LMFDB - Embedded newform 925.2.y.b.193.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(193,925)] 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("925.193"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.y (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [68] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.11
Character	$\chi$	$=$	925.193
Dual form			925.2.y.b.532.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.713738 - 0.412077i) q^{2} +(-0.475172 - 1.77336i) q^{3} +(-0.660386 + 1.14382i) q^{4} +(-1.06991 - 1.06991i) q^{6} +(-0.320840 - 1.19739i) q^{7} +2.73682i q^{8} +(-0.320958 + 0.185305i) q^{9} +4.12374i q^{11} +(2.34221 + 0.627593i) q^{12} +(4.26154 + 2.46040i) q^{13} +(-0.722412 - 0.722412i) q^{14} +(-0.192990 - 0.334268i) q^{16} +(0.998860 + 1.73008i) q^{17} +(-0.152720 + 0.264518i) q^{18} +(0.608896 + 2.27243i) q^{19} +(-1.97096 + 1.13793i) q^{21} +(1.69930 + 2.94327i) q^{22} +0.794336i q^{23} +(4.85339 - 1.30046i) q^{24} +4.05550 q^{26} +(-3.41346 - 3.41346i) q^{27} +(1.58148 + 0.423756i) q^{28} +(-1.67939 - 1.67939i) q^{29} +(6.42495 - 6.42495i) q^{31} +(-5.01581 - 2.89588i) q^{32} +(7.31290 - 1.95948i) q^{33} +(1.42585 + 0.823214i) q^{34} -0.489491i q^{36} +(6.00606 - 0.962921i) q^{37} +(1.37101 + 1.37101i) q^{38} +(2.33823 - 8.72639i) q^{39} +(9.74356 + 5.62545i) q^{41} +(-0.937830 + 1.62437i) q^{42} +11.4197i q^{43} +(-4.71682 - 2.72326i) q^{44} +(0.327327 + 0.566948i) q^{46} +(2.19390 - 2.19390i) q^{47} +(-0.501076 + 0.501076i) q^{48} +(4.73137 - 2.73166i) q^{49} +(2.59343 - 2.59343i) q^{51} +(-5.62853 + 3.24963i) q^{52} +(0.938365 - 3.50202i) q^{53} +(-3.84292 - 1.02971i) q^{54} +(3.27705 - 0.878082i) q^{56} +(3.74052 - 2.15959i) q^{57} +(-1.89069 - 0.506608i) q^{58} +(-1.41608 - 0.379437i) q^{59} +(-1.72489 - 6.43736i) q^{61} +(1.93816 - 7.23330i) q^{62} +(0.324858 + 0.324858i) q^{63} -4.00134 q^{64} +(4.41203 - 4.41203i) q^{66} +(-5.70687 + 1.52915i) q^{67} -2.63853 q^{68} +(1.40865 - 0.377446i) q^{69} +(-3.30595 + 5.72607i) q^{71} +(-0.507147 - 0.878404i) q^{72} +(-5.14518 + 5.14518i) q^{73} +(3.88996 - 3.16223i) q^{74} +(-3.00136 - 0.804213i) q^{76} +(4.93773 - 1.32306i) q^{77} +(-1.92706 - 7.19188i) q^{78} +(2.30362 + 8.59723i) q^{79} +(-4.98724 + 8.63815i) q^{81} +9.27246 q^{82} +(-0.310366 + 1.15830i) q^{83} -3.00590i q^{84} +(4.70581 + 8.15069i) q^{86} +(-2.18018 + 3.77618i) q^{87} -11.2860 q^{88} +(-1.87621 + 7.00209i) q^{89} +(1.57879 - 5.89213i) q^{91} +(-0.908579 - 0.524568i) q^{92} +(-14.4467 - 8.34083i) q^{93} +(0.661816 - 2.46993i) q^{94} +(-2.75208 + 10.2709i) q^{96} +11.7662 q^{97} +(2.25131 - 3.89938i) q^{98} +(-0.764149 - 1.32355i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Character values

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

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.713738	−	0.412077i	0.504689	−	0.291382i	−0.225959	−	0.974137i	$-0.572552\pi$
$2$	0.713738	−	0.412077i	0.504689	−	0.291382i	0.730648	+	0.682755i	$0.239218\pi$
$3$	−0.475172	−	1.77336i	−0.274340	−	1.02385i	−0.956282	−	0.292446i	$-0.905531\pi$
$3$	−0.475172	−	1.77336i	−0.274340	−	1.02385i	0.681942	−	0.731407i	$-0.261136\pi$
$4$	−0.660386	+	1.14382i	−0.330193	+	0.571911i
$5$		0			0
$5$		0			0
$6$	−1.06991	−	1.06991i	−0.436789	−	0.436789i
$7$	−0.320840	−	1.19739i	−0.121266	−	0.452571i	0.878413	−	0.477902i	$-0.158603\pi$
$7$	−0.320840	−	1.19739i	−0.121266	−	0.452571i	−0.999679	+	0.0253311i	$0.991936\pi$
$8$			2.73682i			0.967614i
$9$	−0.320958	+	0.185305i	−0.106986	+	0.0617683i
$10$		0			0
$11$			4.12374i			1.24335i	0.783273	+	0.621677i	$0.213548\pi$
$11$			4.12374i			1.24335i	−0.783273	+	0.621677i	$0.786452\pi$
$12$	2.34221	+	0.627593i	0.676138	+	0.181171i
$13$	4.26154	+	2.46040i	1.18194	+	0.682393i	0.956463	−	0.291855i	$-0.0942725\pi$
$13$	4.26154	+	2.46040i	1.18194	+	0.682393i	0.225477	+	0.974248i	$0.427606\pi$
$14$	−0.722412	−	0.722412i	−0.193073	−	0.193073i
$15$		0			0
$16$	−0.192990	−	0.334268i	−0.0482475	−	0.0835671i
$17$	0.998860	+	1.73008i	0.242259	+	0.419605i	0.961357	−	0.275303i	$-0.0887783\pi$
$17$	0.998860	+	1.73008i	0.242259	+	0.419605i	−0.719098	+	0.694908i	$0.755445\pi$
$18$	−0.152720	+	0.264518i	−0.0359964	+	0.0623475i
$19$	0.608896	+	2.27243i	0.139690	+	0.521331i	0.999934	+	0.0114491i	$0.00364443\pi$
$19$	0.608896	+	2.27243i	0.139690	+	0.521331i	−0.860244	+	0.509882i	$0.829689\pi$
$20$		0			0
$21$	−1.97096	+	1.13793i	−0.430098	+	0.248317i
$22$	1.69930	+	2.94327i	0.362291	+	0.627507i
$23$			0.794336i			0.165631i	0.996565	+	0.0828153i	$0.0263911\pi$
$23$			0.794336i			0.165631i	−0.996565	+	0.0828153i	$0.973609\pi$
$24$	4.85339	−	1.30046i	0.990694	−	0.265456i
$25$		0			0
$26$	4.05550			0.795349
$27$	−3.41346	−	3.41346i	−0.656920	−	0.656920i
$28$	1.58148	+	0.423756i	0.298871	+	0.0800824i
$29$	−1.67939	−	1.67939i	−0.311856	−	0.311856i	0.533772	−	0.845628i	$-0.320774\pi$
$29$	−1.67939	−	1.67939i	−0.311856	−	0.311856i	−0.845628	+	0.533772i	$0.820774\pi$
$30$		0			0
$31$	6.42495	−	6.42495i	1.15396	−	1.15396i	0.168203	−	0.985752i	$-0.446203\pi$
$31$	6.42495	−	6.42495i	1.15396	−	1.15396i	0.985752	−	0.168203i	$-0.0537965\pi$
$32$	−5.01581	−	2.89588i	−0.886678	−	0.511924i
$33$	7.31290	−	1.95948i	1.27301	−	0.341102i
$34$	1.42585	+	0.823214i	0.244531	+	0.141180i
$35$		0			0
$36$		−	0.489491i		−	0.0815818i
$37$	6.00606	−	0.962921i	0.987391	−	0.158303i
$37$	6.00606	−	0.962921i	0.987391	−	0.158303i
$38$	1.37101	+	1.37101i	0.222407	+	0.222407i
$39$	2.33823	−	8.72639i	0.374416	−	1.39734i
$40$		0			0
$41$	9.74356	+	5.62545i	1.52169	+	0.878547i	0.999672	+	0.0256114i	$0.00815325\pi$
$41$	9.74356	+	5.62545i	1.52169	+	0.878547i	0.522016	+	0.852936i	$0.325180\pi$
$42$	−0.937830	+	1.62437i	−0.144710	+	0.250646i
$43$			11.4197i			1.74149i	0.491732	+	0.870747i	$0.336364\pi$
$43$			11.4197i			1.74149i	−0.491732	+	0.870747i	$0.663636\pi$
$44$	−4.71682	−	2.72326i	−0.711088	−	0.410547i
$45$		0			0
$46$	0.327327	+	0.566948i	0.0482618	+	0.0835919i
$47$	2.19390	−	2.19390i	0.320014	−	0.320014i	−0.528758	−	0.848772i	$-0.677342\pi$
$47$	2.19390	−	2.19390i	0.320014	−	0.320014i	0.848772	+	0.528758i	$0.177342\pi$
$48$	−0.501076	+	0.501076i	−0.0723241	+	0.0723241i
$49$	4.73137	−	2.73166i	0.675910	−	0.390237i
$50$		0			0
$51$	2.59343	−	2.59343i	0.363152	−	0.363152i
$52$	−5.62853	+	3.24963i	−0.780536	+	0.450643i
$53$	0.938365	−	3.50202i	0.128894	−	0.481040i	−0.871054	−	0.491187i	$-0.836563\pi$
$53$	0.938365	−	3.50202i	0.128894	−	0.481040i	0.999949	+	0.0101468i	$0.00322989\pi$
$54$	−3.84292	−	1.02971i	−0.522955	−	0.140125i
$55$		0			0
$56$	3.27705	−	0.878082i	0.437914	−	0.117339i
$57$	3.74052	−	2.15959i	0.495444	−	0.286045i
$58$	−1.89069	−	0.506608i	−0.248259	−	0.0665209i
$59$	−1.41608	−	0.379437i	−0.184358	−	0.0493985i	0.165459	−	0.986217i	$-0.447089\pi$
$59$	−1.41608	−	0.379437i	−0.184358	−	0.0493985i	−0.349817	+	0.936818i	$0.613756\pi$
$60$		0			0
$61$	−1.72489	−	6.43736i	−0.220849	−	0.824220i	−0.984025	−	0.178029i	$-0.943028\pi$
$61$	−1.72489	−	6.43736i	−0.220849	−	0.824220i	0.763176	−	0.646190i	$-0.223639\pi$
$62$	1.93816	−	7.23330i	0.246146	−	0.918631i
$63$	0.324858	+	0.324858i	0.0409283	+	0.0409283i
$64$	−4.00134			−0.500167
$65$		0			0
$66$	4.41203	−	4.41203i	0.543083	−	0.543083i
$67$	−5.70687	+	1.52915i	−0.697205	+	0.186816i	−0.589978	−	0.807419i	$-0.700864\pi$
$67$	−5.70687	+	1.52915i	−0.697205	+	0.186816i	−0.107227	+	0.994235i	$0.534197\pi$
$68$	−2.63853			−0.319969
$69$	1.40865	−	0.377446i	0.169581	−	0.0454392i
$70$		0			0
$71$	−3.30595	+	5.72607i	−0.392344	+	0.679559i	−0.992758	−	0.120130i	$-0.961669\pi$
$71$	−3.30595	+	5.72607i	−0.392344	+	0.679559i	0.600414	+	0.799689i	$0.295002\pi$
$72$	−0.507147	−	0.878404i	−0.0597679	−	0.103521i
$73$	−5.14518	+	5.14518i	−0.602197	+	0.602197i	−0.940895	−	0.338698i	$-0.890014\pi$
$73$	−5.14518	+	5.14518i	−0.602197	+	0.602197i	0.338698	+	0.940895i	$0.390014\pi$
$74$	3.88996	−	3.16223i	0.452198	−	0.367602i
$75$		0			0
$76$	−3.00136	−	0.804213i	−0.344280	−	0.0922495i
$77$	4.93773	−	1.32306i	0.562706	−	0.150777i
