LMFDB - Embedded newform 925.2.bb.d.151.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(151,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.151"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [78,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			151.10
Character	$\chi$	$=$	925.151
Dual form			925.2.bb.d.876.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.12720 - 1.34335i) q^{2} +(-1.57550 + 1.32200i) q^{3} +(-0.186702 - 1.05884i) q^{4} +3.60661i q^{6} +(3.02288 + 1.10024i) q^{7} +(1.40451 + 0.810896i) q^{8} +(0.213569 - 1.21121i) q^{9} +(-2.19070 + 3.79440i) q^{11} +(1.69394 + 1.42138i) q^{12} +(-4.72516 + 0.833174i) q^{13} +(4.88541 - 2.82059i) q^{14} +(4.69315 - 1.70817i) q^{16} +(-6.77975 - 1.19545i) q^{17} +(-1.38634 - 1.65217i) q^{18} +(-0.999689 - 1.19138i) q^{19} +(-6.21707 + 2.26283i) q^{21} +(2.62784 + 7.21993i) q^{22} +(1.49959 - 0.865791i) q^{23} +(-3.28482 + 0.579202i) q^{24} +(-4.20698 + 7.28670i) q^{26} +(-1.82026 - 3.15279i) q^{27} +(0.600598 - 3.40616i) q^{28} +(7.16270 + 4.13539i) q^{29} +7.52042i q^{31} +(1.88610 - 5.18202i) q^{32} +(-1.56476 - 8.87419i) q^{33} +(-9.24806 + 7.76005i) q^{34} -1.32235 q^{36} +(-5.88477 - 1.53933i) q^{37} -2.72730 q^{38} +(6.34304 - 7.55934i) q^{39} +(1.04807 + 5.94389i) q^{41} +(-3.96814 + 10.9024i) q^{42} +7.74103i q^{43} +(4.42667 + 1.61118i) q^{44} +(0.527288 - 2.99040i) q^{46} +(1.89010 + 3.27374i) q^{47} +(-5.13586 + 8.89558i) q^{48} +(2.56498 + 2.15227i) q^{49} +(12.2619 - 7.07940i) q^{51} +(1.76439 + 4.84763i) q^{52} +(2.40878 - 0.876724i) q^{53} +(-6.28710 - 1.10859i) q^{54} +(3.35350 + 3.99654i) q^{56} +(3.15002 + 0.555434i) q^{57} +(13.6291 - 4.96058i) q^{58} +(0.456794 + 1.25503i) q^{59} +(4.15361 - 0.732394i) q^{61} +(10.1025 + 8.47705i) q^{62} +(1.97821 - 3.42636i) q^{63} +(0.159107 + 0.275582i) q^{64} +(-13.6849 - 7.90100i) q^{66} +(-0.577235 - 0.210097i) q^{67} +7.40185i q^{68} +(-1.21803 + 3.34652i) q^{69} +(11.0001 - 9.23018i) q^{71} +(1.28212 - 1.52797i) q^{72} -3.69283 q^{73} +(-8.70118 + 6.17015i) q^{74} +(-1.07484 + 1.28094i) q^{76} +(-10.7970 + 9.05974i) q^{77} +(-3.00494 - 17.0418i) q^{78} +(-0.649592 + 1.78474i) q^{79} +(10.5030 + 3.82277i) q^{81} +(9.16610 + 5.29205i) q^{82} +(1.01140 - 5.73596i) q^{83} +(3.55671 + 6.16040i) q^{84} +(10.3989 + 8.72572i) q^{86} +(-16.7518 + 2.95380i) q^{87} +(-6.15373 + 3.55286i) q^{88} +(1.16409 + 3.19832i) q^{89} +(-15.2003 - 2.68022i) q^{91} +(-1.19671 - 1.42618i) q^{92} +(-9.94201 - 11.8484i) q^{93} +(6.52830 + 1.15112i) q^{94} +(3.87909 + 10.6577i) q^{96} +(9.54884 - 5.51302i) q^{97} +(5.78251 - 1.01961i) q^{98} +(4.12794 + 3.46375i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q + 3 q^{2} + 3 q^{4} - 6 q^{7} + 18 q^{8} + 15 q^{12} - 27 q^{13} - 18 q^{14} + 9 q^{16} - 15 q^{18} + 3 q^{21} - 30 q^{22} + 15 q^{24} + 36 q^{27} + 27 q^{28} - 9 q^{29} - 18 q^{32} - 6 q^{33} - 51 q^{34}+ \cdots - 183 q^{99}+O(q^{100}) $ 78 * q + 3 * q^2 + 3 * q^4 - 6 * q^7 + 18 * q^8 + 15 * q^12 - 27 * q^13 - 18 * q^14 + 9 * q^16 - 15 * q^18 + 3 * q^21 - 30 * q^22 + 15 * q^24 + 36 * q^27 + 27 * q^28 - 9 * q^29 - 18 * q^32 - 6 * q^33 - 51 * q^34 - 108 * q^36 + 6 * q^37 + 84 * q^38 - 33 * q^39 - 21 * q^41 + 42 * q^42 - 3 * q^44 + 36 * q^46 - 57 * q^47 + 54 * q^48 + 54 * q^49 + 90 * q^51 + 75 * q^52 - 24 * q^53 - 39 * q^54 - 48 * q^56 - 9 * q^57 + 9 * q^58 + 15 * q^59 - 18 * q^61 - 120 * q^63 + 66 * q^64 + 126 * q^66 - 24 * q^67 + 45 * q^69 + 48 * q^71 + 132 * q^72 - 60 * q^73 - 12 * q^74 + 81 * q^76 + 21 * q^77 - 258 * q^78 + 84 * q^79 + 48 * q^81 + 234 * q^82 + 42 * q^83 + 57 * q^84 - 66 * q^86 + 24 * q^87 - 90 * q^88 + 39 * q^89 + 57 * q^91 - 87 * q^92 - 12 * q^93 + 78 * q^94 - 78 * q^96 - 36 * q^97 + 126 * q^98 - 183 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$

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 $

$2$	1.12720	−	1.34335i	0.797053	−	0.949891i	−0.202515	−	0.979279i	$-0.564911\pi$
$2$	1.12720	−	1.34335i	0.797053	−	0.949891i	0.999568	+	0.0293882i	$0.00935590\pi$
$3$	−1.57550	+	1.32200i	−0.909616	+	0.763258i	−0.972046	−	0.234791i	$-0.924559\pi$
$3$	−1.57550	+	1.32200i	−0.909616	+	0.763258i	0.0624301	+	0.998049i	$0.480115\pi$
$4$	−0.186702	−	1.05884i	−0.0933509	−	0.529419i
$5$		0			0
$5$		0			0
$6$			3.60661i			1.47239i
$7$	3.02288	+	1.10024i	1.14254	+	0.415851i	0.842831	−	0.538179i	$-0.180887\pi$
$7$	3.02288	+	1.10024i	1.14254	+	0.415851i	0.299711	+	0.954030i	$0.403110\pi$
$8$	1.40451	+	0.810896i	0.496570	+	0.286695i
$9$	0.213569	−	1.21121i	0.0711895	−	0.403736i
$10$		0			0
$11$	−2.19070	+	3.79440i	−0.660521	+	1.14406i	0.319959	+	0.947432i	$0.396331\pi$
$11$	−2.19070	+	3.79440i	−0.660521	+	1.14406i	−0.980479	+	0.196624i	$0.937002\pi$
$12$	1.69394	+	1.42138i	0.488997	+	0.410317i
$13$	−4.72516	+	0.833174i	−1.31052	+	0.231081i	−0.784893	−	0.619631i	$-0.787282\pi$
$13$	−4.72516	+	0.833174i	−1.31052	+	0.231081i	−0.525632	+	0.850712i	$0.676171\pi$
$14$	4.88541	−	2.82059i	1.30568	−	0.753835i
$15$		0			0
$16$	4.69315	−	1.70817i	1.17329	−	0.427042i
$17$	−6.77975	−	1.19545i	−1.64433	−	0.289940i	−0.726575	−	0.687087i	$-0.758889\pi$
$17$	−6.77975	−	1.19545i	−1.64433	−	0.289940i	−0.917755	+	0.397147i	$0.870000\pi$
$18$	−1.38634	−	1.65217i	−0.326763	−	0.389421i
$19$	−0.999689	−	1.19138i	−0.229344	−	0.273322i	0.639084	−	0.769137i	$-0.279314\pi$
$19$	−0.999689	−	1.19138i	−0.229344	−	0.273322i	−0.868428	+	0.495815i	$0.834869\pi$
$20$		0			0
$21$	−6.21707	+	2.26283i	−1.35668	+	0.493790i
$22$	2.62784	+	7.21993i	0.560258	+	1.53930i
$23$	1.49959	−	0.865791i	0.312687	−	0.180530i	−0.335441	−	0.942061i	$-0.608885\pi$
$23$	1.49959	−	0.865791i	0.312687	−	0.180530i	0.648128	+	0.761531i	$0.275552\pi$
$24$	−3.28482	+	0.579202i	−0.670511	+	0.118229i
$25$		0			0
$26$	−4.20698	+	7.28670i	−0.825056	+	1.42904i
$27$	−1.82026	−	3.15279i	−0.350310	−	0.606755i
$28$	0.600598	−	3.40616i	0.113502	−	0.643704i
$29$	7.16270	+	4.13539i	1.33008	+	0.767922i	0.985312	−	0.170766i	$-0.0546241\pi$
$29$	7.16270	+	4.13539i	1.33008	+	0.767922i	0.344768	+	0.938688i	$0.387957\pi$
$30$		0			0
$31$			7.52042i			1.35071i	0.737494	+	0.675354i	$0.236009\pi$
$31$			7.52042i			1.35071i	−0.737494	+	0.675354i	$0.763991\pi$
$32$	1.88610	−	5.18202i	0.333419	−	0.916061i
$33$	−1.56476	−	8.87419i	−0.272390	−	1.54480i
$34$	−9.24806	+	7.76005i	−1.58603	+	1.33084i
$35$		0			0
$36$	−1.32235			−0.220391
$37$	−5.88477	−	1.53933i	−0.967449	−	0.253064i
$37$	−5.88477	−	1.53933i	−0.967449	−	0.253064i
$38$	−2.72730			−0.442426
$39$	6.34304	−	7.55934i	1.01570	−	1.21046i
$40$		0			0
$41$	1.04807	+	5.94389i	0.163681	+	0.928280i	0.950414	+	0.310987i	$0.100659\pi$
$41$	1.04807	+	5.94389i	0.163681	+	0.928280i	−0.786734	+	0.617293i	$0.788229\pi$
$42$	−3.96814	+	10.9024i	−0.612297	+	1.68227i
$43$			7.74103i			1.18050i	0.807222	+	0.590248i	$0.200970\pi$
$43$			7.74103i			1.18050i	−0.807222	+	0.590248i	$0.799030\pi$
$44$	4.42667	+	1.61118i	0.667345	+	0.242894i
$45$		0			0
$46$	0.527288	−	2.99040i	0.0777444	−	0.440910i
$47$	1.89010	+	3.27374i	0.275699	+	0.477525i	0.970311	−	0.241860i	$-0.0777574\pi$
$47$	1.89010	+	3.27374i	0.275699	+	0.477525i	−0.694612	+	0.719384i	$0.744424\pi$
$48$	−5.13586	+	8.89558i	−0.741298	+	1.28397i
$49$	2.56498	+	2.15227i	0.366426	+	0.307468i
$50$		0			0
$51$	12.2619	−	7.07940i	1.71701	−	0.991315i
$52$	1.76439	+	4.84763i	0.244677	+	0.672246i
$53$	2.40878	−	0.876724i	0.330871	−	0.120427i	−0.171242	−	0.985229i	$-0.554778\pi$
$53$	2.40878	−	0.876724i	0.330871	−	0.120427i	0.502114	+	0.864802i	$0.332556\pi$
$54$	−6.28710	−	1.10859i	−0.855566	−	0.150859i
$55$		0			0
$56$	3.35350	+	3.99654i	0.448130	+	0.534061i
$57$	3.15002	+	0.555434i	0.417231	+	0.0735690i
$58$	13.6291	−	4.96058i	1.78959	−	0.651356i
$59$	0.456794	+	1.25503i	0.0594695	+	0.163391i	0.965869	−	0.259030i	$-0.0834027\pi$
$59$	0.456794	+	1.25503i	0.0594695	+	0.163391i	−0.906400	+	0.422421i	$0.861181\pi$
$60$		0			0
$61$	4.15361	−	0.732394i	0.531815	−	0.0937734i	0.0987092	−	0.995116i	$-0.468529\pi$
$61$	4.15361	−	0.732394i	0.531815	−	0.0937734i	0.433106	+	0.901343i	$0.357418\pi$
$62$	10.1025	+	8.47705i	1.28303	+	1.07659i
$63$	1.97821	−	3.42636i	0.249231	−	0.431681i
$64$	0.159107	+	0.275582i	0.0198884	+	0.0344477i
$65$		0			0
$66$	−13.6849	−	7.90100i	−1.68450	−	0.972546i
$67$	−0.577235	−	0.210097i	−0.0705205	−	0.0256674i	0.306519	−	0.951865i	$-0.400836\pi$
