LMFDB - Embedded newform 802.2.e.b.45.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [802,2,Mod(45,802)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(802, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("802.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 802 = 2 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	802.e (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.40400224211$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			45.12
Character	$\chi$	$=$	802.45
Dual form			802.2.e.b.303.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(1.29760 + 0.537484i) q^{3} +1.00000i q^{4} +2.57737 q^{5} +(0.537484 + 1.29760i) q^{6} +(-3.54527 + 3.54527i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.726439 - 0.726439i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(1.29760 + 0.537484i) q^{3} +1.00000i q^{4} +2.57737 q^{5} +(0.537484 + 1.29760i) q^{6} +(-3.54527 + 3.54527i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.726439 - 0.726439i) q^{9} +(1.82248 + 1.82248i) q^{10} +(1.49177 + 1.49177i) q^{11} +(-0.537484 + 1.29760i) q^{12} +(6.40667 - 2.65373i) q^{13} -5.01376 q^{14} +(3.34441 + 1.38530i) q^{15} -1.00000 q^{16} +(-5.24548 + 2.17275i) q^{17} -1.02734i q^{18} +(1.72226 + 4.15791i) q^{19} +2.57737i q^{20} +(-6.50587 + 2.69482i) q^{21} +2.10968i q^{22} +(-0.467071 - 1.12761i) q^{23} +(-1.29760 + 0.537484i) q^{24} +1.64286 q^{25} +(6.40667 + 2.65373i) q^{26} +(-2.16463 - 5.22588i) q^{27} +(-3.54527 - 3.54527i) q^{28} +4.16647 q^{29} +(1.38530 + 3.34441i) q^{30} +(-0.913776 - 2.20605i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.13392 + 2.73753i) q^{33} +(-5.24548 - 2.17275i) q^{34} +(-9.13748 + 9.13748i) q^{35} +(0.726439 - 0.726439i) q^{36} +(1.92510 + 0.797401i) q^{37} +(-1.72226 + 4.15791i) q^{38} +9.73965 q^{39} +(-1.82248 + 1.82248i) q^{40} +1.48663 q^{41} +(-6.50587 - 2.69482i) q^{42} +(-5.46952 + 5.46952i) q^{43} +(-1.49177 + 1.49177i) q^{44} +(-1.87230 - 1.87230i) q^{45} +(0.467071 - 1.12761i) q^{46} +(3.02869 + 3.02869i) q^{47} +(-1.29760 - 0.537484i) q^{48} -18.1378i q^{49} +(1.16167 + 1.16167i) q^{50} -7.97436 q^{51} +(2.65373 + 6.40667i) q^{52} +(4.88522 - 11.7940i) q^{53} +(2.16463 - 5.22588i) q^{54} +(3.84485 + 3.84485i) q^{55} -5.01376i q^{56} +6.32100i q^{57} +(2.94614 + 2.94614i) q^{58} +(10.8810 - 4.50706i) q^{59} +(-1.38530 + 3.34441i) q^{60} +(-1.42792 - 3.44731i) q^{61} +(0.913776 - 2.20605i) q^{62} +5.15084 q^{63} -1.00000i q^{64} +(16.5124 - 6.83966i) q^{65} +(-1.13392 + 2.73753i) q^{66} +(1.68487 - 4.06765i) q^{67} +(-2.17275 - 5.24548i) q^{68} -1.71423i q^{69} -12.9223 q^{70} +(-3.97870 + 9.60544i) q^{71} +1.02734 q^{72} +(1.73902 - 1.73902i) q^{73} +(0.797401 + 1.92510i) q^{74} +(2.13177 + 0.883009i) q^{75} +(-4.15791 + 1.72226i) q^{76} -10.5774 q^{77} +(6.88697 + 6.88697i) q^{78} +(-5.62912 - 13.5899i) q^{79} -2.57737 q^{80} -4.86255i q^{81} +(1.05121 + 1.05121i) q^{82} +3.58226 q^{83} +(-2.69482 - 6.50587i) q^{84} +(-13.5196 + 5.59999i) q^{85} -7.73507 q^{86} +(5.40642 + 2.23941i) q^{87} -2.10968 q^{88} +(-2.73801 + 2.73801i) q^{89} -2.64784i q^{90} +(-13.3052 + 32.1215i) q^{91} +(1.12761 - 0.467071i) q^{92} -3.35372i q^{93} +4.28322i q^{94} +(4.43891 + 10.7165i) q^{95} +(-0.537484 - 1.29760i) q^{96} +(0.0220137 + 0.0531457i) q^{97} +(12.8254 - 12.8254i) q^{98} -2.16736i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{6} + 20 q^{9}+O(q^{10}) $ 68 * q + 4 * q^6 + 20 * q^9	$ 68 q + 4 q^{6} + 20 q^{9} - 4 q^{10} + 12 q^{11} - 4 q^{12} - 8 q^{13} + 8 q^{14} - 4 q^{15} - 68 q^{16} + 4 q^{17} + 20 q^{19} - 40 q^{21} - 16 q^{23} + 20 q^{25} - 8 q^{26} - 12 q^{27} + 16 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{34} + 16 q^{35} - 20 q^{36} + 12 q^{37} - 20 q^{38} + 40 q^{39} + 4 q^{40} + 24 q^{41} - 40 q^{42} + 40 q^{43} - 12 q^{44} + 28 q^{45} + 16 q^{46} + 4 q^{47} - 8 q^{50} + 24 q^{51} + 4 q^{52} + 12 q^{53} + 12 q^{54} - 24 q^{55} - 4 q^{58} + 4 q^{59} + 4 q^{60} - 20 q^{61} + 8 q^{62} - 16 q^{63} + 36 q^{65} - 8 q^{66} + 48 q^{67} + 8 q^{68} - 16 q^{71} - 68 q^{72} + 40 q^{73} - 8 q^{74} - 96 q^{75} - 16 q^{77} + 32 q^{78} + 28 q^{79} - 16 q^{82} + 16 q^{83} - 4 q^{84} + 16 q^{85} - 32 q^{86} + 8 q^{87} + 8 q^{88} - 20 q^{89} - 4 q^{91} + 8 q^{92} - 24 q^{95} - 4 q^{96} + 24 q^{97} + 24 q^{98}+O(q^{100}) $ 68 * q + 4 * q^6 + 20 * q^9 - 4 * q^10 + 12 * q^11 - 4 * q^12 - 8 * q^13 + 8 * q^14 - 4 * q^15 - 68 * q^16 + 4 * q^17 + 20 * q^19 - 40 * q^21 - 16 * q^23 + 20 * q^25 - 8 * q^26 - 12 * q^27 + 16 * q^29 - 4 * q^30 - 8 * q^31 + 8 * q^33 + 4 * q^34 + 16 * q^35 - 20 * q^36 + 12 * q^37 - 20 * q^38 + 40 * q^39 + 4 * q^40 + 24 * q^41 - 40 * q^42 + 40 * q^43 - 12 * q^44 + 28 * q^45 + 16 * q^46 + 4 * q^47 - 8 * q^50 + 24 * q^51 + 4 * q^52 + 12 * q^53 + 12 * q^54 - 24 * q^55 - 4 * q^58 + 4 * q^59 + 4 * q^60 - 20 * q^61 + 8 * q^62 - 16 * q^63 + 36 * q^65 - 8 * q^66 + 48 * q^67 + 8 * q^68 - 16 * q^71 - 68 * q^72 + 40 * q^73 - 8 * q^74 - 96 * q^75 - 16 * q^77 + 32 * q^78 + 28 * q^79 - 16 * q^82 + 16 * q^83 - 4 * q^84 + 16 * q^85 - 32 * q^86 + 8 * q^87 + 8 * q^88 - 20 * q^89 - 4 * q^91 + 8 * q^92 - 24 * q^95 - 4 * q^96 + 24 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/802\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	1.29760	+	0.537484i	0.749171	+	0.310317i	0.724403	−	0.689377i	$-0.242115\pi$
$3$	1.29760	+	0.537484i	0.749171	+	0.310317i	0.0247676	+	0.999693i	$0.492115\pi$
$4$			1.00000i			0.500000i
$5$	2.57737			1.15264			0.576318	−	0.817225i	$-0.304489\pi$
$5$	2.57737			1.15264			0.576318	+	0.817225i	$0.304489\pi$
$6$	0.537484	+	1.29760i	0.219427	+	0.529744i
$7$	−3.54527	+	3.54527i	−1.33998	+	1.33998i	−0.443917	+	0.896068i	$0.646411\pi$
$7$	−3.54527	+	3.54527i	−1.33998	+	1.33998i	−0.896068	+	0.443917i	$0.853589\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.726439	−	0.726439i	−0.242146	−	0.242146i
$10$	1.82248	+	1.82248i	0.576318	+	0.576318i
$11$	1.49177	+	1.49177i	0.449785	+	0.449785i	0.895283	−	0.445498i	$-0.146973\pi$
$11$	1.49177	+	1.49177i	0.449785	+	0.449785i	−0.445498	+	0.895283i	$0.646973\pi$
$12$	−0.537484	+	1.29760i	−0.155158	+	0.374585i
$13$	6.40667	−	2.65373i	1.77689	−	0.736013i	0.783479	−	0.621418i	$-0.213443\pi$
$13$	6.40667	−	2.65373i	1.77689	−	0.736013i	0.993412	−	0.114594i	$-0.0365568\pi$
$14$	−5.01376			−1.33998
$15$	3.34441	+	1.38530i	0.863522	+	0.357682i
$16$	−1.00000			−0.250000
$17$	−5.24548	+	2.17275i	−1.27222	+	0.526969i	−0.913637	−	0.406531i	$-0.866738\pi$
$17$	−5.24548	+	2.17275i	−1.27222	+	0.526969i	−0.358579	+	0.933500i	$0.616738\pi$
$18$		−	1.02734i		−	0.242146i
$19$	1.72226	+	4.15791i	0.395114	+	0.953890i	0.988807	+	0.149198i	$0.0476693\pi$
$19$	1.72226	+	4.15791i	0.395114	+	0.953890i	−0.593693	+	0.804691i	$0.702331\pi$
$20$			2.57737i			0.576318i
$21$	−6.50587	+	2.69482i	−1.41970	+	0.588058i
$22$			2.10968i			0.449785i
$23$	−0.467071	−	1.12761i	−0.0973911	−	0.235123i	0.867674	−	0.497134i	$-0.165614\pi$
$23$	−0.467071	−	1.12761i	−0.0973911	−	0.235123i	−0.965065	+	0.262011i	$0.915614\pi$
$24$	−1.29760	+	0.537484i	−0.264872	+	0.109714i
$25$	1.64286			0.328571
$26$	6.40667	+	2.65373i	1.25645	+	0.520439i
$27$	−2.16463	−	5.22588i	−0.416584	−	1.00572i
$28$	−3.54527	−	3.54527i	−0.669992	−	0.669992i
$29$	4.16647			0.773693			0.386847	−	0.922144i	$-0.373564\pi$
$29$	4.16647			0.773693			0.386847	+	0.922144i	$0.373564\pi$
$30$	1.38530	+	3.34441i	0.252920	+	0.610602i
$31$	−0.913776	−	2.20605i	−0.164119	−	0.396218i	0.820330	−	0.571891i	$-0.193790\pi$
$31$	−0.913776	−	2.20605i	−0.164119	−	0.396218i	−0.984449	+	0.175673i	$0.943790\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	1.13392	+	2.73753i	0.197390	+	0.476542i
$34$	−5.24548	−	2.17275i	−0.899592	−	0.372623i
$35$	−9.13748	+	9.13748i	−1.54452	+	1.54452i
$36$	0.726439	−	0.726439i	0.121073	−	0.121073i
$37$	1.92510	+	0.797401i	0.316484	+	0.131092i	0.535270	−	0.844681i	$-0.320210\pi$
$37$	1.92510	+	0.797401i	0.316484	+	0.131092i	−0.218786	+	0.975773i	$0.570210\pi$
$38$	−1.72226	+	4.15791i	−0.279388	+	0.674502i
$39$	9.73965			1.55959
$40$	−1.82248	+	1.82248i	−0.288159	+	0.288159i
$41$	1.48663			0.232172			0.116086	−	0.993239i	$-0.462965\pi$
$41$	1.48663			0.232172			0.116086	+	0.993239i	$0.462965\pi$
$42$	−6.50587	−	2.69482i	−1.00388	−	0.415820i
$43$	−5.46952	+	5.46952i	−0.834094	+	0.834094i	−0.988074	−	0.153980i	$-0.950791\pi$
$43$	−5.46952	+	5.46952i	−0.834094	+	0.834094i	0.153980	+	0.988074i	$0.450791\pi$
$44$	−1.49177	+	1.49177i	−0.224893	+	0.224893i
$45$	−1.87230	−	1.87230i	−0.279107	−	0.279107i
$46$	0.467071	−	1.12761i	0.0688659	−	0.166257i
$47$	3.02869	+	3.02869i	0.441780	+	0.441780i	0.892610	−	0.450830i	$-0.148872\pi$
$47$	3.02869	+	3.02869i	0.441780	+	0.441780i	−0.450830	+	0.892610i	$0.648872\pi$
$48$	−1.29760	−	0.537484i	−0.187293	−	0.0775792i
$49$		−	18.1378i		−	2.59112i
$50$	1.16167	+	1.16167i	0.164286	+	0.164286i
$51$	−7.97436			−1.11663
$52$	2.65373	+	6.40667i	0.368006	+	0.888446i
$53$	4.88522	−	11.7940i	0.671037	−	1.62003i	−0.108816	−	0.994062i	$-0.534706\pi$
