LMFDB - Embedded newform 153.2.s.a.11.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,2,Mod(5,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([40, 15]))

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

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

chi := DirichletCharacter("153.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.s (of order $48$, degree $16$, 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:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			11.16
Character	$\chi$	$=$	153.11
Dual form			153.2.s.a.14.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.45899 + 1.90139i) q^{2} +(0.889766 - 1.48604i) q^{3} +(-0.969004 + 3.61637i) q^{4} +(-0.502973 - 0.0329666i) q^{5} +(4.12371 - 0.476323i) q^{6} +(0.0485612 + 0.740900i) q^{7} +(-3.86148 + 1.59948i) q^{8} +(-1.41663 - 2.64446i) q^{9} +O(q^{10})$	\(q+(1.45899 + 1.90139i) q^{2} +(0.889766 - 1.48604i) q^{3} +(-0.969004 + 3.61637i) q^{4} +(-0.502973 - 0.0329666i) q^{5} +(4.12371 - 0.476323i) q^{6} +(0.0485612 + 0.740900i) q^{7} +(-3.86148 + 1.59948i) q^{8} +(-1.41663 - 2.64446i) q^{9} +(-0.671150 - 1.00445i) q^{10} +(0.767594 + 0.673162i) q^{11} +(4.51189 + 4.65771i) q^{12} +(-5.20440 - 1.39452i) q^{13} +(-1.33789 + 1.17330i) q^{14} +(-0.496518 + 0.718106i) q^{15} +(-2.19038 - 1.26462i) q^{16} +(3.71857 - 1.78107i) q^{17} +(2.96130 - 6.55181i) q^{18} +(-3.37354 - 1.39737i) q^{19} +(0.606603 - 1.78699i) q^{20} +(1.14422 + 0.587064i) q^{21} +(-0.160033 + 2.44163i) q^{22} +(-0.172029 - 0.506782i) q^{23} +(-1.05893 + 7.16147i) q^{24} +(-4.70533 - 0.619468i) q^{25} +(-4.94165 - 11.9302i) q^{26} +(-5.19024 - 0.247775i) q^{27} +(-2.72643 - 0.542320i) q^{28} +(5.67976 - 2.80095i) q^{29} +(-2.08982 + 0.103633i) q^{30} +(-0.677946 - 0.773049i) q^{31} +(0.299892 + 2.27790i) q^{32} +(1.68332 - 0.541719i) q^{33} +(8.81188 + 4.47190i) q^{34} -0.374254i q^{35} +(10.9361 - 2.56058i) q^{36} +(2.20919 + 11.1064i) q^{37} +(-2.26502 - 8.45317i) q^{38} +(-6.70301 + 6.49316i) q^{39} +(1.99495 - 0.677194i) q^{40} +(-2.96507 + 6.01257i) q^{41} +(0.553160 + 3.03212i) q^{42} +(0.384182 - 2.91815i) q^{43} +(-3.17821 + 2.12361i) q^{44} +(0.625350 + 1.37679i) q^{45} +(0.712603 - 1.06649i) q^{46} +(11.4370 - 3.06452i) q^{47} +(-3.82820 + 2.12978i) q^{48} +(6.39354 - 0.841725i) q^{49} +(-5.68718 - 9.85048i) q^{50} +(0.661916 - 7.11069i) q^{51} +(10.0862 - 17.4698i) q^{52} +(-3.30651 + 7.98262i) q^{53} +(-7.10139 - 10.2302i) q^{54} +(-0.363887 - 0.363887i) q^{55} +(-1.37257 - 2.78330i) q^{56} +(-5.07821 + 3.76989i) q^{57} +(13.6124 + 6.71290i) q^{58} +(-6.97647 - 5.35323i) q^{59} +(-2.11581 - 2.49144i) q^{60} +(6.35837 - 0.416750i) q^{61} +(0.480754 - 2.41691i) q^{62} +(1.89049 - 1.17800i) q^{63} +(-7.47053 + 7.47053i) q^{64} +(2.57170 + 0.872975i) q^{65} +(3.48597 + 2.41030i) q^{66} +(-8.82398 + 5.09452i) q^{67} +(2.83771 + 15.1736i) q^{68} +(-0.906165 - 0.195275i) q^{69} +(0.711604 - 0.546033i) q^{70} +(4.19907 - 0.835247i) q^{71} +(9.70004 + 7.94564i) q^{72} +(2.65455 + 1.77371i) q^{73} +(-17.8943 + 20.4046i) q^{74} +(-5.10720 + 6.44113i) q^{75} +(8.32238 - 10.8459i) q^{76} +(-0.461470 + 0.601400i) q^{77} +(-22.1257 - 3.27159i) q^{78} +(-6.82883 + 7.78679i) q^{79} +(1.06001 + 0.708279i) q^{80} +(-4.98630 + 7.49245i) q^{81} +(-15.7583 + 3.13452i) q^{82} +(1.02986 - 0.790239i) q^{83} +(-3.23179 + 3.56904i) q^{84} +(-1.92906 + 0.773243i) q^{85} +(6.10907 - 3.52707i) q^{86} +(0.891337 - 10.9325i) q^{87} +(-4.04075 - 1.37165i) q^{88} +(2.39586 - 2.39586i) q^{89} +(-1.70544 + 3.19776i) q^{90} +(0.780465 - 3.92366i) q^{91} +(1.99941 - 0.131048i) q^{92} +(-1.75200 + 0.319622i) q^{93} +(22.5133 + 17.2750i) q^{94} +(1.65074 + 0.814053i) q^{95} +(3.65189 + 1.58115i) q^{96} +(-7.04839 - 14.2927i) q^{97} +(10.9286 + 10.9286i) q^{98} +(0.692749 - 2.98349i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.45899	+	1.90139i	1.03166	+	1.34449i	0.937136	+	0.348965i	$0.113467\pi$
$2$	1.45899	+	1.90139i	1.03166	+	1.34449i	0.0945260	+	0.995522i	$0.469866\pi$
$3$	0.889766	−	1.48604i	0.513707	−	0.857966i
$3$	0.889766	−	1.48604i	0.513707	−	0.857966i
$4$	−0.969004	+	3.61637i	−0.484502	+	1.80819i
$5$	−0.502973	−	0.0329666i	−0.224936	−	0.0147431i	−0.0474819	−	0.998872i	$-0.515120\pi$
$5$	−0.502973	−	0.0329666i	−0.224936	−	0.0147431i	−0.177455	+	0.984129i	$0.556786\pi$
$6$	4.12371	−	0.476323i	1.68350	−	0.194458i
$7$	0.0485612	+	0.740900i	0.0183544	+	0.280034i	0.997164	+	0.0752609i	$0.0239790\pi$
$7$	0.0485612	+	0.740900i	0.0183544	+	0.280034i	−0.978809	+	0.204773i	$0.934354\pi$
$8$	−3.86148	+	1.59948i	−1.36524	+	0.565500i
$9$	−1.41663	−	2.64446i	−0.472211	−	0.881486i
$10$	−0.671150	−	1.00445i	−0.212236	−	0.317634i
$11$	0.767594	+	0.673162i	0.231438	+	0.202966i	0.767208	−	0.641398i	$-0.221645\pi$
$11$	0.767594	+	0.673162i	0.231438	+	0.202966i	−0.535770	+	0.844364i	$0.679979\pi$
$12$	4.51189	+	4.65771i	1.30247	+	1.34456i
$13$	−5.20440	−	1.39452i	−1.44344	−	0.386769i	−0.549704	−	0.835360i	$-0.685259\pi$
$13$	−5.20440	−	1.39452i	−1.44344	−	0.386769i	−0.893737	+	0.448591i	$0.851926\pi$
$14$	−1.33789	+	1.17330i	−0.357567	+	0.313578i
$15$	−0.496518	+	0.718106i	−0.128200	+	0.185414i
$16$	−2.19038	−	1.26462i	−0.547596	−	0.316155i
$17$	3.71857	−	1.78107i	0.901886	−	0.431973i
$17$	3.71857	−	1.78107i	0.901886	−	0.431973i
$18$	2.96130	−	6.55181i	0.697985	−	1.54428i
$19$	−3.37354	−	1.39737i	−0.773944	−	0.320578i	−0.0394751	−	0.999221i	$-0.512569\pi$
$19$	−3.37354	−	1.39737i	−0.773944	−	0.320578i	−0.734469	+	0.678643i	$0.762569\pi$
$20$	0.606603	−	1.78699i	0.135641	−	0.399584i
$21$	1.14422	+	0.587064i	0.249688	+	0.128108i
$22$	−0.160033	+	2.44163i	−0.0341192	+	0.520558i
$23$	−0.172029	−	0.506782i	−0.0358706	−	0.105671i	0.927520	−	0.373774i	$-0.121937\pi$
$23$	−0.172029	−	0.506782i	−0.0358706	−	0.105671i	−0.963390	+	0.268103i	$0.913603\pi$
$24$	−1.05893	+	7.16147i	−0.216152	+	1.46183i
$25$	−4.70533	−	0.619468i	−0.941066	−	0.123894i
$26$	−4.94165	−	11.9302i	−0.969137	−	2.33970i
$27$	−5.19024	−	0.247775i	−0.998862	−	0.0476843i
$28$	−2.72643	−	0.542320i	−0.515246	−	0.102489i
$29$	5.67976	−	2.80095i	1.05471	−	0.520123i	0.169600	−	0.985513i	$-0.445753\pi$
$29$	5.67976	−	2.80095i	1.05471	−	0.520123i	0.885106	+	0.465390i	$0.154086\pi$
$30$	−2.08982	+	0.103633i	−0.381547	+	0.0189208i
$31$	−0.677946	−	0.773049i	−0.121763	−	0.138844i	0.687747	−	0.725951i	$-0.258600\pi$
$31$	−0.677946	−	0.773049i	−0.121763	−	0.138844i	−0.809509	+	0.587107i	$0.800267\pi$
$32$	0.299892	+	2.27790i	0.0530139	+	0.402680i
$33$	1.68332	−	0.541719i	0.293029	−	0.0943012i
$34$	8.81188	+	4.47190i	1.51122	+	0.766925i
$35$		−	0.374254i		−	0.0632604i
$36$	10.9361	−	2.56058i	1.82268	−	0.426764i
$37$	2.20919	+	11.1064i	0.363189	+	1.82587i	0.540045	+	0.841636i	$0.318407\pi$
$37$	2.20919	+	11.1064i	0.363189	+	1.82587i	−0.176856	+	0.984237i	$0.556593\pi$
$38$	−2.26502	−	8.45317i	−0.367435	−	1.37129i
$39$	−6.70301	+	6.49316i	−1.07334	+	1.03974i
$40$	1.99495	−	0.677194i	0.315429	−	0.107074i
$41$	−2.96507	+	6.01257i	−0.463067	+	0.939006i	0.532631	+	0.846347i	$0.321203\pi$
$41$	−2.96507	+	6.01257i	−0.463067	+	0.939006i	−0.995698	+	0.0926589i	$0.970463\pi$
$42$	0.553160	+	3.03212i	0.0853544	+	0.467867i
$43$	0.384182	−	2.91815i	0.0585872	−	0.445014i	−0.936860	−	0.349704i	$-0.886282\pi$
$43$	0.384182	−	2.91815i	0.0585872	−	0.445014i	0.995448	−	0.0953104i	$-0.0303844\pi$
$44$	−3.17821	+	2.12361i	−0.479133	+	0.320146i
$45$	0.625350	+	1.37679i	0.0932216	+	0.205240i
$46$	0.712603	−	1.06649i	0.105068	−	0.157245i
$47$	11.4370	−	3.06452i	1.66825	−	0.447007i	0.703614	−	0.710583i	$-0.251569\pi$
$47$	11.4370	−	3.06452i	1.66825	−	0.447007i	0.964639	+	0.263576i	$0.0849019\pi$
$48$	−3.82820	+	2.12978i	−0.552554	+	0.307408i
$49$	6.39354	−	0.841725i	0.913363	−	0.120246i
$50$	−5.68718	−	9.85048i	−0.804288	−	1.39307i
$51$	0.661916	−	7.11069i	0.0926868	−	0.995695i
$52$	10.0862	−	17.4698i	1.39870	−	2.42262i
$53$	−3.30651	+	7.98262i	−0.454184	+	1.09650i	0.516532	+	0.856268i	$0.327223\pi$
$53$	−3.30651	+	7.98262i	−0.454184	+	1.09650i	−0.970716	+	0.240230i	$0.922777\pi$
$54$	−7.10139	−	10.2302i	−0.966377	−	1.39215i
$55$	−0.363887	−	0.363887i	−0.0490666	−	0.0490666i
$56$	−1.37257	−	2.78330i	−0.183417	−	0.371934i
$57$	−5.07821	+	3.76989i	−0.672625	+	0.499334i
$58$	13.6124	+	6.71290i	1.78740	+	0.881447i
$59$	−6.97647	−	5.35323i	−0.908259	−	0.696932i	0.0450319	−	0.998986i	$-0.485661\pi$
$59$	−6.97647	−	5.35323i	−0.908259	−	0.696932i	−0.953291	+	0.302054i	$0.902328\pi$
$60$	−2.11581	−	2.49144i	−0.273150	−	0.321644i
$61$	6.35837	−	0.416750i	0.814106	−	0.0533593i	0.347339	−	0.937740i	$-0.387085\pi$
$61$	6.35837	−	0.416750i	0.814106	−	0.0533593i	0.466767	+	0.884380i	$0.345419\pi$
$62$	0.480754	−	2.41691i	0.0610558	−	0.306948i
$63$	1.89049	−	1.17800i	0.238179	−	0.148414i
$64$	−7.47053	+	7.47053i	−0.933817	+	0.933817i
$65$	2.57170	+	0.872975i	0.318980	+	0.108279i
$66$	3.48597	+	2.41030i	0.429094	+	0.296687i
$67$	−8.82398	+	5.09452i	−1.07802	+	0.622395i	−0.930362	−	0.366643i	$-0.880507\pi$
$67$	−8.82398	+	5.09452i	−1.07802	+	0.622395i	−0.147659	+	0.989038i	$0.547174\pi$
$68$	2.83771	+	15.1736i	0.344122	+	1.84007i
$69$	−0.906165	−	0.195275i	−0.109089	−	0.0235084i
$70$	0.711604	−	0.546033i	0.0850529	−	0.0652634i
$71$	4.19907	−	0.835247i	0.498338	−	0.0991255i	0.0604793	−	0.998169i	$-0.480737\pi$
$71$	4.19907	−	0.835247i	0.498338	−	0.0991255i	0.437858	+	0.899044i	$0.355737\pi$
