LMFDB - Embedded newform 572.2.bk.a.31.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(31,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 12, 15]))

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

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

chi := DirichletCharacter("572.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bk (of order $20$, degree $8$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$80$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			31.17
Character	$\chi$	$=$	572.31
Dual form			572.2.bk.a.203.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13998 - 0.836921i) q^{2} +(-1.62851 - 2.24145i) q^{3} +(0.599125 + 1.90815i) q^{4} +(2.91084 + 1.48315i) q^{5} +(-0.0194442 + 3.91816i) q^{6} +(-4.55254 + 0.721051i) q^{7} +(0.913981 - 2.67668i) q^{8} +(-1.44502 + 4.44730i) q^{9} +O(q^{10})$	\(q+(-1.13998 - 0.836921i) q^{2} +(-1.62851 - 2.24145i) q^{3} +(0.599125 + 1.90815i) q^{4} +(2.91084 + 1.48315i) q^{5} +(-0.0194442 + 3.91816i) q^{6} +(-4.55254 + 0.721051i) q^{7} +(0.913981 - 2.67668i) q^{8} +(-1.44502 + 4.44730i) q^{9} +(-2.07704 - 4.12691i) q^{10} +(2.56483 + 2.10277i) q^{11} +(3.30136 - 4.45036i) q^{12} +(-3.18197 - 1.69560i) q^{13} +(5.79328 + 2.98813i) q^{14} +(-1.41593 - 8.93985i) q^{15} +(-3.28210 + 2.28645i) q^{16} +(3.96347 - 1.28781i) q^{17} +(5.36934 - 3.86049i) q^{18} +(4.75150 + 0.752564i) q^{19} +(-1.08612 + 6.44293i) q^{20} +(9.03007 + 9.03007i) q^{21} +(-1.16401 - 4.54368i) q^{22} +4.93054 q^{23} +(-7.48810 + 2.31036i) q^{24} +(3.33435 + 4.58934i) q^{25} +(2.20831 + 4.59602i) q^{26} +(4.41669 - 1.43507i) q^{27} +(-4.10342 - 8.25494i) q^{28} +(0.708501 + 0.514756i) q^{29} +(-5.86781 + 11.3763i) q^{30} +(7.88162 - 4.01588i) q^{31} +(5.65511 + 0.140348i) q^{32} +(0.536402 - 9.17334i) q^{33} +(-5.59609 - 1.84903i) q^{34} +(-14.3212 - 4.65322i) q^{35} +(-9.35188 - 0.0928215i) q^{36} +(-0.197253 - 1.24541i) q^{37} +(-4.78680 - 4.83455i) q^{38} +(1.38126 + 9.89355i) q^{39} +(6.63038 - 6.43584i) q^{40} +(0.571993 - 3.61142i) q^{41} +(-2.73667 - 17.8516i) q^{42} -3.41144 q^{43} +(-2.47575 + 6.15391i) q^{44} +(-10.8022 + 10.8022i) q^{45} +(-5.62073 - 4.12647i) q^{46} +(-0.360302 + 2.27486i) q^{47} +(10.4699 + 3.63317i) q^{48} +(13.5483 - 4.40211i) q^{49} +(0.0398118 - 8.02237i) q^{50} +(-9.34113 - 6.78673i) q^{51} +(1.32907 - 7.08756i) q^{52} +(1.39374 - 4.28948i) q^{53} +(-6.23600 - 2.06047i) q^{54} +(4.34711 + 9.92486i) q^{55} +(-2.23091 + 12.8447i) q^{56} +(-6.05104 - 11.8758i) q^{57} +(-0.376869 - 1.17977i) q^{58} +(2.57466 - 0.407786i) q^{59} +(16.2103 - 8.05791i) q^{60} +(0.657419 + 2.02333i) q^{61} +(-12.3459 - 2.01825i) q^{62} +(3.37176 - 21.2884i) q^{63} +(-6.32928 - 4.89288i) q^{64} +(-6.74739 - 9.65497i) q^{65} +(-8.28885 + 10.0085i) q^{66} +(6.32540 + 6.32540i) q^{67} +(4.83195 + 6.79135i) q^{68} +(-8.02944 - 11.0516i) q^{69} +(12.4315 + 17.2903i) q^{70} +(2.28645 - 4.48741i) q^{71} +(10.5833 + 7.93261i) q^{72} +(0.683121 + 4.31306i) q^{73} +(-0.817441 + 1.58483i) q^{74} +(4.85677 - 14.9476i) q^{75} +(1.41074 + 9.51748i) q^{76} +(-13.1927 - 7.72356i) q^{77} +(6.70551 - 12.4345i) q^{78} +(-11.9681 - 3.88866i) q^{79} +(-12.9448 + 1.78764i) q^{80} +(0.940025 + 0.682968i) q^{81} +(-3.67454 + 3.63825i) q^{82} +(2.52104 - 4.94781i) q^{83} +(-11.8206 + 22.6409i) q^{84} +(13.4471 + 2.12980i) q^{85} +(3.88899 + 2.85511i) q^{86} -2.42636i q^{87} +(7.97266 - 4.94335i) q^{88} +(-0.113348 - 0.113348i) q^{89} +(21.3550 - 3.27375i) q^{90} +(15.7087 + 5.42493i) q^{91} +(2.95401 + 9.40822i) q^{92} +(-21.8367 - 11.1264i) q^{93} +(2.31462 - 2.29176i) q^{94} +(12.7147 + 9.23779i) q^{95} +(-8.89484 - 12.9042i) q^{96} +(7.27341 + 14.2749i) q^{97} +(-19.1290 - 6.32052i) q^{98} +(-13.0579 + 8.36805i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9}+O(q^{10}) $ 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9	$ 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9} - 12 q^{13} + 4 q^{14} - 36 q^{16} - 10 q^{18} - 60 q^{20} - 56 q^{21} - 44 q^{22} - 14 q^{24} + 26 q^{26} - 14 q^{28} - 24 q^{29} - 16 q^{32} - 28 q^{33} + 12 q^{34} - 12 q^{37} + 4 q^{40} - 36 q^{41} - 8 q^{42} + 26 q^{44} - 16 q^{45} - 50 q^{46} + 48 q^{48} + 36 q^{50} - 52 q^{52} - 40 q^{53} + 116 q^{54} - 36 q^{57} - 70 q^{58} + 52 q^{60} - 8 q^{61} - 48 q^{65} - 228 q^{66} - 44 q^{68} - 68 q^{70} - 38 q^{72} - 12 q^{73} - 12 q^{74} + 108 q^{76} + 108 q^{78} + 62 q^{80} - 168 q^{81} - 36 q^{84} - 52 q^{85} - 62 q^{86} + 16 q^{89} - 80 q^{92} - 4 q^{93} - 124 q^{94} - 132 q^{96} - 4 q^{97} - 108 q^{98}+O(q^{100}) $ 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9 - 12 * q^13 + 4 * q^14 - 36 * q^16 - 10 * q^18 - 60 * q^20 - 56 * q^21 - 44 * q^22 - 14 * q^24 + 26 * q^26 - 14 * q^28 - 24 * q^29 - 16 * q^32 - 28 * q^33 + 12 * q^34 - 12 * q^37 + 4 * q^40 - 36 * q^41 - 8 * q^42 + 26 * q^44 - 16 * q^45 - 50 * q^46 + 48 * q^48 + 36 * q^50 - 52 * q^52 - 40 * q^53 + 116 * q^54 - 36 * q^57 - 70 * q^58 + 52 * q^60 - 8 * q^61 - 48 * q^65 - 228 * q^66 - 44 * q^68 - 68 * q^70 - 38 * q^72 - 12 * q^73 - 12 * q^74 + 108 * q^76 + 108 * q^78 + 62 * q^80 - 168 * q^81 - 36 * q^84 - 52 * q^85 - 62 * q^86 + 16 * q^89 - 80 * q^92 - 4 * q^93 - 124 * q^94 - 132 * q^96 - 4 * q^97 - 108 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.13998	−	0.836921i	−0.806090	−	0.591793i
$2$	−1.13998	−	0.836921i	−0.806090	−	0.591793i
$3$	−1.62851	−	2.24145i	−0.940222	−	1.29410i	−0.955736	−	0.294225i	$-0.904939\pi$
$3$	−1.62851	−	2.24145i	−0.940222	−	1.29410i	0.0155143	−	0.999880i	$-0.495061\pi$
$4$	0.599125	+	1.90815i	0.299563	+	0.954077i
$5$	2.91084	+	1.48315i	1.30177	+	0.663284i	0.960918	−	0.276833i	$-0.0892849\pi$
$5$	2.91084	+	1.48315i	1.30177	+	0.663284i	0.340851	+	0.940117i	$0.389285\pi$
$6$	−0.0194442	+	3.91816i	−0.00793807	+	1.59958i
$7$	−4.55254	+	0.721051i	−1.72070	+	0.272532i	−0.937182	−	0.348841i	$-0.886575\pi$
$7$	−4.55254	+	0.721051i	−1.72070	+	0.272532i	−0.783515	+	0.621372i	$0.786575\pi$
$8$	0.913981	−	2.67668i	0.323141	−	0.946351i
$9$	−1.44502	+	4.44730i	−0.481672	+	1.48243i
$10$	−2.07704	−	4.12691i	−0.656816	−	1.30504i
$11$	2.56483	+	2.10277i	0.773326	+	0.634009i
$11$	2.56483	+	2.10277i	0.773326	+	0.634009i
$12$	3.30136	−	4.45036i	0.953020	−	1.28471i
$13$	−3.18197	−	1.69560i	−0.882520	−	0.470275i
$13$	−3.18197	−	1.69560i	−0.882520	−	0.470275i
$14$	5.79328	+	2.98813i	1.54832	+	0.798611i
$15$	−1.41593	−	8.93985i	−0.365592	−	2.30826i
$16$	−3.28210	+	2.28645i	−0.820525	+	0.571611i
$17$	3.96347	−	1.28781i	0.961283	−	0.312340i	0.213991	−	0.976836i	$-0.431354\pi$
$17$	3.96347	−	1.28781i	0.961283	−	0.312340i	0.747292	+	0.664496i	$0.231354\pi$
$18$	5.36934	−	3.86049i	1.26557	−	0.909926i
$19$	4.75150	+	0.752564i	1.09007	+	0.172650i	0.675495	−	0.737365i	$-0.263930\pi$
$19$	4.75150	+	0.752564i	1.09007	+	0.172650i	0.414575	+	0.910015i	$0.363930\pi$
$20$	−1.08612	+	6.44293i	−0.242863	+	1.44068i
$21$	9.03007	+	9.03007i	1.97052	+	1.97052i
$22$	−1.16401	−	4.54368i	−0.248169	−	0.968717i
$23$	4.93054			1.02809			0.514044	−	0.857764i	$-0.328147\pi$
$23$	4.93054			1.02809			0.514044	+	0.857764i	$0.328147\pi$
$24$	−7.48810	+	2.31036i	−1.52850	+	0.471601i
$25$	3.33435	+	4.58934i	0.666871	+	0.917869i
$26$	2.20831	+	4.59602i	0.433085	+	0.901353i
$27$	4.41669	−	1.43507i	0.849993	−	0.276179i
$28$	−4.10342	−	8.25494i	−0.775473	−	1.56004i
$29$	0.708501	+	0.514756i	0.131565	+	0.0955879i	0.651622	−	0.758544i	$-0.274089\pi$
$29$	0.708501	+	0.514756i	0.131565	+	0.0955879i	−0.520056	+	0.854132i	$0.674089\pi$
$30$	−5.86781	+	11.3763i	−1.07131	+	2.07702i
$31$	7.88162	−	4.01588i	1.41558	−	0.721274i	0.432021	−	0.901863i	$-0.357800\pi$
$31$	7.88162	−	4.01588i	1.41558	−	0.721274i	0.983559	+	0.180589i	$0.0578005\pi$
$32$	5.65511	+	0.140348i	0.999692	+	0.0248102i
$33$	0.536402	−	9.17334i	0.0933755	−	1.59687i
$34$	−5.59609	−	1.84903i	−0.959721	−	0.317106i
$35$	−14.3212	−	4.65322i	−2.42072	−	0.786538i
$36$	−9.35188	−	0.0928215i	−1.55865	−	0.0154702i
$37$	−0.197253	−	1.24541i	−0.0324282	−	0.204743i	0.966155	−	0.257964i	$-0.0830515\pi$
$37$	−0.197253	−	1.24541i	−0.0324282	−	0.204743i	−0.998583	+	0.0532202i	$0.983051\pi$
$38$	−4.78680	−	4.83455i	−0.776522	−	0.784267i
$39$	1.38126	+	9.89355i	0.221179	+	1.58424i
$40$	6.63038	−	6.43584i	1.04835	−	1.01760i
$41$	0.571993	−	3.61142i	0.0893302	−	0.564009i	−0.901909	−	0.431927i	$-0.857834\pi$
$41$	0.571993	−	3.61142i	0.0893302	−	0.564009i	0.991239	−	0.132082i	$-0.0421662\pi$
$42$	−2.73667	−	17.8516i	−0.422278	−	2.75456i
$43$	−3.41144			−0.520240			−0.260120	−	0.965576i	$-0.583762\pi$
$43$	−3.41144			−0.520240			−0.260120	+	0.965576i	$0.583762\pi$
$44$	−2.47575	+	6.15391i	−0.373233	+	0.927737i
$45$	−10.8022	+	10.8022i	−1.61030	+	1.61030i
$46$	−5.62073	−	4.12647i	−0.828731	−	0.608415i
$47$	−0.360302	+	2.27486i	−0.0525555	+	0.331822i	0.947376	+	0.320123i	$0.103724\pi$
$47$	−0.360302	+	2.27486i	−0.0525555	+	0.331822i	−0.999932	+	0.0116996i	$0.996276\pi$
$48$	10.4699	+	3.63317i	1.51120	+	0.524403i
$49$	13.5483	−	4.40211i	1.93547	−	0.628872i
$50$	0.0398118	−	8.02237i	0.00563023	−	1.13453i
$51$	−9.34113	−	6.78673i	−1.30802	−	0.950332i
$52$	1.32907	−	7.08756i	0.184309	−	0.982868i
$53$	1.39374	−	4.28948i	0.191444	−	0.589205i	−0.808555	−	0.588420i	$-0.799750\pi$
$53$	1.39374	−	4.28948i	0.191444	−	0.589205i	1.00000		0.000785131i	$-0.000249915\pi$
$54$	−6.23600	−	2.06047i	−0.848612	−	0.280394i
$55$	4.34711	+	9.92486i	0.586164	+	1.33827i
$56$	−2.23091	+	12.8447i	−0.298118	+	1.71645i
$57$	−6.05104	−	11.8758i	−0.801480	−	1.57299i
$58$	−0.376869	−	1.17977i	−0.0494854	−	0.154912i
$59$	2.57466	−	0.407786i	0.335192	−	0.0530892i	0.0134300	−	0.999910i	$-0.495725\pi$