$53$	4.88522	−	11.7940i	0.671037	−	1.62003i	0.779852	−	0.625964i	$-0.215294\pi$
$54$	2.16463	−	5.22588i	0.294569	−	0.711153i
$55$	3.84485	+	3.84485i	0.518439	+	0.518439i
$56$		−	5.01376i		−	0.669992i
$57$			6.32100i			0.837237i
$58$	2.94614	+	2.94614i	0.386847	+	0.386847i
$59$	10.8810	−	4.50706i	1.41659	−	0.586770i	0.462586	−	0.886574i	$-0.346921\pi$
$59$	10.8810	−	4.50706i	1.41659	−	0.586770i	0.954001	+	0.299805i	$0.0969215\pi$
$60$	−1.38530	+	3.34441i	−0.178841	+	0.431761i
$61$	−1.42792	−	3.44731i	−0.182827	−	0.441383i	0.805720	−	0.592296i	$-0.201779\pi$
$61$	−1.42792	−	3.44731i	−0.182827	−	0.441383i	−0.988547	+	0.150913i	$0.951779\pi$
$62$	0.913776	−	2.20605i	0.116050	−	0.280169i
$63$	5.15084			0.648945
$64$		−	1.00000i		−	0.125000i
$65$	16.5124	−	6.83966i	2.04811	−	0.848355i
$66$	−1.13392	+	2.73753i	−0.139576	+	0.336966i
$67$	1.68487	−	4.06765i	0.205840	−	0.496942i	−0.786920	−	0.617055i	$-0.788326\pi$
$67$	1.68487	−	4.06765i	0.205840	−	0.496942i	0.992760	+	0.120113i	$0.0383256\pi$
$68$	−2.17275	−	5.24548i	−0.263485	−	0.636108i
$69$		−	1.71423i		−	0.206369i
$70$	−12.9223			−1.54452
$71$	−3.97870	+	9.60544i	−0.472185	+	1.13996i	0.491010	+	0.871154i	$0.336628\pi$
$71$	−3.97870	+	9.60544i	−0.472185	+	1.13996i	−0.963195	+	0.268802i	$0.913372\pi$
$72$	1.02734			0.121073
$73$	1.73902	−	1.73902i	0.203537	−	0.203537i	−0.597977	−	0.801514i	$-0.704028\pi$
$73$	1.73902	−	1.73902i	0.203537	−	0.203537i	0.801514	+	0.597977i	$0.204028\pi$
$74$	0.797401	+	1.92510i	0.0926960	+	0.223788i
$75$	2.13177	+	0.883009i	0.246156	+	0.101961i
$76$	−4.15791	+	1.72226i	−0.476945	+	0.197557i
$77$	−10.5774			−1.20541
$78$	6.88697	+	6.88697i	0.779796	+	0.779796i
$79$	−5.62912	−	13.5899i	−0.633325	−	1.52898i	−0.835417	−	0.549616i	$-0.814774\pi$
$79$	−5.62912	−	13.5899i	−0.633325	−	1.52898i	0.202092	−	0.979367i	$-0.435226\pi$
$80$	−2.57737			−0.288159
$81$		−	4.86255i		−	0.540284i
$82$	1.05121	+	1.05121i	0.116086	+	0.116086i
$83$	3.58226			0.393204			0.196602	−	0.980483i	$-0.437009\pi$
$83$	3.58226			0.393204			0.196602	+	0.980483i	$0.437009\pi$
$84$	−2.69482	−	6.50587i	−0.294029	−	0.709849i
$85$	−13.5196	+	5.59999i	−1.46640	+	0.607404i
$86$	−7.73507			−0.834094
$87$	5.40642	+	2.23941i	0.579629	+	0.240090i
$88$	−2.10968			−0.224893
$89$	−2.73801	+	2.73801i	−0.290229	+	0.290229i	−0.837171	−	0.546942i	$-0.815792\pi$
$89$	−2.73801	+	2.73801i	−0.290229	+	0.290229i	0.546942	+	0.837171i	$0.315792\pi$
$90$		−	2.64784i		−	0.279107i
$91$	−13.3052	+	32.1215i	−1.39476	+	3.36725i
$92$	1.12761	−	0.467071i	0.117561	−	0.0486955i
$93$		−	3.35372i		−	0.347764i
$94$			4.28322i			0.441780i
$95$	4.43891	+	10.7165i	0.455423	+	1.09949i
$96$	−0.537484	−	1.29760i	−0.0548568	−	0.132436i
$97$	0.0220137	+	0.0531457i	0.00223515	+	0.00539612i	0.924993	−	0.379984i	$-0.124070\pi$
$97$	0.0220137	+	0.0531457i	0.00223515	+	0.00539612i	−0.922758	+	0.385380i	$0.874070\pi$
$98$	12.8254	−	12.8254i	1.29556	−	1.29556i
$99$		−	2.16736i		−	0.217828i
$100$			1.64286i			0.164286i
$101$	−3.64294	+	8.79483i	−0.362486	+	0.875118i	0.632449	+	0.774602i	$0.282050\pi$
$101$	−3.64294	+	8.79483i	−0.362486	+	0.875118i	−0.994935	+	0.100517i	$0.967950\pi$
$102$	−5.63873	−	5.63873i	−0.558317	−	0.558317i
$103$	2.76429	−	2.76429i	0.272374	−	0.272374i	−0.557681	−	0.830055i	$-0.688309\pi$
$103$	2.76429	−	2.76429i	0.272374	−	0.272374i	0.830055	+	0.557681i	$0.188309\pi$
$104$	−2.65373	+	6.40667i	−0.260220	+	0.628226i
$105$	−16.7681	+	6.94556i	−1.63639	+	0.677817i
$106$	11.7940	−	4.88522i	1.14553	−	0.474495i
$107$	−4.68670	+	1.94130i	−0.453081	+	0.187672i	−0.597541	−	0.801838i	$-0.703855\pi$
$107$	−4.68670	+	1.94130i	−0.453081	+	0.187672i	0.144460	+	0.989511i	$0.453855\pi$
$108$	5.22588	−	2.16463i	0.502861	−	0.208292i
$109$	10.7229	+	10.7229i	1.02706	+	1.02706i	0.999623	+	0.0274397i	$0.00873543\pi$
$109$	10.7229	+	10.7229i	1.02706	+	1.02706i	0.0274397	+	0.999623i	$0.491265\pi$
$110$			5.43744i			0.518439i
$111$	2.06942	+	2.06942i	0.196421	+	0.196421i
$112$	3.54527	−	3.54527i	0.334996	−	0.334996i
$113$		−	14.9537i		−	1.40672i	−0.710832	−	0.703362i	$-0.751681\pi$
$113$		−	14.9537i		−	1.40672i	0.710832	−	0.703362i	$-0.248319\pi$
$114$	−4.46962	+	4.46962i	−0.418618	+	0.418618i
$115$	−1.20382	−	2.90627i	−0.112257	−	0.271011i
$116$			4.16647i			0.386847i
$117$	−6.58183	−	2.72628i	−0.608490	−	0.252045i
$118$	10.8810	+	4.50706i	1.00168	+	0.414909i
$119$	10.8937	−	26.2996i	0.998619	−	2.41088i
$120$	−3.34441	+	1.38530i	−0.305301	+	0.126460i
$121$		−	6.54925i		−	0.595386i
$122$	1.42792	−	3.44731i	0.129278	−	0.312105i
$123$	1.92905	+	0.799040i	0.173937	+	0.0720470i
$124$	2.20605	−	0.913776i	0.198109	−	0.0820595i
$125$	−8.65262			−0.773914
$126$	3.64219	+	3.64219i	0.324472	+	0.324472i
$127$	0.716413	+	1.72957i	0.0635713	+	0.153475i	0.952473	−	0.304624i	$-0.0985307\pi$
$127$	0.716413	+	1.72957i	0.0635713	+	0.153475i	−0.888901	+	0.458098i	$0.848531\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−10.0370	+	4.15748i	−0.883712	+	0.366046i
$130$	16.5124	+	6.83966i	1.44823	+	0.599878i
$131$	5.89241	−	14.2255i	0.514822	−	1.24289i	−0.426225	−	0.904617i	$-0.640157\pi$
$131$	5.89241	−	14.2255i	0.514822	−	1.24289i	0.941048	−	0.338274i	$-0.109843\pi$
$132$	−2.73753	+	1.13392i	−0.238271	+	0.0986951i
$133$	−20.8468	−	8.63502i	−1.80764	−	0.748751i
$134$	4.06765	−	1.68487i	0.351391	−	0.145551i
$135$	−5.57907	−	13.4691i	−0.480170	−	1.15923i
$136$	2.17275	−	5.24548i	0.186312	−	0.449796i
$137$	13.4013	+	5.55100i	1.14495	+	0.474254i	0.872837	−	0.488012i	$-0.162278\pi$
$137$	13.4013	+	5.55100i	1.14495	+	0.474254i	0.272112	+	0.962265i	$0.412278\pi$
$138$	1.21215	−	1.21215i	0.103185	−	0.103185i
$139$	−12.5415	+	5.19487i	−1.06376	+	0.440623i	−0.844784	−	0.535107i	$-0.820271\pi$
$139$	−12.5415	+	5.19487i	−1.06376	+	0.440623i	−0.218975	+	0.975731i	$0.570271\pi$
$140$	−9.13748	−	9.13748i	−0.772258	−	0.772258i
$141$	2.30216	+	5.55791i	0.193877	+	0.468060i
$142$	−9.60544	+	3.97870i	−0.806071	+	0.333885i
$143$	13.5160	+	5.59853i	1.13027	+	0.468172i
$144$	0.726439	+	0.726439i	0.0605366	+	0.0605366i
$145$	10.7385			0.891787
$146$	2.45935			0.203537
$147$	9.74880	−	23.5357i	0.804067	−	1.94119i
$148$	−0.797401	+	1.92510i	−0.0655460	+	0.158242i
$149$			4.87410i			0.399302i	0.979867	+	0.199651i	$0.0639808\pi$
$149$			4.87410i			0.399302i	−0.979867	+	0.199651i	$0.936019\pi$
$150$	0.883009	+	2.13177i	0.0720974	+	0.174058i
$151$	0.314084	+	0.314084i	0.0255598	+	0.0255598i	0.719771	−	0.694211i	$-0.244247\pi$
$151$	0.314084	+	0.314084i	0.0255598	+	0.0255598i	−0.694211	+	0.719771i	$0.744247\pi$
$152$	−4.15791	−	1.72226i	−0.337251	−	0.139694i
$153$	5.38889	+	2.23215i	0.435666	+	0.180459i
$154$	−7.47938	−	7.47938i	−0.602706	−	0.602706i
$155$	−2.35514	−	5.68582i	−0.189170	−	0.456696i
$156$			9.73965i			0.779796i
$157$	−21.9055	+	9.07357i	−1.74825	+	0.724150i	−0.750238	+	0.661168i	$0.770061\pi$
$157$	−21.9055	+	9.07357i	−1.74825	+	0.724150i	−0.998015	+	0.0629819i	$0.979939\pi$
$158$	5.62912	−	13.5899i	0.447829	−	1.08115i
$159$	12.6781	−	12.6781i	1.00544	−	1.00544i
$160$	−1.82248	−	1.82248i	−0.144080	−	0.144080i
$161$	5.65357	+	2.34179i	0.445564	+	0.184559i
$162$	3.43834	−	3.43834i	0.270142	−	0.270142i
$163$	3.57435	−	1.48054i	0.279965	−	0.115965i	−0.238283	−	0.971196i	$-0.576585\pi$
$163$	3.57435	−	1.48054i	0.279965	−	0.115965i	0.518248	+	0.855231i	$0.326585\pi$
$164$			1.48663i			0.116086i
$165$	2.92254	+	7.05563i	0.227519	+	0.549280i
$166$	2.53304	+	2.53304i	0.196602	+	0.196602i
$167$	−1.80247	−	4.35155i	−0.139479	−	0.336733i	0.838669	−	0.544641i	$-0.183334\pi$
$167$	−1.80247	−	4.35155i	−0.139479	−	0.336733i	−0.978148	+	0.207909i	$0.933334\pi$
$168$	2.69482	−	6.50587i	0.207910	−	0.501939i
$169$	24.8108	−	24.8108i	1.90852	−	1.90852i
$170$	−13.5196	−	5.59999i	−1.03690	−	0.429499i
$171$	1.76935	−	4.27159i	0.135305	−	0.326656i
$172$	−5.46952	−	5.46952i	−0.417047	−	0.417047i
$173$	−16.1960			−1.23136			−0.615679	−	0.787997i	$-0.711118\pi$
$173$	−16.1960			−1.23136			−0.615679	+	0.787997i	$0.711118\pi$
$174$	2.23941	+	5.40642i	0.169769	+	0.409859i
$175$	−5.82436	+	5.82436i	−0.440280	+	0.440280i
$176$	−1.49177	−	1.49177i	−0.112446	−	0.112446i
$177$	16.5417			1.24335
$178$	−3.87213			−0.290229
$179$			6.45630i			0.482566i	0.970455	+	0.241283i	$0.0775682\pi$
$179$			6.45630i			0.482566i	−0.970455	+	0.241283i	$0.922432\pi$
$180$	1.87230	−	1.87230i	0.139553	−	0.139553i
$181$	16.6767	−	16.6767i	1.23957	−	1.23957i	0.279390	−	0.960178i	$-0.409868\pi$
$181$	16.6767	−	16.6767i	1.23957	−	1.23957i	0.960178	−	0.279390i	$-0.0901321\pi$
$182$	−32.1215	+	13.3052i	−2.38101	+	0.986246i
$183$		−	5.24073i		−	0.387406i
$184$	1.12761	+	0.467071i	0.0831285	+	0.0344329i
$185$	4.96170	+	2.05520i	0.364791	+	0.151101i
$186$	2.37143	−	2.37143i	0.173882	−	0.173882i
$187$	−11.0663	−	4.58381i	−0.809247	−	0.335201i
$188$	−3.02869	+	3.02869i	−0.220890	+	0.220890i
$189$	26.2014	+	10.8530i	1.90587	+	0.789436i
$190$	−4.43891	+	10.7165i	−0.322033	+	0.777456i
$191$	−0.814399	−	0.337335i	−0.0589278	−	0.0244087i	0.353025	−	0.935614i	$-0.385153\pi$
