LMFDB - Embedded newform 38.8.c.b.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,8,Mod(7,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("38.7");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	38.c (of order $3$, 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:	$11.8706309684$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
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} + 9740 x^{12} + 37173 x^{11} + 71393485 x^{10} + 196352446 x^{9} + 218671355941 x^{8} + \cdots + 66\!\cdots\!81 $ x^14 - x^13 + 9740x^12 + 37173x^11 + 71393485x^10 + 196352446x^9 + 218671355941x^8 - 33116965187x^7 + 501909199155445x^6 + 488917878843726x^5 + 115037439673768301x^4 + 1132246613431747493x^3 + 24536677825193566084x^2 + 126800218755690130647x + 666410398757822143881
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.3
Root			$8.67249 - 15.0212i$ of defining polynomial
Character	$\chi$	$=$	38.7
Dual form			38.8.c.b.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.00000 + 6.92820i) q^{2} +(-4.67249 - 8.09299i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-40.1604 - 69.5598i) q^{5} +(37.3799 - 64.7439i) q^{6} -541.879 q^{7} -512.000 q^{8} +(1049.84 - 1818.37i) q^{9} +O(q^{10})$	\(q+(4.00000 + 6.92820i) q^{2} +(-4.67249 - 8.09299i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-40.1604 - 69.5598i) q^{5} +(37.3799 - 64.7439i) q^{6} -541.879 q^{7} -512.000 q^{8} +(1049.84 - 1818.37i) q^{9} +(321.283 - 556.478i) q^{10} -6300.13 q^{11} +598.079 q^{12} +(4439.59 - 7689.59i) q^{13} +(-2167.52 - 3754.25i) q^{14} +(-375.298 + 650.035i) q^{15} +(-2048.00 - 3547.24i) q^{16} +(-16934.7 - 29331.7i) q^{17} +16797.4 q^{18} +(2106.13 + 29823.4i) q^{19} +5140.53 q^{20} +(2531.92 + 4385.42i) q^{21} +(-25200.5 - 43648.6i) q^{22} +(39665.2 - 68702.2i) q^{23} +(2392.31 + 4143.61i) q^{24} +(35836.8 - 62071.1i) q^{25} +71033.4 q^{26} -40058.8 q^{27} +(17340.1 - 30034.0i) q^{28} +(-102993. + 178390. i) q^{29} -6004.76 q^{30} -219830. q^{31} +(16384.0 - 28377.9i) q^{32} +(29437.3 + 50986.9i) q^{33} +(135477. - 234654. i) q^{34} +(21762.1 + 37693.0i) q^{35} +(67189.5 + 116376. i) q^{36} -265970. q^{37} +(-198198. + 133885. i) q^{38} -82975.7 q^{39} +(20562.1 + 35614.6i) q^{40} +(267530. + 463376. i) q^{41} +(-20255.4 + 35083.4i) q^{42} +(423436. + 733413. i) q^{43} +(201604. - 349189. i) q^{44} -168647. q^{45} +634644. q^{46} +(-71504.7 + 123850. i) q^{47} +(-19138.5 + 33148.9i) q^{48} -529910. q^{49} +573389. q^{50} +(-158254. + 274104. i) q^{51} +(284134. + 492134. i) q^{52} +(-87517.4 + 151585. i) q^{53} +(-160235. - 277536. i) q^{54} +(253016. + 438236. i) q^{55} +277442. q^{56} +(231520. - 156394. i) q^{57} -1.64789e6 q^{58} +(-572410. - 991444. i) q^{59} +(-24019.1 - 41602.2i) q^{60} +(1.05554e6 - 1.82825e6i) q^{61} +(-879321. - 1.52303e6i) q^{62} +(-568884. + 985336. i) q^{63} +262144. q^{64} -713182. q^{65} +(-235498. + 407895. i) q^{66} +(1.28689e6 - 2.22896e6i) q^{67} +2.16764e6 q^{68} -741341. q^{69} +(-174097. + 301544. i) q^{70} +(-1.55094e6 - 2.68631e6i) q^{71} +(-537516. + 931005. i) q^{72} +(-1.53310e6 - 2.65540e6i) q^{73} +(-1.06388e6 - 1.84270e6i) q^{74} -669788. q^{75} +(-1.72038e6 - 837616. i) q^{76} +3.41391e6 q^{77} +(-331903. - 574872. i) q^{78} +(2.46591e6 + 4.27108e6i) q^{79} +(-164497. + 284917. i) q^{80} +(-2.10882e6 - 3.65258e6i) q^{81} +(-2.14024e6 + 3.70701e6i) q^{82} +7.31863e6 q^{83} -324086. q^{84} +(-1.36020e6 + 2.35594e6i) q^{85} +(-3.38749e6 + 5.86731e6i) q^{86} +1.92494e6 q^{87} +3.22567e6 q^{88} +(3.41889e6 - 5.92170e6i) q^{89} +(-674589. - 1.16842e6i) q^{90} +(-2.40572e6 + 4.16683e6i) q^{91} +(2.53857e6 + 4.39694e6i) q^{92} +(1.02715e6 + 1.77908e6i) q^{93} -1.14407e6 q^{94} +(1.98993e6 - 1.34422e6i) q^{95} -306216. q^{96} +(2.97919e6 + 5.16011e6i) q^{97} +(-2.11964e6 - 3.67132e6i) q^{98} +(-6.61411e6 + 1.14560e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 56 q^{2} + 55 q^{3} - 448 q^{4} - 126 q^{5} - 440 q^{6} + 1928 q^{7} - 7168 q^{8} - 4602 q^{9}+O(q^{10}) $ 14 * q + 56 * q^2 + 55 * q^3 - 448 * q^4 - 126 * q^5 - 440 * q^6 + 1928 * q^7 - 7168 * q^8 - 4602 * q^9	\( 14 q + 56 q^{2} + 55 q^{3} - 448 q^{4} - 126 q^{5} - 440 q^{6} + 1928 q^{7} - 7168 q^{8} - 4602 q^{9} + 1008 q^{10} + 646 q^{11} - 7040 q^{12} - 1308 q^{13} + 7712 q^{14} + 8740 q^{15} - 28672 q^{16} + 10528 q^{17} - 73632 q^{18} - 87463 q^{19} + 16128 q^{20} - 30584 q^{21} + 2584 q^{22} - 113822 q^{23} - 28160 q^{24} - 50143 q^{25} - 20928 q^{26} - 319898 q^{27} - 61696 q^{28} + 167706 q^{29} + 139840 q^{30} + 201780 q^{31} + 229376 q^{32} + 377473 q^{33} - 84224 q^{34} - 33168 q^{35} - 294528 q^{36} + 380924 q^{37} - 384064 q^{38} + 1379564 q^{39} + 64512 q^{40} + 66301 q^{41} + 244672 q^{42} + 726564 q^{43} - 20672 q^{44} + 428936 q^{45} - 1821152 q^{46} - 2373788 q^{47} + 225280 q^{48} + 5898846 q^{49} - 802288 q^{50} + 3264054 q^{51} - 83712 q^{52} + 161792 q^{53} - 1279592 q^{54} - 53424 q^{55} - 987136 q^{56} - 4487994 q^{57} + 2683296 q^{58} - 1845767 q^{59} + 559360 q^{60} - 1600418 q^{61} + 807120 q^{62} - 3064040 q^{63} + 3670016 q^{64} + 6534852 q^{65} - 3019784 q^{66} - 8911929 q^{67} - 1347584 q^{68} - 8860208 q^{69} + 265344 q^{70} + 517154 q^{71} + 2356224 q^{72} - 9558049 q^{73} + 1523696 q^{74} - 24621450 q^{75} + 2525120 q^{76} - 9188192 q^{77} + 5518256 q^{78} + 7963520 q^{79} - 516096 q^{80} - 4125855 q^{81} - 530408 q^{82} + 30616886 q^{83} + 3914752 q^{84} + 6973266 q^{85} - 5812512 q^{86} + 25084136 q^{87} - 330752 q^{88} + 11829436 q^{89} + 1715744 q^{90} + 4017336 q^{91} - 7284608 q^{92} + 396810 q^{93} - 37980608 q^{94} + 7058892 q^{95} + 3604480 q^{96} - 8033723 q^{97} + 23595384 q^{98} + 24812606 q^{99}+O(q^{100}) \) 14 * q + 56 * q^2 + 55 * q^3 - 448 * q^4 - 126 * q^5 - 440 * q^6 + 1928 * q^7 - 7168 * q^8 - 4602 * q^9 + 1008 * q^10 + 646 * q^11 - 7040 * q^12 - 1308 * q^13 + 7712 * q^14 + 8740 * q^15 - 28672 * q^16 + 10528 * q^17 - 73632 * q^18 - 87463 * q^19 + 16128 * q^20 - 30584 * q^21 + 2584 * q^22 - 113822 * q^23 - 28160 * q^24 - 50143 * q^25 - 20928 * q^26 - 319898 * q^27 - 61696 * q^28 + 167706 * q^29 + 139840 * q^30 + 201780 * q^31 + 229376 * q^32 + 377473 * q^33 - 84224 * q^34 - 33168 * q^35 - 294528 * q^36 + 380924 * q^37 - 384064 * q^38 + 1379564 * q^39 + 64512 * q^40 + 66301 * q^41 + 244672 * q^42 + 726564 * q^43 - 20672 * q^44 + 428936 * q^45 - 1821152 * q^46 - 2373788 * q^47 + 225280 * q^48 + 5898846 * q^49 - 802288 * q^50 + 3264054 * q^51 - 83712 * q^52 + 161792 * q^53 - 1279592 * q^54 - 53424 * q^55 - 987136 * q^56 - 4487994 * q^57 + 2683296 * q^58 - 1845767 * q^59 + 559360 * q^60 - 1600418 * q^61 + 807120 * q^62 - 3064040 * q^63 + 3670016 * q^64 + 6534852 * q^65 - 3019784 * q^66 - 8911929 * q^67 - 1347584 * q^68 - 8860208 * q^69 + 265344 * q^70 + 517154 * q^71 + 2356224 * q^72 - 9558049 * q^73 + 1523696 * q^74 - 24621450 * q^75 + 2525120 * q^76 - 9188192 * q^77 + 5518256 * q^78 + 7963520 * q^79 - 516096 * q^80 - 4125855 * q^81 - 530408 * q^82 + 30616886 * q^83 + 3914752 * q^84 + 6973266 * q^85 - 5812512 * q^86 + 25084136 * q^87 - 330752 * q^88 + 11829436 * q^89 + 1715744 * q^90 + 4017336 * q^91 - 7284608 * q^92 + 396810 * q^93 - 37980608 * q^94 + 7058892 * q^95 + 3604480 * q^96 - 8033723 * q^97 + 23595384 * q^98 + 24812606 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	4.00000	+	6.92820i	0.353553	+	0.612372i
$2$	4.00000	+	6.92820i	0.353553	+	0.612372i
$3$	−4.67249	−	8.09299i	−0.0999134	−	0.173055i	0.811735	−	0.584026i	$-0.198523\pi$
$3$	−4.67249	−	8.09299i	−0.0999134	−	0.173055i	−0.911649	+	0.410970i	$0.865190\pi$
$4$	−32.0000	+	55.4256i	−0.250000	+	0.433013i
$5$	−40.1604	−	69.5598i	−0.143682	−	0.248865i	0.785198	−	0.619244i	$-0.212561\pi$
$5$	−40.1604	−	69.5598i	−0.143682	−	0.248865i	−0.928880	+	0.370380i	$0.879228\pi$
$6$	37.3799	−	64.7439i	0.0706495	−	0.122368i
$7$	−541.879			−0.597117			−0.298558	−	0.954391i	$-0.596506\pi$
$7$	−541.879			−0.597117			−0.298558	+	0.954391i	$0.596506\pi$
$8$	−512.000			−0.353553
$9$	1049.84	−	1818.37i	0.480035	−	0.831444i
$10$	321.283	−	556.478i	0.101599	−	0.175974i
$11$	−6300.13			−1.42717			−0.713584	−	0.700569i	$-0.752930\pi$
$11$	−6300.13			−1.42717			−0.713584	+	0.700569i	$0.752930\pi$
$12$	598.079			0.0999134
$13$	4439.59	−	7689.59i	0.560455	−	0.970737i	−0.437002	−	0.899461i	$-0.643960\pi$
$13$	4439.59	−	7689.59i	0.560455	−	0.970737i	0.997457	−	0.0712758i	$-0.0227071\pi$
$14$	−2167.52	−	3754.25i	−0.211113	−	0.365658i
$15$	−375.298	+	650.035i	−0.0287115	+	0.0497298i
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	−16934.7	−	29331.7i	−0.835998	−	1.44799i	−0.893215	−	0.449629i	$-0.851556\pi$
$17$	−16934.7	−	29331.7i	−0.835998	−	1.44799i	0.0572172	−	0.998362i	$-0.481777\pi$
$18$	16797.4			0.678871
$19$	2106.13	+	29823.4i	0.0704444	+	0.997516i
$19$	2106.13	+	29823.4i	0.0704444	+	0.997516i
$20$	5140.53			0.143682
$21$	2531.92	+	4385.42i	0.0596600	+	0.103334i
$22$	−25200.5	−	43648.6i	−0.504580	−	0.873959i
$23$	39665.2	−	68702.2i	0.679771	−	1.17740i	−0.295279	−	0.955411i	$-0.595413\pi$
$23$	39665.2	−	68702.2i	0.679771	−	1.17740i	0.975050	−	0.221986i	$-0.0712540\pi$
$24$	2392.31	+	4143.61i	0.0353247	+	0.0611842i
$25$	35836.8	−	62071.1i	0.458711	−	0.794511i
$26$	71033.4			0.792603
$27$	−40058.8			−0.391674
$28$	17340.1	−	30034.0i	0.149279	−	0.258559i
$29$	−102993.	+	178390.i	−0.784180	+	1.35824i	0.145307	+	0.989387i	$0.453583\pi$
$29$	−102993.	+	178390.i	−0.784180	+	1.35824i	−0.929487	+	0.368854i	$0.879750\pi$
$30$	−6004.76			−0.0406043
$31$	−219830.			−1.32532			−0.662661	−	0.748919i	$-0.730573\pi$
$31$	−219830.			−1.32532			−0.662661	+	0.748919i	$0.730573\pi$
$32$	16384.0	−	28377.9i	0.0883883	−	0.153093i
$33$	29437.3	+	50986.9i	0.142593	+	0.246979i
