LMFDB - Embedded newform 930.2.k.a.433.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(247,930)]

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([0, 1, 2]))

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

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

chi := DirichletCharacter("930.247");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.k (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:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			433.4
Character	$\chi$	$=$	930.433
Dual form			930.2.k.a.247.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-0.899839 - 2.04702i) q^{5} +1.00000i q^{6} +(2.95191 - 2.95191i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-0.899839 - 2.04702i) q^{5} +1.00000i q^{6} +(2.95191 - 2.95191i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(2.08374 + 0.811179i) q^{10} +4.03469i q^{11} +(-0.707107 - 0.707107i) q^{12} +(2.80675 - 2.80675i) q^{13} +4.17463i q^{14} +(-2.08374 - 0.811179i) q^{15} -1.00000 q^{16} +(2.66235 + 2.66235i) q^{17} +(0.707107 + 0.707107i) q^{18} -1.01510i q^{19} +(-2.04702 + 0.899839i) q^{20} -4.17463i q^{21} +(-2.85296 - 2.85296i) q^{22} +(2.02478 - 2.02478i) q^{23} +1.00000 q^{24} +(-3.38058 + 3.68398i) q^{25} +3.96934i q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.95191 - 2.95191i) q^{28} +4.35667 q^{29} +(2.04702 - 0.899839i) q^{30} +(-2.75488 - 4.83845i) q^{31} +(0.707107 - 0.707107i) q^{32} +(2.85296 + 2.85296i) q^{33} -3.76514 q^{34} +(-8.69886 - 3.38637i) q^{35} -1.00000 q^{36} +(-4.51858 - 4.51858i) q^{37} +(0.717783 + 0.717783i) q^{38} -3.96934i q^{39} +(0.811179 - 2.08374i) q^{40} -8.01545 q^{41} +(2.95191 + 2.95191i) q^{42} +(0.805022 - 0.805022i) q^{43} +4.03469 q^{44} +(-2.04702 + 0.899839i) q^{45} +2.86347i q^{46} +(-0.485909 + 0.485909i) q^{47} +(-0.707107 + 0.707107i) q^{48} -10.4275i q^{49} +(-0.214533 - 4.99540i) q^{50} +3.76514 q^{51} +(-2.80675 - 2.80675i) q^{52} +(2.97139 - 2.97139i) q^{53} +1.00000 q^{54} +(8.25909 - 3.63057i) q^{55} +4.17463 q^{56} +(-0.717783 - 0.717783i) q^{57} +(-3.08063 + 3.08063i) q^{58} -12.9765i q^{59} +(-0.811179 + 2.08374i) q^{60} +8.09893i q^{61} +(5.36930 + 1.47331i) q^{62} +(-2.95191 - 2.95191i) q^{63} +1.00000i q^{64} +(-8.27109 - 3.21985i) q^{65} -4.03469 q^{66} +(-4.92097 + 4.92097i) q^{67} +(2.66235 - 2.66235i) q^{68} -2.86347i q^{69} +(8.54555 - 3.75649i) q^{70} +6.49419 q^{71} +(0.707107 - 0.707107i) q^{72} +(-6.55280 + 6.55280i) q^{73} +6.39023 q^{74} +(0.214533 + 4.99540i) q^{75} -1.01510 q^{76} +(11.9100 + 11.9100i) q^{77} +(2.80675 + 2.80675i) q^{78} +9.44004 q^{79} +(0.899839 + 2.04702i) q^{80} -1.00000 q^{81} +(5.66778 - 5.66778i) q^{82} +(-7.59317 + 7.59317i) q^{83} -4.17463 q^{84} +(3.05420 - 7.84558i) q^{85} +1.13847i q^{86} +(3.08063 - 3.08063i) q^{87} +(-2.85296 + 2.85296i) q^{88} -5.03739 q^{89} +(0.811179 - 2.08374i) q^{90} -16.5705i q^{91} +(-2.02478 - 2.02478i) q^{92} +(-5.36930 - 1.47331i) q^{93} -0.687180i q^{94} +(-2.07793 + 0.913425i) q^{95} -1.00000i q^{96} +(8.30027 - 8.30027i) q^{97} +(7.37338 + 7.37338i) q^{98} +4.03469 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{7}+O(q^{10}) $ 32 * q - 4 * q^7	$ 32 q - 4 q^{7} + 4 q^{10} - 4 q^{15} - 32 q^{16} - 8 q^{17} + 4 q^{22} + 32 q^{24} + 8 q^{25} + 4 q^{28} - 8 q^{29} - 20 q^{31} - 4 q^{33} - 24 q^{35} - 32 q^{36} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 4 q^{42} + 16 q^{43} + 8 q^{44} - 8 q^{47} - 16 q^{50} + 24 q^{53} + 32 q^{54} + 28 q^{55} - 16 q^{57} - 20 q^{58} + 16 q^{62} + 4 q^{63} - 56 q^{65} - 8 q^{66} + 32 q^{67} - 8 q^{68} - 28 q^{70} + 16 q^{71} + 20 q^{73} - 24 q^{74} + 16 q^{75} - 16 q^{76} + 40 q^{77} + 56 q^{79} - 32 q^{81} + 16 q^{82} - 72 q^{83} + 32 q^{85} + 20 q^{87} + 4 q^{88} + 64 q^{89} - 16 q^{93} + 32 q^{95} - 4 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) $ 32 * q - 4 * q^7 + 4 * q^10 - 4 * q^15 - 32 * q^16 - 8 * q^17 + 4 * q^22 + 32 * q^24 + 8 * q^25 + 4 * q^28 - 8 * q^29 - 20 * q^31 - 4 * q^33 - 24 * q^35 - 32 * q^36 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 4 * q^42 + 16 * q^43 + 8 * q^44 - 8 * q^47 - 16 * q^50 + 24 * q^53 + 32 * q^54 + 28 * q^55 - 16 * q^57 - 20 * q^58 + 16 * q^62 + 4 * q^63 - 56 * q^65 - 8 * q^66 + 32 * q^67 - 8 * q^68 - 28 * q^70 + 16 * q^71 + 20 * q^73 - 24 * q^74 + 16 * q^75 - 16 * q^76 + 40 * q^77 + 56 * q^79 - 32 * q^81 + 16 * q^82 - 72 * q^83 + 32 * q^85 + 20 * q^87 + 4 * q^88 + 64 * q^89 - 16 * q^93 + 32 * q^95 - 4 * q^97 + 16 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	−0.899839	−	2.04702i	−0.402420	−	0.915455i
$5$	−0.899839	−	2.04702i	−0.402420	−	0.915455i
$6$			1.00000i			0.408248i
$7$	2.95191	−	2.95191i	1.11572	−	1.11572i	0.123354	−	0.992363i	$-0.460635\pi$
$7$	2.95191	−	2.95191i	1.11572	−	1.11572i	0.992363	−	0.123354i	$-0.0393651\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	2.08374	+	0.811179i	0.658938	+	0.256517i
$11$			4.03469i			1.21650i	0.793744	+	0.608252i	$0.208129\pi$
$11$			4.03469i			1.21650i	−0.793744	+	0.608252i	$0.791871\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	2.80675	−	2.80675i	0.778452	−	0.778452i	−0.201115	−	0.979568i	$-0.564457\pi$
$13$	2.80675	−	2.80675i	0.778452	−	0.778452i	0.979568	+	0.201115i	$0.0644566\pi$
$14$			4.17463i			1.11572i
$15$	−2.08374	−	0.811179i	−0.538020	−	0.209446i
$16$	−1.00000			−0.250000
$17$	2.66235	+	2.66235i	0.645716	+	0.645716i	0.951955	−	0.306239i	$-0.0990707\pi$
$17$	2.66235	+	2.66235i	0.645716	+	0.645716i	−0.306239	+	0.951955i	$0.599071\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$		−	1.01510i		−	0.232879i	−0.993198	−	0.116440i	$-0.962852\pi$
$19$		−	1.01510i		−	0.232879i	0.993198	−	0.116440i	$-0.0371482\pi$
$20$	−2.04702	+	0.899839i	−0.457728	+	0.201210i
$21$		−	4.17463i		−	0.910979i
$22$	−2.85296	−	2.85296i	−0.608252	−	0.608252i
$23$	2.02478	−	2.02478i	0.422196	−	0.422196i	−0.463763	−	0.885959i	$-0.653501\pi$
$23$	2.02478	−	2.02478i	0.422196	−	0.422196i	0.885959	+	0.463763i	$0.153501\pi$
$24$	1.00000			0.204124
$25$	−3.38058	+	3.68398i	−0.676116	+	0.736795i
$26$			3.96934i			0.778452i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−2.95191	−	2.95191i	−0.557858	−	0.557858i
$29$	4.35667			0.809013			0.404506	−	0.914535i	$-0.367443\pi$
$29$	4.35667			0.809013			0.404506	+	0.914535i	$0.367443\pi$
$30$	2.04702	−	0.899839i	0.373733	−	0.164287i
$31$	−2.75488	−	4.83845i	−0.494791	−	0.869012i
$31$	−2.75488	−	4.83845i	−0.494791	−	0.869012i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	2.85296	+	2.85296i	0.496636	+	0.496636i
$34$	−3.76514			−0.645716
$35$	−8.69886	−	3.38637i	−1.47038	−	0.572402i
$36$	−1.00000			−0.166667
$37$	−4.51858	−	4.51858i	−0.742849	−	0.742849i	0.230276	−	0.973125i	$-0.426037\pi$
$37$	−4.51858	−	4.51858i	−0.742849	−	0.742849i	−0.973125	+	0.230276i	$0.926037\pi$
$38$	0.717783	+	0.717783i	0.116440	+	0.116440i
$39$		−	3.96934i		−	0.635604i
$40$	0.811179	−	2.08374i	0.128259	−	0.329469i
$41$	−8.01545			−1.25180			−0.625902	−	0.779902i	$-0.715269\pi$
$41$	−8.01545			−1.25180			−0.625902	+	0.779902i	$0.715269\pi$
$42$	2.95191	+	2.95191i	0.455490	+	0.455490i
$43$	0.805022	−	0.805022i	0.122765	−	0.122765i	−0.643055	−	0.765820i	$-0.722333\pi$
$43$	0.805022	−	0.805022i	0.122765	−	0.122765i	0.765820	+	0.643055i	$0.222333\pi$
$44$	4.03469			0.608252
$45$	−2.04702	+	0.899839i	−0.305152	+	0.134140i
$46$			2.86347i			0.422196i
$47$	−0.485909	+	0.485909i	−0.0708772	+	0.0708772i	−0.741657	−	0.670780i	$-0.765960\pi$
$47$	−0.485909	+	0.485909i	−0.0708772	+	0.0708772i	0.670780	+	0.741657i	$0.265960\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$		−	10.4275i		−	1.48965i
$50$	−0.214533	−	4.99540i	−0.0303396	−	0.706456i
$51$	3.76514			0.527225
$52$	−2.80675	−	2.80675i	−0.389226	−	0.389226i
$53$	2.97139	−	2.97139i	0.408152	−	0.408152i	−0.472942	−	0.881094i	$-0.656808\pi$
$53$	2.97139	−	2.97139i	0.408152	−	0.408152i	0.881094	+	0.472942i	$0.156808\pi$
$54$	1.00000			0.136083
$55$	8.25909	−	3.63057i	1.11366	−	0.489546i
$56$	4.17463			0.557858
$57$	−0.717783	−	0.717783i	−0.0950727	−	0.0950727i
$58$	−3.08063	+	3.08063i	−0.404506	+	0.404506i
$59$		−	12.9765i		−	1.68940i	−0.535241	−	0.844699i	$-0.679779\pi$
$59$		−	12.9765i		−	1.68940i	0.535241	−	0.844699i	$-0.320221\pi$
$60$	−0.811179	+	2.08374i	−0.104723	+	0.269010i
$61$			8.09893i			1.03696i	0.855089	+	0.518481i	$0.173502\pi$
$61$			8.09893i			1.03696i	−0.855089	+	0.518481i	$0.826498\pi$
