LMFDB - Embedded newform 950.2.q.g.293.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(107,950)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("950.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.q (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			293.5
Character	$\chi$	$=$	950.293
Dual form			950.2.q.g.107.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(-0.407975 - 1.52258i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.788148 - 1.36511i) q^{6} +(-2.78714 + 2.78714i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.446257 - 0.257647i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(-0.407975 - 1.52258i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.788148 - 1.36511i) q^{6} +(-2.78714 + 2.78714i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.446257 - 0.257647i) q^{9} -3.61156 q^{11} +(-1.11461 - 1.11461i) q^{12} +(-4.02492 - 1.07847i) q^{13} +(-1.97080 + 3.41353i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.78974 - 6.67939i) q^{17} +(0.364368 - 0.364368i) q^{18} +(-4.35847 - 0.0613000i) q^{19} +(5.38074 + 3.10657i) q^{21} +(-3.48850 + 0.934740i) q^{22} +(-0.826722 + 3.08537i) q^{23} +(-1.36511 - 0.788148i) q^{24} -4.16690 q^{26} +(-3.91818 - 3.91818i) q^{27} +(-1.02016 + 3.80730i) q^{28} +(-0.966822 - 1.67459i) q^{29} -2.38055i q^{31} +(0.258819 - 0.965926i) q^{32} +(1.47343 + 5.49890i) q^{33} +(-3.45751 - 5.98858i) q^{34} +(0.257647 - 0.446257i) q^{36} +(-5.07600 - 5.07600i) q^{37} +(-4.22582 + 1.06884i) q^{38} +6.56826i q^{39} +(1.72256 + 0.994522i) q^{41} +(6.00143 + 1.60808i) q^{42} +(7.85704 - 2.10529i) q^{43} +(-3.12770 + 1.80578i) q^{44} +3.19421i q^{46} +(5.79010 + 1.55145i) q^{47} +(-1.52258 - 0.407975i) q^{48} -8.53628i q^{49} +(-9.43977 + 5.45005i) q^{51} +(-4.02492 + 1.07847i) q^{52} +(12.1460 + 3.25451i) q^{53} +(-4.79877 - 2.77057i) q^{54} +3.94161i q^{56} +(1.68481 + 6.66114i) q^{57} +(-1.36729 - 1.36729i) q^{58} +(-4.99297 + 8.64808i) q^{59} +(1.12826 + 1.95420i) q^{61} +(-0.616133 - 2.29944i) q^{62} +(-0.525684 + 1.96188i) q^{63} -1.00000i q^{64} +(2.84644 + 4.93018i) q^{66} +(-1.12871 + 4.21239i) q^{67} +(-4.88965 - 4.88965i) q^{68} +5.03501 q^{69} +(4.67273 + 2.69780i) q^{71} +(0.133368 - 0.497736i) q^{72} +(-13.2038 + 3.53796i) q^{73} +(-6.21680 - 3.58927i) q^{74} +(-3.80519 + 2.12615i) q^{76} +(10.0659 - 10.0659i) q^{77} +(1.69999 + 6.34445i) q^{78} +(-0.484828 + 0.839746i) q^{79} +(-3.59430 + 6.22550i) q^{81} +(1.92127 + 0.514803i) q^{82} +(-4.90713 - 4.90713i) q^{83} +6.21314 q^{84} +(7.04443 - 4.06711i) q^{86} +(-2.15526 + 2.15526i) q^{87} +(-2.55376 + 2.55376i) q^{88} +(-0.366642 - 0.635043i) q^{89} +(14.2238 - 8.21214i) q^{91} +(0.826722 + 3.08537i) q^{92} +(-3.62459 + 0.971207i) q^{93} +5.99435 q^{94} -1.57630 q^{96} +(11.9625 - 3.20535i) q^{97} +(-2.20935 - 8.24541i) q^{98} +(-1.61168 + 0.930507i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{3} - 24 q^{7}+O(q^{10}) $ 32 * q + 12 * q^3 - 24 * q^7	$ 32 q + 12 q^{3} - 24 q^{7} - 16 q^{11} - 24 q^{13} + 16 q^{16} + 8 q^{17} + 12 q^{22} - 4 q^{23} - 16 q^{26} + 12 q^{28} + 24 q^{33} - 8 q^{36} - 16 q^{38} + 24 q^{41} - 20 q^{42} + 24 q^{43} + 36 q^{47} + 12 q^{48} + 24 q^{51} - 24 q^{52} + 72 q^{53} + 24 q^{57} - 24 q^{58} - 48 q^{61} + 4 q^{62} - 16 q^{63} + 32 q^{66} - 36 q^{67} - 16 q^{68} + 24 q^{71} - 8 q^{73} + 24 q^{77} + 24 q^{78} + 56 q^{81} - 8 q^{82} - 24 q^{83} - 104 q^{87} - 24 q^{91} + 4 q^{92} - 52 q^{93} + 24 q^{97} - 72 q^{98}+O(q^{100}) $ 32 * q + 12 * q^3 - 24 * q^7 - 16 * q^11 - 24 * q^13 + 16 * q^16 + 8 * q^17 + 12 * q^22 - 4 * q^23 - 16 * q^26 + 12 * q^28 + 24 * q^33 - 8 * q^36 - 16 * q^38 + 24 * q^41 - 20 * q^42 + 24 * q^43 + 36 * q^47 + 12 * q^48 + 24 * q^51 - 24 * q^52 + 72 * q^53 + 24 * q^57 - 24 * q^58 - 48 * q^61 + 4 * q^62 - 16 * q^63 + 32 * q^66 - 36 * q^67 - 16 * q^68 + 24 * q^71 - 8 * q^73 + 24 * q^77 + 24 * q^78 + 56 * q^81 - 8 * q^82 - 24 * q^83 - 104 * q^87 - 24 * q^91 + 4 * q^92 - 52 * q^93 + 24 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	−0.407975	−	1.52258i	−0.235545	−	0.879064i	−0.977903	−	0.209061i	$-0.932959\pi$
$3$	−0.407975	−	1.52258i	−0.235545	−	0.879064i	0.742358	−	0.670003i	$-0.233707\pi$
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$	−0.788148	−	1.36511i	−0.321760	−	0.557304i
$7$	−2.78714	+	2.78714i	−1.05344	+	1.05344i	−0.0549500	+	0.998489i	$0.517500\pi$
$7$	−2.78714	+	2.78714i	−1.05344	+	1.05344i	−0.998489	+	0.0549500i	$0.982500\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.446257	−	0.257647i	0.148752	−	0.0858823i
$10$		0			0
$11$	−3.61156			−1.08893			−0.544463	−	0.838785i	$-0.683266\pi$
$11$	−3.61156			−1.08893			−0.544463	+	0.838785i	$0.683266\pi$
$12$	−1.11461	−	1.11461i	−0.321760	−	0.321760i
$13$	−4.02492	−	1.07847i	−1.11631	−	0.299115i	−0.346921	−	0.937894i	$-0.612773\pi$
$13$	−4.02492	−	1.07847i	−1.11631	−	0.299115i	−0.769390	+	0.638780i	$0.779439\pi$
$14$	−1.97080	+	3.41353i	−0.526720	+	0.912305i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.78974	−	6.67939i	−0.434075	−	1.61999i	−0.743270	−	0.668991i	$-0.766726\pi$
$17$	−1.78974	−	6.67939i	−0.434075	−	1.61999i	0.309195	−	0.950999i	$-0.399940\pi$
$18$	0.364368	−	0.364368i	0.0858823	−	0.0858823i
$19$	−4.35847	−	0.0613000i	−0.999901	−	0.0140632i
$19$	−4.35847	−	0.0613000i	−0.999901	−	0.0140632i
$20$		0			0
$21$	5.38074	+	3.10657i	1.17417	+	0.677909i
$22$	−3.48850	+	0.934740i	−0.743750	+	0.199287i
$23$	−0.826722	+	3.08537i	−0.172383	+	0.643344i	0.824599	+	0.565717i	$0.191401\pi$
$23$	−0.826722	+	3.08537i	−0.172383	+	0.643344i	−0.996983	+	0.0776261i	$0.975266\pi$
$24$	−1.36511	−	0.788148i	−0.278652	−	0.160880i
$25$		0			0
$26$	−4.16690			−0.817196
$27$	−3.91818	−	3.91818i	−0.754054	−	0.754054i
$28$	−1.02016	+	3.80730i	−0.192793	+	0.719512i
$29$	−0.966822	−	1.67459i	−0.179534	−	0.310963i	0.762187	−	0.647357i	$-0.224126\pi$
$29$	−0.966822	−	1.67459i	−0.179534	−	0.310963i	−0.941721	+	0.336395i	$0.890792\pi$
$30$		0			0
$31$		−	2.38055i		−	0.427560i	−0.976882	−	0.213780i	$-0.931422\pi$
$31$		−	2.38055i		−	0.427560i	0.976882	−	0.213780i	$-0.0685776\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	1.47343	+	5.49890i	0.256491	+	0.957236i
$34$	−3.45751	−	5.98858i	−0.592958	−	1.02703i
$35$		0			0
$36$	0.257647	−	0.446257i	0.0429411	−	0.0743762i
$37$	−5.07600	−	5.07600i	−0.834489	−	0.834489i	0.153639	−	0.988127i	$-0.450901\pi$
$37$	−5.07600	−	5.07600i	−0.834489	−	0.834489i	−0.988127	+	0.153639i	$0.950901\pi$
$38$	−4.22582	+	1.06884i	−0.685519	+	0.173389i
$39$			6.56826i			1.05176i
$40$		0			0
$41$	1.72256	+	0.994522i	0.269019	+	0.155318i	0.628442	−	0.777857i	$-0.283693\pi$
$41$	1.72256	+	0.994522i	0.269019	+	0.155318i	−0.359423	+	0.933175i	$0.617026\pi$
$42$	6.00143	+	1.60808i	0.926041	+	0.248132i
$43$	7.85704	−	2.10529i	1.19819	−	0.321054i	0.396071	−	0.918220i	$-0.370374\pi$
$43$	7.85704	−	2.10529i	1.19819	−	0.321054i	0.802117	+	0.597167i	$0.203707\pi$
$44$	−3.12770	+	1.80578i	−0.471519	+	0.272231i
$45$		0			0
$46$			3.19421i			0.470960i
$47$	5.79010	+	1.55145i	0.844573	+	0.226303i	0.655061	−	0.755576i	$-0.272643\pi$
$47$	5.79010	+	1.55145i	0.844573	+	0.226303i	0.189512	+	0.981878i	$0.439310\pi$
$48$	−1.52258	−	0.407975i	−0.219766	−	0.0588861i
$49$		−	8.53628i		−	1.21947i
$50$		0			0
$51$	−9.43977	+	5.45005i	−1.32183	+	0.763160i
$52$	−4.02492	+	1.07847i	−0.558155	+	0.149557i
$53$	12.1460	+	3.25451i	1.66838	+	0.447041i	0.964673	−	0.263449i	$-0.0848602\pi$
$53$	12.1460	+	3.25451i	1.66838	+	0.447041i	0.703707	+	0.710490i	$0.251527\pi$
$54$	−4.79877	−	2.77057i	−0.653030	−	0.377027i
$55$		0			0
$56$			3.94161i			0.526720i
$57$	1.68481	+	6.66114i	0.223159	+	0.882290i
$58$	−1.36729	−	1.36729i	−0.179534	−	0.179534i
$59$	−4.99297	+	8.64808i	−0.650030	+	1.12588i	0.333085	+	0.942897i	$0.391910\pi$
$59$	−4.99297	+	8.64808i	−0.650030	+	1.12588i	−0.983115	+	0.182988i	$0.941423\pi$
$60$		0			0
$61$	1.12826	+	1.95420i	0.144459	+	0.250210i	0.929171	−	0.369650i	$-0.120523\pi$
$61$	1.12826	+	1.95420i	0.144459	+	0.250210i	−0.784712	+	0.619860i	$0.787189\pi$
$62$	−0.616133	−	2.29944i	−0.0782489	−	0.292029i
$63$	−0.525684	+	1.96188i	−0.0662299	+	0.247173i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	2.84644	+	4.93018i	0.350373	+	0.606863i
$67$	−1.12871	+	4.21239i	−0.137893	+	0.514625i	0.862076	+	0.506779i	$0.169164\pi$
