LMFDB - Embedded newform 930.2.j.g.497.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(497,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("930.497");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (of order $4$, degree $2$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			497.6
Character	$\chi$	$=$	930.497
Dual form			930.2.j.g.683.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.0444250 - 1.73148i) q^{3} -1.00000i q^{4} +(-0.142194 - 2.23154i) q^{5} +(1.19293 + 1.25576i) q^{6} +(2.34383 + 2.34383i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.99605 - 0.153842i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.0444250 - 1.73148i) q^{3} -1.00000i q^{4} +(-0.142194 - 2.23154i) q^{5} +(1.19293 + 1.25576i) q^{6} +(2.34383 + 2.34383i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.99605 - 0.153842i) q^{9} +(1.67849 + 1.47739i) q^{10} +5.32287i q^{11} +(-1.73148 - 0.0444250i) q^{12} +(-2.57481 + 2.57481i) q^{13} -3.31467 q^{14} +(-3.87019 + 0.147070i) q^{15} -1.00000 q^{16} +(-2.33223 + 2.33223i) q^{17} +(2.22731 - 2.00975i) q^{18} +5.87131i q^{19} +(-2.23154 + 0.142194i) q^{20} +(4.16242 - 3.95417i) q^{21} +(-3.76384 - 3.76384i) q^{22} +(2.05643 + 2.05643i) q^{23} +(1.25576 - 1.19293i) q^{24} +(-4.95956 + 0.634625i) q^{25} -3.64134i q^{26} +(-0.399474 + 5.18077i) q^{27} +(2.34383 - 2.34383i) q^{28} -4.07771 q^{29} +(2.63264 - 2.84063i) q^{30} +1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(9.21645 + 0.236468i) q^{33} -3.29827i q^{34} +(4.89707 - 5.56363i) q^{35} +(-0.153842 + 2.99605i) q^{36} +(0.718205 + 0.718205i) q^{37} +(-4.15164 - 4.15164i) q^{38} +(4.34385 + 4.57263i) q^{39} +(1.47739 - 1.67849i) q^{40} -9.62849i q^{41} +(-0.147254 + 5.73929i) q^{42} +(1.71966 - 1.71966i) q^{43} +5.32287 q^{44} +(0.0827162 + 6.70769i) q^{45} -2.90823 q^{46} +(-6.49628 + 6.49628i) q^{47} +(-0.0444250 + 1.73148i) q^{48} +3.98705i q^{49} +(3.05819 - 3.95569i) q^{50} +(3.93461 + 4.14183i) q^{51} +(2.57481 + 2.57481i) q^{52} +(5.55295 + 5.55295i) q^{53} +(-3.38089 - 3.94583i) q^{54} +(11.8782 - 0.756881i) q^{55} +3.31467i q^{56} +(10.1661 + 0.260833i) q^{57} +(2.88338 - 2.88338i) q^{58} +6.86460 q^{59} +(0.147070 + 3.87019i) q^{60} -0.913500 q^{61} +(-0.707107 + 0.707107i) q^{62} +(-6.66165 - 7.38281i) q^{63} +1.00000i q^{64} +(6.11193 + 5.37968i) q^{65} +(-6.68422 + 6.34980i) q^{66} +(-9.72000 - 9.72000i) q^{67} +(2.33223 + 2.33223i) q^{68} +(3.65203 - 3.46932i) q^{69} +(0.471327 + 7.39683i) q^{70} +8.59895i q^{71} +(-2.00975 - 2.22731i) q^{72} +(-5.80419 + 5.80419i) q^{73} -1.01570 q^{74} +(0.878512 + 8.61558i) q^{75} +5.87131 q^{76} +(-12.4759 + 12.4759i) q^{77} +(-6.30490 - 0.161766i) q^{78} -10.0091i q^{79} +(0.142194 + 2.23154i) q^{80} +(8.95267 + 0.921838i) q^{81} +(6.80837 + 6.80837i) q^{82} +(4.35290 + 4.35290i) q^{83} +(-3.95417 - 4.16242i) q^{84} +(5.53610 + 4.87285i) q^{85} +2.43196i q^{86} +(-0.181152 + 7.06048i) q^{87} +(-3.76384 + 3.76384i) q^{88} +3.15398 q^{89} +(-4.80155 - 4.68457i) q^{90} -12.0698 q^{91} +(2.05643 - 2.05643i) q^{92} +(0.0444250 - 1.73148i) q^{93} -9.18712i q^{94} +(13.1021 - 0.834866i) q^{95} +(-1.19293 - 1.25576i) q^{96} +(-7.10018 - 7.10018i) q^{97} +(-2.81927 - 2.81927i) q^{98} +(0.818881 - 15.9476i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} - 8 q^{7}+O(q^{10}) $ 40 * q - 4 * q^3 - 8 * q^7	$ 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40} - 20 q^{42} - 48 q^{43} - 4 q^{45} - 80 q^{46} + 4 q^{48} + 48 q^{51} + 20 q^{52} + 164 q^{55} + 40 q^{57} + 56 q^{58} + 24 q^{60} - 128 q^{61} + 56 q^{63} + 8 q^{66} - 4 q^{67} - 56 q^{70} - 16 q^{72} - 48 q^{73} - 48 q^{75} - 40 q^{76} - 36 q^{78} - 24 q^{81} - 16 q^{82} - 56 q^{85} - 12 q^{87} - 4 q^{88} - 28 q^{90} - 32 q^{91} - 4 q^{93} - 52 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.0444250	−	1.73148i	0.0256488	−	0.999671i
$3$	0.0444250	−	1.73148i	0.0256488	−	0.999671i
$4$		−	1.00000i		−	0.500000i
$5$	−0.142194	−	2.23154i	−0.0635912	−	0.997976i
$5$	−0.142194	−	2.23154i	−0.0635912	−	0.997976i
$6$	1.19293	+	1.25576i	0.487011	+	0.512660i
$7$	2.34383	+	2.34383i	0.885883	+	0.885883i	0.994125	−	0.108241i	$-0.0345219\pi$
$7$	2.34383	+	2.34383i	0.885883	+	0.885883i	−0.108241	+	0.994125i	$0.534522\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.99605	−	0.153842i	−0.998684	−	0.0512807i
$10$	1.67849	+	1.47739i	0.530784	+	0.467192i
$11$			5.32287i			1.60491i	0.596716	+	0.802453i	$0.296472\pi$
$11$			5.32287i			1.60491i	−0.596716	+	0.802453i	$0.703528\pi$
$12$	−1.73148	−	0.0444250i	−0.499836	−	0.0128244i
$13$	−2.57481	+	2.57481i	−0.714125	+	0.714125i	−0.967395	−	0.253271i	$-0.918494\pi$
$13$	−2.57481	+	2.57481i	−0.714125	+	0.714125i	0.253271	+	0.967395i	$0.418494\pi$
$14$	−3.31467			−0.885883
$15$	−3.87019	+	0.147070i	−0.999279	+	0.0379734i
$16$	−1.00000			−0.250000
$17$	−2.33223	+	2.33223i	−0.565649	+	0.565649i	−0.930907	−	0.365257i	$-0.880981\pi$
$17$	−2.33223	+	2.33223i	−0.565649	+	0.565649i	0.365257	+	0.930907i	$0.380981\pi$
$18$	2.22731	−	2.00975i	0.524982	−	0.473702i
$19$			5.87131i			1.34697i	0.739201	+	0.673485i	$0.235204\pi$
$19$			5.87131i			1.34697i	−0.739201	+	0.673485i	$0.764796\pi$
$20$	−2.23154	+	0.142194i	−0.498988	+	0.0317956i
$21$	4.16242	−	3.95417i	0.908314	−	0.862870i
$22$	−3.76384	−	3.76384i	−0.802453	−	0.802453i
$23$	2.05643	+	2.05643i	0.428796	+	0.428796i	0.888218	−	0.459422i	$-0.151943\pi$
$23$	2.05643	+	2.05643i	0.428796	+	0.428796i	−0.459422	+	0.888218i	$0.651943\pi$
$24$	1.25576	−	1.19293i	0.256330	−	0.243506i
$25$	−4.95956	+	0.634625i	−0.991912	+	0.126925i
$26$		−	3.64134i		−	0.714125i
$27$	−0.399474	+	5.18077i	−0.0768789	+	0.997040i
$28$	2.34383	−	2.34383i	0.442942	−	0.442942i
$29$	−4.07771			−0.757212			−0.378606	−	0.925558i	$-0.623597\pi$
$29$	−4.07771			−0.757212			−0.378606	+	0.925558i	$0.623597\pi$
$30$	2.63264	−	2.84063i	0.480653	−	0.518626i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	9.21645	+	0.236468i	1.60438	+	0.0411639i
$34$		−	3.29827i		−	0.565649i
$35$	4.89707	−	5.56363i	0.827756	−	0.940425i
$36$	−0.153842	+	2.99605i	−0.0256403	+	0.499342i
$37$	0.718205	+	0.718205i	0.118072	+	0.118072i	0.763674	−	0.645602i	$-0.223393\pi$
$37$	0.718205	+	0.718205i	0.118072	+	0.118072i	−0.645602	+	0.763674i	$0.723393\pi$
$38$	−4.15164	−	4.15164i	−0.673485	−	0.673485i
$39$	4.34385	+	4.57263i	0.695573	+	0.732206i
$40$	1.47739	−	1.67849i	0.233596	−	0.265392i
$41$		−	9.62849i		−	1.50372i	−0.659325	−	0.751858i	$-0.729158\pi$
$41$		−	9.62849i		−	1.50372i	0.659325	−	0.751858i	$-0.270842\pi$
$42$	−0.147254	+	5.73929i	−0.0227218	+	0.885592i
$43$	1.71966	−	1.71966i	0.262245	−	0.262245i	−0.563720	−	0.825966i	$-0.690630\pi$
$43$	1.71966	−	1.71966i	0.262245	−	0.262245i	0.825966	+	0.563720i	$0.190630\pi$
$44$	5.32287			0.802453
$45$	0.0827162	+	6.70769i	0.0123306	+	0.999924i
$46$	−2.90823			−0.428796
$47$	−6.49628	+	6.49628i	−0.947579	+	0.947579i	−0.998693	−	0.0511135i	$-0.983723\pi$
$47$	−6.49628	+	6.49628i	−0.947579	+	0.947579i	0.0511135	+	0.998693i	$0.483723\pi$
$48$	−0.0444250	+	1.73148i	−0.00641220	+	0.249918i
$49$			3.98705i			0.569578i
$50$	3.05819	−	3.95569i	0.432494	−	0.559419i
$51$	3.93461	+	4.14183i	0.550955	+	0.579972i
$52$	2.57481	+	2.57481i	0.357062	+	0.357062i
$53$	5.55295	+	5.55295i	0.762756	+	0.762756i	0.976820	−	0.214064i	$-0.0686700\pi$
$53$	5.55295	+	5.55295i	0.762756	+	0.762756i	−0.214064	+	0.976820i	$0.568670\pi$
$54$	−3.38089	−	3.94583i	−0.460081	−	0.536960i
$55$	11.8782	−	0.756881i	1.60166	−	0.102058i
$56$			3.31467i			0.442942i
$57$	10.1661	+	0.260833i	1.34653	+	0.0345482i
$58$	2.88338	−	2.88338i	0.378606	−	0.378606i
$59$	6.86460			0.893694			0.446847	−	0.894610i	$-0.352547\pi$
$59$	6.86460			0.893694			0.446847	+	0.894610i	$0.352547\pi$
$60$	0.147070	+	3.87019i	0.0189867	+	0.499639i
$61$	−0.913500			−0.116962			−0.0584808	−	0.998289i	$-0.518626\pi$
$61$	−0.913500			−0.116962			−0.0584808	+	0.998289i	$0.518626\pi$
$62$	−0.707107	+	0.707107i	−0.0898027	+	0.0898027i
$63$	−6.66165	−	7.38281i	−0.839289	−	0.930146i
$64$			1.00000i			0.125000i
$65$	6.11193	+	5.37968i	0.758091	+	0.667267i
$66$	−6.68422	+	6.34980i	−0.822771	+	0.781607i
$67$	−9.72000	−	9.72000i	−1.18749	−	1.18749i	−0.977760	−	0.209727i	$-0.932743\pi$
$67$	−9.72000	−	9.72000i	−1.18749	−	1.18749i	−0.209727	−	0.977760i	$-0.567257\pi$
$68$	2.33223	+	2.33223i	0.282825	+	0.282825i
$69$	3.65203	−	3.46932i	0.439653	−	0.417657i
$70$	0.471327	+	7.39683i	0.0563344	+	0.884090i
$71$			8.59895i			1.02051i	0.860024	+	0.510254i	$0.170449\pi$
$71$			8.59895i			1.02051i	−0.860024	+	0.510254i	$0.829551\pi$
$72$	−2.00975	−	2.22731i	−0.236851	−	0.262491i