$62$	5.36930	+	1.47331i	0.681901	+	0.187111i
$63$	−2.95191	−	2.95191i	−0.371906	−	0.371906i
$64$			1.00000i			0.125000i
$65$	−8.27109	−	3.21985i	−1.02590	−	0.399373i
$66$	−4.03469			−0.496636
$67$	−4.92097	+	4.92097i	−0.601192	+	0.601192i	−0.940629	−	0.339437i	$-0.889764\pi$
$67$	−4.92097	+	4.92097i	−0.601192	+	0.601192i	0.339437	+	0.940629i	$0.389764\pi$
$68$	2.66235	−	2.66235i	0.322858	−	0.322858i
$69$		−	2.86347i		−	0.344722i
$70$	8.54555	−	3.75649i	1.02139	−	0.448987i
$71$	6.49419			0.770718			0.385359	−	0.922767i	$-0.374078\pi$
$71$	6.49419			0.770718			0.385359	+	0.922767i	$0.374078\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	−6.55280	+	6.55280i	−0.766947	+	0.766947i	−0.977568	−	0.210621i	$-0.932451\pi$
$73$	−6.55280	+	6.55280i	−0.766947	+	0.766947i	0.210621	+	0.977568i	$0.432451\pi$
$74$	6.39023			0.742849
$75$	0.214533	+	4.99540i	0.0247722	+	0.576819i
$76$	−1.01510			−0.116440
$77$	11.9100	+	11.9100i	1.35727	+	1.35727i
$78$	2.80675	+	2.80675i	0.317802	+	0.317802i
$79$	9.44004			1.06209			0.531044	−	0.847344i	$-0.321800\pi$
$79$	9.44004			1.06209			0.531044	+	0.847344i	$0.321800\pi$
$80$	0.899839	+	2.04702i	0.100605	+	0.228864i
$81$	−1.00000			−0.111111
$82$	5.66778	−	5.66778i	0.625902	−	0.625902i
$83$	−7.59317	+	7.59317i	−0.833459	+	0.833459i	−0.987988	−	0.154529i	$-0.950614\pi$
$83$	−7.59317	+	7.59317i	−0.833459	+	0.833459i	0.154529	+	0.987988i	$0.450614\pi$
$84$	−4.17463			−0.455490
$85$	3.05420	−	7.84558i	0.331275	−	0.850973i
$86$			1.13847i			0.122765i
$87$	3.08063	−	3.08063i	0.330278	−	0.330278i
$88$	−2.85296	+	2.85296i	−0.304126	+	0.304126i
$89$	−5.03739			−0.533962			−0.266981	−	0.963702i	$-0.586026\pi$
$89$	−5.03739			−0.533962			−0.266981	+	0.963702i	$0.586026\pi$
$90$	0.811179	−	2.08374i	0.0855058	−	0.219646i
$91$		−	16.5705i		−	1.73706i
$92$	−2.02478	−	2.02478i	−0.211098	−	0.211098i
$93$	−5.36930	−	1.47331i	−0.556770	−	0.152775i
$94$		−	0.687180i		−	0.0708772i
$95$	−2.07793	+	0.913425i	−0.213191	+	0.0937154i
$96$		−	1.00000i		−	0.102062i
$97$	8.30027	−	8.30027i	0.842764	−	0.842764i	−0.146453	−	0.989218i	$-0.546786\pi$
$97$	8.30027	−	8.30027i	0.842764	−	0.842764i	0.989218	+	0.146453i	$0.0467858\pi$
$98$	7.37338	+	7.37338i	0.744824	+	0.744824i
$99$	4.03469			0.405502
$100$	3.68398	+	3.38058i	0.368398	+	0.338058i
$101$	−2.88110			−0.286680			−0.143340	−	0.989674i	$-0.545784\pi$
$101$	−2.88110			−0.286680			−0.143340	+	0.989674i	$0.545784\pi$
$102$	−2.66235	+	2.66235i	−0.263612	+	0.263612i
$103$	8.65254	+	8.65254i	0.852560	+	0.852560i	0.990448	−	0.137888i	$-0.0440314\pi$
$103$	8.65254	+	8.65254i	0.852560	+	0.852560i	−0.137888	+	0.990448i	$0.544031\pi$
$104$	3.96934			0.389226
$105$	−8.54555	+	3.75649i	−0.833960	+	0.366596i
$106$			4.20218i			0.408152i
$107$	−11.2782	+	11.2782i	−1.09031	+	1.09031i	−0.0948132	+	0.995495i	$0.530225\pi$
$107$	−11.2782	+	11.2782i	−1.09031	+	1.09031i	−0.995495	+	0.0948132i	$0.969775\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$		−	14.0311i		−	1.34394i	−0.740579	−	0.671970i	$-0.765448\pi$
$109$		−	14.0311i		−	1.34394i	0.740579	−	0.671970i	$-0.234552\pi$
$110$	−3.27286	+	8.40726i	−0.312055	+	0.801601i
$111$	−6.39023			−0.606534
$112$	−2.95191	+	2.95191i	−0.278929	+	0.278929i
$113$	6.42328	+	6.42328i	0.604251	+	0.604251i	0.941438	−	0.337187i	$-0.109475\pi$
$113$	6.42328	+	6.42328i	0.604251	+	0.604251i	−0.337187	+	0.941438i	$0.609475\pi$
$114$	1.01510			0.0950727
$115$	−5.96674	−	2.32279i	−0.556402	−	0.216601i
$116$		−	4.35667i		−	0.404506i
$117$	−2.80675	−	2.80675i	−0.259484	−	0.259484i
$118$	9.17578	+	9.17578i	0.844699	+	0.844699i
$119$	15.7181			1.44087
$120$	−0.899839	−	2.04702i	−0.0821437	−	0.186866i
$121$	−5.27872			−0.479884
$122$	−5.72681	−	5.72681i	−0.518481	−	0.518481i
$123$	−5.66778	+	5.66778i	−0.511047	+	0.511047i
$124$	−4.83845	+	2.75488i	−0.434506	+	0.247395i
$125$	10.5831	+	3.60513i	0.946586	+	0.322453i
$126$	4.17463			0.371906
$127$	0.444118	+	0.444118i	0.0394091	+	0.0394091i	0.726537	−	0.687128i	$-0.241129\pi$
$127$	0.444118	+	0.444118i	0.0394091	+	0.0394091i	−0.687128	+	0.726537i	$0.741129\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		−	1.13847i		−	0.100237i
$130$	8.12532	−	3.57177i	0.712638	−	0.313265i
$131$	−12.9824			−1.13427			−0.567137	−	0.823624i	$-0.691949\pi$
$131$	−12.9824			−1.13427			−0.567137	+	0.823624i	$0.691949\pi$
$132$	2.85296	−	2.85296i	0.248318	−	0.248318i
$133$	−2.99648	−	2.99648i	−0.259828	−	0.259828i
$134$		−	6.95930i		−	0.601192i
$135$	−0.811179	+	2.08374i	−0.0698152	+	0.179340i
$136$			3.76514i			0.322858i
$137$	13.4768	+	13.4768i	1.15140	+	1.15140i	0.986272	+	0.165130i	$0.0528043\pi$
$137$	13.4768	+	13.4768i	1.15140	+	1.15140i	0.165130	+	0.986272i	$0.447196\pi$
$138$	2.02478	+	2.02478i	0.172361	+	0.172361i
$139$	21.5110			1.82454			0.912268	−	0.409593i	$-0.134329\pi$
$139$	21.5110			1.82454			0.912268	+	0.409593i	$0.134329\pi$
$140$	−3.38637	+	8.69886i	−0.286201	+	0.735188i
$141$			0.687180i			0.0578710i
$142$	−4.59208	+	4.59208i	−0.385359	+	0.385359i
$143$	11.3244	+	11.3244i	0.946991	+	0.946991i
$144$			1.00000i			0.0833333i
$145$	−3.92030	−	8.91819i	−0.325563	−	0.740615i
$146$		−	9.26705i		−	0.766947i
$147$	−7.37338	−	7.37338i	−0.608146	−	0.608146i
$148$	−4.51858	+	4.51858i	−0.371425	+	0.371425i
$149$			0.221568i			0.0181515i	0.999959	+	0.00907577i	$0.00288895\pi$
$149$			0.221568i			0.0181515i	−0.999959	+	0.00907577i	$0.997111\pi$
$150$	−3.68398	−	3.38058i	−0.300795	−	0.276023i
$151$			11.4689i			0.933324i	0.884436	+	0.466662i	$0.154544\pi$
$151$			11.4689i			0.933324i	−0.884436	+	0.466662i	$0.845456\pi$
$152$	0.717783	−	0.717783i	0.0582199	−	0.0582199i
$153$	2.66235	−	2.66235i	0.215239	−	0.215239i
$154$	−16.8433			−1.35727
$155$	−7.42546	+	9.99312i	−0.596428	+	0.802667i
$156$	−3.96934			−0.317802
$157$	10.0308	−	10.0308i	0.800549	−	0.800549i	−0.182633	−	0.983181i	$-0.558462\pi$
$157$	10.0308	−	10.0308i	0.800549	−	0.800549i	0.983181	+	0.182633i	$0.0584619\pi$
$158$	−6.67512	+	6.67512i	−0.531044	+	0.531044i
$159$		−	4.20218i		−	0.333255i
$160$	−2.08374	−	0.811179i	−0.164734	−	0.0641294i
$161$		−	11.9539i		−	0.942103i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−2.82330	−	2.82330i	−0.221138	−	0.221138i	0.587840	−	0.808977i	$-0.299979\pi$
$163$	−2.82330	−	2.82330i	−0.221138	−	0.221138i	−0.808977	+	0.587840i	$0.799979\pi$
$164$			8.01545i			0.625902i
$165$	3.27286	−	8.40726i	0.254792	−	0.654504i
$166$		−	10.7384i		−	0.833459i
$167$	−14.2859	−	14.2859i	−1.10547	−	1.10547i	−0.993738	−	0.111736i	$-0.964359\pi$
$167$	−14.2859	−	14.2859i	−1.10547	−	1.10547i	−0.111736	−	0.993738i	$-0.535641\pi$
$168$	2.95191	−	2.95191i	0.227745	−	0.227745i
$169$		−	2.75569i		−	0.211976i
$170$	3.38802	+	7.70731i	0.259849	+	0.591124i
$171$	−1.01510			−0.0776265
$172$	−0.805022	−	0.805022i	−0.0613823	−	0.0613823i
$173$	−12.5526	−	12.5526i	−0.954360	−	0.954360i	0.0446433	−	0.999003i	$-0.485785\pi$
$173$	−12.5526	−	12.5526i	−0.954360	−	0.954360i	−0.999003	+	0.0446433i	$0.985785\pi$
$174$			4.35667i			0.330278i
$175$	0.895598	+	20.8539i	0.0677008	+	1.57641i
$176$		−	4.03469i		−	0.304126i
$177$	−9.17578	−	9.17578i	−0.689694	−	0.689694i
$178$	3.56197	−	3.56197i	0.266981	−	0.266981i
$179$	22.2553			1.66344			0.831720	−	0.555195i	$-0.187356\pi$
$179$	22.2553			1.66344			0.831720	+	0.555195i	$0.187356\pi$
$180$	0.899839	+	2.04702i	0.0670700	+	0.152576i
$181$		−	3.14386i		−	0.233681i	−0.993151	−	0.116841i	$-0.962723\pi$
$181$		−	3.14386i		−	0.233681i	0.993151	−	0.116841i	$-0.0372767\pi$
$182$	11.7171	+	11.7171i	0.868532	+	0.868532i
$183$	5.72681	+	5.72681i	0.423338	+	0.423338i
$184$	2.86347			0.211098
$185$	−5.18362	+	13.3156i	−0.381108	+	0.978983i
$186$	4.83845	−	2.75488i	0.354773	−	0.201998i
$187$	−10.7418	+	10.7418i	−0.785516	+	0.785516i
$188$	0.485909	+	0.485909i	0.0354386	+	0.0354386i
$189$	−4.17463			−0.303660
$190$	0.823427	−	2.11520i	0.0597377	−	0.153453i
$191$	−14.4881			−1.04832			−0.524162	−	0.851618i	$-0.675621\pi$
$191$	−14.4881			−1.04832			−0.524162	+	0.851618i	$0.675621\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	11.6924	+	11.6924i	0.841640	+	0.841640i	0.989072	−	0.147432i	$-0.0471007\pi$
$193$	11.6924	+	11.6924i	0.841640	+	0.841640i	−0.147432	+	0.989072i	$0.547101\pi$
$194$			11.7383i			0.842764i
$195$	−8.12532	+	3.57177i	−0.581867	+	0.255780i
$196$	−10.4275			−0.744824
$197$	15.6591	+	15.6591i	1.11567	+	1.11567i	0.992370	+	0.123297i	$0.0393467\pi$
