LMFDB - Embedded newform 570.2.bb.a.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(41,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 13]))

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

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

chi := DirichletCharacter("570.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bb (of order $18$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.1
Character	$\chi$	$=$	570.41
Dual form			570.2.bb.a.431.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(-1.71569 + 0.237506i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.984808 - 0.173648i) q^{5} +(-1.46696 - 0.920884i) q^{6} +(-2.15391 - 3.73068i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.88718 - 0.814973i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(-1.71569 + 0.237506i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.984808 - 0.173648i) q^{5} +(-1.46696 - 0.920884i) q^{6} +(-2.15391 - 3.73068i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.88718 - 0.814973i) q^{9} +(-0.642788 - 0.766044i) q^{10} +(5.10344 + 2.94647i) q^{11} +(-0.531824 - 1.64838i) q^{12} +(-0.685059 + 1.88218i) q^{13} +(0.748044 - 4.24237i) q^{14} +(1.73087 + 0.0640285i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(3.33131 - 3.97010i) q^{17} +(2.73556 + 1.23154i) q^{18} +(3.66401 - 2.36115i) q^{19} -1.00000i q^{20} +(4.58150 + 5.88912i) q^{21} +(2.01551 + 5.53756i) q^{22} +(4.33308 - 0.764038i) q^{23} +(0.652159 - 1.60458i) q^{24} +(0.939693 + 0.342020i) q^{25} +(-1.73463 + 1.00149i) q^{26} +(-4.75995 + 2.08396i) q^{27} +(3.29998 - 2.76901i) q^{28} +(-4.72289 + 3.96297i) q^{29} +(1.28476 + 1.16163i) q^{30} +(8.95735 - 5.17153i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-9.45573 - 3.84314i) q^{33} +(5.10386 - 0.899949i) q^{34} +(1.47336 + 4.04802i) q^{35} +(1.30395 + 2.70180i) q^{36} +4.61808i q^{37} +(4.32451 + 0.546433i) q^{38} +(0.728319 - 3.39195i) q^{39} +(0.642788 - 0.766044i) q^{40} +(2.23666 - 0.814078i) q^{41} +(-0.275823 + 7.45626i) q^{42} +(1.19559 - 6.78053i) q^{43} +(-2.01551 + 5.53756i) q^{44} +(-2.98484 + 0.301238i) q^{45} +(3.81044 + 2.19996i) q^{46} +(-1.62871 - 1.94102i) q^{47} +(1.53099 - 0.809983i) q^{48} +(-5.77864 + 10.0089i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-4.77257 + 7.60267i) q^{51} +(-1.97255 - 0.347814i) q^{52} +(0.495259 + 2.80876i) q^{53} +(-4.98588 - 1.46323i) q^{54} +(-4.51426 - 3.78791i) q^{55} +4.30782 q^{56} +(-5.72552 + 4.92123i) q^{57} -6.16529 q^{58} +(-4.64246 - 3.89548i) q^{59} +(0.237506 + 1.71569i) q^{60} +(-0.709610 - 4.02440i) q^{61} +(10.1859 + 1.79605i) q^{62} +(-9.25913 - 9.01577i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.00149 - 1.73463i) q^{65} +(-4.77319 - 9.02204i) q^{66} +(3.70272 + 4.41273i) q^{67} +(4.48826 + 2.59130i) q^{68} +(-7.25275 + 2.33998i) q^{69} +(-1.47336 + 4.04802i) q^{70} +(0.178695 - 1.01343i) q^{71} +(-0.737803 + 2.90786i) q^{72} +(12.0120 - 4.37201i) q^{73} +(-2.96845 + 3.53766i) q^{74} +(-1.69345 - 0.363618i) q^{75} +(2.96153 + 3.19834i) q^{76} -25.3857i q^{77} +(2.73823 - 2.13023i) q^{78} +(-2.16679 - 5.95320i) q^{79} +(0.984808 - 0.173648i) q^{80} +(7.67164 - 4.70595i) q^{81} +(2.23666 + 0.814078i) q^{82} +(5.69611 - 3.28865i) q^{83} +(-5.00408 + 5.53453i) q^{84} +(-3.97010 + 3.33131i) q^{85} +(5.27431 - 4.42568i) q^{86} +(7.16178 - 7.92095i) q^{87} +(-5.10344 + 2.94647i) q^{88} +(-6.78349 - 2.46899i) q^{89} +(-2.48015 - 1.68785i) q^{90} +(8.49738 - 1.49832i) q^{91} +(1.50486 + 4.13457i) q^{92} +(-14.1398 + 11.0002i) q^{93} -2.53383i q^{94} +(-4.01835 + 1.68903i) q^{95} +(1.69345 + 0.363618i) q^{96} +(1.32366 - 1.57748i) q^{97} +(-10.8603 + 3.95282i) q^{98} +(17.1359 + 4.34784i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9}+O(q^{10}) $ 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9	$ 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9} + 24 q^{13} + 24 q^{14} - 12 q^{17} - 12 q^{19} + 36 q^{22} - 6 q^{24} - 6 q^{27} - 12 q^{28} + 12 q^{29} - 6 q^{33} + 12 q^{34} - 18 q^{38} + 12 q^{39} - 6 q^{41} + 24 q^{43} - 36 q^{44} - 12 q^{47} - 54 q^{49} + 42 q^{50} - 54 q^{51} + 12 q^{52} + 60 q^{53} - 54 q^{54} - 60 q^{57} - 24 q^{58} + 18 q^{59} - 48 q^{61} + 12 q^{62} + 18 q^{63} - 42 q^{64} + 54 q^{66} + 6 q^{67} + 54 q^{68} - 60 q^{69} - 48 q^{71} - 12 q^{72} + 84 q^{73} - 24 q^{74} + 36 q^{78} - 12 q^{79} + 114 q^{81} - 6 q^{82} - 36 q^{83} - 18 q^{84} - 12 q^{86} + 6 q^{87} + 12 q^{89} + 24 q^{91} + 6 q^{93} + 12 q^{95} - 42 q^{97} - 36 q^{98} + 102 q^{99}+O(q^{100}) $ 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9 + 24 * q^13 + 24 * q^14 - 12 * q^17 - 12 * q^19 + 36 * q^22 - 6 * q^24 - 6 * q^27 - 12 * q^28 + 12 * q^29 - 6 * q^33 + 12 * q^34 - 18 * q^38 + 12 * q^39 - 6 * q^41 + 24 * q^43 - 36 * q^44 - 12 * q^47 - 54 * q^49 + 42 * q^50 - 54 * q^51 + 12 * q^52 + 60 * q^53 - 54 * q^54 - 60 * q^57 - 24 * q^58 + 18 * q^59 - 48 * q^61 + 12 * q^62 + 18 * q^63 - 42 * q^64 + 54 * q^66 + 6 * q^67 + 54 * q^68 - 60 * q^69 - 48 * q^71 - 12 * q^72 + 84 * q^73 - 24 * q^74 + 36 * q^78 - 12 * q^79 + 114 * q^81 - 6 * q^82 - 36 * q^83 - 18 * q^84 - 12 * q^86 + 6 * q^87 + 12 * q^89 + 24 * q^91 + 6 * q^93 + 12 * q^95 - 42 * q^97 - 36 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$	$1$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	−1.71569	+	0.237506i	−0.990554	+	0.137124i
$3$	−1.71569	+	0.237506i	−0.990554	+	0.137124i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.984808	−	0.173648i	−0.440419	−	0.0776578i
$5$	−0.984808	−	0.173648i	−0.440419	−	0.0776578i
$6$	−1.46696	−	0.920884i	−0.598884	−	0.375949i
$7$	−2.15391	−	3.73068i	−0.814101	−	1.41006i	−0.909972	−	0.414670i	$-0.863897\pi$
$7$	−2.15391	−	3.73068i	−0.814101	−	1.41006i	0.0958711	−	0.995394i	$-0.469436\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	2.88718	−	0.814973i	0.962394	−	0.271658i
$10$	−0.642788	−	0.766044i	−0.203267	−	0.242245i
$11$	5.10344	+	2.94647i	1.53875	+	0.888395i	0.998913	+	0.0466234i	$0.0148461\pi$
$11$	5.10344	+	2.94647i	1.53875	+	0.888395i	0.539833	+	0.841772i	$0.318487\pi$
$12$	−0.531824	−	1.64838i	−0.153524	−	0.475847i
$13$	−0.685059	+	1.88218i	−0.190001	+	0.522024i	−0.997716	−	0.0675494i	$-0.978482\pi$
$13$	−0.685059	+	1.88218i	−0.190001	+	0.522024i	0.807715	+	0.589574i	$0.200704\pi$
$14$	0.748044	−	4.24237i	0.199923	−	1.13382i
$15$	1.73087	+	0.0640285i	0.446908	+	0.0165321i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	3.33131	−	3.97010i	0.807962	−	0.962891i	−0.191867	−	0.981421i	$-0.561454\pi$
$17$	3.33131	−	3.97010i	0.807962	−	0.962891i	0.999828	+	0.0185298i	$0.00589856\pi$
$18$	2.73556	+	1.23154i	0.644779	+	0.290276i
$19$	3.66401	−	2.36115i	0.840581	−	0.541685i
$19$	3.66401	−	2.36115i	0.840581	−	0.541685i
$20$		−	1.00000i		−	0.223607i
$21$	4.58150	+	5.88912i	0.999764	+	1.28511i
$22$	2.01551	+	5.53756i	0.429708	+	1.18061i
$23$	4.33308	−	0.764038i	0.903509	−	0.159313i	0.297454	−	0.954736i	$-0.403862\pi$
$23$	4.33308	−	0.764038i	0.903509	−	0.159313i	0.606055	+	0.795423i	$0.292751\pi$
$24$	0.652159	−	1.60458i	0.133121	−	0.327534i
$25$	0.939693	+	0.342020i	0.187939	+	0.0684040i
$26$	−1.73463	+	1.00149i	−0.340189	+	0.196408i
$27$	−4.75995	+	2.08396i	−0.916052	+	0.401059i
$28$	3.29998	−	2.76901i	0.623637	−	0.523294i
$29$	−4.72289	+	3.96297i	−0.877018	+	0.735906i	−0.965564	−	0.260166i	$-0.916223\pi$
$29$	−4.72289	+	3.96297i	−0.877018	+	0.735906i	0.0885454	+	0.996072i	$0.471778\pi$
$30$	1.28476	+	1.16163i	0.234565	+	0.212083i
$31$	8.95735	−	5.17153i	1.60879	−	0.928834i	0.619145	−	0.785276i	$-0.287479\pi$
$31$	8.95735	−	5.17153i	1.60879	−	0.928834i	0.989642	−	0.143557i	$-0.0458542\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	−9.45573	−	3.84314i	−1.64603	−	0.669004i
$34$	5.10386	−	0.899949i	0.875306	−	0.154340i
$35$	1.47336	+	4.04802i	0.249043	+	0.684241i
$36$	1.30395	+	2.70180i	0.217324	+	0.450300i
$37$			4.61808i			0.759208i	0.925149	+	0.379604i	$0.123940\pi$
$37$			4.61808i			0.759208i	−0.925149	+	0.379604i	$0.876060\pi$
$38$	4.32451	+	0.546433i	0.701529	+	0.0886432i
$39$	0.728319	−	3.39195i	0.116624	−	0.543147i
$40$	0.642788	−	0.766044i	0.101634	−	0.121122i
$41$	2.23666	−	0.814078i	0.349308	−	0.127138i	−0.161407	−	0.986888i	$-0.551603\pi$
$41$	2.23666	−	0.814078i	0.349308	−	0.127138i	0.510715	+	0.859750i	$0.329381\pi$
$42$	−0.275823	+	7.45626i	−0.0425604	+	1.15053i
$43$	1.19559	−	6.78053i	0.182326	−	1.03402i	−0.747018	−	0.664804i	$-0.768515\pi$
$43$	1.19559	−	6.78053i	0.182326	−	1.03402i	0.929343	−	0.369217i	$-0.120374\pi$
$44$	−2.01551	+	5.53756i	−0.303849	+	0.834819i
$45$	−2.98484	+	0.301238i	−0.444953	+	0.0449060i
$46$	3.81044	+	2.19996i	0.561819	+	0.324367i
$47$	−1.62871	−	1.94102i	−0.237572	−	0.283127i	0.634064	−	0.773280i	$-0.281385\pi$
$47$	−1.62871	−	1.94102i	−0.237572	−	0.283127i	−0.871636	+	0.490153i	$0.836941\pi$
$48$	1.53099	−	0.809983i	0.220979	−	0.116911i
$49$	−5.77864	+	10.0089i	−0.825520	+	1.42984i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−4.77257	+	7.60267i	−0.668294	+	1.06459i
$52$	−1.97255	−	0.347814i	−0.273543	−	0.0482331i
$53$	0.495259	+	2.80876i	0.0680291	+	0.385812i	0.999744	+	0.0226220i	$0.00720141\pi$
$53$	0.495259	+	2.80876i	0.0680291	+	0.385812i	−0.931715	+	0.363190i	$0.881687\pi$
$54$	−4.98588	−	1.46323i	−0.678492	−	0.199120i
$55$	−4.51426	−	3.78791i	−0.608703	−	0.510762i
$56$	4.30782			0.575656
$57$	−5.72552	+	4.92123i	−0.758363	+	0.651832i
$58$	−6.16529			−0.809543
$59$	−4.64246	−	3.89548i	−0.604396	−	0.507149i	0.288459	−	0.957492i	$-0.406857\pi$
$59$	−4.64246	−	3.89548i	−0.604396	−	0.507149i	−0.892855	+	0.450343i	$0.851302\pi$
