LMFDB - Embedded newform 547.2.m.a.10.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(10,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(182))

chi = DirichletCharacter(H, H._module([60]))

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

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

chi := DirichletCharacter("547.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.m (of order $91$, degree $72$, 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:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$3168$
Relative dimension:	$44$ over $\Q(\zeta_{91})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{91}]$

Embedding invariants

Embedding label			10.11
Character	$\chi$	$=$	547.10
Dual form			547.2.m.a.383.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.882718 - 1.48907i) q^{2} +(0.304921 + 1.33595i) q^{3} +(-0.478271 + 0.874256i) q^{4} +(-3.64866 - 0.126013i) q^{5} +(1.72016 - 1.63331i) q^{6} +(2.07032 - 0.287726i) q^{7} +(-1.73602 + 0.0599566i) q^{8} +(1.01113 - 0.486934i) q^{9} +O(q^{10})$	\(q+(-0.882718 - 1.48907i) q^{2} +(0.304921 + 1.33595i) q^{3} +(-0.478271 + 0.874256i) q^{4} +(-3.64866 - 0.126013i) q^{5} +(1.72016 - 1.63331i) q^{6} +(2.07032 - 0.287726i) q^{7} +(-1.73602 + 0.0599566i) q^{8} +(1.01113 - 0.486934i) q^{9} +(3.03310 + 5.54435i) q^{10} +(0.304699 + 0.0751016i) q^{11} +(-1.31379 - 0.372365i) q^{12} +(-1.48308 - 1.85973i) q^{13} +(-2.25595 - 2.82887i) q^{14} +(-0.944207 - 4.91284i) q^{15} +(2.69659 + 4.21049i) q^{16} +(-2.75758 + 2.27807i) q^{17} +(-1.61762 - 1.07582i) q^{18} +(-5.42447 + 3.34347i) q^{19} +(1.85521 - 3.12959i) q^{20} +(1.01567 + 2.67810i) q^{21} +(-0.157132 - 0.520013i) q^{22} +(-1.12438 + 3.72102i) q^{23} +(-0.609450 - 2.30095i) q^{24} +(8.30875 + 0.574600i) q^{25} +(-1.46013 + 3.85003i) q^{26} +(3.52194 + 4.41638i) q^{27} +(-0.738627 + 1.94760i) q^{28} +(-3.48723 + 1.98669i) q^{29} +(-6.48211 + 5.74264i) q^{30} +(-0.442988 + 0.159313i) q^{31} +(2.32823 - 4.62851i) q^{32} +(-0.00742253 + 0.429962i) q^{33} +(5.82638 + 2.09535i) q^{34} +(-7.59015 + 0.788927i) q^{35} +(-0.0578884 + 1.11687i) q^{36} +(-1.23384 + 7.87815i) q^{37} +(9.76695 + 5.12609i) q^{38} +(2.03227 - 2.54839i) q^{39} +6.34172 q^{40} -11.7546 q^{41} +(3.09134 - 3.87642i) q^{42} +(-5.43468 + 3.89148i) q^{43} +(-0.211387 + 0.230466i) q^{44} +(-3.75063 + 1.64924i) q^{45} +(6.53338 - 1.61033i) q^{46} +(4.71588 - 6.83213i) q^{47} +(-4.80275 + 4.88638i) q^{48} +(-2.53129 + 0.717435i) q^{49} +(-6.47867 - 12.8795i) q^{50} +(-3.88422 - 2.98936i) q^{51} +(2.33519 - 0.407141i) q^{52} +(2.01770 + 10.4984i) q^{53} +(3.46742 - 9.14284i) q^{54} +(-1.10228 - 0.312416i) q^{55} +(-3.57687 + 0.623628i) q^{56} +(-6.12074 - 6.22731i) q^{57} +(6.03656 + 3.43905i) q^{58} +(-1.38758 - 11.4277i) q^{59} +(4.74667 + 1.52419i) q^{60} +(0.258664 + 2.98956i) q^{61} +(0.628261 + 0.519013i) q^{62} +(1.95326 - 1.29904i) q^{63} +(1.02879 - 0.0711467i) q^{64} +(5.17692 + 6.97240i) q^{65} +(0.646797 - 0.368483i) q^{66} +(0.724183 + 0.205253i) q^{67} +(-0.672742 - 3.50037i) q^{68} +(-5.31394 - 0.367490i) q^{69} +(7.87473 + 10.6059i) q^{70} +(1.40343 + 4.12463i) q^{71} +(-1.72615 + 0.905953i) q^{72} +(1.63820 - 8.52380i) q^{73} +(12.8203 - 5.11691i) q^{74} +(1.76588 + 11.2753i) q^{75} +(-0.328683 - 6.34146i) q^{76} +(0.652434 + 0.0678145i) q^{77} +(-5.58867 - 0.776693i) q^{78} +(12.7895 - 9.15785i) q^{79} +(-9.30838 - 15.7025i) q^{80} +(-2.72696 + 3.41950i) q^{81} +(10.3760 + 17.5034i) q^{82} +(7.41358 + 3.89095i) q^{83} +(-2.82711 - 0.392902i) q^{84} +(10.3486 - 7.96440i) q^{85} +(10.5920 + 4.65756i) q^{86} +(-3.71744 - 4.05297i) q^{87} +(-0.533468 - 0.112110i) q^{88} +(0.665022 - 7.68612i) q^{89} +(5.76658 + 4.12914i) q^{90} +(-3.60555 - 3.42351i) q^{91} +(-2.71537 - 2.76265i) q^{92} +(-0.347910 - 0.543230i) q^{93} +(-14.3363 - 0.991442i) q^{94} +(20.2134 - 11.5156i) q^{95} +(6.89337 + 1.69906i) q^{96} +(1.75398 + 1.34989i) q^{97} +(3.30272 + 3.13597i) q^{98} +(0.344660 - 0.0724310i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9}+O(q^{10}) $ 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9	\( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9} - 91 q^{10} - 61 q^{11} - 31 q^{12} - 72 q^{13} - 21 q^{14} - 46 q^{15} + 24 q^{16} - 91 q^{17} + 9 q^{18} - 89 q^{19} - 108 q^{20} - 81 q^{21} - 50 q^{22} - 86 q^{23} - 33 q^{24} - 15 q^{25} + 137 q^{26} + 163 q^{27} - 47 q^{28} - 12 q^{29} + 29 q^{30} - 53 q^{31} - 122 q^{32} - 21 q^{33} - 80 q^{34} - 75 q^{35} - 8 q^{36} - 49 q^{37} - 47 q^{38} + 128 q^{39} - 246 q^{40} - 686 q^{41} - 466 q^{42} - 9 q^{43} - 43 q^{44} + 156 q^{45} - 91 q^{46} - 72 q^{47} + 21 q^{48} - 8 q^{49} - 84 q^{50} + 93 q^{51} + 4 q^{52} - 32 q^{53} - 71 q^{54} - 34 q^{55} - 263 q^{56} - 61 q^{57} - 36 q^{58} - 23 q^{59} + 87 q^{60} + 38 q^{61} + 26 q^{62} + 133 q^{63} + 343 q^{64} + 143 q^{65} - 65 q^{66} - 50 q^{67} - 213 q^{68} - 140 q^{69} + 372 q^{70} - 75 q^{71} + 147 q^{72} - 18 q^{73} - 85 q^{74} + 97 q^{75} - 47 q^{76} + 11 q^{77} + 55 q^{78} - 37 q^{79} - 142 q^{80} - 532 q^{81} - 94 q^{82} - 279 q^{83} + 395 q^{84} - 75 q^{85} - 147 q^{86} + 84 q^{87} + 345 q^{88} + 8 q^{89} + 278 q^{90} - 38 q^{91} - 78 q^{92} - 83 q^{93} - 540 q^{94} + 35 q^{95} + 123 q^{96} - 735 q^{97} - 90 q^{98} + 351 q^{99}+O(q^{100}) \) 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9 - 91 * q^10 - 61 * q^11 - 31 * q^12 - 72 * q^13 - 21 * q^14 - 46 * q^15 + 24 * q^16 - 91 * q^17 + 9 * q^18 - 89 * q^19 - 108 * q^20 - 81 * q^21 - 50 * q^22 - 86 * q^23 - 33 * q^24 - 15 * q^25 + 137 * q^26 + 163 * q^27 - 47 * q^28 - 12 * q^29 + 29 * q^30 - 53 * q^31 - 122 * q^32 - 21 * q^33 - 80 * q^34 - 75 * q^35 - 8 * q^36 - 49 * q^37 - 47 * q^38 + 128 * q^39 - 246 * q^40 - 686 * q^41 - 466 * q^42 - 9 * q^43 - 43 * q^44 + 156 * q^45 - 91 * q^46 - 72 * q^47 + 21 * q^48 - 8 * q^49 - 84 * q^50 + 93 * q^51 + 4 * q^52 - 32 * q^53 - 71 * q^54 - 34 * q^55 - 263 * q^56 - 61 * q^57 - 36 * q^58 - 23 * q^59 + 87 * q^60 + 38 * q^61 + 26 * q^62 + 133 * q^63 + 343 * q^64 + 143 * q^65 - 65 * q^66 - 50 * q^67 - 213 * q^68 - 140 * q^69 + 372 * q^70 - 75 * q^71 + 147 * q^72 - 18 * q^73 - 85 * q^74 + 97 * q^75 - 47 * q^76 + 11 * q^77 + 55 * q^78 - 37 * q^79 - 142 * q^80 - 532 * q^81 - 94 * q^82 - 279 * q^83 + 395 * q^84 - 75 * q^85 - 147 * q^86 + 84 * q^87 + 345 * q^88 + 8 * q^89 + 278 * q^90 - 38 * q^91 - 78 * q^92 - 83 * q^93 - 540 * q^94 + 35 * q^95 + 123 * q^96 - 735 * q^97 - 90 * q^98 + 351 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{30}{91}\right)$

Coefficient data

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

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

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

$2$	−0.882718	−	1.48907i	−0.624176	−	1.05293i	−0.992383	−	0.123189i	$-0.960688\pi$
$2$	−0.882718	−	1.48907i	−0.624176	−	1.05293i	0.368207	−	0.929744i	$-0.379972\pi$
$3$	0.304921	+	1.33595i	0.176046	+	0.771309i	0.983431	+	0.181284i	$0.0580252\pi$
$3$	0.304921	+	1.33595i	0.176046	+	0.771309i	−0.807385	+	0.590026i	$0.799118\pi$
$4$	−0.478271	+	0.874256i	−0.239135	+	0.437128i
$5$	−3.64866	−	0.126013i	−1.63173	−	0.0563546i	−0.795930	−	0.605388i	$-0.793018\pi$
$5$	−3.64866	−	0.126013i	−1.63173	−	0.0563546i	−0.835800	+	0.549034i	$0.814996\pi$
$6$	1.72016	−	1.63331i	0.702253	−	0.666798i
$7$	2.07032	−	0.287726i	0.782507	−	0.108750i	0.264795	−	0.964305i	$-0.414696\pi$
$7$	2.07032	−	0.287726i	0.782507	−	0.108750i	0.517712	+	0.855555i	$0.326784\pi$
$8$	−1.73602	+	0.0599566i	−0.613777	+	0.0211979i
$9$	1.01113	−	0.486934i	0.337043	−	0.162311i
$10$	3.03310	+	5.54435i	0.959149	+	1.75328i
$11$	0.304699	+	0.0751016i	0.0918703	+	0.0226440i	0.284983	−	0.958533i	$-0.408012\pi$
$11$	0.304699	+	0.0751016i	0.0918703	+	0.0226440i	−0.193113	+	0.981177i	$0.561858\pi$
$12$	−1.31379	−	0.372365i	−0.379260	−	0.107493i
$13$	−1.48308	−	1.85973i	−0.411333	−	0.515796i	0.532404	−	0.846490i	$-0.321289\pi$
$13$	−1.48308	−	1.85973i	−0.411333	−	0.515796i	−0.943738	+	0.330694i	$0.892717\pi$
$14$	−2.25595	−	2.82887i	−0.602929	−	0.756049i
$15$	−0.944207	−	4.91284i	−0.243793	−	1.26849i
$16$	2.69659	+	4.21049i	0.674148	+	1.05262i
$17$	−2.75758	+	2.27807i	−0.668812	+	0.552512i	−0.908265	−	0.418396i	$-0.862593\pi$
$17$	−2.75758	+	2.27807i	−0.668812	+	0.552512i	0.239452	+	0.970908i	$0.423032\pi$
$18$	−1.61762	−	1.07582i	−0.381277	−	0.253573i
$19$	−5.42447	+	3.34347i	−1.24446	+	0.767045i	−0.980315	−	0.197439i	$-0.936738\pi$
$19$	−5.42447	+	3.34347i	−1.24446	+	0.767045i	−0.264144	+	0.964483i	$0.585089\pi$
$20$	1.85521	−	3.12959i	0.414839	−	0.699799i
$21$	1.01567	+	2.67810i	0.221637	+	0.584410i
$22$	−0.157132	−	0.520013i	−0.0335006	−	0.110867i
$23$	−1.12438	+	3.72102i	−0.234449	+	0.775887i	0.757894	+	0.652377i	$0.226228\pi$
$23$	−1.12438	+	3.72102i	−0.234449	+	0.775887i	−0.992343	+	0.123510i	$0.960585\pi$
$24$	−0.609450	−	2.30095i	−0.124403	−	0.469680i
$25$	8.30875	+	0.574600i	1.66175	+	0.114920i
$26$	−1.46013	+	3.85003i	−0.286354	+	0.755054i
$27$	3.52194	+	4.41638i	0.677798	+	0.849932i
$28$	−0.738627	+	1.94760i	−0.139587	+	0.368062i
$29$	−3.48723	+	1.98669i	−0.647562	+	0.368919i	−0.783138	−	0.621848i	$-0.786382\pi$
$29$	−3.48723	+	1.98669i	−0.647562	+	0.368919i	0.135575	+	0.990767i	$0.456712\pi$
$30$	−6.48211	+	5.74264i	−1.18347	+	1.04846i
$31$	−0.442988	+	0.159313i	−0.0795630	+	0.0286134i	−0.377892	−	0.925850i	$-0.623351\pi$
$31$	−0.442988	+	0.159313i	−0.0795630	+	0.0286134i	0.298329	+	0.954463i	$0.403571\pi$
$32$	2.32823	−	4.62851i	0.411577	−	0.818213i
$33$	−0.00742253	+	0.429962i	−0.00129210	+	0.0748468i
$34$	5.82638	+	2.09535i	0.999215	+	0.359350i
$35$	−7.59015	+	0.788927i	−1.28297	+	0.133353i
$36$	−0.0578884	+	1.11687i	−0.00964807	+	0.186145i
$37$	−1.23384	+	7.87815i	−0.202842	+	1.29516i	0.644701	+	0.764434i	$0.276982\pi$
$37$	−1.23384	+	7.87815i	−0.202842	+	1.29516i	−0.847544	+	0.530726i	$0.821919\pi$
$38$	9.76695	+	5.12609i	1.58441	+	0.831562i
$39$	2.03227	−	2.54839i	0.325424	−	0.408069i
$40$	6.34172			1.00271
$41$	−11.7546			−1.83576			−0.917878	−	0.396862i	$-0.870099\pi$
$41$	−11.7546			−1.83576			−0.917878	+	0.396862i	$0.870099\pi$
