LMFDB - Embedded newform 804.2.j.a.499.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(499,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("804.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.15
Character	$\chi$	$=$	804.499
Dual form			804.2.j.a.775.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.411062 + 1.35315i) q^{2} -1.00000 q^{3} +(-1.66206 - 1.11246i) q^{4} +0.264773i q^{5} +(0.411062 - 1.35315i) q^{6} +(-0.135503 + 0.234697i) q^{7} +(2.18854 - 1.79173i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.411062 + 1.35315i) q^{2} -1.00000 q^{3} +(-1.66206 - 1.11246i) q^{4} +0.264773i q^{5} +(0.411062 - 1.35315i) q^{6} +(-0.135503 + 0.234697i) q^{7} +(2.18854 - 1.79173i) q^{8} +1.00000 q^{9} +(-0.358279 - 0.108838i) q^{10} +(0.751460 - 1.30157i) q^{11} +(1.66206 + 1.11246i) q^{12} +(-0.859489 + 0.496226i) q^{13} +(-0.261882 - 0.279831i) q^{14} -0.264773i q^{15} +(1.52486 + 3.69794i) q^{16} +(1.75421 + 3.03838i) q^{17} +(-0.411062 + 1.35315i) q^{18} +(-6.01588 + 3.47327i) q^{19} +(0.294550 - 0.440068i) q^{20} +(0.135503 - 0.234697i) q^{21} +(1.45232 + 1.55187i) q^{22} +(-1.36375 + 0.787364i) q^{23} +(-2.18854 + 1.79173i) q^{24} +4.92990 q^{25} +(-0.318168 - 1.36700i) q^{26} -1.00000 q^{27} +(0.486304 - 0.239339i) q^{28} +(-2.13180 + 3.69238i) q^{29} +(0.358279 + 0.108838i) q^{30} +(-0.419440 + 0.726491i) q^{31} +(-5.63070 + 0.543290i) q^{32} +(-0.751460 + 1.30157i) q^{33} +(-4.83248 + 1.12475i) q^{34} +(-0.0621415 - 0.0358774i) q^{35} +(-1.66206 - 1.11246i) q^{36} +(3.43401 + 5.94788i) q^{37} +(-2.22698 - 9.56815i) q^{38} +(0.859489 - 0.496226i) q^{39} +(0.474402 + 0.579467i) q^{40} +(-8.20489 - 4.73710i) q^{41} +(0.261882 + 0.279831i) q^{42} -6.70100 q^{43} +(-2.69691 + 1.32731i) q^{44} +0.264773i q^{45} +(-0.504838 - 2.16903i) q^{46} +(-10.3897 - 5.99851i) q^{47} +(-1.52486 - 3.69794i) q^{48} +(3.46328 + 5.99857i) q^{49} +(-2.02649 + 6.67091i) q^{50} +(-1.75421 - 3.03838i) q^{51} +(1.98055 + 0.131392i) q^{52} -4.07367i q^{53} +(0.411062 - 1.35315i) q^{54} +(0.344620 + 0.198966i) q^{55} +(0.123961 + 0.756428i) q^{56} +(6.01588 - 3.47327i) q^{57} +(-4.12006 - 4.40245i) q^{58} -1.35341i q^{59} +(-0.294550 + 0.440068i) q^{60} +(-12.3123 + 7.10852i) q^{61} +(-0.810639 - 0.866199i) q^{62} +(-0.135503 + 0.234697i) q^{63} +(1.57941 - 7.84254i) q^{64} +(-0.131387 - 0.227570i) q^{65} +(-1.45232 - 1.55187i) q^{66} +(2.59693 + 7.76247i) q^{67} +(0.464483 - 7.00144i) q^{68} +(1.36375 - 0.787364i) q^{69} +(0.0740918 - 0.0693393i) q^{70} +(3.35364 + 1.93622i) q^{71} +(2.18854 - 1.79173i) q^{72} +(0.753239 + 1.30465i) q^{73} +(-9.46000 + 2.20180i) q^{74} -4.92990 q^{75} +(13.8626 + 0.919661i) q^{76} +(0.203649 + 0.352731i) q^{77} +(0.318168 + 1.36700i) q^{78} +(-5.31673 + 9.20885i) q^{79} +(-0.979117 + 0.403743i) q^{80} +1.00000 q^{81} +(9.78275 - 9.15525i) q^{82} +(-9.69920 + 5.59984i) q^{83} +(-0.486304 + 0.239339i) q^{84} +(-0.804481 + 0.464467i) q^{85} +(2.75453 - 9.06749i) q^{86} +(2.13180 - 3.69238i) q^{87} +(-0.687455 - 4.19494i) q^{88} -3.57586 q^{89} +(-0.358279 - 0.108838i) q^{90} -0.268960i q^{91} +(3.14255 + 0.208480i) q^{92} +(0.419440 - 0.726491i) q^{93} +(12.3877 - 11.5932i) q^{94} +(-0.919630 - 1.59285i) q^{95} +(5.63070 - 0.543290i) q^{96} +(9.74602 - 5.62687i) q^{97} +(-9.54062 + 2.22057i) q^{98} +(0.751460 - 1.30157i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.411062	+	1.35315i	−0.290665	+	0.956825i
$2$	−0.411062	+	1.35315i	−0.290665	+	0.956825i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.66206	−	1.11246i	−0.831028	−	0.556230i
$5$			0.264773i			0.118410i	0.998246	+	0.0592051i	$0.0188566\pi$
$5$			0.264773i			0.118410i	−0.998246	+	0.0592051i	$0.981143\pi$
$6$	0.411062	−	1.35315i	0.167815	−	0.552423i
$7$	−0.135503	+	0.234697i	−0.0512151	+	0.0887072i	−0.890496	−	0.454990i	$-0.849643\pi$
$7$	−0.135503	+	0.234697i	−0.0512151	+	0.0887072i	0.839281	+	0.543697i	$0.182976\pi$
$8$	2.18854	−	1.79173i	0.773766	−	0.633472i
$9$	1.00000			0.333333
$10$	−0.358279	−	0.108838i	−0.113298	−	0.0344177i
$11$	0.751460	−	1.30157i	0.226574	−	0.392437i	−0.730217	−	0.683216i	$-0.760581\pi$
$11$	0.751460	−	1.30157i	0.226574	−	0.392437i	0.956790	+	0.290778i	$0.0939143\pi$
$12$	1.66206	+	1.11246i	0.479794	+	0.321140i
$13$	−0.859489	+	0.496226i	−0.238379	+	0.137628i	−0.614432	−	0.788970i	$-0.710615\pi$
$13$	−0.859489	+	0.496226i	−0.238379	+	0.137628i	0.376052	+	0.926598i	$0.377281\pi$
$14$	−0.261882	−	0.279831i	−0.0699909	−	0.0747880i
$15$		−	0.264773i		−	0.0683641i
$16$	1.52486	+	3.69794i	0.381216	+	0.924486i
$17$	1.75421	+	3.03838i	0.425458	+	0.736914i	0.996463	−	0.0840319i	$-0.0267798\pi$
$17$	1.75421	+	3.03838i	0.425458	+	0.736914i	−0.571005	+	0.820946i	$0.693446\pi$
$18$	−0.411062	+	1.35315i	−0.0968882	+	0.318942i
$19$	−6.01588	+	3.47327i	−1.38014	+	0.796823i	−0.992175	−	0.124851i	$-0.960155\pi$
$19$	−6.01588	+	3.47327i	−1.38014	+	0.796823i	−0.387963	+	0.921675i	$0.626821\pi$
$20$	0.294550	−	0.440068i	0.0658633	−	0.0984022i
$21$	0.135503	−	0.234697i	0.0295691	−	0.0512151i
$22$	1.45232	+	1.55187i	0.309637	+	0.330859i
$23$	−1.36375	+	0.787364i	−0.284362	+	0.164177i	−0.635397	−	0.772186i	$-0.719163\pi$
$23$	−1.36375	+	0.787364i	−0.284362	+	0.164177i	0.351034	+	0.936363i	$0.385830\pi$
$24$	−2.18854	+	1.79173i	−0.446734	+	0.365735i
$25$	4.92990			0.985979
$26$	−0.318168	−	1.36700i	−0.0623978	−	0.268091i
$27$	−1.00000			−0.192450
$28$	0.486304	−	0.239339i	0.0919029	−	0.0452308i
$29$	−2.13180	+	3.69238i	−0.395865	+	0.685658i	−0.993211	−	0.116326i	$-0.962888\pi$
$29$	−2.13180	+	3.69238i	−0.395865	+	0.685658i	0.597346	+	0.801983i	$0.296222\pi$
$30$	0.358279	+	0.108838i	0.0654125	+	0.0198710i
$31$	−0.419440	+	0.726491i	−0.0753336	+	0.130482i	−0.901231	−	0.433338i	$-0.857335\pi$
$31$	−0.419440	+	0.726491i	−0.0753336	+	0.130482i	0.825898	+	0.563820i	$0.190669\pi$
$32$	−5.63070	+	0.543290i	−0.995377	+	0.0960411i
$33$	−0.751460	+	1.30157i	−0.130812	+	0.226574i
$34$	−4.83248	+	1.12475i	−0.828764	+	0.192894i
$35$	−0.0621415	−	0.0358774i	−0.0105038	−	0.00606439i
$36$	−1.66206	−	1.11246i	−0.277009	−	0.185410i
$37$	3.43401	+	5.94788i	0.564548	+	0.977826i	0.997092	+	0.0762129i	$0.0242829\pi$
$37$	3.43401	+	5.94788i	0.564548	+	0.977826i	−0.432543	+	0.901613i	$0.642384\pi$
$38$	−2.22698	−	9.56815i	−0.361263	−	1.55216i
$39$	0.859489	−	0.496226i	0.137628	−	0.0794598i
$40$	0.474402	+	0.579467i	0.0750095	+	0.0916217i
$41$	−8.20489	−	4.73710i	−1.28139	−	0.739810i	−0.304287	−	0.952580i	$-0.598418\pi$
$41$	−8.20489	−	4.73710i	−1.28139	−	0.739810i	−0.977102	+	0.212770i	$0.931751\pi$
$42$	0.261882	+	0.279831i	0.0404092	+	0.0431789i
$43$	−6.70100			−1.02189			−0.510947	−	0.859612i	$-0.670705\pi$
$43$	−6.70100			−1.02189			−0.510947	+	0.859612i	$0.670705\pi$
$44$	−2.69691	+	1.32731i	−0.406574	+	0.200099i
$45$			0.264773i			0.0394701i
$46$	−0.504838	−	2.16903i	−0.0744343	−	0.319805i
$47$	−10.3897	−	5.99851i	−1.51550	−	0.874973i	−0.999835	−	0.0181816i	$-0.994212\pi$
$47$	−10.3897	−	5.99851i	−1.51550	−	0.874973i	−0.515663	−	0.856791i	$-0.672454\pi$
$48$	−1.52486	−	3.69794i	−0.220095	−	0.533752i
$49$	3.46328	+	5.99857i	0.494754	+	0.856939i
$50$	−2.02649	+	6.67091i	−0.286589	+	0.943409i
$51$	−1.75421	−	3.03838i	−0.245638	−	0.425458i
$52$	1.98055	+	0.131392i	0.274653	+	0.0182208i
$53$		−	4.07367i		−	0.559562i	−0.960064	−	0.279781i	$-0.909738\pi$
$53$		−	4.07367i		−	0.559562i	0.960064	−	0.279781i	$-0.0902619\pi$
$54$	0.411062	−	1.35315i	0.0559384	−	0.184141i
$55$	0.344620	+	0.198966i	0.0464685	+	0.0268286i
$56$	0.123961	+	0.756428i	0.0165650	+	0.101082i
$57$	6.01588	−	3.47327i	0.796823	−	0.460046i
$58$	−4.12006	−	4.40245i	−0.540991	−	0.578070i
$59$		−	1.35341i		−	0.176199i	−0.996112	−	0.0880997i	$-0.971921\pi$
$59$		−	1.35341i		−	0.176199i	0.996112	−	0.0880997i	$-0.0280794\pi$
$60$	−0.294550	+	0.440068i	−0.0380262	+	0.0568125i
$61$	−12.3123	+	7.10852i	−1.57643	+	0.910152i	−0.581078	+	0.813848i	$0.697369\pi$
$61$	−12.3123	+	7.10852i	−1.57643	+	0.910152i	−0.995352	+	0.0963041i	$0.969298\pi$
$62$	−0.810639	−	0.866199i	−0.102951	−	0.110007i
$63$	−0.135503	+	0.234697i	−0.0170717	+	0.0295691i
$64$	1.57941	−	7.84254i	0.197427	−	0.980318i
$65$	−0.131387	−	0.227570i	−0.0162966	−	0.0282265i
$66$	−1.45232	−	1.55187i	−0.178769	−	0.191021i
$67$	2.59693	+	7.76247i	0.317265	+	0.948337i
$67$	2.59693	+	7.76247i	0.317265	+	0.948337i
$68$	0.464483	−	7.00144i	0.0563268	−	0.849049i
$69$	1.36375	−	0.787364i	0.164177	−	0.0947875i
$70$	0.0740918	−	0.0693393i	0.00885566	−	0.00828763i
$71$	3.35364	+	1.93622i	0.398004	+	0.229788i	0.685622	−	0.727958i	$-0.259530\pi$
$71$	3.35364	+	1.93622i	0.398004	+	0.229788i	−0.287619	+	0.957745i	$0.592864\pi$
$72$	2.18854	−	1.79173i	0.257922	−	0.211157i
$73$	0.753239	+	1.30465i	0.0881600	+	0.152698i	0.906733	−	0.421704i	$-0.138568\pi$
$73$	0.753239	+	1.30465i	0.0881600	+	0.152698i	−0.818573	+	0.574402i	$0.805235\pi$
$74$	−9.46000	+	2.20180i	−1.09970	+	0.255954i