$60$	0.237506	+	1.71569i	0.0306619	+	0.221495i
$61$	−0.709610	−	4.02440i	−0.0908563	−	0.515272i	−0.995939	−	0.0900351i	$-0.971302\pi$
$61$	−0.709610	−	4.02440i	−0.0908563	−	0.515272i	0.905082	−	0.425236i	$-0.139809\pi$
$62$	10.1859	+	1.79605i	1.29361	+	0.228099i
$63$	−9.25913	−	9.01577i	−1.16654	−	1.13588i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	1.00149	−	1.73463i	0.124219	−	0.215154i
$66$	−4.77319	−	9.02204i	−0.587539	−	1.11054i
$67$	3.70272	+	4.41273i	0.452359	+	0.539101i	0.943234	−	0.332130i	$-0.107767\pi$
$67$	3.70272	+	4.41273i	0.452359	+	0.539101i	−0.490875	+	0.871230i	$0.663323\pi$
$68$	4.48826	+	2.59130i	0.544282	+	0.314241i
$69$	−7.25275	+	2.33998i	−0.873129	+	0.281701i
$70$	−1.47336	+	4.04802i	−0.176100	+	0.483831i
$71$	0.178695	−	1.01343i	0.0212072	−	0.120272i	−0.972366	−	0.233460i	$-0.924995\pi$
$71$	0.178695	−	1.01343i	0.0212072	−	0.120272i	0.993574	+	0.113188i	$0.0361063\pi$
$72$	−0.737803	+	2.90786i	−0.0869509	+	0.342695i
$73$	12.0120	−	4.37201i	1.40590	−	0.511705i	0.475974	−	0.879459i	$-0.342096\pi$
$73$	12.0120	−	4.37201i	1.40590	−	0.511705i	0.929923	+	0.367755i	$0.119873\pi$
$74$	−2.96845	+	3.53766i	−0.345075	+	0.411244i
$75$	−1.69345	−	0.363618i	−0.195543	−	0.0419870i
$76$	2.96153	+	3.19834i	0.339711	+	0.366874i
$77$		−	25.3857i		−	2.89297i
$78$	2.73823	−	2.13023i	0.310043	−	0.241201i
$79$	−2.16679	−	5.95320i	−0.243783	−	0.669787i	−0.999882	−	0.0153308i	$-0.995120\pi$
$79$	−2.16679	−	5.95320i	−0.243783	−	0.669787i	0.756100	−	0.654456i	$-0.227102\pi$
$80$	0.984808	−	0.173648i	0.110105	−	0.0194145i
$81$	7.67164	−	4.70595i	0.852404	−	0.522884i
$82$	2.23666	+	0.814078i	0.246998	+	0.0898999i
$83$	5.69611	−	3.28865i	0.625229	−	0.360976i	−0.153673	−	0.988122i	$-0.549110\pi$
$83$	5.69611	−	3.28865i	0.625229	−	0.360976i	0.778902	+	0.627146i	$0.215777\pi$
$84$	−5.00408	+	5.53453i	−0.545990	+	0.603867i
$85$	−3.97010	+	3.33131i	−0.430618	+	0.361331i
$86$	5.27431	−	4.42568i	0.568744	−	0.477233i
$87$	7.16178	−	7.92095i	0.767823	−	0.849215i
$88$	−5.10344	+	2.94647i	−0.544029	+	0.314095i
$89$	−6.78349	−	2.46899i	−0.719049	−	0.261712i	−0.0435268	−	0.999052i	$-0.513859\pi$
$89$	−6.78349	−	2.46899i	−0.719049	−	0.261712i	−0.675522	+	0.737340i	$0.736082\pi$
$90$	−2.48015	−	1.68785i	−0.261431	−	0.177916i
$91$	8.49738	−	1.49832i	0.890767	−	0.157066i
$92$	1.50486	+	4.13457i	0.156893	+	0.431059i
$93$	−14.1398	+	11.0002i	−1.46622	+	1.14066i
$94$		−	2.53383i		−	0.261344i
$95$	−4.01835	+	1.68903i	−0.412274	+	0.173291i
$96$	1.69345	+	0.363618i	0.172837	+	0.0371116i
$97$	1.32366	−	1.57748i	0.134398	−	0.160169i	−0.694648	−	0.719350i	$-0.744440\pi$
$97$	1.32366	−	1.57748i	0.134398	−	0.160169i	0.829046	+	0.559181i	$0.188884\pi$
$98$	−10.8603	+	3.95282i	−1.09705	+	0.399295i
$99$	17.1359	+	4.34784i	1.72222	+	0.436974i
$100$	−0.173648	+	0.984808i	−0.0173648	+	0.0984808i
$101$	−6.60827	+	18.1561i	−0.657548	+	1.80660i	−0.0697877	+	0.997562i	$0.522232\pi$
$101$	−6.60827	+	18.1561i	−0.657548	+	1.80660i	−0.587760	+	0.809035i	$0.699990\pi$
$102$	−8.54290	+	2.75623i	−0.845874	+	0.272908i
$103$	−5.33712	−	3.08139i	−0.525882	−	0.303618i	0.213456	−	0.976953i	$-0.431528\pi$
$103$	−5.33712	−	3.08139i	−0.525882	−	0.303618i	−0.739338	+	0.673335i	$0.764861\pi$
$104$	−1.28749	−	1.53437i	−0.126249	−	0.150457i
$105$	−3.48926	−	6.59522i	−0.340517	−	0.643627i
$106$	−1.42604	+	2.46998i	−0.138510	+	0.239906i
$107$	−0.270503	−	0.468526i	−0.0261505	−	0.0452941i	0.852654	−	0.522476i	$-0.174992\pi$
$107$	−0.270503	−	0.468526i	−0.0261505	−	0.0452941i	−0.878805	+	0.477182i	$0.841658\pi$
$108$	−2.87886	−	4.32576i	−0.277018	−	0.416246i
$109$	−8.29811	−	1.46318i	−0.794815	−	0.140147i	−0.238526	−	0.971136i	$-0.576664\pi$
$109$	−8.29811	−	1.46318i	−0.794815	−	0.140147i	−0.556289	+	0.830989i	$0.687775\pi$
$110$	−1.02330	−	5.80342i	−0.0975678	−	0.553334i
$111$	−1.09682	−	7.92320i	−0.104106	−	0.752037i
$112$	3.29998	+	2.76901i	0.311819	+	0.261647i
$113$	−1.20824			−0.113662			−0.0568308	−	0.998384i	$-0.518100\pi$
$113$	−1.20824			−0.113662			−0.0568308	+	0.998384i	$0.518100\pi$
$114$	−7.54930	+	0.0895880i	−0.707057	+	0.00839068i
$115$	−4.39992			−0.410295
$116$	−4.72289	−	3.96297i	−0.438509	−	0.367953i
$117$	−0.443960	+	5.99251i	−0.0410441	+	0.554008i
$118$	−1.05236	−	5.96823i	−0.0968776	−	0.549420i
$119$	−21.9865	−	3.87682i	−2.01550	−	0.355387i
$120$	−0.920884	+	1.46696i	−0.0840648	+	0.133915i
$121$	11.8634	+	20.5480i	1.07849	+	1.86800i
$122$	2.04324	−	3.53900i	0.184986	−	0.320406i
$123$	−3.64407	+	1.92793i	−0.328575	+	0.173835i
$124$	6.64839	+	7.92324i	0.597043	+	0.711528i
$125$	−0.866025	−	0.500000i	−0.0774597	−	0.0447214i
$126$	−1.29768	−	12.8581i	−0.115606	−	1.14549i
$127$	−0.0757411	+	0.208097i	−0.00672094	+	0.0184656i	−0.943008	−	0.332771i	$-0.892016\pi$
$127$	−0.0757411	+	0.208097i	−0.00672094	+	0.0184656i	0.936287	+	0.351236i	$0.114239\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	−0.440845	+	11.9172i	−0.0388142	+	1.04925i
$130$	1.88218	−	0.685059i	0.165079	−	0.0600837i
$131$	3.86634	−	4.60773i	0.337804	−	0.402579i	−0.570224	−	0.821489i	$-0.693143\pi$
$131$	3.86634	−	4.60773i	0.337804	−	0.402579i	0.908028	+	0.418911i	$0.137588\pi$
$132$	2.14278	−	9.97943i	0.186505	−	0.868598i
$133$	−16.7006	−	8.58354i	−1.44813	−	0.744287i
$134$			5.76041i			0.497623i
$135$	5.04951	−	1.22575i	0.434593	−	0.105496i
$136$	1.77255	+	4.87005i	0.151995	+	0.417603i
$137$	−20.1604	+	3.55483i	−1.72242	+	0.303709i	−0.945436	−	0.325808i	$-0.894364\pi$
$137$	−20.1604	+	3.55483i	−1.72242	+	0.303709i	−0.776986	+	0.629518i	$0.783252\pi$
$138$	−7.06004	−	2.86945i	−0.600991	−	0.244264i
$139$	14.8501	+	5.40498i	1.25957	+	0.458445i	0.883624	−	0.468198i	$-0.155097\pi$
$139$	14.8501	+	5.40498i	1.25957	+	0.458445i	0.375943	+	0.926643i	$0.377319\pi$
$140$	−3.73068	+	2.15391i	−0.315300	+	0.182038i
$141$	3.25537	+	2.94336i	0.274151	+	0.247876i
$142$	0.788308	−	0.661469i	0.0661533	−	0.0555092i
$143$	−9.04197	+	7.58711i	−0.756127	+	0.634466i
$144$	−2.43433	+	1.75330i	−0.202861	+	0.146108i
$145$	5.33930	−	3.08265i	0.443405	−	0.256000i
$146$	12.0120	+	4.37201i	0.994119	+	0.361830i
$147$	7.53718	−	18.5446i	0.621656	−	1.52953i
$148$	−4.54792	+	0.801922i	−0.373837	+	0.0659176i
$149$	−1.52610	−	4.19293i	−0.125023	−	0.343498i	0.861352	−	0.508008i	$-0.169618\pi$
$149$	−1.52610	−	4.19293i	−0.125023	−	0.343498i	−0.986375	+	0.164510i	$0.947396\pi$
$150$	−1.06353	−	1.36708i	−0.0868370	−	0.111621i
$151$			14.0808i			1.14588i	0.819598	+	0.572939i	$0.194197\pi$
$151$			14.0808i			1.14588i	−0.819598	+	0.572939i	$0.805803\pi$
$152$	0.212812	+	4.35370i	0.0172613	+	0.353132i
$153$	6.38257	−	14.1773i	0.516000	−	1.14617i
$154$	16.3176	−	19.4466i	1.31491	−	1.56705i
$155$	−9.71929	+	3.53753i	−0.780672	+	0.284142i
$156$	3.46689	+	0.128248i	0.277573	+	0.0102680i
$157$	−0.545175	+	3.09184i	−0.0435097	+	0.246756i	−0.998804	−	0.0489022i	$-0.984428\pi$
$157$	−0.545175	+	3.09184i	−0.0435097	+	0.246756i	0.955294	+	0.295658i	$0.0955388\pi$
$158$	2.16679	−	5.95320i	0.172380	−	0.473611i
$159$	−1.51681	−	4.70133i	−0.120291	−	0.372839i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	−12.1834	−	14.5196i	−0.960189	−	1.14431i
$162$	8.90174	+	1.32626i	0.699387	+	0.104201i
$163$	−9.86741	+	17.0908i	−0.772875	+	1.33866i	0.163106	+	0.986609i	$0.447849\pi$
$163$	−9.86741	+	17.0908i	−0.772875	+	1.33866i	−0.935981	+	0.352050i	$0.885485\pi$
$164$	1.19010	+	2.06132i	0.0929314	+	0.160962i
$165$	8.64472	+	5.42672i	0.672991	+	0.422470i
$166$	6.47737	+	1.14214i	0.502742	+	0.0886469i
$167$	4.24877	+	24.0960i	0.328780	+	1.86460i	0.481662	+	0.876357i	$0.340033\pi$
$167$	4.24877	+	24.0960i	0.328780	+	1.86460i	−0.152882	+	0.988244i	$0.548855\pi$
$168$	−7.39088	+	1.02313i	−0.570218	+	0.0789364i
$169$	6.88526	+	5.77742i	0.529636	+	0.444417i
$170$	−5.18260			−0.397487
$171$	8.65439	−	9.80314i	0.661817	−	0.749665i
$172$	6.88513			0.524986
$173$	−6.31947	−	5.30267i	−0.480461	−	0.403154i	0.370132	−	0.928979i	$-0.379312\pi$
$173$	−6.31947	−	5.30267i	−0.480461	−	0.403154i	−0.850593	+	0.525825i	$0.823757\pi$
$174$	10.5777	−	1.46429i	0.801896	−	0.111008i
$175$	−0.748044	−	4.24237i	−0.0565468	−	0.320693i
$176$	−5.80342	−	1.02330i	−0.437449	−	0.0771341i
$177$	8.89022	+	5.58083i	0.668230	+	0.419481i
$178$	−3.60942	−	6.25170i	−0.270538	−	0.468585i
$179$	7.61972	−	13.1977i	0.569525	−	0.986446i	−0.427088	−	0.904210i	$-0.640461\pi$
$179$	7.61972	−	13.1977i	0.569525	−	0.986446i	0.996613	−	0.0822356i	$-0.0262060\pi$
$180$	−0.814973	−	2.88718i	−0.0607445	−	0.215198i
$181$	−7.65703	−	9.12530i	−0.569143	−	0.678278i	0.402312	−	0.915503i	$-0.368207\pi$
$181$	−7.65703	−	9.12530i	−0.569143	−	0.678278i	−0.971455	+	0.237225i	$0.923762\pi$
$182$	7.47247	+	4.31423i	0.553896	+	0.319792i
$183$	2.17329	+	6.73608i	0.160654	+	0.497946i
$184$	−1.50486	+	4.13457i	−0.110940	+	0.304805i
$185$	0.801922	−	4.54792i	0.0589585	−	0.334370i
$186$	−17.9025	−	0.662251i	−1.31267	−	0.0485586i
$187$	28.6990	−	10.4456i	2.09868	−	0.763855i
$188$	1.62871	−	1.94102i	0.118786	−	0.141564i
$189$	18.0271	+	13.2692i	1.31128	+	0.965189i
$190$	−4.16393	−	1.28908i	−0.302083	−	0.0935194i
$191$			0.532682i			0.0385435i	0.999814	+	0.0192717i	$0.00613477\pi$
$191$			0.532682i			0.0385435i	−0.999814	+	0.0192717i	$0.993865\pi$
$192$	1.06353	+	1.36708i	0.0767537	+	0.0986603i
$193$	−0.495387	−	1.36106i	−0.0356587	−	0.0979715i	0.920586	−	0.390541i	$-0.127712\pi$
$193$	−0.495387	−	1.36106i	−0.0356587	−	0.0979715i	−0.956244	+	0.292569i	$0.905490\pi$
$194$	2.02797	−	0.357586i	0.145600	−	0.0256732i
$195$	−1.30626	+	3.21395i	−0.0935432	+	0.230156i
