LMFDB - Embedded newform 731.2.m.b.87.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$29$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			87.8
Character	$\chi$	$=$	731.87
Dual form			731.2.m.b.689.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09522 - 1.09522i) q^{2} +(2.12589 - 0.880571i) q^{3} +0.399034i q^{4} +(-0.733376 - 1.77053i) q^{5} +(-3.29275 - 1.36390i) q^{6} +(-0.642781 + 1.55181i) q^{7} +(-1.75342 + 1.75342i) q^{8} +(1.62267 - 1.62267i) q^{9} +O(q^{10})$	\(q+(-1.09522 - 1.09522i) q^{2} +(2.12589 - 0.880571i) q^{3} +0.399034i q^{4} +(-0.733376 - 1.77053i) q^{5} +(-3.29275 - 1.36390i) q^{6} +(-0.642781 + 1.55181i) q^{7} +(-1.75342 + 1.75342i) q^{8} +(1.62267 - 1.62267i) q^{9} +(-1.13591 + 2.74234i) q^{10} +(-1.51016 - 0.625530i) q^{11} +(0.351378 + 0.848301i) q^{12} +0.507373i q^{13} +(2.40357 - 0.995592i) q^{14} +(-3.11815 - 3.11815i) q^{15} +4.63884 q^{16} +(-3.59771 - 2.01406i) q^{17} -3.55438 q^{18} +(-4.59362 - 4.59362i) q^{19} +(0.706500 - 0.292642i) q^{20} +3.86499i q^{21} +(0.968872 + 2.33906i) q^{22} +(-6.92729 - 2.86938i) q^{23} +(-2.18356 + 5.27158i) q^{24} +(0.938610 - 0.938610i) q^{25} +(0.555687 - 0.555687i) q^{26} +(-0.620976 + 1.49917i) q^{27} +(-0.619225 - 0.256491i) q^{28} +(-1.37217 - 3.31271i) q^{29} +6.83015i q^{30} +(-6.25705 + 2.59175i) q^{31} +(-1.57374 - 1.57374i) q^{32} -3.76126 q^{33} +(1.73445 + 6.14616i) q^{34} +3.21892 q^{35} +(0.647500 + 0.647500i) q^{36} +(4.59788 - 1.90450i) q^{37} +10.0621i q^{38} +(0.446778 + 1.07862i) q^{39} +(4.39039 + 1.81856i) q^{40} +(3.95930 - 9.55860i) q^{41} +(4.23303 - 4.23303i) q^{42} +(0.707107 - 0.707107i) q^{43} +(0.249607 - 0.602606i) q^{44} +(-4.06301 - 1.68295i) q^{45} +(4.44432 + 10.7295i) q^{46} +7.95145i q^{47} +(9.86165 - 4.08483i) q^{48} +(2.95480 + 2.95480i) q^{49} -2.05598 q^{50} +(-9.42186 - 1.11363i) q^{51} -0.202459 q^{52} +(1.64672 + 1.64672i) q^{53} +(2.32203 - 0.961818i) q^{54} +3.13253i q^{55} +(-1.59391 - 3.84804i) q^{56} +(-13.8105 - 5.72051i) q^{57} +(-2.12533 + 5.13100i) q^{58} +(5.72936 - 5.72936i) q^{59} +(1.24425 - 1.24425i) q^{60} +(5.49422 - 13.2642i) q^{61} +(9.69143 + 4.01432i) q^{62} +(1.47506 + 3.56110i) q^{63} -5.83049i q^{64} +(0.898318 - 0.372095i) q^{65} +(4.11942 + 4.11942i) q^{66} +10.0492 q^{67} +(0.803679 - 1.43561i) q^{68} -17.2533 q^{69} +(-3.52544 - 3.52544i) q^{70} +(2.94784 - 1.22104i) q^{71} +5.69044i q^{72} +(2.62461 + 6.33637i) q^{73} +(-7.12157 - 2.94985i) q^{74} +(1.16887 - 2.82189i) q^{75} +(1.83301 - 1.83301i) q^{76} +(1.94141 - 1.94141i) q^{77} +(0.692006 - 1.67065i) q^{78} +(10.8345 + 4.48779i) q^{79} +(-3.40201 - 8.21319i) q^{80} +10.6183i q^{81} +(-14.8051 + 6.13249i) q^{82} +(-9.96741 - 9.96741i) q^{83} -1.54226 q^{84} +(-0.927477 + 7.84691i) q^{85} -1.54888 q^{86} +(-5.83416 - 5.83416i) q^{87} +(3.74476 - 1.55113i) q^{88} +10.8047i q^{89} +(2.60670 + 6.29312i) q^{90} +(-0.787347 - 0.326130i) q^{91} +(1.14498 - 2.76422i) q^{92} +(-11.0196 + 11.0196i) q^{93} +(8.70862 - 8.70862i) q^{94} +(-4.76427 + 11.5020i) q^{95} +(-4.73137 - 1.95980i) q^{96} +(-0.595519 - 1.43771i) q^{97} -6.47233i q^{98} +(-3.46553 + 1.43547i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 8 q^{6}+O(q^{10}) $ 116 * q - 8 * q^6	$ 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) $ 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	−1.09522	−	1.09522i	−0.774441	−	0.774441i	0.204439	−	0.978879i	$-0.434463\pi$
$2$	−1.09522	−	1.09522i	−0.774441	−	0.774441i	−0.978879	+	0.204439i	$0.934463\pi$
$3$	2.12589	−	0.880571i	1.22738	−	0.508398i	0.327632	−	0.944805i	$-0.393749\pi$
$3$	2.12589	−	0.880571i	1.22738	−	0.508398i	0.899749	+	0.436407i	$0.143749\pi$
$4$			0.399034i			0.199517i
$5$	−0.733376	−	1.77053i	−0.327976	−	0.791804i	−0.998742	−	0.0501351i	$-0.984035\pi$
$5$	−0.733376	−	1.77053i	−0.327976	−	0.791804i	0.670767	−	0.741668i	$-0.265965\pi$
$6$	−3.29275	−	1.36390i	−1.34426	−	0.556810i
$7$	−0.642781	+	1.55181i	−0.242948	+	0.586530i	−0.997573	−	0.0696273i	$-0.977819\pi$
$7$	−0.642781	+	1.55181i	−0.242948	+	0.586530i	0.754625	+	0.656157i	$0.227819\pi$
$8$	−1.75342	+	1.75342i	−0.619927	+	0.619927i
$9$	1.62267	−	1.62267i	0.540890	−	0.540890i
$10$	−1.13591	+	2.74234i	−0.359207	+	0.867203i
$11$	−1.51016	−	0.625530i	−0.455331	−	0.188604i	0.143217	−	0.989691i	$-0.454255\pi$
$11$	−1.51016	−	0.625530i	−0.455331	−	0.188604i	−0.598548	+	0.801087i	$0.704255\pi$
$12$	0.351378	+	0.848301i	0.101434	+	0.244883i
$13$			0.507373i			0.140720i	0.997522	+	0.0703600i	$0.0224148\pi$
$13$			0.507373i			0.140720i	−0.997522	+	0.0703600i	$0.977585\pi$
$14$	2.40357	−	0.995592i	0.642382	−	0.266083i
$15$	−3.11815	−	3.11815i	−0.805103	−	0.805103i
$16$	4.63884			1.15971
$17$	−3.59771	−	2.01406i	−0.872574	−	0.488482i
$17$	−3.59771	−	2.01406i	−0.872574	−	0.488482i
$18$	−3.55438			−0.837775
$19$	−4.59362	−	4.59362i	−1.05385	−	1.05385i	−0.998465	−	0.0553833i	$-0.982362\pi$
$19$	−4.59362	−	4.59362i	−1.05385	−	1.05385i	−0.0553833	−	0.998465i	$-0.517638\pi$
$20$	0.706500	−	0.292642i	0.157978	−	0.0654367i
$21$			3.86499i			0.843410i
$22$	0.968872	+	2.33906i	0.206564	+	0.498690i
$23$	−6.92729	−	2.86938i	−1.44444	−	0.598306i	−0.483569	−	0.875306i	$-0.660660\pi$
$23$	−6.92729	−	2.86938i	−1.44444	−	0.598306i	−0.960870	+	0.277000i	$0.910660\pi$
$24$	−2.18356	+	5.27158i	−0.445717	+	1.07606i
$25$	0.938610	−	0.938610i	0.187722	−	0.187722i
$26$	0.555687	−	0.555687i	0.108979	−	0.108979i
$27$	−0.620976	+	1.49917i	−0.119507	+	0.288515i
$28$	−0.619225	−	0.256491i	−0.117022	−	0.0484723i
$29$	−1.37217	−	3.31271i	−0.254805	−	0.615155i	0.743774	−	0.668431i	$-0.233034\pi$
$29$	−1.37217	−	3.31271i	−0.254805	−	0.615155i	−0.998580	+	0.0532759i	$0.983034\pi$
$30$			6.83015i			1.24701i
$31$	−6.25705	+	2.59175i	−1.12380	+	0.465493i	−0.865669	−	0.500617i	$-0.833106\pi$
$31$	−6.25705	+	2.59175i	−1.12380	+	0.465493i	−0.258130	+	0.966110i	$0.583106\pi$
$32$	−1.57374	−	1.57374i	−0.278200	−	0.278200i
$33$	−3.76126			−0.654751
$34$	1.73445	+	6.14616i	0.297456	+	1.05406i
$35$	3.21892			0.544097
$36$	0.647500	+	0.647500i	0.107917	+	0.107917i
$37$	4.59788	−	1.90450i	0.755887	−	0.313099i	0.0287460	−	0.999587i	$-0.490849\pi$
$37$	4.59788	−	1.90450i	0.755887	−	0.313099i	0.727141	+	0.686488i	$0.240849\pi$
$38$			10.0621i			1.63229i
$39$	0.446778	+	1.07862i	0.0715418	+	0.172717i
$40$	4.39039	+	1.81856i	0.694181	+	0.287539i
$41$	3.95930	−	9.55860i	0.618339	−	1.49280i	−0.235293	−	0.971925i	$-0.575605\pi$
$41$	3.95930	−	9.55860i	0.618339	−	1.49280i	0.853631	−	0.520878i	$-0.174395\pi$
$42$	4.23303	−	4.23303i	0.653171	−	0.653171i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$44$	0.249607	−	0.602606i	0.0376297	−	0.0908462i
$45$	−4.06301	−	1.68295i	−0.605678	−	0.250880i
$46$	4.44432	+	10.7295i	0.655280	+	1.58199i
$47$			7.95145i			1.15984i	0.814674	+	0.579919i	$0.196916\pi$
$47$			7.95145i			1.15984i	−0.814674	+	0.579919i	$0.803084\pi$
$48$	9.86165	−	4.08483i	1.42341	−	0.589594i
$49$	2.95480	+	2.95480i	0.422114	+	0.422114i
$50$	−2.05598			−0.290759
$51$	−9.42186	−	1.11363i	−1.31932	−	0.155939i
$52$	−0.202459			−0.0280760
$53$	1.64672	+	1.64672i	0.226195	+	0.226195i	0.811101	−	0.584906i	$-0.198869\pi$
$53$	1.64672	+	1.64672i	0.226195	+	0.226195i	−0.584906	+	0.811101i	$0.698869\pi$
$54$	2.32203	−	0.961818i	0.315989	−	0.130887i
$55$			3.13253i			0.422391i
$56$	−1.59391	−	3.84804i	−0.212995	−	0.514216i
$57$	−13.8105	−	5.72051i	−1.82925	−	0.757700i
$58$	−2.12533	+	5.13100i	−0.279069	+	0.673733i
$59$	5.72936	−	5.72936i	0.745899	−	0.745899i	−0.227807	−	0.973706i	$-0.573156\pi$
$59$	5.72936	−	5.72936i	0.745899	−	0.745899i	0.973706	+	0.227807i	$0.0731556\pi$
$60$	1.24425	−	1.24425i	0.160632	−	0.160632i
$61$	5.49422	−	13.2642i	0.703463	−	1.69831i	−0.0122595	−	0.999925i	$-0.503902\pi$
$61$	5.49422	−	13.2642i	0.703463	−	1.69831i	0.715722	−	0.698385i	$-0.246098\pi$
$62$	9.69143	+	4.01432i	1.23081	+	0.509819i
$63$	1.47506	+	3.56110i	0.185840	+	0.448657i
$64$		−	5.83049i		−	0.728811i
$65$	0.898318	−	0.372095i	0.111423	−	0.0461527i
$66$	4.11942	+	4.11942i	0.507066	+	0.507066i
$67$	10.0492			1.22770			0.613850	−	0.789423i	$-0.289620\pi$
$67$	10.0492			1.22770			0.613850	+	0.789423i	$0.289620\pi$
$68$	0.803679	−	1.43561i	0.0974605	−	0.174093i
$69$	−17.2533			−2.07706
$70$	−3.52544	−	3.52544i	−0.421371	−	0.421371i
$71$	2.94784	−	1.22104i	0.349844	−	0.144910i	−0.200840	−	0.979624i	$-0.564367\pi$
$71$	2.94784	−	1.22104i	0.349844	−	0.144910i	0.550684	+	0.834714i	$0.314367\pi$
$72$			5.69044i			0.670625i
$73$	2.62461	+	6.33637i	0.307188	+	0.741616i	0.999794	+	0.0203007i	$0.00646235\pi$
$73$	2.62461	+	6.33637i	0.307188	+	0.741616i	−0.692606	+	0.721316i	$0.743538\pi$