$73$	−5.80419	+	5.80419i	−0.679329	+	0.679329i	−0.959848	−	0.280519i	$-0.909493\pi$
$73$	−5.80419	+	5.80419i	−0.679329	+	0.679329i	0.280519	+	0.959848i	$0.409493\pi$
$74$	−1.01570			−0.118072
$75$	0.878512	+	8.61558i	0.101442	+	0.994841i
$76$	5.87131			0.673485
$77$	−12.4759	+	12.4759i	−1.42176	+	1.42176i
$78$	−6.30490	−	0.161766i	−0.713890	−	0.0183164i
$79$		−	10.0091i		−	1.12611i	−0.826419	−	0.563056i	$-0.809626\pi$
$79$		−	10.0091i		−	1.12611i	0.826419	−	0.563056i	$-0.190374\pi$
$80$	0.142194	+	2.23154i	0.0158978	+	0.249494i
$81$	8.95267	+	0.921838i	0.994741	+	0.102426i
$82$	6.80837	+	6.80837i	0.751858	+	0.751858i
$83$	4.35290	+	4.35290i	0.477793	+	0.477793i	0.904425	−	0.426632i	$-0.140300\pi$
$83$	4.35290	+	4.35290i	0.477793	+	0.477793i	−0.426632	+	0.904425i	$0.640300\pi$
$84$	−3.95417	−	4.16242i	−0.431435	−	0.454157i
$85$	5.53610	+	4.87285i	0.600475	+	0.528534i
$86$			2.43196i			0.262245i
$87$	−0.181152	+	7.06048i	−0.0194216	+	0.756963i
$88$	−3.76384	+	3.76384i	−0.401226	+	0.401226i
$89$	3.15398			0.334322			0.167161	−	0.985930i	$-0.446540\pi$
$89$	3.15398			0.334322			0.167161	+	0.985930i	$0.446540\pi$
$90$	−4.80155	−	4.68457i	−0.506127	−	0.493797i
$91$	−12.0698			−1.26526
$92$	2.05643	−	2.05643i	0.214398	−	0.214398i
$93$	0.0444250	−	1.73148i	0.00460666	−	0.179546i
$94$		−	9.18712i		−	0.947579i
$95$	13.1021	−	0.834866i	1.34424	−	0.0856554i
$96$	−1.19293	−	1.25576i	−0.121753	−	0.128165i
$97$	−7.10018	−	7.10018i	−0.720914	−	0.720914i	0.247878	−	0.968791i	$-0.420267\pi$
$97$	−7.10018	−	7.10018i	−0.720914	−	0.720914i	−0.968791	+	0.247878i	$0.920267\pi$
$98$	−2.81927	−	2.81927i	−0.284789	−	0.284789i
$99$	0.818881	−	15.9476i	0.0823007	−	1.60279i
$100$	0.634625	+	4.95956i	0.0634625	+	0.495956i
$101$		−	12.6296i		−	1.25669i	−0.777933	−	0.628347i	$-0.783732\pi$
$101$		−	12.6296i		−	1.25669i	0.777933	−	0.628347i	$-0.216268\pi$
$102$	−5.71090	−	0.146526i	−0.565463	−	0.0145082i
$103$	−8.68173	+	8.68173i	−0.855436	+	0.855436i	−0.990796	−	0.135360i	$-0.956781\pi$
$103$	−8.68173	+	8.68173i	−0.855436	+	0.855436i	0.135360	+	0.990796i	$0.456781\pi$
$104$	−3.64134			−0.357062
$105$	−9.41576	−	8.72635i	−0.918884	−	0.851604i
$106$	−7.85306			−0.762756
$107$	7.38945	−	7.38945i	0.714365	−	0.714365i	−0.253080	−	0.967445i	$-0.581444\pi$
$107$	7.38945	−	7.38945i	0.714365	−	0.714365i	0.967445	+	0.253080i	$0.0814437\pi$
$108$	5.18077	+	0.399474i	0.498520	+	0.0384394i
$109$		−	7.31869i		−	0.701004i	−0.936562	−	0.350502i	$-0.886011\pi$
$109$		−	7.31869i		−	0.701004i	0.936562	−	0.350502i	$-0.113989\pi$
$110$	−7.86397	+	8.93436i	−0.749800	+	0.851857i
$111$	1.27546	−	1.21165i	0.121062	−	0.115005i
$112$	−2.34383	−	2.34383i	−0.221471	−	0.221471i
$113$	10.6053	+	10.6053i	0.997665	+	0.997665i	0.999997	−	0.00233179i	$-0.000742233\pi$
$113$	10.6053	+	10.6053i	0.997665	+	0.997665i	−0.00233179	+	0.999997i	$0.500742\pi$
$114$	−7.37293	+	7.00405i	−0.690538	+	0.655990i
$115$	4.29660	−	4.88143i	0.400660	−	0.455196i
$116$			4.07771i			0.378606i
$117$	8.11039	−	7.31816i	0.749806	−	0.676564i
$118$	−4.85400	+	4.85400i	−0.446847	+	0.446847i
$119$	−10.9327			−1.00220
$120$	−2.84063	−	2.63264i	−0.259313	−	0.240326i
$121$	−17.3329			−1.57572
$122$	0.645942	−	0.645942i	0.0584808	−	0.0584808i
$123$	−16.6715	−	0.427745i	−1.50322	−	0.0385685i
$124$		−	1.00000i		−	0.0898027i
$125$	2.12141	+	10.9772i	0.189745	+	0.981833i
$126$	9.93093	+	0.509936i	0.884718	+	0.0454287i
$127$	11.9179	+	11.9179i	1.05754	+	1.05754i	0.998240	+	0.0593044i	$0.0188883\pi$
$127$	11.9179	+	11.9179i	1.05754	+	1.05754i	0.0593044	+	0.998240i	$0.481112\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−2.90116	−	3.05395i	−0.255433	−	0.268885i
$130$	−8.12579	+	0.517777i	−0.712679	+	0.0454120i
$131$		−	9.02710i		−	0.788701i	−0.918960	−	0.394351i	$-0.870970\pi$
$131$		−	9.02710i		−	0.788701i	0.918960	−	0.394351i	$-0.129030\pi$
$132$	0.236468	−	9.21645i	0.0205819	−	0.802189i
$133$	−13.7613	+	13.7613i	−1.19326	+	1.19326i
$134$	13.7462			1.18749
$135$	11.6179	+	0.154768i	0.999911	+	0.0133203i
$136$	−3.29827			−0.282825
$137$	−4.99130	+	4.99130i	−0.426435	+	0.426435i	−0.887412	−	0.460977i	$-0.847499\pi$
$137$	−4.99130	+	4.99130i	−0.426435	+	0.426435i	0.460977	+	0.887412i	$0.347499\pi$
$138$	−0.129198	+	5.03555i	−0.0109981	+	0.428655i
$139$		−	5.06021i		−	0.429202i	−0.976702	−	0.214601i	$-0.931155\pi$
$139$		−	5.06021i		−	0.429202i	0.976702	−	0.214601i	$-0.0688451\pi$
$140$	−5.56363	−	4.89707i	−0.470212	−	0.413878i
$141$	10.9596	+	11.5368i	0.922963	+	0.971572i
$142$	−6.08038	−	6.08038i	−0.510254	−	0.510254i
$143$	−13.7054	−	13.7054i	−1.14610	−	1.14610i
$144$	2.99605	+	0.153842i	0.249671	+	0.0128202i
$145$	0.579827	+	9.09959i	0.0481520	+	0.755680i
$146$		−	8.20836i		−	0.679329i
$147$	6.90350	+	0.177125i	0.569391	+	0.0146090i
$148$	0.718205	−	0.718205i	0.0590361	−	0.0590361i
$149$	−7.97693			−0.653496			−0.326748	−	0.945112i	$-0.605953\pi$
$149$	−7.97693			−0.653496			−0.326748	+	0.945112i	$0.605953\pi$
$150$	−6.71334	−	5.47093i	−0.548142	−	0.446700i
$151$	3.74299			0.304601			0.152300	−	0.988334i	$-0.451332\pi$
$151$	3.74299			0.304601			0.152300	+	0.988334i	$0.451332\pi$
$152$	−4.15164	+	4.15164i	−0.336743	+	0.336743i
$153$	7.34629	−	6.62870i	0.593912	−	0.535898i
$154$		−	17.6436i		−	1.42176i
$155$	−0.142194	−	2.23154i	−0.0114213	−	0.179242i
$156$	4.57263	−	4.34385i	0.366103	−	0.347787i
$157$	13.3446	+	13.3446i	1.06501	+	1.06501i	0.997734	+	0.0672799i	$0.0214320\pi$
$157$	13.3446	+	13.3446i	1.06501	+	1.06501i	0.0672799	+	0.997734i	$0.478568\pi$
$158$	7.07750	+	7.07750i	0.563056	+	0.563056i
$159$	9.86151	−	9.36814i	0.782069	−	0.742941i
$160$	−1.67849	−	1.47739i	−0.132696	−	0.116798i
$161$			9.63984i			0.759726i
$162$	−6.98233	+	5.67865i	−0.548584	+	0.446157i
$163$	−3.35423	+	3.35423i	−0.262723	+	0.262723i	−0.826160	−	0.563436i	$-0.809479\pi$
$163$	−3.35423	+	3.35423i	−0.262723	+	0.262723i	0.563436	+	0.826160i	$0.309479\pi$
$164$	−9.62849			−0.751858
$165$	−0.782836	−	20.6005i	−0.0609437	−	1.60375i
$166$	−6.15593			−0.477793
$167$	−16.7823	+	16.7823i	−1.29865	+	1.29865i	−0.369370	+	0.929282i	$0.620427\pi$
$167$	−16.7823	+	16.7823i	−1.29865	+	1.29865i	−0.929282	+	0.369370i	$0.879573\pi$
$168$	5.73929	+	0.147254i	0.442796	+	0.0113609i
$169$		−	0.259324i		−	0.0199480i
$170$	−7.36024	+	0.468995i	−0.564505	+	0.0359703i
$171$	0.903254	−	17.5908i	0.0690736	−	1.34520i
$172$	−1.71966	−	1.71966i	−0.131123	−	0.131123i
$173$	5.10781	+	5.10781i	0.388339	+	0.388339i	0.874095	−	0.485756i	$-0.161455\pi$
$173$	5.10781	+	5.10781i	0.388339	+	0.388339i	−0.485756	+	0.874095i	$0.661455\pi$
$174$	−4.86442	−	5.12061i	−0.368771	−	0.388192i
$175$	−13.1118	−	10.1369i	−0.991159	−	0.766278i
$176$		−	5.32287i		−	0.401226i
$177$	0.304960	−	11.8859i	0.0229222	−	0.893400i
$178$	−2.23020	+	2.23020i	−0.167161	+	0.167161i
$179$	17.1413			1.28120			0.640602	−	0.767873i	$-0.278685\pi$
$179$	17.1413			1.28120			0.640602	+	0.767873i	$0.278685\pi$
$180$	6.70769	−	0.0827162i	0.499962	−	0.00616530i
$181$	9.34856			0.694873			0.347436	−	0.937704i	$-0.387052\pi$
$181$	9.34856			0.694873			0.347436	+	0.937704i	$0.387052\pi$
$182$	8.53466	−	8.53466i	0.632631	−	0.632631i
$183$	−0.0405822	+	1.58171i	−0.00299992	+	0.116923i
$184$			2.90823i			0.214398i
$185$	1.50058	−	1.70483i	0.110325	−	0.125342i
$186$	1.19293	+	1.25576i	0.0874698	+	0.0920764i
$187$	−12.4142	−	12.4142i	−0.907814	−	0.907814i
$188$	6.49628	+	6.49628i	0.473790	+	0.473790i
$189$	−13.0791	+	11.2065i	−0.951367	+	0.815156i
$190$	−8.67423	+	9.85490i	−0.629294	+	0.714950i
$191$		−	19.7911i		−	1.43203i	−0.698083	−	0.716017i	$-0.745963\pi$
$191$		−	19.7911i		−	1.43203i	0.698083	−	0.716017i	$-0.254037\pi$
$192$	1.73148	+	0.0444250i	0.124959	+	0.00320610i
$193$	−0.289823	+	0.289823i	−0.0208619	+	0.0208619i	−0.717461	−	0.696599i	$-0.754696\pi$
$193$	−0.289823	+	0.289823i	−0.0208619	+	0.0208619i	0.696599	+	0.717461i	$0.254696\pi$
$194$	10.0412			0.720914
$195$	9.58634	−	10.3437i	0.686492	−	0.740727i
$196$	3.98705			0.284789
$197$	12.1490	−	12.1490i	0.865584	−	0.865584i	−0.126396	−	0.991980i	$-0.540341\pi$
$197$	12.1490	−	12.1490i	0.865584	−	0.865584i	0.991980	+	0.126396i	$0.0403410\pi$
$198$	10.6976	+	11.8557i	0.760247	+	0.842547i
$199$		−	16.3567i		−	1.15950i	−0.814796	−	0.579748i	$-0.803151\pi$
$199$		−	16.3567i		−	1.15950i	0.814796	−	0.579748i	$-0.196849\pi$
$200$	−3.95569	−	3.05819i	−0.279709	−	0.216247i
$201$	−17.2618	+	16.3982i	−1.21755	+	1.15664i
$202$	8.93049	+	8.93049i	0.628347	+	0.628347i
$203$	−9.55746	−	9.55746i	−0.670802	−	0.670802i
$204$	4.14183	−	3.93461i	0.289986	−	0.275478i
