LMFDB - Embedded newform 9.9.d.a.2.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,9,Mod(2,9)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("9.2");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	9.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.66640749055$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 427 x^{12} - 1362 x^{11} + 135762 x^{10} - 371244 x^{9} + 18261508 x^{8} + \cdots + 872385888256 $ x^14 - x^13 + 427x^12 - 1362x^11 + 135762x^10 - 371244x^9 + 18261508x^8 - 29352736x^7 + 1757083840x^6 - 1434930432x^5 + 61638378240x^4 + 183604924416x^3 + 1254910111744x^2 + 1078377512960x + 872385888256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{21} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2.3
Root			$4.05115 + 7.01679i$ of defining polynomial
Character	$\chi$	$=$	9.2
Dual form			9.9.d.a.5.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.1534 - 7.01679i) q^{2} +(54.3339 + 60.0735i) q^{3} +(-29.5292 - 51.1461i) q^{4} +(676.216 - 390.413i) q^{5} +(-238.821 - 1111.35i) q^{6} +(2168.61 - 3756.14i) q^{7} +4421.40i q^{8} +(-656.650 + 6528.06i) q^{9} +O(q^{10})$	\(q+(-12.1534 - 7.01679i) q^{2} +(54.3339 + 60.0735i) q^{3} +(-29.5292 - 51.1461i) q^{4} +(676.216 - 390.413i) q^{5} +(-238.821 - 1111.35i) q^{6} +(2168.61 - 3756.14i) q^{7} +4421.40i q^{8} +(-656.650 + 6528.06i) q^{9} -10957.8 q^{10} +(5607.04 + 3237.22i) q^{11} +(1468.09 - 4552.89i) q^{12} +(-8497.75 - 14718.5i) q^{13} +(-52712.1 + 30433.3i) q^{14} +(60194.9 + 19410.0i) q^{15} +(23464.6 - 40641.8i) q^{16} +29881.7i q^{17} +(53786.6 - 74730.8i) q^{18} -91768.1 q^{19} +(-39936.2 - 23057.2i) q^{20} +(343473. - 73809.9i) q^{21} +(-45429.9 - 78686.9i) q^{22} +(-106388. + 61423.0i) q^{23} +(-265609. + 240232. i) q^{24} +(109532. - 189716. i) q^{25} +238508. i q^{26} +(-427842. + 315248. i) q^{27} -256149. q^{28} +(434568. + 250898. i) q^{29} +(-595380. - 658273. i) q^{30} +(505931. + 876298. i) q^{31} +(409885. - 236647. i) q^{32} +(110181. + 512725. i) q^{33} +(209673. - 363165. i) q^{34} -3.38661e6i q^{35} +(353275. - 159183. i) q^{36} +190279. q^{37} +(1.11530e6 + 643918. i) q^{38} +(422478. - 1.31021e6i) q^{39} +(1.72617e6 + 2.98982e6i) q^{40} +(-1.95619e6 + 1.12941e6i) q^{41} +(-4.69229e6 - 1.51304e6i) q^{42} +(-1.64497e6 + 2.84917e6i) q^{43} -382371. i q^{44} +(2.10460e6 + 4.67074e6i) q^{45} +1.72397e6 q^{46} +(-110171. - 63607.2i) q^{47} +(3.71642e6 - 798631. i) q^{48} +(-6.52331e6 - 1.12987e7i) q^{49} +(-2.66239e6 + 1.53713e6i) q^{50} +(-1.79510e6 + 1.62359e6i) q^{51} +(-501864. + 869254. i) q^{52} +1.40856e6i q^{53} +(7.41178e6 - 829268. i) q^{54} +5.05542e6 q^{55} +(1.66074e7 + 9.58828e6i) q^{56} +(-4.98612e6 - 5.51283e6i) q^{57} +(-3.52099e6 - 6.09854e6i) q^{58} +(-1.79370e7 + 1.03560e7i) q^{59} +(-784766. - 3.65190e6i) q^{60} +(9.62157e6 - 1.66651e7i) q^{61} -1.42000e7i q^{62} +(2.30963e7 + 1.66233e7i) q^{63} -1.86559e7 q^{64} +(-1.14926e7 - 6.63527e6i) q^{65} +(2.25861e6 - 7.00450e6i) q^{66} +(1.17156e7 + 2.02920e7i) q^{67} +(1.52833e6 - 882382. i) q^{68} +(-9.47036e6 - 3.05373e6i) q^{69} +(-2.37632e7 + 4.11590e7i) q^{70} +9.12361e6i q^{71} +(-2.88632e7 - 2.90331e6i) q^{72} +1.43931e7 q^{73} +(-2.31255e6 - 1.33515e6i) q^{74} +(1.73482e7 - 3.72800e6i) q^{75} +(2.70984e6 + 4.69358e6i) q^{76} +(2.43189e7 - 1.40405e7i) q^{77} +(-1.43280e7 + 1.29591e7i) q^{78} +(2.69804e7 - 4.67314e7i) q^{79} -3.66435e7i q^{80} +(-4.21843e7 - 8.57330e6i) q^{81} +3.16992e7 q^{82} +(2.66155e7 + 1.53664e7i) q^{83} +(-1.39176e7 - 1.53878e7i) q^{84} +(1.16662e7 + 2.02064e7i) q^{85} +(3.99841e7 - 2.30848e7i) q^{86} +(8.53946e6 + 3.97382e7i) q^{87} +(-1.43131e7 + 2.47910e7i) q^{88} -2.32435e7i q^{89} +(7.19544e6 - 7.15331e7i) q^{90} -7.37131e7 q^{91} +(6.28309e6 + 3.62755e6i) q^{92} +(-2.51531e7 + 7.80057e7i) q^{93} +(892637. + 1.54609e6i) q^{94} +(-6.20550e7 + 3.58275e7i) q^{95} +(3.64869e7 + 1.17652e7i) q^{96} +(2.46595e7 - 4.27114e7i) q^{97} +1.83091e8i q^{98} +(-2.48147e7 + 3.44773e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{2} - 93 q^{3} + 767 q^{4} + 438 q^{5} - 2259 q^{6} + 922 q^{7} + 17973 q^{9}+O(q^{10}) $ 14 * q - 3 * q^2 - 93 * q^3 + 767 * q^4 + 438 * q^5 - 2259 * q^6 + 922 * q^7 + 17973 * q^9	\( 14 q - 3 q^{2} - 93 q^{3} + 767 q^{4} + 438 q^{5} - 2259 q^{6} + 922 q^{7} + 17973 q^{9} - 516 q^{10} - 28677 q^{11} - 55110 q^{12} + 1684 q^{13} + 120966 q^{14} - 75276 q^{15} - 65281 q^{16} + 243324 q^{18} - 269630 q^{19} + 539454 q^{20} + 354054 q^{21} + 61311 q^{22} - 1000452 q^{23} - 1125513 q^{24} + 65177 q^{25} - 524826 q^{27} + 1075708 q^{28} + 3797682 q^{29} + 2372562 q^{30} - 164132 q^{31} - 8461881 q^{32} - 5761521 q^{33} + 654993 q^{34} + 12958047 q^{36} - 1671668 q^{37} + 10967691 q^{38} + 3383976 q^{39} + 613326 q^{40} - 10239447 q^{41} - 35844228 q^{42} + 791815 q^{43} + 27631638 q^{45} + 1189536 q^{46} + 31148628 q^{47} + 17088189 q^{48} - 4826637 q^{49} - 63849453 q^{50} - 47946573 q^{51} - 5552720 q^{52} + 36967995 q^{54} + 8107476 q^{55} + 116638674 q^{56} + 37276797 q^{57} + 14211822 q^{58} - 83493795 q^{59} - 109012050 q^{60} - 5255600 q^{61} + 38322432 q^{63} - 26813830 q^{64} + 69232992 q^{65} + 36133866 q^{66} - 8288855 q^{67} - 77746743 q^{68} - 62108640 q^{69} + 27813756 q^{70} + 88821171 q^{72} - 36721682 q^{73} - 10383450 q^{74} + 13792011 q^{75} - 42822959 q^{76} + 56158710 q^{77} + 27355140 q^{78} - 32771822 q^{79} - 16336971 q^{81} + 236099418 q^{82} - 198915996 q^{83} - 187060614 q^{84} + 97486146 q^{85} + 146190669 q^{86} + 114294006 q^{87} + 24955827 q^{88} - 222035850 q^{90} - 201514504 q^{91} - 295365804 q^{92} + 94187784 q^{93} - 36698244 q^{94} + 386813838 q^{95} + 768275928 q^{96} + 127049161 q^{97} - 511060752 q^{99}+O(q^{100}) \) 14 * q - 3 * q^2 - 93 * q^3 + 767 * q^4 + 438 * q^5 - 2259 * q^6 + 922 * q^7 + 17973 * q^9 - 516 * q^10 - 28677 * q^11 - 55110 * q^12 + 1684 * q^13 + 120966 * q^14 - 75276 * q^15 - 65281 * q^16 + 243324 * q^18 - 269630 * q^19 + 539454 * q^20 + 354054 * q^21 + 61311 * q^22 - 1000452 * q^23 - 1125513 * q^24 + 65177 * q^25 - 524826 * q^27 + 1075708 * q^28 + 3797682 * q^29 + 2372562 * q^30 - 164132 * q^31 - 8461881 * q^32 - 5761521 * q^33 + 654993 * q^34 + 12958047 * q^36 - 1671668 * q^37 + 10967691 * q^38 + 3383976 * q^39 + 613326 * q^40 - 10239447 * q^41 - 35844228 * q^42 + 791815 * q^43 + 27631638 * q^45 + 1189536 * q^46 + 31148628 * q^47 + 17088189 * q^48 - 4826637 * q^49 - 63849453 * q^50 - 47946573 * q^51 - 5552720 * q^52 + 36967995 * q^54 + 8107476 * q^55 + 116638674 * q^56 + 37276797 * q^57 + 14211822 * q^58 - 83493795 * q^59 - 109012050 * q^60 - 5255600 * q^61 + 38322432 * q^63 - 26813830 * q^64 + 69232992 * q^65 + 36133866 * q^66 - 8288855 * q^67 - 77746743 * q^68 - 62108640 * q^69 + 27813756 * q^70 + 88821171 * q^72 - 36721682 * q^73 - 10383450 * q^74 + 13792011 * q^75 - 42822959 * q^76 + 56158710 * q^77 + 27355140 * q^78 - 32771822 * q^79 - 16336971 * q^81 + 236099418 * q^82 - 198915996 * q^83 - 187060614 * q^84 + 97486146 * q^85 + 146190669 * q^86 + 114294006 * q^87 + 24955827 * q^88 - 222035850 * q^90 - 201514504 * q^91 - 295365804 * q^92 + 94187784 * q^93 - 36698244 * q^94 + 386813838 * q^95 + 768275928 * q^96 + 127049161 * q^97 - 511060752 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−12.1534	−	7.01679i	−0.759590	−	0.438550i	0.0695584	−	0.997578i	$-0.477841\pi$
$2$	−12.1534	−	7.01679i	−0.759590	−	0.438550i	−0.829149	+	0.559028i	$0.811174\pi$
$3$	54.3339	+	60.0735i	0.670789	+	0.741648i
$3$	54.3339	+	60.0735i	0.670789	+	0.741648i
$4$	−29.5292	−	51.1461i	−0.115349	−	0.199789i
$5$	676.216	−	390.413i	1.08194	−	0.624661i	0.150524	−	0.988606i	$-0.451904\pi$
$5$	676.216	−	390.413i	1.08194	−	0.624661i	0.931420	+	0.363945i	$0.118570\pi$
$6$	−238.821	−	1111.35i	−0.184275	−	0.857523i
$7$	2168.61	−	3756.14i	0.903210	−	1.56441i	0.0799078	−	0.996802i	$-0.474537\pi$
$7$	2168.61	−	3756.14i	0.903210	−	1.56441i	0.823302	−	0.567603i	$-0.192129\pi$
$8$			4421.40i			1.07944i
$9$	−656.650	+	6528.06i	−0.100084	+	0.994979i
$10$	−10957.8			−1.09578
$11$	5607.04	+	3237.22i	0.382968	+	0.221107i	0.679109	−	0.734038i	$-0.262366\pi$
$11$	5607.04	+	3237.22i	0.382968	+	0.221107i	−0.296141	+	0.955144i	$0.595700\pi$
$12$	1468.09	−	4552.89i	0.0707990	−	0.219565i
$13$	−8497.75	−	14718.5i	−0.297530	−	0.515337i	0.678040	−	0.735025i	$-0.262829\pi$
$13$	−8497.75	−	14718.5i	−0.297530	−	0.515337i	−0.975570	+	0.219688i	$0.929496\pi$
$14$	−52712.1	+	30433.3i	−1.37214	+	0.792205i
$15$	60194.9	+	19410.0i	1.18904	+	0.383406i
$16$	23464.6	−	40641.8i	0.358041	−	0.620145i
$17$			29881.7i			0.357774i	0.983870	+	0.178887i	$0.0572497\pi$
$17$			29881.7i			0.357774i	−0.983870	+	0.178887i	$0.942750\pi$
$18$	53786.6	−	74730.8i	0.512370	−	0.711885i
$19$	−91768.1			−0.704170			−0.352085	−	0.935968i	$-0.614527\pi$
$19$	−91768.1			−0.704170			−0.352085	+	0.935968i	$0.614527\pi$
$20$	−39936.2	−	23057.2i	−0.249601	−	0.144107i
$21$	343473.	−	73809.9i	1.76610	−	0.379522i
$22$	−45429.9	−	78686.9i	−0.193933	−	0.335901i
$23$	−106388.	+	61423.0i	−0.380172	+	0.219492i	−0.677893	−	0.735160i	$-0.737107\pi$
$23$	−106388.	+	61423.0i	−0.380172	+	0.219492i	0.297721	+	0.954653i	$0.403773\pi$
$24$	−265609.	+	240232.i	−0.800567	+	0.724079i
$25$	109532.	−	189716.i	0.280403	−	0.485672i
$26$			238508.i			0.521926i
$27$	−427842.	+	315248.i	−0.805059	+	0.593194i
$28$	−256149.			−0.416736
$29$	434568.	+	250898.i	0.614420	+	0.354736i	0.774693	−	0.632337i	$-0.217904\pi$
$29$	434568.	+	250898.i	0.614420	+	0.354736i	−0.160273	+	0.987073i	$0.551238\pi$
$30$	−595380.	−	658273.i	−0.735037	−	0.812683i
$31$	505931.	+	876298.i	0.547828	+	0.948866i	0.998423	+	0.0561377i	$0.0178786\pi$
$31$	505931.	+	876298.i	0.547828	+	0.948866i	−0.450595	+	0.892729i	$0.648788\pi$
$32$	409885.	−	236647.i	0.390897	−	0.225684i
$33$	110181.	+	512725.i	0.0929075	+	0.432344i
$34$	209673.	−	363165.i	0.156902	−	0.271762i
$35$		−	3.38661e6i		−	2.25680i
$36$	353275.	−	159183.i	0.210331	−	0.0947736i
$37$	190279.			0.101528			0.0507638	−	0.998711i	$-0.483834\pi$
$37$	190279.			0.101528			0.0507638	+	0.998711i	$0.483834\pi$
$38$	1.11530e6	+	643918.i	0.534880	+	0.308813i
$39$	422478.	−	1.31021e6i	0.182619	−	0.566345i
$40$	1.72617e6	+	2.98982e6i	0.674286	+	1.16790i
