LMFDB - Embedded newform 73.2.k.a.12.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [73,2,Mod(6,73)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(73, base_ring=CyclotomicField(36))

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

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

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

chi := DirichletCharacter("73.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	73.k (of order $36$, degree $12$, 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:	$0.582907934755$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			12.1
Character	$\chi$	$=$	73.12
Dual form			73.2.k.a.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.421521 - 2.39057i) q^{2} +(-2.81166 + 1.62332i) q^{3} +(-3.65774 + 1.33131i) q^{4} +(-0.771420 - 1.10170i) q^{5} +(5.06582 + 6.03721i) q^{6} +(-2.96706 - 0.795022i) q^{7} +(2.29696 + 3.97845i) q^{8} +(3.77030 - 6.53036i) q^{9} +O(q^{10})$	\(q+(-0.421521 - 2.39057i) q^{2} +(-2.81166 + 1.62332i) q^{3} +(-3.65774 + 1.33131i) q^{4} +(-0.771420 - 1.10170i) q^{5} +(5.06582 + 6.03721i) q^{6} +(-2.96706 - 0.795022i) q^{7} +(2.29696 + 3.97845i) q^{8} +(3.77030 - 6.53036i) q^{9} +(-2.30852 + 2.30852i) q^{10} +(1.57674 - 1.10405i) q^{11} +(8.12321 - 9.68087i) q^{12} +(-2.41081 - 0.210918i) q^{13} +(-0.649873 + 7.42808i) q^{14} +(3.95739 + 1.84536i) q^{15} +(2.57888 - 2.16394i) q^{16} +(-0.0367704 - 0.137229i) q^{17} +(-17.2005 - 6.26048i) q^{18} +(-3.44475 + 0.607402i) q^{19} +(4.28837 + 3.00275i) q^{20} +(9.63295 - 2.58114i) q^{21} +(-3.30393 - 3.30393i) q^{22} +(0.209310 + 0.0369070i) q^{23} +(-12.9165 - 7.45737i) q^{24} +(1.09144 - 2.99871i) q^{25} +(0.511992 + 5.85210i) q^{26} +14.7417i q^{27} +(11.9112 - 1.04209i) q^{28} +(1.96575 - 2.80739i) q^{29} +(2.74333 - 10.2383i) q^{30} +(-0.991677 - 2.12666i) q^{31} +(0.778184 + 0.652974i) q^{32} +(-2.64105 + 5.66376i) q^{33} +(-0.312555 + 0.145747i) q^{34} +(1.41297 + 3.88212i) q^{35} +(-5.09687 + 28.9058i) q^{36} +(-1.03582 + 5.87441i) q^{37} +(2.90407 + 7.97887i) q^{38} +(7.12076 - 3.32047i) q^{39} +(2.61114 - 5.59962i) q^{40} +(-4.14349 - 3.47680i) q^{41} +(-10.2309 - 21.9402i) q^{42} +(0.322907 - 1.20511i) q^{43} +(-4.29749 + 6.13745i) q^{44} +(-10.1030 + 0.883898i) q^{45} -0.515927i q^{46} +(-1.13332 - 12.9539i) q^{47} +(-3.73820 + 10.2706i) q^{48} +(2.10922 + 1.21776i) q^{49} +(-7.62869 - 1.34514i) q^{50} +(0.326152 + 0.326152i) q^{51} +(9.09891 - 2.43804i) q^{52} +(-3.99598 - 2.79801i) q^{53} +(35.2409 - 6.21393i) q^{54} +(-2.43266 - 0.885417i) q^{55} +(-3.65226 - 13.6304i) q^{56} +(8.69948 - 7.29973i) q^{57} +(-7.53985 - 3.51589i) q^{58} +(-1.15518 + 13.2037i) q^{59} +(-16.9318 - 1.48134i) q^{60} +(-5.32131 + 6.34169i) q^{61} +(-4.66591 + 3.26710i) q^{62} +(-16.3785 + 16.3785i) q^{63} +(4.59945 - 7.96648i) q^{64} +(1.62738 + 2.81870i) q^{65} +(14.6528 + 3.92622i) q^{66} +(-6.79441 - 8.09726i) q^{67} +(0.317191 + 0.452996i) q^{68} +(-0.648421 + 0.236006i) q^{69} +(8.68486 - 5.01421i) q^{70} +(-1.40155 - 7.94856i) q^{71} +34.6409 q^{72} +(7.19155 + 4.61319i) q^{73} +14.4798 q^{74} +(1.79909 + 10.2031i) q^{75} +(11.7914 - 6.80775i) q^{76} +(-5.55603 + 2.02223i) q^{77} +(-10.9393 - 15.6230i) q^{78} +(6.05041 + 7.21060i) q^{79} +(-4.37342 - 1.17186i) q^{80} +(-12.6195 - 21.8576i) q^{81} +(-6.56495 + 11.3708i) q^{82} +(11.1294 - 11.1294i) q^{83} +(-31.7986 + 22.2656i) q^{84} +(-0.122820 + 0.146371i) q^{85} +(-3.01700 - 0.263953i) q^{86} +(-0.969765 + 11.0845i) q^{87} +(8.01410 + 3.73704i) q^{88} +(10.5446 - 8.84801i) q^{89} +(6.37165 + 23.7793i) q^{90} +(6.98533 + 2.54245i) q^{91} +(-0.814737 + 0.143660i) q^{92} +(6.24050 + 4.36965i) q^{93} +(-30.4895 + 8.16963i) q^{94} +(3.32653 + 3.32653i) q^{95} +(-3.24797 - 0.572705i) q^{96} +(7.40709 + 4.27649i) q^{97} +(2.02205 - 5.55555i) q^{98} +(-1.26502 - 14.4593i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) $ 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9	\( 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9} - 6 q^{11} + 6 q^{12} - 12 q^{13} - 12 q^{14} - 30 q^{15} + 30 q^{17} - 12 q^{18} - 6 q^{19} + 60 q^{20} - 30 q^{21} - 12 q^{22} - 12 q^{23} - 18 q^{24} + 36 q^{25} + 12 q^{26} + 120 q^{28} - 6 q^{29} - 72 q^{30} - 18 q^{31} - 18 q^{32} - 60 q^{33} - 60 q^{34} - 36 q^{35} + 60 q^{36} - 6 q^{37} + 48 q^{38} + 78 q^{39} - 18 q^{40} + 54 q^{42} - 24 q^{43} + 48 q^{44} + 36 q^{47} + 30 q^{48} - 18 q^{49} + 132 q^{50} - 18 q^{51} - 24 q^{53} - 6 q^{54} + 72 q^{55} + 24 q^{56} - 6 q^{57} - 18 q^{58} - 66 q^{60} - 36 q^{61} - 36 q^{62} + 12 q^{63} - 84 q^{64} + 24 q^{65} + 156 q^{66} - 54 q^{67} - 84 q^{68} - 6 q^{69} - 162 q^{70} + 48 q^{71} - 72 q^{72} - 36 q^{73} + 144 q^{74} + 6 q^{75} - 180 q^{76} - 24 q^{77} - 198 q^{78} - 36 q^{79} - 126 q^{80} - 48 q^{81} + 30 q^{82} - 48 q^{83} - 126 q^{84} - 6 q^{85} - 120 q^{86} + 6 q^{87} + 6 q^{88} + 6 q^{89} + 210 q^{90} + 48 q^{91} + 96 q^{92} + 144 q^{93} - 6 q^{94} - 12 q^{95} + 162 q^{96} - 18 q^{97} + 186 q^{98} + 78 q^{99}+O(q^{100}) \) 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9 - 6 * q^11 + 6 * q^12 - 12 * q^13 - 12 * q^14 - 30 * q^15 + 30 * q^17 - 12 * q^18 - 6 * q^19 + 60 * q^20 - 30 * q^21 - 12 * q^22 - 12 * q^23 - 18 * q^24 + 36 * q^25 + 12 * q^26 + 120 * q^28 - 6 * q^29 - 72 * q^30 - 18 * q^31 - 18 * q^32 - 60 * q^33 - 60 * q^34 - 36 * q^35 + 60 * q^36 - 6 * q^37 + 48 * q^38 + 78 * q^39 - 18 * q^40 + 54 * q^42 - 24 * q^43 + 48 * q^44 + 36 * q^47 + 30 * q^48 - 18 * q^49 + 132 * q^50 - 18 * q^51 - 24 * q^53 - 6 * q^54 + 72 * q^55 + 24 * q^56 - 6 * q^57 - 18 * q^58 - 66 * q^60 - 36 * q^61 - 36 * q^62 + 12 * q^63 - 84 * q^64 + 24 * q^65 + 156 * q^66 - 54 * q^67 - 84 * q^68 - 6 * q^69 - 162 * q^70 + 48 * q^71 - 72 * q^72 - 36 * q^73 + 144 * q^74 + 6 * q^75 - 180 * q^76 - 24 * q^77 - 198 * q^78 - 36 * q^79 - 126 * q^80 - 48 * q^81 + 30 * q^82 - 48 * q^83 - 126 * q^84 - 6 * q^85 - 120 * q^86 + 6 * q^87 + 6 * q^88 + 6 * q^89 + 210 * q^90 + 48 * q^91 + 96 * q^92 + 144 * q^93 - 6 * q^94 - 12 * q^95 + 162 * q^96 - 18 * q^97 + 186 * q^98 + 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/73\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{11}{36}\right)$

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 $

$2$	−0.421521	−	2.39057i	−0.298061	−	1.69039i	−0.654496	−	0.756066i	$-0.727119\pi$
$2$	−0.421521	−	2.39057i	−0.298061	−	1.69039i	0.356435	−	0.934320i	$-0.383992\pi$
$3$	−2.81166	+	1.62332i	−1.62332	+	0.937221i	−0.637290	+	0.770624i	$0.719945\pi$
$3$	−2.81166	+	1.62332i	−1.62332	+	0.937221i	−0.986025	+	0.166597i	$0.946722\pi$
$4$	−3.65774	+	1.33131i	−1.82887	+	0.665655i
$5$	−0.771420	−	1.10170i	−0.344990	−	0.492696i	0.608737	−	0.793372i	$-0.291677\pi$
$5$	−0.771420	−	1.10170i	−0.344990	−	0.492696i	−0.953726	+	0.300676i	$0.902788\pi$
$6$	5.06582	+	6.03721i	2.06811	+	2.46468i
$7$	−2.96706	−	0.795022i	−1.12144	−	0.300490i	−0.349976	−	0.936758i	$-0.613810\pi$
$7$	−2.96706	−	0.795022i	−1.12144	−	0.300490i	−0.771468	+	0.636268i	$0.780477\pi$
$8$	2.29696	+	3.97845i	0.812097	+	1.40659i
$9$	3.77030	−	6.53036i	1.25677	−	2.17679i
$10$	−2.30852	+	2.30852i	−0.730019	+	0.730019i
$11$	1.57674	−	1.10405i	0.475406	−	0.332883i	−0.311194	−	0.950347i	$-0.600729\pi$
$11$	1.57674	−	1.10405i	0.475406	−	0.332883i	0.786599	+	0.617464i	$0.211840\pi$
$12$	8.12321	−	9.68087i	2.34497	−	2.79463i
$13$	−2.41081	−	0.210918i	−0.668637	−	0.0584982i	−0.252217	−	0.967671i	$-0.581160\pi$
$13$	−2.41081	−	0.210918i	−0.668637	−	0.0584982i	−0.416420	+	0.909172i	$0.636715\pi$
$14$	−0.649873	+	7.42808i	−0.173686	+	1.98524i
$15$	3.95739	+	1.84536i	1.02179	+	0.476470i
$16$	2.57888	−	2.16394i	0.644721	−	0.540985i
$17$	−0.0367704	−	0.137229i	−0.00891813	−	0.0332829i	0.961323	−	0.275422i	$-0.0888176\pi$
$17$	−0.0367704	−	0.137229i	−0.00891813	−	0.0332829i	−0.970242	+	0.242139i	$0.922151\pi$
$18$	−17.2005	−	6.26048i	−4.05420	−	1.47561i
$19$	−3.44475	+	0.607402i	−0.790280	+	0.139348i	−0.554197	−	0.832385i	$-0.686975\pi$
$19$	−3.44475	+	0.607402i	−0.790280	+	0.139348i	−0.236083	+	0.971733i	$0.575864\pi$
$20$	4.28837	+	3.00275i	0.958908	+	0.671434i
$21$	9.63295	−	2.58114i	2.10208	−	0.563251i
$22$	−3.30393	−	3.30393i	−0.704400	−	0.704400i
$23$	0.209310	+	0.0369070i	0.0436442	+	0.00769565i	0.195428	−	0.980718i	$-0.437391\pi$
$23$	0.209310	+	0.0369070i	0.0436442	+	0.00769565i	−0.151783	+	0.988414i	$0.548502\pi$
$24$	−12.9165	−	7.45737i	−2.63658	−	1.52223i
$25$	1.09144	−	2.99871i	0.218288	−	0.599742i
$26$	0.511992	+	5.85210i	0.100410	+	1.14769i
$27$			14.7417i			2.83704i
$28$	11.9112	−	1.04209i	2.25100	−	0.196937i
$29$	1.96575	−	2.80739i	0.365031	−	0.521318i	−0.594058	−	0.804422i	$-0.702475\pi$
$29$	1.96575	−	2.80739i	0.365031	−	0.521318i	0.959089	+	0.283104i	$0.0913640\pi$
$30$	2.74333	−	10.2383i	0.500862	−	1.86924i
$31$	−0.991677	−	2.12666i	−0.178111	−	0.381959i	0.796902	−	0.604108i	$-0.206471\pi$
$31$	−0.991677	−	2.12666i	−0.178111	−	0.381959i	−0.975013	+	0.222149i	$0.928693\pi$
$32$	0.778184	+	0.652974i	0.137565	+	0.115431i
$33$	−2.64105	+	5.66376i	−0.459748	+	0.985934i
$34$	−0.312555	+	0.145747i	−0.0536028	+	0.0249954i
$35$	1.41297	+	3.88212i	0.238836	+	0.656197i
$36$	−5.09687	+	28.9058i	−0.849479	+	4.81764i
$37$	−1.03582	+	5.87441i	−0.170287	+	0.965747i	0.773157	+	0.634215i	$0.218677\pi$
$37$	−1.03582	+	5.87441i	−0.170287	+	0.965747i	−0.943444	+	0.331532i	$0.892435\pi$
$38$	2.90407	+	7.97887i	0.471103	+	1.29434i
$39$	7.12076	−	3.32047i	1.14023	−	0.531700i
$40$	2.61114	−	5.59962i	0.412858	−	0.885377i
$41$	−4.14349	−	3.47680i	−0.647104	−	0.542985i	0.259087	−	0.965854i	$-0.416578\pi$
$41$	−4.14349	−	3.47680i	−0.647104	−	0.542985i	−0.906191	+	0.422869i	$0.861023\pi$
$42$	−10.2309	−	21.9402i	−1.57866	−	3.38545i
$43$	0.322907	−	1.20511i	0.0492429	−	0.183777i	−0.936924	−	0.349534i	$-0.886340\pi$
$43$	0.322907	−	1.20511i	0.0492429	−	0.183777i	0.986167	+	0.165757i	$0.0530067\pi$