$67$	−1.12871	+	4.21239i	−0.137893	+	0.514625i	−0.999969	+	0.00784566i	$0.997503\pi$
$68$	−4.88965	−	4.88965i	−0.592958	−	0.592958i
$69$	5.03501			0.606144
$70$		0			0
$71$	4.67273	+	2.69780i	0.554551	+	0.320170i	0.750955	−	0.660353i	$-0.229593\pi$
$71$	4.67273	+	2.69780i	0.554551	+	0.320170i	−0.196405	+	0.980523i	$0.562927\pi$
$72$	0.133368	−	0.497736i	0.0157176	−	0.0586587i
$73$	−13.2038	+	3.53796i	−1.54539	+	0.414087i	−0.928003	−	0.372572i	$-0.878476\pi$
$73$	−13.2038	+	3.53796i	−1.54539	+	0.414087i	−0.617389	+	0.786658i	$0.711809\pi$
$74$	−6.21680	−	3.58927i	−0.722688	−	0.417244i
$75$		0			0
$76$	−3.80519	+	2.12615i	−0.436486	+	0.243886i
$77$	10.0659	−	10.0659i	1.14712	−	1.14712i
$78$	1.69999	+	6.34445i	0.192486	+	0.718368i
$79$	−0.484828	+	0.839746i	−0.0545474	+	0.0944788i	−0.892010	−	0.452016i	$-0.850705\pi$
$79$	−0.484828	+	0.839746i	−0.0545474	+	0.0944788i	0.837462	+	0.546495i	$0.184038\pi$
$80$		0			0
$81$	−3.59430	+	6.22550i	−0.399366	+	0.691723i
$82$	1.92127	+	0.514803i	0.212169	+	0.0568504i
$83$	−4.90713	−	4.90713i	−0.538628	−	0.538628i	0.384498	−	0.923126i	$-0.374375\pi$
$83$	−4.90713	−	4.90713i	−0.538628	−	0.538628i	−0.923126	+	0.384498i	$0.874375\pi$
$84$	6.21314			0.677909
$85$		0			0
$86$	7.04443	−	4.06711i	0.759621	−	0.438567i
$87$	−2.15526	+	2.15526i	−0.231068	+	0.231068i
$88$	−2.55376	+	2.55376i	−0.272231	+	0.272231i
$89$	−0.366642	−	0.635043i	−0.0388640	−	0.0673144i	0.845939	−	0.533279i	$-0.179041\pi$
$89$	−0.366642	−	0.635043i	−0.0388640	−	0.0673144i	−0.884803	+	0.465965i	$0.845707\pi$
$90$		0			0
$91$	14.2238	−	8.21214i	1.49106	−	0.860866i
$92$	0.826722	+	3.08537i	0.0861917	+	0.321672i
$93$	−3.62459	+	0.971207i	−0.375853	+	0.100709i
$94$	5.99435			0.618270
$95$		0			0
$96$	−1.57630			−0.160880
$97$	11.9625	−	3.20535i	1.21461	−	0.325454i	0.406042	−	0.913854i	$-0.366909\pi$
$97$	11.9625	−	3.20535i	1.21461	−	0.325454i	0.808570	+	0.588400i	$0.200242\pi$
$98$	−2.20935	−	8.24541i	−0.223178	−	0.832912i
$99$	−1.61168	+	0.930507i	−0.161980	+	0.0935194i
$100$		0			0
$101$	−7.62872	−	13.2133i	−0.759086	−	1.31478i	−0.943317	−	0.331893i	$-0.892313\pi$
$101$	−7.62872	−	13.2133i	−0.759086	−	1.31478i	0.184231	−	0.982883i	$-0.441021\pi$
$102$	−7.70754	+	7.70754i	−0.763160	+	0.763160i
$103$	7.87126	−	7.87126i	0.775578	−	0.775578i	−0.203497	−	0.979076i	$-0.565231\pi$
$103$	7.87126	−	7.87126i	0.775578	−	0.775578i	0.979076	+	0.203497i	$0.0652307\pi$
$104$	−3.60864	+	2.08345i	−0.353856	+	0.204299i
$105$		0			0
$106$	12.5745			1.22134
$107$	0.402059	+	0.402059i	0.0388685	+	0.0388685i	0.726274	−	0.687405i	$-0.241250\pi$
$107$	0.402059	+	0.402059i	0.0388685	+	0.0388685i	−0.687405	+	0.726274i	$0.741250\pi$
$108$	−5.35233	−	1.43415i	−0.515028	−	0.138001i
$109$	0.204284	−	0.353831i	0.0195669	−	0.0338909i	−0.856076	−	0.516850i	$-0.827105\pi$
$109$	0.204284	−	0.353831i	0.0195669	−	0.0338909i	0.875643	+	0.482959i	$0.160438\pi$
$110$		0			0
$111$	−5.65775	+	9.79951i	−0.537010	+	0.930128i
$112$	1.02016	+	3.80730i	0.0963964	+	0.359756i
$113$	1.30484	−	1.30484i	0.122749	−	0.122749i	−0.643064	−	0.765813i	$-0.722337\pi$
$113$	1.30484	−	1.30484i	0.122749	−	0.122749i	0.765813	+	0.643064i	$0.222337\pi$
$114$	3.35143	+	5.99811i	0.313891	+	0.561774i
$115$		0			0
$116$	−1.67459	−	0.966822i	−0.155481	−	0.0897672i
$117$	−2.07401	+	0.555730i	−0.191743	+	0.0513773i
$118$	−2.58455	+	9.64569i	−0.237927	+	0.887957i
$119$	23.6046	+	13.6281i	2.16383	+	1.24929i
$120$		0			0
$121$	2.04335			0.185760
$122$	1.59560	+	1.59560i	0.144459	+	0.144459i
$123$	0.811481	−	3.02849i	0.0731688	−	0.273070i
$124$	−1.19028	−	2.06162i	−0.106890	−	0.185139i
$125$		0			0
$126$			2.03109i			0.180944i
$127$	3.18666	−	11.8928i	0.282770	−	1.05531i	−0.667683	−	0.744446i	$-0.732714\pi$
$127$	3.18666	−	11.8928i	0.282770	−	1.05531i	0.950453	−	0.310867i	$-0.100619\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−6.41096	−	11.1041i	−0.564453	−	0.977662i
$130$		0			0
$131$	5.43736	−	9.41778i	0.475064	−	0.822835i	−0.524528	−	0.851393i	$-0.675758\pi$
$131$	5.43736	−	9.41778i	0.475064	−	0.822835i	0.999592	+	0.0285582i	$0.00909160\pi$
$132$	4.02548	+	4.02548i	0.350373	+	0.350373i
$133$	12.3185	−	11.9768i	1.06815	−	1.03852i
$134$			4.36098i			0.376732i
$135$		0			0
$136$	−5.98858	−	3.45751i	−0.513516	−	0.296479i
$137$	−12.4149	−	3.32656i	−1.06068	−	0.284207i	−0.314019	−	0.949417i	$-0.601676\pi$
$137$	−12.4149	−	3.32656i	−1.06068	−	0.284207i	−0.746657	+	0.665209i	$0.768342\pi$
$138$	4.86345	−	1.30316i	0.414004	−	0.110932i
$139$	−11.0016	+	6.35176i	−0.933141	+	0.538749i	−0.887803	−	0.460223i	$-0.847770\pi$
$139$	−11.0016	+	6.35176i	−0.933141	+	0.538749i	−0.0453372	+	0.998972i	$0.514436\pi$
$140$		0			0
$141$		−	9.44887i		−	0.795738i
$142$	5.21175	+	1.39648i	0.437360	+	0.117190i
$143$	14.5362	+	3.89497i	1.21558	+	0.325714i
$144$		−	0.515294i		−	0.0429411i
$145$		0			0
$146$	−11.8382	+	6.83481i	−0.979739	+	0.565653i
$147$	−12.9972	+	3.48259i	−1.07199	+	0.287239i
$148$	−6.93394	−	1.85794i	−0.569966	−	0.152722i
$149$	1.05966	+	0.611793i	0.0868105	+	0.0501201i	0.542777	−	0.839877i	$-0.317373\pi$
$149$	1.05966	+	0.611793i	0.0868105	+	0.0501201i	−0.455966	+	0.889997i	$0.650706\pi$
$150$		0			0
$151$			0.201292i			0.0163809i	0.999966	+	0.00819047i	$0.00260714\pi$
$151$			0.201292i			0.0163809i	−0.999966	+	0.00819047i	$0.997393\pi$
$152$	−3.12525	+	3.03856i	−0.253491	+	0.246459i
$153$	−2.51961	−	2.51961i	−0.203698	−	0.203698i
$154$	7.11767	−	12.3282i	0.573559	−	0.993433i
$155$		0			0
$156$	3.28413	+	5.68828i	0.262941	+	0.455427i
$157$	−4.12977	−	15.4125i	−0.329591	−	1.23005i	−0.909615	−	0.415452i	$-0.863623\pi$
$157$	−4.12977	−	15.4125i	−0.329591	−	1.23005i	0.580024	−	0.814600i	$-0.303043\pi$
$158$	−0.250965	+	0.936615i	−0.0199657	+	0.0745131i
$159$		−	19.8211i		−	1.57191i
$160$		0			0
$161$	−6.29516	−	10.9035i	−0.496128	−	0.859319i
$162$	−1.86054	+	6.94365i	−0.146178	+	0.545544i
$163$	3.38517	+	3.38517i	0.265147	+	0.265147i	0.827141	−	0.561994i	$-0.189966\pi$
$163$	3.38517	+	3.38517i	0.265147	+	0.265147i	−0.561994	+	0.827141i	$0.689966\pi$
$164$	1.98904			0.155318
$165$		0			0
$166$	−6.00999	−	3.46987i	−0.466465	−	0.269314i
$167$	−3.71737	+	13.8734i	−0.287659	+	1.07356i	0.659216	+	0.751954i	$0.270888\pi$
$167$	−3.71737	+	13.8734i	−0.287659	+	1.07356i	−0.946874	+	0.321603i	$0.895778\pi$
$168$	6.00143	−	1.60808i	0.463020	−	0.124066i
$169$	3.77851	+	2.18152i	0.290655	+	0.167810i
$170$		0			0
$171$	−1.96079	+	1.09559i	−0.149946	+	0.0837819i
$172$	5.75176	−	5.75176i	0.438567	−	0.438567i
$173$	−1.71219	−	6.38997i	−0.130175	−	0.485820i	0.869796	−	0.493411i	$-0.164250\pi$
$173$	−1.71219	−	6.38997i	−0.130175	−	0.485820i	−0.999971	+	0.00759123i	$0.997584\pi$
$174$	−1.52400	+	2.63964i	−0.115534	+	0.200111i
$175$		0			0
$176$	−1.80578	+	3.12770i	−0.136116	+	0.235759i
$177$	15.2044	+	4.07402i	1.14284	+	0.306222i
$178$	−0.518510	−	0.518510i	−0.0388640	−	0.0388640i
$179$	−6.55743			−0.490126			−0.245063	−	0.969507i	$-0.578809\pi$
$179$	−6.55743			−0.490126			−0.245063	+	0.969507i	$0.578809\pi$
$180$		0			0
$181$	0.989823	−	0.571474i	0.0735729	−	0.0424774i	−0.462762	−	0.886482i	$-0.653142\pi$
$181$	0.989823	−	0.571474i	0.0735729	−	0.0424774i	0.536335	+	0.844005i	$0.319808\pi$
$182$	11.6137	−	11.6137i	0.860866	−	0.860866i
$183$	2.51514	−	2.51514i	0.185924	−	0.185924i
$184$	1.59710	+	2.76626i	0.117740	+	0.203932i
$185$		0			0
$186$	−3.24972	+	1.87623i	−0.238281	+	0.137572i
$187$	6.46374	+	24.1230i	0.472676	+	1.76405i
$188$	5.79010	−	1.55145i	0.422286	−	0.113151i
$189$	21.8410			1.58870
$190$		0			0
$191$	8.77547			0.634970			0.317485	−	0.948263i	$-0.397162\pi$
$191$	8.77547			0.634970			0.317485	+	0.948263i	$0.397162\pi$
$192$	−1.52258	+	0.407975i	−0.109883	+	0.0294431i
$193$	−1.40965	−	5.26087i	−0.101469	−	0.378686i	0.896452	−	0.443141i	$-0.146136\pi$
$193$	−1.40965	−	5.26087i	−0.101469	−	0.378686i	−0.997921	+	0.0644549i	$0.979469\pi$
$194$	10.7253	−	6.19227i	0.770033	−	0.444579i
$195$		0			0
$196$	−4.26814	−	7.39263i	−0.304867	−	0.528045i
$197$	−6.21372	+	6.21372i	−0.442710	+	0.442710i	−0.892922	−	0.450212i	$-0.851348\pi$
$197$	−6.21372	+	6.21372i	−0.442710	+	0.442710i	0.450212	+	0.892922i	$0.351348\pi$
$198$	−1.31594	+	1.31594i	−0.0935194	+	0.0935194i
