LMFDB - Embedded newform 690.2.m.g.151.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			151.3
Character	$\chi$	$=$	690.151
Dual form			690.2.m.g.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 - 0.755750i) q^{2} +(0.841254 + 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(2.52297 + 0.740810i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.654861 - 0.755750i) q^{2} +(0.841254 + 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(2.52297 + 0.740810i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +(-0.959493 + 0.281733i) q^{10} +(3.03251 - 3.49970i) q^{11} +(-0.654861 + 0.755750i) q^{12} +(-2.32534 + 0.682783i) q^{13} +(-1.09233 - 2.39186i) q^{14} +(0.841254 - 0.540641i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.246429 + 1.71395i) q^{17} +(0.415415 - 0.909632i) q^{18} +(-0.221233 + 1.53871i) q^{19} +(0.841254 + 0.540641i) q^{20} +(1.72194 + 1.98723i) q^{21} -4.63077 q^{22} +(3.48568 - 3.29394i) q^{23} +1.00000 q^{24} +(-0.654861 - 0.755750i) q^{25} +(2.03879 + 1.31025i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(-1.09233 + 2.39186i) q^{28} +(0.675716 + 4.69971i) q^{29} +(-0.959493 - 0.281733i) q^{30} +(0.508109 - 0.326542i) q^{31} +(0.415415 + 0.909632i) q^{32} +(4.44319 - 1.30464i) q^{33} +(1.13394 - 1.30864i) q^{34} +(1.72194 - 1.98723i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-0.955451 - 2.09215i) q^{37} +(1.30776 - 0.840445i) q^{38} +(-2.32534 - 0.682783i) q^{39} +(-0.142315 - 0.989821i) q^{40} +(3.21189 - 7.03307i) q^{41} +(0.374214 - 2.60272i) q^{42} +(5.14961 + 3.30945i) q^{43} +(3.03251 + 3.49970i) q^{44} +1.00000 q^{45} +(-4.77203 - 0.477227i) q^{46} +3.51124 q^{47} +(-0.654861 - 0.755750i) q^{48} +(-0.0722037 - 0.0464025i) q^{49} +(-0.142315 + 0.989821i) q^{50} +(-0.719323 + 1.57510i) q^{51} +(-0.344902 - 2.39885i) q^{52} +(7.92060 + 2.32570i) q^{53} +(0.841254 - 0.540641i) q^{54} +(-1.92369 - 4.21230i) q^{55} +(2.52297 - 0.740810i) q^{56} +(-1.01800 + 1.17484i) q^{57} +(3.10930 - 3.58832i) q^{58} +(-3.27844 + 0.962636i) q^{59} +(0.415415 + 0.909632i) q^{60} +(1.54224 - 0.991137i) q^{61} +(-0.579524 - 0.170164i) q^{62} +(0.374214 + 2.60272i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.344902 + 2.39885i) q^{65} +(-3.89565 - 2.50358i) q^{66} +(-0.0237093 - 0.0273620i) q^{67} -1.73158 q^{68} +(4.71318 - 0.886540i) q^{69} -2.62948 q^{70} +(-10.3059 - 11.8936i) q^{71} +(0.841254 + 0.540641i) q^{72} +(-1.31721 + 9.16139i) q^{73} +(-0.955451 + 2.09215i) q^{74} +(-0.142315 - 0.989821i) q^{75} +(-1.49156 - 0.437963i) q^{76} +(10.2435 - 6.58313i) q^{77} +(1.00676 + 2.20451i) q^{78} +(-4.05050 + 1.18933i) q^{79} +(-0.654861 + 0.755750i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-7.41858 + 2.17829i) q^{82} +(3.05120 + 6.68119i) q^{83} +(-2.21206 + 1.42160i) q^{84} +(1.66144 + 0.487842i) q^{85} +(-0.871159 - 6.05905i) q^{86} +(-1.97240 + 4.31896i) q^{87} +(0.659028 - 4.58364i) q^{88} +(6.01448 + 3.86527i) q^{89} +(-0.654861 - 0.755750i) q^{90} -6.37258 q^{91} +(2.76435 + 3.91898i) q^{92} +0.603990 q^{93} +(-2.29937 - 2.65362i) q^{94} +(1.30776 + 0.840445i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(0.932704 - 2.04234i) q^{97} +(0.0122147 + 0.0849551i) q^{98} +(4.44319 + 1.30464i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{11}\right)$

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 $

$2$	−0.654861	−	0.755750i	−0.463056	−	0.534396i
$2$	−0.654861	−	0.755750i	−0.463056	−	0.534396i
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$4$	−0.142315	+	0.989821i	−0.0711574	+	0.494911i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$6$	−0.142315	−	0.989821i	−0.0580998	−	0.404093i
$7$	2.52297	+	0.740810i	0.953593	+	0.280000i	0.721282	−	0.692642i	$-0.243553\pi$
$7$	2.52297	+	0.740810i	0.953593	+	0.280000i	0.232311	+	0.972642i	$0.425371\pi$
$8$	0.841254	−	0.540641i	0.297428	−	0.191145i
$9$	0.415415	+	0.909632i	0.138472	+	0.303211i
$10$	−0.959493	+	0.281733i	−0.303418	+	0.0890917i
$11$	3.03251	−	3.49970i	0.914336	−	1.05520i	−0.0839376	−	0.996471i	$-0.526750\pi$
$11$	3.03251	−	3.49970i	0.914336	−	1.05520i	0.998274	−	0.0587294i	$-0.0187049\pi$
$12$	−0.654861	+	0.755750i	−0.189042	+	0.218166i
$13$	−2.32534	+	0.682783i	−0.644934	+	0.189370i	−0.587812	−	0.808997i	$-0.700011\pi$
$13$	−2.32534	+	0.682783i	−0.644934	+	0.189370i	−0.0571221	+	0.998367i	$0.518192\pi$
$14$	−1.09233	−	2.39186i	−0.291936	−	0.639252i
$15$	0.841254	−	0.540641i	0.217211	−	0.139593i
$16$	−0.959493	−	0.281733i	−0.239873	−	0.0704331i
$17$	0.246429	+	1.71395i	0.0597678	+	0.415694i	0.997637	+	0.0687053i	$0.0218868\pi$
$17$	0.246429	+	1.71395i	0.0597678	+	0.415694i	−0.937869	+	0.346989i	$0.887204\pi$
$18$	0.415415	−	0.909632i	0.0979143	−	0.214402i
$19$	−0.221233	+	1.53871i	−0.0507544	+	0.353005i	0.948580	+	0.316536i	$0.102520\pi$
$19$	−0.221233	+	1.53871i	−0.0507544	+	0.353005i	−0.999335	+	0.0364683i	$0.988389\pi$
$20$	0.841254	+	0.540641i	0.188110	+	0.120891i
$21$	1.72194	+	1.98723i	0.375759	+	0.433649i
$22$	−4.63077			−0.987284
$23$	3.48568	−	3.29394i	0.726814	−	0.686834i
$23$	3.48568	−	3.29394i	0.726814	−	0.686834i
$24$	1.00000			0.204124
$25$	−0.654861	−	0.755750i	−0.130972	−	0.151150i
$26$	2.03879	+	1.31025i	0.399839	+	0.256961i
$27$	−0.142315	+	0.989821i	−0.0273885	+	0.190491i
$28$	−1.09233	+	2.39186i	−0.206430	+	0.452019i
$29$	0.675716	+	4.69971i	0.125477	+	0.872713i	0.951186	+	0.308617i	$0.0998662\pi$
$29$	0.675716	+	4.69971i	0.125477	+	0.872713i	−0.825709	+	0.564096i	$0.809225\pi$
$30$	−0.959493	−	0.281733i	−0.175179	−	0.0514371i
$31$	0.508109	−	0.326542i	0.0912591	−	0.0586486i	−0.494215	−	0.869339i	$-0.664545\pi$
$31$	0.508109	−	0.326542i	0.0912591	−	0.0586486i	0.585474	+	0.810691i	$0.300908\pi$
$32$	0.415415	+	0.909632i	0.0734357	+	0.160802i
$33$	4.44319	−	1.30464i	0.773461	−	0.227109i
$34$	1.13394	−	1.30864i	0.194469	−	0.224430i
$35$	1.72194	−	1.98723i	0.291062	−	0.335903i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	−0.955451	−	2.09215i	−0.157075	−	0.343947i	0.814690	−	0.579897i	$-0.196907\pi$
$37$	−0.955451	−	2.09215i	−0.157075	−	0.343947i	−0.971765	+	0.235950i	$0.924180\pi$
$38$	1.30776	−	0.840445i	0.212146	−	0.136338i
$39$	−2.32534	−	0.682783i	−0.372353	−	0.109333i
$40$	−0.142315	−	0.989821i	−0.0225020	−	0.156505i
$41$	3.21189	−	7.03307i	0.501614	−	1.09838i	−0.474328	−	0.880348i	$-0.657309\pi$
$41$	3.21189	−	7.03307i	0.501614	−	1.09838i	0.975942	−	0.218032i	$-0.0699639\pi$
$42$	0.374214	−	2.60272i	0.0577425	−	0.401608i
$43$	5.14961	+	3.30945i	0.785308	+	0.504687i	0.870791	−	0.491653i	$-0.163607\pi$
$43$	5.14961	+	3.30945i	0.785308	+	0.504687i	−0.0854833	+	0.996340i	$0.527243\pi$
$44$	3.03251	+	3.49970i	0.457168	+	0.527600i
$45$	1.00000			0.149071
$46$	−4.77203	−	0.477227i	−0.703597	−	0.0703633i
$47$	3.51124			0.512167			0.256083	−	0.966655i	$-0.417568\pi$
$47$	3.51124			0.512167			0.256083	+	0.966655i	$0.417568\pi$
$48$	−0.654861	−	0.755750i	−0.0945210	−	0.109083i
$49$	−0.0722037	−	0.0464025i	−0.0103148	−	0.00662893i
$50$	−0.142315	+	0.989821i	−0.0201264	+	0.139982i
$51$	−0.719323	+	1.57510i	−0.100725	+	0.220558i
$52$	−0.344902	−	2.39885i	−0.0478293	−	0.332660i
$53$	7.92060	+	2.32570i	1.08798	+	0.319459i	0.776066	−	0.630651i	$-0.217212\pi$
$53$	7.92060	+	2.32570i	1.08798	+	0.319459i	0.311912	+	0.950111i	$0.399030\pi$
$54$	0.841254	−	0.540641i	0.114480	−	0.0735719i
$55$	−1.92369	−	4.21230i	−0.259391	−	0.567986i
$56$	2.52297	−	0.740810i	0.337146	−	0.0989950i
$57$	−1.01800	+	1.17484i	−0.134838	+	0.155611i
$58$	3.10930	−	3.58832i	0.408271	−	0.471170i
$59$	−3.27844	+	0.962636i	−0.426816	+	0.125324i	−0.488084	−	0.872797i	$-0.662304\pi$
$59$	−3.27844	+	0.962636i	−0.426816	+	0.125324i	0.0612676	+	0.998121i	$0.480486\pi$
$60$	0.415415	+	0.909632i	0.0536298	+	0.117433i
$61$	1.54224	−	0.991137i	0.197463	−	0.126902i	−0.438173	−	0.898891i	$-0.644374\pi$
$61$	1.54224	−	0.991137i	0.197463	−	0.126902i	0.635636	+	0.771989i	$0.280738\pi$
$62$	−0.579524	−	0.170164i	−0.0735997	−	0.0216108i
$63$	0.374214	+	2.60272i	0.0471466	+	0.327912i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	−0.344902	+	2.39885i	−0.0427798	+	0.297540i
$66$	−3.89565	−	2.50358i	−0.479522	−	0.308170i
$67$	−0.0237093	−	0.0273620i	−0.00289655	−	0.00334280i	0.754299	−	0.656531i	$-0.227977\pi$
$67$	−0.0237093	−	0.0273620i	−0.00289655	−	0.00334280i	−0.757196	+	0.653188i	$0.773431\pi$
$68$	−1.73158			−0.209985
$69$	4.71318	−	0.886540i	0.567400	−	0.106727i
$70$	−2.62948			−0.314283
$71$	−10.3059	−	11.8936i	−1.22309	−	1.41152i	−0.881844	−	0.471541i	$-0.843698\pi$
$71$	−10.3059	−	11.8936i	−1.22309	−	1.41152i	−0.341242	−	0.939976i	$-0.610848\pi$
$72$	0.841254	+	0.540641i	0.0991427	+	0.0637151i
$73$	−1.31721	+	9.16139i	−0.154168	+	1.07226i	0.754968	+	0.655761i	$0.227652\pi$
$73$	−1.31721	+	9.16139i	−0.154168	+	1.07226i	−0.909136	+	0.416499i	$0.863257\pi$
$74$	−0.955451	+	2.09215i	−0.111069	+	0.243207i
$75$	−0.142315	−	0.989821i	−0.0164331	−	0.114295i
$76$	−1.49156	−	0.437963i	−0.171094	−	0.0502378i
$77$	10.2435	−	6.58313i	1.16736	−	0.750217i
$78$	1.00676	+	2.20451i	0.113994	+	0.249611i
$79$	−4.05050	+	1.18933i	−0.455716	+	0.133810i	−0.501531	−	0.865140i	$-0.667230\pi$