$41$	−1.95619e6	+	1.12941e6i	−0.692269	+	0.399682i	−0.804462	−	0.594005i	$-0.797546\pi$
$41$	−1.95619e6	+	1.12941e6i	−0.692269	+	0.399682i	0.112192	+	0.993687i	$0.464213\pi$
$42$	−4.69229e6	−	1.51304e6i	−1.50795	−	0.486242i
$43$	−1.64497e6	+	2.84917e6i	−0.481154	+	0.833383i	−0.999766	−	0.0216266i	$-0.993115\pi$
$43$	−1.64497e6	+	2.84917e6i	−0.481154	+	0.833383i	0.518612	+	0.855010i	$0.326449\pi$
$44$		−	382371.i		−	0.102017i
$45$	2.10460e6	+	4.67074e6i	0.513240	+	1.13903i
$46$	1.72397e6			0.385033
$47$	−110171.	−	63607.2i	−0.0225775	−	0.0130351i	0.488669	−	0.872469i	$-0.337483\pi$
$47$	−110171.	−	63607.2i	−0.0225775	−	0.0130351i	−0.511246	+	0.859434i	$0.670816\pi$
$48$	3.71642e6	−	798631.i	0.700099	−	0.150446i
$49$	−6.52331e6	−	1.12987e7i	−1.13158	−	1.95995i
$50$	−2.66239e6	+	1.53713e6i	−0.425983	+	0.245941i
$51$	−1.79510e6	+	1.62359e6i	−0.265343	+	0.239991i
$52$	−501864.	+	869254.i	−0.0686393	+	0.118887i
$53$			1.40856e6i			0.178514i	0.996009	+	0.0892571i	$0.0284493\pi$
$53$			1.40856e6i			0.178514i	−0.996009	+	0.0892571i	$0.971551\pi$
$54$	7.41178e6	−	829268.i	0.871660	−	0.0975259i
$55$	5.05542e6			0.552467
$56$	1.66074e7	+	9.58828e6i	1.68869	+	0.974964i
$57$	−4.98612e6	−	5.51283e6i	−0.472349	−	0.522246i
$58$	−3.52099e6	−	6.09854e6i	−0.311138	−	0.538907i
$59$	−1.79370e7	+	1.03560e7i	−1.48028	+	0.854638i	−0.999750	−	0.0223421i	$-0.992888\pi$
$59$	−1.79370e7	+	1.03560e7i	−1.48028	+	0.854638i	−0.480526	+	0.876980i	$0.659554\pi$
$60$	−784766.	−	3.65190e6i	−0.0605529	−	0.281782i
$61$	9.62157e6	−	1.66651e7i	0.694907	−	1.20361i	−0.275305	−	0.961357i	$-0.588779\pi$
$61$	9.62157e6	−	1.66651e7i	0.694907	−	1.20361i	0.970212	−	0.242258i	$-0.0778879\pi$
$62$		−	1.42000e7i		−	0.960999i
$63$	2.30963e7	+	1.66233e7i	1.46615	+	1.05525i
$64$	−1.86559e7			−1.11198
$65$	−1.14926e7	−	6.63527e6i	−0.643822	−	0.371711i
$66$	2.25861e6	−	7.00450e6i	0.119033	−	0.369149i
$67$	1.17156e7	+	2.02920e7i	0.581386	+	1.00699i	0.995315	+	0.0966815i	$0.0308228\pi$
$67$	1.17156e7	+	2.02920e7i	0.581386	+	1.00699i	−0.413929	+	0.910309i	$0.635844\pi$
$68$	1.52833e6	−	882382.i	0.0714795	−	0.0412687i
$69$	−9.47036e6	−	3.05373e6i	−0.417801	−	0.134721i
$70$	−2.37632e7	+	4.11590e7i	−0.989719	+	1.71424i
$71$			9.12361e6i			0.359032i	0.983755	+	0.179516i	$0.0574532\pi$
$71$			9.12361e6i			0.359032i	−0.983755	+	0.179516i	$0.942547\pi$
$72$	−2.88632e7	−	2.90331e6i	−1.07402	−	0.108035i
$73$	1.43931e7			0.506832			0.253416	−	0.967357i	$-0.418446\pi$
$73$	1.43931e7			0.506832			0.253416	+	0.967357i	$0.418446\pi$
$74$	−2.31255e6	−	1.33515e6i	−0.0771194	−	0.0445249i
$75$	1.73482e7	−	3.72800e6i	0.548289	−	0.117823i
$76$	2.70984e6	+	4.69358e6i	0.0812249	+	0.140686i
$77$	2.43189e7	−	1.40405e7i	0.691801	−	0.399412i
$78$	−1.43280e7	+	1.29591e7i	−0.387086	+	0.350103i
$79$	2.69804e7	−	4.67314e7i	0.692691	−	1.19978i	−0.278262	−	0.960505i	$-0.589758\pi$
$79$	2.69804e7	−	4.67314e7i	0.692691	−	1.19978i	0.970953	−	0.239271i	$-0.0769083\pi$
$80$		−	3.66435e7i		−	0.894617i
$81$	−4.21843e7	−	8.57330e6i	−0.979966	−	0.199163i
$82$	3.16992e7			0.701121
$83$	2.66155e7	+	1.53664e7i	0.560818	+	0.323788i	0.753474	−	0.657478i	$-0.228377\pi$
$83$	2.66155e7	+	1.53664e7i	0.560818	+	0.323788i	−0.192656	+	0.981266i	$0.561710\pi$
$84$	−1.39176e7	−	1.53878e7i	−0.279542	−	0.309071i
$85$	1.16662e7	+	2.02064e7i	0.223488	+	0.387092i
$86$	3.99841e7	−	2.30848e7i	0.730959	−	0.422020i
$87$	8.53946e6	+	3.97382e7i	0.149057	+	0.693636i
$88$	−1.43131e7	+	2.47910e7i	−0.238672	+	0.413393i
$89$		−	2.32435e7i		−	0.370460i	−0.982695	−	0.185230i	$-0.940697\pi$
$89$		−	2.32435e7i		−	0.370460i	0.982695	−	0.185230i	$-0.0593030\pi$
$90$	7.19544e6	−	7.15331e7i	0.109670	−	1.09028i
$91$	−7.37131e7			−1.07493
$92$	6.28309e6	+	3.62755e6i	0.0877046	+	0.0506363i
$93$	−2.51531e7	+	7.80057e7i	−0.336248	+	1.04278i
$94$	892637.	+	1.54609e6i	0.0114331	+	0.0198027i
$95$	−6.20550e7	+	3.58275e7i	−0.761873	+	0.439867i
$96$	3.64869e7	+	1.17652e7i	0.429588	+	0.138521i
$97$	2.46595e7	−	4.27114e7i	0.278546	−	0.482455i	−0.692478	−	0.721439i	$-0.743481\pi$
$97$	2.46595e7	−	4.27114e7i	0.278546	−	0.482455i	0.971024	+	0.238984i	$0.0768143\pi$
$98$			1.83091e8i			1.98501i
$99$	−2.48147e7	+	3.44773e7i	−0.258326	+	0.358916i
$100$	−1.29376e7			−0.129376
$101$	−1.76236e8	−	1.01750e8i	−1.69359	−	0.977795i	−0.951576	−	0.307412i	$-0.900537\pi$
$101$	−1.76236e8	−	1.01750e8i	−1.69359	−	0.977795i	−0.742015	−	0.670383i	$-0.766130\pi$
$102$	3.32090e7	−	7.13636e6i	0.306800	−	0.0659290i
$103$	9.75328e6	+	1.68932e7i	0.0866566	+	0.150094i	0.906096	−	0.423072i	$-0.139048\pi$
$103$	9.75328e6	+	1.68932e7i	0.0866566	+	0.150094i	−0.819439	+	0.573166i	$0.805715\pi$
$104$	6.50765e7	−	3.75720e7i	0.556277	−	0.321167i
$105$	2.03446e8	−	1.84008e8i	1.67375	−	1.51384i
$106$	9.88360e6	−	1.71189e7i	0.0782874	−	0.135598i
$107$			9.76742e7i			0.745152i	0.928002	+	0.372576i	$0.121525\pi$
$107$			9.76742e7i			0.745152i	−0.928002	+	0.372576i	$0.878475\pi$
$108$	2.87575e7	+	1.25734e7i	0.211376	+	0.0924184i
$109$	−6.46331e7			−0.457877			−0.228939	−	0.973441i	$-0.573526\pi$
$109$	−6.46331e7			−0.457877			−0.228939	+	0.973441i	$0.573526\pi$
$110$	−6.14408e7	−	3.54728e7i	−0.419649	−	0.242284i
$111$	1.03386e7	+	1.14307e7i	0.0681036	+	0.0752978i
$112$	−1.01771e8	−	1.76272e8i	−0.646772	−	1.12024i
$113$	1.15273e8	−	6.65528e7i	0.706989	−	0.408181i	−0.102956	−	0.994686i	$-0.532830\pi$
$113$	1.15273e8	−	6.65528e7i	0.706989	−	0.408181i	0.809945	+	0.586505i	$0.199497\pi$
$114$	2.19161e7	+	1.01986e8i	0.129761	+	0.603842i
$115$	−4.79607e7	+	8.30704e7i	−0.274217	+	0.474957i
$116$		−	2.96353e7i		−	0.163673i
$117$	1.01663e8	−	4.58089e7i	0.542527	−	0.244459i
$118$	2.90663e8			1.49920
$119$	1.12240e8	+	6.48016e7i	0.559704	+	0.323145i
$120$	−8.58192e7	+	2.66146e8i	−0.413866	+	1.28350i
$121$	−8.62202e7	−	1.49338e8i	−0.402224	−	0.696672i
$122$	−2.33871e8	+	1.35025e8i	−1.05569	+	0.609503i
$123$	−1.74135e8	−	5.61500e7i	−0.760790	−	0.245318i
$124$	2.98795e7	−	5.17528e7i	0.126382	−	0.218901i
$125$			1.33959e8i			0.548695i
$126$	−1.64057e8	−	3.64092e8i	−0.650898	−	1.44454i
$127$	−2.04396e7			−0.0785702			−0.0392851	−	0.999228i	$-0.512508\pi$
$127$	−2.04396e7			−0.0785702			−0.0392851	+	0.999228i	$0.512508\pi$
$128$	1.21803e8	+	7.03228e7i	0.453750	+	0.261973i
$129$	−2.60537e8	+	5.59875e7i	−0.940830	+	0.202177i
$130$	9.31166e7	+	1.61283e8i	0.326027	+	0.564696i
$131$	4.48695e8	−	2.59054e8i	1.52358	−	0.879641i	0.523972	−	0.851736i	$-0.324450\pi$
$131$	4.48695e8	−	2.59054e8i	1.52358	−	0.879641i	0.999611	−	0.0279052i	$-0.00888364\pi$
$132$	2.29704e7	−	2.07757e7i	0.0756610	−	0.0684321i
$133$	−1.99009e8	+	3.44694e8i	−0.636013	+	1.10161i
$134$		−	3.28823e8i		−	1.01987i
$135$	−1.66236e8	+	3.80210e8i	−0.500485	+	1.14469i
$136$	−1.32119e8			−0.386197
$137$	−2.57339e8	−	1.48575e8i	−0.730506	−	0.421758i	0.0881015	−	0.996111i	$-0.471920\pi$
$137$	−2.57339e8	−	1.48575e8i	−0.730506	−	0.421758i	−0.818607	+	0.574354i	$0.805253\pi$
$138$	9.36700e7	+	1.03565e8i	0.258276	+	0.285559i
$139$	2.45532e8	+	4.25274e8i	0.657732	+	1.13923i	0.981201	+	0.192987i	$0.0618174\pi$
$139$	2.45532e8	+	4.25274e8i	0.657732	+	1.13923i	−0.323469	+	0.946239i	$0.604849\pi$
$140$	−1.73212e8	+	1.00004e8i	−0.450885	+	0.260319i
$141$	−2.16491e6	−	1.00744e7i	−0.00547726	−	0.0254884i
$142$	6.40185e7	−	1.10883e8i	0.157453	−	0.272717i
$143$		−	1.10037e8i		−	0.263144i
$144$	2.49904e8	+	1.79866e8i	0.581197	+	0.418310i
$145$	3.91815e8			0.886358
$146$	−1.74926e8	−	1.00994e8i	−0.384985	−	0.222271i
$147$	3.24316e8	−	1.00578e9i	0.694543	−	2.15394i
$148$	−5.61880e6	−	9.73204e6i	−0.0117111	−	0.0202842i
$149$	3.16813e8	−	1.82912e8i	0.642774	−	0.371106i	−0.142908	−	0.989736i	$-0.545645\pi$
$149$	3.16813e8	−	1.82912e8i	0.642774	−	0.371106i	0.785682	+	0.618630i	$0.212312\pi$
$150$	−2.36999e8	−	7.64208e7i	−0.468147	−	0.150955i
$151$	1.21077e8	−	2.09712e8i	0.232892	−	0.403381i	−0.725766	−	0.687942i	$-0.758514\pi$
$151$	1.21077e8	−	2.09712e8i	0.232892	−	0.403381i	0.958658	+	0.284561i	$0.0918477\pi$
$152$		−	4.05743e8i		−	0.760111i
$153$	−1.95069e8	−	1.96218e7i	−0.355978	−	0.0358074i
$154$	−3.94078e8			−0.700647
$155$	6.84237e8	+	3.95044e8i	1.18544	+	0.684414i
$156$	−7.94873e7	+	1.70812e7i	−0.134215	+	0.0288417i
$157$	1.04126e8	+	1.80351e8i	0.171380	+	0.296839i	0.938903	−	0.344183i	$-0.111844\pi$
$157$	1.04126e8	+	1.80351e8i	0.171380	+	0.296839i	−0.767523	+	0.641022i	$0.778511\pi$
$158$	−6.55809e8	+	3.78631e8i	−1.05232	+	0.607559i
$159$	−8.46173e7	+	7.65328e7i	−0.132395	+	0.119745i
$160$	1.84780e8	−	3.20049e8i	0.281952	−	0.488356i
$161$			5.32809e8i			0.792991i
$162$	4.52528e8	+	4.00194e8i	0.657030	+	0.581046i
$163$	−1.01916e9			−1.44374			−0.721872	−	0.692027i	$-0.756718\pi$
$163$	−1.01916e9			−1.44374			−0.721872	+	0.692027i	$0.756718\pi$
$164$	1.15529e8	+	6.67009e7i	0.159704	+	0.0922054i
$165$	2.74681e8	+	3.03697e8i	0.370589	+	0.409736i
$166$	−2.15646e8	−	3.73511e8i	−0.283994	−	0.491893i
$167$	−1.28831e9	+	7.43808e8i	−1.65636	+	0.956302i	−0.681991	+	0.731360i	$0.738886\pi$
$167$	−1.28831e9	+	7.43808e8i	−1.65636	+	0.956302i	−0.974372	+	0.224941i	$0.927781\pi$
$168$	3.26343e8	+	1.51863e9i	0.409673	+	1.90641i
$169$	2.63442e8	−	4.56295e8i	0.322952	−	0.559369i
$170$		−	3.27437e8i		−	0.392042i
$171$	6.02595e7	−	5.99067e8i	0.0704760	−	0.700634i
$172$	1.94299e8			0.222002
$173$	4.86514e8	+	2.80889e8i	0.543139	+	0.313582i	0.746350	−	0.665553i	$-0.231804\pi$
$173$	4.86514e8	+	2.80889e8i	0.543139	+	0.313582i	−0.203211	+	0.979135i	$0.565138\pi$
$174$	1.75051e8	−	5.42876e8i	0.190971	−	0.592248i
$175$	−4.75066e8	−	8.22838e8i	−0.506526	−	0.877328i
$176$	2.63133e8	−	1.51920e8i	0.274237	−	0.158331i
$177$	−1.59671e9	−	5.14861e8i	−1.62679	−	0.524562i
$178$	−1.63095e8	+	2.82488e8i	−0.162465	+	0.281398i
$179$			3.03038e7i			0.0295178i	0.999891	+	0.0147589i	$0.00469808\pi$
$179$			3.03038e7i			0.0295178i	−0.999891	+	0.0147589i	$0.995302\pi$
$180$	1.76743e8	−	2.45565e8i	0.168365	−	0.233925i
$181$	7.49672e8			0.698485			0.349243	−	0.937032i	$-0.386439\pi$
$181$	7.49672e8			0.698485			0.349243	+	0.937032i	$0.386439\pi$
$182$	8.95868e8	+	5.17230e8i	0.816505	+	0.471409i
$183$	1.52391e9	−	3.27476e8i	1.35879	−	0.291995i
$184$	−2.71576e8	−	4.70383e8i	−0.236930	−	0.410374i
$185$	1.28670e8	−	7.42875e7i	0.109847	−	0.0634204i