$34$	135477.	−	234654.i	0.591140	−	1.02388i
$35$	21762.1	+	37693.0i	0.0857950	+	0.148601i
$36$	67189.5	+	116376.i	0.240017	+	0.415722i
$37$	−265970.			−0.863231			−0.431615	−	0.902058i	$-0.642056\pi$
$37$	−265970.			−0.863231			−0.431615	+	0.902058i	$0.642056\pi$
$38$	−198198.	+	133885.i	−0.585945	+	0.395813i
$39$	−82975.7			−0.223988
$40$	20562.1	+	35614.6i	0.0507993	+	0.0879870i
$41$	267530.	+	463376.i	0.606218	+	1.05000i	0.991858	+	0.127352i	$0.0406476\pi$
$41$	267530.	+	463376.i	0.606218	+	1.05000i	−0.385639	+	0.922650i	$0.626019\pi$
$42$	−20255.4	+	35083.4i	−0.0421860	+	0.0730683i
$43$	423436.	+	733413.i	0.812173	+	1.40673i	0.911340	+	0.411654i	$0.135049\pi$
$43$	423436.	+	733413.i	0.812173	+	1.40673i	−0.0991668	+	0.995071i	$0.531618\pi$
$44$	201604.	−	349189.i	0.356792	−	0.617982i
$45$	−168647.			−0.275890
$46$	634644.			0.961341
$47$	−71504.7	+	123850.i	−0.100460	+	0.174001i	−0.911874	−	0.410470i	$-0.865365\pi$
$47$	−71504.7	+	123850.i	−0.100460	+	0.174001i	0.811414	+	0.584471i	$0.198698\pi$
$48$	−19138.5	+	33148.9i	−0.0249784	+	0.0432638i
$49$	−529910.			−0.643451
$50$	573389.			0.648715
$51$	−158254.	+	274104.i	−0.167055	+	0.289348i
$52$	284134.	+	492134.i	0.280228	+	0.485368i
$53$	−87517.4	+	151585.i	−0.0807475	+	0.139859i	−0.903571	−	0.428438i	$-0.859064\pi$
$53$	−87517.4	+	151585.i	−0.0807475	+	0.139859i	0.822824	+	0.568297i	$0.192397\pi$
$54$	−160235.	−	277536.i	−0.138478	−	0.239851i
$55$	253016.	+	438236.i	0.205059	+	0.355172i
$56$	277442.			0.211113
$57$	231520.	−	156394.i	0.165587	−	0.111856i
$58$	−1.64789e6			−1.10900
$59$	−572410.	−	991444.i	−0.362849	−	0.628472i	0.625580	−	0.780160i	$-0.284862\pi$
$59$	−572410.	−	991444.i	−0.362849	−	0.628472i	−0.988428	+	0.151688i	$0.951529\pi$
$60$	−24019.1	−	41602.2i	−0.0143558	−	0.0248649i
$61$	1.05554e6	−	1.82825e6i	0.595415	−	1.03129i	−0.398073	−	0.917354i	$-0.630321\pi$
$61$	1.05554e6	−	1.82825e6i	0.595415	−	1.03129i	0.993488	−	0.113936i	$-0.0363458\pi$
$62$	−879321.	−	1.52303e6i	−0.468572	−	0.811591i
$63$	−568884.	+	985336.i	−0.286637	+	0.496470i
$64$	262144.			0.125000
$65$	−713182.			−0.322109
$66$	−235498.	+	407895.i	−0.100829	+	0.174640i
$67$	1.28689e6	−	2.22896e6i	0.522732	−	0.905399i	−0.476918	−	0.878948i	$-0.658246\pi$
$67$	1.28689e6	−	2.22896e6i	0.522732	−	0.905399i	0.999650	−	0.0264510i	$-0.00842059\pi$
$68$	2.16764e6			0.835998
$69$	−741341.			−0.271673
$70$	−174097.	+	301544.i	−0.0606662	+	0.105077i
$71$	−1.55094e6	−	2.68631e6i	−0.514271	−	0.890744i	−0.999863	−	0.0165579i	$-0.994729\pi$
$71$	−1.55094e6	−	2.68631e6i	−0.514271	−	0.890744i	0.485592	−	0.874186i	$-0.338604\pi$
$72$	−537516.	+	931005.i	−0.169718	+	0.293960i
$73$	−1.53310e6	−	2.65540e6i	−0.461253	−	0.798914i	0.537770	−	0.843091i	$-0.319267\pi$
$73$	−1.53310e6	−	2.65540e6i	−0.461253	−	0.798914i	−0.999024	+	0.0441772i	$0.985933\pi$
$74$	−1.06388e6	−	1.84270e6i	−0.305198	−	0.528619i
$75$	−669788.			−0.183326
$76$	−1.72038e6	−	837616.i	−0.449548	−	0.218876i
$77$	3.41391e6			0.852187
$78$	−331903.	−	574872.i	−0.0791917	−	0.137164i
$79$	2.46591e6	+	4.27108e6i	0.562707	+	0.974637i	0.997259	+	0.0739905i	$0.0235734\pi$
$79$	2.46591e6	+	4.27108e6i	0.562707	+	0.974637i	−0.434552	+	0.900647i	$0.643093\pi$
$80$	−164497.	+	284917.i	−0.0359205	+	0.0622162i
$81$	−2.10882e6	−	3.65258e6i	−0.440901	−	0.763663i
$82$	−2.14024e6	+	3.70701e6i	−0.428661	+	0.742463i
$83$	7.31863e6			1.40493			0.702467	−	0.711716i	$-0.252082\pi$
$83$	7.31863e6			1.40493			0.702467	+	0.711716i	$0.252082\pi$
$84$	−324086.			−0.0596600
$85$	−1.36020e6	+	2.35594e6i	−0.240236	+	0.416101i
$86$	−3.38749e6	+	5.86731e6i	−0.574293	+	0.994705i
$87$	1.92494e6			0.313401
$88$	3.22567e6			0.504580
$89$	3.41889e6	−	5.92170e6i	0.514068	−	0.890392i	−0.485799	−	0.874071i	$-0.661471\pi$
$89$	3.41889e6	−	5.92170e6i	0.514068	−	0.890392i	0.999867	−	0.0163214i	$-0.00519551\pi$
$90$	−674589.	−	1.16842e6i	−0.0975417	−	0.168947i
$91$	−2.40572e6	+	4.16683e6i	−0.334657	+	0.579643i
$92$	2.53857e6	+	4.39694e6i	0.339885	+	0.588699i
$93$	1.02715e6	+	1.77908e6i	0.132418	+	0.229354i
$94$	−1.14407e6			−0.142071
$95$	1.98993e6	−	1.34422e6i	0.238125	−	0.160856i
$96$	−306216.			−0.0353247
$97$	2.97919e6	+	5.16011e6i	0.331434	+	0.574061i	0.982793	−	0.184709i	$-0.0591341\pi$
$97$	2.97919e6	+	5.16011e6i	0.331434	+	0.574061i	−0.651359	+	0.758770i	$0.725801\pi$
$98$	−2.11964e6	−	3.67132e6i	−0.227494	−	0.394032i
$99$	−6.61411e6	+	1.14560e7i	−0.685090	+	1.18661i
$100$	2.29355e6	+	3.97255e6i	0.229355	+	0.397255i
$101$	4.93228e6	−	8.54297e6i	0.476347	−	0.825057i	−0.523286	−	0.852157i	$-0.675294\pi$
$101$	4.93228e6	−	8.54297e6i	0.476347	−	0.825057i	0.999633	+	0.0271002i	$0.00862732\pi$
$102$	−2.53206e6			−0.236251
$103$	2.60566e6			0.234956			0.117478	−	0.993075i	$-0.462519\pi$
$103$	2.60566e6			0.234956			0.117478	+	0.993075i	$0.462519\pi$
$104$	−2.27307e6	+	3.93707e6i	−0.198151	+	0.343207i
$105$	203366.	−	352240.i	0.0171441	−	0.0296945i
$106$	−1.40028e6			−0.114194
$107$	−5.58579e6			−0.440800			−0.220400	−	0.975410i	$-0.570736\pi$
$107$	−5.58579e6			−0.440800			−0.220400	+	0.975410i	$0.570736\pi$
$108$	1.28188e6	−	2.22029e6i	0.0979186	−	0.169600i
$109$	7.87860e6	+	1.36461e7i	0.582715	+	1.00929i	0.995156	+	0.0983082i	$0.0313431\pi$
$109$	7.87860e6	+	1.36461e7i	0.582715	+	1.00929i	−0.412441	+	0.910985i	$0.635324\pi$
$110$	−2.02413e6	+	3.50589e6i	−0.144998	+	0.251145i
$111$	1.24274e6	+	2.15249e6i	0.0862483	+	0.149387i
$112$	1.10977e6	+	1.92218e6i	0.0746396	+	0.129280i
$113$	−2.57335e7			−1.67774			−0.838870	−	0.544332i	$-0.816783\pi$
$113$	−2.57335e7			−1.67774			−0.838870	+	0.544332i	$0.816783\pi$
$114$	2.00961e6	+	978438.i	0.127041	+	0.0618538i
$115$	−6.37188e6			−0.390684
$116$	−6.59157e6	−	1.14169e7i	−0.392090	−	0.679120i
$117$	−9.32167e6	−	1.61456e7i	−0.538076	−	0.931974i
$118$	4.57928e6	−	7.93155e6i	0.256573	−	0.444397i
$119$	9.17654e6	+	1.58942e7i	0.499189	+	0.864620i
$120$	192152.	−	332818.i	0.0101511	−	0.0175822i
$121$	2.02045e7			1.03681
$122$	1.68886e7			0.842044
$123$	2.50006e6	−	4.33024e6i	0.121139	−	0.209818i
$124$	7.03457e6	−	1.21842e7i	0.331331	−	0.573882i
$125$	−1.20319e7			−0.550998
$126$	−9.10215e6			−0.405366
$127$	137615.	−	238356.i	0.00596146	−	0.0103255i	−0.863029	−	0.505154i	$-0.831436\pi$
$127$	137615.	−	238356.i	0.00596146	−	0.0103255i	0.868991	+	0.494828i	$0.164769\pi$
$128$	1.04858e6	+	1.81619e6i	0.0441942	+	0.0765466i
$129$	3.95700e6	−	6.85373e6i	0.162294	−	0.281101i
$130$	−2.85273e6	−	4.94107e6i	−0.113883	−	0.197251i
$131$	−1.66126e7	−	2.87739e7i	−0.645637	−	1.11828i	−0.984154	−	0.177315i	$-0.943259\pi$
$131$	−1.66126e7	−	2.87739e7i	−0.645637	−	1.11828i	0.338518	−	0.940960i	$-0.390075\pi$
$132$	−3.76797e6			−0.142593
$133$	−1.14127e6	−	1.61607e7i	−0.0420636	−	0.595634i
$134$	2.05902e7			0.739255
$135$	1.60878e6	+	2.78649e6i	0.0562766	+	0.0974739i
$136$	8.67055e6	+	1.50178e7i	0.295570	+	0.511942i
$137$	1.79982e7	−	3.11738e7i	0.598008	−	1.03578i	−0.395107	−	0.918635i	$-0.629293\pi$
$137$	1.79982e7	−	3.11738e7i	0.598008	−	1.03578i	0.993115	−	0.117145i	$-0.0373741\pi$
$138$	−2.96536e6	−	5.13616e6i	−0.0960509	−	0.166365i
$139$	−1.91369e7	+	3.31461e7i	−0.604393	+	1.04684i	0.387754	+	0.921763i	$0.373251\pi$
$139$	−1.91369e7	+	3.31461e7i	−0.604393	+	1.04684i	−0.992147	+	0.125077i	$0.960082\pi$
$140$	−2.78555e6			−0.0857950
$141$	1.33642e6			0.0401491
$142$	1.24076e7	−	2.14905e7i	0.363645	−	0.629851i
$143$	−2.79700e7	+	4.84454e7i	−0.799864	+	1.38541i
$144$	−8.60025e6			−0.240017
$145$	1.65450e7			0.450691
$146$	1.22648e7	−	2.12432e7i	0.326155	−	0.564918i
$147$	2.47600e6	+	4.28855e6i	0.0642894	+	0.111353i
$148$	8.51105e6	−	1.47416e7i	0.215808	−	0.373790i
$149$	−2.10791e7	−	3.65101e7i	−0.522036	−	0.904193i	−0.999671	−	0.0256345i	$-0.991839\pi$
$149$	−2.10791e7	−	3.65101e7i	−0.522036	−	0.904193i	0.477636	−	0.878558i	$-0.341494\pi$
$150$	−2.67915e6	−	4.64043e6i	−0.0648154	−	0.112263i
$151$	5.01127e7			1.18448			0.592241	−	0.805761i	$-0.298243\pi$
$151$	5.01127e7			1.18448			0.592241	+	0.805761i	$0.298243\pi$
$152$	−1.07834e6	−	1.52696e7i	−0.0249059	−	0.352675i
$153$	−7.11144e7			−1.60523
$154$	1.36556e7	+	2.36523e7i	0.301294	+	0.521856i
$155$	8.82847e6	+	1.52913e7i	0.190425	+	0.329826i
$156$	2.65522e6	−	4.59898e6i	0.0559970	−	0.0969896i
$157$	−1.03720e7	−	1.79648e7i	−0.213901	−	0.370487i	0.739031	−	0.673671i	$-0.235284\pi$
$157$	−1.03720e7	−	1.79648e7i	−0.213901	−	0.370487i	−0.952932	+	0.303184i	$0.901950\pi$
$158$	−1.97273e7	+	3.41687e7i	−0.397894	+	0.689173i
$159$	1.63570e6			0.0322710
$160$	−2.63195e6			−0.0507993
$161$	−2.14938e7	+	3.72283e7i	−0.405903	+	0.703044i
$162$	1.68705e7	−	2.92206e7i	0.311764	−	0.539991i
$163$	3.16858e7			0.573071			0.286536	−	0.958070i	$-0.407496\pi$
$163$	3.16858e7			0.573071			0.286536	+	0.958070i	$0.407496\pi$
$164$	−3.42439e7			−0.606218
$165$	2.36443e6	−	4.09531e6i	0.0409762	−	0.0709729i
$166$	2.92745e7	+	5.07049e7i	0.496720	+	0.860343i
$167$	−2.68482e7	+	4.65025e7i	−0.446075	+	0.772625i	−0.998126	−	0.0611855i	$-0.980512\pi$
$167$	−2.68482e7	+	4.65025e7i	−0.446075	+	0.772625i	0.552051	+	0.833810i	$0.313845\pi$
$168$	−1.29635e6	−	2.24534e6i	−0.0210930	−	0.0365341i
$169$	−8.04559e6	−	1.39354e7i	−0.128220	−	0.222083i
$170$	−2.17633e7			−0.339745
$171$	5.64410e7	+	2.74800e7i	0.863195	+	0.420271i
$172$	−5.41999e7			−0.812173
$173$	−1.09756e7	−	1.90104e7i	−0.161164	−	0.279144i	0.774122	−	0.633036i	$-0.218191\pi$
$173$	−1.09756e7	−	1.90104e7i	−0.161164	−	0.279144i	−0.935286	+	0.353892i	$0.884858\pi$
$174$	7.69976e6	+	1.33364e7i	0.110804	+	0.191918i
$175$	−1.94192e7	+	3.36351e7i	−0.273904	+	0.474416i
$176$	1.29027e7	+	2.23481e7i	0.178396	+	0.308991i
$177$	−5.34916e6	+	9.26502e6i	−0.0725069	+	0.125586i
$178$	5.47023e7			0.727002
$179$	1.62960e7			0.212372			0.106186	−	0.994346i	$-0.466136\pi$