$191$	−0.814399	−	0.337335i	−0.0589278	−	0.0244087i	−0.411953	+	0.911205i	$0.635153\pi$
$192$	0.537484	−	1.29760i	0.0387896	−	0.0936464i
$193$	13.2997	−	5.50890i	0.957331	−	0.396540i	0.151350	−	0.988480i	$-0.451638\pi$
$193$	13.2997	−	5.50890i	0.957331	−	0.396540i	0.805981	+	0.591941i	$0.201638\pi$
$194$	−0.0220137	+	0.0531457i	−0.00158049	+	0.00381564i
$195$	25.1027			1.79764
$196$	18.1378			1.29556
$197$		−	5.50208i		−	0.392007i	−0.980603	−	0.196003i	$-0.937204\pi$
$197$		−	5.50208i		−	0.392007i	0.980603	−	0.196003i	$-0.0627964\pi$
$198$	1.53255	−	1.53255i	0.108914	−	0.108914i
$199$	6.53567	−	2.70716i	0.463301	−	0.191906i	−0.138808	−	0.990319i	$-0.544327\pi$
$199$	6.53567	−	2.70716i	0.463301	−	0.191906i	0.602109	+	0.798414i	$0.294327\pi$
$200$	−1.16167	+	1.16167i	−0.0821428	+	0.0821428i
$201$	4.37259	−	4.37259i	0.308419	−	0.308419i
$202$	−8.79483	+	3.64294i	−0.618802	+	0.256316i
$203$	−14.7712	+	14.7712i	−1.03674	+	1.03674i
$204$		−	7.97436i		−	0.558317i
$205$	3.83160			0.267610
$206$	3.90930			0.272374
$207$	−0.479841	+	1.15844i	−0.0333512	+	0.0805170i
$208$	−6.40667	+	2.65373i	−0.444223	+	0.184003i
$209$	−3.63342	+	8.77186i	−0.251329	+	0.606762i
$210$	−16.7681	−	6.94556i	−1.15711	−	0.479289i
$211$	6.02251	−	14.5396i	0.414607	−	1.00095i	−0.569278	−	0.822145i	$-0.692777\pi$
$211$	6.02251	−	14.5396i	0.414607	−	1.00095i	0.983885	−	0.178804i	$-0.0572228\pi$
$212$	11.7940	+	4.88522i	0.810013	+	0.335518i
$213$	−10.3255	+	10.3255i	−0.707495	+	0.707495i
$214$	−4.68670	−	1.94130i	−0.320376	−	0.132704i
$215$	−14.0970	+	14.0970i	−0.961407	+	0.961407i
$216$	5.22588	+	2.16463i	0.355576	+	0.147285i
$217$	11.0606	+	4.58146i	0.750844	+	0.311010i
$218$			15.1644i			1.02706i
$219$	3.19125	−	1.32186i	0.215645	−	0.0893230i
$220$	−3.84485	+	3.84485i	−0.259220	+	0.259220i
$221$	−27.8402	+	27.8402i	−1.87273	+	1.87273i
$222$			2.92660i			0.196421i
$223$	−18.0924			−1.21156			−0.605780	−	0.795632i	$-0.707139\pi$
$223$	−18.0924			−1.21156			−0.605780	+	0.795632i	$0.707139\pi$
$224$	5.01376			0.334996
$225$	−1.19343	−	1.19343i	−0.0795623	−	0.0795623i
$226$	10.5738	−	10.5738i	0.703362	−	0.703362i
$227$	−5.51180	−	13.3067i	−0.365831	−	0.883194i	−0.994424	−	0.105459i	$-0.966369\pi$
$227$	−5.51180	−	13.3067i	−0.365831	−	0.883194i	0.628593	−	0.777735i	$-0.283631\pi$
$228$	−6.32100			−0.418618
$229$	1.47132	+	1.47132i	0.0972274	+	0.0972274i	0.754047	−	0.656820i	$-0.228099\pi$
$229$	1.47132	+	1.47132i	0.0972274	+	0.0972274i	−0.656820	+	0.754047i	$0.728099\pi$
$230$	1.20382	−	2.90627i	0.0793774	−	0.191634i
$231$	−13.7253	−	5.68521i	−0.903059	−	0.374059i
$232$	−2.94614	+	2.94614i	−0.193423	+	0.193423i
$233$	−9.48658	+	22.9026i	−0.621486	+	1.50040i	0.228472	+	0.973550i	$0.426627\pi$
$233$	−9.48658	+	22.9026i	−0.621486	+	1.50040i	−0.849958	+	0.526850i	$0.823373\pi$
$234$	−2.72628	−	6.58183i	−0.178223	−	0.430268i
$235$	7.80607	+	7.80607i	0.509212	+	0.509212i
$236$	4.50706	+	10.8810i	0.293385	+	0.708294i
$237$		−	20.6598i		−	1.34200i
$238$	26.2996	−	10.8937i	1.70475	−	0.706131i
$239$	2.97114	−	2.97114i	0.192187	−	0.192187i	−0.604453	−	0.796641i	$-0.706608\pi$
$239$	2.97114	−	2.97114i	0.192187	−	0.192187i	0.796641	+	0.604453i	$0.206608\pi$
$240$	−3.34441	−	1.38530i	−0.215880	−	0.0894206i
$241$	20.5235	+	20.5235i	1.32203	+	1.32203i	0.912128	+	0.409906i	$0.134439\pi$
$241$	20.5235	+	20.5235i	1.32203	+	1.32203i	0.409906	+	0.912128i	$0.365561\pi$
$242$	4.63102	−	4.63102i	0.297693	−	0.297693i
$243$	−3.88035	+	9.36799i	−0.248925	+	0.600957i
$244$	3.44731	−	1.42792i	0.220692	−	0.0914134i
$245$		−	46.7480i		−	2.98662i
$246$	0.799040	+	1.92905i	0.0509449	+	0.122992i
$247$	22.0679	+	22.0679i	1.40415	+	1.40415i
$248$	2.20605	+	0.913776i	0.140084	+	0.0580248i
$249$	4.64835	+	1.92541i	0.294577	+	0.122018i
$250$	−6.11832	−	6.11832i	−0.386957	−	0.386957i
$251$	0.678902	+	1.63901i	0.0428519	+	0.103454i	0.943856	−	0.330356i	$-0.107169\pi$
$251$	0.678902	+	1.63901i	0.0428519	+	0.103454i	−0.901004	+	0.433810i	$0.857169\pi$
$252$			5.15084i			0.324472i
$253$	0.985371	−	2.37890i	0.0619498	−	0.149560i
$254$	−0.716413	+	1.72957i	−0.0449517	+	0.108523i
$255$	−20.5529			−1.28707
$256$	1.00000			0.0625000
$257$	−17.1892	−	17.1892i	−1.07224	−	1.07224i	−0.997179	−	0.0750559i	$-0.976086\pi$
$257$	−17.1892	−	17.1892i	−1.07224	−	1.07224i	−0.0750559	−	0.997179i	$-0.523914\pi$
$258$	−10.0370	−	4.15748i	−0.624879	−	0.258833i
$259$	−9.65198	+	3.99798i	−0.599745	+	0.248423i
$260$	6.83966	+	16.5124i	0.424177	+	1.02405i
$261$	−3.02668	−	3.02668i	−0.187347	−	0.187347i
$262$	14.2255	−	5.89241i	0.878857	−	0.364034i
$263$	2.04138	−	2.04138i	0.125877	−	0.125877i	−0.641362	−	0.767239i	$-0.721630\pi$
$263$	2.04138	−	2.04138i	0.125877	−	0.125877i	0.767239	+	0.641362i	$0.221630\pi$
$264$	−2.73753	−	1.13392i	−0.168483	−	0.0697880i
$265$	12.5910	−	30.3975i	0.773461	−	1.86730i
$266$	−8.63502	−	20.8468i	−0.529447	−	1.27820i
$267$	−5.02449	+	2.08121i	−0.307494	+	0.127368i
$268$	4.06765	+	1.68487i	0.248471	+	0.102920i
$269$	−23.0687	+	9.55535i	−1.40652	+	0.582600i	−0.951436	−	0.307847i	$-0.900391\pi$
$269$	−23.0687	+	9.55535i	−1.40652	+	0.582600i	−0.455086	+	0.890448i	$0.650391\pi$
$270$	5.57907	−	13.4691i	0.339531	−	0.819701i
$271$	−12.2841	−	5.08823i	−0.746204	−	0.309088i	−0.0230125	−	0.999735i	$-0.507326\pi$
$271$	−12.2841	−	5.08823i	−0.746204	−	0.309088i	−0.723192	+	0.690647i	$0.757326\pi$
$272$	5.24548	−	2.17275i	0.318054	−	0.131742i
$273$	−34.5297	+	34.5297i	−2.08983	+	2.08983i
$274$	5.55100	+	13.4013i	0.335348	+	0.809602i
$275$	2.45076	+	2.45076i	0.147786	+	0.147786i
$276$	1.71423			0.103185
$277$	−1.33280	+	0.552064i	−0.0800803	+	0.0331703i	−0.422364	−	0.906426i	$-0.638800\pi$
$277$	−1.33280	+	0.552064i	−0.0800803	+	0.0331703i	0.342284	+	0.939597i	$0.388800\pi$
$278$	−12.5415	−	5.19487i	−0.752191	−	0.311568i
$279$	−0.938758	+	2.26636i	−0.0562020	+	0.135684i
$280$		−	12.9223i		−	0.772258i
$281$	−14.7911	+	6.12666i	−0.882360	+	0.365486i	−0.777412	−	0.628992i	$-0.783468\pi$
$281$	−14.7911	+	6.12666i	−0.882360	+	0.365486i	−0.104949	+	0.994478i	$0.533468\pi$
$282$	−2.30216	+	5.55791i	−0.137092	+	0.330969i
$283$	29.5999	+	12.2607i	1.75953	+	0.728823i	0.996604	+	0.0823404i	$0.0262395\pi$
$283$	29.5999	+	12.2607i	1.75953	+	0.728823i	0.762929	+	0.646482i	$0.223761\pi$
$284$	−9.60544	−	3.97870i	−0.569978	−	0.236093i
$285$			16.2916i			0.965030i
$286$	5.59853	+	13.5160i	0.331048	+	0.799220i
$287$	−5.27050	+	5.27050i	−0.311108	+	0.311108i
$288$			1.02734i			0.0605366i
$289$	10.7734	−	10.7734i	0.633730	−	0.633730i
$290$	7.59330	+	7.59330i	0.445894	+	0.445894i
$291$			0.0807939i			0.00473622i
$292$	1.73902	+	1.73902i	0.101768	+	0.101768i
$293$	−24.0734	+	9.97152i	−1.40638	+	0.582543i	−0.951400	−	0.307958i	$-0.900354\pi$
$293$	−24.0734	+	9.97152i	−1.40638	+	0.582543i	−0.454982	+	0.890500i	$0.650354\pi$
$294$	23.5357	−	9.74880i	1.37263	−	0.568562i
$295$	28.0444	−	11.6164i	1.63281	−	0.676332i
$296$	−1.92510	+	0.797401i	−0.111894	+	0.0463480i
$297$	4.56668	−	11.0249i	0.264986	−	0.639732i
$298$	−3.44651	+	3.44651i	−0.199651	+	0.199651i
$299$	−5.98475	−	5.98475i	−0.346107	−	0.346107i
$300$	−0.883009	+	2.13177i	−0.0509805	+	0.123078i
$301$		−	38.7818i		−	2.23535i
$302$			0.444181i			0.0255598i
$303$	−9.45417	+	9.45417i	−0.543128	+	0.543128i
$304$	−1.72226	−	4.15791i	−0.0987785	−	0.238472i
$305$	−3.68029	−	8.88501i	−0.210733	−	0.508754i
$306$	2.23215	+	5.38889i	0.127604	+	0.308062i
$307$			2.40510i			0.137266i	0.997642	+	0.0686331i	$0.0218638\pi$
$307$			2.40510i			0.137266i	−0.997642	+	0.0686331i	$0.978136\pi$
$308$		−	10.5774i		−	0.602706i
$309$	5.07271	−	2.10119i	0.288577	−	0.119532i
$310$	2.35514	−	5.68582i	0.133763	−	0.322933i
$311$			10.5679i			0.599250i	0.954057	+	0.299625i	$0.0968616\pi$
$311$			10.5679i			0.599250i	−0.954057	+	0.299625i	$0.903138\pi$
$312$	−6.88697	+	6.88697i	−0.389898	+	0.389898i
$313$	−20.3834			−1.15214			−0.576070	−	0.817401i	$-0.695414\pi$
$313$	−20.3834			−1.15214			−0.576070	+	0.817401i	$0.695414\pi$
$314$	−21.9055	−	9.07357i	−1.23620	−	0.512051i
$315$	13.2756			0.747997
$316$	13.5899	−	5.62912i	0.764491	−	0.316663i
$317$	5.83108	+	14.0775i	0.327506	+	0.790670i	0.998776	+	0.0494571i	$0.0157491\pi$
$317$	5.83108	+	14.0775i	0.327506	+	0.790670i	−0.671270	+	0.741213i	$0.734251\pi$
$318$	17.9296			1.00544
$319$	6.21541	+	6.21541i	0.347996	+	0.347996i
$320$		−	2.57737i		−	0.144080i
$321$	−7.12489			−0.397673
$322$	2.34179	+	5.65357i	0.130503	+	0.315061i
$323$	−18.0682	−	18.0682i	−1.00534	−	1.00534i
$324$	4.86255			0.270142
$325$	10.5252	−	4.35970i	0.583835	−	0.241832i
$326$	3.57435	+	1.48054i	0.197965	+	0.0819998i
$327$	8.15063	+	19.6774i	0.450731	+	1.08816i
$328$	−1.05121	+	1.05121i	−0.0580431	+	0.0580431i
$329$	−21.4750			−1.18396
$330$	−2.92254	+	7.05563i	−0.160880	+	0.388400i
$331$	−2.41622			−0.132807			−0.0664037	−	0.997793i	$-0.521153\pi$
$331$	−2.41622			−0.132807			−0.0664037	+	0.997793i	$0.521153\pi$
$332$			3.58226i			0.196602i
$333$	−0.819202	−	1.97773i	−0.0448920	−	0.108379i
$334$	1.80247	−	4.35155i	0.0986267	−	0.238106i
$335$	4.34255	−	10.4838i	0.237259	−	0.572794i