$59$	2.57466	−	0.407786i	0.335192	−	0.0530892i	0.321762	+	0.946821i	$0.395725\pi$
$60$	16.2103	−	8.05791i	2.09274	−	1.04027i
$61$	0.657419	+	2.02333i	0.0841738	+	0.259060i	0.984281	−	0.176607i	$-0.0565123\pi$
$61$	0.657419	+	2.02333i	0.0841738	+	0.259060i	−0.900108	+	0.435668i	$0.856512\pi$
$62$	−12.3459	−	2.01825i	−1.56793	−	0.256318i
$63$	3.37176	−	21.2884i	0.424802	−	2.68209i
$64$	−6.32928	−	4.89288i	−0.791159	−	0.611610i
$65$	−6.74739	−	9.65497i	−0.836910	−	1.19755i
$66$	−8.28885	+	10.0085i	−1.02029	+	1.23196i
$67$	6.32540	+	6.32540i	0.772771	+	0.772771i	0.978590	−	0.205819i	$-0.0659859\pi$
$67$	6.32540	+	6.32540i	0.772771	+	0.772771i	−0.205819	+	0.978590i	$0.565986\pi$
$68$	4.83195	+	6.79135i	0.585960	+	0.823572i
$69$	−8.02944	−	11.0516i	−0.966631	−	1.33045i
$70$	12.4315	+	17.2903i	1.48585	+	2.06658i
$71$	2.28645	−	4.48741i	0.271352	−	0.532557i	−0.714611	−	0.699522i	$-0.753396\pi$
$71$	2.28645	−	4.48741i	0.271352	−	0.532557i	0.985963	+	0.166964i	$0.0533964\pi$
$72$	10.5833	+	7.93261i	1.24725	+	0.934866i
$73$	0.683121	+	4.31306i	0.0799533	+	0.504805i	0.994870	+	0.101162i	$0.0322562\pi$
$73$	0.683121	+	4.31306i	0.0799533	+	0.504805i	−0.914917	+	0.403643i	$0.867744\pi$
$74$	−0.817441	+	1.58483i	−0.0950256	+	0.184232i
$75$	4.85677	−	14.9476i	0.560812	−	1.72600i
$76$	1.41074	+	9.51748i	0.161823	+	1.09173i
$77$	−13.1927	−	7.72356i	−1.50345	−	0.880181i
$78$	6.70551	−	12.4345i	0.759249	−	1.40793i
$79$	−11.9681	−	3.88866i	−1.34651	−	0.437508i	−0.454995	−	0.890494i	$-0.650359\pi$
$79$	−11.9681	−	3.88866i	−1.34651	−	0.437508i	−0.891518	+	0.452986i	$0.850359\pi$
$80$	−12.9448	+	1.78764i	−1.44727	+	0.199865i
$81$	0.940025	+	0.682968i	0.104447	+	0.0758854i
$82$	−3.67454	+	3.63825i	−0.405785	+	0.401777i
$83$	2.52104	−	4.94781i	0.276720	−	0.543093i	−0.710260	−	0.703940i	$-0.751422\pi$
$83$	2.52104	−	4.94781i	0.276720	−	0.543093i	0.986979	+	0.160847i	$0.0514225\pi$
$84$	−11.8206	+	22.6409i	−1.28973	+	2.47032i
$85$	13.4471	+	2.12980i	1.45854	+	0.231010i
$86$	3.88899	+	2.85511i	0.419360	+	0.307874i
$87$		−	2.42636i		−	0.260133i
$88$	7.97266	−	4.94335i	0.849888	−	0.526963i
$89$	−0.113348	−	0.113348i	−0.0120149	−	0.0120149i	0.701074	−	0.713089i	$-0.252704\pi$
$89$	−0.113348	−	0.113348i	−0.0120149	−	0.0120149i	−0.713089	+	0.701074i	$0.752704\pi$
$90$	21.3550	−	3.27375i	2.25101	−	0.345083i
$91$	15.7087	+	5.42493i	1.64671	+	0.568687i
$92$	2.95401	+	9.40822i	0.307977	+	0.980875i
$93$	−21.8367	−	11.1264i	−2.26436	−	1.15375i
$94$	2.31462	−	2.29176i	0.238735	−	0.236377i
$95$	12.7147	+	9.23779i	1.30450	+	0.947777i
$96$	−8.89484	−	12.9042i	−0.907826	−	1.31703i
$97$	7.27341	+	14.2749i	0.738503	+	1.44939i	0.887621	+	0.460575i	$0.152357\pi$
$97$	7.27341	+	14.2749i	0.738503	+	1.44939i	−0.149118	+	0.988819i	$0.547643\pi$
$98$	−19.1290	−	6.32052i	−1.93233	−	0.638469i
$99$	−13.0579	+	8.36805i	−1.31237	+	0.841021i
$100$	−6.75948	+	9.11205i	−0.675948	+	0.911205i
$101$	2.97156	+	0.965518i	0.295681	+	0.0960726i	0.453101	−	0.891459i	$-0.350318\pi$
$101$	2.97156	+	0.965518i	0.295681	+	0.0960726i	−0.157420	+	0.987532i	$0.550318\pi$
$102$	4.96878	+	15.5545i	0.491982	+	1.54013i
$103$	3.15877	+	2.29498i	0.311243	+	0.226131i	0.732430	−	0.680843i	$-0.238386\pi$
$103$	3.15877	+	2.29498i	0.311243	+	0.226131i	−0.421187	+	0.906974i	$0.638386\pi$
$104$	−7.44685	+	6.96738i	−0.730224	+	0.683208i
$105$	12.8922	+	39.6780i	1.25815	+	3.87218i
$106$	−5.17879	+	3.72349i	−0.503009	+	0.361657i
$107$	9.16336	+	12.6123i	0.885856	+	1.21928i	0.974764	+	0.223236i	$0.0716621\pi$
$107$	9.16336	+	12.6123i	0.885856	+	1.21928i	−0.0889086	+	0.996040i	$0.528338\pi$
$108$	5.38449	+	7.56794i	0.518122	+	0.728225i
$109$	8.00435	−	8.00435i	0.766677	−	0.766677i	−0.210843	−	0.977520i	$-0.567621\pi$
$109$	8.00435	−	8.00435i	0.766677	−	0.766677i	0.977520	+	0.210843i	$0.0676208\pi$
$110$	3.35070	−	14.9524i	0.319477	−	1.42565i
$111$	−2.47029	+	2.47029i	−0.234470	+	0.234470i
$112$	13.2932	−	12.7757i	1.25609	−	1.20719i
$113$	−13.6719	+	9.93319i	−1.28614	+	0.934436i	−0.999720	−	0.0236682i	$-0.992465\pi$
$113$	−13.6719	+	9.93319i	−1.28614	+	0.934436i	−0.286421	+	0.958104i	$0.592465\pi$
$114$	−3.04106	+	18.6025i	−0.284821	+	1.74229i
$115$	14.3520	+	7.31272i	1.33833	+	0.681915i
$116$	−0.557753	+	1.66033i	−0.0517861	+	0.154158i
$117$	12.1389	−	11.7010i	1.12224	−	1.08176i
$118$	−3.27635	−	1.68992i	−0.301613	−	0.155569i
$119$	−17.1153	+	8.72067i	−1.56895	+	0.799422i
$120$	−25.2233	−	4.38085i	−2.30256	−	0.399915i
$121$	2.15673	+	10.7865i	0.196066	+	0.980591i
$122$	0.943919	−	2.85677i	0.0854584	−	0.258640i
$123$	−9.02633	+	4.59914i	−0.813877	+	0.414691i
$124$	12.3850	+	12.6333i	1.11221	+	1.13451i
$125$	0.343810	+	2.17073i	0.0307513	+	0.194156i
$126$	−21.6605	+	21.4466i	−1.92967	+	1.91061i
$127$	1.35414	+	4.16760i	0.120160	+	0.369815i	0.992988	−	0.118213i	$-0.0377165\pi$
$127$	1.35414	+	4.16760i	0.120160	+	0.369815i	−0.872828	+	0.488028i	$0.837716\pi$
$128$	3.12032	+	10.8749i	0.275800	+	0.961215i
$129$	5.55558	+	7.64659i	0.489141	+	0.673245i
$130$	−0.388538	+	16.6535i	−0.0340770	+	1.46061i
$131$			1.12945i			0.0986808i	0.998782	+	0.0493404i	$0.0157119\pi$
$131$			1.12945i			0.0986808i	−0.998782	+	0.0493404i	$0.984288\pi$
$132$	17.8255	−	4.47244i	1.55151	−	0.389276i
$133$	−22.1740			−1.92273
$134$	−1.91699	−	12.5047i	−0.165603	−	1.08024i
$135$	14.9847	+	2.37335i	1.28968	+	0.204265i
$136$	0.175479	−	11.7860i	0.0150472	−	1.01064i
$137$	6.00133	−	11.7783i	0.512728	−	1.00629i	−0.478986	−	0.877822i	$-0.658996\pi$
$137$	6.00133	−	11.7783i	0.512728	−	1.00629i	0.991714	−	0.128463i	$-0.0410044\pi$
$138$	−0.0958705	+	19.3186i	−0.00816104	+	1.64451i
$139$	9.71474	−	13.3712i	0.823994	−	1.13413i	−0.165018	−	0.986291i	$-0.552768\pi$
$139$	9.71474	−	13.3712i	0.823994	−	1.13413i	0.989011	−	0.147839i	$-0.0472319\pi$
$140$	0.298903	−	30.1148i	0.0252619	−	2.54517i
$141$	5.68575	−	2.89704i	0.478827	−	0.243974i
$142$	−6.36212	+	3.20199i	−0.533897	+	0.268705i
$143$	−4.59576	−	11.0399i	−0.384317	−	0.923201i
$144$	−5.42583	−	17.9004i	−0.452153	−	1.49170i
$145$	1.29888	+	2.54919i	0.107866	+	0.211699i
$146$	2.83094	−	5.48853i	0.234291	−	0.454234i
$147$	−31.9307	−	23.1990i	−2.63360	−	1.91342i
$148$	2.25825	−	1.12254i	0.185627	−	0.0922724i
$149$	−11.1788	−	5.69590i	−0.915806	−	0.466626i	−0.0684514	−	0.997654i	$-0.521806\pi$
$149$	−11.1788	−	5.69590i	−0.915806	−	0.466626i	−0.847354	+	0.531028i	$0.821806\pi$
$150$	−18.0466	+	12.9753i	−1.47350	+	1.05943i
$151$	1.78742	−	11.2854i	0.145459	−	0.918389i	−0.801724	−	0.597694i	$-0.796084\pi$
$151$	1.78742	−	11.2854i	0.145459	−	0.918389i	0.947183	−	0.320695i	$-0.103916\pi$
$152$	6.35716	−	12.0304i	0.515634	−	0.975798i
$153$			19.4877i			1.57548i
$154$	8.57545	+	19.8460i	0.691029	+	1.59923i
$155$	28.8983			2.32117
$156$	−18.0509	+	8.56314i	−1.44523	+	0.685600i
$157$	4.86295	−	3.53314i	0.388106	−	0.281976i	−0.376573	−	0.926387i	$-0.622898\pi$
$157$	4.86295	−	3.53314i	0.388106	−	0.281976i	0.764679	+	0.644411i	$0.222898\pi$
$158$	10.3889	+	14.4493i	0.826496	+	1.14953i
$159$	−11.8844	+	3.86147i	−0.942494	+	0.306235i
$160$	16.2530	+	8.79591i	1.28491	+	0.695377i
$161$	−22.4465	+	3.55517i	−1.76903	+	0.280187i
$162$	−0.500023	−	1.56530i	−0.0392855	−	0.122982i
$163$	−1.25384	−	2.46081i	−0.0982087	−	0.192745i	0.836675	−	0.547700i	$-0.184496\pi$
$163$	−1.25384	−	2.46081i	−0.0982087	−	0.192745i	−0.934884	+	0.354954i	$0.884496\pi$
$164$	7.23384	−	1.07224i	0.564868	−	0.0837281i
$165$	15.1668	−	25.9066i	1.18073	−	2.01683i
$166$	−7.01487	+	3.53052i	−0.544460	+	0.274021i
$167$	8.31084	+	16.3109i	0.643112	+	1.26218i	0.950539	+	0.310606i	$0.100532\pi$
$167$	8.31084	+	16.3109i	0.643112	+	1.26218i	−0.307427	+	0.951572i	$0.599468\pi$
$168$	32.4239	−	15.9173i	2.50156	−	1.22805i
$169$	7.24987	+	10.7907i	0.557682	+	0.830055i
$170$	−13.5469	−	13.6821i	−1.03900	−	1.04937i
$171$	−10.2129	+	20.0439i	−0.780999	+	1.53280i
$172$	−2.04388	−	6.50955i	−0.155844	−	0.496349i
$173$	1.23567	+	1.70076i	0.0939465	+	0.129306i	0.853403	−	0.521252i	$-0.174535\pi$
$173$	1.23567	+	1.70076i	0.0939465	+	0.129306i	−0.759456	+	0.650558i	$0.774535\pi$
$174$	−2.03067	+	2.76601i	−0.153945	+	0.209691i
$175$	−18.4889	−	18.4889i	−1.39763	−	1.39763i
$176$	−13.2259	−	1.03715i	−0.996939	−	0.0781778i
$177$	−5.10689	−	5.10689i	−0.383858	−	0.383858i
$178$	0.0343515	+	0.224078i	0.00257475	+	0.0167954i
$179$	−5.91633	+	4.29846i	−0.442207	+	0.321282i	−0.786511	−	0.617576i	$-0.788115\pi$
$179$	−5.91633	+	4.29846i	−0.442207	+	0.321282i	0.344304	+	0.938858i	$0.388115\pi$
$180$	−27.0842	−	14.1404i	−2.01874	−	1.05396i
$181$	6.46916	−	2.10196i	0.480849	−	0.156237i	−0.0585556	−	0.998284i	$-0.518649\pi$
$181$	6.46916	−	2.10196i	0.480849	−	0.156237i	0.539404	+	0.842047i	$0.318649\pi$
$182$	−13.3674	−	19.3312i	−0.990855	−	1.43293i
$183$	3.46458	−	4.76859i	0.256109	−	0.352504i
$184$	4.50642	−	13.1975i	0.332218	−	0.972932i
$185$	1.27295	−	3.91774i	0.0935891	−	0.288038i
$186$	15.5816	+	30.9595i	1.14250	+	2.27006i
$187$	12.8736	+	5.03125i	0.941411	+	0.367921i
$188$	−4.55665	+	0.675414i	−0.332328	+	0.0492596i
$189$	−19.0724	+	9.71787i	−1.38731	+	0.706871i
$190$	−6.76327	−	21.1721i	−0.490659	−	1.53599i
$191$	2.71221	−	3.73303i	0.196248	−	0.270113i	−0.699540	−	0.714593i	$-0.746612\pi$
$191$	2.71221	−	3.73303i	0.196248	−	0.270113i	0.895788	+	0.444481i	$0.146612\pi$
$192$	−0.659864	+	22.1549i	−0.0476216	+	1.59889i
$193$	5.70345	−	11.1936i	0.410543	−	0.805736i	−0.589455	−	0.807801i	$-0.700657\pi$
$193$	5.70345	−	11.1936i	0.410543	−	0.805736i	0.999998	+	0.00206533i	$0.000657414\pi$
$194$	3.65538	−	22.3604i	0.262441	−	1.60538i
$195$	−10.6530	+	30.8472i	−0.762875	+	2.20901i
