LMFDB - Embedded newform 27.9.d.a.8.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,9,Mod(8,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, 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("27.8");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	27.d (of order $6$, degree $2$, not 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:	$10.9992224717$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{30} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			8.5
Root			$4.05115 + 7.01679i$ of defining polynomial
Character	$\chi$	$=$	27.8
Dual form			27.9.d.a.17.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(12.1534 + 7.01679i) q^{2} +(-29.5292 - 51.1461i) q^{4} +(-676.216 + 390.413i) q^{5} +(2168.61 - 3756.14i) q^{7} -4421.40i q^{8} +O(q^{10})$	\(q+(12.1534 + 7.01679i) q^{2} +(-29.5292 - 51.1461i) q^{4} +(-676.216 + 390.413i) q^{5} +(2168.61 - 3756.14i) q^{7} -4421.40i q^{8} -10957.8 q^{10} +(-5607.04 - 3237.22i) q^{11} +(-8497.75 - 14718.5i) q^{13} +(52712.1 - 30433.3i) q^{14} +(23464.6 - 40641.8i) q^{16} -29881.7i q^{17} -91768.1 q^{19} +(39936.2 + 23057.2i) q^{20} +(-45429.9 - 78686.9i) q^{22} +(106388. - 61423.0i) q^{23} +(109532. - 189716. i) q^{25} -238508. i q^{26} -256149. q^{28} +(-434568. - 250898. i) q^{29} +(505931. + 876298. i) q^{31} +(-409885. + 236647. i) q^{32} +(209673. - 363165. i) q^{34} +3.38661e6i q^{35} +190279. q^{37} +(-1.11530e6 - 643918. i) q^{38} +(1.72617e6 + 2.98982e6i) q^{40} +(1.95619e6 - 1.12941e6i) q^{41} +(-1.64497e6 + 2.84917e6i) q^{43} +382371. i q^{44} +1.72397e6 q^{46} +(110171. + 63607.2i) q^{47} +(-6.52331e6 - 1.12987e7i) q^{49} +(2.66239e6 - 1.53713e6i) q^{50} +(-501864. + 869254. i) q^{52} -1.40856e6i q^{53} +5.05542e6 q^{55} +(-1.66074e7 - 9.58828e6i) q^{56} +(-3.52099e6 - 6.09854e6i) q^{58} +(1.79370e7 - 1.03560e7i) q^{59} +(9.62157e6 - 1.66651e7i) q^{61} +1.42000e7i q^{62} -1.86559e7 q^{64} +(1.14926e7 + 6.63527e6i) q^{65} +(1.17156e7 + 2.02920e7i) q^{67} +(-1.52833e6 + 882382. i) q^{68} +(-2.37632e7 + 4.11590e7i) q^{70} -9.12361e6i q^{71} +1.43931e7 q^{73} +(2.31255e6 + 1.33515e6i) q^{74} +(2.70984e6 + 4.69358e6i) q^{76} +(-2.43189e7 + 1.40405e7i) q^{77} +(2.69804e7 - 4.67314e7i) q^{79} +3.66435e7i q^{80} +3.16992e7 q^{82} +(-2.66155e7 - 1.53664e7i) q^{83} +(1.16662e7 + 2.02064e7i) q^{85} +(-3.99841e7 + 2.30848e7i) q^{86} +(-1.43131e7 + 2.47910e7i) q^{88} +2.32435e7i q^{89} -7.37131e7 q^{91} +(-6.28309e6 - 3.62755e6i) q^{92} +(892637. + 1.54609e6i) q^{94} +(6.20550e7 - 3.58275e7i) q^{95} +(2.46595e7 - 4.27114e7i) q^{97} -1.83091e8i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{2} + 767 q^{4} - 438 q^{5} + 922 q^{7}+O(q^{10}) $ 14 * q + 3 * q^2 + 767 * q^4 - 438 * q^5 + 922 * q^7	$ 14 q + 3 q^{2} + 767 q^{4} - 438 q^{5} + 922 q^{7} - 516 q^{10} + 28677 q^{11} + 1684 q^{13} - 120966 q^{14} - 65281 q^{16} - 269630 q^{19} - 539454 q^{20} + 61311 q^{22} + 1000452 q^{23} + 65177 q^{25} + 1075708 q^{28} - 3797682 q^{29} - 164132 q^{31} + 8461881 q^{32} + 654993 q^{34} - 1671668 q^{37} - 10967691 q^{38} + 613326 q^{40} + 10239447 q^{41} + 791815 q^{43} + 1189536 q^{46} - 31148628 q^{47} - 4826637 q^{49} + 63849453 q^{50} - 5552720 q^{52} + 8107476 q^{55} - 116638674 q^{56} + 14211822 q^{58} + 83493795 q^{59} - 5255600 q^{61} - 26813830 q^{64} - 69232992 q^{65} - 8288855 q^{67} + 77746743 q^{68} + 27813756 q^{70} - 36721682 q^{73} + 10383450 q^{74} - 42822959 q^{76} - 56158710 q^{77} - 32771822 q^{79} + 236099418 q^{82} + 198915996 q^{83} + 97486146 q^{85} - 146190669 q^{86} + 24955827 q^{88} - 201514504 q^{91} + 295365804 q^{92} - 36698244 q^{94} - 386813838 q^{95} + 127049161 q^{97}+O(q^{100}) $ 14 * q + 3 * q^2 + 767 * q^4 - 438 * q^5 + 922 * q^7 - 516 * q^10 + 28677 * q^11 + 1684 * q^13 - 120966 * q^14 - 65281 * q^16 - 269630 * q^19 - 539454 * q^20 + 61311 * q^22 + 1000452 * q^23 + 65177 * q^25 + 1075708 * q^28 - 3797682 * q^29 - 164132 * q^31 + 8461881 * q^32 + 654993 * q^34 - 1671668 * q^37 - 10967691 * q^38 + 613326 * q^40 + 10239447 * q^41 + 791815 * q^43 + 1189536 * q^46 - 31148628 * q^47 - 4826637 * q^49 + 63849453 * q^50 - 5552720 * q^52 + 8107476 * q^55 - 116638674 * q^56 + 14211822 * q^58 + 83493795 * q^59 - 5255600 * q^61 - 26813830 * q^64 - 69232992 * q^65 - 8288855 * q^67 + 77746743 * q^68 + 27813756 * q^70 - 36721682 * q^73 + 10383450 * q^74 - 42822959 * q^76 - 56158710 * q^77 - 32771822 * q^79 + 236099418 * q^82 + 198915996 * q^83 + 97486146 * q^85 - 146190669 * q^86 + 24955827 * q^88 - 201514504 * q^91 + 295365804 * q^92 - 36698244 * q^94 - 386813838 * q^95 + 127049161 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

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

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	0.829149	−	0.559028i	$-0.188826\pi$
$2$	12.1534	+	7.01679i	0.759590	+	0.438550i	−0.0695584	+	0.997578i	$0.522159\pi$
$3$		0			0
$3$		0			0
$4$	−29.5292	−	51.1461i	−0.115349	−	0.199789i
$5$	−676.216	+	390.413i	−1.08194	+	0.624661i	−0.931420	−	0.363945i	$-0.881430\pi$
$5$	−676.216	+	390.413i	−1.08194	+	0.624661i	−0.150524	+	0.988606i	$0.548096\pi$
$6$		0			0
$7$	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
$9$		0			0
$10$	−10957.8			−1.09578
$11$	−5607.04	−	3237.22i	−0.382968	−	0.221107i	0.296141	−	0.955144i	$-0.404300\pi$
$11$	−5607.04	−	3237.22i	−0.382968	−	0.221107i	−0.679109	+	0.734038i	$0.737634\pi$
$12$		0			0
$13$	−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
$15$		0			0
$16$	23464.6	−	40641.8i	0.358041	−	0.620145i
$17$		−	29881.7i		−	0.357774i	−0.983870	−	0.178887i	$-0.942750\pi$
$17$		−	29881.7i		−	0.357774i	0.983870	−	0.178887i	$-0.0572497\pi$
$18$		0			0
$19$	−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
$21$		0			0
$22$	−45429.9	−	78686.9i	−0.193933	−	0.335901i
$23$	106388.	−	61423.0i	0.380172	−	0.219492i	−0.297721	−	0.954653i	$-0.596227\pi$
$23$	106388.	−	61423.0i	0.380172	−	0.219492i	0.677893	+	0.735160i	$0.262893\pi$
$24$		0			0
$25$	109532.	−	189716.i	0.280403	−	0.485672i
$26$		−	238508.i		−	0.521926i
$27$		0			0
$28$	−256149.			−0.416736
$29$	−434568.	−	250898.i	−0.614420	−	0.354736i	0.160273	−	0.987073i	$-0.448762\pi$
$29$	−434568.	−	250898.i	−0.614420	−	0.354736i	−0.774693	+	0.632337i	$0.782096\pi$
$30$		0			0
$31$	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
$33$		0			0
$34$	209673.	−	363165.i	0.156902	−	0.271762i
$35$			3.38661e6i			2.25680i
$36$		0			0
$37$	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
