LMFDB - Embedded newform 930.2.j.g.497.19

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			497.19
Character	$\chi$	$=$	930.497
Dual form			930.2.j.g.683.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.59589 + 0.673165i) q^{3} -1.00000i q^{4} +(1.55932 + 1.60266i) q^{5} +(1.60446 - 0.652462i) q^{6} +(-0.700251 - 0.700251i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.09370 + 2.14859i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.59589 + 0.673165i) q^{3} -1.00000i q^{4} +(1.55932 + 1.60266i) q^{5} +(1.60446 - 0.652462i) q^{6} +(-0.700251 - 0.700251i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.09370 + 2.14859i) q^{9} +(2.23586 + 0.0306496i) q^{10} +4.42224i q^{11} +(0.673165 - 1.59589i) q^{12} +(0.282488 - 0.282488i) q^{13} -0.990304 q^{14} +(1.40964 + 3.60734i) q^{15} -1.00000 q^{16} +(1.25971 - 1.25971i) q^{17} +(2.99975 + 0.0388113i) q^{18} -5.10691i q^{19} +(1.60266 - 1.55932i) q^{20} +(-0.646136 - 1.58890i) q^{21} +(3.12700 + 3.12700i) q^{22} +(3.17479 + 3.17479i) q^{23} +(-0.652462 - 1.60446i) q^{24} +(-0.137056 + 4.99812i) q^{25} -0.399498i q^{26} +(1.89495 + 4.83830i) q^{27} +(-0.700251 + 0.700251i) q^{28} -0.862782 q^{29} +(3.54754 + 1.55401i) q^{30} +1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.97689 + 7.05739i) q^{33} -1.78149i q^{34} +(0.0303525 - 2.21418i) q^{35} +(2.14859 - 2.09370i) q^{36} +(-1.12067 - 1.12067i) q^{37} +(-3.61113 - 3.61113i) q^{38} +(0.640978 - 0.260657i) q^{39} +(0.0306496 - 2.23586i) q^{40} -9.40638i q^{41} +(-1.58041 - 0.666638i) q^{42} +(-5.61274 + 5.61274i) q^{43} +4.42224 q^{44} +(-0.178718 + 6.70582i) q^{45} +4.48983 q^{46} +(5.96081 - 5.96081i) q^{47} +(-1.59589 - 0.673165i) q^{48} -6.01930i q^{49} +(3.43729 + 3.63112i) q^{50} +(2.85834 - 1.16236i) q^{51} +(-0.282488 - 0.282488i) q^{52} +(-7.34070 - 7.34070i) q^{53} +(4.76113 + 2.08126i) q^{54} +(-7.08736 + 6.89568i) q^{55} +0.990304i q^{56} +(3.43779 - 8.15004i) q^{57} +(-0.610079 + 0.610079i) q^{58} -0.852824 q^{59} +(3.60734 - 1.40964i) q^{60} -3.32914 q^{61} +(0.707107 - 0.707107i) q^{62} +(0.0384350 - 2.97066i) q^{63} +1.00000i q^{64} +(0.893220 + 0.0122445i) q^{65} +(2.88534 + 7.09531i) q^{66} +(7.00567 + 7.00567i) q^{67} +(-1.25971 - 1.25971i) q^{68} +(2.92945 + 7.20376i) q^{69} +(-1.54420 - 1.58712i) q^{70} +2.54520i q^{71} +(0.0388113 - 2.99975i) q^{72} +(-8.92808 + 8.92808i) q^{73} -1.58487 q^{74} +(-3.58328 + 7.88417i) q^{75} -5.10691 q^{76} +(3.09668 - 3.09668i) q^{77} +(0.268928 - 0.637553i) q^{78} -2.12954i q^{79} +(-1.55932 - 1.60266i) q^{80} +(-0.232848 + 8.99699i) q^{81} +(-6.65131 - 6.65131i) q^{82} +(-3.12488 - 3.12488i) q^{83} +(-1.58890 + 0.646136i) q^{84} +(3.98317 + 0.0546021i) q^{85} +7.93762i q^{86} +(-1.37690 - 0.580794i) q^{87} +(3.12700 - 3.12700i) q^{88} -2.60883 q^{89} +(4.61536 + 4.86811i) q^{90} -0.395624 q^{91} +(3.17479 - 3.17479i) q^{92} +(1.59589 + 0.673165i) q^{93} -8.42986i q^{94} +(8.18466 - 7.96330i) q^{95} +(-1.60446 + 0.652462i) q^{96} +(-11.2793 - 11.2793i) q^{97} +(-4.25629 - 4.25629i) q^{98} +(-9.50156 + 9.25884i) 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
$3$	1.59589	+	0.673165i	0.921385	+	0.388652i
$3$	1.59589	+	0.673165i	0.921385	+	0.388652i
$4$		−	1.00000i		−	0.500000i
$5$	1.55932	+	1.60266i	0.697348	+	0.716733i
$5$	1.55932	+	1.60266i	0.697348	+	0.716733i
$6$	1.60446	−	0.652462i	0.655018	−	0.266367i
$7$	−0.700251	−	0.700251i	−0.264670	−	0.264670i	0.562278	−	0.826948i	$-0.309925\pi$
$7$	−0.700251	−	0.700251i	−0.264670	−	0.264670i	−0.826948	+	0.562278i	$0.809925\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.09370	+	2.14859i	0.697900	+	0.716196i
$10$	2.23586	+	0.0306496i	0.707040	+	0.00969227i
$11$			4.42224i			1.33336i	0.745346	+	0.666678i	$0.232284\pi$
$11$			4.42224i			1.33336i	−0.745346	+	0.666678i	$0.767716\pi$
$12$	0.673165	−	1.59589i	0.194326	−	0.460692i
$13$	0.282488	−	0.282488i	0.0783480	−	0.0783480i	−0.666847	−	0.745195i	$-0.732356\pi$
$13$	0.282488	−	0.282488i	0.0783480	−	0.0783480i	0.745195	+	0.666847i	$0.232356\pi$
$14$	−0.990304			−0.264670
$15$	1.40964	+	3.60734i	0.363967	+	0.931412i
$16$	−1.00000			−0.250000
$17$	1.25971	−	1.25971i	0.305524	−	0.305524i	−0.537647	−	0.843170i	$-0.680687\pi$
$17$	1.25971	−	1.25971i	0.305524	−	0.305524i	0.843170	+	0.537647i	$0.180687\pi$
$18$	2.99975	+	0.0388113i	0.707048	+	0.00914792i
$19$		−	5.10691i		−	1.17161i	−0.810454	−	0.585803i	$-0.800779\pi$
$19$		−	5.10691i		−	1.17161i	0.810454	−	0.585803i	$-0.199221\pi$
$20$	1.60266	−	1.55932i	0.358366	−	0.348674i
$21$	−0.646136	−	1.58890i	−0.140998	−	0.346727i
$22$	3.12700	+	3.12700i	0.666678	+	0.666678i
$23$	3.17479	+	3.17479i	0.661990	+	0.661990i	0.955849	−	0.293859i	$-0.0949396\pi$
$23$	3.17479	+	3.17479i	0.661990	+	0.661990i	−0.293859	+	0.955849i	$0.594940\pi$
$24$	−0.652462	−	1.60446i	−0.133183	−	0.327509i
$25$	−0.137056	+	4.99812i	−0.0274113	+	0.999624i
$26$		−	0.399498i		−	0.0783480i
$27$	1.89495	+	4.83830i	0.364684	+	0.931132i
$28$	−0.700251	+	0.700251i	−0.132335	+	0.132335i
$29$	−0.862782			−0.160215			−0.0801073	−	0.996786i	$-0.525526\pi$
$29$	−0.862782			−0.160215			−0.0801073	+	0.996786i	$0.525526\pi$
$30$	3.54754	+	1.55401i	0.647689	+	0.283723i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−2.97689	+	7.05739i	−0.518211	+	1.22853i
$34$		−	1.78149i		−	0.305524i
$35$	0.0303525	−	2.21418i	0.00513050	−	0.374265i
$36$	2.14859	−	2.09370i	0.358098	−	0.348950i
$37$	−1.12067	−	1.12067i	−0.184238	−	0.184238i	0.608962	−	0.793200i	$-0.291586\pi$
$37$	−1.12067	−	1.12067i	−0.184238	−	0.184238i	−0.793200	+	0.608962i	$0.791586\pi$
$38$	−3.61113	−	3.61113i	−0.585803	−	0.585803i
$39$	0.640978	−	0.260657i	0.102639	−	0.0417385i
$40$	0.0306496	−	2.23586i	0.00484613	−	0.353520i
$41$		−	9.40638i		−	1.46903i	−0.678593	−	0.734515i	$-0.737410\pi$
$41$		−	9.40638i		−	1.46903i	0.678593	−	0.734515i	$-0.262590\pi$
$42$	−1.58041	−	0.666638i	−0.243863	−	0.102864i
$43$	−5.61274	+	5.61274i	−0.855935	+	0.855935i	−0.990856	−	0.134921i	$-0.956922\pi$
$43$	−5.61274	+	5.61274i	−0.855935	+	0.855935i	0.134921	+	0.990856i	$0.456922\pi$
$44$	4.42224			0.666678
$45$	−0.178718	+	6.70582i	−0.0266417	+	0.999645i
$46$	4.48983			0.661990
$47$	5.96081	−	5.96081i	0.869473	−	0.869473i	−0.122941	−	0.992414i	$-0.539232\pi$
$47$	5.96081	−	5.96081i	0.869473	−	0.869473i	0.992414	+	0.122941i	$0.0392325\pi$
$48$	−1.59589	−	0.673165i	−0.230346	−	0.0971629i
$49$		−	6.01930i		−	0.859900i
$50$	3.43729	+	3.63112i	0.486106	+	0.513518i
$51$	2.85834	−	1.16236i	0.400247	−	0.162763i
$52$	−0.282488	−	0.282488i	−0.0391740	−	0.0391740i
$53$	−7.34070	−	7.34070i	−1.00832	−	1.00832i	−0.999965	−	0.00835762i	$-0.997340\pi$
$53$	−7.34070	−	7.34070i	−1.00832	−	1.00832i	−0.00835762	−	0.999965i	$-0.502660\pi$
$54$	4.76113	+	2.08126i	0.647908	+	0.283224i
$55$	−7.08736	+	6.89568i	−0.955659	+	0.929813i
$56$			0.990304i			0.132335i
$57$	3.43779	−	8.15004i	0.455347	−	1.07950i
$58$	−0.610079	+	0.610079i	−0.0801073	+	0.0801073i
$59$	−0.852824			−0.111028			−0.0555141	−	0.998458i	$-0.517680\pi$
$59$	−0.852824			−0.111028			−0.0555141	+	0.998458i	$0.517680\pi$
$60$	3.60734	−	1.40964i	0.465706	−	0.181983i
$61$	−3.32914			−0.426253			−0.213126	−	0.977025i	$-0.568365\pi$
$61$	−3.32914			−0.426253			−0.213126	+	0.977025i	$0.568365\pi$
$62$	0.707107	−	0.707107i	0.0898027	−	0.0898027i
$63$	0.0384350	−	2.97066i	0.00484236	−	0.374268i
$64$			1.00000i			0.125000i
$65$	0.893220	+	0.0122445i	0.110790	+	0.00151874i
$66$	2.88534	+	7.09531i	0.355161	+	0.873372i
$67$	7.00567	+	7.00567i	0.855879	+	0.855879i	0.990850	−	0.134970i	$-0.0430939\pi$
$67$	7.00567	+	7.00567i	0.855879	+	0.855879i	−0.134970	+	0.990850i	$0.543094\pi$
$68$	−1.25971	−	1.25971i	−0.152762	−	0.152762i
$69$	2.92945	+	7.20376i	0.352664	+	0.867231i
$70$	−1.54420	−	1.58712i	−0.184567	−	0.189698i
$71$			2.54520i			0.302060i	0.988529	+	0.151030i	$0.0482589\pi$
$71$			2.54520i			0.302060i	−0.988529	+	0.151030i	$0.951741\pi$
$72$	0.0388113	−	2.99975i	0.00457396	−	0.353524i
$73$	−8.92808	+	8.92808i	−1.04495	+	1.04495i	−0.0460116	+	0.998941i	$0.514651\pi$
$73$	−8.92808	+	8.92808i	−1.04495	+	1.04495i	−0.998941	+	0.0460116i	$0.985349\pi$
$74$	−1.58487			−0.184238
$75$	−3.58328	+	7.88417i	−0.413762	+	0.910385i
$76$	−5.10691			−0.585803
$77$	3.09668	−	3.09668i	0.352899	−	0.352899i
$78$	0.268928	−	0.637553i	0.0304501	−	0.0721886i
$79$		−	2.12954i		−	0.239592i	−0.992799	−	0.119796i	$-0.961776\pi$
$79$		−	2.12954i		−	0.239592i	0.992799	−	0.119796i	$-0.0382241\pi$
$80$	−1.55932	−	1.60266i	−0.174337	−	0.179183i
