LMFDB - Embedded newform 231.2.be.a.2.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(2,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 10, 3]))

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

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

chi := DirichletCharacter("231.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.be (of order $30$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			2.18
Character	$\chi$	$=$	231.2
Dual form			231.2.be.a.116.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.590583 + 0.655909i) q^{2} +(-1.65683 - 0.504891i) q^{3} +(0.127629 - 1.21431i) q^{4} +(-0.627181 + 2.95066i) q^{5} +(-0.647333 - 1.38491i) q^{6} +(2.53863 - 0.745226i) q^{7} +(2.29995 - 1.67101i) q^{8} +(2.49017 + 1.67304i) q^{9} +O(q^{10})$	\(q+(0.590583 + 0.655909i) q^{2} +(-1.65683 - 0.504891i) q^{3} +(0.127629 - 1.21431i) q^{4} +(-0.627181 + 2.95066i) q^{5} +(-0.647333 - 1.38491i) q^{6} +(2.53863 - 0.745226i) q^{7} +(2.29995 - 1.67101i) q^{8} +(2.49017 + 1.67304i) q^{9} +(-2.30576 + 1.33123i) q^{10} +(3.06443 + 1.26857i) q^{11} +(-0.824552 + 1.94746i) q^{12} +(1.56018 + 0.506933i) q^{13} +(1.98807 + 1.22499i) q^{14} +(2.52889 - 4.57208i) q^{15} +(0.0657108 + 0.0139673i) q^{16} +(0.0265497 - 0.0294864i) q^{17} +(0.373293 + 2.62139i) q^{18} +(-1.72384 + 0.181182i) q^{19} +(3.50296 + 1.13818i) q^{20} +(-4.58233 - 0.0470180i) q^{21} +(0.977730 + 2.75918i) q^{22} +(3.55849 + 2.05449i) q^{23} +(-4.65430 + 1.60736i) q^{24} +(-3.74529 - 1.66751i) q^{25} +(0.588913 + 1.32272i) q^{26} +(-3.28109 - 4.02920i) q^{27} +(-0.580931 - 3.17779i) q^{28} +(-6.87050 - 4.99171i) q^{29} +(4.49239 - 1.04147i) q^{30} +(5.15337 - 1.09538i) q^{31} +(-2.81324 - 4.87268i) q^{32} +(-4.43674 - 3.64901i) q^{33} +0.0350201 q^{34} +(0.606725 + 7.95801i) q^{35} +(2.34940 - 2.81030i) q^{36} +(-8.45969 + 3.76649i) q^{37} +(-1.13691 - 1.02368i) q^{38} +(-2.32901 - 1.62762i) q^{39} +(3.48809 + 7.83438i) q^{40} +(-4.13780 + 3.00629i) q^{41} +(-2.67541 - 3.03336i) q^{42} +0.302979i q^{43} +(1.93155 - 3.55925i) q^{44} +(-6.49834 + 6.29834i) q^{45} +(0.754021 + 3.54739i) q^{46} +(-0.405927 + 0.0426647i) q^{47} +(-0.101820 - 0.0563182i) q^{48} +(5.88928 - 3.78371i) q^{49} +(-1.11817 - 3.44137i) q^{50} +(-0.0588757 + 0.0354492i) q^{51} +(0.814696 - 1.82984i) q^{52} +(1.49246 + 7.02148i) q^{53} +(0.705034 - 4.53167i) q^{54} +(-5.66508 + 8.24645i) q^{55} +(4.59343 - 5.95605i) q^{56} +(2.94758 + 0.570161i) q^{57} +(-0.783494 - 7.45444i) q^{58} +(-9.86546 - 1.03690i) q^{59} +(-5.22914 - 3.65438i) q^{60} +(2.87377 - 13.5200i) q^{61} +(3.76196 + 2.73323i) q^{62} +(7.56841 + 2.39148i) q^{63} +(1.57610 - 4.85074i) q^{64} +(-2.47430 + 4.28561i) q^{65} +(-0.226845 - 5.06514i) q^{66} +(-4.09951 - 7.10057i) q^{67} +(-0.0324170 - 0.0360027i) q^{68} +(-4.85851 - 5.20059i) q^{69} +(-4.86141 + 5.09782i) q^{70} +(6.15655 - 2.00038i) q^{71} +(8.52292 - 0.313202i) q^{72} +(5.63692 + 0.592464i) q^{73} +(-7.46662 - 3.32435i) q^{74} +(5.36339 + 4.65374i) q^{75} +2.11639i q^{76} +(8.72482 + 0.936749i) q^{77} +(-0.307899 - 2.48886i) q^{78} +(1.10418 - 0.994206i) q^{79} +(-0.0824252 + 0.185130i) q^{80} +(3.40190 + 8.33229i) q^{81} +(-4.41557 - 0.938558i) q^{82} +(4.09272 + 12.5961i) q^{83} +(-0.641932 + 5.55836i) q^{84} +(0.0703527 + 0.0968322i) q^{85} +(-0.198727 + 0.178934i) q^{86} +(8.86298 + 11.7393i) q^{87} +(9.16782 - 2.20303i) q^{88} +(-13.1138 - 7.57127i) q^{89} +(-7.96895 - 0.542630i) q^{90} +(4.33850 + 0.124229i) q^{91} +(2.94895 - 4.05888i) q^{92} +(-9.09131 - 0.787027i) q^{93} +(-0.267718 - 0.241054i) q^{94} +(0.546551 - 5.20008i) q^{95} +(2.20089 + 9.49359i) q^{96} +(-1.75630 + 5.40534i) q^{97} +(5.95987 + 1.62824i) q^{98} +(5.50858 + 8.28587i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) $ 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9	$ 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9} - 16 q^{12} - 40 q^{13} + 12 q^{15} + 34 q^{16} - 5 q^{18} - 10 q^{19} - 76 q^{22} - 25 q^{24} - 18 q^{25} + 6 q^{27} + 10 q^{28} - 35 q^{30} - 8 q^{33} - 96 q^{34} - 48 q^{36} - 10 q^{37} - 45 q^{39} - 120 q^{40} + 34 q^{42} - 24 q^{45} - 50 q^{46} + 14 q^{48} - 56 q^{49} - 45 q^{51} - 10 q^{52} + 48 q^{55} + 60 q^{57} + 44 q^{58} - 47 q^{60} - 50 q^{61} + 60 q^{63} - 72 q^{64} + 77 q^{66} - 80 q^{67} + 78 q^{69} + 36 q^{70} + 55 q^{72} - 70 q^{73} - 11 q^{75} + 36 q^{78} - 90 q^{79} + 23 q^{81} - 6 q^{82} + 125 q^{84} + 160 q^{85} + 86 q^{88} + 30 q^{90} - 128 q^{91} - 38 q^{93} - 210 q^{94} + 135 q^{96} + 40 q^{97} + 80 q^{99}+O(q^{100}) $ 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9 - 16 * q^12 - 40 * q^13 + 12 * q^15 + 34 * q^16 - 5 * q^18 - 10 * q^19 - 76 * q^22 - 25 * q^24 - 18 * q^25 + 6 * q^27 + 10 * q^28 - 35 * q^30 - 8 * q^33 - 96 * q^34 - 48 * q^36 - 10 * q^37 - 45 * q^39 - 120 * q^40 + 34 * q^42 - 24 * q^45 - 50 * q^46 + 14 * q^48 - 56 * q^49 - 45 * q^51 - 10 * q^52 + 48 * q^55 + 60 * q^57 + 44 * q^58 - 47 * q^60 - 50 * q^61 + 60 * q^63 - 72 * q^64 + 77 * q^66 - 80 * q^67 + 78 * q^69 + 36 * q^70 + 55 * q^72 - 70 * q^73 - 11 * q^75 + 36 * q^78 - 90 * q^79 + 23 * q^81 - 6 * q^82 + 125 * q^84 + 160 * q^85 + 86 * q^88 + 30 * q^90 - 128 * q^91 - 38 * q^93 - 210 * q^94 + 135 * q^96 + 40 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	0.590583	+	0.655909i	0.417605	+	0.463798i	0.914839	−	0.403819i	$-0.132317\pi$
$2$	0.590583	+	0.655909i	0.417605	+	0.463798i	−0.497234	+	0.867617i	$0.665651\pi$
$3$	−1.65683	−	0.504891i	−0.956571	−	0.291499i
$3$	−1.65683	−	0.504891i	−0.956571	−	0.291499i
$4$	0.127629	−	1.21431i	0.0638144	−	0.607153i
$5$	−0.627181	+	2.95066i	−0.280484	+	1.31957i	0.581876	+	0.813278i	$0.302319\pi$
$5$	−0.627181	+	2.95066i	−0.280484	+	1.31957i	−0.862360	+	0.506296i	$0.831014\pi$
$6$	−0.647333	−	1.38491i	−0.264273	−	0.565387i
$7$	2.53863	−	0.745226i	0.959512	−	0.281669i
$7$	2.53863	−	0.745226i	0.959512	−	0.281669i
$8$	2.29995	−	1.67101i	0.813154	−	0.590791i
$9$	2.49017	+	1.67304i	0.830057	+	0.557679i
$10$	−2.30576	+	1.33123i	−0.729147	+	0.420973i
$11$	3.06443	+	1.26857i	0.923960	+	0.382490i
$11$	3.06443	+	1.26857i	0.923960	+	0.382490i
$12$	−0.824552	+	1.94746i	−0.238028	+	0.562184i
$13$	1.56018	+	0.506933i	0.432716	+	0.140598i	0.517272	−	0.855821i	$-0.326947\pi$
$13$	1.56018	+	0.506933i	0.432716	+	0.140598i	−0.0845567	+	0.996419i	$0.526947\pi$
$14$	1.98807	+	1.22499i	0.531334	+	0.327393i
$15$	2.52889	−	4.57208i	0.652957	−	1.18051i
$16$	0.0657108	+	0.0139673i	0.0164277	+	0.00349182i
$17$	0.0265497	−	0.0294864i	0.00643924	−	0.00715150i	−0.739917	−	0.672699i	$-0.765135\pi$
$17$	0.0265497	−	0.0294864i	0.00643924	−	0.00715150i	0.746356	+	0.665547i	$0.231802\pi$
$18$	0.373293	+	2.62139i	0.0879859	+	0.617868i
$19$	−1.72384	+	0.181182i	−0.395475	+	0.0415661i	−0.300179	−	0.953883i	$-0.597046\pi$
$19$	−1.72384	+	0.181182i	−0.395475	+	0.0415661i	−0.0952960	+	0.995449i	$0.530380\pi$
$20$	3.50296	+	1.13818i	0.783285	+	0.254505i
$21$	−4.58233	−	0.0470180i	−0.999947	−	0.0102602i
$22$	0.977730	+	2.75918i	0.208453	+	0.588260i
$23$	3.55849	+	2.05449i	0.741995	+	0.428391i	0.822794	−	0.568339i	$-0.192414\pi$
$23$	3.55849	+	2.05449i	0.741995	+	0.428391i	−0.0807989	+	0.996730i	$0.525747\pi$
$24$	−4.65430	+	1.60736i	−0.950054	+	0.328100i
$25$	−3.74529	−	1.66751i	−0.749058	−	0.333502i
$26$	0.588913	+	1.32272i	0.115495	+	0.259407i
$27$	−3.28109	−	4.02920i	−0.631446	−	0.775420i
$28$	−0.580931	−	3.17779i	−0.109786	−	0.600545i
$29$	−6.87050	−	4.99171i	−1.27582	−	0.926938i	−0.276402	−	0.961042i	$-0.589142\pi$
$29$	−6.87050	−	4.99171i	−1.27582	−	0.926938i	−0.999418	+	0.0341044i	$0.989142\pi$
$30$	4.49239	−	1.04147i	0.820194	−	0.190145i
$31$	5.15337	−	1.09538i	0.925573	−	0.196737i	0.279617	−	0.960112i	$-0.409792\pi$
$31$	5.15337	−	1.09538i	0.925573	−	0.196737i	0.645956	+	0.763375i	$0.276459\pi$
$32$	−2.81324	−	4.87268i	−0.497316	−	0.861376i
$33$	−4.43674	−	3.64901i	−0.772338	−	0.635212i
$34$	0.0350201			0.00600591
$35$	0.606725	+	7.95801i	0.102555	+	1.34515i
$36$	2.34940	−	2.81030i	0.391566	−	0.468384i
$37$	−8.45969	+	3.76649i	−1.39076	+	0.619208i	−0.959162	−	0.282856i	$-0.908718\pi$
$37$	−8.45969	+	3.76649i	−1.39076	+	0.619208i	−0.431602	+	0.902064i	$0.642051\pi$
$38$	−1.13691	−	1.02368i	−0.184431	−	0.166062i
$39$	−2.32901	−	1.62762i	−0.372939	−	0.260628i
$40$	3.48809	+	7.83438i	0.551515	+	1.23872i
$41$	−4.13780	+	3.00629i	−0.646216	+	0.469503i	−0.861980	−	0.506942i	$-0.830776\pi$
$41$	−4.13780	+	3.00629i	−0.646216	+	0.469503i	0.215764	+	0.976446i	$0.430776\pi$
$42$	−2.67541	−	3.03336i	−0.412825	−	0.468058i
$43$			0.302979i			0.0462039i	0.999733	+	0.0231020i	$0.00735424\pi$
$43$			0.302979i			0.0462039i	−0.999733	+	0.0231020i	$0.992646\pi$
$44$	1.93155	−	3.55925i	0.291192	−	0.536577i
$45$	−6.49834	+	6.29834i	−0.968716	+	0.938901i
$46$	0.754021	+	3.54739i	0.111174	+	0.523034i
$47$	−0.405927	+	0.0426647i	−0.0592106	+	0.00622328i	−0.134087	−	0.990970i	$-0.542810\pi$
$47$	−0.405927	+	0.0426647i	−0.0592106	+	0.00622328i	0.0748768	+	0.997193i	$0.476144\pi$
$48$	−0.101820	−	0.0563182i	−0.0146964	−	0.00812883i
$49$	5.88928	−	3.78371i	0.841325	−	0.540529i
$50$	−1.11817	−	3.44137i	−0.158133	−	0.486683i
$51$	−0.0588757	+	0.0354492i	−0.00824424	+	0.00496389i
$52$	0.814696	−	1.82984i	0.112978	−	0.253753i
$53$	1.49246	+	7.02148i	0.205005	+	0.964474i	0.953514	+	0.301349i	$0.0974370\pi$
$53$	1.49246	+	7.02148i	0.205005	+	0.964474i	−0.748509	+	0.663125i	$0.769230\pi$
$54$	0.705034	−	4.53167i	0.0959430	−	0.616682i
$55$	−5.66508	+	8.24645i	−0.763879	+	1.11195i
$56$	4.59343	−	5.95605i	0.613823	−	0.795911i
$57$	2.94758	+	0.570161i	0.390416	+	0.0755196i
$58$	−0.783494	−	7.45444i	−0.102878	−	0.978816i
$59$	−9.86546	−	1.03690i	−1.28437	−	0.134993i	−0.562372	−	0.826884i	$-0.690111\pi$
$59$	−9.86546	−	1.03690i	−1.28437	−	0.134993i	−0.722002	+	0.691891i	$0.756778\pi$