$75$	−4.92990			−0.569255
$76$	13.8626	+	0.919661i	1.59015	+	0.105492i
$77$	0.203649	+	0.352731i	0.0232080	+	0.0401974i
$78$	0.318168	+	1.36700i	0.0360254	+	0.154782i
$79$	−5.31673	+	9.20885i	−0.598179	+	1.03608i	0.394910	+	0.918720i	$0.370776\pi$
$79$	−5.31673	+	9.20885i	−0.598179	+	1.03608i	−0.993090	+	0.117357i	$0.962558\pi$
$80$	−0.979117	+	0.403743i	−0.109469	+	0.0451398i
$81$	1.00000			0.111111
$82$	9.78275	−	9.15525i	1.08032	−	1.01103i
$83$	−9.69920	+	5.59984i	−1.06463	+	0.614662i	−0.926708	−	0.375782i	$-0.877374\pi$
$83$	−9.69920	+	5.59984i	−1.06463	+	0.614662i	−0.137918	+	0.990444i	$0.544041\pi$
$84$	−0.486304	+	0.239339i	−0.0530602	+	0.0261140i
$85$	−0.804481	+	0.464467i	−0.0872582	+	0.0503785i
$86$	2.75453	−	9.06749i	0.297028	−	0.977773i
$87$	2.13180	−	3.69238i	0.228553	−	0.395865i
$88$	−0.687455	−	4.19494i	−0.0732830	−	0.447182i
$89$	−3.57586			−0.379041			−0.189520	−	0.981877i	$-0.560693\pi$
$89$	−3.57586			−0.379041			−0.189520	+	0.981877i	$0.560693\pi$
$90$	−0.358279	−	0.108838i	−0.0377659	−	0.0114726i
$91$		−	0.268960i		−	0.0281946i
$92$	3.14255	+	0.208480i	0.327633	+	0.0217355i
$93$	0.419440	−	0.726491i	0.0434939	−	0.0753336i
$94$	12.3877	−	11.5932i	1.27770	−	1.19574i
$95$	−0.919630	−	1.59285i	−0.0943520	−	0.163422i
$96$	5.63070	−	0.543290i	0.574681	−	0.0554493i
$97$	9.74602	−	5.62687i	0.989558	−	0.571322i	0.0844159	−	0.996431i	$-0.473098\pi$
$97$	9.74602	−	5.62687i	0.989558	−	0.571322i	0.905142	+	0.425109i	$0.139764\pi$
$98$	−9.54062	+	2.22057i	−0.963748	+	0.224311i
$99$	0.751460	−	1.30157i	0.0755245	−	0.130812i
$100$	−8.19376	−	5.48432i	−0.819376	−	0.548432i
$101$	9.33645	+	5.39040i	0.929012	+	0.536365i	0.886499	−	0.462731i	$-0.153130\pi$
$101$	9.33645	+	5.39040i	0.929012	+	0.536365i	0.0425130	+	0.999096i	$0.486464\pi$
$102$	4.83248	−	1.12475i	0.478487	−	0.111367i
$103$	−5.70949	−	3.29638i	−0.562573	−	0.324802i	0.191605	−	0.981472i	$-0.438631\pi$
$103$	−5.70949	−	3.29638i	−0.562573	−	0.324802i	−0.754178	+	0.656670i	$0.771964\pi$
$104$	−0.991922	+	2.62598i	−0.0972660	+	0.257499i
$105$	0.0621415	+	0.0358774i	0.00606439	+	0.00350128i
$106$	5.51231	+	1.67453i	0.535403	+	0.162645i
$107$		−	4.50016i		−	0.435047i	−0.976055	−	0.217524i	$-0.930202\pi$
$107$		−	4.50016i		−	0.435047i	0.976055	−	0.217524i	$-0.0697979\pi$
$108$	1.66206	+	1.11246i	0.159931	+	0.107047i
$109$			1.38215i			0.132386i	0.997807	+	0.0661929i	$0.0210853\pi$
$109$			1.38215i			0.132386i	−0.997807	+	0.0661929i	$0.978915\pi$
$110$	−0.410892	+	0.384537i	−0.0391771	+	0.0366641i
$111$	−3.43401	−	5.94788i	−0.325942	−	0.564548i
$112$	−1.07452	−	0.143200i	−0.101533	−	0.0135311i
$113$	2.58877	+	1.49463i	0.243531	+	0.140603i	0.616799	−	0.787121i	$-0.288429\pi$
$113$	2.58877	+	1.49463i	0.243531	+	0.140603i	−0.373267	+	0.927724i	$0.621763\pi$
$114$	2.22698	+	9.56815i	0.208575	+	0.896140i
$115$	−0.208473	−	0.361086i	−0.0194402	−	0.0336714i
$116$	7.65079	−	3.76540i	0.710358	−	0.349609i
$117$	−0.859489	+	0.496226i	−0.0794598	+	0.0458761i
$118$	1.83138	+	0.556336i	0.168592	+	0.0512149i
$119$	−0.950798			−0.0871595
$120$	−0.474402	−	0.579467i	−0.0433068	−	0.0528978i
$121$	4.37062	+	7.57013i	0.397329	+	0.688194i
$122$	−4.55780	−	19.5825i	−0.412644	−	1.77292i
$123$	8.20489	+	4.73710i	0.739810	+	0.427130i
$124$	1.50532	−	0.740858i	0.135182	−	0.0665310i
$125$			2.62917i			0.235160i
$126$	−0.261882	−	0.279831i	−0.0233303	−	0.0249293i
$127$	13.1015	+	7.56416i	1.16257	+	0.671210i	0.951919	−	0.306351i	$-0.0991080\pi$
$127$	13.1015	+	7.56416i	1.16257	+	0.671210i	0.210652	+	0.977561i	$0.432441\pi$
$128$	9.96294	+	5.36096i	0.880608	+	0.473846i
$129$	6.70100			0.589990
$130$	0.361945	−	0.0842423i	0.0317447	−	0.00738854i
$131$			4.02225i			0.351426i	0.984441	+	0.175713i	$0.0562230\pi$
$131$			4.02225i			0.351426i	−0.984441	+	0.175713i	$0.943777\pi$
$132$	2.69691	−	1.32731i	0.234736	−	0.115527i
$133$		−	1.88255i		−	0.163238i
$134$	−11.5713	+	0.323189i	−0.999610	+	0.0279193i
$135$		−	0.264773i		−	0.0227880i
$136$	9.28310	+	3.50654i	0.796019	+	0.300684i
$137$		−	1.59001i		−	0.135844i	−0.997691	−	0.0679219i	$-0.978363\pi$
$137$		−	1.59001i		−	0.135844i	0.997691	−	0.0679219i	$-0.0216369\pi$
$138$	0.504838	+	2.16903i	0.0429747	+	0.184640i
$139$	10.7761			0.914019			0.457009	−	0.889462i	$-0.348921\pi$
$139$	10.7761			0.914019			0.457009	+	0.889462i	$0.348921\pi$
$140$	0.0633705	+	0.128760i	0.00535579	+	0.0108822i
$141$	10.3897	+	5.99851i	0.874973	+	0.505166i
$142$	−3.99856	+	3.74208i	−0.335552	+	0.314029i
$143$			1.49158i			0.124732i
$144$	1.52486	+	3.69794i	0.127072	+	0.308162i
$145$	−0.977643	−	0.564443i	−0.0811889	−	0.0468744i
$146$	−2.07502	+	0.482958i	−0.171730	+	0.0399699i
$147$	−3.46328	−	5.99857i	−0.285646	−	0.494754i
$148$	0.909266	−	13.7059i	0.0747412	−	1.12662i
$149$	−13.4189			−1.09932			−0.549660	−	0.835389i	$-0.685243\pi$
$149$	−13.4189			−1.09932			−0.549660	+	0.835389i	$0.685243\pi$
$150$	2.02649	−	6.67091i	0.165462	−	0.544678i
$151$	−2.14543	+	1.23867i	−0.174593	+	0.100801i	−0.584750	−	0.811214i	$-0.698807\pi$
$151$	−2.14543	+	1.23867i	−0.174593	+	0.100801i	0.410157	+	0.912015i	$0.365474\pi$
$152$	−6.94284	+	18.3802i	−0.563139	+	1.49083i
$153$	1.75421	+	3.03838i	0.141819	+	0.245638i
$154$	−0.561012	+	0.130575i	−0.0452077	+	0.0105220i
$155$	−0.192355	−	0.111056i	−0.0154503	−	0.00892026i
$156$	−1.98055	−	0.131392i	−0.158571	−	0.0105198i
$157$	−6.79981	−	11.7776i	−0.542684	−	0.939956i	−0.998749	−	0.0500094i	$-0.984075\pi$
$157$	−6.79981	−	11.7776i	−0.542684	−	0.939956i	0.456065	−	0.889946i	$-0.349258\pi$
$158$	−10.2755	−	10.9798i	−0.817475	−	0.873504i
$159$			4.07367i			0.323063i
$160$	−0.143849	−	1.49086i	−0.0113722	−	0.117863i
$161$		−	0.426759i		−	0.0336333i
$162$	−0.411062	+	1.35315i	−0.0322961	+	0.106314i
$163$	10.3003	+	5.94691i	0.806786	+	0.465798i	0.845838	−	0.533439i	$-0.179101\pi$
$163$	10.3003	+	5.94691i	0.806786	+	0.465798i	−0.0390528	+	0.999237i	$0.512434\pi$
$164$	8.36716	+	17.0009i	0.653365	+	1.32755i
$165$	−0.344620	−	0.198966i	−0.0268286	−	0.0154895i
$166$	−3.59047	−	15.4264i	−0.278675	−	1.19732i
$167$	2.15345	+	1.24329i	0.166639	+	0.0962090i	0.581000	−	0.813904i	$-0.302662\pi$
$167$	2.15345	+	1.24329i	0.166639	+	0.0962090i	−0.414361	+	0.910113i	$0.635995\pi$
$168$	−0.123961	−	0.756428i	−0.00956382	−	0.0583597i
$169$	−6.00752	+	10.4053i	−0.462117	+	0.800410i
$170$	−0.297805	−	1.27951i	−0.0228406	−	0.0981341i
$171$	−6.01588	+	3.47327i	−0.460046	+	0.265608i
$172$	11.1374	+	7.45460i	0.849222	+	0.568408i
$173$	−3.13698	−	5.43341i	−0.238500	−	0.413094i	0.721784	−	0.692118i	$-0.243322\pi$
$173$	−3.13698	−	5.43341i	−0.238500	−	0.413094i	−0.960284	+	0.279024i	$0.909989\pi$
$174$	4.12006	+	4.40245i	0.312341	+	0.333749i
$175$	−0.668013	+	1.15703i	−0.0504971	+	0.0874635i
$176$	5.95899	+	0.794147i	0.449176	+	0.0598611i
$177$			1.35341i			0.101729i
$178$	1.46990	−	4.83870i	0.110174	−	0.362676i
$179$	15.3648			1.14842			0.574210	−	0.818708i	$-0.305309\pi$
$179$	15.3648			1.14842			0.574210	+	0.818708i	$0.305309\pi$
$180$	0.294550	−	0.440068i	0.0219544	−	0.0328007i
$181$	0.892907	−	1.54656i	0.0663693	−	0.114955i	−0.830931	−	0.556375i	$-0.812192\pi$
$181$	0.892907	−	1.54656i	0.0663693	−	0.114955i	0.897301	+	0.441420i	$0.145525\pi$
$182$	0.363944	+	0.110559i	0.0269773	+	0.00819518i
$183$	12.3123	−	7.10852i	0.910152	−	0.525477i
$184$	−1.57389	+	4.16666i	−0.116029	+	0.307170i
$185$	−1.57484	+	0.909234i	−0.115785	+	0.0668482i
$186$	0.810639	+	0.866199i	0.0594389	+	0.0635128i
$187$	5.27286			0.385590
$188$	10.5952	+	21.5280i	0.772735	+	1.57009i
$189$	0.135503	−	0.234697i	0.00985636	−	0.0170717i
$190$	2.53339	−	0.589643i	0.183791	−	0.0427772i
$191$	4.20479	+	7.28292i	0.304248	+	0.526973i	0.977094	−	0.212810i	$-0.0682614\pi$
$191$	4.20479	+	7.28292i	0.304248	+	0.526973i	−0.672845	+	0.739783i	$0.734928\pi$
$192$	−1.57941	+	7.84254i	−0.113984	+	0.565987i
$193$	−22.7797			−1.63972			−0.819860	−	0.572564i	$-0.805949\pi$
$193$	−22.7797			−1.63972			−0.819860	+	0.572564i	$0.805949\pi$
$194$	3.60780	+	15.5009i	0.259025	+	1.11290i
$195$	0.131387	+	0.227570i	0.00940884	+	0.0162966i
$196$	0.917015	−	13.8227i	0.0655011	−	0.987338i
$197$	−1.52264	−	0.879097i	−0.108484	−	0.0626331i	0.444776	−	0.895642i	$-0.353283\pi$
$197$	−1.52264	−	0.879097i	−0.108484	−	0.0626331i	−0.553260	+	0.833009i	$0.686616\pi$
$198$	1.45232	+	1.55187i	0.103212	+	0.110286i
$199$	23.9212	−	13.8109i	1.69573	−	0.979030i	0.746005	−	0.665940i	$-0.231969\pi$
$199$	23.9212	−	13.8109i	1.69573	−	0.979030i	0.949724	−	0.313090i	$-0.101364\pi$
$200$	10.7893	−	8.83304i	0.762917	−	0.624590i
$201$	−2.59693	−	7.76247i	−0.183173	−	0.547523i
$202$	−11.1319	+	10.4179i	−0.783239	+	0.732999i
$203$	−0.577728	−	1.00065i	−0.0405485	−	0.0702321i
$204$	−0.464483	+	7.00144i	−0.0325203	+	0.490199i
$205$	1.25426	−	2.17244i	0.0876011	−	0.151730i
$206$	6.80746	−	6.37081i	0.474299	−	0.443876i
$207$	−1.36375	+	0.787364i	−0.0947875	+	0.0547256i
$208$	−3.14562	−	2.42167i	−0.218109	−	0.167912i