$186$	8.53047e8	−	7.71544e8i	0.712723	−	0.644628i
$187$	−9.67336e7	+	1.67548e8i	−0.0791063	+	0.137016i
$188$			7.51308e6i			0.00601432i
$189$	2.56293e8	+	2.29068e9i	0.200858	+	1.79522i
$190$	1.00558e9			0.771615
$191$	−1.95265e9	−	1.12736e9i	−1.46721	−	0.847092i	−0.467879	−	0.883792i	$-0.654982\pi$
$191$	−1.95265e9	−	1.12736e9i	−1.46721	−	0.847092i	−0.999326	+	0.0367008i	$0.988315\pi$
$192$	−1.01365e9	−	1.12072e9i	−0.745902	−	0.824696i
$193$	4.35948e8	+	7.55084e8i	0.314199	+	0.544209i	0.979267	−	0.202574i	$-0.0649306\pi$
$193$	4.35948e8	+	7.55084e8i	0.314199	+	0.544209i	−0.665068	+	0.746783i	$0.731597\pi$
$194$	−5.99395e8	+	3.46061e8i	−0.423161	+	0.244312i
$195$	−2.25835e8	−	1.05092e9i	−0.156190	−	0.726829i
$196$	−3.85257e8	+	6.67284e8i	−0.261051	+	0.452154i
$197$		−	1.82586e9i		−	1.21228i	−0.795358	−	0.606140i	$-0.792717\pi$
$197$		−	1.82586e9i		−	1.21228i	0.795358	−	0.606140i	$-0.207283\pi$
$198$	5.43504e8	−	2.44899e8i	0.353624	−	0.159341i
$199$	−1.16593e9			−0.743467			−0.371734	−	0.928339i	$-0.621236\pi$
$199$	−1.16593e9			−0.743467			−0.371734	+	0.928339i	$0.621236\pi$
$200$	8.38809e8	+	4.84287e8i	0.524256	+	0.302679i
$201$	−5.82457e8	+	1.80634e9i	−0.356845	+	1.10666i
$202$	1.42791e9	+	2.47322e9i	0.857624	+	1.48545i
$203$	1.88481e9	−	1.08820e9i	1.10990	−	0.640801i
$204$	1.36048e8	+	4.38689e7i	0.0785546	+	0.0253300i
$205$	−8.81869e8	+	1.52744e9i	−0.499331	+	0.864867i
$206$		−	2.73747e8i		−	0.152013i
$207$	−3.31113e8	−	7.34839e8i	−0.180341	−	0.400231i
$208$	−7.97584e8			−0.426112
$209$	−5.14547e8	−	2.97074e8i	−0.269675	−	0.155697i
$210$	−3.76371e9	+	8.08794e8i	−1.93526	+	0.415873i
$211$	−6.72025e8	−	1.16398e9i	−0.339044	−	0.587241i	0.645210	−	0.764006i	$-0.276770\pi$
$211$	−6.72025e8	−	1.16398e9i	−0.339044	−	0.587241i	−0.984253	+	0.176765i	$0.943437\pi$
$212$	7.20425e7	−	4.15938e7i	0.0356653	−	0.0205914i
$213$	−5.48087e8	+	4.95721e8i	−0.266275	+	0.240835i
$214$	6.85360e8	−	1.18708e9i	0.326786	−	0.566010i
$215$			2.56887e9i			1.20223i
$216$	−1.39384e9	−	1.89166e9i	−0.640319	−	0.869016i
$217$	4.38866e9			1.97922
$218$	7.85515e8	+	4.53517e8i	0.347799	+	0.200802i
$219$	7.82036e8	+	8.64646e8i	0.339978	+	0.375891i
$220$	−1.49283e8	−	2.58565e8i	−0.0637263	−	0.110377i
$221$	4.39814e8	−	2.53927e8i	0.184374	−	0.106449i
$222$	−4.54426e7	−	2.11467e8i	−0.0187090	−	0.0870623i
$223$	3.94241e8	−	6.82846e8i	0.159420	−	0.276123i	−0.775240	−	0.631667i	$-0.782371\pi$
$223$	3.94241e8	−	6.82846e8i	0.159420	−	0.276123i	0.934660	+	0.355544i	$0.115704\pi$
$224$		−	2.05278e9i		−	0.815361i
$225$	1.16655e9	+	8.39611e8i	0.455170	+	0.327603i
$226$	−1.86795e9			−0.716030
$227$	−8.42559e8	−	4.86452e8i	−0.317320	−	0.183205i	0.332878	−	0.942970i	$-0.391980\pi$
$227$	−8.42559e8	−	4.86452e8i	−0.317320	−	0.183205i	−0.650197	+	0.759765i	$0.725314\pi$
$228$	−1.34724e8	+	4.17810e8i	−0.0498545	+	0.154611i
$229$	−1.18623e9	−	2.05461e9i	−0.431348	−	0.747116i	0.565642	−	0.824651i	$-0.308628\pi$
$229$	−1.18623e9	−	2.05461e9i	−0.431348	−	0.747116i	−0.996990	+	0.0775347i	$0.975295\pi$
$230$	1.16578e9	−	6.73061e8i	0.416585	−	0.240515i
$231$	2.16481e9	+	6.98045e8i	0.760276	+	0.245152i
$232$	−1.10932e9	+	1.92140e9i	−0.382917	+	0.663232i
$233$			3.05248e9i			1.03569i	0.855475	+	0.517844i	$0.173265\pi$
$233$			3.05248e9i			1.03569i	−0.855475	+	0.517844i	$0.826735\pi$
$234$	−1.55699e9	−	1.56616e8i	−0.519306	−	0.0522364i
$235$	−9.93323e7			−0.0325701
$236$	1.05933e9	+	6.11607e8i	0.341495	+	0.197162i
$237$	4.27327e9	−	9.18293e8i	1.35446	−	0.291064i
$238$	−9.09399e8	−	1.57512e9i	−0.283430	−	0.490916i
$239$	3.19031e9	−	1.84193e9i	0.977782	−	0.564522i	0.0761819	−	0.997094i	$-0.475727\pi$
$239$	3.19031e9	−	1.84193e9i	0.977782	−	0.564522i	0.901600	+	0.432572i	$0.142394\pi$
$240$	2.20130e9	−	1.99099e9i	0.663491	−	0.600099i
$241$	9.21301e8	−	1.59574e9i	0.273107	−	0.473036i	−0.696549	−	0.717510i	$-0.745282\pi$
$241$	9.21301e8	−	1.59574e9i	0.273107	−	0.473036i	0.969656	+	0.244474i	$0.0786153\pi$
$242$			2.41996e9i			0.705580i
$243$	−1.77701e9	−	2.99998e9i	−0.509642	−	0.860386i
$244$	−1.13647e9			−0.320626
$245$	−8.82233e9	−	5.09358e9i	−2.44861	−	1.41370i
$246$	1.72234e9	+	1.90428e9i	0.470304	+	0.519985i
$247$	7.79822e8	+	1.35069e9i	0.209512	+	0.362885i
$248$	−3.87446e9	+	2.23692e9i	−1.02425	+	0.591350i
$249$	5.23007e8	+	2.43380e9i	0.136054	+	0.633123i
$250$	9.39960e8	−	1.62806e9i	0.240630	−	0.416783i
$251$			5.83943e9i			1.47121i	0.677409	+	0.735606i	$0.263103\pi$
$251$			5.83943e9i			1.47121i	−0.677409	+	0.735606i	$0.736897\pi$
$252$	1.68200e8	−	1.67216e9i	0.0417085	−	0.414643i
$253$	−7.95360e8			−0.194125
$254$	2.48412e8	+	1.43421e8i	0.0596811	+	0.0344569i
$255$	−5.80002e8	+	1.79872e9i	−0.137173	+	0.425406i
$256$	1.40107e9	+	2.42673e9i	0.326212	+	0.565016i
$257$	−4.71548e9	+	2.72248e9i	−1.08092	+	0.624069i	−0.931144	−	0.364651i	$-0.881188\pi$
$257$	−4.71548e9	+	2.72248e9i	−1.08092	+	0.624069i	−0.149775	+	0.988720i	$0.547855\pi$
$258$	3.55928e9	+	1.14769e9i	0.803310	+	0.259029i
$259$	4.12641e8	−	7.14715e8i	0.0917008	−	0.158830i
$260$			7.83737e8i			0.171505i
$261$	−1.92323e9	+	2.67213e9i	−0.414448	+	0.575832i
$262$	−7.27092e9			−1.54306
$263$	5.14084e9	+	2.96807e9i	1.07451	+	0.620369i	0.929411	−	0.369047i	$-0.120316\pi$
$263$	5.14084e9	+	2.96807e9i	1.07451	+	0.620369i	0.145101	+	0.989417i	$0.453649\pi$
$264$	−2.26696e9	+	4.87154e8i	−0.466691	+	0.100288i
$265$	5.49922e8	+	9.52492e8i	0.111511	+	0.193143i
$266$	4.83729e9	−	2.79281e9i	0.966219	−	0.557847i
$267$	1.39632e9	−	1.26291e9i	0.274751	−	0.248500i
$268$	6.91904e8	−	1.19841e9i	0.134124	−	0.232310i
$269$		−	8.12664e9i		−	1.55204i	−0.630711	−	0.776018i	$-0.717237\pi$
$269$		−	8.12664e9i		−	1.55204i	0.630711	−	0.776018i	$-0.282763\pi$
$270$	4.68820e9	−	3.45442e9i	0.882168	−	0.650010i
$271$	−4.85074e9			−0.899355			−0.449677	−	0.893191i	$-0.648461\pi$
$271$	−4.85074e9			−0.899355			−0.449677	+	0.893191i	$0.648461\pi$
$272$	1.21445e9	+	7.01160e8i	0.221872	+	0.128098i
$273$	−4.00512e9	−	4.42821e9i	−0.721050	−	0.797218i
$274$	2.08504e9	+	3.61139e9i	0.369923	+	0.640726i
$275$	1.22831e9	−	7.09162e8i	0.214771	−	0.123998i
$276$	1.23466e8	+	5.74546e8i	0.0212770	+	0.0990122i
$277$	2.69682e9	−	4.67102e9i	0.458070	−	0.793401i	−0.540789	−	0.841158i	$-0.681874\pi$
$277$	2.69682e9	−	4.67102e9i	0.458070	−	0.793401i	0.998859	+	0.0477575i	$0.0152075\pi$
$278$		−	6.89139e9i		−	1.15379i
$279$	−6.05274e9	+	2.72732e9i	−0.998931	+	0.450111i
$280$	1.49736e10			2.43609
$281$	3.14649e9	+	1.81663e9i	0.504663	+	0.291367i	0.730637	−	0.682766i	$-0.239223\pi$
$281$	3.14649e9	+	1.81663e9i	0.504663	+	0.291367i	−0.225974	+	0.974133i	$0.572556\pi$
$282$	−4.43787e7	+	1.37629e8i	−0.00701743	+	0.0217628i
$283$	−4.07016e9	−	7.04973e9i	−0.634550	−	1.09907i	−0.986610	−	0.163096i	$-0.947852\pi$
$283$	−4.07016e9	−	7.04973e9i	−0.634550	−	1.09907i	0.352060	−	0.935977i	$-0.385481\pi$
$284$	4.66637e8	−	2.69413e8i	0.0717308	−	0.0414138i
$285$	−5.52397e9	−	1.78121e9i	−0.837283	−	0.269983i
$286$	−7.72104e8	+	1.33732e9i	−0.115401	+	0.199881i
$287$			9.79695e9i			1.44399i
$288$	1.27569e9	+	2.83115e9i	0.185429	+	0.411521i
$289$	6.08284e9			0.871998
$290$	−4.76190e9	−	2.74929e9i	−0.673269	−	0.388712i
$291$	3.90567e9	−	8.39300e8i	0.544658	−	0.117043i
$292$	−4.25018e8	−	7.36153e8i	−0.0584623	−	0.101260i
$293$	8.58256e9	−	4.95514e9i	1.16452	−	0.672335i	0.212135	−	0.977240i	$-0.431958\pi$
$293$	8.58256e9	−	4.95514e9i	1.16452	−	0.672335i	0.952383	+	0.304906i	$0.0986249\pi$
$294$	−1.09989e10	+	9.94805e9i	−1.47218	+	1.33152i
$295$	−8.08621e9	+	1.40057e10i	−1.06772	+	1.84934i
$296$			8.41300e8i			0.109593i
$297$	−3.41945e9	+	3.82586e8i	−0.439471	+	0.0491704i
$298$	−5.13383e9			−0.650993
$299$	1.80811e9	+	1.04391e9i	0.226225	+	0.130611i
$300$	−7.02952e8	−	7.77209e8i	−0.0867842	−	0.0959517i
$301$	7.13458e9	+	1.23575e10i	0.869166	+	1.50544i
$302$	−2.94301e9	+	1.69915e9i	−0.353805	+	0.204270i
$303$	−3.46312e9	−	1.61156e10i	−0.410863	−	1.91194i
$304$	−2.15330e9	+	3.72962e9i	−0.252122	+	0.436687i
$305$		−	1.50256e10i		−	1.73633i
$306$	2.23308e9	+	1.60723e9i	0.254694	+	0.183313i
$307$	3.22198e9			0.362718			0.181359	−	0.983417i	$-0.441950\pi$
$307$	3.22198e9			0.362718			0.181359	+	0.983417i	$0.441950\pi$
$308$	−1.43624e9	−	8.29212e8i	−0.159597	−	0.0921431i
$309$	−4.84898e8	+	1.50379e9i	−0.0531884	+	0.164950i
$310$	−5.54389e9	−	9.60229e9i	−0.600299	−	1.03975i
$311$	−9.85438e9	+	5.68943e9i	−1.05339	+	0.608173i	−0.923595	−	0.383369i	$-0.874764\pi$
$311$	−9.85438e9	+	5.68943e9i	−1.05339	+	0.608173i	−0.129791	+	0.991541i	$0.541431\pi$
$312$	5.79294e9	+	1.86794e9i	0.611337	+	0.197127i
$313$	−7.25584e8	+	1.25675e9i	−0.0755980	+	0.130940i	−0.901346	−	0.433099i	$-0.857420\pi$
$313$	−7.25584e8	+	1.25675e9i	−0.0755980	+	0.130940i	0.825748	+	0.564039i	$0.190753\pi$
$314$		−	2.92252e9i		−	0.300634i
$315$	2.21080e10	+	2.22382e9i	2.24547	+	0.225869i
$316$	−3.18684e9			−0.319603
$317$	9.96977e8	+	5.75605e8i	0.0987297	+	0.0570016i	0.548552	−	0.836117i	$-0.315179\pi$
$317$	9.96977e8	+	5.75605e8i	0.0987297	+	0.0570016i	−0.449822	+	0.893118i	$0.648513\pi$
$318$	1.56541e9	−	3.36394e8i	0.153080	−	0.0328958i
$319$	1.62442e9	+	2.81359e9i	0.156869	+	0.271705i
$320$	−1.26154e10	+	7.28350e9i	−1.20310	+	0.694609i
$321$	−5.86763e9	+	5.30702e9i	−0.552641	+	0.499840i
$322$	3.73861e9	−	6.47547e9i	0.347766	−	0.602348i
$323$		−	2.74218e9i		−	0.251934i
$324$	8.07180e8	+	2.41073e9i	0.0732471	+	0.218760i
$325$	−3.72312e9			−0.333713
$326$	1.23863e10	+	7.15121e9i	1.09665	+	0.633153i
$327$	−3.51177e9	−	3.88274e9i	−0.307139	−	0.339584i
$328$	−4.99355e9	−	8.64909e9i	−0.431434	−	0.747265i
$329$	−4.77835e8	+	2.75878e8i	−0.0407844	+	0.0235469i
$330$	−1.20734e9	−	5.61834e9i	−0.101806	−	0.473753i
$331$	3.79423e9	−	6.57179e9i	0.316090	−	0.547485i	−0.663578	−	0.748107i	$-0.730963\pi$
$331$	3.79423e9	−	6.57179e9i	0.316090	−	0.547485i	0.979669	+	0.200622i	$0.0642964\pi$
$332$		−	1.81504e9i		−	0.149394i
$333$	−1.24947e8	+	1.24215e9i	−0.0101613	+	0.101018i
$334$	2.08766e10			1.67754
$335$	1.58445e10	+	9.14784e9i	1.25806	+	0.726339i
$336$	5.05968e9	−	1.56913e10i	0.396978	−	1.23112i
$337$	−2.99639e9	−	5.18990e9i	−0.232316	−	0.402383i	0.726173	−	0.687512i	$-0.241297\pi$
$337$	−2.99639e9	−	5.18990e9i	−0.232316	−	0.402383i	−0.958489	+	0.285129i	$0.907964\pi$