$67$	−0.577235	−	0.210097i	−0.0705205	−	0.0256674i	−0.377040	+	0.926197i	$0.623058\pi$
$68$			7.40185i			0.897607i
$69$	−1.21803	+	3.34652i	−0.146634	+	0.402874i
$70$		0			0
$71$	11.0001	−	9.23018i	1.30547	−	1.09542i	0.316299	−	0.948660i	$-0.397560\pi$
$71$	11.0001	−	9.23018i	1.30547	−	1.09542i	0.989172	−	0.146761i	$-0.0468848\pi$
$72$	1.28212	−	1.52797i	0.151100	−	0.180074i
$73$	−3.69283			−0.432213			−0.216107	−	0.976370i	$-0.569336\pi$
$73$	−3.69283			−0.432213			−0.216107	+	0.976370i	$0.569336\pi$
$74$	−8.70118	+	6.17015i	−1.01149	+	0.717266i
$75$		0			0
$76$	−1.07484	+	1.28094i	−0.123293	+	0.146934i
$77$	−10.7970	+	9.05974i	−1.23043	+	1.03245i
$78$	−3.00494	−	17.0418i	−0.340242	−	1.92961i
$79$	−0.649592	+	1.78474i	−0.0730849	+	0.200799i	−0.970856	−	0.239663i	$-0.922963\pi$
$79$	−0.649592	+	1.78474i	−0.0730849	+	0.200799i	0.897771	+	0.440462i	$0.145185\pi$
$80$		0			0
$81$	10.5030	+	3.82277i	1.16700	+	0.424753i
$82$	9.16610	+	5.29205i	1.01223	+	0.584409i
$83$	1.01140	−	5.73596i	0.111016	−	0.629604i	−0.877630	−	0.479339i	$-0.840876\pi$
$83$	1.01140	−	5.73596i	0.111016	−	0.629604i	0.988646	−	0.150264i	$-0.0480125\pi$
$84$	3.55671	+	6.16040i	0.388069	+	0.672155i
$85$		0			0
$86$	10.3989	+	8.72572i	1.12134	+	0.940918i
$87$	−16.7518	+	2.95380i	−1.79598	+	0.316681i
$88$	−6.15373	+	3.55286i	−0.655990	+	0.378736i
$89$	1.16409	+	3.19832i	0.123394	+	0.339021i	0.985974	−	0.166899i	$-0.0533754\pi$
$89$	1.16409	+	3.19832i	0.123394	+	0.339021i	−0.862580	+	0.505920i	$0.831153\pi$
$90$		0			0
$91$	−15.2003	−	2.68022i	−1.59343	−	0.280964i
$92$	−1.19671	−	1.42618i	−0.124766	−	0.148690i
$93$	−9.94201	−	11.8484i	−1.03094	−	1.22863i
$94$	6.52830	+	1.15112i	0.673343	+	0.118729i
$95$		0			0
$96$	3.87909	+	10.6577i	0.395908	+	1.08775i
$97$	9.54884	−	5.51302i	0.969538	−	0.559763i	0.0704424	−	0.997516i	$-0.477559\pi$
$97$	9.54884	−	5.51302i	0.969538	−	0.559763i	0.899095	+	0.437753i	$0.144226\pi$
$98$	5.78251	−	1.01961i	0.584122	−	0.102996i
$99$	4.12794	+	3.46375i	0.414874	+	0.348120i
$100$		0			0
$101$	−3.31022	−	5.73346i	−0.329379	−	0.570501i	0.653010	−	0.757349i	$-0.273506\pi$
$101$	−3.31022	−	5.73346i	−0.329379	−	0.570501i	−0.982389	+	0.186849i	$0.940173\pi$
$102$	4.31153	−	24.4519i	0.426905	−	2.42110i
$103$	17.4276	+	10.0618i	1.71719	+	0.991422i	0.923945	+	0.382525i	$0.124945\pi$
$103$	17.4276	+	10.0618i	1.71719	+	0.991422i	0.793249	+	0.608897i	$0.208388\pi$
$104$	−7.31217	−	2.66141i	−0.717018	−	0.260973i
$105$		0			0
$106$	1.53744	−	4.22408i	0.149329	−	0.410279i
$107$	−2.48077	−	14.0691i	−0.239825	−	1.36011i	−0.832211	−	0.554460i	$-0.812925\pi$
$107$	−2.48077	−	14.0691i	−0.239825	−	1.36011i	0.592386	−	0.805654i	$-0.298186\pi$
$108$	−2.99845	+	2.51600i	−0.288526	+	0.242102i
$109$	−9.83113	+	11.7163i	−0.941652	+	1.12222i	0.0506926	+	0.998714i	$0.483857\pi$
$109$	−9.83113	+	11.7163i	−0.941652	+	1.12222i	−0.992344	+	0.123502i	$0.960587\pi$
$110$		0			0
$111$	11.3064	−	5.35446i	1.07316	−	0.508223i
$112$	16.0662			1.51812
$113$	1.73564	−	2.06846i	0.163276	−	0.194584i	−0.678203	−	0.734875i	$-0.737241\pi$
$113$	1.73564	−	2.06846i	0.163276	−	0.194584i	0.841479	+	0.540290i	$0.181685\pi$
$114$	4.29686	−	3.60549i	0.402438	−	0.337685i
$115$		0			0
$116$	3.04142	−	8.35623i	0.282389	−	0.775857i
$117$			5.90109i			0.545556i
$118$	2.20084	+	0.801041i	0.202604	+	0.0737418i
$119$	−19.1791	−	11.0731i	−1.75814	−	1.01507i
$120$		0			0
$121$	−4.09832	−	7.09850i	−0.372575	−	0.645318i
$122$	3.69810	−	6.40531i	0.334811	−	0.579909i
$123$	−9.50907	−	7.97905i	−0.857404	−	0.719447i
$124$	7.96292	−	1.40408i	0.715091	−	0.126090i
$125$		0			0
$126$	−2.37295	−	6.51963i	−0.211399	−	0.580815i
$127$	−5.41324	+	1.97026i	−0.480347	+	0.174832i	−0.570834	−	0.821066i	$-0.693380\pi$
$127$	−5.41324	+	1.97026i	−0.480347	+	0.174832i	0.0904867	+	0.995898i	$0.471158\pi$
$128$	11.4112	+	2.01210i	1.00861	+	0.177846i
$129$	−10.2337	−	12.1960i	−0.901023	−	1.07380i
$130$		0			0
$131$	−6.49151	−	1.14463i	−0.567166	−	0.100007i	−0.117290	−	0.993098i	$-0.537421\pi$
$131$	−6.49151	−	1.14463i	−0.567166	−	0.100007i	−0.449876	+	0.893091i	$0.648532\pi$
$132$	−9.10420	+	3.31366i	−0.792419	+	0.288417i
$133$	−1.71114	−	4.70131i	−0.148374	−	0.407655i
$134$	−0.932895	+	0.538607i	−0.0805898	+	0.0465286i
$135$		0			0
$136$	−8.55286	−	7.17670i	−0.733401	−	0.615397i
$137$	0.00576235	−	0.00998069i	0.000492311	−	0.000852708i	−0.865779	−	0.500426i	$-0.833177\pi$
$137$	0.00576235	−	0.00998069i	0.000492311	−	0.000852708i	0.866271	+	0.499574i	$0.166510\pi$
$138$	3.12257	+	5.40845i	0.265811	+	0.460398i
$139$	2.73652	−	15.5196i	0.232108	−	1.31635i	−0.616510	−	0.787347i	$-0.711454\pi$
$139$	2.73652	−	15.5196i	0.232108	−	1.31635i	0.848619	−	0.529005i	$-0.177435\pi$
$140$		0			0
$141$	−7.30575	−	2.65907i	−0.615255	−	0.223934i
$142$		−	25.1812i		−	2.11316i
$143$	7.19002	−	19.7544i	0.601259	−	1.65195i
$144$	−1.06664	−	6.04919i	−0.0888863	−	0.504099i
$145$		0			0
$146$	−4.16257	+	4.96076i	−0.344497	+	0.410555i
$147$	−6.88644			−0.567984
$148$	−0.531206	+	6.51841i	−0.0436649	+	0.535810i
$149$	13.7308			1.12487			0.562435	−	0.826842i	$-0.309865\pi$
$149$	13.7308			1.12487			0.562435	+	0.826842i	$0.309865\pi$
$150$		0			0
$151$	−5.23411	+	4.39194i	−0.425945	+	0.357411i	−0.830419	−	0.557139i	$-0.811899\pi$
$151$	−5.23411	+	4.39194i	−0.425945	+	0.357411i	0.404474	+	0.914550i	$0.367455\pi$
$152$	−0.437989	−	2.48396i	−0.0355256	−	0.201476i
$153$	−2.89588	+	7.95637i	−0.234118	+	0.643234i
$154$			24.7163i			1.99169i
$155$		0			0
$156$	−9.18839	−	5.30492i	−0.735660	−	0.424733i
$157$	−4.18302	+	23.7231i	−0.333841	+	1.89331i	0.104545	+	0.994520i	$0.466661\pi$
$157$	−4.18302	+	23.7231i	−0.333841	+	1.89331i	−0.438386	+	0.898787i	$0.644450\pi$
$158$	1.66531	+	2.88440i	0.132485	+	0.229470i
$159$	−2.63600	+	4.56569i	−0.209049	+	0.362083i
$160$		0			0
$161$	5.48567	−	0.967272i	0.432332	−	0.0762317i
$162$	16.9743	−	9.80013i	1.33363	−	0.769971i
$163$	0.528659	+	1.45248i	0.0414078	+	0.113767i	0.958673	−	0.284509i	$-0.0918307\pi$
$163$	0.528659	+	1.45248i	0.0414078	+	0.113767i	−0.917265	+	0.398276i	$0.869608\pi$
$164$	6.09795	−	2.21947i	0.476170	−	0.173312i
$165$		0			0
$166$	−6.56534	−	7.82426i	−0.509569	−	0.607281i
$167$	−10.0623	−	11.9918i	−0.778643	−	0.927950i	0.220229	−	0.975448i	$-0.429320\pi$
$167$	−10.0623	−	11.9918i	−0.778643	−	0.927950i	−0.998871	+	0.0474981i	$0.984875\pi$
$168$	−10.5669	−	1.86323i	−0.815252	−	0.143751i
$169$	9.41700	−	3.42751i	0.724384	−	0.263654i
$170$		0			0
$171$	−1.65651	+	0.956389i	−0.126677	+	0.0731369i
$172$	8.19650	−	1.44526i	0.624978	−	0.110200i
$173$	−5.73151	−	4.80931i	−0.435759	−	0.365645i	0.398361	−	0.917229i	$-0.369579\pi$
$173$	−5.73151	−	4.80931i	−0.435759	−	0.365645i	−0.834119	+	0.551584i	$0.814024\pi$
$174$	−14.9147	+	25.8331i	−1.13068	+	1.95840i
$175$		0			0
$176$	−3.79981	+	21.5498i	−0.286421	+	1.62438i
$177$	−2.37883	−	1.37342i	−0.178804	−	0.103233i
$178$	5.60862	+	2.04137i	0.420384	+	0.153007i
$179$		−	18.9882i		−	1.41925i	−0.704581	−	0.709624i	$-0.748865\pi$
$179$		−	18.9882i		−	1.41925i	0.704581	−	0.709624i	$-0.251135\pi$
$180$		0			0
$181$	−0.728700	−	4.13266i	−0.0541638	−	0.307178i	0.945675	−	0.325112i	$-0.105402\pi$
$181$	−0.728700	−	4.13266i	−0.0541638	−	0.307178i	−0.999839	+	0.0179342i	$0.994291\pi$
$182$	−20.7343	+	17.3982i	−1.53693	+	1.28964i
$183$	−5.57579	+	6.64497i	−0.412174	+	0.491210i
$184$	2.80827			0.207028
$185$		0			0
$186$	−27.1232			−1.98877
$187$	19.3884	−	23.1062i	1.41782	−	1.68969i
$188$	3.11348	−	2.61252i	0.227074	−	0.190538i
$189$	−2.03362	−	11.5332i	−0.147924	−	0.838920i
$190$		0			0
$191$			13.5388i			0.979636i	0.871825	+	0.489818i	$0.162937\pi$
$191$			13.5388i			0.979636i	−0.871825	+	0.489818i	$0.837063\pi$
$192$	−0.614993	−	0.223839i	−0.0443833	−	0.0161542i
$193$	18.1770	+	10.4945i	1.30841	+	0.755411i	0.981831	−	0.189758i	$-0.0607704\pi$
$193$	18.1770	+	10.4945i	1.30841	+	0.755411i	0.326580	+	0.945170i	$0.394104\pi$
$194$	3.35757	−	19.0417i	0.241059	−	1.36712i
$195$		0			0
$196$	1.80002	−	3.11773i	0.128573	−	0.222695i
$197$	6.77491	+	5.68483i	0.482693	+	0.405027i	0.851399	−	0.524519i	$-0.175755\pi$
$197$	6.77491	+	5.68483i	0.482693	+	0.405027i	−0.368706	+	0.929546i	$0.620199\pi$
$198$	9.30606	−	1.64091i	0.661353	−	0.116614i
$199$	14.8467	−	8.57173i	1.05245	−	0.607634i	0.129118	−	0.991629i	$-0.458786\pi$