$209$			10.4401i			0.722157i
$210$	−0.0740918	+	0.0693393i	−0.00511282	+	0.00478487i
$211$	−10.8677	+	6.27445i	−0.748160	+	0.431951i	−0.825029	−	0.565091i	$-0.808841\pi$
$211$	−10.8677	+	6.27445i	−0.748160	+	0.431951i	0.0768684	+	0.997041i	$0.475508\pi$
$212$	−4.53180	+	6.77067i	−0.311245	+	0.465012i
$213$	−3.35364	−	1.93622i	−0.229788	−	0.132668i
$214$	6.08942	+	1.84985i	0.416264	+	0.126453i
$215$		−	1.77425i		−	0.121003i
$216$	−2.18854	+	1.79173i	−0.148911	+	0.121912i
$217$	−0.113670	−	0.196883i	−0.00771644	−	0.0133653i
$218$	−1.87026	−	0.568149i	−0.126670	−	0.0384799i
$219$	−0.753239	−	1.30465i	−0.0508992	−	0.0881600i
$220$	−0.351435	−	0.714070i	−0.0236938	−	0.0481426i
$221$	−3.01544	−	1.74097i	−0.202841	−	0.117110i
$222$	9.46000	−	2.20180i	0.634914	−	0.147775i
$223$			20.5523i			1.37628i	0.725576	+	0.688142i	$0.241573\pi$
$223$			20.5523i			1.37628i	−0.725576	+	0.688142i	$0.758427\pi$
$224$	0.635466	−	1.39513i	0.0424589	−	0.0932159i
$225$	4.92990			0.328660
$226$	−3.08661	+	2.88862i	−0.205318	+	0.192148i
$227$	1.64227	+	0.948166i	0.109001	+	0.0629320i	0.553510	−	0.832843i	$-0.313288\pi$
$227$	1.64227	+	0.948166i	0.109001	+	0.0629320i	−0.444508	+	0.895775i	$0.646622\pi$
$228$	−13.8626	−	0.919661i	−0.918074	−	0.0609061i
$229$	−11.2710	+	6.50731i	−0.744809	+	0.430015i	−0.823815	−	0.566859i	$-0.808159\pi$
$229$	−11.2710	+	6.50731i	−0.744809	+	0.430015i	0.0790065	+	0.996874i	$0.474825\pi$
$230$	0.574300	−	0.133668i	0.0378682	−	0.00881378i
$231$	−0.203649	−	0.352731i	−0.0133991	−	0.0232080i
$232$	1.95022	+	11.9005i	0.128038	+	0.781308i
$233$	5.01455	+	2.89515i	0.328514	+	0.189668i	0.655181	−	0.755472i	$-0.272592\pi$
$233$	5.01455	+	2.89515i	0.328514	+	0.189668i	−0.326667	+	0.945139i	$0.605926\pi$
$234$	−0.318168	−	1.36700i	−0.0207993	−	0.0893637i
$235$	1.58825	−	2.75092i	0.103606	−	0.179450i
$236$	−1.50562	+	2.24945i	−0.0980074	+	0.146427i
$237$	5.31673	−	9.20885i	0.345359	−	0.598179i
$238$	0.390837	−	1.28658i	0.0253342	−	0.0833964i
$239$	−1.82097	+	3.15402i	−0.117789	+	0.204016i	−0.918891	−	0.394511i	$-0.870914\pi$
$239$	−1.82097	+	3.15402i	−0.117789	+	0.204016i	0.801102	+	0.598528i	$0.204247\pi$
$240$	0.979117	−	0.403743i	0.0632017	−	0.0260615i
$241$	1.64815			0.106167			0.0530834	−	0.998590i	$-0.483095\pi$
$241$	1.64815			0.106167			0.0530834	+	0.998590i	$0.483095\pi$
$242$	−12.0402	+	2.80233i	−0.773970	+	0.180141i
$243$	−1.00000			−0.0641500
$244$	28.3717	+	1.88221i	1.81631	+	0.120496i
$245$	−1.58826	+	0.916983i	−0.101470	+	0.0585839i
$246$	−9.78275	+	9.15525i	−0.623725	+	0.583718i
$247$	3.44706	−	5.97048i	0.219331	−	0.379892i
$248$	0.383714	+	2.34148i	0.0243659	+	0.148684i
$249$	9.69920	−	5.59984i	0.614662	−	0.354875i
$250$	−3.55767	−	1.08075i	−0.225007	−	0.0683527i
$251$	0.000837772		0.00145106i	5.28797e−5		9.15903e-5i	0.866052	−	0.499954i	$-0.166650\pi$
$251$	0.000837772		0.00145106i	5.28797e−5		9.15903e-5i	−0.865999	+	0.500046i	$0.833317\pi$
$252$	0.486304	−	0.239339i	0.0306343	−	0.0150769i
$253$			2.36669i			0.148792i
$254$	−15.6210	+	14.6190i	−0.980149	+	0.917279i
$255$	0.804481	−	0.464467i	0.0503785	−	0.0290861i
$256$	−11.3496	+	11.2777i	−0.709349	+	0.704857i
$257$	13.3489	−	23.1209i	0.832681	−	1.44225i	−0.0632244	−	0.997999i	$-0.520138\pi$
$257$	13.3489	−	23.1209i	0.832681	−	1.44225i	0.895905	−	0.444246i	$-0.146528\pi$
$258$	−2.75453	+	9.06749i	−0.171489	+	0.564518i
$259$	−1.86127			−0.115654
$260$	−0.0347891	+	0.524397i	−0.00215753	+	0.0325217i
$261$	−2.13180	+	3.69238i	−0.131955	+	0.228553i
$262$	−5.44273	−	1.65339i	−0.336253	−	0.102147i
$263$		−	30.4038i		−	1.87478i	−0.348280	−	0.937390i	$-0.613234\pi$
$263$		−	30.4038i		−	1.87478i	0.348280	−	0.937390i	$-0.386766\pi$
$264$	0.687455	+	4.19494i	0.0423099	+	0.258181i
$265$	1.07860			0.0662578
$266$	2.54738	+	0.773844i	0.156190	+	0.0474474i
$267$	3.57586			0.218839
$268$	4.31921	−	15.7906i	0.263837	−	0.964567i
$269$	−12.1032			−0.737947			−0.368974	−	0.929440i	$-0.620291\pi$
$269$	−12.1032			−0.737947			−0.368974	+	0.929440i	$0.620291\pi$
$270$	0.358279	+	0.108838i	0.0218042	+	0.00662368i
$271$	19.7568			1.20014			0.600070	−	0.799947i	$-0.295139\pi$
$271$	19.7568			1.20014			0.600070	+	0.799947i	$0.295139\pi$
$272$	−8.56082	+	11.1201i	−0.519076	+	0.674253i
$273$			0.268960i			0.0162782i
$274$	2.15153	+	0.653593i	0.129979	+	0.0394850i
$275$	3.70462	−	6.41659i	0.223397	−	0.386935i
$276$	−3.14255	−	0.208480i	−0.189159	−	0.0125490i
$277$	−19.0612			−1.14527			−0.572637	−	0.819809i	$-0.694080\pi$
$277$	−19.0612			−1.14527			−0.572637	+	0.819809i	$0.694080\pi$
$278$	−4.42965	+	14.5818i	−0.265673	+	0.874556i
$279$	−0.419440	+	0.726491i	−0.0251112	+	0.0434939i
$280$	−0.200282	+	0.0328216i	−0.0119691	+	0.00196147i
$281$	23.9867	−	13.8487i	1.43093	−	0.826146i	0.433735	−	0.901040i	$-0.357195\pi$
$281$	23.9867	−	13.8487i	1.43093	−	0.826146i	0.997191	+	0.0748944i	$0.0238620\pi$
$282$	−12.3877	+	11.5932i	−0.737679	+	0.690362i
$283$		−	5.38099i		−	0.319866i	−0.987128	−	0.159933i	$-0.948872\pi$
$283$		−	5.38099i		−	0.319866i	0.987128	−	0.159933i	$-0.0511279\pi$
$284$	−3.41996	−	6.94890i	−0.202937	−	0.412342i
$285$	0.919630	+	1.59285i	0.0544742	+	0.0943520i
$286$	−2.01833	−	0.613130i	−0.119347	−	0.0362551i
$287$	2.22357	−	1.28378i	0.131253	−	0.0757790i
$288$	−5.63070	+	0.543290i	−0.331792	+	0.0320137i
$289$	2.34551	−	4.06255i	0.137971	−	0.238974i
$290$	1.16565	−	1.09088i	0.0684493	−	0.0640588i
$291$	−9.74602	+	5.62687i	−0.571322	+	0.329853i
$292$	0.199444	−	3.00635i	0.0116716	−	0.175933i
$293$	−2.41748			−0.141231			−0.0706153	−	0.997504i	$-0.522496\pi$
$293$	−2.41748			−0.141231			−0.0706153	+	0.997504i	$0.522496\pi$
$294$	9.54062	−	2.22057i	0.556420	−	0.129506i
$295$	0.358347			0.0208638
$296$	18.1725	+	6.86436i	1.05625	+	0.398983i
$297$	−0.751460	+	1.30157i	−0.0436041	+	0.0755245i
$298$	5.51600	−	18.1579i	0.319533	−	1.05186i
$299$	0.781421	−	1.35346i	0.0451907	−	0.0782727i
$300$	8.19376	+	5.48432i	0.473067	+	0.316637i
$301$	0.908003	−	1.57271i	0.0523364	−	0.0906493i
$302$	−0.794201	−	3.41227i	−0.0457011	−	0.196354i
$303$	−9.33645	−	5.39040i	−0.536365	−	0.309671i
$304$	−22.0174	−	16.9501i	−1.26278	−	0.972158i
$305$	−1.88214	−	3.25997i	−0.107771	−	0.186665i
$306$	−4.83248	+	1.12475i	−0.276255	+	0.0642979i
$307$	−8.14044	+	4.69988i	−0.464599	+	0.268237i	−0.713976	−	0.700170i	$-0.753108\pi$
$307$	−8.14044	+	4.69988i	−0.464599	+	0.268237i	0.249377	+	0.968407i	$0.419774\pi$
$308$	0.0539228	−	0.812811i	0.00307253	−	0.0463142i
$309$	5.70949	+	3.29638i	0.324802	+	0.187524i
$310$	0.229346	−	0.214635i	0.0130260	−	0.0121905i
$311$	4.33041			0.245555			0.122778	−	0.992434i	$-0.460820\pi$
$311$	4.33041			0.245555			0.122778	+	0.992434i	$0.460820\pi$
$312$	0.991922	−	2.62598i	0.0561566	−	0.148667i
$313$		−	16.4951i		−	0.932356i	−0.884691	−	0.466178i	$-0.845631\pi$
$313$		−	16.4951i		−	0.932356i	0.884691	−	0.466178i	$-0.154369\pi$
$314$	18.7321	−	4.35987i	1.05711	−	0.246041i
$315$	−0.0621415	−	0.0358774i	−0.00350128	−	0.00202146i
$316$	19.0812	−	9.39098i	1.07340	−	0.528284i
$317$	2.76164	+	4.78330i	0.155109	+	0.268657i	0.933099	−	0.359620i	$-0.117094\pi$
$317$	2.76164	+	4.78330i	0.155109	+	0.268657i	−0.777990	+	0.628277i	$0.783760\pi$
$318$	−5.51231	−	1.67453i	−0.309115	−	0.0939031i
$319$	3.20392	+	5.54935i	0.179385	+	0.310704i
$320$	2.07649	+	0.418186i	0.116080	+	0.0233773i
$321$			4.50016i			0.251175i
$322$	0.577471	+	0.175424i	0.0321812	+	0.00977602i
$323$	−21.1062	−	12.1857i	−1.17438	−	0.678029i
$324$	−1.66206	−	1.11246i	−0.0923365	−	0.0618034i
$325$	−4.23719	+	2.44634i	−0.235037	+	0.135699i
$326$	−12.2812	+	11.4934i	−0.680191	+	0.636562i
$327$		−	1.38215i		−	0.0764330i
$328$	−26.4443	+	4.33362i	−1.46014	+	0.239284i
$329$	2.81567	−	1.62563i	0.155233	−	0.0896237i
$330$	0.410892	−	0.384537i	0.0226189	−	0.0211680i
$331$	1.38336	−	2.39604i	0.0760362	−	0.131699i	−0.825500	−	0.564402i	$-0.809107\pi$
$331$	1.38336	−	2.39604i	0.0760362	−	0.131699i	0.901536	+	0.432703i	$0.142440\pi$
$332$	22.3502	+	1.48274i	1.22663	+	0.0813758i
$333$	3.43401	+	5.94788i	0.188183	+	0.325942i
$334$	−2.56757	+	2.40288i	−0.140491	+	0.131480i
$335$	−2.05529	+	0.687597i	−0.112293	+	0.0375674i
$336$	1.07452	+	0.143200i	0.0586199	+	0.00781220i
$337$	−3.41878	+	1.97383i	−0.186233	+	0.107522i	−0.590218	−	0.807244i	$-0.700958\pi$
$337$	−3.41878	+	1.97383i	−0.186233	+	0.107522i	0.403985	+	0.914766i	$0.367625\pi$
$338$	−11.6106	−	12.4063i	−0.631531	−	0.674816i
$339$	−2.58877	−	1.49463i	−0.140603	−	0.0811770i
$340$	1.85379	+	0.122983i	0.100536	+	0.00666967i
$341$	0.630384	+	1.09186i	0.0341372	+	0.0591274i
$342$	−2.22698	−	9.56815i	−0.120421	−	0.517387i
$343$	−3.77417			−0.203786
$344$	−14.6654	+	12.0064i	−0.790706	+	0.647341i
$345$	0.208473	+	0.361086i	0.0112238	+	0.0194402i
$346$	8.64174	−	2.01135i	0.464583	−	0.108131i
$347$	9.56629	−	16.5693i	0.513546	−	0.889487i	−0.486331	−	0.873775i	$-0.661665\pi$
$347$	9.56629	−	16.5693i	0.513546	−	0.889487i	0.999877	−	0.0157123i	$-0.00500159\pi$