$60$	−5.22914	−	3.65438i	−0.675080	−	0.471778i
$61$	2.87377	−	13.5200i	0.367949	−	1.73106i	−0.271686	−	0.962386i	$-0.587581\pi$
$61$	2.87377	−	13.5200i	0.367949	−	1.73106i	0.639635	−	0.768679i	$-0.279085\pi$
$62$	3.76196	+	2.73323i	0.477770	+	0.347120i
$63$	7.56841	+	2.39148i	0.953530	+	0.301298i
$64$	1.57610	−	4.85074i	0.197012	−	0.606342i
$65$	−2.47430	+	4.28561i	−0.306899	+	0.531565i
$66$	−0.226845	−	5.06514i	−0.0279227	−	0.623476i
$67$	−4.09951	−	7.10057i	−0.500835	−	0.867472i	−1.00000		0.000964734i	$-0.999693\pi$
$67$	−4.09951	−	7.10057i	−0.500835	−	0.867472i	0.499164	−	0.866507i	$-0.333640\pi$
$68$	−0.0324170	−	0.0360027i	−0.00393114	−	0.00436597i
$69$	−4.85851	−	5.20059i	−0.584896	−	0.626078i
$70$	−4.86141	+	5.09782i	−0.581050	+	0.609306i
$71$	6.15655	−	2.00038i	0.730648	−	0.237402i	0.0800145	−	0.996794i	$-0.474503\pi$
$71$	6.15655	−	2.00038i	0.730648	−	0.237402i	0.650634	+	0.759392i	$0.274503\pi$
$72$	8.52292	−	0.313202i	1.00444	−	0.0369112i
$73$	5.63692	+	0.592464i	0.659752	+	0.0693427i	0.428487	−	0.903548i	$-0.359047\pi$
$73$	5.63692	+	0.592464i	0.659752	+	0.0693427i	0.231265	+	0.972891i	$0.425714\pi$
$74$	−7.46662	−	3.32435i	−0.867977	−	0.386448i
$75$	5.36339	+	4.65374i	0.619311	+	0.537368i
$76$			2.11639i			0.242767i
$77$	8.72482	+	0.936749i	0.994286	+	0.106752i
$78$	−0.307899	−	2.48886i	−0.0348627	−	0.281808i
$79$	1.10418	−	0.994206i	0.124230	−	0.111857i	−0.604674	−	0.796473i	$-0.706697\pi$
$79$	1.10418	−	0.994206i	0.124230	−	0.111857i	0.728904	+	0.684616i	$0.240030\pi$
$80$	−0.0824252	+	0.185130i	−0.00921542	+	0.0206982i
$81$	3.40190	+	8.33229i	0.377988	+	0.925810i
$82$	−4.41557	−	0.938558i	−0.487618	−	0.103646i
$83$	4.09272	+	12.5961i	0.449234	+	1.38260i	0.877773	+	0.479078i	$0.159029\pi$
$83$	4.09272	+	12.5961i	0.449234	+	1.38260i	−0.428538	+	0.903524i	$0.640971\pi$
$84$	−0.641932	+	5.55836i	−0.0700405	+	0.606467i
$85$	0.0703527	+	0.0968322i	0.00763082	+	0.0105029i
$86$	−0.198727	+	0.178934i	−0.0214293	+	0.0192950i
$87$	8.86298	+	11.7393i	0.950212	+	1.25858i
$88$	9.16782	−	2.20303i	0.977293	−	0.234844i
$89$	−13.1138	−	7.57127i	−1.39006	−	0.802553i	−0.396742	−	0.917930i	$-0.629859\pi$
$89$	−13.1138	−	7.57127i	−1.39006	−	0.802553i	−0.993322	+	0.115377i	$0.963192\pi$
$90$	−7.96895	−	0.542630i	−0.840001	−	0.0571982i
$91$	4.33850	+	0.124229i	0.454798	+	0.0130227i
$92$	2.94895	−	4.05888i	0.307449	−	0.423168i
$93$	−9.09131	−	0.787027i	−0.942725	−	0.0816109i
$94$	−0.267718	−	0.241054i	−0.0276130	−	0.0248629i
$95$	0.546551	−	5.20008i	0.0560749	−	0.533517i
$96$	2.20089	+	9.49359i	0.224628	+	0.968935i
$97$	−1.75630	+	5.40534i	−0.178325	+	0.548829i	−0.999770	−	0.0214595i	$-0.993169\pi$
$97$	−1.75630	+	5.40534i	−0.178325	+	0.548829i	0.821444	+	0.570289i	$0.193169\pi$
$98$	5.95987	+	1.62824i	0.602038	+	0.164477i
$99$	5.50858	+	8.28587i	0.553633	+	0.832761i
$100$	−2.50287	+	4.33511i	−0.250287	+	0.433511i
$101$	−0.551559	+	0.117238i	−0.0548822	+	0.0116656i	−0.235271	−	0.971930i	$-0.575598\pi$
$101$	−0.551559	+	0.117238i	−0.0548822	+	0.0116656i	0.180389	+	0.983595i	$0.442264\pi$
$102$	−0.0580224	−	0.0176814i	−0.00574508	−	0.00175071i
$103$	−11.9055	+	5.30069i	−1.17309	+	0.522292i	−0.898373	−	0.439234i	$-0.855250\pi$
$103$	−11.9055	+	5.30069i	−1.17309	+	0.522292i	−0.274714	+	0.961526i	$0.588583\pi$
$104$	4.43542	−	1.44115i	0.434928	−	0.141317i
$105$	3.01269	−	13.4914i	0.294008	−	1.31663i
$106$	−3.72403	+	5.12568i	−0.361710	+	0.497850i
$107$	1.08312	+	10.3052i	0.104709	+	0.996239i	0.913140	+	0.407647i	$0.133651\pi$
$107$	1.08312	+	10.3052i	0.104709	+	0.996239i	−0.808431	+	0.588591i	$0.799683\pi$
$108$	−5.31145	+	3.47000i	−0.511094	+	0.333901i
$109$	−1.21388	+	0.700832i	−0.116268	+	0.0671275i	−0.557006	−	0.830508i	$-0.688050\pi$
$109$	−1.21388	+	0.700832i	−0.116268	+	0.0671275i	0.440738	+	0.897636i	$0.354717\pi$
$110$	−8.75462	+	1.15444i	−0.834720	+	0.110071i
$111$	15.9179	−	1.96922i	1.51086	−	0.186910i
$112$	0.177224	−	0.0135117i	0.0167461	−	0.00127674i
$113$	−11.4288	−	15.7304i	−1.07513	−	1.47979i	−0.864773	−	0.502162i	$-0.832538\pi$
$113$	−11.4288	−	15.7304i	−1.07513	−	1.47979i	−0.210355	−	0.977625i	$-0.567462\pi$
$114$	1.36682	+	2.27007i	0.128014	+	0.212612i
$115$	−8.29392	+	9.21133i	−0.773412	+	0.858961i
$116$	−6.93834	+	7.70581i	−0.644209	+	0.715467i
$117$	3.03699	+	3.87259i	0.280770	+	0.358021i
$118$	−5.14626	−	7.08322i	−0.473752	−	0.652063i
$119$	0.0454257	−	0.0946405i	0.00416417	−	0.00867568i
$120$	−1.82366	−	14.7413i	−0.166477	−	1.34569i
$121$	7.78144	+	7.77491i	0.707403	+	0.706810i
$122$	10.5651	−	6.09977i	0.956521	−	0.552248i
$123$	8.37348	−	2.89177i	0.755011	−	0.260742i
$124$	−0.672412	−	6.39758i	−0.0603844	−	0.574519i
$125$	−1.59627	+	2.19708i	−0.142775	+	0.196513i
$126$	2.90118	+	6.37655i	0.258458	+	0.568069i
$127$	−7.37346	+	2.39578i	−0.654289	+	0.212591i	−0.617304	−	0.786725i	$-0.711775\pi$
$127$	−7.37346	+	2.39578i	−0.654289	+	0.212591i	−0.0369846	+	0.999316i	$0.511775\pi$
$128$	−6.16765	+	2.74601i	−0.545148	+	0.242716i
$129$	0.152972	−	0.501985i	0.0134684	−	0.0441973i
$130$	−4.27225	+	0.908095i	−0.374701	+	0.0796452i
$131$	9.77773	−	16.9355i	0.854284	−	1.47966i	−0.0230238	−	0.999735i	$-0.507329\pi$
$131$	9.77773	−	16.9355i	0.854284	−	1.47966i	0.877308	−	0.479928i	$-0.159337\pi$
$132$	−4.99728	+	4.92185i	−0.434957	+	0.428392i
$133$	−4.24116	+	1.74460i	−0.367755	+	0.151276i
$134$	2.23622	−	6.88238i	0.193180	−	0.594547i
$135$	13.9466	−	7.15432i	1.20033	−	0.615746i
$136$	0.0117908	−	0.112182i	0.00101105	−	0.00961951i
$137$	4.88851	+	4.40163i	0.417653	+	0.376057i	0.850996	−	0.525173i	$-0.175999\pi$
$137$	4.88851	+	4.40163i	0.417653	+	0.376057i	−0.433342	+	0.901229i	$0.642666\pi$
$138$	0.541760	−	6.25812i	0.0461177	−	0.532727i
$139$	5.96489	−	8.20997i	0.505935	−	0.696360i	−0.477292	−	0.878745i	$-0.658382\pi$
$139$	5.96489	−	8.20997i	0.505935	−	0.696360i	0.983227	+	0.182384i	$0.0583815\pi$
$140$	9.74091	+	0.278921i	0.823257	+	0.0235732i
$141$	0.694094	+	0.134261i	0.0584532	+	0.0113068i
$142$	4.94802	+	2.85674i	0.415229	+	0.239733i
$143$	4.13797	+	3.53266i	0.346035	+	0.295416i
$144$	0.140263	+	0.144717i	0.0116886	+	0.0120598i
$145$	19.0379	−	17.1418i	1.58101	−	1.42355i
$146$	2.94047	+	4.04721i	0.243355	+	0.334949i
$147$	−11.6679	+	3.29551i	−0.962351	+	0.271809i
$148$	3.49398	+	10.7534i	0.287203	+	0.883921i
$149$	−14.4232	−	3.06575i	−1.18159	−	0.251156i	−0.425094	−	0.905149i	$-0.639759\pi$
$149$	−14.4232	−	3.06575i	−1.18159	−	0.251156i	−0.756500	+	0.653993i	$0.773092\pi$
$150$	0.115099	+	6.26632i	0.00939780	+	0.511643i
$151$	−1.15489	+	2.59393i	−0.0939839	+	0.211091i	−0.954420	−	0.298467i	$-0.903525\pi$
$151$	−1.15489	+	2.59393i	−0.0939839	+	0.211091i	0.860436	+	0.509559i	$0.170191\pi$
$152$	−3.66197	+	3.29725i	−0.297025	+	0.267443i
$153$	0.115445	−	0.0290076i	0.00933317	−	0.00234512i
$154$	4.53831	+	6.27591i	0.365707	+	0.505728i
$155$			15.8928i			1.27654i
$156$	−2.27368	+	2.62040i	−0.182040	+	0.209800i
$157$	−7.84006	−	3.49062i	−0.625705	−	0.278582i	0.0692899	−	0.997597i	$-0.477927\pi$
$157$	−7.84006	−	3.49062i	−0.625705	−	0.278582i	−0.694995	+	0.719015i	$0.744593\pi$
$158$	1.30422	+	0.137079i	0.103758	+	0.0109054i
$159$	1.07233	−	12.3869i	0.0850410	−	0.982347i
$160$	16.1420	−	5.24486i	1.27614	−	0.414643i
$161$	10.5647	+	2.56372i	0.832618	+	0.202049i
$162$	−3.45612	+	7.15224i	−0.271539	+	0.561933i
$163$	10.2002	+	11.3284i	0.798940	+	0.887312i	0.995652	−	0.0931488i	$-0.0296932\pi$
$163$	10.2002	+	11.3284i	0.798940	+	0.887312i	−0.196713	+	0.980461i	$0.563027\pi$
$164$	3.12245	+	5.40825i	0.243823	+	0.422313i
$165$	13.5496	−	10.8027i	1.05484	−	0.840990i
$166$	−5.84480	+	10.1235i	−0.453644	+	0.785735i
$167$	3.26943	−	10.0623i	0.252996	−	0.778642i	−0.741222	−	0.671260i	$-0.765753\pi$
$167$	3.26943	−	10.0623i	0.252996	−	0.778642i	0.994218	−	0.107382i	$-0.0342467\pi$
$168$	−10.6177	+	7.54898i	−0.819173	+	0.582417i
$169$	−8.34004	−	6.05940i	−0.641542	−	0.466107i
$170$	−0.0219640	+	0.103332i	−0.00168456	+	0.00792523i
$171$	−4.59577	−	2.43287i	−0.351447	−	0.186046i
$172$	0.367910	+	0.0386689i	0.0280529	+	0.00294847i
$173$	−0.828685	−	7.88441i	−0.0630038	−	0.599441i	−0.979785	−	0.200052i	$-0.935889\pi$
$173$	−0.828685	−	7.88441i	−0.0630038	−	0.599441i	0.916782	−	0.399389i	$-0.130778\pi$
$174$	−2.46557	+	12.7463i	−0.186914	+	0.966296i
$175$	−10.7506	−	1.44210i	−0.812667	−	0.109013i
$176$	0.183648	+	0.126161i	0.0138430	+	0.00950972i
$177$	15.8219	+	6.69895i	1.18924	+	0.503524i
$178$	−2.77874	−	13.0729i	−0.208275	−	0.979858i
$179$	−2.72773	+	6.12657i	−0.203880	+	0.457922i	−0.986328	−	0.164794i	$-0.947304\pi$
$179$	−2.72773	+	6.12657i	−0.203880	+	0.457922i	0.782448	+	0.622716i	$0.213971\pi$
$180$	6.81874	+	8.69483i	0.508239	+	0.648075i
$181$	−2.55100	−	7.85116i	−0.189614	−	0.583572i	0.810383	−	0.585900i	$-0.199259\pi$
$181$	−2.55100	−	7.85116i	−0.189614	−	0.583572i	−0.999997	+	0.00232806i	$0.999259\pi$
$182$	2.48076	+	2.91902i	0.183886	+	0.216372i
$183$	−11.5875	+	20.9495i	−0.856573	+	1.54863i
$184$	11.6174	−	1.22104i	0.856446	−	0.0900161i
$185$	−5.80787	−	27.3239i	−0.427003	−	2.00889i
$186$	−4.85295	−	6.42787i	−0.355836	−	0.471315i
$187$	0.118765	−	0.0566787i	0.00868497	−	0.00414475i
$188$			0.498366i			0.0363471i
$189$	−11.3321	−	7.78350i	−0.824291	−	0.566166i
$190$	3.73356	−	2.71259i	0.270861	−	0.196792i
$191$	−7.26950	−	16.3276i	−0.526003	−	1.18142i	−0.959870	−	0.280445i	$-0.909518\pi$
$191$	−7.26950	−	16.3276i	−0.526003	−	1.18142i	0.433868	−	0.900977i	$-0.357149\pi$
$192$	−5.06042	+	7.24108i	−0.365204	+	0.522580i
$193$	16.1648	+	14.5548i	1.16357	+	1.04768i	0.998109	+	0.0614631i	$0.0195767\pi$
$193$	16.1648	+	14.5548i	1.16357	+	1.04768i	0.165457	+	0.986217i	$0.447090\pi$
$194$	−4.58265	+	2.04033i	−0.329015	+	0.146487i
$195$	6.26326	−	5.85128i	0.448521	−	0.419019i
$196$	−3.84294	−	7.63430i	−0.274496	−	0.545307i
