LMFDB - Embedded newform 189.2.bd.a.185.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(47,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 15]))

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

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

chi := DirichletCharacter("189.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.bd (of order $18$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			185.10
Character	$\chi$	$=$	189.185
Dual form			189.2.bd.a.47.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.313923 + 0.0553531i) q^{2} +(1.24200 + 1.20725i) q^{3} +(-1.78390 + 0.649287i) q^{4} +(-2.68563 + 0.977491i) q^{5} +(-0.456717 - 0.310234i) q^{6} +(-2.48320 - 0.913082i) q^{7} +(1.07619 - 0.621337i) q^{8} +(0.0851152 + 2.99879i) q^{9} +O(q^{10})$	\(q+(-0.313923 + 0.0553531i) q^{2} +(1.24200 + 1.20725i) q^{3} +(-1.78390 + 0.649287i) q^{4} +(-2.68563 + 0.977491i) q^{5} +(-0.456717 - 0.310234i) q^{6} +(-2.48320 - 0.913082i) q^{7} +(1.07619 - 0.621337i) q^{8} +(0.0851152 + 2.99879i) q^{9} +(0.788975 - 0.455515i) q^{10} +(-1.16543 + 3.20200i) q^{11} +(-2.99945 - 1.34719i) q^{12} +(-1.17022 - 3.21516i) q^{13} +(0.830076 + 0.149185i) q^{14} +(-4.51562 - 2.02818i) q^{15} +(2.60505 - 2.18590i) q^{16} +(2.33161 + 4.03847i) q^{17} +(-0.192712 - 0.936679i) q^{18} +(4.78098 + 2.76030i) q^{19} +(4.15623 - 3.48749i) q^{20} +(-1.98181 - 4.13188i) q^{21} +(0.188615 - 1.06969i) q^{22} +(-1.35415 - 0.238774i) q^{23} +(2.08673 + 0.527523i) q^{24} +(2.42692 - 2.03643i) q^{25} +(0.545329 + 0.944538i) q^{26} +(-3.51457 + 3.82725i) q^{27} +(5.02264 + 0.0165384i) q^{28} +(-2.81504 + 7.73427i) q^{29} +(1.52982 + 0.386739i) q^{30} +(0.756904 + 2.07958i) q^{31} +(-2.29434 + 2.73429i) q^{32} +(-5.31306 + 2.56991i) q^{33} +(-0.955489 - 1.13871i) q^{34} +(7.56149 + 0.0248983i) q^{35} +(-2.09891 - 5.29429i) q^{36} -1.76484 q^{37} +(-1.65365 - 0.601880i) q^{38} +(2.42808 - 5.40597i) q^{39} +(-2.28289 + 2.72064i) q^{40} +(4.96713 - 1.80789i) q^{41} +(0.850850 + 1.18739i) q^{42} +(-1.57831 - 8.95103i) q^{43} -6.46875i q^{44} +(-3.15988 - 7.97046i) q^{45} +0.438317 q^{46} +(2.87974 + 1.04814i) q^{47} +(5.87439 + 0.430058i) q^{48} +(5.33256 + 4.53473i) q^{49} +(-0.649143 + 0.773618i) q^{50} +(-1.97957 + 7.83060i) q^{51} +(4.17513 + 4.97572i) q^{52} +(1.30996 + 0.756305i) q^{53} +(0.891454 - 1.39600i) q^{54} -9.73859i q^{55} +(-3.23972 + 0.560257i) q^{56} +(2.60560 + 9.20011i) q^{57} +(0.455592 - 2.58379i) q^{58} +(-5.25805 - 4.41203i) q^{59} +(9.37229 + 0.686137i) q^{60} +(3.36646 - 9.24926i) q^{61} +(-0.352721 - 0.610930i) q^{62} +(2.52678 - 7.52432i) q^{63} +(-2.83176 + 4.90475i) q^{64} +(6.28558 + 7.49087i) q^{65} +(1.52564 - 1.10085i) q^{66} +(-1.66553 + 9.44568i) q^{67} +(-6.78150 - 5.69035i) q^{68} +(-1.39360 - 1.93135i) q^{69} +(-2.37511 + 0.410736i) q^{70} +(-9.64722 - 5.56983i) q^{71} +(1.95486 + 3.17438i) q^{72} -5.91133i q^{73} +(0.554024 - 0.0976893i) q^{74} +(5.47269 + 0.400651i) q^{75} +(-10.3210 - 1.81988i) q^{76} +(5.81769 - 6.88707i) q^{77} +(-0.462992 + 1.83146i) q^{78} +(1.98492 + 11.2570i) q^{79} +(-4.85952 + 8.41694i) q^{80} +(-8.98551 + 0.510486i) q^{81} +(-1.45922 + 0.842484i) q^{82} +(6.72578 + 2.44798i) q^{83} +(6.21814 + 6.08410i) q^{84} +(-10.2094 - 8.56673i) q^{85} +(0.990935 + 2.72257i) q^{86} +(-12.8334 + 6.20749i) q^{87} +(0.735296 + 4.17007i) q^{88} +(6.12929 - 10.6162i) q^{89} +(1.43315 + 2.32720i) q^{90} +(-0.0298075 + 9.05240i) q^{91} +(2.57071 - 0.453286i) q^{92} +(-1.57049 + 3.49660i) q^{93} +(-0.962036 - 0.169633i) q^{94} +(-15.5381 - 2.73979i) q^{95} +(-6.15052 + 0.626146i) q^{96} +(-2.47531 + 0.436465i) q^{97} +(-1.92503 - 1.12838i) q^{98} +(-9.70132 - 3.22235i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.313923	+	0.0553531i	−0.221977	+	0.0391406i	−0.283530	−	0.958963i	$-0.591506\pi$
$2$	−0.313923	+	0.0553531i	−0.221977	+	0.0391406i	0.0615533	+	0.998104i	$0.480395\pi$
$3$	1.24200	+	1.20725i	0.717068	+	0.697004i
$3$	1.24200	+	1.20725i	0.717068	+	0.697004i
$4$	−1.78390	+	0.649287i	−0.891951	+	0.324644i
$5$	−2.68563	+	0.977491i	−1.20105	+	0.437147i	−0.863591	−	0.504193i	$-0.831790\pi$
$5$	−2.68563	+	0.977491i	−1.20105	+	0.437147i	−0.337461	+	0.941340i	$0.609568\pi$
$6$	−0.456717	−	0.310234i	−0.186454	−	0.126652i
$7$	−2.48320	−	0.913082i	−0.938561	−	0.345112i
$7$	−2.48320	−	0.913082i	−0.938561	−	0.345112i
$8$	1.07619	−	0.621337i	0.380489	−	0.219676i
$9$	0.0851152	+	2.99879i	0.0283717	+	0.999597i
$10$	0.788975	−	0.455515i	0.249496	−	0.144047i
$11$	−1.16543	+	3.20200i	−0.351391	+	0.965439i	0.630533	+	0.776162i	$0.282836\pi$
$11$	−1.16543	+	3.20200i	−0.351391	+	0.965439i	−0.981924	+	0.189276i	$0.939386\pi$
$12$	−2.99945	−	1.34719i	−0.865867	−	0.388902i
$13$	−1.17022	−	3.21516i	−0.324562	−	0.891726i	−0.989462	−	0.144794i	$-0.953748\pi$
$13$	−1.17022	−	3.21516i	−0.324562	−	0.891726i	0.664900	−	0.746932i	$-0.268474\pi$
$14$	0.830076	+	0.149185i	0.221847	+	0.0398713i
$15$	−4.51562	−	2.02818i	−1.16593	−	0.523674i
$16$	2.60505	−	2.18590i	0.651263	−	0.546475i
$17$	2.33161	+	4.03847i	0.565499	+	0.979474i	0.997003	+	0.0773624i	$0.0246498\pi$
$17$	2.33161	+	4.03847i	0.565499	+	0.979474i	−0.431504	+	0.902111i	$0.642017\pi$
$18$	−0.192712	−	0.936679i	−0.0454227	−	0.220777i
$19$	4.78098	+	2.76030i	1.09683	+	0.633256i	0.935387	−	0.353625i	$-0.115051\pi$
$19$	4.78098	+	2.76030i	1.09683	+	0.633256i	0.161445	+	0.986882i	$0.448385\pi$
$20$	4.15623	−	3.48749i	0.929362	−	0.779827i
$21$	−1.98181	−	4.13188i	−0.432467	−	0.901650i
$22$	0.188615	−	1.06969i	0.0402129	−	0.228059i
$23$	−1.35415	−	0.238774i	−0.282361	−	0.0497878i	0.0306742	−	0.999529i	$-0.490235\pi$
$23$	−1.35415	−	0.238774i	−0.282361	−	0.0497878i	−0.313035	+	0.949742i	$0.601346\pi$
$24$	2.08673	+	0.527523i	0.425951	+	0.107680i
$25$	2.42692	−	2.03643i	0.485383	−	0.407285i
$26$	0.545329	+	0.944538i	0.106948	+	0.185239i
$27$	−3.51457	+	3.82725i	−0.676379	+	0.736554i
$28$	5.02264	+	0.0165384i	0.949189	+	0.00312546i
$29$	−2.81504	+	7.73427i	−0.522741	+	1.43622i	0.344717	+	0.938707i	$0.387975\pi$
$29$	−2.81504	+	7.73427i	−0.522741	+	1.43622i	−0.867458	+	0.497511i	$0.834247\pi$
$30$	1.52982	+	0.386739i	0.279306	+	0.0706085i
$31$	0.756904	+	2.07958i	0.135944	+	0.373503i	0.988920	−	0.148446i	$-0.0474272\pi$
$31$	0.756904	+	2.07958i	0.135944	+	0.373503i	−0.852977	+	0.521949i	$0.825205\pi$
$32$	−2.29434	+	2.73429i	−0.405586	+	0.483358i
$33$	−5.31306	+	2.56991i	−0.924885	+	0.447364i
$34$	−0.955489	−	1.13871i	−0.163865	−	0.195287i
$35$	7.56149	+	0.0248983i	1.27813	+	0.00420858i
$36$	−2.09891	−	5.29429i	−0.349819	−	0.882381i
$37$	−1.76484			−0.290138			−0.145069	−	0.989422i	$-0.546340\pi$
$37$	−1.76484			−0.290138			−0.145069	+	0.989422i	$0.546340\pi$
$38$	−1.65365	−	0.601880i	−0.268258	−	0.0976378i
$39$	2.42808	−	5.40597i	0.388803	−	0.865648i
$40$	−2.28289	+	2.72064i	−0.360957	+	0.430172i
$41$	4.96713	−	1.80789i	0.775735	−	0.282344i	0.0763420	−	0.997082i	$-0.475676\pi$
$41$	4.96713	−	1.80789i	0.775735	−	0.282344i	0.699393	+	0.714737i	$0.253454\pi$
$42$	0.850850	+	1.18739i	0.131289	+	0.183219i
$43$	−1.57831	−	8.95103i	−0.240690	−	1.36502i	−0.830293	−	0.557327i	$-0.811827\pi$
$43$	−1.57831	−	8.95103i	−0.240690	−	1.36502i	0.589603	−	0.807693i	$-0.299284\pi$
$44$		−	6.46875i		−	0.975200i
$45$	−3.15988	−	7.97046i	−0.471047	−	1.18817i
$46$	0.438317			0.0646263
$47$	2.87974	+	1.04814i	0.420054	+	0.152887i	0.543395	−	0.839477i	$-0.317139\pi$
$47$	2.87974	+	1.04814i	0.420054	+	0.152887i	−0.123341	+	0.992364i	$0.539361\pi$
$48$	5.87439	+	0.430058i	0.847895	+	0.0620736i
$49$	5.33256	+	4.53473i	0.761795	+	0.647818i
$50$	−0.649143	+	0.773618i	−0.0918027	+	0.109406i
$51$	−1.97957	+	7.83060i	−0.277195	+	1.09650i
$52$	4.17513	+	4.97572i	0.578986	+	0.690009i
$53$	1.30996	+	0.756305i	0.179937	+	0.103886i	0.587263	−	0.809396i	$-0.300205\pi$
$53$	1.30996	+	0.756305i	0.179937	+	0.103886i	−0.407326	+	0.913283i	$0.633539\pi$
$54$	0.891454	−	1.39600i	0.121311	−	0.189972i
$55$		−	9.73859i		−	1.31315i
$56$	−3.23972	+	0.560257i	−0.432925	+	0.0748675i
$57$	2.60560	+	9.20011i	0.345121	+	1.21858i
$58$	0.455592	−	2.58379i	0.0598221	−	0.339268i
$59$	−5.25805	−	4.41203i	−0.684540	−	0.574397i	0.232789	−	0.972527i	$-0.425215\pi$
$59$	−5.25805	−	4.41203i	−0.684540	−	0.574397i	−0.917329	+	0.398130i	$0.869659\pi$
$60$	9.37229	+	0.686137i	1.20996	+	0.0885799i
$61$	3.36646	−	9.24926i	0.431031	−	1.18425i	−0.514150	−	0.857700i	$-0.671893\pi$
$61$	3.36646	−	9.24926i	0.431031	−	1.18425i	0.945181	−	0.326547i	$-0.105885\pi$
$62$	−0.352721	−	0.610930i	−0.0447956	−	0.0775882i
$63$	2.52678	−	7.52432i	0.318345	−	0.947975i
$64$	−2.83176	+	4.90475i	−0.353970	+	0.613094i
$65$	6.28558	+	7.49087i	0.779631	+	0.929128i
$66$	1.52564	−	1.10085i	0.187793	−	0.135505i
$67$	−1.66553	+	9.44568i	−0.203477	+	1.15397i	0.696342	+	0.717710i	$0.254810\pi$
$67$	−1.66553	+	9.44568i	−0.203477	+	1.15397i	−0.899819	+	0.436264i	$0.856302\pi$
$68$	−6.78150	−	5.69035i	−0.822377	−	0.690056i
$69$	−1.39360	−	1.93135i	−0.167769	−	0.232508i
$70$	−2.37511	+	0.410736i	−0.283879	+	0.0490924i
$71$	−9.64722	−	5.56983i	−1.14491	−	0.661017i	−0.197272	−	0.980349i	$-0.563208\pi$
$71$	−9.64722	−	5.56983i	−1.14491	−	0.661017i	−0.947643	+	0.319332i	$0.896541\pi$
$72$	1.95486	+	3.17438i	0.230382	+	0.374104i