$74$	−7.12157	−	2.94985i	−0.827866	−	0.342913i
$75$	1.16887	−	2.82189i	0.134969	−	0.325844i
$76$	1.83301	−	1.83301i	0.210260	−	0.210260i
$77$	1.94141	−	1.94141i	0.221244	−	0.221244i
$78$	0.692006	−	1.67065i	0.0783543	−	0.189164i
$79$	10.8345	+	4.48779i	1.21897	+	0.504915i	0.897083	−	0.441862i	$-0.145682\pi$
$79$	10.8345	+	4.48779i	1.21897	+	0.504915i	0.321890	+	0.946777i	$0.395682\pi$
$80$	−3.40201	−	8.21319i	−0.380357	−	0.918262i
$81$			10.6183i			1.17981i
$82$	−14.8051	+	6.13249i	−1.63495	+	0.677220i
$83$	−9.96741	−	9.96741i	−1.09406	−	1.09406i	−0.995090	−	0.0989750i	$-0.968444\pi$
$83$	−9.96741	−	9.96741i	−1.09406	−	1.09406i	−0.0989750	−	0.995090i	$-0.531556\pi$
$84$	−1.54226			−0.168275
$85$	−0.927477	+	7.84691i	−0.100599	+	0.851117i
$86$	−1.54888			−0.167020
$87$	−5.83416	−	5.83416i	−0.625487	−	0.625487i
$88$	3.74476	−	1.55113i	0.399193	−	0.165351i
$89$			10.8047i			1.14530i	0.819800	+	0.572650i	$0.194085\pi$
$89$			10.8047i			1.14530i	−0.819800	+	0.572650i	$0.805915\pi$
$90$	2.60670	+	6.29312i	0.274770	+	0.663353i
$91$	−0.787347	−	0.326130i	−0.0825364	−	0.0341877i
$92$	1.14498	−	2.76422i	0.119372	−	0.288190i
$93$	−11.0196	+	11.0196i	−1.14267	+	1.14267i
$94$	8.70862	−	8.70862i	0.898226	−	0.898226i
$95$	−4.76427	+	11.5020i	−0.488804	+	1.18008i
$96$	−4.73137	−	1.95980i	−0.482894	−	0.200021i
$97$	−0.595519	−	1.43771i	−0.0604657	−	0.145977i	0.890759	−	0.454476i	$-0.150173\pi$
$97$	−0.595519	−	1.43771i	−0.0604657	−	0.145977i	−0.951225	+	0.308499i	$0.900173\pi$
$98$		−	6.47233i		−	0.653804i
$99$	−3.46553	+	1.43547i	−0.348299	+	0.144270i
$100$	0.374537	+	0.374537i	0.0374537	+	0.0374537i
$101$	7.48757			0.745041			0.372520	−	0.928024i	$-0.378494\pi$
$101$	7.48757			0.745041			0.372520	+	0.928024i	$0.378494\pi$
$102$	9.09938	+	11.5387i	0.900973	+	1.14250i
$103$	1.61105			0.158741			0.0793705	−	0.996845i	$-0.474709\pi$
$103$	1.61105			0.158741			0.0793705	+	0.996845i	$0.474709\pi$
$104$	−0.889637	−	0.889637i	−0.0872361	−	0.0872361i
$105$	6.84307	−	2.83449i	0.667815	−	0.276618i
$106$		−	3.60706i		−	0.350349i
$107$	−5.08830	−	12.2843i	−0.491905	−	1.18756i	−0.953749	−	0.300603i	$-0.902812\pi$
$107$	−5.08830	−	12.2843i	−0.491905	−	1.18756i	0.461845	−	0.886961i	$-0.347188\pi$
$108$	−0.598218	−	0.247790i	−0.0575636	−	0.0238436i
$109$	−5.84079	+	14.1009i	−0.559446	+	1.35062i	0.350759	+	0.936466i	$0.385924\pi$
$109$	−5.84079	+	14.1009i	−0.559446	+	1.35062i	−0.910205	+	0.414157i	$0.864076\pi$
$110$	3.43083	−	3.43083i	0.327116	−	0.327116i
$111$	8.09753	−	8.09753i	0.768583	−	0.768583i
$112$	−2.98176	+	7.19860i	−0.281750	+	0.680204i
$113$	8.88699	+	3.68111i	0.836018	+	0.346290i	0.759282	−	0.650762i	$-0.225550\pi$
$113$	8.88699	+	3.68111i	0.836018	+	0.346290i	0.0767355	+	0.997051i	$0.475550\pi$
$114$	8.86039	+	21.3909i	0.829851	+	2.00344i
$115$			14.3693i			1.33994i
$116$	1.32188	−	0.547542i	0.122734	−	0.0508380i
$117$	0.823300	+	0.823300i	0.0761141	+	0.0761141i
$118$	−12.5499			−1.15531
$119$	5.43799	−	4.28837i	0.498500	−	0.393114i
$120$	10.9348			0.998210
$121$	−5.88887	−	5.88887i	−0.535352	−	0.535352i
$122$	−20.5447	+	8.50990i	−1.86003	+	0.770450i
$123$		−	23.8070i		−	2.14660i
$124$	−1.03420	−	2.49677i	−0.0928737	−	0.224217i
$125$	−11.2028	−	4.64036i	−1.00201	−	0.415046i
$126$	2.28469	−	5.51572i	0.203536	−	0.491380i
$127$	1.75601	−	1.75601i	0.155821	−	0.155821i	−0.624891	−	0.780712i	$-0.714857\pi$
$127$	1.75601	−	1.75601i	0.155821	−	0.155821i	0.780712	+	0.624891i	$0.214857\pi$
$128$	−9.53317	+	9.53317i	−0.842621	+	0.842621i
$129$	0.880571	−	2.12589i	0.0775300	−	0.187174i
$130$	−1.39139	−	0.576331i	−0.122033	−	0.0505476i
$131$	−8.45056	−	20.4015i	−0.738329	−	1.78248i	−0.612560	−	0.790424i	$-0.709860\pi$
$131$	−8.45056	−	20.4015i	−0.738329	−	1.78248i	−0.125769	−	0.992059i	$-0.540140\pi$
$132$		−	1.50087i		−	0.130634i
$133$	10.0811	−	4.17574i	0.874144	−	0.362082i
$134$	−11.0061	−	11.0061i	−0.950780	−	0.950780i
$135$	3.10973			0.267643
$136$	9.83979	−	2.77680i	0.843755	−	0.238109i
$137$	−0.764902			−0.0653500			−0.0326750	−	0.999466i	$-0.510403\pi$
$137$	−0.764902			−0.0653500			−0.0326750	+	0.999466i	$0.510403\pi$
$138$	18.8963	+	18.8963i	1.60856	+	1.60856i
$139$	−18.2658	+	7.56592i	−1.54928	+	0.641733i	−0.983186	−	0.182607i	$-0.941546\pi$
$139$	−18.2658	+	7.56592i	−1.54928	+	0.641733i	−0.566095	+	0.824340i	$0.691546\pi$
$140$			1.28446i			0.108557i
$141$	7.00182	+	16.9039i	0.589659	+	1.42356i
$142$	−4.56585	−	1.89124i	−0.383158	−	0.158709i
$143$	0.317377	−	0.766216i	0.0265404	−	0.0640742i
$144$	7.52731	−	7.52731i	0.627276	−	0.627276i
$145$	−4.85893	+	4.85893i	−0.403512	+	0.403512i
$146$	4.06521	−	9.81429i	0.336439	−	0.812237i
$147$	8.88348	+	3.67966i	0.732697	+	0.303493i
$148$	0.759961	+	1.83471i	0.0624684	+	0.150812i
$149$			12.1609i			0.996262i	0.867102	+	0.498131i	$0.165980\pi$
$149$			12.1609i			0.996262i	−0.867102	+	0.498131i	$0.834020\pi$
$150$	−4.37078	+	1.81043i	−0.356872	+	0.147821i
$151$	−9.70908	−	9.70908i	−0.790114	−	0.790114i	0.191399	−	0.981512i	$-0.438698\pi$
$151$	−9.70908	−	9.70908i	−0.790114	−	0.790114i	−0.981512	+	0.191399i	$0.938698\pi$
$152$	16.1091			1.30662
$153$	−9.10607	+	2.56974i	−0.736182	+	0.207751i
$154$	−4.25256			−0.342681
$155$	9.17754	+	9.17754i	0.737158	+	0.737158i
$156$	−0.430405	+	0.178280i	−0.0344600	+	0.0142738i
$157$		−	17.1372i		−	1.36770i	−0.729624	−	0.683848i	$-0.760305\pi$
$157$		−	17.1372i		−	1.36770i	0.729624	−	0.683848i	$-0.239695\pi$
$158$	−6.95105	−	16.7813i	−0.552996	−	1.33505i
$159$	4.95080	+	2.05069i	0.392624	+	0.162630i
$160$	−1.63220	+	3.94048i	−0.129037	+	0.311522i
$161$	8.90546	−	8.90546i	0.701849	−	0.701849i
$162$	11.6294	−	11.6294i	0.913693	−	0.913693i
$163$	−1.36626	+	3.29844i	−0.107014	+	0.258354i	−0.968311	−	0.249747i	$-0.919652\pi$
$163$	−1.36626	+	3.29844i	−0.107014	+	0.258354i	0.861297	+	0.508101i	$0.169652\pi$
$164$	3.81420	+	1.57989i	0.297839	+	0.123369i
$165$	2.75842	+	6.65941i	0.214743	+	0.518434i
$166$			21.8331i			1.69458i
$167$	2.41196	−	0.999066i	0.186643	−	0.0773101i	−0.287405	−	0.957809i	$-0.592792\pi$
$167$	2.41196	−	0.999066i	0.186643	−	0.0773101i	0.474048	+	0.880499i	$0.342792\pi$
$168$	−6.77694	−	6.77694i	−0.522853	−	0.522853i
$169$	12.7426			0.980198
$170$	9.60993	−	7.57834i	0.737048	−	0.581232i
$171$	−14.9079			−1.14003
$172$	0.282159	+	0.282159i	0.0215145	+	0.0215145i
$173$	11.1617	−	4.62333i	0.848609	−	0.351505i	0.0843669	−	0.996435i	$-0.473113\pi$
$173$	11.1617	−	4.62333i	0.848609	−	0.351505i	0.764242	+	0.644929i	$0.223113\pi$
$174$			12.7794i			0.968805i
$175$	0.853225	+	2.05987i	0.0644977	+	0.155711i
$176$	−7.00540	−	2.90173i	−0.528052	−	0.218726i
$177$	7.13486	−	17.2251i	0.536289	−	1.29472i
$178$	11.8336	−	11.8336i	0.886967	−	0.886967i
$179$	5.29950	−	5.29950i	0.396103	−	0.396103i	−0.480753	−	0.876856i	$-0.659637\pi$
$179$	5.29950	−	5.29950i	0.396103	−	0.396103i	0.876856	+	0.480753i	$0.159637\pi$
$180$	0.671555	−	1.62128i	0.0500548	−	0.120843i
$181$	−10.3559	−	4.28954i	−0.769745	−	0.318839i	−0.0369762	−	0.999316i	$-0.511773\pi$
$181$	−10.3559	−	4.28954i	−0.769745	−	0.318839i	−0.732769	+	0.680477i	$0.761773\pi$
$182$	0.505137	+	1.21951i	0.0374432	+	0.0903959i
$183$		−	33.0363i		−	2.44211i
$184$	17.1776	−	7.11521i	1.26635	−	0.524540i
$185$	−6.74395	−	6.74395i	−0.495825	−	0.495825i
$186$	24.1378			1.76987
$187$	4.17328	+	5.29204i	0.305180	+	0.386993i
$188$	−3.17290			−0.231407
$189$	−1.92727	−	1.92727i	−0.140189	−	0.140189i
$190$	17.8152	−	7.37930i	1.29245	−	0.535350i
$191$		−	15.4321i		−	1.11662i	−0.829631	−	0.558312i	$-0.811449\pi$
$191$		−	15.4321i		−	1.11662i	0.829631	−	0.558312i	$-0.188551\pi$
$192$	−5.13416	−	12.3950i	−0.370526	−	0.894530i
$193$	−10.9287	−	4.52682i	−0.786666	−	0.325848i	−0.0470635	−	0.998892i	$-0.514986\pi$
$193$	−10.9287	−	4.52682i	−0.786666	−	0.325848i	−0.739602	+	0.673044i	$0.764986\pi$
$194$	−0.922388	+	2.22684i	−0.0662236	+	0.159878i
$195$	1.58207	−	1.58207i	0.113294	−	0.113294i
$196$	−1.17906	+	1.17906i	−0.0842188	+	0.0842188i
$197$	0.694816	−	1.67744i	0.0495036	−	0.119512i	−0.897193	−	0.441638i	$-0.854397\pi$
$197$	0.694816	−	1.67744i	0.0495036	−	0.119512i	0.946697	+	0.322126i	$0.104397\pi$
$198$	5.36769	+	2.22337i	0.381465	+	0.158008i
$199$	8.86923	+	21.4122i	0.628723	+	1.51787i	0.841211	+	0.540708i	$0.181843\pi$
$199$	8.86923	+	21.4122i	0.628723	+	1.51787i	−0.212488	+	0.977164i	$0.568157\pi$
$200$			3.29155i			0.232748i
$201$	21.3634	−	8.84900i	1.50686	−	0.624160i
$202$	−8.20057	−	8.20057i	−0.576990	−	0.576990i
$203$	6.02271			0.422711
$204$	0.444376	−	3.75964i	0.0311125	−	0.263227i
$205$	−19.8274			−1.38481
$206$	−1.76446	−	1.76446i	−0.122936	−	0.122936i
$207$	−15.8968	+	6.58465i	−1.10490	+	0.457665i
