LMFDB - Embedded newform 961.2.c.i.521.5

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 = [16,4,-3,16,-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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			521.5
Root			$-2.16544i$ of defining polynomial
Character	$\chi$	$=$	961.521
Dual form			961.2.c.i.439.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.23217 q^{2} +(1.03749 + 1.79698i) q^{3} -0.481752 q^{4} +(0.772811 - 1.33855i) q^{5} +(1.27836 + 2.21419i) q^{6} +(1.90188 + 3.29415i) q^{7} -3.05795 q^{8} +(-0.652760 + 1.13061i) q^{9} +(0.952237 - 1.64932i) q^{10} +(-1.88076 + 3.25758i) q^{11} +(-0.499811 - 0.865698i) q^{12} +(-1.31753 + 2.28203i) q^{13} +(2.34344 + 4.05896i) q^{14} +3.20713 q^{15} -2.80441 q^{16} +(1.88717 + 3.26867i) q^{17} +(-0.804313 + 1.39311i) q^{18} +(-3.04916 - 5.28130i) q^{19} +(-0.372303 + 0.644848i) q^{20} +(-3.94635 + 6.83528i) q^{21} +(-2.31742 + 4.01389i) q^{22} -0.909847 q^{23} +(-3.17258 - 5.49507i) q^{24} +(1.30553 + 2.26124i) q^{25} +(-1.62343 + 2.81186i) q^{26} +3.51600 q^{27} +(-0.916233 - 1.58696i) q^{28} +6.80859 q^{29} +3.95173 q^{30} +2.66037 q^{32} -7.80507 q^{33} +(2.32532 + 4.02757i) q^{34} +5.87917 q^{35} +(0.314468 - 0.544675i) q^{36} +(-0.907032 - 1.57103i) q^{37} +(-3.75709 - 6.50747i) q^{38} -5.46769 q^{39} +(-2.36321 + 4.09321i) q^{40} +(-0.168572 + 0.291976i) q^{41} +(-4.86258 + 8.42224i) q^{42} +(1.94200 + 3.36364i) q^{43} +(0.906060 - 1.56934i) q^{44} +(1.00892 + 1.74750i) q^{45} -1.12109 q^{46} -1.18915 q^{47} +(-2.90954 - 5.03948i) q^{48} +(-3.73429 + 6.46798i) q^{49} +(1.60863 + 2.78623i) q^{50} +(-3.91583 + 6.78242i) q^{51} +(0.634723 - 1.09937i) q^{52} +(-1.17206 + 2.03007i) q^{53} +4.33232 q^{54} +(2.90695 + 5.03498i) q^{55} +(-5.81584 - 10.0733i) q^{56} +(6.32692 - 10.9586i) q^{57} +8.38936 q^{58} +(-3.88942 - 6.73667i) q^{59} -1.54504 q^{60} +2.72343 q^{61} -4.96588 q^{63} +8.88686 q^{64} +(2.03641 + 3.52716i) q^{65} -9.61719 q^{66} +(3.71059 - 6.42693i) q^{67} +(-0.909147 - 1.57469i) q^{68} +(-0.943955 - 1.63498i) q^{69} +7.24416 q^{70} +(2.54909 - 4.41515i) q^{71} +(1.99610 - 3.45735i) q^{72} +(2.69587 - 4.66939i) q^{73} +(-1.11762 - 1.93577i) q^{74} +(-2.70893 + 4.69201i) q^{75} +(1.46894 + 2.54427i) q^{76} -14.3079 q^{77} -6.73714 q^{78} +(-4.86861 - 8.43268i) q^{79} +(-2.16728 + 3.75384i) q^{80} +(5.60609 + 9.71003i) q^{81} +(-0.207710 + 0.359765i) q^{82} +(-4.19757 + 7.27041i) q^{83} +(1.90116 - 3.29291i) q^{84} +5.83370 q^{85} +(2.39288 + 4.14458i) q^{86} +(7.06383 + 12.2349i) q^{87} +(5.75127 - 9.96149i) q^{88} -5.09560 q^{89} +(1.24316 + 2.15322i) q^{90} -10.0231 q^{91} +0.438320 q^{92} -1.46523 q^{94} -9.42569 q^{95} +(2.76010 + 4.78064i) q^{96} +10.9142 q^{97} +(-4.60129 + 7.96966i) q^{98} +(-2.45537 - 4.25283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 3 q^{3} + 16 q^{4} - 3 q^{5} - 11 q^{6} + 2 q^{7} - 18 q^{8} - 5 q^{9} + 13 q^{10} - 18 q^{11} - 8 q^{13} + 9 q^{14} + 36 q^{15} + 8 q^{16} - 14 q^{17} - 23 q^{18} + 6 q^{19} + 7 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 3 * q^3 + 16 * q^4 - 3 * q^5 - 11 * q^6 + 2 * q^7 - 18 * q^8 - 5 * q^9 + 13 * q^10 - 18 * q^11 - 8 * q^13 + 9 * q^14 + 36 * q^15 + 8 * q^16 - 14 * q^17 - 23 * q^18 + 6 * q^19 + 7 * q^20 + q^21 - 4 * q^22 + 44 * q^23 - 30 * q^24 - 13 * q^25 - 9 * q^26 + 36 * q^27 + 5 * q^28 + 24 * q^29 + 22 * q^30 - 42 * q^32 + 12 * q^33 + 7 * q^34 - 24 * q^35 + q^36 + 8 * q^37 - 7 * q^38 + 2 * q^39 - 11 * q^40 + 22 * q^41 + 6 * q^42 + 2 * q^43 - 4 * q^44 + 36 * q^46 - 36 * q^47 + q^48 + 2 * q^49 - 27 * q^50 - 2 * q^51 + q^52 - 6 * q^53 - 14 * q^54 - 28 * q^55 - 30 * q^56 + 17 * q^57 - 10 * q^58 + 4 * q^59 - 80 * q^60 + 60 * q^61 - 46 * q^63 + 18 * q^64 - 3 * q^65 + 20 * q^66 + 13 * q^67 - 30 * q^68 - 22 * q^69 - 78 * q^70 + q^71 - 3 * q^72 - 2 * q^73 - 8 * q^74 - 23 * q^75 + 33 * q^76 - 48 * q^77 - 8 * q^79 - 24 * q^80 + 28 * q^81 + 19 * q^82 - 39 * q^83 - 8 * q^84 - 52 * q^85 + 16 * q^86 + 15 * q^87 + 17 * q^88 + 54 * q^89 - 8 * q^90 + 32 * q^91 + 64 * q^92 + 44 * q^94 - 12 * q^95 + 12 * q^96 + 68 * q^97 - 10 * q^98 - 6 * 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 $

$2$	1.23217			0.871277			0.435639	−	0.900122i	$-0.356523\pi$
$2$	1.23217			0.871277			0.435639	+	0.900122i	$0.356523\pi$
$3$	1.03749	+	1.79698i	0.598994	+	1.03749i	0.992970	+	0.118367i	$0.0377659\pi$
$3$	1.03749	+	1.79698i	0.598994	+	1.03749i	−0.393976	+	0.919121i	$0.628901\pi$
$4$	−0.481752			−0.240876
$5$	0.772811	−	1.33855i	0.345612	−	0.598617i	−0.639853	−	0.768497i	$-0.721005\pi$
$5$	0.772811	−	1.33855i	0.345612	−	0.598617i	0.985465	+	0.169880i	$0.0543381\pi$
$6$	1.27836	+	2.21419i	0.521890	+	0.903939i
$7$	1.90188	+	3.29415i	0.718843	+	1.24507i	0.961459	+	0.274950i	$0.0886612\pi$
$7$	1.90188	+	3.29415i	0.718843	+	1.24507i	−0.242616	+	0.970122i	$0.578005\pi$
$8$	−3.05795			−1.08115
$9$	−0.652760	+	1.13061i	−0.217587	+	0.376871i
$10$	0.952237	−	1.64932i	0.301124	−	0.521562i
$11$	−1.88076	+	3.25758i	−0.567071	+	0.982196i	0.429783	+	0.902932i	$0.358590\pi$
$11$	−1.88076	+	3.25758i	−0.567071	+	0.982196i	−0.996854	+	0.0792636i	$0.974743\pi$
$12$	−0.499811	−	0.865698i	−0.144283	−	0.249906i
$13$	−1.31753	+	2.28203i	−0.365418	+	0.632922i	−0.988843	−	0.148961i	$-0.952407\pi$
$13$	−1.31753	+	2.28203i	−0.365418	+	0.632922i	0.623426	+	0.781883i	$0.285740\pi$
$14$	2.34344	+	4.05896i	0.626311	+	1.08480i
$15$	3.20713			0.828077
$16$	−2.80441			−0.701103
$17$	1.88717	+	3.26867i	0.457706	+	0.792770i	0.998839	−	0.0481669i	$-0.0153379\pi$
$17$	1.88717	+	3.26867i	0.457706	+	0.792770i	−0.541133	+	0.840937i	$0.682005\pi$
$18$	−0.804313	+	1.39311i	−0.189578	+	0.328359i
$19$	−3.04916	−	5.28130i	−0.699525	−	1.21161i	−0.968631	−	0.248502i	$-0.920062\pi$
$19$	−3.04916	−	5.28130i	−0.699525	−	1.21161i	0.269107	−	0.963110i	$-0.413272\pi$
$20$	−0.372303	+	0.644848i	−0.0832495	+	0.144192i
$21$	−3.94635	+	6.83528i	−0.861164	+	1.49158i
$22$	−2.31742	+	4.01389i	−0.494076	+	0.855765i
$23$	−0.909847			−0.189716			−0.0948581	−	0.995491i	$-0.530240\pi$
$23$	−0.909847			−0.189716			−0.0948581	+	0.995491i	$0.530240\pi$
$24$	−3.17258	−	5.49507i	−0.647600	−	1.12168i
$25$	1.30553	+	2.26124i	0.261105	+	0.452247i
$26$	−1.62343	+	2.81186i	−0.318380	+	0.551450i
$27$	3.51600			0.676655
$28$	−0.916233	−	1.58696i	−0.173152	−	0.299908i
$29$	6.80859			1.26432			0.632162	−	0.774836i	$-0.282168\pi$
$29$	6.80859			1.26432			0.632162	+	0.774836i	$0.282168\pi$
$30$	3.95173			0.721485
$31$		0			0
$31$		0			0
$32$	2.66037			0.470292
$33$	−7.80507			−1.35869
$34$	2.32532	+	4.02757i	0.398789	+	0.690722i
$35$	5.87917			0.993762
$36$	0.314468	−	0.544675i	0.0524114	−	0.0907792i
$37$	−0.907032	−	1.57103i	−0.149115	−	0.258275i	0.781786	−	0.623547i	$-0.214309\pi$
$37$	−0.907032	−	1.57103i	−0.149115	−	0.258275i	−0.930901	+	0.365272i	$0.880976\pi$
$38$	−3.75709	−	6.50747i	−0.609480	−	1.05565i
$39$	−5.46769			−0.875531
$40$	−2.36321	+	4.09321i	−0.373657	+	0.647193i
$41$	−0.168572	+	0.291976i	−0.0263266	+	0.0455990i	−0.878889	−	0.477027i	$-0.841714\pi$
$41$	−0.168572	+	0.291976i	−0.0263266	+	0.0455990i	0.852562	+	0.522626i	$0.175048\pi$
$42$	−4.86258	+	8.42224i	−0.750313	+	1.29958i
$43$	1.94200	+	3.36364i	0.296152	+	0.512950i	0.975252	−	0.221095i	$-0.0709632\pi$
$43$	1.94200	+	3.36364i	0.296152	+	0.512950i	−0.679100	+	0.734045i	$0.737630\pi$
$44$	0.906060	−	1.56934i	0.136594	−	0.236587i
$45$	1.00892	+	1.74750i	0.150401	+	0.260502i
$46$	−1.12109			−0.165295
$47$	−1.18915			−0.173455			−0.0867275	−	0.996232i	$-0.527641\pi$
$47$	−1.18915			−0.173455			−0.0867275	+	0.996232i	$0.527641\pi$
$48$	−2.90954	−	5.03948i	−0.419956	−	0.727386i
$49$	−3.73429	+	6.46798i	−0.533470	+	0.923997i
$50$	1.60863	+	2.78623i	0.227495	+	0.394033i
$51$	−3.91583	+	6.78242i	−0.548326	+	0.949728i
$52$	0.634723	−	1.09937i	0.0880202	−	0.152456i
$53$	−1.17206	+	2.03007i	−0.160995	+	0.278852i	−0.935226	−	0.354052i	$-0.884804\pi$
$53$	−1.17206	+	2.03007i	−0.160995	+	0.278852i	0.774231	+	0.632904i	$0.218137\pi$
$54$	4.33232			0.589554
$55$	2.90695	+	5.03498i	0.391973	+	0.678917i
$56$	−5.81584	−	10.0733i	−0.777175	−	1.34611i
$57$	6.32692	−	10.9586i	0.838022	−	1.45150i
$58$	8.38936			1.10158
$59$	−3.88942	−	6.73667i	−0.506359	−	0.877039i	−0.999973	−	0.00735816i	$-0.997658\pi$
$59$	−3.88942	−	6.73667i	−0.506359	−	0.877039i	0.493614	−	0.869681i	$-0.335676\pi$
$60$	−1.54504			−0.199464
$61$	2.72343			0.348700			0.174350	−	0.984684i	$-0.444218\pi$
$61$	2.72343			0.348700			0.174350	+	0.984684i	$0.444218\pi$
$62$		0			0
$63$	−4.96588			−0.625642
$64$	8.88686			1.11086
$65$	2.03641	+	3.52716i	0.252585	+	0.437490i
$66$	−9.61719			−1.18379
$67$	3.71059	−	6.42693i	0.453321	−	0.785175i	−0.545269	−	0.838261i	$-0.683573\pi$
