LMFDB - Embedded newform 961.2.d.q.531.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(374,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.374"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,4,6,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == 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:	$4$ over $\Q(\zeta_{5})$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			531.4
Root			$1.42343i$ of defining polynomial
Character	$\chi$	$=$	961.531
Dual form			961.2.d.q.628.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.713065 + 2.19459i) q^{2} +(0.785745 - 2.41827i) q^{3} +(-2.68972 + 1.95420i) q^{4} -2.49846 q^{5} +5.86740 q^{6} +(-1.29595 + 0.941560i) q^{7} +(-2.47295 - 1.79670i) q^{8} +(-2.80360 - 2.03694i) q^{9} +(-1.78156 - 5.48309i) q^{10} +(0.593541 - 0.431233i) q^{11} +(2.61235 + 8.03999i) q^{12} +(0.585889 - 1.80318i) q^{13} +(-2.99043 - 2.17268i) q^{14} +(-1.96315 + 6.04196i) q^{15} +(0.124885 - 0.384356i) q^{16} +(-3.54288 - 2.57405i) q^{17} +(2.47109 - 7.60523i) q^{18} +(-1.43323 - 4.41103i) q^{19} +(6.72016 - 4.88248i) q^{20} +(1.25867 + 3.87378i) q^{21} +(1.36961 + 0.995081i) q^{22} +(-5.75896 - 4.18413i) q^{23} +(-6.28803 + 4.56852i) q^{24} +1.24230 q^{25} +4.37501 q^{26} +(-0.957471 + 0.695643i) q^{27} +(1.64574 - 5.06507i) q^{28} +(0.0398443 + 0.122628i) q^{29} -14.6595 q^{30} -5.18091 q^{32} +(-0.576467 - 1.77418i) q^{33} +(3.12268 - 9.61063i) q^{34} +(3.23787 - 2.35245i) q^{35} +11.5215 q^{36} -8.42948 q^{37} +(8.65840 - 6.29069i) q^{38} +(-3.90022 - 2.83368i) q^{39} +(6.17856 + 4.48899i) q^{40} +(-2.27869 - 7.01307i) q^{41} +(-7.60384 + 5.52452i) q^{42} +(-0.0712259 - 0.219211i) q^{43} +(-0.753746 + 2.31979i) q^{44} +(7.00469 + 5.08921i) q^{45} +(5.07593 - 15.6221i) q^{46} +(-2.48342 + 7.64319i) q^{47} +(-0.831350 - 0.604011i) q^{48} +(-1.37018 + 4.21697i) q^{49} +(0.885840 + 2.72634i) q^{50} +(-9.00856 + 6.54511i) q^{51} +(1.94789 + 5.99500i) q^{52} +(4.63910 + 3.37050i) q^{53} +(-2.20939 - 1.60522i) q^{54} +(-1.48294 + 1.07742i) q^{55} +4.89652 q^{56} -11.7932 q^{57} +(-0.240707 + 0.174884i) q^{58} +(2.93681 - 9.03857i) q^{59} +(-6.52685 - 20.0876i) q^{60} +7.84044 q^{61} +5.55122 q^{63} +(-3.94410 - 12.1387i) q^{64} +(-1.46382 + 4.50517i) q^{65} +(3.48254 - 2.53022i) q^{66} +4.82658 q^{67} +14.5596 q^{68} +(-14.6434 + 10.6391i) q^{69} +(7.47147 + 5.42834i) q^{70} +(2.75472 + 2.00142i) q^{71} +(3.27340 + 10.0745i) q^{72} +(2.17791 - 1.58234i) q^{73} +(-6.01076 - 18.4992i) q^{74} +(0.976130 - 3.00422i) q^{75} +(12.4750 + 9.06362i) q^{76} +(-0.363166 + 1.11771i) q^{77} +(3.43765 - 10.5800i) q^{78} +(3.66318 + 2.66146i) q^{79} +(-0.312019 + 0.960297i) q^{80} +(-2.28272 - 7.02548i) q^{81} +(13.7660 - 10.0016i) q^{82} +(-0.825183 - 2.53965i) q^{83} +(-10.9556 - 7.95971i) q^{84} +(8.85174 + 6.43117i) q^{85} +(0.430288 - 0.312623i) q^{86} +0.327856 q^{87} -2.24259 q^{88} +(-1.78355 + 1.29582i) q^{89} +(-6.17391 + 19.0013i) q^{90} +(0.938522 + 2.88847i) q^{91} +23.6666 q^{92} -18.5445 q^{94} +(3.58086 + 11.0208i) q^{95} +(-4.07088 + 12.5289i) q^{96} +(-9.94271 + 7.22380i) q^{97} -10.2315 q^{98} -2.54245 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 22 q^{6} - 9 q^{7} - 8 q^{8} - 10 q^{9} - 6 q^{10} - 4 q^{11} + 5 q^{12} - 9 q^{13} - 18 q^{14} - 4 q^{15} - 2 q^{16} - 17 q^{17} - 14 q^{18} - 7 q^{19} + 36 q^{20}+ \cdots + 12 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 22 * q^6 - 9 * q^7 - 8 * q^8 - 10 * q^9 - 6 * q^10 - 4 * q^11 + 5 * q^12 - 9 * q^13 - 18 * q^14 - 4 * q^15 - 2 * q^16 - 17 * q^17 - 14 * q^18 - 7 * q^19 + 36 * q^20 - 2 * q^21 + 8 * q^22 - 21 * q^23 - 5 * q^24 + 26 * q^25 + 18 * q^26 - 9 * q^27 + 20 * q^28 - 26 * q^29 + 22 * q^30 - 42 * q^32 + 7 * q^33 + 56 * q^34 + 21 * q^35 - 2 * q^36 - 16 * q^37 + 24 * q^38 + 2 * q^39 - 13 * q^40 + 6 * q^41 - 12 * q^42 + 16 * q^43 - 37 * q^44 - 5 * q^45 + 16 * q^46 + 4 * q^47 - 37 * q^48 - 39 * q^49 - 21 * q^50 - 11 * q^51 + 18 * q^52 - 3 * q^53 - 39 * q^54 - 29 * q^55 + 60 * q^56 - 34 * q^57 - 10 * q^58 - 3 * q^59 - 35 * q^60 + 60 * q^61 - 46 * q^63 - 32 * q^64 - 9 * q^65 + 20 * q^66 - 26 * q^67 + 60 * q^68 - 21 * q^69 + 27 * q^70 + 18 * q^71 - 4 * q^72 + 9 * q^73 - 64 * q^74 - 19 * q^75 + 9 * q^76 + 42 * q^77 + 15 * q^78 - 14 * q^79 + 18 * q^80 + 29 * q^81 + 32 * q^82 - 67 * q^83 - 39 * q^84 + 63 * q^85 + 23 * q^86 - 30 * q^87 - 34 * q^88 - 26 * q^89 - 24 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 + 28 * q^95 - 4 * q^96 - 37 * q^97 + 20 * q^98 + 12 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.713065	+	2.19459i	0.504213	+	1.55181i	0.802089	+	0.597204i	$0.203722\pi$
$2$	0.713065	+	2.19459i	0.504213	+	1.55181i	−0.297876	+	0.954604i	$0.596278\pi$
$3$	0.785745	−	2.41827i	0.453650	−	1.39619i	−0.419063	−	0.907957i	$-0.637641\pi$
$3$	0.785745	−	2.41827i	0.453650	−	1.39619i	0.872713	−	0.488234i	$-0.162359\pi$
$4$	−2.68972	+	1.95420i	−1.34486	+	0.977099i
$5$	−2.49846			−1.11735			−0.558673	−	0.829388i	$-0.688689\pi$
$5$	−2.49846			−1.11735			−0.558673	+	0.829388i	$0.688689\pi$
$6$	5.86740			2.39536
$7$	−1.29595	+	0.941560i	−0.489822	+	0.355876i	−0.805116	−	0.593118i	$-0.797897\pi$
$7$	−1.29595	+	0.941560i	−0.489822	+	0.355876i	0.315294	+	0.948994i	$0.397897\pi$
$8$	−2.47295	−	1.79670i	−0.874320	−	0.635230i
$9$	−2.80360	−	2.03694i	−0.934535	−	0.678979i
$10$	−1.78156	−	5.48309i	−0.563380	−	1.73391i
$11$	0.593541	−	0.431233i	0.178959	−	0.130022i	−0.494699	−	0.869064i	$-0.664722\pi$
$11$	0.593541	−	0.431233i	0.178959	−	0.130022i	0.673659	+	0.739043i	$0.264722\pi$
$12$	2.61235	+	8.03999i	0.754121	+	2.32094i
$13$	0.585889	−	1.80318i	0.162496	−	0.500112i	−0.836347	−	0.548201i	$-0.815313\pi$
$13$	0.585889	−	1.80318i	0.162496	−	0.500112i	0.998843	+	0.0480886i	$0.0153130\pi$
$14$	−2.99043	−	2.17268i	−0.799227	−	0.580672i
$15$	−1.96315	+	6.04196i	−0.506884	+	1.56003i
$16$	0.124885	−	0.384356i	0.0312212	−	0.0960889i
$17$	−3.54288	−	2.57405i	−0.859274	−	0.624299i	0.0684130	−	0.997657i	$-0.478206\pi$
$17$	−3.54288	−	2.57405i	−0.859274	−	0.624299i	−0.927687	+	0.373358i	$0.878206\pi$
$18$	2.47109	−	7.60523i	0.582441	−	1.79257i
$19$	−1.43323	−	4.41103i	−0.328805	−	1.01196i	−0.969694	−	0.244324i	$-0.921434\pi$
$19$	−1.43323	−	4.41103i	−0.328805	−	1.01196i	0.640888	−	0.767634i	$-0.278566\pi$
$20$	6.72016	−	4.88248i	1.50267	−	1.09176i
$21$	1.25867	+	3.87378i	0.274664	+	0.845328i
$22$	1.36961	+	0.995081i	0.292002	+	0.212152i
$23$	−5.75896	−	4.18413i	−1.20083	−	0.872451i	−0.206460	−	0.978455i	$-0.566194\pi$
$23$	−5.75896	−	4.18413i	−1.20083	−	0.872451i	−0.994366	+	0.106004i	$0.966194\pi$
$24$	−6.28803	+	4.56852i	−1.28354	+	0.932545i
$25$	1.24230			0.248460
$26$	4.37501			0.858011
$27$	−0.957471	+	0.695643i	−0.184265	+	0.133877i
$28$	1.64574	−	5.06507i	0.311016	−	0.957209i
$29$	0.0398443	+	0.122628i	0.00739891	+	0.0227715i	0.954688	−	0.297609i	$-0.0961892\pi$
$29$	0.0398443	+	0.122628i	0.00739891	+	0.0227715i	−0.947289	+	0.320381i	$0.896189\pi$
$30$	−14.6595			−2.67644
$31$		0			0
$31$		0			0
$32$	−5.18091			−0.915865
$33$	−0.576467	−	1.77418i	−0.100350	−	0.308846i
$34$	3.12268	−	9.61063i	0.535536	−	1.64821i
$35$	3.23787	−	2.35245i	0.547300	−	0.397637i
$36$	11.5215			1.92025
$37$	−8.42948			−1.38580			−0.692899	−	0.721035i	$-0.743667\pi$
$37$	−8.42948			−1.38580			−0.692899	+	0.721035i	$0.743667\pi$
$38$	8.65840	−	6.29069i	1.40458	−	1.02049i
$39$	−3.90022	−	2.83368i	−0.624536	−	0.453752i
$40$	6.17856	+	4.48899i	0.976917	+	0.709772i
$41$	−2.27869	−	7.01307i	−0.355871	−	1.09526i	−0.955503	−	0.294982i	$-0.904686\pi$
$41$	−2.27869	−	7.01307i	−0.355871	−	1.09526i	0.599632	−	0.800276i	$-0.295314\pi$
$42$	−7.60384	+	5.52452i	−1.17330	+	0.852451i
$43$	−0.0712259	−	0.219211i	−0.0108618	−	0.0334293i	0.945479	−	0.325684i	$-0.105595\pi$
$43$	−0.0712259	−	0.219211i	−0.0108618	−	0.0334293i	−0.956341	+	0.292255i	$0.905595\pi$
$44$	−0.753746	+	2.31979i	−0.113631	+	0.349722i
$45$	7.00469	+	5.08921i	1.04420	+	0.758654i
$46$	5.07593	−	15.6221i	0.748404	−	2.30335i
$47$	−2.48342	+	7.64319i	−0.362244	+	1.11487i	0.589444	+	0.807809i	$0.299347\pi$
$47$	−2.48342	+	7.64319i	−0.362244	+	1.11487i	−0.951689	+	0.307065i	$0.900653\pi$
$48$	−0.831350	−	0.604011i	−0.119995	−	0.0871815i
$49$	−1.37018	+	4.21697i	−0.195740	+	0.602424i
$50$	0.885840	+	2.72634i	0.125277	+	0.385562i
$51$	−9.00856	+	6.54511i	−1.26145	+	0.916498i
$52$	1.94789	+	5.99500i	0.270124	+	0.831356i
$53$	4.63910	+	3.37050i	0.637229	+	0.462974i	0.858897	−	0.512148i	$-0.171150\pi$
$53$	4.63910	+	3.37050i	0.637229	+	0.462974i	−0.221668	+	0.975122i	$0.571150\pi$
$54$	−2.20939	−	1.60522i	−0.300660	−	0.218442i
$55$	−1.48294	+	1.07742i	−0.199959	+	0.145279i
$56$	4.89652			0.654324
$57$	−11.7932			−1.56205
$58$	−0.240707	+	0.174884i	−0.0316064	+	0.0229634i
$59$	2.93681	−	9.03857i	0.382340	−	1.17672i	−0.556051	−	0.831148i	$-0.687684\pi$
$59$	2.93681	−	9.03857i	0.382340	−	1.17672i	0.938392	−	0.345574i	$-0.112316\pi$
$60$	−6.52685	−	20.0876i	−0.842613	−	2.59330i
$61$	7.84044			1.00387			0.501933	−	0.864907i	$-0.332623\pi$
$61$	7.84044			1.00387			0.501933	+	0.864907i	$0.332623\pi$
$62$		0			0
$63$	5.55122			0.699388
$64$	−3.94410	−	12.1387i	−0.493012	−	1.51734i