$205$	−21.4864	+	1.36911i	−1.50067	+	0.0956231i
$206$		−	12.2778i		−	0.855436i
$207$	−5.84481	−	6.47755i	−0.406243	−	0.450221i
$208$	2.57481	−	2.57481i	0.178531	−	0.178531i
$209$	−31.2522			−2.16176
$210$	12.8284	−	0.487490i	0.885244	−	0.0336400i
$211$	19.7796			1.36168			0.680841	−	0.732431i	$-0.261614\pi$
$211$	19.7796			1.36168			0.680841	+	0.732431i	$0.261614\pi$
$212$	5.55295	−	5.55295i	0.381378	−	0.381378i
$213$	14.8889	+	0.382008i	1.02017	+	0.0261748i
$214$			10.4503i			0.714365i
$215$	−4.08201	−	3.59296i	−0.278391	−	0.245038i
$216$	−3.94583	+	3.38089i	−0.268480	+	0.230040i
$217$	2.34383	+	2.34383i	0.159109	+	0.159109i
$218$	5.17510	+	5.17510i	0.350502	+	0.350502i
$219$	9.79199	+	10.3077i	0.661681	+	0.696529i
$220$	−0.756881	−	11.8782i	−0.0510289	−	0.800829i
$221$		−	12.0101i		−	0.807888i
$222$	−0.0451223	+	1.75866i	−0.00302841	+	0.118033i
$223$	4.74368	−	4.74368i	0.317660	−	0.317660i	−0.530208	−	0.847868i	$-0.677886\pi$
$223$	4.74368	−	4.74368i	0.317660	−	0.317660i	0.847868	+	0.530208i	$0.177886\pi$
$224$	3.31467			0.221471
$225$	14.9567	−	1.13838i	0.997116	−	0.0758920i
$226$	−14.9982			−0.997665
$227$	−1.30263	+	1.30263i	−0.0864587	+	0.0864587i	−0.749013	−	0.662555i	$-0.769472\pi$
$227$	−1.30263	+	1.30263i	−0.0864587	+	0.0864587i	0.662555	+	0.749013i	$0.269472\pi$
$228$	0.260833	−	10.1661i	0.0172741	−	0.673264i
$229$			17.4858i			1.15550i	0.816215	+	0.577748i	$0.196068\pi$
$229$			17.4858i			1.15550i	−0.816215	+	0.577748i	$0.803932\pi$
$230$	0.413534	+	6.48985i	0.0272676	+	0.427928i
$231$	21.0475	+	22.1560i	1.38482	+	1.45776i
$232$	−2.88338	−	2.88338i	−0.189303	−	0.189303i
$233$	10.5213	+	10.5213i	0.689271	+	0.689271i	0.962071	−	0.272800i	$-0.0879497\pi$
$233$	10.5213	+	10.5213i	0.689271	+	0.689271i	−0.272800	+	0.962071i	$0.587950\pi$
$234$	−0.560191	+	10.9096i	−0.0366208	+	0.713185i
$235$	15.4204	+	13.5730i	1.00592	+	0.885404i
$236$		−	6.86460i		−	0.446847i
$237$	−17.3306	−	0.444654i	−1.12574	−	0.0288834i
$238$	7.73058	−	7.73058i	0.501099	−	0.501099i
$239$	−6.58020			−0.425638			−0.212819	−	0.977092i	$-0.568264\pi$
$239$	−6.58020			−0.425638			−0.212819	+	0.977092i	$0.568264\pi$
$240$	3.87019	−	0.147070i	0.249820	−	0.00949335i
$241$	6.44072			0.414883			0.207442	−	0.978247i	$-0.433486\pi$
$241$	6.44072			0.414883			0.207442	+	0.978247i	$0.433486\pi$
$242$	12.2562	−	12.2562i	0.787861	−	0.787861i
$243$	1.99387	−	15.4604i	0.127907	−	0.991786i
$244$			0.913500i			0.0584808i
$245$	8.89727	−	0.566935i	0.568426	−	0.0362202i
$246$	12.0910	−	11.4861i	0.770895	−	0.732327i
$247$	−15.1175	−	15.1175i	−0.961905	−	0.961905i
$248$	0.707107	+	0.707107i	0.0449013	+	0.0449013i
$249$	7.73034	−	7.34358i	0.489890	−	0.465381i
$250$	−9.26214	−	6.26201i	−0.585789	−	0.396044i
$251$		−	5.87064i		−	0.370551i	−0.982687	−	0.185276i	$-0.940682\pi$
$251$		−	5.87064i		−	0.370551i	0.982687	−	0.185276i	$-0.0593178\pi$
$252$	−7.38281	+	6.66165i	−0.465073	+	0.419645i
$253$	−10.9461	+	10.9461i	−0.688177	+	0.688177i
$254$	−16.8545			−1.05754
$255$	8.68318	−	9.36918i	0.543762	−	0.586721i
$256$	1.00000			0.0625000
$257$	2.94491	−	2.94491i	0.183698	−	0.183698i	−0.609267	−	0.792965i	$-0.708536\pi$
$257$	2.94491	−	2.94491i	0.183698	−	0.183698i	0.792965	+	0.609267i	$0.208536\pi$
$258$	4.21090	+	0.108040i	0.262159	+	0.00672627i
$259$			3.36670i			0.209196i
$260$	5.37968	−	6.11193i	0.333634	−	0.379046i
$261$	12.2170	+	0.627324i	0.756216	+	0.0388304i
$262$	6.38312	+	6.38312i	0.394351	+	0.394351i
$263$	−1.15541	−	1.15541i	−0.0712457	−	0.0712457i	0.670586	−	0.741832i	$-0.266043\pi$
$263$	−1.15541	−	1.15541i	−0.0712457	−	0.0712457i	−0.741832	+	0.670586i	$0.766043\pi$
$264$	6.34980	+	6.68422i	0.390803	+	0.411385i
$265$	11.6020	−	13.1812i	0.712708	−	0.809717i
$266$		−	19.4615i		−	1.19326i
$267$	0.140116	−	5.46106i	0.00857495	−	0.334212i
$268$	−9.72000	+	9.72000i	−0.593743	+	0.593743i
$269$	19.2490			1.17363			0.586817	−	0.809720i	$-0.300381\pi$
$269$	19.2490			1.17363			0.586817	+	0.809720i	$0.300381\pi$
$270$	−8.32455	+	8.10567i	−0.506616	+	0.493295i
$271$	−10.0388			−0.609816			−0.304908	−	0.952382i	$-0.598626\pi$
$271$	−10.0388			−0.609816			−0.304908	+	0.952382i	$0.598626\pi$
$272$	2.33223	−	2.33223i	0.141412	−	0.141412i
$273$	−0.536202	+	20.8987i	−0.0324524	+	1.26485i
$274$		−	7.05876i		−	0.426435i
$275$	−3.37802	−	26.3991i	−0.203703	−	1.59193i
$276$	−3.46932	−	3.65203i	−0.208828	−	0.219826i
$277$	−12.1820	−	12.1820i	−0.731945	−	0.731945i	0.239060	−	0.971005i	$-0.423161\pi$
$277$	−12.1820	−	12.1820i	−0.731945	−	0.731945i	−0.971005	+	0.239060i	$0.923161\pi$
$278$	3.57811	+	3.57811i	0.214601	+	0.214601i
$279$	−2.99605	−	0.153842i	−0.179369	−	0.00921028i
$280$	7.39683	−	0.471327i	0.442045	−	0.0281672i
$281$			26.5997i			1.58681i	0.608697	+	0.793403i	$0.291692\pi$
$281$			26.5997i			1.58681i	−0.608697	+	0.793403i	$0.708308\pi$
$282$	−15.9073	−	0.408138i	−0.947268	−	0.0243043i
$283$	−12.7232	+	12.7232i	−0.756315	+	0.756315i	−0.975650	−	0.219335i	$-0.929611\pi$
$283$	−12.7232	+	12.7232i	−0.756315	+	0.756315i	0.219335	+	0.975650i	$0.429611\pi$
$284$	8.59895			0.510254
$285$	−0.863495	−	22.7231i	−0.0511490	−	1.34600i
$286$	19.3824			1.14610
$287$	22.5675	−	22.5675i	1.33212	−	1.33212i
$288$	−2.22731	+	2.00975i	−0.131246	+	0.118425i
$289$			6.12138i			0.360081i
$290$	−6.84438	−	6.02438i	−0.401916	−	0.353764i
$291$	−12.6092	+	11.9784i	−0.739167	+	0.702186i
$292$	5.80419	+	5.80419i	0.339664	+	0.339664i
$293$	−9.75762	−	9.75762i	−0.570046	−	0.570046i	0.362095	−	0.932141i	$-0.382062\pi$
$293$	−9.75762	−	9.75762i	−0.570046	−	0.570046i	−0.932141	+	0.362095i	$0.882062\pi$
$294$	−5.00676	+	4.75627i	−0.292000	+	0.277391i
$295$	−0.976106	−	15.3186i	−0.0568311	−	0.891885i
$296$			1.01570i			0.0590361i
$297$	−27.5766	−	2.12635i	−1.60016	−	0.123383i
$298$	5.64054	−	5.64054i	0.326748	−	0.326748i
$299$	−10.5899			−0.612427
$300$	8.61558	−	0.878512i	0.497421	−	0.0507209i
$301$	8.06116			0.464637
$302$	−2.64670	+	2.64670i	−0.152300	+	0.152300i
$303$	−21.8680	−	0.561071i	−1.25628	−	0.0322327i
$304$		−	5.87131i		−	0.336743i
$305$	0.129894	+	2.03851i	0.00743773	+	0.116725i
$306$	−0.507413	+	9.88180i	−0.0290069	+	0.564905i
$307$	0.0921439	+	0.0921439i	0.00525893	+	0.00525893i	0.709731	−	0.704472i	$-0.248816\pi$
$307$	0.0921439	+	0.0921439i	0.00525893	+	0.00525893i	−0.704472	+	0.709731i	$0.748816\pi$
$308$	12.4759	+	12.4759i	0.710879	+	0.710879i
$309$	14.6466	+	15.4179i	0.833214	+	0.877096i
$310$	1.67849	+	1.47739i	0.0953315	+	0.0839102i
$311$		−	8.45397i		−	0.479381i	−0.970849	−	0.239690i	$-0.922954\pi$
$311$		−	8.45397i		−	0.479381i	0.970849	−	0.239690i	$-0.0770459\pi$
$312$	−0.161766	+	6.30490i	−0.00915821	+	0.356945i
$313$	−23.0864	+	23.0864i	−1.30492	+	1.30492i	−0.379885	+	0.925034i	$0.624036\pi$
$313$	−23.0864	+	23.0864i	−1.30492	+	1.30492i	−0.925034	+	0.379885i	$0.875964\pi$
$314$	−18.8721			−1.06501
$315$	−15.5278	+	15.9155i	−0.874892	+	0.896739i
$316$	−10.0091			−0.563056
$317$	−9.01722	+	9.01722i	−0.506458	+	0.506458i	−0.913437	−	0.406980i	$-0.866582\pi$
$317$	−9.01722	+	9.01722i	−0.506458	+	0.506458i	0.406980	+	0.913437i	$0.366582\pi$
$318$	−0.348872	+	13.5974i	−0.0195638	+	0.762505i
$319$		−	21.7051i		−	1.21525i
$320$	2.23154	−	0.142194i	0.124747	−	0.00794890i
$321$	−12.4664	−	13.1230i	−0.695807	−	0.732452i
$322$	−6.81640	−	6.81640i	−0.379863	−	0.379863i
$323$	−13.6933	−	13.6933i	−0.761913	−	0.761913i
$324$	0.921838	−	8.95267i	0.0512132	−	0.497370i
$325$	11.1359	−	14.4040i	0.617709	−	0.798989i
$326$		−	4.74360i		−	0.262723i
$327$	−12.6722	−	0.325133i	−0.700773	−	0.0179799i
$328$	6.80837	−	6.80837i	0.375929	−	0.375929i
$329$	−30.4523			−1.67889
$330$	15.1203	+	14.0132i	0.832346	+	0.771402i
$331$	23.1909			1.27469			0.637344	−	0.770580i	$-0.280033\pi$
$331$	23.1909			1.27469			0.637344	+	0.770580i	$0.280033\pi$
$332$	4.35290	−	4.35290i	0.238896	−	0.238896i
$333$	−2.04129	−	2.26227i	−0.111862	−	0.123972i
$334$		−	23.7337i		−	1.29865i
$335$	−20.3085	+	23.0727i	−1.10957	+	1.26060i
$336$	−4.16242	+	3.95417i	−0.227078	+	0.215718i
$337$	−12.6434	−	12.6434i	−0.688728	−	0.688728i	0.273223	−	0.961951i	$-0.411910\pi$
$337$	−12.6434	−	12.6434i	−0.688728	−	0.688728i	−0.961951	+	0.273223i	$0.911910\pi$
$338$	0.183370	+	0.183370i	0.00997402	+	0.00997402i
$339$	18.8341	−	17.8918i	1.02293	−	0.971748i
$340$	4.87285	−	5.53610i	0.264267	−	0.300237i
$341$			5.32287i			0.288250i
$342$	11.7998	+	13.0772i	0.638062	+	0.707136i
$343$	7.06184	−	7.06184i	0.381303	−	0.381303i
$344$	2.43196			0.131123
$345$	−8.26122	−	7.65634i	−0.444769	−	0.412204i
$346$	−7.22353			−0.388339
$347$	22.9418	−	22.9418i	1.23158	−	1.23158i	0.268225	−	0.963356i	$-0.413563\pi$