$78$	−1.92706	−	7.19188i	−0.218196	−	0.814320i
$79$	2.30362	+	8.59723i	0.259178	+	0.967264i	0.965718	+	0.259592i	$0.0835880\pi$
$79$	2.30362	+	8.59723i	0.259178	+	0.967264i	−0.706541	+	0.707672i	$0.749745\pi$
$80$		0			0
$81$	−4.98724	+	8.63815i	−0.554138	+	0.959795i
$82$	9.27246			1.02397
$83$	−0.310366	+	1.15830i	−0.0340671	+	0.127140i	−0.980865	−	0.194688i	$-0.937631\pi$
$83$	−0.310366	+	1.15830i	−0.0340671	+	0.127140i	0.946798	+	0.321828i	$0.104297\pi$
$84$		−	3.00590i		−	0.327970i
$85$		0			0
$86$	4.70581	+	8.15069i	0.507440	+	0.878912i
$87$	−2.18018	+	3.77618i	−0.233740	+	0.404849i
$88$	−11.2860			−1.20309
$89$	−1.87621	+	7.00209i	−0.198877	+	0.742220i	0.792352	+	0.610065i	$0.208857\pi$
$89$	−1.87621	+	7.00209i	−0.198877	+	0.742220i	−0.991229	+	0.132156i	$0.957810\pi$
$90$		0			0
$91$	1.57879	−	5.89213i	0.165502	−	0.617663i
$92$	−0.908579	−	0.524568i	−0.0947259	−	0.0546900i
$93$	−14.4467	−	8.34083i	−1.49806	−	0.864904i
$94$	0.661816	−	2.46993i	0.0682611	−	0.254754i
$95$		0			0
$96$	−2.75208	+	10.2709i	−0.280883	+	1.04827i
$97$	11.7662			1.19468			0.597338	−	0.801990i	$-0.296225\pi$
$97$	11.7662			1.19468			0.597338	+	0.801990i	$0.296225\pi$
$98$	2.25131	−	3.89938i	0.227416	−	0.393896i
$99$	−0.764149	−	1.32355i	−0.0767999	−	0.133021i
$100$		0			0
$101$		−	3.14602i		−	0.313041i	−0.987675	−	0.156521i	$-0.949972\pi$
$101$		−	3.14602i		−	0.313041i	0.987675	−	0.156521i	$-0.0500277\pi$
$102$	0.782335	−	2.91972i	0.0774628	−	0.289095i
$103$	7.98036			0.786328			0.393164	−	0.919468i	$-0.371380\pi$
$103$	7.98036			0.786328			0.393164	+	0.919468i	$0.371380\pi$
$104$	−6.73369	+	11.6631i	−0.660293	+	1.14366i
$105$		0			0
$106$	−0.773356	−	2.88620i	−0.0751150	−	0.280333i
$107$	−0.559856	−	2.08941i	−0.0541233	−	0.201991i	0.933570	−	0.358396i	$-0.116676\pi$
$107$	−0.559856	−	2.08941i	−0.0541233	−	0.201991i	−0.987693	+	0.156405i	$0.950010\pi$
$108$	6.15858	−	1.65019i	0.592610	−	0.158789i
$109$	−10.4305	−	2.79484i	−0.999059	−	0.267697i	−0.278008	−	0.960579i	$-0.589674\pi$
$109$	−10.4305	−	2.79484i	−0.999059	−	0.267697i	−0.721051	+	0.692882i	$0.756341\pi$
$110$		0			0
$111$	−4.56152	−	10.1934i	−0.432960	−	0.967513i
$112$	−0.338331	+	0.338331i	−0.0319692	+	0.0319692i
$113$	1.07951	+	1.86976i	0.101552	+	0.175892i	0.912324	−	0.409469i	$-0.134286\pi$
$113$	1.07951	+	1.86976i	0.101552	+	0.175892i	−0.810773	+	0.585361i	$0.800953\pi$
$114$	1.77983	−	3.08276i	0.166697	−	0.288727i
$115$		0			0
$116$	3.02998	−	0.811879i	0.281326	−	0.0753811i
$117$	−1.82370			−0.168601
$118$	−1.16707	+	0.312715i	−0.107437	+	0.0287877i
$119$	1.75110	−	1.75110i	0.160523	−	0.160523i
$120$		0			0
$121$	−6.00524			−0.545931
$122$	−3.88380	−	3.88380i	−0.351623	−	0.351623i
$123$	5.34610	−	19.9519i	0.482042	−	1.79901i
$124$	3.10605	+	11.5919i	0.278932	+	1.04099i
$125$		0			0
$126$	0.365730	+	0.0979971i	0.0325818	+	0.00873027i
$127$	−3.65534	−	0.979445i	−0.324359	−	0.0869117i	0.0929655	−	0.995669i	$-0.470365\pi$
$127$	−3.65534	−	0.979445i	−0.324359	−	0.0869117i	−0.417324	+	0.908758i	$0.637032\pi$
$128$	7.17571	−	4.14290i	0.634249	−	0.366184i
$129$	20.2514	−	5.42633i	1.78303	−	0.477762i
$130$		0			0
$131$	−9.54260	−	2.55693i	−0.833741	−	0.223400i	−0.183396	−	0.983039i	$-0.558709\pi$
$131$	−9.54260	−	2.55693i	−0.833741	−	0.223400i	−0.650345	+	0.759639i	$0.725376\pi$
$132$	−2.58803	+	9.65866i	−0.225259	+	0.840679i
$133$	2.52563	−	1.45817i	0.219000	−	0.126440i
$134$	−3.44308	+	3.44308i	−0.297437	+	0.297437i
$135$		0			0
$136$	−4.73491	+	2.73370i	−0.406016	+	0.234413i
$137$	−14.9643	+	14.9643i	−1.27849	+	1.27849i	−0.336976	+	0.941513i	$0.609404\pi$
$137$	−14.9643	+	14.9643i	−1.27849	+	1.27849i	−0.941513	+	0.336976i	$0.890596\pi$
$138$	0.849868	−	0.849868i	0.0723456	−	0.0723456i
$139$	−11.0779	−	19.1876i	−0.939619	−	1.62747i	−0.766183	−	0.642623i	$-0.777846\pi$
$139$	−11.0779	−	19.1876i	−0.939619	−	1.62747i	−0.173436	−	0.984845i	$-0.555487\pi$
$140$		0			0
$141$	−4.93307	−	2.84811i	−0.415440	−	0.239854i
$142$			5.44922i			0.457288i
$143$	−10.1461	+	17.5735i	−0.848457	+	1.46957i
$144$	0.123883	+	0.0715239i	0.0103236	+	0.00596033i
$145$		0			0
$146$	−1.55210	+	5.79251i	−0.128453	+	0.479392i
$147$	−7.09244	−	7.09244i	−0.584975	−	0.584975i
$148$	−2.86491	+	7.50576i	−0.235494	+	0.616970i
$149$		−	15.3831i		−	1.26024i	−0.776499	−	0.630118i	$-0.783006\pi$
$149$		−	15.3831i		−	1.26024i	0.776499	−	0.630118i	$-0.216994\pi$
$150$		0			0
$151$	−14.2305	−	8.21599i	−1.15806	−	0.668608i	−0.207224	−	0.978294i	$-0.566443\pi$
$151$	−14.2305	−	8.21599i	−1.15806	−	0.668608i	−0.950839	+	0.309686i	$0.899776\pi$
$152$	−6.21925	+	1.66644i	−0.504447	+	0.135166i
$153$	−0.641183	−	0.370187i	−0.0518366	−	0.0299279i
$154$	2.97904	−	2.97904i	0.240058	−	0.240058i
$155$		0			0
$156$	8.43730	+	8.43730i	0.675524	+	0.675524i
$157$	8.19871	+	2.19684i	0.654328	+	0.175327i	0.570685	−	0.821169i	$-0.306678\pi$
$157$	8.19871	+	2.19684i	0.654328	+	0.175327i	0.0836433	+	0.996496i	$0.473344\pi$
$158$	5.18690	+	5.18690i	0.412647	+	0.412647i
$159$	−6.65625			−0.527875
$160$		0			0
$161$	0.951131	−	0.254855i	0.0749596	−	0.0200854i
$162$			8.22050i			0.645863i
$163$	0.474073	+	0.821119i	0.0371323	+	0.0643150i	0.883994	−	0.467498i	$-0.154844\pi$
$163$	0.474073	+	0.821119i	0.0371323	+	0.0643150i	−0.846862	+	0.531813i	$0.821511\pi$
$164$	−12.8690	+	7.42993i	−1.00490	+	0.580180i
$165$		0			0
$166$	0.255789	+	0.954618i	0.0198531	+	0.0740928i
$167$	−0.925739	+	1.60343i	−0.0716358	+	0.124077i	−0.899618	−	0.436677i	$-0.856155\pi$
$167$	−0.925739	+	1.60343i	−0.0716358	+	0.124077i	0.827983	+	0.560754i	$0.189489\pi$
$168$	−3.11432	−	5.39416i	−0.240275	−	0.416168i
$169$	5.60717	+	9.71191i	0.431321	+	0.747070i
$170$		0			0
$171$	−0.616522	−	0.616522i	−0.0471467	−	0.0471467i
$172$	−13.0621	−	7.54143i	−0.995979	−	0.575029i
$173$	1.94070	+	0.520009i	0.147549	+	0.0395356i	0.331837	−	0.943337i	$-0.392331\pi$
$173$	1.94070	+	0.520009i	0.147549	+	0.0395356i	−0.184289	+	0.982872i	$0.558998\pi$
$174$			3.59360i			0.272430i
$175$		0			0
$176$	1.37844	−	0.795840i	0.103903	−	0.0599887i
$177$			2.69152i			0.202307i
$178$	1.54628	+	5.77080i	0.115899	+	0.432540i
$179$	16.5221	+	16.5221i	1.23492	+	1.23492i	0.962052	+	0.272865i	$0.0879712\pi$
$179$	16.5221	+	16.5221i	1.23492	+	1.23492i	0.272865	+	0.962052i	$0.412029\pi$
$180$		0			0
$181$	−0.609064	+	1.05493i	−0.0452713	+	0.0784123i	−0.887773	−	0.460281i	$-0.847749\pi$
$181$	−0.609064	+	1.05493i	−0.0452713	+	0.0784123i	0.842502	+	0.538693i	$0.181082\pi$
$182$	−1.30117	−	4.85602i	−0.0964488	−	0.359952i
$183$	−10.5962	+	6.11770i	−0.783292	+	0.452234i
$184$	−2.17396			−0.160266
$185$		0			0
$186$	−13.7482			−1.00807
$187$	−7.13438	+	4.11904i	−0.521718	+	0.301214i
$188$	1.06061	+	3.95826i	0.0773531	+	0.288686i
$189$	−2.99207	+	5.18241i	−0.217641	+	0.376965i
$190$		0			0
$191$	−5.47122	−	5.47122i	−0.395883	−	0.395883i	0.480895	−	0.876778i	$-0.340312\pi$
$191$	−5.47122	−	5.47122i	−0.395883	−	0.395883i	−0.876778	+	0.480895i	$0.840312\pi$
$192$	1.90132	+	7.09583i	0.137216	+	0.512097i
$193$		−	20.4352i		−	1.47096i	−0.677546	−	0.735480i	$-0.736957\pi$
$193$		−	20.4352i		−	1.47096i	0.677546	−	0.735480i	$-0.263043\pi$
$194$	8.39797	−	4.84857i	0.602939	−	0.348107i
$195$		0			0
$196$			7.21579i			0.515414i
$197$	26.8016	+	7.18146i	1.90953	+	0.511658i	0.993995	+	0.109426i	$0.0349012\pi$
$197$	26.8016	+	7.18146i	1.90953	+	0.511658i	0.915538	+	0.402232i	$0.131765\pi$
$198$	−1.09080	−	0.629776i	−0.0775201	−	0.0447562i
$199$	12.8241	+	12.8241i	0.909074	+	0.909074i	0.996198	−	0.0871235i	$-0.0277675\pi$
$199$	12.8241	+	12.8241i	0.909074	+	0.909074i	−0.0871235	+	0.996198i	$0.527767\pi$
$200$		0			0
$201$	5.42349	+	9.39375i	0.382543	+	0.662584i
$202$	−1.29640	−	2.24544i	−0.0912146	−	0.157988i
$203$	−1.47207	+	2.54971i	−0.103319	+	0.178954i
$204$	1.25375	+	4.67908i	0.0877804	+	0.327601i
$205$		0			0
$206$	5.69588	−	3.28852i	0.396851	−	0.229122i
$207$	−0.147194	−	0.254948i	−0.0102307	−	0.0177201i
$208$		−	1.89933i		−	0.131695i
$209$	−9.37092	+	2.51093i	−0.648200	+	0.173685i