$197$	−11.7938			−0.840272			−0.420136	−	0.907461i	$-0.638018\pi$
$197$	−11.7938			−0.840272			−0.420136	+	0.907461i	$0.638018\pi$
$198$	−2.18150	+	8.50661i	−0.155033	+	0.604539i
$199$	0.846848	+	1.46678i	0.0600314	+	0.103978i	0.894479	−	0.447109i	$-0.147547\pi$
$199$	0.846848	+	1.46678i	0.0600314	+	0.103978i	−0.834448	+	0.551087i	$0.814213\pi$
$200$	−11.4004	+	2.42323i	−0.806129	+	0.171348i
$201$	3.20718	+	13.8342i	0.226217	+	0.975792i
$202$	−0.402639	−	0.292534i	−0.0283295	−	0.0205826i
$203$	−21.1616	−	7.55203i	−1.48525	−	0.530049i
$204$	0.0355320	+	0.0760175i	0.00248774	+	0.00532229i
$205$	−6.27537	−	14.0947i	−0.438291	−	0.984418i
$206$	−10.5080	−	4.67845i	−0.732125	−	0.325963i
$207$	5.42399	+	11.0695i	0.376994	+	0.769384i
$208$	0.0954401	+	0.0551024i	0.00661758	+	0.00382066i
$209$	−5.51241	−	1.63159i	−0.381302	−	0.112860i
$210$	10.6284	−	5.99174i	0.733427	−	0.413470i
$211$	9.41386	+	3.05875i	0.648077	+	0.210573i	0.614566	−	0.788866i	$-0.289331\pi$
$211$	9.41386	+	3.05875i	0.648077	+	0.210573i	0.0335107	+	0.999438i	$0.489331\pi$
$212$	8.71671	−	0.916163i	0.598666	−	0.0629224i
$213$	−11.2103	+	0.205910i	−0.768119	+	0.0141087i
$214$	−6.11958	+	6.79648i	−0.418326	+	0.464598i
$215$	−0.893988	−	0.190023i	−0.0609695	−	0.0129595i
$216$	−14.2792	−	3.78422i	−0.971574	−	0.257484i
$217$	12.2662	−	6.62120i	0.832683	−	0.449476i
$218$	−1.17658	−	0.382293i	−0.0796878	−	0.0258921i
$219$	−9.04029	−	3.82764i	−0.610886	−	0.258648i
$220$	9.29069	+	7.93163i	0.626378	+	0.534750i
$221$	0.0563698	−	0.0325451i	0.00379184	−	0.00218922i
$222$	10.6925	+	9.27772i	0.717633	+	0.622680i
$223$	14.9963	−	10.8954i	1.00423	−	0.729612i	0.0412352	−	0.999149i	$-0.486871\pi$
$223$	14.9963	−	10.8954i	1.00423	−	0.729612i	0.962990	+	0.269537i	$0.0868707\pi$
$224$	−10.7730	−	10.2734i	−0.719803	−	0.686422i
$225$	−6.53660	−	10.4184i	−0.435773	−	0.694559i
$226$	3.56804	−	16.7863i	0.237343	−	1.11661i
$227$	0.0558625	−	0.531496i	0.00370772	−	0.0352766i	−0.992512	−	0.122150i	$-0.961021\pi$
$227$	0.0558625	−	0.531496i	0.00370772	−	0.0352766i	0.996219	+	0.0868737i	$0.0276877\pi$
$228$	1.06855	−	3.50650i	0.0707662	−	0.232223i
$229$	−4.14188	−	4.60003i	−0.273703	−	0.303978i	0.590585	−	0.806976i	$-0.298897\pi$
$229$	−4.14188	−	4.60003i	−0.273703	−	0.303978i	−0.864288	+	0.502997i	$0.832231\pi$
$230$	−10.9400			−0.721365
$231$	−13.9826	−	5.95712i	−0.919987	−	0.391949i
$232$	−24.1430			−1.58506
$233$	−5.45941	−	6.06329i	−0.357658	−	0.397220i	0.537284	−	0.843401i	$-0.319450\pi$
$233$	−5.45941	−	6.06329i	−0.357658	−	0.397220i	−0.894942	+	0.446182i	$0.852784\pi$
$234$	−0.746466	+	4.27907i	−0.0487980	+	0.279732i
$235$	0.128701	−	1.22451i	0.00839554	−	0.0798783i
$236$	−2.51823	+	11.8474i	−0.163923	+	0.771197i
$237$	−2.33140	+	1.08974i	−0.151441	+	0.0707863i
$238$	0.0889032	−	0.0260979i	0.00576274	−	0.00169168i
$239$	7.75836	−	5.63678i	0.501847	−	0.364613i	−0.307875	−	0.951427i	$-0.599618\pi$
$239$	7.75836	−	5.63678i	0.501847	−	0.364613i	0.809722	+	0.586814i	$0.199618\pi$
$240$	0.230035	−	0.265113i	0.0148487	−	0.0171130i
$241$	2.84020	−	1.63979i	0.182953	−	0.105628i	−0.405726	−	0.913995i	$-0.632981\pi$
$241$	2.84020	−	1.63979i	0.182953	−	0.105628i	0.588679	+	0.808367i	$0.299648\pi$
$242$	−0.504048	+	9.69564i	−0.0324014	+	0.623259i
$243$	−1.42946	−	15.5228i	−0.0917002	−	0.995787i
$244$	−16.0507	−	5.21519i	−1.02754	−	0.333868i
$245$	7.47077	+	19.7503i	0.477290	+	1.26180i
$246$	6.84197	+	3.78441i	0.436228	+	0.241285i
$247$	−2.78134	−	0.591192i	−0.176972	−	0.0376166i
$248$	10.0221	−	11.1307i	0.636403	−	0.706797i
$249$	−0.421286	−	22.9360i	−0.0266979	−	1.45351i
$250$	−2.38381	+	0.250549i	−0.150766	+	0.0158461i
$251$	−3.99903	−	1.29936i	−0.252417	−	0.0820152i	0.180076	−	0.983653i	$-0.442366\pi$
$251$	−3.99903	−	1.29936i	−0.252417	−	0.0820152i	−0.432492	+	0.901638i	$0.642366\pi$
$252$	3.86994	−	8.88515i	0.243783	−	0.559712i
$253$	8.29845	+	10.8100i	0.521719	+	0.679622i
$254$	−5.92605	−	3.42141i	−0.371834	−	0.214678i
$255$	−0.0676728	−	0.195955i	−0.00423783	−	0.0122712i
$256$	−14.7625	−	6.57268i	−0.922654	−	0.410792i
$257$	10.5666	+	23.7331i	0.659129	+	1.48043i	0.864960	+	0.501841i	$0.167344\pi$
$257$	10.5666	+	23.7331i	0.659129	+	1.48043i	−0.205831	+	0.978588i	$0.565990\pi$
$258$	0.419599	−	0.196129i	0.0261231	−	0.0122104i
$259$	−18.6691	+	15.8661i	−1.16004	+	0.985872i
$260$	4.88826	+	3.55153i	0.303157	+	0.220256i
$261$	−8.75740	−	23.9248i	−0.542070	−	1.48091i
$262$	16.8827	−	3.58853i	1.04302	−	0.221700i
$263$	−4.99074	−	8.64422i	−0.307742	−	0.533025i	0.670126	−	0.742247i	$-0.266240\pi$
$263$	−4.99074	−	8.64422i	−0.307742	−	0.533025i	−0.977868	+	0.209222i	$0.932907\pi$
$264$	−16.3018	−	0.978698i	−1.00331	−	0.0602347i
$265$	−21.6540			−1.33020
$266$	−3.64906	−	1.75148i	−0.223738	−	0.107390i
$267$	17.9047	+	19.1654i	1.09575	+	1.17290i
$268$	−9.14548	+	4.07183i	−0.558649	+	0.248727i
$269$	2.90623	+	2.61678i	0.177196	+	0.159548i	0.752956	−	0.658071i	$-0.228627\pi$
$269$	2.90623	+	2.61678i	0.177196	+	0.159548i	−0.575760	+	0.817618i	$0.695294\pi$
$270$	12.9292	+	4.92249i	0.786847	+	0.299573i
$271$	3.20158	+	7.19086i	0.194482	+	0.436813i	0.984294	−	0.176535i	$-0.0564889\pi$
$271$	3.20158	+	7.19086i	0.194482	+	0.436813i	−0.789813	+	0.613348i	$0.789822\pi$
$272$	0.00215644	−	0.00156675i	0.000130754	−	9.49980e-5i
$273$	−7.12543	−	2.39629i	−0.431250	−	0.145030i
$274$			5.80594i			0.350750i
$275$	−9.36180	−	9.86114i	−0.564538	−	0.594649i
$276$	−6.93520	+	5.23598i	−0.417450	+	0.315169i
$277$	6.84007	+	32.1800i	0.410980	+	1.93351i	0.354350	+	0.935113i	$0.384702\pi$
$277$	6.84007	+	32.1800i	0.410980	+	1.93351i	0.0566295	+	0.998395i	$0.481965\pi$
$278$	8.90775	−	0.936243i	0.534252	−	0.0561521i
$279$	14.6654	+	5.89409i	0.877994	+	0.352870i
$280$	14.6933	+	17.2892i	0.878095	+	1.03323i
$281$	5.87610	+	18.0848i	0.350538	+	1.07885i	0.958551	+	0.284919i	$0.0919668\pi$
$281$	5.87610	+	18.0848i	0.350538	+	1.07885i	−0.608013	+	0.793927i	$0.708033\pi$
$282$	0.321857	+	0.534554i	0.0191663	+	0.0318322i
$283$	−1.07903	+	2.42354i	−0.0641418	+	0.144065i	−0.942772	−	0.333438i	$-0.891791\pi$
$283$	−1.07903	+	2.42354i	−0.0641418	+	0.144065i	0.878630	+	0.477503i	$0.158458\pi$
$284$	−1.64333	−	7.73125i	−0.0975136	−	0.458765i
$285$	−3.53101	+	8.33970i	−0.209159	+	0.494001i
$286$	0.126712	+	4.80046i	0.00749266	+	0.283857i
$287$	−8.26398	+	10.7155i	−0.487807	+	0.632513i
$288$	1.14672	−	16.8405i	0.0675710	−	0.992334i
$289$	1.77682	+	16.9053i	0.104519	+	0.994430i
$290$	22.4869	+	2.36347i	1.32048	+	0.138788i
$291$	5.63900	−	8.06899i	0.330564	−	0.473013i
$292$	1.43887	−	6.76934i	0.0842033	−	0.396146i
$293$	15.6864	+	11.3968i	0.916407	+	0.665808i	0.942627	−	0.333848i	$-0.108347\pi$
$293$	15.6864	+	11.3968i	0.916407	+	0.665808i	−0.0262203	+	0.999656i	$0.508347\pi$
$294$	−9.05241	−	5.70680i	−0.527947	−	0.332827i
$295$	9.24697	−	28.4593i	0.538380	−	1.65696i
$296$	−13.1630	+	22.7989i	−0.765083	+	1.32516i
$297$	−4.94331	−	16.5095i	−0.286840	−	0.957978i
$298$	−6.50725	−	11.2709i	−0.376955	−	0.652905i
$299$	4.51038	+	5.00929i	0.260842	+	0.289695i
$300$	6.33559	−	5.91885i	0.365786	−	0.341725i
$301$	0.225788	+	0.769152i	0.0130142	+	0.0443332i
$302$	−2.38344	+	0.774428i	−0.137152	+	0.0445633i
$303$	0.973032	+	0.0842346i	0.0558992	+	0.00483915i
$304$	−0.115805	−	0.0121716i	−0.00664189	−	0.000698090i
$305$	38.0906	+	16.9590i	2.18106	+	0.971072i
$306$	0.0872061	+	0.0585900i	0.00498524	+	0.00334937i
$307$			26.9617i			1.53879i	0.638775	+	0.769394i	$0.279442\pi$
$307$			26.9617i			1.53879i	−0.638775	+	0.769394i	$0.720558\pi$
$308$	2.25104	−	10.4751i	0.128265	−	0.596872i
$309$	22.4017	−	2.77134i	1.27439	−	0.157656i
$310$	−10.4242	+	9.38603i	−0.592057	+	0.533091i
$311$	4.13641	−	9.29053i	0.234554	−	0.526817i	−0.757469	−	0.652871i	$-0.773564\pi$
$311$	4.13641	−	9.29053i	0.234554	−	0.526817i	0.992023	+	0.126053i	$0.0402311\pi$
$312$	−8.07636	+	0.148346i	−0.457234	+	0.00839843i
$313$	−20.4456	−	4.34584i	−1.15565	−	0.245642i	−0.410070	−	0.912054i	$-0.634496\pi$
$313$	−20.4456	−	4.34584i	−1.15565	−	0.245642i	−0.745583	+	0.666412i	$0.767829\pi$
$314$	−2.34068	−	7.20386i	−0.132092	−	0.406538i
$315$	−11.8032	+	20.8319i	−0.665035	+	1.17374i
$316$	−1.06635	−	1.46770i	−0.0599866	−	0.0825645i
$317$	−7.30172	+	6.57449i	−0.410105	+	0.369260i	−0.848207	−	0.529665i	$-0.822318\pi$
$317$	−7.30172	+	6.57449i	−0.410105	+	0.369260i	0.438102	+	0.898925i	$0.355651\pi$
$318$	8.75799	−	6.61216i	0.491124	−	0.370791i
$319$	−14.7218	−	24.0125i	−0.824263	−	1.34444i
$320$	13.3244	+	7.69282i	0.744854	+	0.430042i
$321$	3.40845	−	17.6208i	0.190241	−	0.983496i
$322$	4.55779	+	8.44359i	0.253996	+	0.470543i
$323$	−0.0404248	+	0.0556400i	−0.00224930	+	0.00309589i
$324$	10.5521	−	3.06751i	0.586230	−	0.170417i
$325$	−4.99800	−	4.50022i	−0.277239	−	0.249627i
$326$	−1.40638	+	13.3808i	−0.0778920	+	0.741093i
$327$	2.36503	−	0.548284i	0.130786	−	0.0303202i
$328$	−4.49319	+	13.8286i	−0.248095	+	0.763557i
$329$	−0.998704	+	0.410818i	−0.0550604	+	0.0226491i
$330$	15.0878	+	2.50742i	0.830555	+	0.138029i
$331$	6.26895	−	10.8581i	0.344573	−	0.596817i	−0.640703	−	0.767789i	$-0.721357\pi$
$331$	6.26895	−	10.8581i	0.344573	−	0.596817i	0.985276	+	0.170971i	$0.0546905\pi$
$332$	15.8179	−	3.36219i	0.868119	−	0.184524i
$333$	−27.3675	−	4.77415i	−1.49973	−	0.261622i
$334$	8.53080	−	3.79816i	0.466785	−	0.207826i
$335$	23.5225	−	7.64291i	1.28517	−	0.417577i
$336$	−0.300452	−	0.0670923i	−0.0163910	−	0.00366018i
$337$	14.5199	−	19.9849i	0.790950	−	1.08865i	−0.203039	−	0.979171i	$-0.565082\pi$
$337$	14.5199	−	19.9849i	0.790950	−	1.08865i	0.993989	−	0.109479i	$-0.0349181\pi$
$338$	−0.951076	−	9.04888i	−0.0517317	−	0.492194i
$339$	10.9934	+	31.8328i	0.597080	+	1.72892i
$340$	0.126563	−	0.0730712i	0.00686384	−	0.00396284i
$341$	17.1817	+	3.18071i	0.930442	+	0.172245i
$342$	−1.11845	−	4.45121i	−0.0604786	−	0.240694i
