LMFDB - Embedded newform 125.2.g.a.11.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(6,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("125.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.g (of order $25$, degree $20$, 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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$11$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			11.9
Character	$\chi$	$=$	125.11
Dual form			125.2.g.a.91.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03453 - 0.971489i) q^{2} +(-1.68964 - 2.66244i) q^{3} +(0.000881745 - 0.0140149i) q^{4} +(-2.20603 + 0.365290i) q^{5} +(-4.33451 - 1.11291i) q^{6} +(1.16348 - 3.58083i) q^{7} +(1.79652 + 2.17162i) q^{8} +(-2.95638 + 6.28262i) q^{9} +O(q^{10})$	\(q+(1.03453 - 0.971489i) q^{2} +(-1.68964 - 2.66244i) q^{3} +(0.000881745 - 0.0140149i) q^{4} +(-2.20603 + 0.365290i) q^{5} +(-4.33451 - 1.11291i) q^{6} +(1.16348 - 3.58083i) q^{7} +(1.79652 + 2.17162i) q^{8} +(-2.95638 + 6.28262i) q^{9} +(-1.92733 + 2.52104i) q^{10} +(2.88022 - 2.70470i) q^{11} +(-0.0388037 + 0.0213325i) q^{12} +(0.800374 - 1.70088i) q^{13} +(-2.27507 - 4.83478i) q^{14} +(4.69995 + 5.25621i) q^{15} +(3.99613 + 0.504828i) q^{16} +(-0.0265474 - 0.421958i) q^{17} +(3.04503 + 9.37165i) q^{18} +(0.185873 - 0.292888i) q^{19} +(0.00317437 + 0.0312394i) q^{20} +(-11.4996 + 2.95259i) q^{21} +(0.352083 - 5.59619i) q^{22} +(-0.871083 + 4.56638i) q^{23} +(2.74635 - 8.45238i) q^{24} +(4.73313 - 1.61168i) q^{25} +(-0.824376 - 2.53717i) q^{26} +(12.3369 - 1.55852i) q^{27} +(-0.0491591 - 0.0194635i) q^{28} +(2.33719 + 0.925361i) q^{29} +(9.96859 + 0.871763i) q^{30} +(0.0524853 + 0.834229i) q^{31} +(0.0642649 - 0.0466911i) q^{32} +(-12.0676 - 3.09844i) q^{33} +(-0.437392 - 0.410738i) q^{34} +(-1.25863 + 8.32441i) q^{35} +(0.0854438 + 0.0469731i) q^{36} +(0.445573 + 0.0562889i) q^{37} +(-0.0922469 - 0.483575i) q^{38} +(-5.88084 + 0.742922i) q^{39} +(-4.75645 - 4.13441i) q^{40} +(2.20608 + 11.5647i) q^{41} +(-9.02826 + 14.2263i) q^{42} +(-2.24054 - 1.62785i) q^{43} +(-0.0353666 - 0.0427509i) q^{44} +(4.22687 - 14.9396i) q^{45} +(3.53502 + 5.57030i) q^{46} +(-2.93448 + 3.54718i) q^{47} +(-5.40792 - 11.4924i) q^{48} +(-5.80551 - 4.21795i) q^{49} +(3.33083 - 6.26551i) q^{50} +(-1.07858 + 0.783636i) q^{51} +(-0.0231320 - 0.0127169i) q^{52} +(-3.27123 + 0.839910i) q^{53} +(11.2488 - 13.5975i) q^{54} +(-5.36584 + 7.01877i) q^{55} +(9.86642 - 3.90639i) q^{56} -1.09385 q^{57} +(3.31688 - 1.31324i) q^{58} +(-4.96681 + 2.73053i) q^{59} +(0.0778096 - 0.0612348i) q^{60} +(2.62966 - 13.7852i) q^{61} +(0.864742 + 0.812046i) q^{62} +(19.0573 + 17.8960i) q^{63} +(-1.48838 + 7.80235i) q^{64} +(-1.14433 + 4.04456i) q^{65} +(-15.4944 + 8.51813i) q^{66} +(1.43733 - 0.569080i) q^{67} -0.00593712 q^{68} +(13.6295 - 5.39631i) q^{69} +(6.78498 + 9.83460i) q^{70} +(4.46025 - 5.39152i) q^{71} +(-18.9547 + 4.86673i) q^{72} +(-0.448600 - 0.246620i) q^{73} +(0.515642 - 0.374636i) q^{74} +(-12.2883 - 9.87850i) q^{75} +(-0.00394092 - 0.00286324i) q^{76} +(-6.33399 - 13.4604i) q^{77} +(-5.36216 + 6.48174i) q^{78} +(0.574079 + 0.904603i) q^{79} +(-8.99998 + 0.346081i) q^{80} +(-11.7166 - 14.1629i) q^{81} +(13.5172 + 9.82084i) q^{82} +(6.32789 - 9.97116i) q^{83} +(0.0312407 + 0.163769i) q^{84} +(0.212702 + 0.921154i) q^{85} +(-3.89935 + 0.492602i) q^{86} +(-1.48529 - 7.78616i) q^{87} +(11.0480 + 1.39568i) q^{88} +(-8.08154 - 4.44286i) q^{89} +(-10.1408 - 19.5618i) q^{90} +(-5.15934 - 4.84494i) q^{91} +(0.0632294 + 0.0162346i) q^{92} +(2.13240 - 1.54928i) q^{93} +(0.410233 + 6.52047i) q^{94} +(-0.303051 + 0.714018i) q^{95} +(-0.232897 - 0.0922102i) q^{96} +(13.8825 + 5.49646i) q^{97} +(-10.1037 + 1.27639i) q^{98} +(8.47762 + 26.0914i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9}+O(q^{10}) $ 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9} - 20 q^{10} - 15 q^{11} - 100 q^{12} - 20 q^{13} - 10 q^{14} - 15 q^{17} + 10 q^{18} - 10 q^{19} + 5 q^{20} - 5 q^{21} + 25 q^{22} - 90 q^{23} + 15 q^{24} - 45 q^{25} + 15 q^{26} + 10 q^{27} + 30 q^{28} - 10 q^{29} + 40 q^{30} - 10 q^{31} + 20 q^{32} + 15 q^{33} + 5 q^{34} + 10 q^{35} - 210 q^{36} + 20 q^{37} + 30 q^{38} + 45 q^{40} - 5 q^{41} + 70 q^{42} + 25 q^{43} + 15 q^{44} - 100 q^{45} - 100 q^{47} + 105 q^{48} - 20 q^{49} + 60 q^{50} + 25 q^{51} + 85 q^{52} + 20 q^{53} + 60 q^{54} + 15 q^{55} - 105 q^{56} + 40 q^{57} - 225 q^{58} + 5 q^{59} - 35 q^{60} + 65 q^{62} + 85 q^{63} + 45 q^{64} + 45 q^{65} + 55 q^{66} - 105 q^{67} + 80 q^{68} + 40 q^{69} + 95 q^{70} - 85 q^{71} + 160 q^{72} + 40 q^{73} + 35 q^{74} + 55 q^{75} + 35 q^{76} + 75 q^{77} - 10 q^{78} - 330 q^{80} + 55 q^{81} - 95 q^{82} + 50 q^{83} + 115 q^{84} + 85 q^{85} + 40 q^{86} + 95 q^{87} + 165 q^{88} + 55 q^{89} + 170 q^{90} - 105 q^{91} + 155 q^{92} - 185 q^{93} + 60 q^{94} + 30 q^{95} + 135 q^{96} + 65 q^{97} + 135 q^{98} + 45 q^{99}+O(q^{100}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9 - 20 * q^10 - 15 * q^11 - 100 * q^12 - 20 * q^13 - 10 * q^14 - 15 * q^17 + 10 * q^18 - 10 * q^19 + 5 * q^20 - 5 * q^21 + 25 * q^22 - 90 * q^23 + 15 * q^24 - 45 * q^25 + 15 * q^26 + 10 * q^27 + 30 * q^28 - 10 * q^29 + 40 * q^30 - 10 * q^31 + 20 * q^32 + 15 * q^33 + 5 * q^34 + 10 * q^35 - 210 * q^36 + 20 * q^37 + 30 * q^38 + 45 * q^40 - 5 * q^41 + 70 * q^42 + 25 * q^43 + 15 * q^44 - 100 * q^45 - 100 * q^47 + 105 * q^48 - 20 * q^49 + 60 * q^50 + 25 * q^51 + 85 * q^52 + 20 * q^53 + 60 * q^54 + 15 * q^55 - 105 * q^56 + 40 * q^57 - 225 * q^58 + 5 * q^59 - 35 * q^60 + 65 * q^62 + 85 * q^63 + 45 * q^64 + 45 * q^65 + 55 * q^66 - 105 * q^67 + 80 * q^68 + 40 * q^69 + 95 * q^70 - 85 * q^71 + 160 * q^72 + 40 * q^73 + 35 * q^74 + 55 * q^75 + 35 * q^76 + 75 * q^77 - 10 * q^78 - 330 * q^80 + 55 * q^81 - 95 * q^82 + 50 * q^83 + 115 * q^84 + 85 * q^85 + 40 * q^86 + 95 * q^87 + 165 * q^88 + 55 * q^89 + 170 * q^90 - 105 * q^91 + 155 * q^92 - 185 * q^93 + 60 * q^94 + 30 * q^95 + 135 * q^96 + 65 * q^97 + 135 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{19}{25}\right)$

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 $

$2$	1.03453	−	0.971489i	0.731523	−	0.686946i	−0.226379	−	0.974039i	$-0.572689\pi$
$2$	1.03453	−	0.971489i	0.731523	−	0.686946i	0.957903	+	0.287093i	$0.0926889\pi$
$3$	−1.68964	−	2.66244i	−0.975511	−	1.53716i	−0.837290	−	0.546759i	$-0.815862\pi$
$3$	−1.68964	−	2.66244i	−0.975511	−	1.53716i	−0.138221	−	0.990401i	$-0.544138\pi$
$4$	0.000881745	−	0.0140149i	0.000440872	−	0.00700747i
$5$	−2.20603	+	0.365290i	−0.986566	+	0.163363i
$5$	−2.20603	+	0.365290i	−0.986566	+	0.163363i
$6$	−4.33451	−	1.11291i	−1.76956	−	0.454345i
$7$	1.16348	−	3.58083i	0.439754	−	1.35342i	−0.448381	−	0.893843i	$-0.647999\pi$
$7$	1.16348	−	3.58083i	0.439754	−	1.35342i	0.888135	−	0.459582i	$-0.152001\pi$
$8$	1.79652	+	2.17162i	0.635167	+	0.767785i
$9$	−2.95638	+	6.28262i	−0.985459	+	2.09421i
$10$	−1.92733	+	2.52104i	−0.609475	+	0.797221i
$11$	2.88022	−	2.70470i	0.868418	−	0.815499i	−0.115650	−	0.993290i	$-0.536895\pi$
$11$	2.88022	−	2.70470i	0.868418	−	0.815499i	0.984068	+	0.177791i	$0.0568952\pi$
$12$	−0.0388037	+	0.0213325i	−0.0112017	+	0.00615817i
$13$	0.800374	−	1.70088i	0.221984	−	0.471740i	−0.762551	−	0.646928i	$-0.776053\pi$
$13$	0.800374	−	1.70088i	0.221984	−	0.471740i	0.984535	+	0.175188i	$0.0560534\pi$
$14$	−2.27507	−	4.83478i	−0.608039	−	1.29215i
$15$	4.69995	+	5.25621i	1.21352	+	1.35715i
$16$	3.99613	+	0.504828i	0.999032	+	0.126207i
$17$	−0.0265474	−	0.421958i	−0.00643868	−	0.102340i	0.993495	−	0.113878i	$-0.0363273\pi$
$17$	−0.0265474	−	0.421958i	−0.00643868	−	0.102340i	−0.999933	+	0.0115380i	$0.996327\pi$
$18$	3.04503	+	9.37165i	0.717721	+	2.20892i
$19$	0.185873	−	0.292888i	0.0426421	−	0.0671932i	−0.822338	−	0.568999i	$-0.807331\pi$
$19$	0.185873	−	0.292888i	0.0426421	−	0.0671932i	0.864980	+	0.501806i	$0.167331\pi$
$20$	0.00317437	+	0.0312394i	0.000709810	+	0.00698535i
$21$	−11.4996	+	2.95259i	−2.50942	+	0.644309i
$22$	0.352083	−	5.59619i	0.0750643	−	1.19311i
$23$	−0.871083	+	4.56638i	−0.181633	+	0.952155i	0.768391	+	0.639980i	$0.221058\pi$
$23$	−0.871083	+	4.56638i	−0.181633	+	0.952155i	−0.950025	+	0.312175i	$0.898942\pi$
$24$	2.74635	−	8.45238i	0.560595	−	1.72534i
$25$	4.73313	−	1.61168i	0.946625	−	0.322337i
$26$	−0.824376	−	2.53717i	−0.161673	−	0.497580i
$27$	12.3369	−	1.55852i	2.37424	−	0.299936i
$28$	−0.0491591	−	0.0194635i	−0.00929020	−	0.00367825i
$29$	2.33719	+	0.925361i	0.434006	+	0.171835i	0.574961	−	0.818181i	$-0.305017\pi$
$29$	2.33719	+	0.925361i	0.434006	+	0.171835i	−0.140955	+	0.990016i	$0.545017\pi$
$30$	9.96859	+	0.871763i	1.82001	+	0.159161i
$31$	0.0524853	+	0.834229i	0.00942663	+	0.149832i	0.999924	+	0.0123026i	$0.00391614\pi$
$31$	0.0524853	+	0.834229i	0.00942663	+	0.149832i	−0.990498	+	0.137529i	$0.956084\pi$
$32$	0.0642649	−	0.0466911i	0.0113605	−	0.00825391i
$33$	−12.0676	−	3.09844i	−2.10070	−	0.539369i
$34$	−0.437392	−	0.410738i	−0.0750120	−	0.0704410i
$35$	−1.25863	+	8.32441i	−0.212747	+	1.40708i
$36$	0.0854438	+	0.0469731i	0.0142406	+	0.00782885i
$37$	0.445573	+	0.0562889i	0.0732517	+	0.00925384i	0.161874	−	0.986811i	$-0.448246\pi$
$37$	0.445573	+	0.0562889i	0.0732517	+	0.00925384i	−0.0886220	+	0.996065i	$0.528246\pi$
$38$	−0.0922469	−	0.483575i	−0.0149644	−	0.0784462i
$39$	−5.88084	+	0.742922i	−0.941687	+	0.118963i
$40$	−4.75645	−	4.13441i	−0.752061	−	0.653708i
$41$	2.20608	+	11.5647i	0.344532	+	1.80610i	0.558774	+	0.829320i	$0.311272\pi$
$41$	2.20608	+	11.5647i	0.344532	+	1.80610i	−0.214242	+	0.976781i	$0.568728\pi$
$42$	−9.02826	+	14.2263i	−1.39309	+	2.19516i
$43$	−2.24054	−	1.62785i	−0.341680	−	0.248245i	0.403691	−	0.914896i	$-0.367727\pi$
$43$	−2.24054	−	1.62785i	−0.341680	−	0.248245i	−0.745370	+	0.666651i	$0.767727\pi$
$44$	−0.0353666	−	0.0427509i	−0.00533172	−	0.00644494i
$45$	4.22687	−	14.9396i	0.630105	−	2.22706i
$46$	3.53502	+	5.57030i	0.521210	+	0.821296i
$47$	−2.93448	+	3.54718i	−0.428038	+	0.517409i	−0.939803	−	0.341717i	$-0.888992\pi$
$47$	−2.93448	+	3.54718i	−0.428038	+	0.517409i	0.511765	+	0.859125i	$0.328992\pi$
