LMFDB - Embedded newform 731.2.k.a.188.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(35,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("731.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.k (of order $7$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$30$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			188.7
Character	$\chi$	$=$	731.188
Dual form			731.2.k.a.35.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.396271 - 1.73618i) q^{2} +(-0.0213391 + 0.0934929i) q^{3} +(-1.05534 + 0.508225i) q^{4} +(-1.30201 - 1.63267i) q^{5} +0.170776 q^{6} -1.70084 q^{7} +(-0.920084 - 1.15375i) q^{8} +(2.69462 + 1.29766i) q^{9} +O(q^{10})$	\(q+(-0.396271 - 1.73618i) q^{2} +(-0.0213391 + 0.0934929i) q^{3} +(-1.05534 + 0.508225i) q^{4} +(-1.30201 - 1.63267i) q^{5} +0.170776 q^{6} -1.70084 q^{7} +(-0.920084 - 1.15375i) q^{8} +(2.69462 + 1.29766i) q^{9} +(-2.31865 + 2.90749i) q^{10} +(-1.66630 - 0.802449i) q^{11} +(-0.0249954 - 0.109512i) q^{12} +(-1.34014 - 1.68048i) q^{13} +(0.673994 + 2.95296i) q^{14} +(0.180427 - 0.0868888i) q^{15} +(-3.09915 + 3.88621i) q^{16} +(0.623490 - 0.781831i) q^{17} +(1.18517 - 5.19256i) q^{18} +(-5.46595 + 2.63226i) q^{19} +(2.20382 + 1.06131i) q^{20} +(0.0362945 - 0.159017i) q^{21} +(-0.732885 + 3.21098i) q^{22} +(-1.05819 - 0.509599i) q^{23} +(0.127501 - 0.0614013i) q^{24} +(0.142229 - 0.623147i) q^{25} +(-2.38655 + 2.99264i) q^{26} +(-0.358196 + 0.449163i) q^{27} +(1.79497 - 0.864410i) q^{28} +(2.35300 + 10.3092i) q^{29} +(-0.222352 - 0.278821i) q^{30} +(-1.69205 - 7.41336i) q^{31} +(5.31612 + 2.56011i) q^{32} +(0.110581 - 0.138664i) q^{33} +(-1.60447 - 0.772671i) q^{34} +(2.21451 + 2.77691i) q^{35} -3.50324 q^{36} -6.51903 q^{37} +(6.73607 + 8.44676i) q^{38} +(0.185710 - 0.0894334i) q^{39} +(-0.685731 + 3.00438i) q^{40} +(2.34635 + 10.2800i) q^{41} -0.290463 q^{42} +(-0.943496 - 6.48921i) q^{43} +2.16634 q^{44} +(-1.38977 - 6.08898i) q^{45} +(-0.465423 + 2.03915i) q^{46} +(1.05986 - 0.510404i) q^{47} +(-0.297200 - 0.372676i) q^{48} -4.10714 q^{49} -1.13825 q^{50} +(0.0597910 + 0.0749755i) q^{51} +(2.26836 + 1.09239i) q^{52} +(-3.38532 + 4.24506i) q^{53} +(0.921770 + 0.443901i) q^{54} +(0.859408 + 3.76531i) q^{55} +(1.56492 + 1.96235i) q^{56} +(-0.129459 - 0.567197i) q^{57} +(16.9661 - 8.17043i) q^{58} +(5.16638 - 6.47844i) q^{59} +(-0.146252 + 0.183395i) q^{60} +(-0.727539 + 3.18756i) q^{61} +(-12.2004 + 5.87540i) q^{62} +(-4.58313 - 2.20712i) q^{63} +(0.126031 - 0.552176i) q^{64} +(-0.998793 + 4.37600i) q^{65} +(-0.284565 - 0.137039i) q^{66} +(-4.62193 + 2.22581i) q^{67} +(-0.260647 + 1.14197i) q^{68} +(0.0702248 - 0.0880592i) q^{69} +(3.94366 - 4.94519i) q^{70} +(-1.28705 + 0.619812i) q^{71} +(-0.982103 - 4.30288i) q^{72} +(-1.16712 - 1.46352i) q^{73} +(2.58330 + 11.3182i) q^{74} +(0.0552248 + 0.0265948i) q^{75} +(4.43065 - 5.55586i) q^{76} +(2.83412 + 1.36484i) q^{77} +(-0.228864 - 0.286986i) q^{78} -12.6103 q^{79} +10.3800 q^{80} +(5.55986 + 6.97184i) q^{81} +(16.9181 - 8.14734i) q^{82} +(3.78855 - 16.5987i) q^{83} +(0.0425132 + 0.186262i) q^{84} -2.08826 q^{85} +(-10.8925 + 4.20956i) q^{86} -1.01404 q^{87} +(0.607314 + 2.66082i) q^{88} +(3.19548 - 14.0003i) q^{89} +(-10.0208 + 4.82578i) q^{90} +(2.27936 + 2.85823i) q^{91} +1.37574 q^{92} +0.729203 q^{93} +(-1.30614 - 1.63785i) q^{94} +(11.4143 + 5.49684i) q^{95} +(-0.352793 + 0.442389i) q^{96} +(10.0400 + 4.83503i) q^{97} +(1.62754 + 7.13071i) q^{98} +(-3.44875 - 4.32459i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - 4 q^{2} - 6 q^{3} - 34 q^{4} - 6 q^{5} - 14 q^{6} + 66 q^{7} + 2 q^{8} - 26 q^{9}+O(q^{10}) $ 180 * q - 4 * q^2 - 6 * q^3 - 34 * q^4 - 6 * q^5 - 14 * q^6 + 66 * q^7 + 2 * q^8 - 26 * q^9	\( 180 q - 4 q^{2} - 6 q^{3} - 34 q^{4} - 6 q^{5} - 14 q^{6} + 66 q^{7} + 2 q^{8} - 26 q^{9} - 8 q^{10} - 12 q^{11} - 24 q^{12} - 5 q^{13} - 8 q^{14} - q^{15} - 58 q^{16} - 30 q^{17} + 36 q^{18} - 24 q^{19} - 36 q^{20} - 28 q^{21} + 5 q^{22} + 27 q^{23} - 46 q^{24} - 38 q^{25} + 6 q^{26} - 36 q^{27} - 54 q^{28} + 28 q^{29} - 21 q^{30} + 36 q^{31} + 11 q^{32} + 5 q^{33} - 4 q^{34} + 6 q^{35} + 192 q^{36} + 164 q^{37} + 32 q^{38} - 34 q^{39} + 2 q^{40} + 42 q^{41} - 2 q^{42} - 22 q^{43} + 14 q^{44} + 58 q^{45} - 53 q^{46} + 21 q^{47} - 20 q^{48} + 166 q^{49} + 18 q^{50} - 6 q^{51} + 54 q^{52} + 8 q^{53} - 154 q^{54} - 5 q^{55} - 35 q^{56} + 8 q^{57} + 9 q^{58} - 13 q^{59} - 88 q^{60} - 34 q^{61} - 36 q^{62} - 31 q^{63} - 18 q^{64} + 9 q^{65} + 222 q^{66} - 48 q^{67} - 27 q^{68} + 2 q^{69} - 64 q^{70} - 42 q^{71} + 77 q^{72} - 44 q^{73} - 35 q^{74} - 21 q^{75} + 44 q^{76} - 32 q^{77} + 124 q^{78} - 96 q^{79} + 490 q^{80} - 12 q^{81} - 130 q^{82} - 8 q^{83} + 170 q^{84} + 22 q^{85} - 12 q^{86} - 90 q^{87} - 122 q^{88} - 81 q^{89} + 49 q^{90} - 27 q^{91} - 116 q^{92} + 18 q^{93} - 124 q^{94} + 117 q^{95} + 52 q^{96} - 79 q^{97} - 54 q^{98} - 39 q^{99}+O(q^{100}) \) 180 * q - 4 * q^2 - 6 * q^3 - 34 * q^4 - 6 * q^5 - 14 * q^6 + 66 * q^7 + 2 * q^8 - 26 * q^9 - 8 * q^10 - 12 * q^11 - 24 * q^12 - 5 * q^13 - 8 * q^14 - q^15 - 58 * q^16 - 30 * q^17 + 36 * q^18 - 24 * q^19 - 36 * q^20 - 28 * q^21 + 5 * q^22 + 27 * q^23 - 46 * q^24 - 38 * q^25 + 6 * q^26 - 36 * q^27 - 54 * q^28 + 28 * q^29 - 21 * q^30 + 36 * q^31 + 11 * q^32 + 5 * q^33 - 4 * q^34 + 6 * q^35 + 192 * q^36 + 164 * q^37 + 32 * q^38 - 34 * q^39 + 2 * q^40 + 42 * q^41 - 2 * q^42 - 22 * q^43 + 14 * q^44 + 58 * q^45 - 53 * q^46 + 21 * q^47 - 20 * q^48 + 166 * q^49 + 18 * q^50 - 6 * q^51 + 54 * q^52 + 8 * q^53 - 154 * q^54 - 5 * q^55 - 35 * q^56 + 8 * q^57 + 9 * q^58 - 13 * q^59 - 88 * q^60 - 34 * q^61 - 36 * q^62 - 31 * q^63 - 18 * q^64 + 9 * q^65 + 222 * q^66 - 48 * q^67 - 27 * q^68 + 2 * q^69 - 64 * q^70 - 42 * q^71 + 77 * q^72 - 44 * q^73 - 35 * q^74 - 21 * q^75 + 44 * q^76 - 32 * q^77 + 124 * q^78 - 96 * q^79 + 490 * q^80 - 12 * q^81 - 130 * q^82 - 8 * q^83 + 170 * q^84 + 22 * q^85 - 12 * q^86 - 90 * q^87 - 122 * q^88 - 81 * q^89 + 49 * q^90 - 27 * q^91 - 116 * q^92 + 18 * q^93 - 124 * q^94 + 117 * q^95 + 52 * q^96 - 79 * q^97 - 54 * q^98 - 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{4}{7}\right)$

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 $

$2$	−0.396271	−	1.73618i	−0.280206	−	1.22766i	−0.897530	−	0.440953i	$-0.854640\pi$
$2$	−0.396271	−	1.73618i	−0.280206	−	1.22766i	0.617324	−	0.786709i	$-0.288217\pi$
$3$	−0.0213391	+	0.0934929i	−0.0123202	+	0.0539782i	−0.980714	−	0.195447i	$-0.937384\pi$
$3$	−0.0213391	+	0.0934929i	−0.0123202	+	0.0539782i	0.968394	+	0.249425i	$0.0802415\pi$
$4$	−1.05534	+	0.508225i	−0.527670	+	0.254112i
$5$	−1.30201	−	1.63267i	−0.582276	−	0.730151i	0.400223	−	0.916418i	$-0.368933\pi$
$5$	−1.30201	−	1.63267i	−0.582276	−	0.730151i	−0.982499	+	0.186267i	$0.940361\pi$
$6$	0.170776			0.0697191
$7$	−1.70084			−0.642858			−0.321429	−	0.946934i	$-0.604163\pi$
$7$	−1.70084			−0.642858			−0.321429	+	0.946934i	$0.604163\pi$
$8$	−0.920084	−	1.15375i	−0.325299	−	0.407912i
$9$	2.69462	+	1.29766i	0.898207	+	0.432554i
$10$	−2.31865	+	2.90749i	−0.733221	+	0.919431i
$11$	−1.66630	−	0.802449i	−0.502409	−	0.241947i	0.165473	−	0.986214i	$-0.447085\pi$
$11$	−1.66630	−	0.802449i	−0.502409	−	0.241947i	−0.667882	+	0.744267i	$0.732799\pi$
$12$	−0.0249954	−	0.109512i	−0.00721554	−	0.0316134i
$13$	−1.34014	−	1.68048i	−0.371688	−	0.466081i	0.560449	−	0.828189i	$-0.310629\pi$
$13$	−1.34014	−	1.68048i	−0.371688	−	0.466081i	−0.932136	+	0.362108i	$0.882057\pi$
$14$	0.673994	+	2.95296i	0.180133	+	0.789212i
$15$	0.180427	−	0.0868888i	0.0465859	−	0.0224346i
$16$	−3.09915	+	3.88621i	−0.774786	+	0.971551i
$17$	0.623490	−	0.781831i	0.151218	−	0.189622i
$17$	0.623490	−	0.781831i	0.151218	−	0.189622i
$18$	1.18517	−	5.19256i	0.279347	−	1.22390i
$19$	−5.46595	+	2.63226i	−1.25397	+	0.603882i	−0.938574	−	0.345077i	$-0.887853\pi$
$19$	−5.46595	+	2.63226i	−1.25397	+	0.603882i	−0.315400	+	0.948959i	$0.602139\pi$
$20$	2.20382	+	1.06131i	0.492790	+	0.237315i
$21$	0.0362945	−	0.159017i	0.00792011	−	0.0347003i
$22$	−0.732885	+	3.21098i	−0.156252	+	0.684583i
$23$	−1.05819	−	0.509599i	−0.220649	−	0.106259i	0.320294	−	0.947318i	$-0.396218\pi$
$23$	−1.05819	−	0.509599i	−0.220649	−	0.106259i	−0.540943	+	0.841059i	$0.681932\pi$
$24$	0.127501	−	0.0614013i	0.0260261	−	0.0125335i
$25$	0.142229	−	0.623147i	0.0284458	−	0.124629i
$26$	−2.38655	+	2.99264i	−0.468041	+	0.586905i
$27$	−0.358196	+	0.449163i	−0.0689348	+	0.0864415i
$28$	1.79497	−	0.864410i	0.339217	−	0.163358i
$29$	2.35300	+	10.3092i	0.436940	+	1.91436i	0.403645	+	0.914916i	$0.367743\pi$
$29$	2.35300	+	10.3092i	0.436940	+	1.91436i	0.0332953	+	0.999446i	$0.489400\pi$
$30$	−0.222352	−	0.278821i	−0.0405958	−	0.0509055i
$31$	−1.69205	−	7.41336i	−0.303901	−	1.33148i	−0.864184	−	0.503177i	$-0.832164\pi$
$31$	−1.69205	−	7.41336i	−0.303901	−	1.33148i	0.560282	−	0.828302i	$-0.310693\pi$
$32$	5.31612	+	2.56011i	0.939766	+	0.452567i
$33$	0.110581	−	0.138664i	0.0192496	−	0.0241383i
$34$	−1.60447	−	0.772671i	−0.275164	−	0.132512i
$35$	2.21451	+	2.77691i	0.374321	+	0.469383i
$36$	−3.50324			−0.583874
$37$	−6.51903			−1.07172			−0.535861	−	0.844306i	$-0.680013\pi$
$37$	−6.51903			−1.07172			−0.535861	+	0.844306i	$0.680013\pi$
$38$	6.73607	+	8.44676i	1.09273	+	1.37025i
$39$	0.185710	−	0.0894334i	0.0297375	−	0.0143208i
$40$	−0.685731	+	3.00438i	−0.108424	+	0.475035i
$41$	2.34635	+	10.2800i	0.366438	+	1.60547i	0.736484	+	0.676455i	$0.236485\pi$
$41$	2.34635	+	10.2800i	0.366438	+	1.60547i	−0.370046	+	0.929013i	$0.620658\pi$
$42$	−0.290463			−0.0448195
$43$	−0.943496	−	6.48921i	−0.143882	−	0.989595i
$43$	−0.943496	−	6.48921i	−0.143882	−	0.989595i
$44$	2.16634			0.326588
$45$	−1.38977	−	6.08898i	−0.207175	−	0.907692i