$42$	3.09134	−	3.87642i	0.477004	−	0.598144i
$43$	−5.43468	+	3.89148i	−0.828782	+	0.593446i	−0.915285	−	0.402806i	$-0.868035\pi$
$43$	−5.43468	+	3.89148i	−0.828782	+	0.593446i	0.0865038	+	0.996252i	$0.472431\pi$
$44$	−0.211387	+	0.230466i	−0.0318678	+	0.0347441i
$45$	−3.75063	+	1.64924i	−0.559110	+	0.245854i
$46$	6.53338	−	1.61033i	0.963295	−	0.237431i
$47$	4.71588	−	6.83213i	0.687881	−	0.996568i	−0.311052	−	0.950393i	$-0.600681\pi$
$47$	4.71588	−	6.83213i	0.687881	−	0.996568i	0.998933	−	0.0461753i	$-0.0147033\pi$
$48$	−4.80275	+	4.88638i	−0.693217	+	0.705288i
$49$	−2.53129	+	0.717435i	−0.361612	+	0.102491i
$50$	−6.47867	−	12.8795i	−0.916222	−	1.82144i
$51$	−3.88422	−	2.98936i	−0.543900	−	0.418594i
$52$	2.33519	−	0.407141i	0.323833	−	0.0564603i
$53$	2.01770	+	10.4984i	0.277153	+	1.44206i	0.805278	+	0.592897i	$0.202016\pi$
$53$	2.01770	+	10.4984i	0.277153	+	1.44206i	−0.528126	+	0.849166i	$0.677105\pi$
$54$	3.46742	−	9.14284i	0.471857	−	1.24418i
$55$	−1.10228	−	0.312416i	−0.148631	−	0.0421262i
$56$	−3.57687	+	0.623628i	−0.477980	+	0.0833358i
$57$	−6.12074	−	6.22731i	−0.810711	−	0.824828i
$58$	6.03656	+	3.43905i	0.792639	+	0.451570i
$59$	−1.38758	−	11.4277i	−0.180647	−	1.48776i	−0.747676	−	0.664064i	$-0.768830\pi$
$59$	−1.38758	−	11.4277i	−0.180647	−	1.48776i	0.567029	−	0.823698i	$-0.308093\pi$
$60$	4.74667	+	1.52419i	0.612792	+	0.196772i
$61$	0.258664	+	2.98956i	0.0331186	+	0.382775i	0.994281	+	0.106792i	$0.0340580\pi$
$61$	0.258664	+	2.98956i	0.0331186	+	0.382775i	−0.961163	+	0.275982i	$0.910997\pi$
$62$	0.628261	+	0.519013i	0.0797893	+	0.0659147i
$63$	1.95326	−	1.29904i	0.246087	−	0.163663i
$64$	1.02879	−	0.0711467i	0.128598	−	0.00889334i
$65$	5.17692	+	6.97240i	0.642118	+	0.864820i
$66$	0.646797	−	0.368483i	0.0796152	−	0.0453571i
$67$	0.724183	+	0.205253i	0.0884730	+	0.0250757i	0.316634	−	0.948548i	$-0.397447\pi$
$67$	0.724183	+	0.205253i	0.0884730	+	0.0250757i	−0.228161	+	0.973623i	$0.573271\pi$
$68$	−0.672742	−	3.50037i	−0.0815819	−	0.424482i
$69$	−5.31394	−	0.367490i	−0.639723	−	0.0442406i
$70$	7.87473	+	10.6059i	0.941210	+	1.26765i
$71$	1.40343	+	4.12463i	0.166557	+	0.489504i	0.997792	−	0.0664174i	$-0.0211569\pi$
$71$	1.40343	+	4.12463i	0.166557	+	0.489504i	−0.831235	+	0.555921i	$0.812366\pi$
$72$	−1.72615	+	0.905953i	−0.203429	+	0.106768i
$73$	1.63820	−	8.52380i	0.191737	−	0.997636i	−0.750038	−	0.661394i	$-0.769965\pi$
$73$	1.63820	−	8.52380i	0.191737	−	0.997636i	0.941776	−	0.336241i	$-0.109156\pi$
$74$	12.8203	−	5.11691i	1.49033	−	0.594828i
$75$	1.76588	+	11.2753i	0.203906	+	1.30196i
$76$	−0.328683	−	6.34146i	−0.0377025	−	0.727415i
$77$	0.652434	+	0.0678145i	0.0743517	+	0.00772818i
$78$	−5.58867	−	0.776693i	−0.632792	−	0.0879432i
$79$	12.7895	−	9.15785i	1.43893	−	1.03034i	0.448281	−	0.893893i	$-0.352036\pi$
$79$	12.7895	−	9.15785i	1.43893	−	1.03034i	0.990647	−	0.136446i	$-0.0435680\pi$
$80$	−9.30838	−	15.7025i	−1.04071	−	1.75559i
$81$	−2.72696	+	3.41950i	−0.302996	+	0.379945i
$82$	10.3760	+	17.5034i	1.14583	+	1.93293i
$83$	7.41358	+	3.89095i	0.813747	+	0.427087i	0.819628	−	0.572896i	$-0.194180\pi$
$83$	7.41358	+	3.89095i	0.813747	+	0.427087i	−0.00588180	+	0.999983i	$0.501872\pi$
$84$	−2.82711	−	0.392902i	−0.308463	−	0.0428692i
$85$	10.3486	−	7.96440i	1.12246	−	0.863861i
$86$	10.5920	+	4.65756i	1.14216	+	0.502237i
$87$	−3.71744	−	4.05297i	−0.398551	−	0.434524i
$88$	−0.533468	−	0.112110i	−0.0568679	−	0.0119509i
$89$	0.665022	−	7.68612i	0.0704922	−	0.814727i	−0.873943	−	0.486029i	$-0.838445\pi$
$89$	0.665022	−	7.68612i	0.0704922	−	0.814727i	0.944435	−	0.328698i	$-0.106610\pi$
$90$	5.76658	+	4.12914i	0.607851	+	0.435249i
$91$	−3.60555	−	3.42351i	−0.377964	−	0.358881i
$92$	−2.71537	−	2.76265i	−0.283097	−	0.288026i
$93$	−0.347910	−	0.543230i	−0.0360766	−	0.0563304i
$94$	−14.3363	−	0.991442i	−1.47868	−	0.102259i
$95$	20.2134	−	11.5156i	2.07385	−	1.18148i
$96$	6.89337	+	1.69906i	0.703552	+	0.173410i
$97$	1.75398	+	1.34989i	0.178090	+	0.137061i	0.695085	−	0.718928i	$-0.255367\pi$
$97$	1.75398	+	1.34989i	0.178090	+	0.137061i	−0.516995	+	0.855989i	$0.672949\pi$
$98$	3.30272	+	3.13597i	0.333625	+	0.316781i
$99$	0.344660	−	0.0724310i	0.0346396	−	0.00727959i
$100$	−4.47618	+	6.98916i	−0.447618	+	0.698916i
$101$	−6.11720	+	8.23880i	−0.608684	+	0.819791i	−0.994713	−	0.102696i	$-0.967253\pi$
$101$	−6.11720	+	8.23880i	−0.608684	+	0.819791i	0.386029	+	0.922487i	$0.373847\pi$
$102$	−1.02269	+	8.42265i	−0.101262	+	0.833966i
$103$	−4.25311	+	9.23618i	−0.419071	+	0.910068i	0.576592	+	0.817032i	$0.304382\pi$
$103$	−4.25311	+	9.23618i	−0.419071	+	0.910068i	−0.995663	+	0.0930357i	$0.970343\pi$
$104$	2.68617	+	3.13961i	0.263401	+	0.307864i
$105$	−3.36836	−	9.89948i	−0.328718	−	0.966090i
$106$	13.8518	−	12.2716i	1.34540	−	1.19192i
$107$	−10.1119	−	2.49235i	−0.977550	−	0.240944i	−0.281994	−	0.959416i	$-0.590996\pi$
$107$	−10.1119	−	2.49235i	−0.977550	−	0.240944i	−0.695556	+	0.718472i	$0.744842\pi$
$108$	−5.54549	+	0.966856i	−0.533615	+	0.0930358i
$109$	−3.39495	−	5.30092i	−0.325177	−	0.507736i	0.640334	−	0.768097i	$-0.278796\pi$
$109$	−3.39495	−	5.30092i	−0.325177	−	0.507736i	−0.965511	+	0.260361i	$0.916159\pi$
$110$	0.507792	+	1.91715i	0.0484161	+	0.182793i
$111$	−10.9010	+	0.753870i	−1.03468	+	0.0715542i
$112$	6.79428	+	7.94119i	0.641999	+	0.750372i
$113$	−11.6449	−	7.17756i	−1.09546	−	0.675208i	−0.146062	−	0.989275i	$-0.546660\pi$
$113$	−11.6449	−	7.17756i	−1.09546	−	0.675208i	−0.949401	+	0.314067i	$0.898308\pi$
$114$	−3.87003	+	14.6112i	−0.362462	+	1.36846i
$115$	4.57137	−	13.4351i	0.426282	−	1.25283i
$116$	−0.0690340	−	3.99891i	−0.00640964	−	0.371289i
$117$	−2.40515	−	1.15826i	−0.222357	−	0.107081i
$118$	−15.7919	+	12.1536i	−1.45376	+	1.11883i
$119$	−5.05362	+	5.50975i	−0.463265	+	0.505078i
$120$	1.93372	+	8.47220i	0.176524	+	0.773403i
$121$	−9.65281	−	5.06619i	−0.877529	−	0.460563i
$122$	4.22335	−	3.02411i	0.382364	−	0.273790i
$123$	−3.58422	−	15.7035i	−0.323178	−	1.41594i
$124$	0.0725880	−	0.463479i	0.00651860	−	0.0416217i
$125$	−12.0871	−	1.25634i	−1.08110	−	0.112370i
$126$	−3.65853	−	1.76186i	−0.325928	−	0.156959i
$127$	−3.66418	−	0.638850i	−0.325143	−	0.0566887i	0.00683257	−	0.999977i	$-0.497825\pi$
$127$	−3.66418	−	0.638850i	−0.325143	−	0.0566887i	−0.331976	+	0.943288i	$0.607715\pi$
$128$	−6.90047	−	9.99706i	−0.609921	−	0.883623i
$129$	−6.85597	−	6.07386i	−0.603634	−	0.534773i
$130$	5.81265	−	13.8635i	0.509804	−	1.21591i
$131$	−2.20056	+	0.462453i	−0.192264	+	0.0404047i	−0.300797	−	0.953688i	$-0.597253\pi$
$131$	−2.20056	+	0.462453i	−0.192264	+	0.0404047i	0.108533	+	0.994093i	$0.465385\pi$
$132$	−0.372347	−	0.212128i	−0.0324087	−	0.0184633i
$133$	−10.2684	+	8.48281i	−0.890382	+	0.735553i
$134$	−0.333612	−	1.25954i	−0.0288197	−	0.108808i
$135$	−12.2939	−	16.5577i	−1.05809	−	1.42506i
$136$	4.65065	−	4.12012i	0.398790	−	0.353297i
$137$	2.65929	+	4.86106i	0.227199	+	0.415308i	0.965972	−	0.258645i	$-0.0832761\pi$
$137$	2.65929	+	4.86106i	0.227199	+	0.415308i	−0.738774	+	0.673953i	$0.764595\pi$
$138$	4.14349	+	8.23723i	0.352717	+	0.701200i
$139$	−15.2451	−	10.9162i	−1.29307	−	0.925898i	−0.293522	−	0.955952i	$-0.594827\pi$
$139$	−15.2451	−	10.9162i	−1.29307	−	0.925898i	−0.999548	+	0.0300546i	$0.990432\pi$
$140$	2.94042	−	7.01305i	0.248511	−	0.592711i
$141$	10.5653	+	4.21690i	0.889761	+	0.355127i
$142$	4.90304	−	5.73070i	0.411454	−	0.480910i
$143$	−0.312226	−	0.678040i	−0.0261097	−	0.0567006i
$144$	4.77684	+	2.94429i	0.398070	+	0.245357i
$145$	12.9741	−	6.80931i	1.07744	−	0.565483i
$146$	−14.1386	+	5.08471i	−1.17012	+	0.420813i
$147$	−1.73030	−	3.16290i	−0.142713	−	0.260872i
$148$	−6.29741	−	4.84658i	−0.517644	−	0.398387i
$149$	16.4504	+	16.7368i	1.34767	+	1.37113i	0.870376	+	0.492387i	$0.163875\pi$
$149$	16.4504	+	16.7368i	1.34767	+	1.37113i	0.477290	+	0.878746i	$0.341619\pi$
$150$	15.2309	−	12.5824i	1.24360	−	1.02735i
$151$	0.965675	−	3.19581i	0.0785855	−	0.260071i	−0.909087	−	0.416607i	$-0.863219\pi$
$151$	0.965675	−	3.19581i	0.0785855	−	0.260071i	0.987672	+	0.156535i	$0.0500325\pi$
$152$	9.21655	−	6.12958i	0.747561	−	0.497175i
$153$	−1.67901	+	3.64618i	−0.135740	+	0.294776i
$154$	−0.474934	−	1.03138i	−0.0382713	−	0.0831111i
$155$	1.63639	−	0.525456i	0.131438	−	0.0422056i
$156$	1.25597	+	2.99555i	0.100558	+	0.239836i
$157$	21.3423	+	3.72103i	1.70330	+	0.296970i	0.937982	−	0.346684i	$-0.112692\pi$
$157$	21.3423	+	3.72103i	1.70330	+	0.296970i	0.765316	+	0.643654i	$0.222583\pi$
$158$	−24.9262	−	10.9607i	−1.98302	−	0.871983i
$159$	−13.4100	+	5.89672i	−1.06349	+	0.467640i
$160$	−9.07818	+	16.5945i	−0.717693	+	1.31191i
$161$	−1.25719	+	8.02722i	−0.0990802	+	0.632634i
$162$	7.49902	+	1.04219i	0.589179	+	0.0818820i
$163$	3.23659	−	3.52872i	0.253509	−	0.276391i	−0.597125	−	0.802148i	$-0.703691\pi$
$163$	3.23659	−	3.52872i	0.253509	−	0.276391i	0.850635	+	0.525757i	$0.176218\pi$
$164$	5.62187	−	10.2765i	0.438994	−	0.802461i
$165$	0.0812630	−	1.56785i	0.00632632	−	0.122057i
$166$	−0.750198	−	14.4740i	−0.0582267	−	1.12340i
$167$	0.303248	+	17.5661i	0.0234660	+	1.35931i	0.745063	+	0.666994i	$0.232420\pi$
$167$	0.303248	+	17.5661i	0.0234660	+	1.35931i	−0.721597	+	0.692314i	$0.756591\pi$
$168$	−1.92380	−	4.58836i	−0.148424	−	0.353999i
$169$	1.63372	−	7.15780i	0.125671	−	0.550600i
$170$	−20.9944	−	8.37943i	−1.61020	−	0.642673i
$171$	−3.85679	+	6.02204i	−0.294936	+	0.460517i
$172$	−0.802901	−	6.61249i	−0.0612207	−	0.504197i
$173$	−7.78267	−	5.17596i	−0.591705	−	0.393521i	0.221788	−	0.975095i	$-0.428811\pi$
$173$	−7.78267	−	5.17596i	−0.591705	−	0.393521i	−0.813493	+	0.581574i	$0.802437\pi$
$174$	−2.75372	+	9.11317i	−0.208759	+	0.690867i
$175$	17.3671	−	1.20104i	1.31283	−	0.0907899i
$176$	0.505435	+	1.48545i	0.0380986	+	0.111970i
$177$	14.8437	−	5.33828i	1.11572	−	0.401250i
$178$	−12.0322	+	5.79441i	−0.901853	+	0.434309i
$179$	12.1163	−	3.43408i	0.905611	−	0.256675i	0.212208	−	0.977225i	$-0.431935\pi$
$179$	12.1163	−	3.43408i	0.905611	−	0.256675i	0.693403	+	0.720550i	$0.256110\pi$
$180$	0.351955	−	4.06779i	0.0262332	−	0.303195i
$181$	3.40195	+	3.01386i	0.252865	+	0.224019i	0.780027	−	0.625746i	$-0.215205\pi$