$196$	−10.8603	−	3.95282i	−0.775735	−	0.282344i
$197$	0.425344	−	0.245573i	0.0303045	−	0.0174963i	−0.484771	−	0.874641i	$-0.661097\pi$
$197$	0.425344	−	0.245573i	0.0303045	−	0.0174963i	0.515076	+	0.857145i	$0.327764\pi$
$198$	10.3321	+	14.3454i	0.734270	+	1.01948i
$199$	3.05485	−	2.56332i	0.216552	−	0.181709i	−0.528058	−	0.849208i	$-0.677080\pi$
$199$	3.05485	−	2.56332i	0.216552	−	0.181709i	0.744611	+	0.667499i	$0.232635\pi$
$200$	−0.766044	+	0.642788i	−0.0541675	+	0.0454519i
$201$	−7.40077	−	6.69145i	−0.522010	−	0.471979i
$202$	−16.7327	+	9.66065i	−1.17731	+	0.679721i
$203$	24.9572	+	9.08370i	1.75166	+	0.637550i
$204$	−8.31592	−	3.37988i	−0.582231	−	0.236639i
$205$	−2.34405	+	0.413318i	−0.163715	+	0.0288674i
$206$	−2.10779	−	5.79111i	−0.146857	−	0.403486i
$207$	11.8877	−	5.73726i	0.826253	−	0.398767i
$208$		−	2.00298i		−	0.138882i
$209$	25.6561	−	1.25409i	1.77467	−	0.0867472i
$210$	1.56640	−	7.29508i	0.108092	−	0.503409i
$211$	8.58556	−	10.2319i	0.591054	−	0.704391i	−0.384754	−	0.923019i	$-0.625714\pi$
$211$	8.58556	−	10.2319i	0.591054	−	0.704391i	0.975808	+	0.218628i	$0.0701581\pi$
$212$	−2.68008	+	0.975471i	−0.184069	+	0.0669956i
$213$	−0.0658894	+	1.78117i	−0.00451467	+	0.122044i
$214$	0.0939448	−	0.532788i	0.00642194	−	0.0364206i
$215$	−2.35485	+	6.46991i	−0.160600	+	0.441244i
$216$	0.575207	−	5.16422i	0.0391379	−	0.351380i
$217$	−38.5866	−	22.2780i	−2.61943	−	1.51233i
$218$	−5.41621	−	6.45478i	−0.366832	−	0.437173i
$219$	−19.5705	+	10.3539i	−1.32245	+	0.699653i
$220$	2.94647	−	5.10344i	0.198651	−	0.344074i
$221$	5.19032	+	8.98990i	0.349139	+	0.604726i
$222$	4.25272	−	6.77455i	0.285424	−	0.454678i
$223$	0.0146314	+	0.00257991i	0.000979791	+	0.000172764i	0.174138	−	0.984721i	$-0.444286\pi$
$223$	0.0146314	+	0.00257991i	0.000979791	+	0.000172764i	−0.173158	+	0.984894i	$0.555397\pi$
$224$	0.748044	+	4.24237i	0.0499808	+	0.283455i
$225$	2.99180	+	0.221650i	0.199453	+	0.0147767i
$226$	−0.925565	−	0.776641i	−0.0615677	−	0.0516614i
$227$	−10.6199			−0.704866			−0.352433	−	0.935837i	$-0.614645\pi$
$227$	−10.6199			−0.704866			−0.352433	+	0.935837i	$0.614645\pi$
$228$	−5.84069	−	4.78397i	−0.386809	−	0.316826i
$229$	14.0898			0.931077			0.465539	−	0.885028i	$-0.345861\pi$
$229$	14.0898			0.931077			0.465539	+	0.885028i	$0.345861\pi$
$230$	−3.37054	−	2.82822i	−0.222247	−	0.186487i
$231$	6.02927	+	43.5540i	0.396697	+	2.86565i
$232$	−1.07059	−	6.07163i	−0.0702878	−	0.398622i
$233$	23.0906	+	4.07150i	1.51272	+	0.266733i	0.867566	−	0.497322i	$-0.165683\pi$
$233$	23.0906	+	4.07150i	1.51272	+	0.266733i	0.645151	+	0.764055i	$0.276794\pi$
$234$	−4.19201	+	4.30516i	−0.274040	+	0.281437i
$235$	1.26691	+	2.19436i	0.0826443	+	0.143144i
$236$	3.03015	−	5.24837i	0.197246	−	0.341640i
$237$	5.13145	+	9.69921i	0.333324	+	0.630032i
$238$	−14.3507	−	17.1025i	−0.930216	−	1.10859i
$239$	−18.5149	−	10.6896i	−1.19763	−	0.691453i	−0.237605	−	0.971362i	$-0.576362\pi$
$239$	−18.5149	−	10.6896i	−1.19763	−	0.691453i	−0.960027	+	0.279909i	$0.909696\pi$
$240$	−1.64838	+	0.531824i	−0.106403	+	0.0343291i
$241$	−8.27165	+	22.7262i	−0.532824	+	1.46392i	0.322873	+	0.946442i	$0.395351\pi$
$241$	−8.27165	+	22.7262i	−0.532824	+	1.46392i	−0.855696	+	0.517478i	$0.826871\pi$
$242$	−4.12012	+	23.3664i	−0.264851	+	1.50205i
$243$	−12.0445	+	9.89601i	−0.772652	+	0.634830i
$244$	3.84004	−	1.39766i	0.245833	−	0.0894760i
$245$	7.42888	−	8.85339i	0.474613	−	0.565622i
$246$	−4.03077	−	0.865485i	−0.256992	−	0.0551813i
$247$	1.93406	+	8.51387i	0.123061	+	0.541725i
$248$			10.3431i			0.656785i
$249$	−8.99168	+	6.99516i	−0.569824	+	0.443300i
$250$	−0.342020	−	0.939693i	−0.0216313	−	0.0594314i
$251$	−12.9411	+	2.28187i	−0.816836	+	0.144030i	−0.566429	−	0.824110i	$-0.691676\pi$
$251$	−12.9411	+	2.28187i	−0.816836	+	0.144030i	−0.250407	+	0.968141i	$0.580564\pi$
$252$	7.27097	−	10.6840i	0.458028	−	0.673031i
$253$	24.3648	+	8.86807i	1.53180	+	0.557531i
$254$	−0.191783	+	0.110726i	−0.0120336	+	0.00694758i
$255$	6.02026	−	6.65842i	0.377003	−	0.416966i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	15.5721	−	13.0666i	0.971363	−	0.815070i	−0.0114010	−	0.999935i	$-0.503629\pi$
$257$	15.5721	−	13.0666i	0.971363	−	0.815070i	0.982764	+	0.184865i	$0.0591847\pi$
$258$	−7.99796	+	8.84577i	−0.497931	+	0.550713i
$259$	17.2286	−	9.94693i	1.07053	−	0.618072i
$260$	1.88218	+	0.685059i	0.116728	+	0.0424856i
$261$	−10.4061	+	15.2909i	−0.644123	+	0.946480i
$262$	5.92358	−	1.04449i	0.365960	−	0.0645286i
$263$	−2.82249	−	7.75474i	−0.174042	−	0.478178i	0.821746	−	0.569853i	$-0.193000\pi$
$263$	−2.82249	−	7.75474i	−0.174042	−	0.478178i	−0.995789	+	0.0916755i	$0.970778\pi$
$264$	8.05612	−	6.26733i	0.495820	−	0.385728i
$265$		−	2.85209i		−	0.175202i
$266$	−7.27604	−	17.3103i	−0.446122	−	1.06136i
$267$	12.2248	+	2.62490i	0.748144	+	0.160641i
$268$	−3.70272	+	4.41273i	−0.226180	+	0.269550i
$269$	7.14462	−	2.60043i	0.435615	−	0.158551i	−0.114898	−	0.993377i	$-0.536654\pi$
$269$	7.14462	−	2.60043i	0.435615	−	0.158551i	0.550513	+	0.834826i	$0.314432\pi$
$270$	4.65604	+	2.30678i	0.283358	+	0.140386i
$271$	3.06363	−	17.3747i	0.186103	−	1.05544i	−0.738428	−	0.674332i	$-0.764432\pi$
$271$	3.06363	−	17.3747i	0.186103	−	1.05544i	0.924531	−	0.381108i	$-0.124457\pi$
$272$	−1.77255	+	4.87005i	−0.107477	+	0.295290i
$273$	−14.2230	+	4.58883i	−0.860816	+	0.277728i
$274$	−17.7288	−	10.2357i	−1.07104	−	0.618362i
$275$	3.78791	+	4.51426i	0.228420	+	0.272220i
$276$	−3.56386	−	6.73623i	−0.214519	−	0.405474i
$277$	−13.5646	+	23.4946i	−0.815019	+	1.41165i	0.0942960	+	0.995544i	$0.469940\pi$
$277$	−13.5646	+	23.4946i	−0.815019	+	1.41165i	−0.909315	+	0.416109i	$0.863393\pi$
$278$	7.90156	+	13.6859i	0.473904	+	0.820826i
$279$	21.6468	−	22.2311i	1.29596	−	1.33094i
$280$	−4.24237	−	0.748044i	−0.253530	−	0.0447042i
$281$	2.83820	+	16.0962i	0.169313	+	0.960221i	0.944505	+	0.328496i	$0.106542\pi$
$281$	2.83820	+	16.0962i	0.169313	+	0.960221i	−0.775192	+	0.631725i	$0.782347\pi$
$282$	0.601799	+	4.34726i	0.0358366	+	0.258875i
$283$	−10.2346	−	8.58788i	−0.608386	−	0.510497i	0.285743	−	0.958306i	$-0.407760\pi$
$283$	−10.2346	−	8.58788i	−0.608386	−	0.510497i	−0.894129	+	0.447810i	$0.852204\pi$
$284$	1.02906			0.0610637
$285$	6.49309	−	3.85224i	0.384618	−	0.228187i
$286$	−11.8035			−0.697953
$287$	−7.85463	−	6.59082i	−0.463644	−	0.389044i
$288$	−2.99180	−	0.221650i	−0.176294	−	0.0130608i
$289$	−1.71206	−	9.70956i	−0.100709	−	0.571151i
$290$	6.07163	+	1.07059i	0.356538	+	0.0628673i
$291$	−1.89633	+	3.02085i	−0.111165	+	0.177085i
$292$	6.39145	+	11.0703i	0.374031	+	0.647841i
$293$	−8.04841	+	13.9403i	−0.470193	+	0.814398i	−0.999419	−	0.0340825i	$-0.989149\pi$
$293$	−8.04841	+	13.9403i	−0.470193	+	0.814398i	0.529226	+	0.848481i	$0.322482\pi$
$294$	17.6941	−	9.36120i	1.03194	−	0.545956i
$295$	3.89548	+	4.64246i	0.226804	+	0.270294i
$296$	−3.99938	−	2.30904i	−0.232459	−	0.134210i
$297$	−30.4325	−	3.38966i	−1.76587	−	0.196688i
$298$	1.52610	−	4.19293i	0.0884047	−	0.242890i
$299$	−1.53035	+	8.67906i	−0.0885026	+	0.501923i
$300$	0.0640285	−	1.73087i	0.00369669	−	0.0999316i
$301$	−27.8712	+	10.1443i	−1.60647	+	0.584706i
$302$	−9.05096	+	10.7865i	−0.520824	+	0.620694i
$303$	7.02556	−	32.7197i	0.403608	−	1.87970i
$304$	−2.63548	+	3.47192i	−0.151155	+	0.199128i
$305$			4.08648i			0.233991i
$306$	14.0024	−	6.75783i	0.800461	−	0.386319i
$307$	7.23407	+	19.8755i	0.412870	+	1.13435i	0.955657	+	0.294481i	$0.0951469\pi$
$307$	7.23407	+	19.8755i	0.412870	+	1.13435i	−0.542787	+	0.839870i	$0.682631\pi$
$308$	25.0001	−	4.40819i	1.42451	−	0.251180i
$309$	9.88868	+	4.01910i	0.562548	+	0.228639i
$310$	−9.71929	−	3.53753i	−0.552019	−	0.200918i
$311$	−0.773439	+	0.446545i	−0.0438577	+	0.0253212i	−0.521769	−	0.853087i	$-0.674728\pi$
$311$	−0.773439	+	0.446545i	−0.0438577	+	0.0253212i	0.477911	+	0.878408i	$0.341394\pi$
$312$	2.57336	+	2.32672i	0.145688	+	0.131724i
$313$	−13.2099	+	11.0844i	−0.746668	+	0.626529i	−0.934619	−	0.355650i	$-0.884260\pi$
$313$	−13.2099	+	11.0844i	−0.746668	+	0.626529i	0.187952	+	0.982178i	$0.439815\pi$
$314$	−2.40502	+	2.01806i	−0.135723	+	0.113885i
$315$	7.55289	+	10.4866i	0.425557	+	0.590855i
$316$	5.48650	−	3.16763i	0.308640	−	0.178193i
$317$	25.4354	+	9.25774i	1.42860	+	0.519966i	0.936529	−	0.350591i	$-0.114019\pi$
$317$	25.4354	+	9.25774i	1.42860	+	0.519966i	0.492067	+	0.870557i	$0.336241\pi$
$318$	1.86001	−	4.57641i	0.104304	−	0.256632i
$319$	−35.7798	+	6.30894i	−2.00328	+	0.353233i
$320$	0.342020	+	0.939693i	0.0191195	+	0.0525304i
$321$	0.575377	+	0.739598i	0.0321144	+	0.0412803i
$322$		−	18.9541i		−	1.05627i
$323$	2.83195	−	22.4122i	0.157574	−	1.24705i
$324$	5.96662	+	6.73791i	0.331479	+	0.374328i
$325$	−1.28749	+	1.53437i	−0.0714171	+	0.0851116i
$326$	−18.5447	+	6.74970i	−1.02709	+	0.373831i
$327$	14.5845	+	0.539512i	0.806525	+	0.0298351i
$328$	−0.413318	+	2.34405i	−0.0228217	+	0.129428i
$329$	−3.73324	+	10.2570i	−0.205820	+	0.565486i
$330$	3.13401	+	9.71383i	0.172522	+	0.534729i
$331$	−2.05129	−	1.18431i	−0.112749	−	0.0650958i	0.442565	−	0.896736i	$-0.354069\pi$
$331$	−2.05129	−	1.18431i	−0.112749	−	0.0650958i	−0.555314	+	0.831641i	$0.687402\pi$
$332$	4.22781	+	5.03850i	0.232031	+	0.276524i
$333$	3.76362	+	13.3332i	0.206245	+	0.730657i
$334$	−12.2338	+	21.1896i	−0.669406	+	1.15945i
$335$	−2.88020	−	4.98866i	−0.157362	−	0.272560i
$336$	−6.31940	−	3.96700i	−0.344751	−	0.216417i
$337$	−10.7599	−	1.89726i	−0.586128	−	0.103350i	−0.127283	−	0.991866i	$-0.540626\pi$
$337$	−10.7599	−	1.89726i	−0.586128	−	0.103350i	−0.458845	+	0.888516i	$0.651737\pi$
$338$	1.56076	+	8.85153i	0.0848943	+	0.481459i
$339$	2.07296	−	0.286964i	0.112588	−	0.0155858i