$39$		0			0
$40$	1.72617e6	+	2.98982e6i	0.674286	+	1.16790i
$41$	1.95619e6	−	1.12941e6i	0.692269	−	0.399682i	−0.112192	−	0.993687i	$-0.535787\pi$
$41$	1.95619e6	−	1.12941e6i	0.692269	−	0.399682i	0.804462	+	0.594005i	$0.202454\pi$
$42$		0			0
$43$	−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
$45$		0			0
$46$	1.72397e6			0.385033
$47$	110171.	+	63607.2i	0.0225775	+	0.0130351i	0.511246	−	0.859434i	$-0.329184\pi$
$47$	110171.	+	63607.2i	0.0225775	+	0.0130351i	−0.488669	+	0.872469i	$0.662517\pi$
$48$		0			0
$49$	−6.52331e6	−	1.12987e7i	−1.13158	−	1.95995i
$50$	2.66239e6	−	1.53713e6i	0.425983	−	0.245941i
$51$		0			0
$52$	−501864.	+	869254.i	−0.0686393	+	0.118887i
$53$		−	1.40856e6i		−	0.178514i	−0.996009	−	0.0892571i	$-0.971551\pi$
$53$		−	1.40856e6i		−	0.178514i	0.996009	−	0.0892571i	$-0.0284493\pi$
$54$		0			0
$55$	5.05542e6			0.552467
$56$	−1.66074e7	−	9.58828e6i	−1.68869	−	0.974964i
$57$		0			0
$58$	−3.52099e6	−	6.09854e6i	−0.311138	−	0.538907i
$59$	1.79370e7	−	1.03560e7i	1.48028	−	0.854638i	0.480526	−	0.876980i	$-0.340446\pi$
$59$	1.79370e7	−	1.03560e7i	1.48028	−	0.854638i	0.999750	+	0.0223421i	$0.00711229\pi$
$60$		0			0
$61$	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
$63$		0			0
$64$	−1.86559e7			−1.11198
$65$	1.14926e7	+	6.63527e6i	0.643822	+	0.371711i
$66$		0			0
$67$	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
$69$		0			0
$70$	−2.37632e7	+	4.11590e7i	−0.989719	+	1.71424i
$71$		−	9.12361e6i		−	0.359032i	−0.983755	−	0.179516i	$-0.942547\pi$
$71$		−	9.12361e6i		−	0.359032i	0.983755	−	0.179516i	$-0.0574532\pi$
$72$		0			0
$73$	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
$75$		0			0
$76$	2.70984e6	+	4.69358e6i	0.0812249	+	0.140686i
$77$	−2.43189e7	+	1.40405e7i	−0.691801	+	0.399412i
$78$		0			0
$79$	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
$81$		0			0
$82$	3.16992e7			0.701121
$83$	−2.66155e7	−	1.53664e7i	−0.560818	−	0.323788i	0.192656	−	0.981266i	$-0.438290\pi$
$83$	−2.66155e7	−	1.53664e7i	−0.560818	−	0.323788i	−0.753474	+	0.657478i	$0.771623\pi$
$84$		0			0
$85$	1.16662e7	+	2.02064e7i	0.223488	+	0.387092i
$86$	−3.99841e7	+	2.30848e7i	−0.730959	+	0.422020i
$87$		0			0
$88$	−1.43131e7	+	2.47910e7i	−0.238672	+	0.413393i
$89$			2.32435e7i			0.370460i	0.982695	+	0.185230i	$0.0593030\pi$
$89$			2.32435e7i			0.370460i	−0.982695	+	0.185230i	$0.940697\pi$
$90$		0			0
$91$	−7.37131e7			−1.07493
$92$	−6.28309e6	−	3.62755e6i	−0.0877046	−	0.0506363i
$93$		0			0
$94$	892637.	+	1.54609e6i	0.0114331	+	0.0198027i
$95$	6.20550e7	−	3.58275e7i	0.761873	−	0.439867i
$96$		0			0
$97$	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
$99$		0			0
$100$	−1.29376e7			−0.129376
$101$	1.76236e8	+	1.01750e8i	1.69359	+	0.977795i	0.951576	+	0.307412i	$0.0994630\pi$
$101$	1.76236e8	+	1.01750e8i	1.69359	+	0.977795i	0.742015	+	0.670383i	$0.233870\pi$
$102$		0			0
$103$	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
$105$		0			0
$106$	9.88360e6	−	1.71189e7i	0.0782874	−	0.135598i
$107$		−	9.76742e7i		−	0.745152i	−0.928002	−	0.372576i	$-0.878475\pi$
$107$		−	9.76742e7i		−	0.745152i	0.928002	−	0.372576i	$-0.121525\pi$
$108$		0			0
$109$	−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
$111$		0			0
$112$	−1.01771e8	−	1.76272e8i	−0.646772	−	1.12024i
$113$	−1.15273e8	+	6.65528e7i	−0.706989	+	0.408181i	−0.809945	−	0.586505i	$-0.800503\pi$
$113$	−1.15273e8	+	6.65528e7i	−0.706989	+	0.408181i	0.102956	+	0.994686i	$0.467170\pi$
$114$		0			0
$115$	−4.79607e7	+	8.30704e7i	−0.274217	+	0.474957i
$116$			2.96353e7i			0.163673i
$117$		0			0
$118$	2.90663e8			1.49920
$119$	−1.12240e8	−	6.48016e7i	−0.559704	−	0.323145i
$120$		0			0
$121$	−8.62202e7	−	1.49338e8i	−0.402224	−	0.696672i
$122$	2.33871e8	−	1.35025e8i	1.05569	−	0.609503i
$123$		0			0
$124$	2.98795e7	−	5.17528e7i	0.126382	−	0.218901i
$125$		−	1.33959e8i		−	0.548695i
$126$		0			0
$127$	−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
$129$		0			0
$130$	9.31166e7	+	1.61283e8i	0.326027	+	0.564696i
$131$	−4.48695e8	+	2.59054e8i	−1.52358	+	0.879641i	−0.523972	+	0.851736i	$0.675550\pi$
$131$	−4.48695e8	+	2.59054e8i	−1.52358	+	0.879641i	−0.999611	+	0.0279052i	$0.991116\pi$
$132$		0			0
$133$	−1.99009e8	+	3.44694e8i	−0.636013	+	1.10161i
$134$			3.28823e8i			1.01987i
$135$		0			0
$136$	−1.32119e8			−0.386197
$137$	2.57339e8	+	1.48575e8i	0.730506	+	0.421758i	0.818607	−	0.574354i	$-0.194747\pi$
$137$	2.57339e8	+	1.48575e8i	0.730506	+	0.421758i	−0.0881015	+	0.996111i	$0.528080\pi$
$138$		0			0
$139$	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
$141$		0			0
$142$	6.40185e7	−	1.10883e8i	0.157453	−	0.272717i
$143$			1.10037e8i			0.263144i
$144$		0			0
$145$	3.91815e8			0.886358
$146$	1.74926e8	+	1.00994e8i	0.384985	+	0.222271i
$147$		0			0
$148$	−5.61880e6	−	9.73204e6i	−0.0117111	−	0.0202842i
$149$	−3.16813e8	+	1.82912e8i	−0.642774	+	0.371106i	−0.785682	−	0.618630i	$-0.787688\pi$
$149$	−3.16813e8	+	1.82912e8i	−0.642774	+	0.371106i	0.142908	+	0.989736i	$0.454355\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$	−3.94078e8			−0.700647
$155$	−6.84237e8	−	3.95044e8i	−1.18544	−	0.684414i
$156$		0			0
$157$	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
$159$		0			0
$160$	1.84780e8	−	3.20049e8i	0.281952	−	0.488356i
$161$		−	5.32809e8i		−	0.792991i
$162$		0			0
$163$	−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
$165$		0			0
$166$	−2.15646e8	−	3.73511e8i	−0.283994	−	0.491893i
$167$	1.28831e9	−	7.43808e8i	1.65636	−	0.956302i	0.681991	−	0.731360i	$-0.261114\pi$
$167$	1.28831e9	−	7.43808e8i	1.65636	−	0.956302i	0.974372	−	0.224941i	$-0.0722191\pi$
$168$		0			0
$169$	2.63442e8	−	4.56295e8i	0.322952	−	0.559369i
$170$			3.27437e8i			0.392042i
$171$		0			0
$172$	1.94299e8			0.222002
$173$	−4.86514e8	−	2.80889e8i	−0.543139	−	0.313582i	0.203211	−	0.979135i	$-0.434862\pi$
$173$	−4.86514e8	−	2.80889e8i	−0.543139	−	0.313582i	−0.746350	+	0.665553i	$0.768196\pi$
$174$		0			0
$175$	−4.75066e8	−	8.22838e8i	−0.506526	−	0.877328i
$176$	−2.63133e8	+	1.51920e8i	−0.274237	+	0.158331i
$177$		0			0
$178$	−1.63095e8	+	2.82488e8i	−0.162465	+	0.281398i
$179$		−	3.03038e7i		−	0.0295178i	−0.999891	−	0.0147589i	$-0.995302\pi$
$179$		−	3.03038e7i		−	0.0295178i	0.999891	−	0.0147589i	$-0.00469808\pi$
$180$		0			0
$181$	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
$183$		0			0
$184$	−2.71576e8	−	4.70383e8i	−0.236930	−	0.410374i
$185$	−1.28670e8	+	7.42875e7i	−0.109847	+	0.0634204i
$186$		0			0