$348$	−7.65079	+	3.76540i	−0.410126	+	0.201847i
$349$	−18.3235			−0.980834			−0.490417	−	0.871488i	$-0.663155\pi$
$349$	−18.3235			−0.980834			−0.490417	+	0.871488i	$0.663155\pi$
$350$	−1.29105	−	1.37954i	−0.0690095	−	0.0737394i
$351$	0.859489	−	0.496226i	0.0458761	−	0.0264866i
$352$	−3.52412	+	7.73700i	−0.187836	+	0.412383i
$353$	30.6203	−	17.6786i	1.62975	−	0.940937i	0.645586	−	0.763688i	$-0.276613\pi$
$353$	30.6203	−	17.6786i	1.62975	−	0.940937i	0.984166	−	0.177250i	$-0.0567200\pi$
$354$	−1.83138	−	0.556336i	−0.0973366	−	0.0295689i
$355$	−0.512660	+	0.887954i	−0.0272092	+	0.0471277i
$356$	5.94329	+	3.97801i	0.314994	+	0.210834i
$357$	0.950798			0.0503216
$358$	−6.31588	+	20.7910i	−0.333805	+	1.09884i
$359$			35.3618i			1.86633i	0.359452	+	0.933164i	$0.382964\pi$
$359$			35.3618i			1.86633i	−0.359452	+	0.933164i	$0.617036\pi$
$360$	0.474402	+	0.579467i	0.0250032	+	0.0305406i
$361$	14.6272	−	25.3351i	0.769855	−	1.33343i
$362$	1.72570	+	1.84397i	0.0907006	+	0.0969171i
$363$	−4.37062	−	7.57013i	−0.229398	−	0.397329i
$364$	−0.299207	+	0.447026i	−0.0156827	+	0.0234305i
$365$	−0.345436	+	0.199438i	−0.0180809	+	0.0104390i
$366$	4.55780	+	19.5825i	0.238240	+	1.02359i
$367$	8.86155	−	15.3487i	0.462569	−	0.801194i	−0.536519	−	0.843888i	$-0.680261\pi$
$367$	8.86155	−	15.3487i	0.462569	−	0.801194i	0.999088	+	0.0426948i	$0.0135943\pi$
$368$	−4.99117	−	3.84247i	−0.260182	−	0.200302i
$369$	−8.20489	−	4.73710i	−0.427130	−	0.246603i
$370$	−0.582978	−	2.50475i	−0.0303076	−	0.130216i
$371$	0.956080	+	0.551993i	0.0496372	+	0.0286581i
$372$	−1.50532	+	0.740858i	−0.0780474	+	0.0384117i
$373$	−17.1160	−	9.88191i	−0.886231	−	0.511666i	−0.0135232	−	0.999909i	$-0.504305\pi$
$373$	−17.1160	−	9.88191i	−0.886231	−	0.511666i	−0.872708	+	0.488243i	$0.837638\pi$
$374$	−2.16747	+	7.13500i	−0.112077	+	0.368942i
$375$		−	2.62917i		−	0.135770i
$376$	−33.4860	+	5.48760i	−1.72691	+	0.283001i
$377$		−	4.23141i		−	0.217929i
$378$	0.261882	+	0.279831i	0.0134697	+	0.0143930i
$379$	−3.58647	−	6.21194i	−0.184224	−	0.319086i	0.759091	−	0.650985i	$-0.225644\pi$
$379$	−3.58647	−	6.21194i	−0.184224	−	0.319086i	−0.943315	+	0.331899i	$0.892311\pi$
$380$	−0.243502	+	3.67045i	−0.0124914	+	0.188290i
$381$	−13.1015	−	7.56416i	−0.671210	−	0.387524i
$382$	−11.5833	+	2.69601i	−0.592656	+	0.137940i
$383$	−15.1874	−	26.3054i	−0.776041	−	1.34414i	−0.934208	−	0.356730i	$-0.883892\pi$
$383$	−15.1874	−	26.3054i	−0.776041	−	1.34414i	0.158167	−	0.987412i	$-0.449442\pi$
$384$	−9.96294	−	5.36096i	−0.508419	−	0.273575i
$385$	−0.0933937	+	0.0539209i	−0.00475979	+	0.00274806i
$386$	9.36387	−	30.8245i	0.476609	−	1.56893i
$387$	−6.70100			−0.340631
$388$	−22.4581	−	1.48989i	−1.14014	−	0.0756379i
$389$	0.580758	+	1.00590i	0.0294456	+	0.0510013i	0.880373	−	0.474283i	$-0.157292\pi$
$389$	0.580758	+	1.00590i	0.0294456	+	0.0510013i	−0.850927	+	0.525284i	$0.823959\pi$
$390$	−0.361945	+	0.0842423i	−0.0183278	+	0.00426577i
$391$	−4.78462	−	2.76240i	−0.241968	−	0.139701i
$392$	18.3273	+	6.92286i	0.925671	+	0.349657i
$393$		−	4.02225i		−	0.202896i
$394$	1.81545	−	1.69901i	0.0914613	−	0.0855947i
$395$	−2.43826	−	1.40773i	−0.122682	−	0.0708305i
$396$	−2.69691	+	1.32731i	−0.135525	+	0.0666997i
$397$	10.5427			0.529125			0.264563	−	0.964369i	$-0.414772\pi$
$397$	10.5427			0.529125			0.264563	+	0.964369i	$0.414772\pi$
$398$	8.85521	+	38.0462i	0.443871	+	1.90709i
$399$			1.88255i			0.0942453i
$400$	7.51741	+	18.2305i	0.375870	+	0.911524i
$401$		−	14.4238i		−	0.720291i	−0.932896	−	0.360145i	$-0.882727\pi$
$401$		−	14.4238i		−	0.720291i	0.932896	−	0.360145i	$-0.117273\pi$
$402$	11.5713	−	0.323189i	0.577125	−	0.0161192i
$403$		−	0.832547i		−	0.0414721i
$404$	−9.52110	−	19.3456i	−0.473692	−	0.962479i
$405$			0.264773i			0.0131567i
$406$	1.59152	−	0.370424i	0.0789859	−	0.0183839i
$407$	10.3221			0.511647
$408$	−9.28310	−	3.50654i	−0.459582	−	0.173600i
$409$	−29.0669	−	16.7818i	−1.43726	−	0.829805i	−0.439605	−	0.898191i	$-0.644882\pi$
$409$	−29.0669	−	16.7818i	−1.43726	−	0.829805i	−0.997659	+	0.0683863i	$0.978215\pi$
$410$	2.42407	+	2.59021i	0.119716	+	0.127921i
$411$			1.59001i			0.0784295i
$412$	5.82241	+	11.8304i	0.286849	+	0.582840i
$413$	0.317642	+	0.183391i	0.0156302	+	0.00902407i
$414$	−0.504838	−	2.16903i	−0.0248114	−	0.106602i
$415$	−1.48269	−	2.56809i	−0.0727822	−	0.126063i
$416$	4.56993	−	3.26105i	0.224059	−	0.159886i
$417$	−10.7761			−0.527709
$418$	−14.1271	−	4.29153i	−0.690978	−	0.209905i
$419$	25.8102	−	14.9015i	1.26091	−	0.727987i	0.287660	−	0.957732i	$-0.407123\pi$
$419$	25.8102	−	14.9015i	1.26091	−	0.727987i	0.973251	+	0.229745i	$0.0737893\pi$
$420$	−0.0633705	−	0.128760i	−0.00309216	−	0.00628286i
$421$	12.6264	+	21.8696i	0.615375	+	1.06586i	0.990319	+	0.138813i	$0.0443285\pi$
$421$	12.6264	+	21.8696i	0.615375	+	1.06586i	−0.374944	+	0.927047i	$0.622338\pi$
$422$	−4.02302	−	17.2848i	−0.195837	−	0.841411i
$423$	−10.3897	−	5.99851i	−0.505166	−	0.291658i
$424$	−7.29892	−	8.91540i	−0.354467	−	0.432970i
$425$	8.64806	+	14.9789i	0.419492	+	0.726582i
$426$	3.99856	−	3.74208i	0.193731	−	0.181305i
$427$		−	3.85289i		−	0.186454i
$428$	−5.00626	+	7.47953i	−0.241987	+	0.361537i
$429$		−	1.49158i		−	0.0720140i
$430$	2.40083	+	0.729325i	0.115778	+	0.0351712i
$431$	11.3272	+	6.53977i	0.545613	+	0.315010i	0.747351	−	0.664430i	$-0.231326\pi$
$431$	11.3272	+	6.53977i	0.545613	+	0.315010i	−0.201738	+	0.979440i	$0.564659\pi$
$432$	−1.52486	−	3.69794i	−0.0733650	−	0.177917i
$433$	10.0791	+	5.81915i	0.484369	+	0.279650i	0.722235	−	0.691647i	$-0.243115\pi$
$433$	10.0791	+	5.81915i	0.484369	+	0.279650i	−0.237867	+	0.971298i	$0.576448\pi$
$434$	0.313138	−	0.0728825i	0.0150311	−	0.00349847i
$435$	0.977643	+	0.564443i	0.0468744	+	0.0270630i
$436$	1.53759	−	2.29721i	0.0736370	−	0.110016i
$437$	5.46946	−	9.47338i	0.261640	−	0.453173i
$438$	2.07502	−	0.482958i	0.0991482	−	0.0230766i
$439$	−3.95291	+	2.28221i	−0.188662	+	0.108924i	−0.591356	−	0.806411i	$-0.701407\pi$
$439$	−3.95291	+	2.28221i	−0.188662	+	0.108924i	0.402694	+	0.915335i	$0.368074\pi$
$440$	1.11071	−	0.182020i	0.0529509	−	0.00867745i
$441$	3.46328	+	5.99857i	0.164918	+	0.285646i
$442$	3.59533	−	3.36472i	0.171012	−	0.160043i
$443$	−7.78655	+	13.4867i	−0.369950	+	0.640773i	−0.989557	−	0.144139i	$-0.953959\pi$
$443$	−7.78655	+	13.4867i	−0.369950	+	0.640773i	0.619607	+	0.784912i	$0.287292\pi$
$444$	−0.909266	+	13.7059i	−0.0431518	+	0.650454i
$445$		−	0.946793i		−	0.0448823i
$446$	−27.8104	−	8.44827i	−1.31686	−	0.400037i
$447$	13.4189			0.634692
$448$	1.62661	+	1.43337i	0.0768500	+	0.0677203i
$449$	−14.5224	+	25.1536i	−0.685355	+	1.18707i	0.287970	+	0.957639i	$0.407020\pi$
$449$	−14.5224	+	25.1536i	−0.685355	+	1.18707i	−0.973325	+	0.229430i	$0.926314\pi$
$450$	−2.02649	+	6.67091i	−0.0955297	+	0.314470i
$451$	−12.3313	+	7.11948i	−0.580658	+	0.335243i
$452$	−2.63997	−	5.36406i	−0.124174	−	0.252304i
$453$	2.14543	−	1.23867i	0.100801	−	0.0581976i
$454$	−1.95809	+	1.83249i	−0.0918977	+	0.0860031i
$455$	0.0712133			0.00333853
$456$	6.94284	−	18.3802i	0.325128	−	0.860733i
$457$	11.7523	−	20.3555i	0.549748	−	0.952192i	−0.448543	−	0.893761i	$-0.648057\pi$
$457$	11.7523	−	20.3555i	0.549748	−	0.952192i	0.998291	−	0.0584307i	$-0.0186097\pi$
$458$	−4.17233	−	17.9263i	−0.194960	−	0.837642i
$459$	−1.75421	−	3.03838i	−0.0818794	−	0.141819i
$460$	−0.0551999	+	0.832062i	−0.00257371	+	0.0387951i
$461$	3.36035			0.156507			0.0782536	−	0.996933i	$-0.475066\pi$
$461$	3.36035			0.156507			0.0782536	+	0.996933i	$0.475066\pi$
$462$	0.561012	−	0.130575i	0.0261007	−	0.00607489i
$463$	−7.88841	−	13.6631i	−0.366605	−	0.634979i	0.622427	−	0.782678i	$-0.286147\pi$
$463$	−7.88841	−	13.6631i	−0.366605	−	0.634979i	−0.989032	+	0.147699i	$0.952813\pi$
$464$	−16.9049	−	2.25290i	−0.784791	−	0.104588i
$465$	0.192355	+	0.111056i	0.00892026	+	0.00515011i
$466$	−5.97888	+	5.59538i	−0.276966	+	0.259201i
$467$	−18.5595	+	10.7153i	−0.858832	+	0.495847i	−0.863621	−	0.504142i	$-0.831809\pi$
$467$	−18.5595	+	10.7153i	−0.858832	+	0.495847i	0.00478923	+	0.999989i	$0.498476\pi$
$468$	1.98055	+	0.131392i	0.0915510	+	0.00607359i
$469$	−2.17372	−	0.442343i	−0.100373	−	0.0204255i
$470$	3.06956	+	3.27994i	0.141588	+	0.151292i
$471$	6.79981	+	11.7776i	0.313319	+	0.542684i
$472$	−2.42495	−	2.96200i	−0.111617	−	0.136337i
$473$	−5.03553	+	8.72180i	−0.231534	+	0.401029i
$474$	10.2755	+	10.9798i	0.471969	+	0.504318i
$475$	−29.6577	+	17.1229i	−1.36079	+	0.785651i
$476$	1.58028	+	1.05773i	0.0724320	+	0.0484808i
$477$		−	4.07367i		−	0.186521i
$478$	−3.51934	−	3.76055i	−0.160971	−	0.172004i
$479$	−15.2222	+	8.78855i	−0.695520	+	0.401559i	−0.805677	−	0.592355i	$-0.798198\pi$
$479$	−15.2222	+	8.78855i	−0.695520	+	0.401559i	0.110156	+	0.993914i	$0.464865\pi$
$480$	0.143849	+	1.49086i	0.00656577	+	0.0680481i
$481$	−5.90299	−	3.40809i	−0.269153	−	0.155396i
$482$	−0.677493	+	2.23021i	−0.0308590	+	0.101583i
$483$			0.426759i			0.0194182i
