LMFDB - Embedded newform 315.2.be.b.236.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(236,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 5]))

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

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

chi := DirichletCharacter("315.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.be (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			236.14
Character	$\chi$	$=$	315.236
Dual form			315.2.be.b.311.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.03201 - 1.17318i) q^{2} +(-0.909209 - 1.47423i) q^{3} +(1.75271 - 3.03578i) q^{4} +1.00000 q^{5} +(-3.57705 - 1.92897i) q^{6} +(0.498797 - 2.59831i) q^{7} -3.53226i q^{8} +(-1.34668 + 2.68076i) q^{9} +O(q^{10})$	\(q+(2.03201 - 1.17318i) q^{2} +(-0.909209 - 1.47423i) q^{3} +(1.75271 - 3.03578i) q^{4} +1.00000 q^{5} +(-3.57705 - 1.92897i) q^{6} +(0.498797 - 2.59831i) q^{7} -3.53226i q^{8} +(-1.34668 + 2.68076i) q^{9} +(2.03201 - 1.17318i) q^{10} +5.55854i q^{11} +(-6.06901 + 0.176271i) q^{12} +(0.0395039 - 0.0228076i) q^{13} +(-2.03473 - 5.86497i) q^{14} +(-0.909209 - 1.47423i) q^{15} +(-0.638563 - 1.10602i) q^{16} +(0.320160 + 0.554533i) q^{17} +(0.408548 + 7.02722i) q^{18} +(-5.73840 - 3.31307i) q^{19} +(1.75271 - 3.03578i) q^{20} +(-4.28400 + 1.62706i) q^{21} +(6.52118 + 11.2950i) q^{22} -6.04027i q^{23} +(-5.20735 + 3.21156i) q^{24} +1.00000 q^{25} +(0.0535149 - 0.0926905i) q^{26} +(5.17645 - 0.452058i) q^{27} +(-7.01365 - 6.06832i) q^{28} +(5.95930 + 3.44060i) q^{29} +(-3.57705 - 1.92897i) q^{30} +(5.61264 + 3.24046i) q^{31} +(3.52292 + 2.03396i) q^{32} +(8.19454 - 5.05387i) q^{33} +(1.30114 + 0.751211i) q^{34} +(0.498797 - 2.59831i) q^{35} +(5.77785 + 8.78681i) q^{36} +(-3.67259 + 6.36111i) q^{37} -15.5473 q^{38} +(-0.0695408 - 0.0375008i) q^{39} -3.53226i q^{40} +(-0.580801 - 1.00598i) q^{41} +(-6.79629 + 8.33212i) q^{42} +(-2.08247 + 3.60695i) q^{43} +(16.8745 + 9.74251i) q^{44} +(-1.34668 + 2.68076i) q^{45} +(-7.08634 - 12.2739i) q^{46} +(-2.79236 - 4.83651i) q^{47} +(-1.04994 + 1.94699i) q^{48} +(-6.50240 - 2.59206i) q^{49} +(2.03201 - 1.17318i) q^{50} +(0.526414 - 0.976173i) q^{51} -0.159900i q^{52} +(5.08648 - 2.93668i) q^{53} +(9.98825 - 6.99150i) q^{54} +5.55854i q^{55} +(-9.17790 - 1.76188i) q^{56} +(0.333196 + 11.4720i) q^{57} +16.1458 q^{58} +(-1.47910 + 2.56187i) q^{59} +(-6.06901 + 0.176271i) q^{60} +(-5.79128 + 3.34359i) q^{61} +15.2066 q^{62} +(6.29371 + 4.83624i) q^{63} +12.0991 q^{64} +(0.0395039 - 0.0228076i) q^{65} +(10.7223 - 19.8832i) q^{66} +(-1.75146 + 3.03361i) q^{67} +2.24459 q^{68} +(-8.90472 + 5.49187i) q^{69} +(-2.03473 - 5.86497i) q^{70} -7.67660i q^{71} +(9.46913 + 4.75682i) q^{72} +(-3.76739 + 2.17511i) q^{73} +17.2344i q^{74} +(-0.909209 - 1.47423i) q^{75} +(-20.1155 + 11.6137i) q^{76} +(14.4428 + 2.77259i) q^{77} +(-0.185303 + 0.00538201i) q^{78} +(-4.28313 - 7.41859i) q^{79} +(-0.638563 - 1.10602i) q^{80} +(-5.37291 - 7.22024i) q^{81} +(-2.36039 - 1.36277i) q^{82} +(0.725553 - 1.25670i) q^{83} +(-2.56920 + 15.8571i) q^{84} +(0.320160 + 0.554533i) q^{85} +9.77248i q^{86} +(-0.346023 - 11.9136i) q^{87} +19.6342 q^{88} +(-9.24246 + 16.0084i) q^{89} +(0.408548 + 7.02722i) q^{90} +(-0.0395567 - 0.114020i) q^{91} +(-18.3370 - 10.5868i) q^{92} +(-0.325894 - 11.2205i) q^{93} +(-11.3482 - 6.55189i) q^{94} +(-5.73840 - 3.31307i) q^{95} +(-0.204556 - 7.04287i) q^{96} +(5.49921 + 3.17497i) q^{97} +(-16.2539 + 2.36141i) q^{98} +(-14.9011 - 7.48557i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9	$ 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9} + 3 q^{10} - 18 q^{12} + 12 q^{13} - 9 q^{14} - q^{15} - 21 q^{16} + 3 q^{17} - 22 q^{18} + 15 q^{20} - 10 q^{21} + 15 q^{22} + 2 q^{24} + 30 q^{25} - 24 q^{26} + 5 q^{27} + 27 q^{28} + q^{30} + 6 q^{31} + 9 q^{32} - 17 q^{33} - 48 q^{34} + 6 q^{35} + 21 q^{36} - 3 q^{37} - 60 q^{38} + 12 q^{39} + 18 q^{41} - 47 q^{42} + 12 q^{43} - 15 q^{44} - 5 q^{45} + 9 q^{46} - 30 q^{47} + 40 q^{48} - 24 q^{49} + 3 q^{50} + 33 q^{51} + 30 q^{53} + 13 q^{54} + 72 q^{56} - 21 q^{57} + 15 q^{59} - 18 q^{60} - 30 q^{61} - 12 q^{62} + 10 q^{63} - 138 q^{64} + 12 q^{65} + 44 q^{66} - 6 q^{67} - 42 q^{68} - 32 q^{69} - 9 q^{70} - 137 q^{72} + 6 q^{73} - q^{75} + 54 q^{76} - 21 q^{77} - 18 q^{78} - 12 q^{79} - 21 q^{80} - 17 q^{81} + 6 q^{82} + 6 q^{83} - 12 q^{84} + 3 q^{85} - 47 q^{87} + 96 q^{88} + 3 q^{89} - 22 q^{90} + 15 q^{91} - 3 q^{92} - 18 q^{93} + 3 q^{94} + 60 q^{96} - 36 q^{97} - 24 q^{98} - q^{99}+O(q^{100}) $ 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9 + 3 * q^10 - 18 * q^12 + 12 * q^13 - 9 * q^14 - q^15 - 21 * q^16 + 3 * q^17 - 22 * q^18 + 15 * q^20 - 10 * q^21 + 15 * q^22 + 2 * q^24 + 30 * q^25 - 24 * q^26 + 5 * q^27 + 27 * q^28 + q^30 + 6 * q^31 + 9 * q^32 - 17 * q^33 - 48 * q^34 + 6 * q^35 + 21 * q^36 - 3 * q^37 - 60 * q^38 + 12 * q^39 + 18 * q^41 - 47 * q^42 + 12 * q^43 - 15 * q^44 - 5 * q^45 + 9 * q^46 - 30 * q^47 + 40 * q^48 - 24 * q^49 + 3 * q^50 + 33 * q^51 + 30 * q^53 + 13 * q^54 + 72 * q^56 - 21 * q^57 + 15 * q^59 - 18 * q^60 - 30 * q^61 - 12 * q^62 + 10 * q^63 - 138 * q^64 + 12 * q^65 + 44 * q^66 - 6 * q^67 - 42 * q^68 - 32 * q^69 - 9 * q^70 - 137 * q^72 + 6 * q^73 - q^75 + 54 * q^76 - 21 * q^77 - 18 * q^78 - 12 * q^79 - 21 * q^80 - 17 * q^81 + 6 * q^82 + 6 * q^83 - 12 * q^84 + 3 * q^85 - 47 * q^87 + 96 * q^88 + 3 * q^89 - 22 * q^90 + 15 * q^91 - 3 * q^92 - 18 * q^93 + 3 * q^94 + 60 * q^96 - 36 * q^97 - 24 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.03201	−	1.17318i	1.43685	−	0.829565i	0.439219	−	0.898380i	$-0.355255\pi$
$2$	2.03201	−	1.17318i	1.43685	−	0.829565i	0.997629	+	0.0688156i	$0.0219220\pi$
$3$	−0.909209	−	1.47423i	−0.524932	−	0.851144i
$3$	−0.909209	−	1.47423i	−0.524932	−	0.851144i
$4$	1.75271	−	3.03578i	0.876355	−	1.51789i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−3.57705	−	1.92897i	−1.46033	−	0.787500i
$7$	0.498797	−	2.59831i	0.188528	−	0.982068i
$7$	0.498797	−	2.59831i	0.188528	−	0.982068i
$8$		−	3.53226i		−	1.24884i
$9$	−1.34668	+	2.68076i	−0.448893	+	0.893585i
$10$	2.03201	−	1.17318i	0.642578	−	0.370993i
$11$			5.55854i			1.67596i	0.545698	+	0.837982i	$0.316264\pi$
$11$			5.55854i			1.67596i	−0.545698	+	0.837982i	$0.683736\pi$
$12$	−6.06901	+	0.176271i	−1.75197	+	0.0508850i
$13$	0.0395039	−	0.0228076i	0.0109564	−	0.00632569i	−0.494512	−	0.869171i	$-0.664653\pi$
$13$	0.0395039	−	0.0228076i	0.0109564	−	0.00632569i	0.505468	+	0.862845i	$0.331320\pi$
$14$	−2.03473	−	5.86497i	−0.543803	−	1.56748i
$15$	−0.909209	−	1.47423i	−0.234757	−	0.380643i
$16$	−0.638563	−	1.10602i	−0.159641	−	0.276506i
$17$	0.320160	+	0.554533i	0.0776501	+	0.134494i	0.902236	−	0.431243i	$-0.141925\pi$
$17$	0.320160	+	0.554533i	0.0776501	+	0.134494i	−0.824586	+	0.565737i	$0.808592\pi$
$18$	0.408548	+	7.02722i	0.0962957	+	1.65633i
$19$	−5.73840	−	3.31307i	−1.31648	−	0.760069i	−0.333319	−	0.942814i	$-0.608168\pi$
$19$	−5.73840	−	3.31307i	−1.31648	−	0.760069i	−0.983160	+	0.182745i	$0.941502\pi$
$20$	1.75271	−	3.03578i	0.391918	−	0.678822i
$21$	−4.28400	+	1.62706i	−0.934846	+	0.355054i
$22$	6.52118	+	11.2950i	1.39032	+	2.40810i
$23$		−	6.04027i		−	1.25948i	−0.776804	−	0.629742i	$-0.783161\pi$
$23$		−	6.04027i		−	1.25948i	0.776804	−	0.629742i	$-0.216839\pi$
$24$	−5.20735	+	3.21156i	−1.06295	+	0.655557i
$25$	1.00000			0.200000
$26$	0.0535149	−	0.0926905i	0.0104951	−	0.0181781i
$27$	5.17645	−	0.452058i	0.996208	−	0.0869987i
$28$	−7.01365	−	6.06832i	−1.32545	−	1.14680i
$29$	5.95930	+	3.44060i	1.10661	+	0.638904i	0.937950	−	0.346770i	$-0.112722\pi$
$29$	5.95930	+	3.44060i	1.10661	+	0.638904i	0.168663	+	0.985674i	$0.446055\pi$
$30$	−3.57705	−	1.92897i	−0.653078	−	0.352181i
$31$	5.61264	+	3.24046i	1.00806	+	0.582003i	0.910623	−	0.413238i	$-0.135602\pi$
$31$	5.61264	+	3.24046i	1.00806	+	0.582003i	0.0974365	+	0.995242i	$0.468936\pi$
$32$	3.52292	+	2.03396i	0.622770	+	0.359557i
$33$	8.19454	−	5.05387i	1.42649	−	0.879766i
$34$	1.30114	+	0.751211i	0.223143	+	0.128832i
$35$	0.498797	−	2.59831i	0.0843121	−	0.439194i
$36$	5.77785	+	8.78681i	0.962976	+	1.46447i
$37$	−3.67259	+	6.36111i	−0.603770	+	1.04576i	0.388475	+	0.921459i	$0.373002\pi$
$37$	−3.67259	+	6.36111i	−0.603770	+	1.04576i	−0.992245	+	0.124300i	$0.960331\pi$
$38$	−15.5473			−2.52211
$39$	−0.0695408	−	0.0375008i	−0.0111354	−	0.00600493i
$40$		−	3.53226i		−	0.558499i
$41$	−0.580801	−	1.00598i	−0.0907059	−	0.157107i	0.817102	−	0.576493i	$-0.195579\pi$
$41$	−0.580801	−	1.00598i	−0.0907059	−	0.157107i	−0.907808	+	0.419385i	$0.862246\pi$
$42$	−6.79629	+	8.33212i	−1.04869	+	1.28567i
$43$	−2.08247	+	3.60695i	−0.317574	+	0.550055i	−0.979981	−	0.199089i	$-0.936202\pi$
$43$	−2.08247	+	3.60695i	−0.317574	+	0.550055i	0.662407	+	0.749144i	$0.269535\pi$
$44$	16.8745	+	9.74251i	2.54393	+	1.46874i
$45$	−1.34668	+	2.68076i	−0.200751	+	0.399624i
$46$	−7.08634	−	12.2739i	−1.04482	−	1.80969i
$47$	−2.79236	−	4.83651i	−0.407308	−	0.705478i	0.587279	−	0.809384i	$-0.300199\pi$
$47$	−2.79236	−	4.83651i	−0.407308	−	0.705478i	−0.994587	+	0.103907i	$0.966866\pi$
$48$	−1.04994	+	1.94699i	−0.151546	+	0.281024i
$49$	−6.50240	−	2.59206i	−0.928915	−	0.370294i
$50$	2.03201	−	1.17318i	0.287370	−	0.165913i
$51$	0.526414	−	0.976173i	0.0737127	−	0.136692i
$52$		−	0.159900i		−	0.0221742i