$347$	22.9418	−	22.9418i	1.23158	−	1.23158i	0.963356	−	0.268225i	$-0.0864372\pi$
$348$	7.06048	+	0.181152i	0.378482	+	0.00971079i
$349$		−	35.3989i		−	1.89486i	−0.319965	−	0.947429i	$-0.603671\pi$
$349$		−	35.3989i		−	1.89486i	0.319965	−	0.947429i	$-0.396329\pi$
$350$	16.4393	−	2.10357i	0.878719	−	0.112441i
$351$	−12.3110	−	14.3681i	−0.657110	−	0.766912i
$352$	3.76384	+	3.76384i	0.200613	+	0.200613i
$353$	15.6878	+	15.6878i	0.834976	+	0.834976i	0.988193	−	0.153217i	$-0.0489633\pi$
$353$	15.6878	+	15.6878i	0.834976	+	0.834976i	−0.153217	+	0.988193i	$0.548963\pi$
$354$	8.18897	+	8.62025i	0.435239	+	0.458161i
$355$	19.1889	−	1.22272i	1.01844	−	0.0648953i
$356$		−	3.15398i		−	0.167161i
$357$	−0.485685	+	18.9298i	−0.0257052	+	1.00187i
$358$	−12.1208	+	12.1208i	−0.640602	+	0.640602i
$359$	−31.0215			−1.63725			−0.818626	−	0.574327i	$-0.805264\pi$
$359$	−31.0215			−1.63725			−0.818626	+	0.574327i	$0.805264\pi$
$360$	−4.68457	+	4.80155i	−0.246898	+	0.253064i
$361$	−15.4723			−0.814330
$362$	−6.61043	+	6.61043i	−0.347436	+	0.347436i
$363$	−0.770016	+	30.0116i	−0.0404153	+	1.57520i
$364$			12.0698i			0.632631i
$365$	13.7776	+	12.1270i	0.721153	+	0.634755i
$366$	−1.08974	−	1.14713i	−0.0569616	−	0.0599615i
$367$	18.5964	+	18.5964i	0.970723	+	0.970723i	0.999583	−	0.0288601i	$-0.00918772\pi$
$367$	18.5964	+	18.5964i	0.970723	+	0.970723i	−0.0288601	+	0.999583i	$0.509188\pi$
$368$	−2.05643	−	2.05643i	−0.107199	−	0.107199i
$369$	−1.48127	+	28.8475i	−0.0771116	+	1.50174i
$370$	0.144426	+	2.26657i	0.00750835	+	0.117833i
$371$			26.0303i			1.35143i
$372$	−1.73148	−	0.0444250i	−0.0897731	−	0.00230333i
$373$	7.03959	−	7.03959i	0.364496	−	0.364496i	−0.500969	−	0.865465i	$-0.667023\pi$
$373$	7.03959	−	7.03959i	0.364496	−	0.364496i	0.865465	+	0.500969i	$0.167023\pi$
$374$	17.5563			0.907814
$375$	19.1011	−	3.18552i	0.986377	−	0.164500i
$376$	−9.18712			−0.473790
$377$	10.4994	−	10.4994i	0.540744	−	0.540744i
$378$	1.32413	−	17.1726i	0.0681057	−	0.883261i
$379$			31.2352i			1.60444i	0.597027	+	0.802221i	$0.296349\pi$
$379$			31.2352i			1.60444i	−0.597027	+	0.802221i	$0.703651\pi$
$380$	−0.834866	−	13.1021i	−0.0428277	−	0.672122i
$381$	21.1651	−	20.1062i	1.08432	−	1.03007i
$382$	13.9944	+	13.9944i	0.716017	+	0.716017i
$383$	−15.8078	−	15.8078i	−0.807742	−	0.807742i	0.176550	−	0.984292i	$-0.443506\pi$
$383$	−15.8078	−	15.8078i	−0.807742	−	0.807742i	−0.984292	+	0.176550i	$0.943506\pi$
$384$	−1.25576	+	1.19293i	−0.0640825	+	0.0608764i
$385$	29.6145	+	26.0665i	1.50929	+	1.32847i
$386$		−	0.409872i		−	0.0208619i
$387$	−5.41674	+	4.88763i	−0.275348	+	0.248452i
$388$	−7.10018	+	7.10018i	−0.360457	+	0.360457i
$389$	12.8441			0.651220			0.325610	−	0.945504i	$-0.394430\pi$
$389$	12.8441			0.651220			0.325610	+	0.945504i	$0.394430\pi$
$390$	0.535532	+	14.0927i	0.0271177	+	0.713610i
$391$	−9.59216			−0.485096
$392$	−2.81927	+	2.81927i	−0.142395	+	0.142395i
$393$	−15.6302	−	0.401029i	−0.788442	−	0.0202292i
$394$			17.1814i			0.865584i
$395$	−22.3357	+	1.42324i	−1.12383	+	0.0716108i
$396$	−15.9476	−	0.818881i	−0.801397	−	0.0411503i
$397$	−19.6869	−	19.6869i	−0.988058	−	0.988058i	0.0118711	−	0.999930i	$-0.496221\pi$
$397$	−19.6869	−	19.6869i	−0.988058	−	0.988058i	−0.999930	+	0.0118711i	$0.996221\pi$
$398$	11.5659	+	11.5659i	0.579748	+	0.579748i
$399$	23.2161	+	24.4388i	1.16226	+	1.22347i
$400$	4.95956	−	0.634625i	0.247978	−	0.0317312i
$401$			38.0122i			1.89824i	0.314916	+	0.949119i	$0.398024\pi$
$401$			38.0122i			1.89824i	−0.314916	+	0.949119i	$0.601976\pi$
$402$	0.610673	−	23.8012i	0.0304576	−	1.18710i
$403$	−2.57481	+	2.57481i	−0.128261	+	0.128261i
$404$	−12.6296			−0.628347
$405$	0.784103	−	20.1093i	0.0389624	−	0.999241i
$406$	13.5163			0.670802
$407$	−3.82291	+	3.82291i	−0.189495	+	0.189495i
$408$	−0.146526	+	5.71090i	−0.00725411	+	0.282732i
$409$			17.6761i			0.874026i	0.899455	+	0.437013i	$0.143964\pi$
$409$			17.6761i			0.874026i	−0.899455	+	0.437013i	$0.856036\pi$
$410$	14.2251	−	16.1613i	0.702525	−	0.798148i
$411$	8.42060	+	8.86408i	0.415358	+	0.437233i
$412$	8.68173	+	8.68173i	0.427718	+	0.427718i
$413$	16.0894	+	16.0894i	0.791709	+	0.791709i
$414$	8.71323	+	0.447409i	0.428232	+	0.0219889i
$415$	9.09472	−	10.3326i	0.446442	−	0.507209i
$416$			3.64134i			0.178531i
$417$	−8.76167	−	0.224800i	−0.429061	−	0.0110085i
$418$	22.0986	−	22.0986i	1.08088	−	1.08088i
$419$	−24.1973			−1.18212			−0.591058	−	0.806629i	$-0.701290\pi$
$419$	−24.1973			−1.18212			−0.591058	+	0.806629i	$0.701290\pi$
$420$	−8.72635	+	9.41576i	−0.425802	+	0.459442i
$421$	20.5246			1.00031			0.500154	−	0.865936i	$-0.333277\pi$
$421$	20.5246			1.00031			0.500154	+	0.865936i	$0.333277\pi$
$422$	−13.9863	+	13.9863i	−0.680841	+	0.680841i
$423$	20.4626	−	18.4638i	0.994925	−	0.897740i
$424$			7.85306i			0.381378i
$425$	10.0868	−	13.0469i	0.489280	−	0.632870i
$426$	−10.7982	+	10.2579i	−0.523174	+	0.496999i
$427$	−2.14109	−	2.14109i	−0.103614	−	0.103614i
$428$	−7.38945	−	7.38945i	−0.357182	−	0.357182i
$429$	−24.3395	+	23.1218i	−1.17512	+	1.11633i
$430$	5.42703	−	0.345811i	0.261714	−	0.0166765i
$431$			23.9070i			1.15156i	0.817605	+	0.575780i	$0.195302\pi$
$431$			23.9070i			1.15156i	−0.817605	+	0.575780i	$0.804698\pi$
$432$	0.399474	−	5.18077i	0.0192197	−	0.249260i
$433$	−8.97114	+	8.97114i	−0.431125	+	0.431125i	−0.889011	−	0.457886i	$-0.848607\pi$
$433$	−8.97114	+	8.97114i	−0.431125	+	0.431125i	0.457886	+	0.889011i	$0.348607\pi$
$434$	−3.31467			−0.159109
$435$	15.7815	−	0.599710i	0.756666	−	0.0287539i
$436$	−7.31869			−0.350502
$437$	−12.0740	+	12.0740i	−0.577575	+	0.577575i
$438$	−14.2126	−	0.364656i	−0.679105	−	0.0174240i
$439$			28.6135i			1.36565i	0.730583	+	0.682824i	$0.239248\pi$
$439$			28.6135i			1.36565i	−0.730583	+	0.682824i	$0.760752\pi$
$440$	8.93436	+	7.86397i	0.425929	+	0.374900i
$441$	0.613376	−	11.9454i	0.0292084	−	0.568829i
$442$	8.49244	+	8.49244i	0.403944	+	0.403944i
$443$	21.3536	+	21.3536i	1.01454	+	1.01454i	0.999893	+	0.0146498i	$0.00466334\pi$
$443$	21.3536	+	21.3536i	1.01454	+	1.01454i	0.0146498	+	0.999893i	$0.495337\pi$
$444$	−1.21165	−	1.27546i	−0.0575025	−	0.0605309i
$445$	−0.448478	−	7.03825i	−0.0212599	−	0.333645i
$446$			6.70857i			0.317660i
$447$	−0.354375	+	13.8119i	−0.0167614	+	0.653281i
$448$	−2.34383	+	2.34383i	−0.110735	+	0.110735i
$449$	−38.9162			−1.83657			−0.918285	−	0.395921i	$-0.870425\pi$
$449$	−38.9162			−1.83657			−0.918285	+	0.395921i	$0.870425\pi$
$450$	−9.77106	+	11.3810i	−0.460612	+	0.536504i
$451$	51.2512			2.41332
$452$	10.6053	−	10.6053i	0.498833	−	0.498833i
$453$	0.166282	−	6.48092i	0.00781263	−	0.304500i
$454$		−	1.84220i		−	0.0864587i
$455$	1.71626	+	26.9343i	0.0804595	+	1.26270i
$456$	7.00405	+	7.37293i	0.327995	+	0.345269i
$457$	2.63616	+	2.63616i	0.123314	+	0.123314i	0.766071	−	0.642756i	$-0.222209\pi$
$457$	2.63616	+	2.63616i	0.123314	+	0.123314i	−0.642756	+	0.766071i	$0.722209\pi$
$458$	−12.3644	−	12.3644i	−0.577748	−	0.577748i
$459$	−11.1511	−	13.0144i	−0.520489	−	0.607462i
$460$	−4.88143	−	4.29660i	−0.227598	−	0.200330i
$461$		−	27.1612i		−	1.26502i	−0.774552	−	0.632511i	$-0.782024\pi$
$461$		−	27.1612i		−	1.26502i	0.774552	−	0.632511i	$-0.217976\pi$
$462$	−30.5495	−	0.783815i	−1.42129	−	0.0364664i
$463$	−13.7006	+	13.7006i	−0.636723	+	0.636723i	−0.949746	−	0.313023i	$-0.898658\pi$
$463$	−13.7006	+	13.7006i	−0.636723	+	0.636723i	0.313023	+	0.949746i	$0.398658\pi$
$464$	4.07771			0.189303
$465$	−3.87019	+	0.147070i	−0.179476	+	0.00682022i
$466$	−14.8793			−0.689271
$467$	−17.5028	+	17.5028i	−0.809934	+	0.809934i	−0.984624	−	0.174690i	$-0.944108\pi$
$467$	−17.5028	+	17.5028i	−0.809934	+	0.809934i	0.174690	+	0.984624i	$0.444108\pi$
$468$	−7.31816	−	8.11039i	−0.338282	−	0.374903i
$469$		−	45.5640i		−	2.10395i
$470$	−20.5015	+	1.30636i	−0.945662	+	0.0602577i
$471$	23.6987	−	22.5131i	1.09198	−	1.03735i
$472$	4.85400	+	4.85400i	0.223424	+	0.223424i
$473$	9.15351	+	9.15351i	0.420879	+	0.420879i
$474$	12.5690	−	11.9401i	0.577312	−	0.548429i
$475$	−3.72608	−	29.1191i	−0.170964	−	1.33608i
$476$			10.9327i			0.501099i
$477$	−15.7827	−	17.4912i	−0.722638	−	0.800867i
$478$	4.65290	−	4.65290i	0.212819	−	0.212819i
$479$	−8.40205			−0.383899			−0.191950	−	0.981405i	$-0.561481\pi$
$479$	−8.40205			−0.383899			−0.191950	+	0.981405i	$0.561481\pi$
$480$	−2.63264	+	2.84063i	−0.120163	+	0.129657i
$481$	−3.69849			−0.168637
$482$	−4.55428	+	4.55428i	−0.207442	+	0.207442i
$483$	16.6912	+	0.428250i	0.759476	+	0.0194861i
$484$			17.3329i			0.787861i
$485$	−14.8347	+	16.8539i	−0.673611	+	0.765298i
$486$	9.52229	+	12.3420i	0.431940	+	0.559846i