$199$	14.8467	−	8.57173i	1.05245	−	0.607634i	0.923335	+	0.383996i	$0.125452\pi$
$200$		0			0
$201$	1.18718	−	0.432099i	0.0837374	−	0.0304779i
$202$	−11.4333	−	2.01600i	−0.804446	−	0.141846i
$203$	17.1021	+	20.3815i	1.20033	+	1.43050i
$204$	−9.78527	−	11.6616i	−0.685106	−	0.816477i
$205$		0			0
$206$	33.1610	−	12.0696i	2.31044	−	0.840931i
$207$	−0.728386	−	2.00122i	−0.0506263	−	0.139095i
$208$	−20.7527	+	11.9816i	−1.43894	+	0.830774i
$209$	6.71061	−	1.18326i	0.464182	−	0.0818479i
$210$		0			0
$211$	−7.25915	+	12.5732i	−0.499740	+	0.865576i	−1.00000		0.000299773i	$-0.999905\pi$
$211$	−7.25915	+	12.5732i	−0.499740	+	0.865576i	0.500260	+	0.865875i	$0.333238\pi$
$212$	−1.37803	−	2.38682i	−0.0946437	−	0.163928i
$213$	−5.12835	+	29.0843i	−0.351389	+	1.99282i
$214$	−21.6961	−	12.5262i	−1.48311	−	0.856276i
$215$		0			0
$216$		−	5.90418i		−	0.401729i
$217$	−8.27426	+	22.7334i	−0.561694	+	1.54324i
$218$	4.65737	+	26.4133i	0.315437	+	1.78893i
$219$	5.81806	−	4.88193i	0.393148	−	0.329890i
$220$		0			0
$221$	33.0314			2.22194
$222$	5.55177	−	21.2241i	0.372610	−	1.42447i
$223$	11.6690			0.781416			0.390708	−	0.920515i	$-0.372230\pi$
$223$	11.6690			0.781416			0.390708	+	0.920515i	$0.372230\pi$
$224$	11.4029	−	13.5895i	0.761890	−	0.907985i
$225$		0			0
$226$	−0.822240	−	4.66315i	−0.0546946	−	0.310188i
$227$	9.76325	−	26.8243i	0.648009	−	1.78039i	0.0230496	−	0.999734i	$-0.492662\pi$
$227$	9.76325	−	26.8243i	0.648009	−	1.78039i	0.624960	−	0.780657i	$-0.285115\pi$
$228$		−	3.43907i		−	0.227758i
$229$	−0.725757	−	0.264154i	−0.0479594	−	0.0174558i	0.317929	−	0.948114i	$-0.397013\pi$
$229$	−0.725757	−	0.264154i	−0.0479594	−	0.0174558i	−0.365888	+	0.930659i	$0.619235\pi$
$230$		0			0
$231$	5.03365	−	28.5472i	0.331190	−	1.87827i
$232$	6.70674	+	11.6164i	0.440319	+	0.762655i
$233$	7.26745	−	12.5876i	0.476106	−	0.824641i	−0.523519	−	0.852014i	$-0.675381\pi$
$233$	7.26745	−	12.5876i	0.476106	−	0.824641i	0.999625	+	0.0273736i	$0.00871436\pi$
$234$	7.92723	+	6.65173i	0.518219	+	0.434837i
$235$		0			0
$236$	1.24359	−	0.717988i	0.0809509	−	0.0467370i
$237$	−1.33600	−	3.67062i	−0.0867824	−	0.238433i
$238$	−36.4937	+	13.2826i	−2.36554	+	0.860985i
$239$	21.4898	+	3.78923i	1.39006	+	0.245105i	0.818052	−	0.575145i	$-0.195054\pi$
$239$	21.4898	+	3.78923i	1.39006	+	0.245105i	0.572006	+	0.820249i	$0.306165\pi$
$240$		0			0
$241$	7.08091	+	8.43870i	0.456121	+	0.543584i	0.944268	−	0.329177i	$-0.106771\pi$
$241$	7.08091	+	8.43870i	0.456121	+	0.543584i	−0.488147	+	0.872762i	$0.662327\pi$
$242$	−14.1554	−	2.49598i	−0.909944	−	0.160448i
$243$	−11.3382	+	4.12678i	−0.727348	+	0.264733i
$244$	−1.55097	−	4.26127i	−0.0992909	−	0.272800i
$245$		0			0
$246$	−21.4373	+	3.77997i	−1.36679	+	0.241002i
$247$	5.71633	+	4.79657i	0.363721	+	0.305198i
$248$	−6.09828	+	10.5625i	−0.387241	+	0.670721i
$249$	5.98948	+	10.3741i	0.379568	+	0.657431i
$250$		0			0
$251$	−14.6931	−	8.48306i	−0.927419	−	0.535446i	−0.0414249	−	0.999142i	$-0.513190\pi$
$251$	−14.6931	−	8.48306i	−0.927419	−	0.535446i	−0.885994	+	0.463696i	$0.846523\pi$
$252$	−3.99730	−	1.45490i	−0.251806	−	0.0916500i
$253$			7.58675i			0.476975i
$254$	−3.45508	+	9.49275i	−0.216791	+	0.595628i
$255$		0			0
$256$	15.0781	−	12.6521i	0.942383	−	0.790753i
$257$	−1.60229	+	1.90953i	−0.0999478	+	0.119113i	−0.813700	−	0.581285i	$-0.802550\pi$
$257$	−1.60229	+	1.90953i	−0.0999478	+	0.119113i	0.713752	+	0.700399i	$0.246994\pi$
$258$	−27.9189			−1.73815
$259$	−16.0953	−	11.1279i	−1.00011	−	0.691452i
$260$		0			0
$261$	6.53854	−	7.79233i	0.404725	−	0.482333i
$262$	−8.85488	+	7.43013i	−0.547057	+	0.459035i
$263$	−2.57340	−	14.5945i	−0.158683	−	0.899934i	−0.955341	−	0.295505i	$-0.904512\pi$
$263$	−2.57340	−	14.5945i	−0.158683	−	0.899934i	0.796659	−	0.604429i	$-0.206599\pi$
$264$	4.99832	−	13.7328i	0.307625	−	0.845194i
$265$		0			0
$266$	−8.24430	−	3.00068i	−0.505490	−	0.183983i
$267$	−6.06221	−	3.50002i	−0.371001	−	0.214198i
$268$	−0.114687	+	0.650425i	−0.00700565	+	0.0397310i
$269$	6.86296	+	11.8870i	0.418442	+	0.724763i	0.995783	−	0.0917405i	$-0.0292430\pi$
$269$	6.86296	+	11.8870i	0.418442	+	0.724763i	−0.577341	+	0.816503i	$0.695910\pi$
$270$		0			0
$271$	4.05881	+	3.40575i	0.246555	+	0.206885i	0.757687	−	0.652618i	$-0.226329\pi$
$271$	4.05881	+	3.40575i	0.246555	+	0.206885i	−0.511132	+	0.859502i	$0.670774\pi$
$272$	−33.8604	+	5.97051i	−2.05309	+	0.362015i
$273$	27.4914	−	15.8721i	1.66385	−	0.960626i
$274$	−0.00691220	−	0.0189911i	−0.000417581	−	0.00114730i
$275$		0			0
$276$	3.77084	+	0.664900i	0.226978	+	0.0400223i
$277$	21.1153	+	25.1643i	1.26870	+	1.51197i	0.758074	+	0.652169i	$0.226141\pi$
$277$	21.1153	+	25.1643i	1.26870	+	1.51197i	0.510622	+	0.859805i	$0.329415\pi$
$278$	−17.7636	−	21.1698i	−1.06539	−	1.26968i
$279$	9.10879	+	1.60613i	0.545329	+	0.0961562i
$280$		0			0
$281$	−5.27920	−	14.5045i	−0.314930	−	0.865264i	−0.991642	−	0.129017i	$-0.958818\pi$
$281$	−5.27920	−	14.5045i	−0.314930	−	0.865264i	0.676712	−	0.736248i	$-0.263404\pi$
$282$	−11.8071	+	6.81685i	−0.703104	+	0.405937i
$283$	−14.6157	+	2.57714i	−0.868814	+	0.153195i	−0.590248	−	0.807222i	$-0.700970\pi$
$283$	−14.6157	+	2.57714i	−0.868814	+	0.153195i	−0.278566	+	0.960417i	$0.589859\pi$
$284$	−11.8270	−	9.92404i	−0.701804	−	0.588883i
$285$		0			0
$286$	−18.4324	−	31.9259i	−1.08993	−	1.88782i
$287$	−3.37151	+	19.1208i	−0.199014	+	1.12867i
$288$	−5.87369	−	3.39118i	−0.346111	−	0.199827i
$289$	28.5611	+	10.3954i	1.68006	+	0.611494i
$290$		0			0
$291$	−7.75597	+	21.3094i	−0.454663	+	1.24918i
$292$	0.689459	+	3.91011i	0.0403475	+	0.228822i
$293$	−23.4131	+	19.6459i	−1.36781	+	1.14773i	−0.394324	+	0.918972i	$0.629021\pi$
$293$	−23.4131	+	19.6459i	−1.36781	+	1.14773i	−0.973484	+	0.228755i	$0.926534\pi$
$294$	−7.76242	+	9.25089i	−0.452713	+	0.539523i
$295$		0			0
$296$	−7.01699	−	6.93394i	−0.407854	−	0.403027i
$297$	15.9506			0.925548
$298$	15.4774	−	18.4452i	0.896581	−	1.06850i
$299$	−6.36447	+	5.34043i	−0.368067	+	0.308845i
$300$		0			0
$301$	−8.51699	+	23.4002i	−0.490911	+	1.34877i
$302$			11.9818i			0.689477i
$303$	12.7949	+	4.65696i	0.735048	+	0.267535i
$304$	−6.72678	−	3.88371i	−0.385807	−	0.222746i
$305$		0			0
$306$	7.42393	+	12.8586i	0.424398	+	0.735079i
$307$	−8.59435	+	14.8859i	−0.490506	+	0.849580i	−0.999940	−	0.0109288i	$-0.996521\pi$
$307$	−8.59435	+	14.8859i	−0.490506	+	0.849580i	0.509435	+	0.860509i	$0.329855\pi$
$308$	11.6086	+	9.74079i	0.661462	+	0.555033i
$309$	−40.7590	+	7.18691i	−2.31870	+	0.408849i
$310$		0			0
$311$	−6.65618	−	18.2877i	−0.377437	−	1.03700i	−0.972415	−	0.233258i	$-0.925061\pi$
$311$	−6.65618	−	18.2877i	−0.377437	−	1.03700i	0.594978	−	0.803742i	$-0.297161\pi$
$312$	15.0387	−	5.47365i	0.851400	−	0.309884i
$313$	18.0010	+	3.17405i	1.01747	+	0.179408i	0.657421	−	0.753524i	$-0.271647\pi$
$313$	18.0010	+	3.17405i	1.01747	+	0.179408i	0.360053	+	0.932932i	$0.382758\pi$
$314$	27.1532	+	32.3600i	1.53235	+	1.82618i
$315$		0			0
$316$	2.01103	+	0.354599i	0.113129	+	0.0199478i
$317$	−9.74489	+	3.54685i	−0.547328	+	0.199211i	−0.600859	−	0.799355i	$-0.705175\pi$
$317$	−9.74489	+	3.54685i	−0.547328	+	0.199211i	0.0535311	+	0.998566i	$0.482952\pi$
$318$	3.16200	+	8.68753i	0.177316	+	0.487173i
$319$	−31.3826	+	18.1188i	−1.75709	+	1.01446i
$320$		0			0
$321$	22.5079	+	18.8863i	1.25627	+	1.05413i
$322$	4.88409	−	8.45948i	0.272179	−	0.471429i
$323$	5.35340	+	9.27236i	0.297871	+	0.515928i
$324$	2.08677	−	11.8347i	0.115932	−	0.657483i
$325$		0			0
$326$	2.54709	+	0.927066i	0.141070	+	0.0513454i
$327$		−	31.4558i		−	1.73951i
$328$	−3.34785	+	9.19814i	−0.184854	+	0.507883i
$329$	2.11164	+	11.9757i	0.116418	+	0.660242i
$330$		0			0
$331$	−9.57025	+	11.4054i	−0.526028	+	0.626896i	−0.961995	−	0.273067i	$-0.911962\pi$
$331$	−9.57025	+	11.4054i	−0.526028	+	0.626896i	0.435967	+	0.899963i	$0.356407\pi$
$332$	−6.26229			−0.343688
$333$	−3.12125	+	6.79892i	−0.171043	+	0.372578i
$334$	−27.4513			−1.50207
$335$		0			0
$336$	−25.3124	+	21.2396i	−1.38090	+	1.15872i
$337$	−4.44396	−	25.2029i	−0.242078	−	1.37289i	−0.827182	−	0.561934i	$-0.810058\pi$
$337$	−4.44396	−	25.2029i	−0.242078	−	1.37289i	0.585104	−	0.810958i	$-0.301054\pi$
$338$	6.01053	−	16.5138i	0.326930	−	0.898233i
$339$			5.55339i			0.301619i
$340$		0			0
$341$	−28.5355	−	16.4750i	−1.54528	−	0.892170i
$342$	−0.582465	+	3.30332i	−0.0314961	+	0.178623i
$343$	−5.87348	−	10.1732i	−0.317138	−	0.549299i
