LMFDB - Embedded newform 961.2.c.d.521.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(439,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.439"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,2,-2,-2,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			521.1
Root			$-0.309017 - 0.535233i$ of defining polynomial
Character	$\chi$	$=$	961.521
Dual form			961.2.c.d.439.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.618034 q^{2} +(-0.500000 - 0.866025i) q^{3} -1.61803 q^{4} +(1.30902 - 2.26728i) q^{5} +(0.309017 + 0.535233i) q^{6} +(-1.50000 - 2.59808i) q^{7} +2.23607 q^{8} +(1.00000 - 1.73205i) q^{9} +(-0.809017 + 1.40126i) q^{10} +(-0.381966 + 0.661585i) q^{11} +(0.809017 + 1.40126i) q^{12} +(2.42705 - 4.20378i) q^{13} +(0.927051 + 1.60570i) q^{14} -2.61803 q^{15} +1.85410 q^{16} +(0.118034 + 0.204441i) q^{17} +(-0.618034 + 1.07047i) q^{18} +(-2.50000 - 4.33013i) q^{19} +(-2.11803 + 3.66854i) q^{20} +(-1.50000 + 2.59808i) q^{21} +(0.236068 - 0.408882i) q^{22} +5.47214 q^{23} +(-1.11803 - 1.93649i) q^{24} +(-0.927051 - 1.60570i) q^{25} +(-1.50000 + 2.59808i) q^{26} -5.00000 q^{27} +(2.42705 + 4.20378i) q^{28} +8.61803 q^{29} +1.61803 q^{30} -5.61803 q^{32} +0.763932 q^{33} +(-0.0729490 - 0.126351i) q^{34} -7.85410 q^{35} +(-1.61803 + 2.80252i) q^{36} +(0.118034 + 0.204441i) q^{37} +(1.54508 + 2.67617i) q^{38} -4.85410 q^{39} +(2.92705 - 5.06980i) q^{40} +(-3.23607 + 5.60503i) q^{41} +(0.927051 - 1.60570i) q^{42} +(-2.30902 - 3.99933i) q^{43} +(0.618034 - 1.07047i) q^{44} +(-2.61803 - 4.53457i) q^{45} -3.38197 q^{46} -3.38197 q^{47} +(-0.927051 - 1.60570i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(0.572949 + 0.992377i) q^{50} +(0.118034 - 0.204441i) q^{51} +(-3.92705 + 6.80185i) q^{52} +(-6.35410 + 11.0056i) q^{53} +3.09017 q^{54} +(1.00000 + 1.73205i) q^{55} +(-3.35410 - 5.80948i) q^{56} +(-2.50000 + 4.33013i) q^{57} -5.32624 q^{58} +(-4.73607 - 8.20311i) q^{59} +4.23607 q^{60} +6.94427 q^{61} -6.00000 q^{63} -0.236068 q^{64} +(-6.35410 - 11.0056i) q^{65} -0.472136 q^{66} +(2.11803 - 3.66854i) q^{67} +(-0.190983 - 0.330792i) q^{68} +(-2.73607 - 4.73901i) q^{69} +4.85410 q^{70} +(-0.0450850 + 0.0780895i) q^{71} +(2.23607 - 3.87298i) q^{72} +(-4.28115 + 7.41517i) q^{73} +(-0.0729490 - 0.126351i) q^{74} +(-0.927051 + 1.60570i) q^{75} +(4.04508 + 7.00629i) q^{76} +2.29180 q^{77} +3.00000 q^{78} +(2.42705 - 4.20378i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.00000 - 3.46410i) q^{82} +(-2.04508 + 3.54219i) q^{83} +(2.42705 - 4.20378i) q^{84} +0.618034 q^{85} +(1.42705 + 2.47172i) q^{86} +(-4.30902 - 7.46344i) q^{87} +(-0.854102 + 1.47935i) q^{88} +6.38197 q^{89} +(1.61803 + 2.80252i) q^{90} -14.5623 q^{91} -8.85410 q^{92} +2.09017 q^{94} -13.0902 q^{95} +(2.80902 + 4.86536i) q^{96} -5.29180 q^{97} +(0.618034 - 1.07047i) q^{98} +(0.763932 + 1.32317i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 3 q^{5} - q^{6} - 6 q^{7} + 4 q^{9} - q^{10} - 6 q^{11} + q^{12} + 3 q^{13} - 3 q^{14} - 6 q^{15} - 6 q^{16} - 4 q^{17} + 2 q^{18} - 10 q^{19} - 4 q^{20} - 6 q^{21}+ \cdots + 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 3 * q^5 - q^6 - 6 * q^7 + 4 * q^9 - q^10 - 6 * q^11 + q^12 + 3 * q^13 - 3 * q^14 - 6 * q^15 - 6 * q^16 - 4 * q^17 + 2 * q^18 - 10 * q^19 - 4 * q^20 - 6 * q^21 - 8 * q^22 + 4 * q^23 + 3 * q^25 - 6 * q^26 - 20 * q^27 + 3 * q^28 + 30 * q^29 + 2 * q^30 - 18 * q^32 + 12 * q^33 - 7 * q^34 - 18 * q^35 - 2 * q^36 - 4 * q^37 - 5 * q^38 - 6 * q^39 + 5 * q^40 - 4 * q^41 - 3 * q^42 - 7 * q^43 - 2 * q^44 - 6 * q^45 - 18 * q^46 - 18 * q^47 + 3 * q^48 - 4 * q^49 + 9 * q^50 - 4 * q^51 - 9 * q^52 - 12 * q^53 - 10 * q^54 + 4 * q^55 - 10 * q^57 + 10 * q^58 - 10 * q^59 + 8 * q^60 - 8 * q^61 - 24 * q^63 + 8 * q^64 - 12 * q^65 + 16 * q^66 + 4 * q^67 - 3 * q^68 - 2 * q^69 + 6 * q^70 + 11 * q^71 + 3 * q^73 - 7 * q^74 + 3 * q^75 + 5 * q^76 + 36 * q^77 + 12 * q^78 + 3 * q^80 - 2 * q^81 + 8 * q^82 + 3 * q^83 + 3 * q^84 - 2 * q^85 - q^86 - 15 * q^87 + 10 * q^88 + 30 * q^89 + 2 * q^90 - 18 * q^91 - 22 * q^92 - 14 * q^94 - 30 * q^95 + 9 * q^96 - 48 * q^97 - 2 * q^98 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.618034			−0.437016			−0.218508	−	0.975835i	$-0.570119\pi$
$2$	−0.618034			−0.437016			−0.218508	+	0.975835i	$0.570119\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$	−1.61803			−0.809017
$5$	1.30902	−	2.26728i	0.585410	−	1.01396i	−0.409414	−	0.912349i	$-0.634267\pi$
$5$	1.30902	−	2.26728i	0.585410	−	1.01396i	0.994824	−	0.101611i	$-0.0323999\pi$
$6$	0.309017	+	0.535233i	0.126156	+	0.218508i
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	−0.996866	−	0.0791130i	$-0.974791\pi$
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	0.429919	−	0.902867i	$-0.358542\pi$
$8$	2.23607			0.790569
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$	−0.809017	+	1.40126i	−0.255834	+	0.443117i
$11$	−0.381966	+	0.661585i	−0.115167	+	0.199475i	−0.917847	−	0.396935i	$-0.870074\pi$
$11$	−0.381966	+	0.661585i	−0.115167	+	0.199475i	0.802679	+	0.596411i	$0.203407\pi$
$12$	0.809017	+	1.40126i	0.233543	+	0.404508i
$13$	2.42705	−	4.20378i	0.673143	−	1.16592i	−0.303865	−	0.952715i	$-0.598277\pi$
$13$	2.42705	−	4.20378i	0.673143	−	1.16592i	0.977008	−	0.213203i	$-0.0683894\pi$
$14$	0.927051	+	1.60570i	0.247765	+	0.429141i
$15$	−2.61803			−0.675973
$16$	1.85410			0.463525
$17$	0.118034	+	0.204441i	0.0286274	+	0.0495842i	0.879984	−	0.475003i	$-0.157553\pi$
$17$	0.118034	+	0.204441i	0.0286274	+	0.0495842i	−0.851357	+	0.524587i	$0.824220\pi$
$18$	−0.618034	+	1.07047i	−0.145672	+	0.252311i
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	−0.996199	−	0.0871106i	$-0.972237\pi$
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	0.422659	−	0.906289i	$-0.361097\pi$
$20$	−2.11803	+	3.66854i	−0.473607	+	0.820311i
$21$	−1.50000	+	2.59808i	−0.327327	+	0.566947i
$22$	0.236068	−	0.408882i	0.0503299	−	0.0871739i
$23$	5.47214			1.14102			0.570510	−	0.821291i	$-0.306746\pi$
$23$	5.47214			1.14102			0.570510	+	0.821291i	$0.306746\pi$
$24$	−1.11803	−	1.93649i	−0.228218	−	0.395285i
$25$	−0.927051	−	1.60570i	−0.185410	−	0.321140i
$26$	−1.50000	+	2.59808i	−0.294174	+	0.509525i
$27$	−5.00000			−0.962250
$28$	2.42705	+	4.20378i	0.458670	+	0.794439i
$29$	8.61803			1.60033			0.800164	−	0.599781i	$-0.204746\pi$
$29$	8.61803			1.60033			0.800164	+	0.599781i	$0.204746\pi$
$30$	1.61803			0.295411
$31$		0			0
$31$		0			0
$32$	−5.61803			−0.993137
$33$	0.763932			0.132983
$34$	−0.0729490	−	0.126351i	−0.0125107	−	0.0216691i
$35$	−7.85410			−1.32759
$36$	−1.61803	+	2.80252i	−0.269672	+	0.467086i
$37$	0.118034	+	0.204441i	0.0194047	+	0.0336099i	0.875565	−	0.483101i	$-0.160490\pi$
$37$	0.118034	+	0.204441i	0.0194047	+	0.0336099i	−0.856160	+	0.516711i	$0.827156\pi$
$38$	1.54508	+	2.67617i	0.250646	+	0.434131i
$39$	−4.85410			−0.777278
$40$	2.92705	−	5.06980i	0.462807	−	0.801606i
$41$	−3.23607	+	5.60503i	−0.505389	+	0.875359i	0.494592	+	0.869125i	$0.335318\pi$
$41$	−3.23607	+	5.60503i	−0.505389	+	0.875359i	−0.999981	+	0.00623380i	$0.998016\pi$
$42$	0.927051	−	1.60570i	0.143047	−	0.247765i
$43$	−2.30902	−	3.99933i	−0.352122	−	0.609893i	0.634499	−	0.772924i	$-0.281206\pi$
$43$	−2.30902	−	3.99933i	−0.352122	−	0.609893i	−0.986621	+	0.163031i	$0.947873\pi$
$44$	0.618034	−	1.07047i	0.0931721	−	0.161379i
$45$	−2.61803	−	4.53457i	−0.390273	−	0.675973i
$46$	−3.38197			−0.498644
$47$	−3.38197			−0.493310			−0.246655	−	0.969103i	$-0.579332\pi$
$47$	−3.38197			−0.493310			−0.246655	+	0.969103i	$0.579332\pi$
$48$	−0.927051	−	1.60570i	−0.133808	−	0.231763i
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$	0.572949	+	0.992377i	0.0810272	+	0.140343i
$51$	0.118034	−	0.204441i	0.0165281	−	0.0286274i
$52$	−3.92705	+	6.80185i	−0.544584	+	0.943247i
$53$	−6.35410	+	11.0056i	−0.872803	+	1.51174i	−0.0137182	+	0.999906i	$0.504367\pi$
$53$	−6.35410	+	11.0056i	−0.872803	+	1.51174i	−0.859085	+	0.511833i	$0.828967\pi$
$54$	3.09017			0.420519
$55$	1.00000	+	1.73205i	0.134840	+	0.233550i
$56$	−3.35410	−	5.80948i	−0.448211	−	0.776324i
$57$	−2.50000	+	4.33013i	−0.331133	+	0.573539i
$58$	−5.32624			−0.699369
$59$	−4.73607	−	8.20311i	−0.616584	−	1.06795i	−0.990104	−	0.140332i	$-0.955183\pi$
$59$	−4.73607	−	8.20311i	−0.616584	−	1.06795i	0.373521	−	0.927622i	$-0.378150\pi$
$60$	4.23607			0.546874
$61$	6.94427			0.889123			0.444561	−	0.895748i	$-0.353360\pi$
$61$	6.94427			0.889123			0.444561	+	0.895748i	$0.353360\pi$
$62$		0			0
$63$	−6.00000			−0.755929
$64$	−0.236068			−0.0295085
$65$	−6.35410	−	11.0056i	−0.788129	−	1.36508i
$66$	−0.472136			−0.0581159
$67$	2.11803	−	3.66854i	0.258759	−	0.448184i	−0.707151	−	0.707063i	$-0.750020\pi$
$67$	2.11803	−	3.66854i	0.258759	−	0.448184i	0.965910	+	0.258879i	$0.0833531\pi$