$338$	−6.40345e9	+	3.69703e9i	−0.490622	+	0.283261i
$339$	1.02613e10	+	3.30877e9i	0.776967	+	0.250534i
$340$	6.88987e8	−	1.19336e9i	0.0515579	−	0.0893010i
$341$			6.55125e9i			0.484514i
$342$	−4.93589e9	+	6.85790e9i	−0.360796	+	0.501287i
$343$	−3.15828e10			−2.28178
$344$	−1.25973e10	−	7.27307e9i	−0.899590	−	0.519378i
$345$	−7.59622e9	+	1.63237e9i	−0.536193	+	0.115224i
$346$	−3.94188e9	−	6.82754e9i	−0.275042	−	0.476387i
$347$	2.63578e9	−	1.52177e9i	0.181799	−	0.104962i	−0.406339	−	0.913723i	$-0.633195\pi$
$347$	2.63578e9	−	1.52177e9i	0.181799	−	0.104962i	0.588138	+	0.808761i	$0.299861\pi$
$348$	1.78029e9	−	1.61020e9i	0.121388	−	0.109790i
$349$	9.34951e9	−	1.61938e10i	0.630213	−	1.09156i	−0.357295	−	0.933992i	$-0.616301\pi$
$349$	9.34951e9	−	1.61938e10i	0.630213	−	1.09156i	0.987508	−	0.157569i	$-0.0503657\pi$
$350$			1.33338e10i			0.888547i
$351$	8.27568e9	+	3.61831e9i	0.545224	+	0.238384i
$352$	3.06432e9			0.199601
$353$	−2.85996e9	−	1.65120e9i	−0.184188	−	0.106341i	0.405071	−	0.914285i	$-0.367247\pi$
$353$	−2.85996e9	−	1.65120e9i	−0.184188	−	0.106341i	−0.589259	+	0.807944i	$0.700580\pi$
$354$	1.57928e10	+	1.74611e10i	1.00565	+	1.11188i
$355$	3.56198e9	+	6.16953e9i	0.224273	+	0.388453i
$356$	−1.18881e9	+	6.86362e8i	−0.0740140	+	0.0427320i
$357$	2.20556e9	+	1.02636e10i	0.135783	+	0.631866i
$358$	2.12635e8	−	3.68295e8i	0.0129450	−	0.0224215i
$359$		−	4.04837e8i		−	0.0243726i	−0.999926	−	0.0121863i	$-0.996121\pi$
$359$		−	4.04837e8i		−	0.0243726i	0.999926	−	0.0121863i	$-0.00387912\pi$
$360$	−2.06512e10	+	9.30529e9i	−1.22952	+	0.554013i
$361$	−8.56218e9			−0.504145
$362$	−9.11110e9	−	5.26030e9i	−0.530562	−	0.306320i
$363$	4.28656e9	−	1.32937e10i	0.246878	−	0.765628i
$364$	2.17669e9	+	3.77014e9i	0.123991	+	0.214759i
$365$	9.73287e9	−	5.61927e9i	0.548364	−	0.316598i
$366$	−2.08185e10	−	6.71297e9i	−1.16018	−	0.374102i
$367$	−1.54013e10	+	2.66758e10i	−0.848970	+	1.47046i	0.0331587	+	0.999450i	$0.489443\pi$
$367$	−1.54013e10	+	2.66758e10i	−0.848970	+	1.47046i	−0.882129	+	0.471009i	$0.843890\pi$
$368$			5.76506e9i			0.314349i
$369$	−6.08829e9	−	1.35117e10i	−0.328390	−	0.728795i
$370$	−2.08504e9			−0.111252
$371$	5.29076e9	+	3.05462e9i	0.279269	+	0.161236i
$372$	4.73244e9	−	1.01697e9i	0.247123	−	0.0531049i
$373$	5.49331e9	+	9.51470e9i	0.283791	+	0.491541i	0.972315	−	0.233673i	$-0.0750744\pi$
$373$	5.49331e9	+	9.51470e9i	0.283791	+	0.491541i	−0.688524	+	0.725213i	$0.741741\pi$
$374$	2.35129e9	−	1.35752e9i	0.120177	−	0.0693841i
$375$	−8.04736e9	+	7.27850e9i	−0.406938	+	0.368058i
$376$	2.81233e8	−	4.87110e8i	0.0140707	−	0.0243711i
$377$		−	8.52826e9i		−	0.422178i
$378$	1.29584e10	−	2.96380e10i	0.634722	−	1.45172i
$379$	3.02748e10			1.46732			0.733659	−	0.679517i	$-0.237811\pi$
$379$	3.02748e10			1.46732			0.733659	+	0.679517i	$0.237811\pi$
$380$	3.66487e9	+	2.11591e9i	0.175762	+	0.101476i
$381$	−1.11056e9	−	1.22788e9i	−0.0527040	−	0.0582714i
$382$	1.58209e10	+	2.74027e10i	0.742983	+	1.28688i
$383$	−8.03555e9	+	4.63933e9i	−0.373440	+	0.215606i	−0.674960	−	0.737854i	$-0.735839\pi$
$383$	−8.03555e9	+	4.63933e9i	−0.373440	+	0.215606i	0.301520	+	0.953460i	$0.402506\pi$
$384$	2.39348e9	+	1.11380e10i	0.110079	+	0.512251i
$385$	1.09632e10	−	1.89889e10i	0.498994	−	0.864283i
$386$		−	1.22358e10i		−	0.551168i
$387$	−1.75194e10	−	1.26094e10i	−0.781043	−	0.562146i
$388$	−2.91270e9			−0.128519
$389$	−3.34709e10	−	1.93244e10i	−1.46174	−	0.843934i	−0.462645	−	0.886543i	$-0.653100\pi$
$389$	−3.34709e10	−	1.93244e10i	−1.46174	−	0.843934i	−0.999092	+	0.0426090i	$0.986433\pi$
$390$	−4.62943e9	+	1.43570e10i	−0.200110	+	0.620589i
$391$	−1.83542e9	−	3.17904e9i	−0.0785287	−	0.136016i
$392$	4.99561e10	−	2.88422e10i	2.11565	−	1.22147i
$393$	3.99416e10	+	1.28792e10i	1.67439	+	0.539909i
$394$	−1.28117e10	+	2.21905e10i	−0.531645	+	0.920836i
$395$		−	4.21340e10i		−	1.73079i
$396$	2.49614e9	+	2.51084e8i	0.101505	+	0.0102103i
$397$	1.60205e9			0.0644933			0.0322466	−	0.999480i	$-0.489734\pi$
$397$	1.60205e9			0.0644933			0.0322466	+	0.999480i	$0.489734\pi$
$398$	1.41701e10	+	8.18112e9i	0.564730	+	0.326047i
$399$	−3.15199e10	+	6.77339e9i	−1.24364	+	0.267248i
$400$	−5.14026e9	−	8.90320e9i	−0.200792	−	0.347781i
$401$	−1.29788e10	+	7.49329e9i	−0.501945	+	0.289798i	−0.729516	−	0.683963i	$-0.760255\pi$
$401$	−1.29788e10	+	7.49329e9i	−0.501945	+	0.289798i	0.227572	+	0.973761i	$0.426921\pi$
$402$	1.97536e10	−	1.78663e10i	0.756382	−	0.684116i
$403$	8.59855e9	−	1.48931e10i	0.325991	−	0.564632i
$404$			1.20184e10i			0.451149i
$405$	−3.18728e10	+	1.06719e10i	−1.18468	+	0.396664i
$406$	−3.05426e10			−1.12409
$407$	1.06690e9	+	6.15976e8i	0.0388819	+	0.0224485i
$408$	−7.17853e9	−	7.93684e9i	−0.259057	−	0.286422i
$409$	8.26473e9	+	1.43149e10i	0.295349	+	0.511560i	0.975066	−	0.221915i	$-0.0712307\pi$
$409$	8.26473e9	+	1.43149e10i	0.295349	+	0.511560i	−0.679717	+	0.733474i	$0.737897\pi$
$410$	2.14355e10	−	1.23758e10i	0.758574	−	0.437963i
$411$	−5.05683e9	−	2.35319e10i	−0.177219	−	0.824688i
$412$	5.76013e8	−	9.97684e8i	0.0199914	−	0.0346262i
$413$			8.98320e10i			3.08767i
$414$	−1.13204e9	+	1.12542e10i	−0.0385356	+	0.383100i
$415$	2.39971e10			0.809032
$416$	−6.96620e9	−	4.02194e9i	−0.232607	−	0.134296i
$417$	−1.22070e10	+	3.78568e10i	−0.403705	+	1.25199i
$418$	4.16901e9	+	7.22094e9i	0.136561	+	0.236531i
$419$	−1.89762e10	+	1.09559e10i	−0.615676	+	0.355461i	−0.775184	−	0.631736i	$-0.782343\pi$
$419$	−1.89762e10	+	1.09559e10i	−0.615676	+	0.355461i	0.159507	+	0.987197i	$0.449009\pi$
$420$	−1.54189e10	−	4.97184e9i	−0.495514	−	0.159779i
$421$	−1.72487e10	+	2.98757e10i	−0.549071	+	0.951020i	0.449267	+	0.893398i	$0.351685\pi$
$421$	−1.72487e10	+	2.98757e10i	−0.549071	+	0.951020i	−0.998338	+	0.0576222i	$0.981648\pi$
$422$			1.88618e10i			0.594750i
$423$	4.87575e8	−	6.77434e8i	0.0152293	−	0.0211595i
$424$	−6.22782e9			−0.192696
$425$	5.66902e9	+	3.27301e9i	0.173761	+	0.100321i
$426$	1.01395e10	−	2.17891e9i	0.307878	−	0.0661608i
$427$	−4.17308e10	−	7.22799e10i	−1.25529	−	2.17423i
$428$	4.99566e9	−	2.88424e9i	0.148874	−	0.0859522i
$429$	6.61028e9	−	5.97872e9i	0.195160	−	0.176514i
$430$	1.80252e10	−	3.12206e10i	0.527239	−	0.913204i
$431$		−	1.04363e10i		−	0.302440i	−0.988500	−	0.151220i	$-0.951680\pi$
$431$		−	1.04363e10i		−	0.302440i	0.988500	−	0.151220i	$-0.0483202\pi$
$432$	2.77312e9	+	2.47854e10i	0.0796222	+	0.711641i
$433$	9.48759e9			0.269901			0.134950	−	0.990852i	$-0.456912\pi$
$433$	9.48759e9			0.269901			0.134950	+	0.990852i	$0.456912\pi$
$434$	−5.33373e10	−	3.07943e10i	−1.50339	−	0.867984i
$435$	2.12889e10	+	2.35377e10i	0.594559	+	0.657366i
$436$	1.90857e9	+	3.30573e9i	0.0528155	+	0.0914791i
$437$	9.76300e9	−	5.63667e9i	0.267706	−	0.154560i
$438$	−3.43738e9	−	1.59958e10i	−0.0933967	−	0.434620i
$439$	2.99022e10	−	5.17921e10i	0.805091	−	1.39446i	−0.111138	−	0.993805i	$-0.535450\pi$
$439$	2.99022e10	−	5.17921e10i	0.805091	−	1.39446i	0.916229	−	0.400654i	$-0.131217\pi$
$440$			2.23520e10i			0.596357i
$441$	7.80422e10	−	3.51653e10i	2.06336	−	0.929736i
$442$	−7.12701e9			−0.186732
$443$	2.90683e10	+	1.67826e10i	0.754753	+	0.435757i	0.827409	−	0.561600i	$-0.189814\pi$
$443$	2.90683e10	+	1.67826e10i	0.754753	+	0.435757i	−0.0726555	+	0.997357i	$0.523147\pi$
$444$	2.79346e8	−	8.66320e8i	0.00718805	−	0.0222919i
$445$	−9.07456e9	−	1.57176e10i	−0.231412	−	0.400817i
$446$	−9.58278e9	+	5.53262e9i	−0.242188	+	0.139827i
$447$	2.82019e10	+	9.09374e9i	0.706396	+	0.227778i
$448$	−4.04573e10	+	7.00740e10i	−1.00435	+	1.73958i
$449$		−	6.27667e10i		−	1.54434i	−0.635413	−	0.772172i	$-0.719170\pi$
$449$		−	6.27667e10i		−	1.54434i	0.635413	−	0.772172i	$-0.280830\pi$
$450$	−8.28623e9	−	1.83896e10i	−0.202072	−	0.448459i
$451$	−1.46246e10			−0.353489
$452$	−6.80783e9	−	3.93050e9i	−0.163100	−	0.0941660i
$453$	1.91767e10	−	4.12094e9i	0.455389	−	0.0978596i
$454$	6.82666e9	+	1.18241e10i	0.160689	+	0.278321i
$455$	−4.98460e10	+	2.87786e10i	−1.16301	+	0.671466i
$456$	2.43744e10	−	2.20456e10i	0.563735	−	0.509874i
$457$	−1.95241e10	+	3.38167e10i	−0.447616	+	0.775294i	−0.998230	−	0.0594657i	$-0.981060\pi$
$457$	−1.95241e10	+	3.38167e10i	−0.447616	+	0.775294i	0.550614	+	0.834760i	$0.314394\pi$
$458$			3.32942e10i			0.756670i
$459$	−9.42012e9	−	1.27846e10i	−0.212230	−	0.288029i
$460$	5.66497e9			0.126522
$461$	2.09686e10	+	1.21062e10i	0.464264	+	0.268043i	0.713836	−	0.700313i	$-0.246956\pi$
$461$	2.09686e10	+	1.21062e10i	0.464264	+	0.268043i	−0.249571	+	0.968356i	$0.580290\pi$
$462$	−2.14118e10	−	2.36737e10i	−0.469987	−	0.519634i
$463$	1.41145e10	+	2.44470e10i	0.307144	+	0.531988i	0.977736	−	0.209837i	$-0.0672935\pi$
$463$	1.41145e10	+	2.44470e10i	0.307144	+	0.531988i	−0.670593	+	0.741826i	$0.733960\pi$
$464$	2.03939e10	−	1.17744e10i	0.439975	−	0.254020i
$465$	1.34456e10	+	6.25688e10i	0.287586	+	1.33828i
$466$	2.14186e10	−	3.70981e10i	0.454200	−	0.786698i
$467$		−	3.95095e8i		−	0.00830681i	−0.999991	−	0.00415341i	$-0.998678\pi$
$467$		−	3.95095e8i		−	0.00830681i	0.999991	−	0.00415341i	$-0.00132207\pi$
$468$	−5.34499e9	−	3.84699e9i	−0.111420	−	0.0801933i
$469$	1.01626e11			2.10046
$470$	1.20723e9	+	6.96995e8i	0.0247399	+	0.0142836i
$471$	−5.17677e9	+	1.60544e10i	−0.105190	+	0.326220i
$472$	−4.57878e10	−	7.93069e10i	−0.922534	−	1.59787i
$473$	−1.84468e10	+	1.06503e10i	−0.368533	+	0.212773i
$474$	−5.83784e10	−	1.88242e10i	−1.15648	−	0.372909i
$475$	−1.00516e10	+	1.74099e10i	−0.197451	+	0.341996i
$476$		−	7.65416e9i		−	0.149097i
$477$	−9.19518e9	−	9.24933e8i	−0.177618	−	0.0178664i
$478$	−5.16977e10			−0.990284
$479$	−4.38005e10	−	2.52882e10i	−0.832026	−	0.480370i	0.0225201	−	0.999746i	$-0.492831\pi$
$479$	−4.38005e10	−	2.52882e10i	−0.832026	−	0.480370i	−0.854546	+	0.519376i	$0.826164\pi$
$480$	2.92663e10	−	6.28911e9i	0.551319	−	0.118474i
$481$	−1.61695e9	−	2.80063e9i	−0.0302075	−	0.0523209i
$482$	−2.23940e10	+	1.29292e10i	−0.414899	+	0.239542i
$483$	−3.20077e10	+	2.89496e10i	−0.588120	+	0.531930i
$484$	−5.09203e9	+	8.81965e9i	−0.0927918	+	0.160720i
$485$		−	3.85095e10i		−	0.695987i
$486$	5.46567e8	+	4.89290e10i	0.00979711	+	0.877044i
$487$	−5.77961e10			−1.02750			−0.513751	−	0.857940i	$-0.671744\pi$
$487$	−5.77961e10			−1.02750			−0.513751	+	0.857940i	$0.671744\pi$
$488$	7.36829e10	+	4.25408e10i	1.29923	+	0.750113i
$489$	−5.53747e10	−	6.12243e10i	−0.968448	−	1.07075i