$67$	3.71059	−	6.42693i	0.453321	−	0.785175i	0.998590	+	0.0530864i	$0.0169059\pi$
$68$	−0.909147	−	1.57469i	−0.110250	−	0.190959i
$69$	−0.943955	−	1.63498i	−0.113639	−	0.196828i
$70$	7.24416			0.865842
$71$	2.54909	−	4.41515i	0.302521	−	0.523982i	−0.674185	−	0.738562i	$-0.735505\pi$
$71$	2.54909	−	4.41515i	0.302521	−	0.523982i	0.976706	+	0.214580i	$0.0688383\pi$
$72$	1.99610	−	3.45735i	0.235243	−	0.407453i
$73$	2.69587	−	4.66939i	0.315528	−	0.546510i	−0.664022	−	0.747713i	$-0.731152\pi$
$73$	2.69587	−	4.66939i	0.315528	−	0.546510i	0.979550	+	0.201203i	$0.0644851\pi$
$74$	−1.11762	−	1.93577i	−0.129921	−	0.225029i
$75$	−2.70893	+	4.69201i	−0.312801	+	0.541786i
$76$	1.46894	+	2.54427i	0.168499	+	0.291848i
$77$	−14.3079			−1.63054
$78$	−6.73714			−0.762830
$79$	−4.86861	−	8.43268i	−0.547762	−	0.948751i	−0.998427	−	0.0560584i	$-0.982147\pi$
$79$	−4.86861	−	8.43268i	−0.547762	−	0.948751i	0.450666	−	0.892693i	$-0.351187\pi$
$80$	−2.16728	+	3.75384i	−0.242309	+	0.419692i
$81$	5.60609	+	9.71003i	0.622899	+	1.07889i
$82$	−0.207710	+	0.359765i	−0.0229377	+	0.0397293i
$83$	−4.19757	+	7.27041i	−0.460743	+	0.798031i	−0.998998	−	0.0447511i	$-0.985751\pi$
$83$	−4.19757	+	7.27041i	−0.460743	+	0.798031i	0.538255	+	0.842782i	$0.319084\pi$
$84$	1.90116	−	3.29291i	0.207434	−	0.359286i
$85$	5.83370			0.632754
$86$	2.39288	+	4.14458i	0.258030	+	0.446922i
$87$	7.06383	+	12.2349i	0.757322	+	1.31172i
$88$	5.75127	−	9.96149i	0.613087	−	1.06190i
$89$	−5.09560			−0.540132			−0.270066	−	0.962842i	$-0.587046\pi$
$89$	−5.09560			−0.540132			−0.270066	+	0.962842i	$0.587046\pi$
$90$	1.24316	+	2.15322i	0.131041	+	0.226970i
$91$	−10.0231			−1.05071
$92$	0.438320			0.0456980
$93$		0			0
$94$	−1.46523			−0.151127
$95$	−9.42569			−0.967056
$96$	2.76010	+	4.78064i	0.281702	+	0.487922i
$97$	10.9142			1.10817			0.554086	−	0.832460i	$-0.313068\pi$
$97$	10.9142			1.10817			0.554086	+	0.832460i	$0.313068\pi$
$98$	−4.60129	+	7.96966i	−0.464800	+	0.805057i
$99$	−2.45537	−	4.25283i	−0.246774	−	0.427426i
$100$	−0.628939	−	1.08935i	−0.0628939	−	0.108935i
$101$	−0.398727			−0.0396748			−0.0198374	−	0.999803i	$-0.506315\pi$
$101$	−0.398727			−0.0396748			−0.0198374	+	0.999803i	$0.506315\pi$
$102$	−4.82498	+	8.35710i	−0.477744	+	0.827477i
$103$	−1.63840	+	2.83779i	−0.161436	+	0.279616i	−0.935384	−	0.353633i	$-0.884946\pi$
$103$	−1.63840	+	2.83779i	−0.161436	+	0.279616i	0.773948	+	0.633250i	$0.218279\pi$
$104$	4.02894	−	6.97833i	0.395070	−	0.684281i
$105$	6.09957	+	10.5648i	0.595257	+	1.03102i
$106$	−1.44418	+	2.50140i	−0.140271	+	0.242957i
$107$	−1.57842	−	2.73391i	−0.152592	−	0.264297i	0.779588	−	0.626293i	$-0.215429\pi$
$107$	−1.57842	−	2.73391i	−0.152592	−	0.264297i	−0.932180	+	0.361996i	$0.882095\pi$
$108$	−1.69384			−0.162990
$109$	6.95622			0.666285			0.333142	−	0.942877i	$-0.391891\pi$
$109$	6.95622			0.666285			0.333142	+	0.942877i	$0.391891\pi$
$110$	3.58186	+	6.20397i	0.341517	+	0.591525i
$111$	1.88207	−	3.25984i	0.178638	−	0.309410i
$112$	−5.33365	−	9.23816i	−0.503983	−	0.872924i
$113$	7.62339	−	13.2041i	0.717148	−	1.24214i	−0.244977	−	0.969529i	$-0.578780\pi$
$113$	7.62339	−	13.2041i	0.717148	−	1.24214i	0.962125	−	0.272609i	$-0.0878864\pi$
$114$	7.79586	−	13.5028i	0.730149	−	1.26466i
$115$	−0.703140	+	1.21787i	−0.0655682	+	0.113567i
$116$	−3.28005			−0.304545
$117$	−1.72006	−	2.97924i	−0.159020	−	0.275431i
$118$	−4.79243	−	8.30073i	−0.441179	−	0.764144i
$119$	−7.17834	+	12.4332i	−0.658037	+	1.13975i
$120$	−9.80722			−0.895273
$121$	−1.57453	−	2.72717i	−0.143139	−	0.247925i
$122$	3.35574			0.303814
$123$	−0.699567			−0.0630778
$124$		0			0
$125$	11.7638			1.05219
$126$	−6.11882			−0.545108
$127$	−10.1132	−	17.5165i	−0.897400	−	1.55434i	−0.830806	−	0.556562i	$-0.812120\pi$
$127$	−10.1132	−	17.5165i	−0.897400	−	1.55434i	−0.0665942	−	0.997780i	$-0.521213\pi$
$128$	5.62940			0.497573
$129$	−4.02960	+	6.97946i	−0.354786	+	0.614508i
$130$	2.50920	+	4.34607i	0.220072	+	0.381175i
$131$	−6.32564	−	10.9563i	−0.552674	−	0.957259i	−0.998080	−	0.0619307i	$-0.980274\pi$
$131$	−6.32564	−	10.9563i	−0.552674	−	0.957259i	0.445407	−	0.895328i	$-0.353059\pi$
$132$	3.76010			0.327275
$133$	11.5983	−	20.0888i	1.00570	−	1.74192i
$134$	4.57209	−	7.91909i	0.394968	−	0.684105i
$135$	2.71721	−	4.70634i	0.233860	−	0.405057i
$136$	−5.77086	−	9.99543i	−0.494847	−	0.857101i
$137$	−4.93901	+	8.55461i	−0.421968	+	0.730870i	−0.996132	−	0.0878706i	$-0.971994\pi$
$137$	−4.93901	+	8.55461i	−0.421968	+	0.730870i	0.574164	+	0.818740i	$0.305327\pi$
$138$	−1.16311	−	2.01457i	−0.0990109	−	0.171492i
$139$	15.4990			1.31461			0.657303	−	0.753626i	$-0.271697\pi$
$139$	15.4990			1.31461			0.657303	+	0.753626i	$0.271697\pi$
$140$	−2.83230			−0.239373
$141$	−1.23373	−	2.13687i	−0.103898	−	0.179957i
$142$	3.14092	−	5.44023i	0.263580	−	0.456534i
$143$	−4.95593	−	8.58392i	−0.414435	−	0.717823i
$144$	1.83061	−	3.17071i	0.152551	−	0.264226i
$145$	5.26176	−	9.11363i	0.436965	−	0.756846i
$146$	3.32178	−	5.75349i	0.274912	−	0.476162i
$147$	−15.4971			−1.27818
$148$	0.436964	+	0.756844i	0.0359182	+	0.0622122i
$149$	7.62162	+	13.2010i	0.624388	+	1.08147i	0.988659	+	0.150178i	$0.0479848\pi$
$149$	7.62162	+	13.2010i	0.624388	+	1.08147i	−0.364271	+	0.931293i	$0.618682\pi$
$150$	−3.33787	+	5.78136i	−0.272536	+	0.472046i
$151$	0.261828			0.0213073			0.0106536	−	0.999943i	$-0.496609\pi$
$151$	0.261828			0.0213073			0.0106536	+	0.999943i	$0.496609\pi$
$152$	9.32416	+	16.1499i	0.756289	+	1.30993i
$153$	−4.92748			−0.398363
$154$	−17.6298			−1.42065
$155$		0			0
$156$	2.63407			0.210894
$157$	15.9265			1.27108			0.635538	−	0.772070i	$-0.280778\pi$
$157$	15.9265			1.27108			0.635538	+	0.772070i	$0.280778\pi$
$158$	−5.99897	−	10.3905i	−0.477252	−	0.826625i
$159$	−4.86400			−0.385740
$160$	2.05597	−	3.56104i	0.162538	−	0.281525i
$161$	−1.73042	−	2.99717i	−0.136376	−	0.236210i
$162$	6.90767	+	11.9644i	0.542718	+	0.940014i
$163$	−0.133175			−0.0104311			−0.00521555	−	0.999986i	$-0.501660\pi$
$163$	−0.133175			−0.0104311			−0.00521555	+	0.999986i	$0.501660\pi$
$164$	0.0812100	−	0.140660i	0.00634143	−	0.0109837i
$165$	−6.03185	+	10.4475i	−0.469579	+	0.813334i
$166$	−5.17213	+	8.95840i	−0.401435	+	0.695306i
$167$	−1.97439	−	3.41974i	−0.152783	−	0.264628i	0.779467	−	0.626444i	$-0.215490\pi$
$167$	−1.97439	−	3.41974i	−0.152783	−	0.264628i	−0.932250	+	0.361816i	$0.882157\pi$
$168$	12.0677	−	20.9019i	0.931045	−	1.61262i
$169$	3.02822	+	5.24503i	0.232940	+	0.403464i
$170$	7.18813			0.551304
$171$	7.96147			0.608829
$172$	−0.935560	−	1.62044i	−0.0713358	−	0.123557i
$173$	7.22847	−	12.5201i	0.549570	−	0.951884i	−0.448733	−	0.893666i	$-0.648125\pi$
$173$	7.22847	−	12.5201i	0.549570	−	0.951884i	0.998304	−	0.0582182i	$-0.0185419\pi$
$174$	8.70385	+	15.0755i	0.659837	+	1.14287i
$175$	−4.96590	+	8.60120i	−0.375387	+	0.650189i
$176$	5.27443	−	9.13559i	0.397575	−	0.688621i
$177$	8.07044	−	13.9784i	0.606611	−	1.05068i
$178$	−6.27865			−0.470605
$179$	−8.85994	−	15.3459i	−0.662223	−	1.14700i	−0.980030	−	0.198849i	$-0.936280\pi$
$179$	−8.85994	−	15.3459i	−0.662223	−	1.14700i	0.317807	−	0.948155i	$-0.397054\pi$
$180$	−0.486049	−	0.841862i	−0.0362280	−	0.0627487i
$181$	−6.02958	+	10.4435i	−0.448175	+	0.776262i	−0.998267	−	0.0588418i	$-0.981259\pi$
$181$	−6.02958	+	10.4435i	−0.448175	+	0.776262i	0.550092	+	0.835104i	$0.314593\pi$
$182$	−12.3502			−0.915461
$183$	2.82553	+	4.89396i	0.208869	+	0.361772i
$184$	2.78226			0.205111
$185$	−2.80386			−0.206144
$186$		0			0
$187$	−14.1973			−1.03821
$188$	0.572874			0.0417811
$189$	6.68701	+	11.5822i	0.486409	+	0.842484i
$190$	−11.6141			−0.842574
$191$	−2.53576	+	4.39207i	−0.183481	+	0.317799i	−0.943064	−	0.332612i	$-0.892070\pi$
$191$	−2.53576	+	4.39207i	−0.183481	+	0.317799i	0.759583	+	0.650411i	$0.225403\pi$
$192$	9.22001	+	15.9695i	0.665397	+	1.15250i
$193$	10.0209	+	17.3567i	0.721318	+	1.24936i	0.960472	+	0.278378i	$0.0897968\pi$
$193$	10.0209	+	17.3567i	0.721318	+	1.24936i	−0.239153	+	0.970982i	$0.576870\pi$
$194$	13.4482			0.965525
$195$	−4.22549	+	7.31877i	−0.302594	+	0.524108i
$196$	1.79900	−	3.11596i	0.128500	−	0.222568i
$197$	10.8542	−	18.8000i	0.773328	−	1.33944i	−0.162401	−	0.986725i	$-0.551924\pi$
$197$	10.8542	−	18.8000i	0.773328	−	1.33944i	0.935729	−	0.352719i	$-0.114743\pi$
$198$	−3.02544	−	5.24022i	−0.215009	−	0.372406i
$199$	7.58275	−	13.1337i	0.537527	−	0.931024i	−0.461509	−	0.887135i	$-0.652692\pi$
$199$	7.58275	−	13.1337i	0.537527	−	0.931024i	0.999036	−	0.0438890i	$-0.0139748\pi$
$200$	−3.99222	−	6.91474i	−0.282293	−	0.488946i
$201$	15.3988			1.08615
$202$	−0.491300			−0.0345678
$203$	12.9491	+	22.4285i	0.908850	+	1.57417i
$204$	1.88646	−	3.26744i	0.132078	−	0.228767i
$205$	0.260549	+	0.451284i	0.0181975	+	0.0315191i
$206$	−2.01879	+	3.49665i	−0.140656	+	0.243623i