$81$	−0.232848	+	8.99699i	−0.0258720	+	0.999665i
$82$	−6.65131	−	6.65131i	−0.734515	−	0.734515i
$83$	−3.12488	−	3.12488i	−0.343000	−	0.343000i	0.514494	−	0.857494i	$-0.327980\pi$
$83$	−3.12488	−	3.12488i	−0.343000	−	0.343000i	−0.857494	+	0.514494i	$0.827980\pi$
$84$	−1.58890	+	0.646136i	−0.173364	+	0.0704992i
$85$	3.98317	+	0.0546021i	0.432035	+	0.00592243i
$86$			7.93762i			0.855935i
$87$	−1.37690	−	0.580794i	−0.147619	−	0.0622677i
$88$	3.12700	−	3.12700i	0.333339	−	0.333339i
$89$	−2.60883			−0.276536			−0.138268	−	0.990395i	$-0.544153\pi$
$89$	−2.60883			−0.276536			−0.138268	+	0.990395i	$0.544153\pi$
$90$	4.61536	+	4.86811i	0.486502	+	0.513143i
$91$	−0.395624			−0.0414727
$92$	3.17479	−	3.17479i	0.330995	−	0.330995i
$93$	1.59589	+	0.673165i	0.165486	+	0.0698039i
$94$		−	8.42986i		−	0.869473i
$95$	8.18466	−	7.96330i	0.839728	−	0.817017i
$96$	−1.60446	+	0.652462i	−0.163755	+	0.0665916i
$97$	−11.2793	−	11.2793i	−1.14524	−	1.14524i	−0.987477	−	0.157762i	$-0.949572\pi$
$97$	−11.2793	−	11.2793i	−1.14524	−	1.14524i	−0.157762	−	0.987477i	$-0.550428\pi$
$98$	−4.25629	−	4.25629i	−0.429950	−	0.429950i
$99$	−9.50156	+	9.25884i	−0.954943	+	0.930548i
$100$	4.99812	+	0.137056i	0.499812	+	0.0137056i
$101$		−	3.97281i		−	0.395309i	−0.980272	−	0.197655i	$-0.936668\pi$
$101$		−	3.97281i		−	0.395309i	0.980272	−	0.197655i	$-0.0633325\pi$
$102$	1.19924	−	2.84306i	0.118742	−	0.281505i
$103$	4.23054	−	4.23054i	0.416848	−	0.416848i	−0.467268	−	0.884116i	$-0.654762\pi$
$103$	4.23054	−	4.23054i	0.416848	−	0.416848i	0.884116	+	0.467268i	$0.154762\pi$
$104$	−0.399498			−0.0391740
$105$	1.53895	−	3.51314i	0.150186	−	0.342848i
$106$	−10.3813			−1.00832
$107$	10.3058	−	10.3058i	0.996300	−	0.996300i	−0.00369355	−	0.999993i	$-0.501176\pi$
$107$	10.3058	−	10.3058i	0.996300	−	0.996300i	0.999993	+	0.00369355i	$0.00117570\pi$
$108$	4.83830	−	1.89495i	0.465566	−	0.182342i
$109$		−	6.25281i		−	0.598911i	−0.954110	−	0.299455i	$-0.903195\pi$
$109$		−	6.25281i		−	0.598911i	0.954110	−	0.299455i	$-0.0968050\pi$
$110$	−0.135540	+	9.88750i	−0.0129232	+	0.942736i
$111$	−1.03407	−	2.54287i	−0.0981496	−	0.241358i
$112$	0.700251	+	0.700251i	0.0661675	+	0.0661675i
$113$	8.71474	+	8.71474i	0.819814	+	0.819814i	0.986081	−	0.166267i	$-0.0531714\pi$
$113$	8.71474	+	8.71474i	0.819814	+	0.819814i	−0.166267	+	0.986081i	$0.553171\pi$
$114$	−3.33207	−	8.19384i	−0.312077	−	0.767423i
$115$	−0.137612	+	10.0386i	−0.0128324	+	0.936107i
$116$			0.862782i			0.0801073i
$117$	1.19839	+	0.0155050i	0.110791	+	0.00143344i
$118$	−0.603038	+	0.603038i	−0.0555141	+	0.0555141i
$119$	−1.76422			−0.161726
$120$	1.55401	−	3.54754i	0.141861	−	0.323845i
$121$	−8.55620			−0.777836
$122$	−2.35406	+	2.35406i	−0.213126	+	0.213126i
$123$	6.33204	−	15.0115i	0.570941	−	1.35354i
$124$		−	1.00000i		−	0.0898027i
$125$	−8.22402	+	7.57400i	−0.735579	+	0.677439i
$126$	−2.07340	−	2.12775i	−0.184713	−	0.189555i
$127$	−9.03363	−	9.03363i	−0.801605	−	0.801605i	0.181742	−	0.983346i	$-0.441827\pi$
$127$	−9.03363	−	9.03363i	−0.801605	−	0.801605i	−0.983346	+	0.181742i	$0.941827\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−12.7356	+	5.17899i	−1.12131	+	0.455985i
$130$	0.640260	−	0.622944i	0.0561545	−	0.0546358i
$131$			10.6882i			0.933831i	0.884302	+	0.466915i	$0.154635\pi$
$131$			10.6882i			0.933831i	−0.884302	+	0.466915i	$0.845365\pi$
$132$	7.05739	+	2.97689i	0.614267	+	0.259105i
$133$	−3.57612	+	3.57612i	−0.310089	+	0.310089i
$134$	9.90752			0.855879
$135$	−4.79934	+	10.5814i	−0.413061	+	0.910703i
$136$	−1.78149			−0.152762
$137$	3.13371	−	3.13371i	0.267731	−	0.267731i	−0.560455	−	0.828185i	$-0.689374\pi$
$137$	3.13371	−	3.13371i	0.267731	−	0.267731i	0.828185	+	0.560455i	$0.189374\pi$
$138$	7.16526	+	3.02240i	0.609947	+	0.257283i
$139$		−	21.5733i		−	1.82982i	−0.403657	−	0.914911i	$-0.632261\pi$
$139$		−	21.5733i		−	1.82982i	0.403657	−	0.914911i	$-0.367739\pi$
$140$	−2.21418	−	0.0303525i	−0.187132	−	0.00256525i
$141$	13.5254	−	5.50016i	1.13904	−	0.463197i
$142$	1.79973	+	1.79973i	0.151030	+	0.151030i
$143$	1.24923	+	1.24923i	0.104466	+	0.104466i
$144$	−2.09370	−	2.14859i	−0.174475	−	0.179049i
$145$	−1.34535	−	1.38275i	−0.111725	−	0.114831i
$146$			12.6262i			1.04495i
$147$	4.05198	−	9.60611i	0.334201	−	0.792298i
$148$	−1.12067	+	1.12067i	−0.0921189	+	0.0921189i
$149$	6.21215			0.508919			0.254460	−	0.967083i	$-0.418102\pi$
$149$	6.21215			0.508919			0.254460	+	0.967083i	$0.418102\pi$
$150$	3.04118	+	8.10871i	0.248312	+	0.662074i
$151$	14.5620			1.18504			0.592521	−	0.805555i	$-0.298133\pi$
$151$	14.5620			1.18504			0.592521	+	0.805555i	$0.298133\pi$
$152$	−3.61113	+	3.61113i	−0.292901	+	0.292901i
$153$	5.34403	+	0.0691421i	0.432040	+	0.00558981i
$154$		−	4.37936i		−	0.352899i
$155$	1.55932	+	1.60266i	0.125247	+	0.128729i
$156$	−0.260657	−	0.640978i	−0.0208693	−	0.0513193i
$157$	−11.2599	−	11.2599i	−0.898639	−	0.898639i	0.0966771	−	0.995316i	$-0.469179\pi$
$157$	−11.2599	−	11.2599i	−0.898639	−	0.898639i	−0.995316	+	0.0966771i	$0.969179\pi$
$158$	−1.50581	−	1.50581i	−0.119796	−	0.119796i
$159$	−6.77342	−	16.6564i	−0.537167	−	1.32094i
$160$	−2.23586	−	0.0306496i	−0.176760	−	0.00242307i
$161$		−	4.44630i		−	0.350418i
$162$	6.19718	+	6.52648i	0.486897	+	0.512769i
$163$	−13.8251	+	13.8251i	−1.08287	+	1.08287i	−0.0866262	+	0.996241i	$0.527609\pi$
$163$	−13.8251	+	13.8251i	−1.08287	+	1.08287i	−0.996241	+	0.0866262i	$0.972391\pi$
$164$	−9.40638			−0.734515
$165$	−15.9525	+	6.23375i	−1.24190	+	0.485297i
$166$	−4.41925			−0.343000
$167$	−18.0679	+	18.0679i	−1.39814	+	1.39814i	−0.592759	+	0.805380i	$0.701962\pi$
$167$	−18.0679	+	18.0679i	−1.39814	+	1.39814i	−0.805380	+	0.592759i	$0.798038\pi$
$168$	−0.666638	+	1.58041i	−0.0514322	+	0.121931i
$169$			12.8404i			0.987723i
$170$	2.85513	−	2.77791i	0.218979	−	0.213056i
$171$	10.9726	−	10.6923i	0.839099	−	0.817663i
$172$	5.61274	+	5.61274i	0.427968	+	0.427968i
$173$	−8.14142	−	8.14142i	−0.618980	−	0.618980i	0.326290	−	0.945270i	$-0.394202\pi$
$173$	−8.14142	−	8.14142i	−0.618980	−	0.618980i	−0.945270	+	0.326290i	$0.894202\pi$
$174$	−1.38430	+	0.562933i	−0.104943	+	0.0426758i
$175$	3.59591	−	3.40396i	0.271825	−	0.257316i
$176$		−	4.42224i		−	0.333339i
$177$	−1.36101	−	0.574091i	−0.102300	−	0.0431513i
$178$	−1.84472	+	1.84472i	−0.138268	+	0.138268i
$179$	−12.7857			−0.955645			−0.477822	−	0.878456i	$-0.658574\pi$
$179$	−12.7857			−0.955645			−0.477822	+	0.878456i	$0.658574\pi$
$180$	6.70582	+	0.178718i	0.499823	+	0.0133208i
$181$	2.73755			0.203480			0.101740	−	0.994811i	$-0.467559\pi$
$181$	2.73755			0.203480			0.101740	+	0.994811i	$0.467559\pi$
$182$	−0.279749	+	0.279749i	−0.0207364	+	0.0207364i
$183$	−5.31292	−	2.24106i	−0.392743	−	0.165664i
$184$		−	4.48983i		−	0.330995i
$185$	0.0485758	−	3.54355i	0.00357136	−	0.260527i
$186$	1.60446	−	0.652462i	0.117645	−	0.0478408i
$187$	5.57072	+	5.57072i	0.407372	+	0.407372i
$188$	−5.96081	−	5.96081i	−0.434737	−	0.434737i
$189$	2.06108	−	4.71497i	0.149922	−	0.342963i
$190$	0.156525	−	11.4183i	0.0113555	−	0.828372i
$191$		−	6.29907i		−	0.455785i	−0.973686	−	0.227892i	$-0.926817\pi$
$191$		−	6.29907i		−	0.455785i	0.973686	−	0.227892i	$-0.0731835\pi$
$192$	−0.673165	+	1.59589i	−0.0485815	+	0.115173i
$193$	−8.56703	+	8.56703i	−0.616668	+	0.616668i	−0.944675	−	0.328007i	$-0.893623\pi$
$193$	−8.56703	+	8.56703i	−0.616668	+	0.616668i	0.328007	+	0.944675i	$0.393623\pi$
$194$	−15.9513			−1.14524
$195$	1.41723	+	0.620825i	0.101490	+	0.0444582i
$196$	−6.01930			−0.429950
$197$	0.661707	−	0.661707i	0.0471447	−	0.0471447i	−0.683141	−	0.730286i	$-0.739387\pi$
$197$	0.661707	−	0.661707i	0.0471447	−	0.0471447i	0.730286	+	0.683141i	$0.239387\pi$
$198$	−0.171633	+	13.2656i	−0.0121974	+	0.942746i
$199$			16.9809i			1.20375i	0.798592	+	0.601873i	$0.205579\pi$
$199$			16.9809i			1.20375i	−0.798592	+	0.601873i	$0.794421\pi$
$200$	3.63112	−	3.43729i	0.256759	−	0.243053i
$201$	6.46428	+	15.8962i	0.455955	+	1.12123i
$202$	−2.80920	−	2.80920i	−0.197655	−	0.197655i
$203$	0.604164	+	0.604164i	0.0424040	+	0.0424040i
$204$	−1.16236	−	2.85834i	−0.0813813	−	0.200124i
$205$	15.0753	−	14.6675i	1.05290	−	1.02442i
$206$		−	5.98289i		−	0.416848i
$207$	−0.174256	+	13.4684i	−0.0121117	+	0.936116i
$208$	−0.282488	+	0.282488i	−0.0195870	+	0.0195870i
$209$	22.5840			1.56217
$210$	−1.39597	−	3.57237i	−0.0963310	−	0.246517i
$211$	−10.8572			−0.747442			−0.373721	−	0.927541i	$-0.621918\pi$
$211$	−10.8572			−0.747442			−0.373721	+	0.927541i	$0.621918\pi$
$212$	−7.34070	+	7.34070i	−0.504161	+	0.504161i