$336$	6.50587	−	2.69482i	0.354924	−	0.147014i
$337$		−	7.97411i		−	0.434377i	−0.976130	−	0.217189i	$-0.930311\pi$
$337$		−	7.97411i		−	0.434377i	0.976130	−	0.217189i	$-0.0696887\pi$
$338$	35.0877			1.90852
$339$	8.03736	−	19.4039i	0.436530	−	1.05388i
$340$	−5.59999	−	13.5196i	−0.303702	−	0.733201i
$341$	1.92778	−	4.65406i	0.104395	−	0.252032i
$342$	4.27159	−	1.76935i	0.230981	−	0.0956754i
$343$	39.4866	+	39.4866i	2.13208	+	2.13208i
$344$		−	7.73507i		−	0.417047i
$345$		−	4.41822i		−	0.237869i
$346$	−11.4523	−	11.4523i	−0.615679	−	0.615679i
$347$	−8.83084	+	21.3195i	−0.474065	+	1.14449i	0.488287	+	0.872683i	$0.337622\pi$
$347$	−8.83084	+	21.3195i	−0.474065	+	1.14449i	−0.962351	+	0.271810i	$0.912378\pi$
$348$	−2.23941	+	5.40642i	−0.120045	+	0.289814i
$349$	12.3823	+	29.8936i	0.662810	+	1.60017i	0.793380	+	0.608726i	$0.208319\pi$
$349$	12.3823	+	29.8936i	0.662810	+	1.60017i	−0.130570	+	0.991439i	$0.541681\pi$
$350$	−8.23689			−0.440280
$351$	−27.7362	−	27.7362i	−1.48045	−	1.48045i
$352$		−	2.10968i		−	0.112446i
$353$	−26.5489	−	10.9969i	−1.41306	−	0.585308i	−0.459951	−	0.887944i	$-0.652133\pi$
$353$	−26.5489	−	10.9969i	−1.41306	−	0.585308i	−0.953106	+	0.302636i	$0.902133\pi$
$354$	11.6967	+	11.6967i	0.621675	+	0.621675i
$355$	−10.2546	+	24.7568i	−0.544258	+	1.31396i
$356$	−2.73801	−	2.73801i	−0.145114	−	0.145114i
$357$	28.2712	−	28.2712i	1.49627	−	1.49627i
$358$	−4.56529	+	4.56529i	−0.241283	+	0.241283i
$359$	3.04981	+	1.26327i	0.160963	+	0.0666729i	0.461710	−	0.887031i	$-0.347236\pi$
$359$	3.04981	+	1.26327i	0.160963	+	0.0666729i	−0.300747	+	0.953704i	$0.597236\pi$
$360$	2.64784			0.139553
$361$	−0.886991	+	0.886991i	−0.0466838	+	0.0466838i
$362$	23.5844			1.23957
$363$	3.52012	−	8.49831i	0.184758	−	0.446046i
$364$	−32.1215	−	13.3052i	−1.68363	−	0.697381i
$365$	4.48210	−	4.48210i	0.234604	−	0.234604i
$366$	3.70575	−	3.70575i	0.193703	−	0.193703i
$367$	−18.5583	−	7.68711i	−0.968737	−	0.401264i	−0.158495	−	0.987360i	$-0.550664\pi$
$367$	−18.5583	−	7.68711i	−0.968737	−	0.401264i	−0.810242	+	0.586096i	$0.800664\pi$
$368$	0.467071	+	1.12761i	0.0243478	+	0.0587807i
$369$	−1.07995	−	1.07995i	−0.0562197	−	0.0562197i
$370$	2.05520	+	4.96170i	0.106845	+	0.257946i
$371$	24.4933	+	59.1322i	1.27163	+	3.06999i
$372$	3.35372			0.173882
$373$	−12.0195	−	12.0195i	−0.622347	−	0.622347i	0.323784	−	0.946131i	$-0.395045\pi$
$373$	−12.0195	−	12.0195i	−0.622347	−	0.622347i	−0.946131	+	0.323784i	$0.895045\pi$
$374$	−4.58381	−	11.0663i	−0.237023	−	0.572224i
$375$	−11.2277	−	4.65065i	−0.579793	−	0.240158i
$376$	−4.28322			−0.220890
$377$	26.6932	−	11.0567i	1.37477	−	0.569448i
$378$	10.8530	+	26.2014i	0.558216	+	1.34765i
$379$			33.7546i			1.73386i	0.498432	+	0.866929i	$0.333910\pi$
$379$			33.7546i			1.73386i	−0.498432	+	0.866929i	$0.666090\pi$
$380$	−10.7165	+	4.43891i	−0.549744	+	0.227711i
$381$			2.62936i			0.134706i
$382$	−0.337335	−	0.814399i	−0.0172596	−	0.0416683i
$383$			2.53402i			0.129482i	0.997902	+	0.0647412i	$0.0206222\pi$
$383$			2.53402i			0.129482i	−0.997902	+	0.0647412i	$0.979378\pi$
$384$	1.29760	−	0.537484i	0.0662180	−	0.0274284i
$385$	−27.2620			−1.38940
$386$	13.2997	+	5.50890i	0.676935	+	0.280396i
$387$	7.94654			0.403946
$388$	−0.0531457	+	0.0220137i	−0.00269806	+	0.00111757i
$389$	−7.58766	+	18.3182i	−0.384710	+	0.928772i	0.606331	+	0.795212i	$0.292641\pi$
$389$	−7.58766	+	18.3182i	−0.384710	+	0.928772i	−0.991041	+	0.133559i	$0.957359\pi$
$390$	17.7503	+	17.7503i	0.898821	+	0.898821i
$391$	4.90003	+	4.90003i	0.247805	+	0.247805i
$392$	12.8254	+	12.8254i	0.647780	+	0.647780i
$393$	15.2920	−	15.2920i	0.771380	−	0.771380i
$394$	3.89056	−	3.89056i	0.196003	−	0.196003i
$395$	−14.5083	−	35.0262i	−0.729994	−	1.76236i
$396$	2.16736			0.108914
$397$		−	14.3890i		−	0.722161i	−0.932535	−	0.361081i	$-0.882408\pi$
$397$		−	14.3890i		−	0.722161i	0.932535	−	0.361081i	$-0.117592\pi$
$398$	6.53567	+	2.70716i	0.327603	+	0.135698i
$399$	−22.4096	−	22.4096i	−1.12188	−	1.12188i
$400$	−1.64286			−0.0821428
$401$	12.0701	+	15.9785i	0.602754	+	0.797927i
$401$	12.0701	+	15.9785i	0.602754	+	0.797927i
$402$	6.18378			0.308419
$403$	−11.7085	−	11.7085i	−0.583243	−	0.583243i
$404$	−8.79483	−	3.64294i	−0.437559	−	0.181243i
$405$		−	12.5326i		−	0.622751i
$406$	−20.8897			−1.03674
$407$	1.68226	+	4.06134i	0.0833867	+	0.201313i
$408$	5.63873	−	5.63873i	0.279159	−	0.279159i
$409$	−14.2690	+	14.2690i	−0.705557	+	0.705557i	−0.965598	−	0.260041i	$-0.916264\pi$
$409$	−14.2690	+	14.2690i	−0.705557	+	0.705557i	0.260041	+	0.965598i	$0.416264\pi$
$410$	2.70935	+	2.70935i	0.133805	+	0.133805i
$411$	14.4060	+	14.4060i	0.710594	+	0.710594i
$412$	2.76429	+	2.76429i	0.136187	+	0.136187i
$413$	−22.5973	+	54.5548i	−1.11194	+	2.68447i
$414$	−1.15844	+	0.479841i	−0.0569341	+	0.0235829i
$415$	9.23282			0.453222
$416$	−6.40667	−	2.65373i	−0.314113	−	0.130110i
$417$	−19.0661			−0.933670
$418$	−8.77186	+	3.63342i	−0.429046	+	0.177717i
$419$		−	2.70223i		−	0.132013i	−0.997819	−	0.0660063i	$-0.978974\pi$
$419$		−	2.70223i		−	0.132013i	0.997819	−	0.0660063i	$-0.0210257\pi$
$420$	−6.94556	−	16.7681i	−0.338908	−	0.818197i
$421$			2.22277i			0.108331i	0.998532	+	0.0541656i	$0.0172499\pi$
$421$			2.22277i			0.108331i	−0.998532	+	0.0541656i	$0.982750\pi$
$422$	14.5396	−	6.02251i	0.707778	−	0.293171i
$423$		−	4.40032i		−	0.213951i
$424$	4.88522	+	11.7940i	0.237247	+	0.572766i
$425$	−8.61756	+	3.56951i	−0.418013	+	0.173147i
$426$	−14.6025			−0.707495
$427$	17.2840	+	7.15927i	0.836432	+	0.346461i
$428$	−1.94130	−	4.68670i	−0.0938361	−	0.226540i
$429$	14.5293	+	14.5293i	0.701482	+	0.701482i
$430$	−19.9362			−0.961407
$431$	−0.0830107	−	0.200406i	−0.00399848	−	0.00965319i	0.921868	−	0.387505i	$-0.126663\pi$
$431$	−0.0830107	−	0.200406i	−0.00399848	−	0.00965319i	−0.925866	+	0.377852i	$0.876663\pi$
$432$	2.16463	+	5.22588i	0.104146	+	0.251430i
$433$	7.55400	+	7.55400i	0.363022	+	0.363022i	0.864924	−	0.501902i	$-0.167366\pi$
$433$	7.55400	+	7.55400i	0.363022	+	0.363022i	−0.501902	+	0.864924i	$0.667366\pi$
$434$	4.58146	+	11.0606i	0.219917	+	0.530927i
$435$	13.9344	+	5.77180i	0.668101	+	0.276737i
$436$	−10.7229	+	10.7229i	−0.513532	+	0.513532i
$437$	3.88408	−	3.88408i	0.185801	−	0.185801i
$438$	3.19125	+	1.32186i	0.152484	+	0.0631609i
$439$	−2.85948	+	6.90339i	−0.136475	+	0.329481i	−0.977311	−	0.211810i	$-0.932064\pi$
$439$	−2.85948	+	6.90339i	−0.136475	+	0.329481i	0.840835	+	0.541291i	$0.182064\pi$
$440$	−5.43744			−0.259220
$441$	−13.1760	+	13.1760i	−0.627430	+	0.627430i
$442$	−39.3720			−1.87273
$443$	−19.4376	−	8.05130i	−0.923507	−	0.382529i	−0.130295	−	0.991475i	$-0.541592\pi$
$443$	−19.4376	−	8.05130i	−0.923507	−	0.382529i	−0.793211	+	0.608946i	$0.791592\pi$
$444$	−2.06942	+	2.06942i	−0.0982103	+	0.0982103i
$445$	−7.05688	+	7.05688i	−0.334528	+	0.334528i
$446$	−12.7933	−	12.7933i	−0.605780	−	0.605780i
$447$	−2.61975	+	6.32464i	−0.123910	+	0.299145i
$448$	3.54527	+	3.54527i	0.167498	+	0.167498i
$449$	−15.9144	−	6.59194i	−0.751045	−	0.311093i	−0.0258771	−	0.999665i	$-0.508238\pi$
$449$	−15.9144	−	6.59194i	−0.751045	−	0.311093i	−0.725168	+	0.688572i	$0.758238\pi$
$450$		−	1.68777i		−	0.0795623i
$451$	2.21771	+	2.21771i	0.104428	+	0.104428i
$452$	14.9537			0.703362
$453$	0.238740	+	0.576370i	0.0112170	+	0.0270802i
$454$	5.51180	−	13.3067i	0.258682	−	0.624513i
$455$	−34.2924	+	82.7892i	−1.60765	+	3.88122i
$456$	−4.46962	−	4.46962i	−0.209309	−	0.209309i
$457$		−	4.03499i		−	0.188749i	−0.995537	−	0.0943745i	$-0.969915\pi$
$457$		−	4.03499i		−	0.188749i	0.995537	−	0.0943745i	$-0.0300851\pi$
$458$			2.08076i			0.0972274i
$459$	22.7091	+	22.7091i	1.05997	+	1.05997i
$460$	2.90627	−	1.20382i	0.135506	−	0.0561283i
$461$	3.88158	−	9.37096i	0.180783	−	0.436449i	−0.807345	−	0.590079i	$-0.799096\pi$
$461$	3.88158	−	9.37096i	0.180783	−	0.436449i	0.988128	+	0.153630i	$0.0490964\pi$
$462$	−5.68521	−	13.7253i	−0.264500	−	0.638559i
$463$	−9.87765	+	23.8468i	−0.459054	+	1.10825i	0.509728	+	0.860336i	$0.329746\pi$
$463$	−9.87765	+	23.8468i	−0.459054	+	1.10825i	−0.968781	+	0.247917i	$0.920254\pi$
$464$	−4.16647			−0.193423
$465$		−	8.64378i		−	0.400846i
$466$	−22.9026	+	9.48658i	−1.06094	+	0.439457i
$467$	−3.15135	+	7.60803i	−0.145827	+	0.352058i	−0.979868	−	0.199644i	$-0.936021\pi$
$467$	−3.15135	+	7.60803i	−0.145827	+	0.352058i	0.834041	+	0.551702i	$0.186021\pi$
$468$	2.72628	−	6.58183i	0.126022	−	0.304245i
$469$	8.44756	+	20.3942i	0.390072	+	0.941717i
$470$			11.0394i			0.509212i
$471$	−33.3016			−1.53446
$472$	−4.50706	+	10.8810i	−0.207454	+	0.500839i
$473$	−16.3185			−0.750327
$474$	14.6087	−	14.6087i	0.671000	−	0.671000i
$475$	2.82943	+	6.83084i	0.129823	+	0.313421i
$476$	26.2996	+	10.8937i	1.20544	+	0.499310i
$477$	−12.1164	+	5.01878i	−0.554772	+	0.229794i
$478$	4.20183			0.192187
$479$	−1.75907	−	1.75907i	−0.0803739	−	0.0803739i	0.665777	−	0.746151i	$-0.268100\pi$
$479$	−1.75907	−	1.75907i	−0.0803739	−	0.0803739i	−0.746151	+	0.665777i	$0.768100\pi$
$480$	−1.38530	−	3.34441i	−0.0632299	−	0.152651i
$481$	14.4496			0.658843
$482$			29.0246i			1.32203i