$490$	7.14811e10	+	1.23809e11i	1.23996	+	2.14767i
$491$	6.06996e10	−	3.50449e10i	1.04438	−	0.602975i	0.123312	−	0.992368i	$-0.460648\pi$
$491$	6.06996e10	−	3.50449e10i	1.04438	−	0.602975i	0.921072	+	0.389393i	$0.127315\pi$
$492$	2.27021e9	+	1.05644e10i	0.0387440	+	0.180295i
$493$	−7.49724e9	+	1.29856e10i	−0.126915	+	0.219824i
$494$		−	2.18874e10i		−	0.367525i
$495$	−3.31964e9	+	3.30021e10i	−0.0552931	+	0.549693i
$496$	4.74858e10			0.784580
$497$	3.42695e10	+	1.97855e10i	0.561672	+	0.324281i
$498$	1.07212e10	−	3.32489e10i	0.174311	−	0.540580i
$499$	4.15944e10	+	7.20436e10i	0.670861	+	1.16196i	0.977660	+	0.210191i	$0.0674085\pi$
$499$	4.15944e10	+	7.20436e10i	0.670861	+	1.16196i	−0.306800	+	0.951774i	$0.599258\pi$
$500$	6.85146e9	−	3.95569e9i	0.109623	−	0.0632911i
$501$	−1.14682e11	−	3.69795e10i	−1.82031	−	0.586962i
$502$	4.09741e10	−	7.09691e10i	0.645200	−	1.11752i
$503$		−	3.33685e10i		−	0.521272i	−0.965437	−	0.260636i	$-0.916068\pi$
$503$		−	3.33685e10i		−	0.521272i	0.965437	−	0.260636i	$-0.0839323\pi$
$504$	−7.34981e10	+	1.02118e11i	−1.13908	+	1.58263i
$505$	−1.58898e11			−2.44316
$506$	9.66636e9	+	5.58088e9i	0.147456	+	0.0851335i
$507$	4.17250e10	−	8.96640e9i	0.631488	−	0.135702i
$508$	6.03566e8	+	1.04541e9i	0.00906295	+	0.0156975i
$509$	1.17263e10	−	6.77018e9i	0.174699	−	0.100862i	−0.410101	−	0.912040i	$-0.634506\pi$
$509$	1.17263e10	−	6.77018e9i	0.174699	−	0.100862i	0.584800	+	0.811178i	$0.301173\pi$
$510$	1.96703e10	−	1.77909e10i	0.290757	−	0.262977i
$511$	3.12131e10	−	5.40626e10i	0.457776	−	0.792891i
$512$		−	7.53294e10i		−	1.09619i
$513$	3.92622e10	−	2.89297e10i	0.566898	−	0.417709i
$514$	7.64124e10			1.09474
$515$	1.31906e10	+	7.61562e9i	0.187515	+	0.108262i
$516$	1.05570e10	+	1.16722e10i	0.148916	+	0.164647i
$517$	−4.11822e8	−	7.13296e8i	−0.00576430	−	0.00998407i
$518$	−1.00300e10	+	5.79083e9i	−0.139310	+	0.0804307i
$519$	9.56023e9	+	4.44884e10i	0.131765	+	0.613165i
$520$	2.93372e10	−	5.08135e10i	0.401241	−	0.694969i
$521$			3.88502e10i			0.527281i	0.964621	+	0.263641i	$0.0849233\pi$
$521$			3.88502e10i			0.527281i	−0.964621	+	0.263641i	$0.915077\pi$
$522$	4.21237e10	−	1.89806e10i	0.567341	−	0.255640i
$523$	7.89795e10			1.05562			0.527810	−	0.849362i	$-0.323013\pi$
$523$	7.89795e10			1.05562			0.527810	+	0.849362i	$0.323013\pi$
$524$	−2.64992e10	−	1.52993e10i	−0.351486	−	0.202930i
$525$	2.36186e10	−	7.32469e10i	0.310897	−	0.964166i
$526$	−4.16526e10	−	7.21444e10i	−0.544126	−	0.942453i
$527$	−2.61852e10	+	1.51181e10i	−0.339480	+	0.195999i
$528$	2.34234e10	+	7.55293e9i	0.301381	+	0.0971806i
$529$	−3.16099e10	+	5.47500e10i	−0.403646	+	0.699136i
$530$		−	1.54347e10i		−	0.195612i
$531$	−5.58259e10	−	1.23894e11i	−0.702195	−	1.55838i
$532$	2.35063e10			0.293453
$533$	3.32464e10	+	1.91948e10i	0.411942	+	0.237835i
$534$	−2.58316e10	+	5.55103e9i	−0.317678	+	0.0682666i
$535$	3.81333e10	+	6.60488e10i	0.465468	+	0.806213i
$536$	−8.97190e10	+	5.17993e10i	−1.08699	+	0.627574i
$537$	−1.82045e9	+	1.64652e9i	−0.0218918	+	0.0198002i
$538$	−5.70229e10	+	9.87666e10i	−0.680645	+	1.17891i
$539$		−	8.44697e10i		−	1.00080i
$540$	2.43551e10	−	2.72498e9i	0.286428	−	0.0320470i
$541$	−9.12585e10			−1.06533			−0.532665	−	0.846326i	$-0.678809\pi$
$541$	−9.12585e10			−1.06533			−0.532665	+	0.846326i	$0.678809\pi$
$542$	5.89532e10	+	3.40367e10i	0.683141	+	0.394412i
$543$	4.07326e10	+	4.50354e10i	0.468536	+	0.518030i
$544$	7.07141e9	+	1.22480e10i	0.0807440	+	0.139853i
$545$	−4.37059e10	+	2.52336e10i	−0.495398	+	0.286018i
$546$	1.76042e10	+	8.19211e10i	0.198083	+	0.921775i
$547$	−6.11129e10	+	1.05851e11i	−0.682627	+	1.18234i	0.291549	+	0.956556i	$0.405829\pi$
$547$	−6.11129e10	+	1.05851e11i	−0.682627	+	1.18234i	−0.974176	+	0.225789i	$0.927504\pi$
$548$			1.75492e10i			0.194596i
$549$	1.02472e11	+	7.37533e10i	1.12802	+	0.811880i
$550$	−1.99042e10			−0.217517
$551$	−3.98794e10	−	2.30244e10i	−0.432656	−	0.249794i
$552$	1.35018e10	−	4.18722e10i	0.145423	−	0.450993i
$553$	−1.17020e11	−	2.02684e11i	−1.25129	−	2.16730i
$554$	−6.55512e10	+	3.78460e10i	−0.695891	+	0.401773i
$555$	1.14538e10	+	3.69331e9i	0.120720	+	0.0389264i
$556$	1.45007e10	−	2.51160e10i	0.151737	−	0.262816i
$557$			8.31342e10i			0.863692i	0.901947	+	0.431846i	$0.142138\pi$
$557$			8.31342e10i			0.863692i	−0.901947	+	0.431846i	$0.857862\pi$
$558$	9.26987e10	+	9.32447e9i	0.956174	+	0.0961805i
$559$	5.59142e10			0.572631
$560$	−1.37638e11	−	7.94654e10i	−1.39954	−	0.808027i
$561$	−1.53211e10	+	3.29239e9i	−0.154681	+	0.0332399i
$562$	−2.54938e10	−	4.41566e10i	−0.255558	−	0.442640i
$563$	4.30743e9	−	2.48690e9i	0.0428731	−	0.0247528i	−0.478410	−	0.878136i	$-0.658787\pi$
$563$	4.30743e9	−	2.48690e9i	0.0428731	−	0.0247528i	0.521283	+	0.853384i	$0.325453\pi$
$564$	−4.51337e8	+	4.08215e8i	−0.00446051	+	0.00403434i
$565$	5.19661e10	−	9.00080e10i	0.509949	−	0.883258i
$566$			1.14238e11i			1.11313i
$567$	−1.23684e11	+	1.39858e11i	−1.19669	+	1.35318i
$568$	−4.03391e10			−0.387555
$569$	1.40620e11	+	8.11870e10i	1.34152	+	0.774528i	0.987031	−	0.160531i	$-0.0513206\pi$
$569$	1.40620e11	+	8.11870e10i	1.34152	+	0.774528i	0.354492	+	0.935059i	$0.384654\pi$
$570$	5.46369e10	+	6.04085e10i	0.517591	+	0.572267i
$571$	3.84545e10	+	6.66051e10i	0.361745	+	0.626561i	0.988248	−	0.152858i	$-0.0488477\pi$
$571$	3.84545e10	+	6.66051e10i	0.361745	+	0.626561i	−0.626503	+	0.779419i	$0.715514\pi$
$572$	−5.62794e9	+	3.24929e9i	−0.0525733	+	0.0303532i
$573$	−3.83705e10	−	1.78557e11i	−0.355942	−	1.65637i
$574$	6.87431e10	−	1.19067e11i	0.633260	−	1.09684i
$575$			2.69112e10i			0.246185i
$576$	1.22504e10	−	1.21787e11i	0.111291	−	1.10639i
$577$	1.27866e11			1.15359			0.576796	−	0.816888i	$-0.304303\pi$
$577$	1.27866e11			1.15359			0.576796	+	0.816888i	$0.304303\pi$
$578$	−7.39275e10	−	4.26821e10i	−0.662361	−	0.382414i
$579$	−2.16738e10	+	6.72156e10i	−0.192850	+	0.598075i
$580$	−1.15700e10	−	2.00398e10i	−0.102240	−	0.177085i
$581$	1.15437e11	−	6.66476e10i	1.01307	−	0.584898i
$582$	−5.33565e10	−	1.72049e10i	−0.465046	−	0.149955i
$583$	−4.55984e9	+	7.89787e9i	−0.0394707	+	0.0683653i
$584$			6.36378e10i			0.547097i
$585$	5.08620e10	−	7.06674e10i	0.434281	−	0.603387i
$586$	−1.39077e11			−1.17941
$587$	4.13335e10	+	2.38639e10i	0.348137	+	0.200997i	0.663864	−	0.747853i	$-0.268915\pi$
$587$	4.13335e10	+	2.38639e10i	0.348137	+	0.200997i	−0.315728	+	0.948850i	$0.602249\pi$
$588$	−6.10186e10	+	1.31124e10i	−0.510450	+	0.109692i
$589$	−4.64283e10	−	8.04162e10i	−0.385764	−	0.668163i
$590$	1.96551e11	−	1.13478e11i	1.62206	−	0.936495i
$591$	1.09686e11	−	9.92062e10i	0.899085	−	0.813184i
$592$	4.46482e9	−	7.73329e9i	0.0363511	−	0.0629619i
$593$			1.18090e11i			0.954983i	0.878636	+	0.477492i	$0.158454\pi$
$593$			1.18090e11i			0.954983i	−0.878636	+	0.477492i	$0.841546\pi$
$594$	4.42426e10	+	1.93438e10i	0.355382	+	0.155381i
$595$	1.01198e11			0.807425
$596$	−1.87105e10	−	1.08025e10i	−0.148286	−	0.0856130i
$597$	−6.33498e10	−	7.00417e10i	−0.498710	−	0.551391i
$598$	−1.46499e10	−	2.53743e10i	−0.114559	−	0.198422i
$599$	1.84255e10	−	1.06380e10i	0.143124	−	0.0826327i	−0.426728	−	0.904380i	$-0.640334\pi$
$599$	1.84255e10	−	1.06380e10i	0.143124	−	0.0826327i	0.569852	+	0.821747i	$0.307000\pi$
$600$	1.64830e10	+	7.67034e10i	0.127184	+	0.591847i
$601$	−1.78722e10	+	3.09555e10i	−0.136987	+	0.237269i	−0.926355	−	0.376652i	$-0.877075\pi$
$601$	−1.78722e10	+	3.09555e10i	−0.136987	+	0.237269i	0.789368	+	0.613921i	$0.210409\pi$
$602$		−	2.00248e11i		−	1.52469i
$603$	−1.40160e11	+	6.31553e10i	−1.06012	+	0.477684i
$604$	−1.43013e10			−0.107455
$605$	−1.16607e11	−	6.73230e10i	−0.870367	−	0.502507i
$606$	−7.09908e10	+	2.20160e11i	−0.526395	+	1.63248i
$607$	7.23802e10	+	1.25366e11i	0.533169	+	0.923476i	0.999250	+	0.0387335i	$0.0123323\pi$
$607$	7.23802e10	+	1.25366e11i	0.533169	+	0.923476i	−0.466081	+	0.884742i	$0.654334\pi$
$608$	−3.76143e10	+	2.17167e10i	−0.275258	+	0.158920i
$609$	1.67781e11	+	5.41013e10i	1.21976	+	0.393313i
$610$	−1.05431e11	+	1.82612e11i	−0.761465	+	1.31890i
$611$			2.16207e9i			0.0155133i
$612$	4.75666e9	+	1.05564e10i	0.0339076	+	0.0752510i
$613$	−6.24369e10			−0.442180			−0.221090	−	0.975253i	$-0.570961\pi$
$613$	−6.24369e10			−0.442180			−0.221090	+	0.975253i	$0.570961\pi$
$614$	−3.91582e10	−	2.26080e10i	−0.275517	−	0.159070i
$615$	−1.39674e11	+	3.00150e10i	−0.976373	+	0.209815i
$616$	6.20788e10	+	1.07524e11i	0.431142	+	0.746760i
$617$	−2.52991e10	+	1.46064e10i	−0.174568	+	0.100787i	−0.584738	−	0.811222i	$-0.698803\pi$
$617$	−2.52991e10	+	1.46064e10i	−0.174568	+	0.100787i	0.410170	+	0.912009i	$0.365469\pi$
$618$	1.64449e10	−	1.48737e10i	0.112740	−	0.101969i
$619$	9.88162e9	−	1.71155e10i	0.0673078	−	0.116581i	−0.830408	−	0.557156i	$-0.811892\pi$
$619$	9.88162e9	−	1.71155e10i	0.0673078	−	0.116581i	0.897715	+	0.440576i	$0.145226\pi$
$620$		−	4.66614e10i		−	0.315785i
$621$	2.61536e10	−	5.98178e10i	0.175859	−	0.402220i
$622$	1.59686e11			1.06686
$623$	−8.73057e10	−	5.04060e10i	−0.579550	−	0.334603i
$624$	−4.33359e10	−	4.79137e10i	−0.285831	−	0.316025i
$625$	9.50853e10	+	1.64693e11i	0.623151	+	1.07933i
$626$	1.76367e10	−	1.01825e10i	0.114847	−	0.0663069i
$627$	−1.01111e10	−	4.70518e10i	−0.0654226	−	0.304443i
$628$	6.14951e9	−	1.06513e10i	0.0395368	−	0.0684798i
$629$			5.68586e9i			0.0363240i
$630$	−2.53084e11	−	1.82154e11i	−1.60658	−	1.15632i
$631$	−4.61313e10			−0.290990			−0.145495	−	0.989359i	$-0.546477\pi$
$631$	−4.61313e10			−0.290990			−0.145495	+	0.989359i	$0.546477\pi$
$632$	2.06618e11	+	1.19291e11i	1.29509	+	0.747721i
$633$	3.34107e10	−	1.03615e11i	0.208099	−	0.645366i
$634$	−8.07780e9	−	1.39912e10i	−0.0499961	−	0.0865958i
$635$	−1.38216e10	+	7.97989e9i	−0.0850086	+	0.0490797i
$636$	6.41304e9	+	2.06789e9i	0.0391954	+	0.0126386i
$637$	−1.10867e11	+	1.92027e11i	−0.673356	+	1.16629i
$638$		−	4.55930e10i		−	0.275179i
$639$	−5.95594e10	−	5.99102e9i	−0.357229	−	0.0359333i
$640$	1.09820e11			0.654577
$641$	−1.75989e11	−	1.01607e11i	−1.04244	−	0.601855i	−0.121919	−	0.992540i	$-0.538905\pi$
$641$	−1.75989e11	−	1.01607e11i	−1.04244	−	0.601855i	−0.920525	+	0.390685i	$0.872238\pi$
$642$	1.08550e11	−	2.33266e10i	0.638985	−	0.137313i
$643$	−8.38984e10	−	1.45316e11i	−0.490806	−	0.850101i	0.509138	−	0.860685i	$-0.329964\pi$