$53$	5.08648	−	2.93668i	0.698682	−	0.403384i	−0.108174	−	0.994132i	$-0.534500\pi$
$53$	5.08648	−	2.93668i	0.698682	−	0.403384i	0.806856	+	0.590748i	$0.201167\pi$
$54$	9.98825	−	6.99150i	1.35923	−	0.951423i
$55$			5.55854i			0.749514i
$56$	−9.17790	−	1.76188i	−1.22645	−	0.235441i
$57$	0.333196	+	11.4720i	0.0441329	+	1.51950i
$58$	16.1458			2.12005
$59$	−1.47910	+	2.56187i	−0.192562	+	0.333527i	−0.946099	−	0.323879i	$-0.895013\pi$
$59$	−1.47910	+	2.56187i	−0.192562	+	0.333527i	0.753536	+	0.657406i	$0.228346\pi$
$60$	−6.06901	+	0.176271i	−0.783505	+	0.0227565i
$61$	−5.79128	+	3.34359i	−0.741497	+	0.428103i	−0.822613	−	0.568601i	$-0.807485\pi$
$61$	−5.79128	+	3.34359i	−0.741497	+	0.428103i	0.0811165	+	0.996705i	$0.474151\pi$
$62$	15.2066			1.93124
$63$	6.29371	+	4.83624i	0.792933	+	0.609309i
$64$	12.0991			1.51238
$65$	0.0395039	−	0.0228076i	0.00489986	−	0.00282893i
$66$	10.7223	−	19.8832i	1.31982	−	2.44745i
$67$	−1.75146	+	3.03361i	−0.213974	+	0.370615i	−0.952955	−	0.303112i	$-0.901974\pi$
$67$	−1.75146	+	3.03361i	−0.213974	+	0.370615i	0.738980	+	0.673727i	$0.235308\pi$
$68$	2.24459			0.272196
$69$	−8.90472	+	5.49187i	−1.07200	+	0.661143i
$70$	−2.03473	−	5.86497i	−0.243196	−	0.700998i
$71$		−	7.67660i		−	0.911045i	−0.890224	−	0.455523i	$-0.849452\pi$
$71$		−	7.67660i		−	0.911045i	0.890224	−	0.455523i	$-0.150548\pi$
$72$	9.46913	+	4.75682i	1.11595	+	0.560597i
$73$	−3.76739	+	2.17511i	−0.440940	+	0.254577i	−0.703996	−	0.710204i	$-0.748603\pi$
$73$	−3.76739	+	2.17511i	−0.440940	+	0.254577i	0.263056	+	0.964781i	$0.415270\pi$
$74$			17.2344i			2.00346i
$75$	−0.909209	−	1.47423i	−0.104986	−	0.170229i
$76$	−20.1155	+	11.6137i	−2.30741	+	1.33218i
$77$	14.4428	+	2.77259i	1.64591	+	0.315965i
$78$	−0.185303	+	0.00538201i	−0.0209814	+	0.000609393i
$79$	−4.28313	−	7.41859i	−0.481889	−	0.834657i	0.517894	−	0.855445i	$-0.326716\pi$
$79$	−4.28313	−	7.41859i	−0.481889	−	0.834657i	−0.999784	+	0.0207875i	$0.993383\pi$
$80$	−0.638563	−	1.10602i	−0.0713935	−	0.123657i
$81$	−5.37291	−	7.22024i	−0.596990	−	0.802249i
$82$	−2.36039	−	1.36277i	−0.260661	−	0.150493i
$83$	0.725553	−	1.25670i	0.0796398	−	0.137940i	−0.823455	−	0.567382i	$-0.807956\pi$
$83$	0.725553	−	1.25670i	0.0796398	−	0.137940i	0.903095	+	0.429442i	$0.141290\pi$
$84$	−2.56920	+	15.8571i	−0.280322	+	1.73015i
$85$	0.320160	+	0.554533i	0.0347262	+	0.0601475i
$86$			9.77248i			1.05379i
$87$	−0.346023	−	11.9136i	−0.0370975	−	1.27727i
$88$	19.6342			2.09301
$89$	−9.24246	+	16.0084i	−0.979699	+	1.69689i	−0.316232	+	0.948682i	$0.602418\pi$
$89$	−9.24246	+	16.0084i	−0.979699	+	1.69689i	−0.663467	+	0.748206i	$0.730916\pi$
$90$	0.408548	+	7.02722i	0.0430647	+	0.740734i
$91$	−0.0395567	−	0.114020i	−0.00414667	−	0.0119525i
$92$	−18.3370	−	10.5868i	−1.91176	−	1.10376i
$93$	−0.325894	−	11.2205i	−0.0337937	−	1.16352i
$94$	−11.3482	−	6.55189i	−1.17048	−	0.675776i
$95$	−5.73840	−	3.31307i	−0.588747	−	0.339913i
$96$	−0.204556	−	7.04287i	−0.0208774	−	0.718810i
$97$	5.49921	+	3.17497i	0.558360	+	0.322369i	0.752487	−	0.658607i	$-0.228854\pi$
$97$	5.49921	+	3.17497i	0.558360	+	0.322369i	−0.194127	+	0.980976i	$0.562187\pi$
$98$	−16.2539	+	2.36141i	−1.64189	+	0.238539i
$99$	−14.9011	−	7.48557i	−1.49762	−	0.752328i
$100$	1.75271	−	3.03578i	0.175271	−	0.303578i
$101$	11.2252			1.11695			0.558473	−	0.829522i	$-0.311387\pi$
$101$	11.2252			1.11695			0.558473	+	0.829522i	$0.311387\pi$
$102$	−0.0755496	−	2.60117i	−0.00748052	−	0.257555i
$103$		−	10.7382i		−	1.05807i	−0.848600	−	0.529034i	$-0.822554\pi$
$103$		−	10.7382i		−	1.05807i	0.848600	−	0.529034i	$-0.177446\pi$
$104$	−0.0805623	−	0.139538i	−0.00789979	−	0.0136828i
$105$	−4.28400	+	1.62706i	−0.418076	+	0.158785i
$106$	6.89052	−	11.9347i	0.669267	−	1.15920i
$107$	1.55054	+	0.895206i	0.149897	+	0.0865429i	0.573072	−	0.819505i	$-0.305751\pi$
$107$	1.55054	+	0.895206i	0.149897	+	0.0865429i	−0.423176	+	0.906048i	$0.639085\pi$
$108$	7.70046	−	16.5069i	0.740978	−	1.58838i
$109$	−9.14606	−	15.8414i	−0.876034	−	1.51733i	−0.855657	−	0.517543i	$-0.826847\pi$
$109$	−9.14606	−	15.8414i	−0.876034	−	1.51733i	−0.0203763	−	0.999792i	$-0.506486\pi$
$110$	6.52118	+	11.2950i	0.621770	+	1.07694i
$111$	12.7169	−	0.369354i	1.20703	−	0.0350575i
$112$	−3.19230	+	1.10750i	−0.301644	+	0.104649i
$113$	−5.20067	+	3.00261i	−0.489238	+	0.282461i	−0.724258	−	0.689529i	$-0.757818\pi$
$113$	−5.20067	+	3.00261i	−0.489238	+	0.282461i	0.235021	+	0.971990i	$0.424484\pi$
$114$	14.1357	+	22.9202i	1.32393	+	2.14668i
$115$		−	6.04027i		−	0.563259i
$116$	20.8898	−	12.0607i	1.93957	−	1.11981i
$117$	0.00794250	+	0.136615i	0.000734284	+	0.0126300i
$118$			6.94100i			0.638971i
$119$	1.60054	−	0.555274i	0.146721	−	0.0509019i
$120$	−5.20735	+	3.21156i	−0.475364	+	0.293174i
$121$	−19.8974			−1.80885
$122$	−7.84529	+	13.5884i	−0.710279	+	1.23024i
$123$	−0.954968	+	1.77088i	−0.0861065	+	0.159674i
$124$	19.6746	−	11.3592i	1.76684	−	1.02008i
$125$	1.00000			0.0894427
$126$	18.4627	+	2.44363i	1.64479	+	0.217696i
$127$	−15.6793			−1.39132			−0.695658	−	0.718373i	$-0.744887\pi$
$127$	−15.6793			−1.39132			−0.695658	+	0.718373i	$0.744887\pi$
$128$	17.5396	−	10.1265i	1.55029	−	0.895063i
$129$	7.21086	−	0.209435i	0.634881	−	0.0184397i
$130$	0.0535149	−	0.0926905i	0.00469357	−	0.00812949i
$131$	−15.8843			−1.38782			−0.693910	−	0.720062i	$-0.744113\pi$
$131$	−15.8843			−1.38782			−0.693910	+	0.720062i	$0.744113\pi$
$132$	−0.979808	−	33.7348i	−0.0852814	−	2.93624i
$133$	−11.4707	+	13.2576i	−0.994632	+	1.14958i
$134$			8.21911i			0.710023i
$135$	5.17645	−	0.452058i	0.445518	−	0.0389070i
$136$	1.95875	−	1.13089i	0.167962	−	0.0969728i
$137$			10.7542i			0.918796i	0.888230	+	0.459398i	$0.151935\pi$
$137$			10.7542i			0.918796i	−0.888230	+	0.459398i	$0.848065\pi$
$138$	−11.6515	+	21.6064i	−0.991844	+	1.83926i
$139$	−5.11830	+	2.95505i	−0.434129	+	0.250644i	−0.701104	−	0.713059i	$-0.747309\pi$
$139$	−5.11830	+	2.95505i	−0.434129	+	0.250644i	0.266975	+	0.963703i	$0.413976\pi$
$140$	−7.01365	−	6.06832i	−0.592761	−	0.512867i
$141$	−4.59127	+	8.51397i	−0.386654	+	0.717005i
$142$	−9.00605	−	15.5989i	−0.755771	−	1.30903i
$143$	0.126777	+	0.219584i	0.0106016	+	0.0183625i
$144$	3.82492	−	0.222373i	0.318743	−	0.0185311i
$145$	5.95930	+	3.44060i	0.494893	+	0.285726i
$146$	−5.10359	+	8.83968i	−0.422376	+	0.731577i
$147$	2.09076	+	11.9427i	0.172443	+	0.985019i
$148$	12.8740	+	22.2983i	1.05823	+	1.83291i
$149$		−	7.18431i		−	0.588562i	−0.955719	−	0.294281i	$-0.904920\pi$
$149$		−	7.18431i		−	0.588562i	0.955719	−	0.294281i	$-0.0950801\pi$
$150$	−3.57705	−	1.92897i	−0.292065	−	0.157500i
$151$	13.7310			1.11741			0.558706	−	0.829366i	$-0.311298\pi$
$151$	13.7310			1.11741			0.558706	+	0.829366i	$0.311298\pi$
$152$	−11.7026	+	20.2695i	−0.949207	+	1.64407i
$153$	−1.91772	+	0.111492i	−0.155038	+	0.00901361i
$154$	32.6007	−	11.3101i	2.62704	−	0.911394i
$155$	5.61264	+	3.24046i	0.450818	+	0.260280i
$156$	−0.235729	+	0.145383i	−0.0188734	+	0.0116399i
$157$	−1.74911	−	1.00985i	−0.139594	−	0.0805945i	0.428577	−	0.903505i	$-0.359015\pi$
$157$	−1.74911	−	1.00985i	−0.139594	−	0.0805945i	−0.568170	+	0.822911i	$0.692349\pi$
$158$	−17.4067	−	10.0498i	−1.38480	−	0.799517i
$159$	−8.95400	−	4.82856i	−0.710099	−	0.382930i
$160$	3.52292	+	2.03396i	0.278511	+	0.160799i
$161$	−15.6945	−	3.01287i	−1.23690	−	0.237448i
$162$	−19.3885	−	8.36820i	−1.52330	−	0.657468i
$163$	4.14847	−	7.18537i	0.324934	−	0.562801i	−0.656565	−	0.754269i	$-0.727991\pi$
$163$	4.14847	−	7.18537i	0.324934	−	0.562801i	0.981499	+	0.191468i	$0.0613247\pi$
$164$	−4.07190			−0.317962
$165$	8.19454	−	5.05387i	0.637944	−	0.393444i
$166$		−	3.40482i		−	0.264266i
$167$	1.67285	+	2.89747i	0.129449	+	0.224213i	0.923463	−	0.383687i	$-0.125346\pi$
$167$	1.67285	+	2.89747i	0.129449	+	0.224213i	−0.794014	+	0.607899i	$0.792012\pi$
$168$	5.74721	+	15.1322i	0.443407	+	1.16748i
$169$	−6.49896	+	11.2565i	−0.499920	+	0.865887i
$170$	1.30114	+	0.751211i	0.0997925	+	0.0576152i
$171$	16.6093	−	10.9216i	1.27015	−	0.835196i
$172$	7.29994	+	12.6439i	0.556615	+	0.964086i
$173$	6.73971	+	11.6735i	0.512411	+	0.887522i	0.999896	+	0.0143905i	$0.00458081\pi$
$173$	6.73971	+	11.6735i	0.512411	+	0.887522i	−0.487486	+	0.873131i	$0.662086\pi$
$174$	−14.6799	−	23.8025i	−1.11288	−	1.80447i
$175$	0.498797	−	2.59831i	0.0377055	−	0.196414i
$176$	6.14788	−	3.54948i	0.463414	−	0.267552i
$177$	5.12159	−	0.148754i	0.384962	−	0.0111810i
$178$			43.3723i			3.25089i
$179$	17.5857	−	10.1531i	1.31442	−	0.758881i	0.331596	−	0.943422i	$-0.392413\pi$
$179$	17.5857	−	10.1531i	1.31442	−	0.758881i	0.982825	+	0.184541i	$0.0590797\pi$
$180$	5.77785	+	8.78681i	0.430656	+	0.654930i
$181$			7.86227i			0.584398i	0.956358	+	0.292199i	$0.0943870\pi$
$181$			7.86227i			0.584398i	−0.956358	+	0.292199i	$0.905613\pi$
$182$	−0.214145	−	0.185282i	−0.0158735	−	0.0137340i
$183$	10.1947	+	5.49762i	0.753613	+	0.406396i
$184$	−21.3358			−1.57290
$185$	−3.67259	+	6.36111i	−0.270014	+	0.467678i
$186$	−13.8260	−	22.4179i	−1.01377	−	1.64376i
$187$	−3.08239	+	1.77962i	−0.225407	+	0.130139i
$188$	−19.5768			−1.42778
$189$	1.40741	−	13.6755i	0.102374	−	0.994746i
$190$	−15.5473			−1.12792
$191$	1.43930	−	0.830978i	0.104144	−	0.0601274i	−0.447023	−	0.894522i	$-0.647516\pi$
$191$	1.43930	−	0.830978i	0.104144	−	0.0601274i	0.551167	+	0.834395i	$0.314183\pi$