$179$	1.62960e7			0.212372			0.106186	+	0.994346i	$0.466136\pi$
$180$	5.39671e6	−	9.34737e6i	0.0689724	−	0.119464i
$181$	6.37200e7	−	1.10366e8i	0.798732	−	1.38344i	−0.121710	−	0.992566i	$-0.538838\pi$
$181$	6.37200e7	−	1.10366e8i	0.798732	−	1.38344i	0.920442	−	0.390879i	$-0.127829\pi$
$182$	−3.84915e7			−0.473277
$183$	−1.97280e7			−0.237960
$184$	−2.03086e7	+	3.51755e7i	−0.240335	+	0.416273i
$185$	1.06815e7	+	1.85008e7i	0.124031	+	0.214828i
$186$	−8.21724e6	+	1.42327e7i	−0.0936333	+	0.162178i
$187$	1.06691e8	+	1.84794e8i	1.19311	+	2.06653i
$188$	−4.57630e6	−	7.92638e6i	−0.0502298	−	0.0870006i
$189$	2.17071e7			0.233875
$190$	1.72727e7	+	8.40974e6i	0.182694	+	0.0889498i
$191$	−1.12140e8			−1.16451			−0.582257	−	0.813005i	$-0.697830\pi$
$191$	−1.12140e8			−1.16451			−0.582257	+	0.813005i	$0.697830\pi$
$192$	−1.22486e6	−	2.12153e6i	−0.0124892	−	0.0216319i
$193$	3.30980e7	+	5.73274e7i	0.331399	+	0.574000i	0.982786	−	0.184746i	$-0.0591461\pi$
$193$	3.30980e7	+	5.73274e7i	0.331399	+	0.574000i	−0.651388	+	0.758745i	$0.725813\pi$
$194$	−2.38335e7	+	4.12809e7i	−0.234359	+	0.405923i
$195$	3.33233e6	+	5.77177e6i	0.0321831	+	0.0557427i
$196$	1.69571e7	−	2.93706e7i	0.160863	−	0.278623i
$197$	1.20337e8			1.12142			0.560708	−	0.828014i	$-0.310529\pi$
$197$	1.20337e8			1.12142			0.560708	+	0.828014i	$0.310529\pi$
$198$	−1.05826e8			−0.968864
$199$	3.61781e7	−	6.26623e7i	0.325432	−	0.563664i	−0.656168	−	0.754615i	$-0.727824\pi$
$199$	3.61781e7	−	6.26623e7i	0.325432	−	0.563664i	0.981600	+	0.190951i	$0.0611570\pi$
$200$	−1.83484e7	+	3.17804e7i	−0.162179	+	0.280902i
$201$	−2.40519e7			−0.208912
$202$	7.89166e7			0.673656
$203$	5.58099e7	−	9.66657e7i	0.468247	−	0.811028i
$204$	−1.01283e7	−	1.75427e7i	−0.0835274	−	0.144674i
$205$	2.14882e7	−	3.72187e7i	0.174205	−	0.301733i
$206$	1.04226e7	+	1.80525e7i	0.0830695	+	0.143881i
$207$	−8.32839e7	−	1.44252e8i	−0.652627	−	1.13038i
$208$	−3.63691e7			−0.280228
$209$	−1.32689e7	−	1.87891e8i	−0.100536	−	1.42362i
$210$	3.25386e6			0.0242455
$211$	−5.51115e7	−	9.54560e7i	−0.403881	−	0.699543i	0.590309	−	0.807177i	$-0.299006\pi$
$211$	−5.51115e7	−	9.54560e7i	−0.403881	−	0.699543i	−0.994191	+	0.107634i	$0.965672\pi$
$212$	−5.60111e6	−	9.70141e6i	−0.0403737	−	0.0699294i
$213$	−1.44935e7	+	2.51036e7i	−0.102765	+	0.177994i
$214$	−2.23432e7	−	3.86995e7i	−0.155846	−	0.269934i
$215$	3.40107e7	−	5.89083e7i	0.233389	−	0.404242i
$216$	2.05101e7			0.138478
$217$	1.19121e8			0.791373
$218$	−6.30288e7	+	1.09169e8i	−0.412042	+	0.713678i
$219$	−1.43268e7	+	2.48147e7i	−0.0921708	+	0.159644i
$220$	−3.23860e7			−0.205059
$221$	−3.00732e8			−1.87416
$222$	−9.94194e6	+	1.72199e7i	−0.0609868	+	0.105632i
$223$	1.18727e8	+	2.05642e8i	0.716941	+	1.24178i	0.962206	+	0.272322i	$0.0877915\pi$
$223$	1.18727e8	+	2.05642e8i	0.716941	+	1.24178i	−0.245266	+	0.969456i	$0.578875\pi$
$224$	−8.87815e6	+	1.53774e7i	−0.0527782	+	0.0914145i
$225$	−7.52455e7	−	1.30329e8i	−0.440394	−	0.762785i
$226$	−1.02934e8	−	1.78287e8i	−0.593171	−	1.02740i
$227$	520153.			0.00295148			0.00147574	−	0.999999i	$-0.499530\pi$
$227$	520153.			0.00295148			0.00147574	+	0.999999i	$0.499530\pi$
$228$	1.25963e6	+	1.78367e7i	0.00703834	+	0.0996652i
$229$	1.41720e8			0.779841			0.389920	−	0.920849i	$-0.372503\pi$
$229$	1.41720e8			0.779841			0.389920	+	0.920849i	$0.372503\pi$
$230$	−2.54875e7	−	4.41457e7i	−0.138127	−	0.239244i
$231$	−1.59515e7	−	2.76288e7i	−0.0851449	−	0.147475i
$232$	5.27326e7	−	9.13355e7i	0.277250	−	0.480211i
$233$	−8.93149e7	−	1.54698e8i	−0.462571	−	0.801196i	0.536518	−	0.843889i	$-0.319740\pi$
$233$	−8.93149e7	−	1.54698e8i	−0.462571	−	0.801196i	−0.999088	+	0.0426932i	$0.986406\pi$
$234$	7.45734e7	−	1.29165e8i	0.380477	−	0.659005i
$235$	1.14866e7			0.0577370
$236$	7.32685e7			0.362849
$237$	2.30439e7	−	3.99132e7i	0.112444	−	0.194759i
$238$	−7.34123e7	+	1.27154e8i	−0.352980	+	0.611379i
$239$	−2.08990e8			−0.990221			−0.495111	−	0.868830i	$-0.664872\pi$
$239$	−2.08990e8			−0.990221			−0.495111	+	0.868830i	$0.664872\pi$
$240$	3.07444e6			0.0143558
$241$	1.70437e7	−	2.95205e7i	0.0784339	−	0.135852i	−0.824140	−	0.566385i	$-0.808341\pi$
$241$	1.70437e7	−	2.95205e7i	0.0784339	−	0.135852i	0.902574	+	0.430534i	$0.141675\pi$
$242$	8.08181e7	+	1.39981e8i	0.366568	+	0.634915i
$243$	−6.35112e7	+	1.10005e8i	−0.283941	+	0.491800i
$244$	6.75545e7	+	1.17008e8i	0.297708	+	0.515645i
$245$	2.12814e7	+	3.68604e7i	0.0924524	+	0.160132i
$246$	4.00010e7			0.171316
$247$	2.38680e8	+	1.16208e8i	1.00781	+	0.490680i
$248$	1.12553e8			0.468572
$249$	−3.41962e7	−	5.92295e7i	−0.140372	−	0.243131i
$250$	−4.81277e7	−	8.33597e7i	−0.194807	−	0.337416i
$251$	3.86193e7	−	6.68905e7i	0.154151	−	0.266997i	−0.778599	−	0.627522i	$-0.784069\pi$
$251$	3.86193e7	−	6.68905e7i	0.154151	−	0.266997i	0.932750	+	0.360525i	$0.117402\pi$
$252$	−3.64086e7	−	6.30615e7i	−0.143318	−	0.248235i
$253$	−2.49896e8	+	4.32833e8i	−0.970148	+	1.68034i
$254$	2.20184e6			0.00843077
$255$	2.54222e7			0.0960112
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	5.15591e6	−	8.93030e6i	0.0189470	−	0.0328171i	−0.856396	−	0.516319i	$-0.827302\pi$
$257$	5.15591e6	−	8.93030e6i	0.0189470	−	0.0328171i	0.875343	+	0.483502i	$0.160635\pi$
$258$	6.33121e7			0.229518
$259$	1.44124e8			0.515450
$260$	2.28218e7	−	3.95285e7i	0.0805274	−	0.139477i
$261$	2.16252e8	+	3.74560e8i	0.752868	+	1.30400i
$262$	1.32901e8	−	2.30191e8i	0.456534	−	0.790740i
$263$	1.57347e7	+	2.72533e7i	0.0533351	+	0.0923791i	0.891460	−	0.453099i	$-0.149682\pi$
$263$	1.57347e7	+	2.72533e7i	0.0533351	+	0.0923791i	−0.838125	+	0.545478i	$0.816348\pi$
$264$	−1.50719e7	−	2.61053e7i	−0.0504144	−	0.0873202i
$265$	1.40589e7			0.0464079
$266$	1.07399e8	−	7.25497e7i	0.349878	−	0.236347i
$267$	−6.38990e7			−0.205449
$268$	8.23609e7	+	1.42653e8i	0.261366	+	0.452699i
$269$	2.15542e8	+	3.73329e8i	0.675147	+	1.16939i	0.976426	+	0.215853i	$0.0692531\pi$
$269$	2.15542e8	+	3.73329e8i	0.675147	+	1.16939i	−0.301279	+	0.953536i	$0.597414\pi$
$270$	−1.28702e7	+	2.22919e7i	−0.0397936	+	0.0689245i
$271$	−3.33326e6	−	5.77337e6i	−0.0101736	−	0.0176213i	0.860894	−	0.508785i	$-0.169905\pi$
$271$	−3.33326e6	−	5.77337e6i	−0.0101736	−	0.0176213i	−0.871067	+	0.491163i	$0.836572\pi$
$272$	−6.93644e7	+	1.20143e8i	−0.209000	+	0.361998i
$273$	4.49628e7			0.133747
$274$	2.87971e8			0.845711
$275$	−2.25777e8	+	3.91057e8i	−0.654658	+	1.13390i
$276$	2.37229e7	−	4.10893e7i	0.0679182	−	0.117638i
$277$	−3.04940e8			−0.862056			−0.431028	−	0.902339i	$-0.641849\pi$
$277$	−3.04940e8			−0.862056			−0.431028	+	0.902339i	$0.641849\pi$
$278$	−3.06190e8			−0.854741
$279$	−2.30786e8	+	3.99733e8i	−0.636201	+	1.10193i
$280$	−1.11422e7	−	1.92988e7i	−0.0303331	−	0.0525385i
$281$	1.83243e8	−	3.17387e8i	0.492670	−	0.853329i	−0.507294	−	0.861773i	$-0.669354\pi$
$281$	1.83243e8	−	3.17387e8i	0.492670	−	0.853329i	0.999964	+	0.00844353i	$0.00268769\pi$
$282$	5.34567e6	+	9.25898e6i	0.0141948	+	0.0245862i
$283$	−3.02262e8	−	5.23533e8i	−0.792740	−	1.37307i	−0.924265	−	0.381753i	$-0.875321\pi$
$283$	−3.02262e8	−	5.23533e8i	−0.792740	−	1.37307i	0.131525	−	0.991313i	$-0.458013\pi$
$284$	1.98521e8			0.514271
$285$	−2.01767e7	−	9.82360e6i	−0.0516289	−	0.0251370i
$286$	−4.47520e8			−1.13118
$287$	−1.44969e8	−	2.51094e8i	−0.361983	−	0.626974i
$288$	−3.44010e7	−	5.95843e7i	−0.0848589	−	0.146980i
$289$	−3.68396e8	+	6.38081e8i	−0.897785	+	1.55501i
$290$	6.61800e7	+	1.14627e8i	0.159343	+	0.275991i
$291$	2.78405e7	−	4.82211e7i	0.0662295	−	0.114713i
$292$	1.96236e8			0.461253
$293$	4.58358e8			1.06456			0.532278	−	0.846570i	$-0.321336\pi$
$293$	4.58358e8			1.06456			0.532278	+	0.846570i	$0.321336\pi$
$294$	−1.98080e7	+	3.43084e7i	−0.0454595	+	0.0787381i
$295$	−4.59764e7	+	7.96335e7i	−0.104270	+	0.180600i
$296$	1.36177e8			0.305198
$297$	2.52376e8			0.558986
$298$	1.68633e8	−	2.92081e8i	0.369135	−	0.639361i
$299$	−3.52194e8	−	6.10018e8i	−0.761962	−	1.31976i
$300$	2.14332e7	−	3.71234e7i	0.0458314	−	0.0793823i
$301$	−2.29451e8	−	3.97422e8i	−0.484962	−	0.839980i
$302$	2.00451e8	+	3.47191e8i	0.418777	+	0.725344i
$303$	−9.21842e7			−0.190374
$304$	1.01477e8	−	6.85493e7i	0.207163	−	0.139941i
$305$	−1.69563e8			−0.342202
$306$	−2.84458e8	−	4.92695e8i	−0.567535	−	0.983000i
$307$	1.06376e8	+	1.84248e8i	0.209825	+	0.363428i	0.951659	−	0.307156i	$-0.0993772\pi$
$307$	1.06376e8	+	1.84248e8i	0.209825	+	0.363428i	−0.741834	+	0.670583i	$0.766044\pi$
$308$	−1.09245e8	+	1.89218e8i	−0.213047	+	0.369008i
$309$	−1.21749e7	−	2.10875e7i	−0.0234753	−	0.0406604i
$310$	−7.06277e7	+	1.22331e8i	−0.134651	+	0.233222i
$311$	5.09193e8			0.959890			0.479945	−	0.877299i	$-0.340657\pi$
$311$	5.09193e8			0.959890			0.479945	+	0.877299i	$0.340657\pi$
$312$	4.24835e7			0.0791917
$313$	−3.86251e8	+	6.69006e8i	−0.711974	+	1.23318i	0.252141	+	0.967691i	$0.418865\pi$
$313$	−3.86251e8	+	6.69006e8i	−0.711974	+	1.23318i	−0.964115	+	0.265485i	$0.914468\pi$
$314$	8.29757e7	−	1.43718e8i	0.151251	−	0.261974i
$315$	9.13864e7			0.164738
$316$	−3.15636e8			−0.562707
$317$	1.88340e8	−	3.26215e8i	0.332075	−	0.575170i	−0.650844	−	0.759212i	$-0.725585\pi$
$317$	1.88340e8	−	3.26215e8i	0.332075	−	0.575170i	0.982918	+	0.184041i	$0.0589181\pi$
$318$	6.54279e6	+	1.13324e7i	0.0114095	+	0.0197619i
$319$	6.48872e8	−	1.12388e9i	1.11916	−	1.93844i
$320$	−1.05278e7	−	1.82347e7i	−0.0179603	−	0.0311081i
$321$	2.60995e7	+	4.52057e7i	0.0440418	+	0.0762827i
$322$	−3.43900e8			−0.574033
$323$	8.39105e8	−	5.66826e8i	1.38550	−	0.935924i
$324$	2.69928e8			0.440901
$325$	−3.18201e8	−	5.51140e8i	−0.514174	−	0.890575i
$326$	1.26743e8	+	2.19526e8i	0.202611	+	0.350933i
$327$	7.36254e7	−	1.27523e8i	0.116442	−	0.201684i
$328$	−1.36975e8	−	2.37248e8i	−0.214331	−	0.371231i
$329$	3.87469e7	−	6.71116e7i	0.0599862	−	0.103899i
$330$	3.78308e7			0.0579491