$483$	6.07741	+	6.07741i	0.276532	+	0.276532i
$484$	6.54925			0.297693
$485$	0.0567374	+	0.136976i	0.00257631	+	0.00621977i
$486$	−9.36799	+	3.88035i	−0.424941	+	0.176016i
$487$	−39.0646			−1.77019			−0.885093	−	0.465414i	$-0.845905\pi$
$487$	−39.0646			−1.77019			−0.885093	+	0.465414i	$0.845905\pi$
$488$	3.44731	+	1.42792i	0.156052	+	0.0646391i
$489$	5.43386			0.245727
$490$	33.0558	−	33.0558i	1.49331	−	1.49331i
$491$		−	41.9935i		−	1.89514i	−0.319546	−	0.947571i	$-0.603530\pi$
$491$		−	41.9935i		−	1.89514i	0.319546	−	0.947571i	$-0.396470\pi$
$492$	−0.799040	+	1.92905i	−0.0360235	+	0.0869684i
$493$	−21.8551	+	9.05269i	−0.984305	+	0.407713i
$494$			31.2088i			1.40415i
$495$		−	5.58609i		−	0.251076i
$496$	0.913776	+	2.20605i	0.0410298	+	0.0990546i
$497$	−19.9483	−	48.1594i	−0.894803	−	2.16024i
$498$	1.92541	+	4.64835i	0.0862796	+	0.208297i
$499$	13.1503	−	13.1503i	0.588689	−	0.588689i	−0.348588	−	0.937276i	$-0.613339\pi$
$499$	13.1503	−	13.1503i	0.588689	−	0.588689i	0.937276	+	0.348588i	$0.113339\pi$
$500$		−	8.65262i		−	0.386957i
$501$		−	6.61537i		−	0.295553i
$502$	−0.678902	+	1.63901i	−0.0303009	+	0.0731528i
$503$	8.06535	+	8.06535i	0.359616	+	0.359616i	0.863671	−	0.504055i	$-0.168159\pi$
$503$	8.06535	+	8.06535i	0.359616	+	0.359616i	−0.504055	+	0.863671i	$0.668159\pi$
$504$	−3.64219	+	3.64219i	−0.162236	+	0.162236i
$505$	−9.38921	+	22.6676i	−0.417814	+	1.00869i
$506$	2.37890	−	0.985371i	0.105755	−	0.0438051i
$507$	45.5299	−	18.8591i	2.02206	−	0.837563i
$508$	−1.72957	+	0.716413i	−0.0767374	+	0.0317857i
$509$	7.48409	−	3.10001i	0.331727	−	0.137406i	−0.210603	−	0.977572i	$-0.567543\pi$
$509$	7.48409	−	3.10001i	0.331727	−	0.137406i	0.542329	+	0.840166i	$0.317543\pi$
$510$	−14.5331	−	14.5331i	−0.643537	−	0.643537i
$511$			12.3306i			0.545473i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	18.0007	−	18.0007i	0.794750	−	0.794750i
$514$		−	24.3093i		−	1.07224i
$515$	7.12461	−	7.12461i	0.313948	−	0.313948i
$516$	−4.15748	−	10.0370i	−0.183023	−	0.441856i
$517$			9.03622i			0.397412i
$518$	−9.65198	−	3.99798i	−0.424084	−	0.175661i
$519$	−21.0159	−	8.70509i	−0.922497	−	0.382111i
$520$	−6.83966	+	16.5124i	−0.299939	+	0.724116i
$521$	21.7793	−	9.02128i	0.954168	−	0.395229i	0.149372	−	0.988781i	$-0.452275\pi$
$521$	21.7793	−	9.02128i	0.954168	−	0.395229i	0.804796	+	0.593552i	$0.202275\pi$
$522$		−	4.28038i		−	0.187347i
$523$	12.3879	−	29.9071i	0.541686	−	1.30775i	−0.381846	−	0.924226i	$-0.624712\pi$
$523$	12.3879	−	29.9071i	0.541686	−	1.30775i	0.923532	−	0.383521i	$-0.125288\pi$
$524$	14.2255	+	5.89241i	0.621446	+	0.257411i
$525$	−10.6882	+	4.42720i	−0.466471	+	0.193219i
$526$	2.88694			0.125877
$527$	9.58639	+	9.58639i	0.417590	+	0.417590i
$528$	−1.13392	−	2.73753i	−0.0493476	−	0.119136i
$529$	15.2101	−	15.2101i	0.661309	−	0.661309i
$530$	30.3975	−	12.5910i	1.32038	−	0.546920i
$531$	−11.1785	−	4.63028i	−0.485105	−	0.200937i
$532$	8.63502	−	20.8468i	0.374375	−	0.903822i
$533$	9.52435	−	3.94511i	0.412545	−	0.170882i
$534$	−5.02449	−	2.08121i	−0.217431	−	0.0900628i
$535$	−12.0794	+	5.00345i	−0.522237	+	0.216318i
$536$	1.68487	+	4.06765i	0.0727755	+	0.175696i
$537$	−3.47016	+	8.37770i	−0.149748	+	0.361524i
$538$	−23.0687	−	9.55535i	−0.994561	−	0.411961i
$539$	27.0575	−	27.0575i	1.16545	−	1.16545i
$540$	13.4691	−	5.57907i	0.579616	−	0.240085i
$541$	−6.14548	−	6.14548i	−0.264215	−	0.264215i	0.562549	−	0.826764i	$-0.309821\pi$
$541$	−6.14548	−	6.14548i	−0.264215	−	0.264215i	−0.826764	+	0.562549i	$0.809821\pi$
$542$	−5.08823	−	12.2841i	−0.218558	−	0.527646i
$543$	30.6031	−	12.6762i	1.31331	−	0.543989i
$544$	5.24548	+	2.17275i	0.224898	+	0.0931558i
$545$	27.6368	+	27.6368i	1.18383	+	1.18383i
$546$	−48.8323			−2.08983
$547$	−5.40428			−0.231070			−0.115535	−	0.993303i	$-0.536858\pi$
$547$	−5.40428			−0.231070			−0.115535	+	0.993303i	$0.536858\pi$
$548$	−5.55100	+	13.4013i	−0.237127	+	0.572475i
$549$	−1.46696	+	3.54156i	−0.0626084	+	0.151150i
$550$			3.46590i			0.147786i
$551$	7.17575	+	17.3238i	0.305697	+	0.738018i
$552$	1.21215	+	1.21215i	0.0515923	+	0.0515923i
$553$	68.1365	+	28.2231i	2.89746	+	1.20017i
$554$	−1.33280	−	0.552064i	−0.0566253	−	0.0234550i
$555$	5.33367	+	5.33367i	0.226402	+	0.226402i
$556$	−5.19487	−	12.5415i	−0.220312	−	0.531879i
$557$			24.6612i			1.04493i	0.852661	+	0.522464i	$0.174987\pi$
$557$			24.6612i			1.04493i	−0.852661	+	0.522464i	$0.825013\pi$
$558$	−2.26636	+	0.938758i	−0.0959428	+	0.0397408i
$559$	−20.5268	+	49.5561i	−0.868191	+	2.09600i
$560$	9.13748	−	9.13748i	0.386129	−	0.386129i
$561$	−11.8959	−	11.8959i	−0.502246	−	0.502246i
$562$	−14.7911	−	6.12666i	−0.623923	−	0.258437i
$563$	−29.4356	+	29.4356i	−1.24056	+	1.24056i	−0.280793	+	0.959768i	$0.590598\pi$
$563$	−29.4356	+	29.4356i	−1.24056	+	1.24056i	−0.959768	+	0.280793i	$0.909402\pi$
$564$	−5.55791	+	2.30216i	−0.234030	+	0.0969385i
$565$		−	38.5412i		−	1.62144i
$566$	12.2607	+	29.5999i	0.515355	+	1.24418i
$567$	17.2390	+	17.2390i	0.723972	+	0.723972i
$568$	−3.97870	−	9.60544i	−0.166943	−	0.403035i
$569$	2.12767	−	5.13666i	0.0891967	−	0.215340i	−0.872986	−	0.487746i	$-0.837819\pi$
$569$	2.12767	−	5.13666i	0.0891967	−	0.215340i	0.962182	+	0.272406i	$0.0878193\pi$
$570$	−11.5199	+	11.5199i	−0.482515	+	0.482515i
$571$	20.0666	+	8.31186i	0.839761	+	0.347841i	0.760760	−	0.649034i	$-0.224827\pi$
$571$	20.0666	+	8.31186i	0.839761	+	0.347841i	0.0790020	+	0.996874i	$0.474827\pi$
$572$	−5.59853	+	13.5160i	−0.234086	+	0.565134i
$573$	−0.875453	−	0.875453i	−0.0365726	−	0.0365726i
$574$	−7.45361			−0.311108
$575$	−0.767330	−	1.85250i	−0.0319999	−	0.0772546i
$576$	−0.726439	+	0.726439i	−0.0302683	+	0.0302683i
$577$	21.8950	+	21.8950i	0.911499	+	0.911499i	0.996390	−	0.0848915i	$-0.0270544\pi$
$577$	21.8950	+	21.8950i	0.911499	+	0.911499i	−0.0848915	+	0.996390i	$0.527054\pi$
$578$	15.2359			0.633730
$579$	20.2186			0.840257
$580$			10.7385i			0.445894i
$581$	−12.7001	+	12.7001i	−0.526888	+	0.526888i
$582$	−0.0571299	+	0.0571299i	−0.00236811	+	0.00236811i
$583$	24.8815	−	10.3063i	1.03049	−	0.426842i
$584$			2.45935i			0.101768i
$585$	−16.9638	−	7.02665i	−0.701368	−	0.290516i
$586$	−24.0734	−	9.97152i	−0.994463	−	0.411920i
$587$	−6.34409	+	6.34409i	−0.261849	+	0.261849i	−0.825805	−	0.563956i	$-0.809279\pi$
$587$	−6.34409	+	6.34409i	−0.261849	+	0.261849i	0.563956	+	0.825805i	$0.309279\pi$
$588$	23.5357	+	9.74880i	0.970595	+	0.402034i
$589$	7.59879	−	7.59879i	0.313103	−	0.313103i
$590$	28.0444	+	11.6164i	1.15457	+	0.478239i
$591$	2.95728	−	7.13951i	0.121646	−	0.293680i
$592$	−1.92510	−	0.797401i	−0.0791210	−	0.0327730i
$593$	16.6856	−	40.2825i	0.685194	−	1.65421i	−0.0690518	−	0.997613i	$-0.521997\pi$
$593$	16.6856	−	40.2825i	0.685194	−	1.65421i	0.754246	−	0.656592i	$-0.228003\pi$
$594$	11.0249	−	4.56668i	0.452359	−	0.187373i
$595$	28.0770	−	67.7839i	1.15105	−	2.77887i
$596$	−4.87410			−0.199651
$597$	9.93575			0.406643
$598$		−	8.46371i		−	0.346107i
$599$	16.5687	−	16.5687i	0.676977	−	0.676977i	−0.282338	−	0.959315i	$-0.591110\pi$
$599$	16.5687	−	16.5687i	0.676977	−	0.676977i	0.959315	+	0.282338i	$0.0911100\pi$
$600$	−2.13177	+	0.883009i	−0.0870292	+	0.0360487i
$601$	9.20834	−	9.20834i	0.375616	−	0.375616i	−0.493902	−	0.869518i	$-0.664430\pi$
$601$	9.20834	−	9.20834i	0.375616	−	0.375616i	0.869518	+	0.493902i	$0.164430\pi$
$602$	27.4229	−	27.4229i	1.11767	−	1.11767i
$603$	−4.17885	+	1.73094i	−0.170176	+	0.0704893i
$604$	−0.314084	+	0.314084i	−0.0127799	+	0.0127799i
$605$		−	16.8799i		−	0.686264i
$606$	−13.3702			−0.543128
$607$	−26.9496			−1.09385			−0.546926	−	0.837181i	$-0.684202\pi$
$607$	−26.9496			−1.09385			−0.546926	+	0.837181i	$0.684202\pi$
$608$	1.72226	−	4.15791i	0.0698470	−	0.168625i
$609$	−27.1065	+	11.2279i	−1.09841	+	0.454977i
$610$	3.68029	−	8.88501i	0.149011	−	0.359744i
$611$	27.4412	+	11.3665i	1.11015	+	0.459839i
$612$	−2.23215	+	5.38889i	−0.0902294	+	0.217833i
$613$	−9.31639	−	3.85897i	−0.376285	−	0.155863i	0.186522	−	0.982451i	$-0.440279\pi$
$613$	−9.31639	−	3.85897i	−0.376285	−	0.155863i	−0.562807	+	0.826588i	$0.690279\pi$
$614$	−1.70066	+	1.70066i	−0.0686331	+	0.0686331i
$615$	4.97189	+	2.05942i	0.200486	+	0.0830440i
$616$	7.47938	−	7.47938i	0.301353	−	0.301353i
$617$	−25.3423	−	10.4971i	−1.02024	−	0.422598i	−0.191062	−	0.981578i	$-0.561193\pi$
$617$	−25.3423	−	10.4971i	−1.02024	−	0.422598i	−0.829181	+	0.558980i	$0.811193\pi$
$618$	5.07271	+	2.10119i	0.204054	+	0.0845221i
$619$			24.3407i			0.978334i	0.872190	+	0.489167i	$0.162699\pi$
$619$			24.3407i			0.978334i	−0.872190	+	0.489167i	$0.837301\pi$
$620$	5.68582	−	2.35514i	0.228348	−	0.0945848i
$621$	−4.88172	+	4.88172i	−0.195897	+	0.195897i
$622$	−7.47263	+	7.47263i	−0.299625	+	0.299625i
$623$		−	19.4140i		−	0.777804i
$624$	−9.73965			−0.389898
$625$	−30.5153			−1.22061
$626$	−14.4133	−	14.4133i	−0.576070	−	0.576070i
$627$	−9.42948	+	9.42948i	−0.376577	+	0.376577i
$628$	−9.07357	−	21.9055i	−0.362075	−	0.874126i
$629$	−11.8306			−0.471717
$630$	9.38729	+	9.38729i	0.373999	+	0.373999i
$631$	−5.58977	+	13.4949i	−0.222525	+	0.537223i	−0.995232	−	0.0975404i	$-0.968902\pi$
