LMFDB - Embedded newform 31.2.g.a.18.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [31,2,Mod(7,31)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(31, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([28]))

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

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

chi := DirichletCharacter("31.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	31.g (of order $15$, degree $8$, 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:	$0.247536246266$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			18.1
Root			$-1.42343i$ of defining polynomial
Character	$\chi$	$=$	31.18
Dual form			31.2.g.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86683 + 1.35633i) q^{2} +(-2.32289 + 1.03422i) q^{3} +(1.02738 - 3.16196i) q^{4} +(1.24923 + 2.16373i) q^{5} +(2.93370 - 5.08132i) q^{6} +(1.07187 + 1.19043i) q^{7} +(0.944583 + 2.90713i) q^{8} +(2.31884 - 2.57533i) q^{9} +O(q^{10})$	\(q+(-1.86683 + 1.35633i) q^{2} +(-2.32289 + 1.03422i) q^{3} +(1.02738 - 3.16196i) q^{4} +(1.24923 + 2.16373i) q^{5} +(2.93370 - 5.08132i) q^{6} +(1.07187 + 1.19043i) q^{7} +(0.944583 + 2.90713i) q^{8} +(2.31884 - 2.57533i) q^{9} +(-5.26683 - 2.34494i) q^{10} +(-0.717625 + 0.152536i) q^{11} +(0.883657 + 8.40743i) q^{12} +(0.198183 - 1.88559i) q^{13} +(-3.61560 - 0.768520i) q^{14} +(-5.13960 - 3.73414i) q^{15} +(-0.326952 - 0.237545i) q^{16} +(4.28354 + 0.910495i) q^{17} +(-0.835873 + 7.95280i) q^{18} +(0.484806 + 4.61262i) q^{19} +(8.12506 - 1.72703i) q^{20} +(-3.72099 - 1.65669i) q^{21} +(1.13279 - 1.25809i) q^{22} +(-2.19973 - 6.77006i) q^{23} +(-5.20077 - 5.77604i) q^{24} +(-0.621150 + 1.07586i) q^{25} +(2.18751 + 3.78887i) q^{26} +(-0.365721 + 1.12557i) q^{27} +(4.86530 - 2.16617i) q^{28} +(0.104314 - 0.0757884i) q^{29} +14.6595 q^{30} +(4.81795 - 2.79058i) q^{31} -5.18091 q^{32} +(1.50921 - 1.09651i) q^{33} +(-9.23157 + 4.11016i) q^{34} +(-1.23676 + 3.80635i) q^{35} +(-5.76075 - 9.97791i) q^{36} +(-4.21474 + 7.30014i) q^{37} +(-7.16128 - 7.95341i) q^{38} +(1.48975 + 4.58499i) q^{39} +(-5.11023 + 5.67549i) q^{40} +(-6.73647 - 2.99927i) q^{41} +(9.19348 - 1.95413i) q^{42} +(-0.0240929 - 0.229229i) q^{43} +(-0.254963 + 2.42581i) q^{44} +(8.46907 + 1.80016i) q^{45} +(13.2889 + 9.65498i) q^{46} +(6.50168 + 4.72375i) q^{47} +(1.00515 + 0.213651i) q^{48} +(0.463478 - 4.40970i) q^{49} +(-0.299645 - 2.85094i) q^{50} +(-10.8919 + 2.31514i) q^{51} +(-5.75854 - 2.56387i) q^{52} +(3.83695 - 4.26137i) q^{53} +(-0.843912 - 2.59729i) q^{54} +(-1.22652 - 1.36219i) q^{55} +(-2.44826 + 4.24051i) q^{56} +(-5.89661 - 10.2132i) q^{57} +(-0.0919419 + 0.282968i) q^{58} +(8.68208 - 3.86551i) q^{59} +(-17.0875 + 12.4148i) q^{60} -7.84044 q^{61} +(-5.20934 + 11.7443i) q^{62} +5.55122 q^{63} +(10.3258 - 7.50212i) q^{64} +(4.32748 - 1.92672i) q^{65} +(-1.33021 + 4.09397i) q^{66} +(-2.41329 - 4.17994i) q^{67} +(7.27978 - 12.6090i) q^{68} +(12.1115 + 13.4511i) q^{69} +(-2.85385 - 8.78324i) q^{70} +(-2.27840 + 2.53042i) q^{71} +(9.67714 + 4.30854i) q^{72} +(-2.63322 + 0.559708i) q^{73} +(-2.03321 - 19.3447i) q^{74} +(0.330187 - 3.14152i) q^{75} +(15.0830 + 3.20599i) q^{76} +(-0.950780 - 0.690782i) q^{77} +(-8.99987 - 6.53879i) q^{78} +(-4.42900 - 0.941413i) q^{79} +(0.105544 - 1.00418i) q^{80} +(0.772154 + 7.34656i) q^{81} +(16.6438 - 3.53775i) q^{82} +(2.43949 + 1.08613i) q^{83} +(-9.06128 + 10.0636i) q^{84} +(3.38106 + 10.4058i) q^{85} +(0.355888 + 0.395253i) q^{86} +(-0.163928 + 0.283932i) q^{87} +(-1.12130 - 1.94214i) q^{88} +(-0.681255 + 2.09669i) q^{89} +(-18.2519 + 8.12627i) q^{90} +(2.45708 - 1.78518i) q^{91} -23.6666 q^{92} +(-8.30552 + 11.4650i) q^{93} -18.5445 q^{94} +(-9.37482 + 6.81121i) q^{95} +(12.0347 - 5.35820i) q^{96} +(3.79778 - 11.6884i) q^{97} +(5.11577 + 8.86077i) q^{98} +(-1.27122 + 2.20182i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9	\( 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9} - 2 q^{10} - 7 q^{11} + 5 q^{12} - 7 q^{13} - 6 q^{14} + 14 q^{15} - 2 q^{16} - 6 q^{17} - 3 q^{18} + 16 q^{19} + 37 q^{20} + 9 q^{21} + 9 q^{22} + q^{23} - 20 q^{24} - 13 q^{25} + 9 q^{26} + 9 q^{27} - 30 q^{28} - 14 q^{29} - 22 q^{30} + 15 q^{31} - 42 q^{32} - 13 q^{33} - 32 q^{34} - 9 q^{35} + q^{36} - 8 q^{37} + 8 q^{38} - 3 q^{39} - q^{40} - 8 q^{41} + 69 q^{42} + 23 q^{43} + 39 q^{44} + 65 q^{45} + 34 q^{46} + 14 q^{47} + 34 q^{48} + 2 q^{49} + 3 q^{50} - 42 q^{51} + 29 q^{52} + 6 q^{53} - 46 q^{54} - 7 q^{55} - 30 q^{56} - 17 q^{57} - 15 q^{58} + 4 q^{59} - 75 q^{60} - 60 q^{61} - 25 q^{62} - 46 q^{63} + 23 q^{64} - 12 q^{65} - 30 q^{66} + 13 q^{67} + 30 q^{68} + 38 q^{69} + 12 q^{70} - 14 q^{71} + 37 q^{72} + 2 q^{73} + 13 q^{74} + 13 q^{75} - 12 q^{76} + 18 q^{77} - 15 q^{78} + 18 q^{79} + 36 q^{80} + 23 q^{81} + 14 q^{82} - 16 q^{83} + 8 q^{84} + 37 q^{85} - 26 q^{86} + 15 q^{87} - 17 q^{88} + q^{89} - 23 q^{90} + 8 q^{91} - 64 q^{92} + 17 q^{93} + 44 q^{94} - 22 q^{95} + 8 q^{96} + 3 q^{97} - 10 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9 - 2 * q^10 - 7 * q^11 + 5 * q^12 - 7 * q^13 - 6 * q^14 + 14 * q^15 - 2 * q^16 - 6 * q^17 - 3 * q^18 + 16 * q^19 + 37 * q^20 + 9 * q^21 + 9 * q^22 + q^23 - 20 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 - 30 * q^28 - 14 * q^29 - 22 * q^30 + 15 * q^31 - 42 * q^32 - 13 * q^33 - 32 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 8 * q^38 - 3 * q^39 - q^40 - 8 * q^41 + 69 * q^42 + 23 * q^43 + 39 * q^44 + 65 * q^45 + 34 * q^46 + 14 * q^47 + 34 * q^48 + 2 * q^49 + 3 * q^50 - 42 * q^51 + 29 * q^52 + 6 * q^53 - 46 * q^54 - 7 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 + 4 * q^59 - 75 * q^60 - 60 * q^61 - 25 * q^62 - 46 * q^63 + 23 * q^64 - 12 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 + 38 * q^69 + 12 * q^70 - 14 * q^71 + 37 * q^72 + 2 * q^73 + 13 * q^74 + 13 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 + 18 * q^79 + 36 * q^80 + 23 * q^81 + 14 * q^82 - 16 * q^83 + 8 * q^84 + 37 * q^85 - 26 * q^86 + 15 * q^87 - 17 * q^88 + q^89 - 23 * q^90 + 8 * q^91 - 64 * q^92 + 17 * q^93 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{13}{15}\right)$

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 $

$2$	−1.86683	+	1.35633i	−1.32005	+	0.959070i	−0.320115	+	0.947379i	$0.603722\pi$
$2$	−1.86683	+	1.35633i	−1.32005	+	0.959070i	−0.999932	+	0.0116917i	$0.996278\pi$
$3$	−2.32289	+	1.03422i	−1.34112	+	0.597107i	−0.946787	−	0.321860i	$-0.895692\pi$
$3$	−2.32289	+	1.03422i	−1.34112	+	0.597107i	−0.394336	+	0.918966i	$0.629025\pi$
$4$	1.02738	−	3.16196i	0.513691	−	1.58098i
$5$	1.24923	+	2.16373i	0.558673	+	0.967649i	0.997608	+	0.0691304i	$0.0220225\pi$
$5$	1.24923	+	2.16373i	0.558673	+	0.967649i	−0.438935	+	0.898519i	$0.644644\pi$
$6$	2.93370	−	5.08132i	1.19768	−	2.07444i
$7$	1.07187	+	1.19043i	0.405127	+	0.449939i	0.910838	−	0.412764i	$-0.135436\pi$
$7$	1.07187	+	1.19043i	0.405127	+	0.449939i	−0.505711	+	0.862703i	$0.668770\pi$
$8$	0.944583	+	2.90713i	0.333960	+	1.02782i
$9$	2.31884	−	2.57533i	0.772945	−	0.858443i
$10$	−5.26683	−	2.34494i	−1.66552	−	0.741536i
$11$	−0.717625	+	0.152536i	−0.216372	+	0.0459913i	−0.314822	−	0.949151i	$-0.601945\pi$
$11$	−0.717625	+	0.152536i	−0.216372	+	0.0459913i	0.0984501	+	0.995142i	$0.468612\pi$
$12$	0.883657	+	8.40743i	0.255090	+	2.42702i
$13$	0.198183	−	1.88559i	0.0549662	−	0.522968i	−0.932048	−	0.362335i	$-0.881980\pi$
$13$	0.198183	−	1.88559i	0.0549662	−	0.522968i	0.987014	−	0.160633i	$-0.0513537\pi$
$14$	−3.61560	−	0.768520i	−0.966310	−	0.205396i
$15$	−5.13960	−	3.73414i	−1.32704	−	0.964150i
$16$	−0.326952	−	0.237545i	−0.0817381	−	0.0593862i
$17$	4.28354	+	0.910495i	1.03891	+	0.220828i	0.695626	−	0.718404i	$-0.255127\pi$
$17$	4.28354	+	0.910495i	1.03891	+	0.220828i	0.343285	+	0.939231i	$0.388460\pi$
$18$	−0.835873	+	7.95280i	−0.197017	+	1.87449i
$19$	0.484806	+	4.61262i	0.111222	+	1.05821i	0.897706	+	0.440596i	$0.145233\pi$
$19$	0.484806	+	4.61262i	0.111222	+	1.05821i	−0.786483	+	0.617611i	$0.788100\pi$
$20$	8.12506	−	1.72703i	1.81682	−	0.386177i
$21$	−3.72099	−	1.65669i	−0.811987	−	0.361520i
$22$	1.13279	−	1.25809i	0.241512	−	0.268227i
$23$	−2.19973	−	6.77006i	−0.458675	−	1.41166i	−0.866766	−	0.498714i	$-0.833806\pi$
$23$	−2.19973	−	6.77006i	−0.458675	−	1.41166i	0.408092	−	0.912941i	$-0.366194\pi$
$24$	−5.20077	−	5.77604i	−1.06160	−	1.17903i
$25$	−0.621150	+	1.07586i	−0.124230	+	0.215173i
$26$	2.18751	+	3.78887i	0.429005	+	0.743059i
$27$	−0.365721	+	1.12557i	−0.0703831	+	0.216617i
$28$	4.86530	−	2.16617i	0.919455	−	0.409368i
$29$	0.104314	−	0.0757884i	0.0193706	−	0.0140736i	−0.578058	−	0.815996i	$-0.696189\pi$
$29$	0.104314	−	0.0757884i	0.0193706	−	0.0140736i	0.597428	+	0.801922i	$0.296189\pi$
$30$	14.6595			2.67644
$31$	4.81795	−	2.79058i	0.865330	−	0.501203i
$31$	4.81795	−	2.79058i	0.865330	−	0.501203i
$32$	−5.18091			−0.915865
$33$	1.50921	−	1.09651i	0.262720	−	0.190877i
$34$	−9.23157	+	4.11016i	−1.58320	+	0.704887i
$35$	−1.23676	+	3.80635i	−0.209050	+	0.643390i
$36$	−5.76075	−	9.97791i	−0.960125	−	1.66298i
$37$	−4.21474	+	7.30014i	−0.692899	+	1.20014i	0.277985	+	0.960585i	$0.410333\pi$
$37$	−4.21474	+	7.30014i	−0.692899	+	1.20014i	−0.970884	+	0.239550i	$0.923000\pi$
$38$	−7.16128	−	7.95341i	−1.16171	−	1.29021i
$39$	1.48975	+	4.58499i	0.238551	+	0.734186i
$40$	−5.11023	+	5.67549i	−0.807999	+	0.897374i
$41$	−6.73647	−	2.99927i	−1.05206	−	0.468407i	−0.193489	−	0.981102i	$-0.561980\pi$
$41$	−6.73647	−	2.99927i	−1.05206	−	0.468407i	−0.858570	+	0.512696i	$0.828647\pi$
$42$	9.19348	−	1.95413i	1.41858	−	0.301529i
$43$	−0.0240929	−	0.229229i	−0.00367414	−	0.0349571i	0.992531	−	0.121991i	$-0.0389279\pi$
$43$	−0.0240929	−	0.229229i	−0.00367414	−	0.0349571i	−0.996205	+	0.0870338i	$0.972261\pi$
$44$	−0.254963	+	2.42581i	−0.0384371	+	0.365705i
$45$	8.46907	+	1.80016i	1.26249	+	0.268351i
$46$	13.2889	+	9.65498i	1.95935	+	1.42355i
$47$	6.50168	+	4.72375i	0.948368	+	0.689030i	0.950420	−	0.310968i	$-0.100653\pi$
$47$	6.50168	+	4.72375i	0.948368	+	0.689030i	−0.00205222	+	0.999998i	$0.500653\pi$
$48$	1.00515	+	0.213651i	0.145081	+	0.0308379i
$49$	0.463478	−	4.40970i	0.0662111	−	0.629957i