$44$	−4.29749	+	6.13745i	−0.647871	+	0.925256i
$45$	−10.1030	+	0.883898i	−1.50607	+	0.131764i
$46$		−	0.515927i		−	0.0760693i
$47$	−1.13332	−	12.9539i	−0.165312	−	1.88952i	−0.398615	−	0.917118i	$-0.630509\pi$
$47$	−1.13332	−	12.9539i	−0.165312	−	1.88952i	0.233303	−	0.972404i	$-0.425047\pi$
$48$	−3.73820	+	10.2706i	−0.539563	+	1.48244i
$49$	2.10922	+	1.21776i	0.301317	+	0.173966i
$50$	−7.62869	−	1.34514i	−1.07886	−	0.190232i
$51$	0.326152	+	0.326152i	0.0456704	+	0.0456704i
$52$	9.09891	−	2.43804i	1.26179	−	0.338096i
$53$	−3.99598	−	2.79801i	−0.548889	−	0.384337i	0.265982	−	0.963978i	$-0.414304\pi$
$53$	−3.99598	−	2.79801i	−0.548889	−	0.384337i	−0.814872	+	0.579641i	$0.803193\pi$
$54$	35.2409	−	6.21393i	4.79569	−	0.845609i
$55$	−2.43266	−	0.885417i	−0.328020	−	0.119390i
$56$	−3.65226	−	13.6304i	−0.488054	−	1.82144i
$57$	8.69948	−	7.29973i	1.15227	−	0.966873i
$58$	−7.53985	−	3.51589i	−0.990031	−	0.461659i
$59$	−1.15518	+	13.2037i	−0.150391	+	1.71898i	0.428474	+	0.903554i	$0.359051\pi$
$59$	−1.15518	+	13.2037i	−0.150391	+	1.71898i	−0.578865	+	0.815424i	$0.696504\pi$
$60$	−16.9318	−	1.48134i	−2.18589	−	0.191241i
$61$	−5.32131	+	6.34169i	−0.681324	+	0.811970i	−0.990277	−	0.139107i	$-0.955577\pi$
$61$	−5.32131	+	6.34169i	−0.681324	+	0.811970i	0.308953	+	0.951077i	$0.400021\pi$
$62$	−4.66591	+	3.26710i	−0.592571	+	0.414923i
$63$	−16.3785	+	16.3785i	−2.06350	+	2.06350i
$64$	4.59945	−	7.96648i	0.574931	−	0.995810i
$65$	1.62738	+	2.81870i	0.201851	+	0.349616i
$66$	14.6528	+	3.92622i	1.80364	+	0.483284i
$67$	−6.79441	−	8.09726i	−0.830069	−	0.989238i	−0.999993	−	0.00378054i	$-0.998797\pi$
$67$	−6.79441	−	8.09726i	−0.830069	−	0.989238i	0.169924	−	0.985457i	$-0.445648\pi$
$68$	0.317191	+	0.452996i	0.0384650	+	0.0549338i
$69$	−0.648421	+	0.236006i	−0.0780608	+	0.0284118i
$70$	8.68486	−	5.01421i	1.03804	−	0.599312i
$71$	−1.40155	−	7.94856i	−0.166333	−	0.943320i	−0.947680	−	0.319223i	$-0.896578\pi$
$71$	−1.40155	−	7.94856i	−0.166333	−	0.943320i	0.781347	−	0.624097i	$-0.214533\pi$
$72$	34.6409			4.08247
$73$	7.19155	+	4.61319i	0.841708	+	0.539933i
$73$	7.19155	+	4.61319i	0.841708	+	0.539933i
$74$	14.4798			1.68324
$75$	1.79909	+	10.2031i	0.207741	+	1.17816i
$76$	11.7914	−	6.80775i	1.35256	−	0.780903i
$77$	−5.55603	+	2.02223i	−0.633169	+	0.230455i
$78$	−10.9393	−	15.6230i	−1.23864	−	1.76896i
$79$	6.05041	+	7.21060i	0.680724	+	0.811256i	0.990201	−	0.139652i	$-0.0445982\pi$
$79$	6.05041	+	7.21060i	0.680724	+	0.811256i	−0.309476	+	0.950907i	$0.600154\pi$
$80$	−4.37342	−	1.17186i	−0.488964	−	0.131017i
$81$	−12.6195	−	21.8576i	−1.40216	−	2.42862i
$82$	−6.56495	+	11.3708i	−0.724978	+	1.25570i
$83$	11.1294	−	11.1294i	1.22162	−	1.22162i	0.254558	−	0.967057i	$-0.418070\pi$
$83$	11.1294	−	11.1294i	1.22162	−	1.22162i	0.967057	−	0.254558i	$-0.0819301\pi$
$84$	−31.7986	+	22.2656i	−3.46951	+	2.42938i
$85$	−0.122820	+	0.146371i	−0.0133217	+	0.0158762i
$86$	−3.01700	−	0.263953i	−0.325331	−	0.0284628i
$87$	−0.969765	+	11.0845i	−0.103970	+	1.18838i
$88$	8.01410	+	3.73704i	0.854306	+	0.398369i
$89$	10.5446	−	8.84801i	1.11773	−	0.937887i	0.119243	−	0.992865i	$-0.461953\pi$
$89$	10.5446	−	8.84801i	1.11773	−	0.937887i	0.998488	+	0.0549777i	$0.0175088\pi$
$90$	6.37165	+	23.7793i	0.671631	+	2.50656i
$91$	6.98533	+	2.54245i	0.732261	+	0.266521i
$92$	−0.814737	+	0.143660i	−0.0849422	+	0.0149776i
$93$	6.24050	+	4.36965i	0.647110	+	0.453111i
$94$	−30.4895	+	8.16963i	−3.14475	+	0.842633i
$95$	3.32653	+	3.32653i	0.341295	+	0.341295i
$96$	−3.24797	−	0.572705i	−0.331495	−	0.0584515i
$97$	7.40709	+	4.27649i	0.752076	+	0.434211i	0.826444	−	0.563019i	$-0.190360\pi$
$97$	7.40709	+	4.27649i	0.752076	+	0.434211i	−0.0743673	+	0.997231i	$0.523694\pi$
$98$	2.02205	−	5.55555i	0.204258	−	0.561195i
$99$	−1.26502	−	14.4593i	−0.127140	−	1.45321i
$100$			12.4216i			1.24216i
$101$	−7.85681	+	0.687381i	−0.781781	+	0.0683970i	−0.471057	−	0.882103i	$-0.656127\pi$
$101$	−7.85681	+	0.687381i	−0.781781	+	0.0683970i	−0.310725	+	0.950500i	$0.600572\pi$
$102$	0.642208	−	0.917168i	0.0635880	−	0.0908131i
$103$	1.54323	−	5.75939i	0.152058	−	0.567490i	−0.847281	−	0.531145i	$-0.821762\pi$
$103$	1.54323	−	5.75939i	0.152058	−	0.567490i	0.999339	−	0.0363448i	$-0.0115715\pi$
$104$	−4.69839	−	10.0757i	−0.460715	−	0.988007i
$105$	−10.2747	−	8.62150i	−1.00271	−	0.841373i
$106$	−5.00445	+	10.7321i	−0.486075	+	1.04239i
$107$	7.11860	−	3.31946i	0.688181	−	0.320904i	−0.0468843	−	0.998900i	$-0.514929\pi$
$107$	7.11860	−	3.31946i	0.688181	−	0.320904i	0.735065	+	0.677996i	$0.237151\pi$
$108$	−19.6257	−	53.9213i	−1.88849	−	5.18857i
$109$	0.442257	−	2.50816i	0.0423605	−	0.240238i	−0.956274	−	0.292471i	$-0.905523\pi$
$109$	0.442257	−	2.50816i	0.0423605	−	0.240238i	0.998635	+	0.0522325i	$0.0166337\pi$
$110$	−1.09123	+	6.18866i	−0.104045	+	0.590066i
$111$	−6.62365	−	18.1983i	−0.628689	−	1.72731i
$112$	−9.37209	+	4.37028i	−0.885579	+	0.412952i
$113$	−2.30716	+	4.94771i	−0.217039	+	0.465442i	−0.984439	−	0.175727i	$-0.943772\pi$
$113$	−2.30716	+	4.94771i	−0.217039	+	0.465442i	0.767400	+	0.641169i	$0.221550\pi$
$114$	−21.1175	−	17.7197i	−1.97784	−	1.65960i
$115$	−0.120806	−	0.259068i	−0.0112652	−	0.0241582i
$116$	−3.45272	+	12.8857i	−0.320577	+	1.19641i
$117$	−10.4668	+	14.9482i	−0.967660	+	1.38196i
$118$	32.0513	−	2.80413i	2.95056	−	0.258141i
$119$			0.436400i			0.0400047i
$120$	1.74828	+	19.9830i	0.159596	+	1.82419i
$121$	−2.49503	+	6.85503i	−0.226820	+	0.623184i
$122$	17.4033	+	10.0478i	1.57562	+	0.909684i
$123$	17.2940	+	3.04941i	1.55935	+	0.274956i
$124$	6.45854	+	6.45854i	0.579994	+	0.579994i
$125$	−10.6412	+	2.85129i	−0.951775	+	0.255027i
$126$	46.0578	+	32.2500i	4.10315	+	2.87306i
$127$	−17.3057	+	3.05147i	−1.53563	+	0.270774i	−0.876556	−	0.481300i	$-0.840165\pi$
$127$	−17.3057	+	3.05147i	−1.53563	+	0.270774i	−0.659079	+	0.752074i	$0.729054\pi$
$128$	−19.0740	−	6.94237i	−1.68592	−	0.613625i
$129$	1.04836	+	3.91253i	0.0923030	+	0.344479i
$130$	6.05231	−	5.07849i	0.530823	−	0.445413i
$131$	3.47436	+	1.62012i	0.303556	+	0.141550i	0.568428	−	0.822733i	$-0.307552\pi$
$131$	3.47436	+	1.62012i	0.303556	+	0.141550i	−0.264872	+	0.964284i	$0.585330\pi$
$132$	2.12008	−	24.2326i	0.184529	−	2.10918i
$133$	10.7037	+	0.936451i	0.928128	+	0.0812006i
$134$	−16.4931	+	19.6557i	−1.42478	+	1.69799i
$135$	16.2409	−	11.3720i	1.39780	−	0.978748i
$136$	0.461498	−	0.461498i	0.0395731	−	0.0395731i
$137$	4.07964	−	7.06615i	0.348547	−	0.603702i	−0.637444	−	0.770496i	$-0.720008\pi$
$137$	4.07964	−	7.06615i	0.348547	−	0.603702i	0.985992	+	0.166795i	$0.0533417\pi$
$138$	0.837512	+	1.45061i	0.0712937	+	0.123484i
$139$	−3.53299	−	0.946663i	−0.299665	−	0.0802949i	0.105854	−	0.994382i	$-0.466242\pi$
$139$	−3.53299	−	0.946663i	−0.299665	−	0.0802949i	−0.405519	+	0.914087i	$0.632909\pi$
$140$	−10.3366	−	12.3187i	−0.873602	−	1.04112i
$141$	24.2148	+	34.5823i	2.03925	+	2.91236i
$142$	−18.4108	+	6.70098i	−1.54500	+	0.562333i
$143$	−4.03408	+	2.32908i	−0.337347	+	0.194767i
$144$	−4.40813	−	24.9998i	−0.367344	−	2.08331i
$145$	−4.60933			−0.382784
$146$	7.99675	−	19.1364i	0.661816	−	1.58374i
$147$	−7.90723			−0.652177
$148$	−4.03190	−	22.8661i	−0.331421	−	1.87958i
$149$	−0.231102	+	0.133427i	−0.0189326	+	0.0109308i	−0.509436	−	0.860508i	$-0.670146\pi$
$149$	−0.231102	+	0.133427i	−0.0189326	+	0.0109308i	0.490504	+	0.871439i	$0.336813\pi$
$150$	23.6329	−	8.60167i	1.92962	−	0.702323i
$151$	−0.822278	−	1.17433i	−0.0669160	−	0.0955660i	0.784299	−	0.620383i	$-0.213023\pi$
$151$	−0.822278	−	1.17433i	−0.0669160	−	0.0955660i	−0.851215	+	0.524817i	$0.824134\pi$
$152$	−10.3290	−	12.3096i	−0.837789	−	0.998439i
$153$	−1.03479	−	0.277271i	−0.0836578	−	0.0224160i
$154$	7.17626	+	12.4297i	0.578280	+	1.00161i
$155$	−1.57795	+	2.73308i	−0.126744	+	0.219526i
$156$	−21.6254	+	21.6254i	−1.73141	+	1.73141i
$157$	6.07950	−	4.25691i	0.485197	−	0.339738i	−0.305247	−	0.952273i	$-0.598739\pi$
$157$	6.07950	−	4.25691i	0.485197	−	0.339738i	0.790444	+	0.612535i	$0.209850\pi$
$158$	14.6870	−	17.5033i	1.16844	−	1.39249i
$159$	15.7774	+	1.38034i	1.25123	+	0.109468i
$160$	0.119076	−	1.36104i	0.00941378	−	0.107600i
$161$	−0.591694	−	0.275912i	−0.0466320	−	0.0217449i
$162$	−46.9326	+	39.3811i	−3.68737	+	3.09407i
$163$	0.230175	+	0.859026i	0.0180287	+	0.0672841i	0.974354	−	0.225020i	$-0.0722447\pi$
$163$	0.230175	+	0.859026i	0.0180287	+	0.0672841i	−0.956325	+	0.292304i	$0.905578\pi$
$164$	19.7845	+	7.20097i	1.54491	+	0.562302i
$165$	8.27714	−	1.45948i	0.644374	−	0.113621i
$166$	−31.2970	−	21.9144i	−2.42912	−	1.70089i
$167$	2.95026	−	0.790519i	0.228298	−	0.0611722i	−0.142857	−	0.989743i	$-0.545629\pi$
$167$	2.95026	−	0.790519i	0.228298	−	0.0611722i	0.371154	+	0.928571i	$0.378962\pi$
$168$	32.3954	+	32.3954i	2.49936	+	2.49936i
$169$	−7.03500	−	1.24046i	−0.541154	−	0.0954201i
$170$	0.401682	+	0.231911i	0.0308076	+	0.0177868i
$171$	−9.02120	+	24.7855i	−0.689868	+	1.89540i
$172$	0.423258	+	4.83786i	0.0322731	+	0.368883i
$173$			5.62558i			0.427705i	0.976866	+	0.213852i	$0.0686011\pi$
$173$			5.62558i			0.427705i	−0.976866	+	0.213852i	$0.931399\pi$
$174$	26.9069	−	2.35405i	2.03981	−	0.178460i
$175$	−5.62242	+	8.02964i	−0.425015	+	0.606984i
$176$	1.67714	−	6.25919i	0.126419	−	0.471804i
$177$	−18.1858	−	38.9996i	−1.36693	−	2.93139i
$178$	−25.5966	−	21.4781i	−1.91854	−	1.60985i
$179$	1.22044	−	2.61725i	0.0912201	−	0.195622i	−0.855404	−	0.517961i	$-0.826691\pi$
$179$	1.22044	−	2.61725i	0.0912201	−	0.195622i	0.946624	+	0.322339i	$0.104469\pi$
$180$	35.7774	−	16.6833i	2.66669	−	1.24350i
$181$	−4.21785	−	11.5884i	−0.313510	−	0.861362i	−0.991941	−	0.126698i	$-0.959562\pi$
$181$	−4.21785	−	11.5884i	−0.313510	−	0.861362i	0.678431	−	0.734664i	$-0.262660\pi$
$182$	3.13343	−	17.7706i	0.232266	−	1.31724i
$183$	4.66718	−	26.4689i	0.345008	−	1.95664i
$184$	0.333944	+	0.917503i	0.0246187	+	0.0676392i
$185$	7.27090	−	3.39048i	0.534567	−	0.249273i