$197$	15.6591	+	15.6591i	1.11567	+	1.11567i	0.123297	+	0.992370i	$0.460653\pi$
$198$	−2.85296	+	2.85296i	−0.202751	+	0.202751i
$199$	−14.4567			−1.02481			−0.512406	−	0.858743i	$-0.671246\pi$
$199$	−14.4567			−1.02481			−0.512406	+	0.858743i	$0.671246\pi$
$200$	−4.99540	+	0.214533i	−0.353228	+	0.0151698i
$201$			6.95930i			0.490871i
$202$	2.03724	−	2.03724i	0.143340	−	0.143340i
$203$	12.8605	−	12.8605i	0.902629	−	0.902629i
$204$		−	3.76514i		−	0.263612i
$205$	7.21261	+	16.4078i	0.503751	+	1.14597i
$206$	−12.2365			−0.852560
$207$	−2.02478	−	2.02478i	−0.140732	−	0.140732i
$208$	−2.80675	+	2.80675i	−0.194613	+	0.194613i
$209$	4.09561			0.283299
$210$	3.38637	−	8.69886i	0.233682	−	0.600278i
$211$	−8.27591			−0.569737			−0.284869	−	0.958567i	$-0.591950\pi$
$211$	−8.27591			−0.569737			−0.284869	+	0.958567i	$0.591950\pi$
$212$	−2.97139	−	2.97139i	−0.204076	−	0.204076i
$213$	4.59208	−	4.59208i	0.314644	−	0.314644i
$214$		−	15.9498i		−	1.09031i
$215$	−2.37229	−	0.923506i	−0.161789	−	0.0629826i
$216$		−	1.00000i		−	0.0680414i
$217$	−22.4148	−	6.15052i	−1.52162	−	0.417525i
$218$	9.92151	+	9.92151i	0.671970	+	0.671970i
$219$			9.26705i			0.626209i
$220$	−3.63057	−	8.25909i	−0.244773	−	0.556828i
$221$	14.9451			1.00532
$222$	4.51858	−	4.51858i	0.303267	−	0.303267i
$223$	−1.91786	+	1.91786i	−0.128429	+	0.128429i	−0.768400	−	0.639970i	$-0.778947\pi$
$223$	−1.91786	+	1.91786i	−0.128429	+	0.128429i	0.639970	+	0.768400i	$0.278947\pi$
$224$		−	4.17463i		−	0.278929i
$225$	3.68398	+	3.38058i	0.245598	+	0.225372i
$226$	−9.08389			−0.604251
$227$	−5.61156	+	5.61156i	−0.372452	+	0.372452i	−0.868370	−	0.495917i	$-0.834832\pi$
$227$	−5.61156	+	5.61156i	−0.372452	+	0.372452i	0.495917	+	0.868370i	$0.334832\pi$
$228$	−0.717783	+	0.717783i	−0.0475363	+	0.0475363i
$229$	−5.55524			−0.367101			−0.183550	−	0.983010i	$-0.558759\pi$
$229$	−5.55524			−0.367101			−0.183550	+	0.983010i	$0.558759\pi$
$230$	5.86159	−	2.57666i	0.386502	−	0.169900i
$231$	16.8433			1.10821
$232$	3.08063	+	3.08063i	0.202253	+	0.202253i
$233$	12.4453	+	12.4453i	0.815317	+	0.815317i	0.985425	−	0.170108i	$-0.0544118\pi$
$233$	12.4453	+	12.4453i	0.815317	+	0.815317i	−0.170108	+	0.985425i	$0.554412\pi$
$234$	3.96934			0.259484
$235$	1.43191	+	0.557426i	0.0934073	+	0.0363625i
$236$	−12.9765			−0.844699
$237$	6.67512	−	6.67512i	0.433595	−	0.433595i
$238$	−11.1143	+	11.1143i	−0.720436	+	0.720436i
$239$	−24.6462			−1.59423			−0.797114	−	0.603829i	$-0.793641\pi$
$239$	−24.6462			−1.59423			−0.797114	+	0.603829i	$0.793641\pi$
$240$	2.08374	+	0.811179i	0.134505	+	0.0523614i
$241$			15.1372i			0.975071i	0.873103	+	0.487535i	$0.162104\pi$
$241$			15.1372i			0.975071i	−0.873103	+	0.487535i	$0.837896\pi$
$242$	3.73262	−	3.73262i	0.239942	−	0.239942i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	8.09893			0.518481
$245$	−21.3454	+	9.38311i	−1.36371	+	0.599465i
$246$		−	8.01545i		−	0.511047i
$247$	−2.84913	−	2.84913i	−0.181286	−	0.181286i
$248$	1.47331	−	5.36930i	0.0935553	−	0.340951i
$249$			10.7384i			0.680516i
$250$	−10.0326	+	4.93421i	−0.634519	+	0.312067i
$251$		−	0.385808i		−	0.0243520i	−0.999926	−	0.0121760i	$-0.996124\pi$
$251$		−	0.385808i		−	0.0243520i	0.999926	−	0.0121760i	$-0.00387584\pi$
$252$	−2.95191	+	2.95191i	−0.185953	+	0.185953i
$253$	8.16936	+	8.16936i	0.513603	+	0.513603i
$254$	−0.628077			−0.0394091
$255$	−3.38802	−	7.70731i	−0.212166	−	0.482650i
$256$	1.00000			0.0625000
$257$	14.6768	−	14.6768i	0.915514	−	0.915514i	−0.0811847	−	0.996699i	$-0.525870\pi$
$257$	14.6768	−	14.6768i	0.915514	−	0.915514i	0.996699	+	0.0811847i	$0.0258703\pi$
$258$	0.805022	+	0.805022i	0.0501185	+	0.0501185i
$259$	−26.6769			−1.65762
$260$	−3.21985	+	8.27109i	−0.199687	+	0.512952i
$261$		−	4.35667i		−	0.269671i
$262$	9.17991	−	9.17991i	0.567137	−	0.567137i
$263$	−21.5005	+	21.5005i	−1.32578	+	1.32578i	−0.416757	+	0.909018i	$0.636833\pi$
$263$	−21.5005	+	21.5005i	−1.32578	+	1.32578i	−0.909018	+	0.416757i	$0.863167\pi$
$264$			4.03469i			0.248318i
$265$	−8.75627	−	3.40873i	−0.537894	−	0.209396i
$266$	4.23766			0.259828
$267$	−3.56197	+	3.56197i	−0.217989	+	0.217989i
$268$	4.92097	+	4.92097i	0.300596	+	0.300596i
$269$	−20.9881			−1.27967			−0.639833	−	0.768514i	$-0.720996\pi$
$269$	−20.9881			−1.27967			−0.639833	+	0.768514i	$0.720996\pi$
$270$	−0.899839	−	2.04702i	−0.0547625	−	0.124578i
$271$			13.3550i			0.811257i	0.914038	+	0.405629i	$0.132947\pi$
$271$			13.3550i			0.811257i	−0.914038	+	0.405629i	$0.867053\pi$
$272$	−2.66235	−	2.66235i	−0.161429	−	0.161429i
$273$	−11.7171	−	11.7171i	−0.709154	−	0.709154i
$274$	−19.0591			−1.15140
$275$	−14.8637	−	13.6396i	−0.896315	−	0.822498i
$276$	−2.86347			−0.172361
$277$	22.7574	+	22.7574i	1.36736	+	1.36736i	0.864181	+	0.503182i	$0.167837\pi$
$277$	22.7574	+	22.7574i	1.36736	+	1.36736i	0.503182	+	0.864181i	$0.332163\pi$
$278$	−15.2106	+	15.2106i	−0.912268	+	0.912268i
$279$	−4.83845	+	2.75488i	−0.289671	+	0.164930i
$280$	−3.75649	−	8.54555i	−0.224494	−	0.510694i
$281$	11.7181			0.699046			0.349523	−	0.936928i	$-0.386344\pi$
$281$	11.7181			0.699046			0.349523	+	0.936928i	$0.386344\pi$
$282$	−0.485909	−	0.485909i	−0.0289355	−	0.0289355i
$283$	16.4024	+	16.4024i	0.975023	+	0.975023i	0.999696	−	0.0246725i	$-0.00785430\pi$
$283$	16.4024	+	16.4024i	0.975023	+	0.975023i	−0.0246725	+	0.999696i	$0.507854\pi$
$284$		−	6.49419i		−	0.385359i
$285$	−0.823427	+	2.11520i	−0.0487756	+	0.125294i
$286$	−16.0151			−0.946991
$287$	−23.6609	+	23.6609i	−1.39666	+	1.39666i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$		−	2.82375i		−	0.166103i
$290$	9.07818	+	3.53404i	0.533089	+	0.207526i
$291$		−	11.7383i		−	0.688114i
$292$	6.55280	+	6.55280i	0.383473	+	0.383473i
$293$	−1.36623	−	1.36623i	−0.0798158	−	0.0798158i	0.666072	−	0.745888i	$-0.267974\pi$
$293$	−1.36623	−	1.36623i	−0.0798158	−	0.0798158i	−0.745888	+	0.666072i	$0.767974\pi$
$294$	10.4275			0.608146
$295$	−26.5632	+	11.6768i	−1.54657	+	0.679848i
$296$		−	6.39023i		−	0.371425i
$297$	2.85296	−	2.85296i	0.165545	−	0.165545i
$298$	−0.156672	−	0.156672i	−0.00907577	−	0.00907577i
$299$		−	11.3661i		−	0.657319i
$300$	4.99540	−	0.214533i	0.288409	−	0.0123861i
$301$		−	4.75270i		−	0.273941i
$302$	−8.10972	−	8.10972i	−0.466662	−	0.466662i
$303$	−2.03724	+	2.03724i	−0.117037	+	0.117037i
$304$			1.01510i			0.0582199i
$305$	16.5787	−	7.28774i	0.949292	−	0.417295i
$306$			3.76514i			0.215239i
$307$	0.502871	−	0.502871i	0.0287004	−	0.0287004i	−0.692611	−	0.721311i	$-0.743540\pi$
$307$	0.502871	−	0.502871i	0.0287004	−	0.0287004i	0.721311	+	0.692611i	$0.243540\pi$
$308$	11.9100	−	11.9100i	0.678637	−	0.678637i
$309$	12.2365			0.696112
$310$	−1.81561	−	12.3168i	−0.103120	−	0.699547i
$311$	23.6115			1.33889			0.669443	−	0.742864i	$-0.266533\pi$
$311$	23.6115			1.33889			0.669443	+	0.742864i	$0.266533\pi$
$312$	2.80675	−	2.80675i	0.158901	−	0.158901i
$313$	12.8877	−	12.8877i	0.728458	−	0.728458i	−0.241854	−	0.970313i	$-0.577756\pi$
$313$	12.8877	−	12.8877i	0.728458	−	0.728458i	0.970313	+	0.241854i	$0.0777557\pi$
$314$			14.1858i			0.800549i
$315$	−3.38637	+	8.69886i	−0.190801	+	0.490125i
$316$		−	9.44004i		−	0.531044i
$317$	−1.52562	+	1.52562i	−0.0856873	+	0.0856873i	−0.748651	−	0.662964i	$-0.769298\pi$
$317$	−1.52562	+	1.52562i	−0.0856873	+	0.0856873i	0.662964	+	0.748651i	$0.269298\pi$
$318$	2.97139	+	2.97139i	0.166627	+	0.166627i
$319$			17.5778i			0.984168i
$320$	2.04702	−	0.899839i	0.114432	−	0.0503025i
$321$			15.9498i			0.890233i
$322$	8.45271	+	8.45271i	0.471051	+	0.471051i
$323$	2.70255	−	2.70255i	0.150374	−	0.150374i
$324$			1.00000i			0.0555556i
$325$	0.851557	+	19.8284i	0.0472359	+	1.09988i
$326$	3.99275			0.221138
$327$	−9.92151	−	9.92151i	−0.548661	−	0.548661i
$328$	−5.66778	−	5.66778i	−0.312951	−	0.312951i
$329$			2.86872i			0.158158i
$330$	3.63057	+	8.25909i	0.199856	+	0.454648i
$331$			10.2406i			0.562872i	0.959580	+	0.281436i	$0.0908107\pi$
$331$			10.2406i			0.562872i	−0.959580	+	0.281436i	$0.909189\pi$
$332$	7.59317	+	7.59317i	0.416729	+	0.416729i
$333$	−4.51858	+	4.51858i	−0.247616	+	0.247616i
$334$	20.2033			1.10547
$335$	14.5014	+	5.64524i	0.792296	+	0.308433i
$336$			4.17463i			0.227745i
$337$	18.5342	+	18.5342i	1.00962	+	1.00962i	0.999953	+	0.00966899i	$0.00307778\pi$
$337$	18.5342	+	18.5342i	1.00962	+	1.00962i	0.00966899	+	0.999953i	$0.496922\pi$
$338$	1.94856	+	1.94856i	0.105988	+	0.105988i
$339$	9.08389			0.493369
$340$	−7.84558	−	3.05420i	−0.425486	−	0.165637i
$341$	19.5217	−	11.1151i	1.05716	−	0.601916i