$50$	−0.299645	−	2.85094i	−0.0423763	−	0.403183i
$51$	−10.8919	+	2.31514i	−1.52517	+	0.324184i
$52$	−5.75854	−	2.56387i	−0.798566	−	0.355545i
$53$	3.83695	−	4.26137i	0.527046	−	0.585344i	−0.419563	−	0.907726i	$-0.637817\pi$
$53$	3.83695	−	4.26137i	0.527046	−	0.585344i	0.946610	+	0.322382i	$0.104483\pi$
$54$	−0.843912	−	2.59729i	−0.114842	−	0.353447i
$55$	−1.22652	−	1.36219i	−0.165384	−	0.183678i
$56$	−2.44826	+	4.24051i	−0.327162	+	0.566662i
$57$	−5.89661	−	10.2132i	−0.781025	−	1.35278i
$58$	−0.0919419	+	0.282968i	−0.0120726	+	0.0371555i
$59$	8.68208	−	3.86551i	1.13031	−	0.503247i	0.245592	−	0.969373i	$-0.421018\pi$
$59$	8.68208	−	3.86551i	1.13031	−	0.503247i	0.884718	+	0.466127i	$0.154351\pi$
$60$	−17.0875	+	12.4148i	−2.20599	+	1.60274i
$61$	−7.84044			−1.00387			−0.501933	−	0.864907i	$-0.667377\pi$
$61$	−7.84044			−1.00387			−0.501933	+	0.864907i	$0.667377\pi$
$62$	−5.20934	+	11.7443i	−0.661587	+	1.49152i
$63$	5.55122			0.699388
$64$	10.3258	−	7.50212i	1.29072	−	0.937765i
$65$	4.32748	−	1.92672i	0.536758	−	0.238980i
$66$	−1.33021	+	4.09397i	−0.163738	+	0.503933i
$67$	−2.41329	−	4.17994i	−0.294830	−	0.510661i	0.680115	−	0.733105i	$-0.261930\pi$
$67$	−2.41329	−	4.17994i	−0.294830	−	0.510661i	−0.974945	+	0.222444i	$0.928596\pi$
$68$	7.27978	−	12.6090i	0.882804	−	1.52906i
$69$	12.1115	+	13.4511i	1.45805	+	1.61933i
$70$	−2.85385	−	8.78324i	−0.341100	−	1.04980i
$71$	−2.27840	+	2.53042i	−0.270396	+	0.300306i	−0.863016	−	0.505177i	$-0.831427\pi$
$71$	−2.27840	+	2.53042i	−0.270396	+	0.300306i	0.592619	+	0.805483i	$0.298094\pi$
$72$	9.67714	+	4.30854i	1.14046	+	0.507766i
$73$	−2.63322	+	0.559708i	−0.308195	+	0.0655088i	−0.359413	−	0.933179i	$-0.617023\pi$
$73$	−2.63322	+	0.559708i	−0.308195	+	0.0655088i	0.0512180	+	0.998687i	$0.483690\pi$
$74$	−2.03321	−	19.3447i	−0.236356	−	2.24877i
$75$	0.330187	−	3.14152i	0.0381267	−	0.362751i
$76$	15.0830	+	3.20599i	1.73014	+	0.367752i
$77$	−0.950780	−	0.690782i	−0.108351	−	0.0787219i
$78$	−8.99987	−	6.53879i	−1.01903	−	0.740372i
$79$	−4.42900	−	0.941413i	−0.498301	−	0.105917i	−0.0480968	−	0.998843i	$-0.515316\pi$
$79$	−4.42900	−	0.941413i	−0.498301	−	0.105917i	−0.450204	+	0.892925i	$0.648649\pi$
$80$	0.105544	−	1.00418i	0.0118002	−	0.112271i
$81$	0.772154	+	7.34656i	0.0857949	+	0.816284i
$82$	16.6438	−	3.53775i	1.83800	−	0.390680i
$83$	2.43949	+	1.08613i	0.267768	+	0.119218i	0.536229	−	0.844072i	$-0.319848\pi$
$83$	2.43949	+	1.08613i	0.267768	+	0.119218i	−0.268461	+	0.963291i	$0.586515\pi$
$84$	−9.06128	+	10.0636i	−0.988666	+	1.09803i
$85$	3.38106	+	10.4058i	0.366728	+	1.12867i
$86$	0.355888	+	0.395253i	0.0383764	+	0.0426213i
$87$	−0.163928	+	0.283932i	−0.0175749	+	0.0304407i
$88$	−1.12130	−	1.94214i	−0.119531	−	0.207033i
$89$	−0.681255	+	2.09669i	−0.0722129	+	0.222248i	−0.980649	−	0.195776i	$-0.937277\pi$
$89$	−0.681255	+	2.09669i	−0.0722129	+	0.222248i	0.908436	+	0.418025i	$0.137277\pi$
$90$	−18.2519	+	8.12627i	−1.92392	+	0.856584i
$91$	2.45708	−	1.78518i	0.257572	−	0.187137i
$92$	−23.6666			−2.46741
$93$	−8.30552	+	11.4650i	−0.861243	+	1.18887i
$94$	−18.5445			−1.91272
$95$	−9.37482	+	6.81121i	−0.961837	+	0.698815i
$96$	12.0347	−	5.35820i	1.22829	−	0.546869i
$97$	3.79778	−	11.6884i	0.385606	−	1.18677i	−0.550434	−	0.834879i	$-0.685538\pi$
$97$	3.79778	−	11.6884i	0.385606	−	1.18677i	0.936040	−	0.351894i	$-0.114462\pi$
$98$	5.11577	+	8.86077i	0.516771	+	0.895073i
$99$	−1.27122	+	2.20182i	−0.127763	+	0.221292i
$100$	2.76367	+	3.06937i	0.276367	+	0.306937i
$101$	2.26952	+	6.98486i	0.225826	+	0.695020i	0.998207	+	0.0598605i	$0.0190656\pi$
$101$	2.26952	+	6.98486i	0.225826	+	0.695020i	−0.772381	+	0.635159i	$0.780934\pi$
$102$	17.1932	−	19.0949i	1.70238	−	1.89068i
$103$	5.10558	+	2.27315i	0.503068	+	0.223980i	0.642549	−	0.766245i	$-0.277877\pi$
$103$	5.10558	+	2.27315i	0.503068	+	0.223980i	−0.139481	+	0.990225i	$0.544544\pi$
$104$	5.66885	−	1.20495i	0.555876	−	0.118155i
$105$	−1.06374	−	10.1208i	−0.103810	−	0.987690i
$106$	−1.38311	+	13.1594i	−0.134340	+	1.27816i
$107$	−1.78430	−	0.379264i	−0.172495	−	0.0366649i	0.120855	−	0.992670i	$-0.461437\pi$
$107$	−1.78430	−	0.379264i	−0.172495	−	0.0366649i	−0.293349	+	0.956005i	$0.594770\pi$
$108$	3.18328	+	2.31279i	0.306312	+	0.222548i
$109$	−9.51832	−	6.91546i	−0.911689	−	0.662381i	0.0297521	−	0.999557i	$-0.490528\pi$
$109$	−9.51832	−	6.91546i	−0.911689	−	0.662381i	−0.941442	+	0.337176i	$0.890528\pi$
$110$	4.13729	+	0.879409i	0.394475	+	0.0838483i
$111$	2.24045	−	21.3164i	0.212654	−	2.02326i
$112$	−0.0676692	−	0.643829i	−0.00639414	−	0.0608361i
$113$	−10.8130	+	2.29837i	−1.01720	+	0.216212i	−0.686195	−	0.727417i	$-0.740720\pi$
$113$	−10.8130	+	2.29837i	−1.01720	+	0.216212i	−0.331003	+	0.943630i	$0.607387\pi$
$114$	24.8605	+	11.0686i	2.32840	+	1.03667i
$115$	11.9006	−	13.2170i	1.10974	−	1.23249i
$116$	−0.132470	−	0.407700i	−0.0122995	−	0.0378540i
$117$	−4.39646	−	4.88276i	−0.406452	−	0.451411i
$118$	−10.9650	+	18.9920i	−1.00941	+	1.74836i
$119$	3.50750	+	6.07518i	0.321532	+	0.556911i
$120$	6.00083	−	18.4687i	0.547799	−	1.68595i
$121$	−9.55728	+	4.25518i	−0.868844	+	0.386834i
$122$	14.6368	−	10.6342i	1.32515	−	0.962777i
$123$	18.7500			1.69063
$124$	−3.87381	−	18.1012i	−0.347879	−	1.62553i
$125$	9.38846			0.839730
$126$	−10.3632	+	7.52929i	−0.923225	+	0.670762i
$127$	−1.17576	+	0.523483i	−0.104332	+	0.0464516i	−0.458239	−	0.888829i	$-0.651520\pi$
$127$	−1.17576	+	0.523483i	−0.104332	+	0.0464516i	0.353907	+	0.935281i	$0.384853\pi$
$128$	−5.89913	+	18.1557i	−0.521414	+	1.60475i
$129$	0.293038	+	0.507557i	0.0258006	+	0.0446879i
$130$	−5.46540	+	9.46635i	−0.479347	+	0.830254i
$131$	−5.36666	−	5.96028i	−0.468888	−	0.520752i	0.461594	−	0.887091i	$-0.347278\pi$
$131$	−5.36666	−	5.96028i	−0.468888	−	0.520752i	−0.930481	+	0.366339i	$0.880611\pi$
$132$	−1.91657	−	5.89859i	−0.166816	−	0.513406i
$133$	−4.97134	+	5.52123i	−0.431070	+	0.478752i
$134$	10.1746	+	4.53001i	0.878949	+	0.391334i
$135$	−2.89231	+	0.614779i	−0.248930	+	0.0529118i
$136$	1.39924	+	13.3128i	0.119983	+	1.14157i
$137$	1.72229	−	16.3865i	0.147145	−	1.39999i	−0.632883	−	0.774248i	$-0.718128\pi$
$137$	1.72229	−	16.3865i	0.147145	−	1.39999i	0.780028	−	0.625745i	$-0.215205\pi$
$138$	−40.8542	−	8.68382i	−3.47774	−	0.739216i
$139$	−5.93804	−	4.31424i	−0.503658	−	0.365929i	0.306755	−	0.951789i	$-0.400757\pi$
$139$	−5.93804	−	4.31424i	−0.503658	−	0.365929i	−0.810412	+	0.585860i	$0.800757\pi$
$140$	10.7649	+	7.82114i	0.909799	+	0.661007i
$141$	−19.9881	−	4.24861i	−1.68330	−	0.357797i
$142$	0.821298	−	7.81413i	0.0689218	−	0.655747i
$143$	0.145399	+	1.38338i	0.0121588	+	0.115684i
$144$	−1.36990	+	0.291182i	−0.114159	+	0.0242652i
$145$	0.294298	+	0.131030i	0.0244401	+	0.0108814i
$146$	4.15662	−	4.61639i	0.344004	−	0.382055i
$147$	3.48398	+	10.7226i	0.287354	+	0.884385i
$148$	18.7526	+	20.8269i	1.54145	+	1.71196i
$149$	3.18096	−	5.50959i	0.260595	−	0.451363i	−0.705805	−	0.708406i	$-0.749415\pi$
$149$	3.18096	−	5.50959i	0.260595	−	0.451363i	0.966400	+	0.257043i	$0.0827480\pi$
$150$	3.64454	+	6.31252i	0.297575	+	0.515415i
$151$	−1.70724	+	5.25433i	−0.138933	+	0.427592i	−0.996181	−	0.0873120i	$-0.972172\pi$
$151$	−1.70724	+	5.25433i	−0.138933	+	0.427592i	0.857248	+	0.514904i	$0.172172\pi$
$152$	−12.9515	+	5.76639i	−1.05051	+	0.467716i
$153$	12.2777	−	8.92024i	0.992590	−	0.721159i
$154$	2.71187			0.218529
$155$	12.0568	+	6.93867i	0.968424	+	0.557327i
$156$	16.0281			1.28327
$157$	−6.46767	+	4.69903i	−0.516176	+	0.375024i	−0.815161	−	0.579234i	$-0.803352\pi$
$157$	−6.46767	+	4.69903i	−0.516176	+	0.375024i	0.298985	+	0.954258i	$0.403352\pi$
$158$	9.54505	−	4.24973i	0.759363	−	0.338090i
$159$	−4.50565	+	13.8670i	−0.357321	+	1.09972i
$160$	−6.47215	−	11.2101i	−0.511669	−	0.886236i
$161$	5.70146	−	9.87521i	0.449338	−	0.778276i
$162$	−11.4058	−	12.6675i	−0.896127	−	0.995250i
$163$	−5.27350	−	16.2302i	−0.413052	−	1.27124i	−0.913981	−	0.405756i	$-0.867008\pi$
$163$	−5.27350	−	16.2302i	−0.413052	−	1.27124i	0.500929	−	0.865488i	$-0.332992\pi$
$164$	−16.4045	+	18.2190i	−1.28098	+	1.42267i
$165$	4.25789	+	1.89574i	0.331476	+	0.147583i
$166$	−6.02725	+	1.28113i	−0.467805	+	0.0994351i
$167$	2.54759	+	24.2387i	0.197138	+	1.87565i	0.429570	+	0.903034i	$0.358665\pi$
$167$	2.54759	+	24.2387i	0.197138	+	1.87565i	−0.232431	+	0.972613i	$0.574668\pi$
$168$	1.30143	−	12.3823i	0.100408	−	0.955314i
$169$	9.19975	+	1.95547i	0.707673	+	0.150421i
$170$	−20.4256	−	14.8401i	−1.56657	−	1.13818i
$171$	13.0032	+	9.44737i	0.994379	+	0.722458i
$172$	−0.749565	−	0.159325i	−0.0571538	−	0.0121484i
$173$	−0.937997	+	8.92444i	−0.0713146	+	0.678513i	0.899211	+	0.437515i	$0.144141\pi$
$173$	−0.937997	+	8.92444i	−0.0713146	+	0.678513i	−0.970526	+	0.240998i	$0.922525\pi$
$174$	−0.0790797	−	0.752393i	−0.00599501	−	0.0570387i
$175$	−1.94653	+	0.413747i	−0.147144	+	0.0312763i
$176$	0.270863	+	0.120596i	0.0204171	+	0.00909027i
$177$	−16.1698	+	17.9583i	−1.21539	+	1.34983i
$178$	−1.57201	−	4.83816i	−0.117827	−	0.362635i
$179$	−7.55483	−	8.39049i	−0.564675	−	0.627135i	0.391413	−	0.920215i	$-0.371986\pi$
$179$	−7.55483	−	8.39049i	−0.564675	−	0.627135i	−0.956088	+	0.293080i	$0.905320\pi$
$180$	14.3930	−	24.9294i	1.07279	−	1.85813i
$181$	7.47052	+	12.9393i	0.555279	+	0.961772i	0.997882	+	0.0650542i	$0.0207220\pi$
$181$	7.47052	+	12.9393i	0.555279	+	0.961772i	−0.442602	+	0.896718i	$0.645945\pi$
$182$	−2.16567	+	6.66523i	−0.160530	+	0.494060i
$183$	18.2125	−	8.10873i	1.34631	−	0.599415i
$184$	17.6036	−	12.7898i	1.29775	−	0.942874i
$185$	−21.0607			−1.54841
$186$	−0.0453903	−	32.6683i	−0.00332818	−	2.39536i
$187$	−3.21286			−0.234947
$188$	21.6160	−	15.7050i	1.57651	−	1.14540i
$189$	−1.73192	+	0.771100i	−0.125979	+	0.0560893i
$190$	8.26294	−	25.4307i	0.599457	−	1.84494i
$191$	−1.13046	−	1.95802i	−0.0817975	−	0.141677i	0.822225	−	0.569163i	$-0.192733\pi$
$191$	−1.13046	−	1.95802i	−0.0817975	−	0.141677i	−0.904022	+	0.427486i	$0.859399\pi$
$192$	−16.2269	+	28.1057i	−1.17107	+	2.02836i
$193$	17.1727	+	19.0723i	1.23612	+	1.37285i	0.902813	+	0.430033i	$0.141498\pi$
$193$	17.1727	+	19.0723i	1.23612	+	1.37285i	0.333307	+	0.942818i	$0.391835\pi$