$79$	−4.05050	+	1.18933i	−0.455716	+	0.133810i	0.0458149	+	0.998950i	$0.485412\pi$
$80$	−0.654861	+	0.755750i	−0.0732157	+	0.0844954i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	−7.41858	+	2.17829i	−0.819245	+	0.240552i
$83$	3.05120	+	6.68119i	0.334913	+	0.733356i	0.999909	−	0.0134903i	$-0.00429423\pi$
$83$	3.05120	+	6.68119i	0.334913	+	0.733356i	−0.664996	+	0.746847i	$0.731567\pi$
$84$	−2.21206	+	1.42160i	−0.241356	+	0.155110i
$85$	1.66144	+	0.487842i	0.180208	+	0.0529139i
$86$	−0.871159	−	6.05905i	−0.0939395	−	0.653364i
$87$	−1.97240	+	4.31896i	−0.211464	+	0.463041i
$88$	0.659028	−	4.58364i	0.0702526	−	0.488617i
$89$	6.01448	+	3.86527i	0.637534	+	0.409718i	0.819092	−	0.573662i	$-0.194478\pi$
$89$	6.01448	+	3.86527i	0.637534	+	0.409718i	−0.181558	+	0.983380i	$0.558114\pi$
$90$	−0.654861	−	0.755750i	−0.0690284	−	0.0796630i
$91$	−6.37258			−0.668028
$92$	2.76435	+	3.91898i	0.288203	+	0.408581i
$93$	0.603990			0.0626309
$94$	−2.29937	−	2.65362i	−0.237162	−	0.273700i
$95$	1.30776	+	0.840445i	0.134173	+	0.0862278i
$96$	−0.142315	+	0.989821i	−0.0145249	+	0.101023i
$97$	0.932704	−	2.04234i	0.0947017	−	0.207368i	−0.856353	−	0.516391i	$-0.827275\pi$
$97$	0.932704	−	2.04234i	0.0947017	−	0.207368i	0.951054	+	0.309024i	$0.100002\pi$
$98$	0.0122147	+	0.0849551i	0.00123387	+	0.00858176i
$99$	4.44319	+	1.30464i	0.446558	+	0.131121i
$100$	0.841254	−	0.540641i	0.0841254	−	0.0540641i
$101$	−4.49613	−	9.84516i	−0.447382	−	0.979630i	−0.990184	−	0.139769i	$-0.955364\pi$
$101$	−4.49613	−	9.84516i	−0.447382	−	0.979630i	0.542802	−	0.839861i	$-0.317363\pi$
$102$	1.66144	−	0.487842i	0.164507	−	0.0483035i
$103$	−7.13350	+	8.23250i	−0.702885	+	0.811172i	−0.989139	−	0.146981i	$-0.953044\pi$
$103$	−7.13350	+	8.23250i	−0.702885	+	0.811172i	0.286254	+	0.958154i	$0.407590\pi$
$104$	−1.58706	+	1.83157i	−0.155624	+	0.179600i
$105$	2.52297	−	0.740810i	0.246217	−	0.0722957i
$106$	−3.42925	−	7.50900i	−0.333078	−	0.729339i
$107$	−2.37886	+	1.52880i	−0.229973	+	0.147795i	−0.650553	−	0.759461i	$-0.725463\pi$
$107$	−2.37886	+	1.52880i	−0.229973	+	0.147795i	0.420580	+	0.907255i	$0.361827\pi$
$108$	−0.959493	−	0.281733i	−0.0923273	−	0.0271097i
$109$	−1.60853	−	11.1876i	−0.154069	−	1.07158i	−0.909308	−	0.416125i	$-0.863388\pi$
$109$	−1.60853	−	11.1876i	−0.154069	−	1.07158i	0.755238	−	0.655450i	$-0.227521\pi$
$110$	−1.92369	+	4.21230i	−0.183417	+	0.401627i
$111$	0.327323	−	2.27658i	0.0310681	−	0.216084i
$112$	−2.21206	−	1.42160i	−0.209020	−	0.134329i
$113$	−6.05205	−	6.98443i	−0.569329	−	0.657040i	0.395947	−	0.918273i	$-0.370416\pi$
$113$	−6.05205	−	6.98443i	−0.569329	−	0.657040i	−0.965276	+	0.261233i	$0.915871\pi$
$114$	1.55453			0.145595
$115$	−1.54827	−	4.53904i	−0.144377	−	0.423267i
$116$	−4.74803			−0.440844
$117$	−1.58706	−	1.83157i	−0.146724	−	0.169329i
$118$	2.87443	+	1.84728i	0.264613	+	0.170056i
$119$	−0.647981	+	4.50680i	−0.0594003	+	0.413138i
$120$	0.415415	−	0.909632i	0.0379220	−	0.0830377i
$121$	−1.48634	−	10.3377i	−0.135122	−	0.939795i
$122$	−1.75900	−	0.516490i	−0.159253	−	0.0467608i
$123$	6.50438	−	4.18011i	0.586480	−	0.376908i
$124$	0.250907	+	0.549409i	0.0225321	+	0.0493384i
$125$	−0.959493	+	0.281733i	−0.0858197	+	0.0251989i
$126$	1.72194	−	1.98723i	0.153403	−	0.177036i
$127$	−8.59219	+	9.91591i	−0.762433	+	0.879895i	−0.995711	−	0.0925151i	$-0.970509\pi$
$127$	−8.59219	+	9.91591i	−0.762433	+	0.879895i	0.233278	+	0.972410i	$0.425055\pi$
$128$	−0.959493	+	0.281733i	−0.0848080	+	0.0249019i
$129$	2.54290	+	5.56818i	0.223890	+	0.490251i
$130$	2.03879	−	1.31025i	0.178814	−	0.114917i
$131$	1.18852	+	0.348980i	0.103841	+	0.0304905i	0.333240	−	0.942842i	$-0.391858\pi$
$131$	1.18852	+	0.348980i	0.103841	+	0.0304905i	−0.229399	+	0.973332i	$0.573676\pi$
$132$	0.659028	+	4.58364i	0.0573610	+	0.398954i
$133$	−1.69806	+	3.71823i	−0.147240	+	0.322411i
$134$	−0.00515253	+	0.0358366i	−0.000445110	+	0.00309581i
$135$	0.841254	+	0.540641i	0.0724036	+	0.0465310i
$136$	1.13394	+	1.30864i	0.0972347	+	0.112215i
$137$	−11.0294			−0.942309			−0.471155	−	0.882051i	$-0.656163\pi$
$137$	−11.0294			−0.942309			−0.471155	+	0.882051i	$0.656163\pi$
$138$	−3.75648	−	2.98142i	−0.319773	−	0.253796i
$139$	1.80556			0.153146			0.0765730	−	0.997064i	$-0.475602\pi$
$139$	1.80556			0.153146			0.0765730	+	0.997064i	$0.475602\pi$
$140$	1.72194	+	1.98723i	0.145531	+	0.167952i
$141$	2.95384	+	1.89832i	0.248758	+	0.159867i
$142$	−2.23969	+	15.5774i	−0.187950	+	1.30722i
$143$	−4.66209	+	10.2086i	−0.389864	+	0.853683i
$144$	−0.142315	−	0.989821i	−0.0118596	−	0.0824851i
$145$	4.55570	+	1.33768i	0.378331	+	0.111088i
$146$	7.78631	−	5.00396i	0.644399	−	0.414130i
$147$	−0.0356545	−	0.0780726i	−0.00294074	−	0.00643932i
$148$	2.20683	−	0.647983i	0.181400	−	0.0532639i
$149$	1.27596	−	1.47253i	0.104530	−	0.120634i	−0.701074	−	0.713089i	$-0.747296\pi$
$149$	1.27596	−	1.47253i	0.104530	−	0.120634i	0.805604	+	0.592455i	$0.201841\pi$
$150$	−0.654861	+	0.755750i	−0.0534692	+	0.0617067i
$151$	−18.7992	+	5.51994i	−1.52986	+	0.449206i	−0.935007	−	0.354630i	$-0.884607\pi$
$151$	−18.7992	+	5.51994i	−1.52986	+	0.449206i	−0.594850	+	0.803837i	$0.702789\pi$
$152$	0.645777	+	1.41405i	0.0523794	+	0.114695i
$153$	−1.45670	+	0.936161i	−0.117767	+	0.0756842i
$154$	−11.6833	−	3.43052i	−0.941467	−	0.276440i
$155$	−0.0859568	−	0.597843i	−0.00690421	−	0.0480199i
$156$	1.00676	−	2.20451i	0.0806056	−	0.176502i
$157$	−1.58238	+	11.0057i	−0.126288	+	0.878352i	0.823913	+	0.566716i	$0.191786\pi$
$157$	−1.58238	+	11.0057i	−0.126288	+	0.878352i	−0.950201	+	0.311637i	$0.899123\pi$
$158$	3.55135	+	2.28231i	0.282530	+	0.181571i
$159$	5.40587	+	6.23870i	0.428713	+	0.494761i
$160$	1.00000			0.0790569
$161$	11.2344	−	5.72828i	0.885398	−	0.451452i
$162$	1.00000			0.0785674
$163$	−6.78365	−	7.82875i	−0.531337	−	0.613195i	0.425096	−	0.905148i	$-0.360240\pi$
$163$	−6.78365	−	7.82875i	−0.531337	−	0.613195i	−0.956433	+	0.291953i	$0.905695\pi$
$164$	6.50438	+	4.18011i	0.507907	+	0.326412i
$165$	0.659028	−	4.58364i	0.0513052	−	0.356836i
$166$	3.05120	−	6.68119i	0.236819	−	0.518561i
$167$	2.59006	+	18.0143i	0.200425	+	1.39399i	0.803026	+	0.595944i	$0.203222\pi$
$167$	2.59006	+	18.0143i	0.200425	+	1.39399i	−0.602601	+	0.798043i	$0.705869\pi$
$168$	2.52297	+	0.740810i	0.194651	+	0.0571548i
$169$	−5.99526	+	3.85292i	−0.461174	+	0.296379i
$170$	−0.719323	−	1.57510i	−0.0551696	−	0.120804i
$171$	−1.49156	+	0.437963i	−0.114063	+	0.0334919i
$172$	−4.00863	+	4.62621i	−0.305655	+	0.352745i
$173$	−15.7674	+	18.1965i	−1.19877	+	1.38346i	−0.294971	+	0.955506i	$0.595310\pi$
$173$	−15.7674	+	18.1965i	−1.19877	+	1.38346i	−0.903802	+	0.427951i	$0.859235\pi$
$174$	4.55570	−	1.33768i	0.345367	−	0.101409i
$175$	−1.09233	−	2.39186i	−0.0825721	−	0.180808i
$176$	−3.89565	+	2.50358i	−0.293646	+	0.188715i
$177$	−3.27844	−	0.962636i	−0.246422	−	0.0723561i
$178$	−1.01747	−	7.07666i	−0.0762626	−	0.530418i
$179$	−4.45101	+	9.74635i	−0.332684	+	0.728477i	−0.999865	−	0.0164189i	$-0.994773\pi$
$179$	−4.45101	+	9.74635i	−0.332684	+	0.728477i	0.667181	+	0.744896i	$0.267501\pi$
$180$	−0.142315	+	0.989821i	−0.0106075	+	0.0737769i
$181$	−2.49370	−	1.60260i	−0.185355	−	0.119121i	0.444672	−	0.895693i	$-0.353320\pi$
$181$	−2.49370	−	1.60260i	−0.185355	−	0.119121i	−0.630028	+	0.776573i	$0.716956\pi$
$182$	4.17315	+	4.81608i	0.309335	+	0.356991i
$183$	1.83326			0.135519
$184$	1.15150	−	4.65554i	0.0848897	−	0.343211i
$185$	−2.29999			−0.169099
$186$	−0.395530	−	0.456465i	−0.0290016	−	0.0334697i
$187$	6.74562	+	4.33515i	0.493289	+	0.317017i
$188$	−0.499701	+	3.47550i	−0.0364445	+	0.253477i
$189$	−1.09233	+	2.39186i	−0.0794550	+	0.173982i
$190$	−0.221233	−	1.53871i	−0.0160499	−	0.111630i
$191$	−12.8582	−	3.77550i	−0.930385	−	0.273186i	−0.218787	−	0.975773i	$-0.570210\pi$
$191$	−12.8582	−	3.77550i	−0.930385	−	0.273186i	−0.711598	+	0.702587i	$0.752028\pi$
$192$	0.841254	−	0.540641i	0.0607122	−	0.0390174i
$193$	5.12498	+	11.2221i	0.368904	+	0.807787i	0.999498	+	0.0316743i	$0.0100839\pi$
$193$	5.12498	+	11.2221i	0.368904	+	0.807787i	−0.630594	+	0.776113i	$0.717189\pi$
$194$	−2.15429	+	0.632555i	−0.154669	+	0.0454148i
$195$	−1.58706	+	1.83157i	−0.113652	+	0.131161i
$196$	0.0562059	−	0.0648650i	0.00401470	−	0.00463322i
$197$	13.9884	−	4.10735i	0.996629	−	0.292637i	0.257557	−	0.966263i	$-0.417082\pi$
$197$	13.9884	−	4.10735i	0.996629	−	0.292637i	0.739072	+	0.673626i	$0.235264\pi$
$198$	−1.92369	−	4.21230i	−0.136711	−	0.299355i
$199$	−14.1739	+	9.10902i	−1.00476	+	0.645722i	−0.936032	−	0.351914i	$-0.885531\pi$
$199$	−14.1739	+	9.10902i	−1.00476	+	0.645722i	−0.0687300	+	0.997635i	$0.521895\pi$
$200$	−0.959493	−	0.281733i	−0.0678464	−	0.0199215i
$201$	−0.00515253	−	0.0358366i	−0.000363431	−	0.00252772i
$202$	−4.49613	+	9.84516i	−0.316347	+	0.692703i
$203$	−1.77678	+	12.3578i	−0.124706	+	0.867347i
$204$	−1.45670	−	0.936161i	−0.101989	−	0.0655444i
$205$	−5.06323	−	5.84328i	−0.353632	−	0.408113i
$206$	10.8932			0.758962
$207$	4.44428	+	1.80233i	0.308899	+	0.125271i
$208$	2.42351			0.168040
$209$	4.71414	+	5.44041i	0.326084	+	0.376321i
$210$	−2.21206	−	1.42160i	−0.152647	−	0.0981001i
$211$	−0.546521	+	3.80113i	−0.0376240	+	0.261681i	−0.999948	−	0.0102256i	$-0.996745\pi$