$186$	7.81543	−	16.7602i	0.573055	−	1.22892i
$187$	−0.209485	−	0.175778i	−0.0153190	−	0.0128542i
$188$	21.3911	+	45.8733i	1.56010	+	3.34565i
$189$	11.7200	−	43.7395i	0.852501	−	3.18158i
$190$	6.55008	−	9.35449i	0.475193	−	0.678646i
$191$	−12.3581	+	1.08119i	−0.894201	+	0.0782324i	−0.524985	−	0.851111i	$-0.675929\pi$
$191$	−12.3581	+	1.08119i	−0.894201	+	0.0782324i	−0.369216	+	0.929344i	$0.620374\pi$
$192$			29.8654i			2.15535i
$193$	1.72070	+	19.6677i	0.123859	+	1.41571i	0.762889	+	0.646529i	$0.223780\pi$
$193$	1.72070	+	19.6677i	0.123859	+	1.41571i	−0.639031	+	0.769181i	$0.720664\pi$
$194$	7.10098	−	19.5098i	0.509821	−	1.40072i
$195$	−9.15127	−	5.28349i	−0.655336	−	0.378358i
$196$	−9.33621	−	1.64623i	−0.666872	−	0.117588i
$197$	−1.84370	−	1.84370i	−0.131358	−	0.131358i	0.638371	−	0.769729i	$-0.279609\pi$
$197$	−1.84370	−	1.84370i	−0.131358	−	0.131358i	−0.769729	+	0.638371i	$0.779609\pi$
$198$	−34.0326	+	9.11902i	−2.41859	+	0.648060i
$199$	−21.4117	−	14.9926i	−1.51783	−	1.06280i	−0.974798	−	0.223089i	$-0.928386\pi$
$199$	−21.4117	−	14.9926i	−1.51783	−	1.06280i	−0.543035	−	0.839710i	$-0.682725\pi$
$200$	14.4372	−	2.54567i	1.02086	−	0.180006i
$201$	32.2480	+	11.7373i	2.27460	+	0.827886i
$202$	4.95504	+	18.4925i	0.348636	+	1.30113i
$203$	−8.06444	+	6.76687i	−0.566013	+	0.474941i
$204$	−1.62719	−	0.758771i	−0.113926	−	0.0531246i
$205$	−0.634027	+	7.24697i	−0.0442824	+	0.506150i
$206$	−14.4187	−	1.26147i	−1.00460	−	0.0878911i
$207$	1.03018	−	1.22772i	0.0716024	−	0.0853324i
$208$	−6.67360	+	4.67291i	−0.462731	+	0.324008i
$209$	−4.76088	+	4.76088i	−0.329317	+	0.329317i
$210$	−16.2793	+	28.1965i	−1.12338	+	1.94575i
$211$	5.24213	+	9.07964i	0.360883	+	0.625068i	0.988106	−	0.153771i	$-0.0491419\pi$
$211$	5.24213	+	9.07964i	0.360883	+	0.625068i	−0.627223	+	0.778840i	$0.715809\pi$
$212$	18.3413	+	4.91453i	1.25968	+	0.337531i
$213$	16.8437	+	20.0735i	1.15411	+	1.37542i
$214$	−10.9360	−	15.6183i	−0.747571	−	1.06764i
$215$	−1.57677	+	0.573896i	−0.107535	+	0.0391394i
$216$	−58.6489	+	33.8610i	−3.99056	+	2.30395i
$217$	1.25163	+	7.09834i	0.0849661	+	0.481866i
$218$	−6.18235			−0.418722
$219$	−27.7089	−	1.29659i	−1.87239	−	0.0876154i
$220$	10.0768			0.679379
$221$	0.0597022	+	0.338588i	0.00401600	+	0.0227759i
$222$	−40.7123	+	23.5052i	−2.73243	+	1.57757i
$223$	12.0962	−	4.40266i	0.810022	−	0.294824i	0.0963894	−	0.995344i	$-0.469271\pi$
$223$	12.0962	−	4.40266i	0.810022	−	0.294824i	0.713633	+	0.700520i	$0.247048\pi$
$224$	−1.78979	−	2.55609i	−0.119585	−	0.170786i
$225$	−15.4676	−	18.4336i	−1.03117	−	1.22890i
$226$	12.8004	+	3.42984i	0.851467	+	0.228150i
$227$	4.08478	+	7.07505i	0.271117	+	0.469588i	0.969148	−	0.246479i	$-0.0792737\pi$
$227$	4.08478	+	7.07505i	0.271117	+	0.469588i	−0.698031	+	0.716067i	$0.745940\pi$
$228$	−22.1023	+	38.2822i	−1.46376	+	2.53530i
$229$	16.6804	−	16.6804i	1.10227	−	1.10227i	0.108136	−	0.994136i	$-0.465512\pi$
$229$	16.6804	−	16.6804i	1.10227	−	1.10227i	0.994136	−	0.108136i	$-0.0344883\pi$
$230$	−0.568398	+	0.397997i	−0.0374791	+	0.0262431i
$231$	12.3390	−	14.7050i	0.811845	−	0.967520i
$232$	15.6843	+	1.37220i	1.02972	+	0.0900891i
$233$	−0.306016	+	3.49777i	−0.0200477	+	0.229147i	0.979560	+	0.201151i	$0.0644681\pi$
$233$	−0.306016	+	3.49777i	−0.0200477	+	0.229147i	−0.999608	+	0.0279960i	$0.991087\pi$
$234$	40.1467	+	18.7207i	2.62447	+	1.22381i
$235$	−13.3971	+	11.2415i	−0.873930	+	0.733314i
$236$	−13.3529	−	49.8337i	−0.869200	−	3.24390i
$237$	−28.7168	−	10.4521i	−1.86536	−	0.678934i
$238$	1.04324	−	0.183952i	0.0676234	−	0.0119238i
$239$	−2.71239	−	1.89923i	−0.175450	−	0.122851i	0.482553	−	0.875867i	$-0.339710\pi$
$239$	−2.71239	−	1.89923i	−0.175450	−	0.122851i	−0.658003	+	0.753016i	$0.728598\pi$
$240$	14.1989	−	3.80458i	0.916534	−	0.245585i
$241$	14.8886	+	14.8886i	0.959061	+	0.959061i	0.999194	−	0.0401333i	$-0.0127783\pi$
$241$	14.8886	+	14.8886i	0.959061	+	0.959061i	−0.0401333	+	0.999194i	$0.512778\pi$
$242$	17.4391	+	3.07498i	1.12103	+	0.197667i
$243$	32.6634	+	18.8582i	2.09536	+	1.20976i
$244$	11.0212	−	30.2806i	0.705562	−	1.93852i
$245$	−0.285488	−	3.26314i	−0.0182391	−	0.208474i
$246$		−	42.6279i		−	2.71786i
$247$	8.43274	−	0.737769i	0.536562	−	0.0469431i
$248$	6.18296	−	8.83018i	0.392618	−	0.560717i
$249$	−13.2257	+	49.3589i	−0.838143	+	3.12799i
$250$	11.3017	+	24.2365i	0.714781	+	1.53285i
$251$	−8.17156	−	6.85675i	−0.515784	−	0.432794i	0.347375	−	0.937726i	$-0.387073\pi$
$251$	−8.17156	−	6.85675i	−0.515784	−	0.432794i	−0.863159	+	0.504932i	$0.831518\pi$
$252$	38.1035	−	81.7132i	2.40030	−	5.14745i
$253$	0.370775	−	0.172895i	0.0233104	−	0.0108698i
$254$	14.5895	+	40.0842i	0.915425	+	2.51511i
$255$	0.107722	−	0.610922i	0.00674582	−	0.0382574i
$256$	−5.36135	+	30.4057i	−0.335085	+	1.90036i
$257$	−0.374632	−	1.02929i	−0.0233689	−	0.0642055i	0.927460	−	0.373923i	$-0.121988\pi$
$257$	−0.374632	−	1.02929i	−0.0233689	−	0.0642055i	−0.950829	+	0.309718i	$0.899765\pi$
$258$	8.91127	−	4.15539i	0.554791	−	0.258703i
$259$	7.74361	−	16.6062i	0.481165	−	1.03186i
$260$	−9.70508	−	8.14353i	−0.601884	−	0.505040i
$261$	−10.9217	−	23.4218i	−0.676039	−	1.44977i
$262$	2.40849	−	8.98860i	0.148797	−	0.555317i
$263$	8.72119	−	12.4552i	0.537772	−	0.768018i	−0.454680	−	0.890655i	$-0.650246\pi$
$263$	8.72119	−	12.4552i	0.537772	−	0.768018i	0.992452	+	0.122637i	$0.0391352\pi$
$264$	−28.5993	+	2.50212i	−1.76017	+	0.153995i
$265$			6.56082i			0.403028i
$266$	−2.27318	−	25.9826i	−0.139378	−	1.59310i
$267$	−15.2849	+	41.9949i	−0.935421	+	2.57005i
$268$	35.6322	+	20.5722i	2.17658	+	1.25665i
$269$	−15.1593	−	2.67299i	−0.924278	−	0.162975i	−0.308798	−	0.951128i	$-0.599927\pi$
$269$	−15.1593	−	2.67299i	−0.924278	−	0.162975i	−0.615480	+	0.788152i	$0.711038\pi$
$270$	−34.0315	−	34.0315i	−2.07109	−	2.07109i
$271$	17.8259	−	4.77644i	1.08285	−	0.290148i	0.327085	−	0.944995i	$-0.393933\pi$
$271$	17.8259	−	4.77644i	1.08285	−	0.290148i	0.755762	+	0.654847i	$0.227267\pi$
$272$	−0.391782	−	0.274329i	−0.0237553	−	0.0166336i
$273$	−23.7676	+	4.19087i	−1.43848	+	0.253643i
$274$	−18.6118	−	6.77412i	−1.12438	−	0.409240i
$275$	−1.58980	−	5.93320i	−0.0958682	−	0.357785i
$276$	2.05756	−	1.72650i	0.123851	−	0.103923i
$277$	−5.11585	−	2.38556i	−0.307382	−	0.143334i	0.262807	−	0.964849i	$-0.415352\pi$
$277$	−5.11585	−	2.38556i	−0.307382	−	0.143334i	−0.570188	+	0.821514i	$0.693130\pi$
$278$	−0.773828	+	8.84490i	−0.0464111	+	0.530482i
$279$	−17.6268	−	1.54214i	−1.05529	−	0.0923257i
$280$	−12.1992	+	14.5385i	−0.729045	+	0.868842i
$281$	−10.7505	+	7.52757i	−0.641320	+	0.449057i	−0.848464	−	0.529253i	$-0.822472\pi$
$281$	−10.7505	+	7.52757i	−0.641320	+	0.449057i	0.207144	+	0.978311i	$0.433583\pi$
$282$	72.4643	−	72.4643i	4.31519	−	4.31519i
$283$	4.03665	−	6.99169i	0.239954	−	0.415613i	−0.720747	−	0.693198i	$-0.756201\pi$
$283$	4.03665	−	6.99169i	0.239954	−	0.415613i	0.960701	+	0.277586i	$0.0895343\pi$
$284$	15.7085	+	27.2079i	0.932127	+	1.61449i
$285$	−14.7531	−	3.95308i	−0.873897	−	0.234160i
$286$	7.26827	+	8.66198i	0.429782	+	0.512194i
$287$	9.52986	+	13.6100i	0.562530	+	0.803375i
$288$	7.19814	−	2.61991i	0.424155	−	0.154380i
$289$	14.7050	−	8.48991i	0.864997	−	0.499406i
$290$	1.94293	+	11.0189i	0.114093	+	0.647052i
$291$	−27.7683			−1.62781
$292$	−32.4464	−	7.29969i	−1.89878	−	0.427182i
$293$	−13.6581			−0.797915			−0.398957	−	0.916969i	$-0.630628\pi$
$293$	−13.6581			−0.797915			−0.398957	+	0.916969i	$0.630628\pi$
$294$	3.33307	+	18.9028i	0.194388	+	1.10243i
$295$	15.4377	−	8.91296i	0.898818	−	0.518933i
$296$	−25.7502	+	9.37232i	−1.49670	+	0.544755i
$297$	16.2755	+	23.2438i	0.944400	+	1.34874i
$298$	0.416381	+	0.496223i	0.0241203	+	0.0287454i
$299$	−0.496822	−	0.133123i	−0.0287319	−	0.00769870i
$300$	−20.1641	−	34.9253i	−1.16418	−	2.01641i
$301$	−1.91617	+	3.31891i	−0.110446	+	0.191299i
$302$	−2.46072	+	2.46072i	−0.141598	+	0.141598i
$303$	20.9749	−	14.6868i	1.20497	−	0.843732i
$304$	−7.56923	+	9.02066i	−0.434125	+	0.517370i
$305$	11.0916	+	0.970392i	0.635105	+	0.0555645i
$306$	−0.226649	+	2.59061i	−0.0129567	+	0.148095i
$307$	−11.3329	−	5.28462i	−0.646802	−	0.301609i	0.0713952	−	0.997448i	$-0.477255\pi$
$307$	−11.3329	−	5.28462i	−0.646802	−	0.301609i	−0.718198	+	0.695839i	$0.755033\pi$
$308$	17.6303	−	14.7936i	1.00458	−	0.842944i
$309$	5.01028	+	18.6986i	0.285025	+	1.06373i
$310$	7.19875	+	2.62013i	0.408862	+	0.148813i
$311$	−22.0945	+	3.89586i	−1.25286	+	0.220914i	−0.760421	−	0.649431i	$-0.775007\pi$
$311$	−22.0945	+	3.89586i	−1.25286	+	0.220914i	−0.492444	+	0.870344i	$0.663896\pi$
$312$	29.5664	+	20.7026i	1.67387	+	1.17205i
$313$	−20.2099	+	5.41522i	−1.14233	+	0.306086i	−0.779887	−	0.625920i	$-0.784724\pi$
$313$	−20.2099	+	5.41522i	−1.14233	+	0.306086i	−0.362442	+	0.932006i	$0.618057\pi$
$314$	−12.7391	−	12.7391i	−0.718907	−	0.718907i
$315$	30.6790	+	5.40953i	1.72856	+	0.304792i
$316$	−31.7304	−	18.3195i	−1.78497	−	1.03056i
$317$	6.21421	−	17.0734i	0.349025	−	0.958938i	−0.633653	−	0.773617i	$-0.718445\pi$
$317$	6.21421	−	17.0734i	0.349025	−	0.958938i	0.982678	−	0.185321i	$-0.0593325\pi$
$318$	−3.35071	−	38.2988i	−0.187898	−	2.14769i
$319$		−	6.59680i		−	0.369350i
$320$	−12.3248	+	1.07828i	−0.688978	+	0.0602777i
$321$	−14.6266	+	20.8889i	−0.816377	+	1.16591i
$322$	−0.410173	+	1.53079i	−0.0228581	+	0.0853074i
$323$	0.210018	+	0.450385i	0.0116857	+	0.0250601i
$324$	75.2579	+	63.1489i	4.18100	+	3.50827i
$325$	−3.26374	+	6.99910i	−0.181040	+	0.388240i
$326$	1.95654	−	0.912348i	0.108362	−	0.0505303i
$327$	2.82806	+	7.77003i	0.156392	+	0.429684i
$328$	4.31484	−	24.4707i	0.238247	−	1.35117i
$329$	−6.93601	+	39.3361i	−0.382395	+	2.16867i
$330$	−6.97798	−	19.1718i	−0.384125	−	1.05538i
$331$	25.7343	−	12.0001i	1.41449	−	0.659586i	0.442965	−	0.896539i	$-0.353927\pi$
$331$	25.7343	−	12.0001i	1.41449	−	0.659586i	0.971521	+	0.236953i	$0.0761487\pi$
$332$	−25.8919	+	55.5254i	−1.42100	+	3.04735i