$207$	0.593912	−	1.02869i	0.0412797	−	0.0714986i
$208$	3.69490	−	6.39976i	0.256195	−	0.443743i
$209$	22.9390			1.58672
$210$	7.51572	+	13.0176i	0.518634	+	0.898300i
$211$	−3.15220	−	5.45978i	−0.217007	−	0.375867i	0.736885	−	0.676018i	$-0.236296\pi$
$211$	−3.15220	−	5.45978i	−0.217007	−	0.375867i	−0.953891	+	0.300152i	$0.902963\pi$
$212$	0.564643	−	0.977990i	0.0387798	−	0.0671687i
$213$	10.5786			0.724833
$214$	−1.94489	−	3.36865i	−0.132950	−	0.230276i
$215$	6.00319			0.409414
$216$	−10.7517			−0.731564
$217$		0			0
$218$	8.57126			0.580519
$219$	11.1877			0.755997
$220$	−1.40043	−	2.42561i	−0.0944168	−	0.163535i
$221$	−9.94562			−0.669015
$222$	2.31903	−	4.01668i	0.155643	−	0.269582i
$223$	3.69455	+	6.39915i	0.247406	+	0.428519i	0.962805	−	0.270196i	$-0.0870887\pi$
$223$	3.69455	+	6.39915i	0.247406	+	0.428519i	−0.715400	+	0.698716i	$0.753755\pi$
$224$	5.05971	+	8.76367i	0.338066	+	0.585547i
$225$	−3.40878			−0.227252
$226$	9.39333	−	16.2697i	0.624835	−	1.08225i
$227$	−9.61989	+	16.6621i	−0.638495	+	1.10591i	0.347269	+	0.937766i	$0.387109\pi$
$227$	−9.61989	+	16.6621i	−0.638495	+	1.10591i	−0.985763	+	0.168140i	$0.946224\pi$
$228$	−3.04801	+	5.27930i	−0.201859	+	0.349630i
$229$	−3.04355	−	5.27159i	−0.201124	−	0.348356i	0.747767	−	0.663961i	$-0.231126\pi$
$229$	−3.04355	−	5.27159i	−0.201124	−	0.348356i	−0.948891	+	0.315605i	$0.897793\pi$
$230$	−0.866390	+	1.50063i	−0.0571280	+	0.0989487i
$231$	−14.8443	−	25.7111i	−0.976683	−	1.69166i
$232$	−20.8203			−1.36692
$233$	17.5280			1.14830			0.574150	−	0.818750i	$-0.305333\pi$
$233$	17.5280			1.14830			0.574150	+	0.818750i	$0.305333\pi$
$234$	−2.11942	−	3.67094i	−0.138551	−	0.239977i
$235$	−0.918986	+	1.59173i	−0.0599481	+	0.103833i
$236$	1.87373	+	3.24540i	0.121970	+	0.211257i
$237$	10.1022	−	17.4976i	0.656212	−	1.13659i
$238$	−8.84495	+	15.3199i	−0.573333	+	0.993042i
$239$	−13.9560	+	24.1725i	−0.902740	+	1.56359i	−0.0788174	+	0.996889i	$0.525114\pi$
$239$	−13.9560	+	24.1725i	−0.902740	+	1.56359i	−0.823923	+	0.566702i	$0.808219\pi$
$240$	−8.99411			−0.580567
$241$	11.3749	+	19.7018i	0.732720	+	1.26911i	0.955717	+	0.294289i	$0.0950827\pi$
$241$	11.3749	+	19.7018i	0.732720	+	1.26911i	−0.222997	+	0.974819i	$0.571584\pi$
$242$	−1.94010	−	3.36034i	−0.124714	−	0.216011i
$243$	−6.35849	+	11.0132i	−0.407897	+	0.706499i
$244$	−1.31202			−0.0839933
$245$	5.77180	+	9.99705i	0.368747	+	0.638688i
$246$	−0.861987			−0.0549583
$247$	16.0694			1.02247
$248$		0			0
$249$	−17.4197			−1.10393
$250$	14.4950			0.916747
$251$	−8.11725	−	14.0595i	−0.512356	−	0.887427i	−0.999897	−	0.0143270i	$-0.995439\pi$
$251$	−8.11725	−	14.0595i	−0.512356	−	0.887427i	0.487541	−	0.873100i	$-0.337894\pi$
$252$	2.39232			0.150702
$253$	1.71121	−	2.96390i	0.107583	−	0.186339i
$254$	−12.4612	−	21.5834i	−0.781884	−	1.35426i
$255$	6.05239	+	10.4831i	0.379016	+	0.656474i
$256$	−10.8373			−0.677333
$257$	−11.6761	+	20.2235i	−0.728332	+	1.26151i	0.229256	+	0.973366i	$0.426371\pi$
$257$	−11.6761	+	20.2235i	−0.728332	+	1.26151i	−0.957588	+	0.288142i	$0.906963\pi$
$258$	−4.96516	+	8.59990i	−0.309117	+	0.535407i
$259$	3.45013	−	5.97580i	0.214381	−	0.371318i
$260$	−0.981042	−	1.69921i	−0.0608417	−	0.105381i
$261$	−4.44438	+	7.69789i	−0.275100	+	0.476487i
$262$	−7.79428	−	13.5001i	−0.481532	−	0.834038i
$263$	10.3944			0.640944			0.320472	−	0.947258i	$-0.396159\pi$
$263$	10.3944			0.640944			0.320472	+	0.947258i	$0.396159\pi$
$264$	23.8675			1.46894
$265$	1.81157	+	3.13773i	0.111284	+	0.192749i
$266$	14.2911	−	24.7528i	0.876240	−	1.51769i
$267$	−5.28662	−	9.15669i	−0.323536	−	0.560380i
$268$	−1.78758	+	3.09618i	−0.109194	+	0.189130i
$269$	−2.20902	+	3.82614i	−0.134686	+	0.233284i	−0.925478	−	0.378802i	$-0.876336\pi$
$269$	−2.20902	+	3.82614i	−0.134686	+	0.233284i	0.790791	+	0.612086i	$0.209669\pi$
$270$	3.34807	−	5.79902i	0.203757	−	0.352917i
$271$	−6.15286			−0.373760			−0.186880	−	0.982383i	$-0.559838\pi$
$271$	−6.15286			−0.373760			−0.186880	+	0.982383i	$0.559838\pi$
$272$	−5.29240	−	9.16671i	−0.320899	−	0.555813i
$273$	−10.3989	−	18.0114i	−0.629369	−	1.09010i
$274$	−6.08571	+	10.5408i	−0.367651	+	0.636790i
$275$	−9.82153			−0.592261
$276$	0.454752	+	0.787653i	0.0273728	+	0.0474111i
$277$	−22.0474			−1.32470			−0.662350	−	0.749194i	$-0.730441\pi$
$277$	−22.0474			−1.32470			−0.662350	+	0.749194i	$0.730441\pi$
$278$	19.0974			1.14539
$279$		0			0
$280$	−17.9782			−1.07440
$281$	−30.7736			−1.83580			−0.917899	−	0.396815i	$-0.870115\pi$
$281$	−30.7736			−1.83580			−0.917899	+	0.396815i	$0.870115\pi$
$282$	−1.52016	−	2.63300i	−0.0905243	−	0.156793i
$283$	−21.3453			−1.26884			−0.634422	−	0.772987i	$-0.718762\pi$
$283$	−21.3453			−1.26884			−0.634422	+	0.772987i	$0.718762\pi$
$284$	−1.22803	+	2.12701i	−0.0728701	+	0.126215i
$285$	−9.77904	−	16.9378i	−0.579260	−	1.00331i
$286$	−6.10656	−	10.5769i	−0.361088	−	0.625423i
$287$	−1.28242			−0.0756987
$288$	−1.73658	+	3.00785i	−0.102329	+	0.177239i
$289$	1.37718	−	2.38535i	0.0810107	−	0.140315i
$290$	6.48339	−	11.2296i	0.380718	−	0.659422i
$291$	11.3234	+	19.6126i	0.663788	+	1.14971i
$292$	−1.29874	+	2.24948i	−0.0760030	+	0.131641i
$293$	0.899514	+	1.55800i	0.0525501	+	0.0910195i	0.891104	−	0.453799i	$-0.149932\pi$
$293$	0.899514	+	1.55800i	0.0525501	+	0.0910195i	−0.838554	+	0.544819i	$0.816598\pi$
$294$	−19.0951			−1.11365
$295$	−12.0231			−0.700014
$296$	2.77365	+	4.80411i	0.161215	+	0.279233i
$297$	−6.61276	+	11.4536i	−0.383712	+	0.664608i
$298$	9.39115	+	16.2660i	0.544015	+	0.942261i
$299$	1.19875	−	2.07630i	0.0693256	−	0.120076i
$300$	1.30503	−	2.26038i	0.0753461	−	0.130503i
$301$	−7.38689	+	12.7945i	−0.425773	+	0.737461i
$302$	0.322617			0.0185645
$303$	−0.413674	−	0.716505i	−0.0237650	−	0.0411621i
$304$	8.55109	+	14.8109i	0.490439	+	0.849465i
$305$	2.10470	−	3.64545i	0.120515	−	0.208738i
$306$	−6.07150			−0.347085
$307$	−13.3847	−	23.1830i	−0.763905	−	1.32312i	−0.940823	−	0.338897i	$-0.889946\pi$
$307$	−13.3847	−	23.1830i	−0.763905	−	1.32312i	0.176918	−	0.984226i	$-0.443387\pi$
$308$	6.89287			0.392758
$309$	−6.79928			−0.386798
$310$		0			0
$311$	4.18114			0.237090			0.118545	−	0.992949i	$-0.462177\pi$
$311$	4.18114			0.237090			0.118545	+	0.992949i	$0.462177\pi$
$312$	16.7199			0.946578
$313$	−5.67141	−	9.82318i	−0.320567	−	0.555239i	0.660038	−	0.751232i	$-0.270540\pi$
$313$	−5.67141	−	9.82318i	−0.320567	−	0.555239i	−0.980605	+	0.195993i	$0.937207\pi$
$314$	19.6242			1.10746
$315$	−3.83769	+	6.64708i	−0.216229	+	0.374520i
$316$	2.34546	+	4.06246i	0.131943	+	0.228531i
$317$	−12.9407	−	22.4139i	−0.726820	−	1.25889i	−0.958220	−	0.286031i	$-0.907664\pi$
$317$	−12.9407	−	22.4139i	−0.726820	−	1.25889i	0.231400	−	0.972859i	$-0.425669\pi$
$318$	−5.99329			−0.336087
$319$	−12.8053	+	22.1795i	−0.716961	+	1.24181i
$320$	6.86787	−	11.8955i	0.383925	−	0.664978i
$321$	3.27519	−	5.67279i	0.182803	−	0.316624i
$322$	−2.13217	−	3.69303i	−0.118821	−	0.205805i
$323$	11.5086	−	19.9334i	0.640353	−	1.10912i
$324$	−2.70074	−	4.67782i	−0.150041	−	0.259879i
$325$	−6.88028			−0.381649
$326$	−0.164095			−0.00908838
$327$	7.21699	+	12.5002i	0.399100	+	0.691262i
$328$	0.515485	−	0.892846i	0.0284629	−	0.0492992i
$329$	−2.26161	−	3.91723i	−0.124687	−	0.215964i
$330$	−7.43227	+	12.8731i	−0.409133	+	0.708639i
$331$	0.382894	−	0.663192i	0.0210457	−	0.0364523i	−0.855311	−	0.518115i	$-0.826634\pi$
$331$	0.382894	−	0.663192i	0.0210457	−	0.0364523i	0.876356	+	0.481663i	$0.159967\pi$
$332$	2.02219	−	3.50253i	0.110982	−	0.192226i
$333$	2.36830			0.129782
$334$	−2.43279	−	4.21371i	−0.133116	−	0.230564i
$335$	−5.73517	−	9.93361i	−0.313346	−	0.542731i
$336$	11.0672	−	19.1689i	0.603765	−	1.04575i
$337$	−2.39434			−0.130428			−0.0652140	−	0.997871i	$-0.520773\pi$
$337$	−2.39434			−0.130428			−0.0652140	+	0.997871i	$0.520773\pi$
$338$	3.73129	+	6.46278i	0.202955	+	0.351529i
$339$	31.6367			1.71827
$340$	−2.81040			−0.152415
$341$		0			0
$342$	9.80991			0.530459
$343$	−1.78235			−0.0962378
$344$	−5.93852	−	10.2858i	−0.320184	−	0.554574i
$345$	−2.91800			−0.157100
$346$	8.90672	−	15.4269i	0.478828	−	0.829355i
$347$	2.82890	+	4.89980i	0.151863	+	0.263035i	0.931912	−	0.362683i	$-0.118139\pi$
$347$	2.82890	+	4.89980i	0.151863	+	0.263035i	−0.780049	+	0.625718i	$0.784806\pi$
$348$	−3.40301	−	5.89419i	−0.182420	−	0.315962i
$349$	29.0676			1.55595			0.777977	−	0.628293i	$-0.216246\pi$
$349$	29.0676			1.55595			0.777977	+	0.628293i	$0.216246\pi$
$350$	−6.11885	+	10.5982i	−0.327066	+	0.566495i
$351$	−4.63244	+	8.02363i	−0.247262	+	0.428270i
$352$	−5.00353	+	8.66636i	−0.266689	+	0.461919i
$353$	−9.63760	−	16.6928i	−0.512958	−	0.888469i	−0.999887	−	0.0150275i	$-0.995216\pi$
$353$	−9.63760	−	16.6928i	−0.512958	−	0.888469i	0.486929	−	0.873441i	$-0.338117\pi$