$211$	−0.546521	+	3.80113i	−0.0376240	+	0.261681i	0.962324	+	0.271906i	$0.0876541\pi$
$212$	−3.42925	+	7.50900i	−0.235522	+	0.515720i
$213$	−2.23969	−	15.5774i	−0.153461	−	1.06734i
$214$	2.71322	+	0.796672i	0.185472	+	0.0544594i
$215$	5.14961	−	3.30945i	0.351200	−	0.225703i
$216$	0.415415	+	0.909632i	0.0282654	+	0.0618926i
$217$	1.52385	−	0.447442i	0.103446	−	0.0303744i
$218$	−7.40164	+	8.54195i	−0.501302	+	0.578534i
$219$	−6.06113	+	6.99492i	−0.409573	+	0.472673i
$220$	4.44319	−	1.30464i	0.299560	−	0.0879588i
$221$	−1.74329	−	3.81727i	−0.117266	−	0.256777i
$222$	−1.93488	+	1.24347i	−0.129860	+	0.0834562i
$223$	19.8896	+	5.84013i	1.33191	+	0.391084i	0.868776	−	0.495205i	$-0.164907\pi$
$223$	19.8896	+	5.84013i	1.33191	+	0.391084i	0.463133	+	0.886289i	$0.346725\pi$
$224$	0.374214	+	2.60272i	0.0250032	+	0.173901i
$225$	0.415415	−	0.909632i	0.0276943	−	0.0606421i
$226$	−1.31524	+	9.14766i	−0.0874882	+	0.608494i
$227$	−1.49944	−	0.963629i	−0.0995211	−	0.0639583i	0.489934	−	0.871760i	$-0.337021\pi$
$227$	−1.49944	−	0.963629i	−0.0995211	−	0.0639583i	−0.589455	+	0.807801i	$0.700657\pi$
$228$	−1.01800	−	1.17484i	−0.0674189	−	0.0778056i
$229$	−2.21141			−0.146134			−0.0730671	−	0.997327i	$-0.523279\pi$
$229$	−2.21141			−0.146134			−0.0730671	+	0.997327i	$0.523279\pi$
$230$	−2.41647	+	4.14254i	−0.159338	+	0.273151i
$231$	12.1765			0.801157
$232$	3.10930	+	3.58832i	0.204136	+	0.235585i
$233$	−17.5448	−	11.2754i	−1.14940	−	0.738674i	−0.179880	−	0.983689i	$-0.557571\pi$
$233$	−17.5448	−	11.2754i	−1.14940	−	0.738674i	−0.969519	+	0.245015i	$0.921207\pi$
$234$	−0.344902	+	2.39885i	−0.0225469	+	0.156817i
$235$	1.45862	−	3.19393i	0.0951499	−	0.208349i
$236$	−0.486267	−	3.38206i	−0.0316533	−	0.220154i
$237$	−4.05050	−	1.18933i	−0.263108	−	0.0772555i
$238$	3.83035	−	2.46162i	0.248285	−	0.159563i
$239$	−11.8931	−	26.0422i	−0.769300	−	1.68453i	−0.728188	−	0.685378i	$-0.759637\pi$
$239$	−11.8931	−	26.0422i	−0.769300	−	1.68453i	−0.0411123	−	0.999155i	$-0.513090\pi$
$240$	−0.959493	+	0.281733i	−0.0619350	+	0.0181858i
$241$	−10.1465	+	11.7097i	−0.653594	+	0.754287i	−0.981717	−	0.190348i	$-0.939038\pi$
$241$	−10.1465	+	11.7097i	−0.653594	+	0.754287i	0.328123	+	0.944635i	$0.393584\pi$
$242$	−6.83940	+	7.89308i	−0.439653	+	0.507387i
$243$	−0.959493	+	0.281733i	−0.0615515	+	0.0180732i
$244$	0.761565	+	1.66759i	0.0487542	+	0.106757i
$245$	−0.0722037	+	0.0464025i	−0.00461293	+	0.00296455i
$246$	−7.41858	−	2.17829i	−0.472992	−	0.138883i
$247$	−0.536162	−	3.72909i	−0.0341152	−	0.237276i
$248$	0.250907	−	0.549409i	0.0159326	−	0.0348875i
$249$	−1.04529	+	7.27018i	−0.0662428	+	0.460729i
$250$	0.841254	+	0.540641i	0.0532055	+	0.0341931i
$251$	2.38739	+	2.75519i	0.150691	+	0.173906i	0.826076	−	0.563559i	$-0.190568\pi$
$251$	2.38739	+	2.75519i	0.150691	+	0.173906i	−0.675385	+	0.737465i	$0.736023\pi$
$252$	−2.62948			−0.165642
$253$	−0.957463	−	22.1878i	−0.0601952	−	1.39493i
$254$	13.1206			0.823262
$255$	1.13394	+	1.30864i	0.0710102	+	0.0819501i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	2.51404	−	17.4855i	0.156822	−	1.09072i	−0.747622	−	0.664124i	$-0.768805\pi$
$257$	2.51404	−	17.4855i	0.156822	−	1.09072i	0.904444	−	0.426593i	$-0.140286\pi$
$258$	2.54290	−	5.56818i	0.158314	−	0.346660i
$259$	−0.860690	−	5.98623i	−0.0534807	−	0.371966i
$260$	−2.32534	−	0.682783i	−0.144212	−	0.0423444i
$261$	−3.99430	+	2.56698i	−0.247241	+	0.158892i
$262$	−0.514571	−	1.12675i	−0.0317903	−	0.0696110i
$263$	−27.9776	+	8.21496i	−1.72517	+	0.506556i	−0.985969	−	0.166927i	$-0.946616\pi$
$263$	−27.9776	+	8.21496i	−1.72517	+	0.506556i	−0.739203	+	0.673483i	$0.764797\pi$
$264$	3.03251	−	3.49970i	0.186638	−	0.215392i
$265$	5.40587	−	6.23870i	0.332080	−	0.383241i
$266$	3.92204	−	1.15162i	0.240476	−	0.0706100i
$267$	2.96998	+	6.50335i	0.181760	+	0.397998i
$268$	0.0304577	−	0.0195740i	0.00186050	−	0.00119567i
$269$	−29.1567	−	8.56118i	−1.77771	−	0.521984i	−0.782761	−	0.622322i	$-0.786189\pi$
$269$	−29.1567	−	8.56118i	−1.77771	−	0.521984i	−0.994953	+	0.100338i	$0.968008\pi$
$270$	−0.142315	−	0.989821i	−0.00866101	−	0.0602386i
$271$	4.44397	−	9.73094i	0.269952	−	0.591112i	−0.725301	−	0.688432i	$-0.758300\pi$
$271$	4.44397	−	9.73094i	0.269952	−	0.591112i	0.995253	+	0.0973192i	$0.0310268\pi$
$272$	0.246429	−	1.71395i	0.0149420	−	0.103924i
$273$	−5.36096	−	3.44528i	−0.324460	−	0.208518i
$274$	7.22275	+	8.33550i	0.436342	+	0.503566i
$275$	−4.63077			−0.279246
$276$	0.206761	+	4.79137i	0.0124455	+	0.288407i
$277$	31.1418			1.87113			0.935565	−	0.353153i	$-0.114891\pi$
$277$	31.1418			1.87113			0.935565	+	0.353153i	$0.114891\pi$
$278$	−1.18239	−	1.36455i	−0.0709153	−	0.0818406i
$279$	0.508109	+	0.326542i	0.0304197	+	0.0195495i
$280$	0.374214	−	2.60272i	0.0223636	−	0.155542i
$281$	10.6853	−	23.3975i	0.637429	−	1.39578i	−0.264709	−	0.964328i	$-0.585276\pi$
$281$	10.6853	−	23.3975i	0.637429	−	1.39578i	0.902138	−	0.431447i	$-0.141997\pi$
$282$	−0.499701	−	3.47550i	−0.0297568	−	0.206963i
$283$	23.8589	+	7.00561i	1.41827	+	0.416440i	0.898916	−	0.438122i	$-0.144356\pi$
$283$	23.8589	+	7.00561i	1.41827	+	0.416440i	0.519350	+	0.854562i	$0.326174\pi$
$284$	13.2393	−	8.50836i	0.785606	−	0.504879i
$285$	0.645777	+	1.41405i	0.0382525	+	0.0837613i
$286$	10.7681	−	3.16181i	0.636733	−	0.186962i
$287$	13.3137	−	15.3648i	0.785882	−	0.906956i
$288$	−0.654861	+	0.755750i	−0.0385880	+	0.0445330i
$289$	13.4345	−	3.94472i	0.790263	−	0.232042i
$290$	−1.97240	−	4.31896i	−0.115824	−	0.253618i
$291$	1.88881	−	1.21386i	0.110724	−	0.0711580i
$292$	−8.88069	−	2.60760i	−0.519703	−	0.152599i
$293$	−3.41890	−	23.7790i	−0.199734	−	1.38918i	−0.805055	−	0.593200i	$-0.797864\pi$
$293$	−3.41890	−	23.7790i	−0.199734	−	1.38918i	0.605321	−	0.795981i	$-0.293045\pi$
$294$	−0.0356545	+	0.0780726i	−0.00207942	+	0.00455328i
$295$	−0.486267	+	3.38206i	−0.0283116	+	0.196911i
$296$	−1.93488	−	1.24347i	−0.112462	−	0.0722752i
$297$	3.03251	+	3.49970i	0.175964	+	0.203073i
$298$	−1.94844			−0.112870
$299$	−5.85635	+	10.0395i	−0.338682	+	0.580600i
$300$	1.00000			0.0577350
$301$	10.5406	+	12.1645i	0.607552	+	0.701152i
$302$	16.4825	+	10.5927i	0.948464	+	0.609541i
$303$	1.54031	−	10.7131i	0.0884883	−	0.615450i
$304$	0.645777	−	1.41405i	0.0370378	−	0.0811016i
$305$	−0.260900	−	1.81460i	−0.0149391	−	0.103904i
$306$	1.66144	+	0.487842i	0.0949780	+	0.0278880i
$307$	28.5463	−	18.3456i	1.62922	−	1.04704i	0.679632	−	0.733553i	$-0.262140\pi$
$307$	28.5463	−	18.3456i	1.62922	−	1.04704i	0.949593	−	0.313486i	$-0.101497\pi$
$308$	5.05831	+	11.0762i	0.288224	+	0.631123i
$309$	−10.4519	+	3.06896i	−0.594588	+	0.174587i
$310$	−0.395530	+	0.456465i	−0.0224646	+	0.0259255i
$311$	−8.50781	+	9.81853i	−0.482433	+	0.556758i	−0.943828	−	0.330437i	$-0.892804\pi$
$311$	−8.50781	+	9.81853i	−0.482433	+	0.556758i	0.461395	+	0.887195i	$0.347349\pi$
$312$	−2.32534	+	0.682783i	−0.131647	+	0.0386550i
$313$	−9.11583	−	19.9609i	−0.515257	−	1.12826i	−0.971204	−	0.238249i	$-0.923427\pi$
$313$	−9.11583	−	19.9609i	−0.515257	−	1.12826i	0.455947	−	0.890007i	$-0.349301\pi$
$314$	9.35381	−	6.01133i	0.527866	−	0.339239i
$315$	2.52297	+	0.740810i	0.142153	+	0.0417399i
$316$	−0.600781	−	4.17853i	−0.0337966	−	0.235060i
$317$	−1.52163	+	3.33191i	−0.0854634	+	0.187139i	−0.947538	−	0.319642i	$-0.896437\pi$
$317$	−1.52163	+	3.33191i	−0.0854634	+	0.187139i	0.862075	+	0.506781i	$0.169165\pi$
$318$	1.17481	−	8.17097i	0.0658799	−	0.458205i
$319$	18.4967	+	11.8871i	1.03562	+	0.665550i
$320$	−0.654861	−	0.755750i	−0.0366078	−	0.0422477i
$321$	−2.82776			−0.157830
$322$	−11.6861	−	4.73920i	−0.651243	−	0.264105i
$323$	−2.69180			−0.149776
$324$	−0.654861	−	0.755750i	−0.0363812	−	0.0419861i
$325$	2.03879	+	1.31025i	0.113092	+	0.0726796i
$326$	−1.47423	+	10.2535i	−0.0816499	+	0.567888i
$327$	4.69528	−	10.2812i	0.259649	−	0.568553i
$328$	−1.10035	−	7.65307i	−0.0607564	−	0.422570i
$329$	8.85874	+	2.60116i	0.488398	+	0.143407i
$330$	−3.89565	+	2.50358i	−0.214449	+	0.137818i
$331$	4.54633	+	9.95507i	0.249889	+	0.547180i	0.992457	−	0.122590i	$-0.0391200\pi$
$331$	4.54633	+	9.95507i	0.249889	+	0.547180i	−0.742569	+	0.669770i	$0.766393\pi$
$332$	−7.04742	+	2.06931i	−0.386777	+	0.113568i
$333$	1.50617	−	1.73822i	0.0825379	−	0.0952538i
$334$	11.9182	−	13.7543i	0.652132	−	0.752601i
$335$	−0.0347386	+	0.0102002i	−0.00189797	+	0.000557294i
$336$	−1.09233	−	2.39186i	−0.0595913	−	0.130487i
$337$	−21.2544	+	13.6594i	−1.15780	+	0.744075i	−0.971178	−	0.238357i	$-0.923391\pi$
$337$	−21.2544	+	13.6594i	−1.15780	+	0.744075i	−0.186625	+	0.982431i	$0.559755\pi$
$338$	6.83791	+	2.00779i	0.371933	+	0.109209i
$339$	−1.31524	−	9.14766i	−0.0714338	−	0.496833i
$340$	−0.719323	+	1.57510i	−0.0390108	+	0.0854217i
$341$	0.398046	−	2.76847i	0.0215554	−	0.149921i
$342$	1.30776	+	0.840445i	0.0707154	+	0.0454460i
$343$	−12.2014	−	14.0812i	−0.658814	−	0.760312i
$344$	6.12135			0.330041
$345$	1.15150	−	4.65554i	0.0619947	−	0.250646i
$346$	24.0775			1.29441
$347$	6.24255	+	7.20429i	0.335118	+	0.386747i	0.898151	−	0.439688i	$-0.144911\pi$
$347$	6.24255	+	7.20429i	0.335118	+	0.386747i	−0.563033	+	0.826435i	$0.690366\pi$
$348$	−3.99430	−	2.56698i	−0.214117	−	0.137605i