$331$	−1.05467e9			−1.59853			−0.799263	−	0.600981i	$-0.794777\pi$
$331$	−1.05467e9			−1.59853			−0.799263	+	0.600981i	$0.794777\pi$
$332$	−2.34196e8	+	4.05639e8i	−0.351234	+	0.608355i
$333$	−2.79225e8	+	4.83632e8i	−0.414381	+	0.717728i
$334$	−4.29572e8			−0.630845
$335$	−2.06728e8			−0.300429
$336$	1.03708e7	−	1.79627e7i	0.0149150	−	0.0258335i
$337$	2.07716e8	+	3.59775e8i	0.295642	+	0.512067i	0.975134	−	0.221616i	$-0.0711331\pi$
$337$	2.07716e8	+	3.59775e8i	0.295642	+	0.512067i	−0.679492	+	0.733683i	$0.737800\pi$
$338$	6.43647e7	−	1.11483e8i	0.0906650	−	0.157036i
$339$	1.20240e8	+	2.08261e8i	0.167629	+	0.290341i
$340$	−8.70531e7	−	1.50780e8i	−0.120118	−	0.208050i
$341$	1.38496e9			1.89146
$342$	3.53774e7	+	5.00955e8i	0.0478227	+	0.677185i
$343$	7.33408e8			0.981333
$344$	−2.16799e8	−	3.75508e8i	−0.287147	−	0.497352i
$345$	2.97725e7	+	5.15675e7i	0.0390345	+	0.0676098i
$346$	8.78050e7	−	1.52083e8i	0.113960	−	0.197385i
$347$	−3.68219e8	−	6.37775e8i	−0.473101	−	0.819434i	0.526425	−	0.850221i	$-0.323532\pi$
$347$	−3.68219e8	−	6.37775e8i	−0.473101	−	0.819434i	−0.999526	+	0.0307869i	$0.990199\pi$
$348$	−6.15981e7	+	1.06691e8i	−0.0783502	+	0.135706i
$349$	8.62191e8			1.08571			0.542856	−	0.839826i	$-0.317343\pi$
$349$	8.62191e8			1.08571			0.542856	+	0.839826i	$0.317343\pi$
$350$	−3.10707e8			−0.387359
$351$	−1.77845e8	+	3.08036e8i	−0.219516	+	0.380213i
$352$	−1.03221e8	+	1.78785e8i	−0.126145	+	0.218490i
$353$	−9.64172e8			−1.16666			−0.583328	−	0.812237i	$-0.698250\pi$
$353$	−9.64172e8			−1.16666			−0.583328	+	0.812237i	$0.698250\pi$
$354$	−8.55866e7			−0.102540
$355$	−1.24573e8	+	2.15767e8i	−0.147783	+	0.255968i
$356$	2.18809e8	+	3.78989e8i	0.257034	+	0.445196i
$357$	8.57546e7	−	1.48531e8i	0.0997513	−	0.172774i
$358$	6.51842e7	+	1.12902e8i	0.0750847	+	0.130051i
$359$	−4.02024e8	−	6.96326e8i	−0.458587	−	0.794295i	0.540300	−	0.841473i	$-0.318311\pi$
$359$	−4.02024e8	−	6.96326e8i	−0.458587	−	0.794295i	−0.998887	+	0.0471771i	$0.984977\pi$
$360$	8.63473e7			0.0975417
$361$	−8.85000e8	+	1.25624e8i	−0.990075	+	0.140539i
$362$	1.01952e9			1.12958
$363$	−9.44054e7	−	1.63515e8i	−0.103591	−	0.179426i
$364$	−1.53966e8	−	2.66677e8i	−0.167329	−	0.289822i
$365$	−1.23139e8	+	2.13284e8i	−0.132548	+	0.229579i
$366$	−7.89119e7	−	1.36679e8i	−0.0841316	−	0.145720i
$367$	−2.06829e7	+	3.58238e7i	−0.0218413	+	0.0378303i	−0.876739	−	0.480966i	$-0.840286\pi$
$367$	−2.06829e7	+	3.58238e7i	−0.0218413	+	0.0378303i	0.854898	+	0.518796i	$0.173620\pi$
$368$	−3.24937e8			−0.339885
$369$	1.12345e9			1.16402
$370$	−8.54517e7	+	1.48007e8i	−0.0877030	+	0.151906i
$371$	4.74239e7	−	8.21406e7i	0.0482157	−	0.0835120i
$372$	−1.31476e8			−0.132418
$373$	−1.48246e8			−0.147911			−0.0739557	−	0.997262i	$-0.523562\pi$
$373$	−1.48246e8			−0.147911			−0.0739557	+	0.997262i	$0.523562\pi$
$374$	−8.53525e8	+	1.47835e9i	−0.843656	+	1.46126i
$375$	5.62191e7	+	9.73743e7i	0.0550521	+	0.0953531i
$376$	3.66104e7	−	6.34110e7i	0.0355179	−	0.0615187i
$377$	9.14495e8	+	1.58395e9i	0.878996	+	1.52247i
$378$	8.68282e7	+	1.50391e8i	0.0826875	+	0.143219i
$379$	8.34027e8			0.786943			0.393471	−	0.919337i	$-0.371274\pi$
$379$	8.34027e8			0.786943			0.393471	+	0.919337i	$0.371274\pi$
$380$	1.08266e7	+	1.53308e8i	0.0101216	+	0.143325i
$381$	−2.57202e6			−0.00238252
$382$	−4.48561e8	−	7.76930e8i	−0.411718	−	0.713116i
$383$	−8.31138e7	−	1.43957e8i	−0.0755923	−	0.130930i	0.825751	−	0.564034i	$-0.190751\pi$
$383$	−8.31138e7	−	1.43957e8i	−0.0755923	−	0.130930i	−0.901344	+	0.433105i	$0.857418\pi$
$384$	9.79892e6	−	1.69722e7i	0.00883118	−	0.0152961i
$385$	−1.37104e8	−	2.37471e8i	−0.122444	−	0.212079i
$386$	−2.64784e8	+	4.58619e8i	−0.234334	+	0.405879i
$387$	1.77815e9			1.55948
$388$	−3.81337e8			−0.331434
$389$	−5.95231e8	+	1.03097e9i	−0.512699	+	0.888020i	0.487193	+	0.873294i	$0.338021\pi$
$389$	−5.95231e8	+	1.03097e9i	−0.512699	+	0.888020i	−0.999892	+	0.0147259i	$0.995312\pi$
$390$	−2.66587e7	+	4.61742e7i	−0.0227569	+	0.0394160i
$391$	−2.68687e9			−2.27315
$392$	2.71314e8			0.227494
$393$	−1.55244e8	+	2.68891e8i	−0.129016	+	0.223461i
$394$	4.81347e8	+	8.33718e8i	0.396481	+	0.686724i
$395$	1.98064e8	−	3.43056e8i	0.161702	−	0.280076i
$396$	−4.23303e8	−	7.33182e8i	−0.342545	−	0.593306i
$397$	6.43364e8	+	1.11434e9i	0.516048	+	0.893821i	0.999826	+	0.0186308i	$0.00593073\pi$
$397$	6.43364e8	+	1.11434e9i	0.516048	+	0.893821i	−0.483778	+	0.875191i	$0.660736\pi$
$398$	5.78849e8			0.460230
$399$	−1.25456e8	+	8.47469e7i	−0.0988747	+	0.0667911i
$400$	−2.93575e8			−0.229355
$401$	−1.24837e9	−	2.16224e9i	−0.966801	−	1.67455i	−0.704696	−	0.709509i	$-0.748917\pi$
$401$	−1.24837e9	−	2.16224e9i	−0.966801	−	1.67455i	−0.262105	−	0.965039i	$-0.584417\pi$
$402$	−9.62076e7	−	1.66636e8i	−0.0738615	−	0.127932i
$403$	−9.75956e8	+	1.69040e9i	−0.742784	+	1.28654i
$404$	3.15666e8	+	5.46750e8i	0.238173	+	0.412529i
$405$	−1.69382e8	+	2.93378e8i	−0.126699	+	0.219449i
$406$	8.92959e8			0.662202
$407$	1.67565e9			1.23198
$408$	8.10261e7	−	1.40341e8i	0.0590628	−	0.102300i
$409$	2.90598e7	−	5.03330e7i	0.0210020	−	0.0363765i	−0.855333	−	0.518078i	$-0.826648\pi$
$409$	2.90598e7	−	5.03330e7i	0.0210020	−	0.0363765i	0.876335	+	0.481701i	$0.159981\pi$
$410$	3.43811e8			0.246364
$411$	−3.36385e8			−0.238996
$412$	−8.33810e7	+	1.44420e8i	−0.0587390	+	0.101739i
$413$	3.10177e8	+	5.37243e8i	0.216663	+	0.375271i
$414$	6.66271e8	−	1.15402e9i	0.461477	−	0.799301i
$415$	−2.93919e8	−	5.09082e8i	−0.201864	−	0.349639i
$416$	−1.45476e8	−	2.51972e8i	−0.0990754	−	0.171604i
$417$	3.57668e8			0.241548
$418$	1.24868e9	−	8.43495e8i	0.836243	−	0.564892i
$419$	1.16319e9			0.772506			0.386253	−	0.922393i	$-0.373769\pi$
$419$	1.16319e9			0.772506			0.386253	+	0.922393i	$0.373769\pi$
$420$	1.30154e7	+	2.25434e7i	0.00857207	+	0.0148473i
$421$	−1.70499e8	−	2.95313e8i	−0.111361	−	0.192884i	0.804958	−	0.593332i	$-0.202188\pi$
$421$	−1.70499e8	−	2.95313e8i	−0.111361	−	0.192884i	−0.916319	+	0.400448i	$0.868854\pi$
$422$	4.40892e8	−	7.63648e8i	0.285587	−	0.494652i
$423$	1.50136e8	+	2.60044e8i	0.0964482	+	0.167053i
$424$	4.48089e7	−	7.76113e7i	0.0285485	−	0.0494475i
$425$	−2.42754e9			−1.53393
$426$	−2.31897e8			−0.145332
$427$	−5.71975e8	+	9.90690e8i	−0.355533	+	0.615801i
$428$	1.78745e8	−	3.09596e8i	0.110200	−	0.190872i
$429$	5.22758e8			0.319669
$430$	5.44172e8			0.330063
$431$	−2.18370e7	+	3.78228e7i	−0.0131378	+	0.0227554i	−0.872520	−	0.488579i	$-0.837515\pi$
$431$	−2.18370e7	+	3.78228e7i	−0.0131378	+	0.0227554i	0.859382	+	0.511335i	$0.170849\pi$
$432$	8.20405e7	+	1.42098e8i	0.0489593	+	0.0848000i
$433$	1.25534e9	−	2.17431e9i	0.743110	−	1.28710i	−0.207963	−	0.978137i	$-0.566683\pi$
$433$	1.25534e9	−	2.17431e9i	0.743110	−	1.28710i	0.951073	−	0.308968i	$-0.0999835\pi$
$434$	4.76486e8	+	8.25298e8i	0.279792	+	0.484615i
$435$	−7.73063e7	−	1.33898e8i	−0.0450301	−	0.0779944i
$436$	−1.00846e9			−0.582715
$437$	2.13247e9	+	1.03826e9i	1.22236	+	0.595141i
$438$	−2.29228e8			−0.130349
$439$	−1.16409e9	−	2.01626e9i	−0.656689	−	1.13742i	−0.981468	−	0.191628i	$-0.938623\pi$
$439$	−1.16409e9	−	2.01626e9i	−0.656689	−	1.13742i	0.324779	−	0.945790i	$-0.394710\pi$
$440$	−1.29544e8	−	2.24377e8i	−0.0724992	−	0.125572i
$441$	−5.56318e8	+	9.63571e8i	−0.308879	+	0.534994i
$442$	−1.20293e9	−	2.08353e9i	−0.662615	−	1.14768i
$443$	1.47943e8	−	2.56245e8i	0.0808503	−	0.140037i	−0.822765	−	0.568382i	$-0.807570\pi$
$443$	1.47943e8	−	2.56245e8i	0.0808503	−	0.140037i	0.903615	+	0.428345i	$0.140903\pi$
$444$	−1.59071e8			−0.0862483
$445$	−5.49216e8			−0.295450
$446$	−9.49818e8	+	1.64513e9i	−0.506954	+	0.878069i
$447$	−1.96984e8	+	3.41186e8i	−0.104317	+	0.180682i
$448$	−1.42050e8			−0.0746396
$449$	−4.42606e8			−0.230757			−0.115379	−	0.993322i	$-0.536808\pi$
$449$	−4.42606e8			−0.230757			−0.115379	+	0.993322i	$0.536808\pi$
$450$	6.01964e8	−	1.04263e9i	0.311406	−	0.539371i
$451$	−1.68548e9	−	2.91933e9i	−0.865176	−	1.49853i
$452$	8.23472e8	−	1.42630e9i	0.419435	−	0.726483i
$453$	−2.34151e8	−	4.05561e8i	−0.118346	−	0.204981i
$454$	2.08061e6	+	3.60372e6i	0.00104351	+	0.00180741i
$455$	3.86458e8			0.192337
$456$	−1.18538e8	+	8.00739e7i	−0.0585438	+	0.0395471i
$457$	−1.33254e9			−0.653092			−0.326546	−	0.945181i	$-0.605885\pi$
$457$	−1.33254e9			−0.653092			−0.326546	+	0.945181i	$0.605885\pi$
$458$	5.66879e8	+	9.81863e8i	0.275715	+	0.477553i
$459$	6.78383e8	+	1.17499e9i	0.327439	+	0.567141i
$460$	2.03900e8	−	3.53165e8i	0.0976709	−	0.169171i
$461$	−3.56731e8	−	6.17876e8i	−0.169585	−	0.293730i	0.768689	−	0.639623i	$-0.220909\pi$
$461$	−3.56731e8	−	6.17876e8i	−0.169585	−	0.293730i	−0.938274	+	0.345893i	$0.887576\pi$
$462$	1.27612e8	−	2.21030e8i	0.0602065	−	0.104281i
$463$	9.69585e8			0.453996			0.226998	−	0.973895i	$-0.427109\pi$
$463$	9.69585e8			0.453996			0.226998	+	0.973895i	$0.427109\pi$
$464$	8.43721e8			0.392090
$465$	8.25018e7	−	1.42897e8i	0.0380521	−	0.0659081i
$466$	7.14519e8	−	1.23758e9i	0.327087	−	0.566531i
$467$	−2.95089e9			−1.34074			−0.670369	−	0.742028i	$-0.733864\pi$
$467$	−2.95089e9			−1.34074			−0.670369	+	0.742028i	$0.733864\pi$
$468$	1.19317e9			0.538076
$469$	−6.97339e8	+	1.20783e9i	−0.312132	+	0.540629i
$470$	4.59464e7	+	7.95816e7i	0.0204131	+	0.0353566i
$471$	−9.69258e7	+	1.67880e8i	−0.0427431	+	0.0740333i
$472$	2.93074e8	+	5.07619e8i	0.128286	+	0.222198i
$473$	−2.66771e9	−	4.62060e9i	−1.15911	−	2.00763i
$474$	3.68702e8			0.159020
$475$	1.92665e9	+	9.38046e8i	0.824850	+	0.401602i
$476$	−1.17460e9			−0.499189
$477$	1.83758e8	+	3.18278e8i	0.0775232	+	0.134274i
$478$	−8.35959e8	−	1.44792e9i	−0.350096	−	0.606384i
$479$	−1.50881e9	+	2.61334e9i	−0.627278	+	1.08648i	0.360817	+	0.932637i	$0.382498\pi$
$479$	−1.50881e9	+	2.61334e9i	−0.627278	+	1.08648i	−0.988096	+	0.153842i	$0.950835\pi$
$480$	1.22978e7	+	2.13003e7i	0.00507553	+	0.00879108i