$72$	9.70004	+	7.94564i	1.14316	+	0.936403i
$73$	2.65455	+	1.77371i	0.310691	+	0.207597i	0.701133	−	0.713030i	$-0.252678\pi$
$73$	2.65455	+	1.77371i	0.310691	+	0.207597i	−0.390442	+	0.920627i	$0.627678\pi$
$74$	−17.8943	+	20.4046i	−2.08018	+	2.37199i
$75$	−5.10720	+	6.44113i	−0.589728	+	0.743757i
$76$	8.32238	−	10.8459i	0.954642	−	1.24411i
$77$	−0.461470	+	0.601400i	−0.0525894	+	0.0685359i
$78$	−22.1257	−	3.27159i	−2.50524	−	0.370435i
$79$	−6.82883	+	7.78679i	−0.768304	+	0.876083i	−0.995203	−	0.0978357i	$-0.968808\pi$
$79$	−6.82883	+	7.78679i	−0.768304	+	0.876083i	0.226899	+	0.973918i	$0.427141\pi$
$80$	1.06001	+	0.708279i	0.118513	+	0.0791880i
$81$	−4.98630	+	7.49245i	−0.554034	+	0.832494i
$82$	−15.7583	+	3.13452i	−1.74021	+	0.346149i
$83$	1.02986	−	0.790239i	0.113042	−	0.0867400i	−0.550694	−	0.834707i	$-0.685637\pi$
$83$	1.02986	−	0.790239i	0.113042	−	0.0867400i	0.663735	+	0.747967i	$0.268970\pi$
$84$	−3.23179	+	3.56904i	−0.352618	+	0.389415i
$85$	−1.92906	+	0.773243i	−0.209236	+	0.0838699i
$86$	6.10907	−	3.52707i	0.658758	−	0.380334i
$87$	0.891337	−	10.9325i	0.0955613	−	1.17209i
$88$	−4.04075	−	1.37165i	−0.430746	−	0.146218i
$89$	2.39586	−	2.39586i	0.253961	−	0.253961i	−0.568632	−	0.822592i	$-0.692527\pi$
$89$	2.39586	−	2.39586i	0.253961	−	0.253961i	0.822592	+	0.568632i	$0.192527\pi$
$90$	−1.70544	+	3.19776i	−0.179770	+	0.337074i
$91$	0.780465	−	3.92366i	0.0818149	−	0.411311i
$92$	1.99941	−	0.131048i	0.208453	−	0.0136627i
$93$	−1.75200	+	0.319622i	−0.181673	+	0.0331433i
$94$	22.5133	+	17.2750i	2.32207	+	1.78178i
$95$	1.65074	+	0.814053i	0.169362	+	0.0835200i
$96$	3.65189	+	1.58115i	0.372720	+	0.161376i
$97$	−7.04839	−	14.2927i	−0.715656	−	1.45121i	−0.884972	−	0.465644i	$-0.845823\pi$
$97$	−7.04839	−	14.2927i	−0.715656	−	1.45121i	0.169316	−	0.985562i	$-0.445844\pi$
$98$	10.9286	+	10.9286i	1.10395	+	1.10395i
$99$	0.692749	−	2.98349i	0.0696239	−	0.299852i
$100$	6.79971	−	16.4160i	0.679971	−	1.64160i
$101$	−6.54019	+	11.3279i	−0.650773	+	1.12717i	0.332163	+	0.943222i	$0.392222\pi$
$101$	−6.54019	+	11.3279i	−0.650773	+	1.12717i	−0.982936	+	0.183949i	$0.941112\pi$
$102$	14.4859	−	9.11586i	1.43432	−	0.902604i
$103$	−3.23969	−	5.61131i	−0.319216	−	0.552899i	0.661108	−	0.750290i	$-0.270086\pi$
$103$	−3.23969	−	5.61131i	−0.319216	−	0.552899i	−0.980325	+	0.197391i	$0.936753\pi$
$104$	22.3272	−	2.93943i	2.18936	−	0.288235i
$105$	−0.556156	−	0.332998i	−0.0542753	−	0.0324973i
$106$	−20.0023	+	5.35959i	−1.94279	+	0.520570i
$107$	8.20002	−	12.2722i	0.792726	−	1.18640i	−0.186266	−	0.982499i	$-0.559639\pi$
$107$	8.20002	−	12.2722i	0.792726	−	1.18640i	0.978992	−	0.203899i	$-0.0653614\pi$
$108$	5.92541	−	18.5298i	0.570173	−	1.78303i
$109$	0.866335	−	0.578867i	0.0829798	−	0.0554454i	−0.513388	−	0.858156i	$-0.671610\pi$
$109$	0.866335	−	0.578867i	0.0829798	−	0.0554454i	0.596368	+	0.802711i	$0.296610\pi$
$110$	0.160985	−	1.22280i	0.0153493	−	0.116589i
$111$	18.4702	+	6.59911i	1.75311	+	0.626360i
$112$	0.830589	−	1.68427i	0.0784832	−	0.159148i
$113$	4.50947	−	1.53076i	0.424215	−	0.144002i	−0.101164	−	0.994870i	$-0.532257\pi$
$113$	4.50947	−	1.53076i	0.424215	−	0.144002i	0.525379	+	0.850868i	$0.323923\pi$
$114$	−14.5771	−	4.15543i	−1.36527	−	0.389192i
$115$	0.0698193	+	0.260569i	0.00651068	+	0.0242982i
$116$	4.62556	+	23.2543i	0.429473	+	2.15911i
$117$	3.68499	+	15.7383i	0.340677	+	1.45501i
$118$		−	21.0753i		−	1.94014i
$119$	1.50017	+	2.66860i	0.137521	+	0.244630i
$120$	0.768700	−	3.56712i	0.0701724	−	0.325632i
$121$	−1.29973	−	9.87246i	−0.118158	−	0.897497i
$122$	10.0692	+	11.4817i	0.911623	+	1.03951i
$123$	6.29671	+	9.75600i	0.567755	+	0.879669i
$124$	3.45257	−	1.70262i	0.310050	−	0.152900i
$125$	4.81807	+	0.958374i	0.430941	+	0.0857195i
$126$	4.99804	+	1.87586i	0.445261	+	0.167115i
$127$	−2.87472	−	6.94019i	−0.255090	−	0.615843i	0.743510	−	0.668724i	$-0.233159\pi$
$127$	−2.87472	−	6.94019i	−0.255090	−	0.615843i	−0.998601	+	0.0528818i	$0.983159\pi$
$128$	−20.5480	−	2.70520i	−1.81621	−	0.239108i
$129$	−3.99466	−	3.16738i	−0.351710	−	0.278872i
$130$	2.09222	+	6.16348i	0.183500	+	0.540573i
$131$	0.287829	−	4.39143i	0.0251478	−	0.383681i	−0.966671	−	0.256023i	$-0.917588\pi$
$131$	0.287829	−	4.39143i	0.0251478	−	0.383681i	0.991818	−	0.127657i	$-0.0407458\pi$
$132$	0.327910	+	6.61246i	0.0285409	+	0.575541i
$133$	0.871486	−	2.56732i	0.0755675	−	0.222615i
$134$	−22.5608	−	9.34498i	−1.94895	−	0.807284i
$135$	2.60238	+	0.295729i	0.223978	+	0.0254523i
$136$	−11.5104	+	12.8253i	−0.987009	+	1.09976i
$137$	5.46680	+	3.15626i	0.467060	+	0.269657i	0.715008	−	0.699116i	$-0.246423\pi$
$137$	5.46680	+	3.15626i	0.467060	+	0.269657i	−0.247948	+	0.968773i	$0.579756\pi$
$138$	−0.950791	−	2.00788i	−0.0809367	−	0.170922i
$139$	11.3931	−	9.99145i	0.966347	−	0.847463i	−0.0219884	−	0.999758i	$-0.507000\pi$
$139$	11.3931	−	9.99145i	0.966347	−	0.847463i	0.988335	+	0.152295i	$0.0486664\pi$
$140$	1.35344	+	0.362654i	0.114387	+	0.0306498i
$141$	5.62221	−	19.7225i	0.473476	−	1.66093i
$142$	7.71453	+	6.76546i	0.647389	+	0.567745i
$143$	−3.05613	−	4.57383i	−0.255567	−	0.382483i
$144$	−0.241261	+	7.58388i	−0.0201050	+	0.631990i
$145$	−2.94911	+	1.22156i	−0.244910	+	0.101445i
$146$	0.500435	+	7.63516i	0.0414163	+	0.631890i
$147$	4.43792	−	10.2500i	0.366033	−	0.845405i
$148$	−42.3054	−	2.77284i	−3.47749	−	0.227926i
$149$	−1.91554	+	7.14890i	−0.156927	+	0.585661i	0.842005	+	0.539469i	$0.181375\pi$
$149$	−1.91554	+	7.14890i	−0.156927	+	0.585661i	−0.998933	+	0.0461915i	$0.985292\pi$
$150$	−19.6985	−	0.313247i	−1.60837	−	0.0255765i
$151$	−1.49586	−	1.94944i	−0.121731	−	0.158643i	0.728512	−	0.685033i	$-0.240212\pi$
$151$	−1.49586	−	1.94944i	−0.121731	−	0.158643i	−0.850244	+	0.526389i	$0.823545\pi$
$152$	15.2619			1.23790
$153$	−9.97782	−	7.31048i	−0.806659	−	0.591017i
$154$	−1.81678			−0.146400
$155$	0.315504	+	0.411173i	0.0253419	+	0.0330262i
$156$	−16.9864	−	30.5325i	−1.36000	−	2.44455i
$157$	−2.48072	+	9.25817i	−0.197983	+	0.738883i	0.793491	+	0.608581i	$0.208261\pi$
$157$	−2.48072	+	9.25817i	−0.197983	+	0.738883i	−0.991474	+	0.130301i	$0.958406\pi$
$158$	−24.7689	−	1.62344i	−1.97051	−	0.129154i
$159$	8.92048	+	12.0163i	0.707440	+	0.952953i
$160$	−0.0757428	−	1.15561i	−0.00598799	−	0.0913591i
$161$	0.367121	−	0.152067i	0.0289332	−	0.0119845i
$162$	−21.5211	+	1.45048i	−1.69085	+	0.113961i
$163$	3.62885	+	5.43096i	0.284234	+	0.425386i	0.945922	−	0.324393i	$-0.105160\pi$
$163$	3.62885	+	5.43096i	0.284234	+	0.425386i	−0.661689	+	0.749779i	$0.730160\pi$
$164$	−18.8705	−	16.5490i	−1.47354	−	1.29226i
$165$	−0.864526	+	0.216977i	−0.0673033	+	0.0168916i
$166$	3.00511	+	0.805217i	0.233242	+	0.0624970i
$167$	3.06714	−	2.68981i	0.237343	−	0.208144i	−0.532409	−	0.846487i	$-0.678713\pi$
$167$	3.06714	−	2.68981i	0.237343	−	0.208144i	0.769752	+	0.638343i	$0.220380\pi$
$168$	−5.35736	−	0.436788i	−0.413329	−	0.0336990i
$169$	13.8828	+	8.01523i	1.06791	+	0.616556i
$170$	−4.28471	−	2.53974i	−0.328623	−	0.194790i
$171$	1.08379	+	10.9007i	0.0828798	+	0.833601i
$172$	10.1809	+	4.21705i	0.776283	+	0.321547i
$173$	−2.64623	+	7.79554i	−0.201189	+	0.592684i	−0.999960	−	0.00895141i	$-0.997151\pi$
$173$	−2.64623	+	7.79554i	−0.201189	+	0.592684i	0.798771	+	0.601635i	$0.205484\pi$
$174$	22.0875	−	14.2557i	1.67445	−	1.08072i
$175$	0.230468	−	3.51626i	0.0174217	−	0.265804i
$176$	−0.830032	−	2.44520i	−0.0625660	−	0.184314i
$177$	−14.1625	+	5.60419i	−1.06452	+	0.421237i
$178$	8.05100	+	1.05993i	0.603448	+	0.0794455i
$179$	−4.54443	−	10.9712i	−0.339667	−	0.820028i	−0.997748	−	0.0670807i	$-0.978631\pi$
$179$	−4.54443	−	10.9712i	−0.339667	−	0.820028i	0.658081	−	0.752947i	$-0.271369\pi$
$180$	−5.58496	+	0.927379i	−0.416279	+	0.0691228i
$181$	17.5732	+	3.49554i	1.30621	+	0.259821i	0.798650	−	0.601796i	$-0.205548\pi$
$181$	17.5732	+	3.49554i	1.30621	+	0.259821i	0.507559	+	0.861617i	$0.330548\pi$
$182$	8.59911	−	4.24061i	0.637408	−	0.314335i
$183$	5.03816	−	9.81961i	0.372431	−	0.725886i
$184$	1.47487	+	1.68177i	0.108729	+	0.123982i
$185$	−0.745025	−	5.65903i	−0.0547753	−	0.416060i
$186$	−3.16387	−	2.86491i	−0.231986	−	0.210065i
$187$	4.05330	+	1.13606i	0.296407	+	0.0830771i
$188$			44.3299i			3.23309i
$189$	−0.0684678	−	3.85748i	−0.00498030	−	0.280591i
$190$	0.860573	+	4.32639i	0.0624325	+	0.313869i
$191$	−5.55608	−	20.7356i	−0.402024	−	1.50037i	−0.809479	−	0.587148i	$-0.800251\pi$
$191$	−5.55608	−	20.7356i	−0.402024	−	1.50037i	0.407456	−	0.913225i	$-0.366416\pi$
$192$	4.45449	+	17.7485i	0.321475	+	1.28089i
$193$	8.52695	−	2.89451i	0.613783	−	0.208351i	0.00280156	−	0.999996i	$-0.499108\pi$
$193$	8.52695	−	2.89451i	0.613783	−	0.208351i	0.610982	+	0.791645i	$0.290775\pi$
$194$	16.8925	−	34.2547i	1.21281	−	2.45934i
$195$	3.58549	−	3.04491i	0.256762	−	0.218051i
$196$	−3.15137	+	23.9371i	−0.225098	+	1.70979i
$197$	−15.1511	+	10.1237i	−1.07947	+	0.721281i	−0.962344	−	0.271836i	$-0.912369\pi$
$197$	−15.1511	+	10.1237i	−1.07947	+	0.721281i	−0.117130	+	0.993117i	$0.537369\pi$
$198$	6.68350	−	3.03570i	0.474976	−	0.215738i
$199$	13.9975	−	20.9487i	0.992255	−	1.48501i	0.121929	−	0.992539i	$-0.461092\pi$
$199$	13.9975	−	20.9487i	0.992255	−	1.48501i	0.870326	−	0.492476i	$-0.163908\pi$
$200$	19.1603	−	5.13400i	1.35484	−	0.363029i
$201$	−0.280604	+	17.6457i	−0.0197923	+	1.24463i
$202$	−31.0809	+	4.09188i	−2.18685	+	0.287904i
$203$	2.35104	+	4.07212i	0.165011	+	0.285807i
$204$	25.0735	+	9.28402i	1.75550	+	0.650012i
$205$	1.68957	−	2.92642i	0.118004	−	0.204390i