$354$	9.94417	−	17.2238i	0.528527	−	0.915435i
$355$	−3.93993	−	6.82416i	−0.209110	−	0.362189i
$356$	2.45481			0.130105
$357$	−29.7897			−1.57664
$358$	−10.9170	−	18.9088i	−0.576980	−	0.999359i
$359$	−5.17214	+	8.95840i	−0.272975	+	0.472806i	−0.969622	−	0.244607i	$-0.921341\pi$
$359$	−5.17214	+	8.95840i	−0.272975	+	0.472806i	0.696647	+	0.717414i	$0.254674\pi$
$360$	−3.08522	−	5.34377i	−0.162606	−	0.281641i
$361$	−9.09472	+	15.7525i	−0.478669	+	0.829080i
$362$	−7.42948	+	12.8682i	−0.390485	+	0.676340i
$363$	3.26712	−	5.65881i	0.171479	−	0.297010i
$364$	4.82867			0.253091
$365$	−4.16680	−	7.21711i	−0.218100	−	0.377761i
$366$	3.48154	+	6.03020i	0.181983	+	0.315203i
$367$	−0.0682819	+	0.118268i	−0.00356428	+	0.00617352i	−0.867802	−	0.496910i	$-0.834468\pi$
$367$	−0.0682819	+	0.118268i	−0.00356428	+	0.00617352i	0.864238	+	0.503084i	$0.167801\pi$
$368$	2.55159			0.133011
$369$	−0.220075	−	0.381180i	−0.0114566	−	0.0198435i
$370$	−3.45484			−0.179608
$371$	−8.91649			−0.462921
$372$		0			0
$373$	−7.36393			−0.381290			−0.190645	−	0.981659i	$-0.561058\pi$
$373$	−7.36393			−0.381290			−0.190645	+	0.981659i	$0.561058\pi$
$374$	−17.4935			−0.904566
$375$	12.2048	+	21.1393i	0.630254	+	1.09163i
$376$	3.63635			0.187530
$377$	−8.97053	+	15.5374i	−0.462006	+	0.800218i
$378$	8.23955	+	14.2713i	0.423797	+	0.734038i
$379$	2.30407	+	3.99076i	0.118352	+	0.204992i	0.919115	−	0.393990i	$-0.128906\pi$
$379$	2.30407	+	3.99076i	0.118352	+	0.204992i	−0.800763	+	0.598982i	$0.795572\pi$
$380$	4.54084			0.232940
$381$	20.9846	−	36.3464i	1.07507	−	1.86208i
$382$	−3.12449	+	5.41178i	−0.159863	+	0.276891i
$383$	−16.1474	+	27.9681i	−0.825093	+	1.42910i	0.0767550	+	0.997050i	$0.475544\pi$
$383$	−16.1474	+	27.9681i	−0.825093	+	1.42910i	−0.901848	+	0.432053i	$0.857789\pi$
$384$	5.84043	+	10.1159i	0.298043	+	0.516226i
$385$	−11.0573	+	19.1519i	−0.563534	+	0.976069i
$386$	12.3474	+	21.3864i	0.628468	+	1.08854i
$387$	−5.07063			−0.257755
$388$	−5.25794			−0.266932
$389$	−17.6356	−	30.5458i	−0.894162	−	1.54873i	−0.834838	−	0.550496i	$-0.814439\pi$
$389$	−17.6356	−	30.5458i	−0.894162	−	1.54873i	−0.0593242	−	0.998239i	$-0.518895\pi$
$390$	−5.20653	+	9.01798i	−0.263643	+	0.456643i
$391$	−1.71704	−	2.97399i	−0.0868342	−	0.150401i
$392$	11.4192	−	19.7787i	0.576759	−	0.998976i
$393$	13.1255	−	22.7341i	0.662096	−	1.14678i
$394$	13.3742	−	23.1648i	0.673783	−	1.16703i
$395$	−15.0501			−0.757252
$396$	1.18288	+	2.04881i	0.0594419	+	0.102956i
$397$	2.01701	+	3.49356i	0.101231	+	0.175337i	0.912192	−	0.409763i	$-0.134389\pi$
$397$	2.01701	+	3.49356i	0.101231	+	0.175337i	−0.810961	+	0.585100i	$0.801055\pi$
$398$	9.34326	−	16.1830i	0.468335	−	0.811181i
$399$	48.1322			2.40962
$400$	−3.66123	−	6.34144i	−0.183062	−	0.317072i
$401$	−24.8832			−1.24261			−0.621304	−	0.783570i	$-0.713397\pi$
$401$	−24.8832			−1.24261			−0.621304	+	0.783570i	$0.713397\pi$
$402$	18.9739			0.946334
$403$		0			0
$404$	0.192087			0.00955671
$405$	17.3298			0.861124
$406$	15.9555	+	27.6358i	0.791860	+	1.37154i
$407$	6.82365			0.338236
$408$	11.9744	−	20.7403i	0.592821	−	1.02680i
$409$	1.75361	+	3.03734i	0.0867105	+	0.150187i	0.906119	−	0.423023i	$-0.139031\pi$
$409$	1.75361	+	3.03734i	0.0867105	+	0.150187i	−0.819408	+	0.573210i	$0.805698\pi$
$410$	0.321042	+	0.556060i	0.0158551	+	0.0274619i
$411$	−20.4966			−1.01102
$412$	0.789302	−	1.36711i	0.0388861	−	0.0673528i
$413$	14.7944	−	25.6246i	0.727985	−	1.26091i
$414$	0.731802	−	1.26752i	0.0359661	−	0.0622951i
$415$	6.48786	+	11.2373i	0.318477	+	0.551618i
$416$	−3.50512	+	6.07105i	−0.171853	+	0.297658i
$417$	16.0800	+	27.8514i	0.787441	+	1.36389i
$418$	28.2647			1.38247
$419$	4.12031			0.201290			0.100645	−	0.994922i	$-0.467909\pi$
$419$	4.12031			0.201290			0.100645	+	0.994922i	$0.467909\pi$
$420$	−2.93848	−	5.08959i	−0.143383	−	0.248347i
$421$	−13.8007	+	23.9035i	−0.672605	+	1.16499i	0.304558	+	0.952494i	$0.401491\pi$
$421$	−13.8007	+	23.9035i	−0.672605	+	1.16499i	−0.977163	+	0.212492i	$0.931842\pi$
$422$	−3.88406	−	6.72739i	−0.189073	−	0.327484i
$423$	0.776228	−	1.34447i	0.0377415	−	0.0653702i
$424$	3.58410	−	6.20785i	0.174059	−	0.301480i
$425$	−4.92750	+	8.53467i	−0.239019	+	0.413992i
$426$	13.0347			0.631531
$427$	5.17964	+	8.97140i	0.250660	+	0.434156i
$428$	0.760408	+	1.31706i	0.0367557	+	0.0636627i
$429$	10.2834	−	17.8114i	0.496488	−	0.859943i
$430$	7.39697			0.356713
$431$	7.43697	+	12.8812i	0.358226	+	0.620466i	0.987665	−	0.156584i	$-0.0500483\pi$
$431$	7.43697	+	12.8812i	0.358226	+	0.620466i	−0.629438	+	0.777050i	$0.716715\pi$
$432$	−9.86032			−0.474405
$433$	−9.26195			−0.445101			−0.222550	−	0.974921i	$-0.571438\pi$
$433$	−9.26195			−0.445101			−0.222550	+	0.974921i	$0.571438\pi$
$434$		0			0
$435$	21.8360			1.04696
$436$	−3.35117			−0.160492
$437$	2.77427	+	4.80517i	0.132711	+	0.229863i
$438$	13.7852			0.658683
$439$	−8.85909	+	15.3444i	−0.422821	+	0.732348i	−0.996214	−	0.0869324i	$-0.972294\pi$
$439$	−8.85909	+	15.3444i	−0.422821	+	0.732348i	0.573393	+	0.819281i	$0.305627\pi$
$440$	−8.88929	−	15.3967i	−0.423780	−	0.734009i
$441$	−4.87519	−	8.44407i	−0.232152	−	0.402099i
$442$	−12.2547			−0.582898
$443$	9.22512	−	15.9784i	0.438299	−	0.759155i	−0.559260	−	0.828992i	$-0.688915\pi$
$443$	9.22512	−	15.9784i	0.438299	−	0.759155i	0.997558	+	0.0698371i	$0.0222479\pi$
$444$	−0.906689	+	1.57043i	−0.0430296	+	0.0745294i
$445$	−3.93794	+	6.82070i	−0.186676	+	0.323332i
$446$	4.55233	+	7.88486i	0.215559	+	0.373359i
$447$	−15.8147	+	27.3918i	−0.748009	+	1.29559i
$448$	16.9017	+	29.2747i	0.798532	+	1.38310i
$449$	−22.7102			−1.07176			−0.535881	−	0.844294i	$-0.680020\pi$
$449$	−22.7102			−1.07176			−0.535881	+	0.844294i	$0.680020\pi$
$450$	−4.20020			−0.197999
$451$	−0.634089	−	1.09827i	−0.0298581	−	0.0517157i
$452$	−3.67258	+	6.36110i	−0.172744	+	0.299201i
$453$	0.271643	+	0.470500i	0.0127629	+	0.0221060i
$454$	−11.8534	+	20.5306i	−0.556306	+	0.963550i
$455$	−7.74600	+	13.4165i	−0.363138	+	0.628974i
$456$	−19.3474	+	33.5107i	−0.906025	+	1.56928i
$457$	16.1619			0.756020			0.378010	−	0.925802i	$-0.376608\pi$
$457$	16.1619			0.756020			0.378010	+	0.925802i	$0.376608\pi$
$458$	−3.75018	−	6.49550i	−0.175234	−	0.303515i
$459$	6.63529	+	11.4927i	0.309709	+	0.536432i
$460$	0.338739	−	0.586713i	0.0157938	−	0.0273556i
$461$	−21.5388			−1.00316			−0.501580	−	0.865111i	$-0.667248\pi$
$461$	−21.5388			−1.00316			−0.501580	+	0.865111i	$0.667248\pi$
$462$	−18.2907	−	31.6805i	−0.850962	−	1.47391i
$463$	17.5098			0.813750			0.406875	−	0.913484i	$-0.366619\pi$
$463$	17.5098			0.813750			0.406875	+	0.913484i	$0.366619\pi$
$464$	−19.0941			−0.886421
$465$		0			0
$466$	21.5976			1.00049
$467$	−11.8066			−0.546346			−0.273173	−	0.961965i	$-0.588073\pi$
$467$	−11.8066			−0.546346			−0.273173	+	0.961965i	$0.588073\pi$
$468$	0.828644	+	1.43525i	0.0383041	+	0.0663446i
$469$	28.2284			1.30347
$470$	−1.13235	+	1.96129i	−0.0522314	+	0.0904674i
$471$	16.5236	+	28.6197i	0.761366	+	1.31872i
$472$	11.8936	+	20.6004i	0.547448	+	0.948208i
$473$	−14.6097			−0.671757
$474$	12.4477	−	21.5601i	0.571742	−	0.990287i
$475$	7.96150	−	13.7897i	0.365299	−	0.632716i
$476$	3.45818	−	5.98973i	0.158505	−	0.274539i
$477$	−1.53015	−	2.65030i	−0.0700608	−	0.121349i
$478$	−17.1962	+	29.7847i	−0.786537	+	1.36232i
$479$	7.90436	+	13.6908i	0.361159	+	0.625546i	0.988152	−	0.153479i	$-0.0490477\pi$
$479$	7.90436	+	13.6908i	0.361159	+	0.625546i	−0.626993	+	0.779025i	$0.715714\pi$
$480$	8.53215			0.389438
$481$	4.78017			0.217957
$482$	14.0158	+	24.2761i	0.638402	+	1.10574i
$483$	3.59058	−	6.21906i	0.163377	−	0.282977i
$484$	0.758534	+	1.31382i	0.0344788	+	0.0597190i
$485$	8.43464	−	14.6092i	0.382997	−	0.663370i
$486$	−7.83475	+	13.5702i	−0.355392	+	0.615556i
$487$	6.39582	−	11.0779i	0.289822	−	0.501987i	−0.683945	−	0.729534i	$-0.739737\pi$
$487$	6.39582	−	11.0779i	0.289822	−	0.501987i	0.973767	+	0.227547i	$0.0730705\pi$
$488$	−8.32811			−0.376996
$489$	−0.138168	−	0.239314i	−0.00624816	−	0.0108221i
$490$	7.11185	+	12.3181i	0.321281	+	0.556475i
$491$	−9.26410	+	16.0459i	−0.418083	+	0.724141i	−0.995747	−	0.0921341i	$-0.970631\pi$
$491$	−9.26410	+	16.0459i	−0.418083	+	0.724141i	0.577664	+	0.816275i	$0.303964\pi$
$492$	0.337017			0.0151939
$493$	12.8490	+	22.2551i	0.578688	+	1.00232i
$494$	19.8003			0.890859
$495$	−7.59016			−0.341152
$496$		0			0
$497$	19.3922			0.869861
$498$	−21.4641			−0.961829
$499$	20.4436	+	35.4094i	0.915182	+	1.58514i	0.806634	+	0.591051i	$0.201287\pi$
$499$	20.4436	+	35.4094i	0.915182	+	1.58514i	0.108548	+	0.994091i	$0.465380\pi$
$500$	−5.66723			−0.253446
$501$	4.09681	−	7.09588i	0.183032	−	0.317021i
$502$	−10.0018	−	17.3237i	−0.446404	−	0.773195i
$503$	−10.0385	−	17.3873i	−0.447597	−	0.775260i	0.550632	−	0.834748i	$-0.314387\pi$