$208$			2.35362i			0.163194i
$209$	4.06367	+	9.81056i	0.281090	+	0.678611i
$210$	−10.5991	−	4.39029i	−0.731408	−	0.302959i
$211$	6.87102	−	16.5881i	0.473020	−	1.14197i	−0.489801	−	0.871834i	$-0.662931\pi$
$211$	6.87102	−	16.5881i	0.473020	−	1.14197i	0.962822	−	0.270138i	$-0.0870693\pi$
$212$	−0.657098	+	0.657098i	−0.0451297	+	0.0451297i
$213$	5.19157	−	5.19157i	0.355720	−	0.355720i
$214$	−7.88118	+	19.0269i	−0.538746	+	1.30065i
$215$	−1.77053	−	0.733376i	−0.120749	−	0.0500158i
$216$	−1.53984	−	3.71750i	−0.104773	−	0.252944i
$217$		−	11.3757i		−	0.772232i
$218$	21.8406	−	9.04669i	1.47924	−	0.612719i
$219$	11.1593	+	11.1593i	0.754073	+	0.754073i
$220$	−1.24999			−0.0842740
$221$	1.02188	−	1.82538i	0.0687392	−	0.122789i
$222$	−17.7372			−1.19044
$223$	12.3731	+	12.3731i	0.828563	+	0.828563i	0.987318	−	0.158755i	$-0.0507479\pi$
$223$	12.3731	+	12.3731i	0.828563	+	0.828563i	−0.158755	+	0.987318i	$0.550748\pi$
$224$	3.45371	−	1.43057i	0.230761	−	0.0955842i
$225$		−	3.04611i		−	0.203074i
$226$	−5.70160	−	13.7649i	−0.379265	−	0.915627i
$227$	−14.1848	−	5.87555i	−0.941481	−	0.389974i	−0.141458	−	0.989944i	$-0.545179\pi$
$227$	−14.1848	−	5.87555i	−0.941481	−	0.389974i	−0.800022	+	0.599970i	$0.795179\pi$
$228$	2.28267	−	5.51086i	0.151174	−	0.364966i
$229$	−0.678979	+	0.678979i	−0.0448682	+	0.0448682i	−0.729185	−	0.684317i	$-0.760101\pi$
$229$	−0.678979	+	0.678979i	−0.0448682	+	0.0448682i	0.684317	+	0.729185i	$0.260101\pi$
$230$	15.7376	−	15.7376i	1.03771	−	1.03771i
$231$	2.41767	−	5.83677i	0.159071	−	0.384031i
$232$	8.21455	+	3.40258i	0.539312	+	0.223390i
$233$	0.566286	+	1.36714i	0.0370986	+	0.0895640i	0.941343	−	0.337452i	$-0.109565\pi$
$233$	0.566286	+	1.36714i	0.0370986	+	0.0895640i	−0.904244	+	0.427016i	$0.859565\pi$
$234$		−	1.80340i		−	0.117892i
$235$	14.0783	−	5.83140i	0.918364	−	0.380399i
$236$	2.28621	+	2.28621i	0.148819	+	0.148819i
$237$	26.9847			1.75284
$238$	−10.6525	−	1.25909i	−0.690502	−	0.0816149i
$239$	7.14970			0.462476			0.231238	−	0.972897i	$-0.425722\pi$
$239$	7.14970			0.462476			0.231238	+	0.972897i	$0.425722\pi$
$240$	−14.4646	−	14.4646i	−0.933686	−	0.933686i
$241$	−18.7576	+	7.76965i	−1.20828	+	0.500487i	−0.893667	−	0.448732i	$-0.851876\pi$
$241$	−18.7576	+	7.76965i	−1.20828	+	0.500487i	−0.314616	+	0.949219i	$0.601876\pi$
$242$			12.8993i			0.829197i
$243$	7.48723	+	18.0758i	0.480306	+	1.15956i
$244$	5.29287	+	2.19238i	0.338841	+	0.140353i
$245$	3.06457	−	7.39852i	0.195788	−	0.472674i
$246$	−26.0740	+	26.0740i	−1.66241	+	1.66241i
$247$	2.33068	−	2.33068i	0.148298	−	0.148298i
$248$	6.42679	−	15.5156i	0.408102	−	0.985245i
$249$	−29.9666	−	12.4126i	−1.89906	−	0.786615i
$250$	7.18737	+	17.3518i	0.454569	+	1.09743i
$251$		−	27.6889i		−	1.74771i	−0.486190	−	0.873853i	$-0.661614\pi$
$251$		−	27.6889i		−	1.74771i	0.486190	−	0.873853i	$-0.338386\pi$
$252$	−1.42100	+	0.588597i	−0.0895146	+	0.0370781i
$253$	8.66645	+	8.66645i	0.544855	+	0.544855i
$254$	−3.84645			−0.241348
$255$	4.93806	+	17.4984i	0.309233	+	1.09579i
$256$	9.22094			0.576309
$257$	2.49953	+	2.49953i	0.155917	+	0.155917i	0.780755	−	0.624838i	$-0.214835\pi$
$257$	2.49953	+	2.49953i	0.155917	+	0.155917i	−0.624838	+	0.780755i	$0.714835\pi$
$258$	−3.29275	+	1.36390i	−0.204998	+	0.0849127i
$259$			8.35922i			0.519417i
$260$	0.148479	+	0.358459i	0.00920825	+	0.0222307i
$261$	−7.60202	−	3.14886i	−0.470553	−	0.194910i
$262$	−13.0889	+	31.5994i	−0.808636	+	1.95222i
$263$	−17.4764	+	17.4764i	−1.07764	+	1.07764i	−0.0809174	+	0.996721i	$0.525785\pi$
$263$	−17.4764	+	17.4764i	−1.07764	+	1.07764i	−0.996721	+	0.0809174i	$0.974215\pi$
$264$	6.59506	−	6.59506i	0.405898	−	0.405898i
$265$	1.70790	−	4.12323i	0.104915	−	0.253288i
$266$	−15.6145	−	6.46772i	−0.957384	−	0.396561i
$267$	9.51434	+	22.9697i	0.582268	+	1.40572i
$268$			4.00995i			0.244947i
$269$	−14.3710	+	5.95268i	−0.876218	+	0.362941i	−0.775029	−	0.631926i	$-0.782265\pi$
$269$	−14.3710	+	5.95268i	−0.876218	+	0.362941i	−0.101189	+	0.994867i	$0.532265\pi$
$270$	−3.40585	−	3.40585i	−0.207273	−	0.207273i
$271$	−8.06026			−0.489626			−0.244813	−	0.969570i	$-0.578727\pi$
$271$	−8.06026			−0.489626			−0.244813	+	0.969570i	$0.578727\pi$
$272$	−16.6892	−	9.34292i	−1.01193	−	0.566498i
$273$	−1.96099			−0.118685
$274$	0.837740	+	0.837740i	0.0506097	+	0.0506097i
$275$	−2.00458	+	0.830325i	−0.120881	+	0.0500705i
$276$		−	6.88466i		−	0.414408i
$277$	−1.05823	−	2.55479i	−0.0635829	−	0.153503i	0.888895	−	0.458112i	$-0.151474\pi$
$277$	−1.05823	−	2.55479i	−0.0635829	−	0.153503i	−0.952477	+	0.304609i	$0.901474\pi$
$278$	28.2915	+	11.7187i	1.69681	+	0.702842i
$279$	−5.94757	+	14.3587i	−0.356072	+	0.859633i
$280$	−5.64412	+	5.64412i	−0.337301	+	0.337301i
$281$	−3.24105	+	3.24105i	−0.193345	+	0.193345i	−0.797140	−	0.603795i	$-0.793655\pi$
$281$	−3.24105	+	3.24105i	−0.193345	+	0.193345i	0.603795	+	0.797140i	$0.293655\pi$
$282$	10.8450	−	26.1821i	0.645810	−	1.55912i
$283$	17.1184	+	7.09067i	1.01758	+	0.421497i	0.828216	−	0.560410i	$-0.189356\pi$
$283$	17.1184	+	7.09067i	1.01758	+	0.421497i	0.189367	+	0.981906i	$0.439356\pi$
$284$	0.487234	+	1.17629i	0.0289120	+	0.0697998i
$285$			28.6472i			1.69691i
$286$	−1.18678	+	0.491579i	−0.0701756	+	0.0290677i
$287$	12.2882	+	12.2882i	0.725348	+	0.725348i
$288$	−5.10731			−0.300951
$289$	8.88709	+	14.4921i	0.522770	+	0.852474i
$290$	10.6432			0.624992
$291$	−2.53201	−	2.53201i	−0.148429	−	0.148429i
$292$	−2.52843	+	1.04731i	−0.147965	+	0.0612891i
$293$			7.33193i			0.428336i	0.976797	+	0.214168i	$0.0687040\pi$
$293$			7.33193i			0.428336i	−0.976797	+	0.214168i	$0.931296\pi$
$294$	−5.69935	−	13.7595i	−0.332393	−	0.802467i
$295$	−14.3458	−	5.94221i	−0.835242	−	0.345969i
$296$	−4.72261	+	11.4014i	−0.274496	+	0.662693i
$297$	1.87555	−	1.87555i	0.108830	−	0.108830i
$298$	13.3189	−	13.3189i	0.771546	−	0.771546i
$299$	1.45584	−	3.51472i	0.0841936	−	0.203261i
$300$	1.12603	+	0.466417i	0.0650114	+	0.0269286i
$301$	0.642781	+	1.55181i	0.0370493	+	0.0894449i
$302$			21.2672i			1.22379i
$303$	15.9177	−	6.59334i	0.914449	−	0.378777i
$304$	−21.3091	−	21.3091i	−1.22216	−	1.22216i
$305$	−27.5140			−1.57545
$306$	12.7876	+	7.15875i	0.731021	+	0.409238i
$307$	−6.95910			−0.397177			−0.198588	−	0.980083i	$-0.563636\pi$
$307$	−6.95910			−0.397177			−0.198588	+	0.980083i	$0.563636\pi$
$308$	0.774687	+	0.774687i	0.0441419	+	0.0441419i
$309$	3.42490	−	1.41864i	0.194836	−	0.0807037i
$310$		−	20.1029i		−	1.14177i
$311$	5.11933	+	12.3591i	0.290290	+	0.700823i	0.999993	−	0.00367825i	$-0.00117083\pi$
$311$	5.11933	+	12.3591i	0.290290	+	0.700823i	−0.709703	+	0.704501i	$0.751171\pi$
$312$	−2.67466	−	1.10788i	−0.151423	−	0.0627213i
$313$	1.82402	−	4.40358i	0.103100	−	0.248905i	−0.863909	−	0.503648i	$-0.831991\pi$
$313$	1.82402	−	4.40358i	0.103100	−	0.248905i	0.967009	+	0.254743i	$0.0819908\pi$
$314$	−18.7691	+	18.7691i	−1.05920	+	1.05920i
$315$	5.22325	−	5.22325i	0.294297	−	0.294297i
$316$	−1.79078	+	4.32332i	−0.100739	+	0.243206i
$317$	28.3958	+	11.7619i	1.59487	+	0.660616i	0.990678	−	0.136223i	$-0.0434964\pi$
$317$	28.3958	+	11.7619i	1.59487	+	0.660616i	0.604191	+	0.796840i	$0.293496\pi$
$318$	−3.17628	−	7.66821i	−0.178117	−	0.430012i
$319$			5.86106i			0.328157i
$320$	−10.3230	+	4.27594i	−0.577076	+	0.239033i
$321$	−21.6343	−	21.6343i	−1.20751	−	1.20751i
$322$	−19.5070			−1.08708
$323$	7.27468	+	25.7784i	0.404774	+	1.43435i
$324$	−4.23705			−0.235392
$325$	0.476225	+	0.476225i	0.0264162	+	0.0264162i
$326$	5.10889	−	2.11617i	0.282955	−	0.117204i
$327$			35.1202i			1.94215i
$328$	9.81791	+	23.7025i	0.542103	+	1.30875i
$329$	−12.3391	−	5.11104i	−0.680279	−	0.281781i
$330$	4.27246	−	10.3146i	0.235191	−	0.567802i
$331$	−16.1779	+	16.1779i	−0.889219	+	0.889219i	−0.994448	−	0.105229i	$-0.966442\pi$
$331$	−16.1779	+	16.1779i	−0.889219	+	0.889219i	0.105229	+	0.994448i	$0.466442\pi$
$332$	3.97733	−	3.97733i	0.218284	−	0.218284i
$333$	4.37046	−	10.5512i	0.239500	−	0.578204i
$334$	−3.73584	−	1.54744i	−0.204416	−	0.0846719i
$335$	−7.36981	−	17.7923i	−0.402656	−	0.972097i
$336$			17.9291i			0.978111i
$337$	25.5027	−	10.5635i	1.38922	−	0.575433i	0.442289	−	0.896873i	$-0.354167\pi$
$337$	25.5027	−	10.5635i	1.38922	−	0.575433i	0.946930	+	0.321440i	$0.104167\pi$
$338$	−13.9560	−	13.9560i	−0.759105	−	0.759105i
$339$	22.1342			1.20217
$340$	−3.13118	−	0.370095i	−0.169812	−	0.0200712i
$341$	11.0704			0.599495
$342$	16.3275	+	16.3275i	0.882888	+	0.882888i
$343$	−17.3473	+	7.18547i	−0.936664	+	0.387979i
$344$			2.47971i			0.133697i
$345$	12.6532	+	30.5475i	0.681224	+	1.64462i
$346$	−17.2882	−	7.16099i	−0.929417	−	0.384977i
$347$	−4.46014	+	10.7677i	−0.239433	+	0.578042i	−0.997224	−	0.0744545i	$-0.976278\pi$