$194$	8.76347	+	26.9712i	0.629181	+	1.93642i
$195$	−8.05963	+	8.95113i	−0.577162	+	0.641004i
$196$	−13.4671	−	5.99594i	−0.961936	−	0.428282i
$197$	6.06032	−	1.28816i	0.431780	−	0.0917776i	0.0131056	−	0.999914i	$-0.495828\pi$
$197$	6.06032	−	1.28816i	0.431780	−	0.0917776i	0.418674	+	0.908136i	$0.362495\pi$
$198$	−0.613244	−	5.83463i	−0.0435813	−	0.414649i
$199$	0.477625	−	4.54430i	0.0338579	−	0.322137i	−0.964463	−	0.264217i	$-0.914887\pi$
$199$	0.477625	−	4.54430i	0.0338579	−	0.322137i	0.998321	−	0.0579199i	$-0.0184468\pi$
$200$	−3.71440	−	0.789519i	−0.262647	−	0.0558274i
$201$	9.92879	+	7.21369i	0.700323	+	0.508814i
$202$	−13.7106	−	9.96132i	−0.964673	−	0.700876i
$203$	0.202031	+	0.0429430i	0.0141798	+	0.00301401i
$204$	−3.86974	+	36.8182i	−0.270936	+	2.57779i
$205$	−1.92579	−	18.3227i	−0.134503	−	1.27971i
$206$	−12.6144	+	2.68127i	−0.878886	+	0.186813i
$207$	−22.5359	−	10.0336i	−1.56636	−	0.697386i
$208$	−0.512708	+	0.569420i	−0.0355499	+	0.0394822i
$209$	−1.05150	−	3.23618i	−0.0727336	−	0.223851i
$210$	15.7130	+	17.4510i	1.08430	+	1.20424i
$211$	9.30839	−	16.1226i	0.640816	−	1.10993i	−0.344435	−	0.938810i	$-0.611930\pi$
$211$	9.30839	−	16.1226i	0.640816	−	1.10993i	0.985251	−	0.171115i	$-0.0547371\pi$
$212$	−9.53225	−	16.5103i	−0.654678	−	1.13394i
$213$	2.67547	−	8.23426i	0.183321	−	0.564203i
$214$	3.84539	−	1.71208i	0.262865	−	0.117035i
$215$	0.465892	−	0.338490i	0.0317736	−	0.0230849i
$216$	−3.61764			−0.246149
$217$	8.48618	+	2.74430i	0.576080	+	0.186295i
$218$	27.1487			1.83874
$219$	5.53783	−	4.02347i	0.374212	−	0.271881i
$220$	−5.56731	+	2.47872i	−0.375348	+	0.167116i
$221$	2.56575	−	7.89656i	0.172591	−	0.531180i
$222$	24.7296	+	42.8329i	1.65974	+	2.87475i
$223$	−3.10748	+	5.38231i	−0.208092	+	0.360426i	−0.951113	−	0.308842i	$-0.900059\pi$
$223$	−3.10748	+	5.38231i	−0.208092	+	0.360426i	0.743021	+	0.669268i	$0.233392\pi$
$224$	−5.55324	−	6.16750i	−0.371042	−	0.412084i
$225$	1.33036	+	4.09441i	0.0886904	+	0.272961i
$226$	17.0686	−	18.9566i	1.13539	−	1.26097i
$227$	−11.9198	−	5.30702i	−0.791142	−	0.352239i	−0.0289423	−	0.999581i	$-0.509214\pi$
$227$	−11.9198	−	5.30702i	−0.791142	−	0.352239i	−0.762200	+	0.647342i	$0.775881\pi$
$228$	−38.3519	+	8.15194i	−2.53992	+	0.539876i
$229$	−1.59698	−	15.1942i	−0.105531	−	1.00406i	−0.911275	−	0.411799i	$-0.864901\pi$
$229$	−1.59698	−	15.1942i	−0.105531	−	1.00406i	0.805743	−	0.592265i	$-0.201766\pi$
$230$	−4.28983	+	40.8150i	−0.282863	+	2.69126i
$231$	2.92298	+	0.621299i	0.192318	+	0.0408785i
$232$	0.318860	+	0.231665i	0.0209342	+	0.0152096i
$233$	−10.5668	−	7.67721i	−0.692253	−	0.502951i	0.185147	−	0.982711i	$-0.440724\pi$
$233$	−10.5668	−	7.67721i	−0.692253	−	0.502951i	−0.877400	+	0.479760i	$0.840724\pi$
$234$	14.8301	+	3.15223i	0.969471	+	0.206068i
$235$	−2.09882	+	19.9689i	−0.136912	+	1.30263i
$236$	−3.30277	−	31.4237i	−0.214992	−	2.04551i
$237$	11.2617	−	2.39375i	0.731527	−	0.155491i
$238$	−14.7879	−	6.58398i	−0.958554	−	0.426776i
$239$	−15.6859	+	17.4210i	−1.01464	+	1.12687i	−0.0227507	+	0.999741i	$0.507242\pi$
$239$	−15.6859	+	17.4210i	−1.01464	+	1.12687i	−0.991886	+	0.127128i	$0.959424\pi$
$240$	0.793379	+	2.44177i	0.0512124	+	0.157616i
$241$	16.5356	+	18.3647i	1.06515	+	1.18297i	0.982475	+	0.186395i	$0.0596805\pi$
$241$	16.5356	+	18.3647i	1.06515	+	1.18297i	0.0826776	+	0.996576i	$0.473653\pi$
$242$	12.0704	−	20.9065i	0.775914	−	1.34392i
$243$	−11.1668	−	19.3415i	−0.716353	−	1.24076i
$244$	−8.05513	+	24.7911i	−0.515677	+	1.58709i
$245$	10.1204	−	4.50588i	0.646567	−	0.287870i
$246$	−35.0030	+	25.4312i	−2.23171	+	1.62143i
$247$	8.79358			0.559522
$248$	12.6635	+	11.3705i	0.804134	+	0.722025i
$249$	−6.78996			−0.430296
$250$	−17.5266	+	12.7339i	−1.10848	+	0.805360i
$251$	−21.1889	+	9.43391i	−1.33743	+	0.595463i	−0.945827	−	0.324671i	$-0.894747\pi$
$251$	−21.1889	+	9.43391i	−1.33743	+	0.595463i	−0.391605	+	0.920134i	$0.628080\pi$
$252$	5.70323	−	17.5527i	0.359270	−	1.10572i
$253$	2.61125	+	4.52282i	0.164168	+	0.284348i
$254$	1.48493	−	2.57198i	0.0931729	−	0.161380i
$255$	−18.6158	−	20.6749i	−1.16577	−	1.29471i
$256$	−5.72420	−	17.6173i	−0.357763	−	1.10108i
$257$	10.2686	−	11.4044i	0.640535	−	0.711386i	−0.332225	−	0.943200i	$-0.607799\pi$
$257$	10.2686	−	11.4044i	0.640535	−	0.711386i	0.972760	+	0.231814i	$0.0744661\pi$
$258$	−1.23547	−	0.550066i	−0.0769169	−	0.0342456i
$259$	−13.2079	+	2.80743i	−0.820700	+	0.174445i
$260$	−1.64623	−	15.6628i	−0.102095	−	0.971365i
$261$	0.0467066	−	0.444383i	0.00289106	−	0.0275066i
$262$	18.1028	+	3.84786i	1.11839	+	0.237722i
$263$	5.50607	+	4.00039i	0.339519	+	0.246675i	0.744459	−	0.667668i	$-0.232708\pi$
$263$	5.50607	+	4.00039i	0.339519	+	0.246675i	−0.404940	+	0.914343i	$0.632708\pi$
$264$	4.61325	+	3.35173i	0.283926	+	0.206284i
$265$	14.0137	+	2.97870i	0.860854	+	0.182980i
$266$	1.79202	−	17.0500i	0.109876	−	1.04540i
$267$	−0.585951	−	5.57495i	−0.0358596	−	0.341181i
$268$	−15.6962	+	3.33632i	−0.958796	+	0.203798i
$269$	9.61017	+	4.27873i	0.585943	+	0.260878i	0.678225	−	0.734854i	$-0.262750\pi$
$269$	9.61017	+	4.27873i	0.585943	+	0.260878i	−0.0922822	+	0.995733i	$0.529416\pi$
$270$	4.56560	−	5.07061i	0.277854	−	0.308588i
$271$	−0.487363	−	1.49995i	−0.0296052	−	0.0911154i	0.935162	−	0.354220i	$-0.115254\pi$
$271$	−0.487363	−	1.49995i	−0.0296052	−	0.0911154i	−0.964767	+	0.263105i	$0.915254\pi$
$272$	−1.18423	−	1.31522i	−0.0718046	−	0.0797470i
$273$	−3.86128	+	6.68794i	−0.233695	+	0.404772i
$274$	19.0103	+	32.9268i	1.14845	+	1.98918i
$275$	0.281645	−	0.866813i	0.0169838	−	0.0522708i
$276$	54.9750	−	24.4765i	3.30911	−	1.47331i
$277$	−9.79020	+	7.11300i	−0.588236	+	0.427379i	−0.841684	−	0.539970i	$-0.818435\pi$
$277$	−9.79020	+	7.11300i	−0.588236	+	0.427379i	0.253448	+	0.967349i	$0.418435\pi$
$278$	16.9368			1.01580
$279$	3.98538	−	18.8787i	0.238599	−	1.13024i
$280$	−12.2337			−0.731106
$281$	17.3718	−	12.6214i	1.03632	−	0.752927i	0.0667525	−	0.997770i	$-0.478736\pi$
$281$	17.3718	−	12.6214i	1.03632	−	0.752927i	0.969563	+	0.244842i	$0.0787362\pi$
$282$	43.0769	−	19.1791i	2.56519	−	1.14210i
$283$	−0.212853	+	0.655094i	−0.0126528	+	0.0389413i	−0.957184	−	0.289482i	$-0.906517\pi$
$283$	−0.212853	+	0.655094i	−0.0126528	+	0.0389413i	0.944531	+	0.328423i	$0.106517\pi$
$284$	5.66030	+	9.80392i	0.335877	+	0.581756i
$285$	14.7324	−	25.5173i	0.872675	−	1.51152i
$286$	−2.14775	−	2.38532i	−0.126999	−	0.141047i
$287$	−3.65018	−	11.2341i	−0.215463	−	0.663127i
$288$	−12.0137	+	13.3426i	−0.707913	+	0.786217i
$289$	1.98947	+	0.885767i	0.117027	+	0.0521040i
$290$	−0.727123	+	0.154555i	−0.0426981	+	0.00907576i
$291$	3.26649	+	31.0785i	0.191485	+	1.82186i
$292$	−0.935550	+	8.90116i	−0.0547489	+	0.520901i
$293$	−8.81495	−	1.87368i	−0.514975	−	0.109461i	−0.0569086	−	0.998379i	$-0.518124\pi$
$293$	−8.81495	−	1.87368i	−0.514975	−	0.109461i	−0.458066	+	0.888918i	$0.651458\pi$
$294$	−21.0474	−	15.2918i	−1.22751	−	0.891837i
$295$	19.2098	+	13.9568i	1.11844	+	0.812594i
$296$	−25.2036	−	5.35719i	−1.46493	−	0.311380i
$297$	0.0907602	−	0.863526i	0.00526644	−	0.0501068i
$298$	1.53451	+	14.5999i	0.0888918	+	0.845749i
$299$	−13.2015	+	2.80607i	−0.763463	+	0.162279i
$300$	−9.59413	−	4.27158i	−0.553917	−	0.246620i
$301$	0.247056	−	0.274384i	0.0142401	−	0.0158152i
$302$	−3.93949	−	12.1245i	−0.226692	−	0.697688i
$303$	−12.4957	−	13.8779i	−0.717861	−	0.797265i
$304$	0.937195	−	1.62327i	0.0537518	−	0.0931009i
$305$	−9.79451	−	16.9646i	−0.560832	−	0.971389i
$306$	−10.8215	+	33.3051i	−0.618623	+	1.90393i
$307$	−28.6238	+	12.7441i	−1.63365	+	0.727346i	−0.998968	−	0.0454296i	$-0.985534\pi$
$307$	−28.6238	+	12.7441i	−1.63365	+	0.727346i	−0.634679	+	0.772776i	$0.718868\pi$
$308$	−3.16104	+	2.29663i	−0.180117	+	0.130863i
$309$	−14.2107			−0.808416
$310$	−31.9191	+	3.39968i	−1.81288	+	0.193089i
$311$	−17.7139			−1.00447			−0.502233	−	0.864732i	$-0.667488\pi$
$311$	−17.7139			−1.00447			−0.502233	+	0.864732i	$0.667488\pi$
$312$	−11.9219	+	8.66180i	−0.674947	+	0.490378i
$313$	−19.7953	+	8.81346i	−1.11890	+	0.498166i	−0.880996	−	0.473123i	$-0.843127\pi$
$313$	−19.7953	+	8.81346i	−1.11890	+	0.498166i	−0.237903	+	0.971289i	$0.576460\pi$
$314$	5.70058	−	17.5446i	0.321702	−	0.990098i
$315$	6.93475	+	12.0113i	0.390729	+	0.676762i
$316$	−7.52698	+	13.0371i	−0.423426	+	0.733395i
$317$	0.679868	+	0.755070i	0.0381852	+	0.0424089i	0.761935	−	0.647654i	$-0.224250\pi$
$317$	0.679868	+	0.755070i	0.0381852	+	0.0424089i	−0.723750	+	0.690063i	$0.757583\pi$
$318$	−10.3969	−	31.9984i	−0.583030	−	1.79438i
$319$	−0.0632977	+	0.0702992i	−0.00354399	+	0.00393600i
$320$	29.1318	+	12.9703i	1.62852	+	0.725063i
$321$	4.53698	−	0.964364i	0.253229	−	0.0538256i
$322$	2.75041	+	26.1684i	0.153274	+	1.45831i
$323$	−2.12308	+	20.1998i	−0.118131	+	1.12394i
$324$	24.0228	+	5.10620i	1.33460	+	0.283678i
$325$	1.90553	+	1.38445i	0.105700	+	0.0767955i
$326$	31.8582	+	23.1463i	1.76446	+	1.28196i
$327$	29.2621	+	6.21986i	1.61820	+	0.343959i
$328$	2.35610	−	22.4168i	0.130094	−	1.23776i
$329$	1.34565	+	12.8030i	0.0741881	+	0.705853i
$330$	−10.5200	+	2.23609i	−0.579107	+	0.123093i
$331$	24.3820	+	10.8556i	1.34016	+	0.596676i	0.946537	−	0.322597i	$-0.104556\pi$
$331$	24.3820	+	10.8556i	1.34016	+	0.596676i	0.393621	+	0.919273i	$0.371222\pi$
$332$	5.94058	−	6.59768i	0.326032	−	0.362095i
$333$	9.02697	+	27.7822i	0.494675	+	1.52245i
$334$	−37.6316	−	41.7941i	−2.05911	−	2.28687i
$335$	6.02951	−	10.4434i	0.329427	−	0.570584i
$336$	0.823049	+	1.42556i	0.0449010	+	0.0777708i
$337$	9.87048	−	30.3782i	0.537679	−	1.65481i	−0.200108	−	0.979774i	$-0.564129\pi$
$337$	9.87048	−	30.3782i	0.537679	−	1.65481i	0.737788	−	0.675033i	$-0.235871\pi$
$338$	−19.8266	+	8.82738i	−1.07843	+	0.480146i
$339$	22.7404	−	16.5218i	1.23509	−	0.897343i
$340$	36.3765			1.97279
$341$	−3.03182	+	2.73750i	−0.164182	+	0.148244i
$342$	−37.0885			−2.00552
$343$	14.8178	−	10.7658i	0.800088	−	0.581298i
$344$	0.643640	−	0.286567i	0.0347027	−	0.0154507i
$345$	−13.9746	+	43.0095i	−0.752368	+	2.31555i
$346$	−10.3534	−	17.9326i	−0.556603	−	0.964065i
$347$	−1.56066	+	2.70314i	−0.0837804	+	0.145112i	−0.904871	−	0.425686i	$-0.860033\pi$
$347$	−1.56066	+	2.70314i	−0.0837804	+	0.145112i	0.821090	+	0.570798i	$0.193366\pi$