$344$	−6.27717	+	10.8724i	−0.338442	+	0.586199i
$345$		0			0
$346$	−12.9212	+	2.27835i	−0.694646	+	0.122485i
$347$	−27.6503	+	15.9639i	−1.48435	+	0.856989i	−0.999842	−	0.0177991i	$-0.994334\pi$
$347$	−27.6503	+	15.9639i	−1.48435	+	0.856989i	−0.484506	+	0.874788i	$0.661001\pi$
$348$	6.25520	+	17.1860i	0.335314	+	0.921267i
$349$	20.9061	−	7.60919i	1.11908	−	0.407310i	0.284761	−	0.958598i	$-0.408086\pi$
$349$	20.9061	−	7.60919i	1.11908	−	0.407310i	0.834315	+	0.551288i	$0.185863\pi$
$350$		0			0
$351$	11.2279	+	13.3809i	0.599299	+	0.714217i
$352$	15.5308	+	18.5089i	0.827794	+	0.986526i
$353$	20.1857	+	3.55928i	1.07438	+	0.189441i	0.682727	−	0.730673i	$-0.260794\pi$
$353$	20.1857	+	3.55928i	1.07438	+	0.189441i	0.391649	+	0.920115i	$0.371905\pi$
$354$	−4.52641	+	1.64748i	−0.240576	+	0.0875625i
$355$		0			0
$356$	3.16916	−	1.82972i	0.167965	−	0.0969748i
$357$	44.8553	−	7.90920i	2.37399	−	0.418599i
$358$	−25.5078	−	21.4036i	−1.34813	−	1.13122i
$359$	11.6733	−	20.2188i	0.616095	−	1.06711i	−0.374096	−	0.927390i	$-0.622047\pi$
$359$	11.6733	−	20.2188i	0.616095	−	1.06711i	0.990191	−	0.139718i	$-0.0446196\pi$
$360$		0			0
$361$	2.87930	−	16.3293i	0.151542	−	0.859438i
$362$	−6.37300	−	3.67945i	−0.334957	−	0.193388i
$363$	15.8411	+	5.76571i	0.831444	+	0.302621i
$364$			16.5951i			0.869819i
$365$		0			0
$366$	2.64146	+	14.9805i	0.138071	+	0.783041i
$367$	2.00564	−	1.68293i	0.104693	−	0.0878481i	−0.588938	−	0.808178i	$-0.700454\pi$
$367$	2.00564	−	1.68293i	0.104693	−	0.0878481i	0.693632	+	0.720330i	$0.256010\pi$
$368$	5.55891	−	6.62485i	0.289778	−	0.345344i
$369$	7.42312			0.386432
$370$		0			0
$371$	8.24606			0.428114
$372$	−10.6894	+	12.7391i	−0.554219	+	0.660492i
$373$	11.5442	−	9.68673i	0.597736	−	0.501560i	−0.292981	−	0.956118i	$-0.594647\pi$
$373$	11.5442	−	9.68673i	0.597736	−	0.501560i	0.890717	+	0.454558i	$0.150203\pi$
$374$	−9.18501	−	52.0908i	−0.474946	−	2.69355i
$375$		0			0
$376$			6.13069i			0.316166i
$377$	−37.2904	−	13.5726i	−1.92056	−	0.699025i
$378$	−17.7855	−	10.2684i	−0.914786	−	0.528152i
$379$	−0.502227	+	2.84827i	−0.0257977	+	0.146306i	−0.994986	−	0.100016i	$-0.968111\pi$
$379$	−0.502227	+	2.84827i	−0.0257977	+	0.146306i	0.969188	+	0.246321i	$0.0792219\pi$
$380$		0			0
$381$	5.92388	−	10.2605i	0.303489	−	0.525659i
$382$	18.1874	+	15.2610i	0.930547	+	0.780822i
$383$	−6.76491	+	1.19284i	−0.345671	+	0.0609511i	−0.343788	−	0.939047i	$-0.611710\pi$
$383$	−6.76491	+	1.19284i	−0.345671	+	0.0609511i	−0.00188233	+	0.999998i	$0.500599\pi$
$384$	−20.6383	+	11.9155i	−1.05319	+	0.608062i
$385$		0			0
$386$	34.5870	−	12.5886i	1.76043	−	0.640745i
$387$	9.37599	+	1.65324i	0.476608	+	0.0840389i
$388$	−7.62019	−	9.08139i	−0.386857	−	0.461038i
$389$	−17.6601	−	21.0465i	−0.895405	−	1.06710i	−0.997382	−	0.0723154i	$-0.976961\pi$
$389$	−17.6601	−	21.0465i	−0.895405	−	1.06710i	0.101977	−	0.994787i	$-0.467483\pi$
$390$		0			0
$391$	−11.2019	+	4.07715i	−0.566503	+	0.206190i
$392$	1.85728	+	5.10283i	0.0938067	+	0.257732i
$393$	11.7406	−	6.77843i	0.592234	−	0.341926i
$394$	15.2734	−	2.69311i	0.769463	−	0.135677i
$395$		0			0
$396$	2.89686	−	5.01752i	0.145573	−	0.252140i
$397$	7.30017	+	12.6443i	0.366385	+	0.634598i	0.988997	−	0.147933i	$-0.0472619\pi$
$397$	7.30017	+	12.6443i	0.366385	+	0.634598i	−0.622612	+	0.782530i	$0.713929\pi$
$398$	5.22040	−	29.6063i	0.261675	−	1.48403i
$399$	8.91104	+	5.14479i	0.446110	+	0.257562i
$400$		0			0
$401$			0.325878i			0.0162736i	0.999967	+	0.00813678i	$0.00259005\pi$
$401$			0.325878i			0.0162736i	−0.999967	+	0.00813678i	$0.997410\pi$
$402$	0.757737	−	2.08186i	0.0377925	−	0.103834i
$403$	−6.26582	−	35.5352i	−0.312123	−	1.77014i
$404$	−5.45279	+	4.57543i	−0.271286	+	0.227636i
$405$		0			0
$406$	46.6570			2.31555
$407$	18.7326	−	18.9570i	0.928540	−	0.939661i
$408$	22.9626			1.13682
$409$	2.40904	−	2.87098i	0.119119	−	0.141961i	−0.703189	−	0.711003i	$-0.748241\pi$
$409$	2.40904	−	2.87098i	0.119119	−	0.141961i	0.822309	+	0.569042i	$0.192686\pi$
$410$		0			0
$411$	0.00411590	+	0.0233424i	0.000203022	+	0.00115140i
$412$	7.40010	−	20.3316i	0.364577	−	1.00167i
$413$			4.29639i			0.211412i
$414$	−3.50938	−	1.27731i	−0.172477	−	0.0627764i
$415$		0			0
$416$	−4.59461	+	26.0574i	−0.225270	+	1.27757i
$417$	16.2055	+	28.0688i	0.793587	+	1.37453i
$418$	5.97469	−	10.3485i	0.292231	−	0.506160i
$419$	4.28124	+	3.59239i	0.209152	+	0.175500i	0.741346	−	0.671123i	$-0.234188\pi$
$419$	4.28124	+	3.59239i	0.209152	+	0.175500i	−0.532194	+	0.846623i	$0.678632\pi$
$420$		0			0
$421$	−12.8128	+	7.39749i	−0.624459	+	0.360531i	−0.778603	−	0.627517i	$-0.784071\pi$
$421$	−12.8128	+	7.39749i	−0.624459	+	0.360531i	0.154144	+	0.988048i	$0.450738\pi$
$422$	8.70767	+	23.9241i	0.423883	+	1.16461i
$423$	4.36885	−	1.59013i	0.212421	−	0.0773148i
$424$	4.09409	+	0.721899i	0.198827	+	0.0350585i
$425$		0			0
$426$	33.2897	+	39.6731i	1.61289	+	1.92217i
$427$	13.3617	+	2.35603i	0.646617	+	0.114016i
$428$	−14.4338	+	5.25347i	−0.697683	+	0.253936i
$429$	14.7875	+	40.6283i	0.713947	+	1.96155i
$430$		0			0
$431$	2.03515	−	0.358852i	0.0980297	−	0.0172853i	−0.124418	−	0.992230i	$-0.539706\pi$
$431$	2.03515	−	0.358852i	0.0980297	−	0.0172853i	0.222448	+	0.974945i	$0.428595\pi$
$432$	−13.9283	−	11.6872i	−0.670124	−	0.562301i
$433$	−11.0184	+	19.0844i	−0.529510	+	0.917138i	0.469898	+	0.882721i	$0.344291\pi$
$433$	−11.0184	+	19.0844i	−0.529510	+	0.917138i	−0.999408	+	0.0344171i	$0.989043\pi$
$434$	21.2120	+	36.7403i	1.01821	+	1.76359i
$435$		0			0
$436$	14.2412	+	8.22213i	0.682027	+	0.393769i
$437$	−2.53062	−	0.921069i	−0.121056	−	0.0440607i
$438$		−	13.3186i		−	0.636388i
$439$	−2.21596	+	6.08830i	−0.105762	+	0.290579i	−0.981274	−	0.192618i	$-0.938302\pi$
$439$	−2.21596	+	6.08830i	−0.105762	+	0.290579i	0.875512	+	0.483197i	$0.160524\pi$
$440$		0			0
$441$	3.15465	−	2.64706i	0.150221	−	0.126051i
$442$	37.2332	−	44.3727i	1.77100	−	2.11060i
$443$	30.0998			1.43008			0.715042	−	0.699082i	$-0.246408\pi$
$443$	30.0998			1.43008			0.715042	+	0.699082i	$0.246408\pi$
$444$	−7.78044	−	10.9720i	−0.369243	−	0.520709i
$445$		0			0
$446$	13.1534	−	15.6756i	0.622830	−	0.742260i
$447$	−21.6329	+	18.1521i	−1.02320	+	0.858566i
$448$	0.177757	+	1.00811i	0.00839821	+	0.0476286i
$449$	2.33595	−	6.41796i	0.110240	−	0.302882i	−0.872289	−	0.488990i	$-0.837365\pi$
$449$	2.33595	−	6.41796i	0.110240	−	0.302882i	0.982529	+	0.186108i	$0.0595875\pi$
$450$		0			0
$451$	−24.8495	−	9.04448i	−1.17012	−	0.425888i
$452$	−2.51422	−	1.45158i	−0.118259	−	0.0682767i
$453$	2.44019	−	13.8390i	0.114650	−	0.650213i
$454$	−25.0292	−	43.3519i	−1.17468	−	2.03460i
$455$		0			0
$456$	3.97385	+	3.33446i	0.186093	+	0.156150i
$457$	10.1562	−	1.79082i	0.475089	−	0.0837709i	0.0690233	−	0.997615i	$-0.478012\pi$
$457$	10.1562	−	1.79082i	0.475089	−	0.0837709i	0.406065	+	0.913844i	$0.366901\pi$
$458$	−1.17293	+	0.677189i	−0.0548072	+	0.0316430i
$459$	8.57192	+	23.5512i	0.400103	+	1.09927i
$460$		0			0
$461$	21.0722	+	3.71560i	0.981430	+	0.173053i	0.641270	−	0.767315i	$-0.278408\pi$
$461$	21.0722	+	3.71560i	0.981430	+	0.173053i	0.340160	+	0.940368i	$0.389519\pi$
$462$	−32.6750	−	38.9405i	−1.52018	−	1.81168i
$463$	−3.03186	−	3.61323i	−0.140903	−	0.167921i	0.690978	−	0.722876i	$-0.257180\pi$
$463$	−3.03186	−	3.61323i	−0.140903	−	0.167921i	−0.831881	+	0.554955i	$0.812736\pi$
$464$	40.6796	+	7.17291i	1.88850	+	0.332994i
$465$		0			0
$466$	−8.71763	−	23.9515i	−0.403836	−	1.10953i
$467$	19.0762	−	11.0136i	0.882740	−	0.509650i	0.0111794	−	0.999938i	$-0.496441\pi$
$467$	19.0762	−	11.0136i	0.882740	−	0.509650i	0.871561	+	0.490287i	$0.163108\pi$
$468$	6.24831	−	1.10175i	0.288828	−	0.0509282i
$469$	−1.51376	−	1.27019i	−0.0698989	−	0.0586521i
$470$		0			0
$471$	−24.7716	−	42.9057i	−1.14142	−	1.97699i
$472$	−0.376126	+	2.13312i	−0.0173126	+	0.0981848i
$473$	−29.3726	−	16.9583i	−1.35055	−	0.779742i
$474$	−6.43687	−	2.34283i	−0.295655	−	0.107610i
$475$		0			0
$476$	−8.14381	+	22.3749i	−0.373271	+	1.02555i
$477$	−0.547455	−	3.10477i	−0.0250662	−	0.142158i
$478$	29.3136	−	24.5970i	1.34077	−	1.12504i
$479$	−8.33131	+	9.92887i	−0.380667	+	0.453661i	−0.922025	−	0.387131i	$-0.873466\pi$
$479$	−8.33131	+	9.92887i	−0.380667	+	0.453661i	0.541358	+	0.840792i	$0.317911\pi$
$480$		0			0
$481$	29.0890	+	2.37055i	1.32634	+	0.108088i
$482$	19.3177			0.879899
$483$	−7.36395	+	8.77601i	−0.335071	+	0.399322i