$481$	−1.18080e9	+	2.04520e9i	−0.483802	+	0.837970i
$482$	2.72699e8			0.110922
$483$	4.01717e8			0.162220
$484$	−6.46545e8	+	1.11985e9i	−0.259203	+	0.448952i
$485$	2.39291e8	−	4.14464e8i	0.0952424	−	0.164965i
$486$	−1.01618e9			−0.401553
$487$	6.05815e8			0.237678			0.118839	−	0.992914i	$-0.462083\pi$
$487$	6.05815e8			0.237678			0.118839	+	0.992914i	$0.462083\pi$
$488$	−5.40436e8	+	9.36063e8i	−0.210511	+	0.364616i
$489$	−1.48052e8	−	2.56433e8i	−0.0572575	−	0.0991729i
$490$	−1.70251e8	+	2.94883e8i	−0.0653737	+	0.113231i
$491$	−3.23608e8	−	5.60506e8i	−0.123377	−	0.213695i	0.797720	−	0.603028i	$-0.206039\pi$
$491$	−3.23608e8	−	5.60506e8i	−0.123377	−	0.213695i	−0.921097	+	0.389332i	$0.872706\pi$
$492$	1.60004e8	+	2.77135e8i	0.0605694	+	0.104909i
$493$	6.97663e9			2.62229
$494$	1.49605e8	+	2.11846e9i	0.0558345	+	0.790634i
$495$	1.06250e9			0.393741
$496$	4.50212e8	+	7.79791e8i	0.165665	+	0.286941i
$497$	8.40425e8	+	1.45566e9i	0.307080	+	0.531878i
$498$	2.73570e8	−	4.73836e8i	0.0992579	−	0.171920i
$499$	1.23002e9	+	2.13045e9i	0.443159	+	0.767574i	0.997922	−	0.0644347i	$-0.0205244\pi$
$499$	1.23002e9	+	2.13045e9i	0.443159	+	0.767574i	−0.554763	+	0.832008i	$0.687191\pi$
$500$	3.85022e8	−	6.66877e8i	0.137750	−	0.238589i
$501$	5.01792e8			0.178276
$502$	6.17908e8			0.218002
$503$	5.66714e8	−	9.81577e8i	0.198553	−	0.343903i	−0.749507	−	0.661997i	$-0.769709\pi$
$503$	5.66714e8	−	9.81577e8i	0.198553	−	0.343903i	0.948059	+	0.318093i	$0.103043\pi$
$504$	2.91269e8	−	5.04492e8i	0.101341	−	0.175528i
$505$	−7.92329e8			−0.273770
$506$	−3.99834e9			−1.37200
$507$	−7.51859e7	+	1.30226e8i	−0.0256217	+	0.0443781i
$508$	8.80735e6	+	1.52548e7i	0.00298073	+	0.00516277i
$509$	−3.88236e8	+	6.72445e8i	−0.130492	+	0.226019i	−0.923866	−	0.382715i	$-0.874989\pi$
$509$	−3.88236e8	+	6.72445e8i	−0.130492	+	0.226019i	0.793374	+	0.608734i	$0.208322\pi$
$510$	1.01689e8	+	1.76130e8i	0.0339451	+	0.0587946i
$511$	8.30753e8	+	1.43891e9i	0.275422	+	0.477045i
$512$	−1.34218e8			−0.0441942
$513$	−8.43689e7	−	1.19469e9i	−0.0275913	−	0.390701i
$514$	8.24946e7			0.0267950
$515$	−1.04644e8	−	1.81249e8i	−0.0337590	−	0.0584723i
$516$	2.53248e8	+	4.38639e8i	0.0811470	+	0.140551i
$517$	4.50489e8	−	7.80270e8i	0.143373	−	0.248329i
$518$	5.76495e8	+	9.98519e8i	0.182239	+	0.315647i
$519$	−1.02567e8	+	1.77651e8i	−0.0322049	+	0.0557805i
$520$	3.65149e8			0.113883
$521$	−1.46962e9			−0.455274			−0.227637	−	0.973746i	$-0.573100\pi$
$521$	−1.46962e9			−0.455274			−0.227637	+	0.973746i	$0.573100\pi$
$522$	−1.73002e9	+	2.99648e9i	−0.532358	+	0.922071i
$523$	−1.12377e9	+	1.94643e9i	−0.343497	+	0.594955i	−0.985080	−	0.172100i	$-0.944945\pi$
$523$	−1.12377e9	+	1.94643e9i	−0.343497	+	0.594955i	0.641582	+	0.767054i	$0.278278\pi$
$524$	2.12641e9			0.645637
$525$	3.62944e8			0.109467
$526$	−1.25878e8	+	2.18026e8i	−0.0377136	+	0.0653219i
$527$	3.72275e9	+	6.44799e9i	1.10797	+	1.91906i
$528$	1.20575e8	−	2.08842e8i	0.0356483	−	0.0617447i
$529$	−1.44425e9	−	2.50151e9i	−0.424176	−	0.734695i
$530$	5.62357e7	+	9.74031e7i	0.0164077	+	0.0284189i
$531$	−2.40375e9			−0.696719
$532$	9.32237e8	+	4.53887e8i	0.268433	+	0.130694i
$533$	4.75089e9			1.35903
$534$	−2.55596e8	−	4.42705e8i	−0.0726373	−	0.125811i
$535$	2.24327e8	+	3.88546e8i	0.0633350	+	0.109700i
$536$	−6.58887e8	+	1.14123e9i	−0.184814	+	0.320107i
$537$	−7.61431e7	−	1.31884e8i	−0.0212188	−	0.0367520i
$538$	−1.72433e9	+	2.98663e9i	−0.477401	+	0.826883i
$539$	3.33850e9			0.918314
$540$	−2.05924e8			−0.0562766
$541$	4.93456e6	−	8.54690e6i	0.00133985	−	0.00232070i	−0.865355	−	0.501160i	$-0.832907\pi$
$541$	4.93456e6	−	8.54690e6i	0.00133985	−	0.00232070i	0.866695	+	0.498839i	$0.166240\pi$
$542$	2.66661e7	−	4.61870e7i	0.00719385	−	0.0124601i
$543$	−1.19092e9			−0.319216
$544$	−1.10983e9			−0.295570
$545$	6.32815e8	−	1.09607e9i	0.167452	−	0.290035i
$546$	1.79851e8	+	3.11511e8i	0.0472867	+	0.0819030i
$547$	−1.21492e9	+	2.10429e9i	−0.317388	+	0.549732i	−0.979942	−	0.199282i	$-0.936139\pi$
$547$	−1.21492e9	+	2.10429e9i	−0.317388	+	0.549732i	0.662554	+	0.749014i	$0.269472\pi$
$548$	1.15188e9	+	1.99512e9i	0.299004	+	0.517890i
$549$	−2.21629e9	−	3.83872e9i	−0.571640	−	0.990109i
$550$	−3.61243e9			−0.925826
$551$	−5.53710e9	−	2.69590e9i	−1.41011	−	0.686552i
$552$	3.79567e8			0.0960509
$553$	−1.33623e9	−	2.31441e9i	−0.336002	−	0.581973i
$554$	−1.21976e9	−	2.11269e9i	−0.304783	−	0.527899i
$555$	9.98180e7	−	1.72890e8i	0.0247847	−	0.0429283i
$556$	−1.22476e9	−	2.12135e9i	−0.302197	−	0.523420i
$557$	3.10811e9	−	5.38341e9i	0.762086	−	1.31997i	−0.179688	−	0.983724i	$-0.557509\pi$
$557$	3.10811e9	−	5.38341e9i	0.762086	−	1.31997i	0.941774	−	0.336247i	$-0.109158\pi$
$558$	−3.69257e9			−0.899724
$559$	7.51953e9			1.82075
$560$	8.91374e7	−	1.54391e8i	0.0214488	−	0.0371503i
$561$	9.97021e8	−	1.72689e9i	0.238416	−	0.412948i
$562$	2.93189e9			0.696740
$563$	2.18977e9			0.517153			0.258577	−	0.965991i	$-0.416747\pi$
$563$	2.18977e9			0.517153			0.258577	+	0.965991i	$0.416747\pi$
$564$	−4.27654e7	+	7.40718e7i	−0.0100373	+	0.0173851i
$565$	1.03347e9	+	1.79002e9i	0.241061	+	0.417530i
$566$	2.41809e9	−	4.18826e9i	0.560552	−	0.970904i
$567$	1.14272e9	+	1.97926e9i	0.263270	+	0.455996i
$568$	7.94084e8	+	1.37539e9i	0.181822	+	0.314925i
$569$	−4.33477e9			−0.986446			−0.493223	−	0.869903i	$-0.664181\pi$
$569$	−4.33477e9			−0.986446			−0.493223	+	0.869903i	$0.664181\pi$
$570$	−1.26468e7	−	1.79083e8i	−0.00286034	−	0.0405034i
$571$	−5.27200e9			−1.18508			−0.592542	−	0.805539i	$-0.701876\pi$
$571$	−5.27200e9			−1.18508			−0.592542	+	0.805539i	$0.701876\pi$
$572$	−1.79008e9	−	3.10051e9i	−0.399932	−	0.692703i
$573$	5.23974e8	+	9.07549e8i	0.116351	+	0.201525i
$574$	1.15975e9	−	2.00875e9i	0.255961	−	0.443337i
$575$	−2.84295e9	−	4.92413e9i	−0.623636	−	1.08017i
$576$	2.75208e8	−	4.76674e8i	0.0600043	−	0.103931i
$577$	−4.53756e8			−0.0983347			−0.0491674	−	0.998791i	$-0.515657\pi$
$577$	−4.53756e8			−0.0983347			−0.0491674	+	0.998791i	$0.515657\pi$
$578$	−5.89434e9			−1.26966
$579$	3.09300e8	−	5.35723e8i	0.0662224	−	0.114701i
$580$	−5.29440e8	+	9.17017e8i	−0.112673	+	0.195155i
$581$	−3.96581e9			−0.838911
$582$	4.45448e8			0.0936626
$583$	5.51371e8	−	9.55003e8i	0.115240	−	0.199602i
$584$	7.84945e8	+	1.35957e9i	0.163078	+	0.282459i
$585$	−7.48724e8	+	1.29683e9i	−0.154624	+	0.267816i
$586$	1.83343e9	+	3.17560e9i	0.376377	+	0.651905i
$587$	2.10572e9	+	3.64721e9i	0.429701	+	0.744264i	0.996847	−	0.0793535i	$-0.0252856\pi$
$587$	2.10572e9	+	3.64721e9i	0.429701	+	0.744264i	−0.567145	+	0.823618i	$0.691952\pi$
$588$	−3.16928e8			−0.0642894
$589$	−4.62990e8	−	6.55609e9i	−0.0933616	−	1.32203i
$590$	−7.35623e8			−0.147460
$591$	−5.62273e8	−	9.73885e8i	−0.112045	−	0.194067i
$592$	5.44707e8	+	9.43460e8i	0.107904	+	0.186895i
$593$	−5.25018e8	+	9.09358e8i	−0.103391	+	0.179078i	−0.913080	−	0.407781i	$-0.866303\pi$
$593$	−5.25018e8	+	9.09358e8i	−0.103391	+	0.179078i	0.809689	+	0.586860i	$0.199636\pi$
$594$	1.00950e9	+	1.74851e9i	0.197631	+	0.342307i
$595$	7.37067e8	−	1.27664e9i	0.143449	−	0.248461i
$596$	2.69813e9			0.522036
$597$	−6.76167e8			−0.130060
$598$	2.81755e9	−	4.88015e9i	0.538788	−	0.933209i
$599$	−4.41818e8	+	7.65251e8i	−0.0839943	+	0.145482i	−0.904962	−	0.425492i	$-0.860101\pi$
$599$	−4.41818e8	+	7.65251e8i	−0.0839943	+	0.145482i	0.820968	+	0.570974i	$0.193434\pi$
$600$	3.42931e8			0.0648154
$601$	−1.28488e9			−0.241436			−0.120718	−	0.992687i	$-0.538520\pi$
$601$	−1.28488e9			−0.241436			−0.120718	+	0.992687i	$0.538520\pi$
$602$	1.83561e9	−	3.17937e9i	0.342920	−	0.593955i
$603$	−2.70204e9	−	4.68008e9i	−0.501859	−	0.869246i
$604$	−1.60361e9	+	2.77753e9i	−0.296120	+	0.512895i
$605$	−8.11421e8	−	1.40542e9i	−0.148971	−	0.258026i
$606$	−3.68737e8	−	6.38671e8i	−0.0673073	−	0.116580i
$607$	8.02707e9			1.45679			0.728395	−	0.685158i	$-0.240267\pi$
$607$	8.02707e9			1.45679			0.728395	+	0.685158i	$0.240267\pi$
$608$	8.80833e8	+	4.28859e8i	0.158939	+	0.0773842i
$609$	−1.04309e9			−0.187137
$610$	−6.78254e8	−	1.17477e9i	−0.120987	−	0.209555i
$611$	6.34902e8	+	1.09968e9i	0.112606	+	0.195040i
$612$	2.27566e9	−	3.94156e9i	0.401308	−	0.695086i
$613$	3.68140e9	+	6.37637e9i	0.645507	+	1.11805i	0.984184	+	0.177149i	$0.0566873\pi$
$613$	3.68140e9	+	6.37637e9i	0.645507	+	1.11805i	−0.338677	+	0.940903i	$0.609979\pi$
$614$	−8.51004e8	+	1.47398e9i	−0.148369	+	0.256982i
$615$	−4.01614e8			−0.0696219
$616$	−1.74792e9			−0.301294
$617$	2.50499e9	−	4.33877e9i	0.429346	−	0.743649i	−0.567469	−	0.823395i	$-0.692077\pi$
$617$	2.50499e9	−	4.33877e9i	0.429346	−	0.743649i	0.996815	+	0.0797455i	$0.0254107\pi$
$618$	9.73992e7	−	1.68700e8i	0.0165995	−	0.0287512i
$619$	5.93273e9			1.00540			0.502698	−	0.864462i	$-0.332341\pi$
$619$	5.93273e9			1.00540			0.502698	+	0.864462i	$0.332341\pi$
$620$	−1.13004e9			−0.190425
$621$	−1.58894e9	+	2.75213e9i	−0.266249	+	0.461157i
$622$	2.03677e9	+	3.52779e9i	0.339372	+	0.587810i
$623$	−1.85263e9	+	3.20885e9i	−0.306959	+	0.531668i
$624$	1.69934e8	+	2.94335e8i	0.0279985	+	0.0484948i
$625$	−2.31654e9	−	4.01237e9i	−0.379542	−	0.657387i
$626$	−6.18001e9			−1.00688
$627$	−1.45860e9	+	9.85306e8i	−0.236320	+	0.159637i
$628$	1.32761e9			0.213901
$629$	4.50411e9	+	7.80135e9i	0.721659	+	1.24995i
$630$	3.65546e8	+	6.33144e8i	0.0582438	+	0.100881i
$631$	−1.21699e9	+	2.10790e9i	−0.192835	+	0.334000i	−0.946189	−	0.323616i	$-0.895102\pi$
$631$	−1.21699e9	+	2.10790e9i	−0.192835	+	0.334000i	0.753354	+	0.657616i	$0.228435\pi$
$632$	−1.26255e9	−	2.18679e9i	−0.198947	−	0.344586i
$633$	−5.15016e8	+	8.92034e8i	−0.0807063	+	0.139787i
$634$	3.01344e9			0.469625
$635$	−2.21067e7			−0.00342622
$636$	−5.23423e7	+	9.06595e7i	−0.00806776	+	0.0139738i
$637$	−2.35258e9	+	4.07479e9i	−0.360626	+	0.624622i
$638$	1.03819e10			1.58273