$213$	−1.71334	+	4.06185i	−0.117396	+	0.278313i
$214$		−	14.5746i		−	0.996300i
$215$	−17.7474	−	0.243285i	−1.21036	−	0.0165919i
$216$	2.08126	−	4.76113i	0.141612	−	0.323954i
$217$	−0.700251	−	0.700251i	−0.0475361	−	0.0475361i
$218$	−4.42141	−	4.42141i	−0.299455	−	0.299455i
$219$	−20.2583	+	8.23812i	−1.36893	+	0.556681i
$220$	6.89568	+	7.08736i	0.464906	+	0.477830i
$221$		−	0.711703i		−	0.0478743i
$222$	−2.52928	−	1.06688i	−0.169754	−	0.0716043i
$223$	−0.145214	+	0.145214i	−0.00972426	+	0.00972426i	−0.711952	−	0.702228i	$-0.752189\pi$
$223$	−0.145214	+	0.145214i	−0.00972426	+	0.00972426i	0.702228	+	0.711952i	$0.252189\pi$
$224$	0.990304			0.0661675
$225$	−11.0259	+	10.1701i	−0.735057	+	0.678006i
$226$	12.3245			0.819814
$227$	−14.9233	+	14.9233i	−0.990492	+	0.990492i	−0.999955	−	0.00946342i	$-0.996988\pi$
$227$	−14.9233	+	14.9233i	−0.990492	+	0.990492i	0.00946342	+	0.999955i	$0.496988\pi$
$228$	−8.15004	−	3.43779i	−0.539750	−	0.227673i
$229$		−	18.0957i		−	1.19579i	−0.801573	−	0.597897i	$-0.796003\pi$
$229$		−	18.0957i		−	1.19579i	0.801573	−	0.597897i	$-0.203997\pi$
$230$	7.00108	+	7.19569i	0.461637	+	0.474470i
$231$	7.02651	−	2.85737i	0.462311	−	0.188001i
$232$	0.610079	+	0.610079i	0.0400537	+	0.0400537i
$233$	12.6901	+	12.6901i	0.831358	+	0.831358i	0.987703	−	0.156344i	$-0.0499709\pi$
$233$	12.6901	+	12.6901i	0.831358	+	0.831358i	−0.156344	+	0.987703i	$0.549971\pi$
$234$	0.858356	−	0.836428i	0.0561125	−	0.0546790i
$235$	18.8480	+	0.258372i	1.22951	+	0.0168543i
$236$			0.852824i			0.0555141i
$237$	1.43353	−	3.39850i	0.0931179	−	0.220757i
$238$	−1.24749	+	1.24749i	−0.0808629	+	0.0808629i
$239$	10.4687			0.677162			0.338581	−	0.940937i	$-0.390053\pi$
$239$	10.4687			0.677162			0.338581	+	0.940937i	$0.390053\pi$
$240$	−1.40964	−	3.60734i	−0.0909916	−	0.232853i
$241$	−6.58071			−0.423901			−0.211950	−	0.977280i	$-0.567982\pi$
$241$	−6.58071			−0.423901			−0.211950	+	0.977280i	$0.567982\pi$
$242$	−6.05015	+	6.05015i	−0.388918	+	0.388918i
$243$	−6.42805	+	14.2014i	−0.412360	+	0.911021i
$244$			3.32914i			0.213126i
$245$	9.64690	−	9.38600i	0.616318	−	0.599649i
$246$	−6.13730	−	15.0922i	−0.391300	−	0.962241i
$247$	−1.44264	−	1.44264i	−0.0917929	−	0.0917929i
$248$	−0.707107	−	0.707107i	−0.0449013	−	0.0449013i
$249$	−2.88339	−	7.09050i	−0.182727	−	0.449342i
$250$	−0.459629	+	11.1709i	−0.0290695	+	0.706509i
$251$			2.94903i			0.186141i	0.995660	+	0.0930705i	$0.0296682\pi$
$251$			2.94903i			0.186141i	−0.995660	+	0.0930705i	$0.970332\pi$
$252$	−2.97066	−	0.0384350i	−0.187134	−	0.00242118i
$253$	−14.0397	+	14.0397i	−0.882667	+	0.882667i
$254$	−12.7755			−0.801605
$255$	6.31992	+	2.76847i	0.395769	+	0.173368i
$256$	1.00000			0.0625000
$257$	−3.32257	+	3.32257i	−0.207256	+	0.207256i	−0.803100	−	0.595844i	$-0.796818\pi$
$257$	−3.32257	+	3.32257i	−0.207256	+	0.207256i	0.595844	+	0.803100i	$0.296818\pi$
$258$	−5.34332	+	12.6675i	−0.332661	+	0.788646i
$259$			1.56951i			0.0975244i
$260$	0.0122445	−	0.893220i	0.000759369	−	0.0553952i
$261$	−1.80641	−	1.85376i	−0.111814	−	0.114745i
$262$	7.55769	+	7.55769i	0.466915	+	0.466915i
$263$	14.3978	+	14.3978i	0.887805	+	0.887805i	0.994312	−	0.106507i	$-0.0339666\pi$
$263$	14.3978	+	14.3978i	0.887805	+	0.887805i	−0.106507	+	0.994312i	$0.533967\pi$
$264$	7.09531	−	2.88534i	0.436686	−	0.177581i
$265$	0.318184	−	23.2112i	0.0195459	−	1.42585i
$266$			5.05740i			0.310089i
$267$	−4.16340	−	1.75617i	−0.254796	−	0.107476i
$268$	7.00567	−	7.00567i	0.427940	−	0.427940i
$269$	24.5047			1.49408			0.747038	−	0.664781i	$-0.231475\pi$
$269$	24.5047			1.49408			0.747038	+	0.664781i	$0.231475\pi$
$270$	4.08855	+	10.8758i	0.248821	+	0.661882i
$271$	25.1352			1.52686			0.763428	−	0.645893i	$-0.223515\pi$
$271$	25.1352			1.52686			0.763428	+	0.645893i	$0.223515\pi$
$272$	−1.25971	+	1.25971i	−0.0763809	+	0.0763809i
$273$	−0.631371	−	0.266320i	−0.0382123	−	0.0161184i
$274$		−	4.43173i		−	0.267731i
$275$	−22.1029	−	0.606097i	−1.33285	−	0.0365490i
$276$	7.20376	−	2.92945i	0.433615	−	0.176332i
$277$	−11.6986	−	11.6986i	−0.702902	−	0.702902i	0.262131	−	0.965032i	$-0.415575\pi$
$277$	−11.6986	−	11.6986i	−0.702902	−	0.702902i	−0.965032	+	0.262131i	$0.915575\pi$
$278$	−15.2546	−	15.2546i	−0.914911	−	0.914911i
$279$	2.09370	+	2.14859i	0.125346	+	0.128633i
$280$	−1.58712	+	1.54420i	−0.0948488	+	0.0922835i
$281$		−	8.51957i		−	0.508235i	−0.967173	−	0.254118i	$-0.918215\pi$
$281$		−	8.51957i		−	0.508235i	0.967173	−	0.254118i	$-0.0817850\pi$
$282$	5.67468	−	13.4531i	0.337922	−	0.801119i
$283$	14.1299	−	14.1299i	0.839937	−	0.839937i	−0.148913	−	0.988850i	$-0.547577\pi$
$283$	14.1299	−	14.1299i	0.839937	−	0.839937i	0.988850	+	0.148913i	$0.0475774\pi$
$284$	2.54520			0.151030
$285$	18.4224	−	7.19889i	1.09125	−	0.426425i
$286$	1.76667			0.104466
$287$	−6.58682	+	6.58682i	−0.388808	+	0.388808i
$288$	−2.99975	−	0.0388113i	−0.176762	−	0.00228698i
$289$			13.8263i			0.813311i
$290$	−1.92906	−	0.0264440i	−0.113278	−	0.00155284i
$291$	−10.4076	−	25.5933i	−0.610107	−	1.50031i
$292$	8.92808	+	8.92808i	0.522476	+	0.522476i
$293$	−20.0654	−	20.0654i	−1.17223	−	1.17223i	−0.981676	−	0.190558i	$-0.938970\pi$
$293$	−20.0654	−	20.0654i	−1.17223	−	1.17223i	−0.190558	−	0.981676i	$-0.561030\pi$
$294$	−3.92736	−	9.65772i	−0.229048	−	0.563250i
$295$	−1.32982	−	1.36679i	−0.0774254	−	0.0795776i
$296$			1.58487i			0.0921189i
$297$	−21.3961	+	8.37993i	−1.24153	+	0.486253i
$298$	4.39266	−	4.39266i	0.254460	−	0.254460i
$299$	1.79368			0.103731
$300$	7.88417	+	3.58328i	0.455193	+	0.206881i
$301$	7.86066			0.453081
$302$	10.2969	−	10.2969i	0.592521	−	0.592521i
$303$	2.67436	−	6.34015i	0.153638	−	0.364232i
$304$			5.10691i			0.292901i
$305$	−5.19119	−	5.33549i	−0.297246	−	0.305509i
$306$	3.82769	−	3.72991i	0.218815	−	0.213225i
$307$	3.42153	+	3.42153i	0.195277	+	0.195277i	0.797972	−	0.602695i	$-0.205906\pi$
$307$	3.42153	+	3.42153i	0.195277	+	0.195277i	−0.602695	+	0.797972i	$0.705906\pi$
$308$	−3.09668	−	3.09668i	−0.176450	−	0.176450i
$309$	9.59931	−	3.90361i	0.546086	−	0.222069i
$310$	2.23586	+	0.0306496i	0.126988	+	0.00174078i
$311$			13.5393i			0.767745i	0.923386	+	0.383872i	$0.125410\pi$
$311$			13.5393i			0.767745i	−0.923386	+	0.383872i	$0.874590\pi$
$312$	−0.637553	−	0.268928i	−0.0360943	−	0.0152250i
$313$	−14.6089	+	14.6089i	−0.825742	+	0.825742i	−0.986925	−	0.161183i	$-0.948469\pi$
$313$	−14.6089	+	14.6089i	−0.825742	+	0.825742i	0.161183	+	0.986925i	$0.448469\pi$
$314$	−15.9239			−0.898639
$315$	4.82091	−	4.57061i	0.271627	−	0.257525i
$316$	−2.12954			−0.119796
$317$	1.18936	−	1.18936i	0.0668012	−	0.0668012i	−0.672917	−	0.739718i	$-0.734959\pi$
$317$	1.18936	−	1.18936i	0.0668012	−	0.0668012i	0.739718	+	0.672917i	$0.234959\pi$
$318$	−16.5674	−	6.98833i	−0.929053	−	0.391886i
$319$		−	3.81543i		−	0.213623i
$320$	−1.60266	+	1.55932i	−0.0895916	+	0.0871685i
$321$	23.3844	−	9.50938i	1.30519	−	0.530762i
$322$	−3.14401	−	3.14401i	−0.175209	−	0.175209i
$323$	−6.43321	−	6.43321i	−0.357953	−	0.357953i
$324$	8.99699	+	0.232848i	0.499833	+	0.0129360i
$325$	1.37319	+	1.45062i	0.0761709	+	0.0804661i
$326$			19.5517i			1.08287i
$327$	4.20917	−	9.97877i	0.232768	−	0.551827i
$328$	−6.65131	+	6.65131i	−0.367257	+	0.367257i
$329$	−8.34812			−0.460247
$330$	−6.87222	+	15.6881i	−0.378303	+	0.863600i
$331$	−13.6823			−0.752048			−0.376024	−	0.926610i	$-0.622709\pi$
$331$	−13.6823			−0.752048			−0.376024	+	0.926610i	$0.622709\pi$
$332$	−3.12488	+	3.12488i	−0.171500	+	0.171500i
$333$	0.0615110	−	4.75422i	0.00337078	−	0.260530i
$334$			25.5519i			1.39814i
$335$	−0.303662	+	22.1518i	−0.0165908	+	1.21028i
$336$	0.646136	+	1.58890i	0.0352496	+	0.0866818i
$337$	−0.457008	−	0.457008i	−0.0248948	−	0.0248948i	0.694550	−	0.719445i	$-0.255604\pi$
$337$	−0.457008	−	0.457008i	−0.0248948	−	0.0248948i	−0.719445	+	0.694550i	$0.755604\pi$
$338$	9.07953	+	9.07953i	0.493862	+	0.493862i
$339$	8.04127	+	19.7742i	0.436742	+	1.07399i
$340$	0.0546021	−	3.98317i	0.00296122	−	0.216018i
$341$			4.42224i			0.239478i
$342$	0.198206	−	15.3194i	0.0107177	−	0.828381i
$343$	−9.11677	+	9.11677i	−0.492260	+	0.492260i
$344$	7.93762			0.427968
$345$	−6.97726	+	15.9279i	−0.375643	+	0.857527i
$346$	−11.5137			−0.618980
$347$	−9.05827	+	9.05827i	−0.486273	+	0.486273i	−0.907128	−	0.420855i	$-0.861730\pi$
$347$	−9.05827	+	9.05827i	−0.486273	+	0.486273i	0.420855	+	0.907128i	$0.361730\pi$
$348$	−0.580794	+	1.37690i	−0.0311338	+	0.0738097i
$349$		−	0.0529227i		−	0.00283289i	−0.999999	−	0.00141644i	$-0.999549\pi$