$349$	2.93421	−	20.4079i	0.157065	−	1.09241i	−0.746941	−	0.664890i	$-0.768478\pi$
$349$	2.93421	−	20.4079i	0.157065	−	1.09241i	0.904006	−	0.427520i	$-0.140613\pi$
$350$	−1.09233	+	2.39186i	−0.0583873	+	0.127850i
$351$	−0.344902	−	2.39885i	−0.0184095	−	0.128041i
$352$	4.44319	+	1.30464i	0.236823	+	0.0695375i
$353$	18.1529	−	11.6662i	0.966183	−	0.620928i	0.0404808	−	0.999180i	$-0.487111\pi$
$353$	18.1529	−	11.6662i	0.966183	−	0.620928i	0.925703	+	0.378252i	$0.123475\pi$
$354$	1.41941	+	3.10807i	0.0754407	+	0.165192i
$355$	−15.1001	+	4.43378i	−0.801429	+	0.235321i
$356$	−4.68188	+	5.40318i	−0.248139	+	0.286368i
$357$	−2.98168	+	3.44104i	−0.157807	+	0.182119i
$358$	10.2806	−	3.01866i	0.543346	−	0.159541i
$359$	−10.2871	−	22.5257i	−0.542935	−	1.18886i	−0.960004	−	0.279987i	$-0.909670\pi$
$359$	−10.2871	−	22.5257i	−0.542935	−	1.18886i	0.417069	−	0.908875i	$-0.363057\pi$
$360$	0.841254	−	0.540641i	0.0443380	−	0.0284943i
$361$	15.9117	+	4.67209i	0.837457	+	0.245899i
$362$	0.421859	+	2.93409i	0.0221724	+	0.154213i
$363$	4.33861	−	9.50024i	0.227718	−	0.498633i
$364$	0.906913	−	6.30772i	0.0475352	−	0.330614i
$365$	7.78631	+	5.00396i	0.407554	+	0.261919i
$366$	−1.20053	−	1.38549i	−0.0627528	−	0.0724206i
$367$	0.759831			0.0396629			0.0198314	−	0.999803i	$-0.493687\pi$
$367$	0.759831			0.0396629			0.0198314	+	0.999803i	$0.493687\pi$
$368$	−4.27249	+	2.17848i	−0.222719	+	0.113561i
$369$	7.73177			0.402500
$370$	1.50617	+	1.73822i	0.0783023	+	0.0903657i
$371$	18.2605	+	11.7353i	0.948040	+	0.609268i
$372$	−0.0859568	+	0.597843i	−0.00445665	+	0.0309967i
$373$	−0.246462	+	0.539677i	−0.0127613	+	0.0279434i	−0.915905	−	0.401394i	$-0.868526\pi$
$373$	−0.246462	+	0.539677i	−0.0127613	+	0.0279434i	0.903144	+	0.429338i	$0.141253\pi$
$374$	−1.14116	−	7.93692i	−0.0590078	−	0.410408i
$375$	−0.959493	−	0.281733i	−0.0495480	−	0.0145486i
$376$	2.95384	−	1.89832i	0.152333	−	0.0978983i
$377$	−4.78015	−	10.4671i	−0.246190	−	0.539081i
$378$	2.52297	−	0.740810i	0.129768	−	0.0381032i
$379$	−12.1411	+	14.0116i	−0.623648	+	0.719728i	−0.976395	−	0.215991i	$-0.930702\pi$
$379$	−12.1411	+	14.0116i	−0.623648	+	0.719728i	0.352748	+	0.935718i	$0.385247\pi$
$380$	−1.01800	+	1.17484i	−0.0522225	+	0.0602679i
$381$	−12.5892	+	3.69651i	−0.644962	+	0.189378i
$382$	5.56698	+	12.1900i	0.284832	+	0.623694i
$383$	−28.4725	+	18.2981i	−1.45488	+	0.934991i	−0.455886	+	0.890038i	$0.650678\pi$
$383$	−28.4725	+	18.2981i	−1.45488	+	0.934991i	−0.998989	+	0.0449533i	$0.985686\pi$
$384$	−0.959493	−	0.281733i	−0.0489639	−	0.0143771i
$385$	−1.73290	−	12.0526i	−0.0883168	−	0.614257i
$386$	5.12498	−	11.2221i	0.260854	−	0.571192i
$387$	−0.871159	+	6.05905i	−0.0442835	+	0.307999i
$388$	1.88881	+	1.21386i	0.0958898	+	0.0616246i
$389$	13.0053	+	15.0089i	0.659393	+	0.760980i	0.982678	−	0.185322i	$-0.0593328\pi$
$389$	13.0053	+	15.0089i	0.659393	+	0.760980i	−0.323285	+	0.946302i	$0.604787\pi$
$390$	2.42351			0.122719
$391$	6.50463	+	5.16256i	0.328953	+	0.261082i
$392$	−0.0858287			−0.00433501
$393$	0.811170	+	0.936140i	0.0409181	+	0.0472220i
$394$	−12.2646	−	7.88195i	−0.617880	−	0.397087i
$395$	−0.600781	+	4.17853i	−0.0302286	+	0.210244i
$396$	−1.92369	+	4.21230i	−0.0966692	+	0.211676i
$397$	−0.195089	−	1.35687i	−0.00979124	−	0.0680996i	0.984340	−	0.176280i	$-0.0564065\pi$
$397$	−0.195089	−	1.35687i	−0.00979124	−	0.0680996i	−0.994131	+	0.108181i	$0.965497\pi$
$398$	16.1661	+	4.74679i	0.810333	+	0.237935i
$399$	−3.43872	+	2.20993i	−0.172151	+	0.110635i
$400$	0.415415	+	0.909632i	0.0207708	+	0.0454816i
$401$	15.9769	−	4.69123i	0.797846	−	0.234269i	0.142695	−	0.989767i	$-0.454423\pi$
$401$	15.9769	−	4.69123i	0.797846	−	0.234269i	0.655151	+	0.755498i	$0.272605\pi$
$402$	−0.0237093	+	0.0273620i	−0.00118251	+	0.00136469i
$403$	−0.958571	+	1.10625i	−0.0477498	+	0.0551062i
$404$	10.3848	−	3.04926i	0.516664	−	0.151706i
$405$	0.415415	+	0.909632i	0.0206421	+	0.0452000i
$406$	10.5029	−	6.74983i	0.521252	−	0.334988i
$407$	−10.2193	−	3.00066i	−0.506552	−	0.148737i
$408$	0.246429	+	1.71395i	0.0122001	+	0.0848533i
$409$	−3.99742	+	8.75313i	−0.197660	+	0.432814i	−0.982345	−	0.187081i	$-0.940097\pi$
$409$	−3.99742	+	8.75313i	−0.197660	+	0.432814i	0.784685	+	0.619895i	$0.212825\pi$
$410$	−1.10035	+	7.65307i	−0.0543422	+	0.377958i
$411$	−9.27856	−	5.96297i	−0.457678	−	0.294132i
$412$	−7.13350	−	8.23250i	−0.351442	−	0.405586i
$413$	−8.98452			−0.442099
$414$	−1.54827	−	4.53904i	−0.0760934	−	0.223081i
$415$	7.34494			0.360549
$416$	−1.58706	−	1.83157i	−0.0778122	−	0.0898001i
$417$	1.51894	+	0.976162i	0.0743827	+	0.0478029i
$418$	1.02448	−	7.12542i	0.0501090	−	0.348516i
$419$	0.393389	−	0.861401i	0.0192183	−	0.0420822i	−0.899779	−	0.436345i	$-0.856273\pi$
$419$	0.393389	−	0.861401i	0.0192183	−	0.0420822i	0.918998	+	0.394263i	$0.129000\pi$
$420$	0.374214	+	2.60272i	0.0182598	+	0.127000i
$421$	−6.57274	−	1.92993i	−0.320336	−	0.0940591i	0.117612	−	0.993060i	$-0.462476\pi$
$421$	−6.57274	−	1.92993i	−0.320336	−	0.0940591i	−0.437947	+	0.899001i	$0.644294\pi$
$422$	3.23060	−	2.07618i	0.157263	−	0.101067i
$423$	1.45862	+	3.19393i	0.0709206	+	0.155294i
$424$	7.92060	−	2.32570i	0.384659	−	0.112946i
$425$	1.13394	−	1.30864i	0.0550043	−	0.0634783i
$426$	−10.3059	+	11.8936i	−0.499323	+	0.576249i
$427$	4.62526	−	1.35810i	0.223832	−	0.0657231i
$428$	−1.17469	−	2.57222i	−0.0567810	−	0.124333i
$429$	−9.44117	+	6.06747i	−0.455824	+	0.292940i
$430$	−5.87339	−	1.72458i	−0.283240	−	0.0831668i
$431$	−5.01418	−	34.8744i	−0.241525	−	1.67984i	−0.644480	−	0.764621i	$-0.722926\pi$
$431$	−5.01418	−	34.8744i	−0.241525	−	1.67984i	0.402955	−	0.915220i	$-0.367983\pi$
$432$	0.415415	−	0.909632i	0.0199867	−	0.0437647i
$433$	0.469980	−	3.26878i	0.0225858	−	0.157088i	−0.975407	−	0.220410i	$-0.929260\pi$
$433$	0.469980	−	3.26878i	0.0225858	−	0.157088i	0.997993	+	0.0633222i	$0.0201696\pi$
$434$	−1.33606	−	0.858636i	−0.0641331	−	0.0412158i
$435$	3.10930	+	3.58832i	0.149080	+	0.172047i
$436$	11.3026			0.541297
$437$	4.29728	+	6.09218i	0.205567	+	0.291429i
$438$	9.25560			0.442250
$439$	13.9891	+	16.1442i	0.667661	+	0.770522i	0.984009	−	0.178121i	$-0.0570019\pi$
$439$	13.9891	+	16.1442i	0.667661	+	0.770522i	−0.316347	+	0.948643i	$0.602456\pi$
$440$	−3.89565	−	2.50358i	−0.185718	−	0.119354i
$441$	0.0122147	−	0.0849551i	0.000581652	−	0.00404548i
$442$	−1.74329	+	3.81727i	−0.0829198	+	0.181569i
$443$	5.74553	+	39.9611i	0.272978	+	1.89861i	0.416791	+	0.909002i	$0.363155\pi$
$443$	5.74553	+	39.9611i	0.272978	+	1.89861i	−0.143813	+	0.989605i	$0.545936\pi$
$444$	2.20683	+	0.647983i	0.104731	+	0.0307519i
$445$	6.01448	−	3.86527i	0.285114	−	0.183231i
$446$	−8.61127	−	18.8561i	−0.407756	−	0.892860i
$447$	1.86951	−	0.548938i	0.0884249	−	0.0259639i
$448$	1.72194	−	1.98723i	0.0813542	−	0.0938878i
$449$	1.00664	−	1.16173i	0.0475063	−	0.0548252i	−0.731499	−	0.681842i	$-0.761179\pi$
$449$	1.00664	−	1.16173i	0.0475063	−	0.0548252i	0.779005	+	0.627017i	$0.215724\pi$
$450$	−0.959493	+	0.281733i	−0.0452309	+	0.0132810i
$451$	−14.8736	−	32.5685i	−0.700368	−	1.53359i
$452$	7.77464	−	4.99646i	0.365688	−	0.235014i
$453$	−18.7992	−	5.51994i	−0.883263	−	0.259349i
$454$	0.253660	+	1.76424i	0.0119048	+	0.0827999i
$455$	−2.64727	+	5.79671i	−0.124106	+	0.271754i
$456$	−0.221233	+	1.53871i	−0.0103602	+	0.0720567i
$457$	23.3109	+	14.9810i	1.09044	+	0.700782i	0.956945	−	0.290268i	$-0.0937446\pi$
$457$	23.3109	+	14.9810i	1.09044	+	0.700782i	0.133492	+	0.991050i	$0.457381\pi$
$458$	1.44817	+	1.67127i	0.0676683	+	0.0780934i
$459$	−1.73158			−0.0808231
$460$	4.71318	−	0.886540i	0.219753	−	0.0413351i
$461$	42.7699			1.99199			0.995996	−	0.0893985i	$-0.0284945\pi$
$461$	42.7699			1.99199			0.995996	+	0.0893985i	$0.0284945\pi$
$462$	−7.97393	−	9.20241i	−0.370981	−	0.428135i
$463$	9.54201	+	6.13228i	0.443455	+	0.284991i	0.743252	−	0.669012i	$-0.233283\pi$
$463$	9.54201	+	6.13228i	0.443455	+	0.284991i	−0.299797	+	0.954003i	$0.596919\pi$
$464$	0.675716	−	4.69971i	0.0313693	−	0.218178i
$465$	0.250907	−	0.549409i	0.0116355	−	0.0254782i
$466$	2.96806	+	20.6433i	0.137493	+	0.956282i
$467$	−33.2956	−	9.77648i	−1.54074	−	0.452402i	−0.602422	−	0.798178i	$-0.705797\pi$
$467$	−33.2956	−	9.77648i	−1.54074	−	0.452402i	−0.938317	+	0.345776i	$0.887616\pi$
$468$	2.03879	−	1.31025i	0.0942431	−	0.0605663i
$469$	−0.0395478	−	0.0865976i	−0.00182615	−	0.00399870i
$470$	−3.36901	+	0.989230i	−0.155401	+	0.0456298i
$471$	−7.28133	+	8.40310i	−0.335506	+	0.387194i
$472$	−2.23756	+	2.58228i	−0.102992	+	0.118859i
$473$	27.1983	−	7.98616i	1.25058	−	0.367204i
$474$	1.75367	+	3.84001i	0.0805488	+	0.176377i
$475$	1.30776	−	0.840445i	0.0600040	−	0.0385622i
$476$	−4.36871	−	1.28277i	−0.200240	−	0.0587957i
$477$	1.17481	+	8.17097i	0.0537907	+	0.374123i
$478$	−11.8931	+	26.0422i	−0.543977	+	1.19114i
$479$	−4.82203	+	33.5380i	−0.220324	+	1.53239i	0.516489	+	0.856294i	$0.327239\pi$
$479$	−4.82203	+	33.5380i	−0.220324	+	1.53239i	−0.736814	+	0.676096i	$0.763670\pi$
$480$	0.841254	+	0.540641i	0.0383978	+	0.0246768i
$481$	3.65023	+	4.21260i	0.166436	+	0.192078i
$482$	15.4941			0.705739
$483$	12.5480	+	1.25486i	0.570952	+	0.0570981i
$484$	10.4440			0.474729
$485$	−1.47032	−	1.69683i	−0.0667636	−	0.0770493i