$340$	−3.97010	−	3.33131i	−0.215309	−	0.180666i
$341$	60.9511			3.30069
$342$	12.9310	−	1.94671i	0.699227	−	0.105266i
$343$	19.6319			1.06002
$344$	5.27431	+	4.42568i	0.284372	+	0.238616i
$345$	7.54890	−	1.04501i	0.406419	−	0.0562614i
$346$	−1.43251	−	8.12416i	−0.0770121	−	0.436757i
$347$	8.44952	+	1.48988i	0.453594	+	0.0799809i	0.395778	−	0.918346i	$-0.370475\pi$
$347$	8.44952	+	1.48988i	0.453594	+	0.0799809i	0.0578164	+	0.998327i	$0.481586\pi$
$348$	9.04424	+	5.67752i	0.484822	+	0.304347i
$349$	−15.1347	−	26.2140i	−0.810140	−	1.40320i	−0.912765	−	0.408484i	$-0.866058\pi$
$349$	−15.1347	−	26.2140i	−0.810140	−	1.40320i	0.102625	−	0.994720i	$-0.467276\pi$
$350$	2.15391	−	3.73068i	0.115131	−	0.199413i
$351$	−0.661561	−	10.3867i	−0.0353115	−	0.554403i
$352$	−3.78791	−	4.51426i	−0.201896	−	0.240611i
$353$	−22.8646	−	13.2009i	−1.21696	−	0.702611i	−0.252691	−	0.967547i	$-0.581316\pi$
$353$	−22.8646	−	13.2009i	−1.21696	−	0.702611i	−0.964266	+	0.264936i	$0.914649\pi$
$354$	3.22301	+	9.98968i	0.171301	+	0.530946i
$355$	−0.351960	+	0.967003i	−0.0186801	+	0.0513232i
$356$	1.25354	−	7.10917i	0.0664374	−	0.376785i
$357$	38.6428	+	1.42948i	2.04519	+	0.0756562i
$358$	14.3204	−	5.21220i	0.756856	−	0.275473i
$359$	1.63105	−	1.94381i	0.0860835	−	0.102590i	−0.721283	−	0.692640i	$-0.756447\pi$
$359$	1.63105	−	1.94381i	0.0860835	−	0.102590i	0.807367	+	0.590050i	$0.200892\pi$
$360$	1.23154	−	2.73556i	0.0649078	−	0.144177i
$361$	7.84993	−	17.3026i	0.413154	−	0.910661i
$362$		−	11.9122i		−	0.626093i
$363$	−25.2342	−	32.4364i	−1.32445	−	1.70247i
$364$	2.95111	+	8.10811i	0.154680	+	0.424980i
$365$	−12.5887	+	2.21973i	−0.658922	+	0.116186i
$366$	−2.66503	+	6.55710i	−0.139304	+	0.342745i
$367$	−32.9140	−	11.9797i	−1.71810	−	0.625337i	−0.720427	−	0.693531i	$-0.756054\pi$
$367$	−32.9140	−	11.9797i	−1.71810	−	0.625337i	−0.997672	+	0.0681942i	$0.978276\pi$
$368$	−3.81044	+	2.19996i	−0.198633	+	0.114681i
$369$	5.79420	−	4.17321i	0.301634	−	0.217249i
$370$	3.53766	−	2.96845i	0.183914	−	0.154322i
$371$	9.41182	−	7.89746i	0.488637	−	0.410015i
$372$	−13.2884	−	12.0148i	−0.688971	−	0.622938i
$373$	17.7079	−	10.2236i	0.916878	−	0.529360i	0.0342404	−	0.999414i	$-0.489099\pi$
$373$	17.7079	−	10.2236i	0.916878	−	0.529360i	0.882638	+	0.470054i	$0.155765\pi$
$374$	28.6990	+	10.4456i	1.48399	+	0.540127i
$375$	1.60458	+	0.652159i	0.0828604	+	0.0336773i
$376$	2.49533	−	0.439994i	0.128687	−	0.0226910i
$377$	−4.22359	−	11.6042i	−0.217526	−	0.597648i
$378$	5.28030	+	21.7524i	0.271589	+	1.11882i
$379$			12.2034i			0.626848i	0.949613	+	0.313424i	$0.101476\pi$
$379$			12.2034i			0.626848i	−0.949613	+	0.313424i	$0.898524\pi$
$380$	−2.36115	−	3.66401i	−0.121124	−	0.187960i
$381$	0.0805240	−	0.375019i	0.00412537	−	0.0192128i
$382$	−0.342401	+	0.408058i	−0.0175188	+	0.0208781i
$383$	−22.8863	+	8.32992i	−1.16943	+	0.425639i	−0.852459	−	0.522794i	$-0.824890\pi$
$383$	−22.8863	+	8.32992i	−1.16943	+	0.425639i	−0.316975	+	0.948434i	$0.602667\pi$
$384$	−0.0640285	+	1.73087i	−0.00326744	+	0.0883279i
$385$	−4.40819	+	25.0001i	−0.224662	+	1.27412i
$386$	0.495387	−	1.36106i	0.0252145	−	0.0692763i
$387$	−2.07406	−	20.5510i	−0.105431	−	1.04467i
$388$	1.78337	+	1.02963i	0.0905368	+	0.0522714i
$389$	−4.58436	−	5.46342i	−0.232436	−	0.277007i	0.637201	−	0.770697i	$-0.280092\pi$
$389$	−4.58436	−	5.46342i	−0.232436	−	0.277007i	−0.869638	+	0.493691i	$0.835647\pi$
$390$	−3.06654	+	1.62238i	−0.155280	+	0.0821524i
$391$	11.4015	−	19.7480i	0.576600	−	0.998700i
$392$	−5.77864	−	10.0089i	−0.291865	−	0.505526i
$393$	−5.53908	+	8.82371i	−0.279410	+	0.445097i
$394$	0.483684	+	0.0852865i	0.0243676	+	0.00429667i
$395$	1.10011	+	6.23901i	0.0553524	+	0.313919i
$396$	−1.30617	+	17.6305i	−0.0656375	+	0.885967i
$397$	24.8411	+	20.8442i	1.24674	+	1.04614i	0.996966	+	0.0778351i	$0.0248008\pi$
$397$	24.8411	+	20.8442i	1.24674	+	1.04614i	0.249774	+	0.968304i	$0.419644\pi$
$398$	3.98782			0.199891
$399$	30.6917	+	10.7602i	1.53651	+	0.538683i
$400$	−1.00000			−0.0500000
$401$	−8.22032	−	6.89767i	−0.410503	−	0.344453i	0.414033	−	0.910262i	$-0.364120\pi$
$401$	−8.22032	−	6.89767i	−0.410503	−	0.344453i	−0.824537	+	0.565809i	$0.808564\pi$
$402$	−1.36813	−	9.88307i	−0.0682362	−	0.492923i
$403$	3.59746	+	20.4022i	0.179202	+	1.01631i
$404$	−19.0278	−	3.35511i	−0.946666	−	0.166923i
$405$	−8.37227	+	3.30229i	−0.416021	+	0.164092i
$406$	13.2795	+	23.0007i	0.659049	+	1.14151i
$407$	−13.6071	+	23.5681i	−0.674477	+	1.16823i
$408$	−4.19782	−	7.93450i	−0.207823	−	0.392816i
$409$	3.58064	+	4.26724i	0.177051	+	0.211001i	0.847270	−	0.531162i	$-0.178244\pi$
$409$	3.58064	+	4.26724i	0.177051	+	0.211001i	−0.670219	+	0.742163i	$0.733800\pi$
$410$	−2.06132	−	1.19010i	−0.101801	−	0.0587750i
$411$	33.7447	−	10.8872i	1.66451	−	0.537026i
$412$	2.10779	−	5.79111i	0.103843	−	0.285308i
$413$	−4.53337	+	25.7100i	−0.223073	+	1.26511i
$414$	12.7944	+	3.24628i	0.628808	+	0.159546i
$415$	−6.18064	+	2.24957i	−0.303396	+	0.110427i
$416$	1.28749	−	1.53437i	0.0631244	−	0.0752287i
$417$	−26.7618	−	5.74629i	−1.31053	−	0.281397i
$418$	20.4599	+	15.5308i	1.00072	+	0.759634i
$419$		−	7.31485i		−	0.357354i	−0.983908	−	0.178677i	$-0.942818\pi$
$419$		−	7.31485i		−	0.357354i	0.983908	−	0.178677i	$-0.0571817\pi$
$420$	5.88912	−	4.58150i	0.287360	−	0.223554i
$421$	−3.91654	−	10.7606i	−0.190881	−	0.524440i	0.806925	−	0.590654i	$-0.201130\pi$
$421$	−3.91654	−	10.7606i	−0.190881	−	0.524440i	−0.997805	+	0.0662140i	$0.978908\pi$
$422$	13.1538	−	2.31938i	0.640319	−	0.112906i
$423$	−6.28427	−	4.27673i	−0.305552	−	0.207942i
$424$	−2.68008	−	0.975471i	−0.130156	−	0.0473730i
$425$	4.48826	−	2.59130i	0.217713	−	0.125697i
$426$	−1.19539	+	1.32210i	−0.0579168	+	0.0640561i
$427$	−13.4853	+	11.3155i	−0.652600	+	0.547596i
$428$	0.414435	−	0.347752i	0.0200325	−	0.0168092i
$429$	13.7112	−	15.1647i	0.661984	−	0.732156i
$430$	−5.96270	+	3.44256i	−0.287547	+	0.166015i
$431$	36.5805	+	13.3142i	1.76202	+	0.641323i	0.999981	−	0.00620540i	$-0.00197525\pi$
$431$	36.5805	+	13.3142i	1.76202	+	0.641323i	0.762041	+	0.647529i	$0.224197\pi$
$432$	3.76013	−	3.58628i	0.180909	−	0.172545i
$433$	20.8334	−	3.67349i	1.00119	−	0.176537i	0.351054	−	0.936355i	$-0.385823\pi$
$433$	20.8334	−	3.67349i	1.00119	−	0.176537i	0.650135	+	0.759818i	$0.274712\pi$
$434$	−15.2390	−	41.8689i	−0.731497	−	2.00977i
$435$	−8.42844	+	6.55698i	−0.404113	+	0.314383i
$436$		−	8.42612i		−	0.403538i
$437$	14.0724	−	13.0305i	0.673175	−	0.623333i
$438$	−21.6472	−	4.64809i	−1.03434	−	0.222094i
$439$	−24.5603	+	29.2698i	−1.17220	+	1.39697i	−0.271549	+	0.962425i	$0.587536\pi$
$439$	−24.5603	+	29.2698i	−1.17220	+	1.39697i	−0.900649	+	0.434547i	$0.856909\pi$
$440$	5.53756	−	2.01551i	0.263993	−	0.0960855i
$441$	−8.52700	+	33.6069i	−0.406047	+	1.60033i
$442$	−1.80258	+	10.2229i	−0.0857400	+	0.486255i
$443$	6.56413	−	18.0348i	0.311871	−	0.856859i	−0.680408	−	0.732833i	$-0.738197\pi$
$443$	6.56413	−	18.0348i	0.311871	−	0.856859i	0.992279	−	0.124025i	$-0.0395803\pi$
$444$	7.61237	−	2.45601i	0.361267	−	0.116557i
$445$	6.25170	+	3.60942i	0.296359	+	0.171103i
$446$	0.00954996	+	0.0113812i	0.000452204	+	0.000538916i
$447$	3.61416	+	6.83131i	0.170944	+	0.323110i
$448$	−2.15391	+	3.73068i	−0.101763	+	0.176258i
$449$	−9.71597	−	16.8285i	−0.458525	−	0.794188i	0.540359	−	0.841435i	$-0.318289\pi$
$449$	−9.71597	−	16.8285i	−0.458525	−	0.794188i	−0.998883	+	0.0472467i	$0.984955\pi$
$450$	2.14938	+	2.09289i	0.101323	+	0.0986596i
$451$	13.8133	+	2.43566i	0.650445	+	0.114691i
$452$	−0.209809	−	1.18988i	−0.00986857	−	0.0559674i
$453$	−3.34427	−	24.1583i	−0.157128	−	1.13505i
$454$	−8.13529	−	6.82632i	−0.381808	−	0.320375i
$455$	−8.62847			−0.404509
$456$	−1.39915	−	7.41906i	−0.0655212	−	0.347429i
$457$	−16.0643			−0.751457			−0.375728	−	0.926730i	$-0.622607\pi$
$457$	−16.0643			−0.751457			−0.375728	+	0.926730i	$0.622607\pi$
$458$	10.7934	+	9.05672i	0.504342	+	0.423193i
$459$	−7.58331	+	25.8398i	−0.353959	+	1.20610i
$460$	−0.764038	−	4.33308i	−0.0356235	−	0.202031i
$461$	−10.4637	−	1.84504i	−0.487344	−	0.0859319i	−0.0754234	−	0.997152i	$-0.524031\pi$
$461$	−10.4637	−	1.84504i	−0.487344	−	0.0859319i	−0.411921	+	0.911220i	$0.635142\pi$
$462$	−23.3773	+	37.2399i	−1.08761	+	1.73256i
$463$	−7.34362	−	12.7195i	−0.341287	−	0.591126i	0.643385	−	0.765543i	$-0.277529\pi$
$463$	−7.34362	−	12.7195i	−0.341287	−	0.591126i	−0.984672	+	0.174417i	$0.944196\pi$
$464$	3.08265	−	5.33930i	0.143108	−	0.247871i
$465$	15.8351	−	8.37770i	0.734335	−	0.388507i
$466$	15.0713	+	17.9613i	0.698166	+	0.832042i
$467$	−30.7467	−	17.7516i	−1.42279	−	0.821446i	−0.426249	−	0.904606i	$-0.640165\pi$
$467$	−30.7467	−	17.7516i	−1.42279	−	0.821446i	−0.996536	+	0.0831601i	$0.973499\pi$
$468$	−5.97857	+	0.603374i	−0.276359	+	0.0278910i
$469$	8.48715	−	23.3183i	0.391900	−	1.07674i
$470$	−0.439994	+	2.49533i	−0.0202954	+	0.115101i
$471$	0.201020	−	5.43412i	0.00926251	−	0.250391i
$472$	5.69482	−	2.07274i	0.262125	−	0.0954058i
$473$	26.0803	−	31.0813i	1.19917	−	1.42912i
$474$	−2.30361	+	10.7285i	−0.105808	+	0.492775i
$475$	4.25060	−	0.965591i	0.195031	−	0.0443044i
$476$		−	22.3257i		−	1.02330i
$477$	3.71897	+	7.70577i	0.170280	+	0.352823i
$478$	−7.31212	−	20.0899i	−0.334449	−	0.918890i
$479$	−11.1407	+	1.96440i	−0.509031	+	0.0897558i	−0.422264	−	0.906473i	$-0.638765\pi$
$479$	−11.1407	+	1.96440i	−0.509031	+	0.0897558i	−0.0867666	+	0.996229i	$0.527653\pi$
$480$	−1.60458	−	0.652159i	−0.0732389	−	0.0297668i
$481$	−8.69209	−	3.16366i	−0.396325	−	0.144251i
$482$	−20.9445	+	12.0923i	−0.953998	+	0.550791i
$483$	24.3515	+	22.0176i	1.10803	+	1.00183i