$206$	5.94263	−	14.3468i	0.414043	−	0.999587i
$207$	−1.09646	+	1.17285i	−0.0762094	+	0.0815186i
$208$	9.63611	+	9.63611i	0.668144	+	0.668144i
$209$	−1.64886	−	3.34355i	−0.114054	−	0.231278i
$210$	−0.178266	−	1.54331i	−0.0123015	−	0.106499i
$211$	−13.5539	−	6.68404i	−0.933088	−	0.460148i	−0.0888071	−	0.996049i	$-0.528305\pi$
$211$	−13.5539	−	6.68404i	−0.933088	−	0.460148i	−0.844281	+	0.535901i	$0.819972\pi$
$212$	−25.6641	−	19.6928i	−1.76262	−	1.35251i
$213$	2.49498	−	6.98316i	0.170953	−	0.478478i
$214$	35.2980	−	2.31355i	2.41292	−	0.158151i
$215$	−0.289435	+	1.45509i	−0.0197393	+	0.0992361i
$216$	20.4383	−	7.34489i	1.39065	−	0.499757i
$217$	0.539830	−	0.539830i	0.0366461	−	0.0366461i
$218$	2.36463	+	0.802683i	0.160153	+	0.0543645i
$219$	4.99773	−	2.36657i	0.337715	−	0.159918i
$220$	1.66856	−	0.963344i	0.112494	−	0.0649487i
$221$	−21.8367	+	4.08380i	−1.46889	+	0.274706i
$222$	14.4003	+	44.7470i	0.966483	+	3.00322i
$223$	−12.2180	+	9.37523i	−0.818180	+	0.627812i	−0.930678	−	0.365840i	$-0.880782\pi$
$223$	−12.2180	+	9.37523i	−0.818180	+	0.627812i	0.112497	+	0.993652i	$0.464115\pi$
$224$	−1.67314	+	0.332808i	−0.111791	+	0.0222366i
$225$	5.02757	+	13.3206i	0.335171	+	0.888040i
$226$	9.48984	+	6.34091i	0.631255	+	0.421791i
$227$	−11.7400	+	13.3870i	−0.779214	+	0.888523i	−0.996150	−	0.0876626i	$-0.972060\pi$
$227$	−11.7400	+	13.3870i	−0.779214	+	0.888523i	0.216936	+	0.976186i	$0.430394\pi$
$228$	−8.71253	−	22.0177i	−0.577001	−	1.45816i
$229$	4.83506	−	6.30117i	0.319509	−	0.416393i	−0.605793	−	0.795622i	$-0.707144\pi$
$229$	4.83506	−	6.30117i	0.319509	−	0.416393i	0.925303	+	0.379229i	$0.123811\pi$
$230$	−0.393579	+	0.512922i	−0.0259518	+	0.0338211i
$231$	0.483104	+	1.22087i	0.0317859	+	0.0803273i
$232$	−17.4522	+	19.9004i	−1.14579	+	1.30653i
$233$	15.3673	+	10.2681i	1.00675	+	0.672687i	0.945563	−	0.325440i	$-0.105512\pi$
$233$	15.3673	+	10.2681i	1.00675	+	0.672687i	0.0611841	+	0.998126i	$0.480512\pi$
$234$	−24.5484	+	29.9687i	−1.60478	+	1.95911i
$235$	−5.85351	+	1.16434i	−0.381841	+	0.0759529i
$236$	26.1195	−	20.0422i	1.70024	−	1.30464i
$237$	5.49542	+	17.0763i	0.356966	+	1.10923i
$238$	−2.88532	+	6.74588i	−0.187027	+	0.437271i
$239$	14.9969	−	8.65844i	0.970067	−	0.560068i	0.0708101	−	0.997490i	$-0.477442\pi$
$239$	14.9969	−	8.65844i	0.970067	−	0.560068i	0.899257	+	0.437422i	$0.144108\pi$
$240$	1.99570	−	0.945022i	0.128822	−	0.0610009i
$241$	−11.7751	−	3.99711i	−0.758501	−	0.257476i	−0.0847170	−	0.996405i	$-0.526999\pi$
$241$	−11.7751	−	3.99711i	−0.758501	−	0.257476i	−0.673784	+	0.738929i	$0.735332\pi$
$242$	16.8751	−	16.8751i	1.08477	−	1.08477i
$243$	6.69744	+	14.0764i	0.429641	+	0.903000i
$244$	−4.65417	+	23.3981i	−0.297953	+	1.49791i
$245$	−3.24353	+	0.212592i	−0.207221	+	0.0135820i
$246$	−9.36316	+	26.2064i	−0.596973	+	1.67086i
$247$	15.6086	+	11.9769i	0.993153	+	0.762073i
$248$	3.85435	+	1.90075i	0.244751	+	0.120698i
$249$	−0.257993	−	2.23354i	−0.0163497	−	0.141545i
$250$	5.20727	+	10.5593i	0.329337	+	0.667829i
$251$	−12.5986	−	12.5986i	−0.795218	−	0.795218i	0.187119	−	0.982337i	$-0.440085\pi$
$251$	−12.5986	−	12.5986i	−0.795218	−	0.795218i	−0.982337	+	0.187119i	$0.940085\pi$
$252$	2.42820	+	7.97819i	0.152962	+	0.502579i
$253$	0.209098	−	0.504807i	0.0131459	−	0.0317369i
$254$	9.00184	−	15.5916i	0.564826	−	0.978307i
$255$	−0.567341	+	3.55466i	−0.0355283	+	0.222602i
$256$	−14.2708	−	24.7178i	−0.891925	−	1.54486i
$257$	−11.1120	+	1.46292i	−0.693147	+	0.0912545i	−0.468865	−	0.883270i	$-0.655337\pi$
$257$	−11.1120	+	1.46292i	−0.693147	+	0.0912545i	−0.224282	+	0.974524i	$0.572004\pi$
$258$	0.194270	−	12.2166i	0.0120947	−	0.760572i
$259$	−8.12142	+	2.17613i	−0.504640	+	0.135218i
$260$	−5.64900	+	8.45432i	−0.350336	+	0.524315i
$261$	−15.4531	−	11.0520i	−0.956525	−	0.684100i
$262$	8.76977	−	5.85977i	0.541798	−	0.362018i
$263$	−2.18215	+	16.5751i	−0.134557	+	1.02206i	0.782316	+	0.622882i	$0.214038\pi$
$263$	−2.18215	+	16.5751i	−0.134557	+	1.02206i	−0.916873	+	0.399180i	$0.869295\pi$
$264$	−5.63365	+	4.78427i	−0.346727	+	0.294452i
$265$	1.92625	−	3.90604i	0.118328	−	0.239946i
$266$	6.15297	−	2.08865i	0.377263	−	0.128063i
$267$	−1.42859	−	5.69210i	−0.0874282	−	0.348351i
$268$	−9.87323	−	36.8474i	−0.603104	−	2.25081i
$269$	−1.87839	−	9.44333i	−0.114528	−	0.575770i	−0.994847	−	0.101388i	$-0.967672\pi$
$269$	−1.87839	−	9.44333i	−0.114528	−	0.575770i	0.880319	−	0.474382i	$-0.157328\pi$
$270$	3.23456	+	5.37962i	0.196849	+	0.327393i
$271$			21.5828i			1.31106i	0.755168	+	0.655531i	$0.227555\pi$
$271$			21.5828i			1.31106i	−0.755168	+	0.655531i	$0.772445\pi$
$272$	−10.3975	−	0.801347i	−0.630440	−	0.0485888i
$273$	−5.13629	−	4.65094i	−0.310862	−	0.281488i
$274$	1.97472	+	14.9995i	0.119297	+	0.906152i
$275$	−3.19478	−	3.64295i	−0.192652	−	0.219678i
$276$	1.58427	−	3.08781i	0.0953616	−	0.185864i
$277$	−23.0315	+	11.3579i	−1.38383	+	0.682428i	−0.973325	−	0.229432i	$-0.926313\pi$
$277$	−23.0315	+	11.3579i	−1.38383	+	0.682428i	−0.410502	+	0.911860i	$0.634647\pi$
$278$	35.6200	+	7.08526i	2.13635	+	0.424946i
$279$	−1.08389	+	2.88793i	−0.0648911	+	0.172896i
$280$	0.598610	+	1.44517i	0.0357738	+	0.0863656i
$281$	11.5690	+	1.52308i	0.690147	+	0.0908595i	0.467439	−	0.884026i	$-0.345177\pi$
$281$	11.5690	+	1.52308i	0.690147	+	0.0908595i	0.222708	+	0.974885i	$0.428510\pi$
$282$	45.7030	−	18.0849i	2.72157	−	1.07694i
$283$	0.351485	+	1.03544i	0.0208936	+	0.0615506i	0.956877	−	0.290494i	$-0.0938197\pi$
$283$	0.351485	+	1.03544i	0.0208936	+	0.0615506i	−0.935983	+	0.352045i	$0.885486\pi$
$284$	−1.04835	+	15.9948i	−0.0622082	+	0.949114i
$285$	2.67848	−	1.72874i	0.158660	−	0.102402i
$286$	4.23777	−	12.4841i	0.250585	−	0.738199i
$287$	−4.59870	−	1.90485i	−0.271453	−	0.112439i
$288$	5.59898	−	4.02000i	0.329923	−	0.236881i
$289$	10.6556	−	13.2461i	0.626798	−	0.779182i
$290$	−6.62538	−	3.82517i	−0.389056	−	0.224622i
$291$	−27.5110	−	2.24299i	−1.61272	−	0.131486i
$292$	−8.98667	+	7.88110i	−0.525905	+	0.461206i
$293$	2.28133	+	0.611280i	0.133276	+	0.0357113i	0.324841	−	0.945769i	$-0.394689\pi$
$293$	2.28133	+	0.611280i	0.133276	+	0.0357113i	−0.191564	+	0.981480i	$0.561356\pi$
$294$	25.9641	−	6.51642i	1.51426	−	0.380045i
$295$	3.33250	+	2.92252i	0.194026	+	0.170156i
$296$	−26.2951	−	39.3534i	−1.52837	−	2.28737i
$297$	−3.81721	−	3.68406i	−0.221497	−	0.213771i
$298$	−16.3876	+	6.78798i	−0.949310	+	0.393217i
$299$	0.188595	+	2.87740i	0.0109067	+	0.166404i
$300$	−18.3446	−	24.7110i	−1.05913	−	1.42669i
$301$	2.18072	+	0.142932i	0.125694	+	0.00823844i
$302$	1.52421	−	5.68844i	0.0877086	−	0.327333i
$303$	11.0145	+	19.7982i	0.632768	+	1.13738i
$304$	5.62222	+	7.32702i	0.322456	+	0.420233i
$305$	−3.21183			−0.183909
$306$	−0.657439	−	29.6377i	−0.0375833	−	1.69427i
$307$	−31.4910			−1.79729			−0.898644	−	0.438678i	$-0.855447\pi$
$307$	−31.4910			−1.79729			−0.898644	+	0.438678i	$0.855447\pi$
$308$	−1.72772	−	2.25161i	−0.0984460	−	0.128297i
$309$	−11.2212	−	0.178441i	−0.638352	−	0.0101512i
$310$	−0.321484	+	1.19979i	−0.0182590	+	0.0681437i
$311$	−11.2499	−	0.737360i	−0.637926	−	0.0418119i	−0.256991	−	0.966414i	$-0.582731\pi$
$311$	−11.2499	−	0.737360i	−0.637926	−	0.0418119i	−0.380935	+	0.924602i	$0.624398\pi$
$312$	15.4978	−	35.7945i	0.877393	−	2.02646i
$313$	−0.550274	−	8.39557i	−0.0311034	−	0.474545i	−0.984791	−	0.173745i	$-0.944413\pi$
$313$	−0.550274	−	8.39557i	−0.0311034	−	0.474545i	0.953687	−	0.300800i	$-0.0972537\pi$
$314$	−21.2228	+	8.79076i	−1.19767	+	0.496091i
$315$	−0.989698	+	0.530180i	−0.0557632	+	0.0298723i
$316$	−21.5428	−	32.2411i	−1.21188	−	1.81370i
$317$	0.973224	+	0.853495i	0.0546617	+	0.0479371i	0.686241	−	0.727374i	$-0.259260\pi$
$317$	0.973224	+	0.853495i	0.0546617	+	0.0479371i	−0.631579	+	0.775311i	$0.717593\pi$
$318$	−9.83277	+	34.4930i	−0.551394	+	1.93427i
$319$	6.24524	+	1.67341i	0.349667	+	0.0936929i
$320$	4.00376	−	3.51120i	0.223817	−	0.196282i
$321$	−10.9409	−	23.1050i	−0.610661	−	1.28959i
$322$	0.824764	+	0.476178i	0.0459623	+	0.0265364i
$323$	−15.0336	+	0.812309i	−0.836491	+	0.0451981i
$324$	−22.2637	−	25.2926i	−1.23687	−	1.40514i
$325$	23.6246	+	9.78561i	1.31045	+	0.542808i
$326$	−5.03193	+	14.8236i	−0.278693	+	0.821003i
$327$	−0.0893836	−	1.80246i	−0.00494292	−	0.0996765i
$328$	1.83259	−	27.9600i	0.101188	−	1.54383i
$329$	2.82590	+	8.32483i	0.155797	+	0.458963i
$330$	−1.67389	−	1.32724i	−0.0921448	−	0.0730620i
$331$	−6.58097	−	0.866401i	−0.361723	−	0.0476217i	−0.0525254	−	0.998620i	$-0.516727\pi$
$331$	−6.58097	−	0.866401i	−0.361723	−	0.0476217i	−0.309197	+	0.950998i	$0.600060\pi$
$332$	1.85986	+	4.49010i	0.102073	+	0.246426i
$333$	26.2407	−	21.5757i	1.43798	−	1.18234i
$334$	9.58932	+	1.90744i	0.524705	+	0.104370i
$335$	4.60617	−	2.27151i	0.251662	−	0.124106i
$336$	−1.76386	−	2.73289i	−0.0962264	−	0.149091i
$337$	−4.97913	−	5.67761i	−0.271230	−	0.309279i	0.600150	−	0.799888i	$-0.295108\pi$
$337$	−4.97913	−	5.67761i	−0.271230	−	0.309279i	−0.871380	+	0.490609i	$0.836774\pi$
$338$	5.01475	+	38.0908i	0.272766	+	2.07186i
$339$	1.73760	−	8.06327i	0.0943736	−	0.437937i
$340$	−0.927068	−	7.72547i	−0.0502773	−	0.418973i
$341$		−	1.04976i		−	0.0568474i
$342$	−19.1454	+	17.9648i	−1.03526	+	0.971425i
$343$	1.94808	+	9.79366i	0.105186	+	0.528808i
$344$	3.18400	+	11.8829i	0.171670	+	0.640681i
$345$	0.449339	+	0.128091i	0.0241916	+	0.00689621i
$346$	−18.6832	+	6.34209i	−1.00442	+	0.340953i
$347$	−12.1309	+	24.5991i	−0.651223	+	1.32055i	0.281362	+	0.959602i	$0.409214\pi$