$349$		−	0.0529227i		−	0.00283289i	0.999999	−	0.00141644i	$-0.000450868\pi$
$350$	0.135728	−	4.94966i	0.00725495	−	0.264570i
$351$	1.90206	+	0.831460i	0.101524	+	0.0443800i
$352$	−3.12700	−	3.12700i	−0.166669	−	0.166669i
$353$	2.59840	+	2.59840i	0.138299	+	0.138299i	0.772867	−	0.634568i	$-0.218822\pi$
$353$	2.59840	+	2.59840i	0.138299	+	0.138299i	−0.634568	+	0.772867i	$0.718822\pi$
$354$	−1.36832	+	0.556436i	−0.0727255	+	0.0295742i
$355$	−4.07910	+	3.96877i	−0.216496	+	0.210641i
$356$			2.60883i			0.138268i
$357$	−2.81549	−	1.18761i	−0.149012	−	0.0628550i
$358$	−9.04082	+	9.04082i	−0.477822	+	0.477822i
$359$	21.5350			1.13658			0.568288	−	0.822830i	$-0.307606\pi$
$359$	21.5350			1.13658			0.568288	+	0.822830i	$0.307606\pi$
$360$	4.86811	−	4.61536i	0.256572	−	0.243251i
$361$	−7.08053			−0.372660
$362$	1.93574	−	1.93574i	0.101740	−	0.101740i
$363$	−13.6547	−	5.75973i	−0.716686	−	0.302307i
$364$			0.395624i			0.0207364i
$365$	−28.2304	−	0.386989i	−1.47765	−	0.0202559i
$366$	−5.34147	+	2.17214i	−0.279203	+	0.113539i
$367$	20.7979	+	20.7979i	1.08564	+	1.08564i	0.995972	+	0.0896685i	$0.0285807\pi$
$367$	20.7979	+	20.7979i	1.08564	+	1.08564i	0.0896685	+	0.995972i	$0.471419\pi$
$368$	−3.17479	−	3.17479i	−0.165497	−	0.165497i
$369$	20.2104	−	19.6941i	1.05211	−	1.02524i
$370$	−2.47132	−	2.54002i	−0.128478	−	0.132049i
$371$			10.2807i			0.533745i
$372$	0.673165	−	1.59589i	0.0349020	−	0.0827428i
$373$	13.2229	−	13.2229i	0.684658	−	0.684658i	−0.276388	−	0.961046i	$-0.589138\pi$
$373$	13.2229	−	13.2229i	0.684658	−	0.684658i	0.961046	+	0.276388i	$0.0891376\pi$
$374$	7.87819			0.407372
$375$	−18.2231	+	6.55112i	−0.941039	+	0.338299i
$376$	−8.42986			−0.434737
$377$	−0.243725	+	0.243725i	−0.0125525	+	0.0125525i
$378$	−1.87658	−	4.79139i	−0.0965208	−	0.246443i
$379$		−	8.35532i		−	0.429184i	−0.976704	−	0.214592i	$-0.931158\pi$
$379$		−	8.35532i		−	0.429184i	0.976704	−	0.214592i	$-0.0688422\pi$
$380$	−7.96330	−	8.18466i	−0.408508	−	0.419864i
$381$	−8.33551	−	20.4977i	−0.427041	−	1.05013i
$382$	−4.45412	−	4.45412i	−0.227892	−	0.227892i
$383$	5.02031	+	5.02031i	0.256526	+	0.256526i	0.823640	−	0.567114i	$-0.191940\pi$
$383$	5.02031	+	5.02031i	0.256526	+	0.256526i	−0.567114	+	0.823640i	$0.691940\pi$
$384$	0.652462	+	1.60446i	0.0332958	+	0.0818773i
$385$	9.79163	+	0.134226i	0.499028	+	0.00684078i
$386$			12.1156i			0.616668i
$387$	−23.8109	−	0.308069i	−1.21037	−	0.0156600i
$388$	−11.2793	+	11.2793i	−0.572620	+	0.572620i
$389$	28.9564			1.46815			0.734073	−	0.679071i	$-0.237617\pi$
$389$	28.9564			1.46815			0.734073	+	0.679071i	$0.237617\pi$
$390$	1.44113	−	0.563147i	0.0729742	−	0.0285160i
$391$	7.99861			0.404507
$392$	−4.25629	+	4.25629i	−0.214975	+	0.214975i
$393$	−7.19490	+	17.0571i	−0.362935	+	0.860417i
$394$		−	0.935795i		−	0.0471447i
$395$	3.41294	−	3.32063i	0.171724	−	0.167079i
$396$	9.25884	+	9.50156i	0.465274	+	0.477472i
$397$	−18.5427	−	18.5427i	−0.930629	−	0.930629i	0.0671160	−	0.997745i	$-0.478620\pi$
$397$	−18.5427	−	18.5427i	−0.930629	−	0.930629i	−0.997745	+	0.0671160i	$0.978620\pi$
$398$	12.0073	+	12.0073i	0.601873	+	0.601873i
$399$	−8.11439	+	3.29976i	−0.406228	+	0.165195i
$400$	0.137056	−	4.99812i	0.00685282	−	0.249906i
$401$			21.3665i			1.06699i	0.845803	+	0.533496i	$0.179122\pi$
$401$			21.3665i			1.06699i	−0.845803	+	0.533496i	$0.820878\pi$
$402$	15.8113	+	6.66939i	0.788594	+	0.332639i
$403$	0.282488	−	0.282488i	0.0140717	−	0.0140717i
$404$	−3.97281			−0.197655
$405$	−14.7822	+	13.6560i	−0.734535	+	0.678571i
$406$	0.854417			0.0424040
$407$	4.95589	−	4.95589i	0.245654	−	0.245654i
$408$	−2.84306	−	1.19924i	−0.140752	−	0.0593711i
$409$		−	12.6304i		−	0.624535i	−0.949994	−	0.312267i	$-0.898911\pi$
$409$		−	12.6304i		−	0.624535i	0.949994	−	0.312267i	$-0.101089\pi$
$410$	0.288302	−	21.0313i	0.0142382	−	1.03866i
$411$	7.11053	−	2.89153i	0.350737	−	0.142629i
$412$	−4.23054	−	4.23054i	−0.208424	−	0.208424i
$413$	0.597191	+	0.597191i	0.0293858	+	0.0293858i
$414$	9.40036	+	9.64679i	0.462002	+	0.474114i
$415$	0.135448	−	9.88080i	0.00664889	−	0.485030i
$416$			0.399498i			0.0195870i
$417$	14.5224	−	34.4285i	0.711163	−	1.68597i
$418$	15.9693	−	15.9693i	0.781083	−	0.781083i
$419$	27.4856			1.34276			0.671381	−	0.741113i	$-0.265702\pi$
$419$	27.4856			1.34276			0.671381	+	0.741113i	$0.265702\pi$
$420$	−3.51314	−	1.53895i	−0.171424	−	0.0750929i
$421$	−12.5192			−0.610147			−0.305073	−	0.952329i	$-0.598681\pi$
$421$	−12.5192			−0.610147			−0.305073	+	0.952329i	$0.598681\pi$
$422$	−7.67721	+	7.67721i	−0.373721	+	0.373721i
$423$	25.2875	+	0.327174i	1.22952	+	0.0159077i
$424$			10.3813i			0.504161i
$425$	6.12351	+	6.46882i	0.297034	+	0.313784i
$426$	1.66065	+	4.08367i	0.0804586	+	0.197855i
$427$	2.33123	+	2.33123i	0.112816	+	0.112816i
$428$	−10.3058	−	10.3058i	−0.498150	−	0.498150i
$429$	1.15269	+	2.83456i	0.0556523	+	0.136854i
$430$	−12.7213	+	12.3773i	−0.613477	+	0.596885i
$431$		−	9.08020i		−	0.437378i	−0.975795	−	0.218689i	$-0.929822\pi$
$431$		−	9.08020i		−	0.437378i	0.975795	−	0.218689i	$-0.0701780\pi$
$432$	−1.89495	−	4.83830i	−0.0911709	−	0.232783i
$433$	−6.99720	+	6.99720i	−0.336264	+	0.336264i	−0.854959	−	0.518695i	$-0.826418\pi$
$433$	−6.99720	+	6.99720i	−0.336264	+	0.336264i	0.518695	+	0.854959i	$0.326418\pi$
$434$	−0.990304			−0.0475361
$435$	−1.21621	−	3.11235i	−0.0583128	−	0.149226i
$436$	−6.25281			−0.299455
$437$	16.2134	−	16.2134i	0.775591	−	0.775591i
$438$	−8.49952	+	20.1500i	−0.406123	+	0.962803i
$439$		−	37.6408i		−	1.79650i	−0.439486	−	0.898249i	$-0.644840\pi$
$439$		−	37.6408i		−	1.79650i	0.439486	−	0.898249i	$-0.355160\pi$
$440$	9.88750	+	0.135540i	0.471368	+	0.00646162i
$441$	12.9330	−	12.6026i	0.615856	−	0.600124i
$442$	−0.503250	−	0.503250i	−0.0239372	−	0.0239372i
$443$	14.9275	+	14.9275i	0.709225	+	0.709225i	0.966372	−	0.257147i	$-0.0827824\pi$
$443$	14.9275	+	14.9275i	0.709225	+	0.709225i	−0.257147	+	0.966372i	$0.582782\pi$
$444$	−2.54287	+	1.03407i	−0.120679	+	0.0490748i
$445$	−4.06800	−	4.18108i	−0.192842	−	0.198202i
$446$			0.205364i			0.00972426i
$447$	9.91388	+	4.18180i	0.468911	+	0.197792i
$448$	0.700251	−	0.700251i	0.0330837	−	0.0330837i
$449$	20.5392			0.969305			0.484653	−	0.874707i	$-0.338946\pi$
$449$	20.5392			0.969305			0.484653	+	0.874707i	$0.338946\pi$
$450$	−0.605119	+	14.9878i	−0.0285256	+	0.706531i
$451$	41.5972			1.95874
$452$	8.71474	−	8.71474i	0.409907	−	0.409907i
$453$	23.2393	+	9.80265i	1.09188	+	0.460569i
$454$			21.1047i			0.990492i
$455$	−0.616904	−	0.634052i	−0.0289209	−	0.0297248i
$456$	−8.19384	+	3.33207i	−0.383712	+	0.156038i
$457$	1.21507	+	1.21507i	0.0568387	+	0.0568387i	0.734955	−	0.678116i	$-0.237203\pi$
$457$	1.21507	+	1.21507i	0.0568387	+	0.0568387i	−0.678116	+	0.734955i	$0.737203\pi$
$458$	−12.7956	−	12.7956i	−0.597897	−	0.597897i
$459$	8.48192	+	3.70776i	0.395902	+	0.173063i
$460$	10.0386	+	0.137612i	0.468053	+	0.00641618i
$461$		−	5.57688i		−	0.259741i	−0.991531	−	0.129871i	$-0.958544\pi$
$461$		−	5.57688i		−	0.259741i	0.991531	−	0.129871i	$-0.0414562\pi$
$462$	2.94803	−	6.98896i	0.137155	−	0.325156i
$463$	−15.0409	+	15.0409i	−0.699009	+	0.699009i	−0.964197	−	0.265188i	$-0.914566\pi$
$463$	−15.0409	+	15.0409i	−0.699009	+	0.699009i	0.265188	+	0.964197i	$0.414566\pi$
$464$	0.862782			0.0400537
$465$	1.40964	+	3.60734i	0.0653703	+	0.167287i
$466$	17.9466			0.831358
$467$	23.1199	−	23.1199i	1.06986	−	1.06986i	0.0724925	−	0.997369i	$-0.476905\pi$
$467$	23.1199	−	23.1199i	1.06986	−	1.06986i	0.997369	−	0.0724925i	$-0.0230953\pi$
$468$	0.0155050	−	1.19839i	0.000716721	−	0.0553957i
$469$		−	9.81146i		−	0.453051i
$470$	13.5102	−	13.1448i	0.623180	−	0.606326i
$471$	−10.3898	−	25.5493i	−0.478735	−	1.17725i
$472$	0.603038	+	0.603038i	0.0277571	+	0.0277571i
$473$	−24.8209	−	24.8209i	−1.14127	−	1.14127i
$474$	−1.38945	−	3.41677i	−0.0638193	−	0.156937i
$475$	25.5250	+	0.699935i	1.17117	+	0.0321152i
$476$			1.76422i			0.0808629i
$477$	0.402913	−	31.1413i	0.0184481	−	1.42586i
$478$	7.40247	−	7.40247i	0.338581	−	0.338581i
$479$	35.0571			1.60180			0.800900	−	0.598799i	$-0.204355\pi$
$479$	35.0571			1.60180			0.800900	+	0.598799i	$0.204355\pi$
$480$	−3.54754	−	1.55401i	−0.161922	−	0.0709307i
$481$	−0.633153			−0.0288693
$482$	−4.65326	+	4.65326i	−0.211950	+	0.211950i
$483$	2.99309	−	7.09578i	0.136190	−	0.322869i
$484$			8.55620i			0.388918i
$485$	0.488903	−	35.6649i	0.0221999	−	1.61946i
$486$	5.49660	+	14.5872i	0.249331	+	0.661690i
$487$	9.20945	+	9.20945i	0.417320	+	0.417320i	0.884279	−	0.466959i	$-0.154650\pi$