$484$	−18.1758	+	15.2513i	−0.826173	+	0.693242i
$485$	−1.57748	+	1.32366i	−0.0716297	+	0.0601045i
$486$	−15.5876	−	0.161239i	−0.707069	−	0.00731395i
$487$	2.50443	−	1.44594i	0.113487	−	0.0655216i	−0.442182	−	0.896925i	$-0.645796\pi$
$487$	2.50443	−	1.44594i	0.113487	−	0.0655216i	0.555669	+	0.831404i	$0.312462\pi$
$488$	3.84004	+	1.39766i	0.173830	+	0.0632691i
$489$	12.8702	−	31.6662i	0.582012	−	1.43199i
$490$	11.3817	−	2.00690i	0.514173	−	0.0906625i
$491$	7.66548	+	21.0607i	0.345938	+	0.950457i	0.983635	+	0.180170i	$0.0576649\pi$
$491$	7.66548	+	21.0607i	0.345938	+	0.950457i	−0.637697	+	0.770287i	$0.720113\pi$
$492$	−2.53142	−	3.25393i	−0.114125	−	0.146698i
$493$			31.9522i			1.43906i
$494$	−3.99104	+	7.76519i	−0.179565	+	0.349373i
$495$	−16.1205	−	7.25739i	−0.724564	−	0.326196i
$496$	−6.64839	+	7.92324i	−0.298521	+	0.355764i
$497$	−4.16567	+	1.51618i	−0.186856	+	0.0680100i
$498$	−11.3844	−	0.421135i	−0.510148	−	0.0188715i
$499$	2.70379	−	15.3339i	0.121038	−	0.686441i	−0.862544	−	0.505982i	$-0.831130\pi$
$499$	2.70379	−	15.3339i	0.121038	−	0.686441i	0.983582	−	0.180460i	$-0.0577585\pi$
$500$	0.342020	−	0.939693i	0.0152956	−	0.0420243i
$501$	−13.0125	−	40.3321i	−0.581356	−	1.80190i
$502$	−11.3802	−	6.57038i	−0.507924	−	0.293250i
$503$	7.76205	+	9.25046i	0.346093	+	0.412457i	0.910809	−	0.412828i	$-0.135459\pi$
$503$	7.76205	+	9.25046i	0.346093	+	0.412457i	−0.564716	+	0.825285i	$0.691014\pi$
$504$	12.4374	−	3.51076i	0.554008	−	0.156381i
$505$	9.66065	−	16.7327i	0.429893	−	0.744597i
$506$	12.9643	+	22.4547i	0.576331	+	0.998235i
$507$	−13.1851	−	8.27697i	−0.585573	−	0.367593i
$508$	−0.218088	−	0.0384548i	−0.00967609	−	0.00170616i
$509$	−5.58286	−	31.6620i	−0.247456	−	1.40339i	−0.814719	−	0.579856i	$-0.803109\pi$
$509$	−5.58286	−	31.6620i	−0.247456	−	1.40339i	0.567263	−	0.823537i	$-0.308002\pi$
$510$	8.89173	−	1.23090i	0.393733	−	0.0545051i
$511$	−42.1833	−	35.3960i	−1.86608	−	1.56583i
$512$	1.00000			0.0441942
$513$	−12.5199	+	18.8746i	−0.552769	+	0.833335i
$514$	20.3280			0.896629
$515$	4.72096	+	3.96135i	0.208030	+	0.174558i
$516$	−11.8127	+	1.63526i	−0.520027	+	0.0719883i
$517$	−2.59286	−	14.7049i	−0.114034	−	0.646719i
$518$	19.5916	+	3.45453i	0.860806	+	0.151783i
$519$	12.1017	+	7.59682i	0.531204	+	0.333463i
$520$	1.00149	+	1.73463i	0.0439182	+	0.0760686i
$521$	−14.9350	+	25.8681i	−0.654313	+	1.13330i	0.327752	+	0.944764i	$0.393709\pi$
$521$	−14.9350	+	25.8681i	−0.654313	+	1.13330i	−0.982066	+	0.188540i	$0.939625\pi$
$522$	−17.8003	+	5.02455i	−0.779099	+	0.219919i
$523$	−11.5730	−	13.7922i	−0.506053	−	0.603090i	0.451171	−	0.892437i	$-0.351006\pi$
$523$	−11.5730	−	13.7922i	−0.506053	−	0.603090i	−0.957224	+	0.289347i	$0.906562\pi$
$524$	5.20911	+	3.00748i	0.227561	+	0.131382i
$525$	2.29100	+	7.10093i	0.0999875	+	0.309910i
$526$	2.82249	−	7.75474i	0.123067	−	0.338123i
$527$	9.30822	−	52.7896i	0.405473	−	2.29955i
$528$	10.1999	+	0.377317i	0.443894	+	0.0164206i
$529$	−3.42113	+	1.24519i	−0.148745	+	0.0541386i
$530$	1.83329	−	2.18482i	0.0796328	−	0.0949027i
$531$	−16.5783	−	7.46349i	−0.719438	−	0.323888i
$532$	5.55310	−	17.9374i	0.240757	−	0.777686i
$533$			4.76750i			0.206503i
$534$	7.67746	+	9.86872i	0.332236	+	0.427061i
$535$	0.185035	+	0.508380i	0.00799977	+	0.0219792i
$536$	−5.67289	+	1.00028i	−0.245032	+	0.0432057i
$537$	−9.93853	+	24.4530i	−0.428879	+	1.05522i
$538$	7.14462	+	2.60043i	0.308026	+	0.112112i
$539$	−58.9819	+	34.0532i	−2.54053	+	1.46678i
$540$	2.08396	+	4.75995i	0.0896796	+	0.204835i
$541$	8.60840	−	7.22330i	0.370104	−	0.310554i	−0.438699	−	0.898634i	$-0.644560\pi$
$541$	8.60840	−	7.22330i	0.370104	−	0.310554i	0.808803	+	0.588080i	$0.200116\pi$
$542$	13.5151	−	11.3406i	0.580525	−	0.487118i
$543$	15.3044	+	13.8376i	0.656775	+	0.593828i
$544$	−4.48826	+	2.59130i	−0.192433	+	0.111101i
$545$	7.91797	+	2.88190i	0.339168	+	0.123447i
$546$	−13.8451	−	5.62713i	−0.592515	−	0.240819i
$547$	31.4826	−	5.55123i	1.34610	−	0.237353i	0.546284	−	0.837600i	$-0.316042\pi$
$547$	31.4826	−	5.55123i	1.34610	−	0.237353i	0.799815	+	0.600247i	$0.204931\pi$
$548$	−7.00164	−	19.2369i	−0.299095	−	0.821758i
$549$	−5.32855	−	11.0409i	−0.227417	−	0.471212i
$550$			5.89295i			0.251276i
$551$	−7.94753	+	25.6718i	−0.338576	+	1.09366i
$552$	1.59989	−	7.45106i	0.0680958	−	0.317138i
$553$	−17.5424	+	20.9062i	−0.745979	+	0.889023i
$554$	−25.4931	+	9.27874i	−1.08310	+	0.394216i
$555$	−0.295689	+	7.99329i	−0.0125513	+	0.339296i
$556$	−2.74418	+	15.5630i	−0.116379	+	0.660020i
$557$	−5.05407	+	13.8860i	−0.214148	+	0.588367i	−0.999530	−	0.0306442i	$-0.990244\pi$
$557$	−5.05407	+	13.8860i	−0.214148	+	0.588367i	0.785382	+	0.619011i	$0.212466\pi$
$558$	30.8723	−	3.11572i	1.30693	−	0.131899i
$559$	11.9432	+	6.89539i	0.505142	+	0.291644i
$560$	−2.76901	−	3.29998i	−0.117012	−	0.139450i
$561$	−46.7576	+	24.7375i	−1.97411	+	1.04442i
$562$	−8.17227	+	14.1548i	−0.344727	+	0.597084i
$563$	−2.27891	−	3.94719i	−0.0960446	−	0.166354i	0.813999	−	0.580866i	$-0.197286\pi$
$563$	−2.27891	−	3.94719i	−0.0960446	−	0.166354i	−0.910044	+	0.414511i	$0.863952\pi$
$564$	−2.33336	+	3.71702i	−0.0982521	+	0.156515i
$565$	1.18988	+	0.209809i	0.0500588	+	0.00882671i
$566$	−2.32000	−	13.1574i	−0.0975171	−	0.553047i
$567$	−34.0804	−	18.4842i	−1.43124	−	0.776264i
$568$	0.788308	+	0.661469i	0.0330767	+	0.0277546i
$569$	−1.56319			−0.0655323			−0.0327661	−	0.999463i	$-0.510432\pi$
$569$	−1.56319			−0.0655323			−0.0327661	+	0.999463i	$0.510432\pi$
$570$	7.45017	+	1.22270i	0.312053	+	0.0512131i
$571$	−47.6500			−1.99409			−0.997045	−	0.0768217i	$-0.975523\pi$
$571$	−47.6500			−1.99409			−0.997045	+	0.0768217i	$0.975523\pi$
$572$	−9.04197	−	7.58711i	−0.378064	−	0.317233i
$573$	−0.126515	−	0.913917i	−0.00528525	−	0.0381794i
$574$	−1.78050	−	10.0977i	−0.0743166	−	0.421471i
$575$	4.33308	+	0.764038i	0.180702	+	0.0318626i
$576$	−2.14938	−	2.09289i	−0.0895574	−	0.0872036i
$577$	−11.2727	−	19.5250i	−0.469290	−	0.812834i	0.530093	−	0.847939i	$-0.322157\pi$
$577$	−11.2727	−	19.5250i	−0.469290	−	0.812834i	−0.999384	+	0.0351048i	$0.988824\pi$
$578$	4.92967	−	8.53844i	0.205047	−	0.355152i
$579$	1.17319	+	2.21751i	0.0487562	+	0.0921564i
$580$	3.96297	+	4.72289i	0.164554	+	0.196107i
$581$	−24.5378	−	14.1669i	−1.01800	−	0.587742i
$582$	−3.39444	+	1.09516i	−0.140704	+	0.0453959i
$583$	−5.74840	+	15.7936i	−0.238074	+	0.654104i
$584$	−2.21973	+	12.5887i	−0.0918529	+	0.520924i
$585$	1.47780	−	5.82438i	0.0610997	−	0.240809i
$586$	−15.1261	+	5.50544i	−0.624852	+	0.227428i
$587$	−18.1473	+	21.6271i	−0.749018	+	0.892645i	−0.997101	−	0.0760938i	$-0.975755\pi$
$587$	−18.1473	+	21.6271i	−0.749018	+	0.892645i	0.248083	+	0.968739i	$0.420200\pi$
$588$	19.5717	+	4.20243i	0.807124	+	0.173305i
$589$	20.6091	−	40.0982i	0.849181	−	1.65222i
$590$			6.06030i			0.249498i
$591$	−0.671434	+	0.522349i	−0.0276191	+	0.0214865i
$592$	−1.57948	−	4.33958i	−0.0649161	−	0.178356i
$593$	20.2794	−	3.57581i	0.832776	−	0.146841i	0.259025	−	0.965871i	$-0.416599\pi$
$593$	20.2794	−	3.57581i	0.832776	−	0.146841i	0.573751	+	0.819030i	$0.305488\pi$
$594$	−21.1338	−	22.1582i	−0.867130	−	0.909164i
$595$	20.9793	+	7.63583i	0.860067	+	0.313039i
$596$	3.86422	−	2.23101i	0.158285	−	0.0913858i
$597$	−4.63237	+	5.12341i	−0.189590	+	0.209687i
$598$	−6.75111	+	5.66486i	−0.276074	+	0.231653i
$599$	−23.9964	+	20.1354i	−0.980467	+	0.822709i	−0.984160	−	0.177284i	$-0.943269\pi$
$599$	−23.9964	+	20.1354i	−0.980467	+	0.822709i	0.00369286	+	0.999993i	$0.498825\pi$
$600$	1.16163	−	1.28476i	0.0474233	−	0.0524503i
$601$	−13.1442	+	7.58884i	−0.536165	+	0.309555i	−0.743523	−	0.668710i	$-0.766847\pi$
$601$	−13.1442	+	7.58884i	−0.536165	+	0.309555i	0.207358	+	0.978265i	$0.433513\pi$
$602$	−27.8712	−	10.1443i	−1.13594	−	0.413450i
$603$	14.2867	+	9.72273i	0.581799	+	0.395940i
$604$	−13.8669	+	2.44510i	−0.564235	+	0.0994899i
$605$	−8.11506	−	22.2959i	−0.329924	−	0.906459i
$606$	26.4137	−	20.5488i	1.07298	−	0.834738i
$607$		−	17.6987i		−	0.718368i	−0.933267	−	0.359184i	$-0.883055\pi$
$607$		−	17.6987i		−	0.718368i	0.933267	−	0.359184i	$-0.116945\pi$
$608$	−4.25060	+	0.965591i	−0.172385	+	0.0391599i
$609$	−44.9763	−	9.65730i	−1.82253	−	0.391334i
$610$	−2.62674	+	3.13043i	−0.106354	+	0.126747i
$611$	4.76913	−	1.73582i	0.192938	−	0.0702238i
$612$	15.0703	+	3.82374i	0.609180	+	0.154565i
$613$	1.19312	−	6.76652i	0.0481896	−	0.273297i	−0.951186	−	0.308617i	$-0.900134\pi$
$613$	1.19312	−	6.76652i	0.0481896	−	0.273297i	0.999376	+	0.0353199i	$0.0112450\pi$
$614$	−7.23407	+	19.8755i	−0.291943	+	0.802108i
$615$	3.92349	−	1.26585i	0.158210	−	0.0510440i
$616$	21.9847	+	12.6929i	0.885788	+	0.511410i
$617$	7.98239	+	9.51304i	0.321359	+	0.382981i	0.902404	−	0.430891i	$-0.141801\pi$
$617$	7.98239	+	9.51304i	0.321359	+	0.382981i	−0.581045	+	0.813871i	$0.697356\pi$
$618$	4.99174	+	9.43514i	0.200797	+	0.379537i
$619$	−7.96450	+	13.7949i	−0.320120	+	0.554465i	−0.980513	−	0.196456i	$-0.937057\pi$
$619$	−7.96450	+	13.7949i	−0.320120	+	0.554465i	0.660392	+	0.750921i	$0.270390\pi$
$620$	−5.17153	−	8.95735i	−0.207694	−	0.359736i
$621$	−19.0330	+	12.6668i	−0.763767	+	0.508300i
$622$	−0.879522	−	0.155083i	−0.0352656	−	0.00621828i
$623$	5.40001	+	30.6250i	0.216347	+	1.22696i
$624$	0.475720	+	3.43649i	0.0190440	+	0.137570i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	−17.2443			−0.689221
$627$	−43.7201	+	8.24512i	−1.74601	+	0.329278i
$628$	−3.13954			−0.125281
$629$	18.3343	+	15.3843i	0.731035	+	0.613411i
$630$	−0.954826	+	12.8881i	−0.0380412	+	0.513475i
$631$	−4.35930	−	24.7228i	−0.173541	−	0.984200i	−0.939814	−	0.341685i	$-0.889002\pi$
$631$	−4.35930	−	24.7228i	−0.173541	−	0.984200i	0.766273	−	0.642515i	$-0.222109\pi$