$181$	3.40195	+	3.01386i	0.252865	+	0.224019i	−0.527162	+	0.849765i	$0.676744\pi$
$182$	−1.91517	+	8.39092i	−0.141962	+	0.621976i
$183$	−3.91503	+	1.25714i	−0.289407	+	0.0929307i
$184$	1.72885	−	6.52720i	0.127452	−	0.481192i
$185$	5.49461	−	28.5892i	0.403972	−	2.10192i
$186$	−0.501803	+	0.997582i	−0.0367940	+	0.0731463i
$187$	−1.01132	+	0.487026i	−0.0739551	+	0.0356149i
$188$	3.71756	+	7.39049i	0.271131	+	0.539007i
$189$	8.56225	+	8.12996i	0.622812	+	0.591367i
$190$	−34.9903	−	19.9341i	−2.53846	−	1.44617i
$191$	−10.7713	−	7.16360i	−0.779385	−	0.518340i	0.0996922	−	0.995018i	$-0.468214\pi$
$191$	−10.7713	−	7.16360i	−0.779385	−	0.518340i	−0.879078	+	0.476679i	$0.841841\pi$
$192$	0.408747	+	1.35271i	0.0294988	+	0.0976235i
$193$	−6.05407	−	5.00133i	−0.435782	−	0.360003i	0.393035	−	0.919523i	$-0.371425\pi$
$193$	−6.05407	−	5.00133i	−0.435782	−	0.360003i	−0.828817	+	0.559520i	$0.810986\pi$
$194$	0.461814	−	3.80338i	0.0331563	−	0.273067i
$195$	−7.73621	+	9.04212i	−0.554002	+	0.647520i
$196$	0.583418	−	2.55612i	0.0416727	−	0.182580i
$197$	−3.58663	−	5.19612i	−0.255536	−	0.370209i	0.674129	−	0.738614i	$-0.264519\pi$
$197$	−3.58663	−	5.19612i	−0.255536	−	0.370209i	−0.929665	+	0.368405i	$0.879904\pi$
$198$	−0.412093	−	0.449287i	−0.0292861	−	0.0319295i
$199$	−10.0269	+	2.47140i	−0.710785	+	0.175193i	−0.578101	−	0.815965i	$-0.696206\pi$
$199$	−10.0269	+	2.47140i	−0.710785	+	0.175193i	−0.132685	+	0.991158i	$0.542360\pi$
$200$	−14.4587	−	0.499354i	−1.02238	−	0.0353097i
$201$	−0.0533887	+	1.03006i	−0.00376575	+	0.0726545i
$202$	17.6679	+	1.83642i	1.24311	+	0.129210i
$203$	−6.64806	+	5.11644i	−0.466602	+	0.359104i
$204$	4.47117	−	1.96608i	0.313045	−	0.137653i
$205$	42.8885	+	1.48123i	2.99546	+	0.103453i
$206$	17.5076	−	1.81976i	1.21981	−	0.126789i
$207$	0.675002	+	4.30993i	0.0469159	+	0.299561i
$208$	3.83110	−	11.2594i	0.265639	−	0.780702i
$209$	−1.90393	+	0.611367i	−0.131698	+	0.0422891i
$210$	−11.7677	+	13.7542i	−0.812050	+	0.949128i
$211$	−6.75621	+	9.09943i	−0.465116	+	0.626430i	−0.971830	−	0.235684i	$-0.924267\pi$
$211$	−6.75621	+	9.09943i	−0.465116	+	0.626430i	0.506713	+	0.862115i	$0.330860\pi$
$212$	−10.1433	−	3.25708i	−0.696643	−	0.223697i
$213$	−5.08235	+	3.13260i	−0.348237	+	0.214642i
$214$	5.21463	+	17.2573i	0.356465	+	1.17969i
$215$	20.3197	−	13.5139i	1.38579	−	0.921637i
$216$	−6.37897	−	7.45578i	−0.434034	−	0.507301i
$217$	−0.871288	+	0.457287i	−0.0591469	+	0.0310427i
$218$	−4.89667	+	9.73454i	−0.331644	+	0.659307i
$219$	11.8869	−	0.410534i	0.803240	−	0.0277413i
$220$	0.800320	−	0.814256i	0.0539576	−	0.0548971i
$221$	8.32631	+	1.74979i	0.560089	+	0.117704i
$222$	10.7451	+	15.5669i	0.721163	+	1.04479i
$223$	−0.236765	−	0.564697i	−0.0158550	−	0.0378149i	0.914098	−	0.405493i	$-0.132900\pi$
$223$	−0.236765	−	0.564697i	−0.0158550	−	0.0378149i	−0.929953	+	0.367678i	$0.880153\pi$
$224$	3.48844	−	10.2524i	0.233081	−	0.685017i
$225$	8.68101	−	3.46482i	0.578734	−	0.230988i
$226$	−0.408722	+	23.6759i	−0.0271878	+	1.57490i
$227$	−27.6493	+	0.954916i	−1.83515	+	0.0633800i	−0.931253	−	0.364374i	$-0.881283\pi$
$227$	−27.6493	+	0.954916i	−1.83515	+	0.0633800i	−0.903895	+	0.427754i	$0.859305\pi$
$228$	8.37163	−	2.37275i	0.554425	−	0.157139i
$229$	−11.1175	−	7.96063i	−0.734664	−	0.526053i	0.152049	−	0.988373i	$-0.451413\pi$
$229$	−11.1175	−	7.96063i	−0.734664	−	0.526053i	−0.886713	+	0.462320i	$0.847017\pi$
$230$	−24.0410	+	5.05227i	−1.58522	+	0.333137i
$231$	0.108344	+	0.892295i	0.00712853	+	0.0587087i
$232$	5.93480	−	3.65802i	0.389639	−	0.240161i
$233$	3.14776	+	8.29997i	0.206217	+	0.543749i	0.997725	−	0.0674090i	$-0.0214732\pi$
$233$	3.14776	+	8.29997i	0.206217	+	0.543749i	−0.791509	+	0.611158i	$0.790704\pi$
$234$	0.398338	+	4.60387i	0.0260402	+	0.300964i
$235$	−18.0676	+	24.3339i	−1.17860	+	1.58737i
$236$	10.6544	+	4.25244i	0.693541	+	0.276811i
$237$	16.1342	+	14.2936i	1.04803	+	0.928472i
$238$	12.6653	+	2.66165i	0.820972	+	0.172529i
$239$	3.00657	−	4.35577i	0.194479	−	0.281752i	−0.713597	−	0.700556i	$-0.752935\pi$
$239$	3.00657	−	4.35577i	0.194479	−	0.281752i	0.908076	+	0.418805i	$0.137551\pi$
$240$	18.1393	−	17.2235i	1.17089	−	1.11177i
$241$	−1.72514	+	0.179313i	−0.111126	+	0.0115506i	−0.158786	−	0.987313i	$-0.550758\pi$
$241$	−1.72514	+	0.179313i	−0.111126	+	0.0115506i	0.0476594	+	0.998864i	$0.484824\pi$
$242$	0.976791	+	18.8458i	0.0627905	+	1.21145i
$243$	9.86828	+	4.75232i	0.633051	+	0.304861i
$244$	−2.73736	−	1.20368i	−0.175241	−	0.0770579i
$245$	9.32621	−	2.29870i	0.595829	−	0.146859i
$246$	−20.2198	+	19.1989i	−1.28917	+	1.22408i
$247$	14.2629	+	5.12940i	0.907526	+	0.326376i
$248$	0.759486	−	0.303131i	0.0482274	−	0.0192488i
$249$	−2.93754	+	11.0906i	−0.186159	+	0.702838i
$250$	8.79868	+	19.1075i	0.556477	+	1.20846i
$251$	1.41310	−	11.6379i	0.0891941	−	0.734579i	−0.877666	−	0.479273i	$-0.840900\pi$
$251$	1.41310	−	11.6379i	0.0891941	−	0.734579i	0.966860	−	0.255307i	$-0.0821764\pi$
$252$	0.201505	+	2.32894i	0.0126936	+	0.146709i
$253$	−0.622052	+	1.04935i	−0.0391081	+	0.0659721i
$254$	2.28314	+	6.02015i	0.143257	+	0.377738i
$255$	13.7955	+	11.3966i	0.863908	+	0.713683i
$256$	−7.93250	+	17.2265i	−0.495781	+	1.07665i
$257$	21.5439	+	13.2790i	1.34387	+	0.828321i	0.994095	−	0.108511i	$-0.0346083\pi$
$257$	21.5439	+	13.2790i	1.34387	+	0.828321i	0.349779	+	0.936832i	$0.386257\pi$
$258$	−2.99253	+	15.5705i	−0.186307	+	0.969379i
$259$	−0.287697	+	16.6653i	−0.0178766	+	1.03553i
$260$	−8.57163	+	1.19126i	−0.531590	+	0.0738786i
$261$	−2.55865	+	3.70685i	−0.158377	+	0.229448i
$262$	2.63110	+	2.86858i	0.162550	+	0.177222i
$263$	19.5856	+	3.41474i	1.20770	+	0.210562i	0.739558	−	0.673093i	$-0.235034\pi$
$263$	19.5856	+	3.41474i	1.20770	+	0.210562i	0.468139	+	0.883655i	$0.344925\pi$
$264$	−0.0128934	−	0.746870i	−0.000793533	−	0.0459667i
$265$	−6.03898	−	38.5593i	−0.370972	−	2.36868i
$266$	21.6956	+	7.80244i	1.33024	+	0.478398i
$267$	10.4710	−	1.45523i	0.640817	−	0.0890585i
$268$	−0.525799	+	0.534955i	−0.0321183	+	0.0326775i
$269$	0.348075	−	4.02295i	0.0212225	−	0.245284i	−0.978089	−	0.208187i	$-0.933244\pi$
$269$	0.348075	−	4.02295i	0.0212225	−	0.245284i	0.999312	−	0.0370970i	$-0.0118111\pi$
$270$	−13.8036	+	32.9222i	−0.840058	+	2.00358i
$271$	−3.72614	+	5.81804i	−0.226347	+	0.353421i	−0.936525	−	0.350602i	$-0.885977\pi$
$271$	−3.72614	+	5.81804i	−0.226347	+	0.353421i	0.710178	+	0.704022i	$0.248614\pi$
$272$	−17.0279	−	5.46777i	−1.03247	−	0.331532i
$273$	3.47422	−	5.86072i	0.210269	−	0.354707i
$274$	4.89106	−	8.25082i	0.295480	−	0.498450i
$275$	2.48852	+	0.799081i	0.150063	+	0.0481864i
$276$	2.86278	−	4.46998i	0.172319	−	0.269061i
$277$	0.136479	−	0.325510i	0.00820024	−	0.0195580i	−0.918068	−	0.396424i	$-0.870251\pi$
$277$	0.136479	−	0.325510i	0.00820024	−	0.0195580i	0.926268	+	0.376866i	$0.122998\pi$
$278$	−2.79787	+	32.3369i	−0.167805	+	1.93944i
$279$	−0.370343	+	0.376792i	−0.0221719	+	0.0225579i
$280$	13.1294	−	1.82468i	0.784631	−	0.109045i
$281$	19.1601	+	6.89058i	1.14299	+	0.411057i	0.840349	−	0.542046i	$-0.182350\pi$
$281$	19.1601	+	6.89058i	1.14299	+	0.411057i	0.302645	+	0.953103i	$0.402130\pi$
$282$	−3.04693	−	19.4549i	−0.181442	−	1.15852i
$283$	0.388900	+	22.5277i	0.0231177	+	1.33913i	0.754111	+	0.656746i	$0.228068\pi$
$283$	0.388900	+	22.5277i	0.0231177	+	1.33913i	−0.730994	+	0.682384i	$0.760943\pi$
$284$	−4.27720	−	0.745731i	−0.253805	−	0.0442510i
$285$	21.5478	+	23.4926i	1.27638	+	1.39158i
$286$	−0.734043	+	1.06345i	−0.0434049	+	0.0628828i
$287$	−24.3357	+	3.38210i	−1.43649	+	0.199639i
$288$	0.100363	−	5.81372i	0.00591397	−	0.342577i
$289$	−0.793857	+	4.13054i	−0.0466975	+	0.242973i
$290$	−21.5920	−	13.3086i	−1.26793	−	0.781509i
$291$	−1.26856	+	2.75484i	−0.0743641	+	0.161492i
$292$	6.66848	+	5.50889i	0.390243	+	0.322384i
$293$	−6.96788	−	18.3728i	−0.407068	−	1.07335i	−0.969194	−	0.246298i	$-0.920786\pi$
$293$	−6.96788	−	18.3728i	−0.407068	−	1.07335i	0.562127	−	0.827051i	$-0.309983\pi$
$294$	−3.18242	+	5.36849i	−0.185603	+	0.313097i
$295$	3.62275	+	41.8707i	0.210925	+	2.43781i
$296$	1.66963	−	13.7506i	0.0970453	−	0.799240i
$297$	0.741457	+	1.61017i	0.0430237	+	0.0934316i
$298$	10.4013	−	39.2697i	0.602530	−	2.27483i
$299$	8.58764	−	3.42755i	0.496636	−	0.198221i
$300$	−10.7020	−	3.84880i	−0.617882	−	0.222210i
$301$	−10.1319	+	9.62031i	−0.583990	+	0.554505i
$302$	−5.61121	+	1.38304i	−0.322889	+	0.0795850i
$303$	−12.8719	−	5.66007i	−0.739469	−	0.325163i
$304$	−28.7053	−	13.8237i	−1.64636	−	0.792845i
$305$	−0.567055	−	10.9405i	−0.0324695	−	0.626451i
$306$	6.91152	−	0.718389i	0.395105	−	0.0410676i
$307$	−16.0387	+	15.2289i	−0.915376	+	0.869160i	−0.991785	−	0.127916i	$-0.959171\pi$
$307$	−16.0387	+	15.2289i	−0.915376	+	0.869160i	0.0764089	+	0.997077i	$0.475655\pi$
$308$	−0.371327	+	0.537960i	−0.0211583	+	0.0306531i
$309$	−13.6359	−	2.86562i	−0.775720	−	0.163019i
$310$	−2.22691	−	1.97287i	−0.126480	−	0.112051i
$311$	−3.76302	−	1.50192i	−0.213381	−	0.0851661i	0.261546	−	0.965191i	$-0.415768\pi$
$311$	−3.76302	−	1.50192i	−0.213381	−	0.0851661i	−0.474928	+	0.880025i	$0.657526\pi$
$312$	−3.37529	+	4.54592i	−0.191088	+	0.257362i
$313$	−0.303570	−	3.50857i	−0.0171588	−	0.198316i	−0.999910	−	0.0133857i	$-0.995739\pi$
$313$	−0.303570	−	3.50857i	−0.0171588	−	0.198316i	0.982752	−	0.184930i	$-0.0592060\pi$
$314$	−13.2983	−	35.0648i	−0.750468	−	1.97882i
$315$	−7.29046	+	4.49361i	−0.410771	+	0.253186i
$316$	1.88947	+	15.5612i	0.106291	+	0.875386i
$317$	32.0290	−	6.73096i	1.79893	−	0.378049i	0.818434	−	0.574601i	$-0.194843\pi$
$317$	32.0290	−	6.73096i	1.79893	−	0.378049i	0.980493	+	0.196552i	$0.0629745\pi$
$318$	20.6179	+	14.7634i	1.15620	+	0.827889i
$319$	−1.21176	+	0.343446i	−0.0678455	+	0.0192293i
$320$	−3.76266	+	0.129950i	−0.210339	+	0.00726442i
$321$	0.246327	−	14.2689i	0.0137486	−	0.796411i
$322$	13.0629	−	5.21373i	0.727964	−	0.290550i
$323$	7.34179	−	21.5772i	0.408508	−	1.20059i
$324$	−1.68529	−	4.01951i	−0.0936274	−	0.223306i
$325$	−11.2540	−	16.3042i	−0.624259	−	0.904395i
$326$	−8.11151	−	1.70465i	−0.449255	−	0.0944119i
$327$	6.04655	−	6.15184i	0.334375	−	0.340197i
$328$	20.4062	−	0.704765i	1.12675	−	0.0389141i