$199$	−0.834214	+	0.481634i	−0.0591359	+	0.0341421i	−0.529276	−	0.848449i	$-0.677537\pi$
$199$	−0.834214	+	0.481634i	−0.0591359	+	0.0341421i	0.470141	+	0.882592i	$0.344203\pi$
$200$		0			0
$201$	6.87420			0.484868
$202$	−10.7886	−	10.7886i	−0.759086	−	0.759086i
$203$	7.36197	+	1.97263i	0.516709	+	0.138452i
$204$	−5.45005	+	9.43977i	−0.381580	+	0.660916i
$205$		0			0
$206$	5.56582	−	9.64029i	0.387789	−	0.671671i
$207$	0.426005	+	1.58987i	0.0296094	+	0.110504i
$208$	−2.94644	+	2.94644i	−0.204299	+	0.204299i
$209$	15.7409	+	0.221389i	1.08882	+	0.0153138i
$210$		0			0
$211$	−2.74108	−	1.58257i	−0.188704	−	0.108948i	0.402672	−	0.915344i	$-0.368082\pi$
$211$	−2.74108	−	1.58257i	−0.188704	−	0.108948i	−0.591376	+	0.806396i	$0.701415\pi$
$212$	12.1460	−	3.25451i	0.834190	−	0.223521i
$213$	2.20127	−	8.21526i	0.150829	−	0.562900i
$214$	0.492419	+	0.284298i	0.0336611	+	0.0194342i
$215$		0			0
$216$	−5.54114			−0.377027
$217$	6.63493	+	6.63493i	0.450409	+	0.450409i
$218$	0.105745	−	0.394647i	0.00716198	−	0.0267289i
$219$	10.7737	+	18.6606i	0.728017	+	1.26096i
$220$		0			0
$221$			28.8142i			1.93825i
$222$	−2.92867	+	10.9299i	−0.196559	+	0.733569i
$223$	6.29264	+	23.4845i	0.421386	+	1.57264i	0.771690	+	0.635999i	$0.219412\pi$
$223$	6.29264	+	23.4845i	0.421386	+	1.57264i	−0.350303	+	0.936636i	$0.613921\pi$
$224$	1.97080	+	3.41353i	0.131680	+	0.228076i
$225$		0			0
$226$	0.922661	−	1.59810i	0.0613745	−	0.106304i
$227$	−16.3802	−	16.3802i	−1.08719	−	1.08719i	−0.995817	−	0.0913721i	$-0.970875\pi$
$227$	−16.3802	−	16.3802i	−1.08719	−	1.08719i	−0.0913721	−	0.995817i	$-0.529125\pi$
$228$	4.78966	+	4.92631i	0.317203	+	0.326253i
$229$		−	17.5273i		−	1.15823i	−0.815244	−	0.579117i	$-0.803397\pi$
$229$		−	17.5273i		−	1.15823i	0.815244	−	0.579117i	$-0.196603\pi$
$230$		0			0
$231$	−19.4328	−	11.2196i	−1.27859	−	0.738193i
$232$	−1.86776	−	0.500464i	−0.122624	−	0.0328571i
$233$	−9.95158	+	2.66652i	−0.651950	+	0.174689i	−0.569610	−	0.821915i	$-0.692906\pi$
$233$	−9.95158	+	2.66652i	−0.651950	+	0.174689i	−0.0823394	+	0.996604i	$0.526239\pi$
$234$	−1.85951	+	1.07359i	−0.121560	+	0.0701827i
$235$		0			0
$236$			9.98595i			0.650030i
$237$	1.47638	+	0.395595i	0.0959013	+	0.0256967i
$238$	26.3275	+	7.05444i	1.70656	+	0.457272i
$239$		−	16.7248i		−	1.08184i	−0.841075	−	0.540919i	$-0.818076\pi$
$239$		−	16.7248i		−	1.08184i	0.841075	−	0.540919i	$-0.181924\pi$
$240$		0			0
$241$	17.2849	−	9.97943i	1.11342	−	0.642831i	0.173704	−	0.984798i	$-0.444426\pi$
$241$	17.2849	−	9.97943i	1.11342	−	0.642831i	0.939712	+	0.341967i	$0.111093\pi$
$242$	1.97373	−	0.528859i	0.126876	−	0.0339964i
$243$	−5.11176	−	1.36969i	−0.327919	−	0.0878657i
$244$	1.95420	+	1.12826i	0.125105	+	0.0722294i
$245$		0			0
$246$		−	3.13532i		−	0.199901i
$247$	17.4764	+	4.94722i	1.11199	+	0.314784i
$248$	−1.68331	−	1.68331i	−0.106890	−	0.106890i
$249$	−5.46954	+	9.47351i	−0.346618	+	0.600359i
$250$		0			0
$251$	−2.47482	−	4.28651i	−0.156209	−	0.270562i	0.777289	−	0.629143i	$-0.216594\pi$
$251$	−2.47482	−	4.28651i	−0.156209	−	0.270562i	−0.933499	+	0.358581i	$0.883261\pi$
$252$	0.525684	+	1.96188i	0.0331150	+	0.123587i
$253$	2.98575	−	11.1430i	0.187713	−	0.700553i
$254$		−	12.3123i		−	0.772543i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.02199	+	11.2782i	−0.188506	+	0.703515i	0.805346	+	0.592805i	$0.201979\pi$
$257$	−3.02199	+	11.2782i	−0.188506	+	0.703515i	−0.993853	+	0.110711i	$0.964687\pi$
$258$	−9.06646	−	9.06646i	−0.564453	−	0.564453i
$259$	28.2950			1.75817
$260$		0			0
$261$	−0.862903	−	0.498197i	−0.0534124	−	0.0308376i
$262$	2.81458	−	10.5042i	0.173885	−	0.648949i
$263$	−12.8749	+	3.44981i	−0.793898	+	0.212724i	−0.632903	−	0.774231i	$-0.718137\pi$
$263$	−12.8749	+	3.44981i	−0.793898	+	0.212724i	−0.160995	+	0.986955i	$0.551470\pi$
$264$	4.93018	+	2.84644i	0.303432	+	0.175186i
$265$		0			0
$266$	8.79894	−	14.7570i	0.539497	−	0.904807i
$267$	−0.817326	+	0.817326i	−0.0500195	+	0.0500195i
$268$	1.12871	+	4.21239i	0.0689467	+	0.257312i
$269$	−11.7656	+	20.3787i	−0.717363	+	1.24251i	0.244678	+	0.969604i	$0.421318\pi$
$269$	−11.7656	+	20.3787i	−0.717363	+	1.24251i	−0.962041	+	0.272905i	$0.912016\pi$
$270$		0			0
$271$	13.5007	−	23.3839i	0.820109	−	1.42047i	−0.0854913	−	0.996339i	$-0.527246\pi$
$271$	13.5007	−	23.3839i	0.820109	−	1.42047i	0.905600	−	0.424132i	$-0.139421\pi$
$272$	−6.67939	−	1.78974i	−0.404998	−	0.108519i
$273$	−18.3067	−	18.3067i	−1.10797	−	1.10797i
$274$	−12.8528			−0.776469
$275$		0			0
$276$	4.36045	−	2.51751i	0.262468	−	0.151536i
$277$	19.2785	−	19.2785i	1.15833	−	1.15833i	0.173495	−	0.984835i	$-0.444494\pi$
$277$	19.2785	−	19.2785i	1.15833	−	1.15833i	0.984835	−	0.173495i	$-0.0555062\pi$
$278$	−8.98274	+	8.98274i	−0.538749	+	0.538749i
$279$	−0.613342	−	1.06234i	−0.0367199	−	0.0636006i
$280$		0			0
$281$	18.1717	−	10.4914i	1.08403	−	0.625865i	0.152050	−	0.988373i	$-0.451413\pi$
$281$	18.1717	−	10.4914i	1.08403	−	0.625865i	0.931981	+	0.362507i	$0.118079\pi$
$282$	−2.44555	−	9.12691i	−0.145630	−	0.543499i
$283$	−2.05427	+	0.550440i	−0.122114	+	0.0327202i	−0.319358	−	0.947634i	$-0.603467\pi$
$283$	−2.05427	+	0.550440i	−0.122114	+	0.0327202i	0.197245	+	0.980354i	$0.436801\pi$
$284$	5.39560			0.320170
$285$		0			0
$286$	15.0490			0.889866
$287$	−7.57289	+	2.02915i	−0.447014	+	0.119777i
$288$	−0.133368	−	0.497736i	−0.00785878	−	0.0293293i
$289$	−26.6887	+	15.4087i	−1.56992	+	0.906395i
$290$		0			0
$291$	−9.76084	−	16.9063i	−0.572190	−	0.991063i
$292$	−9.66588	+	9.66588i	−0.565653	+	0.565653i
$293$	−9.87528	+	9.87528i	−0.576920	+	0.576920i	−0.934053	−	0.357133i	$-0.883754\pi$
$293$	−9.87528	+	9.87528i	−0.576920	+	0.576920i	0.357133	+	0.934053i	$0.383754\pi$
$294$	−11.6530	+	6.72784i	−0.679615	+	0.392376i
$295$		0			0
$296$	−7.17854			−0.417244
$297$	14.1507	+	14.1507i	0.821109	+	0.821109i
$298$	1.18189	+	0.316688i	0.0684653	+	0.0183452i
$299$	6.65497	−	11.5267i	0.384867	−	0.666609i
$300$		0			0
$301$	−16.0309	+	27.7664i	−0.924008	+	1.60043i
$302$	0.0520983	+	0.194434i	0.00299792	+	0.0111884i
$303$	−17.0061	+	17.0061i	−0.976974	+	0.976974i
$304$	−2.23232	+	3.74389i	−0.128032	+	0.214727i
$305$		0			0
$306$	−3.08588	−	1.78163i	−0.176408	−	0.101849i
$307$	−21.9228	+	5.87419i	−1.25120	+	0.335258i	−0.822799	−	0.568332i	$-0.807589\pi$
$307$	−21.9228	+	5.87419i	−1.25120	+	0.335258i	−0.428399	+	0.903590i	$0.640922\pi$
$308$	3.68438	−	13.7503i	0.209937	−	0.783496i
$309$	−15.1959	−	8.77338i	−0.864467	−	0.499100i
$310$		0			0
$311$	−10.5277			−0.596971			−0.298485	−	0.954414i	$-0.596481\pi$
$311$	−10.5277			−0.596971			−0.298485	+	0.954414i	$0.596481\pi$
$312$	4.64446	+	4.64446i	0.262941	+	0.262941i
$313$	−4.64875	+	17.3494i	−0.262763	+	0.980644i	0.700843	+	0.713316i	$0.252807\pi$
$313$	−4.64875	+	17.3494i	−0.262763	+	0.980644i	−0.963606	+	0.267328i	$0.913859\pi$
$314$	−7.97810	−	13.8185i	−0.450230	−	0.779822i
$315$		0			0
$316$			0.969655i			0.0545474i
$317$	−7.08176	+	26.4295i	−0.397751	+	1.48443i	0.419292	+	0.907852i	$0.362278\pi$
$317$	−7.08176	+	26.4295i	−0.397751	+	1.48443i	−0.817043	+	0.576577i	$0.804388\pi$
$318$	−5.13007	−	19.1457i	−0.287680	−	1.07364i
$319$	3.49173	+	6.04786i	0.195500	+	0.338615i
$320$		0			0
$321$	0.448138	−	0.776198i	0.0250126	−	0.0433232i
$322$	−8.90270	−	8.90270i	−0.496128	−	0.496128i
$323$	7.39107	+	29.2216i	0.411250	+	1.62593i
$324$			7.18859i			0.399366i
$325$		0			0
$326$	4.14597	+	2.39367i	0.229624	+	0.132573i
$327$	−0.622081	−	0.166686i	−0.0344011	−	0.00921776i
$328$	1.92127	−	0.514803i	0.106084	−	0.0284252i
$329$	−20.4619	+	11.8137i	−1.12810	+	0.651310i
$330$		0			0
$331$			13.5133i			0.742756i	0.928482	+	0.371378i	$0.121115\pi$
$331$			13.5133i			0.742756i	−0.928482	+	0.371378i	$0.878885\pi$
$332$	−6.70327	−	1.79614i	−0.367890	−	0.0985758i
$333$	−3.57302	−	0.957387i	−0.195800	−	0.0524645i
$334$			14.3628i			0.785899i
$335$		0			0
$336$	5.38074	−	3.10657i	0.293543	−	0.169477i
$337$	1.50516	−	0.403307i	0.0819914	−	0.0219695i	−0.217590	−	0.976040i	$-0.569820\pi$
$337$	1.50516	−	0.403307i	0.0819914	−	0.0219695i	0.299582	+	0.954071i	$0.403153\pi$
$338$	4.21438	+	1.12924i	0.229232	+	0.0614226i
$339$	−2.51907	−	1.45439i	−0.136817	−	0.0789914i
$340$		0			0
$341$			8.59751i			0.465581i
$342$	−1.61042	+	1.56575i	−0.0870816	+	0.0846660i
$343$	4.28181	+	4.28181i	0.231196	+	0.231196i
$344$	4.06711	−	7.04443i	0.219284	−	0.379810i