$73$		−	5.91133i		−	0.691869i	−0.938259	−	0.345935i	$-0.887562\pi$
$73$		−	5.91133i		−	0.691869i	0.938259	−	0.345935i	$-0.112438\pi$
$74$	0.554024	−	0.0976893i	0.0644040	−	0.0113562i
$75$	5.47269	+	0.400651i	0.631932	+	0.0462631i
$76$	−10.3210	−	1.81988i	−1.18390	−	0.208754i
$77$	5.81769	−	6.88707i	0.662987	−	0.784854i
$78$	−0.462992	+	1.83146i	−0.0524235	+	0.207372i
$79$	1.98492	+	11.2570i	0.223321	+	1.26652i	0.865869	+	0.500271i	$0.166766\pi$
$79$	1.98492	+	11.2570i	0.223321	+	1.26652i	−0.642548	+	0.766245i	$0.722123\pi$
$80$	−4.85952	+	8.41694i	−0.543311	+	0.941042i
$81$	−8.98551	+	0.510486i	−0.998390	+	0.0567207i
$82$	−1.45922	+	0.842484i	−0.161144	+	0.0930367i
$83$	6.72578	+	2.44798i	0.738250	+	0.268701i	0.683653	−	0.729807i	$-0.260390\pi$
$83$	6.72578	+	2.44798i	0.738250	+	0.268701i	0.0545974	+	0.998508i	$0.482612\pi$
$84$	6.21814	+	6.08410i	0.678454	+	0.663829i
$85$	−10.2094	−	8.56673i	−1.10737	−	0.929192i
$86$	0.990935	+	2.72257i	0.106855	+	0.293582i
$87$	−12.8334	+	6.20749i	−1.37589	+	0.665513i
$88$	0.735296	+	4.17007i	0.0783828	+	0.444531i
$89$	6.12929	−	10.6162i	0.649703	−	1.12532i	−0.333491	−	0.942753i	$-0.608227\pi$
$89$	6.12929	−	10.6162i	0.649703	−	1.12532i	0.983194	−	0.182565i	$-0.0584401\pi$
$90$	1.43315	+	2.32720i	0.151067	+	0.245309i
$91$	−0.0298075	+	9.05240i	−0.00312467	+	0.948949i
$92$	2.57071	−	0.453286i	0.268015	−	0.0472583i
$93$	−1.57049	+	3.49660i	−0.162852	+	0.362580i
$94$	−0.962036	−	0.169633i	−0.0992265	−	0.0174963i
$95$	−15.5381	−	2.73979i	−1.59418	−	0.281097i
$96$	−6.15052	+	0.626146i	−0.627735	+	0.0639058i
$97$	−2.47531	+	0.436465i	−0.251330	+	0.0443163i	−0.297894	−	0.954599i	$-0.596284\pi$
$97$	−2.47531	+	0.436465i	−0.251330	+	0.0443163i	0.0465636	+	0.998915i	$0.485173\pi$
$98$	−1.92503	−	1.12838i	−0.194457	−	0.113984i
$99$	−9.70132	−	3.22235i	−0.975019	−	0.323858i
$100$	−3.00716	+	5.20855i	−0.300716	+	0.520855i
$101$	1.61753	+	9.17347i	0.160950	+	0.912795i	0.953142	+	0.302523i	$0.0978288\pi$
$101$	1.61753	+	9.17347i	0.160950	+	0.912795i	−0.792192	+	0.610272i	$0.791060\pi$
$102$	0.187985	−	2.56778i	0.0186133	−	0.254248i
$103$	3.85481	+	10.5910i	0.379825	+	1.04356i	0.971429	+	0.237332i	$0.0762730\pi$
$103$	3.85481	+	10.5910i	0.379825	+	1.04356i	−0.591603	+	0.806229i	$0.701505\pi$
$104$	−3.25708	−	2.73301i	−0.319383	−	0.267994i
$105$	9.36130	+	9.15950i	0.913569	+	0.893876i
$106$	−0.453090	−	0.164911i	−0.0440080	−	0.0160176i
$107$	−5.79854	+	3.34779i	−0.560566	+	0.323643i	−0.753373	−	0.657594i	$-0.771574\pi$
$107$	−5.79854	+	3.34779i	−0.560566	+	0.323643i	0.192807	+	0.981237i	$0.438241\pi$
$108$	3.78466	−	9.10939i	0.364179	−	0.876552i
$109$	−8.30492	+	14.3845i	−0.795467	+	1.37779i	0.127076	+	0.991893i	$0.459441\pi$
$109$	−8.30492	+	14.3845i	−0.795467	+	1.37779i	−0.922542	+	0.385896i	$0.873892\pi$
$110$	0.539061	+	3.05717i	0.0513975	+	0.291490i
$111$	−2.19193	−	2.13059i	−0.208048	−	0.202227i
$112$	−8.46477	+	3.04940i	−0.799846	+	0.288141i
$113$	10.4246	+	1.83814i	0.980666	+	0.172918i	0.640927	−	0.767602i	$-0.278550\pi$
$113$	10.4246	+	1.83814i	0.980666	+	0.172918i	0.339739	+	0.940520i	$0.389661\pi$
$114$	−1.32721	−	2.74390i	−0.124305	−	0.256990i
$115$	3.87016	−	0.682414i	0.360894	−	0.0636354i
$116$		−	15.6249i		−	1.45074i
$117$	9.54200	−	3.78292i	0.882158	−	0.349731i
$118$	1.89484	+	1.09399i	0.174434	+	0.100710i
$119$	−2.10241	−	12.1573i	−0.192727	−	1.11446i
$120$	−6.11983	+	0.623022i	−0.558662	+	0.0568739i
$121$	−0.468067	−	0.392755i	−0.0425516	−	0.0357050i
$122$	−0.544833	+	3.08990i	−0.0493269	+	0.279747i
$123$	8.35172	+	3.75115i	0.753050	+	0.338230i
$124$	−2.70048	−	3.21831i	−0.242511	−	0.289013i
$125$	2.61776	−	4.53409i	0.234139	−	0.405541i
$126$	−0.376722	+	2.50192i	−0.0335610	+	0.222889i
$127$	8.48685	+	14.6997i	0.753086	+	1.30438i	0.946320	+	0.323231i	$0.104769\pi$
$127$	8.48685	+	14.6997i	0.753086	+	1.30438i	−0.193234	+	0.981153i	$0.561898\pi$
$128$	3.05905	−	8.40466i	0.270384	−	0.742874i
$129$	8.84584	−	13.0226i	0.778833	−	1.14657i
$130$	−2.38783	−	2.00363i	−0.209427	−	0.175730i
$131$	−2.77758	+	15.7524i	−0.242678	+	1.37629i	0.583146	+	0.812367i	$0.301821\pi$
$131$	−2.77758	+	15.7524i	−0.242678	+	1.37629i	−0.825824	+	0.563928i	$0.809290\pi$
$132$	7.80937	−	8.03417i	0.679718	−	0.699285i
$133$	−9.35175	−	11.2198i	−0.810900	−	0.972880i
$134$		−	3.05741i		−	0.264120i
$135$	5.69774	−	13.7140i	0.490383	−	1.18032i
$136$	5.01850	+	2.89743i	0.430333	+	0.248453i
$137$	−8.37647	−	9.98269i	−0.715650	−	0.852879i	0.278550	−	0.960422i	$-0.410146\pi$
$137$	−8.37647	−	9.98269i	−0.715650	−	0.852879i	−0.994200	+	0.107543i	$0.965702\pi$
$138$	0.544389	+	0.529157i	0.0463415	+	0.0450448i
$139$	−2.63292	+	3.13779i	−0.223321	+	0.266144i	−0.866058	−	0.499943i	$-0.833354\pi$
$139$	−2.63292	+	3.13779i	−0.223321	+	0.266144i	0.642737	+	0.766087i	$0.277799\pi$
$140$	−13.5051	+	4.86516i	−1.14139	+	0.411181i
$141$	2.31127	+	4.77835i	0.194644	+	0.402410i
$142$	3.33679	+	1.21449i	0.280017	+	0.101918i
$143$	11.6588			0.974954
$144$	6.77679	+	7.62596i	0.564732	+	0.635497i
$145$		−	23.5231i		−	1.95349i
$146$	0.327211	+	1.85570i	0.0270802	+	0.153579i
$147$	1.14850	+	12.0698i	0.0947265	+	0.995503i
$148$	3.14830	−	1.14589i	0.258789	−	0.0941913i
$149$	−0.958803	+	1.14266i	−0.0785482	+	0.0936101i	−0.803887	−	0.594782i	$-0.797239\pi$
$149$	−0.958803	+	1.14266i	−0.0785482	+	0.0936101i	0.725339	+	0.688392i	$0.241683\pi$
$150$	−1.74018	+	0.177157i	−0.142085	+	0.0144648i
$151$	4.56459	+	1.66138i	0.371461	+	0.135201i	0.521004	−	0.853554i	$-0.325558\pi$
$151$	4.56459	+	1.66138i	0.371461	+	0.135201i	−0.149542	+	0.988755i	$0.547780\pi$
$152$	6.86030			0.556444
$153$	−11.9121	+	7.33576i	−0.963035	+	0.593061i
$154$	−1.44509	+	2.48404i	−0.116448	+	0.200169i
$155$	−4.06553	−	4.84511i	−0.326551	−	0.389169i
$156$	−0.821423	+	11.2202i	−0.0657665	+	0.898338i
$157$	14.4796	−	17.2561i	1.15560	−	1.37719i	0.242149	−	0.970239i	$-0.422148\pi$
$157$	14.4796	−	17.2561i	1.15560	−	1.37719i	0.913450	−	0.406951i	$-0.133408\pi$
$158$	−1.24622	−	3.42397i	−0.0991443	−	0.272397i
$159$	0.713919	+	2.52077i	0.0566175	+	0.199910i
$160$	3.48902	−	9.58599i	0.275831	−	0.757839i
$161$	3.14462	+	1.82938i	0.247830	+	0.144175i
$162$	2.79250	−	0.657629i	0.219400	−	0.0516682i
$163$	−4.81306	−	8.33646i	−0.376988	−	0.652962i	0.613635	−	0.789590i	$-0.289707\pi$
$163$	−4.81306	−	8.33646i	−0.376988	−	0.652962i	−0.990622	+	0.136628i	$0.956374\pi$
$164$	−7.68703	+	6.45018i	−0.600256	+	0.503675i
$165$	11.7569	−	12.0953i	0.915271	−	0.941618i
$166$	−2.24688	−	0.396186i	−0.174392	−	0.0307500i
$167$	1.75065	−	9.92841i	0.135469	−	0.768284i	−0.839063	−	0.544035i	$-0.816896\pi$
$167$	1.75065	−	9.92841i	0.135469	−	0.768284i	0.974532	−	0.224249i	$-0.0719929\pi$
$168$	−4.70009	−	3.21530i	−0.362620	−	0.248066i
$169$	0.990731	−	0.831322i	0.0762101	−	0.0639479i
$170$	3.67917	+	2.12417i	0.282180	+	0.162916i
$171$	−7.87063	+	14.5721i	−0.601882	+	1.11436i
$172$	8.62734	+	14.9430i	0.657828	+	1.13939i
$173$	−9.46890	+	7.94535i	−0.719907	+	0.604074i	−0.927360	−	0.374171i	$-0.877927\pi$
$173$	−9.46890	+	7.94535i	−0.719907	+	0.604074i	0.207452	+	0.978245i	$0.433483\pi$
$174$	3.68511	−	2.65905i	0.279368	−	0.201582i
$175$	−7.88594	+	2.84088i	−0.596121	+	0.214750i
$176$	3.96323	+	10.8889i	0.298740	+	0.820781i
$177$	−1.20408	−	11.8275i	−0.0905044	−	0.889009i
$178$	−1.33648	+	3.67196i	−0.100174	+	0.275225i
$179$	−13.6692	+	7.89190i	−1.02168	+	0.589868i	−0.914591	−	0.404381i	$-0.867487\pi$
$179$	−13.6692	+	7.89190i	−1.02168	+	0.589868i	−0.107091	+	0.994249i	$0.534154\pi$
$180$	10.8120	+	12.1668i	0.805881	+	0.906863i
$181$	11.3602	−	6.55879i	0.844393	−	0.487511i	−0.0143618	−	0.999897i	$-0.504572\pi$
$181$	11.3602	−	6.55879i	0.844393	−	0.487511i	0.858755	+	0.512386i	$0.171238\pi$
$182$	−0.491721	−	2.84341i	−0.0364488	−	0.210767i
$183$	15.3473	−	7.42342i	1.13450	−	0.548755i
$184$	−1.60568	+	0.584420i	−0.118372	+	0.0430840i
$185$	4.73971	−	1.72511i	0.348470	−	0.126833i
$186$	0.299465	−	1.18459i	0.0219578	−	0.0868587i
$187$	−15.6485	+	2.75926i	−1.14433	+	0.201777i
$188$	−5.81773			−0.424301
$189$	12.2220	−	6.29473i	0.889017	−	0.457875i
$190$	5.02943			0.364874
$191$	17.5029	−	3.08624i	1.26647	−	0.223313i	0.500244	−	0.865885i	$-0.333244\pi$
$191$	17.5029	−	3.08624i	1.26647	−	0.223313i	0.766225	+	0.642572i	$0.222133\pi$
$192$	−9.43828	+	2.67306i	−0.681149	+	0.192911i
$193$	12.8024	−	4.65969i	0.921537	−	0.335412i	0.162687	−	0.986678i	$-0.447984\pi$
$193$	12.8024	−	4.65969i	0.921537	−	0.335412i	0.758850	+	0.651266i	$0.225762\pi$
$194$	0.752899	−	0.274033i	0.0540550	−	0.0196744i
$195$	−1.23664	+	16.8919i	−0.0885575	+	1.20965i
$196$	−12.4571	−	4.62715i	−0.889793	−	0.330510i
$197$	7.98620	−	4.61083i	0.568993	−	0.328508i	−0.187754	−	0.982216i	$-0.560121\pi$
$197$	7.98620	−	4.61083i	0.568993	−	0.328508i	0.756747	+	0.653708i	$0.226787\pi$
$198$	3.22384	+	0.474572i	0.229108	+	0.0337263i
$199$	−0.232253	+	0.134091i	−0.0164640	+	0.00950548i	−0.508209	−	0.861234i	$-0.669692\pi$
$199$	−0.232253	+	0.134091i	−0.0164640	+	0.00950548i	0.491745	+	0.870739i	$0.336359\pi$
$200$	1.34651	−	3.69951i	0.0952126	−	0.261595i
$201$	−13.4718	+	9.72081i	−0.950230	+	0.685653i
$202$	−1.01556	−	2.79023i	−0.0714546	−	0.196320i
$203$	14.0523	−	16.6354i	0.986281	−	1.16757i
$204$	−1.55295	−	15.2543i	−0.108728	−	1.06802i
$205$	−11.5727	+	9.71064i	−0.808272	+	0.678221i