$342$	0.717783	−	0.717783i	0.0388132	−	0.0388132i
$343$	−10.1178	−	10.1178i	−0.546309	−	0.546309i
$344$	1.13847			0.0613823
$345$	−5.86159	+	2.57666i	−0.315577	+	0.138723i
$346$	17.7521			0.954360
$347$	−17.5456	−	17.5456i	−0.941899	−	0.941899i	0.0565033	−	0.998402i	$-0.482005\pi$
$347$	−17.5456	−	17.5456i	−0.941899	−	0.941899i	−0.998402	+	0.0565033i	$0.982005\pi$
$348$	−3.08063	−	3.08063i	−0.165139	−	0.165139i
$349$		−	31.1464i		−	1.66723i	−0.552345	−	0.833616i	$-0.686267\pi$
$349$		−	31.1464i		−	1.66723i	0.552345	−	0.833616i	$-0.313733\pi$
$350$	−15.3792	−	14.1127i	−0.822055	−	0.754354i
$351$	−3.96934			−0.211868
$352$	2.85296	+	2.85296i	0.152063	+	0.152063i
$353$	7.56467	−	7.56467i	0.402627	−	0.402627i	−0.476531	−	0.879158i	$-0.658106\pi$
$353$	7.56467	−	7.56467i	0.402627	−	0.402627i	0.879158	+	0.476531i	$0.158106\pi$
$354$	12.9765			0.689694
$355$	−5.84372	−	13.2937i	−0.310153	−	0.705558i
$356$			5.03739i			0.266981i
$357$	11.1143	−	11.1143i	0.588233	−	0.588233i
$358$	−15.7369	+	15.7369i	−0.831720	+	0.831720i
$359$			13.4534i			0.710042i	0.934858	+	0.355021i	$0.115526\pi$
$359$			13.4534i			0.710042i	−0.934858	+	0.355021i	$0.884474\pi$
$360$	−2.08374	−	0.811179i	−0.109823	−	0.0427529i
$361$	17.9696			0.945767
$362$	2.22305	+	2.22305i	0.116841	+	0.116841i
$363$	−3.73262	+	3.73262i	−0.195912	+	0.195912i
$364$	−16.5705			−0.868532
$365$	19.3102	+	7.51724i	1.01074	+	0.393470i
$366$	−8.09893			−0.423338
$367$	15.3254	+	15.3254i	0.799982	+	0.799982i	0.983092	−	0.183111i	$-0.0586167\pi$
$367$	15.3254	+	15.3254i	0.799982	+	0.799982i	−0.183111	+	0.983092i	$0.558617\pi$
$368$	−2.02478	+	2.02478i	−0.105549	+	0.105549i
$369$			8.01545i			0.417268i
$370$	−5.75018	−	13.0809i	−0.298938	−	0.680045i
$371$		−	17.5426i		−	0.910765i
$372$	−1.47331	+	5.36930i	−0.0763876	+	0.278385i
$373$	−18.1490	−	18.1490i	−0.939721	−	0.939721i	0.0585625	−	0.998284i	$-0.481348\pi$
$373$	−18.1490	−	18.1490i	−0.939721	−	0.939721i	−0.998284	+	0.0585625i	$0.981348\pi$
$374$		−	15.1912i		−	0.785516i
$375$	10.0326	−	4.93421i	0.518083	−	0.254801i
$376$	−0.687180			−0.0354386
$377$	12.2281	−	12.2281i	0.629778	−	0.629778i
$378$	2.95191	−	2.95191i	0.151830	−	0.151830i
$379$			12.0805i			0.620535i	0.950649	+	0.310267i	$0.100419\pi$
$379$			12.0805i			0.620535i	−0.950649	+	0.310267i	$0.899581\pi$
$380$	0.913425	+	2.07793i	0.0468577	+	0.106595i
$381$	0.628077			0.0321774
$382$	10.2447	−	10.2447i	0.524162	−	0.524162i
$383$	−5.18617	+	5.18617i	−0.265001	+	0.265001i	−0.827082	−	0.562081i	$-0.810001\pi$
$383$	−5.18617	+	5.18617i	−0.265001	+	0.265001i	0.562081	+	0.827082i	$0.310001\pi$
$384$	−1.00000			−0.0510310
$385$	13.6630	−	35.0972i	0.696329	−	1.78872i
$386$	−16.5356			−0.841640
$387$	−0.805022	−	0.805022i	−0.0409216	−	0.0409216i
$388$	−8.30027	−	8.30027i	−0.421382	−	0.421382i
$389$	5.33947			0.270722			0.135361	−	0.990796i	$-0.456781\pi$
$389$	5.33947			0.270722			0.135361	+	0.990796i	$0.456781\pi$
$390$	3.21985	−	8.27109i	0.163043	−	0.418823i
$391$	10.7814			0.545237
$392$	7.37338	−	7.37338i	0.372412	−	0.372412i
$393$	−9.17991	+	9.17991i	−0.463065	+	0.463065i
$394$	−22.1453			−1.11567
$395$	−8.49451	−	19.3239i	−0.427405	−	0.972293i
$396$		−	4.03469i		−	0.202751i
$397$	−1.41370	+	1.41370i	−0.0709514	+	0.0709514i	−0.741692	−	0.670741i	$-0.765976\pi$
$397$	−1.41370	+	1.41370i	−0.0709514	+	0.0709514i	0.670741	+	0.741692i	$0.265976\pi$
$398$	10.2225	−	10.2225i	0.512406	−	0.512406i
$399$	−4.23766			−0.212148
$400$	3.38058	−	3.68398i	0.169029	−	0.184199i
$401$		−	3.16248i		−	0.157927i	−0.996878	−	0.0789633i	$-0.974839\pi$
$401$		−	3.16248i		−	0.157927i	0.996878	−	0.0789633i	$-0.0251610\pi$
$402$	−4.92097	−	4.92097i	−0.245436	−	0.245436i
$403$	−21.3126	−	5.84807i	−1.06166	−	0.291313i
$404$			2.88110i			0.143340i
$405$	0.899839	+	2.04702i	0.0447134	+	0.101717i
$406$			18.1875i			0.902629i
$407$	18.2311	−	18.2311i	0.903680	−	0.903680i
$408$	2.66235	+	2.66235i	0.131806	+	0.131806i
$409$	5.32872			0.263488			0.131744	−	0.991284i	$-0.457942\pi$
$409$	5.32872			0.263488			0.131744	+	0.991284i	$0.457942\pi$
$410$	−16.7021	−	6.50197i	−0.824860	−	0.321109i
$411$	19.0591			0.940115
$412$	8.65254	−	8.65254i	0.426280	−	0.426280i
$413$	−38.3055	−	38.3055i	−1.88489	−	1.88489i
$414$	2.86347			0.140732
$415$	22.3760	+	8.71074i	1.09839	+	0.427593i
$416$		−	3.96934i		−	0.194613i
$417$	15.2106	−	15.2106i	0.744864	−	0.744864i
$418$	−2.89603	+	2.89603i	−0.141649	+	0.141649i
$419$		−	21.2866i		−	1.03992i	−0.854191	−	0.519959i	$-0.825947\pi$
$419$		−	21.2866i		−	1.03992i	0.854191	−	0.519959i	$-0.174053\pi$
$420$	3.75649	+	8.54555i	0.183298	+	0.416980i
$421$	23.1425			1.12790			0.563949	−	0.825809i	$-0.309281\pi$
$421$	23.1425			1.12790			0.563949	+	0.825809i	$0.309281\pi$
$422$	5.85196	−	5.85196i	0.284869	−	0.284869i
$423$	0.485909	+	0.485909i	0.0236257	+	0.0236257i
$424$	4.20218			0.204076
$425$	−18.8083	+	0.807748i	−0.912339	+	0.0391815i
$426$			6.49419i			0.314644i
$427$	23.9073	+	23.9073i	1.15696	+	1.15696i
$428$	11.2782	+	11.2782i	0.545154	+	0.545154i
$429$	16.0151			0.773215
$430$	2.33048	−	1.02444i	0.112386	−	0.0494030i
$431$	29.9524			1.44276			0.721379	−	0.692541i	$-0.243509\pi$
$431$	29.9524			1.44276			0.721379	+	0.692541i	$0.243509\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	3.11417	−	3.11417i	0.149658	−	0.149658i	−0.628307	−	0.777965i	$-0.716252\pi$
$433$	3.11417	−	3.11417i	0.149658	−	0.149658i	0.777965	+	0.628307i	$0.216252\pi$
$434$	20.1988	−	11.5006i	0.969571	−	0.552047i
$435$	−9.07818	−	3.53404i	−0.435265	−	0.169444i
$436$	−14.0311			−0.671970
$437$	−2.05535	−	2.05535i	−0.0983208	−	0.0983208i
$438$	−6.55280	−	6.55280i	−0.313105	−	0.313105i
$439$		−	28.7403i		−	1.37170i	−0.727743	−	0.685850i	$-0.759430\pi$
$439$		−	28.7403i		−	1.37170i	0.727743	−	0.685850i	$-0.240570\pi$
$440$	8.40726	+	3.27286i	0.400800	+	0.156027i
$441$	−10.4275			−0.496550
$442$	−10.5678	+	10.5678i	−0.502659	+	0.502659i
$443$	−3.15593	−	3.15593i	−0.149943	−	0.149943i	0.628150	−	0.778092i	$-0.283812\pi$
$443$	−3.15593	−	3.15593i	−0.149943	−	0.149943i	−0.778092	+	0.628150i	$0.783812\pi$
$444$			6.39023i			0.303267i
$445$	4.53284	+	10.3116i	0.214877	+	0.488818i
$446$		−	2.71227i		−	0.128429i
$447$	0.156672	+	0.156672i	0.00741033	+	0.00741033i
$448$	2.95191	+	2.95191i	0.139465	+	0.139465i
$449$	18.9024			0.892060			0.446030	−	0.895018i	$-0.352838\pi$
$449$	18.9024			0.892060			0.446030	+	0.895018i	$0.352838\pi$
$450$	−4.99540	+	0.214533i	−0.235485	+	0.0101132i
$451$		−	32.3399i		−	1.52282i
$452$	6.42328	−	6.42328i	0.302126	−	0.302126i
$453$	8.10972	+	8.10972i	0.381028	+	0.381028i
$454$		−	7.93594i		−	0.372452i
$455$	−33.9202	+	14.9108i	−1.59020	+	0.699030i
$456$		−	1.01510i		−	0.0475363i
$457$	−3.87894	−	3.87894i	−0.181449	−	0.181449i	0.610538	−	0.791987i	$-0.290953\pi$
$457$	−3.87894	−	3.87894i	−0.181449	−	0.181449i	−0.791987	+	0.610538i	$0.790953\pi$
$458$	3.92815	−	3.92815i	0.183550	−	0.183550i
$459$		−	3.76514i		−	0.175742i
$460$	−2.32279	+	5.96674i	−0.108301	+	0.278201i
$461$			8.68105i			0.404317i	0.979353	+	0.202158i	$0.0647956\pi$
$461$			8.68105i			0.404317i	−0.979353	+	0.202158i	$0.935204\pi$
$462$	−11.9100	+	11.9100i	−0.554105	+	0.554105i
$463$	17.7693	−	17.7693i	0.825808	−	0.825808i	−0.161126	−	0.986934i	$-0.551512\pi$
$463$	17.7693	−	17.7693i	0.825808	−	0.825808i	0.986934	+	0.161126i	$0.0515124\pi$
$464$	−4.35667			−0.202253
$465$	1.81561	+	12.3168i	0.0841968	+	0.571178i
$466$	−17.6003			−0.815317
$467$	−8.74361	+	8.74361i	−0.404606	+	0.404606i	−0.879853	−	0.475247i	$-0.842359\pi$
$467$	−8.74361	+	8.74361i	−0.404606	+	0.404606i	0.475247	+	0.879853i	$0.342359\pi$
$468$	−2.80675	+	2.80675i	−0.129742	+	0.129742i
$469$			29.0525i			1.34152i
$470$	−1.40667	+	0.618351i	−0.0648849	+	0.0285224i
$471$		−	14.1858i		−	0.653645i
$472$	9.17578	−	9.17578i	0.422350	−	0.422350i
$473$	3.24801	+	3.24801i	0.149344	+	0.149344i
$474$			9.44004i			0.433595i
$475$	3.73960	+	3.43162i	0.171584	+	0.157454i
$476$		−	15.7181i		−	0.720436i
$477$	−2.97139	−	2.97139i	−0.136051	−	0.136051i
$478$	17.4275	−	17.4275i	0.797114	−	0.797114i
$479$		−	9.39464i		−	0.429252i	−0.976696	−	0.214626i	$-0.931147\pi$
$479$		−	9.39464i		−	0.429252i	0.976696	−	0.214626i	$-0.0688532\pi$
$480$	−2.04702	+	0.899839i	−0.0934332	+	0.0410718i
$481$	−25.3650			−1.15655
$482$	−10.7036	−	10.7036i	−0.487535	−	0.487535i
$483$	−8.45271	−	8.45271i	−0.384612	−	0.384612i
$484$			5.27872i			0.239942i