$643$	−8.38984e10	−	1.45316e11i	−0.490806	−	0.850101i	−0.999944	+	0.0105838i	$0.996631\pi$
$644$	2.72511e10	−	1.57334e10i	0.158431	−	0.0914703i
$645$	−1.54321e11	+	1.39577e11i	−0.891633	+	0.806444i
$646$	−1.92413e10	+	3.33270e10i	−0.110485	+	0.191366i
$647$		−	5.14865e10i		−	0.293817i	−0.989150	−	0.146908i	$-0.953068\pi$
$647$		−	5.14865e10i		−	0.293817i	0.989150	−	0.146908i	$-0.0469322\pi$
$648$	3.79060e10	−	1.86514e11i	0.214985	−	1.05782i
$649$	−1.34098e11			−0.755865
$650$	4.52487e10	+	2.61244e10i	0.253485	+	0.146350i
$651$	2.38453e11	+	2.63642e11i	1.32764	+	1.46788i
$652$	3.00949e10	+	5.21259e10i	0.166534	+	0.288445i
$653$	2.87927e11	−	1.66235e11i	1.58354	−	0.914260i	0.589209	−	0.807981i	$-0.299440\pi$
$653$	2.87927e11	−	1.66235e11i	1.58354	−	0.914260i	0.994336	−	0.106279i	$-0.0338937\pi$
$654$	1.54357e10	+	7.18300e10i	0.0843755	+	0.392640i
$655$	2.02276e11	−	3.50353e11i	1.09895	−	1.90345i
$656$			1.06004e11i			0.572410i
$657$	−9.45126e9	+	9.39593e10i	−0.0507257	+	0.504287i
$658$	7.74312e9			0.0413059
$659$	−1.31243e11	−	7.57732e10i	−0.695880	−	0.401767i	0.109931	−	0.993939i	$-0.464937\pi$
$659$	−1.31243e11	−	7.57732e10i	−0.695880	−	0.401767i	−0.805811	+	0.592172i	$0.798270\pi$
$660$	7.42180e9	−	2.30168e10i	0.0391141	−	0.121302i
$661$	9.66735e10	+	1.67443e11i	0.506409	+	0.877127i	0.999972	+	0.00741673i	$0.00236084\pi$
$661$	9.66735e10	+	1.67443e11i	0.506409	+	0.877127i	−0.493563	+	0.869710i	$0.664306\pi$
$662$	−9.22258e10	+	5.32466e10i	−0.480198	+	0.277243i
$663$	3.91511e10	+	1.26243e10i	0.202624	+	0.0653363i
$664$	−6.79412e10	+	1.17678e11i	−0.349511	+	0.605371i
$665$			3.10783e11i			1.58917i
$666$	1.02345e10	−	1.42197e10i	0.0520198	−	0.0722760i
$667$	−6.16435e10			−0.311447
$668$	7.60858e10	+	4.39281e10i	0.382118	+	0.220616i
$669$	6.24416e10	−	1.34182e10i	0.311724	−	0.0669871i
$670$	−1.28377e11	−	2.22355e11i	−0.637071	−	1.10344i
$671$	1.07897e11	−	6.22944e10i	0.532255	−	0.307297i
$672$	1.23318e11	−	1.11535e11i	0.604711	−	0.546935i
$673$	1.66337e11	−	2.88105e11i	0.810830	−	1.40440i	−0.101454	−	0.994840i	$-0.532349\pi$
$673$	1.66337e11	−	2.88105e11i	0.810830	−	1.40440i	0.912284	−	0.409559i	$-0.134317\pi$
$674$			8.41002e10i			0.407528i
$675$	1.29449e10	+	1.15698e11i	0.0623568	+	0.557329i
$676$	−3.11169e10			−0.149008
$677$	−3.43053e11	−	1.98062e11i	−1.63308	−	0.942857i	−0.983137	−	0.182870i	$-0.941461\pi$
$677$	−3.43053e11	−	1.98062e11i	−1.63308	−	0.942857i	−0.649939	−	0.759987i	$-0.725205\pi$
$678$	−1.01493e11	−	1.12214e11i	−0.480305	−	0.531042i
$679$	−1.06953e11	−	1.85249e11i	−0.503171	−	0.871517i
$680$	−8.93408e10	+	5.15809e10i	−0.417844	+	0.241242i
$681$	−1.65567e10	−	7.70463e10i	−0.0769813	−	0.358231i
$682$	4.59688e10	−	7.96202e10i	0.212484	−	0.368032i
$683$		−	5.35678e10i		−	0.246162i	−0.992397	−	0.123081i	$-0.960722\pi$
$683$		−	5.35678e10i		−	0.246162i	0.992397	−	0.123081i	$-0.0392775\pi$
$684$	−3.24194e10	+	1.46079e10i	−0.148109	+	0.0667367i
$685$	−2.32022e11			−1.05382
$686$	3.83840e11	+	2.21610e11i	1.73322	+	1.00068i
$687$	5.89752e10	−	1.82896e11i	0.264754	−	0.821066i
$688$	7.71970e10	+	1.33709e11i	0.344546	+	0.596770i
$689$	2.07320e10	−	1.19696e10i	0.0919950	−	0.0531133i
$690$	1.03774e11	+	3.34622e10i	0.457818	+	0.147624i
$691$	6.61300e10	−	1.14540e11i	0.290059	−	0.502397i	−0.683764	−	0.729703i	$-0.739658\pi$
$691$	6.61300e10	−	1.14540e11i	0.290059	−	0.502397i	0.973823	+	0.227306i	$0.0729918\pi$
$692$		−	3.31777e10i		−	0.144685i
$693$	7.56884e10	+	1.67975e11i	0.328168	+	0.728303i
$694$	−4.27117e10			−0.184124
$695$	3.32065e11	+	1.91718e11i	1.42326	+	0.821719i
$696$	−1.75699e11	+	3.77564e10i	−0.748741	+	0.160899i
$697$	−3.37485e10	−	5.84541e10i	−0.142996	−	0.247676i
$698$	−2.27258e11	+	1.31207e11i	−0.957407	+	0.552759i
$699$	−1.83373e11	+	1.65853e11i	−0.768116	+	0.694728i
$700$	−2.80566e10	+	4.85955e10i	−0.116854	+	0.202397i
$701$			1.27802e11i			0.529256i	0.964351	+	0.264628i	$0.0852491\pi$
$701$			1.27802e11i			0.529256i	−0.964351	+	0.264628i	$0.914751\pi$
$702$	−7.51890e10	−	1.02044e11i	−0.309604	−	0.420182i
$703$	−1.74616e10			−0.0714927
$704$	−1.04604e11	−	6.03933e10i	−0.425852	−	0.245866i
$705$	−5.39712e9	−	5.96724e9i	−0.0218477	−	0.0241556i
$706$	2.31722e10	+	4.01355e10i	0.0932715	+	0.161551i
$707$	−7.64372e11	+	4.41311e11i	−3.05934	+	1.76631i
$708$	2.08164e10	+	9.68689e10i	0.0828462	+	0.385524i
$709$	−1.43783e11	+	2.49040e11i	−0.569014	+	0.985562i	0.427649	+	0.903945i	$0.359342\pi$
$709$	−1.43783e11	+	2.49040e11i	−0.569014	+	0.985562i	−0.996664	+	0.0816172i	$0.973992\pi$
$710$		−	9.99746e10i		−	0.393420i
$711$	2.87348e11	+	2.06816e11i	1.12442	+	0.809291i
$712$	1.02769e11			0.399890
$713$	−1.07650e11	−	6.21516e10i	−0.416538	−	0.240488i
$714$	4.52120e10	−	1.40213e11i	0.173965	−	0.539507i
$715$	−4.29597e10	−	7.44084e10i	−0.164376	−	0.284707i
$716$	1.54992e9	−	8.94846e8i	0.00589735	−	0.00340484i
$717$	2.83993e11	+	9.15741e10i	1.07456	+	0.346494i
$718$	−2.84066e9	+	4.92017e9i	−0.0106886	+	0.0185132i
$719$		−	3.68747e11i		−	1.37979i	−0.723910	−	0.689894i	$-0.757657\pi$
$719$		−	3.68747e11i		−	1.37979i	0.723910	−	0.689894i	$-0.242343\pi$
$720$	2.39211e11	+	2.40620e10i	0.890125	+	0.0895367i
$721$	8.46041e10			0.313076
$722$	1.04060e11	+	6.00791e10i	0.382944	+	0.221093i
$723$	1.45920e11	−	3.13570e10i	0.534023	−	0.114758i
$724$	−2.21372e10	−	3.83428e10i	−0.0805692	−	0.139550i
$725$	9.51985e10	−	5.49629e10i	0.344571	−	0.198938i
$726$	−1.45375e11	+	1.31486e11i	−0.523292	+	0.473295i
$727$	−1.41158e11	+	2.44493e11i	−0.505321	+	0.875242i	0.494660	+	0.869087i	$0.335293\pi$
$727$	−1.41158e11	+	2.44493e11i	−0.505321	+	0.875242i	−0.999981	+	0.00615516i	$0.998041\pi$
$728$		−	3.25915e11i		−	1.16032i
$729$	8.36673e10	−	2.69752e11i	0.296241	−	0.955113i
$730$	−1.57717e11			−0.555376
$731$	−8.51379e10	−	4.91544e10i	−0.298163	−	0.172144i
$732$	−6.17489e10	−	6.82717e10i	−0.215072	−	0.237792i
$733$	9.27774e10	+	1.60695e11i	0.321385	+	0.556656i	0.980774	−	0.195146i	$-0.0625182\pi$
$733$	9.27774e10	+	1.60695e11i	0.321385	+	0.556656i	−0.659389	+	0.751802i	$0.729185\pi$
$734$	3.74357e11	−	2.16135e11i	1.28974	−	0.744631i
$735$	−1.73363e11	−	8.06742e11i	−0.594028	−	2.76430i
$736$	−2.90711e10	+	5.03527e10i	−0.0990720	+	0.171598i
$737$			1.51704e11i			0.514194i
$738$	−2.08153e10	+	2.06934e11i	−0.0701709	+	0.697601i
$739$	2.47928e11			0.831282			0.415641	−	0.909529i	$-0.363557\pi$
$739$	2.47928e11			0.831282			0.415641	+	0.909529i	$0.363557\pi$
$740$	−7.59903e9	−	4.38730e9i	−0.0253414	−	0.0146309i
$741$	−3.87700e10	+	1.20235e11i	−0.128595	+	0.398803i
$742$	−4.28673e10	−	7.42483e10i	−0.141420	−	0.244946i
$743$	3.69180e11	−	2.13146e11i	1.21139	−	0.699395i	0.248327	−	0.968676i	$-0.420119\pi$
$743$	3.69180e11	−	2.13146e11i	1.21139	−	0.699395i	0.963062	+	0.269281i	$0.0867860\pi$
$744$	−3.44895e11	−	1.11212e11i	−1.12563	−	0.362960i
$745$	1.42823e11	−	2.47376e11i	0.463631	−	0.803032i
$746$		−	1.54182e11i		−	0.497826i
$747$	−1.17790e11	+	1.63657e11i	−0.378291	+	0.525596i
$748$	1.14259e10			0.0364992
$749$	3.66878e11	+	2.11817e11i	1.16572	+	0.673029i
$750$	1.48875e11	−	3.19921e10i	0.470518	−	0.101111i
$751$	1.75180e11	+	3.03421e11i	0.550714	+	0.953864i	0.998223	+	0.0595848i	$0.0189777\pi$
$751$	1.75180e11	+	3.03421e11i	0.550714	+	0.953864i	−0.447510	+	0.894279i	$0.647689\pi$
$752$	−5.17022e9	+	2.98503e9i	−0.0161673	+	0.00933421i
$753$	−3.50795e11	+	3.17279e11i	−1.09112	+	0.986873i
$754$	−5.98411e10	+	1.03648e11i	−0.185146	+	0.320682i
$755$		−	1.89081e11i		−	0.581915i
$756$	1.09591e11	−	8.07504e10i	0.335497	−	0.247205i
$757$	6.03226e11			1.83695			0.918473	−	0.395484i	$-0.129423\pi$
$757$	6.03226e11			1.83695			0.918473	+	0.395484i	$0.129423\pi$
$758$	−3.67943e11	−	2.12432e11i	−1.11456	−	0.643492i
$759$	−4.32150e10	−	4.77801e10i	−0.130217	−	0.143973i
$760$	−1.58408e11	−	2.74370e11i	−0.474812	−	0.822398i
$761$	−2.58522e11	+	1.49258e11i	−0.770829	+	0.445038i	−0.833170	−	0.553016i	$-0.813477\pi$
$761$	−2.58522e11	+	1.49258e11i	−0.770829	+	0.445038i	0.0623411	+	0.998055i	$0.480143\pi$
$762$	4.88140e9	+	2.27156e10i	0.0144785	+	0.0673757i
$763$	−1.40164e11	+	2.42771e11i	−0.413559	+	0.716306i
$764$			1.33161e11i			0.390843i
$765$	−1.39569e11	+	6.28890e10i	−0.407516	+	0.183624i
$766$	1.30213e11			0.378215
$767$	3.04849e11	+	1.76005e11i	0.880853	+	0.508561i
$768$	−6.96563e10	+	2.16021e11i	−0.200224	+	0.620942i
$769$	−1.81775e11	−	3.14844e11i	−0.519791	−	0.900305i	−0.999735	−	0.0230059i	$-0.992676\pi$
$769$	−1.81775e11	−	3.14844e11i	−0.519791	−	0.900305i	0.479944	−	0.877299i	$-0.340657\pi$
$770$	−2.66482e11	+	1.53853e11i	−0.758062	+	0.437667i
$771$	−4.19759e11	−	1.35352e11i	−1.18791	−	0.383043i
$772$	2.57464e10	−	4.45941e10i	0.0724848	−	0.125547i
$773$		−	4.05117e10i		−	0.113465i	−0.998389	−	0.0567326i	$-0.981932\pi$
$773$		−	4.05117e10i		−	0.113465i	0.998389	−	0.0567326i	$-0.0180683\pi$
$774$	1.24443e11	+	2.76177e11i	0.346743	+	0.769527i
$775$	2.21663e11			0.614451
$776$	1.88844e11	+	1.09029e11i	0.520783	+	0.300674i
$777$	6.53558e10	−	1.40445e10i	0.179308	−	0.0385320i
$778$	2.71191e11	+	4.69717e11i	0.740214	+	1.28209i
$779$	1.79516e11	−	1.03643e11i	0.487475	−	0.281444i
$780$	−4.70818e10	+	4.25835e10i	−0.127196	+	0.115044i
$781$	−2.95352e10	+	5.11564e10i	−0.0793844	+	0.137498i
$782$			5.15151e10i			0.137755i
$783$	−2.65021e11	+	2.96519e10i	−0.705072	+	0.0788871i
$784$	−6.12267e11			−1.62060
$785$	1.40823e11	+	8.13042e10i	0.370847	+	0.214109i
$786$	−3.95057e11	−	4.36789e11i	−1.03507	−	1.14441i
$787$	−2.03276e11	−	3.52084e11i	−0.529891	−	0.917797i	−0.999392	−	0.0348657i	$-0.988900\pi$
$787$	−2.03276e11	−	3.52084e11i	−0.529891	−	0.917797i	0.469501	−	0.882932i	$-0.344434\pi$
$788$	−9.33857e10	+	5.39163e10i	−0.242201	+	0.139835i
$789$	1.01020e11	+	4.70095e11i	0.260675	+	1.21305i
$790$	−2.95645e11	+	5.12073e11i	−0.759037	+	1.31469i
$791$		−	5.77307e11i		−	1.47469i
$792$	−1.52438e11	−	1.09715e11i	−0.387430	−	0.278848i
$793$	−3.27047e11			−0.827023
$794$	−1.94704e10	−	1.12413e10i	−0.0489884	−	0.0282835i
$795$	−2.73401e10	+	8.47884e10i	−0.0684435	+	0.212260i
$796$	3.44291e10	+	5.96330e10i	0.0857578	+	0.148537i
$797$	4.69140e11	−	2.70858e11i	1.16270	−	0.671287i	0.210753	−	0.977539i	$-0.432409\pi$
$797$	4.69140e11	−	2.70858e11i	1.16270	−	0.671287i	0.951950	+	0.306253i	$0.0990752\pi$