$46$	−0.465423	+	2.03915i	−0.0686228	+	0.300656i
$47$	1.05986	−	0.510404i	0.154597	−	0.0744501i	−0.354985	−	0.934872i	$-0.615514\pi$
$47$	1.05986	−	0.510404i	0.154597	−	0.0744501i	0.509582	+	0.860422i	$0.329800\pi$
$48$	−0.297200	−	0.372676i	−0.0428971	−	0.0537912i
$49$	−4.10714			−0.586734
$50$	−1.13825			−0.160973
$51$	0.0597910	+	0.0749755i	0.00837241	+	0.0104987i
$52$	2.26836	+	1.09239i	0.314565	+	0.151487i
$53$	−3.38532	+	4.24506i	−0.465010	+	0.583104i	−0.957941	−	0.286964i	$-0.907354\pi$
$53$	−3.38532	+	4.24506i	−0.465010	+	0.583104i	0.492932	+	0.870068i	$0.335925\pi$
$54$	0.921770	+	0.443901i	0.125437	+	0.0604073i
$55$	0.859408	+	3.76531i	0.115883	+	0.507714i
$56$	1.56492	+	1.96235i	0.209121	+	0.262229i
$57$	−0.129459	−	0.567197i	−0.0171473	−	0.0751271i
$58$	16.9661	−	8.17043i	2.22776	−	1.07283i
$59$	5.16638	−	6.47844i	0.672606	−	0.843421i	−0.322044	−	0.946725i	$-0.604370\pi$
$59$	5.16638	−	6.47844i	0.672606	−	0.843421i	0.994650	+	0.103304i	$0.0329414\pi$
$60$	−0.146252	+	0.183395i	−0.0188811	+	0.0236761i
$61$	−0.727539	+	3.18756i	−0.0931518	+	0.408125i	−0.999908	−	0.0135295i	$-0.995693\pi$
$61$	−0.727539	+	3.18756i	−0.0931518	+	0.408125i	0.906757	+	0.421654i	$0.138550\pi$
$62$	−12.2004	+	5.87540i	−1.54945	+	0.746176i
$63$	−4.58313	−	2.20712i	−0.577420	−	0.278071i
$64$	0.126031	−	0.552176i	0.0157538	−	0.0690220i
$65$	−0.998793	+	4.37600i	−0.123885	+	0.542776i
$66$	−0.284565	−	0.137039i	−0.0350275	−	0.0168684i
$67$	−4.62193	+	2.22581i	−0.564659	+	0.271925i	−0.694360	−	0.719628i	$-0.744312\pi$
$67$	−4.62193	+	2.22581i	−0.564659	+	0.271925i	0.129701	+	0.991553i	$0.458598\pi$
$68$	−0.260647	+	1.14197i	−0.0316081	+	0.138484i
$69$	0.0702248	−	0.0880592i	0.00845408	−	0.0106011i
$70$	3.94366	−	4.94519i	0.471357	−	0.591063i
$71$	−1.28705	+	0.619812i	−0.152745	+	0.0735581i	−0.508695	−	0.860947i	$-0.669872\pi$
$71$	−1.28705	+	0.619812i	−0.152745	+	0.0735581i	0.355950	+	0.934505i	$0.384157\pi$
$72$	−0.982103	−	4.30288i	−0.115742	−	0.507099i
$73$	−1.16712	−	1.46352i	−0.136601	−	0.171292i	0.708826	−	0.705383i	$-0.249225\pi$
$73$	−1.16712	−	1.46352i	−0.136601	−	0.171292i	−0.845427	+	0.534092i	$0.820654\pi$
$74$	2.58330	+	11.3182i	0.300303	+	1.31571i
$75$	0.0552248	+	0.0265948i	0.00637681	+	0.00307091i
$76$	4.43065	−	5.55586i	0.508230	−	0.637301i
$77$	2.83412	+	1.36484i	0.322978	+	0.155538i
$78$	−0.228864	−	0.286986i	−0.0259137	−	0.0324948i
$79$	−12.6103			−1.41877			−0.709385	−	0.704821i	$-0.751027\pi$
$79$	−12.6103			−1.41877			−0.709385	+	0.704821i	$0.751027\pi$
$80$	10.3800			1.16052
$81$	5.55986	+	6.97184i	0.617762	+	0.774649i
$82$	16.9181	−	8.14734i	1.86829	−	0.899723i
$83$	3.78855	−	16.5987i	0.415847	−	1.82194i	−0.139371	−	0.990240i	$-0.544508\pi$
$83$	3.78855	−	16.5987i	0.415847	−	1.82194i	0.555218	−	0.831705i	$-0.312635\pi$
$84$	0.0425132	+	0.186262i	0.00463857	+	0.0203229i
$85$	−2.08826			−0.226504
$86$	−10.8925	+	4.20956i	−1.17457	+	0.453929i
$87$	−1.01404			−0.108717
$88$	0.607314	+	2.66082i	0.0647399	+	0.283644i
$89$	3.19548	−	14.0003i	0.338720	−	1.48403i	−0.463014	−	0.886351i	$-0.653232\pi$
$89$	3.19548	−	14.0003i	0.338720	−	1.48403i	0.801735	−	0.597680i	$-0.203911\pi$
$90$	−10.0208	+	4.82578i	−1.05629	+	0.508681i
$91$	2.27936	+	2.85823i	0.238942	+	0.299624i
$92$	1.37574			0.143431
$93$	0.729203			0.0756149
$94$	−1.30614	−	1.63785i	−0.134719	−	0.168932i
$95$	11.4143	+	5.49684i	1.17108	+	0.563964i
$96$	−0.352793	+	0.442389i	−0.0360068	+	0.0451511i
$97$	10.0400	+	4.83503i	1.01941	+	0.490923i	0.867482	−	0.497469i	$-0.165737\pi$
$97$	10.0400	+	4.83503i	1.01941	+	0.490923i	0.151930	+	0.988391i	$0.451451\pi$
$98$	1.62754	+	7.13071i	0.164406	+	0.720311i
$99$	−3.44875	−	4.32459i	−0.346612	−	0.434638i
$100$	0.166599	+	0.729916i	0.0166599	+	0.0729916i
$101$	0.426227	−	0.205260i	0.0424111	−	0.0204241i	−0.412558	−	0.910931i	$-0.635365\pi$
$101$	0.426227	−	0.205260i	0.0424111	−	0.0204241i	0.454969	+	0.890507i	$0.349650\pi$
$102$	0.106477	−	0.133518i	0.0105428	−	0.0132203i
$103$	2.48603	−	3.11739i	0.244956	−	0.307165i	−0.644120	−	0.764924i	$-0.722776\pi$
$103$	2.48603	−	3.11739i	0.244956	−	0.307165i	0.889076	+	0.457759i	$0.151348\pi$
$104$	−0.705813	+	3.09237i	−0.0692106	+	0.303232i
$105$	−0.306877	+	0.147784i	−0.0299481	+	0.0144223i
$106$	8.71167	+	4.19532i	0.846152	+	0.407486i
$107$	3.51098	−	15.3826i	0.339419	−	1.48709i	−0.460864	−	0.887471i	$-0.652460\pi$
$107$	3.51098	−	15.3826i	0.339419	−	1.48709i	0.800283	−	0.599623i	$-0.204683\pi$
$108$	0.149742	−	0.656064i	0.0144090	−	0.0631298i
$109$	−6.79192	−	3.27082i	−0.650548	−	0.313287i	0.0793466	−	0.996847i	$-0.474717\pi$
$109$	−6.79192	−	3.27082i	−0.650548	−	0.313287i	−0.729895	+	0.683560i	$0.760431\pi$
$110$	6.19669	−	2.98417i	0.590831	−	0.284529i
$111$	0.139111	−	0.609483i	0.0132038	−	0.0578496i
$112$	5.27116	−	6.60982i	0.498078	−	0.624569i
$113$	−3.00848	+	3.77251i	−0.283014	+	0.354888i	−0.902936	−	0.429775i	$-0.858593\pi$
$113$	−3.00848	+	3.77251i	−0.283014	+	0.354888i	0.619922	+	0.784663i	$0.287164\pi$
$114$	−0.933454	+	0.449528i	−0.0874260	+	0.0421021i
$115$	0.545771	+	2.39118i	0.0508934	+	0.222979i
$116$	−7.72258	−	9.68381i	−0.717023	−	0.899119i
$117$	−1.43047	−	6.26730i	−0.132247	−	0.579412i
$118$	−13.2950	−	6.40253i	−1.22390	−	0.589401i
$119$	−1.06046	+	1.32977i	−0.0972120	+	0.121900i
$120$	−0.266256	−	0.128222i	−0.0243057	−	0.0117050i
$121$	−4.72575	−	5.92590i	−0.429614	−	0.538718i
$122$	5.82246			0.527141
$123$	−1.01118			−0.0911748
$124$	5.55334	+	6.96367i	0.498705	+	0.625356i
$125$	−10.6099	+	5.10944i	−0.948975	+	0.457002i
$126$	−2.01578	+	8.83173i	−0.179580	+	0.786793i
$127$	3.68336	+	16.1379i	0.326846	+	1.43200i	0.825106	+	0.564977i	$0.191115\pi$
$127$	3.68336	+	16.1379i	0.326846	+	1.43200i	−0.498261	+	0.867027i	$0.666028\pi$
$128$	10.7923			0.953911
$129$	0.626828	+	0.0502639i	0.0551892	+	0.00442549i
$130$	7.99330			0.701059
$131$	0.999420	+	4.37875i	0.0873197	+	0.382573i	0.999638	−	0.0269093i	$-0.00856655\pi$
$131$	0.999420	+	4.37875i	0.0873197	+	0.382573i	−0.912318	+	0.409482i	$0.865709\pi$
$132$	−0.0462278	+	0.202537i	−0.00402362	+	0.0176286i
$133$	9.29671	−	4.47706i	0.806127	−	0.388210i
$134$	5.69593	+	7.14247i	0.492053	+	0.617015i
$135$	1.19971			0.103254
$136$	−1.47570			−0.126540
$137$	−8.99246	−	11.2762i	−0.768278	−	0.963390i	0.231678	−	0.972793i	$-0.425578\pi$
$137$	−8.99246	−	11.2762i	−0.768278	−	0.963390i	−0.999956	+	0.00940244i	$0.997007\pi$
$138$	−0.180714	−	0.0870274i	−0.0153834	−	0.00740827i
$139$	7.82332	−	9.81013i	0.663565	−	0.832084i	−0.330161	−	0.943925i	$-0.607103\pi$
$139$	7.82332	−	9.81013i	0.663565	−	0.832084i	0.993726	+	0.111840i	$0.0356746\pi$
$140$	−3.74836	−	1.80511i	−0.316794	−	0.152560i
$141$	0.0251025	+	0.109981i	0.00211402	+	0.00926211i
$142$	1.58612	+	1.98894i	0.133105	+	0.166908i
$143$	0.884576	+	3.87558i	0.0739719	+	0.324092i
$144$	−13.3940	+	6.45021i	−1.11617	+	0.537518i
$145$	13.7678	−	17.2643i	1.14335	−	1.43372i
$146$	−2.07843	+	2.60627i	−0.172012	+	0.215697i
$147$	0.0876428	−	0.383988i	0.00722865	−	0.0316708i
$148$	6.87979	−	3.31313i	0.565516	−	0.272338i
$149$	−19.5710	−	9.42488i	−1.60332	−	0.772117i	−0.603633	−	0.797262i	$-0.706281\pi$
$149$	−19.5710	−	9.42488i	−1.60332	−	0.772117i	−0.999684	+	0.0251458i	$0.991995\pi$
$150$	0.0242894	−	0.106419i	0.00198322	−	0.00868905i
$151$	5.13193	−	22.4845i	0.417631	−	1.82976i	−0.128050	−	0.991768i	$-0.540872\pi$
$151$	5.13193	−	22.4845i	0.417631	−	1.82976i	0.545681	−	0.837993i	$-0.316271\pi$
$152$	8.06610	+	3.88443i	0.654247	+	0.315069i
$153$	2.69462	−	1.29766i	0.217847	−	0.104910i
$154$	1.24652	−	5.46137i	0.100448	−	0.440090i
$155$	−9.90048	+	12.4148i	−0.795226	+	0.997182i
$156$	−0.150535	+	0.188765i	−0.0120525	+	0.0151133i
$157$	−2.99871	+	1.44410i	−0.239323	+	0.115252i	−0.549702	−	0.835361i	$-0.685259\pi$
$157$	−2.99871	+	1.44410i	−0.239323	+	0.115252i	0.310378	+	0.950613i	$0.399544\pi$
$158$	4.99710	+	21.8937i	0.397548	+	1.74177i
$159$	−0.324643	−	0.407089i	−0.0257459	−	0.0322843i
$160$	−2.74183	−	12.0127i	−0.216760	−	0.949690i
$161$	1.79982	+	0.866748i	0.141846	+	0.0683093i
$162$	9.90113	−	12.4156i	0.777907	−	0.975464i
$163$	−20.6207	−	9.93041i	−1.61514	−	0.777809i	−0.615194	−	0.788376i	$-0.710922\pi$
$163$	−20.6207	−	9.93041i	−1.61514	−	0.777809i	−0.999944	+	0.0105664i	$0.996637\pi$
$164$	−7.70075	−	9.65644i	−0.601328	−	0.754041i
$165$	−0.370369			−0.0288332
$166$	−30.3196			−2.35326
$167$	2.34774	+	2.94398i	0.181674	+	0.227812i	0.864326	−	0.502931i	$-0.167745\pi$
$167$	2.34774	+	2.94398i	0.181674	+	0.227812i	−0.682652	+	0.730743i	$0.739174\pi$
$168$	−0.216859	+	0.104434i	−0.0167311	+	0.00805726i
$169$	1.86473	−	8.16991i	0.143441	−	0.628455i
$170$	0.827517	+	3.62559i	0.0634676	+	0.278070i
$171$	−18.1444			−1.38754
$172$	4.29369	+	6.36881i	0.327390	+	0.485617i
$173$	−3.88331			−0.295242			−0.147621	−	0.989044i	$-0.547162\pi$
$173$	−3.88331			−0.295242			−0.147621	+	0.989044i	$0.547162\pi$
$174$	0.401836	+	1.76056i	0.0304631	+	0.133468i
$175$	−0.241909	+	1.05987i	−0.0182866	+	0.0801190i
$176$	8.28259	−	3.98869i	0.624324	−	0.300659i
$177$	0.495442	+	0.621264i	0.0372397	+	0.0466971i
$178$	−25.5733			−1.91680
$179$	8.62734			0.644838			0.322419	−	0.946597i	$-0.395504\pi$
$179$	8.62734			0.644838			0.322419	+	0.946597i	$0.395504\pi$
$180$	4.56125	+	5.71963i	0.339976	+	0.426316i
$181$	−10.9766	−	5.28605i	−0.815884	−	0.392909i	−0.0210821	−	0.999778i	$-0.506711\pi$
$181$	−10.9766	−	5.28605i	−0.815884	−	0.392909i	−0.794802	+	0.606869i	$0.792425\pi$
$182$	4.05915	−	5.09001i	0.300884	−	0.377297i
$183$	−0.282489	−	0.136039i	−0.0208822	−	0.0100563i
$184$	0.385678	+	1.68976i	0.0284325	+	0.124571i
$185$	8.48784	+	10.6434i	0.624038	+	0.782519i