$196$	16.5170	+	23.2148i	1.17979	+	1.65820i
$197$	−1.74908	+	1.74908i	−0.124617	+	0.124617i	−0.766665	−	0.642048i	$-0.778085\pi$
$197$	−1.74908	+	1.74908i	−0.124617	+	0.124617i	0.642048	+	0.766665i	$0.278085\pi$
$198$	21.8892	+	1.38898i	1.55560	+	0.0987102i
$199$	−18.6311			−1.32073			−0.660363	−	0.750947i	$-0.729597\pi$
$199$	−18.6311			−1.32073			−0.660363	+	0.750947i	$0.729597\pi$
$200$	15.3318	−	4.73044i	1.08412	−	0.334492i
$201$	3.87711	−	24.4791i	0.273470	−	1.72662i
$202$	−2.57947	−	3.58764i	−0.181491	−	0.252425i
$203$	−3.59665	−	1.83258i	−0.252435	−	0.128622i
$204$	7.35361	−	21.8904i	0.514856	−	1.53263i
$205$	7.02125	−	9.66393i	0.490386	−	0.674958i
$206$	−1.68023	−	5.25988i	−0.117067	−	0.366473i
$207$	−7.12471	+	21.9276i	−0.495201	+	1.52407i
$208$	14.3204	−	1.71027i	0.992944	−	0.118586i
$209$	10.6043	+	11.9215i	0.733518	+	0.824629i
$210$	18.5105	−	56.0221i	1.27735	−	3.86589i
$211$	8.22256	+	2.67167i	0.566065	+	0.183926i	0.578048	−	0.816003i	$-0.303815\pi$
$211$	8.22256	+	2.67167i	0.566065	+	0.183926i	−0.0119836	+	0.999928i	$0.503815\pi$
$212$	9.02001	+	0.0895275i	0.619497	+	0.00614877i
$213$	−13.7818	+	2.18283i	−0.944316	+	0.149565i
$214$	0.109409	−	22.0468i	0.00747907	−	1.50709i
$215$	−9.93018	−	5.05968i	−0.677232	−	0.345067i
$216$	0.195545	−	13.1337i	0.0133051	−	0.893636i
$217$	−32.9857	+	23.9655i	−2.23922	+	1.62688i
$218$	−15.8238	+	2.42581i	−1.07173	+	0.164297i
$219$	8.55505	−	8.55505i	0.578097	−	0.578097i
$220$	−16.3337	+	14.2412i	−1.10122	+	0.960140i
$221$	−14.7953	−	2.62270i	−0.995237	−	0.176422i
$222$	4.88353	−	0.748652i	0.327761	−	0.0502462i
$223$	1.20407	+	0.190706i	0.0806306	+	0.0127706i	0.196619	−	0.980480i	$-0.437004\pi$
$223$	1.20407	+	0.190706i	0.0806306	+	0.0127706i	−0.115989	+	0.993251i	$0.537004\pi$
$224$	−25.8463	+	3.43869i	−1.72693	+	0.229757i
$225$	−25.2284	+	8.19721i	−1.68189	+	0.546480i
$226$	23.8990	+	0.118601i	1.58974	+	0.00788922i
$227$	−0.229784	−	1.45080i	−0.0152513	−	0.0962931i	0.978888	−	0.204395i	$-0.0655227\pi$
$227$	−0.229784	−	1.45080i	−0.0152513	−	0.0962931i	−0.994140	+	0.108102i	$0.965523\pi$
$228$	19.0356	−	18.6614i	1.26066	−	1.23588i
$229$	−6.98486	+	3.55896i	−0.461572	+	0.235183i	−0.669283	−	0.743007i	$-0.733399\pi$
$229$	−6.98486	+	3.55896i	−0.461572	+	0.235183i	0.207711	+	0.978190i	$0.433399\pi$
$230$	−10.2409	−	20.3479i	−0.675265	−	1.34170i
$231$	4.17246	+	42.1487i	0.274528	+	2.77318i
$232$	2.02540	−	1.42596i	0.132974	−	0.0936186i
$233$	15.5288	+	5.04562i	1.01733	+	0.330550i	0.769769	−	0.638323i	$-0.220372\pi$
$233$	15.5288	+	5.04562i	1.01733	+	0.330550i	0.247559	+	0.968873i	$0.420372\pi$
$234$	−23.6309	+	3.17970i	−1.54480	+	0.207863i
$235$	−4.42274	+	6.08738i	−0.288508	+	0.397097i
$236$	2.32066	+	4.66853i	0.151062	+	0.303895i
$237$	10.7739	+	33.1586i	0.699839	+	2.15388i
$238$	26.8096	+	4.38272i	1.73781	+	0.284090i
$239$	−8.49758	−	1.34588i	−0.549663	−	0.0870580i	−0.124575	−	0.992210i	$-0.539757\pi$
$239$	−8.49758	−	1.34588i	−0.549663	−	0.0870580i	−0.425088	+	0.905152i	$0.639757\pi$
$240$	25.0877	+	26.1040i	1.61940	+	1.68501i
$241$	5.17325	+	5.17325i	0.333238	+	0.333238i	0.853815	−	0.520577i	$-0.174283\pi$
$241$	5.17325	+	5.17325i	0.333238	+	0.333238i	−0.520577	+	0.853815i	$0.674283\pi$
$242$	6.56882	−	14.1014i	0.422260	−	0.906475i
$243$		−	17.1512i		−	1.10025i
$244$	−3.46694	+	2.46668i	−0.221948	+	0.157913i
$245$	45.9659	+	7.28029i	2.93666	+	0.465121i
$246$	14.1390	+	2.31138i	0.901469	+	0.147368i
$247$	−13.8431	−	10.4513i	−0.880815	−	0.665000i
$248$	−3.54560	−	24.7670i	−0.225146	−	1.57271i
$249$	−15.1958	+	2.40678i	−0.962997	+	0.152524i
$250$	1.42480	−	2.76234i	0.0901120	−	0.174706i
$251$	−5.96588	+	18.3611i	−0.376563	+	1.15894i	0.565855	+	0.824505i	$0.308546\pi$
$251$	−5.96588	+	18.3611i	−0.376563	+	1.15894i	−0.942418	+	0.334437i	$0.891454\pi$
$252$	42.6417	−	6.32061i	2.68618	−	0.398161i
$253$	12.6460	+	10.3678i	0.795047	+	0.651817i
$254$	1.94426	−	5.88430i	0.121994	−	0.369214i
$255$	−17.1248	−	33.6094i	−1.07240	−	2.10470i
$256$	5.54433	−	15.0087i	0.346521	−	0.938042i
$257$	−3.95685	+	5.44613i	−0.246821	+	0.339720i	−0.914395	−	0.404823i	$-0.867333\pi$
$257$	−3.95685	+	5.44613i	−0.246821	+	0.339720i	0.667574	+	0.744544i	$0.267333\pi$
$258$	0.0663329	−	13.3666i	0.00412970	−	0.832166i
$259$	1.79600	+	5.52753i	0.111598	+	0.343464i
$260$	14.3806	−	18.6596i	0.891849	−	1.15722i
$261$	−3.31307	+	2.40709i	−0.205074	+	0.148995i
$262$	0.945264	−	1.28756i	0.0583986	−	0.0795457i
$263$			13.4839i			0.831451i	0.909490	+	0.415725i	$0.136472\pi$
$263$			13.4839i			0.831451i	−0.909490	+	0.415725i	$0.863528\pi$
$264$	−24.0639	−	9.82004i	−1.48103	−	0.604382i
$265$	10.4189	−	10.4189i	0.640027	−	0.640027i
$266$	25.2780	+	18.5579i	1.54990	+	1.13786i
$267$	−0.0694758	+	0.438653i	−0.00425185	+	0.0268451i
$268$	−8.28013	+	15.8595i	−0.505789	+	0.968776i
$269$	1.92908	+	5.93709i	0.117618	+	0.361991i	0.992484	−	0.122374i	$-0.0390507\pi$
$269$	1.92908	+	5.93709i	0.117618	+	0.361991i	−0.874866	+	0.484365i	$0.839051\pi$
$270$	−15.0960	−	15.2466i	−0.918715	−	0.927879i
$271$	−24.1905	+	3.83140i	−1.46947	+	0.232741i	−0.839279	−	0.543701i	$-0.817023\pi$
$271$	−24.1905	+	3.83140i	−1.46947	+	0.232741i	−0.630189	+	0.776441i	$0.717023\pi$
$272$	−10.0640	+	13.2890i	−0.610219	+	0.805763i
$273$	−13.4220	−	44.0448i	−0.812337	−	2.66571i
$274$	−16.6989	+	8.40440i	−1.00882	+	0.507728i
$275$	−1.09827	+	18.7823i	−0.0662284	+	1.13261i
$276$	16.2775	−	21.9427i	0.979788	−	1.32079i
$277$	−21.1938	−	6.88629i	−1.27341	−	0.413757i	−0.407157	−	0.913358i	$-0.633480\pi$
$277$	−21.1938	−	6.88629i	−1.27341	−	0.413757i	−0.866255	+	0.499601i	$0.833480\pi$
$278$	−22.2653	+	7.11247i	−1.33538	+	0.426578i
$279$	6.47079	+	40.8550i	0.387396	+	2.44592i
$280$	−25.5445	+	34.0802i	−1.52657	+	2.03668i
$281$	0.902726	−	1.77170i	0.0538521	−	0.105691i	−0.862512	−	0.506037i	$-0.831110\pi$
$281$	0.902726	−	1.77170i	0.0538521	−	0.105691i	0.916364	+	0.400346i	$0.131110\pi$
$282$	−8.90626	−	1.45596i	−0.530360	−	0.0867009i
$283$	−1.48996	+	1.08252i	−0.0885690	+	0.0643491i	−0.631188	−	0.775629i	$-0.717433\pi$
$283$	−1.48996	+	1.08252i	−0.0885690	+	0.0643491i	0.542620	+	0.839979i	$0.317433\pi$
$284$	9.93253	+	1.67438i	0.589387	+	0.0993559i
$285$		−	43.5433i		−	2.57928i
$286$	−4.00042	+	16.4316i	−0.236550	+	0.971619i
$287$			16.8536i			0.994834i
$288$	−8.79590	+	24.9472i	−0.518303	+	1.47003i
$289$	0.297355	−	0.216041i	0.0174915	−	0.0127083i
$290$	0.652773	−	3.99309i	0.0383321	−	0.234482i
$291$	20.1517	−	39.5498i	1.18131	−	2.31845i
$292$	−7.82070	+	3.88756i	−0.457672	+	0.227502i
$293$	−3.06768	−	19.3686i	−0.179216	−	1.13153i	−0.899201	−	0.437536i	$-0.855851\pi$
$293$	−3.06768	−	19.3686i	−0.179216	−	1.13153i	0.719985	−	0.693990i	$-0.244149\pi$
$294$	16.9847	+	53.1699i	0.990569	+	3.10093i
$295$	8.09923	+	2.63160i	0.471555	+	0.153218i
$296$	−3.51384	−	0.610294i	−0.204238	−	0.0354726i
$297$	14.3457	+	5.60657i	0.832422	+	0.325326i
$298$	7.97666	+	15.8490i	0.462076	+	0.918110i
$299$	−15.6888	−	8.36023i	−0.907308	−	0.483484i
$300$	31.4321	+	0.311978i	1.81474	+	0.0180120i
$301$	15.5307	−	2.45982i	0.895176	−	0.141782i
$302$	−11.4826	+	11.3692i	−0.660749	+	0.654223i
$303$	−2.67506	−	8.23297i	−0.153678	−	0.472972i
$304$	−17.3156	+	8.39407i	−0.993118	+	0.481433i
$305$	−1.08725	+	6.86464i	−0.0622559	+	0.393068i
$306$	16.3096	−	22.2156i	0.932360	−	1.26998i
$307$	12.9756	−	12.9756i	0.740557	−	0.740557i	−0.232128	−	0.972685i	$-0.574569\pi$
$307$	12.9756	−	12.9756i	0.740557	−	0.740557i	0.972685	+	0.232128i	$0.0745688\pi$
$308$	6.83366	−	29.8011i	0.389384	−	1.69807i
$309$		−	10.8176i		−	0.615394i
$310$	−32.9436	−	24.1856i	−1.87107	−	1.37365i
$311$	−2.87459	+	2.08851i	−0.163003	+	0.118429i	−0.666297	−	0.745687i	$-0.732122\pi$
$311$	−2.87459	+	2.08851i	−0.163003	+	0.118429i	0.503293	+	0.864116i	$0.332122\pi$
$312$	27.7444	+	5.34532i	1.57071	+	0.302619i
$313$	9.59049	+	29.5165i	0.542086	+	1.66837i	0.727818	+	0.685770i	$0.240534\pi$
$313$	9.59049	+	29.5165i	0.542086	+	1.66837i	−0.185732	+	0.982600i	$0.559466\pi$
$314$	−8.50065	−	0.0421853i	−0.479720	−	0.00238065i
$315$	41.3886	−	56.9665i	2.33198	−	3.20970i
$316$	0.249790	−	25.1667i	0.0140518	−	1.41574i
$317$	−12.5984	−	24.7257i	−0.707595	−	1.38873i	−0.912141	−	0.409876i	$-0.865572\pi$
$317$	−12.5984	−	24.7257i	−0.707595	−	1.38873i	0.204547	−	0.978857i	$-0.434428\pi$
$318$	16.7798	+	5.54429i	0.940962	+	0.310908i
$319$	0.734773	+	2.81008i	0.0411394	+	0.157334i
$320$	−11.1667	−	23.6297i	−0.624236	−	1.32094i
$321$	13.3472	−	41.0785i	0.744969	−	2.29278i
$322$	28.5640	+	14.7331i	1.59181	+	0.821043i
$323$	19.8016	−	3.13627i	1.10179	−	0.174507i
$324$	−0.740015	+	2.20290i	−0.0411120	+	0.122383i
$325$	−2.82811	−	20.2569i	−0.156876	−	1.12365i
$326$	−0.630141	+	3.85465i	−0.0349003	+	0.213489i
$327$	−30.9766	−	4.90620i	−1.71301	−	0.271314i
$328$	−9.14384	−	4.83181i	−0.504884	−	0.266792i
$329$		−	10.6162i		−	0.585289i
$330$	−38.9717	+	16.8397i	−2.14532	+	0.926993i
$331$	−8.88274	−	8.88274i	−0.488239	−	0.488239i	0.419511	−	0.907750i	$-0.362202\pi$
$331$	−8.88274	−	8.88274i	−0.488239	−	0.488239i	−0.907750	+	0.419511i	$0.862202\pi$
$332$	10.9516	+	1.84617i	0.601047	+	0.101321i
$333$	5.82373	+	0.922388i	0.319138	+	0.0505466i
$334$	4.17675	−	25.5497i	0.228542	−	1.39802i
$335$	9.03074	+	27.7938i	0.493402	+	1.51854i
$336$	−50.2843	−	8.99081i	−2.74323	−	0.490489i
$337$	−14.1959	+	19.5390i	−0.773302	+	1.06436i	0.222688	+	0.974890i	$0.428517\pi$
$337$	−14.1959	+	19.5390i	−0.773302	+	1.06436i	−0.995990	+	0.0894686i	$0.971483\pi$
$338$	0.766245	−	18.3688i	0.0416782	−	0.999131i
$339$	44.5296	+	14.4685i	2.41852	+	0.785823i
$340$	3.99248	+	26.9351i	0.216522	+	1.46076i