$347$	−12.1309	+	24.5991i	−0.651223	+	1.32055i	−0.932586	+	0.360949i	$0.882453\pi$
$348$	38.6725	+	13.8171i	2.07306	+	0.740674i
$349$	−1.41604	+	10.7559i	−0.0757990	+	0.575751i	0.910832	+	0.412778i	$0.135442\pi$
$349$	−1.41604	+	10.7559i	−0.0757990	+	0.575751i	−0.986631	+	0.162972i	$0.947892\pi$
$350$	7.02204	−	4.69198i	0.375344	−	0.250797i
$351$	26.6666	+	8.52739i	1.42336	+	0.455158i
$352$	−1.30320	+	1.95038i	−0.0694610	+	0.103956i
$353$	−6.82053	+	1.82756i	−0.363020	+	0.0972710i	−0.435719	−	0.900083i	$-0.643506\pi$
$353$	−6.82053	+	1.82756i	−0.363020	+	0.0972710i	0.0726982	+	0.997354i	$0.476839\pi$
$354$	−31.3188	−	18.7521i	−1.66457	−	0.996663i
$355$	−2.13955	+	0.281678i	−0.113556	+	0.0149499i
$356$	6.34272	+	10.9859i	0.336164	+	0.582253i
$357$	5.30045	+	0.145110i	0.280530	+	0.00768006i
$358$	14.2303	−	24.6477i	0.752096	−	1.30267i
$359$	−1.46983	+	3.54849i	−0.0775748	+	0.187282i	−0.957909	−	0.287072i	$-0.907318\pi$
$359$	−1.46983	+	3.54849i	−0.0775748	+	0.187282i	0.880334	+	0.474354i	$0.157318\pi$
$360$	−4.61692	−	4.31622i	−0.243333	−	0.227485i
$361$	−4.00687	−	4.00687i	−0.210888	−	0.210888i
$362$	18.9928	+	38.5136i	0.998239	+	2.02423i
$363$	−15.8273	−	6.85273i	−0.830720	−	0.359675i
$364$	13.4332	+	6.62450i	0.704088	+	0.347218i
$365$	−1.27669	−	0.979641i	−0.0668251	−	0.0512767i
$366$	26.0216	−	4.74720i	1.36017	−	0.248140i
$367$	14.8625	−	0.974142i	0.775818	−	0.0508498i	0.327650	−	0.944799i	$-0.393743\pi$
$367$	14.8625	−	0.974142i	0.775818	−	0.0508498i	0.448168	+	0.893949i	$0.352077\pi$
$368$	−0.264076	+	1.32760i	−0.0137659	+	0.0692059i
$369$	20.1004	−	0.676600i	1.04639	−	0.0352224i
$370$	9.67305	−	9.67305i	0.502878	−	0.502878i
$371$	−6.07490	−	2.06215i	−0.315393	−	0.107061i
$372$	0.541818	−	6.64559i	0.0280920	−	0.344558i
$373$	−3.87184	+	2.23541i	−0.200476	+	0.115745i	−0.596878	−	0.802332i	$-0.703592\pi$
$373$	−3.87184	+	2.23541i	−0.200476	+	0.115745i	0.396401	+	0.918077i	$0.370259\pi$
$374$	3.75363	+	9.36442i	0.194096	+	0.484223i
$375$	5.71114	−	6.30712i	0.294922	−	0.325698i
$376$	−39.2619	+	30.1267i	−2.02478	+	1.55367i
$377$	−33.4657	+	6.65675i	−1.72357	+	0.342840i
$378$	7.23470	−	5.75821i	0.372113	−	0.296171i
$379$	−12.0411	−	8.04562i	−0.618511	−	0.413276i	0.206457	−	0.978456i	$-0.433807\pi$
$379$	−12.0411	−	8.04562i	−0.618511	−	0.413276i	−0.824968	+	0.565180i	$0.808807\pi$
$380$	−4.54349	+	5.18086i	−0.233076	+	0.265772i
$381$	−12.8712	−	1.90320i	−0.659413	−	0.0975036i
$382$	31.3202	−	40.8173i	1.60248	−	2.08839i
$383$	0.898203	−	1.17056i	0.0458961	−	0.0598129i	−0.769841	−	0.638235i	$-0.779665\pi$
$383$	0.898203	−	1.17056i	0.0458961	−	0.0598129i	0.815737	+	0.578422i	$0.196331\pi$
$384$	−22.3030	+	28.1282i	−1.13814	+	1.43541i
$385$	0.251933	−	0.287275i	0.0128397	−	0.0146409i
$386$	17.9443	+	11.9900i	0.913342	+	0.610276i
$387$	−8.26117	+	3.11800i	−0.419939	+	0.158497i
$388$	58.5178	−	11.6399i	2.97079	−	0.590927i
$389$	30.2791	−	23.2340i	1.53521	−	1.17801i	0.613772	−	0.789484i	$-0.289652\pi$
$389$	30.2791	−	23.2340i	1.53521	−	1.17801i	0.921438	−	0.388525i	$-0.127015\pi$
$390$	11.0208	+	2.37493i	0.558058	+	0.120259i
$391$	−1.54232	−	1.57811i	−0.0779985	−	0.0798085i
$392$	−23.3422	+	13.4766i	−1.17896	+	0.680672i
$393$	−6.26974	−	4.33507i	−0.316266	−	0.218675i
$394$	−41.3544	−	14.0379i	−2.08340	−	0.707221i
$395$	3.69142	−	3.69142i	0.185736	−	0.185736i
$396$	10.1181	+	5.39626i	0.508456	+	0.271172i
$397$	−1.08068	+	5.43296i	−0.0542379	+	0.272673i	−0.998382	−	0.0568600i	$-0.981891\pi$
$397$	−1.08068	+	5.43296i	−0.0542379	+	0.272673i	0.944144	+	0.329533i	$0.106891\pi$
$398$	60.2539	−	3.94925i	3.02026	−	0.197958i
$399$	−3.03972	−	3.57938i	−0.152176	−	0.179193i
$400$	9.52309	+	7.30732i	0.476154	+	0.365366i
$401$	18.3820	+	9.06500i	0.917953	+	0.452684i	0.838961	−	0.544191i	$-0.183163\pi$
$401$	18.3820	+	9.06500i	0.917953	+	0.452684i	0.0789918	+	0.996875i	$0.474830\pi$
$402$	−33.9608	+	25.2114i	−1.69381	+	1.25743i
$403$	2.45027	+	4.96866i	0.122057	+	0.247507i
$404$	−34.6286	−	34.6286i	−1.72284	−	1.72284i
$405$	2.75498	−	3.60412i	0.136896	−	0.179090i
$406$	−4.31256	+	10.4114i	−0.214029	+	0.516711i
$407$	−5.78061	+	10.0123i	−0.286534	+	0.496292i
$408$	8.81740	+	28.5165i	0.436526	+	1.41178i
$409$	11.6707	+	20.2142i	0.577078	+	0.999528i	0.995812	+	0.0914193i	$0.0291404\pi$
$409$	11.6707	+	20.2142i	0.577078	+	0.999528i	−0.418735	+	0.908109i	$0.637526\pi$
$410$	8.02933	−	1.05708i	0.396540	−	0.0522055i
$411$	9.55450	−	5.31555i	0.471289	−	0.262197i
$412$	23.4319	−	6.27855i	1.15441	−	0.309322i
$413$	3.62743	−	5.42883i	0.178494	−	0.267135i
$414$	−3.82977	−	0.373629i	−0.188223	−	0.0183629i
$415$	−0.544044	+	0.363518i	−0.0267060	+	0.0178444i
$416$	1.61581	−	12.2733i	0.0792218	−	0.601750i
$417$	−4.71053	−	25.8206i	−0.230676	−	1.26444i
$418$	3.95174	−	8.01333i	0.193286	−	0.391945i
$419$	32.7941	−	11.1321i	1.60210	−	0.543839i	0.629634	−	0.776892i	$-0.283205\pi$
$419$	32.7941	−	11.1321i	1.60210	−	0.543839i	0.972464	+	0.233053i	$0.0748717\pi$
$420$	1.74316	−	1.68859i	0.0850577	−	0.0823949i
$421$	−0.782462	−	2.92019i	−0.0381349	−	0.142321i	0.944234	−	0.329276i	$-0.106805\pi$
$421$	−0.782462	−	2.92019i	−0.0381349	−	0.142321i	−0.982368	+	0.186955i	$0.940138\pi$
$422$	−7.06601	−	35.5232i	−0.343968	−	1.72924i
$423$	−24.3060	−	25.9032i	−1.18180	−	1.25946i
$424$		−	36.1134i		−	1.75382i
$425$	−18.6004	+	6.07699i	−0.902253	+	0.294777i
$426$	16.9179	−	5.44443i	0.819674	−	0.263783i
$427$	0.617540	+	4.69068i	0.0298849	+	0.226998i
$428$	36.4350	+	41.5462i	1.76115	+	2.00821i
$429$	−9.51613	+	0.471902i	−0.459443	+	0.0227836i
$430$	−3.18897	+	1.57263i	−0.153786	+	0.0758389i
$431$	38.4058	+	7.63939i	1.84994	+	0.367977i	0.989845	−	0.142151i	$-0.0454020\pi$
$431$	38.4058	+	7.63939i	1.84994	+	0.367977i	0.860098	+	0.510128i	$0.170402\pi$
$432$	11.0553	+	7.10640i	0.531897	+	0.341907i
$433$	9.24045	+	22.3084i	0.444068	+	1.07207i	0.974508	+	0.224352i	$0.0720265\pi$
$433$	9.24045	+	22.3084i	0.444068	+	1.07207i	−0.530441	+	0.847722i	$0.677973\pi$
$434$	1.81404	+	0.238822i	0.0870765	+	0.0114638i
$435$	−0.808728	+	5.46940i	−0.0387755	+	0.262237i
$436$	1.25392	+	3.69392i	0.0600517	+	0.176906i
$437$	−0.127812	+	1.95004i	−0.00611410	+	0.0932831i
$438$	11.7914	+	6.04984i	0.563416	+	0.289073i
$439$	−12.2201	+	35.9991i	−0.583231	+	1.71814i	0.106720	+	0.994289i	$0.465965\pi$
$439$	−12.2201	+	35.9991i	−0.583231	+	1.71814i	−0.689952	+	0.723855i	$0.742368\pi$
$440$	1.98717	+	0.823114i	0.0947347	+	0.0392404i
$441$	−11.2832	−	15.7150i	−0.537295	−	0.748334i
$442$	−39.6244	−	35.5619i	−1.88474	−	1.69151i
$443$	−33.1913	−	19.1630i	−1.57697	−	0.910462i	−0.995280	−	0.0970494i	$-0.969060\pi$
$443$	−33.1913	−	19.1630i	−1.57697	−	0.910462i	−0.581687	−	0.813413i	$-0.697607\pi$
$444$	−41.7625	+	60.4004i	−1.98196	+	2.86648i
$445$	−1.28404	+	1.12607i	−0.0608692	+	0.0533808i
$446$	−35.6520	−	9.55292i	−1.68817	−	0.452344i
$447$	8.91917	+	9.20742i	0.421862	+	0.435496i
$448$	−5.89770	−	5.17214i	−0.278640	−	0.244361i
$449$	8.96395	+	13.4155i	0.423035	+	0.633116i	0.980369	−	0.197172i	$-0.0631758\pi$
$449$	8.96395	+	13.4155i	0.423035	+	0.633116i	−0.557334	+	0.830288i	$0.688176\pi$
$450$	−17.9925	+	28.9940i	−0.848176	+	1.36679i
$451$	−6.32341	+	2.61924i	−0.297758	+	0.123335i
$452$	1.16610	+	17.7912i	0.0548487	+	0.836829i
$453$	−4.22792	+	0.488361i	−0.198645	+	0.0229452i
$454$	−42.5825	−	2.79100i	−1.99849	−	0.130988i
$455$	−0.521903	+	1.94777i	−0.0244672	+	0.0913127i
$456$	13.5795	−	22.6798i	0.635920	−	1.06208i
$457$	11.9497	+	15.5731i	0.558983	+	0.728480i	0.984288	−	0.176569i	$-0.0565000\pi$
$457$	11.9497	+	15.5731i	0.558983	+	0.728480i	−0.425306	+	0.905050i	$0.639833\pi$
$458$	19.0353			0.889461
$459$	−19.7416	+	8.32282i	−0.921459	+	0.388476i
$460$	−1.00997			−0.0470901
$461$	−8.16054	−	10.6350i	−0.380074	−	0.495322i	0.563669	−	0.826000i	$-0.309389\pi$
$461$	−8.16054	−	10.6350i	−0.380074	−	0.495322i	−0.943744	+	0.330678i	$0.892723\pi$
$462$	−1.61651	+	2.69981i	−0.0752067	+	0.125606i
$463$	0.244877	−	0.913894i	0.0113804	−	0.0424722i	−0.960002	−	0.279993i	$-0.909668\pi$
$463$	0.244877	−	0.913894i	0.0113804	−	0.0424722i	0.971383	+	0.237520i	$0.0763346\pi$
$464$	−15.9830	−	1.04758i	−0.741992	−	0.0486327i
$465$	0.891744	−	0.103004i	0.0413536	−	0.00477670i
$466$	2.89705	+	44.2004i	0.134203	+	2.04754i
$467$	27.8933	−	11.5538i	1.29075	−	0.534644i	0.371538	−	0.928418i	$-0.378831\pi$
$467$	27.8933	−	11.5538i	1.29075	−	0.534644i	0.919208	+	0.393773i	$0.128831\pi$
$468$	−60.4865	−	1.92421i	−2.79599	−	0.0889468i
$469$	−4.20304	−	6.29029i	−0.194078	−	0.290459i
$470$	−10.7541	−	9.43107i	−0.496049	−	0.435023i
$471$	11.5508	+	11.9241i	0.532231	+	0.549432i
$472$	35.5018	+	9.51269i	1.63410	+	0.437857i
$473$	2.25928	−	1.98134i	0.103882	−	0.0911021i
$474$	−24.4511	+	35.3632i	−1.12307	+	1.62428i
$475$	15.0080	+	8.66488i	0.688614	+	0.397572i
$476$	−11.1043	+	2.83931i	−0.508966	+	0.130139i
$477$	25.7938	−	2.56452i	1.18102	−	0.117421i
$478$	38.3434	+	15.8823i	1.75379	+	0.726442i
$479$	6.91907	−	20.3829i	0.316140	−	0.931319i	−0.666453	−	0.745547i	$-0.732188\pi$
$479$	6.91907	−	20.3829i	0.316140	−	0.931319i	0.982593	−	0.185772i	$-0.0594785\pi$
$480$	−1.78468	−	0.915667i	−0.0814591	−	0.0417943i
$481$	3.99046	−	60.8827i	0.181949	−	2.77601i
$482$	−9.57968	−	28.2208i	−0.436342	−	1.28542i
$483$	0.100675	−	0.680861i	0.00458087	−	0.0309802i
$484$	36.9620	+	4.86614i	1.68009	+	0.221188i