$348$	0.729364	+	0.810041i	0.0390980	+	0.0434227i
$349$	−6.80655	−	20.9484i	−0.364346	−	1.12134i	−0.950389	−	0.311063i	$-0.899315\pi$
$349$	−6.80655	−	20.9484i	−0.364346	−	1.12134i	0.586043	−	0.810280i	$-0.300685\pi$
$350$	3.07265	−	3.41253i	0.164240	−	0.182407i
$351$	2.04989	+	0.912671i	0.109415	+	0.0487147i
$352$	3.71795	−	0.790275i	0.198167	−	0.0421218i
$353$	−0.515575	−	4.90537i	−0.0274413	−	0.261087i	−0.999638	−	0.0269192i	$-0.991430\pi$
$353$	−0.515575	−	4.90537i	−0.0274413	−	0.261087i	0.972196	−	0.234167i	$-0.0752364\pi$
$354$	5.82873	−	55.4567i	0.309794	−	2.94749i
$355$	−8.32139	−	1.76877i	−0.441654	−	0.0938764i
$356$	5.92973	+	4.30820i	0.314275	+	0.228334i
$357$	−14.4306	−	10.4845i	−0.763750	−	0.554897i
$358$	25.4838	+	5.41676i	1.34686	+	0.286285i
$359$	0.0377201	−	0.358883i	0.00199079	−	0.0189411i	−0.993481	−	0.113994i	$-0.963635\pi$
$359$	0.0377201	−	0.358883i	0.00199079	−	0.0189411i	0.995472	+	0.0950532i	$0.0303021\pi$
$360$	2.76645	+	26.3211i	0.145805	+	1.38724i
$361$	−2.45641	+	0.522126i	−0.129285	+	0.0274803i
$362$	−31.4962	−	14.0230i	−1.65540	−	0.737033i
$363$	17.7998	−	19.7686i	0.934246	−	1.03758i
$364$	−3.12029	−	9.60325i	−0.163547	−	0.503347i
$365$	−4.50055	−	4.99837i	−0.235570	−	0.261627i
$366$	−23.0015	+	39.8398i	−1.20231	+	2.08246i
$367$	14.6935	+	25.4498i	0.766992	+	1.32847i	0.939187	+	0.343406i	$0.111581\pi$
$367$	14.6935	+	25.4498i	0.766992	+	1.32847i	−0.172195	+	0.985063i	$0.555086\pi$
$368$	−0.888987	+	2.73602i	−0.0463416	+	0.142625i
$369$	−23.3449	+	10.3938i	−1.21528	+	0.541080i
$370$	39.3167	−	28.5653i	2.04398	−	1.48504i
$371$	9.18555			0.476890
$372$	27.7190	+	38.0407i	1.43716	+	1.97232i
$373$	17.7284			0.917941			0.458971	−	0.888451i	$-0.348218\pi$
$373$	17.7284			0.917941			0.458971	+	0.888451i	$0.348218\pi$
$374$	5.99786	−	4.35770i	0.310142	−	0.225331i
$375$	−21.8084	+	9.70973i	−1.12618	+	0.501408i
$376$	−7.59116	+	23.3632i	−0.391484	+	1.20486i
$377$	−0.122233	−	0.211713i	−0.00629530	−	0.0109038i
$378$	2.18733	−	3.78857i	0.112504	−	0.194863i
$379$	−1.64634	−	1.82845i	−0.0845669	−	0.0939211i	0.699376	−	0.714754i	$-0.253461\pi$
$379$	−1.64634	−	1.82845i	−0.0845669	−	0.0939211i	−0.783943	+	0.620833i	$0.786795\pi$
$380$	11.9052	+	36.6405i	0.610725	+	1.87962i
$381$	2.18978	−	2.43199i	0.112186	−	0.124595i
$382$	4.76611	+	2.12201i	0.243855	+	0.108571i
$383$	18.7001	−	3.97484i	0.955533	−	0.203105i	0.296343	−	0.955082i	$-0.404233\pi$
$383$	18.7001	−	3.97484i	0.955533	−	0.203105i	0.659190	+	0.751977i	$0.270899\pi$
$384$	−5.07387	−	48.2747i	−0.258925	−	2.46351i
$385$	0.306923	−	2.92018i	0.0156422	−	0.148826i
$386$	−57.9268	−	12.3127i	−2.94840	−	0.626701i
$387$	−0.646208	−	0.469497i	−0.0328486	−	0.0238659i
$388$	−33.0563	−	24.0168i	−1.67818	−	1.21927i
$389$	−5.15587	−	1.09591i	−0.261413	−	0.0555651i	0.0753405	−	0.997158i	$-0.475996\pi$
$389$	−5.15587	−	1.09591i	−0.261413	−	0.0555651i	−0.336754	+	0.941593i	$0.609329\pi$
$390$	2.90526	−	27.6417i	0.147114	−	1.39969i
$391$	−3.25851	−	31.0027i	−0.164790	−	1.56787i
$392$	13.2573	−	2.81793i	0.669597	−	0.142327i
$393$	18.6304	+	8.29480i	0.939781	+	0.418417i
$394$	−9.56640	+	10.6246i	−0.481949	+	0.535258i
$395$	−3.49587	−	10.7592i	−0.175897	−	0.541354i
$396$	5.65604	+	6.28167i	0.284227	+	0.315666i
$397$	−8.46275	+	14.6579i	−0.424733	+	0.735660i	−0.996395	−	0.0848295i	$-0.972965\pi$
$397$	−8.46275	+	14.6579i	−0.424733	+	0.735660i	0.571662	+	0.820489i	$0.306299\pi$
$398$	5.27193	+	9.13124i	0.264258	+	0.457708i
$399$	5.83773	−	17.9667i	0.292252	−	0.899460i
$400$	0.458652	−	0.204205i	0.0229326	−	0.0102103i
$401$	−30.7747	+	22.3591i	−1.53682	+	1.11656i	−0.584524	+	0.811377i	$0.698719\pi$
$401$	−30.7747	+	22.3591i	−1.53682	+	1.11656i	−0.952293	+	0.305186i	$0.901281\pi$
$402$	−28.3195			−1.41245
$403$	−4.30705	−	9.63773i	−0.214549	−	0.480089i
$404$	24.4175			1.21482
$405$	−14.9314	+	10.8483i	−0.741945	+	0.539055i
$406$	−0.435402	+	0.193854i	−0.0216087	+	0.00962079i
$407$	1.91107	−	5.88166i	0.0947281	−	0.291543i
$408$	−17.0187	−	29.4772i	−0.842550	−	1.45934i
$409$	−0.249342	+	0.431873i	−0.0123292	+	0.0213547i	−0.872124	−	0.489285i	$-0.837258\pi$
$409$	−0.249342	+	0.431873i	−0.0123292	+	0.0213547i	0.859795	+	0.510639i	$0.170591\pi$
$410$	28.4467	+	31.5933i	1.40488	+	1.56028i
$411$	12.9465	+	39.8453i	0.638605	+	1.96542i
$412$	12.4330	−	13.8082i	0.612529	−	0.680283i
$413$	13.9076	+	6.19208i	0.684350	+	0.304692i
$414$	55.6796	−	11.8351i	2.73650	−	0.581662i
$415$	0.697389	+	6.63521i	0.0342335	+	0.325710i
$416$	−1.02677	+	9.76908i	−0.0503416	+	0.478968i
$417$	18.2553	+	3.88028i	0.893966	+	0.190018i
$418$	6.35229	+	4.61521i	0.310701	+	0.225737i
$419$	−10.9298	−	7.94098i	−0.533957	−	0.387942i	0.287879	−	0.957667i	$-0.407050\pi$
$419$	−10.9298	−	7.94098i	−0.533957	−	0.387942i	−0.821836	+	0.569725i	$0.807050\pi$
$420$	−33.0945	−	7.03444i	−1.61484	−	0.343246i
$421$	3.23151	−	30.7458i	0.157494	−	1.49846i	−0.575264	−	0.817968i	$-0.695101\pi$
$421$	3.23151	−	30.7458i	0.157494	−	1.49846i	0.732758	−	0.680489i	$-0.238233\pi$
$422$	4.49041	+	42.7234i	0.218590	+	2.07974i
$423$	27.2415	−	5.79037i	1.32453	−	0.281537i
$424$	16.0127	+	7.12930i	0.777644	+	0.346229i
$425$	−3.64029	+	4.04295i	−0.176580	+	0.196112i
$426$	6.17373	+	19.0008i	0.299118	+	0.920591i
$427$	−8.40390	−	9.33347i	−0.406693	−	0.451678i
$428$	−3.03237	+	5.25223i	−0.146575	+	0.253876i
$429$	−1.76846	−	3.06306i	−0.0853820	−	0.147886i
$430$	−0.410636	+	1.26381i	−0.0198026	+	0.0609462i
$431$	−11.0126	+	4.90313i	−0.530458	+	0.236175i	−0.654446	−	0.756108i	$-0.727098\pi$
$431$	−11.0126	+	4.90313i	−0.530458	+	0.236175i	0.123988	+	0.992284i	$0.460432\pi$
$432$	0.386948	−	0.281134i	0.0186170	−	0.0135261i
$433$	−32.3919			−1.55665			−0.778327	−	0.627860i	$-0.783931\pi$
$433$	−32.3919			−1.55665			−0.778327	+	0.627860i	$0.783931\pi$
$434$	−19.5644	+	6.38693i	−0.939122	+	0.306583i
$435$	−0.819136			−0.0392745
$436$	−31.6454	+	22.9917i	−1.51554	+	1.10110i
$437$	30.1613	−	13.4287i	1.44281	−	0.642380i
$438$	−4.88102	+	15.0222i	−0.233224	+	0.717790i
$439$	−6.18408	−	10.7111i	−0.295150	−	0.511215i	0.679870	−	0.733333i	$-0.262036\pi$
$439$	−6.18408	−	10.7111i	−0.295150	−	0.511215i	−0.975020	+	0.222118i	$0.928703\pi$
$440$	2.80151	−	4.85236i	0.133557	−	0.231327i
$441$	−10.2817	−	11.4190i	−0.489604	−	0.543760i
$442$	5.92053	+	18.2215i	0.281611	+	0.866709i
$443$	−3.16058	+	3.51017i	−0.150163	+	0.166773i	−0.813533	−	0.581518i	$-0.802459\pi$
$443$	−3.16058	+	3.51017i	−0.150163	+	0.166773i	0.663370	+	0.748292i	$0.269126\pi$
$444$	−65.0998	−	28.9843i	−3.08950	−	1.37553i
$445$	−5.38771	+	1.14519i	−0.255402	+	0.0542873i
$446$	−1.49906	−	14.2626i	−0.0709826	−	0.675354i
$447$	−1.69092	+	16.0880i	−0.0799777	+	0.760937i
$448$	19.9986	+	4.25083i	0.944844	+	0.200833i
$449$	12.9315	+	9.39528i	0.610275	+	0.443390i	0.849511	−	0.527571i	$-0.176897\pi$
$449$	12.9315	+	9.39528i	0.610275	+	0.443390i	−0.239236	+	0.970961i	$0.576897\pi$
$450$	−8.03692	−	5.83917i	−0.378864	−	0.275261i
$451$	5.29175	+	1.12480i	0.249179	+	0.0529646i
$452$	−3.84171	+	36.5515i	−0.180699	+	1.71924i
$453$	−1.46840	−	13.9709i	−0.0689916	−	0.656411i
$454$	29.4502	−	6.25984i	1.38217	−	0.293789i
$455$	6.93210	+	3.08637i	0.324982	+	0.144691i
$456$	24.1213	−	26.7894i	1.12958	−	1.25453i
$457$	1.40842	+	4.33468i	0.0658832	+	0.202768i	0.978579	−	0.205872i	$-0.0660032\pi$
$457$	1.40842	+	4.33468i	0.0658832	+	0.202768i	−0.912696	+	0.408640i	$0.866003\pi$
$458$	23.5897	+	26.1990i	1.10227	+	1.22420i
$459$	−2.59141	+	4.48846i	−0.120957	+	0.209503i
$460$	−29.5650	−	51.2081i	−1.37848	−	2.38759i
$461$	−5.25050	+	16.1594i	−0.244540	+	0.752618i	0.751171	+	0.660107i	$0.229489\pi$
$461$	−5.25050	+	16.1594i	−0.244540	+	0.752618i	−0.995712	+	0.0925105i	$0.970511\pi$
$462$	−6.29939	+	2.80467i	−0.293074	+	0.130485i
$463$	−22.1896	+	16.1217i	−1.03124	+	0.749239i	−0.968556	−	0.248795i	$-0.919965\pi$
$463$	−22.1896	+	16.1217i	−1.03124	+	0.749239i	−0.0626822	+	0.998034i	$0.519965\pi$
$464$	−0.0521088			−0.00241909
$465$	−35.1827	−	3.64844i	−1.63156	−	0.169192i
$466$	30.1392			1.39617
$467$	18.5350	−	13.4665i	0.857697	−	0.623153i	−0.0695608	−	0.997578i	$-0.522160\pi$
$467$	18.5350	−	13.4665i	0.857697	−	0.623153i	0.927257	+	0.374425i	$0.122160\pi$
$468$	−19.9559	+	8.88495i	−0.922463	+	0.410707i
$469$	2.38919	−	7.35318i	0.110323	−	0.339538i
$470$	−23.1663	−	40.1253i	−1.06858	−	1.85084i
$471$	10.1639	−	17.6043i	0.468327	−	0.811165i
$472$	19.4385	+	21.5886i	0.894728	+	0.993696i
$473$	0.0522553	+	0.160825i	0.00240270	+	0.00739476i
$474$	−17.7770	+	19.7433i	−0.816524	+	0.906841i
$475$	−5.26368	−	2.34354i	−0.241514	−	0.107529i
$476$	22.8130	−	4.84905i	1.04563	−	0.222256i
$477$	−2.07716	−	19.7628i	−0.0951065	−	0.904878i
$478$	5.65432	−	53.7972i	0.258622	−	2.46063i
$479$	−8.84935	−	1.88099i	−0.404337	−	0.0859445i	0.00125373	−	0.999999i	$-0.499601\pi$
$479$	−8.84935	−	1.88099i	−0.404337	−	0.0859445i	−0.405591	+	0.914055i	$0.632934\pi$
$480$	26.6278	+	19.3462i	1.21539	+	0.883031i
$481$	12.9298	+	9.39403i	0.589547	+	0.428331i
$482$	−55.7777	−	11.8559i	−2.54060	−	0.540022i
$483$	−3.03075	+	28.8356i	−0.137904	+	1.31207i
$484$	3.63570	+	34.5914i	0.165259	+	1.57234i
$485$	30.0347	−	6.38408i	1.36381	−	0.289886i
$486$	47.0800	+	20.9614i	2.13559	+	0.950828i
$487$	−15.8066	+	17.5551i	−0.716268	+	0.795496i	−0.985876	−	0.167474i	$-0.946439\pi$
$487$	−15.8066	+	17.5551i	−0.716268	+	0.795496i	0.269609	+	0.962970i	$0.413106\pi$
$488$	−7.40594	−	22.7931i	−0.335251	−	1.03180i
$489$	29.0353	+	32.2470i	1.31302	+	1.45826i
$490$	−12.7815	+	22.1383i	−0.577411	+	1.00011i
$491$	−4.61346	−	7.99074i	−0.208202	−	0.360617i	0.742946	−	0.669351i	$-0.233428\pi$
$491$	−4.61346	−	7.99074i	−0.208202	−	0.360617i	−0.951148	+	0.308734i	$0.900095\pi$
$492$	19.2634	−	59.2867i	0.868462	−	2.67285i
$493$	0.515838	−	0.229666i	0.0232322	−	0.0103436i
$494$	−16.4161	+	11.9270i	−0.738596	+	0.536621i
$495$	−6.35220			−0.285510
$496$	−2.23813	−	0.232093i	−0.100495	−	0.0104213i
$497$	−5.45442			−0.244664
$498$	12.6757	−	9.20943i	0.568011	−	0.412684i
$499$	25.9574	−	11.5570i	1.16201	−	0.517362i	0.267130	−	0.963660i	$-0.413925\pi$