$341$	28.6595	+	6.27315i	1.55200	+	0.339710i
$342$	28.4177	−	14.3024i	1.53665	−	0.773383i
$343$	−29.7566	+	15.1618i	−1.60671	+	0.818658i
$344$	−3.11799	+	9.13135i	−0.168111	+	0.492330i
$345$	−6.98131	−	44.0783i	−0.375861	−	2.37309i
$346$	0.0147538	−	2.97300i	0.000793169	−	0.159829i
$347$	−31.7386	+	10.3125i	−1.70381	+	0.553603i	−0.989284	−	0.146002i	$-0.953360\pi$
$347$	−31.7386	+	10.3125i	−1.70381	+	0.553603i	−0.714530	+	0.699604i	$0.753360\pi$
$348$	4.62987	−	1.45369i	0.248187	−	0.0779262i
$349$	−27.1689	−	4.30313i	−1.45432	−	0.230341i	−0.621294	−	0.783577i	$-0.713393\pi$
$349$	−27.1689	−	4.30313i	−1.45432	−	0.230341i	−0.833025	+	0.553236i	$0.813393\pi$
$350$	5.60329	+	36.5508i	0.299509	+	1.95373i
$351$	−16.4871	−	2.92260i	−0.880016	−	0.155997i
$352$	14.2093	+	12.2514i	0.757358	+	0.653000i
$353$	13.0243	−	13.0243i	0.693215	−	0.693215i	−0.269723	−	0.962938i	$-0.586932\pi$
$353$	13.0243	−	13.0243i	0.693215	−	0.693215i	0.962938	+	0.269723i	$0.0869321\pi$
$354$	1.54771	+	10.0958i	0.0822597	+	0.536588i
$355$	13.3110	−	9.67100i	0.706474	−	0.513283i
$356$	0.148376	−	0.284195i	0.00786390	−	0.0150623i
$357$	47.4194	+	24.1614i	2.50970	+	1.27876i
$358$	10.3420	+	0.0513231i	0.546591	+	0.00271251i
$359$	−8.38832	+	1.32858i	−0.442719	+	0.0701197i	−0.373814	−	0.927504i	$-0.621950\pi$
$359$	−8.38832	+	1.32858i	−0.442719	+	0.0701197i	−0.0689042	+	0.997623i	$0.521950\pi$
$360$	19.0411	+	38.7872i	1.00356	+	2.04426i
$361$	3.94037	+	1.28030i	0.207388	+	0.0673844i
$362$	−9.13390	−	3.01798i	−0.480067	−	0.158621i
$363$	20.6652	−	22.4001i	1.08464	−	1.17570i
$364$	−0.940145	+	33.2247i	−0.0492770	+	1.74145i
$365$	−4.40845	+	13.5678i	−0.230749	+	0.710171i
$366$	−7.94050	+	2.53653i	−0.415056	+	0.132586i
$367$	9.87403	−	13.5904i	0.515420	−	0.709415i	−0.469401	−	0.882985i	$-0.655530\pi$
$367$	9.87403	−	13.5904i	0.515420	−	0.709415i	0.984822	+	0.173570i	$0.0555302\pi$
$368$	−16.1825	+	11.2734i	−0.843571	+	0.587667i
$369$	15.2345	+	7.76238i	0.793078	+	0.404094i
$370$	−4.72998	+	3.40080i	−0.245900	+	0.176799i
$371$	−3.25210	+	20.5330i	−0.168841	+	1.06602i
$372$	8.14788	−	48.3339i	0.422448	−	2.50600i
$373$	34.1103			1.76616			0.883082	−	0.469220i	$-0.155465\pi$
$373$	34.1103			1.76616			0.883082	+	0.469220i	$0.155465\pi$
$374$	−10.4649	−	16.5097i	−0.541129	−	0.853698i
$375$	4.30570	−	4.30570i	0.222346	−	0.222346i
$376$	5.75977	+	3.04360i	0.297038	+	0.156961i
$377$	−1.38161	−	2.83928i	−0.0711565	−	0.146230i
$378$	29.8753	+	4.88388i	1.53662	+	0.251200i
$379$	6.66254	−	13.0760i	0.342232	−	0.671668i	−0.654177	−	0.756342i	$-0.726985\pi$
$379$	6.66254	−	13.0760i	0.342232	−	0.671668i	0.996409	+	0.0846737i	$0.0269848\pi$
$380$	−10.0094	+	29.7962i	−0.513472	+	1.52851i
$381$	7.13627	−	9.82223i	0.365602	−	0.503208i
$382$	−6.21613	+	1.98569i	−0.318045	+	0.101597i
$383$	5.14358	−	2.62078i	0.262825	−	0.133916i	−0.317613	−	0.948220i	$-0.602881\pi$
$383$	5.14358	−	2.62078i	0.262825	−	0.133916i	0.580438	+	0.814304i	$0.302881\pi$
$384$	19.2941	−	24.7040i	0.984600	−	1.26067i
$385$	−26.9467	−	42.0488i	−1.37333	−	2.14301i
$386$	−15.8700	+	7.98723i	−0.807763	+	0.406539i
$387$	4.92959	−	15.1717i	0.250585	−	0.771222i
$388$	−22.8810	+	22.4312i	−1.16161	+	1.13877i
$389$	−19.9639	+	27.4779i	−1.01221	+	1.39319i	−0.0946853	+	0.995507i	$0.530184\pi$
$389$	−19.9639	+	27.4779i	−1.01221	+	1.39319i	−0.917524	+	0.397680i	$0.869816\pi$
$390$	37.9609	−	26.2496i	1.92222	−	1.32920i
$391$	19.5420	−	6.34959i	0.988283	−	0.321113i
$392$	0.599837	−	40.2879i	0.0302964	−	2.03485i
$393$	2.53162	−	1.83933i	0.127703	−	0.0927819i
$394$	3.45776	−	0.530080i	0.174200	−	0.0267050i
$395$	−29.0697	−	29.0697i	−1.46266	−	1.46266i
$396$	−23.7908	−	19.9029i	−1.19553	−	1.00016i
$397$	3.24105	+	3.24105i	0.162663	+	0.162663i	0.783746	−	0.621082i	$-0.213307\pi$
$397$	3.24105	+	3.24105i	0.162663	+	0.162663i	−0.621082	+	0.783746i	$0.713307\pi$
$398$	21.2392	+	15.5928i	1.06462	+	0.781596i
$399$	36.1107	+	49.7021i	1.80780	+	2.48822i
$400$	−21.4370	−	7.43886i	−1.07185	−	0.371943i
$401$	−3.60673	+	7.07861i	−0.180112	+	0.353489i	−0.963356	−	0.268225i	$-0.913563\pi$
$401$	−3.60673	+	7.07861i	−0.180112	+	0.353489i	0.783245	+	0.621713i	$0.213563\pi$
$402$	−24.9069	+	24.6609i	−1.24224	+	1.22998i
$403$	−31.8884	−	0.585661i	−1.58847	−	0.0291738i
$404$	−0.0620206	+	6.24866i	−0.00308564	+	0.310882i
$405$	1.72332	+	3.38221i	0.0856326	+	0.168063i
$406$	2.56639	+	5.09922i	0.127368	+	0.253070i
$407$	2.11288	−	3.60903i	0.104732	−	0.178893i
$408$	−26.7035	+	18.8003i	−1.32202	+	0.930754i
$409$	−5.06351	−	9.93770i	−0.250375	−	0.491388i	0.731275	−	0.682083i	$-0.238926\pi$
$409$	−5.06351	−	9.93770i	−0.250375	−	0.491388i	−0.981649	+	0.190695i	$0.938926\pi$
$410$	−16.0921	+	5.14048i	−0.794730	+	0.253870i
$411$	−36.1737	+	5.72935i	−1.78432	+	0.282608i
$412$	−2.48668	+	7.40240i	−0.122510	+	0.364690i
$413$	−11.4272	+	3.71292i	−0.562295	+	0.182701i
$414$	26.4737	−	19.0343i	1.30111	−	0.935484i
$415$	14.6767	−	10.6632i	0.720450	−	0.523438i
$416$	−17.7564	−	10.0354i	−0.870580	−	0.492026i
$417$	−45.7915			−2.24242
$418$	−2.11140	−	22.4653i	−0.103272	−	1.09882i
$419$		−	21.4449i		−	1.04765i	−0.851825	−	0.523827i	$-0.824504\pi$
$419$		−	21.4449i		−	1.04765i	0.851825	−	0.523827i	$-0.175496\pi$
$420$	−67.9878	+	48.3724i	−3.31746	+	2.36033i
$421$	1.48876	−	9.39968i	0.0725579	−	0.458112i	−0.924482	−	0.381226i	$-0.875502\pi$
$421$	1.48876	−	9.39968i	0.0725579	−	0.458112i	0.997040	−	0.0768866i	$-0.0244979\pi$
$422$	−7.13761	−	9.92730i	−0.347453	−	0.483253i
$423$	−9.59635	−	4.88959i	−0.466591	−	0.237740i
$424$	−10.2077	−	7.65110i	−0.495731	−	0.371570i
$425$	19.1258	+	13.8957i	0.927738	+	0.674041i
$426$	17.5379	+	9.04592i	0.849715	+	0.438276i
$427$	−4.45184	−	8.73724i	−0.215440	−	0.422825i
$428$	−18.5762	+	25.0414i	−0.897913	+	1.21042i
$429$	−17.2611	+	28.2798i	−0.833376	+	1.36536i
$430$	7.08568	+	14.0787i	0.341702	+	0.678936i
$431$	12.1659	−	6.19883i	0.586010	−	0.298587i	−0.135736	−	0.990745i	$-0.543340\pi$
$431$	12.1659	−	6.19883i	0.586010	−	0.298587i	0.721746	+	0.692158i	$0.243340\pi$
$432$	−11.2148	+	14.8086i	−0.539573	+	0.712477i
$433$	−7.85929	+	10.8174i	−0.377693	+	0.519850i	−0.954972	−	0.296697i	$-0.904115\pi$
$433$	−7.85929	+	10.8174i	−0.377693	+	0.519850i	0.577278	+	0.816547i	$0.304115\pi$
$434$	57.6604	+	0.286145i	2.76779	+	0.0137354i
$435$	3.59865	−	7.06276i	0.172542	−	0.338633i
$436$	20.0691	+	10.4779i	0.961137	+	0.501801i
$437$	23.4275	+	3.71055i	1.12069	+	0.177499i
$438$	−16.9125	+	2.59271i	−0.808112	+	0.123885i
$439$	−18.0034			−0.859256			−0.429628	−	0.903006i	$-0.641355\pi$
$439$	−18.0034			−0.859256			−0.429628	+	0.903006i	$0.641355\pi$
$440$	30.5389	−	2.56469i	1.45588	−	0.122267i
$441$			66.6145i			3.17212i
$442$	14.6714	+	15.3723i	0.697845	+	0.731186i
$443$	−21.5048	−	29.5989i	−1.02173	−	1.40628i	−0.910987	−	0.412435i	$-0.864679\pi$
$443$	−21.5048	−	29.5989i	−1.02173	−	1.40628i	−0.110738	−	0.993850i	$-0.535321\pi$
$444$	−6.19371	−	3.23368i	−0.293940	−	0.153464i
$445$	−0.161826	−	0.498050i	−0.00767131	−	0.0236099i
$446$	−1.21302	−	1.22511i	−0.0574379	−	0.0580109i
$447$	5.43776	+	34.3327i	0.257197	+	1.62388i
$448$	32.3423	+	17.7113i	1.52803	+	0.836780i
$449$	−29.8768	+	15.2230i	−1.40997	+	0.718416i	−0.982613	−	0.185666i	$-0.940556\pi$
$449$	−29.8768	+	15.2230i	−1.40997	+	0.718416i	−0.427358	+	0.904082i	$0.640556\pi$
$450$	35.6204	+	11.7695i	1.67916	+	0.554820i
$451$	9.06104	−	8.05991i	0.426668	−	0.379526i
$452$	−27.1452	−	20.1368i	−1.27680	−	0.947155i
$453$	−28.2064	+	14.3719i	−1.32525	+	0.675251i
$454$	−0.952257	+	1.84620i	−0.0446916	+	0.0866466i
$455$	37.6795	+	39.0894i	1.76644	+	1.83254i
$456$	−37.3184	+	5.34243i	−1.74760	+	0.250182i
$457$	4.08647	+	2.08216i	0.191157	+	0.0973994i	0.546949	−	0.837166i	$-0.315789\pi$
$457$	4.08647	+	2.08216i	0.191157	+	0.0973994i	−0.355792	+	0.934565i	$0.615789\pi$
$458$	10.9412	+	1.78862i	0.511248	+	0.0835766i
$459$	15.6573	−	11.3757i	0.730822	−	0.530973i
$460$	−5.35513	+	31.7671i	−0.249684	+	1.48115i
$461$	−23.6354	+	23.6354i	−1.10081	+	1.10081i	−0.106495	+	0.994313i	$0.533963\pi$
$461$	−23.6354	+	23.6354i	−1.10081	+	1.10081i	−0.994313	+	0.106495i	$0.966037\pi$
$462$	30.5187	−	51.5409i	1.41986	−	2.39790i
$463$	1.15512	−	1.15512i	0.0536830	−	0.0536830i	−0.679756	−	0.733439i	$-0.737914\pi$
$463$	1.15512	−	1.15512i	0.0536830	−	0.0536830i	0.733439	+	0.679756i	$0.237914\pi$
$464$	−3.50233	−	0.0695312i	−0.162592	−	0.00322790i
$465$	−47.0612	−	64.7742i	−2.18241	−	3.00383i
$466$	−13.4798	−	18.7483i	−0.624441	−	0.868500i
$467$	−2.44551	−	7.52649i	−0.113165	−	0.348285i	0.878395	−	0.477935i	$-0.158615\pi$
$467$	−2.44551	−	7.52649i	−0.113165	−	0.348285i	−0.991560	+	0.129650i	$0.958615\pi$
$468$	29.6000	+	16.1524i	1.36826	+	0.746646i
$469$	−33.3576	−	24.2357i	−1.54031	−	1.11910i
$470$	10.1365	−	3.23803i	0.467562	−	0.149359i
$471$	−15.8388	−	5.14633i	−0.729812	−	0.237130i
$472$	1.26168	−	7.26425i	0.0580733	−	0.334364i
$473$	−8.74978	−	7.17347i	−0.402315	−	0.329837i
$474$	15.4691	−	46.8172i	0.710519	−	2.15038i
$475$	12.3894	+	24.3156i	0.568466	+	1.11568i
$476$	−26.8946	−	27.4338i	−1.23271	−	1.25743i
$477$	17.0626	+	12.3967i	0.781245	+	0.567608i
$478$	8.56070	+	8.64609i	0.391557	+	0.395463i
$479$	−7.24875	−	3.69342i	−0.331204	−	0.168757i	0.280479	−	0.959860i	$-0.409507\pi$
$479$	−7.24875	−	3.69342i	−0.331204	−	0.168757i	−0.611682	+	0.791104i	$0.709507\pi$
$480$	−6.75257	−	50.7546i	−0.308211	−	2.31662i
$481$	−1.48406	+	4.29731i	−0.0676673	+	0.195940i
$482$	−1.56782	−	10.2270i	−0.0714121	−	0.465828i
$483$	44.5231	+	44.5231i	2.02587	+	2.02587i
$484$	−19.2901	+	10.5778i	−0.876825	+	0.480810i
$485$			52.3395i			2.37661i
$486$	−14.3542	+	19.5521i	−0.651120	+	0.886901i