$206$	−1.79636	−	3.11138i	−0.125158	−	0.216780i
$207$	0.600774	−	4.08115i	0.0417567	−	0.283660i
$208$	−10.0765	−	5.81768i	−0.698680	−	0.403383i
$209$	−14.4104	+	12.0917i	−0.996787	+	0.836404i
$210$	−3.44574	−	2.35720i	−0.237778	−	0.162663i
$211$	−2.27165	+	12.8832i	−0.156387	+	0.886914i	0.801120	+	0.598503i	$0.204238\pi$
$211$	−2.27165	+	12.8832i	−0.156387	+	0.886914i	−0.957507	+	0.288410i	$0.906873\pi$
$212$	−2.82789	−	0.498634i	−0.194221	−	0.0342463i
$213$	−5.25768	−	18.5643i	−0.360250	−	1.27200i
$214$	1.63499	−	1.37192i	0.111765	−	0.0937822i
$215$	12.9883	+	22.4964i	0.885795	+	1.53424i
$216$	−1.40432	+	6.30256i	−0.0955519	+	0.428835i
$217$	0.0192796	−	5.85512i	0.00130878	−	0.397471i
$218$	1.81088	−	4.97534i	0.122648	−	0.336973i
$219$	7.13643	−	7.34186i	0.482236	−	0.496117i
$220$	6.32314	+	17.3727i	0.426306	+	1.17127i
$221$	10.2558	−	12.2224i	0.689882	−	0.822170i
$222$	0.806031	+	0.547513i	0.0540973	+	0.0367467i
$223$	9.50475	+	11.3273i	0.636485	+	0.758534i	0.983811	−	0.179211i	$-0.0573545\pi$
$223$	9.50475	+	11.3273i	0.636485	+	0.758534i	−0.347325	+	0.937745i	$0.612910\pi$
$224$	8.19393	−	4.69486i	0.547480	−	0.313689i
$225$	6.31338	+	7.10449i	0.420892	+	0.473633i
$226$	−3.37428			−0.224454
$227$	−8.61703	−	3.13634i	−0.571933	−	0.208166i	0.0398319	−	0.999206i	$-0.487318\pi$
$227$	−8.61703	−	3.13634i	−0.571933	−	0.208166i	−0.611764	+	0.791040i	$0.709540\pi$
$228$	−10.6217	−	14.7203i	−0.703436	−	0.974875i
$229$	8.22374	−	9.80068i	0.543440	−	0.647647i	−0.422515	−	0.906356i	$-0.638853\pi$
$229$	8.22374	−	9.80068i	0.543440	−	0.647647i	0.965955	+	0.258709i	$0.0832971\pi$
$230$	−1.17716	+	0.428451i	−0.0776196	+	0.0282512i
$231$	15.5399	−	1.53034i	1.02245	−	0.100689i
$232$	1.77607	+	10.0726i	0.116605	+	0.661299i
$233$		−	17.0668i		−	1.11808i	−0.829140	−	0.559042i	$-0.811169\pi$
$233$		−	17.0668i		−	1.11808i	0.829140	−	0.559042i	$-0.188831\pi$
$234$	−2.78606	+	1.71572i	−0.182130	+	0.112160i
$235$	−8.75849			−0.571341
$236$	12.2445	+	4.45664i	0.797050	+	0.290103i
$237$	−11.1248	+	16.3775i	−0.722630	+	1.06383i
$238$	1.33294	+	3.70008i	0.0864015	+	0.239841i
$239$	−4.33839	+	5.17029i	−0.280627	+	0.334438i	−0.887884	−	0.460067i	$-0.847825\pi$
$239$	−4.33839	+	5.17029i	−0.280627	+	0.334438i	0.607257	+	0.794505i	$0.292270\pi$
$240$	−16.1968	+	4.58718i	−1.04550	+	0.296101i
$241$	−1.80490	−	2.15100i	−0.116264	−	0.138558i	0.704773	−	0.709432i	$-0.251049\pi$
$241$	−1.80490	−	2.15100i	−0.116264	−	0.138558i	−0.821037	+	0.570875i	$0.806604\pi$
$242$	0.168677	+	0.0973859i	0.0108430	+	0.00626021i
$243$	−11.7763	−	10.2137i	−0.755448	−	0.655209i
$244$			18.6856i			1.19622i
$245$	−18.7540	−	6.96609i	−1.19815	−	0.445047i
$246$	−2.82944	−	0.715280i	−0.180398	−	0.0456046i
$247$	3.28000	−	18.6018i	0.208701	−	1.18360i
$248$	2.10669	+	1.76772i	0.133775	+	0.112250i
$249$	5.39808	+	11.1601i	0.342090	+	0.707240i
$250$	−0.570798	+	1.56826i	−0.0361005	+	0.0991852i
$251$	11.4184	+	19.7772i	0.720720	+	1.24832i	0.960712	+	0.277549i	$0.0895220\pi$
$251$	11.4184	+	19.7772i	0.720720	+	1.24832i	−0.239992	+	0.970775i	$0.577145\pi$
$252$	0.377908	+	15.0633i	0.0238059	+	0.948896i
$253$	2.34273	−	4.05772i	0.147286	−	0.255107i
$254$	−3.47789	−	4.14479i	−0.218222	−	0.260067i
$255$	−2.33794	−	22.9651i	−0.146407	−	1.43813i
$256$	1.47184	−	8.34721i	0.0919899	−	0.521701i
$257$	−9.59035	−	8.04726i	−0.598229	−	0.501974i	0.292647	−	0.956221i	$-0.405464\pi$
$257$	−9.59035	−	8.04726i	−0.598229	−	0.501974i	−0.890876	+	0.454247i	$0.849908\pi$
$258$	−2.05607	+	4.57773i	−0.128006	+	0.284997i
$259$	4.38245	+	1.61144i	0.272312	+	0.100130i
$260$	−16.0766	−	9.28182i	−0.997027	−	0.575634i
$261$	−23.4331	−	7.78343i	−1.45047	−	0.481782i
$262$		−	5.09880i		−	0.315005i
$263$	−12.5268	+	2.20881i	−0.772435	+	0.136201i	−0.545955	−	0.837815i	$-0.683833\pi$
$263$	−12.5268	+	2.20881i	−0.772435	+	0.136201i	−0.226480	+	0.974016i	$0.572722\pi$
$264$	−4.12107	+	6.06690i	−0.253634	+	0.373392i
$265$	−4.25735	−	0.750685i	−0.261527	−	0.0461142i
$266$	3.55678	+	3.00451i	0.218080	+	0.184218i
$267$	20.4290	−	5.78578i	1.25023	−	0.354084i
$268$	−3.16182	−	17.9316i	−0.193139	−	1.09534i
$269$	−9.79421	+	16.9641i	−0.597163	+	1.03432i	0.396074	+	0.918218i	$0.370372\pi$
$269$	−9.79421	+	16.9641i	−0.597163	+	1.03432i	−0.993238	+	0.116099i	$0.962961\pi$
$270$	−1.02954	+	4.62054i	−0.0626556	+	0.281197i
$271$	16.1584	−	9.32907i	0.981555	−	0.566701i	0.0788154	−	0.996889i	$-0.474886\pi$
$271$	16.1584	−	9.32907i	0.981555	−	0.566701i	0.902739	+	0.430188i	$0.141553\pi$
$272$	14.9017	+	5.42376i	0.903546	+	0.328864i
$273$	−10.9655	+	11.2071i	−0.663662	+	0.678283i
$274$	3.18214	+	2.67013i	0.192240	+	0.161309i
$275$	3.69222	+	10.1443i	0.222649	+	0.611724i
$276$	3.74004	+	2.54050i	0.225124	+	0.152920i
$277$	−0.463675	−	2.62963i	−0.0278595	−	0.157999i	0.967704	−	0.252088i	$-0.0811173\pi$
$277$	−0.463675	−	2.62963i	−0.0278595	−	0.157999i	−0.995564	+	0.0940890i	$0.970006\pi$
$278$	0.652848	−	1.13077i	0.0391552	−	0.0678188i
$279$	−6.17179	+	2.44680i	−0.369496	+	0.146486i
$280$	8.15305	−	4.67144i	0.487238	−	0.279172i
$281$	17.0926	−	3.01388i	1.01966	−	0.179793i	0.361261	−	0.932465i	$-0.382346\pi$
$281$	17.0926	−	3.01388i	1.01966	−	0.179793i	0.658396	+	0.752672i	$0.271235\pi$
$282$	−0.990058	−	1.37210i	−0.0589571	−	0.0817073i
$283$	1.07644	+	0.189805i	0.0639875	+	0.0112827i	0.205550	−	0.978647i	$-0.434102\pi$
$283$	1.07644	+	0.189805i	0.0639875	+	0.0112827i	−0.141563	+	0.989929i	$0.545213\pi$
$284$	20.8261	+	3.67221i	1.23580	+	0.217905i
$285$	−15.9907	−	22.1612i	−0.947208	−	1.31271i
$286$	−3.65995	+	0.645349i	−0.216418	+	0.0381603i
$287$	−13.9851	−	0.0460498i	−0.825516	−	0.00271823i
$288$	−8.39485	−	6.64752i	−0.494671	−	0.391709i
$289$	−2.37284	+	4.10988i	−0.139579	+	0.241758i
$290$	1.30208	+	7.38444i	0.0764606	+	0.433629i
$291$	−3.60125	−	2.44623i	−0.211109	−	0.143400i
$292$	3.83815	+	10.5452i	0.224611	+	0.617113i
$293$	16.1311	+	13.5356i	0.942391	+	0.790760i	0.978000	−	0.208606i	$-0.0668926\pi$
$293$	16.1311	+	13.5356i	0.942391	+	0.790760i	−0.0356088	+	0.999366i	$0.511337\pi$
$294$	−1.02864	−	3.72543i	−0.0599917	−	0.217271i
$295$	18.4339	+	6.70940i	1.07326	+	0.390636i
$296$	−1.89930	+	1.09656i	−0.110394	+	0.0637362i
$297$	−8.15885	−	15.7140i	−0.473424	−	0.911820i
$298$	0.237741	−	0.411779i	0.0137720	−	0.0238537i
$299$	0.816966	+	4.63324i	0.0472464	+	0.267947i
$300$	−10.0229	+	2.83863i	−0.578671	+	0.163888i
$301$	−4.25377	+	23.6683i	−0.245183	+	1.36422i
$302$	−1.52489	−	0.268880i	−0.0877478	−	0.0154723i
$303$	−9.06567	+	13.3462i	−0.520809	+	0.766718i
$304$	18.4884	−	3.26001i	1.06039	−	0.186974i
$305$			28.1308i			1.61077i
$306$	3.33342	−	2.96224i	0.190559	−	0.169340i
$307$	−19.7567	−	11.4065i	−1.12757	−	0.651004i	−0.184249	−	0.982880i	$-0.558985\pi$
$307$	−19.7567	−	11.4065i	−1.12757	−	0.651004i	−0.943323	+	0.331876i	$0.892318\pi$
$308$	−5.90650	+	16.0632i	−0.336554	+	0.915285i
$309$	−7.99827	+	17.8077i	−0.455006	+	1.01304i
$310$	1.54446	+	1.29595i	0.0877193	+	0.0736052i
$311$	−3.90921	+	22.1702i	−0.221671	+	1.25716i	0.647277	+	0.762255i	$0.275908\pi$
$311$	−3.90921	+	22.1702i	−0.221671	+	1.25716i	−0.868948	+	0.494903i	$0.835204\pi$
$312$	−0.745864	−	7.32649i	−0.0422262	−	0.414781i
$313$	−0.907448	−	1.08145i	−0.0512920	−	0.0611274i	0.739788	−	0.672839i	$-0.234926\pi$
$313$	−0.907448	−	1.08145i	−0.0512920	−	0.0611274i	−0.791080	+	0.611712i	$0.790481\pi$
$314$	−3.59031	+	6.21859i	−0.202613	+	0.350935i
$315$	0.568934	+	22.6775i	0.0320558	+	1.27773i
$316$	−10.8500	−	18.7927i	−0.610358	−	1.05717i
$317$	−2.34444	+	6.44131i	−0.131677	+	0.361780i	−0.987956	−	0.154733i	$-0.950548\pi$
$317$	−2.34444	+	6.44131i	−0.131677	+	0.361780i	0.856279	+	0.516513i	$0.172770\pi$
$318$	−0.363648	−	0.751810i	−0.0203924	−	0.0421594i
$319$	−21.4844	−	18.0275i	−1.20289	−	1.00935i
$320$	2.81072	−	15.9404i	0.157124	−	0.891095i
$321$	−11.2434	−	2.84232i	−0.627544	−	0.158643i
$322$	−1.08843	−	0.400219i	−0.0606558	−	0.0223034i
$323$			25.7438i			1.43242i
$324$	15.6978	−	6.74483i	0.872101	−	0.374713i
$325$	−9.38747	−	5.41986i	−0.520723	−	0.300640i
$326$	1.97238	+	2.35059i	0.109240	+	0.130187i
$327$	−27.6804	+	7.83948i	−1.53073	+	0.433524i
$328$	4.22225	−	5.03188i	0.233135	−	0.277839i
$329$	−6.19394	−	5.23219i	−0.341483	−	0.288460i
$330$	−3.02124	+	4.44778i	−0.166314	+	0.244842i
$331$	−2.79664	−	1.01790i	−0.153717	−	0.0559486i	0.264015	−	0.964518i	$-0.414953\pi$
$331$	−2.79664	−	1.01790i	−0.153717	−	0.0559486i	−0.417733	+	0.908570i	$0.637175\pi$
$332$	−13.5876			−0.745715
$333$	−0.150215	−	5.29238i	−0.00823171	−	0.290021i
$334$			3.21366i			0.175844i
$335$	−4.76007	−	26.9957i	−0.260070	−	1.47493i
$336$	−14.1946	−	6.43171i	−0.774379	−	0.350879i
$337$	23.6884	−	8.62186i	1.29039	−	0.469663i	0.396534	−	0.918020i	$-0.370213\pi$
$337$	23.6884	−	8.62186i	1.29039	−	0.469663i	0.893854	+	0.448357i	$0.147991\pi$
$338$	−0.264997	+	0.315811i	−0.0144139	+	0.0171779i
$339$	10.7283	+	14.8681i	0.582680	+	0.807522i
$340$	23.7749	+	8.65335i	1.28937	+	0.469294i
$341$	−7.54092			−0.408364
$342$	1.66416	−	5.01019i	0.0899876	−	0.270920i
$343$	−9.10124	−	16.1297i	−0.491421	−	0.870922i
$344$	−7.26016	−	8.65232i	−0.391442	−	0.466502i
$345$	5.63057	+	3.82468i	0.303140	+	0.205914i
$346$	2.53271	−	3.01836i	0.136159	−	0.162268i