$343$	12.1310	−	13.9943i	0.655011	−	0.755619i
$344$	0.506281	+	0.696836i	0.0272969	+	0.0375709i
$345$	18.3923	−	11.0741i	0.990209	−	0.596208i
$346$	4.68205	−	5.19994i	0.251708	−	0.279551i
$347$	16.7156	−	18.5646i	0.897341	−	0.996598i	−0.102658	−	0.994717i	$-0.532735\pi$
$347$	16.7156	−	18.5646i	0.897341	−	0.996598i	0.999998	−	0.00188085i	$-0.000598695\pi$
$348$	15.3863	−	9.26411i	0.824790	−	0.496609i
$349$	2.00287	+	2.75671i	0.107211	+	0.147563i	0.859251	−	0.511554i	$-0.170930\pi$
$349$	2.00287	+	2.75671i	0.107211	+	0.147563i	−0.752040	+	0.659117i	$0.770930\pi$
$350$	−5.40321	−	7.90307i	−0.288814	−	0.422437i
$351$	−3.07655	−	7.94957i	−0.164214	−	0.424316i
$352$	−2.43962	−	18.5008i	−0.130032	−	0.986095i
$353$	16.7987	−	9.69871i	0.894102	−	0.516210i	0.0188200	−	0.999823i	$-0.494009\pi$
$353$	16.7987	−	9.69871i	0.894102	−	0.516210i	0.875282	+	0.483613i	$0.160676\pi$
$354$	4.95022	+	14.3340i	0.263101	+	0.761843i
$355$	2.04117	+	19.4205i	0.108334	+	1.03073i
$356$	−10.8676	+	14.9579i	−0.575979	+	0.792767i
$357$	−0.123046	+	0.133868i	−0.00651227	+	0.00708505i
$358$	−5.62942	+	1.82911i	−0.297524	+	0.0966715i
$359$	−11.4988	+	5.11958i	−0.606882	+	0.270201i	−0.687085	−	0.726577i	$-0.741110\pi$
$359$	−11.4988	+	5.11958i	−0.606882	+	0.270201i	0.0802029	+	0.996779i	$0.474443\pi$
$360$	−4.42126	+	25.3446i	−0.233021	+	1.33578i
$361$	−15.6460	+	3.32566i	−0.823475	+	0.175035i
$362$	3.64307	−	6.30998i	0.191476	−	0.331645i
$363$	−8.96704	−	16.8105i	−0.470647	−	0.882321i
$364$	0.704568	−	5.25241i	0.0369294	−	0.275301i
$365$	−5.28353	+	16.2610i	−0.276553	+	0.851142i
$366$	−20.5843	+	4.77206i	−1.07596	+	0.249439i
$367$	2.28793	−	21.7682i	0.119429	−	1.13629i	−0.756548	−	0.653938i	$-0.773116\pi$
$367$	2.28793	−	21.7682i	0.119429	−	1.13629i	0.875977	−	0.482352i	$-0.160217\pi$
$368$	0.205135	+	0.184705i	0.0106934	+	0.00962840i
$369$	−15.3335	+	0.563477i	−0.798228	+	0.0293335i
$370$	14.4920	−	19.9465i	0.753401	−	1.03697i
$371$	9.02140	+	16.7127i	0.468368	+	0.867681i
$372$	−2.11601	+	10.9392i	−0.109710	+	0.567171i
$373$	12.0201	+	6.93982i	0.622378	+	0.359330i	0.777794	−	0.628519i	$-0.216338\pi$
$373$	12.0201	+	6.93982i	0.622378	+	0.359330i	−0.155416	+	0.987849i	$0.549672\pi$
$374$	0.107317	+	0.0444257i	0.00554922	+	0.00229720i
$375$	3.75404	−	2.83424i	0.193858	−	0.146360i
$376$	−0.862318	+	0.776435i	−0.0444707	+	0.0400416i
$377$	−8.18875	−	11.2708i	−0.421742	−	0.580478i
$378$	−1.58730	−	12.0296i	−0.0816418	−	0.618738i
$379$	1.58680	+	4.88367i	0.0815084	+	0.250857i	0.983503	−	0.180889i	$-0.0578976\pi$
$379$	1.58680	+	4.88367i	0.0815084	+	0.250857i	−0.901995	+	0.431746i	$0.857898\pi$
$380$	−6.24474	−	1.32736i	−0.320348	−	0.0680921i
$381$	13.4262	−	0.246611i	0.687844	−	0.0126343i
$382$	6.41615	−	14.4109i	0.328279	−	0.737326i
$383$	−5.10548	+	4.59700i	−0.260878	+	0.234895i	−0.789182	−	0.614160i	$-0.789495\pi$
$383$	−5.10548	+	4.59700i	−0.260878	+	0.234895i	0.528304	+	0.849056i	$0.322828\pi$
$384$	11.6052	−	1.43569i	0.592224	−	0.0732646i
$385$	−8.23607	+	25.1564i	−0.419749	+	1.28209i
$386$			19.1985i			0.977176i
$387$	−0.506896	+	0.754470i	−0.0257669	+	0.0383519i
$388$	6.33959	+	2.82257i	0.321844	+	0.143294i
$389$	17.5670	+	1.84637i	0.890684	+	0.0936146i	0.538804	−	0.842431i	$-0.318876\pi$
$389$	17.5670	+	1.84637i	0.890684	+	0.0936146i	0.351879	+	0.936045i	$0.385543\pi$
$390$	7.53688	+	0.652462i	0.381645	+	0.0330387i
$391$	0.155056	−	0.0503808i	0.00784152	−	0.00254787i
$392$	7.22242	−	18.5434i	0.364787	−	0.936581i
$393$	−24.7506	+	23.1226i	−1.24850	+	1.16638i
$394$	−6.96520	−	7.73564i	−0.350902	−	0.389716i
$395$	2.24104	+	3.88159i	0.112759	+	0.195304i
$396$	10.7646	−	5.63159i	0.540943	−	0.282998i
$397$	−15.1135	+	26.1773i	−0.758524	+	1.31380i	0.185079	+	0.982724i	$0.440746\pi$
$397$	−15.1135	+	26.1773i	−0.758524	+	1.31380i	−0.943603	+	0.331079i	$0.892587\pi$
$398$	−0.461942	+	1.42171i	−0.0231551	+	0.0712640i
$399$	7.90771	−	0.749187i	0.395881	−	0.0375063i
$400$	−0.222815	−	0.161885i	−0.0111408	−	0.00809424i
$401$	−0.458153	+	2.15544i	−0.0228791	+	0.107638i	−0.988105	−	0.153778i	$-0.950856\pi$
$401$	−0.458153	+	2.15544i	−0.0228791	+	0.107638i	0.965226	+	0.261416i	$0.0841893\pi$
$402$	−7.17989	+	10.2739i	−0.358100	+	0.512415i
$403$	8.59547	+	0.903420i	0.428171	+	0.0450026i
$404$	0.0719675	+	0.684725i	0.00358052	+	0.0340663i
$405$	−26.7193	+	4.81197i	−1.32769	+	0.239109i
$406$	−7.54424	−	18.3402i	−0.374415	−	0.910208i
$407$	−30.7022	+	0.810410i	−1.52185	+	0.0401706i
$408$	−0.0761749	+	0.179913i	−0.00377122	+	0.00890703i
$409$	6.61898	+	31.1398i	0.327287	+	1.53977i	0.767012	+	0.641633i	$0.221743\pi$
$409$	6.61898	+	31.1398i	0.327287	+	1.53977i	−0.439725	+	0.898133i	$0.644924\pi$
$410$	5.53872	−	12.4402i	0.273538	−	0.614376i
$411$	−5.87708	−	9.76092i	−0.289895	−	0.481470i
$412$	4.91717	+	15.1335i	0.242252	+	0.745574i
$413$	−25.8175	+	4.71969i	−1.27039	+	0.232241i
$414$	−4.05727	+	10.0951i	−0.199404	+	0.496148i
$415$	−39.7336	+	4.17617i	−1.95045	+	0.205000i
$416$	−1.91904	−	9.02838i	−0.0940887	−	0.442653i
$417$	−14.0279	+	10.5909i	−0.686952	+	0.518639i
$418$	−2.18536	−	4.57923i	−0.106889	−	0.223978i
$419$		−	20.2477i		−	0.989165i	−0.869131	−	0.494582i	$-0.835321\pi$
$419$		−	20.2477i		−	0.989165i	0.869131	−	0.494582i	$-0.164679\pi$
$420$	−15.9982	−	5.38022i	−0.780632	−	0.262528i
$421$	−23.8800	+	17.3498i	−1.16384	+	0.845579i	−0.990259	−	0.139241i	$-0.955534\pi$
$421$	−23.8800	+	17.3498i	−1.16384	+	0.845579i	−0.173581	+	0.984820i	$0.555534\pi$
$422$	3.55340	+	7.98107i	0.172977	+	0.388513i
$423$	−1.08221	−	0.572889i	−0.0526188	−	0.0278548i
$424$	15.1655	+	13.6551i	0.736504	+	0.663151i
$425$	−0.148605	+	0.0661632i	−0.00720840	+	0.00320939i
$426$	−6.75569	−	7.23135i	−0.327314	−	0.350360i
$427$	−2.78004	−	36.4640i	−0.134536	−	1.76462i
$428$	12.6519			0.611552
$429$	−5.07231	−	7.94225i	−0.244893	−	0.383455i
$430$	−0.403336	−	0.698599i	−0.0194506	−	0.0336894i
$431$	−24.5950	+	5.22783i	−1.18470	+	0.251816i	−0.757802	−	0.652484i	$-0.773727\pi$
$431$	−24.5950	+	5.22783i	−1.18470	+	0.251816i	−0.426898	+	0.904300i	$0.640394\pi$
$432$	−0.159326	−	0.310590i	−0.00766558	−	0.0149433i
$433$	0.569597	+	0.413836i	0.0273731	+	0.0198877i	0.601388	−	0.798957i	$-0.294615\pi$
$433$	0.569597	+	0.413836i	0.0273731	+	0.0198877i	−0.574015	+	0.818845i	$0.694615\pi$
$434$	11.5871	+	4.13514i	0.556199	+	0.198493i
$435$	−40.1973	+	18.7890i	−1.92731	+	0.900862i
$436$	0.696099	+	1.56346i	0.0333371	+	0.0748763i
$437$	−6.50648	−	2.89687i	−0.311247	−	0.138576i
$438$	−2.82846	−	8.19015i	−0.135149	−	0.391340i
$439$	28.3468	+	16.3660i	1.35292	+	0.781108i	0.988657	−	0.150189i	$-0.0479882\pi$
$439$	28.3468	+	16.3660i	1.35292	+	0.781108i	0.364261	+	0.931297i	$0.381322\pi$
$440$	0.750508	+	28.4328i	0.0357791	+	1.35548i
$441$	20.9956	+	0.430905i	0.999789	+	0.0205193i
$442$	0.0546377	+	0.0177529i	0.00259885	+	0.000844418i
$443$	14.5134	−	1.52542i	0.689554	−	0.0724750i	0.246731	−	0.969084i	$-0.420644\pi$
$443$	14.5134	−	1.52542i	0.689554	−	0.0724750i	0.442823	+	0.896609i	$0.353977\pi$
$444$	−0.359654	−	19.5806i	−0.0170684	−	0.929253i
$445$	30.5650	−	33.9458i	1.44892	−	1.60919i
$446$	16.0030	+	3.40153i	0.757762	+	0.161067i
$447$	22.3489	+	12.3616i	1.05707	+	0.584682i
$448$	0.386238	−	13.4888i	0.0182480	−	0.637284i
$449$	26.3661	+	8.56687i	1.24429	+	0.404296i	0.855873	−	0.517186i	$-0.173021\pi$
$449$	26.3661	+	8.56687i	1.24429	+	0.404296i	0.388421	+	0.921482i	$0.373021\pi$
$450$	2.97311	−	10.4403i	0.140154	−	0.492162i
$451$	−16.4937	+	3.96345i	−0.776658	+	0.186631i
$452$	−20.5601	+	11.8704i	−0.967067	+	0.558336i
$453$	3.22311	−	3.71461i	0.151435	−	0.174528i
$454$	0.381604	−	0.277252i	0.0179096	−	0.0130121i
$455$	−3.08758	+	12.7235i	−0.144748	+	0.596487i
$456$	7.73202	−	3.61409i	0.362085	−	0.169245i
$457$	2.39799	−	11.2817i	0.112173	−	0.527734i	−0.885798	−	0.464071i	$-0.846388\pi$
$457$	2.39799	−	11.2817i	0.112173	−	0.527734i	0.997971	−	0.0636633i	$-0.0202784\pi$
$458$	0.571073	−	5.43340i	0.0266845	−	0.253886i
$459$	−0.205918	−	0.0102265i	−0.00961144	−	0.000477333i
$460$	10.1268	+	11.2470i	0.472166	+	0.524394i
$461$	25.3261			1.17955			0.589776	−	0.807567i	$-0.299216\pi$
$461$	25.3261			1.17955			0.589776	+	0.807567i	$0.299216\pi$
$462$	−4.35055	−	12.6895i	−0.202406	−	0.590368i
$463$	20.0145			0.930154			0.465077	−	0.885270i	$-0.346027\pi$
$463$	20.0145			0.930154			0.465077	+	0.885270i	$0.346027\pi$
$464$	−0.381746	−	0.423972i	−0.0177221	−	0.0196824i
$465$	8.02415	−	26.3317i	0.372111	−	1.22110i
$466$	0.752731	−	7.16175i	0.0348696	−	0.331762i
$467$	0.857852	−	4.03588i	0.0396967	−	0.186758i	−0.953832	−	0.300341i	$-0.902899\pi$
$467$	0.857852	−	4.03588i	0.0396967	−	0.186758i	0.993529	+	0.113583i	$0.0362328\pi$
$468$	5.09011	−	3.19359i	0.235291	−	0.147624i
$469$	−15.6987	−	14.9706i	−0.724897	−	0.691280i
$470$	0.879176	−	0.638759i	0.0405534	−	0.0294637i
$471$	11.2273	+	9.74174i	0.517325	+	0.448876i
$472$	−24.4227	+	14.1005i	−1.12415	+	0.649026i
$473$	−0.384352	+	0.928458i	−0.0176725	+	0.0426906i
$474$	−2.09165	−	0.885603i	−0.0960729	−	0.0406771i
$475$	6.75838	+	2.19593i	0.310096	+	0.100756i
$476$	−0.109125	−	0.0672396i	−0.00500173	−	0.00308192i
$477$	−8.03071	+	19.9816i	−0.367701	+	0.914896i
$478$	8.27917	+	1.75979i	0.378680	+	0.0804910i
$479$	3.32919	−	3.69744i	0.152115	−	0.168940i	−0.662271	−	0.749264i	$-0.730407\pi$
$479$	3.32919	−	3.69744i	0.152115	−	0.168940i	0.814386	+	0.580324i	$0.197074\pi$
$480$	−29.3927	+	0.539882i	−1.34159	+	0.0246421i
$481$	−15.1080	+	1.58791i	−0.688865	+	0.0724026i
$482$	2.75292	+	0.894479i	0.125392	+	0.0407424i
$483$	−16.2096	−	9.58168i	−0.737561	−	0.435982i
$484$	10.4343	−	8.45675i	0.474285	−	0.384398i
$485$	−14.8478	−	8.57237i	−0.674203	−	0.389251i
$486$	9.33731	−	10.1051i	0.423549	−	0.458376i
$487$	1.57490	+	0.701192i	0.0713657	+	0.0317741i	0.442109	−	0.896961i	$-0.354230\pi$