$798$	4.30603e11	+	1.38849e11i	1.06185	+	0.342397i
$799$	1.90069e9	−	3.29209e9i	0.00466363	−	0.00807764i
$800$		−	1.03682e11i		−	0.253130i
$801$	1.51735e11	+	1.52628e10i	0.368600	+	0.0370771i
$802$	2.10316e11			0.508363
$803$	8.07029e10	+	4.65938e10i	0.194101	+	0.112064i
$804$	1.09587e11	−	2.35494e10i	0.262261	−	0.0563580i
$805$	2.08016e11	+	3.60294e11i	0.495351	+	0.857973i
$806$	−2.09004e11	+	1.20668e11i	−0.495238	+	0.285926i
$807$	4.88196e11	−	4.41552e11i	1.15106	−	1.04109i
$808$	4.49877e11	−	7.79209e11i	1.05547	−	1.82814i
$809$			8.46989e11i			1.97735i	0.150073	+	0.988675i	$0.452049\pi$
$809$			8.46989e11i			1.97735i	−0.150073	+	0.988675i	$0.547951\pi$
$810$	4.62247e11	+	9.39445e10i	1.07383	+	0.218238i
$811$	−4.04679e11			−0.935464			−0.467732	−	0.883870i	$-0.654929\pi$
$811$	−4.04679e11			−0.935464			−0.467732	+	0.883870i	$0.654929\pi$
$812$	−1.11314e11	−	6.42672e10i	−0.256051	−	0.147831i
$813$	−2.63560e11	−	2.91401e11i	−0.603277	−	0.667005i
$814$	−8.64436e9	−	1.49725e10i	−0.0196895	−	0.0341033i
$815$	−6.89169e11	+	3.97892e11i	−1.56205	+	0.901851i
$816$	2.38644e10	+	1.11053e11i	0.0538258	+	0.250477i
$817$	1.50956e11	−	2.61463e11i	0.338814	−	0.586843i
$818$		−	2.31968e11i		−	0.518101i
$819$	4.84037e10	−	4.81204e11i	0.107583	−	1.06953i
$820$	1.04164e11			0.230389
$821$	−5.97010e11	−	3.44684e11i	−1.31404	−	0.758662i	−0.331278	−	0.943533i	$-0.607480\pi$
$821$	−5.97010e11	−	3.44684e11i	−1.31404	−	0.758662i	−0.982763	+	0.184872i	$0.940813\pi$
$822$	−1.03661e11	+	3.21477e11i	−0.227053	+	0.704145i
$823$	−3.27990e10	−	5.68095e10i	−0.0714926	−	0.123829i	0.828063	−	0.560635i	$-0.189443\pi$
$823$	−3.27990e10	−	5.68095e10i	−0.0714926	−	0.123829i	−0.899556	+	0.436806i	$0.856110\pi$
$824$	−7.46915e10	+	4.31231e10i	−0.162018	+	0.0935409i
$825$	1.09341e11	+	3.52570e10i	0.236029	+	0.0761079i
$826$	6.30333e11	−	1.09177e12i	1.35410	−	2.34536i
$827$			5.43243e11i			1.16137i	0.814127	+	0.580687i	$0.197216\pi$
$827$			5.43243e11i			1.16137i	−0.814127	+	0.580687i	$0.802784\pi$
$828$	−2.78066e10	+	3.86344e10i	−0.0591598	+	0.0821963i
$829$	−1.35770e11			−0.287466			−0.143733	−	0.989616i	$-0.545911\pi$
$829$	−1.35770e11			−0.287466			−0.143733	+	0.989616i	$0.545911\pi$
$830$	−2.91647e11	−	1.68382e11i	−0.614533	−	0.354801i
$831$	4.27133e11	−	9.17878e10i	0.895693	−	0.192478i
$832$	1.58533e11	+	2.74587e11i	0.330846	+	0.573043i
$833$	3.37624e11	−	1.94927e11i	0.701219	−	0.404849i
$834$	4.13990e11	−	3.74436e11i	0.855708	−	0.773951i
$835$	−5.80785e11	+	1.00595e12i	−1.19473	+	2.06933i
$836$			3.50894e10i			0.0718375i
$837$	−4.92709e11	−	2.15423e11i	−1.00390	−	0.438925i
$838$	3.07501e11			0.623549
$839$	2.70550e11	+	1.56202e11i	0.546009	+	0.315239i	0.747511	−	0.664250i	$-0.231249\pi$
$839$	2.70550e11	+	1.56202e11i	0.546009	+	0.315239i	−0.201502	+	0.979488i	$0.564582\pi$
$840$	8.13572e11	+	8.99514e11i	1.63410	+	1.80672i
$841$	−1.24224e11	−	2.15162e11i	−0.248325	−	0.430112i
$842$	4.19263e11	−	2.42062e11i	0.834139	−	0.481590i
$843$	6.18301e10	+	2.87726e11i	0.122430	+	0.569729i
$844$	−3.96887e10	+	6.87429e10i	−0.0782163	+	0.135475i
$845$		−	4.11405e11i		−	0.806942i
$846$	−1.06791e10	+	4.81194e9i	−0.0208475	+	0.00939375i
$847$	−7.47911e11			−1.45317
$848$	5.72466e10	+	3.30513e10i	0.110705	+	0.0639154i
$849$	2.02354e11	−	6.27548e11i	0.389476	−	1.20786i
$850$	−4.59321e10	−	7.95567e10i	−0.0879915	−	0.152406i
$851$	−2.02434e10	+	1.16875e10i	−0.0385980	+	0.0222846i
$852$	4.15388e10	+	1.33943e10i	0.0788307	+	0.0254191i
$853$	−3.97828e10	+	6.89058e10i	−0.0751448	+	0.130155i	−0.901149	−	0.433509i	$-0.857275\pi$
$853$	−3.97828e10	+	6.89058e10i	−0.0751448	+	0.130155i	0.826004	+	0.563664i	$0.190609\pi$
$854$			1.17127e12i			2.20204i
$855$	−1.93135e11	−	4.28625e11i	−0.361408	−	0.802071i
$856$	−4.31857e11			−0.804349
$857$	−7.56463e11	−	4.36744e11i	−1.40238	−	0.809662i	−0.407740	−	0.913098i	$-0.633683\pi$
$857$	−7.56463e11	−	4.36744e11i	−1.40238	−	0.809662i	−0.994636	+	0.103436i	$0.967016\pi$
$858$	−1.22289e11	+	2.62790e10i	−0.225652	+	0.0484909i
$859$	−2.59476e11	−	4.49426e11i	−0.476568	−	0.825440i	0.523072	−	0.852289i	$-0.324786\pi$
$859$	−2.59476e11	−	4.49426e11i	−0.476568	−	0.825440i	−0.999639	+	0.0268491i	$0.991453\pi$
$860$	1.31388e11	−	7.58567e10i	0.240193	−	0.138676i
$861$	−5.88537e11	+	5.32306e11i	−1.07093	+	0.968610i
$862$	−7.32297e10	+	1.26838e11i	−0.132635	+	0.229731i
$863$			5.34241e11i			0.963151i	0.876405	+	0.481575i	$0.159935\pi$
$863$			5.34241e11i			0.963151i	−0.876405	+	0.481575i	$0.840065\pi$
$864$	−1.00763e11	+	2.30463e11i	−0.180820	+	0.413567i
$865$	4.38651e11			0.783529
$866$	−1.15307e11	−	6.65724e10i	−0.205014	−	0.118365i
$867$	3.30505e11	+	3.65418e11i	0.584927	+	0.646715i
$868$	−1.29594e11	−	2.24463e11i	−0.228300	−	0.395426i
$869$	3.02560e11	−	1.74683e11i	0.530557	−	0.306317i
$870$	−9.35736e10	−	4.35444e11i	−0.163334	−	0.760072i
$871$	1.99112e11	−	3.44873e11i	0.345960	−	0.599220i
$872$		−	2.85769e11i		−	0.494253i
$873$	2.62630e11	+	1.89025e11i	0.452155	+	0.325433i
$874$	−1.58205e11			−0.271129
$875$	5.03167e11	+	2.90504e11i	0.858381	+	0.495586i
$876$	2.11304e10	−	6.55304e10i	0.0358832	−	0.111282i
$877$	3.24426e11	+	5.61922e11i	0.548425	+	0.949899i	0.998383	+	0.0568496i	$0.0181055\pi$
$877$	3.24426e11	+	5.61922e11i	0.548425	+	0.949899i	−0.449958	+	0.893050i	$0.648561\pi$
$878$	−7.26830e11	+	4.19635e11i	−1.22308	+	0.706145i
$879$	7.63997e11	+	2.46352e11i	1.27978	+	0.412668i
$880$	1.18623e11	−	2.05462e11i	0.197806	−	0.342610i
$881$		−	4.68554e11i		−	0.777778i	−0.921285	−	0.388889i	$-0.872859\pi$
$881$		−	4.68554e11i		−	0.777778i	0.921285	−	0.388889i	$-0.127141\pi$
$882$	−1.19523e12	−	1.20227e11i	−1.97504	−	0.198667i
$883$	9.85972e11			1.62189			0.810946	−	0.585122i	$-0.198953\pi$
$883$	9.85972e11			1.62189			0.810946	+	0.585122i	$0.198953\pi$
$884$	−2.59747e10	−	1.49965e10i	−0.0425346	−	0.0245574i
$885$	−1.28073e12	+	2.75219e11i	−2.08778	+	0.448648i
$886$	−2.35520e11	−	4.07933e11i	−0.382202	−	0.661994i
$887$	2.45157e11	−	1.41541e11i	0.396050	−	0.228659i	−0.288728	−	0.957411i	$-0.593232\pi$
$887$	2.45157e11	−	1.41541e11i	0.396050	−	0.228659i	0.684778	+	0.728752i	$0.259899\pi$
$888$	−5.05399e10	+	4.57111e10i	−0.0812797	+	0.0735140i
$889$	−4.43255e10	+	7.67740e10i	−0.0709654	+	0.122916i
$890$			2.54697e11i			0.405942i
$891$	−2.08776e11	−	1.84631e11i	−0.331260	−	0.292950i
$892$	−4.65665e10			−0.0735554
$893$	1.01102e10	+	5.83711e9i	0.0158984	+	0.00917893i
$894$	−2.78941e11	−	3.08407e11i	−0.436679	−	0.482808i
$895$	1.18310e10	+	2.04919e10i	0.0184386	+	0.0319367i
$896$	5.28284e11	−	3.05005e11i	0.819663	−	0.473233i
$897$	3.55303e10	+	1.65340e11i	0.0548818	+	0.255392i
$898$	−4.40421e11	+	7.62832e11i	−0.677272	+	1.17307i
$899$			5.07748e11i			0.777337i
$900$	8.49550e9	−	8.44576e10i	0.0129485	−	0.128727i
$901$	−4.20902e10			−0.0638678
$902$	1.77739e11	+	1.02617e11i	0.268507	+	0.155023i
$903$	−3.54706e11	+	1.10003e12i	−0.533479	+	1.65445i
$904$	2.94256e11	+	5.09667e11i	0.440608	+	0.763155i
$905$	5.06940e11	−	2.92682e11i	0.755722	−	0.436316i
$906$	−2.61979e11	−	8.44756e10i	−0.388825	−	0.125377i
$907$	1.71179e10	−	2.96491e10i	0.0252942	−	0.0438108i	−0.853101	−	0.521745i	$-0.825281\pi$
$907$	1.71179e10	−	2.96491e10i	0.0252942	−	0.0438108i	0.878395	+	0.477935i	$0.158614\pi$
$908$			5.74582e10i			0.0845295i
$909$	7.79954e11	−	1.08366e12i	1.14239	−	1.58723i
$910$	8.07733e11			1.17788
$911$	4.92960e11	+	2.84610e11i	0.715711	+	0.413216i	0.813172	−	0.582023i	$-0.197739\pi$
$911$	4.92960e11	+	2.84610e11i	0.715711	+	0.413216i	−0.0974609	+	0.995239i	$0.531072\pi$
$912$	−3.41049e11	+	7.32888e10i	−0.492989	+	0.105940i
$913$	9.94893e10	+	1.72321e11i	0.143184	+	0.248001i
$914$	4.74570e11	−	2.73993e11i	0.680010	−	0.392604i
$915$	9.02638e11	−	8.16398e11i	1.28774	−	1.16471i
$916$	−7.00570e10	+	1.21342e11i	−0.0995107	+	0.172358i
$917$		−	2.24715e12i		−	3.17800i
$918$	2.47799e10	+	2.21476e11i	0.0348923	+	0.311858i
$919$	−6.32730e11			−0.887068			−0.443534	−	0.896258i	$-0.646275\pi$
$919$	−6.32730e11			−0.887068			−0.443534	+	0.896258i	$0.646275\pi$
$920$	−3.67287e11	−	2.12053e11i	−0.512690	−	0.296002i
$921$	1.75063e11	+	1.93556e11i	0.243308	+	0.269009i
$922$	−1.69894e11	−	2.94264e11i	−0.235100	−	0.407206i
$923$	1.34286e11	−	7.75301e10i	0.185022	−	0.106823i
$924$	−2.82227e10	−	1.31334e11i	−0.0387179	−	0.180173i
$925$	2.08417e10	−	3.60990e10i	0.0284687	−	0.0493092i
$926$		−	3.96154e11i		−	0.538791i
$927$	−1.16684e11	+	5.25771e10i	−0.158013	+	0.0711996i
$928$	2.37497e11			0.320233
$929$	−8.64249e11	−	4.98974e11i	−1.16032	−	0.669908i	−0.208936	−	0.977929i	$-0.567000\pi$
$929$	−8.64249e11	−	4.98974e11i	−1.16032	−	0.669908i	−0.951380	+	0.308021i	$0.900333\pi$
$930$	2.75622e11	−	8.54771e11i	0.368453	−	1.14266i
$931$	5.98632e11	+	1.03686e12i	0.796822	+	1.38014i
$932$	1.56122e11	−	9.01373e10i	0.206919	−	0.119465i
$933$	−8.77211e11	−	2.82858e11i	−1.15765	−	0.373286i
$934$	−2.77230e9	+	4.80177e9i	−0.00364295	+	0.00630977i
$935$			1.51064e11i			0.197659i
$936$	2.02539e11	+	4.49495e11i	0.263880	+	0.585628i
$937$	1.76529e11			0.229012			0.114506	−	0.993423i	$-0.463471\pi$
$937$	1.76529e11			0.229012			0.114506	+	0.993423i	$0.463471\pi$
$938$	−1.23511e12	−	7.13089e11i	−1.59549	−	0.921154i
$939$	−1.14921e11	+	2.46957e10i	−0.147821	+	0.0317657i
$940$	2.93321e9	+	5.08046e9i	0.00375691	+	0.00650717i
$941$	−6.73317e11	+	3.88740e11i	−0.858739	+	0.495793i	−0.863590	−	0.504195i	$-0.831789\pi$
$941$	−6.73317e11	+	3.88740e11i	−0.858739	+	0.495793i	0.00485072	+	0.999988i	$0.498456\pi$
$942$	1.75566e11	−	1.58792e11i	0.222965	−	0.201662i
$943$	1.38743e11	−	2.40310e11i	0.175454	−	0.303896i
$944$			9.71993e11i			1.22398i
$945$	1.06762e12	+	1.44893e12i	1.33872	+	1.81686i
$946$	2.98923e11			0.373246
$947$	1.20470e12	+	6.95534e11i	1.49789	+	0.864805i	0.999997	−	0.00243541i	$-0.000775216\pi$
$947$	1.20470e12	+	6.95534e11i	1.49789	+	0.864805i	0.497889	+	0.867241i	$0.334109\pi$
$948$	−1.73153e11	−	1.91444e11i	−0.214387	−	0.237033i
$949$	−1.22309e11	−	2.11846e11i	−0.150798	−	0.261189i
$950$	2.44323e11	−	1.41060e11i	0.299964	−	0.173184i
$951$	1.95911e10	+	9.11667e10i	0.0239517	+	0.111459i
$952$	−2.86514e11	+	4.96256e11i	−0.348817	+	0.604169i
$953$			1.14660e12i			1.39009i	0.718969	+	0.695043i	$0.244615\pi$
$953$			1.14660e12i			1.39009i	−0.718969	+	0.695043i	$0.755385\pi$