$187$	−9.67336e7	+	1.67548e8i	−0.0791063	+	0.137016i
$188$		−	7.51308e6i		−	0.00601432i
$189$		0			0
$190$	1.00558e9			0.771615
$191$	1.95265e9	+	1.12736e9i	1.46721	+	0.847092i	0.999326	−	0.0367008i	$-0.0116849\pi$
$191$	1.95265e9	+	1.12736e9i	1.46721	+	0.847092i	0.467879	+	0.883792i	$0.345018\pi$
$192$		0			0
$193$	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
$195$		0			0
$196$	−3.85257e8	+	6.67284e8i	−0.261051	+	0.452154i
$197$			1.82586e9i			1.21228i	0.795358	+	0.606140i	$0.207283\pi$
$197$			1.82586e9i			1.21228i	−0.795358	+	0.606140i	$0.792717\pi$
$198$		0			0
$199$	−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
$201$		0			0
$202$	1.42791e9	+	2.47322e9i	0.857624	+	1.48545i
$203$	−1.88481e9	+	1.08820e9i	−1.10990	+	0.640801i
$204$		0			0
$205$	−8.81869e8	+	1.52744e9i	−0.499331	+	0.864867i
$206$			2.73747e8i			0.152013i
$207$		0			0
$208$	−7.97584e8			−0.426112
$209$	5.14547e8	+	2.97074e8i	0.269675	+	0.155697i
$210$		0			0
$211$	−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
$213$		0			0
$214$	6.85360e8	−	1.18708e9i	0.326786	−	0.566010i
$215$		−	2.56887e9i		−	1.20223i
$216$		0			0
$217$	4.38866e9			1.97922
$218$	−7.85515e8	−	4.53517e8i	−0.347799	−	0.200802i
$219$		0			0
$220$	−1.49283e8	−	2.58565e8i	−0.0637263	−	0.110377i
$221$	−4.39814e8	+	2.53927e8i	−0.184374	+	0.106449i
$222$		0			0
$223$	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
$225$		0			0
$226$	−1.86795e9			−0.716030
$227$	8.42559e8	+	4.86452e8i	0.317320	+	0.183205i	0.650197	−	0.759765i	$-0.274686\pi$
$227$	8.42559e8	+	4.86452e8i	0.317320	+	0.183205i	−0.332878	+	0.942970i	$0.608020\pi$
$228$		0			0
$229$	−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
$231$		0			0
$232$	−1.10932e9	+	1.92140e9i	−0.382917	+	0.663232i
$233$		−	3.05248e9i		−	1.03569i	−0.855475	−	0.517844i	$-0.826735\pi$
$233$		−	3.05248e9i		−	1.03569i	0.855475	−	0.517844i	$-0.173265\pi$
$234$		0			0
$235$	−9.93323e7			−0.0325701
$236$	−1.05933e9	−	6.11607e8i	−0.341495	−	0.197162i
$237$		0			0
$238$	−9.09399e8	−	1.57512e9i	−0.283430	−	0.490916i
$239$	−3.19031e9	+	1.84193e9i	−0.977782	+	0.564522i	−0.901600	−	0.432572i	$-0.857606\pi$
$239$	−3.19031e9	+	1.84193e9i	−0.977782	+	0.564522i	−0.0761819	+	0.997094i	$0.524273\pi$
$240$		0			0
$241$	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
$243$		0			0
$244$	−1.13647e9			−0.320626
$245$	8.82233e9	+	5.09358e9i	2.44861	+	1.41370i
$246$		0			0
$247$	7.79822e8	+	1.35069e9i	0.209512	+	0.362885i
$248$	3.87446e9	−	2.23692e9i	1.02425	−	0.591350i
$249$		0			0
$250$	9.39960e8	−	1.62806e9i	0.240630	−	0.416783i
$251$		−	5.83943e9i		−	1.47121i	−0.677409	−	0.735606i	$-0.736897\pi$
$251$		−	5.83943e9i		−	1.47121i	0.677409	−	0.735606i	$-0.263103\pi$
$252$		0			0
$253$	−7.95360e8			−0.194125
$254$	−2.48412e8	−	1.43421e8i	−0.0596811	−	0.0344569i
$255$		0			0
$256$	1.40107e9	+	2.42673e9i	0.326212	+	0.565016i
$257$	4.71548e9	−	2.72248e9i	1.08092	−	0.624069i	0.149775	−	0.988720i	$-0.452145\pi$
$257$	4.71548e9	−	2.72248e9i	1.08092	−	0.624069i	0.931144	+	0.364651i	$0.118812\pi$
$258$		0			0
$259$	4.12641e8	−	7.14715e8i	0.0917008	−	0.158830i
$260$		−	7.83737e8i		−	0.171505i
$261$		0			0
$262$	−7.27092e9			−1.54306
$263$	−5.14084e9	−	2.96807e9i	−1.07451	−	0.620369i	−0.145101	−	0.989417i	$-0.546351\pi$
$263$	−5.14084e9	−	2.96807e9i	−1.07451	−	0.620369i	−0.929411	+	0.369047i	$0.879684\pi$
$264$		0			0
$265$	5.49922e8	+	9.52492e8i	0.111511	+	0.193143i
$266$	−4.83729e9	+	2.79281e9i	−0.966219	+	0.557847i
$267$		0			0
$268$	6.91904e8	−	1.19841e9i	0.134124	−	0.232310i
$269$			8.12664e9i			1.55204i	0.630711	+	0.776018i	$0.282763\pi$
$269$			8.12664e9i			1.55204i	−0.630711	+	0.776018i	$0.717237\pi$
$270$		0			0
$271$	−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
$273$		0			0
$274$	2.08504e9	+	3.61139e9i	0.369923	+	0.640726i
$275$	−1.22831e9	+	7.09162e8i	−0.214771	+	0.123998i
$276$		0			0
$277$	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
$279$		0			0
$280$	1.49736e10			2.43609
$281$	−3.14649e9	−	1.81663e9i	−0.504663	−	0.291367i	0.225974	−	0.974133i	$-0.427444\pi$
$281$	−3.14649e9	−	1.81663e9i	−0.504663	−	0.291367i	−0.730637	+	0.682766i	$0.760777\pi$
$282$		0			0
$283$	−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
$285$		0			0
$286$	−7.72104e8	+	1.33732e9i	−0.115401	+	0.199881i
$287$		−	9.79695e9i		−	1.44399i
$288$		0			0
$289$	6.08284e9			0.871998
$290$	4.76190e9	+	2.74929e9i	0.673269	+	0.388712i
$291$		0			0
$292$	−4.25018e8	−	7.36153e8i	−0.0584623	−	0.101260i
$293$	−8.58256e9	+	4.95514e9i	−1.16452	+	0.672335i	−0.952383	−	0.304906i	$-0.901375\pi$
$293$	−8.58256e9	+	4.95514e9i	−1.16452	+	0.672335i	−0.212135	+	0.977240i	$0.568042\pi$
$294$		0			0
$295$	−8.08621e9	+	1.40057e10i	−1.06772	+	1.84934i
$296$		−	8.41300e8i		−	0.109593i
$297$		0			0
$298$	−5.13383e9			−0.650993
$299$	−1.80811e9	−	1.04391e9i	−0.226225	−	0.130611i
$300$		0			0
$301$	7.13458e9	+	1.23575e10i	0.869166	+	1.50544i
$302$	2.94301e9	−	1.69915e9i	0.353805	−	0.204270i
$303$		0			0
$304$	−2.15330e9	+	3.72962e9i	−0.252122	+	0.436687i
$305$			1.50256e10i			1.73633i
$306$		0			0
$307$	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
$309$		0			0
$310$	−5.54389e9	−	9.60229e9i	−0.600299	−	1.03975i
$311$	9.85438e9	−	5.68943e9i	1.05339	−	0.608173i	0.129791	−	0.991541i	$-0.458569\pi$
$311$	9.85438e9	−	5.68943e9i	1.05339	−	0.608173i	0.923595	+	0.383369i	$0.125236\pi$
$312$		0			0
$313$	−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
$315$		0			0
$316$	−3.18684e9			−0.319603
$317$	−9.96977e8	−	5.75605e8i	−0.0987297	−	0.0570016i	0.449822	−	0.893118i	$-0.351487\pi$
$317$	−9.96977e8	−	5.75605e8i	−0.0987297	−	0.0570016i	−0.548552	+	0.836117i	$0.684821\pi$
$318$		0			0
$319$	1.62442e9	+	2.81359e9i	0.156869	+	0.271705i
$320$	1.26154e10	−	7.28350e9i	1.20310	−	0.694609i
$321$		0			0
$322$	3.73861e9	−	6.47547e9i	0.347766	−	0.602348i
$323$			2.74218e9i			0.251934i
$324$		0			0
$325$	−3.72312e9			−0.333713
$326$	−1.23863e10	−	7.15121e9i	−1.09665	−	0.633153i
$327$		0			0
$328$	−4.99355e9	−	8.64909e9i	−0.431434	−	0.747265i
$329$	4.77835e8	−	2.75878e8i	0.0407844	−	0.0235469i
$330$		0			0
$331$	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
$333$		0			0
$334$	2.08766e10			1.67754
$335$	−1.58445e10	−	9.14784e9i	−1.25806	−	0.726339i
$336$		0			0
$337$	−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
$339$		0			0
$340$	6.88987e8	−	1.19336e9i	0.0515579	−	0.0893010i
$341$		−	6.55125e9i		−	0.484514i