$503$	−10.0385	−	17.3873i	−0.447597	−	0.775260i	−0.998229	+	0.0594876i	$0.981053\pi$
$504$	15.1854			0.676411
$505$	−0.308141	+	0.533716i	−0.0137121	+	0.0237500i
$506$	2.10850	−	3.65203i	0.0937343	−	0.162353i
$507$	−6.28348	+	10.8833i	−0.279059	+	0.483345i
$508$	4.87204	+	8.43863i	0.216162	+	0.374403i
$509$	−15.9556	+	27.6359i	−0.707220	+	1.22494i	0.258665	+	0.965967i	$0.416718\pi$
$509$	−15.9556	+	27.6359i	−0.707220	+	1.22494i	−0.965884	+	0.258973i	$0.916616\pi$
$510$	7.45759	+	12.9169i	0.330228	+	0.571971i
$511$	20.5089			0.907260
$512$	−24.6123			−1.08772
$513$	−10.7208	−	18.5690i	−0.473337	−	0.819844i
$514$	−14.3869	+	24.9189i	−0.634579	+	1.09912i
$515$	2.53235	+	4.38616i	0.111589	+	0.193277i
$516$	1.94126	−	3.36237i	0.0854594	−	0.148020i
$517$	2.23650	−	3.87374i	0.0983613	−	0.170367i
$518$	4.25115	−	7.36322i	0.186785	−	0.323521i
$519$	29.9978			1.31676
$520$	−6.22722	−	10.7859i	−0.273082	−	0.472991i
$521$	−1.05378	−	1.82520i	−0.0461670	−	0.0799635i	0.842019	−	0.539449i	$-0.181367\pi$
$521$	−1.05378	−	1.82520i	−0.0461670	−	0.0799635i	−0.888185	+	0.459485i	$0.848034\pi$
$522$	−5.47624	+	9.48512i	−0.239688	+	0.415152i
$523$	−4.90777			−0.214602			−0.107301	−	0.994227i	$-0.534221\pi$
$523$	−4.90777			−0.214602			−0.107301	+	0.994227i	$0.534221\pi$
$524$	3.04739	+	5.27823i	0.133126	+	0.230581i
$525$	−20.6082			−0.899418
$526$	12.8076			0.558440
$527$		0			0
$528$	21.8886			0.952580
$529$	−22.1722			−0.964008
$530$	2.23216	+	3.86622i	0.0969589	+	0.167938i
$531$	10.1554			0.440708
$532$	−5.58748	+	9.67780i	−0.242248	+	0.419586i
$533$	−0.444199	−	0.769375i	−0.0192404	−	0.0333253i
$534$	−6.51402	−	11.2826i	−0.281889	−	0.488247i
$535$	−4.87929			−0.210950
$536$	−11.3468	+	19.6532i	−0.490106	+	0.848889i
$537$	18.3842	−	31.8423i	0.793335	−	1.37410i
$538$	−2.72190	+	4.71446i	−0.117349	+	0.203255i
$539$	−14.0466	−	24.3295i	−0.605031	−	1.04794i
$540$	−1.30902	+	2.26729i	−0.0563312	+	0.0975685i
$541$	6.21851	+	10.7708i	0.267355	+	0.463072i	0.968178	−	0.250263i	$-0.0805172\pi$
$541$	6.21851	+	10.7708i	0.267355	+	0.463072i	−0.700823	+	0.713335i	$0.747184\pi$
$542$	−7.58139			−0.325648
$543$	−25.0225			−1.07382
$544$	5.02057	+	8.69589i	0.215255	+	0.372833i
$545$	5.37584	−	9.31124i	0.230276	−	0.398849i
$546$	−12.8132	−	22.1931i	−0.548355	−	0.949779i
$547$	6.98250	−	12.0941i	0.298550	−	0.517104i	−0.677254	−	0.735749i	$-0.736830\pi$
$547$	6.98250	−	12.0941i	0.298550	−	0.517104i	0.975805	+	0.218645i	$0.0701636\pi$
$548$	2.37937	−	4.12120i	0.101642	−	0.176049i
$549$	−1.77775	+	3.07915i	−0.0758725	+	0.131415i
$550$	−12.1018			−0.516023
$551$	−20.7605	−	35.9582i	−0.884425	−	1.53187i
$552$	2.88656	+	4.99967i	0.122860	+	0.212800i
$553$	18.5190	−	32.0759i	0.787509	−	1.36401i
$554$	−27.1662			−1.15418
$555$	−2.90897	−	5.03848i	−0.123479	−	0.213872i
$556$	−7.46666			−0.316657
$557$	37.2207			1.57709			0.788546	−	0.614976i	$-0.210834\pi$
$557$	37.2207			1.57709			0.788546	+	0.614976i	$0.210834\pi$
$558$		0			0
$559$	−10.2346			−0.432876
$560$	−16.4876			−0.696730
$561$	−14.7295	−	25.5122i	−0.621879	−	1.07713i
$562$	−37.9183			−1.59949
$563$	15.0134	−	26.0039i	0.632738	−	1.09593i	−0.354252	−	0.935150i	$-0.615264\pi$
$563$	15.0134	−	26.0039i	0.632738	−	1.09593i	0.986990	−	0.160784i	$-0.0514023\pi$
$564$	0.594349	+	1.02944i	0.0250266	+	0.0433474i
$565$	−11.7829	−	20.4086i	−0.495710	−	0.858595i
$566$	−26.3010			−1.10551
$567$	−21.3242	+	36.9346i	−0.895532	+	1.55111i
$568$	−7.79498	+	13.5013i	−0.327070	+	0.566502i
$569$	−20.1857	+	34.9626i	−0.846227	+	1.46571i	0.0383249	+	0.999265i	$0.487798\pi$
$569$	−20.1857	+	34.9626i	−0.846227	+	1.46571i	−0.884552	+	0.466442i	$0.845536\pi$
$570$	−12.0495	−	20.8703i	−0.504696	−	0.874160i
$571$	21.3008	−	36.8940i	0.891410	−	1.54397i	0.0532231	−	0.998583i	$-0.483051\pi$
$571$	21.3008	−	36.8940i	0.891410	−	1.54397i	0.838186	−	0.545384i	$-0.183616\pi$
$572$	2.38753	+	4.13532i	0.0998275	+	0.172906i
$573$	−10.5233			−0.439616
$574$	−1.58016			−0.0659545
$575$	−1.18783	−	2.05738i	−0.0495359	−	0.0857986i
$576$	−5.80099	+	10.0476i	−0.241708	+	0.418650i
$577$	3.26888	+	5.66187i	0.136085	+	0.235707i	0.926012	−	0.377495i	$-0.123215\pi$
$577$	3.26888	+	5.66187i	0.136085	+	0.235707i	−0.789926	+	0.613202i	$0.789881\pi$
$578$	1.69692	−	2.93916i	0.0705827	−	0.122253i
$579$	−20.7931	+	36.0146i	−0.864130	+	1.49672i
$580$	−2.53486	+	4.39050i	−0.105254	+	0.182306i
$581$	−31.9331			−1.32481
$582$	13.9523	+	24.1662i	0.578343	+	1.00172i
$583$	−4.40874	−	7.63617i	−0.182591	−	0.316258i
$584$	−8.24383	+	14.2787i	−0.341132	+	0.590858i
$585$	−5.31714			−0.219837
$586$	1.10836	+	1.91973i	0.0457857	+	0.0793032i
$587$	21.3777			0.882352			0.441176	−	0.897421i	$-0.354561\pi$
$587$	21.3777			0.882352			0.441176	+	0.897421i	$0.354561\pi$
$588$	7.46576			0.307883
$589$		0			0
$590$	−14.8146			−0.609907
$591$	45.0443			1.85287
$592$	2.54369	+	4.40580i	0.104545	+	0.181077i
$593$	25.9906			1.06731			0.533653	−	0.845704i	$-0.320819\pi$
$593$	25.9906			1.06731			0.533653	+	0.845704i	$0.320819\pi$
$594$	−8.14807	+	14.1129i	−0.334319	+	0.579058i
$595$	11.0950	+	19.2171i	0.454851	+	0.787824i
$596$	−3.67173	−	6.35962i	−0.150400	−	0.260500i
$597$	31.4680			1.28790
$598$	1.47707	−	2.55836i	0.0604019	−	0.104619i
$599$	4.59398	−	7.95700i	0.187705	−	0.325114i	−0.756780	−	0.653670i	$-0.773228\pi$
$599$	4.59398	−	7.95700i	0.187705	−	0.325114i	0.944485	+	0.328556i	$0.106562\pi$
$600$	8.28377	−	14.3479i	0.338183	−	0.585751i
$601$	16.6595	+	28.8551i	0.679556	+	1.17703i	0.975115	+	0.221701i	$0.0711609\pi$
$601$	16.6595	+	28.8551i	0.679556	+	1.17703i	−0.295559	+	0.955325i	$0.595506\pi$
$602$	−9.10192	+	15.7650i	−0.370967	+	0.642533i
$603$	4.84425	+	8.39049i	0.197273	+	0.341687i
$604$	−0.126136			−0.00513240
$605$	−4.86727			−0.197883
$606$	−0.509718	−	0.882858i	−0.0207059	−	0.0358636i
$607$	24.3504	−	42.1761i	0.988352	−	1.71188i	0.362377	−	0.932032i	$-0.381965\pi$
$607$	24.3504	−	42.1761i	0.988352	−	1.71188i	0.625975	−	0.779843i	$-0.284701\pi$
$608$	−8.11189	−	14.0502i	−0.328981	−	0.569811i
$609$	−26.8691	+	46.5386i	−1.08879	+	1.88584i
$610$	2.59335	−	4.49182i	0.105002	−	0.181868i
$611$	1.56674	−	2.71367i	0.0633835	−	0.109783i
$612$	2.37382			0.0959560
$613$	10.4570	+	18.1121i	0.422354	+	0.731539i	0.996169	−	0.0874458i	$-0.0278705\pi$
$613$	10.4570	+	18.1121i	0.422354	+	0.731539i	−0.573815	+	0.818985i	$0.694537\pi$
$614$	−16.4923	−	28.5654i	−0.665573	−	1.15281i
$615$	−0.540633	+	0.936404i	−0.0218004	+	0.0377594i
$616$	43.7529			1.76285
$617$	−22.6920	−	39.3037i	−0.913545	−	1.58231i	−0.809018	−	0.587784i	$-0.800001\pi$
$617$	−22.6920	−	39.3037i	−0.913545	−	1.58231i	−0.104527	−	0.994522i	$-0.533333\pi$
$618$	−8.37789			−0.337008
$619$	10.2462			0.411832			0.205916	−	0.978570i	$-0.433983\pi$
$619$	10.2462			0.411832			0.205916	+	0.978570i	$0.433983\pi$
$620$		0			0
$621$	−3.19902			−0.128372
$622$	5.15188			0.206572
$623$	−9.69121	−	16.7857i	−0.388270	−	0.672504i
$624$	15.3337			0.613838
$625$	2.56358	−	4.44025i	0.102543	−	0.177610i
$626$	−6.98816	−	12.1038i	−0.279303	−	0.483767i
$627$	23.7989	+	41.2209i	0.950436	+	1.64620i
$628$	−7.67263			−0.306171
$629$	3.42345	−	5.92958i	0.136502	−	0.236428i
$630$	−4.72870	+	8.19034i	−0.188396	+	0.326311i
$631$	−5.33848	+	9.24653i	−0.212522	+	0.368098i	−0.952503	−	0.304529i	$-0.901501\pi$
$631$	−5.33848	+	9.24653i	−0.212522	+	0.368098i	0.739981	+	0.672627i	$0.234834\pi$
$632$	14.8880	+	25.7867i	0.592211	+	1.02574i
$633$	6.54074	−	11.3289i	0.259971	−	0.450283i
$634$	−15.9451	−	27.6178i	−0.633262	−	1.09684i
$635$	−31.2623			−1.24061
$636$	2.34324			0.0929155
$637$	−9.84009	−	17.0435i	−0.389878	−	0.675289i
$638$	−15.7784	+	27.3290i	−0.624672	+	1.08196i
$639$	3.32789	+	5.76407i	0.131649	+	0.228023i
$640$	4.35046	−	7.53522i	0.171967	−	0.297856i
$641$	11.9310	−	20.6652i	0.471248	−	0.816226i	−0.528211	−	0.849113i	$-0.677137\pi$
$641$	11.9310	−	20.6652i	0.471248	−	0.816226i	0.999459	+	0.0328875i	$0.0104703\pi$
$642$	4.03560	−	6.98986i	0.159272	−	0.275868i
$643$	7.93926			0.313094			0.156547	−	0.987671i	$-0.449964\pi$
$643$	7.93926			0.313094			0.156547	+	0.987671i	$0.449964\pi$
$644$	0.833632	+	1.44389i	0.0328497	+	0.0568974i
$645$	6.22823	+	10.7876i	0.245237	+	0.424762i
$646$	14.1805	−	24.5614i	0.557925	−	0.966355i
$647$	−2.47761			−0.0974050			−0.0487025	−	0.998813i	$-0.515509\pi$
$647$	−2.47761			−0.0974050			−0.0487025	+	0.998813i	$0.515509\pi$
$648$	−17.1431	−	29.6927i	−0.673445	−	1.16644i
$649$	29.2603			1.14857
$650$	−8.47769			−0.332523
$651$		0			0
$652$	0.0641574			0.00251260
$653$	22.4940			0.880260			0.440130	−	0.897934i	$-0.354932\pi$
$653$	22.4940			0.880260			0.440130	+	0.897934i	$0.354932\pi$
$654$	8.89257	+	15.4024i	0.347727	+	0.602281i
$655$	−19.5541			−0.764042