$347$	0.787258	+	2.16297i	0.0422622	+	0.116114i	0.959029	−	0.283310i	$-0.0914324\pi$
$347$	0.787258	+	2.16297i	0.0422622	+	0.116114i	−0.916766	+	0.399424i	$0.869210\pi$
$348$	18.8632	−	19.4061i	1.01117	−	1.04028i
$349$	−2.39148	+	6.57053i	−0.128013	+	0.351712i	−0.987097	−	0.160121i	$-0.948811\pi$
$349$	−2.39148	+	6.57053i	−0.128013	+	0.351712i	0.859084	+	0.511834i	$0.171034\pi$
$350$	2.31833	−	1.32833i	0.123920	−	0.0710022i
$351$	16.4180	+	6.82117i	0.876331	+	0.364087i
$352$	−6.08129	−	10.5331i	−0.324134	−	0.561416i
$353$	16.9198	−	14.1974i	0.900550	−	0.755651i	−0.0697482	−	0.997565i	$-0.522220\pi$
$353$	16.9198	−	14.1974i	0.900550	−	0.755651i	0.970298	+	0.241914i	$0.0777751\pi$
$354$	1.03268	+	3.64627i	0.0548862	+	0.193797i
$355$	31.3534	+	5.52844i	1.66406	+	0.293419i
$356$	−4.04106	+	22.9180i	−0.214176	+	1.21465i
$357$	12.0657	−	17.6374i	0.638582	−	0.933472i
$358$	3.85423	−	3.23408i	0.203702	−	0.170926i
$359$	−28.2380	−	16.3032i	−1.49035	−	0.860451i	−0.490407	−	0.871494i	$-0.663152\pi$
$359$	−28.2380	−	16.3032i	−1.49035	−	0.860451i	−0.999939	+	0.0110424i	$0.996485\pi$
$360$	−8.35296	−	6.61435i	−0.440240	−	0.348607i
$361$	5.73852	+	9.93941i	0.302027	+	0.523127i
$362$	−3.20317	+	2.68777i	−0.168355	+	0.141266i
$363$	−0.107186	−	1.05287i	−0.00562583	−	0.0552615i
$364$	−5.82443	−	16.1679i	−0.305283	−	0.847431i
$365$	5.77827	+	15.8757i	0.302449	+	0.830971i
$366$	−4.40695	+	3.17990i	−0.230355	+	0.166216i
$367$	−1.45484	+	3.99714i	−0.0759420	+	0.208649i	−0.971855	−	0.235581i	$-0.924301\pi$
$367$	−1.45484	+	3.99714i	−0.0759420	+	0.208649i	0.895913	+	0.444230i	$0.146523\pi$
$368$	−4.04958	+	2.33803i	−0.211099	+	0.121878i
$369$	5.84426	+	14.7415i	0.304240	+	0.767412i
$370$	−1.39241	+	0.803911i	−0.0723882	+	0.0417933i
$371$	−2.56232	−	3.07415i	−0.133029	−	0.159602i
$372$	0.531299	−	7.25728i	0.0275466	−	0.376273i
$373$	22.9007	−	8.33516i	1.18575	−	0.431578i	0.327521	−	0.944844i	$-0.393787\pi$
$373$	22.9007	−	8.33516i	1.18575	−	0.431578i	0.858230	+	0.513266i	$0.171564\pi$
$374$	4.75970	−	1.73239i	0.246118	−	0.0895797i
$375$	8.72500	−	2.47105i	0.450557	−	0.127604i
$376$	3.75039	−	0.661295i	0.193412	−	0.0341037i
$377$	28.1612			1.45037
$378$	−3.48832	+	2.65259i	−0.179420	+	0.136434i
$379$	−17.8518			−0.916987			−0.458493	−	0.888698i	$-0.651611\pi$
$379$	−17.8518			−0.916987			−0.458493	+	0.888698i	$0.651611\pi$
$380$	29.4974	−	5.20119i	1.51319	−	0.266815i
$381$	−7.20545	+	28.5027i	−0.369147	+	1.46024i
$382$	−5.32375	+	1.93769i	−0.272387	+	0.0991406i
$383$	25.7206	−	9.36155i	1.31426	−	0.478353i	0.412648	−	0.910891i	$-0.364604\pi$
$383$	25.7206	−	9.36155i	1.31426	−	0.478353i	0.901616	+	0.432538i	$0.142382\pi$
$384$	13.9458	−	6.74555i	0.711670	−	0.344232i
$385$	−8.89213	+	24.1829i	−0.453185	+	1.23247i
$386$	−3.76104	+	2.17144i	−0.191432	+	0.110523i
$387$	26.7079	−	5.49489i	1.35764	−	0.279321i
$388$	4.13233	−	2.38580i	0.209787	−	0.121121i
$389$	5.57461	−	15.3161i	0.282644	−	0.776558i	−0.714401	−	0.699736i	$-0.753301\pi$
$389$	5.57461	−	15.3161i	0.282644	−	0.776558i	0.997045	−	0.0768211i	$-0.0244770\pi$
$390$	−0.546809	−	5.37120i	−0.0276887	−	0.271981i
$391$	−2.19308	−	6.02544i	−0.110909	−	0.304720i
$392$	8.55643	+	1.56690i	0.432165	+	0.0791403i
$393$	−22.4668	+	16.2112i	−1.13330	+	0.817749i
$394$	−2.25183	+	1.88951i	−0.113446	+	0.0951921i
$395$	−16.3344	−	28.2920i	−0.821874	−	1.42353i
$396$	19.3984	−	0.550589i	0.974808	−	0.0276681i
$397$	3.94601	+	2.27823i	0.198045	+	0.114341i	0.595743	−	0.803175i	$-0.296858\pi$
$397$	3.94601	+	2.27823i	0.198045	+	0.114341i	−0.397698	+	0.917516i	$0.630191\pi$
$398$	0.0654872	−	0.0549503i	0.00328258	−	0.00275441i
$399$	1.93021	−	25.2248i	0.0966314	−	1.26282i
$400$	1.87083	−	10.6100i	0.0935414	−	0.530499i
$401$	−37.1238	−	6.54593i	−1.85388	−	0.326888i	−0.868289	−	0.496059i	$-0.834780\pi$
$401$	−37.1238	−	6.54593i	−1.85388	−	0.326888i	−0.985587	+	0.169170i	$0.945891\pi$
$402$	3.69104	−	3.79729i	0.184093	−	0.189392i
$403$	5.80043	−	4.86714i	0.288940	−	0.242449i
$404$	−8.84173	−	15.3143i	−0.439893	−	0.761916i
$405$	23.6328	−	10.1542i	1.17432	−	0.504568i
$406$	−3.49053	+	6.00007i	−0.173232	+	0.297778i
$407$	2.05680	−	5.65101i	0.101952	−	0.280110i
$408$	2.73505	+	9.65717i	0.135405	+	0.478101i
$409$	−0.342534	−	0.941105i	−0.0169372	−	0.0465347i	0.930936	−	0.365183i	$-0.118993\pi$
$409$	−0.342534	−	0.941105i	−0.0169372	−	0.0465347i	−0.947873	+	0.318648i	$0.896771\pi$
$410$	3.09542	−	3.68898i	0.152872	−	0.182186i
$411$	1.64800	−	22.5109i	0.0812901	−	1.11038i
$412$	−13.7532	−	16.3904i	−0.677571	−	0.807498i
$413$	9.02825	+	15.7570i	0.444251	+	0.775350i
$414$	0.0373075	+	1.31442i	0.00183356	+	0.0646003i
$415$	−20.4559			−1.00414
$416$	11.4761	+	4.17695i	0.562661	+	0.204792i
$417$	−7.05817	+	0.718548i	−0.345640	+	0.0351874i
$418$	3.85444	−	4.59354i	0.188527	−	0.224677i
$419$	2.20646	−	0.803084i	0.107792	−	0.0392332i	−0.287561	−	0.957762i	$-0.592844\pi$
$419$	2.20646	−	0.803084i	0.107792	−	0.0392332i	0.395353	+	0.918529i	$0.370622\pi$
$420$	−22.6468	−	10.2615i	−1.10505	−	0.500709i
$421$	1.14047	+	6.46793i	0.0555831	+	0.315228i	0.999905	−	0.0137960i	$-0.00439155\pi$
$421$	1.14047	+	6.46793i	0.0555831	+	0.315228i	−0.944322	+	0.329024i	$0.893280\pi$
$422$		−	4.17007i		−	0.202996i
$423$	−2.89805	+	8.72497i	−0.140908	+	0.424223i
$424$	1.87968			0.0912853
$425$	13.8827	+	5.05288i	0.673409	+	0.245101i
$426$	2.67810	+	5.53673i	0.129754	+	0.268255i
$427$	−16.8049	+	19.8939i	−0.813247	+	0.962734i
$428$	8.17035	−	9.73704i	0.394929	−	0.470658i
$429$	14.4801	+	14.0750i	0.699108	+	0.679547i
$430$	−5.32258	−	6.34320i	−0.256677	−	0.305896i
$431$	−13.3456	−	7.70506i	−0.642833	−	0.371140i	0.142872	−	0.989741i	$-0.454366\pi$
$431$	−13.3456	−	7.70506i	−0.642833	−	0.371140i	−0.785705	+	0.618602i	$0.787700\pi$
$432$	−0.789656	+	17.6527i	−0.0379923	+	0.849314i
$433$			9.87188i			0.474412i	0.971459	+	0.237206i	$0.0762317\pi$
$433$			9.87188i			0.474412i	−0.971459	+	0.237206i	$0.923768\pi$
$434$	0.318047	+	1.83912i	0.0152667	+	0.0882808i
$435$	28.3982	−	29.2156i	1.36159	−	1.40078i
$436$	5.47546	−	31.0529i	0.262227	−	1.48716i
$437$	−5.81510	−	4.87945i	−0.278174	−	0.233416i
$438$	−1.83390	+	2.69980i	−0.0876270	+	0.129002i
$439$	−12.0752	+	33.1763i	−0.576317	+	1.58342i	0.218021	+	0.975944i	$0.430040\pi$
$439$	−12.0752	+	33.1763i	−0.576317	+	1.58342i	−0.794339	+	0.607475i	$0.792182\pi$
$440$	−6.05094	−	10.4805i	−0.288467	−	0.499640i
$441$	−13.1448	+	16.3772i	−0.625944	+	0.779868i
$442$	−2.54299	+	4.40460i	−0.120958	+	0.209505i
$443$	2.86061	+	3.40914i	0.135912	+	0.161973i	0.829707	−	0.558199i	$-0.188507\pi$
$443$	2.86061	+	3.40914i	0.135912	+	0.161973i	−0.693796	+	0.720172i	$0.744063\pi$
$444$	5.29355	+	2.37758i	0.251221	+	0.112835i
$445$	−6.08375	+	34.5026i	−0.288397	+	1.63558i
$446$	−3.61076	−	3.02979i	−0.170975	−	0.143465i
$447$	−2.57030	+	0.261666i	−0.121571	+	0.0123764i
$448$	11.5103	−	9.59385i	0.543809	−	0.453267i
$449$	4.96216	+	2.86491i	0.234179	+	0.135203i	0.612498	−	0.790472i	$-0.290165\pi$
$449$	4.96216	+	2.86491i	0.234179	+	0.135203i	−0.378319	+	0.925675i	$0.623498\pi$
$450$	−2.37517	−	1.88080i	−0.111967	−	0.0886617i
$451$			18.0117i			0.848138i
$452$	−19.7900	+	3.48951i	−0.930843	+	0.164133i
$453$	3.66353	+	7.57401i	0.172127	+	0.355858i
$454$	2.87869	+	0.507591i	0.135104	+	0.0238224i
$455$	−8.76859	−	24.3406i	−0.411078	−	1.14110i
$456$	8.52048	+	8.28207i	0.399008	+	0.387844i
$457$	7.09654	+	40.2465i	0.331962	+	1.88265i	0.455384	+	0.890295i	$0.349502\pi$
$457$	7.09654	+	40.2465i	0.331962	+	1.88265i	−0.123422	+	0.992354i	$0.539387\pi$
$458$	−2.03913	+	3.53187i	−0.0952821	+	0.165033i
$459$	−23.6508	−	5.26982i	−1.10393	−	0.245974i
$460$	−6.46090	+	3.73020i	−0.301241	+	0.173922i
$461$	−25.5016	−	9.28183i	−1.18773	−	0.432298i	−0.328803	−	0.944399i	$-0.606645\pi$
$461$	−25.5016	−	9.28183i	−1.18773	−	0.432298i	−0.858925	+	0.512101i	$0.828867\pi$
$462$	−4.79363	+	1.34059i	−0.223020	+	0.0623700i
$463$	−9.76642	−	8.19500i	−0.453884	−	0.380854i	0.386991	−	0.922084i	$-0.373515\pi$
$463$	−9.76642	−	8.19500i	−0.453884	−	0.380854i	−0.840875	+	0.541230i	$0.817959\pi$
$464$	9.57299	+	26.3016i	0.444415	+	1.22102i
$465$	0.799861	−	10.9257i	0.0370927	−	0.506668i
$466$	0.944701	+	5.35766i	0.0437624	+	0.248189i
$467$	11.2722	−	19.5239i	0.521613	−	0.903460i	−0.478071	−	0.878321i	$-0.658664\pi$
$467$	11.2722	−	19.5239i	0.521613	−	0.903460i	0.999684	−	0.0251391i	$-0.00800286\pi$
$468$	−14.5658	+	12.9438i	−0.673304	+	0.598330i
$469$	12.7605	−	21.9347i	0.589226	−	1.01285i
$470$	2.74949	−	0.484810i	0.126825	−	0.0223626i
$471$	38.8160	−	3.95162i	1.78855	−	0.182081i
$472$	−8.40000	−	1.48115i	−0.386641	−	0.0681753i
$473$	30.5006	+	5.37808i	1.40242	+	0.247284i
$474$	2.58577	−	5.75707i	0.118768	−	0.264431i
$475$	17.2242	−	3.03709i	0.790300	−	0.139351i
$476$	11.6441	+	20.3223i	0.533704	+	0.931473i
$477$	−2.15650	+	3.99267i	−0.0987395	+	0.182812i
$478$	1.07573	−	1.86322i	0.0492027	−	0.0852215i
$479$	−5.66597	−	32.1333i	−0.258885	−	1.46821i	−0.785901	−	0.618353i	$-0.787800\pi$
$479$	−5.66597	−	32.1333i	−0.258885	−	1.46821i	0.527016	−	0.849856i	$-0.323311\pi$
$480$	15.9060	−	7.69368i	0.726006	−	0.351167i
$481$	2.06526	+	5.67424i	0.0941676	+	0.258723i
$482$	0.685664	+	0.575340i	0.0312311	+	0.0262060i
$483$	1.69710	+	6.06840i	0.0772206	+	0.276122i
$484$	1.09000	+	0.396726i	0.0495453	+	0.0180330i