$639$	−6.51295e9			−0.987472
$640$	8.42224e7	−	1.45877e8i	0.0126998	−	0.0219967i
$641$	−5.06179e9	−	8.76727e9i	−0.759103	−	1.31480i	−0.943309	−	0.331917i	$-0.892305\pi$
$641$	−5.06179e9	−	8.76727e9i	−0.759103	−	1.31480i	0.184206	−	0.982888i	$-0.441029\pi$
$642$	−2.08796e8	+	3.61646e8i	−0.0311423	+	0.0539400i
$643$	5.00346e8	+	8.66625e8i	0.0742219	+	0.128556i	0.900748	−	0.434343i	$-0.143019\pi$
$643$	5.00346e8	+	8.66625e8i	0.0742219	+	0.128556i	−0.826526	+	0.562899i	$0.809686\pi$
$644$	−1.37560e9	−	2.38261e9i	−0.202951	−	0.351522i
$645$	−6.35659e8			−0.0932750
$646$	7.28350e9	+	3.54619e9i	1.06298	+	0.517544i
$647$	−5.51869e9			−0.801071			−0.400535	−	0.916281i	$-0.631176\pi$
$647$	−5.51869e9			−0.801071			−0.400535	+	0.916281i	$0.631176\pi$
$648$	1.07971e9	+	1.87012e9i	0.155882	+	0.269996i
$649$	3.60626e9	+	6.24623e9i	0.517846	+	0.896936i
$650$	2.54561e9	−	4.40912e9i	0.363576	−	0.629732i
$651$	−5.56594e8	−	9.64049e8i	−0.0790688	−	0.136951i
$652$	−1.01395e9	+	1.75621e9i	−0.143268	+	0.248147i
$653$	5.85703e9			0.823155			0.411577	−	0.911375i	$-0.364978\pi$
$653$	5.85703e9			0.823155			0.411577	+	0.911375i	$0.364978\pi$
$654$	1.17801e9			0.164674
$655$	−1.33434e9	+	2.31114e9i	−0.185533	+	0.321352i
$656$	1.09580e9	−	1.89799e9i	0.151555	−	0.262500i
$657$	−6.43800e9			−0.885670
$658$	6.19950e8			0.0848333
$659$	2.44661e9	−	4.23765e9i	0.333016	−	0.576801i	−0.650086	−	0.759861i	$-0.725267\pi$
$659$	2.44661e9	−	4.23765e9i	0.333016	−	0.576801i	0.983102	+	0.183060i	$0.0586003\pi$
$660$	1.51323e8	+	2.62100e8i	0.0204881	+	0.0354864i
$661$	−3.29616e9	+	5.70911e9i	−0.443918	+	0.768889i	−0.997976	−	0.0635894i	$-0.979745\pi$
$661$	−3.29616e9	+	5.70911e9i	−0.443918	+	0.768889i	0.554058	+	0.832478i	$0.313079\pi$
$662$	−4.21869e9	−	7.30699e9i	−0.565165	−	0.978894i
$663$	1.40516e9	+	2.43382e9i	0.187253	+	0.324333i
$664$	−3.74714e9			−0.496720
$665$	−1.07830e9	+	7.28405e8i	−0.142188	+	0.0960500i
$666$	−4.46760e9			−0.586023
$667$	8.17050e9	+	1.41517e10i	1.06613	+	1.84658i
$668$	−1.71829e9	−	2.97616e9i	−0.223038	−	0.386312i
$669$	1.10950e9	−	1.92172e9i	0.143264	−	0.248141i
$670$	−8.26911e8	−	1.43225e9i	−0.106218	−	0.183974i
$671$	−6.65004e9	+	1.15182e10i	−0.849758	+	1.47182i
$672$	1.65932e8			0.0210930
$673$	−9.16808e9			−1.15938			−0.579690	−	0.814837i	$-0.696826\pi$
$673$	−9.16808e9			−1.15938			−0.579690	+	0.814837i	$0.696826\pi$
$674$	−1.66173e9	+	2.87820e9i	−0.209050	+	0.362086i
$675$	−1.43558e9	+	2.48650e9i	−0.179665	+	0.311190i
$676$	1.02984e9			0.128220
$677$	9.27434e9			1.14874			0.574371	−	0.818595i	$-0.305247\pi$
$677$	9.27434e9			1.14874			0.574371	+	0.818595i	$0.305247\pi$
$678$	−9.61916e8	+	1.66609e9i	−0.118531	+	0.205302i
$679$	−1.61436e9	−	2.79616e9i	−0.197905	−	0.342782i
$680$	6.96425e8	−	1.20624e9i	0.0849362	−	0.147114i
$681$	−2.43041e6	−	4.20959e6i	−0.000294893	−	0.000510769i
$682$	5.53984e9	+	9.59529e9i	0.668732	+	1.15828i
$683$	−7.43197e9			−0.892548			−0.446274	−	0.894896i	$-0.647249\pi$
$683$	−7.43197e9			−0.892548			−0.446274	+	0.894896i	$0.647249\pi$
$684$	−3.32921e9	+	2.24892e9i	−0.397782	+	0.268706i
$685$	−2.89126e9			−0.343692
$686$	2.93363e9	+	5.08120e9i	0.346954	+	0.600941i
$687$	−6.62184e8	−	1.14694e9i	−0.0779166	−	0.134955i
$688$	1.73440e9	−	3.00406e9i	0.203043	−	0.351681i
$689$	7.77082e8	+	1.34595e9i	0.0905106	+	0.156769i
$690$	−2.38180e8	+	4.12540e8i	−0.0276016	+	0.0478073i
$691$	−6.15824e9			−0.710041			−0.355020	−	0.934859i	$-0.615526\pi$
$691$	−6.15824e9			−0.710041			−0.355020	+	0.934859i	$0.615526\pi$
$692$	1.40488e9			0.161164
$693$	3.58405e9	−	6.20775e9i	0.409079	−	0.708546i
$694$	2.94576e9	−	5.10220e9i	0.334533	−	0.579428i
$695$	3.07418e9			0.347362
$696$	−9.85569e8			−0.110804
$697$	9.06106e9	−	1.56942e10i	1.01359	−	1.75560i
$698$	3.44877e9	+	5.97344e9i	0.383857	+	0.664860i
$699$	−8.34646e8	+	1.44565e9i	−0.0924341	+	0.160100i
$700$	−1.24283e9	−	2.15264e9i	−0.136952	−	0.237208i
$701$	3.77012e9	+	6.53004e9i	0.413373	+	0.715983i	0.995256	−	0.0972896i	$-0.0310173\pi$
$701$	3.77012e9	+	6.53004e9i	0.413373	+	0.715983i	−0.581883	+	0.813272i	$0.697684\pi$
$702$	−2.84552e9			−0.310442
$703$	−5.60166e8	−	7.93214e9i	−0.0608098	−	0.861086i
$704$	−1.65154e9			−0.178396
$705$	−5.36711e7	−	9.29610e7i	−0.00576870	−	0.00999169i
$706$	−3.85669e9	−	6.67998e9i	−0.412475	−	0.714428i
$707$	−2.67270e9	+	4.62926e9i	−0.284435	+	0.492656i
$708$	−3.42346e8	−	5.92961e8i	−0.0362534	−	0.0627928i
$709$	5.21123e9	−	9.02611e9i	0.549134	−	0.951128i	−0.449200	−	0.893431i	$-0.648291\pi$
$709$	5.21123e9	−	9.02611e9i	0.549134	−	0.951128i	0.998334	−	0.0576966i	$-0.0183756\pi$
$710$	−1.99317e9			−0.208997
$711$	1.03552e10			1.08048
$712$	−1.75047e9	+	3.03191e9i	−0.181751	+	0.314801i
$713$	−8.71962e9	+	1.51028e10i	−0.900915	+	1.56043i
$714$	1.37207e9			0.141070
$715$	4.49314e9			0.459705
$716$	−5.21473e8	+	9.03218e8i	−0.0530929	+	0.0919596i
$717$	9.76502e8	+	1.69135e9i	0.0989364	+	0.171363i
$718$	3.21619e9	−	5.57061e9i	0.324270	−	0.561652i
$719$	−5.25843e9	−	9.10787e9i	−0.527601	−	0.913831i	−0.999482	−	0.0321692i	$-0.989758\pi$
$719$	−5.25843e9	−	9.10787e9i	−0.527601	−	0.913831i	0.471882	−	0.881662i	$-0.343575\pi$
$720$	3.45389e8	+	5.98232e8i	0.0344862	+	0.0597318i
$721$	−1.41195e9			−0.140296
$722$	−4.41035e9	−	5.62897e9i	−0.436107	−	0.556607i
$723$	−3.18546e8			−0.0313464
$724$	4.07808e9	+	7.06345e9i	0.399366	+	0.691722i
$725$	7.38190e9	+	1.27858e10i	0.719424	+	1.24608i
$726$	7.55243e8	−	1.30812e9i	0.0732502	−	0.126873i
$727$	5.96958e9	+	1.03396e10i	0.576200	+	0.998008i	0.995910	+	0.0903494i	$0.0287984\pi$
$727$	5.96958e9	+	1.03396e10i	0.576200	+	0.998008i	−0.419710	+	0.907658i	$0.637868\pi$
$728$	1.23173e9	−	2.13342e9i	0.118319	−	0.204935i
$729$	−8.03694e9			−0.768324
$730$	−1.97023e9			−0.187451
$731$	1.43415e10	−	2.48402e10i	1.35795	−	2.35204i
$732$	6.31295e8	−	1.09344e9i	0.0594900	−	0.103040i
$733$	6.63762e9			0.622513			0.311257	−	0.950326i	$-0.399250\pi$
$733$	6.63762e9			0.622513			0.311257	+	0.950326i	$0.399250\pi$
$734$	−3.30926e8			−0.0308883
$735$	1.98874e8	−	3.44460e8i	0.0184745	−	0.0319987i
$736$	−1.29975e9	−	2.25123e9i	−0.120168	−	0.208136i
$737$	−8.10757e9	+	1.40427e10i	−0.746027	+	1.29216i
$738$	4.49380e9	+	7.78349e9i	0.411544	+	0.712816i
$739$	−8.43130e9	−	1.46034e10i	−0.768492	−	1.33107i	−0.938381	−	0.345603i	$-0.887674\pi$
$739$	−8.43130e9	−	1.46034e10i	−0.768492	−	1.33107i	0.169889	−	0.985463i	$-0.445659\pi$
$740$	−1.36723e9			−0.124031
$741$	−1.74757e8	−	2.47462e9i	−0.0157787	−	0.223431i
$742$	7.58782e8			0.0681873
$743$	−9.18249e9	−	1.59045e10i	−0.821296	−	1.42253i	−0.904717	−	0.426012i	$-0.859918\pi$
$743$	−9.18249e9	−	1.59045e10i	−0.821296	−	1.42253i	0.0834215	−	0.996514i	$-0.473415\pi$
$744$	−5.25903e8	−	9.10891e8i	−0.0468167	−	0.0810888i
$745$	−1.69309e9	+	2.93252e9i	−0.150014	+	0.259833i
$746$	−5.92983e8	−	1.02708e9i	−0.0522946	−	0.0905769i
$747$	7.68335e9	−	1.33080e10i	0.674417	−	1.16813i
$748$	−1.36564e10			−1.19311
$749$	3.02682e9			0.263209
$750$	−4.49753e8	+	7.78994e8i	−0.0389277	+	0.0674248i
$751$	1.05714e10	−	1.83102e10i	0.910737	−	1.57744i	0.0977109	−	0.995215i	$-0.468848\pi$
$751$	1.05714e10	−	1.83102e10i	0.910737	−	1.57744i	0.813026	−	0.582228i	$-0.197819\pi$
$752$	5.85766e8			0.0502298
$753$	−7.21792e8			−0.0616070
$754$	−7.31596e9	+	1.26716e10i	−0.621544	+	1.07655i
$755$	−2.01254e9	−	3.48583e9i	−0.170189	−	0.294776i
$756$	−6.94626e8	+	1.20313e9i	−0.0584689	+	0.101271i
$757$	−9.32285e8	−	1.61476e9i	−0.0781111	−	0.135292i	0.824324	−	0.566119i	$-0.191556\pi$
$757$	−9.32285e8	−	1.61476e9i	−0.0781111	−	0.135292i	−0.902435	+	0.430826i	$0.858222\pi$
$758$	3.33611e9	+	5.77831e9i	0.278226	+	0.481902i
$759$	4.67055e9			0.387723
$760$	−1.01884e9	+	6.88241e8i	−0.0841898	+	0.0568713i
$761$	6.37154e9			0.524081			0.262040	−	0.965057i	$-0.415605\pi$
$761$	6.37154e9			0.524081			0.262040	+	0.965057i	$0.415605\pi$
$762$	−1.02881e7	−	1.78194e7i	−0.000842347	−	0.00145899i
$763$	−4.26925e9	−	7.39456e9i	−0.347949	−	0.602666i
$764$	3.58849e9	−	6.21544e9i	0.291128	−	0.504249i
$765$	2.85598e9	+	4.94671e9i	0.230643	+	0.399486i
$766$	6.64911e8	−	1.15166e9i	0.0534518	−	0.0925813i
$767$	−1.01651e10			−0.813441
$768$	1.56783e8			0.0124892
$769$	5.68400e9	−	9.84498e9i	0.450725	−	0.780679i	−0.547706	−	0.836671i	$-0.684499\pi$
$769$	5.68400e9	−	9.84498e9i	0.450725	−	0.780679i	0.998431	+	0.0559916i	$0.0178320\pi$
$770$	1.09683e9	−	1.89977e9i	0.0865810	−	0.149963i
$771$	−9.63637e7			−0.00757222
$772$	−4.23654e9			−0.331399
$773$	8.24123e8	−	1.42742e9i	0.0641747	−	0.111154i	−0.832153	−	0.554546i	$-0.812892\pi$
$773$	8.24123e8	−	1.42742e9i	0.0641747	−	0.111154i	0.896328	+	0.443392i	$0.146225\pi$
$774$	7.11262e9	+	1.23194e10i	0.551361	+	0.954986i
$775$	−7.87801e9	+	1.36451e10i	−0.607940	+	1.05298i
$776$	−1.52535e9	−	2.64198e9i	−0.117180	−	0.202961i
$777$	−6.73417e8	−	1.16639e9i	−0.0515004	−	0.0892012i
$778$	−9.52370e9			−0.725066
$779$	−1.32560e10	+	8.95459e9i	−1.00469	+	0.678679i
$780$	−4.26539e8			−0.0321831
$781$	9.77116e9	+	1.69241e10i	0.733952	+	1.27124i
$782$	−1.07475e10	−	1.86152e10i	−0.803679	−	1.39201i
$783$	4.12579e9	−	7.14608e9i	0.307143	−	0.531988i
$784$	1.08526e9	+	1.87972e9i	0.0804314	+	0.139311i
$785$	−8.33084e8	+	1.44294e9i	−0.0614674	+	0.106465i
$786$	−2.48391e9			−0.182456
$787$	−9.13850e9			−0.668288			−0.334144	−	0.942522i	$-0.608447\pi$
$787$	−9.13850e9			−0.668288			−0.334144	+	0.942522i	$0.608447\pi$
$788$	−3.85078e9	+	6.66975e9i	−0.280354	+	0.485588i
$789$	1.47040e8	−	2.54681e8i	0.0106578	−	0.0184598i
$790$	3.16902e9			0.228681
$791$	1.39445e10			1.00181
$792$	3.38642e9	−	5.86546e9i	0.242216	−	0.419531i
$793$	−9.37232e9	−	1.62333e10i	−0.667407	−	1.15598i
$794$	−5.14691e9	+	8.91472e9i	−0.364901	+	0.632027i
$795$	−6.56902e7	−	1.13779e8i	−0.00463677	−	0.00803112i