$186$	−0.288962	−	1.26603i	−0.0211877	−	0.0928295i
$187$	−1.66630	+	0.802449i	−0.121852	+	0.0586809i
$188$	−0.859117	+	1.07730i	−0.0626576	+	0.0785701i
$189$	0.609235	−	0.763956i	0.0443153	−	0.0555696i
$190$	5.02033	−	21.9955i	0.364213	−	1.59572i
$191$	−13.4945	+	6.49860i	−0.976426	+	0.470222i	−0.852875	−	0.522116i	$-0.825143\pi$
$191$	−13.4945	+	6.49860i	−0.976426	+	0.470222i	−0.123552	+	0.992338i	$0.539429\pi$
$192$	0.0489352	+	0.0235659i	0.00353159	+	0.00170072i
$193$	−2.63447	+	11.5424i	−0.189633	+	0.830838i	0.787176	+	0.616728i	$0.211542\pi$
$193$	−2.63447	+	11.5424i	−0.189633	+	0.830838i	−0.976810	+	0.214110i	$0.931315\pi$
$194$	4.41589	−	19.3473i	0.317042	−	1.38905i
$195$	−0.387812	−	0.186760i	−0.0277718	−	0.0133742i
$196$	4.33442	−	2.08735i	0.309602	−	0.149096i
$197$	1.35526	−	5.93780i	0.0965586	−	0.423051i	−0.903425	−	0.428746i	$-0.858956\pi$
$197$	1.35526	−	5.93780i	0.0965586	−	0.423051i	0.999984	+	0.00569485i	$0.00181274\pi$
$198$	−6.14161	+	7.70134i	−0.436465	+	0.547310i
$199$	9.66463	−	12.1191i	0.685107	−	0.859097i	−0.310706	−	0.950506i	$-0.600566\pi$
$199$	9.66463	−	12.1191i	0.685107	−	0.859097i	0.995813	+	0.0914087i	$0.0291370\pi$
$200$	−0.849818	+	0.409251i	−0.0600912	+	0.0289384i
$201$	−0.109469	−	0.479615i	−0.00772134	−	0.0338294i
$202$	−0.525269	−	0.658666i	−0.0369578	−	0.0463436i
$203$	−4.00208	−	17.5342i	−0.280891	−	1.23066i
$204$	−0.101204	−	0.0487374i	−0.00708571	−	0.00341230i
$205$	13.7289	−	17.2155i	0.958866	−	1.20238i
$206$	−6.39748	−	3.08086i	−0.445733	−	0.214654i
$207$	−2.19014	−	2.74635i	−0.152225	−	0.190885i
$208$	10.6840			0.740800
$209$	11.2202			0.776116
$210$	0.378186	+	0.474230i	0.0260973	+	0.0327250i
$211$	−6.63490	+	3.19520i	−0.456766	+	0.219967i	−0.648095	−	0.761559i	$-0.724434\pi$
$211$	−6.63490	+	3.19520i	−0.456766	+	0.219967i	0.191330	+	0.981526i	$0.438720\pi$
$212$	1.41522	−	6.20048i	0.0971977	−	0.425851i
$213$	−0.0304834	−	0.133556i	−0.00208869	−	0.00915114i
$214$	−28.0982			−1.92076
$215$	−9.36628	+	9.98942i	−0.638775	+	0.681273i
$216$	0.847793			0.0576850
$217$	2.87791	+	12.6090i	0.195365	+	0.855952i
$218$	−2.98727	+	13.0881i	−0.202324	+	0.886438i
$219$	0.161734	−	0.0778869i	0.0109290	−	0.00526311i
$220$	−2.82059	−	3.53691i	−0.190164	−	0.238458i
$221$	−2.14942			−0.144585
$222$	−1.11330			−0.0747195
$223$	−10.4216	−	13.0683i	−0.697883	−	0.875117i	0.298981	−	0.954259i	$-0.403353\pi$
$223$	−10.4216	−	13.0683i	−0.697883	−	0.875117i	−0.996863	+	0.0791419i	$0.974782\pi$
$224$	−9.04188	−	4.35434i	−0.604136	−	0.290936i
$225$	1.19189	−	1.49458i	0.0794591	−	0.0996386i
$226$	7.74191	+	3.72831i	0.514984	+	0.248003i
$227$	0.159343	+	0.698128i	0.0105760	+	0.0463364i	0.979941	−	0.199290i	$-0.0638635\pi$
$227$	0.159343	+	0.698128i	0.0105760	+	0.0463364i	−0.969365	+	0.245626i	$0.921006\pi$
$228$	0.424887	+	0.532792i	0.0281388	+	0.0352850i
$229$	0.662384	+	2.90209i	0.0437716	+	0.191776i	0.992087	−	0.125554i	$-0.0400709\pi$
$229$	0.662384	+	2.90209i	0.0437716	+	0.191776i	−0.948315	+	0.317330i	$0.897214\pi$
$230$	3.93524	−	1.89511i	0.259482	−	0.124960i
$231$	−0.188080	+	0.235845i	−0.0123748	+	0.0155175i
$232$	9.72922	−	12.2001i	0.638755	−	0.800973i
$233$	3.44693	−	15.1020i	0.225816	−	0.989364i	−0.727196	−	0.686430i	$-0.759177\pi$
$233$	3.44693	−	15.1020i	0.225816	−	0.989364i	0.953012	−	0.302934i	$-0.0979662\pi$
$234$	−10.3143	+	4.96710i	−0.674266	+	0.324709i
$235$	−2.21327	−	1.06586i	−0.144378	−	0.0695288i
$236$	−2.15979	+	9.46264i	−0.140590	+	0.615965i
$237$	0.269093	−	1.17897i	0.0174795	−	0.0765826i
$238$	2.72895	+	1.31419i	0.176891	+	0.0851864i
$239$	0.0151227	−	0.00728271i	0.000978207	−	0.000471079i	−0.433395	−	0.901204i	$-0.642684\pi$
$239$	0.0151227	−	0.00728271i	0.000978207	−	0.000471079i	0.434373	+	0.900733i	$0.356970\pi$
$240$	−0.221500	+	0.970456i	−0.0142978	+	0.0626426i
$241$	−17.7943	+	22.3134i	−1.14623	+	1.43733i	−0.265251	+	0.964179i	$0.585455\pi$
$241$	−17.7943	+	22.3134i	−1.14623	+	1.43733i	−0.880982	+	0.473151i	$0.843117\pi$
$242$	−8.41573	+	10.5530i	−0.540984	+	0.678372i
$243$	−2.32328	+	1.11883i	−0.149039	+	0.0717733i
$244$	−0.852195	−	3.73371i	−0.0545562	−	0.239026i
$245$	5.34753	+	6.70558i	0.341641	+	0.428404i
$246$	0.400700	+	1.75558i	0.0255477	+	0.111932i
$247$	11.7486	+	5.65782i	0.747545	+	0.359999i
$248$	−6.99633	+	8.77312i	−0.444267	+	0.557094i
$249$	1.47102	+	0.708405i	0.0932219	+	0.0448933i
$250$	13.0753	+	16.3959i	0.826952	+	1.03697i
$251$	22.3435			1.41031			0.705154	−	0.709054i	$-0.250878\pi$
$251$	22.3435			1.41031			0.705154	+	0.709054i	$0.250878\pi$
$252$	5.95847			0.375348
$253$	1.35434	+	1.69829i	0.0851468	+	0.106771i
$254$	26.5586	−	12.7899i	1.66643	−	0.802512i
$255$	0.0445617	−	0.195237i	0.00279056	−	0.0122262i
$256$	−4.52873	−	19.8416i	−0.283045	−	1.24010i
$257$	17.6394			1.10031			0.550157	−	0.835061i	$-0.314568\pi$
$257$	17.6394			1.10031			0.550157	+	0.835061i	$0.314568\pi$
$258$	−0.161127	−	1.10820i	−0.0100313	−	0.0689937i
$259$	11.0878			0.688965
$260$	−1.16993	−	5.12578i	−0.0725557	−	0.317887i
$261$	−7.03735	+	30.8326i	−0.435601	+	1.90849i
$262$	7.20623	−	3.47034i	0.445203	−	0.214398i
$263$	−3.94084	−	4.94166i	−0.243003	−	0.304716i	0.645341	−	0.763894i	$-0.276715\pi$
$263$	−3.94084	−	4.94166i	−0.243003	−	0.304716i	−0.888344	+	0.459179i	$0.848144\pi$
$264$	−0.261727			−0.0161082
$265$	11.3385			0.696517
$266$	−11.4570	−	14.3666i	−0.702473	−	0.880873i
$267$	1.24074	+	0.597510i	0.0759322	+	0.0365670i
$268$	3.74650	−	4.69796i	0.228854	−	0.286974i
$269$	−12.5738	−	6.05524i	−0.766640	−	0.369195i	0.00933613	−	0.999956i	$-0.497028\pi$
$269$	−12.5738	−	6.05524i	−0.766640	−	0.369195i	−0.775976	+	0.630762i	$0.782742\pi$
$270$	−0.475410	−	2.08291i	−0.0289325	−	0.126762i
$271$	9.00525	+	11.2922i	0.547030	+	0.685954i	0.976101	−	0.217317i	$-0.0697305\pi$
$271$	9.00525	+	11.2922i	0.547030	+	0.685954i	−0.429071	+	0.903271i	$0.641159\pi$
$272$	1.10607	+	4.84602i	0.0670655	+	0.293833i
$273$	−0.315864	+	0.152112i	−0.0191170	+	0.00920625i
$274$	−16.0140	+	20.0809i	−0.967442	+	1.21313i
$275$	−0.737040	+	0.924219i	−0.0444452	+	0.0557325i
$276$	−0.0293572	+	0.128622i	−0.00176710	+	0.00774216i
$277$	−8.85394	+	4.26383i	−0.531982	+	0.256189i	−0.680535	−	0.732715i	$-0.738253\pi$
$277$	−8.85394	+	4.26383i	−0.531982	+	0.256189i	0.148553	+	0.988904i	$0.452538\pi$
$278$	−20.1323	−	9.69519i	−1.20745	−	0.581479i
$279$	5.06059	−	22.1719i	0.302970	−	1.32740i
$280$	1.16632	−	5.10998i	0.0697009	−	0.305380i
$281$	12.5380	+	6.03798i	0.747955	+	0.360196i	0.768717	−	0.639589i	$-0.220895\pi$
$281$	12.5380	+	6.03798i	0.747955	+	0.360196i	−0.0207629	+	0.999784i	$0.506610\pi$
$282$	0.181000	−	0.0871649i	0.0107784	−	0.00519059i
$283$	−4.69039	+	20.5500i	−0.278815	+	1.22157i	0.620479	+	0.784223i	$0.286938\pi$
$283$	−4.69039	+	20.5500i	−0.278815	+	1.22157i	−0.899294	+	0.437345i	$0.855919\pi$
$284$	1.04327	−	1.30822i	0.0619069	−	0.0776288i
$285$	−0.757488	+	0.949860i	−0.0448697	+	0.0562648i
$286$	6.37816	−	3.07156i	0.377148	−	0.181625i
$287$	−3.99076	−	17.4847i	−0.235567	−	1.03209i
$288$	11.0028	+	13.7970i	0.648344	+	0.812998i
$289$	−0.222521	−	0.974928i	−0.0130895	−	0.0573487i
$290$	−35.4296	−	17.0620i	−2.08050	−	1.00191i
$291$	−0.666287	+	0.835497i	−0.0390584	+	0.0489777i
$292$	1.97550	+	0.951352i	0.115608	+	0.0556736i
$293$	11.0337	+	13.8358i	0.644594	+	0.808295i	0.991569	−	0.129579i	$-0.0413626\pi$
$293$	11.0337	+	13.8358i	0.644594	+	0.808295i	−0.346975	+	0.937874i	$0.612791\pi$
$294$	−0.701401			−0.0409066
$295$	−17.3038			−1.00747
$296$	5.99806	+	7.52133i	0.348630	+	0.437168i
$297$	0.957293	−	0.461008i	0.0555478	−	0.0267504i
$298$	−8.60785	+	37.7135i	−0.498640	+	2.18468i
$299$	0.561754	+	2.46121i	0.0324871	+	0.142335i
$300$	−0.0717970			−0.00414520
$301$	1.60474	+	11.0371i	0.0924956	+	0.636169i
$302$	−41.0706			−2.36335
$303$	0.0100950	+	0.0442292i	0.000579945	+	0.00254090i
$304$	6.71026	−	29.3996i	0.384860	−	1.68618i
$305$	6.15148	−	2.96240i	0.352233	−	0.169626i
$306$	−3.32077	−	4.16411i	−0.189836	−	0.238046i
$307$	30.4642			1.73868			0.869341	−	0.494213i	$-0.164544\pi$
$307$	30.4642			1.73868			0.869341	+	0.494213i	$0.164544\pi$
$308$	−3.68460			−0.209950
$309$	0.238404	+	0.298949i	0.0135623	+	0.0170066i
$310$	25.4776	+	12.2694i	1.44703	+	0.696852i
$311$	5.64293	−	7.07601i	0.319981	−	0.401244i	−0.595662	−	0.803235i	$-0.703110\pi$
$311$	5.64293	−	7.07601i	0.319981	−	0.401244i	0.915644	+	0.401991i	$0.131682\pi$
$312$	−0.274053	−	0.131977i	−0.0155152	−	0.00747172i
$313$	−6.46935	−	28.3441i	−0.365669	−	1.60210i	−0.738534	−	0.674216i	$-0.764482\pi$
$313$	−6.46935	−	28.3441i	−0.365669	−	1.60210i	0.372864	−	0.927886i	$-0.378376\pi$
$314$	3.69552	+	4.63404i	0.208550	+	0.261514i
$315$	2.36378	+	10.3564i	0.133184	+	0.583517i
$316$	13.3082	−	6.40887i	0.748642	−	0.360527i
$317$	7.20198	−	9.03100i	0.404503	−	0.507231i	−0.537302	−	0.843390i	$-0.680556\pi$
$317$	7.20198	−	9.03100i	0.404503	−	0.507231i	0.941805	+	0.336159i	$0.109128\pi$
$318$	−0.578132	+	0.724955i	−0.0324201	+	0.0406535i
$319$	4.35176	−	19.0663i	0.243652	−	1.06751i
$320$	−1.06561	+	0.513172i	−0.0595696	+	0.0286872i
$321$	1.36324	+	0.656504i	0.0760889	+	0.0366425i
$322$	0.791610	−	3.46827i	0.0441147	−	0.193279i
$323$	−1.34998	+	5.91464i	−0.0751148	+	0.329099i
$324$	−9.41080	−	4.53200i	−0.522822	−	0.251778i
$325$	−1.23779	+	0.596090i	−0.0686604	+	0.0330651i
$326$	−9.06955	+	39.7363i	−0.502316	+	2.20079i
$327$	0.450732	−	0.565200i	0.0249255	−	0.0312556i
$328$	9.70172	−	12.1656i	0.535688	−	0.671732i
$329$	−1.80266	+	0.868116i	−0.0993840	+	0.0478608i
$330$	0.146766	+	0.643026i	0.00807923	+	0.0353974i
$331$	6.04034	+	7.57434i	0.332007	+	0.416324i	0.919614	−	0.392823i	$-0.128501\pi$