$656$	0.472746	−	0.818821i	0.0184576	−	0.0319696i
$657$	3.51952	+	6.09598i	0.137309	+	0.237827i
$658$	−2.78670	−	4.82670i	−0.108637	−	0.188164i
$659$	−11.9596			−0.465881			−0.232941	−	0.972491i	$-0.574835\pi$
$659$	−11.9596			−0.465881			−0.232941	+	0.972491i	$0.574835\pi$
$660$	2.90585	−	5.03308i	0.113110	−	0.195912i
$661$	−11.9180	+	20.6426i	−0.463556	+	0.802902i	−0.999135	−	0.0415827i	$-0.986760\pi$
$661$	−11.9180	+	20.6426i	−0.463556	+	0.802902i	0.535579	+	0.844485i	$0.320093\pi$
$662$	0.471791	−	0.817166i	0.0183367	−	0.0317601i
$663$	−10.3185	−	17.8721i	−0.400736	−	0.694095i
$664$	12.8359	−	22.2325i	0.498131	−	0.862789i
$665$	−17.9265	−	31.0497i	−0.695161	−	1.20405i
$666$	2.91815			0.113076
$667$	−6.19478			−0.239863
$668$	0.951165	+	1.64747i	0.0368017	+	0.0637424i
$669$	−7.66610	+	13.2781i	−0.296389	+	0.513360i
$670$	−7.06672	−	12.2399i	−0.273011	−	0.472869i
$671$	−5.12213	+	8.87179i	−0.197738	+	0.342492i
$672$	−10.4988	+	18.1844i	−0.404998	+	0.701478i
$673$	1.74706	−	3.02600i	0.0673442	−	0.116644i	−0.830387	−	0.557187i	$-0.811881\pi$
$673$	1.74706	−	3.02600i	0.0673442	−	0.116644i	0.897731	+	0.440543i	$0.145214\pi$
$674$	−2.95024			−0.113639
$675$	4.59023	+	7.95051i	0.176678	+	0.306015i
$676$	−1.45885	−	2.52680i	−0.0561096	−	0.0971847i
$677$	−9.62287	+	16.6673i	−0.369837	+	0.640576i	−0.989540	−	0.144260i	$-0.953920\pi$
$677$	−9.62287	+	16.6673i	−0.369837	+	0.640576i	0.619703	+	0.784836i	$0.287253\pi$
$678$	38.9819			1.49709
$679$	20.7575	+	35.9531i	0.796601	+	1.37975i
$680$	−17.8391			−0.684100
$681$	−39.9221			−1.52982
$682$		0			0
$683$	−39.8738			−1.52573			−0.762865	−	0.646558i	$-0.776208\pi$
$683$	−39.8738			−1.52573			−0.762865	+	0.646558i	$0.776208\pi$
$684$	−3.83545			−0.146652
$685$	7.63384	+	13.2222i	0.291674	+	0.505194i
$686$	−2.19616			−0.0838498
$687$	6.31529	−	10.9384i	0.240944	−	0.417326i
$688$	−5.44616	−	9.43303i	−0.207633	−	0.359631i
$689$	−3.08846	−	5.34937i	−0.117661	−	0.203795i
$690$	−3.59547			−0.136877
$691$	−19.2052	+	33.2644i	−0.730601	+	1.26544i	0.226025	+	0.974121i	$0.427427\pi$
$691$	−19.2052	+	33.2644i	−0.730601	+	1.26544i	−0.956627	+	0.291317i	$0.905907\pi$
$692$	−3.48233	+	6.03157i	−0.132378	+	0.229286i
$693$	9.33965	−	16.1767i	0.354784	−	0.614504i
$694$	3.48569	+	6.03740i	0.132315	+	0.229176i
$695$	11.9778	−	20.7461i	0.454343	−	0.786946i
$696$	−21.6008	−	37.4137i	−0.818776	−	1.41816i
$697$	−1.27250			−0.0481993
$698$	35.8163			1.35567
$699$	18.1851	+	31.4976i	0.687825	+	1.19135i
$700$	2.39233	−	4.14364i	0.0904216	−	0.156615i
$701$	17.7127	+	30.6794i	0.669001	+	1.15874i	0.978184	+	0.207741i	$0.0666110\pi$
$701$	17.7127	+	30.6794i	0.669001	+	1.15874i	−0.309183	+	0.951002i	$0.600056\pi$
$702$	−5.70797	+	9.88649i	−0.215433	+	0.373142i
$703$	−5.53137	+	9.58061i	−0.208619	+	0.361339i
$704$	−16.7141	+	28.9496i	−0.629935	+	1.09108i
$705$	−3.81375			−0.143634
$706$	−11.8752	−	20.5684i	−0.446928	−	0.774103i
$707$	−0.758331	−	1.31347i	−0.0285200	−	0.0493980i
$708$	−3.88795	+	6.73412i	−0.146118	+	0.253084i
$709$	25.8093			0.969288			0.484644	−	0.874711i	$-0.338949\pi$
$709$	25.8093			0.969288			0.484644	+	0.874711i	$0.338949\pi$
$710$	−4.85467	−	8.40854i	−0.182193	−	0.315567i
$711$	12.7121			0.476743
$712$	15.5821			0.583962
$713$		0			0
$714$	−36.7061			−1.37369
$715$	−15.3200			−0.572935
$716$	4.26829	+	7.39290i	0.159514	+	0.276286i
$717$	−57.9168			−2.16294
$718$	−6.37296	+	11.0383i	−0.237837	+	0.411945i
$719$	−19.5234	−	33.8155i	−0.728099	−	1.26110i	−0.957686	−	0.287816i	$-0.907071\pi$
$719$	−19.5234	−	33.8155i	−0.728099	−	1.26110i	0.229587	−	0.973288i	$-0.426262\pi$
$720$	−2.82943	−	4.90072i	−0.105447	−	0.182639i
$721$	−12.4642			−0.464190
$722$	−11.2063	+	19.4098i	−0.417054	+	0.722359i
$723$	−23.6026	+	40.8808i	−0.877789	+	1.52037i
$724$	2.90476	−	5.03119i	0.107955	−	0.186983i
$725$	8.88879	+	15.3958i	0.330121	+	0.571787i
$726$	4.02565	−	6.97263i	0.149406	−	0.258779i
$727$	−12.4918	−	21.6365i	−0.463296	−	0.802452i	0.535827	−	0.844328i	$-0.320000\pi$
$727$	−12.4918	−	21.6365i	−0.463296	−	0.802452i	−0.999123	+	0.0418757i	$0.986667\pi$
$728$	30.6502			1.13597
$729$	7.24913			0.268486
$730$	−5.13422	−	8.89272i	−0.190026	−	0.329134i
$731$	−7.32976	+	12.6955i	−0.271101	+	0.469561i
$732$	−1.36120	−	2.35767i	−0.0503115	−	0.0871420i
$733$	8.47452	−	14.6783i	0.313014	−	0.542156i	−0.666000	−	0.745952i	$-0.731995\pi$
$733$	8.47452	−	14.6783i	0.313014	−	0.542156i	0.979013	+	0.203797i	$0.0653281\pi$
$734$	−0.0841350	+	0.145726i	−0.00310548	+	0.00537885i
$735$	−11.9763	+	20.7436i	−0.441754	+	0.765140i
$736$	−2.42053			−0.0892220
$737$	13.9575	+	24.1751i	0.514130	+	0.890500i
$738$	−0.271170	−	0.469680i	−0.00998190	−	0.0172892i
$739$	7.19107	−	12.4553i	0.264528	−	0.458175i	−0.702912	−	0.711277i	$-0.748117\pi$
$739$	7.19107	−	12.4553i	0.264528	−	0.458175i	0.967440	+	0.253101i	$0.0814506\pi$
$740$	1.35076			0.0496550
$741$	16.6718	+	28.8765i	0.612456	+	1.06080i
$742$	−10.9866			−0.403333
$743$	27.7705			1.01880			0.509400	−	0.860530i	$-0.329867\pi$
$743$	27.7705			1.01880			0.509400	+	0.860530i	$0.329867\pi$
$744$		0			0
$745$	23.5603			0.863183
$746$	−9.07363			−0.332209
$747$	−5.48002	−	9.49167i	−0.200503	−	0.347282i
$748$	6.83956			0.250079
$749$	6.00394	−	10.3991i	0.219379	−	0.379976i
$750$	15.0384	+	26.0473i	0.549126	+	0.951113i
$751$	21.7851	+	37.7329i	0.794950	+	1.37689i	0.922871	+	0.385109i	$0.125836\pi$
$751$	21.7851	+	37.7329i	0.794950	+	1.37689i	−0.127922	+	0.991784i	$0.540831\pi$
$752$	3.33486			0.121610
$753$	16.8431	−	29.1731i	0.613796	−	1.06313i
$754$	−11.0532	+	19.1448i	−0.402535	+	0.697212i
$755$	0.202344	−	0.350469i	0.00736404	−	0.0127549i
$756$	−3.22148	−	5.57976i	−0.117164	−	0.202934i
$757$	12.6086	−	21.8387i	0.458266	−	0.793739i	−0.540604	−	0.841277i	$-0.681804\pi$
$757$	12.6086	−	21.8387i	0.458266	−	0.793739i	0.998869	+	0.0475380i	$0.0151375\pi$
$758$	2.83901	+	4.91731i	0.103117	+	0.178605i
$759$	7.10142			0.257765
$760$	28.8233			1.04553
$761$	−1.30797	−	2.26546i	−0.0474137	−	0.0821229i	0.841345	−	0.540499i	$-0.181765\pi$
$761$	−1.30797	−	2.26546i	−0.0474137	−	0.0821229i	−0.888758	+	0.458376i	$0.848431\pi$
$762$	25.8566	−	44.7850i	0.936687	−	1.62239i
$763$	13.2299	+	22.9148i	0.478954	+	0.829573i
$764$	1.22161	−	2.11588i	0.0441962	−	0.0765500i
$765$	−3.80801	+	6.59567i	−0.137679	+	0.238467i
$766$	−19.8964	+	34.4615i	−0.718885	+	1.24515i
$767$	20.4977			0.740130
$768$	−11.2436	−	19.4745i	−0.405718	−	0.702725i
$769$	−5.67534	−	9.82998i	−0.204658	−	0.354478i	0.745366	−	0.666656i	$-0.232275\pi$
$769$	−5.67534	−	9.82998i	−0.204658	−	0.354478i	−0.950024	+	0.312178i	$0.898942\pi$
$770$	−13.6245	+	23.5984i	−0.490994	+	0.850427i
$771$	−48.4550			−1.74507
$772$	−4.82757	−	8.36160i	−0.173748	−	0.300941i
$773$	11.4174			0.410655			0.205327	−	0.978693i	$-0.434174\pi$
$773$	11.4174			0.410655			0.205327	+	0.978693i	$0.434174\pi$
$774$	−6.24789			−0.224576
$775$		0			0
$776$	−33.3751			−1.19810
$777$	14.3179			0.513651
$778$	−21.7301	−	37.6377i	−0.779063	−	1.34938i
$779$	2.05601			0.0736644
$780$	2.03564	−	3.52583i	0.0728875	−	0.126245i
$781$	9.58846	+	16.6077i	0.343102	+	0.594270i
$782$	−2.11568	−	3.66447i	−0.0756567	−	0.131041i
$783$	23.9390			0.855511
$784$	10.4725	−	18.1389i	0.374017	−	0.647817i
$785$	12.3082	−	21.3184i	0.439299	−	0.760888i
$786$	16.1729	−	28.0123i	0.576869	−	0.999167i
$787$	−13.5446	−	23.4599i	−0.482813	−	0.836257i	0.516992	−	0.855990i	$-0.327052\pi$
$787$	−13.5446	−	23.4599i	−0.482813	−	0.836257i	−0.999805	+	0.0197334i	$0.993718\pi$
$788$	−5.22902	+	9.05692i	−0.186276	+	0.322640i
$789$	10.7840	+	18.6785i	0.383921	+	0.664971i
$790$	−18.5443			−0.659776
$791$	57.9951			2.06207
$792$	7.50840	+	13.0049i	0.266799	+	0.462110i
$793$	−3.58821	+	6.21496i	−0.127421	+	0.220700i
$794$	2.48530	+	4.30467i	0.0882001	+	0.152767i
$795$	−3.75896	+	6.51070i	−0.133316	+	0.230911i
$796$	−3.65300	+	6.32719i	−0.129477	+	0.224261i
$797$	24.3279	−	42.1372i	0.861739	−	1.49258i	−0.00851025	−	0.999964i	$-0.502709\pi$
$797$	24.3279	−	42.1372i	0.861739	−	1.49258i	0.870249	−	0.492612i	$-0.163958\pi$
$798$	59.3071			2.09945
$799$	−2.24412	−	3.88693i	−0.0793914	−	0.137510i
$800$	3.47318	+	6.01573i	0.122796	+	0.212688i
$801$	3.32620	−	5.76115i	0.117526	−	0.203560i
$802$	−30.6604			−1.08266
$803$	10.1406	+	17.5640i	0.357854	+	0.619821i
$804$	−7.41838			−0.261626
$805$	−5.34915			−0.188533
$806$		0			0
$807$	−9.16733			−0.322705
$808$	1.21929			0.0428943
$809$	−9.40457	−	16.2892i	−0.330647	−	0.572697i	0.651992	−	0.758226i	$-0.273934\pi$
$809$	−9.40457	−	16.2892i	−0.330647	−	0.572697i	−0.982639	+	0.185529i	$0.940600\pi$
$810$	21.3533			0.750278
$811$	19.7693	−	34.2414i	0.694193	−	1.20238i	−0.276259	−	0.961083i	$-0.589095\pi$