$192$	−11.0006	−	17.8367i	−0.793898	−	1.28726i
$193$	−5.55555	+	9.62250i	−0.399897	+	0.692643i	−0.993713	−	0.111959i	$-0.964288\pi$
$193$	−5.55555	+	9.62250i	−0.399897	+	0.692643i	0.593815	+	0.804601i	$0.297621\pi$
$194$	14.8993			1.06970
$195$	−0.0695408	−	0.0375008i	−0.00497992	−	0.00268549i
$196$	−19.2657	+	15.1968i	−1.37612	+	1.08548i
$197$		−	13.1636i		−	0.937866i	−0.883234	−	0.468933i	$-0.844639\pi$
$197$		−	13.1636i		−	0.937866i	0.883234	−	0.468933i	$-0.155361\pi$
$198$	−39.0611	+	2.27093i	−2.77595	+	0.161388i
$199$	−8.32489	+	4.80638i	−0.590136	+	0.340715i	−0.765151	−	0.643850i	$-0.777336\pi$
$199$	−8.32489	+	4.80638i	−0.590136	+	0.340715i	0.175015	+	0.984566i	$0.444003\pi$
$200$		−	3.53226i		−	0.249769i
$201$	6.06467	−	0.176145i	0.427769	−	0.0124243i
$202$	22.8097	−	13.1692i	1.60488	−	0.926579i
$203$	11.9122	−	13.7679i	0.836074	−	0.966319i
$204$	−2.04080	−	3.30903i	−0.142884	−	0.231678i
$205$	−0.580801	−	1.00598i	−0.0405649	−	0.0702605i
$206$	−12.5979	−	21.8202i	−0.877737	−	1.52028i
$207$	16.1925	+	8.13431i	1.12546	+	0.565374i
$208$	−0.0504515	−	0.0291282i	−0.00349818	−	0.00201967i
$209$	18.4158	−	31.8971i	1.27385	−	2.20637i
$210$	−6.79629	+	8.33212i	−0.468989	+	0.574971i
$211$	5.40390	+	9.35982i	0.372020	+	0.644357i	0.989876	−	0.141934i	$-0.0453321\pi$
$211$	5.40390	+	9.35982i	0.372020	+	0.644357i	−0.617857	+	0.786291i	$0.711999\pi$
$212$		−	20.5886i		−	1.41403i
$213$	−11.3170	+	6.97964i	−0.775431	+	0.478237i
$214$	4.20096			0.287172
$215$	−2.08247	+	3.60695i	−0.142024	+	0.245992i
$216$	−1.59679	−	18.2846i	−0.108648	−	1.24411i
$217$	11.2193	−	12.9670i	0.761614	−	0.880259i
$218$	−37.1698	−	21.4600i	−2.51745	−	1.45345i
$219$	6.63194	+	3.57636i	0.448145	+	0.241668i
$220$	16.8745	+	9.74251i	1.13768	+	0.656840i
$221$	0.0252951	+	0.0146041i	0.00170153	+	0.000982381i
$222$	25.4075	−	15.6697i	1.70524	−	1.05168i
$223$	4.21977	+	2.43629i	0.282577	+	0.163146i	0.634589	−	0.772849i	$-0.281169\pi$
$223$	4.21977	+	2.43629i	0.282577	+	0.163146i	−0.352012	+	0.935995i	$0.614503\pi$
$224$	7.04208	−	8.13910i	0.470518	−	0.543816i
$225$	−1.34668	+	2.68076i	−0.0897786	+	0.178717i
$226$	−7.04520	+	12.2027i	−0.468640	+	0.811708i
$227$	6.75905			0.448614			0.224307	−	0.974519i	$-0.427988\pi$
$227$	6.75905			0.448614			0.224307	+	0.974519i	$0.427988\pi$
$228$	35.4104	+	19.0955i	2.34511	+	1.26463i
$229$		−	7.42469i		−	0.490638i	−0.969442	−	0.245319i	$-0.921107\pi$
$229$		−	7.42469i		−	0.490638i	0.969442	−	0.245319i	$-0.0788926\pi$
$230$	−7.08634	−	12.2739i	−0.467259	−	0.809317i
$231$	−9.04410	−	23.8128i	−0.595058	−	1.56677i
$232$	12.1531	−	21.0498i	0.797890	−	1.38199i
$233$	−16.5989	−	9.58336i	−1.08743	−	0.627827i	−0.154538	−	0.987987i	$-0.549389\pi$
$233$	−16.5989	−	9.58336i	−1.08743	−	0.627827i	−0.932891	+	0.360160i	$0.882722\pi$
$234$	0.176413	+	0.268285i	0.0115325	+	0.0175383i
$235$	−2.79236	−	4.83651i	−0.182154	−	0.315499i
$236$	5.18486	+	8.98044i	0.337506	+	0.584577i
$237$	−7.04242	+	13.0593i	−0.457454	+	0.848295i
$238$	2.60088	−	3.00605i	0.168590	−	0.194853i
$239$	6.68576	−	3.86002i	0.432466	−	0.249684i	−0.267931	−	0.963438i	$-0.586340\pi$
$239$	6.68576	−	3.86002i	0.432466	−	0.249684i	0.700396	+	0.713754i	$0.253007\pi$
$240$	−1.04994	+	1.94699i	−0.0677734	+	0.125678i
$241$		−	19.1353i		−	1.23262i	−0.787505	−	0.616308i	$-0.788628\pi$
$241$		−	19.1353i		−	1.23262i	0.787505	−	0.616308i	$-0.211372\pi$
$242$	−40.4317	+	23.3432i	−2.59905	+	1.50056i
$243$	−5.75916	+	14.4856i	−0.369450	+	0.929250i
$244$			23.4414i			1.50068i
$245$	−6.50240	−	2.59206i	−0.415423	−	0.165600i
$246$	0.137054	+	4.71879i	0.00873827	+	0.300859i
$247$	−0.302252			−0.0192318
$248$	11.4461	−	19.8253i	0.726831	−	1.25891i
$249$	−2.51233	+	0.0729692i	−0.159213	+	0.00462424i
$250$	2.03201	−	1.17318i	0.128516	−	0.0741985i
$251$	10.1633			0.641501			0.320751	−	0.947164i	$-0.396065\pi$
$251$	10.1633			0.641501			0.320751	+	0.947164i	$0.396065\pi$
$252$	25.7128	−	10.6298i	1.61976	−	0.669615i
$253$	33.5751			2.11085
$254$	−31.8606	+	18.3947i	−1.99911	+	1.15419i
$255$	0.526414	−	0.976173i	0.0329653	−	0.0611303i
$256$	11.6613	−	20.1980i	0.728834	−	1.26238i
$257$	−2.98376			−0.186122			−0.0930610	−	0.995660i	$-0.529665\pi$
$257$	−2.98376			−0.186122			−0.0930610	+	0.995660i	$0.529665\pi$
$258$	14.4068	−	8.88522i	0.896930	−	0.553170i
$259$	14.6962	+	12.7154i	0.913180	+	0.790097i
$260$		−	0.159900i		−	0.00991660i
$261$	−17.2487	+	11.3420i	−1.06767	+	0.702054i
$262$	−32.2771	+	18.6352i	−1.99409	+	1.15129i
$263$		−	8.29143i		−	0.511272i	−0.966773	−	0.255636i	$-0.917715\pi$
$263$		−	8.29143i		−	0.511272i	0.966773	−	0.255636i	$-0.0822848\pi$
$264$	−17.8516	−	28.9453i	−1.09869	−	1.78146i
$265$	5.08648	−	2.93668i	0.312460	−	0.180399i
$266$	−7.75496	+	40.3967i	−0.475487	+	2.47688i
$267$	32.0033	−	0.929518i	1.95857	−	0.0568856i
$268$	6.13959	+	10.6341i	0.375035	+	0.649580i
$269$	−10.8332	−	18.7636i	−0.660510	−	1.14404i	−0.980482	−	0.196609i	$-0.937007\pi$
$269$	−10.8332	−	18.7636i	−0.660510	−	1.14404i	0.319972	−	0.947427i	$-0.396326\pi$
$270$	9.98825	−	6.99150i	0.607866	−	0.425489i
$271$	19.4905	+	11.2529i	1.18396	+	0.683562i	0.956928	−	0.290324i	$-0.0937632\pi$
$271$	19.4905	+	11.2529i	1.18396	+	0.683562i	0.227036	+	0.973886i	$0.427097\pi$
$272$	0.408884	−	0.708208i	0.0247922	−	0.0429414i
$273$	−0.132125	+	0.161983i	−0.00799659	+	0.00980366i
$274$	12.6167	+	21.8527i	0.762201	+	1.32017i
$275$			5.55854i			0.335193i
$276$	1.06472	+	36.6585i	0.0640888	+	2.20658i
$277$	5.90124			0.354571			0.177285	−	0.984159i	$-0.443268\pi$
$277$	5.90124			0.354571			0.177285	+	0.984159i	$0.443268\pi$
$278$	−6.93363	+	12.0094i	−0.415851	+	0.720276i
$279$	−16.2453	+	10.6823i	−0.972581	+	0.639530i
$280$	−9.17790	−	1.76188i	−0.548484	−	0.105293i
$281$	11.9850	+	6.91952i	0.714963	+	0.412784i	0.812896	−	0.582409i	$-0.197890\pi$
$281$	11.9850	+	6.91952i	0.714963	+	0.412784i	−0.0979331	+	0.995193i	$0.531223\pi$
$282$	0.658927	+	22.6869i	0.0392385	+	1.35098i
$283$	−16.8407	−	9.72300i	−1.00108	−	0.577972i	−0.0925107	−	0.995712i	$-0.529489\pi$
$283$	−16.8407	−	9.72300i	−1.00108	−	0.577972i	−0.908567	+	0.417739i	$0.862823\pi$
$284$	−23.3045	−	13.4549i	−1.38287	−	0.798399i
$285$	0.333196	+	11.4720i	0.0197369	+	0.679540i
$286$	0.515224	+	0.297465i	0.0304658	+	0.0175895i
$287$	−2.90354	+	1.00732i	−0.171391	+	0.0594603i
$288$	−10.1968	+	6.70500i	−0.600852	+	0.395096i
$289$	8.29500	−	14.3674i	0.487941	−	0.845138i
$290$	16.1458			0.948114
$291$	−0.319308	−	10.9938i	−0.0187182	−	0.644467i
$292$			15.2493i			0.892399i
$293$	10.0926	+	17.4810i	0.589619	+	1.02125i	0.994282	+	0.106784i	$0.0340553\pi$
$293$	10.0926	+	17.4810i	0.589619	+	1.02125i	−0.404664	+	0.914466i	$0.632611\pi$
$294$	18.2594	+	21.8149i	1.06491	+	1.27227i
$295$	−1.47910	+	2.56187i	−0.0861164	+	0.149158i
$296$	22.4691	+	12.9725i	1.30599	+	0.754013i
$297$	2.51278	+	28.7735i	0.145807	+	1.66961i
$298$	−8.42850	−	14.5986i	−0.488250	−	0.845674i
$299$	−0.137764	−	0.238614i	−0.00796710	−	0.0137994i
$300$	−6.06901	+	0.176271i	−0.350394	+	0.0101770i
$301$	8.33323	+	7.21004i	0.480320	+	0.415580i
$302$	27.9015	−	16.1089i	1.60555	−	0.926965i
$303$	−10.2060	−	16.5484i	−0.586321	−	0.950683i
$304$			8.46241i			0.485352i
$305$	−5.79128	+	3.34359i	−0.331607	+	0.191454i
$306$	−3.76602	+	2.47639i	−0.215289	+	0.141566i
$307$		−	14.7616i		−	0.842487i	−0.906947	−	0.421244i	$-0.861594\pi$
$307$		−	14.7616i		−	0.842487i	0.906947	−	0.421244i	$-0.138406\pi$
$308$	33.7310	−	38.9857i	1.92200	−	2.22141i
$309$	−15.8306	+	9.76329i	−0.900569	+	0.555414i
$310$	15.2066			0.863676
$311$	−4.30278	+	7.45264i	−0.243988	+	0.422600i	−0.961847	−	0.273589i	$-0.911789\pi$
$311$	−4.30278	+	7.45264i	−0.243988	+	0.422600i	0.717858	+	0.696189i	$0.245123\pi$
$312$	−0.132463	+	0.245636i	−0.00749922	+	0.0139064i
$313$	15.3880	−	8.88424i	0.869779	−	0.502167i	0.00250423	−	0.999997i	$-0.499203\pi$
$313$	15.3880	−	8.88424i	0.869779	−	0.502167i	0.867275	+	0.497830i	$0.165870\pi$
$314$	−4.73893			−0.267434
$315$	6.29371	+	4.83624i	0.354610	+	0.272491i
$316$	−30.0283			−1.68922
$317$	21.4708	−	12.3962i	1.20592	−	0.696238i	0.244054	−	0.969762i	$-0.421523\pi$
$317$	21.4708	−	12.3962i	1.20592	−	0.696238i	0.961865	+	0.273524i	$0.0881892\pi$
$318$	−23.8594	+	0.692983i	−1.33797	+	0.0388605i
$319$	−19.1247	+	33.1250i	−1.07078	+	1.85464i
$320$	12.0991			0.676358
$321$	−0.0900313	−	3.09978i	−0.00502506	−	0.173013i
$322$	−35.4260	+	12.2903i	−1.97421	+	0.684912i
$323$		−	4.24284i		−	0.236078i
$324$	−31.3362	+	3.65600i	−1.74090	+	0.203111i
$325$	0.0395039	−	0.0228076i	0.00219128	−	0.00126514i
$326$		−	19.4677i		−	1.07821i
$327$	−15.0382	+	27.8865i	−0.831613	+	1.54213i
$328$	−3.55337	+	2.05154i	−0.196202	+	0.113277i
$329$	−13.9596	+	4.84297i	−0.769616	+	0.267002i
$330$	10.7223	−	19.8832i	0.590242	−	1.09453i
$331$	4.28292	+	7.41823i	0.235410	+	0.407743i	0.959392	−	0.282077i	$-0.0910232\pi$
$331$	4.28292	+	7.41823i	0.235410	+	0.407743i	−0.723981	+	0.689819i	$0.757690\pi$
$332$	−2.54337	−	4.40524i	−0.139586	−	0.241769i
$333$	−12.1068	−	18.4117i	−0.663448	−	1.00895i
$334$	6.79851	+	3.92512i	0.371998	+	0.214773i
$335$	−1.75146	+	3.03361i	−0.0956923	+	0.165744i
$336$	4.53518	+	3.69922i	0.247414	+	0.201809i
$337$	−9.72589	−	16.8457i	−0.529803	−	0.917646i	−0.999396	−	0.0347626i	$-0.988932\pi$