$485$	3.07397	+	7.42122i	0.139582	+	0.336980i
$486$	−16.9932	+	33.2717i	−0.770828	+	1.50924i
$487$	−9.83269	−	1.95584i	−0.445562	−	0.0886277i	−0.0327900	−	0.999462i	$-0.510439\pi$
$487$	−9.83269	−	1.95584i	−0.445562	−	0.0886277i	−0.412772	+	0.910835i	$0.635439\pi$
$488$	−23.8861	+	11.7793i	−1.08127	+	0.533226i
$489$	11.2995	−	0.560336i	0.510979	−	0.0253393i
$490$	−5.13650	−	5.85705i	−0.232043	−	0.264595i
$491$	0.564476	+	4.28762i	0.0254744	+	0.193498i	0.999450	−	0.0331544i	$-0.0105553\pi$
$491$	0.564476	+	4.28762i	0.0254744	+	0.193498i	−0.973976	+	0.226652i	$0.927222\pi$
$492$	−41.3829	+	13.3176i	−1.86568	+	0.600405i
$493$	16.1319	−	20.5316i	0.726545	−	0.924697i
$494$			47.1523i			2.12148i
$495$	−0.446790	+	1.47778i	−0.0200817	+	0.0664212i
$496$	0.507349	+	2.55062i	0.0227807	+	0.114526i
$497$	0.822746	+	3.07053i	0.0369052	+	0.137732i
$498$	3.87043	−	3.74926i	0.173438	−	0.168008i
$499$	−22.1611	+	7.52269i	−0.992069	+	0.336762i	−0.769843	−	0.638233i	$-0.779665\pi$
$499$	−22.1611	+	7.52269i	−0.992069	+	0.336762i	−0.222226	+	0.974995i	$0.571332\pi$
$500$	−8.13457	+	16.4953i	−0.363789	+	0.737691i
$501$	−1.26813	−	6.95121i	−0.0566559	−	0.310557i
$502$	5.57367	−	42.3362i	0.248765	−	1.88956i
$503$	−9.17711	+	6.13195i	−0.409187	+	0.273410i	−0.743082	−	0.669200i	$-0.766637\pi$
$503$	−9.17711	+	6.13195i	−0.409187	+	0.273410i	0.333895	+	0.942610i	$0.391637\pi$
$504$	−5.41588	+	7.57261i	−0.241242	+	0.337311i
$505$	3.66298	−	5.48204i	0.163001	−	0.243948i
$506$	1.26491	−	0.338931i	0.0562320	−	0.0150673i
$507$	24.2634	−	13.4987i	1.07758	−	0.599498i
$508$	27.8839	−	3.67099i	1.23715	−	0.162874i
$509$	−13.6706	−	23.6782i	−0.605939	−	1.04952i	−0.991902	−	0.127003i	$-0.959464\pi$
$509$	−13.6706	−	23.6782i	−0.605939	−	1.04952i	0.385963	−	0.922514i	$-0.373869\pi$
$510$	−7.58656	+	4.10748i	−0.335938	+	0.181882i
$511$	−1.18523	+	2.05289i	−0.0524317	+	0.0908144i
$512$	10.3147	−	24.9019i	0.455850	−	1.10052i
$513$	17.1633	+	8.08855i	0.757777	+	0.357118i
$514$	−18.9939	−	18.9939i	−0.837783	−	0.837783i
$515$	1.44449	+	2.92914i	0.0636520	+	0.129073i
$516$	15.3253	−	11.3770i	0.674658	−	0.500843i
$517$	10.8419	+	5.34662i	0.476825	+	0.235144i
$518$	−15.9867	−	12.2671i	−0.702417	−	0.538983i
$519$	9.22996	+	10.8686i	0.405150	+	0.477079i
$520$	−11.3269	+	0.742402i	−0.496716	+	0.0325565i
$521$	−0.254038	+	1.27713i	−0.0111296	+	0.0559523i	−0.985951	−	0.167035i	$-0.946581\pi$
$521$	−0.254038	+	1.27713i	−0.0111296	+	0.0559523i	0.974821	+	0.222987i	$0.0715808\pi$
$522$	−1.53182	−	45.5072i	−0.0670458	−	1.99180i
$523$	−4.98904	+	4.98904i	−0.218155	+	0.218155i	−0.807721	−	0.589565i	$-0.799299\pi$
$523$	−4.98904	+	4.98904i	−0.218155	+	0.218155i	0.589565	+	0.807721i	$0.299299\pi$
$524$	15.6021	+	5.29621i	0.681582	+	0.231366i
$525$	−5.02024	−	3.47113i	−0.219101	−	0.151493i
$526$	−34.6994	+	20.0337i	−1.51297	+	0.873511i
$527$	−3.89785	−	1.66717i	−0.169793	−	0.0726230i
$528$	−4.37220	−	0.942191i	−0.190275	−	0.0410036i
$529$	18.0199	−	13.8271i	0.783474	−	0.601180i
$530$	10.2373	−	2.03632i	0.444680	−	0.0884523i
$531$	−4.27330	+	26.0325i	−0.185445	+	1.12972i
$532$	8.43990	+	5.63936i	0.365916	+	0.244497i
$533$	23.8161	−	27.1570i	1.03159	−	1.17630i
$534$	8.73861	−	11.0210i	0.378157	−	0.476926i
$535$	−4.52896	+	5.90226i	−0.195804	+	0.255177i
$536$	25.9250	−	33.7861i	1.11979	−	1.45934i
$537$	−20.3472	−	3.00862i	−0.878045	−	0.129831i
$538$	15.2149	−	17.3493i	0.655961	−	0.747981i
$539$	5.47426	+	3.65778i	0.235793	+	0.157552i
$540$	−3.59119	+	9.12463i	−0.154540	+	0.392662i
$541$	40.2772	−	8.01163i	1.73165	−	0.344447i	0.774178	−	0.632968i	$-0.218163\pi$
$541$	40.2772	−	8.01163i	1.73165	−	0.344447i	0.957474	+	0.288521i	$0.0931634\pi$
$542$	−41.0374	+	31.4891i	−1.76271	+	1.35257i
$543$	20.8306	−	23.0043i	0.893926	−	0.987211i
$544$	5.17228	+	7.93643i	0.221760	+	0.340271i
$545$	−0.454827	+	0.262594i	−0.0194826	+	0.0112483i
$546$	1.34948	−	16.5518i	0.0577522	−	0.708351i
$547$	34.7372	+	11.7917i	1.48526	+	0.504176i	0.942064	−	0.335433i	$-0.108883\pi$
$547$	34.7372	+	11.7917i	1.48526	+	0.504176i	0.543191	+	0.839609i	$0.317216\pi$
$548$	−16.7116	+	16.7116i	−0.713883	+	0.713883i
$549$	−10.1096	−	16.2241i	−0.431465	−	0.692426i
$550$	2.26552	−	11.3896i	0.0966022	−	0.485652i
$551$	−23.0749	+	1.51241i	−0.983023	+	0.0644307i
$552$	3.81147	−	0.695339i	0.162227	−	0.0295956i
$553$	−6.10085	−	4.68135i	−0.259435	−	0.199071i
$554$	−55.1984	−	27.2209i	−2.34516	−	1.15650i
$555$	−9.07244	−	3.92807i	−0.385104	−	0.166737i
$556$	25.0929	+	50.8833i	1.06417	+	2.15793i
$557$	4.48661	+	4.48661i	0.190104	+	0.190104i	0.795741	−	0.605637i	$-0.207082\pi$
$557$	4.48661	+	4.48661i	0.190104	+	0.190104i	−0.605637	+	0.795741i	$0.707082\pi$
$558$	−7.07247	+	2.15254i	−0.299402	+	0.0911245i
$559$	−6.06884	+	14.6515i	−0.256685	+	0.619692i
$560$	−0.473288	+	0.819760i	−0.0200001	+	0.0346412i
$561$	5.29473	−	5.01254i	0.223544	−	0.211630i
$562$	13.9830	+	24.2193i	0.589838	+	1.02163i
$563$	18.8368	−	2.47992i	0.793878	−	0.104516i	0.277330	−	0.960775i	$-0.410550\pi$
$563$	18.8368	−	2.47992i	0.793878	−	0.104516i	0.516547	+	0.856259i	$0.327217\pi$
$564$	65.8760	+	39.4432i	2.77388	+	1.66086i
$565$	−2.31861	+	0.621268i	−0.0975445	+	0.0261370i
$566$	−1.45597	+	2.17901i	−0.0611989	+	0.0915906i
$567$	−5.79330	−	3.33051i	−0.243296	−	0.139868i
$568$	−14.8786	+	9.94159i	−0.624294	+	0.417140i
$569$	−2.50333	+	19.0147i	−0.104945	+	0.797138i	0.855330	+	0.518084i	$0.173354\pi$
$569$	−2.50333	+	19.0147i	−0.104945	+	0.797138i	−0.960275	+	0.279055i	$0.909979\pi$
$570$	7.19490	+	2.57063i	0.301361	+	0.107672i
$571$	−12.4378	+	25.2214i	−0.520507	+	1.05548i	0.464915	+	0.885355i	$0.346085\pi$
$571$	−12.4378	+	25.2214i	−0.520507	+	1.05548i	−0.985422	+	0.170128i	$0.945582\pi$
$572$	19.5021	−	6.62006i	0.815422	−	0.276799i
$573$	−35.7575	−	10.1932i	−1.49379	−	0.425829i
$574$	−3.08760	−	11.5231i	−0.128874	−	0.480965i
$575$	0.495519	+	2.49114i	0.0206646	+	0.103888i
$576$	30.3385	+	9.17250i	1.26410	+	0.382188i
$577$			44.0005i			1.83176i	0.401449	+	0.915881i	$0.368507\pi$
$577$			44.0005i			1.83176i	−0.401449	+	0.915881i	$0.631493\pi$
$578$	40.7324	+	0.934513i	1.69424	+	0.0388706i
$579$	3.28563	−	15.2468i	0.136546	−	0.633637i
$580$	−1.55992	−	11.8488i	−0.0647722	−	0.491993i
$581$	0.635500	+	0.724648i	0.0263650	+	0.0300635i
$582$	−35.8735	−	55.5817i	−1.48700	−	2.30393i
$583$	−7.91166	+	3.90160i	−0.327667	+	0.161588i
$584$	−13.0875	−	2.60326i	−0.541564	−	0.107724i
$585$	−1.33461	−	8.03744i	−0.0551794	−	0.332307i
$586$	2.16615	+	5.22955i	0.0894828	+	0.216031i
$587$	10.6266	+	1.39901i	0.438605	+	0.0577434i	0.346596	−	0.938015i	$-0.387338\pi$
$587$	10.6266	+	1.39901i	0.438605	+	0.0577434i	0.0920095	+	0.995758i	$0.470671\pi$
$588$	32.7675	+	25.9815i	1.35131	+	1.07146i
$589$	1.20685	+	3.55525i	0.0497272	+	0.146492i
$590$	−0.694782	+	10.6003i	−0.0286037	+	0.436408i
$591$	1.56321	+	31.5229i	0.0643018	+	1.29668i
$592$	9.20632	−	27.1210i	0.378378	−	1.11466i
$593$	17.9488	+	7.43464i	0.737069	+	0.305304i	0.719453	−	0.694541i	$-0.244392\pi$
$593$	17.9488	+	7.43464i	0.737069	+	0.305304i	0.0176157	+	0.999845i	$0.494392\pi$
$594$	1.43559	−	12.6330i	0.0589028	−	0.518339i
$595$	−0.666573	−	1.39169i	−0.0273268	−	0.0570537i
$596$	−23.9969	−	13.8546i	−0.982953	−	0.567508i
$597$	−18.6761	−	39.4403i	−0.764364	−	1.61418i
$598$	−5.19590	+	4.55668i	−0.212476	+	0.186337i
$599$	15.6130	+	4.18348i	0.637929	+	0.170932i	0.563265	−	0.826276i	$-0.309545\pi$
$599$	15.6130	+	4.18348i	0.637929	+	0.170932i	0.0746637	+	0.997209i	$0.476212\pi$
$600$	9.41889	−	33.0411i	0.384525	−	1.34890i
$601$	−13.0141	−	11.4131i	−0.530858	−	0.465550i	0.351460	−	0.936203i	$-0.385685\pi$
$601$	−13.0141	−	11.4131i	−0.530858	−	0.465550i	−0.882319	+	0.470653i	$0.844019\pi$
$602$	2.90987	+	4.35493i	0.118598	+	0.177494i
$603$	25.9726	+	16.1176i	1.05769	+	0.656358i
$604$	8.49941	−	3.52057i	0.345836	−	0.143250i
$605$	0.328270	+	5.00843i	0.0133461	+	0.203622i
$606$	−21.5740	+	49.8283i	−0.876386	+	2.02414i
$607$	−5.60520	−	0.367384i	−0.227508	−	0.0149117i	−0.0487772	−	0.998810i	$-0.515532\pi$
$607$	−5.60520	−	0.367384i	−0.227508	−	0.0149117i	−0.178731	+	0.983898i	$0.557199\pi$
$608$	2.17137	−	8.10367i	0.0880607	−	0.328647i
$609$	8.14321	+	0.129494i	0.329980	+	0.00524738i
$610$	−4.68603	−	6.10695i	−0.189732	−	0.247263i
$611$	−63.7961			−2.58091
$612$	36.1060	−	28.9996i	1.45950	−	1.17224i
$613$	−24.3856			−0.984927			−0.492463	−	0.870333i	$-0.663903\pi$
$613$	−24.3856			−0.984927			−0.492463	+	0.870333i	$0.663903\pi$
$614$	−45.9451	−	59.8768i	−1.85419	−	2.41643i
$615$	−2.84545	−	5.11459i	−0.114740	−	0.206240i
$616$	0.820033	−	3.06040i	0.0330401	−	0.123307i
$617$	18.3824	+	1.20485i	0.740047	+	0.0485053i	0.430764	−	0.902465i	$-0.358244\pi$
$617$	18.3824	+	1.20485i	0.740047	+	0.0485053i	0.309283	+	0.950970i	$0.399911\pi$
$618$	−16.0323	−	21.5963i	−0.644915	−	0.868729i
$619$	−0.609409	−	9.29778i	−0.0244942	−	0.373709i	−0.992455	−	0.122608i	$-0.960874\pi$
$619$	−0.609409	−	9.29778i	−0.0244942	−	0.373709i	0.967961	−	0.251101i	$-0.0807926\pi$
$620$	−1.79268	+	0.742552i	−0.0719957	+	0.0298216i
$621$	0.767306	+	2.67295i	0.0307909	+	0.107262i
$622$	−15.0115	−	22.4664i	−0.601908	−	0.900819i
$623$	1.89144	+	1.65875i	0.0757789	+	0.0664563i
$624$	22.8935	−	5.74576i	0.916474	−	0.230015i
$625$	20.5293	+	5.50082i	0.821173	+	0.220033i
$626$	15.1604	−	13.2953i	0.605932	−	0.531388i
$627$	−6.43575	−	0.524710i	−0.257019	−	0.0209549i
$628$	−31.0772	−	17.9424i	−1.24011	−	0.715981i