$631$	−5.58977	+	13.4949i	−0.222525	+	0.537223i	0.772706	+	0.634763i	$0.218902\pi$
$632$	13.5899	+	5.62912i	0.540577	+	0.223914i
$633$	15.6296	−	15.6296i	0.621223	−	0.621223i
$634$	−5.83108	+	14.0775i	−0.231582	+	0.559088i
$635$	1.84646	+	4.45776i	0.0732747	+	0.176901i
$636$	12.6781	+	12.6781i	0.502721	+	0.502721i
$637$	−48.1329	−	116.203i	−1.90710	−	4.60414i
$638$			8.78992i			0.347996i
$639$	9.86805	−	4.08748i	0.390374	−	0.161698i
$640$	1.82248	−	1.82248i	0.0720398	−	0.0720398i
$641$	7.71194	+	3.19439i	0.304603	+	0.126171i	0.529749	−	0.848154i	$-0.322286\pi$
$641$	7.71194	+	3.19439i	0.304603	+	0.126171i	−0.225146	+	0.974325i	$0.572286\pi$
$642$	−5.03806	−	5.03806i	−0.198836	−	0.198836i
$643$	24.3941	−	24.3941i	0.962010	−	0.962010i	−0.0372940	−	0.999304i	$-0.511874\pi$
$643$	24.3941	−	24.3941i	0.962010	−	0.962010i	0.999304	+	0.0372940i	$0.0118738\pi$
$644$	−2.34179	+	5.65357i	−0.0922793	+	0.222782i
$645$	−25.8692	+	10.7154i	−1.01860	+	0.421918i
$646$		−	25.5523i		−	1.00534i
$647$	13.5244	+	32.6508i	0.531700	+	1.28364i	0.930397	+	0.366554i	$0.119462\pi$
$647$	13.5244	+	32.6508i	0.531700	+	1.28364i	−0.398697	+	0.917083i	$0.630538\pi$
$648$	3.43834	+	3.43834i	0.135071	+	0.135071i
$649$	22.9555	+	9.50846i	0.901081	+	0.373240i
$650$	10.5252	+	4.35970i	0.412834	+	0.171001i
$651$	11.8898	+	11.8898i	0.465999	+	0.465999i
$652$	1.48054	+	3.57435i	0.0579826	+	0.139982i
$653$		−	11.3923i		−	0.445816i	−0.974839	−	0.222908i	$-0.928445\pi$
$653$		−	11.3923i		−	0.445816i	0.974839	−	0.222908i	$-0.0715550\pi$
$654$	−8.15063	+	19.6774i	−0.318715	+	0.769446i
$655$	15.1869	−	36.6645i	0.593403	−	1.43260i
$656$	−1.48663			−0.0580431
$657$	−2.52658			−0.0985714
$658$	−15.1851	−	15.1851i	−0.591978	−	0.591978i
$659$	−25.3852	−	10.5149i	−0.988865	−	0.409601i	−0.171163	−	0.985243i	$-0.554752\pi$
$659$	−25.3852	−	10.5149i	−0.988865	−	0.409601i	−0.817702	+	0.575641i	$0.804752\pi$
$660$	−7.05563	+	2.92254i	−0.274640	+	0.113760i
$661$	18.7617	+	45.2948i	0.729747	+	1.76176i	0.643441	+	0.765495i	$0.277506\pi$
$661$	18.7617	+	45.2948i	0.729747	+	1.76176i	0.0863053	+	0.996269i	$0.472494\pi$
$662$	−1.70852	−	1.70852i	−0.0664037	−	0.0664037i
$663$	−51.0891	+	21.1618i	−1.98414	+	0.821857i
$664$	−2.53304	+	2.53304i	−0.0983010	+	0.0983010i
$665$	−53.7299	−	22.2557i	−2.08356	−	0.863038i
$666$	0.819202	−	1.97773i	0.0317434	−	0.0766354i
$667$	−1.94604	−	4.69815i	−0.0753509	−	0.181913i
$668$	4.35155	−	1.80247i	0.168366	−	0.0697396i
$669$	−23.4768	−	9.72440i	−0.907665	−	0.375967i
$670$	10.4838	−	4.34255i	0.405026	−	0.167767i
$671$	3.01246	−	7.27273i	0.116295	−	0.280761i
$672$	6.50587	+	2.69482i	0.250969	+	0.103955i
$673$	0.901446	−	0.373391i	0.0347482	−	0.0143932i	−0.365242	−	0.930913i	$-0.619014\pi$
$673$	0.901446	−	0.373391i	0.0347482	−	0.0143932i	0.399990	+	0.916520i	$0.369014\pi$
$674$	5.63855	−	5.63855i	0.217189	−	0.217189i
$675$	−3.55618	−	8.58537i	−0.136877	−	0.330451i
$676$	24.8108	+	24.8108i	0.954261	+	0.954261i
$677$	23.4303			0.900498			0.450249	−	0.892903i	$-0.351335\pi$
$677$	23.4303			0.900498			0.450249	+	0.892903i	$0.351335\pi$
$678$	19.4039	−	8.03736i	0.745203	−	0.308673i
$679$	−0.266460	−	0.110371i	−0.0102258	−	0.00423566i
$680$	5.59999	−	13.5196i	0.214750	−	0.518452i
$681$		−	20.2293i		−	0.775187i
$682$	4.65406	−	1.92778i	0.178213	−	0.0738183i
$683$	−18.2867	+	44.1480i	−0.699720	+	1.68927i	0.0244945	+	0.999700i	$0.492202\pi$
$683$	−18.2867	+	44.1480i	−0.699720	+	1.68927i	−0.724215	+	0.689574i	$0.757798\pi$
$684$	4.27159	+	1.76935i	0.163328	+	0.0676527i
$685$	34.5401	+	14.3070i	1.31971	+	0.546642i
$686$			55.8425i			2.13208i
$687$	1.11837	+	2.69999i	0.0426686	+	0.103011i
$688$	5.46952	−	5.46952i	0.208523	−	0.208523i
$689$		−	88.5241i		−	3.37250i
$690$	3.12415	−	3.12415i	0.118934	−	0.118934i
$691$	12.9978	+	12.9978i	0.494458	+	0.494458i	0.909708	−	0.415250i	$-0.136306\pi$
$691$	12.9978	+	12.9978i	0.494458	+	0.494458i	−0.415250	+	0.909708i	$0.636306\pi$
$692$		−	16.1960i		−	0.615679i
$693$	7.68387	+	7.68387i	0.291886	+	0.291886i
$694$	−21.3195	+	8.83084i	−0.809279	+	0.335214i
$695$	−32.3242	+	13.3891i	−1.22613	+	0.507879i
$696$	−5.40642	+	2.23941i	−0.204930	+	0.0848846i
$697$	−7.79808	+	3.23007i	−0.295373	+	0.122348i
$698$	−12.3823	+	29.8936i	−0.468678	+	1.13149i
$699$	−24.6196	+	24.6196i	−0.931199	+	0.931199i
$700$	−5.82436	−	5.82436i	−0.220140	−	0.220140i
$701$	−6.46726	+	15.6133i	−0.244265	+	0.589708i	−0.997698	−	0.0678172i	$-0.978397\pi$
$701$	−6.46726	+	15.6133i	−0.244265	+	0.589708i	0.753433	+	0.657525i	$0.228397\pi$
$702$		−	39.2249i		−	1.48045i
$703$			9.37771i			0.353687i
$704$	1.49177	−	1.49177i	0.0562232	−	0.0562232i
$705$	5.93353	+	14.3248i	0.223470	+	0.539503i
$706$	−10.9969	−	26.5489i	−0.413875	−	0.999183i
$707$	−18.2648	−	44.0952i	−0.686920	−	1.65837i
$708$			16.5417i			0.621675i
$709$		−	10.5283i		−	0.395397i	−0.980263	−	0.197699i	$-0.936653\pi$
$709$		−	10.5283i		−	0.395397i	0.980263	−	0.197699i	$-0.0633467\pi$
$710$	−24.7568	+	10.2546i	−0.929107	+	0.384849i
$711$	−5.78302	+	13.9614i	−0.216880	+	0.523595i
$712$		−	3.87213i		−	0.145114i
$713$	−2.06077	+	2.06077i	−0.0771763	+	0.0771763i
$714$	39.9816			1.49627
$715$	34.8359	+	14.4295i	1.30279	+	0.539632i
$716$	−6.45630			−0.241283
$717$	5.45231	−	2.25842i	0.203620	−	0.0843422i
$718$	1.26327	+	3.04981i	0.0471449	+	0.113818i
$719$	23.6965			0.883729			0.441865	−	0.897082i	$-0.354317\pi$
$719$	23.6965			0.883729			0.441865	+	0.897082i	$0.354317\pi$
$720$	1.87230	+	1.87230i	0.0697767	+	0.0697767i
$721$			19.6003i			0.729953i
$722$	−1.25440			−0.0466838
$723$	15.6003	+	37.6624i	0.580180	+	1.40068i
$724$	16.6767	+	16.6767i	0.619784	+	0.619784i
$725$	6.84490			0.254213
$726$	8.49831	−	3.52012i	0.315402	−	0.130644i
$727$	26.1979	+	10.8515i	0.971626	+	0.402461i	0.811317	−	0.584606i	$-0.198751\pi$
$727$	26.1979	+	10.8515i	0.971626	+	0.402461i	0.160309	+	0.987067i	$0.448751\pi$
$728$	−13.3052	−	32.1215i	−0.493123	−	1.19050i
$729$	−20.3853	+	20.3853i	−0.755012	+	0.755012i
$730$	6.33865			0.234604
$731$	16.8064	−	40.5742i	0.621606	−	1.50069i
$732$	5.24073			0.193703
$733$		−	23.7843i		−	0.878492i	−0.898367	−	0.439246i	$-0.855246\pi$
$733$		−	23.7843i		−	0.878492i	0.898367	−	0.439246i	$-0.144754\pi$
$734$	−7.68711	−	18.5583i	−0.283736	−	0.685000i
$735$	25.1263	−	60.6603i	0.926798	−	2.23749i
$736$	−0.467071	+	1.12761i	−0.0172165	+	0.0415642i
$737$	8.58144	−	3.55455i	0.316101	−	0.130933i
$738$		−	1.52727i		−	0.0562197i
$739$	15.8869			0.584407			0.292204	−	0.956356i	$-0.405611\pi$
$739$	15.8869			0.584407			0.292204	+	0.956356i	$0.405611\pi$
$740$	−2.05520	+	4.96170i	−0.0755507	+	0.182396i
$741$	16.7742	+	40.4966i	0.616217	+	1.48768i
$742$	−24.4933	+	59.1322i	−0.899179	+	2.17081i
$743$	−42.2496	+	17.5004i	−1.54999	+	0.642026i	−0.983314	−	0.181916i	$-0.941770\pi$
$743$	−42.2496	+	17.5004i	−1.54999	+	0.642026i	−0.566674	+	0.823942i	$0.691770\pi$
$744$	2.37143	+	2.37143i	0.0869410	+	0.0869410i
$745$			12.5624i			0.460250i
$746$		−	16.9982i		−	0.622347i
$747$	−2.60229	−	2.60229i	−0.0952129	−	0.0952129i
$748$	4.58381	−	11.0663i	0.167601	−	0.404624i
$749$	9.73320	−	23.4980i	0.355643	−	0.858599i
$750$	−4.65065	−	11.2277i	−0.169818	−	0.409976i
$751$	−13.0652			−0.476755			−0.238378	−	0.971173i	$-0.576616\pi$
$751$	−13.0652			−0.476755			−0.238378	+	0.971173i	$0.576616\pi$
$752$	−3.02869	−	3.02869i	−0.110445	−	0.110445i
$753$			2.49169i			0.0908021i
$754$	26.6932	+	11.0567i	0.972109	+	0.402661i
$755$	0.809511	+	0.809511i	0.0294611	+	0.0294611i
$756$	−10.8530	+	26.2014i	−0.394718	+	0.952934i
$757$	2.81720	+	2.81720i	0.102393	+	0.102393i	0.756447	−	0.654055i	$-0.226933\pi$
$757$	2.81720	+	2.81720i	0.102393	+	0.102393i	−0.654055	+	0.756447i	$0.726933\pi$
$758$	−23.8681	+	23.8681i	−0.866929	+	0.866929i
$759$	2.55724	−	2.55724i	0.0928219	−	0.0928219i
$760$	−10.7165	−	4.43891i	−0.388728	−	0.161016i
$761$	−22.9140			−0.830631			−0.415315	−	0.909678i	$-0.636329\pi$
$761$	−22.9140			−0.830631			−0.415315	+	0.909678i	$0.636329\pi$
$762$	−1.85924	+	1.85924i	−0.0673530	+	0.0673530i
$763$	−76.0308			−2.75250
$764$	0.337335	−	0.814399i	0.0122044	−	0.0294639i
$765$	13.8892	+	5.75309i	0.502165	+	0.208003i
$766$	−1.79182	+	1.79182i	−0.0647412	+	0.0647412i
$767$	57.7506	−	57.7506i	2.08525	−	2.08525i
$768$	1.29760	+	0.537484i	0.0468232	+	0.0193948i
$769$	−7.71138	−	18.6169i	−0.278080	−	0.671343i	0.721703	−	0.692203i	$-0.243360\pi$
$769$	−7.71138	−	18.6169i	−0.278080	−	0.671343i	−0.999782	+	0.0208595i	$0.993360\pi$
$770$	−19.2772	−	19.2772i	−0.694701	−	0.694701i
$771$	−13.0658	−	31.5437i	−0.470555	−	1.13602i
$772$	5.50890	+	13.2997i	0.198270	+	0.478666i
$773$	12.1696			0.437711			0.218855	−	0.975757i	$-0.429768\pi$
$773$	12.1696			0.437711			0.218855	+	0.975757i	$0.429768\pi$
$774$	5.61906	+	5.61906i	0.201973	+	0.201973i
$775$	−1.50120	−	3.62422i	−0.0539247	−	0.130186i
$776$	−0.0531457	−	0.0220137i	−0.00190782	−	0.000790244i
$777$	−14.6733			−0.526401
$778$	−18.3182	+	7.58766i	−0.656741	+	0.272031i
$779$	2.56037	+	6.18127i	0.0917346	+	0.221467i