$65$	−1.46382	+	4.50517i	−0.181564	+	0.558798i
$66$	3.48254	−	2.53022i	0.428671	−	0.311448i
$67$	4.82658			0.589660			0.294830	−	0.955550i	$-0.404737\pi$
$67$	4.82658			0.589660			0.294830	+	0.955550i	$0.404737\pi$
$68$	14.5596			1.76561
$69$	−14.6434	+	10.6391i	−1.76286	+	1.28079i
$70$	7.47147	+	5.42834i	0.893012	+	0.648811i
$71$	2.75472	+	2.00142i	0.326925	+	0.237525i	0.739125	−	0.673569i	$-0.235239\pi$
$71$	2.75472	+	2.00142i	0.326925	+	0.237525i	−0.412200	+	0.911093i	$0.635239\pi$
$72$	3.27340	+	10.0745i	0.385774	+	1.18729i
$73$	2.17791	−	1.58234i	0.254905	−	0.185199i	−0.452993	−	0.891514i	$-0.649644\pi$
$73$	2.17791	−	1.58234i	0.254905	−	0.185199i	0.707898	+	0.706315i	$0.249644\pi$
$74$	−6.01076	−	18.4992i	−0.698737	−	2.15049i
$75$	0.976130	−	3.00422i	0.112714	−	0.346898i
$76$	12.4750	+	9.06362i	1.43098	+	1.03967i
$77$	−0.363166	+	1.11771i	−0.0413866	+	0.127375i
$78$	3.43765	−	10.5800i	0.389237	−	1.19795i
$79$	3.66318	+	2.66146i	0.412140	+	0.299438i	0.774468	−	0.632613i	$-0.218018\pi$
$79$	3.66318	+	2.66146i	0.412140	+	0.299438i	−0.362327	+	0.932051i	$0.618018\pi$
$80$	−0.312019	+	0.960297i	−0.0348848	+	0.107364i
$81$	−2.28272	−	7.02548i	−0.253635	−	0.780609i
$82$	13.7660	−	10.0016i	1.52020	−	1.10449i
$83$	−0.825183	−	2.53965i	−0.0905756	−	0.278763i	0.895500	−	0.445062i	$-0.146818\pi$
$83$	−0.825183	−	2.53965i	−0.0905756	−	0.278763i	−0.986075	+	0.166299i	$0.946818\pi$
$84$	−10.9556	−	7.95971i	−1.19535	−	0.868476i
$85$	8.85174	+	6.43117i	0.960106	+	0.697558i
$86$	0.430288	−	0.312623i	0.0463992	−	0.0337110i
$87$	0.327856			0.0351499
$88$	−2.24259			−0.239061
$89$	−1.78355	+	1.29582i	−0.189056	+	0.137357i	−0.678287	−	0.734797i	$-0.737277\pi$
$89$	−1.78355	+	1.29582i	−0.189056	+	0.137357i	0.489231	+	0.872154i	$0.337277\pi$
$90$	−6.17391	+	19.0013i	−0.650788	+	2.00292i
$91$	0.938522	+	2.88847i	0.0983839	+	0.302794i
$92$	23.6666			2.46741
$93$		0			0
$94$	−18.5445			−1.91272
$95$	3.58086	+	11.0208i	0.367389	+	1.13071i
$96$	−4.07088	+	12.5289i	−0.415482	+	1.27872i
$97$	−9.94271	+	7.22380i	−1.00953	+	0.733466i	−0.964110	−	0.265502i	$-0.914462\pi$
$97$	−9.94271	+	7.22380i	−1.00953	+	0.733466i	−0.0454190	+	0.998968i	$0.514462\pi$
$98$	−10.2315			−1.03354
$99$	−2.54245			−0.255526
$100$	−3.34144	+	2.42770i	−0.334144	+	0.242770i
$101$	−5.94168	−	4.31688i	−0.591219	−	0.429546i	0.251532	−	0.967849i	$-0.419066\pi$
$101$	−5.94168	−	4.31688i	−0.591219	−	0.429546i	−0.842751	+	0.538303i	$0.819066\pi$
$102$	−20.7875	−	15.1030i	−2.05827	−	1.49542i
$103$	1.72702	+	5.31522i	0.170168	+	0.523724i	0.999380	−	0.0352107i	$-0.0112102\pi$
$103$	1.72702	+	5.31522i	0.170168	+	0.523724i	−0.829212	+	0.558935i	$0.811210\pi$
$104$	−4.68865	+	3.40651i	−0.459760	+	0.334035i
$105$	−3.14473	−	9.67849i	−0.306894	−	0.944523i
$106$	−4.08889	+	12.5843i	−0.397148	+	1.22229i
$107$	−1.47578	−	1.07221i	−0.142669	−	0.103655i	0.514162	−	0.857693i	$-0.328103\pi$
$107$	−1.47578	−	1.07221i	−0.142669	−	0.103655i	−0.656830	+	0.754038i	$0.728103\pi$
$108$	1.21591	−	3.74218i	0.117001	−	0.360091i
$109$	3.63567	−	11.1895i	0.348234	−	1.07176i	−0.611595	−	0.791171i	$-0.709472\pi$
$109$	3.63567	−	11.1895i	0.348234	−	1.07176i	0.959829	−	0.280584i	$-0.0905282\pi$
$110$	−3.42192	−	2.48617i	−0.326267	−	0.237047i
$111$	−6.62342	+	20.3848i	−0.628667	+	1.93484i
$112$	0.200050	+	0.615691i	0.0189030	+	0.0581773i
$113$	−8.94331	+	6.49769i	−0.841315	+	0.611251i	−0.922738	−	0.385428i	$-0.874054\pi$
$113$	−8.94331	+	6.49769i	−0.841315	+	0.611251i	0.0814223	+	0.996680i	$0.474054\pi$
$114$	−8.40933	−	25.8813i	−0.787606	−	2.42400i
$115$	14.3885	+	10.4539i	1.34174	+	0.974829i
$116$	−0.346810	−	0.251972i	−0.0322005	−	0.0233950i
$117$	−5.31557	+	3.86198i	−0.491424	+	0.357041i
$118$	21.9301			2.01883
$119$	7.01501			0.643065
$120$	15.7104	−	11.4143i	1.43416	−	1.04197i
$121$	−3.23286	+	9.94971i	−0.293896	+	0.904519i
$122$	5.59074	+	17.2065i	0.506162	+	1.55781i
$123$	−18.7500			−1.69063
$124$		0			0
$125$	9.38846			0.839730
$126$	3.95838	+	12.1826i	0.352641	+	1.08532i
$127$	0.397715	−	1.22404i	0.0352915	−	0.108616i	−0.931859	−	0.362821i	$-0.881814\pi$
$127$	0.397715	−	1.22404i	0.0352915	−	0.108616i	0.967150	+	0.254205i	$0.0818137\pi$
$128$	15.4441	−	11.2208i	1.36508	−	0.991789i
$129$	−0.586077			−0.0516012
$130$	−10.9308			−0.958694
$131$	6.48860	−	4.71425i	0.566912	−	0.411886i	−0.267070	−	0.963677i	$-0.586056\pi$
$131$	6.48860	−	4.71425i	0.566912	−	0.411886i	0.833982	+	0.551792i	$0.186056\pi$
$132$	5.01764	+	3.64553i	0.436730	+	0.317303i
$133$	6.01064	+	4.36698i	0.521188	+	0.378665i
$134$	3.44166	+	10.5924i	0.297315	+	0.915040i
$135$	2.39220	−	1.73804i	0.205888	−	0.149586i
$136$	4.13655	+	12.7310i	0.354707	+	1.09167i
$137$	5.09160	−	15.6703i	0.435005	−	1.33881i	−0.458077	−	0.888912i	$-0.651462\pi$
$137$	5.09160	−	15.6703i	0.435005	−	1.33881i	0.893082	−	0.449894i	$-0.148538\pi$
$138$	−33.7901	−	24.5500i	−2.87641	−	2.08983i
$139$	−2.26813	+	6.98058i	−0.192380	+	0.592085i	0.807617	+	0.589707i	$0.200757\pi$
$139$	−2.26813	+	6.98058i	−0.192380	+	0.592085i	−0.999997	+	0.00237796i	$0.999243\pi$
$140$	−4.11182	+	12.6549i	−0.347512	+	1.06953i
$141$	16.5320	+	12.0112i	1.39224	+	1.01152i
$142$	−2.42800	+	7.47261i	−0.203753	+	0.627088i
$143$	−0.429841	−	1.32292i	−0.0359451	−	0.110628i
$144$	−1.13304	+	0.823199i	−0.0944196	+	0.0685999i
$145$	−0.0995495	−	0.306382i	−0.00826713	−	0.0254436i
$146$	5.02559	+	3.65130i	0.415921	+	0.302184i
$147$	9.12118	+	6.62693i	0.752302	+	0.546580i
$148$	22.6730	−	16.4729i	1.86371	−	1.35406i
$149$	−6.36193			−0.521189			−0.260595	−	0.965448i	$-0.583919\pi$
$149$	−6.36193			−0.521189			−0.260595	+	0.965448i	$0.583919\pi$
$150$	7.28907			0.595150
$151$	−4.46960	+	3.24736i	−0.363731	+	0.264266i	−0.754607	−	0.656177i	$-0.772172\pi$
$151$	−4.46960	+	3.24736i	−0.363731	+	0.264266i	0.390875	+	0.920444i	$0.372172\pi$
$152$	−4.38100	+	13.4833i	−0.355346	+	1.09364i
$153$	4.68965	+	14.4332i	0.379135	+	1.16686i
$154$	−2.71187			−0.218529
$155$		0			0
$156$	16.0281			1.28327
$157$	2.47043	+	7.60320i	0.197162	+	0.606801i	0.999945	+	0.0105298i	$0.00335181\pi$
$157$	2.47043	+	7.60320i	0.197162	+	0.606801i	−0.802783	+	0.596271i	$0.796648\pi$
$158$	−3.22872	+	9.93698i	−0.256863	+	0.790543i
$159$	11.7959	−	8.57025i	0.935479	−	0.679665i
$160$	12.9443			1.02334
$161$	11.4029			0.898675
$162$	13.7903	−	10.0192i	1.08347	−	0.787186i
$163$	13.8062	+	10.0308i	1.08138	+	0.785672i	0.977924	−	0.208961i	$-0.0670083\pi$
$163$	13.8062	+	10.0308i	1.08138	+	0.785672i	0.103461	+	0.994634i	$0.467008\pi$
$164$	19.8340	+	14.4102i	1.54877	+	1.12525i
$165$	1.44028	+	4.43272i	0.112126	+	0.345087i
$166$	4.98508	−	3.62188i	0.386918	−	0.281112i
$167$	7.53143	+	23.1793i	0.582799	+	1.79367i	0.607934	+	0.793988i	$0.291999\pi$
$167$	7.53143	+	23.1793i	0.582799	+	1.79367i	−0.0251344	+	0.999684i	$0.508001\pi$
$168$	3.84741	−	11.8411i	0.296834	−	0.913562i
$169$	7.60903	+	5.52828i	0.585310	+	0.425253i
$170$	−7.80190	+	24.0118i	−0.598378	+	1.84162i
$171$	−4.96678	+	15.2862i	−0.379819	+	1.16896i
$172$	0.619959	+	0.450426i	0.0472714	+	0.0343447i
$173$	2.77300	−	8.53440i	0.210827	−	0.648859i	−0.788597	−	0.614911i	$-0.789192\pi$
$173$	2.77300	−	8.53440i	0.210827	−	0.648859i	0.999424	−	0.0339478i	$-0.0108080\pi$
$174$	0.233783	+	0.719510i	0.0177230	+	0.0545459i
$175$	−1.60995	+	1.16970i	−0.121701	+	0.0884210i
$176$	−0.0916225	−	0.281985i	−0.00690630	−	0.0212554i
$177$	−19.5502	−	14.2040i	−1.46948	−	1.06764i
$178$	−4.11558	−	2.99015i	−0.308476	−	0.224121i
$179$	−9.13422	+	6.63640i	−0.682724	+	0.496028i	−0.874260	−	0.485458i	$-0.838653\pi$
$179$	−9.13422	+	6.63640i	−0.682724	+	0.496028i	0.191536	+	0.981486i	$0.438653\pi$
$180$	−28.7860			−2.14558
$181$	14.9410			1.11056			0.555279	−	0.831664i	$-0.312611\pi$
$181$	14.9410			1.11056			0.555279	+	0.831664i	$0.312611\pi$
$182$	−5.66979	+	4.11934i	−0.420273	+	0.305346i
$183$	6.16058	−	18.9603i	0.455403	−	1.40159i
$184$	6.72398	+	20.6943i	0.495698	+	1.52560i
$185$	21.0607			1.54841
$186$		0			0
$187$	−3.21286			−0.234947
$188$	−8.25658	−	25.4112i	−0.602173	−	1.85330i
$189$	0.585841	−	1.80303i	0.0426137	−	0.131151i
$190$	−21.6327	+	15.7170i	−1.56940	+	1.14023i
$191$	2.26093			0.163595			0.0817975	−	0.996649i	$-0.473934\pi$
$191$	2.26093			0.163595			0.0817975	+	0.996649i	$0.473934\pi$
$192$	−32.4537			−2.34215
$193$	−20.7628	+	15.0851i	−1.49454	+	1.08585i	−0.522047	+	0.852917i	$0.674831\pi$
$193$	−20.7628	+	15.0851i	−1.49454	+	1.08585i	−0.972493	+	0.232930i	$0.925169\pi$
$194$	−22.9431	−	16.6691i	−1.64722	−	1.19677i
$195$	9.74455	+	7.07983i	0.697822	+	0.506997i
$196$	−4.55540	−	14.0201i	−0.325386	−	1.00143i
$197$	−5.01244	+	3.64175i	−0.357121	+	0.259464i	−0.751850	−	0.659334i	$-0.770838\pi$
$197$	−5.01244	+	3.64175i	−0.357121	+	0.259464i	0.394729	+	0.918798i	$0.370838\pi$
$198$	−1.81293	−	5.57962i	−0.128839	−	0.396527i
$199$	1.41200	−	4.34569i	0.100094	−	0.308058i	−0.888454	−	0.458966i	$-0.848220\pi$
$199$	1.41200	−	4.34569i	0.100094	−	0.308058i	0.988548	+	0.150908i	$0.0482199\pi$
$200$	−3.07214	−	2.23204i	−0.217233	−	0.157829i
$201$	3.79246	−	11.6720i	0.267499	−	0.823279i
$202$	5.23698	−	16.1178i	0.368472	−	1.13404i
$203$	−0.167098	−	0.121404i	−0.0117280	−	0.00852088i