$629$	27.9962	+	37.3651i	1.11628	+	1.48984i
$630$	−2.45204	−	1.10828i	−0.0976916	−	0.0441548i
$631$	−5.45994	−	2.26158i	−0.217357	−	0.0900321i	0.271348	−	0.962481i	$-0.412531\pi$
$631$	−5.45994	−	2.26158i	−0.217357	−	0.0900321i	−0.488705	+	0.872449i	$0.662531\pi$
$632$	13.9146	−	40.9911i	0.553493	−	1.63054i
$633$	−21.9925	+	14.1944i	−0.874125	+	0.564177i
$634$	−0.202904	+	3.09572i	−0.00805836	+	0.122947i
$635$	1.21711	+	3.58550i	0.0482997	+	0.142286i
$636$	−52.0993	+	20.6160i	−2.06587	+	0.817476i
$637$	−34.4483	−	4.53521i	−1.36489	−	0.179692i
$638$	5.92994	+	14.3161i	0.234769	+	0.566782i
$639$	−8.15731	−	9.92102i	−0.322698	−	0.392469i
$640$	10.2459	+	2.03804i	0.405006	+	0.0805607i
$641$	−14.0975	+	6.95213i	−0.556819	+	0.274593i	−0.698849	−	0.715270i	$-0.746304\pi$
$641$	−14.0975	+	6.95213i	−0.556819	+	0.274593i	0.142030	+	0.989862i	$0.454637\pi$
$642$	27.9689	−	54.5128i	1.10385	−	2.15145i
$643$	−21.2118	−	24.1874i	−0.836512	−	0.953859i	0.162951	−	0.986634i	$-0.447899\pi$
$643$	−21.2118	−	24.1874i	−0.836512	−	0.953859i	−0.999463	+	0.0327755i	$0.989565\pi$
$644$	0.194188	+	1.47500i	0.00765206	+	0.0581232i
$645$	1.90479	+	1.72480i	0.0750010	+	0.0679139i
$646$	−23.4784	−	27.3996i	−0.923743	−	1.07802i
$647$		−	22.2315i		−	0.874010i	−0.899459	−	0.437005i	$-0.856039\pi$
$647$		−	22.2315i		−	0.874010i	0.899459	−	0.437005i	$-0.143961\pi$
$648$	7.27051	−	36.9074i	0.285613	−	1.44986i
$649$	−1.75150	−	8.80540i	−0.0687525	−	0.345642i
$650$	15.8617	+	59.1967i	0.622147	+	2.32188i
$651$	−0.321887	−	1.28253i	−0.0126157	−	0.0502664i
$652$	−23.1568	+	7.86066i	−0.906889	+	0.307847i
$653$	−1.60076	+	3.24603i	−0.0626428	+	0.127027i	−0.925942	−	0.377665i	$-0.876727\pi$
$653$	−1.60076	+	3.24603i	−0.0626428	+	0.127027i	0.863300	+	0.504692i	$0.168394\pi$
$654$	3.29678	−	2.79973i	0.128914	−	0.109478i
$655$	−0.289541	+	2.19928i	−0.0113133	+	0.0859331i
$656$	14.0983	−	9.42016i	0.550445	−	0.367795i
$657$	0.929986	−	9.53253i	0.0362822	−	0.371899i
$658$	−11.7058	+	17.5190i	−0.456340	+	0.682961i
$659$	−6.95540	+	1.86369i	−0.270944	+	0.0725992i	−0.391733	−	0.920079i	$-0.628124\pi$
$659$	−6.95540	+	1.86369i	−0.270944	+	0.0725992i	0.120789	+	0.992678i	$0.461458\pi$
$660$	0.0530606	−	3.33670i	0.00206538	−	0.129881i
$661$	24.8952	−	3.27751i	0.968310	−	0.127480i	0.370250	−	0.928932i	$-0.379272\pi$
$661$	24.8952	−	3.27751i	0.968310	−	0.127480i	0.598060	+	0.801452i	$0.295939\pi$
$662$	−7.95420	−	13.7771i	−0.309149	−	0.535461i
$663$	−13.3608	+	36.0838i	−0.518892	+	1.40138i
$664$	−2.71281	+	4.69873i	−0.105277	+	0.182346i
$665$	−0.522970	+	1.26256i	−0.0202799	+	0.0489600i
$666$	79.3088	+	18.4150i	3.07315	+	0.713568i
$667$	−2.39656	−	2.39656i	−0.0927951	−	0.0927951i
$668$	6.75529	+	13.6984i	0.261370	+	0.530006i
$669$	3.06078	+	26.4983i	0.118336	+	1.02448i
$670$	11.0394	+	5.44403i	0.426489	+	0.210321i
$671$	5.16119	+	3.96032i	0.199246	+	0.152886i
$672$	−0.994135	+	2.78247i	−0.0383496	+	0.107336i
$673$	−31.5469	+	2.06770i	−1.21605	+	0.0797038i	−0.659882	−	0.751369i	$-0.729394\pi$
$673$	−31.5469	+	2.06770i	−1.21605	+	0.0797038i	−0.556163	+	0.831073i	$0.687727\pi$
$674$	3.53086	−	17.7508i	0.136004	−	0.683737i
$675$	24.2683	+	4.38105i	0.934088	+	0.168627i
$676$	−42.4386	+	42.4386i	−1.63225	+	1.63225i
$677$	−38.8925	−	13.2022i	−1.49476	−	0.507402i	−0.549999	−	0.835165i	$-0.685372\pi$
$677$	−38.8925	−	13.2022i	−1.49476	−	0.507402i	−0.944760	+	0.327763i	$0.893705\pi$
$678$	17.8666	−	8.46036i	0.686162	−	0.324918i
$679$	10.2472	−	5.91623i	0.393252	−	0.227044i
$680$	6.21223	−	6.07134i	0.238228	−	0.232825i
$681$	9.44766	+	29.3574i	0.362035	+	1.12498i
$682$	1.99600	−	1.53158i	0.0764307	−	0.0586473i
$683$	37.3073	−	7.42089i	1.42753	−	0.283953i	0.579961	−	0.814644i	$-0.303068\pi$
$683$	37.3073	−	7.42089i	1.42753	−	0.283953i	0.847565	+	0.530692i	$0.178068\pi$
$684$	−40.4714	−	6.64347i	−1.54746	−	0.254019i
$685$	−2.64560	−	1.76774i	−0.101083	−	0.0675417i
$686$	−15.7794	+	17.9929i	−0.602459	+	0.686973i
$687$	−5.06172	−	12.7917i	−0.193117	−	0.488032i
$688$	−4.53186	+	5.90603i	−0.172775	+	0.225165i
$689$	28.3403	−	36.9338i	1.07968	−	1.40707i
$690$	0.412030	+	1.04125i	0.0156857	+	0.0396399i
$691$	−0.695421	+	0.792975i	−0.0264550	+	0.0301662i	−0.764916	−	0.644130i	$-0.777220\pi$
$691$	−0.695421	+	0.792975i	−0.0264550	+	0.0301662i	0.738461	+	0.674296i	$0.235553\pi$
$692$	−25.6274	−	17.1237i	−0.974207	−	0.650944i
$693$	2.24411	+	0.368376i	0.0852467	+	0.0139934i
$694$	−64.4715	+	12.8242i	−2.44731	+	0.486799i
$695$	−6.05979	+	4.64984i	−0.229861	+	0.176378i
$696$	14.0445	+	43.6415i	0.532354	+	1.65423i
$697$	−0.317018	+	27.6392i	−0.0120079	+	1.04691i
$698$	−22.5172	+	13.0003i	−0.852289	+	0.492069i
$699$	28.9322	−	13.7002i	1.09431	−	0.518191i
$700$	12.4928	+	4.24073i	0.472183	+	0.160285i
$701$	−13.4241	+	13.4241i	−0.507022	+	0.507022i	−0.913611	−	0.406589i	$-0.866718\pi$
$701$	−13.4241	+	13.4241i	−0.507022	+	0.507022i	0.406589	+	0.913611i	$0.366718\pi$
$702$	22.6923	+	63.1450i	0.856467	+	2.38325i
$703$	8.06685	−	40.5548i	0.304247	−	1.52955i
$704$	−10.7632	+	0.705458i	−0.405654	+	0.0265880i
$705$	−3.47801	+	9.73454i	−0.130989	+	0.366624i
$706$	−13.4260	−	10.3021i	−0.505294	−	0.387726i
$707$	−8.71047	−	4.29553i	−0.327591	−	0.161550i
$708$	−6.54328	−	56.6476i	−0.245911	−	2.12895i
$709$	−8.05113	−	16.3261i	−0.302367	−	0.613139i	0.691666	−	0.722217i	$-0.256877\pi$
$709$	−8.05113	−	16.3261i	−0.302367	−	0.613139i	−0.994033	+	0.109078i	$0.965210\pi$
$710$	−3.65717	−	3.65717i	−0.137251	−	0.137251i
$711$	30.2658	+	7.02753i	1.13506	+	0.263553i
$712$	−5.41943	+	13.0837i	−0.203102	+	0.490331i
$713$	−0.275141	+	0.476558i	−0.0103041	+	0.0178472i
$714$	7.45739	+	10.2900i	0.279086	+	0.385092i
$715$	1.38637	+	2.40126i	0.0518473	+	0.0898021i
$716$	44.0796	−	5.80319i	1.64733	−	0.216876i
$717$	0.476904	−	29.9899i	0.0178103	−	1.11999i
$718$	−8.89154	+	2.38248i	−0.331829	+	0.0889134i
$719$	−13.0787	+	19.5737i	−0.487754	+	0.729976i	−0.990955	−	0.134193i	$-0.957156\pi$
$719$	−13.0787	+	19.5737i	−0.487754	+	0.729976i	0.503201	+	0.864170i	$0.332156\pi$
$720$	0.371362	−	3.80653i	0.0138399	−	0.141861i
$721$	4.00010	−	2.67278i	0.148971	−	0.0995395i
$722$	1.77265	−	13.4646i	0.0659713	−	0.501101i
$723$	−16.4169	+	13.9418i	−0.610553	+	0.518500i
$724$	−29.6697	+	60.1642i	−1.10267	+	2.23599i
$725$	−28.4603	+	9.66095i	−1.05699	+	0.358799i
$726$	−10.0622	−	40.0920i	−0.373444	−	1.48796i
$727$	1.11206	+	4.15025i	0.0412439	+	0.153924i	0.983477	−	0.181034i	$-0.0579444\pi$
$727$	1.11206	+	4.15025i	0.0412439	+	0.153924i	−0.942233	+	0.334958i	$0.891278\pi$
$728$	3.26206	+	16.3995i	0.120900	+	0.607804i
$729$	26.8772	+	2.57202i	0.995452	+	0.0952601i
$730$		−	3.85678i		−	0.142746i
$731$	−3.76883	−	11.5356i	−0.139395	−	0.426660i
$732$	30.6294	+	27.7351i	1.13209	+	1.02512i
$733$	1.40148	+	10.6453i	0.0517647	+	0.393192i	0.997640	+	0.0686615i	$0.0218729\pi$
$733$	1.40148	+	10.6453i	0.0517647	+	0.393192i	−0.945875	+	0.324530i	$0.894794\pi$
$734$	23.5365	+	26.8383i	0.868749	+	0.990618i
$735$	−2.57006	+	5.00917i	−0.0947981	+	0.184766i
$736$	1.10281	−	0.543847i	0.0406502	−	0.0200464i
$737$	−10.2027	−	2.02944i	−0.375820	−	0.0747553i
$738$	30.6128	+	37.2316i	1.12687	+	1.37051i
$739$	6.20725	+	14.9856i	0.228337	+	0.551255i	0.995975	−	0.0896286i	$-0.0285680\pi$
$739$	6.20725	+	14.9856i	0.228337	+	0.551255i	−0.767638	+	0.640884i	$0.778568\pi$
$740$	21.1871	+	2.78933i	0.778853	+	0.102538i
$741$	31.6862	−	12.5384i	1.16402	−	0.460609i
$742$	−4.94226	−	14.5594i	−0.181436	−	0.534493i
$743$	−1.12085	+	17.1009i	−0.0411201	+	0.627372i	0.926712	+	0.375773i	$0.122623\pi$
$743$	−1.12085	+	17.1009i	−0.0411201	+	0.627372i	−0.967832	+	0.251598i	$0.919044\pi$
$744$	6.25406	−	4.03649i	0.229285	−	0.147985i
$745$	1.19914	−	3.53256i	0.0439332	−	0.129423i
$746$	−9.89937	−	4.10045i	−0.362442	−	0.150128i
$747$	−3.54869	−	1.60394i	−0.129840	−	0.0586851i
$748$	−8.03609	+	13.5574i	−0.293829	+	0.495708i
$749$	9.49068	+	5.47945i	0.346782	+	0.200215i
$750$	20.3248	+	1.65709i	0.742157	+	0.0605085i
$751$	−5.01816	+	4.40081i	−0.183115	+	0.160588i	−0.745996	−	0.665950i	$-0.768026\pi$
$751$	−5.01816	+	4.40081i	−0.183115	+	0.160588i	0.562881	+	0.826538i	$0.309693\pi$
$752$	−28.9268	−	7.75091i	−1.05485	−	0.282647i
$753$	−29.9319	+	7.51224i	−1.09078	+	0.273761i
$754$	−61.4833	−	53.9194i	−2.23909	−	1.96363i
$755$	0.688111	+	1.02983i	0.0250429	+	0.0374794i
$756$	14.0164	+	3.49031i	0.509773	+	0.126941i
$757$	9.34496	−	3.87081i	0.339648	−	0.140687i	−0.206339	−	0.978481i	$-0.566155\pi$
$757$	9.34496	−	3.87081i	0.339648	−	0.140687i	0.545987	+	0.837794i	$0.316155\pi$
$758$	−2.26999	−	34.6334i	−0.0824499	−	1.25794i
$759$	−0.564115	−	0.759888i	−0.0204761	−	0.0275822i
$760$	−7.67633	−	0.503134i	−0.278450	−	0.0182506i
$761$	−3.16811	+	11.8235i	−0.114844	+	0.428603i	−0.999275	−	0.0380675i	$-0.987880\pi$
$761$	−3.16811	+	11.8235i	−0.114844	+	0.428603i	0.884431	+	0.466670i	$0.154546\pi$
$762$	−15.1603	−	27.2500i	−0.549199	−	0.987164i
$763$	0.470953	+	0.613757i	0.0170496	+	0.0222195i
$764$	80.3714			2.90774
$765$	4.77757	+	4.00591i	0.172734	+	0.144834i
$766$	3.53617			0.127767
$767$	28.8432	+	37.5892i	1.04147	+	1.35727i
$768$	−49.4293	−	0.786031i	−1.78363	−	0.0283634i
$769$	5.80750	−	21.6739i	0.209424	−	0.781581i	−0.778631	−	0.627482i	$-0.784086\pi$
$769$	5.80750	−	21.6739i	0.209424	−	0.781581i	0.988055	−	0.154099i	$-0.0492476\pi$
$770$	0.913791	+	0.0598930i	0.0329307	+	0.00215839i