$796$	2.31540e9	+	4.01039e9i	0.162716	+	0.281832i
$797$	−1.11174e8			−0.00777855			−0.00388928	−	0.999992i	$-0.501238\pi$
$797$	−1.11174e8			−0.00777855			−0.00388928	+	0.999992i	$0.501238\pi$
$798$	−1.08897e9	−	5.30195e8i	−0.0758585	−	0.0369339i
$799$	4.84363e9			0.335936
$800$	−1.17430e9	−	2.03395e9i	−0.0810894	−	0.140451i
$801$	−7.17856e9	−	1.24336e10i	−0.493541	−	0.854838i
$802$	9.98694e9	−	1.72979e10i	0.683632	−	1.18408i
$803$	9.65871e9	+	1.67294e10i	0.658286	+	1.14019i
$804$	7.69661e8	−	1.33309e9i	0.0522280	−	0.0904615i
$805$	3.45279e9			0.233284
$806$	−1.56153e10			−1.05045
$807$	2.01423e9	−	3.48875e9i	0.134912	−	0.233675i
$808$	−2.52533e9	+	4.37400e9i	−0.168414	+	0.291702i
$809$	1.41086e10			0.936834			0.468417	−	0.883508i	$-0.344825\pi$
$809$	1.41086e10			0.936834			0.468417	+	0.883508i	$0.344825\pi$
$810$	−2.71011e9			−0.179180
$811$	1.35499e9	−	2.34690e9i	0.0891994	−	0.154498i	−0.817974	−	0.575256i	$-0.804902\pi$
$811$	1.35499e9	−	2.34690e9i	0.0891994	−	0.154498i	0.907173	+	0.420758i	$0.138236\pi$
$812$	3.57184e9	+	6.18660e9i	0.234124	+	0.405514i
$813$	−3.11492e7	+	5.39520e7i	−0.00203297	+	0.00352120i
$814$	6.70259e9	+	1.16092e10i	0.435569	+	0.754428i
$815$	−1.27251e9	−	2.20406e9i	−0.0823401	−	0.142617i
$816$	1.29642e9			0.0835274
$817$	−2.09811e10	+	1.41730e10i	−1.34602	+	0.909251i
$818$	4.64956e8			0.0297013
$819$	5.05122e9	+	8.74897e9i	0.321294	+	0.556498i
$820$	1.37525e9	+	2.38200e9i	0.0871027	+	0.150866i
$821$	−1.04687e10	+	1.81323e10i	−0.660226	+	1.14354i	0.320331	+	0.947306i	$0.396206\pi$
$821$	−1.04687e10	+	1.81323e10i	−0.660226	+	1.14354i	−0.980556	+	0.196239i	$0.937127\pi$
$822$	−1.34554e9	−	2.33055e9i	−0.0844978	−	0.146355i
$823$	−6.77590e8	+	1.17362e9i	−0.0423709	+	0.0733886i	−0.886433	−	0.462857i	$-0.846824\pi$
$823$	−6.77590e8	+	1.17362e9i	−0.0423709	+	0.0733886i	0.844062	+	0.536245i	$0.180158\pi$
$824$	−1.33410e9			−0.0830695
$825$	4.21975e9			0.261636
$826$	−2.48142e9	+	4.29794e9i	−0.153204	+	0.265357i
$827$	3.60148e9	−	6.23794e9i	0.221417	−	0.383506i	−0.733821	−	0.679343i	$-0.762265\pi$
$827$	3.60148e9	−	6.23794e9i	0.221417	−	0.383506i	0.955239	+	0.295837i	$0.0955984\pi$
$828$	1.06603e10			0.652627
$829$	3.67325e8			0.0223929			0.0111964	−	0.999937i	$-0.496436\pi$
$829$	3.67325e8			0.0223929			0.0111964	+	0.999937i	$0.496436\pi$
$830$	2.35135e9	−	4.07266e9i	0.142739	−	0.247232i
$831$	1.42483e9	+	2.46788e9i	0.0861310	+	0.149183i
$832$	1.16381e9	−	2.01578e9i	0.0700569	−	0.121342i
$833$	8.97384e9	+	1.55432e10i	0.537924	+	0.931712i
$834$	1.43067e9	+	2.47799e9i	0.0854001	+	0.147917i
$835$	4.31294e9			0.256372
$836$	1.08386e10	+	5.27709e9i	0.641581	+	0.312372i
$837$	8.80615e9			0.519095
$838$	4.65276e9	+	8.05882e9i	0.273122	+	0.473061i
$839$	8.54770e9	+	1.48050e10i	0.499669	+	0.865452i	1.00000		0.000382270i	$-0.000121680\pi$
$839$	8.54770e9	+	1.48050e10i	0.499669	+	0.865452i	−0.500331	+	0.865834i	$0.666788\pi$
$840$	−1.04123e8	+	1.80347e8i	−0.00606137	+	0.0104986i
$841$	−1.25903e10	−	2.18070e10i	−0.729878	−	1.26419i
$842$	1.36399e9	−	2.36251e9i	0.0787445	−	0.136389i
$843$	−3.42481e9			−0.196897
$844$	7.05427e9			0.403881
$845$	−6.46228e8	+	1.11930e9i	−0.0368457	+	0.0638187i
$846$	−1.20109e9	+	2.08035e9i	−0.0681992	+	0.118124i
$847$	−1.09484e10			−0.619098
$848$	7.16943e8			0.0403737
$849$	−2.82463e9	+	4.89240e9i	−0.158411	+	0.274375i
$850$	−9.71014e9	−	1.68185e10i	−0.542325	−	0.939334i
$851$	−1.05498e10	+	1.82727e10i	−0.586799	+	1.01637i
$852$	−9.27587e8	−	1.60663e9i	−0.0513826	−	0.0889972i
$853$	1.19417e10	+	2.06836e10i	0.658784	+	1.14105i	0.980931	+	0.194358i	$0.0622623\pi$
$853$	1.19417e10	+	2.06836e10i	0.658784	+	1.14105i	−0.322147	+	0.946690i	$0.604404\pi$
$854$	−9.15160e9			−0.502799
$855$	−3.55192e8	−	5.02963e9i	−0.0194349	−	0.275204i
$856$	2.85992e9			0.155846
$857$	1.45668e10	+	2.52304e10i	0.790553	+	1.36928i	0.925625	+	0.378443i	$0.123540\pi$
$857$	1.45668e10	+	2.52304e10i	0.790553	+	1.36928i	−0.135071	+	0.990836i	$0.543126\pi$
$858$	2.09103e9	+	3.62177e9i	0.113020	+	0.195756i
$859$	−3.42218e9	+	5.92739e9i	−0.184216	+	0.319071i	−0.943312	−	0.331907i	$-0.892308\pi$
$859$	−3.42218e9	+	5.92739e9i	−0.184216	+	0.319071i	0.759096	+	0.650979i	$0.225641\pi$
$860$	2.17669e9	+	3.77013e9i	0.116695	+	0.202121i
$861$	−1.35473e9	+	2.34647e9i	−0.0723340	+	0.125286i
$862$	−3.49392e8			−0.0185797
$863$	−2.24374e10			−1.18832			−0.594162	−	0.804345i	$-0.702516\pi$
$863$	−2.24374e10			−1.18832			−0.594162	+	0.804345i	$0.702516\pi$
$864$	−6.56324e8	+	1.13679e9i	−0.0346195	+	0.0599627i
$865$	−8.81571e8	+	1.52693e9i	−0.0463128	+	0.0802161i
$866$	2.00854e10			1.05092
$867$	6.88531e9			0.358803
$868$	−3.81189e9	+	6.60238e9i	−0.197843	+	0.342674i
$869$	−1.55356e10	−	2.69084e10i	−0.803078	−	1.39097i
$870$	6.18450e8	−	1.07119e9i	0.0318411	−	0.0551503i
$871$	−1.14265e10	−	1.97913e10i	−0.585936	−	1.01487i
$872$	−4.03385e9	−	6.98682e9i	−0.206021	−	0.356839i
$873$	1.25107e10			0.636400
$874$	1.33664e9	+	1.89272e10i	0.0677211	+	0.958953i
$875$	6.51985e9			0.329010
$876$	−9.16912e8	−	1.58814e9i	−0.0460854	−	0.0798222i
$877$	6.14735e9	+	1.06475e10i	0.307744	+	0.533028i	0.977868	−	0.209221i	$-0.0670928\pi$
$877$	6.14735e9	+	1.06475e10i	0.307744	+	0.533028i	−0.670125	+	0.742248i	$0.733759\pi$
$878$	9.31269e9	−	1.61301e10i	0.464349	−	0.804276i
$879$	−2.14167e9	−	3.70949e9i	−0.106363	−	0.184227i
$880$	1.03635e9	−	1.79501e9i	0.0512647	−	0.0887930i
$881$	−2.38790e9			−0.117652			−0.0588262	−	0.998268i	$-0.518736\pi$
$881$	−2.38790e9			−0.117652			−0.0588262	+	0.998268i	$0.518736\pi$
$882$	−8.90109e9			−0.436821
$883$	9.17221e9	−	1.58867e10i	0.448344	−	0.776555i	−0.549934	−	0.835208i	$-0.685347\pi$
$883$	9.17221e9	−	1.58867e10i	0.448344	−	0.776555i	0.998278	+	0.0586529i	$0.0186805\pi$
$884$	9.62341e9	−	1.66682e10i	0.468539	−	0.811534i
$885$	8.59297e8			0.0416718
$886$	2.36709e9			0.114340
$887$	−1.18808e10	+	2.05782e10i	−0.571628	+	0.990089i	0.424771	+	0.905301i	$0.360355\pi$
$887$	−1.18808e10	+	2.05782e10i	−0.571628	+	0.990089i	−0.996399	+	0.0847881i	$0.972979\pi$
$888$	−6.36284e8	−	1.10208e9i	−0.0304934	−	0.0528161i
$889$	−7.45707e7	+	1.29160e8i	−0.00355969	+	0.00616556i
$890$	−2.19687e9	−	3.80508e9i	−0.104457	−	0.180925i
$891$	1.32858e10	+	2.30117e10i	0.629240	+	1.08988i
$892$	−1.51971e10			−0.716941
$893$	−3.84422e9	−	1.87167e9i	−0.180646	−	0.0879527i
$894$	−3.15174e9			−0.147526
$895$	−6.54455e8	−	1.13355e9i	−0.0305140	−	0.0528518i
$896$	−5.68202e8	−	9.84154e8i	−0.0263891	−	0.0457072i
$897$	−3.29125e9	+	5.70061e9i	−0.152260	+	0.263723i
$898$	−1.77043e9	−	3.06647e9i	−0.0815851	−	0.141309i
$899$	2.26410e10	−	3.92154e10i	1.03929	−	1.80011i
$900$	9.63142e9			0.440394
$901$	5.92831e9			0.270019
$902$	1.34838e10	−	2.33546e10i	0.611772	−	1.05962i
$903$	−2.14422e9	+	3.71390e9i	−0.0969085	+	0.167850i
$904$	1.31756e10			0.593171
$905$	−1.02361e10			−0.459054
$906$	1.87321e9	−	3.24449e9i	0.0836830	−	0.144943i
$907$	−1.92190e10	−	3.32882e10i	−0.855272	−	1.48138i	−0.876392	−	0.481598i	$-0.840056\pi$
$907$	−1.92190e10	−	3.32882e10i	−0.855272	−	1.48138i	0.0211197	−	0.999777i	$-0.493277\pi$
$908$	−1.66449e7	+	2.88298e7i	−0.000737871	+	0.00127803i
$909$	−1.03562e10	−	1.79374e10i	−0.457326	−	0.792112i
$910$	1.54583e9	+	2.67746e9i	0.0680014	+	0.117782i
$911$	2.62215e10			1.14906			0.574530	−	0.818484i	$-0.305185\pi$
$911$	2.62215e10			1.14906			0.574530	+	0.818484i	$0.305185\pi$
$912$	−1.02892e9	−	5.00960e8i	−0.0449159	−	0.0218686i
$913$	−4.61083e10			−2.00508
$914$	−5.33017e9	−	9.23213e9i	−0.230903	−	0.399936i
$915$	7.92283e8	+	1.37227e9i	0.0341906	+	0.0592198i
$916$	−4.53503e9	+	7.85490e9i	−0.194960	+	0.337681i
$917$	9.00202e9	+	1.55920e10i	0.385521	+	0.667741i
$918$	−5.42706e9	+	9.39995e9i	−0.231534	+	0.401029i
$919$	−3.71179e10			−1.57754			−0.788768	−	0.614692i	$-0.789280\pi$
$919$	−3.71179e10			−1.57754			−0.788768	+	0.614692i	$0.789280\pi$
$920$	3.26240e9			0.138127
$921$	9.94077e8	−	1.72179e9i	0.0419287	−	0.0726226i
$922$	2.85385e9	−	4.94301e9i	0.119915	−	0.207699i
$923$	−2.75422e10			−1.15290
$924$	2.04179e9			0.0851449
$925$	−9.53152e9	+	1.65091e10i	−0.395973	+	0.685846i
$926$	3.87834e9	+	6.71748e9i	0.160512	+	0.278015i
$927$	2.73551e9	−	4.73804e9i	0.112787	−	0.195353i
$928$	3.37488e9	+	5.84547e9i	0.138625	+	0.240105i
$929$	3.52210e9	+	6.10045e9i	0.144127	+	0.249636i	0.929047	−	0.369962i	$-0.120629\pi$
$929$	3.52210e9	+	6.10045e9i	0.144127	+	0.249636i	−0.784920	+	0.619597i	$0.787296\pi$
$930$	1.32003e9			0.0538137
$931$	−1.11606e9	−	1.58037e10i	−0.0453276	−	0.641853i
$932$	1.14323e10			0.462571
$933$	−2.37920e9	−	4.12089e9i	−0.0959059	−	0.166114i
$934$	−1.18036e10	−	2.04444e10i	−0.474022	−	0.821031i
$935$	8.56947e9	−	1.48428e10i	0.342857	−	0.593846i
$936$	4.77270e9	+	8.26655e9i	0.190238	+	0.329503i
$937$	−8.59209e9	+	1.48819e10i	−0.341201	+	0.590978i	−0.984656	−	0.174506i	$-0.944167\pi$
$937$	−8.59209e9	+	1.48819e10i	−0.341201	+	0.590978i	0.643455	+	0.765484i	$0.277500\pi$
$938$	−1.11574e10			−0.441422
$939$	7.21901e9			0.284543
$940$	−3.67572e8	+	6.36653e8i	−0.0144343	+	0.0250009i
$941$	1.73353e10	−	3.00257e10i	0.678217	−	1.17471i	−0.297300	−	0.954784i	$-0.596086\pi$
$941$	1.73353e10	−	3.00257e10i	0.678217	−	1.17471i	0.975517	−	0.219923i	$-0.0705805\pi$
$942$	−1.55081e9			−0.0604479
$943$	4.24466e10			1.64836
$944$	−2.34459e9	+	4.06095e9i	−0.0907121	+	0.157118i
$945$	−8.71764e8	−	1.50994e9i	−0.0336037	−	0.0582034i
$946$	2.13417e10	−	3.69648e10i	0.819613	−	1.41961i
$947$	2.17761e9	+	3.77174e9i	0.0833212	+	0.144317i	0.904675	−	0.426103i	$-0.140114\pi$
$947$	2.17761e9	+	3.77174e9i	0.0833212	+	0.144317i	−0.821353	+	0.570420i	$0.806781\pi$
$948$	1.47481e9	+	2.55444e9i	0.0562220	+	0.0973794i
$949$	−2.72253e10			−1.03405
$950$	1.20763e9	+	1.71004e10i	0.0456984	+	0.647104i