$487$	21.7600	+	21.7600i	0.986041	+	0.986041i	0.999904	−	0.0138629i	$-0.00441284\pi$
$487$	21.7600	+	21.7600i	0.986041	+	0.986041i	−0.0138629	+	0.999904i	$0.504413\pi$
$488$	−0.645942	−	0.645942i	−0.0292404	−	0.0292404i
$489$	5.65877	+	5.95679i	0.255898	+	0.269376i
$490$	−5.89043	+	6.69220i	−0.266103	+	0.302323i
$491$			19.7006i			0.889074i	0.895760	+	0.444537i	$0.146632\pi$
$491$			19.7006i			0.889074i	−0.895760	+	0.444537i	$0.853368\pi$
$492$	−0.427745	+	16.6715i	−0.0192843	+	0.751611i
$493$	9.51018	−	9.51018i	0.428317	−	0.428317i
$494$	21.3794			0.961905
$495$	−35.7042	+	0.440288i	−1.60478	+	0.0197895i
$496$	−1.00000			−0.0449013
$497$	−20.1545	+	20.1545i	−0.904051	+	0.904051i
$498$	−0.273477	+	10.6589i	−0.0122548	+	0.477636i
$499$			13.1915i			0.590534i	0.955415	+	0.295267i	$0.0954086\pi$
$499$			13.1915i			0.590534i	−0.955415	+	0.295267i	$0.904591\pi$
$500$	10.9772	−	2.12141i	0.490917	−	0.0948725i
$501$	28.3127	+	29.8038i	1.26492	+	1.33153i
$502$	4.15117	+	4.15117i	0.185276	+	0.185276i
$503$	−10.7177	−	10.7177i	−0.477879	−	0.477879i	0.426574	−	0.904453i	$-0.359720\pi$
$503$	−10.7177	−	10.7177i	−0.477879	−	0.477879i	−0.904453	+	0.426574i	$0.859720\pi$
$504$	0.509936	−	9.93093i	0.0227144	−	0.442359i
$505$	−28.1835	+	1.79586i	−1.25415	+	0.0799147i
$506$		−	15.4802i		−	0.688177i
$507$	−0.449015	−	0.0115205i	−0.0199415	−	0.000511643i
$508$	11.9179	−	11.9179i	0.528772	−	0.528772i
$509$	5.08723			0.225487			0.112744	−	0.993624i	$-0.464036\pi$
$509$	5.08723			0.225487			0.112744	+	0.993624i	$0.464036\pi$
$510$	0.485078	+	12.7649i	0.0214796	+	0.565241i
$511$	−27.2080			−1.20361
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−30.4179	−	2.34544i	−1.34298	−	0.103554i
$514$			4.16473i			0.183698i
$515$	20.6081	+	18.1392i	0.908103	+	0.799307i
$516$	−3.05395	+	2.90116i	−0.134443	+	0.127716i
$517$	−34.5788	−	34.5788i	−1.52078	−	1.52078i
$518$	−2.38061	−	2.38061i	−0.104598	−	0.104598i
$519$	9.07098	−	8.61715i	0.398172	−	0.378251i
$520$	0.517777	+	8.12579i	0.0227060	+	0.356340i
$521$		−	39.9892i		−	1.75196i	−0.482348	−	0.875980i	$-0.660216\pi$
$521$		−	39.9892i		−	1.75196i	0.482348	−	0.875980i	$-0.339784\pi$
$522$	−9.08234	+	8.19517i	−0.397523	+	0.358693i
$523$	30.0563	−	30.0563i	1.31427	−	1.31427i	0.396034	−	0.918236i	$-0.370386\pi$
$523$	30.0563	−	30.0563i	1.31427	−	1.31427i	0.918236	−	0.396034i	$-0.129614\pi$
$524$	−9.02710			−0.394351
$525$	−18.1343	+	22.2525i	−0.791448	+	0.971179i
$526$	1.63400			0.0712457
$527$	−2.33223	+	2.33223i	−0.101594	+	0.101594i
$528$	−9.21645	−	0.236468i	−0.401094	−	0.0102910i
$529$		−	14.5422i		−	0.632268i
$530$	1.11666	+	17.5244i	0.0485046	+	0.761212i
$531$	−20.5667	−	1.05606i	−0.892518	−	0.0458293i
$532$	13.7613	+	13.7613i	0.596629	+	0.596629i
$533$	24.7916	+	24.7916i	1.07384	+	1.07384i
$534$	3.76248	+	3.96063i	0.162818	+	0.171393i
$535$	−17.5406	−	15.4391i	−0.758346	−	0.667492i
$536$		−	13.7462i		−	0.593743i
$537$	0.761504	−	29.6799i	0.0328613	−	1.28078i
$538$	−13.6111	+	13.6111i	−0.586817	+	0.586817i
$539$	−21.2225			−0.914119
$540$	0.154768	−	11.6179i	0.00666014	−	0.499956i
$541$	−15.1376			−0.650816			−0.325408	−	0.945574i	$-0.605502\pi$
$541$	−15.1376			−0.650816			−0.325408	+	0.945574i	$0.605502\pi$
$542$	7.09853	−	7.09853i	0.304908	−	0.304908i
$543$	0.415310	−	16.1869i	0.0178226	−	0.694644i
$544$			3.29827i			0.141412i
$545$	−16.3320	+	1.04068i	−0.699585	+	0.0445776i
$546$	−14.3984	−	15.1568i	−0.616197	−	0.648649i
$547$	29.5556	+	29.5556i	1.26371	+	1.26371i	0.949282	+	0.314426i	$0.101812\pi$
$547$	29.5556	+	29.5556i	1.26371	+	1.26371i	0.314426	+	0.949282i	$0.398188\pi$
$548$	4.99130	+	4.99130i	0.213218	+	0.213218i
$549$	2.73689	+	0.140535i	0.116808	+	0.00599787i
$550$	21.0556	+	16.2784i	0.897814	+	0.694111i
$551$		−	23.9415i		−	1.01994i
$552$	5.03555	+	0.129198i	0.214327	+	0.00549905i
$553$	23.4596	−	23.4596i	0.997604	−	0.997604i
$554$	17.2279			0.731945
$555$	−2.88522	−	2.67396i	−0.122471	−	0.113503i
$556$	−5.06021			−0.214601
$557$	9.13927	−	9.13927i	0.387243	−	0.387243i	−0.486460	−	0.873703i	$-0.661712\pi$
$557$	9.13927	−	9.13927i	0.387243	−	0.387243i	0.873703	+	0.486460i	$0.161712\pi$
$558$	2.22731	−	2.00975i	0.0942896	−	0.0850794i
$559$			8.85559i			0.374552i
$560$	−4.89707	+	5.56363i	−0.206939	+	0.235106i
$561$	−22.0464	+	20.9434i	−0.930799	+	0.884231i
$562$	−18.8088	−	18.8088i	−0.793403	−	0.793403i
$563$	−2.02094	−	2.02094i	−0.0851725	−	0.0851725i	0.663237	−	0.748409i	$-0.269182\pi$
$563$	−2.02094	−	2.02094i	−0.0851725	−	0.0851725i	−0.748409	+	0.663237i	$0.769182\pi$
$564$	11.5368	−	10.9596i	0.485786	−	0.461482i
$565$	22.1582	−	25.1743i	0.932204	−	1.05909i
$566$		−	17.9933i		−	0.756315i
$567$	18.8229	+	23.1441i	0.790486	+	0.971962i
$568$	−6.08038	+	6.08038i	−0.255127	+	0.255127i
$569$	−26.1347			−1.09562			−0.547812	−	0.836601i	$-0.684539\pi$
$569$	−26.1347			−1.09562			−0.547812	+	0.836601i	$0.684539\pi$
$570$	16.6782	+	15.4571i	0.698574	+	0.647425i
$571$	12.5432			0.524917			0.262458	−	0.964943i	$-0.415467\pi$
$571$	12.5432			0.524917			0.262458	+	0.964943i	$0.415467\pi$
$572$	−13.7054	+	13.7054i	−0.573051	+	0.573051i
$573$	−34.2679	−	0.879220i	−1.43156	−	0.0367299i
$574$			31.9153i			1.33212i
$575$	−11.5041	−	8.89394i	−0.479753	−	0.370903i
$576$	0.153842	−	2.99605i	0.00641009	−	0.124836i
$577$	16.3900	+	16.3900i	0.682326	+	0.682326i	0.960524	−	0.278198i	$-0.0897372\pi$
$577$	16.3900	+	16.3900i	0.682326	+	0.682326i	−0.278198	+	0.960524i	$0.589737\pi$
$578$	−4.32847	−	4.32847i	−0.180041	−	0.180041i
$579$	0.488948	+	0.514699i	0.0203200	+	0.0213902i
$580$	9.09959	−	0.579827i	0.377840	−	0.0240760i
$581$			20.4049i			0.846537i
$582$	0.446079	−	17.3861i	0.0184906	−	0.720676i
$583$	−29.5576	+	29.5576i	−1.22415	+	1.22415i
$584$	−8.20836			−0.339664
$585$	−17.4840	−	17.0581i	−0.722876	−	0.705265i
$586$	13.7994			0.570046
$587$	28.8017	−	28.8017i	1.18877	−	1.18877i	0.211368	−	0.977407i	$-0.432208\pi$
$587$	28.8017	−	28.8017i	1.18877	−	1.18877i	0.977407	−	0.211368i	$-0.0677917\pi$
$588$	0.177125	−	6.90350i	0.00730450	−	0.284696i
$589$			5.87131i			0.241923i
$590$	11.5221	+	10.1417i	0.474358	+	0.417527i
$591$	−20.4961	−	21.5756i	−0.843098	−	0.887500i
$592$	−0.718205	−	0.718205i	−0.0295180	−	0.0295180i
$593$	10.9951	+	10.9951i	0.451516	+	0.451516i	0.895858	−	0.444341i	$-0.146562\pi$
$593$	10.9951	+	10.9951i	0.451516	+	0.451516i	−0.444341	+	0.895858i	$0.646562\pi$
$594$	21.0031	−	17.9960i	0.861769	−	0.738386i
$595$	1.55457	+	24.3968i	0.0637310	+	1.00017i
$596$			7.97693i			0.326748i
$597$	−28.3213	−	0.726646i	−1.15911	−	0.0297397i
$598$	7.48816	−	7.48816i	0.306214	−	0.306214i
$599$	−4.97456			−0.203255			−0.101627	−	0.994823i	$-0.532405\pi$
$599$	−4.97456			−0.203255			−0.101627	+	0.994823i	$0.532405\pi$
$600$	−5.47093	+	6.71334i	−0.223350	+	0.274071i
$601$	13.7463			0.560723			0.280362	−	0.959894i	$-0.409546\pi$
$601$	13.7463			0.560723			0.280362	+	0.959894i	$0.409546\pi$
$602$	−5.70010	+	5.70010i	−0.232319	+	0.232319i
$603$	27.6263	+	30.6170i	1.12503	+	1.24682i
$604$		−	3.74299i		−	0.152300i
$605$	2.46464	+	38.6792i	0.100202	+	1.57253i
$606$	15.8597	−	15.0662i	0.644257	−	0.612024i
$607$	−9.89383	−	9.89383i	−0.401578	−	0.401578i	0.477211	−	0.878789i	$-0.341648\pi$
$607$	−9.89383	−	9.89383i	−0.401578	−	0.401578i	−0.878789	+	0.477211i	$0.841648\pi$
$608$	4.15164	+	4.15164i	0.168371	+	0.168371i
$609$	−16.9731	+	16.1240i	−0.687786	+	0.653376i
$610$	−1.53330	−	1.34960i	−0.0620813	−	0.0546436i
$611$		−	33.4534i		−	1.35338i
$612$	−6.62870	−	7.34629i	−0.267949	−	0.296956i
$613$	−3.39739	+	3.39739i	−0.137219	+	0.137219i	−0.772380	−	0.635161i	$-0.780934\pi$
$613$	−3.39739	+	3.39739i	−0.137219	+	0.137219i	0.635161	+	0.772380i	$0.280934\pi$
$614$	−0.130311			−0.00525893
$615$	1.41606	+	37.2641i	0.0571012	+	1.50263i
$616$	−17.6436			−0.710879
$617$	−6.92230	+	6.92230i	−0.278681	+	0.278681i	−0.832583	−	0.553901i	$-0.813139\pi$
$617$	−6.92230	+	6.92230i	−0.278681	+	0.278681i	0.553901	+	0.832583i	$0.313139\pi$
$618$	−21.2588	−	0.545442i	−0.855155	−	0.0219409i
$619$			13.4874i			0.542103i	0.962565	+	0.271051i	$0.0873713\pi$
$619$			13.4874i			0.542103i	−0.962565	+	0.271051i	$0.912629\pi$
$620$	−2.23154	+	0.142194i	−0.0896209	+	0.00571066i
$621$	−11.4754	+	9.83242i	−0.460492	+	0.394561i
$622$	5.97786	+	5.97786i	0.239690	+	0.239690i
$623$	7.39239	+	7.39239i	0.296170	+	0.296170i
$624$	−4.34385	−	4.57263i	−0.173893	−	0.183052i
$625$	24.1945	−	6.29492i	0.967780	−	0.251797i
$626$		−	32.6491i		−	1.30492i
$627$	−1.38838	+	54.1126i	−0.0554465	+	2.16105i
$628$	13.3446	−	13.3446i	0.532507	−	0.532507i
$629$	−3.35004			−0.133575
$630$	−0.274177	−	22.2338i	−0.0109235	−	0.885816i