$486$	0.841254	+	0.540641i	0.0381600	+	0.0245240i
$487$	1.75915	−	12.2351i	0.0797145	−	0.554426i	−0.910353	−	0.413833i	$-0.864190\pi$
$487$	1.75915	−	12.2351i	0.0797145	−	0.554426i	0.990067	−	0.140594i	$-0.0449011\pi$
$488$	0.761565	−	1.66759i	0.0344744	−	0.0754884i
$489$	−1.47423	−	10.2535i	−0.0666669	−	0.463678i
$490$	0.0823521	+	0.0241807i	0.00372029	+	0.00109237i
$491$	1.42822	−	0.917859i	0.0644545	−	0.0414224i	−0.508017	−	0.861347i	$-0.669621\pi$
$491$	1.42822	−	0.917859i	0.0644545	−	0.0414224i	0.572471	+	0.819925i	$0.305985\pi$
$492$	3.21189	+	7.03307i	0.144803	+	0.317075i
$493$	−7.88855	+	2.31629i	−0.355283	+	0.104320i
$494$	−2.46714	+	2.84724i	−0.111002	+	0.128103i
$495$	3.03251	−	3.49970i	0.136301	−	0.157300i
$496$	−0.579524	+	0.170164i	−0.0260214	+	0.00764058i
$497$	−17.1905	−	37.6420i	−0.771101	−	1.68848i
$498$	6.17896	−	3.97097i	0.276886	−	0.177944i
$499$	−12.4423	−	3.65340i	−0.556996	−	0.163549i	−0.00889406	−	0.999960i	$-0.502831\pi$
$499$	−12.4423	−	3.65340i	−0.556996	−	0.163549i	−0.548102	+	0.836412i	$0.684649\pi$
$500$	−0.142315	−	0.989821i	−0.00636451	−	0.0442662i
$501$	−7.56036	+	16.5549i	−0.337772	+	0.739617i
$502$	0.518829	−	3.60854i	0.0231565	−	0.161057i
$503$	−5.06142	−	3.25278i	−0.225678	−	0.145034i	0.422916	−	0.906169i	$-0.361006\pi$
$503$	−5.06142	−	3.25278i	−0.225678	−	0.145034i	−0.648594	+	0.761134i	$0.724643\pi$
$504$	1.72194	+	1.98723i	0.0767015	+	0.0885182i
$505$	−10.8232			−0.481627
$506$	−16.1414	+	15.2535i	−0.717572	+	0.678100i
$507$	−7.12658			−0.316503
$508$	−8.59219	−	9.91591i	−0.381217	−	0.439948i
$509$	−7.32733	−	4.70899i	−0.324778	−	0.208722i	0.368084	−	0.929793i	$-0.380014\pi$
$509$	−7.32733	−	4.70899i	−0.324778	−	0.208722i	−0.692862	+	0.721070i	$0.743650\pi$
$510$	0.246429	−	1.71395i	0.0109121	−	0.0758951i
$511$	−10.1101	+	22.1381i	−0.447246	+	0.979332i
$512$	−0.142315	−	0.989821i	−0.00628949	−	0.0437443i
$513$	−1.49156	−	0.437963i	−0.0658542	−	0.0193365i
$514$	−14.8610	+	9.55060i	−0.655492	+	0.421259i
$515$	4.52518	+	9.90877i	0.199403	+	0.436632i
$516$	−5.87339	+	1.72458i	−0.258562	+	0.0759206i
$517$	10.6479	−	12.2883i	0.468293	−	0.540438i
$518$	−3.96046	+	4.57061i	−0.174013	+	0.200821i
$519$	−23.1022	+	6.78341i	−1.01407	+	0.297759i
$520$	1.00676	+	2.20451i	0.0441495	+	0.0966740i
$521$	5.98587	−	3.84688i	0.262246	−	0.168535i	−0.402910	−	0.915239i	$-0.632001\pi$
$521$	5.98587	−	3.84688i	0.262246	−	0.168535i	0.665156	+	0.746704i	$0.268365\pi$
$522$	4.55570	+	1.33768i	0.199398	+	0.0585485i
$523$	1.65098	+	11.4828i	0.0721923	+	0.502108i	0.993550	+	0.113393i	$0.0361719\pi$
$523$	1.65098	+	11.4828i	0.0721923	+	0.502108i	−0.921358	+	0.388715i	$0.872919\pi$
$524$	−0.514571	+	1.12675i	−0.0224791	+	0.0492224i
$525$	0.374214	−	2.60272i	0.0163320	−	0.113592i
$526$	24.5299	+	15.7644i	1.06955	+	0.687360i
$527$	0.684890	+	0.790405i	0.0298343	+	0.0344306i
$528$	−4.63077			−0.201528
$529$	1.29990	−	22.9632i	0.0565175	−	0.998402i
$530$	−8.25499			−0.358574
$531$	−2.23756	−	2.58228i	−0.0971016	−	0.112061i
$532$	−3.43872	−	2.20993i	−0.149088	−	0.0958127i
$533$	−2.66670	+	18.5473i	−0.115508	+	0.803374i
$534$	2.96998	−	6.50335i	0.128524	−	0.281427i
$535$	0.402432	+	2.79898i	0.0173987	+	0.121010i
$536$	−0.0347386	−	0.0102002i	−0.00150048	−	0.000440580i
$537$	−9.01371	+	5.79276i	−0.388970	+	0.249976i
$538$	12.6235	+	27.6415i	0.544236	+	1.19171i
$539$	−0.381354	+	0.111976i	−0.0164261	+	0.00482313i
$540$	−0.654861	+	0.755750i	−0.0281807	+	0.0325223i
$541$	−19.8283	+	22.8830i	−0.852484	+	0.983819i	−0.999986	−	0.00524303i	$-0.998331\pi$
$541$	−19.8283	+	22.8830i	−0.852484	+	0.983819i	0.147503	+	0.989062i	$0.452877\pi$
$542$	−10.2643	+	3.01388i	−0.440891	+	0.129457i
$543$	−1.23140	−	2.69639i	−0.0528445	−	0.115713i
$544$	−1.45670	+	0.936161i	−0.0624553	+	0.0401376i
$545$	−10.8448	−	3.18432i	−0.464539	−	0.136401i
$546$	0.906913	+	6.30772i	0.0388123	+	0.269945i
$547$	10.6861	−	23.3993i	0.456904	−	1.00048i	−0.531279	−	0.847197i	$-0.678288\pi$
$547$	10.6861	−	23.3993i	0.456904	−	1.00048i	0.988182	−	0.153283i	$-0.0489845\pi$
$548$	1.56965	−	10.9172i	0.0670523	−	0.466359i
$549$	1.54224	+	0.991137i	0.0658211	+	0.0423007i
$550$	3.03251	+	3.49970i	0.129307	+	0.149228i
$551$	−7.38098			−0.314440
$552$	3.48568	−	3.29394i	0.148360	−	0.140199i
$553$	−11.1003			−0.472035
$554$	−20.3936	−	23.5354i	−0.866439	−	0.999924i
$555$	−1.93488	−	1.24347i	−0.0821309	−	0.0527824i
$556$	−0.256959	+	1.78719i	−0.0108975	+	0.0757936i
$557$	−2.61508	+	5.72623i	−0.110805	+	0.242628i	−0.956908	−	0.290390i	$-0.906215\pi$
$557$	−2.61508	+	5.72623i	−0.110805	+	0.242628i	0.846104	+	0.533018i	$0.178942\pi$
$558$	−0.0859568	−	0.597843i	−0.00363884	−	0.0253087i
$559$	−14.2342	−	4.17955i	−0.602045	−	0.176776i
$560$	−2.21206	+	1.42160i	−0.0934766	+	0.0600738i
$561$	3.33102	+	7.29392i	0.140636	+	0.307950i
$562$	−24.6800	+	7.24670i	−1.04106	+	0.305683i
$563$	−17.6250	+	20.3403i	−0.742804	+	0.857242i	−0.993850	−	0.110733i	$-0.964680\pi$
$563$	−17.6250	+	20.3403i	−0.742804	+	0.857242i	0.251046	+	0.967975i	$0.419226\pi$
$564$	−2.29937	+	2.65362i	−0.0968210	+	0.111737i
$565$	−8.86738	+	2.60370i	−0.373053	+	0.109538i
$566$	−10.3298	−	22.6191i	−0.434193	−	0.950750i
$567$	−2.21206	+	1.42160i	−0.0928978	+	0.0597018i
$568$	−15.1001	−	4.43378i	−0.633585	−	0.186037i
$569$	4.85262	+	33.7507i	0.203433	+	1.41490i	0.794001	+	0.607917i	$0.207995\pi$
$569$	4.85262	+	33.7507i	0.203433	+	1.41490i	−0.590568	+	0.806988i	$0.701096\pi$
$570$	0.645777	−	1.41405i	0.0270486	−	0.0592282i
$571$	0.814216	−	5.66300i	0.0340739	−	0.236989i	−0.965666	−	0.259786i	$-0.916348\pi$
$571$	0.814216	−	5.66300i	0.0340739	−	0.236989i	0.999740	+	0.0227968i	$0.00725708\pi$
$572$	−9.44117	−	6.06747i	−0.394755	−	0.253694i
$573$	−8.77580	−	10.1278i	−0.366614	−	0.423095i
$574$	−20.3306			−0.848581
$575$	−4.77203	−	0.477227i	−0.199007	−	0.0199017i
$576$	1.00000			0.0416667
$577$	6.50865	+	7.51138i	0.270959	+	0.312703i	0.874879	−	0.484342i	$-0.160941\pi$
$577$	6.50865	+	7.51138i	0.270959	+	0.312703i	−0.603920	+	0.797045i	$0.706395\pi$
$578$	−11.7789	−	7.56986i	−0.489939	−	0.314865i
$579$	−1.75574	+	12.2114i	−0.0729660	+	0.507490i
$580$	−1.97240	+	4.31896i	−0.0818996	+	0.179335i
$581$	2.74858	+	19.1168i	0.114030	+	0.793099i
$582$	−2.15429	−	0.632555i	−0.0892980	−	0.0262203i
$583$	32.1586	−	20.6671i	1.33187	−	0.855942i
$584$	3.84492	+	8.41919i	0.159104	+	0.348389i
$585$	−2.32534	+	0.682783i	−0.0961411	+	0.0282296i
$586$	−15.7320	+	18.1557i	−0.649884	+	0.750006i
$587$	−9.32204	+	10.7582i	−0.384762	+	0.444039i	−0.914783	−	0.403946i	$-0.867639\pi$
$587$	−9.32204	+	10.7582i	−0.384762	+	0.444039i	0.530021	+	0.847984i	$0.322184\pi$
$588$	0.0823521	−	0.0241807i	0.00339614	−	0.000997197i
$589$	0.390043	+	0.854075i	0.0160714	+	0.0351915i
$590$	2.87443	−	1.84728i	0.118338	−	0.0760515i
$591$	13.9884	+	4.10735i	0.575404	+	0.168954i
$592$	0.327323	+	2.27658i	0.0134529	+	0.0935669i
$593$	4.41519	−	9.66792i	0.181310	−	0.397014i	−0.797053	−	0.603910i	$-0.793609\pi$
$593$	4.41519	−	9.66792i	0.181310	−	0.397014i	0.978363	+	0.206896i	$0.0663361\pi$
$594$	0.659028	−	4.58364i	0.0270402	−	0.188069i
$595$	3.83035	+	2.46162i	0.157029	+	0.100917i
$596$	1.27596	+	1.47253i	0.0522652	+	0.0603172i
$597$	−16.8486			−0.689566
$598$	11.4224	−	2.14854i	0.467099	−	0.0878604i
$599$	14.9745			0.611843			0.305921	−	0.952057i	$-0.401036\pi$
$599$	14.9745			0.611843			0.305921	+	0.952057i	$0.401036\pi$
$600$	−0.654861	−	0.755750i	−0.0267346	−	0.0308533i
$601$	21.1093	+	13.5661i	0.861065	+	0.553373i	0.895008	−	0.446051i	$-0.147170\pi$
$601$	21.1093	+	13.5661i	0.861065	+	0.553373i	−0.0339425	+	0.999424i	$0.510806\pi$
$602$	2.29070	−	15.9321i	0.0933618	−	0.649346i
$603$	0.0150401	−	0.0329333i	0.000612482	−	0.00134115i
$604$	−2.78835	−	19.3934i	−0.113456	−	0.789107i
$605$	−10.0210	−	2.94243i	−0.407411	−	0.119627i
$606$	−9.10508	+	5.85148i	−0.369869	+	0.237700i
$607$	−9.49200	−	20.7846i	−0.385268	−	0.843620i	−0.998554	−	0.0537586i	$-0.982880\pi$
$607$	−9.49200	−	20.7846i	−0.385268	−	0.843620i	0.613286	−	0.789861i	$-0.289847\pi$
$608$	−1.49156	+	0.437963i	−0.0604909	+	0.0177617i
$609$	−8.17585	+	9.43543i	−0.331302	+	0.382343i
$610$	−1.20053	+	1.38549i	−0.0486081	+	0.0560967i
$611$	−8.16483	+	2.39741i	−0.330314	+	0.0969889i
$612$	−0.719323	−	1.57510i	−0.0290769	−	0.0636696i
$613$	6.59158	−	4.23615i	0.266231	−	0.171096i	−0.400714	−	0.916203i	$-0.631238\pi$
$613$	6.59158	−	4.23615i	0.266231	−	0.171096i	0.666945	+	0.745107i	$0.267601\pi$
$614$	−32.5586	−	9.56005i	−1.31396	−	0.385812i
$615$	−1.10035	−	7.65307i	−0.0443702	−	0.308602i
$616$	5.05831	−	11.0762i	0.203805	−	0.446271i
$617$	4.24930	−	29.5545i	0.171070	−	1.18982i	−0.705558	−	0.708652i	$-0.749304\pi$
$617$	4.24930	−	29.5545i	0.171070	−	1.18982i	0.876628	−	0.481168i	$-0.159787\pi$
$618$	9.16391	+	5.88929i	0.368627	+	0.236902i
$619$	27.3371	+	31.5487i	1.09877	+	1.26805i	0.960688	+	0.277629i	$0.0895486\pi$
$619$	27.3371	+	31.5487i	1.09877	+	1.26805i	0.138083	+	0.990421i	$0.455906\pi$
$620$	0.603990			0.0242568
$621$	2.76435	+	3.91898i	0.110930	+	0.157263i
$622$	12.9918			0.520923
$623$	12.3109	+	14.2076i	0.493226	+	0.569213i
$624$	2.03879	+	1.31025i	0.0816169	+	0.0524520i