$485$	6.22115	−	3.59178i	0.282488	−	0.163094i
$486$	4.26220	+	2.55446i	0.193337	+	0.115873i
$487$	3.41485	−	5.91469i	0.154741	−	0.268020i	−0.778223	−	0.627988i	$-0.783879\pi$
$487$	3.41485	−	5.91469i	0.154741	−	0.268020i	0.932965	+	0.359967i	$0.117212\pi$
$488$	−2.12397	−	12.0456i	−0.0961476	−	0.545280i
$489$	4.08635	−	16.1644i	0.184791	−	0.730980i
$490$	6.27290	+	1.14873i	0.283381	+	0.0518942i
$491$	−2.93823	−	0.518089i	−0.132601	−	0.0233810i	0.106954	−	0.994264i	$-0.465890\pi$
$491$	−2.93823	−	0.518089i	−0.132601	−	0.0233810i	−0.239554	+	0.970883i	$0.577001\pi$
$492$	−17.3342	−	1.26902i	−0.781487	−	0.0572120i
$493$	−37.7982	+	6.66485i	−1.70235	+	0.300170i
$494$			6.02109i			0.270902i
$495$	29.2040	−	0.828902i	1.31262	−	0.0372564i
$496$	6.51752	+	3.76289i	0.292645	+	0.168959i
$497$	18.8703	+	22.6397i	0.846447	+	1.01553i
$498$	−2.31233	−	3.20460i	−0.103618	−	0.143602i
$499$	23.4393	+	19.6679i	1.04929	+	0.880457i	0.993019	−	0.117958i	$-0.0376349\pi$
$499$	23.4393	+	19.6679i	1.04929	+	0.880457i	0.0562697	+	0.998416i	$0.482079\pi$
$500$	−1.72589	+	9.78804i	−0.0771844	+	0.437734i
$501$	14.1603	−	10.2176i	0.632637	−	0.456489i
$502$	−4.67921	−	5.57647i	−0.208843	−	0.248890i
$503$	−4.53519	+	7.85518i	−0.202214	+	0.350245i	−0.949242	−	0.314548i	$-0.898147\pi$
$503$	−4.53519	+	7.85518i	−0.202214	+	0.350245i	0.747027	+	0.664793i	$0.231480\pi$
$504$	−1.95584	−	9.66755i	−0.0871202	−	0.430627i
$505$	−13.3111	−	23.0555i	−0.592335	−	1.02595i
$506$	−0.510829	+	1.40349i	−0.0227091	+	0.0623928i
$507$	2.23410	+	0.163556i	0.0992197	+	0.00726378i
$508$	−24.6840	−	20.7123i	−1.09518	−	0.918962i
$509$	−1.29588	+	7.34928i	−0.0574387	+	0.325751i	−0.999965	−	0.00838120i	$-0.997332\pi$
$509$	−1.29588	+	7.34928i	−0.0574387	+	0.325751i	0.942526	+	0.334132i	$0.108443\pi$
$510$	2.00513	+	7.07988i	0.0887884	+	0.313502i
$511$	−5.39753	+	14.6790i	−0.238773	+	0.649362i
$512$			20.5900i			0.909956i
$513$	−27.3674	+	8.59674i	−1.20830	+	0.379555i
$514$	3.45607	+	1.99536i	0.152441	+	0.0880117i
$515$	−20.7052	−	24.6755i	−0.912380	−	1.08733i
$516$	−7.32473	+	28.9745i	−0.322453	+	1.27553i
$517$	−6.71229	+	7.99940i	−0.295206	+	0.351813i
$518$	−1.46495	−	0.263287i	−0.0643662	−	0.0115682i
$519$	−21.3523	−	1.56318i	−0.937264	−	0.0686162i
$520$	11.4188	+	4.15611i	0.500748	+	0.182257i
$521$	15.7598			0.690450			0.345225	−	0.938520i	$-0.387803\pi$
$521$	15.7598			0.690450			0.345225	+	0.938520i	$0.387803\pi$
$522$	7.78702	+	1.14630i	0.340829	+	0.0501724i
$523$		−	5.63241i		−	0.246288i	−0.992389	−	0.123144i	$-0.960702\pi$
$523$		−	5.63241i		−	0.246288i	0.992389	−	0.123144i	$-0.0392977\pi$
$524$	−5.27292	−	29.9042i	−0.230348	−	1.30637i
$525$	−13.2240	−	5.99191i	−0.577141	−	0.261508i
$526$	3.81019	−	1.38679i	0.166132	−	0.0604671i
$527$	−6.63351	+	7.90550i	−0.288960	+	0.344369i
$528$	−8.22324	+	18.3086i	−0.357871	+	0.796778i
$529$	−19.8362	−	7.21979i	−0.862444	−	0.313904i
$530$	1.37803			0.0598579
$531$	12.7832	−	16.1433i	0.554744	−	0.700561i
$532$	23.9675	+	13.9431i	1.03912	+	0.604508i
$533$	−11.6253	−	13.8545i	−0.503548	−	0.600105i
$534$	−6.09286	+	2.94710i	−0.263664	+	0.127533i
$535$	12.3003	−	14.6590i	0.531789	−	0.633762i
$536$	4.07653	+	11.2002i	0.176079	+	0.483774i
$537$	−26.5045	−	6.70033i	−1.14375	−	0.289141i
$538$	2.13561	−	5.86755i	0.0920729	−	0.252968i
$539$	−20.7349	+	11.7899i	−0.893117	+	0.507829i
$540$	−1.25986	+	28.1640i	−0.0542156	+	1.21198i
$541$	−0.446747	−	0.773788i	−0.0192071	−	0.0332677i	0.856262	−	0.516542i	$-0.172781\pi$
$541$	−0.446747	−	0.773788i	−0.0192071	−	0.0332677i	−0.875469	+	0.483274i	$0.839448\pi$
$542$	−4.55611	+	3.82303i	−0.195702	+	0.164213i
$543$	22.0273	+	5.56850i	0.945284	+	0.238967i
$544$	−16.3919	−	2.89033i	−0.702795	−	0.123922i
$545$	8.24321	−	46.7496i	0.353100	−	2.00253i
$546$	2.82198	−	4.12513i	0.120769	−	0.176539i
$547$	4.87449	−	4.09018i	0.208418	−	0.174884i	−0.532603	−	0.846365i	$-0.678786\pi$
$547$	4.87449	−	4.09018i	0.208418	−	0.174884i	0.741021	+	0.671481i	$0.234342\pi$
$548$	21.4244	+	12.3694i	0.915207	+	0.528395i
$549$	28.0232	+	9.30805i	1.19600	+	0.397258i
$550$	−1.72059	−	2.98015i	−0.0733663	−	0.127074i
$551$	−34.8076	+	29.2070i	−1.48285	+	1.24426i
$552$	−2.69979	−	1.21260i	−0.114911	−	0.0516118i
$553$	5.34965	−	29.7659i	0.227490	−	1.26577i
$554$	0.291117	+	0.799836i	0.0123684	+	0.0339818i
$555$	7.96934	+	3.57941i	0.338280	+	0.151937i
$556$	2.65954	−	7.30703i	0.112790	−	0.309887i
$557$	−14.9657	+	8.64047i	−0.634119	+	0.366109i	−0.782345	−	0.622845i	$-0.785977\pi$
$557$	−14.9657	+	8.64047i	−0.634119	+	0.366109i	0.148227	+	0.988953i	$0.452643\pi$
$558$	1.80203	−	1.10974i	0.0762860	−	0.0469789i
$559$	−26.9320	+	15.5492i	−1.13910	+	0.657662i
$560$	19.7525	−	16.4638i	0.834696	−	0.695722i
$561$	−22.7665	−	15.4646i	−0.961203	−	0.652917i
$562$	−5.19892	+	1.89225i	−0.219303	+	0.0798199i
$563$	−1.75211	+	0.637716i	−0.0738426	+	0.0268765i	−0.378677	−	0.925529i	$-0.623621\pi$
$563$	−1.75211	+	0.637716i	−0.0738426	+	0.0268765i	0.304835	+	0.952405i	$0.401399\pi$
$564$	−7.22560	−	7.02342i	−0.304253	−	0.295740i
$565$	−29.7935	+	5.25340i	−1.25342	+	0.221012i
$566$	−0.348424			−0.0146454
$567$	22.7789	+	6.93687i	0.956625	+	0.291321i
$568$	−13.8429			−0.580837
$569$	−25.3007	+	4.46119i	−1.06066	+	0.187023i	−0.676648	−	0.736306i	$-0.736568\pi$
$569$	−25.3007	+	4.46119i	−1.06066	+	0.187023i	−0.384010	+	0.923329i	$0.625457\pi$
$570$	6.24655	+	6.07176i	0.261639	+	0.254318i
$571$	2.05601	−	0.748326i	0.0860413	−	0.0313165i	−0.298641	−	0.954366i	$-0.596533\pi$
$571$	2.05601	−	0.748326i	0.0860413	−	0.0313165i	0.384682	+	0.923049i	$0.374311\pi$
$572$	−20.7981	+	7.56988i	−0.869611	+	0.316513i
$573$	25.4645	+	17.2973i	1.06379	+	0.722603i
$574$	4.39280	−	0.759664i	0.183352	−	0.0317078i
$575$	−3.77267	+	2.17815i	−0.157331	+	0.0908351i
$576$	−14.9494	−	8.07439i	−0.622890	−	0.336433i
$577$	12.3597	−	7.13589i	0.514542	−	0.297071i	−0.220157	−	0.975464i	$-0.570657\pi$
$577$	12.3597	−	7.13589i	0.514542	−	0.297071i	0.734699	+	0.678394i	$0.237324\pi$
$578$	0.517395	−	1.42153i	0.0215208	−	0.0591279i
$579$	21.5259	+	9.66832i	0.894588	+	0.401802i
$580$	15.2732	+	41.9629i	0.634187	+	1.74241i
$581$	−14.4662	−	12.2200i	−0.600161	−	0.506972i
$582$	1.26592	+	0.568586i	0.0524742	+	0.0235686i
$583$	−3.94835	+	3.31306i	−0.163524	+	0.137213i
$584$	−3.67293	−	6.36170i	−0.151987	−	0.263249i
$585$	−21.9286	+	19.4867i	−0.906634	+	0.805678i
$586$	−5.81318	−	3.35624i	−0.240140	−	0.138645i
$587$	−20.9075	+	17.5435i	−0.862947	+	0.724098i	−0.962601	−	0.270924i	$-0.912671\pi$
$587$	−20.9075	+	17.5435i	−0.862947	+	0.724098i	0.0996541	+	0.995022i	$0.468226\pi$
$588$	−9.88559	−	20.7857i	−0.407675	−	0.857188i
$589$	−2.12151	+	12.0317i	−0.0874154	+	0.495757i
$590$	−6.15822	−	1.08586i	−0.253530	−	0.0447042i
$591$	15.4853	+	3.91466i	0.636978	+	0.161028i
$592$	−4.59750	+	3.85776i	−0.188956	+	0.158553i
$593$	−9.81715	−	17.0038i	−0.403142	−	0.698262i	0.590961	−	0.806700i	$-0.298749\pi$
$593$	−9.81715	−	17.0038i	−0.403142	−	0.698262i	−0.994103	+	0.108438i	$0.965415\pi$
$594$	3.43107	+	4.48138i	0.140779	+	0.183873i
$595$	17.5299	+	30.5949i	0.718657	+	1.25427i
$596$	0.968498	−	2.66093i	0.0396712	−	0.108996i
$597$	−0.450339	−	0.113845i	−0.0184311	−	0.00465938i
$598$	−0.512929	−	1.40926i	−0.0209752	−	0.0576290i
$599$	12.4046	−	14.7832i	0.506837	−	0.604025i	−0.450579	−	0.892737i	$-0.648782\pi$
$599$	12.4046	−	14.7832i	0.506837	−	0.604025i	0.957416	+	0.288712i	$0.0932269\pi$
$600$	6.13858	−	2.96921i	0.250606	−	0.121217i
$601$	−13.5997	−	16.2075i	−0.554743	−	0.661116i	0.413683	−	0.910421i	$-0.364242\pi$
$601$	−13.5997	−	16.2075i	−0.554743	−	0.661116i	−0.968425	+	0.249305i	$0.919798\pi$
$602$	0.0252407	−	7.66549i	0.00102873	−	0.312422i
$603$	−28.4674	−	4.19060i	−1.15928	−	0.170654i
$604$	−9.22150			−0.375217
$605$	1.64097	+	0.597265i	0.0667150	+	0.0242823i
$606$	2.10717	−	4.69149i	0.0855979	−	0.190579i
$607$	−9.60228	+	11.4436i	−0.389745	+	0.464480i	−0.924865	−	0.380296i	$-0.875822\pi$
$607$	−9.60228	+	11.4436i	−0.389745	+	0.464480i	0.535120	+	0.844776i	$0.320266\pi$
$608$	−18.5167	+	6.73951i	−0.750949	+	0.273323i
$609$	37.5360	−	3.69647i	1.52103	−	0.149788i
$610$	−1.55713	−	8.83091i	−0.0630463	−	0.357553i
$611$		−	10.4854i		−	0.424194i
$612$	16.4870	−	20.8206i	0.666446	−	0.841624i
$613$	5.58886			0.225732			0.112866	−	0.993610i	$-0.463997\pi$
$613$	5.58886			0.225732			0.112866	+	0.993610i	$0.463997\pi$
$614$	6.83346	+	2.48717i	0.275776	+	0.100374i
$615$	−26.0964	−	1.91049i	−1.05231	−	0.0770385i
$616$	1.98173	−	11.0265i	0.0798462	−	0.444271i
$617$	4.78146	−	5.69832i	0.192494	−	0.229406i	−0.661161	−	0.750244i	$-0.729936\pi$
$617$	4.78146	−	5.69832i	0.192494	−	0.229406i	0.853655	+	0.520838i	$0.174381\pi$
$618$	1.52513	−	6.03297i	0.0613498	−	0.242682i
$619$	9.85761	+	11.7478i	0.396211	+	0.472185i	0.926861	−	0.375406i	$-0.122497\pi$
$619$	9.85761	+	11.7478i	0.396211	+	0.472185i	−0.530650	+	0.847591i	$0.678052\pi$
$620$	10.3984	+	6.00351i	0.417609	+	0.241107i
$621$	5.67311	−	4.34350i	0.227654	−	0.174298i
$622$		−	7.17613i		−	0.287737i
$623$	−24.9137	+	20.7657i	−0.998148	+	0.831960i
$624$	−5.49164	−	19.3904i	−0.219841	−	0.776236i
$625$	−5.34899	+	30.3356i	−0.213960	+	1.21343i
$626$	0.344731	+	0.289263i	0.0137782	+	0.0115613i
$627$	−32.4954	−	2.37896i	−1.29774	−	0.0950063i