$632$	6.23901	+	1.10011i	0.248175	+	0.0437599i
$633$	−12.3000	+	19.5938i	−0.488882	+	0.778785i
$634$	13.5339	+	23.4414i	0.537500	+	0.930977i
$635$	0.110726	−	0.191783i	0.00439403	−	0.00761069i
$636$	4.36651	−	2.31014i	0.173143	−	0.0916031i
$637$	−14.8799	−	17.7332i	−0.589562	−	0.702613i
$638$	−31.4642	−	18.1659i	−1.24568	−	0.719194i
$639$	−0.309993	−	3.07159i	−0.0122631	−	0.121510i
$640$	−0.342020	+	0.939693i	−0.0135195	+	0.0371446i
$641$	−2.78972	+	15.8213i	−0.110187	+	0.624902i	0.878834	+	0.477128i	$0.158322\pi$
$641$	−2.78972	+	15.8213i	−0.110187	+	0.624902i	−0.989021	+	0.147774i	$0.952789\pi$
$642$	−0.0346399	+	0.936411i	−0.00136713	+	0.0369572i
$643$	17.9021	−	6.51584i	0.705991	−	0.256960i	0.0360241	−	0.999351i	$-0.488531\pi$
$643$	17.9021	−	6.51584i	0.705991	−	0.256960i	0.669966	+	0.742391i	$0.266308\pi$
$644$	12.1834	−	14.5196i	0.480094	−	0.572154i
$645$	2.50355	−	11.6596i	0.0985774	−	0.459098i
$646$	16.5757	−	15.3484i	0.652162	−	0.603875i
$647$			12.1782i			0.478773i	0.970924	+	0.239387i	$0.0769464\pi$
$647$			12.1782i			0.478773i	−0.970924	+	0.239387i	$0.923054\pi$
$648$	0.239656	+	8.99681i	0.00941459	+	0.353428i
$649$	−12.2146	−	33.5593i	−0.479464	−	1.31732i
$650$	−1.97255	+	0.347814i	−0.0773698	+	0.0136424i
$651$	71.4938	+	29.0576i	2.80206	+	1.13886i
$652$	−18.5447	−	6.74970i	−0.726265	−	0.264339i
$653$	−22.2400	+	12.8403i	−0.870319	+	0.502479i	−0.867454	−	0.497517i	$-0.834245\pi$
$653$	−22.2400	+	12.8403i	−0.870319	+	0.502479i	−0.00286485	+	0.999996i	$0.500912\pi$
$654$	10.8256	+	9.78802i	0.423314	+	0.382742i
$655$	−4.60773	+	3.86634i	−0.180039	+	0.151070i
$656$	−1.82334	+	1.52997i	−0.0711896	+	0.0597352i
$657$	31.1177	−	22.4122i	1.21402	−	0.874384i
$658$	−9.45289	+	5.45763i	−0.368512	+	0.212760i
$659$	−11.1034	−	4.04131i	−0.432528	−	0.157427i	0.116575	−	0.993182i	$-0.462808\pi$
$659$	−11.1034	−	4.04131i	−0.432528	−	0.157427i	−0.549103	+	0.835755i	$0.685031\pi$
$660$	−3.84314	+	9.45573i	−0.149594	+	0.368064i
$661$	−30.1118	+	5.30953i	−1.17121	+	0.206517i	−0.725219	−	0.688518i	$-0.758261\pi$
$661$	−30.1118	+	5.30953i	−1.17121	+	0.206517i	−0.445996	+	0.895035i	$0.647150\pi$
$662$	−0.810119	−	2.22578i	−0.0314862	−	0.0865075i
$663$	−11.0401	−	14.1911i	−0.428763	−	0.551138i
$664$			6.57730i			0.255249i
$665$	14.9564	+	11.3532i	0.579984	+	0.440257i
$666$	−5.68735	+	12.6331i	−0.220380	+	0.489521i
$667$	−17.4368	+	20.7803i	−0.675155	+	0.804618i
$668$	−22.9921	+	8.36844i	−0.889591	+	0.323785i
$669$	−0.0257157		0.000951279i	−0.000994225		3.67786e-5i
$670$	1.00028	−	5.67289i	0.0386444	−	0.219163i
$671$	8.23633	−	22.6291i	0.317960	−	0.873588i
$672$	−2.29100	−	7.10093i	−0.0883773	−	0.273924i
$673$	24.2930	+	14.0255i	0.936425	+	0.540645i	0.888838	−	0.458222i	$-0.151514\pi$
$673$	24.2930	+	14.0255i	0.936425	+	0.540645i	0.0475869	+	0.998867i	$0.484847\pi$
$674$	−7.02301	−	8.36970i	−0.270516	−	0.322389i
$675$	−5.18564	+	0.330289i	−0.199596	+	0.0127128i
$676$	−4.49404	+	7.78390i	−0.172848	+	0.299381i
$677$	4.15320	+	7.19355i	0.159620	+	0.276471i	0.934732	−	0.355354i	$-0.115640\pi$
$677$	4.15320	+	7.19355i	0.159620	+	0.276471i	−0.775111	+	0.631825i	$0.782306\pi$
$678$	1.77244	+	1.11265i	0.0680701	+	0.0427310i
$679$	−8.73612	−	1.54041i	−0.335262	−	0.0591157i
$680$	−0.899949	−	5.10386i	−0.0345115	−	0.195724i
$681$	18.2204	−	2.52228i	0.698207	−	0.0966541i
$682$	46.6912	+	39.1786i	1.78790	+	1.50023i
$683$	30.5693			1.16970			0.584851	−	0.811141i	$-0.301153\pi$
$683$	30.5693			1.16970			0.584851	+	0.811141i	$0.301153\pi$
$684$	11.1570	+	6.82061i	0.426600	+	0.260792i
$685$	20.4714			0.782173
$686$	15.0389	+	12.6192i	0.574189	+	0.481802i
$687$	−24.1737	+	3.34640i	−0.922282	+	0.127673i
$688$	1.19559	+	6.78053i	0.0455814	+	0.258505i
$689$	−5.62588	−	0.991994i	−0.214329	−	0.0377920i
$690$	6.45451	+	4.05182i	0.245719	+	0.154250i
$691$	9.98171	+	17.2888i	0.379722	+	0.657698i	0.991022	−	0.133701i	$-0.0426862\pi$
$691$	9.98171	+	17.2888i	0.379722	+	0.657698i	−0.611299	+	0.791399i	$0.709353\pi$
$692$	4.12474	−	7.14427i	0.156799	−	0.271584i
$693$	−20.6887	−	73.2932i	−0.785899	−	2.78418i
$694$	5.51503	+	6.57256i	0.209348	+	0.249491i
$695$	−13.6859	−	7.90156i	−0.519136	−	0.299723i
$696$	3.27885	+	10.1628i	0.124285	+	0.385218i
$697$	4.21904	−	11.5917i	0.159808	−	0.439068i
$698$	5.25622	−	29.8095i	0.198951	−	1.12831i
$699$	−40.5833	−	1.50127i	−1.53500	−	0.0567831i
$700$	4.04802	−	1.47336i	0.153001	−	0.0556878i
$701$	10.7471	−	12.8079i	0.405912	−	0.483747i	−0.523901	−	0.851779i	$-0.675524\pi$
$701$	10.7471	−	12.8079i	0.405912	−	0.483747i	0.929813	+	0.368032i	$0.119968\pi$
$702$	6.16968	−	8.38195i	0.232860	−	0.316356i
$703$	10.9040	+	16.9207i	0.411252	+	0.638176i
$704$		−	5.89295i		−	0.222099i
$705$	−2.69480	−	3.46394i	−0.101492	−	0.130459i
$706$	−9.02992	−	24.8095i	−0.339845	−	0.933718i
$707$	81.9681	−	14.4532i	3.08273	−	0.543568i
$708$	−3.95227	+	9.72426i	−0.148536	+	0.365460i
$709$	37.4907	+	13.6455i	1.40799	+	0.512468i	0.930540	−	0.366189i	$-0.119338\pi$
$709$	37.4907	+	13.6455i	1.40799	+	0.512468i	0.477453	+	0.878657i	$0.341560\pi$
$710$	−0.891195	+	0.514531i	−0.0334459	+	0.0193100i
$711$	−11.1076	−	15.4221i	−0.416568	−	0.578373i
$712$	5.52995	−	4.64018i	0.207244	−	0.173898i
$713$	34.8616	−	29.2524i	1.30558	−	1.09551i
$714$	28.6832	+	25.9342i	1.07344	+	0.970561i
$715$	10.2221	−	5.90173i	0.382284	−	0.220712i
$716$	14.3204	+	5.21220i	0.535178	+	0.194789i
$717$	34.3047	+	13.9426i	1.28113	+	0.520697i
$718$	2.49891	−	0.440626i	0.0932586	−	0.0164440i
$719$	9.16925	+	25.1923i	0.341955	+	0.939515i	0.984827	+	0.173541i	$0.0555208\pi$
$719$	9.16925	+	25.1923i	0.341955	+	0.939515i	−0.642871	+	0.765974i	$0.722257\pi$
$720$	2.70180	−	1.30395i	0.100690	−	0.0485952i
$721$			26.5481i			0.988702i
$722$	17.1353	−	8.20869i	0.637709	−	0.305496i
$723$	8.79398	−	40.9556i	0.327052	−	1.52316i
$724$	7.65703	−	9.12530i	0.284571	−	0.339139i
$725$	−5.79348	+	2.10865i	−0.215164	+	0.0783135i
$726$	1.51919	−	41.0680i	0.0563826	−	1.52418i
$727$	−1.16125	+	6.58576i	−0.0430682	+	0.244252i	−0.998740	−	0.0501817i	$-0.984020\pi$
$727$	−1.16125	+	6.58576i	−0.0430682	+	0.244252i	0.955672	+	0.294434i	$0.0951311\pi$
$728$	−2.95111	+	8.10811i	−0.109375	+	0.300506i
$729$	18.3142	−	19.8391i	0.678303	−	0.734782i
$730$	−11.0703	−	6.39145i	−0.409730	−	0.236558i
$731$	−22.9365	−	27.3347i	−0.848337	−	1.01101i
$732$	−6.25636	+	3.30998i	−0.231242	+	0.122340i
$733$	−3.15795	+	5.46972i	−0.116641	+	0.202029i	−0.918435	−	0.395573i	$-0.870546\pi$
$733$	−3.15795	+	5.46972i	−0.116641	+	0.202029i	0.801793	+	0.597601i	$0.203879\pi$
$734$	−17.5132	−	30.3337i	−0.646424	−	1.11964i
$735$	−10.6429	+	16.9541i	−0.392570	+	0.625360i
$736$	−4.33308	−	0.764038i	−0.159719	−	0.0281628i
$737$	5.89462	+	33.4301i	0.217131	+	1.23141i
$738$	7.12110	+	0.527572i	0.262131	+	0.0194202i
$739$	30.6961	+	25.7571i	1.12917	+	0.947489i	0.999031	−	0.0440062i	$-0.0140121\pi$
$739$	30.6961	+	25.7571i	1.12917	+	0.947489i	0.130142	+	0.991495i	$0.458457\pi$
$740$	4.61808			0.169764
$741$	−5.34034	−	14.1478i	−0.196182	−	0.519733i
$742$	12.2863			0.451043
$743$	29.2213	+	24.5196i	1.07203	+	0.899536i	0.995234	−	0.0975107i	$-0.0310880\pi$
$743$	29.2213	+	24.5196i	1.07203	+	0.899536i	0.0767913	+	0.997047i	$0.475532\pi$
$744$	−2.45654	−	17.7455i	−0.0900611	−	0.650581i
$745$	0.774822	+	4.39423i	0.0283873	+	0.160992i
$746$	20.1366	+	3.55063i	0.737255	+	0.129998i
$747$	13.7655	−	14.1371i	0.503655	−	0.517250i
$748$	15.2704	+	26.4491i	0.558341	+	0.967075i
$749$	−1.16528	+	2.01832i	−0.0425784	+	0.0737479i
$750$	0.809983	+	1.53099i	0.0295764	+	0.0559038i
$751$	−12.4306	−	14.8142i	−0.453598	−	0.540577i	0.489977	−	0.871735i	$-0.337005\pi$
$751$	−12.4306	−	14.8142i	−0.453598	−	0.540577i	−0.943575	+	0.331158i	$0.892561\pi$
$752$	2.19436	+	1.26691i	0.0800200	+	0.0461995i
$753$	21.6610	−	6.98857i	0.789370	−	0.254678i
$754$	4.22359	−	11.6042i	0.153814	−	0.422601i
$755$	2.44510	−	13.8669i	0.0889864	−	0.504667i
$756$	−9.93720	+	20.0574i	−0.361412	+	0.729480i
$757$	15.2886	−	5.56461i	0.555675	−	0.202249i	−0.0488910	−	0.998804i	$-0.515569\pi$
$757$	15.2886	−	5.56461i	0.555675	−	0.202249i	0.604566	+	0.796555i	$0.293346\pi$
$758$	−7.84421	+	9.34837i	−0.284915	+	0.339548i
$759$	−43.9087	−	9.42807i	−1.59379	−	0.342217i
$760$	0.546433	−	4.32451i	0.0198212	−	0.156867i
$761$		−	41.5644i		−	1.50671i	−0.657615	−	0.753354i	$-0.728435\pi$
$761$		−	41.5644i		−	1.50671i	0.657615	−	0.753354i	$-0.271565\pi$
$762$	0.302742	−	0.235521i	0.0109672	−	0.00853204i
$763$	12.4147	+	34.1091i	0.449443	+	1.23483i
$764$	−0.524589	+	0.0924992i	−0.0189790	+	0.00334650i
$765$	−8.74748	+	12.8536i	−0.316266	+	0.464724i
$766$	−22.8863	−	8.32992i	−0.826915	−	0.300972i
$767$	10.5124	−	6.06933i	0.379580	−	0.219151i
$768$	−1.16163	+	1.28476i	−0.0419167	+	0.0463599i
$769$	−9.03109	+	7.57798i	−0.325669	+	0.273269i	−0.790933	−	0.611903i	$-0.790404\pi$
$769$	−9.03109	+	7.57798i	−0.325669	+	0.273269i	0.465263	+	0.885172i	$0.345960\pi$
$770$	−19.4466	+	16.3176i	−0.700807	+	0.588047i
$771$	−23.6136	+	26.1167i	−0.850422	+	0.940568i
$772$	1.25436	−	0.724207i	0.0451455	−	0.0260648i
$773$	−50.4818	−	18.3739i	−1.81570	−	0.660862i	−0.996130	−	0.0878876i	$-0.971988\pi$
$773$	−50.4818	−	18.3739i	−1.81570	−	0.660862i	−0.819573	−	0.572974i	$-0.805789\pi$
$774$	11.6211	−	17.0762i	0.417712	−	0.613790i
$775$	10.1859	−	1.79605i	0.365889	−	0.0645161i
$776$	0.704307	+	1.93507i	0.0252831	+	0.0694649i
$777$	−27.1964	+	21.1577i	−0.975667	+	0.759029i
$778$		−	7.13199i		−	0.255694i
$779$	6.27299	−	8.26389i	0.224753	−	0.296085i
$780$	−3.39195	−	0.728319i	−0.121451	−	0.0260780i