$485$	−24.4597	−	9.52191i	−1.11066	−	0.432367i
$486$		−	1.00000i		−	0.0453609i
$487$	22.3244	+	22.3244i	1.01162	+	1.01162i	0.999932	+	0.0116856i	$0.00371973\pi$
$487$	22.3244	+	22.3244i	1.01162	+	1.01162i	0.0116856	+	0.999932i	$0.496280\pi$
$488$	−5.72681	+	5.72681i	−0.259241	+	0.259241i
$489$	−3.99275			−0.180558
$490$	8.45861	−	21.7283i	0.382121	−	0.981585i
$491$			5.51033i			0.248678i	0.992240	+	0.124339i	$0.0396810\pi$
$491$			5.51033i			0.248678i	−0.992240	+	0.124339i	$0.960319\pi$
$492$	5.66778	+	5.66778i	0.255523	+	0.255523i
$493$	11.5990	+	11.5990i	0.522392	+	0.522392i
$494$	4.02927			0.181286
$495$	−3.63057	−	8.25909i	−0.163182	−	0.371218i
$496$	2.75488	+	4.83845i	0.123698	+	0.217253i
$497$	19.1702	−	19.1702i	0.859903	−	0.859903i
$498$	−7.59317	−	7.59317i	−0.340258	−	0.340258i
$499$	−12.0284			−0.538464			−0.269232	−	0.963075i	$-0.586770\pi$
$499$	−12.0284			−0.538464			−0.269232	+	0.963075i	$0.586770\pi$
$500$	3.60513	−	10.5831i	0.161226	−	0.473293i
$501$	−20.2033			−0.902615
$502$	0.272808	+	0.272808i	0.0121760	+	0.0121760i
$503$	4.36837	+	4.36837i	0.194776	+	0.194776i	0.797756	−	0.602980i	$-0.206020\pi$
$503$	4.36837	+	4.36837i	0.194776	+	0.194776i	−0.602980	+	0.797756i	$0.706020\pi$
$504$		−	4.17463i		−	0.185953i
$505$	2.59252	+	5.89767i	0.115366	+	0.262443i
$506$	−11.5532			−0.513603
$507$	−1.94856	−	1.94856i	−0.0865388	−	0.0865388i
$508$	0.444118	−	0.444118i	0.0197045	−	0.0197045i
$509$	−14.7406			−0.653367			−0.326684	−	0.945134i	$-0.605931\pi$
$509$	−14.7406			−0.653367			−0.326684	+	0.945134i	$0.605931\pi$
$510$	7.84558	+	3.05420i	0.347408	+	0.135242i
$511$			38.6865i			1.71139i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−0.717783	+	0.717783i	−0.0316909	+	0.0316909i
$514$			20.7561i			0.915514i
$515$	9.92603	−	25.4978i	0.437393	−	1.12357i
$516$	−1.13847			−0.0501185
$517$	−1.96049	−	1.96049i	−0.0862224	−	0.0862224i
$518$	18.8634	−	18.8634i	0.828810	−	0.828810i
$519$	−17.7521			−0.779231
$520$	−3.57177	−	8.12532i	−0.156632	−	0.356319i
$521$	5.07786			0.222465			0.111233	−	0.993794i	$-0.464520\pi$
$521$	5.07786			0.222465			0.111233	+	0.993794i	$0.464520\pi$
$522$	3.08063	+	3.08063i	0.134835	+	0.134835i
$523$	11.5844	−	11.5844i	0.506552	−	0.506552i	−0.406915	−	0.913466i	$-0.633395\pi$
$523$	11.5844	−	11.5844i	0.506552	−	0.506552i	0.913466	+	0.406915i	$0.133395\pi$
$524$			12.9824i			0.567137i
$525$	15.3792	+	14.1127i	0.671205	+	0.615928i
$526$		−	30.4062i		−	1.32578i
$527$	5.54721	−	20.2161i	0.241640	−	0.880629i
$528$	−2.85296	−	2.85296i	−0.124159	−	0.124159i
$529$			14.8005i			0.643501i
$530$	8.60195	−	3.78129i	0.373645	−	0.164249i
$531$	−12.9765			−0.563133
$532$	−2.99648	+	2.99648i	−0.129914	+	0.129914i
$533$	−22.4974	+	22.4974i	−0.974469	+	0.974469i
$534$		−	5.03739i		−	0.217989i
$535$	33.2354	+	12.9382i	1.43689	+	0.559366i
$536$	−6.95930			−0.300596
$537$	15.7369	−	15.7369i	0.679097	−	0.679097i
$538$	14.8408	−	14.8408i	0.639833	−	0.639833i
$539$	42.0719			1.81216
$540$	2.08374	+	0.811179i	0.0896701	+	0.0349076i
$541$	5.34555			0.229823			0.114911	−	0.993376i	$-0.463342\pi$
$541$	5.34555			0.229823			0.114911	+	0.993376i	$0.463342\pi$
$542$	−9.44340	−	9.44340i	−0.405629	−	0.405629i
$543$	−2.22305	−	2.22305i	−0.0954000	−	0.0954000i
$544$	3.76514			0.161429
$545$	−28.7220	+	12.6258i	−1.23032	+	0.540828i
$546$	16.5705			0.709154
$547$	−30.0130	+	30.0130i	−1.28326	+	1.28326i	−0.344464	+	0.938800i	$0.611939\pi$
$547$	−30.0130	+	30.0130i	−1.28326	+	1.28326i	−0.938800	+	0.344464i	$0.888061\pi$
$548$	13.4768	−	13.4768i	0.575701	−	0.575701i
$549$	8.09893			0.345654
$550$	20.1549	−	0.865576i	0.859407	−	0.0369083i
$551$		−	4.42245i		−	0.188403i
$552$	2.02478	−	2.02478i	0.0861804	−	0.0861804i
$553$	27.8661	−	27.8661i	1.18499	−	1.18499i
$554$	−32.1839			−1.36736
$555$	5.75018	+	13.0809i	0.244081	+	0.555255i
$556$		−	21.5110i		−	0.912268i
$557$	−26.7109	−	26.7109i	−1.13178	−	1.13178i	−0.989882	−	0.141895i	$-0.954680\pi$
$557$	−26.7109	−	26.7109i	−1.13178	−	1.13178i	−0.141895	−	0.989882i	$-0.545320\pi$
$558$	1.47331	−	5.36930i	0.0623702	−	0.227300i
$559$		−	4.51899i		−	0.191133i
$560$	8.69886	+	3.38637i	0.367594	+	0.143100i
$561$			15.1912i			0.641371i
$562$	−8.28598	+	8.28598i	−0.349523	+	0.349523i
$563$	16.5013	+	16.5013i	0.695446	+	0.695446i	0.963425	−	0.267978i	$-0.0863556\pi$
$563$	16.5013	+	16.5013i	0.695446	+	0.695446i	−0.267978	+	0.963425i	$0.586356\pi$
$564$	0.687180			0.0289355
$565$	7.36866	−	18.9285i	0.310002	−	0.796328i
$566$	−23.1965			−0.975023
$567$	−2.95191	+	2.95191i	−0.123969	+	0.123969i
$568$	4.59208	+	4.59208i	0.192680	+	0.192680i
$569$	−24.1381			−1.01192			−0.505962	−	0.862556i	$-0.668862\pi$
$569$	−24.1381			−1.01192			−0.505962	+	0.862556i	$0.668862\pi$
$570$	−0.913425	−	2.07793i	−0.0382592	−	0.0870347i
$571$			4.16201i			0.174175i	0.996201	+	0.0870875i	$0.0277560\pi$
$571$			4.16201i			0.174175i	−0.996201	+	0.0870875i	$0.972244\pi$
$572$	11.3244	−	11.3244i	0.473495	−	0.473495i
$573$	−10.2447	+	10.2447i	−0.427977	+	0.427977i
$574$		−	33.4615i		−	1.39666i
$575$	0.614311	+	14.3042i	0.0256185	+	0.596526i
$576$	1.00000			0.0416667
$577$	7.51725	−	7.51725i	0.312947	−	0.312947i	−0.533103	−	0.846050i	$-0.678974\pi$
$577$	7.51725	−	7.51725i	0.312947	−	0.312947i	0.846050	+	0.533103i	$0.178974\pi$
$578$	1.99669	+	1.99669i	0.0830514	+	0.0830514i
$579$	16.5356			0.687197
$580$	−8.91819	+	3.92030i	−0.370308	+	0.162782i
$581$			44.8287i			1.85981i
$582$	8.30027	+	8.30027i	0.344057	+	0.344057i
$583$	11.9886	+	11.9886i	0.496519	+	0.496519i
$584$	−9.26705			−0.383473
$585$	−3.21985	+	8.27109i	−0.133124	+	0.341968i
$586$	1.93214			0.0798158
$587$	13.1654	+	13.1654i	0.543396	+	0.543396i	0.924523	−	0.381127i	$-0.124464\pi$
$587$	13.1654	+	13.1654i	0.543396	+	0.543396i	−0.381127	+	0.924523i	$0.624464\pi$
$588$	−7.37338	+	7.37338i	−0.304073	+	0.304073i
$589$	−4.91151	+	2.79647i	−0.202375	+	0.115227i
$590$	10.5263	−	27.0397i	0.433360	−	1.11321i
$591$	22.1453			0.910938
$592$	4.51858	+	4.51858i	0.185712	+	0.185712i
$593$	7.98738	+	7.98738i	0.328002	+	0.328002i	0.851826	−	0.523824i	$-0.175495\pi$
$593$	7.98738	+	7.98738i	0.328002	+	0.328002i	−0.523824	+	0.851826i	$0.675495\pi$
$594$			4.03469i			0.165545i
$595$	−14.1437	−	32.1752i	−0.579836	−	1.31905i
$596$	0.221568			0.00907577
$597$	−10.2225	+	10.2225i	−0.418378	+	0.418378i
$598$	8.03705	+	8.03705i	0.328659	+	0.328659i
$599$		−	3.56015i		−	0.145464i	−0.997352	−	0.0727318i	$-0.976828\pi$
$599$		−	3.56015i		−	0.145464i	0.997352	−	0.0727318i	$-0.0231717\pi$
$600$	−3.38058	+	3.68398i	−0.138012	+	0.150398i
$601$			21.1871i			0.864239i	0.901816	+	0.432120i	$0.142234\pi$
$601$			21.1871i			0.864239i	−0.901816	+	0.432120i	$0.857766\pi$
$602$	3.36067	+	3.36067i	0.136971	+	0.136971i
$603$	4.92097	+	4.92097i	0.200397	+	0.200397i
$604$	11.4689			0.466662
$605$	4.75000	+	10.8056i	0.193115	+	0.439312i
$606$		−	2.88110i		−	0.117037i
$607$	−11.0204	+	11.0204i	−0.447305	+	0.447305i	−0.894458	−	0.447153i	$-0.852438\pi$
$607$	−11.0204	+	11.0204i	−0.447305	+	0.447305i	0.447153	+	0.894458i	$0.352438\pi$
$608$	−0.717783	−	0.717783i	−0.0291099	−	0.0291099i
$609$		−	18.1875i		−	0.736994i
$610$	−6.56969	+	16.8761i	−0.265999	+	0.683293i
$611$			2.72765i			0.110349i
$612$	−2.66235	−	2.66235i	−0.107619	−	0.107619i
$613$	29.3900	−	29.3900i	1.18705	−	1.18705i	0.209171	−	0.977879i	$-0.432923\pi$
$613$	29.3900	−	29.3900i	1.18705	−	1.18705i	0.977879	−	0.209171i	$-0.0670766\pi$
$614$			0.711167i			0.0287004i
$615$	16.7021	+	6.50197i	0.673496	+	0.262185i
$616$			16.8433i			0.678637i
$617$	−7.25887	+	7.25887i	−0.292231	+	0.292231i	−0.837961	−	0.545730i	$-0.816252\pi$
$617$	−7.25887	+	7.25887i	−0.292231	+	0.292231i	0.545730	+	0.837961i	$0.316252\pi$
$618$	−8.65254	+	8.65254i	−0.348056	+	0.348056i
$619$	−42.3564			−1.70245			−0.851224	−	0.524803i	$-0.824139\pi$
$619$	−42.3564			−1.70245			−0.851224	+	0.524803i	$0.824139\pi$
$620$	9.99312	+	7.42546i	0.401333	+	0.298214i
$621$	−2.86347			−0.114907
$622$	−16.6959	+	16.6959i	−0.669443	+	0.669443i
$623$	−14.8699	+	14.8699i	−0.595750	+	0.595750i
$624$			3.96934i			0.158901i
$625$	−2.14336	−	24.9080i	−0.0857343	−	0.996318i
$626$			18.2260i			0.728458i
$627$	2.89603	−	2.89603i	0.115656	−	0.115656i
$628$	−10.0308	−	10.0308i	−0.400274	−	0.400274i
$629$		−	24.0601i		−	0.959339i
$630$	−3.75649	−	8.54555i	−0.149662	−	0.340463i
$631$			34.7320i			1.38266i	0.722540	+	0.691329i	$0.242975\pi$
$631$			34.7320i			1.38266i	−0.722540	+	0.691329i	$0.757025\pi$