$487$	1.57490	+	0.701192i	0.0713657	+	0.0317741i	−0.370743	+	0.928735i	$0.620897\pi$
$488$	−15.9826	−	35.8975i	−0.723498	−	1.62500i
$489$	−11.1803	−	23.9193i	−0.505592	−	1.08167i
$490$	−8.54229	+	16.5643i	−0.385901	+	0.748300i
$491$	−1.33662	−	0.971113i	−0.0603209	−	0.0438257i	0.557216	−	0.830367i	$-0.311869\pi$
$491$	−1.33662	−	0.971113i	−0.0603209	−	0.0438257i	−0.617537	+	0.786542i	$0.711869\pi$
$492$	−2.44280	−	10.5370i	−0.110130	−	0.475047i
$493$	−0.329597	+	0.0700580i	−0.0148443	+	0.00315525i
$494$	−1.25484	−	2.17345i	−0.0564581	−	0.0977883i
$495$	−27.9036	+	11.0572i	−1.25417	+	0.496983i
$496$	0.353932			0.0158920
$497$	14.1385	−	9.66626i	0.634197	−	0.433591i
$498$	14.7951	−	13.8219i	0.662984	−	0.619375i
$499$	35.8312	−	15.9531i	1.60403	−	0.714158i	0.607258	−	0.794505i	$-0.292269\pi$
$499$	35.8312	−	15.9531i	1.60403	−	0.714158i	0.996767	+	0.0803466i	$0.0256027\pi$
$500$	2.46420	+	2.21877i	0.110202	+	0.0992266i
$501$	−10.4972	+	15.0208i	−0.468982	+	0.671079i
$502$	−1.50950	−	3.39038i	−0.0673721	−	0.151320i
$503$	−29.2551	+	21.2551i	−1.30442	+	0.947717i	−0.999988	−	0.00481705i	$-0.998467\pi$
$503$	−29.2551	+	21.2551i	−1.30442	+	0.947717i	−0.304432	+	0.952534i	$0.598467\pi$
$504$	21.4031	−	7.14660i	0.953371	−	0.318335i
$505$		−	1.70099i		−	0.0756931i
$506$	−2.18949	+	11.8273i	−0.0973345	+	0.525785i
$507$	10.7587	+	14.2502i	0.477811	+	0.632874i
$508$	1.96815	+	9.25941i	0.0873225	+	0.410820i
$509$	−39.6559	+	4.16800i	−1.75772	+	0.184743i	−0.927783	−	0.373119i	$-0.878288\pi$
$509$	−39.6559	+	4.16800i	−1.75772	+	0.184743i	−0.829933	+	0.557863i	$0.811622\pi$
$510$	0.0885622	−	0.160115i	0.00392160	−	0.00709000i
$511$	14.7516	−	2.69673i	0.652571	−	0.119296i
$512$	−0.234836	−	0.722751i	−0.0103784	−	0.0319414i
$513$	6.38608	+	6.35121i	0.281952	+	0.280413i
$514$	−9.32625	+	20.9471i	−0.411363	+	0.923937i
$515$	−8.17357	−	38.4536i	−0.360171	−	1.69447i
$516$	−0.590040	−	0.249822i	−0.0259751	−	0.0109978i
$517$	−1.29806	−	0.384206i	−0.0570886	−	0.0168974i
$518$	−21.4324	−	2.87498i	−0.941685	−	0.126319i
$519$	−2.60778	+	13.4815i	−0.114469	+	0.591773i
$520$	1.47054	+	13.9913i	0.0644875	+	0.613557i
$521$	−5.16137	−	0.542482i	−0.226124	−	0.0237666i	−0.00921104	−	0.999958i	$-0.502932\pi$
$521$	−5.16137	−	0.542482i	−0.226124	−	0.0237666i	−0.216913	+	0.976191i	$0.569599\pi$
$522$	10.5205	−	19.8736i	0.460471	−	0.869846i
$523$	1.13775	−	5.35269i	0.0497503	−	0.234057i	−0.946246	−	0.323447i	$-0.895158\pi$
$523$	1.13775	−	5.35269i	0.0497503	−	0.234057i	0.995997	+	0.0893899i	$0.0284917\pi$
$524$	−19.3170	−	14.0346i	−0.843867	−	0.613105i
$525$	17.0838	+	7.81718i	0.745596	+	0.341170i
$526$	2.72237	−	8.37860i	0.118701	−	0.365324i
$527$	0.104521	−	0.181036i	0.00455302	−	0.00788607i
$528$	−0.240575	−	0.301749i	−0.0104697	−	0.0131319i
$529$	−3.05812	−	5.29682i	−0.132962	−	0.230297i
$530$	−12.7885	−	14.2031i	−0.555497	−	0.616941i
$531$	−22.8319	−	19.0873i	−0.990820	−	0.828320i
$532$	1.57719	+	5.37273i	0.0683798	+	0.232937i
$533$	−7.97970	+	2.59276i	−0.345639	+	0.112305i
$534$	−1.99651	+	23.0626i	−0.0863975	+	0.998016i
$535$	−31.0863	−	3.26730i	−1.34398	−	0.141258i
$536$	−21.2938	−	9.48060i	−0.919751	−	0.409499i
$537$	7.61263	−	8.77348i	0.328509	−	0.378604i
$538$			3.45164i			0.148811i
$539$	22.8472	−	4.12391i	0.984097	−	0.177629i
$540$	−6.90755	−	17.8486i	−0.297254	−	0.768081i
$541$	−11.5313	+	10.3828i	−0.495768	+	0.446392i	−0.878693	−	0.477388i	$-0.841584\pi$
$541$	−11.5313	+	10.3828i	−0.495768	+	0.446392i	0.382924	+	0.923780i	$0.374917\pi$
$542$	−2.82575	+	6.34674i	−0.121376	+	0.272616i
$543$	0.262588	+	14.2960i	0.0112687	+	0.613501i
$544$	−0.218368	−	0.0464156i	−0.00936247	−	0.00199005i
$545$	−1.30659	−	4.02128i	−0.0559683	−	0.172253i
$546$	−2.63641	−	6.08884i	−0.112828	−	0.260578i
$547$	10.0257	+	13.7991i	0.428666	+	0.590009i	0.967646	−	0.252310i	$-0.0811902\pi$
$547$	10.0257	+	13.7991i	0.428666	+	0.590009i	−0.538980	+	0.842318i	$0.681190\pi$
$548$	5.96884	−	5.37437i	0.254976	−	0.229582i
$549$	29.7757	−	28.8593i	1.27080	−	1.23168i
$550$	0.939086	−	11.9643i	0.0400428	−	0.510160i
$551$	12.7480	+	7.36008i	0.543084	+	0.313550i
$552$	−19.8645	−	3.84247i	−0.845491	−	0.163546i
$553$	2.06219	−	3.34678i	0.0876932	−	0.142320i
$554$	−17.0675	+	23.4914i	−0.725129	+	0.998054i
$555$	−4.17293	+	48.2034i	−0.177131	+	2.04612i
$556$	−9.20813	−	8.29104i	−0.390512	−	0.351618i
$557$	−0.879733	+	8.37010i	−0.0372755	+	0.354653i	0.959948	+	0.280180i	$0.0903941\pi$
$557$	−0.879733	+	8.37010i	−0.0372755	+	0.354653i	−0.997223	+	0.0744729i	$0.976273\pi$
$558$	4.79514	+	13.1001i	0.202995	+	0.554572i
$559$	−0.153590	+	0.472702i	−0.00649617	+	0.0199932i
$560$	−0.0712833	+	0.531402i	−0.00301227	+	0.0224558i
$561$	−0.225390	+	0.0339435i	−0.00951598	+	0.00143309i
$562$	−8.39163	+	14.5347i	−0.353980	+	0.613111i
$563$	0.656382	−	0.139518i	0.0276632	−	0.00587999i	−0.194059	−	0.980990i	$-0.562165\pi$
$563$	0.656382	−	0.139518i	0.0276632	−	0.00587999i	0.221722	+	0.975110i	$0.428832\pi$
$564$	0.251620	−	0.825707i	0.0105951	−	0.0347685i
$565$	53.5828	−	23.8566i	2.25424	−	1.00365i
$566$	−2.22688	+	0.723558i	−0.0936028	+	0.0304134i
$567$	14.8456	+	18.6174i	0.623456	+	0.781858i
$568$	10.8171	−	14.8884i	0.453875	−	0.624705i
$569$	−1.44992	−	13.7951i	−0.0607840	−	0.578321i	−0.981949	−	0.189148i	$-0.939427\pi$
$569$	−1.44992	−	13.7951i	−0.0607840	−	0.578321i	0.921165	−	0.389173i	$-0.127239\pi$
$570$	−7.55544	+	2.60926i	−0.316463	+	0.109290i
$571$	−19.9419	+	11.5135i	−0.834542	+	0.481823i	−0.855405	−	0.517959i	$-0.826692\pi$
$571$	−19.9419	+	11.5135i	−0.834542	+	0.481823i	0.0208634	+	0.999782i	$0.493358\pi$
$572$	4.81786	−	4.57390i	0.201445	−	0.191244i
$573$	3.80069	+	30.7223i	0.158776	+	1.28344i
$574$	−11.9089	+	0.907945i	−0.497069	+	0.0378969i
$575$	−9.90167	−	13.6285i	−0.412928	−	0.568347i
$576$	12.0402	−	9.44228i	0.501676	−	0.393429i
$577$	6.19531	−	6.88058i	0.257914	−	0.286442i	−0.600256	−	0.799808i	$-0.704935\pi$
$577$	6.19531	−	6.88058i	0.257914	−	0.286442i	0.858170	+	0.513365i	$0.171601\pi$
$578$	−10.0390	+	11.1494i	−0.417567	+	0.463755i
$579$	−19.4337	−	32.2763i	−0.807637	−	1.34136i
$580$	−18.3856	−	25.3056i	−0.763421	−	1.05076i
$581$	19.7768	+	28.9268i	0.820482	+	1.20009i
$582$	8.62282	−	1.06674i	0.357427	−	0.0442177i
$583$	−4.33373	+	23.4101i	−0.179485	+	0.969548i
$584$	13.9546	−	8.05671i	0.577447	−	0.333389i
$585$	−13.3314	+	6.53231i	−0.551186	+	0.270078i
$586$	1.78883	+	17.0196i	0.0738959	+	0.703072i
$587$	10.2371	−	14.0902i	0.422531	−	0.581565i	−0.543687	−	0.839288i	$-0.682972\pi$
$587$	10.2371	−	14.0902i	0.422531	−	0.581565i	0.966219	+	0.257723i	$0.0829723\pi$
$588$	2.51261	+	14.5890i	0.103618	+	0.601640i
$589$	−8.68510	+	2.82196i	−0.357863	+	0.116277i
$590$	24.1278	−	10.7424i	0.993325	−	0.442257i
$591$	19.5403	+	5.95457i	0.803780	+	0.244938i
$592$	−0.608500	+	0.129341i	−0.0250092	+	0.00531587i
$593$	−4.00225	+	6.93209i	−0.164353	+	0.284667i	−0.936425	−	0.350867i	$-0.885887\pi$
$593$	−4.00225	+	6.93209i	−0.164353	+	0.284667i	0.772073	+	0.635534i	$0.219220\pi$
$594$	7.90929	−	12.9926i	0.324522	−	0.533093i
$595$	0.250761	+	0.193392i	0.0102802	+	0.00792832i
$596$	−5.56357	+	17.1229i	−0.227893	+	0.701382i
$597$	−0.662517	−	2.85778i	−0.0271150	−	0.116961i
$598$	−0.621881	+	5.91680i	−0.0254306	+	0.241956i
$599$	−6.13877	−	5.52737i	−0.250823	−	0.225842i	0.534122	−	0.845407i	$-0.320642\pi$
$599$	−6.13877	−	5.52737i	−0.250823	−	0.225842i	−0.784945	+	0.619565i	$0.787309\pi$
$600$	20.1120	+	1.74108i	0.821067	+	0.0710792i
$601$	4.40591	−	6.06421i	0.179721	−	0.247364i	−0.709646	−	0.704558i	$-0.751145\pi$
$601$	4.40591	−	6.06421i	0.179721	−	0.247364i	0.889367	+	0.457194i	$0.151145\pi$
$602$	−0.371147	+	0.602344i	−0.0151268	+	0.0245497i
$603$	1.67102	−	24.5403i	0.0680492	−	0.999356i
$604$	3.00243	+	1.73346i	0.122167	+	0.0705333i
$605$	−27.8215	+	18.0841i	−1.13110	+	0.735222i
$606$	0.519406	+	0.687968i	0.0210994	+	0.0279468i
$607$	12.8890	−	11.6053i	0.523147	−	0.471044i	−0.364737	−	0.931110i	$-0.618841\pi$
$607$	12.8890	−	11.6053i	0.523147	−	0.471044i	0.887884	+	0.460067i	$0.152175\pi$
$608$	5.73241	+	7.88999i	0.232480	+	0.319981i
$609$	31.2482	+	23.1967i	1.26624	+	0.939979i
$610$	11.3721	+	34.9997i	0.460443	+	1.41710i
$611$	−0.654947	−	0.139213i	−0.0264963	−	0.00563197i
$612$	−0.0204900	−	0.143888i	−0.000828258	−	0.00581632i
$613$	−0.251599	+	0.565101i	−0.0101620	+	0.0228242i	−0.918555	−	0.395293i	$-0.870643\pi$
$613$	−0.251599	+	0.565101i	−0.0101620	+	0.0228242i	0.908393	+	0.418117i	$0.137310\pi$
$614$	−17.6844	+	15.9231i	−0.713686	+	0.642606i
$615$	3.28093	+	26.5209i	0.132300	+	1.06943i
$616$	21.6319	−	12.4248i	0.871576	−	0.500609i
$617$		−	32.9052i		−	1.32471i	−0.749189	−	0.662356i	$-0.769557\pi$
$617$		−	32.9052i		−	1.32471i	0.749189	−	0.662356i	$-0.230443\pi$
$618$	15.0478	+	13.0568i	0.605312	+	0.525221i
$619$	15.9565	+	7.10431i	0.641348	+	0.285546i	0.701529	−	0.712641i	$-0.252501\pi$
$619$	15.9565	+	7.10431i	0.641348	+	0.285546i	−0.0601811	+	0.998187i	$0.519168\pi$
$620$	19.2988	+	2.02838i	0.775057	+	0.0814618i
$621$	−3.39774	−	21.0788i	−0.136347	−	0.845864i
$622$	8.53663	−	2.77372i	0.342288	−	0.111216i
$623$	−38.9335	−	9.44789i	−1.55984	−	0.378522i
$624$	−0.130307	−	0.139482i	−0.00521647	−	0.00558376i
$625$	−19.1979	−	21.3215i	−0.767918	−	0.852859i
$626$	−9.22434	−	15.9770i	−0.368679	−	0.638570i
$627$	8.30936	+	5.48644i	0.331844	+	0.219107i
$628$	−5.23930	+	9.07473i	−0.209071	+	0.362121i
$629$	−0.113541	+	0.349445i	−0.00452719	+	0.0139333i
$630$	−20.6346	+	4.56113i	−0.822101	+	0.181720i
$631$	−24.1139	−	17.5198i	−0.959959	−	0.697451i	−0.00681806	−	0.999977i	$-0.502170\pi$
$631$	−24.1139	−	17.5198i	−0.959959	−	0.697451i	−0.953141	+	0.302525i	$0.902170\pi$
$632$	0.878222	−	4.13171i	0.0349338	−	0.164351i
$633$	−14.0528	−	9.82079i	−0.558550	−	0.390342i
$634$	−8.62454	−	0.906475i	−0.342524	−	0.0360007i
$635$	−2.44463	−	23.2591i	−0.0970123	−	0.923011i