$499$	25.9574	−	11.5570i	1.16201	−	0.517362i	0.894884	+	0.446298i	$0.147258\pi$
$500$	9.64554	−	29.6859i	0.431362	−	1.32759i
$501$	−30.9859	−	53.6692i	−1.38435	−	2.39776i
$502$	26.7606	−	46.3506i	1.19438	−	2.06873i
$503$	12.2304	+	13.5833i	0.545327	+	0.605647i	0.951311	−	0.308233i	$-0.0997377\pi$
$503$	12.2304	+	13.5833i	0.545327	+	0.605647i	−0.405984	+	0.913880i	$0.633071\pi$
$504$	5.24359	+	16.1381i	0.233568	+	0.718848i
$505$	−12.2782	+	13.6363i	−0.546373	+	0.606808i
$506$	−11.0092	−	4.90161i	−0.489419	−	0.217903i
$507$	−23.3924	+	4.97221i	−1.03889	+	0.220824i
$508$	0.447274	+	4.25553i	0.0198446	+	0.188809i
$509$	−1.08567	+	10.3295i	−0.0481215	+	0.457845i	0.943756	+	0.330644i	$0.107266\pi$
$509$	−1.08567	+	10.3295i	−0.0481215	+	0.457845i	−0.991877	+	0.127201i	$0.959401\pi$
$510$	62.7945	+	13.3474i	2.78059	+	0.591032i
$511$	−3.48875	−	2.53472i	−0.154333	−	0.112130i
$512$	3.69272	+	2.68292i	0.163197	+	0.118569i
$513$	−5.36915	−	1.14125i	−0.237054	−	0.0503873i
$514$	−3.70152	+	35.2176i	−0.163267	+	1.55338i
$515$	1.45956	+	13.8868i	0.0643159	+	0.611924i
$516$	1.90594	−	0.405120i	0.0839042	−	0.0178344i
$517$	−5.38631	−	2.39814i	−0.236890	−	0.105470i
$518$	20.8491	−	23.1553i	0.916058	−	1.01739i
$519$	−7.05096	−	21.7006i	−0.309503	−	0.952552i
$520$	9.68888	+	10.7606i	0.424885	+	0.471883i
$521$	−4.62522	+	8.01111i	−0.202635	+	0.350973i	−0.949376	−	0.314141i	$-0.898284\pi$
$521$	−4.62522	+	8.01111i	−0.202635	+	0.350973i	0.746742	+	0.665114i	$0.231617\pi$
$522$	0.515537	+	0.892937i	0.0225645	+	0.0390828i
$523$	−2.03184	+	6.25335i	−0.0888461	+	0.273440i	−0.985601	−	0.169087i	$-0.945918\pi$
$523$	−2.03184	+	6.25335i	−0.0888461	+	0.273440i	0.896755	+	0.442527i	$0.145918\pi$
$524$	−24.3598	+	10.8457i	−1.06416	+	0.473796i
$525$	4.09367	−	2.97422i	0.178662	−	0.129806i
$526$	−15.7047			−0.684759
$527$	23.1787	−	7.56684i	1.00968	−	0.329617i
$528$	−0.753909			−0.0328097
$529$	−22.3875	+	16.2655i	−0.973371	+	0.707195i
$530$	−30.2013	+	13.4465i	−1.31186	+	0.584077i
$531$	10.1774	−	31.3227i	0.441660	−	1.35929i
$532$	12.3504	+	21.3916i	0.535460	+	0.927443i
$533$	−6.99044	+	12.1078i	−0.302790	+	0.524447i
$534$	8.65534	+	9.61273i	0.374553	+	0.415983i
$535$	−1.40837	−	4.33453i	−0.0608893	−	0.187398i
$536$	9.87206	−	10.9640i	0.426408	−	0.473574i
$537$	26.2267	+	11.6769i	1.13176	+	0.503894i
$538$	−23.7439	+	5.04692i	−1.02367	+	0.217588i
$539$	0.340034	+	3.23520i	0.0146463	+	0.139350i
$540$	−1.02760	+	9.77697i	−0.0442209	+	0.420734i
$541$	2.15513	+	0.458087i	0.0926562	+	0.0196947i	0.254006	−	0.967203i	$-0.418252\pi$
$541$	2.15513	+	0.458087i	0.0926562	+	0.0196947i	−0.161350	+	0.986897i	$0.551585\pi$
$542$	2.94425	+	2.13912i	0.126466	+	0.0918831i
$543$	−30.7353	−	22.3305i	−1.31898	−	0.958294i
$544$	−22.1927	−	4.71720i	−0.951503	−	0.202248i
$545$	3.07262	−	29.2341i	0.131617	−	1.25225i
$546$	−1.86270	−	17.7224i	−0.0797162	−	0.758449i
$547$	4.75717	−	1.01117i	0.203402	−	0.0432344i	−0.105084	−	0.994463i	$-0.533511\pi$
$547$	4.75717	−	1.01117i	0.203402	−	0.0432344i	0.308486	+	0.951229i	$0.400178\pi$
$548$	−50.0440	−	22.2810i	−2.13777	−	0.951797i
$549$	−18.1807	+	20.1917i	−0.775933	+	0.861761i
$550$	0.649903	+	2.00019i	0.0277119	+	0.0852886i
$551$	0.400155	+	0.444417i	0.0170472	+	0.0189328i
$552$	−27.6639	+	47.9152i	−1.17745	+	2.03941i
$553$	−3.62661	−	6.28147i	−0.154219	−	0.267115i
$554$	8.62905	−	26.5575i	0.366613	−	1.12832i
$555$	48.9218	−	21.7814i	2.07661	−	0.924568i
$556$	−19.7421	+	14.3435i	−0.837251	+	0.608298i
$557$	11.0363			0.467623			0.233811	−	0.972282i	$-0.424880\pi$
$557$	11.0363			0.467623			0.233811	+	0.972282i	$0.424880\pi$
$558$	18.1657	+	40.6488i	0.769016	+	1.72080i
$559$	−0.437007			−0.0184834
$560$	1.30854	−	0.950708i	0.0552958	−	0.0401748i
$561$	7.46313	−	3.32280i	0.315094	−	0.140289i
$562$	−15.3115	+	47.1238i	−0.645875	+	1.98780i
$563$	5.59621	+	9.69292i	0.235852	+	0.408508i	0.959520	−	0.281641i	$-0.0908786\pi$
$563$	5.59621	+	9.69292i	0.235852	+	0.408508i	−0.723668	+	0.690148i	$0.757545\pi$
$564$	−33.9694	+	58.8366i	−1.43037	+	2.47747i
$565$	−18.4809	−	20.5251i	−0.777498	−	0.863499i
$566$	−0.491164	−	1.51165i	−0.0206452	−	0.0635393i
$567$	−7.91790	+	8.79372i	−0.332521	+	0.369301i
$568$	−9.50839	−	4.23341i	−0.398963	−	0.177630i
$569$	45.8966	−	9.75563i	1.92409	−	0.408977i	0.924471	−	0.381252i	$-0.124507\pi$
$569$	45.8966	−	9.75563i	1.92409	−	0.408977i	0.999616	−	0.0277250i	$-0.00882627\pi$
$570$	7.10700	+	67.6185i	0.297679	+	2.83223i
$571$	2.13862	−	20.3476i	0.0894983	−	0.851520i	−0.854029	−	0.520225i	$-0.825848\pi$
$571$	2.13862	−	20.3476i	0.0894983	−	0.851520i	0.943527	−	0.331295i	$-0.107485\pi$
$572$	4.52355	+	0.961511i	0.189139	+	0.0402028i
$573$	4.65097	+	3.37913i	0.194297	+	0.141165i
$574$	22.0514	+	16.0213i	0.920407	+	0.668715i
$575$	8.65001	+	1.83862i	0.360731	+	0.0766756i
$576$	4.62337	−	43.9885i	0.192641	−	1.83285i
$577$	−0.381356	−	3.62836i	−0.0158761	−	0.151051i	0.983712	−	0.179752i	$-0.0575295\pi$
$577$	−0.381356	−	3.62836i	−0.0158761	−	0.151051i	−0.999588	+	0.0287013i	$0.990863\pi$
$578$	−4.91538	+	1.04480i	−0.204453	+	0.0434578i
$579$	−59.6153	−	26.5425i	−2.47753	−	1.10307i
$580$	0.716667	−	0.795939i	0.0297580	−	0.0330496i
$581$	1.32184	+	4.06822i	0.0548393	+	0.168778i
$582$	−48.2507	−	53.5879i	−2.00006	−	2.22129i
$583$	−2.10348	+	3.64334i	−0.0871173	+	0.150892i
$584$	−4.11443	−	7.12641i	−0.170256	−	0.294893i
$585$	5.07279	−	15.6124i	0.209734	−	0.645494i
$586$	18.9973	−	8.45815i	0.784772	−	0.349403i
$587$	18.5043	−	13.4442i	0.763755	−	0.554901i	−0.136305	−	0.990667i	$-0.543523\pi$
$587$	18.5043	−	13.4442i	0.763755	−	0.554901i	0.900060	+	0.435766i	$0.143523\pi$
$588$	37.4838			1.54580
$589$	15.2076	+	20.8705i	0.626620	+	0.859954i
$590$	−54.7914			−2.25573
$591$	−12.7452	+	9.25996i	−0.524269	+	0.380904i
$592$	3.11213	−	1.38561i	0.127908	−	0.0569482i
$593$	−6.01340	+	18.5073i	−0.246941	+	0.760005i	0.748371	+	0.663281i	$0.230837\pi$
$593$	−6.01340	+	18.5073i	−0.246941	+	0.760005i	−0.995311	+	0.0967243i	$0.969163\pi$
$594$	1.00179	+	1.73515i	0.0411040	+	0.0711943i
$595$	−8.76336	+	15.1786i	−0.359263	+	0.622261i
$596$	−14.1530	−	15.7185i	−0.579731	−	0.643856i
$597$	3.59033	+	11.0499i	0.146942	+	0.452242i
$598$	20.8390	−	23.1440i	0.852169	−	0.946430i
$599$	32.1311	+	14.3057i	1.31284	+	0.584514i	0.939299	−	0.343099i	$-0.111477\pi$
$599$	32.1311	+	14.3057i	1.31284	+	0.584514i	0.373541	+	0.927614i	$0.378143\pi$
$600$	9.44469	−	2.00753i	0.385578	−	0.0819571i
$601$	−0.615470	−	5.85580i	−0.0251055	−	0.238863i	−0.999877	−	0.0156596i	$-0.995015\pi$
$601$	−0.615470	−	5.85580i	−0.0251055	−	0.238863i	0.974772	−	0.223204i	$-0.0716515\pi$
$602$	−0.0890566	+	0.847317i	−0.00362968	+	0.0345341i
$603$	−16.3607	−	3.47758i	−0.666261	−	0.141618i
$604$	14.8600	+	10.7964i	0.604645	+	0.439300i
$605$	−21.1463	−	15.3637i	−0.859719	−	0.624622i
$606$	42.1504	+	8.95935i	1.71224	+	0.363949i
$607$	−4.06457	+	38.6718i	−0.164976	+	1.56964i	0.528356	+	0.849023i	$0.322809\pi$
$607$	−4.06457	+	38.6718i	−0.164976	+	1.56964i	−0.693332	+	0.720618i	$0.743858\pi$
$608$	−2.51174	−	23.8976i	−0.101864	−	0.969175i
$609$	−0.513709	+	0.109192i	−0.0208166	+	0.00442469i
$610$	41.2942	+	18.3854i	1.67195	+	0.744402i
$611$	10.1956	−	11.3233i	0.412469	−	0.458093i
$612$	−15.5916	−	47.9859i	−0.630252	−	1.93972i
$613$	−30.5139	−	33.8892i	−1.23245	−	1.36877i	−0.905845	−	0.423609i	$-0.860763\pi$
$613$	−30.5139	−	33.8892i	−1.23245	−	1.36877i	−0.326602	−	0.945162i	$-0.605904\pi$
$614$	36.1505	−	62.6144i	1.45891	−	2.52691i
$615$	23.4231	+	40.5699i	0.944509	+	1.63594i
$616$	1.11010	−	3.41654i	0.0447272	−	0.137656i
$617$	−6.05359	+	2.69523i	−0.243708	+	0.108506i	−0.524956	−	0.851129i	$-0.675918\pi$
$617$	−6.05359	+	2.69523i	−0.243708	+	0.108506i	0.281248	+	0.959635i	$0.409252\pi$
$618$	26.5288	−	19.2743i	1.06715	−	0.775328i
$619$	41.5360			1.66947			0.834736	−	0.550650i	$-0.185620\pi$
$619$	41.5360			1.66947			0.834736	+	0.550650i	$0.185620\pi$
$620$	34.3267	−	30.9944i	1.37859	−	1.24476i
$621$	8.42469			0.338071
$622$	33.0689	−	24.0260i	1.32594	−	0.963353i
$623$	−3.22617	+	1.43638i	−0.129254	+	0.0575474i
$624$	0.602062	−	1.85296i	0.0241018	−	0.0741776i
$625$	14.8341	+	25.6934i	0.593364	+	1.02774i
$626$	25.0006	−	43.3022i	0.999223	−	1.73071i
$627$	5.78944	+	6.42982i	0.231208	+	0.256782i
$628$	8.21338	+	25.2782i	0.327750	+	1.00871i
$629$	−24.7008	+	27.4330i	−0.984884	+	1.09382i
$630$	−29.2373	−	13.0173i	−1.16484	−	0.518622i
$631$	−10.9012	+	2.31712i	−0.433969	+	0.0922429i	−0.419716	−	0.907655i	$-0.637870\pi$
$631$	−10.9012	+	2.31712i	−0.433969	+	0.0922429i	−0.0142529	+	0.999898i	$0.504537\pi$
$632$	−1.44675	−	13.7649i	−0.0575486	−	0.547538i
$633$	−4.94810	+	47.0780i	−0.196669	+	1.87118i
$634$	−2.29332	−	0.487460i	−0.0910794	−	0.0193595i
$635$	−2.60147	−	1.89008i	−0.103236	−	0.0750056i
$636$	39.2177	+	28.4934i	1.55508	+	1.12983i
$637$	−8.22302	−	1.74786i	−0.325808	−	0.0692526i
$638$	0.0228170	−	0.217089i	0.000903334	−	0.00859464i
$639$	1.23343	+	11.7353i	0.0487936	+	0.464240i
$640$	−46.6533	+	9.91646i	−1.84413	+	0.391983i
$641$	16.0357	+	7.13957i	0.633374	+	0.281996i	0.698203	−	0.715900i	$-0.253983\pi$
$641$	16.0357	+	7.13957i	0.633374	+	0.281996i	−0.0648289	+	0.997896i	$0.520650\pi$
$642$	−7.16176	+	7.95394i	−0.282652	+	0.313917i
$643$	−0.678617	−	2.08857i	−0.0267621	−	0.0823651i	0.936783	−	0.349910i	$-0.113788\pi$
$643$	−0.678617	−	2.08857i	−0.0267621	−	0.0823651i	−0.963545	+	0.267545i	$0.913788\pi$
$644$	−25.3674	−	28.1734i	−0.999617	−	1.11019i
$645$	−0.732145	+	1.26811i	−0.0288282	+	0.0499318i
$646$	−23.4341	−	40.5891i	−0.922003	−	1.59696i
$647$	−10.0259	+	30.8566i	−0.394160	+	1.21310i	0.535454	+	0.844564i	$0.320140\pi$
$647$	−10.0259	+	30.8566i	−0.394160	+	1.21310i	−0.929614	+	0.368535i	$0.879860\pi$
$648$	−20.6280	+	9.18418i	−0.810345	+	0.360789i
$649$	−5.64084	+	4.09831i	−0.221422	+	0.160873i
$650$	−5.43508			−0.213181
$651$	−22.5507	+	2.40186i	−0.883832	+	0.0941362i
$652$	−56.7370			−2.22199
$653$	−13.3407	+	9.69256i	−0.522061	+	0.379299i	−0.817380	−	0.576099i	$-0.804574\pi$
$653$	−13.3407	+	9.69256i	−0.522061	+	0.379299i	0.295319	+	0.955399i	$0.404574\pi$
$654$	−63.0636	+	28.0777i	−2.46598	+	1.09793i