$48$	−5.40792	−	11.4924i	−0.780566	−	1.65879i
$49$	−5.80551	−	4.21795i	−0.829358	−	0.602564i
$50$	3.33083	−	6.26551i	0.471051	−	0.886077i
$51$	−1.07858	+	0.783636i	−0.151032	+	0.109731i
$52$	−0.0231320	−	0.0127169i	−0.00320783	−	0.00176352i
$53$	−3.27123	+	0.839910i	−0.449339	+	0.115371i	−0.466576	−	0.884481i	$-0.654513\pi$
$53$	−3.27123	+	0.839910i	−0.449339	+	0.115371i	0.0172379	+	0.999851i	$0.494513\pi$
$54$	11.2488	−	13.5975i	1.53077	−	1.85039i
$55$	−5.36584	+	7.01877i	−0.723529	+	0.946410i
$56$	9.86642	−	3.90639i	1.31846	−	0.522014i
$57$	−1.09385			−0.144885
$58$	3.31688	−	1.31324i	0.435527	−	0.172437i
$59$	−4.96681	+	2.73053i	−0.646624	+	0.355485i	−0.771078	−	0.636741i	$-0.780282\pi$
$59$	−4.96681	+	2.73053i	−0.646624	+	0.355485i	0.124454	+	0.992225i	$0.460282\pi$
$60$	0.0778096	−	0.0612348i	0.0100452	−	0.00790538i
$61$	2.62966	−	13.7852i	0.336693	−	1.76501i	−0.263016	−	0.964791i	$-0.584717\pi$
$61$	2.62966	−	13.7852i	0.336693	−	1.76501i	0.599710	−	0.800218i	$-0.295283\pi$
$62$	0.864742	+	0.812046i	0.109822	+	0.103130i
$63$	19.0573	+	17.8960i	2.40099	+	2.25468i
$64$	−1.48838	+	7.80235i	−0.186047	+	0.975294i
$65$	−1.14433	+	4.04456i	−0.141937	+	0.501666i
$66$	−15.4944	+	8.51813i	−1.90723	+	1.04851i
$67$	1.43733	−	0.569080i	0.175598	−	0.0695242i	−0.278680	−	0.960384i	$-0.589897\pi$
$67$	1.43733	−	0.569080i	0.175598	−	0.0695242i	0.454279	+	0.890860i	$0.349897\pi$
$68$	−0.00593712			−0.000719982
$69$	13.6295	−	5.39631i	1.64080	−	0.649639i
$70$	6.78498	+	9.83460i	0.810960	+	1.17546i
$71$	4.46025	−	5.39152i	0.529334	−	0.639855i	−0.436287	−	0.899808i	$-0.643707\pi$
$71$	4.46025	−	5.39152i	0.529334	−	0.639855i	0.965622	+	0.259952i	$0.0837068\pi$
$72$	−18.9547	+	4.86673i	−2.23383	+	0.573550i
$73$	−0.448600	−	0.246620i	−0.0525046	−	0.0288647i	0.455285	−	0.890346i	$-0.349537\pi$
$73$	−0.448600	−	0.246620i	−0.0525046	−	0.0288647i	−0.507790	+	0.861481i	$0.669537\pi$
$74$	0.515642	−	0.374636i	0.0599422	−	0.0435506i
$75$	−12.2883	−	9.87850i	−1.41893	−	1.14067i
$76$	−0.00394092	−	0.00286324i	−0.000452054	−	0.000328437i
$77$	−6.33399	−	13.4604i	−0.721825	−	1.53396i
$78$	−5.36216	+	6.48174i	−0.607145	+	0.733912i
$79$	0.574079	+	0.904603i	0.0645889	+	0.101776i	0.875087	−	0.483965i	$-0.160804\pi$
$79$	0.574079	+	0.904603i	0.0645889	+	0.101776i	−0.810499	+	0.585741i	$0.800804\pi$
$80$	−8.99998	+	0.346081i	−1.00623	+	0.0386931i
$81$	−11.7166	−	14.1629i	−1.30184	−	1.57366i
$82$	13.5172	+	9.82084i	1.49273	+	1.08453i
$83$	6.32789	−	9.97116i	0.694576	−	1.09448i	−0.295689	−	0.955284i	$-0.595549\pi$
$83$	6.32789	−	9.97116i	0.694576	−	1.09448i	0.990265	−	0.139193i	$-0.0444507\pi$
$84$	0.0312407	+	0.163769i	0.00340864	+	0.0178687i
$85$	0.212702	+	0.921154i	0.0230707	+	0.0999132i
$86$	−3.89935	+	0.492602i	−0.420477	+	0.0531186i
$87$	−1.48529	−	7.78616i	−0.159240	−	0.834764i
$88$	11.0480	+	1.39568i	1.17772	+	0.148780i
$89$	−8.08154	−	4.44286i	−0.856641	−	0.470943i	−0.00803522	−	0.999968i	$-0.502558\pi$
$89$	−8.08154	−	4.44286i	−0.856641	−	0.470943i	−0.848606	+	0.529025i	$0.822558\pi$
$90$	−10.1408	−	19.5618i	−1.06893	−	2.06200i
$91$	−5.15934	−	4.84494i	−0.540846	−	0.507888i
$92$	0.0632294	+	0.0162346i	0.00659212	+	0.00169257i
$93$	2.13240	−	1.54928i	0.221120	−	0.160653i
$94$	0.410233	+	6.52047i	0.0423123	+	0.672535i
$95$	−0.303051	+	0.714018i	−0.0310924	+	0.0732567i
$96$	−0.232897	−	0.0922102i	−0.0237699	−	0.00941117i
$97$	13.8825	+	5.49646i	1.40955	+	0.558080i	0.944884	−	0.327405i	$-0.106174\pi$
$97$	13.8825	+	5.49646i	1.40955	+	0.558080i	0.464666	+	0.885486i	$0.346174\pi$
$98$	−10.1037	+	1.27639i	−1.02062	+	0.128935i
$99$	8.47762	+	26.0914i	0.852033	+	2.62229i
$100$	−0.0184142	−	0.0677555i	−0.00184142	−	0.00677555i
$101$	−5.24732	+	16.1496i	−0.522128	+	1.60694i	0.247798	+	0.968812i	$0.420293\pi$
$101$	−5.24732	+	16.1496i	−0.522128	+	1.60694i	−0.769926	+	0.638133i	$0.779707\pi$
$102$	−0.354533	+	1.85853i	−0.0351040	+	0.184021i
$103$	0.115081	−	1.82915i	0.0113392	−	0.180232i	−0.988280	−	0.152650i	$-0.951219\pi$
$103$	0.115081	−	1.82915i	0.0113392	−	0.180232i	0.999620	−	0.0275818i	$-0.00878069\pi$
$104$	5.13156	−	1.31756i	0.503191	−	0.129198i
$105$	24.2899	−	10.7142i	2.37045	−	1.04560i
$106$	−2.56823	+	4.04688i	−0.249448	+	0.393068i
$107$	0.742965	+	2.28661i	0.0718251	+	0.221055i	0.980525	−	0.196396i	$-0.0629237\pi$
$107$	0.742965	+	2.28661i	0.0718251	+	0.221055i	−0.908700	+	0.417451i	$0.862924\pi$
$108$	−0.0109645	−	0.174275i	−0.00105506	−	0.0167697i
$109$	−2.52062	−	0.318428i	−0.241431	−	0.0304999i	0.00368630	−	0.999993i	$-0.498827\pi$
$109$	−2.52062	−	0.318428i	−0.241431	−	0.0304999i	−0.245118	+	0.969493i	$0.578827\pi$
$110$	1.26753	+	12.4740i	0.120854	+	1.18935i
$111$	−0.602990	−	1.28142i	−0.0572332	−	0.121627i
$112$	6.45712	−	13.7221i	0.610140	−	1.29661i
$113$	−11.9140	+	6.54976i	−1.12077	+	0.616150i	−0.930760	−	0.365632i	$-0.880853\pi$
$113$	−11.9140	+	6.54976i	−1.12077	+	0.616150i	−0.190013	+	0.981782i	$0.560853\pi$
$114$	−1.13163	+	1.06267i	−0.105986	+	0.0995279i
$115$	0.253580	−	10.3918i	0.0236465	−	0.969036i
$116$	0.0150297	−	0.0319397i	0.00139547	−	0.00296553i
$117$	8.31979	+	10.0569i	0.769165	+	0.929760i
$118$	−2.48564	+	7.65002i	−0.228822	+	0.704241i
$119$	−1.54185	−	0.395879i	−0.141341	−	0.0362901i
$120$	−2.97094	+	19.6494i	−0.271209	+	1.79374i
$121$	0.289531	−	4.60196i	0.0263210	−	0.418360i
$122$	−10.6717	−	16.8159i	−0.966167	−	1.52244i
$123$	27.0628	−	25.4137i	2.44017	−	2.29147i
$124$	0.0117379			0.00105410
$125$	−9.85268	+	5.28438i	−0.881250	+	0.472650i
$126$	37.1011			3.30523
$127$	1.39603	−	1.31096i	0.123878	−	0.116329i	−0.620133	−	0.784497i	$-0.712921\pi$
$127$	1.39603	−	1.31096i	0.123878	−	0.116329i	0.744011	+	0.668168i	$0.232921\pi$
$128$	6.12525	+	9.65185i	0.541401	+	0.853111i
$129$	−0.548350	+	8.71578i	−0.0482796	+	0.767382i
$130$	2.74540	+	5.29593i	0.240788	+	0.464484i
$131$	14.1606	+	3.63583i	1.23722	+	0.317664i	0.809971	−	0.586470i	$-0.199483\pi$
$131$	14.1606	+	3.63583i	1.23722	+	0.317664i	0.427249	+	0.904134i	$0.359483\pi$
$132$	−0.0540650	+	0.166395i	−0.00470575	+	0.0144828i
$133$	−0.832523	−	1.00635i	−0.0721889	−	0.0872614i
$134$	0.934109	−	1.98508i	0.0806948	−	0.171485i
$135$	−26.6463	+	7.94469i	−2.29335	+	0.683770i
$136$	0.868641	−	0.815708i	0.0744853	−	0.0699464i
$137$	−9.76708	+	5.36950i	−0.834458	+	0.458747i	−0.840873	−	0.541232i	$-0.817958\pi$
$137$	−9.76708	+	5.36950i	−0.834458	+	0.458747i	0.00641505	+	0.999979i	$0.497958\pi$
$138$	8.85769	−	18.8236i	0.754017	−	1.60237i
$139$	9.34962	+	19.8689i	0.793024	+	1.68526i	0.726186	+	0.687498i	$0.241291\pi$
$139$	9.34962	+	19.8689i	0.793024	+	1.68526i	0.0668384	+	0.997764i	$0.478709\pi$
$140$	0.115556	+	0.0249796i	0.00976629	+	0.00211116i
$141$	14.4023	+	1.81944i	1.21290	+	0.153224i
$142$	−0.623533	−	9.91077i	−0.0523257	−	0.831693i
$143$	−2.29513	−	7.06368i	−0.191928	−	0.590695i
$144$	−14.9857	+	23.6137i	−1.24881	+	1.96781i
$145$	−5.49394	−	1.18762i	−0.456247	−	0.0986263i
$146$	−0.703678	+	0.180674i	−0.0582368	+	0.0149527i
$147$	−1.42084	+	22.5836i	−0.117189	+	1.86266i
$148$	0.00118177	−	0.00619504i	9.71406e−5	−	0.000509229i
$149$	5.68527	−	17.4975i	0.465756	−	1.43345i	−0.392274	−	0.919848i	$-0.628312\pi$
$149$	5.68527	−	17.4975i	0.465756	−	1.43345i	0.858030	−	0.513600i	$-0.171688\pi$
$150$	−22.3094	+	1.71830i	−1.82156	+	0.140298i
$151$	−1.66909	−	5.13694i	−0.135829	−	0.418038i	0.859889	−	0.510481i	$-0.170533\pi$
$151$	−1.66909	−	5.13694i	−0.135829	−	0.418038i	−0.995718	+	0.0924426i	$0.970533\pi$
$152$	0.969967	−	0.122535i	0.0786747	−	0.00993893i
$153$	2.72949	+	1.08068i	0.220666	+	0.0873678i
$154$	−19.6293	−	7.77181i	−1.58178	−	0.626270i
$155$	−0.420520	−	1.82116i	−0.0337770	−	0.146279i
$156$	0.00522661	+	0.0830746i	0.000418464	+	0.00665129i
$157$	−15.5069	+	11.2664i	−1.23759	+	0.899159i	−0.997435	−	0.0715772i	$-0.977197\pi$
$157$	−15.5069	+	11.2664i	−1.23759	+	0.899159i	−0.240150	+	0.970736i	$0.577197\pi$
$158$	1.47271	+	0.378128i	0.117163	+	0.0300823i
$159$	7.76340	+	7.29032i	0.615678	+	0.578160i
$160$	−0.124714	+	0.126477i	−0.00985953	+	0.00999891i
$161$	15.3379	+	8.43209i	1.20880	+	0.664542i
$162$	−25.8803	−	3.26944i	−2.03335	−	0.256871i
$163$	−2.07513	−	10.8782i	−0.162537	−	0.852048i	−0.966363	−	0.257183i	$-0.917206\pi$
$163$	−2.07513	−	10.8782i	−0.162537	−	0.852048i	0.803826	−	0.594865i	$-0.202794\pi$
$164$	0.164024	−	0.0207210i	0.0128081	−	0.00161804i
$165$	27.7533	+	2.42706i	2.16060	+	0.188946i
$166$	−3.14047	−	16.4629i	−0.243748	−	1.27777i
$167$	3.98299	−	6.27619i	0.308213	−	0.485666i	−0.654548	−	0.756021i	$-0.727141\pi$
$167$	3.98299	−	6.27619i	0.308213	−	0.485666i	0.962761	+	0.270354i	$0.0871409\pi$
$168$	−27.0712	−	19.6684i	−2.08859	−	1.51745i
$169$	6.03411	+	7.29399i	0.464162	+	0.561076i
$170$	1.11494	+	0.746325i	0.0855118	+	0.0572405i
$171$	1.29060	+	2.03366i	0.0986944	+	0.155518i
$172$	−0.0247898	+	0.0299657i	−0.00189020	+	0.00228486i
$173$	−5.13958	−	10.9222i	−0.390755	−	0.830397i	−0.999319	−	0.0368922i	$-0.988254\pi$
$173$	−5.13958	−	10.9222i	−0.390755	−	0.830397i	0.608564	−	0.793505i	$-0.291746\pi$
$174$	−9.10074	−	6.61208i	−0.689925	−	0.501260i
$175$	−0.264253	−	18.8237i	−0.0199757	−	1.42293i
$176$	12.8751	−	9.35432i	0.970499	−	0.705108i
$177$	15.6620	+	8.61024i	1.17723	+	0.647186i
$178$	−12.6768	+	3.25485i	−0.950165	+	0.243961i
$179$	1.89815	−	2.29447i	0.141874	−	0.171496i	−0.694790	−	0.719213i	$-0.744503\pi$
$179$	1.89815	−	2.29447i	0.141874	−	0.171496i	0.836664	+	0.547716i	$0.184503\pi$
$180$	−0.205650	−	0.0724122i	−0.0153283	−	0.00539729i
$181$	−15.0746	+	5.96846i	−1.12049	+	0.443632i	−0.854035	−	0.520216i	$-0.825851\pi$
$181$	−15.0746	+	5.96846i	−1.12049	+	0.443632i	−0.266452	+	0.963848i	$0.585851\pi$
$182$	−10.0443			−0.744533
$183$	−41.1453	+	16.2906i	−3.04155	+	1.20423i
$184$	−11.4814	+	6.31194i	−0.846418	+	0.465322i
$185$	−1.00351	+	0.0385885i	−0.0737794	+	0.00283708i
$186$	0.700926	−	3.67438i	0.0513944	−	0.269419i
$187$	−1.21773	−	1.14353i	−0.0890495	−	0.0836230i
$188$	0.0471260	+	0.0442542i	0.00343701	+	0.00322757i
$189$	8.77300	−	45.9897i	0.638142	−	3.34526i
$190$	0.380145	+	1.03308i	0.0275786	+	0.0749477i