$204$	11.4401	−	35.2090i	0.800968	−	2.46513i
$205$	5.69320	+	17.5219i	0.397630	+	1.22378i
$206$	−10.4332	+	7.58019i	−0.726918	+	0.528137i
$207$	7.62303	+	23.4613i	0.529837	+	1.63067i
$208$	−0.619894	−	0.450379i	−0.0429819	−	0.0312282i
$209$	−2.75286	−	2.00007i	−0.190419	−	0.138348i
$210$	18.9979	−	13.8028i	1.31098	−	0.952482i
$211$	−18.6168			−1.28163			−0.640816	−	0.767695i	$-0.721404\pi$
$211$	−18.6168			−1.28163			−0.640816	+	0.767695i	$0.721404\pi$
$212$	−19.0645			−1.30936
$213$	7.00448	−	5.08906i	0.479939	−	0.348696i
$214$	1.30074	−	4.00328i	0.0889171	−	0.273659i
$215$	0.177955	+	0.547689i	0.0121364	+	0.0373521i
$216$	3.61764			0.246149
$217$		0			0
$218$	27.1487			1.83874
$219$	−2.11526	−	6.51010i	−0.142936	−	0.439912i
$220$	1.88320	−	5.79591i	0.126966	−	0.390760i
$221$	−6.71721	+	4.88034i	−0.451849	+	0.328287i
$222$	−49.4591			−3.31948
$223$	−6.21495			−0.416184			−0.208092	−	0.978109i	$-0.566725\pi$
$223$	−6.21495			−0.416184			−0.208092	+	0.978109i	$0.566725\pi$
$224$	6.71419	−	4.87814i	0.448611	−	0.325935i
$225$	−3.48292	−	2.53049i	−0.232194	−	0.168699i
$226$	−20.6369	−	14.9936i	−1.37275	−	0.997359i
$227$	−4.03199	−	12.4092i	−0.267613	−	0.823627i	−0.991080	−	0.133268i	$-0.957453\pi$
$227$	−4.03199	−	12.4092i	−0.267613	−	0.823627i	0.723467	−	0.690359i	$-0.242547\pi$
$228$	31.7205	−	23.0463i	2.10074	−	1.52628i
$229$	−4.72114	−	14.5302i	−0.311982	−	0.960181i	−0.976979	−	0.213335i	$-0.931567\pi$
$229$	−4.72114	−	14.5302i	−0.311982	−	0.960181i	0.664997	−	0.746846i	$-0.268433\pi$
$230$	−12.6820	+	39.0312i	−0.836226	+	2.57364i
$231$	2.41757	+	1.75647i	0.159065	+	0.115567i
$232$	0.121794	−	0.374842i	0.00799614	−	0.0246096i
$233$	4.03615	−	12.4220i	0.264417	−	0.813792i	−0.727410	−	0.686203i	$-0.759276\pi$
$233$	4.03615	−	12.4220i	0.264417	−	0.813792i	0.991827	−	0.127589i	$-0.0407238\pi$
$234$	−12.2658	−	8.91163i	−0.801841	−	0.582572i
$235$	6.20473	−	19.0962i	0.404752	−	1.24570i
$236$	9.76395	+	30.0504i	0.635579	+	1.95611i
$237$	9.31447	−	6.76736i	0.605040	−	0.439587i
$238$	5.00216	+	15.3951i	0.324242	+	0.997913i
$239$	−18.9652	−	13.7790i	−1.22675	−	0.891289i	−0.230111	−	0.973164i	$-0.573909\pi$
$239$	−18.9652	−	13.7790i	−1.22675	−	0.891289i	−0.996643	+	0.0818753i	$0.973909\pi$
$240$	2.07709	+	1.50910i	0.134076	+	0.0974118i
$241$	19.9925	−	14.5254i	1.28783	−	0.935663i	0.288071	−	0.957609i	$-0.406986\pi$
$241$	19.9925	−	14.5254i	1.28783	−	0.935663i	0.999759	+	0.0219459i	$0.00698616\pi$
$242$	−24.1408			−1.55183
$243$	−22.3337			−1.43271
$244$	−21.0886	+	15.3218i	−1.35006	+	0.980875i
$245$	3.42333	−	10.5359i	0.218709	−	0.673116i
$246$	−13.3700	−	41.1485i	−0.852438	−	2.62353i
$247$	−8.79358			−0.559522
$248$		0			0
$249$	−6.78996			−0.430296
$250$	6.69458	+	20.6038i	0.423403	+	1.30310i
$251$	7.16738	−	22.0589i	0.452401	−	1.39235i	−0.421758	−	0.906709i	$-0.638587\pi$
$251$	7.16738	−	22.0589i	0.452401	−	1.39235i	0.874159	−	0.485640i	$-0.161413\pi$
$252$	−14.9312	+	10.8482i	−0.940580	+	0.683371i
$253$	−5.22251			−0.328336
$254$	2.96986			0.186346
$255$	22.5075	−	16.3527i	1.40948	−	1.02404i
$256$	14.9862	+	10.8881i	0.936635	+	0.680505i
$257$	−12.4153	−	9.02022i	−0.774443	−	0.562666i	0.128863	−	0.991662i	$-0.458867\pi$
$257$	−12.4153	−	9.02022i	−0.774443	−	0.562666i	−0.903306	+	0.428997i	$0.858867\pi$
$258$	−0.417911	−	1.28620i	−0.0260180	−	0.0800752i
$259$	10.9242	−	7.93686i	0.678794	−	0.493173i
$260$	−4.86673	−	14.9783i	−0.301822	−	0.928912i
$261$	0.138078	−	0.424962i	0.00854684	−	0.0263045i
$262$	14.9726	+	10.8782i	0.925012	+	0.672060i
$263$	2.10313	−	6.47277i	0.129685	−	0.399128i	−0.865041	−	0.501701i	$-0.832708\pi$
$263$	2.10313	−	6.47277i	0.129685	−	0.399128i	0.994725	+	0.102573i	$0.0327076\pi$
$264$	−1.76211	+	5.42321i	−0.108450	+	0.333775i
$265$	−11.5906	−	8.42106i	−0.712005	−	0.517302i
$266$	−5.29775	+	16.3048i	−0.324826	+	0.999712i
$267$	1.73224	+	5.33129i	0.106012	+	0.326270i
$268$	−12.9822	+	9.43209i	−0.793011	+	0.576157i
$269$	−3.25075	−	10.0048i	−0.198202	−	0.610002i	−0.999924	−	0.0123058i	$-0.996083\pi$
$269$	−3.25075	−	10.0048i	−0.198202	−	0.610002i	0.801723	−	0.597696i	$-0.203917\pi$
$270$	5.52007	+	4.01057i	0.335941	+	0.244075i
$271$	−1.27593	−	0.927019i	−0.0775074	−	0.0563124i	0.548357	−	0.836244i	$-0.315254\pi$
$271$	−1.27593	−	0.927019i	−0.0775074	−	0.0563124i	−0.625864	+	0.779932i	$0.715254\pi$
$272$	−1.43180	+	1.04027i	−0.0868158	+	0.0630754i
$273$	7.72256			0.467391
$274$	38.0206			2.29691
$275$	0.737355	−	0.535720i	0.0444642	−	0.0323051i
$276$	18.5959	−	57.2323i	1.11934	−	3.44498i
$277$	−3.73952	−	11.5091i	−0.224686	−	0.691513i	−0.998323	−	0.0578841i	$-0.981565\pi$
$277$	−3.73952	−	11.5091i	−0.224686	−	0.691513i	0.773637	−	0.633629i	$-0.218435\pi$
$278$	−16.9368			−1.01580
$279$		0			0
$280$	−12.2337			−0.731106
$281$	−6.63544	−	20.4218i	−0.395837	−	1.21826i	−0.928308	−	0.371813i	$-0.878736\pi$
$281$	−6.63544	−	20.4218i	−0.395837	−	1.21826i	0.532470	−	0.846449i	$-0.321264\pi$
$282$	−14.5712	+	44.8457i	−0.867705	+	2.67052i
$283$	0.557256	−	0.404870i	0.0331254	−	0.0240670i	−0.571099	−	0.820881i	$-0.693483\pi$
$283$	0.557256	−	0.404870i	0.0331254	−	0.0240670i	0.604225	+	0.796814i	$0.293483\pi$
$284$	−11.3206			−0.671753
$285$	29.4649			1.74535
$286$	2.59675	−	1.88665i	0.153549	−	0.111560i
$287$	9.55629	+	6.94305i	0.564090	+	0.409835i
$288$	14.5252	+	10.5532i	0.855908	+	0.621853i
$289$	0.672959	+	2.07116i	0.0395858	+	0.121833i
$290$	0.601397	−	0.436940i	0.0353152	−	0.0256580i
$291$	9.65670	+	29.7203i	0.566086	+	1.74223i
$292$	−2.76576	+	8.51214i	−0.161854	+	0.498135i
$293$	−7.29076	−	5.29705i	−0.425931	−	0.309457i	0.354089	−	0.935212i	$-0.384791\pi$
$293$	−7.29076	−	5.29705i	−0.425931	−	0.309457i	−0.780020	+	0.625755i	$0.784791\pi$
$294$	−8.03938	+	24.7427i	−0.468866	+	1.44302i
$295$	−7.33750	+	22.5825i	−0.427206	+	1.31480i
$296$	20.8457	+	15.1453i	1.21163	+	0.880301i
$297$	−0.268314	+	0.825785i	−0.0155692	+	0.0479169i
$298$	−4.53647	−	13.9618i	−0.262791	−	0.808786i
$299$	−10.9188	+	7.93300i	−0.631453	+	0.458777i
$300$	3.24532	+	9.98807i	0.187369	+	0.576662i
$301$	0.298705	+	0.217022i	0.0172171	+	0.0125089i
$302$	−10.3137	−	7.49336i	−0.593488	−	0.431195i
$303$	−15.1081	+	10.9766i	−0.867935	+	0.630592i
$304$	−1.87439			−0.107504
$305$	−19.5890			−1.12166
$306$	−28.3310	+	20.5837i	−1.61958	+	1.17669i
$307$	−9.68232	+	29.7991i	−0.552599	+	1.70073i	0.149601	+	0.988746i	$0.452201\pi$
$307$	−9.68232	+	29.7991i	−0.552599	+	1.70073i	−0.702201	+	0.711979i	$0.747799\pi$
$308$	−1.20741	−	3.71602i	−0.0687985	−	0.211740i
$309$	14.2107			0.808416
$310$		0			0
$311$	−17.7139			−1.00447			−0.502233	−	0.864732i	$-0.667488\pi$
$311$	−17.7139			−1.00447			−0.502233	+	0.864732i	$0.667488\pi$
$312$	4.55378	+	14.0151i	0.257807	+	0.793448i
$313$	6.69600	−	20.6082i	0.378480	−	1.16484i	−0.562620	−	0.826715i	$-0.690207\pi$
$313$	6.69600	−	20.6082i	0.378480	−	1.16484i	0.941101	−	0.338127i	$-0.109793\pi$
$314$	−14.9243	+	10.8431i	−0.842228	+	0.611914i
$315$	−13.8695			−0.781458
$316$	−15.0540			−0.846852
$317$	−0.821999	+	0.597217i	−0.0461681	+	0.0335431i	−0.610630	−	0.791916i	$-0.709084\pi$
$317$	−0.821999	+	0.597217i	−0.0461681	+	0.0335431i	0.564462	+	0.825459i	$0.309084\pi$
$318$	27.2195	+	19.7761i	1.52639	+	1.10899i
$319$	0.0765305	+	0.0556027i	0.00428489	+	0.00311315i
$320$	9.85417	+	30.3280i	0.550865	+	1.69539i
$321$	−3.75249	+	2.72635i	−0.209444	+	0.152170i
$322$	8.13102	+	25.0247i	0.453124	+	1.39457i
$323$	−6.27645	+	19.3169i	−0.349231	+	1.07482i
$324$	19.8690	+	14.4357i	1.10384	+	0.801984i
$325$	0.727849	−	2.24009i	0.0403738	−	0.124258i
$326$	−12.1687	+	37.4515i	−0.673964	+	2.07425i
$327$	−24.2025	−	17.5841i	−1.33840	−	0.972404i
$328$	−6.96533	+	21.4371i	−0.384596	+	1.18367i
$329$	−3.97814	−	12.2435i	−0.219322	−	0.675004i
$330$	−8.70099	+	6.32164i	−0.478974	+	0.347995i
$331$	−8.24749	−	25.3832i	−0.453323	−	1.39519i	−0.873093	−	0.487554i	$-0.837889\pi$
$331$	−8.24749	−	25.3832i	−0.453323	−	1.39519i	0.419769	−	0.907631i	$-0.362111\pi$
$332$	7.18250	+	5.21839i	0.394191	+	0.286396i
$333$	23.6329	+	17.1703i	1.29508	+	0.940928i
$334$	−45.4987	+	33.0568i	−2.48958	+	1.80879i
$335$	−12.0590			−0.658854
$336$	1.64610			0.0898020
$337$	25.8412	−	18.7748i	1.40766	−	1.02273i	0.414005	−	0.910274i	$-0.364129\pi$
$337$	25.8412	−	18.7748i	1.40766	−	1.02273i	0.993657	−	0.112452i	$-0.0358705\pi$
$338$	−6.70657	+	20.6407i	−0.364789	+	1.12271i
$339$	8.68604	+	26.7329i	0.471761	+	1.45193i
$340$	−36.3765			−1.97279
$341$		0			0
$342$	−37.0885			−2.00552
$343$	−5.65991	−	17.4194i	−0.305606	−	0.940560i
$344$	−0.217718	+	0.670069i	−0.0117386	+	0.0361277i
$345$	36.5860	−	26.5813i	1.96973	−	1.43109i
$346$	20.7068			1.11321
$347$	−3.12131			−0.167561			−0.0837804	−	0.996484i	$-0.526699\pi$
$347$	−3.12131			−0.167561			−0.0837804	+	0.996484i	$0.526699\pi$
$348$	−0.881842	+	0.640696i	−0.0472717	+	0.0343449i
$349$	17.8198	+	12.9468i	0.953871	+	0.693028i	0.951719	−	0.306970i	$-0.0993151\pi$
$349$	17.8198	+	12.9468i	0.953871	+	0.693028i	0.00215168	+	0.999998i	$0.499315\pi$
$350$	−3.71501	−	2.69911i	−0.198576	−	0.144274i
$351$	0.693399	+	2.13406i	0.0370109	+	0.113908i
$352$	−3.07508	+	2.23418i	−0.163903	+	0.119082i