$487$	8.74291	+	1.38474i	0.396179	+	0.0627486i	0.351345	−	0.936246i	$-0.385724\pi$
$487$	8.74291	+	1.38474i	0.396179	+	0.0627486i	0.0448335	+	0.998994i	$0.485724\pi$
$488$	6.01667	+	0.0895808i	0.272362	+	0.00405513i
$489$	−3.47389	+	6.81789i	−0.157095	+	0.308316i
$490$	−46.3074	−	46.7693i	−2.09195	−	2.11282i
$491$	24.6948	+	17.9418i	1.11446	+	0.809703i	0.983360	−	0.181666i	$-0.0581489\pi$
$491$	24.6948	+	17.9418i	1.11446	+	0.809703i	0.131101	+	0.991369i	$0.458149\pi$
$492$	−14.1838	−	14.4682i	−0.639454	−	0.652275i
$493$	3.47103	+	1.12781i	0.156327	+	0.0507939i
$494$	7.03399	+	23.4999i	0.316474	+	1.05731i
$495$	−50.4205	+	4.99131i	−2.26623	+	0.224343i
$496$	−16.6861	+	31.2014i	−0.749230	+	1.40098i
$497$	−7.17349	+	22.0777i	−0.321775	+	0.990322i
$498$	19.3373	+	9.97403i	0.866525	+	0.446947i
$499$	−5.47042	−	34.5389i	−0.244890	−	1.54617i	−0.737152	−	0.675727i	$-0.763830\pi$
$499$	−5.47042	−	34.5389i	−0.244890	−	1.54617i	0.492262	−	0.870447i	$-0.336170\pi$
$500$	−3.93611	+	1.95658i	−0.176028	+	0.0875011i
$501$	23.0259	−	45.1909i	1.02872	−	2.01898i
$502$	22.1678	−	15.9384i	0.989398	−	0.711365i
$503$	20.5798	+	28.3256i	0.917606	+	1.26298i	0.964502	+	0.264077i	$0.0850672\pi$
$503$	20.5798	+	28.3256i	0.917606	+	1.26298i	−0.0468956	+	0.998900i	$0.514933\pi$
$504$	−53.9007	−	28.4824i	−2.40093	−	1.26871i
$505$	7.21774	+	7.21774i	0.321185	+	0.321185i
$506$	−5.73921	−	22.4028i	−0.255139	−	0.995926i
$507$	12.3804	−	33.8231i	0.549832	−	1.50213i
$508$	−7.14113	+	5.08082i	−0.316836	+	0.225425i
$509$	5.54729	−	35.0242i	0.245879	−	1.55242i	−0.487818	−	0.872945i	$-0.662207\pi$
$509$	5.54729	−	35.0242i	0.245879	−	1.55242i	0.733698	−	0.679476i	$-0.237793\pi$
$510$	−8.60638	+	52.6463i	−0.381097	+	2.33122i
$511$	−6.21987	−	19.1428i	−0.275151	−	0.846827i
$512$	−18.8815	+	12.4695i	−0.834454	+	0.551078i
$513$	22.0659	−	3.49490i	0.974234	−	0.154304i
$514$	9.06872	−	2.89693i	0.400004	−	0.127778i
$515$	5.79089	+	11.3653i	0.255177	+	0.500813i
$516$	−11.2624	+	15.1822i	−0.495799	+	0.668357i
$517$	−5.70762	+	5.07700i	−0.251021	+	0.223286i
$518$	2.57869	−	7.80440i	0.113301	−	0.342906i
$519$	1.79986	−	5.53941i	0.0790053	−	0.243153i
$520$	−32.0103	+	9.23616i	−1.40374	+	0.405033i
$521$	3.66742	+	2.66454i	0.160673	+	0.116736i	0.665216	−	0.746651i	$-0.268339\pi$
$521$	3.66742	+	2.66454i	0.160673	+	0.116736i	−0.504544	+	0.863386i	$0.668339\pi$
$522$	5.79139	+	0.0287403i	0.253482	+	0.00125793i
$523$	−23.7104	+	7.70397i	−1.03678	+	0.336871i	−0.777468	−	0.628922i	$-0.783496\pi$
$523$	−23.7104	+	7.70397i	−1.03678	+	0.336871i	−0.259314	+	0.965793i	$0.583496\pi$
$524$	−2.15517	+	0.676684i	−0.0941491	+	0.0295611i
$525$	−11.3326	+	71.5515i	−0.494597	+	3.12276i
$526$	11.2849	−	15.3714i	0.492046	−	0.670224i
$527$	26.0669	−	26.0669i	1.13549	−	1.13549i
$528$	19.2138	+	31.3343i	0.836174	+	1.36365i
$529$	1.31019			0.0569647
$530$	−20.5971	+	3.15757i	−0.894683	+	0.137156i
$531$	−1.90688	+	12.0395i	−0.0827513	+	0.522471i
$532$	−13.2850	−	42.3115i	−0.575979	−	1.83443i
$533$	−7.94359	+	10.5216i	−0.344075	+	0.455739i
$534$	0.446320	−	0.441912i	0.0193141	−	0.0191234i
$535$	7.96722	+	50.3030i	0.344453	+	2.17479i
$536$	22.7124	−	11.1498i	0.981026	−	0.481598i
$537$	19.2696	+	6.26108i	0.831545	+	0.270185i
$538$	2.76976	−	8.38267i	0.119413	−	0.361403i
$539$	44.0057	+	17.1983i	1.89546	+	0.740782i
$540$	4.44901	+	30.0151i	0.191455	+	1.29164i
$541$	30.1340	−	15.3540i	1.29556	−	0.660121i	0.336064	−	0.941839i	$-0.390904\pi$
$541$	30.1340	−	15.3540i	1.29556	−	0.660121i	0.959497	+	0.281718i	$0.0909043\pi$
$542$	30.7834	+	15.8778i	1.32226	+	0.682011i
$543$	−15.2465	−	11.0773i	−0.654292	−	0.475371i
$544$	22.5946	−	6.72644i	0.968736	−	0.288394i
$545$	35.1710	−	11.4278i	1.50656	−	0.489512i
$546$	−21.5612	+	61.4435i	−0.922733	+	2.62954i
$547$	−12.7230	−	17.5117i	−0.543996	−	0.748747i	0.445186	−	0.895438i	$-0.353138\pi$
$547$	−12.7230	−	17.5117i	−0.543996	−	0.748747i	−0.989182	+	0.146691i	$0.953138\pi$
$548$	26.0703	+	4.39480i	1.11367	+	0.187736i
$549$	−9.94833			−0.424584
$550$	16.9713	−	20.4923i	0.723659	−	0.873795i
$551$	2.97906	+	2.97906i	0.126912	+	0.126912i
$552$	−36.9203	+	11.3913i	−1.57143	+	0.484848i
$553$	57.2890	+	9.07369i	2.43618	+	0.385852i
$554$	18.3973	+	25.5878i	0.781627	+	1.08712i
$555$	−10.8544	+	3.52682i	−0.460745	+	0.149705i
$556$	31.3346	+	10.5262i	1.32888	+	0.446410i
$557$	−1.06573	−	6.72874i	−0.0451563	−	0.285106i	0.954769	−	0.297350i	$-0.0961027\pi$
$557$	−1.06573	−	6.72874i	−0.0451563	−	0.285106i	−0.999925	+	0.0122436i	$0.996103\pi$
$558$	26.8158	−	51.9895i	1.13520	−	2.20089i
$559$	10.8551	+	5.78445i	0.459122	+	0.244656i
$560$	57.6428	−	17.4722i	2.43585	−	0.738335i
$561$	−9.68750	−	37.0490i	−0.409007	−	1.56421i
$562$	−2.51187	+	1.26420i	−0.105957	+	0.0533270i
$563$	6.74328	−	20.7537i	0.284195	−	0.874663i	−0.702443	−	0.711740i	$-0.747908\pi$
$563$	6.74328	−	20.7537i	0.284195	−	0.874663i	0.986639	−	0.162924i	$-0.0520924\pi$
$564$	8.93447	+	9.11360i	0.376209	+	0.383752i
$565$	−54.5290	+	8.63655i	−2.29405	+	0.363343i
$566$	2.60452	+	0.0129252i	0.109476	+	0.000543285i
$567$	−4.77195	−	2.43143i	−0.200403	−	0.102111i
$568$	−9.92160	−	10.2215i	−0.416301	−	0.428885i
$569$	20.4642	+	28.1666i	0.857904	+	1.18080i	0.982065	+	0.188541i	$0.0603759\pi$
$569$	20.4642	+	28.1666i	0.857904	+	1.18080i	−0.124161	+	0.992262i	$0.539624\pi$
$570$	−36.4423	+	49.6387i	−1.52640	+	2.07914i
$571$	−11.2746			−0.471826			−0.235913	−	0.971774i	$-0.575808\pi$
$571$	−11.2746			−0.471826			−0.235913	+	0.971774i	$0.575808\pi$
$572$	18.3124	−	15.3837i	0.765678	−	0.643224i
$573$	−12.7843			−0.534071
$574$	14.1051	−	19.2128i	0.588736	−	0.801926i
$575$	16.4402	+	22.6279i	0.685602	+	0.943650i
$576$	30.9060	−	21.0779i	1.28775	−	0.878247i
$577$	20.1444	+	10.2641i	0.838621	+	0.427299i	0.819887	−	0.572526i	$-0.194036\pi$
$577$	20.1444	+	10.2641i	0.838621	+	0.427299i	0.0187344	+	0.999824i	$0.494036\pi$
$578$	−0.519789	−	0.00257950i	−0.0216204	−	0.000107293i
$579$	−34.3782	+	5.44497i	−1.42871	+	0.226285i
$580$	−4.08605	+	4.00574i	−0.169664	+	0.166329i
$581$	−7.90949	+	24.3429i	−0.328141	+	1.00991i
$582$	−56.0727	+	28.2208i	−2.32429	+	1.16979i
$583$	12.5945	−	8.07109i	0.521610	−	0.334270i
$584$	12.1691	+	2.11355i	0.503559	+	0.0874595i
$585$	52.6887	−	16.0561i	2.17841	−	0.663838i
$586$	−12.7129	+	24.6473i	−0.525164	+	1.01817i
$587$	−1.96938	−	12.4341i	−0.0812848	−	0.513212i	−0.994415	−	0.105543i	$-0.966342\pi$
$587$	−1.96938	−	12.4341i	−0.0812848	−	0.513212i	0.913130	−	0.407669i	$-0.133658\pi$
$588$	25.1368	−	74.8277i	1.03662	−	3.08584i
$589$	40.4717	−	13.1501i	1.66761	−	0.541839i
$590$	−7.03055	−	9.77840i	−0.289443	−	0.402570i
$591$	6.76888	+	1.07208i	0.278434	+	0.0440997i
$592$	3.49495	+	3.63654i	0.143642	+	0.149461i
$593$	7.28414	+	7.28414i	0.299124	+	0.299124i	0.840671	−	0.541547i	$-0.182161\pi$
$593$	7.28414	+	7.28414i	0.299124	+	0.299124i	−0.541547	+	0.840671i	$0.682161\pi$
$594$	−11.6616	−	18.3976i	−0.478481	−	0.754863i
$595$	−62.7539			−2.57266
$596$	4.17113	−	24.7435i	0.170856	−	1.01353i
$597$	30.3410	+	41.7608i	1.24178	+	1.70916i
$598$	10.8881	+	22.6608i	0.445249	+	0.926670i
$599$	5.36441	−	1.74300i	0.219184	−	0.0712171i	−0.197367	−	0.980330i	$-0.563239\pi$
$599$	5.36441	−	1.74300i	0.219184	−	0.0712171i	0.416550	+	0.909113i	$0.363239\pi$
$600$	−35.5710	−	26.6619i	−1.45218	−	1.08847i
$601$	24.4186	+	17.7411i	0.996055	+	0.723676i	0.961239	−	0.275718i	$-0.0889155\pi$
$601$	24.4186	+	17.7411i	0.996055	+	0.723676i	0.0348160	+	0.999394i	$0.488915\pi$
$602$	−19.7634	−	10.1938i	−0.805498	−	0.415470i
$603$	−37.2713	+	18.9907i	−1.51780	+	0.773360i
$604$	22.6051	−	3.35066i	0.919787	−	0.136336i
$605$	−9.72009	+	34.5966i	−0.395178	+	1.40655i
$606$	−3.84083	+	11.6243i	−0.156023	+	0.472203i
$607$	−25.4850	−	8.28057i	−1.03440	−	0.336098i	−0.257874	−	0.966179i	$-0.583022\pi$
$607$	−25.4850	−	8.28057i	−1.03440	−	0.336098i	−0.776530	+	0.630080i	$0.783022\pi$
$608$	26.7647	+	4.92270i	1.08545	+	0.199642i
$609$	1.74953	+	11.0461i	0.0708945	+	0.447611i
$610$	6.98461	−	6.91563i	0.282799	−	0.280006i
$611$	5.00373	−	6.62761i	0.202429	−	0.268124i
$612$	−37.1854	+	11.6755i	−1.50313	+	0.471956i
$613$	−3.97673	+	25.1081i	−0.160619	+	1.01411i	0.767291	+	0.641300i	$0.221604\pi$
$613$	−3.97673	+	25.1081i	−0.160619	+	1.01411i	−0.927909	+	0.372806i	$0.878396\pi$
$614$	−25.6516	+	3.93242i	−1.03521	+	0.158699i
$615$	−33.0954			−1.33454
$616$	−32.7314	+	28.2535i	−1.31879	+	1.13837i
$617$	27.3745	−	27.3745i	1.10206	−	1.10206i	0.107895	−	0.994162i	$-0.465589\pi$
$617$	27.3745	−	27.3745i	1.10206	−	1.10206i	0.994162	−	0.107895i	$-0.0344112\pi$
$618$	−9.05352	+	12.3319i	−0.364186	+	0.496063i
$619$	1.28461	−	8.11073i	0.0516329	−	0.325998i	−0.948329	−	0.317288i	$-0.897228\pi$
$619$	1.28461	−	8.11073i	0.0516329	−	0.325998i	0.999962	−	0.00870928i	$-0.00277229\pi$
$620$	17.3137	+	55.1424i	0.695335	+	2.21457i
$621$	21.7767	−	7.07567i	0.873867	−	0.283937i
$622$	5.02491	+	0.0249366i	0.201481	+	0.000999866i
$623$	0.597751	+	0.434291i	0.0239484	+	0.0173995i
$624$	−27.1545	−	29.3134i	−1.08705	−	1.17348i
$625$	6.54613	−	20.1469i	0.261845	−	0.805876i
$626$	13.7700	−	41.6748i	0.550359	−	1.66566i
$627$	9.45224	−	43.1835i	0.377486	−	1.72458i
$628$	9.65530	+	7.16247i	0.385288	+	0.285814i
$629$	−2.38565	−	4.68210i	−0.0951221	−	0.186688i
$630$	−94.8588	+	30.3019i	−3.77927	+	1.20726i
$631$	−9.82939	+	1.55682i	−0.391302	+	0.0619761i	−0.348985	−	0.937128i	$-0.613474\pi$
$631$	−9.82939	+	1.55682i	−0.391302	+	0.0619761i	−0.0423164	+	0.999104i	$0.513474\pi$
$632$	−21.3473	+	28.4806i	−0.849150	+	1.13290i
$633$	−7.40211	−	22.7814i	−0.294207	−	0.905477i
$634$	−6.33152	+	38.7307i	−0.251457	+	1.53819i