$347$	−4.46014	+	10.7677i	−0.239433	+	0.578042i	0.757791	+	0.652497i	$0.226278\pi$
$348$	2.32802	−	2.32802i	0.124795	−	0.124795i
$349$	−1.47628	+	1.47628i	−0.0790236	+	0.0790236i	−0.745514	−	0.666490i	$-0.767796\pi$
$349$	−1.47628	+	1.47628i	−0.0790236	+	0.0790236i	0.666490	+	0.745514i	$0.267796\pi$
$350$	1.32154	−	3.19049i	0.0706395	−	0.170539i
$351$	−0.760637	−	0.315066i	−0.0405998	−	0.0168170i
$352$	1.39218	+	3.36102i	0.0742033	+	0.179143i
$353$		−	3.51168i		−	0.186908i	−0.995624	−	0.0934540i	$-0.970209\pi$
$353$		−	3.51168i		−	0.186908i	0.995624	−	0.0934540i	$-0.0297908\pi$
$354$	−26.6796	+	11.0511i	−1.41801	+	0.587357i
$355$	−4.32375	−	4.32375i	−0.229481	−	0.229481i
$356$	−4.31145			−0.228507
$357$	7.78434	−	13.9051i	0.411991	−	0.735938i
$358$	−11.6083			−0.613516
$359$	−1.52421	−	1.52421i	−0.0804448	−	0.0804448i	0.665739	−	0.746184i	$-0.268116\pi$
$359$	−1.52421	−	1.52421i	−0.0804448	−	0.0804448i	−0.746184	+	0.665739i	$0.768116\pi$
$360$	10.0751	−	4.17323i	0.531003	−	0.219949i
$361$			23.2027i			1.22119i
$362$	6.64399	+	16.0400i	0.349200	+	0.843044i
$363$	−17.7046	−	7.33351i	−0.929253	−	0.384909i
$364$	0.130137	−	0.314178i	0.00682102	−	0.0164674i
$365$	9.29389	−	9.29389i	0.486464	−	0.486464i
$366$	−36.1822	+	36.1822i	−1.89127	+	1.89127i
$367$	−5.78033	+	13.9549i	−0.301731	+	0.728442i	0.698191	+	0.715912i	$0.253989\pi$
$367$	−5.78033	+	13.9549i	−0.301731	+	0.728442i	−0.999921	+	0.0125306i	$0.996011\pi$
$368$	−32.1346	−	13.3106i	−1.67513	−	0.693862i
$369$	−9.08582	−	21.9351i	−0.472989	−	1.14190i
$370$			14.7723i			0.767975i
$371$	−3.61389	+	1.49692i	−0.187624	+	0.0777162i
$372$	−4.39717	−	4.39717i	−0.227983	−	0.227983i
$373$	10.5876			0.548207			0.274104	−	0.961700i	$-0.411619\pi$
$373$	10.5876			0.548207			0.274104	+	0.961700i	$0.411619\pi$
$374$	1.22530	−	10.3666i	0.0633588	−	0.536047i
$375$	−27.9021			−1.44086
$376$	−13.9422	−	13.9422i	−0.719015	−	0.719015i
$377$	1.68078	−	0.696202i	0.0865646	−	0.0358562i
$378$			4.22160i			0.217135i
$379$	−1.19170	−	2.87703i	−0.0612137	−	0.147783i	0.890313	−	0.455349i	$-0.150485\pi$
$379$	−1.19170	−	2.87703i	−0.0612137	−	0.147783i	−0.951527	+	0.307566i	$0.900485\pi$
$380$	−4.58967	−	1.90111i	−0.235445	−	0.0975247i
$381$	2.18679	−	5.27937i	0.112032	−	0.270470i
$382$	−16.9016	+	16.9016i	−0.864760	+	0.864760i
$383$	−3.95134	+	3.95134i	−0.201904	+	0.201904i	−0.800815	−	0.598911i	$-0.795600\pi$
$383$	−3.95134	+	3.95134i	−0.201904	+	0.201904i	0.598911	+	0.800815i	$0.295600\pi$
$384$	−11.8718	+	28.6611i	−0.605831	+	1.46260i
$385$	−4.86110	−	2.01353i	−0.247745	−	0.102619i
$386$	7.01151	+	16.9273i	0.356876	+	0.861575i
$387$		−	2.29480i		−	0.116651i
$388$	0.573694	−	0.237632i	0.0291249	−	0.0120639i
$389$	−26.9332	−	26.9332i	−1.36557	−	1.36557i	−0.866648	−	0.498920i	$-0.833730\pi$
$389$	−26.9332	−	26.9332i	−1.36557	−	1.36557i	−0.498920	−	0.866648i	$-0.666270\pi$
$390$	−3.46543			−0.175479
$391$	19.1433	+	24.2752i	0.968118	+	1.22765i
$392$	−10.3620			−0.523359
$393$	−35.9299	−	35.9299i	−1.81242	−	1.81242i
$394$	−2.59815	+	1.07619i	−0.130893	+	0.0542176i
$395$		−	22.4740i		−	1.13079i
$396$	−0.572800	−	1.38286i	−0.0287843	−	0.0694914i
$397$	6.71080	+	2.77970i	0.336805	+	0.139509i	0.544675	−	0.838647i	$-0.316653\pi$
$397$	6.71080	+	2.77970i	0.336805	+	0.139509i	−0.207870	+	0.978157i	$0.566653\pi$
$398$	13.7374	−	33.1650i	0.688593	−	1.66241i
$399$	17.7543	−	17.7543i	0.888826	−	0.888826i
$400$	4.35406	−	4.35406i	0.217703	−	0.217703i
$401$	6.23416	−	15.0506i	0.311319	−	0.751591i	−0.688338	−	0.725390i	$-0.741659\pi$
$401$	6.23416	−	15.0506i	0.311319	−	0.751591i	0.999657	−	0.0262003i	$-0.00834078\pi$
$402$	−33.0893	−	13.7060i	−1.65035	−	0.683595i
$403$	−1.31499	−	3.17466i	−0.0655041	−	0.158141i
$404$			2.98779i			0.148648i
$405$	18.8000	−	7.78720i	0.934178	−	0.386949i
$406$	−6.59622	−	6.59622i	−0.327365	−	0.327365i
$407$	−8.13487			−0.403231
$408$	18.4731	−	14.5678i	0.914556	−	0.721214i
$409$	6.91066			0.341710			0.170855	−	0.985296i	$-0.445347\pi$
$409$	6.91066			0.341710			0.170855	+	0.985296i	$0.445347\pi$
$410$	21.7155	+	21.7155i	1.07245	+	1.07245i
$411$	−1.62610	+	0.673551i	−0.0802094	+	0.0332238i
$412$			0.642861i			0.0316715i
$413$	5.20816	+	12.5736i	0.256277	+	0.618707i
$414$	24.6222	+	10.1988i	1.21012	+	0.501246i
$415$	−10.3377	+	24.9574i	−0.507458	+	1.22511i
$416$	0.798471	−	0.798471i	0.0391483	−	0.0391483i
$417$	−32.1686	+	32.1686i	−1.57530	+	1.57530i
$418$	6.29414	−	15.1954i	0.307856	−	0.743231i
$419$	−15.6393	−	6.47800i	−0.764029	−	0.316471i	−0.0335779	−	0.999436i	$-0.510690\pi$
$419$	−15.6393	−	6.47800i	−0.764029	−	0.316471i	−0.730451	+	0.682965i	$0.760690\pi$
$420$	1.13106	+	2.73061i	0.0551900	+	0.133240i
$421$		−	36.9402i		−	1.80036i	−0.435523	−	0.900178i	$-0.643436\pi$
$421$		−	36.9402i		−	1.80036i	0.435523	−	0.900178i	$-0.356564\pi$
$422$	−25.6930	+	10.6424i	−1.25072	+	0.518063i
$423$	12.9026	+	12.9026i	0.627345	+	0.627345i
$424$	−5.77479			−0.280448
$425$	−5.26727	+	1.48643i	−0.255500	+	0.0721024i
$426$	−11.3719			−0.550969
$427$	17.0520	+	17.0520i	0.825204	+	0.825204i
$428$	4.90183	−	2.03040i	0.236939	−	0.0981433i
$429$		−	1.90836i		−	0.0921366i
$430$	1.13591	+	2.74234i	0.0547786	+	0.132247i
$431$	0.714535	+	0.295970i	0.0344180	+	0.0142564i	0.399826	−	0.916591i	$-0.369071\pi$
$431$	0.714535	+	0.295970i	0.0344180	+	0.0142564i	−0.365408	+	0.930847i	$0.619071\pi$
$432$	−2.88061	+	6.95440i	−0.138593	+	0.334594i
$433$	10.2952	−	10.2952i	0.494755	−	0.494755i	−0.415046	−	0.909801i	$-0.636234\pi$
$433$	10.2952	−	10.2952i	0.494755	−	0.494755i	0.909801	+	0.415046i	$0.136234\pi$
$434$	−12.4589	+	12.4589i	−0.598048	+	0.598048i
$435$	−6.05090	+	14.6082i	−0.290118	+	0.700408i
$436$	−5.62674	−	2.33067i	−0.269472	−	0.111619i
$437$	18.6405	+	45.0021i	0.891696	+	2.15274i
$438$		−	24.4438i		−	1.16797i
$439$	3.60238	−	1.49215i	0.171932	−	0.0712166i	−0.295057	−	0.955480i	$-0.595339\pi$
$439$	3.60238	−	1.49215i	0.171932	−	0.0712166i	0.466989	+	0.884263i	$0.345339\pi$
$440$	−5.49264	−	5.49264i	−0.261851	−	0.261851i
$441$	9.58933			0.456635
$442$	−3.11839	+	0.880014i	−0.148327	+	0.0418580i
$443$	14.8787			0.706910			0.353455	−	0.935451i	$-0.385007\pi$
$443$	14.8787			0.706910			0.353455	+	0.935451i	$0.385007\pi$
$444$	3.23119	+	3.23119i	0.153345	+	0.153345i
$445$	19.1301	−	7.92394i	0.906853	−	0.375631i
$446$		−	27.1026i		−	1.28335i
$447$	10.7086	+	25.8528i	0.506498	+	1.22279i
$448$	9.04782	+	3.74773i	0.427469	+	0.177064i
$449$	7.57890	−	18.2971i	0.357670	−	0.863492i	−0.637957	−	0.770072i	$-0.720220\pi$
$449$	7.57890	−	18.2971i	0.357670	−	0.863492i	0.995627	−	0.0934199i	$-0.0297799\pi$
$450$	−3.33618	+	3.33618i	−0.157269	+	0.157269i
$451$	−11.9584	+	11.9584i	−0.563098	+	0.563098i
$452$	−1.46889	+	3.54621i	−0.0690906	+	0.166800i
$453$	−29.1900	−	12.0909i	−1.37146	−	0.568079i
$454$	9.10053	+	21.9706i	0.427109	+	1.03113i
$455$			1.63320i			0.0765654i
$456$	34.2461	−	14.1852i	1.60372	−	0.664282i
$457$	−20.8473	−	20.8473i	−0.975198	−	0.975198i	0.0245023	−	0.999700i	$-0.492200\pi$
$457$	−20.8473	−	20.8473i	−0.975198	−	0.975198i	−0.999700	+	0.0245023i	$0.992200\pi$
$458$	1.48727			0.0694955
$459$	5.25351	−	4.14289i	0.245213	−	0.193374i
$460$	−5.73382			−0.267341
$461$	4.68896	+	4.68896i	0.218387	+	0.218387i	0.807818	−	0.589432i	$-0.200648\pi$
$461$	4.68896	+	4.68896i	0.218387	+	0.218387i	−0.589432	+	0.807818i	$0.700648\pi$
$462$	−9.04046	+	3.74468i	−0.420600	+	0.174218i
$463$		−	8.52670i		−	0.396269i	−0.980175	−	0.198135i	$-0.936512\pi$
$463$		−	8.52670i		−	0.396269i	0.980175	−	0.198135i	$-0.0634883\pi$
$464$	−6.36527	−	15.3671i	−0.295500	−	0.713401i
$465$	27.5919	+	11.4289i	1.27954	+	0.530004i
$466$	0.877110	−	2.11753i	0.0406313	−	0.0980927i
$467$	−8.50270	+	8.50270i	−0.393458	+	0.393458i	−0.875918	−	0.482460i	$-0.839743\pi$
$467$	−8.50270	+	8.50270i	−0.393458	+	0.393458i	0.482460	+	0.875918i	$0.339743\pi$
$468$	−0.328524	+	0.328524i	−0.0151860	+	0.0151860i
$469$	−6.45941	+	15.5944i	−0.298268	+	0.720082i
$470$	−21.8055	−	9.03215i	−1.00581	−	0.416622i
$471$	−15.0905	−	36.4317i	−0.695335	−	1.67869i
$472$			20.0919i			0.924805i
$473$	−1.51016	+	0.625530i	−0.0694374	+	0.0287619i
$474$	−29.5543	−	29.5543i	−1.35747	−	1.35747i
$475$	−8.62323			−0.395661
$476$	1.71120	+	2.16994i	0.0784329	+	0.0994591i
$477$	5.34418			0.244693
$478$	−7.83053	−	7.83053i	−0.358160	−	0.358160i
$479$	−0.856998	+	0.354980i	−0.0391573	+	0.0162195i	−0.402176	−	0.915562i	$-0.631746\pi$
$479$	−0.856998	+	0.354980i	−0.0391573	+	0.0162195i	0.363019	+	0.931782i	$0.381746\pi$
$480$			9.81429i			0.447959i
$481$	0.966294	+	2.33284i	0.0440592	+	0.106368i
$482$	29.0533	+	12.0343i	1.32334	+	0.548146i