$484$	1.15726	−	17.4441i	0.0526028	−	0.792915i
$485$	1.48984	+	2.58048i	0.0676503	+	0.117174i
$486$	0.411062	−	1.35315i	0.0186461	−	0.0613804i
$487$	5.35309	+	9.27182i	0.242572	+	0.420146i	0.961446	−	0.274994i	$-0.0886757\pi$
$487$	5.35309	+	9.27182i	0.242572	+	0.420146i	−0.718874	+	0.695140i	$0.755342\pi$
$488$	−14.2094	+	37.6176i	−0.643231	+	1.70287i
$489$	−10.3003	−	5.94691i	−0.465798	−	0.268929i
$490$	−0.587947	−	2.52610i	−0.0265607	−	0.114118i
$491$		−	16.7422i		−	0.755565i	−0.925894	−	0.377783i	$-0.876687\pi$
$491$		−	16.7422i		−	0.755565i	0.925894	−	0.377783i	$-0.123313\pi$
$492$	−8.36716	−	17.0009i	−0.377221	−	0.766462i
$493$	−14.9585			−0.673695
$494$	6.66203	+	7.11864i	0.299739	+	0.320283i
$495$	0.344620	+	0.198966i	0.0154895	+	0.00894288i
$496$	−3.32611	−	0.443266i	−0.149347	−	0.0199032i
$497$	−0.908853	+	0.524727i	−0.0407676	+	0.0235372i
$498$	3.59047	+	15.4264i	0.160893	+	0.691274i
$499$	18.0168	+	31.2061i	0.806545	+	1.39698i	0.915243	+	0.402901i	$0.131998\pi$
$499$	18.0168	+	31.2061i	0.806545	+	1.39698i	−0.108699	+	0.994075i	$0.534668\pi$
$500$	2.92485	−	4.36983i	0.130803	−	0.195425i
$501$	−2.15345	−	1.24329i	−0.0962090	−	0.0555463i
$502$	−0.00230789		0.000537158i	−0.000103006		2.39746e-5i
$503$	−8.50492	+	14.7310i	−0.379216	+	0.656821i	−0.990948	−	0.134244i	$-0.957139\pi$
$503$	−8.50492	+	14.7310i	−0.379216	+	0.656821i	0.611733	+	0.791065i	$0.290473\pi$
$504$	0.123961	+	0.756428i	0.00552168	+	0.0336940i
$505$	−1.42723	+	2.47204i	−0.0635111	+	0.110004i
$506$	−3.20250	−	0.972856i	−0.142368	−	0.0432487i
$507$	6.00752	−	10.4053i	0.266803	−	0.462117i
$508$	−13.3606	−	27.1470i	−0.592781	−	1.20445i
$509$	−18.0815			−0.801450			−0.400725	−	0.916198i	$-0.631242\pi$
$509$	−18.0815			−0.801450			−0.400725	+	0.916198i	$0.631242\pi$
$510$	0.297805	+	1.27951i	0.0131870	+	0.0566577i
$511$	−0.408263			−0.0180605
$512$	−10.5951	−	19.9936i	−0.468242	−	0.883600i
$513$	6.01588	−	3.47327i	0.265608	−	0.153349i
$514$	25.7990	+	27.5672i	1.13795	+	1.21594i
$515$	0.872792	−	1.51172i	0.0384598	−	0.0666144i
$516$	−11.1374	−	7.45460i	−0.490299	−	0.328171i
$517$	−15.6149	+	9.01528i	−0.686744	+	0.396492i
$518$	0.765097	−	2.51859i	0.0336164	−	0.110660i
$519$	3.13698	+	5.43341i	0.137698	+	0.238500i
$520$	−0.695290	−	0.262635i	−0.0304905	−	0.0115173i
$521$			25.1190i			1.10049i	0.835005	+	0.550243i	$0.185465\pi$
$521$			25.1190i			1.10049i	−0.835005	+	0.550243i	$0.814535\pi$
$522$	−4.12006	−	4.40245i	−0.180330	−	0.192690i
$523$	−21.3639	+	12.3345i	−0.934179	+	0.539349i	−0.888131	−	0.459590i	$-0.847996\pi$
$523$	−21.3639	+	12.3345i	−0.934179	+	0.539349i	−0.0460484	+	0.998939i	$0.514663\pi$
$524$	4.47460	−	6.68521i	0.195474	−	0.292045i
$525$	0.668013	−	1.15703i	0.0291545	−	0.0504971i
$526$	41.1411	+	12.4979i	1.79384	+	0.544933i
$527$	−2.94314			−0.128205
$528$	−5.95899	−	0.794147i	−0.259332	−	0.0345608i
$529$	−10.2601	+	17.7710i	−0.446092	+	0.772654i
$530$	−0.443371	+	1.45951i	−0.0192588	+	0.0633972i
$531$		−	1.35341i		−	0.0587331i
$532$	−2.09426	+	3.12890i	−0.0907978	+	0.135655i
$533$	9.40269			0.407276
$534$	−1.46990	+	4.83870i	−0.0636089	+	0.209391i
$535$	1.19152			0.0515140
$536$	19.5917	+	12.3355i	0.846234	+	0.532812i
$537$	−15.3648			−0.663040
$538$	4.97518	−	16.3775i	0.214495	−	0.706086i
$539$	10.4101			0.448393
$540$	−0.294550	+	0.440068i	−0.0126754	+	0.0189375i
$541$			3.62686i			0.155931i	0.996956	+	0.0779654i	$0.0248424\pi$
$541$			3.62686i			0.155931i	−0.996956	+	0.0779654i	$0.975158\pi$
$542$	−8.12127	+	26.7340i	−0.348838	+	1.14832i
$543$	−0.892907	+	1.54656i	−0.0383183	+	0.0663693i
$544$	−11.5281	−	16.1552i	−0.494265	−	0.692647i
$545$	−0.365956			−0.0156758
$546$	−0.363944	−	0.110559i	−0.0155754	−	0.00473149i
$547$	14.3899	−	24.9241i	0.615269	−	1.06568i	−0.375068	−	0.926997i	$-0.622381\pi$
$547$	14.3899	−	24.9241i	0.615269	−	1.06568i	0.990337	−	0.138680i	$-0.0442860\pi$
$548$	−1.76883	+	2.64269i	−0.0755605	+	0.112890i
$549$	−12.3123	+	7.10852i	−0.525477	+	0.303384i
$550$	7.15981	+	7.65054i	0.305295	+	0.326220i
$551$		−	29.6172i		−	1.26174i
$552$	1.57389	−	4.16666i	0.0669891	−	0.177345i
$553$	−1.44086	−	2.49565i	−0.0612717	−	0.106126i
$554$	7.83532	−	25.7927i	0.332891	−	1.09583i
$555$	1.57484	−	0.909234i	0.0668482	−	0.0385949i
$556$	−17.9105	−	11.9880i	−0.759575	−	0.508405i
$557$	8.57117	−	14.8457i	0.363172	−	0.629033i	−0.625309	−	0.780377i	$-0.715027\pi$
$557$	8.57117	−	14.8457i	0.363172	−	0.629033i	0.988481	+	0.151345i	$0.0483604\pi$
$558$	−0.810639	−	0.866199i	−0.0343171	−	0.0366691i
$559$	5.75944	−	3.32521i	0.243598	−	0.140641i
$560$	0.0379155	−	0.284504i	0.00160222	−	0.0120225i
$561$	−5.27286			−0.222621
$562$	8.87946	+	38.1504i	0.374557	+	1.60928i
$563$	19.3939			0.817354			0.408677	−	0.912679i	$-0.365990\pi$
$563$	19.3939			0.817354			0.408677	+	0.912679i	$0.365990\pi$
$564$	−10.5952	−	21.5280i	−0.446139	−	0.906494i
$565$	−0.395737	+	0.685437i	−0.0166488	+	0.0288366i
$566$	7.28131	+	2.21192i	0.306056	+	0.0929739i
$567$	−0.135503	+	0.234697i	−0.00569057	+	0.00985636i
$568$	10.8088	−	1.77131i	0.453526	−	0.0743225i
$569$	21.9491	−	38.0169i	0.920154	−	1.59375i	0.120979	−	0.992655i	$-0.461397\pi$
$569$	21.9491	−	38.0169i	0.920154	−	1.59375i	0.799175	−	0.601098i	$-0.205270\pi$
$570$	−2.53339	+	0.589643i	−0.106112	+	0.0246974i
$571$	19.1701	+	11.0679i	0.802245	+	0.463176i	0.844256	−	0.535941i	$-0.180043\pi$
$571$	19.1701	+	11.0679i	0.802245	+	0.463176i	−0.0420107	+	0.999117i	$0.513376\pi$
$572$	1.65932	−	2.47908i	0.0693796	−	0.103656i
$573$	−4.20479	−	7.28292i	−0.175658	−	0.304248i
$574$	0.823126	+	3.53654i	0.0343566	+	0.147612i
$575$	−6.72317	+	3.88162i	−0.280375	+	0.161875i
$576$	1.57941	−	7.84254i	0.0658088	−	0.326773i
$577$	16.6661	+	9.62216i	0.693817	+	0.400576i	0.805041	−	0.593220i	$-0.202144\pi$
$577$	16.6661	+	9.62216i	0.693817	+	0.400576i	−0.111223	+	0.993795i	$0.535477\pi$
$578$	4.53311	+	4.84380i	0.188552	+	0.201476i
$579$	22.7797			0.946693
$580$	0.996978	+	2.02573i	0.0413973	+	0.0841137i
$581$		−	3.03517i		−	0.125920i
$582$	−3.60780	−	15.5009i	−0.149548	−	0.642531i
$583$	−5.30216	−	3.06120i	−0.219593	−	0.126782i
$584$	3.98607	+	1.50567i	0.164945	+	0.0623052i
$585$	−0.131387	−	0.227570i	−0.00543220	−	0.00940884i
$586$	0.993733	−	3.27122i	0.0410507	−	0.135133i
$587$	8.35039	+	14.4633i	0.344658	+	0.596965i	0.985292	−	0.170882i	$-0.0546617\pi$
$587$	8.35039	+	14.4633i	0.344658	+	0.596965i	−0.640634	+	0.767847i	$0.721328\pi$
$588$	−0.917015	+	13.8227i	−0.0378171	+	0.570040i
$589$		−	5.82731i		−	0.240110i
$590$	−0.147303	+	0.484900i	−0.00606437	+	0.0199630i
$591$	1.52264	+	0.879097i	0.0626331	+	0.0361612i
$592$	−16.7585	+	21.7685i	−0.688772	+	0.894679i
$593$	13.0159	−	7.51471i	0.534497	−	0.308592i	−0.208349	−	0.978055i	$-0.566809\pi$
$593$	13.0159	−	7.51471i	0.534497	−	0.308592i	0.742846	+	0.669462i	$0.233475\pi$
$594$	−1.45232	−	1.55187i	−0.0595896	−	0.0636738i
$595$		−	0.251746i		−	0.0103206i
$596$	22.3030	+	14.9280i	0.913565	+	0.611475i
$597$	−23.9212	+	13.8109i	−0.979030	+	0.565243i
$598$	1.51023	+	1.61374i	0.0617579	+	0.0659907i
$599$	−19.6336	+	34.0064i	−0.802208	+	1.38946i	0.115952	+	0.993255i	$0.463008\pi$
$599$	−19.6336	+	34.0064i	−0.802208	+	1.38946i	−0.918160	+	0.396210i	$0.870325\pi$
$600$	−10.7893	+	8.83304i	−0.440470	+	0.360607i
$601$	14.3165	+	24.7969i	0.583983	+	1.01149i	0.995001	+	0.0998613i	$0.0318399\pi$
$601$	14.3165	+	24.7969i	0.583983	+	1.01149i	−0.411018	+	0.911627i	$0.634827\pi$
$602$	1.75487	+	1.87515i	0.0715232	+	0.0764253i
$603$	2.59693	+	7.76247i	0.105755	+	0.316112i
$604$	4.94380	+	0.327977i	0.201160	+	0.0133452i
$605$	−2.00437	+	1.15722i	−0.0814891	+	0.0470478i
$606$	11.1319	−	10.4179i	0.452203	−	0.423197i
$607$	19.0186	+	10.9804i	0.771942	+	0.445681i	0.833567	−	0.552418i	$-0.186295\pi$
$607$	19.0186	+	10.9804i	0.771942	+	0.445681i	−0.0616249	+	0.998099i	$0.519628\pi$
$608$	31.9867	−	22.8253i	1.29723	−	0.925690i
$609$	0.577728	+	1.00065i	0.0234107	+	0.0405485i
$610$	5.18492	−	1.20678i	0.209931	−	0.0488612i
$611$	11.9065			0.481684
$612$	0.464483	−	7.00144i	0.0187756	−	0.283016i
$613$	7.23577	+	12.5327i	0.292250	+	0.506192i	0.974341	−	0.225075i	$-0.0722628\pi$
$613$	7.23577	+	12.5327i	0.292250	+	0.506192i	−0.682092	+	0.731267i	$0.738929\pi$
$614$	−3.01345	−	12.9472i	−0.121613	−	0.522507i
$615$	−1.25426	+	2.17244i	−0.0505765	+	0.0876011i
$616$	1.07769	+	0.407081i	0.0434215	+	0.0164018i
$617$	20.3360			0.818697			0.409349	−	0.912378i	$-0.365756\pi$
$617$	20.3360			0.818697			0.409349	+	0.912378i	$0.365756\pi$
$618$	−6.80746	+	6.37081i	−0.273836	+	0.256272i
$619$	1.03218	−	0.595930i	0.0414869	−	0.0239524i	−0.479113	−	0.877753i	$-0.659042\pi$
$619$	1.03218	−	0.595930i	0.0414869	−	0.0239524i	0.520600	+	0.853801i	$0.325708\pi$
$620$	0.196159	+	0.398570i	0.00787795	+	0.0160069i
$621$	1.36375	−	0.787364i	0.0547256	−	0.0315958i
$622$	−1.78007	+	5.85972i	−0.0713742	+	0.234953i
$623$	0.484539	−	0.839246i	0.0194126	−	0.0336237i
$624$	3.14562	+	2.42167i	0.125926	+	0.0969442i