$811$	19.7693	−	34.2414i	0.694193	−	1.20238i	0.970452	−	0.241294i	$-0.0775720\pi$
$812$	−6.23826	−	10.8050i	−0.218920	−	0.379180i
$813$	−6.38352	−	11.0566i	−0.223880	−	0.387771i
$814$	8.40791			0.294697
$815$	−0.102919	+	0.178262i	−0.00360511	+	0.00624423i
$816$	10.9816	−	19.0207i	0.384433	−	0.665857i
$817$	11.8429	−	20.5125i	0.414331	−	0.717642i
$818$	2.16075	+	3.74253i	0.0755489	+	0.130855i
$819$	6.54271	−	11.3323i	0.228621	−	0.395983i
$820$	−0.125520	−	0.217407i	−0.00438335	−	0.00759218i
$821$	14.6367			0.510825			0.255412	−	0.966832i	$-0.417789\pi$
$821$	14.6367			0.510825			0.255412	+	0.966832i	$0.417789\pi$
$822$	−25.2554			−0.880882
$823$	20.8934	+	36.1883i	0.728296	+	1.26145i	0.957603	+	0.288092i	$0.0930210\pi$
$823$	20.8934	+	36.1883i	0.728296	+	1.26145i	−0.229306	+	0.973354i	$0.573646\pi$
$824$	5.01014	−	8.67782i	0.174537	−	0.302306i
$825$	−10.1897	−	17.6491i	−0.354760	−	0.614463i
$826$	18.2292	−	31.5740i	0.634277	−	1.09860i
$827$	−4.70307	+	8.14595i	−0.163542	+	0.283262i	−0.936136	−	0.351637i	$-0.885625\pi$
$827$	−4.70307	+	8.14595i	−0.163542	+	0.283262i	0.772595	+	0.634899i	$0.218958\pi$
$828$	−0.286118	+	0.495571i	−0.00994329	+	0.0172223i
$829$	−40.3307			−1.40074			−0.700372	−	0.713778i	$-0.746983\pi$
$829$	−40.3307			−1.40074			−0.700372	+	0.713778i	$0.746983\pi$
$830$	7.99417	+	13.8463i	0.277482	+	0.480612i
$831$	−22.8739	−	39.6188i	−0.793487	−	1.37436i
$832$	−11.7087	+	20.2801i	−0.405927	+	0.703086i
$833$	−28.1889			−0.976689
$834$	19.8133	+	34.3177i	0.686079	+	1.18832i
$835$	−6.10332			−0.211214
$836$	−11.0509			−0.382203
$837$		0			0
$838$	5.07693			0.175380
$839$	7.14965			0.246833			0.123417	−	0.992355i	$-0.460615\pi$
$839$	7.14965			0.246833			0.123417	+	0.992355i	$0.460615\pi$
$840$	−18.6522	−	32.3065i	−0.643560	−	1.11468i
$841$	17.3569			0.598514
$842$	−17.0048	+	29.4532i	−0.586025	+	1.01503i
$843$	−31.9272	−	55.2995i	−1.09963	−	1.90462i
$844$	1.51858	+	2.63026i	0.0522716	+	0.0905371i
$845$	9.36097			0.322027
$846$	0.956446	−	1.65661i	0.0328833	−	0.0569556i
$847$	5.98914	−	10.3735i	0.205789	−	0.356438i
$848$	3.28695	−	5.69316i	0.112874	−	0.195504i
$849$	−22.1454	−	38.3570i	−0.760029	−	1.31641i
$850$	−6.07152	+	10.5162i	−0.208252	+	0.360702i
$851$	0.825260	+	1.42939i	0.0282896	+	0.0489990i
$852$	−5.09625			−0.174595
$853$	1.12667			0.0385765			0.0192882	−	0.999814i	$-0.493860\pi$
$853$	1.12667			0.0385765			0.0192882	+	0.999814i	$0.493860\pi$
$854$	6.38221	+	11.0543i	0.218395	+	0.378271i
$855$	6.15272	−	10.6568i	0.210418	−	0.364455i
$856$	4.82673	+	8.36014i	0.164974	+	0.285744i
$857$	11.9270	−	20.6582i	0.407419	−	0.705671i	−0.587181	−	0.809456i	$-0.699762\pi$
$857$	11.9270	−	20.6582i	0.407419	−	0.705671i	0.994600	+	0.103785i	$0.0330955\pi$
$858$	12.6710	−	21.9467i	0.432579	−	0.749249i
$859$	16.2328	−	28.1161i	0.553857	−	0.959309i	−0.444134	−	0.895960i	$-0.646489\pi$
$859$	16.2328	−	28.1161i	0.553857	−	0.959309i	0.997991	−	0.0633488i	$-0.0201781\pi$
$860$	−2.89205			−0.0986180
$861$	−1.33049	−	2.30448i	−0.0453430	−	0.0785364i
$862$	9.16363	+	15.8719i	0.312114	+	0.540598i
$863$	−11.9209	+	20.6476i	−0.405793	+	0.702853i	−0.994413	−	0.105556i	$-0.966338\pi$
$863$	−11.9209	+	20.6476i	−0.405793	+	0.702853i	0.588621	+	0.808409i	$0.299671\pi$
$864$	9.35387			0.318225
$865$	−11.1725	−	19.3513i	−0.379876	−	0.657964i
$866$	−11.4123			−0.387806
$867$	5.71523			0.194099
$868$		0			0
$869$	36.6268			1.24248
$870$	26.9057			0.912190
$871$	9.77764	+	16.9354i	0.331303	+	0.573833i
$872$	−21.2717			−0.720352
$873$	−7.12437	+	12.3398i	−0.241123	+	0.417638i
$874$	3.41837	+	5.92080i	0.115628	+	0.200274i
$875$	22.3733	+	38.7518i	0.756357	+	1.31005i
$876$	−5.38971			−0.182101
$877$	−14.6373	+	25.3526i	−0.494267	+	0.856096i	−0.999978	−	0.00660717i	$-0.997897\pi$
$877$	−14.6373	+	25.3526i	−0.494267	+	0.856096i	0.505711	+	0.862703i	$0.331230\pi$
$878$	−10.9159	+	18.9069i	−0.368395	+	0.638078i
$879$	−1.86647	+	3.23282i	−0.0629544	+	0.109040i
$880$	−8.15228	−	14.1202i	−0.274813	−	0.475991i
$881$	4.51504	−	7.82028i	0.152116	−	0.263472i	−0.779889	−	0.625917i	$-0.784725\pi$
$881$	4.51504	−	7.82028i	0.152116	−	0.263472i	0.932005	+	0.362445i	$0.118058\pi$
$882$	−6.00707	−	10.4046i	−0.202269	−	0.350340i
$883$	−21.4076			−0.720422			−0.360211	−	0.932871i	$-0.617295\pi$
$883$	−21.4076			−0.720422			−0.360211	+	0.932871i	$0.617295\pi$
$884$	4.79132			0.161150
$885$	−12.4739	−	21.6054i	−0.419304	−	0.726256i
$886$	11.3669	−	19.6881i	0.381880	−	0.661435i
$887$	−12.2975	−	21.2999i	−0.412910	−	0.715181i	0.582297	−	0.812976i	$-0.302154\pi$
$887$	−12.2975	−	21.2999i	−0.412910	−	0.715181i	−0.995207	+	0.0977956i	$0.968821\pi$
$888$	−5.75526	+	9.96841i	−0.193134	+	0.334518i
$889$	38.4681	−	66.6287i	1.29018	−	2.23466i
$890$	−4.85222	+	8.40428i	−0.162647	+	0.281712i
$891$	−42.1749			−1.41291
$892$	−1.77986	−	3.08280i	−0.0595940	−	0.103220i
$893$	3.62590	+	6.28024i	0.121336	+	0.210160i
$894$	−19.4864	+	33.7514i	−0.651723	+	1.12882i
$895$	−27.3883			−0.915488
$896$	10.7064	+	18.5441i	0.357677	+	0.619515i
$897$	4.97476			0.166102
$898$	−27.9829			−0.933801
$899$		0			0
$900$	1.64218			0.0547395
$901$	−8.84753			−0.294754
$902$	−0.781307	−	1.35326i	−0.0260147	−	0.0450587i
$903$	−30.6552			−1.02014
$904$	−23.3119	+	40.3774i	−0.775343	+	1.34293i
$905$	9.31946	+	16.1418i	0.309789	+	0.536571i
$906$	0.334711	+	0.579737i	0.0111200	+	0.0192605i
$907$	−19.7663			−0.656329			−0.328165	−	0.944621i	$-0.606430\pi$
$907$	−19.7663			−0.656329			−0.328165	+	0.944621i	$0.606430\pi$
$908$	4.63440	−	8.02701i	0.153798	−	0.266386i
$909$	0.260273	−	0.450806i	0.00863272	−	0.0149523i
$910$	−9.54441	+	16.5314i	−0.316394	+	0.548010i
$911$	−17.8108	−	30.8492i	−0.590098	−	1.02208i	−0.994219	−	0.107374i	$-0.965756\pi$
$911$	−17.8108	−	30.8492i	−0.590098	−	1.02208i	0.404121	−	0.914706i	$-0.367578\pi$
$912$	−17.7433	+	30.7323i	−0.587540	+	1.01765i
$913$	−15.7893	−	27.3478i	−0.522549	−	0.905081i
$914$	19.9142			0.658703
$915$	8.73440			0.288750
$916$	1.46624	+	2.53960i	0.0484458	+	0.0839106i
$917$	24.0612	−	41.6752i	0.794571	−	1.37624i
$918$	8.17582	+	14.1609i	0.269842	+	0.467381i
$919$	8.57816	−	14.8578i	0.282968	−	0.490114i	−0.689147	−	0.724622i	$-0.742014\pi$
$919$	8.57816	−	14.8578i	0.282968	−	0.490114i	0.972114	+	0.234508i	$0.0753478\pi$
$920$	2.15016	−	3.72419i	0.0708888	−	0.122783i
$921$	27.7729	−	48.1041i	0.915149	−	1.58508i
$922$	−26.5395			−0.874030
$923$	6.71701	+	11.6342i	0.221093	+	0.382945i
$924$	7.15126	+	12.3863i	0.235259	+	0.407481i
$925$	2.36831	−	4.10203i	0.0778694	−	0.134874i
$926$	21.5751			0.709002
$927$	−2.13897	−	3.70480i	−0.0702529	−	0.121682i
$928$	18.1134			0.594601
$929$	−45.5222			−1.49353			−0.746767	−	0.665086i	$-0.768395\pi$
$929$	−45.5222			−1.49353			−0.746767	+	0.665086i	$0.768395\pi$
$930$		0			0
$931$	45.5457			1.49270
$932$	−8.44416			−0.276598
$933$	4.33788	+	7.51342i	0.142016	+	0.245978i
$934$	−14.5478			−0.476018
$935$	−10.9718	+	19.0037i	−0.358817	+	0.621489i
$936$	5.25986	+	9.11035i	0.171924	+	0.297781i
$937$	−12.8087	−	22.1854i	−0.418443	−	0.724765i	0.577340	−	0.816504i	$-0.304091\pi$
$937$	−12.8087	−	22.1854i	−0.418443	−	0.724765i	−0.995783	+	0.0917389i	$0.970757\pi$
$938$	34.7822			1.13568
$939$	11.7680	−	20.3828i	0.384036	−	0.665169i
$940$	0.442723	−	0.766819i	0.0144400	−	0.0250109i
$941$	6.06192	−	10.4996i	0.197613	−	0.342276i	−0.750141	−	0.661278i	$-0.770014\pi$
$941$	6.06192	−	10.4996i	0.197613	−	0.342276i	0.947754	+	0.319002i	$0.103348\pi$
$942$	20.3599	+	35.2644i	0.663361	+	1.14898i
$943$	0.153375	−	0.265653i	0.00499458	−	0.00865086i
$944$	10.9075	+	18.8924i	0.355010	+	0.614895i
$945$	20.6712			0.672434
$946$	−18.0017			−0.585286
$947$	−13.6005	−	23.5568i	−0.441958	−	0.765494i	0.555877	−	0.831265i	$-0.312383\pi$
$947$	−13.6005	−	23.5568i	−0.441958	−	0.765494i	−0.997835	+	0.0657711i	$0.979049\pi$
$948$	−4.86677	+	8.42950i	−0.158065	+	0.273777i
$949$	7.10379	+	12.3041i	0.230599	+	0.399409i
$950$	9.80994	−	16.9913i	0.318277	−	0.551271i
$951$	26.8516	−	46.5083i	0.870722	−	1.50813i
$952$	21.9510	−	38.0202i	0.711435	−	1.23224i
$953$	−24.8927			−0.806353			−0.403177	−	0.915122i	$-0.632094\pi$
$953$	−24.8927			−0.806353			−0.403177	+	0.915122i	$0.632094\pi$
$954$	−1.88541	−	3.26563i	−0.0610424	−	0.105729i
$955$	3.91933	+	6.78848i	0.126826	+	0.219670i
$956$	6.72333	−	11.6452i	0.217448	−	0.376631i
$957$	−53.1415			−1.71782
$958$	9.73953	+	16.8694i	0.314670	+	0.545024i
$959$	−37.5736			−1.21331
$960$	28.5013			0.919876
$961$		0			0
$962$	5.89000			0.189901
$963$	4.12133			0.132808
$964$	−5.47986	−	9.49140i	−0.176494	−	0.305697i
$965$	30.9770			0.997184
$966$	4.42421	−	7.66295i	0.142347	−	0.246551i
$967$	26.0999	+	45.2064i	0.839316	+	1.45374i	0.890467	+	0.455048i	$0.150378\pi$