$483$	11.0901	−	26.7739i	0.504618	−	1.21825i
$484$	2.34986	−	2.34986i	0.106812	−	0.106812i
$485$	−2.10876	+	2.10876i	−0.0957540	+	0.0957540i
$486$	11.5968	−	27.9972i	0.526043	−	1.26998i
$487$	−3.24726	−	1.34506i	−0.147147	−	0.0609504i	0.307894	−	0.951421i	$-0.400376\pi$
$487$	−3.24726	−	1.34506i	−0.147147	−	0.0609504i	−0.455042	+	0.890470i	$0.650376\pi$
$488$	13.6241	+	32.8914i	0.616732	+	1.48892i
$489$			8.21520i			0.371504i
$490$	−11.4594	+	4.74665i	−0.517685	+	0.214432i
$491$	23.8811	+	23.8811i	1.07774	+	1.07774i	0.996712	+	0.0810248i	$0.0258193\pi$
$491$	23.8811	+	23.8811i	1.07774	+	1.07774i	0.0810248	+	0.996712i	$0.474181\pi$
$492$	9.49977			0.428283
$493$	−1.73534	+	14.6818i	−0.0781557	+	0.661236i
$494$	−5.10523			−0.229695
$495$	5.08307	+	5.08307i	0.228467	+	0.228467i
$496$	−29.0254	+	12.0227i	−1.30328	+	0.539837i
$497$			5.35935i			0.240400i
$498$	19.2256	+	46.4147i	0.861520	+	2.07989i
$499$	−25.9728	−	10.7583i	−1.16270	−	0.481608i	−0.283929	−	0.958845i	$-0.591638\pi$
$499$	−25.9728	−	10.7583i	−1.16270	−	0.481608i	−0.878774	+	0.477237i	$0.841638\pi$
$500$	1.85166	−	4.47030i	0.0828087	−	0.199918i
$501$	4.24780	−	4.24780i	0.189778	−	0.189778i
$502$	−30.3255	+	30.3255i	−1.35349	+	1.35349i
$503$	7.00396	−	16.9091i	0.312291	−	0.753938i	−0.687328	−	0.726347i	$-0.741217\pi$
$503$	7.00396	−	16.9091i	0.312291	−	0.753938i	0.999619	−	0.0275907i	$-0.00878350\pi$
$504$	−8.83049	−	3.65771i	−0.393341	−	0.162927i
$505$	−5.49120	−	13.2569i	−0.244355	−	0.589926i
$506$		−	18.9834i		−	0.843916i
$507$	27.0893	−	11.2207i	1.20308	−	0.498331i
$508$	0.700707	+	0.700707i	0.0310888	+	0.0310888i
$509$	19.6261			0.869910			0.434955	−	0.900452i	$-0.356764\pi$
$509$	19.6261			0.869910			0.434955	+	0.900452i	$0.356764\pi$
$510$	13.7564	−	24.5729i	0.609142	−	1.08811i
$511$	−11.5199			−0.509611
$512$	8.96734	+	8.96734i	0.396304	+	0.396304i
$513$	9.73913	−	4.03408i	0.429993	−	0.178109i
$514$		−	5.47510i		−	0.241496i
$515$	−1.18150	−	2.85240i	−0.0520632	−	0.125692i
$516$	0.848301	+	0.351378i	0.0373444	+	0.0154685i
$517$	4.97387	−	12.0080i	0.218750	−	0.528110i
$518$	9.15523	−	9.15523i	0.402258	−	0.402258i
$519$	19.6574	−	19.6574i	0.862863	−	0.862863i
$520$	−0.922687	+	2.22756i	−0.0404625	+	0.0976852i
$521$	16.9278	+	7.01170i	0.741618	+	0.307188i	0.721317	−	0.692606i	$-0.243537\pi$
$521$	16.9278	+	7.01170i	0.741618	+	0.307188i	0.0203018	+	0.999794i	$0.493537\pi$
$522$	4.87721	+	11.7746i	0.213470	+	0.515361i
$523$		−	13.6685i		−	0.597680i	−0.954303	−	0.298840i	$-0.903400\pi$
$523$		−	13.6685i		−	0.597680i	0.954303	−	0.298840i	$-0.0965997\pi$
$524$	8.14087	−	3.37206i	0.355636	−	0.147309i
$525$	3.62772	+	3.62772i	0.158327	+	0.158327i
$526$	38.2811			1.66913
$527$	27.7310	+	3.27771i	1.20798	+	0.142779i
$528$	−17.4479			−0.759322
$529$	23.4905	+	23.4905i	1.02133	+	1.02133i
$530$	−6.38640	+	2.64533i	−0.277408	+	0.114906i
$531$		−	18.5937i		−	0.806899i
$532$	1.66626	+	4.02271i	0.0722415	+	0.174406i
$533$	4.84977	+	2.00884i	0.210067	+	0.0870126i
$534$	14.7366	−	35.5773i	0.637715	−	1.53958i
$535$	−18.0180	+	18.0180i	−0.778984	+	0.778984i
$536$	−17.6204	+	17.6204i	−0.761084	+	0.761084i
$537$	6.59955	−	15.9327i	0.284791	−	0.687547i
$538$	22.2590	+	9.22000i	0.959656	+	0.397502i
$539$	−2.61391	−	6.31054i	−0.112589	−	0.271814i
$540$			1.24089i			0.0533992i
$541$	−12.8080	+	5.30523i	−0.550657	+	0.228090i	−0.640623	−	0.767855i	$-0.721324\pi$
$541$	−12.8080	+	5.30523i	−0.550657	+	0.228090i	0.0899664	+	0.995945i	$0.471324\pi$
$542$	8.82780	+	8.82780i	0.379186	+	0.379186i
$543$	−25.7927			−1.10687
$544$	2.49224	+	8.83145i	0.106854	+	0.378645i
$545$	29.2495			1.25291
$546$	2.14773	+	2.14773i	0.0919142	+	0.0919142i
$547$	39.5244	−	16.3715i	1.68994	−	0.699996i	0.690219	−	0.723600i	$-0.257514\pi$
$547$	39.5244	−	16.3715i	1.68994	−	0.699996i	0.999721	+	0.0236039i	$0.00751405\pi$
$548$		−	0.305222i		−	0.0130384i
$549$	−12.6082	−	30.4388i	−0.538103	−	1.29910i
$550$	3.10486	+	1.28608i	0.132392	+	0.0548384i
$551$	−8.91410	+	21.5206i	−0.379754	+	0.916806i
$552$	30.2523	−	30.2523i	1.28762	−	1.28762i
$553$	−13.9284	+	13.9284i	−0.592296	+	0.592296i
$554$	−1.63907	+	3.95707i	−0.0696375	+	0.168120i
$555$	−20.2754	−	8.39835i	−0.860644	−	0.356490i
$556$	−3.01906	−	7.28865i	−0.128037	−	0.309108i
$557$			16.5864i			0.702789i	0.936228	+	0.351394i	$0.114292\pi$
$557$			16.5864i			0.702789i	−0.936228	+	0.351394i	$0.885708\pi$
$558$	22.2399	−	9.21208i	0.941491	−	0.389978i
$559$	0.358767	+	0.358767i	0.0151742	+	0.0151742i
$560$	14.9321			0.630995
$561$	13.5319	+	7.57542i	0.571319	+	0.319834i
$562$	7.09935			0.299468
$563$	1.56463	+	1.56463i	0.0659412	+	0.0659412i	0.739308	−	0.673367i	$-0.235153\pi$
$563$	1.56463	+	1.56463i	0.0659412	+	0.0659412i	−0.673367	+	0.739308i	$0.735153\pi$
$564$	−6.74522	+	2.79396i	−0.284025	+	0.117647i
$565$		−	18.4343i		−	0.775536i
$566$	−10.9826	−	26.5144i	−0.461634	−	1.11448i
$567$	−16.4776	−	6.82524i	−0.691993	−	0.286633i
$568$	−3.02781	+	7.30978i	−0.127044	+	0.306712i
$569$	7.86909	−	7.86909i	0.329889	−	0.329889i	−0.522655	−	0.852544i	$-0.675058\pi$
$569$	7.86909	−	7.86909i	0.329889	−	0.329889i	0.852544	+	0.522655i	$0.175058\pi$
$570$	31.3751	−	31.3751i	1.31416	−	1.31416i
$571$	9.72938	−	23.4888i	0.407162	−	0.982976i	−0.578719	−	0.815527i	$-0.696447\pi$
$571$	9.72938	−	23.4888i	0.407162	−	0.982976i	0.985881	−	0.167449i	$-0.0535529\pi$
$572$	0.305746	+	0.126644i	0.0127839	+	0.00529526i
$573$	−13.5890	−	32.8068i	−0.567690	−	1.37052i
$574$		−	26.9166i		−	1.12348i
$575$	−9.19524	+	3.80880i	−0.383468	+	0.158838i
$576$	−9.46097	−	9.46097i	−0.394207	−	0.394207i
$577$	−32.9034			−1.36979			−0.684893	−	0.728644i	$-0.740151\pi$
$577$	−32.9034			−1.36979			−0.684893	+	0.728644i	$0.740151\pi$
$578$	6.13870	−	25.6054i	0.255336	−	1.06504i
$579$	−27.2194			−1.13120
$580$	−1.93887	−	1.93887i	−0.0805074	−	0.0805074i
$581$	21.8744	−	9.06067i	0.907503	−	0.375900i
$582$			5.54624i			0.229899i
$583$	−1.45675	−	3.51689i	−0.0603322	−	0.145655i
$584$	−15.7124	−	6.50827i	−0.650182	−	0.269314i
$585$	0.853886	−	2.06146i	0.0353038	−	0.0852310i
$586$	8.03011	−	8.03011i	0.331721	−	0.331721i
$587$	−28.1828	+	28.1828i	−1.16323	+	1.16323i	−0.179462	+	0.983765i	$0.557436\pi$
$587$	−28.1828	+	28.1828i	−1.16323	+	1.16323i	−0.983765	+	0.179462i	$0.942564\pi$
$588$	−1.46831	+	3.54481i	−0.0605519	+	0.146185i
$589$	40.6480	+	16.8370i	1.67487	+	0.693755i
$590$	9.20377	+	22.2199i	0.378913	+	0.914778i
$591$		−	4.17787i		−	0.171855i
$592$	21.3288	−	8.83469i	0.876610	−	0.363104i
$593$	11.4849	+	11.4849i	0.471630	+	0.471630i	0.902442	−	0.430812i	$-0.141773\pi$
$593$	11.4849	+	11.4849i	0.471630	+	0.471630i	−0.430812	+	0.902442i	$0.641773\pi$
$594$	−4.10829			−0.168565
$595$	−11.5808	−	6.48312i	−0.474765	−	0.265782i
$596$	−4.85262			−0.198771
$597$	37.7100	+	37.7100i	1.54337	+	1.54337i
$598$	−5.44388	+	2.25493i	−0.222617	+	0.0922109i
$599$			34.0997i			1.39327i	0.717424	+	0.696637i	$0.245321\pi$
$599$			34.0997i			1.39327i	−0.717424	+	0.696637i	$0.754679\pi$
$600$	2.89845	+	6.99747i	0.118329	+	0.285670i
$601$	−12.1848	−	5.04710i	−0.497027	−	0.205875i	0.120065	−	0.992766i	$-0.461690\pi$
$601$	−12.1848	−	5.04710i	−0.497027	−	0.205875i	−0.617093	+	0.786891i	$0.711690\pi$
$602$	0.995592	−	2.40357i	0.0405773	−	0.0979623i
$603$	16.3065	−	16.3065i	0.664051	−	0.664051i
$604$	3.87425	−	3.87425i	0.157641	−	0.157641i
$605$	−6.10765	+	14.7452i	−0.248311	+	0.599476i
$606$	−24.6547	−	10.2123i	−1.00153	−	0.414846i
$607$	1.08439	+	2.61794i	0.0440139	+	0.106259i	0.944358	−	0.328921i	$-0.106685\pi$
$607$	1.08439	+	2.61794i	0.0440139	+	0.106259i	−0.900344	+	0.435180i	$0.856685\pi$
$608$			14.4583i			0.586361i
$609$	12.8036	−	5.30342i	0.518828	−	0.214906i
$610$	30.1340	+	30.1340i	1.22009	+	1.22009i
$611$	−4.03435			−0.163212
$612$	−1.02541	−	3.63363i	−0.0414499	−	0.146881i
$613$	15.3857			0.621423			0.310711	−	0.950504i	$-0.399433\pi$
$613$	15.3857			0.621423			0.310711	+	0.950504i	$0.399433\pi$
$614$	7.62177	+	7.62177i	0.307590	+	0.307590i
$615$	−42.1508	+	17.4594i	−1.69969	+	0.704033i
$616$			6.80820i			0.274310i
$617$	5.58490	+	13.4831i	0.224840	+	0.542811i	0.995535	−	0.0943928i	$-0.0300909\pi$
$617$	5.58490	+	13.4831i	0.224840	+	0.542811i	−0.770695	+	0.637204i	$0.780091\pi$
$618$	−5.30477	−	2.19731i	−0.213389	−	0.0883886i
$619$	7.43915	−	17.9597i	0.299005	−	0.721861i	−0.700958	−	0.713203i	$-0.747244\pi$
$619$	7.43915	−	17.9597i	0.299005	−	0.721861i	0.999963	−	0.00865823i	$-0.00275603\pi$
$620$	−3.66215	+	3.66215i	−0.147075	+	0.147075i
$621$	8.60335	−	8.60335i	0.345241	−	0.345241i
$622$	7.92923	−	19.1429i	0.317933	−	0.767558i
$623$	−16.7669	−	6.94508i	−0.671752	−	0.278249i
$624$	2.07253	+	5.00354i	0.0829677	+	0.200302i