$337$	−9.72589	−	16.8457i	−0.529803	−	0.917646i	0.469592	−	0.882883i	$-0.344401\pi$
$338$			30.4978i			1.65886i
$339$	9.15501	+	4.93696i	0.497232	+	0.268139i
$340$	2.24459			0.121730
$341$	−18.0122	+	31.1981i	−0.975416	+	1.68947i
$342$	20.9372	−	41.6786i	1.13216	−	2.25372i
$343$	−9.97834	+	15.6023i	−0.538780	+	0.842447i
$344$	12.7407	+	7.35584i	0.686932	+	0.396600i
$345$	−8.90472	+	5.49187i	−0.479414	+	0.295672i
$346$	27.3903	+	15.8138i	1.47251	+	0.850156i
$347$	8.37116	+	4.83309i	0.449387	+	0.259454i	0.707571	−	0.706642i	$-0.249791\pi$
$347$	8.37116	+	4.83309i	0.449387	+	0.259454i	−0.258184	+	0.966096i	$0.583124\pi$
$348$	−36.7735	−	19.8306i	−1.97127	−	1.06303i
$349$	22.7845	+	13.1546i	1.21962	+	0.704151i	0.964838	−	0.262847i	$-0.0846613\pi$
$349$	22.7845	+	13.1546i	1.21962	+	0.704151i	0.254787	+	0.966997i	$0.417995\pi$
$350$	−2.03473	−	5.86497i	−0.108761	−	0.313496i
$351$	0.194180	−	0.135920i	0.0103645	−	0.00725490i
$352$	−11.3058	+	19.5823i	−0.602604	+	1.04374i
$353$	25.3336			1.34837			0.674186	−	0.738562i	$-0.264495\pi$
$353$	25.3336			1.34837			0.674186	+	0.738562i	$0.264495\pi$
$354$	10.2326	−	6.31082i	0.543857	−	0.335416i
$355$		−	7.67660i		−	0.407432i
$356$	32.3987	+	56.1162i	1.71713	+	2.97415i
$357$	−2.27382	−	1.85470i	−0.120344	−	0.0981611i
$358$	23.8229	−	41.2625i	1.25908	−	2.18079i
$359$	−3.18127	−	1.83671i	−0.167901	−	0.0969378i	0.413695	−	0.910416i	$-0.364238\pi$
$359$	−3.18127	−	1.83671i	−0.167901	−	0.0969378i	−0.581596	+	0.813478i	$0.697571\pi$
$360$	9.46913	+	4.75682i	0.499067	+	0.250707i
$361$	12.4528	+	21.5689i	0.655411	+	1.13521i
$362$	9.22387	+	15.9762i	0.484796	+	0.839691i
$363$	18.0909	+	29.3332i	0.949524	+	1.53959i
$364$	−0.415470	−	0.0797579i	−0.0217766	−	0.00418045i
$365$	−3.76739	+	2.17511i	−0.197194	+	0.113850i
$366$	27.1654	−	0.789004i	1.41996	−	0.0412419i
$367$		−	34.4340i		−	1.79744i	−0.438523	−	0.898720i	$-0.644498\pi$
$367$		−	34.4340i		−	1.79744i	0.438523	−	0.898720i	$-0.355502\pi$
$368$	−6.68069	+	3.85710i	−0.348255	+	0.201065i
$369$	3.47893	−	0.202258i	0.181106	−	0.0105291i
$370$			17.2344i			0.895976i
$371$	−5.09328	−	14.6811i	−0.264430	−	0.762202i
$372$	−34.6343	−	18.6770i	−1.79571	−	0.968358i
$373$	6.06138			0.313847			0.156923	−	0.987611i	$-0.449842\pi$
$373$	6.06138			0.313847			0.156923	+	0.987611i	$0.449842\pi$
$374$	−4.17564	+	7.23241i	−0.215917	+	0.373979i
$375$	−0.909209	−	1.47423i	−0.0469513	−	0.0761287i
$376$	−17.0838	+	9.86335i	−0.881030	+	0.508663i
$377$	0.313887			0.0161660
$378$	−13.1840	−	29.4399i	−0.678110	−	1.51422i
$379$	−23.3855			−1.20123			−0.600616	−	0.799537i	$-0.705078\pi$
$379$	−23.3855			−1.20123			−0.600616	+	0.799537i	$0.705078\pi$
$380$	−20.1155	+	11.6137i	−1.03190	+	0.595769i
$381$	14.2558	+	23.1149i	0.730346	+	1.18421i
$382$	1.94978	−	3.37711i	0.0997592	−	0.172788i
$383$	7.62794			0.389770			0.194885	−	0.980826i	$-0.437567\pi$
$383$	7.62794			0.389770			0.194885	+	0.980826i	$0.437567\pi$
$384$	−30.8759	−	16.6502i	−1.57563	−	0.849677i
$385$	14.4428	+	2.77259i	0.736073	+	0.141304i
$386$			26.0707i			1.32696i
$387$	−6.86493	−	10.4400i	−0.348964	−	0.530696i
$388$	19.2770	−	11.1296i	0.978643	−	0.565020i
$389$			28.4591i			1.44293i	0.692449	+	0.721467i	$0.256532\pi$
$389$			28.4591i			1.44293i	−0.692449	+	0.721467i	$0.743468\pi$
$390$	−0.185303	+	0.00538201i	−0.00938317	+	0.000272529i
$391$	3.34953	−	1.93385i	0.169393	−	0.0977991i
$392$	−9.15582	+	22.9682i	−0.462439	+	1.16007i
$393$	14.4422	+	23.4171i	0.728511	+	1.18124i
$394$	−15.4433	−	26.7485i	−0.778020	−	1.34757i
$395$	−4.28313	−	7.41859i	−0.215508	−	0.373270i
$396$	−48.8419	+	32.1164i	−2.45440	+	1.61391i
$397$	−4.05711	−	2.34237i	−0.203620	−	0.117560i	0.394723	−	0.918800i	$-0.370841\pi$
$397$	−4.05711	−	2.34237i	−0.203620	−	0.117560i	−0.598343	+	0.801240i	$0.704174\pi$
$398$	−11.2775	+	19.5332i	−0.565291	+	0.979112i
$399$	29.9739	+	4.85644i	1.50057	+	0.243126i
$400$	−0.638563	−	1.10602i	−0.0319282	−	0.0553012i
$401$		−	31.7700i		−	1.58652i	−0.608885	−	0.793258i	$-0.708383\pi$
$401$		−	31.7700i		−	1.58652i	0.608885	−	0.793258i	$-0.291617\pi$
$402$	12.1168	−	7.47288i	0.604332	−	0.372713i
$403$	0.295628			0.0147263
$404$	19.6745	−	34.0772i	0.978842	−	1.69540i
$405$	−5.37291	−	7.22024i	−0.266982	−	0.358777i
$406$	8.05348	−	41.9517i	0.399688	−	2.08203i
$407$	−35.3585	−	20.4142i	−1.75265	−	1.01190i
$408$	−3.44810	−	1.85943i	−0.170706	−	0.0920556i
$409$	−18.3401	−	10.5887i	−0.906862	−	0.523577i	−0.0274415	−	0.999623i	$-0.508736\pi$
$409$	−18.3401	−	10.5887i	−0.906862	−	0.523577i	−0.879420	+	0.476047i	$0.842069\pi$
$410$	−2.36039	−	1.36277i	−0.116571	−	0.0673025i
$411$	15.8542	−	9.77784i	0.782028	−	0.482305i
$412$	−32.5989	−	18.8210i	−1.60603	−	0.927244i
$413$	5.91876	+	5.12101i	0.291243	+	0.251988i
$414$	42.4464	−	2.46774i	2.08612	−	0.121283i
$415$	0.725553	−	1.25670i	0.0356160	−	0.0616888i
$416$	0.185559			0.00909777
$417$	9.01002	+	4.85877i	0.441222	+	0.237935i
$418$		−	86.4204i		−	4.22696i
$419$	4.78529	+	8.28837i	0.233777	+	0.404913i	0.958917	−	0.283688i	$-0.0915582\pi$
$419$	4.78529	+	8.28837i	0.233777	+	0.404913i	−0.725140	+	0.688602i	$0.758225\pi$
$420$	−2.56920	+	15.8571i	−0.125364	+	0.773745i
$421$	9.69705	−	16.7958i	0.472605	−	0.818576i	−0.526903	−	0.849925i	$-0.676647\pi$
$421$	9.69705	−	16.7958i	0.472605	−	0.818576i	0.999509	+	0.0313489i	$0.00998031\pi$
$422$	21.9615	+	12.6795i	1.06907	+	0.617228i
$423$	16.7259	−	0.972410i	0.813242	−	0.0472802i
$424$	−10.3731	−	17.9668i	−0.503763	−	0.872544i
$425$	0.320160	+	0.554533i	0.0155300	+	0.0268988i
$426$	−14.8080	+	27.4596i	−0.717448	+	1.33042i
$427$	5.79901	+	16.7153i	0.280634	+	0.808910i
$428$	5.43530	−	3.13807i	0.262725	−	0.151685i
$429$	0.208450	−	0.386545i	0.0100640	−	0.0186626i
$430$			9.77248i			0.471271i
$431$	10.4849	−	6.05345i	0.505039	−	0.291585i	−0.225753	−	0.974185i	$-0.572484\pi$
$431$	10.4849	−	6.05345i	0.505039	−	0.291585i	0.730792	+	0.682600i	$0.239151\pi$
$432$	−3.80548	−	5.43661i	−0.183091	−	0.261569i
$433$		−	31.4855i		−	1.51310i	−0.653937	−	0.756549i	$-0.726884\pi$
$433$		−	31.4855i		−	1.51310i	0.653937	−	0.756549i	$-0.273116\pi$
$434$	7.58500	−	39.5114i	0.364092	−	1.89661i
$435$	−0.346023	−	11.9136i	−0.0165905	−	0.571212i
$436$	−64.1216			−3.07087
$437$	−20.0118	+	34.6615i	−0.957296	+	1.65808i
$438$	17.6719	−	0.513270i	0.844396	−	0.0245250i
$439$	−19.5592	+	11.2925i	−0.933509	+	0.538962i	−0.887920	−	0.459998i	$-0.847850\pi$
$439$	−19.5592	+	11.2925i	−0.933509	+	0.538962i	−0.0455896	+	0.998960i	$0.514517\pi$
$440$	19.6342			0.936024
$441$	15.7053	−	13.9407i	0.747873	−	0.663842i
$442$	0.0685332			0.00325979
$443$	7.38535	−	4.26393i	0.350889	−	0.202586i	−0.314188	−	0.949361i	$-0.601732\pi$
$443$	7.38535	−	4.26393i	0.350889	−	0.202586i	0.665077	+	0.746775i	$0.268399\pi$
$444$	21.1677	−	39.2530i	1.00457	−	1.86286i
$445$	−9.24246	+	16.0084i	−0.438135	+	0.758871i
$446$	11.4328			0.541360
$447$	−10.5913	+	6.53204i	−0.500951	+	0.308955i
$448$	6.03498	−	31.4371i	0.285126	−	1.48526i
$449$			9.99820i			0.471844i	0.971772	+	0.235922i	$0.0758110\pi$
$449$			9.99820i			0.471844i	−0.971772	+	0.235922i	$0.924189\pi$
$450$	0.408548	+	7.02722i	0.0192591	+	0.331266i
$451$	5.59177	−	3.22841i	0.263306	−	0.152020i
$452$			21.0508i			0.990146i
$453$	−12.4843	−	20.2426i	−0.586565	−	0.951078i
$454$	13.7345	−	7.92959i	0.644590	−	0.372154i
$455$	−0.0395567	−	0.114020i	−0.00185445	−	0.00534532i
$456$	40.5219	−	1.17694i	1.89761	−	0.0551151i
$457$	−16.9345	−	29.3314i	−0.792162	−	1.37206i	−0.924626	−	0.380877i	$-0.875622\pi$
$457$	−16.9345	−	29.3314i	−0.792162	−	1.37206i	0.132464	−	0.991188i	$-0.457711\pi$
$458$	−8.71051	−	15.0871i	−0.407016	−	0.704972i
$459$	1.90797	+	2.72578i	0.0890565	+	0.127229i
$460$	−18.3370	−	10.5868i	−0.854965	−	0.493614i
$461$	−17.8667	+	30.9461i	−0.832136	+	1.44130i	0.0642045	+	0.997937i	$0.479549\pi$
$461$	−17.8667	+	30.9461i	−0.832136	+	1.44130i	−0.896341	+	0.443366i	$0.853784\pi$
$462$	−46.3144	−	37.7775i	−2.15474	−	1.75757i
$463$	−2.36387	−	4.09435i	−0.109858	−	0.190280i	0.805854	−	0.592114i	$-0.201706\pi$
$463$	−2.36387	−	4.09435i	−0.109858	−	0.190280i	−0.915713	+	0.401833i	$0.868373\pi$
$464$		−	8.78816i		−	0.407980i
$465$	−0.325894	−	11.2205i	−0.0151130	−	0.520340i
$466$	−44.9721			−2.08329
$467$	14.7227	−	25.5005i	0.681285	−	1.18002i	−0.293304	−	0.956019i	$-0.594755\pi$
$467$	14.7227	−	25.5005i	0.681285	−	1.18002i	0.974589	−	0.224001i	$-0.0719120\pi$
$468$	0.428654	+	0.215334i	0.0198145	+	0.00995384i
$469$	7.00863	+	6.06398i	0.323629	+	0.280009i
$470$	−11.3482	−	6.55189i	−0.523454	−	0.302216i
$471$	0.101561	+	3.49674i	0.00467967	+	0.161121i
$472$	9.04920	+	5.22456i	0.416523	+	0.240480i
$473$	−20.0494	−	11.5755i	−0.921872	−	0.532243i
$474$	1.01071	+	34.7988i	0.0464234	+	1.59836i
$475$	−5.73840	−	3.31307i	−0.263296	−	0.152014i
$476$	1.11959	−	5.83213i	0.0513165	−	0.267315i
$477$	1.02267	+	17.5904i	0.0468247	+	0.805408i
$478$	9.05702	−	15.6872i	0.414258	−	0.717516i
$479$	−35.7156			−1.63189			−0.815944	−	0.578131i	$-0.803782\pi$
$479$	−35.7156			−1.63189			−0.815944	+	0.578131i	$0.803782\pi$
$480$	−0.204556	−	7.04287i	−0.00933667	−	0.321462i
$481$			0.335051i			0.0152770i
$482$	−22.4492	−	38.8832i	−1.02253	−	1.77108i
$483$	9.82791	+	25.8765i	0.447186	+	1.17742i
$484$	−34.8743	+	60.4041i	−1.58520	+	2.74564i
$485$	5.49921	+	3.17497i	0.249706	+	0.144168i