$771$	−7.71311	+	17.8145i	−0.277781	+	0.641574i
$772$	2.20498	+	33.6414i	0.0793588	+	1.21078i
$773$	−29.2000	+	12.0950i	−1.05025	+	0.435029i	−0.839982	−	0.542615i	$-0.817434\pi$
$773$	−29.2000	+	12.0950i	−1.05025	+	0.435029i	−0.210270	+	0.977643i	$0.567434\pi$
$774$	−17.9815	−	11.1586i	−0.646332	−	0.401088i
$775$	2.71108	+	4.05742i	0.0973848	+	0.145747i
$776$	50.0781	+	43.9173i	1.79770	+	1.57654i
$777$	−3.99235	+	14.0050i	−0.143225	+	0.502427i
$778$	88.3537	+	23.6743i	3.16763	+	0.848765i
$779$	18.4046	−	16.1404i	0.659412	−	0.578289i
$780$	7.53718	+	15.9170i	0.269874	+	0.569920i
$781$	3.78544	+	2.18552i	0.135454	+	0.0782041i
$782$	0.750379	−	5.23500i	0.0268335	−	0.187203i
$783$	−30.1733	+	13.1303i	−1.07831	+	0.469239i
$784$	−15.0688	−	6.24169i	−0.538170	−	0.222917i
$785$	1.55295	−	4.57483i	0.0554270	−	0.163283i
$786$	−0.904816	−	18.2461i	−0.0322737	−	0.650815i
$787$	−1.88137	+	28.7041i	−0.0670635	+	1.02319i	0.823202	+	0.567749i	$0.192186\pi$
$787$	−1.88137	+	28.7041i	−0.0670635	+	1.02319i	−0.890265	+	0.455443i	$0.849481\pi$
$788$	−21.9294	−	64.6020i	−0.781204	−	2.30135i
$789$	22.6896	+	17.9907i	0.807771	+	0.640485i
$790$	12.4046	+	1.63310i	0.441336	+	0.0581030i
$791$	1.35312	+	3.26673i	0.0481115	+	0.116152i
$792$	2.09699	+	12.6287i	0.0745133	+	0.448742i
$793$	−33.6727	−	6.69791i	−1.19575	−	0.237850i
$794$	−11.9069	+	5.87183i	−0.422560	+	0.208384i
$795$	−4.09063	−	6.33794i	−0.145080	−	0.224784i
$796$	62.1947	+	70.9195i	2.20443	+	2.51368i
$797$	−3.32560	−	25.2604i	−0.117799	−	0.894770i	−0.943665	−	0.330903i	$-0.892647\pi$
$797$	−3.32560	−	25.2604i	−0.117799	−	0.894770i	0.825866	−	0.563866i	$-0.190687\pi$
$798$	2.37088	−	11.0020i	0.0839283	−	0.389465i
$799$	37.0710	−	31.7657i	1.31148	−	1.12379i
$800$		−	10.9041i		−	0.385517i
$801$	−9.72980	−	2.94169i	−0.343785	−	0.103940i
$802$	9.58303	+	48.1771i	0.338389	+	1.70119i
$803$	0.843619	+	3.14843i	0.0297707	+	0.111106i
$804$	−63.5416	−	18.1136i	−2.24094	−	0.638816i
$805$	−0.189665	+	0.0643827i	−0.00668482	+	0.00226919i
$806$	−5.87246	+	11.9082i	−0.206848	+	0.419447i
$807$	−15.7045	−	5.61098i	−0.552824	−	0.197516i
$808$	7.13602	−	54.2034i	0.251044	−	1.90687i
$809$	1.47986	−	0.988813i	0.0520292	−	0.0347648i	−0.529284	−	0.848445i	$-0.677539\pi$
$809$	1.47986	−	0.988813i	0.0520292	−	0.0347648i	0.581313	+	0.813680i	$0.302539\pi$
$810$	10.8723	−	0.0200779i	0.382015	−	0.000705467i
$811$	27.6326	−	41.3552i	0.970314	−	1.45218i	0.0800181	−	0.996793i	$-0.474502\pi$
$811$	27.6326	−	41.3552i	0.970314	−	1.45218i	0.890295	−	0.455383i	$-0.150498\pi$
$812$	−17.0045	+	4.55634i	−0.596740	+	0.159896i
$813$	32.0729	+	19.2037i	1.12485	+	0.673501i
$814$	−27.4712	+	3.61665i	−0.962865	+	0.126764i
$815$	−1.64618	−	2.85126i	−0.0576630	−	0.0998752i
$816$	−10.4422	+	14.7381i	−0.365549	+	0.515935i
$817$	−5.37378	+	9.30767i	−0.188005	+	0.325634i
$818$	−21.4077	+	51.6828i	−0.748504	+	1.80705i
$819$	−11.4816	+	3.49448i	−0.401199	+	0.122107i
$820$	8.94581	+	8.94581i	0.312401	+	0.312401i
$821$	−16.3205	−	33.0947i	−0.569589	−	1.15501i	−0.970992	−	0.239111i	$-0.923144\pi$
$821$	−16.3205	−	33.0947i	−0.569589	−	1.15501i	0.401404	−	0.915901i	$-0.368523\pi$
$822$	24.0469	+	10.4115i	0.838731	+	0.363143i
$823$	9.90115	+	4.88271i	0.345132	+	0.170200i	0.606591	−	0.795014i	$-0.292537\pi$
$823$	9.90115	+	4.88271i	0.345132	+	0.170200i	−0.261458	+	0.965215i	$0.584203\pi$
$824$	21.4852	+	16.4861i	0.748471	+	0.574322i
$825$	−8.25618	+	1.50620i	−0.287443	+	0.0524392i
$826$	15.6147	−	1.02344i	0.543305	−	0.0356101i
$827$	−4.01743	+	20.1970i	−0.139700	+	0.702318i	0.845916	+	0.533316i	$0.179054\pi$
$827$	−4.01743	+	20.1970i	−0.139700	+	0.702318i	−0.985616	+	0.169002i	$0.945946\pi$
$828$	−3.17898	−	5.10171i	−0.110477	−	0.177297i
$829$	−10.5506	+	10.5506i	−0.366437	+	0.366437i	−0.866176	−	0.499739i	$-0.833429\pi$
$829$	−10.5506	+	10.5506i	−0.366437	+	0.366437i	0.499739	+	0.866176i	$0.333429\pi$
$830$	−1.48494	−	0.504071i	−0.0515432	−	0.0174966i
$831$	−3.61438	+	44.3315i	−0.125381	+	1.53784i
$832$	49.2974	−	28.4619i	1.70908	−	0.986738i
$833$	22.2757	−	14.5174i	0.771806	−	0.502997i
$834$	42.2225	−	46.6286i	1.46204	−	1.61462i
$835$	−1.63137	+	1.25179i	−0.0564557	+	0.0433200i
$836$	13.6893	−	2.72297i	0.473454	−	0.0941758i
$837$	3.32716	+	4.18029i	0.115004	+	0.144492i
$838$	69.0128	+	46.1129i	2.38401	+	1.59294i
$839$	14.6052	−	16.6541i	0.504228	−	0.574962i	−0.442593	−	0.896723i	$-0.645941\pi$
$839$	14.6052	−	16.6541i	0.504228	−	0.574962i	0.946821	+	0.321761i	$0.104275\pi$
$840$	2.68021	+	0.396307i	0.0924760	+	0.0136739i
$841$	6.76031	−	8.81021i	0.233114	−	0.303800i
$842$	4.41082	−	5.74829i	0.152007	−	0.198099i
$843$	12.5570	−	15.8368i	0.432487	−	0.545447i
$844$	37.3058	−	42.5391i	1.28412	−	1.46425i
$845$	−6.71844	−	4.48912i	−0.231121	−	0.154430i
$846$	13.7901	−	84.0078i	0.474112	−	2.88825i
$847$	7.25139	−	1.44239i	0.249161	−	0.0495612i
$848$	17.3375	−	13.3035i	0.595372	−	0.456845i
$849$	1.85145	+	0.398980i	0.0635415	+	0.0136930i
$850$	−38.6926	−	26.5004i	−1.32714	−	0.908958i
$851$	5.24846	−	3.03020i	0.179915	−	0.103874i
$852$	22.8361	+	15.7895i	0.782351	+	0.540939i
$853$	−25.7146	−	8.72894i	−0.880452	−	0.298873i	−0.155635	−	0.987815i	$-0.549742\pi$
$853$	−25.7146	−	8.72894i	−0.880452	−	0.298873i	−0.724817	+	0.688941i	$0.758076\pi$
$854$	−8.01784	+	8.01784i	−0.274365	+	0.274365i
$855$	−0.185759	−	5.51851i	−0.00635281	−	0.188729i
$856$	−12.0351	+	60.5046i	−0.411351	+	2.06800i
$857$	33.3011	−	2.18267i	1.13754	−	0.0745585i	0.515033	−	0.857170i	$-0.327780\pi$
$857$	33.3011	−	2.18267i	1.13754	−	0.0745585i	0.622510	+	0.782612i	$0.286113\pi$
$858$	−14.7812	−	17.4054i	−0.504622	−	0.594211i
$859$	−11.1148	−	8.52870i	−0.379233	−	0.290995i	0.401502	−	0.915858i	$-0.368488\pi$
$859$	−11.1148	−	8.52870i	−0.379233	−	0.290995i	−0.780735	+	0.624863i	$0.785155\pi$
$860$	−4.98168	−	2.45669i	−0.169874	−	0.0837725i
$861$	−6.92245	+	5.13899i	−0.235916	+	0.175136i
$862$	41.5082	+	84.1703i	1.41378	+	2.86685i
$863$	−4.06464	−	4.06464i	−0.138362	−	0.138362i	0.634533	−	0.772895i	$-0.281192\pi$
$863$	−4.06464	−	4.06464i	−0.138362	−	0.138362i	−0.772895	+	0.634533i	$0.781192\pi$
$864$	−0.992104	−	11.8972i	−0.0337521	−	0.404750i
$865$	1.58798	−	3.83371i	0.0539928	−	0.130350i
$866$	−28.9353	+	50.1175i	−0.983263	+	1.70306i
$867$	−10.2033	−	27.6205i	−0.346521	−	0.938042i
$868$	1.42913	+	2.47533i	0.0485078	+	0.0840181i
$869$	−10.4835	+	1.38018i	−0.355630	+	0.0468196i
$870$	−11.5794	+	6.44208i	−0.392578	+	0.218407i
$871$	53.0279	−	14.2088i	1.79678	−	0.481446i
$872$	−2.41945	+	3.62096i	−0.0819329	+	0.122621i
$873$	−27.8115	+	38.8867i	−0.941277	+	1.31612i
$874$	−3.89427	+	2.60207i	−0.131726	+	0.0880163i
$875$	−0.476088	+	3.61625i	−0.0160947	+	0.122251i
$876$	3.71560	+	20.3669i	0.125538	+	0.688133i
$877$	−2.88801	+	5.85631i	−0.0975213	+	0.197754i	−0.940166	−	0.340716i	$-0.889331\pi$
$877$	−2.88801	+	5.85631i	−0.0975213	+	0.197754i	0.842645	+	0.538469i	$0.180997\pi$
$878$	−86.2774	+	29.2872i	−2.91172	+	0.988396i
$879$	2.93823	−	2.84625i	0.0991041	−	0.0960015i
$880$	0.336874	+	1.25723i	0.0113560	+	0.0423813i
$881$	−5.82712	−	29.2949i	−0.196321	−	0.986971i	−0.945752	−	0.324889i	$-0.894673\pi$
$881$	−5.82712	−	29.2949i	−0.196321	−	0.986971i	0.749431	−	0.662082i	$-0.230327\pi$
$882$	13.4184	−	44.3819i	0.451819	−	1.49441i
$883$		−	49.5960i		−	1.66904i	−0.550978	−	0.834520i	$-0.685745\pi$
$883$		−	49.5960i		−	1.66904i	0.550978	−	0.834520i	$-0.314255\pi$
$884$	6.39127	−	82.9268i	0.214962	−	2.78913i
$885$	7.30813	−	2.35187i	0.245660	−	0.0790571i
$886$	−11.9894	−	91.0683i	−0.402791	−	3.05950i
$887$	−10.0838	−	11.4984i	−0.338583	−	0.386079i	0.557344	−	0.830282i	$-0.311820\pi$
$887$	−10.0838	−	11.4984i	−0.338583	−	0.386079i	−0.895926	+	0.444202i	$0.853487\pi$
$888$	−81.8772	+	4.06026i	−2.74762	+	0.136253i
$889$	5.00239	−	2.46691i	0.167775	−	0.0827374i
$890$	−4.01450	−	0.798533i	−0.134566	−	0.0267669i
$891$	−8.87109	+	2.39457i	−0.297193	+	0.0802210i
$892$	−22.0650	−	53.2696i	−0.738791	−	1.78360i
$893$	−42.8653	−	5.64333i	−1.43443	−	0.188847i
$894$	−4.49395	+	30.3924i	−0.150300	+	1.01647i
$895$	1.92404	+	5.66805i	0.0643137	+	0.189462i
$896$	1.00645	−	15.3554i	0.0336230	−	0.512988i
$897$	4.44373	+	2.27995i	0.148372	+	0.0761253i
$898$	−12.4298	+	36.6170i	−0.414788	+	1.22193i
$899$	−6.01584	−	2.49184i	−0.200640	−	0.0831077i
$900$	−53.0440	+	5.27384i	−1.76813	+	0.175795i
$901$	1.92212	+	35.5731i	0.0640351	+	1.18511i
$902$	−14.2060	−	8.20183i	−0.473008	−	0.273091i
$903$	2.15273	−	3.11346i	0.0716383	−	0.103609i
$904$	−14.9648	+	13.1238i	−0.497722	+	0.436490i
$905$	−8.72364	−	2.33749i	−0.289983	−	0.0777008i
$906$	−7.09706	−	7.32642i	−0.235784	−	0.243404i
$907$	−0.239945	−	0.210426i	−0.00796724	−	0.00698708i	0.655353	−	0.755323i	$-0.272520\pi$
$907$	−0.239945	−	0.210426i	−0.00796724	−	0.00698708i	−0.663320	+	0.748336i	$0.730853\pi$
$908$	−37.0361	−	55.4284i	−1.22909	−	1.83946i
$909$	39.2213	+	1.24772i	1.30089	+	0.0413842i
$910$	−4.46492	+	1.84943i	−0.148011	+	0.0613080i
$911$	−1.06415	−	16.2358i	−0.0352569	−	0.537916i	−0.978557	−	0.205975i	$-0.933963\pi$
$911$	−1.06415	−	16.2358i	−0.0352569	−	0.537916i	0.943300	−	0.331941i	$-0.107703\pi$
$912$	15.8907	−	1.83551i	0.526194	−	0.0607799i
$913$	1.32247	+	0.0866795i	0.0437675	+	0.00286867i
$914$	−12.1762	+	45.4421i	−0.402752	+	1.50309i
$915$	−2.85778	+	4.77291i	−0.0944752	+	0.157788i
$916$	18.1022	+	23.5912i	0.598113	+	0.779476i
$917$	3.26759			0.107905