$625$			16.6010i			0.664042i
$626$	−6.82063	+	2.82520i	−0.272607	+	0.112918i
$627$	17.2778	+	17.2778i	0.690009	+	0.690009i
$628$	6.83832			0.272878
$629$	−20.3777	−	2.40857i	−0.812510	−	0.0960358i
$630$	−11.4413			−0.455831
$631$	−3.47265	−	3.47265i	−0.138244	−	0.138244i	0.634598	−	0.772842i	$-0.281166\pi$
$631$	−3.47265	−	3.47265i	−0.138244	−	0.138244i	−0.772842	+	0.634598i	$0.781166\pi$
$632$	−26.8663	+	11.1284i	−1.06868	+	0.442664i
$633$		−	41.3149i		−	1.64212i
$634$	−18.2179	−	43.9818i	−0.723523	−	1.74674i
$635$	−4.39688	−	1.82125i	−0.174485	−	0.0722739i
$636$	−0.818294	+	1.97554i	−0.0324475	+	0.0783352i
$637$	−1.49918	+	1.49918i	−0.0593999	+	0.0593999i
$638$	6.41918	−	6.41918i	0.254138	−	0.254138i
$639$	2.80204	−	6.76471i	0.110847	−	0.267608i
$640$	23.8701	+	9.88733i	0.943550	+	0.390831i
$641$	−18.9378	−	45.7199i	−0.747998	−	1.80583i	−0.569704	−	0.821850i	$-0.692942\pi$
$641$	−18.9378	−	45.7199i	−0.747998	−	1.80583i	−0.178294	−	0.983977i	$-0.557058\pi$
$642$			47.3889i			1.87029i
$643$	−10.2054	+	4.22722i	−0.402462	+	0.166705i	−0.574727	−	0.818346i	$-0.694892\pi$
$643$	−10.2054	+	4.22722i	−0.402462	+	0.166705i	0.172265	+	0.985051i	$0.444892\pi$
$644$	3.55358	+	3.55358i	0.140031	+	0.140031i
$645$	−4.40973			−0.173633
$646$	20.2657	−	36.2005i	0.797343	−	1.42429i
$647$	3.27038			0.128572			0.0642859	−	0.997932i	$-0.479523\pi$
$647$	3.27038			0.128572			0.0642859	+	0.997932i	$0.479523\pi$
$648$	−18.6183	−	18.6183i	−0.731396	−	0.731396i
$649$	−12.2361	+	5.06838i	−0.480311	+	0.198951i
$650$		−	1.04315i		−	0.0409156i
$651$	−10.0171	−	24.1834i	−0.392601	−	0.947824i
$652$	−1.31619	−	0.545183i	−0.0515459	−	0.0213510i
$653$	9.55568	−	23.0695i	0.373943	−	0.902778i	−0.619131	−	0.785287i	$-0.712515\pi$
$653$	9.55568	−	23.0695i	0.373943	−	0.902778i	0.993074	−	0.117490i	$-0.0374849\pi$
$654$	38.4645	−	38.4645i	1.50408	−	1.50408i
$655$	−29.9239	+	29.9239i	−1.16922	+	1.16922i
$656$	18.3666	−	44.3408i	0.717094	−	1.73122i
$657$	14.5407	+	6.02297i	0.567288	+	0.234978i
$658$	7.91640	+	19.1119i	0.308613	+	0.745058i
$659$			9.85211i			0.383784i	0.981416	+	0.191892i	$0.0614623\pi$
$659$			9.85211i			0.383784i	−0.981416	+	0.191892i	$0.938538\pi$
$660$	−2.65733	+	1.10070i	−0.103436	+	0.0428448i
$661$	24.2117	+	24.2117i	0.941725	+	0.941725i	0.998393	−	0.0566685i	$-0.0180478\pi$
$661$	24.2117	+	24.2117i	0.941725	+	0.941725i	−0.0566685	+	0.998393i	$0.518048\pi$
$662$	35.4369			1.37729
$663$	0.565026	−	4.78040i	0.0219438	−	0.185655i
$664$	34.9541			1.35648
$665$	−14.7865	−	14.7865i	−0.573396	−	0.573396i
$666$	−16.3426	+	6.76933i	−0.633263	+	0.262306i
$667$			26.8854i			1.04101i
$668$	0.398661	+	0.962453i	0.0154247	+	0.0372384i
$669$	37.1992	+	15.4084i	1.43820	+	0.595723i
$670$	−11.4150	+	27.5582i	−0.440998	+	1.06466i
$671$	−16.5943	+	16.5943i	−0.640617	+	0.640617i
$672$	6.08247	−	6.08247i	0.234636	−	0.234636i
$673$	16.4848	−	39.7977i	0.635441	−	1.53409i	−0.197251	−	0.980353i	$-0.563201\pi$
$673$	16.4848	−	39.7977i	0.635441	−	1.53409i	0.832692	−	0.553737i	$-0.186799\pi$
$674$	−39.5006	−	16.3617i	−1.52151	−	0.630229i
$675$	0.824280	+	1.98999i	0.0317266	+	0.0765947i
$676$			5.08471i			0.195566i
$677$	−35.1857	+	14.5744i	−1.35229	+	0.560139i	−0.936930	−	0.349516i	$-0.886346\pi$
$677$	−35.1857	+	14.5744i	−1.35229	+	0.560139i	−0.415365	+	0.909655i	$0.636346\pi$
$678$	−24.2419	−	24.2419i	−0.931006	−	0.931006i
$679$	2.61384			0.100310
$680$	−12.1327	−	15.3852i	−0.465266	−	0.589995i
$681$	−35.3292			−1.35382
$682$	−12.1246	−	12.1246i	−0.464273	−	0.464273i
$683$	−18.9120	+	7.83359i	−0.723646	+	0.299744i	−0.713938	−	0.700209i	$-0.753090\pi$
$683$	−18.9120	+	7.83359i	−0.723646	+	0.299744i	−0.00970823	+	0.999953i	$0.503090\pi$
$684$		−	5.94874i		−	0.227456i
$685$	0.560961	+	1.35428i	0.0214332	+	0.0517444i
$686$	26.8688	+	11.1294i	1.02586	+	0.424924i
$687$	−0.845543	+	2.04132i	−0.0322595	+	0.0778813i
$688$	3.28015	−	3.28015i	0.125055	−	0.125055i
$689$	−0.835503	+	0.835503i	−0.0318301	+	0.0318301i
$690$	19.5983	−	47.3144i	0.746093	−	1.80123i
$691$	−33.0869	−	13.7050i	−1.25868	−	0.521364i	−0.349178	−	0.937056i	$-0.613539\pi$
$691$	−33.0869	−	13.7050i	−1.25868	−	0.521364i	−0.909505	+	0.415693i	$0.863539\pi$
$692$	1.84486	+	4.45390i	0.0701312	+	0.169312i
$693$		−	6.30054i		−	0.239338i
$694$	16.6779	−	6.90823i	0.633086	−	0.262233i
$695$	26.7913	+	26.7913i	1.01625	+	1.01625i
$696$	20.4594			0.775512
$697$	−33.4961	+	26.4148i	−1.26875	+	1.00053i
$698$	3.23372			0.122398
$699$	2.40772	+	2.40772i	0.0910684	+	0.0910684i
$700$	−0.821956	+	0.340465i	−0.0310670	+	0.0128684i
$701$		−	7.66830i		−	0.289628i	−0.989459	−	0.144814i	$-0.953742\pi$
$701$		−	7.66830i		−	0.289628i	0.989459	−	0.144814i	$-0.0462583\pi$
$702$	0.488000	+	1.17814i	0.0184184	+	0.0444659i
$703$	−29.8695	−	12.3723i	−1.12655	−	0.466632i
$704$	−3.64715	+	8.80499i	−0.137457	+	0.331851i
$705$	24.7938	−	24.7938i	0.933789	−	0.933789i
$706$	−3.84608	+	3.84608i	−0.144749	+	0.144749i
$707$	−4.81287	+	11.6193i	−0.181006	+	0.436988i
$708$	6.87339	+	2.84705i	0.258318	+	0.106999i
$709$	−3.81874	−	9.21926i	−0.143416	−	0.346236i	0.835807	−	0.549023i	$-0.185000\pi$
$709$	−3.81874	−	9.21926i	−0.143416	−	0.346236i	−0.979223	+	0.202787i	$0.935000\pi$
$710$			9.47096i			0.355439i
$711$	24.8630	−	10.2986i	0.932435	−	0.386227i
$712$	−18.9452	−	18.9452i	−0.710002	−	0.710002i
$713$	50.7811			1.90177
$714$	−23.7548	+	6.70364i	−0.889003	+	0.250877i
$715$	−1.58936			−0.0594388
$716$	2.11468	+	2.11468i	0.0790292	+	0.0790292i
$717$	15.1995	−	6.29582i	0.567634	−	0.235122i
$718$			3.33871i			0.124599i
$719$	−5.57285	−	13.4540i	−0.207832	−	0.501751i	0.785249	−	0.619180i	$-0.212535\pi$
$719$	−5.57285	−	13.4540i	−0.207832	−	0.501751i	−0.993081	+	0.117429i	$0.962535\pi$
$720$	−18.8477	−	7.80695i	−0.702411	−	0.290948i
$721$	−1.03555	+	2.50004i	−0.0385659	+	0.0931063i
$722$	25.4121	−	25.4121i	0.945742	−	0.945742i
$723$	−33.0348	+	33.0348i	−1.22858	+	1.22858i
$724$	1.71167	−	4.13234i	0.0636137	−	0.153577i
$725$	−4.39727	−	1.82141i	−0.163311	−	0.0676455i
$726$	11.3587	+	27.4224i	0.421562	+	1.01774i
$727$			43.9629i			1.63050i	0.579112	+	0.815248i	$0.303399\pi$
$727$			43.9629i			1.63050i	−0.579112	+	0.815248i	$0.696601\pi$
$728$	1.95239	−	0.808707i	0.0723604	−	0.0299727i
$729$	9.30924	+	9.30924i	0.344787	+	0.344787i
$730$	−20.3578			−0.753476
$731$	−3.96813	+	1.11981i	−0.146766	+	0.0414176i
$732$	13.1826			0.487243
$733$	30.1341	+	30.1341i	1.11303	+	1.11303i	0.992739	+	0.120288i	$0.0383817\pi$
$733$	30.1341	+	30.1341i	1.11303	+	1.11303i	0.120288	+	0.992739i	$0.461618\pi$
$734$	21.6146	−	8.95304i	0.797808	−	0.330463i
$735$		−	18.4270i		−	0.679690i
$736$	6.38608	+	15.4174i	0.235394	+	0.568291i
$737$	−15.1759	−	6.28605i	−0.559010	−	0.231549i
$738$	−14.0729	+	33.9749i	−0.518029	+	1.25063i
$739$	7.17701	−	7.17701i	0.264011	−	0.264011i	−0.562671	−	0.826681i	$-0.690226\pi$
$739$	7.17701	−	7.17701i	0.264011	−	0.264011i	0.826681	+	0.562671i	$0.190226\pi$
$740$	2.69106	−	2.69106i	0.0989255	−	0.0989255i
$741$	2.90243	−	7.00709i	0.106623	−	0.257412i
$742$	5.59748	+	2.31855i	0.205490	+	0.0851167i
$743$	16.0919	+	38.8494i	0.590356	+	1.42524i	0.883160	+	0.469072i	$0.155412\pi$
$743$	16.0919	+	38.8494i	0.590356	+	1.42524i	−0.292804	+	0.956172i	$0.594588\pi$
$744$		−	38.6438i		−	1.41675i
$745$	21.5312	−	8.91853i	0.788844	−	0.326750i
$746$	−11.5958	−	11.5958i	−0.424554	−	0.424554i
$747$	−32.3476			−1.18354
$748$	−2.11170	+	1.66528i	−0.0772115	+	0.0608886i
$749$	22.3335			0.816049
$750$	30.5591	+	30.5591i	1.11586	+	1.11586i
$751$	−8.34470	+	3.45649i	−0.304503	+	0.126129i	−0.529703	−	0.848183i	$-0.677696\pi$
$751$	−8.34470	+	3.45649i	−0.304503	+	0.126129i	0.225200	+	0.974313i	$0.427696\pi$
$752$			36.8855i			1.34508i
$753$	−24.3820	−	58.8634i	−0.888531	−	2.14510i
$754$	−2.60333	−	1.07833i	−0.0948076	−	0.0392706i
$755$	−10.0698	+	24.3106i	−0.366477	+	0.884753i
$756$	0.769047	−	0.769047i	0.0279700	−	0.0279700i
$757$	7.34107	−	7.34107i	0.266816	−	0.266816i	−0.561000	−	0.827816i	$-0.689583\pi$
$757$	7.34107	−	7.34107i	0.266816	−	0.266816i	0.827816	+	0.561000i	$0.189583\pi$
$758$	−1.84581	+	4.45617i	−0.0670427	+	0.161855i
$759$	26.0553	+	10.7925i	0.945748	+	0.391742i
$760$	−11.8140	−	28.5215i	−0.428539	−	1.03458i
$761$			28.5843i			1.03618i	0.855326	+	0.518090i	$0.173357\pi$
$761$			28.5843i			1.03618i	−0.855326	+	0.518090i	$0.826643\pi$
$762$	−8.17712	+	3.38707i	−0.296226	+	0.122701i
$763$	−18.1276	−	18.1276i	−0.656264	−	0.656264i
$764$	6.15791			0.222785
$765$	11.2280	+	14.2380i	0.405948	+	0.514774i
$766$	8.65522			0.312726
$767$	2.90692	+	2.90692i	0.104963	+	0.104963i
$768$	19.6027	−	8.11969i	0.707351	−	0.292994i