$635$	−2.23950	+	14.1396i	−0.0888717	+	0.561114i
$636$	−14.4885	−	20.3637i	−0.574507	−	0.807475i
$637$	−50.5745	−	8.96514i	−2.00383	−	0.355212i
$638$	1.51419	−	3.81839i	0.0599472	−	0.151172i
$639$	16.6529	+	16.6529i	0.658779	+	0.658779i
$640$	−7.04636	+	36.2831i	−0.278532	+	1.43421i
$641$	−24.3449	−	33.5079i	−0.961566	−	1.32348i	−0.946194	−	0.323600i	$-0.895107\pi$
$641$	−24.3449	−	33.5079i	−0.961566	−	1.32348i	−0.0153720	−	0.999882i	$-0.504893\pi$
$642$	−49.5951	+	35.6583i	−1.95736	+	1.40732i
$643$	−15.8676	+	31.1418i	−0.625756	+	1.22811i	0.332743	+	0.943018i	$0.392026\pi$
$643$	−15.8676	+	31.1418i	−0.625756	+	1.22811i	−0.958499	+	0.285097i	$0.907974\pi$
$644$	−20.2320	−	40.7013i	−0.797254	−	1.60386i
$645$	4.83037	+	30.4978i	0.190196	+	1.20085i
$646$	−25.1983	−	12.9971i	−0.991415	−	0.511364i
$647$	9.68652	−	29.8121i	0.380817	−	1.17203i	−0.558653	−	0.829401i	$-0.688682\pi$
$647$	9.68652	−	29.8121i	0.380817	−	1.17203i	0.939470	−	0.342632i	$-0.111318\pi$
$648$	2.68726	−	1.89193i	0.105565	−	0.0743220i
$649$	7.46104	+	4.36801i	0.292871	+	0.171459i
$650$	−13.7294	+	25.4594i	−0.538512	+	0.998601i
$651$	107.435	+	34.9078i	4.21072	+	1.36815i
$652$	3.94439	−	3.86686i	0.154474	−	0.151438i
$653$	−39.3284	−	28.5738i	−1.53904	−	1.11818i	−0.950934	−	0.309393i	$-0.899874\pi$
$653$	−39.3284	−	28.5738i	−1.53904	−	1.11818i	−0.588105	−	0.808785i	$-0.700126\pi$
$654$	31.2067	+	31.5179i	1.22028	+	1.23245i
$655$	−1.67515	+	3.28766i	−0.0654535	+	0.128460i
$656$	6.37998	+	13.1609i	0.249096	+	0.513845i
$657$	−20.1686	−	3.19439i	−0.786852	−	0.124625i
$658$	−8.88491	+	12.1023i	−0.346370	+	0.471796i
$659$		−	12.4981i		−	0.486857i	−0.969919	−	0.243429i	$-0.921728\pi$
$659$		−	12.4981i		−	0.486857i	0.969919	−	0.243429i	$-0.0782721\pi$
$660$	58.5206	+	13.4193i	2.27791	+	0.522346i
$661$	−6.86205	−	6.86205i	−0.266903	−	0.266903i	0.560948	−	0.827851i	$-0.310437\pi$
$661$	−6.86205	−	6.86205i	−0.266903	−	0.266903i	−0.827851	+	0.560948i	$0.810437\pi$
$662$	2.69202	+	17.5603i	0.104628	+	0.682502i
$663$	18.2156	+	37.4340i	0.707435	+	1.45382i
$664$	−10.9396	−	11.2702i	−0.424537	−	0.437370i
$665$	−64.5452	−	32.8874i	−2.50295	−	1.27532i
$666$	−5.86699	−	5.92551i	−0.227341	−	0.229609i
$667$	3.49329	+	2.53803i	0.135261	+	0.0982727i
$668$	−26.1445	+	25.6306i	−1.01156	+	0.991679i
$669$	−1.53339	−	3.00944i	−0.0592841	−	0.116352i
$670$	12.9663	−	39.2425i	0.500932	−	1.51607i
$671$	−2.56842	+	6.57189i	−0.0991528	+	0.253705i
$672$	49.7987	+	52.3334i	1.92103	+	2.01880i
$673$	−11.4006	−	3.70427i	−0.439460	−	0.142789i	0.0809265	−	0.996720i	$-0.474212\pi$
$673$	−11.4006	−	3.70427i	−0.439460	−	0.142789i	−0.520386	+	0.853931i	$0.674212\pi$
$674$	32.5358	−	10.3933i	1.25323	−	0.400334i
$675$	21.3128	+	15.4847i	0.820332	+	0.596006i
$676$	−16.2467	+	20.2988i	−0.624875	+	0.780725i
$677$	2.84512	+	8.75639i	0.109347	+	0.336535i	0.990726	−	0.135874i	$-0.0433843\pi$
$677$	2.84512	+	8.75639i	0.109347	+	0.336535i	−0.881379	+	0.472410i	$0.843384\pi$
$678$	−38.6540	−	53.7617i	−1.48450	−	2.06470i
$679$	−43.4054	−	59.7424i	−1.66575	−	2.29270i
$680$	17.9912	−	34.0469i	0.689930	−	1.30564i
$681$	−2.87770	+	2.87770i	−0.110274	+	0.110274i
$682$	−27.4212	−	31.1370i	−1.05001	−	1.19230i
$683$	6.24457	−	6.24457i	0.238942	−	0.238942i	−0.577470	−	0.816412i	$-0.695960\pi$
$683$	6.24457	−	6.24457i	0.238942	−	0.238942i	0.816412	+	0.577470i	$0.195960\pi$
$684$	−44.3657	−	7.47894i	−1.69636	−	0.285964i
$685$	34.9379	−	25.3838i	1.33491	−	0.969867i
$686$	46.6113	+	7.61980i	1.77963	+	0.290925i
$687$	19.3522	+	9.86043i	0.738332	+	0.376199i
$688$	11.1967	−	7.80008i	0.426870	−	0.297375i
$689$	−11.7081	+	11.2858i	−0.446042	+	0.429954i
$690$	−28.9315	+	56.0913i	−1.10140	+	2.13536i
$691$	15.5815	−	7.93916i	0.592747	−	0.302020i	−0.131766	−	0.991281i	$-0.542065\pi$
$691$	15.5815	−	7.93916i	0.592747	−	0.302020i	0.724513	+	0.689261i	$0.242065\pi$
$692$	−2.50499	+	3.37682i	−0.0952253	+	0.128368i
$693$	53.4127	−	47.5113i	2.02898	−	1.80480i
$694$	44.8122	+	14.8066i	1.70105	+	0.562051i
$695$	48.1096	−	24.5131i	1.82490	−	0.929833i
$696$	−6.49460	−	2.21765i	−0.246177	−	0.0840598i
$697$	−2.38374	−	15.0504i	−0.0902907	−	0.570073i
$698$	27.3707	+	27.6438i	1.03600	+	1.04633i
$699$	−13.9794	−	43.0240i	−0.528748	−	1.62732i
$700$	24.2025	−	46.3569i	0.914769	−	1.75213i
$701$	−23.3628	−	32.1561i	−0.882401	−	1.21452i	−0.975750	−	0.218887i	$-0.929757\pi$
$701$	−23.3628	−	32.1561i	−0.882401	−	1.21452i	0.0933497	−	0.995633i	$-0.470243\pi$
$702$	16.3490	+	17.1301i	0.617054	+	0.646535i
$703$		−	6.06600i		−	0.228783i
$704$	−5.94493	−	25.8584i	−0.224058	−	0.974576i
$705$	20.8471			0.785146
$706$	−25.7479	+	3.94718i	−0.969033	+	0.148554i
$707$	−14.2243	−	2.25291i	−0.534961	−	0.0847295i
$708$	6.68507	−	12.8044i	0.251240	−	0.481219i
$709$	−14.0704	+	27.6147i	−0.528424	+	1.03709i	0.460359	+	0.887733i	$0.347721\pi$
$709$	−14.0704	+	27.6147i	−0.528424	+	1.03709i	−0.988783	+	0.149358i	$0.952279\pi$
$710$	−23.2682	−	0.115471i	−0.873239	−	0.00433353i
$711$	34.5881	−	47.6064i	1.29716	−	1.78538i
$712$	−0.406995	+	0.199799i	−0.0152528	+	0.00748778i
$713$	38.8606	−	19.8005i	1.45534	−	0.741533i
$714$	−33.8362	−	67.2299i	−1.26629	−	2.51602i
$715$	2.99625	−	38.9516i	0.112053	−	1.45671i
$716$	−11.7467	−	8.71394i	−0.438996	−	0.325655i
$717$	10.8217	+	21.2387i	0.404143	+	0.793175i
$718$	10.6745	+	5.50581i	0.398367	+	0.205475i
$719$	−22.9980	−	16.7091i	−0.857682	−	0.623143i	0.0695710	−	0.997577i	$-0.477837\pi$
$719$	−22.9980	−	16.7091i	−0.857682	−	0.623143i	−0.927253	+	0.374434i	$0.877837\pi$
$720$	10.7553	−	60.1527i	0.400825	−	2.24176i
$721$	−16.0352	−	8.17035i	−0.597183	−	0.304280i
$722$	−3.42044	−	4.75731i	−0.127296	−	0.177049i
$723$	3.17091	−	20.0203i	0.117927	−	0.744564i
$724$	7.88669	+	11.0848i	0.293107	+	0.411964i
$725$			4.96794i			0.184505i
$726$	−42.3051	+	8.24066i	−1.57009	+	0.305839i
$727$	−41.0232			−1.52147			−0.760734	−	0.649064i	$-0.775161\pi$
$727$	−41.0232			−1.52147			−0.760734	+	0.649064i	$0.775161\pi$
$728$	28.8782	−	37.0888i	1.07030	−	1.37460i
$729$	−35.6236	+	25.8820i	−1.31939	+	0.958594i
$730$	16.3807	−	11.7776i	0.606279	−	0.435907i
$731$	−13.5212	+	4.39329i	−0.500098	+	0.162492i
$732$	11.1749	+	3.75397i	0.413037	+	0.138751i
$733$	39.9992	−	6.33525i	1.47740	−	0.233998i	0.634861	−	0.772626i	$-0.281057\pi$
$733$	39.9992	−	6.33525i	1.47740	−	0.233998i	0.842543	+	0.538629i	$0.181057\pi$
$734$	−22.6304	+	7.22909i	−0.835302	+	0.266831i
$735$	−58.5376	−	114.887i	−2.15919	−	4.23766i
$736$	27.8827	+	0.691990i	1.02777	+	0.0255071i
$737$	2.92273	+	29.5244i	0.107660	+	1.08755i
$738$	−10.8706	−	21.5991i	−0.400153	−	0.795074i
$739$	22.8424	+	44.8308i	0.840272	+	1.64913i	0.757757	+	0.652537i	$0.226295\pi$
$739$	22.8424	+	44.8308i	0.840272	+	1.64913i	0.0825148	+	0.996590i	$0.473705\pi$
$740$	8.23830	+	0.0817687i	0.302846	+	0.00300588i
$741$	−0.882460	+	48.0487i	−0.0324180	+	1.76511i
$742$	20.8918	−	20.6855i	0.766963	−	0.759389i
$743$	−17.4807	+	34.3078i	−0.641305	+	1.25863i	0.310104	+	0.950703i	$0.399636\pi$
$743$	−17.4807	+	34.3078i	−0.641305	+	1.25863i	−0.951409	+	0.307930i	$0.900364\pi$
$744$	−49.7401	+	48.2807i	−1.82356	+	1.77006i
$745$	−24.0920	−	33.1597i	−0.882661	−	1.21488i
$746$	−38.8852	−	28.5476i	−1.42369	−	1.04520i
$747$	18.3615	+	18.3615i	0.671812	+	0.671812i
$748$	−1.88749	+	27.5792i	−0.0690136	+	1.00839i
$749$	−50.8107	−	50.8107i	−1.85658	−	1.85658i
$750$	−8.51196	+	1.30490i	−0.310813	+	0.0476481i
$751$	26.8192	−	19.4853i	0.978648	−	0.711029i	0.0212416	−	0.999774i	$-0.493238\pi$
$751$	26.8192	−	19.4853i	0.978648	−	0.711029i	0.957406	+	0.288745i	$0.0932381\pi$
$752$	−4.01880	−	8.29013i	−0.146550	−	0.302310i
$753$	50.8711	−	16.5290i	1.85385	−	0.602351i
$754$	−0.801240	+	4.39303i	−0.0291794	+	0.159985i
$755$	21.9408	−	30.1989i	0.798506	−	1.09905i
$756$	−29.9699	−	30.5708i	−1.09000	−	1.11185i
$757$	−8.03642	+	24.7336i	−0.292089	+	0.898957i	0.692095	+	0.721806i	$0.256688\pi$
$757$	−8.03642	+	24.7336i	−0.292089	+	0.898957i	−0.984184	+	0.177150i	$0.943312\pi$
$758$	−18.5388	+	9.33038i	−0.673358	+	0.338895i
$759$	2.64475	−	45.2295i	0.0959982	−	1.64173i
$760$	36.3477	−	25.5901i	1.31847	−	0.928252i
$761$	−23.0033	+	11.7208i	−0.833870	+	0.424878i	−0.818154	−	0.574999i	$-0.805003\pi$
$761$	−23.0033	+	11.7208i	−0.833870	+	0.424878i	−0.0157153	+	0.999877i	$0.505003\pi$
$762$	−16.3557	+	5.22468i	−0.592503	+	0.189270i
$763$	−30.6685	+	42.2116i	−1.11028	+	1.52816i
$764$	8.74815	+	2.93875i	0.316497	+	0.106320i
$765$	−28.9031	+	56.7255i	−1.04499	+	2.05092i
$766$	−8.05699	−	1.31712i	−0.291111	−	0.0475895i
$767$	−8.88392	−	3.06803i	−0.320780	−	0.110780i
$768$	−42.6703	+	12.0144i	−1.53973	+	0.433534i
$769$	−34.7808	+	34.7808i	−1.25423	+	1.25423i	−0.300421	+	0.953807i	$0.597127\pi$
$769$	−34.7808	+	34.7808i	−1.25423	+	1.25423i	−0.953807	+	0.300421i	$0.902873\pi$
$770$	−4.47276	+	70.4872i	−0.161187	+	2.54018i
$771$	18.6510			0.671700
$772$	24.7763	+	4.17666i	0.891717	+	0.150321i
$773$	−3.21284	+	20.2851i	−0.115558	+	0.729603i	0.860071	+	0.510175i	$0.170419\pi$
$773$	−3.21284	+	20.2851i	−0.115558	+	0.729603i	−0.975629	+	0.219429i	$0.929581\pi$
$774$	−18.3172	+	13.1698i	−0.658398	+	0.473380i
$775$	44.7104	+	22.7811i	1.60604	+	0.818320i
$776$	44.8571	−	6.42166i	1.61028	−	0.230524i
$777$	9.46489	−	13.0273i	0.339551	−	0.467352i
$778$	45.7554	−	14.6162i	1.64041	−	0.524016i
$779$	5.43565	−	16.7292i	0.194752	−	0.599386i
$780$	−65.2436	−	1.84617i	−2.33610	−	0.0661034i
$781$	15.3003	−	6.70158i	0.547489	−	0.239801i
$782$	−27.5917	−	9.11672i	−0.986677	−	0.326013i
$783$	3.86794	+	1.25677i	0.138229	+	0.0449133i
$784$	−34.4016	+	45.4256i	−1.22863	+	1.62234i