$918$	−44.6277	−	25.3936i	−1.47294	−	0.838114i
$919$	−32.6543			−1.07716			−0.538582	−	0.842573i	$-0.681040\pi$
$919$	−32.6543			−1.07716			−0.538582	+	0.842573i	$0.681040\pi$
$920$	−0.686380	−	0.894508i	−0.0226293	−	0.0294910i
$921$	−28.0197	+	46.7970i	−0.923279	+	1.54201i
$922$	8.31521	−	31.0328i	0.273847	−	1.02201i
$923$	−23.0184	−	1.50871i	−0.757660	−	0.0496597i
$924$	−4.88325	+	0.564057i	−0.160647	+	0.0185561i
$925$	−3.51494	−	53.6276i	−0.115570	−	1.76326i
$926$	2.09494	−	0.867754i	0.0688441	−	0.0285162i
$927$	−10.2494	+	16.5164i	−0.336635	+	0.542470i
$928$	8.08361	+	12.0980i	0.265357	+	0.397136i
$929$	10.6468	+	9.33703i	0.349312	+	0.306338i	0.815964	−	0.578103i	$-0.196207\pi$
$929$	10.6468	+	9.33703i	0.349312	+	0.306338i	−0.466652	+	0.884441i	$0.654540\pi$
$930$	1.49690	+	1.54527i	0.0490852	+	0.0506715i
$931$	−22.7451	−	6.09453i	−0.745440	−	0.199740i
$932$	−52.0244	+	45.6241i	−1.70411	+	1.49447i
$933$	−11.1056	+	16.0618i	−0.363580	+	0.525839i
$934$	62.6642	+	36.1792i	2.05044	+	1.18382i
$935$	−2.00125	−	0.705032i	−0.0654479	−	0.0230570i
$936$	−39.4026	−	54.8791i	−1.28791	−	1.79378i
$937$	−25.9564	−	10.7515i	−0.847959	−	0.351236i	−0.0839723	−	0.996468i	$-0.526761\pi$
$937$	−25.9564	−	10.7515i	−0.847959	−	0.351236i	−0.763987	+	0.645232i	$0.776761\pi$
$938$	5.82812	−	17.1691i	0.190295	−	0.560591i
$939$	−12.9658	−	6.65236i	−0.423122	−	0.217092i
$940$	1.46141	−	22.2967i	0.0476658	−	0.727239i
$941$	1.79655	+	5.29248i	0.0585660	+	0.172530i	0.972276	−	0.233838i	$-0.0751285\pi$
$941$	1.79655	+	5.29248i	0.0585660	+	0.172530i	−0.913710	+	0.406368i	$0.866795\pi$
$942$	−5.81988	+	39.3596i	−0.189622	+	1.28241i
$943$	3.55715	+	0.468307i	0.115837	+	0.0152502i
$944$	8.51135	+	20.5482i	0.277021	+	0.668787i
$945$	−0.0927307	+	1.94247i	−0.00301653	+	0.0631885i
$946$	7.06358	+	1.40503i	0.229657	+	0.0456816i
$947$	−25.5947	+	12.6219i	−0.831717	+	0.410158i	−0.807728	−	0.589555i	$-0.799303\pi$
$947$	−25.5947	+	12.6219i	−0.831717	+	0.410158i	−0.0239887	+	0.999712i	$0.507637\pi$
$948$	−67.0795	+	3.32645i	−2.17864	+	0.108038i
$949$	−11.3419	−	12.9329i	−0.368172	−	0.419820i
$950$	5.42120	+	41.1781i	0.175887	+	1.33599i
$951$	2.13427	−	0.686840i	0.0692085	−	0.0222723i
$952$	−10.0613	−	7.90525i	−0.326087	−	0.256210i
$953$		−	37.4674i		−	1.21369i	−0.794821	−	0.606844i	$-0.792435\pi$
$953$		−	37.4674i		−	1.21369i	0.794821	−	0.606844i	$-0.207565\pi$
$954$	42.5091	+	45.3026i	1.37628	+	1.46672i
$955$	2.11098	+	10.6126i	0.0683096	+	0.343416i
$956$	16.7801	+	62.6243i	0.542709	+	2.02542i
$957$	8.04356	−	7.79174i	0.260011	−	0.251871i
$958$	48.8508	−	16.5826i	1.57830	−	0.535760i
$959$	−2.07300	+	4.20362i	−0.0669406	+	0.135742i
$960$	−1.65538	−	9.07389i	−0.0534271	−	0.292859i
$961$	3.90832	−	29.6866i	0.126075	−	0.957633i
$962$	121.584	−	81.2398i	3.92002	−	2.61927i
$963$	−44.0697	−	4.29941i	−1.42013	−	0.138546i
$964$	25.8651	−	38.7099i	0.833060	−	1.24676i
$965$	−4.38425	+	1.17476i	−0.141134	+	0.0378167i
$966$	1.44147	−	0.801946i	0.0463784	−	0.0258022i
$967$	4.60784	−	0.606634i	0.148178	−	0.0195080i	−0.0560721	−	0.998427i	$-0.517858\pi$
$967$	4.60784	−	0.606634i	0.148178	−	0.0195080i	0.204250	+	0.978919i	$0.434524\pi$
$968$	20.8097	+	36.0434i	0.668848	+	1.15848i
$969$	−12.1692	+	23.0633i	−0.390932	+	0.740899i
$970$	−9.62576	+	16.6723i	−0.309065	+	0.535316i
$971$	−17.1196	+	41.3304i	−0.549394	+	1.32636i	0.368536	+	0.929614i	$0.379859\pi$
$971$	−17.1196	+	41.3304i	−0.549394	+	1.32636i	−0.917930	+	0.396742i	$0.870141\pi$
$972$	−57.3953	+	10.5804i	−1.84095	+	0.339365i
$973$	7.95592	+	7.95592i	0.255055	+	0.255055i
$974$	−10.6270	−	21.5494i	−0.340510	−	0.690486i
$975$	35.5622	−	26.4001i	1.13890	−	0.845481i
$976$	−14.4543	−	7.12808i	−0.462671	−	0.228164i
$977$	23.5464	+	18.0678i	0.753317	+	0.578040i	0.912436	−	0.409219i	$-0.134199\pi$
$977$	23.5464	+	18.0678i	0.753317	+	0.578040i	−0.159120	+	0.987259i	$0.550866\pi$
$978$	17.5512	+	20.6672i	0.561226	+	0.660864i
$979$	3.45185	−	0.226246i	0.110322	−	0.00723086i
$980$	2.37418	−	11.9358i	0.0758404	−	0.381276i
$981$	−2.75807	−	1.47094i	−0.0880583	−	0.0469636i
$982$	−7.32889	+	7.32889i	−0.233874	+	0.233874i
$983$	27.3926	+	9.29854i	0.873688	+	0.296577i	0.722035	−	0.691857i	$-0.243207\pi$
$983$	27.3926	+	9.29854i	0.873688	+	0.296577i	0.151653	+	0.988434i	$0.451540\pi$
$984$	−39.9191	−	27.6011i	−1.27257	−	0.879893i
$985$	7.95436	−	4.59245i	0.253447	−	0.146328i
$986$	62.5749	+	0.717727i	1.99279	+	0.0228571i
$987$	14.8854	+	3.20775i	0.473808	+	0.102104i
$988$	−58.4378	+	44.8409i	−1.85915	+	1.42658i
$989$	−1.54496	+	0.307311i	−0.0491268	+	0.00977193i
$990$	−3.46170	+	1.30654i	−0.110020	+	0.0415246i
$991$	−15.8269	−	10.5752i	−0.502759	−	0.335933i	0.278191	−	0.960526i	$-0.410265\pi$
$991$	−15.8269	−	10.5752i	−0.502759	−	0.335933i	−0.780951	+	0.624593i	$0.785265\pi$
$992$	1.55762	−	1.77613i	0.0494545	−	0.0563921i
$993$	−7.14303	+	9.00870i	−0.226677	+	0.285882i
$994$	−4.63790	+	6.04424i	−0.147105	+	0.191711i
$995$	−7.73097	+	10.0752i	−0.245088	+	0.319405i
$996$	8.32732	+	1.23131i	0.263861	+	0.0390156i
$997$	−21.1273	+	24.0911i	−0.669108	+	0.762972i	−0.982421	−	0.186678i	$-0.940228\pi$
$997$	−21.1273	+	24.0911i	−0.669108	+	0.762972i	0.313313	+	0.949650i	$0.398561\pi$
$998$	−46.6365	−	31.1615i	−1.47625	−	0.986400i
$999$	−8.71436	−	58.1920i	−0.275710	−	1.84111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.s.a.11.16	✓	256
3.2	odd	2		459.2.y.a.62.1		256
9.4	even	3		459.2.y.a.368.1		256
9.5	odd	6	inner	153.2.s.a.113.16	yes	256
17.14	odd	16	inner	153.2.s.a.65.16	yes	256
51.14	even	16		459.2.y.a.116.1		256
153.14	even	48	inner	153.2.s.a.14.16	yes	256
153.31	odd	48		459.2.y.a.422.1		256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.16	✓	256	1.1	even	1	trivial
153.2.s.a.14.16	yes	256	153.14	even	48	inner
153.2.s.a.65.16	yes	256	17.14	odd	16	inner
153.2.s.a.113.16	yes	256	9.5	odd	6	inner
459.2.y.a.62.1		256	3.2	odd	2
459.2.y.a.116.1		256	51.14	even	16
459.2.y.a.368.1		256	9.4	even	3
459.2.y.a.422.1		256	153.31	odd	48

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.s (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.45899 + 1.90139i) q^{2} +(0.889766 - 1.48604i) q^{3} +(-0.969004 + 3.61637i) q^{4} +(-0.502973 - 0.0329666i) q^{5} +(4.12371 - 0.476323i) q^{6} +(0.0485612 + 0.740900i) q^{7} +(-3.86148 + 1.59948i) q^{8} +(-1.41663 - 2.64446i) q^{9} +O(q^{10})\)	\(q+(1.45899 + 1.90139i) q^{2} +(0.889766 - 1.48604i) q^{3} +(-0.969004 + 3.61637i) q^{4} +(-0.502973 - 0.0329666i) q^{5} +(4.12371 - 0.476323i) q^{6} +(0.0485612 + 0.740900i) q^{7} +(-3.86148 + 1.59948i) q^{8} +(-1.41663 - 2.64446i) q^{9} +(-0.671150 - 1.00445i) q^{10} +(0.767594 + 0.673162i) q^{11} +(4.51189 + 4.65771i) q^{12} +(-5.20440 - 1.39452i) q^{13} +(-1.33789 + 1.17330i) q^{14} +(-0.496518 + 0.718106i) q^{15} +(-2.19038 - 1.26462i) q^{16} +(3.71857 - 1.78107i) q^{17} +(2.96130 - 6.55181i) q^{18} +(-3.37354 - 1.39737i) q^{19} +(0.606603 - 1.78699i) q^{20} +(1.14422 + 0.587064i) q^{21} +(-0.160033 + 2.44163i) q^{22} +(-0.172029 - 0.506782i) q^{23} +(-1.05893 + 7.16147i) q^{24} +(-4.70533 - 0.619468i) q^{25} +(-4.94165 - 11.9302i) q^{26} +(-5.19024 - 0.247775i) q^{27} +(-2.72643 - 0.542320i) q^{28} +(5.67976 - 2.80095i) q^{29} +(-2.08982 + 0.103633i) q^{30} +(-0.677946 - 0.773049i) q^{31} +(0.299892 + 2.27790i) q^{32} +(1.68332 - 0.541719i) q^{33} +(8.81188 + 4.47190i) q^{34} -0.374254i q^{35} +(10.9361 - 2.56058i) q^{36} +(2.20919 + 11.1064i) q^{37} +(-2.26502 - 8.45317i) q^{38} +(-6.70301 + 6.49316i) q^{39} +(1.99495 - 0.677194i) q^{40} +(-2.96507 + 6.01257i) q^{41} +(0.553160 + 3.03212i) q^{42} +(0.384182 - 2.91815i) q^{43} +(-3.17821 + 2.12361i) q^{44} +(0.625350 + 1.37679i) q^{45} +(0.712603 - 1.06649i) q^{46} +(11.4370 - 3.06452i) q^{47} +(-3.82820 + 2.12978i) q^{48} +(6.39354 - 0.841725i) q^{49} +(-5.68718 - 9.85048i) q^{50} +(0.661916 - 7.11069i) q^{51} +(10.0862 - 17.4698i) q^{52} +(-3.30651 + 7.98262i) q^{53} +(-7.10139 - 10.2302i) q^{54} +(-0.363887 - 0.363887i) q^{55} +(-1.37257 - 2.78330i) q^{56} +(-5.07821 + 3.76989i) q^{57} +(13.6124 + 6.71290i) q^{58} +(-6.97647 - 5.35323i) q^{59} +(-2.11581 - 2.49144i) q^{60} +(6.35837 - 0.416750i) q^{61} +(0.480754 - 2.41691i) q^{62} +(1.89049 - 1.17800i) q^{63} +(-7.47053 + 7.47053i) q^{64} +(2.57170 + 0.872975i) q^{65} +(3.48597 + 2.41030i) q^{66} +(-8.82398 + 5.09452i) q^{67} +(2.83771 + 15.1736i) q^{68} +(-0.906165 - 0.195275i) q^{69} +(0.711604 - 0.546033i) q^{70} +(4.19907 - 0.835247i) q^{71} +(9.70004 + 7.94564i) q^{72} +(2.65455 + 1.77371i) q^{73} +(-17.8943 + 20.4046i) q^{74} +(-5.10720 + 6.44113i) q^{75} +(8.32238 - 10.8459i) q^{76} +(-0.461470 + 0.601400i) q^{77} +(-22.1257 - 3.27159i) q^{78} +(-6.82883 + 7.78679i) q^{79} +(1.06001 + 0.708279i) q^{80} +(-4.98630 + 7.49245i) q^{81} +(-15.7583 + 3.13452i) q^{82} +(1.02986 - 0.790239i) q^{83} +(-3.23179 + 3.56904i) q^{84} +(-1.92906 + 0.773243i) q^{85} +(6.10907 - 3.52707i) q^{86} +(0.891337 - 10.9325i) q^{87} +(-4.04075 - 1.37165i) q^{88} +(2.39586 - 2.39586i) q^{89} +(-1.70544 + 3.19776i) q^{90} +(0.780465 - 3.92366i) q^{91} +(1.99941 - 0.131048i) q^{92} +(-1.75200 + 0.319622i) q^{93} +(22.5133 + 17.2750i) q^{94} +(1.65074 + 0.814053i) q^{95} +(3.65189 + 1.58115i) q^{96} +(-7.04839 - 14.2927i) q^{97} +(10.9286 + 10.9286i) q^{98} +(0.692749 - 2.98349i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

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