$769$		−	40.0256i		−	1.44336i	−0.692227	−	0.721680i	$-0.743370\pi$
$769$		−	40.0256i		−	1.44336i	0.692227	−	0.721680i	$-0.256630\pi$
$770$	3.11872	+	7.52927i	0.112391	+	0.271336i
$771$	7.51474	+	3.11271i	0.270637	+	0.112101i
$772$	1.80635	−	4.36092i	0.0650121	−	0.156953i
$773$	−12.4539	+	12.4539i	−0.447936	+	0.447936i	−0.894668	−	0.446732i	$-0.852588\pi$
$773$	−12.4539	+	12.4539i	−0.447936	+	0.447936i	0.446732	+	0.894668i	$0.352588\pi$
$774$	−2.51333	+	2.51333i	−0.0903396	+	0.0903396i
$775$	−3.44028	+	8.30557i	−0.123579	+	0.298345i
$776$	3.56510	+	1.47671i	0.127980	+	0.0530109i
$777$	7.36089	+	17.7708i	0.264071	+	0.637523i
$778$			58.9958i			2.11510i
$779$	−62.0961	+	25.7210i	−2.22482	+	0.921552i
$780$	0.631297	+	0.631297i	0.0226041	+	0.0226041i
$781$	−5.21551			−0.186626
$782$	5.62059	−	47.5530i	0.200992	−	1.70049i
$783$	5.81839			0.207932
$784$	13.7068	+	13.7068i	0.489530	+	0.489530i
$785$	−30.3419	+	12.5680i	−1.08295	+	0.448571i
$786$			78.7026i			2.80723i
$787$	−17.7929	−	42.9558i	−0.634248	−	1.53121i	−0.834233	−	0.551412i	$-0.814089\pi$
$787$	−17.7929	−	42.9558i	−0.634248	−	1.53121i	0.199985	−	0.979799i	$-0.435911\pi$
$788$	0.669353	+	0.277255i	0.0238447	+	0.00987681i
$789$	−21.7636	+	52.5419i	−0.774804	+	1.87054i
$790$	−24.6140	+	24.6140i	−0.875728	+	0.875728i
$791$	−11.4248	+	11.4248i	−0.406218	+	0.406218i
$792$	3.55954	−	8.59349i	0.126483	−	0.305356i
$793$	6.72991	+	2.78762i	0.238986	+	0.0989913i
$794$	−4.30543	−	10.3942i	−0.152794	−	0.368878i
$795$		−	10.2695i		−	0.364220i
$796$	−8.54419	+	3.53912i	−0.302841	+	0.125441i
$797$	25.3028	+	25.3028i	0.896271	+	0.896271i	0.995104	−	0.0988329i	$-0.0315109\pi$
$797$	25.3028	+	25.3028i	0.896271	+	0.896271i	−0.0988329	+	0.995104i	$0.531511\pi$
$798$	−38.8899			−1.37669
$799$	16.0147	−	28.6070i	0.566560	−	1.01204i
$800$	−2.95425			−0.104448
$801$	17.5325	+	17.5325i	0.619482	+	0.619482i
$802$	−23.3116	+	9.65598i	−0.823161	+	0.340964i
$803$		−	11.2107i		−	0.395618i
$804$	3.53105	+	8.52470i	0.124530	+	0.300643i
$805$	−22.2984	−	9.23630i	−0.785916	−	0.325537i
$806$	−2.03676	+	4.91717i	−0.0717417	+	0.173200i
$807$	−25.3095	+	25.3095i	−0.890935	+	0.890935i
$808$	−13.1288	+	13.1288i	−0.461871	+	0.461871i
$809$	−8.55063	+	20.6431i	−0.300624	+	0.725771i	0.699316	+	0.714813i	$0.253488\pi$
$809$	−8.55063	+	20.6431i	−0.300624	+	0.725771i	−0.999940	+	0.0109582i	$0.996512\pi$
$810$	−29.1189	−	12.0614i	−1.02313	−	0.423796i
$811$	−13.2487	−	31.9853i	−0.465226	−	1.12315i	−0.966223	−	0.257706i	$-0.917033\pi$
$811$	−13.2487	−	31.9853i	−0.465226	−	1.12315i	0.500998	−	0.865449i	$-0.332967\pi$
$812$			2.40326i			0.0843380i
$813$	−17.1352	+	7.09764i	−0.600958	+	0.248925i
$814$	8.90951	+	8.90951i	0.312278	+	0.312278i
$815$	6.84196			0.239663
$816$	−43.7065	−	5.16595i	−1.53003	−	0.180845i
$817$	−6.49636			−0.227279
$818$	−7.56873	−	7.56873i	−0.264634	−	0.264634i
$819$	−1.80681	+	0.748404i	−0.0631350	+	0.0261514i
$820$		−	7.91180i		−	0.276292i
$821$	3.99087	+	9.63481i	0.139282	+	0.336257i	0.978094	−	0.208165i	$-0.0667491\pi$
$821$	3.99087	+	9.63481i	0.139282	+	0.336257i	−0.838812	+	0.544422i	$0.816749\pi$
$822$	2.51863	+	1.04325i	0.0878473	+	0.0363875i
$823$	0.228758	−	0.552270i	0.00797399	−	0.0192509i	−0.919842	−	0.392288i	$-0.871684\pi$
$823$	0.228758	−	0.552270i	0.00797399	−	0.0192509i	0.927816	+	0.373037i	$0.121684\pi$
$824$	−2.82484	+	2.82484i	−0.0984078	+	0.0984078i
$825$	−3.53036	+	3.53036i	−0.122911	+	0.122911i
$826$	8.06682	−	19.4750i	0.280681	−	0.677623i
$827$	40.5206	+	16.7842i	1.40904	+	0.583643i	0.952081	−	0.305846i	$-0.0989393\pi$
$827$	40.5206	+	16.7842i	1.40904	+	0.583643i	0.456957	+	0.889489i	$0.348939\pi$
$828$	−2.62750	−	6.34334i	−0.0913119	−	0.220446i
$829$			33.5401i			1.16489i	0.812868	+	0.582447i	$0.197905\pi$
$829$			33.5401i			1.16489i	−0.812868	+	0.582447i	$0.802095\pi$
$830$	38.6561	−	16.0119i	1.34177	−	0.555780i
$831$	−4.49936	−	4.49936i	−0.156081	−	0.156081i
$832$	2.95823			0.102558
$833$	−4.67936	−	16.5817i	−0.162130	−	0.574521i
$834$	70.4637			2.43996
$835$	−3.53775	−	3.53775i	−0.122429	−	0.122429i
$836$	−3.91474	+	1.62154i	−0.135394	+	0.0560821i
$837$		−	10.9898i		−	0.379863i
$838$	10.0337	+	24.2234i	0.346607	+	0.836783i
$839$	−33.2756	−	13.7832i	−1.14880	−	0.475849i	−0.274669	−	0.961539i	$-0.588568\pi$
$839$	−33.2756	−	13.7832i	−1.14880	−	0.475849i	−0.874131	+	0.485690i	$0.838568\pi$
$840$	−7.02871	+	16.9688i	−0.242514	+	0.585479i
$841$	11.4149	−	11.4149i	0.393617	−	0.393617i
$842$	−40.4578	+	40.4578i	−1.39427	+	1.39427i
$843$	−4.03613	+	9.74408i	−0.139012	+	0.335604i
$844$	6.61921	+	2.74177i	0.227843	+	0.0943755i
$845$	−9.34510	−	22.5611i	−0.321481	−	0.776124i
$846$		−	28.2625i		−	0.971683i
$847$	12.9237	−	5.35316i	0.444063	−	0.183937i
$848$	7.63888	+	7.63888i	0.262320	+	0.262320i
$849$	42.6356			1.46325
$850$	7.39682	+	4.14087i	0.253709	+	0.142031i
$851$	−37.3156			−1.27916
$852$	2.07161	+	2.07161i	0.0709722	+	0.0709722i
$853$	52.4102	−	21.7090i	1.79449	−	0.743303i	0.806023	−	0.591884i	$-0.201616\pi$
$853$	52.4102	−	21.7090i	1.79449	−	0.743303i	0.988470	−	0.151419i	$-0.0483842\pi$
$854$		−	37.3515i		−	1.27814i
$855$	10.9331	+	26.3948i	0.373903	+	0.902682i
$856$	30.4613	+	12.6175i	1.04115	+	0.431257i
$857$	−7.50886	+	18.1280i	−0.256498	+	0.619240i	−0.998702	−	0.0509334i	$-0.983780\pi$
$857$	−7.50886	+	18.1280i	−0.256498	+	0.619240i	0.742204	+	0.670174i	$0.233780\pi$
$858$	−2.09008	+	2.09008i	−0.0713543	+	0.0713543i
$859$	28.7185	−	28.7185i	0.979864	−	0.979864i	−0.0199374	−	0.999801i	$-0.506347\pi$
$859$	28.7185	−	28.7185i	0.979864	−	0.979864i	0.999801	+	0.0199374i	$0.00634668\pi$
$860$	0.292642	−	0.706500i	0.00997900	−	0.0240914i
$861$	36.9439	+	15.3027i	1.25904	+	0.521513i
$862$	−0.458423	−	1.10673i	−0.0156139	−	0.0376954i
$863$		−	15.2726i		−	0.519886i	−0.965624	−	0.259943i	$-0.916296\pi$
$863$		−	15.2726i		−	0.519886i	0.965624	−	0.259943i	$-0.0837038\pi$
$864$	3.33655	−	1.38204i	0.113512	−	0.0470180i
$865$	−16.3715	−	16.3715i	−0.556646	−	0.556646i
$866$	−22.5511			−0.766316
$867$	31.6542	+	22.9828i	1.07503	+	0.780536i
$868$	4.53928			0.154073
$869$	−13.5546	−	13.5546i	−0.459807	−	0.459807i
$870$	22.6263	−	9.37212i	0.767104	−	0.317745i
$871$			5.09867i			0.172762i
$872$	−14.4835	−	34.9661i	−0.490472	−	1.18410i
$873$	−3.29926	−	1.36660i	−0.111663	−	0.0462523i
$874$	28.8719	−	69.7030i	0.976607	−	2.35774i
$875$	14.4019	−	14.4019i	0.486874	−	0.486874i
$876$	−4.45292	+	4.45292i	−0.150450	+	0.150450i
$877$	16.3605	−	39.4977i	0.552454	−	1.33374i	−0.363177	−	0.931720i	$-0.618308\pi$
$877$	16.3605	−	39.4977i	0.552454	−	1.33374i	0.915630	−	0.402021i	$-0.131692\pi$
$878$	−5.57965	−	2.31117i	−0.188304	−	0.0779981i
$879$	6.45629	+	15.5869i	0.217765	+	0.525732i
$880$			14.5313i			0.489850i
$881$	−24.8985	+	10.3133i	−0.838853	+	0.347464i	−0.760401	−	0.649454i	$-0.774998\pi$
$881$	−24.8985	+	10.3133i	−0.838853	+	0.347464i	−0.0784515	+	0.996918i	$0.524998\pi$
$882$	−10.5025	−	10.5025i	−0.353636	−	0.353636i
$883$	−3.88994			−0.130907			−0.0654535	−	0.997856i	$-0.520849\pi$
$883$	−3.88994			−0.130907			−0.0654535	+	0.997856i	$0.520849\pi$
$884$	0.728389	+	0.407765i	0.0244984	+	0.0137146i
$885$	−35.7300			−1.20105
$886$	−16.2956	−	16.2956i	−0.547460	−	0.547460i
$887$	21.2440	−	8.79954i	0.713302	−	0.295460i	0.00363206	−	0.999993i	$-0.498844\pi$
$887$	21.2440	−	8.79954i	0.713302	−	0.295460i	0.709670	+	0.704534i	$0.248844\pi$
$888$			28.3967i			0.952931i
$889$	1.59627	+	3.85372i	0.0535370	+	0.129250i
$890$	−29.6302	−	12.2732i	−0.993207	−	0.411400i
$891$	6.64206	−	16.0353i	0.222517	−	0.537204i
$892$	−4.93728	+	4.93728i	−0.165312	+	0.165312i
$893$	36.5259	−	36.5259i	1.22229	−	1.22229i
$894$	16.5863	−	40.0429i	0.554729	−	1.33923i
$895$	−13.2694	−	5.49637i	−0.443548	−	0.183724i
$896$	−8.66594	−	20.9214i	−0.289509	−	0.698936i
$897$		−	8.75387i		−	0.292283i
$898$	−28.3400	+	11.7388i	−0.945718	+	0.391729i
$899$	17.1715	+	17.1715i	0.572700	+	0.572700i
$900$	1.21550			0.0405167
$901$	−2.60783	−	9.24104i	−0.0868795	−	0.307864i
$902$	26.1942			0.872172
$903$	2.73296	+	2.73296i	0.0909473	+	0.0909473i
$904$	−22.0371	+	9.12808i	−0.732944	+	0.303595i
$905$			21.4812i			0.714059i
$906$	18.7273	+	45.2118i	0.622174	+	1.50206i
$907$	38.0707	+	15.7694i	1.26412	+	0.523615i	0.911171	−	0.412029i	$-0.135180\pi$
$907$	38.0707	+	15.7694i	1.26412	+	0.523615i	0.352947	+	0.935643i	$0.385180\pi$
$908$	2.34454	−	5.66023i	0.0778064	−	0.187841i
$909$	12.1499	−	12.1499i	0.402985	−	0.402985i
$910$	1.78872	−	1.78872i	0.0592953	−	0.0592953i
$911$	−0.709994	+	1.71408i	−0.0235231	+	0.0567899i	−0.935205	−	0.354108i	$-0.884785\pi$
$911$	−0.709994	+	1.71408i	−0.0235231	+	0.0567899i	0.911682	+	0.410898i	$0.134785\pi$