$625$	23.9533			0.958134
$626$	22.3204	+	6.78049i	0.892101	+	0.271003i
$627$		−	10.4401i		−	0.416937i
$628$	−1.80047	+	27.1396i	−0.0718465	+	1.08299i
$629$	−12.0479	+	20.8676i	−0.480383	+	0.832047i
$630$	0.0740918	−	0.0693393i	0.00295189	−	0.00276254i
$631$	−17.5037	−	30.3173i	−0.696812	−	1.20691i	−0.969566	−	0.244830i	$-0.921268\pi$
$631$	−17.5037	−	30.3173i	−0.696812	−	1.20691i	0.272754	−	0.962084i	$-0.412066\pi$
$632$	4.86389	+	29.6801i	0.193475	+	1.18061i
$633$	10.8677	−	6.27445i	0.431951	−	0.249387i
$634$	−7.60775	+	1.77069i	−0.302142	+	0.0703232i
$635$	−2.00279	+	3.46893i	−0.0794781	+	0.137660i
$636$	4.53180	−	6.77067i	0.179698	−	0.268475i
$637$	−5.95330	−	3.43714i	−0.235878	−	0.136184i
$638$	−8.82614	+	2.05427i	−0.349430	+	0.0813294i
$639$	3.35364	+	1.93622i	0.132668	+	0.0765958i
$640$	−1.41944	+	2.63792i	−0.0561082	+	0.104273i
$641$	28.8909	+	16.6802i	1.14112	+	0.658828i	0.946708	−	0.322092i	$-0.104386\pi$
$641$	28.8909	+	16.6802i	1.14112	+	0.658828i	0.194415	+	0.980919i	$0.437719\pi$
$642$	−6.08942	−	1.84985i	−0.240330	−	0.0730076i
$643$		−	2.04944i		−	0.0808220i	−0.999183	−	0.0404110i	$-0.987133\pi$
$643$		−	2.04944i		−	0.0808220i	0.999183	−	0.0404110i	$-0.0128667\pi$
$644$	−0.474753	+	0.709298i	−0.0187079	+	0.0279502i
$645$			1.77425i			0.0698609i
$646$	25.1651	−	23.5509i	0.990107	−	0.926598i
$647$	−12.6017	−	21.8268i	−0.495425	−	0.858100i	0.504562	−	0.863376i	$-0.331654\pi$
$647$	−12.6017	−	21.8268i	−0.495425	−	0.858100i	−0.999986	+	0.00527529i	$0.998321\pi$
$648$	2.18854	−	1.79173i	0.0859740	−	0.0703858i
$649$	−1.76156	−	1.01704i	−0.0691472	−	0.0399221i
$650$	−1.56853	−	6.73917i	−0.0615229	−	0.264332i
$651$	0.113670	+	0.196883i	0.00445509	+	0.00771644i
$652$	−10.5041	−	21.3428i	−0.411371	−	0.835850i
$653$	−23.6162	+	13.6348i	−0.924172	+	0.533571i	−0.884964	−	0.465660i	$-0.845817\pi$
$653$	−23.6162	+	13.6348i	−0.924172	+	0.533571i	−0.0392087	+	0.999231i	$0.512484\pi$
$654$	1.87026	+	0.568149i	0.0731330	+	0.0222164i
$655$	−1.06498			−0.0416124
$656$	5.00620	−	37.5647i	0.195459	−	1.46665i
$657$	0.753239	+	1.30465i	0.0293867	+	0.0508992i
$658$	1.04231	+	4.47827i	0.0406335	+	0.174581i
$659$	11.6956	+	6.75245i	0.455595	+	0.263038i	0.710190	−	0.704010i	$-0.248609\pi$
$659$	11.6956	+	6.75245i	0.455595	+	0.263038i	−0.254595	+	0.967048i	$0.581942\pi$
$660$	0.351435	+	0.714070i	0.0136796	+	0.0277951i
$661$			31.8361i			1.23828i	0.785281	+	0.619140i	$0.212519\pi$
$661$			31.8361i			1.23828i	−0.785281	+	0.619140i	$0.787481\pi$
$662$	2.67357	+	2.85682i	0.103911	+	0.111033i
$663$	3.01544	+	1.74097i	0.117110	+	0.0676135i
$664$	−11.1937	+	29.6338i	−0.434400	+	1.15001i
$665$	0.498449			0.0193290
$666$	−9.46000	+	2.20180i	−0.366568	+	0.0853181i
$667$		−	6.71400i		−	0.259967i
$668$	−2.19604	−	4.46205i	−0.0849673	−	0.172642i
$669$		−	20.5523i		−	0.794598i
$670$	−0.0855717	−	3.06378i	−0.00330592	−	0.118364i
$671$			21.3671i			0.824866i
$672$	−0.635466	+	1.39513i	−0.0245136	+	0.0538182i
$673$			22.8614i			0.881243i	0.897693	+	0.440622i	$0.145242\pi$
$673$			22.8614i			0.881243i	−0.897693	+	0.440622i	$0.854758\pi$
$674$	−1.26557	−	5.43751i	−0.0487480	−	0.209445i
$675$	−4.92990			−0.189752
$676$	21.5604	−	10.6111i	0.829244	−	0.408120i
$677$	−38.0858	−	21.9889i	−1.46376	−	0.845101i	−0.464576	−	0.885533i	$-0.653793\pi$
$677$	−38.0858	−	21.9889i	−1.46376	−	0.845101i	−0.999182	+	0.0404325i	$0.987126\pi$
$678$	3.08661	−	2.88862i	0.118540	−	0.110937i
$679$			3.04982i			0.117041i
$680$	−0.928438	+	2.45792i	−0.0356040	+	0.0942568i
$681$	−1.64227	−	0.948166i	−0.0629320	−	0.0363338i
$682$	−1.73658	+	0.404186i	−0.0664970	+	0.0154771i
$683$	−1.82949	−	3.16877i	−0.0700034	−	0.121249i	0.828899	−	0.559398i	$-0.188968\pi$
$683$	−1.82949	−	3.16877i	−0.0700034	−	0.121249i	−0.898903	+	0.438149i	$0.855634\pi$
$684$	13.8626	+	0.919661i	0.530050	+	0.0351641i
$685$	0.420992			0.0160853
$686$	1.55142	−	5.10703i	0.0592333	−	0.194987i
$687$	11.2710	−	6.50731i	0.430015	−	0.248270i
$688$	−10.2181	−	24.7799i	−0.389562	−	0.944726i
$689$	2.02146	+	3.50128i	0.0770116	+	0.133388i
$690$	−0.574300	+	0.133668i	−0.0218632	+	0.00508864i
$691$	37.1663	+	21.4580i	1.41387	+	0.816300i	0.995751	−	0.0920901i	$-0.0293548\pi$
$691$	37.1663	+	21.4580i	1.41387	+	0.816300i	0.418123	+	0.908390i	$0.362688\pi$
$692$	−0.830617	+	12.5204i	−0.0315753	+	0.475954i
$693$	0.203649	+	0.352731i	0.00773600	+	0.0133991i
$694$	18.4885	+	19.7557i	0.701814	+	0.749916i
$695$			2.85323i			0.108229i
$696$	−1.95022	−	11.9005i	−0.0739231	−	0.451088i
$697$		−	33.2394i		−	1.25903i
$698$	7.53209	−	24.7945i	0.285094	−	0.938486i
$699$	−5.01455	−	2.89515i	−0.189668	−	0.109505i
$700$	2.39743	−	1.17992i	0.0906143	−	0.0445966i
$701$	3.81476	+	2.20245i	0.144082	+	0.0831856i	0.570308	−	0.821431i	$-0.306824\pi$
$701$	3.81476	+	2.20245i	0.144082	+	0.0831856i	−0.426226	+	0.904617i	$0.640157\pi$
$702$	0.318168	+	1.36700i	0.0120085	+	0.0515941i
$703$	−41.3172	−	23.8545i	−1.55831	−	0.899690i
$704$	−9.02072	−	7.94906i	−0.339981	−	0.299592i
$705$	−1.58825	+	2.75092i	−0.0598168	+	0.103606i
$706$	11.3351	+	48.7009i	0.426601	+	1.83288i
$707$	−2.53023	+	1.46083i	−0.0951590	+	0.0549400i
$708$	1.50562	−	2.24945i	0.0565846	−	0.0845394i
$709$	−9.15430	−	15.8557i	−0.343797	−	0.595474i	0.641337	−	0.767259i	$-0.278380\pi$
$709$	−9.15430	−	15.8557i	−0.343797	−	0.595474i	−0.985134	+	0.171785i	$0.945047\pi$
$710$	−0.990804	−	1.05871i	−0.0371842	−	0.0397328i
$711$	−5.31673	+	9.20885i	−0.199393	+	0.345359i
$712$	−7.82592	+	6.40698i	−0.293289	+	0.240112i
$713$		−	1.32101i		−	0.0494721i
$714$	−0.390837	+	1.28658i	−0.0146267	+	0.0481489i
$715$	−0.394929			−0.0147695
$716$	−25.5372	−	17.0927i	−0.954369	−	0.638786i
$717$	1.82097	−	3.15402i	0.0680055	−	0.117789i
$718$	−47.8501	−	14.5359i	−1.78575	−	0.542475i
$719$	−10.2908	+	5.94142i	−0.383784	+	0.221578i	−0.679463	−	0.733710i	$-0.737787\pi$
$719$	−10.2908	+	5.94142i	−0.383784	+	0.221578i	0.295680	+	0.955287i	$0.404454\pi$
$720$	−0.979117	+	0.403743i	−0.0364895	+	0.0150466i
$721$	1.54730	−	0.893335i	0.0576245	−	0.0332695i
$722$	28.2697	+	30.2072i	1.05209	+	1.12420i
$723$	−1.64815			−0.0612955
$724$	−3.20455	+	1.57715i	−0.119096	+	0.0586142i
$725$	−10.5095	+	18.2030i	−0.390314	+	0.676044i
$726$	12.0402	−	2.80233i	0.446852	−	0.104004i
$727$	16.3949	+	28.3968i	0.608052	+	1.05318i	0.991561	+	0.129640i	$0.0413822\pi$
$727$	16.3949	+	28.3968i	0.608052	+	1.05318i	−0.383509	+	0.923537i	$0.625284\pi$
$728$	−0.481903	−	0.588629i	−0.0178605	−	0.0218160i
$729$	1.00000			0.0370370
$730$	−0.127874	−	0.549409i	−0.00473284	−	0.0203346i
$731$	−11.7549	−	20.3602i	−0.434772	−	0.753048i
$732$	−28.3717	−	1.88221i	−1.04865	−	0.0695685i
$733$	9.93994	+	5.73883i	0.367140	+	0.211968i	0.672208	−	0.740362i	$-0.265346\pi$
$733$	9.93994	+	5.73883i	0.367140	+	0.211968i	−0.305068	+	0.952331i	$0.598679\pi$
$734$	17.1265	+	18.3003i	0.632149	+	0.675476i
$735$	1.58826	−	0.916983i	0.0585839	−	0.0338234i
$736$	7.25113	−	5.17433i	0.267280	−	0.190728i
$737$	12.0549	+	2.45311i	0.444046	+	0.0903615i
$738$	9.78275	−	9.15525i	0.360108	−	0.337009i
$739$	8.38688	+	14.5265i	0.308516	+	0.534366i	0.978038	−	0.208426i	$-0.0668342\pi$
$739$	8.38688	+	14.5265i	0.308516	+	0.534366i	−0.669522	+	0.742793i	$0.733501\pi$
$740$	3.62896	+	0.240749i	0.133403	+	0.00885012i
$741$	−3.44706	+	5.97048i	−0.126631	+	0.219331i
$742$	−1.13994	+	1.06682i	−0.0418485	+	0.0391642i
$743$	−4.33334	+	2.50185i	−0.158975	+	0.0917841i	−0.577377	−	0.816478i	$-0.695924\pi$
$743$	−4.33334	+	2.50185i	−0.158975	+	0.0917841i	0.418402	+	0.908262i	$0.362590\pi$
$744$	−0.383714	−	2.34148i	−0.0140677	−	0.0858427i
$745$		−	3.55297i		−	0.130171i
$746$	20.4075	−	19.0985i	0.747171	−	0.699245i
$747$	−9.69920	+	5.59984i	−0.354875	+	0.204887i
$748$	−8.76380	−	5.86585i	−0.320436	−	0.214477i
$749$	1.05618	+	0.609784i	0.0385918	+	0.0222810i
$750$	3.55767	+	1.08075i	0.129908	+	0.0394635i
$751$			6.28773i			0.229442i	0.993398	+	0.114721i	$0.0365975\pi$
$751$			6.28773i			0.229442i	−0.993398	+	0.114721i	$0.963403\pi$
$752$	6.33927	−	47.5676i	0.231169	−	1.73461i
$753$	−0.000837772	−	0.00145106i	−3.05301e−5	−	5.28797e-5i
$754$	5.72576	+	1.73937i	0.208520	+	0.0633442i
$755$	−0.327965	−	0.568053i	−0.0119359	−	0.0206736i
$756$	−0.486304	+	0.239339i	−0.0176867	+	0.00870467i
$757$	26.4882	+	15.2930i	0.962731	+	0.555833i	0.897012	−	0.442005i	$-0.145733\pi$
$757$	26.4882	+	15.2930i	0.962731	+	0.555833i	0.0657183	+	0.997838i	$0.479066\pi$
$758$	9.87998	−	2.29955i	0.358857	−	0.0835235i
$759$		−	2.36669i		−	0.0859054i
$760$	−4.86659	−	1.83828i	−0.176530	−	0.0666813i
$761$	9.53430			0.345618			0.172809	−	0.984955i	$-0.444716\pi$
$761$	9.53430			0.345618			0.172809	+	0.984955i	$0.444716\pi$
$762$	15.6210	−	14.6190i	0.565889	−	0.529592i
$763$	−0.324387	−	0.187285i	−0.0117436	−	0.00678016i
$764$	1.11336	−	16.7823i	0.0402798	−	0.607162i
$765$	−0.804481	+	0.464467i	−0.0290861	+	0.0167928i
$766$	41.8382	−	9.73779i	1.51168	−	0.351841i