$636$	−14.9047	−	2.88306i	−0.591009	−	0.114321i
$637$	11.1064	−	2.91779i	0.440052	−	0.115607i
$638$	7.05556	−	23.8375i	0.279332	−	0.943737i
$639$	18.6776	+	5.31884i	0.738874	+	0.210410i
$640$	−4.23431	−	19.9209i	−0.167376	−	0.787441i
$641$	−6.42935	+	14.4406i	−0.253944	+	0.570368i	−0.994863	−	0.101226i	$-0.967723\pi$
$641$	−6.42935	+	14.4406i	−0.253944	+	0.570368i	0.740919	+	0.671594i	$0.234390\pi$
$642$	13.5706	−	8.17090i	0.535588	−	0.322480i
$643$	−4.12229	−	12.6871i	−0.162567	−	0.500330i	0.836282	−	0.548300i	$-0.184725\pi$
$643$	−4.12229	−	12.6871i	−0.162567	−	0.500330i	−0.998849	+	0.0479699i	$0.984725\pi$
$644$	4.46151	−	12.5016i	0.175808	−	0.492633i
$645$	1.38524	+	0.766202i	0.0545440	+	0.0301692i
$646$	−0.0603690	+	0.00634504i	−0.00237519	+	0.000249642i
$647$	9.33920	+	43.9375i	0.367162	+	1.72736i	0.642743	+	0.766082i	$0.277796\pi$
$647$	9.33920	+	43.9375i	0.367162	+	1.72736i	−0.275581	+	0.961278i	$0.588870\pi$
$648$	21.7475	+	13.4792i	0.854323	+	0.529514i
$649$	−28.9166	−	15.6926i	−1.13508	−	0.615988i
$650$		−	5.93599i		−	0.232829i
$651$	−23.6660	+	4.77711i	−0.927543	+	0.187230i
$652$	15.0580	−	10.9403i	0.589719	−	0.428456i
$653$	0.475340	+	1.06763i	0.0186015	+	0.0417797i	0.922607	−	0.385740i	$-0.126054\pi$
$653$	0.475340	+	1.06763i	0.0186015	+	0.0417797i	−0.904006	+	0.427520i	$0.859387\pi$
$654$	1.75637	+	1.22744i	0.0686795	+	0.0479966i
$655$	43.8385	+	39.4723i	1.71291	+	1.54231i
$656$	−0.313888	+	0.139752i	−0.0122553	+	0.00545640i
$657$	13.0457	+	10.9061i	0.508961	+	0.425488i
$658$	−0.859277	−	0.412437i	−0.0334981	−	0.0160785i
$659$	22.3699			0.871406			0.435703	−	0.900090i	$-0.356500\pi$
$659$	22.3699			0.871406			0.435703	+	0.900090i	$0.356500\pi$
$660$	−11.3885	−	17.8321i	−0.443296	−	0.694115i
$661$	1.72647	+	2.99033i	0.0671518	+	0.116310i	0.897647	−	0.440716i	$-0.145275\pi$
$661$	1.72647	+	2.99033i	0.0671518	+	0.116310i	−0.830495	+	0.557027i	$0.811942\pi$
$662$	10.8243	−	2.30077i	0.420698	−	0.0894221i
$663$	−0.109827	+	0.0254611i	−0.00426533	+	0.000988829i
$664$	30.4612	+	22.1314i	1.18212	+	0.858864i
$665$	−2.48775	−	13.6084i	−0.0964707	−	0.527710i
$666$	−13.0314	−	20.7701i	−0.504956	−	0.804827i
$667$	−14.1931	−	31.8783i	−0.549561	−	1.23433i
$668$	−11.8014	−	5.25433i	−0.456610	−	0.203296i
$669$	−30.3473	+	10.4804i	−1.17329	+	0.405196i
$670$	18.9050	+	10.9148i	0.730365	+	0.421676i
$671$	25.9577	−	37.7856i	1.00208	−	1.45870i
$672$	12.6621	+	22.4605i	0.488452	+	0.866434i
$673$	−31.6299	−	10.2772i	−1.21924	−	0.396156i	−0.372436	−	0.928058i	$-0.621477\pi$
$673$	−31.6299	−	10.2772i	−1.21924	−	0.396156i	−0.846806	+	0.531902i	$0.821477\pi$
$674$	21.6835	−	2.27903i	0.835218	−	0.0877849i
$675$	5.56988	+	20.5618i	0.214385	+	0.791423i
$676$	−8.42240	+	9.35402i	−0.323938	+	0.359770i
$677$	17.5630	+	3.73314i	0.675003	+	0.143476i	0.532645	−	0.846339i	$-0.321198\pi$
$677$	17.5630	+	3.73314i	0.675003	+	0.143476i	0.142358	+	0.989815i	$0.454532\pi$
$678$	−14.3869	+	26.0106i	−0.552525	+	0.998931i
$679$	−0.430398	+	15.0310i	−0.0165172	+	0.576837i
$680$	0.323615	+	0.105149i	0.0124101	+	0.00403228i
$681$	−0.360902	+	0.852394i	−0.0138298	+	0.0326638i
$682$	8.06097	+	13.1481i	0.308670	+	0.503467i
$683$	8.40895	−	4.85491i	0.321760	−	0.185768i	−0.330417	−	0.943835i	$-0.607189\pi$
$683$	8.40895	−	4.85491i	0.321760	−	0.185768i	0.652177	+	0.758067i	$0.273856\pi$
$684$	−3.54080	+	5.27017i	−0.135386	+	0.201510i
$685$	−16.0537	+	11.6637i	−0.613380	+	0.445646i
$686$	16.3433	−	0.307963i	0.623990	−	0.0117581i
$687$	4.53988	+	9.71266i	0.173207	+	0.370561i
$688$	−0.00423179	+	0.0199090i	−0.000161336	+	0.000759024i
$689$	−1.23091	+	11.7113i	−0.0468940	+	0.446167i
$690$	18.1258	+	5.52352i	0.690037	+	0.210277i
$691$	−1.37462	−	1.52667i	−0.0522929	−	0.0580771i	0.716431	−	0.697658i	$-0.245775\pi$
$691$	−1.37462	−	1.52667i	−0.0522929	−	0.0580771i	−0.768724	+	0.639581i	$0.779108\pi$
$692$	−9.67986			−0.367973
$693$	20.1591	+	16.9296i	0.765780	+	0.643103i
$694$	22.0486			0.836954
$695$	20.4837	+	22.7495i	0.776992	+	0.862937i
$696$	40.0008	+	12.1896i	1.51623	+	0.462045i
$697$	−0.0212126	+	0.201825i	−0.000803486	+	0.00764466i
$698$	−0.625291	+	2.94177i	−0.0236676	+	0.111347i
$699$	5.98402	+	12.8023i	0.226336	+	0.484226i
$700$	−3.12324	+	12.8704i	−0.118047	+	0.486457i
$701$	22.2188	−	16.1429i	0.839193	−	0.609709i	−0.0829521	−	0.996554i	$-0.526435\pi$
$701$	22.2188	−	16.1429i	0.839193	−	0.609709i	0.922145	+	0.386844i	$0.126435\pi$
$702$	3.39723	−	6.71281i	0.128220	−	0.253359i
$703$	13.9007	−	8.02556i	0.524274	−	0.302690i
$704$	10.9834	−	12.8653i	0.413951	−	0.484880i
$705$	−0.831480	+	1.96383i	−0.0313154	+	0.0739620i
$706$	16.2825	+	5.29049i	0.612799	+	0.199110i
$707$	−1.31284	+	0.708659i	−0.0493743	+	0.0266519i
$708$	10.1539	−	18.3576i	0.381607	−	0.689922i
$709$	−7.15493	−	1.52083i	−0.268709	−	0.0571159i	0.0715865	−	0.997434i	$-0.477194\pi$
$709$	−7.15493	−	1.52083i	−0.268709	−	0.0571159i	−0.340296	+	0.940319i	$0.610527\pi$
$710$	−11.5326	+	12.8082i	−0.432810	+	0.480684i
$711$	4.41293	−	0.628412i	0.165498	−	0.0235673i
$712$	−42.8128	+	4.49980i	−1.60448	+	0.168637i
$713$	20.5887	+	6.68966i	0.771051	+	0.250530i
$714$	−0.160474	−	0.00164658i	−0.00600559	−	6.16217e-5i
$715$	−13.0189	+	9.99412i	−0.486880	+	0.373759i
$716$	7.09140	+	4.09422i	0.265018	+	0.153008i
$717$	−15.7002	+	5.42206i	−0.586336	+	0.202491i
$718$	−10.1490	−	4.51861i	−0.378756	−	0.168633i
$719$	−6.91639	−	15.5345i	−0.257938	−	0.579338i	0.737436	−	0.675417i	$-0.236036\pi$
$719$	−6.91639	−	15.5345i	−0.257938	−	0.579338i	−0.995374	+	0.0960795i	$0.969370\pi$
$720$	−0.514982	+	0.323105i	−0.0191922	+	0.0120414i
$721$	−26.2735	+	22.3288i	−0.978477	+	0.831568i
$722$	−11.4216	−	8.29828i	−0.425068	−	0.308830i
$723$	−5.53364	+	1.28286i	−0.205798	+	0.0477101i
$724$	−9.85930	+	2.09566i	−0.366418	+	0.0778845i
$725$	17.4083	+	30.1520i	0.646527	+	1.11982i
$726$	5.73036	−	15.8095i	0.212674	−	0.586747i
$727$	−32.3373			−1.19932			−0.599662	−	0.800253i	$-0.704698\pi$
$727$	−32.3373			−1.19932			−0.599662	+	0.800253i	$0.704698\pi$
$728$	10.1859	−	6.96395i	0.377514	−	0.258101i
$729$	−5.46893	+	26.4403i	−0.202553	+	0.979271i
$730$	−13.7861	+	6.13798i	−0.510247	+	0.227177i
$731$	0.00893376	+	0.00804400i	0.000330427	+	0.000297518i
$732$	23.9602	+	16.7445i	0.885594	+	0.618896i
$733$	7.06916	+	15.8776i	0.261105	+	0.586452i	0.995760	−	0.0919889i	$-0.0293224\pi$
$733$	7.06916	+	15.8776i	0.261105	+	0.586452i	−0.734655	+	0.678441i	$0.762656\pi$
$734$	15.6292	−	11.3552i	0.576883	−	0.419130i
$735$	−2.40605	−	36.4948i	−0.0887484	−	1.34613i
$736$		−	23.1192i		−	0.852183i
$737$	−3.55507	−	26.9597i	−0.130953	−	0.993074i
$738$	−9.42527	−	9.72457i	−0.346949	−	0.357966i
$739$	−1.69537	−	7.97608i	−0.0623651	−	0.293405i	0.935901	−	0.352262i	$-0.114588\pi$
$739$	−1.69537	−	7.97608i	−0.0623651	−	0.293405i	−0.998266	+	0.0588576i	$0.981254\pi$
$740$	−33.9208	+	3.56522i	−1.24696	+	0.131060i
$741$	4.30972	+	2.38378i	0.158321	+	0.0875703i
$742$	−5.63413	+	15.7875i	−0.206835	+	0.579576i
$743$	−10.1027	−	31.0928i	−0.370631	−	1.14069i	−0.946379	−	0.323058i	$-0.895289\pi$
$743$	−10.1027	−	31.0928i	−0.370631	−	1.14069i	0.575748	−	0.817627i	$-0.304711\pi$
$744$	−22.2247	+	13.3815i	−0.814795	+	0.490591i
$745$	18.0919	−	40.6351i	0.662837	−	1.48876i
$746$	2.54699	+	11.9826i	0.0932519	+	0.438716i
$747$	−10.8822	+	38.2137i	−0.398158	+	1.39817i
$748$	−0.0536674	−	0.151451i	−0.00196228	−	0.00553760i
$749$	10.4293	+	25.3538i	0.381079	+	0.926409i
$750$	4.07607	+	0.788449i	0.148837	+	0.0287901i
$751$	0.278494	+	2.64970i	0.0101624	+	0.0966888i	0.998427	−	0.0560605i	$-0.0178540\pi$
$751$	0.278494	+	2.64970i	0.0101624	+	0.0966888i	−0.988265	+	0.152749i	$0.951187\pi$
$752$	−0.0272697	−	0.00286616i	−0.000994425	−	0.000104518i
$753$	5.96968	+	4.17190i	0.217547	+	0.152033i
$754$	2.55651	−	12.0274i	0.0931027	−	0.438014i
$755$	−6.92948	−	5.03456i	−0.252189	−	0.183226i
$756$	−10.8979	+	12.7673i	−0.396351	+	0.464342i
$757$	0.652391	−	2.00785i	0.0237116	−	0.0729767i	−0.938501	−	0.345278i	$-0.887785\pi$
$757$	0.652391	−	2.00785i	0.0237116	−	0.0729767i	0.962212	+	0.272301i	$0.0877847\pi$
$758$	−2.26610	+	3.92501i	−0.0823086	+	0.142563i
$759$	−8.29122	−	22.1002i	−0.300952	−	0.802187i
$760$	−7.43234	−	12.8732i	−0.269599	−	0.466960i
$761$	15.0974	+	16.7673i	0.547279	+	0.607815i	0.951802	−	0.306713i	$-0.0992292\pi$
$761$	15.0974	+	16.7673i	0.547279	+	0.607815i	−0.404523	+	0.914528i	$0.632562\pi$
$762$	8.09103	+	8.66070i	0.293107	+	0.313744i
$763$	−2.55930	+	2.68376i	−0.0926530	+	0.0971588i
$764$	−20.7545	+	6.74354i	−0.750870	+	0.243973i
$765$	0.0131864	+	0.358831i	0.000476756	+	0.0129736i
$766$	−6.03042	−	0.633823i	−0.217888	−	0.0229009i
$767$	−14.8662	−	6.61888i	−0.536789	−	0.238994i
$768$	21.1404	+	18.3432i	0.762839	+	0.661905i
$769$		−	21.0411i		−	0.758763i	−0.925240	−	0.379381i	$-0.876137\pi$
$769$		−	21.0411i		−	0.758763i	0.925240	−	0.379381i	$-0.123863\pi$
$770$	−21.3644	+	9.45485i	−0.769920	+	0.340729i
$771$	−5.52452	−	44.6567i	−0.198961	−	1.60827i
$772$	19.7371	−	17.7714i	0.710355	−	0.639606i
$773$	−9.12635	+	20.4981i	−0.328252	+	0.737266i	−0.999994	−	0.00351930i	$-0.998880\pi$
$773$	−9.12635	+	20.4981i	−0.328252	+	0.737266i	0.671742	+	0.740785i	$0.265546\pi$
$774$	−0.794227	+	0.113100i	−0.0285479	+	0.00406529i
$775$	−21.1274	−	4.49077i	−0.758919	−	0.161313i
$776$	4.99297	+	15.3668i	0.179237	+	0.551636i
$777$	38.9422	−	16.8616i	1.39704	−	0.604906i
$778$	9.16374	+	12.6128i	0.328536	+	0.452191i
$779$	6.58820	−	5.93205i	0.236047	−	0.212538i
$780$	−6.30588	−	8.35231i	−0.225787	−	0.299061i
$781$	21.4039	+	1.68001i	0.765893	+	0.0601154i
$782$	0.124619	+	0.0719486i	0.00445635	+	0.00257288i
$783$	2.43010	+	44.0609i	0.0868449	+	1.57461i
$784$	0.439837	−	0.166373i	0.0157085	−	0.00594190i
$785$	15.2168	−	20.9441i	0.543109	−	0.747526i
$786$	−29.7836	−	2.57834i	−1.06235	−	0.0919664i