$487$	9.20945	+	9.20945i	0.417320	+	0.417320i	−0.466959	+	0.884279i	$0.654650\pi$
$488$	2.35406	+	2.35406i	0.106563	+	0.106563i
$489$	−31.3699	+	12.7567i	−1.41860	+	0.576879i
$490$	0.184489	−	13.4583i	0.00833438	−	0.607984i
$491$		−	32.9660i		−	1.48774i	−0.668326	−	0.743868i	$-0.732989\pi$
$491$		−	32.9660i		−	1.48774i	0.668326	−	0.743868i	$-0.267011\pi$
$492$	−15.0115	−	6.33204i	−0.676771	−	0.285470i
$493$	−1.08685	+	1.08685i	−0.0489494	+	0.0489494i
$494$	−2.04020			−0.0917929
$495$	−29.6548	−	0.790333i	−1.33288	−	0.0355228i
$496$	−1.00000			−0.0449013
$497$	1.78228	−	1.78228i	0.0799461	−	0.0799461i
$498$	−7.05261	−	2.97488i	−0.316035	−	0.133308i
$499$			28.0406i			1.25527i	0.778508	+	0.627635i	$0.215977\pi$
$499$			28.0406i			1.25527i	−0.778508	+	0.627635i	$0.784023\pi$
$500$	7.57400	+	8.22402i	0.338720	+	0.367789i
$501$	−40.9970	+	16.6717i	−1.83161	+	0.744835i
$502$	2.08528	+	2.08528i	0.0930705	+	0.0930705i
$503$	26.9938	+	26.9938i	1.20360	+	1.20360i	0.973065	+	0.230530i	$0.0740461\pi$
$503$	26.9938	+	26.9938i	1.20360	+	1.20360i	0.230530	+	0.973065i	$0.425954\pi$
$504$	−2.12775	+	2.07340i	−0.0947777	+	0.0923565i
$505$	6.36708	−	6.19487i	0.283331	−	0.275668i
$506$			19.8551i			0.882667i
$507$	−8.64370	+	20.4918i	−0.383880	+	0.910073i
$508$	−9.03363	+	9.03363i	−0.400802	+	0.400802i
$509$	30.0807			1.33330			0.666652	−	0.745369i	$-0.267727\pi$
$509$	30.0807			1.33330			0.666652	+	0.745369i	$0.267727\pi$
$510$	6.42646	−	2.51126i	0.284568	−	0.111200i
$511$	12.5038			0.553135
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	24.7088	−	9.67735i	1.09092	−	0.427265i
$514$			4.69882i			0.207256i
$515$	13.3769	+	0.183373i	0.589456	+	0.00808040i
$516$	5.17899	+	12.7356i	0.227992	+	0.560653i
$517$	26.3601	+	26.3601i	1.15932	+	1.15932i
$518$	1.10981	+	1.10981i	0.0487622	+	0.0487622i
$519$	−7.51225	−	18.4733i	−0.329751	−	0.810887i
$520$	−0.622944	−	0.640260i	−0.0273179	−	0.0280773i
$521$			24.4421i			1.07083i	0.844589	+	0.535415i	$0.179845\pi$
$521$			24.4421i			1.07083i	−0.844589	+	0.535415i	$0.820155\pi$
$522$	−2.58813	−	0.0334857i	−0.113279	−	0.00146563i
$523$	−6.56960	+	6.56960i	−0.287269	+	0.287269i	−0.835999	−	0.548731i	$-0.815111\pi$
$523$	−6.56960	+	6.56960i	−0.287269	+	0.287269i	0.548731	+	0.835999i	$0.315111\pi$
$524$	10.6882			0.466915
$525$	8.03009	−	3.01170i	0.350462	−	0.131441i
$526$	20.3615			0.887805
$527$	1.25971	−	1.25971i	0.0548737	−	0.0548737i
$528$	2.97689	−	7.05739i	0.129553	−	0.307133i
$529$		−	2.84140i		−	0.123539i
$530$	−16.1878	−	16.6378i	−0.703152	−	0.722698i
$531$	−1.78556	−	1.83237i	−0.0774866	−	0.0795180i
$532$	3.57612	+	3.57612i	0.155044	+	0.155044i
$533$	−2.65718	−	2.65718i	−0.115095	−	0.115095i
$534$	−4.18577	+	1.70216i	−0.181136	+	0.0736598i
$535$	32.5868	+	0.446706i	1.40885	+	0.0193128i
$536$		−	9.90752i		−	0.427940i
$537$	−20.4044	−	8.60685i	−0.880517	−	0.371413i
$538$	17.3274	−	17.3274i	0.747038	−	0.747038i
$539$	26.6188			1.14655
$540$	10.5814	+	4.79934i	0.455352	+	0.206531i
$541$	−11.5909			−0.498330			−0.249165	−	0.968461i	$-0.580156\pi$
$541$	−11.5909			−0.498330			−0.249165	+	0.968461i	$0.580156\pi$
$542$	17.7733	−	17.7733i	0.763428	−	0.763428i
$543$	4.36881	+	1.84282i	0.187484	+	0.0790830i
$544$			1.78149i			0.0763809i
$545$	10.0212	−	9.75012i	0.429259	−	0.417649i
$546$	−0.634764	+	0.258130i	−0.0271654	+	0.0110469i
$547$	1.55467	+	1.55467i	0.0664731	+	0.0664731i	0.739562	−	0.673089i	$-0.235033\pi$
$547$	1.55467	+	1.55467i	0.0664731	+	0.0664731i	−0.673089	+	0.739562i	$0.735033\pi$
$548$	−3.13371	−	3.13371i	−0.133865	−	0.133865i
$549$	−6.97022	−	7.15294i	−0.297482	−	0.305280i
$550$	−16.0577	+	15.2005i	−0.684702	+	0.648153i
$551$			4.40615i			0.187708i
$552$	3.02240	−	7.16526i	0.128642	−	0.304974i
$553$	−1.49121	+	1.49121i	−0.0634129	+	0.0634129i
$554$	−16.5443			−0.702902
$555$	2.46291	−	5.62240i	0.104545	−	0.238658i
$556$	−21.5733			−0.914911
$557$	−13.8257	+	13.8257i	−0.585812	+	0.585812i	−0.936494	−	0.350682i	$-0.885950\pi$
$557$	−13.8257	+	13.8257i	−0.585812	+	0.585812i	0.350682	+	0.936494i	$0.385950\pi$
$558$	2.99975	+	0.0388113i	0.126989	+	0.00164301i
$559$			3.17106i			0.134122i
$560$	−0.0303525	+	2.21418i	−0.00128263	+	0.0935662i
$561$	5.14022	+	12.6402i	0.217020	+	0.533672i
$562$	−6.02425	−	6.02425i	−0.254118	−	0.254118i
$563$	20.7731	+	20.7731i	0.875481	+	0.875481i	0.993063	−	0.117582i	$-0.0375144\pi$
$563$	20.7731	+	20.7731i	0.875481	+	0.875481i	−0.117582	+	0.993063i	$0.537514\pi$
$564$	−5.50016	−	13.5254i	−0.231599	−	0.569521i
$565$	−0.377742	+	27.5558i	−0.0158917	+	1.15928i
$566$		−	19.9827i		−	0.839937i
$567$	6.46320	−	6.13710i	0.271429	−	0.257734i
$568$	1.79973	−	1.79973i	0.0755149	−	0.0755149i
$569$	7.64700			0.320579			0.160290	−	0.987070i	$-0.448757\pi$
$569$	7.64700			0.320579			0.160290	+	0.987070i	$0.448757\pi$
$570$	7.93621	−	18.1170i	0.332411	−	0.758836i
$571$	11.8402			0.495498			0.247749	−	0.968824i	$-0.420309\pi$
$571$	11.8402			0.495498			0.247749	+	0.968824i	$0.420309\pi$
$572$	1.24923	−	1.24923i	0.0522328	−	0.0522328i
$573$	4.24031	−	10.0526i	0.177142	−	0.419953i
$574$			9.31517i			0.388808i
$575$	−16.3031	+	15.4329i	−0.679887	+	0.643595i
$576$	−2.14859	+	2.09370i	−0.0895244	+	0.0872375i
$577$	1.73481	+	1.73481i	0.0722212	+	0.0722212i	0.742295	−	0.670074i	$-0.233737\pi$
$577$	1.73481	+	1.73481i	0.0722212	+	0.0722212i	−0.670074	+	0.742295i	$0.733737\pi$
$578$	9.77666	+	9.77666i	0.406655	+	0.406655i
$579$	−19.4390	+	7.90497i	−0.807858	+	0.328519i
$580$	−1.38275	+	1.34535i	−0.0574155	+	0.0558627i
$581$			4.37640i			0.181564i
$582$	−25.4565	−	10.7379i	−1.05521	−	0.445099i
$583$	32.4623	−	32.4623i	1.34445	−	1.34445i
$584$	12.6262			0.522476
$585$	1.84383	+	1.94480i	0.0762328	+	0.0804075i
$586$	−28.3768			−1.17223
$587$	6.61726	−	6.61726i	0.273124	−	0.273124i	−0.557233	−	0.830356i	$-0.688137\pi$
$587$	6.61726	−	6.61726i	0.273124	−	0.273124i	0.830356	+	0.557233i	$0.188137\pi$
$588$	−9.60611	−	4.05198i	−0.396149	−	0.167101i
$589$		−	5.10691i		−	0.210427i
$590$	−1.90679	−	0.0261388i	−0.0785015	−	0.00107612i
$591$	1.50145	−	0.610571i	0.0617612	−	0.0251155i
$592$	1.12067	+	1.12067i	0.0460594	+	0.0460594i
$593$	−31.9338	−	31.9338i	−1.31137	−	1.31137i	−0.920409	−	0.390957i	$-0.872144\pi$
$593$	−31.9338	−	31.9338i	−1.31137	−	1.31137i	−0.390957	−	0.920409i	$-0.627856\pi$
$594$	−9.20384	+	21.0548i	−0.377638	+	0.863891i
$595$	−2.75098	−	2.82745i	−0.112779	−	0.115914i
$596$		−	6.21215i		−	0.254460i
$597$	−11.4310	+	27.0996i	−0.467838	+	1.10911i
$598$	1.26832	−	1.26832i	0.0518655	−	0.0518655i
$599$	−41.0791			−1.67845			−0.839223	−	0.543787i	$-0.816990\pi$
$599$	−41.0791			−1.67845			−0.839223	+	0.543787i	$0.816990\pi$
$600$	8.10871	−	3.04118i	0.331037	−	0.124156i
$601$	23.6759			0.965761			0.482880	−	0.875686i	$-0.339591\pi$
$601$	23.6759			0.965761			0.482880	+	0.875686i	$0.339591\pi$
$602$	5.55832	−	5.55832i	0.226540	−	0.226540i
$603$	−0.384524	+	29.7201i	−0.0156590	+	1.21029i
$604$		−	14.5620i		−	0.592521i
$605$	−13.3418	−	13.7127i	−0.542423	−	0.557501i
$606$	−2.59211	−	6.37422i	−0.105297	−	0.258935i
$607$	5.00888	+	5.00888i	0.203304	+	0.203304i	0.801414	−	0.598110i	$-0.204081\pi$
$607$	5.00888	+	5.00888i	0.203304	+	0.203304i	−0.598110	+	0.801414i	$0.704081\pi$
$608$	3.61113	+	3.61113i	0.146451	+	0.146451i
$609$	0.557475	+	1.37088i	0.0225900	+	0.0555508i
$610$	−7.44348	−	0.102037i	−0.301378	−	0.00413135i
$611$		−	3.36771i		−	0.136243i
$612$	0.0691421	−	5.34403i	0.00279490	−	0.216020i
$613$	15.0946	−	15.0946i	0.609664	−	0.609664i	−0.333194	−	0.942858i	$-0.608127\pi$
$613$	15.0946	−	15.0946i	0.609664	−	0.609664i	0.942858	+	0.333194i	$0.108127\pi$
$614$	4.83877			0.195277
$615$	33.9320	−	13.2596i	1.36827	−	0.534677i
$616$	−4.37936			−0.176450
$617$	−26.1869	+	26.1869i	−1.05425	+	1.05425i	−0.0558042	+	0.998442i	$0.517772\pi$
$617$	−26.1869	+	26.1869i	−1.05425	+	1.05425i	−0.998442	+	0.0558042i	$0.982228\pi$
$618$	4.02747	−	9.54800i	0.162009	−	0.384077i
$619$			33.2037i			1.33457i	0.744803	+	0.667284i	$0.232543\pi$
$619$			33.2037i			1.33457i	−0.744803	+	0.667284i	$0.767457\pi$
$620$	1.60266	−	1.55932i	0.0643645	−	0.0626237i
$621$	−9.34452	+	21.3767i	−0.374983	+	0.857816i
$622$	9.57375	+	9.57375i	0.383872	+	0.383872i
$623$	1.82684	+	1.82684i	0.0731907	+	0.0731907i
$624$	−0.640978	+	0.260657i	−0.0256597	+	0.0104346i
$625$	−24.9624	−	1.37005i	−0.998497	−	0.0548020i
$626$			20.6601i			0.825742i
$627$	36.0414	+	15.2027i	1.43936	+	0.607139i
$628$	−11.2599	+	11.2599i	−0.449319	+	0.449319i
$629$	−2.82344			−0.112578