$631$	38.3139			1.52525			0.762627	−	0.646839i	$-0.223909\pi$
$631$	38.3139			1.52525			0.762627	+	0.646839i	$0.223909\pi$
$632$	7.07750	−	7.07750i	0.281528	−	0.281528i
$633$	0.878707	−	34.2480i	0.0349255	−	1.36123i
$634$		−	12.7523i		−	0.506458i
$635$	24.9007	−	28.2900i	0.988153	−	1.12265i
$636$	−9.36814	−	9.86151i	−0.371471	−	0.391035i
$637$	−10.2659	−	10.2659i	−0.406750	−	0.406750i
$638$	15.3479	+	15.3479i	0.607627	+	0.607627i
$639$	1.32288	−	25.7629i	0.0523324	−	1.01917i
$640$	−1.47739	+	1.67849i	−0.0583991	+	0.0663480i
$641$			17.1624i			0.677873i	0.940809	+	0.338936i	$0.110067\pi$
$641$			17.1624i			0.677873i	−0.940809	+	0.338936i	$0.889933\pi$
$642$	18.0944	+	0.464253i	0.714130	+	0.0183226i
$643$	8.57949	−	8.57949i	0.338342	−	0.338342i	−0.517401	−	0.855743i	$-0.673100\pi$
$643$	8.57949	−	8.57949i	0.338342	−	0.338342i	0.855743	+	0.517401i	$0.173100\pi$
$644$	9.63984			0.379863
$645$	−6.40249	+	6.90831i	−0.252098	+	0.272014i
$646$	19.3652			0.761913
$647$	24.5435	−	24.5435i	0.964905	−	0.964905i	−0.0344995	−	0.999405i	$-0.510984\pi$
$647$	24.5435	−	24.5435i	0.964905	−	0.964905i	0.999405	+	0.0344995i	$0.0109837\pi$
$648$	5.67865	+	6.98233i	0.223079	+	0.274292i
$649$			36.5393i			1.43429i
$650$	2.31088	+	18.0594i	0.0906402	+	0.708349i
$651$	4.16242	−	3.95417i	0.163138	−	0.154976i
$652$	3.35423	+	3.35423i	0.131362	+	0.131362i
$653$	9.73348	+	9.73348i	0.380901	+	0.380901i	0.871427	−	0.490526i	$-0.163195\pi$
$653$	9.73348	+	9.73348i	0.380901	+	0.380901i	−0.490526	+	0.871427i	$0.663195\pi$
$654$	9.19049	−	8.73068i	0.359377	−	0.341397i
$655$	−20.1444	+	1.28360i	−0.787105	+	0.0501544i
$656$			9.62849i			0.375929i
$657$	18.2826	−	16.4967i	0.713271	−	0.643599i
$658$	21.5330	−	21.5330i	0.839445	−	0.839445i
$659$	−4.25839			−0.165883			−0.0829417	−	0.996554i	$-0.526432\pi$
$659$	−4.25839			−0.165883			−0.0829417	+	0.996554i	$0.526432\pi$
$660$	−20.6005	+	0.782836i	−0.801874	+	0.0304718i
$661$	0.330451			0.0128530			0.00642652	−	0.999979i	$-0.497954\pi$
$661$	0.330451			0.0128530			0.00642652	+	0.999979i	$0.497954\pi$
$662$	−16.3984	+	16.3984i	−0.637344	+	0.637344i
$663$	−20.7953	−	0.533550i	−0.807623	−	0.0207214i
$664$			6.15593i			0.238896i
$665$	32.6658	+	28.7522i	1.26672	+	1.11496i
$666$	3.04308	+	0.156257i	0.117917	+	0.00605482i
$667$	−8.38554	−	8.38554i	−0.324690	−	0.324690i
$668$	16.7823	+	16.7823i	0.649326	+	0.649326i
$669$	−8.00285	−	8.42432i	−0.309408	−	0.325703i
$670$	−1.95462	−	30.6751i	−0.0755137	−	1.18508i
$671$		−	4.86244i		−	0.187712i
$672$	0.147254	−	5.73929i	0.00568046	−	0.221398i
$673$	30.2191	−	30.2191i	1.16486	−	1.16486i	0.181464	−	0.983398i	$-0.441916\pi$
$673$	30.2191	−	30.2191i	1.16486	−	1.16486i	0.983398	−	0.181464i	$-0.0580837\pi$
$674$	17.8804			0.688728
$675$	−1.30663	−	25.9479i	−0.0502922	−	0.998735i
$676$	−0.259324			−0.00997402
$677$	17.5604	−	17.5604i	0.674901	−	0.674901i	−0.283941	−	0.958842i	$-0.591642\pi$
$677$	17.5604	−	17.5604i	0.674901	−	0.674901i	0.958842	+	0.283941i	$0.0916419\pi$
$678$	−0.666295	+	25.9691i	−0.0255889	+	0.997337i
$679$		−	33.2832i		−	1.27729i
$680$	0.468995	+	7.36024i	0.0179852	+	0.282252i
$681$	2.19761	+	2.31335i	0.0842127	+	0.0886478i
$682$	−3.76384	−	3.76384i	−0.144125	−	0.144125i
$683$	−28.7718	−	28.7718i	−1.10092	−	1.10092i	−0.994300	−	0.106622i	$-0.965997\pi$
$683$	−28.7718	−	28.7718i	−1.10092	−	1.10092i	−0.106622	−	0.994300i	$-0.534003\pi$
$684$	−17.5908	−	0.903254i	−0.672599	−	0.0345368i
$685$	11.8480	+	10.4286i	0.452690	+	0.398455i
$686$			9.98694i			0.381303i
$687$	30.2764	+	0.776808i	1.15512	+	0.0296371i
$688$	−1.71966	+	1.71966i	−0.0655613	+	0.0655613i
$689$	−28.5956			−1.08941
$690$	11.2554	−	0.427715i	0.428487	−	0.0162828i
$691$	29.8168			1.13429			0.567143	−	0.823620i	$-0.308049\pi$
$691$	29.8168			1.13429			0.567143	+	0.823620i	$0.308049\pi$
$692$	5.10781	−	5.10781i	0.194170	−	0.194170i
$693$	39.2977	−	35.4591i	1.49280	−	1.34698i
$694$			32.4446i			1.23158i
$695$	−11.2921	+	0.719533i	−0.428333	+	0.0272934i
$696$	−5.12061	+	4.86442i	−0.194096	+	0.184385i
$697$	22.4559	+	22.4559i	0.850577	+	0.850577i
$698$	25.0308	+	25.0308i	0.947429	+	0.947429i
$699$	18.6848	−	17.7500i	0.706723	−	0.671365i
$700$	−10.1369	+	13.1118i	−0.383139	+	0.495580i
$701$		−	17.0513i		−	0.644020i	−0.946736	−	0.322010i	$-0.895641\pi$
$701$		−	17.0513i		−	0.644020i	0.946736	−	0.322010i	$-0.104359\pi$
$702$	18.8649	+	1.45462i	0.712011	+	0.0549011i
$703$	−4.21680	+	4.21680i	−0.159040	+	0.159040i
$704$	−5.32287			−0.200613
$705$	24.1864	−	26.0972i	0.910913	−	0.982879i
$706$	−22.1859			−0.834976
$707$	29.6017	−	29.6017i	1.11328	−	1.11328i
$708$	−11.8859	−	0.304960i	−0.446700	−	0.0114611i
$709$			24.4984i			0.920059i	0.887904	+	0.460029i	$0.152161\pi$
$709$			24.4984i			0.920059i	−0.887904	+	0.460029i	$0.847839\pi$
$710$	−12.7040	+	14.4332i	−0.476774	+	0.541669i
$711$	−1.53982	+	29.9878i	−0.0577478	+	1.12463i
$712$	2.23020	+	2.23020i	0.0835804	+	0.0835804i
$713$	2.05643	+	2.05643i	0.0770140	+	0.0770140i
$714$	−13.0419	−	13.7288i	−0.488082	−	0.513787i
$715$	−28.6353	+	32.5330i	−1.07090	+	1.21666i
$716$		−	17.1413i		−	0.640602i
$717$	−0.292325	+	11.3935i	−0.0109171	+	0.425498i
$718$	21.9355	−	21.9355i	0.818626	−	0.818626i
$719$	−11.2341			−0.418963			−0.209481	−	0.977813i	$-0.567178\pi$
$719$	−11.2341			−0.418963			−0.209481	+	0.977813i	$0.567178\pi$
$720$	−0.0827162	−	6.70769i	−0.00308265	−	0.249981i
$721$	−40.6969			−1.51563
$722$	10.9405	−	10.9405i	0.407165	−	0.407165i
$723$	0.286129	−	11.1520i	0.0106412	−	0.414747i
$724$		−	9.34856i		−	0.347436i
$725$	20.2237	−	2.58782i	0.751088	−	0.0961091i
$726$	−20.6770	−	21.7659i	−0.767394	−	0.807809i
$727$	27.4216	+	27.4216i	1.01701	+	1.01701i	0.999853	+	0.0171593i	$0.00546226\pi$
$727$	27.4216	+	27.4216i	1.01701	+	1.01701i	0.0171593	+	0.999853i	$0.494538\pi$
$728$	−8.53466	−	8.53466i	−0.316316	−	0.316316i
$729$	−26.6808	−	4.13917i	−0.988179	−	0.153303i
$730$	−18.3173	+	1.16718i	−0.677954	+	0.0431993i
$731$			8.02128i			0.296678i
$732$	1.58171	+	0.0405822i	0.0584616	+	0.00149996i
$733$	8.57269	−	8.57269i	0.316639	−	0.316639i	−0.530836	−	0.847475i	$-0.678122\pi$
$733$	8.57269	−	8.57269i	0.316639	−	0.316639i	0.847475	+	0.530836i	$0.178122\pi$
$734$	−26.2993			−0.970723
$735$	−0.586376	−	15.4306i	−0.0216288	−	0.569168i
$736$	2.90823			0.107199
$737$	51.7383	−	51.7383i	1.90580	−	1.90580i
$738$	−19.3508	−	21.4456i	−0.712313	−	0.789425i
$739$		−	8.21308i		−	0.302123i	−0.988524	−	0.151062i	$-0.951731\pi$
$739$		−	8.21308i		−	0.302123i	0.988524	−	0.151062i	$-0.0482692\pi$
$740$	−1.70483	−	1.50058i	−0.0626708	−	0.0551624i
$741$	−26.8473	+	25.5041i	−0.986260	+	0.936917i
$742$	−18.4062	−	18.4062i	−0.675713	−	0.675713i
$743$	2.02106	+	2.02106i	0.0741456	+	0.0741456i	0.743207	−	0.669061i	$-0.233304\pi$
$743$	2.02106	+	2.02106i	0.0741456	+	0.0741456i	−0.669061	+	0.743207i	$0.733304\pi$
$744$	1.25576	−	1.19293i	0.0460382	−	0.0437349i
$745$	1.13427	+	17.8009i	0.0415566	+	0.652173i
$746$			9.95549i			0.364496i
$747$	−12.3719	−	13.7112i	−0.452663	−	0.501666i
$748$	−12.4142	+	12.4142i	−0.453907	+	0.453907i
$749$	34.6392			1.26569
$750$	−11.2540	+	15.7590i	−0.410939	+	0.575438i
$751$	9.64510			0.351955			0.175977	−	0.984394i	$-0.443691\pi$
$751$	9.64510			0.351955			0.175977	+	0.984394i	$0.443691\pi$
$752$	6.49628	−	6.49628i	0.236895	−	0.236895i
$753$	−10.1649	−	0.260803i	−0.370430	−	0.00950419i
$754$			14.8483i			0.540744i
$755$	−0.532232	−	8.35265i	−0.0193699	−	0.303984i
$756$	11.2065	+	13.0791i	0.407578	+	0.475684i
$757$	29.8289	+	29.8289i	1.08415	+	1.08415i	0.996118	+	0.0880304i	$0.0280573\pi$
$757$	29.8289	+	29.8289i	1.08415	+	1.08415i	0.0880304	+	0.996118i	$0.471943\pi$
$758$	−22.0866	−	22.0866i	−0.802221	−	0.802221i
$759$	18.4667	+	19.4393i	0.670299	+	0.705601i
$760$	9.85490	+	8.67423i	0.357475	+	0.314647i
$761$			1.75145i			0.0634902i	0.999496	+	0.0317451i	$0.0101065\pi$
$761$			1.75145i			0.0634902i	−0.999496	+	0.0317451i	$0.989894\pi$
$762$	−0.748760	+	29.1832i	−0.0271247	+	1.05720i
$763$	17.1538	−	17.1538i	0.621008	−	0.621008i
$764$	−19.7911			−0.716017
$765$	−15.8368	−	15.4510i	−0.572581	−	0.558632i
$766$	22.3556			0.807742
$767$	−17.6751	+	17.6751i	−0.638209	+	0.638209i
$768$	0.0444250	−	1.73148i	0.00160305	−	0.0624794i
$769$		−	20.9102i		−	0.754042i	−0.926205	−	0.377021i	$-0.876948\pi$
$769$		−	20.9102i		−	0.754042i	0.926205	−	0.377021i	$-0.123052\pi$
$770$	−39.3724	+	2.50881i	−1.41888	+	0.0904113i
$771$	−4.96822	−	5.22988i	−0.178926	−	0.188349i
$772$	0.289823	+	0.289823i	0.0104310	+	0.0104310i
$773$	−35.1192	−	35.1192i	−1.26315	−	1.26315i	−0.949557	−	0.313593i	$-0.898467\pi$