$767$	0.671599	+	1.16324i	0.0242500	+	0.0420023i
$768$	11.3496	−	11.2777i	0.409543	−	0.406949i
$769$	1.14006	+	0.658215i	0.0411117	+	0.0237358i	0.520415	−	0.853913i	$-0.325777\pi$
$769$	1.14006	+	0.658215i	0.0411117	+	0.0237358i	−0.479303	+	0.877649i	$0.659111\pi$
$770$	−0.0345727	−	0.148541i	−0.00124591	−	0.00535305i
$771$	−13.3489	+	23.1209i	−0.480748	+	0.832681i
$772$	37.8612	+	25.3415i	1.36265	+	0.912062i
$773$	−9.92859	+	17.1968i	−0.357107	+	0.618527i	−0.987476	−	0.157768i	$-0.949570\pi$
$773$	−9.92859	+	17.1968i	−0.357107	+	0.618527i	0.630370	+	0.776295i	$0.282903\pi$
$774$	2.75453	−	9.06749i	0.0990094	−	0.325924i
$775$	−2.06779	+	3.58152i	−0.0742773	+	0.128652i
$776$	11.2477	−	29.7768i	0.403770	−	1.06893i
$777$	1.86127			0.0667727
$778$	−1.59987	+	0.372367i	−0.0573581	+	0.0133500i
$779$	65.8129			2.35799
$780$	0.0347891	−	0.524397i	0.00124565	−	0.0187764i
$781$	5.04025	−	2.90999i	0.180354	−	0.104128i
$782$	5.70473	−	5.33881i	0.204001	−	0.190915i
$783$	2.13180	−	3.69238i	0.0761842	−	0.131955i
$784$	−16.9014	+	21.9540i	−0.603620	+	0.784072i
$785$	3.11840	−	1.80041i	0.111300	−	0.0642593i
$786$	5.44273	+	1.65339i	0.194136	+	0.0589746i
$787$	−20.6928	−	35.8411i	−0.737620	−	1.27760i	−0.953564	−	0.301190i	$-0.902616\pi$
$787$	−20.6928	−	35.8411i	−0.737620	−	1.27760i	0.215944	−	0.976406i	$-0.430717\pi$
$788$	1.55275	+	3.15499i	0.0553146	+	0.112392i
$789$			30.4038i			1.08241i
$790$	2.90715	−	2.72068i	0.103432	−	0.0967973i
$791$	−0.701570	+	0.405052i	−0.0249450	+	0.0144020i
$792$	−0.687455	−	4.19494i	−0.0244277	−	0.149061i
$793$	7.05486	−	12.2194i	0.250525	−	0.433923i
$794$	−4.33372	+	14.2660i	−0.153798	+	0.506280i
$795$	−1.07860			−0.0382540
$796$	−55.1225	−	3.65689i	−1.95376	−	0.129615i
$797$	−23.5736	+	40.8307i	−0.835021	+	1.44630i	0.0589927	+	0.998258i	$0.481211\pi$
$797$	−23.5736	+	40.8307i	−0.835021	+	1.44630i	−0.894013	+	0.448040i	$0.852122\pi$
$798$	−2.54738	−	0.773844i	−0.0901763	−	0.0273938i
$799$		−	42.0905i		−	1.48906i
$800$	−27.7588	+	2.67836i	−0.981421	+	0.0946945i
$801$	−3.57586			−0.126347
$802$	19.5177	+	5.92908i	0.689192	+	0.209363i
$803$	2.26412			0.0798989
$804$	−4.31921	+	15.7906i	−0.152327	+	0.556893i
$805$	0.112994			0.00398253
$806$	1.12657	+	0.342228i	0.0396816	+	0.0120545i
$807$	12.1032			0.426054
$808$	30.0913	−	4.93128i	1.05861	−	0.173482i
$809$		−	53.6849i		−	1.88746i	−0.330715	−	0.943731i	$-0.607290\pi$
$809$		−	53.6849i		−	1.88746i	0.330715	−	0.943731i	$-0.392710\pi$
$810$	−0.358279	−	0.108838i	−0.0125886	−	0.00382418i
$811$	−5.35427	+	9.27387i	−0.188014	+	0.325650i	−0.944588	−	0.328258i	$-0.893538\pi$
$811$	−5.35427	+	9.27387i	−0.188014	+	0.325650i	0.756574	+	0.653908i	$0.226872\pi$
$812$	−0.152972	+	2.30584i	−0.00536827	+	0.0809192i
$813$	−19.7568			−0.692901
$814$	−4.24302	+	13.9674i	−0.148718	+	0.489557i
$815$	−1.57458	+	2.72726i	−0.0551552	+	0.0955316i
$816$	8.56082	−	11.1201i	0.299689	−	0.389280i
$817$	40.3125	−	23.2744i	1.41035	−	0.814268i
$818$	34.6566	−	32.4336i	1.21174	−	1.13402i
$819$		−	0.268960i		−	0.00939821i
$820$	−4.50140	+	2.21540i	−0.157196	+	0.0773651i
$821$	5.85297	+	10.1376i	0.204270	+	0.353806i	0.949900	−	0.312554i	$-0.101185\pi$
$821$	5.85297	+	10.1376i	0.204270	+	0.353806i	−0.745630	+	0.666360i	$0.767851\pi$
$822$	−2.15153	−	0.653593i	−0.0750433	−	0.0227967i
$823$	−31.1760	+	17.9995i	−1.08673	+	0.627421i	−0.932703	−	0.360646i	$-0.882556\pi$
$823$	−31.1760	+	17.9995i	−1.08673	+	0.627421i	−0.154023	+	0.988067i	$0.549223\pi$
$824$	−18.4017	+	3.01561i	−0.641053	+	0.105054i
$825$	−3.70462	+	6.41659i	−0.128978	+	0.223397i
$826$	−0.378727	+	0.354434i	−0.0131776	+	0.0123323i
$827$	17.6005	−	10.1616i	0.612028	−	0.353354i	−0.161731	−	0.986835i	$-0.551708\pi$
$827$	17.6005	−	10.1616i	0.612028	−	0.353354i	0.773759	+	0.633481i	$0.218374\pi$
$828$	3.14255	+	0.208480i	0.109211	+	0.00724518i
$829$	45.0358			1.56416			0.782079	−	0.623179i	$-0.214159\pi$
$829$	45.0358			1.56416			0.782079	+	0.623179i	$0.214159\pi$
$830$	4.08450	−	0.950661i	0.141775	−	0.0329979i
$831$	19.0612			0.661224
$832$	2.53419	+	7.52432i	0.0878571	+	0.260859i
$833$	−12.1506	+	21.0455i	−0.420994	+	0.729183i
$834$	4.42965	−	14.5818i	0.153386	−	0.504925i
$835$	−0.329191	+	0.570176i	−0.0113921	+	0.0197317i
$836$	11.6142	−	17.3520i	0.401686	−	0.600133i
$837$	0.419440	−	0.726491i	0.0144980	−	0.0251112i
$838$	9.55449	+	41.0507i	0.330054	+	1.41807i
$839$	−42.8633	−	24.7471i	−1.47980	−	0.854366i	−0.480066	−	0.877232i	$-0.659387\pi$
$839$	−42.8633	−	24.7471i	−1.47980	−	0.854366i	−0.999739	+	0.0228666i	$0.992721\pi$
$840$	0.200282	−	0.0328216i	0.00691038	−	0.00113245i
$841$	5.41089	+	9.37193i	0.186582	+	0.323170i
$842$	−34.7832	+	8.09575i	−1.19871	+	0.278998i
$843$	−23.9867	+	13.8487i	−0.826146	+	0.476976i
$844$	25.0427	+	1.66136i	0.862006	+	0.0571864i
$845$	−2.75505	−	1.59063i	−0.0947767	−	0.0547193i
$846$	12.3877	−	11.5932i	0.425899	−	0.398581i
$847$	−2.36892			−0.0813970
$848$	15.0642	−	6.21179i	0.517307	−	0.213314i
$849$			5.38099i			0.184675i
$850$	−23.8236	+	5.54492i	−0.817144	+	0.190189i
$851$	−9.36630	−	5.40763i	−0.321073	−	0.185371i
$852$	3.41996	+	6.94890i	0.117166	+	0.238066i
$853$	−17.0829	−	29.5884i	−0.584906	−	1.01309i	−0.994887	−	0.100993i	$-0.967798\pi$
$853$	−17.0829	−	29.5884i	−0.584906	−	1.01309i	0.409982	−	0.912094i	$-0.365535\pi$
$854$	5.21355	+	1.58378i	0.178404	+	0.0541957i
$855$	−0.919630	−	1.59285i	−0.0314507	−	0.0544742i
$856$	−8.06308	−	9.84879i	−0.275590	−	0.336625i
$857$			28.6575i			0.978921i	0.872026	+	0.489460i	$0.162806\pi$
$857$			28.6575i			0.978921i	−0.872026	+	0.489460i	$0.837194\pi$
$858$	2.01833	+	0.613130i	0.0689047	+	0.0209319i
$859$	−16.4976	−	9.52492i	−0.562892	−	0.324986i	0.191413	−	0.981510i	$-0.438693\pi$
$859$	−16.4976	−	9.52492i	−0.562892	−	0.324986i	−0.754306	+	0.656524i	$0.772026\pi$
$860$	−1.97378	+	2.94890i	−0.0673053	+	0.100557i
$861$	−2.22357	+	1.28378i	−0.0757790	+	0.0437510i
$862$	−13.5055	+	12.6392i	−0.459999	+	0.430494i
$863$			32.1293i			1.09369i	0.837232	+	0.546847i	$0.184172\pi$
$863$			32.1293i			1.09369i	−0.837232	+	0.546847i	$0.815828\pi$
$864$	5.63070	−	0.543290i	0.191560	−	0.0184831i
$865$	1.43862	−	0.830588i	0.0489146	−	0.0282408i
$866$	−12.0173	+	11.2465i	−0.408365	+	0.382172i
$867$	−2.34551	+	4.06255i	−0.0796578	+	0.137971i
$868$	−0.0300979	+	0.453684i	−0.00102159	+	0.0153990i
$869$	7.99062	+	13.8402i	0.271063	+	0.469495i
$870$	−1.16565	+	1.09088i	−0.0395192	+	0.0369844i
$871$	−6.08397	−	5.38309i	−0.206147	−	0.182399i
$872$	2.47644	+	3.02489i	0.0838627	+	0.102436i
$873$	9.74602	−	5.62687i	0.329853	−	0.190441i
$874$	10.5707	+	11.2952i	0.357558	+	0.382065i
$875$	−0.617059	−	0.356259i	−0.0208604	−	0.0120438i
$876$	−0.199444	+	3.00635i	−0.00673860	+	0.101575i
$877$	−10.3986	−	18.0108i	−0.351134	−	0.608183i	0.635314	−	0.772254i	$-0.280871\pi$
$877$	−10.3986	−	18.0108i	−0.351134	−	0.608183i	−0.986448	+	0.164071i	$0.947537\pi$
$878$	−1.46330	−	6.28703i	−0.0493839	−	0.212177i
$879$	2.41748			0.0815395
$880$	−0.210269	+	1.57778i	−0.00708817	+	0.0531870i
$881$	1.60309	+	2.77664i	0.0540096	+	0.0935474i	0.891766	−	0.452496i	$-0.149466\pi$
$881$	1.60309	+	2.77664i	0.0540096	+	0.0935474i	−0.837757	+	0.546044i	$0.816133\pi$
$882$	−9.54062	+	2.22057i	−0.321249	+	0.0747704i
$883$	9.46771	−	16.3986i	0.318614	−	0.551856i	−0.661585	−	0.749870i	$-0.730116\pi$
$883$	9.46771	−	16.3986i	0.318614	−	0.551856i	0.980199	+	0.198015i	$0.0634493\pi$
$884$	3.07508	+	6.24815i	0.103426	+	0.210148i
$885$	−0.358347			−0.0120457
$886$	−15.0488	−	16.0803i	−0.505576	−	0.540228i
$887$	13.1715	−	7.60457i	0.442256	−	0.255336i	−0.262298	−	0.964987i	$-0.584480\pi$
$887$	13.1715	−	7.60457i	0.442256	−	0.255336i	0.704554	+	0.709650i	$0.251147\pi$
$888$	−18.1725	−	6.86436i	−0.609828	−	0.230353i
$889$	−3.55057	+	2.04992i	−0.119082	+	0.0687523i
$890$	1.28116	+	0.389191i	0.0429445	+	0.0130457i
$891$	0.751460	−	1.30157i	0.0251748	−	0.0436041i
$892$	22.8636	−	34.1591i	0.765531	−	1.14373i
$893$	83.3379			2.78880
$894$	−5.51600	+	18.1579i	−0.184483	+	0.607289i
$895$			4.06819i			0.135985i
$896$	−2.60821	+	1.61185i	−0.0871340	+	0.0538481i
$897$	−0.781421	+	1.35346i	−0.0260909	+	0.0451907i
$898$	−28.0670	−	29.9907i	−0.936609	−	1.00080i
$899$	−1.78832	−	3.09746i	−0.0596438	−	0.103306i
$900$	−8.19376	−	5.48432i	−0.273125	−	0.182811i
$901$	12.3774	−	7.14607i	0.412349	−	0.238070i
$902$	−4.56483	−	19.6127i	−0.151992	−	0.653031i
$903$	−0.908003	+	1.57271i	−0.0302164	+	0.0523364i
$904$	8.34360	−	1.36733i	0.277504	−	0.0454766i
$905$	0.409488	+	0.236418i	0.0136118	+	0.00785880i
$906$	0.794201	+	3.41227i	0.0263856	+	0.113365i
$907$	−38.5702	−	22.2685i	−1.28070	−	0.739414i	−0.303726	−	0.952759i	$-0.598231\pi$
$907$	−38.5702	−	22.2685i	−1.28070	−	0.739414i	−0.976977	+	0.213345i	$0.931564\pi$
$908$	−1.67475	−	3.40287i	−0.0555785	−	0.112928i
$909$	9.33645	+	5.39040i	0.309671	+	0.178788i
$910$	−0.0292731	+	0.0963626i	−0.000970393	+	0.00319439i