$345$		0			0
$346$	−3.30769	−	5.72909i	−0.177823	−	0.307998i
$347$	−2.61710	−	9.76714i	−0.140493	−	0.524328i	−0.999915	−	0.0130599i	$-0.995843\pi$
$347$	−2.61710	−	9.76714i	−0.140493	−	0.524328i	0.859422	−	0.511268i	$-0.170824\pi$
$348$	−0.788879	+	2.94414i	−0.0422883	+	0.157822i
$349$		−	1.48199i		−	0.0793290i	−0.999213	−	0.0396645i	$-0.987371\pi$
$349$		−	1.48199i		−	0.0793290i	0.999213	−	0.0396645i	$-0.0126289\pi$
$350$		0			0
$351$	11.5447	+	19.9960i	0.616210	+	1.06731i
$352$	−0.934740	+	3.48850i	−0.0498218	+	0.185938i
$353$	6.58908	+	6.58908i	0.350701	+	0.350701i	0.860370	−	0.509669i	$-0.170232\pi$
$353$	6.58908	+	6.58908i	0.350701	+	0.350701i	−0.509669	+	0.860370i	$0.670232\pi$
$354$	15.7408			0.836614
$355$		0			0
$356$	−0.635043	−	0.366642i	−0.0336572	−	0.0194320i
$357$	11.1199	−	41.5000i	0.588527	−	2.19641i
$358$	−6.33399	+	1.69719i	−0.334762	+	0.0896992i
$359$	14.2064	+	8.20209i	0.749787	+	0.432890i	0.825617	−	0.564231i	$-0.190827\pi$
$359$	14.2064	+	8.20209i	0.749787	+	0.432890i	−0.0758297	+	0.997121i	$0.524161\pi$
$360$		0			0
$361$	18.9925	+	0.534348i	0.999604	+	0.0281236i
$362$	0.808187	−	0.808187i	0.0424774	−	0.0424774i
$363$	−0.833638	−	3.11118i	−0.0437547	−	0.163295i
$364$	8.21214	−	14.2238i	0.430433	−	0.745532i
$365$		0			0
$366$	1.77847	−	3.08040i	0.0929621	−	0.161015i
$367$	−4.67874	−	1.25366i	−0.244228	−	0.0654408i	0.134628	−	0.990896i	$-0.457016\pi$
$367$	−4.67874	−	1.25366i	−0.244228	−	0.0654408i	−0.378857	+	0.925455i	$0.623683\pi$
$368$	2.25865	+	2.25865i	0.117740	+	0.117740i
$369$	1.02494			0.0533564
$370$		0			0
$371$	−42.9233	+	24.7818i	−2.22847	+	1.28661i
$372$	−2.65339	+	2.65339i	−0.137572	+	0.137572i
$373$	14.9024	−	14.9024i	0.771618	−	0.771618i	−0.206771	−	0.978389i	$-0.566296\pi$
$373$	14.9024	−	14.9024i	0.771618	−	0.771618i	0.978389	+	0.206771i	$0.0662956\pi$
$374$	12.4870	+	21.6281i	0.645687	+	1.11836i
$375$		0			0
$376$	5.19126	−	2.99718i	0.267719	−	0.154568i
$377$	2.08538	+	7.78276i	0.107403	+	0.400832i
$378$	21.0968	−	5.65287i	1.08510	−	0.290752i
$379$	−17.7195			−0.910187			−0.455094	−	0.890444i	$-0.650394\pi$
$379$	−17.7195			−0.910187			−0.455094	+	0.890444i	$0.650394\pi$
$380$		0			0
$381$	−19.4078			−0.994293
$382$	8.47645	−	2.27126i	0.433693	−	0.116208i
$383$	−4.20625	−	15.6979i	−0.214929	−	0.802127i	−0.986191	−	0.165609i	$-0.947041\pi$
$383$	−4.20625	−	15.6979i	−0.214929	−	0.802127i	0.771262	−	0.636518i	$-0.219626\pi$
$384$	−1.36511	+	0.788148i	−0.0696631	+	0.0402200i
$385$		0			0
$386$	−2.72323	−	4.71677i	−0.138609	−	0.240077i
$387$	2.96384	−	2.96384i	0.150661	−	0.150661i
$388$	8.75719	−	8.75719i	0.444579	−	0.444579i
$389$	14.6085	−	8.43424i	0.740682	−	0.427633i	−0.0816355	−	0.996662i	$-0.526014\pi$
$389$	14.6085	−	8.43424i	0.740682	−	0.427633i	0.822317	+	0.569030i	$0.192681\pi$
$390$		0			0
$391$	22.0880			1.11704
$392$	−6.03606	−	6.03606i	−0.304867	−	0.304867i
$393$	−16.5577	−	4.43661i	−0.835224	−	0.223797i
$394$	−4.39377	+	7.61023i	−0.221355	+	0.383398i
$395$		0			0
$396$	−0.930507	+	1.61168i	−0.0467597	+	0.0809902i
$397$	−1.67463	−	6.24979i	−0.0840471	−	0.313668i	0.911085	−	0.412219i	$-0.135246\pi$
$397$	−1.67463	−	6.24979i	−0.0840471	−	0.313668i	−0.995132	+	0.0985507i	$0.968579\pi$
$398$	−0.681133	+	0.681133i	−0.0341421	+	0.0341421i
$399$	−23.2613	−	13.8697i	−1.16452	−	0.694354i
$400$		0			0
$401$	2.05818	+	1.18829i	0.102781	+	0.0593405i	0.550509	−	0.834829i	$-0.314434\pi$
$401$	2.05818	+	1.18829i	0.102781	+	0.0593405i	−0.447729	+	0.894170i	$0.647767\pi$
$402$	6.63996	−	1.77917i	0.331171	−	0.0887371i
$403$	−2.56736	+	9.58153i	−0.127889	+	0.477290i
$404$	−13.2133	−	7.62872i	−0.657388	−	0.379543i
$405$		0			0
$406$	7.62167			0.378257
$407$	18.3323	+	18.3323i	0.908696	+	0.908696i
$408$	−2.82115	+	10.5287i	−0.139668	+	0.521248i
$409$	−2.23584	−	3.87260i	−0.110555	−	0.191488i	0.805439	−	0.592679i	$-0.201930\pi$
$409$	−2.23584	−	3.87260i	−0.110555	−	0.191488i	−0.915994	+	0.401191i	$0.868596\pi$
$410$		0			0
$411$			20.2599i			0.999346i
$412$	2.88108	−	10.7523i	0.141941	−	0.529730i
$413$	−10.1873	−	38.0195i	−0.501284	−	1.87082i
$414$	0.822978	+	1.42544i	0.0404471	+	0.0700565i
$415$		0			0
$416$	−2.08345	+	3.60864i	−0.102150	+	0.176928i
$417$	14.1595	+	14.1595i	0.693391	+	0.693391i
$418$	15.2618	−	3.86019i	0.746479	−	0.188808i
$419$		−	15.3593i		−	0.750351i	−0.926954	−	0.375175i	$-0.877583\pi$
$419$		−	15.3593i		−	0.750351i	0.926954	−	0.375175i	$-0.122417\pi$
$420$		0			0
$421$	−18.8271	−	10.8698i	−0.917578	−	0.529764i	−0.0347163	−	0.999397i	$-0.511053\pi$
$421$	−18.8271	−	10.8698i	−0.917578	−	0.529764i	−0.882862	+	0.469633i	$0.844386\pi$
$422$	−3.05728	−	0.819196i	−0.148826	−	0.0398779i
$423$	2.98360	−	0.799454i	0.145068	−	0.0388708i
$424$	10.8898	−	6.28723i	0.528855	−	0.305335i
$425$		0			0
$426$		−	8.50506i		−	0.412072i
$427$	−8.59125	−	2.30202i	−0.415759	−	0.111402i
$428$	0.549222	+	0.147164i	0.0265477	+	0.00711343i
$429$		−	23.7217i		−	1.14529i
$430$		0			0
$431$	−34.4917	+	19.9138i	−1.66141	+	0.959213i	−0.689360	+	0.724419i	$0.742108\pi$
$431$	−34.4917	+	19.9138i	−1.66141	+	0.959213i	−0.972045	+	0.234794i	$0.924558\pi$
$432$	−5.35233	+	1.43415i	−0.257514	+	0.0690007i
$433$	36.8281	+	9.86805i	1.76984	+	0.474228i	0.988673	−	0.150088i	$-0.0479558\pi$
$433$	36.8281	+	9.86805i	1.76984	+	0.474228i	0.781172	+	0.624316i	$0.214622\pi$
$434$	8.12610	+	4.69161i	0.390065	+	0.225204i
$435$		0			0
$436$		−	0.408569i		−	0.0195669i
$437$	3.79237	−	13.3968i	0.181414	−	0.640856i
$438$	15.2363	+	15.2363i	0.728017	+	0.728017i
$439$	10.2735	−	17.7943i	0.490330	−	0.849276i	−0.509608	−	0.860406i	$-0.670210\pi$
$439$	10.2735	−	17.7943i	0.490330	−	0.849276i	0.999938	+	0.0111305i	$0.00354303\pi$
$440$		0			0
$441$	−2.19934	−	3.80938i	−0.104731	−	0.181399i
$442$	7.45765	+	27.8323i	0.354724	+	1.32385i
$443$	1.61024	−	6.00948i	0.0765046	−	0.285519i	−0.917066	−	0.398736i	$-0.869449\pi$
$443$	1.61024	−	6.00948i	0.0765046	−	0.285519i	0.993570	+	0.113217i	$0.0361155\pi$
$444$			11.3155i			0.537010i
$445$		0			0
$446$	12.1565	+	21.0556i	0.575625	+	0.997011i
$447$	0.499193	−	1.86301i	0.0236110	−	0.0881175i
$448$	2.78714	+	2.78714i	0.131680	+	0.131680i
$449$	−13.7989			−0.651212			−0.325606	−	0.945505i	$-0.605568\pi$
$449$	−13.7989			−0.651212			−0.325606	+	0.945505i	$0.605568\pi$
$450$		0			0
$451$	−6.22114	−	3.59178i	−0.292942	−	0.169130i
$452$	0.477604	−	1.78244i	0.0224646	−	0.0838391i
$453$	0.306485	−	0.0821223i	0.0143999	−	0.00385844i
$454$	−20.0615	−	11.5825i	−0.941533	−	0.543594i
$455$		0			0
$456$	5.90148	+	3.51880i	0.276362	+	0.164783i
$457$	19.3387	−	19.3387i	0.904625	−	0.904625i	−0.0912068	−	0.995832i	$-0.529072\pi$
$457$	19.3387	−	19.3387i	0.904625	−	0.904625i	0.995832	+	0.0912068i	$0.0290724\pi$
$458$	−4.53639	−	16.9300i	−0.211972	−	0.791089i
$459$	−19.1585	+	33.1835i	−0.894244	+	1.54888i
$460$		0			0
$461$	8.15000	−	14.1162i	0.379583	−	0.657457i	−0.611418	−	0.791307i	$-0.709401\pi$
$461$	8.15000	−	14.1162i	0.379583	−	0.657457i	0.991002	+	0.133850i	$0.0427341\pi$
$462$	−21.6745	−	5.80767i	−1.00839	−	0.270197i
$463$	0.446318	+	0.446318i	0.0207422	+	0.0207422i	0.717402	−	0.696660i	$-0.245331\pi$
$463$	0.446318	+	0.446318i	0.0207422	+	0.0207422i	−0.696660	+	0.717402i	$0.745331\pi$
$464$	−1.93364			−0.0897672
$465$		0			0
$466$	−8.92234	+	5.15132i	−0.413319	+	0.238630i
$467$	−19.6340	+	19.6340i	−0.908553	+	0.908553i	−0.996155	−	0.0876026i	$-0.972079\pi$
$467$	−19.6340	+	19.6340i	−0.908553	+	0.908553i	0.0876026	+	0.996155i	$0.472079\pi$
$468$	−1.51828	+	1.51828i	−0.0701827	+	0.0701827i
$469$	−8.59464	−	14.8864i	−0.396864	−	0.687388i
$470$		0			0
$471$	−21.7820	+	12.5758i	−1.00366	+	0.579464i
$472$	2.58455	+	9.64569i	0.118964	+	0.443979i
$473$	−28.3762	+	7.60337i	−1.30474	+	0.349603i
$474$	1.52846			0.0702046
$475$		0			0
$476$	27.2563			1.24929
$477$	6.25875	−	1.67703i	0.286569	−	0.0767858i
$478$	−4.32870	−	16.1549i	−0.197990	−	0.738909i
$479$	17.5576	−	10.1369i	0.802229	−	0.463167i	−0.0420209	−	0.999117i	$-0.513380\pi$
$479$	17.5576	−	10.1369i	0.802229	−	0.463167i	0.844250	+	0.535950i	$0.180046\pi$
$480$		0			0
$481$	14.9561	+	25.9048i	0.681941	+	1.18116i
$482$	14.1130	−	14.1130i	0.642831	−	0.642831i
$483$	−14.0333	+	14.0333i	−0.638536	+	0.638536i
$484$	1.76960	−	1.02168i	0.0804362	−	0.0464399i