$210$		0			0
$211$	−18.6491			−1.28386			−0.641928	−	0.766765i	$-0.721865\pi$
$211$	−18.6491			−1.28386			−0.641928	+	0.766765i	$0.721865\pi$
$212$	3.38601	+	3.38601i	0.232552	+	0.232552i
$213$	11.7253	+	3.14179i	0.803404	+	0.215272i
$214$	−1.26059	−	1.26059i	−0.0861720	−	0.0861720i
$215$		0			0
$216$	9.34203	−	9.34203i	0.635645	−	0.635645i
$217$	−9.75456	−	5.63180i	−0.662182	−	0.382311i
$218$	−8.59632	+	2.30338i	−0.582216	+	0.156004i
$219$	11.5691	+	6.67943i	0.781768	+	0.451354i
$220$		0			0
$221$			9.83039i			0.661264i
$222$	−7.45618	−	5.39571i	−0.500426	−	0.362136i
$223$	−7.82604	−	7.82604i	−0.524071	−	0.524071i	0.394728	−	0.918798i	$-0.370839\pi$
$223$	−7.82604	−	7.82604i	−0.524071	−	0.524071i	−0.918798	+	0.394728i	$0.870839\pi$
$224$	−1.85823	+	6.93499i	−0.124158	+	0.463364i
$225$		0			0
$226$	1.54097	+	0.889680i	0.102504	+	0.0591806i
$227$	−4.20907	+	7.29033i	−0.279366	+	0.483876i	−0.971227	−	0.238154i	$-0.923458\pi$
$227$	−4.20907	+	7.29033i	−0.279366	+	0.483876i	0.691861	+	0.722030i	$0.256791\pi$
$228$			5.70465i			0.377800i
$229$	−17.6546	−	10.1929i	−1.16665	−	0.673566i	−0.213762	−	0.976886i	$-0.568572\pi$
$229$	−17.6546	−	10.1929i	−1.16665	−	0.673566i	−0.952889	+	0.303319i	$0.901905\pi$
$230$		0			0
$231$	−4.69254	−	8.12771i	−0.308746	−	0.534764i
$232$	4.59621	−	4.59621i	0.301756	−	0.301756i
$233$	6.42167	−	6.42167i	0.420698	−	0.420698i	−0.464746	−	0.885444i	$-0.653854\pi$
$233$	6.42167	−	6.42167i	0.420698	−	0.420698i	0.885444	+	0.464746i	$0.153854\pi$
$234$	−1.30164	+	0.751504i	−0.0850911	+	0.0491274i
$235$		0			0
$236$	1.36917	−	1.36917i	0.0891252	−	0.0891252i
$237$	14.1514	−	8.17032i	0.919233	−	0.530719i
$238$	0.528239	−	1.97142i	0.0342407	−	0.127788i
$239$	−5.80797	−	1.55624i	−0.375686	−	0.100665i	0.0660347	−	0.997817i	$-0.478965\pi$
$239$	−5.80797	−	1.55624i	−0.375686	−	0.100665i	−0.441721	+	0.897152i	$0.645632\pi$
$240$		0			0
$241$	−0.252833	+	0.0677464i	−0.0162864	+	0.00436393i	−0.266953	−	0.963710i	$-0.586017\pi$
$241$	−0.252833	+	0.0677464i	−0.0162864	+	0.00436393i	0.250667	+	0.968073i	$0.419350\pi$
$242$	−4.28616	+	2.47462i	−0.275525	+	0.159074i
$243$	3.69978	+	0.991354i	0.237341	+	0.0635954i
$244$	8.50228	+	2.27818i	0.544303	+	0.145846i
$245$		0			0
$246$	−4.40601	−	16.4435i	−0.280917	−	1.04840i
$247$	−2.99626	+	11.1822i	−0.190647	+	0.711506i
$248$	17.5840	+	17.5840i	1.11658	+	1.11658i
$249$	2.20157			0.139519
$250$		0			0
$251$	−17.9819	+	17.9819i	−1.13500	+	1.13500i	−0.145672	+	0.989333i	$0.546534\pi$
$251$	−17.9819	+	17.9819i	−1.13500	+	1.13500i	−0.989333	+	0.145672i	$0.953466\pi$
$252$	−0.586112	+	0.157048i	−0.0369216	+	0.00989310i
$253$	−3.27564			−0.205938
$254$	−3.01256	+	0.807212i	−0.189025	+	0.0506490i
$255$		0			0
$256$	7.41572	−	12.8444i	0.463482	−	0.802775i
$257$	−7.05043	−	12.2117i	−0.439794	−	0.761745i	0.557879	−	0.829922i	$-0.311615\pi$
$257$	−7.05043	−	12.2117i	−0.439794	−	0.761745i	−0.997673	+	0.0681767i	$0.978282\pi$
$258$	12.2181	−	12.2181i	0.760665	−	0.760665i
$259$	−3.07998	−	6.88266i	−0.191380	−	0.427667i
$260$		0			0
$261$	0.850214	+	0.227814i	0.0526269	+	0.0141013i
$262$	−7.86457	+	2.10730i	−0.485875	+	0.130190i
$263$	−3.04678	−	11.3707i	−0.187872	−	0.701149i	−0.993997	−	0.109404i	$-0.965106\pi$
$263$	−3.04678	−	11.3707i	−0.187872	−	0.701149i	0.806125	−	0.591745i	$-0.201561\pi$
$264$	5.36277	+	20.0141i	0.330055	+	1.23178i
$265$		0			0
$266$	1.20176	−	2.08151i	0.0736845	−	0.127625i
$267$	13.3088			0.814484
$268$	2.01966	−	7.53747i	0.123370	−	0.460424i
$269$			23.2856i			1.41975i	0.704328	+	0.709875i	$0.251248\pi$
$269$			23.2856i			1.41975i	−0.704328	+	0.709875i	$0.748752\pi$
$270$		0			0
$271$	3.22003	+	5.57726i	0.195603	+	0.338794i	0.947098	−	0.320944i	$-0.104000\pi$
$271$	3.22003	+	5.57726i	0.195603	+	0.338794i	−0.751495	+	0.659739i	$0.770667\pi$
$272$	0.385540	−	0.667774i	0.0233768	−	0.0404898i
$273$	−11.1991			−0.677800
$274$	−4.51416	+	16.8471i	−0.272710	+	1.01777i
$275$		0			0
$276$	−0.498520	+	1.86050i	−0.0300074	+	0.111989i
$277$	15.9026	+	9.18139i	0.955497	+	0.551656i	0.894784	−	0.446499i	$-0.147329\pi$
$277$	15.9026	+	9.18139i	0.955497	+	0.551656i	0.0607125	+	0.998155i	$0.480663\pi$
$278$	−15.8135	−	9.12992i	−0.948430	−	0.547576i
$279$	−0.871562	+	3.25271i	−0.0521790	+	0.194735i
$280$		0			0
$281$	5.16431	−	19.2735i	0.308077	−	1.14976i	−0.622188	−	0.782868i	$-0.713756\pi$
$281$	5.16431	−	19.2735i	0.308077	−	1.14976i	0.930264	−	0.366890i	$-0.119577\pi$
$282$	−4.69456			−0.279557
$283$	5.55937	−	9.62911i	0.330470	−	0.572391i	−0.652134	−	0.758104i	$-0.726126\pi$
$283$	5.55937	−	9.62911i	0.330470	−	0.572391i	0.982604	+	0.185713i	$0.0594594\pi$
$284$	−4.36640	−	7.56283i	−0.259098	−	0.448771i
$285$		0			0
$286$			16.7238i			0.988901i
$287$	3.60973	−	13.4717i	0.213076	−	0.795210i
$288$	2.14648			0.126483
$289$	6.50456	−	11.2662i	0.382621	−	0.662719i
$290$		0			0
$291$	−5.59096	−	20.8657i	−0.327748	−	1.22317i
$292$	−2.48736	−	9.28297i	−0.145562	−	0.543244i
$293$	−28.1127	+	7.53277i	−1.64236	+	0.440069i	−0.957459	−	0.288568i	$-0.906821\pi$
$293$	−28.1127	+	7.53277i	−1.64236	+	0.440069i	−0.684900	+	0.728637i	$0.740154\pi$
$294$	−7.98477	−	2.13951i	−0.465681	−	0.124779i
$295$		0			0
$296$	2.63535	+	16.4375i	0.153176	+	0.955413i
$297$	14.0762	−	14.0762i	0.816784	−	0.816784i
$298$	−6.33904	−	10.9795i	−0.367211	−	0.636027i
$299$	−1.95439	+	3.38510i	−0.113025	+	0.195765i
$300$		0			0
$301$	13.6739	−	3.66390i	0.788149	−	0.211184i
$302$	−13.5425			−0.779282
$303$	−5.57905	+	1.49490i	−0.320508	+	0.0858798i
$304$	0.642091	−	0.642091i	0.0368264	−	0.0368264i
$305$		0			0
$306$	−0.610182			−0.0348818
$307$	−17.5892	−	17.5892i	−1.00387	−	1.00387i	−0.999992	−	0.00387509i	$-0.998767\pi$
$307$	−17.5892	−	17.5892i	−1.00387	−	1.00387i	−0.00387509	−	0.999992i	$-0.501233\pi$
$308$	−1.74746	+	6.52161i	−0.0995708	+	0.371603i
$309$	−3.79204	−	14.1521i	−0.215722	−	0.805084i
$310$		0			0
$311$	21.0337	+	5.63596i	1.19271	+	0.319586i	0.799957	−	0.600058i	$-0.204856\pi$
$311$	21.0337	+	5.63596i	1.19271	+	0.319586i	0.392754	+	0.919644i	$0.371522\pi$
$312$	23.8826	+	6.39932i	1.35209	+	0.362290i
$313$	25.0189	−	14.4447i	1.41415	−	0.816460i	0.418374	−	0.908275i	$-0.362600\pi$
$313$	25.0189	−	14.4447i	1.41415	−	0.816460i	0.995776	+	0.0918148i	$0.0292668\pi$
$314$	6.75699	−	1.81053i	0.381319	−	0.102174i
$315$		0			0
$316$	−11.3550	−	3.04256i	−0.638767	−	0.171157i
$317$	−0.284851	+	1.06308i	−0.0159988	+	0.0597084i	−0.973464	−	0.228841i	$-0.926506\pi$
$317$	−0.284851	+	1.06308i	−0.0159988	+	0.0597084i	0.957465	+	0.288550i	$0.0931730\pi$
$318$	−4.75082	+	2.74289i	−0.266413	+	0.153813i
$319$	6.92539	−	6.92539i	0.387747	−	0.387747i
$320$		0			0
$321$	−3.43926	+	1.98566i	−0.191961	+	0.110829i
$322$	0.573838	−	0.573838i	0.0319787	−	0.0319787i
$323$	−3.32328	+	3.32328i	−0.184912	+	0.184912i
$324$	−6.58700	−	11.4090i	−0.365945	−	0.633835i
$325$		0			0
$326$	0.676728	+	0.390709i	0.0374805	+	0.0216394i
$327$			19.8251i			1.09633i
$328$	−15.3959	+	26.6664i	−0.850094	+	1.47241i
$329$	−3.33085	−	1.92307i	−0.183636	−	0.106022i
$330$		0			0
$331$	0.504686	−	1.88351i	0.0277400	−	0.103527i	−0.950668	−	0.310211i	$-0.899600\pi$
$331$	0.504686	−	1.88351i	0.0277400	−	0.103527i	0.978408	+	0.206684i	$0.0662670\pi$
$332$	−1.11993	−	1.11993i	−0.0614641	−	0.0614641i
$333$	−1.74926	+	1.42201i	−0.0958587	+	0.0779257i
$334$			1.52590i			0.0834936i
$335$		0			0
$336$	0.760749	+	0.439219i	0.0415023	+	0.0239613i
$337$	0.813925	−	0.218091i	0.0443373	−	0.0118802i	−0.236582	−	0.971611i	$-0.576027\pi$
$337$	0.813925	−	0.218091i	0.0443373	−	0.0118802i	0.280920	+	0.959731i	$0.409361\pi$
$338$	8.00410	+	4.62117i	0.435366	+	0.251359i
$339$	2.80282	−	2.80282i	0.152228	−	0.152228i
$340$		0			0
$341$	26.4948	+	26.4948i	1.43478	+	1.43478i
$342$	−0.694090	−	0.185981i	−0.0375321	−	0.0100567i
$343$	−10.9247	−	10.9247i	−0.589880	−	0.589880i
$344$	−31.2538			−1.68509
$345$		0			0
$346$	1.59944	−	0.428568i	0.0859862	−	0.0230399i
$347$		−	25.8472i		−	1.38755i	−0.720191	−	0.693776i	$-0.755946\pi$