$484$	−6.75101	+	5.66477i	−0.306864	+	0.257489i
$485$		0			0
$486$	−7.23680	+	19.8829i	−0.328268	+	0.901908i
$487$			18.4532i			0.836195i	0.908402	+	0.418097i	$0.137303\pi$
$487$			18.4532i			0.836195i	−0.908402	+	0.418097i	$0.862697\pi$
$488$	6.42770	+	2.33949i	0.290968	+	0.105904i
$489$	−2.75308	−	1.58949i	−0.124499	−	0.0718794i
$490$		0			0
$491$	11.2150	+	19.4250i	0.506126	+	0.876637i	0.999975	+	0.00708861i	$0.00225639\pi$
$491$	11.2150	+	19.4250i	0.506126	+	0.876637i	−0.493849	+	0.869548i	$0.664410\pi$
$492$	−6.67317	+	11.5583i	−0.300850	+	0.521087i
$493$	−43.6176	−	36.5996i	−1.96444	−	1.64836i
$494$	12.8869	−	2.27231i	0.579810	−	0.102236i
$495$		0			0
$496$	12.8461	+	35.2945i	0.576809	+	1.58477i
$497$	43.4074	−	15.7990i	1.94709	−	0.708682i
$498$	20.6874	+	3.64774i	0.927024	+	0.163459i
$499$	0.153311	+	0.182709i	0.00686316	+	0.00817919i	0.769465	−	0.638689i	$-0.220523\pi$
$499$	0.153311	+	0.182709i	0.00686316	+	0.00817919i	−0.762602	+	0.646868i	$0.776078\pi$
$500$		0			0
$501$	31.7063	+	5.59067i	1.41653	+	0.249773i
$502$	−27.9578	+	10.1758i	−1.24782	+	0.454168i
$503$	−2.60284	−	7.15125i	−0.116055	−	0.318859i	0.868042	−	0.496491i	$-0.165378\pi$
$503$	−2.60284	−	7.15125i	−0.116055	−	0.318859i	−0.984097	+	0.177632i	$0.943156\pi$
$504$	5.55684	−	3.20825i	0.247522	−	0.142907i
$505$		0			0
$506$	10.1916	+	8.55181i	0.453074	+	0.380174i
$507$	−10.3053	+	17.8493i	−0.457675	+	0.792717i
$508$	3.09685	+	5.36390i	0.137400	+	0.237984i
$509$	3.60422	−	20.4406i	0.159754	−	0.906011i	−0.794555	−	0.607192i	$-0.792296\pi$
$509$	3.60422	−	20.4406i	0.159754	−	0.906011i	0.954310	−	0.298820i	$-0.0965929\pi$
$510$		0			0
$511$	−11.1630	−	4.06300i	−0.493822	−	0.179736i
$512$		−	11.3422i		−	0.501259i
$513$	−1.93648	+	5.32044i	−0.0854978	+	0.234903i
$514$	0.759063	+	4.30486i	0.0334808	+	0.189879i
$515$		0			0
$516$	−11.0030	+	13.1128i	−0.484378	+	0.577259i
$517$	−16.5625			−0.728419
$518$	−33.0913	+	9.07826i	−1.45395	+	0.398876i
$519$	15.3879			0.675455
$520$		0			0
$521$	−33.1731	+	27.8355i	−1.45334	+	1.21950i	−0.523243	+	0.852184i	$0.675278\pi$
$521$	−33.1731	+	27.8355i	−1.45334	+	1.21950i	−0.930097	+	0.367313i	$0.880278\pi$
$522$	−3.09755	−	17.5671i	−0.135576	−	0.768890i
$523$	−3.83800	+	10.5448i	−0.167824	+	0.461092i	−0.994884	−	0.101021i	$-0.967789\pi$
$523$	−3.83800	+	10.5448i	−0.167824	+	0.461092i	0.827060	+	0.562113i	$0.190011\pi$
$524$			7.08717i			0.309604i
$525$		0			0
$526$	−22.5062	−	12.9940i	−0.981318	−	0.566564i
$527$	8.99031	−	50.9866i	0.391624	−	2.22101i
$528$	−22.5023	−	38.9751i	−0.979285	−	1.69617i
$529$	−10.0008	+	17.3219i	−0.434818	+	0.753127i
$530$		0			0
$531$	1.61766	−	0.285237i	0.0702004	−	0.0123782i
$532$	−4.65846	+	2.68956i	−0.201970	+	0.116607i
$533$	−9.90459	−	27.2126i	−0.429015	−	1.17871i
$534$	−11.5351	+	4.19843i	−0.499172	+	0.181684i
$535$		0			0
$536$	−0.640368	−	0.763161i	−0.0276597	−	0.0329635i
$537$	25.1025	+	29.9160i	1.08325	+	1.29097i
$538$	23.7043	+	4.17971i	1.02197	+	0.180200i
$539$	−13.7857	+	5.01758i	−0.593792	+	0.216123i
$540$		0			0
$541$	−21.7090	+	12.5337i	−0.933345	+	0.538867i	−0.887868	−	0.460098i	$-0.847814\pi$
$541$	−21.7090	+	12.5337i	−0.933345	+	0.538867i	−0.0454770	+	0.998965i	$0.514481\pi$
$542$	9.15022	−	1.61343i	0.393035	−	0.0693028i
$543$	6.61145	+	5.54767i	0.283725	+	0.238073i
$544$	−18.9822	+	32.8781i	−0.813853	+	1.40963i
$545$		0			0
$546$	9.66653	−	54.8216i	0.413689	−	2.34615i
$547$	−13.4913	−	7.78922i	−0.576848	−	0.333043i	0.183032	−	0.983107i	$-0.441409\pi$
$547$	−13.4913	−	7.78922i	−0.576848	−	0.333043i	−0.759880	+	0.650064i	$0.774742\pi$
$548$	−0.0116438	−	0.00423799i	−0.000497398	−	0.000181038i
$549$		−	5.18730i		−	0.221389i
$550$		0			0
$551$	−2.23364	−	12.6676i	−0.0951564	−	0.539659i
$552$	−4.42442	+	3.71253i	−0.188316	+	0.158016i
$553$	−3.92728	+	4.68035i	−0.167005	+	0.199029i
$554$	57.6056			2.44743
$555$		0			0
$556$	−16.9436			−0.718570
$557$	−22.8889	+	27.2780i	−0.969836	+	1.15581i	0.0179265	+	0.999839i	$0.494294\pi$
$557$	−22.8889	+	27.2780i	−0.969836	+	1.15581i	−0.987762	+	0.155966i	$0.950151\pi$
$558$	12.4250	−	10.4259i	0.525994	−	0.441361i
$559$	−6.44963	−	36.5776i	−0.272790	−	1.54707i
$560$		0			0
$561$			62.0354i			2.61914i
$562$	−25.4353	−	9.25769i	−1.07292	−	0.390512i
$563$	11.8413	+	6.83659i	0.499052	+	0.288128i	0.728322	−	0.685235i	$-0.240300\pi$
$563$	11.8413	+	6.83659i	0.499052	+	0.288128i	−0.229270	+	0.973363i	$0.573634\pi$
$564$	−1.45153	+	8.23206i	−0.0611206	+	0.346632i
$565$		0			0
$566$	−13.0129	+	22.5390i	−0.546972	+	0.947383i
$567$	27.5433	+	23.1116i	1.15671	+	0.970595i
$568$	22.9345	−	4.04397i	0.962310	−	0.169681i
$569$	0.229444	−	0.132470i	0.00961879	−	0.00555341i	−0.495183	−	0.868789i	$-0.664899\pi$
$569$	0.229444	−	0.132470i	0.00961879	−	0.00555341i	0.504802	+	0.863235i	$0.331566\pi$
$570$		0			0
$571$	25.7734	−	9.38074i	1.07858	−	0.392572i	0.259203	−	0.965823i	$-0.416540\pi$
$571$	25.7734	−	9.38074i	1.07858	−	0.392572i	0.819380	+	0.573251i	$0.194318\pi$
$572$	−22.2591	−	3.92488i	−0.930701	−	0.164108i
$573$	−17.8984	−	21.3304i	−0.747715	−	0.891092i
$574$	21.8855	+	26.0822i	0.913484	+	1.08865i
$575$		0			0
$576$	0.367767	−	0.133856i	0.0153236	−	0.00557734i
$577$	−1.12251	−	3.08407i	−0.0467308	−	0.128392i	0.914132	−	0.405417i	$-0.132874\pi$
$577$	−1.12251	−	3.08407i	−0.0467308	−	0.128392i	−0.960863	+	0.277025i	$0.910651\pi$
$578$	46.1588	−	26.6498i	1.91995	−	1.10849i
$579$	−42.5117	+	7.49596i	−1.76673	+	0.311521i
$580$		0			0
$581$	9.36829	−	16.2263i	0.388662	−	0.673182i
$582$	19.8833	+	34.4390i	0.824191	+	1.42754i
$583$	−1.95027	+	11.0605i	−0.0807718	+	0.458080i
$584$	−5.18663	−	2.99450i	−0.214624	−	0.123913i
$585$		0			0
$586$			53.5969i			2.21407i
$587$	−4.42689	+	12.1628i	−0.182717	+	0.502012i	−0.996907	−	0.0785868i	$-0.974959\pi$
$587$	−4.42689	+	12.1628i	−0.182717	+	0.502012i	0.814190	+	0.580599i	$0.197181\pi$
$588$	1.28571	+	7.29163i	0.0530218	+	0.300702i
$589$	8.95971	−	7.51809i	0.369178	−	0.309777i
$590$		0			0
$591$	−18.1892			−0.748205
$592$	−30.2475	+	2.82786i	−1.24317	+	0.116224i
$593$	44.1954			1.81489			0.907444	−	0.420174i	$-0.138031\pi$
$593$	44.1954			1.81489			0.907444	+	0.420174i	$0.138031\pi$
$594$	17.9796	−	21.4272i	0.737711	−	0.879169i
$595$		0			0
$596$	−2.56356	−	14.5387i	−0.105008	−	0.595528i
$597$	−12.0591	+	33.1321i	−0.493546	+	1.35601i
$598$			14.5695i			0.595789i
$599$	7.69706	+	2.80150i	0.314493	+	0.114466i	0.494444	−	0.869209i	$-0.335372\pi$
$599$	7.69706	+	2.80150i	0.314493	+	0.114466i	−0.179951	+	0.983676i	$0.557594\pi$
$600$		0			0
$601$	6.99477	−	39.6693i	0.285323	−	1.61815i	−0.418808	−	0.908075i	$-0.637552\pi$
$601$	6.99477	−	39.6693i	0.285323	−	1.61815i	0.704130	−	0.710071i	$-0.251337\pi$
$602$	21.8343	+	37.8181i	0.889899	+	1.54135i
$603$	−0.377750	+	0.654282i	−0.0153832	+	0.0266444i
$604$	5.62757	+	4.72209i	0.228983	+	0.192139i
$605$		0			0
$606$	20.6784	−	11.9387i	0.840002	−	0.484975i
$607$	1.89386	+	5.20335i	0.0768696	+	0.211197i	0.972175	−	0.234255i	$-0.0752651\pi$
$607$	1.89386	+	5.20335i	0.0768696	+	0.211197i	−0.895306	+	0.445452i	$0.853043\pi$
$608$	−8.05929	+	2.93334i	−0.326847	+	0.118963i
$609$	−53.8887	−	9.50203i	−2.18368	−	0.385042i
$610$		0			0
$611$	−11.6586	−	13.8942i	−0.471657	−	0.562099i
$612$	8.96518	+	1.58080i	0.362396	+	0.0639002i
$613$	−17.6777	+	6.43414i	−0.713994	+	0.259873i	−0.673374	−	0.739302i	$-0.735156\pi$
$613$	−17.6777	+	6.43414i	−0.713994	+	0.259873i	−0.0406202	+	0.999175i	$0.512933\pi$
$614$	10.3093	+	28.3246i	0.416050	+	1.14309i
$615$		0			0
$616$	−22.5110	+	3.96930i	−0.906994	+	0.159927i
$617$	10.6984	+	8.97703i	0.430702	+	0.361402i	0.832216	−	0.554451i	$-0.187072\pi$
$617$	10.6984	+	8.97703i	0.430702	+	0.361402i	−0.401515	+	0.915853i	$0.631516\pi$
$618$	−36.2892	+	62.8547i	−1.45976	+	2.52838i
$619$	−8.84392	−	15.3181i	−0.355467	−	0.615687i	0.631731	−	0.775188i	$-0.282345\pi$
$619$	−8.84392	−	15.3181i	−0.355467	−	0.615687i	−0.987198	+	0.159501i	$0.949012\pi$
$620$		0			0
$621$	−5.45931	−	3.15194i	−0.219075	−	0.126483i
$622$	−32.0696	−	11.6724i	−1.28587	−	0.468020i
$623$			10.9489i			0.438659i
$624$	16.8562	−	46.3121i	0.674790	−	1.85397i
$625$		0			0
$626$	24.5546	−	20.6038i	0.981399	−	0.823492i
$627$	−9.00829	+	10.7357i	−0.359756	+	0.428741i
$628$	25.8999			1.03352
$629$	38.0570	+	17.4712i	1.51743	+	0.696623i
$630$		0			0