$353$	−1.52419	−	4.69098i	−0.0811246	−	0.249676i	0.902265	−	0.431181i	$-0.141903\pi$
$353$	−1.52419	−	4.69098i	−0.0811246	−	0.249676i	−0.983390	+	0.181505i	$0.941903\pi$
$354$	17.2315	−	53.0330i	0.915841	−	2.81867i
$355$	−6.88255	−	5.00046i	−0.365288	−	0.265397i
$356$	2.26495	−	6.97081i	0.120042	−	0.369452i
$357$	5.51201	−	16.9642i	0.291726	−	0.897842i
$358$	−21.0775	−	15.3137i	−1.11398	−	0.809353i
$359$	−0.111512	+	0.343198i	−0.00588537	+	0.0181133i	−0.953956	−	0.299946i	$-0.903031\pi$
$359$	−0.111512	+	0.343198i	−0.00588537	+	0.0181133i	0.948071	+	0.318060i	$0.103031\pi$
$360$	−8.17846	−	25.1707i	−0.431042	−	1.32661i
$361$	−2.03167	+	1.47610i	−0.106930	+	0.0776893i
$362$	10.6539	+	32.7894i	0.559958	+	1.72337i
$363$	21.5209	+	15.6359i	1.12956	+	0.820671i
$364$	−8.16902	−	5.93514i	−0.428173	−	0.311086i
$365$	−5.44142	+	3.95342i	−0.284817	+	0.206932i
$366$	46.0030			2.40462
$367$	29.3869			1.53398			0.766992	−	0.641657i	$-0.221753\pi$
$367$	29.3869			1.53398			0.766992	+	0.641657i	$0.221753\pi$
$368$	−2.32740	+	1.69095i	−0.121324	+	0.0881470i
$369$	−7.89666	+	24.3034i	−0.411084	+	1.26519i
$370$	15.0177	+	46.2196i	0.780731	+	2.40284i
$371$	−9.18555			−0.476890
$372$		0			0
$373$	17.7284			0.917941			0.458971	−	0.888451i	$-0.348218\pi$
$373$	17.7284			0.917941			0.458971	+	0.888451i	$0.348218\pi$
$374$	−2.29098	−	7.05090i	−0.118464	−	0.364593i
$375$	7.37694	−	22.7039i	0.380943	−	1.17242i
$376$	19.8739	−	14.4392i	1.02492	−	0.744647i
$377$	0.244465			0.0125906
$378$	4.37466			0.225008
$379$	1.99052	−	1.44620i	0.102246	−	0.0742862i	−0.535487	−	0.844543i	$-0.679872\pi$
$379$	1.99052	−	1.44620i	0.102246	−	0.0742862i	0.637734	+	0.770257i	$0.279872\pi$
$380$	−31.1683	−	22.6451i	−1.59890	−	1.16167i
$381$	−2.64756	−	1.92357i	−0.135639	−	0.0985474i
$382$	1.61219	+	4.96181i	0.0824868	+	0.253868i
$383$	−15.4667	+	11.2372i	−0.790312	+	0.574196i	−0.908056	−	0.418848i	$-0.862434\pi$
$383$	−15.4667	+	11.2372i	−0.790312	+	0.574196i	0.117744	+	0.993044i	$0.462434\pi$
$384$	−14.9999	−	46.1648i	−0.765458	−	2.35584i
$385$	0.907355	−	2.79255i	0.0462431	−	0.142322i
$386$	−47.9108	−	34.8092i	−2.43859	−	1.77174i
$387$	−0.246829	+	0.759663i	−0.0125470	+	0.0386158i
$388$	12.6264	−	38.8600i	0.641008	−	1.97282i
$389$	4.26438	+	3.09825i	0.216212	+	0.157088i	0.690620	−	0.723218i	$-0.257338\pi$
$389$	4.26438	+	3.09825i	0.216212	+	0.157088i	−0.474408	+	0.880305i	$0.657338\pi$
$390$	−8.58882	+	26.4337i	−0.434912	+	1.33852i
$391$	9.63313	+	29.6477i	0.487168	+	1.49935i
$392$	10.9650	−	7.96656i	0.553817	−	0.402372i
$393$	−6.30195	−	19.3954i	−0.317891	−	0.978369i
$394$	−11.5663	−	8.40343i	−0.582703	−	0.423359i
$395$	−9.15232	−	6.64955i	−0.460503	−	0.334575i
$396$	6.83848	−	4.96844i	0.343646	−	0.249674i
$397$	16.9255			0.849467			0.424733	−	0.905319i	$-0.360368\pi$
$397$	16.9255			0.849467			0.424733	+	0.905319i	$0.360368\pi$
$398$	10.5439			0.528516
$399$	15.2834	−	11.1040i	0.765126	−	0.555897i
$400$	0.155144	−	0.477485i	0.00775721	−	0.0238742i
$401$	−11.7549	−	36.1779i	−0.587012	−	1.80664i	−0.591037	−	0.806644i	$-0.701281\pi$
$401$	−11.7549	−	36.1779i	−0.587012	−	1.80664i	0.00402560	−	0.999992i	$-0.498719\pi$
$402$	28.3195			1.41245
$403$		0			0
$404$	24.4175			1.21482
$405$	5.70327	+	17.5529i	0.283398	+	0.872209i
$406$	0.147280	−	0.453280i	0.00730937	−	0.0224959i
$407$	−5.00324	+	3.63507i	−0.248001	+	0.180183i
$408$	34.0373			1.68510
$409$	−0.498684			−0.0246583			−0.0123292	−	0.999924i	$-0.503925\pi$
$409$	−0.498684			−0.0246583			−0.0123292	+	0.999924i	$0.503925\pi$
$410$	−34.3937	+	24.9885i	−1.69858	+	1.23409i
$411$	−33.8944	−	24.6258i	−1.67189	−	1.21470i
$412$	−15.0322	−	10.9215i	−0.740583	−	0.538065i
$413$	4.70441	+	14.4787i	0.231489	+	0.712450i
$414$	−46.0521	+	33.4588i	−2.26334	+	1.64441i
$415$	2.06169	+	6.34522i	0.101204	+	0.311475i
$416$	−3.03544	+	9.34212i	−0.148825	+	0.458035i
$417$	15.0988	+	10.9699i	0.739391	+	0.537199i
$418$	2.42636	−	7.46757i	0.118677	−	0.365251i
$419$	4.17482	−	12.8488i	0.203953	−	0.627704i	−0.795801	−	0.605558i	$-0.792950\pi$
$419$	4.17482	−	12.8488i	0.203953	−	0.627704i	0.999755	−	0.0221460i	$-0.00704986\pi$
$420$	27.3721	+	19.8870i	1.33562	+	0.970387i
$421$	−9.55329	+	29.4020i	−0.465599	+	1.43297i	0.392628	+	0.919697i	$0.371566\pi$
$421$	−9.55329	+	29.4020i	−0.465599	+	1.43297i	−0.858227	+	0.513269i	$0.828434\pi$
$422$	−13.2750	−	40.8561i	−0.646215	−	1.98885i
$423$	22.5312	−	16.3699i	1.09551	−	0.795932i
$424$	−5.41646	−	16.6702i	−0.263047	−	0.809574i
$425$	−4.40132	−	3.19774i	−0.213495	−	0.155113i
$426$	16.1630	+	11.7431i	0.783102	+	0.568957i
$427$	−10.1608	+	7.38225i	−0.491715	+	0.357252i
$428$	6.06475			0.293151
$429$	−3.53692			−0.170764
$430$	−1.07506	+	0.781076i	−0.0518439	+	0.0376668i
$431$	−3.72514	+	11.4648i	−0.179434	+	0.552240i	−0.999808	−	0.0195869i	$-0.993765\pi$
$431$	−3.72514	+	11.4648i	−0.179434	+	0.552240i	0.820375	+	0.571826i	$0.193765\pi$
$432$	0.147801	+	0.454884i	0.00711108	+	0.0218856i
$433$	32.3919			1.55665			0.778327	−	0.627860i	$-0.216069\pi$
$433$	32.3919			1.55665			0.778327	+	0.627860i	$0.216069\pi$
$434$		0			0
$435$	−0.819136			−0.0392745
$436$	12.0875	+	37.2013i	0.578884	+	1.78162i
$437$	−10.2024	+	31.3997i	−0.488046	+	1.50205i
$438$	12.7787	−	9.28426i	0.610589	−	0.443619i
$439$	12.3682			0.590300			0.295150	−	0.955451i	$-0.404630\pi$
$439$	12.3682			0.590300			0.295150	+	0.955451i	$0.404630\pi$
$440$	5.60303			0.267114
$441$	12.4311	−	9.03175i	0.591959	−	0.430083i
$442$	−15.5001	−	11.2615i	−0.737267	−	0.535656i
$443$	3.82132	+	2.77635i	0.181556	+	0.131908i	0.674851	−	0.737954i	$-0.264208\pi$
$443$	3.82132	+	2.77635i	0.181556	+	0.131908i	−0.493295	+	0.869862i	$0.664208\pi$
$444$	−22.0207	−	67.7729i	−1.04506	−	3.21636i
$445$	4.45612	−	3.23756i	0.211240	−	0.153475i
$446$	−4.43167	−	13.6393i	−0.209845	−	0.645838i
$447$	−4.99885	+	15.3849i	−0.236438	+	0.727680i
$448$	16.5406	+	12.0175i	0.781472	+	0.567773i
$449$	4.93939	−	15.2019i	0.233104	−	0.717421i	−0.764263	−	0.644905i	$-0.776897\pi$
$449$	4.93939	−	15.2019i	0.233104	−	0.717421i	0.997367	−	0.0725162i	$-0.0231029\pi$
$450$	3.06983	−	9.44797i	0.144713	−	0.445381i
$451$	−4.37676	−	3.17990i	−0.206093	−	0.149736i
$452$	11.3572	−	34.9540i	0.534199	−	1.64410i
$453$	4.34103	+	13.3603i	0.203959	+	0.627723i
$454$	24.3580	−	17.6971i	1.14318	−	0.830567i
$455$	−2.34486	−	7.21674i	−0.109929	−	0.338326i
$456$	29.1640	+	21.1889i	1.36573	+	0.992262i
$457$	3.68730	+	2.67898i	0.172484	+	0.125317i	0.670678	−	0.741748i	$-0.266003\pi$
$457$	3.68730	+	2.67898i	0.172484	+	0.125317i	−0.498194	+	0.867066i	$0.666003\pi$
$458$	28.5213	−	20.7219i	1.33271	−	0.968272i
$459$	5.18283			0.241914
$460$	−59.1301			−2.75695
$461$	−13.7460	+	9.98705i	−0.640215	+	0.465143i	−0.859924	−	0.510422i	$-0.829489\pi$
$461$	−13.7460	+	9.98705i	−0.640215	+	0.465143i	0.219709	+	0.975565i	$0.429489\pi$
$462$	−2.13084	+	6.55805i	−0.0991356	+	0.305108i
$463$	−8.47567	−	26.0854i	−0.393898	−	1.21229i	−0.929816	−	0.368024i	$-0.880035\pi$
$463$	−8.47567	−	26.0854i	−0.393898	−	1.21229i	0.535918	−	0.844270i	$-0.319965\pi$
$464$	0.0521088			0.00241909
$465$		0			0
$466$	30.1392			1.39617
$467$	−7.07973	−	21.7892i	−0.327611	−	1.00828i	−0.970248	−	0.242112i	$-0.922160\pi$
$467$	−7.07973	−	21.7892i	−0.327611	−	1.00828i	0.642637	−	0.766171i	$-0.277840\pi$
$468$	6.75031	−	20.7753i	0.312033	−	0.960340i
$469$	−6.25499	+	4.54452i	−0.288829	+	0.209846i
$470$	46.3327			2.13717
$471$	20.3277			0.936653
$472$	−23.5022	+	17.0754i	−1.08178	+	0.785957i
$473$	−0.136806	−	0.0993955i	−0.00629036	−	0.00457021i
$474$	21.4934	+	15.6159i	0.987224	+	0.717260i
$475$	−1.78050	−	5.47981i	−0.0816949	−	0.251431i
$476$	−18.8684	+	13.7087i	−0.864833	+	0.628338i
$477$	−6.14069	−	18.8991i	−0.281163	−	0.865330i
$478$	16.7158	−	51.4460i	0.764564	−	2.35309i
$479$	−7.31922	−	5.31772i	−0.334424	−	0.242973i	0.407882	−	0.913035i	$-0.366268\pi$
$479$	−7.31922	−	5.31772i	−0.334424	−	0.242973i	−0.742305	+	0.670062i	$0.766268\pi$
$480$	10.1709	−	31.3029i	0.464237	−	1.42877i
$481$	−4.93874	+	15.1999i	−0.225187	+	0.693054i
$482$	46.1332	+	33.5177i	2.10131	+	1.52669i
$483$	8.95978	−	27.5754i	0.407684	−	1.25472i
$484$	−10.7482	−	33.0796i	−0.488555	−	1.50362i
$485$	24.8415	−	18.0484i	1.12799	−	0.819535i
$486$	−15.9254	−	49.0132i	−0.722389	−	2.22328i
$487$	−19.1111	−	13.8851i	−0.866008	−	0.629192i	0.0635046	−	0.997982i	$-0.479772\pi$
$487$	−19.1111	−	13.8851i	−0.866008	−	0.629192i	−0.929513	+	0.368790i	$0.879772\pi$
$488$	−19.3890	−	14.0869i	−0.877699	−	0.637686i
$489$	35.1054	−	25.5055i	1.58752	−	1.15340i
$490$	25.5631			1.15482
$491$	−9.22692			−0.416405			−0.208202	−	0.978086i	$-0.566761\pi$
$491$	−9.22692			−0.416405			−0.208202	+	0.978086i	$0.566761\pi$
$492$	50.4323	−	36.6412i	2.27366	−	1.65191i
$493$	0.174488	−	0.537019i	0.00785854	−	0.0241861i
$494$	−6.27040	−	19.2983i	−0.282119	−	0.868271i
$495$	6.35220			0.285510
$496$		0			0
$497$	−5.45442			−0.244664
$498$	−4.84168	−	14.9012i	−0.216961	−	0.667737i
$499$	−8.78039	+	27.0233i	−0.393064	+	1.20973i	0.537394	+	0.843331i	$0.319409\pi$
$499$	−8.78039	+	27.0233i	−0.393064	+	1.20973i	−0.930459	+	0.366397i	$0.880591\pi$
$500$	−25.2524	+	18.3469i	−1.12932	+	0.820499i