$347$		−	25.8472i		−	1.38755i	0.720191	−	0.693776i	$-0.244054\pi$
$348$	−2.87952	−	4.98747i	−0.154358	−	0.267356i
$349$	15.4393	−	8.91390i	0.826448	−	0.477150i	−0.0261867	−	0.999657i	$-0.508336\pi$
$349$	15.4393	−	8.91390i	0.826448	−	0.477150i	0.852635	+	0.522507i	$0.175003\pi$
$350$		0			0
$351$	−6.14811	−	22.9451i	−0.328162	−	1.22472i
$352$	11.9418	−	20.6839i	0.636503	−	1.10245i
$353$	−3.51992	−	6.09669i	−0.187347	−	0.324494i	0.757018	−	0.653394i	$-0.226655\pi$
$353$	−3.51992	−	6.09669i	−0.187347	−	0.324494i	−0.944365	+	0.328900i	$0.893322\pi$
$354$	1.10911	+	1.92104i	0.0589487	+	0.102102i
$355$		0			0
$356$	−6.77013	−	6.77013i	−0.358816	−	0.358816i
$357$	−3.93742	−	2.27327i	−0.208390	−	0.120314i
$358$	18.6008	+	4.98406i	0.983082	+	0.263416i
$359$		−	18.3910i		−	0.970639i	−0.874337	−	0.485320i	$-0.838703\pi$
$359$		−	18.3910i		−	0.970639i	0.874337	−	0.485320i	$-0.161297\pi$
$360$		0			0
$361$	11.6613	−	6.73265i	0.613752	−	0.354350i
$362$			1.00392i			0.0527650i
$363$	2.85352	+	10.6495i	0.149771	+	0.558952i
$364$	5.69693	+	5.69693i	0.298600	+	0.298600i
$365$		0			0
$366$	−5.04192	+	8.73287i	−0.263546	+	0.456474i
$367$	4.24206	+	15.8316i	0.221434	+	0.826402i	0.983802	+	0.179258i	$0.0573698\pi$
$367$	4.24206	+	15.8316i	0.221434	+	0.826402i	−0.762368	+	0.647143i	$0.775964\pi$
$368$	0.265521	−	0.153299i	0.0138413	−	0.00799125i
$369$	−4.16969			−0.217065
$370$		0			0
$371$	−4.49435			−0.233335
$372$	19.0808	−	11.0163i	0.989295	−	0.571170i
$373$	−1.39064	−	5.18993i	−0.0720045	−	0.268724i	0.920533	−	0.390665i	$-0.127755\pi$
$373$	−1.39064	−	5.18993i	−0.0720045	−	0.268724i	−0.992537	+	0.121941i	$0.961088\pi$
$374$	−3.39472	+	5.87983i	−0.175537	+	0.304039i
$375$		0			0
$376$	6.00433	+	6.00433i	0.309650	+	0.309650i
$377$	−3.02483	−	11.2888i	−0.155786	−	0.581403i
$378$			4.93184i			0.253667i
$379$	17.5612	−	10.1389i	0.902057	−	0.520803i	0.0241899	−	0.999707i	$-0.492299\pi$
$379$	17.5612	−	10.1389i	0.902057	−	0.520803i	0.877867	+	0.478905i	$0.158966\pi$
$380$		0			0
$381$			6.94765i			0.355939i
$382$	−6.15958	−	1.65045i	−0.315151	−	0.0844445i
$383$	−5.99456	−	3.46096i	−0.306308	−	0.176847i	0.338965	−	0.940799i	$-0.389923\pi$
$383$	−5.99456	−	3.46096i	−0.306308	−	0.176847i	−0.645273	+	0.763952i	$0.723256\pi$
$384$	−10.7566	−	10.7566i	−0.548919	−	0.548919i
$385$		0			0
$386$	−8.42088	−	14.5854i	−0.428612	−	0.742377i
$387$	−2.11613	−	3.66525i	−0.107569	−	0.186315i
$388$	−7.77022	+	13.4584i	−0.394473	+	0.683248i
$389$	−9.03222	−	33.7087i	−0.457952	−	1.70910i	−0.679262	−	0.733896i	$-0.737700\pi$
$389$	−9.03222	−	33.7087i	−0.457952	−	1.70910i	0.221311	−	0.975203i	$-0.428967\pi$
$390$		0			0
$391$	−1.37426	+	0.793431i	−0.0694994	+	0.0401255i
$392$	7.47607	+	12.9489i	0.377599	+	0.654020i
$393$			18.1375i			0.914916i
$394$	22.0886	−	5.91862i	1.11281	−	0.298176i
$395$		0			0
$396$	2.01853			0.101435
$397$	−8.75997	−	8.75997i	−0.439650	−	0.439650i	0.452244	−	0.891894i	$-0.350624\pi$
$397$	−8.75997	−	8.75997i	−0.439650	−	0.439650i	−0.891894	+	0.452244i	$0.850624\pi$
$398$	14.4375	+	3.86852i	0.723687	+	0.193911i
$399$	−3.78598	−	3.78598i	−0.189536	−	0.189536i
$400$		0			0
$401$	−22.1660	+	22.1660i	−1.10692	+	1.10692i	−0.113365	+	0.993553i	$0.536163\pi$
$401$	−22.1660	+	22.1660i	−1.10692	+	1.10692i	−0.993553	+	0.113365i	$0.963837\pi$
$402$	7.74189	+	4.46978i	0.386130	+	0.222933i
$403$	43.1882	−	11.5722i	2.15136	−	0.576455i
$404$	3.59849	+	2.07759i	0.179032	+	0.103364i
$405$		0			0
$406$			2.42643i			0.120422i
$407$	3.97084	+	24.7674i	0.196827	+	1.22768i
$408$	7.09775	+	7.09775i	0.351391	+	0.351391i
$409$	7.06463	−	26.3656i	0.349324	−	1.30369i	−0.538156	−	0.842845i	$-0.680879\pi$
$409$	7.06463	−	26.3656i	0.349324	−	1.30369i	0.887479	−	0.460848i	$-0.152455\pi$
$410$		0			0
$411$	33.6478	+	19.4266i	1.65973	+	0.958243i
$412$	−5.27011	+	9.12810i	−0.259640	+	0.449709i
$413$			1.81734i			0.0894254i
$414$	−0.210116	−	0.121311i	−0.0103267	−	0.00596210i
$415$		0			0
$416$	−14.2501	−	24.6818i	−0.698667	−	1.21013i
$417$	−28.7626	+	28.7626i	−1.40851	+	1.40851i
$418$	−5.65368	+	5.65368i	−0.276531	+	0.276531i
$419$	−30.6436	+	17.6921i	−1.49704	+	0.864315i	−0.999994	−	0.00341085i	$-0.998914\pi$
$419$	−30.6436	+	17.6921i	−1.49704	+	0.864315i	−0.497043	+	0.867726i	$0.665581\pi$
$420$		0			0
$421$	6.45054	−	6.45054i	0.314380	−	0.314380i	−0.532224	−	0.846604i	$-0.678643\pi$
$421$	6.45054	−	6.45054i	0.314380	−	0.314380i	0.846604	+	0.532224i	$0.178643\pi$
$422$	−13.3105	+	7.68485i	−0.647947	+	0.374093i
$423$	−0.297609	+	1.11069i	−0.0144702	+	0.0540037i
$424$	9.58443	+	2.56814i	0.465461	+	0.124720i
$425$		0			0
$426$	9.66345	−	2.58931i	0.468195	−	0.125453i
$427$	−7.15462	+	4.13072i	−0.346236	+	0.199900i
$428$	2.75963	+	0.739442i	0.133392	+	0.0357423i
$429$	35.9854	+	9.64225i	1.73739	+	0.465532i
$430$		0			0
$431$	−6.64876	−	24.8135i	−0.320259	−	1.19522i	−0.918992	−	0.394276i	$-0.870996\pi$
$431$	−6.64876	−	24.8135i	−0.320259	−	1.19522i	0.598733	−	0.800949i	$-0.295671\pi$
$432$	−0.482247	+	1.79977i	−0.0232021	+	0.0865916i
$433$	17.0203	+	17.0203i	0.817941	+	0.817941i	0.985809	−	0.167868i	$-0.0536882\pi$
$433$	17.0203	+	17.0203i	0.817941	+	0.817941i	−0.167868	+	0.985809i	$0.553688\pi$
$434$	−9.28293			−0.445595
$435$		0			0
$436$	10.0849	−	10.0849i	0.482981	−	0.482981i
$437$	−1.80507	+	0.483668i	−0.0863484	+	0.0231370i
$438$	11.0098			0.526066
$439$	−14.3903	+	3.85588i	−0.686814	+	0.184031i	−0.585317	−	0.810805i	$-0.699030\pi$
$439$	−14.3903	+	3.85588i	−0.686814	+	0.184031i	−0.101497	+	0.994836i	$0.532363\pi$
$440$		0			0
$441$	−1.01238	+	1.75349i	−0.0482086	+	0.0834997i
$442$	4.05088	+	7.01632i	0.192681	+	0.333732i
$443$	19.1200	−	19.1200i	0.908420	−	0.908420i	−0.0877248	−	0.996145i	$-0.527960\pi$
$443$	19.1200	−	19.1200i	0.908420	−	0.908420i	0.996145	+	0.0877248i	$0.0279596\pi$
$444$	14.6718	+	1.51400i	0.696292	+	0.0718512i
$445$		0			0
$446$	−8.81067	−	2.36081i	−0.417197	−	0.111788i
$447$	−27.2799	+	7.30964i	−1.29030	+	0.345734i
$448$	1.28379	+	4.79116i	0.0606533	+	0.226361i
$449$	1.83666	+	6.85450i	0.0866772	+	0.323484i	0.995627	−	0.0934229i	$-0.0297809\pi$
$449$	1.83666	+	6.85450i	0.0866772	+	0.323484i	−0.908949	+	0.416907i	$0.863114\pi$
$450$		0			0
$451$	−23.1979	+	40.1799i	−1.09235	+	1.89200i
$452$	−2.85157			−0.134126
$453$	−7.80801	+	29.1399i	−0.366852	+	1.36911i
$454$			6.93784i			0.325609i
$455$		0			0
$456$	5.91042	+	10.2371i	0.276781	+	0.479398i
$457$	−6.55090	+	11.3465i	−0.306438	+	0.530767i	−0.977581	−	0.210562i	$-0.932471\pi$
$457$	−6.55090	+	11.3465i	−0.306438	+	0.530767i	0.671142	+	0.741329i	$0.265804\pi$
$458$	−16.8010			−0.785061
$459$	2.49597	−	9.31510i	0.116502	−	0.434792i
$460$		0			0
$461$	−5.66561	+	21.1444i	−0.263874	+	0.984791i	0.699062	+	0.715061i	$0.253601\pi$
$461$	−5.66561	+	21.1444i	−0.263874	+	0.984791i	−0.962936	+	0.269730i	$0.913066\pi$
$462$	−6.69848	−	3.86737i	−0.311641	−	0.179926i
$463$	−23.5293	−	13.5846i	−1.09350	−	0.631331i	−0.158992	−	0.987280i	$-0.550824\pi$
$463$	−23.5293	−	13.5846i	−1.09350	−	0.631331i	−0.934506	+	0.355949i	$0.884158\pi$
$464$	−0.237262	+	0.885474i	−0.0110146	+	0.0411071i
$465$		0			0
$466$	1.93717	−	7.22961i	0.0897376	−	0.334905i
$467$	−11.4311			−0.528967			−0.264483	−	0.964390i	$-0.585201\pi$
$467$	−11.4311			−0.528967			−0.264483	+	0.964390i	$0.585201\pi$
$468$	1.20435	−	2.08599i	0.0556709	−	0.0964248i
$469$	3.66198	+	6.34274i	0.169095	+	0.292880i
$470$		0			0
$471$		−	15.5832i		−	0.718035i
$472$	1.03845	−	3.87556i	0.0477987	−	0.178387i
$473$	−47.0920			−2.16529
$474$	6.73360	−	11.6629i	0.309284	−	0.535696i
$475$		0			0
$476$	0.846546	+	3.15935i	0.0388014	+	0.144809i
$477$	0.347767	+	1.29788i	0.0159232	+	0.0594261i
$478$	−4.78666	+	1.28258i	−0.218937	+	0.0586639i
$479$	−9.48503	−	2.54151i	−0.433382	−	0.116124i	0.0355313	−	0.999369i	$-0.488688\pi$
$479$	−9.48503	−	2.54151i	−0.433382	−	0.116124i	−0.468913	+	0.883244i	$0.655354\pi$
$480$		0			0
$481$	27.9643	+	10.6738i	1.27506	+	0.486684i
$482$	−0.152540	+	0.152540i	−0.00694799	+	0.00694799i
$483$	−0.903900	−	1.56560i	−0.0411289	−	0.0712373i