$631$	−8.73458	+	10.4095i	−0.347718	+	0.414394i	−0.911350	−	0.411631i	$-0.864959\pi$
$631$	−8.73458	+	10.4095i	−0.347718	+	0.414394i	0.563632	+	0.826026i	$0.309404\pi$
$632$	−2.35960	+	1.97994i	−0.0938599	+	0.0787578i
$633$	−5.18502	−	29.4057i	−0.206086	−	1.16877i
$634$	−6.21982	+	17.0888i	−0.247021	+	0.678683i
$635$		0			0
$636$	5.32648	+	1.93868i	0.211209	+	0.0768736i
$637$	−13.9132	−	8.03277i	−0.551260	−	0.318270i
$638$	−11.0348	+	62.5814i	−0.436871	+	2.47762i
$639$	−8.83038	−	15.2947i	−0.349325	−	0.605048i
$640$		0			0
$641$	−7.68670	−	6.44991i	−0.303607	−	0.254756i	0.478237	−	0.878231i	$-0.341276\pi$
$641$	−7.68670	−	6.44991i	−0.303607	−	0.254756i	−0.781844	+	0.623475i	$0.785720\pi$
$642$	50.7419	−	8.94716i	2.00262	−	0.353116i
$643$	−41.8732	+	24.1755i	−1.65132	+	0.953388i	−0.674784	+	0.738015i	$0.735763\pi$
$643$	−41.8732	+	24.1755i	−1.65132	+	0.953388i	−0.976532	+	0.215373i	$0.930903\pi$
$644$	−2.04837	−	5.62785i	−0.0807171	−	0.221768i
$645$		0			0
$646$	18.4904	+	3.26035i	0.727494	+	0.128277i
$647$	−13.9394	−	16.6124i	−0.548015	−	0.653099i	0.418950	−	0.908009i	$-0.362398\pi$
$647$	−13.9394	−	16.6124i	−0.548015	−	0.653099i	−0.966965	+	0.254911i	$0.917954\pi$
$648$	11.6517	+	13.8860i	0.457722	+	0.545492i
$649$	−5.76279	−	1.01613i	−0.226209	−	0.0398868i
$650$		0			0
$651$	−17.0174	−	46.7550i	−0.666966	−	1.83247i
$652$	1.43924	−	0.830946i	0.0563650	−	0.0325424i
$653$	−29.7905	+	5.25287i	−1.16579	+	0.205561i	−0.722860	−	0.690994i	$-0.757173\pi$
$653$	−29.7905	+	5.25287i	−1.16579	+	0.205561i	−0.442932	+	0.896555i	$0.646062\pi$
$654$	−42.2561	−	35.4571i	−1.65234	−	1.38648i
$655$		0			0
$656$	15.0719	+	26.1053i	0.588459	+	1.01924i
$657$	−0.788673	+	4.47278i	−0.0307690	+	0.174500i
$658$	18.4678	+	10.6624i	0.719950	+	0.415663i
$659$	22.7270	+	8.27195i	0.885318	+	0.322229i	0.744354	−	0.667785i	$-0.232758\pi$
$659$	22.7270	+	8.27195i	0.885318	+	0.322229i	0.140964	+	0.990015i	$0.454980\pi$
$660$		0			0
$661$	−8.25434	+	22.6786i	−0.321057	+	0.882096i	0.669230	+	0.743055i	$0.266624\pi$
$661$	−8.25434	+	22.6786i	−0.321057	+	0.882096i	−0.990287	+	0.139040i	$0.955598\pi$
$662$	4.53378	+	25.7124i	0.176210	+	0.999339i
$663$	−52.0411	+	43.6676i	−2.02111	+	1.69591i
$664$	6.07180	−	7.23609i	0.235632	−	0.280815i
$665$		0			0
$666$	5.61504	+	11.8567i	0.217578	+	0.459437i
$667$	14.3215			0.554532
$668$	−10.8187	+	12.8932i	−0.418588	+	0.498854i
$669$	−18.3846	+	15.4265i	−0.710789	+	0.596422i
$670$		0			0
$671$	−6.32032	+	17.3649i	−0.243993	+	0.670365i
$672$			36.4849i			1.40744i
$673$	−44.8878	−	16.3378i	−1.73030	−	0.629777i	−0.731645	−	0.681686i	$-0.761247\pi$
$673$	−44.8878	−	16.3378i	−1.73030	−	0.629777i	−0.998652	+	0.0519090i	$0.983469\pi$
$674$	−38.8656	−	22.4391i	−1.49705	−	0.864320i
$675$		0			0
$676$	−5.38735	−	9.33116i	−0.207206	−	0.358891i
$677$	10.2443	−	17.7436i	0.393719	−	0.681941i	−0.599218	−	0.800586i	$-0.704522\pi$
$677$	10.2443	−	17.7436i	0.393719	−	0.681941i	0.992937	+	0.118645i	$0.0378551\pi$
$678$	7.46014	+	6.25980i	0.286505	+	0.240406i
$679$	34.9307	−	6.15922i	1.34052	−	0.236369i
$680$		0			0
$681$	20.0798	+	55.1687i	0.769459	+	2.11407i
$682$	−54.2970	+	19.7625i	−2.07914	+	0.756744i
$683$	39.5691	+	6.97710i	1.51407	+	0.266971i	0.868099	−	0.496391i	$-0.165342\pi$
$683$	39.5691	+	6.97710i	1.51407	+	0.266971i	0.645970	+	0.763363i	$0.276453\pi$
$684$	1.32194	+	1.57542i	0.0505455	+	0.0602378i
$685$		0			0
$686$	−20.2867	−	3.57709i	−0.774550	−	0.136574i
$687$	1.49264	−	0.543277i	0.0569479	−	0.0207273i
$688$	13.2230	+	36.3298i	0.504121	+	1.38506i
$689$	−10.6514	+	6.14960i	−0.405787	+	0.234281i
$690$		0			0
$691$	−29.5876	−	24.8270i	−1.12557	−	0.944463i	−0.126694	−	0.991942i	$-0.540437\pi$
$691$	−29.5876	−	24.8270i	−1.12557	−	0.944463i	−0.998872	+	0.0474792i	$0.984881\pi$
$692$	−4.02220	+	6.96666i	−0.152901	+	0.264833i
$693$	8.66733	+	15.0122i	0.329244	+	0.570268i
$694$	−9.72243	+	55.1386i	−0.369058	+	2.09303i
$695$		0			0
$696$	−25.9234	−	9.43534i	−0.982624	−	0.357646i
$697$		−	41.5510i		−	1.57386i
$698$	13.3436	−	36.6612i	0.505063	−	1.38765i
$699$	5.19095	+	29.4393i	0.196340	+	1.11350i
$700$		0			0
$701$	−15.0201	+	17.9003i	−0.567302	+	0.676085i	−0.971075	−	0.238775i	$-0.923254\pi$
$701$	−15.0201	+	17.9003i	−0.567302	+	0.676085i	0.403773	+	0.914859i	$0.367699\pi$
$702$	30.6312			1.15610
$703$	4.04900	+	8.54986i	0.152711	+	0.322464i
$704$	−1.39422			−0.0525468
$705$		0			0
$706$	27.5347	−	23.1044i	1.03628	−	0.869545i
$707$	−3.69821	−	20.9736i	−0.139086	−	0.788794i
$708$	−1.01010	+	2.77522i	−0.0379618	+	0.104299i
$709$			23.3205i			0.875820i	0.899019	+	0.437910i	$0.144281\pi$
$709$			23.3205i			0.875820i	−0.899019	+	0.437910i	$0.855719\pi$
$710$		0			0
$711$	2.02296	+	1.16796i	0.0758669	+	0.0438018i
$712$	−0.958520	+	5.43603i	−0.0359220	+	0.203724i
$713$	6.51111	+	11.2776i	0.243843	+	0.422349i
$714$	39.9362	−	69.1716i	1.49458	−	2.58868i
$715$		0			0
$716$	−20.1055	+	3.54514i	−0.751377	+	0.132488i
$717$	−38.8665	+	22.4396i	−1.45150	+	0.838022i
$718$	−14.0027	−	38.4721i	−0.522576	−	1.43576i
$719$	−24.1407	+	8.78650i	−0.900296	+	0.327681i	−0.750371	−	0.661016i	$-0.770125\pi$
$719$	−24.1407	+	8.78650i	−0.900296	+	0.327681i	−0.149925	+	0.988697i	$0.547903\pi$
$720$		0			0
$721$	41.6112	+	49.5903i	1.54968	+	1.84684i
$722$	−18.6904	−	22.2744i	−0.695585	−	0.828966i
$723$	−22.3120	−	3.93420i	−0.829791	−	0.146314i
$724$	−4.23977	+	1.54315i	−0.157570	+	0.0573508i
$725$		0			0
$726$	25.6015	−	14.7811i	0.950162	−	0.548577i
$727$	6.35393	−	1.12037i	0.235654	−	0.0415522i	−0.0545738	−	0.998510i	$-0.517380\pi$
$727$	6.35393	−	1.12037i	0.235654	−	0.0415522i	0.290228	+	0.956958i	$0.406269\pi$
$728$	−19.1756	−	16.0903i	−0.710697	−	0.596345i
$729$	−4.35777	+	7.54788i	−0.161399	+	0.279551i
$730$		0			0
$731$	9.25403	−	52.4822i	0.342273	−	1.94113i
$732$	8.07696	+	4.66324i	0.298533	+	0.172358i
$733$	34.7153	+	12.6353i	1.28224	+	0.466696i	0.891171	−	0.453667i	$-0.149884\pi$
$733$	34.7153	+	12.6353i	1.28224	+	0.466696i	0.391066	+	0.920363i	$0.372107\pi$
$734$		−	4.59127i		−	0.169467i
$735$		0			0
$736$	−1.65816	−	9.40390i	−0.0611206	−	0.346632i
$737$	2.06174	−	1.73000i	0.0759451	−	0.0637255i
$738$	8.36736	−	9.97183i	0.308007	−	0.367068i
$739$	37.1558			1.36680			0.683399	−	0.730045i	$-0.260501\pi$
$739$	37.1558			1.36680			0.683399	+	0.730045i	$0.260501\pi$
$740$		0			0
$741$	−15.3471			−0.563792
$742$	9.29499	−	11.0773i	0.341230	−	0.406662i
$743$	−12.3663	+	10.3766i	−0.453676	+	0.380680i	−0.840798	−	0.541349i	$-0.817914\pi$
$743$	−12.3663	+	10.3766i	−0.453676	+	0.380680i	0.387122	+	0.922029i	$0.373469\pi$
$744$	−4.35584	−	24.7032i	−0.159693	−	0.905664i
$745$		0			0
$746$		−	26.4268i		−	0.967554i
$747$	−6.73143	−	2.45004i	−0.246290	−	0.0896423i
$748$	−28.0856	−	16.2152i	−1.02691	−	0.592888i
$749$	7.98034	−	45.2588i	0.291595	−	1.65372i
$750$		0			0
$751$	17.3180	−	29.9957i	0.631944	−	1.09456i	−0.355210	−	0.934786i	$-0.615591\pi$
$751$	17.3180	−	29.9957i	0.631944	−	1.09456i	0.987154	−	0.159772i	$-0.0510760\pi$
$752$	14.4626	+	12.1356i	0.527398	+	0.442539i
$753$	34.3636	−	6.05923i	1.25228	−	0.220811i
$754$	−60.2667	+	34.7950i	−2.19478	+	1.26716i
$755$		0			0
$756$	−11.8322	+	4.30655i	−0.430332	+	0.156628i
$757$	−46.3966	−	8.18097i	−1.68631	−	0.297343i	−0.753432	−	0.657526i	$-0.771603\pi$
$757$	−46.3966	−	8.18097i	−1.68631	−	0.297343i	−0.932882	+	0.360183i	$0.882714\pi$
$758$	3.26011	+	3.88525i	0.118412	+	0.141118i
$759$	−10.0297	−	11.9529i	−0.364055	−	0.433864i
$760$		0			0
$761$	−24.3058	+	8.84660i	−0.881086	+	0.320689i	−0.742648	−	0.669682i	$-0.766430\pi$
$761$	−24.3058	+	8.84660i	−0.881086	+	0.320689i	−0.138438	+	0.990371i	$0.544208\pi$
$762$	−7.10595	−	19.5235i	−0.257422	−	0.707260i
$763$	−42.6091	+	24.6004i	−1.54255	+	0.890593i
$764$	14.3354	−	2.52773i	0.518638	−	0.0914499i
$765$		0			0
$766$	−6.02303	+	10.4322i	−0.217621	+	0.376931i
$767$	−3.20408	−	5.54964i	−0.115693	−	0.200386i
$768$	−7.02956	+	39.8666i	−0.253658	+	1.43856i
$769$	−37.4568	−	21.6257i	−1.35073	−	0.779843i	−0.362376	−	0.932032i	$-0.618035\pi$
$769$	−37.4568	−	21.6257i	−1.35073	−	0.779843i	−0.988351	+	0.152189i	$0.951368\pi$
$770$		0			0
$771$		−	5.12669i		−	0.184633i
$772$	7.71831	−	21.2059i	0.277788	−	0.763217i
$773$	5.03198	+	28.5378i	0.180988	+	1.02643i	0.931003	+	0.365012i	$0.118935\pi$
$773$	5.03198	+	28.5378i	0.180988	+	1.02643i	−0.750015	+	0.661421i	$0.769954\pi$