$632$	6.67512	+	6.67512i	0.265522	+	0.265522i
$633$	−5.85196	+	5.85196i	−0.232594	+	0.232594i
$634$		−	2.15755i		−	0.0856873i
$635$	0.509483	−	1.30875i	0.0202182	−	0.0519362i
$636$	−4.20218			−0.166627
$637$	−29.2675	−	29.2675i	−1.15962	−	1.15962i
$638$	−12.4294	−	12.4294i	−0.492084	−	0.492084i
$639$		−	6.49419i		−	0.256906i
$640$	−0.811179	+	2.08374i	−0.0320647	+	0.0823672i
$641$		−	24.4321i		−	0.965011i	−0.875893	−	0.482505i	$-0.839727\pi$
$641$		−	24.4321i		−	0.965011i	0.875893	−	0.482505i	$-0.160273\pi$
$642$	−11.2782	−	11.2782i	−0.445116	−	0.445116i
$643$	−29.6839	+	29.6839i	−1.17062	+	1.17062i	−0.188557	+	0.982062i	$0.560381\pi$
$643$	−29.6839	+	29.6839i	−1.17062	+	1.17062i	−0.982062	+	0.188557i	$0.939619\pi$
$644$	−11.9539			−0.471051
$645$	−2.33048	+	1.02444i	−0.0917624	+	0.0403374i
$646$			3.82198i			0.150374i
$647$	−1.52435	−	1.52435i	−0.0599282	−	0.0599282i	0.676507	−	0.736436i	$-0.263493\pi$
$647$	−1.52435	−	1.52435i	−0.0599282	−	0.0599282i	−0.736436	+	0.676507i	$0.763493\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	52.3562			2.05516
$650$	−14.6230	−	13.4187i	−0.573560	−	0.526324i
$651$	−20.1988	+	11.5006i	−0.791652	+	0.450744i
$652$	−2.82330	+	2.82330i	−0.110569	+	0.110569i
$653$	−23.7269	−	23.7269i	−0.928504	−	0.928504i	0.0691055	−	0.997609i	$-0.477985\pi$
$653$	−23.7269	−	23.7269i	−0.928504	−	0.928504i	−0.997609	+	0.0691055i	$0.977985\pi$
$654$	14.0311			0.548661
$655$	11.6820	+	26.5751i	0.456455	+	1.03838i
$656$	8.01545			0.312951
$657$	6.55280	+	6.55280i	0.255649	+	0.255649i
$658$	−2.02849	−	2.02849i	−0.0790789	−	0.0790789i
$659$			39.5459i			1.54049i	0.637747	+	0.770246i	$0.279866\pi$
$659$			39.5459i			1.54049i	−0.637747	+	0.770246i	$0.720134\pi$
$660$	−8.40726	−	3.27286i	−0.327252	−	0.127396i
$661$	15.6588			0.609057			0.304529	−	0.952503i	$-0.401501\pi$
$661$	15.6588			0.609057			0.304529	+	0.952503i	$0.401501\pi$
$662$	−7.24116	−	7.24116i	−0.281436	−	0.281436i
$663$	10.5678	−	10.5678i	0.410419	−	0.410419i
$664$	−10.7384			−0.416729
$665$	−3.43750	+	8.83020i	−0.133301	+	0.342420i
$666$		−	6.39023i		−	0.247616i
$667$	8.82130	−	8.82130i	0.341562	−	0.341562i
$668$	−14.2859	+	14.2859i	−0.552737	+	0.552737i
$669$			2.71227i			0.104862i
$670$	−14.2458	+	6.26225i	−0.550365	+	0.241932i
$671$	−32.6767			−1.26147
$672$	−2.95191	−	2.95191i	−0.113872	−	0.113872i
$673$	12.3713	−	12.3713i	0.476880	−	0.476880i	−0.427253	−	0.904132i	$-0.640519\pi$
$673$	12.3713	−	12.3713i	0.476880	−	0.476880i	0.904132	+	0.427253i	$0.140519\pi$
$674$	−26.2113			−1.00962
$675$	4.99540	−	0.214533i	0.192273	−	0.00825740i
$676$	−2.75569			−0.105988
$677$	27.6460	+	27.6460i	1.06252	+	1.06252i	0.997911	+	0.0646102i	$0.0205804\pi$
$677$	27.6460	+	27.6460i	1.06252	+	1.06252i	0.0646102	+	0.997911i	$0.479420\pi$
$678$	−6.42328	+	6.42328i	−0.246685	+	0.246685i
$679$		−	49.0033i		−	1.88057i
$680$	7.70731	−	3.38802i	0.295562	−	0.129924i
$681$			7.93594i			0.304106i
$682$	−5.94435	+	21.6634i	−0.227621	+	0.829536i
$683$	−16.3646	−	16.3646i	−0.626174	−	0.626174i	0.320929	−	0.947103i	$-0.396005\pi$
$683$	−16.3646	−	16.3646i	−0.626174	−	0.626174i	−0.947103	+	0.320929i	$0.896005\pi$
$684$			1.01510i			0.0388132i
$685$	15.4603	−	39.7143i	0.590709	−	1.51740i
$686$	14.3087			0.546309
$687$	−3.92815	+	3.92815i	−0.149868	+	0.149868i
$688$	−0.805022	+	0.805022i	−0.0306912	+	0.0306912i
$689$		−	16.6799i		−	0.635454i
$690$	2.32279	−	5.96674i	0.0884271	−	0.227150i
$691$	−34.2989			−1.30479			−0.652395	−	0.757879i	$-0.726236\pi$
$691$	−34.2989			−1.30479			−0.652395	+	0.757879i	$0.726236\pi$
$692$	−12.5526	+	12.5526i	−0.477180	+	0.477180i
$693$	11.9100	−	11.9100i	0.452425	−	0.452425i
$694$	24.8133			0.941899
$695$	−19.3564	−	44.0334i	−0.734230	−	1.67028i
$696$	4.35667			0.165139
$697$	−21.3400	−	21.3400i	−0.808309	−	0.808309i
$698$	22.0239	+	22.0239i	0.833616	+	0.833616i
$699$	17.6003			0.665703
$700$	20.8539	−	0.895598i	0.788204	−	0.0338504i
$701$	26.5443			1.00257			0.501283	−	0.865283i	$-0.332862\pi$
$701$	26.5443			1.00257			0.501283	+	0.865283i	$0.332862\pi$
$702$	2.80675	−	2.80675i	0.105934	−	0.105934i
$703$	−4.58680	+	4.58680i	−0.172994	+	0.172994i
$704$	−4.03469			−0.152063
$705$	1.40667	−	0.618351i	0.0529783	−	0.0232884i
$706$			10.6981i			0.402627i
$707$	−8.50474	+	8.50474i	−0.319854	+	0.319854i
$708$	−9.17578	+	9.17578i	−0.344847	+	0.344847i
$709$	−42.1917			−1.58454			−0.792272	−	0.610169i	$-0.791102\pi$
$709$	−42.1917			−1.58454			−0.792272	+	0.610169i	$0.791102\pi$
$710$	13.5322	+	5.26795i	0.507855	+	0.197703i
$711$		−	9.44004i		−	0.354029i
$712$	−3.56197	−	3.56197i	−0.133490	−	0.133490i
$713$	−15.3748	−	4.21878i	−0.575792	−	0.157995i
$714$			15.7181i			0.588233i
$715$	12.9911	−	33.3713i	0.485839	−	1.24802i
$716$		−	22.2553i		−	0.831720i
$717$	−17.4275	+	17.4275i	−0.650841	+	0.650841i
$718$	−9.51297	−	9.51297i	−0.355021	−	0.355021i
$719$	39.9630			1.49037			0.745183	−	0.666860i	$-0.232362\pi$
$719$	39.9630			1.49037			0.745183	+	0.666860i	$0.232362\pi$
$720$	2.04702	−	0.899839i	0.0762879	−	0.0335350i
$721$	51.0830			1.90243
$722$	−12.7064	+	12.7064i	−0.472884	+	0.472884i
$723$	10.7036	+	10.7036i	0.398071	+	0.398071i
$724$	−3.14386			−0.116841
$725$	−14.7281	+	16.0499i	−0.546987	+	0.596077i
$726$		−	5.27872i		−	0.195912i
$727$	−27.1518	+	27.1518i	−1.00700	+	1.00700i	−0.00702780	+	0.999975i	$0.502237\pi$
$727$	−27.1518	+	27.1518i	−1.00700	+	1.00700i	−0.999975	+	0.00702780i	$0.997763\pi$
$728$	11.7171	−	11.7171i	0.434266	−	0.434266i
$729$			1.00000i			0.0370370i
$730$	−18.9698	+	8.33885i	−0.702105	+	0.308635i
$731$	4.28651			0.158542
$732$	5.72681	−	5.72681i	0.211669	−	0.211669i
$733$	34.0779	+	34.0779i	1.25870	+	1.25870i	0.951716	+	0.306979i	$0.0993183\pi$
$733$	34.0779	+	34.0779i	1.25870	+	1.25870i	0.306979	+	0.951716i	$0.400682\pi$
$734$	−21.6734			−0.799982
$735$	−8.45861	+	21.7283i	−0.312000	+	0.801461i
$736$		−	2.86347i		−	0.105549i
$737$	−19.8546	−	19.8546i	−0.731353	−	0.731353i
$738$	−5.66778	−	5.66778i	−0.208634	−	0.208634i
$739$	16.9876			0.624897			0.312449	−	0.949935i	$-0.398851\pi$
$739$	16.9876			0.624897			0.312449	+	0.949935i	$0.398851\pi$
$740$	13.3156	+	5.18362i	0.489491	+	0.190554i
$741$	−4.02927			−0.148019
$742$	12.4045	+	12.4045i	0.455382	+	0.455382i
$743$	−19.2665	+	19.2665i	−0.706818	+	0.706818i	−0.965865	−	0.259047i	$-0.916592\pi$
$743$	−19.2665	+	19.2665i	−0.706818	+	0.706818i	0.259047	+	0.965865i	$0.416592\pi$
$744$	−2.75488	−	4.83845i	−0.100999	−	0.177386i
$745$	0.453553	−	0.199375i	0.0166169	−	0.00730454i
$746$	25.6666			0.939721
$747$	7.59317	+	7.59317i	0.277820	+	0.277820i
$748$	10.7418	+	10.7418i	0.392758	+	0.392758i
$749$			66.5847i			2.43295i
$750$	−3.60513	+	10.5831i	−0.131641	+	0.386442i
$751$	−40.8167			−1.48942			−0.744710	−	0.667388i	$-0.767412\pi$
$751$	−40.8167			−1.48942			−0.744710	+	0.667388i	$0.767412\pi$
$752$	0.485909	−	0.485909i	0.0177193	−	0.0177193i
$753$	−0.272808	−	0.272808i	−0.00994166	−	0.00994166i
$754$			17.2931i			0.629778i
$755$	23.4770	−	10.3201i	0.854416	−	0.375588i
$756$			4.17463i			0.151830i
$757$	−16.0389	−	16.0389i	−0.582943	−	0.582943i	0.352768	−	0.935711i	$-0.385241\pi$
$757$	−16.0389	−	16.0389i	−0.582943	−	0.582943i	−0.935711	+	0.352768i	$0.885241\pi$
$758$	−8.54222	−	8.54222i	−0.310267	−	0.310267i
$759$	11.5532			0.419355
$760$	−2.11520	−	0.823427i	−0.0767265	−	0.0298688i
$761$		−	16.2603i		−	0.589437i	−0.955584	−	0.294718i	$-0.904774\pi$
$761$		−	16.2603i		−	0.589437i	0.955584	−	0.294718i	$-0.0952258\pi$
$762$	−0.444118	+	0.444118i	−0.0160887	+	0.0160887i
$763$	−41.4187	−	41.4187i	−1.49946	−	1.49946i
$764$			14.4881i			0.524162i
$765$	−7.84558	−	3.05420i	−0.283658	−	0.110425i
$766$		−	7.33434i		−	0.265001i
$767$	−36.4218	−	36.4218i	−1.31512	−	1.31512i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$		−	7.52534i		−	0.271371i	−0.990752	−	0.135685i	$-0.956676\pi$
$769$		−	7.52534i		−	0.271371i	0.990752	−	0.135685i	$-0.0433236\pi$
$770$	15.1563	+	34.4786i	0.546195	+	1.24252i
$771$		−	20.7561i		−	0.747514i
$772$	11.6924	−	11.6924i	0.420820	−	0.420820i
$773$	−6.55832	+	6.55832i	−0.235886	+	0.235886i	−0.815144	−	0.579258i	$-0.803342\pi$
$773$	−6.55832	+	6.55832i	−0.235886	+	0.235886i	0.579258	+	0.815144i	$0.303342\pi$
$774$	1.13847			0.0409216
$775$	27.1378	+	6.20787i	0.974820	+	0.222993i
$776$	11.7383			0.421382
$777$	−18.8634	+	18.8634i	−0.676720	+	0.676720i
$778$	−3.77557	+	3.77557i	−0.135361	+	0.135361i