$68$	−0.190983	−	0.330792i	−0.0231601	−	0.0401145i
$69$	−2.73607	−	4.73901i	−0.329384	−	0.570510i
$70$	4.85410			0.580176
$71$	−0.0450850	+	0.0780895i	−0.00535060	+	0.00926751i	−0.868688	−	0.495359i	$-0.835036\pi$
$71$	−0.0450850	+	0.0780895i	−0.00535060	+	0.00926751i	0.863338	+	0.504627i	$0.168370\pi$
$72$	2.23607	−	3.87298i	0.263523	−	0.456435i
$73$	−4.28115	+	7.41517i	−0.501071	+	0.867881i	0.498928	+	0.866643i	$0.333727\pi$
$73$	−4.28115	+	7.41517i	−0.501071	+	0.867881i	−0.999999	+	0.00123719i	$0.999606\pi$
$74$	−0.0729490	−	0.126351i	−0.00848015	−	0.0146881i
$75$	−0.927051	+	1.60570i	−0.107047	+	0.185410i
$76$	4.04508	+	7.00629i	0.464003	+	0.803677i
$77$	2.29180			0.261174
$78$	3.00000			0.339683
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	2.42705	−	4.20378i	0.271353	−	0.469996i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.00000	−	3.46410i	0.220863	−	0.382546i
$83$	−2.04508	+	3.54219i	−0.224477	+	0.388806i	−0.956162	−	0.292837i	$-0.905401\pi$
$83$	−2.04508	+	3.54219i	−0.224477	+	0.388806i	0.731685	+	0.681643i	$0.238734\pi$
$84$	2.42705	−	4.20378i	0.264813	−	0.458670i
$85$	0.618034			0.0670352
$86$	1.42705	+	2.47172i	0.153883	+	0.266533i
$87$	−4.30902	−	7.46344i	−0.461975	−	0.800164i
$88$	−0.854102	+	1.47935i	−0.0910476	+	0.157699i
$89$	6.38197			0.676487			0.338244	−	0.941059i	$-0.390167\pi$
$89$	6.38197			0.676487			0.338244	+	0.941059i	$0.390167\pi$
$90$	1.61803	+	2.80252i	0.170556	+	0.295411i
$91$	−14.5623			−1.52654
$92$	−8.85410			−0.923104
$93$		0			0
$94$	2.09017			0.215585
$95$	−13.0902			−1.34302
$96$	2.80902	+	4.86536i	0.286694	+	0.496569i
$97$	−5.29180			−0.537300			−0.268650	−	0.963238i	$-0.586578\pi$
$97$	−5.29180			−0.537300			−0.268650	+	0.963238i	$0.586578\pi$
$98$	0.618034	−	1.07047i	0.0624309	−	0.108133i
$99$	0.763932	+	1.32317i	0.0767781	+	0.132983i
$100$	1.50000	+	2.59808i	0.150000	+	0.259808i
$101$	4.76393			0.474029			0.237014	−	0.971506i	$-0.423831\pi$
$101$	4.76393			0.474029			0.237014	+	0.971506i	$0.423831\pi$
$102$	−0.0729490	+	0.126351i	−0.00722303	+	0.0125107i
$103$	0.0729490	−	0.126351i	0.00718788	−	0.0124498i	−0.862409	−	0.506212i	$-0.831045\pi$
$103$	0.0729490	−	0.126351i	0.00718788	−	0.0124498i	0.869597	+	0.493762i	$0.164379\pi$
$104$	5.42705	−	9.39993i	0.532166	−	0.921739i
$105$	3.92705	+	6.80185i	0.383241	+	0.663793i
$106$	3.92705	−	6.80185i	0.381429	−	0.660654i
$107$	−0.545085	−	0.944115i	−0.0526954	−	0.0912710i	0.838475	−	0.544941i	$-0.183448\pi$
$107$	−0.545085	−	0.944115i	−0.0526954	−	0.0912710i	−0.891170	+	0.453670i	$0.850115\pi$
$108$	8.09017			0.778477
$109$	−8.41641			−0.806146			−0.403073	−	0.915168i	$-0.632058\pi$
$109$	−8.41641			−0.806146			−0.403073	+	0.915168i	$0.632058\pi$
$110$	−0.618034	−	1.07047i	−0.0589272	−	0.102065i
$111$	0.118034	−	0.204441i	0.0112033	−	0.0194047i
$112$	−2.78115	−	4.81710i	−0.262794	−	0.455173i
$113$	0.927051	−	1.60570i	0.0872096	−	0.151051i	−0.819121	−	0.573621i	$-0.805538\pi$
$113$	0.927051	−	1.60570i	0.0872096	−	0.151051i	0.906331	+	0.422569i	$0.138872\pi$
$114$	1.54508	−	2.67617i	0.144710	−	0.250646i
$115$	7.16312	−	12.4069i	0.667964	−	1.15695i
$116$	−13.9443			−1.29469
$117$	−4.85410	−	8.40755i	−0.448762	−	0.777278i
$118$	2.92705	+	5.06980i	0.269457	+	0.466713i
$119$	0.354102	−	0.613323i	0.0324605	−	0.0562232i
$120$	−5.85410			−0.534404
$121$	5.20820	+	9.02087i	0.473473	+	0.820079i
$122$	−4.29180			−0.388561
$123$	6.47214			0.583573
$124$		0			0
$125$	8.23607			0.736656
$126$	3.70820			0.330353
$127$	5.11803	+	8.86469i	0.454152	+	0.786614i	0.998639	−	0.0521549i	$-0.0166089\pi$
$127$	5.11803	+	8.86469i	0.454152	+	0.786614i	−0.544487	+	0.838769i	$0.683276\pi$
$128$	11.3820			1.00603
$129$	−2.30902	+	3.99933i	−0.203298	+	0.352122i
$130$	3.92705	+	6.80185i	0.344425	+	0.596562i
$131$	−0.0450850	−	0.0780895i	−0.00393909	−	0.00682271i	0.864049	−	0.503407i	$-0.167921\pi$
$131$	−0.0450850	−	0.0780895i	−0.00393909	−	0.00682271i	−0.867988	+	0.496585i	$0.834587\pi$
$132$	−1.23607			−0.107586
$133$	−7.50000	+	12.9904i	−0.650332	+	1.12641i
$134$	−1.30902	+	2.26728i	−0.113082	+	0.195864i
$135$	−6.54508	+	11.3364i	−0.563311	+	0.975684i
$136$	0.263932	+	0.457144i	0.0226320	+	0.0391997i
$137$	−3.23607	+	5.60503i	−0.276476	+	0.478870i	−0.970506	−	0.241075i	$-0.922500\pi$
$137$	−3.23607	+	5.60503i	−0.276476	+	0.478870i	0.694030	+	0.719946i	$0.255833\pi$
$138$	1.69098	+	2.92887i	0.143946	+	0.249322i
$139$	−5.85410			−0.496538			−0.248269	−	0.968691i	$-0.579862\pi$
$139$	−5.85410			−0.496538			−0.248269	+	0.968691i	$0.579862\pi$
$140$	12.7082			1.07404
$141$	1.69098	+	2.92887i	0.142406	+	0.246655i
$142$	0.0278640	−	0.0482619i	0.00233830	−	0.00405005i
$143$	1.85410	+	3.21140i	0.155048	+	0.268551i
$144$	1.85410	−	3.21140i	0.154508	−	0.267617i
$145$	11.2812	−	19.5395i	0.936849	−	1.62267i
$146$	2.64590	−	4.58283i	0.218976	−	0.379278i
$147$	2.00000			0.164957
$148$	−0.190983	−	0.330792i	−0.0156987	−	0.0271910i
$149$	8.51722	+	14.7523i	0.697758	+	1.20855i	0.969242	+	0.246109i	$0.0791522\pi$
$149$	8.51722	+	14.7523i	0.697758	+	1.20855i	−0.271484	+	0.962443i	$0.587514\pi$
$150$	0.572949	−	0.992377i	0.0467811	−	0.0810272i
$151$	19.5066			1.58742			0.793711	−	0.608295i	$-0.208146\pi$
$151$	19.5066			1.58742			0.793711	+	0.608295i	$0.208146\pi$
$152$	−5.59017	−	9.68246i	−0.453423	−	0.785351i
$153$	0.472136			0.0381699
$154$	−1.41641			−0.114137
$155$		0			0
$156$	7.85410			0.628831
$157$	9.70820			0.774799			0.387400	−	0.921912i	$-0.373373\pi$
$157$	9.70820			0.774799			0.387400	+	0.921912i	$0.373373\pi$
$158$		0			0
$159$	12.7082			1.00783
$160$	−7.35410	+	12.7377i	−0.581393	+	1.00700i
$161$	−8.20820	−	14.2170i	−0.646897	−	1.12046i
$162$	0.309017	+	0.535233i	0.0242787	+	0.0420519i
$163$	−12.7082			−0.995383			−0.497692	−	0.867354i	$-0.665819\pi$
$163$	−12.7082			−0.995383			−0.497692	+	0.867354i	$0.665819\pi$
$164$	5.23607	−	9.06914i	0.408868	−	0.708181i
$165$	1.00000	−	1.73205i	0.0778499	−	0.134840i
$166$	1.26393	−	2.18919i	0.0981002	−	0.169914i
$167$	−4.61803	−	7.99867i	−0.357354	−	0.618956i	0.630164	−	0.776462i	$-0.282988\pi$
$167$	−4.61803	−	7.99867i	−0.357354	−	0.618956i	−0.987518	+	0.157507i	$0.949654\pi$
$168$	−3.35410	+	5.80948i	−0.258775	+	0.448211i
$169$	−5.28115	−	9.14723i	−0.406243	−	0.703633i
$170$	−0.381966			−0.0292955
$171$	−10.0000			−0.764719
$172$	3.73607	+	6.47106i	0.284873	+	0.493414i
$173$	−0.454915	+	0.787936i	−0.0345865	+	0.0599057i	−0.882801	−	0.469748i	$-0.844345\pi$
$173$	−0.454915	+	0.787936i	−0.0345865	+	0.0599057i	0.848214	+	0.529654i	$0.177678\pi$
$174$	2.66312	+	4.61266i	0.201891	+	0.349685i
$175$	−2.78115	+	4.81710i	−0.210235	+	0.364138i
$176$	−0.708204	+	1.22665i	−0.0533829	+	0.0924619i
$177$	−4.73607	+	8.20311i	−0.355985	+	0.616584i
$178$	−3.94427			−0.295636
$179$	9.89919	+	17.1459i	0.739900	+	1.28154i	0.952540	+	0.304414i	$0.0984605\pi$
$179$	9.89919	+	17.1459i	0.739900	+	1.28154i	−0.212640	+	0.977131i	$0.568206\pi$
$180$	4.23607	+	7.33708i	0.315738	+	0.546874i
$181$	8.50000	−	14.7224i	0.631800	−	1.09431i	−0.355383	−	0.934721i	$-0.615650\pi$
$181$	8.50000	−	14.7224i	0.631800	−	1.09431i	0.987184	−	0.159589i	$-0.0510169\pi$
$182$	9.00000			0.667124
$183$	−3.47214	−	6.01392i	−0.256668	−	0.444561i
$184$	12.2361			0.902055
$185$	0.618034			0.0454388
$186$		0			0
$187$	−0.180340			−0.0131878
$188$	5.47214			0.399097
$189$	7.50000	+	12.9904i	0.545545	+	0.944911i
$190$	8.09017			0.586923
$191$	8.04508	−	13.9345i	0.582122	−	1.00826i	−0.413106	−	0.910683i	$-0.635556\pi$
$191$	8.04508	−	13.9345i	0.582122	−	1.00826i	0.995228	−	0.0975816i	$-0.0311107\pi$
$192$	0.118034	+	0.204441i	0.00851837	+	0.0147542i
$193$	1.19098	+	2.06284i	0.0857288	+	0.148487i	0.905702	−	0.423916i	$-0.139345\pi$
$193$	1.19098	+	2.06284i	0.0857288	+	0.148487i	−0.819973	+	0.572403i	$0.806011\pi$
$194$	3.27051			0.234809
$195$	−6.35410	+	11.0056i	−0.455027	+	0.788129i
$196$	1.61803	−	2.80252i	0.115574	−	0.200180i
$197$	8.20820	−	14.2170i	0.584810	−	1.01292i	−0.410089	−	0.912046i	$-0.634502\pi$
$197$	8.20820	−	14.2170i	0.584810	−	1.01292i	0.994899	−	0.100876i	$-0.0321644\pi$
$198$	−0.472136	−	0.817763i	−0.0335532	−	0.0581159i
$199$	−13.3541	+	23.1300i	−0.946647	+	1.63964i	−0.194228	+	0.980956i	$0.562220\pi$
$199$	−13.3541	+	23.1300i	−0.946647	+	1.63964i	−0.752419	+	0.658685i	$0.771113\pi$
$200$	−2.07295	−	3.59045i	−0.146580	−	0.253883i
$201$	−4.23607			−0.298789
$202$	−2.94427			−0.207158
$203$	−12.9271	−	22.3903i	−0.907301	−	1.57149i
$204$	−0.190983	+	0.330792i	−0.0133715	+	0.0231601i
$205$	8.47214	+	14.6742i	0.591720	+	1.02489i
$206$	−0.0450850	+	0.0780895i	−0.00314122	+	0.00544075i
$207$	5.47214	−	9.47802i	0.380340	−	0.658768i