$780$			25.1027i			0.898821i
$781$	−20.2644	+	8.39380i	−0.725118	+	0.300354i
$782$			6.92968i			0.247805i
$783$	−9.01887	−	21.7735i	−0.322308	−	0.778120i
$784$			18.1378i			0.647780i
$785$	−56.4588	+	23.3860i	−2.01510	+	0.834682i
$786$	21.6262			0.771380
$787$	18.9987	+	7.86954i	0.677232	+	0.280519i	0.694669	−	0.719329i	$-0.255551\pi$
$787$	18.9987	+	7.86954i	0.677232	+	0.280519i	−0.0174372	+	0.999848i	$0.505551\pi$
$788$	5.50208			0.196003
$789$	3.74610	−	1.55169i	0.133365	−	0.0552415i
$790$	14.5083	−	35.0262i	0.516184	−	1.24618i
$791$	53.0148	+	53.0148i	1.88499	+	1.88499i
$792$	1.53255	+	1.53255i	0.0544570	+	0.0544570i
$793$	−18.2965	−	18.2965i	−0.649727	−	0.649727i
$794$	10.1745	−	10.1745i	0.361081	−	0.361081i
$795$	32.6763	−	32.6763i	1.15891	−	1.15891i
$796$	2.70716	+	6.53567i	0.0959528	+	0.231651i
$797$	9.60579			0.340254			0.170127	−	0.985422i	$-0.445582\pi$
$797$	9.60579			0.340254			0.170127	+	0.985422i	$0.445582\pi$
$798$		−	31.6920i		−	1.12188i
$799$	−22.4675	−	9.30635i	−0.794844	−	0.329235i
$800$	−1.16167	−	1.16167i	−0.0410714	−	0.0410714i
$801$	3.97800			0.140556
$802$	−2.76361	+	19.8334i	−0.0975864	+	0.700341i
$803$	5.18843			0.183096
$804$	4.37259	+	4.37259i	0.154209	+	0.154209i
$805$	14.5714	+	6.03566i	0.513573	+	0.212729i
$806$		−	16.5584i		−	0.583243i
$807$	−35.0698			−1.23452
$808$	−3.64294	−	8.79483i	−0.128158	−	0.309401i
$809$	13.3007	−	13.3007i	0.467627	−	0.467627i	−0.433518	−	0.901145i	$-0.642728\pi$
$809$	13.3007	−	13.3007i	0.467627	−	0.467627i	0.901145	+	0.433518i	$0.142728\pi$
$810$	8.86190	−	8.86190i	0.311375	−	0.311375i
$811$	−11.5933	−	11.5933i	−0.407095	−	0.407095i	0.473630	−	0.880724i	$-0.342944\pi$
$811$	−11.5933	−	11.5933i	−0.407095	−	0.407095i	−0.880724	+	0.473630i	$0.842944\pi$
$812$	−14.7712	−	14.7712i	−0.518369	−	0.518369i
$813$	−13.2050	−	13.2050i	−0.463119	−	0.463119i
$814$	−1.68226	+	4.06134i	−0.0589633	+	0.142350i
$815$	9.21244	−	3.81592i	0.322698	−	0.133666i
$816$	7.97436			0.279159
$817$	−32.1617	−	13.3218i	−1.12520	−	0.466071i
$818$	−20.1794			−0.705557
$819$	32.9997	−	13.6689i	1.15310	−	0.477631i
$820$			3.83160i			0.133805i
$821$	9.56712	+	23.0971i	0.333895	+	0.806093i	0.998276	+	0.0586991i	$0.0186953\pi$
$821$	9.56712	+	23.0971i	0.333895	+	0.806093i	−0.664381	+	0.747394i	$0.731305\pi$
$822$			20.3731i			0.710594i
$823$	17.8662	−	7.40043i	0.622778	−	0.257963i	−0.0489033	−	0.998804i	$-0.515573\pi$
$823$	17.8662	−	7.40043i	0.622778	−	0.257963i	0.671681	+	0.740841i	$0.265573\pi$
$824$			3.90930i			0.136187i
$825$	1.86287	+	4.49736i	0.0648567	+	0.156578i
$826$	−54.5548	+	22.5973i	−1.89821	+	0.786262i
$827$	−0.188118			−0.00654149			−0.00327075	−	0.999995i	$-0.501041\pi$
$827$	−0.188118			−0.00654149			−0.00327075	+	0.999995i	$0.501041\pi$
$828$	−1.15844	−	0.479841i	−0.0402585	−	0.0166756i
$829$	−21.2854	−	51.3874i	−0.739271	−	1.78476i	−0.608829	−	0.793302i	$-0.708360\pi$
$829$	−21.2854	−	51.3874i	−0.739271	−	1.78476i	−0.130442	−	0.991456i	$-0.541640\pi$
$830$	6.52859	+	6.52859i	0.226611	+	0.226611i
$831$	−2.02617			−0.0702871
$832$	−2.65373	−	6.40667i	−0.0920016	−	0.222111i
$833$	39.4090	+	95.1416i	1.36544	+	3.29646i
$834$	−13.4818	−	13.4818i	−0.466835	−	0.466835i
$835$	−4.64564	−	11.2156i	−0.160769	−	0.388130i
$836$	−8.77186	−	3.63342i	−0.303381	−	0.125665i
$837$	−9.55057	+	9.55057i	−0.330116	+	0.330116i
$838$	1.91077	−	1.91077i	0.0660063	−	0.0660063i
$839$	−33.4982	−	13.8754i	−1.15649	−	0.479032i	−0.279782	−	0.960064i	$-0.590262\pi$
$839$	−33.4982	−	13.8754i	−1.15649	−	0.479032i	−0.876703	+	0.481032i	$0.840262\pi$
$840$	6.94556	−	16.7681i	0.239644	−	0.578553i
$841$	−11.6406			−0.401398
$842$	−1.57174	+	1.57174i	−0.0541656	+	0.0541656i
$843$	−22.4859			−0.774455
$844$	14.5396	+	6.02251i	0.500475	+	0.207303i
$845$	63.9467	−	63.9467i	2.19983	−	2.19983i
$846$	3.11149	−	3.11149i	0.106975	−	0.106975i
$847$	23.2188	+	23.2188i	0.797808	+	0.797808i
$848$	−4.88522	+	11.7940i	−0.167759	+	0.405006i
$849$	31.8190	+	31.8190i	1.09203	+	1.09203i
$850$	−8.61756	−	3.56951i	−0.295580	−	0.122433i
$851$		−	2.54320i		−	0.0871798i
$852$	−10.3255	−	10.3255i	−0.353747	−	0.353747i
$853$	37.9272			1.29860			0.649301	−	0.760531i	$-0.275061\pi$
$853$	37.9272			1.29860			0.649301	+	0.760531i	$0.275061\pi$
$854$	7.15927	+	17.2840i	0.244985	+	0.591447i
$855$	4.56027	−	11.0095i	0.155958	−	0.376516i
$856$	1.94130	−	4.68670i	0.0663521	−	0.160188i
$857$	14.7666	+	14.7666i	0.504416	+	0.504416i	0.912807	−	0.408391i	$-0.133910\pi$
$857$	14.7666	+	14.7666i	0.504416	+	0.504416i	−0.408391	+	0.912807i	$0.633910\pi$
$858$			20.5476i			0.701482i
$859$		−	53.9657i		−	1.84129i	−0.390404	−	0.920644i	$-0.627665\pi$
$859$		−	53.9657i		−	1.84129i	0.390404	−	0.920644i	$-0.372335\pi$
$860$	−14.0970	−	14.0970i	−0.480704	−	0.480704i
$861$	−9.67182	+	4.00620i	−0.329615	+	0.136531i
$862$	0.0830107	−	0.200406i	0.00282736	−	0.00682584i
$863$	−3.90626	−	9.43054i	−0.132970	−	0.321019i	0.843344	−	0.537373i	$-0.180583\pi$
$863$	−3.90626	−	9.43054i	−0.132970	−	0.321019i	−0.976315	+	0.216354i	$0.930583\pi$
$864$	−2.16463	+	5.22588i	−0.0736423	+	0.177788i
$865$	−41.7431			−1.41931
$866$			10.6830i			0.363022i
$867$	19.7701	−	8.18906i	0.671429	−	0.278115i
$868$	−4.58146	+	11.0606i	−0.155505	+	0.375422i
$869$	11.8756	−	28.6703i	0.402854	−	0.972575i
$870$	5.77180	+	13.9344i	0.195682	+	0.472419i
$871$		−	30.5313i		−	1.03451i
$872$	−15.1644			−0.513532
$873$	0.0226155	−	0.0545987i	0.000765419	−	0.00184788i
$874$	5.49292			0.185801
$875$	30.6758	−	30.6758i	1.03703	−	1.03703i
$876$	1.32186	+	3.19125i	0.0446615	+	0.107822i
$877$	37.9210	+	15.7074i	1.28050	+	0.530400i	0.916140	−	0.400858i	$-0.131288\pi$
$877$	37.9210	+	15.7074i	1.28050	+	0.530400i	0.364360	+	0.931258i	$0.381288\pi$
$878$	−6.90339	+	2.85948i	−0.232978	+	0.0965027i
$879$	−36.5972			−1.23439
$880$	−3.84485	−	3.84485i	−0.129610	−	0.129610i
$881$	−7.20047	−	17.3835i	−0.242590	−	0.585664i	0.754948	−	0.655784i	$-0.227662\pi$
$881$	−7.20047	−	17.3835i	−0.242590	−	0.585664i	−0.997539	+	0.0701198i	$0.977662\pi$
$882$	−18.6337			−0.627430
$883$		−	18.0980i		−	0.609046i	−0.952505	−	0.304523i	$-0.901503\pi$
$883$		−	18.0980i		−	0.609046i	0.952505	−	0.304523i	$-0.0984970\pi$
$884$	−27.8402	−	27.8402i	−0.936367	−	0.936367i
$885$	42.6341			1.43313
$886$	−8.05130	−	19.4376i	−0.270489	−	0.653018i
$887$	−30.9218	+	12.8082i	−1.03825	+	0.430058i	−0.835684	−	0.549211i	$-0.814928\pi$
$887$	−30.9218	+	12.8082i	−1.03825	+	0.430058i	−0.202567	+	0.979268i	$0.564928\pi$
$888$	−2.92660			−0.0982103
$889$	−8.67167	−	3.59192i	−0.290839	−	0.120469i
$890$	−9.97993			−0.334528
$891$	7.25381	−	7.25381i	0.243012	−	0.243012i
$892$		−	18.0924i		−	0.605780i
$893$	−7.37682	+	17.8092i	−0.246856	+	0.595963i
$894$	−6.32464	+	2.61975i	−0.211528	+	0.0876177i
$895$			16.6403i			0.556223i
$896$			5.01376i			0.167498i
$897$	−4.54911	−	10.9825i	−0.151890	−	0.366696i
$898$	−6.59194	−	15.9144i	−0.219976	−	0.531069i
$899$	−3.80722	−	9.19144i	−0.126978	−	0.306552i
$900$	1.19343	−	1.19343i	0.0397811	−	0.0397811i
$901$			72.4794i			2.41464i
$902$			3.13631i			0.104428i
$903$	20.8446	−	50.3234i	0.693665	−	1.67466i
$904$	10.5738	+	10.5738i	0.351681	+	0.351681i
$905$	42.9820	−	42.9820i	1.42877	−	1.42877i
$906$	−0.238740	+	0.576370i	−0.00793162	+	0.0191486i
$907$	30.9452	−	12.8179i	1.02752	−	0.425612i	0.195703	−	0.980663i	$-0.437301\pi$
$907$	30.9452	−	12.8179i	1.02752	−	0.425612i	0.831816	+	0.555051i	$0.187301\pi$
$908$	13.3067	−	5.51180i	0.441597	−	0.182915i
$909$	9.03528	−	3.74254i	0.299681	−	0.124132i
$910$	−82.7892	+	34.2924i	−2.74444	+	1.13678i
$911$	7.85275	+	7.85275i	0.260173	+	0.260173i	0.825124	−	0.564951i	$-0.191105\pi$
$911$	7.85275	+	7.85275i	0.260173	+	0.260173i	−0.564951	+	0.825124i	$0.691105\pi$
$912$		−	6.32100i		−	0.209309i
$913$	5.34391	+	5.34391i	0.176858	+	0.176858i
$914$	2.85317	−	2.85317i	0.0943745	−	0.0943745i
$915$		−	13.5073i		−	0.446538i
$916$	−1.47132	+	1.47132i	−0.0486137	+	0.0486137i
$917$	29.5432	+	71.3235i	0.975601	+	2.35531i
$918$			32.1155i			1.05997i
$919$	36.1258	+	14.9638i	1.19168	+	0.493611i	0.888302	−	0.459259i	$-0.151885\pi$
$919$	36.1258	+	14.9638i	1.19168	+	0.493611i	0.303379	+	0.952870i	$0.401885\pi$
$920$	2.90627	+	1.20382i	0.0958169	+	0.0396887i
$921$	−1.29270	+	3.12086i	−0.0425960	+	0.102836i
$922$	9.37096	−	3.88158i	0.308616	−	0.127833i
$923$			72.0973i			2.37311i
$924$	5.68521	−	13.7253i	0.187030	−	0.451530i
$925$	3.16266	+	1.31001i	0.103987	+	0.0430730i
$926$	−23.8468	+	9.87765i	−0.783653	+	0.324600i
$927$	−4.01618			−0.131909
$928$	−2.94614	−	2.94614i	−0.0967117	−	0.0967117i
$929$	−11.1046	−	26.8089i	−0.364331	−	0.879572i	−0.994656	−	0.103241i	$-0.967079\pi$
$929$	−11.1046	−	26.8089i	−0.364331	−	0.879572i	0.630326	−	0.776331i	$-0.282921\pi$
$930$	6.11207	−	6.11207i	0.200423	−	0.200423i
$931$	75.4155	−	31.2381i	2.47164	−	1.02379i
$932$	−22.9026	−	9.48658i	−0.750200	−	0.310743i
$933$	−5.68007	+	13.7129i	−0.185957	+	0.448941i
$934$	−7.60803	+	3.15135i	−0.248942	+	0.103115i
$935$	−28.5220	−	11.8142i	−0.932768	−	0.386365i
$936$	6.58183	−	2.72628i	0.215134	−	0.0891114i