$333$	34.4566	+	28.9125i	1.88821	+	1.58440i
$334$	−3.13338	−	6.71956i	−0.171451	−	0.367678i
$335$	−3.67943	+	13.7318i	−0.201029	+	0.750249i
$336$	19.2568	−	27.5016i	1.05055	−	1.50034i
$337$	15.6628	−	1.37031i	0.853206	−	0.0746458i	0.347843	−	0.937553i	$-0.386914\pi$
$337$	15.6628	−	1.37031i	0.853206	−	0.0746458i	0.505363	+	0.862907i	$0.331359\pi$
$338$			17.3405i			0.943200i
$339$	−1.54475	−	17.6565i	−0.0838992	−	0.958972i
$340$	0.254379	−	0.698900i	0.0137956	−	0.0379032i
$341$	−3.91155	−	2.25833i	−0.211822	−	0.122296i
$342$	63.0541	+	11.1181i	3.40958	+	0.601200i
$343$	9.91424	+	9.91424i	0.535318	+	0.535318i
$344$	5.53615	−	1.48341i	0.298489	−	0.0799800i
$345$	0.760214	+	0.532308i	0.0409286	+	0.0286585i
$346$	13.4483	−	2.37130i	0.722986	−	0.127482i
$347$	−5.55467	−	2.02173i	−0.298190	−	0.108532i	0.188593	−	0.982055i	$-0.439607\pi$
$347$	−5.55467	−	2.02173i	−0.298190	−	0.108532i	−0.486783	+	0.873523i	$0.661830\pi$
$348$	−11.2097	−	41.8352i	−0.600903	−	2.24260i
$349$	2.37884	−	1.99609i	0.127337	−	0.106848i	−0.576895	−	0.816818i	$-0.695736\pi$
$349$	2.37884	−	1.99609i	0.127337	−	0.106848i	0.704232	+	0.709970i	$0.251292\pi$
$350$	21.5654	+	10.0561i	1.15272	+	0.537521i
$351$	3.10929	−	35.5393i	0.165961	−	1.89695i
$352$	1.94791	+	0.170420i	0.103824	+	0.00908341i
$353$	12.0514	−	14.3623i	0.641432	−	0.764428i	−0.343164	−	0.939275i	$-0.611499\pi$
$353$	12.0514	−	14.3623i	0.641432	−	0.764428i	0.984596	+	0.174847i	$0.0559431\pi$
$354$	−85.5655	+	59.9136i	−4.54776	+	3.18437i
$355$	−7.67577	+	7.67577i	−0.407387	+	0.407387i
$356$	−26.7902	+	46.4020i	−1.41988	+	2.45930i
$357$	−0.708415	−	1.22701i	−0.0374933	−	0.0649403i
$358$	−6.77115	−	1.81432i	−0.357866	−	0.0958899i
$359$	−11.9293	−	14.2168i	−0.629605	−	0.750334i	0.353085	−	0.935591i	$-0.385133\pi$
$359$	−11.9293	−	14.2168i	−0.629605	−	0.750334i	−0.982690	+	0.185257i	$0.940688\pi$
$360$	−26.7227	−	38.1640i	−1.40841	−	2.01142i
$361$	−6.35679	+	2.31368i	−0.334568	+	0.121773i
$362$	−25.9250	+	14.9678i	−1.36259	+	0.786691i
$363$	−4.11269	−	23.3242i	−0.215860	−	1.22421i
$364$	−28.9353			−1.51662
$365$	−0.465346	−	11.4817i	−0.0243573	−	0.600978i
$366$	−65.2429			−3.41030
$367$	2.06258	+	11.6975i	0.107666	+	0.610604i	0.990122	+	0.140209i	$0.0447774\pi$
$367$	2.06258	+	11.6975i	0.107666	+	0.610604i	−0.882456	+	0.470395i	$0.844111\pi$
$368$	0.619651	−	0.357756i	0.0323016	−	0.0186493i
$369$	−38.3269	+	13.9499i	−1.99522	+	0.726201i
$370$	−11.1700	−	15.9524i	−0.580701	−	0.829326i
$371$	9.63183	+	11.4788i	0.500060	+	0.595948i
$372$	−28.6435	−	7.67500i	−1.48510	−	0.397930i
$373$	11.3797	+	19.7103i	0.589221	+	1.02056i	0.994335	+	0.106294i	$0.0338984\pi$
$373$	11.3797	+	19.7103i	0.589221	+	1.02056i	−0.405114	+	0.914266i	$0.632768\pi$
$374$	−0.331908	+	0.574881i	−0.0171625	+	0.0297264i
$375$	25.2908	−	25.2908i	1.30601	−	1.30601i
$376$	48.9333	−	34.2634i	2.52354	−	1.76700i
$377$	−5.33118	+	6.35345i	−0.274569	+	0.327219i
$378$	−109.502	−	9.58021i	−5.63219	−	0.492753i
$379$	2.66366	−	30.4458i	0.136823	−	1.56389i	−0.548811	−	0.835947i	$-0.684919\pi$
$379$	2.66366	−	30.4458i	0.136823	−	1.56389i	0.685634	−	0.727947i	$-0.259525\pi$
$380$	−16.5962	−	7.73895i	−0.851368	−	0.397000i
$381$	43.7044	−	36.6723i	2.23904	−	1.87878i
$382$	7.79387	+	29.0871i	0.398769	+	1.48823i
$383$	21.4904	+	7.82186i	1.09811	+	0.399679i	0.826618	−	0.562763i	$-0.190262\pi$
$383$	21.4904	+	7.82186i	1.09811	+	0.399679i	0.271489	+	0.962441i	$0.412484\pi$
$384$	64.8994	−	11.4435i	3.31188	−	0.583974i
$385$	6.51393	+	4.56111i	0.331981	+	0.232455i
$386$	46.2916	−	12.4038i	2.35618	−	0.631336i
$387$	−6.65231	−	6.65231i	−0.338156	−	0.338156i
$388$	−32.7866	−	5.78116i	−1.66449	−	0.293494i
$389$	0.823690	+	0.475558i	0.0417628	+	0.0241117i	0.520736	−	0.853718i	$-0.325658\pi$
$389$	0.823690	+	0.475558i	0.0417628	+	0.0241117i	−0.478973	+	0.877829i	$0.658991\pi$
$390$	−8.77307	+	24.1038i	−0.444242	+	1.22054i
$391$	−0.00263170	−	0.0300805i	−0.000133091	−	0.00152124i
$392$			11.1886i			0.565108i
$393$	−12.3987	+	1.08474i	−0.625431	+	0.0547181i
$394$	−3.63033	+	5.18465i	−0.182893	+	0.261199i
$395$	3.27652	−	12.2282i	0.164860	−	0.615265i
$396$	23.8769	+	51.2042i	1.19986	+	2.57311i
$397$	−9.52786	−	7.99482i	−0.478190	−	0.401249i	0.371582	−	0.928400i	$-0.378816\pi$
$397$	−9.52786	−	7.99482i	−0.478190	−	0.401249i	−0.849771	+	0.527152i	$0.823260\pi$
$398$	−26.8154	+	57.5057i	−1.34413	+	2.88250i
$399$	−31.6153	+	14.7425i	−1.58275	+	0.738047i
$400$	−3.67433	−	10.0951i	−0.183717	−	0.504757i
$401$	−2.92100	+	16.5658i	−0.145868	+	0.827256i	0.820799	+	0.571217i	$0.193529\pi$
$401$	−2.92100	+	16.5658i	−0.145868	+	0.827256i	−0.966666	+	0.256039i	$0.917583\pi$
$402$	14.4656	−	82.0385i	0.721479	−	4.09171i
$403$	1.94219	+	5.33612i	0.0967474	+	0.265811i
$404$	27.8231	−	12.9741i	1.38425	−	0.645486i
$405$	−14.3456	+	30.7643i	−0.712839	+	1.52869i
$406$	19.5760	+	16.4262i	0.971540	+	0.815219i
$407$	4.85240	+	10.4060i	0.240525	+	0.515807i
$408$	−0.548421	+	2.04673i	−0.0271509	+	0.101328i
$409$	8.97742	−	12.8211i	0.443905	−	0.633962i	−0.533384	−	0.845873i	$-0.679080\pi$
$409$	8.97742	−	12.8211i	0.443905	−	0.633962i	0.977289	+	0.211911i	$0.0679688\pi$
$410$	17.5916	−	1.53907i	0.868788	−	0.0760091i
$411$			26.4902i			1.30666i
$412$	2.02282	+	23.1209i	0.0996570	+	1.13908i
$413$	13.9247	−	38.2579i	0.685191	−	1.88255i
$414$	−3.36919	−	1.94520i	−0.165586	−	0.0956014i
$415$	−20.8468	−	3.67586i	−1.02333	−	0.180441i
$416$	−1.73833	−	1.73833i	−0.0852284	−	0.0852284i
$417$	11.4703	−	3.07346i	0.561704	−	0.150508i
$418$	13.3880	+	9.37439i	0.654829	+	0.458517i
$419$	−3.52066	+	0.620787i	−0.171995	+	0.0303274i	−0.258983	−	0.965882i	$-0.583387\pi$
$419$	−3.52066	+	0.620787i	−0.171995	+	0.0303274i	0.0869871	+	0.996209i	$0.472276\pi$
$420$	49.0601	+	17.8564i	2.39389	+	0.871305i
$421$	−5.93630	−	22.1546i	−0.289317	−	1.07975i	−0.945626	−	0.325255i	$-0.894550\pi$
$421$	−5.93630	−	22.1546i	−0.289317	−	1.07975i	0.656309	−	0.754492i	$-0.272117\pi$
$422$	19.4958	−	16.3589i	0.949041	−	0.796340i
$423$	−88.8666	−	41.4392i	−4.32084	−	2.01484i
$424$	1.95316	−	22.3247i	0.0948537	−	1.08418i
$425$	−0.451643	−	0.0395136i	−0.0219079	−	0.00191669i
$426$	40.8871	−	48.7274i	1.98099	−	2.36085i
$427$	20.8304	−	14.5856i	1.00806	−	0.705848i
$428$	−21.6188	+	21.6188i	−1.04498	+	1.04498i
$429$	7.56165	−	13.0972i	0.365080	−	0.632337i
$430$	2.03658	+	3.52745i	0.0982124	+	0.170109i
$431$	23.7800	+	6.37182i	1.14544	+	0.306920i	0.781137	−	0.624360i	$-0.214640\pi$
$431$	23.7800	+	6.37182i	1.14544	+	0.306920i	0.364304	+	0.931280i	$0.381307\pi$
$432$	31.9001	+	38.0171i	1.53479	+	1.82910i
$433$	−11.3176	−	16.1632i	−0.543888	−	0.776752i	0.449287	−	0.893387i	$-0.351678\pi$
$433$	−11.3176	−	16.1632i	−0.543888	−	0.776752i	−0.993175	+	0.116635i	$0.962789\pi$
$434$	16.4415	−	5.98420i	0.789215	−	0.287251i
$435$	12.9599	−	7.48239i	0.621378	−	0.358753i
$436$	1.72148	+	9.76299i	0.0824439	+	0.467563i
$437$	−0.743439			−0.0355635
$438$	8.58031	+	66.7865i	0.409983	+	3.19118i
$439$	26.3114			1.25578			0.627888	−	0.778304i	$-0.283920\pi$
$439$	26.3114			1.25578			0.627888	+	0.778304i	$0.283920\pi$
$440$	−2.06514	−	11.7120i	−0.0984516	−	0.558347i
$441$	15.9048	−	9.18265i	0.757372	−	0.437269i
$442$	0.784251	−	0.285444i	0.0373030	−	0.0135772i
$443$	12.4970	+	17.8476i	0.593752	+	0.847966i	0.997767	−	0.0667864i	$-0.0212746\pi$
$443$	12.4970	+	17.8476i	0.593752	+	0.847966i	−0.404015	+	0.914752i	$0.632386\pi$
$444$	48.4552	+	57.7466i	2.29958	+	2.74053i
$445$	−17.8822	−	4.79153i	−0.847699	−	0.227140i
$446$	−15.6237	−	27.0610i	−0.739802	−	1.28138i
$447$	0.433188	−	0.750304i	0.0204891	−	0.0354881i
$448$	−19.9804	+	19.9804i	−0.943985	+	0.943985i
$449$	27.1040	−	18.9784i	1.27912	−	0.895647i	0.281167	−	0.959659i	$-0.409279\pi$
$449$	27.1040	−	18.9784i	1.27912	−	0.895647i	0.997949	+	0.0640124i	$0.0203897\pi$
$450$	−37.5467	+	44.7464i	−1.76997	+	2.10937i
$451$	−10.3718	−	0.907411i	−0.488387	−	0.0427283i
$452$	1.85205	−	21.1690i	0.0871130	−	0.995706i
$453$	4.21828	+	1.96702i	0.198192	+	0.0924186i
$454$	15.1916	−	12.7472i	0.712976	−	0.598257i
$455$	−2.58760	−	9.65705i	−0.121309	−	0.452730i
$456$	49.0239	+	17.8432i	2.29575	+	0.835586i
$457$	−18.0534	+	3.18330i	−0.844502	+	0.148909i	−0.579128	−	0.815237i	$-0.696607\pi$
$457$	−18.0534	+	3.18330i	−0.844502	+	0.148909i	−0.265375	+	0.964145i	$0.585496\pi$
$458$	−46.9068	−	32.8445i	−2.19181	−	1.53472i
$459$	2.02298	−	0.542057i	0.0944248	−	0.0253011i
$460$	0.786776	+	0.786776i	0.0366836	+	0.0366836i
$461$	−23.9596	−	4.22472i	−1.11591	−	0.196765i	−0.414866	−	0.909883i	$-0.636171\pi$
$461$	−23.9596	−	4.22472i	−1.11591	−	0.196765i	−0.701044	+	0.713118i	$0.747282\pi$
$462$	−40.3545	−	23.2987i	−1.87746	−	1.08395i
$463$	−14.6476	+	40.2439i	−0.680731	+	1.87029i	−0.248051	+	0.968747i	$0.579790\pi$
$463$	−14.6476	+	40.2439i	−0.680731	+	1.87029i	−0.432680	+	0.901547i	$0.642432\pi$
$464$	−1.00557	−	11.4937i	−0.0466823	−	0.533581i
$465$		−	10.2460i		−	0.475147i
$466$	8.49065	−	0.742836i	0.393322	−	0.0344112i
$467$	11.0876	−	15.8347i	0.513072	−	0.732743i	−0.476118	−	0.879381i	$-0.657957\pi$
$467$	11.0876	−	15.8347i	0.513072	−	0.732743i	0.989190	+	0.146639i	$0.0468454\pi$
$468$	18.3843	−	68.6113i	0.849816	−	3.17156i
$469$	13.7219	+	29.4268i	0.633620	+	1.35880i
$470$	32.5207	+	27.2881i	1.50007	+	1.25871i
$471$	−10.1832	+	21.8379i	−0.469217	+	1.00624i
$472$	−55.1837	+	25.7326i	−2.54003	+	1.18444i
$473$	−0.821352	−	2.25665i	−0.0377658	−	0.103761i
$474$	−12.8816	+	73.0552i	−0.591671	+	3.35554i
$475$	−1.93832	+	10.9928i	−0.0889362	+	0.504382i
$476$	−0.580984	−	1.59624i	−0.0266293	−	0.0731635i
$477$	−33.3381	+	15.5458i	−1.52644	+	0.711793i
$478$	−3.39692	+	7.28471i	−0.155371	+	0.333195i
$479$	7.88287	+	6.61451i	0.360177	+	0.302225i	0.804861	−	0.593463i	$-0.202240\pi$
$479$	7.88287	+	6.61451i	0.360177	+	0.302225i	−0.444684	+	0.895687i	$0.646684\pi$
$480$	1.87460	+	4.02010i	0.0855635	+	0.183492i