$208$	4.50000	−	7.79423i	0.312019	−	0.540433i
$209$	3.81966			0.264211
$210$	−2.42705	−	4.20378i	−0.167482	−	0.290088i
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	0.970229	−	0.242190i	$-0.0778659\pi$
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	−0.694857	+	0.719148i	$0.744533\pi$
$212$	10.2812	−	17.8075i	0.706112	−	1.22302i
$213$	0.0901699			0.00617834
$214$	0.336881	+	0.583495i	0.0230287	+	0.0398869i
$215$	−12.0902			−0.824543
$216$	−11.1803			−0.760726
$217$		0			0
$218$	5.20163			0.352299
$219$	8.56231			0.578587
$220$	−1.61803	−	2.80252i	−0.109088	−	0.188946i
$221$	1.14590			0.0770814
$222$	−0.0729490	+	0.126351i	−0.00489602	+	0.00848015i
$223$	0.354102	+	0.613323i	0.0237124	+	0.0410711i	0.877638	−	0.479324i	$-0.159118\pi$
$223$	0.354102	+	0.613323i	0.0237124	+	0.0410711i	−0.853926	+	0.520395i	$0.825785\pi$
$224$	8.42705	+	14.5961i	0.563056	+	0.975242i
$225$	−3.70820			−0.247214
$226$	−0.572949	+	0.992377i	−0.0381120	+	0.0660119i
$227$	10.3713	−	17.9637i	0.688369	−	1.19229i	−0.283996	−	0.958825i	$-0.591660\pi$
$227$	10.3713	−	17.9637i	0.688369	−	1.19229i	0.972365	−	0.233465i	$-0.0750063\pi$
$228$	4.04508	−	7.00629i	0.267892	−	0.464003i
$229$	−3.61803	−	6.26662i	−0.239086	−	0.414110i	0.721366	−	0.692554i	$-0.243515\pi$
$229$	−3.61803	−	6.26662i	−0.239086	−	0.414110i	−0.960452	+	0.278444i	$0.910181\pi$
$230$	−4.42705	+	7.66788i	−0.291911	+	0.505605i
$231$	−1.14590	−	1.98475i	−0.0753946	−	0.130587i
$232$	19.2705			1.26517
$233$	18.7984			1.23152			0.615761	−	0.787933i	$-0.288849\pi$
$233$	18.7984			1.23152			0.615761	+	0.787933i	$0.288849\pi$
$234$	3.00000	+	5.19615i	0.196116	+	0.339683i
$235$	−4.42705	+	7.66788i	−0.288789	+	0.500197i
$236$	7.66312	+	13.2729i	0.498827	+	0.863993i
$237$		0			0
$238$	−0.218847	+	0.379054i	−0.0141857	+	0.0245704i
$239$	−6.70820	+	11.6190i	−0.433918	+	0.751567i	−0.997207	−	0.0746926i	$-0.976202\pi$
$239$	−6.70820	+	11.6190i	−0.433918	+	0.751567i	0.563289	+	0.826260i	$0.309536\pi$
$240$	−4.85410			−0.313331
$241$	−4.26393	−	7.38535i	−0.274664	−	0.475732i	0.695386	−	0.718636i	$-0.255233\pi$
$241$	−4.26393	−	7.38535i	−0.274664	−	0.475732i	−0.970050	+	0.242904i	$0.921900\pi$
$242$	−3.21885	−	5.57521i	−0.206915	−	0.358388i
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$	−11.2361			−0.719316
$245$	2.61803	+	4.53457i	0.167260	+	0.289703i
$246$	−4.00000			−0.255031
$247$	−24.2705			−1.54430
$248$		0			0
$249$	4.09017			0.259204
$250$	−5.09017			−0.321931
$251$	0.472136	+	0.817763i	0.0298010	+	0.0516168i	0.880541	−	0.473970i	$-0.157179\pi$
$251$	0.472136	+	0.817763i	0.0298010	+	0.0516168i	−0.850740	+	0.525586i	$0.823846\pi$
$252$	9.70820			0.611559
$253$	−2.09017	+	3.62028i	−0.131408	+	0.227605i
$254$	−3.16312	−	5.47868i	−0.198472	−	0.343763i
$255$	−0.309017	−	0.535233i	−0.0193514	−	0.0335176i
$256$	−6.56231			−0.410144
$257$	−0.708204	+	1.22665i	−0.0441765	+	0.0765160i	−0.887268	−	0.461254i	$-0.847400\pi$
$257$	−0.708204	+	1.22665i	−0.0441765	+	0.0765160i	0.843092	+	0.537770i	$0.180733\pi$
$258$	1.42705	−	2.47172i	0.0888443	−	0.153883i
$259$	0.354102	−	0.613323i	0.0220028	−	0.0381100i
$260$	10.2812	+	17.8075i	0.637610	+	1.10437i
$261$	8.61803	−	14.9269i	0.533443	−	0.923950i
$262$	0.0278640	+	0.0482619i	0.00172145	+	0.00298163i
$263$	10.7984			0.665856			0.332928	−	0.942952i	$-0.391963\pi$
$263$	10.7984			0.665856			0.332928	+	0.942952i	$0.391963\pi$
$264$	1.70820			0.105133
$265$	16.6353	+	28.8131i	1.02190	+	1.76998i
$266$	4.63525	−	8.02850i	0.284206	−	0.492259i
$267$	−3.19098	−	5.52694i	−0.195285	−	0.338244i
$268$	−3.42705	+	5.93583i	−0.209340	+	0.362588i
$269$	−0.690983	+	1.19682i	−0.0421300	+	0.0729713i	−0.886321	−	0.463070i	$-0.846748\pi$
$269$	−0.690983	+	1.19682i	−0.0421300	+	0.0729713i	0.844192	+	0.536042i	$0.180081\pi$
$270$	4.04508	−	7.00629i	0.246176	−	0.426389i
$271$	−9.56231			−0.580869			−0.290434	−	0.956895i	$-0.593800\pi$
$271$	−9.56231			−0.580869			−0.290434	+	0.956895i	$0.593800\pi$
$272$	0.218847	+	0.379054i	0.0132696	+	0.0229835i
$273$	7.28115	+	12.6113i	0.440675	+	0.763272i
$274$	2.00000	−	3.46410i	0.120824	−	0.209274i
$275$	1.41641			0.0854126
$276$	4.42705	+	7.66788i	0.266477	+	0.461552i
$277$	−13.3262			−0.800696			−0.400348	−	0.916363i	$-0.631111\pi$
$277$	−13.3262			−0.800696			−0.400348	+	0.916363i	$0.631111\pi$
$278$	3.61803			0.216995
$279$		0			0
$280$	−17.5623			−1.04955
$281$	19.0344			1.13550			0.567750	−	0.823201i	$-0.307814\pi$
$281$	19.0344			1.13550			0.567750	+	0.823201i	$0.307814\pi$
$282$	−1.04508	−	1.81014i	−0.0622339	−	0.107792i
$283$	6.56231			0.390089			0.195044	−	0.980794i	$-0.437515\pi$
$283$	6.56231			0.390089			0.195044	+	0.980794i	$0.437515\pi$
$284$	0.0729490	−	0.126351i	0.00432873	−	0.00749758i
$285$	6.54508	+	11.3364i	0.387697	+	0.671512i
$286$	−1.14590	−	1.98475i	−0.0677584	−	0.117361i
$287$	19.4164			1.14611
$288$	−5.61803	+	9.73072i	−0.331046	+	0.573388i
$289$	8.47214	−	14.6742i	0.498361	−	0.863186i
$290$	−6.97214	+	12.0761i	−0.409418	+	0.709133i
$291$	2.64590	+	4.58283i	0.155105	+	0.268650i
$292$	6.92705	−	11.9980i	0.405375	−	0.702130i
$293$	4.11803	+	7.13264i	0.240578	+	0.416694i	0.960879	−	0.276968i	$-0.0893296\pi$
$293$	4.11803	+	7.13264i	0.240578	+	0.416694i	−0.720301	+	0.693662i	$0.755996\pi$
$294$	−1.23607			−0.0720889
$295$	−24.7984			−1.44382
$296$	0.263932	+	0.457144i	0.0153407	+	0.0265709i
$297$	1.90983	−	3.30792i	0.110820	−	0.191945i
$298$	−5.26393	−	9.11740i	−0.304931	−	0.528157i
$299$	13.2812	−	23.0036i	0.768069	−	1.33033i
$300$	1.50000	−	2.59808i	0.0866025	−	0.150000i
$301$	−6.92705	+	11.9980i	−0.399269	+	0.691553i
$302$	−12.0557			−0.693729
$303$	−2.38197	−	4.12569i	−0.136840	−	0.237014i
$304$	−4.63525	−	8.02850i	−0.265850	−	0.460466i
$305$	9.09017	−	15.7446i	0.520502	−	0.901535i
$306$	−0.291796			−0.0166809
$307$	−3.04508	−	5.27424i	−0.173792	−	0.301017i	0.765950	−	0.642900i	$-0.222269\pi$
$307$	−3.04508	−	5.27424i	−0.173792	−	0.301017i	−0.939743	+	0.341883i	$0.888935\pi$
$308$	−3.70820			−0.211295
$309$	−0.145898			−0.00829985
$310$		0			0
$311$	16.4721			0.934049			0.467025	−	0.884244i	$-0.345326\pi$
$311$	16.4721			0.934049			0.467025	+	0.884244i	$0.345326\pi$
$312$	−10.8541			−0.614493
$313$	0.618034	+	1.07047i	0.0349333	+	0.0605063i	0.882963	−	0.469442i	$-0.155545\pi$
$313$	0.618034	+	1.07047i	0.0349333	+	0.0605063i	−0.848030	+	0.529948i	$0.822211\pi$
$314$	−6.00000			−0.338600
$315$	−7.85410	+	13.6037i	−0.442529	+	0.766482i
$316$		0			0
$317$	−12.9443	−	22.4201i	−0.727023	−	1.25924i	−0.958136	−	0.286313i	$-0.907570\pi$
$317$	−12.9443	−	22.4201i	−0.727023	−	1.25924i	0.231113	−	0.972927i	$-0.425763\pi$
$318$	−7.85410			−0.440436
$319$	−3.29180	+	5.70156i	−0.184305	+	0.319226i
$320$	−0.309017	+	0.535233i	−0.0172746	+	0.0299204i
$321$	−0.545085	+	0.944115i	−0.0304237	+	0.0526954i
$322$	5.07295	+	8.78661i	0.282704	+	0.489658i
$323$	0.590170	−	1.02220i	0.0328379	−	0.0568770i
$324$	0.809017	+	1.40126i	0.0449454	+	0.0778477i
$325$	−9.00000			−0.499230
$326$	7.85410			0.434998
$327$	4.20820	+	7.28882i	0.232714	+	0.403073i
$328$	−7.23607	+	12.5332i	−0.399545	+	0.692032i
$329$	5.07295	+	8.78661i	0.279681	+	0.484421i
$330$	−0.618034	+	1.07047i	−0.0340217	+	0.0589272i
$331$	5.63525	−	9.76055i	0.309742	−	0.536488i	−0.668564	−	0.743654i	$-0.733091\pi$
$331$	5.63525	−	9.76055i	0.309742	−	0.536488i	0.978306	+	0.207166i	$0.0664241\pi$
$332$	3.30902	−	5.73139i	0.181606	−	0.314551i
$333$	0.472136			0.0258729
$334$	2.85410	+	4.94345i	0.156170	+	0.270494i
$335$	−5.54508	−	9.60437i	−0.302960	−	0.524743i
$336$	−2.78115	+	4.81710i	−0.151724	+	0.262794i
$337$	−18.9787			−1.03384			−0.516918	−	0.856035i	$-0.672921\pi$
$337$	−18.9787			−1.03384			−0.516918	+	0.856035i	$0.672921\pi$
$338$	3.26393	+	5.65330i	0.177534	+	0.307499i
$339$	−1.85410			−0.100701
$340$	−1.00000			−0.0542326
$341$		0			0
$342$	6.18034			0.334195
$343$	−15.0000			−0.809924
$344$	−5.16312	−	8.94278i	−0.278377	−	0.482163i
$345$	−14.3262			−0.771299
$346$	0.281153	−	0.486971i	0.0151149	−	0.0261797i
$347$	4.06231	+	7.03612i	0.218076	+	0.377719i	0.954220	−	0.299107i	$-0.0966886\pi$
$347$	4.06231	+	7.03612i	0.218076	+	0.377719i	−0.736144	+	0.676825i	$0.763355\pi$
$348$	6.97214	+	12.0761i	0.373746	+	0.647347i
$349$	−16.7082			−0.894370			−0.447185	−	0.894442i	$-0.647573\pi$
$349$	−16.7082			−0.894370			−0.447185	+	0.894442i	$0.647573\pi$
$350$	1.71885	−	2.97713i	0.0918762	−	0.159134i
$351$	−12.1353	+	21.0189i	−0.647732	+	1.12190i
$352$	2.14590	−	3.71680i	0.114377	−	0.198106i
$353$	−16.1910	−	28.0436i	−0.861759	−	1.49261i	−0.870230	−	0.492646i	$-0.836030\pi$
$353$	−16.1910	−	28.0436i	−0.861759	−	1.49261i	0.00847052	−	0.999964i	$-0.497304\pi$
$354$	2.92705	−	5.06980i	0.155571	−	0.269457i