$485$		0			0
$486$	−5.29208			−0.240054
$487$	−5.10239	−	5.10239i	−0.231211	−	0.231211i	0.581987	−	0.813198i	$-0.302276\pi$
$487$	−5.10239	−	5.10239i	−0.231211	−	0.231211i	−0.813198	+	0.581987i	$0.802276\pi$
$488$	2.17963	+	0.584030i	0.0986672	+	0.0264378i
$489$	3.77314	−	6.53526i	0.170627	−	0.295535i
$490$		0			0
$491$	−3.92645	+	6.80081i	−0.177198	+	0.306916i	−0.940920	−	0.338629i	$-0.890037\pi$
$491$	−3.92645	+	6.80081i	−0.177198	+	0.306916i	0.763722	+	0.645546i	$0.223370\pi$
$492$	−0.811481	−	3.02849i	−0.0365844	−	0.136535i
$493$	−9.45485	+	9.45485i	−0.425825	+	0.425825i
$494$	18.1613	+	0.255431i	0.817115	+	0.0114924i
$495$		0			0
$496$	−2.06162	−	1.19028i	−0.0925695	−	0.0534450i
$497$	−20.5427	+	5.50439i	−0.921465	+	0.246906i
$498$	−2.83124	+	10.5663i	−0.126871	+	0.473489i
$499$	−35.2137	−	20.3307i	−1.57638	−	0.910125i	−0.995358	−	0.0962394i	$-0.969319\pi$
$499$	−35.2137	−	20.3307i	−1.57638	−	0.910125i	−0.581025	−	0.813886i	$-0.697348\pi$
$500$		0			0
$501$	22.6400			1.01148
$502$	−3.49992	−	3.49992i	−0.156209	−	0.156209i
$503$	0.873798	−	3.26106i	0.0389607	−	0.145403i	−0.943706	−	0.330787i	$-0.892686\pi$
$503$	0.873798	−	3.26106i	0.0389607	−	0.145403i	0.982666	+	0.185383i	$0.0593526\pi$
$504$	1.01554	+	1.75897i	0.0452359	+	0.0783508i
$505$		0			0
$506$		−	11.5361i		−	0.512841i
$507$	1.78002	−	6.64311i	0.0790533	−	0.295031i
$508$	−3.18666	−	11.8928i	−0.141385	−	0.527657i
$509$	5.84142	+	10.1176i	0.258917	+	0.448457i	0.965952	−	0.258722i	$-0.0833012\pi$
$509$	5.84142	+	10.1176i	0.258917	+	0.448457i	−0.707035	+	0.707178i	$0.749968\pi$
$510$		0			0
$511$	26.9401	−	46.6617i	1.19176	−	2.06419i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	16.8371	+	17.3174i	0.743375	+	0.764584i
$514$			11.6761i			0.515009i
$515$		0			0
$516$	−11.1041	−	6.41096i	−0.488831	−	0.282227i
$517$	−20.9113	−	5.60316i	−0.919677	−	0.246427i
$518$	27.3309	−	7.32329i	1.20085	−	0.321767i
$519$	−9.03073	+	5.21390i	−0.396405	+	0.228865i
$520$		0			0
$521$			14.2880i			0.625967i	0.949759	+	0.312984i	$0.101328\pi$
$521$			14.2880i			0.625967i	−0.949759	+	0.312984i	$0.898672\pi$
$522$	−0.962444	−	0.257886i	−0.0421250	−	0.0112874i
$523$	−39.0089	−	10.4524i	−1.70574	−	0.457052i	−0.731366	−	0.681986i	$-0.761117\pi$
$523$	−39.0089	−	10.4524i	−1.70574	−	0.457052i	−0.974374	+	0.224934i	$0.927783\pi$
$524$		−	10.8747i		−	0.475064i
$525$		0			0
$526$	−11.5433	+	6.66452i	−0.503311	+	0.290587i
$527$	−15.9007	+	4.26057i	−0.692643	+	0.185593i
$528$	5.49890	+	1.47343i	0.239309	+	0.0641226i
$529$	11.0826	+	6.39852i	0.481850	+	0.278197i
$530$		0			0
$531$			5.14570i			0.223304i
$532$	4.67974	−	16.5315i	0.202892	−	0.716730i
$533$	−5.86061	−	5.86061i	−0.253851	−	0.253851i
$534$	−0.577936	+	1.00102i	−0.0250098	+	0.0433182i
$535$		0			0
$536$	2.18049	+	3.77672i	0.0941829	+	0.163130i
$537$	2.67527	+	9.98425i	0.115446	+	0.430852i
$538$	−6.09034	+	22.7294i	−0.262573	+	0.979936i
$539$			30.8293i			1.32791i
$540$		0			0
$541$	12.6688	+	21.9431i	0.544676	+	0.943406i	0.998627	+	0.0523799i	$0.0166807\pi$
$541$	12.6688	+	21.9431i	0.544676	+	0.943406i	−0.453951	+	0.891026i	$0.649986\pi$
$542$	6.98848	−	26.0814i	0.300181	−	1.12029i
$543$	−1.27394	−	1.27394i	−0.0546700	−	0.0546700i
$544$	−6.91501			−0.296479
$545$		0			0
$546$	−22.4210	−	12.9448i	−0.959529	−	0.553985i
$547$	−4.10436	+	15.3177i	−0.175490	+	0.654936i	0.820978	+	0.570960i	$0.193429\pi$
$547$	−4.10436	+	15.3177i	−0.175490	+	0.654936i	−0.996468	+	0.0839766i	$0.973238\pi$
$548$	−12.4149	+	3.32656i	−0.530338	+	0.142104i
$549$	1.00699	+	0.581385i	0.0429772	+	0.0248129i
$550$		0			0
$551$	4.11121	+	7.35789i	0.175143	+	0.313457i
$552$	3.56029	−	3.56029i	0.151536	−	0.151536i
$553$	−0.989207	−	3.69177i	−0.0420653	−	0.156990i
$554$	13.6319	−	23.6112i	0.579165	−	1.00314i
$555$		0			0
$556$	−6.35176	+	11.0016i	−0.269375	+	0.466570i
$557$	−39.0361	−	10.4597i	−1.65401	−	0.443192i	−0.693282	−	0.720667i	$-0.743836\pi$
$557$	−39.0361	−	10.4597i	−1.65401	−	0.443192i	−0.960733	+	0.277475i	$0.910502\pi$
$558$	−0.867397	−	0.867397i	−0.0367199	−	0.0367199i
$559$	−33.8944			−1.43358
$560$		0			0
$561$	34.0923	−	19.6832i	1.43938	−	0.831024i
$562$	14.8371	−	14.8371i	0.625865	−	0.625865i
$563$	26.6238	−	26.6238i	1.12206	−	1.12206i	0.130630	−	0.991431i	$-0.458300\pi$
$563$	26.6238	−	26.6238i	1.12206	−	1.12206i	0.991431	−	0.130630i	$-0.0417000\pi$
$564$	−4.72443	−	8.18296i	−0.198935	−	0.344565i
$565$		0			0
$566$	−1.84181	+	1.06337i	−0.0774169	+	0.0446967i
$567$	−7.33354	−	27.3691i	−0.307980	−	1.14940i
$568$	5.21175	−	1.39648i	0.218680	−	0.0585952i
$569$	12.3169			0.516351			0.258175	−	0.966098i	$-0.416879\pi$
$569$	12.3169			0.516351			0.258175	+	0.966098i	$0.416879\pi$
$570$		0			0
$571$	1.74090			0.0728543			0.0364271	−	0.999336i	$-0.488402\pi$
$571$	1.74090			0.0728543			0.0364271	+	0.999336i	$0.488402\pi$
$572$	14.5362	−	3.89497i	0.607790	−	0.162857i
$573$	−3.58017	−	13.3614i	−0.149564	−	0.558180i
$574$	−6.78967	+	3.92002i	−0.283395	+	0.163618i
$575$		0			0
$576$	−0.257647	−	0.446257i	−0.0107353	−	0.0185941i
$577$	12.6036	−	12.6036i	0.524693	−	0.524693i	−0.394292	−	0.918985i	$-0.629010\pi$
$577$	12.6036	−	12.6036i	0.524693	−	0.524693i	0.918985	+	0.394292i	$0.129010\pi$
$578$	−21.7912	+	21.7912i	−0.906395	+	0.906395i
$579$	−7.43502	+	4.29261i	−0.308989	+	0.178395i
$580$		0			0
$581$	27.3537			1.13482
$582$	−13.8039	−	13.8039i	−0.572190	−	0.572190i
$583$	−43.8660	−	11.7538i	−1.81674	−	0.486795i
$584$	−6.83481	+	11.8382i	−0.282826	+	0.489870i
$585$		0			0
$586$	−6.98288	+	12.0947i	−0.288460	+	0.499627i
$587$	−1.83576	−	6.85116i	−0.0757701	−	0.282778i	0.917637	−	0.397420i	$-0.130094\pi$
$587$	−1.83576	−	6.85116i	−0.0757701	−	0.282778i	−0.993407	+	0.114642i	$0.963428\pi$
$588$	−9.51461	+	9.51461i	−0.392376	+	0.392376i
$589$	−0.145928	+	10.3756i	−0.00601286	+	0.427518i
$590$		0			0
$591$	11.9960	+	6.92587i	0.493448	+	0.284892i
$592$	−6.93394	+	1.85794i	−0.284983	+	0.0763610i
$593$	−5.31834	+	19.8483i	−0.218398	+	0.815073i	0.766545	+	0.642191i	$0.221974\pi$
$593$	−5.31834	+	19.8483i	−0.218398	+	0.815073i	−0.984943	+	0.172881i	$0.944692\pi$
$594$	17.3310	+	10.0061i	0.711101	+	0.410554i
$595$		0			0
$596$	1.22359			0.0501201
$597$	1.07367	+	1.07367i	0.0439423	+	0.0439423i
$598$	3.44487	−	12.8564i	0.140871	−	0.525738i
$599$	4.61719	+	7.99720i	0.188653	+	0.326757i	0.944801	−	0.327644i	$-0.106254\pi$
$599$	4.61719	+	7.99720i	0.188653	+	0.326757i	−0.756148	+	0.654400i	$0.772921\pi$
$600$		0			0
$601$		−	47.7643i		−	1.94834i	−0.225805	−	0.974172i	$-0.572501\pi$
$601$		−	47.7643i		−	1.94834i	0.225805	−	0.974172i	$-0.427499\pi$
$602$	−8.29822	+	30.9694i	−0.338210	+	1.26222i
$603$	0.581615	+	2.17062i	0.0236852	+	0.0883943i
$604$	0.100646	+	0.174324i	0.00409524	+	0.00709316i
$605$		0			0
$606$	−12.0251	+	20.8281i	−0.488487	+	0.846084i
$607$	16.6738	+	16.6738i	0.676771	+	0.676771i	0.959268	−	0.282497i	$-0.0911629\pi$
$607$	16.6738	+	16.6738i	0.676771	+	0.676771i	−0.282497	+	0.959268i	$0.591163\pi$
$608$	−1.18727	+	4.19409i	−0.0481500	+	0.170093i
$609$		−	12.0140i		−	0.486832i
$610$		0			0
$611$	−21.6315	−	12.4889i	−0.875115	−	0.505248i
$612$	−3.44185	−	0.922240i	−0.139128	−	0.0372794i
$613$	−22.4123	+	6.00537i	−0.905226	+	0.242555i	−0.681259	−	0.732042i	$-0.738567\pi$
$613$	−22.4123	+	6.00537i	−0.905226	+	0.242555i	−0.223967	+	0.974597i	$0.571901\pi$
$614$	−19.6554	+	11.3481i	−0.793228	+	0.457970i
$615$		0			0
$616$		−	14.2353i		−	0.573559i
$617$	34.2648	+	9.18124i	1.37945	+	0.369623i	0.870921	−	0.491422i	$-0.163523\pi$
$617$	34.2648	+	9.18124i	1.37945	+	0.369623i	0.508529	+	0.861045i	$0.330189\pi$
$618$	−16.9489	−	4.54144i	−0.681783	−	0.182683i
$619$		−	32.1839i		−	1.29358i	−0.762668	−	0.646790i	$-0.776111\pi$
$619$		−	32.1839i		−	1.29358i	0.762668	−	0.646790i	$-0.223889\pi$
$620$		0			0
$621$	15.3283	−	8.84978i	0.615102	−	0.355129i
$622$	−10.1690	+	2.72477i	−0.407739	+	0.109253i
$623$	2.79184	+	0.748070i	0.111853	+	0.0299708i
$624$	5.68828	+	3.28413i	0.227714	+	0.131470i
$625$		0			0
$626$			17.9614i			0.717881i
$627$	−6.08480	−	24.0571i	−0.243003	−	0.960748i
$628$	−11.2827	−	11.2827i	−0.450230	−	0.450230i
$629$	−24.8199	+	42.9893i	−0.989633	+	1.71409i
$630$		0			0
$631$	14.7239	+	25.5025i	0.586148	+	1.01524i	0.994731	+	0.102517i	$0.0326898\pi$