$329$	7.79759	−	15.5016i	0.429895	−	0.854629i
$330$	−2.40638	+	1.26296i	−0.132467	+	0.0695238i
$331$	−3.99198	−	4.66585i	−0.219419	−	0.256458i	0.639238	−	0.769009i	$-0.279250\pi$
$331$	−3.99198	−	4.66585i	−0.219419	−	0.256458i	−0.858657	+	0.512551i	$0.828701\pi$
$332$	−6.94739	+	4.62044i	−0.381287	+	0.253580i
$333$	2.58857	+	8.56663i	0.141853	+	0.469448i
$334$	25.8896	−	15.9575i	1.41661	−	0.873155i
$335$	−2.61643	−	0.840155i	−0.142951	−	0.0459026i
$336$	−8.53729	+	11.4982i	−0.465747	+	0.627280i
$337$	−9.46338	+	11.0609i	−0.515503	+	0.602523i	−0.955323	−	0.295563i	$-0.904493\pi$
$337$	−9.46338	+	11.0609i	−0.515503	+	0.602523i	0.439820	+	0.898086i	$0.355042\pi$
$338$	−12.1006	+	3.88559i	−0.658185	+	0.211348i
$339$	6.03806	−	17.7456i	0.327942	−	0.963809i
$340$	2.01351	+	12.8564i	0.109198	+	0.697237i
$341$	−0.146943	+	0.0152734i	−0.00795740	+	0.000827099i
$342$	12.3717	+	0.427278i	0.668986	+	0.0231046i
$343$	−18.4280	+	8.10322i	−0.995016	+	0.437533i
$344$	9.20143	−	7.08155i	0.496108	−	0.381812i
$345$	19.3424	+	2.01047i	1.04136	+	0.108240i
$346$	−0.837476	+	16.1579i	−0.0450230	+	0.868652i
$347$	32.2476	+	1.11373i	1.73114	+	0.0597880i	0.882826	−	0.469700i	$-0.155638\pi$
$347$	32.2476	+	1.11373i	1.73114	+	0.0597880i	0.848318	+	0.529488i	$0.177616\pi$
$348$	5.32128	−	1.31158i	0.285250	−	0.0703079i
$349$	−12.0978	−	13.1897i	−0.647578	−	0.706028i	0.323112	−	0.946361i	$-0.395271\pi$
$349$	−12.0978	−	13.1897i	−0.647578	−	0.706028i	−0.970691	+	0.240333i	$0.922743\pi$
$350$	−17.1187	−	24.8007i	−0.915032	−	1.32565i
$351$	2.98992	−	13.0997i	0.159590	−	0.699211i
$352$	1.05702	−	1.23545i	0.0563394	−	0.0658497i
$353$	−0.429124	+	3.53415i	−0.0228400	+	0.188104i	−0.999663	−	0.0259425i	$-0.991741\pi$
$353$	−0.429124	+	3.53415i	−0.0228400	+	0.188104i	0.976823	+	0.214046i	$0.0686644\pi$
$354$	−21.0519	−	17.3912i	−1.11890	−	0.924331i
$355$	−4.60089	−	15.2262i	−0.244190	−	0.808124i
$356$	6.40158	+	4.25745i	0.339283	+	0.225644i
$357$	−8.90170	−	5.07133i	−0.471128	−	0.268403i
$358$	−15.8088	−	15.0107i	−0.835522	−	0.793338i
$359$	3.51568	+	6.98916i	0.185551	+	0.368874i	0.966874	−	0.255252i	$-0.0821585\pi$
$359$	3.51568	+	6.98916i	0.185551	+	0.368874i	−0.781324	+	0.624126i	$0.785455\pi$
$360$	6.41230	−	3.08800i	0.337958	−	0.162752i
$361$	9.70806	−	19.2996i	0.510950	−	1.01577i
$362$	1.48490	−	7.72613i	0.0780446	−	0.406077i
$363$	3.82481	−	14.4404i	0.200751	−	0.757926i
$364$	4.71745	−	1.51481i	0.247262	−	0.0793975i
$365$	−7.05136	+	30.8940i	−0.369085	+	1.61707i
$366$	5.32784	+	4.72006i	0.278491	+	0.246721i
$367$	0.617097	−	7.13222i	0.0322122	−	0.372299i	−0.962627	−	0.270832i	$-0.912701\pi$
$367$	0.617097	−	7.13222i	0.0322122	−	0.372299i	0.994839	−	0.101467i	$-0.0323537\pi$
$368$	−18.6993	+	5.29990i	−0.974771	+	0.276277i
$369$	−11.8854	+	5.72371i	−0.618729	+	0.297964i
$370$	−47.4216	+	17.0543i	−2.46533	+	0.886613i
$371$	7.19794	+	21.1545i	0.373699	+	1.09828i
$372$	0.641317	−	0.0443509i	0.0332508	−	0.00229949i
$373$	−10.6397	+	35.2110i	−0.550902	+	1.82316i	0.0167091	+	0.999860i	$0.494681\pi$
$373$	−10.6397	+	35.2110i	−0.550902	+	1.82316i	−0.567611	+	0.823297i	$0.692132\pi$
$374$	1.61793	+	1.07602i	0.0836611	+	0.0556398i
$375$	−2.00720	−	16.5307i	−0.103651	−	0.853644i
$376$	−7.77725	+	12.1435i	−0.401081	+	0.626253i
$377$	8.86655	+	3.53888i	0.456651	+	0.182261i
$378$	4.54804	−	19.9263i	0.233926	−	1.02490i
$379$	−2.69716	−	6.43286i	−0.138544	−	0.330434i	0.838028	−	0.545628i	$-0.183709\pi$
$379$	−2.69716	−	6.43286i	−0.138544	−	0.330434i	−0.976571	+	0.215194i	$0.930962\pi$
$380$	0.400148	+	23.1793i	0.0205272	+	1.18907i
$381$	−0.263816	−	5.08995i	−0.0135157	−	0.260766i
$382$	−1.15908	+	22.3627i	−0.0593036	+	1.14418i
$383$	−12.1883	+	22.2796i	−0.622791	+	1.13843i	0.356177	+	0.934419i	$0.384080\pi$
$383$	−12.1883	+	22.2796i	−0.622791	+	1.13843i	−0.978968	+	0.204014i	$0.934601\pi$
$384$	11.2514	−	12.2670i	0.574173	−	0.625997i
$385$	−2.37196	−	0.329647i	−0.120886	−	0.0168004i
$386$	−2.10330	+	13.4297i	−0.107055	+	0.683554i
$387$	−3.60027	+	6.58112i	−0.183012	+	0.334537i
$388$	−2.01903	+	0.887816i	−0.102501	+	0.0450721i
$389$	−3.64639	−	1.60341i	−0.184879	−	0.0812959i	0.308030	−	0.951377i	$-0.400330\pi$
$389$	−3.64639	−	1.60341i	−0.184879	−	0.0812959i	−0.492909	+	0.870081i	$0.664067\pi$
$390$	20.2933	+	3.53813i	1.02759	+	0.179160i
$391$	−5.37618	−	12.8224i	−0.271885	−	0.648459i
$392$	4.35136	−	1.39725i	0.219777	−	0.0705719i
$393$	−1.28881	−	2.79882i	−0.0650119	−	0.141182i
$394$	−4.57143	+	9.92746i	−0.230305	+	0.500138i
$395$	−47.8185	+	31.8022i	−2.40601	+	1.60014i
$396$	−0.101517	+	0.335963i	−0.00510145	+	0.0168828i
$397$	9.87579	−	8.15848i	0.495651	−	0.409462i	−0.355263	−	0.934766i	$-0.615609\pi$
$397$	9.87579	−	8.15848i	0.495651	−	0.409462i	0.850915	+	0.525304i	$0.176048\pi$
$398$	12.5310	+	12.7492i	0.628121	+	0.639058i
$399$	−14.4636	−	11.1314i	−0.724087	−	0.557269i
$400$	19.9860	+	36.5334i	0.999299	+	1.82667i
$401$	30.9319	−	11.1241i	1.54467	−	0.555512i	0.579007	−	0.815322i	$-0.303440\pi$
$401$	30.9319	−	11.1241i	1.54467	−	0.555512i	0.965660	+	0.259810i	$0.0836601\pi$
$402$	1.58095	−	0.829749i	0.0788509	−	0.0413841i
$403$	0.953266	+	0.587563i	0.0474856	+	0.0292686i
$404$	−4.27714	−	9.28837i	−0.212796	−	0.462114i
$405$	10.3807	−	12.1330i	0.515819	−	0.602892i
$406$	13.4871	+	5.38306i	0.669354	+	0.267157i
$407$	−0.967613	+	2.30780i	−0.0479628	+	0.114394i
$408$	6.92234	+	4.95671i	0.342707	+	0.245394i
$409$	−3.25635	−	6.47361i	−0.161016	−	0.320100i	0.798383	−	0.602150i	$-0.205689\pi$
$409$	−3.25635	−	6.47361i	−0.161016	−	0.320100i	−0.959400	+	0.282050i	$0.908986\pi$
$410$	−35.6528	−	65.1715i	−1.76076	−	3.21859i
$411$	−5.68324	+	5.03491i	−0.280334	+	0.248354i
$412$	−6.04065	−	8.13570i	−0.297602	−	0.400817i
$413$	−6.16077	−	23.2598i	−0.303152	−	1.14454i
$414$	5.82197	−	4.80958i	0.286134	−	0.236378i
$415$	−26.5593	−	15.1310i	−1.30375	−	0.742749i
$416$	−12.0607	+	2.53459i	−0.591326	+	0.124269i
$417$	9.93488	−	23.6952i	0.486513	−	1.16036i
$418$	2.59100	+	2.29543i	0.126730	+	0.112273i
$419$	−2.43764	−	3.53154i	−0.119087	−	0.172527i	0.758907	−	0.651199i	$-0.225734\pi$
$419$	−2.43764	−	3.53154i	−0.119087	−	0.172527i	−0.877994	+	0.478672i	$0.841118\pi$
$420$	10.2657	+	1.78982i	0.500913	+	0.0873342i
$421$	8.95617	+	4.31306i	0.436497	+	0.210206i	0.639210	−	0.769032i	$-0.279262\pi$
$421$	8.95617	+	4.31306i	0.436497	+	0.210206i	−0.202713	+	0.979238i	$0.564976\pi$
$422$	19.5135	+	2.02825i	0.949904	+	0.0987339i
$423$	1.44156	−	9.20448i	0.0700913	−	0.447537i
$424$	−4.13223	−	18.1045i	−0.200679	−	0.879231i
$425$	−24.2211	+	17.3434i	−1.17489	+	0.841278i
$426$	9.15095	+	4.80279i	0.443365	+	0.232696i
$427$	1.39569	+	6.11493i	0.0675423	+	0.295922i
$428$	7.01515	−	7.64833i	0.339090	−	0.369696i
$429$	0.810621	−	0.623866i	0.0391372	−	0.0301205i
$430$	−38.0597	−	18.3286i	−1.83540	−	0.883882i
$431$	0.166563	+	9.64846i	0.00802308	+	0.464750i	0.976485	+	0.215587i	$0.0691665\pi$
$431$	0.166563	+	9.64846i	0.00802308	+	0.464750i	−0.968462	+	0.249163i	$0.919844\pi$
$432$	−9.09788	+	26.7383i	−0.437722	+	1.28645i
$433$	3.56245	−	13.4499i	0.171200	−	0.646361i	−0.825442	−	0.564486i	$-0.809074\pi$
$433$	3.56245	−	13.4499i	0.171200	−	0.646361i	0.996643	−	0.0818742i	$-0.0260906\pi$
$434$	1.45003	+	0.893755i	0.0696039	+	0.0429016i
$435$	13.0530	+	15.2564i	0.625841	+	0.731486i
$436$	6.25807	−	0.432782i	0.299707	−	0.0207265i
$437$	−6.34198	−	23.9439i	−0.303378	−	1.14539i
$438$	−11.1041	−	17.3380i	−0.530573	−	0.828443i
$439$	−6.48356	+	1.13041i	−0.309444	+	0.0539515i	−0.324349	−	0.945937i	$-0.605145\pi$
$439$	−6.48356	+	1.13041i	−0.309444	+	0.0539515i	0.0149057	+	0.999889i	$0.495255\pi$
$440$	1.93232	+	0.476274i	0.0921196	+	0.0227055i
$441$	−2.21011	+	1.95799i	−0.105243	+	0.0932376i
$442$	−4.74422	−	13.9431i	−0.225659	−	0.663204i
$443$	12.7496	+	14.9018i	0.605750	+	0.708004i	0.975220	−	0.221239i	$-0.0710099\pi$
$443$	12.7496	+	14.9018i	0.605750	+	0.708004i	−0.369469	+	0.929243i	$0.620460\pi$
$444$	4.55456	−	9.89083i	0.216150	−	0.469398i
$445$	−3.39499	+	27.9602i	−0.160938	+	1.32544i
$446$	−0.631877	+	0.851028i	−0.0299203	+	0.0402974i
$447$	−17.3434	+	27.0802i	−0.820316	+	1.28085i
$448$	2.10945	−	0.443305i	0.0996620	−	0.0209442i
$449$	−19.6473	−	18.6553i	−0.927213	−	0.880400i	0.0658679	−	0.997828i	$-0.479018\pi$
$449$	−19.6473	−	18.6553i	−0.927213	−	0.880400i	−0.993081	+	0.117429i	$0.962535\pi$
$450$	−12.8223	−	9.86820i	−0.604447	−	0.465191i
$451$	−3.58161	−	0.882788i	−0.168652	−	0.0415689i
$452$	11.8445	−	6.74783i	0.557116	−	0.317391i
$453$	4.56389	+	0.315620i	0.214430	+	0.0148291i
$454$	25.8285	+	40.3289i	1.21219	+	1.89273i
$455$	12.7240	+	12.9456i	0.596511	+	0.606898i
$456$	10.9991	+	10.4438i	0.515081	+	0.489075i
$457$	6.94520	+	4.97308i	0.324883	+	0.232631i	0.732889	−	0.680348i	$-0.238171\pi$
$457$	6.94520	+	4.97308i	0.324883	+	0.232631i	−0.408006	+	0.912979i	$0.633776\pi$
$458$	−2.04035	+	23.5817i	−0.0953392	+	1.10190i
$459$	−19.7729	−	4.15531i	−0.922918	−	0.193953i
$460$	9.55934	+	10.4221i	0.445706	+	0.485935i
$461$	−16.7096	−	7.34761i	−0.778243	−	0.342212i	−0.0247714	−	0.999693i	$-0.507886\pi$
$461$	−16.7096	−	7.34761i	−0.778243	−	0.342212i	−0.753471	+	0.657481i	$0.771622\pi$
$462$	1.23305	−	0.948977i	0.0573669	−	0.0441504i
$463$	13.7271	+	1.90775i	0.637953	+	0.0886605i	0.449297	−	0.893383i	$-0.351675\pi$
$463$	13.7271	+	1.90775i	0.637953	+	0.0886605i	0.188656	+	0.982043i	$0.439587\pi$
$464$	−17.7686	−	9.32567i	−0.824886	−	0.432933i
$465$	1.20095	+	2.02590i	0.0556927	+	0.0939491i
$466$	9.58067	−	12.0138i	0.443816	−	0.556527i
$467$	−11.3750	−	19.1887i	−0.526372	−	0.887947i	−0.999974	−	0.00720772i	$-0.997706\pi$
$467$	−11.3750	−	19.1887i	−0.526372	−	0.887947i	0.473602	−	0.880739i	$-0.342954\pi$
$468$	2.16293	−	1.54876i	0.0999815	−	0.0715914i
$469$	1.55835	+	0.216574i	0.0719577	+	0.0100004i
$470$	52.1834	+	5.42399i	2.40704	+	0.250190i
$471$	1.53662	+	29.6468i	0.0708035	+	1.36605i
$472$	3.09403	+	19.7556i	0.142414	+	0.909325i
$473$	−1.94820	+	0.777578i	−0.0895784	+	0.0357531i
$474$	7.04233	−	36.6422i	0.323465	−	1.68303i
$475$	−46.9918	+	24.6632i	−2.15613	+	1.13162i