$655$	6.19225	−	19.0578i	0.241951	−	0.744649i
$656$	1.49004	+	2.58083i	0.0581764	+	0.100764i
$657$	−4.66457	+	8.07927i	−0.181982	+	0.315202i
$658$	−19.8772	−	22.0759i	−0.774894	−	0.860607i
$659$	−6.10043	−	18.7752i	−0.237639	−	0.731377i	−0.996760	−	0.0804282i	$-0.974371\pi$
$659$	−6.10043	−	18.7752i	−0.237639	−	0.731377i	0.759122	−	0.650949i	$-0.225629\pi$
$660$	10.3687	−	11.5156i	0.403602	−	0.448245i
$661$	10.7623	+	4.79169i	0.418605	+	0.186375i	0.605220	−	0.796058i	$-0.293085\pi$
$661$	10.7623	+	4.79169i	0.418605	+	0.186375i	−0.186615	+	0.982433i	$0.559752\pi$
$662$	−60.2408	+	12.8046i	−2.34132	+	0.497664i
$663$	2.20681	+	20.9964i	0.0857055	+	0.815433i
$664$	−0.853219	+	8.11783i	−0.0331113	+	0.315033i
$665$	−18.1568	−	3.85935i	−0.704091	−	0.149659i
$666$	−54.5336	−	39.6210i	−2.11313	−	1.53528i
$667$	−0.742554	−	0.539497i	−0.0287518	−	0.0208894i
$668$	79.2591	+	16.8470i	3.06663	+	0.651832i
$669$	1.65185	−	15.7163i	0.0638644	−	0.607629i
$670$	2.90866	+	27.6741i	0.112371	+	1.06914i
$671$	5.62649	−	1.19595i	0.217208	−	0.0461690i
$672$	19.2781	+	8.58318i	0.743671	+	0.331104i
$673$	33.7122	−	37.4412i	1.29951	−	1.44325i	0.472217	−	0.881482i	$-0.343454\pi$
$673$	33.7122	−	37.4412i	1.29951	−	1.44325i	0.827293	−	0.561770i	$-0.189880\pi$
$674$	22.7764	+	70.0985i	0.877314	+	2.70009i
$675$	−0.983796	−	1.09262i	−0.0378663	−	0.0420548i
$676$	15.6348	−	27.0802i	0.601337	−	1.04155i
$677$	1.98998	+	3.44674i	0.0764810	+	0.132469i	0.901729	−	0.432301i	$-0.142298\pi$
$677$	1.98998	+	3.44674i	0.0764810	+	0.132469i	−0.825248	+	0.564770i	$0.808965\pi$
$678$	−20.0433	+	61.6869i	−0.769758	+	2.36907i
$679$	17.9849	−	8.00737i	0.690195	−	0.307295i
$680$	−27.0574	+	19.6584i	−1.03760	+	0.753864i
$681$	33.1770			1.27134
$682$	1.94693	−	9.22259i	0.0745519	−	0.353151i
$683$	5.23244			0.200214			0.100107	−	0.994977i	$-0.468082\pi$
$683$	5.23244			0.200214			0.100107	+	0.994977i	$0.468082\pi$
$684$	43.2314	−	31.4095i	1.65300	−	1.20097i
$685$	37.6075	−	16.7439i	1.43691	−	0.639753i
$686$	−13.0604	+	40.1958i	−0.498648	+	1.53468i
$687$	19.4238	+	33.6430i	0.741064	+	1.28356i
$688$	−0.0465749	+	0.0806701i	−0.00177565	+	0.00307552i
$689$	−7.27477	−	8.07945i	−0.277147	−	0.307803i
$690$	−32.2468	−	99.2455i	−1.22762	−	3.77821i
$691$	6.15301	−	6.83361i	0.234072	−	0.259963i	−0.614653	−	0.788797i	$-0.710704\pi$
$691$	6.15301	−	6.83361i	0.234072	−	0.259963i	0.848725	+	0.528834i	$0.177371\pi$
$692$	27.2550	+	12.1347i	1.03608	+	0.461293i
$693$	−3.98369	+	0.846760i	−0.151328	+	0.0321658i
$694$	−0.752867	−	7.16305i	−0.0285785	−	0.271906i
$695$	1.91687	−	18.2378i	0.0727110	−	0.691799i
$696$	−0.980270	−	0.208363i	−0.0371570	−	0.00789797i
$697$	−26.1251	−	18.9810i	−0.989560	−	0.718957i
$698$	41.1196	+	29.8751i	1.55640	+	1.13079i
$699$	32.4854	+	6.90499i	1.22871	+	0.261171i
$700$	−0.691576	+	6.57991i	−0.0261391	+	0.248697i
$701$	4.23908	+	40.3321i	0.160108	+	1.52332i	0.719542	+	0.694449i	$0.244352\pi$
$701$	4.23908	+	40.3321i	0.160108	+	1.52332i	−0.559434	+	0.828875i	$0.688981\pi$
$702$	−5.06468	+	1.07653i	−0.191154	+	0.0406310i
$703$	−35.7161	−	15.9018i	−1.34706	−	0.599749i
$704$	−6.26569	+	6.95876i	−0.236147	+	0.262268i
$705$	−15.7769	−	48.5564i	−0.594193	−	1.82874i
$706$	7.61579	+	8.45820i	0.286624	+	0.318328i
$707$	−5.88235	+	10.1885i	−0.221229	+	0.383179i
$708$	40.1710	+	69.5782i	1.50972	+	2.61491i
$709$	−11.5220	+	35.4612i	−0.432719	+	1.33177i	0.462687	+	0.886521i	$0.346885\pi$
$709$	−11.5220	+	35.4612i	−0.432719	+	1.33177i	−0.895406	+	0.445250i	$0.853115\pi$
$710$	17.9336	−	7.98457i	0.673038	−	0.299656i
$711$	−12.6946	+	9.22314i	−0.476083	+	0.345895i
$712$	−6.73883			−0.252548
$713$	−29.4906	−	26.4793i	−1.10443	−	0.991658i
$714$	41.1599			1.54037
$715$	−2.81161	+	2.04276i	−0.105148	+	0.0763948i
$716$	−34.2921	+	15.2678i	−1.28156	+	0.570585i
$717$	18.4196	−	56.6897i	0.687893	−	2.11712i
$718$	0.416347	+	0.721134i	0.0155379	+	0.0269125i
$719$	9.28994	−	16.0906i	0.346456	−	0.600080i	−0.639161	−	0.769073i	$-0.720718\pi$
$719$	9.28994	−	16.0906i	0.346456	−	0.600080i	0.985617	+	0.168993i	$0.0540516\pi$
$720$	−2.34136	−	2.60035i	−0.0872575	−	0.0969093i
$721$	2.76647	+	8.51433i	0.103029	+	0.317090i
$722$	3.87752	−	4.30642i	0.144306	−	0.160268i
$723$	−57.4036	−	25.5577i	−2.13486	−	0.950501i
$724$	48.5887	−	10.3278i	1.80578	−	0.383831i
$725$	0.0167435	+	0.159303i	0.000621836	+	0.00591638i
$726$	−6.41630	+	61.0470i	−0.238131	+	2.26567i
$727$	−16.0193	−	3.40501i	−0.594123	−	0.126285i	−0.0989697	−	0.995090i	$-0.531555\pi$
$727$	−16.0193	−	3.40501i	−0.594123	−	0.126285i	−0.495153	+	0.868806i	$0.664888\pi$
$728$	7.51065	+	5.45681i	0.278363	+	0.202243i
$729$	28.0140	+	20.3534i	1.03756	+	0.753829i
$730$	15.1812	+	3.22686i	0.561881	+	0.119432i
$731$	0.105509	−	1.00385i	0.00390238	−	0.0371287i
$732$	−6.92826	−	65.9179i	−0.256076	−	2.43640i
$733$	1.12618	−	0.239377i	0.0415964	−	0.00884158i	−0.187067	−	0.982347i	$-0.559898\pi$
$733$	1.12618	−	0.239377i	0.0415964	−	0.00884158i	0.228663	+	0.973506i	$0.426565\pi$
$734$	−61.9485	−	27.5812i	−2.28656	−	1.01804i
$735$	−18.8485	+	20.9334i	−0.695237	+	0.772139i
$736$	11.3966	+	35.0751i	0.420084	+	1.29289i
$737$	2.36943	+	2.63151i	0.0872789	+	0.0969331i
$738$	29.4834	−	51.0668i	1.08530	−	1.87979i
$739$	10.3579	+	17.9404i	0.381022	+	0.659949i	0.991209	−	0.132309i	$-0.0422390\pi$
$739$	10.3579	+	17.9404i	0.381022	+	0.659949i	−0.610187	+	0.792257i	$0.708906\pi$
$740$	−21.6374	+	66.5931i	−0.795407	+	2.44801i
$741$	−20.4266	+	9.09449i	−0.750389	+	0.334095i
$742$	−17.1479	+	12.4586i	−0.629517	+	0.457371i
$743$	−35.2367			−1.29271			−0.646354	−	0.763038i	$-0.723707\pi$
$743$	−35.2367			−1.29271			−0.646354	+	0.763038i	$0.723707\pi$
$744$	−41.1756	−	13.3155i	−1.50957	−	0.488171i
$745$	15.8950			0.582348
$746$	−33.0959	+	24.0456i	−1.21173	+	0.880370i
$747$	8.45390	−	3.76392i	0.309312	−	0.137715i
$748$	−3.30083	+	10.1589i	−0.120690	+	0.371447i
$749$	−1.46104	−	2.53060i	−0.0533853	−	0.0924660i
$750$	27.5429	−	47.7058i	1.00573	−	1.74197i
$751$	−28.8702	−	32.0636i	−1.05349	−	1.17002i	−0.985033	−	0.172364i	$-0.944859\pi$
$751$	−28.8702	−	32.0636i	−1.05349	−	1.17002i	−0.0684559	−	0.997654i	$-0.521807\pi$
$752$	−1.00364	−	3.08888i	−0.0365989	−	0.112640i
$753$	39.4629	−	43.8279i	1.43811	−	1.59718i
$754$	0.515340	+	0.229444i	0.0187676	+	0.00835586i
$755$	−13.5017	+	2.86987i	−0.491377	+	0.104445i
$756$	0.658843	+	6.26847i	0.0239619	+	0.227982i
$757$	2.85766	−	27.1888i	0.103863	−	0.988194i	−0.811168	−	0.584813i	$-0.801168\pi$
$757$	2.85766	−	27.1888i	0.103863	−	0.988194i	0.915032	−	0.403382i	$-0.132165\pi$
$758$	5.55342	+	1.18042i	0.201709	+	0.0428746i
$759$	−10.7433	−	7.80543i	−0.389955	−	0.283319i
$760$	−28.6563	−	20.8201i	−1.03947	−	0.755223i
$761$	−16.8163	−	3.57441i	−0.609589	−	0.129572i	−0.107235	−	0.994234i	$-0.534200\pi$
$761$	−16.8163	−	3.57441i	−0.609589	−	0.129572i	−0.502355	+	0.864662i	$0.667533\pi$
$762$	−0.789351	+	7.51017i	−0.0285952	+	0.272065i
$763$	−1.97000	−	18.7433i	−0.0713189	−	0.678554i
$764$	−7.35260	+	1.56284i	−0.266008	+	0.0565417i
$765$	34.6386	+	15.4221i	1.25236	+	0.557587i
$766$	−29.5188	+	32.7839i	−1.06656	+	1.18453i
$767$	−5.56812	−	17.1369i	−0.201053	−	0.618778i
$768$	31.5169	+	35.0030i	1.13727	+	1.26306i
$769$	−7.02837	+	12.1735i	−0.253450	+	0.438987i	−0.964473	−	0.264181i	$-0.914899\pi$
$769$	−7.02837	+	12.1735i	−0.253450	+	0.438987i	0.711024	+	0.703168i	$0.248232\pi$
$770$	3.38775	+	5.86776i	0.122086	+	0.211459i
$771$	−12.0581	+	37.1111i	−0.434263	+	1.33652i
$772$	77.9486	−	34.7050i	2.80543	−	1.24906i
$773$	17.9900	−	13.0705i	0.647054	−	0.470112i	−0.215212	−	0.976567i	$-0.569044\pi$
$773$	17.9900	−	13.0705i	0.647054	−	0.470112i	0.862266	+	0.506455i	$0.169044\pi$
$774$	1.84315			0.0662507
$775$	0.00961044	+	6.91682i	0.000345217	+	0.248460i
$776$	37.5668			1.34857
$777$	27.7771	−	20.1813i	0.996498	−	0.723998i
$778$	11.1116	−	4.94718i	0.398369	−	0.177365i
$779$	10.5686	−	32.5268i	0.378659	−	1.16539i
$780$	20.0228	+	34.6804i	0.716930	+	1.24176i
$781$	1.24906	−	2.16343i	0.0446948	−	0.0774136i
$782$	48.1330	+	53.4571i	1.72123	+	1.91162i
$783$	0.0471557	+	0.145130i	0.00168521	+	0.00518654i
$784$	−1.19904	+	1.33166i	−0.0428227	+	0.0475594i
$785$	−18.2470	−	8.12411i	−0.651265	−	0.289962i
$786$	−46.0303	+	9.78404i	−1.64185	+	0.348985i
$787$	−3.34845	−	31.8583i	−0.119359	−	1.13563i	−0.876173	−	0.481997i	$-0.839912\pi$
$787$	−3.34845	−	31.8583i	−0.119359	−	1.13563i	0.756814	−	0.653630i	$-0.226755\pi$
$788$	2.15316	−	20.4859i	0.0767030	−	0.729780i
$789$	−16.9273	−	3.59801i	−0.602628	−	0.128093i
$790$	21.1192	+	15.3440i	0.751388	+	0.545915i
$791$	−14.3261	−	10.4085i	−0.509377	−	0.370084i
$792$	−7.60176	−	1.61580i	−0.270117	−	0.0574151i
$793$	−1.55384	+	14.7838i	−0.0551786	+	0.524990i
$794$	−4.08247	−	38.8421i	−0.144881	−	1.37845i
$795$	−35.6329	+	7.57402i	−1.26377	+	0.268623i
$796$	−13.8782	−	6.17896i	−0.491899	−	0.219008i
$797$	17.4304	−	19.3584i	0.617415	−	0.685709i	−0.350622	−	0.936517i	$-0.614030\pi$
$797$	17.4304	−	19.3584i	0.617415	−	0.685709i	0.968037	+	0.250808i	$0.0806964\pi$
$798$	13.4707	+	41.4586i	0.476859	+	1.46762i
$799$	23.5493	+	26.1541i	0.833114	+	0.925267i
$800$	3.21812	−	5.57395i	0.113778	−	0.197069i
$801$	3.81994	+	6.61633i	0.134971	+	0.233776i
$802$	27.1247	−	83.4814i	0.957808	−	2.94783i
$803$	1.80429	−	0.803320i	0.0636719	−	0.0283485i
$804$	33.0100	−	23.9832i	1.16417	−	0.845822i
$805$	28.4897			1.00413
$806$	21.1125	+	12.1502i	0.743655	+	0.427973i
$807$	−26.7486			−0.941594
$808$	−18.1621	+	13.1956i	−0.638942	+	0.464218i
$809$	−7.97472	+	3.55057i	−0.280376	+	0.124831i	−0.542107	−	0.840309i	$-0.682373\pi$
$809$	−7.97472	+	3.55057i	−0.280376	+	0.124831i	0.261731	+	0.965141i	$0.415707\pi$
$810$	13.1605	−	40.5037i	0.462411	−	1.42316i
$811$	25.0392	+	43.3692i	0.879245	+	1.52290i	0.852170	+	0.523264i	$0.175286\pi$
$811$	25.0392	+	43.3692i	0.879245	+	1.52290i	0.0270750	+	0.999633i	$0.491381\pi$
$812$	0.343347	−	0.594695i	0.0120491	−	0.0208697i
$813$	2.68337	+	2.98018i	0.0941098	+	0.104520i
$814$	4.40984	+	13.5721i	0.154565	+	0.475701i
$815$	28.5299	−	31.6856i	0.999358	−	1.10990i
$816$	4.11107	+	1.83037i	0.143916	+	0.0640756i