$628$	−14.6260	+	40.1847i	−0.583642	+	1.60354i
$629$	−4.11492	−	7.12725i	−0.164073	−	0.284182i
$630$	−1.43387	−	7.08749i	−0.0571268	−	0.282372i
$631$	−12.0123	+	20.8060i	−0.478203	+	0.828272i	−0.999688	−	0.0249886i	$-0.992045\pi$
$631$	−12.0123	+	20.8060i	−0.478203	+	0.828272i	0.521485	+	0.853261i	$0.325378\pi$
$632$	9.13056	+	10.8814i	0.363194	+	0.432838i
$633$	−18.3745	+	13.2584i	−0.730322	+	0.526975i
$634$	0.379429	−	2.15185i	0.0150690	−	0.0854608i
$635$	−37.1614	−	31.1821i	−1.47470	−	1.23742i
$636$	−2.91026	−	4.03327i	−0.115399	−	0.159929i
$637$	8.33960	−	22.4517i	0.330427	−	0.889569i
$638$	7.74232	+	4.47003i	0.306521	+	0.176970i
$639$	15.8816	−	29.4041i	0.628267	−	1.16321i
$640$			25.5620i			1.01043i
$641$	44.3011	−	7.81149i	1.74979	−	0.308535i	0.795176	−	0.606379i	$-0.207379\pi$
$641$	44.3011	−	7.81149i	1.74979	−	0.308535i	0.954615	+	0.297844i	$0.0962676\pi$
$642$	3.68689	+	0.269914i	0.145510	+	0.0106526i
$643$	−5.46038	−	0.962813i	−0.215337	−	0.0379696i	0.0649390	−	0.997889i	$-0.479315\pi$
$643$	−5.46038	−	0.962813i	−0.215337	−	0.0379696i	−0.280276	+	0.959920i	$0.590426\pi$
$644$	−6.79747	−	1.22167i	−0.267858	−	0.0481405i
$645$	−11.0273	+	43.6206i	−0.434198	+	1.71756i
$646$	−1.42500	−	8.08158i	−0.0560659	−	0.317965i
$647$	17.8595	−	30.9335i	0.702127	−	1.21612i	−0.265591	−	0.964086i	$-0.585567\pi$
$647$	17.8595	−	30.9335i	0.702127	−	1.21612i	0.967718	−	0.252035i	$-0.0810997\pi$
$648$	−9.35290	+	6.13241i	−0.367417	+	0.240904i
$649$	20.2552	−	11.6943i	0.795086	−	0.459043i
$650$	3.24695	+	1.18179i	0.127356	+	0.0463538i
$651$	7.09251	−	7.24877i	0.277978	−	0.284102i
$652$	13.9988	+	11.7464i	0.548235	+	0.460023i
$653$	9.10992	+	25.0293i	0.356499	+	0.979472i	0.980235	+	0.197837i	$0.0633917\pi$
$653$	9.10992	+	25.0293i	0.356499	+	0.979472i	−0.623736	+	0.781635i	$0.714386\pi$
$654$	8.25557	−	3.99319i	0.322818	−	0.156146i
$655$	−7.93829	−	45.0203i	−0.310175	−	1.75909i
$656$	8.98777	−	15.5673i	0.350914	−	0.607800i
$657$	17.7269	−	0.503145i	0.691591	−	0.0196295i
$658$	2.23404	+	1.29965i	0.0870919	+	0.0506656i
$659$	27.7440	−	4.89202i	1.08075	−	0.190566i	0.395205	−	0.918593i	$-0.370673\pi$
$659$	27.7440	−	4.89202i	1.08075	−	0.190566i	0.685549	+	0.728027i	$0.259562\pi$
$660$	−13.1198	+	29.2104i	−0.510687	+	1.13701i
$661$	−32.7012	−	5.76611i	−1.27193	−	0.224276i	−0.503380	−	0.864065i	$-0.667910\pi$
$661$	−32.7012	−	5.76611i	−1.27193	−	0.224276i	−0.768550	+	0.639790i	$0.779021\pi$
$662$	0.934275	+	0.164738i	0.0363116	+	0.00640272i
$663$	27.4932	−	2.79891i	1.06775	−	0.108701i
$664$	8.75922	−	1.54449i	0.339924	−	0.0599377i
$665$	36.0826	+	20.9910i	1.39922	+	0.813997i
$666$	0.340106	+	1.65309i	0.0131788	+	0.0640558i
$667$	5.65875	−	9.80124i	0.219108	−	0.379505i
$668$	3.32341	+	18.8480i	0.128587	+	0.729250i
$669$	−1.86998	+	25.5431i	−0.0722978	+	0.987553i
$670$	2.98859	+	8.21108i	0.115459	+	0.317222i
$671$	25.6927	+	21.5588i	0.991857	+	0.832267i
$672$	15.8447	+	4.06108i	0.611223	+	0.156660i
$673$	2.51415	+	0.915077i	0.0969135	+	0.0352736i	0.390022	−	0.920806i	$-0.372467\pi$
$673$	2.51415	+	0.915077i	0.0969135	+	0.0352736i	−0.293108	+	0.956079i	$0.594690\pi$
$674$	−6.95908	+	4.01783i	−0.268054	+	0.154761i
$675$	−0.735658	+	16.4456i	−0.0283155	+	0.632990i
$676$	−1.22760	+	2.12627i	−0.0472154	+	0.0817795i
$677$	6.89486	+	39.1027i	0.264991	+	1.50284i	0.769060	+	0.639176i	$0.220725\pi$
$677$	6.89486	+	39.1027i	0.264991	+	1.50284i	−0.504069	+	0.863663i	$0.668164\pi$
$678$	−4.19084	−	4.07358i	−0.160948	−	0.156445i
$679$	6.54523	+	1.17634i	0.251183	+	0.0451436i
$680$	−16.3101	−	2.87591i	−0.625463	−	0.110286i
$681$	−6.91599	−	14.2982i	−0.265022	−	0.547908i
$682$	2.36727	−	0.417413i	0.0906474	−	0.0159836i
$683$			19.6212i			0.750783i	0.926866	+	0.375392i	$0.122492\pi$
$683$			19.6212i			0.750783i	−0.926866	+	0.375392i	$0.877508\pi$
$684$	4.57895	−	31.1055i	0.175081	−	1.18935i
$685$	32.2541	+	18.6219i	1.23237	+	0.711507i
$686$	3.74992	+	4.55971i	0.143173	+	0.174090i
$687$	22.0457	−	2.24433i	0.841096	−	0.0856267i
$688$	−23.6776	−	19.8679i	−0.902701	−	0.757456i
$689$	0.898699	−	5.09677i	0.0342377	−	0.194172i
$690$	−1.97927	−	0.888986i	−0.0753497	−	0.0338431i
$691$	−3.58492	−	4.27234i	−0.136377	−	0.162527i	0.693534	−	0.720424i	$-0.256053\pi$
$691$	−3.58492	−	4.27234i	−0.136377	−	0.162527i	−0.829910	+	0.557897i	$0.811608\pi$
$692$	11.7328	−	20.3218i	0.446013	−	0.772517i
$693$	21.1481	+	16.8598i	0.803348	+	0.640452i
$694$	−0.366866	−	0.635430i	−0.0139260	−	0.0241206i
$695$	4.00390	−	11.0006i	0.151876	−	0.417277i
$696$	−9.95424	+	14.6543i	−0.377314	+	0.555470i
$697$	18.8825	+	15.8443i	0.715227	+	0.600146i
$698$	0.387041	−	2.19502i	0.0146497	−	0.0830826i
$699$	20.6038	−	21.1969i	0.779308	−	0.801741i
$700$	12.2232	−	10.1881i	0.461994	−	0.385073i
$701$		−	46.9342i		−	1.77268i	−0.463033	−	0.886341i	$-0.653239\pi$
$701$		−	46.9342i		−	1.77268i	0.463033	−	0.886341i	$-0.346761\pi$
$702$	−5.53158	−	1.23253i	−0.208776	−	0.0465189i
$703$	−8.43766	−	4.87149i	−0.318232	−	0.183732i
$704$	−12.4048	−	14.7834i	−0.467523	−	0.557172i
$705$	−10.8780	−	10.5736i	−0.409690	−	0.398227i
$706$	−4.52564	+	5.39345i	−0.170325	+	0.202985i
$707$	4.35948	−	24.2565i	0.163955	−	0.912260i
$708$	9.82740	+	20.3173i	0.369336	+	0.763570i
$709$	16.3092	+	5.93606i	0.612505	+	0.222934i	0.629599	−	0.776920i	$-0.283219\pi$
$709$	16.3092	+	5.93606i	0.612505	+	0.222934i	−0.0170941	+	0.999854i	$0.505441\pi$
$710$	−10.1486			−0.380869
$711$	−33.5886	+	6.91051i	−1.25967	+	0.259164i
$712$		−	15.2334i		−	0.570896i
$713$	−0.528416	−	2.99680i	−0.0197893	−	0.112231i
$714$	−2.81140	+	6.20467i	−0.105214	+	0.232204i
$715$	−31.3111	+	11.3963i	−1.17097	+	0.426198i
$716$	19.2603	−	22.9536i	0.719793	−	0.857816i
$717$	−11.6301	+	1.18399i	−0.434333	+	0.0442167i
$718$	9.76700	+	3.55490i	0.364501	+	0.132668i
$719$	26.6722			0.994706			0.497353	−	0.867548i	$-0.334305\pi$
$719$	26.6722			0.994706			0.497353	+	0.867548i	$0.334305\pi$
$720$	−25.6543	−	13.8563i	−0.956078	−	0.516393i
$721$	0.0981882	−	29.8193i	0.00365672	−	1.11053i
$722$	−2.35163	−	2.80257i	−0.0875187	−	0.104301i
$723$	0.355100	−	4.85049i	0.0132063	−	0.180392i
$724$	−16.0069	+	19.0762i	−0.594890	+	0.708962i
$725$	8.91838	+	24.5031i	0.331220	+	0.910021i
$726$	0.0919281	+	0.324588i	0.00341177	+	0.0120466i
$727$	11.6117	−	31.9029i	0.430654	−	1.18321i	−0.514758	−	0.857336i	$-0.672118\pi$
$727$	11.6117	−	31.9029i	0.430654	−	1.18321i	0.945412	−	0.325878i	$-0.105660\pi$
$728$	5.59251	+	9.76059i	0.207272	+	0.361752i
$729$	−2.29564	−	26.9022i	−0.0850239	−	0.996379i
$730$	−2.69270	−	4.66390i	−0.0996614	−	0.172619i
$731$	32.4685	−	27.2443i	1.20089	−	1.00767i
$732$	−22.5581	+	23.2074i	−0.833770	+	0.857771i
$733$	15.0444	+	2.65274i	0.555679	+	0.0979811i	0.444433	−	0.895812i	$-0.353405\pi$
$733$	15.0444	+	2.65274i	0.555679	+	0.0979811i	0.111245	+	0.993793i	$0.464516\pi$
$734$	0.235454	−	1.33532i	0.00869076	−	0.0492877i
$735$	−14.8826	−	31.2925i	−0.548953	−	1.15424i
$736$	3.75977	−	3.15482i	0.138587	−	0.116288i
$737$	−28.3040	−	16.3413i	−1.04259	−	0.601940i
$738$	−2.65064	−	4.30420i	−0.0975712	−	0.158440i
$739$	15.5321	+	26.9024i	0.571359	+	0.989622i	0.996427	+	0.0844608i	$0.0269168\pi$
$739$	15.5321	+	26.9024i	0.571359	+	0.989622i	−0.425068	+	0.905161i	$0.639750\pi$
$740$	−7.33508	+	6.15486i	−0.269643	+	0.226257i
$741$	26.5307	−	19.1436i	0.974629	−	0.703259i
$742$	0.974535	+	0.823216i	0.0357763	+	0.0302212i
$743$	−10.8218	−	29.7328i	−0.397015	−	1.09079i	−0.963731	−	0.266876i	$-0.914008\pi$
$743$	−10.8218	−	29.7328i	−0.397015	−	1.09079i	0.566716	−	0.823913i	$-0.308214\pi$
$744$	0.482427	+	4.73879i	0.0176866	+	0.173733i
$745$	1.45806	−	4.00598i	0.0534191	−	0.146768i
$746$	−6.72767	+	3.88422i	−0.246317	+	0.142211i
$747$	−6.76853	+	20.3776i	−0.247648	+	0.745577i
$748$	26.1239	−	15.0826i	0.955183	−	0.551475i
$749$	17.4557	−	3.01869i	0.637819	−	0.110300i
$750$	−2.60220	+	1.25868i	−0.0950189	+	0.0459603i
$751$	19.7899	−	7.20294i	0.722145	−	0.262839i	0.0453087	−	0.998973i	$-0.485573\pi$
$751$	19.7899	−	7.20294i	0.722145	−	0.262839i	0.676836	+	0.736134i	$0.263351\pi$
$752$	9.79302	−	3.56437i	0.357115	−	0.129979i
$753$	−9.69434	+	38.3479i	−0.353281	+	1.39748i
$754$	−8.84044	+	1.55881i	−0.321950	+	0.0567685i
$755$	−13.8828			−0.505247
$756$	−17.7157	+	19.1647i	−0.644313	+	0.697015i
$757$	−13.1053			−0.476322			−0.238161	−	0.971226i	$-0.576545\pi$
$757$	−13.1053			−0.476322			−0.238161	+	0.971226i	$0.576545\pi$
$758$	5.60410	−	0.988154i	0.203550	−	0.0358914i
$759$	7.80833	−	2.21143i	0.283424	−	0.0802700i
$760$	−18.4243	+	6.70588i	−0.668318	+	0.243248i
$761$	−9.52482	+	3.46675i	−0.345274	+	0.125670i	−0.508836	−	0.860864i	$-0.669924\pi$
$761$	−9.52482	+	3.46675i	−0.345274	+	0.125670i	0.163561	+	0.986533i	$0.447702\pi$
$762$	0.684248	−	9.34649i	0.0247877	−	0.338588i
$763$	33.7570	−	28.1366i	1.22209	−	1.01861i
$764$	−29.2197	+	16.8700i	−1.05713	+	0.610335i
$765$	24.8209	−	31.3451i	0.897400	−	1.13328i
$766$	−7.55611	+	4.36252i	−0.273013	+	0.157624i
$767$	−8.03230	+	22.0685i	−0.290029	+	0.796849i
$768$	11.9052	−	8.59034i	0.429590	−	0.309977i
$769$	−7.15123	−	19.6478i	−0.257880	−	0.708519i	−0.999298	−	0.0374752i	$-0.988068\pi$
$769$	−7.15123	−	19.6478i	−0.257880	−	0.708519i	0.741418	−	0.671044i	$-0.234154\pi$
$770$	1.45285	−	8.08377i	0.0523570	−	0.291319i