$774$	12.7895	−	10.7317i	0.459710	−	0.385743i
$775$		0			0
$776$	17.8820			0.641925
$777$	40.0692	−	3.74609i	1.43748	−	0.134390i
$778$	−48.1794			−1.72732
$779$	6.03371	−	7.19069i	0.216180	−	0.257633i
$780$		0			0
$781$	10.9251	+	61.9593i	0.390931	+	2.21708i
$782$	−7.14976	+	19.6438i	−0.255675	+	0.702461i
$783$		−	30.1100i		−	1.07604i
$784$	15.7143	+	5.71953i	0.561225	+	0.204269i
$785$		0			0
$786$	4.12823	−	23.4124i	0.147249	−	0.835091i
$787$	−9.74581	−	16.8802i	−0.347401	−	0.601715i	0.638386	−	0.769716i	$-0.279602\pi$
$787$	−9.74581	−	16.8802i	−0.347401	−	0.601715i	−0.985787	+	0.168001i	$0.946269\pi$
$788$	4.75443	−	8.23491i	0.169370	−	0.293357i
$789$	23.3483	+	19.5916i	0.831222	+	0.697478i
$790$		0			0
$791$	7.52245	−	4.34309i	0.267468	−	0.154423i
$792$	2.98900	+	8.21222i	0.106210	+	0.291809i
$793$	−19.0163	+	6.92136i	−0.675288	+	0.245785i
$794$	25.2144	+	4.44599i	0.894827	+	0.157782i
$795$		0			0
$796$	−11.8480	−	14.1199i	−0.419941	−	0.500466i
$797$	15.4434	+	2.72309i	0.547034	+	0.0964568i	0.440333	−	0.897834i	$-0.354860\pi$
$797$	15.4434	+	2.72309i	0.547034	+	0.0964568i	0.106700	+	0.994291i	$0.465971\pi$
$798$	16.9558	−	6.17141i	0.600229	−	0.218465i
$799$	−8.90078	−	24.4547i	−0.314887	−	0.865145i
$800$		0			0
$801$	4.12244	−	0.726897i	0.145659	−	0.0256836i
$802$	0.437768	+	0.367331i	0.0154581	+	0.0129709i
$803$	8.08988	−	14.0121i	0.285486	−	0.494476i
$804$	−0.679173	−	1.17636i	−0.0239526	−	0.0414871i
$805$		0			0
$806$	−54.7991	−	31.6383i	−1.93021	−	1.11441i
$807$	−26.5272	−	9.65512i	−0.933802	−	0.339876i
$808$		−	10.7370i		−	0.377725i
$809$	−2.79448	+	7.67776i	−0.0982486	+	0.269936i	−0.979074	−	0.203506i	$-0.934766\pi$
$809$	−2.79448	+	7.67776i	−0.0982486	+	0.269936i	0.880825	+	0.473442i	$0.156989\pi$
$810$		0			0
$811$	31.2095	−	26.1879i	1.09591	−	0.919580i	0.0987695	−	0.995110i	$-0.468509\pi$
$811$	31.2095	−	26.1879i	1.09591	−	0.919580i	0.997144	+	0.0755301i	$0.0240649\pi$
$812$	18.3877	−	21.9136i	0.645282	−	0.769017i
$813$	−10.8971			−0.382177
$814$	−4.35037	−	46.5327i	−0.152480	−	1.63097i
$815$		0			0
$816$	45.4541	−	54.1701i	1.59121	−	1.89633i
$817$	9.22254	−	7.73863i	0.322656	−	0.270740i
$818$	−1.14125	−	6.47235i	−0.0399029	−	0.226301i
$819$	−6.49261	+	17.8383i	−0.226870	+	0.623321i
$820$		0			0
$821$	−26.2164	−	9.54200i	−0.914959	−	0.333018i	−0.158728	−	0.987322i	$-0.550739\pi$
$821$	−26.2164	−	9.54200i	−0.914959	−	0.333018i	−0.756231	+	0.654304i	$0.772962\pi$
$822$	0.0359965	+	0.0207826i	0.00125552	+	0.000724875i
$823$	−2.04791	+	11.6143i	−0.0713857	+	0.404849i	0.928087	+	0.372365i	$0.121453\pi$
$823$	−2.04791	+	11.6143i	−0.0713857	+	0.404849i	−0.999472	+	0.0324840i	$0.989658\pi$
$824$	16.3182	+	28.2640i	0.568472	+	0.984622i
$825$		0			0
$826$	5.77155	+	4.84291i	0.200818	+	0.168506i
$827$	43.4424	−	7.66006i	1.51064	−	0.266366i	0.643893	−	0.765116i	$-0.277318\pi$
$827$	43.4424	−	7.66006i	1.51064	−	0.266366i	0.866746	+	0.498749i	$0.166207\pi$
$828$	−1.98298	+	1.14488i	−0.0689134	+	0.0397872i
$829$	7.55135	+	20.7472i	0.262269	+	0.720579i	0.999014	+	0.0444072i	$0.0141399\pi$
$829$	7.55135	+	20.7472i	0.262269	+	0.720579i	−0.736744	+	0.676171i	$0.763638\pi$
$830$		0			0
$831$	−66.5344	−	11.7318i	−2.30805	−	0.406972i
$832$	−0.981415	−	1.16961i	−0.0340245	−	0.0405488i
$833$	−14.8170	−	17.6582i	−0.513378	−	0.611820i
$834$	55.9730	+	9.86955i	1.93819	+	0.341755i
$835$		0			0
$836$	−2.50577	−	6.88453i	−0.0866637	−	0.238107i
$837$	23.7103	−	13.6892i	0.819548	−	0.473166i
$838$	9.65166	−	1.70185i	0.333411	−	0.0587894i
$839$	−2.07653	−	1.74242i	−0.0716899	−	0.0601549i	0.606239	−	0.795283i	$-0.292678\pi$
$839$	−2.07653	−	1.74242i	−0.0716899	−	0.0601549i	−0.677928	+	0.735128i	$0.737122\pi$
$840$		0			0
$841$	19.7029	+	34.1263i	0.679409	+	1.17677i
$842$	−4.50525	+	25.5506i	−0.155261	+	0.880531i
$843$	27.4923	+	15.8727i	0.946886	+	0.546685i
$844$	14.6683	+	5.33883i	0.504904	+	0.183770i
$845$		0			0
$846$	2.78848	−	7.66129i	0.0958699	−	0.263401i
$847$	−4.57870	−	25.9671i	−0.157326	−	0.892239i
$848$	9.80718	−	8.22920i	0.336780	−	0.282592i
$849$	19.6201	−	23.3823i	0.673359	−	0.802478i
$850$		0			0
$851$	−10.1575	+	2.78661i	−0.348194	+	0.0955236i
$852$	31.7531			1.08784
$853$	−27.8851	+	33.2322i	−0.954769	+	1.13785i	0.0355963	+	0.999366i	$0.488667\pi$
$853$	−27.8851	+	33.2322i	−0.954769	+	1.13785i	−0.990365	+	0.138483i	$0.955777\pi$
$854$	18.2263	−	15.2937i	0.623691	−	0.523339i
$855$		0			0
$856$	7.92433	−	21.7719i	0.270848	−	0.744149i
$857$			16.3581i			0.558780i	0.960178	+	0.279390i	$0.0901323\pi$
$857$			16.3581i			0.558780i	−0.960178	+	0.279390i	$0.909868\pi$
$858$	71.2465	+	25.9316i	2.43231	+	0.885290i
$859$	−16.4757	−	9.51227i	−0.562145	−	0.324555i	0.191861	−	0.981422i	$-0.438548\pi$
$859$	−16.4757	−	9.51227i	−0.562145	−	0.324555i	−0.754006	+	0.656868i	$0.771881\pi$
$860$		0			0
$861$	−19.9659	−	34.5820i	−0.680437	−	1.17855i
$862$	1.81196	−	3.13841i	0.0617158	−	0.106895i
$863$	20.8635	+	17.5065i	0.710200	+	0.595929i	0.924655	−	0.380805i	$-0.124353\pi$
$863$	20.8635	+	17.5065i	0.710200	+	0.595929i	−0.214455	+	0.976734i	$0.568798\pi$
$864$	−19.7710	+	3.48617i	−0.672624	+	0.118602i
$865$		0			0
$866$	13.2170	+	36.3135i	0.449134	+	1.23398i
$867$	−58.7408	+	21.3799i	−1.99494	+	0.726099i
$868$	25.6158	+	4.51675i	0.869456	+	0.153309i
$869$	−5.34896	−	6.37464i	−0.181451	−	0.216245i
$870$		0			0
$871$	2.90258	+	0.511803i	0.0983501	+	0.0173418i
$872$	−23.3086	+	8.48365i	−0.789330	+	0.287293i
$873$	−4.63808	−	12.7430i	−0.156975	−	0.431286i
$874$	−4.08984	+	2.36127i	−0.138341	+	0.0798711i
$875$		0			0
$876$	−6.25542	−	5.24892i	−0.211351	−	0.177345i
$877$	23.7911	−	41.2075i	0.803370	−	1.39148i	−0.114016	−	0.993479i	$-0.536372\pi$
$877$	23.7911	−	41.2075i	0.803370	−	1.39148i	0.917386	−	0.397998i	$-0.130295\pi$
$878$	5.68087	+	9.83955i	0.191720	+	0.332069i
$879$	10.9154	−	61.9043i	0.368167	−	2.08798i
$880$		0			0
$881$	7.27907	+	2.64937i	0.245238	+	0.0892594i	0.461715	−	0.887028i	$-0.347234\pi$
$881$	7.27907	+	2.64937i	0.245238	+	0.0892594i	−0.216477	+	0.976288i	$0.569457\pi$
$882$		−	7.22157i		−	0.243163i
$883$	16.2458	−	44.6349i	0.546714	−	1.50209i	−0.291406	−	0.956599i	$-0.594123\pi$
$883$	16.2458	−	44.6349i	0.546714	−	1.50209i	0.838120	−	0.545486i	$-0.183655\pi$
$884$	−6.16703	−	34.9750i	−0.207420	−	1.17634i
$885$		0			0
$886$	33.9286	−	40.4345i	1.13985	−	1.35842i
$887$	−0.179153			−0.00601537			−0.00300769	−	0.999995i	$-0.500957\pi$
$887$	−0.179153			−0.00601537			−0.00300769	+	0.999995i	$0.500957\pi$
$888$	20.2220	+	1.64795i	0.678605	+	0.0553016i
$889$	−18.5313			−0.621521
$890$		0			0
$891$	−37.5140	+	31.4780i	−1.25677	+	1.05455i
$892$	−2.17863	−	12.3556i	−0.0729460	−	0.413697i
$893$	2.01077	−	5.52456i	0.0672880	−	0.184872i
$894$			49.5216i			1.65625i
$895$		0			0
$896$	32.2808	+	18.6374i	1.07843	+	0.622630i
$897$	2.96718	−	16.8277i	0.0990711	−	0.561860i
$898$	−5.98847	−	10.3723i	−0.199838	−	0.346129i
$899$	−31.0999	+	53.8665i	−1.03724	+	1.79655i
$900$		0			0
$901$	−17.3790	+	3.06439i	−0.578978	+	0.102090i
$902$	−40.1603	+	23.1866i	−1.33719	+	0.772029i
$903$	−17.5166	−	48.1265i	−0.582917	−	1.60155i
$904$	4.11504	−	1.49775i	0.136864	−	0.0498145i
$905$		0			0
$906$	−15.8400	−	18.8774i	−0.526249	−	0.627159i
$907$	−1.50821	−	1.79742i	−0.0500793	−	0.0596822i	0.740423	−	0.672141i	$-0.234625\pi$
$907$	−1.50821	−	1.79742i	−0.0500793	−	0.0596822i	−0.790503	+	0.612459i	$0.790181\pi$
$908$	−30.2254	−	5.32956i	−1.00307	−	0.176868i
$909$	−7.65137	+	2.78487i	−0.253780	+	0.0923683i
$910$		0			0
$911$	3.92335	−	2.26514i	0.129986	−	0.0750476i	−0.433597	−	0.901107i	$-0.642756\pi$
$911$	3.92335	−	2.26514i	0.129986	−	0.0750476i	0.563583	+	0.826059i	$0.309422\pi$
$912$	15.7323	−	2.77403i	0.520949	−	0.0918573i
$913$	19.5489	+	16.4034i	0.646973	+	0.542875i
$914$	9.04245	−	15.6620i	0.299098	−	0.518052i
$915$		0			0
$916$	−0.144196	+	0.817778i	−0.00476438	+	0.0270201i
$917$	−18.3637	−	10.6023i	−0.606423	−	0.350118i
$918$	41.2997	+	15.0319i	1.36309	+	0.496126i
$919$		−	3.16709i		−	0.104473i	−0.998635	−	0.0522363i	$-0.983365\pi$
$919$		−	3.16709i		−	0.104473i	0.998635	−	0.0522363i	$-0.0166349\pi$
$920$		0			0
$921$	−6.13872	−	34.8144i	−0.202278	−	1.14717i
$922$	28.7440	−	24.1191i	0.946633	−	0.794320i
$923$	−44.2869	+	52.7791i	−1.45772	+	1.73725i
$924$	−31.1667			−1.02531
$925$		0			0
$926$	−8.27135			−0.271814