$481$	3.73617	−	13.9436i	0.170355	−	0.635773i
$482$	29.3164	−	41.8681i	1.33532	−	1.90704i
$483$	2.11154	−	0.184736i	0.0960783	−	0.00840576i
$484$		−	28.3956i		−	1.29071i
$485$	−1.00257	−	11.4594i	−0.0455242	−	0.520344i
$486$	31.3135	−	86.0332i	1.42041	−	3.90255i
$487$	0.327139	+	0.188874i	0.0148241	+	0.00855869i	0.507394	−	0.861714i	$-0.330609\pi$
$487$	0.327139	+	0.188874i	0.0148241	+	0.00855869i	−0.492570	+	0.870273i	$0.663942\pi$
$488$	−37.4529	−	6.60396i	−1.69541	−	0.298947i
$489$	−2.04165	−	2.04165i	−0.0923264	−	0.0923264i
$490$	−7.68041	+	2.05796i	−0.346966	+	0.0929692i
$491$	33.0752	+	23.1595i	1.49266	+	1.04517i	0.982748	+	0.184948i	$0.0592117\pi$
$491$	33.0752	+	23.1595i	1.49266	+	1.04517i	0.509914	+	0.860225i	$0.329677\pi$
$492$	−67.3169	+	11.8698i	−3.03488	+	0.535131i
$493$	−0.457536	−	0.166529i	−0.0206064	−	0.00750011i
$494$	−5.31826	−	19.8480i	−0.239280	−	0.893005i
$495$	−14.9540	+	12.5479i	−0.672131	+	0.563984i
$496$	−7.15939	−	3.33848i	−0.321466	−	0.149902i
$497$	−2.16081	+	24.6981i	−0.0969254	+	1.10786i
$498$	123.571	+	10.8110i	5.53733	+	0.484454i
$499$	−10.0808	+	12.0139i	−0.451280	+	0.537814i	−0.942936	−	0.332975i	$-0.891947\pi$
$499$	−10.0808	+	12.0139i	−0.451280	+	0.537814i	0.491656	+	0.870790i	$0.336392\pi$
$500$	35.1267	−	24.5960i	1.57091	−	1.09997i
$501$	−7.01187	+	7.01187i	−0.313267	+	0.313267i
$502$	−12.9470	+	22.4249i	−0.577855	+	1.00087i
$503$	−8.18912	−	14.1840i	−0.365135	−	0.632432i	0.623663	−	0.781693i	$-0.285644\pi$
$503$	−8.18912	−	14.1840i	−0.365135	−	0.632432i	−0.988798	+	0.149261i	$0.952310\pi$
$504$	−102.782	−	27.5403i	−4.57826	−	1.22674i
$505$	6.81819	+	8.12560i	0.303405	+	0.361585i
$506$	−0.569607	−	0.813483i	−0.0253221	−	0.0361638i
$507$	21.7937	−	7.93227i	0.967893	−	0.352284i
$508$	59.2375	−	34.2008i	2.62824	−	1.51741i
$509$	−1.90747	−	10.8178i	−0.0845469	−	0.479489i	−0.997453	−	0.0713207i	$-0.977279\pi$
$509$	−1.90747	−	10.8178i	−0.0845469	−	0.479489i	0.912907	−	0.408169i	$-0.133832\pi$
$510$	−1.50586			−0.0666805
$511$	−17.6702	−	19.4051i	−0.781684	−	0.858430i
$512$	34.3506			1.51810
$513$	−8.95413	−	50.7814i	−0.395334	−	2.24205i
$514$	−2.30268	+	1.32945i	−0.101567	+	0.0586396i
$515$	−7.53562	+	2.74274i	−0.332059	+	0.120860i
$516$	−9.04343	−	12.9154i	−0.398115	−	0.568567i
$517$	−16.0887	−	19.1737i	−0.707579	−	0.843260i
$518$	−42.9624	−	11.5117i	−1.88766	−	0.505797i
$519$	−9.13208	−	15.8172i	−0.400854	−	0.694299i
$520$	−7.47602	+	12.9489i	−0.327845	+	0.567845i
$521$	−7.93560	+	7.93560i	−0.347665	+	0.347665i	−0.859239	−	0.511574i	$-0.829063\pi$
$521$	−7.93560	+	7.93560i	−0.347665	+	0.347665i	0.511574	+	0.859239i	$0.329063\pi$
$522$	−51.3875	+	35.9819i	−2.24917	+	1.57489i
$523$	−17.1035	+	20.3832i	−0.747884	+	0.891293i	−0.997018	−	0.0771757i	$-0.975410\pi$
$523$	−17.1035	+	20.3832i	−0.747884	+	0.891293i	0.249133	+	0.968469i	$0.419854\pi$
$524$	−14.8652	−	1.30054i	−0.649389	−	0.0568141i
$525$	2.77371	−	31.7036i	0.121054	−	1.38366i
$526$	−33.4510	−	15.5985i	−1.45853	−	0.680126i
$527$	−0.255375	+	0.214285i	−0.0111243	+	0.00933440i
$528$	5.44506	+	20.3213i	0.236966	+	0.884369i
$529$	−21.5705	−	7.85101i	−0.937847	−	0.341348i
$530$	15.6841	−	2.76553i	0.681273	−	0.120127i
$531$	81.8696	+	57.3257i	3.55284	+	2.48773i
$532$	−40.3981	+	10.8246i	−1.75148	+	0.469307i
$533$	9.25582	+	9.25582i	0.400914	+	0.400914i
$534$	106.835	+	18.8378i	4.62318	+	0.815192i
$535$	−9.14849	−	5.28188i	−0.395524	−	0.228356i
$536$	16.6081	−	45.6302i	0.717359	−	1.97093i
$537$	0.817142	+	9.33998i	0.0352623	+	0.403050i
$538$			37.3660i			1.61096i
$539$	4.67016	−	0.408586i	0.201158	−	0.0175991i
$540$	−44.2655	+	63.2177i	−1.90488	+	2.72046i
$541$	10.0287	−	37.4277i	0.431168	−	1.60914i	−0.318904	−	0.947787i	$-0.603315\pi$
$541$	10.0287	−	37.4277i	0.431168	−	1.60914i	0.750073	−	0.661355i	$-0.230019\pi$
$542$	−18.9324	−	40.6007i	−0.813216	−	1.74395i
$543$	30.6709	+	25.7359i	1.31621	+	1.10443i
$544$	0.0609928	−	0.130799i	0.00261504	−	0.00560798i
$545$	−3.10441	+	1.44761i	−0.132979	+	0.0620089i
$546$	20.0371	+	55.0515i	0.857509	+	2.35599i
$547$	3.30380	−	18.7368i	0.141260	−	0.801126i	−0.829034	−	0.559198i	$-0.811109\pi$
$547$	3.30380	−	18.7368i	0.141260	−	0.801126i	0.970294	−	0.241928i	$-0.0777798\pi$
$548$	−5.51505	+	31.2774i	−0.235591	+	1.33611i
$549$	21.3506	+	58.6602i	0.911219	+	2.50355i
$550$	−13.5136	+	6.30148i	−0.576220	+	0.268696i
$551$	−5.06631	+	10.8647i	−0.215832	+	0.462854i
$552$	−2.42833	−	2.03761i	−0.103357	−	0.0867266i
$553$	−12.2194	−	26.2045i	−0.519620	−	1.11433i
$554$	−3.54640	+	13.2353i	−0.150672	+	0.562316i
$555$	−14.9395	+	21.3358i	−0.634147	+	0.905656i
$556$	14.1831	−	1.24086i	0.601497	−	0.0526242i
$557$		−	13.9653i		−	0.591729i	−0.955230	−	0.295865i	$-0.904392\pi$
$557$		−	13.9653i		−	0.591729i	0.955230	−	0.295865i	$-0.0956077\pi$
$558$	3.74347	+	42.7880i	0.158474	+	1.81136i
$559$	−1.03265	+	2.83717i	−0.0436762	+	0.119999i
$560$	12.0446	+	6.95394i	0.508976	+	0.293857i
$561$	0.874344	+	0.154170i	0.0369148	+	0.00650908i
$562$	22.5267	+	22.5267i	0.950232	+	0.950232i
$563$	−12.0580	+	3.23092i	−0.508183	+	0.136167i	−0.503795	−	0.863823i	$-0.668063\pi$
$563$	−12.0580	+	3.23092i	−0.508183	+	0.136167i	−0.00438772	+	0.999990i	$0.501397\pi$
$564$	−134.611	−	94.2559i	−5.66816	−	3.96889i
$565$	7.23070	−	1.27497i	0.304198	−	0.0536383i
$566$	−18.4156	−	6.70274i	−0.774067	−	0.281737i
$567$	20.0655	+	74.8855i	0.842672	+	3.14489i
$568$	28.4036	−	23.8335i	1.19179	−	1.00003i
$569$	30.6792	+	14.3059i	1.28614	+	0.599736i	0.940870	−	0.338767i	$-0.110010\pi$
$569$	30.6792	+	14.3059i	1.28614	+	0.599736i	0.345269	+	0.938504i	$0.387788\pi$
$570$	−3.23135	+	36.9345i	−0.135346	+	1.54702i
$571$	−29.8772	−	2.61391i	−1.25032	−	0.109389i	−0.557303	−	0.830309i	$-0.688164\pi$
$571$	−29.8772	−	2.61391i	−1.25032	−	0.109389i	−0.693018	+	0.720920i	$0.743719\pi$
$572$	11.6549	−	13.8898i	0.487316	−	0.580761i
$573$	32.9917	−	23.1010i	1.37825	−	0.965060i
$574$	28.5187	−	28.5187i	1.19035	−	1.19035i
$575$	0.339123	−	0.587379i	0.0141424	−	0.0244954i
$576$	−34.6827	−	60.0721i	−1.44511	−	2.50300i
$577$	16.2259	+	4.34773i	0.675495	+	0.180998i	0.580229	−	0.814453i	$-0.302963\pi$
$577$	16.2259	+	4.34773i	0.675495	+	0.180998i	0.0952662	+	0.995452i	$0.469630\pi$
$578$	−26.4941	−	31.5745i	−1.10201	−	1.31333i
$579$	−36.7649	−	52.5057i	−1.52790	−	2.18206i
$580$	16.8597	−	6.13644i	0.700062	−	0.254802i
$581$	−41.8699	+	24.1736i	−1.73706	+	1.00289i
$582$	11.7050	+	66.3821i	0.485186	+	2.75163i
$583$	−9.38976			−0.388884
$584$	−1.83465	+	39.2075i	−0.0759182	+	1.62242i
$585$	24.5428			1.01472
$586$	5.75718	+	32.6506i	0.237827	+	1.34878i
$587$	−14.5210	+	8.38371i	−0.599346	+	0.346033i	−0.768784	−	0.639508i	$-0.779138\pi$
$587$	−14.5210	+	8.38371i	−0.599346	+	0.346033i	0.169438	+	0.985541i	$0.445805\pi$
$588$	28.9226	−	10.5270i	1.19275	−	0.434125i
$589$	4.70782	+	6.72346i	0.193982	+	0.277035i
$590$	−27.8143	−	33.1478i	−1.14510	−	1.36468i
$591$	8.17677	+	2.19096i	0.336347	+	0.0901240i
$592$	10.0406	+	17.3909i	0.412667	+	0.714760i
$593$	22.8219	−	39.5287i	0.937184	−	1.62325i	0.166493	−	0.986043i	$-0.446756\pi$
$593$	22.8219	−	39.5287i	0.937184	−	1.62325i	0.770692	−	0.637208i	$-0.219911\pi$
$594$	48.7054	−	48.7054i	1.99841	−	1.99841i
$595$	0.480783	−	0.336648i	0.0197102	−	0.0138012i
$596$	0.667680	−	0.795710i	0.0273492	−	0.0325936i
$597$	84.5402	+	7.39631i	3.46000	+	0.302711i
$598$	−0.108818	+	1.24380i	−0.00444991	+	0.0508627i
$599$	40.2968	+	18.7907i	1.64648	+	0.767768i	0.999988	+	0.00485030i	$0.00154391\pi$
$599$	40.2968	+	18.7907i	1.64648	+	0.767768i	0.646496	+	0.762918i	$0.276234\pi$
$600$	−36.4601	+	30.5937i	−1.48848	+	1.24898i
$601$	5.35536	+	19.9865i	0.218450	+	0.815265i	0.984924	+	0.172990i	$0.0553428\pi$
$601$	5.35536	+	19.9865i	0.218450	+	0.815265i	−0.766474	+	0.642275i	$0.777991\pi$
$602$	8.74177	+	3.18175i	0.356288	+	0.129678i
$603$	−78.4950	+	13.8408i	−3.19656	+	0.563640i
$604$	4.57108	+	3.20071i	0.185995	+	0.130235i
$605$	9.47691	−	2.53933i	0.385291	−	0.103239i
$606$	−43.9510	−	43.9510i	−1.78539	−	1.78539i
$607$	22.9100	+	4.03965i	0.929889	+	0.163965i	0.618022	−	0.786161i	$-0.287934\pi$
$607$	22.9100	+	4.03965i	0.929889	+	0.163965i	0.311867	+	0.950126i	$0.399046\pi$
$608$	−3.07727	−	1.77666i	−0.124800	−	0.0720531i
$609$	11.6897	−	32.1173i	0.473692	−	1.30146i
$610$	−2.35557	−	26.9243i	−0.0953743	−	1.09013i
$611$			31.4684i			1.27308i
$612$	4.15413	−	0.363439i	0.167921	−	0.0146912i
$613$	−5.45803	+	7.79487i	−0.220448	+	0.314832i	−0.914108	−	0.405470i	$-0.867108\pi$
$613$	−5.45803	+	7.79487i	−0.220448	+	0.314832i	0.693661	+	0.720302i	$0.255997\pi$
$614$	−7.85617	+	29.3196i	−0.317049	+	1.18324i
$615$	−9.98144	−	21.4053i	−0.402490	−	0.863143i
$616$	−20.8073	−	17.4594i	−0.838350	−	0.703459i
$617$	17.4863	−	37.4994i	0.703971	−	1.50967i	−0.149630	−	0.988742i	$-0.547808\pi$
$617$	17.4863	−	37.4994i	0.703971	−	1.50967i	0.853601	−	0.520928i	$-0.174414\pi$
$618$	42.5884	−	19.8593i	1.71316	−	0.798857i
$619$	−0.445145	−	1.22302i	−0.0178919	−	0.0491575i	0.930425	−	0.366482i	$-0.119438\pi$
$619$	−0.445145	−	1.22302i	−0.0178919	−	0.0491575i	−0.948317	+	0.317324i	$0.897216\pi$
$620$	2.13314	−	12.0976i	0.0856690	−	0.485853i
$621$	−0.544071	+	3.08558i	−0.0218328	+	0.123820i
$622$	18.6266	+	51.1762i	0.746859	+	2.05198i
$623$	−38.3210	+	17.8694i	−1.53530	+	0.715921i
$624$	11.1783	−	23.9720i	0.447491	−	0.959648i
$625$	−0.872772	−	0.732342i	−0.0349109	−	0.0292937i
$626$	21.4643	+	46.0304i	0.857887	+	1.83975i
$627$	5.65759	−	21.1144i	0.225942	−	0.843228i
$628$	−16.5700	+	23.6644i	−0.661214	+	0.944312i
$629$	0.844226	−	0.0738602i	0.0336615	−	0.00294500i
$630$		−	75.6203i		−	3.01279i
$631$	1.60334	+	18.3262i	0.0638278	+	0.729555i	0.958920	+	0.283675i	$0.0915537\pi$
$631$	1.60334	+	18.3262i	0.0638278	+	0.729555i	−0.895093	+	0.445880i	$0.852891\pi$
$632$	−14.7894	+	40.6337i	−0.588292	+	1.61632i
$633$	−29.4782	−	17.0193i	−1.17165	−	0.676455i