$355$	0.118034	+	0.204441i	0.00626459	+	0.0108506i
$356$	−10.3262			−0.547290
$357$	−0.708204			−0.0374821
$358$	−6.11803	−	10.5967i	−0.323348	−	0.560055i
$359$	12.6631	−	21.9332i	0.668334	−	1.15759i	−0.310036	−	0.950725i	$-0.600341\pi$
$359$	12.6631	−	21.9332i	0.668334	−	1.15759i	0.978370	−	0.206863i	$-0.0663256\pi$
$360$	−5.85410	−	10.1396i	−0.308538	−	0.534404i
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	−5.25329	+	9.09896i	−0.276107	+	0.478231i
$363$	5.20820	−	9.02087i	0.273360	−	0.473473i
$364$	23.5623			1.23500
$365$	11.2082	+	19.4132i	0.586664	+	1.01613i
$366$	2.14590	+	3.71680i	0.112168	+	0.194280i
$367$	−18.1353	+	31.4112i	−0.946653	+	1.63965i	−0.194245	+	0.980953i	$0.562226\pi$
$367$	−18.1353	+	31.4112i	−0.946653	+	1.63965i	−0.752408	+	0.658697i	$0.771108\pi$
$368$	10.1459			0.528891
$369$	6.47214	+	11.2101i	0.336926	+	0.583573i
$370$	−0.381966			−0.0198575
$371$	38.1246			1.97933
$372$		0			0
$373$	−0.347524			−0.0179941			−0.00899706	−	0.999960i	$-0.502864\pi$
$373$	−0.347524			−0.0179941			−0.00899706	+	0.999960i	$0.502864\pi$
$374$	0.111456			0.00576326
$375$	−4.11803	−	7.13264i	−0.212654	−	0.368328i
$376$	−7.56231			−0.389996
$377$	20.9164	−	36.2283i	1.07725	−	1.86585i
$378$	−4.63525	−	8.02850i	−0.238412	−	0.412941i
$379$	9.20820	+	15.9491i	0.472994	+	0.819249i	0.999522	−	0.0309084i	$-0.00984001\pi$
$379$	9.20820	+	15.9491i	0.472994	+	0.819249i	−0.526529	+	0.850157i	$0.676507\pi$
$380$	21.1803			1.08653
$381$	5.11803	−	8.86469i	0.262205	−	0.454152i
$382$	−4.97214	+	8.61199i	−0.254397	+	0.440628i
$383$	−8.42705	+	14.5961i	−0.430602	+	0.745825i	−0.996925	−	0.0783585i	$-0.975032\pi$
$383$	−8.42705	+	14.5961i	−0.430602	+	0.745825i	0.566323	+	0.824183i	$0.308365\pi$
$384$	−5.69098	−	9.85707i	−0.290417	−	0.503017i
$385$	3.00000	−	5.19615i	0.152894	−	0.264820i
$386$	−0.736068	−	1.27491i	−0.0374649	−	0.0648911i
$387$	−9.23607			−0.469496
$388$	8.56231			0.434685
$389$	−14.5344	−	25.1744i	−0.736925	−	1.27639i	−0.953873	−	0.300209i	$-0.902944\pi$
$389$	−14.5344	−	25.1744i	−0.736925	−	1.27639i	0.216948	−	0.976183i	$-0.430390\pi$
$390$	3.92705	−	6.80185i	0.198854	−	0.344425i
$391$	0.645898	+	1.11873i	0.0326645	+	0.0565765i
$392$	−2.23607	+	3.87298i	−0.112938	+	0.195615i
$393$	−0.0450850	+	0.0780895i	−0.00227424	+	0.00393909i
$394$	−5.07295	+	8.78661i	−0.255571	+	0.442663i
$395$		0			0
$396$	−1.23607	−	2.14093i	−0.0621148	−	0.107586i
$397$	−8.14590	−	14.1091i	−0.408831	−	0.708116i	0.585928	−	0.810363i	$-0.300730\pi$
$397$	−8.14590	−	14.1091i	−0.408831	−	0.708116i	−0.994759	+	0.102247i	$0.967397\pi$
$398$	8.25329	−	14.2951i	0.413700	−	0.716549i
$399$	15.0000			0.750939
$400$	−1.71885	−	2.97713i	−0.0859424	−	0.148857i
$401$	29.8328			1.48978			0.744890	−	0.667187i	$-0.232502\pi$
$401$	29.8328			1.48978			0.744890	+	0.667187i	$0.232502\pi$
$402$	2.61803			0.130576
$403$		0			0
$404$	−7.70820			−0.383497
$405$	−2.61803			−0.130091
$406$	7.98936	+	13.8380i	0.396505	+	0.686767i
$407$	−0.180340			−0.00893912
$408$	0.263932	−	0.457144i	0.0130666	−	0.0226320i
$409$	−3.09017	−	5.35233i	−0.152799	−	0.264656i	0.779456	−	0.626457i	$-0.215495\pi$
$409$	−3.09017	−	5.35233i	−0.152799	−	0.264656i	−0.932255	+	0.361801i	$0.882162\pi$
$410$	−5.23607	−	9.06914i	−0.258591	−	0.447893i
$411$	6.47214			0.319247
$412$	−0.118034	+	0.204441i	−0.00581512	+	0.0100721i
$413$	−14.2082	+	24.6093i	−0.699140	+	1.21095i
$414$	−3.38197	+	5.85774i	−0.166215	+	0.287892i
$415$	5.35410	+	9.27358i	0.262823	+	0.455222i
$416$	−13.6353	+	23.6170i	−0.668523	+	1.15792i
$417$	2.92705	+	5.06980i	0.143338	+	0.248269i
$418$	−2.36068			−0.115465
$419$	4.47214			0.218478			0.109239	−	0.994016i	$-0.465159\pi$
$419$	4.47214			0.218478			0.109239	+	0.994016i	$0.465159\pi$
$420$	−6.35410	−	11.0056i	−0.310048	−	0.537020i
$421$	−7.38197	+	12.7859i	−0.359775	+	0.623149i	−0.987923	−	0.154945i	$-0.950480\pi$
$421$	−7.38197	+	12.7859i	−0.359775	+	0.623149i	0.628148	+	0.778094i	$0.283813\pi$
$422$	−2.47214	−	4.28187i	−0.120342	−	0.208438i
$423$	−3.38197	+	5.85774i	−0.164437	+	0.284813i
$424$	−14.2082	+	24.6093i	−0.690011	+	1.19513i
$425$	0.218847	−	0.379054i	0.0106156	−	0.0183868i
$426$	−0.0557281			−0.00270003
$427$	−10.4164	−	18.0417i	−0.504085	−	0.873101i
$428$	0.881966	+	1.52761i	0.0426314	+	0.0738398i
$429$	1.85410	−	3.21140i	0.0895169	−	0.155048i
$430$	7.47214			0.360338
$431$	−14.6180	−	25.3192i	−0.704126	−	1.21958i	−0.967006	−	0.254753i	$-0.918006\pi$
$431$	−14.6180	−	25.3192i	−0.704126	−	1.21958i	0.262880	−	0.964828i	$-0.415328\pi$
$432$	−9.27051			−0.446028
$433$	−0.583592			−0.0280456			−0.0140228	−	0.999902i	$-0.504464\pi$
$433$	−0.583592			−0.0280456			−0.0140228	+	0.999902i	$0.504464\pi$
$434$		0			0
$435$	−22.5623			−1.08178
$436$	13.6180			0.652186
$437$	−13.6803	−	23.6950i	−0.654419	−	1.13349i
$438$	−5.29180			−0.252852
$439$	−20.9164	+	36.2283i	−0.998286	+	1.72908i	−0.448455	+	0.893805i	$0.648026\pi$
$439$	−20.9164	+	36.2283i	−0.998286	+	1.72908i	−0.549831	+	0.835276i	$0.685308\pi$
$440$	2.23607	+	3.87298i	0.106600	+	0.184637i
$441$	2.00000	+	3.46410i	0.0952381	+	0.164957i
$442$	−0.708204			−0.0336858
$443$	20.5623	−	35.6150i	0.976945	−	1.69212i	0.303582	−	0.952805i	$-0.401817\pi$
$443$	20.5623	−	35.6150i	0.976945	−	1.69212i	0.673363	−	0.739312i	$-0.264849\pi$
$444$	−0.190983	+	0.330792i	−0.00906365	+	0.0156987i
$445$	8.35410	−	14.4697i	0.396022	−	0.685931i
$446$	−0.218847	−	0.379054i	−0.0103627	−	0.0179487i
$447$	8.51722	−	14.7523i	0.402851	−	0.697758i
$448$	0.354102	+	0.613323i	0.0167297	+	0.0289768i
$449$	−24.0689			−1.13588			−0.567940	−	0.823070i	$-0.692260\pi$
$449$	−24.0689			−1.13588			−0.567940	+	0.823070i	$0.692260\pi$
$450$	2.29180			0.108036
$451$	−2.47214	−	4.28187i	−0.116408	−	0.201625i
$452$	−1.50000	+	2.59808i	−0.0705541	+	0.122203i
$453$	−9.75329	−	16.8932i	−0.458249	−	0.793711i
$454$	−6.40983	+	11.1022i	−0.300828	+	0.521050i
$455$	−19.0623	+	33.0169i	−0.893655	+	1.54786i
$456$	−5.59017	+	9.68246i	−0.261784	+	0.453423i
$457$	15.7426			0.736410			0.368205	−	0.929745i	$-0.379972\pi$
$457$	15.7426			0.736410			0.368205	+	0.929745i	$0.379972\pi$
$458$	2.23607	+	3.87298i	0.104485	+	0.180973i
$459$	−0.590170	−	1.02220i	−0.0275468	−	0.0477124i
$460$	−11.5902	+	20.0748i	−0.540394	+	0.935991i
$461$	−10.7426			−0.500335			−0.250167	−	0.968203i	$-0.580486\pi$
$461$	−10.7426			−0.500335			−0.250167	+	0.968203i	$0.580486\pi$
$462$	0.708204	+	1.22665i	0.0329486	+	0.0570687i
$463$	31.1246			1.44648			0.723242	−	0.690595i	$-0.242651\pi$
$463$	31.1246			1.44648			0.723242	+	0.690595i	$0.242651\pi$
$464$	15.9787			0.741793
$465$		0			0
$466$	−11.6180			−0.538195
$467$	−32.7771			−1.51674			−0.758371	−	0.651823i	$-0.774005\pi$
$467$	−32.7771			−1.51674			−0.758371	+	0.651823i	$0.774005\pi$
$468$	7.85410	+	13.6037i	0.363056	+	0.628831i
$469$	−12.7082			−0.586810
$470$	2.73607	−	4.73901i	0.126205	−	0.218594i
$471$	−4.85410	−	8.40755i	−0.223665	−	0.387400i
$472$	−10.5902	−	18.3427i	−0.487452	−	0.844292i
$473$	3.52786			0.162211
$474$		0			0
$475$	−4.63525	+	8.02850i	−0.212680	+	0.368373i
$476$	−0.572949	+	0.992377i	−0.0262611	+	0.0454855i
$477$	12.7082	+	22.0113i	0.581869	+	1.00783i
$478$	4.14590	−	7.18091i	0.189629	−	0.328447i
$479$	4.47214	+	7.74597i	0.204337	+	0.353922i	0.949921	−	0.312489i	$-0.101163\pi$
$479$	4.47214	+	7.74597i	0.204337	+	0.353922i	−0.745584	+	0.666411i	$0.767829\pi$
$480$	14.7082			0.671335
$481$	1.14590			0.0522485
$482$	2.63525	+	4.56440i	0.120033	+	0.207903i
$483$	−8.20820	+	14.2170i	−0.373486	+	0.646897i
$484$	−8.42705	−	14.5961i	−0.383048	−	0.663458i
$485$	−6.92705	+	11.9980i	−0.314541	+	0.544801i
$486$	4.94427	−	8.56373i	0.224277	−	0.388459i
$487$	11.4615	−	19.8519i	0.519370	−	0.899575i	−0.480377	−	0.877062i	$-0.659500\pi$
$487$	11.4615	−	19.8519i	0.519370	−	0.899575i	0.999747	−	0.0225127i	$-0.00716661\pi$
$488$	15.5279			0.702913
$489$	6.35410	+	11.0056i	0.287342	+	0.497692i
$490$	−1.61803	−	2.80252i	−0.0730953	−	0.126605i
$491$	−13.7984	+	23.8995i	−0.622712	+	1.07857i	0.366267	+	0.930510i	$0.380636\pi$
$491$	−13.7984	+	23.8995i	−0.622712	+	1.07857i	−0.988979	+	0.148059i	$0.952698\pi$
$492$	−10.4721			−0.472120
$493$	1.01722	+	1.76188i	0.0458133	+	0.0793510i
$494$	15.0000			0.674882
$495$	4.00000			0.179787
$496$		0			0
$497$	0.270510			0.0121340
$498$	−2.52786			−0.113276
$499$	2.07295	+	3.59045i	0.0927979	+	0.160731i	0.908687	−	0.417477i	$-0.137086\pi$
$499$	2.07295	+	3.59045i	0.0927979	+	0.160731i	−0.815889	+	0.578208i	$0.803752\pi$
$500$	−13.3262			−0.595967
$501$	−4.61803	+	7.99867i	−0.206319	+	0.357354i
$502$	−0.291796	−	0.505406i	−0.0130235	−	0.0225574i
$503$	−6.57295	−	11.3847i	−0.293073	−	0.507618i	0.681462	−	0.731854i	$-0.261345\pi$