$484$	3.96577	−	6.86892i	0.180262	−	0.312224i
$485$		0			0
$486$	3.04919	−	0.817028i	0.138314	−	0.0370611i
$487$	28.7566			1.30308			0.651542	−	0.758613i	$-0.274122\pi$
$487$	28.7566			1.30308			0.651542	+	0.758613i	$0.274122\pi$
$488$	17.6179	−	4.72071i	0.797526	−	0.213696i
$489$	1.23088	−	1.23088i	0.0556622	−	0.0556622i
$490$		0			0
$491$	31.5099			1.42202			0.711010	−	0.703182i	$-0.248238\pi$
$491$	31.5099			1.42202			0.711010	+	0.703182i	$0.248238\pi$
$492$	19.2910	+	19.2910i	0.869704	+	0.869704i
$493$	1.22800	−	4.58296i	0.0553063	−	0.206406i
$494$	2.46938	+	9.21584i	0.111103	+	0.414640i
$495$		0			0
$496$	−3.38761	−	0.907707i	−0.152108	−	0.0407572i
$497$	7.91702	+	2.12136i	0.355127	+	0.0951560i
$498$	1.57134	−	0.907215i	0.0704136	−	0.0406533i
$499$	−28.6886	+	7.68709i	−1.28428	+	0.344121i	−0.835485	−	0.549514i	$-0.814813\pi$
$499$	−28.6886	+	7.68709i	−1.28428	+	0.344121i	−0.448794	+	0.893635i	$0.648146\pi$
$500$		0			0
$501$	3.28334	+	0.879770i	0.146689	+	0.0393052i
$502$	−5.42443	+	20.2442i	−0.242104	+	0.903544i
$503$	15.0571	−	8.69325i	0.671365	−	0.387613i	−0.125229	−	0.992128i	$-0.539966\pi$
$503$	15.0571	−	8.69325i	0.671365	−	0.387613i	0.796594	+	0.604515i	$0.206633\pi$
$504$	−0.889080	+	0.889080i	−0.0396028	+	0.0396028i
$505$		0			0
$506$	−2.33795	+	1.34981i	−0.103934	+	0.0600065i
$507$	14.5584	−	14.5584i	0.646561	−	0.646561i
$508$	3.53424	−	3.53424i	0.156807	−	0.156807i
$509$	4.46764	+	7.73818i	0.198025	+	0.342989i	0.947888	−	0.318604i	$-0.103214\pi$
$509$	4.46764	+	7.73818i	0.198025	+	0.342989i	−0.749863	+	0.661593i	$0.769881\pi$
$510$		0			0
$511$	7.81156	+	4.51001i	0.345563	+	0.199511i
$512$			4.34822i			0.192166i
$513$	5.67840	−	9.83528i	0.250708	−	0.434238i
$514$	−10.0643	−	5.81064i	−0.443918	−	0.256296i
$515$		0			0
$516$	−7.16695	+	26.7474i	−0.315507	+	1.17749i
$517$	9.04709	+	9.04709i	0.397891	+	0.397891i
$518$	−5.03448	−	3.64323i	−0.221202	−	0.160074i
$519$		−	3.68867i		−	0.161914i
$520$		0			0
$521$	5.50222	+	3.17671i	0.241057	+	0.139174i	0.615662	−	0.788010i	$-0.288889\pi$
$521$	5.50222	+	3.17671i	0.241057	+	0.139174i	−0.374606	+	0.927184i	$0.622222\pi$
$522$	0.700707	−	0.187754i	0.0306691	−	0.00821776i
$523$	2.70312	+	1.56065i	0.118199	+	0.0682423i	0.557934	−	0.829885i	$-0.311594\pi$
$523$	2.70312	+	1.56065i	0.118199	+	0.0682423i	−0.439735	+	0.898128i	$0.644928\pi$
$524$	9.22647	−	9.22647i	0.403060	−	0.403060i
$525$		0			0
$526$	−6.86021	−	6.86021i	−0.299119	−	0.299119i
$527$	17.5333	+	4.69803i	0.763762	+	0.204649i
$528$	−2.06631	−	2.06631i	−0.0899245	−	0.0899245i
$529$	22.3690			0.972567
$530$		0			0
$531$	0.524813	−	0.140623i	0.0227749	−	0.00610253i
$532$			3.85183i			0.166998i
$533$	27.6817	+	47.9462i	1.19903	+	2.07678i
$534$	9.49898	−	5.48424i	0.411061	−	0.237326i
$535$		0			0
$536$	−4.18502	−	15.6187i	−0.180765	−	0.674625i
$537$	21.4488	−	37.1505i	0.925585	−	1.60316i
$538$	9.59546	+	16.6198i	0.413690	+	0.716531i
$539$	11.2647	+	19.5110i	0.485203	+	0.840396i
$540$		0			0
$541$	−2.14088	−	2.14088i	−0.0920435	−	0.0920435i	0.659586	−	0.751629i	$-0.270732\pi$
$541$	−2.14088	−	2.14088i	−0.0920435	−	0.0920435i	−0.751629	+	0.659586i	$0.770732\pi$
$542$	4.59651	+	2.65380i	0.197437	+	0.113990i
$543$	2.16018	+	0.578819i	0.0927023	+	0.0248395i
$544$		−	11.5703i		−	0.496073i
$545$		0			0
$546$	−7.99321	+	4.61488i	−0.342078	+	0.197499i
$547$		−	45.1561i		−	1.93074i	−0.260891	−	0.965368i	$-0.584016\pi$
$547$		−	45.1561i		−	1.93074i	0.260891	−	0.965368i	$-0.415984\pi$
$548$	−7.23429	−	26.9988i	−0.309034	−	1.15333i
$549$	1.74649	+	1.74649i	0.0745384	+	0.0745384i
$550$		0			0
$551$	2.79373	−	4.83888i	0.119017	−	0.206143i
$552$	1.03300	+	3.85522i	0.0439676	+	0.164089i
$553$	9.55515	−	5.51667i	0.406326	−	0.234593i
$554$	15.1337			0.642971
$555$		0			0
$556$	29.2629			1.24102
$557$	1.00267	−	0.578894i	0.0424847	−	0.0245285i	−0.478607	−	0.878029i	$-0.658858\pi$
$557$	1.00267	−	0.578894i	0.0424847	−	0.0245285i	0.521092	+	0.853501i	$0.325525\pi$
$558$	0.718300	+	2.68073i	0.0304081	+	0.113485i
$559$	−28.0972	+	48.6657i	−1.18838	+	2.05834i
$560$		0			0
$561$	10.6946	+	10.6946i	0.451527	+	0.451527i
$562$	−4.25618	−	15.8843i	−0.179536	−	0.670038i
$563$		−	9.05216i		−	0.381503i	−0.981638	−	0.190751i	$-0.938908\pi$
$563$		−	9.05216i		−	0.381503i	0.981638	−	0.190751i	$-0.0610925\pi$
$564$	6.51546	−	3.76170i	0.274350	−	0.158396i
$565$		0			0
$566$		−	9.16354i		−	0.385172i
$567$	11.9433	+	3.20021i	0.501573	+	0.134396i
$568$	−15.6712	−	9.04780i	−0.657551	−	0.379637i
$569$	−0.221126	−	0.221126i	−0.00927008	−	0.00927008i	0.702457	−	0.711727i	$-0.252087\pi$
$569$	−0.221126	−	0.221126i	−0.00927008	−	0.00927008i	−0.711727	+	0.702457i	$0.752087\pi$
$570$		0			0
$571$	−14.6005	−	25.2888i	−0.611012	−	1.05830i	−0.991070	−	0.133342i	$-0.957429\pi$
$571$	−14.6005	−	25.2888i	−0.611012	−	1.05830i	0.380058	−	0.924963i	$-0.375904\pi$
$572$	−13.4006	−	23.2106i	−0.560309	−	0.970483i
$573$	−7.10270	+	12.3022i	−0.296719	+	0.513933i
$574$	−2.97497	−	11.1028i	−0.124173	−	0.463420i
$575$		0			0
$576$	1.28426	−	0.741467i	0.0535108	−	0.0308945i
$577$	7.37214	+	12.7689i	0.306906	+	0.531577i	0.977684	−	0.210081i	$-0.0673729\pi$
$577$	7.37214	+	12.7689i	0.306906	+	0.531577i	−0.670778	+	0.741658i	$0.734040\pi$
$578$		−	10.7215i		−	0.445956i
$579$	−36.2391	+	9.71024i	−1.50605	+	0.403544i
$580$		0			0
$581$	1.48652			0.0616711
$582$	−12.5888	−	12.5888i	−0.521821	−	0.521821i
$583$	14.4414	+	3.86957i	0.598103	+	0.160261i
$584$	−14.0814	−	14.0814i	−0.582694	−	0.582694i
$585$		0			0
$586$	−16.9610	+	16.9610i	−0.700652	+	0.700652i
$587$	−29.6366	−	17.1107i	−1.22323	−	0.706233i	−0.257627	−	0.966245i	$-0.582940\pi$
$587$	−29.6366	−	17.1107i	−1.22323	−	0.706233i	−0.965606	+	0.260011i	$0.916274\pi$
$588$	12.7962	−	3.42874i	0.527708	−	0.141399i
$589$	18.5124	+	10.6881i	0.762790	+	0.440397i
$590$		0			0
$591$		−	50.9414i		−	2.09545i
$592$	−1.48098	−	1.82180i	−0.0608680	−	0.0748756i
$593$	−2.15764	−	2.15764i	−0.0886036	−	0.0886036i	0.661416	−	0.750019i	$-0.269956\pi$
$593$	−2.15764	−	2.15764i	−0.0886036	−	0.0886036i	−0.750019	+	0.661416i	$0.769956\pi$
$594$	4.24624	−	15.8472i	0.174225	−	0.650218i
$595$		0			0
$596$	17.5956	+	10.1588i	0.720743	+	0.416121i
$597$	16.6481	−	28.8354i	0.681362	−	1.18015i
$598$			3.22143i			0.131734i
$599$	−6.31443	−	3.64564i	−0.258000	−	0.148957i	0.365422	−	0.930842i	$-0.380925\pi$
$599$	−6.31443	−	3.64564i	−0.258000	−	0.148957i	−0.623422	+	0.781885i	$0.714258\pi$
$600$		0			0
$601$	−6.91912	−	11.9843i	−0.282237	−	0.488849i	0.689699	−	0.724097i	$-0.257743\pi$
$601$	−6.91912	−	11.9843i	−0.282237	−	0.488849i	−0.971935	+	0.235248i	$0.924410\pi$
$602$	8.24975	−	8.24975i	0.336235	−	0.336235i
$603$	1.54830	−	1.54830i	0.0630518	−	0.0630518i
$604$	18.7953	−	10.8514i	0.764768	−	0.441539i
$605$		0			0
$606$	−3.36596	+	3.36596i	−0.136733	+	0.136733i
$607$	8.17078	−	4.71740i	0.331642	−	0.191473i	−0.324928	−	0.945739i	$-0.605340\pi$
$607$	8.17078	−	4.71740i	0.331642	−	0.191473i	0.656570	+	0.754265i	$0.272007\pi$
$608$	3.52658	−	13.1614i	0.143022	−	0.533764i
$609$	5.22105	+	1.39898i	0.211568	+	0.0566893i
$610$		0			0
$611$	14.7473	−	3.95153i	0.596612	−	0.159862i
$612$	0.846856	−	0.488933i	0.0342321	−	0.0197639i
$613$	−25.9670	−	6.95785i	−1.04880	−	0.281025i	−0.307043	−	0.951696i	$-0.599340\pi$
$613$	−25.9670	−	6.95785i	−1.04880	−	0.281025i	−0.741755	+	0.670671i	$0.766006\pi$
$614$	−19.8022	−	5.30597i	−0.799150	−	0.214132i
$615$		0			0
$616$	3.62098	+	13.5137i	0.145894	+	0.544482i
$617$	−7.44729	+	27.7937i	−0.299817	+	1.11893i	0.637499	+	0.770451i	$0.279969\pi$
$617$	−7.44729	+	27.7937i	−0.299817	+	1.11893i	−0.937316	+	0.348481i	$0.886698\pi$
$618$	−8.53826	−	8.53826i	−0.343459	−	0.343459i
$619$	−33.9719			−1.36544			−0.682722	−	0.730678i	$-0.739204\pi$
$619$	−33.9719			−1.36544			−0.682722	+	0.730678i	$0.739204\pi$
$620$		0			0
$621$	2.71143	−	2.71143i	0.108806	−	0.108806i
$622$	17.3350	−	4.64489i	0.695069	−	0.186243i
$623$	8.98620			0.360025
$624$	−3.36821	+	0.902509i	−0.134836	+	0.0361293i
$625$		0			0