$342$		0			0
$343$	−3.15828e10			−2.28178
$344$	1.25973e10	+	7.27307e9i	0.899590	+	0.519378i
$345$		0			0
$346$	−3.94188e9	−	6.82754e9i	−0.275042	−	0.476387i
$347$	−2.63578e9	+	1.52177e9i	−0.181799	+	0.104962i	−0.588138	−	0.808761i	$-0.700139\pi$
$347$	−2.63578e9	+	1.52177e9i	−0.181799	+	0.104962i	0.406339	+	0.913723i	$0.366805\pi$
$348$		0			0
$349$	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
$351$		0			0
$352$	3.06432e9			0.199601
$353$	2.85996e9	+	1.65120e9i	0.184188	+	0.106341i	0.589259	−	0.807944i	$-0.299420\pi$
$353$	2.85996e9	+	1.65120e9i	0.184188	+	0.106341i	−0.405071	+	0.914285i	$0.632753\pi$
$354$		0			0
$355$	3.56198e9	+	6.16953e9i	0.224273	+	0.388453i
$356$	1.18881e9	−	6.86362e8i	0.0740140	−	0.0427320i
$357$		0			0
$358$	2.12635e8	−	3.68295e8i	0.0129450	−	0.0224215i
$359$			4.04837e8i			0.0243726i	0.999926	+	0.0121863i	$0.00387912\pi$
$359$			4.04837e8i			0.0243726i	−0.999926	+	0.0121863i	$0.996121\pi$
$360$		0			0
$361$	−8.56218e9			−0.504145
$362$	9.11110e9	+	5.26030e9i	0.530562	+	0.306320i
$363$		0			0
$364$	2.17669e9	+	3.77014e9i	0.123991	+	0.214759i
$365$	−9.73287e9	+	5.61927e9i	−0.548364	+	0.316598i
$366$		0			0
$367$	−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
$369$		0			0
$370$	−2.08504e9			−0.111252
$371$	−5.29076e9	−	3.05462e9i	−0.279269	−	0.161236i
$372$		0			0
$373$	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
$375$		0			0
$376$	2.81233e8	−	4.87110e8i	0.0140707	−	0.0243711i
$377$			8.52826e9i			0.422178i
$378$		0			0
$379$	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
$381$		0			0
$382$	1.58209e10	+	2.74027e10i	0.742983	+	1.28688i
$383$	8.03555e9	−	4.63933e9i	0.373440	−	0.215606i	−0.301520	−	0.953460i	$-0.597494\pi$
$383$	8.03555e9	−	4.63933e9i	0.373440	−	0.215606i	0.674960	+	0.737854i	$0.264161\pi$
$384$		0			0
$385$	1.09632e10	−	1.89889e10i	0.498994	−	0.864283i
$386$			1.22358e10i			0.551168i
$387$		0			0
$388$	−2.91270e9			−0.128519
$389$	3.34709e10	+	1.93244e10i	1.46174	+	0.843934i	0.999092	−	0.0426090i	$-0.0135670\pi$
$389$	3.34709e10	+	1.93244e10i	1.46174	+	0.843934i	0.462645	+	0.886543i	$0.346900\pi$
$390$		0			0
$391$	−1.83542e9	−	3.17904e9i	−0.0785287	−	0.136016i
$392$	−4.99561e10	+	2.88422e10i	−2.11565	+	1.22147i
$393$		0			0
$394$	−1.28117e10	+	2.21905e10i	−0.531645	+	0.920836i
$395$			4.21340e10i			1.73079i
$396$		0			0
$397$	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
$399$		0			0
$400$	−5.14026e9	−	8.90320e9i	−0.200792	−	0.347781i
$401$	1.29788e10	−	7.49329e9i	0.501945	−	0.289798i	−0.227572	−	0.973761i	$-0.573079\pi$
$401$	1.29788e10	−	7.49329e9i	0.501945	−	0.289798i	0.729516	+	0.683963i	$0.239745\pi$
$402$		0			0
$403$	8.59855e9	−	1.48931e10i	0.325991	−	0.564632i
$404$		−	1.20184e10i		−	0.451149i
$405$		0			0
$406$	−3.05426e10			−1.12409
$407$	−1.06690e9	−	6.15976e8i	−0.0388819	−	0.0224485i
$408$		0			0
$409$	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
$411$		0			0
$412$	5.76013e8	−	9.97684e8i	0.0199914	−	0.0346262i
$413$		−	8.98320e10i		−	3.08767i
$414$		0			0
$415$	2.39971e10			0.809032
$416$	6.96620e9	+	4.02194e9i	0.232607	+	0.134296i
$417$		0			0
$418$	4.16901e9	+	7.22094e9i	0.136561	+	0.236531i
$419$	1.89762e10	−	1.09559e10i	0.615676	−	0.355461i	−0.159507	−	0.987197i	$-0.550991\pi$
$419$	1.89762e10	−	1.09559e10i	0.615676	−	0.355461i	0.775184	+	0.631736i	$0.217657\pi$
$420$		0			0
$421$	−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
$423$		0			0
$424$	−6.22782e9			−0.192696
$425$	−5.66902e9	−	3.27301e9i	−0.173761	−	0.100321i
$426$		0			0
$427$	−4.17308e10	−	7.22799e10i	−1.25529	−	2.17423i
$428$	−4.99566e9	+	2.88424e9i	−0.148874	+	0.0859522i
$429$		0			0
$430$	1.80252e10	−	3.12206e10i	0.527239	−	0.913204i
$431$			1.04363e10i			0.302440i	0.988500	+	0.151220i	$0.0483202\pi$
$431$			1.04363e10i			0.302440i	−0.988500	+	0.151220i	$0.951680\pi$
$432$		0			0
$433$	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
$435$		0			0
$436$	1.90857e9	+	3.30573e9i	0.0528155	+	0.0914791i
$437$	−9.76300e9	+	5.63667e9i	−0.267706	+	0.154560i
$438$		0			0
$439$	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
$441$		0			0
$442$	−7.12701e9			−0.186732
$443$	−2.90683e10	−	1.67826e10i	−0.754753	−	0.435757i	0.0726555	−	0.997357i	$-0.476853\pi$
$443$	−2.90683e10	−	1.67826e10i	−0.754753	−	0.435757i	−0.827409	+	0.561600i	$0.810186\pi$
$444$		0			0
$445$	−9.07456e9	−	1.57176e10i	−0.231412	−	0.400817i
$446$	9.58278e9	−	5.53262e9i	0.242188	−	0.139827i
$447$		0			0
$448$	−4.04573e10	+	7.00740e10i	−1.00435	+	1.73958i
$449$			6.27667e10i			1.54434i	0.635413	+	0.772172i	$0.280830\pi$
$449$			6.27667e10i			1.54434i	−0.635413	+	0.772172i	$0.719170\pi$
$450$		0			0
$451$	−1.46246e10			−0.353489
$452$	6.80783e9	+	3.93050e9i	0.163100	+	0.0941660i
$453$		0			0
$454$	6.82666e9	+	1.18241e10i	0.160689	+	0.278321i
$455$	4.98460e10	−	2.87786e10i	1.16301	−	0.671466i
$456$		0			0
$457$	−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
$459$		0			0
$460$	5.66497e9			0.126522
$461$	−2.09686e10	−	1.21062e10i	−0.464264	−	0.268043i	0.249571	−	0.968356i	$-0.419710\pi$
$461$	−2.09686e10	−	1.21062e10i	−0.464264	−	0.268043i	−0.713836	+	0.700313i	$0.753044\pi$
$462$		0			0
$463$	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
$465$		0			0
$466$	2.14186e10	−	3.70981e10i	0.454200	−	0.786698i
$467$			3.95095e8i			0.00830681i	0.999991	+	0.00415341i	$0.00132207\pi$
$467$			3.95095e8i			0.00830681i	−0.999991	+	0.00415341i	$0.998678\pi$
$468$		0			0
$469$	1.01626e11			2.10046
$470$	−1.20723e9	−	6.96995e8i	−0.0247399	−	0.0142836i
$471$		0			0
$472$	−4.57878e10	−	7.93069e10i	−0.922534	−	1.59787i
$473$	1.84468e10	−	1.06503e10i	0.368533	−	0.212773i
$474$		0			0
$475$	−1.00516e10	+	1.74099e10i	−0.197451	+	0.341996i
$476$			7.65416e9i			0.149097i
$477$		0			0
$478$	−5.16977e10			−0.990284
$479$	4.38005e10	+	2.52882e10i	0.832026	+	0.480370i	0.854546	−	0.519376i	$-0.173836\pi$
$479$	4.38005e10	+	2.52882e10i	0.832026	+	0.480370i	−0.0225201	+	0.999746i	$0.507169\pi$
$480$		0			0
$481$	−1.61695e9	−	2.80063e9i	−0.0302075	−	0.0523209i
$482$	2.23940e10	−	1.29292e10i	0.414899	−	0.239542i
$483$		0			0
$484$	−5.09203e9	+	8.81965e9i	−0.0927918	+	0.160720i
$485$			3.85095e10i			0.695987i
$486$		0			0
$487$	−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
$489$		0			0
$490$	7.14811e10	+	1.23809e11i	1.23996	+	2.14767i
$491$	−6.06996e10	+	3.50449e10i	−1.04438	+	0.602975i	−0.921072	−	0.389393i	$-0.872685\pi$