$476$	−2.39994	−	7.05331i	−0.110001	−	0.323288i
$477$	7.15218	+	9.63273i	0.327476	+	0.441052i
$478$	−9.14002	−	0.632086i	−0.418055	−	0.0289110i
$479$	−2.27551	−	11.8398i	−0.103971	−	0.540975i	−0.996027	−	0.0890504i	$-0.971617\pi$
$479$	−2.27551	−	11.8398i	−0.103971	−	0.540975i	0.892056	−	0.451924i	$-0.149262\pi$
$480$	−24.9375	−	7.06796i	−1.13823	−	0.322607i
$481$	16.4811	−	9.38935i	0.751474	−	0.428118i
$482$	1.78982	+	2.41058i	0.0815243	+	0.109799i
$483$	−11.1073	+	0.768135i	−0.505399	+	0.0349513i
$484$	9.04580	−	6.01602i	0.411173	−	0.273456i
$485$	−6.22958	−	5.14632i	−0.282871	−	0.233682i
$486$	−1.63437	−	18.8895i	−0.0741365	−	0.856847i
$487$	−35.6145	−	11.4361i	−1.61385	−	0.518218i	−0.644644	−	0.764483i	$-0.722994\pi$
$487$	−35.6145	−	11.4361i	−1.61385	−	0.518218i	−0.969203	+	0.246265i	$0.920797\pi$
$488$	−0.628292	−	5.17445i	−0.0284414	−	0.234236i
$489$	5.70108	+	3.24793i	0.257812	+	0.146876i
$490$	−11.6553	−	11.8583i	−0.526535	−	0.535703i
$491$	4.42433	−	0.771383i	0.199667	−	0.0348120i	−0.0710411	−	0.997473i	$-0.522632\pi$
$491$	4.42433	−	0.771383i	0.199667	−	0.0348120i	0.270708	+	0.962661i	$0.412742\pi$
$492$	15.4431	+	4.37700i	0.696229	+	0.197330i
$493$	5.09052	−	13.4226i	0.229266	−	0.604524i
$494$	−4.95207	−	25.7663i	−0.222804	−	1.15928i
$495$	−1.26667	+	0.220845i	−0.0569328	+	0.00992623i
$496$	−1.86534	−	1.43560i	−0.0837564	−	0.0644602i
$497$	4.09232	+	8.13550i	0.183566	+	0.364927i
$498$	19.1077	−	5.41565i	0.856237	−	0.242681i
$499$	−9.48646	+	9.65164i	−0.424672	+	0.432067i	−0.892012	−	0.452011i	$-0.850707\pi$
$499$	−9.48646	+	9.65164i	−0.424672	+	0.432067i	0.467340	+	0.884078i	$0.345212\pi$
$500$	6.87924	−	9.96631i	0.307649	−	0.445707i
$501$	−23.3750	+	5.76141i	−1.04432	+	0.257401i
$502$	−18.5771	+	8.16880i	−0.829136	+	0.364591i
$503$	8.33710	−	9.08959i	0.371733	−	0.405285i	−0.522679	−	0.852530i	$-0.675067\pi$
$503$	8.33710	−	9.08959i	0.371733	−	0.405285i	0.894412	+	0.447245i	$0.147595\pi$
$504$	−3.31302	+	2.37227i	−0.147573	+	0.105669i
$505$	23.3578	−	29.2897i	1.03941	−	1.30338i
$506$	2.11166			0.0938746
$507$	10.0606			0.446807
$508$	2.31099	−	2.89789i	0.102533	−	0.128573i
$509$	2.09160	+	1.09776i	0.0927085	+	0.0486572i	0.510440	−	0.859913i	$-0.329482\pi$
$509$	2.09160	+	1.09776i	0.0927085	+	0.0486572i	−0.417732	+	0.908570i	$0.637175\pi$
$510$	4.79282	−	30.6025i	0.212230	−	1.35510i
$511$	0.939089	−	18.1183i	0.0415428	−	0.801508i
$512$	8.48915	−	0.882370i	0.375171	−	0.0389956i
$513$	−33.8707	−	12.1810i	−1.49543	−	0.537804i
$514$	0.756165	−	43.8021i	0.0333530	−	1.93203i
$515$	16.6820	−	33.1637i	0.735097	−	1.46137i
$516$	8.58911	−	3.08892i	0.378115	−	0.135982i
$517$	1.95003	−	1.72757i	0.0857622	−	0.0759787i
$518$	25.0698	−	14.2824i	1.10150	−	0.627531i
$519$	4.54170	−	11.9755i	0.199359	−	0.525666i
$520$	−9.40530	−	11.7939i	−0.412450	−	0.517196i
$521$	8.66553	−	22.8491i	0.379644	−	1.00104i	−0.599948	−	0.800039i	$-0.704812\pi$
$521$	8.66553	−	22.8491i	0.379644	−	1.00104i	0.979591	−	0.200999i	$-0.0644189\pi$
$522$	7.77834	+	0.537918i	0.340448	+	0.0235440i
$523$	4.97437	+	18.7806i	0.217514	+	0.821217i	0.983883	+	0.178816i	$0.0572266\pi$
$523$	4.97437	+	18.7806i	0.217514	+	0.821217i	−0.766368	+	0.642401i	$0.777938\pi$
$524$	0.648163	−	2.14503i	0.0283151	−	0.0937062i
$525$	6.90012	+	22.8353i	0.301146	+	0.996614i
$526$	−12.2037	−	32.1786i	−0.532108	−	1.40305i
$527$	0.858651	−	1.44847i	0.0374034	−	0.0630965i
$528$	−1.83037	+	1.12818i	−0.0796566	+	0.0490978i
$529$	6.56953	+	4.36915i	0.285632	+	0.189963i
$530$	−52.0868	+	43.0294i	−2.26251	+	1.86908i
$531$	−6.96756	−	10.8792i	−0.302366	−	0.472119i
$532$	−2.50508	−	13.0343i	−0.108609	−	0.565108i
$533$	17.4330	+	21.8603i	0.755108	+	0.946876i
$534$	−11.4099	−	14.3076i	−0.493755	−	0.619149i
$535$	36.5806	+	10.3680i	1.58152	+	0.448246i
$536$	−1.26951	−	0.312905i	−0.0548343	−	0.0135154i
$537$	8.28225	+	15.1395i	0.357405	+	0.653320i
$538$	−6.29772	+	3.03282i	−0.271514	+	0.130754i
$539$	−0.825162	+	0.0284984i	−0.0355422	+	0.00122751i
$540$	20.3554	−	2.82893i	0.875958	−	0.121738i
$541$	−33.0515	+	31.3828i	−1.42100	+	1.34925i	−0.572661	+	0.819792i	$0.694089\pi$
$541$	−33.0515	+	31.3828i	−1.42100	+	1.34925i	−0.848335	+	0.529460i	$0.822395\pi$
$542$	11.9526	+	0.412804i	0.513408	+	0.0177314i
$543$	−2.98903	+	5.46381i	−0.128272	+	0.234475i
$544$	4.12376	+	18.0674i	0.176805	+	0.774633i
$545$	11.7190	+	19.7691i	0.501989	+	0.846813i
$546$	−11.7938			−0.504728
$547$	−15.8480	+	17.2000i	−0.677613	+	0.735418i
$547$	−15.8480	+	17.2000i	−0.677613	+	0.735418i
$548$	−5.52167			−0.235874
$549$	1.71726	+	2.89688i	0.0732910	+	0.123636i
$550$	−1.00677	−	4.41095i	−0.0429288	−	0.188083i
$551$	12.2739	−	22.4362i	0.522888	−	0.955814i
$552$	9.24716	+	0.319367i	0.393585	+	0.0135931i
$553$	23.8434	−	22.6395i	1.01392	−	0.962731i
$554$	−0.605180	+	0.0841058i	−0.0257116	+	0.00357331i
$555$	39.8691	−	1.37695i	1.69235	−	0.0584482i
$556$	16.8348	−	8.10721i	0.713955	−	0.343822i
$557$	4.92350	+	8.99992i	0.208615	+	0.381339i	0.960640	−	0.277796i	$-0.0896040\pi$
$557$	4.92350	+	8.99992i	0.208615	+	0.381339i	−0.752025	+	0.659135i	$0.770923\pi$
$558$	0.887978	+	0.218867i	0.0375911	+	0.00926538i
$559$	15.2972	+	4.33564i	0.647002	+	0.183378i
$560$	−23.7893	−	29.8309i	−1.00528	−	1.26058i
$561$	−0.959015	−	1.20257i	−0.0404896	−	0.0507724i
$562$	−6.65237	−	34.6132i	−0.280613	−	1.46007i
$563$	18.7215	+	29.2320i	0.789018	+	1.23198i	0.968694	+	0.248256i	$0.0798576\pi$
$563$	18.7215	+	29.2320i	0.789018	+	1.23198i	−0.179676	+	0.983726i	$0.557505\pi$
$564$	−8.73974	+	7.21998i	−0.368009	+	0.304016i
$565$	41.5839	+	27.6559i	1.74945	+	1.16349i
$566$	33.2020	−	20.4647i	1.39559	−	0.860194i
$567$	−4.66180	+	7.86408i	−0.195777	+	0.330260i
$568$	−2.68369	−	7.07632i	−0.112605	−	0.296916i
$569$	7.38600	+	24.4433i	0.309637	+	1.02472i	0.963412	+	0.268026i	$0.0863714\pi$
$569$	7.38600	+	24.4433i	0.309637	+	1.02472i	−0.653774	+	0.756690i	$0.726815\pi$
$570$	15.9616	−	52.8235i	0.668559	−	2.21253i
$571$	−4.68153	−	17.6749i	−0.195916	−	0.739673i	−0.991079	−	0.133277i	$-0.957450\pi$
$571$	−4.68153	−	17.6749i	−0.195916	−	0.739673i	0.795163	−	0.606396i	$-0.207385\pi$
$572$	0.742109	+	0.0513212i	0.0310291	+	0.00214585i
$573$	6.28578	−	16.5742i	0.262592	−	0.692399i
$574$	26.5178	+	33.2522i	1.10683	+	1.38792i
$575$	−11.4803	+	30.2710i	−0.478761	+	1.26239i
$576$	1.00559	−	0.572890i	0.0418997	−	0.0238704i
$577$	−22.4383	+	19.8786i	−0.934117	+	0.827556i	−0.985247	−	0.171136i	$-0.945256\pi$
$577$	−22.4383	+	19.8786i	−0.934117	+	0.827556i	0.0511301	+	0.998692i	$0.483718\pi$
$578$	6.85143	−	2.46400i	0.284982	−	0.102489i
$579$	4.83549	−	9.61293i	0.200956	−	0.399500i
$580$	−0.252032	+	14.5993i	−0.0104650	+	0.606205i
$581$	16.4680	+	5.92243i	0.683208	+	0.245704i
$582$	5.22193	−	0.542772i	0.216456	−	0.0224986i
$583$	−0.173653	+	3.35038i	−0.00719198	+	0.138759i
$584$	−2.33291	+	14.8958i	−0.0965363	+	0.616391i
$585$	8.62963	+	4.52918i	0.356791	+	0.187259i
$586$	−21.2077	+	26.5936i	−0.876083	+	1.09857i
$587$	−32.9707			−1.36085			−0.680423	−	0.732819i	$-0.738204\pi$
$587$	−32.9707			−1.36085			−0.680423	+	0.732819i	$0.738204\pi$
$588$	3.59274			0.148162
$589$	1.87032	−	2.34530i	0.0770651	−	0.0966366i
$590$	59.1506	−	42.3546i	2.43519	−	1.74371i
$591$	5.84811	−	6.37595i	0.240559	−	0.262272i
$592$	−36.4981	+	16.0491i	−1.50006	+	0.659614i
$593$	36.9091	−	9.09727i	1.51567	−	0.373580i	0.608232	−	0.793759i	$-0.291879\pi$
$593$	36.9091	−	9.09727i	1.51567	−	0.373580i	0.907441	+	0.420179i	$0.138033\pi$
$594$	1.74316	−	2.52541i	0.0715229	−	0.103619i
$595$	19.1332	−	19.4664i	0.784387	−	0.798045i
$596$	−22.5000	+	6.37711i	−0.921635	+	0.261217i
$597$	−6.35906	−	12.6418i	−0.260259	−	0.517393i
$598$	−12.6843	−	9.76206i	−0.518701	−	0.399200i
$599$	−32.8767	+	5.73206i	−1.34331	+	0.234206i	−0.797304	−	0.603578i	$-0.793741\pi$
$599$	−32.8767	+	5.73206i	−1.34331	+	0.234206i	−0.546003	+	0.837783i	$0.683851\pi$
$600$	−3.74164	−	19.4683i	−0.152752	−	0.794788i
$601$	3.58179	−	9.44441i	0.146104	−	0.385246i	−0.841908	−	0.539621i	$-0.818567\pi$
$601$	3.58179	−	9.44441i	0.146104	−	0.385246i	0.988012	+	0.154376i	$0.0493366\pi$
$602$	23.2689	+	6.59504i	0.948370	+	0.268794i
$603$	0.832187	−	0.145092i	0.0338893	−	0.00590860i
$604$	2.33210	+	2.37271i	0.0948919	+	0.0965442i
$605$	34.5814	+	19.7012i	1.40594	+	0.800967i
$606$	2.93396	+	24.1634i	0.119184	+	0.981570i
$607$	−5.28047	−	1.69560i	−0.214328	−	0.0688222i	0.196625	−	0.980479i	$-0.437002\pi$
$607$	−5.28047	−	1.69560i	−0.214328	−	0.0688222i	−0.410953	+	0.911657i	$0.634804\pi$
$608$	2.84586	+	32.8916i	0.115415	+	1.33393i
$609$	−8.86243	−	7.32134i	−0.359124	−	0.296676i
$610$	−15.7906	+	10.5018i	−0.639345	+	0.425204i
$611$	−19.6999	+	1.36237i	−0.796974	+	0.0551155i
$612$	−2.38468	−	3.21174i	−0.0963948	−	0.129827i
$613$	20.4993	−	11.6785i	0.827959	−	0.471692i	−0.0212335	−	0.999775i	$-0.506759\pi$
$613$	20.4993	−	11.6785i	0.827959	−	0.471692i	0.849193	+	0.528083i	$0.177089\pi$
$614$	36.8346	+	10.4399i	1.48652	+	0.421321i
$615$	11.0988	+	57.7484i	0.447545	+	2.32864i
$616$	−1.13671	−	0.0786100i	−0.0457992	−	0.00316729i
$617$	0.430932	+	0.580389i	0.0173487	+	0.0233656i	0.811475	−	0.584387i	$-0.198665\pi$
$617$	0.430932	+	0.580389i	0.0173487	+	0.0233656i	−0.794127	+	0.607752i	$0.792071\pi$
$618$	7.76955	+	22.8344i	0.312537	+	0.918534i
$619$	−19.3025	+	10.1307i	−0.775833	+	0.407188i	−0.805669	−	0.592366i	$-0.798194\pi$
$619$	−19.3025	+	10.1307i	−0.775833	+	0.407188i	0.0298360	+	0.999555i	$0.490502\pi$
$620$	−0.323253	+	1.68193i	−0.0129822	+	0.0675480i
$621$	−20.3934	+	8.13956i	−0.818361	+	0.326629i
$622$	1.08522	+	6.92918i	0.0435133	+	0.277835i
$623$	−0.834687	−	16.1041i	−0.0334410	−	0.645196i
$624$	16.2102	+	1.68490i	0.648928	+	0.0674501i
$625$	2.69665	+	0.374771i	0.107866	+	0.0149908i
$626$	−4.95655	+	3.54912i	−0.198104	+	0.141851i
$627$	−1.39730	−	2.35714i	−0.0558029	−	0.0941349i
$628$	−13.4605	+	16.8789i	−0.537133	+	0.673543i
$629$	−14.5445	−	24.5354i	−0.579929	−	0.978292i
$630$	13.1267	+	6.88944i	0.522981	+	0.274482i
$631$	48.9123	+	6.79767i	1.94717	+	0.270611i	0.998901	−	0.0468609i	$-0.0149217\pi$