$937$	−2.38353	−	5.75434i	−0.0778664	−	0.187986i	0.880153	−	0.474691i	$-0.157440\pi$
$937$	−2.38353	−	5.75434i	−0.0778664	−	0.187986i	−0.958019	+	0.286705i	$0.907440\pi$
$938$	−8.44756	+	20.3942i	−0.275823	+	0.665895i
$939$	−26.4496	−	10.9558i	−0.863149	−	0.357528i
$940$	−7.80607	+	7.80607i	−0.254606	+	0.254606i
$941$	2.80498	−	1.16186i	0.0914399	−	0.0378756i	−0.336495	−	0.941685i	$-0.609241\pi$
$941$	2.80498	−	1.16186i	0.0914399	−	0.0378756i	0.427935	+	0.903810i	$0.359241\pi$
$942$	−23.5478	−	23.5478i	−0.767228	−	0.767228i
$943$	−0.694362	−	1.67634i	−0.0226115	−	0.0545891i
$944$	−10.8810	+	4.50706i	−0.354147	+	0.146692i
$945$	67.5307	+	27.9721i	2.19677	+	0.909933i
$946$	−11.5389	−	11.5389i	−0.375163	−	0.375163i
$947$	−54.8314			−1.78178			−0.890891	−	0.454217i	$-0.849919\pi$
$947$	−54.8314			−1.78178			−0.890891	+	0.454217i	$0.849919\pi$
$948$	20.6598			0.671000
$949$	6.52644	−	15.7562i	0.211857	−	0.511469i
$950$	−2.82943	+	6.83084i	−0.0917987	+	0.221622i
$951$			21.4011i			0.693977i
$952$	10.8937	+	26.2996i	0.353065	+	0.852375i
$953$	−37.4845	−	37.4845i	−1.21424	−	1.21424i	−0.969618	−	0.244626i	$-0.921335\pi$
$953$	−37.4845	−	37.4845i	−1.21424	−	1.21424i	−0.244626	−	0.969618i	$-0.578665\pi$
$954$	−12.1164	−	5.01878i	−0.392283	−	0.162489i
$955$	−2.09901	−	0.869438i	−0.0679224	−	0.0281344i
$956$	2.97114	+	2.97114i	0.0960937	+	0.0960937i
$957$	4.72444	+	11.4058i	0.152720	+	0.368698i
$958$		−	2.48770i		−	0.0803739i
$959$	−67.1909	+	27.8314i	−2.16971	+	0.898722i
$960$	1.38530	−	3.34441i	0.0447103	−	0.107940i
$961$	17.8886	−	17.8886i	0.577053	−	0.577053i
$962$	10.2174	+	10.2174i	0.329422	+	0.329422i
$963$	4.81484	+	1.99437i	0.155156	+	0.0642677i
$964$	−20.5235	+	20.5235i	−0.661017	+	0.661017i
$965$	34.2782	−	14.1985i	1.10345	−	0.457066i
$966$			8.59476i			0.276532i
$967$	−10.9128	−	26.3458i	−0.350932	−	0.847224i	−0.996506	−	0.0835261i	$-0.973382\pi$
$967$	−10.9128	−	26.3458i	−0.350932	−	0.847224i	0.645574	−	0.763698i	$-0.276618\pi$
$968$	4.63102	+	4.63102i	0.148847	+	0.148847i
$969$	−13.7339	−	33.1567i	−0.441198	−	1.06515i
$970$	−0.0567374	+	0.136976i	−0.00182173	+	0.00439804i
$971$	−15.9859	+	15.9859i	−0.513012	+	0.513012i	−0.915448	−	0.402436i	$-0.868164\pi$
$971$	−15.9859	+	15.9859i	−0.513012	+	0.513012i	0.402436	+	0.915448i	$0.368164\pi$
$972$	−9.36799	−	3.88035i	−0.300479	−	0.124462i
$973$	26.0459	−	62.8803i	0.834992	−	2.01585i
$974$	−27.6228	−	27.6228i	−0.885093	−	0.885093i
$975$	16.0008			0.512437
$976$	1.42792	+	3.44731i	0.0457067	+	0.110346i
$977$	16.9434	−	16.9434i	0.542068	−	0.542068i	−0.382067	−	0.924135i	$-0.624788\pi$
$977$	16.9434	−	16.9434i	0.542068	−	0.542068i	0.924135	+	0.382067i	$0.124788\pi$
$978$	3.84232	+	3.84232i	0.122864	+	0.122864i
$979$	−8.16897			−0.261081
$980$	46.7480			1.49331
$981$		−	15.5790i		−	0.497399i
$982$	29.6939	−	29.6939i	0.947571	−	0.947571i
$983$	13.7131	−	13.7131i	0.437380	−	0.437380i	−0.453750	−	0.891129i	$-0.649914\pi$
$983$	13.7131	−	13.7131i	0.437380	−	0.437380i	0.891129	+	0.453750i	$0.149914\pi$
$984$	−1.92905	+	0.799040i	−0.0614960	+	0.0254725i
$985$		−	14.1809i		−	0.451841i
$986$	−21.8551	−	9.05269i	−0.696009	−	0.288296i
$987$	−27.8660	−	11.5425i	−0.886986	−	0.367402i
$988$	−22.0679	+	22.0679i	−0.702075	+	0.702075i
$989$	8.72214	+	3.61283i	0.277348	+	0.114881i
$990$	3.94997	−	3.94997i	0.125538	−	0.125538i
$991$	−36.5120	−	15.1238i	−1.15984	−	0.480423i	−0.282020	−	0.959408i	$-0.591005\pi$
$991$	−36.5120	−	15.1238i	−1.15984	−	0.480423i	−0.877823	+	0.478986i	$0.841005\pi$
$992$	−0.913776	+	2.20605i	−0.0290124	+	0.0700422i
$993$	−3.13529	−	1.29868i	−0.0994954	−	0.0412124i
$994$	19.9483	−	48.1594i	0.632721	−	1.52752i
$995$	16.8449	−	6.97737i	0.534018	−	0.221197i
$996$	−1.92541	+	4.64835i	−0.0610089	+	0.147289i
$997$	26.8114			0.849127			0.424564	−	0.905398i	$-0.360428\pi$
$997$	26.8114			0.849127			0.424564	+	0.905398i	$0.360428\pi$
$998$	18.5973			0.588689
$999$		−	11.7864i		−	0.372906i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	802.2.e.b.45.12	✓	68
401.303	even	8	inner	802.2.e.b.303.12	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
802.2.e.b.45.12	✓	68	1.1	even	1	trivial
802.2.e.b.303.12	yes	68	401.303	even	8	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:	\( N \)	\(=\)	\( 802 = 2 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	802.e (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.29760 + 0.537484i) q^{3} +1.00000i q^{4} +2.57737 q^{5} +(0.537484 + 1.29760i) q^{6} +(-3.54527 + 3.54527i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.726439 - 0.726439i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.29760 + 0.537484i) q^{3} +1.00000i q^{4} +2.57737 q^{5} +(0.537484 + 1.29760i) q^{6} +(-3.54527 + 3.54527i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.726439 - 0.726439i) q^{9} +(1.82248 + 1.82248i) q^{10} +(1.49177 + 1.49177i) q^{11} +(-0.537484 + 1.29760i) q^{12} +(6.40667 - 2.65373i) q^{13} -5.01376 q^{14} +(3.34441 + 1.38530i) q^{15} -1.00000 q^{16} +(-5.24548 + 2.17275i) q^{17} -1.02734i q^{18} +(1.72226 + 4.15791i) q^{19} +2.57737i q^{20} +(-6.50587 + 2.69482i) q^{21} +2.10968i q^{22} +(-0.467071 - 1.12761i) q^{23} +(-1.29760 + 0.537484i) q^{24} +1.64286 q^{25} +(6.40667 + 2.65373i) q^{26} +(-2.16463 - 5.22588i) q^{27} +(-3.54527 - 3.54527i) q^{28} +4.16647 q^{29} +(1.38530 + 3.34441i) q^{30} +(-0.913776 - 2.20605i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.13392 + 2.73753i) q^{33} +(-5.24548 - 2.17275i) q^{34} +(-9.13748 + 9.13748i) q^{35} +(0.726439 - 0.726439i) q^{36} +(1.92510 + 0.797401i) q^{37} +(-1.72226 + 4.15791i) q^{38} +9.73965 q^{39} +(-1.82248 + 1.82248i) q^{40} +1.48663 q^{41} +(-6.50587 - 2.69482i) q^{42} +(-5.46952 + 5.46952i) q^{43} +(-1.49177 + 1.49177i) q^{44} +(-1.87230 - 1.87230i) q^{45} +(0.467071 - 1.12761i) q^{46} +(3.02869 + 3.02869i) q^{47} +(-1.29760 - 0.537484i) q^{48} -18.1378i q^{49} +(1.16167 + 1.16167i) q^{50} -7.97436 q^{51} +(2.65373 + 6.40667i) q^{52} +(4.88522 - 11.7940i) q^{53} +(2.16463 - 5.22588i) q^{54} +(3.84485 + 3.84485i) q^{55} -5.01376i q^{56} +6.32100i q^{57} +(2.94614 + 2.94614i) q^{58} +(10.8810 - 4.50706i) q^{59} +(-1.38530 + 3.34441i) q^{60} +(-1.42792 - 3.44731i) q^{61} +(0.913776 - 2.20605i) q^{62} +5.15084 q^{63} -1.00000i q^{64} +(16.5124 - 6.83966i) q^{65} +(-1.13392 + 2.73753i) q^{66} +(1.68487 - 4.06765i) q^{67} +(-2.17275 - 5.24548i) q^{68} -1.71423i q^{69} -12.9223 q^{70} +(-3.97870 + 9.60544i) q^{71} +1.02734 q^{72} +(1.73902 - 1.73902i) q^{73} +(0.797401 + 1.92510i) q^{74} +(2.13177 + 0.883009i) q^{75} +(-4.15791 + 1.72226i) q^{76} -10.5774 q^{77} +(6.88697 + 6.88697i) q^{78} +(-5.62912 - 13.5899i) q^{79} -2.57737 q^{80} -4.86255i q^{81} +(1.05121 + 1.05121i) q^{82} +3.58226 q^{83} +(-2.69482 - 6.50587i) q^{84} +(-13.5196 + 5.59999i) q^{85} -7.73507 q^{86} +(5.40642 + 2.23941i) q^{87} -2.10968 q^{88} +(-2.73801 + 2.73801i) q^{89} -2.64784i q^{90} +(-13.3052 + 32.1215i) q^{91} +(1.12761 - 0.467071i) q^{92} -3.35372i q^{93} +4.28322i q^{94} +(4.43891 + 10.7165i) q^{95} +(-0.537484 - 1.29760i) q^{96} +(0.0220137 + 0.0531457i) q^{97} +(12.8254 - 12.8254i) q^{98} -2.16736i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{6} + 20 q^{9}+O(q^{10}) \) 68 * q + 4 * q^6 + 20 * q^9	\( 68 q + 4 q^{6} + 20 q^{9} - 4 q^{10} + 12 q^{11} - 4 q^{12} - 8 q^{13} + 8 q^{14} - 4 q^{15} - 68 q^{16} + 4 q^{17} + 20 q^{19} - 40 q^{21} - 16 q^{23} + 20 q^{25} - 8 q^{26} - 12 q^{27} + 16 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{34} + 16 q^{35} - 20 q^{36} + 12 q^{37} - 20 q^{38} + 40 q^{39} + 4 q^{40} + 24 q^{41} - 40 q^{42} + 40 q^{43} - 12 q^{44} + 28 q^{45} + 16 q^{46} + 4 q^{47} - 8 q^{50} + 24 q^{51} + 4 q^{52} + 12 q^{53} + 12 q^{54} - 24 q^{55} - 4 q^{58} + 4 q^{59} + 4 q^{60} - 20 q^{61} + 8 q^{62} - 16 q^{63} + 36 q^{65} - 8 q^{66} + 48 q^{67} + 8 q^{68} - 16 q^{71} - 68 q^{72} + 40 q^{73} - 8 q^{74} - 96 q^{75} - 16 q^{77} + 32 q^{78} + 28 q^{79} - 16 q^{82} + 16 q^{83} - 4 q^{84} + 16 q^{85} - 32 q^{86} + 8 q^{87} + 8 q^{88} - 20 q^{89} - 4 q^{91} + 8 q^{92} - 24 q^{95} - 4 q^{96} + 24 q^{97} + 24 q^{98}+O(q^{100}) \) 68 * q + 4 * q^6 + 20 * q^9 - 4 * q^10 + 12 * q^11 - 4 * q^12 - 8 * q^13 + 8 * q^14 - 4 * q^15 - 68 * q^16 + 4 * q^17 + 20 * q^19 - 40 * q^21 - 16 * q^23 + 20 * q^25 - 8 * q^26 - 12 * q^27 + 16 * q^29 - 4 * q^30 - 8 * q^31 + 8 * q^33 + 4 * q^34 + 16 * q^35 - 20 * q^36 + 12 * q^37 - 20 * q^38 + 40 * q^39 + 4 * q^40 + 24 * q^41 - 40 * q^42 + 40 * q^43 - 12 * q^44 + 28 * q^45 + 16 * q^46 + 4 * q^47 - 8 * q^50 + 24 * q^51 + 4 * q^52 + 12 * q^53 + 12 * q^54 - 24 * q^55 - 4 * q^58 + 4 * q^59 + 4 * q^60 - 20 * q^61 + 8 * q^62 - 16 * q^63 + 36 * q^65 - 8 * q^66 + 48 * q^67 + 8 * q^68 - 16 * q^71 - 68 * q^72 + 40 * q^73 - 8 * q^74 - 96 * q^75 - 16 * q^77 + 32 * q^78 + 28 * q^79 - 16 * q^82 + 16 * q^83 - 4 * q^84 + 16 * q^85 - 32 * q^86 + 8 * q^87 + 8 * q^88 - 20 * q^89 - 4 * q^91 + 8 * q^92 - 24 * q^95 - 4 * q^96 + 24 * q^97 + 24 * q^98

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