$191$	−13.7768	+	7.57386i	−0.996854	+	0.548025i	−0.894664	−	0.446740i	$-0.852585\pi$
$191$	−13.7768	+	7.57386i	−0.996854	+	0.548025i	−0.102190	+	0.994765i	$0.532585\pi$
$192$	23.2881	−	9.22041i	1.68067	−	0.665426i
$193$	12.1363			0.873594			0.436797	−	0.899560i	$-0.356113\pi$
$193$	12.1363			0.873594			0.436797	+	0.899560i	$0.356113\pi$
$194$	19.7016	−	7.80040i	1.41449	−	0.560036i
$195$	12.7019	−	3.78712i	0.909603	−	0.271201i
$196$	−0.0642332	+	0.0776446i	−0.00458809	+	0.00554604i
$197$	−0.128650	+	0.0330317i	−0.00916593	+	0.00235341i	−0.253270	−	0.967396i	$-0.581506\pi$
$197$	−0.128650	+	0.0330317i	−0.00916593	+	0.00235341i	0.244104	+	0.969749i	$0.421506\pi$
$198$	34.1179	+	18.7565i	2.42465	+	1.33296i
$199$	−18.9905	+	13.7974i	−1.34620	+	0.978070i	−0.347007	+	0.937862i	$0.612802\pi$
$199$	−18.9905	+	13.7974i	−1.34620	+	0.978070i	−0.999191	+	0.0402080i	$0.987198\pi$
$200$	12.0031	+	7.38314i	0.848750	+	0.522067i
$201$	−3.94371	−	2.86527i	−0.278168	−	0.202101i
$202$	10.2606	+	21.8050i	0.721936	+	1.53419i
$203$	6.03284	−	7.29245i	0.423422	−	0.511829i
$204$	0.0100316	+	0.0158072i	0.000702351	+	0.00110673i
$205$	−9.09115	−	24.7062i	−0.634954	−	1.72555i
$206$	−1.65795	−	2.00411i	−0.115515	−	0.139633i
$207$	−26.1136	−	18.9726i	−1.81502	−	1.31869i
$208$	4.05705	−	6.39289i	0.281306	−	0.443267i
$209$	−0.256823	−	1.34631i	−0.0177648	−	0.0931263i
$210$	14.7199	−	34.6815i	1.01577	−	2.39325i
$211$	1.95708	−	0.247236i	0.134731	−	0.0170204i	−0.0576786	−	0.998335i	$-0.518370\pi$
$211$	1.95708	−	0.247236i	0.134731	−	0.0170204i	0.192409	+	0.981315i	$0.438370\pi$
$212$	0.00888689	+	0.0465867i	0.000610354	+	0.00319959i
$213$	−21.8908	−	2.76545i	−1.49993	−	0.189485i
$214$	2.99004	+	1.64379i	0.204395	+	0.112367i
$215$	5.53734	+	2.77263i	0.377643	+	0.189092i
$216$	25.5481	+	23.9912i	1.73833	+	1.63240i
$217$	3.04829	+	0.782669i	0.206932	+	0.0531310i
$218$	−2.91700	+	2.11933i	−0.197564	+	0.143539i
$219$	0.101360	+	1.61107i	0.00684926	+	0.108866i
$220$	0.0936363	+	0.0813906i	0.00631296	+	0.00548735i
$221$	−0.738949	−	0.292570i	−0.0497071	−	0.0196804i
$222$	−1.86869	−	0.739868i	−0.125419	−	0.0496567i
$223$	−7.53706	+	0.952153i	−0.504719	+	0.0637608i	−0.373570	−	0.927602i	$-0.621867\pi$
$223$	−7.53706	+	0.952153i	−0.504719	+	0.0637608i	−0.131149	+	0.991363i	$0.541867\pi$
$224$	−0.0924219	−	0.284445i	−0.00617520	−	0.0190053i
$225$	−3.86731	+	34.5012i	−0.257821	+	2.30008i
$226$	−5.96235	+	18.3502i	−0.396609	+	1.22064i
$227$	1.11712	−	5.85616i	0.0741460	−	0.388687i	−0.925797	−	0.378021i	$-0.876605\pi$
$227$	1.11712	−	5.85616i	0.0741460	−	0.388687i	0.999943	−	0.0106662i	$-0.00339521\pi$
$228$	−0.000964500		0.0153303i	−6.38756e−5		0.00101527i
$229$	0.376745	−	0.0967318i	0.0248960	−	0.00639222i	−0.236221	−	0.971699i	$-0.575909\pi$
$229$	0.376745	−	0.0967318i	0.0248960	−	0.00639222i	0.261117	+	0.965307i	$0.415909\pi$
$230$	−9.83314	−	10.9969i	−0.648378	−	0.725117i
$231$	−25.1354	+	39.6071i	−1.65379	+	2.60595i
$232$	2.18929	+	6.73793i	0.143734	+	0.442367i
$233$	−0.611395	−	9.71784i	−0.0400538	−	0.636637i	−0.965929	−	0.258807i	$-0.916671\pi$
$233$	−0.611395	−	9.71784i	−0.0400538	−	0.636637i	0.925875	−	0.377829i	$-0.123329\pi$
$234$	18.3772	+	2.32158i	1.20136	+	0.151767i
$235$	5.17780	−	8.89711i	0.337762	−	0.580383i
$236$	0.0338887	+	0.0720172i	0.00220597	+	0.00468792i
$237$	1.43847	−	3.05690i	0.0934385	−	0.198567i
$238$	−1.97968	+	1.08834i	−0.128323	+	0.0705464i
$239$	5.88232	−	5.52386i	0.380495	−	0.357309i	−0.470575	−	0.882360i	$-0.655954\pi$
$239$	5.88232	−	5.52386i	0.380495	−	0.357309i	0.851071	+	0.525051i	$0.175954\pi$
$240$	16.1281	+	23.3771i	1.04106	+	1.50899i
$241$	3.90466	−	8.29783i	0.251521	−	0.534510i	−0.738697	−	0.674038i	$-0.764558\pi$
$241$	3.90466	−	8.29783i	0.251521	−	0.534510i	0.990218	+	0.139528i	$0.0445584\pi$
$242$	−4.17122	−	5.04214i	−0.268136	−	0.324121i
$243$	−6.38330	+	19.6458i	−0.409489	+	1.26028i
$244$	−0.190879	−	0.0490095i	−0.0122198	−	0.00313751i
$245$	14.3479	+	7.18422i	0.916653	+	0.458983i
$246$	3.30820	−	52.5824i	0.210923	−	3.35253i
$247$	−0.349401	−	0.550568i	−0.0222318	−	0.0350318i
$248$	−1.71734	+	1.61269i	−0.109051	+	0.102406i
$249$	−37.2394			−2.35995
$250$	−5.05918	+	15.0386i	−0.319970	+	0.951126i
$251$	1.40763			0.0888490			0.0444245	−	0.999013i	$-0.485855\pi$
$251$	1.40763			0.0888490			0.0444245	+	0.999013i	$0.485855\pi$
$252$	0.267615	−	0.251307i	0.0168581	−	0.0158308i
$253$	9.84179	+	15.5082i	0.618748	+	0.974990i
$254$	0.170654	−	2.71246i	0.0107078	−	0.170195i
$255$	2.09313	−	2.12272i	0.131077	−	0.132930i
$256$	0.326419	+	0.0838102i	0.0204012	+	0.00523814i
$257$	−5.68429	+	17.4944i	−0.354576	+	1.09127i	0.601679	+	0.798738i	$0.294499\pi$
$257$	−5.68429	+	17.4944i	−0.354576	+	1.09127i	−0.956255	+	0.292535i	$0.905501\pi$
$258$	7.90000	+	9.54945i	0.491832	+	0.594523i
$259$	0.719976	−	1.53003i	0.0447371	−	0.0950712i
$260$	0.0556753	+	0.0196040i	0.00345283	+	0.00121579i
$261$	−12.7233	+	11.9480i	−0.787554	+	0.739562i
$262$	18.1818	−	9.99551i	1.12327	−	0.617525i
$263$	−1.34276	+	2.85351i	−0.0827980	+	0.175955i	−0.941939	−	0.335784i	$-0.890999\pi$
$263$	−1.34276	+	2.85351i	−0.0827980	+	0.175955i	0.859141	+	0.511739i	$0.170999\pi$
$264$	−14.9511	−	31.7727i	−0.920177	−	1.95548i
$265$	6.90963	−	3.04782i	0.424455	−	0.187226i
$266$	−1.83892	−	0.232310i	−0.112752	−	0.0142439i
$267$	1.82600	+	29.0234i	0.111749	+	1.77620i
$268$	−0.00670826	−	0.0206459i	−0.000409772	−	0.00126115i
$269$	12.2382	−	19.2843i	0.746174	−	1.17578i	−0.232944	−	0.972490i	$-0.574836\pi$
$269$	12.2382	−	19.2843i	0.746174	−	1.17578i	0.979118	−	0.203292i	$-0.0651641\pi$
$270$	−19.8482	+	34.1056i	−1.20792	+	2.07560i
$271$	−13.1786	+	3.38369i	−0.800543	+	0.205545i	−0.626732	−	0.779235i	$-0.715608\pi$
$271$	−13.1786	+	3.38369i	−0.800543	+	0.205545i	−0.173811	+	0.984779i	$0.555608\pi$
$272$	0.106930	−	1.69960i	0.00648357	−	0.103053i
$273$	−4.18196	+	21.9226i	−0.253104	+	1.32682i
$274$	−4.88793	+	15.0435i	−0.295291	+	0.908812i
$275$	9.27330	−	17.4437i	0.559201	−	1.05189i
$276$	−0.0636111	−	0.195775i	−0.00382894	−	0.0117843i
$277$	−23.9239	+	3.02229i	−1.43745	+	0.181592i	−0.805121	−	0.593111i	$-0.797900\pi$
$277$	−23.9239	+	3.02229i	−1.43745	+	0.181592i	−0.632326	+	0.774702i	$0.717900\pi$
$278$	28.9749	+	11.4720i	1.73780	+	0.688044i
$279$	−5.39631	−	2.13655i	−0.323069	−	0.127912i
$280$	−20.3386	+	12.2217i	−1.21547	+	0.730388i
$281$	0.926913	+	14.7329i	0.0552950	+	0.878888i	0.923720	+	0.383068i	$0.125133\pi$
$281$	0.926913	+	14.7329i	0.0552950	+	0.878888i	−0.868425	+	0.495820i	$0.834867\pi$
$282$	16.6672	−	12.1094i	0.992518	−	0.721107i
$283$	9.10360	+	2.33741i	0.541153	+	0.138944i	0.509366	−	0.860550i	$-0.329880\pi$
$283$	9.10360	+	2.33741i	0.541153	+	0.138944i	0.0317873	+	0.999495i	$0.489880\pi$
$284$	−0.0716290	−	0.0672641i	−0.00425040	−	0.00399139i
$285$	2.41307	−	0.399575i	0.142938	−	0.0236688i
$286$	−9.23667	−	5.07790i	−0.546175	−	0.300263i
$287$	43.9779	+	5.55570i	2.59593	+	0.327942i
$288$	0.103352	+	0.541788i	0.00609005	+	0.0319252i
$289$	16.6886	−	2.10826i	0.981683	−	0.124015i
$290$	−6.83741	+	4.10868i	−0.401506	+	0.241270i
$291$	−8.82232	−	46.2482i	−0.517173	−	2.71112i
$292$	−0.00385191	+	0.00606964i	−0.000225416	+	0.000355199i
$293$	10.2195	+	7.42493i	0.597032	+	0.433769i	0.844824	−	0.535044i	$-0.179705\pi$
$293$	10.2195	+	7.42493i	0.597032	+	0.433769i	−0.247792	+	0.968813i	$0.579705\pi$
$294$	20.4698	+	24.7437i	1.19382	+	1.44308i
$295$	9.95950	−	7.83796i	0.579865	−	0.456343i
$296$	0.678243	+	1.06874i	0.0394221	+	0.0621193i
$297$	31.3177	−	37.8566i	1.81724	−	2.19666i
$298$	−11.1170	−	23.6248i	−0.643991	−	1.36855i
$299$	7.06968	+	5.13642i	0.408850	+	0.297047i
$300$	−0.149282	+	0.163509i	−0.00861878	+	0.00944019i
$301$	−8.43587	+	6.12902i	−0.486236	+	0.353271i
$302$	−6.71720	−	3.69281i	−0.386532	−	0.212498i
$303$	51.8634	−	13.3163i	2.97947	−	0.764999i
$304$	0.890629	−	1.07659i	0.0510811	−	0.0617464i
$305$	−0.765518	+	31.3711i	−0.0438334	+	1.79630i
$306$	3.87361	−	1.53367i	0.221439	−	0.0876740i
$307$	−16.3274			−0.931853			−0.465927	−	0.884823i	$-0.654279\pi$
$307$	−16.3274			−0.931853			−0.465927	+	0.884823i	$0.654279\pi$
$308$	−0.194232	+	0.0769018i	−0.0110674	+	0.00438189i
$309$	−5.06445	+	2.78421i	−0.288107	+	0.158388i
$310$	−2.20428	−	1.47552i	−0.125195	−	0.0838037i
$311$	4.19900	−	22.0119i	0.238103	−	1.24818i	−0.639499	−	0.768792i	$-0.720858\pi$
$311$	4.19900	−	22.0119i	0.238103	−	1.24818i	0.877602	−	0.479390i	$-0.159142\pi$
$312$	−12.1784	−	11.4363i	−0.689466	−	0.647452i
$313$	−13.8838	−	13.0378i	−0.784760	−	0.736939i	0.184538	−	0.982825i	$-0.440921\pi$
$313$	−13.8838	−	13.0378i	−0.784760	−	0.736939i	−0.969299	+	0.245886i	$0.920921\pi$
$314$	−5.09716	+	26.7202i	−0.287649	+	1.50791i
$315$	−48.5781	−	32.5176i	−2.73707	−	1.83216i
$316$	0.0131841	−	0.00724804i	0.000741666	−	0.000407734i
$317$	−17.9772	+	7.11767i	−1.00970	+	0.399768i	−0.813981	−	0.580892i	$-0.802704\pi$
$317$	−17.9772	+	7.11767i	−1.00970	+	0.399768i	−0.195719	+	0.980660i	$0.562704\pi$
$318$	15.1139			0.847547
$319$	9.23445	−	3.65618i	0.517030	−	0.204707i
$320$	0.433280	−	17.7559i	0.0242211	−	0.992585i
$321$	4.83262	−	5.84164i	0.269731	−	0.326048i
$322$	24.0592	−	6.17736i	1.34077	−	0.344251i
$323$	−0.128521	−	0.0706550i	−0.00715110	−	0.00393135i
$324$	−0.208823	+	0.151719i	−0.0116013	+	0.00842884i
$325$	1.04699	−	9.34044i	0.0580766	−	0.518114i
$326$	−12.7149	−	9.23789i	−0.704211	−	0.511639i
$327$	3.41113	+	7.24902i	0.188636	+	0.400872i
$328$	−21.1509	+	25.5670i	−1.16786	+	1.41170i
$329$	9.28761	+	14.6349i	0.512042	+	0.806850i
$330$	31.0695	−	24.4512i	1.71032	−	1.34599i
$331$	−0.704819	−	0.851980i	−0.0387404	−	0.0468291i	0.750787	−	0.660544i	$-0.229674\pi$
$331$	−0.704819	−	0.851980i	−0.0387404	−	0.0468291i	−0.789528	+	0.613715i	$0.789674\pi$
$332$	−0.134166	−	0.0974770i	−0.00736329	−	0.00534974i
$333$	−1.67092	+	2.63295i	−0.0915660	+	0.144285i
$334$	−1.97672	−	10.3623i	−0.108161	−	0.567002i
$335$	−2.96292	+	1.78045i	−0.161882	+	0.0972765i
$336$	−47.4444	+	5.99362i	−2.58830	+	0.326979i
$337$	−4.10069	−	21.4966i	−0.223379	−	1.17099i	−0.900411	−	0.435039i	$-0.856734\pi$