$331$	6.04034	+	7.57434i	0.332007	+	0.416324i	−0.587607	+	0.809146i	$0.699930\pi$
$332$	4.43767	+	19.4427i	0.243549	+	1.06706i
$333$	−17.5663	−	8.45950i	−0.962629	−	0.463577i
$334$	4.18092	−	5.24271i	0.228770	−	0.286868i
$335$	9.65179	+	4.64806i	0.527334	+	0.253951i
$336$	0.505490	+	0.633864i	0.0275767	+	0.0345801i
$337$	27.5671			1.50168			0.750838	−	0.660487i	$-0.229650\pi$
$337$	27.5671			1.50168			0.750838	+	0.660487i	$0.229650\pi$
$338$	−14.9233			−0.811723
$339$	−0.288505	−	0.361773i	−0.0156694	−	0.0196488i
$340$	2.20382	−	1.06131i	0.119519	−	0.0575574i
$341$	−3.12937	+	13.7107i	−0.169465	+	0.742475i
$342$	7.19011	+	31.5019i	0.388797	+	1.70343i
$343$	18.8915			1.02004
$344$	−6.61882	+	7.05918i	−0.356863	+	0.380605i
$345$	−0.235205			−0.0126630
$346$	1.53884	+	6.74210i	0.0827286	+	0.362458i
$347$	−3.89724	+	17.0749i	−0.209215	+	0.916630i	0.755876	+	0.654715i	$0.227211\pi$
$347$	−3.89724	+	17.0749i	−0.209215	+	0.916630i	−0.965091	+	0.261915i	$0.915646\pi$
$348$	1.07016	−	0.515362i	0.0573666	−	0.0276263i
$349$	20.7448	+	26.0131i	1.11044	+	1.39245i	0.910933	+	0.412554i	$0.135363\pi$
$349$	20.7448	+	26.0131i	1.11044	+	1.39245i	0.199509	+	0.979896i	$0.436065\pi$
$350$	1.93599			0.103483
$351$	1.23484			0.0659110
$352$	−6.80390	−	8.53182i	−0.362649	−	0.454748i
$353$	22.5148	+	10.8426i	1.19834	+	0.577092i	0.923203	−	0.384312i	$-0.125561\pi$
$353$	22.5148	+	10.8426i	1.19834	+	0.577092i	0.275141	+	0.961404i	$0.411276\pi$
$354$	0.882295	−	1.10636i	0.0468935	−	0.0588025i
$355$	2.68770	+	1.29433i	0.142648	+	0.0686958i
$356$	3.74299	+	16.3991i	0.198378	+	0.869151i
$357$	−0.101695	−	0.127521i	−0.00538227	−	0.00674915i
$358$	−3.41877	−	14.9786i	−0.180687	−	0.791643i
$359$	16.9761	−	8.17527i	0.895965	−	0.431474i	0.0715352	−	0.997438i	$-0.477210\pi$
$359$	16.9761	−	8.17527i	0.895965	−	0.431474i	0.824430	+	0.565964i	$0.191496\pi$
$360$	−5.74646	+	7.20583i	−0.302865	+	0.379780i
$361$	11.1015	−	13.9208i	0.584288	−	0.732674i
$362$	−4.82781	+	21.1520i	−0.253744	+	1.11173i
$363$	0.654873	−	0.315370i	0.0343719	−	0.0165527i
$364$	−3.85813	−	1.85798i	−0.202221	−	0.0973844i
$365$	−0.869842	+	3.81103i	−0.0455296	+	0.199478i
$366$	−0.124246	+	0.544359i	−0.00649446	+	0.0284541i
$367$	13.0313	+	6.27554i	0.680228	+	0.327581i	0.741895	−	0.670516i	$-0.233927\pi$
$367$	13.0313	+	6.27554i	0.680228	+	0.327581i	−0.0616668	+	0.998097i	$0.519642\pi$
$368$	5.25990	−	2.53304i	0.274191	−	0.132044i
$369$	−7.01746	+	30.7455i	−0.365314	+	1.60055i
$370$	15.1154	−	18.9541i	0.785810	−	0.985374i
$371$	5.75790	−	7.22017i	0.298935	−	0.374853i
$372$	−0.769557	+	0.370599i	−0.0398997	+	0.0192147i
$373$	−3.02909	−	13.2713i	−0.156840	−	0.687163i	−0.990800	−	0.135337i	$-0.956788\pi$
$373$	−3.02909	−	13.2713i	−0.156840	−	0.687163i	0.833959	−	0.551826i	$-0.186069\pi$
$374$	2.05350	+	2.57501i	0.106184	+	0.133150i
$375$	−0.251291	−	1.10098i	−0.0129766	−	0.0568542i
$376$	−1.56404	−	0.753203i	−0.0806594	−	0.0388435i
$377$	14.1710	−	17.7699i	0.729843	−	0.915194i
$378$	−1.56778	−	0.755005i	−0.0806381	−	0.0388333i
$379$	−0.851098	−	1.06724i	−0.0437179	−	0.0548206i	0.759492	−	0.650517i	$-0.225448\pi$
$379$	−0.851098	−	1.06724i	−0.0437179	−	0.0548206i	−0.803210	+	0.595696i	$0.796876\pi$
$380$	−14.8396			−0.761256
$381$	−1.58738			−0.0813238
$382$	16.6302	+	20.8536i	0.850874	+	1.06696i
$383$	−2.65390	+	1.27805i	−0.135608	+	0.0653054i	−0.500457	−	0.865761i	$-0.666835\pi$
$383$	−2.65390	+	1.27805i	−0.135608	+	0.0653054i	0.364849	+	0.931067i	$0.381121\pi$
$384$	−0.230298	+	1.00900i	−0.0117523	+	0.0514904i
$385$	−1.46172	−	6.40420i	−0.0744960	−	0.326388i
$386$	21.0836			1.07312
$387$	5.87843	−	18.7103i	0.298817	−	0.951098i
$388$	−13.0529			−0.662662
$389$	7.54073	+	33.0381i	0.382330	+	1.67510i	0.690160	+	0.723657i	$0.257540\pi$
$389$	7.54073	+	33.0381i	0.382330	+	1.67510i	−0.307830	+	0.951441i	$0.599603\pi$
$390$	−0.170570	+	0.747317i	−0.00863716	+	0.0378419i
$391$	−1.05819	+	0.509599i	−0.0535151	+	0.0257715i
$392$	3.77891	+	4.73861i	0.190864	+	0.239336i
$393$	−0.430708			−0.0217264
$394$	−10.8461			−0.546420
$395$	16.4187	+	20.5884i	0.826116	+	1.03592i
$396$	5.83746	+	2.81117i	0.293344	+	0.141267i
$397$	−18.6738	+	23.4162i	−0.937210	+	1.17522i	0.0471208	+	0.998889i	$0.484995\pi$
$397$	−18.6738	+	23.4162i	−0.937210	+	1.17522i	−0.984330	+	0.176334i	$0.943576\pi$
$398$	−24.8706	−	11.9771i	−1.24665	−	0.600356i
$399$	0.220190	+	0.964713i	0.0110233	+	0.0482961i
$400$	1.98089	+	2.48395i	0.0990444	+	0.124198i
$401$	7.96226	+	34.8849i	0.397616	+	1.74207i	0.636737	+	0.771081i	$0.280284\pi$
$401$	7.96226	+	34.8849i	0.397616	+	1.74207i	−0.239120	+	0.970990i	$0.576859\pi$
$402$	−0.789316	+	0.380115i	−0.0393675	+	0.0189584i
$403$	−10.1904	+	12.7784i	−0.507621	+	0.636537i
$404$	−0.345496	+	0.433238i	−0.0171891	+	0.0215544i
$405$	4.14371	−	18.1548i	0.205903	−	0.902119i
$406$	−28.8566	+	13.8966i	−1.43213	+	0.689678i
$407$	10.8627	+	5.23119i	0.538443	+	0.259300i
$408$	0.0314902	−	0.137968i	0.00155900	−	0.00683041i
$409$	−6.08737	+	26.6705i	−0.301001	+	1.31877i	0.567618	+	0.823292i	$0.307865\pi$
$409$	−6.08737	+	26.6705i	−0.301001	+	1.31877i	−0.868619	+	0.495480i	$0.834992\pi$
$410$	−35.3294	−	17.0138i	−1.74480	−	0.840250i
$411$	1.24614	−	0.600107i	0.0614673	−	0.0296011i
$412$	−1.03928	+	4.55337i	−0.0512015	+	0.224328i
$413$	−8.78720	+	11.0188i	−0.432390	+	0.542200i
$414$	−3.90026	+	4.89077i	−0.191687	+	0.240368i
$415$	−32.0329	+	15.4262i	−1.57243	+	0.757244i
$416$	−2.82212	−	12.3645i	−0.138366	−	0.606221i
$417$	0.750234	+	0.940764i	0.0367391	+	0.0460694i
$418$	−4.44623	−	19.4802i	−0.217472	−	0.952808i
$419$	−29.9063	−	14.4021i	−1.46102	−	0.703589i	−0.476548	−	0.879148i	$-0.658112\pi$
$419$	−29.9063	−	14.4021i	−1.46102	−	0.703589i	−0.984469	+	0.175560i	$0.943826\pi$
$420$	0.248752	−	0.311925i	0.0121379	−	0.0152204i
$421$	−9.07414	−	4.36988i	−0.442246	−	0.212975i	0.199490	−	0.979900i	$-0.436071\pi$
$421$	−9.07414	−	4.36988i	−0.442246	−	0.212975i	−0.641737	+	0.766925i	$0.721786\pi$
$422$	8.17665	+	10.2532i	0.398033	+	0.499118i
$423$	3.51826			0.171064
$424$	8.01251			0.389122
$425$	−0.398517	−	0.499725i	−0.0193309	−	0.0242402i
$426$	−0.219798	+	0.105849i	−0.0106492	+	0.00512841i
$427$	1.23743	−	5.42153i	0.0598834	−	0.262366i
$428$	4.11255	+	18.0183i	0.198788	+	0.870945i
$429$	−0.381215			−0.0184052
$430$	21.0550	+	12.3030i	1.01536	+	0.593303i
$431$	−38.1564			−1.83793			−0.918965	−	0.394338i	$-0.870974\pi$
$431$	−38.1564			−1.83793			−0.918965	+	0.394338i	$0.870974\pi$
$432$	−0.635440	−	2.78405i	−0.0305726	−	0.133947i
$433$	6.77306	−	29.6747i	0.325492	−	1.42607i	−0.502131	−	0.864791i	$-0.667451\pi$
$433$	6.77306	−	29.6747i	0.325492	−	1.42607i	0.827624	−	0.561283i	$-0.189692\pi$
$434$	20.7509	−	9.99312i	0.996077	−	0.479685i
$435$	1.32029	+	1.65560i	0.0633032	+	0.0793797i
$436$	8.83010			0.422885
$437$	7.12543			0.340855
$438$	−0.199316	−	0.249934i	−0.00952368	−	0.0119423i
$439$	5.58128	+	2.68780i	0.266380	+	0.128282i	0.562307	−	0.826929i	$-0.309914\pi$
$439$	5.58128	+	2.68780i	0.266380	+	0.128282i	−0.295927	+	0.955211i	$0.595628\pi$
$440$	3.55350	−	4.45595i	0.169406	−	0.212429i
$441$	−11.0672	−	5.32967i	−0.527008	−	0.253794i
$442$	0.851751	+	3.73176i	0.0405136	+	0.177502i
$443$	−7.97335	−	9.99826i	−0.378825	−	0.475032i	0.555468	−	0.831538i	$-0.312539\pi$
$443$	−7.97335	−	9.99826i	−0.378825	−	0.475032i	−0.934293	+	0.356506i	$0.883968\pi$
$444$	0.162946	+	0.713911i	0.00773306	+	0.0338807i
$445$	−27.0184	+	13.0114i	−1.28080	+	0.616798i
$446$	−18.5591	+	23.2723i	−0.878797	+	1.10198i
$447$	1.29879	−	1.62863i	0.0614306	−	0.0770315i
$448$	−0.214358	+	0.939165i	−0.0101275	+	0.0443714i
$449$	7.51425	−	3.61867i	0.354620	−	0.170776i	−0.248089	−	0.968737i	$-0.579803\pi$
$449$	7.51425	−	3.61867i	0.354620	−	0.170776i	0.602708	+	0.797962i	$0.294088\pi$
$450$	−3.06716	−	1.47707i	−0.144587	−	0.0696297i
$451$	4.33946	−	19.0124i	0.204337	−	0.895260i
$452$	1.25768	−	5.51026i	0.0591564	−	0.259181i
$453$	1.99263	+	0.959599i	0.0936218	+	0.0450859i
$454$	1.14893	−	0.553296i	0.0539220	−	0.0259675i
$455$	1.69879	−	7.44288i	0.0796405	−	0.348928i
$456$	−0.535290	+	0.671233i	−0.0250673	+	0.0314334i
$457$	14.1470	−	17.7398i	0.661770	−	0.829833i	−0.331765	−	0.943362i	$-0.607644\pi$
$457$	14.1470	−	17.7398i	0.661770	−	0.829833i	0.993535	+	0.113529i	$0.0362155\pi$
$458$	4.77606	−	2.30003i	0.223171	−	0.107473i
$459$	0.127839	+	0.560098i	0.00596700	+	0.0261431i
$460$	−1.79123	−	2.24613i	−0.0835166	−	0.104726i
$461$	−3.51747	−	15.4110i	−0.163825	−	0.717763i	−0.988383	−	0.151986i	$-0.951433\pi$
$461$	−3.51747	−	15.4110i	−0.163825	−	0.717763i	0.824558	−	0.565777i	$-0.191424\pi$
$462$	0.484000	+	0.233082i	0.0225177	+	0.0108440i
$463$	−9.07301	+	11.3772i	−0.421658	+	0.528743i	−0.946606	−	0.322391i	$-0.895513\pi$
$463$	−9.07301	+	11.3772i	−0.421658	+	0.528743i	0.524948	+	0.851134i	$0.324085\pi$
$464$	−47.3558	−	22.8053i	−2.19844	−	1.05871i
$465$	−0.949429	−	1.19055i	−0.0440287	−	0.0552103i
$466$	−27.5856			−1.27788
$467$	2.83398			0.131141			0.0655704	−	0.997848i	$-0.479113\pi$
$467$	2.83398			0.131141			0.0655704	+	0.997848i	$0.479113\pi$
$468$	4.69483	+	5.88713i	0.217019	+	0.272133i
$469$	7.86118	−	3.78574i	0.362995	−	0.174809i
$470$	−0.973458	+	4.26500i	−0.0449023	+	0.196730i
$471$	−0.0710235	−	0.311174i	−0.00327259	−	0.0143382i
$472$	−12.2280			−0.562839
$473$	−3.63511	+	11.5701i	−0.167142	+	0.531993i
$474$	−2.15354			−0.0989154
$475$	0.862868	+	3.78047i	0.0395911	+	0.173460i
$476$	0.443320	−	1.94231i	0.0203195	−	0.0890257i
$477$	−14.6308	+	7.04582i	−0.669898	+	0.322606i
$478$	−0.0186368	−	0.0233698i	−0.000852426	−	0.00106891i
$479$	−17.6305			−0.805559			−0.402779	−	0.915297i	$-0.631956\pi$