$501$	61.9718			2.76870
$502$	53.5211			2.38876
$503$	−14.7873	+	10.7436i	−0.659332	+	0.479033i	−0.866437	−	0.499286i	$-0.833596\pi$
$503$	−14.7873	+	10.7436i	−0.659332	+	0.479033i	0.207105	+	0.978319i	$0.433596\pi$
$504$	−13.7279	−	9.97390i	−0.611489	−	0.444273i
$505$	14.8450	+	10.7856i	0.660596	+	0.479951i
$506$	−3.72399	−	11.4613i	−0.165551	−	0.509515i
$507$	19.3477	−	14.0569i	0.859260	−	0.624289i
$508$	1.32227	+	4.06954i	0.0586665	+	0.180557i
$509$	−3.20956	+	9.87801i	−0.142261	+	0.437835i	−0.996649	−	0.0818015i	$-0.973933\pi$
$509$	−3.20956	+	9.87801i	−0.142261	+	0.437835i	0.854387	+	0.519637i	$0.173933\pi$
$510$	51.9367	+	37.7342i	2.29980	+	1.67090i
$511$	−1.33258	+	4.10127i	−0.0589500	+	0.181429i
$512$	−1.41050	+	4.34106i	−0.0623357	+	0.191849i
$513$	4.44078	+	3.22641i	0.196065	+	0.142450i
$514$	10.9428	−	33.6784i	0.482665	−	1.48549i
$515$	−4.31489	−	13.2799i	−0.190137	−	0.585180i
$516$	1.57638	−	1.14531i	0.0693964	−	0.0504195i
$517$	1.82198	+	5.60748i	0.0801306	+	0.246617i
$518$	25.2078	+	18.3145i	1.10757	+	0.804694i
$519$	−18.4597	−	13.4117i	−0.810289	−	0.588710i
$520$	11.7144	−	8.51101i	0.513711	−	0.373233i
$521$	9.25044			0.405269			0.202635	−	0.979254i	$-0.435050\pi$
$521$	9.25044			0.405269			0.202635	+	0.979254i	$0.435050\pi$
$522$	1.03107			0.0451289
$523$	−5.31942	+	3.86478i	−0.232602	+	0.168995i	−0.697981	−	0.716116i	$-0.745918\pi$
$523$	−5.31942	+	3.86478i	−0.232602	+	0.168995i	0.465379	+	0.885111i	$0.345918\pi$
$524$	−8.23997	+	25.3600i	−0.359965	+	1.10786i
$525$	1.56364	+	4.81240i	0.0682429	+	0.210030i
$526$	15.7047			0.684759
$527$		0			0
$528$	−0.753909			−0.0328097
$529$	8.55127	+	26.3181i	0.371794	+	1.14427i
$530$	10.2159	−	31.4413i	0.443751	−	1.36572i
$531$	−26.6447	+	19.3585i	−1.15628	+	0.840086i
$532$	−24.7009			−1.07092
$533$	−13.9809			−0.605579
$534$	−10.4648	+	7.60312i	−0.452856	+	0.329019i
$535$	3.68717	+	2.67888i	0.159410	+	0.115818i
$536$	−11.9359	−	8.67193i	−0.515552	−	0.374570i
$537$	8.87147	+	27.3036i	0.382832	+	1.17824i
$538$	19.6384	−	14.2681i	0.846670	−	0.615142i
$539$	1.00524	+	3.09381i	0.0432987	+	0.133260i
$540$	−3.03789	+	9.34967i	−0.130730	+	0.402346i
$541$	1.78249	+	1.29505i	0.0766351	+	0.0556787i	0.625443	−	0.780270i	$-0.284918\pi$
$541$	1.78249	+	1.29505i	0.0766351	+	0.0556787i	−0.548808	+	0.835948i	$0.684918\pi$
$542$	1.12460	−	3.46117i	0.0483058	−	0.148670i
$543$	11.7398	−	36.1315i	0.503805	−	1.55055i
$544$	18.3554	+	13.3359i	0.786979	+	0.571774i
$545$	−9.08358	+	27.9564i	−0.389098	+	1.19752i
$546$	5.50669	+	16.9478i	0.235665	+	0.725301i
$547$	3.93461	−	2.85866i	0.168232	−	0.122228i	−0.500484	−	0.865746i	$-0.666844\pi$
$547$	3.93461	−	2.85866i	0.168232	−	0.122228i	0.668715	+	0.743518i	$0.266844\pi$
$548$	16.9279	+	52.0988i	0.723125	+	2.22555i
$549$	−21.9815	−	15.9705i	−0.938147	−	0.681604i
$550$	1.70147	+	1.23619i	0.0725508	+	0.0527112i
$551$	0.483810	−	0.351509i	0.0206110	−	0.0149748i
$552$	55.3277			2.35491
$553$	−7.25322			−0.308438
$554$	22.5911	−	16.4134i	0.959806	−	0.697340i
$555$	16.5483	−	50.9306i	0.702438	−	2.16188i
$556$	−7.54080	−	23.2082i	−0.319801	−	0.984247i
$557$	−11.0363			−0.467623			−0.233811	−	0.972282i	$-0.575120\pi$
$557$	−11.0363			−0.467623			−0.233811	+	0.972282i	$0.575120\pi$
$558$		0			0
$559$	−0.437007			−0.0184834
$560$	−0.499817	−	1.53828i	−0.0211211	−	0.0650041i
$561$	−2.52449	+	7.76957i	−0.106584	+	0.328032i
$562$	40.0859	−	29.1241i	1.69092	−	1.22853i
$563$	−11.1924			−0.471704			−0.235852	−	0.971789i	$-0.575788\pi$
$563$	−11.1924			−0.471704			−0.235852	+	0.971789i	$0.575788\pi$
$564$	−67.9387			−2.86074
$565$	22.3445	−	16.2342i	0.940040	−	0.682979i
$566$	1.28588	+	0.934249i	0.0540497	+	0.0392694i
$567$	9.57319	+	6.95533i	0.402036	+	0.292096i
$568$	−3.21632	−	9.89881i	−0.134954	−	0.415345i
$569$	−37.9607	+	27.5800i	−1.59139	+	1.15622i	−0.689477	+	0.724308i	$0.742160\pi$
$569$	−37.9607	+	27.5800i	−1.59139	+	1.15622i	−0.901918	+	0.431908i	$0.857840\pi$
$570$	21.0104	+	64.6633i	0.880028	+	2.70845i
$571$	6.32238	−	19.4583i	0.264584	−	0.814304i	−0.727206	−	0.686420i	$-0.759181\pi$
$571$	6.32238	−	19.4583i	0.264584	−	0.814304i	0.991789	−	0.127885i	$-0.0408187\pi$
$572$	3.74139	+	2.71828i	0.156435	+	0.113657i
$573$	1.77651	−	5.46755i	0.0742149	−	0.228410i
$574$	−8.42288	+	25.9230i	−0.351564	+	1.08200i
$575$	−7.15435	−	5.19794i	−0.298357	−	0.216769i
$576$	−13.6681	+	42.0659i	−0.569502	+	1.75275i
$577$	1.12740	+	3.46978i	0.0469343	+	0.144449i	0.971777	−	0.235900i	$-0.0758038\pi$
$577$	1.12740	+	3.46978i	0.0469343	+	0.144449i	−0.924843	+	0.380349i	$0.875804\pi$
$578$	−4.06547	+	2.95374i	−0.169101	+	0.122859i
$579$	20.1656	+	62.0632i	0.838052	+	2.57926i
$580$	0.866491	+	0.629543i	0.0359791	+	0.0261403i
$581$	3.46063	+	2.51430i	0.143571	+	0.104311i
$582$	−58.3379	+	42.3850i	−2.41818	+	1.75691i
$583$	4.20696			0.174235
$584$	−8.22887			−0.340513
$585$	13.2807	−	9.64901i	0.549090	−	0.398938i
$586$	6.42606	−	19.7774i	0.265458	−	0.816995i
$587$	7.06802	+	21.7531i	0.291729	+	0.897848i	0.984301	+	0.176500i	$0.0564774\pi$
$587$	7.06802	+	21.7531i	0.291729	+	0.897848i	−0.692572	+	0.721349i	$0.743523\pi$
$588$	−37.4838			−1.54580
$589$		0			0
$590$	−54.7914			−2.25573
$591$	4.86825	+	14.9829i	0.200253	+	0.616315i
$592$	−1.05271	+	3.23992i	−0.0432662	+	0.133160i
$593$	15.7433	−	11.4382i	0.646499	−	0.469709i	−0.215578	−	0.976487i	$-0.569163\pi$
$593$	15.7433	−	11.4382i	0.646499	−	0.469709i	0.862077	+	0.506778i	$0.169163\pi$
$594$	−2.00358			−0.0822081
$595$	−17.5267			−0.718525
$596$	17.1118	−	12.4325i	0.700927	−	0.509254i
$597$	−9.39960	−	6.82921i	−0.384700	−	0.279501i
$598$	−25.1955	−	18.3056i	−1.03032	−	0.748572i
$599$	10.8687	+	33.4504i	0.444083	+	1.36675i	0.883486	+	0.468457i	$0.155190\pi$
$599$	10.8687	+	33.4504i	0.444083	+	1.36675i	−0.439403	+	0.898290i	$0.644810\pi$
$600$	−7.81161	+	5.67547i	−0.318908	+	0.231700i
$601$	−1.81951	−	5.59988i	−0.0742194	−	0.228424i	0.907064	−	0.420992i	$-0.138318\pi$
$601$	−1.81951	−	5.59988i	−0.0742194	−	0.228424i	−0.981283	+	0.192569i	$0.938318\pi$
$602$	−0.263278	+	0.810285i	−0.0107304	+	0.0330248i
$603$	−13.5318	−	9.83144i	−0.551058	−	0.400367i
$604$	5.67602	−	17.4690i	0.230954	−	0.710803i
$605$	8.07716	−	24.8590i	0.328383	−	1.01066i
$606$	−34.8622	−	25.3289i	−1.41618	−	1.02892i
$607$	12.0161	−	36.9817i	0.487717	−	1.50104i	−0.340289	−	0.940321i	$-0.610525\pi$
$607$	12.0161	−	36.9817i	0.487717	−	1.50104i	0.828006	−	0.560719i	$-0.189475\pi$
$608$	7.42544	+	22.8531i	0.301141	+	0.926817i
$609$	−0.424884	+	0.308697i	−0.0172172	+	0.0125090i
$610$	−13.9682	−	42.9898i	−0.565557	−	1.74061i
$611$	12.3270	+	8.95612i	0.498698	+	0.362326i
$612$	−40.8193	−	29.6569i	−1.65002	−	1.19881i
$613$	−36.8931	+	26.8044i	−1.49010	+	1.08262i	−0.515975	+	0.856604i	$0.672570\pi$
$613$	−36.8931	+	26.8044i	−1.49010	+	1.08262i	−0.974124	+	0.226016i	$0.927430\pi$
$614$	−72.3009			−2.91783
$615$	46.8461			1.88902
$616$	2.90628	−	2.11154i	0.117097	−	0.0850762i
$617$	−2.04769	+	6.30216i	−0.0824371	+	0.253715i	−0.983777	−	0.179398i	$-0.942585\pi$
$617$	−2.04769	+	6.30216i	−0.0824371	+	0.253715i	0.901339	+	0.433113i	$0.142585\pi$
$618$	10.1331	+	31.1865i	0.407614	+	1.25451i
$619$	−41.5360			−1.66947			−0.834736	−	0.550650i	$-0.814380\pi$
$619$	−41.5360			−1.66947			−0.834736	+	0.550650i	$0.814380\pi$
$620$		0			0
$621$	8.42469			0.338071
$622$	−12.6312	−	38.8748i	−0.506465	−	1.55874i
$623$	1.09129	−	3.35864i	0.0437215	−	0.134561i
$624$	−1.57622	+	1.14519i	−0.0630992	+	0.0458443i
$625$	−29.6682			−1.18673
$626$	50.0011			1.99845
$627$	−6.99976	+	5.08562i	−0.279543	+	0.203100i
$628$	−21.5029	−	15.6228i	−0.858060	−	0.623417i
$629$	29.8646	+	21.6979i	1.19078	+	0.865153i
$630$	−9.88986	−	30.4378i	−0.394021	−	1.21267i
$631$	9.01626	−	6.55070i	0.358932	−	0.260779i	−0.393675	−	0.919250i	$-0.628796\pi$
$631$	9.01626	−	6.55070i	0.358932	−	0.260779i	0.752606	+	0.658471i	$0.228796\pi$
$632$	−4.27702	−	13.1633i	−0.170131	−	0.523608i
$633$	−14.6280	+	45.0205i	−0.581412	+	1.78940i
$634$	−1.89678	−	1.37809i	−0.0753309	−	0.0547311i
$635$	−0.993675	+	3.05822i	−0.0394328	+	0.121362i
$636$	−14.9798	+	46.1032i	−0.593989	+	1.82811i
$637$	6.80119	+	4.94135i	0.269473	+	0.195783i
$638$	−0.0674538	+	0.207601i	−0.00267052	+	0.00821902i
$639$	−3.64637	−	11.2224i	−0.144248	−	0.443950i
$640$	−38.5865	+	28.0347i	−1.52527	+	1.10817i
$641$	−5.42427	−	16.6942i	−0.214246	−	0.659381i	−0.999206	−	0.0398348i	$-0.987317\pi$
$641$	−5.42427	−	16.6942i	−0.214246	−	0.659381i	0.784961	−	0.619546i	$-0.212683\pi$
$642$	−8.65898	−	6.29111i	−0.341743	−	0.248290i
$643$	−1.77664	−	1.29081i	−0.0700640	−	0.0509044i	0.552202	−	0.833710i	$-0.313788\pi$
$643$	−1.77664	−	1.29081i	−0.0700640	−	0.0509044i	−0.622266	+	0.782806i	$0.713788\pi$
$644$	−30.6707	+	22.2835i	−1.20859	+	0.878095i
$645$	1.46429			0.0576563
$646$	−46.8682			−1.84401
$647$	−26.2482	+	19.0704i	−1.03192	+	0.749737i	−0.968693	−	0.248262i	$-0.920140\pi$
$647$	−26.2482	+	19.0704i	−1.03192	+	0.749737i	−0.0632310	+	0.997999i	$0.520140\pi$
$648$	−6.97765	+	21.4750i	−0.274108	+	0.843618i
$649$	−2.15461	−	6.63121i	−0.0845759	−	0.260298i
$650$	5.43508			0.213181
$651$		0			0
$652$	−56.7370			−2.22199