$781$	3.89800	−	4.64546i	0.139481	−	0.166228i
$782$	21.4278	−	7.79910i	0.766258	−	0.278895i
$783$	14.2220	−	28.7059i	0.508253	−	1.02586i
$784$	2.00690	−	11.3817i	0.0716750	−	0.406489i
$785$	1.07378	−	2.95020i	0.0383250	−	0.105297i
$786$	−9.91495	+	3.19890i	−0.353655	+	0.114101i
$787$	−6.58751	−	3.80330i	−0.234819	−	0.135573i	0.377974	−	0.925816i	$-0.376621\pi$
$787$	−6.58751	−	3.80330i	−0.234819	−	0.135573i	−0.612793	+	0.790243i	$0.709954\pi$
$788$	0.315702	+	0.376239i	0.0112464	+	0.0134030i
$789$	6.68432	+	12.6344i	0.237968	+	0.449795i
$790$	−3.16763	+	5.48650i	−0.112699	+	0.195201i
$791$	2.60244	+	4.50755i	0.0925320	+	0.160270i
$792$	−12.3333	+	12.6662i	−0.438244	+	0.450073i
$793$	8.06079	+	1.42133i	0.286247	+	0.0504731i
$794$	5.63103	+	31.9351i	0.199838	+	1.13334i
$795$	0.677388	+	4.89329i	0.0240245	+	0.173547i
$796$	3.05485	+	2.56332i	0.108276	+	0.0908545i
$797$	−6.33081			−0.224249			−0.112124	−	0.993694i	$-0.535766\pi$
$797$	−6.33081			−0.224249			−0.112124	+	0.993694i	$0.535766\pi$
$798$	16.5947	+	27.9711i	0.587447	+	0.990165i
$799$	−13.1318			−0.464570
$800$	−0.766044	−	0.642788i	−0.0270838	−	0.0227260i
$801$	−21.5973	−	1.60005i	−0.763104	−	0.0565351i
$802$	−1.86340	−	10.5678i	−0.0657988	−	0.373164i
$803$	74.1845	+	13.0807i	2.61791	+	0.461609i
$804$	5.30467	−	8.45029i	0.187081	−	0.298019i
$805$	9.47703	+	16.4147i	0.334021	+	0.578542i
$806$	−10.3585	+	17.9414i	−0.364861	+	0.631958i
$807$	−11.6403	+	6.15842i	−0.409759	+	0.216787i
$808$	−12.4195	−	14.8010i	−0.436916	−	0.520696i
$809$	16.4139	+	9.47658i	0.577083	+	0.333179i	0.759973	−	0.649954i	$-0.225212\pi$
$809$	16.4139	+	9.47658i	0.577083	+	0.333179i	−0.182891	+	0.983133i	$0.558545\pi$
$810$	−8.53620	−	2.85189i	−0.299932	−	0.100205i
$811$	15.0123	−	41.2459i	0.527153	−	1.44834i	−0.335256	−	0.942127i	$-0.608823\pi$
$811$	15.0123	−	41.2459i	0.527153	−	1.44834i	0.862408	−	0.506213i	$-0.168955\pi$
$812$	−4.61191	+	26.1555i	−0.161846	+	0.917877i
$813$	−1.12964	+	30.5373i	−0.0396182	+	1.07099i
$814$	−25.5729	+	9.30778i	−0.896330	+	0.326237i
$815$	12.6853	−	15.1177i	0.444346	−	0.529551i
$816$	1.88449	−	8.77649i	0.0659702	−	0.307239i
$817$	−11.6292	−	27.6669i	−0.406854	−	0.967942i
$818$			5.57048i			0.194767i
$819$	23.3124	−	11.2511i	0.814601	−	0.393144i
$820$	−0.814078	−	2.23666i	−0.0284289	−	0.0781076i
$821$	−2.27585	+	0.401294i	−0.0794278	+	0.0140053i	−0.213221	−	0.977004i	$-0.568395\pi$
$821$	−2.27585	+	0.401294i	−0.0794278	+	0.0140053i	0.133793	+	0.991009i	$0.457284\pi$
$822$	32.8481	+	13.3506i	1.14571	+	0.465656i
$823$	25.3073	+	9.21111i	0.882157	+	0.321079i	0.743080	−	0.669202i	$-0.233364\pi$
$823$	25.3073	+	9.21111i	0.882157	+	0.321079i	0.139077	+	0.990282i	$0.455586\pi$
$824$	5.33712	−	3.08139i	0.185927	−	0.107345i
$825$	−7.57105	−	6.84542i	−0.263590	−	0.238327i
$826$	−19.9989	+	16.7810i	−0.695849	+	0.583887i
$827$	−29.8958	+	25.0856i	−1.03958	+	0.872311i	−0.991960	−	0.126555i	$-0.959608\pi$
$827$	−29.8958	+	25.0856i	−1.03958	+	0.872311i	−0.0476200	+	0.998866i	$0.515164\pi$
$828$	7.71438	+	10.7108i	0.268093	+	0.372228i
$829$	−31.9176	+	18.4276i	−1.10854	+	0.640018i	−0.938452	−	0.345410i	$-0.887740\pi$
$829$	−31.9176	+	18.4276i	−1.10854	+	0.640018i	−0.170092	+	0.985428i	$0.554407\pi$
$830$	−6.18064	−	2.24957i	−0.214533	−	0.0780837i
$831$	17.6926	−	43.5311i	0.613748	−	1.51008i
$832$	1.97255	−	0.347814i	0.0683858	−	0.0120583i
$833$	20.4859	+	56.2845i	0.709794	+	1.95014i
$834$	−16.8071	−	21.6041i	−0.581983	−	0.748089i
$835$		−	24.4677i		−	0.846739i
$836$	5.69018	+	25.0486i	0.196799	+	0.866324i
$837$	−31.8592	+	43.2830i	−1.10122	+	1.49608i
$838$	4.70189	−	5.60350i	0.162424	−	0.193570i
$839$	−8.65886	+	3.15157i	−0.298937	+	0.108804i	−0.487134	−	0.873327i	$-0.661958\pi$
$839$	−8.65886	+	3.15157i	−0.298937	+	0.108804i	0.188197	+	0.982131i	$0.439736\pi$
$840$	7.45626	+	0.275823i	0.257265	+	0.00951680i
$841$	1.56472	−	8.87395i	0.0539557	−	0.305998i
$842$	3.91654	−	10.7606i	0.134973	−	0.370835i
$843$	−8.69243	−	26.9421i	−0.299383	−	0.927934i
$844$	11.5673	+	6.67838i	0.398163	+	0.229879i
$845$	−5.77742	−	6.88526i	−0.198749	−	0.236860i
$846$	−2.06500	−	7.31561i	−0.0709962	−	0.251516i
$847$	51.1054	−	88.5172i	1.75600	−	3.04149i
$848$	−1.42604	−	2.46998i	−0.0489705	−	0.0848194i
$849$	19.5991	+	12.3034i	0.672641	+	0.422250i
$850$	5.10386	+	0.899949i	0.175061	+	0.0308680i
$851$	3.52839	+	20.0105i	0.120952	+	0.685952i
$852$	−1.76555	+	0.244409i	−0.0604868	+	0.00837330i
$853$	14.4371	+	12.1142i	0.494317	+	0.414781i	0.855570	−	0.517686i	$-0.173207\pi$
$853$	14.4371	+	12.1142i	0.494317	+	0.414781i	−0.361253	+	0.932468i	$0.617651\pi$
$854$	−17.6038			−0.602390
$855$	−10.2252	+	8.15139i	−0.349695	+	0.278772i
$856$	0.541007			0.0184912
$857$	−7.12863	−	5.98163i	−0.243509	−	0.204329i	0.512862	−	0.858471i	$-0.328585\pi$
$857$	−7.12863	−	5.98163i	−0.243509	−	0.204329i	−0.756371	+	0.654142i	$0.773030\pi$
$858$	20.2511	−	2.80339i	0.691360	−	0.0957062i
$859$	5.42514	+	30.7675i	0.185103	+	1.04977i	0.925822	+	0.377959i	$0.123374\pi$
$859$	5.42514	+	30.7675i	0.185103	+	1.04977i	−0.740719	+	0.671815i	$0.765515\pi$
$860$	−6.78053	−	1.19559i	−0.231214	−	0.0407693i
$861$	15.0415	+	9.44227i	0.512612	+	0.321792i
$862$	19.4641	+	33.7128i	0.662949	+	1.14826i
$863$	7.02997	−	12.1763i	0.239303	−	0.414485i	−0.721212	−	0.692715i	$-0.756414\pi$
$863$	7.02997	−	12.1763i	0.239303	−	0.414485i	0.960514	+	0.278230i	$0.0897478\pi$
$864$	5.18564	−	0.330289i	0.176419	−	0.0112366i
$865$	5.30267	+	6.31947i	0.180296	+	0.214869i
$866$	18.3206	+	10.5774i	0.622559	+	0.359435i
$867$	5.24344	+	16.2520i	0.178076	+	0.551946i
$868$	15.2390	−	41.8689i	0.517247	−	1.42112i
$869$	6.48287	−	36.7662i	0.219916	−	1.24721i
$870$	−10.6713	−	0.394755i	−0.361791	−	0.0133834i
$871$	−10.8422	+	3.94622i	−0.367372	+	0.133713i
$872$	5.41621	−	6.45478i	0.183416	−	0.218587i
$873$	2.53605	−	5.63323i	0.0858324	−	0.190656i
$874$	19.1559	−	0.936356i	0.647959	−	0.0316727i
$875$			4.30782i			0.145631i
$876$	−13.5950	−	17.4752i	−0.459333	−	0.590432i
$877$	11.3611	+	31.2145i	0.383638	+	1.05404i	0.969812	+	0.243852i	$0.0784112\pi$
$877$	11.3611	+	31.2145i	0.383638	+	1.05404i	−0.586174	+	0.810185i	$0.699367\pi$
$878$	−37.6285	+	6.63493i	−1.26990	+	0.223918i
$879$	10.4977	−	25.8287i	0.354078	−	0.871180i
$880$	5.53756	+	2.01551i	0.186671	+	0.0679427i
$881$	−0.0879764	+	0.0507932i	−0.00296400	+	0.00171127i	−0.501481	−	0.865169i	$-0.667211\pi$
$881$	−0.0879764	+	0.0507932i	−0.00296400	+	0.00171127i	0.498517	+	0.866880i	$0.333878\pi$
$882$	−28.1342	+	20.2634i	−0.947327	+	0.682303i
$883$	−12.9042	+	10.8279i	−0.434262	+	0.364389i	−0.833557	−	0.552433i	$-0.813699\pi$
$883$	−12.9042	+	10.8279i	−0.434262	+	0.364389i	0.399295	+	0.916823i	$0.369255\pi$
$884$	−7.95203	+	6.67255i	−0.267456	+	0.224422i
$885$	−7.78605	−	7.03981i	−0.261725	−	0.236641i
$886$	16.6209	−	9.59611i	0.558392	−	0.322388i
$887$	32.0388	+	11.6612i	1.07576	+	0.391544i	0.818327	−	0.574752i	$-0.194902\pi$
$887$	32.0388	+	11.6612i	1.07576	+	0.391544i	0.257431	+	0.966297i	$0.417124\pi$
$888$	7.41010	+	3.01172i	0.248667	+	0.101067i
$889$	0.939483	−	0.165656i	0.0315092	−	0.00555593i
$890$	2.46899	+	6.78349i	0.0827607	+	0.227383i
$891$	53.0177	−	1.41228i	1.77616	−	0.0473133i
$892$			0.0148571i			0.000497453i
$893$	−10.5507	−	3.26629i	−0.353064	−	0.109302i
$894$	−1.62247	+	7.55622i	−0.0542635	+	0.252718i
$895$	−9.79572	+	11.6741i	−0.327435	+	0.390222i
$896$	−4.04802	+	1.47336i	−0.135235	+	0.0492215i
$897$	0.564280	−	15.2540i	0.0188408	−	0.509318i
$898$	3.37432	−	19.1367i	0.112602	−	0.638600i
$899$	−21.8099	+	59.9223i	−0.727402	+	1.99852i
$900$	0.301238	+	2.98484i	0.0100413	+	0.0994946i
$901$	12.8009	+	7.39061i	0.426460	+	0.246217i
$902$	9.01602	+	10.7449i	0.300200	+	0.357765i
$903$	45.4089	−	24.0240i	1.51111	−	0.799468i
$904$	0.604120	−	1.04637i	0.0200927	−	0.0348016i
$905$	5.95611	+	10.3163i	0.197988	+	0.342925i
$906$	12.9668	−	20.6560i	0.430792	−	0.686248i
$907$	−33.6821	−	5.93906i	−1.11840	−	0.197203i	−0.416259	−	0.909246i	$-0.636659\pi$
$907$	−33.6821	−	5.93906i	−1.11840	−	0.197203i	−0.702136	+	0.712043i	$0.747770\pi$
$908$	−1.84412	−	10.4585i	−0.0611993	−	0.347079i
$909$	−4.28256	+	57.8055i	−0.142044	+	1.91729i
$910$	−6.60979	−	5.54627i	−0.219112	−	0.183857i
$911$	−16.7009			−0.553326			−0.276663	−	0.960967i	$-0.589229\pi$
$911$	−16.7009			−0.553326			−0.276663	+	0.960967i	$0.589229\pi$
$912$	3.69707	−	6.58268i	0.122422	−	0.217974i
$913$	38.7597			1.28276
$914$	−12.3060	−	10.3259i	−0.407045	−	0.341552i
$915$	−0.970564	−	7.01114i	−0.0320859	−	0.231781i
$916$	2.44666	+	13.8757i	0.0808399	+	0.458466i
$917$	−25.5177	−	4.49946i	−0.842668	−	0.148585i
$918$	−22.4187	+	14.9200i	−0.739926	+	0.492433i
$919$	9.95271	+	17.2386i	0.328310	+	0.568649i	0.982177	−	0.187960i	$-0.0601877\pi$
$919$	9.95271	+	17.2386i	0.328310	+	0.568649i	−0.653867	+	0.756610i	$0.726854\pi$
$920$	2.19996	−	3.81044i	0.0725306	−	0.125627i
$921$	−17.1320	−	32.3820i	−0.564517	−	1.06702i
$922$	−6.82971	−	8.13933i	−0.224925	−	0.268055i
$923$	1.78504	+	1.03060i	0.0587555	+	0.0339225i
$924$	−41.8454	+	13.5007i	−1.37661	+	0.444142i
$925$	−1.57948	+	4.33958i	−0.0519329	+	0.142684i
$926$	2.55041	−	14.4641i	0.0838117	−	0.475320i
$927$	−17.9205	−	4.54691i	−0.588586	−	0.149340i
$928$	5.79348	−	2.10865i	0.190180	−	0.0692200i
$929$	2.91834	−	3.47794i	0.0957475	−	0.114107i	−0.716043	−	0.698056i	$-0.754049\pi$
$929$	2.91834	−	3.47794i	0.0957475	−	0.114107i	0.811791	+	0.583949i	$0.198493\pi$
$930$	17.5155	+	3.76092i	0.574355	+	0.123325i
$931$	2.45953	+	50.3169i	0.0806077	+	1.64907i
$932$			23.4468i			0.768026i