$954$	1.05263e11	+	7.57618e10i	0.127082	+	0.0914654i
$955$	−1.76055e12			−2.11658
$956$	−1.88415e11	−	1.08781e11i	−0.225571	−	0.130234i
$957$	−8.07606e10	+	2.50458e11i	−0.0962835	+	0.298598i
$958$	3.54884e11	+	6.14678e11i	0.421332	+	0.729769i
$959$	−1.11613e12	+	6.44401e11i	−1.31960	+	0.761871i
$960$	−1.12299e12	−	3.62110e11i	−1.32218	−	0.426339i
$961$	−8.54865e10	+	1.48067e11i	−0.100231	+	0.173606i
$962$			4.53831e10i			0.0529900i
$963$	−6.37623e11	−	6.41378e10i	−0.741411	−	0.0745777i
$964$	−1.08821e11			−0.126010
$965$	5.89589e11	+	3.40400e11i	0.679893	+	0.392536i
$966$	5.92137e11	−	1.27246e11i	0.680008	−	0.146129i
$967$	−5.71613e11	−	9.90063e11i	−0.653727	−	1.13229i	−0.982211	−	0.187778i	$-0.939871\pi$
$967$	−5.71613e11	−	9.90063e11i	−0.653727	−	1.13229i	0.328485	−	0.944509i	$-0.393462\pi$
$968$	6.60282e11	−	3.81214e11i	0.752018	−	0.434178i
$969$	1.64733e11	−	1.48994e11i	0.186846	−	0.168994i
$970$	−2.70213e11	+	4.68023e11i	−0.305225	+	0.528665i
$971$		−	5.95098e11i		−	0.669440i	−0.942318	−	0.334720i	$-0.891358\pi$
$971$		−	5.95098e11i		−	0.669440i	0.942318	−	0.334720i	$-0.108642\pi$
$972$	−1.00964e11	+	1.79474e11i	−0.113110	+	0.201065i
$973$	2.12985e12			2.37628
$974$	7.02421e11	+	4.05543e11i	0.780480	+	0.450610i
$975$	−2.02292e11	−	2.23661e11i	−0.223851	−	0.247498i
$976$	−4.51532e11	−	7.82077e11i	−0.497610	−	0.861887i
$977$	−1.19400e12	+	6.89357e11i	−1.31047	+	0.756600i	−0.982174	−	0.187975i	$-0.939807\pi$
$977$	−1.19400e12	+	6.89357e11i	−1.31047	+	0.756600i	−0.328295	+	0.944575i	$0.606474\pi$
$978$	2.43396e11	+	1.13264e12i	0.266046	+	1.23804i
$979$	7.52444e10	−	1.30327e11i	0.0819112	−	0.141874i
$980$			6.01637e11i			0.652275i
$981$	4.24414e10	−	4.21929e11i	0.0458261	−	0.455578i
$982$	−9.83613e11			−1.05774
$983$	−4.07742e11	−	2.35410e11i	−0.436688	−	0.252122i	0.265504	−	0.964110i	$-0.414462\pi$
$983$	−4.07742e11	−	2.35410e11i	−0.436688	−	0.252122i	−0.702192	+	0.711988i	$0.747795\pi$
$984$	2.48262e11	−	7.69919e11i	0.264807	−	0.821230i
$985$	−7.12841e11	−	1.23468e12i	−0.757264	−	1.31162i
$986$	1.82235e11	−	1.05213e11i	0.192807	−	0.111317i
$987$	−4.25356e10	−	1.37157e10i	−0.0448212	−	0.0144527i
$988$	4.60551e10	−	7.97698e10i	0.0483337	−	0.0837164i
$989$		−	4.04156e11i		−	0.422439i
$990$	2.71914e11	−	3.77796e11i	0.283068	−	0.393293i
$991$	1.46045e12			1.51423			0.757117	−	0.653279i	$-0.226607\pi$
$991$	1.46045e12			1.51423			0.757117	+	0.653279i	$0.226607\pi$
$992$	4.14747e11	+	2.39454e11i	0.428288	+	0.247272i
$993$	6.00946e11	−	1.29139e11i	0.618071	−	0.132819i
$994$	−2.77662e11	−	4.80924e11i	−0.284427	−	0.492642i
$995$	−7.88423e11	+	4.55196e11i	−0.804390	+	0.464415i
$996$	1.09036e11	−	9.86181e10i	0.110798	−	0.100212i
$997$	7.72426e11	−	1.33788e12i	0.781765	−	1.35406i	−0.149148	−	0.988815i	$-0.547653\pi$
$997$	7.72426e11	−	1.33788e12i	0.781765	−	1.35406i	0.930913	−	0.365241i	$-0.119014\pi$
$998$		−	1.16744e12i		−	1.17682i
$999$	−8.14093e10	+	5.99851e10i	−0.0817358	+	0.0602256i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.9.d.a.2.3	✓	14
3.2	odd	2		27.9.d.a.8.5		14
4.3	odd	2		144.9.q.a.65.2		14
9.2	odd	6		81.9.b.a.80.5		14
9.4	even	3		27.9.d.a.17.5		14
9.5	odd	6	inner	9.9.d.a.5.3	yes	14
9.7	even	3		81.9.b.a.80.10		14
12.11	even	2		432.9.q.a.305.1		14
36.23	even	6		144.9.q.a.113.2		14
36.31	odd	6		432.9.q.a.17.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.9.d.a.2.3	✓	14	1.1	even	1	trivial
9.9.d.a.5.3	yes	14	9.5	odd	6	inner
27.9.d.a.8.5		14	3.2	odd	2
27.9.d.a.17.5		14	9.4	even	3
81.9.b.a.80.5		14	9.2	odd	6
81.9.b.a.80.10		14	9.7	even	3
144.9.q.a.65.2		14	4.3	odd	2
144.9.q.a.113.2		14	36.23	even	6
432.9.q.a.17.1		14	36.31	odd	6
432.9.q.a.305.1		14	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	9.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-12.1534 - 7.01679i) q^{2} +(54.3339 + 60.0735i) q^{3} +(-29.5292 - 51.1461i) q^{4} +(676.216 - 390.413i) q^{5} +(-238.821 - 1111.35i) q^{6} +(2168.61 - 3756.14i) q^{7} +4421.40i q^{8} +(-656.650 + 6528.06i) q^{9} +O(q^{10})\)	\(q+(-12.1534 - 7.01679i) q^{2} +(54.3339 + 60.0735i) q^{3} +(-29.5292 - 51.1461i) q^{4} +(676.216 - 390.413i) q^{5} +(-238.821 - 1111.35i) q^{6} +(2168.61 - 3756.14i) q^{7} +4421.40i q^{8} +(-656.650 + 6528.06i) q^{9} -10957.8 q^{10} +(5607.04 + 3237.22i) q^{11} +(1468.09 - 4552.89i) q^{12} +(-8497.75 - 14718.5i) q^{13} +(-52712.1 + 30433.3i) q^{14} +(60194.9 + 19410.0i) q^{15} +(23464.6 - 40641.8i) q^{16} +29881.7i q^{17} +(53786.6 - 74730.8i) q^{18} -91768.1 q^{19} +(-39936.2 - 23057.2i) q^{20} +(343473. - 73809.9i) q^{21} +(-45429.9 - 78686.9i) q^{22} +(-106388. + 61423.0i) q^{23} +(-265609. + 240232. i) q^{24} +(109532. - 189716. i) q^{25} +238508. i q^{26} +(-427842. + 315248. i) q^{27} -256149. q^{28} +(434568. + 250898. i) q^{29} +(-595380. - 658273. i) q^{30} +(505931. + 876298. i) q^{31} +(409885. - 236647. i) q^{32} +(110181. + 512725. i) q^{33} +(209673. - 363165. i) q^{34} -3.38661e6i q^{35} +(353275. - 159183. i) q^{36} +190279. q^{37} +(1.11530e6 + 643918. i) q^{38} +(422478. - 1.31021e6i) q^{39} +(1.72617e6 + 2.98982e6i) q^{40} +(-1.95619e6 + 1.12941e6i) q^{41} +(-4.69229e6 - 1.51304e6i) q^{42} +(-1.64497e6 + 2.84917e6i) q^{43} -382371. i q^{44} +(2.10460e6 + 4.67074e6i) q^{45} +1.72397e6 q^{46} +(-110171. - 63607.2i) q^{47} +(3.71642e6 - 798631. i) q^{48} +(-6.52331e6 - 1.12987e7i) q^{49} +(-2.66239e6 + 1.53713e6i) q^{50} +(-1.79510e6 + 1.62359e6i) q^{51} +(-501864. + 869254. i) q^{52} +1.40856e6i q^{53} +(7.41178e6 - 829268. i) q^{54} +5.05542e6 q^{55} +(1.66074e7 + 9.58828e6i) q^{56} +(-4.98612e6 - 5.51283e6i) q^{57} +(-3.52099e6 - 6.09854e6i) q^{58} +(-1.79370e7 + 1.03560e7i) q^{59} +(-784766. - 3.65190e6i) q^{60} +(9.62157e6 - 1.66651e7i) q^{61} -1.42000e7i q^{62} +(2.30963e7 + 1.66233e7i) q^{63} -1.86559e7 q^{64} +(-1.14926e7 - 6.63527e6i) q^{65} +(2.25861e6 - 7.00450e6i) q^{66} +(1.17156e7 + 2.02920e7i) q^{67} +(1.52833e6 - 882382. i) q^{68} +(-9.47036e6 - 3.05373e6i) q^{69} +(-2.37632e7 + 4.11590e7i) q^{70} +9.12361e6i q^{71} +(-2.88632e7 - 2.90331e6i) q^{72} +1.43931e7 q^{73} +(-2.31255e6 - 1.33515e6i) q^{74} +(1.73482e7 - 3.72800e6i) q^{75} +(2.70984e6 + 4.69358e6i) q^{76} +(2.43189e7 - 1.40405e7i) q^{77} +(-1.43280e7 + 1.29591e7i) q^{78} +(2.69804e7 - 4.67314e7i) q^{79} -3.66435e7i q^{80} +(-4.21843e7 - 8.57330e6i) q^{81} +3.16992e7 q^{82} +(2.66155e7 + 1.53664e7i) q^{83} +(-1.39176e7 - 1.53878e7i) q^{84} +(1.16662e7 + 2.02064e7i) q^{85} +(3.99841e7 - 2.30848e7i) q^{86} +(8.53946e6 + 3.97382e7i) q^{87} +(-1.43131e7 + 2.47910e7i) q^{88} -2.32435e7i q^{89} +(7.19544e6 - 7.15331e7i) q^{90} -7.37131e7 q^{91} +(6.28309e6 + 3.62755e6i) q^{92} +(-2.51531e7 + 7.80057e7i) q^{93} +(892637. + 1.54609e6i) q^{94} +(-6.20550e7 + 3.58275e7i) q^{95} +(3.64869e7 + 1.17652e7i) q^{96} +(2.46595e7 - 4.27114e7i) q^{97} +1.83091e8i q^{98} +(-2.48147e7 + 3.44773e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{2} - 93 q^{3} + 767 q^{4} + 438 q^{5} - 2259 q^{6} + 922 q^{7} + 17973 q^{9}+O(q^{10}) \) 14 * q - 3 * q^2 - 93 * q^3 + 767 * q^4 + 438 * q^5 - 2259 * q^6 + 922 * q^7 + 17973 * q^9	\( 14 q - 3 q^{2} - 93 q^{3} + 767 q^{4} + 438 q^{5} - 2259 q^{6} + 922 q^{7} + 17973 q^{9} - 516 q^{10} - 28677 q^{11} - 55110 q^{12} + 1684 q^{13} + 120966 q^{14} - 75276 q^{15} - 65281 q^{16} + 243324 q^{18} - 269630 q^{19} + 539454 q^{20} + 354054 q^{21} + 61311 q^{22} - 1000452 q^{23} - 1125513 q^{24} + 65177 q^{25} - 524826 q^{27} + 1075708 q^{28} + 3797682 q^{29} + 2372562 q^{30} - 164132 q^{31} - 8461881 q^{32} - 5761521 q^{33} + 654993 q^{34} + 12958047 q^{36} - 1671668 q^{37} + 10967691 q^{38} + 3383976 q^{39} + 613326 q^{40} - 10239447 q^{41} - 35844228 q^{42} + 791815 q^{43} + 27631638 q^{45} + 1189536 q^{46} + 31148628 q^{47} + 17088189 q^{48} - 4826637 q^{49} - 63849453 q^{50} - 47946573 q^{51} - 5552720 q^{52} + 36967995 q^{54} + 8107476 q^{55} + 116638674 q^{56} + 37276797 q^{57} + 14211822 q^{58} - 83493795 q^{59} - 109012050 q^{60} - 5255600 q^{61} + 38322432 q^{63} - 26813830 q^{64} + 69232992 q^{65} + 36133866 q^{66} - 8288855 q^{67} - 77746743 q^{68} - 62108640 q^{69} + 27813756 q^{70} + 88821171 q^{72} - 36721682 q^{73} - 10383450 q^{74} + 13792011 q^{75} - 42822959 q^{76} + 56158710 q^{77} + 27355140 q^{78} - 32771822 q^{79} - 16336971 q^{81} + 236099418 q^{82} - 198915996 q^{83} - 187060614 q^{84} + 97486146 q^{85} + 146190669 q^{86} + 114294006 q^{87} + 24955827 q^{88} - 222035850 q^{90} - 201514504 q^{91} - 295365804 q^{92} + 94187784 q^{93} - 36698244 q^{94} + 386813838 q^{95} + 768275928 q^{96} + 127049161 q^{97} - 511060752 q^{99}+O(q^{100}) \) 14 * q - 3 * q^2 - 93 * q^3 + 767 * q^4 + 438 * q^5 - 2259 * q^6 + 922 * q^7 + 17973 * q^9 - 516 * q^10 - 28677 * q^11 - 55110 * q^12 + 1684 * q^13 + 120966 * q^14 - 75276 * q^15 - 65281 * q^16 + 243324 * q^18 - 269630 * q^19 + 539454 * q^20 + 354054 * q^21 + 61311 * q^22 - 1000452 * q^23 - 1125513 * q^24 + 65177 * q^25 - 524826 * q^27 + 1075708 * q^28 + 3797682 * q^29 + 2372562 * q^30 - 164132 * q^31 - 8461881 * q^32 - 5761521 * q^33 + 654993 * q^34 + 12958047 * q^36 - 1671668 * q^37 + 10967691 * q^38 + 3383976 * q^39 + 613326 * q^40 - 10239447 * q^41 - 35844228 * q^42 + 791815 * q^43 + 27631638 * q^45 + 1189536 * q^46 + 31148628 * q^47 + 17088189 * q^48 - 4826637 * q^49 - 63849453 * q^50 - 47946573 * q^51 - 5552720 * q^52 + 36967995 * q^54 + 8107476 * q^55 + 116638674 * q^56 + 37276797 * q^57 + 14211822 * q^58 - 83493795 * q^59 - 109012050 * q^60 - 5255600 * q^61 + 38322432 * q^63 - 26813830 * q^64 + 69232992 * q^65 + 36133866 * q^66 - 8288855 * q^67 - 77746743 * q^68 - 62108640 * q^69 + 27813756 * q^70 + 88821171 * q^72 - 36721682 * q^73 - 10383450 * q^74 + 13792011 * q^75 - 42822959 * q^76 + 56158710 * q^77 + 27355140 * q^78 - 32771822 * q^79 - 16336971 * q^81 + 236099418 * q^82 - 198915996 * q^83 - 187060614 * q^84 + 97486146 * q^85 + 146190669 * q^86 + 114294006 * q^87 + 24955827 * q^88 - 222035850 * q^90 - 201514504 * q^91 - 295365804 * q^92 + 94187784 * q^93 - 36698244 * q^94 + 386813838 * q^95 + 768275928 * q^96 + 127049161 * q^97 - 511060752 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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