$491$	−6.06996e10	+	3.50449e10i	−1.04438	+	0.602975i	−0.123312	+	0.992368i	$0.539352\pi$
$492$		0			0
$493$	−7.49724e9	+	1.29856e10i	−0.126915	+	0.219824i
$494$			2.18874e10i			0.367525i
$495$		0			0
$496$	4.74858e10			0.784580
$497$	−3.42695e10	−	1.97855e10i	−0.561672	−	0.324281i
$498$		0			0
$499$	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
$501$		0			0
$502$	4.09741e10	−	7.09691e10i	0.645200	−	1.11752i
$503$			3.33685e10i			0.521272i	0.965437	+	0.260636i	$0.0839323\pi$
$503$			3.33685e10i			0.521272i	−0.965437	+	0.260636i	$0.916068\pi$
$504$		0			0
$505$	−1.58898e11			−2.44316
$506$	−9.66636e9	−	5.58088e9i	−0.147456	−	0.0851335i
$507$		0			0
$508$	6.03566e8	+	1.04541e9i	0.00906295	+	0.0156975i
$509$	−1.17263e10	+	6.77018e9i	−0.174699	+	0.100862i	−0.584800	−	0.811178i	$-0.698827\pi$
$509$	−1.17263e10	+	6.77018e9i	−0.174699	+	0.100862i	0.410101	+	0.912040i	$0.365494\pi$
$510$		0			0
$511$	3.12131e10	−	5.40626e10i	0.457776	−	0.792891i
$512$			7.53294e10i			1.09619i
$513$		0			0
$514$	7.64124e10			1.09474
$515$	−1.31906e10	−	7.61562e9i	−0.187515	−	0.108262i
$516$		0			0
$517$	−4.11822e8	−	7.13296e8i	−0.00576430	−	0.00998407i
$518$	1.00300e10	−	5.79083e9i	0.139310	−	0.0804307i
$519$		0			0
$520$	2.93372e10	−	5.08135e10i	0.401241	−	0.694969i
$521$		−	3.88502e10i		−	0.527281i	−0.964621	−	0.263641i	$-0.915077\pi$
$521$		−	3.88502e10i		−	0.527281i	0.964621	−	0.263641i	$-0.0849233\pi$
$522$		0			0
$523$	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
$525$		0			0
$526$	−4.16526e10	−	7.21444e10i	−0.544126	−	0.942453i
$527$	2.61852e10	−	1.51181e10i	0.339480	−	0.195999i
$528$		0			0
$529$	−3.16099e10	+	5.47500e10i	−0.403646	+	0.699136i
$530$			1.54347e10i			0.195612i
$531$		0			0
$532$	2.35063e10			0.293453
$533$	−3.32464e10	−	1.91948e10i	−0.411942	−	0.237835i
$534$		0			0
$535$	3.81333e10	+	6.60488e10i	0.465468	+	0.806213i
$536$	8.97190e10	−	5.17993e10i	1.08699	−	0.627574i
$537$		0			0
$538$	−5.70229e10	+	9.87666e10i	−0.680645	+	1.17891i
$539$			8.44697e10i			1.00080i
$540$		0			0
$541$	−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
$543$		0			0
$544$	7.07141e9	+	1.22480e10i	0.0807440	+	0.139853i
$545$	4.37059e10	−	2.52336e10i	0.495398	−	0.286018i
$546$		0			0
$547$	−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
$549$		0			0
$550$	−1.99042e10			−0.217517
$551$	3.98794e10	+	2.30244e10i	0.432656	+	0.249794i
$552$		0			0
$553$	−1.17020e11	−	2.02684e11i	−1.25129	−	2.16730i
$554$	6.55512e10	−	3.78460e10i	0.695891	−	0.401773i
$555$		0			0
$556$	1.45007e10	−	2.51160e10i	0.151737	−	0.262816i
$557$		−	8.31342e10i		−	0.863692i	−0.901947	−	0.431846i	$-0.857862\pi$
$557$		−	8.31342e10i		−	0.863692i	0.901947	−	0.431846i	$-0.142138\pi$
$558$		0			0
$559$	5.59142e10			0.572631
$560$	1.37638e11	+	7.94654e10i	1.39954	+	0.808027i
$561$		0			0
$562$	−2.54938e10	−	4.41566e10i	−0.255558	−	0.442640i
$563$	−4.30743e9	+	2.48690e9i	−0.0428731	+	0.0247528i	−0.521283	−	0.853384i	$-0.674547\pi$
$563$	−4.30743e9	+	2.48690e9i	−0.0428731	+	0.0247528i	0.478410	+	0.878136i	$0.341213\pi$
$564$		0			0
$565$	5.19661e10	−	9.00080e10i	0.509949	−	0.883258i
$566$		−	1.14238e11i		−	1.11313i
$567$		0			0
$568$	−4.03391e10			−0.387555
$569$	−1.40620e11	−	8.11870e10i	−1.34152	−	0.774528i	−0.354492	−	0.935059i	$-0.615346\pi$
$569$	−1.40620e11	−	8.11870e10i	−1.34152	−	0.774528i	−0.987031	+	0.160531i	$0.948679\pi$
$570$		0			0
$571$	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
$573$		0			0
$574$	6.87431e10	−	1.19067e11i	0.633260	−	1.09684i
$575$		−	2.69112e10i		−	0.246185i
$576$		0			0
$577$	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
$579$		0			0
$580$	−1.15700e10	−	2.00398e10i	−0.102240	−	0.177085i
$581$	−1.15437e11	+	6.66476e10i	−1.01307	+	0.584898i
$582$		0			0
$583$	−4.55984e9	+	7.89787e9i	−0.0394707	+	0.0683653i
$584$		−	6.36378e10i		−	0.547097i
$585$		0			0
$586$	−1.39077e11			−1.17941
$587$	−4.13335e10	−	2.38639e10i	−0.348137	−	0.200997i	0.315728	−	0.948850i	$-0.397751\pi$
$587$	−4.13335e10	−	2.38639e10i	−0.348137	−	0.200997i	−0.663864	+	0.747853i	$0.731085\pi$
$588$		0			0
$589$	−4.64283e10	−	8.04162e10i	−0.385764	−	0.668163i
$590$	−1.96551e11	+	1.13478e11i	−1.62206	+	0.936495i
$591$		0			0
$592$	4.46482e9	−	7.73329e9i	0.0363511	−	0.0629619i
$593$		−	1.18090e11i		−	0.954983i	−0.878636	−	0.477492i	$-0.841546\pi$
$593$		−	1.18090e11i		−	0.954983i	0.878636	−	0.477492i	$-0.158454\pi$
$594$		0			0
$595$	1.01198e11			0.807425
$596$	1.87105e10	+	1.08025e10i	0.148286	+	0.0856130i
$597$		0			0
$598$	−1.46499e10	−	2.53743e10i	−0.114559	−	0.198422i
$599$	−1.84255e10	+	1.06380e10i	−0.143124	+	0.0826327i	−0.569852	−	0.821747i	$-0.693000\pi$
$599$	−1.84255e10	+	1.06380e10i	−0.143124	+	0.0826327i	0.426728	+	0.904380i	$0.359666\pi$
$600$		0			0
$601$	−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
$603$		0			0
$604$	−1.43013e10			−0.107455
$605$	1.16607e11	+	6.73230e10i	0.870367	+	0.502507i
$606$		0			0
$607$	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
$609$		0			0
$610$	−1.05431e11	+	1.82612e11i	−0.761465	+	1.31890i
$611$		−	2.16207e9i		−	0.0155133i
$612$		0			0
$613$	−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
$615$		0			0
$616$	6.20788e10	+	1.07524e11i	0.431142	+	0.746760i
$617$	2.52991e10	−	1.46064e10i	0.174568	−	0.100787i	−0.410170	−	0.912009i	$-0.634531\pi$
$617$	2.52991e10	−	1.46064e10i	0.174568	−	0.100787i	0.584738	+	0.811222i	$0.301197\pi$
$618$		0			0
$619$	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
$621$		0			0
$622$	1.59686e11			1.06686
$623$	8.73057e10	+	5.04060e10i	0.579550	+	0.334603i
$624$		0			0
$625$	9.50853e10	+	1.64693e11i	0.623151	+	1.07933i
$626$	−1.76367e10	+	1.01825e10i	−0.114847	+	0.0663069i
$627$		0			0
$628$	6.14951e9	−	1.06513e10i	0.0395368	−	0.0684798i
$629$		−	5.68586e9i		−	0.0363240i
$630$		0			0
$631$	−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
$633$		0			0
$634$	−8.07780e9	−	1.39912e10i	−0.0499961	−	0.0865958i
$635$	1.38216e10	−	7.97989e9i	0.0850086	−	0.0490797i
$636$		0			0
$637$	−1.10867e11	+	1.92027e11i	−0.673356	+	1.16629i
$638$			4.55930e10i			0.275179i
$639$		0			0
$640$	1.09820e11			0.654577
$641$	1.75989e11	+	1.01607e11i	1.04244	+	0.601855i	0.920525	−	0.390685i	$-0.127762\pi$
$641$	1.75989e11	+	1.01607e11i	1.04244	+	0.601855i	0.121919	+	0.992540i	$0.461095\pi$
$642$		0			0
$643$	−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
$645$		0			0
$646$	−1.92413e10	+	3.33270e10i	−0.110485	+	0.191366i