$631$	48.9123	+	6.79767i	1.94717	+	0.270611i	0.948268	+	0.317472i	$0.102834\pi$
$632$	−21.6538	+	16.6651i	−0.861341	+	0.662901i
$633$	−14.2165	−	6.25133i	−0.565054	−	0.248468i
$634$	−38.2954	−	41.7519i	−1.52091	−	1.65818i
$635$	13.2888	+	2.79268i	0.527351	+	0.110824i
$636$	1.25839	−	14.5440i	0.0498982	−	0.576709i
$637$	5.08834	+	3.64349i	0.201607	+	0.144360i
$638$	1.58106	+	1.50123i	0.0625947	+	0.0594344i
$639$	3.42748	+	3.48716i	0.135589	+	0.137950i
$640$	23.9177	+	37.3454i	0.945431	+	1.47621i
$641$	−48.9362	−	3.38423i	−1.93286	−	0.133669i	−0.949316	−	0.314324i	$-0.898222\pi$
$641$	−48.9362	−	3.38423i	−1.93286	−	0.133669i	−0.983547	+	0.180655i	$0.942178\pi$
$642$	−21.4648	+	12.2286i	−0.847149	+	0.482624i
$643$	9.49133	+	2.33940i	0.374301	+	0.0922570i	0.421979	−	0.906606i	$-0.361336\pi$
$643$	9.49133	+	2.33940i	0.374301	+	0.0922570i	−0.0476772	+	0.998863i	$0.515182\pi$
$644$	−6.41657	−	4.93829i	−0.252848	−	0.194596i
$645$	24.2497	+	23.0254i	0.954831	+	0.906623i
$646$	−38.6108	+	8.11414i	−1.51912	+	0.319246i
$647$	2.81926	−	4.40203i	0.110837	−	0.173062i	−0.782225	−	0.622996i	$-0.785915\pi$
$647$	2.81926	−	4.40203i	0.110837	−	0.173062i	0.893062	+	0.449934i	$0.148553\pi$
$648$	4.52905	−	6.09984i	0.177918	−	0.239624i
$649$	0.435447	−	3.58623i	0.0170928	−	0.140772i
$650$	−14.3441	+	31.1500i	−0.562620	+	1.22180i
$651$	−0.876586	−	1.02456i	−0.0343561	−	0.0401556i
$652$	1.53704	+	4.51729i	0.0601950	+	0.176911i
$653$	−2.63972	+	2.33859i	−0.103300	+	0.0915161i	−0.713192	−	0.700969i	$-0.752751\pi$
$653$	−2.63972	+	2.33859i	−0.103300	+	0.0915161i	0.609892	+	0.792485i	$0.291213\pi$
$654$	−14.4979	−	3.57342i	−0.566914	−	0.139732i
$655$	8.08738	−	1.41004i	0.316000	−	0.0550947i
$656$	−31.6973	−	49.4926i	−1.23757	−	1.93236i
$657$	−2.49409	−	9.41636i	−0.0973039	−	0.367367i
$658$	−29.9660	+	2.07233i	−1.16820	+	0.0807878i
$659$	−23.9245	−	27.9630i	−0.931965	−	1.08929i	−0.995821	−	0.0913262i	$-0.970889\pi$
$659$	−23.9245	−	27.9630i	−0.931965	−	1.08929i	0.0638564	−	0.997959i	$-0.479660\pi$
$660$	1.33184	+	0.820902i	0.0518417	+	0.0319536i
$661$	−3.02753	+	11.4303i	−0.117757	+	0.444588i	−0.999639	−	0.0268833i	$-0.991442\pi$
$661$	−3.02753	+	11.4303i	−0.117757	+	0.444588i	0.881881	+	0.471471i	$0.156277\pi$
$662$	−3.42400	+	10.0630i	−0.133077	+	0.391109i
$663$	0.201238	+	11.6571i	0.00781545	+	0.452723i
$664$	−13.1035	−	6.31029i	−0.508513	−	0.244887i
$665$	38.5348	−	29.6569i	1.49432	−	1.15005i
$666$	10.4714	−	11.4165i	0.405757	−	0.442380i
$667$	−3.47155	−	15.2099i	−0.134419	−	0.588928i
$668$	−15.5023	−	8.13625i	−0.599803	−	0.314801i
$669$	0.682210	−	0.488494i	0.0263758	−	0.0188863i
$670$	1.05852	+	4.63768i	0.0408942	+	0.179169i
$671$	−0.145706	+	0.930345i	−0.00562493	+	0.0359156i
$672$	14.7604	+	1.53420i	0.569393	+	0.0591832i
$673$	12.0854	+	5.82004i	0.465859	+	0.224346i	0.652062	−	0.758165i	$-0.273904\pi$
$673$	12.0854	+	5.82004i	0.465859	+	0.224346i	−0.186203	+	0.982511i	$0.559618\pi$
$674$	24.8239	+	4.32805i	0.956181	+	0.166710i
$675$	26.7253	+	38.7183i	1.02866	+	1.49027i
$676$	5.47639	+	4.85165i	0.210630	+	0.186602i
$677$	−10.3474	+	24.6790i	−0.397682	+	0.948491i	0.592095	+	0.805868i	$0.298301\pi$
$677$	−10.3474	+	24.6790i	−0.397682	+	0.948491i	−0.989777	+	0.142623i	$0.954446\pi$
$678$	−31.7544	+	6.67325i	−1.21952	+	0.256285i
$679$	4.01970	+	2.29004i	0.154262	+	0.0878837i
$680$	−17.4878	+	14.4469i	−0.670627	+	0.554012i
$681$	−9.70657	−	36.6468i	−0.371957	−	1.40431i
$682$	0.152452	+	0.205326i	0.00583769	+	0.00786235i
$683$	−5.58443	+	4.94738i	−0.213682	+	0.189306i	−0.763174	−	0.646193i	$-0.776360\pi$
$683$	−5.58443	+	4.94738i	−0.213682	+	0.189306i	0.549491	+	0.835499i	$0.314822\pi$
$684$	−3.42021	−	6.25199i	−0.130775	−	0.239051i
$685$	−9.09029	−	18.0714i	−0.347322	−	0.690474i
$686$	28.3330	+	20.2877i	1.08176	+	0.774588i
$687$	7.24502	−	17.2797i	0.276415	−	0.659263i
$688$	−31.0402	−	12.3890i	−1.18340	−	0.472325i
$689$	16.5317	−	19.3224i	0.629808	−	0.736123i
$690$	−14.0802	−	30.5770i	−0.536023	−	1.16405i
$691$	19.3457	+	11.9241i	0.735947	+	0.453614i	0.841126	−	0.540839i	$-0.181893\pi$
$691$	19.3457	+	11.9241i	0.735947	+	0.453614i	−0.105179	+	0.994453i	$0.533542\pi$
$692$	8.24733	−	4.32853i	0.313517	−	0.164546i
$693$	0.692716	−	0.249123i	0.0263141	−	0.00946340i
$694$	−26.8071	−	49.0022i	−1.01759	−	1.86010i
$695$	54.2485	+	41.7505i	2.05776	+	1.58369i
$696$	6.69657	+	6.81317i	0.253833	+	0.258253i
$697$	32.4142	−	26.7777i	1.22778	−	1.01428i
$698$	−8.96149	+	29.6572i	−0.339197	+	1.12254i
$699$	−10.1285	+	6.73608i	−0.383095	+	0.254782i
$700$	−7.25616	+	15.7577i	−0.274257	+	0.595586i
$701$	10.2917	+	22.3499i	0.388714	+	0.844144i	0.998663	+	0.0517026i	$0.0164648\pi$
$701$	10.2917	+	22.3499i	0.388714	+	0.844144i	−0.609949	+	0.792441i	$0.708810\pi$
$702$	−22.1457	+	7.11114i	−0.835835	+	0.268393i
$703$	−19.6474	−	46.8601i	−0.741017	−	1.76736i
$704$	0.318814	+	0.0555852i	0.0120157	+	0.00209495i
$705$	−38.0179	−	16.7174i	−1.43184	−	0.629614i
$706$	5.64140	−	2.48066i	0.212317	−	0.0933610i
$707$	−10.2940	+	18.8170i	−0.387147	+	0.707687i
$708$	−2.43229	+	15.5304i	−0.0914112	+	0.583666i
$709$	−19.0702	−	2.65031i	−0.716196	−	0.0995344i	−0.229756	−	0.973248i	$-0.573793\pi$
$709$	−19.0702	−	2.65031i	−0.716196	−	0.0995344i	−0.486440	+	0.873714i	$0.661705\pi$
$710$	−18.6117	+	20.2915i	−0.698483	+	0.761527i
$711$	8.47254	−	15.4874i	0.317745	−	0.580823i
$712$	−0.693661	+	13.3832i	−0.0259960	+	0.501555i
$713$	−0.0947207	−	1.82750i	−0.00354732	−	0.0684403i
$714$	0.306108	+	17.7318i	0.0114558	+	0.663597i
$715$	1.05376	+	2.51328i	0.0394086	+	0.0939914i
$716$	−2.79259	+	12.2351i	−0.104364	+	0.457248i
$717$	6.73585	+	2.68845i	0.251555	+	0.100402i
$718$	7.30400	−	11.4046i	0.272583	−	0.425614i
$719$	6.35993	+	52.3787i	0.237185	+	1.95340i	0.296165	+	0.955137i	$0.404292\pi$
$719$	6.35993	+	52.3787i	0.237185	+	1.95340i	−0.0589794	+	0.998259i	$0.518785\pi$
$720$	−17.0580	−	11.3447i	−0.635716	−	0.422790i
$721$	−6.14780	+	20.3456i	−0.228956	+	0.757709i
$722$	−37.3079	+	2.58006i	−1.38846	+	0.0960200i
$723$	−0.765585	−	2.25002i	−0.0284724	−	0.0836793i
$724$	−4.26194	+	1.53273i	−0.158394	+	0.0569635i
$725$	−30.1161	+	14.5031i	−1.11848	+	0.538633i
$726$	−24.8791	+	7.05141i	−0.923349	+	0.261702i
$727$	3.03634	−	35.0931i	0.112612	−	1.30153i	−0.698065	−	0.716035i	$-0.745955\pi$
$727$	3.03634	−	35.0931i	0.112612	−	1.30153i	0.810676	−	0.585495i	$-0.199100\pi$
$728$	6.46458	+	5.72712i	0.239593	+	0.212261i
$729$	−6.25952	+	27.4247i	−0.231834	+	1.01573i
$730$	52.2278	−	16.7707i	1.93304	−	0.620712i
$731$	6.12154	−	23.1117i	0.226413	−	0.854816i
$732$	0.773378	−	4.02399i	0.0285849	−	0.148731i
$733$	7.44319	−	14.7970i	0.274921	−	0.546540i	−0.713063	−	0.701100i	$-0.752693\pi$
$733$	7.44319	−	14.7970i	0.274921	−	0.546540i	0.987983	+	0.154560i	$0.0493959\pi$
$734$	−11.1651	+	5.37684i	−0.412112	+	0.198463i
$735$	5.91470	+	11.7584i	0.218167	+	0.433715i
$736$	14.6050	+	13.8676i	0.538347	+	0.511167i
$737$	0.205243	+	0.116928i	0.00756023	+	0.00430709i
$738$	19.0145	+	12.6458i	0.699932	+	0.465498i
$739$	−3.78703	−	12.5328i	−0.139308	−	0.461028i	0.859430	−	0.511254i	$-0.170819\pi$
$739$	−3.78703	−	12.5328i	−0.139308	−	0.461028i	−0.998738	+	0.0502264i	$0.984006\pi$
$740$	22.3664	+	18.4771i	0.822205	+	0.679231i
$741$	−2.50354	+	20.6185i	−0.0919700	+	0.757441i
$742$	25.1468	−	29.3917i	0.923167	−	1.07900i
$743$	−3.07635	+	13.4784i	−0.112860	+	0.494474i	0.886628	+	0.462484i	$0.153042\pi$
$743$	−3.07635	+	13.4784i	−0.112860	+	0.494474i	−0.999488	+	0.0319902i	$0.989815\pi$
$744$	0.636550	+	0.922202i	0.0233371	+	0.0338096i
$745$	−57.9128	−	63.1399i	−2.12176	−	2.31327i
$746$	61.8236	−	15.2381i	2.26352	−	0.557908i
$747$	9.39073	+	0.324325i	0.343589	+	0.0118664i
$748$	0.0578994	−	1.11708i	0.00211701	−	0.0408446i
$749$	−21.6519	−	2.25052i	−0.791142	−	0.0822320i
$750$	−22.8437	+	17.5808i	−0.834133	+	0.641962i
$751$	14.6276	−	6.43213i	0.533770	−	0.234712i	−0.118155	−	0.992995i	$-0.537698\pi$
$751$	14.6276	−	6.43213i	0.533770	−	0.234712i	0.651925	+	0.758283i	$0.273962\pi$
$752$	41.4834	+	1.43270i	1.51275	+	0.0522453i
$753$	15.9785	−	1.66082i	0.582290	−	0.0605238i
$754$	−2.55702	−	16.3268i	−0.0931213	−	0.594586i
$755$	−3.92613	+	11.5387i	−0.142887	+	0.419938i
$756$	−11.2027	+	3.59728i	−0.407440	+	0.130832i
$757$	20.0007	−	23.3770i	0.726939	−	0.849650i	−0.266521	−	0.963829i	$-0.585874\pi$
$757$	20.0007	−	23.3770i	0.726939	−	0.849650i	0.993460	+	0.114179i	$0.0364237\pi$
$758$	−7.19816	+	9.69466i	−0.261449	+	0.352126i
$759$	−1.59155	−	0.511060i	−0.0577698	−	0.0185503i
$760$	−34.4005	+	21.2034i	−1.24784	+	0.769126i
$761$	5.18595	+	17.1624i	0.187991	+	0.622137i	0.999296	+	0.0375149i	$0.0119442\pi$
$761$	5.18595	+	17.1624i	0.187991	+	0.622137i	−0.811305	+	0.584622i	$0.801243\pi$
$762$	−7.34642	+	4.88583i	−0.266133	+	0.176995i
$763$	−8.55385	−	9.99778i	−0.309670	−	0.361944i
$764$	11.4144	−	5.99075i	0.412959	−	0.216738i
$765$	6.58558	−	13.0921i	0.238102	−	0.473346i
$766$	43.9347	−	1.51736i	1.58742	−	0.0548244i
$767$	−19.1946	+	19.5288i	−0.693075	+	0.705143i
$768$	−25.4324	−	5.34468i	−0.917714	−	0.192860i
$769$	11.0237	+	15.9706i	0.397525	+	0.575914i	0.969725	−	0.244200i	$-0.0785253\pi$
$769$	11.0237	+	15.9706i	0.397525	+	0.575914i	−0.572200	+	0.820114i	$0.693910\pi$
$770$	1.60291	+	3.82301i	0.0577647	+	0.137772i
$771$	−11.1708	+	32.8306i	−0.402308	+	1.18237i
$772$	7.26793	−	2.90082i	0.261578	−	0.104403i
$773$	−0.563492	+	32.6412i	−0.0202674	+	1.17402i	0.799261	+	0.600984i	$0.205225\pi$
$773$	−0.563492	+	32.6412i	−0.0202674	+	1.17402i	−0.819528	+	0.573039i	$0.805764\pi$
$774$	12.9778	−	0.448210i	0.466477	−	0.0161106i
$775$	−3.77222	+	1.06915i	−0.135502	+	0.0384050i
$776$	−3.12589	−	2.23828i	−0.112213	−	0.0803496i
$777$	−22.3517	+	4.69726i	−0.801862	+	0.168513i
$778$	0.831144	+	6.84509i	0.0297980	+	0.245408i
$779$	63.7624	−	39.3011i	2.28452	−	1.40811i
$780$	−4.20513	−	11.0880i	−0.150568	−	0.397014i
$781$	0.117858	+	1.36217i	0.00421731	+	0.0487424i
$782$	−14.3479	+	19.3241i	−0.513080	+	0.691029i
$783$	−21.0558	−	8.40392i	−0.752473	−	0.300332i
$784$	−9.84660	−	8.72333i	−0.351664	−	0.311548i
$785$	−77.4018	−	16.2662i	−2.76259	−	0.580564i