$625$	−0.142315	+	0.989821i	−0.00569259	+	0.0395929i
$626$	−9.11583	+	19.9609i	−0.364342	+	0.797797i
$627$	1.02448	+	7.12542i	0.0409138	+	0.284562i
$628$	−10.6685	−	3.13256i	−0.425720	−	0.125003i
$629$	3.35039	−	2.15316i	0.133589	−	0.0858523i
$630$	−1.09233	−	2.39186i	−0.0435193	−	0.0952940i
$631$	−30.2231	+	8.87432i	−1.20316	+	0.353281i	−0.821062	−	0.570839i	$-0.806618\pi$
$631$	−30.2231	+	8.87432i	−1.20316	+	0.353281i	−0.382102	+	0.924120i	$0.624800\pi$
$632$	−2.76449	+	3.19039i	−0.109966	+	0.126907i
$633$	−2.51481	+	2.90225i	−0.0999547	+	0.115354i
$634$	3.51455	−	1.03196i	0.139580	−	0.0409845i
$635$	5.45051	+	11.9349i	0.216297	+	0.473624i
$636$	−6.94454	+	4.46298i	−0.275369	+	0.176969i
$637$	0.199581	+	0.0586024i	0.00790770	+	0.00232191i
$638$	−3.12908	−	21.7633i	−0.123882	−	0.861616i
$639$	6.53762	−	14.3154i	0.258624	−	0.566308i
$640$	−0.142315	+	0.989821i	−0.00562549	+	0.0391261i
$641$	33.6762	+	21.6424i	1.33013	+	0.854823i	0.996142	−	0.0877545i	$-0.0279691\pi$
$641$	33.6762	+	21.6424i	1.33013	+	0.854823i	0.333988	+	0.942577i	$0.391605\pi$
$642$	1.85179	+	2.13708i	0.0730843	+	0.0843438i
$643$	22.3075			0.879724			0.439862	−	0.898065i	$-0.355027\pi$
$643$	22.3075			0.879724			0.439862	+	0.898065i	$0.355027\pi$
$644$	4.07115	+	11.9353i	0.160426	+	0.470317i
$645$	6.12135			0.241028
$646$	1.76275	+	2.03432i	0.0693545	+	0.0800394i
$647$	−16.3984	−	10.5386i	−0.644687	−	0.414315i	0.177034	−	0.984205i	$-0.443350\pi$
$647$	−16.3984	−	10.5386i	−0.644687	−	0.414315i	−0.821721	+	0.569889i	$0.806986\pi$
$648$	−0.142315	+	0.989821i	−0.00559065	+	0.0388839i
$649$	−6.57295	+	14.3928i	−0.258011	+	0.564965i
$650$	−0.344902	−	2.39885i	−0.0135282	−	0.0940905i
$651$	1.52385	+	0.447442i	0.0597243	+	0.0175366i
$652$	8.71448	−	5.60046i	0.341285	−	0.219331i
$653$	7.76331	+	16.9993i	0.303802	+	0.665233i	0.998539	−	0.0540301i	$-0.0172067\pi$
$653$	7.76331	+	16.9993i	0.303802	+	0.665233i	−0.694737	+	0.719263i	$0.744479\pi$
$654$	−10.8448	+	3.18432i	−0.424065	+	0.124517i
$655$	0.811170	−	0.936140i	0.0316950	−	0.0365780i
$656$	−5.06323	+	5.84328i	−0.197686	+	0.228142i
$657$	−8.88069	+	2.60760i	−0.346469	+	0.101732i
$658$	−3.83542	−	8.39839i	−0.149520	−	0.327403i
$659$	42.5663	−	27.3557i	1.65815	−	1.06563i	0.737407	−	0.675448i	$-0.236050\pi$
$659$	42.5663	−	27.3557i	1.65815	−	1.06563i	0.920739	−	0.390178i	$-0.127587\pi$
$660$	4.44319	+	1.30464i	0.172951	+	0.0507830i
$661$	6.29657	+	43.7936i	0.244908	+	1.70337i	0.626811	+	0.779171i	$0.284360\pi$
$661$	6.29657	+	43.7936i	0.244908	+	1.70337i	−0.381903	+	0.924203i	$0.624731\pi$
$662$	4.54633	−	9.95507i	0.176698	−	0.386915i
$663$	0.597224	−	4.15379i	0.0231943	−	0.161320i
$664$	6.17896	+	3.97097i	0.239790	+	0.154104i
$665$	2.67682	+	3.08922i	0.103803	+	0.119795i
$666$	−2.29999			−0.0891229
$667$	17.8359	+	14.1559i	0.690608	+	0.548118i
$668$	−18.1995			−0.704161
$669$	13.5748	+	15.6662i	0.524833	+	0.605690i
$670$	0.0304577	+	0.0195740i	0.00117668	+	0.000756208i
$671$	1.20817	−	8.40301i	0.0466409	−	0.324395i
$672$	−1.09233	+	2.39186i	−0.0421374	+	0.0922680i
$673$	−2.46522	−	17.1460i	−0.0950271	−	0.660928i	−0.980541	−	0.196315i	$-0.937102\pi$
$673$	−2.46522	−	17.1460i	−0.0950271	−	0.660928i	0.885514	−	0.464613i	$-0.153807\pi$
$674$	24.2418	+	7.11803i	0.933758	+	0.274176i
$675$	0.841254	−	0.540641i	0.0323799	−	0.0208093i
$676$	−2.96049	−	6.48257i	−0.113865	−	0.249330i
$677$	24.1309	−	7.08548i	0.927427	−	0.272317i	0.217068	−	0.976156i	$-0.430351\pi$
$677$	24.1309	−	7.08548i	0.927427	−	0.272317i	0.710359	+	0.703839i	$0.248532\pi$
$678$	−6.05205	+	6.98443i	−0.232427	+	0.268236i
$679$	3.86617	−	4.46179i	0.148370	−	0.171228i
$680$	1.66144	−	0.487842i	0.0637132	−	0.0187079i
$681$	−0.740429	−	1.62131i	−0.0283733	−	0.0621288i
$682$	−2.35294	+	1.51214i	−0.0900986	+	0.0579029i
$683$	−6.35447	−	1.86584i	−0.243147	−	0.0713944i	0.157888	−	0.987457i	$-0.449531\pi$
$683$	−6.35447	−	1.86584i	−0.243147	−	0.0713944i	−0.401035	+	0.916063i	$0.631350\pi$
$684$	−0.221233	−	1.53871i	−0.00845906	−	0.0588341i
$685$	−4.58180	+	10.0327i	−0.175062	+	0.383331i
$686$	−2.65162	+	18.4424i	−0.101239	+	0.704134i
$687$	−1.86036	−	1.19558i	−0.0709770	−	0.0456142i
$688$	−4.00863	−	4.62621i	−0.152828	−	0.176373i
$689$	−20.0061			−0.762171
$690$	−4.27249	+	2.17848i	−0.162651	+	0.0829335i
$691$	3.78464			0.143974			0.0719872	−	0.997406i	$-0.477066\pi$
$691$	3.78464			0.143974			0.0719872	+	0.997406i	$0.477066\pi$
$692$	−15.7674	−	18.1965i	−0.599386	−	0.691729i
$693$	10.2435	+	6.58313i	0.389120	+	0.250072i
$694$	1.35664	−	9.43562i	0.0514972	−	0.358171i
$695$	0.750059	−	1.64240i	0.0284514	−	0.0622998i
$696$	0.675716	+	4.69971i	0.0256129	+	0.178142i
$697$	12.8458	+	3.77188i	0.486571	+	0.142870i
$698$	−17.3448	+	11.1468i	−0.656509	+	0.421913i
$699$	−8.66371	−	18.9709i	−0.327692	−	0.717545i
$700$	2.52297	−	0.740810i	0.0953593	−	0.0280000i
$701$	−9.86836	+	11.3887i	−0.372723	+	0.430145i	−0.910862	−	0.412711i	$-0.864582\pi$
$701$	−9.86836	+	11.3887i	−0.372723	+	0.430145i	0.538139	+	0.842856i	$0.319127\pi$
$702$	−1.58706	+	1.83157i	−0.0598999	+	0.0691281i
$703$	3.43059	−	1.00731i	0.129387	−	0.0379915i
$704$	−1.92369	−	4.21230i	−0.0725019	−	0.158757i
$705$	2.95384	−	1.89832i	0.111248	−	0.0714948i
$706$	−20.7044	−	6.07935i	−0.779219	−	0.228799i
$707$	−4.05021	−	28.1698i	−0.152324	−	1.05943i
$708$	1.41941	−	3.10807i	0.0533446	−	0.116808i
$709$	5.04581	−	35.0944i	0.189499	−	1.31800i	−0.643808	−	0.765187i	$-0.722646\pi$
$709$	5.04581	−	35.0944i	0.189499	−	1.31800i	0.833307	−	0.552810i	$-0.186445\pi$
$710$	13.2393	+	8.50836i	0.496861	+	0.319313i
$711$	−2.76449	−	3.19039i	−0.103677	−	0.119649i
$712$	7.14943			0.267936
$713$	0.695495	−	2.81190i	0.0260465	−	0.105307i
$714$	4.55315			0.170397
$715$	7.34933	+	8.48158i	0.274849	+	0.317193i
$716$	−9.01371	−	5.79276i	−0.336858	−	0.216485i
$717$	4.07439	−	28.3380i	0.152161	−	1.05830i
$718$	−10.2871	+	22.5257i	−0.383913	+	0.840652i
$719$	−0.900112	−	6.26041i	−0.0335685	−	0.233474i	0.966129	−	0.258059i	$-0.0830828\pi$
$719$	−0.900112	−	6.26041i	−0.0335685	−	0.233474i	−0.999698	+	0.0245846i	$0.992174\pi$
$720$	−0.959493	−	0.281733i	−0.0357582	−	0.0104996i
$721$	−24.0963	+	15.4858i	−0.897394	+	0.576720i
$722$	−6.88900	−	15.0848i	−0.256382	−	0.561399i
$723$	−14.8665	+	4.36520i	−0.552892	+	0.162344i
$724$	1.94118	−	2.24024i	0.0721434	−	0.0832580i
$725$	3.10930	−	3.58832i	0.115477	−	0.133267i
$726$	−10.0210	+	2.94243i	−0.371914	+	0.109204i
$727$	−10.1097	−	22.1371i	−0.374947	−	0.821019i	−0.999208	−	0.0398026i	$-0.987327\pi$
$727$	−10.1097	−	22.1371i	−0.374947	−	0.821019i	0.624261	−	0.781216i	$-0.285400\pi$
$728$	−5.36096	+	3.44528i	−0.198690	+	0.127691i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	−1.31721	−	9.16139i	−0.0487521	−	0.339078i
$731$	−4.40323	+	9.64173i	−0.162859	+	0.356612i
$732$	−0.260900	+	1.81460i	−0.00964316	+	0.0670696i
$733$	−21.1151	−	13.5698i	−0.779903	−	0.501213i	0.0890984	−	0.996023i	$-0.471601\pi$
$733$	−21.1151	−	13.5698i	−0.779903	−	0.501213i	−0.869001	+	0.494810i	$0.835238\pi$
$734$	−0.497584	−	0.574242i	−0.0183661	−	0.0211957i
$735$	−0.0858287			−0.00316584
$736$	4.44428	+	1.80233i	0.163818	+	0.0664348i
$737$	−0.167658			−0.00617575
$738$	−5.06323	−	5.84328i	−0.186380	−	0.215094i
$739$	16.6576	+	10.7052i	0.612759	+	0.393796i	0.809891	−	0.586581i	$-0.199526\pi$
$739$	16.6576	+	10.7052i	0.612759	+	0.393796i	−0.197132	+	0.980377i	$0.563163\pi$
$740$	0.327323	−	2.27658i	0.0120326	−	0.0836888i
$741$	1.56505	−	3.42698i	0.0574935	−	0.125893i
$742$	−3.08913	−	21.4854i	−0.113406	−	0.788754i
$743$	−3.57025	−	1.04832i	−0.130980	−	0.0384591i	0.215586	−	0.976485i	$-0.430834\pi$
$743$	−3.57025	−	1.04832i	−0.130980	−	0.0384591i	−0.346565	+	0.938026i	$0.612652\pi$
$744$	0.508109	−	0.326542i	0.0186282	−	0.0119716i
$745$	−0.809410	−	1.77236i	−0.0296545	−	0.0649343i
$746$	0.569260	−	0.167150i	0.0208421	−	0.00611978i
$747$	−4.80991	+	5.55094i	−0.175986	+	0.203098i
$748$	−5.25103	+	6.06001i	−0.191997	+	0.221576i
$749$	−7.13435	+	2.09483i	−0.260684	+	0.0765436i
$750$	0.415415	+	0.909632i	0.0151688	+	0.0332151i
$751$	−12.6366	+	8.12104i	−0.461116	+	0.296341i	−0.750498	−	0.660873i	$-0.770186\pi$
$751$	−12.6366	+	8.12104i	−0.461116	+	0.296341i	0.289383	+	0.957214i	$0.406550\pi$
$752$	−3.36901	−	0.989230i	−0.122855	−	0.0360735i
$753$	0.518829	+	3.60854i	0.0189072	+	0.131502i
$754$	−4.78015	+	10.4671i	−0.174083	+	0.381188i
$755$	−2.78835	+	19.3934i	−0.101479	+	0.705799i
$756$	−2.21206	−	1.42160i	−0.0804519	−	0.0517033i
$757$	−4.32002	−	4.98557i	−0.157014	−	0.181204i	0.671792	−	0.740740i	$-0.265525\pi$
$757$	−4.32002	−	4.98557i	−0.157014	−	0.181204i	−0.828806	+	0.559536i	$0.810979\pi$
$758$	18.5400			0.673404
$759$	11.1901	−	19.1832i	0.406176	−	0.696305i
$760$	1.55453			0.0563889
$761$	1.32332	+	1.52719i	0.0479702	+	0.0553606i	0.779228	−	0.626741i	$-0.215612\pi$
$761$	1.32332	+	1.52719i	0.0479702	+	0.0553606i	−0.731257	+	0.682102i	$0.761066\pi$
$762$	11.0378	+	7.09355i	0.399857	+	0.256972i
$763$	4.22960	−	29.4175i	0.153122	−	1.06499i
$764$	5.56698	−	12.1900i	0.201406	−	0.441018i
$765$	0.246429	+	1.71395i	0.00890966	+	0.0619681i
$766$	32.4743	+	9.53532i	1.17334	+	0.344525i