$653$	5.09568	+	15.6829i	0.199409	+	0.613719i	0.999897	+	0.0143694i	$0.00457408\pi$
$653$	5.09568	+	15.6829i	0.199409	+	0.613719i	−0.800487	+	0.599350i	$0.795426\pi$
$654$	21.3320	−	65.6530i	0.834146	−	2.56724i
$655$	−16.2115	+	11.7784i	−0.633436	+	0.460218i
$656$	−2.98009			−0.116353
$657$	−9.32914			−0.363964
$658$	24.0327	−	17.4608i	0.936891	−	0.680691i
$659$	15.9711	+	11.6037i	0.622147	+	0.452016i	0.853671	−	0.520813i	$-0.174371\pi$
$659$	15.9711	+	11.6037i	0.622147	+	0.452016i	−0.231524	+	0.972829i	$0.574371\pi$
$660$	−12.5364	−	9.10821i	−0.487978	−	0.354536i
$661$	3.64047	+	11.2042i	0.141598	+	0.435794i	0.996558	−	0.0829005i	$-0.0264184\pi$
$661$	3.64047	+	11.2042i	0.141598	+	0.435794i	−0.854960	+	0.518694i	$0.826418\pi$
$662$	49.8246	−	36.1997i	1.93649	−	1.40694i
$663$	6.52399	+	20.0788i	0.253371	+	0.779795i
$664$	−2.52237	+	7.76304i	−0.0978868	+	0.301265i
$665$	−15.0173	−	10.9107i	−0.582347	−	0.423100i
$666$	−20.8300	+	64.1081i	−0.807145	+	2.48414i
$667$	0.283630	−	0.872925i	0.0109822	−	0.0337998i
$668$	−65.5545	−	47.6281i	−2.53638	−	1.84279i
$669$	−4.88337	+	15.0295i	−0.188802	+	0.581073i
$670$	−8.59886	−	26.4646i	−0.332203	−	1.02242i
$671$	4.65362	−	3.38105i	0.179651	−	0.130524i
$672$	−6.52105	−	20.0697i	−0.251555	−	0.774207i
$673$	40.7600	+	29.6139i	1.57118	+	1.14153i	0.926013	+	0.377490i	$0.123213\pi$
$673$	40.7600	+	29.6139i	1.57118	+	1.14153i	0.645169	+	0.764040i	$0.276787\pi$
$674$	59.6294	+	43.3233i	2.29684	+	1.66875i
$675$	−1.18947	+	0.864197i	−0.0457826	+	0.0332630i
$676$	−31.2695			−1.20267
$677$	3.97995			0.152962			0.0764810	−	0.997071i	$-0.475632\pi$
$677$	3.97995			0.152962			0.0764810	+	0.997071i	$0.475632\pi$
$678$	−52.4740	+	38.1246i	−2.01525	+	1.46417i
$679$	6.08358	−	18.7233i	0.233466	−	0.718535i
$680$	−10.3350	−	31.8079i	−0.396330	−	1.21978i
$681$	−33.1770			−1.27134
$682$		0			0
$683$	5.23244			0.200214			0.100107	−	0.994977i	$-0.468082\pi$
$683$	5.23244			0.200214			0.100107	+	0.994977i	$0.468082\pi$
$684$	−16.5129	−	50.8216i	−0.631388	−	1.94321i
$685$	−12.7211	+	39.1517i	−0.486050	+	1.49591i
$686$	34.1926	−	24.8423i	1.30548	−	0.948485i
$687$	−38.8476			−1.48213
$688$	−0.0931499			−0.00355130
$689$	8.79561	−	6.39039i	0.335086	−	0.243454i
$690$	84.4233	+	61.3371i	3.21394	+	2.33506i
$691$	−7.43934	−	5.40500i	−0.283006	−	0.205616i	0.437222	−	0.899354i	$-0.355963\pi$
$691$	−7.43934	−	5.40500i	−0.283006	−	0.205616i	−0.720227	+	0.693738i	$0.755963\pi$
$692$	9.21932	+	28.3742i	0.350466	+	1.07862i
$693$	3.29488	−	2.39387i	0.125162	−	0.0909355i
$694$	−2.22570	−	6.84999i	−0.0844863	−	0.260022i
$695$	5.66683	−	17.4407i	0.214955	−	0.661564i
$696$	−0.810772	−	0.589060i	−0.0307322	−	0.0223283i
$697$	−9.97891	+	30.7119i	−0.377978	+	1.16330i
$698$	−15.7063	+	48.3390i	−0.594492	+	1.82966i
$699$	−26.8684	−	19.5210i	−1.01626	−	0.738353i
$700$	2.04450	−	6.29234i	0.0772750	−	0.237828i
$701$	−12.5320	−	38.5694i	−0.473326	−	1.45675i	−0.848202	−	0.529673i	$-0.822315\pi$
$701$	−12.5320	−	38.5694i	−0.473326	−	1.45675i	0.374876	−	0.927075i	$-0.377685\pi$
$702$	−4.18895	+	3.04345i	−0.158102	+	0.114868i
$703$	12.0814	+	37.1826i	0.455657	+	1.40237i
$704$	−7.57558	−	5.50398i	−0.285515	−	0.207439i
$705$	−41.3045	−	30.0095i	−1.55562	−	1.13022i
$706$	9.20793	−	6.68995i	0.346545	−	0.251780i
$707$	11.7647			0.442457
$708$	80.3420			3.01944
$709$	−30.1651	+	21.9162i	−1.13287	+	0.823080i	−0.986110	−	0.166092i	$-0.946885\pi$
$709$	−30.1651	+	21.9162i	−1.13287	+	0.823080i	−0.146762	+	0.989172i	$0.546885\pi$
$710$	6.06626	−	18.6700i	0.227663	−	0.700673i
$711$	−4.84889	−	14.9234i	−0.181848	−	0.559670i
$712$	6.73883			0.252548
$713$		0			0
$714$	41.1599			1.54037
$715$	1.07394	+	3.30525i	0.0401631	+	0.123609i
$716$	11.5997	−	35.7001i	0.433500	−	1.33418i
$717$	−48.2232	+	35.0362i	−1.80093	+	1.30845i
$718$	−0.832694			−0.0310759
$719$	18.5799			0.692912			0.346456	−	0.938066i	$-0.387385\pi$
$719$	18.5799			0.692912			0.346456	+	0.938066i	$0.387385\pi$
$720$	2.83084	−	2.05673i	0.105499	−	0.0766497i
$721$	−7.24272	−	5.26215i	−0.269733	−	0.195973i
$722$	−4.68814	−	3.40613i	−0.174475	−	0.126763i
$723$	−19.4174	−	59.7606i	−0.722141	−	2.22252i
$724$	−40.1873	+	29.1978i	−1.49355	+	1.08513i
$725$	0.0494986	+	0.152341i	0.00183833	+	0.00565780i
$726$	−18.9685	+	58.3790i	−0.703986	+	2.16665i
$727$	−13.2494	−	9.62626i	−0.491394	−	0.357018i	0.314326	−	0.949315i	$-0.398221\pi$
$727$	−13.2494	−	9.62626i	−0.491394	−	0.357018i	−0.805720	+	0.592297i	$0.798221\pi$
$728$	2.86881	−	8.82930i	0.106325	−	0.327236i
$729$	−10.7004	+	32.9325i	−0.396312	+	1.21972i
$730$	−12.5562	−	9.12263i	−0.464727	−	0.337644i
$731$	−0.311915	+	0.959976i	−0.0115366	+	0.0355060i
$732$	20.4820	+	63.0370i	0.757035	+	2.32992i
$733$	0.931452	−	0.676740i	0.0344040	−	0.0249959i	−0.570450	−	0.821332i	$-0.693231\pi$
$733$	0.931452	−	0.676740i	0.0344040	−	0.0249959i	0.604854	+	0.796336i	$0.293231\pi$
$734$	20.9548	+	64.4922i	0.773455	+	2.38045i
$735$	−22.7889	−	16.5571i	−0.840581	−	0.610718i
$736$	29.8367	+	21.6776i	1.09979	+	0.799047i
$737$	2.86477	−	2.08138i	0.105525	−	0.0766685i
$738$	−58.9668			−2.17060
$739$	20.7158			0.762043			0.381022	−	0.924566i	$-0.375572\pi$
$739$	20.7158			0.762043			0.381022	+	0.924566i	$0.375572\pi$
$740$	−56.6474	+	41.1568i	−2.08240	+	1.51295i
$741$	−6.90951	+	21.2653i	−0.253827	+	0.781200i
$742$	−6.54990	−	20.1585i	−0.240454	−	0.740042i
$743$	35.2367			1.29271			0.646354	−	0.763038i	$-0.276293\pi$
$743$	35.2367			1.29271			0.646354	+	0.763038i	$0.276293\pi$
$744$		0			0
$745$	15.8950			0.582348
$746$	12.6415	+	38.9065i	0.462838	+	1.42447i
$747$	−2.85963	+	8.80103i	−0.104628	+	0.322013i
$748$	8.64170	−	6.27856i	0.315972	−	0.229567i
$749$	2.92208			0.106771
$750$	55.0859			2.01145
$751$	34.9057	−	25.3605i	1.27373	−	0.925418i	0.274384	−	0.961620i	$-0.411526\pi$
$751$	34.9057	−	25.3605i	1.27373	−	0.925418i	0.999344	+	0.0362024i	$0.0115261\pi$
$752$	2.62756	+	1.90903i	0.0958173	+	0.0696153i
$753$	−47.7128	−	34.6654i	−1.73875	−	1.26328i
$754$	0.174320	+	0.536500i	0.00634834	+	0.0195382i
$755$	11.1671	−	8.11339i	0.406413	−	0.295277i
$756$	1.94773	+	5.99451i	0.0708384	+	0.218018i
$757$	8.44808	−	26.0005i	0.307051	−	0.945005i	−0.671853	−	0.740684i	$-0.734501\pi$
$757$	8.44808	−	26.0005i	0.307051	−	0.945005i	0.978904	−	0.204321i	$-0.0654986\pi$
$758$	4.59318	+	3.33714i	0.166832	+	0.121210i
$759$	−4.10356	+	12.6295i	−0.148950	+	0.458420i
$760$	10.9457	−	33.6875i	0.397044	−	1.22198i
$761$	13.9086	+	10.1052i	0.504186	+	0.366312i	0.810614	−	0.585581i	$-0.199134\pi$
$761$	13.9086	+	10.1052i	0.504186	+	0.366312i	−0.306428	+	0.951894i	$0.599134\pi$
$762$	2.33355	−	7.18194i	0.0845357	−	0.260174i
$763$	5.82391	+	17.9241i	0.210840	+	0.648898i
$764$	−6.08127	+	4.41830i	−0.220013	+	0.159849i
$765$	−11.7169	−	36.0609i	−0.423625	−	1.30378i
$766$	−35.6899	−	25.9302i	−1.28953	−	0.936896i
$767$	−14.5775	−	10.5912i	−0.526364	−	0.382426i
$768$	38.1057	−	27.6854i	1.37502	−	0.999011i
$769$	14.0567			0.506899			0.253450	−	0.967349i	$-0.418435\pi$
$769$	14.0567			0.506899			0.253450	+	0.967349i	$0.418435\pi$
$770$	6.77550			0.244172
$771$	−31.5686	+	22.9359i	−1.13691	+	0.826017i
$772$	26.3670	−	81.1493i	0.948969	−	2.92063i
$773$	6.87156	+	21.1485i	0.247153	+	0.760658i	0.995275	+	0.0970970i	$0.0309557\pi$
$773$	6.87156	+	21.1485i	0.247153	+	0.760658i	−0.748122	+	0.663561i	$0.769044\pi$
$774$	−1.84315			−0.0662507
$775$		0			0
$776$	37.5668			1.34857
$777$	−10.6099	−	32.6539i	−0.380628	−	1.17145i
$778$	−3.75861	+	11.5678i	−0.134753	+	0.414726i
$779$	−27.6690	+	20.1027i	−0.991343	+	0.720253i
$780$	−40.0455			−1.43386
$781$	2.49811			0.0893895
$782$	−58.1955	+	42.2815i	−2.08107	+	1.51198i
$783$	−0.123455	−	0.0896956i	−0.00441193	−	0.00320546i
$784$	1.44970	+	1.05327i	0.0517751	+	0.0376168i
$785$	−6.17227	−	18.9963i	−0.220298	−	0.678006i
$786$	38.0712	−	27.6604i	1.35796	−	0.986613i
$787$	−9.89899	−	30.4660i	−0.352861	−	1.08599i	−0.957239	−	0.289297i	$-0.906578\pi$
$787$	−9.89899	−	30.4660i	−0.352861	−	1.08599i	0.604378	−	0.796697i	$-0.293422\pi$
$788$	6.36536	−	19.5906i	0.226757	−	0.697885i
$789$	−14.0004	−	10.1719i	−0.498428	−	0.362129i
$790$	8.06682	−	24.8271i	0.287005	−	0.883310i
$791$	5.47208	−	16.8413i	0.194565	−	0.598809i
$792$	6.28734	+	4.56802i	0.223411	+	0.162318i
$793$	4.59362	−	14.1377i	0.163124	−	0.502045i
$794$	12.0690	+	37.1445i	0.428312	+	1.31821i
$795$	−29.4717	+	21.4124i	−1.04525	+	0.759421i
$796$	4.69445	+	14.4480i	0.166390	+	0.512097i
$797$	21.0743	+	15.3114i	0.746490	+	0.542357i	0.894737	−	0.446594i	$-0.147363\pi$
$797$	21.0743	+	15.3114i	0.746490	+	0.542357i	−0.148247	+	0.988950i	$0.547363\pi$
$798$	35.2668	+	25.6228i	1.24843	+	0.907039i
$799$	28.4724	−	20.6864i	1.00728	−	0.731833i
$800$	−6.43625			−0.227556
$801$	7.63987			0.269942
$802$	71.0135	−	51.5943i	2.50757	−	1.82186i
$803$	0.610320	−	1.87837i	0.0215377	−	0.0662863i
$804$	12.6087	+	38.8056i	0.444675	+	1.36857i
$805$	−28.4897			−1.00413
$806$		0			0
$807$	−26.7486			−0.941594
$808$	6.93732	+	21.3509i	0.244054	+	0.751121i
$809$	2.69754	−	8.30217i	0.0948404	−	0.291889i	−0.892372	−	0.451301i	$-0.850960\pi$
$809$	2.69754	−	8.30217i	0.0948404	−	0.291889i	0.987212	+	0.159413i	$0.0509600\pi$