$631$	14.7239	+	25.5025i	0.586148	+	1.01524i	−0.408583	+	0.912721i	$0.633977\pi$
$632$	0.250965	+	0.936615i	0.00998286	+	0.0372565i
$633$	−1.29130	+	4.81918i	−0.0513244	+	0.191545i
$634$			27.3618i			1.08668i
$635$		0			0
$636$	−9.91053	−	17.1655i	−0.392978	−	0.680658i
$637$	−9.20614	+	34.3578i	−0.364761	+	1.36131i
$638$	4.93806	+	4.93806i	0.195500	+	0.195500i
$639$	2.78032			0.109988
$640$		0			0
$641$	−29.2550	−	16.8904i	−1.15550	−	0.667129i	−0.205280	−	0.978703i	$-0.565810\pi$
$641$	−29.2550	−	16.8904i	−1.15550	−	0.667129i	−0.950222	+	0.311574i	$0.899144\pi$
$642$	0.231973	−	0.865737i	0.00915526	−	0.0341679i
$643$	9.15447	−	2.45293i	0.361017	−	0.0967342i	−0.0737511	−	0.997277i	$-0.523497\pi$
$643$	9.15447	−	2.45293i	0.361017	−	0.0967342i	0.434768	+	0.900542i	$0.356830\pi$
$644$	−10.9035	−	6.29516i	−0.429659	−	0.248064i
$645$		0			0
$646$	14.7023	+	26.3130i	0.578456	+	1.03527i
$647$	−30.6637	+	30.6637i	−1.20552	+	1.20552i	−0.233052	+	0.972464i	$0.574871\pi$
$647$	−30.6637	+	30.6637i	−1.20552	+	1.20552i	−0.972464	+	0.233052i	$0.925129\pi$
$648$	1.86054	+	6.94365i	0.0730891	+	0.272772i
$649$	18.0324	−	31.2331i	0.707834	−	1.22600i
$650$		0			0
$651$	7.39536	−	12.8091i	0.289847	−	0.502030i
$652$	4.62422	+	1.23906i	0.181099	+	0.0485252i
$653$	28.6028	+	28.6028i	1.11931	+	1.11931i	0.991842	+	0.127471i	$0.0406859\pi$
$653$	28.6028	+	28.6028i	1.11931	+	1.11931i	0.127471	+	0.991842i	$0.459314\pi$
$654$	−0.644025			−0.0251834
$655$		0			0
$656$	1.72256	−	0.994522i	0.0672548	−	0.0388296i
$657$	−4.98077	+	4.98077i	−0.194318	+	0.194318i
$658$	−16.7071	+	16.7071i	−0.651310	+	0.651310i
$659$	5.18753	+	8.98507i	0.202078	+	0.350009i	0.949198	−	0.314680i	$-0.101897\pi$
$659$	5.18753	+	8.98507i	0.202078	+	0.350009i	−0.747120	+	0.664689i	$0.768564\pi$
$660$		0			0
$661$	−9.46554	+	5.46493i	−0.368167	+	0.212561i	−0.672657	−	0.739954i	$-0.734847\pi$
$661$	−9.46554	+	5.46493i	−0.368167	+	0.212561i	0.304490	+	0.952515i	$0.401514\pi$
$662$	3.49749	+	13.0528i	0.135934	+	0.507311i
$663$	43.8720	−	11.7555i	1.70385	−	0.456544i
$664$	−6.93974			−0.269314
$665$		0			0
$666$	−3.69906			−0.143336
$667$	5.96600	−	1.59859i	0.231005	−	0.0618975i
$668$	3.71737	+	13.8734i	0.143829	+	0.536779i
$669$	33.1898	−	19.1622i	1.28319	−	0.740852i
$670$		0			0
$671$	−4.07477	−	7.05772i	−0.157305	−	0.272460i
$672$	4.39335	−	4.39335i	0.169477	−	0.169477i
$673$	12.8831	−	12.8831i	0.496607	−	0.496607i	−0.413773	−	0.910380i	$-0.635789\pi$
$673$	12.8831	−	12.8831i	0.496607	−	0.496607i	0.910380	+	0.413773i	$0.135789\pi$
$674$	1.34949	−	0.779129i	0.0519805	−	0.0300109i
$675$		0			0
$676$	4.36305			0.167810
$677$	24.6947	+	24.6947i	0.949096	+	0.949096i	0.998766	−	0.0496700i	$-0.0158170\pi$
$677$	24.6947	+	24.6947i	0.949096	+	0.949096i	−0.0496700	+	0.998766i	$0.515817\pi$
$678$	−2.80966	−	0.752846i	−0.107904	−	0.0289129i
$679$	−24.4075	+	42.2750i	−0.936673	+	1.62237i
$680$		0			0
$681$	−18.2575	+	31.6229i	−0.699628	+	1.21179i
$682$	2.22520	+	8.30456i	0.0852073	+	0.317998i
$683$	−14.3969	+	14.3969i	−0.550881	+	0.550881i	−0.926695	−	0.375814i	$-0.877363\pi$
$683$	−14.3969	+	14.3969i	−0.550881	+	0.550881i	0.375814	+	0.926695i	$0.377363\pi$
$684$	−1.15030	+	1.92921i	−0.0439829	+	0.0737650i
$685$		0			0
$686$	5.24413	+	3.02770i	0.200222	+	0.115598i
$687$	−26.6867	+	7.15069i	−1.01816	+	0.272816i
$688$	2.10529	−	7.85704i	0.0802634	−	0.299547i
$689$	−45.3767	−	26.1982i	−1.72871	−	0.998073i
$690$		0			0
$691$	−18.4198			−0.700722			−0.350361	−	0.936615i	$-0.613941\pi$
$691$	−18.4198			−0.700722			−0.350361	+	0.936615i	$0.613941\pi$
$692$	−4.67778	−	4.67778i	−0.177823	−	0.177823i
$693$	1.89854	−	7.08544i	0.0721195	−	0.269154i
$694$	−5.05584	−	8.75698i	−0.191917	−	0.332410i
$695$		0			0
$696$			3.04799i			0.115534i
$697$	3.55987	−	13.2856i	0.134840	−	0.503228i
$698$	−0.383567	−	1.43149i	−0.0145182	−	0.0541827i
$699$	8.11999	+	14.0642i	0.307126	+	0.531959i
$700$		0			0
$701$	−4.23908	+	7.34231i	−0.160108	+	0.277315i	−0.934907	−	0.354892i	$-0.884518\pi$
$701$	−4.23908	+	7.34231i	−0.160108	+	0.277315i	0.774799	+	0.632207i	$0.217851\pi$
$702$	16.3267	+	16.3267i	0.616210	+	0.616210i
$703$	21.8124	+	22.4347i	0.822670	+	0.846142i
$704$			3.61156i			0.136116i
$705$		0			0
$706$	8.06994	+	4.65918i	0.303716	+	0.175351i
$707$	58.0897	+	15.5651i	2.18469	+	0.585385i
$708$	15.2044	−	4.07402i	0.571418	−	0.153111i
$709$	37.5241	−	21.6645i	1.40925	−	0.813629i	0.413931	−	0.910308i	$-0.364155\pi$
$709$	37.5241	−	21.6645i	1.40925	−	0.813629i	0.995316	+	0.0966793i	$0.0308221\pi$
$710$		0			0
$711$			0.499657i			0.0187386i
$712$	−0.708298	−	0.189788i	−0.0265446	−	0.00711261i
$713$	7.34489	+	1.96806i	0.275068	+	0.0737043i
$714$		−	42.9639i		−	1.60788i
$715$		0			0
$716$	−5.67890	+	3.27872i	−0.212231	+	0.122531i
$717$	−25.4649	+	6.82331i	−0.951006	+	0.254821i
$718$	15.8452	+	4.24572i	0.591339	+	0.158449i
$719$	0.0416220	+	0.0240305i	0.00155224	+	0.000896185i	0.500776	−	0.865577i	$-0.333048\pi$
$719$	0.0416220	+	0.0240305i	0.00155224	+	0.000896185i	−0.499224	+	0.866473i	$0.666381\pi$
$720$		0			0
$721$			43.8766i			1.63405i
$722$	18.4836	−	4.39948i	0.687890	−	0.163732i
$723$	−22.2463	−	22.2463i	−0.827349	−	0.827349i
$724$	0.571474	−	0.989823i	0.0212387	−	0.0367865i
$725$		0			0
$726$	−1.61047	−	2.78941i	−0.0597700	−	0.103525i
$727$	−10.6952	−	39.9150i	−0.396663	−	1.48036i	−0.818930	−	0.573894i	$-0.805432\pi$
$727$	−10.6952	−	39.9150i	−0.396663	−	1.48036i	0.422267	−	0.906471i	$-0.361234\pi$
$728$	4.25092	−	15.8646i	0.157549	−	0.587983i
$729$			29.9077i			1.10769i
$730$		0			0
$731$	−28.1241	−	48.7124i	−1.04021	−	1.80169i
$732$	0.920604	−	3.43574i	0.0340265	−	0.126989i
$733$	30.0046	+	30.0046i	1.10825	+	1.10825i	0.993381	+	0.114864i	$0.0366434\pi$
$733$	30.0046	+	30.0046i	1.10825	+	1.10825i	0.114864	+	0.993381i	$0.463357\pi$
$734$	−4.84379			−0.178787
$735$		0			0
$736$	2.76626	+	1.59710i	0.101966	+	0.0588700i
$737$	4.07639	−	15.2133i	0.150156	−	0.560388i
$738$	0.990018	−	0.265275i	0.0364431	−	0.00976489i
$739$	9.49745	+	5.48336i	0.349369	+	0.201708i	0.664407	−	0.747371i	$-0.268684\pi$
$739$	9.49745	+	5.48336i	0.349369	+	0.201708i	−0.315038	+	0.949079i	$0.602017\pi$
$740$		0			0
$741$	0.402635	−	28.6276i	0.0147912	−	1.05166i
$742$	−35.0467	+	35.0467i	−1.28661	+	1.28661i
$743$	1.34854	+	5.03281i	0.0494730	+	0.184636i	0.986241	−	0.165316i	$-0.0528645\pi$
$743$	1.34854	+	5.03281i	0.0494730	+	0.184636i	−0.936768	+	0.349952i	$0.886198\pi$
$744$	−1.87623	+	3.24972i	−0.0687859	+	0.119141i
$745$		0			0
$746$	10.5376	−	18.2517i	0.385809	−	0.668241i
$747$	−3.45415	−	0.925537i	−0.126381	−	0.0338636i
$748$	17.6593	+	17.6593i	0.645687	+	0.645687i
$749$	−2.24119			−0.0818912
$750$		0			0
$751$	−33.5017	+	19.3422i	−1.22250	+	0.705808i	−0.965449	−	0.260591i	$-0.916083\pi$
$751$	−33.5017	+	19.3422i	−1.22250	+	0.705808i	−0.257047	+	0.966399i	$0.582749\pi$
$752$	4.23865	−	4.23865i	0.154568	−	0.154568i
$753$	−5.51691	+	5.51691i	−0.201047	+	0.201047i
$754$	4.02865	+	6.97783i	0.146715	+	0.254117i
$755$		0			0
$756$	18.9149	−	10.9205i	0.687927	−	0.397175i
$757$	−5.22710	−	19.5078i	−0.189982	−	0.709023i	−0.993509	−	0.113755i	$-0.963712\pi$
$757$	−5.22710	−	19.5078i	−0.189982	−	0.709023i	0.803527	−	0.595269i	$-0.202954\pi$
$758$	−17.1157	+	4.58613i	−0.621669	+	0.166576i
$759$	−18.1842			−0.660046
$760$		0			0
$761$	−15.1951			−0.550821			−0.275411	−	0.961327i	$-0.588814\pi$
$761$	−15.1951			−0.550821			−0.275411	+	0.961327i	$0.588814\pi$
$762$	−18.7465	+	5.02312i	−0.679115	+	0.181968i
$763$	0.416807	+	1.55555i	0.0150894	+	0.0563145i
$764$	7.59978	−	4.38773i	0.274950	−	0.158743i
$765$		0			0
$766$	−8.12585	−	14.0744i	−0.293599	−	0.508528i
$767$	29.4230	−	29.4230i	1.06240	−	1.06240i
$768$	−1.11461	+	1.11461i	−0.0402200	+	0.0402200i
$769$	−19.8012	+	11.4323i	−0.714051	+	0.412258i	−0.812559	−	0.582879i	$-0.801926\pi$
$769$	−19.8012	+	11.4323i	−0.714051	+	0.412258i	0.0985081	+	0.995136i	$0.468593\pi$
$770$		0			0
$771$	18.4049			0.662837
$772$	−3.85123	−	3.85123i	−0.138609	−	0.138609i
$773$	29.9577	+	8.02714i	1.07750	+	0.288716i	0.753573	−	0.657365i	$-0.228329\pi$
$773$	29.9577	+	8.02714i	1.07750	+	0.288716i	0.323931	+	0.946081i	$0.394996\pi$
$774$	2.09575	−	3.62995i	0.0753303	−	0.130476i
$775$		0			0
$776$	6.19227	−	10.7253i	0.222289	−	0.385017i
$777$	−11.5437	−	43.0815i	−0.414126	−	1.54554i