$767$	6.96622	−	4.47692i	0.251536	−	0.161652i
$768$	0.415415	+	0.909632i	0.0149900	+	0.0328235i
$769$	9.15955	−	2.68949i	0.330302	−	0.0969854i	−0.112377	−	0.993666i	$-0.535846\pi$
$769$	9.15955	−	2.68949i	0.330302	−	0.0969854i	0.442679	+	0.896680i	$0.354028\pi$
$770$	−7.97393	+	9.20241i	−0.287360	+	0.331632i
$771$	11.5683	−	13.3506i	0.416624	−	0.480809i
$772$	−11.8373	+	3.47574i	−0.426033	+	0.125094i
$773$	−17.2728	−	37.8221i	−0.621258	−	1.36037i	−0.914600	−	0.404359i	$-0.867495\pi$
$773$	−17.2728	−	37.8221i	−0.621258	−	1.36037i	0.293342	−	0.956008i	$-0.405233\pi$
$774$	5.14961	−	3.30945i	0.185099	−	0.118956i
$775$	−0.579524	−	0.170164i	−0.0208171	−	0.00611246i
$776$	−0.319530	−	2.22238i	−0.0114705	−	0.0797788i
$777$	2.51234	−	5.50126i	0.0901297	−	0.197357i
$778$	2.82631	−	19.6574i	0.101328	−	0.704753i
$779$	10.1113	+	6.49813i	0.362274	+	0.232820i
$780$	−1.58706	−	1.83157i	−0.0568260	−	0.0655807i
$781$	−72.8770			−2.60774
$782$	−0.358023	−	8.29663i	−0.0128029	−	0.296687i
$783$	−4.74803			−0.169681
$784$	0.0562059	+	0.0648650i	0.00200735	+	0.00231661i
$785$	9.35381	+	6.01133i	0.333852	+	0.214554i
$786$	0.176284	−	1.22608i	0.00628785	−	0.0437329i
$787$	−11.7588	+	25.7482i	−0.419156	+	0.917823i	0.575808	+	0.817585i	$0.304688\pi$
$787$	−11.7588	+	25.7482i	−0.419156	+	0.917823i	−0.994964	+	0.100238i	$0.968040\pi$
$788$	2.07480	+	14.4305i	0.0739115	+	0.514066i
$789$	−27.9776	−	8.21496i	−0.996029	−	0.292460i
$790$	3.55135	−	2.28231i	0.126351	−	0.0812010i
$791$	−10.0950	−	22.1049i	−0.358936	−	0.785961i
$792$	4.44319	−	1.30464i	0.157882	−	0.0463583i
$793$	−2.90950	+	3.35775i	−0.103320	+	0.119237i
$794$	−0.897701	+	1.03600i	−0.0318582	+	0.0367664i
$795$	7.92060	−	2.32570i	0.280915	−	0.0824841i
$796$	−6.99915	−	15.3260i	−0.248078	−	0.543216i
$797$	16.5737	−	10.6513i	0.587070	−	0.377287i	−0.213126	−	0.977025i	$-0.568365\pi$
$797$	16.5737	−	10.6513i	0.587070	−	0.377287i	0.800197	+	0.599737i	$0.204728\pi$
$798$	3.92204	+	1.15162i	0.138839	+	0.0407667i
$799$	0.865271	+	6.01809i	0.0306111	+	0.212905i
$800$	0.415415	−	0.909632i	0.0146871	−	0.0321603i
$801$	−1.01747	+	7.07666i	−0.0359505	+	0.250041i
$802$	−14.0080	−	9.00241i	−0.494640	−	0.317886i
$803$	28.0677	+	32.3919i	0.990488	+	1.14308i
$804$	0.0362051			0.00127686
$805$	−0.543674	−	12.5988i	−0.0191620	−	0.444050i
$806$	1.46378			0.0515594
$807$	−19.8996	−	22.9654i	−0.700501	−	0.808421i
$808$	−9.10508	−	5.85148i	−0.320316	−	0.205854i
$809$	5.38793	−	37.4739i	0.189429	−	1.31751i	−0.644060	−	0.764975i	$-0.722751\pi$
$809$	5.38793	−	37.4739i	0.189429	−	1.31751i	0.833489	−	0.552536i	$-0.186340\pi$
$810$	0.415415	−	0.909632i	0.0145962	−	0.0319612i
$811$	1.39351	+	9.69204i	0.0489326	+	0.340334i	0.999551	+	0.0299708i	$0.00954143\pi$
$811$	1.39351	+	9.69204i	0.0489326	+	0.340334i	−0.950618	+	0.310363i	$0.899549\pi$
$812$	−11.9791	−	3.51739i	−0.420385	−	0.123436i
$813$	8.99945	−	5.78359i	0.315624	−	0.202840i
$814$	4.42448	+	9.68825i	0.155078	+	0.339573i
$815$	−9.93931	+	2.91845i	−0.348159	+	0.102229i
$816$	1.13394	−	1.30864i	0.0396959	−	0.0458115i
$817$	−6.23156	+	7.19160i	−0.218015	+	0.251602i
$818$	9.23292	−	2.71103i	0.322822	−	0.0947890i
$819$	−2.64727	−	5.79671i	−0.0925030	−	0.202553i
$820$	6.50438	−	4.18011i	0.227143	−	0.145976i
$821$	31.1362	+	9.14241i	1.08666	+	0.319072i	0.775540	−	0.631298i	$-0.217478\pi$
$821$	31.1362	+	9.14241i	1.08666	+	0.319072i	0.311120	+	0.950371i	$0.399296\pi$
$822$	1.56965	+	10.9172i	0.0547480	+	0.380781i
$823$	−3.90407	+	8.54873i	−0.136087	+	0.297990i	−0.965390	−	0.260810i	$-0.916011\pi$
$823$	−3.90407	+	8.54873i	−0.136087	+	0.297990i	0.829303	+	0.558799i	$0.188738\pi$
$824$	−1.55026	+	10.7823i	−0.0540058	+	0.375619i
$825$	−3.89565	−	2.50358i	−0.135629	−	0.0871636i
$826$	5.88361	+	6.79005i	0.204717	+	0.236256i
$827$	9.10545			0.316627			0.158314	−	0.987389i	$-0.449394\pi$
$827$	9.10545			0.316627			0.158314	+	0.987389i	$0.449394\pi$
$828$	−2.41647	+	4.14254i	−0.0839782	+	0.143963i
$829$	−30.7206			−1.06697			−0.533485	−	0.845810i	$-0.679118\pi$
$829$	−30.7206			−1.06697			−0.533485	+	0.845810i	$0.679118\pi$
$830$	−4.80991	−	5.55094i	−0.166955	−	0.192676i
$831$	26.1982	+	16.8365i	0.908804	+	0.584053i
$832$	−0.344902	+	2.39885i	−0.0119573	+	0.0831650i
$833$	0.0617386	−	0.135189i	0.00213912	−	0.00468401i
$834$	−0.256959	−	1.78719i	−0.00889775	−	0.0618852i
$835$	17.4623	+	5.12740i	0.604308	+	0.177441i
$836$	−6.05593	+	3.89191i	−0.209449	+	0.134604i
$837$	0.250907	+	0.549409i	0.00867260	+	0.0189903i
$838$	−0.908618	+	0.266794i	−0.0313877	+	0.00921626i
$839$	−9.91270	+	11.4399i	−0.342224	+	0.394948i	−0.900606	−	0.434636i	$-0.856877\pi$
$839$	−9.91270	+	11.4399i	−0.342224	+	0.394948i	0.558382	+	0.829584i	$0.311422\pi$
$840$	1.72194	−	1.98723i	0.0594127	−	0.0685659i
$841$	6.19466	−	1.81892i	0.213609	−	0.0627212i
$842$	2.84568	+	6.23118i	0.0980688	+	0.214741i
$843$	21.6386	−	13.9063i	0.745274	−	0.478959i
$844$	−3.68467	−	1.08192i	−0.126831	−	0.0372411i
$845$	1.01422	+	7.05404i	0.0348902	+	0.242667i
$846$	1.45862	−	3.19393i	0.0501484	−	0.109810i
$847$	3.90831	−	27.1829i	0.134291	−	0.934015i
$848$	−6.94454	−	4.46298i	−0.238476	−	0.153260i
$849$	16.2839	+	18.7926i	0.558861	+	0.644960i
$850$	−1.73158			−0.0593926
$851$	−10.2218	−	4.14535i	−0.350399	−	0.142101i
$852$	15.7376			0.539160
$853$	1.02965	+	1.18828i	0.0352545	+	0.0406858i	0.773103	−	0.634281i	$-0.218704\pi$
$853$	1.02965	+	1.18828i	0.0352545	+	0.0406858i	−0.737848	+	0.674966i	$0.764158\pi$
$854$	−4.05529	−	2.60617i	−0.138769	−	0.0891815i
$855$	−0.221233	+	1.53871i	−0.00756602	+	0.0526228i
$856$	−1.17469	+	2.57222i	−0.0401502	+	0.0879167i
$857$	7.75946	+	53.9682i	0.265058	+	1.84352i	0.493230	+	0.869899i	$0.335816\pi$
$857$	7.75946	+	53.9682i	0.265058	+	1.84352i	−0.228171	+	0.973621i	$0.573275\pi$
$858$	10.7681	+	3.16181i	0.367618	+	0.107942i
$859$	37.4308	−	24.0553i	1.27712	−	0.820756i	0.286591	−	0.958053i	$-0.407478\pi$
$859$	37.4308	−	24.0553i	1.27712	−	0.820756i	0.990530	+	0.137297i	$0.0438415\pi$
$860$	2.54290	+	5.56818i	0.0867122	+	0.189873i
$861$	19.5070	−	5.72778i	0.664798	−	0.195202i
$862$	−23.0727	+	26.6273i	−0.785860	+	0.906931i
$863$	−29.5420	+	34.0933i	−1.00562	+	1.16055i	−0.0186236	+	0.999827i	$0.505928\pi$
$863$	−29.5420	+	34.0933i	−1.00562	+	1.16055i	−0.986999	+	0.160724i	$0.948617\pi$
$864$	−0.959493	+	0.281733i	−0.0326426	+	0.00958474i
$865$	10.0021	+	21.9016i	0.340083	+	0.744678i
$866$	−2.77815	+	1.78541i	−0.0944055	+	0.0606707i
$867$	13.4345	+	3.94472i	0.456259	+	0.133970i
$868$	0.226022	+	1.57202i	0.00767168	+	0.0533577i
$869$	−8.12086	+	17.7822i	−0.275481	+	0.603220i
$870$	0.675716	−	4.69971i	0.0229089	−	0.159335i
$871$	0.0738146	+	0.0474378i	0.00250111	+	0.00160737i
$872$	−7.40164	−	8.54195i	−0.250651	−	0.289267i
$873$	2.24523			0.0759896
$874$	1.79005	−	7.23719i	0.0605492	−	0.244802i
$875$	−2.62948			−0.0888927
$876$	−6.06113	−	6.99492i	−0.204787	−	0.236336i
$877$	−39.8608	−	25.6170i	−1.34600	−	0.865024i	−0.348616	−	0.937266i	$-0.613348\pi$
$877$	−39.8608	−	25.6170i	−1.34600	−	0.865024i	−0.997387	+	0.0722420i	$0.976985\pi$
$878$	3.04011	−	21.1445i	0.102599	−	0.713591i
$879$	9.97971	−	21.8525i	0.336607	−	0.737067i
$880$	0.659028	+	4.58364i	0.0222158	+	0.154514i
$881$	25.1216	+	7.37638i	0.846370	+	0.248517i	0.676035	−	0.736870i	$-0.263697\pi$
$881$	25.1216	+	7.37638i	0.846370	+	0.248517i	0.170335	+	0.985386i	$0.445515\pi$
$882$	−0.0722037	+	0.0464025i	−0.00243123	+	0.00156245i
$883$	9.63247	+	21.0922i	0.324158	+	0.709808i	0.999619	−	0.0275880i	$-0.00878264\pi$
$883$	9.63247	+	21.0922i	0.324158	+	0.709808i	−0.675461	+	0.737396i	$0.736055\pi$
$884$	4.02651	−	1.18229i	0.135426	−	0.0397647i
$885$	−2.23756	+	2.58228i	−0.0752146	+	0.0868023i
$886$	26.4380	−	30.5111i	0.888203	−	1.02504i
$887$	25.0615	−	7.35871i	0.841481	−	0.247081i	0.167539	−	0.985865i	$-0.446418\pi$
$887$	25.0615	−	7.35871i	0.841481	−	0.247081i	0.673942	+	0.738784i	$0.264600\pi$
$888$	−0.955451	−	2.09215i	−0.0320628	−	0.0702078i
$889$	−29.0236	+	18.6524i	−0.973421	+	0.625580i
$890$	−6.85982	−	2.01423i	−0.229942	−	0.0675170i
$891$	0.659028	+	4.58364i	0.0220783	+	0.153558i
$892$	−8.61127	+	18.8561i	−0.288327	+	0.631348i
$893$	−0.776802	+	5.40278i	−0.0259947	+	0.180797i
$894$	−1.63913	−	1.05340i	−0.0548207	−	0.0352311i
$895$	7.01658	+	8.09756i	0.234538	+	0.270672i
$896$	−2.62948			−0.0878448
$897$	−10.3544	+	5.27959i	−0.345725	+	0.176280i
$898$	−1.53718			−0.0512965
$899$	1.87799	+	2.16731i	0.0626344	+	0.0722839i
$900$	0.841254	+	0.540641i	0.0280418	+	0.0180214i
$901$	−2.03427	+	14.1487i	−0.0677713	+	0.471360i
$902$	−14.8736	+	32.5685i	−0.495235	+	1.08441i
$903$	2.29070	+	15.9321i	0.0762296	+	0.530189i
$904$	−8.86738	−	2.60370i	−0.294925	−	0.0865977i
$905$	−2.49370	+	1.60260i	−0.0828934	+	0.0532723i
$906$	8.13916	+	17.8223i	0.270405	+	0.592105i
$907$	−39.4758	+	11.5911i	−1.31077	+	0.384877i	−0.861154	−	0.508344i	$-0.830258\pi$
$907$	−39.4758	+	11.5911i	−1.31077	+	0.384877i	−0.449617	+	0.893221i	$0.648440\pi$
$908$	1.16721	−	1.34704i	0.0387353	−	0.0447029i
$909$	7.08771	−	8.17965i	0.235084	−	0.271302i
$910$	6.11445	−	1.79536i	0.202692	−	0.0595157i
$911$	−14.5039	−	31.7590i	−0.480535	−	1.05222i	−0.982316	−	0.187230i	$-0.940049\pi$