$967$	26.0999	+	45.2064i	0.839316	+	1.45374i	−0.0511507	+	0.998691i	$0.516289\pi$
$968$	4.81483	+	8.33954i	0.154755	+	0.268043i
$969$	47.7599			1.53427
$970$	10.3929	−	18.0011i	0.333697	−	0.577980i
$971$	9.98042	−	17.2866i	0.320287	−	0.554753i	−0.660260	−	0.751037i	$-0.729554\pi$
$971$	9.98042	−	17.2866i	0.320287	−	0.554753i	0.980547	+	0.196284i	$0.0628874\pi$
$972$	3.06321	−	5.30564i	0.0982526	−	0.170178i
$973$	29.4772	+	51.0560i	0.944995	+	1.63678i
$974$	7.88075	−	13.6499i	0.252516	−	0.437370i
$975$	−7.13821	−	12.3637i	−0.228606	−	0.395957i
$976$	−7.63763			−0.244475
$977$	−60.2506			−1.92759			−0.963794	−	0.266648i	$-0.914084\pi$
$977$	−60.2506			−1.92759			−0.963794	+	0.266648i	$0.914084\pi$
$978$	−0.170246	−	0.294876i	−0.00544388	−	0.00942908i
$979$	9.58361	−	16.5993i	0.306293	−	0.530516i
$980$	−2.78057	−	4.81609i	−0.0888222	−	0.153845i
$981$	−4.54074	+	7.86480i	−0.144975	+	0.251104i
$982$	−11.4150	+	19.7713i	−0.364266	+	0.630927i
$983$	−5.76936	+	9.99283i	−0.184014	+	0.318722i	−0.943244	−	0.332101i	$-0.892243\pi$
$983$	−5.76936	+	9.99283i	−0.184014	+	0.318722i	0.759230	+	0.650823i	$0.225576\pi$
$984$	2.13924			0.0681964
$985$	−16.7765	−	29.0577i	−0.534543	−	0.925855i
$986$	15.8321	+	27.4221i	0.504198	+	0.873297i
$987$	4.69279	−	8.12816i	0.149373	−	0.258722i
$988$	−7.74148			−0.246289
$989$	−1.76692	−	3.06040i	−0.0561848	−	0.0973149i
$990$	−9.35239			−0.297238
$991$	−37.3423			−1.18622			−0.593109	−	0.805122i	$-0.702100\pi$
$991$	−37.3423			−1.18622			−0.593109	+	0.805122i	$0.702100\pi$
$992$		0			0
$993$	1.58899			0.0504251
$994$	23.8946			0.757890
$995$	−11.7201	−	20.2998i	−0.371551	−	0.643546i
$996$	8.39197			0.265910
$997$	−10.4012	+	18.0154i	−0.329410	+	0.570555i	−0.982395	−	0.186816i	$-0.940183\pi$
$997$	−10.4012	+	18.0154i	−0.329410	+	0.570555i	0.652985	+	0.757371i	$0.273516\pi$
$998$	25.1901	+	43.6305i	0.797378	+	1.38110i
$999$	−3.18913	−	5.52373i	−0.100900	−	0.174763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.c.i.521.5		16
31.2	even	5		961.2.g.l.844.2		16
31.3	odd	30		961.2.d.o.628.3		16
31.4	even	5		961.2.g.m.338.1		16
31.5	even	3	inner	961.2.c.i.439.5		16
31.6	odd	6		961.2.a.i.1.5		8
31.7	even	15		961.2.d.q.388.2		16
31.8	even	5		961.2.g.n.732.1		16
31.9	even	15		961.2.g.m.816.1		16
31.10	even	15		961.2.g.j.547.2		16
31.11	odd	30		961.2.g.t.235.1		16
31.12	odd	30		961.2.d.o.531.3		16
31.13	odd	30		31.2.g.a.9.2	yes	16
31.14	even	15		961.2.d.q.374.2		16
31.15	odd	10		961.2.g.k.448.2		16
31.16	even	5		961.2.g.j.448.2		16
31.17	odd	30		961.2.d.p.374.2		16
31.18	even	15		961.2.g.l.846.2		16
31.19	even	15		961.2.d.n.531.3		16
31.20	even	15		961.2.g.n.235.1		16
31.21	odd	30		961.2.g.k.547.2		16
31.22	odd	30		961.2.g.s.816.1		16
31.23	odd	10		961.2.g.t.732.1		16
31.24	odd	30		961.2.d.p.388.2		16
31.25	even	3		961.2.a.j.1.5		8
31.26	odd	6		961.2.c.j.439.5		16
31.27	odd	10		961.2.g.s.338.1		16
31.28	even	15		961.2.d.n.628.3		16
31.29	odd	10		31.2.g.a.7.2	✓	16
31.30	odd	2		961.2.c.j.521.5		16
93.29	even	10		279.2.y.c.100.1		16
93.44	even	30		279.2.y.c.226.1		16
93.56	odd	6		8649.2.a.be.1.4		8
93.68	even	6		8649.2.a.bf.1.4		8
124.75	even	30		496.2.bg.c.257.2		16
124.91	even	10		496.2.bg.c.193.2		16
155.13	even	60		775.2.ck.a.474.2		32
155.29	odd	10		775.2.bl.a.751.1		16
155.44	odd	30		775.2.bl.a.226.1		16
155.122	even	20		775.2.ck.a.224.2		32
155.137	even	60		775.2.ck.a.474.3		32
155.153	even	20		775.2.ck.a.224.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.7.2	✓	16	31.29	odd	10
31.2.g.a.9.2	yes	16	31.13	odd	30
279.2.y.c.100.1		16	93.29	even	10
279.2.y.c.226.1		16	93.44	even	30
496.2.bg.c.193.2		16	124.91	even	10
496.2.bg.c.257.2		16	124.75	even	30
775.2.bl.a.226.1		16	155.44	odd	30
775.2.bl.a.751.1		16	155.29	odd	10
775.2.ck.a.224.2		32	155.122	even	20
775.2.ck.a.224.3		32	155.153	even	20
775.2.ck.a.474.2		32	155.13	even	60
775.2.ck.a.474.3		32	155.137	even	60
961.2.a.i.1.5		8	31.6	odd	6
961.2.a.j.1.5		8	31.25	even	3
961.2.c.i.439.5		16	31.5	even	3	inner
961.2.c.i.521.5		16	1.1	even	1	trivial
961.2.c.j.439.5		16	31.26	odd	6
961.2.c.j.521.5		16	31.30	odd	2
961.2.d.n.531.3		16	31.19	even	15
961.2.d.n.628.3		16	31.28	even	15
961.2.d.o.531.3		16	31.12	odd	30
961.2.d.o.628.3		16	31.3	odd	30
961.2.d.p.374.2		16	31.17	odd	30
961.2.d.p.388.2		16	31.24	odd	30
961.2.d.q.374.2		16	31.14	even	15
961.2.d.q.388.2		16	31.7	even	15
961.2.g.j.448.2		16	31.16	even	5
961.2.g.j.547.2		16	31.10	even	15
961.2.g.k.448.2		16	31.15	odd	10
961.2.g.k.547.2		16	31.21	odd	30
961.2.g.l.844.2		16	31.2	even	5
961.2.g.l.846.2		16	31.18	even	15
961.2.g.m.338.1		16	31.4	even	5
961.2.g.m.816.1		16	31.9	even	15
961.2.g.n.235.1		16	31.20	even	15
961.2.g.n.732.1		16	31.8	even	5
961.2.g.s.338.1		16	31.27	odd	10
961.2.g.s.816.1		16	31.22	odd	30
961.2.g.t.235.1		16	31.11	odd	30
961.2.g.t.732.1		16	31.23	odd	10
8649.2.a.be.1.4		8	93.56	odd	6
8649.2.a.bf.1.4		8	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+1.23217 q^{2} +(1.03749 + 1.79698i) q^{3} -0.481752 q^{4} +(0.772811 - 1.33855i) q^{5} +(1.27836 + 2.21419i) q^{6} +(1.90188 + 3.29415i) q^{7} -3.05795 q^{8} +(-0.652760 + 1.13061i) q^{9} +(0.952237 - 1.64932i) q^{10} +(-1.88076 + 3.25758i) q^{11} +(-0.499811 - 0.865698i) q^{12} +(-1.31753 + 2.28203i) q^{13} +(2.34344 + 4.05896i) q^{14} +3.20713 q^{15} -2.80441 q^{16} +(1.88717 + 3.26867i) q^{17} +(-0.804313 + 1.39311i) q^{18} +(-3.04916 - 5.28130i) q^{19} +(-0.372303 + 0.644848i) q^{20} +(-3.94635 + 6.83528i) q^{21} +(-2.31742 + 4.01389i) q^{22} -0.909847 q^{23} +(-3.17258 - 5.49507i) q^{24} +(1.30553 + 2.26124i) q^{25} +(-1.62343 + 2.81186i) q^{26} +3.51600 q^{27} +(-0.916233 - 1.58696i) q^{28} +6.80859 q^{29} +3.95173 q^{30} +2.66037 q^{32} -7.80507 q^{33} +(2.32532 + 4.02757i) q^{34} +5.87917 q^{35} +(0.314468 - 0.544675i) q^{36} +(-0.907032 - 1.57103i) q^{37} +(-3.75709 - 6.50747i) q^{38} -5.46769 q^{39} +(-2.36321 + 4.09321i) q^{40} +(-0.168572 + 0.291976i) q^{41} +(-4.86258 + 8.42224i) q^{42} +(1.94200 + 3.36364i) q^{43} +(0.906060 - 1.56934i) q^{44} +(1.00892 + 1.74750i) q^{45} -1.12109 q^{46} -1.18915 q^{47} +(-2.90954 - 5.03948i) q^{48} +(-3.73429 + 6.46798i) q^{49} +(1.60863 + 2.78623i) q^{50} +(-3.91583 + 6.78242i) q^{51} +(0.634723 - 1.09937i) q^{52} +(-1.17206 + 2.03007i) q^{53} +4.33232 q^{54} +(2.90695 + 5.03498i) q^{55} +(-5.81584 - 10.0733i) q^{56} +(6.32692 - 10.9586i) q^{57} +8.38936 q^{58} +(-3.88942 - 6.73667i) q^{59} -1.54504 q^{60} +2.72343 q^{61} -4.96588 q^{63} +8.88686 q^{64} +(2.03641 + 3.52716i) q^{65} -9.61719 q^{66} +(3.71059 - 6.42693i) q^{67} +(-0.909147 - 1.57469i) q^{68} +(-0.943955 - 1.63498i) q^{69} +7.24416 q^{70} +(2.54909 - 4.41515i) q^{71} +(1.99610 - 3.45735i) q^{72} +(2.69587 - 4.66939i) q^{73} +(-1.11762 - 1.93577i) q^{74} +(-2.70893 + 4.69201i) q^{75} +(1.46894 + 2.54427i) q^{76} -14.3079 q^{77} -6.73714 q^{78} +(-4.86861 - 8.43268i) q^{79} +(-2.16728 + 3.75384i) q^{80} +(5.60609 + 9.71003i) q^{81} +(-0.207710 + 0.359765i) q^{82} +(-4.19757 + 7.27041i) q^{83} +(1.90116 - 3.29291i) q^{84} +5.83370 q^{85} +(2.39288 + 4.14458i) q^{86} +(7.06383 + 12.2349i) q^{87} +(5.75127 - 9.96149i) q^{88} -5.09560 q^{89} +(1.24316 + 2.15322i) q^{90} -10.0231 q^{91} +0.438320 q^{92} -1.46523 q^{94} -9.42569 q^{95} +(2.76010 + 4.78064i) q^{96} +10.9142 q^{97} +(-4.60129 + 7.96966i) q^{98} +(-2.45537 - 4.25283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 3 q^{3} + 16 q^{4} - 3 q^{5} - 11 q^{6} + 2 q^{7} - 18 q^{8} - 5 q^{9} + 13 q^{10} - 18 q^{11} - 8 q^{13} + 9 q^{14} + 36 q^{15} + 8 q^{16} - 14 q^{17} - 23 q^{18} + 6 q^{19} + 7 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 3 * q^3 + 16 * q^4 - 3 * q^5 - 11 * q^6 + 2 * q^7 - 18 * q^8 - 5 * q^9 + 13 * q^10 - 18 * q^11 - 8 * q^13 + 9 * q^14 + 36 * q^15 + 8 * q^16 - 14 * q^17 - 23 * q^18 + 6 * q^19 + 7 * q^20 + q^21 - 4 * q^22 + 44 * q^23 - 30 * q^24 - 13 * q^25 - 9 * q^26 + 36 * q^27 + 5 * q^28 + 24 * q^29 + 22 * q^30 - 42 * q^32 + 12 * q^33 + 7 * q^34 - 24 * q^35 + q^36 + 8 * q^37 - 7 * q^38 + 2 * q^39 - 11 * q^40 + 22 * q^41 + 6 * q^42 + 2 * q^43 - 4 * q^44 + 36 * q^46 - 36 * q^47 + q^48 + 2 * q^49 - 27 * q^50 - 2 * q^51 + q^52 - 6 * q^53 - 14 * q^54 - 28 * q^55 - 30 * q^56 + 17 * q^57 - 10 * q^58 + 4 * q^59 - 80 * q^60 + 60 * q^61 - 46 * q^63 + 18 * q^64 - 3 * q^65 + 20 * q^66 + 13 * q^67 - 30 * q^68 - 22 * q^69 - 78 * q^70 + q^71 - 3 * q^72 - 2 * q^73 - 8 * q^74 - 23 * q^75 + 33 * q^76 - 48 * q^77 - 8 * q^79 - 24 * q^80 + 28 * q^81 + 19 * q^82 - 39 * q^83 - 8 * q^84 - 52 * q^85 + 16 * q^86 + 15 * q^87 + 17 * q^88 + 54 * q^89 - 8 * q^90 + 32 * q^91 + 64 * q^92 + 44 * q^94 - 12 * q^95 + 12 * q^96 + 68 * q^97 - 10 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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