$817$	1.04567	−	0.222263i	0.0365832	−	0.00777600i
$818$	−0.120284	−	1.14442i	−0.00420562	−	0.0400138i
$819$	1.10016	−	10.4673i	0.0384427	−	0.365758i
$820$	−59.9140	−	12.7351i	−2.09229	−	0.444730i
$821$	41.0844	+	29.8495i	1.43385	+	1.04176i	0.989283	+	0.146013i	$0.0466441\pi$
$821$	41.0844	+	29.8495i	1.43385	+	1.04176i	0.444572	+	0.895743i	$0.353356\pi$
$822$	−78.2123	−	56.8246i	−2.72797	−	1.98199i
$823$	6.19089	+	1.31592i	0.215801	+	0.0458699i	0.314543	−	0.949243i	$-0.398149\pi$
$823$	6.19089	+	1.31592i	0.215801	+	0.0458699i	−0.0987423	+	0.995113i	$0.531482\pi$
$824$	−1.78569	+	16.9897i	−0.0622076	+	0.591866i
$825$	0.242244	+	2.30480i	0.00843385	+	0.0802427i
$826$	−34.3617	+	7.30380i	−1.19560	+	0.254132i
$827$	3.37779	+	1.50389i	0.117457	+	0.0522953i	0.464624	−	0.885508i	$-0.346190\pi$
$827$	3.37779	+	1.50389i	0.117457	+	0.0522953i	−0.347167	+	0.937803i	$0.612856\pi$
$828$	−54.8790	+	60.9493i	−1.90718	+	2.11813i
$829$	8.04729	+	24.7670i	0.279494	+	0.860193i	0.987995	+	0.154484i	$0.0493715\pi$
$829$	8.04729	+	24.7670i	0.279494	+	0.860193i	−0.708501	+	0.705709i	$0.750628\pi$
$830$	−10.3014	−	11.4409i	−0.357568	−	0.397120i
$831$	15.3852	−	26.6479i	0.533707	−	0.924407i
$832$	−12.0995	−	20.9570i	−0.419475	−	0.726553i
$833$	6.00033	−	18.4671i	0.207899	−	0.639848i
$834$	−39.3425	+	17.5164i	−1.36232	+	0.606543i
$835$	−49.2635	+	35.7920i	−1.70483	+	1.23863i
$836$	−11.3130			−0.391267
$837$	1.37898	+	6.44354i	0.0476644	+	0.222721i
$838$	31.1747			1.07691
$839$	−6.06196	+	4.40427i	−0.209282	+	0.152052i	−0.687489	−	0.726195i	$-0.741287\pi$
$839$	−6.06196	+	4.40427i	−0.209282	+	0.152052i	0.478207	+	0.878247i	$0.341287\pi$
$840$	28.4177	−	12.6524i	0.980504	−	0.436548i
$841$	−8.95636	+	27.5648i	−0.308840	+	0.950511i
$842$	35.6687	+	61.7800i	1.22923	+	2.12908i
$843$	−27.2996	+	47.2843i	−0.940249	+	1.62856i
$844$	−41.4157	−	45.9968i	−1.42559	−	1.58328i
$845$	7.26150	+	22.3486i	0.249803	+	0.768815i
$846$	−43.0016	+	47.7581i	−1.47843	+	1.64196i
$847$	−15.3096	−	6.81627i	−0.526044	−	0.234210i
$848$	−2.26677	+	0.481816i	−0.0778411	+	0.0165456i
$849$	−0.183076	−	1.74185i	−0.00628315	−	0.0597801i
$850$	1.31222	−	12.4849i	0.0450087	−	0.428230i
$851$	58.6937	+	12.4757i	2.01199	+	0.427662i
$852$	−23.2877	−	16.9195i	−0.797822	−	0.579652i
$853$	35.2626	+	25.6198i	1.20737	+	0.877204i	0.994989	−	0.0999836i	$-0.0318790\pi$
$853$	35.2626	+	25.6198i	1.20737	+	0.877204i	0.212378	+	0.977187i	$0.431879\pi$
$854$	28.3479	+	6.02553i	0.970045	+	0.206189i
$855$	−4.19758	+	39.9373i	−0.143554	+	1.36583i
$856$	−0.582848	−	5.54543i	−0.0199213	−	0.189539i
$857$	−38.3657	+	8.15487i	−1.31055	+	0.278565i	−0.809635	−	0.586933i	$-0.800335\pi$
$857$	−38.3657	+	8.15487i	−1.31055	+	0.278565i	−0.500911	+	0.865499i	$0.667002\pi$
$858$	7.45593	+	3.31959i	0.254541	+	0.113329i
$859$	−12.1790	+	13.5262i	−0.415544	+	0.461508i	−0.914183	−	0.405302i	$-0.867167\pi$
$859$	−12.1790	+	13.5262i	−0.415544	+	0.461508i	0.498639	+	0.866809i	$0.333833\pi$
$860$	−0.591643	−	1.82089i	−0.0201749	−	0.0620918i
$861$	20.0975	+	22.3205i	0.684920	+	0.760681i
$862$	13.9084	−	24.0900i	0.473721	−	0.820509i
$863$	−22.4738	−	38.9258i	−0.765018	−	1.32505i	−0.940237	−	0.340521i	$-0.889397\pi$
$863$	−22.4738	−	38.9258i	−0.765018	−	1.32505i	0.175219	−	0.984530i	$-0.443937\pi$
$864$	1.89477	−	5.83151i	0.0644614	−	0.198392i
$865$	−20.4819	+	9.11911i	−0.696404	+	0.310059i
$866$	60.4700	−	43.9340i	2.05486	−	1.49294i
$867$	−5.53740			−0.188060
$868$	17.3959	−	24.0135i	0.590456	−	0.815072i
$869$	3.32196			0.112690
$870$	1.52919	−	1.11102i	0.0518442	−	0.0376670i
$871$	−8.35992	+	3.72208i	−0.283265	+	0.126118i
$872$	11.1133	−	34.2032i	0.376343	−	1.15827i
$873$	−21.2949	−	36.8839i	−0.720724	−	1.24833i
$874$	−38.0922	+	65.9776i	−1.28849	+	2.23173i
$875$	10.0632	+	11.1763i	0.340197	+	0.377827i
$876$	−7.03257	−	21.6440i	−0.237608	−	0.731283i
$877$	−28.5391	+	31.6959i	−0.963698	+	1.07029i	0.0337881	+	0.999429i	$0.489243\pi$
$877$	−28.5391	+	31.6959i	−0.963698	+	1.07029i	−0.997486	+	0.0708657i	$0.977424\pi$
$878$	26.0725	+	11.6082i	0.879903	+	0.391758i
$879$	22.4140	−	4.76424i	0.756005	−	0.160694i
$880$	0.0774331	+	0.736727i	0.00261027	+	0.0248350i
$881$	0.932030	−	8.86768i	0.0314009	−	0.298760i	−0.967539	−	0.252722i	$-0.918674\pi$
$881$	0.932030	−	8.86768i	0.0314009	−	0.298760i	0.998940	−	0.0460372i	$-0.0146593\pi$
$882$	34.6820	+	7.37189i	1.16780	+	0.248225i
$883$	−38.0791	−	27.6661i	−1.28146	−	0.931038i	−0.281867	−	0.959453i	$-0.590954\pi$
$883$	−38.0791	−	27.6661i	−1.28146	−	0.931038i	−0.999596	+	0.0284158i	$0.990954\pi$
$884$	−22.3326	−	16.2256i	−0.751126	−	0.545725i
$885$	−59.0567	−	12.5529i	−1.98517	−	0.421961i
$886$	1.13930	−	10.8397i	0.0382754	−	0.364166i
$887$	−0.329951	−	3.13928i	−0.0110787	−	0.105407i	0.987585	−	0.157085i	$-0.0502096\pi$
$887$	−0.329951	−	3.13928i	−0.0110787	−	0.105407i	−0.998664	+	0.0516783i	$0.983543\pi$
$888$	64.0858	−	13.6219i	2.15058	−	0.457120i
$889$	−1.88343	−	0.838557i	−0.0631682	−	0.0281243i
$890$	8.50466	−	9.44538i	0.285077	−	0.316610i
$891$	−1.67473	−	5.15429i	−0.0561056	−	0.172675i
$892$	13.8261	+	15.3554i	0.462931	+	0.514137i
$893$	−18.6368	+	32.2799i	−0.623657	+	1.08021i
$894$	−18.6640	−	32.3270i	−0.624217	−	1.08118i
$895$	8.71703	−	26.8283i	0.291378	−	0.896770i
$896$	−27.9361	+	12.4379i	−0.933279	+	0.415522i
$897$	27.7636	−	20.1714i	0.927000	−	0.673505i
$898$	−36.8840			−1.23083
$899$	0.291086	−	0.656241i	0.00970825	−	0.0218869i
$900$	14.3131			0.477105
$901$	20.3157	−	14.7602i	0.676815	−	0.491735i
$902$	−11.4044	+	5.07756i	−0.379724	+	0.169064i
$903$	−0.290113	+	0.892875i	−0.00965434	+	0.0297130i
$904$	−16.8954	−	29.2637i	−0.561932	−	0.973295i
$905$	−18.6648	+	32.3284i	−0.620439	+	1.07463i
$906$	21.6904	+	24.0897i	0.720616	+	0.800326i
$907$	8.33208	+	25.6435i	0.276662	+	0.851478i	0.988775	+	0.149413i	$0.0477384\pi$
$907$	8.33208	+	25.6435i	0.276662	+	0.851478i	−0.712113	+	0.702065i	$0.752262\pi$
$908$	−29.0267	+	32.2374i	−0.963285	+	1.06984i
$909$	23.2510	+	10.3520i	0.771185	+	0.343354i
$910$	−17.1272	+	3.64049i	−0.567760	+	0.120681i
$911$	−0.530798	−	5.05020i	−0.0175861	−	0.167321i	0.982204	−	0.187818i	$-0.0601416\pi$
$911$	−0.530798	−	5.05020i	−0.0175861	−	0.167321i	−0.999790	+	0.0204976i	$0.993475\pi$
$912$	−0.498189	+	4.73995i	−0.0164967	+	0.156955i
$913$	−1.91631	−	0.407324i	−0.0634206	−	0.0134805i
$914$	−8.50854	−	6.18181i	−0.281437	−	0.204476i
$915$	40.2967	+	29.2773i	1.33217	+	0.967876i
$916$	−49.6843	−	10.5607i	−1.64161	−	0.348936i
$917$	1.34294	−	12.7772i	0.0443479	−	0.421942i
$918$	−1.25011	−	11.8940i	−0.0412598	−	0.392560i
$919$	48.2001	−	10.2453i	1.58998	−	0.337960i	0.673856	−	0.738863i	$-0.264637\pi$
$919$	48.2001	−	10.2453i	1.58998	−	0.337960i	0.916120	+	0.400903i	$0.131304\pi$
$920$	49.6645	+	22.1121i	1.63739	+	0.729013i
$921$	53.3098	−	59.2066i	1.75662	−	1.95092i
$922$	−12.1157	−	37.2882i	−0.399009	−	1.22802i
$923$	4.31979	+	4.79762i	0.142188	+	0.157915i
$924$	4.96754	−	8.60403i	0.163420	−	0.283052i
$925$	−5.23597	−	9.06896i	−0.172158	−	0.298186i
$926$	19.5578	−	60.1929i	0.642711	−	1.97806i
$927$	17.6931	−	7.87748i	0.581118	−	0.258730i
$928$	−0.540441	+	0.392653i	−0.0177408	+	0.0128895i
$929$	−39.9606			−1.31107			−0.655533	−	0.755167i	$-0.727556\pi$
$929$	−39.9606			−1.31107			−0.655533	+	0.755167i	$0.727556\pi$
$930$	70.6286	−	40.9084i	2.31600	−	1.34144i
$931$	20.5649			0.673989
$932$	−35.1311	+	25.5243i	−1.15076	+	0.836075i
$933$	41.1476	−	18.3201i	1.34711	−	0.599773i
$934$	−16.3367	+	50.2791i	−0.534552	+	1.64518i
$935$	−4.01360	−	6.95176i	−0.131259	−	0.227347i
$936$	10.0420	−	17.3932i	0.328232	−	0.568515i
$937$	30.1706	+	33.5079i	0.985631	+	1.09465i	0.995506	+	0.0947033i	$0.0301903\pi$
$937$	30.1706	+	33.5079i	0.985631	+	1.09465i	−0.00987411	+	0.999951i	$0.503143\pi$
$938$	5.51313	+	16.9677i	0.180010	+	0.554014i
$939$	36.8674	−	40.9454i	1.20312	−	1.33620i
$940$	60.9846	+	27.1521i	1.98910	+	0.885604i
$941$	−49.0955	+	10.4356i	−1.60047	+	0.340190i	−0.919795	−	0.392398i	$-0.871646\pi$
$941$	−49.0955	+	10.4356i	−1.60047	+	0.340190i	−0.680672	+	0.732588i	$0.738312\pi$
$942$	4.90310	+	46.6499i	0.159752	+	1.51993i
$943$	−5.48684	+	52.2038i	−0.178676	+	1.69999i
$944$	−3.75686	−	0.798545i	−0.122275	−	0.0259904i
$945$	−3.83202	−	2.78412i	−0.124656	−	0.0905675i
$946$	−0.315684	−	0.229358i	−0.0102638	−	0.00745707i
$947$	−29.6633	−	6.30512i	−0.963926	−	0.204889i	−0.301042	−	0.953611i	$-0.597334\pi$
$947$	−29.6633	−	6.30512i	−0.963926	−	0.204889i	−0.662884	+	0.748722i	$0.730668\pi$
$948$	4.00115	−	38.0684i	0.129951	−	1.23640i
$949$	0.533519	+	5.07609i	0.0173188	+	0.164777i
$950$	13.0050	−	2.76430i	0.421938	−	0.0896857i
$951$	−2.36017	−	1.05081i	−0.0765337	−	0.0340750i
$952$	−14.3482	+	15.9353i	−0.465027	+	0.516465i
$953$	−10.9631	−	33.7411i	−0.355131	−	1.09298i	−0.955934	−	0.293583i	$-0.905152\pi$
$953$	−10.9631	−	33.7411i	−0.355131	−	1.09298i	0.600803	−	0.799397i	$-0.294848\pi$
$954$	30.6826	+	34.0765i	0.993387	+	1.10327i
$955$	2.82442	−	4.89204i	0.0913961	−	0.158303i
$956$	38.9689	+	67.4962i	1.26035	+	2.18298i
$957$	0.0743291	−	0.228761i	0.00240272	−	0.00739481i
$958$	19.0715	−	8.49116i	0.616171	−	0.274337i
$959$	21.3530	−	15.5139i	0.689524	−	0.500969i
$960$	−81.0843			−2.61698
$961$	15.4253	−	26.8898i	0.497592	−	0.867411i
$962$	−36.8791			−1.18903
$963$	−5.11422	+	3.71570i	−0.164804	+	0.119737i
$964$	75.0567	−	33.4174i	2.41741	−	1.07630i
$965$	−19.8145	+	60.9828i	−0.637852	+	1.96311i
$966$	−33.4527	−	57.9418i	−1.07632	−	1.86425i
$967$	17.7222	−	30.6957i	0.569906	−	0.987107i	−0.426668	−	0.904408i	$-0.640313\pi$
$967$	17.7222	−	30.6957i	0.569906	−	0.987107i	0.996575	−	0.0826987i	$-0.0263539\pi$
$968$	−21.3980	−	23.7649i	−0.687757	−	0.763832i
$969$	−15.9593	−	49.1176i	−0.512686	−	1.57789i
$970$	−47.4108	+	52.6550i	−1.52227	+	1.69065i
$971$	−36.6306	−	16.3090i	−1.17553	−	0.523381i	−0.276394	−	0.961044i	$-0.589140\pi$
$971$	−36.6306	−	16.3090i	−1.17553	−	0.523381i	−0.899139	+	0.437663i	$0.855806\pi$
$972$	−72.6297	+	15.4379i	−2.32960	+	0.495171i
$973$	−1.22899	−	11.6931i	−0.0393997	−	0.374863i
$974$	5.69784	−	54.2113i	0.182571	−	1.73704i
$975$	−5.85818	−	1.24519i	−0.187612	−	0.0398781i