$479$	−17.6305			−0.805559			−0.402779	+	0.915297i	$0.631956\pi$
$480$	1.18161			0.0539330
$481$	8.73641	+	10.9551i	0.398346	+	0.499510i
$482$	45.7913	+	22.0519i	2.08574	+	1.00444i
$483$	−0.119441	+	0.149775i	−0.00543477	+	0.00681499i
$484$	7.99896	+	3.85210i	0.363589	+	0.175095i
$485$	−5.17823	−	22.6873i	−0.235131	−	1.03018i
$486$	2.86314	+	3.59027i	0.129875	+	0.162858i
$487$	−8.67324	−	38.0000i	−0.393022	−	1.72194i	−0.653909	−	0.756573i	$-0.726872\pi$
$487$	−8.67324	−	38.0000i	−0.393022	−	1.72194i	0.260887	−	0.965369i	$-0.415985\pi$
$488$	4.34704	−	2.09342i	0.196781	−	0.0947648i
$489$	1.36845	−	1.71598i	0.0618835	−	0.0775994i
$490$	9.52301	−	11.9415i	0.430206	−	0.539461i
$491$	1.98935	−	8.71590i	0.0897780	−	0.393343i	−0.909996	−	0.414618i	$-0.863915\pi$
$491$	1.98935	−	8.71590i	0.0897780	−	0.393343i	0.999774	+	0.0212746i	$0.00677242\pi$
$492$	1.06714	−	0.513906i	0.0481102	−	0.0231687i
$493$	9.52709	+	4.58800i	0.429078	+	0.206633i
$494$	5.16735	−	22.6397i	0.232490	−	1.01861i
$495$	−2.57032	+	11.2613i	−0.115527	+	0.506158i
$496$	34.0537	+	16.3994i	1.52906	+	0.736356i
$497$	2.18907	−	1.05420i	0.0981933	−	0.0472874i
$498$	0.646994	−	2.83467i	0.0289925	−	0.127024i
$499$	−20.5046	+	25.7119i	−0.917911	+	1.15102i	0.0702385	+	0.997530i	$0.477624\pi$
$499$	−20.5046	+	25.7119i	−0.917911	+	1.15102i	−0.988150	+	0.153494i	$0.950947\pi$
$500$	8.60026	−	10.7844i	0.384615	−	0.482293i
$501$	−0.325340	+	0.156675i	−0.0145351	+	0.00699974i
$502$	−8.85408	−	38.7922i	−0.395177	−	1.73138i
$503$	8.89237	+	11.1507i	0.396491	+	0.497184i	0.939503	−	0.342541i	$-0.111288\pi$
$503$	8.89237	+	11.1507i	0.396491	+	0.497184i	−0.543012	+	0.839725i	$0.682716\pi$
$504$	1.67040	+	7.31851i	0.0744056	+	0.325992i
$505$	−0.890072	−	0.428636i	−0.0396077	−	0.0190741i
$506$	2.41185	−	3.02436i	0.107220	−	0.134449i
$507$	0.724037	+	0.348678i	0.0321556	+	0.0154853i
$508$	−12.0889	−	15.1590i	−0.536357	−	0.672570i
$509$	−4.28244			−0.189816			−0.0949078	−	0.995486i	$-0.530256\pi$
$509$	−4.28244			−0.189816			−0.0949078	+	0.995486i	$0.530256\pi$
$510$	−0.356625			−0.0157916
$511$	1.98508	+	2.48921i	0.0878149	+	0.110116i
$512$	−13.2070	+	6.36015i	−0.583672	+	0.281081i
$513$	0.775564	−	3.39797i	0.0342420	−	0.150024i
$514$	−6.98997	−	30.6251i	−0.308314	−	1.35081i
$515$	−8.32649			−0.366909
$516$	−0.687062	+	0.265524i	−0.0302462	+	0.0116891i
$517$	−2.17563			−0.0956840
$518$	−4.39379	−	19.2505i	−0.193052	−	0.845816i
$519$	0.0828664	−	0.363062i	0.00363743	−	0.0159366i
$520$	5.96778	−	2.87393i	0.261704	−	0.126030i
$521$	16.6824	+	20.9191i	0.730870	+	0.916482i	0.998898	−	0.0469290i	$-0.0149434\pi$
$521$	16.6824	+	20.9191i	0.730870	+	0.916482i	−0.268028	+	0.963411i	$0.586372\pi$
$522$	56.3196			2.46504
$523$	−35.9068			−1.57009			−0.785046	−	0.619437i	$-0.787361\pi$
$523$	−35.9068			−1.57009			−0.785046	+	0.619437i	$0.787361\pi$
$524$	−3.28012	−	4.11313i	−0.143293	−	0.179683i
$525$	−0.0939286	−	0.0452336i	−0.00409938	−	0.00197416i
$526$	−7.01795	+	8.80023i	−0.305997	+	0.383708i
$527$	−6.85097	−	3.29926i	−0.298433	−	0.143718i
$528$	0.196170	+	0.859479i	0.00853722	+	0.0374040i
$529$	−13.4802	−	16.9036i	−0.586095	−	0.734940i
$530$	−4.49311	−	19.6856i	−0.195168	−	0.855088i
$531$	22.3283	−	10.7527i	0.968964	−	0.466628i
$532$	−7.53584	+	9.44964i	−0.326720	+	0.409694i
$533$	14.1309	−	17.7196i	0.612079	−	0.767522i
$534$	0.545712	−	2.39092i	0.0236153	−	0.103465i
$535$	−29.6860	+	14.2960i	−1.28344	+	0.618071i
$536$	6.82059	+	3.28462i	0.294605	+	0.141874i
$537$	−0.184100	+	0.806596i	−0.00794451	+	0.0348072i
$538$	−5.53032	+	24.2299i	−0.238429	+	1.04463i
$539$	6.84373	+	3.29577i	0.294780	+	0.141959i
$540$	−1.26610	+	0.609722i	−0.0544843	+	0.0262382i
$541$	5.66700	−	24.8287i	0.243643	−	1.06747i	−0.694028	−	0.719948i	$-0.744166\pi$
$541$	5.66700	−	24.8287i	0.243643	−	1.06747i	0.937671	−	0.347523i	$-0.112977\pi$
$542$	16.0368	−	20.1095i	0.688839	−	0.863776i
$543$	0.728440	−	0.913434i	0.0312603	−	0.0391992i
$544$	5.31612	−	2.56011i	0.227927	−	0.109764i
$545$	3.50298	+	15.3476i	0.150051	+	0.657418i
$546$	0.389261	+	0.488118i	0.0166588	+	0.0208895i
$547$	−0.724301	−	3.17337i	−0.0309689	−	0.135684i	0.957080	−	0.289823i	$-0.0935965\pi$
$547$	−0.724301	−	3.17337i	−0.0309689	−	0.135684i	−0.988049	+	0.154140i	$0.950739\pi$
$548$	15.2209	+	7.33002i	0.650207	+	0.313123i
$549$	−6.09681	+	7.64516i	−0.260205	+	0.326287i
$550$	1.89667	+	0.913390i	0.0808745	+	0.0389471i
$551$	−39.9977	−	50.1556i	−1.70396	−	2.13670i
$552$	−0.166211			−0.00707441
$553$	21.4481			0.912068
$554$	10.9113	+	13.6824i	0.463578	+	0.581308i
$555$	−1.17621	+	0.566431i	−0.0499272	+	0.0240437i
$556$	−3.27051	+	14.3290i	−0.138700	+	0.607686i
$557$	−5.45612	−	23.9048i	−0.231183	−	1.01288i	−0.948660	−	0.316298i	$-0.897560\pi$
$557$	−5.45612	−	23.9048i	−0.231183	−	1.01288i	0.717476	−	0.696583i	$-0.245297\pi$
$558$	−40.4997			−1.71449
$559$	−9.64057	+	10.2820i	−0.407753	+	0.434881i
$560$	−17.6547			−0.746049
$561$	−0.0394658	−	0.172911i	−0.00166625	−	0.00730031i
$562$	5.51456	−	24.1609i	0.232618	−	1.01916i
$563$	−8.95704	+	4.31348i	−0.377494	+	0.181792i	−0.613003	−	0.790081i	$-0.710039\pi$
$563$	−8.95704	+	4.31348i	−0.377494	+	0.181792i	0.235509	+	0.971872i	$0.424324\pi$
$564$	−0.0823870	−	0.103310i	−0.00346912	−	0.00435014i
$565$	10.0763			0.423914
$566$	37.5370			1.57780
$567$	−9.45644	−	11.8580i	−0.397133	−	0.497989i
$568$	1.89930	+	0.914656i	0.0796930	+	0.0383781i
$569$	5.20643	−	6.52866i	0.218265	−	0.273696i	−0.660629	−	0.750712i	$-0.729710\pi$
$569$	5.20643	−	6.52866i	0.218265	−	0.273696i	0.878894	+	0.477017i	$0.158282\pi$
$570$	1.94929	+	0.938731i	0.0816469	+	0.0393191i
$571$	5.89616	+	25.8328i	0.246747	+	1.08107i	0.934735	+	0.355346i	$0.115637\pi$
$571$	5.89616	+	25.8328i	0.246747	+	1.08107i	−0.687988	+	0.725722i	$0.741506\pi$
$572$	−2.90319	−	3.64049i	−0.121389	−	0.152217i
$573$	−0.319612	−	1.40031i	−0.0133520	−	0.0584989i
$574$	−28.7751	+	13.8573i	−1.20105	+	0.578394i
$575$	−0.468061	+	0.586930i	−0.0195195	+	0.0244767i
$576$	1.05614	−	1.32436i	0.0440059	−	0.0551817i
$577$	4.58169	−	20.0737i	0.190738	−	0.835679i	−0.785480	−	0.618887i	$-0.787584\pi$
$577$	4.58169	−	20.0737i	0.190738	−	0.835679i	0.976218	−	0.216791i	$-0.0695591\pi$
$578$	−1.60447	+	0.772671i	−0.0667371	+	0.0321389i
$579$	−1.02291	−	0.492609i	−0.0425108	−	0.0204721i
$580$	−5.75557	+	25.2168i	−0.238987	+	1.04707i
$581$	−6.44372	+	28.2318i	−0.267331	+	1.17125i
$582$	1.71460	+	0.825708i	0.0710725	+	0.0342267i
$583$	9.04741	−	4.35700i	0.374705	−	0.180449i
$584$	−0.614687	+	2.69312i	−0.0254359	+	0.111442i
$585$	−8.36993	+	10.4956i	−0.346054	+	0.433938i
$586$	19.6490	−	24.6391i	0.811695	−	1.01783i
$587$	−30.3133	+	14.5981i	−1.25116	+	0.602529i	−0.937824	−	0.347112i	$-0.887162\pi$
$587$	−30.3133	+	14.5981i	−1.25116	+	0.602529i	−0.313340	+	0.949641i	$0.601448\pi$
$588$	0.102659	+	0.449780i	0.00423360	+	0.0185486i
$589$	28.7626	+	36.0671i	1.18514	+	1.48612i
$590$	6.85699	+	30.0425i	0.282298	+	1.23683i
$591$	0.526222	+	0.253415i	0.0216459	+	0.0104241i
$592$	20.2034	−	25.3343i	0.830356	−	1.04123i
$593$	−7.69649	−	3.70643i	−0.316057	−	0.152205i	0.269129	−	0.963104i	$-0.413264\pi$
$593$	−7.69649	−	3.70643i	−0.316057	−	0.152205i	−0.585186	+	0.810899i	$0.698978\pi$
$594$	−1.17974	−	1.47935i	−0.0484053	−	0.0606983i
$595$	3.55180			0.145610
$596$	25.4440			1.04223
$597$	0.926811	+	1.16218i	0.0379319	+	0.0475650i
$598$	4.05048	−	1.95061i	0.165637	−	0.0797663i
$599$	5.07694	−	22.2435i	0.207438	−	0.908846i	−0.758826	−	0.651293i	$-0.774227\pi$
$599$	5.07694	−	22.2435i	0.207438	−	0.908846i	0.966264	−	0.257553i	$-0.0829161\pi$
$600$	−0.0201277	−	0.0881850i	−0.000821708	−	0.00360014i
$601$	17.0521			0.695571			0.347786	−	0.937574i	$-0.386934\pi$
$601$	17.0521			0.695571			0.347786	+	0.937574i	$0.386934\pi$
$602$	18.5265	−	7.15980i	0.755083	−	0.291812i
$603$	−15.3427			−0.624803
$604$	6.01123	+	26.3369i	0.244594	+	1.07163i
$605$	−3.52206	+	15.4312i	−0.143192	+	0.627366i
$606$	0.0727894	−	0.0350535i	0.00295687	−	0.00142395i
$607$	9.23963	+	11.5861i	0.375025	+	0.470266i	0.933148	−	0.359492i	$-0.117050\pi$
$607$	9.23963	+	11.5861i	0.375025	+	0.470266i	−0.558123	+	0.829758i	$0.688478\pi$
$608$	−35.7965			−1.45174
$609$	1.72473			0.0698895
$610$	−7.58090	−	9.50614i	−0.306941	−	0.384892i
$611$	−2.27809	−	1.09707i	−0.0921616	−	0.0443827i
$612$	−2.18424	+	2.73895i	−0.0882926	+	0.110715i
$613$	−31.1241	−	14.9886i	−1.25709	−	0.605383i	−0.317687	−	0.948196i	$-0.602906\pi$
$613$	−31.1241	−	14.9886i	−1.25709	−	0.605383i	−0.939404	+	0.342812i	$0.888620\pi$
$614$	−12.0721	−	52.8912i	−0.487189	−	2.13451i
$615$	1.31656	+	1.65092i	0.0530889	+	0.0665714i
$616$	−1.03294	−	4.52563i	−0.0416185	−	0.182343i
$617$	28.7440	−	13.8424i	1.15719	−	0.557273i	0.246003	−	0.969269i	$-0.420883\pi$
$617$	28.7440	−	13.8424i	1.15719	−	0.557273i	0.911185	+	0.411996i	$0.135168\pi$
$618$	0.424556	−	0.532376i	0.0170781	−	0.0214153i
$619$	−3.87958	+	4.86484i	−0.155934	+	0.195535i	−0.853661	−	0.520828i	$-0.825623\pi$
$619$	−3.87958	+	4.86484i	−0.155934	+	0.195535i	0.697728	+	0.716363i	$0.254195\pi$
$620$	4.13886	−	18.1335i	0.166220	−	0.728260i
$621$	0.607934	−	0.292766i	0.0243955	−	0.0117483i
$622$	−14.5213	−	6.99311i	−0.582252	−	0.280398i
$623$	−5.43501	+	23.8123i	−0.217749	+	0.954021i
$624$	−0.227987	+	0.998876i	−0.00912678	+	0.0399870i
$625$	19.2768	+	9.28320i	0.771071	+	0.371328i
$626$	−46.6467	+	22.4639i	−1.86438	+	0.897837i
$627$	−0.239429	+	1.04901i	−0.00956187	+	0.0418933i
$628$	2.43073	−	3.04804i	0.0969967	−	0.121630i
$629$	−4.06455	+	5.09678i	−0.162064	+	0.203222i
$630$	17.0438	−	8.20788i	0.679043	−	0.327010i
$631$	6.49915	+	28.4746i	0.258727	+	1.13356i	0.922614	+	0.385724i	$0.126048\pi$