$773$	−35.1192	−	35.1192i	−1.26315	−	1.26315i	−0.313593	−	0.949557i	$-0.601533\pi$
$774$	0.374138	−	7.28629i	0.0134481	−	0.261900i
$775$	−4.95956	+	0.634625i	−0.178153	+	0.0227964i
$776$		−	10.0412i		−	0.360457i
$777$	5.82937	+	0.149565i	0.209128	+	0.00536563i
$778$	−9.08213	+	9.08213i	−0.325610	+	0.325610i
$779$	56.5318			2.02546
$780$	−10.3437	−	9.58634i	−0.370364	−	0.343246i
$781$	−45.7711			−1.63782
$782$	6.78268	−	6.78268i	0.242548	−	0.242548i
$783$	1.62894	−	21.1257i	0.0582136	−	0.754971i
$784$		−	3.98705i		−	0.142395i
$785$	27.8815	−	31.6765i	0.995133	−	1.13058i
$786$	11.3358	−	10.7687i	0.404336	−	0.384106i
$787$	−11.5196	−	11.5196i	−0.410629	−	0.410629i	0.471329	−	0.881957i	$-0.343774\pi$
$787$	−11.5196	−	11.5196i	−0.410629	−	0.410629i	−0.881957	+	0.471329i	$0.843774\pi$
$788$	−12.1490	−	12.1490i	−0.432792	−	0.432792i
$789$	−2.05190	+	1.94924i	−0.0730496	+	0.0693949i
$790$	14.7874	−	16.8001i	0.526111	−	0.597722i
$791$			49.7141i			1.76763i
$792$	11.8557	−	10.6976i	0.421274	−	0.380123i
$793$	2.35209	−	2.35209i	0.0835252	−	0.0835252i
$794$	27.8415			0.988058
$795$	−22.3076	−	20.6743i	−0.791170	−	0.733242i
$796$	−16.3567			−0.579748
$797$	−0.995608	+	0.995608i	−0.0352662	+	0.0352662i	−0.724520	−	0.689254i	$-0.757939\pi$
$797$	−0.995608	+	0.995608i	−0.0352662	+	0.0352662i	0.689254	+	0.724520i	$0.257939\pi$
$798$	−33.6971	−	0.864575i	−1.19287	−	0.0306056i
$799$		−	30.3017i		−	1.07200i
$800$	−3.05819	+	3.95569i	−0.108123	+	0.139855i
$801$	−9.44951	−	0.485216i	−0.333882	−	0.0171442i
$802$	−26.8787	−	26.8787i	−0.949119	−	0.949119i
$803$	−30.8949	−	30.8949i	−1.09026	−	1.09026i
$804$	16.3982	+	17.2618i	0.578319	+	0.608777i
$805$	21.5117	−	1.37073i	0.758188	−	0.0483119i
$806$		−	3.64134i		−	0.128261i
$807$	0.855138	−	33.3293i	0.0301023	−	1.17325i
$808$	8.93049	−	8.93049i	0.314174	−	0.314174i
$809$	38.0612			1.33816			0.669080	−	0.743190i	$-0.266688\pi$
$809$	38.0612			1.33816			0.669080	+	0.743190i	$0.266688\pi$
$810$	13.6650	+	14.7739i	0.480139	+	0.519102i
$811$	−49.7487			−1.74691			−0.873457	−	0.486901i	$-0.838127\pi$
$811$	−49.7487			−1.74691			−0.873457	+	0.486901i	$0.838127\pi$
$812$	−9.55746	+	9.55746i	−0.335401	+	0.335401i
$813$	−0.445976	+	17.3821i	−0.0156410	+	0.609616i
$814$		−	5.40641i		−	0.189495i
$815$	7.96205	+	7.00815i	0.278899	+	0.245485i
$816$	−3.93461	−	4.14183i	−0.137739	−	0.144993i
$817$	10.0966	+	10.0966i	0.353237	+	0.353237i
$818$	−12.4989	−	12.4989i	−0.437013	−	0.437013i
$819$	36.1619	+	1.85685i	1.26360	+	0.0648835i
$820$	1.36911	+	21.4864i	0.0478116	+	0.750337i
$821$		−	28.4532i		−	0.993025i	−0.868030	−	0.496512i	$-0.834614\pi$
$821$		−	28.4532i		−	0.993025i	0.868030	−	0.496512i	$-0.165386\pi$
$822$	−12.2221	−	0.313585i	−0.426295	−	0.0109375i
$823$	5.51218	−	5.51218i	0.192142	−	0.192142i	−0.604479	−	0.796621i	$-0.706619\pi$
$823$	5.51218	−	5.51218i	0.192142	−	0.192142i	0.796621	+	0.604479i	$0.206619\pi$
$824$	−12.2778			−0.427718
$825$	−45.8596	+	4.67620i	−1.59663	+	0.162805i
$826$	−22.7539			−0.791709
$827$	10.3809	−	10.3809i	0.360978	−	0.360978i	−0.503195	−	0.864173i	$-0.667842\pi$
$827$	10.3809	−	10.3809i	0.360978	−	0.360978i	0.864173	+	0.503195i	$0.167842\pi$
$828$	−6.47755	+	5.84481i	−0.225110	+	0.203121i
$829$		−	22.4738i		−	0.780549i	−0.920699	−	0.390274i	$-0.872380\pi$
$829$		−	22.4738i		−	0.780549i	0.920699	−	0.390274i	$-0.127620\pi$
$830$	0.875337	+	13.7372i	0.0303834	+	0.476826i
$831$	−21.6341	+	20.5517i	−0.750478	+	0.712931i
$832$	−2.57481	−	2.57481i	−0.0892656	−	0.0892656i
$833$	−9.29872	−	9.29872i	−0.322182	−	0.322182i
$834$	6.35439	−	6.03648i	0.220035	−	0.209026i
$835$	39.8367	+	35.0640i	1.37861	+	1.21344i
$836$			31.2522i			1.08088i
$837$	−0.399474	+	5.18077i	−0.0138078	+	0.179074i
$838$	17.1101	−	17.1101i	0.591058	−	0.591058i
$839$	5.01157			0.173019			0.0865093	−	0.996251i	$-0.472429\pi$
$839$	5.01157			0.173019			0.0865093	+	0.996251i	$0.472429\pi$
$840$	−0.487490	−	12.8284i	−0.0168200	−	0.442622i
$841$	−12.3722			−0.426629
$842$	−14.5131	+	14.5131i	−0.500154	+	0.500154i
$843$	46.0569	+	1.18169i	1.58628	+	0.0406996i
$844$		−	19.7796i		−	0.680841i
$845$	−0.578693	+	0.0368744i	−0.0199077	+	0.00126852i
$846$	−1.41337	+	27.5251i	−0.0485925	+	0.946333i
$847$	−40.6254	−	40.6254i	−1.39591	−	1.39591i
$848$	−5.55295	−	5.55295i	−0.190689	−	0.190689i
$849$	21.4647	+	22.5952i	0.736668	+	0.775465i
$850$	2.09317	+	16.3580i	0.0717950	+	0.561075i
$851$			2.95388i			0.101258i
$852$	0.382008	−	14.8889i	0.0130874	−	0.510086i
$853$	−15.5225	+	15.5225i	−0.531480	+	0.531480i	−0.921013	−	0.389532i	$-0.872637\pi$
$853$	−15.5225	+	15.5225i	−0.531480	+	0.531480i	0.389532	+	0.921013i	$0.372637\pi$
$854$	3.02795			0.103614
$855$	−39.3829	+	0.485652i	−1.34687	+	0.0166090i
$856$	10.4503			0.357182
$857$	6.05485	−	6.05485i	0.206830	−	0.206830i	−0.596089	−	0.802919i	$-0.703279\pi$
$857$	6.05485	−	6.05485i	0.206830	−	0.206830i	0.802919	+	0.596089i	$0.203279\pi$
$858$	0.861061	−	33.5602i	0.0293961	−	1.14573i
$859$		−	36.8937i		−	1.25880i	−0.777082	−	0.629399i	$-0.783301\pi$
$859$		−	36.8937i		−	1.25880i	0.777082	−	0.629399i	$-0.216699\pi$
$860$	−3.59296	+	4.08201i	−0.122519	+	0.139195i
$861$	−38.0726	−	40.0778i	−1.29751	−	1.36585i
$862$	−16.9048	−	16.9048i	−0.575780	−	0.575780i
$863$	11.9650	+	11.9650i	0.407292	+	0.407292i	0.880793	−	0.473501i	$-0.157010\pi$
$863$	11.9650	+	11.9650i	0.407292	+	0.407292i	−0.473501	+	0.880793i	$0.657010\pi$
$864$	3.38089	+	3.94583i	0.115020	+	0.134240i
$865$	10.6720	−	12.1246i	0.362858	−	0.412248i
$866$		−	12.6871i		−	0.431125i
$867$	10.5991	+	0.271942i	0.359963	+	0.00923565i
$868$	2.34383	−	2.34383i	0.0795547	−	0.0795547i
$869$	53.2771			1.80730
$870$	−10.7352	+	11.5833i	−0.363956	+	0.392710i
$871$	50.0544			1.69603
$872$	5.17510	−	5.17510i	0.175251	−	0.175251i
$873$	20.1802	+	22.3648i	0.682996	+	0.756934i
$874$		−	17.0751i		−	0.577575i
$875$	−20.7565	+	30.7010i	−0.701698	+	1.03788i
$876$	10.3077	−	9.79199i	0.348265	−	0.330841i
$877$	−2.74612	−	2.74612i	−0.0927299	−	0.0927299i	0.659220	−	0.751950i	$-0.270887\pi$
$877$	−2.74612	−	2.74612i	−0.0927299	−	0.0927299i	−0.751950	+	0.659220i	$0.770887\pi$
$878$	−20.2328	−	20.2328i	−0.682824	−	0.682824i
$879$	−17.3286	+	16.4616i	−0.584480	+	0.555238i
$880$	−11.8782	+	0.756881i	−0.400414	+	0.0255145i
$881$			24.1429i			0.813393i	0.913563	+	0.406697i	$0.133319\pi$
$881$			24.1429i			0.813393i	−0.913563	+	0.406697i	$0.866681\pi$
$882$	8.01296	+	8.88040i	0.269810	+	0.299019i
$883$	−10.9140	+	10.9140i	−0.367287	+	0.367287i	−0.866487	−	0.499200i	$-0.833627\pi$
$883$	−10.9140	+	10.9140i	−0.367287	+	0.367287i	0.499200	+	0.866487i	$0.333627\pi$
$884$	−12.0101			−0.403944
$885$	−26.5673	+	1.00958i	−0.893050	+	0.0339366i
$886$	−30.1986			−1.01454
$887$	19.5350	−	19.5350i	0.655920	−	0.655920i	−0.298492	−	0.954412i	$-0.596484\pi$
$887$	19.5350	−	19.5350i	0.655920	−	0.655920i	0.954412	+	0.298492i	$0.0964835\pi$
$888$	1.75866	+	0.0451223i	0.0590167	+	0.00151420i
$889$			55.8671i			1.87372i
$890$	5.29392	+	4.65967i	0.177452	+	0.156193i
$891$	−4.90682	+	47.6539i	−0.164385	+	1.59646i
$892$	−4.74368	−	4.74368i	−0.158830	−	0.158830i
$893$	−38.1416	−	38.1416i	−1.27636	−	1.27636i
$894$	−9.51591	−	10.0171i	−0.318260	−	0.335021i
$895$	−2.43740	−	38.2516i	−0.0814733	−	1.27861i
$896$		−	3.31467i		−	0.110735i
$897$	−0.470454	+	18.3361i	−0.0157080	+	0.612226i
$898$	27.5179	−	27.5179i	0.918285	−	0.918285i
$899$	−4.07771			−0.135999
$900$	−1.13838	−	14.9567i	−0.0379460	−	0.498558i
$901$	−25.9015			−0.862905
$902$	−36.2401	+	36.2401i	−1.20666	+	1.20666i
$903$	0.358117	−	13.9577i	0.0119174	−	0.464484i
$904$			14.9982i			0.498833i
$905$	−1.32931	−	20.8617i	−0.0441878	−	0.693467i
$906$	4.46512	+	4.70028i	0.148344	+	0.156156i
$907$	6.70921	+	6.70921i	0.222776	+	0.222776i	0.809666	−	0.586891i	$-0.199648\pi$
$907$	6.70921	+	6.70921i	0.222776	+	0.222776i	−0.586891	+	0.809666i	$0.699648\pi$
$908$	1.30263	+	1.30263i	0.0432293	+	0.0432293i
$909$	−1.94297	+	37.8390i	−0.0644442	+	1.25504i
$910$	−20.2590	−	17.8319i	−0.671580	−	0.591121i
$911$		−	4.06585i		−	0.134708i	−0.997729	−	0.0673539i	$-0.978544\pi$
$911$		−	4.06585i		−	0.134708i	0.997729	−	0.0673539i	$-0.0214557\pi$
$912$	−10.1661	−	0.260833i	−0.336632	−	0.00863704i
$913$	−23.1699	+	23.1699i	−0.766812	+	0.766812i
$914$	−3.72809			−0.123314
$915$	3.53542	−	0.134349i	0.116877	−	0.00444143i
$916$	17.4858			0.577748
$917$	21.1580	−	21.1580i	0.698697	−	0.698697i
$918$	17.0876	+	1.31758i	0.563975	+	0.0434865i
$919$			21.3756i			0.705116i	0.935790	+	0.352558i	$0.114688\pi$
$919$			21.3756i			0.705116i	−0.935790	+	0.352558i	$0.885312\pi$