$626$	11.9046	−	20.6194i	0.475804	−	0.824116i
$627$	8.90559	+	15.4249i	0.355655	+	0.616012i
$628$	−7.92710	+	7.92710i	−0.316326	+	0.316326i
$629$	7.66514	+	9.42912i	0.305629	+	0.375964i
$630$		0			0
$631$	24.1532	+	6.47184i	0.961525	+	0.257640i	0.705246	−	0.708963i	$-0.250837\pi$
$631$	24.1532	+	6.47184i	0.961525	+	0.257640i	0.256279	+	0.966603i	$0.417503\pi$
$632$	−23.5291	+	6.30461i	−0.935938	+	0.250784i
$633$	8.86151	+	33.0716i	0.352213	+	1.31448i
$634$	0.234761	+	0.876139i	0.00932355	+	0.0347959i
$635$		0			0
$636$	4.39569	−	7.61356i	0.174301	−	0.301897i
$637$	26.8839			1.06518
$638$	2.08912	−	7.79670i	0.0827090	−	0.308674i
$639$		−	2.45043i		−	0.0969377i
$640$		0			0
$641$	−0.440835	−	0.763549i	−0.0174119	−	0.0301584i	0.857188	−	0.515003i	$-0.172209\pi$
$641$	−0.440835	−	0.763549i	−0.0174119	−	0.0301584i	−0.874600	+	0.484845i	$0.838876\pi$
$642$	−1.63649	+	2.83448i	−0.0645870	+	0.111868i
$643$	27.9848			1.10361			0.551807	−	0.833972i	$-0.313938\pi$
$643$	27.9848			1.10361			0.551807	+	0.833972i	$0.313938\pi$
$644$	−0.336605	+	1.25623i	−0.0132641	+	0.0495022i
$645$		0			0
$646$	−1.00250	+	3.74139i	−0.0394430	+	0.147203i
$647$	−20.1484	−	11.6327i	−0.792114	−	0.457327i	0.0485920	−	0.998819i	$-0.484527\pi$
$647$	−20.1484	−	11.6327i	−0.792114	−	0.457327i	−0.840706	+	0.541491i	$0.817860\pi$
$648$	−23.6411	−	13.6492i	−0.928710	−	0.536191i
$649$	1.56470	−	5.83955i	0.0614199	−	0.229222i
$650$		0			0
$651$	−5.35214	+	19.9745i	−0.209767	+	0.782861i
$652$	−1.25228			−0.0490433
$653$	−19.9298	+	34.5194i	−0.779914	+	1.35085i	0.152077	+	0.988369i	$0.451404\pi$
$653$	−19.9298	+	34.5194i	−0.779914	+	1.35085i	−0.931991	+	0.362482i	$0.881930\pi$
$654$	8.16945	+	14.1499i	0.319451	+	0.553305i
$655$		0			0
$656$		−	4.34262i		−	0.169551i
$657$	0.697957	−	2.60481i	0.0272299	−	0.101623i
$658$	−3.16981			−0.123572
$659$	−5.64501	+	9.77745i	−0.219898	+	0.380875i	−0.954777	−	0.297324i	$-0.903906\pi$
$659$	−5.64501	+	9.77745i	−0.219898	+	0.380875i	0.734878	+	0.678199i	$0.237239\pi$
$660$		0			0
$661$	1.49956	+	5.59642i	0.0583259	+	0.217675i	0.988937	−	0.148333i	$-0.0473908\pi$
$661$	1.49956	+	5.59642i	0.0583259	+	0.217675i	−0.930612	+	0.366008i	$0.880724\pi$
$662$	−0.415939	−	1.55230i	−0.0161659	−	0.0603320i
$663$	17.4329	−	4.67112i	0.677037	−	0.181411i
$664$	−3.17007	−	0.849418i	−0.123023	−	0.0329638i
$665$		0			0
$666$	−0.662534	+	1.73577i	−0.0256727	+	0.0672597i
$667$	1.33400	−	1.33400i	0.0516528	−	0.0516528i
$668$	−1.22269	−	2.11776i	−0.0473073	−	0.0819386i
$669$	−10.1597	+	17.5971i	−0.392797	+	0.680345i
$670$		0			0
$671$	26.5460	−	7.11298i	1.02480	−	0.274594i
$672$	13.1812			0.508478
$673$	−34.1375	+	9.14711i	−1.31590	+	0.352595i	−0.847442	−	0.530888i	$-0.821858\pi$
$673$	−34.1375	+	9.14711i	−1.31590	+	0.352595i	−0.468462	+	0.883484i	$0.655192\pi$
$674$	0.491059	−	0.491059i	0.0189149	−	0.0189149i
$675$		0			0
$676$	−14.8116			−0.569676
$677$	−26.8736	−	26.8736i	−1.03284	−	1.03284i	−0.999442	−	0.0333951i	$-0.989368\pi$
$677$	−26.8736	−	26.8736i	−1.03284	−	1.03284i	−0.0333951	−	0.999442i	$-0.510632\pi$
$678$	0.845501	−	3.15545i	0.0324713	−	0.121184i
$679$	−3.77506	−	14.0887i	−0.144874	−	0.540675i
$680$		0			0
$681$	14.9284	+	4.00006i	0.572059	+	0.153283i
$682$	29.8283	+	7.99246i	1.14218	+	0.306047i
$683$	−9.59406	+	5.53913i	−0.367107	+	0.211949i	−0.672194	−	0.740375i	$-0.734648\pi$
$683$	−9.59406	+	5.53913i	−0.367107	+	0.211949i	0.305087	+	0.952324i	$0.401314\pi$
$684$	1.11233	−	0.298049i	0.0425312	−	0.0113962i
$685$		0			0
$686$	−12.2992	−	3.29556i	−0.469586	−	0.125825i
$687$	−9.68676	+	36.1515i	−0.369573	+	1.37927i
$688$	3.81725	−	2.20389i	0.145531	−	0.0840226i
$689$	12.6153	−	12.6153i	0.480604	−	0.480604i
$690$		0			0
$691$	3.68751	−	2.12898i	0.140279	−	0.0809904i	−0.428218	−	0.903676i	$-0.640858\pi$
$691$	3.68751	−	2.12898i	0.140279	−	0.0809904i	0.568497	+	0.822685i	$0.307525\pi$
$692$	−1.87641	+	1.87641i	−0.0713304	+	0.0713304i
$693$	−1.33963	+	1.33963i	−0.0508884	+	0.0508884i
$694$	−10.6510	−	18.4481i	−0.404308	−	0.700281i
$695$		0			0
$696$	−10.3347	−	5.96676i	−0.391737	−	0.226170i
$697$			22.4761i			0.851344i
$698$	7.34642	−	12.7244i	0.278066	−	0.481625i
$699$	−14.4394	−	8.33657i	−0.546147	−	0.315318i
$700$		0			0
$701$	−9.60225	+	35.8361i	−0.362672	+	1.35351i	0.507878	+	0.861429i	$0.330430\pi$
$701$	−9.60225	+	35.8361i	−0.362672	+	1.35351i	−0.870549	+	0.492081i	$0.836236\pi$
$702$	−13.8433	−	13.8433i	−0.522481	−	0.522481i
$703$	5.84524	+	13.0620i	0.220457	+	0.492644i
$704$		−	16.5005i		−	0.621885i
$705$		0			0
$706$	−5.02460	−	2.90096i	−0.189103	−	0.109179i
$707$	−3.76702	+	1.00937i	−0.141673	+	0.0379612i
$708$	−3.07862	−	1.77744i	−0.115702	−	0.0668004i
$709$	25.2496	−	25.2496i	0.948269	−	0.948269i	−0.0504569	−	0.998726i	$-0.516068\pi$
$709$	25.2496	−	25.2496i	0.948269	−	0.948269i	0.998726	+	0.0504569i	$0.0160677\pi$
$710$		0			0
$711$	−2.33247	−	2.33247i	−0.0874746	−	0.0874746i
$712$	−19.1635	−	5.13484i	−0.718183	−	0.192436i
$713$	5.10357	+	5.10357i	0.191130	+	0.191130i
$714$	−3.74704			−0.140230
$715$		0			0
$716$	−29.8092	+	7.98736i	−1.11402	+	0.298502i
$717$			11.0391i			0.412264i
$718$	−7.57849	−	13.1263i	−0.282827	−	0.489871i
$719$	37.1866	−	21.4697i	1.38683	−	0.800685i	0.393871	−	0.919166i	$-0.371136\pi$
$719$	37.1866	−	21.4697i	1.38683	−	0.800685i	0.992956	+	0.118480i	$0.0378022\pi$
$720$		0			0
$721$	−2.56042	−	9.55560i	−0.0953549	−	0.355869i
$722$	5.54874	−	9.61069i	0.206503	−	0.357673i
$723$	0.240278	+	0.416174i	0.00893604	+	0.0154777i
$724$	−0.804434	−	1.39332i	−0.0298965	−	0.0517823i
$725$		0			0
$726$	6.42506	+	6.42506i	0.238456	+	0.238456i
$727$	−5.97867	−	3.45179i	−0.221737	−	0.128020i	0.385017	−	0.922909i	$-0.374195\pi$
$727$	−5.97867	−	3.45179i	−0.221737	−	0.128020i	−0.606754	+	0.794890i	$0.707529\pi$
$728$	16.1257	+	4.32087i	0.597659	+	0.160142i
$729$			22.8913i			0.847826i
$730$		0			0
$731$	−19.7570	+	11.4067i	−0.730739	+	0.421893i
$732$		−	16.1602i		−	0.597297i
$733$	1.90920	+	7.12522i	0.0705178	+	0.263176i	0.992180	−	0.124818i	$-0.0398347\pi$
$733$	1.90920	+	7.12522i	0.0705178	+	0.263176i	−0.921662	+	0.387994i	$0.873168\pi$
$734$	9.55154	+	9.55154i	0.352554	+	0.352554i
$735$		0			0
$736$	2.30030	−	3.98424i	0.0847902	−	0.146861i
$737$	−6.30582	−	23.5337i	−0.232278	−	0.866873i
$738$	−2.97607	+	1.71823i	−0.109550	+	0.0632490i
$739$	−14.9613			−0.550359			−0.275179	−	0.961393i	$-0.588737\pi$
$739$	−14.9613			−0.550359			−0.275179	+	0.961393i	$0.588737\pi$
$740$		0			0
$741$	21.2538			0.780780
$742$	−3.20779	+	1.85202i	−0.117762	+	0.0679897i
$743$	4.39484	+	16.4018i	0.161231	+	0.601723i	0.998491	+	0.0549175i	$0.0174896\pi$
$743$	4.39484	+	16.4018i	0.161231	+	0.601723i	−0.837260	+	0.546805i	$0.815844\pi$
$744$	22.8274	−	39.5382i	0.836893	−	1.44954i
$745$		0			0
$746$	−3.13120	−	3.13120i	−0.114641	−	0.114641i
$747$	−0.115025	−	0.429278i	−0.00420853	−	0.0157065i
$748$		−	10.8806i		−	0.397835i
$749$	−2.32222	+	1.34073i	−0.0848519	+	0.0489893i
$750$		0			0
$751$		−	25.3188i		−	0.923895i	−0.886907	−	0.461947i	$-0.847151\pi$
$751$		−	25.3188i		−	0.923895i	0.886907	−	0.461947i	$-0.152849\pi$
$752$	−1.15675	−	0.309951i	−0.0421825	−	0.0113028i
$753$	40.4329	+	23.3439i	1.47346	+	0.850700i
$754$	−6.81078	−	6.81078i	−0.248034	−	0.248034i
$755$		0			0
$756$	−3.95184	−	6.84478i	−0.143727	−	0.248942i
$757$	8.53899	+	14.7900i	0.310355	+	0.537551i	0.978439	−	0.206535i	$-0.0662188\pi$
$757$	8.53899	+	14.7900i	0.310355	+	0.537551i	−0.668084	+	0.744086i	$0.732885\pi$
$758$	8.35605	−	14.4731i	0.303505	−	0.525687i
$759$	1.55649	+	5.80890i	0.0564970	+	0.210850i
$760$		0			0
$761$	−44.0238	+	25.4171i	−1.59586	+	0.921370i	−0.603587	+	0.797297i	$0.706262\pi$
$761$	−44.0238	+	25.4171i	−1.59586	+	0.921370i	−0.992273	+	0.124073i	$0.960404\pi$
$762$	2.86296	+	4.95880i	0.103714	+	0.179638i
$763$			13.3861i			0.484608i
$764$	9.87121	−	2.64498i	0.357128	−	0.0956921i
$765$		0			0
$766$	−5.70472			−0.206120
$767$	−5.10112	−	5.10112i	−0.184191	−	0.184191i
$768$	−26.3015	−	7.04748i	−0.949075	−	0.254304i