$503$	−6.57295	−	11.3847i	−0.293073	−	0.507618i	−0.974535	+	0.224236i	$0.928011\pi$
$504$	−13.4164			−0.597614
$505$	6.23607	−	10.8012i	0.277501	−	0.480646i
$506$	1.29180	−	2.23746i	0.0574273	−	0.0994671i
$507$	−5.28115	+	9.14723i	−0.234544	+	0.406243i
$508$	−8.28115	−	14.3434i	−0.367417	−	0.636384i
$509$	−0.954915	+	1.65396i	−0.0423259	+	0.0733105i	−0.886412	−	0.462897i	$-0.846810\pi$
$509$	−0.954915	+	1.65396i	−0.0423259	+	0.0733105i	0.844086	+	0.536207i	$0.180143\pi$
$510$	0.190983	+	0.330792i	0.00845687	+	0.0146477i
$511$	25.6869			1.13632
$512$	−18.7082			−0.826794
$513$	12.5000	+	21.6506i	0.551888	+	0.955899i
$514$	0.437694	−	0.758108i	0.0193059	−	0.0334387i
$515$	−0.190983	−	0.330792i	−0.00841572	−	0.0145764i
$516$	3.73607	−	6.47106i	0.164471	−	0.284873i
$517$	1.29180	−	2.23746i	0.0568131	−	0.0984032i
$518$	−0.218847	+	0.379054i	−0.00961559	+	0.0166547i
$519$	0.909830			0.0399371
$520$	−14.2082	−	24.6093i	−0.623071	−	1.07919i
$521$	−15.5344	−	26.9064i	−0.680576	−	1.17879i	−0.974805	−	0.223058i	$-0.928396\pi$
$521$	−15.5344	−	26.9064i	−0.680576	−	1.17879i	0.294229	−	0.955735i	$-0.404937\pi$
$522$	−5.32624	+	9.22531i	−0.233123	+	0.403781i
$523$	−34.1246			−1.49217			−0.746083	−	0.665853i	$-0.768068\pi$
$523$	−34.1246			−1.49217			−0.746083	+	0.665853i	$0.768068\pi$
$524$	0.0729490	+	0.126351i	0.00318679	+	0.00551969i
$525$	5.56231			0.242759
$526$	−6.67376			−0.290990
$527$		0			0
$528$	1.41641			0.0616412
$529$	6.94427			0.301925
$530$	−10.2812	−	17.8075i	−0.446585	−	0.773507i
$531$	−18.9443			−0.822111
$532$	12.1353	−	21.0189i	0.526130	−	0.911284i
$533$	15.7082	+	27.2074i	0.680398	+	1.17848i
$534$	1.97214	+	3.41584i	0.0853427	+	0.147818i
$535$	−2.85410			−0.123394
$536$	4.73607	−	8.20311i	0.204567	−	0.354320i
$537$	9.89919	−	17.1459i	0.427181	−	0.739900i
$538$	0.427051	−	0.739674i	0.0184115	−	0.0318896i
$539$	−0.763932	−	1.32317i	−0.0329049	−	0.0569929i
$540$	10.5902	−	18.3427i	0.455728	−	0.789345i
$541$	−11.0000	−	19.0526i	−0.472927	−	0.819133i	0.526593	−	0.850118i	$-0.323469\pi$
$541$	−11.0000	−	19.0526i	−0.472927	−	0.819133i	−0.999520	+	0.0309841i	$0.990136\pi$
$542$	5.90983			0.253849
$543$	−17.0000			−0.729540
$544$	−0.663119	−	1.14856i	−0.0284310	−	0.0492439i
$545$	−11.0172	+	19.0824i	−0.471926	+	0.817400i
$546$	−4.50000	−	7.79423i	−0.192582	−	0.333562i
$547$	11.8541	−	20.5319i	0.506845	−	0.877881i	−0.493124	−	0.869959i	$-0.664145\pi$
$547$	11.8541	−	20.5319i	0.506845	−	0.877881i	0.999969	−	0.00792181i	$-0.00252162\pi$
$548$	5.23607	−	9.06914i	0.223674	−	0.387414i
$549$	6.94427	−	12.0278i	0.296374	−	0.513335i
$550$	−0.875388			−0.0373267
$551$	−21.5451	−	37.3172i	−0.917851	−	1.58977i
$552$	−6.11803	−	10.5967i	−0.260401	−	0.451027i
$553$		0			0
$554$	8.23607			0.349917
$555$	−0.309017	−	0.535233i	−0.0131170	−	0.0227194i
$556$	9.47214			0.401708
$557$	−35.8885			−1.52065			−0.760323	−	0.649545i	$-0.774959\pi$
$557$	−35.8885			−1.52065			−0.760323	+	0.649545i	$0.774959\pi$
$558$		0			0
$559$	−22.4164			−0.948113
$560$	−14.5623			−0.615370
$561$	0.0901699	+	0.156179i	0.00380698	+	0.00659388i
$562$	−11.7639			−0.496232
$563$	4.28115	−	7.41517i	0.180429	−	0.312512i	−0.761598	−	0.648050i	$-0.775585\pi$
$563$	4.28115	−	7.41517i	0.180429	−	0.312512i	0.942027	+	0.335538i	$0.108918\pi$
$564$	−2.73607	−	4.73901i	−0.115209	−	0.199548i
$565$	−2.42705	−	4.20378i	−0.102107	−	0.176854i
$566$	−4.05573			−0.170475
$567$	−1.50000	+	2.59808i	−0.0629941	+	0.109109i
$568$	−0.100813	+	0.174613i	−0.00423002	+	0.00732661i
$569$	7.76393	−	13.4475i	0.325481	−	0.563750i	−0.656129	−	0.754649i	$-0.727807\pi$
$569$	7.76393	−	13.4475i	0.325481	−	0.563750i	0.981610	+	0.190900i	$0.0611405\pi$
$570$	−4.04508	−	7.00629i	−0.169430	−	0.293461i
$571$	3.50000	−	6.06218i	0.146470	−	0.253694i	−0.783450	−	0.621455i	$-0.786542\pi$
$571$	3.50000	−	6.06218i	0.146470	−	0.253694i	0.929921	+	0.367760i	$0.119875\pi$
$572$	−3.00000	−	5.19615i	−0.125436	−	0.217262i
$573$	−16.0902			−0.672176
$574$	−12.0000			−0.500870
$575$	−5.07295	−	8.78661i	−0.211557	−	0.366427i
$576$	−0.236068	+	0.408882i	−0.00983617	+	0.0170367i
$577$	−19.4894	−	33.7566i	−0.811353	−	1.40530i	−0.911918	−	0.410373i	$-0.865398\pi$
$577$	−19.4894	−	33.7566i	−0.811353	−	1.40530i	0.100565	−	0.994930i	$-0.467935\pi$
$578$	−5.23607	+	9.06914i	−0.217792	+	0.377226i
$579$	1.19098	−	2.06284i	0.0494956	−	0.0857288i
$580$	−18.2533	+	31.6156i	−0.757927	+	1.31277i
$581$	12.2705			0.509067
$582$	−1.63525	−	2.83234i	−0.0677835	−	0.117404i
$583$	−4.85410	−	8.40755i	−0.201036	−	0.348205i
$584$	−9.57295	+	16.5808i	−0.396131	+	0.686120i
$585$	−25.4164			−1.05084
$586$	−2.54508	−	4.40822i	−0.105136	−	0.182102i
$587$	−36.0132			−1.48642			−0.743211	−	0.669057i	$-0.766698\pi$
$587$	−36.0132			−1.48642			−0.743211	+	0.669057i	$0.766698\pi$
$588$	−3.23607			−0.133453
$589$		0			0
$590$	15.3262			0.630971
$591$	−16.4164			−0.675281
$592$	0.218847	+	0.379054i	0.00899456	+	0.0155790i
$593$	6.11146			0.250967			0.125484	−	0.992096i	$-0.459952\pi$
$593$	6.11146			0.250967			0.125484	+	0.992096i	$0.459952\pi$
$594$	−1.18034	+	2.04441i	−0.0484299	+	0.0838831i
$595$	−0.927051	−	1.60570i	−0.0380054	−	0.0658273i
$596$	−13.7812	−	23.8697i	−0.564498	−	0.977739i
$597$	26.7082			1.09309
$598$	−8.20820	+	14.2170i	−0.335658	+	0.581377i
$599$	−14.8992	+	25.8061i	−0.608764	+	1.05441i	0.382680	+	0.923881i	$0.375001\pi$
$599$	−14.8992	+	25.8061i	−0.608764	+	1.05441i	−0.991444	+	0.130530i	$0.958332\pi$
$600$	−2.07295	+	3.59045i	−0.0846278	+	0.146580i
$601$	11.0000	+	19.0526i	0.448699	+	0.777170i	0.998302	−	0.0582563i	$-0.0185541\pi$
$601$	11.0000	+	19.0526i	0.448699	+	0.777170i	−0.549602	+	0.835426i	$0.685221\pi$
$602$	4.28115	−	7.41517i	0.174487	−	0.302220i
$603$	−4.23607	−	7.33708i	−0.172506	−	0.298789i
$604$	−31.5623			−1.28425
$605$	27.2705			1.10870
$606$	1.47214	+	2.54981i	0.0598014	+	0.103579i
$607$	12.7082	−	22.0113i	0.515810	−	0.893409i	−0.484021	−	0.875056i	$-0.660824\pi$
$607$	12.7082	−	22.0113i	0.515810	−	0.893409i	0.999832	−	0.0183532i	$-0.00584232\pi$
$608$	14.0451	+	24.3268i	0.569603	+	0.986582i
$609$	−12.9271	+	22.3903i	−0.523831	+	0.907301i
$610$	−5.61803	+	9.73072i	−0.227468	+	0.393985i
$611$	−8.20820	+	14.2170i	−0.332068	+	0.575159i
$612$	−0.763932			−0.0308801
$613$	12.5279	+	21.6989i	0.505996	+	0.876410i	0.999976	+	0.00693709i	$0.00220816\pi$
$613$	12.5279	+	21.6989i	0.505996	+	0.876410i	−0.493980	+	0.869473i	$0.664459\pi$
$614$	1.88197	+	3.25966i	0.0759500	+	0.131549i
$615$	8.47214	−	14.6742i	0.341629	−	0.591720i
$616$	5.12461			0.206476
$617$	7.11803	+	12.3288i	0.286561	+	0.496339i	0.972987	−	0.230862i	$-0.0741545\pi$
$617$	7.11803	+	12.3288i	0.286561	+	0.496339i	−0.686425	+	0.727200i	$0.740821\pi$
$618$	0.0901699			0.00362717
$619$	40.0000			1.60774			0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000			1.60774			0.803868	+	0.594808i	$0.202772\pi$
$620$		0			0
$621$	−27.3607			−1.09795
$622$	−10.1803			−0.408194
$623$	−9.57295	−	16.5808i	−0.383532	−	0.664297i
$624$	−9.00000			−0.360288
$625$	15.4164	−	26.7020i	0.616656	−	1.06808i
$626$	−0.381966	−	0.661585i	−0.0152664	−	0.0264422i
$627$	−1.90983	−	3.30792i	−0.0762713	−	0.132106i
$628$	−15.7082			−0.626826
$629$	−0.0278640	+	0.0482619i	−0.00111101	+	0.00192433i
$630$	4.85410	−	8.40755i	0.193392	−	0.334965i
$631$	−4.36475	+	7.55996i	−0.173758	+	0.300957i	−0.939731	−	0.341916i	$-0.888924\pi$
$631$	−4.36475	+	7.55996i	−0.173758	+	0.300957i	0.765973	+	0.642873i	$0.222258\pi$
$632$		0			0
$633$	4.00000	−	6.92820i	0.158986	−	0.275371i
$634$	8.00000	+	13.8564i	0.317721	+	0.550308i
$635$	26.7984			1.06346
$636$	−20.5623			−0.815348
$637$	4.85410	+	8.40755i	0.192327	+	0.333119i
$638$	2.03444	−	3.52376i	0.0805443	−	0.139507i
$639$	0.0901699	+	0.156179i	0.00356707	+	0.00617834i
$640$	14.8992	−	25.8061i	0.588942	−	1.02008i
$641$	−20.5451	+	35.5851i	−0.811482	+	1.40553i	0.100345	+	0.994953i	$0.468005\pi$
$641$	−20.5451	+	35.5851i	−0.811482	+	1.40553i	−0.911827	+	0.410575i	$0.865328\pi$
$642$	0.336881	−	0.583495i	0.0132956	−	0.0230287i
$643$	−8.14590			−0.321243			−0.160621	−	0.987016i	$-0.551350\pi$
$643$	−8.14590			−0.321243			−0.160621	+	0.987016i	$0.551350\pi$
$644$	13.2812	+	23.0036i	0.523351	+	0.906470i
$645$	6.04508	+	10.4704i	0.238025	+	0.412271i
$646$	−0.364745	+	0.631757i	−0.0143507	+	0.0248561i
$647$	29.8885			1.17504			0.587520	−	0.809210i	$-0.300104\pi$
$647$	29.8885			1.17504			0.587520	+	0.809210i	$0.300104\pi$
$648$	−1.11803	−	1.93649i	−0.0439205	−	0.0760726i
$649$	7.23607			0.284041
$650$	5.56231			0.218172
$651$		0			0
$652$	20.5623			0.805282
$653$	39.6525			1.55172			0.775861	−	0.630904i	$-0.217316\pi$
$653$	39.6525			1.55172			0.775861	+	0.630904i	$0.217316\pi$