$486$	5.29154	+	36.1914i	0.240029	+	1.64167i
$487$	−5.47609	−	9.48486i	−0.248145	−	0.429800i	0.714866	−	0.699261i	$-0.246488\pi$
$487$	−5.47609	−	9.48486i	−0.248145	−	0.429800i	−0.963011	+	0.269461i	$0.913154\pi$
$488$	11.8104	+	20.4563i	0.534634	+	0.926013i
$489$	−14.3647	+	0.417214i	−0.649593	+	0.0188671i
$490$	−16.2539	+	2.36141i	−0.734276	+	0.106678i
$491$	−2.96611	+	1.71249i	−0.133859	+	0.0772834i	−0.565434	−	0.824794i	$-0.691291\pi$
$491$	−2.96611	+	1.71249i	−0.133859	+	0.0772834i	0.431575	+	0.902077i	$0.357958\pi$
$492$	3.70221	+	6.00290i	0.166909	+	0.270632i
$493$			4.40617i			0.198444i
$494$	−0.614179	+	0.354597i	−0.0276332	+	0.0159541i
$495$	−14.9011	−	7.48557i	−0.669754	−	0.336451i
$496$		−	8.27695i		−	0.371646i
$497$	−19.9462	−	3.82907i	−0.894708	−	0.171757i
$498$	−5.01948	+	3.09570i	−0.224928	+	0.138721i
$499$	39.8402			1.78349			0.891746	−	0.452536i	$-0.149481\pi$
$499$	39.8402			1.78349			0.891746	+	0.452536i	$0.149481\pi$
$500$	1.75271	−	3.03578i	0.0783836	−	0.135764i
$501$	2.75054	−	5.10056i	0.122885	−	0.227876i
$502$	20.6519	−	11.9234i	0.921740	−	0.532167i
$503$	−13.7558			−0.613339			−0.306669	−	0.951816i	$-0.599215\pi$
$503$	−13.7558			−0.613339			−0.306669	+	0.951816i	$0.599215\pi$
$504$	17.0829	−	22.2310i	0.760931	−	0.990248i
$505$	11.2252			0.499514
$506$	68.2250	−	39.3897i	3.03297	−	1.75109i
$507$	22.5036	−	0.653603i	0.999418	−	0.0290275i
$508$	−27.4813	+	47.5991i	−1.21929	+	2.11187i
$509$	−10.0525			−0.445570			−0.222785	−	0.974868i	$-0.571515\pi$
$509$	−10.0525			−0.445570			−0.222785	+	0.974868i	$0.571515\pi$
$510$	−0.0755496	−	2.60117i	−0.00334539	−	0.115182i
$511$	3.77243	+	10.8738i	0.166882	+	0.481028i
$512$		−	14.2175i		−	0.628332i
$513$	−31.2022	−	14.5558i	−1.37761	−	0.642656i
$514$	−6.06304	+	3.50050i	−0.267429	+	0.154400i
$515$		−	10.7382i		−	0.473183i
$516$	12.0027	−	22.2577i	0.528391	−	0.979840i
$517$	26.8839	−	15.5215i	1.18235	−	0.682633i
$518$	44.7804	+	8.59650i	1.96754	+	0.377708i
$519$	11.0816	−	20.5495i	0.486428	−	0.902024i
$520$	−0.0805623	−	0.139538i	−0.00353289	−	0.00611915i
$521$	16.0928	+	27.8735i	0.705038	+	1.22116i	0.966678	+	0.255996i	$0.0824035\pi$
$521$	16.0928	+	27.8735i	0.705038	+	1.22116i	−0.261640	+	0.965166i	$0.584263\pi$
$522$	−21.7432	+	43.2830i	−0.951675	+	1.89444i
$523$	−13.2068	−	7.62493i	−0.577492	−	0.333415i	0.182644	−	0.983179i	$-0.441534\pi$
$523$	−13.2068	−	7.62493i	−0.577492	−	0.333415i	−0.760136	+	0.649764i	$0.774868\pi$
$524$	−27.8406	+	48.2214i	−1.21622	+	2.10656i
$525$	−4.28400	+	1.62706i	−0.186969	+	0.0710109i
$526$	−9.72735	−	16.8483i	−0.424133	−	0.734619i
$527$			4.14985i			0.180771i
$528$	−10.8224	−	5.83614i	−0.470986	−	0.253985i
$529$	−13.4849			−0.586301
$530$	6.89052	−	11.9347i	0.299305	−	0.518412i
$531$	−4.87589	−	7.41512i	−0.211595	−	0.321789i
$532$	20.1424	+	58.0591i	0.873283	+	2.51718i
$533$	−0.0458878	−	0.0264934i	−0.00198762	−	0.00114755i
$534$	63.9406	−	39.4345i	2.76698	−	1.70650i
$535$	1.55054	+	0.895206i	0.0670358	+	0.0387031i
$536$	10.7155	+	6.18660i	0.462839	+	0.267220i
$537$	−30.9571	−	16.6940i	−1.33590	−	0.720401i
$538$	−44.0262	−	25.4185i	−1.89810	−	1.09587i
$539$	14.4081	−	36.1439i	0.620599	−	1.55683i
$540$	7.70046	−	16.5069i	0.331375	−	0.710344i
$541$	5.21897	−	9.03953i	0.224381	−	0.388640i	−0.731752	−	0.681571i	$-0.761297\pi$
$541$	5.21897	−	9.03953i	0.224381	−	0.388640i	0.956134	+	0.292931i	$0.0946306\pi$
$542$	52.8065			2.26824
$543$	11.5908	−	7.14845i	0.497407	−	0.306769i
$544$			2.60477i			0.111678i
$545$	−9.14606	−	15.8414i	−0.391774	−	0.678573i
$546$	−0.0784444	+	0.484158i	−0.00335711	+	0.0207201i
$547$	0.223525	−	0.387157i	0.00955724	−	0.0165536i	−0.861207	−	0.508254i	$-0.830291\pi$
$547$	0.223525	−	0.387157i	0.00955724	−	0.0165536i	0.870764	+	0.491700i	$0.163624\pi$
$548$	32.6475	+	18.8490i	1.39463	+	0.805191i
$549$	−1.16437	−	20.0277i	−0.0496941	−	0.854763i
$550$	6.52118	+	11.2950i	0.278064	+	0.481621i
$551$	−22.7979	−	39.4871i	−0.971222	−	1.68221i
$552$	19.3987	+	31.4538i	0.825664	+	1.33876i
$553$	−21.4122	+	7.42851i	−0.910539	+	0.315892i
$554$	11.9914	−	6.92322i	0.509465	−	0.294140i
$555$	12.7169	−	0.369354i	0.539800	−	0.0156782i
$556$			20.7174i			0.878613i
$557$	31.9305	−	18.4351i	1.35294	−	0.781120i	0.364280	−	0.931290i	$-0.381315\pi$
$557$	31.9305	−	18.4351i	1.35294	−	0.781120i	0.988660	+	0.150169i	$0.0479819\pi$
$558$	−20.4784	+	40.7651i	−0.866919	+	1.72573i
$559$			0.189985i			0.00803550i
$560$	−3.19230	+	1.10750i	−0.134899	+	0.0468005i
$561$	5.42610	+	2.92609i	0.229090	+	0.123540i
$562$	32.4714			1.36972
$563$	−16.3191	+	28.2655i	−0.687767	+	1.19125i	0.284792	+	0.958589i	$0.408076\pi$
$563$	−16.3191	+	28.2655i	−0.687767	+	1.19125i	−0.972559	+	0.232658i	$0.925258\pi$
$564$	17.7994	+	28.8606i	0.749489	+	1.21525i
$565$	−5.20067	+	3.00261i	−0.218794	+	0.126321i
$566$	−45.6274			−1.91786
$567$	−21.4404	+	10.3590i	−0.900412	+	0.435039i
$568$	−27.1158			−1.13775
$569$	−3.96228	+	2.28762i	−0.166108	+	0.0959022i	−0.580749	−	0.814083i	$-0.697240\pi$
$569$	−3.96228	+	2.28762i	−0.166108	+	0.0959022i	0.414642	+	0.909985i	$0.363907\pi$
$570$	14.1357	+	22.9202i	0.592081	+	0.960023i
$571$	0.453916	−	0.786206i	0.0189958	−	0.0329017i	−0.856371	−	0.516361i	$-0.827286\pi$
$571$	0.453916	−	0.786206i	0.0189958	−	0.0329017i	0.875367	+	0.483459i	$0.160620\pi$
$572$	0.888813			0.0371631
$573$	−2.53367	−	1.36631i	−0.105846	−	0.0570786i
$574$	−4.71825	+	5.45327i	−0.196936	+	0.227615i
$575$		−	6.04027i		−	0.251897i
$576$	−16.2936	+	32.4347i	−0.678898	+	1.35144i
$577$	−1.41559	+	0.817294i	−0.0589319	+	0.0340244i	−0.529176	−	0.848512i	$-0.677499\pi$
$577$	−1.41559	+	0.817294i	−0.0589319	+	0.0340244i	0.470245	+	0.882536i	$0.344166\pi$
$578$		−	38.9261i		−	1.61911i
$579$	19.2369	−	0.558724i	0.799458	−	0.0232198i
$580$	20.8898	−	12.0607i	0.867403	−	0.500795i
$581$	−2.90338	−	2.51205i	−0.120452	−	0.104217i
$582$	−13.5465	−	21.9649i	−0.561522	−	0.910473i
$583$	16.3237	+	28.2734i	0.676057	+	1.17097i
$584$	7.68304	+	13.3074i	0.317927	+	0.550665i
$585$	0.00794250	+	0.136615i	0.000328382	+	0.00564833i
$586$	41.0167	+	23.6810i	1.69438	+	0.978254i
$587$	−13.7267	+	23.7753i	−0.566561	+	0.981312i	0.430342	+	0.902666i	$0.358393\pi$
$587$	−13.7267	+	23.7753i	−0.566561	+	0.981312i	−0.996903	+	0.0786460i	$0.974940\pi$
$588$	39.9200	+	14.5850i	1.64627	+	0.601476i
$589$	−21.4717	−	37.1901i	−0.884726	−	1.53239i
$590$			6.94100i			0.285757i
$591$	−19.4061	+	11.9684i	−0.798259	+	0.492316i
$592$	9.38071			0.385545
$593$	12.8076	−	22.1834i	0.525944	−	0.910961i	−0.473600	−	0.880740i	$-0.657046\pi$
$593$	12.8076	−	22.1834i	0.525944	−	0.910961i	0.999543	−	0.0302209i	$-0.00962106\pi$
$594$	38.8626	+	55.5201i	1.59455	+	2.27802i
$595$	1.60054	−	0.555274i	0.0656158	−	0.0227640i
$596$	−21.8100	−	12.5920i	−0.893373	−	0.515789i
$597$	14.6548	+	7.90277i	0.599779	+	0.323439i
$598$	−0.559876	−	0.323245i	−0.0228950	−	0.0132185i
$599$	3.97627	+	2.29570i	0.162466	+	0.0937998i	0.579029	−	0.815307i	$-0.303432\pi$
$599$	3.97627	+	2.29570i	0.162466	+	0.0937998i	−0.416563	+	0.909107i	$0.636765\pi$
$600$	−5.20735	+	3.21156i	−0.212589	+	0.131111i
$601$	1.61392	+	0.931798i	0.0658333	+	0.0380088i	0.532555	−	0.846395i	$-0.321232\pi$
$601$	1.61392	+	0.931798i	0.0658333	+	0.0380088i	−0.466722	+	0.884404i	$0.654565\pi$
$602$	25.3919	+	4.87449i	1.03490	+	0.198669i
$603$	−5.77372	−	8.78053i	−0.235124	−	0.357571i
$604$	24.0664	−	41.6843i	0.979249	−	1.69611i
$605$	−19.8974			−0.808944
$606$	−40.1531	−	21.6531i	−1.63111	−	0.879596i
$607$			37.1028i			1.50595i	0.658046	+	0.752977i	$0.271383\pi$
$607$			37.1028i			1.50595i	−0.658046	+	0.752977i	$0.728617\pi$
$608$	−13.4773	−	23.3433i	−0.546576	−	0.946698i
$609$	−31.1277	−	5.04338i	−1.26136	−	0.204368i
$610$	−7.84529	+	13.5884i	−0.317646	+	0.550180i
$611$	−0.220618	−	0.127374i	−0.00892526	−	0.00515300i
$612$	−3.02274	+	6.01719i	−0.122187	+	0.243231i
$613$	21.2995	+	36.8918i	0.860278	+	1.49005i	0.871661	+	0.490110i	$0.163043\pi$
$613$	21.2995	+	36.8918i	0.860278	+	1.49005i	−0.0113827	+	0.999935i	$0.503623\pi$
$614$	−17.3180	−	29.9957i	−0.698898	−	1.21053i
$615$	−0.954968	+	1.77088i	−0.0385080	+	0.0714086i
$616$	9.79349	−	51.0157i	0.394591	−	2.05548i
$617$	−0.787957	+	0.454927i	−0.0317220	+	0.0183147i	−0.515777	−	0.856723i	$-0.672497\pi$
$617$	−0.787957	+	0.454927i	−0.0317220	+	0.0183147i	0.484055	+	0.875037i	$0.339163\pi$
$618$	−20.7138	+	38.4112i	−0.833229	+	1.54513i
$619$			33.4500i			1.34447i	0.740337	+	0.672235i	$0.234666\pi$
$619$			33.4500i			1.34447i	−0.740337	+	0.672235i	$0.765334\pi$
$620$	19.6746	−	11.3592i	0.790153	−	0.456195i
$621$	−2.73056	−	31.2672i	−0.109573	−	1.25471i
$622$			20.1918i			0.809616i
$623$	36.9846	+	31.9997i	1.48176	+	1.28204i
$624$	0.00292943	+	0.100860i	0.000117271	+	0.00403765i
$625$	1.00000			0.0400000
$626$	20.8457	−	36.1057i	0.833160	−	1.44308i
$627$	−63.7674	+	1.85209i	−2.54662	+	0.0739652i
$628$	−6.13135	+	3.53994i	−0.244667	+	0.141259i
$629$	−4.70326			−0.187531
$630$	18.4627	+	2.44363i	0.735570	+	0.0973564i
$631$	−25.0870			−0.998697			−0.499348	−	0.866401i	$-0.666427\pi$
$631$	−25.0870			−0.998697			−0.499348	+	0.866401i	$0.666427\pi$
$632$	−26.2044	+	15.1291i	−1.04236	+	0.601804i
$633$	8.88522	−	16.4766i	0.353156	−	0.654886i
$634$	29.0859	−	50.3783i	1.15515	−	2.00078i