$786$	−3.03000	+	4.38971i	−0.108076	+	0.156576i
$787$	−36.6307	+	34.7813i	−1.30574	+	1.23982i	−0.353153	+	0.935566i	$0.614890\pi$
$787$	−36.6307	+	34.7813i	−1.30574	+	1.23982i	−0.952591	+	0.304253i	$0.901593\pi$
$788$	6.25812	−	0.650475i	0.222936	−	0.0231722i
$789$	1.41014	+	27.2065i	0.0502022	+	0.968577i
$790$	89.5661	+	43.1327i	3.18662	+	1.53459i
$791$	−26.1739	−	11.5093i	−0.930636	−	0.409223i
$792$	−0.593995	+	0.146407i	−0.0211067	+	0.00520234i
$793$	5.17616	−	4.91482i	0.183811	−	0.174530i
$794$	−20.8661	−	7.50412i	−0.740510	−	0.266311i
$795$	49.6717	−	19.8253i	1.76168	−	0.703131i
$796$	2.63492	−	9.94804i	0.0933922	−	0.352599i
$797$	−17.8893	−	38.8489i	−0.633671	−	1.37610i	−0.909827	−	0.414987i	$-0.863786\pi$
$797$	−17.8893	−	38.8489i	−0.633671	−	1.37610i	0.276157	−	0.961113i	$-0.410939\pi$
$798$	−3.80820	+	31.3633i	−0.134809	+	1.11025i
$799$	2.55961	+	29.5833i	0.0905527	+	1.04658i
$800$	22.0043	−	37.1194i	0.777968	−	1.31237i
$801$	−3.07021	−	8.09548i	−0.108481	−	0.286040i
$802$	−43.8688	−	36.2404i	−1.54906	−	1.27969i
$803$	1.13931	−	2.47417i	0.0402054	−	0.0873114i
$804$	−0.874998	−	0.539321i	−0.0308588	−	0.0190204i
$805$	5.59858	−	29.1302i	0.197324	−	1.02670i
$806$	0.0334584	−	1.93813i	0.00117852	−	0.0682679i
$807$	5.48058	−	0.761672i	0.192926	−	0.0268121i
$808$	10.1256	−	14.6695i	0.356219	−	0.516072i
$809$	13.0903	+	14.2718i	0.460231	+	0.501771i	0.923049	−	0.384683i	$-0.125689\pi$
$809$	13.0903	+	14.2718i	0.460231	+	0.501771i	−0.462818	+	0.886453i	$0.653162\pi$
$810$	−27.2301	−	4.74756i	−0.956767	−	0.166812i
$811$	−0.501713	−	29.0625i	−0.0176175	−	1.02052i	−0.868655	−	0.495418i	$-0.835015\pi$
$811$	−0.501713	−	29.0625i	−0.0176175	−	1.02052i	0.851037	−	0.525105i	$-0.175974\pi$
$812$	−1.29351	−	8.25915i	−0.0453933	−	0.289839i
$813$	−8.90877	−	3.20388i	−0.312444	−	0.112365i
$814$	4.29062	−	0.596295i	0.150386	−	0.0209001i
$815$	−12.2539	+	12.4672i	−0.429234	+	0.436708i
$816$	2.11249	−	24.4156i	0.0739521	−	0.854716i
$817$	16.4692	−	39.2799i	0.576186	−	1.37423i
$818$	−6.76523	+	10.5633i	−0.236541	+	0.369338i
$819$	−5.31270	−	1.70595i	−0.185641	−	0.0596106i
$820$	−21.8073	+	36.7871i	−0.761543	+	1.28466i
$821$	25.7688	−	43.4699i	0.899338	−	1.51711i	0.0440046	−	0.999031i	$-0.485988\pi$
$821$	25.7688	−	43.4699i	0.899338	−	1.51711i	0.855333	−	0.518078i	$-0.173352\pi$
$822$	12.5140	+	4.01835i	0.436477	+	0.140156i
$823$	−11.8883	+	18.5626i	−0.414401	+	0.647051i	−0.984674	−	0.174404i	$-0.944200\pi$
$823$	−11.8883	+	18.5626i	−0.414401	+	0.647051i	0.570273	+	0.821455i	$0.306837\pi$
$824$	6.82973	−	16.2892i	0.237925	−	0.567463i
$825$	−0.308728	+	3.56819i	−0.0107485	+	0.124228i
$826$	−29.1973	+	29.7057i	−1.01590	+	1.03359i
$827$	5.19707	−	0.722271i	0.180720	−	0.0251158i	−0.0467196	−	0.998908i	$-0.514877\pi$
$827$	5.19707	−	0.722271i	0.180720	−	0.0251158i	0.227439	+	0.973792i	$0.426965\pi$
$828$	−4.09082	−	1.47119i	−0.142166	−	0.0511274i
$829$	1.96638	+	12.5555i	0.0682952	+	0.436069i	0.997745	+	0.0671204i	$0.0213812\pi$
$829$	1.96638	+	12.5555i	0.0682952	+	0.436069i	−0.929450	+	0.368949i	$0.879718\pi$
$830$	0.913313	+	52.9051i	0.0317015	+	1.83636i
$831$	0.476479	+	0.0830742i	0.0165289	+	0.00288181i
$832$	−1.65809	−	1.80775i	−0.0574839	−	0.0626724i
$833$	5.34587	−	7.74483i	0.185223	−	0.268342i
$834$	−44.0535	+	6.12241i	−1.52545	+	0.212002i
$835$	1.10711	−	64.1311i	0.0383131	−	2.21935i
$836$	0.376105	−	1.95692i	0.0130078	−	0.0676816i
$837$	−2.26376	−	1.39531i	−0.0782471	−	0.0482290i
$838$	−3.10696	+	6.74718i	−0.107328	+	0.233077i
$839$	−10.6441	−	8.79317i	−0.367474	−	0.303574i	0.434803	−	0.900526i	$-0.356818\pi$
$839$	−10.6441	−	8.79317i	−0.367474	−	0.303574i	−0.802277	+	0.596952i	$0.796378\pi$
$840$	6.44110	+	16.9838i	0.222239	+	0.585996i
$841$	−6.57420	+	11.0901i	−0.226697	+	0.382419i
$842$	−1.48331	−	17.1436i	−0.0511181	−	0.590807i
$843$	−3.36314	+	27.6979i	−0.115833	+	0.953967i
$844$	−4.72393	−	10.2586i	−0.162604	−	0.353117i
$845$	−6.86286	+	25.9105i	−0.236090	+	0.891348i
$846$	−14.9786	+	5.97837i	−0.514976	+	0.205541i
$847$	−21.4421	−	7.71126i	−0.736759	−	0.264962i
$848$	−38.7624	+	36.8054i	−1.33111	+	1.26390i
$849$	−29.9772	+	7.38871i	−1.02881	+	0.253580i
$850$	47.2059	+	20.7576i	1.61915	+	0.711980i
$851$	−27.9275	−	13.4492i	−0.957342	−	0.461032i
$852$	−0.307953	−	5.94151i	−0.0105503	−	0.203553i
$853$	−0.0962060	+	0.00999974i	−0.00329403	+	0.000342385i	−0.105031	−	0.994469i	$-0.533494\pi$
$853$	−0.0962060	+	0.00999974i	−0.00329403	+	0.000342385i	0.101737	+	0.994811i	$0.467560\pi$
$854$	7.87357	−	7.47604i	0.269428	−	0.255825i
$855$	14.8310	−	21.4864i	0.507209	−	0.734818i
$856$	17.7039	+	3.72050i	0.605105	+	0.127164i
$857$	−10.6979	−	9.47750i	−0.365433	−	0.323745i	0.460346	−	0.887740i	$-0.347725\pi$
$857$	−10.6979	−	9.47750i	−0.365433	−	0.323745i	−0.825779	+	0.563994i	$0.809264\pi$
$858$	−1.64453	−	0.656376i	−0.0561434	−	0.0224083i
$859$	−3.46392	+	4.66530i	−0.118188	+	0.159178i	−0.858025	−	0.513607i	$-0.828309\pi$
$859$	−3.46392	+	4.66530i	−0.118188	+	0.159178i	0.739838	+	0.672785i	$0.234902\pi$
$860$	2.09626	+	24.2279i	0.0714817	+	0.826164i
$861$	−11.9388	−	31.4800i	−0.406873	−	1.07283i
$862$	14.2202	−	8.76489i	0.484343	−	0.298533i
$863$	3.54840	+	29.2237i	0.120789	+	0.994787i	0.919505	+	0.393079i	$0.128590\pi$
$863$	3.54840	+	29.2237i	0.120789	+	0.994787i	−0.798716	+	0.601709i	$0.794487\pi$
$864$	28.6412	−	6.01900i	0.974392	−	0.204771i
$865$	27.7441	+	19.8660i	0.943327	+	0.675465i
$866$	−23.1725	+	6.56772i	−0.787433	+	0.223180i
$867$	−5.76025	+	0.198940i	−0.195628	+	0.00675636i
$868$	0.0169255	−	0.980436i	0.000574488	−	0.0332782i
$869$	4.58472	−	1.82988i	0.155526	−	0.0620744i
$870$	11.1957	−	32.9038i	0.379571	−	1.11554i
$871$	−0.692309	−	1.65119i	−0.0234580	−	0.0559485i
$872$	6.21155	+	8.99898i	0.210349	+	0.304744i
$873$	2.43081	+	0.510840i	0.0822705	+	0.0172893i
$874$	−30.0560	+	30.5794i	−1.01666	+	1.03436i
$875$	−25.3855	+	0.876733i	−0.858188	+	0.0296390i
$876$	−5.32623	+	10.5885i	−0.179957	+	0.357753i
$877$	−39.7350	+	20.8545i	−1.34176	+	0.704208i	−0.974177	−	0.225785i	$-0.927505\pi$
$877$	−39.7350	+	20.8545i	−1.34176	+	0.704208i	−0.367579	+	0.929992i	$0.619813\pi$
$878$	7.40642	+	8.65666i	0.249955	+	0.292148i
$879$	22.4204	−	14.9110i	0.756222	−	0.502934i
$880$	−1.65698	−	5.48361i	−0.0558566	−	0.184852i
$881$	−23.3708	+	14.4050i	−0.787383	+	0.485318i	−0.858914	−	0.512121i	$-0.828860\pi$
$881$	−23.3708	+	14.4050i	−0.787383	+	0.485318i	0.0715304	+	0.997438i	$0.477212\pi$
$882$	4.86649	+	1.56267i	0.163863	+	0.0526177i
$883$	−0.785071	+	1.05735i	−0.0264197	+	0.0355828i	−0.815899	−	0.578195i	$-0.803757\pi$
$883$	−0.785071	+	1.05735i	−0.0264197	+	0.0355828i	0.789479	+	0.613777i	$0.210351\pi$
$884$	−5.51200	+	6.44245i	−0.185389	+	0.216683i
$885$	−54.8324	+	17.6071i	−1.84317	+	0.591855i
$886$	10.9355	−	32.1391i	0.367387	−	1.07973i
$887$	3.91377	+	24.9896i	0.131411	+	0.839070i	0.960160	+	0.279450i	$0.0901520\pi$
$887$	3.91377	+	24.9896i	0.131411	+	0.839070i	−0.828749	+	0.559621i	$0.810947\pi$
$888$	18.8792	−	1.96232i	0.633546	−	0.0658513i
$889$	−7.76983	−	0.268344i	−0.260592	−	0.00899998i
$890$	44.6316	−	19.6256i	1.49606	−	0.657852i
$891$	−1.08771	+	0.837121i	−0.0364398	+	0.0280446i
$892$	0.606927	+	0.0630846i	0.0203214	+	0.00211223i
$893$	−2.73812	+	52.8281i	−0.0916278	+	1.76782i
$894$	55.6338	+	1.92141i	1.86067	+	0.0642615i
$895$	−44.6408	+	11.0030i	−1.49218	+	0.367789i
$896$	−17.1626	−	18.7117i	−0.573362	−	0.625113i
$897$	7.19758	+	10.4275i	0.240320	+	0.348164i
$898$	−10.4361	+	45.7237i	−0.348258	+	1.52582i
$899$	1.22830	−	1.43564i	0.0409660	−	0.0478812i
$900$	−1.12273	+	9.24655i	−0.0374245	+	0.308218i
$901$	−29.4800	−	24.3537i	−0.982121	−	0.811340i
$902$	1.84702	+	6.11253i	0.0614990	+	0.203525i
$903$	−15.9416	−	10.6022i	−0.530505	−	0.352819i
$904$	20.6462	+	11.7622i	0.686683	+	0.391206i
$905$	−12.0328	−	11.4252i	−0.399982	−	0.379788i
$906$	−3.55865	−	7.07456i	−0.118228	−	0.235037i
$907$	47.6436	−	22.9439i	1.58198	−	0.761841i	0.583253	−	0.812291i	$-0.301780\pi$
$907$	47.6436	−	22.9439i	1.58198	−	0.761841i	0.998727	+	0.0504497i	$0.0160655\pi$
$908$	12.3890	−	24.6293i	0.411144	−	0.817351i
$909$	−2.17353	+	11.3092i	−0.0720913	+	0.375101i
$910$	8.04517	−	30.3743i	0.266695	−	1.00690i
$911$	49.6699	−	15.9494i	1.64564	−	0.528426i	0.668988	−	0.743273i	$-0.266728\pi$
$911$	49.6699	−	15.9494i	1.64564	−	0.528426i	0.976648	+	0.214847i	$0.0689253\pi$
$912$	9.71492	−	42.5639i	0.321693	−	1.40943i
$913$	1.96670	+	1.74234i	0.0650882	+	0.0576631i
$914$	1.27463	−	14.7317i	0.0421609	−	0.487283i
$915$	14.4430	−	4.09355i	0.477472	−	0.135328i
$916$	12.2768	−	5.91219i	0.405637	−	0.195344i
$917$	−4.42281	+	1.59058i	−0.146054	+	0.0525257i
$918$	11.2663	+	33.1112i	0.371843	+	1.09283i
$919$	15.2542	−	1.05492i	0.503190	−	0.0347986i	0.184834	−	0.982770i	$-0.440825\pi$
$919$	15.2542	−	1.05492i	0.503190	−	0.0347986i	0.318356	+	0.947971i	$0.396869\pi$
$920$	−7.13049	+	23.5977i	−0.235085	+	0.777993i
$921$	−25.2356	−	16.7832i	−0.831540	−	0.553026i
$922$	3.80872	+	31.3676i	0.125434	+	1.03304i
$923$	5.58929	−	8.72718i	0.183974	−	0.287259i
$924$	−0.831912	−	0.332038i	−0.0273679	−	0.0109232i
$925$	−14.7785	+	64.7487i	−0.485913	+	2.12892i
$926$	−9.27640	−	22.1247i	−0.304841	−	0.727062i
$927$	0.196972	+	11.4100i	0.00646942	+	0.374752i
$928$	1.07633	+	20.7662i	0.0353322	+	0.681683i
$929$	−1.55265	+	29.9561i	−0.0509408	+	0.982828i	0.843916	+	0.536475i	$0.180245\pi$
$929$	−1.55265	+	29.9561i	−0.0509408	+	0.982828i	−0.894857	+	0.446353i	$0.852723\pi$
$930$	1.95662	−	3.57660i	0.0641600	−	0.117281i
$931$	11.3322	−	12.3550i	0.371397	−	0.404918i
$932$	−8.76178	−	1.21768i	−0.287002	−	0.0398865i
$933$	0.859062	−	5.48517i	0.0281244	−	0.179576i
$934$	−18.5324	+	33.8764i	−0.606400	+	1.10847i
$935$	3.75134	−	1.64955i	0.122682	−	0.0539462i
$936$	4.24485	+	1.86657i	0.138747	+	0.0610106i
$937$	−11.9810	−	2.08889i	−0.391402	−	0.0682409i	−0.0273650	−	0.999626i	$-0.508712\pi$
$937$	−11.9810	−	2.08889i	−0.391402	−	0.0682409i	−0.364037	+	0.931385i	$0.618602\pi$
$938$	−1.05309	−	2.51166i	−0.0343845	−	0.0820087i
$939$	4.59470	−	1.47539i	0.149942	−	0.0481476i