$654$	−2.60081	−	4.50474i	−0.101700	−	0.176149i
$655$	−0.236068			−0.00922394
$656$	−6.00000	+	10.3923i	−0.234261	+	0.405751i
$657$	8.56231	+	14.8303i	0.334047	+	0.578587i
$658$	−3.13525	−	5.43042i	−0.122225	−	0.211700i
$659$	22.6869			0.883757			0.441878	−	0.897075i	$-0.354312\pi$
$659$	22.6869			0.883757			0.441878	+	0.897075i	$0.354312\pi$
$660$	−1.61803	+	2.80252i	−0.0629819	+	0.109088i
$661$	8.30902	−	14.3916i	0.323183	−	0.559770i	−0.657960	−	0.753053i	$-0.728580\pi$
$661$	8.30902	−	14.3916i	0.323183	−	0.559770i	0.981143	+	0.193283i	$0.0619136\pi$
$662$	−3.48278	+	6.03235i	−0.135362	+	0.234454i
$663$	−0.572949	−	0.992377i	−0.0222515	−	0.0385407i
$664$	−4.57295	+	7.92058i	−0.177465	+	0.307378i
$665$	19.6353	+	34.0093i	0.761423	+	1.31882i
$666$	−0.291796			−0.0113069
$667$	47.1591			1.82601
$668$	7.47214	+	12.9421i	0.289106	+	0.500746i
$669$	0.354102	−	0.613323i	0.0136904	−	0.0237124i
$670$	3.42705	+	5.93583i	0.132399	+	0.229321i
$671$	−2.65248	+	4.59422i	−0.102398	+	0.177358i
$672$	8.42705	−	14.5961i	0.325081	−	0.563056i
$673$	−2.20820	+	3.82472i	−0.0851200	+	0.147432i	−0.905442	−	0.424469i	$-0.860461\pi$
$673$	−2.20820	+	3.82472i	−0.0851200	+	0.147432i	0.820322	+	0.571901i	$0.193794\pi$
$674$	11.7295			0.451803
$675$	4.63525	+	8.02850i	0.178411	+	0.309017i
$676$	8.54508	+	14.8005i	0.328657	+	0.569251i
$677$	14.3262	−	24.8138i	0.550602	−	0.953671i	−0.447629	−	0.894219i	$-0.647732\pi$
$677$	14.3262	−	24.8138i	0.550602	−	0.953671i	0.998231	−	0.0594514i	$-0.0189351\pi$
$678$	1.14590			0.0440079
$679$	7.93769	+	13.7485i	0.304621	+	0.527619i
$680$	1.38197			0.0529960
$681$	−20.7426			−0.794860
$682$		0			0
$683$	10.0557			0.384772			0.192386	−	0.981319i	$-0.438377\pi$
$683$	10.0557			0.384772			0.192386	+	0.981319i	$0.438377\pi$
$684$	16.1803			0.618671
$685$	8.47214	+	14.6742i	0.323704	+	0.560671i
$686$	9.27051			0.353950
$687$	−3.61803	+	6.26662i	−0.138037	+	0.239086i
$688$	−4.28115	−	7.41517i	−0.163217	−	0.282701i
$689$	30.8435	+	53.4224i	1.17504	+	2.03523i
$690$	8.85410			0.337070
$691$	−1.91641	+	3.31932i	−0.0729036	+	0.126273i	−0.900173	−	0.435533i	$-0.856560\pi$
$691$	−1.91641	+	3.31932i	−0.0729036	+	0.126273i	0.827269	+	0.561806i	$0.189893\pi$
$692$	0.736068	−	1.27491i	0.0279811	−	0.0484647i
$693$	2.29180	−	3.96951i	0.0870581	−	0.150789i
$694$	−2.51064	−	4.34856i	−0.0953027	−	0.165069i
$695$	−7.66312	+	13.2729i	−0.290679	+	0.503470i
$696$	−9.63525	−	16.6888i	−0.365223	−	0.632585i
$697$	−1.52786			−0.0578720
$698$	10.3262			0.390854
$699$	−9.39919	−	16.2799i	−0.355510	−	0.615761i
$700$	4.50000	−	7.79423i	0.170084	−	0.294594i
$701$	15.0172	+	26.0106i	0.567193	+	0.982406i	0.996842	+	0.0794106i	$0.0253038\pi$
$701$	15.0172	+	26.0106i	0.567193	+	0.982406i	−0.429649	+	0.902996i	$0.641363\pi$
$702$	7.50000	−	12.9904i	0.283069	−	0.490290i
$703$	0.590170	−	1.02220i	0.0222587	−	0.0385532i
$704$	0.0901699	−	0.156179i	0.00339841	−	0.00588621i
$705$	8.85410			0.333465
$706$	10.0066	+	17.3319i	0.376603	+	0.652295i
$707$	−7.14590	−	12.3771i	−0.268749	−	0.465487i
$708$	7.66312	−	13.2729i	0.287998	−	0.498827i
$709$	−4.14590			−0.155702			−0.0778512	−	0.996965i	$-0.524806\pi$
$709$	−4.14590			−0.155702			−0.0778512	+	0.996965i	$0.524806\pi$
$710$	−0.0729490	−	0.126351i	−0.00273773	−	0.00474188i
$711$		0			0
$712$	14.2705			0.534810
$713$		0			0
$714$	0.437694			0.0163803
$715$	9.70820			0.363066
$716$	−16.0172	−	27.7426i	−0.598592	−	1.03679i
$717$	13.4164			0.501045
$718$	−7.82624	+	13.5554i	−0.292073	+	0.505885i
$719$	−20.6910	−	35.8378i	−0.771643	−	1.33653i	−0.936662	−	0.350235i	$-0.886102\pi$
$719$	−20.6910	−	35.8378i	−0.771643	−	1.33653i	0.165018	−	0.986290i	$-0.447232\pi$
$720$	−4.85410	−	8.40755i	−0.180902	−	0.313331i
$721$	−0.437694			−0.0163006
$722$	1.85410	−	3.21140i	0.0690025	−	0.119516i
$723$	−4.26393	+	7.38535i	−0.158577	+	0.274664i
$724$	−13.7533	+	23.8214i	−0.511137	+	0.885315i
$725$	−7.98936	−	13.8380i	−0.296717	−	0.513929i
$726$	−3.21885	+	5.57521i	−0.119463	+	0.206915i
$727$	11.9164	+	20.6398i	0.441955	+	0.765489i	0.997835	−	0.0657742i	$-0.0209517\pi$
$727$	11.9164	+	20.6398i	0.441955	+	0.765489i	−0.555879	+	0.831263i	$0.687618\pi$
$728$	−32.5623			−1.20684
$729$	13.0000			0.481481
$730$	−6.92705	−	11.9980i	−0.256382	−	0.444066i
$731$	0.545085	−	0.944115i	0.0201607	−	0.0349193i
$732$	5.61803	+	9.73072i	0.207649	+	0.359658i
$733$	−13.9721	+	24.2004i	−0.516073	+	0.893864i	0.483753	+	0.875204i	$0.339273\pi$
$733$	−13.9721	+	24.2004i	−0.516073	+	0.893864i	−0.999826	+	0.0186596i	$0.994060\pi$
$734$	11.2082	−	19.4132i	0.413702	−	0.716554i
$735$	2.61803	−	4.53457i	0.0965676	−	0.167260i
$736$	−30.7426			−1.13319
$737$	1.61803	+	2.80252i	0.0596010	+	0.103232i
$738$	−4.00000	−	6.92820i	−0.147242	−	0.255031i
$739$	10.8541	−	18.7999i	0.399275	−	0.691564i	−0.594362	−	0.804198i	$-0.702595\pi$
$739$	10.8541	−	18.7999i	0.399275	−	0.691564i	0.993637	+	0.112634i	$0.0359287\pi$
$740$	−1.00000			−0.0367607
$741$	12.1353	+	21.0189i	0.445800	+	0.772148i
$742$	−23.5623			−0.864999
$743$	3.43769			0.126117			0.0630584	−	0.998010i	$-0.479915\pi$
$743$	3.43769			0.126117			0.0630584	+	0.998010i	$0.479915\pi$
$744$		0			0
$745$	44.5967			1.63390
$746$	0.214782			0.00786372
$747$	4.09017	+	7.08438i	0.149651	+	0.259204i
$748$	0.291796			0.0106691
$749$	−1.63525	+	2.83234i	−0.0597509	+	0.103492i
$750$	2.54508	+	4.40822i	0.0929334	+	0.160965i
$751$	19.9164	+	34.4962i	0.726760	+	1.25879i	0.958245	+	0.285947i	$0.0923081\pi$
$751$	19.9164	+	34.4962i	0.726760	+	1.25879i	−0.231485	+	0.972838i	$0.574359\pi$
$752$	−6.27051			−0.228662
$753$	0.472136	−	0.817763i	0.0172056	−	0.0298010i
$754$	−12.9271	+	22.3903i	−0.470775	+	0.815407i
$755$	25.5344	−	44.2270i	0.929293	−	1.60958i
$756$	−12.1353	−	21.0189i	−0.441355	−	0.764449i
$757$	21.5623	−	37.3470i	0.783695	−	1.35740i	−0.146080	−	0.989273i	$-0.546666\pi$
$757$	21.5623	−	37.3470i	0.783695	−	1.35740i	0.929775	−	0.368127i	$-0.120001\pi$
$758$	−5.69098	−	9.85707i	−0.206706	−	0.358025i
$759$	4.18034			0.151737
$760$	−29.2705			−1.06175
$761$	1.75329	+	3.03679i	0.0635567	+	0.110083i	0.896053	−	0.443947i	$-0.146422\pi$
$761$	1.75329	+	3.03679i	0.0635567	+	0.110083i	−0.832496	+	0.554031i	$0.813089\pi$
$762$	−3.16312	+	5.47868i	−0.114588	+	0.198472i
$763$	12.6246	+	21.8665i	0.457042	+	0.791619i
$764$	−13.0172	+	22.5465i	−0.470947	+	0.815703i
$765$	0.618034	−	1.07047i	0.0223451	−	0.0387028i
$766$	5.20820	−	9.02087i	0.188180	−	0.325937i
$767$	−45.9787			−1.66020
$768$	3.28115	+	5.68312i	0.118398	+	0.205072i
$769$	26.8713	+	46.5425i	0.969005	+	1.67837i	0.698447	+	0.715662i	$0.253875\pi$
$769$	26.8713	+	46.5425i	0.969005	+	1.67837i	0.270557	+	0.962704i	$0.412792\pi$
$770$	−1.85410	+	3.21140i	−0.0668172	+	0.115731i
$771$	1.41641			0.0510107
$772$	−1.92705	−	3.33775i	−0.0693561	−	0.120128i
$773$	19.0902			0.686626			0.343313	−	0.939221i	$-0.388451\pi$
$773$	19.0902			0.686626			0.343313	+	0.939221i	$0.388451\pi$
$774$	5.70820			0.205177
$775$		0			0
$776$	−11.8328			−0.424773
$777$	−0.708204			−0.0254067
$778$	8.98278	+	15.5586i	0.322048	+	0.557804i
$779$	32.3607			1.15944
$780$	10.2812	−	17.8075i	0.368124	−	0.637610i
$781$	−0.0344419	−	0.0596550i	−0.00123243	−	0.00213463i
$782$	−0.399187	−	0.691412i	−0.0142749	−	0.0247248i
$783$	−43.0902			−1.53992
$784$	−1.85410	+	3.21140i	−0.0662179	+	0.114693i
$785$	12.7082	−	22.0113i	0.453575	−	0.785615i
$786$	0.0278640	−	0.0482619i	0.000993878	−	0.00172145i
$787$	15.6459	+	27.0995i	0.557716	+	0.965993i	0.997687	+	0.0679803i	$0.0216555\pi$
$787$	15.6459	+	27.0995i	0.557716	+	0.965993i	−0.439971	+	0.898012i	$0.645011\pi$
$788$	−13.2812	+	23.0036i	−0.473121	+	0.819470i
$789$	−5.39919	−	9.35167i	−0.192216	−	0.332928i
$790$		0			0
$791$	−5.56231			−0.197773
$792$	1.70820	+	2.95870i	0.0606984	+	0.105133i
$793$	16.8541	−	29.1922i	0.598507	−	1.03664i
$794$	5.03444	+	8.71991i	0.178666	+	0.309458i
$795$	16.6353	−	28.8131i	0.589992	−	1.02190i
$796$	21.6074	−	37.4251i	0.765854	−	1.32650i
$797$	4.52786	−	7.84249i	0.160385	−	0.277795i	−0.774622	−	0.632425i	$-0.782060\pi$
$797$	4.52786	−	7.84249i	0.160385	−	0.277795i	0.935007	+	0.354630i	$0.115393\pi$
$798$	−9.27051			−0.328172
$799$	−0.399187	−	0.691412i	−0.0141222	−	0.0244604i
$800$	5.20820	+	9.02087i	0.184138	+	0.318936i
$801$	6.38197	−	11.0539i	0.225496	−	0.390570i
$802$	−18.4377			−0.651058
$803$	−3.27051	−	5.66469i	−0.115414	−	0.199903i
$804$	6.85410			0.241726
$805$	−42.9787			−1.51480
$806$		0			0
$807$	1.38197			0.0486475
$808$	10.6525			0.374753
$809$	27.3992	+	47.4568i	0.963304	+	1.66849i	0.714104	+	0.700040i	$0.246834\pi$
$809$	27.3992	+	47.4568i	0.963304	+	1.66849i	0.249200	+	0.968452i	$0.419832\pi$
$810$	1.61803			0.0568519
$811$	−21.3885	+	37.0460i	−0.751053	+	1.30086i	0.196259	+	0.980552i	$0.437121\pi$