$771$	−2.19617	−	21.5726i	−0.0790931	−	0.776917i
$772$	−19.8127	+	16.6249i	−0.713076	+	0.598342i
$773$	10.5944	+	18.3500i	0.381054	+	0.660005i	0.991213	−	0.132274i	$-0.0422279\pi$
$773$	10.5944	+	18.3500i	0.381054	+	0.660005i	−0.610159	+	0.792279i	$0.708895\pi$
$774$	−8.08008	+	3.20334i	−0.290433	+	0.115142i
$775$	6.07185	+	3.50558i	0.218107	+	0.125924i
$776$	−2.39271	+	2.00772i	−0.0858932	+	0.0720730i
$777$	3.49758	+	7.29210i	0.125475	+	0.261603i
$778$	−0.902204	+	5.11665i	−0.0323456	+	0.183441i
$779$	28.7381	+	5.06729i	1.02965	+	0.181555i
$780$	−8.76164	−	30.9364i	−0.313717	−	1.10770i
$781$	29.0777	−	24.3991i	1.04048	−	0.873069i
$782$	1.02199	+	1.77013i	0.0365462	+	0.0632998i
$783$	−19.7073	−	37.9565i	−0.704282	−	1.35645i
$784$	23.8041	+	0.156764i	0.850145	+	0.00559873i
$785$	−22.0192	+	60.4974i	−0.785900	+	2.15924i
$786$	6.15550	−	6.33269i	0.219559	−	0.225880i
$787$	−7.46006	−	20.4964i	−0.265923	−	0.730616i	−0.998740	−	0.0501905i	$-0.984017\pi$
$787$	−7.46006	−	20.4964i	−0.265923	−	0.730616i	0.732817	−	0.680426i	$-0.238205\pi$
$788$	−11.2528	+	13.4106i	−0.400866	+	0.477733i
$789$	−18.2248	−	12.3796i	−0.648821	−	0.440725i
$790$	6.69381	+	7.97737i	0.238155	+	0.283822i
$791$	−24.2081	−	14.0830i	−0.860739	−	0.500734i
$792$	−12.4426	+	2.55994i	−0.442128	+	0.0909634i
$793$	−33.6774			−1.19592
$794$	−1.36485	−	0.496765i	−0.0484368	−	0.0176295i
$795$	−4.38135	−	6.07201i	−0.155391	−	0.215352i
$796$	0.327253	−	0.390005i	0.0115992	−	0.0138233i
$797$	−14.4170	+	5.24735i	−0.510676	+	0.185871i	−0.584490	−	0.811401i	$-0.698705\pi$
$797$	−14.4170	+	5.24735i	−0.510676	+	0.185871i	0.0738137	+	0.997272i	$0.476483\pi$
$798$	0.790335	+	8.02550i	0.0279776	+	0.284100i
$799$	2.48156	+	14.0736i	0.0877913	+	0.497889i
$800$			11.3081i			0.399803i
$801$	32.3576	+	17.4769i	1.14330	+	0.617514i
$802$	12.0164			0.424313
$803$	18.9281	+	6.88926i	0.667957	+	0.243117i
$804$	17.7208	−	26.0881i	0.624966	−	0.920055i
$805$	−10.2335	−	1.83920i	−0.360683	−	0.0648234i
$806$	−1.55148	+	1.84898i	−0.0546485	+	0.0651275i
$807$	−32.6442	+	9.24531i	−1.14913	+	0.325450i
$808$	7.44058	+	8.86734i	0.261759	+	0.311952i
$809$	11.6471	+	6.72444i	0.409489	+	0.236419i	0.690570	−	0.723265i	$-0.257360\pi$
$809$	11.6471	+	6.72444i	0.409489	+	0.236419i	−0.281081	+	0.959684i	$0.590693\pi$
$810$	−6.85681	+	4.49580i	−0.240924	+	0.157966i
$811$		−	3.07886i		−	0.108113i	−0.998538	−	0.0540566i	$-0.982785\pi$
$811$		−	3.07886i		−	0.108113i	0.998538	−	0.0540566i	$-0.0172152\pi$
$812$	−14.2669	+	38.7999i	−0.500668	+	1.36161i
$813$	31.3312	+	7.92051i	1.09883	+	0.277784i
$814$	−0.332876	+	1.88783i	−0.0116673	+	0.0661685i
$815$	21.0749	+	17.6840i	0.738223	+	0.619442i
$816$	11.9600	+	24.7263i	0.418684	+	0.865593i
$817$	17.1617	−	47.1513i	0.600411	−	1.64962i
$818$	0.159623	+	0.276474i	0.00558107	+	0.00966670i
$819$	−27.1488	+	0.681111i	−0.948656	+	0.0237999i
$820$	14.3395	−	24.8368i	0.500759	−	0.867340i
$821$	−2.90182	−	3.45825i	−0.101274	−	0.120694i	0.713027	−	0.701137i	$-0.247324\pi$
$821$	−2.90182	−	3.45825i	−0.101274	−	0.120694i	−0.814301	+	0.580443i	$0.802879\pi$
$822$	0.728704	+	7.15793i	0.0254165	+	0.249661i
$823$	5.31672	−	30.1526i	0.185329	−	1.05105i	−0.740202	−	0.672384i	$-0.765270\pi$
$823$	5.31672	−	30.1526i	0.185329	−	1.05105i	0.925532	−	0.378670i	$-0.123619\pi$
$824$	10.7291	+	9.00275i	0.373765	+	0.313626i
$825$	−7.66093	+	17.0566i	−0.266719	+	0.593835i
$826$	−3.70637	−	4.44674i	−0.128961	−	0.154722i
$827$	12.8966	+	7.44587i	0.448459	+	0.258918i	0.707179	−	0.707034i	$-0.249967\pi$
$827$	12.8966	+	7.44587i	0.448459	+	0.258918i	−0.258720	+	0.965952i	$0.583301\pi$
$828$	1.57812	+	7.67045i	0.0548433	+	0.266566i
$829$			25.2709i			0.877695i	0.898561	+	0.438848i	$0.144613\pi$
$829$			25.2709i			0.877695i	−0.898561	+	0.438848i	$0.855387\pi$
$830$	6.42157	−	1.13230i	0.222896	−	0.0393026i
$831$	2.59873	−	3.82576i	0.0901489	−	0.132714i
$832$	19.0834	+	3.36491i	0.661597	+	0.116657i
$833$	−5.87990	+	32.1086i	−0.203727	+	1.11250i
$834$	2.17595	−	0.616260i	0.0753469	−	0.0213394i
$835$	5.00334	+	28.3753i	0.173148	+	0.981969i
$836$	17.8557	−	30.9270i	0.617552	−	1.06963i
$837$	−10.6192	−	4.41195i	−0.367055	−	0.152499i
$838$	−0.648204	+	0.374241i	−0.0223918	+	0.0129279i
$839$	16.6975	+	6.07738i	0.576460	+	0.209814i	0.613764	−	0.789490i	$-0.289655\pi$
$839$	16.6975	+	6.07738i	0.576460	+	0.209814i	−0.0373037	+	0.999304i	$0.511877\pi$
$840$	15.7656	+	4.04082i	0.543966	+	0.139422i
$841$	−29.6792	−	24.9038i	−1.02342	−	0.858751i
$842$	−0.716040	−	1.96730i	−0.0246764	−	0.0677978i
$843$	24.8674	+	16.8917i	0.856479	+	0.581781i
$844$	−4.31247	−	24.4572i	−0.148441	−	0.841853i
$845$	−1.84813	+	3.20106i	−0.0635776	+	0.110120i
$846$	0.426810	−	2.89939i	0.0146740	−	0.0996829i
$847$	0.803687	+	1.40267i	0.0276150	+	0.0481964i
$848$	5.06571	−	0.893222i	0.173957	−	0.0306734i
$849$	1.10779	+	1.53526i	0.0380192	+	0.0526900i
$850$	−4.63779	−	0.817767i	−0.159075	−	0.0280492i
$851$	2.38986	+	0.421397i	0.0819235	+	0.0144453i
$852$	21.4327	+	29.7031i	0.734273	+	1.01761i
$853$	−13.7587	+	2.42603i	−0.471089	+	0.0830656i	−0.404152	−	0.914692i	$-0.632433\pi$
$853$	−13.7587	+	2.42603i	−0.471089	+	0.0830656i	−0.0669361	+	0.997757i	$0.521322\pi$
$854$	4.17426	−	7.17537i	0.142840	−	0.245536i
$855$	6.89353	−	46.8288i	0.235754	−	1.60151i
$856$	−4.16021	+	7.20569i	−0.142193	+	0.246286i
$857$	3.71073	+	21.0446i	0.126756	+	0.718869i	0.980249	+	0.197765i	$0.0633684\pi$
$857$	3.71073	+	21.0446i	0.126756	+	0.718869i	−0.853493	+	0.521104i	$0.825520\pi$
$858$	−5.32475	−	3.61694i	−0.181784	−	0.123480i
$859$	−4.24094	−	11.6519i	−0.144699	−	0.397557i	0.846078	−	0.533059i	$-0.178958\pi$
$859$	−4.24094	−	11.6519i	−0.144699	−	0.397557i	−0.990777	+	0.135502i	$0.956735\pi$
$860$	−37.7765	−	31.6982i	−1.28817	−	1.08090i
$861$	−17.3139	−	16.9407i	−0.590056	−	0.577337i
$862$	4.61598	+	1.68008i	0.157221	+	0.0572237i
$863$	−9.03144	+	5.21430i	−0.307434	+	0.177497i	−0.645778	−	0.763526i	$-0.723467\pi$
$863$	−9.03144	+	5.21430i	−0.307434	+	0.177497i	0.338344	+	0.941023i	$0.390133\pi$
$864$	−2.40119	−	18.3908i	−0.0816900	−	0.625669i
$865$	17.6635	−	30.5941i	0.600577	−	1.04023i
$866$	−0.546439	−	3.09901i	−0.0185688	−	0.105309i
$867$	−7.90870	+	2.23986i	−0.268594	+	0.0760696i
$868$	3.76726	+	10.4575i	0.127869	+	0.354950i
$869$	−38.3583	−	6.76360i	−1.30122	−	0.229440i
$870$	−7.29766	+	10.7434i	−0.247414	+	0.364235i
$871$	32.3184	−	5.69861i	1.09507	−	0.193090i
$872$			20.6406i			0.698979i
$873$	−1.51955	−	7.38580i	−0.0514291	−	0.249972i
$874$	2.09559	+	1.20989i	0.0708843	+	0.0409250i
$875$	−10.6404	+	8.86882i	−0.359711	+	0.299821i
$876$	−7.96372	+	17.7308i	−0.269069	+	0.599067i
$877$	31.4881	+	26.4217i	1.06328	+	0.892197i	0.994427	−	0.105430i	$-0.0336218\pi$
$877$	31.4881	+	26.4217i	1.06328	+	0.892197i	0.0688523	+	0.997627i	$0.478066\pi$
$878$	1.95427	−	11.0832i	0.0659534	−	0.374040i
$879$	3.69400	+	36.2855i	0.124595	+	1.22388i
$880$	−21.2876	−	25.3695i	−0.717604	−	0.855207i
$881$	−14.4200	+	24.9761i	−0.485821	+	0.841467i	−0.999867	−	0.0162958i	$-0.994813\pi$
$881$	−14.4200	+	24.9761i	−0.485821	+	0.841467i	0.514046	+	0.857762i	$0.328146\pi$
$882$	3.21994	−	5.86880i	0.108421	−	0.197613i
$883$	24.3484	+	42.1726i	0.819388	+	1.41922i	0.906134	+	0.422991i	$0.139020\pi$
$883$	24.3484	+	42.1726i	0.819388	+	1.41922i	−0.0867455	+	0.996231i	$0.527647\pi$
$884$	−10.3595	+	28.4626i	−0.348429	+	0.957301i
$885$	14.7950	+	30.5873i	0.497328	+	1.02818i
$886$	−1.08672	−	0.911864i	−0.0365090	−	0.0306347i
$887$	−1.38081	+	7.83099i	−0.0463632	+	0.262939i	−0.999174	−	0.0406244i	$-0.987065\pi$
$887$	−1.38081	+	7.83099i	−0.0463632	+	0.262939i	0.952811	+	0.303563i	$0.0981764\pi$
$888$	−3.68274	−	0.930994i	−0.123585	−	0.0312421i
$889$	−7.65256	−	44.2514i	−0.256659	−	1.48414i
$890$		−	11.1679i		−	0.374350i
$891$	8.83743	−	29.3665i	0.296065	−	0.983815i
$892$	−24.3102	−	14.0355i	−0.813967	−	0.469944i
$893$	10.8748	+	12.9601i	0.363912	+	0.433693i
$894$	0.792393	−	0.224417i	0.0265016	−	0.00750563i
$895$	28.9961	−	34.5562i	0.969233	−	1.15509i
$896$	−15.2704	+	18.0773i	−0.510147	+	0.603920i
$897$	−4.57880	+	6.74076i	−0.152882	+	0.225067i
$898$	−1.71632	−	0.624689i	−0.0572743	−	0.0208461i
$899$	−18.2147			−0.607495
$900$	−15.8753	−	8.57451i	−0.529177	−	0.285817i
$901$			7.05364i			0.234991i
$902$	−0.997004	−	5.65429i	−0.0331966	−	0.188267i
$903$	−33.8567	+	24.2607i	−1.12668	+	0.807344i
$904$	12.3609	−	4.49902i	0.411119	−	0.149635i
$905$	−24.0981	+	28.7189i	−0.801046	+	0.954650i
$906$	−1.56931	−	2.17487i	−0.0521369	−	0.0722552i
$907$	−40.7073	−	14.8163i	−1.35167	−	0.491966i	−0.438198	−	0.898878i	$-0.644383\pi$
$907$	−40.7073	−	14.8163i	−1.35167	−	0.491966i	−0.913467	+	0.406913i	$0.866605\pi$
$908$	17.4083			0.577716
$909$	−27.3717	+	5.63144i	−0.907861	+	0.186783i
$910$	4.09999	+	7.15570i	0.135913	+	0.237209i
$911$	−32.8056	−	39.0962i	−1.08690	−	1.29531i	−0.952551	−	0.304379i	$-0.901551\pi$
$911$	−32.8056	−	39.0962i	−1.08690	−	1.29531i	−0.134346	−	0.990934i	$-0.542893\pi$
$912$	26.8982	+	18.2712i	0.890690	+	0.605019i
$913$	−15.6769	+	18.6830i	−0.518829	+	0.618316i
$914$	−4.45553	−	12.2415i	−0.147376	−	0.404912i
$915$	−33.9608	+	34.9384i	−1.12271	+	1.15503i
$916$	−8.30690	+	22.8230i	−0.274468	+	0.754094i
$917$	21.2805	−	36.5802i	0.702745	−	1.20799i
$918$	7.71625	+	0.345170i	0.254674	+	0.0113923i