$785$	19.3955	−	3.07194i	0.692254	−	0.109642i
$786$	−4.42538	−	0.0219614i	−0.157848	−	0.000783336i
$787$	28.6719	+	14.6090i	1.02204	+	0.520756i	0.882922	−	0.469520i	$-0.155573\pi$
$787$	28.6719	+	14.6090i	1.02204	+	0.520756i	0.139119	+	0.990276i	$0.455573\pi$
$788$	−4.38543	−	2.28959i	−0.156224	−	0.0815634i
$789$	30.2235	−	21.9586i	1.07598	−	0.781748i
$790$	8.80993	+	57.4681i	0.313443	+	2.04462i
$791$	55.0793	−	55.0793i	1.95840	−	1.95840i
$792$	10.4640	+	42.6001i	0.371821	+	1.51373i
$793$	1.33887	−	7.55288i	0.0475447	−	0.268211i
$794$	−0.982239	−	6.40724i	−0.0348583	−	0.227384i
$795$	−40.3207	−	6.38618i	−1.43003	−	0.226494i
$796$	−11.1624	−	35.5510i	−0.395640	−	1.26007i
$797$	1.07948	−	0.350744i	0.0382371	−	0.0124240i	−0.289836	−	0.957076i	$-0.593601\pi$
$797$	1.07948	−	0.350744i	0.0382371	−	0.0124240i	0.328073	+	0.944652i	$0.393601\pi$
$798$	0.431157	−	86.8814i	0.0152628	−	3.07557i
$799$	1.50154	+	9.48034i	0.0531206	+	0.335390i
$800$	18.2120	+	26.4212i	0.643893	+	0.934132i
$801$	0.667883	−	0.340303i	0.0235985	−	0.0120240i
$802$	10.0359	−	5.05095i	0.354378	−	0.178355i
$803$	−7.31727	+	12.4987i	−0.258221	+	0.441070i
$804$	49.0327	−	7.26792i	1.72925	−	0.256320i
$805$	−70.6110	−	22.9429i	−2.48871	−	0.808631i
$806$	35.8621	+	27.3557i	1.26319	+	0.963565i
$807$	10.1662	−	13.9926i	0.357867	−	0.492562i
$808$	5.30034	−	7.07146i	0.186465	−	0.248773i
$809$	1.01679	+	3.12935i	0.0357484	+	0.110022i	0.967338	−	0.253489i	$-0.0815780\pi$
$809$	1.01679	+	3.12935i	0.0357484	+	0.110022i	−0.931590	+	0.363511i	$0.881578\pi$
$810$	0.866085	−	5.29795i	0.0304311	−	0.186151i
$811$	44.4599	+	7.04176i	1.56120	+	0.247270i	0.876444	−	0.481503i	$-0.159909\pi$
$811$	44.4599	+	7.04176i	1.56120	+	0.247270i	0.684755	+	0.728773i	$0.259909\pi$
$812$	1.34201	−	7.96090i	0.0470952	−	0.279373i
$813$	47.9824	+	47.9824i	1.68282	+	1.68282i
$814$	−5.42912	+	2.34592i	−0.190291	+	0.0822246i
$815$		−	9.02266i		−	0.316050i
$816$	46.1760	+	0.916723i	1.61648	+	0.0320917i
$817$	−16.2095	−	2.56733i	−0.567098	−	0.0898195i
$818$	−2.54475	+	15.5666i	−0.0889753	+	0.544273i
$819$	−46.8256	+	62.0220i	−1.63622	+	2.16723i
$820$	22.6469	+	7.60773i	0.790863	+	0.265673i
$821$	4.91905	−	0.779101i	0.171676	−	0.0271908i	−0.0700046	−	0.997547i	$-0.522301\pi$
$821$	4.91905	−	0.779101i	0.171676	−	0.0271908i	0.241681	+	0.970356i	$0.422301\pi$
$822$	46.0324	+	23.7432i	1.60557	+	0.828138i
$823$	6.58943	−	20.2802i	0.229693	−	0.706922i	−0.768088	−	0.640344i	$-0.778792\pi$
$823$	6.58943	−	20.2802i	0.229693	−	0.706922i	0.997781	−	0.0665783i	$-0.0212082\pi$
$824$	9.03000	−	6.35746i	0.314575	−	0.221473i
$825$	43.8882	−	28.1254i	1.52799	−	0.979202i
$826$	16.1342	+	5.33099i	0.561382	+	0.185489i
$827$	−13.9531	−	27.3846i	−0.485198	−	0.952255i	−0.995723	−	0.0923916i	$-0.970549\pi$
$827$	−13.9531	−	27.3846i	−0.485198	−	0.952255i	0.510525	−	0.859863i	$-0.329451\pi$
$828$	−46.1098	−	0.457660i	−1.60243	−	0.0159048i
$829$	−5.54743	+	7.63538i	−0.192670	+	0.265188i	−0.894412	−	0.447243i	$-0.852406\pi$
$829$	−5.54743	+	7.63538i	−0.192670	+	0.265188i	0.701742	+	0.712431i	$0.252406\pi$
$830$	−25.6555	−	0.127318i	−0.890515	−	0.00441926i
$831$	19.0791	+	58.7194i	0.661846	+	2.03695i
$832$	11.8432	+	26.3009i	0.410589	+	0.911821i
$833$	48.0292	−	34.8952i	1.66411	−	1.20905i
$834$	52.2016	+	38.3239i	1.80759	+	1.32705i
$835$			59.8048i			2.06963i
$836$	−16.3948	+	27.3772i	−0.567025	+	0.946860i
$837$	29.0476	−	29.0476i	1.00403	−	1.00403i
$838$	−17.9477	+	24.4469i	−0.619994	+	0.844503i
$839$	−6.28669	+	39.6926i	−0.217041	+	1.37034i	0.602865	+	0.797843i	$0.294026\pi$
$839$	−6.28669	+	39.6926i	−0.217041	+	1.37034i	−0.819906	+	0.572498i	$0.805974\pi$
$840$	117.989	+	1.75671i	4.07100	+	0.0606121i
$841$	−8.72449	−	26.8512i	−0.300845	−	0.925904i
$842$	−9.56396	+	9.46950i	−0.329596	+	0.326341i
$843$	−5.44128	+	0.861815i	−0.187408	+	0.0296825i
$844$	−0.171616	+	17.2906i	−0.00590728	+	0.595166i
$845$	5.09900	+	42.1627i	0.175411	+	1.45044i
$846$	6.84748	+	13.6054i	0.235421	+	0.467765i
$847$	−17.5962	−	47.5508i	−0.604612	−	1.63387i
$848$	5.23328	+	17.2652i	0.179712	+	0.592889i
$849$	4.85284	+	1.57678i	0.166549	+	0.0541151i
$850$	−10.1735	−	31.8477i	−0.348948	−	1.09237i
$851$	−0.972562	−	6.14052i	−0.0333390	−	0.210494i
$852$	−12.4222	−	24.9901i	−0.425578	−	0.856145i
$853$	−18.2232	+	35.7650i	−0.623949	+	1.22457i	0.335327	+	0.942102i	$0.391153\pi$
$853$	−18.2232	+	35.7650i	−0.623949	+	1.22457i	−0.959277	+	0.282468i	$0.908847\pi$
$854$	−2.23735	+	13.6862i	−0.0765606	+	0.468330i
$855$	−59.4562	+	43.1975i	−2.03336	+	1.47732i
$856$	42.1343	−	13.0000i	1.44012	−	0.444332i
$857$		−	28.1719i		−	0.962334i	−0.876629	−	0.481167i	$-0.840213\pi$
$857$		−	28.1719i		−	0.962334i	0.876629	−	0.481167i	$-0.159787\pi$
$858$	43.3454	−	17.7923i	1.47979	−	0.607417i
$859$			47.9543i			1.63618i	0.575092	+	0.818089i	$0.304966\pi$
$859$			47.9543i			1.63618i	−0.575092	+	0.818089i	$0.695034\pi$
$860$	3.70522	−	21.9797i	0.126347	−	0.749501i
$861$	37.7765	−	27.4462i	1.28742	−	0.935365i
$862$	−19.0569	−	3.11533i	−0.649079	−	0.106109i
$863$	−24.1813	+	47.4585i	−0.823141	+	1.61551i	−0.0355008	+	0.999370i	$0.511303\pi$
$863$	−24.1813	+	47.4585i	−0.823141	+	1.61551i	−0.787640	+	0.616136i	$0.788697\pi$
$864$	25.1783	−	7.49561i	0.856583	−	0.255006i
$865$	1.07437	+	6.78333i	0.0365298	+	0.230640i
$866$	18.0128	−	5.75403i	0.612098	−	0.195530i
$867$	−0.968492	−	0.314682i	−0.0328917	−	0.0106872i
$868$	−65.4924	−	48.5834i	−2.22296	−	1.64903i
$869$	−22.5191	−	35.1398i	−0.763909	−	1.19204i
$870$	−10.0134	+	5.03964i	−0.339485	+	0.170860i
$871$	−9.40187	−	30.8526i	−0.318570	−	1.04540i
$872$	−14.1093	−	28.7409i	−0.477801	−	0.973291i
$873$	−73.9949	+	11.7196i	−2.50435	+	0.396650i
$874$	−23.6015	−	23.8369i	−0.798332	−	0.806296i
$875$	−3.13042	−	9.63444i	−0.105828	−	0.325704i
$876$	21.4499	+	11.1988i	0.724725	+	0.378373i
$877$	5.90541	−	37.2853i	0.199412	−	1.25903i	−0.661370	−	0.750060i	$-0.730025\pi$
$877$	5.90541	−	37.2853i	0.199412	−	1.25903i	0.860781	−	0.508975i	$-0.169975\pi$
$878$	20.5236	+	15.0674i	0.692638	+	0.508502i
$879$	−38.4181	+	38.4181i	−1.29581	+	1.29581i
$880$	−36.9603	−	22.6349i	−1.24593	−	0.763024i
$881$			39.2949i			1.32388i	0.749557	+	0.661940i	$0.230266\pi$
$881$			39.2949i			1.32388i	−0.749557	+	0.661940i	$0.769734\pi$
$882$	55.7511	−	75.9394i	1.87724	−	2.55701i
$883$	3.16191	−	2.29726i	0.106407	−	0.0773090i	−0.533309	−	0.845920i	$-0.679052\pi$
$883$	3.16191	−	2.29726i	0.106407	−	0.0773090i	0.639716	+	0.768611i	$0.279052\pi$
$884$	−3.85970	−	29.8029i	−0.129816	−	1.00238i
$885$	−7.29108	−	22.4396i	−0.245087	−	0.754301i
$886$	−0.256765	+	51.7401i	−0.00862619	+	1.73824i
$887$	−14.4828	+	19.9338i	−0.486284	+	0.669312i	−0.979697	−	0.200483i	$-0.935749\pi$
$887$	−14.4828	+	19.9338i	−0.486284	+	0.669312i	0.493413	+	0.869795i	$0.335749\pi$
$888$	4.35439	+	8.86999i	0.146124	+	0.297657i
$889$	−9.16981	−	17.9968i	−0.307546	−	0.603592i
$890$	−0.232350	+	0.703205i	−0.00778838	+	0.0235715i
$891$	0.974882	+	3.72835i	0.0326598	+	0.124905i
$892$	0.357493	+	2.41181i	0.0119697	+	0.0807534i
$893$	−3.42396	+	10.5379i	−0.114578	+	0.352636i
$894$	22.5348	−	43.6897i	0.753676	−	1.46120i
$895$	−23.5968	+	3.73736i	−0.788753	+	0.124926i
$896$	−22.0467	−	47.2585i	−0.736529	−	1.57880i
$897$	6.81036	+	48.7805i	0.227391	+	1.62873i
$898$	46.7994	+	7.65056i	1.56172	+	0.255303i
$899$	7.65134	+	1.21185i	0.255186	+	0.0404176i
$900$	−30.7565	−	43.2285i	−1.02522	−	1.44095i
$901$		−	18.7961i		−	0.626189i
$902$	−17.0750	+	1.60479i	−0.568534	+	0.0534336i
$903$	−30.8056	−	30.8056i	−1.02514	−	1.02514i
$904$	14.0922	+	45.6740i	0.468699	+	1.51909i
$905$	21.9482	+	3.47626i	0.729583	+	0.115555i
$906$	44.1830	+	7.22285i	1.46788	+	0.239963i
$907$	−15.7708	−	48.5376i	−0.523661	−	1.61166i	−0.766948	−	0.641710i	$-0.778225\pi$
$907$	−15.7708	−	48.5376i	−0.523661	−	1.61166i	0.243286	−	0.969955i	$-0.421775\pi$
$908$	2.63068	−	1.30768i	0.0873023	−	0.0433968i
$909$	−8.58790	+	11.8202i	−0.284843	+	0.392052i
$910$	−10.2392	−	76.0960i	−0.339427	−	2.52256i
$911$	30.9666	+	10.0617i	1.02597	+	0.333357i	0.773195	−	0.634168i	$-0.218657\pi$
$911$	30.9666	+	10.0617i	1.02597	+	0.333357i	0.252773	+	0.967526i	$0.418657\pi$
$912$	47.0136	+	25.1423i	1.55678	+	0.832545i
$913$	16.8701	−	7.38915i	0.558320	−	0.244545i
$914$	−2.91591	−	5.79369i	−0.0964496	−	0.191638i
$915$	17.1574	−	8.74212i	0.567205	−	0.289006i
$916$	−10.9758	−	11.1959i	−0.362652	−	0.369923i
$917$	−0.814394	−	5.14188i	−0.0268937	−	0.169800i
$918$	−27.3697	−	0.135825i	−0.903334	−	0.00448288i
$919$	28.1703	−	9.15309i	0.929253	−	0.301933i	0.194996	−	0.980804i	$-0.437531\pi$
$919$	28.1703	−	9.15309i	0.929253	−	0.301933i	0.734257	+	0.678872i	$0.237531\pi$
$920$	32.6913	−	31.7321i	1.07780	−	1.04618i
$921$	−50.2152	−	7.95330i	−1.65465	−	0.262070i
$922$	46.7248	−	7.16298i	1.53880	−	0.235900i
$923$	−14.8843	+	10.4019i	−0.489922	+	0.342382i
$924$	−77.9264	+	33.2141i	−2.56359	+	1.09266i
$925$	5.05788	−	5.05788i	0.166302	−	0.166302i
$926$	−2.28356	+	0.350074i	−0.0750426	+	0.0115041i
$927$	−14.7710	+	10.7317i	−0.485142	+	0.352476i
$928$	3.93441	+	3.01044i	0.129153	+	0.0988226i
$929$	3.20253	+	1.63177i	0.105072	+	0.0535366i	0.505736	−	0.862688i	$-0.331221\pi$
$929$	3.20253	+	1.63177i	0.105072	+	0.0535366i	−0.400665	+	0.916225i	$0.631221\pi$
$930$	−0.561905	+	113.228i	−0.0184256	+	3.71290i
$931$	67.6876	−	10.7207i	2.21837	−	0.351356i
$932$	−0.324108	+	32.6543i	−0.0106165	+	1.06963i
$933$	9.36262	+	3.04210i	0.306518	+	0.0995939i
$934$	−3.51125	+	10.6268i	−0.114891	+	0.347719i
$935$	30.0110	+	33.7386i	0.981463	+	1.10337i
$936$	−20.2252	−	43.1864i	−0.661082	−	1.41159i
$937$	9.97896	−	30.7121i	0.325998	−	1.00332i	−0.644990	−	0.764191i	$-0.723138\pi$