$811$	−21.3885	+	37.0460i	−0.751053	+	1.30086i	−0.947313	+	0.320311i	$0.896213\pi$
$812$	20.9164	+	36.2283i	0.734022	+	1.27136i
$813$	4.78115	+	8.28120i	0.167682	+	0.290434i
$814$	0.111456			0.00390654
$815$	−16.6353	+	28.8131i	−0.582708	+	1.00928i
$816$	0.218847	−	0.379054i	0.00766118	−	0.0132696i
$817$	−11.5451	+	19.9967i	−0.403911	+	0.699595i
$818$	1.90983	+	3.30792i	0.0667756	+	0.115659i
$819$	−14.5623	+	25.2227i	−0.508848	+	0.881351i
$820$	−13.7082	−	23.7433i	−0.478711	−	0.829152i
$821$	32.4721			1.13329			0.566643	−	0.823964i	$-0.308242\pi$
$821$	32.4721			1.13329			0.566643	+	0.823964i	$0.308242\pi$
$822$	−4.00000			−0.139516
$823$	−3.06231	−	5.30407i	−0.106745	−	0.184888i	0.807705	−	0.589587i	$-0.200710\pi$
$823$	−3.06231	−	5.30407i	−0.106745	−	0.184888i	−0.914450	+	0.404699i	$0.867376\pi$
$824$	0.163119	−	0.282530i	0.00568252	−	0.00984241i
$825$	−0.708204	−	1.22665i	−0.0246565	−	0.0427063i
$826$	8.78115	−	15.2094i	0.305535	−	0.529203i
$827$	1.33688	−	2.31555i	0.0464879	−	0.0805194i	−0.841845	−	0.539719i	$-0.818530\pi$
$827$	1.33688	−	2.31555i	0.0464879	−	0.0805194i	0.888333	+	0.459200i	$0.151864\pi$
$828$	−8.85410	+	15.3358i	−0.307701	+	0.532954i
$829$	21.7082			0.753957			0.376979	−	0.926222i	$-0.376963\pi$
$829$	21.7082			0.753957			0.376979	+	0.926222i	$0.376963\pi$
$830$	−3.30902	−	5.73139i	−0.114858	−	0.198939i
$831$	6.66312	+	11.5409i	0.231141	+	0.400348i
$832$	−0.572949	+	0.992377i	−0.0198634	+	0.0344045i
$833$	−0.472136			−0.0163585
$834$	−1.80902	−	3.13331i	−0.0626411	−	0.108498i
$835$	−24.1803			−0.836795
$836$	−6.18034			−0.213752
$837$		0			0
$838$	−2.76393			−0.0954784
$839$	11.1803			0.385988			0.192994	−	0.981200i	$-0.438180\pi$
$839$	11.1803			0.385988			0.192994	+	0.981200i	$0.438180\pi$
$840$	8.78115	+	15.2094i	0.302979	+	0.524774i
$841$	45.2705			1.56105
$842$	4.56231	−	7.90215i	0.157227	−	0.272326i
$843$	−9.51722	−	16.4843i	−0.327791	−	0.567750i
$844$	−6.47214	−	11.2101i	−0.222780	−	0.385866i
$845$	−27.6525			−0.951274
$846$	2.09017	−	3.62028i	0.0718615	−	0.124468i
$847$	15.6246	−	27.0626i	0.536868	−	0.929883i
$848$	−11.7812	+	20.4056i	−0.404566	+	0.700730i
$849$	−3.28115	−	5.68312i	−0.112609	−	0.195044i
$850$	−0.135255	+	0.234268i	−0.00463921	+	0.00803534i
$851$	0.645898	+	1.11873i	0.0221411	+	0.0383495i
$852$	−0.145898			−0.00499838
$853$	4.00000			0.136957			0.0684787	−	0.997653i	$-0.478185\pi$
$853$	4.00000			0.136957			0.0684787	+	0.997653i	$0.478185\pi$
$854$	6.43769	+	11.1504i	0.220293	+	0.381559i
$855$	−13.0902	+	22.6728i	−0.447674	+	0.775395i
$856$	−1.21885	−	2.11111i	−0.0416593	−	0.0721561i
$857$	4.09017	−	7.08438i	0.139718	−	0.241998i	−0.787672	−	0.616095i	$-0.788714\pi$
$857$	4.09017	−	7.08438i	0.139718	−	0.241998i	0.927390	+	0.374097i	$0.122047\pi$
$858$	−1.14590	+	1.98475i	−0.0391203	+	0.0677584i
$859$	21.6459	−	37.4918i	0.738549	−	1.27920i	−0.214600	−	0.976702i	$-0.568845\pi$
$859$	21.6459	−	37.4918i	0.738549	−	1.27920i	0.953149	−	0.302502i	$-0.0978218\pi$
$860$	19.5623			0.667069
$861$	−9.70820	−	16.8151i	−0.330855	−	0.573057i
$862$	9.03444	+	15.6481i	0.307714	+	0.532977i
$863$	1.24671	−	2.15937i	0.0424385	−	0.0735057i	−0.844026	−	0.536302i	$-0.819821\pi$
$863$	1.24671	−	2.15937i	0.0424385	−	0.0735057i	0.886464	+	0.462797i	$0.153154\pi$
$864$	28.0902			0.955647
$865$	1.19098	+	2.06284i	0.0404946	+	0.0701388i
$866$	0.360680			0.0122564
$867$	−16.9443			−0.575458
$868$		0			0
$869$		0			0
$870$	13.9443			0.472755
$871$	−10.2812	−	17.8075i	−0.348364	−	0.603383i
$872$	−18.8197			−0.637314
$873$	−5.29180	+	9.16566i	−0.179100	+	0.310211i
$874$	8.45492	+	14.6443i	0.285992	+	0.495352i
$875$	−12.3541	−	21.3979i	−0.417645	−	0.723382i
$876$	−13.8541			−0.468087
$877$	−8.14590	+	14.1091i	−0.275067	+	0.476431i	−0.970152	−	0.242497i	$-0.922034\pi$
$877$	−8.14590	+	14.1091i	−0.275067	+	0.476431i	0.695085	+	0.718928i	$0.255367\pi$
$878$	12.9271	−	22.3903i	0.436267	−	0.755636i
$879$	4.11803	−	7.13264i	0.138898	−	0.240578i
$880$	1.85410	+	3.21140i	0.0625018	+	0.108256i
$881$	−7.68034	+	13.3027i	−0.258757	+	0.448181i	−0.965909	−	0.258881i	$-0.916646\pi$
$881$	−7.68034	+	13.3027i	−0.258757	+	0.448181i	0.707152	+	0.707062i	$0.249980\pi$
$882$	−1.23607	−	2.14093i	−0.0416206	−	0.0720889i
$883$	1.00000			0.0336527			0.0168263	−	0.999858i	$-0.494644\pi$
$883$	1.00000			0.0336527			0.0168263	+	0.999858i	$0.494644\pi$
$884$	−1.85410			−0.0623602
$885$	12.3992	+	21.4760i	0.416794	+	0.721909i
$886$	−12.7082	+	22.0113i	−0.426940	+	0.739483i
$887$	−19.5517	−	33.8645i	−0.656481	−	1.13706i	−0.981520	−	0.191357i	$-0.938711\pi$
$887$	−19.5517	−	33.8645i	−0.656481	−	1.13706i	0.325040	−	0.945700i	$-0.394622\pi$
$888$	0.263932	−	0.457144i	0.00885698	−	0.0153407i
$889$	15.3541	−	26.5941i	0.514960	−	0.891937i
$890$	−5.16312	+	8.94278i	−0.173068	+	0.299763i
$891$	0.763932			0.0255927
$892$	−0.572949	−	0.992377i	−0.0191838	−	0.0332272i
$893$	8.45492	+	14.6443i	0.282933	+	0.490054i
$894$	−5.26393	+	9.11740i	−0.176052	+	0.304931i
$895$	51.8328			1.73258
$896$	−17.0729	−	29.5712i	−0.570367	−	0.987905i
$897$	−26.5623			−0.886890
$898$	14.8754			0.496398
$899$		0			0
$900$	6.00000			0.200000
$901$	−3.00000			−0.0999445
$902$	1.52786	+	2.64634i	0.0508723	+	0.0881134i
$903$	13.8541			0.461036
$904$	2.07295	−	3.59045i	0.0689453	−	0.119417i
$905$	−22.2533	−	38.5438i	−0.739724	−	1.28124i
$906$	6.02786	+	10.4406i	0.200262	+	0.346865i
$907$	52.9230			1.75728			0.878639	−	0.477486i	$-0.158452\pi$
$907$	52.9230			1.75728			0.878639	+	0.477486i	$0.158452\pi$
$908$	−16.7812	+	29.0658i	−0.556902	+	0.964583i
$909$	4.76393	−	8.25137i	0.158010	−	0.273681i
$910$	11.7812	−	20.4056i	0.390541	−	0.676438i
$911$	4.09017	+	7.08438i	0.135513	+	0.234716i	0.925793	−	0.378030i	$-0.123398\pi$
$911$	4.09017	+	7.08438i	0.135513	+	0.234716i	−0.790280	+	0.612746i	$0.790065\pi$
$912$	−4.63525	+	8.02850i	−0.153489	+	0.265850i
$913$	−1.56231	−	2.70599i	−0.0517048	−	0.0895553i
$914$	−9.72949			−0.321823
$915$	−18.1803			−0.601023
$916$	5.85410	+	10.1396i	0.193425	+	0.335022i
$917$	−0.135255	+	0.234268i	−0.00446651	+	0.00773622i
$918$	0.364745	+	0.631757i	0.0120384	+	0.0208511i
$919$	−4.93769	+	8.55234i	−0.162879	+	0.282116i	−0.935900	−	0.352265i	$-0.885412\pi$
$919$	−4.93769	+	8.55234i	−0.162879	+	0.282116i	0.773021	+	0.634381i	$0.218745\pi$
$920$	16.0172	−	27.7426i	0.528072	−	0.914648i
$921$	−3.04508	+	5.27424i	−0.100339	+	0.173792i
$922$	6.63932			0.218654
$923$	0.218847	+	0.379054i	0.00720344	+	0.0124767i
$924$	1.85410	+	3.21140i	0.0609955	+	0.105647i
$925$	0.218847	−	0.379054i	0.00719565	−	0.0124632i
$926$	−19.2361			−0.632136
$927$	−0.145898	−	0.252703i	−0.00479192	−	0.00829985i
$928$	−48.4164			−1.58935
$929$	−33.5410			−1.10045			−0.550223	−	0.835018i	$-0.685457\pi$
$929$	−33.5410			−1.10045			−0.550223	+	0.835018i	$0.685457\pi$
$930$		0			0
$931$	10.0000			0.327737
$932$	−30.4164			−0.996323
$933$	−8.23607	−	14.2653i	−0.269637	−	0.467025i
$934$	20.2574			0.662841
$935$	−0.236068	+	0.408882i	−0.00772025	+	0.0133719i
$936$	−10.8541	−	18.7999i	−0.354777	−	0.614493i
$937$	−20.2426	−	35.0613i	−0.661298	−	1.14540i	−0.980275	−	0.197640i	$-0.936672\pi$
$937$	−20.2426	−	35.0613i	−0.661298	−	1.14540i	0.318976	−	0.947763i	$-0.396661\pi$
$938$	7.85410			0.256446
$939$	0.618034	−	1.07047i	0.0201688	−	0.0349333i
$940$	7.16312	−	12.4069i	0.233635	−	0.404668i
$941$	14.2918	−	24.7541i	0.465899	−	0.806961i	−0.533342	−	0.845899i	$-0.679064\pi$
$941$	14.2918	−	24.7541i	0.465899	−	0.806961i	0.999242	+	0.0389383i	$0.0123976\pi$
$942$	3.00000	+	5.19615i	0.0977453	+	0.169300i
$943$	−17.7082	+	30.6715i	−0.576658	+	0.998802i
$944$	−8.78115	−	15.2094i	−0.285802	−	0.495024i
$945$	39.2705			1.27747
$946$	−2.18034			−0.0708890
$947$	11.0344	+	19.1122i	0.358571	+	0.621064i	0.987722	−	0.156219i	$-0.0499307\pi$
$947$	11.0344	+	19.1122i	0.358571	+	0.621064i	−0.629151	+	0.777283i	$0.716597\pi$
$948$		0			0
$949$	20.7812	+	35.9940i	0.674585	+	1.16842i
$950$	2.86475	−	4.96188i	0.0929446	−	0.160985i
$951$	−12.9443	+	22.4201i	−0.419747	+	0.727023i
$952$	0.791796	−	1.37143i	0.0256623	−	0.0444483i
$953$	−42.2148			−1.36747			−0.683735	−	0.729730i	$-0.739646\pi$
$953$	−42.2148			−1.36747			−0.683735	+	0.729730i	$0.739646\pi$
$954$	−7.85410	−	13.6037i	−0.254286	−	0.440436i
$955$	−21.0623	−	36.4810i	−0.681560	−	1.18050i
$956$	10.8541	−	18.7999i	0.351047	−	0.608031i
$957$	6.58359			0.212817
$958$	−2.76393	−	4.78727i	−0.0892986	−	0.154670i
$959$	19.4164			0.626989
$960$	0.618034			0.0199470
$961$		0			0
$962$	−0.708204			−0.0228334
$963$	−2.18034			−0.0702605
$964$	6.89919	+	11.9497i	0.222208	+	0.384875i
$965$	6.23607			0.200746
$966$	5.07295	−	8.78661i	0.163219	−	0.282704i