$951$	−3.52007e9			−0.132715
$952$	−4.69839e9	−	8.13785e9i	−0.176490	−	0.305689i
$953$	−1.85556e10	−	3.21393e10i	−0.694464	−	1.20285i	−0.970361	−	0.241660i	$-0.922308\pi$
$953$	−1.85556e10	−	3.21393e10i	−0.694464	−	1.20285i	0.275897	−	0.961187i	$-0.411025\pi$
$954$	−1.47006e9	+	2.54622e9i	−0.0548172	+	0.0949461i
$955$	4.50359e9	+	7.80045e9i	0.167320	+	0.289806i
$956$	6.68767e9	−	1.15834e10i	0.247555	−	0.428778i
$957$	−1.21274e10			−0.447276
$958$	−2.41410e10			−0.887106
$959$	−9.75285e9	+	1.68924e10i	−0.357081	+	0.618482i
$960$	−9.83820e7	+	1.70403e8i	−0.00358894	+	0.00621623i
$961$	2.08127e10			0.756480
$962$	−1.88928e10			−0.684199
$963$	−5.86416e9	+	1.01570e10i	−0.211599	+	0.366501i
$964$	1.09080e9	+	1.88931e9i	0.0392170	+	0.0679258i
$965$	2.65845e9	−	4.60458e9i	0.0952322	−	0.164947i
$966$	1.60687e9	+	2.78318e9i	0.0573536	+	0.0993394i
$967$	−1.24982e10	−	2.16475e10i	−0.444482	−	0.769865i	0.553534	−	0.832826i	$-0.313279\pi$
$967$	−1.24982e10	−	2.16475e10i	−0.444482	−	0.769865i	−0.998016	+	0.0629617i	$0.979945\pi$
$968$	−1.03447e10			−0.366568
$969$	−8.50802e9	−	4.14238e9i	−0.300397	−	0.146257i
$970$	3.82866e9			0.134693
$971$	1.02047e10	+	1.76750e10i	0.357711	+	0.619574i	0.987578	−	0.157129i	$-0.0502239\pi$
$971$	1.02047e10	+	1.76750e10i	0.357711	+	0.619574i	−0.629867	+	0.776703i	$0.716891\pi$
$972$	−4.06472e9	−	7.04029e9i	−0.141971	−	0.245900i
$973$	1.03699e10	−	1.79612e10i	0.360894	−	0.625086i
$974$	2.42326e9	+	4.19721e9i	0.0840318	+	0.145547i
$975$	−2.97358e9	+	5.15039e9i	−0.102746	+	0.177961i
$976$	−8.64698e9			−0.297708
$977$	4.76770e10			1.63560			0.817802	−	0.575499i	$-0.195192\pi$
$977$	4.76770e10			1.63560			0.817802	+	0.575499i	$0.195192\pi$
$978$	1.18441e9	−	2.05146e9i	0.0404872	−	0.0701258i
$979$	−2.15395e10	+	3.73075e10i	−0.733662	+	1.27074i
$980$	−2.72402e9			−0.0924524
$981$	3.30850e10			1.11889
$982$	2.58887e9	−	4.48405e9i	0.0872408	−	0.151105i
$983$	−2.23886e9	−	3.87781e9i	−0.0751777	−	0.130212i	0.825986	−	0.563691i	$-0.190619\pi$
$983$	−2.23886e9	−	3.87781e9i	−0.0751777	−	0.130212i	−0.901164	+	0.433479i	$0.857286\pi$
$984$	−1.28003e9	+	2.21708e9i	−0.0428290	+	0.0741820i
$985$	−4.83277e9	−	8.37061e9i	−0.161127	−	0.279081i
$986$	2.79065e10	+	4.83355e10i	0.927121	+	1.60582i
$987$	−7.24178e8			−0.0239737
$988$	−1.40787e10	+	9.51033e9i	−0.464422	+	0.313723i
$989$	6.71828e10			2.20837
$990$	4.25000e9	+	7.36121e9i	0.139208	+	0.241116i
$991$	2.02319e10	+	3.50427e10i	0.660358	+	1.14377i	0.980522	+	0.196412i	$0.0629288\pi$
$991$	2.02319e10	+	3.50427e10i	0.660358	+	1.14377i	−0.320163	+	0.947362i	$0.603738\pi$
$992$	−3.60170e9	+	6.23833e9i	−0.117143	+	0.202898i
$993$	4.92795e9	+	8.53546e9i	0.159714	+	0.276633i
$994$	−6.72340e9	+	1.16453e10i	−0.217138	+	0.376095i
$995$	−5.81170e9			−0.187035
$996$	4.37711e9			0.140372
$997$	5.81136e9	−	1.00656e10i	0.185714	−	0.321666i	−0.758103	−	0.652135i	$-0.773874\pi$
$997$	5.81136e9	−	1.00656e10i	0.185714	−	0.321666i	0.943817	+	0.330469i	$0.107207\pi$
$998$	−9.84014e9	+	1.70436e10i	−0.313361	+	0.542757i
$999$	1.06545e10			0.338105

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.8.c.b.7.3	✓	14
19.11	even	3	inner	38.8.c.b.11.3	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.8.c.b.7.3	✓	14	1.1	even	1	trivial
38.8.c.b.11.3	yes	14	19.11	even	3	inner

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 + 6.92820i) q^{2} +(-4.67249 - 8.09299i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-40.1604 - 69.5598i) q^{5} +(37.3799 - 64.7439i) q^{6} -541.879 q^{7} -512.000 q^{8} +(1049.84 - 1818.37i) q^{9} +O(q^{10})\)	\(q+(4.00000 + 6.92820i) q^{2} +(-4.67249 - 8.09299i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-40.1604 - 69.5598i) q^{5} +(37.3799 - 64.7439i) q^{6} -541.879 q^{7} -512.000 q^{8} +(1049.84 - 1818.37i) q^{9} +(321.283 - 556.478i) q^{10} -6300.13 q^{11} +598.079 q^{12} +(4439.59 - 7689.59i) q^{13} +(-2167.52 - 3754.25i) q^{14} +(-375.298 + 650.035i) q^{15} +(-2048.00 - 3547.24i) q^{16} +(-16934.7 - 29331.7i) q^{17} +16797.4 q^{18} +(2106.13 + 29823.4i) q^{19} +5140.53 q^{20} +(2531.92 + 4385.42i) q^{21} +(-25200.5 - 43648.6i) q^{22} +(39665.2 - 68702.2i) q^{23} +(2392.31 + 4143.61i) q^{24} +(35836.8 - 62071.1i) q^{25} +71033.4 q^{26} -40058.8 q^{27} +(17340.1 - 30034.0i) q^{28} +(-102993. + 178390. i) q^{29} -6004.76 q^{30} -219830. q^{31} +(16384.0 - 28377.9i) q^{32} +(29437.3 + 50986.9i) q^{33} +(135477. - 234654. i) q^{34} +(21762.1 + 37693.0i) q^{35} +(67189.5 + 116376. i) q^{36} -265970. q^{37} +(-198198. + 133885. i) q^{38} -82975.7 q^{39} +(20562.1 + 35614.6i) q^{40} +(267530. + 463376. i) q^{41} +(-20255.4 + 35083.4i) q^{42} +(423436. + 733413. i) q^{43} +(201604. - 349189. i) q^{44} -168647. q^{45} +634644. q^{46} +(-71504.7 + 123850. i) q^{47} +(-19138.5 + 33148.9i) q^{48} -529910. q^{49} +573389. q^{50} +(-158254. + 274104. i) q^{51} +(284134. + 492134. i) q^{52} +(-87517.4 + 151585. i) q^{53} +(-160235. - 277536. i) q^{54} +(253016. + 438236. i) q^{55} +277442. q^{56} +(231520. - 156394. i) q^{57} -1.64789e6 q^{58} +(-572410. - 991444. i) q^{59} +(-24019.1 - 41602.2i) q^{60} +(1.05554e6 - 1.82825e6i) q^{61} +(-879321. - 1.52303e6i) q^{62} +(-568884. + 985336. i) q^{63} +262144. q^{64} -713182. q^{65} +(-235498. + 407895. i) q^{66} +(1.28689e6 - 2.22896e6i) q^{67} +2.16764e6 q^{68} -741341. q^{69} +(-174097. + 301544. i) q^{70} +(-1.55094e6 - 2.68631e6i) q^{71} +(-537516. + 931005. i) q^{72} +(-1.53310e6 - 2.65540e6i) q^{73} +(-1.06388e6 - 1.84270e6i) q^{74} -669788. q^{75} +(-1.72038e6 - 837616. i) q^{76} +3.41391e6 q^{77} +(-331903. - 574872. i) q^{78} +(2.46591e6 + 4.27108e6i) q^{79} +(-164497. + 284917. i) q^{80} +(-2.10882e6 - 3.65258e6i) q^{81} +(-2.14024e6 + 3.70701e6i) q^{82} +7.31863e6 q^{83} -324086. q^{84} +(-1.36020e6 + 2.35594e6i) q^{85} +(-3.38749e6 + 5.86731e6i) q^{86} +1.92494e6 q^{87} +3.22567e6 q^{88} +(3.41889e6 - 5.92170e6i) q^{89} +(-674589. - 1.16842e6i) q^{90} +(-2.40572e6 + 4.16683e6i) q^{91} +(2.53857e6 + 4.39694e6i) q^{92} +(1.02715e6 + 1.77908e6i) q^{93} -1.14407e6 q^{94} +(1.98993e6 - 1.34422e6i) q^{95} -306216. q^{96} +(2.97919e6 + 5.16011e6i) q^{97} +(-2.11964e6 - 3.67132e6i) q^{98} +(-6.61411e6 + 1.14560e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 56 q^{2} + 55 q^{3} - 448 q^{4} - 126 q^{5} - 440 q^{6} + 1928 q^{7} - 7168 q^{8} - 4602 q^{9}+O(q^{10}) \) 14 * q + 56 * q^2 + 55 * q^3 - 448 * q^4 - 126 * q^5 - 440 * q^6 + 1928 * q^7 - 7168 * q^8 - 4602 * q^9	\( 14 q + 56 q^{2} + 55 q^{3} - 448 q^{4} - 126 q^{5} - 440 q^{6} + 1928 q^{7} - 7168 q^{8} - 4602 q^{9} + 1008 q^{10} + 646 q^{11} - 7040 q^{12} - 1308 q^{13} + 7712 q^{14} + 8740 q^{15} - 28672 q^{16} + 10528 q^{17} - 73632 q^{18} - 87463 q^{19} + 16128 q^{20} - 30584 q^{21} + 2584 q^{22} - 113822 q^{23} - 28160 q^{24} - 50143 q^{25} - 20928 q^{26} - 319898 q^{27} - 61696 q^{28} + 167706 q^{29} + 139840 q^{30} + 201780 q^{31} + 229376 q^{32} + 377473 q^{33} - 84224 q^{34} - 33168 q^{35} - 294528 q^{36} + 380924 q^{37} - 384064 q^{38} + 1379564 q^{39} + 64512 q^{40} + 66301 q^{41} + 244672 q^{42} + 726564 q^{43} - 20672 q^{44} + 428936 q^{45} - 1821152 q^{46} - 2373788 q^{47} + 225280 q^{48} + 5898846 q^{49} - 802288 q^{50} + 3264054 q^{51} - 83712 q^{52} + 161792 q^{53} - 1279592 q^{54} - 53424 q^{55} - 987136 q^{56} - 4487994 q^{57} + 2683296 q^{58} - 1845767 q^{59} + 559360 q^{60} - 1600418 q^{61} + 807120 q^{62} - 3064040 q^{63} + 3670016 q^{64} + 6534852 q^{65} - 3019784 q^{66} - 8911929 q^{67} - 1347584 q^{68} - 8860208 q^{69} + 265344 q^{70} + 517154 q^{71} + 2356224 q^{72} - 9558049 q^{73} + 1523696 q^{74} - 24621450 q^{75} + 2525120 q^{76} - 9188192 q^{77} + 5518256 q^{78} + 7963520 q^{79} - 516096 q^{80} - 4125855 q^{81} - 530408 q^{82} + 30616886 q^{83} + 3914752 q^{84} + 6973266 q^{85} - 5812512 q^{86} + 25084136 q^{87} - 330752 q^{88} + 11829436 q^{89} + 1715744 q^{90} + 4017336 q^{91} - 7284608 q^{92} + 396810 q^{93} - 37980608 q^{94} + 7058892 q^{95} + 3604480 q^{96} - 8033723 q^{97} + 23595384 q^{98} + 24812606 q^{99}+O(q^{100}) \) 14 * q + 56 * q^2 + 55 * q^3 - 448 * q^4 - 126 * q^5 - 440 * q^6 + 1928 * q^7 - 7168 * q^8 - 4602 * q^9 + 1008 * q^10 + 646 * q^11 - 7040 * q^12 - 1308 * q^13 + 7712 * q^14 + 8740 * q^15 - 28672 * q^16 + 10528 * q^17 - 73632 * q^18 - 87463 * q^19 + 16128 * q^20 - 30584 * q^21 + 2584 * q^22 - 113822 * q^23 - 28160 * q^24 - 50143 * q^25 - 20928 * q^26 - 319898 * q^27 - 61696 * q^28 + 167706 * q^29 + 139840 * q^30 + 201780 * q^31 + 229376 * q^32 + 377473 * q^33 - 84224 * q^34 - 33168 * q^35 - 294528 * q^36 + 380924 * q^37 - 384064 * q^38 + 1379564 * q^39 + 64512 * q^40 + 66301 * q^41 + 244672 * q^42 + 726564 * q^43 - 20672 * q^44 + 428936 * q^45 - 1821152 * q^46 - 2373788 * q^47 + 225280 * q^48 + 5898846 * q^49 - 802288 * q^50 + 3264054 * q^51 - 83712 * q^52 + 161792 * q^53 - 1279592 * q^54 - 53424 * q^55 - 987136 * q^56 - 4487994 * q^57 + 2683296 * q^58 - 1845767 * q^59 + 559360 * q^60 - 1600418 * q^61 + 807120 * q^62 - 3064040 * q^63 + 3670016 * q^64 + 6534852 * q^65 - 3019784 * q^66 - 8911929 * q^67 - 1347584 * q^68 - 8860208 * q^69 + 265344 * q^70 + 517154 * q^71 + 2356224 * q^72 - 9558049 * q^73 + 1523696 * q^74 - 24621450 * q^75 + 2525120 * q^76 - 9188192 * q^77 + 5518256 * q^78 + 7963520 * q^79 - 516096 * q^80 - 4125855 * q^81 - 530408 * q^82 + 30616886 * q^83 + 3914752 * q^84 + 6973266 * q^85 - 5812512 * q^86 + 25084136 * q^87 - 330752 * q^88 + 11829436 * q^89 + 1715744 * q^90 + 4017336 * q^91 - 7284608 * q^92 + 396810 * q^93 - 37980608 * q^94 + 7058892 * q^95 + 3604480 * q^96 - 8033723 * q^97 + 23595384 * q^98 + 24812606 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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