$911$			20.6168i			0.683065i	0.939870	+	0.341533i	$0.110946\pi$
$911$			20.6168i			0.683065i	−0.939870	+	0.341533i	$0.889054\pi$
$912$	22.0174	+	16.9501i	0.729068	+	0.561276i
$913$			16.8322i			0.557065i
$914$	22.7133	+	24.2700i	0.751289	+	0.802781i
$915$	1.88214	+	3.25997i	0.0622218	+	0.107771i
$916$	25.9722	+	1.72302i	0.858144	+	0.0569302i
$917$	−0.944011	−	0.545025i	−0.0311740	−	0.0179983i
$918$	4.83248	−	1.12475i	0.159496	−	0.0371224i
$919$	6.59713	+	11.4266i	0.217619	+	0.376927i	0.954080	−	0.299553i	$-0.0968376\pi$
$919$	6.59713	+	11.4266i	0.217619	+	0.376927i	−0.736460	+	0.676481i	$0.763504\pi$
$920$	−1.10322	−	0.416723i	−0.0363720	−	0.0137390i
$921$	8.14044	−	4.69988i	0.268237	−	0.154866i
$922$	−1.38131	+	4.54707i	−0.0454911	+	0.149750i
$923$	−3.84322			−0.126501
$924$	−0.0539228	+	0.812811i	−0.00177393	+	0.0267395i
$925$	16.9293	+	29.3224i	0.556633	+	0.964116i
$926$	21.7309	−	5.05785i	0.714123	−	0.166211i
$927$	−5.70949	−	3.29638i	−0.187524	−	0.108267i
$928$	9.99748	−	21.9489i	0.328183	−	0.720508i
$929$			29.0403i			0.952780i	0.879234	+	0.476390i	$0.158055\pi$
$929$			29.0403i			0.952780i	−0.879234	+	0.476390i	$0.841945\pi$
$930$	−0.229346	+	0.214635i	−0.00752056	+	0.00703817i
$931$	−41.6694	−	24.0578i	−1.36566	−	0.788463i
$932$	−5.11372	−	10.3904i	−0.167506	−	0.340349i
$933$	−4.33041			−0.141771
$934$	−6.87040	−	29.5186i	−0.224806	−	0.965877i
$935$			1.39611i			0.0456578i
$936$	−0.991922	+	2.62598i	−0.0324220	+	0.0858329i
$937$			20.3024i			0.663249i	0.943411	+	0.331624i	$0.107597\pi$
$937$			20.3024i			0.663249i	−0.943411	+	0.331624i	$0.892403\pi$
$938$	1.49209	−	2.75955i	0.0487185	−	0.0901025i
$939$			16.4951i			0.538296i
$940$	−5.70005	+	2.80533i	−0.185915	+	0.0914997i
$941$		−	45.5215i		−	1.48396i	−0.670424	−	0.741979i	$-0.733888\pi$
$941$		−	45.5215i		−	1.48396i	0.670424	−	0.741979i	$-0.266112\pi$
$942$	−18.7321	+	4.35987i	−0.610324	+	0.142052i
$943$	14.9193			0.485839
$944$	5.00485	−	2.06377i	0.162894	−	0.0671699i
$945$	0.0621415	+	0.0358774i	0.00202146	+	0.00116709i
$946$	−9.73203	−	10.3991i	−0.316416	−	0.338102i
$947$			8.30388i			0.269840i	0.990857	+	0.134920i	$0.0430777\pi$
$947$			8.30388i			0.269840i	−0.990857	+	0.134920i	$0.956922\pi$
$948$	−19.0812	+	9.39098i	−0.619729	+	0.305005i
$949$	−1.29480	−	0.747554i	−0.0420310	−	0.0242666i
$950$	−10.9788	−	47.1700i	−0.356198	−	1.53040i
$951$	−2.76164	−	4.78330i	−0.0895522	−	0.155109i
$952$	−2.08086	+	1.70357i	−0.0674410	+	0.0552131i
$953$	0.931842			0.0301853			0.0150927	−	0.999886i	$-0.495196\pi$
$953$	0.931842			0.0301853			0.0150927	+	0.999886i	$0.495196\pi$
$954$	5.51231	+	1.67453i	0.178468	+	0.0542150i
$955$	−1.92832	+	1.11332i	−0.0623990	+	0.0360261i
$956$	6.53528	−	3.21639i	0.211366	−	0.104026i
$957$	−3.20392	−	5.54935i	−0.103568	−	0.179385i
$958$	−5.63499	−	24.2106i	−0.182058	−	0.782210i
$959$	0.373171	+	0.215451i	0.0120503	+	0.00695726i
$960$	−2.07649	−	0.418186i	−0.0670186	−	0.0134969i
$961$	15.1481	+	26.2373i	0.488650	+	0.846366i
$962$	7.03817	−	6.58672i	0.226920	−	0.212364i
$963$		−	4.50016i		−	0.145016i
$964$	−2.73932	−	1.83351i	−0.0882276	−	0.0590532i
$965$		−	6.03146i		−	0.194160i
$966$	−0.577471	−	0.175424i	−0.0185798	−	0.00564419i
$967$	6.46682	+	3.73362i	0.207959	+	0.120065i	0.600362	−	0.799728i	$-0.295023\pi$
$967$	6.46682	+	3.73362i	0.207959	+	0.120065i	−0.392404	+	0.919793i	$0.628356\pi$
$968$	23.1289	+	8.73657i	0.743391	+	0.280804i
$969$	21.1062	+	12.1857i	0.678029	+	0.391460i
$970$	−4.10421	+	0.955250i	−0.131778	+	0.0306712i
$971$	32.3294	+	18.6654i	1.03750	+	0.599001i	0.919124	−	0.393968i	$-0.128898\pi$
$971$	32.3294	+	18.6654i	1.03750	+	0.599001i	0.118376	+	0.992969i	$0.462231\pi$
$972$	1.66206	+	1.11246i	0.0533105	+	0.0356822i
$973$	−1.46019	+	2.52913i	−0.0468116	+	0.0810801i
$974$	−14.7467	+	3.43227i	−0.472514	+	0.109977i
$975$	4.23719	−	2.44634i	0.135699	−	0.0783457i
$976$	−45.0615	−	34.6907i	−1.44238	−	1.11042i
$977$	−22.4295	−	38.8491i	−0.717585	−	1.24289i	−0.961954	−	0.273211i	$-0.911914\pi$
$977$	−22.4295	−	38.8491i	−0.717585	−	1.24289i	0.244370	−	0.969682i	$-0.421419\pi$
$978$	12.2812	−	11.4934i	0.392709	−	0.367519i
$979$	−2.68712	+	4.65422i	−0.0858807	+	0.148750i
$980$	3.65989	+	0.242801i	0.116911	+	0.00775599i
$981$			1.38215i			0.0441286i
$982$	22.6548	+	6.88208i	0.722944	+	0.219616i
$983$	−35.9938			−1.14802			−0.574012	−	0.818847i	$-0.694614\pi$
$983$	−35.9938			−1.14802			−0.574012	+	0.818847i	$0.694614\pi$
$984$	26.4443	−	4.33362i	0.843015	−	0.138151i
$985$	0.232761	−	0.403155i	0.00741639	−	0.0128456i
$986$	6.14885	−	20.2411i	0.195819	−	0.644608i
$987$	−2.81567	+	1.62563i	−0.0896237	+	0.0517443i
$988$	−12.3711	+	6.08855i	−0.393578	+	0.193703i
$989$	9.13852	−	5.27613i	0.290588	−	0.167771i
$990$	−0.410892	+	0.384537i	−0.0130590	+	0.0122214i
$991$	−41.4181			−1.31569			−0.657844	−	0.753154i	$-0.728532\pi$
$991$	−41.4181			−1.31569			−0.657844	+	0.753154i	$0.728532\pi$
$992$	1.96704	−	4.31853i	0.0624537	−	0.137114i
$993$	−1.38336	+	2.39604i	−0.0438995	+	0.0760362i
$994$	−0.336441	−	1.44551i	−0.0106713	−	0.0458489i
$995$	3.65676	+	6.33369i	0.115927	+	0.200792i
$996$	−22.3502	−	1.48274i	−0.708194	−	0.0469823i
$997$	−21.3806			−0.677130			−0.338565	−	0.940943i	$-0.609941\pi$
$997$	−21.3806			−0.677130			−0.338565	+	0.940943i	$0.609941\pi$
$998$	−49.6327	+	11.5519i	−1.57110	+	0.365670i
$999$	−3.43401	−	5.94788i	−0.108647	−	0.188183i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.j.a.499.15	✓	68
4.3	odd	2		804.2.j.b.499.3	yes	68
67.38	odd	6		804.2.j.b.775.3	yes	68
268.239	even	6	inner	804.2.j.a.775.15	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.j.a.499.15	✓	68	1.1	even	1	trivial
804.2.j.a.775.15	yes	68	268.239	even	6	inner
804.2.j.b.499.3	yes	68	4.3	odd	2
804.2.j.b.775.3	yes	68	67.38	odd	6

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.411062 + 1.35315i) q^{2} -1.00000 q^{3} +(-1.66206 - 1.11246i) q^{4} +0.264773i q^{5} +(0.411062 - 1.35315i) q^{6} +(-0.135503 + 0.234697i) q^{7} +(2.18854 - 1.79173i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.411062 + 1.35315i) q^{2} -1.00000 q^{3} +(-1.66206 - 1.11246i) q^{4} +0.264773i q^{5} +(0.411062 - 1.35315i) q^{6} +(-0.135503 + 0.234697i) q^{7} +(2.18854 - 1.79173i) q^{8} +1.00000 q^{9} +(-0.358279 - 0.108838i) q^{10} +(0.751460 - 1.30157i) q^{11} +(1.66206 + 1.11246i) q^{12} +(-0.859489 + 0.496226i) q^{13} +(-0.261882 - 0.279831i) q^{14} -0.264773i q^{15} +(1.52486 + 3.69794i) q^{16} +(1.75421 + 3.03838i) q^{17} +(-0.411062 + 1.35315i) q^{18} +(-6.01588 + 3.47327i) q^{19} +(0.294550 - 0.440068i) q^{20} +(0.135503 - 0.234697i) q^{21} +(1.45232 + 1.55187i) q^{22} +(-1.36375 + 0.787364i) q^{23} +(-2.18854 + 1.79173i) q^{24} +4.92990 q^{25} +(-0.318168 - 1.36700i) q^{26} -1.00000 q^{27} +(0.486304 - 0.239339i) q^{28} +(-2.13180 + 3.69238i) q^{29} +(0.358279 + 0.108838i) q^{30} +(-0.419440 + 0.726491i) q^{31} +(-5.63070 + 0.543290i) q^{32} +(-0.751460 + 1.30157i) q^{33} +(-4.83248 + 1.12475i) q^{34} +(-0.0621415 - 0.0358774i) q^{35} +(-1.66206 - 1.11246i) q^{36} +(3.43401 + 5.94788i) q^{37} +(-2.22698 - 9.56815i) q^{38} +(0.859489 - 0.496226i) q^{39} +(0.474402 + 0.579467i) q^{40} +(-8.20489 - 4.73710i) q^{41} +(0.261882 + 0.279831i) q^{42} -6.70100 q^{43} +(-2.69691 + 1.32731i) q^{44} +0.264773i q^{45} +(-0.504838 - 2.16903i) q^{46} +(-10.3897 - 5.99851i) q^{47} +(-1.52486 - 3.69794i) q^{48} +(3.46328 + 5.99857i) q^{49} +(-2.02649 + 6.67091i) q^{50} +(-1.75421 - 3.03838i) q^{51} +(1.98055 + 0.131392i) q^{52} -4.07367i q^{53} +(0.411062 - 1.35315i) q^{54} +(0.344620 + 0.198966i) q^{55} +(0.123961 + 0.756428i) q^{56} +(6.01588 - 3.47327i) q^{57} +(-4.12006 - 4.40245i) q^{58} -1.35341i q^{59} +(-0.294550 + 0.440068i) q^{60} +(-12.3123 + 7.10852i) q^{61} +(-0.810639 - 0.866199i) q^{62} +(-0.135503 + 0.234697i) q^{63} +(1.57941 - 7.84254i) q^{64} +(-0.131387 - 0.227570i) q^{65} +(-1.45232 - 1.55187i) q^{66} +(2.59693 + 7.76247i) q^{67} +(0.464483 - 7.00144i) q^{68} +(1.36375 - 0.787364i) q^{69} +(0.0740918 - 0.0693393i) q^{70} +(3.35364 + 1.93622i) q^{71} +(2.18854 - 1.79173i) q^{72} +(0.753239 + 1.30465i) q^{73} +(-9.46000 + 2.20180i) q^{74} -4.92990 q^{75} +(13.8626 + 0.919661i) q^{76} +(0.203649 + 0.352731i) q^{77} +(0.318168 + 1.36700i) q^{78} +(-5.31673 + 9.20885i) q^{79} +(-0.979117 + 0.403743i) q^{80} +1.00000 q^{81} +(9.78275 - 9.15525i) q^{82} +(-9.69920 + 5.59984i) q^{83} +(-0.486304 + 0.239339i) q^{84} +(-0.804481 + 0.464467i) q^{85} +(2.75453 - 9.06749i) q^{86} +(2.13180 - 3.69238i) q^{87} +(-0.687455 - 4.19494i) q^{88} -3.57586 q^{89} +(-0.358279 - 0.108838i) q^{90} -0.268960i q^{91} +(3.14255 + 0.208480i) q^{92} +(0.419440 - 0.726491i) q^{93} +(12.3877 - 11.5932i) q^{94} +(-0.919630 - 1.59285i) q^{95} +(5.63070 - 0.543290i) q^{96} +(9.74602 - 5.62687i) q^{97} +(-9.54062 + 2.22057i) q^{98} +(0.751460 - 1.30157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

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