$778$	11.9278	−	11.9278i	0.427633	−	0.427633i
$779$	−7.44677	−	4.44019i	−0.266808	−	0.159086i
$780$		0			0
$781$	−16.8758	−	9.74326i	−0.603865	−	0.348641i
$782$	21.3354	−	5.71679i	0.762951	−	0.204432i
$783$	−2.77314	+	10.3495i	−0.0991040	+	0.369861i
$784$	−7.39263	−	4.26814i	−0.264023	−	0.152433i
$785$		0			0
$786$	−17.1418			−0.611426
$787$	−9.84741	−	9.84741i	−0.351022	−	0.351022i	0.509468	−	0.860490i	$-0.329842\pi$
$787$	−9.84741	−	9.84741i	−0.351022	−	0.351022i	−0.860490	+	0.509468i	$0.829842\pi$
$788$	−2.27438	+	8.48811i	−0.0810215	+	0.302376i
$789$	10.5053	+	18.1956i	0.373997	+	0.647782i
$790$		0			0
$791$			7.27354i			0.258617i
$792$	−0.481666	+	1.79760i	−0.0171152	+	0.0638750i
$793$	−2.43359	−	9.08230i	−0.0864195	−	0.322522i
$794$	−3.23513	−	5.60341i	−0.114810	−	0.198858i
$795$		0			0
$796$	−0.481634	+	0.834214i	−0.0170711	+	0.0295679i
$797$	7.07080	+	7.07080i	0.250460	+	0.250460i	0.821159	−	0.570699i	$-0.193328\pi$
$797$	7.07080	+	7.07080i	0.250460	+	0.250460i	−0.570699	+	0.821159i	$0.693328\pi$
$798$	−26.0585	−	7.37665i	−0.922460	−	0.261130i
$799$		−	41.4510i		−	1.46643i
$800$		0			0
$801$	−0.327234	−	0.188928i	−0.0115622	−	0.00667546i
$802$	2.29560	+	0.615105i	0.0810606	+	0.0217201i
$803$	47.6864	−	12.7775i	1.68282	−	0.450910i
$804$	5.95323	−	3.43710i	0.209954	−	0.121217i
$805$		0			0
$806$			9.91953i			0.349401i
$807$	35.8283	+	9.60017i	1.26122	+	0.337942i
$808$	−14.7376	−	3.94892i	−0.518465	−	0.138922i
$809$			19.1687i			0.673936i	0.941516	+	0.336968i	$0.109401\pi$
$809$			19.1687i			0.673936i	−0.941516	+	0.336968i	$0.890599\pi$
$810$		0			0
$811$	16.5436	−	9.55142i	0.580923	−	0.335396i	−0.180577	−	0.983561i	$-0.557797\pi$
$811$	16.5436	−	9.55142i	0.580923	−	0.335396i	0.761500	+	0.648165i	$0.224463\pi$
$812$	7.36197	−	1.97263i	0.258354	−	0.0692258i
$813$	−41.1119	−	11.0159i	−1.44186	−	0.386345i
$814$	22.4523	+	12.9629i	0.786954	+	0.454348i
$815$		0			0
$816$			10.9001i			0.381580i
$817$	−34.3737	+	8.69420i	−1.20258	+	0.304171i
$818$	−3.16196	−	3.16196i	−0.110555	−	0.110555i
$819$	4.23167	−	7.32946i	0.147866	−	0.256112i
$820$		0			0
$821$	8.36444	+	14.4876i	0.291921	+	0.505622i	0.974264	−	0.225410i	$-0.0723723\pi$
$821$	8.36444	+	14.4876i	0.291921	+	0.505622i	−0.682343	+	0.731032i	$0.739039\pi$
$822$	5.24364	+	19.5695i	0.182893	+	0.682566i
$823$	−1.75505	+	6.54992i	−0.0611771	+	0.228316i	−0.989745	−	0.142847i	$-0.954374\pi$
$823$	−1.75505	+	6.54992i	−0.0611771	+	0.228316i	0.928568	+	0.371163i	$0.121041\pi$
$824$		−	11.1316i		−	0.387789i
$825$		0			0
$826$	−19.6803	−	34.0874i	−0.684767	−	1.18605i
$827$	11.1098	−	41.4624i	0.386326	−	1.44179i	−0.449739	−	0.893160i	$-0.648483\pi$
$827$	11.1098	−	41.4624i	0.386326	−	1.44179i	0.836066	−	0.548629i	$-0.184850\pi$
$828$	1.16387	+	1.16387i	0.0404471	+	0.0404471i
$829$	37.4534			1.30081			0.650405	−	0.759588i	$-0.274599\pi$
$829$	37.4534			1.30081			0.650405	+	0.759588i	$0.274599\pi$
$830$		0			0
$831$	−37.2182	−	21.4879i	−1.29109	−	0.745408i
$832$	−1.07847	+	4.02492i	−0.0373893	+	0.139539i
$833$	−57.0171	+	15.2777i	−1.97553	+	0.529341i
$834$	17.3417	+	10.0122i	0.600494	+	0.346696i
$835$		0			0
$836$	13.7427	−	7.67870i	0.475301	−	0.265573i
$837$	−9.32744	+	9.32744i	−0.322403	+	0.322403i
$838$	−3.97528	−	14.8359i	−0.137324	−	0.512499i
$839$	−0.365101	+	0.632373i	−0.0126047	+	0.0218320i	−0.872259	−	0.489044i	$-0.837346\pi$
$839$	−0.365101	+	0.632373i	−0.0126047	+	0.0218320i	0.859654	+	0.510876i	$0.170679\pi$
$840$		0			0
$841$	12.6305	−	21.8767i	0.435535	−	0.754368i
$842$	−20.9989	−	5.62665i	−0.723671	−	0.193907i
$843$	−23.3877	−	23.3877i	−0.805514	−	0.805514i
$844$	−3.16513			−0.108948
$845$		0			0
$846$	2.67502	−	1.54443i	0.0919692	−	0.0530985i
$847$	−5.69511	+	5.69511i	−0.195686	+	0.195686i
$848$	8.89148	−	8.89148i	0.305335	−	0.305335i
$849$	1.67618	+	2.90323i	0.0575264	+	0.0996386i
$850$		0			0
$851$	19.8577	−	11.4649i	0.680715	−	0.393011i
$852$	−2.20127	−	8.21526i	−0.0754143	−	0.281450i
$853$	29.2374	−	7.83414i	1.00107	−	0.268236i	0.279176	−	0.960240i	$-0.409939\pi$
$853$	29.2374	−	7.83414i	1.00107	−	0.268236i	0.721894	+	0.692004i	$0.243272\pi$
$854$	−8.89431			−0.304357
$855$		0			0
$856$	0.568597			0.0194342
$857$	−36.9078	+	9.88942i	−1.26075	+	0.337816i	−0.826479	−	0.562968i	$-0.809660\pi$
$857$	−36.9078	+	9.88942i	−1.26075	+	0.337816i	−0.434268	+	0.900784i	$0.642993\pi$
$858$	−6.13962	−	22.9134i	−0.209603	−	0.782250i
$859$	48.6836	−	28.1075i	1.66106	−	0.959015i	0.688854	−	0.724900i	$-0.258114\pi$
$859$	48.6836	−	28.1075i	1.66106	−	0.959015i	0.972209	−	0.234115i	$-0.0752193\pi$
$860$		0			0
$861$	6.17910	+	10.7025i	0.210583	+	0.364741i
$862$	−28.1623	+	28.1623i	−0.959213	+	0.959213i
$863$	4.35182	−	4.35182i	0.148138	−	0.148138i	−0.629148	−	0.777286i	$-0.716596\pi$
$863$	4.35182	−	4.35182i	0.148138	−	0.148138i	0.777286	+	0.629148i	$0.216596\pi$
$864$	−4.79877	+	2.77057i	−0.163257	+	0.0942567i
$865$		0			0
$866$	38.1272			1.29562
$867$	34.3494	+	34.3494i	1.16657	+	1.16657i
$868$	9.06349	+	2.42855i	0.307635	+	0.0824305i
$869$	1.75098	−	3.03279i	0.0593980	−	0.102880i
$870$		0			0
$871$	9.08589	−	15.7372i	0.307864	−	0.533235i
$872$	−0.105745	−	0.394647i	−0.00358099	−	0.0133644i
$873$	4.51252	−	4.51252i	0.152726	−	0.152726i
$874$	0.195805	−	13.9219i	0.00662320	−	0.470914i
$875$		0			0
$876$	18.6606	+	10.7737i	0.630482	+	0.364009i
$877$	13.1510	−	3.52380i	0.444077	−	0.118990i	−0.0298495	−	0.999554i	$-0.509503\pi$
$877$	13.1510	−	3.52380i	0.444077	−	0.118990i	0.473927	+	0.880564i	$0.342836\pi$
$878$	5.31798	−	19.8470i	0.179473	−	0.669803i
$879$	19.0648	+	11.0071i	0.643040	+	0.371259i
$880$		0			0
$881$	−40.0134			−1.34808			−0.674042	−	0.738693i	$-0.735443\pi$
$881$	−40.0134			−1.34808			−0.674042	+	0.738693i	$0.735443\pi$
$882$	−3.11034	−	3.11034i	−0.104731	−	0.104731i
$883$	4.03148	−	15.0457i	0.135670	−	0.506328i	−0.864324	−	0.502935i	$-0.832253\pi$
$883$	4.03148	−	15.0457i	0.135670	−	0.506328i	0.999994	−	0.00339283i	$-0.00107997\pi$
$884$	14.4071	+	24.9538i	0.484563	+	0.839287i
$885$		0			0
$886$		−	6.22148i		−	0.209015i
$887$	−4.16017	+	15.5260i	−0.139685	+	0.521311i	0.860250	+	0.509873i	$0.170308\pi$
$887$	−4.16017	+	15.5260i	−0.139685	+	0.521311i	−0.999935	+	0.0114381i	$0.996359\pi$
$888$	2.92867	+	10.9299i	0.0982796	+	0.366785i
$889$	24.2651	+	42.0285i	0.813827	+	1.40959i
$890$		0			0
$891$	12.9810	−	22.4838i	0.434880	−	0.753235i
$892$	17.1918	+	17.1918i	0.575625	+	0.575625i
$893$	−25.1409	−	7.11689i	−0.841307	−	0.238158i
$894$		−	1.92873i		−	0.0645065i
$895$		0			0
$896$	3.41353	+	1.97080i	0.114038	+	0.0658399i
$897$	−20.2655	−	5.43013i	−0.676645	−	0.181307i
$898$	−13.3288	+	3.57143i	−0.444786	+	0.119180i
$899$	−3.98644	+	2.30157i	−0.132955	+	0.0767618i
$900$		0			0
$901$		−	86.9525i		−	2.89681i
$902$	−6.93878	−	1.85924i	−0.231036	−	0.0619059i
$903$	48.8169	+	13.0804i	1.62452	+	0.435290i
$904$		−	1.84532i		−	0.0613745i
$905$		0			0
$906$	0.274787	−	0.158648i	0.00912918	−	0.00527073i
$907$	34.8329	−	9.33344i	1.15661	−	0.309912i	0.370997	−	0.928634i	$-0.379016\pi$
$907$	34.8329	−	9.33344i	1.15661	−	0.309912i	0.785610	+	0.618722i	$0.212349\pi$
$908$	−22.3757	−	5.99555i	−0.742564	−	0.198969i
$909$	−6.80875	−	3.93103i	−0.225832	−	0.130384i
$910$		0			0
$911$			32.3119i			1.07054i	0.844680	+	0.535271i	$0.179791\pi$
$911$			32.3119i			1.07054i	−0.844680	+	0.535271i	$0.820209\pi$
$912$	6.61113	+	1.87148i	0.218916	+	0.0619709i
$913$	17.7224	+	17.7224i	0.586526	+	0.586526i
$914$	13.6745	−	23.6849i	0.452313	−	0.783428i
$915$		0			0
$916$	−8.76364	−	15.1791i	−0.289559	−	0.501530i
$917$	11.0940	+	41.4033i	0.366356	+	1.36726i
$918$	−9.91719	+	37.0114i	−0.327316	+	1.22156i
$919$		−	4.70255i		−	0.155123i	−0.996988	−	0.0775614i	$-0.975287\pi$
$919$		−	4.70255i		−	0.155123i	0.996988	−	0.0775614i	$-0.0247134\pi$
$920$		0			0
$921$	17.8879	+	30.9827i	0.589426	+	1.02092i
$922$	4.21875	−	15.7446i	0.138937	−	0.518520i
$923$	−15.8978	−	15.8978i	−0.523283	−	0.523283i
$924$	−22.4391			−0.738193
$925$		0			0
$926$	0.546626	+	0.315594i	0.0179632	+	0.0103711i
$927$	1.48460	−	5.54062i	0.0487608	−	0.181978i
$928$	−1.86776	+	0.500464i	−0.0613121	+	0.0164285i
$929$	−11.6040	−	6.69959i	−0.380716	−	0.219807i	0.297414	−	0.954749i	$-0.403876\pi$
$929$	−11.6040	−	6.69959i	−0.380716	−	0.219807i	−0.678130	+	0.734942i	$0.737209\pi$