$779$			8.13647i			0.291519i
$780$	3.57177	+	8.12532i	0.127890	+	0.290933i
$781$			26.2020i			0.937582i
$782$	−7.62358	+	7.62358i	−0.272619	+	0.272619i
$783$	−3.08063	−	3.08063i	−0.110093	−	0.110093i
$784$			10.4275i			0.372412i
$785$	−29.5595	−	11.5072i	−1.05502	−	0.410709i
$786$		−	12.9824i		−	0.463065i
$787$	−30.6420	−	30.6420i	−1.09227	−	1.09227i	−0.995286	−	0.0969850i	$-0.969080\pi$
$787$	−30.6420	−	30.6420i	−1.09227	−	1.09227i	−0.0969850	−	0.995286i	$-0.530920\pi$
$788$	15.6591	−	15.6591i	0.557833	−	0.557833i
$789$			30.4062i			1.08249i
$790$	19.6706	+	7.65756i	0.699849	+	0.272444i
$791$	37.9219			1.34835
$792$	2.85296	+	2.85296i	0.101375	+	0.101375i
$793$	22.7317	+	22.7317i	0.807226	+	0.807226i
$794$		−	1.99927i		−	0.0709514i
$795$	−8.60195	+	3.78129i	−0.305080	+	0.134108i
$796$			14.4567i			0.512406i
$797$	2.53778	+	2.53778i	0.0898928	+	0.0898928i	0.750623	−	0.660730i	$-0.229753\pi$
$797$	2.53778	+	2.53778i	0.0898928	+	0.0898928i	−0.660730	+	0.750623i	$0.729753\pi$
$798$	2.99648	−	2.99648i	0.106074	−	0.106074i
$799$	−2.58733			−0.0915330
$800$	0.214533	+	4.99540i	0.00758490	+	0.176614i
$801$			5.03739i			0.177987i
$802$	2.23621	+	2.23621i	0.0789633	+	0.0789633i
$803$	−26.4385	−	26.4385i	−0.932994	−	0.932994i
$804$	6.95930			0.245436
$805$	−24.4700	+	10.7566i	−0.862453	+	0.379121i
$806$	19.2055	−	10.9351i	0.676484	−	0.385171i
$807$	−14.8408	+	14.8408i	−0.522421	+	0.522421i
$808$	−2.03724	−	2.03724i	−0.0716700	−	0.0716700i
$809$	5.85839			0.205970			0.102985	−	0.994683i	$-0.467161\pi$
$809$	5.85839			0.205970			0.102985	+	0.994683i	$0.467161\pi$
$810$	−2.08374	−	0.811179i	−0.0732153	−	0.0285019i
$811$	−39.7619			−1.39623			−0.698115	−	0.715986i	$-0.745977\pi$
$811$	−39.7619			−1.39623			−0.698115	+	0.715986i	$0.745977\pi$
$812$	−12.8605	−	12.8605i	−0.451315	−	0.451315i
$813$	9.44340	+	9.44340i	0.331194	+	0.331194i
$814$			25.7826i			0.903680i
$815$	−3.23884	+	8.31986i	−0.113451	+	0.291432i
$816$	−3.76514			−0.131806
$817$	−0.817176	−	0.817176i	−0.0285894	−	0.0285894i
$818$	−3.76797	+	3.76797i	−0.131744	+	0.131744i
$819$	−16.5705			−0.579022
$820$	16.4078	−	7.21261i	0.572985	−	0.251875i
$821$		−	50.6248i		−	1.76682i	−0.468604	−	0.883408i	$-0.655243\pi$
$821$		−	50.6248i		−	1.76682i	0.468604	−	0.883408i	$-0.344757\pi$
$822$	−13.4768	+	13.4768i	−0.470058	+	0.470058i
$823$	−32.2721	+	32.2721i	−1.12493	+	1.12493i	−0.133945	+	0.990989i	$0.542764\pi$
$823$	−32.2721	+	32.2721i	−1.12493	+	1.12493i	−0.990989	+	0.133945i	$0.957236\pi$
$824$			12.2365i			0.426280i
$825$	−20.1549	+	0.865576i	−0.701702	+	0.0301355i
$826$	54.1722			1.88489
$827$	19.7409	+	19.7409i	0.686460	+	0.686460i	0.961448	−	0.274988i	$-0.0886738\pi$
$827$	19.7409	+	19.7409i	0.686460	+	0.686460i	−0.274988	+	0.961448i	$0.588674\pi$
$828$	−2.02478	+	2.02478i	−0.0703660	+	0.0703660i
$829$	−52.4332			−1.82108			−0.910540	−	0.413421i	$-0.864334\pi$
$829$	−52.4332			−1.82108			−0.910540	+	0.413421i	$0.864334\pi$
$830$	−21.9816	+	9.66280i	−0.762994	+	0.335401i
$831$	32.1839			1.11645
$832$	2.80675	+	2.80675i	0.0973065	+	0.0973065i
$833$	27.7618	−	27.7618i	0.961889	−	0.961889i
$834$			21.5110i			0.744864i
$835$	−16.3885	+	42.0984i	−0.567147	+	1.45688i
$836$		−	4.09561i		−	0.141649i
$837$	−1.47331	+	5.36930i	−0.0509250	+	0.185590i
$838$	15.0519	+	15.0519i	0.519959	+	0.519959i
$839$			35.4933i			1.22537i	0.790329	+	0.612683i	$0.209910\pi$
$839$			35.4933i			1.22537i	−0.790329	+	0.612683i	$0.790090\pi$
$840$	−8.69886	−	3.38637i	−0.300139	−	0.116841i
$841$	−10.0194			−0.345498
$842$	−16.3643	+	16.3643i	−0.563949	+	0.563949i
$843$	8.28598	−	8.28598i	0.285384	−	0.285384i
$844$			8.27591i			0.284869i
$845$	−5.64095	+	2.47967i	−0.194054	+	0.0853034i
$846$	−0.687180			−0.0236257
$847$	−15.5823	+	15.5823i	−0.535414	+	0.535414i
$848$	−2.97139	+	2.97139i	−0.102038	+	0.102038i
$849$	23.1965			0.796103
$850$	12.7283	−	13.8707i	0.436579	−	0.475760i
$851$	−18.2983			−0.627256
$852$	−4.59208	−	4.59208i	−0.157322	−	0.157322i
$853$	−20.1909	−	20.1909i	−0.691323	−	0.691323i	0.271200	−	0.962523i	$-0.412580\pi$
$853$	−20.1909	−	20.1909i	−0.691323	−	0.691323i	−0.962523	+	0.271200i	$0.912580\pi$
$854$	−33.8101			−1.15696
$855$	0.913425	+	2.07793i	0.0312385	+	0.0710636i
$856$	−15.9498			−0.545154
$857$	31.3119	−	31.3119i	1.06959	−	1.06959i	0.0722034	−	0.997390i	$-0.476997\pi$
$857$	31.3119	−	31.3119i	1.06959	−	1.06959i	0.997390	−	0.0722034i	$-0.0230031\pi$
$858$	−11.3244	+	11.3244i	−0.386607	+	0.386607i
$859$	−24.2766			−0.828308			−0.414154	−	0.910207i	$-0.635922\pi$
$859$	−24.2766			−0.828308			−0.414154	+	0.910207i	$0.635922\pi$
$860$	−0.923506	+	2.37229i	−0.0314913	+	0.0808943i
$861$			33.4615i			1.14037i
$862$	−21.1796	+	21.1796i	−0.721379	+	0.721379i
$863$	20.5511	−	20.5511i	0.699568	−	0.699568i	−0.264749	−	0.964317i	$-0.585289\pi$
$863$	20.5511	−	20.5511i	0.699568	−	0.699568i	0.964317	+	0.264749i	$0.0852892\pi$
$864$	−1.00000			−0.0340207
$865$	−14.4002	+	36.9909i	−0.489620	+	1.25773i
$866$			4.40411i			0.149658i
$867$	−1.99669	−	1.99669i	−0.0678112	−	0.0678112i
$868$	−6.15052	+	22.4148i	−0.208762	+	0.760809i
$869$			38.0876i			1.29203i
$870$	8.91819	−	3.92030i	0.302355	−	0.132911i
$871$			27.6239i			0.935999i
$872$	9.92151	−	9.92151i	0.335985	−	0.335985i
$873$	−8.30027	−	8.30027i	−0.280921	−	0.280921i
$874$	2.90671			0.0983208
$875$	41.8825	−	20.5985i	1.41589	−	0.696356i
$876$	9.26705			0.313105
$877$	−4.50607	+	4.50607i	−0.152159	+	0.152159i	−0.779082	−	0.626922i	$-0.784314\pi$
$877$	−4.50607	+	4.50607i	−0.152159	+	0.152159i	0.626922	+	0.779082i	$0.284314\pi$
$878$	20.3225	+	20.3225i	0.685850	+	0.685850i
$879$	−1.93214			−0.0651694
$880$	−8.25909	+	3.63057i	−0.278414	+	0.122387i
$881$		−	9.83063i		−	0.331202i	−0.986193	−	0.165601i	$-0.947044\pi$
$881$		−	9.83063i		−	0.331202i	0.986193	−	0.165601i	$-0.0529565\pi$
$882$	7.37338	−	7.37338i	0.248275	−	0.248275i
$883$	18.4307	−	18.4307i	0.620241	−	0.620241i	−0.325352	−	0.945593i	$-0.605483\pi$
$883$	18.4307	−	18.4307i	0.620241	−	0.620241i	0.945593	+	0.325352i	$0.105483\pi$
$884$		−	14.9451i		−	0.502659i
$885$	−10.5263	+	27.0397i	−0.353837	+	0.908931i
$886$	4.46315			0.149943
$887$	6.97326	−	6.97326i	0.234139	−	0.234139i	−0.580279	−	0.814418i	$-0.697056\pi$
$887$	6.97326	−	6.97326i	0.234139	−	0.234139i	0.814418	+	0.580279i	$0.197056\pi$
$888$	−4.51858	−	4.51858i	−0.151633	−	0.151633i
$889$	2.62199			0.0879387
$890$	−10.4966	−	4.08622i	−0.351848	−	0.136971i
$891$		−	4.03469i		−	0.135167i
$892$	1.91786	+	1.91786i	0.0642147	+	0.0642147i
$893$	0.493246	+	0.493246i	0.0165058	+	0.0165058i
$894$	−0.221568			−0.00741033
$895$	−20.0262	−	45.5571i	−0.669402	−	1.52281i
$896$	−4.17463			−0.139465
$897$	−8.03705	−	8.03705i	−0.268349	−	0.268349i
$898$	−13.3660	+	13.3660i	−0.446030	+	0.446030i
$899$	−12.0021	−	21.0795i	−0.400292	−	0.703042i
$900$	3.38058	−	3.68398i	0.112686	−	0.122799i
$901$	15.8218			0.527100
$902$	22.8677	+	22.8677i	0.761412	+	0.761412i
$903$	−3.36067	−	3.36067i	−0.111836	−	0.111836i
$904$			9.08389i			0.302126i
$905$	−6.43555	+	2.82897i	−0.213925	+	0.0940381i
$906$	−11.4689			−0.381028
$907$	36.7566	−	36.7566i	1.22048	−	1.22048i	0.253020	−	0.967461i	$-0.418576\pi$
$907$	36.7566	−	36.7566i	1.22048	−	1.22048i	0.967461	−	0.253020i	$-0.0814240\pi$
$908$	5.61156	+	5.61156i	0.186226	+	0.186226i
$909$			2.88110i			0.0955600i
$910$	13.4417	−	34.5288i	0.445587	−	1.14462i
$911$		−	53.0903i		−	1.75896i	−0.475935	−	0.879481i	$-0.657890\pi$
$911$		−	53.0903i		−	1.75896i	0.475935	−	0.879481i	$-0.342110\pi$
$912$	0.717783	+	0.717783i	0.0237682	+	0.0237682i
$913$	−30.6361	−	30.6361i	−1.01391	−	1.01391i
$914$	5.48565			0.181449
$915$	6.56969	−	16.8761i	0.217187	−	0.557907i
$916$			5.55524i			0.183550i
$917$	−38.3227	+	38.3227i	−1.26553	+	1.26553i
$918$	2.66235	+	2.66235i	0.0878708	+	0.0878708i
$919$			20.9427i			0.690836i	0.938449	+	0.345418i	$0.112263\pi$
$919$			20.9427i			0.690836i	−0.938449	+	0.345418i	$0.887737\pi$
$920$	−2.57666	−	5.86159i	−0.0849501	−	0.193251i
$921$		−	0.711167i		−	0.0234338i
$922$	−6.13843	−	6.13843i	−0.202158	−	0.202158i
$923$	18.2276	−	18.2276i	0.599967	−	0.599967i
$924$		−	16.8433i		−	0.554105i
$925$	31.9217	−	1.37092i	1.04958	−	0.0450755i
$926$			25.1296i			0.825808i
$927$	8.65254	−	8.65254i	0.284187	−	0.284187i
$928$	3.08063	−	3.08063i	0.101127	−	0.101127i
$929$	7.44039			0.244111			0.122056	−	0.992523i	$-0.461051\pi$
$929$	7.44039			0.244111			0.122056	+	0.992523i	$0.461051\pi$