$631$	6.49915	+	28.4746i	0.258727	+	1.13356i	−0.663887	+	0.747833i	$0.731094\pi$
$632$	11.6025	+	14.5491i	0.461525	+	0.578733i
$633$	−0.157145	−	0.688499i	−0.00624597	−	0.0273654i
$634$	−18.5333	−	8.92518i	−0.736053	−	0.354464i
$635$	21.5520	−	27.0254i	0.855265	−	1.07247i
$636$	0.549502	+	0.264626i	0.0217892	+	0.0104931i
$637$	5.50413	+	6.90196i	0.218082	+	0.273466i
$638$	−34.8270			−1.37881
$639$	−4.27242			−0.169014
$640$	−14.0516	−	17.6202i	−0.555440	−	0.696499i
$641$	11.2599	−	5.42249i	0.444740	−	0.214175i	−0.198091	−	0.980184i	$-0.563474\pi$
$641$	11.2599	−	5.42249i	0.444740	−	0.214175i	0.642831	+	0.766008i	$0.277760\pi$
$642$	0.599592	−	2.62699i	0.0236640	−	0.103679i
$643$	−1.21129	−	5.30701i	−0.0477686	−	0.209288i	0.945411	−	0.325879i	$-0.105660\pi$
$643$	−1.21129	−	5.30701i	−0.0477686	−	0.209288i	−0.993180	+	0.116591i	$0.962803\pi$
$644$	−2.33992			−0.0922059
$645$	−0.734072	−	1.08885i	−0.0289040	−	0.0428733i
$646$	10.8038			0.425070
$647$	−1.07898	−	4.72731i	−0.0424190	−	0.185850i	0.949280	−	0.314433i	$-0.101814\pi$
$647$	−1.07898	−	4.72731i	−0.0424190	−	0.185850i	−0.991699	+	0.128583i	$0.958957\pi$
$648$	2.92822	−	12.8294i	0.115031	−	0.503985i
$649$	−13.8074	+	6.64928i	−0.541986	+	0.261007i
$650$	1.52542	+	1.91281i	0.0598318	+	0.0750267i
$651$	−1.24026			−0.0486096
$652$	26.8087			1.04991
$653$	4.38730	+	5.50150i	0.171688	+	0.215290i	0.860230	−	0.509907i	$-0.170320\pi$
$653$	4.38730	+	5.50150i	0.171688	+	0.215290i	−0.688541	+	0.725197i	$0.741749\pi$
$654$	−1.15990	−	0.558578i	−0.0453556	−	0.0218421i
$655$	5.84778	−	7.33288i	0.228492	−	0.286520i
$656$	−47.2219	−	22.7409i	−1.84371	−	0.887882i
$657$	−1.24579	−	5.45815i	−0.0486028	−	0.212943i
$658$	2.22155	+	2.78573i	0.0866049	+	0.108599i
$659$	6.34052	+	27.7796i	0.246992	+	1.08214i	0.934500	+	0.355964i	$0.115847\pi$
$659$	6.34052	+	27.7796i	0.246992	+	1.08214i	−0.687508	+	0.726177i	$0.741295\pi$
$660$	0.390865	−	0.188231i	0.0152144	−	0.00732687i
$661$	−3.59329	+	4.50584i	−0.139763	+	0.175257i	−0.846787	−	0.531933i	$-0.821466\pi$
$661$	−3.59329	+	4.50584i	−0.139763	+	0.175257i	0.707024	+	0.707190i	$0.250037\pi$
$662$	10.7568	−	13.4886i	0.418074	−	0.524249i
$663$	0.0458667	−	0.200955i	0.00178131	−	0.00780445i
$664$	−22.6365	+	10.9012i	−0.878468	+	0.423048i
$665$	−19.4139	−	9.34927i	−0.752841	−	0.362549i
$666$	−7.72615	+	33.8505i	−0.299382	+	1.31168i
$667$	2.76361	−	12.1082i	0.107007	−	0.468830i
$668$	−3.97387	−	1.91372i	−0.153754	−	0.0740439i
$669$	1.44418	−	0.695481i	0.0558352	−	0.0268888i
$670$	4.24512	−	18.5991i	0.164003	−	0.718546i
$671$	3.77015	−	4.72762i	0.145545	−	0.182508i
$672$	0.600046	−	0.752434i	0.0231473	−	0.0290258i
$673$	4.78010	−	2.30198i	0.184259	−	0.0887346i	−0.339480	−	0.940613i	$-0.610251\pi$
$673$	4.78010	−	2.30198i	0.184259	−	0.0887346i	0.523739	+	0.851879i	$0.324537\pi$
$674$	−10.9240	−	47.8613i	−0.420778	−	1.84355i
$675$	0.228949	+	0.287093i	0.00881225	+	0.0110502i
$676$	2.18423	+	9.56973i	0.0840088	+	0.368067i
$677$	−8.73637	−	4.20721i	−0.335766	−	0.161696i	0.258402	−	0.966038i	$-0.416804\pi$
$677$	−8.73637	−	4.20721i	−0.335766	−	0.161696i	−0.594168	+	0.804341i	$0.702518\pi$
$678$	−0.513776	+	0.644255i	−0.0197315	+	0.0247425i
$679$	−17.0765	−	8.22362i	−0.655337	−	0.315594i
$680$	1.92138	+	2.40933i	0.0736814	+	0.0923935i
$681$	−0.0686703			−0.00263145
$682$	25.0442			0.958993
$683$	−5.93499	−	7.44224i	−0.227096	−	0.284770i	0.655209	−	0.755448i	$-0.272581\pi$
$683$	−5.93499	−	7.44224i	−0.227096	−	0.284770i	−0.882305	+	0.470678i	$0.844009\pi$
$684$	19.1485	−	9.22145i	0.732163	−	0.352591i
$685$	−6.70200	+	29.3634i	−0.256070	+	1.12192i
$686$	−7.48615	−	32.7989i	−0.285822	−	1.25227i
$687$	−0.285460			−0.0108910
$688$	28.1424	+	16.4444i	1.07292	+	0.626936i
$689$	11.6705			0.444612
$690$	0.0932048	+	0.408357i	0.00354824	+	0.0155459i
$691$	−3.59882	+	15.7674i	−0.136905	+	0.599822i	0.859199	+	0.511641i	$0.170962\pi$
$691$	−3.59882	+	15.7674i	−0.136905	+	0.599822i	−0.996105	+	0.0881806i	$0.971895\pi$
$692$	4.09821	−	1.97359i	0.155790	−	0.0750247i
$693$	5.86577	+	7.35545i	0.222822	+	0.279410i
$694$	31.1894			1.18394
$695$	−26.2027			−0.993925
$696$	0.933006	+	1.16995i	0.0353655	+	0.0443469i
$697$	9.50016	+	4.57504i	0.359844	+	0.173292i
$698$	36.9428	−	46.3248i	1.39831	−	1.75342i
$699$	1.33837	+	0.644527i	0.0506220	+	0.0243783i
$700$	−0.283358	−	1.24147i	−0.0107099	−	0.0469232i
$701$	18.0984	+	22.6946i	0.683566	+	0.857165i	0.995677	−	0.0928807i	$-0.0296075\pi$
$701$	18.0984	+	22.6946i	0.683566	+	0.857165i	−0.312111	+	0.950046i	$0.601036\pi$
$702$	−0.489332	−	2.14390i	−0.0184687	−	0.0809165i
$703$	35.6327	−	17.1598i	1.34391	−	0.647194i
$704$	−0.653098	+	0.818959i	−0.0246146	+	0.0308657i
$705$	0.146879	−	0.184181i	0.00553179	−	0.00693665i
$706$	9.90265	−	43.3863i	0.372691	−	1.63287i
$707$	−0.724944	+	0.349115i	−0.0272643	+	0.0131298i
$708$	−0.838601	−	0.403849i	−0.0315166	−	0.0151776i
$709$	6.14043	−	26.9030i	0.230609	−	1.01036i	−0.718528	−	0.695498i	$-0.755184\pi$
$709$	6.14043	−	26.9030i	0.230609	−	1.01036i	0.949137	−	0.314864i	$-0.101959\pi$
$710$	1.18212	−	5.17922i	0.0443643	−	0.194373i
$711$	−33.9800	−	16.3639i	−1.27435	−	0.613694i
$712$	−19.0930	+	9.19469i	−0.715539	+	0.344586i
$713$	−1.98732	+	8.70704i	−0.0744259	+	0.326081i
$714$	−0.181101	+	0.227093i	−0.00677754	+	0.00849876i
$715$	5.17581	−	6.49026i	0.193564	−	0.242722i
$716$	−9.10478	+	4.38463i	−0.340262	+	0.163861i
$717$	0.000358176		0.00156927i	1.33763e−5		5.86056e-5i
$718$	−20.9208	−	26.2339i	−0.780759	−	0.979041i
$719$	1.95599	+	8.56975i	0.0729461	+	0.319598i	0.998216	−	0.0597127i	$-0.0190184\pi$
$719$	1.95599	+	8.56975i	0.0729461	+	0.319598i	−0.925270	+	0.379310i	$0.876161\pi$
$720$	27.9701	+	13.4697i	1.04239	+	0.501987i
$721$	−4.22835	+	5.30218i	−0.157472	+	0.197464i
$722$	−28.5682	−	13.7577i	−1.06320	−	0.512009i
$723$	−1.70643	−	2.13979i	−0.0634627	−	0.0795797i
$724$	14.2705			0.530361
$725$	6.75878			0.251015
$726$	−0.807046	−	1.01200i	−0.0299523	−	0.0375590i
$727$	−38.5410	+	18.5603i	−1.42940	+	0.688365i	−0.978887	−	0.204402i	$-0.934475\pi$
$727$	−38.5410	+	18.5603i	−1.42940	+	0.688365i	−0.450518	+	0.892767i	$0.648761\pi$
$728$	1.20048	−	5.25963i	0.0444926	−	0.194935i
$729$	5.89784	+	25.8401i	0.218439	+	0.957042i
$730$	6.96131			0.257650
$731$	−5.66173	−	3.30830i	−0.209407	−	0.122362i
$732$	0.367260			0.0135743
$733$	1.10957	+	4.86133i	0.0409828	+	0.179557i	0.991277	−	0.131797i	$-0.0420746\pi$
$733$	1.10957	+	4.86133i	0.0409828	+	0.179557i	−0.950294	+	0.311354i	$0.899217\pi$
$734$	5.73152	−	25.1114i	0.211554	−	0.926880i
$735$	−0.741036	+	0.356864i	−0.0273335	+	0.0131631i
$736$	−4.32085	−	5.41818i	−0.159269	−	0.199717i
$737$	9.48763			0.349481
$738$	56.1604			2.06729
$739$	−6.79667	−	8.52275i	−0.250019	−	0.313514i	0.640946	−	0.767586i	$-0.278542\pi$
$739$	−6.79667	−	8.52275i	−0.250019	−	0.313514i	−0.890965	+	0.454072i	$0.849971\pi$
$740$	−14.3668	−	6.91868i	−0.528134	−	0.254336i
$741$	−0.779671	+	0.977677i	−0.0286419	+	0.0359158i
$742$	−14.8172	−	7.13558i	−0.543956	−	0.261955i
$743$	1.93635	+	8.48370i	0.0710377	+	0.311237i	0.997947	−	0.0640496i	$-0.0204016\pi$
$743$	1.93635	+	8.48370i	0.0710377	+	0.311237i	−0.926909	+	0.375286i	$0.877544\pi$
$744$	−0.670929	−	0.841318i	−0.0245974	−	0.0308442i
$745$	10.0939	+	44.2242i	0.369811	+	1.62025i
$746$	−21.8410	+	10.5181i	−0.799656	+	0.385094i
$747$	31.7482	−	39.8110i	1.16161	−	1.45661i
$748$	1.35069	−	1.69371i	0.0493861	−	0.0619282i
$749$	−5.97163	+	26.1634i	−0.218198	+	0.955990i
$750$	−1.81191	+	0.872571i	−0.0661617	+	0.0318618i
$751$	14.7566	+	7.10638i	0.538474	+	0.259316i	0.683295	−	0.730142i	$-0.260546\pi$
$751$	14.7566	+	7.10638i	0.538474	+	0.259316i	−0.144821	+	0.989458i	$0.546261\pi$
$752$	−1.30114	+	5.70067i	−0.0474477	+	0.207882i
$753$	−0.476791	+	2.08896i	−0.0173752	+	0.0761259i
$754$	−36.4671	−	17.5617i	−1.32806	−	0.639558i
$755$	−43.3915	+	20.8962i	−1.57918	+	0.760492i
$756$	−0.254688	+	1.11586i	−0.00926292	+	0.0405835i
$757$	−2.95827	+	3.70956i	−0.107520	+	0.134826i	−0.832680	−	0.553755i	$-0.813195\pi$
$757$	−2.95827	+	3.70956i	−0.107520	+	0.134826i	0.725160	+	0.688581i	$0.241766\pi$
$758$	−1.51566	+	1.90057i	−0.0550511	+	0.0690319i
$759$	−0.187679	+	0.0903813i	−0.00681231	+	0.00328063i
$760$	−4.16015	−	18.2268i	−0.150905	−	0.661156i
$761$	−1.46927	−	1.84241i	−0.0532610	−	0.0667871i	0.754488	−	0.656314i	$-0.227885\pi$
$761$	−1.46927	−	1.84241i	−0.0532610	−	0.0667871i	−0.807748	+	0.589527i	$0.799314\pi$
$762$	0.629031	+	2.75597i	0.0227874	+	0.0998381i
$763$	11.5520	+	5.56314i	0.418210	+	0.201399i
$764$	10.9385	−	13.7165i	0.395742	−	0.496244i
$765$	−5.62707	−	2.70985i	−0.203447	−	0.0979749i
$766$	3.27059	+	4.10119i	0.118171	+	0.148182i
$767$	−17.8106			−0.643102
$768$	1.95169			0.0704256
$769$	18.1075	+	22.7061i	0.652975	+	0.818805i	0.992558	−	0.121771i	$-0.0388575\pi$
$769$	18.1075	+	22.7061i	0.652975	+	0.818805i	−0.339583	+	0.940576i	$0.610286\pi$
$770$	−10.5396	+	5.07560i	−0.379820	+	0.182912i
$771$	−0.376409	+	1.64916i	−0.0135560	+	0.0593929i
$772$	−3.08586	−	13.5200i	−0.111062	−	0.486596i
$773$	39.3293			1.41458			0.707288	−	0.706926i	$-0.249918\pi$
$773$	39.3293			1.41458			0.707288	+	0.706926i	$0.249918\pi$
$774$	−34.8138	−	2.79164i	−1.25136	−	0.100343i
$775$	−4.86027			−0.174586
$776$	−3.65927	−	16.0323i	−0.131360	−	0.575527i
$777$	−0.236605	+	1.03664i	−0.00848816	+	0.0371891i
$778$	54.3718	−	26.1841i	1.94932	−	0.938745i
$779$	−39.8847	−	50.0138i	−1.42902	−	1.79193i
$780$	0.504189			0.0180529
$781$	2.64198			0.0945376
$782$	1.30409	+	1.63527i	0.0466340	+	0.0584772i
$783$	−5.47333	−	2.63582i	−0.195601	−	0.0941964i
$784$	12.7286	−	15.9612i	0.454593	−	0.570042i
$785$	6.26209	+	3.01566i	0.223504	+	0.107634i