$919$	19.5951	+	33.9398i	0.646384	+	1.11957i	0.983980	+	0.178279i	$0.0570529\pi$
$919$	19.5951	+	33.9398i	0.646384	+	1.11957i	−0.337596	+	0.941291i	$0.609614\pi$
$920$	3.74101	−	3.13908i	0.123337	−	0.103492i
$921$	−10.7673	−	38.0180i	−0.354793	−	1.25274i
$922$	8.51932	+	1.50219i	0.280569	+	0.0494719i
$923$	−6.61849	+	37.5353i	−0.217850	+	1.23549i
$924$	−26.7281	+	12.8199i	−0.879289	+	0.421742i
$925$	−4.28312	+	3.59396i	−0.140828	+	0.118169i
$926$	3.51952	+	2.03200i	0.115659	+	0.0667756i
$927$	−31.4321	+	12.4612i	−1.03237	+	0.409280i
$928$	−14.6891	−	25.4422i	−0.482192	−	0.835181i
$929$	−23.4335	+	19.6630i	−0.768828	+	0.645123i	−0.940409	−	0.340047i	$-0.889557\pi$
$929$	−23.4335	+	19.6630i	−0.768828	+	0.645123i	0.171581	+	0.985170i	$0.445113\pi$
$930$	0.353677	+	3.47411i	0.0115975	+	0.113921i
$931$	12.9777	+	36.3999i	0.425326	+	1.19296i
$932$	11.0813	+	30.4455i	0.362979	+	0.997275i
$933$	−31.6201	+	22.8160i	−1.03520	+	0.746962i
$934$	−2.45788	+	6.75297i	−0.0804242	+	0.220964i
$935$	39.3290	−	22.7066i	1.28620	−	0.742586i
$936$	7.91851	−	9.99992i	0.258825	−	0.326858i
$937$	−4.39414	+	2.53696i	−0.143550	+	0.0828787i	−0.570055	−	0.821607i	$-0.693078\pi$
$937$	−4.39414	+	2.53696i	−0.143550	+	0.0828787i	0.426505	+	0.904485i	$0.359745\pi$
$938$	−2.79166	+	7.59216i	−0.0911511	+	0.247893i
$939$	0.178533	−	2.43868i	0.00582621	−	0.0795832i
$940$	15.6243	−	5.68677i	0.509608	−	0.185482i
$941$	−13.6748	+	4.97722i	−0.445785	+	0.162253i	−0.555152	−	0.831749i	$-0.687340\pi$
$941$	−13.6748	+	4.97722i	−0.445785	+	0.162253i	0.109367	+	0.994001i	$0.465118\pi$
$942$	−11.9665	+	3.38909i	−0.389890	+	0.110423i
$943$	−7.15793	+	1.26214i	−0.233094	+	0.0411008i
$944$	−23.3417			−0.759709
$945$	−26.6707	+	28.8522i	−0.867597	+	0.938562i
$946$	−9.87254			−0.320984
$947$	53.6444	−	9.45896i	1.74321	−	0.307375i	0.790772	−	0.612110i	$-0.209679\pi$
$947$	53.6444	−	9.45896i	1.74321	−	0.307375i	0.952437	+	0.304735i	$0.0985681\pi$
$948$	9.21176	−	36.4390i	0.299184	−	1.18348i
$949$	−19.0059	+	6.91758i	−0.616958	+	0.224554i
$950$	−5.23896	+	1.90683i	−0.169974	+	0.0618656i
$951$	−10.6880	+	5.16977i	−0.346583	+	0.167641i
$952$	−9.81635	−	11.7772i	−0.318150	−	0.381702i
$953$	19.6055	−	11.3192i	0.635084	−	0.366666i	−0.147634	−	0.989042i	$-0.547166\pi$
$953$	19.6055	−	11.3192i	0.635084	−	0.366666i	0.782718	+	0.622376i	$0.213833\pi$
$954$	0.455970	−	1.37276i	0.0147626	−	0.0444447i
$955$	−43.9897	+	25.3975i	−1.42347	+	0.821843i
$956$	4.38225	−	12.0401i	0.141732	−	0.389406i
$957$	−4.91988	−	48.3271i	−0.159037	−	1.56219i
$958$	3.55736	+	9.77376i	0.114933	+	0.315776i
$959$	11.6854	+	32.4374i	0.377343	+	1.04746i
$960$	22.7349	−	16.4047i	0.733765	−	0.529459i
$961$	19.9956	−	16.7783i	0.645021	−	0.541237i
$962$	−0.962419	−	1.66696i	−0.0310296	−	0.0537449i
$963$	−10.5329	−	17.1037i	−0.339417	−	0.551158i
$964$	4.61638	+	2.66527i	0.148683	+	0.0858424i
$965$	−29.8277	+	25.0284i	−0.960189	+	0.805694i
$966$	−0.868663	−	1.81107i	−0.0279488	−	0.0582703i
$967$	5.14316	−	29.1683i	0.165393	−	0.937990i	−0.783265	−	0.621687i	$-0.786447\pi$
$967$	5.14316	−	29.1683i	0.165393	−	0.937990i	0.948658	−	0.316303i	$-0.102441\pi$
$968$	−0.747761	−	0.131850i	−0.0240339	−	0.00423783i
$969$	−31.0791	+	31.9738i	−0.998405	+	1.02714i
$970$	−1.75415	+	1.47190i	−0.0563222	+	0.0472600i
$971$	7.12855	+	12.3470i	0.228766	+	0.396234i	0.957443	−	0.288623i	$-0.0931976\pi$
$971$	7.12855	+	12.3470i	0.228766	+	0.396234i	−0.728677	+	0.684858i	$0.759864\pi$
$972$	27.6393	+	10.5741i	0.886531	+	0.339163i
$973$	9.40313	−	5.38769i	0.301450	−	0.172722i
$974$	−0.744603	+	2.04578i	−0.0238586	+	0.0655510i
$975$	−5.11611	−	18.0644i	−0.163847	−	0.578525i
$976$	−11.4482	−	31.4535i	−0.366447	−	1.00680i
$977$	12.8962	−	15.3691i	0.412587	−	0.491702i	−0.519228	−	0.854636i	$-0.673780\pi$
$977$	12.8962	−	15.3691i	0.412587	−	0.491702i	0.931815	+	0.362934i	$0.118225\pi$
$978$	−0.388050	+	5.30058i	−0.0124085	+	0.169494i
$979$	26.8499	+	31.9985i	0.858126	+	1.02268i
$980$	37.9782	+	0.250110i	1.21317	+	0.00798947i
$981$	−43.8431	−	23.6804i	−1.39980	−	0.756056i
$982$	0.951057			0.0303494
$983$	−15.7312	−	5.72570i	−0.501748	−	0.182621i	0.0787320	−	0.996896i	$-0.474913\pi$
$983$	−15.7312	−	5.72570i	−0.501748	−	0.182621i	−0.580480	+	0.814274i	$0.697135\pi$
$984$	11.3187	−	1.15229i	0.360828	−	0.0367337i
$985$	−16.9410	+	20.1894i	−0.539784	+	0.643289i
$986$	11.4968	−	4.18450i	0.366133	−	0.133262i
$987$	−1.37633	−	13.9760i	−0.0438089	−	0.444860i
$988$	6.22671	+	35.3134i	0.198098	+	1.12347i
$989$			12.4979i			0.397411i
$990$	−9.12193	+	1.87674i	−0.289914	+	0.0596469i
$991$	22.1202			0.702671			0.351335	−	0.936250i	$-0.385728\pi$
$991$	22.1202			0.702671			0.351335	+	0.936250i	$0.385728\pi$
$992$	−7.42276	−	2.70166i	−0.235673	−	0.0857779i
$993$	−2.24457	−	4.64046i	−0.0712294	−	0.147261i
$994$	−7.17699	−	6.06260i	−0.227640	−	0.192294i
$995$	0.492673	−	0.587145i	0.0156188	−	0.0186138i
$996$	−16.8757	−	16.4035i	−0.534728	−	0.519766i
$997$	−28.6879	−	34.1890i	−0.908556	−	1.08277i	−0.996241	−	0.0866267i	$-0.972391\pi$
$997$	−28.6879	−	34.1890i	−0.908556	−	1.08277i	0.0876848	−	0.996148i	$-0.472053\pi$
$998$	−8.44683	−	4.87678i	−0.267380	−	0.154372i
$999$	6.20264	−	6.75447i	0.196243	−	0.213702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.bd.a.185.10	yes	132
3.2	odd	2		567.2.bd.a.17.13		132
7.5	odd	6		189.2.ba.a.131.13	yes	132
21.5	even	6		567.2.ba.a.341.10		132
27.7	even	9		567.2.ba.a.143.10		132
27.20	odd	18		189.2.ba.a.101.13	✓	132
189.47	even	18	inner	189.2.bd.a.47.10	yes	132
189.61	odd	18		567.2.bd.a.467.13		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.13	✓	132	27.20	odd	18
189.2.ba.a.131.13	yes	132	7.5	odd	6
189.2.bd.a.47.10	yes	132	189.47	even	18	inner
189.2.bd.a.185.10	yes	132	1.1	even	1	trivial
567.2.ba.a.143.10		132	27.7	even	9
567.2.ba.a.341.10		132	21.5	even	6
567.2.bd.a.17.13		132	3.2	odd	2
567.2.bd.a.467.13		132	189.61	odd	18

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.bd (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.313923 + 0.0553531i) q^{2} +(1.24200 + 1.20725i) q^{3} +(-1.78390 + 0.649287i) q^{4} +(-2.68563 + 0.977491i) q^{5} +(-0.456717 - 0.310234i) q^{6} +(-2.48320 - 0.913082i) q^{7} +(1.07619 - 0.621337i) q^{8} +(0.0851152 + 2.99879i) q^{9} +O(q^{10})\)	\(q+(-0.313923 + 0.0553531i) q^{2} +(1.24200 + 1.20725i) q^{3} +(-1.78390 + 0.649287i) q^{4} +(-2.68563 + 0.977491i) q^{5} +(-0.456717 - 0.310234i) q^{6} +(-2.48320 - 0.913082i) q^{7} +(1.07619 - 0.621337i) q^{8} +(0.0851152 + 2.99879i) q^{9} +(0.788975 - 0.455515i) q^{10} +(-1.16543 + 3.20200i) q^{11} +(-2.99945 - 1.34719i) q^{12} +(-1.17022 - 3.21516i) q^{13} +(0.830076 + 0.149185i) q^{14} +(-4.51562 - 2.02818i) q^{15} +(2.60505 - 2.18590i) q^{16} +(2.33161 + 4.03847i) q^{17} +(-0.192712 - 0.936679i) q^{18} +(4.78098 + 2.76030i) q^{19} +(4.15623 - 3.48749i) q^{20} +(-1.98181 - 4.13188i) q^{21} +(0.188615 - 1.06969i) q^{22} +(-1.35415 - 0.238774i) q^{23} +(2.08673 + 0.527523i) q^{24} +(2.42692 - 2.03643i) q^{25} +(0.545329 + 0.944538i) q^{26} +(-3.51457 + 3.82725i) q^{27} +(5.02264 + 0.0165384i) q^{28} +(-2.81504 + 7.73427i) q^{29} +(1.52982 + 0.386739i) q^{30} +(0.756904 + 2.07958i) q^{31} +(-2.29434 + 2.73429i) q^{32} +(-5.31306 + 2.56991i) q^{33} +(-0.955489 - 1.13871i) q^{34} +(7.56149 + 0.0248983i) q^{35} +(-2.09891 - 5.29429i) q^{36} -1.76484 q^{37} +(-1.65365 - 0.601880i) q^{38} +(2.42808 - 5.40597i) q^{39} +(-2.28289 + 2.72064i) q^{40} +(4.96713 - 1.80789i) q^{41} +(0.850850 + 1.18739i) q^{42} +(-1.57831 - 8.95103i) q^{43} -6.46875i q^{44} +(-3.15988 - 7.97046i) q^{45} +0.438317 q^{46} +(2.87974 + 1.04814i) q^{47} +(5.87439 + 0.430058i) q^{48} +(5.33256 + 4.53473i) q^{49} +(-0.649143 + 0.773618i) q^{50} +(-1.97957 + 7.83060i) q^{51} +(4.17513 + 4.97572i) q^{52} +(1.30996 + 0.756305i) q^{53} +(0.891454 - 1.39600i) q^{54} -9.73859i q^{55} +(-3.23972 + 0.560257i) q^{56} +(2.60560 + 9.20011i) q^{57} +(0.455592 - 2.58379i) q^{58} +(-5.25805 - 4.41203i) q^{59} +(9.37229 + 0.686137i) q^{60} +(3.36646 - 9.24926i) q^{61} +(-0.352721 - 0.610930i) q^{62} +(2.52678 - 7.52432i) q^{63} +(-2.83176 + 4.90475i) q^{64} +(6.28558 + 7.49087i) q^{65} +(1.52564 - 1.10085i) q^{66} +(-1.66553 + 9.44568i) q^{67} +(-6.78150 - 5.69035i) q^{68} +(-1.39360 - 1.93135i) q^{69} +(-2.37511 + 0.410736i) q^{70} +(-9.64722 - 5.56983i) q^{71} +(1.95486 + 3.17438i) q^{72} -5.91133i q^{73} +(0.554024 - 0.0976893i) q^{74} +(5.47269 + 0.400651i) q^{75} +(-10.3210 - 1.81988i) q^{76} +(5.81769 - 6.88707i) q^{77} +(-0.462992 + 1.83146i) q^{78} +(1.98492 + 11.2570i) q^{79} +(-4.85952 + 8.41694i) q^{80} +(-8.98551 + 0.510486i) q^{81} +(-1.45922 + 0.842484i) q^{82} +(6.72578 + 2.44798i) q^{83} +(6.21814 + 6.08410i) q^{84} +(-10.2094 - 8.56673i) q^{85} +(0.990935 + 2.72257i) q^{86} +(-12.8334 + 6.20749i) q^{87} +(0.735296 + 4.17007i) q^{88} +(6.12929 - 10.6162i) q^{89} +(1.43315 + 2.32720i) q^{90} +(-0.0298075 + 9.05240i) q^{91} +(2.57071 - 0.453286i) q^{92} +(-1.57049 + 3.49660i) q^{93} +(-0.962036 - 0.169633i) q^{94} +(-15.5381 - 2.73979i) q^{95} +(-6.15052 + 0.626146i) q^{96} +(-2.47531 + 0.436465i) q^{97} +(-1.92503 - 1.12838i) q^{98} +(-9.70132 - 3.22235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

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