$930$	−9.99312	−	7.42546i	−0.327687	−	0.243491i
$931$	−10.5850			−0.346909
$932$	12.4453	−	12.4453i	0.407658	−	0.407658i
$933$	16.6959	−	16.6959i	0.546598	−	0.546598i
$934$		−	12.3653i		−	0.404606i
$935$	31.6545	+	12.3228i	1.03521	+	0.402997i
$936$		−	3.96934i		−	0.129742i
$937$	5.93410	−	5.93410i	0.193859	−	0.193859i	−0.603502	−	0.797361i	$-0.706229\pi$
$937$	5.93410	−	5.93410i	0.193859	−	0.193859i	0.797361	+	0.603502i	$0.206229\pi$
$938$	−20.5432	−	20.5432i	−0.670760	−	0.670760i
$939$		−	18.2260i		−	0.594784i
$940$	0.557426	−	1.43191i	0.0181812	−	0.0467036i
$941$			54.9327i			1.79076i	0.445308	+	0.895378i	$0.353094\pi$
$941$			54.9327i			1.79076i	−0.445308	+	0.895378i	$0.646906\pi$
$942$	10.0308	+	10.0308i	0.326823	+	0.326823i
$943$	−16.2295	+	16.2295i	−0.528506	+	0.528506i
$944$			12.9765i			0.422350i
$945$	3.75649	+	8.54555i	0.122199	+	0.277987i
$946$	−4.59338			−0.149344
$947$	−32.0224	−	32.0224i	−1.04059	−	1.04059i	−0.999141	−	0.0414489i	$-0.986803\pi$
$947$	−32.0224	−	32.0224i	−1.04059	−	1.04059i	−0.0414489	−	0.999141i	$-0.513197\pi$
$948$	−6.67512	−	6.67512i	−0.216798	−	0.216798i
$949$			36.7841i			1.19406i
$950$	−5.07082	+	0.217772i	−0.164519	+	0.00706547i
$951$			2.15755i			0.0699634i
$952$	11.1143	+	11.1143i	0.360218	+	0.360218i
$953$	−26.2199	+	26.2199i	−0.849345	+	0.849345i	−0.990051	−	0.140707i	$-0.955063\pi$
$953$	−26.2199	+	26.2199i	−0.849345	+	0.849345i	0.140707	+	0.990051i	$0.455063\pi$
$954$	4.20218			0.136051
$955$	13.0370	+	29.6575i	0.421867	+	0.959694i
$956$			24.6462i			0.797114i
$957$	12.4294	+	12.4294i	0.401785	+	0.401785i
$958$	6.64301	+	6.64301i	0.214626	+	0.214626i
$959$	79.5646			2.56928
$960$	0.811179	−	2.08374i	0.0261807	−	0.0672525i
$961$	−15.8213	+	26.6587i	−0.510364	+	0.859959i
$962$	17.9358	−	17.9358i	0.578273	−	0.578273i
$963$	11.2782	+	11.2782i	0.363436	+	0.363436i
$964$	15.1372			0.487535
$965$	13.4133	−	34.4560i	0.431791	−	1.10918i
$966$	11.9539			0.384612
$967$	18.2620	+	18.2620i	0.587267	+	0.587267i	0.936890	−	0.349623i	$-0.113690\pi$
$967$	18.2620	+	18.2620i	0.587267	+	0.587267i	−0.349623	+	0.936890i	$0.613690\pi$
$968$	−3.73262	−	3.73262i	−0.119971	−	0.119971i
$969$		−	3.82198i		−	0.122780i
$970$	24.0286	−	10.5626i	0.771513	−	0.339145i
$971$	−21.3719			−0.685858			−0.342929	−	0.939361i	$-0.611419\pi$
$971$	−21.3719			−0.685858			−0.342929	+	0.939361i	$0.611419\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	63.4984	−	63.4984i	2.03567	−	2.03567i
$974$	−31.5715			−1.01162
$975$	14.6230	+	13.4187i	0.468310	+	0.429742i
$976$		−	8.09893i		−	0.259241i
$977$	−13.4924	+	13.4924i	−0.431659	+	0.431659i	−0.889193	−	0.457533i	$-0.848733\pi$
$977$	−13.4924	+	13.4924i	−0.431659	+	0.431659i	0.457533	+	0.889193i	$0.348733\pi$
$978$	2.82330	−	2.82330i	0.0902792	−	0.0902792i
$979$		−	20.3243i		−	0.649567i
$980$	9.38311	+	21.3454i	0.299732	+	0.681853i
$981$	−14.0311			−0.447980
$982$	−3.89639	−	3.89639i	−0.124339	−	0.124339i
$983$	5.92278	−	5.92278i	0.188907	−	0.188907i	−0.606316	−	0.795224i	$-0.707353\pi$
$983$	5.92278	−	5.92278i	0.188907	−	0.188907i	0.795224	+	0.606316i	$0.207353\pi$
$984$	−8.01545			−0.255523
$985$	17.9638	−	46.1452i	0.572376	−	1.47031i
$986$	−16.4035			−0.522392
$987$	2.02849	+	2.02849i	0.0645676	+	0.0645676i
$988$	−2.84913	+	2.84913i	−0.0906428	+	0.0906428i
$989$		−	3.25999i		−	0.103662i
$990$	8.40726	+	3.27286i	0.267200	+	0.104018i
$991$		−	15.0645i		−	0.478541i	−0.970953	−	0.239270i	$-0.923092\pi$
$991$		−	15.0645i		−	0.478541i	0.970953	−	0.239270i	$-0.0769083\pi$
$992$	−5.36930	−	1.47331i	−0.170475	−	0.0467776i
$993$	7.24116	+	7.24116i	0.229791	+	0.229791i
$994$			27.1108i			0.859903i
$995$	13.0087	+	29.5932i	0.412405	+	0.938169i
$996$	10.7384			0.340258
$997$	22.5763	−	22.5763i	0.714998	−	0.714998i	−0.252579	−	0.967576i	$-0.581279\pi$
$997$	22.5763	−	22.5763i	0.714998	−	0.714998i	0.967576	+	0.252579i	$0.0812787\pi$
$998$	8.50535	−	8.50535i	0.269232	−	0.269232i
$999$			6.39023i			0.202178i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.k.a.433.4	yes	32
5.2	odd	4		930.2.k.b.247.4	yes	32
31.30	odd	2		930.2.k.b.433.4	yes	32
155.92	even	4	inner	930.2.k.a.247.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.k.a.247.4	✓	32	155.92	even	4	inner
930.2.k.a.433.4	yes	32	1.1	even	1	trivial
930.2.k.b.247.4	yes	32	5.2	odd	4
930.2.k.b.433.4	yes	32	31.30	odd	2

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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-0.899839 - 2.04702i) q^{5} +1.00000i q^{6} +(2.95191 - 2.95191i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-0.899839 - 2.04702i) q^{5} +1.00000i q^{6} +(2.95191 - 2.95191i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(2.08374 + 0.811179i) q^{10} +4.03469i q^{11} +(-0.707107 - 0.707107i) q^{12} +(2.80675 - 2.80675i) q^{13} +4.17463i q^{14} +(-2.08374 - 0.811179i) q^{15} -1.00000 q^{16} +(2.66235 + 2.66235i) q^{17} +(0.707107 + 0.707107i) q^{18} -1.01510i q^{19} +(-2.04702 + 0.899839i) q^{20} -4.17463i q^{21} +(-2.85296 - 2.85296i) q^{22} +(2.02478 - 2.02478i) q^{23} +1.00000 q^{24} +(-3.38058 + 3.68398i) q^{25} +3.96934i q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.95191 - 2.95191i) q^{28} +4.35667 q^{29} +(2.04702 - 0.899839i) q^{30} +(-2.75488 - 4.83845i) q^{31} +(0.707107 - 0.707107i) q^{32} +(2.85296 + 2.85296i) q^{33} -3.76514 q^{34} +(-8.69886 - 3.38637i) q^{35} -1.00000 q^{36} +(-4.51858 - 4.51858i) q^{37} +(0.717783 + 0.717783i) q^{38} -3.96934i q^{39} +(0.811179 - 2.08374i) q^{40} -8.01545 q^{41} +(2.95191 + 2.95191i) q^{42} +(0.805022 - 0.805022i) q^{43} +4.03469 q^{44} +(-2.04702 + 0.899839i) q^{45} +2.86347i q^{46} +(-0.485909 + 0.485909i) q^{47} +(-0.707107 + 0.707107i) q^{48} -10.4275i q^{49} +(-0.214533 - 4.99540i) q^{50} +3.76514 q^{51} +(-2.80675 - 2.80675i) q^{52} +(2.97139 - 2.97139i) q^{53} +1.00000 q^{54} +(8.25909 - 3.63057i) q^{55} +4.17463 q^{56} +(-0.717783 - 0.717783i) q^{57} +(-3.08063 + 3.08063i) q^{58} -12.9765i q^{59} +(-0.811179 + 2.08374i) q^{60} +8.09893i q^{61} +(5.36930 + 1.47331i) q^{62} +(-2.95191 - 2.95191i) q^{63} +1.00000i q^{64} +(-8.27109 - 3.21985i) q^{65} -4.03469 q^{66} +(-4.92097 + 4.92097i) q^{67} +(2.66235 - 2.66235i) q^{68} -2.86347i q^{69} +(8.54555 - 3.75649i) q^{70} +6.49419 q^{71} +(0.707107 - 0.707107i) q^{72} +(-6.55280 + 6.55280i) q^{73} +6.39023 q^{74} +(0.214533 + 4.99540i) q^{75} -1.01510 q^{76} +(11.9100 + 11.9100i) q^{77} +(2.80675 + 2.80675i) q^{78} +9.44004 q^{79} +(0.899839 + 2.04702i) q^{80} -1.00000 q^{81} +(5.66778 - 5.66778i) q^{82} +(-7.59317 + 7.59317i) q^{83} -4.17463 q^{84} +(3.05420 - 7.84558i) q^{85} +1.13847i q^{86} +(3.08063 - 3.08063i) q^{87} +(-2.85296 + 2.85296i) q^{88} -5.03739 q^{89} +(0.811179 - 2.08374i) q^{90} -16.5705i q^{91} +(-2.02478 - 2.02478i) q^{92} +(-5.36930 - 1.47331i) q^{93} -0.687180i q^{94} +(-2.07793 + 0.913425i) q^{95} -1.00000i q^{96} +(8.30027 - 8.30027i) q^{97} +(7.37338 + 7.37338i) q^{98} +4.03469 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{7}+O(q^{10}) \) 32 * q - 4 * q^7	\( 32 q - 4 q^{7} + 4 q^{10} - 4 q^{15} - 32 q^{16} - 8 q^{17} + 4 q^{22} + 32 q^{24} + 8 q^{25} + 4 q^{28} - 8 q^{29} - 20 q^{31} - 4 q^{33} - 24 q^{35} - 32 q^{36} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 4 q^{42} + 16 q^{43} + 8 q^{44} - 8 q^{47} - 16 q^{50} + 24 q^{53} + 32 q^{54} + 28 q^{55} - 16 q^{57} - 20 q^{58} + 16 q^{62} + 4 q^{63} - 56 q^{65} - 8 q^{66} + 32 q^{67} - 8 q^{68} - 28 q^{70} + 16 q^{71} + 20 q^{73} - 24 q^{74} + 16 q^{75} - 16 q^{76} + 40 q^{77} + 56 q^{79} - 32 q^{81} + 16 q^{82} - 72 q^{83} + 32 q^{85} + 20 q^{87} + 4 q^{88} + 64 q^{89} - 16 q^{93} + 32 q^{95} - 4 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - 4 * q^7 + 4 * q^10 - 4 * q^15 - 32 * q^16 - 8 * q^17 + 4 * q^22 + 32 * q^24 + 8 * q^25 + 4 * q^28 - 8 * q^29 - 20 * q^31 - 4 * q^33 - 24 * q^35 - 32 * q^36 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 4 * q^42 + 16 * q^43 + 8 * q^44 - 8 * q^47 - 16 * q^50 + 24 * q^53 + 32 * q^54 + 28 * q^55 - 16 * q^57 - 20 * q^58 + 16 * q^62 + 4 * q^63 - 56 * q^65 - 8 * q^66 + 32 * q^67 - 8 * q^68 - 28 * q^70 + 16 * q^71 + 20 * q^73 - 24 * q^74 + 16 * q^75 - 16 * q^76 + 40 * q^77 + 56 * q^79 - 32 * q^81 + 16 * q^82 - 72 * q^83 + 32 * q^85 + 20 * q^87 + 4 * q^88 + 64 * q^89 - 16 * q^93 + 32 * q^95 - 4 * q^97 + 16 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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