$937$	9.97896	−	30.7121i	0.325998	−	1.00332i	0.970988	−	0.239129i	$-0.0768617\pi$
$938$	17.7437	+	55.5459i	0.579353	+	1.81364i
$939$	50.5416	−	69.5646i	1.64936	−	2.27016i
$940$	−14.2654	−	4.79216i	−0.465287	−	0.156303i
$941$	0.706475	+	0.359967i	0.0230304	+	0.0117346i	0.465468	−	0.885065i	$-0.345886\pi$
$941$	0.706475	+	0.359967i	0.0230304	+	0.0117346i	−0.442437	+	0.896799i	$0.645886\pi$
$942$	13.7489	+	19.1225i	0.447962	+	0.623046i
$943$	2.82023	−	17.8062i	0.0918393	−	0.579851i
$944$	−7.51790	+	7.22520i	−0.244687	+	0.235160i
$945$	−69.9298			−2.27482
$946$	3.97097	+	15.5005i	0.129107	+	0.503965i
$947$	−3.96047	+	3.96047i	−0.128698	+	0.128698i	−0.768522	−	0.639824i	$-0.779007\pi$
$947$	−3.96047	+	3.96047i	−0.128698	+	0.128698i	0.639824	+	0.768522i	$0.279007\pi$
$948$	−56.8168	+	40.4244i	−1.84532	+	1.31292i
$949$	5.13956	−	14.8823i	0.166837	−	0.483101i
$950$	6.22652	−	38.0884i	0.202015	−	1.23575i
$951$	−34.9049	+	68.5047i	−1.13187	+	2.22142i
$952$	7.69943	+	53.7827i	0.249540	+	1.74311i
$953$	10.6092	−	14.6024i	0.343667	−	0.473017i	−0.601841	−	0.798616i	$-0.705566\pi$
$953$	10.6092	−	14.6024i	0.343667	−	0.473017i	0.945508	+	0.325599i	$0.105566\pi$
$954$	−9.07604	−	28.4122i	−0.293848	−	0.919878i
$955$	13.4315	−	6.84367i	0.434632	−	0.221456i
$956$	−2.52296	−	17.0210i	−0.0815984	−	0.550500i
$957$	5.10208	−	6.22321i	0.164927	−	0.201168i
$958$	5.17235	+	10.2771i	0.167111	+	0.332037i
$959$	−18.8285	+	57.9483i	−0.608005	+	1.87125i
$960$	−34.7798	+	63.5108i	−1.12251	+	2.04980i
$961$	27.7712	−	38.2238i	0.895845	−	1.23303i
$962$	5.28831	−	3.65682i	0.170502	−	0.117901i
$963$	−69.3319	+	22.5273i	−2.23419	+	0.725932i
$964$	−6.77193	+	12.9708i	−0.218109	+	0.417761i
$965$	33.2037	−	24.1239i	1.06886	−	0.776575i
$966$	−13.4933	−	88.0179i	−0.434139	−	2.83193i
$967$	28.5850	+	28.5850i	0.919233	+	0.919233i	0.996974	−	0.0777405i	$-0.0247706\pi$
$967$	28.5850	+	28.5850i	0.919233	+	0.919233i	−0.0777405	+	0.996974i	$0.524771\pi$
$968$	30.8433	+	4.08579i	0.991340	+	0.131322i
$969$	−39.2770	−	39.2770i	−1.26176	−	1.26176i
$970$	43.8040	−	59.6662i	1.40646	−	1.91577i
$971$	−22.0830	−	30.3946i	−0.708676	−	0.975409i	−0.999825	−	0.0187311i	$-0.994037\pi$
$971$	−22.0830	−	30.3946i	−0.708676	−	0.975409i	0.291148	−	0.956678i	$-0.405963\pi$
$972$	32.7271	−	10.2757i	1.04972	−	0.329594i
$973$	−34.5854	+	67.8777i	−1.10876	+	2.17606i
$974$	−8.80785	−	8.89571i	−0.282222	−	0.285037i
$975$	−40.7993	+	39.3277i	−1.30662	+	1.25949i
$976$	−6.78394	−	5.13760i	−0.217149	−	0.164451i
$977$	−10.9446	−	21.4800i	−0.350150	−	0.687208i	0.647013	−	0.762479i	$-0.276018\pi$
$977$	−10.9446	−	21.4800i	−0.350150	−	0.687208i	−0.997163	+	0.0752710i	$0.976018\pi$
$978$	9.66621	−	4.86491i	0.309091	−	0.155563i
$979$	−0.0523739	−	0.529063i	−0.00167388	−	0.0169089i
$980$	13.6474	+	92.0718i	0.435952	+	2.94113i
$981$	24.0313	+	47.1642i	0.767262	+	1.50584i
$982$	−13.1358	−	41.1210i	−0.419179	−	1.31222i
$983$	−10.0749	+	1.59571i	−0.321341	+	0.0508953i	−0.315021	−	0.949085i	$-0.602012\pi$
$983$	−10.0749	+	1.59571i	−0.321341	+	0.0508953i	−0.00631952	+	0.999980i	$0.502012\pi$
$984$	4.06056	+	28.3642i	0.129446	+	0.904216i
$985$	−7.68544	+	2.49715i	−0.244878	+	0.0795658i
$986$	−3.01303	−	4.19066i	−0.0959546	−	0.133458i
$987$	−23.7957	+	17.2886i	−0.757425	+	0.550302i
$988$	11.6489	−	32.6764i	0.370602	−	1.03957i
$989$	−16.8202			−0.534852
$990$	61.6559	+	36.5080i	1.95955	+	1.16030i
$991$		−	47.8988i		−	1.52156i	−0.649012	−	0.760778i	$-0.724817\pi$
$991$		−	47.8988i		−	1.52156i	0.649012	−	0.760778i	$-0.275183\pi$
$992$	45.1350	−	21.6041i	1.43304	−	0.685931i
$993$	−5.44461	+	34.3759i	−0.172779	+	1.09089i
$994$	26.6550	−	19.1646i	0.845445	−	0.607865i
$995$	−54.2323	−	27.6327i	−1.71928	−	0.876017i
$996$	−13.6967	−	27.5540i	−0.433997	−	0.873083i
$997$	1.06804	+	0.775974i	0.0338250	+	0.0245753i	0.604569	−	0.796553i	$-0.293345\pi$
$997$	1.06804	+	0.775974i	0.0338250	+	0.0245753i	−0.570744	+	0.821128i	$0.693345\pi$
$998$	−22.6702	+	43.9521i	−0.717611	+	1.39128i
$999$	−2.65845	−	5.21750i	−0.0841096	−	0.165074i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bk.a.31.17	✓	640
4.3	odd	2	inner	572.2.bk.a.31.40	yes	640
11.5	even	5	inner	572.2.bk.a.291.80	yes	640
13.8	odd	4	inner	572.2.bk.a.515.57	yes	640
44.27	odd	10	inner	572.2.bk.a.291.57	yes	640
52.47	even	4	inner	572.2.bk.a.515.80	yes	640
143.60	odd	20	inner	572.2.bk.a.203.40	yes	640
572.203	even	20	inner	572.2.bk.a.203.17	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bk.a.31.17	✓	640	1.1	even	1	trivial
572.2.bk.a.31.40	yes	640	4.3	odd	2	inner
572.2.bk.a.203.17	yes	640	572.203	even	20	inner
572.2.bk.a.203.40	yes	640	143.60	odd	20	inner
572.2.bk.a.291.57	yes	640	44.27	odd	10	inner
572.2.bk.a.291.80	yes	640	11.5	even	5	inner
572.2.bk.a.515.57	yes	640	13.8	odd	4	inner
572.2.bk.a.515.80	yes	640	52.47	even	4	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13998 - 0.836921i) q^{2} +(-1.62851 - 2.24145i) q^{3} +(0.599125 + 1.90815i) q^{4} +(2.91084 + 1.48315i) q^{5} +(-0.0194442 + 3.91816i) q^{6} +(-4.55254 + 0.721051i) q^{7} +(0.913981 - 2.67668i) q^{8} +(-1.44502 + 4.44730i) q^{9} +O(q^{10})\)	\(q+(-1.13998 - 0.836921i) q^{2} +(-1.62851 - 2.24145i) q^{3} +(0.599125 + 1.90815i) q^{4} +(2.91084 + 1.48315i) q^{5} +(-0.0194442 + 3.91816i) q^{6} +(-4.55254 + 0.721051i) q^{7} +(0.913981 - 2.67668i) q^{8} +(-1.44502 + 4.44730i) q^{9} +(-2.07704 - 4.12691i) q^{10} +(2.56483 + 2.10277i) q^{11} +(3.30136 - 4.45036i) q^{12} +(-3.18197 - 1.69560i) q^{13} +(5.79328 + 2.98813i) q^{14} +(-1.41593 - 8.93985i) q^{15} +(-3.28210 + 2.28645i) q^{16} +(3.96347 - 1.28781i) q^{17} +(5.36934 - 3.86049i) q^{18} +(4.75150 + 0.752564i) q^{19} +(-1.08612 + 6.44293i) q^{20} +(9.03007 + 9.03007i) q^{21} +(-1.16401 - 4.54368i) q^{22} +4.93054 q^{23} +(-7.48810 + 2.31036i) q^{24} +(3.33435 + 4.58934i) q^{25} +(2.20831 + 4.59602i) q^{26} +(4.41669 - 1.43507i) q^{27} +(-4.10342 - 8.25494i) q^{28} +(0.708501 + 0.514756i) q^{29} +(-5.86781 + 11.3763i) q^{30} +(7.88162 - 4.01588i) q^{31} +(5.65511 + 0.140348i) q^{32} +(0.536402 - 9.17334i) q^{33} +(-5.59609 - 1.84903i) q^{34} +(-14.3212 - 4.65322i) q^{35} +(-9.35188 - 0.0928215i) q^{36} +(-0.197253 - 1.24541i) q^{37} +(-4.78680 - 4.83455i) q^{38} +(1.38126 + 9.89355i) q^{39} +(6.63038 - 6.43584i) q^{40} +(0.571993 - 3.61142i) q^{41} +(-2.73667 - 17.8516i) q^{42} -3.41144 q^{43} +(-2.47575 + 6.15391i) q^{44} +(-10.8022 + 10.8022i) q^{45} +(-5.62073 - 4.12647i) q^{46} +(-0.360302 + 2.27486i) q^{47} +(10.4699 + 3.63317i) q^{48} +(13.5483 - 4.40211i) q^{49} +(0.0398118 - 8.02237i) q^{50} +(-9.34113 - 6.78673i) q^{51} +(1.32907 - 7.08756i) q^{52} +(1.39374 - 4.28948i) q^{53} +(-6.23600 - 2.06047i) q^{54} +(4.34711 + 9.92486i) q^{55} +(-2.23091 + 12.8447i) q^{56} +(-6.05104 - 11.8758i) q^{57} +(-0.376869 - 1.17977i) q^{58} +(2.57466 - 0.407786i) q^{59} +(16.2103 - 8.05791i) q^{60} +(0.657419 + 2.02333i) q^{61} +(-12.3459 - 2.01825i) q^{62} +(3.37176 - 21.2884i) q^{63} +(-6.32928 - 4.89288i) q^{64} +(-6.74739 - 9.65497i) q^{65} +(-8.28885 + 10.0085i) q^{66} +(6.32540 + 6.32540i) q^{67} +(4.83195 + 6.79135i) q^{68} +(-8.02944 - 11.0516i) q^{69} +(12.4315 + 17.2903i) q^{70} +(2.28645 - 4.48741i) q^{71} +(10.5833 + 7.93261i) q^{72} +(0.683121 + 4.31306i) q^{73} +(-0.817441 + 1.58483i) q^{74} +(4.85677 - 14.9476i) q^{75} +(1.41074 + 9.51748i) q^{76} +(-13.1927 - 7.72356i) q^{77} +(6.70551 - 12.4345i) q^{78} +(-11.9681 - 3.88866i) q^{79} +(-12.9448 + 1.78764i) q^{80} +(0.940025 + 0.682968i) q^{81} +(-3.67454 + 3.63825i) q^{82} +(2.52104 - 4.94781i) q^{83} +(-11.8206 + 22.6409i) q^{84} +(13.4471 + 2.12980i) q^{85} +(3.88899 + 2.85511i) q^{86} -2.42636i q^{87} +(7.97266 - 4.94335i) q^{88} +(-0.113348 - 0.113348i) q^{89} +(21.3550 - 3.27375i) q^{90} +(15.7087 + 5.42493i) q^{91} +(2.95401 + 9.40822i) q^{92} +(-21.8367 - 11.1264i) q^{93} +(2.31462 - 2.29176i) q^{94} +(12.7147 + 9.23779i) q^{95} +(-8.89484 - 12.9042i) q^{96} +(7.27341 + 14.2749i) q^{97} +(-19.1290 - 6.32052i) q^{98} +(-13.0579 + 8.36805i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9}+O(q^{10}) \) 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9	\( 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9} - 12 q^{13} + 4 q^{14} - 36 q^{16} - 10 q^{18} - 60 q^{20} - 56 q^{21} - 44 q^{22} - 14 q^{24} + 26 q^{26} - 14 q^{28} - 24 q^{29} - 16 q^{32} - 28 q^{33} + 12 q^{34} - 12 q^{37} + 4 q^{40} - 36 q^{41} - 8 q^{42} + 26 q^{44} - 16 q^{45} - 50 q^{46} + 48 q^{48} + 36 q^{50} - 52 q^{52} - 40 q^{53} + 116 q^{54} - 36 q^{57} - 70 q^{58} + 52 q^{60} - 8 q^{61} - 48 q^{65} - 228 q^{66} - 44 q^{68} - 68 q^{70} - 38 q^{72} - 12 q^{73} - 12 q^{74} + 108 q^{76} + 108 q^{78} + 62 q^{80} - 168 q^{81} - 36 q^{84} - 52 q^{85} - 62 q^{86} + 16 q^{89} - 80 q^{92} - 4 q^{93} - 124 q^{94} - 132 q^{96} - 4 q^{97} - 108 q^{98}+O(q^{100}) \) 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9 - 12 * q^13 + 4 * q^14 - 36 * q^16 - 10 * q^18 - 60 * q^20 - 56 * q^21 - 44 * q^22 - 14 * q^24 + 26 * q^26 - 14 * q^28 - 24 * q^29 - 16 * q^32 - 28 * q^33 + 12 * q^34 - 12 * q^37 + 4 * q^40 - 36 * q^41 - 8 * q^42 + 26 * q^44 - 16 * q^45 - 50 * q^46 + 48 * q^48 + 36 * q^50 - 52 * q^52 - 40 * q^53 + 116 * q^54 - 36 * q^57 - 70 * q^58 + 52 * q^60 - 8 * q^61 - 48 * q^65 - 228 * q^66 - 44 * q^68 - 68 * q^70 - 38 * q^72 - 12 * q^73 - 12 * q^74 + 108 * q^76 + 108 * q^78 + 62 * q^80 - 168 * q^81 - 36 * q^84 - 52 * q^85 - 62 * q^86 + 16 * q^89 - 80 * q^92 - 4 * q^93 - 124 * q^94 - 132 * q^96 - 4 * q^97 - 108 * q^98

Introduction

L-functions

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