$911$	−14.5039	−	31.7590i	−0.480535	−	1.05222i	0.501782	−	0.864994i	$-0.332678\pi$
$912$	1.30776	−	0.840445i	0.0433042	−	0.0278299i
$913$	32.6350	+	9.58250i	1.08006	+	0.317134i
$914$	−3.94350	−	27.4277i	−0.130439	−	0.907226i
$915$	0.761565	−	1.66759i	0.0251766	−	0.0551290i
$916$	0.314717	−	2.18890i	0.0103985	−	0.0723233i
$917$	2.74006	+	1.76093i	0.0904847	+	0.0581510i
$918$	1.13394	+	1.30864i	0.0374257	+	0.0431915i
$919$	−18.9946			−0.626573			−0.313286	−	0.949659i	$-0.601430\pi$
$919$	−18.9946			−0.626573			−0.313286	+	0.949659i	$0.601430\pi$
$920$	−3.75648	−	2.98142i	−0.123847	−	0.0982946i
$921$	33.9331			1.11813
$922$	−28.0083	−	32.3233i	−0.922405	−	1.06451i
$923$	32.0856	+	20.6201i	1.05611	+	0.678720i
$924$	−1.73290	+	12.0526i	−0.0570082	+	0.396501i
$925$	−0.955451	+	2.09215i	−0.0314150	+	0.0687894i
$926$	−1.61422	−	11.2272i	−0.0530466	−	0.368947i
$927$	−10.4519	−	3.06896i	−0.343286	−	0.100798i
$928$	−3.99430	+	2.56698i	−0.131119	+	0.0842653i
$929$	4.75757	+	10.4176i	0.156091	+	0.341791i	0.971480	−	0.237122i	$-0.0762042\pi$
$929$	4.75757	+	10.4176i	0.156091	+	0.341791i	−0.815389	+	0.578913i	$0.803477\pi$
$930$	−0.579524	+	0.170164i	−0.0190034	+	0.00557989i
$931$	0.0873739	−	0.100835i	0.00286356	−	0.00330473i
$932$	13.6575	−	15.7616i	0.447366	−	0.516288i
$933$	−12.4655	+	3.66021i	−0.408103	+	0.119830i
$934$	14.4154	+	31.5654i	0.471688	+	1.03285i
$935$	6.74562	−	4.33515i	0.220605	−	0.141775i
$936$	−2.32534	−	0.682783i	−0.0760062	−	0.0223174i
$937$	1.06082	+	7.37817i	0.0346555	+	0.241034i	0.999785	−	0.0207389i	$-0.00660188\pi$
$937$	1.06082	+	7.37817i	0.0346555	+	0.241034i	−0.965129	+	0.261773i	$0.915693\pi$
$938$	−0.0395478	+	0.0865976i	−0.00129128	+	0.00282751i
$939$	3.12294	−	21.7206i	0.101913	−	0.708824i
$940$	2.95384	+	1.89832i	0.0963437	+	0.0619163i
$941$	10.6533	+	12.2945i	0.347287	+	0.400790i	0.902340	−	0.431024i	$-0.141848\pi$
$941$	10.6533	+	12.2945i	0.347287	+	0.400790i	−0.555054	+	0.831815i	$0.687302\pi$
$942$	11.1189			0.362273
$943$	−11.9709	−	35.0948i	−0.389826	−	1.14284i
$944$	3.41684			0.111209
$945$	1.72194	+	1.98723i	0.0560148	+	0.0646446i
$946$	−23.8467	−	15.3253i	−0.775322	−	0.498269i
$947$	−0.540412	+	3.75864i	−0.0175610	+	0.122140i	−0.996716	−	0.0809739i	$-0.974197\pi$
$947$	−0.540412	+	3.75864i	−0.0175610	+	0.122140i	0.979155	+	0.203113i	$0.0651060\pi$
$948$	1.75367	−	3.84001i	0.0569566	−	0.124718i
$949$	−3.19227	−	22.2028i	−0.103626	−	0.720732i
$950$	−1.49156	−	0.437963i	−0.0483927	−	0.0142094i
$951$	−3.08144	+	1.98032i	−0.0999227	+	0.0642164i
$952$	1.89145	+	4.14169i	0.0613021	+	0.134233i
$953$	1.41358	−	0.415064i	0.0457903	−	0.0134452i	−0.258757	−	0.965942i	$-0.583313\pi$
$953$	1.41358	−	0.415064i	0.0457903	−	0.0134452i	0.304547	+	0.952497i	$0.401495\pi$
$954$	5.40587	−	6.23870i	0.175021	−	0.201986i
$955$	−8.77580	+	10.1278i	−0.283978	+	0.327728i
$956$	27.4697	−	8.06584i	0.888434	−	0.260868i
$957$	9.13375	+	20.0001i	0.295252	+	0.646512i
$958$	28.5041	−	18.3185i	0.920925	−	0.591843i
$959$	−27.8270	−	8.17073i	−0.898579	−	0.263847i
$960$	−0.142315	−	0.989821i	−0.00459319	−	0.0319463i
$961$	−12.7263	+	27.8668i	−0.410526	+	0.898928i
$962$	0.793272	−	5.51733i	0.0255761	−	0.177886i
$963$	−2.37886	−	1.52880i	−0.0766578	−	0.0492650i
$964$	−10.1465	−	11.7097i	−0.326797	−	0.377144i
$965$	12.3370			0.397142
$966$	−7.26881	−	10.3049i	−0.233870	−	0.331554i
$967$	27.0197			0.868894			0.434447	−	0.900697i	$-0.356944\pi$
$967$	27.0197			0.868894			0.434447	+	0.900697i	$0.356944\pi$
$968$	−6.83940	−	7.89308i	−0.219827	−	0.253693i
$969$	−2.26448	−	1.45529i	−0.0727457	−	0.0467508i
$970$	−0.319530	+	2.22238i	−0.0102595	+	0.0713563i
$971$	2.58166	−	5.65305i	0.0828494	−	0.181415i	−0.863673	−	0.504052i	$-0.831842\pi$
$971$	2.58166	−	5.65305i	0.0828494	−	0.181415i	0.946523	+	0.322637i	$0.104569\pi$
$972$	−0.142315	−	0.989821i	−0.00456475	−	0.0317485i
$973$	4.55538	+	1.33758i	0.146039	+	0.0428809i
$974$	−10.3987	+	6.68283i	−0.333195	+	0.214132i
$975$	1.00676	+	2.20451i	0.0322422	+	0.0706007i
$976$	−1.75900	+	0.516490i	−0.0563043	+	0.0165324i
$977$	−21.6405	+	24.9745i	−0.692341	+	0.799004i	−0.987696	−	0.156384i	$-0.950016\pi$
$977$	−21.6405	+	24.9745i	−0.692341	+	0.799004i	0.295356	+	0.955387i	$0.404562\pi$
$978$	−6.78365	+	7.82875i	−0.216917	+	0.250336i
$979$	31.7663	−	9.32742i	1.01525	−	0.298106i
$980$	−0.0356545	−	0.0780726i	−0.00113894	−	0.00249394i
$981$	9.50837	−	6.11066i	0.303579	−	0.195098i
$982$	−1.62896	−	0.478304i	−0.0519820	−	0.0152633i
$983$	−1.61183	−	11.2105i	−0.0514095	−	0.357561i	−0.999247	−	0.0388063i	$-0.987644\pi$
$983$	−1.61183	−	11.2105i	−0.0514095	−	0.357561i	0.947837	−	0.318755i	$-0.103265\pi$
$984$	3.21189	−	7.03307i	0.102391	−	0.224206i
$985$	2.07480	−	14.4305i	0.0661085	−	0.459794i
$986$	6.91644	+	4.44492i	0.220264	+	0.141555i
$987$	6.04615	+	6.97763i	0.192451	+	0.222101i
$988$	3.76743			0.119858
$989$	28.8510	−	5.42682i	0.917409	−	0.172563i
$990$	−4.63077			−0.147176
$991$	−36.9234	−	42.6119i	−1.17291	−	1.35361i	−0.922746	−	0.385407i	$-0.874061\pi$
$991$	−36.9234	−	42.6119i	−1.17291	−	1.35361i	−0.250164	−	0.968203i	$-0.580485\pi$
$992$	0.508109	+	0.326542i	0.0161325	+	0.0103677i
$993$	−1.55750	+	10.8327i	−0.0494258	+	0.343764i
$994$	−17.1905	+	37.6420i	−0.545251	+	1.19393i
$995$	2.39780	+	16.6771i	0.0760154	+	0.528699i
$996$	−7.04742	−	2.06931i	−0.223306	−	0.0655686i
$997$	33.9560	−	21.8222i	1.07540	−	0.691115i	0.121907	−	0.992542i	$-0.461099\pi$
$997$	33.9560	−	21.8222i	1.07540	−	0.691115i	0.953490	+	0.301426i	$0.0974627\pi$
$998$	5.38694	+	11.7958i	0.170521	+	0.373388i
$999$	2.20683	−	0.647983i	0.0698209	−	0.0205013i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.g.151.3	✓	30
23.16	even	11	inner	690.2.m.g.361.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.g.151.3	✓	30	1.1	even	1	trivial
690.2.m.g.361.3	yes	30	23.16	even	11	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 - 0.755750i) q^{2} +(0.841254 + 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(2.52297 + 0.740810i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.654861 - 0.755750i) q^{2} +(0.841254 + 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(2.52297 + 0.740810i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +(-0.959493 + 0.281733i) q^{10} +(3.03251 - 3.49970i) q^{11} +(-0.654861 + 0.755750i) q^{12} +(-2.32534 + 0.682783i) q^{13} +(-1.09233 - 2.39186i) q^{14} +(0.841254 - 0.540641i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.246429 + 1.71395i) q^{17} +(0.415415 - 0.909632i) q^{18} +(-0.221233 + 1.53871i) q^{19} +(0.841254 + 0.540641i) q^{20} +(1.72194 + 1.98723i) q^{21} -4.63077 q^{22} +(3.48568 - 3.29394i) q^{23} +1.00000 q^{24} +(-0.654861 - 0.755750i) q^{25} +(2.03879 + 1.31025i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(-1.09233 + 2.39186i) q^{28} +(0.675716 + 4.69971i) q^{29} +(-0.959493 - 0.281733i) q^{30} +(0.508109 - 0.326542i) q^{31} +(0.415415 + 0.909632i) q^{32} +(4.44319 - 1.30464i) q^{33} +(1.13394 - 1.30864i) q^{34} +(1.72194 - 1.98723i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-0.955451 - 2.09215i) q^{37} +(1.30776 - 0.840445i) q^{38} +(-2.32534 - 0.682783i) q^{39} +(-0.142315 - 0.989821i) q^{40} +(3.21189 - 7.03307i) q^{41} +(0.374214 - 2.60272i) q^{42} +(5.14961 + 3.30945i) q^{43} +(3.03251 + 3.49970i) q^{44} +1.00000 q^{45} +(-4.77203 - 0.477227i) q^{46} +3.51124 q^{47} +(-0.654861 - 0.755750i) q^{48} +(-0.0722037 - 0.0464025i) q^{49} +(-0.142315 + 0.989821i) q^{50} +(-0.719323 + 1.57510i) q^{51} +(-0.344902 - 2.39885i) q^{52} +(7.92060 + 2.32570i) q^{53} +(0.841254 - 0.540641i) q^{54} +(-1.92369 - 4.21230i) q^{55} +(2.52297 - 0.740810i) q^{56} +(-1.01800 + 1.17484i) q^{57} +(3.10930 - 3.58832i) q^{58} +(-3.27844 + 0.962636i) q^{59} +(0.415415 + 0.909632i) q^{60} +(1.54224 - 0.991137i) q^{61} +(-0.579524 - 0.170164i) q^{62} +(0.374214 + 2.60272i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.344902 + 2.39885i) q^{65} +(-3.89565 - 2.50358i) q^{66} +(-0.0237093 - 0.0273620i) q^{67} -1.73158 q^{68} +(4.71318 - 0.886540i) q^{69} -2.62948 q^{70} +(-10.3059 - 11.8936i) q^{71} +(0.841254 + 0.540641i) q^{72} +(-1.31721 + 9.16139i) q^{73} +(-0.955451 + 2.09215i) q^{74} +(-0.142315 - 0.989821i) q^{75} +(-1.49156 - 0.437963i) q^{76} +(10.2435 - 6.58313i) q^{77} +(1.00676 + 2.20451i) q^{78} +(-4.05050 + 1.18933i) q^{79} +(-0.654861 + 0.755750i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-7.41858 + 2.17829i) q^{82} +(3.05120 + 6.68119i) q^{83} +(-2.21206 + 1.42160i) q^{84} +(1.66144 + 0.487842i) q^{85} +(-0.871159 - 6.05905i) q^{86} +(-1.97240 + 4.31896i) q^{87} +(0.659028 - 4.58364i) q^{88} +(6.01448 + 3.86527i) q^{89} +(-0.654861 - 0.755750i) q^{90} -6.37258 q^{91} +(2.76435 + 3.91898i) q^{92} +0.603990 q^{93} +(-2.29937 - 2.65362i) q^{94} +(1.30776 + 0.840445i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(0.932704 - 2.04234i) q^{97} +(0.0122147 + 0.0849551i) q^{98} +(4.44319 + 1.30464i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * q^99

Introduction

L-functions

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Database

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