$634$	−43.4346	−	7.65868i	−1.72501	−	0.304165i
$635$	16.7118	+	16.7118i	0.663187	+	0.663187i
$636$	−59.5473	+	15.9557i	−2.36121	+	0.632683i
$637$	−4.82808	−	3.38066i	−0.191295	−	0.133946i
$638$	−15.7701	+	2.78069i	−0.624344	+	0.110089i
$639$	−57.1912	−	20.8159i	−2.26245	−	0.823464i
$640$	7.06565	+	26.3694i	0.279294	+	1.04234i
$641$	−27.5925	+	23.1529i	−1.08984	+	0.914484i	−0.996700	−	0.0811690i	$-0.974135\pi$
$641$	−27.5925	+	23.1529i	−1.08984	+	0.914484i	−0.0931393	+	0.995653i	$0.529690\pi$
$642$	56.1018	+	26.1607i	2.21416	+	1.03248i
$643$	3.75375	−	42.9056i	0.148033	−	1.69203i	−0.451970	−	0.892033i	$-0.649279\pi$
$643$	3.75375	−	42.9056i	0.148033	−	1.69203i	0.600004	−	0.799997i	$-0.295166\pi$
$644$	2.53159	+	0.221485i	0.0997586	+	0.00872775i
$645$	3.50172	−	4.17319i	0.137880	−	0.164319i
$646$	0.988149	−	0.691909i	0.0388782	−	0.0272228i
$647$	−14.2344	+	14.2344i	−0.559611	+	0.559611i	−0.929197	−	0.369585i	$-0.879500\pi$
$647$	−14.2344	+	14.2344i	−0.559611	+	0.559611i	0.369585	+	0.929197i	$0.379500\pi$
$648$	57.9727	−	100.412i	2.27738	−	3.94455i
$649$	12.7561	+	22.0942i	0.500721	+	0.867274i
$650$	18.1076	+	4.85191i	0.710237	+	0.190307i
$651$	−15.0420	−	17.9263i	−0.589542	−	0.702589i
$652$	−1.98555	−	2.83566i	−0.0777602	−	0.111053i
$653$	9.21118	−	3.35259i	0.360461	−	0.131197i	−0.155440	−	0.987845i	$-0.549679\pi$
$653$	9.21118	−	3.35259i	0.360461	−	0.131197i	0.515901	+	0.856648i	$0.327457\pi$
$654$	17.3827	−	10.0359i	0.679717	−	0.392435i
$655$	−0.895300	−	5.07750i	−0.0349823	−	0.198394i
$656$	−18.2092			−0.710948
$657$	57.2401	−	29.5703i	2.23315	−	1.15365i
$658$	96.9592			3.77986
$659$	0.542959	+	3.07928i	0.0211507	+	0.119952i	0.993555	−	0.113350i	$-0.0361582\pi$
$659$	0.542959	+	3.07928i	0.0211507	+	0.119952i	−0.972404	+	0.233302i	$0.925047\pi$
$660$	−28.3326	+	16.3578i	−1.10285	+	0.636728i
$661$	−23.0282	+	8.38159i	−0.895694	+	0.326006i	−0.748526	−	0.663105i	$-0.769238\pi$
$661$	−23.0282	+	8.38159i	−0.895694	+	0.326006i	−0.147168	+	0.989111i	$0.547016\pi$
$662$	−39.5346	−	56.4613i	−1.53656	−	2.19443i
$663$	−0.717497	−	0.855080i	−0.0278653	−	0.0332086i
$664$	69.8418	+	18.7140i	2.71039	+	0.726246i
$665$	−7.22535	−	12.5147i	−0.280187	−	0.485298i
$666$	54.5932	−	94.5581i	2.11544	−	3.66405i
$667$	0.515064	−	0.515064i	0.0199434	−	0.0199434i
$668$	−9.73885	+	6.81922i	−0.376808	+	0.263843i
$669$	−26.8636	+	32.0148i	−1.03861	+	1.23776i
$670$	34.3778	+	3.00766i	1.32813	+	0.116196i
$671$	−1.38881	+	15.8742i	−0.0536145	+	0.612816i
$672$	9.18163	+	4.28146i	0.354189	+	0.165161i
$673$	−34.6908	+	29.1090i	−1.33723	+	1.12207i	−0.354903	+	0.934903i	$0.615486\pi$
$673$	−34.6908	+	29.1090i	−1.33723	+	1.12207i	−0.982328	+	0.187167i	$0.940070\pi$
$674$	−9.87802	−	36.8653i	−0.380487	−	1.42000i
$675$	44.2060	+	16.0897i	1.70149	+	0.619292i
$676$	27.3837	−	4.82848i	1.05322	−	0.185711i
$677$	−7.20656	−	5.04609i	−0.276971	−	0.193937i	0.426835	−	0.904330i	$-0.359629\pi$
$677$	−7.20656	−	5.04609i	−0.276971	−	0.193937i	−0.703806	+	0.710393i	$0.748517\pi$
$678$	−41.5580	+	11.1354i	−1.59603	+	0.427654i
$679$	−18.5774	−	18.5774i	−0.712935	−	0.712935i
$680$	−0.864443	−	0.152425i	−0.0331499	−	0.00584521i
$681$	−22.9701	−	13.2618i	−0.880216	−	0.508193i
$682$	−3.74990	+	10.3028i	−0.143591	+	0.394513i
$683$	1.89009	+	21.6038i	0.0723222	+	0.826646i	0.942565	+	0.334023i	$0.108406\pi$
$683$	1.89009	+	21.6038i	0.0723222	+	0.826646i	−0.870243	+	0.492623i	$0.836038\pi$
$684$		−	102.669i		−	3.92565i
$685$	−10.9319	+	0.956418i	−0.417687	+	0.0365429i
$686$	19.5216	−	27.8797i	0.745337	−	1.06445i
$687$	−19.8221	+	73.9773i	−0.756262	+	2.82241i
$688$	−1.77504	−	3.80658i	−0.0676727	−	0.145125i
$689$	9.04337	+	7.58829i	0.344525	+	0.289091i
$690$	0.952070	−	2.04172i	0.0362447	−	0.0777270i
$691$	−10.3496	+	4.82608i	−0.393716	+	0.183593i	−0.609386	−	0.792873i	$-0.708584\pi$
$691$	−10.3496	+	4.82608i	−0.393716	+	0.183593i	0.215670	+	0.976466i	$0.430806\pi$
$692$	−7.48938	−	20.5769i	−0.284704	−	0.782217i
$693$	−7.74204	+	43.9073i	−0.294096	+	1.66790i
$694$	−2.49168	+	14.1310i	−0.0945828	+	0.536406i
$695$	1.68248	+	4.62259i	0.0638202	+	0.175345i
$696$	−46.3264	+	21.6024i	−1.75600	+	0.818836i
$697$	−0.324760	+	0.696450i	−0.0123012	+	0.0263799i
$698$	−5.77451	−	4.84539i	−0.218568	−	0.183401i
$699$	−4.81758	−	10.3313i	−0.182217	−	0.390767i
$700$	9.87542	−	36.8556i	0.373256	−	1.39301i
$701$	3.81353	−	5.44628i	0.144035	−	0.205703i	−0.740652	−	0.671889i	$-0.765483\pi$
$701$	3.81353	−	5.44628i	0.144035	−	0.205703i	0.884687	+	0.466186i	$0.154372\pi$
$702$	−86.2697	+	7.54762i	−3.25604	+	0.284867i
$703$		−	20.8650i		−	0.786939i
$704$	−1.54322	−	17.6391i	−0.0581623	−	0.664798i
$705$	19.4196	−	53.3550i	0.731386	−	2.00947i
$706$	−39.4140	−	22.7557i	−1.48336	−	0.856421i
$707$	23.8581	+	4.20683i	0.897277	+	0.158214i
$708$	118.440	+	118.440i	4.45124	+	4.45124i
$709$	37.7015	−	10.1021i	1.41591	−	0.379392i	0.531879	−	0.846821i	$-0.321486\pi$
$709$	37.7015	−	10.1021i	1.41591	−	0.379392i	0.884031	+	0.467429i	$0.154820\pi$
$710$	21.5849	+	15.1139i	0.810068	+	0.567216i
$711$	69.8997	−	12.3252i	2.62144	−	0.462231i
$712$	59.4219	+	21.6278i	2.22693	+	0.810537i
$713$	−0.129079	−	0.481731i	−0.00483406	−	0.0180410i
$714$	−2.63464	+	2.21072i	−0.0985989	+	0.0827343i
$715$	5.67792	+	2.64766i	0.212342	+	0.0990169i
$716$	−0.979698	+	11.1980i	−0.0366130	+	0.418489i
$717$	10.7094	+	0.936949i	0.399949	+	0.0349910i
$718$	−28.9578	+	34.5105i	−1.08069	+	1.28792i
$719$	12.2352	−	8.56718i	0.456296	−	0.319502i	−0.322733	−	0.946490i	$-0.604601\pi$
$719$	12.2352	−	8.56718i	0.456296	−	0.319502i	0.779029	+	0.626988i	$0.215713\pi$
$720$	−24.1418	+	24.1418i	−0.899711	+	0.899711i
$721$	−9.15769	+	15.8616i	−0.341050	+	0.590716i
$722$	8.21054	+	14.2211i	0.305564	+	0.529253i
$723$	−66.0308	−	17.6929i	−2.45571	−	0.658006i
$724$	30.8556	+	36.7723i	1.14674	+	1.36663i
$725$	−6.27303	−	8.95882i	−0.232975	−	0.332722i
$726$	−54.0246	+	19.6633i	−2.00504	+	0.729775i
$727$	−10.5840	+	6.11068i	−0.392539	+	0.226633i	−0.683260	−	0.730175i	$-0.739438\pi$
$727$	−10.5840	+	6.11068i	−0.392539	+	0.226633i	0.290720	+	0.956808i	$0.406105\pi$
$728$	5.92999	+	33.6306i	0.219780	+	1.24643i
$729$	−46.7346			−1.73091
$730$	−27.2515	+	5.95221i	−1.00862	+	0.220301i
$731$	−0.177249			−0.00655579
$732$	18.1669	+	103.030i	0.671469	+	3.80809i
$733$	−16.5792	+	9.57201i	−0.612367	+	0.353550i	−0.773891	−	0.633319i	$-0.781692\pi$
$733$	−16.5792	+	9.57201i	−0.612367	+	0.353550i	0.161524	+	0.986869i	$0.448359\pi$
$734$	27.0942	−	9.86148i	1.00006	−	0.363994i
$735$	6.09980	+	8.71142i	0.224995	+	0.321325i
$736$	0.138782	+	0.165394i	0.00511559	+	0.00609652i
$737$	−19.6528	−	5.26595i	−0.723919	−	0.193974i
$738$	49.5037	+	85.7430i	1.82226	+	3.15624i
$739$	−6.28135	+	10.8796i	−0.231063	+	0.400213i	−0.958121	−	0.286363i	$-0.907554\pi$
$739$	−6.28135	+	10.8796i	−0.231063	+	0.400213i	0.727058	+	0.686576i	$0.240887\pi$
$740$	−22.0813	+	22.0813i	−0.811725	+	0.811725i
$741$	−22.5124	+	15.7633i	−0.827013	+	0.579081i
$742$	23.3807	−	27.8641i	0.858334	−	1.02292i
$743$	−10.9133	−	0.954793i	−0.400371	−	0.0350280i	−0.114808	−	0.993388i	$-0.536625\pi$
$743$	−10.9133	−	0.954793i	−0.400371	−	0.0350280i	−0.285564	+	0.958360i	$0.592181\pi$
$744$	−3.05024	+	34.8644i	−0.111827	+	1.27819i
$745$	0.325274	+	0.151678i	0.0119171	+	0.00555704i
$746$	42.3219	−	35.5123i	1.54952	−	1.30020i
$747$	−30.7179	−	114.641i	−1.12391	−	4.19448i
$748$	1.00026	+	0.364064i	0.0365730	+	0.0133115i
$749$	−23.7604	+	4.18960i	−0.868185	+	0.153084i
$750$	−71.1201	−	49.7988i	−2.59694	−	1.81840i
$751$	−10.8660	+	2.91154i	−0.396506	+	0.106244i	−0.451562	−	0.892240i	$-0.649133\pi$
$751$	−10.8660	+	2.91154i	−0.396506	+	0.106244i	0.0550557	+	0.998483i	$0.482466\pi$
$752$	−30.9542	−	30.9542i	−1.12878	−	1.12878i
$753$	34.1064	+	6.01387i	1.24290	+	0.219158i
$754$	17.4355	+	10.0664i	0.634965	+	0.366597i
$755$	−0.659445	+	1.81181i	−0.0239997	+	0.0659386i
$756$	15.3622	+	175.591i	0.558717	+	6.38617i
$757$		−	19.4901i		−	0.708380i	−0.935174	−	0.354190i	$-0.884757\pi$
$757$		−	19.4901i		−	0.708380i	0.935174	−	0.354190i	$-0.115243\pi$
$758$	−73.9054	+	6.46588i	−2.68436	+	0.234851i
$759$	−0.761832	+	1.08801i	−0.0276527	+	0.0394922i
$760$	−5.59352	+	20.8753i	−0.202898	+	0.757227i
$761$	−2.05137	−	4.39918i	−0.0743621	−	0.159470i	0.865612	−	0.500715i	$-0.166929\pi$
$761$	−2.05137	−	4.39918i	−0.0743621	−	0.159470i	−0.939975	+	0.341244i	$0.889152\pi$
$762$	−106.090	−	89.0201i	−3.84324	−	3.22486i
$763$	−3.30625	+	7.09027i	−0.119694	+	0.256685i
$764$	43.7634	−	20.4072i	1.58330	−	0.738306i
$765$	0.492788	+	1.35392i	0.0178168	+	0.0489512i
$766$	9.64003	−	54.6713i	0.348308	−	1.97535i
$767$	5.56981	−	31.5880i	0.201114	−	1.14057i
$768$	−34.2838	−	94.1939i	−1.23711	−	3.39893i
$769$	14.4572	−	6.74150i	0.521340	−	0.243105i	−0.144091	−	0.989564i	$-0.546026\pi$
$769$	14.4572	−	6.74150i	0.521340	−	0.243105i	0.665431	+	0.746460i	$0.268248\pi$
$770$	8.15787	−	17.4946i	0.293989	−	0.630462i
$771$	2.72420	+	2.28588i	0.0981098	+	0.0823239i
$772$	−32.4776	−	69.6485i	−1.16890	−	2.50671i
$773$	3.35803	−	12.5323i	0.120780	−	0.450757i	−0.878874	−	0.477054i	$-0.841705\pi$
$773$	3.35803	−	12.5323i	0.120780	−	0.450757i	0.999654	+	0.0262966i	$0.00837144\pi$
$774$	−13.0987	+	18.7069i	−0.470823	+	0.672405i
$775$	−7.45959	+	0.652630i	−0.267957	+	0.0234432i
$776$			39.2916i			1.41049i
$777$	5.18471	+	59.2615i	0.186000	+	2.12599i
$778$	0.789650	−	2.16954i	0.0283103	−	0.0777819i
$779$	16.3851	+	9.45994i	0.587057	+	0.338938i
$780$	40.5069	+	7.14247i	1.45038	+	0.255741i
$781$	−10.9855	−	10.9855i	−0.393090	−	0.393090i
$782$	−0.0708001	+	0.0189708i	−0.00253181	+	0.000678396i
$783$	41.3856	+	28.9785i	1.47900	+	1.03561i
$784$	8.07460	−	1.42377i	0.288379	−	0.0508489i
$785$	−9.37970	−	3.41393i	−0.334776	−	0.121848i
$786$	7.81947	+	29.1826i	0.278911	+	1.04091i
$787$	−36.7866	+	30.8676i	−1.31130	+	1.10031i	−0.323228	+	0.946321i	$0.604768\pi$