$787$	7.84057	+	7.05968i	0.279486	+	0.251650i	0.796937	−	0.604063i	$-0.206452\pi$
$787$	7.84057	+	7.05968i	0.279486	+	0.251650i	−0.517451	+	0.855713i	$0.673119\pi$
$788$	−1.50523	+	14.3213i	−0.0536214	+	0.510174i
$789$	3.90442	+	16.8418i	0.139001	+	0.599583i
$790$	−1.22245	+	3.76232i	−0.0434929	+	0.133857i
$791$	−40.7361	−	31.4165i	−1.44841	−	1.11704i
$792$	26.5152	+	9.85217i	0.942176	+	0.350082i
$793$	11.3374	−	19.6369i	0.402601	−	0.697326i
$794$	−26.0957	+	5.54681i	−0.926102	+	0.196849i
$795$	35.8770	+	10.9329i	1.27243	+	0.387751i
$796$	1.88921	−	0.841129i	0.0669612	−	0.0298130i
$797$	−24.8016	+	8.05854i	−0.878519	+	0.285448i	−0.713342	−	0.700816i	$-0.752819\pi$
$797$	−24.8016	+	8.05854i	−0.878519	+	0.285448i	−0.165177	+	0.986264i	$0.552819\pi$
$798$	5.16156	+	4.74428i	0.182717	+	0.167946i
$799$	−0.00951921	+	0.0131021i	−0.000336765	+	0.000463518i
$800$	2.41117	+	22.9407i	0.0852476	+	0.811076i
$801$	−19.9887	−	40.7937i	−0.706264	−	1.44137i
$802$	−1.68435	+	0.972460i	−0.0594765	+	0.0343388i
$803$	16.5224	+	8.96642i	0.583061	+	0.316418i
$804$	17.2083	−	2.12886i	0.606891	−	0.0750791i
$805$	−14.1907	+	29.5650i	−0.500155	+	1.04203i
$806$	4.48377	+	6.17139i	0.157934	+	0.217378i
$807$	−3.49393	−	5.80288i	−0.122992	−	0.204271i
$808$	−1.07265	+	1.19130i	−0.0377358	+	0.0419098i
$809$	25.7790	−	28.6305i	0.906341	−	1.00659i	−0.0935985	−	0.995610i	$-0.529837\pi$
$809$	25.7790	−	28.6305i	0.906341	−	1.00659i	0.999940	−	0.0109839i	$-0.00349634\pi$
$810$	−18.9362	−	14.6836i	−0.665350	−	0.515928i
$811$	5.99313	+	8.24884i	0.210447	+	0.289656i	0.901172	−	0.433462i	$-0.142708\pi$
$811$	5.99313	+	8.24884i	0.210447	+	0.289656i	−0.690724	+	0.723118i	$0.742708\pi$
$812$	−11.8713	+	24.7328i	−0.416601	+	0.867952i
$813$	−1.67387	−	13.5305i	−0.0587051	−	0.474534i
$814$	−18.6637	−	19.6592i	−0.654164	−	0.689055i
$815$	−39.8237	+	22.9922i	−1.39496	+	0.805383i
$816$	−0.00436390	+	0.00150707i	−0.000152767	+	5.27579e-5i
$817$	−0.0548945	−	0.522287i	−0.00192052	−	0.0182725i
$818$	−16.5158	+	22.7321i	−0.577463	+	0.794809i
$819$	10.5958	+	7.56781i	0.370246	+	0.264441i
$820$	−17.9162	+	5.82134i	−0.625662	+	0.203290i
$821$	32.2665	−	14.3660i	1.12611	−	0.501376i	0.242758	−	0.970087i	$-0.421948\pi$
$821$	32.2665	−	14.3660i	1.12611	−	0.501376i	0.883352	+	0.468711i	$0.155281\pi$
$822$	2.93137	−	9.61946i	0.102243	−	0.335517i
$823$	−43.5714	+	9.26139i	−1.51880	+	0.322832i	−0.890445	−	0.455091i	$-0.849607\pi$
$823$	−43.5714	+	9.26139i	−1.51880	+	0.322832i	−0.628359	+	0.777923i	$0.716273\pi$
$824$	−18.5246	+	32.0856i	−0.645335	+	1.11775i
$825$	10.5321	+	21.0649i	0.366681	+	0.733386i
$826$	−18.3430	−	14.1465i	−0.638236	−	0.492221i
$827$	10.4625	−	32.2003i	0.363817	−	1.11971i	−0.586902	−	0.809658i	$-0.699653\pi$
$827$	10.4625	−	32.2003i	0.363817	−	1.11971i	0.950719	−	0.310055i	$-0.100347\pi$
$828$	14.1340	−	5.17360i	0.491192	−	0.179795i
$829$	1.84575	−	17.5611i	0.0641054	−	0.609922i	−0.914558	−	0.404454i	$-0.867462\pi$
$829$	1.84575	−	17.5611i	0.0641054	−	0.609922i	0.978664	−	0.205468i	$-0.0658717\pi$
$830$	−26.2052	−	23.5953i	−0.909595	−	0.819003i
$831$	4.91456	−	56.7703i	0.170484	−	1.96934i
$832$	4.91799	−	6.76904i	0.170501	−	0.234674i
$833$	0.0447905	−	0.274110i	0.00155190	−	0.00949733i
$834$	−15.2313	−	2.94625i	−0.527418	−	0.102020i
$835$	27.6398	+	15.9578i	0.956514	+	0.552244i
$836$	−2.68480	+	6.48552i	−0.0928557	+	0.224307i
$837$	−21.3222	−	17.1699i	−0.737002	−	0.593479i
$838$	13.2806	−	11.9579i	0.458772	−	0.413080i
$839$	2.81951	+	3.88072i	0.0973402	+	0.133977i	0.854909	−	0.518778i	$-0.173613\pi$
$839$	2.81951	+	3.88072i	0.0973402	+	0.133977i	−0.757569	+	0.652755i	$0.773613\pi$
$840$	−15.6152	−	36.0637i	−0.538777	−	1.24432i
$841$	13.3251	+	41.0105i	0.459487	+	1.41416i
$842$	−25.4830	−	5.41658i	−0.878203	−	0.186668i
$843$	−0.604858	−	32.9302i	−0.0208324	−	1.13417i
$844$	4.91574	−	11.0409i	0.169207	−	0.380044i
$845$	23.1099	−	20.8083i	0.795005	−	0.715826i
$846$	−0.263371	−	1.04817i	−0.00905487	−	0.0360368i
$847$	25.5483	+	13.9387i	0.877848	+	0.478939i
$848$			0.482233i			0.0165599i
$849$	3.01140	−	3.47061i	0.103351	−	0.119111i
$850$	−0.131161	−	0.0583964i	−0.00449877	−	0.00200298i
$851$	−37.8419	−	3.97734i	−1.29720	−	0.136342i
$852$	−1.18072	+	13.6391i	−0.0404509	+	0.467267i
$853$	0.126171	−	0.0409955i	0.00432002	−	0.00140366i	−0.306856	−	0.951756i	$-0.599277\pi$
$853$	0.126171	−	0.0409955i	0.00432002	−	0.00140366i	0.311176	+	0.950352i	$0.399277\pi$
$854$	22.2752	−	23.3585i	0.762242	−	0.799310i
$855$	10.0609	−	12.0347i	0.344077	−	0.411578i
$856$	19.7111	+	21.8914i	0.673713	+	0.748234i
$857$	−11.1965	−	19.3928i	−0.382464	−	0.662446i	0.608950	−	0.793208i	$-0.291591\pi$
$857$	−11.1965	−	19.3928i	−0.382464	−	0.662446i	−0.991414	+	0.130762i	$0.958258\pi$
$858$	2.21377	−	8.01753i	0.0755768	−	0.273714i
$859$	2.34009	−	4.05315i	0.0798427	−	0.138292i	−0.823339	−	0.567550i	$-0.807892\pi$
$859$	2.34009	−	4.05315i	0.0798427	−	0.138292i	0.903182	+	0.429258i	$0.141225\pi$
$860$	−0.344845	+	1.06132i	−0.0117591	+	0.0361908i
$861$	19.1021	−	13.5813i	0.650999	−	0.462848i
$862$	−17.9544	−	13.0446i	−0.611529	−	0.444301i
$863$	0.000154560	0	0.000727149i	5.26129e−6	0	2.47524e-5i	−0.978145	−	0.207924i	$-0.933329\pi$
$863$	0.000154560	0	0.000727149i	5.26129e−6	0	2.47524e-5i	0.978150	+	0.207899i	$0.0666626\pi$
$864$	−10.4025	+	27.3228i	−0.353901	+	0.929541i
$865$	23.7839	+	2.49979i	0.808678	+	0.0849955i
$866$	0.0649553	+	0.618008i	0.00220727	+	0.0210008i
$867$	5.59145	−	28.9063i	0.189896	−	0.981710i
$868$	−6.47465	−	15.7400i	−0.219764	−	0.534250i
$869$	4.64490	−	1.64594i	0.157567	−	0.0558347i
$870$	−36.0637	−	15.2693i	−1.22267	−	0.517677i
$871$	−2.79646	−	13.1563i	−0.0947546	−	0.445785i
$872$	−1.62075	+	3.64027i	−0.0548856	+	0.123275i
$873$	−13.4168	+	10.5219i	−0.454091	+	0.356111i
$874$	−1.94253	−	5.97850i	−0.0657072	−	0.202226i
$875$	−2.41502	+	6.76715i	−0.0816426	+	0.228771i
$876$	−5.80173	+	10.4892i	−0.196022	+	0.354396i
$877$	35.5128	−	3.73254i	1.19918	−	0.126039i	0.516195	−	0.856471i	$-0.327348\pi$
$877$	35.5128	−	3.73254i	1.19918	−	0.126039i	0.682986	+	0.730432i	$0.260681\pi$
$878$	6.00651	+	28.2584i	0.202710	+	0.953675i
$879$	−20.2355	−	26.8025i	−0.682526	−	0.904025i
$880$	−0.487437	+	0.462755i	−0.0164315	+	0.0155995i
$881$			8.31743i			0.280221i	0.990136	+	0.140111i	$0.0447458\pi$
$881$			8.31743i			0.280221i	−0.990136	+	0.140111i	$0.955254\pi$
$882$	12.1170	+	14.0257i	0.408000	+	0.472269i
$883$	15.9804	−	11.6104i	0.537784	−	0.390723i	−0.285478	−	0.958385i	$-0.592152\pi$
$883$	15.9804	−	11.6104i	0.537784	−	0.390723i	0.823261	+	0.567663i	$0.192152\pi$
$884$	−0.0323254	−	0.0726040i	−0.00108722	−	0.00244194i
$885$	−29.6895	+	42.4834i	−0.998001	+	1.42806i
$886$	9.57192	+	8.61860i	0.321575	+	0.289547i
$887$	10.2562	−	4.56636i	0.344370	−	0.153323i	−0.227262	−	0.973834i	$-0.572977\pi$
$887$	10.2562	−	4.56636i	0.344370	−	0.153323i	0.571632	+	0.820510i	$0.306311\pi$
$888$	33.3198	−	31.1281i	1.11814	−	1.04459i
$889$	−16.9331	+	11.5769i	−0.567917	+	0.388277i
$890$	40.3165			1.35141
$891$	−0.145268	+	29.8493i	−0.00486665	+	0.999988i
$892$	−11.3164	−	19.6007i	−0.378903	−	0.656279i
$893$	0.692022	−	0.147094i	0.0231576	−	0.00492231i
$894$	5.09083	+	21.9594i	0.170263	+	0.734432i
$895$	−16.3666	−	11.8911i	−0.547076	−	0.397474i
$896$	−13.6110	+	11.5674i	−0.454711	+	0.386440i
$897$	−4.94379	−	10.5768i	−0.165068	−	0.353149i
$898$	9.95229	+	22.3532i	0.332112	+	0.745936i
$899$	−40.8741	−	18.1983i	−1.36323	−	0.606948i
$900$	−13.4854	+	6.60775i	−0.449513	+	0.220258i
$901$	0.246662	+	0.142411i	0.00821751	+	0.00474438i
$902$	−12.3406	−	8.47762i	−0.410896	−	0.282274i
$903$	0.0142455	−	1.38835i	0.000474060	−	0.0462015i
$904$	−52.5711	−	17.0814i	−1.74849	−	0.568119i
$905$	24.7660	−	2.60301i	0.823250	−	0.0865271i
$906$	4.33996	−	0.0797160i	0.144186	−	0.00264839i
$907$	0.423039	−	0.469832i	0.0140468	−	0.0156005i	−0.736080	−	0.676894i	$-0.763326\pi$
$907$	0.423039	−	0.469832i	0.0140468	−	0.0156005i	0.750127	+	0.661293i	$0.229992\pi$
$908$	−0.638270	−	0.135668i	−0.0211817	−	0.00450232i
$909$	−1.56962	−	0.630837i	−0.0520610	−	0.0209236i
$910$	−10.1689	+	5.48911i	−0.337096	+	0.181962i
$911$	−15.6806	−	5.09492i	−0.519520	−	0.168802i	0.0375074	−	0.999296i	$-0.488058\pi$
$911$	−15.6806	−	5.09492i	−0.519520	−	0.168802i	−0.557028	+	0.830494i	$0.688058\pi$
$912$	0.185724	+	0.0786353i	0.00614995	+	0.00260388i
$913$	−3.43724	+	43.7918i	−0.113756	+	1.44930i
$914$	8.81596	−	5.08990i	0.291606	−	0.168359i
$915$	−54.5472	−	47.3299i	−1.80328	−	1.56468i
$916$	−6.11447	+	4.44242i	−0.202028	+	0.146782i
$917$	12.2012	−	50.2796i	0.402920	−	1.66038i
$918$	−0.114904	−	0.141103i	−0.00379240	−	0.00465710i
$919$	−6.40792	+	30.1469i	−0.211378	+	0.994454i	0.736652	+	0.676272i	$0.236406\pi$
$919$	−6.40792	+	30.1469i	−0.211378	+	0.994454i	−0.948030	+	0.318182i	$0.896928\pi$
$920$	−3.68335	+	35.0448i	−0.121437	+	1.15539i
$921$	13.6127	−	44.6710i	0.448555	−	1.47196i
$922$	14.9571	+	16.6116i	0.492587	+	0.547073i
$923$	10.6194			0.349541
$924$	−9.01835	+	16.2189i	−0.296682	+	0.533561i
$925$	37.9646			1.24827
$926$	11.8202	+	13.1277i	0.388437	+	0.431403i
$927$	−38.5151	−	6.71879i	−1.26500	−	0.220674i
$928$	−4.99462	+	47.5207i	−0.163957	+	1.55994i
$929$	0.144380	−	0.679256i	0.00473696	−	0.0222857i	−0.975716	−	0.219041i	$-0.929707\pi$
$929$	0.144380	−	0.679256i	0.00473696	−	0.0222857i	0.980453	+	0.196755i	$0.0630405\pi$
$930$	22.0101	−	10.2880i	0.721740	−	0.337355i
$931$	−9.46660	+	7.58952i	−0.310255	+	0.248736i
$932$	−8.05948	+	5.85555i	−0.263997	+	0.191805i
$933$	−11.5440	+	13.3044i	−0.377934	+	0.435566i
$934$	3.15380	−	1.82085i	0.103195	−	0.0595799i
$935$	0.0927520	+	0.385983i	0.00303331	+	0.0126230i
$936$	13.4560	+	3.83190i	0.439825	+	0.125249i
$937$	49.8661	+	16.2025i	1.62905	+	0.529312i	0.974054	−	0.226318i	$-0.0726687\pi$