$337$	−4.10069	−	21.4966i	−0.223379	−	1.17099i	0.677033	−	0.735953i	$-0.263266\pi$
$338$	13.3285	+	1.68378i	0.724975	+	0.0915856i
$339$	37.5686	+	20.6535i	2.04045	+	1.12175i
$340$	0.0130975	−	0.00216877i	0.000710310	−	0.000117618i
$341$	2.40751	+	2.26080i	0.130374	+	0.122429i
$342$	3.31083	+	0.850078i	0.179029	+	0.0459669i
$343$	−0.536099	+	0.389499i	−0.0289466	+	0.0210310i
$344$	−0.490110	−	7.79008i	−0.0264250	−	0.420013i
$345$	−28.0959	+	16.8831i	−1.51263	+	0.908958i
$346$	−15.9278	−	6.30627i	−0.856284	−	0.339027i
$347$	−12.1989	−	4.82990i	−0.654873	−	0.259283i	0.0171048	−	0.999854i	$-0.494555\pi$
$347$	−12.1989	−	4.82990i	−0.654873	−	0.259283i	−0.671978	+	0.740571i	$0.734555\pi$
$348$	−0.110432	+	0.0139508i	−0.00591978	+	0.000747843i
$349$	−2.70191	−	8.31562i	−0.144630	−	0.445125i	0.852333	−	0.522999i	$-0.175187\pi$
$349$	−2.70191	−	8.31562i	−0.144630	−	0.445125i	−0.996963	+	0.0778740i	$0.975187\pi$
$350$	−18.5603	−	19.2169i	−0.992092	−	1.02719i
$351$	7.22330	−	22.2310i	0.385551	−	1.18661i
$352$	0.0588110	−	0.308298i	0.00313464	−	0.0164323i
$353$	−2.27669	+	36.1869i	−0.121176	+	1.92603i	0.201433	+	0.979502i	$0.435440\pi$
$353$	−2.27669	+	36.1869i	−0.121176	+	1.92603i	−0.322609	+	0.946532i	$0.604560\pi$
$354$	24.5675	−	6.30787i	1.30575	−	0.335260i
$355$	−7.86997	+	13.5231i	−0.417695	+	0.717733i
$356$	−0.0693923	+	0.109345i	−0.00367778	+	0.00579526i
$357$	1.55115	+	4.77396i	0.0820958	+	0.252665i
$358$	−0.265357	−	4.21772i	−0.0140245	−	0.222914i
$359$	−16.3064	−	2.05997i	−0.860618	−	0.108721i	−0.317378	−	0.948299i	$-0.602802\pi$
$359$	−16.3064	−	2.05997i	−0.860618	−	0.108721i	−0.543240	+	0.839578i	$0.682802\pi$
$360$	40.0368	−	17.6601i	2.11012	−	0.930770i
$361$	8.03857	+	17.0828i	0.423083	+	0.899097i
$362$	−9.79685	+	20.8194i	−0.514911	+	1.09424i
$363$	−12.7416	+	7.00478i	−0.668763	+	0.367655i
$364$	−0.0724508	+	0.0680358i	−0.00379745	+	0.00356605i
$365$	1.07971	+	0.380181i	0.0565147	+	0.0198996i
$366$	−26.7400	+	56.8253i	−1.39772	+	2.97031i
$367$	2.67625	+	3.23503i	0.139699	+	0.168867i	0.835723	−	0.549152i	$-0.185049\pi$
$367$	2.67625	+	3.23503i	0.139699	+	0.168867i	−0.696024	+	0.718019i	$0.745049\pi$
$368$	−5.78619	+	17.8081i	−0.301626	+	0.928310i
$369$	−79.1786	−	20.3296i	−4.12187	−	1.05832i
$370$	−1.00067	+	1.01482i	−0.0520224	+	0.0527578i
$371$	−0.798446	+	12.6909i	−0.0414533	+	0.658881i
$372$	−0.0198328	−	0.0312516i	−0.00102829	−	0.00162032i
$373$	−13.9504	+	13.1003i	−0.722324	+	0.678308i	−0.955788	−	0.294058i	$-0.904994\pi$
$373$	−13.9504	+	13.1003i	−0.722324	+	0.678308i	0.233463	+	0.972366i	$0.424994\pi$
$374$	−2.37071			−0.122586
$375$	30.7168	+	17.3035i	1.58621	+	0.893548i
$376$	−12.9750			−0.669134
$377$	3.44456	−	3.23466i	0.177404	−	0.166593i
$378$	−35.6025	−	56.1006i	−1.83120	−	2.88550i
$379$	1.03398	−	16.4346i	0.0531118	−	0.844188i	−0.877819	−	0.478992i	$-0.841002\pi$
$379$	1.03398	−	16.4346i	0.0531118	−	0.844188i	0.930931	−	0.365195i	$-0.118998\pi$
$380$	0.00973970	+	0.00487682i	0.000499636	+	0.000250176i
$381$	−5.84915	−	1.50181i	−0.299661	−	0.0769399i
$382$	−6.89460	+	21.2194i	−0.352758	+	1.08568i
$383$	17.3854	+	21.0153i	0.888350	+	1.07383i	0.996816	+	0.0797309i	$0.0254061\pi$
$383$	17.3854	+	21.0153i	0.888350	+	1.07383i	−0.108466	+	0.994100i	$0.534594\pi$
$384$	15.3480	−	32.6162i	0.783226	−	1.66444i
$385$	18.8899	+	27.3803i	0.962720	+	1.39543i
$386$	12.5554	−	11.7903i	0.639054	−	0.600112i
$387$	16.8511	−	9.26394i	0.856587	−	0.470913i
$388$	0.0892732	−	0.189715i	0.00453216	−	0.00963134i
$389$	−4.56487	−	9.70085i	−0.231448	−	0.491852i	0.755041	−	0.655677i	$-0.227617\pi$
$389$	−4.56487	−	9.70085i	−0.231448	−	0.491852i	−0.986489	+	0.163825i	$0.947617\pi$
$390$	9.46136	−	16.2576i	0.479095	−	0.823238i
$391$	1.94994	+	0.246335i	0.0986130	+	0.0124577i
$392$	−1.26993	−	20.1850i	−0.0641413	−	1.01950i
$393$	−14.2461	−	43.8450i	−0.718621	−	2.21169i
$394$	−0.101002	+	0.159154i	−0.00508842	+	0.00801807i
$395$	−1.59688	−	1.78588i	−0.0803476	−	0.0898571i
$396$	0.373145	−	0.0958073i	0.0187512	−	0.00481450i
$397$	−1.60034	+	25.4367i	−0.0803188	+	1.27663i	0.727050	+	0.686584i	$0.240891\pi$
$397$	−1.60034	+	25.4367i	−0.0803188	+	1.27663i	−0.807369	+	0.590047i	$0.799109\pi$
$398$	−6.24221	+	32.7228i	−0.312894	+	1.64025i
$399$	−1.27268	+	3.91690i	−0.0637136	+	0.196090i
$400$	19.7278	−	4.05107i	0.986390	−	0.202554i
$401$	−7.04218	−	21.6736i	−0.351670	−	1.08233i	−0.957915	−	0.287051i	$-0.907325\pi$
$401$	−7.04218	−	21.6736i	−0.351670	−	1.08233i	0.606246	−	0.795277i	$-0.292675\pi$
$402$	−6.86347	+	0.867058i	−0.342319	+	0.0432449i
$403$	1.46093	+	0.578424i	0.0727743	+	0.0288134i
$404$	0.221709	+	0.0877807i	0.0110304	+	0.00436725i
$405$	31.0207	+	26.9639i	1.54143	+	1.33984i
$406$	−0.843376	−	13.4051i	−0.0418561	−	0.665283i
$407$	1.43559	−	1.04302i	0.0711596	−	0.0517005i
$408$	−3.63946	−	0.934454i	−0.180180	−	0.0462624i
$409$	14.9062	+	13.9978i	0.737062	+	0.692147i	0.959156	−	0.282878i	$-0.0912891\pi$
$409$	14.9062	+	13.9978i	0.737062	+	0.692147i	−0.222094	+	0.975025i	$0.571289\pi$
$410$	−33.4068	−	16.7273i	−1.64985	−	0.826104i
$411$	30.7988	+	16.9318i	1.51919	+	0.835183i
$412$	−0.0255340	−	0.00322569i	−0.00125797	−	0.000158918i
$413$	3.99876	+	20.9622i	0.196766	+	1.03148i
$414$	−45.4470	+	5.74129i	−2.23360	+	0.282169i
$415$	−10.3171	+	24.3082i	−0.506448	+	1.19324i
$416$	−0.0279802	−	0.146677i	−0.00137184	−	0.00719145i
$417$	37.1024	−	58.4641i	1.81691	−	2.86300i
$418$	−1.57362	−	1.14330i	−0.0769681	−	0.0559206i
$419$	−9.75158	−	11.7876i	−0.476396	−	0.575864i	0.476495	−	0.879177i	$-0.341907\pi$
$419$	−9.75158	−	11.7876i	−0.476396	−	0.575864i	−0.952891	+	0.303313i	$0.901907\pi$
$420$	−0.128741	−	0.349868i	−0.00628193	−	0.0170718i
$421$	3.11789	+	4.91301i	0.151957	+	0.239445i	0.911775	−	0.410690i	$-0.134712\pi$
$421$	3.11789	+	4.91301i	0.151957	+	0.239445i	−0.759818	+	0.650135i	$0.774712\pi$
$422$	1.78447	−	2.15705i	0.0868665	−	0.105004i
$423$	−13.6101	−	28.9230i	−0.661747	−	1.40628i
$424$	−7.70081	−	5.59497i	−0.373985	−	0.271716i
$425$	−0.805715	−	1.95439i	−0.0390829	−	0.0948021i
$426$	−25.3333	+	18.4057i	−1.22740	+	0.891759i
$427$	−46.3027	−	25.4551i	−2.24074	−	1.23186i
$428$	0.0327018	−	0.00839639i	0.00158070	−	0.000405855i
$429$	−14.9287	+	18.0457i	−0.720764	+	0.871254i
$430$	8.42213	−	2.51109i	0.406151	−	0.121095i
$431$	27.0613	−	10.7143i	1.30350	−	0.516092i	0.389208	−	0.921150i	$-0.372749\pi$
$431$	27.0613	−	10.7143i	1.30350	−	0.516092i	0.914291	+	0.405058i	$0.132749\pi$
$432$	50.0867			2.40980
$433$	31.0720	−	12.3023i	1.49322	−	0.591209i	0.527218	−	0.849730i	$-0.323235\pi$
$433$	31.0720	−	12.3023i	1.49322	−	0.591209i	0.966006	+	0.258521i	$0.0832353\pi$
$434$	3.91391	−	2.15169i	0.187874	−	0.103284i
$435$	6.12080	+	16.6339i	0.293470	+	0.797536i
$436$	−0.00668529	+	0.0350455i	−0.000320167	+	0.00167838i
$437$	1.17553	+	1.10389i	0.0562331	+	0.0528064i
$438$	1.66999	+	1.56823i	0.0797953	+	0.0749328i
$439$	6.46741	−	33.9034i	0.308673	−	1.61812i	−0.402720	−	0.915323i	$-0.631935\pi$
$439$	6.46741	−	33.9034i	0.308673	−	1.61812i	0.711392	−	0.702795i	$-0.248065\pi$
$440$	−24.8820	+	0.956800i	−1.18620	+	0.0456137i
$441$	43.6630	−	24.0040i	2.07919	−	1.14305i
$442$	−1.04869	+	0.415207i	−0.0498813	+	0.0197494i
$443$	−34.7900			−1.65292			−0.826461	−	0.562994i	$-0.809649\pi$
$443$	−34.7900			−1.65292			−0.826461	+	0.562994i	$0.809649\pi$
$444$	−0.0184907	+	0.00732097i	−0.000877528	+	0.000347438i
$445$	19.4510	+	6.84898i	0.922068	+	0.324673i
$446$	−6.87231	+	8.30720i	−0.325414	+	0.393357i
$447$	−56.1920	+	14.4276i	−2.65779	+	0.682404i
$448$	26.2072	+	14.4075i	1.23817	+	0.680691i
$449$	29.1799	−	21.2005i	1.37709	−	1.00051i	0.379940	−	0.925011i	$-0.375944\pi$
$449$	29.1799	−	21.2005i	1.37709	−	1.00051i	0.997146	−	0.0755007i	$-0.0240555\pi$
$450$	29.5166	+	39.4496i	1.39143	+	1.85967i
$451$	37.6330	+	27.3420i	1.77207	+	1.28748i
$452$	0.0812894	+	0.172749i	0.00382353	+	0.00812542i
$453$	−10.8566	+	13.1234i	−0.510089	+	0.616592i
$454$	−4.53349	−	7.14364i	−0.212767	−	0.335268i
$455$	13.1515	+	8.80343i	0.616550	+	0.412711i
$456$	−1.96513	−	2.37544i	−0.0920258	−	0.111240i
$457$	29.2896	+	21.2801i	1.37011	+	0.995443i	0.997729	+	0.0673628i	$0.0214585\pi$
$457$	29.2896	+	21.2801i	1.37011	+	0.995443i	0.372381	+	0.928080i	$0.378542\pi$
$458$	0.295781	−	0.466076i	0.0138209	−	0.0217783i
$459$	−0.985141	−	5.16429i	−0.0459824	−	0.241048i
$460$	−0.145416	−	0.0127168i	−0.00678007	−	0.000592923i
$461$	10.7274	−	1.35518i	0.499623	−	0.0631171i	0.128517	−	0.991707i	$-0.458978\pi$
$461$	10.7274	−	1.35518i	0.499623	−	0.0631171i	0.371107	+	0.928590i	$0.378978\pi$
$462$	12.4745	+	65.3935i	0.580365	+	3.04238i
$463$	−14.8437	−	1.87520i	−0.689846	−	0.0871478i	−0.227408	−	0.973800i	$-0.573025\pi$
$463$	−14.8437	−	1.87520i	−0.689846	−	0.0871478i	−0.462438	+	0.886652i	$0.653025\pi$
$464$	8.87258	+	4.87774i	0.411899	+	0.226443i
$465$	−4.13821	+	4.19671i	−0.191905	+	0.194618i
$466$	−10.0733	−	9.45943i	−0.466635	−	0.438200i
$467$	−1.99626	−	0.512552i	−0.0923758	−	0.0237181i	0.202219	−	0.979340i	$-0.435185\pi$
$467$	−1.99626	−	0.512552i	−0.0923758	−	0.0237181i	−0.294595	+	0.955622i	$0.595185\pi$
$468$	0.148283	−	0.107734i	0.00685437	−	0.00497999i
$469$	−0.365468	−	5.80895i	−0.0168758	−	0.268233i
$470$	−3.28685	−	14.2345i	−0.151611	−	0.656588i
$471$	56.1972	+	22.2500i	2.58943	+	1.02523i
$472$	−14.8527	−	5.88059i	−0.683650	−	0.270676i
$473$	−10.8561	+	1.37144i	−0.499164	+	0.0630591i
$474$	−1.48160	−	4.55991i	−0.0680523	−	0.209444i
$475$	0.407715	−	1.68584i	0.0187073	−	0.0773519i
$476$	−0.00690773	+	0.0212598i	−0.000316615	+	0.000974441i
$477$	4.39416	−	23.0350i	0.201195	−	1.05470i
$478$	0.719065	−	11.4292i	0.0328893	−	0.522760i
$479$	−4.45883	+	1.14483i	−0.203729	+	0.0523087i	−0.349175	−	0.937057i	$-0.613538\pi$
$479$	−4.45883	+	1.14483i	−0.203729	+	0.0523087i	0.145446	+	0.989366i	$0.453538\pi$
$480$	0.547460	+	0.118344i	0.0249880	+	0.00540162i
$481$	0.452366	−	0.712814i	0.0206261	−	0.0325015i
$482$	−4.02176	−	12.3777i	−0.183186	−	0.563788i
$483$	−3.46555	−	55.0834i	−0.157688	−	2.50638i