$769$	34.2637	+	34.2637i	1.23558	+	1.23558i	0.961790	+	0.273790i	$0.0882772\pi$
$769$	34.2637	+	34.2637i	1.23558	+	1.23558i	0.273790	+	0.961790i	$0.411723\pi$
$770$		0			0
$771$	−18.3056	+	18.3056i	−0.659262	+	0.659262i
$772$	23.3743	+	13.4951i	0.841258	+	0.485701i
$773$	6.87810	−	1.84298i	0.247388	−	0.0662874i	−0.132994	−	0.991117i	$-0.542459\pi$
$773$	6.87810	−	1.84298i	0.247388	−	0.0662874i	0.380382	+	0.924829i	$0.375792\pi$
$774$	−3.02073	−	1.74402i	−0.108578	−	0.0626874i
$775$		0			0
$776$			32.2020i			1.15598i
$777$	−10.7419	+	8.73236i	−0.385365	+	0.313272i
$778$	−20.3372	−	20.3372i	−0.729124	−	0.729124i
$779$	−6.85062	+	25.5669i	−0.245449	+	0.916028i
$780$		0			0
$781$	−23.6128	−	13.6329i	−0.844933	−	0.487822i
$782$	−0.653908	+	1.13260i	−0.0233837	+	0.0405018i
$783$			11.4651i			0.409728i
$784$	−1.82621	−	1.05436i	−0.0652219	−	0.0376559i
$785$		0			0
$786$	7.47404	+	12.9454i	0.266590	+	0.461748i
$787$	19.6130	−	19.6130i	0.699129	−	0.699129i	−0.265094	−	0.964223i	$-0.585403\pi$
$787$	19.6130	−	19.6130i	0.699129	−	0.699129i	0.964223	+	0.265094i	$0.0854029\pi$
$788$	−25.9137	+	25.9137i	−0.923137	+	0.923137i
$789$	−18.7167	+	10.8061i	−0.666332	+	0.384707i
$790$		0			0
$791$	1.89249	−	1.89249i	0.0672891	−	0.0672891i
$792$	3.62231	−	2.09134i	0.128713	−	0.0743126i
$793$	8.48783	−	31.6770i	0.301412	−	1.12488i
$794$	−9.86210	−	2.64254i	−0.349993	−	0.0937803i
$795$		0			0
$796$	−23.1373	+	6.19961i	−0.820079	+	0.219739i
$797$	−43.0504	+	24.8552i	−1.52492	+	0.880415i	−0.525359	+	0.850881i	$0.676069\pi$
$797$	−43.0504	+	24.8552i	−1.52492	+	0.880415i	−0.999564	+	0.0295340i	$0.990598\pi$
$798$	−4.26231	−	1.14208i	−0.150884	−	0.0404293i
$799$	5.98703	+	1.60422i	0.211806	+	0.0567532i
$800$		0			0
$801$	−0.695340	−	2.59504i	−0.0245686	−	0.0916914i
$802$	−6.68662	+	24.9548i	−0.236113	+	0.881185i
$803$	−21.2174	−	21.2174i	−0.748745	−	0.748745i
$804$	−14.3264			−0.505252
$805$		0			0
$806$	26.0564	−	26.0564i	0.917797	−	0.917797i
$807$	41.2939	−	11.0647i	1.45361	−	0.389495i
$808$	8.61011			0.302903
$809$	−15.7995	+	4.23346i	−0.555480	+	0.148841i	−0.525629	−	0.850714i	$-0.676170\pi$
$809$	−15.7995	+	4.23346i	−0.555480	+	0.148841i	−0.0298512	+	0.999554i	$0.509503\pi$
$810$		0			0
$811$	−7.45897	+	12.9193i	−0.261920	+	0.453659i	−0.966752	−	0.255716i	$-0.917689\pi$
$811$	−7.45897	+	12.9193i	−0.261920	+	0.453659i	0.704832	+	0.709374i	$0.251022\pi$
$812$	−1.94427	−	3.36758i	−0.0682306	−	0.118179i
$813$	8.36044	−	8.36044i	0.293214	−	0.293214i
$814$	13.0402	+	16.0412i	0.457060	+	0.562243i
$815$		0			0
$816$	−1.36740	−	0.366395i	−0.0478687	−	0.0128264i
$817$	−25.9506	+	6.95343i	−0.907895	+	0.243270i
$818$	−5.82234	−	21.7293i	−0.203573	−	0.759746i
$819$	0.585115	+	2.18368i	0.0204456	+	0.0763040i
$820$		0			0
$821$	5.80160	−	10.0487i	0.202477	−	0.350701i	−0.746849	−	0.664994i	$-0.768434\pi$
$821$	5.80160	−	10.0487i	0.202477	−	0.350701i	0.949326	+	0.314293i	$0.101767\pi$
$822$	32.0210			1.11686
$823$	6.12304	−	22.8515i	0.213436	−	0.796553i	−0.773276	−	0.634070i	$-0.781383\pi$
$823$	6.12304	−	22.8515i	0.213436	−	0.796553i	0.986711	−	0.162483i	$-0.0519503\pi$
$824$			21.8408i			0.760862i
$825$		0			0
$826$	0.748883	+	1.29710i	0.0260570	+	0.0451320i
$827$	−3.22817	+	5.59136i	−0.112255	+	0.194431i	−0.916679	−	0.399624i	$-0.869141\pi$
$827$	−3.22817	+	5.59136i	−0.112255	+	0.194431i	0.804424	+	0.594055i	$0.202474\pi$
$828$	0.388820			0.0135124
$829$	−2.90505	+	10.8418i	−0.100897	+	0.376551i	−0.997847	−	0.0655791i	$-0.979111\pi$
$829$	−2.90505	+	10.8418i	−0.100897	+	0.376551i	0.896951	+	0.442131i	$0.145777\pi$
$830$		0			0
$831$	8.72547	−	32.5639i	0.302683	−	1.12963i
$832$	−17.0519	−	9.84490i	−0.591167	−	0.341310i
$833$	9.45196	+	5.45709i	0.327491	+	0.189077i
$834$	−8.67656	+	32.3814i	−0.300445	+	1.12127i
$835$		0			0
$836$	3.31636	−	12.3768i	0.114699	−	0.428062i
$837$	−43.8626			−1.51611
$838$	−14.5810	+	25.2550i	−0.503692	+	0.872420i
$839$	19.3905	+	33.5854i	0.669435	+	1.15950i	0.978062	+	0.208312i	$0.0667970\pi$
$839$	19.3905	+	33.5854i	0.669435	+	1.15950i	−0.308628	+	0.951183i	$0.599870\pi$
$840$		0			0
$841$		−	23.3593i		−	0.805492i
$842$	1.94588	−	7.26211i	0.0670593	−	0.250269i
$843$	−36.6328			−1.26170
$844$	12.3156	−	21.3312i	0.423920	−	0.734251i
$845$		0			0
$846$	0.245275	+	0.915380i	0.00843274	+	0.0314714i
$847$	1.92672	+	7.19061i	0.0662028	+	0.247072i
$848$	−1.35171	+	0.362190i	−0.0464179	+	0.0124376i
$849$	−19.7176	−	5.28331i	−0.676705	−	0.181323i
$850$		0			0
$851$	0.764883	+	4.77083i	0.0262199	+	0.163542i
$852$	−11.3369	+	11.3369i	−0.388395	+	0.388395i
$853$	−19.3647	−	33.5407i	−0.663035	−	1.14841i	−0.979814	−	0.199911i	$-0.935935\pi$
$853$	−19.3647	−	33.5407i	−0.663035	−	1.14841i	0.316779	−	0.948499i	$-0.397399\pi$
$854$	−3.40435	+	5.89651i	−0.116494	+	0.201774i
$855$		0			0
$856$	5.71835	−	1.53223i	0.195449	−	0.0523705i
$857$	32.5958			1.11345			0.556726	−	0.830696i	$-0.312057\pi$
$857$	32.5958			1.11345			0.556726	+	0.830696i	$0.312057\pi$
$858$	29.6574	−	7.94669i	1.01249	−	0.271295i
$859$	25.5200	−	25.5200i	0.870731	−	0.870731i	−0.121821	−	0.992552i	$-0.538873\pi$
$859$	25.5200	−	25.5200i	0.870731	−	0.870731i	0.992552	+	0.121821i	$0.0388734\pi$
$860$		0			0
$861$	−25.6055			−0.872633
$862$	−14.9705	−	14.9705i	−0.509898	−	0.509898i
$863$	−2.11358	+	7.88799i	−0.0719471	+	0.268510i	−0.992524	−	0.122052i	$-0.961053\pi$
$863$	−2.11358	+	7.88799i	−0.0719471	+	0.268510i	0.920577	+	0.390562i	$0.127719\pi$
$864$	7.23629	+	27.0062i	0.246183	+	0.918769i
$865$		0			0
$866$	19.1617	+	5.13435i	0.651139	+	0.174472i
$867$	−23.0699	−	6.18156i	−0.783495	−	0.209937i
$868$	12.8835	−	7.43831i	0.437296	−	0.252473i
$869$	−35.4527	+	9.49953i	−1.20265	+	0.322250i
$870$		0			0
$871$	−28.0824	−	7.52466i	−0.951536	−	0.254963i
$872$	7.64898	−	28.5464i	0.259027	−	0.966703i
$873$	−3.77645	+	2.18033i	−0.127813	+	0.0737931i
$874$	−1.08904	+	1.08904i	−0.0368374	+	0.0368374i
$875$		0			0
$876$	−15.2802	+	8.82200i	−0.516269	+	0.298068i
$877$	−9.48217	+	9.48217i	−0.320190	+	0.320190i	−0.848840	−	0.528650i	$-0.822698\pi$
$877$	−9.48217	+	9.48217i	−0.320190	+	0.320190i	0.528650	+	0.848840i	$0.322698\pi$
$878$	−8.68201	+	8.68201i	−0.293004	+	0.293004i
$879$	26.7167	+	46.2747i	0.901131	+	1.56081i
$880$		0			0
$881$	−18.1684	−	10.4895i	−0.612110	−	0.353402i	0.161681	−	0.986843i	$-0.448308\pi$
$881$	−18.1684	−	10.4895i	−0.612110	−	0.353402i	−0.773791	+	0.633441i	$0.781642\pi$
$882$			1.66871i			0.0561885i
$883$	12.2856	−	21.2792i	0.413442	−	0.716103i	−0.581822	−	0.813316i	$-0.697660\pi$
$883$	12.2856	−	21.2792i	0.413442	−	0.716103i	0.995264	+	0.0972140i	$0.0309931\pi$
$884$	−11.2442	−	6.49185i	−0.378184	−	0.218345i
$885$		0			0
$886$	5.76777	−	21.5256i	0.193772	−	0.723167i
$887$	7.43917	+	7.43917i	0.249783	+	0.249783i	0.820881	−	0.571099i	$-0.193483\pi$
$887$	7.43917	+	7.43917i	0.249783	+	0.249783i	−0.571099	+	0.820881i	$0.693483\pi$
$888$	27.8975	−	12.4841i	0.936179	−	0.418938i
$889$			4.69111i			0.157335i
$890$		0			0
$891$	−35.6215	−	20.5661i	−1.19336	−	0.688990i
$892$	14.1198	−	3.78339i	0.472766	−	0.126677i
$893$	6.32136	+	3.64964i	0.211536	+	0.122130i
$894$	−16.4586	+	16.4586i	−0.550457	+	0.550457i
$895$		0			0
$896$	−7.26292	−	7.26292i	−0.242637	−	0.242637i
$897$	6.93168	+	1.85734i	0.231442	+	0.0620148i
$898$	4.13547	+	4.13547i	0.138002	+	0.138002i
$899$	−21.5801			−0.719735
$900$		0			0
$901$	6.99606	−	1.87459i	0.233073	−	0.0624516i
$902$			38.2372i			1.27316i
$903$	−12.9949	−	22.5078i	−0.432442	−	0.749012i
$904$	−5.11721	+	2.95442i	−0.170196	+	0.0982627i
$905$		0			0
$906$	6.43500	+	24.0157i	0.213788	+	0.797870i
$907$	−17.8411	+	30.9017i	−0.592404	+	1.02607i	0.401504	+	0.915857i	$0.368488\pi$
$907$	−17.8411	+	30.9017i	−0.592404	+	1.02607i	−0.993908	+	0.110216i	$0.964846\pi$
$908$	−5.55922	−	9.62885i	−0.184489	−	0.319545i
$909$	0.582974	+	1.00974i	0.0193360	+	0.0334910i
$910$		0			0
$911$	−14.7906	−	14.7906i	−0.490033	−	0.490033i	0.418283	−	0.908317i	$-0.362632\pi$
$911$	−14.7906	−	14.7906i	−0.490033	−	0.490033i	−0.908317	+	0.418283i	$0.862632\pi$