$787$	−36.7866	+	30.8676i	−1.31130	+	1.10031i	−0.988072	+	0.153991i	$0.950787\pi$
$788$	9.19832	+	4.28925i	0.327676	+	0.152798i
$789$	−4.30243	+	49.1770i	−0.153170	+	1.75075i
$790$	−30.6133	−	2.67832i	−1.08917	−	0.0952904i
$791$	10.7790	−	12.8459i	0.383258	−	0.456749i
$792$	54.6198	−	38.2452i	1.94083	−	1.35898i
$793$	14.1662	−	14.1662i	0.503057	−	0.503057i
$794$	−15.0960	+	26.1470i	−0.535736	+	0.927921i
$795$	−10.6503	−	18.4468i	−0.377726	−	0.654241i
$796$	98.2782	+	26.3336i	3.48338	+	0.933369i
$797$	−15.1214	−	18.0210i	−0.535627	−	0.638336i	0.428574	−	0.903507i	$-0.359016\pi$
$797$	−15.1214	−	18.0210i	−0.535627	−	0.638336i	−0.964201	+	0.265171i	$0.914572\pi$
$798$	48.5694	+	69.3643i	1.71934	+	2.45547i
$799$	−1.73598	+	0.631845i	−0.0614145	+	0.0223531i
$800$	2.80742	−	1.62087i	0.0992574	−	0.0573063i
$801$	−18.0241	−	102.220i	−0.636852	−	3.61177i
$802$	40.8329			1.44186
$803$	16.4324	−	0.665997i	0.579887	−	0.0235025i
$804$	−133.581			−4.71103
$805$	0.152473	+	0.864715i	0.00537395	+	0.0304772i
$806$	11.9377	−	6.89223i	0.420487	−	0.242768i
$807$	46.9619	−	17.0927i	1.65314	−	0.601693i
$808$	−20.7815	−	29.6790i	−0.731089	−	1.04410i
$809$	−25.0058	−	29.8007i	−0.879157	−	1.04774i	−0.998493	−	0.0548842i	$-0.982521\pi$
$809$	−25.0058	−	29.8007i	−0.879157	−	1.04774i	0.119336	−	0.992854i	$-0.461923\pi$
$810$	79.5910	+	21.3263i	2.79654	+	0.749331i
$811$	9.01343	+	15.6117i	0.316504	+	0.548201i	0.979756	−	0.200195i	$-0.0641575\pi$
$811$	9.01343	+	15.6117i	0.316504	+	0.548201i	−0.663252	+	0.748396i	$0.730824\pi$
$812$	20.4889	−	35.4878i	0.719018	−	1.24538i
$813$	−42.3668	+	42.3668i	−1.48587	+	1.48587i
$814$	22.8309	−	15.9864i	0.800222	−	0.560321i
$815$	0.768829	−	0.916255i	0.0269309	−	0.0320950i
$816$	1.54688	+	0.135335i	0.0541517	+	0.00473766i
$817$	−0.380350	+	4.34742i	−0.0133068	+	0.152097i
$818$	−34.4338	−	16.0568i	−1.20395	−	0.561411i
$819$	42.9399	−	36.0309i	1.50044	−	1.25902i
$820$	−7.32885	−	27.3516i	−0.255934	−	0.955160i
$821$	−24.4279	−	8.89102i	−0.852539	−	0.310299i	−0.121464	−	0.992596i	$-0.538759\pi$
$821$	−24.4279	−	8.89102i	−0.852539	−	0.310299i	−0.731075	+	0.682297i	$0.760981\pi$
$822$	63.3265	−	11.1662i	2.20877	−	0.389465i
$823$	26.0016	+	18.2065i	0.906359	+	0.634639i	0.930985	−	0.365057i	$-0.118951\pi$
$823$	26.0016	+	18.2065i	0.906359	+	0.634639i	−0.0246262	+	0.999697i	$0.507840\pi$
$824$	26.4582	−	7.08944i	0.921714	−	0.246972i
$825$	14.1014	+	14.1014i	0.490948	+	0.490948i
$826$	−97.3276	−	17.1615i	−3.38646	−	0.597124i
$827$	8.60576	+	4.96854i	0.299251	+	0.172773i	0.642107	−	0.766615i	$-0.278061\pi$
$827$	8.60576	+	4.96854i	0.299251	+	0.172773i	−0.342855	+	0.939388i	$0.611394\pi$
$828$	−2.13365	+	5.86217i	−0.0741496	+	0.203724i
$829$	2.88425	+	32.9671i	0.100174	+	1.14499i	0.865348	+	0.501171i	$0.167097\pi$
$829$	2.88425	+	32.9671i	0.100174	+	1.14499i	−0.765174	+	0.643824i	$0.777347\pi$
$830$			51.3852i			1.78361i
$831$	18.2566	−	1.59724i	0.633313	−	0.0554077i
$832$	−12.7687	+	18.2355i	−0.442674	+	0.632203i
$833$	0.0895550	−	0.334224i	0.00310290	−	0.0115802i
$834$	−12.1823	−	26.1251i	−0.421839	−	0.904637i
$835$	−3.14680	−	2.64048i	−0.108900	−	0.0913777i
$836$	11.0759	−	23.7523i	0.383067	−	0.821490i
$837$	31.3505	−	14.6190i	1.08363	−	0.505306i
$838$	2.96807	+	8.15469i	0.102530	+	0.281699i
$839$	6.61090	−	37.4923i	0.228234	−	1.29438i	−0.628173	−	0.778074i	$-0.716197\pi$
$839$	6.61090	−	37.4923i	0.228234	−	1.29438i	0.856406	−	0.516303i	$-0.172692\pi$
$840$	10.6996	−	60.6806i	0.369172	−	2.09368i
$841$	5.90135	+	16.2138i	0.203495	+	0.559098i
$842$	−50.4597	+	23.5297i	−1.73896	+	0.810888i
$843$	18.0071	−	38.6164i	0.620199	−	1.33002i
$844$	−31.2622	−	26.2321i	−1.07609	−	0.902946i
$845$	4.06033	+	8.70740i	0.139679	+	0.299544i
$846$	−61.6040	+	229.909i	−2.11799	+	7.90444i
$847$	12.8528	−	18.3557i	0.441627	−	0.630709i
$848$	−16.3599	+	1.43131i	−0.561801	+	0.0491512i
$849$			26.2110i			0.899560i
$850$	0.0959171	+	1.09634i	0.00328993	+	0.0376041i
$851$	−0.433614	+	1.19134i	−0.0148641	+	0.0408387i
$852$	−88.3340	−	50.9996i	−3.02627	−	1.74722i
$853$	36.2521	+	6.39222i	1.24125	+	0.218865i	0.755450	−	0.655206i	$-0.227418\pi$
$853$	36.2521	+	6.39222i	1.24125	+	0.218865i	0.485797	+	0.874072i	$0.338529\pi$
$854$	−43.6484	−	43.6484i	−1.49362	−	1.49362i
$855$	34.2654	−	9.18140i	1.17185	−	0.313997i
$856$	29.5574	+	20.6963i	1.01025	+	0.707386i
$857$	−16.0718	+	2.83390i	−0.549003	+	0.0968040i	−0.441268	−	0.897376i	$-0.645471\pi$
$857$	−16.0718	+	2.83390i	−0.549003	+	0.0968040i	−0.107735	+	0.994180i	$0.534360\pi$
$858$	−34.4971	−	12.5559i	−1.17771	−	0.428651i
$859$	2.46085	+	9.18400i	0.0839630	+	0.313354i	0.995116	−	0.0987145i	$-0.0314731\pi$
$859$	2.46085	+	9.18400i	0.0839630	+	0.313354i	−0.911153	+	0.412069i	$0.864806\pi$
$860$	5.00337	−	4.19833i	0.170614	−	0.143162i
$861$	−48.8881	−	22.7969i	−1.66610	−	0.776917i
$862$	5.20850	−	59.5335i	0.177402	−	2.02772i
$863$	50.4010	+	4.40952i	1.71567	+	0.150102i	0.902146	−	0.431430i	$-0.141991\pi$
$863$	50.4010	+	4.40952i	1.71567	+	0.150102i	0.813523	+	0.581532i	$0.197547\pi$
$864$	−9.62592	+	11.4717i	−0.327481	+	0.390276i
$865$	6.19771	−	4.33968i	0.210729	−	0.147554i
$866$	−33.8685	+	33.8685i	−1.15090	+	1.15090i
$867$	−27.5636	+	47.7415i	−0.936109	+	1.62139i
$868$	−14.0282	−	24.2976i	−0.476149	−	0.824714i
$869$	17.5008	+	4.68932i	0.593673	+	0.159074i
$870$	−23.3500	−	27.8275i	−0.791639	−	0.943439i
$871$	14.6721	+	20.9540i	0.497146	+	0.709999i
$872$	10.9944	−	4.00165i	0.372318	−	0.135513i
$873$	55.8540	−	32.2473i	1.89037	−	1.09141i
$874$	0.313375	+	1.77724i	0.0106001	+	0.0601160i
$875$	33.8398			1.14400
$876$	103.078	−	32.1465i	3.48269	−	1.08613i
$877$	−52.7313			−1.78061			−0.890304	−	0.455366i	$-0.849508\pi$
$877$	−52.7313			−1.78061			−0.890304	+	0.455366i	$0.849508\pi$
$878$	−11.0908	−	62.8992i	−0.374297	−	2.12275i
$879$	38.4020	−	22.1714i	1.29527	−	0.747823i
$880$	−8.18954	+	2.98075i	−0.276069	+	0.100481i
$881$	6.06735	+	8.66507i	0.204414	+	0.291934i	0.908249	−	0.418430i	$-0.137419\pi$
$881$	6.06735	+	8.66507i	0.204414	+	0.291934i	−0.703835	+	0.710364i	$0.748531\pi$
$882$	−28.6560	−	34.1508i	−0.964896	−	1.14992i
$883$	5.89563	+	1.57973i	0.198404	+	0.0531621i	0.356652	−	0.934237i	$-0.383918\pi$
$883$	5.89563	+	1.57973i	0.198404	+	0.0531621i	−0.158249	+	0.987399i	$0.550585\pi$
$884$	−0.669141	−	1.15899i	−0.0225056	−	0.0389809i
$885$	−28.9371	+	50.1205i	−0.972709	+	1.68478i
$886$	37.3982	−	37.3982i	1.25642	−	1.25642i
$887$	−6.58626	+	4.61175i	−0.221145	+	0.154847i	−0.678899	−	0.734231i	$-0.737543\pi$
$887$	−6.58626	+	4.61175i	−0.221145	+	0.154847i	0.457754	+	0.889079i	$0.348654\pi$
$888$	57.1868	−	68.1526i	1.91906	−	2.28705i
$889$	53.7731	+	4.70454i	1.80349	+	0.157785i
$890$	−3.91673	+	44.7684i	−0.131289	+	1.50064i
$891$	−44.0294	−	20.5312i	−1.47504	−	0.687823i
$892$	−38.3835	+	32.2076i	−1.28518	+	1.07839i
$893$	11.7722	+	43.9346i	0.393943	+	1.47022i
$894$	−1.97625	−	0.719296i	−0.0660956	−	0.0240568i
$895$	−3.82490	+	0.674433i	−0.127852	+	0.0225438i
$896$	51.0744	+	35.7627i	1.70628	+	1.19475i
$897$	1.61300	−	0.432201i	0.0538564	−	0.0144308i
$898$	−56.7941	−	56.7941i	−1.89524	−	1.89524i
$899$	−7.91974	−	1.39646i	−0.264138	−	0.0465747i
$900$	81.1172	+	46.8331i	2.70391	+	1.56110i
$901$	−0.237035	+	0.651248i	−0.00789677	+	0.0216962i
$902$	2.20269	+	25.1769i	0.0733416	+	0.838298i
$903$		−	12.4422i		−	0.414050i
$904$	−24.9836	+	2.18579i	−0.830944	+	0.0726982i
$905$	−9.51328	+	13.5864i	−0.316232	+	0.451626i
$906$	2.92419	−	10.9132i	0.0971497	−	0.362568i
$907$	2.25487	+	4.83558i	0.0748716	+	0.160563i	0.940181	−	0.340676i	$-0.110656\pi$
$907$	2.25487	+	4.83558i	0.0748716	+	0.160563i	−0.865309	+	0.501238i	$0.832878\pi$
$908$	−24.3602	−	20.4406i	−0.808421	−	0.678346i
$909$	−25.1337	+	53.8994i	−0.833632	+	1.78773i
$910$	−21.9951	+	10.2565i	−0.729130	+	0.339999i
$911$	0.332271	+	0.912906i	0.0110086	+	0.0302459i	0.945075	−	0.326853i	$-0.105988\pi$
$911$	0.332271	+	0.912906i	0.0110086	+	0.0302459i	−0.934067	+	0.357099i	$0.883766\pi$
$912$	6.63877	−	37.6503i	0.219831	−	1.24673i
$913$	5.26084	−	29.8357i	0.174108	−	0.987418i
$914$	15.2198	+	41.8160i	0.503426	+	1.38315i
$915$	−32.7612	+	15.2768i	−1.08305	+	0.505035i
$916$	−38.8059	+	83.2195i	−1.28218	+	2.74965i
$917$	−9.02060	−	7.56918i	−0.297887	−	0.249956i
$918$	−2.14855	−	4.60759i	−0.0709129	−	0.152073i
$919$	−14.2530	+	53.1928i	−0.470162	+	1.75467i	0.169021	+	0.985613i	$0.445940\pi$
$919$	−14.2530	+	53.1928i	−0.470162	+	1.75467i	−0.639182	+	0.769055i	$0.720727\pi$
$920$	0.753204	−	1.07569i	0.0248324	−	0.0354644i
$921$	40.4429	−	3.53829i	1.33264	−	0.116591i
$922$			59.0578i			1.94497i
$923$	1.70236	+	19.4580i	0.0560338	+	0.640469i
$924$	−25.5559	+	70.2142i	−0.840727	+	2.30988i
$925$	16.4851	+	9.51769i	0.542027	+	0.312940i
$926$	102.380	+	18.0524i	3.36442	+	0.593238i
$927$	−31.7925	−	31.7925i	−1.04420	−	1.04420i
$928$	3.36287	−	0.901077i	0.110391	−	0.0295793i
$929$	−5.84543	−	4.09301i	−0.191782	−	0.134287i	0.473742	−	0.880664i	$-0.342903\pi$
$929$	−5.84543	−	4.09301i	−0.191782	−	0.134287i	−0.665524	+	0.746376i	$0.731792\pi$
$930$	−24.4938	+	4.31891i	−0.803183	+	0.141623i
$931$	−8.00541	−	2.91373i	−0.262367	−	0.0954937i
$932$	−3.53729	−	13.2014i	−0.115868	−	0.432425i
$933$	55.7981	−	46.8202i	1.82675	−	1.53282i
$934$	−42.5276	−	19.8309i	−1.39154	−	0.648888i
$935$	−0.0320549	+	0.366389i	−0.00104831	+	0.0119822i
$936$	−83.5125	−	7.30639i	−2.72969	−	0.238817i
$937$	26.2941	−	31.3361i	0.858992	−	1.02371i	−0.140443	−	0.990089i	$-0.544853\pi$
$937$	26.2941	−	31.3361i	0.858992	−	1.02371i	0.999435	−	0.0336180i	$-0.0107029\pi$
$938$	64.5626	−	45.2072i	2.10804	−	1.47607i
$939$	48.0328	−	48.0328i	1.56749	−	1.56749i
$940$	34.0372	−	58.9542i	1.11017	−	1.92287i
$941$	11.2903	+	19.5554i	0.368053	+	0.637487i	0.989261	−	0.146159i	$-0.0466912\pi$
$941$	11.2903	+	19.5554i	0.368053	+	0.637487i	−0.621208	+	0.783646i	$0.713358\pi$