$635$	−15.6793			−0.622216
$636$	−30.3522	+	18.7193i	−1.20354	+	0.742270i
$637$	−0.315989	+	0.0459077i	−0.0125199	+	0.00181893i
$638$			89.7471i			3.55312i
$639$	20.5791	+	10.3379i	0.814097	+	0.408962i
$640$	17.5396	−	10.1265i	0.693313	−	0.400284i
$641$			30.3204i			1.19758i	0.800905	+	0.598792i	$0.204352\pi$
$641$			30.3204i			1.19758i	−0.800905	+	0.598792i	$0.795648\pi$
$642$	−3.81955	−	6.19316i	−0.150746	−	0.244424i
$643$	3.01202	−	1.73899i	0.118782	−	0.0685790i	−0.439432	−	0.898276i	$-0.644820\pi$
$643$	3.01202	−	1.73899i	0.118782	−	0.0685790i	0.558214	+	0.829697i	$0.311487\pi$
$644$	−36.6543	+	42.3644i	−1.44438	+	1.66939i
$645$	7.21086	−	0.209435i	0.283927	−	0.00824651i
$646$	−4.97762	−	8.62149i	−0.195842	−	0.339208i
$647$	−14.6521	−	25.3782i	−0.576035	−	0.997721i	−0.995928	−	0.0901479i	$-0.971266\pi$
$647$	−14.6521	−	25.3782i	−0.576035	−	0.997721i	0.419894	−	0.907573i	$-0.362067\pi$
$648$	−25.5038	+	18.9785i	−1.00188	+	0.745546i
$649$	−14.2403	−	8.22163i	−0.558980	−	0.322727i
$650$	0.0535149	−	0.0926905i	0.00209903	−	0.00363562i
$651$	−29.3170	−	4.75000i	−1.14902	−	0.186167i
$652$	−14.5421	−	25.1877i	−0.569514	−	0.986427i
$653$			28.9947i			1.13465i	0.823494	+	0.567325i	$0.192022\pi$
$653$			28.9947i			1.13465i	−0.823494	+	0.567325i	$0.807978\pi$
$654$	2.15824	+	74.3082i	0.0843938	+	2.90568i
$655$	−15.8843			−0.620652
$656$	−0.741757	+	1.28476i	−0.0289607	+	0.0501615i
$657$	−0.757458	−	13.0286i	−0.0295512	−	0.508296i
$658$	−22.6843	+	26.2181i	−0.884326	+	1.02209i
$659$	23.0794	+	13.3249i	0.899047	+	0.519065i	0.876891	−	0.480689i	$-0.159614\pi$
$659$	23.0794	+	13.3249i	0.899047	+	0.519065i	0.0221563	+	0.999755i	$0.492947\pi$
$660$	−0.979808	−	33.7348i	−0.0381390	−	1.31313i
$661$	−10.2516	−	5.91874i	−0.398740	−	0.230212i	0.287200	−	0.957871i	$-0.407275\pi$
$661$	−10.2516	−	5.91874i	−0.398740	−	0.230212i	−0.685940	+	0.727658i	$0.740609\pi$
$662$	17.4059	+	10.0493i	0.676498	+	0.390576i
$663$	−0.00146874	−	0.0505689i	−5.70413e−5	−	0.00196393i
$664$	−4.43898	−	2.56284i	−0.172266	−	0.0994576i
$665$	−11.4707	+	13.2576i	−0.444813	+	0.514107i
$666$	−46.2013	−	23.2093i	−1.79027	−	0.899341i
$667$	20.7822	−	35.9958i	0.804689	−	1.39376i
$668$	11.7281			0.453774
$669$	−0.245019	−	8.43599i	−0.00947296	−	0.326154i
$670$			8.21911i			0.317532i
$671$	−18.5855	−	32.1910i	−0.717486	−	1.24272i
$672$	−18.4016	−	2.98147i	−0.709856	−	0.115013i
$673$	−2.82034	+	4.88498i	−0.108716	+	0.188302i	−0.915250	−	0.402885i	$-0.868007\pi$
$673$	−2.82034	+	4.88498i	−0.108716	+	0.188302i	0.806534	+	0.591187i	$0.201341\pi$
$674$	−39.5262	−	22.8205i	−1.52249	−	0.879012i
$675$	5.17645	−	0.452058i	0.199242	−	0.0173997i
$676$	22.7816	+	39.4589i	0.876215	+	1.51765i
$677$	−9.41239	−	16.3027i	−0.361748	−	0.626565i	0.626501	−	0.779421i	$-0.284486\pi$
$677$	−9.41239	−	16.3027i	−0.361748	−	0.626565i	−0.988249	+	0.152856i	$0.951153\pi$
$678$	24.3950	−	0.708539i	0.936885	−	0.0272113i
$679$	10.9925	−	12.7050i	0.421855	−	0.487572i
$680$	1.95875	−	1.13089i	0.0751148	−	0.0433675i
$681$	−6.14539	−	9.96436i	−0.235492	−	0.381835i
$682$			84.5264i			3.23668i
$683$	−24.2727	+	14.0138i	−0.928769	+	0.536225i	−0.886422	−	0.462878i	$-0.846817\pi$
$683$	−24.2727	+	14.0138i	−0.928769	+	0.536225i	−0.0423467	+	0.999103i	$0.513483\pi$
$684$	−4.04434	−	69.5646i	−0.154639	−	2.65987i
$685$			10.7542i			0.410898i
$686$	−1.97173	+	43.4105i	−0.0752810	+	1.65742i
$687$	−10.9457	+	6.75060i	−0.417603	+	0.257551i
$688$	5.31916			0.202791
$689$	0.133957	−	0.232021i	0.00510336	−	0.00883929i
$690$	−11.6515	+	21.6064i	−0.443566	+	0.822541i
$691$	29.1277	−	16.8169i	1.10807	−	0.639745i	0.169742	−	0.985489i	$-0.445707\pi$
$691$	29.1277	−	16.8169i	1.10807	−	0.639745i	0.938329	+	0.345744i	$0.112373\pi$
$692$	47.2510			1.79621
$693$	−26.8824	+	34.9838i	−1.02118	+	1.32893i
$694$	22.6804			0.860935
$695$	−5.11830	+	2.95505i	−0.194148	+	0.112092i
$696$	−42.0818	+	1.22224i	−1.59511	+	0.0463290i
$697$	0.371898	−	0.644147i	0.0140867	−	0.0243988i
$698$	61.7310			2.33655
$699$	0.963803	+	33.1837i	0.0364544	+	1.25512i
$700$	−7.01365	−	6.06832i	−0.265091	−	0.229361i
$701$			34.5173i			1.30370i	0.758348	+	0.651850i	$0.226007\pi$
$701$			34.5173i			1.30370i	−0.758348	+	0.651850i	$0.773993\pi$
$702$	0.235116	−	0.504000i	0.00887387	−	0.0190222i
$703$	42.1495	−	24.3350i	1.58970	−	0.917814i
$704$			67.2532i			2.53470i
$705$	−4.59127	+	8.51397i	−0.172917	+	0.320655i
$706$	51.4781	−	29.7209i	1.93741	−	1.11856i
$707$	5.59909	−	29.1665i	0.210575	−	1.09692i
$708$	8.52507	−	15.8087i	0.320392	−	0.594129i
$709$	17.6689	+	30.6035i	0.663571	+	1.14934i	0.979671	+	0.200613i	$0.0642933\pi$
$709$	17.6689	+	30.6035i	0.663571	+	1.14934i	−0.316100	+	0.948726i	$0.602373\pi$
$710$	−9.00605	−	15.5989i	−0.337991	−	0.585418i
$711$	25.6554	−	1.49155i	0.962154	−	0.0559376i
$712$	56.5459	+	32.6468i	2.11915	+	1.22349i
$713$	19.5733	−	33.9019i	0.733024	−	1.26963i
$714$	−6.79633	−	1.10116i	−0.254346	−	0.0412098i
$715$	0.126777	+	0.219584i	0.00474119	+	0.00821198i
$716$		−	71.1820i		−	2.66020i
$717$	−11.7693	−	6.34674i	−0.439532	−	0.237023i
$718$	−8.61917			−0.321665
$719$	−11.8838	+	20.5833i	−0.443191	+	0.767629i	−0.997924	−	0.0643994i	$-0.979487\pi$
$719$	−11.8838	+	20.5833i	−0.443191	+	0.767629i	0.554734	+	0.832028i	$0.312820\pi$
$720$	3.82492	−	0.222373i	0.142546	−	0.00828734i
$721$	−27.9012	−	5.35620i	−1.03910	−	0.199475i
$722$	50.6085	+	29.2188i	1.88345	+	1.08741i
$723$	−28.2098	+	17.3980i	−1.04913	+	0.647039i
$724$	23.8682	+	13.7803i	0.887053	+	0.512140i
$725$	5.95930	+	3.44060i	0.221323	+	0.127781i
$726$	71.1740	+	38.3815i	2.64152	+	1.42447i
$727$	13.3342	+	7.69848i	0.494537	+	0.285521i	0.726455	−	0.687214i	$-0.241167\pi$
$727$	13.3342	+	7.69848i	0.494537	+	0.285521i	−0.231918	+	0.972735i	$0.574500\pi$
$728$	−0.402747	+	0.139725i	−0.0149268	+	0.00517853i
$729$	26.5913	−	4.68012i	0.984862	−	0.173338i
$730$	−5.10359	+	8.83968i	−0.188892	+	0.327171i
$731$	−2.66690			−0.0986387
$732$	34.5579	−	21.3131i	1.27730	−	0.787756i
$733$		−	13.1529i		−	0.485813i	−0.970050	−	0.242906i	$-0.921899\pi$
$733$		−	13.1529i		−	0.485813i	0.970050	−	0.242906i	$-0.0781008\pi$
$734$	−40.3973	−	69.9702i	−1.49109	−	2.58265i
$735$	2.09076	+	11.9427i	0.0771190	+	0.440514i
$736$	12.2857	−	21.2794i	0.452856	−	0.784370i
$737$	−16.8625	−	9.73554i	−0.621137	−	0.358613i
$738$	6.83194	−	4.49241i	0.251487	−	0.165368i
$739$	1.91303	+	3.31347i	0.0703721	+	0.121888i	0.899064	−	0.437816i	$-0.144248\pi$
$739$	1.91303	+	3.31347i	0.0703721	+	0.121888i	−0.828692	+	0.559704i	$0.810915\pi$
$740$	12.8740	+	22.2983i	0.473256	+	0.819704i
$741$	0.274810	+	0.445588i	0.0100954	+	0.0163691i
$742$	−27.5731	−	23.8567i	−1.01224	−	0.875807i
$743$	4.53102	−	2.61598i	0.166227	−	0.0959711i	−0.414579	−	0.910014i	$-0.636071\pi$
$743$	4.53102	−	2.61598i	0.166227	−	0.0959711i	0.580806	+	0.814042i	$0.302738\pi$
$744$	−39.6339	+	1.15114i	−1.45305	+	0.0422030i
$745$		−	7.18431i		−	0.263213i
$746$	12.3168	−	7.11110i	0.450950	−	0.260356i
$747$	2.39181	+	3.63740i	0.0875116	+	0.133085i
$748$			12.4766i			0.456191i
$749$	3.09943	−	3.58226i	0.113251	−	0.130893i
$750$	−3.57705	−	1.92897i	−0.130616	−	0.0704361i
$751$	−28.8973			−1.05448			−0.527238	−	0.849717i	$-0.676773\pi$
$751$	−28.8973			−1.05448			−0.527238	+	0.849717i	$0.676773\pi$
$752$	−3.56620	+	6.17683i	−0.130046	+	0.225246i
$753$	−9.24055	−	14.9830i	−0.336745	−	0.546010i
$754$	0.637822	−	0.368247i	0.0232281	−	0.0134108i
$755$	13.7310			0.499722
$756$	−39.0490	−	28.2418i	−1.42020	−	1.02714i
$757$	−12.9857			−0.471973			−0.235987	−	0.971756i	$-0.575832\pi$
$757$	−12.9857			−0.471973			−0.235987	+	0.971756i	$0.575832\pi$
$758$	−47.5196	+	27.4354i	−1.72599	+	0.996500i
$759$	−30.5268	−	49.4973i	−1.10805	−	1.79664i
$760$	−11.7026	+	20.2695i	−0.424498	+	0.735253i
$761$	27.6804			1.00341			0.501707	−	0.865038i	$-0.332705\pi$
$761$	27.6804			1.00341			0.501707	+	0.865038i	$0.332705\pi$
$762$	56.0859	+	30.2450i	2.03178	+	1.09566i
$763$	−45.7230	+	15.8626i	−1.65528	+	0.574265i
$764$		−	5.82585i		−	0.210772i
$765$	−1.91772	+	0.111492i	−0.0693353	+	0.00403101i
$766$	15.5001	−	8.94896i	0.560040	−	0.323339i
$767$			0.134939i			0.00487235i
$768$	−40.3790	+	1.17279i	−1.45705	+	0.0423193i
$769$	7.98441	−	4.60980i	0.287925	−	0.166234i	−0.349081	−	0.937093i	$-0.613506\pi$
$769$	7.98441	−	4.60980i	0.287925	−	0.166234i	0.637006	+	0.770859i	$0.280173\pi$
$770$	32.6007	−	11.3101i	1.17485	−	0.407588i
$771$	2.71286	+	4.39874i	0.0977014	+	0.158417i
$772$	19.4745	+	33.7309i	0.700904	+	1.21400i
$773$	13.3446	+	23.1135i	0.479971	+	0.831335i	0.999736	−	0.0229749i	$-0.00731377\pi$
$773$	13.3446	+	23.1135i	0.479971	+	0.831335i	−0.519765	+	0.854309i	$0.673980\pi$
$774$	−26.1976	−	13.1604i	−0.941655	−	0.473041i
$775$	5.61264	+	3.24046i	0.201612	+	0.116401i
$776$	11.2148	−	19.4246i	0.402589	−	0.697304i
$777$	5.38344	−	33.2265i	0.193130	−	1.19199i
$778$	33.3877	+	57.8292i	1.19701	+	2.07328i
$779$			7.69693i			0.275771i
$780$	−0.235729	+	0.145383i	−0.00844046	+	0.00520554i
$781$	42.6707			1.52688
$782$	4.53752	−	7.85921i	0.162261	−	0.281045i
$783$	32.4034	+	15.1162i	1.15800	+	0.540207i
$784$	1.28532	+	8.84700i	0.0459042	+	0.315964i
$785$	−1.74911	−	1.00985i	−0.0624283	−	0.0360430i
$786$	56.8191	+	30.6404i	2.02667	+	1.09291i
$787$	2.06394	+	1.19162i	0.0735715	+	0.0424765i	0.536334	−	0.844006i	$-0.319809\pi$