$912$	−1.44376	−	0.833558i	−0.0478078	−	0.0276019i
$913$	−4.77654	−	1.27987i	−0.158080	−	0.0423575i
$914$			10.7979i			0.357163i
$915$		0			0
$916$	23.3177	−	13.4625i	0.770440	−	0.444814i
$917$			12.2466i			0.404418i
$918$	−2.05707	−	7.67707i	−0.0678933	−	0.253381i
$919$	11.5779	+	11.5779i	0.381920	+	0.381920i	0.871794	−	0.489873i	$-0.162957\pi$
$919$	11.5779	+	11.5779i	0.381920	+	0.381920i	−0.489873	+	0.871794i	$0.662957\pi$
$920$		0			0
$921$	−22.8342	+	39.5499i	−0.752411	+	1.30321i
$922$	4.66933	+	17.4262i	0.153776	+	0.573901i
$923$	−28.1769	+	16.2679i	−0.927454	+	0.535466i
$924$	12.3955			0.407783
$925$		0			0
$926$	−22.3916			−0.735835
$927$	−2.56136	+	1.47880i	−0.0841259	+	0.0485701i
$928$	3.56020	+	13.2868i	0.116869	+	0.436162i
$929$	7.03355	−	12.1825i	0.230763	−	0.399694i	−0.727270	−	0.686352i	$-0.759211\pi$
$929$	7.03355	−	12.1825i	0.230763	−	0.399694i	0.958033	+	0.286658i	$0.0925443\pi$
$930$		0			0
$931$	9.08842	+	9.08842i	0.297861	+	0.297861i
$932$	3.10447	+	11.5860i	0.101690	+	0.379513i
$933$		−	39.9784i		−	1.30884i
$934$	−8.15879	+	4.71048i	−0.266964	+	0.154132i
$935$		0			0
$936$		−	4.99115i		−	0.163141i
$937$	−24.5217	−	6.57057i	−0.801090	−	0.214651i	−0.165027	−	0.986289i	$-0.552771\pi$
$937$	−24.5217	−	6.57057i	−0.801090	−	0.214651i	−0.636062	+	0.771638i	$0.719438\pi$
$938$	5.22739	+	3.01803i	0.170680	+	0.0985423i
$939$	−37.5039	−	37.5039i	−1.22389	−	1.22389i
$940$		0			0
$941$	29.3296	+	50.8003i	0.956116	+	1.65604i	0.731793	+	0.681527i	$0.238684\pi$
$941$	29.3296	+	50.8003i	0.956116	+	1.65604i	0.224324	+	0.974515i	$0.427983\pi$
$942$	−6.42146	−	11.1223i	−0.209223	−	0.362384i
$943$	−4.46850	+	7.73966i	−0.145514	+	0.252038i
$944$	0.146455	+	0.546578i	0.00476671	+	0.0177896i
$945$		0			0
$946$	−33.6114	+	19.4055i	−1.09280	+	0.630928i
$947$	20.3531	+	35.2526i	0.661386	+	1.14555i	0.980252	+	0.197754i	$0.0633648\pi$
$947$	20.3531	+	35.2526i	0.661386	+	1.14555i	−0.318865	+	0.947800i	$0.603302\pi$
$948$			21.5822i			0.700959i
$949$	−34.5856	+	9.26719i	−1.12270	+	0.300826i
$950$		0			0
$951$	2.02058			0.0655217
$952$	4.79246	+	4.79246i	0.155325	+	0.155325i
$953$	−6.73269	−	1.80402i	−0.218093	−	0.0584379i	0.148118	−	0.988970i	$-0.452679\pi$
$953$	−6.73269	−	1.80402i	−0.218093	−	0.0584379i	−0.366211	+	0.930532i	$0.619345\pi$
$954$	0.783042	+	0.783042i	0.0253519	+	0.0253519i
$955$		0			0
$956$	5.61556	−	5.61556i	0.181620	−	0.181620i
$957$	−15.5720	−	8.99049i	−0.503371	−	0.290621i
$958$	−7.81712	+	2.09459i	−0.252560	+	0.0676731i
$959$	22.7193	+	13.1170i	0.733644	+	0.423570i
$960$		0			0
$961$		−	51.5600i		−	1.66323i
$962$	24.3576	−	3.90513i	0.785320	−	0.125906i
$963$	0.566868	+	0.566868i	0.0182671	+	0.0182671i
$964$	0.0894775	−	0.333935i	0.00288188	−	0.0107553i
$965$		0			0
$966$	−1.29030	−	0.744953i	−0.0415146	−	0.0239685i
$967$	−0.511694	+	0.886281i	−0.0164550	+	0.0285009i	−0.874136	−	0.485682i	$-0.838571\pi$
$967$	−0.511694	+	0.886281i	−0.0164550	+	0.0285009i	0.857681	+	0.514183i	$0.171905\pi$
$968$		−	16.4353i		−	0.528250i
$969$	7.47251	+	4.31425i	0.240052	+	0.138594i
$970$		0			0
$971$	7.81561	+	13.5370i	0.250815	+	0.434424i	0.963750	−	0.266805i	$-0.0859681\pi$
$971$	7.81561	+	13.5370i	0.250815	+	0.434424i	−0.712936	+	0.701230i	$0.752635\pi$
$972$	−3.57722	+	3.57722i	−0.114739	+	0.114739i
$973$	−19.4208	+	19.4208i	−0.622601	+	0.622601i
$974$	20.5246	−	11.8499i	0.657652	−	0.379695i
$975$		0			0
$976$	−1.81892	+	1.81892i	−0.0582222	+	0.0582222i
$977$	18.4196	−	10.6345i	0.589295	−	0.340229i	−0.175524	−	0.984475i	$-0.556162\pi$
$977$	18.4196	−	10.6345i	0.589295	−	0.340229i	0.764819	+	0.644246i	$0.222829\pi$
$978$	0.371308	−	1.38574i	0.0118731	−	0.0443111i
$979$	−28.8748	−	7.73698i	−0.922843	−	0.247275i
$980$		0			0
$981$	3.86564	−	1.03579i	0.123420	−	0.0330704i
$982$	22.4898	−	12.9845i	0.717677	−	0.414351i
$983$	46.1634	+	12.3694i	1.47238	+	0.394524i	0.903748	−	0.428066i	$-0.140805\pi$
$983$	46.1634	+	12.3694i	1.47238	+	0.394524i	0.568635	+	0.822590i	$0.307472\pi$
$984$	54.6049	+	14.6313i	1.74074	+	0.466430i
$985$		0			0
$986$	−1.01206	−	3.77706i	−0.0322306	−	0.120286i
$987$	−1.82757	+	6.82060i	−0.0581723	+	0.217102i
$988$	−10.8118	−	10.8118i	−0.343968	−	0.343968i
$989$	−9.07111			−0.288445
$990$		0			0
$991$	−35.6021	+	35.6021i	−1.13094	+	1.13094i	−0.140916	+	0.990021i	$0.545005\pi$
$991$	−35.6021	+	35.6021i	−1.13094	+	1.13094i	−0.990021	+	0.140916i	$0.954995\pi$
$992$	−50.8322	+	13.6204i	−1.61392	+	0.432450i
$993$	−3.57997			−0.113607
$994$	6.52484	−	1.74833i	0.206955	−	0.0554535i
$995$		0			0
$996$	−1.45388	+	2.51820i	−0.0460681	+	0.0797923i
$997$	−14.7106	−	25.4796i	−0.465891	−	0.806947i	0.533350	−	0.845894i	$-0.320933\pi$
$997$	−14.7106	−	25.4796i	−0.465891	−	0.806947i	−0.999241	+	0.0389477i	$0.987599\pi$
$998$	−17.3085	+	17.3085i	−0.547890	+	0.547890i
$999$	−23.7883	−	17.2145i	−0.752629	−	0.544644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.y.b.193.11		68
5.2	odd	4		925.2.t.b.82.11		68
5.3	odd	4		185.2.p.a.82.7	✓	68
5.4	even	2		185.2.u.a.8.7	yes	68
37.14	odd	12		925.2.t.b.643.11		68
185.14	odd	12		185.2.p.a.88.7	yes	68
185.88	even	12		185.2.u.a.162.7	yes	68
185.162	even	12	inner	925.2.y.b.532.11		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.82.7	✓	68	5.3	odd	4
185.2.p.a.88.7	yes	68	185.14	odd	12
185.2.u.a.8.7	yes	68	5.4	even	2
185.2.u.a.162.7	yes	68	185.88	even	12
925.2.t.b.82.11		68	5.2	odd	4
925.2.t.b.643.11		68	37.14	odd	12
925.2.y.b.193.11		68	1.1	even	1	trivial
925.2.y.b.532.11		68	185.162	even	12	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.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.713738 - 0.412077i) q^{2} +(-0.475172 - 1.77336i) q^{3} +(-0.660386 + 1.14382i) q^{4} +(-1.06991 - 1.06991i) q^{6} +(-0.320840 - 1.19739i) q^{7} +2.73682i q^{8} +(-0.320958 + 0.185305i) q^{9} +4.12374i q^{11} +(2.34221 + 0.627593i) q^{12} +(4.26154 + 2.46040i) q^{13} +(-0.722412 - 0.722412i) q^{14} +(-0.192990 - 0.334268i) q^{16} +(0.998860 + 1.73008i) q^{17} +(-0.152720 + 0.264518i) q^{18} +(0.608896 + 2.27243i) q^{19} +(-1.97096 + 1.13793i) q^{21} +(1.69930 + 2.94327i) q^{22} +0.794336i q^{23} +(4.85339 - 1.30046i) q^{24} +4.05550 q^{26} +(-3.41346 - 3.41346i) q^{27} +(1.58148 + 0.423756i) q^{28} +(-1.67939 - 1.67939i) q^{29} +(6.42495 - 6.42495i) q^{31} +(-5.01581 - 2.89588i) q^{32} +(7.31290 - 1.95948i) q^{33} +(1.42585 + 0.823214i) q^{34} -0.489491i q^{36} +(6.00606 - 0.962921i) q^{37} +(1.37101 + 1.37101i) q^{38} +(2.33823 - 8.72639i) q^{39} +(9.74356 + 5.62545i) q^{41} +(-0.937830 + 1.62437i) q^{42} +11.4197i q^{43} +(-4.71682 - 2.72326i) q^{44} +(0.327327 + 0.566948i) q^{46} +(2.19390 - 2.19390i) q^{47} +(-0.501076 + 0.501076i) q^{48} +(4.73137 - 2.73166i) q^{49} +(2.59343 - 2.59343i) q^{51} +(-5.62853 + 3.24963i) q^{52} +(0.938365 - 3.50202i) q^{53} +(-3.84292 - 1.02971i) q^{54} +(3.27705 - 0.878082i) q^{56} +(3.74052 - 2.15959i) q^{57} +(-1.89069 - 0.506608i) q^{58} +(-1.41608 - 0.379437i) q^{59} +(-1.72489 - 6.43736i) q^{61} +(1.93816 - 7.23330i) q^{62} +(0.324858 + 0.324858i) q^{63} -4.00134 q^{64} +(4.41203 - 4.41203i) q^{66} +(-5.70687 + 1.52915i) q^{67} -2.63853 q^{68} +(1.40865 - 0.377446i) q^{69} +(-3.30595 + 5.72607i) q^{71} +(-0.507147 - 0.878404i) q^{72} +(-5.14518 + 5.14518i) q^{73} +(3.88996 - 3.16223i) q^{74} +(-3.00136 - 0.804213i) q^{76} +(4.93773 - 1.32306i) q^{77} +(-1.92706 - 7.19188i) q^{78} +(2.30362 + 8.59723i) q^{79} +(-4.98724 + 8.63815i) q^{81} +9.27246 q^{82} +(-0.310366 + 1.15830i) q^{83} -3.00590i q^{84} +(4.70581 + 8.15069i) q^{86} +(-2.18018 + 3.77618i) q^{87} -11.2860 q^{88} +(-1.87621 + 7.00209i) q^{89} +(1.57879 - 5.89213i) q^{91} +(-0.908579 - 0.524568i) q^{92} +(-14.4467 - 8.34083i) q^{93} +(0.661816 - 2.46993i) q^{94} +(-2.75208 + 10.2709i) q^{96} +11.7662 q^{97} +(2.25131 - 3.89938i) q^{98} +(-0.764149 - 1.32355i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Introduction

L-functions

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Database

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