$976$	2.56345	+	1.86246i	0.0820540	+	0.0596157i
$977$	31.2854	+	22.7302i	1.00091	+	0.727202i	0.962283	−	0.272052i	$-0.0877022\pi$
$977$	31.2854	+	22.7302i	1.00091	+	0.727202i	0.0386252	+	0.999254i	$0.487702\pi$
$978$	−97.9415	−	20.8181i	−3.13182	−	0.665690i
$979$	0.169065	−	1.60855i	0.00540335	−	0.0514095i
$980$	−3.84991	−	36.6295i	−0.122981	−	1.17009i
$981$	−39.8810	+	8.47697i	−1.27330	+	0.270649i
$982$	19.4506	+	8.65997i	0.620694	+	0.276351i
$983$	−14.4396	+	16.0368i	−0.460551	+	0.511493i	−0.928027	−	0.372512i	$-0.878497\pi$
$983$	−14.4396	+	16.0368i	−0.460551	+	0.511493i	0.467477	+	0.884005i	$0.345163\pi$
$984$	17.7109	+	54.5086i	0.564604	+	1.73767i
$985$	10.3580	+	11.5037i	0.330032	+	0.366538i
$986$	−0.651478	+	1.12839i	−0.0207473	+	0.0359354i
$987$	−16.3669	−	28.3483i	−0.520965	−	0.902338i
$988$	9.03438	−	27.8049i	0.287422	−	0.884593i
$989$	−1.49890	+	0.667352i	−0.0476621	+	0.0212206i
$990$	11.8585	−	8.61568i	0.376887	−	0.273824i
$991$	46.8764			1.48908			0.744538	−	0.667580i	$-0.232670\pi$
$991$	46.8764			1.48908			0.744538	+	0.667580i	$0.232670\pi$
$992$	−24.9614	+	14.4578i	−0.792525	+	0.459034i
$993$	−67.8639			−2.15360
$994$	10.1825	−	7.39800i	0.322968	−	0.234650i
$995$	10.4293	−	4.64342i	0.330631	−	0.147206i
$996$	−6.97589	+	21.4696i	−0.221039	+	0.680290i
$997$	−22.2695	−	38.5718i	−0.705281	−	1.22158i	−0.966590	−	0.256327i	$-0.917488\pi$
$997$	−22.2695	−	38.5718i	−0.705281	−	1.22158i	0.261309	−	0.965255i	$-0.415846\pi$
$998$	−32.7830	+	56.7818i	−1.03773	+	1.79740i
$999$	−6.67543	−	7.41382i	−0.211201	−	0.234563i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.2.g.a.18.1	✓	16
3.2	odd	2		279.2.y.c.235.2		16
4.3	odd	2		496.2.bg.c.49.2		16
5.2	odd	4		775.2.ck.a.49.1		32
5.3	odd	4		775.2.ck.a.49.4		32
5.4	even	2		775.2.bl.a.576.2		16
31.2	even	5		961.2.g.k.816.1		16
31.3	odd	30		961.2.g.m.844.2		16
31.4	even	5		961.2.g.s.846.2		16
31.5	even	3		961.2.d.o.388.1		16
31.6	odd	6		961.2.g.j.338.1		16
31.7	even	15		961.2.g.t.448.2		16
31.8	even	5		961.2.c.j.439.8		16
31.9	even	15		961.2.a.i.1.8		8
31.10	even	15		961.2.d.o.374.1		16
31.11	odd	30		961.2.d.q.628.4		16
31.12	odd	30		961.2.g.l.732.1		16
31.13	odd	30		961.2.d.q.531.4		16
31.14	even	15		961.2.c.j.521.8		16
31.15	odd	10		961.2.g.n.547.2		16
31.16	even	5		961.2.g.t.547.2		16
31.17	odd	30		961.2.c.i.521.8		16
31.18	even	15		961.2.d.p.531.4		16
31.19	even	15	inner	31.2.g.a.19.1	yes	16
31.20	even	15		961.2.d.p.628.4		16
31.21	odd	30		961.2.d.n.374.1		16
31.22	odd	30		961.2.a.j.1.8		8
31.23	odd	10		961.2.c.i.439.8		16
31.24	odd	30		961.2.g.n.448.2		16
31.25	even	3		961.2.g.k.338.1		16
31.26	odd	6		961.2.d.n.388.1		16
31.27	odd	10		961.2.g.m.846.2		16
31.28	even	15		961.2.g.s.844.2		16
31.29	odd	10		961.2.g.j.816.1		16
31.30	odd	2		961.2.g.l.235.1		16
93.50	odd	30		279.2.y.c.19.2		16
93.53	even	30		8649.2.a.be.1.1		8
93.71	odd	30		8649.2.a.bf.1.1		8
124.19	odd	30		496.2.bg.c.81.2		16
155.19	even	30		775.2.bl.a.701.2		16
155.112	odd	60		775.2.ck.a.174.4		32
155.143	odd	60		775.2.ck.a.174.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.18.1	✓	16	1.1	even	1	trivial
31.2.g.a.19.1	yes	16	31.19	even	15	inner
279.2.y.c.19.2		16	93.50	odd	30
279.2.y.c.235.2		16	3.2	odd	2
496.2.bg.c.49.2		16	4.3	odd	2
496.2.bg.c.81.2		16	124.19	odd	30
775.2.bl.a.576.2		16	5.4	even	2
775.2.bl.a.701.2		16	155.19	even	30
775.2.ck.a.49.1		32	5.2	odd	4
775.2.ck.a.49.4		32	5.3	odd	4
775.2.ck.a.174.1		32	155.143	odd	60
775.2.ck.a.174.4		32	155.112	odd	60
961.2.a.i.1.8		8	31.9	even	15
961.2.a.j.1.8		8	31.22	odd	30
961.2.c.i.439.8		16	31.23	odd	10
961.2.c.i.521.8		16	31.17	odd	30
961.2.c.j.439.8		16	31.8	even	5
961.2.c.j.521.8		16	31.14	even	15
961.2.d.n.374.1		16	31.21	odd	30
961.2.d.n.388.1		16	31.26	odd	6
961.2.d.o.374.1		16	31.10	even	15
961.2.d.o.388.1		16	31.5	even	3
961.2.d.p.531.4		16	31.18	even	15
961.2.d.p.628.4		16	31.20	even	15
961.2.d.q.531.4		16	31.13	odd	30
961.2.d.q.628.4		16	31.11	odd	30
961.2.g.j.338.1		16	31.6	odd	6
961.2.g.j.816.1		16	31.29	odd	10
961.2.g.k.338.1		16	31.25	even	3
961.2.g.k.816.1		16	31.2	even	5
961.2.g.l.235.1		16	31.30	odd	2
961.2.g.l.732.1		16	31.12	odd	30
961.2.g.m.844.2		16	31.3	odd	30
961.2.g.m.846.2		16	31.27	odd	10
961.2.g.n.448.2		16	31.24	odd	30
961.2.g.n.547.2		16	31.15	odd	10
961.2.g.s.844.2		16	31.28	even	15
961.2.g.s.846.2		16	31.4	even	5
961.2.g.t.448.2		16	31.7	even	15
961.2.g.t.547.2		16	31.16	even	5
8649.2.a.be.1.1		8	93.53	even	30
8649.2.a.bf.1.1		8	93.71	odd	30

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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	31.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.86683 + 1.35633i) q^{2} +(-2.32289 + 1.03422i) q^{3} +(1.02738 - 3.16196i) q^{4} +(1.24923 + 2.16373i) q^{5} +(2.93370 - 5.08132i) q^{6} +(1.07187 + 1.19043i) q^{7} +(0.944583 + 2.90713i) q^{8} +(2.31884 - 2.57533i) q^{9} +O(q^{10})\)	\(q+(-1.86683 + 1.35633i) q^{2} +(-2.32289 + 1.03422i) q^{3} +(1.02738 - 3.16196i) q^{4} +(1.24923 + 2.16373i) q^{5} +(2.93370 - 5.08132i) q^{6} +(1.07187 + 1.19043i) q^{7} +(0.944583 + 2.90713i) q^{8} +(2.31884 - 2.57533i) q^{9} +(-5.26683 - 2.34494i) q^{10} +(-0.717625 + 0.152536i) q^{11} +(0.883657 + 8.40743i) q^{12} +(0.198183 - 1.88559i) q^{13} +(-3.61560 - 0.768520i) q^{14} +(-5.13960 - 3.73414i) q^{15} +(-0.326952 - 0.237545i) q^{16} +(4.28354 + 0.910495i) q^{17} +(-0.835873 + 7.95280i) q^{18} +(0.484806 + 4.61262i) q^{19} +(8.12506 - 1.72703i) q^{20} +(-3.72099 - 1.65669i) q^{21} +(1.13279 - 1.25809i) q^{22} +(-2.19973 - 6.77006i) q^{23} +(-5.20077 - 5.77604i) q^{24} +(-0.621150 + 1.07586i) q^{25} +(2.18751 + 3.78887i) q^{26} +(-0.365721 + 1.12557i) q^{27} +(4.86530 - 2.16617i) q^{28} +(0.104314 - 0.0757884i) q^{29} +14.6595 q^{30} +(4.81795 - 2.79058i) q^{31} -5.18091 q^{32} +(1.50921 - 1.09651i) q^{33} +(-9.23157 + 4.11016i) q^{34} +(-1.23676 + 3.80635i) q^{35} +(-5.76075 - 9.97791i) q^{36} +(-4.21474 + 7.30014i) q^{37} +(-7.16128 - 7.95341i) q^{38} +(1.48975 + 4.58499i) q^{39} +(-5.11023 + 5.67549i) q^{40} +(-6.73647 - 2.99927i) q^{41} +(9.19348 - 1.95413i) q^{42} +(-0.0240929 - 0.229229i) q^{43} +(-0.254963 + 2.42581i) q^{44} +(8.46907 + 1.80016i) q^{45} +(13.2889 + 9.65498i) q^{46} +(6.50168 + 4.72375i) q^{47} +(1.00515 + 0.213651i) q^{48} +(0.463478 - 4.40970i) q^{49} +(-0.299645 - 2.85094i) q^{50} +(-10.8919 + 2.31514i) q^{51} +(-5.75854 - 2.56387i) q^{52} +(3.83695 - 4.26137i) q^{53} +(-0.843912 - 2.59729i) q^{54} +(-1.22652 - 1.36219i) q^{55} +(-2.44826 + 4.24051i) q^{56} +(-5.89661 - 10.2132i) q^{57} +(-0.0919419 + 0.282968i) q^{58} +(8.68208 - 3.86551i) q^{59} +(-17.0875 + 12.4148i) q^{60} -7.84044 q^{61} +(-5.20934 + 11.7443i) q^{62} +5.55122 q^{63} +(10.3258 - 7.50212i) q^{64} +(4.32748 - 1.92672i) q^{65} +(-1.33021 + 4.09397i) q^{66} +(-2.41329 - 4.17994i) q^{67} +(7.27978 - 12.6090i) q^{68} +(12.1115 + 13.4511i) q^{69} +(-2.85385 - 8.78324i) q^{70} +(-2.27840 + 2.53042i) q^{71} +(9.67714 + 4.30854i) q^{72} +(-2.63322 + 0.559708i) q^{73} +(-2.03321 - 19.3447i) q^{74} +(0.330187 - 3.14152i) q^{75} +(15.0830 + 3.20599i) q^{76} +(-0.950780 - 0.690782i) q^{77} +(-8.99987 - 6.53879i) q^{78} +(-4.42900 - 0.941413i) q^{79} +(0.105544 - 1.00418i) q^{80} +(0.772154 + 7.34656i) q^{81} +(16.6438 - 3.53775i) q^{82} +(2.43949 + 1.08613i) q^{83} +(-9.06128 + 10.0636i) q^{84} +(3.38106 + 10.4058i) q^{85} +(0.355888 + 0.395253i) q^{86} +(-0.163928 + 0.283932i) q^{87} +(-1.12130 - 1.94214i) q^{88} +(-0.681255 + 2.09669i) q^{89} +(-18.2519 + 8.12627i) q^{90} +(2.45708 - 1.78518i) q^{91} -23.6666 q^{92} +(-8.30552 + 11.4650i) q^{93} -18.5445 q^{94} +(-9.37482 + 6.81121i) q^{95} +(12.0347 - 5.35820i) q^{96} +(3.79778 - 11.6884i) q^{97} +(5.11577 + 8.86077i) q^{98} +(-1.27122 + 2.20182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9	\( 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9} - 2 q^{10} - 7 q^{11} + 5 q^{12} - 7 q^{13} - 6 q^{14} + 14 q^{15} - 2 q^{16} - 6 q^{17} - 3 q^{18} + 16 q^{19} + 37 q^{20} + 9 q^{21} + 9 q^{22} + q^{23} - 20 q^{24} - 13 q^{25} + 9 q^{26} + 9 q^{27} - 30 q^{28} - 14 q^{29} - 22 q^{30} + 15 q^{31} - 42 q^{32} - 13 q^{33} - 32 q^{34} - 9 q^{35} + q^{36} - 8 q^{37} + 8 q^{38} - 3 q^{39} - q^{40} - 8 q^{41} + 69 q^{42} + 23 q^{43} + 39 q^{44} + 65 q^{45} + 34 q^{46} + 14 q^{47} + 34 q^{48} + 2 q^{49} + 3 q^{50} - 42 q^{51} + 29 q^{52} + 6 q^{53} - 46 q^{54} - 7 q^{55} - 30 q^{56} - 17 q^{57} - 15 q^{58} + 4 q^{59} - 75 q^{60} - 60 q^{61} - 25 q^{62} - 46 q^{63} + 23 q^{64} - 12 q^{65} - 30 q^{66} + 13 q^{67} + 30 q^{68} + 38 q^{69} + 12 q^{70} - 14 q^{71} + 37 q^{72} + 2 q^{73} + 13 q^{74} + 13 q^{75} - 12 q^{76} + 18 q^{77} - 15 q^{78} + 18 q^{79} + 36 q^{80} + 23 q^{81} + 14 q^{82} - 16 q^{83} + 8 q^{84} + 37 q^{85} - 26 q^{86} + 15 q^{87} - 17 q^{88} + q^{89} - 23 q^{90} + 8 q^{91} - 64 q^{92} + 17 q^{93} + 44 q^{94} - 22 q^{95} + 8 q^{96} + 3 q^{97} - 10 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9 - 2 * q^10 - 7 * q^11 + 5 * q^12 - 7 * q^13 - 6 * q^14 + 14 * q^15 - 2 * q^16 - 6 * q^17 - 3 * q^18 + 16 * q^19 + 37 * q^20 + 9 * q^21 + 9 * q^22 + q^23 - 20 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 - 30 * q^28 - 14 * q^29 - 22 * q^30 + 15 * q^31 - 42 * q^32 - 13 * q^33 - 32 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 8 * q^38 - 3 * q^39 - q^40 - 8 * q^41 + 69 * q^42 + 23 * q^43 + 39 * q^44 + 65 * q^45 + 34 * q^46 + 14 * q^47 + 34 * q^48 + 2 * q^49 + 3 * q^50 - 42 * q^51 + 29 * q^52 + 6 * q^53 - 46 * q^54 - 7 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 + 4 * q^59 - 75 * q^60 - 60 * q^61 - 25 * q^62 - 46 * q^63 + 23 * q^64 - 12 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 + 38 * q^69 + 12 * q^70 - 14 * q^71 + 37 * q^72 + 2 * q^73 + 13 * q^74 + 13 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 + 18 * q^79 + 36 * q^80 + 23 * q^81 + 14 * q^82 - 16 * q^83 + 8 * q^84 + 37 * q^85 - 26 * q^86 + 15 * q^87 - 17 * q^88 + q^89 - 23 * q^90 + 8 * q^91 - 64 * q^92 + 17 * q^93 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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