$647$			5.14865e10i			0.293817i	0.989150	+	0.146908i	$0.0469322\pi$
$647$			5.14865e10i			0.293817i	−0.989150	+	0.146908i	$0.953068\pi$
$648$		0			0
$649$	−1.34098e11			−0.755865
$650$	−4.52487e10	−	2.61244e10i	−0.253485	−	0.146350i
$651$		0			0
$652$	3.00949e10	+	5.21259e10i	0.166534	+	0.288445i
$653$	−2.87927e11	+	1.66235e11i	−1.58354	+	0.914260i	−0.589209	+	0.807981i	$0.700560\pi$
$653$	−2.87927e11	+	1.66235e11i	−1.58354	+	0.914260i	−0.994336	+	0.106279i	$0.966106\pi$
$654$		0			0
$655$	2.02276e11	−	3.50353e11i	1.09895	−	1.90345i
$656$		−	1.06004e11i		−	0.572410i
$657$		0			0
$658$	7.74312e9			0.0413059
$659$	1.31243e11	+	7.57732e10i	0.695880	+	0.401767i	0.805811	−	0.592172i	$-0.201730\pi$
$659$	1.31243e11	+	7.57732e10i	0.695880	+	0.401767i	−0.109931	+	0.993939i	$0.535063\pi$
$660$		0			0
$661$	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
$663$		0			0
$664$	−6.79412e10	+	1.17678e11i	−0.349511	+	0.605371i
$665$		−	3.10783e11i		−	1.58917i
$666$		0			0
$667$	−6.16435e10			−0.311447
$668$	−7.60858e10	−	4.39281e10i	−0.382118	−	0.220616i
$669$		0			0
$670$	−1.28377e11	−	2.22355e11i	−0.637071	−	1.10344i
$671$	−1.07897e11	+	6.22944e10i	−0.532255	+	0.307297i
$672$		0			0
$673$	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
$675$		0			0
$676$	−3.11169e10			−0.149008
$677$	3.43053e11	+	1.98062e11i	1.63308	+	0.942857i	0.983137	+	0.182870i	$0.0585387\pi$
$677$	3.43053e11	+	1.98062e11i	1.63308	+	0.942857i	0.649939	+	0.759987i	$0.274795\pi$
$678$		0			0
$679$	−1.06953e11	−	1.85249e11i	−0.503171	−	0.871517i
$680$	8.93408e10	−	5.15809e10i	0.417844	−	0.241242i
$681$		0			0
$682$	4.59688e10	−	7.96202e10i	0.212484	−	0.368032i
$683$			5.35678e10i			0.246162i	0.992397	+	0.123081i	$0.0392775\pi$
$683$			5.35678e10i			0.246162i	−0.992397	+	0.123081i	$0.960722\pi$
$684$		0			0
$685$	−2.32022e11			−1.05382
$686$	−3.83840e11	−	2.21610e11i	−1.73322	−	1.00068i
$687$		0			0
$688$	7.71970e10	+	1.33709e11i	0.344546	+	0.596770i
$689$	−2.07320e10	+	1.19696e10i	−0.0919950	+	0.0531133i
$690$		0			0
$691$	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
$693$		0			0
$694$	−4.27117e10			−0.184124
$695$	−3.32065e11	−	1.91718e11i	−1.42326	−	0.821719i
$696$		0			0
$697$	−3.37485e10	−	5.84541e10i	−0.142996	−	0.247676i
$698$	2.27258e11	−	1.31207e11i	0.957407	−	0.552759i
$699$		0			0
$700$	−2.80566e10	+	4.85955e10i	−0.116854	+	0.202397i
$701$		−	1.27802e11i		−	0.529256i	−0.964351	−	0.264628i	$-0.914751\pi$
$701$		−	1.27802e11i		−	0.529256i	0.964351	−	0.264628i	$-0.0852491\pi$
$702$		0			0
$703$	−1.74616e10			−0.0714927
$704$	1.04604e11	+	6.03933e10i	0.425852	+	0.245866i
$705$		0			0
$706$	2.31722e10	+	4.01355e10i	0.0932715	+	0.161551i
$707$	7.64372e11	−	4.41311e11i	3.05934	−	1.76631i
$708$		0			0
$709$	−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
$711$		0			0
$712$	1.02769e11			0.399890
$713$	1.07650e11	+	6.21516e10i	0.416538	+	0.240488i
$714$		0			0
$715$	−4.29597e10	−	7.44084e10i	−0.164376	−	0.284707i
$716$	−1.54992e9	+	8.94846e8i	−0.00589735	+	0.00340484i
$717$		0			0
$718$	−2.84066e9	+	4.92017e9i	−0.0106886	+	0.0185132i
$719$			3.68747e11i			1.37979i	0.723910	+	0.689894i	$0.242343\pi$
$719$			3.68747e11i			1.37979i	−0.723910	+	0.689894i	$0.757657\pi$
$720$		0			0
$721$	8.46041e10			0.313076
$722$	−1.04060e11	−	6.00791e10i	−0.382944	−	0.221093i
$723$		0			0
$724$	−2.21372e10	−	3.83428e10i	−0.0805692	−	0.139550i
$725$	−9.51985e10	+	5.49629e10i	−0.344571	+	0.198938i
$726$		0			0
$727$	−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
$729$		0			0
$730$	−1.57717e11			−0.555376
$731$	8.51379e10	+	4.91544e10i	0.298163	+	0.172144i
$732$		0			0
$733$	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
$735$		0			0
$736$	−2.90711e10	+	5.03527e10i	−0.0990720	+	0.171598i
$737$		−	1.51704e11i		−	0.514194i
$738$		0			0
$739$	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
$741$		0			0
$742$	−4.28673e10	−	7.42483e10i	−0.141420	−	0.244946i
$743$	−3.69180e11	+	2.13146e11i	−1.21139	+	0.699395i	−0.963062	−	0.269281i	$-0.913214\pi$
$743$	−3.69180e11	+	2.13146e11i	−1.21139	+	0.699395i	−0.248327	+	0.968676i	$0.579881\pi$
$744$		0			0
$745$	1.42823e11	−	2.47376e11i	0.463631	−	0.803032i
$746$			1.54182e11i			0.497826i
$747$		0			0
$748$	1.14259e10			0.0364992
$749$	−3.66878e11	−	2.11817e11i	−1.16572	−	0.673029i
$750$		0			0
$751$	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
$753$		0			0
$754$	−5.98411e10	+	1.03648e11i	−0.185146	+	0.320682i
$755$			1.89081e11i			0.581915i
$756$		0			0
$757$	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
$759$		0			0
$760$	−1.58408e11	−	2.74370e11i	−0.474812	−	0.822398i
$761$	2.58522e11	−	1.49258e11i	0.770829	−	0.445038i	−0.0623411	−	0.998055i	$-0.519857\pi$
$761$	2.58522e11	−	1.49258e11i	0.770829	−	0.445038i	0.833170	+	0.553016i	$0.186523\pi$
$762$		0			0
$763$	−1.40164e11	+	2.42771e11i	−0.413559	+	0.716306i
$764$		−	1.33161e11i		−	0.390843i
$765$		0			0
$766$	1.30213e11			0.378215
$767$	−3.04849e11	−	1.76005e11i	−0.880853	−	0.508561i
$768$		0			0
$769$	−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
$771$		0			0
$772$	2.57464e10	−	4.45941e10i	0.0724848	−	0.125547i
$773$			4.05117e10i			0.113465i	0.998389	+	0.0567326i	$0.0180683\pi$
$773$			4.05117e10i			0.113465i	−0.998389	+	0.0567326i	$0.981932\pi$
$774$		0			0
$775$	2.21663e11			0.614451
$776$	−1.88844e11	−	1.09029e11i	−0.520783	−	0.300674i
$777$		0			0
$778$	2.71191e11	+	4.69717e11i	0.740214	+	1.28209i
$779$	−1.79516e11	+	1.03643e11i	−0.487475	+	0.281444i
$780$		0			0
$781$	−2.95352e10	+	5.11564e10i	−0.0793844	+	0.137498i
$782$		−	5.15151e10i		−	0.137755i
$783$		0			0
$784$	−6.12267e11			−1.62060
$785$	−1.40823e11	−	8.13042e10i	−0.370847	−	0.214109i
$786$		0			0
$787$	−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
$789$		0			0
$790$	−2.95645e11	+	5.12073e11i	−0.759037	+	1.31469i
$791$			5.77307e11i			1.47469i
$792$		0			0
$793$	−3.27047e11			−0.827023
$794$	1.94704e10	+	1.12413e10i	0.0489884	+	0.0282835i
$795$		0			0
$796$	3.44291e10	+	5.96330e10i	0.0857578	+	0.148537i
$797$	−4.69140e11	+	2.70858e11i	−1.16270	+	0.671287i	−0.951950	−	0.306253i	$-0.900925\pi$
$797$	−4.69140e11	+	2.70858e11i	−1.16270	+	0.671287i	−0.210753	+	0.977539i	$0.567591\pi$
$798$		0			0
$799$	1.90069e9	−	3.29209e9i	0.00466363	−	0.00807764i
$800$			1.03682e11i			0.253130i
$801$		0			0
$802$	2.10316e11			0.508363
$803$	−8.07029e10	−	4.65938e10i	−0.194101	−	0.112064i
$804$		0			0
$805$	2.08016e11	+	3.60294e11i	0.495351	+	0.857973i