$937$	49.8661	+	16.2025i	1.62905	+	0.529312i	0.655000	+	0.755629i	$0.272669\pi$
$938$	0.548006	−	19.1383i	0.0178930	−	0.624888i
$939$	31.6807	+	17.5231i	1.03386	+	0.571845i
$940$	−1.47051	−	0.312566i	−0.0479626	−	0.0101948i
$941$	−19.4052	+	21.5517i	−0.632592	+	0.702565i	−0.971174	−	0.238372i	$-0.923386\pi$
$941$	−19.4052	+	21.5517i	−0.632592	+	0.702565i	0.338581	+	0.940937i	$0.390053\pi$
$942$	0.240938	+	13.1174i	0.00785020	+	0.427387i
$943$	−20.9007	+	2.19675i	−0.680621	+	0.0715361i
$944$	−0.633785	−	0.205929i	−0.0206279	−	0.00670242i
$945$	30.0737	−	28.5556i	0.978298	−	0.928912i
$946$	−0.835976	+	0.296232i	−0.0271799	+	0.00963133i
$947$	−0.740314	−	0.427420i	−0.0240570	−	0.0138893i	0.487923	−	0.872887i	$-0.337755\pi$
$947$	−0.740314	−	0.427420i	−0.0240570	−	0.0138893i	−0.511980	+	0.858997i	$0.671088\pi$
$948$	1.02573	+	2.97012i	0.0333140	+	0.0964649i
$949$	8.49427	+	3.78189i	0.275736	+	0.122765i
$950$	2.55106	+	5.72976i	0.0827672	+	0.185898i
$951$	15.4171	−	7.20625i	0.499934	−	0.233679i
$952$	−0.0536684	−	0.293575i	−0.00173940	−	0.00951481i
$953$	7.45751	+	5.41819i	0.241572	+	0.175513i	0.701983	−	0.712193i	$-0.252298\pi$
$953$	7.45751	+	5.41819i	0.241572	+	0.175513i	−0.460411	+	0.887706i	$0.652298\pi$
$954$	−17.8489	+	6.53339i	−0.577880	+	0.211526i
$955$	52.7363	−	11.2095i	1.70651	−	0.362729i
$956$	−5.85459	−	10.1404i	−0.189351	−	0.327966i
$957$	12.2678	+	47.2175i	0.396563	+	1.52633i
$958$	4.39135			0.141878
$959$	15.6903	+	7.53107i	0.506667	+	0.243191i
$960$	−18.1921	−	19.4730i	−0.587149	−	0.628489i
$961$	−2.96254	+	1.31901i	−0.0955657	+	0.0425486i
$962$	−9.96404	−	8.97166i	−0.321254	−	0.289258i
$963$	−14.5438	+	27.4737i	−0.468667	+	0.885328i
$964$	−1.62872	−	3.65815i	−0.0524574	−	0.117821i
$965$	−53.0846	+	38.5682i	−1.70885	+	1.24155i
$966$	−3.28838	−	16.2908i	−0.105802	−	0.524147i
$967$			11.6400i			0.374319i	0.982330	+	0.187159i	$0.0599281\pi$
$967$			11.6400i			0.374319i	−0.982330	+	0.187159i	$0.940072\pi$
$968$	30.8888	+	4.87903i	0.992805	+	0.156818i
$969$	0.0950692	−	0.0717759i	0.00305406	−	0.00230577i
$970$	−3.14615	−	14.8015i	−0.101017	−	0.475247i
$971$	26.3539	−	2.76991i	0.845737	−	0.0888906i	0.328260	−	0.944587i	$-0.393538\pi$
$971$	26.3539	−	2.76991i	0.845737	−	0.0888906i	0.517477	+	0.855697i	$0.326871\pi$
$972$	−19.0319	−	0.245345i	−0.610447	−	0.00786944i
$973$	9.02436	−	25.2873i	0.289308	−	0.810672i
$974$	0.470193	+	1.44711i	0.0150660	+	0.0463682i
$975$	6.00872	+	9.97955i	0.192433	+	0.319601i
$976$	0.377676	−	0.848274i	0.0120891	−	0.0271526i
$977$	−1.64837	−	7.75496i	−0.0527359	−	0.248103i	0.943881	−	0.330284i	$-0.107145\pi$
$977$	−1.64837	−	7.75496i	−0.0527359	−	0.248103i	−0.996617	+	0.0821813i	$0.973811\pi$
$978$	9.08596	−	21.4596i	0.290537	−	0.686202i
$979$	−30.5817	−	39.8375i	−0.977394	−	1.27321i
$980$	24.9364	−	6.55110i	0.796564	−	0.209267i
$981$	−4.19527	−	0.285669i	−0.133945	−	0.00912071i
$982$	−0.152425	−	1.45022i	−0.00486407	−	0.0462785i
$983$	22.3044	+	2.34429i	0.711400	+	0.0747711i	0.453314	−	0.891351i	$-0.350242\pi$
$983$	22.3044	+	2.34429i	0.711400	+	0.0747711i	0.258086	+	0.966122i	$0.416908\pi$
$984$	14.4264	−	20.6431i	0.459896	−	0.658077i
$985$	7.39684	−	34.7994i	0.235683	−	1.10880i
$986$	−0.240606	−	0.174811i	−0.00766246	−	0.00556710i
$987$	1.86210	−	0.176418i	0.0592713	−	0.00561545i
$988$	−1.07287	+	3.30195i	−0.0341325	+	0.105049i
$989$	−0.622469	+	1.07815i	−0.0197934	+	0.0342831i
$990$	−23.7319	−	11.7721i	−0.754249	−	0.374140i
$991$	−8.57510	−	14.8525i	−0.272397	−	0.471805i	0.697078	−	0.716995i	$-0.254483\pi$
$991$	−8.57510	−	14.8525i	−0.272397	−	0.471805i	−0.969475	+	0.245190i	$0.921150\pi$
$992$	−19.8351	−	22.0292i	−0.629766	−	0.699426i
$993$	−15.8688	+	14.8250i	−0.503580	+	0.470456i
$994$	14.6901	+	3.56481i	0.465942	+	0.113069i
$995$	−4.85910	+	1.57882i	−0.154044	+	0.0500519i
$996$	−27.9051	−	2.41572i	−0.884206	−	0.0765450i
$997$	−45.8062	−	4.81442i	−1.45070	−	0.152474i	−0.653835	−	0.756637i	$-0.726841\pi$
$997$	−45.8062	−	4.81442i	−1.45070	−	0.152474i	−0.796861	+	0.604163i	$0.793508\pi$
$998$	31.6251	+	14.0804i	1.00107	+	0.445707i
$999$	42.9329	+	21.7276i	1.35834	+	0.687430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.be.a.2.18	yes	224
3.2	odd	2	inner	231.2.be.a.2.11	✓	224
7.4	even	3	inner	231.2.be.a.200.11	yes	224
11.6	odd	10	inner	231.2.be.a.149.18	yes	224
21.11	odd	6	inner	231.2.be.a.200.18	yes	224
33.17	even	10	inner	231.2.be.a.149.11	yes	224
77.39	odd	30	inner	231.2.be.a.116.11	yes	224
231.116	even	30	inner	231.2.be.a.116.18	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.be.a.2.11	✓	224	3.2	odd	2	inner
231.2.be.a.2.18	yes	224	1.1	even	1	trivial
231.2.be.a.116.11	yes	224	77.39	odd	30	inner
231.2.be.a.116.18	yes	224	231.116	even	30	inner
231.2.be.a.149.11	yes	224	33.17	even	10	inner
231.2.be.a.149.18	yes	224	11.6	odd	10	inner
231.2.be.a.200.11	yes	224	7.4	even	3	inner
231.2.be.a.200.18	yes	224	21.11	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.be (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.590583 + 0.655909i) q^{2} +(-1.65683 - 0.504891i) q^{3} +(0.127629 - 1.21431i) q^{4} +(-0.627181 + 2.95066i) q^{5} +(-0.647333 - 1.38491i) q^{6} +(2.53863 - 0.745226i) q^{7} +(2.29995 - 1.67101i) q^{8} +(2.49017 + 1.67304i) q^{9} +O(q^{10})\)	\(q+(0.590583 + 0.655909i) q^{2} +(-1.65683 - 0.504891i) q^{3} +(0.127629 - 1.21431i) q^{4} +(-0.627181 + 2.95066i) q^{5} +(-0.647333 - 1.38491i) q^{6} +(2.53863 - 0.745226i) q^{7} +(2.29995 - 1.67101i) q^{8} +(2.49017 + 1.67304i) q^{9} +(-2.30576 + 1.33123i) q^{10} +(3.06443 + 1.26857i) q^{11} +(-0.824552 + 1.94746i) q^{12} +(1.56018 + 0.506933i) q^{13} +(1.98807 + 1.22499i) q^{14} +(2.52889 - 4.57208i) q^{15} +(0.0657108 + 0.0139673i) q^{16} +(0.0265497 - 0.0294864i) q^{17} +(0.373293 + 2.62139i) q^{18} +(-1.72384 + 0.181182i) q^{19} +(3.50296 + 1.13818i) q^{20} +(-4.58233 - 0.0470180i) q^{21} +(0.977730 + 2.75918i) q^{22} +(3.55849 + 2.05449i) q^{23} +(-4.65430 + 1.60736i) q^{24} +(-3.74529 - 1.66751i) q^{25} +(0.588913 + 1.32272i) q^{26} +(-3.28109 - 4.02920i) q^{27} +(-0.580931 - 3.17779i) q^{28} +(-6.87050 - 4.99171i) q^{29} +(4.49239 - 1.04147i) q^{30} +(5.15337 - 1.09538i) q^{31} +(-2.81324 - 4.87268i) q^{32} +(-4.43674 - 3.64901i) q^{33} +0.0350201 q^{34} +(0.606725 + 7.95801i) q^{35} +(2.34940 - 2.81030i) q^{36} +(-8.45969 + 3.76649i) q^{37} +(-1.13691 - 1.02368i) q^{38} +(-2.32901 - 1.62762i) q^{39} +(3.48809 + 7.83438i) q^{40} +(-4.13780 + 3.00629i) q^{41} +(-2.67541 - 3.03336i) q^{42} +0.302979i q^{43} +(1.93155 - 3.55925i) q^{44} +(-6.49834 + 6.29834i) q^{45} +(0.754021 + 3.54739i) q^{46} +(-0.405927 + 0.0426647i) q^{47} +(-0.101820 - 0.0563182i) q^{48} +(5.88928 - 3.78371i) q^{49} +(-1.11817 - 3.44137i) q^{50} +(-0.0588757 + 0.0354492i) q^{51} +(0.814696 - 1.82984i) q^{52} +(1.49246 + 7.02148i) q^{53} +(0.705034 - 4.53167i) q^{54} +(-5.66508 + 8.24645i) q^{55} +(4.59343 - 5.95605i) q^{56} +(2.94758 + 0.570161i) q^{57} +(-0.783494 - 7.45444i) q^{58} +(-9.86546 - 1.03690i) q^{59} +(-5.22914 - 3.65438i) q^{60} +(2.87377 - 13.5200i) q^{61} +(3.76196 + 2.73323i) q^{62} +(7.56841 + 2.39148i) q^{63} +(1.57610 - 4.85074i) q^{64} +(-2.47430 + 4.28561i) q^{65} +(-0.226845 - 5.06514i) q^{66} +(-4.09951 - 7.10057i) q^{67} +(-0.0324170 - 0.0360027i) q^{68} +(-4.85851 - 5.20059i) q^{69} +(-4.86141 + 5.09782i) q^{70} +(6.15655 - 2.00038i) q^{71} +(8.52292 - 0.313202i) q^{72} +(5.63692 + 0.592464i) q^{73} +(-7.46662 - 3.32435i) q^{74} +(5.36339 + 4.65374i) q^{75} +2.11639i q^{76} +(8.72482 + 0.936749i) q^{77} +(-0.307899 - 2.48886i) q^{78} +(1.10418 - 0.994206i) q^{79} +(-0.0824252 + 0.185130i) q^{80} +(3.40190 + 8.33229i) q^{81} +(-4.41557 - 0.938558i) q^{82} +(4.09272 + 12.5961i) q^{83} +(-0.641932 + 5.55836i) q^{84} +(0.0703527 + 0.0968322i) q^{85} +(-0.198727 + 0.178934i) q^{86} +(8.86298 + 11.7393i) q^{87} +(9.16782 - 2.20303i) q^{88} +(-13.1138 - 7.57127i) q^{89} +(-7.96895 - 0.542630i) q^{90} +(4.33850 + 0.124229i) q^{91} +(2.94895 - 4.05888i) q^{92} +(-9.09131 - 0.787027i) q^{93} +(-0.267718 - 0.241054i) q^{94} +(0.546551 - 5.20008i) q^{95} +(2.20089 + 9.49359i) q^{96} +(-1.75630 + 5.40534i) q^{97} +(5.95987 + 1.62824i) q^{98} +(5.50858 + 8.28587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) \) 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9	\( 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9} - 16 q^{12} - 40 q^{13} + 12 q^{15} + 34 q^{16} - 5 q^{18} - 10 q^{19} - 76 q^{22} - 25 q^{24} - 18 q^{25} + 6 q^{27} + 10 q^{28} - 35 q^{30} - 8 q^{33} - 96 q^{34} - 48 q^{36} - 10 q^{37} - 45 q^{39} - 120 q^{40} + 34 q^{42} - 24 q^{45} - 50 q^{46} + 14 q^{48} - 56 q^{49} - 45 q^{51} - 10 q^{52} + 48 q^{55} + 60 q^{57} + 44 q^{58} - 47 q^{60} - 50 q^{61} + 60 q^{63} - 72 q^{64} + 77 q^{66} - 80 q^{67} + 78 q^{69} + 36 q^{70} + 55 q^{72} - 70 q^{73} - 11 q^{75} + 36 q^{78} - 90 q^{79} + 23 q^{81} - 6 q^{82} + 125 q^{84} + 160 q^{85} + 86 q^{88} + 30 q^{90} - 128 q^{91} - 38 q^{93} - 210 q^{94} + 135 q^{96} + 40 q^{97} + 80 q^{99}+O(q^{100}) \) 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9 - 16 * q^12 - 40 * q^13 + 12 * q^15 + 34 * q^16 - 5 * q^18 - 10 * q^19 - 76 * q^22 - 25 * q^24 - 18 * q^25 + 6 * q^27 + 10 * q^28 - 35 * q^30 - 8 * q^33 - 96 * q^34 - 48 * q^36 - 10 * q^37 - 45 * q^39 - 120 * q^40 + 34 * q^42 - 24 * q^45 - 50 * q^46 + 14 * q^48 - 56 * q^49 - 45 * q^51 - 10 * q^52 + 48 * q^55 + 60 * q^57 + 44 * q^58 - 47 * q^60 - 50 * q^61 + 60 * q^63 - 72 * q^64 + 77 * q^66 - 80 * q^67 + 78 * q^69 + 36 * q^70 + 55 * q^72 - 70 * q^73 - 11 * q^75 + 36 * q^78 - 90 * q^79 + 23 * q^81 - 6 * q^82 + 125 * q^84 + 160 * q^85 + 86 * q^88 + 30 * q^90 - 128 * q^91 - 38 * q^93 - 210 * q^94 + 135 * q^96 + 40 * q^97 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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