$786$	0.170677	+	0.747786i	0.00608786	+	0.0266726i
$787$	16.5586	+	20.7638i	0.590251	+	0.740151i	0.983823	−	0.179142i	$-0.0573323\pi$
$787$	16.5586	+	20.7638i	0.590251	+	0.740151i	−0.393572	+	0.919294i	$0.628761\pi$
$788$	1.58747	+	6.95518i	0.0565514	+	0.247768i
$789$	0.546104	−	0.262990i	0.0194418	−	0.00936269i
$790$	29.2389	−	36.6644i	1.04027	−	1.30446i
$791$	5.11694	−	6.41644i	0.181938	−	0.228143i
$792$	−1.81636	+	7.95798i	−0.0645414	+	0.282774i
$793$	6.33163	−	3.04915i	0.224843	−	0.108279i
$794$	48.0545	+	23.1418i	1.70539	+	0.821272i
$795$	−0.241954	+	1.06007i	−0.00858121	+	0.0375967i
$796$	−4.04026	+	17.7015i	−0.143203	+	0.627414i
$797$	−42.1554	−	20.3010i	−1.49322	−	0.719098i	−0.503754	−	0.863847i	$-0.668048\pi$
$797$	−42.1554	−	20.3010i	−1.49322	−	0.719098i	−0.989468	+	0.144749i	$0.953762\pi$
$798$	1.58766	−	0.764576i	0.0562025	−	0.0270657i
$799$	0.261765	−	1.14687i	0.00926058	−	0.0405732i
$800$	2.35143	−	2.94860i	0.0831356	−	0.104249i
$801$	26.7783	−	33.5789i	0.946164	−	1.18645i
$802$	57.4112	−	27.6478i	2.02726	−	0.976277i
$803$	0.770371	+	3.37522i	0.0271858	+	0.119109i
$804$	0.359279	+	0.450522i	0.0126708	+	0.0158887i
$805$	−0.928271	−	4.06702i	−0.0327172	−	0.143344i
$806$	26.2237	+	12.6287i	0.923690	+	0.444826i
$807$	0.834437	−	1.04635i	0.0293736	−	0.0368333i
$808$	−0.628983	−	0.302902i	−0.0221275	−	0.0106561i
$809$	17.9638	+	22.5259i	0.631574	+	0.791968i	0.989921	−	0.141620i	$-0.0452311\pi$
$809$	17.9638	+	22.5259i	0.631574	+	0.791968i	−0.358347	+	0.933588i	$0.616660\pi$
$810$	−33.1619			−1.16519
$811$	16.2719			0.571384			0.285692	−	0.958321i	$-0.407777\pi$
$811$	16.2719			0.571384			0.285692	+	0.958321i	$0.407777\pi$
$812$	13.1349	+	16.4706i	0.460944	+	0.578006i
$813$	−1.24791	+	0.600961i	−0.0437660	+	0.0210766i
$814$	4.77770	−	20.9325i	0.167458	−	0.733683i
$815$	10.6353	+	46.5962i	0.372538	+	1.63219i
$816$	−0.476671			−0.0166868
$817$	22.2384	+	32.9861i	0.778023	+	1.15404i
$818$	48.7170			1.70335
$819$	2.43301	+	10.6597i	0.0850161	+	0.372480i
$820$	−5.73930	+	25.1455i	−0.200425	+	0.878120i
$821$	13.6988	−	6.59698i	0.478090	−	0.230236i	−0.179288	−	0.983797i	$-0.557379\pi$
$821$	13.6988	−	6.59698i	0.478090	−	0.230236i	0.657379	+	0.753560i	$0.271665\pi$
$822$	−1.53570	−	1.92571i	−0.0535637	−	0.0671667i
$823$	−22.8645			−0.797007			−0.398503	−	0.917167i	$-0.630470\pi$
$823$	−22.8645			−0.797007			−0.398503	+	0.917167i	$0.630470\pi$
$824$	−5.88404			−0.204980
$825$	−0.0706801	−	0.0886301i	−0.00246077	−	0.00308570i
$826$	22.6127	+	10.8897i	0.786796	+	0.378901i
$827$	10.0079	−	12.5495i	0.348010	−	0.436390i	−0.576762	−	0.816912i	$-0.695684\pi$
$827$	10.0079	−	12.5495i	0.348010	−	0.436390i	0.924772	+	0.380522i	$0.124256\pi$
$828$	3.70711	+	1.78525i	0.128831	+	0.0620417i
$829$	−11.2657	−	49.3581i	−0.391272	−	1.71428i	−0.660177	−	0.751110i	$-0.729519\pi$
$829$	−11.2657	−	49.3581i	−0.391272	−	1.71428i	0.268905	−	0.963167i	$-0.413338\pi$
$830$	39.4763	+	49.5018i	1.37024	+	1.71823i
$831$	−0.209703	−	0.918767i	−0.00727450	−	0.0318717i
$832$	−1.09682	+	0.528201i	−0.0380254	+	0.0183121i
$833$	−2.56076	+	3.21109i	−0.0887250	+	0.111258i
$834$	1.33604	−	1.67534i	0.0462632	−	0.0580122i
$835$	1.74975	−	7.66617i	0.0605527	−	0.265299i
$836$	−11.8411	+	5.70237i	−0.409533	+	0.197221i
$837$	3.93590	+	1.89543i	0.136044	+	0.0655156i
$838$	−13.1536	+	57.6297i	−0.454384	+	1.99078i
$839$	8.16019	−	35.7521i	0.281721	−	1.23430i	−0.613864	−	0.789412i	$-0.710386\pi$
$839$	8.16019	−	35.7521i	0.281721	−	1.23430i	0.895585	−	0.444890i	$-0.146757\pi$
$840$	0.452859	+	0.218085i	0.0156251	+	0.00752466i
$841$	−74.6139	+	35.9322i	−2.57289	+	1.23904i
$842$	−3.99106	+	17.4860i	−0.137541	+	0.602606i
$843$	−0.832059	+	1.04337i	−0.0286576	+	0.0359355i
$844$	5.37820	−	6.74404i	0.185125	−	0.232140i
$845$	−15.7666	+	7.59281i	−0.542389	+	0.261201i
$846$	−1.39419	−	6.10833i	−0.0479331	−	0.210009i
$847$	8.03776	+	10.0790i	0.276181	+	0.346319i
$848$	−6.00557	−	26.3121i	−0.206232	−	0.903561i
$849$	−1.82119	−	0.877037i	−0.0625029	−	0.0300998i
$850$	−0.709690	+	0.889923i	−0.0243422	+	0.0305241i
$851$	6.89840	+	3.32209i	0.236474	+	0.113880i
$852$	0.100047	+	0.125455i	0.00342756	+	0.00429802i
$853$	4.27072			0.146227			0.0731134	−	0.997324i	$-0.476707\pi$
$853$	4.27072			0.146227			0.0731134	+	0.997324i	$0.476707\pi$
$854$	−9.90309			−0.338877
$855$	23.6242	+	29.6238i	0.807931	+	1.01311i
$856$	−20.9781	+	10.1025i	−0.717016	+	0.345297i
$857$	−7.04582	+	30.8697i	−0.240681	+	1.05449i	0.699719	+	0.714418i	$0.253309\pi$
$857$	−7.04582	+	30.8697i	−0.240681	+	1.05449i	−0.940399	+	0.340072i	$0.889549\pi$
$858$	0.151065	+	0.661857i	0.00515726	+	0.0225954i
$859$	5.48833			0.187259			0.0936296	−	0.995607i	$-0.470153\pi$
$859$	5.48833			0.187259			0.0936296	+	0.995607i	$0.470153\pi$
$860$	4.80773	−	15.3024i	0.163942	−	0.521808i
$861$	1.71985			0.0586124
$862$	15.1203	+	66.2463i	0.514999	+	2.25636i
$863$	3.55799	−	15.5886i	0.121116	−	0.530642i	−0.877573	−	0.479443i	$-0.840839\pi$
$863$	3.55799	−	15.5886i	0.121116	−	0.530642i	0.998688	−	0.0511986i	$-0.0163042\pi$
$864$	−3.05412	+	1.47079i	−0.103903	+	0.0500371i
$865$	5.05610	+	6.34015i	0.171912	+	0.215571i
$866$	−54.2045			−1.84194
$867$	0.0958973			0.00325684
$868$	−9.44536	−	11.8441i	−0.320596	−	0.402015i
$869$	21.0126	+	10.1191i	0.712803	+	0.343268i
$870$	2.35121	−	2.94833i	0.0797135	−	0.0999576i
$871$	9.93445	+	4.78418i	0.336616	+	0.162106i
$872$	2.47544	+	10.8456i	0.0838289	+	0.367278i
$873$	20.7799	+	26.0571i	0.703292	+	0.881900i
$874$	−2.82360	−	12.3710i	−0.0955097	−	0.418455i
$875$	18.0457	−	8.69035i	0.610056	−	0.293787i
$876$	−0.131100	+	0.164394i	−0.00442946	+	0.00555437i
$877$	32.4112	−	40.6423i	1.09445	−	1.37239i	0.172531	−	0.985004i	$-0.444805\pi$
$877$	32.4112	−	40.6423i	1.09445	−	1.37239i	0.921916	−	0.387390i	$-0.126623\pi$
$878$	2.45480	−	10.7552i	0.0828455	−	0.362970i
$879$	−1.52900	+	0.736326i	−0.0515718	+	0.0248357i
$880$	−17.2962	−	8.32941i	−0.583055	−	0.280784i
$881$	8.09121	−	35.4499i	0.272600	−	1.19434i	−0.634332	−	0.773061i	$-0.718725\pi$
$881$	8.09121	−	35.4499i	0.272600	−	1.19434i	0.906932	−	0.421277i	$-0.138418\pi$
$882$	−4.86765	+	21.3266i	−0.163902	+	0.718103i
$883$	−36.3732	−	17.5164i	−1.22406	−	0.589475i	−0.293618	−	0.955923i	$-0.594859\pi$
$883$	−36.3732	−	17.5164i	−1.22406	−	0.589475i	−0.930438	+	0.366448i	$0.880574\pi$
$884$	2.26836	−	1.09239i	0.0762933	−	0.0367409i
$885$	0.369248	−	1.61778i	0.0124122	−	0.0543812i
$886$	−14.1991	+	17.8052i	−0.477029	+	0.598176i
$887$	−4.85333	+	6.08589i	−0.162959	+	0.204344i	−0.856606	−	0.515971i	$-0.827431\pi$
$887$	−4.85333	+	6.08589i	−0.162959	+	0.204344i	0.693647	+	0.720315i	$0.256003\pi$
$888$	−0.831184	+	0.400277i	−0.0278927	+	0.0134324i
$889$	−6.26482	−	27.4480i	−0.210115	−	0.920576i
$890$	33.2967	+	41.7527i	1.11611	+	1.39955i
$891$	−3.66986	−	16.0787i	−0.122945	−	0.538656i
$892$	17.6400	+	8.49496i	0.590630	+	0.284432i
$893$	−4.44965	+	5.57968i	−0.148902	+	0.186717i
$894$	−3.34226	−	1.60955i	−0.111782	−	0.0538313i
$895$	−11.2329	−	14.0856i	−0.375474	−	0.470829i
$896$	−18.3560			−0.613229
$897$	−0.242093			−0.00808324
$898$	−9.26033	−	11.6121i	−0.309021	−	0.387501i
$899$	72.4440	−	34.8872i	2.41614	−	1.16355i
$900$	−0.498264	+	2.18304i	−0.0166088	+	0.0727679i
$901$	1.20821	+	5.29350i	0.0402512	+	0.176352i
$902$	−34.7285			−1.15633
$903$	−1.06614	−	0.0854910i	−0.0354788	−	0.00284496i
$904$	7.12058			0.236827
$905$	5.66126	+	24.8036i	0.188187	+	0.824500i
$906$	0.876413	−	3.83981i	0.0291169	−	0.127569i
$907$	−9.40778	+	4.53055i	−0.312380	+	0.150434i	−0.583504	−	0.812110i	$-0.698319\pi$
$907$	−9.40778	+	4.53055i	−0.312380	+	0.150434i	0.271124	+	0.962544i	$0.412605\pi$
$908$	−0.522967	−	0.655780i	−0.0173553	−	0.0217628i
$909$	1.41488			0.0469285
$910$	−13.5953			−0.450681
$911$	−30.7227	−	38.5250i	−1.01789	−	1.27639i	−0.960571	−	0.278034i	$-0.910317\pi$
$911$	−30.7227	−	38.5250i	−1.01789	−	1.27639i	−0.0573160	−	0.998356i	$-0.518254\pi$
$912$	2.60546	+	1.25472i	0.0862753	+	0.0415480i
$913$	−19.6325	+	24.6183i	−0.649740	+	0.814748i
$914$	−36.4055	−	17.5320i	−1.20419	−	0.579906i
$915$	0.145696	+	0.638335i	0.00481655	+	0.0211027i
$916$	−2.17396	−	2.72605i	−0.0718295	−	0.0900714i
$917$	−1.69986	−	7.44756i	−0.0561342	−	0.245940i
$918$	0.921770	−	0.443901i	0.0304229	−	0.0146509i
$919$	−9.80171	+	12.2910i	−0.323329	+	0.405441i	−0.916757	−	0.399446i	$-0.869203\pi$
$919$	−9.80171	+	12.2910i	−0.323329	+	0.405441i	0.593428	+	0.804887i	$0.297774\pi$
$920$	2.25667	−	2.82977i	0.0744001	−	0.0932948i
$921$	−0.650079	+	2.84818i	−0.0214208	+	0.0938508i
$922$	−25.3624	+	12.2139i	−0.835266	+	0.402243i
$923$	2.76641	+	1.33223i	0.0910575	+	0.0438510i
$924$	0.0786262	−	0.344484i	0.00258661	−	0.0113327i
$925$	−0.927197	+	4.06231i	−0.0304860	+	0.133568i
$926$	23.3482	+	11.2439i	0.767269	+	0.369497i
$927$	10.7442	−	5.17415i	0.352887	−	0.169941i
$928$	−13.8837	+	60.8286i	−0.455756	+	1.99680i
$929$	3.48720	−	4.37282i	0.114411	−	0.143467i	−0.721328	−	0.692594i	$-0.756468\pi$
$929$	3.48720	−	4.37282i	0.114411	−	0.143467i	0.835739	+	0.549126i	$0.185039\pi$
$930$	−1.69077	+	2.12016i	−0.0554424	+	0.0695226i
$931$	22.4494	−	10.8111i	0.735749	−	0.354318i
$932$	4.03752	+	17.6896i	0.132254	+	0.579440i
$933$	0.541142	+	0.678570i	0.0177162	+	0.0222154i
$934$	−1.12302	−	4.92028i	−0.0367464	−	0.160997i
$935$	3.47967	+	1.67572i	0.113797	+	0.0548019i
$936$	−5.91474	+	7.41685i	−0.193329	+	0.242427i
$937$	−9.00618	−	4.33715i	−0.294219	−	0.141688i	0.280951	−	0.959722i	$-0.409350\pi$
$937$	−9.00618	−	4.33715i	−0.294219	−	0.141688i	−0.575171	+	0.818034i	$0.695064\pi$
$938$	−9.68787	−	12.1482i	−0.316320	−	0.396653i
$939$	2.78802			0.0909836
$940$	2.87745			0.0938520