$942$	56.4975	+	15.1385i	1.84079	+	0.493238i
$943$	−0.738956	−	0.880653i	−0.0240637	−	0.0286780i
$944$	25.5930	+	36.5506i	0.832981	+	1.18962i
$945$	−57.2289	+	20.8296i	−1.86166	+	0.677587i
$946$	−5.04844	+	2.91472i	−0.164139	+	0.0947657i
$947$	−1.32147	−	7.49442i	−0.0429419	−	0.243536i	0.955780	−	0.294084i	$-0.0950144\pi$
$947$	−1.32147	−	7.49442i	−0.0429419	−	0.243536i	−0.998722	+	0.0505477i	$0.983903\pi$
$948$	118.954			3.86343
$949$	−16.3644	−	12.6383i	−0.531212	−	0.410258i
$950$	27.0960			0.879109
$951$	10.2432	+	58.0923i	0.332160	+	1.88377i
$952$	−1.73619	+	1.00239i	−0.0562704	+	0.0324877i
$953$	8.80319	−	3.20410i	0.285163	−	0.103791i	−0.195478	−	0.980708i	$-0.562626\pi$
$953$	8.80319	−	3.20410i	0.285163	−	0.103791i	0.480642	+	0.876917i	$0.340404\pi$
$954$	51.2160	+	73.1440i	1.65818	+	2.36812i
$955$	10.7244	+	12.7809i	0.347035	+	0.413580i
$956$	12.4497	+	3.33588i	0.402652	+	0.107890i
$957$	10.7087	+	18.5480i	0.346163	+	0.599572i
$958$	12.4896	−	21.6327i	0.403522	−	0.698920i
$959$	−17.7223	+	17.7223i	−0.572283	+	0.572283i
$960$	32.9028	−	23.0388i	1.06193	−	0.743574i
$961$	16.3872	−	19.5295i	0.528618	−	0.629983i
$962$	−34.9079	−	3.05405i	−1.12548	−	0.0984665i
$963$	5.16204	−	59.0024i	0.166344	−	1.90132i
$964$	−74.2802	−	34.6374i	−2.39240	−	1.11560i
$965$	20.3405	−	17.0677i	0.654785	−	0.549430i
$966$	−1.33168	−	4.96990i	−0.0428461	−	0.159904i
$967$	−12.2986	−	4.47632i	−0.395496	−	0.143949i	0.136613	−	0.990624i	$-0.456378\pi$
$967$	−12.2986	−	4.47632i	−0.395496	−	0.143949i	−0.532109	+	0.846676i	$0.678600\pi$
$968$	−33.0033	+	5.81938i	−1.06077	+	0.187042i
$969$	−1.32162	−	0.925406i	−0.0424565	−	0.0297283i
$970$	−26.9718	+	7.22708i	−0.866013	+	0.232047i
$971$	9.24128	+	9.24128i	0.296567	+	0.296567i	0.839668	−	0.543101i	$-0.182750\pi$
$971$	9.24128	+	9.24128i	0.296567	+	0.296567i	−0.543101	+	0.839668i	$0.682750\pi$
$972$	−144.581	−	25.4934i	−4.63742	−	0.817703i
$973$	9.73000	+	5.61762i	0.311929	+	0.180093i
$974$	0.313619	−	0.861662i	0.0100490	−	0.0276094i
$975$	−2.18522	−	24.9772i	−0.0699831	−	0.799911i
$976$			27.8695i			0.892081i
$977$	−25.3104	+	2.21438i	−0.809753	+	0.0708442i	−0.484509	−	0.874786i	$-0.661002\pi$
$977$	−25.3104	+	2.21438i	−0.809753	+	0.0708442i	−0.325244	+	0.945630i	$0.605446\pi$
$978$	−4.02009	+	5.74129i	−0.128548	+	0.183586i
$979$	6.85757	−	25.5928i	0.219169	−	0.817950i
$980$	5.38849	+	11.5557i	0.172129	+	0.369132i
$981$	−14.7118	−	12.3446i	−0.469710	−	0.394134i
$982$	41.4224	−	88.8307i	1.32184	−	2.83470i
$983$	−19.2839	+	8.99225i	−0.615062	+	0.286808i	−0.705075	−	0.709132i	$-0.749087\pi$
$983$	−19.2839	+	8.99225i	−0.615062	+	0.286808i	0.0900132	+	0.995941i	$0.471309\pi$
$984$	27.5918	+	75.8077i	0.879593	+	2.41666i
$985$	−0.608941	+	3.45348i	−0.0194025	+	0.110037i
$986$	−0.205239	+	1.16397i	−0.00653613	+	0.0370682i
$987$	−44.3531	−	121.859i	−1.41178	−	3.87882i
$988$	−29.8626	+	13.9252i	−0.950055	+	0.443018i
$989$	0.112065	−	0.240323i	0.00356345	−	0.00764184i
$990$	36.2999	+	30.4592i	1.15369	+	0.968058i
$991$	−13.8371	−	29.6738i	−0.439550	−	0.942618i	−0.993895	−	0.110331i	$-0.964809\pi$
$991$	−13.8371	−	29.6738i	−0.439550	−	0.942618i	0.554345	−	0.832287i	$-0.312969\pi$
$992$	0.616945	−	2.30247i	0.0195880	−	0.0731035i
$993$	−52.8763	+	75.5152i	−1.67798	+	2.39640i
$994$	59.9534	−	5.24524i	1.90160	−	0.166369i
$995$			35.1549i			1.11449i
$996$	−17.3358	−	198.150i	−0.549307	−	6.27861i
$997$	10.0164	−	27.5200i	0.317224	−	0.871566i	−0.673924	−	0.738801i	$-0.735392\pi$
$997$	10.0164	−	27.5200i	0.317224	−	0.871566i	0.991148	−	0.132765i	$-0.0423855\pi$
$998$	32.9692	+	19.0348i	1.04362	+	0.602536i
$999$	−86.5986	−	15.2697i	−2.73986	−	0.483111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	73.2.k.a.12.1	✓	72
3.2	odd	2		657.2.cc.d.523.6		72
73.33	odd	72		5329.2.a.o.1.5		72
73.40	odd	72		5329.2.a.o.1.6		72
73.67	even	36	inner	73.2.k.a.67.1	yes	72
219.140	odd	36		657.2.cc.d.505.6		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
73.2.k.a.12.1	✓	72	1.1	even	1	trivial
73.2.k.a.67.1	yes	72	73.67	even	36	inner
657.2.cc.d.505.6		72	219.140	odd	36
657.2.cc.d.523.6		72	3.2	odd	2
5329.2.a.o.1.5		72	73.33	odd	72
5329.2.a.o.1.6		72	73.40	odd	72

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:	\( N \)	\(=\)	\( 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	73.k (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.421521 - 2.39057i) q^{2} +(-2.81166 + 1.62332i) q^{3} +(-3.65774 + 1.33131i) q^{4} +(-0.771420 - 1.10170i) q^{5} +(5.06582 + 6.03721i) q^{6} +(-2.96706 - 0.795022i) q^{7} +(2.29696 + 3.97845i) q^{8} +(3.77030 - 6.53036i) q^{9} +O(q^{10})\)	\(q+(-0.421521 - 2.39057i) q^{2} +(-2.81166 + 1.62332i) q^{3} +(-3.65774 + 1.33131i) q^{4} +(-0.771420 - 1.10170i) q^{5} +(5.06582 + 6.03721i) q^{6} +(-2.96706 - 0.795022i) q^{7} +(2.29696 + 3.97845i) q^{8} +(3.77030 - 6.53036i) q^{9} +(-2.30852 + 2.30852i) q^{10} +(1.57674 - 1.10405i) q^{11} +(8.12321 - 9.68087i) q^{12} +(-2.41081 - 0.210918i) q^{13} +(-0.649873 + 7.42808i) q^{14} +(3.95739 + 1.84536i) q^{15} +(2.57888 - 2.16394i) q^{16} +(-0.0367704 - 0.137229i) q^{17} +(-17.2005 - 6.26048i) q^{18} +(-3.44475 + 0.607402i) q^{19} +(4.28837 + 3.00275i) q^{20} +(9.63295 - 2.58114i) q^{21} +(-3.30393 - 3.30393i) q^{22} +(0.209310 + 0.0369070i) q^{23} +(-12.9165 - 7.45737i) q^{24} +(1.09144 - 2.99871i) q^{25} +(0.511992 + 5.85210i) q^{26} +14.7417i q^{27} +(11.9112 - 1.04209i) q^{28} +(1.96575 - 2.80739i) q^{29} +(2.74333 - 10.2383i) q^{30} +(-0.991677 - 2.12666i) q^{31} +(0.778184 + 0.652974i) q^{32} +(-2.64105 + 5.66376i) q^{33} +(-0.312555 + 0.145747i) q^{34} +(1.41297 + 3.88212i) q^{35} +(-5.09687 + 28.9058i) q^{36} +(-1.03582 + 5.87441i) q^{37} +(2.90407 + 7.97887i) q^{38} +(7.12076 - 3.32047i) q^{39} +(2.61114 - 5.59962i) q^{40} +(-4.14349 - 3.47680i) q^{41} +(-10.2309 - 21.9402i) q^{42} +(0.322907 - 1.20511i) q^{43} +(-4.29749 + 6.13745i) q^{44} +(-10.1030 + 0.883898i) q^{45} -0.515927i q^{46} +(-1.13332 - 12.9539i) q^{47} +(-3.73820 + 10.2706i) q^{48} +(2.10922 + 1.21776i) q^{49} +(-7.62869 - 1.34514i) q^{50} +(0.326152 + 0.326152i) q^{51} +(9.09891 - 2.43804i) q^{52} +(-3.99598 - 2.79801i) q^{53} +(35.2409 - 6.21393i) q^{54} +(-2.43266 - 0.885417i) q^{55} +(-3.65226 - 13.6304i) q^{56} +(8.69948 - 7.29973i) q^{57} +(-7.53985 - 3.51589i) q^{58} +(-1.15518 + 13.2037i) q^{59} +(-16.9318 - 1.48134i) q^{60} +(-5.32131 + 6.34169i) q^{61} +(-4.66591 + 3.26710i) q^{62} +(-16.3785 + 16.3785i) q^{63} +(4.59945 - 7.96648i) q^{64} +(1.62738 + 2.81870i) q^{65} +(14.6528 + 3.92622i) q^{66} +(-6.79441 - 8.09726i) q^{67} +(0.317191 + 0.452996i) q^{68} +(-0.648421 + 0.236006i) q^{69} +(8.68486 - 5.01421i) q^{70} +(-1.40155 - 7.94856i) q^{71} +34.6409 q^{72} +(7.19155 + 4.61319i) q^{73} +14.4798 q^{74} +(1.79909 + 10.2031i) q^{75} +(11.7914 - 6.80775i) q^{76} +(-5.55603 + 2.02223i) q^{77} +(-10.9393 - 15.6230i) q^{78} +(6.05041 + 7.21060i) q^{79} +(-4.37342 - 1.17186i) q^{80} +(-12.6195 - 21.8576i) q^{81} +(-6.56495 + 11.3708i) q^{82} +(11.1294 - 11.1294i) q^{83} +(-31.7986 + 22.2656i) q^{84} +(-0.122820 + 0.146371i) q^{85} +(-3.01700 - 0.263953i) q^{86} +(-0.969765 + 11.0845i) q^{87} +(8.01410 + 3.73704i) q^{88} +(10.5446 - 8.84801i) q^{89} +(6.37165 + 23.7793i) q^{90} +(6.98533 + 2.54245i) q^{91} +(-0.814737 + 0.143660i) q^{92} +(6.24050 + 4.36965i) q^{93} +(-30.4895 + 8.16963i) q^{94} +(3.32653 + 3.32653i) q^{95} +(-3.24797 - 0.572705i) q^{96} +(7.40709 + 4.27649i) q^{97} +(2.02205 - 5.55555i) q^{98} +(-1.26502 - 14.4593i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) \) 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9	\( 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9} - 6 q^{11} + 6 q^{12} - 12 q^{13} - 12 q^{14} - 30 q^{15} + 30 q^{17} - 12 q^{18} - 6 q^{19} + 60 q^{20} - 30 q^{21} - 12 q^{22} - 12 q^{23} - 18 q^{24} + 36 q^{25} + 12 q^{26} + 120 q^{28} - 6 q^{29} - 72 q^{30} - 18 q^{31} - 18 q^{32} - 60 q^{33} - 60 q^{34} - 36 q^{35} + 60 q^{36} - 6 q^{37} + 48 q^{38} + 78 q^{39} - 18 q^{40} + 54 q^{42} - 24 q^{43} + 48 q^{44} + 36 q^{47} + 30 q^{48} - 18 q^{49} + 132 q^{50} - 18 q^{51} - 24 q^{53} - 6 q^{54} + 72 q^{55} + 24 q^{56} - 6 q^{57} - 18 q^{58} - 66 q^{60} - 36 q^{61} - 36 q^{62} + 12 q^{63} - 84 q^{64} + 24 q^{65} + 156 q^{66} - 54 q^{67} - 84 q^{68} - 6 q^{69} - 162 q^{70} + 48 q^{71} - 72 q^{72} - 36 q^{73} + 144 q^{74} + 6 q^{75} - 180 q^{76} - 24 q^{77} - 198 q^{78} - 36 q^{79} - 126 q^{80} - 48 q^{81} + 30 q^{82} - 48 q^{83} - 126 q^{84} - 6 q^{85} - 120 q^{86} + 6 q^{87} + 6 q^{88} + 6 q^{89} + 210 q^{90} + 48 q^{91} + 96 q^{92} + 144 q^{93} - 6 q^{94} - 12 q^{95} + 162 q^{96} - 18 q^{97} + 186 q^{98} + 78 q^{99}+O(q^{100}) \) 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9 - 6 * q^11 + 6 * q^12 - 12 * q^13 - 12 * q^14 - 30 * q^15 + 30 * q^17 - 12 * q^18 - 6 * q^19 + 60 * q^20 - 30 * q^21 - 12 * q^22 - 12 * q^23 - 18 * q^24 + 36 * q^25 + 12 * q^26 + 120 * q^28 - 6 * q^29 - 72 * q^30 - 18 * q^31 - 18 * q^32 - 60 * q^33 - 60 * q^34 - 36 * q^35 + 60 * q^36 - 6 * q^37 + 48 * q^38 + 78 * q^39 - 18 * q^40 + 54 * q^42 - 24 * q^43 + 48 * q^44 + 36 * q^47 + 30 * q^48 - 18 * q^49 + 132 * q^50 - 18 * q^51 - 24 * q^53 - 6 * q^54 + 72 * q^55 + 24 * q^56 - 6 * q^57 - 18 * q^58 - 66 * q^60 - 36 * q^61 - 36 * q^62 + 12 * q^63 - 84 * q^64 + 24 * q^65 + 156 * q^66 - 54 * q^67 - 84 * q^68 - 6 * q^69 - 162 * q^70 + 48 * q^71 - 72 * q^72 - 36 * q^73 + 144 * q^74 + 6 * q^75 - 180 * q^76 - 24 * q^77 - 198 * q^78 - 36 * q^79 - 126 * q^80 - 48 * q^81 + 30 * q^82 - 48 * q^83 - 126 * q^84 - 6 * q^85 - 120 * q^86 + 6 * q^87 + 6 * q^88 + 6 * q^89 + 210 * q^90 + 48 * q^91 + 96 * q^92 + 144 * q^93 - 6 * q^94 - 12 * q^95 + 162 * q^96 - 18 * q^97 + 186 * q^98 + 78 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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