$630$	0.176985	−	6.64080i	0.00705125	−	0.264576i
$631$	−13.2694			−0.528248			−0.264124	−	0.964489i	$-0.585083\pi$
$631$	−13.2694			−0.528248			−0.264124	+	0.964489i	$0.585083\pi$
$632$	−1.50581	+	1.50581i	−0.0598981	+	0.0598981i
$633$	−17.3269	−	7.30870i	−0.688682	−	0.290495i
$634$		−	1.68201i		−	0.0668012i
$635$	0.391564	−	28.5642i	0.0155387	−	1.13353i
$636$	−16.6564	+	6.77342i	−0.660470	+	0.268583i
$637$	−1.70038	−	1.70038i	−0.0673714	−	0.0673714i
$638$	−2.69792	−	2.69792i	−0.106812	−	0.106812i
$639$	−5.46858	+	5.32888i	−0.216334	+	0.210807i
$640$	−0.0306496	+	2.23586i	−0.00121153	+	0.0883800i
$641$		−	39.1022i		−	1.54445i	−0.635352	−	0.772223i	$-0.719145\pi$
$641$		−	39.1022i		−	1.54445i	0.635352	−	0.772223i	$-0.280855\pi$
$642$	9.81111	−	23.2594i	0.387214	−	0.917975i
$643$	10.7210	−	10.7210i	0.422794	−	0.422794i	−0.463371	−	0.886165i	$-0.653360\pi$
$643$	10.7210	−	10.7210i	0.422794	−	0.422794i	0.886165	+	0.463371i	$0.153360\pi$
$644$	−4.44630			−0.175209
$645$	−28.1590	−	12.3352i	−1.10876	−	0.485697i
$646$	−9.09793			−0.357953
$647$	−19.5198	+	19.5198i	−0.767401	+	0.767401i	−0.977648	−	0.210247i	$-0.932573\pi$
$647$	−19.5198	+	19.5198i	−0.767401	+	0.767401i	0.210247	+	0.977648i	$0.432573\pi$
$648$	6.52648	−	6.19718i	0.256384	−	0.243448i
$649$		−	3.77139i		−	0.148040i
$650$	1.99674	+	0.0547538i	0.0783185	+	0.00214762i
$651$	−0.646136	−	1.58890i	−0.0253241	−	0.0622741i
$652$	13.8251	+	13.8251i	0.541434	+	0.541434i
$653$	0.461992	+	0.461992i	0.0180792	+	0.0180792i	0.716089	−	0.698009i	$-0.245931\pi$
$653$	0.461992	+	0.461992i	0.0180792	+	0.0180792i	−0.698009	+	0.716089i	$0.745931\pi$
$654$	−4.07972	−	10.0324i	−0.159530	−	0.392298i
$655$	−17.1296	+	16.6663i	−0.669307	+	0.651205i
$656$			9.40638i			0.367257i
$657$	−37.8755	−	0.490040i	−1.47766	−	0.0191183i
$658$	−5.90301	+	5.90301i	−0.230123	+	0.230123i
$659$	−16.5140			−0.643295			−0.321647	−	0.946860i	$-0.604237\pi$
$659$	−16.5140			−0.643295			−0.321647	+	0.946860i	$0.604237\pi$
$660$	6.23375	+	15.9525i	0.242648	+	0.620952i
$661$	41.4148			1.61085			0.805425	−	0.592697i	$-0.201937\pi$
$661$	41.4148			1.61085			0.805425	+	0.592697i	$0.201937\pi$
$662$	−9.67486	+	9.67486i	−0.376024	+	0.376024i
$663$	0.479093	−	1.13580i	0.0186064	−	0.0441107i
$664$			4.41925i			0.171500i
$665$	−11.3076	−	0.155007i	−0.438491	−	0.00601093i
$666$	−3.31825	−	3.40524i	−0.128579	−	0.131950i
$667$	−2.73915	−	2.73915i	−0.106060	−	0.106060i
$668$	18.0679	+	18.0679i	0.699070	+	0.699070i
$669$	−0.329498	+	0.133992i	−0.0127391	+	0.00518043i
$670$	15.4490	+	15.8784i	0.596846	+	0.613437i
$671$		−	14.7222i		−	0.568346i
$672$	1.58041	+	0.666638i	0.0609657	+	0.0257161i
$673$	−30.2179	+	30.2179i	−1.16481	+	1.16481i	−0.181405	+	0.983409i	$0.558064\pi$
$673$	−30.2179	+	30.2179i	−1.16481	+	1.16481i	−0.983409	+	0.181405i	$0.941936\pi$
$674$	−0.646306			−0.0248948
$675$	−24.4421	+	8.80807i	−0.940778	+	0.339023i
$676$	12.8404			0.493862
$677$	−9.35727	+	9.35727i	−0.359629	+	0.359629i	−0.863676	−	0.504047i	$-0.831844\pi$
$677$	−9.35727	+	9.35727i	−0.359629	+	0.359629i	0.504047	+	0.863676i	$0.331844\pi$
$678$	19.6685	+	8.29642i	0.755364	+	0.318622i
$679$			15.7967i			0.606221i
$680$	−2.77791	−	2.85513i	−0.106528	−	0.109489i
$681$	−33.8616	+	13.7700i	−1.29758	+	0.527668i
$682$	3.12700	+	3.12700i	0.119739	+	0.119739i
$683$	−10.0475	−	10.0475i	−0.384455	−	0.384455i	0.488249	−	0.872704i	$-0.337636\pi$
$683$	−10.0475	−	10.0475i	−0.384455	−	0.384455i	−0.872704	+	0.488249i	$0.837636\pi$
$684$	−10.6923	−	10.9726i	−0.408832	−	0.419549i
$685$	9.90872	+	0.135831i	0.378593	+	0.00518983i
$686$			12.8931i			0.492260i
$687$	12.1814	−	28.8786i	0.464748	−	1.10179i
$688$	5.61274	−	5.61274i	0.213984	−	0.213984i
$689$	−4.14731			−0.158000
$690$	6.32903	+	16.1964i	0.240942	+	0.616585i
$691$	−20.4686			−0.778664			−0.389332	−	0.921098i	$-0.627294\pi$
$691$	−20.4686			−0.778664			−0.389332	+	0.921098i	$0.627294\pi$
$692$	−8.14142	+	8.14142i	−0.309490	+	0.309490i
$693$	13.1370	+	0.169969i	0.499033	+	0.00645658i
$694$			12.8103i			0.486273i
$695$	34.5747	−	33.6396i	1.31149	−	1.27602i
$696$	0.562933	+	1.38430i	0.0213379	+	0.0524717i
$697$	−11.8493	−	11.8493i	−0.448823	−	0.448823i
$698$	−0.0374220	−	0.0374220i	−0.00141644	−	0.00141644i
$699$	11.7095	+	28.7945i	0.442892	+	1.08911i
$700$	−3.40396	−	3.59591i	−0.128658	−	0.135913i
$701$			14.9733i			0.565535i	0.959189	+	0.282767i	$0.0912524\pi$
$701$			14.9733i			0.565535i	−0.959189	+	0.282767i	$0.908748\pi$
$702$	1.93289	−	0.757029i	0.0729523	−	0.0285722i
$703$	−5.72319	+	5.72319i	−0.215854	+	0.215854i
$704$	−4.42224			−0.166669
$705$	29.9053	+	13.1001i	1.12630	+	0.493379i
$706$	3.67469			0.138299
$707$	−2.78196	+	2.78196i	−0.104627	+	0.104627i
$708$	−0.574091	+	1.36101i	−0.0215757	+	0.0511499i
$709$		−	6.59112i		−	0.247535i	−0.992311	−	0.123767i	$-0.960502\pi$
$709$		−	6.59112i		−	0.247535i	0.992311	−	0.123767i	$-0.0394976\pi$
$710$	−0.0780094	+	5.69070i	−0.00292764	+	0.213568i
$711$	4.57551	−	4.45862i	0.171595	−	0.167211i
$712$	1.84472	+	1.84472i	0.0691339	+	0.0691339i
$713$	3.17479	+	3.17479i	0.118897	+	0.118897i
$714$	−2.83062	+	1.15109i	−0.105933	+	0.0430783i
$715$	−0.0541479	+	3.95003i	−0.00202502	+	0.147723i
$716$			12.7857i			0.477822i
$717$	16.7068	+	7.04714i	0.623927	+	0.263180i
$718$	15.2276	−	15.2276i	0.568288	−	0.568288i
$719$	−25.2777			−0.942699			−0.471349	−	0.881947i	$-0.656233\pi$
$719$	−25.2777			−0.942699			−0.471349	+	0.881947i	$0.656233\pi$
$720$	0.178718	−	6.70582i	0.00666042	−	0.249911i
$721$	−5.92488			−0.220654
$722$	−5.00669	+	5.00669i	−0.186330	+	0.186330i
$723$	−10.5021	−	4.42990i	−0.390576	−	0.164750i
$724$		−	2.73755i		−	0.101740i
$725$	0.118250	−	4.31229i	0.00439169	−	0.160154i
$726$	−13.7281	+	5.58259i	−0.509497	+	0.207190i
$727$	2.42912	+	2.42912i	0.0900911	+	0.0900911i	0.750716	−	0.660625i	$-0.229709\pi$
$727$	2.42912	+	2.42912i	0.0900911	+	0.0900911i	−0.660625	+	0.750716i	$0.729709\pi$
$728$	0.279749	+	0.279749i	0.0103682	+	0.0103682i
$729$	−19.8183	+	18.3367i	−0.734012	+	0.679137i
$730$	−20.2356	+	19.6883i	−0.748952	+	0.728696i
$731$			14.1408i			0.523017i
$732$	−2.24106	+	5.31292i	−0.0828319	+	0.196371i
$733$	17.1919	−	17.1919i	0.634998	−	0.634998i	−0.314319	−	0.949317i	$-0.601776\pi$
$733$	17.1919	−	17.1919i	0.634998	−	0.634998i	0.949317	+	0.314319i	$0.101776\pi$
$734$	29.4126			1.08564
$735$	21.7137	−	8.48502i	0.800921	−	0.312975i
$736$	−4.48983			−0.165497
$737$	−30.9808	+	30.9808i	−1.14119	+	1.14119i
$738$	0.365074	−	28.2168i	0.0134386	−	1.03867i
$739$			44.8879i			1.65123i	0.564235	+	0.825614i	$0.309171\pi$
$739$			44.8879i			1.65123i	−0.564235	+	0.825614i	$0.690829\pi$
$740$	−3.54355	−	0.0485758i	−0.130264	−	0.00178568i
$741$	−1.33115	−	3.27342i	−0.0489011	−	0.120252i
$742$	7.26953	+	7.26953i	0.266873	+	0.266873i
$743$	14.7333	+	14.7333i	0.540514	+	0.540514i	0.923680	−	0.383166i	$-0.125166\pi$
$743$	14.7333	+	14.7333i	0.540514	+	0.540514i	−0.383166	+	0.923680i	$0.625166\pi$
$744$	−0.652462	−	1.60446i	−0.0239204	−	0.0588224i
$745$	9.68672	+	9.95599i	0.354894	+	0.364759i
$746$		−	18.7001i		−	0.684658i
$747$	0.171517	−	13.2566i	0.00627547	−	0.485035i
$748$	5.57072	−	5.57072i	0.203686	−	0.203686i
$749$	−14.4333			−0.527381
$750$	−8.25336	+	17.5180i	−0.301370	+	0.639669i
$751$	19.0621			0.695585			0.347792	−	0.937572i	$-0.386931\pi$
$751$	19.0621			0.695585			0.347792	+	0.937572i	$0.386931\pi$
$752$	−5.96081	+	5.96081i	−0.217368	+	0.217368i
$753$	−1.98518	+	4.70631i	−0.0723440	+	0.171507i
$754$			0.344680i			0.0125525i
$755$	22.7068	+	23.3380i	0.826387	+	0.849358i
$756$	−4.71497	−	2.06108i	−0.171482	−	0.0749609i
$757$	31.8979	+	31.8979i	1.15935	+	1.15935i	0.984616	+	0.174734i	$0.0559067\pi$
$757$	31.8979	+	31.8979i	1.15935	+	1.15935i	0.174734	+	0.984616i	$0.444093\pi$
$758$	−5.90811	−	5.90811i	−0.214592	−	0.214592i
$759$	−31.8567	+	12.9547i	−1.15633	+	0.470226i
$760$	−11.4183	−	0.156525i	−0.414186	−	0.00567776i
$761$		−	37.7081i		−	1.36692i	−0.729990	−	0.683458i	$-0.760475\pi$
$761$		−	37.7081i		−	1.36692i	0.729990	−	0.683458i	$-0.239525\pi$
$762$	−20.3882	−	8.60000i	−0.738586	−	0.311545i
$763$	−4.37854	+	4.37854i	−0.158514	+	0.158514i
$764$	−6.29907			−0.227892
$765$	8.22223	+	8.67250i	0.297276	+	0.313555i
$766$	7.09980			0.256526
$767$	−0.240912	+	0.240912i	−0.00869884	+	0.00869884i
$768$	1.59589	+	0.673165i	0.0575865	+	0.0242907i
$769$		−	40.7512i		−	1.46953i	−0.678323	−	0.734764i	$-0.737293\pi$
$769$		−	40.7512i		−	1.46953i	0.678323	−	0.734764i	$-0.262707\pi$