$927$	15.9090	−	18.9596i	0.522519	−	0.622714i
$928$	34.9392	−	29.3175i	1.14694	−	0.962394i
$929$	7.41257	+	42.0387i	0.243198	+	1.37925i	0.824640	+	0.565658i	$0.191378\pi$
$929$	7.41257	+	42.0387i	0.243198	+	1.37925i	−0.581441	+	0.813588i	$0.697511\pi$
$930$		0			0
$931$		−	5.20748i		−	0.170668i
$932$	−14.6851	−	5.34493i	−0.481026	−	0.175079i
$933$	34.6632	+	20.0128i	1.13482	+	0.655190i
$934$	6.70758	−	38.0406i	0.219479	−	1.24473i
$935$		0			0
$936$	−4.78517	+	8.28816i	−0.156408	+	0.270907i
$937$	−5.73390	−	4.81131i	−0.187318	−	0.157179i	0.544306	−	0.838887i	$-0.316793\pi$
$937$	−5.73390	−	4.81131i	−0.187318	−	0.157179i	−0.731624	+	0.681708i	$0.761237\pi$
$938$	−3.41263	+	0.601738i	−0.111426	+	0.0196474i
$939$	−32.5566	+	18.7966i	−1.06245	+	0.613403i
$940$		0			0
$941$	21.0744	−	7.67044i	0.687005	−	0.250049i	0.0251526	−	0.999684i	$-0.491993\pi$
$941$	21.0744	−	7.67044i	0.687005	−	0.250049i	0.661852	+	0.749634i	$0.269771\pi$
$942$	−85.5599	−	15.0865i	−2.78769	−	0.491545i
$943$	6.71784	+	8.00601i	0.218763	+	0.260712i
$944$	4.28761	+	5.10977i	0.139550	+	0.166309i
$945$		0			0
$946$	−55.8897	+	20.3422i	−1.81713	+	0.661382i
$947$	−3.38645	−	9.30421i	−0.110045	−	0.302346i	0.872430	−	0.488738i	$-0.162543\pi$
$947$	−3.38645	−	9.30421i	−0.110045	−	0.302346i	−0.982475	+	0.186392i	$0.940320\pi$
$948$	−3.63717	+	2.09992i	−0.118130	+	0.0682022i
$949$	17.4492	−	3.07677i	0.566426	−	0.0998762i
$950$		0			0
$951$	10.6641	−	18.4708i	0.345808	−	0.598958i
$952$	−17.9582	−	31.1045i	−0.582028	−	1.00810i
$953$	1.49945	−	8.50379i	0.0485719	−	0.275465i	−0.950843	−	0.309674i	$-0.899780\pi$
$953$	1.49945	−	8.50379i	0.0485719	−	0.275465i	0.999415	+	0.0342091i	$0.0108912\pi$
$954$	−4.78788	−	2.76429i	−0.155013	−	0.0894971i
$955$		0			0
$956$		−	23.4617i		−	0.758804i
$957$	25.4903	−	70.0341i	0.823985	−	2.26388i
$958$	3.94685	+	22.3837i	0.127517	+	0.723185i
$959$	0.0284001	−	0.0238305i	0.000917086	−	0.000769526i
$960$		0			0
$961$	−25.5568			−0.824411
$962$	35.9737	−	36.4046i	1.15984	−	1.17373i
$963$	−17.5704			−0.566200
$964$	7.61320	−	9.07306i	0.245205	−	0.292224i
$965$		0			0
$966$	3.48858	+	19.7847i	0.112243	+	0.636562i
$967$	−15.6983	+	43.1306i	−0.504822	+	1.38699i	0.381693	+	0.924289i	$0.375341\pi$
$967$	−15.6983	+	43.1306i	−0.504822	+	1.38699i	−0.886515	+	0.462699i	$0.846881\pi$
$968$		−	13.2933i		−	0.427261i
$969$	−20.6924	−	7.53140i	−0.664735	−	0.241944i
$970$		0			0
$971$	4.23357	−	24.0098i	0.135862	−	0.770510i	−0.838394	−	0.545064i	$-0.816505\pi$
$971$	4.23357	−	24.0098i	0.135862	−	0.770510i	0.974256	−	0.225445i	$-0.0723837\pi$
$972$	6.48647	+	11.2349i	0.208054	+	0.360359i
$973$	25.3474	−	43.9030i	0.812600	−	1.40746i
$974$	24.7891	+	20.8005i	0.794294	+	0.666492i
$975$		0			0
$976$	18.2425	−	10.5323i	0.583928	−	0.337131i
$977$	−6.50697	−	17.8778i	−0.208176	−	0.571960i	0.791031	−	0.611777i	$-0.209545\pi$
$977$	−6.50697	−	17.8778i	−0.208176	−	0.571960i	−0.999207	+	0.0398165i	$0.987323\pi$
$978$	−5.23853	+	1.90667i	−0.167510	+	0.0609686i
$979$	−14.6859	−	2.58952i	−0.469362	−	0.0827613i
$980$		0			0
$981$	12.0912	+	14.4098i	0.386043	+	0.460068i
$982$	38.7361	+	6.83022i	1.23612	+	0.217961i
$983$	37.8892	−	13.7905i	1.20848	−	0.439850i	0.342302	−	0.939590i	$-0.388794\pi$
$983$	37.8892	−	13.7905i	1.20848	−	0.439850i	0.866175	+	0.499741i	$0.166571\pi$
$984$	−6.88542	−	18.9175i	−0.219499	−	0.603069i
$985$		0			0
$986$	−98.3319	+	17.3386i	−3.13153	+	0.552173i
$987$	−19.1588	−	16.0761i	−0.609831	−	0.511709i
$988$	4.01154	−	6.94820i	0.127624	−	0.221052i
$989$	6.70211	+	11.6084i	0.213115	+	0.369126i
$990$		0			0
$991$	48.0133	+	27.7205i	1.52519	+	0.880570i	0.999554	+	0.0298609i	$0.00950644\pi$
$991$	48.0133	+	27.7205i	1.52519	+	0.880570i	0.525637	+	0.850709i	$0.323827\pi$
$992$	38.9710	+	14.1843i	1.23733	+	0.450351i
$993$		−	30.6211i		−	0.971730i
$994$	27.7054	−	76.1200i	0.878762	−	2.41438i
$995$		0			0
$996$	9.86624	−	8.27876i	0.312624	−	0.262323i
$997$	18.1206	−	21.5953i	0.573886	−	0.683930i	−0.398538	−	0.917152i	$-0.630482\pi$
$997$	18.1206	−	21.5953i	0.573886	−	0.683930i	0.972424	+	0.233222i	$0.0749268\pi$
$998$	0.418255			0.0132396
$999$	5.85864	+	21.3554i	0.185359	+	0.675655i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.bb.d.151.10	yes	78
5.2	odd	4		925.2.ba.d.299.20		156
5.3	odd	4		925.2.ba.d.299.7		156
5.4	even	2		925.2.bb.c.151.4	✓	78
37.25	even	18	inner	925.2.bb.d.876.10	yes	78
185.62	odd	36		925.2.ba.d.99.7		156
185.99	even	18		925.2.bb.c.876.4	yes	78
185.173	odd	36		925.2.ba.d.99.20		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.ba.d.99.7		156	185.62	odd	36
925.2.ba.d.99.20		156	185.173	odd	36
925.2.ba.d.299.7		156	5.3	odd	4
925.2.ba.d.299.20		156	5.2	odd	4
925.2.bb.c.151.4	✓	78	5.4	even	2
925.2.bb.c.876.4	yes	78	185.99	even	18
925.2.bb.d.151.10	yes	78	1.1	even	1	trivial
925.2.bb.d.876.10	yes	78	37.25	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.12720 - 1.34335i) q^{2} +(-1.57550 + 1.32200i) q^{3} +(-0.186702 - 1.05884i) q^{4} +3.60661i q^{6} +(3.02288 + 1.10024i) q^{7} +(1.40451 + 0.810896i) q^{8} +(0.213569 - 1.21121i) q^{9} +(-2.19070 + 3.79440i) q^{11} +(1.69394 + 1.42138i) q^{12} +(-4.72516 + 0.833174i) q^{13} +(4.88541 - 2.82059i) q^{14} +(4.69315 - 1.70817i) q^{16} +(-6.77975 - 1.19545i) q^{17} +(-1.38634 - 1.65217i) q^{18} +(-0.999689 - 1.19138i) q^{19} +(-6.21707 + 2.26283i) q^{21} +(2.62784 + 7.21993i) q^{22} +(1.49959 - 0.865791i) q^{23} +(-3.28482 + 0.579202i) q^{24} +(-4.20698 + 7.28670i) q^{26} +(-1.82026 - 3.15279i) q^{27} +(0.600598 - 3.40616i) q^{28} +(7.16270 + 4.13539i) q^{29} +7.52042i q^{31} +(1.88610 - 5.18202i) q^{32} +(-1.56476 - 8.87419i) q^{33} +(-9.24806 + 7.76005i) q^{34} -1.32235 q^{36} +(-5.88477 - 1.53933i) q^{37} -2.72730 q^{38} +(6.34304 - 7.55934i) q^{39} +(1.04807 + 5.94389i) q^{41} +(-3.96814 + 10.9024i) q^{42} +7.74103i q^{43} +(4.42667 + 1.61118i) q^{44} +(0.527288 - 2.99040i) q^{46} +(1.89010 + 3.27374i) q^{47} +(-5.13586 + 8.89558i) q^{48} +(2.56498 + 2.15227i) q^{49} +(12.2619 - 7.07940i) q^{51} +(1.76439 + 4.84763i) q^{52} +(2.40878 - 0.876724i) q^{53} +(-6.28710 - 1.10859i) q^{54} +(3.35350 + 3.99654i) q^{56} +(3.15002 + 0.555434i) q^{57} +(13.6291 - 4.96058i) q^{58} +(0.456794 + 1.25503i) q^{59} +(4.15361 - 0.732394i) q^{61} +(10.1025 + 8.47705i) q^{62} +(1.97821 - 3.42636i) q^{63} +(0.159107 + 0.275582i) q^{64} +(-13.6849 - 7.90100i) q^{66} +(-0.577235 - 0.210097i) q^{67} +7.40185i q^{68} +(-1.21803 + 3.34652i) q^{69} +(11.0001 - 9.23018i) q^{71} +(1.28212 - 1.52797i) q^{72} -3.69283 q^{73} +(-8.70118 + 6.17015i) q^{74} +(-1.07484 + 1.28094i) q^{76} +(-10.7970 + 9.05974i) q^{77} +(-3.00494 - 17.0418i) q^{78} +(-0.649592 + 1.78474i) q^{79} +(10.5030 + 3.82277i) q^{81} +(9.16610 + 5.29205i) q^{82} +(1.01140 - 5.73596i) q^{83} +(3.55671 + 6.16040i) q^{84} +(10.3989 + 8.72572i) q^{86} +(-16.7518 + 2.95380i) q^{87} +(-6.15373 + 3.55286i) q^{88} +(1.16409 + 3.19832i) q^{89} +(-15.2003 - 2.68022i) q^{91} +(-1.19671 - 1.42618i) q^{92} +(-9.94201 - 11.8484i) q^{93} +(6.52830 + 1.15112i) q^{94} +(3.87909 + 10.6577i) q^{96} +(9.54884 - 5.51302i) q^{97} +(5.78251 - 1.01961i) q^{98} +(4.12794 + 3.46375i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 3 q^{2} + 3 q^{4} - 6 q^{7} + 18 q^{8} + 15 q^{12} - 27 q^{13} - 18 q^{14} + 9 q^{16} - 15 q^{18} + 3 q^{21} - 30 q^{22} + 15 q^{24} + 36 q^{27} + 27 q^{28} - 9 q^{29} - 18 q^{32} - 6 q^{33} - 51 q^{34}+ \cdots - 183 q^{99}+O(q^{100}) \) 78 * q + 3 * q^2 + 3 * q^4 - 6 * q^7 + 18 * q^8 + 15 * q^12 - 27 * q^13 - 18 * q^14 + 9 * q^16 - 15 * q^18 + 3 * q^21 - 30 * q^22 + 15 * q^24 + 36 * q^27 + 27 * q^28 - 9 * q^29 - 18 * q^32 - 6 * q^33 - 51 * q^34 - 108 * q^36 + 6 * q^37 + 84 * q^38 - 33 * q^39 - 21 * q^41 + 42 * q^42 - 3 * q^44 + 36 * q^46 - 57 * q^47 + 54 * q^48 + 54 * q^49 + 90 * q^51 + 75 * q^52 - 24 * q^53 - 39 * q^54 - 48 * q^56 - 9 * q^57 + 9 * q^58 + 15 * q^59 - 18 * q^61 - 120 * q^63 + 66 * q^64 + 126 * q^66 - 24 * q^67 + 45 * q^69 + 48 * q^71 + 132 * q^72 - 60 * q^73 - 12 * q^74 + 81 * q^76 + 21 * q^77 - 258 * q^78 + 84 * q^79 + 48 * q^81 + 234 * q^82 + 42 * q^83 + 57 * q^84 - 66 * q^86 + 24 * q^87 - 90 * q^88 + 39 * q^89 + 57 * q^91 - 87 * q^92 - 12 * q^93 + 78 * q^94 - 78 * q^96 - 36 * q^97 + 126 * q^98 - 183 * q^99

Introduction

L-functions

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