$787$	2.06394	+	1.19162i	0.0735715	+	0.0424765i	−0.462763	+	0.886482i	$0.653142\pi$
$788$	−39.9617	−	23.0719i	−1.42358	−	0.821903i
$789$	−12.2234	+	7.53864i	−0.435166	+	0.268383i
$790$	−17.4067	−	10.0498i	−0.619303	−	0.357555i
$791$	5.20762	+	15.0106i	0.185161	+	0.533716i
$792$	−26.4410	+	52.6345i	−0.939540	+	1.87029i
$793$	−0.152519	+	0.264170i	−0.00541610	+	0.00938095i
$794$	−10.9921			−0.390095
$795$	−8.95400	−	4.82856i	−0.317566	−	0.171251i
$796$			33.6968i			1.19435i
$797$	−3.26653	−	5.65780i	−0.115707	−	0.200410i	0.802355	−	0.596847i	$-0.203580\pi$
$797$	−3.26653	−	5.65780i	−0.115707	−	0.200410i	−0.918062	+	0.396437i	$0.870247\pi$
$798$	66.6047	−	25.2965i	2.35778	−	0.895485i
$799$	1.78800	−	3.09691i	0.0632550	−	0.109561i
$800$	3.52292	+	2.03396i	0.124554	+	0.0719113i
$801$	−30.4680	−	46.3350i	−1.07653	−	1.63717i
$802$	−37.2720	−	64.5569i	−1.31612	−	2.27958i
$803$	−12.0904	−	20.9412i	−0.426662	−	0.739000i
$804$	10.0949	−	18.7197i	0.356018	−	0.660194i
$805$	−15.6945	−	3.01287i	−0.553158	−	0.106190i
$806$	0.600719	−	0.346825i	0.0211594	−	0.0122164i
$807$	−17.8122	+	33.0305i	−0.627017	+	1.16273i
$808$		−	39.6502i		−	1.39489i
$809$	41.1230	−	23.7424i	1.44581	−	0.834737i	0.447579	−	0.894244i	$-0.352286\pi$
$809$	41.1230	−	23.7424i	1.44581	−	0.834737i	0.998228	+	0.0595072i	$0.0189529\pi$
$810$	−19.3885	−	8.36820i	−0.681241	−	0.294029i
$811$		−	43.6693i		−	1.53344i	−0.641985	−	0.766718i	$-0.721889\pi$
$811$		−	43.6693i		−	1.53344i	0.641985	−	0.766718i	$-0.278111\pi$
$812$	−20.9177	−	60.2941i	−0.734069	−	2.11591i
$813$	−1.13170	−	38.9646i	−0.0396906	−	1.36655i
$814$	−95.7984			−3.35773
$815$	4.14847	−	7.18537i	0.145315	−	0.251692i
$816$	−1.41582	+	0.0411217i	−0.0495636	+	0.00143955i
$817$	23.9001	−	13.7987i	0.836160	−	0.482757i
$818$	−49.6898			−1.73736
$819$	0.358929	+	0.0475061i	0.0125420	+	0.00166000i
$820$	−4.07190			−0.142197
$821$	−30.6681	+	17.7062i	−1.07032	+	0.617952i	−0.928270	−	0.371907i	$-0.878704\pi$
$821$	−30.6681	+	17.7062i	−1.07032	+	0.617952i	−0.142054	+	0.989859i	$0.545371\pi$
$822$	20.7446	−	38.4685i	0.723552	−	1.34174i
$823$	13.6267	−	23.6021i	0.474996	−	0.822717i	−0.524594	−	0.851352i	$-0.675783\pi$
$823$	13.6267	−	23.6021i	0.474996	−	0.822717i	0.999590	+	0.0286358i	$0.00911630\pi$
$824$	−37.9302			−1.32136
$825$	8.19454	−	5.05387i	0.285297	−	0.175953i
$826$	18.0349	+	3.46215i	0.627513	+	0.120464i
$827$		−	24.8957i		−	0.865708i	−0.901464	−	0.432854i	$-0.857507\pi$
$827$		−	24.8957i		−	0.865708i	0.901464	−	0.432854i	$-0.142493\pi$
$828$	53.0748	−	34.8998i	1.84448	−	1.21285i
$829$	24.5019	−	14.1462i	0.850987	−	0.491318i	−0.00999656	−	0.999950i	$-0.503182\pi$
$829$	24.5019	−	14.1462i	0.850987	−	0.491318i	0.860984	+	0.508632i	$0.169849\pi$
$830$		−	3.40482i		−	0.118183i
$831$	−5.36546	−	8.69975i	−0.186126	−	0.301791i
$832$	0.477960	−	0.275951i	0.0165703	−	0.00956686i
$833$	−0.644426	−	4.43567i	−0.0223280	−	0.153687i
$834$	24.0087	−	0.697318i	0.831352	−	0.0241461i
$835$	1.67285	+	2.89747i	0.0578915	+	0.100271i
$836$	−64.5551	−	111.813i	−2.23269	−	3.86713i
$837$	30.5184	+	14.2368i	1.05487	+	0.492097i
$838$	19.4475	+	11.2280i	0.671804	+	0.387866i
$839$	−3.89651	+	6.74895i	−0.134522	+	0.233000i	−0.925415	−	0.378955i	$-0.876283\pi$
$839$	−3.89651	+	6.74895i	−0.134522	+	0.233000i	0.790892	+	0.611955i	$0.209617\pi$
$840$	5.74721	+	15.1322i	0.198298	+	0.522111i
$841$	9.17547	+	15.8924i	0.316396	+	0.548013i
$842$		−	45.5056i		−	1.56823i
$843$	−0.695899	−	23.9598i	−0.0239680	−	0.825220i
$844$	37.8858			1.30408
$845$	−6.49896	+	11.2565i	−0.223571	+	0.387236i
$846$	32.8464	−	21.5985i	1.12928	−	0.742571i
$847$	−9.92476	+	51.6995i	−0.341019	+	1.77642i
$848$	−6.49608	−	3.75051i	−0.223076	−	0.128793i
$849$	0.977846	+	33.6673i	0.0335596	+	1.15546i
$850$	1.30114	+	0.751211i	0.0446286	+	0.0257663i
$851$	38.4228	+	22.1834i	1.31712	+	0.760438i
$852$	1.35316	+	46.5894i	0.0463585	+	1.59612i
$853$	−2.00649	−	1.15845i	−0.0687008	−	0.0396644i	0.465256	−	0.885176i	$-0.345962\pi$
$853$	−2.00649	−	1.15845i	−0.0687008	−	0.0396644i	−0.533957	+	0.845512i	$0.679296\pi$
$854$	31.3937	+	27.1623i	1.07427	+	0.929476i
$855$	16.6093	−	10.9216i	0.568026	−	0.373511i
$856$	3.16210	−	5.47692i	0.108078	−	0.187197i
$857$	34.9608			1.19424			0.597120	−	0.802152i	$-0.296312\pi$
$857$	34.9608			1.19424			0.597120	+	0.802152i	$0.296312\pi$
$858$	−0.0299162	−	1.03001i	−0.00102132	−	0.0351641i
$859$			39.2526i			1.33928i	0.742685	+	0.669641i	$0.233552\pi$
$859$			39.2526i			1.33928i	−0.742685	+	0.669641i	$0.766448\pi$
$860$	7.29994	+	12.6439i	0.248926	+	0.431153i
$861$	4.12494	+	3.36461i	0.140578	+	0.114666i
$862$	14.2036	−	24.6014i	0.483777	−	0.837926i
$863$	9.76990	+	5.64065i	0.332571	+	0.192010i	0.656982	−	0.753906i	$-0.271833\pi$
$863$	9.76990	+	5.64065i	0.332571	+	0.192010i	−0.324411	+	0.945916i	$0.605166\pi$
$864$	19.1557	+	8.93613i	0.651690	+	0.304013i
$865$	6.73971	+	11.6735i	0.229157	+	0.396912i
$866$	−36.9382	−	63.9789i	−1.25521	−	2.17409i
$867$	−28.7226	+	0.834231i	−0.975470	+	0.0283320i
$868$	−19.7009	−	56.7867i	−0.668693	−	1.92747i
$869$	41.2366	−	23.8079i	1.39885	−	0.807629i
$870$	−14.6799	−	23.8025i	−0.497695	−	0.806982i
$871$			0.159786i			0.00541414i
$872$	−55.9561	+	32.3063i	−1.89491	+	1.09403i
$873$	−15.9170	+	10.4664i	−0.538709	+	0.354233i
$874$			93.9100i			3.17655i
$875$	0.498797	−	2.59831i	0.0168624	−	0.0878388i
$876$	22.4809	−	13.8648i	0.759560	−	0.468449i
$877$	−17.0078			−0.574312			−0.287156	−	0.957884i	$-0.592710\pi$
$877$	−17.0078			−0.574312			−0.287156	+	0.957884i	$0.592710\pi$
$878$	−26.4963	+	45.8930i	−0.894207	+	1.54881i
$879$	16.5946	−	30.7727i	0.559721	−	1.03794i
$880$	6.14788	−	3.54948i	0.207245	−	0.119653i
$881$	3.86189			0.130110			0.0650552	−	0.997882i	$-0.479278\pi$
$881$	3.86189			0.130110			0.0650552	+	0.997882i	$0.479278\pi$
$882$	15.5584	−	46.7528i	0.523879	−	1.57425i
$883$	−45.6227			−1.53533			−0.767663	−	0.640854i	$-0.778580\pi$
$883$	−45.6227			−1.53533			−0.767663	+	0.640854i	$0.778580\pi$
$884$	0.0886700	−	0.0511936i	0.00298229	−	0.00172183i
$885$	5.12159	−	0.148754i	0.172160	−	0.00500030i
$886$	10.0047	−	17.3287i	0.336116	−	0.582169i
$887$	−40.4635			−1.35863			−0.679316	−	0.733846i	$-0.737724\pi$
$887$	−40.4635			−1.35863			−0.679316	+	0.733846i	$0.737724\pi$
$888$	−1.30465	−	44.9192i	−0.0437813	−	1.50739i
$889$	−7.82081	+	40.7398i	−0.262302	+	1.36637i
$890$			43.3723i			1.45384i
$891$	40.1340	−	29.8655i	1.34454	−	1.00053i
$892$	14.7921	−	8.54021i	0.495275	−	0.285947i
$893$			37.0051i			1.23833i
$894$	−13.8583	+	25.6987i	−0.463492	+	0.859492i
$895$	17.5857	−	10.1531i	0.587827	−	0.339382i
$896$	−17.5630	−	50.6243i	−0.586739	−	1.69124i
$897$	−0.226515	+	0.420046i	−0.00756312	+	0.0140249i
$898$	11.7297	+	20.3164i	0.391425	+	0.677968i
$899$	22.2982	+	38.6217i	0.743688	+	1.28811i
$900$	5.77785	+	8.78681i	0.192595	+	0.292894i
$901$	3.25697	+	1.88041i	0.108505	+	0.0626457i
$902$	7.57502	−	13.1203i	0.252221	−	0.436859i
$903$	3.05258	−	18.8405i	0.101584	−	0.626972i
$904$	10.6060	+	18.3701i	0.352750	+	0.610981i
$905$			7.86227i			0.261351i
$906$	−49.1165	−	26.4867i	−1.63179	−	0.879962i
$907$	−42.0634			−1.39669			−0.698346	−	0.715760i	$-0.746080\pi$
$907$	−42.0634			−1.39669			−0.698346	+	0.715760i	$0.746080\pi$
$908$	11.8467	−	20.5190i	0.393145	−	0.680947i
$909$	−15.1167	+	30.0920i	−0.501390	+	0.998087i
$910$	−0.214145	−	0.185282i	−0.00709885	−	0.00614203i
$911$	−6.34565	−	3.66366i	−0.210241	−	0.121382i	0.391183	−	0.920313i	$-0.372066\pi$
$911$	−6.34565	−	3.66366i	−0.210241	−	0.121382i	−0.601423	+	0.798931i	$0.705399\pi$
$912$	12.4755	−	7.69409i	0.413105	−	0.254777i
$913$	6.98539	+	4.03302i	0.231183	+	0.133473i
$914$	−68.8221	−	39.7345i	−2.27643	−	1.31430i
$915$	10.1947	+	5.49762i	0.337026	+	0.181746i
$916$	−22.5398	−	13.0133i	−0.744735	−	0.429973i
$917$	−7.92306	+	41.2724i	−0.261642	+	1.36293i
$918$	7.07485	+	3.30042i	0.233505	+	0.108930i
$919$	−23.8899	+	41.3785i	−0.788054	+	1.36495i	0.139103	+	0.990278i	$0.455578\pi$
$919$	−23.8899	+	41.3785i	−0.788054	+	1.36495i	−0.927157	+	0.374672i	$0.877755\pi$
$920$	−21.3358			−0.703421
$921$	−21.7619	+	13.4213i	−0.717078	+	0.442248i
$922$			83.8436i			2.76124i
$923$	−0.175085	−	0.303256i	−0.00576299	−	0.00998179i
$924$	−88.1421	−	14.2810i	−2.89966	−	0.469810i
$925$	−3.67259	+	6.36111i	−0.120754	+	0.209152i
$926$	−9.60682	−	5.54650i	−0.315700	−	0.182269i
$927$	28.7866	+	14.4609i	0.945475	+	0.474960i
$928$	13.9961	+	24.2419i	0.459444	+	0.795780i
$929$	7.58490	+	13.1374i	0.248853	+	0.431025i	0.963208	−	0.268758i	$-0.0866132\pi$
$929$	7.58490	+	13.1374i	0.248853	+	0.431025i	−0.714355	+	0.699783i	$0.753280\pi$
$930$	−13.8260	−	22.4179i	−0.453371	−	0.735113i
$931$	28.7257	+	36.4171i	0.941447	+	1.19352i
$932$	−58.1860	+	33.5937i	−1.90595	+	1.10040i
$933$	14.8990	−	0.432733i	0.487771	−	0.0141670i
$934$		−	69.0896i		−	2.26068i
$935$	−3.08239	+	1.77962i	−0.100805	+	0.0581998i
$936$	0.482559	−	0.0280550i	0.0157729	−	0.000917006i
$937$		−	34.1681i		−	1.11622i	−0.829765	−	0.558112i	$-0.811526\pi$
$937$		−	34.1681i		−	1.11622i	0.829765	−	0.558112i	$-0.188474\pi$
$938$	21.3558	+	4.09967i	0.697290	+	0.133859i
$939$	−27.0882	−	14.6077i	−0.883991	−	0.476704i
$940$	−19.5768			−0.638525
$941$	−15.6318	+	27.0750i	−0.509582	+	0.882621i	0.490357	+	0.871522i	$0.336866\pi$