$806$	2.09004e11	−	1.20668e11i	0.495238	−	0.285926i
$807$		0			0
$808$	4.49877e11	−	7.79209e11i	1.05547	−	1.82814i
$809$		−	8.46989e11i		−	1.97735i	−0.150073	−	0.988675i	$-0.547951\pi$
$809$		−	8.46989e11i		−	1.97735i	0.150073	−	0.988675i	$-0.452049\pi$
$810$		0			0
$811$	−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
$813$		0			0
$814$	−8.64436e9	−	1.49725e10i	−0.0196895	−	0.0341033i
$815$	6.89169e11	−	3.97892e11i	1.56205	−	0.901851i
$816$		0			0
$817$	1.50956e11	−	2.61463e11i	0.338814	−	0.586843i
$818$			2.31968e11i			0.518101i
$819$		0			0
$820$	1.04164e11			0.230389
$821$	5.97010e11	+	3.44684e11i	1.31404	+	0.758662i	0.982763	−	0.184872i	$-0.0591869\pi$
$821$	5.97010e11	+	3.44684e11i	1.31404	+	0.758662i	0.331278	+	0.943533i	$0.392520\pi$
$822$		0			0
$823$	−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
$825$		0			0
$826$	6.30333e11	−	1.09177e12i	1.35410	−	2.34536i
$827$		−	5.43243e11i		−	1.16137i	−0.814127	−	0.580687i	$-0.802784\pi$
$827$		−	5.43243e11i		−	1.16137i	0.814127	−	0.580687i	$-0.197216\pi$
$828$		0			0
$829$	−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
$831$		0			0
$832$	1.58533e11	+	2.74587e11i	0.330846	+	0.573043i
$833$	−3.37624e11	+	1.94927e11i	−0.701219	+	0.404849i
$834$		0			0
$835$	−5.80785e11	+	1.00595e12i	−1.19473	+	2.06933i
$836$		−	3.50894e10i		−	0.0718375i
$837$		0			0
$838$	3.07501e11			0.623549
$839$	−2.70550e11	−	1.56202e11i	−0.546009	−	0.315239i	0.201502	−	0.979488i	$-0.435418\pi$
$839$	−2.70550e11	−	1.56202e11i	−0.546009	−	0.315239i	−0.747511	+	0.664250i	$0.768751\pi$
$840$		0			0
$841$	−1.24224e11	−	2.15162e11i	−0.248325	−	0.430112i
$842$	−4.19263e11	+	2.42062e11i	−0.834139	+	0.481590i
$843$		0			0
$844$	−3.96887e10	+	6.87429e10i	−0.0782163	+	0.135475i
$845$			4.11405e11i			0.806942i
$846$		0			0
$847$	−7.47911e11			−1.45317
$848$	−5.72466e10	−	3.30513e10i	−0.110705	−	0.0639154i
$849$		0			0
$850$	−4.59321e10	−	7.95567e10i	−0.0879915	−	0.152406i
$851$	2.02434e10	−	1.16875e10i	0.0385980	−	0.0222846i
$852$		0			0
$853$	−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
$855$		0			0
$856$	−4.31857e11			−0.804349
$857$	7.56463e11	+	4.36744e11i	1.40238	+	0.809662i	0.994636	−	0.103436i	$-0.0329837\pi$
$857$	7.56463e11	+	4.36744e11i	1.40238	+	0.809662i	0.407740	+	0.913098i	$0.366317\pi$
$858$		0			0
$859$	−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
$861$		0			0
$862$	−7.32297e10	+	1.26838e11i	−0.132635	+	0.229731i
$863$		−	5.34241e11i		−	0.963151i	−0.876405	−	0.481575i	$-0.840065\pi$
$863$		−	5.34241e11i		−	0.963151i	0.876405	−	0.481575i	$-0.159935\pi$
$864$		0			0
$865$	4.38651e11			0.783529
$866$	1.15307e11	+	6.65724e10i	0.205014	+	0.118365i
$867$		0			0
$868$	−1.29594e11	−	2.24463e11i	−0.228300	−	0.395426i
$869$	−3.02560e11	+	1.74683e11i	−0.530557	+	0.306317i
$870$		0			0
$871$	1.99112e11	−	3.44873e11i	0.345960	−	0.599220i
$872$			2.85769e11i			0.494253i
$873$		0			0
$874$	−1.58205e11			−0.271129
$875$	−5.03167e11	−	2.90504e11i	−0.858381	−	0.495586i
$876$		0			0
$877$	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
$879$		0			0
$880$	1.18623e11	−	2.05462e11i	0.197806	−	0.342610i
$881$			4.68554e11i			0.777778i	0.921285	+	0.388889i	$0.127141\pi$
$881$			4.68554e11i			0.777778i	−0.921285	+	0.388889i	$0.872859\pi$
$882$		0			0
$883$	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
$885$		0			0
$886$	−2.35520e11	−	4.07933e11i	−0.382202	−	0.661994i
$887$	−2.45157e11	+	1.41541e11i	−0.396050	+	0.228659i	−0.684778	−	0.728752i	$-0.740101\pi$
$887$	−2.45157e11	+	1.41541e11i	−0.396050	+	0.228659i	0.288728	+	0.957411i	$0.406768\pi$
$888$		0			0
$889$	−4.43255e10	+	7.67740e10i	−0.0709654	+	0.122916i
$890$		−	2.54697e11i		−	0.405942i
$891$		0			0
$892$	−4.65665e10			−0.0735554
$893$	−1.01102e10	−	5.83711e9i	−0.0158984	−	0.00917893i
$894$		0			0
$895$	1.18310e10	+	2.04919e10i	0.0184386	+	0.0319367i
$896$	−5.28284e11	+	3.05005e11i	−0.819663	+	0.473233i
$897$		0			0
$898$	−4.40421e11	+	7.62832e11i	−0.677272	+	1.17307i
$899$		−	5.07748e11i		−	0.777337i
$900$		0			0
$901$	−4.20902e10			−0.0638678
$902$	−1.77739e11	−	1.02617e11i	−0.268507	−	0.155023i
$903$		0			0
$904$	2.94256e11	+	5.09667e11i	0.440608	+	0.763155i
$905$	−5.06940e11	+	2.92682e11i	−0.755722	+	0.436316i
$906$		0			0
$907$	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
$909$		0			0
$910$	8.07733e11			1.17788
$911$	−4.92960e11	−	2.84610e11i	−0.715711	−	0.413216i	0.0974609	−	0.995239i	$-0.468928\pi$
$911$	−4.92960e11	−	2.84610e11i	−0.715711	−	0.413216i	−0.813172	+	0.582023i	$0.802261\pi$
$912$		0			0
$913$	9.94893e10	+	1.72321e11i	0.143184	+	0.248001i
$914$	−4.74570e11	+	2.73993e11i	−0.680010	+	0.392604i
$915$		0			0
$916$	−7.00570e10	+	1.21342e11i	−0.0995107	+	0.172358i
$917$			2.24715e12i			3.17800i
$918$		0			0
$919$	−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
$921$		0			0
$922$	−1.69894e11	−	2.94264e11i	−0.235100	−	0.407206i
$923$	−1.34286e11	+	7.75301e10i	−0.185022	+	0.106823i
$924$		0			0
$925$	2.08417e10	−	3.60990e10i	0.0284687	−	0.0493092i
$926$			3.96154e11i			0.538791i
$927$		0			0
$928$	2.37497e11			0.320233
$929$	8.64249e11	+	4.98974e11i	1.16032	+	0.669908i	0.951380	−	0.308021i	$-0.0996668\pi$
$929$	8.64249e11	+	4.98974e11i	1.16032	+	0.669908i	0.208936	+	0.977929i	$0.433000\pi$
$930$		0			0
$931$	5.98632e11	+	1.03686e12i	0.796822	+	1.38014i
$932$	−1.56122e11	+	9.01373e10i	−0.206919	+	0.119465i
$933$		0			0
$934$	−2.77230e9	+	4.80177e9i	−0.00364295	+	0.00630977i
$935$		−	1.51064e11i		−	0.197659i
$936$		0			0
$937$	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
$939$		0			0
$940$	2.93321e9	+	5.08046e9i	0.00375691	+	0.00650717i
$941$	6.73317e11	−	3.88740e11i	0.858739	−	0.495793i	−0.00485072	−	0.999988i	$-0.501544\pi$
$941$	6.73317e11	−	3.88740e11i	0.858739	−	0.495793i	0.863590	+	0.504195i	$0.168211\pi$
$942$		0			0
$943$	1.38743e11	−	2.40310e11i	0.175454	−	0.303896i
$944$		−	9.71993e11i		−	1.22398i
$945$		0			0
$946$	2.98923e11			0.373246
$947$	−1.20470e12	−	6.95534e11i	−1.49789	−	0.864805i	−0.497889	−	0.867241i	$-0.665891\pi$
$947$	−1.20470e12	−	6.95534e11i	−1.49789	−	0.864805i	−0.999997	+	0.00243541i	$0.999225\pi$
$948$		0			0
$949$	−1.22309e11	−	2.11846e11i	−0.150798	−	0.261189i
$950$	−2.44323e11	+	1.41060e11i	−0.299964	+	0.173184i
$951$		0			0
$952$	−2.86514e11	+	4.96256e11i	−0.348817	+	0.604169i
$953$		−	1.14660e12i		−	1.39009i	−0.718969	−	0.695043i	$-0.755385\pi$
$953$		−	1.14660e12i		−	1.39009i	0.718969	−	0.695043i	$-0.244615\pi$