$920$	6.48985	−	0.413534i	0.213964	−	0.0136338i
$921$	0.163639	−	0.155452i	0.00539208	−	0.00512231i
$922$	19.2058	+	19.2058i	0.632511	+	0.632511i
$923$	−22.1407	−	22.1407i	−0.728770	−	0.728770i
$924$	22.1560	−	21.0475i	0.728879	−	0.692412i
$925$	−4.01777	−	3.10619i	−0.132104	−	0.102131i
$926$		−	19.3756i		−	0.636723i
$927$	27.3465	−	24.6753i	0.898178	−	0.810443i
$928$	−2.88338	+	2.88338i	−0.0946516	+	0.0946516i
$929$	10.1375			0.332601			0.166300	−	0.986075i	$-0.446818\pi$
$929$	10.1375			0.332601			0.166300	+	0.986075i	$0.446818\pi$
$930$	2.63264	−	2.84063i	0.0863278	−	0.0931480i
$931$	−23.4092			−0.767205
$932$	10.5213	−	10.5213i	0.344636	−	0.344636i
$933$	−14.6379	−	0.375568i	−0.479223	−	0.0122955i
$934$		−	24.7527i		−	0.809934i
$935$	−25.9375	+	29.4680i	−0.848248	+	0.963705i
$936$	10.9096	+	0.560191i	0.356593	+	0.0183104i
$937$	8.17703	+	8.17703i	0.267132	+	0.267132i	0.827944	−	0.560811i	$-0.189511\pi$
$937$	8.17703	+	8.17703i	0.267132	+	0.267132i	−0.560811	+	0.827944i	$0.689511\pi$
$938$	32.2186	+	32.2186i	1.05197	+	1.05197i
$939$	38.9480	+	40.9992i	1.27102	+	1.33796i
$940$	13.5730	−	15.4204i	0.442702	−	0.502960i
$941$			32.3646i			1.05506i	0.849538	+	0.527528i	$0.176881\pi$
$941$			32.3646i			1.05506i	−0.849538	+	0.527528i	$0.823119\pi$
$942$	−0.838393	+	32.6767i	−0.0273163	+	1.06466i
$943$	19.8003	−	19.8003i	0.644788	−	0.644788i
$944$	−6.86460			−0.223424
$945$	26.8676	+	27.5931i	0.874004	+	0.897605i
$946$	−12.9450			−0.420879
$947$	−19.1741	+	19.1741i	−0.623076	+	0.623076i	−0.946317	−	0.323241i	$-0.895228\pi$
$947$	−19.1741	+	19.1741i	−0.623076	+	0.623076i	0.323241	+	0.946317i	$0.395228\pi$
$948$	−0.444654	+	17.3306i	−0.0144417	+	0.562871i
$949$		−	29.8894i		−	0.970251i
$950$	23.2251	+	17.9556i	0.753520	+	0.582556i
$951$	15.2126	+	16.0137i	0.493301	+	0.519281i
$952$	−7.73058	−	7.73058i	−0.250550	−	0.250550i
$953$	20.7857	+	20.7857i	0.673316	+	0.673316i	0.958479	−	0.285163i	$-0.0920477\pi$
$953$	20.7857	+	20.7857i	0.673316	+	0.673316i	−0.285163	+	0.958479i	$0.592048\pi$
$954$	23.5282	+	1.20813i	0.761753	+	0.0391147i
$955$	−44.1647	+	2.81418i	−1.42914	+	0.0910647i
$956$			6.58020i			0.212819i
$957$	−37.5820	−	0.964251i	−1.21485	−	0.0311698i
$958$	5.94114	−	5.94114i	0.191950	−	0.191950i
$959$	−23.3975			−0.755544
$960$	−0.147070	−	3.87019i	−0.00474667	−	0.124910i
$961$	1.00000			0.0322581
$962$	2.61523	−	2.61523i	0.0843183	−	0.0843183i
$963$	−23.2760	+	21.0024i	−0.750058	+	0.676792i
$964$		−	6.44072i		−	0.207442i
$965$	0.687964	+	0.605542i	0.0221464	+	0.0194931i
$966$	−12.1053	+	11.4996i	−0.389481	+	0.369995i
$967$	−26.6176	−	26.6176i	−0.855964	−	0.855964i	0.134896	−	0.990860i	$-0.456930\pi$
$967$	−26.6176	−	26.6176i	−0.855964	−	0.855964i	−0.990860	+	0.134896i	$0.956930\pi$
$968$	−12.2562	−	12.2562i	−0.393930	−	0.393930i
$969$	−24.3179	+	23.1013i	−0.781205	+	0.742120i
$970$	−1.42780	−	22.4073i	−0.0458437	−	0.719454i
$971$			27.0245i			0.867259i	0.901091	+	0.433629i	$0.142767\pi$
$971$			27.0245i			0.867259i	−0.901091	+	0.433629i	$0.857233\pi$
$972$	−15.4604	−	1.99387i	−0.495893	−	0.0639533i
$973$	11.8603	−	11.8603i	0.380223	−	0.380223i
$974$	−30.7733			−0.986041
$975$	−24.4455	−	19.9215i	−0.782883	−	0.637999i
$976$	0.913500			0.0292404
$977$	24.0131	−	24.0131i	0.768246	−	0.768246i	−0.209552	−	0.977798i	$-0.567200\pi$
$977$	24.0131	−	24.0131i	0.768246	−	0.768246i	0.977798	+	0.209552i	$0.0672005\pi$
$978$	−8.21344	−	0.210734i	−0.262637	−	0.00673854i
$979$			16.7882i			0.536555i
$980$	−0.566935	−	8.89727i	−0.0181101	−	0.284213i
$981$	−1.12592	+	21.9272i	−0.0359480	+	0.700081i
$982$	−13.9304	−	13.9304i	−0.444537	−	0.444537i
$983$	20.9700	+	20.9700i	0.668839	+	0.668839i	0.957447	−	0.288609i	$-0.0931926\pi$
$983$	20.9700	+	20.9700i	0.668839	+	0.668839i	−0.288609	+	0.957447i	$0.593193\pi$
$984$	−11.4861	−	12.0910i	−0.366163	−	0.385448i
$985$	−28.8386	−	25.3836i	−0.918876	−	0.808789i
$986$			13.4494i			0.428317i
$987$	−1.35284	+	52.7276i	−0.0430615	+	1.67834i
$988$	−15.1175	+	15.1175i	−0.480952	+	0.480952i
$989$	7.07272			0.224899
$990$	24.9353	−	25.5580i	0.792497	−	0.812286i
$991$	43.3152			1.37595			0.687976	−	0.725733i	$-0.258499\pi$
$991$	43.3152			1.37595			0.687976	+	0.725733i	$0.258499\pi$
$992$	0.707107	−	0.707107i	0.0224507	−	0.0224507i
$993$	1.03026	−	40.1546i	0.0326942	−	1.27427i
$994$		−	28.5027i		−	0.904051i
$995$	−36.5007	+	2.32583i	−1.15715	+	0.0737337i
$996$	−7.34358	−	7.73034i	−0.232690	−	0.244945i
$997$	−31.0340	−	31.0340i	−0.982858	−	0.982858i	0.0169979	−	0.999856i	$-0.494589\pi$
$997$	−31.0340	−	31.0340i	−0.982858	−	0.982858i	−0.999856	+	0.0169979i	$0.994589\pi$
$998$	−9.32782	−	9.32782i	−0.295267	−	0.295267i
$999$	−4.00776	+	3.43395i	−0.126800	+	0.108645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.g.497.6	✓	40
3.2	odd	2	inner	930.2.j.g.497.20	yes	40
5.3	odd	4	inner	930.2.j.g.683.20	yes	40
15.8	even	4	inner	930.2.j.g.683.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.g.497.6	✓	40	1.1	even	1	trivial
930.2.j.g.497.20	yes	40	3.2	odd	2	inner
930.2.j.g.683.6	yes	40	15.8	even	4	inner
930.2.j.g.683.20	yes	40	5.3	odd	4	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.0444250 - 1.73148i) q^{3} -1.00000i q^{4} +(-0.142194 - 2.23154i) q^{5} +(1.19293 + 1.25576i) q^{6} +(2.34383 + 2.34383i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.99605 - 0.153842i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.0444250 - 1.73148i) q^{3} -1.00000i q^{4} +(-0.142194 - 2.23154i) q^{5} +(1.19293 + 1.25576i) q^{6} +(2.34383 + 2.34383i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.99605 - 0.153842i) q^{9} +(1.67849 + 1.47739i) q^{10} +5.32287i q^{11} +(-1.73148 - 0.0444250i) q^{12} +(-2.57481 + 2.57481i) q^{13} -3.31467 q^{14} +(-3.87019 + 0.147070i) q^{15} -1.00000 q^{16} +(-2.33223 + 2.33223i) q^{17} +(2.22731 - 2.00975i) q^{18} +5.87131i q^{19} +(-2.23154 + 0.142194i) q^{20} +(4.16242 - 3.95417i) q^{21} +(-3.76384 - 3.76384i) q^{22} +(2.05643 + 2.05643i) q^{23} +(1.25576 - 1.19293i) q^{24} +(-4.95956 + 0.634625i) q^{25} -3.64134i q^{26} +(-0.399474 + 5.18077i) q^{27} +(2.34383 - 2.34383i) q^{28} -4.07771 q^{29} +(2.63264 - 2.84063i) q^{30} +1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(9.21645 + 0.236468i) q^{33} -3.29827i q^{34} +(4.89707 - 5.56363i) q^{35} +(-0.153842 + 2.99605i) q^{36} +(0.718205 + 0.718205i) q^{37} +(-4.15164 - 4.15164i) q^{38} +(4.34385 + 4.57263i) q^{39} +(1.47739 - 1.67849i) q^{40} -9.62849i q^{41} +(-0.147254 + 5.73929i) q^{42} +(1.71966 - 1.71966i) q^{43} +5.32287 q^{44} +(0.0827162 + 6.70769i) q^{45} -2.90823 q^{46} +(-6.49628 + 6.49628i) q^{47} +(-0.0444250 + 1.73148i) q^{48} +3.98705i q^{49} +(3.05819 - 3.95569i) q^{50} +(3.93461 + 4.14183i) q^{51} +(2.57481 + 2.57481i) q^{52} +(5.55295 + 5.55295i) q^{53} +(-3.38089 - 3.94583i) q^{54} +(11.8782 - 0.756881i) q^{55} +3.31467i q^{56} +(10.1661 + 0.260833i) q^{57} +(2.88338 - 2.88338i) q^{58} +6.86460 q^{59} +(0.147070 + 3.87019i) q^{60} -0.913500 q^{61} +(-0.707107 + 0.707107i) q^{62} +(-6.66165 - 7.38281i) q^{63} +1.00000i q^{64} +(6.11193 + 5.37968i) q^{65} +(-6.68422 + 6.34980i) q^{66} +(-9.72000 - 9.72000i) q^{67} +(2.33223 + 2.33223i) q^{68} +(3.65203 - 3.46932i) q^{69} +(0.471327 + 7.39683i) q^{70} +8.59895i q^{71} +(-2.00975 - 2.22731i) q^{72} +(-5.80419 + 5.80419i) q^{73} -1.01570 q^{74} +(0.878512 + 8.61558i) q^{75} +5.87131 q^{76} +(-12.4759 + 12.4759i) q^{77} +(-6.30490 - 0.161766i) q^{78} -10.0091i q^{79} +(0.142194 + 2.23154i) q^{80} +(8.95267 + 0.921838i) q^{81} +(6.80837 + 6.80837i) q^{82} +(4.35290 + 4.35290i) q^{83} +(-3.95417 - 4.16242i) q^{84} +(5.53610 + 4.87285i) q^{85} +2.43196i q^{86} +(-0.181152 + 7.06048i) q^{87} +(-3.76384 + 3.76384i) q^{88} +3.15398 q^{89} +(-4.80155 - 4.68457i) q^{90} -12.0698 q^{91} +(2.05643 - 2.05643i) q^{92} +(0.0444250 - 1.73148i) q^{93} -9.18712i q^{94} +(13.1021 - 0.834866i) q^{95} +(-1.19293 - 1.25576i) q^{96} +(-7.10018 - 7.10018i) q^{97} +(-2.81927 - 2.81927i) q^{98} +(0.818881 - 15.9476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} - 8 q^{7}+O(q^{10}) \) 40 * q - 4 * q^3 - 8 * q^7	\( 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40} - 20 q^{42} - 48 q^{43} - 4 q^{45} - 80 q^{46} + 4 q^{48} + 48 q^{51} + 20 q^{52} + 164 q^{55} + 40 q^{57} + 56 q^{58} + 24 q^{60} - 128 q^{61} + 56 q^{63} + 8 q^{66} - 4 q^{67} - 56 q^{70} - 16 q^{72} - 48 q^{73} - 48 q^{75} - 40 q^{76} - 36 q^{78} - 24 q^{81} - 16 q^{82} - 56 q^{85} - 12 q^{87} - 4 q^{88} - 28 q^{90} - 32 q^{91} - 4 q^{93} - 52 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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