$484$	−0.0642409	−	0.00811551i	−0.00292004	−	0.000368887i
$485$	−32.6329	−	7.05421i	−1.48178	−	0.320315i
$486$	12.4819	+	26.5254i	0.566192	+	1.20322i
$487$	−14.4193	+	30.6425i	−0.653399	+	1.38854i	0.253558	+	0.967320i	$0.418399\pi$
$487$	−14.4193	+	30.6425i	−0.653399	+	1.38854i	−0.906957	+	0.421223i	$0.861601\pi$
$488$	34.6604	−	19.0547i	1.56900	−	0.862567i
$489$	−25.4564	+	23.9051i	−1.15118	+	1.08103i
$490$	21.8227	−	6.50652i	0.985849	−	0.293935i
$491$	3.26410	−	6.93656i	0.147307	−	0.313042i	−0.817533	−	0.575882i	$-0.804659\pi$
$491$	3.26410	−	6.93656i	0.147307	−	0.313042i	0.964840	+	0.262839i	$0.0846589\pi$
$492$	−0.332308	−	0.401692i	−0.0149816	−	0.0181097i
$493$	0.328417	−	1.01076i	0.0147912	−	0.0455225i
$494$	−0.896336	−	0.230140i	−0.0403281	−	0.0103545i
$495$	−28.2328	−	54.4616i	−1.26897	−	2.44787i
$496$	−0.211405	+	3.36018i	−0.00949235	+	0.150877i
$497$	−14.1167	−	22.2443i	−0.633219	−	0.997794i
$498$	−38.5253	+	36.1777i	−1.72636	+	1.62116i
$499$	25.4067			1.13736			0.568681	−	0.822558i	$-0.307454\pi$
$499$	25.4067			1.13736			0.568681	+	0.822558i	$0.307454\pi$
$500$	0.0653727	+	0.142744i	0.00292356	+	0.00638371i
$501$	−23.4398			−1.04721
$502$	1.45624	−	1.36750i	0.0649951	−	0.0610345i
$503$	−21.5180	−	33.9069i	−0.959438	−	1.51183i	−0.855857	−	0.517212i	$-0.826970\pi$
$503$	−21.5180	−	33.9069i	−0.959438	−	1.51183i	−0.103581	−	0.994621i	$-0.533030\pi$
$504$	−4.62648	+	73.5358i	−0.206080	+	3.27554i
$505$	5.67645	−	37.5433i	0.252599	−	1.67065i
$506$	25.2476	+	6.48249i	1.12239	+	0.288182i
$507$	9.22435	−	28.3896i	0.409668	−	1.26083i
$508$	−0.0171421	−	0.0207213i	−0.000760559	−	0.000919357i
$509$	1.17478	−	2.49653i	0.0520710	−	0.110657i	−0.877098	−	0.480311i	$-0.840524\pi$
$509$	1.17478	−	2.49653i	0.0520710	−	0.110657i	0.929169	+	0.369654i	$0.120524\pi$
$510$	0.103208	−	4.22947i	0.00457011	−	0.187284i
$511$	−1.40504	+	1.31942i	−0.0621553	+	0.0583677i
$512$	−19.6157	+	10.7838i	−0.866900	+	0.476582i
$513$	1.83662	−	3.90303i	0.0810890	−	0.172323i
$514$	11.1151	+	23.6207i	0.490265	+	1.04187i
$515$	0.414301	+	4.07720i	0.0182563	+	0.179663i
$516$	0.121668	+	0.0153702i	0.00535612	+	0.000676635i
$517$	1.14212	+	18.1535i	0.0502305	+	0.798391i
$518$	−0.741567	−	2.28231i	−0.0325826	−	0.100279i
$519$	−20.3956	+	32.1383i	−0.895267	+	1.41071i
$520$	−10.8391	+	4.78109i	−0.475325	+	0.209665i
$521$	−22.2905	+	5.72323i	−0.976564	+	0.250739i	−0.703059	−	0.711131i	$-0.748183\pi$
$521$	−22.2905	+	5.72323i	−0.976564	+	0.250739i	−0.273505	+	0.961871i	$0.588183\pi$
$522$	−1.55532	+	24.7211i	−0.0680745	+	1.08201i
$523$	5.90153	−	30.9369i	0.258056	−	1.35278i	−0.583283	−	0.812269i	$-0.698232\pi$
$523$	5.90153	−	30.9369i	0.258056	−	1.35278i	0.841339	−	0.540508i	$-0.181768\pi$
$524$	0.0634420	−	0.195254i	0.00277148	−	0.00852973i
$525$	−49.6704	+	32.5087i	−2.16779	+	1.41880i
$526$	1.38303	+	4.25651i	0.0603028	+	0.185593i
$527$	0.350616	−	0.0442932i	0.0152731	−	0.00192944i
$528$	−46.6596	−	18.4738i	−2.03060	−	0.803970i
$529$	1.29184	+	0.511477i	0.0561671	+	0.0222381i
$530$	4.18730	−	9.86568i	0.181885	−	0.428538i
$531$	−2.47111	−	39.2771i	−0.107237	−	1.70448i
$532$	−0.0148380	+	0.0107804i	−0.000643307	+	0.000467390i
$533$	21.4359	+	5.50379i	0.928490	+	0.238396i
$534$	30.0850	+	28.2517i	1.30190	+	1.22257i
$535$	−2.47428	−	4.77293i	−0.106972	−	0.206352i
$536$	3.81803	+	2.09898i	0.164914	+	0.0906621i
$537$	−9.31605	−	1.17689i	−0.402017	−	0.0507866i
$538$	−6.07369	−	31.8394i	−0.261855	−	1.37269i
$539$	−28.1294	+	3.55357i	−1.21162	+	0.153063i
$540$	0.0878491	+	0.380451i	0.00378042	+	0.0163720i
$541$	0.441910	+	2.31657i	0.0189992	+	0.0995973i	0.990524	−	0.137342i	$-0.0438558\pi$
$541$	0.441910	+	2.31657i	0.0189992	+	0.0995973i	−0.971525	+	0.236939i	$0.923856\pi$
$542$	−10.3464	+	16.3034i	−0.444418	+	0.700291i
$543$	41.3612	+	30.0507i	1.77498	+	1.28960i
$544$	−0.0214078	−	0.0258775i	−0.000917851	−	0.00110949i
$545$	5.67687	−	0.218296i	0.243171	−	0.00935078i
$546$	16.9712	+	26.7423i	0.726301	+	1.14447i
$547$	7.22428	−	8.73265i	0.308888	−	0.373381i	−0.593110	−	0.805121i	$-0.702100\pi$
$547$	7.22428	−	8.73265i	0.308888	−	0.373381i	0.901998	+	0.431740i	$0.142100\pi$
$548$	0.0666411	+	0.141620i	0.00284677	+	0.00604969i
$549$	78.8327	+	57.2753i	3.36450	+	2.44445i
$550$	−7.35284	−	27.0549i	−0.313526	−	1.15363i
$551$	0.705448	−	0.512538i	0.0300531	−	0.0218348i
$552$	36.2045	+	19.9036i	1.54096	+	0.847152i
$553$	3.90716	−	1.00319i	0.166149	−	0.0426599i
$554$	−21.8139	+	26.3684i	−0.926782	+	1.12029i
$555$	1.79830	+	2.60658i	0.0763337	+	0.110643i
$556$	0.286706	−	0.113515i	0.0121590	−	0.00481411i
$557$	23.2377			0.984614			0.492307	−	0.870422i	$-0.336154\pi$
$557$	23.2377			0.984614			0.492307	+	0.870422i	$0.336154\pi$
$558$	−7.65828	+	3.03213i	−0.324201	+	0.128360i
$559$	−4.56205	+	2.50801i	−0.192954	+	0.106077i
$560$	−9.23205	+	32.6300i	−0.390125	+	1.37887i
$561$	−0.987048	+	5.17429i	−0.0416732	+	0.218459i
$562$	15.2717	+	14.3411i	0.644198	+	0.604943i
$563$	27.6177	+	25.9347i	1.16395	+	1.09302i	0.994202	+	0.107531i	$0.0342943\pi$
$563$	27.6177	+	25.9347i	1.16395	+	1.09302i	0.169745	+	0.985488i	$0.445706\pi$
$564$	0.0381985	−	0.200244i	0.00160845	−	0.00843177i
$565$	23.8900	−	18.8010i	1.00506	−	0.790965i
$566$	11.6887	−	6.42593i	0.491313	−	0.270102i
$567$	−64.3470	+	25.4768i	−2.70232	+	1.06992i
$568$	19.7213			0.827487
$569$	36.2348	−	14.3464i	1.51904	−	0.601432i	0.547188	−	0.837010i	$-0.315698\pi$
$569$	36.2348	−	14.3464i	1.51904	−	0.601432i	0.971855	+	0.235578i	$0.0756983\pi$
$570$	2.10822	−	2.75765i	0.0883034	−	0.115505i
$571$	−8.56531	+	10.3537i	−0.358447	+	0.433288i	−0.918653	−	0.395065i	$-0.870722\pi$
$571$	−8.56531	+	10.3537i	−0.358447	+	0.433288i	0.560206	+	0.828353i	$0.310722\pi$
$572$	−0.101021	+	0.0259377i	−0.00422389	+	0.00108451i
$573$	43.4427	+	23.8828i	1.81485	+	0.997720i
$574$	50.8937	−	36.9765i	2.12426	−	1.54337i
$575$	3.23660	+	23.0171i	0.134976	+	0.959881i
$576$	−44.6190	−	32.4176i	−1.85913	−	1.35073i
$577$	−6.04445	−	12.8451i	−0.251634	−	0.534749i	0.738604	−	0.674140i	$-0.235485\pi$
$577$	−6.04445	−	12.8451i	−0.251634	−	0.534749i	−0.990237	+	0.139391i	$0.955485\pi$
$578$	15.2167	−	18.3938i	0.632932	−	0.765083i
$579$	−20.5060	−	32.3123i	−0.852200	−	1.34285i
$580$	−0.0214886	+	0.0759501i	−0.000892267	+	0.00315365i
$581$	−28.3426	−	34.2603i	−1.17585	−	1.42136i
$582$	−54.0566	−	39.2744i	−2.24072	−	1.62798i
$583$	−7.15015	+	11.2668i	−0.296129	+	0.466625i
$584$	−0.270354	−	1.41725i	−0.0111873	−	0.0586461i
$585$	−22.0274	−	19.1467i	−0.910720	−	0.791617i
$586$	17.7857	−	2.24685i	0.734719	−	0.0928166i
$587$	−0.973487	−	5.10320i	−0.0401801	−	0.210631i	0.956535	−	0.291617i	$-0.0941932\pi$
$587$	−0.973487	−	5.10320i	−0.0401801	−	0.210631i	−0.996715	+	0.0809855i	$0.974193\pi$
$588$	0.315255	+	0.0398259i	0.0130009	+	0.00164239i
$589$	0.254092	+	0.139688i	0.0104697	+	0.00575574i
$590$	2.68892	−	17.7841i	0.110701	−	0.732162i
$591$	0.305316	+	0.286711i	0.0125590	+	0.0117937i
$592$	1.75215	+	0.449875i	0.0720129	+	0.0184898i
$593$	−10.5594	+	7.67186i	−0.433623	+	0.315046i	−0.783096	−	0.621901i	$-0.786361\pi$
$593$	−10.5594	+	7.67186i	−0.433623	+	0.315046i	0.349473	+	0.936946i	$0.386361\pi$
$594$	−4.37814	−	69.5885i	−0.179637	−	2.85525i
$595$	3.54597	+	0.310098i	0.145370	+	0.0127128i
$596$	−0.240213	−	0.0951070i	−0.00983950	−	0.00389573i
$597$	68.8217	+	27.2484i	2.81668	+	1.11520i
$598$	12.3038	−	1.55433i	0.503138	−	0.0635612i
$599$	−9.63970	−	29.6679i	−0.393867	−	1.21220i	−0.929840	−	0.367964i	$-0.880055\pi$
$599$	−9.63970	−	29.6679i	−0.393867	−	1.21220i	0.535973	−	0.844235i	$-0.319945\pi$
$600$	−0.623758	−	44.4324i	−0.0254648	−	1.81395i
$601$	2.01176	−	6.19155i	0.0820612	−	0.252559i	−0.901605	−	0.432560i	$-0.857610\pi$
$601$	2.01176	−	6.19155i	0.0820612	−	0.252559i	0.983666	+	0.180002i	$0.0576103\pi$
$602$	−2.77289	+	14.5360i	−0.113015	+	0.592444i
$603$	−0.673982	+	10.7126i	−0.0274467	+	0.436252i
$604$	−0.0734656	+	0.0188628i	−0.00298927	+	0.000767515i
$605$	1.04234	+	10.2578i	0.0423771	+	0.417040i
$606$	40.7176	−	64.1607i	1.65404	−	2.60635i
$607$	−6.72907	−	20.7099i	−0.273124	−	0.840591i	−0.989710	−	0.143091i	$-0.954296\pi$
$607$	−6.72907	−	20.7099i	−0.273124	−	0.840591i	0.716585	−	0.697500i	$-0.245704\pi$
$608$	−0.00173022	−	0.0275010i	−7.01696e−5	−	0.00111531i
$609$	−29.6090	−	3.74048i	−1.19982	−	0.151572i
$610$	29.6847	+	33.1980i	1.20190	+	1.34415i
$611$	3.68465	+	7.83027i	0.149065	+	0.316779i
$612$	0.0175524	−	0.0373007i	0.000709513	−	0.00150779i
$613$	−3.05098	+	1.67729i	−0.123228	+	0.0677451i	−0.542175	−	0.840265i	$-0.682399\pi$
$613$	−3.05098	+	1.67729i	−0.123228	+	0.0677451i	0.418947	+	0.908010i	$0.362399\pi$
$614$	−16.8912	+	15.8619i	−0.681672	+	0.640133i
$615$	−50.4180	+	65.9491i	−2.03305	+	2.65932i
$616$	17.8518	−	37.9370i	0.719269	−	1.52852i
$617$	−21.8375	−	26.3970i	−0.879143	−	1.06270i	−0.997565	−	0.0697383i	$-0.977784\pi$
$617$	−21.8375	−	26.3970i	−0.879143	−	1.06270i	0.118422	−	0.992963i	$-0.462216\pi$
$618$	−2.53450	+	7.80040i	−0.101953	+	0.313778i
$619$	−42.5109	−	10.9149i	−1.70866	−	0.438708i	−0.737151	−	0.675728i	$-0.763829\pi$
$619$	−42.5109	−	10.9149i	−1.70866	−	0.438708i	−0.971505	+	0.237020i	$0.923829\pi$
$620$	−0.0258942	+	0.00428776i	−0.00103994	+	0.000172201i
$621$	−3.62971	+	57.6926i	−0.145655	+	2.31513i
$622$	−17.0403	−	26.8513i	−0.683255	−	1.07664i
$623$	−25.3118	+	23.7694i	−1.01410	+	0.952301i
$624$	−23.8756			−0.955789
$625$	19.8050	−	15.2566i	0.792198	−	0.610264i
$626$	−27.0293			−1.08031
$627$	−3.15054	+	2.95855i	−0.125820	+	0.118153i
$628$	0.144225	+	0.227262i	0.00575521	+	0.00906875i
$629$	0.0119228	−	0.189507i	0.000475393	−	0.00755615i
$630$	−81.8460	+	13.5527i	−3.26082	+	0.539951i
$631$	0.693825	+	0.178144i	0.0276207	+	0.00709180i	0.262475	−	0.964939i	$-0.415461\pi$
$631$	0.693825	+	0.178144i	0.0276207	+	0.00709180i	−0.234854	+	0.972031i	$0.575461\pi$
$632$	−0.933112	+	2.87182i	−0.0371172	+	0.114235i
$633$	−3.96500	−	4.79286i	−0.157595	−	0.190499i
$634$	−11.6832	+	24.8281i	−0.463999	+	0.986049i
$635$	−2.60081	+	3.40198i	−0.103210	+	0.135003i
$636$	0.109019	−	0.102375i	0.00432287	−	0.00405945i