$770$	7.01864	−	6.82882i	0.252934	−	0.246093i
$771$	−7.53908	+	3.06580i	−0.271513	+	0.110412i
$772$	8.56703	+	8.56703i	0.308334	+	0.308334i
$773$	−22.9415	−	22.9415i	−0.825149	−	0.825149i	0.161692	−	0.986841i	$-0.448305\pi$
$773$	−22.9415	−	22.9415i	−0.825149	−	0.825149i	−0.986841	+	0.161692i	$0.948305\pi$
$774$	−17.0547	+	16.6190i	−0.613017	+	0.597357i
$775$	−0.137056	+	4.99812i	−0.00492321	+	0.179538i
$776$			15.9513i			0.572620i
$777$	−1.05654	+	2.50475i	−0.0379030	+	0.0898575i
$778$	20.4752	−	20.4752i	0.734073	−	0.734073i
$779$	−48.0375			−1.72112
$780$	0.620825	−	1.41723i	0.0222291	−	0.0507451i
$781$	−11.2555			−0.402753
$782$	5.65587	−	5.65587i	0.202253	−	0.202253i
$783$	−1.63493	−	4.17440i	−0.0584276	−	0.149181i
$784$			6.01930i			0.214975i
$785$	0.488062	−	35.6036i	0.0174197	−	1.27075i
$786$	6.97363	+	17.1488i	0.248741	+	0.611676i
$787$	−8.35326	−	8.35326i	−0.297761	−	0.297761i	0.542375	−	0.840136i	$-0.317525\pi$
$787$	−8.35326	−	8.35326i	−0.297761	−	0.297761i	−0.840136	+	0.542375i	$0.817525\pi$
$788$	−0.661707	−	0.661707i	−0.0235723	−	0.0235723i
$789$	13.2851	+	32.6693i	0.472963	+	1.16306i
$790$	0.0652697	−	4.76135i	0.00232219	−	0.169401i
$791$		−	12.2050i		−	0.433960i
$792$	13.2656	+	0.171633i	0.471373	+	0.00609871i
$793$	−0.940441	+	0.940441i	−0.0333960	+	0.0333960i
$794$	−26.2233			−0.930629
$795$	16.1327	−	36.8281i	0.572168	−	1.30616i
$796$	16.9809			0.601873
$797$	−16.8402	+	16.8402i	−0.596509	+	0.596509i	−0.939382	−	0.342873i	$-0.888600\pi$
$797$	−16.8402	+	16.8402i	−0.596509	+	0.596509i	0.342873	+	0.939382i	$0.388600\pi$
$798$	−3.40446	+	8.07102i	−0.120517	+	0.285711i
$799$		−	15.0177i		−	0.531289i
$800$	−3.43729	−	3.63112i	−0.121527	−	0.128379i
$801$	−5.46211	−	5.60530i	−0.192994	−	0.198054i
$802$	15.1084	+	15.1084i	0.533496	+	0.533496i
$803$	−39.4821	−	39.4821i	−1.39329	−	1.39329i
$804$	15.8962	−	6.46428i	0.560617	−	0.227978i
$805$	7.12592	−	6.93319i	0.251156	−	0.244363i
$806$		−	0.399498i		−	0.0140717i
$807$	39.1067	+	16.4957i	1.37662	+	0.580675i
$808$	−2.80920	+	2.80920i	−0.0988274	+	0.0988274i
$809$	37.7696			1.32791			0.663954	−	0.747774i	$-0.268877\pi$
$809$	37.7696			1.32791			0.663954	+	0.747774i	$0.268877\pi$
$810$	−0.796370	+	20.1088i	−0.0279816	+	0.706553i
$811$	−20.1953			−0.709154			−0.354577	−	0.935027i	$-0.615375\pi$
$811$	−20.1953			−0.709154			−0.354577	+	0.935027i	$0.615375\pi$
$812$	0.604164	−	0.604164i	0.0212020	−	0.0212020i
$813$	40.1129	+	16.9201i	1.40682	+	0.593415i
$814$		−	7.00869i		−	0.245654i
$815$	−43.7148	−	0.599252i	−1.53126	−	0.0209909i
$816$	−2.85834	+	1.16236i	−0.100062	+	0.0406906i
$817$	28.6638	+	28.6638i	1.00282	+	1.00282i
$818$	−8.93107	−	8.93107i	−0.312267	−	0.312267i
$819$	−0.828318	−	0.850033i	−0.0289438	−	0.0297026i
$820$	−14.6675	−	15.0753i	−0.512212	−	0.526451i
$821$			33.8991i			1.18309i	0.806273	+	0.591543i	$0.201481\pi$
$821$			33.8991i			1.18309i	−0.806273	+	0.591543i	$0.798519\pi$
$822$	2.98328	−	7.07253i	0.104054	−	0.246683i
$823$	16.1065	−	16.1065i	0.561436	−	0.561436i	−0.368279	−	0.929715i	$-0.620053\pi$
$823$	16.1065	−	16.1065i	0.561436	−	0.561436i	0.929715	+	0.368279i	$0.120053\pi$
$824$	−5.98289			−0.208424
$825$	−34.8657	−	15.8461i	−1.21387	−	0.551692i
$826$	0.844556			0.0293858
$827$	−19.0742	+	19.0742i	−0.663275	+	0.663275i	−0.956151	−	0.292875i	$-0.905388\pi$
$827$	−19.0742	+	19.0742i	−0.663275	+	0.663275i	0.292875	+	0.956151i	$0.405388\pi$
$828$	13.4684	+	0.174256i	0.468058	+	0.00605583i
$829$		−	16.1596i		−	0.561247i	−0.959818	−	0.280623i	$-0.909459\pi$
$829$		−	16.1596i		−	0.561247i	0.959818	−	0.280623i	$-0.0905412\pi$
$830$	−6.89101	−	7.08256i	−0.239190	−	0.245839i
$831$	−10.7946	−	26.5447i	−0.374459	−	0.920827i
$832$	0.282488	+	0.282488i	0.00979350	+	0.00979350i
$833$	−7.58255	−	7.58255i	−0.262720	−	0.262720i
$834$	−14.0757	−	34.6135i	−0.487403	−	1.19857i
$835$	−57.1305	−	0.783157i	−1.97708	−	0.0271023i
$836$		−	22.5840i		−	0.781083i
$837$	1.89495	+	4.83830i	0.0654991	+	0.167236i
$838$	19.4353	−	19.4353i	0.671381	−	0.671381i
$839$	3.57570			0.123447			0.0617234	−	0.998093i	$-0.480340\pi$
$839$	3.57570			0.123447			0.0617234	+	0.998093i	$0.480340\pi$
$840$	−3.57237	+	1.39597i	−0.123258	+	0.0481655i
$841$	−28.2556			−0.974331
$842$	−8.85239	+	8.85239i	−0.305073	+	0.305073i
$843$	5.73507	−	13.5963i	0.197526	−	0.468280i
$844$			10.8572i			0.373721i
$845$	−20.5788	+	20.0223i	−0.707933	+	0.688787i
$846$	18.1123	−	17.6496i	0.622713	−	0.606805i
$847$	5.99149	+	5.99149i	0.205870	+	0.205870i
$848$	7.34070	+	7.34070i	0.252081	+	0.252081i
$849$	32.0615	−	13.0380i	1.10035	−	0.447462i
$850$	8.90412	+	0.244165i	0.305409	+	0.00837480i
$851$		−	7.11582i		−	0.243927i
$852$	4.06185	+	1.71334i	0.139157	+	0.0586980i
$853$	13.5352	−	13.5352i	0.463435	−	0.463435i	−0.436345	−	0.899780i	$-0.643727\pi$
$853$	13.5352	−	13.5352i	0.463435	−	0.463435i	0.899780	+	0.436345i	$0.143727\pi$
$854$	3.29686			0.112816
$855$	34.2460	+	0.912696i	1.17119	+	0.0312135i
$856$	−14.5746			−0.498150
$857$	−20.5962	+	20.5962i	−0.703553	+	0.703553i	−0.965171	−	0.261618i	$-0.915744\pi$
$857$	−20.5962	+	20.5962i	−0.703553	+	0.703553i	0.261618	+	0.965171i	$0.415744\pi$
$858$	2.81941	+	1.18926i	0.0962531	+	0.0406008i
$859$			21.4891i			0.733197i	0.930379	+	0.366599i	$0.119478\pi$
$859$			21.4891i			0.733197i	−0.930379	+	0.366599i	$0.880522\pi$
$860$	−0.243285	+	17.7474i	−0.00829595	+	0.605181i
$861$	−14.9458	+	6.07780i	−0.509352	+	0.207131i
$862$	−6.42067	−	6.42067i	−0.218689	−	0.218689i
$863$	38.3646	+	38.3646i	1.30595	+	1.30595i	0.924315	+	0.381630i	$0.124637\pi$
$863$	38.3646	+	38.3646i	1.30595	+	1.30595i	0.381630	+	0.924315i	$0.375363\pi$
$864$	−4.76113	−	2.08126i	−0.161977	−	0.0708060i
$865$	0.352891	−	25.7430i	0.0119986	−	0.875288i
$866$			9.89553i			0.336264i
$867$	−9.30736	+	22.0652i	−0.316095	+	0.749372i
$868$	−0.700251	+	0.700251i	−0.0237681	+	0.0237681i
$869$	9.41734			0.319462
$870$	−3.06075	−	1.34078i	−0.103769	−	0.0454565i
$871$	3.95803			0.134113
$872$	−4.42141	+	4.42141i	−0.149728	+	0.149728i
$873$	0.619092	−	47.8500i	0.0209531	−	1.61948i
$874$		−	22.9292i		−	0.775591i
$875$	11.0626	+	0.455173i	0.373983	+	0.0153877i
$876$	8.23812	+	20.2583i	0.278340	+	0.684463i
$877$	−15.3051	−	15.3051i	−0.516818	−	0.516818i	0.399789	−	0.916607i	$-0.369083\pi$
$877$	−15.3051	−	15.3051i	−0.516818	−	0.516818i	−0.916607	+	0.399789i	$0.869083\pi$
$878$	−26.6161	−	26.6161i	−0.898249	−	0.898249i
$879$	−18.5148	−	45.5294i	−0.624488	−	1.53567i
$880$	7.08736	−	6.89568i	0.238915	−	0.232453i
$881$			36.8177i			1.24042i	0.784436	+	0.620209i	$0.212952\pi$
$881$			36.8177i			1.24042i	−0.784436	+	0.620209i	$0.787048\pi$
$882$	0.233617	−	18.0564i	0.00786629	−	0.607990i
$883$	−23.4905	+	23.4905i	−0.790519	+	0.790519i	−0.981579	−	0.191059i	$-0.938808\pi$
$883$	−23.4905	+	23.4905i	−0.790519	+	0.790519i	0.191059	+	0.981579i	$0.438808\pi$
$884$	−0.711703			−0.0239372
$885$	−1.20217	−	3.07643i	−0.0404106	−	0.103413i
$886$	21.1106			0.709225
$887$	−17.6666	+	17.6666i	−0.593186	+	0.593186i	−0.938491	−	0.345305i	$-0.887776\pi$
$887$	−17.6666	+	17.6666i	−0.593186	+	0.593186i	0.345305	+	0.938491i	$0.387776\pi$
$888$	−1.06688	+	2.52928i	−0.0358022	+	0.0848769i
$889$			12.6516i			0.424321i
$890$	−5.83298	−	0.0799598i	−0.195522	−	0.00268026i
$891$	−39.7868	−	1.02971i	−1.33291	−	0.0344966i
$892$	0.145214	+	0.145214i	0.00486213	+	0.00486213i
$893$	−30.4413	−	30.4413i	−1.01868	−	1.01868i
$894$	9.96715	−	4.05319i	0.333351	−	0.135559i
$895$	−19.9369	−	20.4911i	−0.666417	−	0.684942i
$896$		−	0.990304i		−	0.0330837i
$897$	2.86250	+	1.20744i	0.0955762	+	0.0403153i
$898$	14.5234	−	14.5234i	0.484653	−	0.484653i
$899$	−0.862782			−0.0287754
$900$	10.1701	+	11.0259i	0.339003	+	0.367528i
$901$	−18.4943			−0.616133
$902$	29.4137	−	29.4137i	0.979369	−	0.979369i
$903$	12.5447	+	5.29151i	0.417462	+	0.176091i
$904$		−	12.3245i		−	0.409907i
$905$	4.26871	+	4.38737i	0.141897	+	0.145841i
$906$	23.3642	−	9.50118i	0.776224	−	0.315655i
$907$	−28.4548	−	28.4548i	−0.944825	−	0.944825i	0.0537306	−	0.998555i	$-0.482889\pi$
$907$	−28.4548	−	28.4548i	−0.944825	−	0.944825i	−0.998555	+	0.0537306i	$0.982889\pi$
$908$	14.9233	+	14.9233i	0.495246	+	0.495246i
$909$	8.53593	−	8.31787i	0.283119	−	0.275886i
$910$	−0.884560	−	0.0121257i	−0.0293229	−	0.000401965i
$911$		−	8.59612i		−	0.284802i	−0.989809	−	0.142401i	$-0.954518\pi$
$911$		−	8.59612i		−	0.284802i	0.989809	−	0.142401i	$-0.0454823\pi$
$912$	−3.43779	+	8.15004i	−0.113837	+	0.269875i
$913$	13.8190	−	13.8190i	0.457341	−	0.457341i