$810$	−34.4545	+	25.0327i	−1.21061	+	0.879559i
$811$	−50.0784			−1.75849			−0.879245	−	0.476369i	$-0.841953\pi$
$811$	−50.0784			−1.75849			−0.879245	+	0.476369i	$0.841953\pi$
$812$	0.686695			0.0240983
$813$	−3.24434	+	2.35715i	−0.113784	+	0.0826690i
$814$	−11.5451	−	8.38801i	−0.404656	−	0.294000i
$815$	−34.4942	−	25.0615i	−1.20828	−	0.877867i
$816$	1.39062	+	4.27988i	0.0486813	+	0.149826i
$817$	−0.864861	+	0.628358i	−0.0302576	+	0.0219835i
$818$	−0.355594	−	1.09441i	−0.0124330	−	0.0382650i
$819$	3.25240	−	10.0099i	0.113648	−	0.349773i
$820$	−49.5543	−	36.0033i	−1.73051	−	1.25729i
$821$	15.6928	−	48.2976i	0.547684	−	1.68560i	−0.166839	−	0.985984i	$-0.553356\pi$
$821$	15.6928	−	48.2976i	0.547684	−	1.68560i	0.714522	−	0.699613i	$-0.246644\pi$
$822$	29.8745	−	91.9441i	1.04199	−	3.20692i
$823$	−5.12043	−	3.72021i	−0.178487	−	0.129678i	0.494955	−	0.868919i	$-0.335185\pi$
$823$	−5.12043	−	3.72021i	−0.178487	−	0.129678i	−0.673442	+	0.739240i	$0.735185\pi$
$824$	5.27904	−	16.2472i	0.183904	−	0.565998i
$825$	−0.716145	−	2.20407i	−0.0249330	−	0.0767357i
$826$	−28.4202	+	20.6485i	−0.988866	+	0.718453i
$827$	−1.14258	−	3.51649i	−0.0397312	−	0.122280i	0.929224	−	0.369518i	$-0.120477\pi$
$827$	−1.14258	−	3.51649i	−0.0397312	−	0.122280i	−0.968955	+	0.247238i	$0.920477\pi$
$828$	−66.3518	−	48.2074i	−2.30588	−	1.67532i
$829$	21.0681	+	15.3068i	0.731724	+	0.531629i	0.890108	−	0.455749i	$-0.150628\pi$
$829$	21.0681	+	15.3068i	0.731724	+	0.531629i	−0.158384	+	0.987378i	$0.550628\pi$
$830$	−12.4550	+	9.04911i	−0.432320	+	0.314099i
$831$	−30.7704			−1.06741
$832$	−24.1990			−0.838951
$833$	15.7091	−	11.4133i	0.544287	−	0.395448i
$834$	−13.3080	+	40.9579i	−0.460819	+	1.41826i
$835$	−18.8170	−	57.9127i	−0.651188	−	2.00415i
$836$	11.3130			0.391267
$837$		0			0
$838$	31.1747			1.07691
$839$	2.31546	+	7.12626i	0.0799387	+	0.246026i	0.983037	−	0.183408i	$-0.0587130\pi$
$839$	2.31546	+	7.12626i	0.0799387	+	0.246026i	−0.903098	+	0.429434i	$0.858713\pi$
$840$	−9.61260	+	29.5846i	−0.331666	+	1.02076i
$841$	23.4480	−	17.0360i	0.808553	−	0.587448i
$842$	−71.3374			−2.45845
$843$	−54.5992			−1.88050
$844$	50.0739	−	36.3809i	1.72362	−	1.25228i
$845$	−19.0108	−	13.8122i	−0.653993	−	0.475154i
$846$	51.9914	+	37.7740i	1.78750	+	1.29870i
$847$	−5.17865	−	15.9382i	−0.177940	−	0.547644i
$848$	1.87482	−	1.36214i	0.0643817	−	0.0467760i
$849$	−0.541226	−	1.66572i	−0.0185748	−	0.0571675i
$850$	3.87931	−	11.9393i	0.133059	−	0.409514i
$851$	48.5450	+	35.2700i	1.66410	+	1.20904i
$852$	−8.89510	+	27.3763i	−0.304741	+	0.937896i
$853$	−13.4691	+	41.4536i	−0.461173	+	1.41935i	0.402559	+	0.915394i	$0.368121\pi$
$853$	−13.4691	+	41.4536i	−0.461173	+	1.41935i	−0.863732	+	0.503951i	$0.831879\pi$
$854$	−23.4463	−	17.0347i	−0.802316	−	0.582916i
$855$	12.4093	−	38.1919i	0.424389	−	1.30613i
$856$	1.72307	+	5.30306i	0.0588933	+	0.181255i
$857$	−31.7319	+	23.0546i	−1.08394	+	0.787529i	−0.978366	−	0.206882i	$-0.933668\pi$
$857$	−31.7319	+	23.0546i	−1.08394	+	0.787529i	−0.105575	+	0.994411i	$0.533668\pi$
$858$	−2.52205	−	7.76208i	−0.0861014	−	0.264993i
$859$	−14.7252	−	10.6985i	−0.502416	−	0.365026i	0.307523	−	0.951541i	$-0.400500\pi$
$859$	−14.7252	−	10.6985i	−0.502416	−	0.365026i	−0.809939	+	0.586514i	$0.800500\pi$
$860$	−1.54894	−	1.12537i	−0.0528185	−	0.0383749i
$861$	24.2990	−	17.6543i	0.828108	−	0.601655i
$862$	−27.8168			−0.947443
$863$	−44.9477			−1.53004			−0.765018	−	0.644009i	$-0.777270\pi$
$863$	−44.9477			−1.53004			−0.765018	+	0.644009i	$0.777270\pi$
$864$	4.96057	−	3.60407i	0.168762	−	0.122613i
$865$	−6.92822	+	21.3229i	−0.235566	+	0.724999i
$866$	23.0975	+	71.0868i	0.784885	+	2.41563i
$867$	5.53740			0.188060
$868$		0			0
$869$	3.32196			0.112690
$870$	−0.584097	−	1.79767i	−0.0198027	−	0.0609466i
$871$	2.82784	−	8.70319i	0.0958176	−	0.294896i
$872$	−29.0950	+	21.1387i	−0.985280	+	0.715848i
$873$	42.5899			1.44145
$874$	−76.1844			−2.57698
$875$	−12.1669	+	8.83981i	−0.411318	+	0.298840i
$876$	18.4115	+	13.3767i	0.622067	+	0.451958i
$877$	34.5054	+	25.0697i	1.16517	+	0.846542i	0.990422	−	0.138072i	$-0.0440905\pi$
$877$	34.5054	+	25.0697i	1.16517	+	0.846542i	0.174743	+	0.984614i	$0.444090\pi$
$878$	8.81930	+	27.1430i	0.297637	+	0.916032i
$879$	−18.5384	+	13.4689i	−0.625285	+	0.454296i
$880$	0.228915	+	0.704528i	0.00771673	+	0.0237496i
$881$	2.75536	−	8.48012i	0.0928303	−	0.285702i	−0.893852	−	0.448362i	$-0.852007\pi$
$881$	2.75536	−	8.48012i	0.0928303	−	0.285702i	0.986682	+	0.162660i	$0.0520074\pi$
$882$	28.6852	+	20.8410i	0.965881	+	0.701753i
$883$	−14.5449	+	44.7647i	−0.489475	+	1.50645i	0.335917	+	0.941892i	$0.390954\pi$
$883$	−14.5449	+	44.7647i	−0.489475	+	1.50645i	−0.825393	+	0.564559i	$0.809046\pi$
$884$	8.53029	−	26.2535i	0.286905	−	0.883002i
$885$	48.8453	+	35.4882i	1.64192	+	1.19292i
$886$	−3.36810	+	10.3659i	−0.113153	+	0.348250i
$887$	0.975433	+	3.00207i	0.0327518	+	0.100800i	0.966096	−	0.258183i	$-0.0831237\pi$
$887$	0.975433	+	3.00207i	0.0327518	+	0.100800i	−0.933344	+	0.358983i	$0.883124\pi$
$888$	53.0048	−	38.5102i	1.77872	−	1.29232i
$889$	0.637091	+	1.96076i	0.0213673	+	0.0657619i
$890$	10.2826	+	7.47076i	0.344674	+	0.250421i
$891$	−4.38450	−	3.18553i	−0.146886	−	0.106719i
$892$	16.7165	−	12.1452i	0.559710	−	0.406653i
$893$	37.2736			1.24731
$894$	−37.3280			−1.24843
$895$	22.8215	−	16.5808i	0.762838	−	0.554234i
$896$	−9.44969	+	29.0832i	−0.315692	+	0.971600i
$897$	10.6048	+	32.6381i	0.354082	+	1.08975i
$898$	36.8840			1.23083
$899$		0			0
$900$	14.3131			0.477105
$901$	−7.75991	−	23.8826i	−0.258520	−	0.795643i
$902$	3.85766	−	11.8727i	0.128446	−	0.395316i
$903$	0.759524	−	0.551827i	0.0252754	−	0.0183636i
$904$	33.7908			1.12386
$905$	−37.3296			−1.24088
$906$	−26.2250	+	19.0536i	−0.871266	+	0.633012i
$907$	−21.8137	−	15.8486i	−0.724311	−	0.526242i	0.163448	−	0.986552i	$-0.447738\pi$
$907$	−21.8137	−	15.8486i	−0.724311	−	0.526242i	−0.887759	+	0.460309i	$0.847738\pi$
$908$	35.0950	+	25.4980i	1.16467	+	0.846180i
$909$	7.86490	+	24.2057i	0.260862	+	0.802851i
$910$	14.1657	−	10.2920i	0.469589	−	0.341177i
$911$	−1.56919	−	4.82948i	−0.0519897	−	0.160008i	0.921691	−	0.387926i	$-0.126808\pi$
$911$	−1.56919	−	4.82948i	−0.0519897	−	0.160008i	−0.973680	+	0.227918i	$0.926808\pi$
$912$	−1.47279	+	4.53279i	−0.0487690	+	0.150096i
$913$	−1.58496	−	1.15154i	−0.0524546	−	0.0381105i
$914$	−3.24997	+	10.0024i	−0.107500	+	0.330849i
$915$	−15.3920	+	47.3716i	−0.508843	+	1.56606i
$916$	41.0934	+	29.8561i	1.35776	+	0.986473i
$917$	−3.97014	+	12.2188i	−0.131105	+	0.403501i
$918$	3.69569	+	11.3742i	0.121976	+	0.375404i
$919$	39.8659	−	28.9643i	1.31505	−	0.955443i	0.315075	−	0.949067i	$-0.397970\pi$
$919$	39.8659	−	28.9643i	1.31505	−	0.955443i	0.999980	−	0.00637645i	$-0.00202970\pi$
$920$	−16.7996	−	51.7038i	−0.553866	−	1.70462i
$921$	64.4546	+	46.8290i	2.12385	+	1.54307i
$922$	−31.7193	−	23.0454i	−1.04462	−	0.758959i
$923$	5.22288	−	3.79464i	0.171913	−	0.124902i
$924$	−9.93508			−0.326840
$925$	−10.4719			−0.344315
$926$	51.2031	−	37.2012i	1.68264	−	1.22251i
$927$	5.98489	−	18.4196i	0.196570	−	0.604979i
$928$	−0.206430	−	0.635327i	−0.00677640	−	0.0208556i
$929$	39.9606			1.31107			0.655533	−	0.755167i	$-0.272444\pi$
$929$	39.9606			1.31107			0.655533	+	0.755167i	$0.272444\pi$
$930$		0			0
$931$	20.5649			0.673989
$932$	13.4189	+	41.2991i	0.439551	+	1.35280i
$933$	−13.9186	+	42.8372i	−0.455676	+	1.40243i
$934$	42.7700	−	31.0742i	1.39948	−	1.01678i
$935$	8.02720			0.262517
$936$	20.0840			0.656465
$937$	−36.4780	+	26.5028i	−1.19168	+	0.865809i	−0.993441	−	0.114343i	$-0.963524\pi$
$937$	−36.4780	+	26.5028i	−1.19168	+	0.865809i	−0.198243	+	0.980153i	$0.563524\pi$
$938$	−14.4336	−	10.4866i	−0.471272	−	0.342399i
$939$	−44.5748	−	32.3855i	−1.45464	−	1.05686i
$940$	20.6287	+	63.4887i	0.672835	+	2.07077i
$941$	40.6064	−	29.5023i	1.32373	−	0.961748i	0.323855	−	0.946107i	$-0.395021\pi$
$941$	40.6064	−	29.5023i	1.32373	−	0.961748i	0.999878	−	0.0156409i	$-0.00497885\pi$
$942$	14.4950	+	44.6110i	0.472273	+	1.45351i
$943$	−16.2207	+	49.9223i	−0.528220	+	1.62569i
$944$	−3.10726	−	2.25756i	−0.101133	−	0.0734773i
$945$	−1.46370	+	4.50481i	−0.0476142	+	0.146541i
$946$	0.120581	−	0.371109i	0.00392041	−	0.0120658i
$947$	24.5342	+	17.8251i	0.797255	+	0.579239i	0.910107	−	0.414372i	$-0.135999\pi$
$947$	24.5342	+	17.8251i	0.797255	+	0.579239i	−0.112853	+	0.993612i	$0.535999\pi$
$948$	−11.8286	+	36.4046i	−0.384174	+	1.18237i
$949$	−1.57724	−	4.85424i	−0.0511993	−	0.157575i
$950$	10.7563	−	7.81493i	0.348981	−	0.253550i
$951$	0.798353	+	2.45708i	0.0258884	+	0.0796762i
$952$	−17.3478	−	12.6039i	−0.562244	−	0.408494i
$953$	−28.7019	−	20.8531i	−0.929745	−	0.675499i	0.0161857	−	0.999869i	$-0.494848\pi$
$953$	−28.7019	−	20.8531i	−0.929745	−	0.675499i	−0.945930	+	0.324370i	$0.894848\pi$
$954$	37.0970	−	26.9526i	1.20106	−	0.872622i
$955$	−5.64884			−0.182792
$956$	77.9379			2.52069
$957$	0.194596	−	0.141382i	0.00629040	−	0.00457024i
$958$	6.45114	−	19.8546i	0.208427	−	0.641472i
$959$	8.15612	+	25.1020i	0.263375	+	0.810584i
$960$	81.0843			2.61698
$961$		0			0
$962$	−36.8791			−1.18903
$963$	1.95346	+	6.01213i	0.0629493	+	0.193738i
$964$	−25.3888	+	78.1386i	−0.817717	+	2.51667i