$930$		0			0
$931$	−0.523274	+	37.2051i	−0.0171496	+	1.21935i
$932$	−7.28506	+	7.28506i	−0.238630	+	0.238630i
$933$	4.29504	+	16.0293i	0.140613	+	0.524776i
$934$	−13.8833	+	24.0466i	−0.454276	+	0.786830i
$935$		0			0
$936$	−1.07359	+	1.85951i	−0.0350913	+	0.0607800i
$937$	47.1914	+	12.6449i	1.54168	+	0.413091i	0.926807	−	0.375539i	$-0.122542\pi$
$937$	47.1914	+	12.6449i	1.54168	+	0.413091i	0.614868	+	0.788630i	$0.289209\pi$
$938$	−12.1547	−	12.1547i	−0.396864	−	0.396864i
$939$	28.3124			0.923941
$940$		0			0
$941$	39.0782	−	22.5618i	1.27391	−	0.735494i	0.298191	−	0.954506i	$-0.403617\pi$
$941$	39.0782	−	22.5618i	1.27391	−	0.735494i	0.975722	+	0.219012i	$0.0702834\pi$
$942$	−17.7849	+	17.7849i	−0.579464	+	0.579464i
$943$	−4.49255	+	4.49255i	−0.146297	+	0.146297i
$944$	4.99297	+	8.64808i	0.162507	+	0.281471i
$945$		0			0
$946$	−25.4414	+	14.6886i	−0.827171	+	0.477567i
$947$	11.2778	+	42.0892i	0.366478	+	1.36771i	0.865406	+	0.501071i	$0.167060\pi$
$947$	11.2778	+	42.0892i	0.366478	+	1.36771i	−0.498929	+	0.866643i	$0.666273\pi$
$948$	1.47638	−	0.395595i	0.0479506	−	0.0128483i
$949$	56.9599			1.84900
$950$		0			0
$951$	43.1303			1.39860
$952$	26.3275	−	7.05444i	0.853280	−	0.228636i
$953$	7.11973	+	26.5712i	0.230631	+	0.860725i	0.980070	+	0.198652i	$0.0636565\pi$
$953$	7.11973	+	26.5712i	0.230631	+	0.860725i	−0.749439	+	0.662073i	$0.769677\pi$
$954$	5.61144	−	3.23977i	0.181677	−	0.104891i
$955$		0			0
$956$	−8.36241	−	14.4841i	−0.270460	−	0.468450i
$957$	7.78384	−	7.78384i	0.251616	−	0.251616i
$958$	14.3358	−	14.3358i	0.463167	−	0.463167i
$959$	43.8736	−	25.3304i	1.41675	−	0.817963i
$960$		0			0
$961$	25.3330			0.817192
$962$	21.1512	+	21.1512i	0.681941	+	0.681941i
$963$	0.283011	+	0.0758325i	0.00911990	+	0.00244367i
$964$	9.97943	−	17.2849i	0.321416	−	0.556708i
$965$		0			0
$966$	−9.92303	+	17.1872i	−0.319268	+	0.552989i
$967$	−1.36339	−	5.08824i	−0.0438436	−	0.163627i	0.940533	−	0.339702i	$-0.110326\pi$
$967$	−1.36339	−	5.08824i	−0.0438436	−	0.163627i	−0.984377	+	0.176076i	$0.943660\pi$
$968$	1.44487	−	1.44487i	0.0464399	−	0.0464399i
$969$	41.4770	−	23.1752i	1.33243	−	0.744495i
$970$		0			0
$971$	22.5946	+	13.0450i	0.725096	+	0.418634i	0.816625	−	0.577168i	$-0.195842\pi$
$971$	22.5946	+	13.0450i	0.725096	+	0.418634i	−0.0915294	+	0.995802i	$0.529176\pi$
$972$	−5.11176	+	1.36969i	−0.163960	+	0.0439329i
$973$	12.9597	−	48.3661i	0.415468	−	1.55055i
$974$	−6.24913	−	3.60794i	−0.200235	−	0.115606i
$975$		0			0
$976$	2.25652			0.0722294
$977$	−6.70444	−	6.70444i	−0.214494	−	0.214494i	0.591679	−	0.806173i	$-0.298465\pi$
$977$	−6.70444	−	6.70444i	−0.214494	−	0.214494i	−0.806173	+	0.591679i	$0.798465\pi$
$978$	1.95312	−	7.28914i	0.0624539	−	0.233081i
$979$	1.32415	+	2.29350i	0.0423200	+	0.0733004i
$980$		0			0
$981$		−	0.210533i		−	0.00672180i
$982$	−2.03248	+	7.58532i	−0.0648591	+	0.242057i
$983$	−14.0105	−	52.2878i	−0.446864	−	1.66772i	−0.710967	−	0.703226i	$-0.751742\pi$
$983$	−14.0105	−	52.2878i	−0.446864	−	1.66772i	0.264102	−	0.964495i	$-0.414924\pi$
$984$	−1.56766	−	2.71527i	−0.0499752	−	0.0865596i
$985$		0			0
$986$	−6.68559	+	11.5798i	−0.212913	+	0.368775i
$987$	26.3353	+	26.3353i	0.838262	+	0.838262i
$988$	17.6086	−	4.45376i	0.560203	−	0.141693i
$989$			25.9824i			0.826191i
$990$		0			0
$991$	39.3012	+	22.6906i	1.24844	+	0.720789i	0.970799	−	0.239895i	$-0.0771129\pi$
$991$	39.3012	+	22.6906i	1.24844	+	0.720789i	0.277645	+	0.960684i	$0.410446\pi$
$992$	−2.29944	−	0.616133i	−0.0730073	−	0.0195622i
$993$	20.5751	−	5.51307i	0.652930	−	0.174952i
$994$	−18.4181	+	10.6337i	−0.584185	+	0.337280i
$995$		0			0
$996$			10.9391i			0.346618i
$997$	−17.3225	−	4.64154i	−0.548608	−	0.146999i	−0.0261407	−	0.999658i	$-0.508322\pi$
$997$	−17.3225	−	4.64154i	−0.548608	−	0.146999i	−0.522468	+	0.852659i	$0.674988\pi$
$998$	−39.2758	−	10.5239i	−1.24325	−	0.333129i
$999$			39.7773i			1.25850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.q.g.293.5		32
5.2	odd	4	inner	950.2.q.g.407.5		32
5.3	odd	4		190.2.m.b.27.4	✓	32
5.4	even	2		190.2.m.b.103.4	yes	32
19.12	odd	6	inner	950.2.q.g.943.5		32
95.12	even	12	inner	950.2.q.g.107.5		32
95.69	odd	6		190.2.m.b.183.4	yes	32
95.88	even	12		190.2.m.b.107.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.m.b.27.4	✓	32	5.3	odd	4
190.2.m.b.103.4	yes	32	5.4	even	2
190.2.m.b.107.4	yes	32	95.88	even	12
190.2.m.b.183.4	yes	32	95.69	odd	6
950.2.q.g.107.5		32	95.12	even	12	inner
950.2.q.g.293.5		32	1.1	even	1	trivial
950.2.q.g.407.5		32	5.2	odd	4	inner
950.2.q.g.943.5		32	19.12	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.407975 - 1.52258i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.788148 - 1.36511i) q^{6} +(-2.78714 + 2.78714i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.446257 - 0.257647i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.407975 - 1.52258i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.788148 - 1.36511i) q^{6} +(-2.78714 + 2.78714i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.446257 - 0.257647i) q^{9} -3.61156 q^{11} +(-1.11461 - 1.11461i) q^{12} +(-4.02492 - 1.07847i) q^{13} +(-1.97080 + 3.41353i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.78974 - 6.67939i) q^{17} +(0.364368 - 0.364368i) q^{18} +(-4.35847 - 0.0613000i) q^{19} +(5.38074 + 3.10657i) q^{21} +(-3.48850 + 0.934740i) q^{22} +(-0.826722 + 3.08537i) q^{23} +(-1.36511 - 0.788148i) q^{24} -4.16690 q^{26} +(-3.91818 - 3.91818i) q^{27} +(-1.02016 + 3.80730i) q^{28} +(-0.966822 - 1.67459i) q^{29} -2.38055i q^{31} +(0.258819 - 0.965926i) q^{32} +(1.47343 + 5.49890i) q^{33} +(-3.45751 - 5.98858i) q^{34} +(0.257647 - 0.446257i) q^{36} +(-5.07600 - 5.07600i) q^{37} +(-4.22582 + 1.06884i) q^{38} +6.56826i q^{39} +(1.72256 + 0.994522i) q^{41} +(6.00143 + 1.60808i) q^{42} +(7.85704 - 2.10529i) q^{43} +(-3.12770 + 1.80578i) q^{44} +3.19421i q^{46} +(5.79010 + 1.55145i) q^{47} +(-1.52258 - 0.407975i) q^{48} -8.53628i q^{49} +(-9.43977 + 5.45005i) q^{51} +(-4.02492 + 1.07847i) q^{52} +(12.1460 + 3.25451i) q^{53} +(-4.79877 - 2.77057i) q^{54} +3.94161i q^{56} +(1.68481 + 6.66114i) q^{57} +(-1.36729 - 1.36729i) q^{58} +(-4.99297 + 8.64808i) q^{59} +(1.12826 + 1.95420i) q^{61} +(-0.616133 - 2.29944i) q^{62} +(-0.525684 + 1.96188i) q^{63} -1.00000i q^{64} +(2.84644 + 4.93018i) q^{66} +(-1.12871 + 4.21239i) q^{67} +(-4.88965 - 4.88965i) q^{68} +5.03501 q^{69} +(4.67273 + 2.69780i) q^{71} +(0.133368 - 0.497736i) q^{72} +(-13.2038 + 3.53796i) q^{73} +(-6.21680 - 3.58927i) q^{74} +(-3.80519 + 2.12615i) q^{76} +(10.0659 - 10.0659i) q^{77} +(1.69999 + 6.34445i) q^{78} +(-0.484828 + 0.839746i) q^{79} +(-3.59430 + 6.22550i) q^{81} +(1.92127 + 0.514803i) q^{82} +(-4.90713 - 4.90713i) q^{83} +6.21314 q^{84} +(7.04443 - 4.06711i) q^{86} +(-2.15526 + 2.15526i) q^{87} +(-2.55376 + 2.55376i) q^{88} +(-0.366642 - 0.635043i) q^{89} +(14.2238 - 8.21214i) q^{91} +(0.826722 + 3.08537i) q^{92} +(-3.62459 + 0.971207i) q^{93} +5.99435 q^{94} -1.57630 q^{96} +(11.9625 - 3.20535i) q^{97} +(-2.20935 - 8.24541i) q^{98} +(-1.61168 + 0.930507i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{3} - 24 q^{7}+O(q^{10}) \) 32 * q + 12 * q^3 - 24 * q^7	\( 32 q + 12 q^{3} - 24 q^{7} - 16 q^{11} - 24 q^{13} + 16 q^{16} + 8 q^{17} + 12 q^{22} - 4 q^{23} - 16 q^{26} + 12 q^{28} + 24 q^{33} - 8 q^{36} - 16 q^{38} + 24 q^{41} - 20 q^{42} + 24 q^{43} + 36 q^{47} + 12 q^{48} + 24 q^{51} - 24 q^{52} + 72 q^{53} + 24 q^{57} - 24 q^{58} - 48 q^{61} + 4 q^{62} - 16 q^{63} + 32 q^{66} - 36 q^{67} - 16 q^{68} + 24 q^{71} - 8 q^{73} + 24 q^{77} + 24 q^{78} + 56 q^{81} - 8 q^{82} - 24 q^{83} - 104 q^{87} - 24 q^{91} + 4 q^{92} - 52 q^{93} + 24 q^{97} - 72 q^{98}+O(q^{100}) \) 32 * q + 12 * q^3 - 24 * q^7 - 16 * q^11 - 24 * q^13 + 16 * q^16 + 8 * q^17 + 12 * q^22 - 4 * q^23 - 16 * q^26 + 12 * q^28 + 24 * q^33 - 8 * q^36 - 16 * q^38 + 24 * q^41 - 20 * q^42 + 24 * q^43 + 36 * q^47 + 12 * q^48 + 24 * q^51 - 24 * q^52 + 72 * q^53 + 24 * q^57 - 24 * q^58 - 48 * q^61 + 4 * q^62 - 16 * q^63 + 32 * q^66 - 36 * q^67 - 16 * q^68 + 24 * q^71 - 8 * q^73 + 24 * q^77 + 24 * q^78 + 56 * q^81 - 8 * q^82 - 24 * q^83 - 104 * q^87 - 24 * q^91 + 4 * q^92 - 52 * q^93 + 24 * q^97 - 72 * q^98

Introduction

L-functions

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