$637$	−11.8208	+	6.49854i	−0.468357	+	0.257482i
$638$	6.00138	−	12.7536i	0.237597	−	0.504919i
$639$	20.6867	+	43.9614i	0.818352	+	1.73909i
$640$	−17.0382	−	19.0548i	−0.673494	−	0.753206i
$641$	−6.93803	−	0.876477i	−0.274036	−	0.0346188i	−0.0128857	−	0.999917i	$-0.504102\pi$
$641$	−6.93803	−	0.876477i	−0.274036	−	0.0346188i	−0.261150	+	0.965298i	$0.584102\pi$
$642$	−0.675589	−	10.7382i	−0.0266634	−	0.423802i
$643$	−4.04892	−	12.4613i	−0.159674	−	0.491425i	0.838931	−	0.544238i	$-0.183181\pi$
$643$	−4.04892	−	12.4613i	−0.159674	−	0.491425i	−0.998604	+	0.0528130i	$0.983181\pi$
$644$	0.131699	−	0.207525i	0.00518968	−	0.00817763i
$645$	−1.97411	−	19.4276i	−0.0777307	−	0.764960i
$646$	−0.201599	+	0.0517619i	−0.00793182	+	0.00203655i
$647$	2.04018	−	32.4277i	0.0802077	−	1.27486i	−0.727840	−	0.685747i	$-0.759476\pi$
$647$	2.04018	−	32.4277i	0.0802077	−	1.27486i	0.808048	−	0.589117i	$-0.200524\pi$
$648$	9.70741	−	50.8880i	0.381343	−	1.99907i
$649$	−6.92023	+	21.2983i	−0.271643	+	0.836030i
$650$	−7.99098	−	10.6801i	−0.313432	−	0.418908i
$651$	−3.06670	−	9.43832i	−0.120193	−	0.369917i
$652$	−0.154287	+	0.0194910i	−0.00604236	+	0.000763327i
$653$	−23.2241	−	9.19506i	−0.908828	−	0.359831i	−0.133250	−	0.991082i	$-0.542541\pi$
$653$	−23.2241	−	9.19506i	−0.908828	−	0.359831i	−0.775578	+	0.631252i	$0.782541\pi$
$654$	10.5713	+	4.18546i	0.413369	+	0.163664i
$655$	−32.5669	−	2.84801i	−1.27249	−	0.111281i
$656$	2.97760	+	47.3277i	0.116256	+	1.84783i
$657$	2.87565	−	2.08928i	0.112190	−	0.0815106i
$658$	23.8260	+	6.11747i	0.928833	+	0.238484i
$659$	8.67490	+	8.14627i	0.337926	+	0.317334i	0.834868	−	0.550450i	$-0.185544\pi$
$659$	8.67490	+	8.14627i	0.337926	+	0.317334i	−0.496942	+	0.867784i	$0.665544\pi$
$660$	0.0584864	−	0.386821i	0.00227658	−	0.0150570i
$661$	−16.7477	−	9.20710i	−0.651408	−	0.358115i	0.121538	−	0.992587i	$-0.461218\pi$
$661$	−16.7477	−	9.20710i	−0.651408	−	0.358115i	−0.772946	+	0.634472i	$0.781218\pi$
$662$	−1.55685	−	0.196675i	−0.0605085	−	0.00764400i
$663$	0.469603	+	2.46174i	0.0182379	+	0.0956062i
$664$	33.0218	−	4.17162i	1.28149	−	0.161890i
$665$	2.20418	+	1.91592i	0.0854744	+	0.0742961i
$666$	0.829264	+	4.34715i	0.0321333	+	0.168449i
$667$	−6.26144	+	9.86644i	−0.242444	+	0.382030i
$668$	−0.0844485	−	0.0613554i	−0.00326741	−	0.00237391i
$669$	15.2699	+	18.4582i	0.590370	+	0.713635i
$670$	−1.33554	+	4.72037i	−0.0515964	+	0.182364i
$671$	−29.7108	−	46.8167i	−1.14697	−	1.80734i
$672$	−0.601159	+	0.726677i	−0.0231902	+	0.0280322i
$673$	13.9452	+	29.6351i	0.537549	+	1.14235i	0.970537	+	0.240951i	$0.0774592\pi$
$673$	13.9452	+	29.6351i	0.537549	+	1.14235i	−0.432988	+	0.901400i	$0.642541\pi$
$674$	−25.1259	−	18.2551i	−0.967815	−	0.703159i
$675$	55.8804	−	27.2599i	2.15084	−	1.04923i
$676$	0.107545	−	0.0781362i	0.00413636	−	0.00300524i
$677$	16.4523	+	9.04472i	0.632313	+	0.347617i	0.765464	−	0.643479i	$-0.222510\pi$
$677$	16.4523	+	9.04472i	0.632313	+	0.347617i	−0.133151	+	0.991096i	$0.542510\pi$
$678$	58.9305	−	15.1308i	2.26321	−	0.581094i
$679$	35.8338	−	43.3157i	1.37518	−	1.66230i
$680$	−1.61828	+	2.11678i	−0.0620581	+	0.0811749i
$681$	−17.4792	+	6.92050i	−0.669804	+	0.265194i
$682$	4.68699			0.179474
$683$	−0.955097	+	0.378150i	−0.0365458	+	0.0144695i	−0.386326	−	0.922362i	$-0.626256\pi$
$683$	−0.955097	+	0.378150i	−0.0365458	+	0.0144695i	0.349781	+	0.936832i	$0.386256\pi$
$684$	0.0296395	−	0.0162945i	0.00113330	−	0.000623035i
$685$	19.5850	−	15.4131i	0.748306	−	0.588904i
$686$	−0.176217	+	0.923762i	−0.00672800	+	0.0352694i
$687$	−0.894105	−	0.839620i	−0.0341122	−	0.0320335i
$688$	−8.13171	−	7.63618i	−0.310018	−	0.291127i
$689$	−1.18962	+	6.23623i	−0.0453210	+	0.237581i
$690$	−12.6643	+	44.7609i	−0.482120	+	1.70402i
$691$	−36.4618	+	20.0451i	−1.38707	+	0.762550i	−0.988012	−	0.154375i	$-0.950664\pi$
$691$	−36.4618	+	20.0451i	−1.38707	+	0.762550i	−0.399061	+	0.916924i	$0.630664\pi$
$692$	−0.157605	+	0.0624003i	−0.00599125	+	0.00237210i
$693$	103.292			3.92375
$694$	−17.3124	+	6.85445i	−0.657168	+	0.260191i
$695$	−27.8835	−	40.4161i	−1.05768	−	1.53307i
$696$	14.2402	−	17.2135i	0.539775	−	0.652476i
$697$	4.82125	−	1.23789i	0.182618	−	0.0468883i
$698$	−10.8737	−	5.97789i	−0.411577	−	0.226266i
$699$	−24.8401	+	18.0474i	−0.939540	+	0.682615i
$700$	−0.264045	−	0.0128942i	−0.00997998	−	0.000487354i
$701$	−30.4346	−	22.1121i	−1.14950	−	0.835161i	−0.161086	−	0.986940i	$-0.551500\pi$
$701$	−30.4346	−	22.1121i	−1.14950	−	0.835161i	−0.988414	+	0.151780i	$0.951500\pi$
$702$	−14.1245	−	30.0160i	−0.533094	−	1.13288i
$703$	0.0993061	−	0.120040i	0.00374540	−	0.00452741i
$704$	16.8162	+	26.4981i	0.633784	+	0.998684i
$705$	−32.4366	+	1.24730i	−1.22163	+	0.0469762i
$706$	32.7999	+	39.6482i	1.23444	+	1.49218i
$707$	51.7237	+	37.5795i	1.94527	+	1.41332i
$708$	0.134482	−	0.211909i	0.00505414	−	0.00796405i
$709$	6.30897	+	33.0728i	0.236938	+	1.24207i	0.879522	+	0.475859i	$0.157863\pi$
$709$	6.30897	+	33.0728i	0.236938	+	1.24207i	−0.642584	+	0.766216i	$0.722137\pi$
$710$	4.99584	+	21.6357i	0.187491	+	0.811972i
$711$	−7.38047	+	0.932370i	−0.276789	+	0.0349666i
$712$	−4.87044	−	25.5318i	−0.182528	−	0.956843i
$713$	−3.85512	−	0.487015i	−0.144376	−	0.0182389i
$714$	6.24256	+	3.43188i	0.233622	+	0.128435i
$715$	7.64342	+	14.7443i	0.285848	+	0.551405i
$716$	−0.0304831	−	0.0286255i	−0.00113921	−	0.00106979i
$717$	−24.6459	−	6.32800i	−0.920419	−	0.236323i
$718$	−18.8707	+	13.7104i	−0.704248	+	0.511666i
$719$	1.33824	+	21.2708i	0.0499081	+	0.793266i	0.940781	+	0.339014i	$0.110093\pi$
$719$	1.33824	+	21.2708i	0.0499081	+	0.793266i	−0.890873	+	0.454252i	$0.849907\pi$
$720$	24.4330	−	57.5666i	0.910566	−	2.14538i
$721$	−6.41598	−	2.54027i	−0.238944	−	0.0946045i
$722$	24.9119	+	9.86333i	0.927126	+	0.367075i
$723$	−28.6899	+	3.62438i	−1.06699	+	0.134792i
$724$	0.0703556	+	0.216532i	0.00261475	+	0.00804736i
$725$	12.5536	+	0.613033i	0.466230	+	0.0227675i
$726$	−6.37655	+	19.6250i	−0.236656	+	0.728353i
$727$	−7.77749	+	40.7710i	−0.288451	+	1.51211i	0.482884	+	0.875684i	$0.339589\pi$
$727$	−7.77749	+	40.7710i	−0.288451	+	1.51211i	−0.771335	+	0.636430i	$0.780411\pi$
$728$	1.25252	−	19.9082i	0.0464214	−	0.737847i
$729$	9.68011	−	2.48543i	0.358523	−	0.0920530i
$730$	1.48634	−	0.655619i	0.0550118	−	0.0242655i
$731$	−0.627404	+	0.988630i	−0.0232054	+	0.0365658i
$732$	0.192032	+	0.591013i	0.00709770	+	0.0218445i
$733$	1.98125	+	31.4911i	0.0731793	+	1.16315i	0.847655	+	0.530548i	$0.178014\pi$
$733$	1.98125	+	31.4911i	0.0731793	+	1.16315i	−0.774476	+	0.632604i	$0.781986\pi$
$734$	5.91146	+	0.746791i	0.218196	+	0.0275645i
$735$	−5.11516	−	50.3391i	−0.188676	−	1.85679i
$736$	0.157229	+	0.334129i	0.00579555	+	0.0123162i
$737$	2.60064	−	5.52663i	0.0957957	−	0.203576i
$738$	−101.663	+	55.8895i	−3.74225	+	2.05732i
$739$	3.10623	−	2.91695i	0.114265	−	0.107302i	−0.625309	−	0.780377i	$-0.715027\pi$
$739$	3.10623	−	2.91695i	0.114265	−	0.107302i	0.739574	+	0.673076i	$0.235027\pi$
$740$	−0.000344023		0.0140981i	−1.26465e−5		0.000518257i
$741$	−0.875493	+	1.86052i	−0.0321620	+	0.0683478i
$742$	11.5031	+	13.9048i	0.422291	+	0.510463i
$743$	8.08462	−	24.8819i	0.296596	−	0.912828i	−0.686085	−	0.727521i	$-0.740672\pi$
$743$	8.08462	−	24.8819i	0.296596	−	0.912828i	0.982681	−	0.185307i	$-0.0593278\pi$
$744$	7.19537	+	1.84746i	0.263795	+	0.0677310i
$745$	−6.15021	+	40.6767i	−0.225326	+	1.49028i
$746$	−1.70532	+	27.1053i	−0.0624362	+	0.992396i
$747$	43.9374	+	69.2342i	1.60759	+	2.53315i
$748$	−0.0171002	+	0.0160582i	−0.000625245	+	0.000587144i
$749$	9.05238			0.330767
$750$	48.5876	−	11.9400i	1.77417	−	0.435988i
$751$	30.3372			1.10702			0.553511	−	0.832842i	$-0.313288\pi$
$751$	30.3372			1.10702			0.553511	+	0.832842i	$0.313288\pi$
$752$	−13.5173	+	12.6936i	−0.492924	+	0.462886i
$753$	−2.37839	−	3.74774i	−0.0866732	−	0.136575i
$754$	0.421069	−	6.69270i	0.0153344	−	0.243734i
$755$	5.55854	+	10.7225i	0.202296	+	0.390233i
$756$	−0.636807	−	0.163504i	−0.0231604	−	0.00594659i
$757$	6.15993	−	18.9583i	0.223887	−	0.689052i	−0.774516	−	0.632554i	$-0.782007\pi$
$757$	6.15993	−	18.9583i	0.223887	−	0.689052i	0.998403	−	0.0564978i	$-0.0179934\pi$
$758$	−14.8963	−	18.0066i	−0.541059	−	0.654028i
$759$	24.6605	−	52.4063i	0.895121	−	1.90223i
$760$	−2.09501	+	0.624636i	−0.0759942	+	0.0226579i
$761$	14.1295	−	13.2685i	0.512193	−	0.480981i	−0.384816	−	0.922993i	$-0.625735\pi$
$761$	14.1295	−	13.2685i	0.512193	−	0.480981i	0.897009	+	0.442012i	$0.145735\pi$
$762$	−7.51011	+	4.12872i	−0.272063	+	0.149568i
$763$	−4.07293	+	8.65541i	−0.147450	+	0.313347i
$764$	0.0939995	+	0.199759i	0.00340078	+	0.00722703i
$765$	−6.41609	−	1.38696i	−0.231974	−	0.0501455i
$766$	38.4018	+	4.85127i	1.38751	+	0.175284i
$767$	0.668997	+	10.6334i	0.0241561	+	0.383950i
$768$	−0.328390	−	1.01068i	−0.0118497	−	0.0364698i
$769$	15.9194	−	25.0850i	0.574069	−	0.904588i	−0.425931	−	0.904756i	$-0.640053\pi$
$769$	15.9194	−	25.0850i	0.574069	−	0.904588i	1.00000		0.000167545i	$5.33312e-5\pi$
$770$	46.1419	+	9.97442i	1.66284	+	0.359453i
$771$	56.1823	−	14.4252i	2.02335	−	0.519509i
$772$	0.0107012	−	0.170090i	0.000385143	−	0.00612168i
$773$	2.76502	−	14.4948i	0.0994510	−	0.521340i	−0.897343	−	0.441333i	$-0.854506\pi$
$773$	2.76502	−	14.4948i	0.0994510	−	0.521340i	0.996794	−	0.0800072i	$-0.0254943\pi$
$774$	8.43311	−	25.9544i	0.303122	−	0.932913i
$775$	1.59293	+	3.86392i	0.0572198	+	0.138796i
$776$	13.0039	+	40.0220i	0.466814	+	1.43671i
$777$	−5.29010	+	0.668295i	−0.189781	+	0.0239750i
$778$	−14.1468	−	5.60110i	−0.507186	−	0.200809i
$779$	3.79721	+	1.50342i	0.136049	+	0.0538657i
$780$	−0.0418764	−	0.181356i	−0.00149942	−	0.00649358i
$781$	−1.73597	−	27.5924i	−0.0621177	−	0.987333i
$782$	2.25659	−	1.63951i	0.0806955	−	0.0586287i
$783$	30.2760	+	7.77355i	1.08197	+	0.277804i
$784$	−21.0702	−	19.7862i	−0.752507	−	0.706651i
$785$	30.0932	−	30.5186i	1.07407	−	1.08925i
$786$	−57.3330	−	31.5191i	−2.04500	−	1.12425i
$787$	−6.83931	−	0.864006i	−0.243795	−	0.0307985i	0.00248599	−	0.999997i	$-0.499209\pi$
$787$	−6.83931	−	0.864006i	−0.243795	−	0.0307985i	−0.246281	+	0.969198i	$0.579209\pi$
$788$	0.000349500		0.00183215i	1.24504e−5		6.52675e-5i