$941$	−21.7157	−	27.2306i	−0.707910	−	0.887692i	0.289676	−	0.957125i	$-0.406452\pi$
$941$	−21.7157	−	27.2306i	−0.707910	−	0.887692i	−0.997587	+	0.0694332i	$0.977881\pi$
$942$	−0.512109	+	0.246619i	−0.0166854	+	0.00803527i
$943$	2.75580	−	12.0739i	0.0897411	−	0.393182i
$944$	9.16517	+	40.1552i	0.298301	+	1.30694i
$945$	−2.04051			−0.0663780
$946$	21.5282	+	1.72630i	0.699942	+	0.0561268i
$947$	−47.7441			−1.55148			−0.775738	−	0.631055i	$-0.782622\pi$
$947$	−47.7441			−1.55148			−0.775738	+	0.631055i	$0.782622\pi$
$948$	0.315199	+	1.38098i	0.0102372	+	0.0448521i
$949$	−0.895316	+	3.92264i	−0.0290632	+	0.127334i
$950$	6.22164	−	2.99618i	0.201857	−	0.0972090i
$951$	0.690650	+	0.866048i	0.0223959	+	0.0280835i
$952$	2.50993			0.0813474
$953$	−0.894600			−0.0289789			−0.0144895	−	0.999895i	$-0.504612\pi$
$953$	−0.894600			−0.0289789			−0.0144895	+	0.999895i	$0.504612\pi$
$954$	18.0306	+	22.6096i	0.583761	+	0.732013i
$955$	28.1800	+	13.5708i	0.911883	+	0.439140i
$956$	−0.0122583	+	0.0153715i	−0.000396463	+	0.000497149i
$957$	1.68970	+	0.813718i	0.0546203	+	0.0263038i
$958$	6.98646	+	30.6097i	0.225722	+	0.988954i
$959$	15.2948	+	19.1790i	0.493894	+	0.619323i
$960$	−0.0252387	−	0.110578i	−0.000814575	−	0.00356889i
$961$	−24.1648	+	11.6372i	−0.779510	+	0.375392i
$962$	15.5580	−	19.5091i	0.501610	−	0.629000i
$963$	29.4222	−	36.8943i	0.948117	−	1.18890i
$964$	7.43884	−	32.5917i	0.239589	−	1.04971i
$965$	22.2750	−	10.7271i	0.717056	−	0.345316i
$966$	0.307367	+	0.148020i	0.00988936	+	0.00476246i
$967$	−10.6713	+	46.7540i	−0.343166	+	1.50351i	0.449183	+	0.893440i	$0.351715\pi$
$967$	−10.6713	+	46.7540i	−0.343166	+	1.50351i	−0.792349	+	0.610068i	$0.791142\pi$
$968$	−2.48892	+	10.9047i	−0.0799968	+	0.350489i
$969$	−0.524169	−	0.252427i	−0.0168387	−	0.00810911i
$970$	−37.3372	+	17.9806i	−1.19882	+	0.577323i
$971$	8.59214	−	37.6446i	0.275735	−	1.20807i	−0.627393	−	0.778702i	$-0.715878\pi$
$971$	8.59214	−	37.6446i	0.275735	−	1.20807i	0.903128	−	0.429371i	$-0.141265\pi$
$972$	1.88323	−	2.36150i	0.0604048	−	0.0757452i
$973$	−13.3062	+	16.6855i	−0.426578	+	0.534912i
$974$	−62.5377	+	30.1166i	−2.00384	+	0.964997i
$975$	−0.0293167	−	0.128445i	−0.000938886	−	0.00411353i
$976$	−10.1327	−	12.7061i	−0.324341	−	0.406711i
$977$	6.94456	+	30.4261i	0.222176	+	0.973417i	0.955836	+	0.293900i	$0.0949533\pi$
$977$	6.94456	+	30.4261i	0.222176	+	0.973417i	−0.733660	+	0.679517i	$0.762190\pi$
$978$	−3.52153	−	1.69588i	−0.112606	−	0.0542282i
$979$	−16.5592	+	20.7645i	−0.529233	+	0.663638i
$980$	−9.05140	−	4.35893i	−0.289136	−	0.139241i
$981$	−14.0572	−	17.6272i	−0.448813	−	0.562794i
$982$	−15.9207			−0.508049
$983$	30.6109			0.976335			0.488168	−	0.872750i	$-0.337665\pi$
$983$	30.6109			0.976335			0.488168	+	0.872750i	$0.337665\pi$
$984$	0.930369	+	1.16665i	0.0296591	+	0.0371913i
$985$	−11.4590	+	5.51837i	−0.365115	+	0.175830i
$986$	4.19028	−	18.3588i	0.133446	−	0.584663i
$987$	−0.0426955	−	0.187061i	−0.00135901	−	0.00595422i
$988$	−15.2742			−0.485937
$989$	−2.30849	+	7.34764i	−0.0734058	+	0.233641i
$990$	20.5702			0.653762
$991$	−8.71944	−	38.2024i	−0.276982	−	1.21354i	−0.901587	−	0.432598i	$-0.857597\pi$
$991$	−8.71944	−	38.2024i	−0.276982	−	1.21354i	0.624605	−	0.780941i	$-0.285260\pi$
$992$	9.98385	−	43.7421i	0.316988	−	1.38881i
$993$	−0.837043	+	0.403099i	−0.0265628	+	0.0127920i
$994$	−2.69775	−	3.38287i	−0.0855673	−	0.107298i
$995$	−32.3698			−1.02619
$996$	−1.91245			−0.0605984
$997$	−3.20953	−	4.02462i	−0.101647	−	0.127461i	0.728406	−	0.685145i	$-0.240261\pi$
$997$	−3.20953	−	4.02462i	−0.101647	−	0.127461i	−0.830053	+	0.557684i	$0.811690\pi$
$998$	52.7658	+	25.4107i	1.67027	+	0.804361i
$999$	2.33509	−	2.92811i	0.0738790	−	0.0926413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.k.a.188.7	yes	180
43.35	even	7	inner	731.2.k.a.35.7	✓	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.k.a.35.7	✓	180	43.35	even	7	inner
731.2.k.a.188.7	yes	180	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.396271 - 1.73618i) q^{2} +(-0.0213391 + 0.0934929i) q^{3} +(-1.05534 + 0.508225i) q^{4} +(-1.30201 - 1.63267i) q^{5} +0.170776 q^{6} -1.70084 q^{7} +(-0.920084 - 1.15375i) q^{8} +(2.69462 + 1.29766i) q^{9} +O(q^{10})\)	\(q+(-0.396271 - 1.73618i) q^{2} +(-0.0213391 + 0.0934929i) q^{3} +(-1.05534 + 0.508225i) q^{4} +(-1.30201 - 1.63267i) q^{5} +0.170776 q^{6} -1.70084 q^{7} +(-0.920084 - 1.15375i) q^{8} +(2.69462 + 1.29766i) q^{9} +(-2.31865 + 2.90749i) q^{10} +(-1.66630 - 0.802449i) q^{11} +(-0.0249954 - 0.109512i) q^{12} +(-1.34014 - 1.68048i) q^{13} +(0.673994 + 2.95296i) q^{14} +(0.180427 - 0.0868888i) q^{15} +(-3.09915 + 3.88621i) q^{16} +(0.623490 - 0.781831i) q^{17} +(1.18517 - 5.19256i) q^{18} +(-5.46595 + 2.63226i) q^{19} +(2.20382 + 1.06131i) q^{20} +(0.0362945 - 0.159017i) q^{21} +(-0.732885 + 3.21098i) q^{22} +(-1.05819 - 0.509599i) q^{23} +(0.127501 - 0.0614013i) q^{24} +(0.142229 - 0.623147i) q^{25} +(-2.38655 + 2.99264i) q^{26} +(-0.358196 + 0.449163i) q^{27} +(1.79497 - 0.864410i) q^{28} +(2.35300 + 10.3092i) q^{29} +(-0.222352 - 0.278821i) q^{30} +(-1.69205 - 7.41336i) q^{31} +(5.31612 + 2.56011i) q^{32} +(0.110581 - 0.138664i) q^{33} +(-1.60447 - 0.772671i) q^{34} +(2.21451 + 2.77691i) q^{35} -3.50324 q^{36} -6.51903 q^{37} +(6.73607 + 8.44676i) q^{38} +(0.185710 - 0.0894334i) q^{39} +(-0.685731 + 3.00438i) q^{40} +(2.34635 + 10.2800i) q^{41} -0.290463 q^{42} +(-0.943496 - 6.48921i) q^{43} +2.16634 q^{44} +(-1.38977 - 6.08898i) q^{45} +(-0.465423 + 2.03915i) q^{46} +(1.05986 - 0.510404i) q^{47} +(-0.297200 - 0.372676i) q^{48} -4.10714 q^{49} -1.13825 q^{50} +(0.0597910 + 0.0749755i) q^{51} +(2.26836 + 1.09239i) q^{52} +(-3.38532 + 4.24506i) q^{53} +(0.921770 + 0.443901i) q^{54} +(0.859408 + 3.76531i) q^{55} +(1.56492 + 1.96235i) q^{56} +(-0.129459 - 0.567197i) q^{57} +(16.9661 - 8.17043i) q^{58} +(5.16638 - 6.47844i) q^{59} +(-0.146252 + 0.183395i) q^{60} +(-0.727539 + 3.18756i) q^{61} +(-12.2004 + 5.87540i) q^{62} +(-4.58313 - 2.20712i) q^{63} +(0.126031 - 0.552176i) q^{64} +(-0.998793 + 4.37600i) q^{65} +(-0.284565 - 0.137039i) q^{66} +(-4.62193 + 2.22581i) q^{67} +(-0.260647 + 1.14197i) q^{68} +(0.0702248 - 0.0880592i) q^{69} +(3.94366 - 4.94519i) q^{70} +(-1.28705 + 0.619812i) q^{71} +(-0.982103 - 4.30288i) q^{72} +(-1.16712 - 1.46352i) q^{73} +(2.58330 + 11.3182i) q^{74} +(0.0552248 + 0.0265948i) q^{75} +(4.43065 - 5.55586i) q^{76} +(2.83412 + 1.36484i) q^{77} +(-0.228864 - 0.286986i) q^{78} -12.6103 q^{79} +10.3800 q^{80} +(5.55986 + 6.97184i) q^{81} +(16.9181 - 8.14734i) q^{82} +(3.78855 - 16.5987i) q^{83} +(0.0425132 + 0.186262i) q^{84} -2.08826 q^{85} +(-10.8925 + 4.20956i) q^{86} -1.01404 q^{87} +(0.607314 + 2.66082i) q^{88} +(3.19548 - 14.0003i) q^{89} +(-10.0208 + 4.82578i) q^{90} +(2.27936 + 2.85823i) q^{91} +1.37574 q^{92} +0.729203 q^{93} +(-1.30614 - 1.63785i) q^{94} +(11.4143 + 5.49684i) q^{95} +(-0.352793 + 0.442389i) q^{96} +(10.0400 + 4.83503i) q^{97} +(1.62754 + 7.13071i) q^{98} +(-3.44875 - 4.32459i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - 4 q^{2} - 6 q^{3} - 34 q^{4} - 6 q^{5} - 14 q^{6} + 66 q^{7} + 2 q^{8} - 26 q^{9}+O(q^{10}) \) 180 * q - 4 * q^2 - 6 * q^3 - 34 * q^4 - 6 * q^5 - 14 * q^6 + 66 * q^7 + 2 * q^8 - 26 * q^9	\( 180 q - 4 q^{2} - 6 q^{3} - 34 q^{4} - 6 q^{5} - 14 q^{6} + 66 q^{7} + 2 q^{8} - 26 q^{9} - 8 q^{10} - 12 q^{11} - 24 q^{12} - 5 q^{13} - 8 q^{14} - q^{15} - 58 q^{16} - 30 q^{17} + 36 q^{18} - 24 q^{19} - 36 q^{20} - 28 q^{21} + 5 q^{22} + 27 q^{23} - 46 q^{24} - 38 q^{25} + 6 q^{26} - 36 q^{27} - 54 q^{28} + 28 q^{29} - 21 q^{30} + 36 q^{31} + 11 q^{32} + 5 q^{33} - 4 q^{34} + 6 q^{35} + 192 q^{36} + 164 q^{37} + 32 q^{38} - 34 q^{39} + 2 q^{40} + 42 q^{41} - 2 q^{42} - 22 q^{43} + 14 q^{44} + 58 q^{45} - 53 q^{46} + 21 q^{47} - 20 q^{48} + 166 q^{49} + 18 q^{50} - 6 q^{51} + 54 q^{52} + 8 q^{53} - 154 q^{54} - 5 q^{55} - 35 q^{56} + 8 q^{57} + 9 q^{58} - 13 q^{59} - 88 q^{60} - 34 q^{61} - 36 q^{62} - 31 q^{63} - 18 q^{64} + 9 q^{65} + 222 q^{66} - 48 q^{67} - 27 q^{68} + 2 q^{69} - 64 q^{70} - 42 q^{71} + 77 q^{72} - 44 q^{73} - 35 q^{74} - 21 q^{75} + 44 q^{76} - 32 q^{77} + 124 q^{78} - 96 q^{79} + 490 q^{80} - 12 q^{81} - 130 q^{82} - 8 q^{83} + 170 q^{84} + 22 q^{85} - 12 q^{86} - 90 q^{87} - 122 q^{88} - 81 q^{89} + 49 q^{90} - 27 q^{91} - 116 q^{92} + 18 q^{93} - 124 q^{94} + 117 q^{95} + 52 q^{96} - 79 q^{97} - 54 q^{98} - 39 q^{99}+O(q^{100}) \) 180 * q - 4 * q^2 - 6 * q^3 - 34 * q^4 - 6 * q^5 - 14 * q^6 + 66 * q^7 + 2 * q^8 - 26 * q^9 - 8 * q^10 - 12 * q^11 - 24 * q^12 - 5 * q^13 - 8 * q^14 - q^15 - 58 * q^16 - 30 * q^17 + 36 * q^18 - 24 * q^19 - 36 * q^20 - 28 * q^21 + 5 * q^22 + 27 * q^23 - 46 * q^24 - 38 * q^25 + 6 * q^26 - 36 * q^27 - 54 * q^28 + 28 * q^29 - 21 * q^30 + 36 * q^31 + 11 * q^32 + 5 * q^33 - 4 * q^34 + 6 * q^35 + 192 * q^36 + 164 * q^37 + 32 * q^38 - 34 * q^39 + 2 * q^40 + 42 * q^41 - 2 * q^42 - 22 * q^43 + 14 * q^44 + 58 * q^45 - 53 * q^46 + 21 * q^47 - 20 * q^48 + 166 * q^49 + 18 * q^50 - 6 * q^51 + 54 * q^52 + 8 * q^53 - 154 * q^54 - 5 * q^55 - 35 * q^56 + 8 * q^57 + 9 * q^58 - 13 * q^59 - 88 * q^60 - 34 * q^61 - 36 * q^62 - 31 * q^63 - 18 * q^64 + 9 * q^65 + 222 * q^66 - 48 * q^67 - 27 * q^68 + 2 * q^69 - 64 * q^70 - 42 * q^71 + 77 * q^72 - 44 * q^73 - 35 * q^74 - 21 * q^75 + 44 * q^76 - 32 * q^77 + 124 * q^78 - 96 * q^79 + 490 * q^80 - 12 * q^81 - 130 * q^82 - 8 * q^83 + 170 * q^84 + 22 * q^85 - 12 * q^86 - 90 * q^87 - 122 * q^88 - 81 * q^89 + 49 * q^90 - 27 * q^91 - 116 * q^92 + 18 * q^93 - 124 * q^94 + 117 * q^95 + 52 * q^96 - 79 * q^97 - 54 * q^98 - 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more