$933$	1.22092	−	0.949829i	0.0399712	−	0.0310960i
$934$	−12.1428	−	33.3621i	−0.397325	−	1.09164i
$935$	−30.0768	+	5.30335i	−0.983617	+	0.173438i
$936$	−4.96769	−	3.38074i	−0.162374	−	0.110503i
$937$	49.3504	+	17.9621i	1.61221	+	0.586795i	0.981875	−	0.189531i	$-0.0606968\pi$
$937$	49.3504	+	17.9621i	1.61221	+	0.586795i	0.630331	+	0.776326i	$0.282919\pi$
$938$	21.4902	−	12.4074i	0.701681	−	0.405116i
$939$	20.0315	−	22.1549i	0.653702	−	0.722997i
$940$	−1.94102	+	1.62871i	−0.0633092	+	0.0531227i
$941$	−13.2451	+	11.1140i	−0.431779	+	0.362306i	−0.832623	−	0.553841i	$-0.813162\pi$
$941$	−13.2451	+	11.1140i	−0.431779	+	0.362306i	0.400843	+	0.916147i	$0.368717\pi$
$942$	3.64698	−	4.03356i	0.118825	−	0.131421i
$943$	9.06964	−	5.23636i	0.295348	−	0.170519i
$944$	5.69482	+	2.07274i	0.185350	+	0.0674621i
$945$	−15.4491	−	16.1979i	−0.502558	−	0.526919i
$946$	39.9573	−	7.04555i	1.29912	−	0.229071i
$947$	−13.1423	−	36.1081i	−0.427067	−	1.17336i	−0.947584	−	0.319505i	$-0.896483\pi$
$947$	−13.1423	−	36.1081i	−0.427067	−	1.17336i	0.520518	−	0.853851i	$-0.325739\pi$
$948$	−8.66079	+	6.73775i	−0.281289	+	0.218832i
$949$			25.6039i			0.831137i
$950$	3.87682	+	1.99255i	0.125781	+	0.0646469i
$951$	−45.8381	−	9.84234i	−1.48640	−	0.319160i
$952$	14.3507	−	17.1025i	0.465108	−	0.554294i
$953$	7.45795	−	2.71447i	0.241587	−	0.0879304i	−0.218389	−	0.975862i	$-0.570080\pi$
$953$	7.45795	−	2.71447i	0.241587	−	0.0879304i	0.459976	+	0.887931i	$0.347858\pi$
$954$	−2.10428	+	8.29346i	−0.0681285	+	0.268511i
$955$	0.0924992	−	0.524589i	0.00299320	−	0.0169753i
$956$	7.31212	−	20.0899i	0.236491	−	0.649753i
$957$	59.8886	−	19.3221i	1.93592	−	0.624595i
$958$	−9.79695	−	5.65627i	−0.316525	−	0.182746i
$959$	56.6856	+	67.5553i	1.83047	+	2.18147i
$960$	−0.809983	−	1.53099i	−0.0261421	−	0.0494125i
$961$	37.9894	−	65.7996i	1.22546	−	2.12257i
$962$	−4.62496	−	8.01067i	−0.149115	−	0.258274i
$963$	−1.16283	−	1.13227i	−0.0374716	−	0.0364867i
$964$	−23.8173	−	4.19963i	−0.767102	−	0.135261i
$965$	0.251515	+	1.42641i	0.00809654	+	0.0459178i
$966$	4.50170	+	32.5193i	0.144840	+	1.04629i
$967$	−13.2565	−	11.1235i	−0.426300	−	0.357708i	0.404254	−	0.914647i	$-0.367531\pi$
$967$	−13.2565	−	11.1235i	−0.426300	−	0.357708i	−0.830554	+	0.556939i	$0.811976\pi$
$968$	−23.7268			−0.762609
$969$	0.464299	+	39.1250i	0.0149154	+	1.25688i
$970$	−2.05926			−0.0661187
$971$	−21.0410	−	17.6555i	−0.675238	−	0.566592i	0.239372	−	0.970928i	$-0.423058\pi$
$971$	−21.0410	−	17.6555i	−0.675238	−	0.566592i	−0.914611	+	0.404336i	$0.867503\pi$
$972$	−11.8372	−	10.1430i	−0.379677	−	0.325338i
$973$	−11.8214	−	67.0427i	−0.378978	−	2.14929i
$974$	2.84794	+	0.502168i	0.0912538	+	0.0160905i
$975$	1.84451	−	2.93829i	0.0590716	−	0.0941006i
$976$	2.04324	+	3.53900i	0.0654026	+	0.113281i
$977$	−21.4130	+	37.0884i	−0.685062	+	1.18656i	0.288356	+	0.957523i	$0.406891\pi$
$977$	−21.4130	+	37.0884i	−0.685062	+	1.18656i	−0.973417	+	0.229038i	$0.926442\pi$
$978$	30.2138	−	15.9849i	0.966130	−	0.511140i
$979$	−27.3444	−	32.5877i	−0.873929	−	1.04151i
$980$	10.0089	+	5.77864i	0.319722	+	0.184592i
$981$	−25.1506	+	2.53827i	−0.802997	+	0.0810408i
$982$	−7.66548	+	21.0607i	−0.244615	+	0.672075i
$983$	1.03929	−	5.89412i	0.0331483	−	0.187993i	−0.963738	−	0.266852i	$-0.914017\pi$
$983$	1.03929	−	5.89412i	0.0331483	−	0.187993i	0.996886	+	0.0788588i	$0.0251276\pi$
$984$	0.152401	−	4.11982i	0.00485837	−	0.131335i
$985$	−0.461526	+	0.167982i	−0.0147054	+	0.00535234i
$986$	−20.5385	+	24.4768i	−0.654079	+	0.779501i
$987$	3.96898	−	18.4845i	0.126334	−	0.588367i
$988$	−8.04868	+	3.38309i	−0.256063	+	0.107631i
$989$		−	30.2940i		−	0.963294i
$990$	−7.68409	−	15.9216i	−0.244216	−	0.506021i
$991$	−4.22440	−	11.6064i	−0.134193	−	0.368691i	0.854337	−	0.519720i	$-0.173964\pi$
$991$	−4.22440	−	11.6064i	−0.134193	−	0.368691i	−0.988529	+	0.151029i	$0.951741\pi$
$992$	−10.1859	+	1.79605i	−0.323403	+	0.0570247i
$993$	3.80066	+	1.54472i	0.120610	+	0.0490202i
$994$	−4.16567	−	1.51618i	−0.132127	−	0.0480903i
$995$	−3.45355	+	1.99391i	−0.109485	+	0.0632112i
$996$	−8.45028	−	7.64038i	−0.267757	−	0.242095i
$997$	−14.9784	+	12.5684i	−0.474372	+	0.398046i	−0.848386	−	0.529377i	$-0.822426\pi$
$997$	−14.9784	+	12.5684i	−0.474372	+	0.398046i	0.374014	+	0.927423i	$0.377981\pi$
$998$	11.9277	−	10.0085i	0.377564	−	0.316814i
$999$	−9.62392	−	21.9818i	−0.304487	−	0.695474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bb.a.41.1	✓	84
3.2	odd	2		570.2.bb.b.41.11	yes	84
19.13	odd	18		570.2.bb.b.431.11	yes	84
57.32	even	18	inner	570.2.bb.a.431.1	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bb.a.41.1	✓	84	1.1	even	1	trivial
570.2.bb.a.431.1	yes	84	57.32	even	18	inner
570.2.bb.b.41.11	yes	84	3.2	odd	2
570.2.bb.b.431.11	yes	84	19.13	odd	18

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(-1.71569 + 0.237506i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.984808 - 0.173648i) q^{5} +(-1.46696 - 0.920884i) q^{6} +(-2.15391 - 3.73068i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.88718 - 0.814973i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(-1.71569 + 0.237506i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.984808 - 0.173648i) q^{5} +(-1.46696 - 0.920884i) q^{6} +(-2.15391 - 3.73068i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.88718 - 0.814973i) q^{9} +(-0.642788 - 0.766044i) q^{10} +(5.10344 + 2.94647i) q^{11} +(-0.531824 - 1.64838i) q^{12} +(-0.685059 + 1.88218i) q^{13} +(0.748044 - 4.24237i) q^{14} +(1.73087 + 0.0640285i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(3.33131 - 3.97010i) q^{17} +(2.73556 + 1.23154i) q^{18} +(3.66401 - 2.36115i) q^{19} -1.00000i q^{20} +(4.58150 + 5.88912i) q^{21} +(2.01551 + 5.53756i) q^{22} +(4.33308 - 0.764038i) q^{23} +(0.652159 - 1.60458i) q^{24} +(0.939693 + 0.342020i) q^{25} +(-1.73463 + 1.00149i) q^{26} +(-4.75995 + 2.08396i) q^{27} +(3.29998 - 2.76901i) q^{28} +(-4.72289 + 3.96297i) q^{29} +(1.28476 + 1.16163i) q^{30} +(8.95735 - 5.17153i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-9.45573 - 3.84314i) q^{33} +(5.10386 - 0.899949i) q^{34} +(1.47336 + 4.04802i) q^{35} +(1.30395 + 2.70180i) q^{36} +4.61808i q^{37} +(4.32451 + 0.546433i) q^{38} +(0.728319 - 3.39195i) q^{39} +(0.642788 - 0.766044i) q^{40} +(2.23666 - 0.814078i) q^{41} +(-0.275823 + 7.45626i) q^{42} +(1.19559 - 6.78053i) q^{43} +(-2.01551 + 5.53756i) q^{44} +(-2.98484 + 0.301238i) q^{45} +(3.81044 + 2.19996i) q^{46} +(-1.62871 - 1.94102i) q^{47} +(1.53099 - 0.809983i) q^{48} +(-5.77864 + 10.0089i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-4.77257 + 7.60267i) q^{51} +(-1.97255 - 0.347814i) q^{52} +(0.495259 + 2.80876i) q^{53} +(-4.98588 - 1.46323i) q^{54} +(-4.51426 - 3.78791i) q^{55} +4.30782 q^{56} +(-5.72552 + 4.92123i) q^{57} -6.16529 q^{58} +(-4.64246 - 3.89548i) q^{59} +(0.237506 + 1.71569i) q^{60} +(-0.709610 - 4.02440i) q^{61} +(10.1859 + 1.79605i) q^{62} +(-9.25913 - 9.01577i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.00149 - 1.73463i) q^{65} +(-4.77319 - 9.02204i) q^{66} +(3.70272 + 4.41273i) q^{67} +(4.48826 + 2.59130i) q^{68} +(-7.25275 + 2.33998i) q^{69} +(-1.47336 + 4.04802i) q^{70} +(0.178695 - 1.01343i) q^{71} +(-0.737803 + 2.90786i) q^{72} +(12.0120 - 4.37201i) q^{73} +(-2.96845 + 3.53766i) q^{74} +(-1.69345 - 0.363618i) q^{75} +(2.96153 + 3.19834i) q^{76} -25.3857i q^{77} +(2.73823 - 2.13023i) q^{78} +(-2.16679 - 5.95320i) q^{79} +(0.984808 - 0.173648i) q^{80} +(7.67164 - 4.70595i) q^{81} +(2.23666 + 0.814078i) q^{82} +(5.69611 - 3.28865i) q^{83} +(-5.00408 + 5.53453i) q^{84} +(-3.97010 + 3.33131i) q^{85} +(5.27431 - 4.42568i) q^{86} +(7.16178 - 7.92095i) q^{87} +(-5.10344 + 2.94647i) q^{88} +(-6.78349 - 2.46899i) q^{89} +(-2.48015 - 1.68785i) q^{90} +(8.49738 - 1.49832i) q^{91} +(1.50486 + 4.13457i) q^{92} +(-14.1398 + 11.0002i) q^{93} -2.53383i q^{94} +(-4.01835 + 1.68903i) q^{95} +(1.69345 + 0.363618i) q^{96} +(1.32366 - 1.57748i) q^{97} +(-10.8603 + 3.95282i) q^{98} +(17.1359 + 4.34784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9}+O(q^{10}) \) 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9	\( 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9} + 24 q^{13} + 24 q^{14} - 12 q^{17} - 12 q^{19} + 36 q^{22} - 6 q^{24} - 6 q^{27} - 12 q^{28} + 12 q^{29} - 6 q^{33} + 12 q^{34} - 18 q^{38} + 12 q^{39} - 6 q^{41} + 24 q^{43} - 36 q^{44} - 12 q^{47} - 54 q^{49} + 42 q^{50} - 54 q^{51} + 12 q^{52} + 60 q^{53} - 54 q^{54} - 60 q^{57} - 24 q^{58} + 18 q^{59} - 48 q^{61} + 12 q^{62} + 18 q^{63} - 42 q^{64} + 54 q^{66} + 6 q^{67} + 54 q^{68} - 60 q^{69} - 48 q^{71} - 12 q^{72} + 84 q^{73} - 24 q^{74} + 36 q^{78} - 12 q^{79} + 114 q^{81} - 6 q^{82} - 36 q^{83} - 18 q^{84} - 12 q^{86} + 6 q^{87} + 12 q^{89} + 24 q^{91} + 6 q^{93} + 12 q^{95} - 42 q^{97} - 36 q^{98} + 102 q^{99}+O(q^{100}) \) 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9 + 24 * q^13 + 24 * q^14 - 12 * q^17 - 12 * q^19 + 36 * q^22 - 6 * q^24 - 6 * q^27 - 12 * q^28 + 12 * q^29 - 6 * q^33 + 12 * q^34 - 18 * q^38 + 12 * q^39 - 6 * q^41 + 24 * q^43 - 36 * q^44 - 12 * q^47 - 54 * q^49 + 42 * q^50 - 54 * q^51 + 12 * q^52 + 60 * q^53 - 54 * q^54 - 60 * q^57 - 24 * q^58 + 18 * q^59 - 48 * q^61 + 12 * q^62 + 18 * q^63 - 42 * q^64 + 54 * q^66 + 6 * q^67 + 54 * q^68 - 60 * q^69 - 48 * q^71 - 12 * q^72 + 84 * q^73 - 24 * q^74 + 36 * q^78 - 12 * q^79 + 114 * q^81 - 6 * q^82 - 36 * q^83 - 18 * q^84 - 12 * q^86 + 6 * q^87 + 12 * q^89 + 24 * q^91 + 6 * q^93 + 12 * q^95 - 42 * q^97 - 36 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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