$789$	9.86606	−	1.24637i	0.351241	−	0.0443721i
$790$	−3.38697	−	0.296194i	−0.120503	−	0.0105381i
$791$	9.59188	+	50.2824i	0.341048	+	1.78784i
$792$	−41.4305	+	65.2840i	−1.47217	+	2.31977i
$793$	−21.3422	−	15.5060i	−0.757884	−	0.550635i
$794$	23.0558	+	27.8697i	0.818221	+	0.989060i
$795$	−19.7894	−	13.2468i	−0.701857	−	0.469814i
$796$	0.176625	+	0.278316i	0.00626029	+	0.00986465i
$797$	−30.2903	+	36.6147i	−1.07294	+	1.29696i	−0.120337	+	0.992733i	$0.538398\pi$
$797$	−30.2903	+	36.6147i	−1.07294	+	1.29696i	−0.952600	+	0.304225i	$0.901602\pi$
$798$	2.48860	+	5.28855i	0.0880955	+	0.187212i
$799$	1.57466	+	1.14406i	0.0557076	+	0.0404739i
$800$	0.228922	−	0.324570i	0.00809363	−	0.0114753i
$801$	51.8049	−	37.6385i	1.83044	−	1.32989i
$802$	−28.3410	−	15.5806i	−1.00076	−	0.550170i
$803$	−1.95910	+	0.503011i	−0.0691350	+	0.0177509i
$804$	−0.0436340	+	0.0527444i	−0.00153885	+	0.00186015i
$805$	−36.9160	−	12.9986i	−1.30112	−	0.458142i
$806$	2.07331	−	0.820882i	0.0730293	−	0.0289143i
$807$	−72.0212			−2.53527
$808$	−44.4978	+	17.6179i	−1.56543	+	0.619796i
$809$	−34.3199	+	18.8675i	−1.20662	+	0.663346i	−0.952710	−	0.303881i	$-0.901717\pi$
$809$	−34.3199	+	18.8675i	−1.20662	+	0.663346i	−0.253912	+	0.967227i	$0.581717\pi$
$810$	58.2869	−	2.24134i	2.04799	−	0.0787527i
$811$	−10.1574	+	53.2468i	−0.356674	+	1.86975i	0.123156	+	0.992387i	$0.460698\pi$
$811$	−10.1574	+	53.2468i	−0.356674	+	1.86975i	−0.479830	+	0.877362i	$0.659302\pi$
$812$	−0.0968837	−	0.0909799i	−0.00339995	−	0.00319277i
$813$	31.2759	+	29.3700i	1.09689	+	1.03005i
$814$	0.471882	−	2.47369i	0.0165395	−	0.0867029i
$815$	8.55151	+	23.2397i	0.299546	+	0.814050i
$816$	−4.70575	+	2.58701i	−0.164734	+	0.0905635i
$817$	−0.893234	+	0.353656i	−0.0312503	+	0.0123729i
$818$	29.0196			1.01465
$819$	45.6919	−	18.0907i	1.59660	−	0.632140i
$820$	−0.354271	+	0.105627i	−0.0123717	+	0.00368867i
$821$	−14.8869	+	17.9952i	−0.519558	+	0.628037i	−0.963400	−	0.268067i	$-0.913615\pi$
$821$	−14.8869	+	17.9952i	−0.519558	+	0.628037i	0.443842	+	0.896105i	$0.353615\pi$
$822$	48.3113	−	12.4042i	1.68505	−	0.432647i
$823$	−22.3107	−	12.2654i	−0.777701	−	0.427545i	0.0428765	−	0.999080i	$-0.486348\pi$
$823$	−22.3107	−	12.2654i	−0.777701	−	0.427545i	−0.820577	+	0.571536i	$0.806348\pi$
$824$	4.17897	−	3.03620i	0.145581	−	0.105771i
$825$	−62.1113	+	4.78387i	−2.16244	+	0.166553i
$826$	24.5014	+	17.8013i	0.852512	+	0.619386i
$827$	5.12630	+	10.8939i	0.178259	+	0.378820i	0.973910	−	0.226936i	$-0.0728709\pi$
$827$	5.12630	+	10.8939i	0.178259	+	0.378820i	−0.795651	+	0.605756i	$0.792871\pi$
$828$	−0.288926	+	0.349251i	−0.0100409	+	0.0121373i
$829$	1.86018	+	2.93117i	0.0646066	+	0.101804i	0.875095	−	0.483950i	$-0.160798\pi$
$829$	1.86018	+	2.93117i	0.0646066	+	0.101804i	−0.810489	+	0.585754i	$0.800798\pi$
$830$	12.9417	+	35.1705i	0.449214	+	1.22079i
$831$	48.4693	+	58.5893i	1.68138	+	2.03244i
$832$	12.0796	+	8.77636i	0.418785	+	0.304265i
$833$	−1.62568	+	2.56166i	−0.0563263	+	0.0887561i
$834$	−18.4136	−	96.5274i	−0.637611	−	3.34247i
$835$	−6.49396	+	15.3004i	−0.224733	+	0.529493i
$836$	−0.0190949	+	0.00241225i	−0.000660412	+	8.34294e-5i
$837$	1.94767	+	10.2100i	0.0673212	+	0.352910i
$838$	−21.5399	−	2.72112i	−0.744082	−	0.0939994i
$839$	−24.3936	−	13.4105i	−0.842160	−	0.462981i	0.00141090	−	0.999999i	$-0.499551\pi$
$839$	−24.3936	−	13.4105i	−0.842160	−	0.462981i	−0.843571	+	0.537018i	$0.819551\pi$
$840$	66.9045	+	33.5001i	2.30842	+	1.15586i
$841$	−16.5339	−	15.5264i	−0.570135	−	0.535392i
$842$	7.99848	+	2.05366i	0.275646	+	0.0707738i
$843$	37.6592	−	27.3610i	1.29705	−	0.942363i
$844$	−0.00173936	−	0.0276463i	−5.98712e−5	−	0.000951625i
$845$	−15.9758	−	13.8865i	−0.549586	−	0.477712i
$846$	−42.1785	−	16.6996i	−1.45013	−	0.574145i
$847$	−16.1420	−	6.39105i	−0.554644	−	0.219599i
$848$	−13.4963	+	1.70498i	−0.463464	+	0.0585491i
$849$	−9.15856	−	28.1872i	−0.314321	−	0.967381i
$850$	−2.73221	−	1.23914i	−0.0937140	−	0.0425021i
$851$	−0.645167	+	1.98562i	−0.0221160	+	0.0680662i
$852$	−0.0580597	+	0.304360i	−0.00198909	+	0.0104272i
$853$	−1.15058	+	18.2880i	−0.0393953	+	0.626170i	0.927950	+	0.372706i	$0.121570\pi$
$853$	−1.15058	+	18.2880i	−0.0393953	+	0.626170i	−0.967345	+	0.253464i	$0.918430\pi$
$854$	−72.6309	+	18.6484i	−2.48538	+	0.638137i
$855$	−3.58997	−	4.01486i	−0.122774	−	0.137305i
$856$	−3.63090	+	5.72139i	−0.124102	+	0.195553i
$857$	−8.19976	−	25.2363i	−0.280098	−	0.862054i	−0.987825	−	0.155568i	$-0.950279\pi$
$857$	−8.19976	−	25.2363i	−0.280098	−	0.862054i	0.707727	−	0.706486i	$-0.249721\pi$
$858$	2.08700	+	33.1719i	0.0712489	+	1.13247i
$859$	−15.0222	−	1.89775i	−0.512551	−	0.0647503i	−0.135196	−	0.990819i	$-0.543166\pi$
$859$	−15.0222	−	1.89775i	−0.512551	−	0.0647503i	−0.377355	+	0.926069i	$0.623166\pi$
$860$	0.0437408	−	0.0751607i	0.00149155	−	0.00256296i
$861$	−59.5148	−	126.475i	−2.02826	−	4.31027i
$862$	17.5869	−	37.3741i	0.599013	−	1.27297i
$863$	18.0568	−	9.92682i	0.614661	−	0.337913i	−0.143824	−	0.989603i	$-0.545940\pi$
$863$	18.0568	−	9.92682i	0.614661	−	0.337913i	0.758485	+	0.651690i	$0.225940\pi$
$864$	0.720062	−	0.676183i	0.0244970	−	0.0230042i
$865$	15.3278	+	22.2172i	0.521162	+	0.755407i
$866$	20.1934	−	42.9131i	0.686199	−	1.45825i
$867$	−33.8108	−	40.8702i	−1.14827	−	1.38802i
$868$	0.0136569	−	0.0420315i	0.000463544	−	0.00142664i
$869$	4.10015	+	1.05274i	0.139088	+	0.0357118i
$870$	22.4918	+	11.2620i	0.762544	+	0.381818i
$871$	0.182466	−	2.90021i	0.00618262	−	0.0982699i
$872$	−3.83684	−	6.04589i	−0.129932	−	0.204740i
$873$	−75.5739	+	70.9687i	−2.55779	+	2.40193i
$874$	2.28854			0.0774110
$875$	7.45905	+	41.4290i	0.252162	+	1.40056i
$876$	0.0226684			0.000765893
$877$	−10.1610	+	9.54186i	−0.343114	+	0.322206i	−0.836877	−	0.547391i	$-0.815621\pi$
$877$	−10.1610	+	9.54186i	−0.343114	+	0.322206i	0.493763	+	0.869597i	$0.335621\pi$
$878$	−26.2460	−	41.3571i	−0.885759	−	1.39573i
$879$	2.50113	−	39.7543i	0.0843611	−	1.34088i
$880$	−24.9858	+	25.3391i	−0.842272	+	0.854180i
$881$	7.92803	+	2.03557i	0.267102	+	0.0685802i	0.379866	−	0.925042i	$-0.375970\pi$
$881$	7.92803	+	2.03557i	0.267102	+	0.0685802i	−0.112763	+	0.993622i	$0.535970\pi$
$882$	21.8512	−	67.2509i	0.735767	−	2.26446i
$883$	20.5946	+	24.8946i	0.693065	+	0.837771i	0.993236	−	0.116114i	$-0.0370438\pi$
$883$	20.5946	+	24.8946i	0.693065	+	0.837771i	−0.300171	+	0.953885i	$0.597044\pi$
$884$	−0.00475192	+	0.0100983i	−0.000159824	+	0.000339644i
$885$	−37.6960	−	13.2733i	−1.26714	−	0.446176i
$886$	−35.9913	+	33.7981i	−1.20915	+	1.13547i
$887$	7.17706	−	3.94562i	0.240982	−	0.132481i	−0.356687	−	0.934224i	$-0.616094\pi$
$887$	7.17706	−	3.94562i	0.240982	−	0.132481i	0.597669	+	0.801743i	$0.296094\pi$
$888$	1.69947	−	3.61156i	0.0570305	−	0.121196i
$889$	−3.07007	−	6.52424i	−0.102967	−	0.218816i
$890$	26.7764	−	11.8110i	0.897547	−	0.395905i
$891$	−72.0528	−	9.10238i	−2.41386	−	0.304941i
$892$	0.00669859	+	0.106471i	0.000224285	+	0.00356491i
$893$	0.493487	+	1.51880i	0.0165139	+	0.0508246i
$894$	−44.1160	+	69.5157i	−1.47546	+	2.32495i
$895$	−3.34922	+	5.75503i	−0.111952	+	0.192370i
$896$	41.6882	−	10.7037i	1.39270	−	0.357586i
$897$	1.73023	−	27.5013i	0.0577708	−	0.918240i
$898$	9.59152	−	50.2805i	0.320073	−	1.67788i
$899$	−0.649295	+	1.99832i	−0.0216552	+	0.0666478i
$900$	0.480122	+	0.0846214i	0.0160041	+	0.00282071i
$901$	0.441250	+	1.35803i	0.0147002	+	0.0452424i
$902$	65.4949	−	8.27394i	2.18074	−	0.275492i
$903$	30.5717	+	12.1042i	1.01736	+	0.402802i
$904$	−35.6273	−	14.1059i	−1.18495	−	0.469154i
$905$	31.0748	−	18.6732i	1.03296	−	0.620718i
$906$	1.51773	+	24.1237i	0.0504233	+	0.801455i
$907$	28.5791	−	20.7639i	0.948954	−	0.689455i	−0.00160526	−	0.999999i	$-0.500511\pi$
$907$	28.5791	−	20.7639i	0.948954	−	0.689455i	0.950559	+	0.310543i	$0.100511\pi$
$908$	−0.0810887	−	0.0208200i	−0.00269102	−	0.000690937i
$909$	−85.9487	−	80.7112i	−2.85074	−	2.67702i
$910$	22.1580	−	3.66909i	0.734531	−	0.121629i
$911$	9.95275	+	5.47157i	0.329749	+	0.181281i	0.638025	−	0.770016i	$-0.279752\pi$
$911$	9.95275	+	5.47157i	0.329749	+	0.181281i	−0.308275	+	0.951297i	$0.599752\pi$
$912$	−4.37118	−	0.552209i	−0.144744	−	0.0182855i
$913$	−8.74333	−	45.8342i	−0.289362	−	1.51689i
$914$	50.9744	−	6.43956i	1.68608	−	0.213002i
$915$	84.8170	−	50.9675i	2.80396	−	1.68493i
$916$	−0.00102350	−	0.00536535i	−3.38173e−5	−	0.000177276i
$917$	29.4949	−	46.4765i	0.974007	−	1.53479i
$918$	−6.03621	−	4.38556i	−0.199224	−	0.144745i
$919$	15.5474	+	18.7936i	0.512861	+	0.619943i	0.961844	−	0.273597i	$-0.0882136\pi$
$919$	15.5474	+	18.7936i	0.512861	+	0.619943i	−0.448983	+	0.893540i	$0.648214\pi$
$920$	23.0225	−	18.1183i	0.759031	−	0.597344i
$921$	27.5873	+	43.4707i	0.909033	+	1.43241i
$922$	9.78124	−	11.8235i	0.322128	−	0.389386i
$923$	−5.60046	−	11.9016i	−0.184342	−	0.391746i
$924$	0.532927	+	0.387194i	0.0175320	+	0.0127378i
$925$	2.19967	−	0.451699i	0.0723247	−	0.0148518i
$926$	−17.1780	+	12.4805i	−0.564504	+	0.410136i
$927$	11.1517	+	6.13067i	0.366268	+	0.201358i
$928$	0.193406	−	0.0496581i	0.00634885	−	0.00163011i
$929$	14.0335	−	16.9635i	0.460423	−	0.556555i	−0.488296	−	0.872678i	$-0.662381\pi$
$929$	14.0335	−	16.9635i	0.460423	−	0.556555i	0.948718	+	0.316123i	$0.102381\pi$
$930$	−0.204046	+	8.36184i	−0.00669093	+	0.274196i
$931$	−2.31447	+	0.916364i	−0.0758537	+	0.0300326i
$932$	−0.136734			−0.00447887
$933$	−65.7002	+	26.0125i	−2.15093	+	0.851613i
$934$	−2.56313	+	1.40909i	−0.0838681	+	0.0461069i
$935$	3.10407	+	2.07783i	0.101514	+	0.0679523i
$936$	−6.89310	+	36.1349i	−0.225308	+	1.18111i
$937$	42.7625	+	40.1566i	1.39699	+	1.31186i	0.894353	+	0.447362i	$0.147636\pi$
$937$	42.7625	+	40.1566i	1.39699	+	1.31186i	0.502636	+	0.864498i	$0.332364\pi$
$938$	−6.02142	−	5.65449i	−0.196606	−	0.184626i
$939$	−11.2537	+	58.9939i	−0.367251	+	1.92519i
$940$	−0.120127	−	0.0804114i	−0.00391811	−	0.00262273i
$941$	−39.3111	+	21.6115i	−1.28151	+	0.704514i	−0.969389	−	0.245529i	$-0.921038\pi$
$941$	−39.3111	+	21.6115i	−1.28151	+	0.704514i	−0.312117	+	0.950044i	$0.601038\pi$
$942$	79.7533	−	31.5766i	2.59850	−	1.02882i
$943$	−54.7304			−1.78227
$944$	−21.2265	+	8.40415i	−0.690863	+	0.273532i