$954$		0			0
$955$	−1.76055e12			−2.11658
$956$	1.88415e11	+	1.08781e11i	0.225571	+	0.130234i
$957$		0			0
$958$	3.54884e11	+	6.14678e11i	0.421332	+	0.729769i
$959$	1.11613e12	−	6.44401e11i	1.31960	−	0.761871i
$960$		0			0
$961$	−8.54865e10	+	1.48067e11i	−0.100231	+	0.173606i
$962$		−	4.53831e10i		−	0.0529900i
$963$		0			0
$964$	−1.08821e11			−0.126010
$965$	−5.89589e11	−	3.40400e11i	−0.679893	−	0.392536i
$966$		0			0
$967$	−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
$969$		0			0
$970$	−2.70213e11	+	4.68023e11i	−0.305225	+	0.528665i
$971$			5.95098e11i			0.669440i	0.942318	+	0.334720i	$0.108642\pi$
$971$			5.95098e11i			0.669440i	−0.942318	+	0.334720i	$0.891358\pi$
$972$		0			0
$973$	2.12985e12			2.37628
$974$	−7.02421e11	−	4.05543e11i	−0.780480	−	0.450610i
$975$		0			0
$976$	−4.51532e11	−	7.82077e11i	−0.497610	−	0.861887i
$977$	1.19400e12	−	6.89357e11i	1.31047	−	0.756600i	0.328295	−	0.944575i	$-0.393526\pi$
$977$	1.19400e12	−	6.89357e11i	1.31047	−	0.756600i	0.982174	+	0.187975i	$0.0601925\pi$
$978$		0			0
$979$	7.52444e10	−	1.30327e11i	0.0819112	−	0.141874i
$980$		−	6.01637e11i		−	0.652275i
$981$		0			0
$982$	−9.83613e11			−1.05774
$983$	4.07742e11	+	2.35410e11i	0.436688	+	0.252122i	0.702192	−	0.711988i	$-0.252205\pi$
$983$	4.07742e11	+	2.35410e11i	0.436688	+	0.252122i	−0.265504	+	0.964110i	$0.585538\pi$
$984$		0			0
$985$	−7.12841e11	−	1.23468e12i	−0.757264	−	1.31162i
$986$	−1.82235e11	+	1.05213e11i	−0.192807	+	0.111317i
$987$		0			0
$988$	4.60551e10	−	7.97698e10i	0.0483337	−	0.0837164i
$989$			4.04156e11i			0.422439i
$990$		0			0
$991$	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
$993$		0			0
$994$	−2.77662e11	−	4.80924e11i	−0.284427	−	0.492642i
$995$	7.88423e11	−	4.55196e11i	0.804390	−	0.464415i
$996$		0			0
$997$	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
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.9.d.a.2.3	✓	14	3.2	odd	2
9.9.d.a.5.3	yes	14	9.4	even	3
27.9.d.a.8.5		14	1.1	even	1	trivial
27.9.d.a.17.5		14	9.5	odd	6	inner
81.9.b.a.80.5		14	9.7	even	3
81.9.b.a.80.10		14	9.2	odd	6
144.9.q.a.65.2		14	12.11	even	2
144.9.q.a.113.2		14	36.31	odd	6
432.9.q.a.17.1		14	36.23	even	6
432.9.q.a.305.1		14	4.3	odd	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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	27.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(12.1534 + 7.01679i) q^{2} +(-29.5292 - 51.1461i) q^{4} +(-676.216 + 390.413i) q^{5} +(2168.61 - 3756.14i) q^{7} -4421.40i q^{8} +O(q^{10})\)	\(q+(12.1534 + 7.01679i) q^{2} +(-29.5292 - 51.1461i) q^{4} +(-676.216 + 390.413i) q^{5} +(2168.61 - 3756.14i) q^{7} -4421.40i q^{8} -10957.8 q^{10} +(-5607.04 - 3237.22i) q^{11} +(-8497.75 - 14718.5i) q^{13} +(52712.1 - 30433.3i) q^{14} +(23464.6 - 40641.8i) q^{16} -29881.7i q^{17} -91768.1 q^{19} +(39936.2 + 23057.2i) q^{20} +(-45429.9 - 78686.9i) q^{22} +(106388. - 61423.0i) q^{23} +(109532. - 189716. i) q^{25} -238508. i q^{26} -256149. q^{28} +(-434568. - 250898. i) q^{29} +(505931. + 876298. i) q^{31} +(-409885. + 236647. i) q^{32} +(209673. - 363165. i) q^{34} +3.38661e6i q^{35} +190279. q^{37} +(-1.11530e6 - 643918. i) q^{38} +(1.72617e6 + 2.98982e6i) q^{40} +(1.95619e6 - 1.12941e6i) q^{41} +(-1.64497e6 + 2.84917e6i) q^{43} +382371. i q^{44} +1.72397e6 q^{46} +(110171. + 63607.2i) q^{47} +(-6.52331e6 - 1.12987e7i) q^{49} +(2.66239e6 - 1.53713e6i) q^{50} +(-501864. + 869254. i) q^{52} -1.40856e6i q^{53} +5.05542e6 q^{55} +(-1.66074e7 - 9.58828e6i) q^{56} +(-3.52099e6 - 6.09854e6i) q^{58} +(1.79370e7 - 1.03560e7i) q^{59} +(9.62157e6 - 1.66651e7i) q^{61} +1.42000e7i q^{62} -1.86559e7 q^{64} +(1.14926e7 + 6.63527e6i) q^{65} +(1.17156e7 + 2.02920e7i) q^{67} +(-1.52833e6 + 882382. i) q^{68} +(-2.37632e7 + 4.11590e7i) q^{70} -9.12361e6i q^{71} +1.43931e7 q^{73} +(2.31255e6 + 1.33515e6i) q^{74} +(2.70984e6 + 4.69358e6i) q^{76} +(-2.43189e7 + 1.40405e7i) q^{77} +(2.69804e7 - 4.67314e7i) q^{79} +3.66435e7i q^{80} +3.16992e7 q^{82} +(-2.66155e7 - 1.53664e7i) q^{83} +(1.16662e7 + 2.02064e7i) q^{85} +(-3.99841e7 + 2.30848e7i) q^{86} +(-1.43131e7 + 2.47910e7i) q^{88} +2.32435e7i q^{89} -7.37131e7 q^{91} +(-6.28309e6 - 3.62755e6i) q^{92} +(892637. + 1.54609e6i) q^{94} +(6.20550e7 - 3.58275e7i) q^{95} +(2.46595e7 - 4.27114e7i) q^{97} -1.83091e8i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{2} + 767 q^{4} - 438 q^{5} + 922 q^{7}+O(q^{10}) \) 14 * q + 3 * q^2 + 767 * q^4 - 438 * q^5 + 922 * q^7	\( 14 q + 3 q^{2} + 767 q^{4} - 438 q^{5} + 922 q^{7} - 516 q^{10} + 28677 q^{11} + 1684 q^{13} - 120966 q^{14} - 65281 q^{16} - 269630 q^{19} - 539454 q^{20} + 61311 q^{22} + 1000452 q^{23} + 65177 q^{25} + 1075708 q^{28} - 3797682 q^{29} - 164132 q^{31} + 8461881 q^{32} + 654993 q^{34} - 1671668 q^{37} - 10967691 q^{38} + 613326 q^{40} + 10239447 q^{41} + 791815 q^{43} + 1189536 q^{46} - 31148628 q^{47} - 4826637 q^{49} + 63849453 q^{50} - 5552720 q^{52} + 8107476 q^{55} - 116638674 q^{56} + 14211822 q^{58} + 83493795 q^{59} - 5255600 q^{61} - 26813830 q^{64} - 69232992 q^{65} - 8288855 q^{67} + 77746743 q^{68} + 27813756 q^{70} - 36721682 q^{73} + 10383450 q^{74} - 42822959 q^{76} - 56158710 q^{77} - 32771822 q^{79} + 236099418 q^{82} + 198915996 q^{83} + 97486146 q^{85} - 146190669 q^{86} + 24955827 q^{88} - 201514504 q^{91} + 295365804 q^{92} - 36698244 q^{94} - 386813838 q^{95} + 127049161 q^{97}+O(q^{100}) \) 14 * q + 3 * q^2 + 767 * q^4 - 438 * q^5 + 922 * q^7 - 516 * q^10 + 28677 * q^11 + 1684 * q^13 - 120966 * q^14 - 65281 * q^16 - 269630 * q^19 - 539454 * q^20 + 61311 * q^22 + 1000452 * q^23 + 65177 * q^25 + 1075708 * q^28 - 3797682 * q^29 - 164132 * q^31 + 8461881 * q^32 + 654993 * q^34 - 1671668 * q^37 - 10967691 * q^38 + 613326 * q^40 + 10239447 * q^41 + 791815 * q^43 + 1189536 * q^46 - 31148628 * q^47 - 4826637 * q^49 + 63849453 * q^50 - 5552720 * q^52 + 8107476 * q^55 - 116638674 * q^56 + 14211822 * q^58 + 83493795 * q^59 - 5255600 * q^61 - 26813830 * q^64 - 69232992 * q^65 - 8288855 * q^67 + 77746743 * q^68 + 27813756 * q^70 - 36721682 * q^73 + 10383450 * q^74 - 42822959 * q^76 - 56158710 * q^77 - 32771822 * q^79 + 236099418 * q^82 + 198915996 * q^83 + 97486146 * q^85 - 146190669 * q^86 + 24955827 * q^88 - 201514504 * q^91 + 295365804 * q^92 - 36698244 * q^94 - 386813838 * q^95 + 127049161 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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