$940$	−12.6328	−	27.4338i	−0.412037	−	0.894793i
$941$	2.59978	−	5.64577i	0.0847505	−	0.184047i	−0.861275	−	0.508139i	$-0.830334\pi$
$941$	2.59978	−	5.64577i	0.0847505	−	0.184047i	0.946025	+	0.324092i	$0.105059\pi$
$942$	42.7898	−	28.4579i	1.39417	−	0.927207i
$943$	13.2166	−	43.7391i	0.430391	−	1.42434i
$944$	44.3746	−	36.6583i	1.44427	−	1.19313i
$945$	−30.2163	−	30.7424i	−0.982935	−	1.00005i
$946$	2.87758	+	2.21463i	0.0935583	+	0.0720039i
$947$	−29.0877	−	53.1709i	−0.945224	−	1.72782i	−0.625309	−	0.780377i	$-0.715027\pi$
$947$	−29.0877	−	53.1709i	−0.945224	−	1.72782i	−0.319914	−	0.947446i	$-0.603654\pi$
$948$	−20.2128	+	7.26918i	−0.656482	+	0.236092i
$949$	−18.2816	+	9.59490i	−0.593444	+	0.311464i
$950$	78.2057	+	48.2035i	2.53733	+	1.56393i
$951$	18.7585	+	40.7366i	0.608287	+	1.32098i
$952$	8.44287	−	9.86807i	0.273635	−	0.319826i
$953$	47.4021	+	18.9194i	1.53551	+	0.612860i	0.976349	−	0.216202i	$-0.0693669\pi$
$953$	47.4021	+	18.9194i	1.53551	+	0.612860i	0.559156	+	0.829062i	$0.311125\pi$
$954$	8.03048	−	19.1531i	0.259996	−	0.620104i
$955$	38.3982	+	27.4949i	1.24254	+	0.889713i
$956$	2.37010	+	4.71175i	0.0766547	+	0.152389i
$957$	−0.828317	−	1.51412i	−0.0267757	−	0.0489447i
$958$	−15.6217	+	13.8396i	−0.504714	+	0.447138i
$959$	6.90423	+	9.29879i	0.222949	+	0.300274i
$960$	−1.32092	−	4.98709i	−0.0426325	−	0.160958i
$961$	−23.7287	+	19.6025i	−0.765442	+	0.632339i
$962$	−28.5296	−	16.2534i	−0.919831	−	0.524031i
$963$	−11.4380	+	2.40372i	−0.368584	+	0.0774588i
$964$	0.668320	−	1.59398i	0.0215251	−	0.0513385i
$965$	21.4590	+	19.0110i	0.690790	+	0.611987i
$966$	10.9484	+	15.8615i	0.352259	+	0.510336i
$967$	−5.64089	−	0.983489i	−0.181399	−	0.0316269i	0.0803302	−	0.996768i	$-0.474403\pi$
$967$	−5.64089	−	0.983489i	−0.181399	−	0.0316269i	−0.261729	+	0.965141i	$0.584293\pi$
$968$	17.0613	+	8.21628i	0.548370	+	0.264081i
$969$	31.0647	+	3.22889i	0.997941	+	0.103727i
$970$	−2.16428	+	13.8190i	−0.0694907	+	0.443703i
$971$	6.93236	+	30.3727i	0.222470	+	0.974705i	0.955612	+	0.294629i	$0.0951961\pi$
$971$	6.93236	+	30.3727i	0.222470	+	0.974705i	−0.733142	+	0.680076i	$0.761947\pi$
$972$	−8.87445	+	6.35451i	−0.284648	+	0.203821i
$973$	−34.7030	−	18.2136i	−1.11253	−	0.583900i
$974$	14.4084	+	63.1274i	0.461675	+	2.02273i
$975$	18.3500	−	20.0062i	0.587670	−	0.640712i
$976$	−11.8900	+	9.15075i	−0.380591	+	0.292908i
$977$	47.3059	+	22.7813i	1.51345	+	0.728839i	0.992211	−	0.124572i	$-0.0397558\pi$
$977$	47.3059	+	22.7813i	1.51345	+	0.728839i	0.521239	+	0.853411i	$0.325470\pi$
$978$	−0.196047	−	11.3563i	−0.00626889	−	0.363135i
$979$	0.779872	−	2.29201i	0.0249248	−	0.0732530i
$980$	−2.45080	+	9.25289i	−0.0782878	+	0.295573i
$981$	−6.01393	−	3.70680i	−0.192010	−	0.118349i
$982$	−5.05408	−	5.90724i	−0.161282	−	0.188508i
$983$	−3.40826	+	0.235701i	−0.108707	+	0.00751771i	−0.123242	−	0.992377i	$-0.539329\pi$
$983$	−3.40826	+	0.235701i	−0.108707	+	0.00751771i	0.0145354	+	0.999894i	$0.495373\pi$
$984$	7.16382	+	27.0468i	0.228374	+	0.862219i
$985$	12.4316	+	19.4109i	0.396104	+	0.618481i
$986$	−24.4807	+	4.26822i	−0.779625	+	0.135928i
$987$	23.0869	+	5.69042i	0.734865	+	0.181128i
$988$	−11.3059	+	10.0162i	−0.359690	+	0.318657i
$989$	−8.36966	−	24.5981i	−0.266140	−	0.782174i
$990$	1.44697	+	1.69123i	0.0459877	+	0.0537507i
$991$	−15.6076	+	33.8940i	−0.495792	+	1.07668i	0.483708	+	0.875230i	$0.339290\pi$
$991$	−15.6076	+	33.8940i	−0.495792	+	1.07668i	−0.979499	+	0.201447i	$0.935435\pi$
$992$	−0.293998	+	2.42129i	−0.00933445	+	0.0768761i
$993$	5.01609	−	6.75579i	0.159181	−	0.214389i
$994$	8.50199	−	13.2751i	0.269667	−	0.421061i
$995$	36.8960	−	7.75378i	1.16968	−	0.245811i
$996$	−8.29107	−	7.87247i	−0.262713	−	0.249449i
$997$	46.6744	+	35.9213i	1.47819	+	1.13764i	0.959153	+	0.282889i	$0.0912927\pi$
$997$	46.6744	+	35.9213i	1.47819	+	1.13764i	0.519040	+	0.854750i	$0.326290\pi$
$998$	22.7459	+	5.60635i	0.720007	+	0.177466i
$999$	−39.1384	+	22.2973i	−1.23828	+	0.705455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.m.a.10.11	✓	3168
547.383	even	91	inner	547.2.m.a.383.11	yes	3168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.m.a.10.11	✓	3168	1.1	even	1	trivial
547.2.m.a.383.11	yes	3168	547.383	even	91	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.m (of order \(91\), degree \(72\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.882718 - 1.48907i) q^{2} +(0.304921 + 1.33595i) q^{3} +(-0.478271 + 0.874256i) q^{4} +(-3.64866 - 0.126013i) q^{5} +(1.72016 - 1.63331i) q^{6} +(2.07032 - 0.287726i) q^{7} +(-1.73602 + 0.0599566i) q^{8} +(1.01113 - 0.486934i) q^{9} +O(q^{10})\)	\(q+(-0.882718 - 1.48907i) q^{2} +(0.304921 + 1.33595i) q^{3} +(-0.478271 + 0.874256i) q^{4} +(-3.64866 - 0.126013i) q^{5} +(1.72016 - 1.63331i) q^{6} +(2.07032 - 0.287726i) q^{7} +(-1.73602 + 0.0599566i) q^{8} +(1.01113 - 0.486934i) q^{9} +(3.03310 + 5.54435i) q^{10} +(0.304699 + 0.0751016i) q^{11} +(-1.31379 - 0.372365i) q^{12} +(-1.48308 - 1.85973i) q^{13} +(-2.25595 - 2.82887i) q^{14} +(-0.944207 - 4.91284i) q^{15} +(2.69659 + 4.21049i) q^{16} +(-2.75758 + 2.27807i) q^{17} +(-1.61762 - 1.07582i) q^{18} +(-5.42447 + 3.34347i) q^{19} +(1.85521 - 3.12959i) q^{20} +(1.01567 + 2.67810i) q^{21} +(-0.157132 - 0.520013i) q^{22} +(-1.12438 + 3.72102i) q^{23} +(-0.609450 - 2.30095i) q^{24} +(8.30875 + 0.574600i) q^{25} +(-1.46013 + 3.85003i) q^{26} +(3.52194 + 4.41638i) q^{27} +(-0.738627 + 1.94760i) q^{28} +(-3.48723 + 1.98669i) q^{29} +(-6.48211 + 5.74264i) q^{30} +(-0.442988 + 0.159313i) q^{31} +(2.32823 - 4.62851i) q^{32} +(-0.00742253 + 0.429962i) q^{33} +(5.82638 + 2.09535i) q^{34} +(-7.59015 + 0.788927i) q^{35} +(-0.0578884 + 1.11687i) q^{36} +(-1.23384 + 7.87815i) q^{37} +(9.76695 + 5.12609i) q^{38} +(2.03227 - 2.54839i) q^{39} +6.34172 q^{40} -11.7546 q^{41} +(3.09134 - 3.87642i) q^{42} +(-5.43468 + 3.89148i) q^{43} +(-0.211387 + 0.230466i) q^{44} +(-3.75063 + 1.64924i) q^{45} +(6.53338 - 1.61033i) q^{46} +(4.71588 - 6.83213i) q^{47} +(-4.80275 + 4.88638i) q^{48} +(-2.53129 + 0.717435i) q^{49} +(-6.47867 - 12.8795i) q^{50} +(-3.88422 - 2.98936i) q^{51} +(2.33519 - 0.407141i) q^{52} +(2.01770 + 10.4984i) q^{53} +(3.46742 - 9.14284i) q^{54} +(-1.10228 - 0.312416i) q^{55} +(-3.57687 + 0.623628i) q^{56} +(-6.12074 - 6.22731i) q^{57} +(6.03656 + 3.43905i) q^{58} +(-1.38758 - 11.4277i) q^{59} +(4.74667 + 1.52419i) q^{60} +(0.258664 + 2.98956i) q^{61} +(0.628261 + 0.519013i) q^{62} +(1.95326 - 1.29904i) q^{63} +(1.02879 - 0.0711467i) q^{64} +(5.17692 + 6.97240i) q^{65} +(0.646797 - 0.368483i) q^{66} +(0.724183 + 0.205253i) q^{67} +(-0.672742 - 3.50037i) q^{68} +(-5.31394 - 0.367490i) q^{69} +(7.87473 + 10.6059i) q^{70} +(1.40343 + 4.12463i) q^{71} +(-1.72615 + 0.905953i) q^{72} +(1.63820 - 8.52380i) q^{73} +(12.8203 - 5.11691i) q^{74} +(1.76588 + 11.2753i) q^{75} +(-0.328683 - 6.34146i) q^{76} +(0.652434 + 0.0678145i) q^{77} +(-5.58867 - 0.776693i) q^{78} +(12.7895 - 9.15785i) q^{79} +(-9.30838 - 15.7025i) q^{80} +(-2.72696 + 3.41950i) q^{81} +(10.3760 + 17.5034i) q^{82} +(7.41358 + 3.89095i) q^{83} +(-2.82711 - 0.392902i) q^{84} +(10.3486 - 7.96440i) q^{85} +(10.5920 + 4.65756i) q^{86} +(-3.71744 - 4.05297i) q^{87} +(-0.533468 - 0.112110i) q^{88} +(0.665022 - 7.68612i) q^{89} +(5.76658 + 4.12914i) q^{90} +(-3.60555 - 3.42351i) q^{91} +(-2.71537 - 2.76265i) q^{92} +(-0.347910 - 0.543230i) q^{93} +(-14.3363 - 0.991442i) q^{94} +(20.2134 - 11.5156i) q^{95} +(6.89337 + 1.69906i) q^{96} +(1.75398 + 1.34989i) q^{97} +(3.30272 + 3.13597i) q^{98} +(0.344660 - 0.0724310i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9}+O(q^{10}) \) 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9	\( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9} - 91 q^{10} - 61 q^{11} - 31 q^{12} - 72 q^{13} - 21 q^{14} - 46 q^{15} + 24 q^{16} - 91 q^{17} + 9 q^{18} - 89 q^{19} - 108 q^{20} - 81 q^{21} - 50 q^{22} - 86 q^{23} - 33 q^{24} - 15 q^{25} + 137 q^{26} + 163 q^{27} - 47 q^{28} - 12 q^{29} + 29 q^{30} - 53 q^{31} - 122 q^{32} - 21 q^{33} - 80 q^{34} - 75 q^{35} - 8 q^{36} - 49 q^{37} - 47 q^{38} + 128 q^{39} - 246 q^{40} - 686 q^{41} - 466 q^{42} - 9 q^{43} - 43 q^{44} + 156 q^{45} - 91 q^{46} - 72 q^{47} + 21 q^{48} - 8 q^{49} - 84 q^{50} + 93 q^{51} + 4 q^{52} - 32 q^{53} - 71 q^{54} - 34 q^{55} - 263 q^{56} - 61 q^{57} - 36 q^{58} - 23 q^{59} + 87 q^{60} + 38 q^{61} + 26 q^{62} + 133 q^{63} + 343 q^{64} + 143 q^{65} - 65 q^{66} - 50 q^{67} - 213 q^{68} - 140 q^{69} + 372 q^{70} - 75 q^{71} + 147 q^{72} - 18 q^{73} - 85 q^{74} + 97 q^{75} - 47 q^{76} + 11 q^{77} + 55 q^{78} - 37 q^{79} - 142 q^{80} - 532 q^{81} - 94 q^{82} - 279 q^{83} + 395 q^{84} - 75 q^{85} - 147 q^{86} + 84 q^{87} + 345 q^{88} + 8 q^{89} + 278 q^{90} - 38 q^{91} - 78 q^{92} - 83 q^{93} - 540 q^{94} + 35 q^{95} + 123 q^{96} - 735 q^{97} - 90 q^{98} + 351 q^{99}+O(q^{100}) \) 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9 - 91 * q^10 - 61 * q^11 - 31 * q^12 - 72 * q^13 - 21 * q^14 - 46 * q^15 + 24 * q^16 - 91 * q^17 + 9 * q^18 - 89 * q^19 - 108 * q^20 - 81 * q^21 - 50 * q^22 - 86 * q^23 - 33 * q^24 - 15 * q^25 + 137 * q^26 + 163 * q^27 - 47 * q^28 - 12 * q^29 + 29 * q^30 - 53 * q^31 - 122 * q^32 - 21 * q^33 - 80 * q^34 - 75 * q^35 - 8 * q^36 - 49 * q^37 - 47 * q^38 + 128 * q^39 - 246 * q^40 - 686 * q^41 - 466 * q^42 - 9 * q^43 - 43 * q^44 + 156 * q^45 - 91 * q^46 - 72 * q^47 + 21 * q^48 - 8 * q^49 - 84 * q^50 + 93 * q^51 + 4 * q^52 - 32 * q^53 - 71 * q^54 - 34 * q^55 - 263 * q^56 - 61 * q^57 - 36 * q^58 - 23 * q^59 + 87 * q^60 + 38 * q^61 + 26 * q^62 + 133 * q^63 + 343 * q^64 + 143 * q^65 - 65 * q^66 - 50 * q^67 - 213 * q^68 - 140 * q^69 + 372 * q^70 - 75 * q^71 + 147 * q^72 - 18 * q^73 - 85 * q^74 + 97 * q^75 - 47 * q^76 + 11 * q^77 + 55 * q^78 - 37 * q^79 - 142 * q^80 - 532 * q^81 - 94 * q^82 - 279 * q^83 + 395 * q^84 - 75 * q^85 - 147 * q^86 + 84 * q^87 + 345 * q^88 + 8 * q^89 + 278 * q^90 - 38 * q^91 - 78 * q^92 - 83 * q^93 - 540 * q^94 + 35 * q^95 + 123 * q^96 - 735 * q^97 - 90 * q^98 + 351 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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