$965$	51.8751	−	37.6894i	1.66992	−	1.21327i
$966$	66.9055			2.15265
$967$	35.4443			1.13981			0.569906	−	0.821710i	$-0.306979\pi$
$967$	35.4443			1.13981			0.569906	+	0.821710i	$0.306979\pi$
$968$	25.8714	−	18.7967i	0.831537	−	0.604147i
$969$	41.7820	+	30.3564i	1.34223	+	0.975187i
$970$	57.3223	+	41.6471i	1.84051	+	1.33721i
$971$	−12.3907	−	38.1347i	−0.397637	−	1.22380i	−0.926889	−	0.375337i	$-0.877527\pi$
$971$	−12.3907	−	38.1347i	−0.397637	−	1.22380i	0.529251	−	0.848465i	$-0.322473\pi$
$972$	60.0713	−	43.6444i	1.92679	−	1.39989i
$973$	−3.63327	−	11.1820i	−0.116477	−	0.358480i
$974$	16.8445	−	51.8420i	0.539732	−	1.66113i
$975$	−4.84525	−	3.52028i	−0.155172	−	0.112739i
$976$	0.979151	−	3.01352i	0.0313418	−	0.0964603i
$977$	−11.9499	+	36.7782i	−0.382313	+	1.17664i	0.556098	+	0.831117i	$0.312298\pi$
$977$	−11.9499	+	36.7782i	−0.382313	+	1.17664i	−0.938411	+	0.345521i	$0.887702\pi$
$978$	81.0065	+	58.8547i	2.59030	+	1.88197i
$979$	−0.499807	+	1.53825i	−0.0159739	+	0.0491626i
$980$	11.3815	+	35.0286i	0.363568	+	1.11895i
$981$	−32.9852	+	23.9652i	−1.05314	+	0.765149i
$982$	−6.57939	−	20.2493i	−0.209957	−	0.646181i
$983$	−17.4583	−	12.6842i	−0.556832	−	0.404562i	0.273466	−	0.961882i	$-0.411830\pi$
$983$	−17.4583	−	12.6842i	−0.556832	−	0.404562i	−0.830298	+	0.557320i	$0.811830\pi$
$984$	46.3678	+	33.6882i	1.47815	+	1.07394i
$985$	12.5234	−	9.09876i	0.399028	−	0.289911i
$986$	1.30296			0.0414946
$987$	−32.7338			−1.04193
$988$	23.6523	−	17.1844i	0.752480	−	0.546709i
$989$	−0.507019	+	1.56044i	−0.0161223	+	0.0496192i
$990$	4.52953	+	13.9405i	0.143958	+	0.443057i
$991$	−46.8764			−1.48908			−0.744538	−	0.667580i	$-0.767330\pi$
$991$	−46.8764			−1.48908			−0.744538	+	0.667580i	$0.767330\pi$
$992$		0			0
$993$	−67.8639			−2.15360
$994$	−3.88936	−	11.9702i	−0.123363	−	0.379672i
$995$	−3.52783	+	10.8575i	−0.111840	+	0.344207i
$996$	18.2631	−	13.2689i	0.578689	−	0.420442i
$997$	44.5389			1.41056			0.705281	−	0.708928i	$-0.250821\pi$
$997$	44.5389			1.41056			0.705281	+	0.708928i	$0.250821\pi$
$998$	−65.5659			−2.07545
$999$	8.07098	−	5.86391i	0.255354	−	0.185526i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.q.531.4		16
31.2	even	5		961.2.d.n.388.1		16
31.3	odd	30		961.2.c.j.439.8		16
31.4	even	5		961.2.d.n.374.1		16
31.5	even	3		961.2.g.m.844.2		16
31.6	odd	6		961.2.g.t.547.2		16
31.7	even	15		961.2.g.j.816.1		16
31.8	even	5	inner	961.2.d.q.628.4		16
31.9	even	15		961.2.g.n.448.2		16
31.10	even	15		961.2.g.j.338.1		16
31.11	odd	30		31.2.g.a.19.1	yes	16
31.12	odd	30		31.2.g.a.18.1	✓	16
31.13	odd	30		961.2.c.j.521.8		16
31.14	even	15		961.2.g.m.846.2		16
31.15	odd	10		961.2.a.i.1.8		8
31.16	even	5		961.2.a.j.1.8		8
31.17	odd	30		961.2.g.s.846.2		16
31.18	even	15		961.2.c.i.521.8		16
31.19	even	15		961.2.g.l.235.1		16
31.20	even	15		961.2.g.l.732.1		16
31.21	odd	30		961.2.g.k.338.1		16
31.22	odd	30		961.2.g.t.448.2		16
31.23	odd	10		961.2.d.p.628.4		16
31.24	odd	30		961.2.g.k.816.1		16
31.25	even	3		961.2.g.n.547.2		16
31.26	odd	6		961.2.g.s.844.2		16
31.27	odd	10		961.2.d.o.374.1		16
31.28	even	15		961.2.c.i.439.8		16
31.29	odd	10		961.2.d.o.388.1		16
31.30	odd	2		961.2.d.p.531.4		16
93.11	even	30		279.2.y.c.19.2		16
93.47	odd	10		8649.2.a.be.1.1		8
93.74	even	30		279.2.y.c.235.2		16
93.77	even	10		8649.2.a.bf.1.1		8
124.11	even	30		496.2.bg.c.81.2		16
124.43	even	30		496.2.bg.c.49.2		16
155.12	even	60		775.2.ck.a.49.1		32
155.42	even	60		775.2.ck.a.174.4		32
155.43	even	60		775.2.ck.a.49.4		32
155.73	even	60		775.2.ck.a.174.1		32
155.74	odd	30		775.2.bl.a.576.2		16
155.104	odd	30		775.2.bl.a.701.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.18.1	✓	16	31.12	odd	30
31.2.g.a.19.1	yes	16	31.11	odd	30
279.2.y.c.19.2		16	93.11	even	30
279.2.y.c.235.2		16	93.74	even	30
496.2.bg.c.49.2		16	124.43	even	30
496.2.bg.c.81.2		16	124.11	even	30
775.2.bl.a.576.2		16	155.74	odd	30
775.2.bl.a.701.2		16	155.104	odd	30
775.2.ck.a.49.1		32	155.12	even	60
775.2.ck.a.49.4		32	155.43	even	60
775.2.ck.a.174.1		32	155.73	even	60
775.2.ck.a.174.4		32	155.42	even	60
961.2.a.i.1.8		8	31.15	odd	10
961.2.a.j.1.8		8	31.16	even	5
961.2.c.i.439.8		16	31.28	even	15
961.2.c.i.521.8		16	31.18	even	15
961.2.c.j.439.8		16	31.3	odd	30
961.2.c.j.521.8		16	31.13	odd	30
961.2.d.n.374.1		16	31.4	even	5
961.2.d.n.388.1		16	31.2	even	5
961.2.d.o.374.1		16	31.27	odd	10
961.2.d.o.388.1		16	31.29	odd	10
961.2.d.p.531.4		16	31.30	odd	2
961.2.d.p.628.4		16	31.23	odd	10
961.2.d.q.531.4		16	1.1	even	1	trivial
961.2.d.q.628.4		16	31.8	even	5	inner
961.2.g.j.338.1		16	31.10	even	15
961.2.g.j.816.1		16	31.7	even	15
961.2.g.k.338.1		16	31.21	odd	30
961.2.g.k.816.1		16	31.24	odd	30
961.2.g.l.235.1		16	31.19	even	15
961.2.g.l.732.1		16	31.20	even	15
961.2.g.m.844.2		16	31.5	even	3
961.2.g.m.846.2		16	31.14	even	15
961.2.g.n.448.2		16	31.9	even	15
961.2.g.n.547.2		16	31.25	even	3
961.2.g.s.844.2		16	31.26	odd	6
961.2.g.s.846.2		16	31.17	odd	30
961.2.g.t.448.2		16	31.22	odd	30
961.2.g.t.547.2		16	31.6	odd	6
8649.2.a.be.1.1		8	93.47	odd	10
8649.2.a.bf.1.1		8	93.77	even	10

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.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.713065 + 2.19459i) q^{2} +(0.785745 - 2.41827i) q^{3} +(-2.68972 + 1.95420i) q^{4} -2.49846 q^{5} +5.86740 q^{6} +(-1.29595 + 0.941560i) q^{7} +(-2.47295 - 1.79670i) q^{8} +(-2.80360 - 2.03694i) q^{9} +(-1.78156 - 5.48309i) q^{10} +(0.593541 - 0.431233i) q^{11} +(2.61235 + 8.03999i) q^{12} +(0.585889 - 1.80318i) q^{13} +(-2.99043 - 2.17268i) q^{14} +(-1.96315 + 6.04196i) q^{15} +(0.124885 - 0.384356i) q^{16} +(-3.54288 - 2.57405i) q^{17} +(2.47109 - 7.60523i) q^{18} +(-1.43323 - 4.41103i) q^{19} +(6.72016 - 4.88248i) q^{20} +(1.25867 + 3.87378i) q^{21} +(1.36961 + 0.995081i) q^{22} +(-5.75896 - 4.18413i) q^{23} +(-6.28803 + 4.56852i) q^{24} +1.24230 q^{25} +4.37501 q^{26} +(-0.957471 + 0.695643i) q^{27} +(1.64574 - 5.06507i) q^{28} +(0.0398443 + 0.122628i) q^{29} -14.6595 q^{30} -5.18091 q^{32} +(-0.576467 - 1.77418i) q^{33} +(3.12268 - 9.61063i) q^{34} +(3.23787 - 2.35245i) q^{35} +11.5215 q^{36} -8.42948 q^{37} +(8.65840 - 6.29069i) q^{38} +(-3.90022 - 2.83368i) q^{39} +(6.17856 + 4.48899i) q^{40} +(-2.27869 - 7.01307i) q^{41} +(-7.60384 + 5.52452i) q^{42} +(-0.0712259 - 0.219211i) q^{43} +(-0.753746 + 2.31979i) q^{44} +(7.00469 + 5.08921i) q^{45} +(5.07593 - 15.6221i) q^{46} +(-2.48342 + 7.64319i) q^{47} +(-0.831350 - 0.604011i) q^{48} +(-1.37018 + 4.21697i) q^{49} +(0.885840 + 2.72634i) q^{50} +(-9.00856 + 6.54511i) q^{51} +(1.94789 + 5.99500i) q^{52} +(4.63910 + 3.37050i) q^{53} +(-2.20939 - 1.60522i) q^{54} +(-1.48294 + 1.07742i) q^{55} +4.89652 q^{56} -11.7932 q^{57} +(-0.240707 + 0.174884i) q^{58} +(2.93681 - 9.03857i) q^{59} +(-6.52685 - 20.0876i) q^{60} +7.84044 q^{61} +5.55122 q^{63} +(-3.94410 - 12.1387i) q^{64} +(-1.46382 + 4.50517i) q^{65} +(3.48254 - 2.53022i) q^{66} +4.82658 q^{67} +14.5596 q^{68} +(-14.6434 + 10.6391i) q^{69} +(7.47147 + 5.42834i) q^{70} +(2.75472 + 2.00142i) q^{71} +(3.27340 + 10.0745i) q^{72} +(2.17791 - 1.58234i) q^{73} +(-6.01076 - 18.4992i) q^{74} +(0.976130 - 3.00422i) q^{75} +(12.4750 + 9.06362i) q^{76} +(-0.363166 + 1.11771i) q^{77} +(3.43765 - 10.5800i) q^{78} +(3.66318 + 2.66146i) q^{79} +(-0.312019 + 0.960297i) q^{80} +(-2.28272 - 7.02548i) q^{81} +(13.7660 - 10.0016i) q^{82} +(-0.825183 - 2.53965i) q^{83} +(-10.9556 - 7.95971i) q^{84} +(8.85174 + 6.43117i) q^{85} +(0.430288 - 0.312623i) q^{86} +0.327856 q^{87} -2.24259 q^{88} +(-1.78355 + 1.29582i) q^{89} +(-6.17391 + 19.0013i) q^{90} +(0.938522 + 2.88847i) q^{91} +23.6666 q^{92} -18.5445 q^{94} +(3.58086 + 11.0208i) q^{95} +(-4.07088 + 12.5289i) q^{96} +(-9.94271 + 7.22380i) q^{97} -10.2315 q^{98} -2.54245 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 22 q^{6} - 9 q^{7} - 8 q^{8} - 10 q^{9} - 6 q^{10} - 4 q^{11} + 5 q^{12} - 9 q^{13} - 18 q^{14} - 4 q^{15} - 2 q^{16} - 17 q^{17} - 14 q^{18} - 7 q^{19} + 36 q^{20}+ \cdots + 12 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 22 * q^6 - 9 * q^7 - 8 * q^8 - 10 * q^9 - 6 * q^10 - 4 * q^11 + 5 * q^12 - 9 * q^13 - 18 * q^14 - 4 * q^15 - 2 * q^16 - 17 * q^17 - 14 * q^18 - 7 * q^19 + 36 * q^20 - 2 * q^21 + 8 * q^22 - 21 * q^23 - 5 * q^24 + 26 * q^25 + 18 * q^26 - 9 * q^27 + 20 * q^28 - 26 * q^29 + 22 * q^30 - 42 * q^32 + 7 * q^33 + 56 * q^34 + 21 * q^35 - 2 * q^36 - 16 * q^37 + 24 * q^38 + 2 * q^39 - 13 * q^40 + 6 * q^41 - 12 * q^42 + 16 * q^43 - 37 * q^44 - 5 * q^45 + 16 * q^46 + 4 * q^47 - 37 * q^48 - 39 * q^49 - 21 * q^50 - 11 * q^51 + 18 * q^52 - 3 * q^53 - 39 * q^54 - 29 * q^55 + 60 * q^56 - 34 * q^57 - 10 * q^58 - 3 * q^59 - 35 * q^60 + 60 * q^61 - 46 * q^63 - 32 * q^64 - 9 * q^65 + 20 * q^66 - 26 * q^67 + 60 * q^68 - 21 * q^69 + 27 * q^70 + 18 * q^71 - 4 * q^72 + 9 * q^73 - 64 * q^74 - 19 * q^75 + 9 * q^76 + 42 * q^77 + 15 * q^78 - 14 * q^79 + 18 * q^80 + 29 * q^81 + 32 * q^82 - 67 * q^83 - 39 * q^84 + 63 * q^85 + 23 * q^86 - 30 * q^87 - 34 * q^88 - 26 * q^89 - 24 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 + 28 * q^95 - 4 * q^96 - 37 * q^97 + 20 * q^98 + 12 * q^99

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