$945$	−2.55390	+	104.659i	−0.0830784	+	3.40456i
$946$	−9.89862	+	11.9654i	−0.321832	+	0.389028i
$947$	−5.23923	+	1.34520i	−0.170252	+	0.0437133i	−0.332854	−	0.942979i	$-0.608011\pi$
$947$	−5.23923	+	1.34520i	−0.170252	+	0.0437133i	0.162602	+	0.986692i	$0.448011\pi$
$948$	−0.0415739	−	0.0228554i	−0.00135026	−	0.000742310i
$949$	−0.778519	+	0.565627i	−0.0252718	+	0.0183610i
$950$	−1.21599	−	2.14015i	−0.0394518	−	0.0694356i
$951$	49.3253	+	35.8369i	1.59948	+	1.16209i
$952$	−1.91026	−	4.05951i	−0.0619119	−	0.131570i
$953$	7.94939	−	9.60916i	0.257506	−	0.311271i	−0.625878	−	0.779921i	$-0.715259\pi$
$953$	7.94939	−	9.60916i	0.257506	−	0.311271i	0.883384	+	0.468650i	$0.155259\pi$
$954$	−17.8324	−	28.0993i	−0.577344	−	0.909748i
$955$	27.6254	−	21.7407i	0.893936	−	0.703512i
$956$	−0.0722299	−	0.0873109i	−0.00233608	−	0.00282384i
$957$	−25.3372	−	18.4086i	−0.819035	−	0.595064i
$958$	−3.50060	+	5.51606i	−0.113099	+	0.178216i
$959$	7.86343	+	41.2215i	0.253923	+	1.33111i
$960$	−48.0061	+	28.8474i	−1.54939	+	0.931046i
$961$	30.0624	−	3.79776i	0.969754	−	0.122508i
$962$	−0.224505	−	1.17690i	−0.00723833	−	0.0379446i
$963$	−16.5624	−	2.09232i	−0.533716	−	0.0674240i
$964$	−0.112851	−	0.0620401i	−0.00363467	−	0.00199818i
$965$	−26.7731	+	4.43329i	−0.861858	+	0.142713i
$966$	−57.0981	−	53.6187i	−1.83710	−	1.72515i
$967$	23.1219	+	5.93668i	0.743549	+	0.190911i	0.601415	−	0.798937i	$-0.294604\pi$
$967$	23.1219	+	5.93668i	0.743549	+	0.190911i	0.142134	+	0.989847i	$0.454604\pi$
$968$	10.5139	−	7.63877i	0.337929	−	0.245519i
$969$	0.0290389	+	0.461561i	0.000932865	+	0.0148275i
$970$	−40.6128	+	24.4047i	−1.30400	+	0.783588i
$971$	9.23783	+	3.65751i	0.296456	+	0.117375i	0.511644	−	0.859197i	$-0.329037\pi$
$971$	9.23783	+	3.65751i	0.296456	+	0.117375i	−0.215188	+	0.976573i	$0.569037\pi$
$972$	0.269706	+	0.106784i	0.00865082	+	0.00342510i
$973$	82.0253	−	10.3622i	2.62961	−	0.332197i
$974$	14.8517	+	45.7087i	0.475878	+	1.46460i
$975$	−26.6374	+	12.9944i	−0.853079	+	0.416153i
$976$	17.4676	−	53.7597i	0.559124	−	1.72081i
$977$	−3.40881	+	17.8696i	−0.109058	+	0.571700i	0.885247	+	0.465122i	$0.153989\pi$
$977$	−3.40881	+	17.8696i	−0.109058	+	0.571700i	−0.994304	+	0.106578i	$0.966011\pi$
$978$	−3.11183	+	49.4612i	−0.0995055	+	1.58159i
$979$	−35.2932	+	9.06175i	−1.12798	+	0.289615i
$980$	0.113337	−	0.194750i	0.00362043	−	0.00622106i
$981$	9.45246	−	14.8947i	0.301794	−	0.475551i
$982$	−3.36198	−	10.3471i	−0.107285	−	0.330190i
$983$	0.915941	+	14.5585i	0.0292140	+	0.464343i	0.985253	+	0.171104i	$0.0547333\pi$
$983$	0.915941	+	14.5585i	0.0292140	+	0.464343i	−0.956039	+	0.293239i	$0.905267\pi$
$984$	103.808	+	13.1140i	3.30927	+	0.418058i
$985$	0.271739	−	0.119863i	0.00865833	−	0.00381917i
$986$	−0.642188	−	1.36472i	−0.0204514	−	0.0434615i
$987$	23.2719	−	49.4554i	0.740754	−	1.57418i
$988$	−0.00802425	+	0.00441137i	−0.000255285	+	0.000140344i
$989$	9.38507	−	8.81317i	0.298428	−	0.280243i
$990$	−82.1166	−	28.9144i	−2.60984	−	0.918959i
$991$	17.6497	−	37.5075i	0.560661	−	1.19146i	−0.400710	−	0.916205i	$-0.631236\pi$
$991$	17.6497	−	37.5075i	0.560661	−	1.19146i	0.961370	−	0.275259i	$-0.0887637\pi$
$992$	0.0423241	+	0.0511610i	0.00134379	+	0.00162436i
$993$	−1.07746	+	3.31607i	−0.0341921	+	0.105232i
$994$	−36.2142	−	9.29823i	−1.14865	−	0.294922i
$995$	36.8535	−	37.3745i	1.16833	−	1.18485i
$996$	−0.0328357	+	0.521908i	−0.00104044	+	0.0165373i
$997$	7.79788	+	12.2875i	0.246961	+	0.389149i	0.945083	−	0.326830i	$-0.105981\pi$
$997$	7.79788	+	12.2875i	0.246961	+	0.389149i	−0.698122	+	0.715979i	$0.745981\pi$
$998$	26.2840	−	24.6823i	0.832006	−	0.781306i
$999$	5.58472			0.176693

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.g.a.11.9	✓	220
5.2	odd	4		625.2.h.b.199.17		440
5.3	odd	4		625.2.h.b.199.6		440
5.4	even	2		625.2.g.a.426.3		220
125.34	even	50		625.2.g.a.201.3		220
125.62	odd	100		625.2.h.b.424.6		440
125.63	odd	100		625.2.h.b.424.17		440
125.91	even	25	inner	125.2.g.a.91.9	yes	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.g.a.11.9	✓	220	1.1	even	1	trivial
125.2.g.a.91.9	yes	220	125.91	even	25	inner
625.2.g.a.201.3		220	125.34	even	50
625.2.g.a.426.3		220	5.4	even	2
625.2.h.b.199.6		440	5.3	odd	4
625.2.h.b.199.17		440	5.2	odd	4
625.2.h.b.424.6		440	125.62	odd	100
625.2.h.b.424.17		440	125.63	odd	100

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.g (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03453 - 0.971489i) q^{2} +(-1.68964 - 2.66244i) q^{3} +(0.000881745 - 0.0140149i) q^{4} +(-2.20603 + 0.365290i) q^{5} +(-4.33451 - 1.11291i) q^{6} +(1.16348 - 3.58083i) q^{7} +(1.79652 + 2.17162i) q^{8} +(-2.95638 + 6.28262i) q^{9} +O(q^{10})\)	\(q+(1.03453 - 0.971489i) q^{2} +(-1.68964 - 2.66244i) q^{3} +(0.000881745 - 0.0140149i) q^{4} +(-2.20603 + 0.365290i) q^{5} +(-4.33451 - 1.11291i) q^{6} +(1.16348 - 3.58083i) q^{7} +(1.79652 + 2.17162i) q^{8} +(-2.95638 + 6.28262i) q^{9} +(-1.92733 + 2.52104i) q^{10} +(2.88022 - 2.70470i) q^{11} +(-0.0388037 + 0.0213325i) q^{12} +(0.800374 - 1.70088i) q^{13} +(-2.27507 - 4.83478i) q^{14} +(4.69995 + 5.25621i) q^{15} +(3.99613 + 0.504828i) q^{16} +(-0.0265474 - 0.421958i) q^{17} +(3.04503 + 9.37165i) q^{18} +(0.185873 - 0.292888i) q^{19} +(0.00317437 + 0.0312394i) q^{20} +(-11.4996 + 2.95259i) q^{21} +(0.352083 - 5.59619i) q^{22} +(-0.871083 + 4.56638i) q^{23} +(2.74635 - 8.45238i) q^{24} +(4.73313 - 1.61168i) q^{25} +(-0.824376 - 2.53717i) q^{26} +(12.3369 - 1.55852i) q^{27} +(-0.0491591 - 0.0194635i) q^{28} +(2.33719 + 0.925361i) q^{29} +(9.96859 + 0.871763i) q^{30} +(0.0524853 + 0.834229i) q^{31} +(0.0642649 - 0.0466911i) q^{32} +(-12.0676 - 3.09844i) q^{33} +(-0.437392 - 0.410738i) q^{34} +(-1.25863 + 8.32441i) q^{35} +(0.0854438 + 0.0469731i) q^{36} +(0.445573 + 0.0562889i) q^{37} +(-0.0922469 - 0.483575i) q^{38} +(-5.88084 + 0.742922i) q^{39} +(-4.75645 - 4.13441i) q^{40} +(2.20608 + 11.5647i) q^{41} +(-9.02826 + 14.2263i) q^{42} +(-2.24054 - 1.62785i) q^{43} +(-0.0353666 - 0.0427509i) q^{44} +(4.22687 - 14.9396i) q^{45} +(3.53502 + 5.57030i) q^{46} +(-2.93448 + 3.54718i) q^{47} +(-5.40792 - 11.4924i) q^{48} +(-5.80551 - 4.21795i) q^{49} +(3.33083 - 6.26551i) q^{50} +(-1.07858 + 0.783636i) q^{51} +(-0.0231320 - 0.0127169i) q^{52} +(-3.27123 + 0.839910i) q^{53} +(11.2488 - 13.5975i) q^{54} +(-5.36584 + 7.01877i) q^{55} +(9.86642 - 3.90639i) q^{56} -1.09385 q^{57} +(3.31688 - 1.31324i) q^{58} +(-4.96681 + 2.73053i) q^{59} +(0.0778096 - 0.0612348i) q^{60} +(2.62966 - 13.7852i) q^{61} +(0.864742 + 0.812046i) q^{62} +(19.0573 + 17.8960i) q^{63} +(-1.48838 + 7.80235i) q^{64} +(-1.14433 + 4.04456i) q^{65} +(-15.4944 + 8.51813i) q^{66} +(1.43733 - 0.569080i) q^{67} -0.00593712 q^{68} +(13.6295 - 5.39631i) q^{69} +(6.78498 + 9.83460i) q^{70} +(4.46025 - 5.39152i) q^{71} +(-18.9547 + 4.86673i) q^{72} +(-0.448600 - 0.246620i) q^{73} +(0.515642 - 0.374636i) q^{74} +(-12.2883 - 9.87850i) q^{75} +(-0.00394092 - 0.00286324i) q^{76} +(-6.33399 - 13.4604i) q^{77} +(-5.36216 + 6.48174i) q^{78} +(0.574079 + 0.904603i) q^{79} +(-8.99998 + 0.346081i) q^{80} +(-11.7166 - 14.1629i) q^{81} +(13.5172 + 9.82084i) q^{82} +(6.32789 - 9.97116i) q^{83} +(0.0312407 + 0.163769i) q^{84} +(0.212702 + 0.921154i) q^{85} +(-3.89935 + 0.492602i) q^{86} +(-1.48529 - 7.78616i) q^{87} +(11.0480 + 1.39568i) q^{88} +(-8.08154 - 4.44286i) q^{89} +(-10.1408 - 19.5618i) q^{90} +(-5.15934 - 4.84494i) q^{91} +(0.0632294 + 0.0162346i) q^{92} +(2.13240 - 1.54928i) q^{93} +(0.410233 + 6.52047i) q^{94} +(-0.303051 + 0.714018i) q^{95} +(-0.232897 - 0.0922102i) q^{96} +(13.8825 + 5.49646i) q^{97} +(-10.1037 + 1.27639i) q^{98} +(8.47762 + 26.0914i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9}+O(q^{10}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9} - 20 q^{10} - 15 q^{11} - 100 q^{12} - 20 q^{13} - 10 q^{14} - 15 q^{17} + 10 q^{18} - 10 q^{19} + 5 q^{20} - 5 q^{21} + 25 q^{22} - 90 q^{23} + 15 q^{24} - 45 q^{25} + 15 q^{26} + 10 q^{27} + 30 q^{28} - 10 q^{29} + 40 q^{30} - 10 q^{31} + 20 q^{32} + 15 q^{33} + 5 q^{34} + 10 q^{35} - 210 q^{36} + 20 q^{37} + 30 q^{38} + 45 q^{40} - 5 q^{41} + 70 q^{42} + 25 q^{43} + 15 q^{44} - 100 q^{45} - 100 q^{47} + 105 q^{48} - 20 q^{49} + 60 q^{50} + 25 q^{51} + 85 q^{52} + 20 q^{53} + 60 q^{54} + 15 q^{55} - 105 q^{56} + 40 q^{57} - 225 q^{58} + 5 q^{59} - 35 q^{60} + 65 q^{62} + 85 q^{63} + 45 q^{64} + 45 q^{65} + 55 q^{66} - 105 q^{67} + 80 q^{68} + 40 q^{69} + 95 q^{70} - 85 q^{71} + 160 q^{72} + 40 q^{73} + 35 q^{74} + 55 q^{75} + 35 q^{76} + 75 q^{77} - 10 q^{78} - 330 q^{80} + 55 q^{81} - 95 q^{82} + 50 q^{83} + 115 q^{84} + 85 q^{85} + 40 q^{86} + 95 q^{87} + 165 q^{88} + 55 q^{89} + 170 q^{90} - 105 q^{91} + 155 q^{92} - 185 q^{93} + 60 q^{94} + 30 q^{95} + 135 q^{96} + 65 q^{97} + 135 q^{98} + 45 q^{99}+O(q^{100}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9 - 20 * q^10 - 15 * q^11 - 100 * q^12 - 20 * q^13 - 10 * q^14 - 15 * q^17 + 10 * q^18 - 10 * q^19 + 5 * q^20 - 5 * q^21 + 25 * q^22 - 90 * q^23 + 15 * q^24 - 45 * q^25 + 15 * q^26 + 10 * q^27 + 30 * q^28 - 10 * q^29 + 40 * q^30 - 10 * q^31 + 20 * q^32 + 15 * q^33 + 5 * q^34 + 10 * q^35 - 210 * q^36 + 20 * q^37 + 30 * q^38 + 45 * q^40 - 5 * q^41 + 70 * q^42 + 25 * q^43 + 15 * q^44 - 100 * q^45 - 100 * q^47 + 105 * q^48 - 20 * q^49 + 60 * q^50 + 25 * q^51 + 85 * q^52 + 20 * q^53 + 60 * q^54 + 15 * q^55 - 105 * q^56 + 40 * q^57 - 225 * q^58 + 5 * q^59 - 35 * q^60 + 65 * q^62 + 85 * q^63 + 45 * q^64 + 45 * q^65 + 55 * q^66 - 105 * q^67 + 80 * q^68 + 40 * q^69 + 95 * q^70 - 85 * q^71 + 160 * q^72 + 40 * q^73 + 35 * q^74 + 55 * q^75 + 35 * q^76 + 75 * q^77 - 10 * q^78 - 330 * q^80 + 55 * q^81 - 95 * q^82 + 50 * q^83 + 115 * q^84 + 85 * q^85 + 40 * q^86 + 95 * q^87 + 165 * q^88 + 55 * q^89 + 170 * q^90 - 105 * q^91 + 155 * q^92 - 185 * q^93 + 60 * q^94 + 30 * q^95 + 135 * q^96 + 65 * q^97 + 135 * q^98 + 45 * q^99

Introduction

L-functions

Modular forms

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Database

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