$941$	−15.6318	+	27.0750i	−0.509582	+	0.882621i	−0.999938	+	0.0110994i	$0.996467\pi$
$942$	4.30868	+	6.98626i	0.140384	+	0.227624i
$943$	−6.07638	+	3.50820i	−0.197874	+	0.114243i
$944$	3.77799			0.122963
$945$	1.40741	−	13.6755i	0.0457832	−	0.444864i
$946$	−54.3207			−1.76612
$947$	1.97819	−	1.14211i	0.0642824	−	0.0371134i	−0.467514	−	0.883985i	$-0.654850\pi$
$947$	1.97819	−	1.14211i	0.0642824	−	0.0371134i	0.531797	+	0.846872i	$0.321517\pi$
$948$	27.3020	+	44.2685i	0.886728	+	1.43777i
$949$	−0.0992179	+	0.171850i	−0.00322075	+	0.00557850i
$950$	−15.5473			−0.504421
$951$	−37.7962	−	20.3821i	−1.22562	−	0.660934i
$952$	−1.96137	−	5.65353i	−0.0635684	−	0.183232i
$953$		−	32.2871i		−	1.04588i	−0.852369	−	0.522940i	$-0.824835\pi$
$953$		−	32.2871i		−	1.04588i	0.852369	−	0.522940i	$-0.175165\pi$
$954$	22.7148	+	34.5441i	0.735418	+	1.11841i
$955$	1.43930	−	0.830978i	0.0465745	−	0.0268898i
$956$		−	27.0620i		−	0.875248i
$957$	66.2221	−	1.92338i	2.14066	−	0.0621741i
$958$	−72.5745	+	41.9009i	−2.34477	+	1.35376i
$959$	27.9428	+	5.36418i	0.902320	+	0.173219i
$960$	−11.0006	−	17.8367i	−0.355042	−	0.575679i
$961$	5.50113	+	9.52824i	0.177456	+	0.307363i
$962$	0.393076	+	0.680828i	0.0126733	+	0.0219508i
$963$	−4.48791	+	2.95107i	−0.144621	+	0.0950970i
$964$	−58.0907	−	33.5387i	−1.87098	−	1.08021i
$965$	−5.55555	+	9.62250i	−0.178840	+	0.309759i
$966$	50.3283	+	41.0515i	1.61929	+	1.32081i
$967$	19.5539	+	33.8684i	0.628811	+	1.08913i	0.987791	+	0.155788i	$0.0497916\pi$
$967$	19.5539	+	33.8684i	0.628811	+	1.08913i	−0.358979	+	0.933346i	$0.616875\pi$
$968$			70.2827i			2.25897i
$969$	−6.25490	+	3.85763i	−0.200936	+	0.123925i
$970$	14.8993			0.478387
$971$	−17.4132	+	30.1605i	−0.558816	+	0.967898i	0.438779	+	0.898595i	$0.355411\pi$
$971$	−17.4132	+	30.1605i	−0.558816	+	0.967898i	−0.997596	+	0.0693032i	$0.977922\pi$
$972$	33.8809	+	42.8726i	1.08673	+	1.37514i
$973$	5.12514	+	14.7729i	0.164304	+	0.473597i
$974$	−22.2549	−	12.8489i	−0.713094	−	0.411705i
$975$	−0.0695408	−	0.0375008i	−0.00222709	−	0.00120099i
$976$	7.39619	+	4.27019i	0.236746	+	0.136685i
$977$	21.9088	+	12.6490i	0.700924	+	0.404678i	0.807691	−	0.589606i	$-0.200717\pi$
$977$	21.9088	+	12.6490i	0.700924	+	0.404678i	−0.106768	+	0.994284i	$0.534050\pi$
$978$	−28.6997	+	17.7002i	−0.917715	+	0.565989i
$979$	−88.9834	−	51.3746i	−2.84392	−	1.64194i
$980$	−19.2657	+	15.1968i	−0.615422	+	0.485442i
$981$	54.7839	−	3.18502i	1.74911	−	0.101690i
$982$	−4.01811	+	6.95958i	−0.128223	+	0.222089i
$983$	−52.6539			−1.67940			−0.839699	−	0.543051i	$-0.817269\pi$
$983$	−52.6539			−1.67940			−0.839699	+	0.543051i	$0.817269\pi$
$984$	6.25519	+	3.37319i	0.199408	+	0.107534i
$985$		−	13.1636i		−	0.419426i
$986$	5.16923	+	8.95337i	0.164622	+	0.285134i
$987$	19.8318	+	16.1763i	0.631253	+	0.514896i
$988$	−0.529760	+	0.917572i	−0.0168539	+	0.0291918i
$989$	21.7870	+	12.5787i	0.692785	+	0.399980i
$990$	−39.0611	+	2.27093i	−1.24144	+	0.0721749i
$991$	−18.6241	−	32.2578i	−0.591613	−	1.02470i	−0.994015	−	0.109240i	$-0.965158\pi$
$991$	−18.6241	−	32.2578i	−0.591613	−	1.02470i	0.402403	−	0.915463i	$-0.368175\pi$
$992$	13.1819	+	22.8318i	0.418526	+	0.724909i
$993$	7.04208	−	13.0587i	0.223474	−	0.414405i
$994$	−45.0230	+	15.6198i	−1.42804	+	0.495429i
$995$	−8.32489	+	4.80638i	−0.263917	+	0.152372i
$996$	−4.18187	+	7.75479i	−0.132508	+	0.245720i
$997$			10.9137i			0.345641i	0.984953	+	0.172820i	$0.0552880\pi$
$997$			10.9137i			0.345641i	−0.984953	+	0.172820i	$0.944712\pi$
$998$	80.9557	−	46.7398i	2.56261	−	1.47952i
$999$	−16.1354	+	34.5882i	−0.510501	+	1.09432i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.be.b.236.14	yes	30
3.2	odd	2		945.2.be.b.656.2		30
7.3	odd	6		315.2.t.b.101.14	✓	30
9.4	even	3		945.2.t.b.341.14		30
9.5	odd	6		315.2.t.b.131.2	yes	30
21.17	even	6		945.2.t.b.521.2		30
63.31	odd	6		945.2.be.b.206.2		30
63.59	even	6	inner	315.2.be.b.311.14	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.b.101.14	✓	30	7.3	odd	6
315.2.t.b.131.2	yes	30	9.5	odd	6
315.2.be.b.236.14	yes	30	1.1	even	1	trivial
315.2.be.b.311.14	yes	30	63.59	even	6	inner
945.2.t.b.341.14		30	9.4	even	3
945.2.t.b.521.2		30	21.17	even	6
945.2.be.b.206.2		30	63.31	odd	6
945.2.be.b.656.2		30	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.03201 - 1.17318i) q^{2} +(-0.909209 - 1.47423i) q^{3} +(1.75271 - 3.03578i) q^{4} +1.00000 q^{5} +(-3.57705 - 1.92897i) q^{6} +(0.498797 - 2.59831i) q^{7} -3.53226i q^{8} +(-1.34668 + 2.68076i) q^{9} +O(q^{10})\)	\(q+(2.03201 - 1.17318i) q^{2} +(-0.909209 - 1.47423i) q^{3} +(1.75271 - 3.03578i) q^{4} +1.00000 q^{5} +(-3.57705 - 1.92897i) q^{6} +(0.498797 - 2.59831i) q^{7} -3.53226i q^{8} +(-1.34668 + 2.68076i) q^{9} +(2.03201 - 1.17318i) q^{10} +5.55854i q^{11} +(-6.06901 + 0.176271i) q^{12} +(0.0395039 - 0.0228076i) q^{13} +(-2.03473 - 5.86497i) q^{14} +(-0.909209 - 1.47423i) q^{15} +(-0.638563 - 1.10602i) q^{16} +(0.320160 + 0.554533i) q^{17} +(0.408548 + 7.02722i) q^{18} +(-5.73840 - 3.31307i) q^{19} +(1.75271 - 3.03578i) q^{20} +(-4.28400 + 1.62706i) q^{21} +(6.52118 + 11.2950i) q^{22} -6.04027i q^{23} +(-5.20735 + 3.21156i) q^{24} +1.00000 q^{25} +(0.0535149 - 0.0926905i) q^{26} +(5.17645 - 0.452058i) q^{27} +(-7.01365 - 6.06832i) q^{28} +(5.95930 + 3.44060i) q^{29} +(-3.57705 - 1.92897i) q^{30} +(5.61264 + 3.24046i) q^{31} +(3.52292 + 2.03396i) q^{32} +(8.19454 - 5.05387i) q^{33} +(1.30114 + 0.751211i) q^{34} +(0.498797 - 2.59831i) q^{35} +(5.77785 + 8.78681i) q^{36} +(-3.67259 + 6.36111i) q^{37} -15.5473 q^{38} +(-0.0695408 - 0.0375008i) q^{39} -3.53226i q^{40} +(-0.580801 - 1.00598i) q^{41} +(-6.79629 + 8.33212i) q^{42} +(-2.08247 + 3.60695i) q^{43} +(16.8745 + 9.74251i) q^{44} +(-1.34668 + 2.68076i) q^{45} +(-7.08634 - 12.2739i) q^{46} +(-2.79236 - 4.83651i) q^{47} +(-1.04994 + 1.94699i) q^{48} +(-6.50240 - 2.59206i) q^{49} +(2.03201 - 1.17318i) q^{50} +(0.526414 - 0.976173i) q^{51} -0.159900i q^{52} +(5.08648 - 2.93668i) q^{53} +(9.98825 - 6.99150i) q^{54} +5.55854i q^{55} +(-9.17790 - 1.76188i) q^{56} +(0.333196 + 11.4720i) q^{57} +16.1458 q^{58} +(-1.47910 + 2.56187i) q^{59} +(-6.06901 + 0.176271i) q^{60} +(-5.79128 + 3.34359i) q^{61} +15.2066 q^{62} +(6.29371 + 4.83624i) q^{63} +12.0991 q^{64} +(0.0395039 - 0.0228076i) q^{65} +(10.7223 - 19.8832i) q^{66} +(-1.75146 + 3.03361i) q^{67} +2.24459 q^{68} +(-8.90472 + 5.49187i) q^{69} +(-2.03473 - 5.86497i) q^{70} -7.67660i q^{71} +(9.46913 + 4.75682i) q^{72} +(-3.76739 + 2.17511i) q^{73} +17.2344i q^{74} +(-0.909209 - 1.47423i) q^{75} +(-20.1155 + 11.6137i) q^{76} +(14.4428 + 2.77259i) q^{77} +(-0.185303 + 0.00538201i) q^{78} +(-4.28313 - 7.41859i) q^{79} +(-0.638563 - 1.10602i) q^{80} +(-5.37291 - 7.22024i) q^{81} +(-2.36039 - 1.36277i) q^{82} +(0.725553 - 1.25670i) q^{83} +(-2.56920 + 15.8571i) q^{84} +(0.320160 + 0.554533i) q^{85} +9.77248i q^{86} +(-0.346023 - 11.9136i) q^{87} +19.6342 q^{88} +(-9.24246 + 16.0084i) q^{89} +(0.408548 + 7.02722i) q^{90} +(-0.0395567 - 0.114020i) q^{91} +(-18.3370 - 10.5868i) q^{92} +(-0.325894 - 11.2205i) q^{93} +(-11.3482 - 6.55189i) q^{94} +(-5.73840 - 3.31307i) q^{95} +(-0.204556 - 7.04287i) q^{96} +(5.49921 + 3.17497i) q^{97} +(-16.2539 + 2.36141i) q^{98} +(-14.9011 - 7.48557i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9	\( 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9} + 3 q^{10} - 18 q^{12} + 12 q^{13} - 9 q^{14} - q^{15} - 21 q^{16} + 3 q^{17} - 22 q^{18} + 15 q^{20} - 10 q^{21} + 15 q^{22} + 2 q^{24} + 30 q^{25} - 24 q^{26} + 5 q^{27} + 27 q^{28} + q^{30} + 6 q^{31} + 9 q^{32} - 17 q^{33} - 48 q^{34} + 6 q^{35} + 21 q^{36} - 3 q^{37} - 60 q^{38} + 12 q^{39} + 18 q^{41} - 47 q^{42} + 12 q^{43} - 15 q^{44} - 5 q^{45} + 9 q^{46} - 30 q^{47} + 40 q^{48} - 24 q^{49} + 3 q^{50} + 33 q^{51} + 30 q^{53} + 13 q^{54} + 72 q^{56} - 21 q^{57} + 15 q^{59} - 18 q^{60} - 30 q^{61} - 12 q^{62} + 10 q^{63} - 138 q^{64} + 12 q^{65} + 44 q^{66} - 6 q^{67} - 42 q^{68} - 32 q^{69} - 9 q^{70} - 137 q^{72} + 6 q^{73} - q^{75} + 54 q^{76} - 21 q^{77} - 18 q^{78} - 12 q^{79} - 21 q^{80} - 17 q^{81} + 6 q^{82} + 6 q^{83} - 12 q^{84} + 3 q^{85} - 47 q^{87} + 96 q^{88} + 3 q^{89} - 22 q^{90} + 15 q^{91} - 3 q^{92} - 18 q^{93} + 3 q^{94} + 60 q^{96} - 36 q^{97} - 24 q^{98} - q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9 + 3 * q^10 - 18 * q^12 + 12 * q^13 - 9 * q^14 - q^15 - 21 * q^16 + 3 * q^17 - 22 * q^18 + 15 * q^20 - 10 * q^21 + 15 * q^22 + 2 * q^24 + 30 * q^25 - 24 * q^26 + 5 * q^27 + 27 * q^28 + q^30 + 6 * q^31 + 9 * q^32 - 17 * q^33 - 48 * q^34 + 6 * q^35 + 21 * q^36 - 3 * q^37 - 60 * q^38 + 12 * q^39 + 18 * q^41 - 47 * q^42 + 12 * q^43 - 15 * q^44 - 5 * q^45 + 9 * q^46 - 30 * q^47 + 40 * q^48 - 24 * q^49 + 3 * q^50 + 33 * q^51 + 30 * q^53 + 13 * q^54 + 72 * q^56 - 21 * q^57 + 15 * q^59 - 18 * q^60 - 30 * q^61 - 12 * q^62 + 10 * q^63 - 138 * q^64 + 12 * q^65 + 44 * q^66 - 6 * q^67 - 42 * q^68 - 32 * q^69 - 9 * q^70 - 137 * q^72 + 6 * q^73 - q^75 + 54 * q^76 - 21 * q^77 - 18 * q^78 - 12 * q^79 - 21 * q^80 - 17 * q^81 + 6 * q^82 + 6 * q^83 - 12 * q^84 + 3 * q^85 - 47 * q^87 + 96 * q^88 + 3 * q^89 - 22 * q^90 + 15 * q^91 - 3 * q^92 - 18 * q^93 + 3 * q^94 + 60 * q^96 - 36 * q^97 - 24 * q^98 - q^99

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