$967$	21.8262	+	37.8042i	0.701884	+	1.21570i	0.967804	+	0.251704i	$0.0809911\pi$
$967$	21.8262	+	37.8042i	0.701884	+	1.21570i	−0.265920	+	0.963995i	$0.585676\pi$
$968$	11.6459	+	20.1713i	0.374313	+	0.648330i
$969$	−1.18034			−0.0379180
$970$	4.28115	−	7.41517i	0.137460	−	0.238087i
$971$	10.2812	−	17.8075i	0.329938	−	0.571469i	−0.652561	−	0.757736i	$-0.726306\pi$
$971$	10.2812	−	17.8075i	0.329938	−	0.571469i	0.982499	+	0.186267i	$0.0596389\pi$
$972$	12.9443	−	22.4201i	0.415188	−	0.719126i
$973$	8.78115	+	15.2094i	0.281511	+	0.487591i
$974$	−7.08359	+	12.2691i	−0.226973	+	0.393129i
$975$	4.50000	+	7.79423i	0.144115	+	0.249615i
$976$	12.8754			0.412131
$977$	−6.06888			−0.194161			−0.0970804	−	0.995277i	$-0.530950\pi$
$977$	−6.06888			−0.194161			−0.0970804	+	0.995277i	$0.530950\pi$
$978$	−3.92705	−	6.80185i	−0.125573	−	0.217499i
$979$	−2.43769	+	4.22221i	−0.0779090	+	0.134942i
$980$	−4.23607	−	7.33708i	−0.135316	−	0.234375i
$981$	−8.41641	+	14.5776i	−0.268715	+	0.465428i
$982$	8.52786	−	14.7707i	0.272135	−	0.471352i
$983$	10.5172	−	18.2164i	0.335447	−	0.581012i	−0.648123	−	0.761535i	$-0.724446\pi$
$983$	10.5172	−	18.2164i	0.335447	−	0.581012i	0.983571	+	0.180524i	$0.0577792\pi$
$984$	14.4721			0.461355
$985$	−21.4894	−	37.2207i	−0.684708	−	1.18595i
$986$	−0.628677	−	1.08890i	−0.0200212	−	0.0346777i
$987$	5.07295	−	8.78661i	0.161474	−	0.279681i
$988$	39.2705			1.24936
$989$	−12.6353	−	21.8849i	−0.401778	−	0.695899i
$990$	−2.47214			−0.0785696
$991$	17.2705			0.548616			0.274308	−	0.961642i	$-0.411551\pi$
$991$	17.2705			0.548616			0.274308	+	0.961642i	$0.411551\pi$
$992$		0			0
$993$	−11.2705			−0.357659
$994$	−0.167184			−0.00530276
$995$	34.9615	+	60.5551i	1.10835	+	1.91973i
$996$	−6.61803			−0.209700
$997$	13.6246	−	23.5985i	0.431496	−	0.747373i	−0.565507	−	0.824744i	$-0.691319\pi$
$997$	13.6246	−	23.5985i	0.431496	−	0.747373i	0.997002	+	0.0773712i	$0.0246526\pi$
$998$	−1.28115	−	2.21902i	−0.0405542	−	0.0702419i
$999$	−0.590170	−	1.02220i	−0.0186722	−	0.0323411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.c.d.521.1		4
31.2	even	5		961.2.g.c.844.1		8
31.3	odd	30		31.2.d.a.8.1	yes	4
31.4	even	5		961.2.g.g.338.1		8
31.5	even	3	inner	961.2.c.d.439.1		4
31.6	odd	6		961.2.a.d.1.1		2
31.7	even	15		961.2.d.e.388.1		4
31.8	even	5		961.2.g.g.732.1		8
31.9	even	15		961.2.g.g.816.1		8
31.10	even	15		961.2.g.c.547.1		8
31.11	odd	30		961.2.g.f.235.1		8
31.12	odd	30		31.2.d.a.4.1	✓	4
31.13	odd	30		961.2.g.b.846.1		8
31.14	even	15		961.2.d.e.374.1		4
31.15	odd	10		961.2.g.b.448.1		8
31.16	even	5		961.2.g.c.448.1		8
31.17	odd	30		961.2.d.f.374.1		4
31.18	even	15		961.2.g.c.846.1		8
31.19	even	15		961.2.d.b.531.1		4
31.20	even	15		961.2.g.g.235.1		8
31.21	odd	30		961.2.g.b.547.1		8
31.22	odd	30		961.2.g.f.816.1		8
31.23	odd	10		961.2.g.f.732.1		8
31.24	odd	30		961.2.d.f.388.1		4
31.25	even	3		961.2.a.e.1.1		2
31.26	odd	6		961.2.c.f.439.1		4
31.27	odd	10		961.2.g.f.338.1		8
31.28	even	15		961.2.d.b.628.1		4
31.29	odd	10		961.2.g.b.844.1		8
31.30	odd	2		961.2.c.f.521.1		4
93.56	odd	6		8649.2.a.f.1.2		2
93.65	even	30		279.2.i.a.163.1		4
93.68	even	6		8649.2.a.g.1.2		2
93.74	even	30		279.2.i.a.190.1		4
124.3	even	30		496.2.n.b.225.1		4
124.43	even	30		496.2.n.b.97.1		4
155.3	even	60		775.2.bf.a.349.2		8
155.12	even	60		775.2.bf.a.624.2		8
155.34	odd	30		775.2.k.c.101.1		4
155.43	even	60		775.2.bf.a.624.1		8
155.74	odd	30		775.2.k.c.376.1		4
155.127	even	60		775.2.bf.a.349.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.d.a.4.1	✓	4	31.12	odd	30
31.2.d.a.8.1	yes	4	31.3	odd	30
279.2.i.a.163.1		4	93.65	even	30
279.2.i.a.190.1		4	93.74	even	30
496.2.n.b.97.1		4	124.43	even	30
496.2.n.b.225.1		4	124.3	even	30
775.2.k.c.101.1		4	155.34	odd	30
775.2.k.c.376.1		4	155.74	odd	30
775.2.bf.a.349.1		8	155.127	even	60
775.2.bf.a.349.2		8	155.3	even	60
775.2.bf.a.624.1		8	155.43	even	60
775.2.bf.a.624.2		8	155.12	even	60
961.2.a.d.1.1		2	31.6	odd	6
961.2.a.e.1.1		2	31.25	even	3
961.2.c.d.439.1		4	31.5	even	3	inner
961.2.c.d.521.1		4	1.1	even	1	trivial
961.2.c.f.439.1		4	31.26	odd	6
961.2.c.f.521.1		4	31.30	odd	2
961.2.d.b.531.1		4	31.19	even	15
961.2.d.b.628.1		4	31.28	even	15
961.2.d.e.374.1		4	31.14	even	15
961.2.d.e.388.1		4	31.7	even	15
961.2.d.f.374.1		4	31.17	odd	30
961.2.d.f.388.1		4	31.24	odd	30
961.2.g.b.448.1		8	31.15	odd	10
961.2.g.b.547.1		8	31.21	odd	30
961.2.g.b.844.1		8	31.29	odd	10
961.2.g.b.846.1		8	31.13	odd	30
961.2.g.c.448.1		8	31.16	even	5
961.2.g.c.547.1		8	31.10	even	15
961.2.g.c.844.1		8	31.2	even	5
961.2.g.c.846.1		8	31.18	even	15
961.2.g.f.235.1		8	31.11	odd	30
961.2.g.f.338.1		8	31.27	odd	10
961.2.g.f.732.1		8	31.23	odd	10
961.2.g.f.816.1		8	31.22	odd	30
961.2.g.g.235.1		8	31.20	even	15
961.2.g.g.338.1		8	31.4	even	5
961.2.g.g.732.1		8	31.8	even	5
961.2.g.g.816.1		8	31.9	even	15
8649.2.a.f.1.2		2	93.56	odd	6
8649.2.a.g.1.2		2	93.68	even	6

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.618034 q^{2} +(-0.500000 - 0.866025i) q^{3} -1.61803 q^{4} +(1.30902 - 2.26728i) q^{5} +(0.309017 + 0.535233i) q^{6} +(-1.50000 - 2.59808i) q^{7} +2.23607 q^{8} +(1.00000 - 1.73205i) q^{9} +(-0.809017 + 1.40126i) q^{10} +(-0.381966 + 0.661585i) q^{11} +(0.809017 + 1.40126i) q^{12} +(2.42705 - 4.20378i) q^{13} +(0.927051 + 1.60570i) q^{14} -2.61803 q^{15} +1.85410 q^{16} +(0.118034 + 0.204441i) q^{17} +(-0.618034 + 1.07047i) q^{18} +(-2.50000 - 4.33013i) q^{19} +(-2.11803 + 3.66854i) q^{20} +(-1.50000 + 2.59808i) q^{21} +(0.236068 - 0.408882i) q^{22} +5.47214 q^{23} +(-1.11803 - 1.93649i) q^{24} +(-0.927051 - 1.60570i) q^{25} +(-1.50000 + 2.59808i) q^{26} -5.00000 q^{27} +(2.42705 + 4.20378i) q^{28} +8.61803 q^{29} +1.61803 q^{30} -5.61803 q^{32} +0.763932 q^{33} +(-0.0729490 - 0.126351i) q^{34} -7.85410 q^{35} +(-1.61803 + 2.80252i) q^{36} +(0.118034 + 0.204441i) q^{37} +(1.54508 + 2.67617i) q^{38} -4.85410 q^{39} +(2.92705 - 5.06980i) q^{40} +(-3.23607 + 5.60503i) q^{41} +(0.927051 - 1.60570i) q^{42} +(-2.30902 - 3.99933i) q^{43} +(0.618034 - 1.07047i) q^{44} +(-2.61803 - 4.53457i) q^{45} -3.38197 q^{46} -3.38197 q^{47} +(-0.927051 - 1.60570i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(0.572949 + 0.992377i) q^{50} +(0.118034 - 0.204441i) q^{51} +(-3.92705 + 6.80185i) q^{52} +(-6.35410 + 11.0056i) q^{53} +3.09017 q^{54} +(1.00000 + 1.73205i) q^{55} +(-3.35410 - 5.80948i) q^{56} +(-2.50000 + 4.33013i) q^{57} -5.32624 q^{58} +(-4.73607 - 8.20311i) q^{59} +4.23607 q^{60} +6.94427 q^{61} -6.00000 q^{63} -0.236068 q^{64} +(-6.35410 - 11.0056i) q^{65} -0.472136 q^{66} +(2.11803 - 3.66854i) q^{67} +(-0.190983 - 0.330792i) q^{68} +(-2.73607 - 4.73901i) q^{69} +4.85410 q^{70} +(-0.0450850 + 0.0780895i) q^{71} +(2.23607 - 3.87298i) q^{72} +(-4.28115 + 7.41517i) q^{73} +(-0.0729490 - 0.126351i) q^{74} +(-0.927051 + 1.60570i) q^{75} +(4.04508 + 7.00629i) q^{76} +2.29180 q^{77} +3.00000 q^{78} +(2.42705 - 4.20378i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.00000 - 3.46410i) q^{82} +(-2.04508 + 3.54219i) q^{83} +(2.42705 - 4.20378i) q^{84} +0.618034 q^{85} +(1.42705 + 2.47172i) q^{86} +(-4.30902 - 7.46344i) q^{87} +(-0.854102 + 1.47935i) q^{88} +6.38197 q^{89} +(1.61803 + 2.80252i) q^{90} -14.5623 q^{91} -8.85410 q^{92} +2.09017 q^{94} -13.0902 q^{95} +(2.80902 + 4.86536i) q^{96} -5.29180 q^{97} +(0.618034 - 1.07047i) q^{98} +(0.763932 + 1.32317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 3 q^{5} - q^{6} - 6 q^{7} + 4 q^{9} - q^{10} - 6 q^{11} + q^{12} + 3 q^{13} - 3 q^{14} - 6 q^{15} - 6 q^{16} - 4 q^{17} + 2 q^{18} - 10 q^{19} - 4 q^{20} - 6 q^{21}+ \cdots + 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 3 * q^5 - q^6 - 6 * q^7 + 4 * q^9 - q^10 - 6 * q^11 + q^12 + 3 * q^13 - 3 * q^14 - 6 * q^15 - 6 * q^16 - 4 * q^17 + 2 * q^18 - 10 * q^19 - 4 * q^20 - 6 * q^21 - 8 * q^22 + 4 * q^23 + 3 * q^25 - 6 * q^26 - 20 * q^27 + 3 * q^28 + 30 * q^29 + 2 * q^30 - 18 * q^32 + 12 * q^33 - 7 * q^34 - 18 * q^35 - 2 * q^36 - 4 * q^37 - 5 * q^38 - 6 * q^39 + 5 * q^40 - 4 * q^41 - 3 * q^42 - 7 * q^43 - 2 * q^44 - 6 * q^45 - 18 * q^46 - 18 * q^47 + 3 * q^48 - 4 * q^49 + 9 * q^50 - 4 * q^51 - 9 * q^52 - 12 * q^53 - 10 * q^54 + 4 * q^55 - 10 * q^57 + 10 * q^58 - 10 * q^59 + 8 * q^60 - 8 * q^61 - 24 * q^63 + 8 * q^64 - 12 * q^65 + 16 * q^66 + 4 * q^67 - 3 * q^68 - 2 * q^69 + 6 * q^70 + 11 * q^71 + 3 * q^73 - 7 * q^74 + 3 * q^75 + 5 * q^76 + 36 * q^77 + 12 * q^78 + 3 * q^80 - 2 * q^81 + 8 * q^82 + 3 * q^83 + 3 * q^84 - 2 * q^85 - q^86 - 15 * q^87 + 10 * q^88 + 30 * q^89 + 2 * q^90 - 18 * q^91 - 22 * q^92 - 14 * q^94 - 30 * q^95 + 9 * q^96 - 48 * q^97 - 2 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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