$914$	1.71837			0.0568387
$915$	−4.69288	−	12.0093i	−0.155142	−	0.397017i
$916$	−18.0957			−0.597897
$917$	7.48441	−	7.48441i	0.247157	−	0.247157i
$918$	8.61940	−	3.37584i	0.284483	−	0.111419i
$919$			43.3194i			1.42897i	0.699648	+	0.714487i	$0.253340\pi$
$919$			43.3194i			1.42897i	−0.699648	+	0.714487i	$0.746660\pi$
$920$	7.19569	−	7.00108i	0.237235	−	0.230819i
$921$	3.15711	+	7.76361i	0.104030	+	0.255820i
$922$	−3.94345	−	3.94345i	−0.129871	−	0.129871i
$923$	0.718987	+	0.718987i	0.0236658	+	0.0236658i
$924$	−2.85737	−	7.02651i	−0.0940005	−	0.231155i
$925$	5.75486	−	5.44767i	0.189219	−	0.179118i
$926$			21.2710i			0.699009i
$927$	17.9472	+	0.232204i	0.589462	+	0.00762657i
$928$	0.610079	−	0.610079i	0.0200268	−	0.0200268i
$929$	49.6565			1.62918			0.814588	−	0.580040i	$-0.196963\pi$
$929$	49.6565			1.62918			0.814588	+	0.580040i	$0.196963\pi$
$930$	3.54754	+	1.55401i	0.116328	+	0.0509581i
$931$	−30.7400			−1.00746
$932$	12.6901	−	12.6901i	0.415679	−	0.415679i
$933$	−9.11419	+	21.6072i	−0.298385	+	0.707388i
$934$		−	32.6965i		−	1.06986i
$935$	−0.241464	+	17.6145i	−0.00789671	+	0.576056i
$936$	−0.836428	−	0.858356i	−0.0273395	−	0.0280562i
$937$	−10.7151	−	10.7151i	−0.350048	−	0.350048i	0.510079	−	0.860128i	$-0.329616\pi$
$937$	−10.7151	−	10.7151i	−0.350048	−	0.350048i	−0.860128	+	0.510079i	$0.829616\pi$
$938$	−6.93775	−	6.93775i	−0.226526	−	0.226526i
$939$	−33.1482	+	13.4799i	−1.08175	+	0.439900i
$940$	0.258372	−	18.8480i	0.00842717	−	0.614753i
$941$		−	41.4459i		−	1.35110i	−0.737316	−	0.675549i	$-0.763907\pi$
$941$		−	41.4459i		−	1.35110i	0.737316	−	0.675549i	$-0.236093\pi$
$942$	−25.4127	−	10.7194i	−0.827992	−	0.349257i
$943$	29.8633	−	29.8633i	0.972482	−	0.972482i
$944$	0.852824			0.0277571
$945$	10.7704	−	4.04891i	0.350361	−	0.131711i
$946$	−35.1020			−1.14127
$947$	9.07927	−	9.07927i	0.295037	−	0.295037i	−0.544029	−	0.839066i	$-0.683102\pi$
$947$	9.07927	−	9.07927i	0.295037	−	0.295037i	0.839066	+	0.544029i	$0.183102\pi$
$948$	−3.39850	−	1.43353i	−0.110378	−	0.0465590i
$949$			5.04414i			0.163740i
$950$	18.5438	−	17.5539i	0.601640	−	0.569525i
$951$	2.69872	−	1.09745i	0.0875120	−	0.0355872i
$952$	1.24749	+	1.24749i	0.0404315	+	0.0404315i
$953$	2.70424	+	2.70424i	0.0875989	+	0.0875989i	0.749548	−	0.661950i	$-0.230271\pi$
$953$	2.70424	+	2.70424i	0.0875989	+	0.0875989i	−0.661950	+	0.749548i	$0.730271\pi$
$954$	−21.7354	−	22.3052i	−0.703708	−	0.722156i
$955$	10.0953	−	9.82226i	0.326676	−	0.317841i
$956$		−	10.4687i		−	0.338581i
$957$	2.56841	−	6.08899i	0.0830249	−	0.196829i
$958$	24.7891	−	24.7891i	0.800900	−	0.800900i
$959$	−4.38876			−0.141720
$960$	−3.60734	+	1.40964i	−0.116427	+	0.0454958i
$961$	1.00000			0.0322581
$962$	−0.447707	+	0.447707i	−0.0144347	+	0.0144347i
$963$	43.7202	+	0.565660i	1.40886	+	0.0182281i
$964$			6.58071i			0.211950i
$965$	−27.0888	−	0.371339i	−0.872018	−	0.0119538i
$966$	−2.90104	−	7.13391i	−0.0933395	−	0.229530i
$967$	8.01011	+	8.01011i	0.257588	+	0.257588i	0.824072	−	0.566485i	$-0.191697\pi$
$967$	8.01011	+	8.01011i	0.257588	+	0.257588i	−0.566485	+	0.824072i	$0.691697\pi$
$968$	6.05015	+	6.05015i	0.194459	+	0.194459i
$969$	−5.93605	−	14.5973i	−0.190693	−	0.468932i
$970$	−24.8732	−	25.5646i	−0.798630	−	0.820830i
$971$			23.2223i			0.745238i	0.927984	+	0.372619i	$0.121540\pi$
$971$			23.2223i			0.745238i	−0.927984	+	0.372619i	$0.878460\pi$
$972$	14.2014	+	6.42805i	0.455511	+	0.206180i
$973$	−15.1067	+	15.1067i	−0.484299	+	0.484299i
$974$	13.0241			0.417320
$975$	1.21495	+	3.23941i	0.0389094	+	0.103744i
$976$	3.32914			0.106563
$977$	36.1374	−	36.1374i	1.15614	−	1.15614i	0.170840	−	0.985299i	$-0.445352\pi$
$977$	36.1374	−	36.1374i	1.15614	−	1.15614i	0.985299	−	0.170840i	$-0.0546482\pi$
$978$	−13.1615	+	31.2022i	−0.420858	+	0.997737i
$979$		−	11.5369i		−	0.368720i
$980$	−9.38600	−	9.64690i	−0.299825	−	0.308159i
$981$	13.4347	−	13.0915i	0.428937	−	0.417980i
$982$	−23.3105	−	23.3105i	−0.743868	−	0.743868i
$983$	−6.21084	−	6.21084i	−0.198095	−	0.198095i	0.601088	−	0.799183i	$-0.294734\pi$
$983$	−6.21084	−	6.21084i	−0.198095	−	0.198095i	−0.799183	+	0.601088i	$0.794734\pi$
$984$	−15.0922	+	6.13730i	−0.481120	+	0.195650i
$985$	2.09230	+	0.0286818i	0.0666663	+	0.000913877i
$986$			1.53704i			0.0489494i
$987$	−13.3226	−	5.61966i	−0.424064	−	0.178876i
$988$	−1.44264	+	1.44264i	−0.0458965	+	0.0458965i
$989$	−35.6386			−1.13324
$990$	−21.5279	+	20.4102i	−0.684202	+	0.648680i
$991$	−29.2313			−0.928564			−0.464282	−	0.885687i	$-0.653688\pi$
$991$	−29.2313			−0.928564			−0.464282	+	0.885687i	$0.653688\pi$
$992$	−0.707107	+	0.707107i	−0.0224507	+	0.0224507i
$993$	−21.8354	−	9.21045i	−0.692926	−	0.292285i
$994$		−	2.52052i		−	0.0799461i
$995$	−27.2147	+	26.4787i	−0.862764	+	0.839430i
$996$	−7.09050	+	2.88339i	−0.224671	+	0.0913637i
$997$	33.1147	+	33.1147i	1.04875	+	1.04875i	0.998749	+	0.0500044i	$0.0159235\pi$
$997$	33.1147	+	33.1147i	1.04875	+	1.04875i	0.0500044	+	0.998749i	$0.484076\pi$
$998$	19.8277	+	19.8277i	0.627635	+	0.627635i
$999$	3.29854	−	7.54579i	0.104361	−	0.238738i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.g.497.19	yes	40
3.2	odd	2	inner	930.2.j.g.497.5	✓	40
5.3	odd	4	inner	930.2.j.g.683.5	yes	40
15.8	even	4	inner	930.2.j.g.683.19	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.g.497.5	✓	40	3.2	odd	2	inner
930.2.j.g.497.19	yes	40	1.1	even	1	trivial
930.2.j.g.683.5	yes	40	5.3	odd	4	inner
930.2.j.g.683.19	yes	40	15.8	even	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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.59589 + 0.673165i) q^{3} -1.00000i q^{4} +(1.55932 + 1.60266i) q^{5} +(1.60446 - 0.652462i) q^{6} +(-0.700251 - 0.700251i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.09370 + 2.14859i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.59589 + 0.673165i) q^{3} -1.00000i q^{4} +(1.55932 + 1.60266i) q^{5} +(1.60446 - 0.652462i) q^{6} +(-0.700251 - 0.700251i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.09370 + 2.14859i) q^{9} +(2.23586 + 0.0306496i) q^{10} +4.42224i q^{11} +(0.673165 - 1.59589i) q^{12} +(0.282488 - 0.282488i) q^{13} -0.990304 q^{14} +(1.40964 + 3.60734i) q^{15} -1.00000 q^{16} +(1.25971 - 1.25971i) q^{17} +(2.99975 + 0.0388113i) q^{18} -5.10691i q^{19} +(1.60266 - 1.55932i) q^{20} +(-0.646136 - 1.58890i) q^{21} +(3.12700 + 3.12700i) q^{22} +(3.17479 + 3.17479i) q^{23} +(-0.652462 - 1.60446i) q^{24} +(-0.137056 + 4.99812i) q^{25} -0.399498i q^{26} +(1.89495 + 4.83830i) q^{27} +(-0.700251 + 0.700251i) q^{28} -0.862782 q^{29} +(3.54754 + 1.55401i) q^{30} +1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.97689 + 7.05739i) q^{33} -1.78149i q^{34} +(0.0303525 - 2.21418i) q^{35} +(2.14859 - 2.09370i) q^{36} +(-1.12067 - 1.12067i) q^{37} +(-3.61113 - 3.61113i) q^{38} +(0.640978 - 0.260657i) q^{39} +(0.0306496 - 2.23586i) q^{40} -9.40638i q^{41} +(-1.58041 - 0.666638i) q^{42} +(-5.61274 + 5.61274i) q^{43} +4.42224 q^{44} +(-0.178718 + 6.70582i) q^{45} +4.48983 q^{46} +(5.96081 - 5.96081i) q^{47} +(-1.59589 - 0.673165i) q^{48} -6.01930i q^{49} +(3.43729 + 3.63112i) q^{50} +(2.85834 - 1.16236i) q^{51} +(-0.282488 - 0.282488i) q^{52} +(-7.34070 - 7.34070i) q^{53} +(4.76113 + 2.08126i) q^{54} +(-7.08736 + 6.89568i) q^{55} +0.990304i q^{56} +(3.43779 - 8.15004i) q^{57} +(-0.610079 + 0.610079i) q^{58} -0.852824 q^{59} +(3.60734 - 1.40964i) q^{60} -3.32914 q^{61} +(0.707107 - 0.707107i) q^{62} +(0.0384350 - 2.97066i) q^{63} +1.00000i q^{64} +(0.893220 + 0.0122445i) q^{65} +(2.88534 + 7.09531i) q^{66} +(7.00567 + 7.00567i) q^{67} +(-1.25971 - 1.25971i) q^{68} +(2.92945 + 7.20376i) q^{69} +(-1.54420 - 1.58712i) q^{70} +2.54520i q^{71} +(0.0388113 - 2.99975i) q^{72} +(-8.92808 + 8.92808i) q^{73} -1.58487 q^{74} +(-3.58328 + 7.88417i) q^{75} -5.10691 q^{76} +(3.09668 - 3.09668i) q^{77} +(0.268928 - 0.637553i) q^{78} -2.12954i q^{79} +(-1.55932 - 1.60266i) q^{80} +(-0.232848 + 8.99699i) q^{81} +(-6.65131 - 6.65131i) q^{82} +(-3.12488 - 3.12488i) q^{83} +(-1.58890 + 0.646136i) q^{84} +(3.98317 + 0.0546021i) q^{85} +7.93762i q^{86} +(-1.37690 - 0.580794i) q^{87} +(3.12700 - 3.12700i) q^{88} -2.60883 q^{89} +(4.61536 + 4.86811i) q^{90} -0.395624 q^{91} +(3.17479 - 3.17479i) q^{92} +(1.59589 + 0.673165i) q^{93} -8.42986i q^{94} +(8.18466 - 7.96330i) q^{95} +(-1.60446 + 0.652462i) q^{96} +(-11.2793 - 11.2793i) q^{97} +(-4.25629 - 4.25629i) q^{98} +(-9.50156 + 9.25884i) 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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