$912$	−64.0648	−	26.5365i	−2.12140	−	0.878712i
$913$	8.81750	+	21.2873i	0.291816	+	0.704507i
$914$			45.6650i			1.51047i
$915$	−58.4916	+	24.2280i	−1.93367	+	0.800954i
$916$	−0.270935	−	0.270935i	−0.00895196	−	0.00895196i
$917$	37.0911			1.22486
$918$	−10.2912	−	1.21638i	−0.339659	−	0.0401465i
$919$	21.4011			0.705958			0.352979	−	0.935631i	$-0.385169\pi$
$919$	21.4011			0.705958			0.352979	+	0.935631i	$0.385169\pi$
$920$	−25.1953	−	25.1953i	−0.830666	−	0.830666i
$921$	−14.7943	+	6.12798i	−0.487487	+	0.201924i
$922$		−	10.2709i		−	0.338255i
$923$	0.619520	+	1.49565i	0.0203918	+	0.0492301i
$924$	2.32907	+	0.964731i	0.0766206	+	0.0317373i
$925$	2.52803	−	6.10320i	0.0831211	−	0.200672i
$926$	−9.33865	+	9.33865i	−0.306887	+	0.306887i
$927$	2.61420	−	2.61420i	0.0858615	−	0.0858615i
$928$	−3.05390	+	7.37276i	−0.100249	+	0.242023i
$929$	46.9139	+	19.4324i	1.53920	+	0.637556i	0.981322	−	0.192371i	$-0.0616176\pi$
$929$	46.9139	+	19.4324i	1.53920	+	0.637556i	0.557873	+	0.829926i	$0.311618\pi$
$930$	−17.7021	−	42.7366i	−0.580474	−	1.40139i
$931$		−	27.1464i		−	0.889688i
$932$	−0.545533	+	0.225967i	−0.0178695	+	0.00740180i
$933$	21.7662	+	21.7662i	0.712594	+	0.712594i
$934$	18.6247			0.609420
$935$	6.30912	−	11.2700i	0.206330	−	0.368567i
$936$	−2.88718			−0.0943703
$937$	−17.3983	−	17.3983i	−0.568379	−	0.568379i	0.363295	−	0.931674i	$-0.381652\pi$
$937$	−17.3983	−	17.3983i	−0.568379	−	0.568379i	−0.931674	+	0.363295i	$0.881652\pi$
$938$	24.1539	−	10.0049i	0.788651	−	0.326670i
$939$		−	10.9677i		−	0.357918i
$940$	2.32693	+	5.61770i	0.0758959	+	0.183229i
$941$	53.9291	+	22.3382i	1.75804	+	0.728203i	0.996818	+	0.0797088i	$0.0253990\pi$
$941$	53.9291	+	22.3382i	1.75804	+	0.728203i	0.761220	+	0.648494i	$0.224601\pi$
$942$	−23.3734	+	56.4284i	−0.761547	+	1.83854i
$943$	−54.8544	+	54.8544i	−1.78631	+	1.78631i
$944$	26.5776	−	26.5776i	0.865026	−	0.865026i
$945$	−1.99887	+	4.82571i	−0.0650234	+	0.156980i
$946$	2.33906	+	0.968872i	0.0760495	+	0.0315007i
$947$	−15.7130	−	37.9346i	−0.510604	−	1.23271i	−0.943533	−	0.331279i	$-0.892520\pi$
$947$	−15.7130	−	37.9346i	−0.510604	−	1.23271i	0.432928	−	0.901428i	$-0.357480\pi$
$948$			10.7678i			0.349722i
$949$	−3.21491	+	1.33166i	−0.104360	+	0.0432274i
$950$	9.44438	+	9.44438i	0.306416	+	0.306416i
$951$	70.7236			2.29337
$952$	−2.01577	+	17.0544i	−0.0653314	+	0.552735i
$953$	−10.1139			−0.327622			−0.163811	−	0.986492i	$-0.552379\pi$
$953$	−10.1139			−0.327622			−0.163811	+	0.986492i	$0.552379\pi$
$954$	−5.85308	−	5.85308i	−0.189500	−	0.189500i
$955$	−27.3229	+	11.3175i	−0.884148	+	0.366226i
$956$			2.85297i			0.0922717i
$957$	5.16109	+	12.4600i	0.166834	+	0.402773i
$958$	1.32739	+	0.549823i	0.0428860	+	0.0177640i
$959$	0.491665	−	1.18698i	0.0158767	−	0.0383297i
$960$	−18.1803	+	18.1803i	−0.586768	+	0.586768i
$961$	10.5132	−	10.5132i	0.339134	−	0.339134i
$962$	1.49668	−	3.61329i	0.0482548	−	0.116497i
$963$	−28.1899	−	11.6767i	−0.908408	−	0.376275i
$964$	−3.10035	−	7.48491i	−0.0998556	−	0.241073i
$965$			22.6694i			0.729755i
$966$	−41.4696	+	17.1773i	−1.33426	+	0.552670i
$967$	35.7839	+	35.7839i	1.15073	+	1.15073i	0.986406	+	0.164329i	$0.0525457\pi$
$967$	35.7839	+	35.7839i	1.15073	+	1.15073i	0.164329	+	0.986406i	$0.447454\pi$
$968$	20.6513			0.663758
$969$	38.1649	+	48.3960i	1.22603	+	1.55470i
$970$	4.61914			0.148312
$971$	27.5183	+	27.5183i	0.883106	+	0.883106i	0.993849	−	0.110743i	$-0.0353232\pi$
$971$	27.5183	+	27.5183i	0.883106	+	0.883106i	−0.110743	+	0.993849i	$0.535323\pi$
$972$	−7.21284	+	2.98766i	−0.231352	+	0.0958292i
$973$		−	33.2082i		−	1.06461i
$974$	2.08334	+	5.02962i	0.0667544	+	0.161159i
$975$	1.43175	+	0.593051i	0.0458528	+	0.0189928i
$976$	25.4868	−	61.5306i	0.815813	−	1.96955i
$977$	−1.40229	+	1.40229i	−0.0448634	+	0.0448634i	−0.729183	−	0.684319i	$-0.760100\pi$
$977$	−1.40229	+	1.40229i	−0.0448634	+	0.0448634i	0.684319	+	0.729183i	$0.260100\pi$
$978$	8.99749	−	8.99749i	0.287708	−	0.287708i
$979$	6.75869	−	16.3169i	0.216009	−	0.521491i
$980$	2.95226	+	1.22287i	0.0943065	+	0.0390630i
$981$	13.4035	+	32.3588i	0.427940	+	1.03314i
$982$		−	52.3102i		−	1.66929i
$983$	−1.50978	+	0.625373i	−0.0481546	+	0.0199463i	−0.406631	−	0.913593i	$-0.633296\pi$
$983$	−1.50978	+	0.625373i	−0.0481546	+	0.0199463i	0.358476	+	0.933539i	$0.383296\pi$
$984$	41.7435	+	41.7435i	1.33074	+	1.33074i
$985$	−3.47951			−0.110866
$986$	17.9805	−	14.1793i	0.572615	−	0.451561i
$987$	−30.7323			−0.978219
$988$	0.930019	+	0.930019i	0.0295878	+	0.0295878i
$989$	−6.92729	+	2.86938i	−0.220275	+	0.0912409i
$990$		−	11.1342i		−	0.353868i
$991$	−2.27040	−	5.48122i	−0.0721216	−	0.174117i	0.883708	−	0.468039i	$-0.155039\pi$
$991$	−2.27040	−	5.48122i	−0.0721216	−	0.174117i	−0.955829	+	0.293922i	$0.905039\pi$
$992$	13.9257	+	5.76820i	0.442141	+	0.183141i
$993$	−20.1466	+	48.6383i	−0.639334	+	1.54349i
$994$	5.86969	−	5.86969i	0.186175	−	0.186175i
$995$	31.4064	−	31.4064i	0.995650	−	0.995650i
$996$	4.95303	−	11.9577i	0.156943	−	0.378894i
$997$	−10.1065	−	4.18624i	−0.320075	−	0.132580i	0.216861	−	0.976203i	$-0.430418\pi$
$997$	−10.1065	−	4.18624i	−0.320075	−	0.132580i	−0.536936	+	0.843623i	$0.680418\pi$
$998$	16.6633	+	40.2288i	0.527469	+	1.27342i
$999$			8.07565i			0.255502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.b.87.8	✓	116
17.9	even	8	inner	731.2.m.b.689.8	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.b.87.8	✓	116	1.1	even	1	trivial
731.2.m.b.689.8	yes	116	17.9	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09522 - 1.09522i) q^{2} +(2.12589 - 0.880571i) q^{3} +0.399034i q^{4} +(-0.733376 - 1.77053i) q^{5} +(-3.29275 - 1.36390i) q^{6} +(-0.642781 + 1.55181i) q^{7} +(-1.75342 + 1.75342i) q^{8} +(1.62267 - 1.62267i) q^{9} +O(q^{10})\)	\(q+(-1.09522 - 1.09522i) q^{2} +(2.12589 - 0.880571i) q^{3} +0.399034i q^{4} +(-0.733376 - 1.77053i) q^{5} +(-3.29275 - 1.36390i) q^{6} +(-0.642781 + 1.55181i) q^{7} +(-1.75342 + 1.75342i) q^{8} +(1.62267 - 1.62267i) q^{9} +(-1.13591 + 2.74234i) q^{10} +(-1.51016 - 0.625530i) q^{11} +(0.351378 + 0.848301i) q^{12} +0.507373i q^{13} +(2.40357 - 0.995592i) q^{14} +(-3.11815 - 3.11815i) q^{15} +4.63884 q^{16} +(-3.59771 - 2.01406i) q^{17} -3.55438 q^{18} +(-4.59362 - 4.59362i) q^{19} +(0.706500 - 0.292642i) q^{20} +3.86499i q^{21} +(0.968872 + 2.33906i) q^{22} +(-6.92729 - 2.86938i) q^{23} +(-2.18356 + 5.27158i) q^{24} +(0.938610 - 0.938610i) q^{25} +(0.555687 - 0.555687i) q^{26} +(-0.620976 + 1.49917i) q^{27} +(-0.619225 - 0.256491i) q^{28} +(-1.37217 - 3.31271i) q^{29} +6.83015i q^{30} +(-6.25705 + 2.59175i) q^{31} +(-1.57374 - 1.57374i) q^{32} -3.76126 q^{33} +(1.73445 + 6.14616i) q^{34} +3.21892 q^{35} +(0.647500 + 0.647500i) q^{36} +(4.59788 - 1.90450i) q^{37} +10.0621i q^{38} +(0.446778 + 1.07862i) q^{39} +(4.39039 + 1.81856i) q^{40} +(3.95930 - 9.55860i) q^{41} +(4.23303 - 4.23303i) q^{42} +(0.707107 - 0.707107i) q^{43} +(0.249607 - 0.602606i) q^{44} +(-4.06301 - 1.68295i) q^{45} +(4.44432 + 10.7295i) q^{46} +7.95145i q^{47} +(9.86165 - 4.08483i) q^{48} +(2.95480 + 2.95480i) q^{49} -2.05598 q^{50} +(-9.42186 - 1.11363i) q^{51} -0.202459 q^{52} +(1.64672 + 1.64672i) q^{53} +(2.32203 - 0.961818i) q^{54} +3.13253i q^{55} +(-1.59391 - 3.84804i) q^{56} +(-13.8105 - 5.72051i) q^{57} +(-2.12533 + 5.13100i) q^{58} +(5.72936 - 5.72936i) q^{59} +(1.24425 - 1.24425i) q^{60} +(5.49422 - 13.2642i) q^{61} +(9.69143 + 4.01432i) q^{62} +(1.47506 + 3.56110i) q^{63} -5.83049i q^{64} +(0.898318 - 0.372095i) q^{65} +(4.11942 + 4.11942i) q^{66} +10.0492 q^{67} +(0.803679 - 1.43561i) q^{68} -17.2533 q^{69} +(-3.52544 - 3.52544i) q^{70} +(2.94784 - 1.22104i) q^{71} +5.69044i q^{72} +(2.62461 + 6.33637i) q^{73} +(-7.12157 - 2.94985i) q^{74} +(1.16887 - 2.82189i) q^{75} +(1.83301 - 1.83301i) q^{76} +(1.94141 - 1.94141i) q^{77} +(0.692006 - 1.67065i) q^{78} +(10.8345 + 4.48779i) q^{79} +(-3.40201 - 8.21319i) q^{80} +10.6183i q^{81} +(-14.8051 + 6.13249i) q^{82} +(-9.96741 - 9.96741i) q^{83} -1.54226 q^{84} +(-0.927477 + 7.84691i) q^{85} -1.54888 q^{86} +(-5.83416 - 5.83416i) q^{87} +(3.74476 - 1.55113i) q^{88} +10.8047i q^{89} +(2.60670 + 6.29312i) q^{90} +(-0.787347 - 0.326130i) q^{91} +(1.14498 - 2.76422i) q^{92} +(-11.0196 + 11.0196i) q^{93} +(8.70862 - 8.70862i) q^{94} +(-4.76427 + 11.5020i) q^{95} +(-4.73137 - 1.95980i) q^{96} +(-0.595519 - 1.43771i) q^{97} -6.47233i q^{98} +(-3.46553 + 1.43547i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 8 q^{6}+O(q^{10}) \) 116 * q - 8 * q^6	\( 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) \) 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

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