LMFDB - Embedded newform 731.2.k.a.188.13

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			188.13
Character	$\chi$	$=$	731.188
Dual form			731.2.k.a.35.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.160022 - 0.701103i) q^{2} +(0.119356 - 0.522931i) q^{3} +(1.33600 - 0.643383i) q^{4} +(-0.180888 - 0.226826i) q^{5} -0.385728 q^{6} -0.492965 q^{7} +(-1.56161 - 1.95820i) q^{8} +(2.44370 + 1.17682i) q^{9} +O(q^{10})$	\(q+(-0.160022 - 0.701103i) q^{2} +(0.119356 - 0.522931i) q^{3} +(1.33600 - 0.643383i) q^{4} +(-0.180888 - 0.226826i) q^{5} -0.385728 q^{6} -0.492965 q^{7} +(-1.56161 - 1.95820i) q^{8} +(2.44370 + 1.17682i) q^{9} +(-0.130083 + 0.163118i) q^{10} +(4.96820 + 2.39256i) q^{11} +(-0.176986 - 0.775427i) q^{12} +(3.72800 + 4.67477i) q^{13} +(0.0788854 + 0.345620i) q^{14} +(-0.140204 + 0.0675189i) q^{15} +(0.726072 - 0.910465i) q^{16} +(0.623490 - 0.781831i) q^{17} +(0.434028 - 1.90160i) q^{18} +(-4.05881 + 1.95462i) q^{19} +(-0.387602 - 0.186659i) q^{20} +(-0.0588382 + 0.257787i) q^{21} +(0.882409 - 3.86608i) q^{22} +(0.664616 + 0.320062i) q^{23} +(-1.21039 + 0.582894i) q^{24} +(1.09387 - 4.79258i) q^{25} +(2.68093 - 3.36178i) q^{26} +(1.91035 - 2.39550i) q^{27} +(-0.658601 + 0.317166i) q^{28} +(-0.712761 - 3.12281i) q^{29} +(0.0697736 + 0.0874933i) q^{30} +(-0.242388 - 1.06197i) q^{31} +(-5.26771 - 2.53680i) q^{32} +(1.84413 - 2.31246i) q^{33} +(-0.647917 - 0.312020i) q^{34} +(0.0891714 + 0.111817i) q^{35} +4.02192 q^{36} -7.55722 q^{37} +(2.01989 + 2.53286i) q^{38} +(2.88954 - 1.39153i) q^{39} +(-0.161694 + 0.708429i) q^{40} +(-1.83204 - 8.02670i) q^{41} +0.190151 q^{42} +(3.38360 + 5.61705i) q^{43} +8.17684 q^{44} +(-0.175101 - 0.767167i) q^{45} +(0.118043 - 0.517181i) q^{46} +(-0.283805 + 0.136673i) q^{47} +(-0.389450 - 0.488355i) q^{48} -6.75699 q^{49} -3.53514 q^{50} +(-0.334427 - 0.419358i) q^{51} +(7.98828 + 3.84695i) q^{52} +(-1.11831 + 1.40231i) q^{53} +(-1.98519 - 0.956017i) q^{54} +(-0.355992 - 1.55970i) q^{55} +(0.769821 + 0.965325i) q^{56} +(0.537690 + 2.35577i) q^{57} +(-2.07535 + 0.999438i) q^{58} +(-5.74421 + 7.20301i) q^{59} +(-0.143872 + 0.180410i) q^{60} +(-0.991234 + 4.34288i) q^{61} +(-0.705764 + 0.339878i) q^{62} +(-1.20466 - 0.580132i) q^{63} +(-0.417341 + 1.82849i) q^{64} +(0.386010 - 1.69122i) q^{65} +(-1.91638 - 0.922878i) q^{66} +(-7.56704 + 3.64410i) q^{67} +(0.329964 - 1.44567i) q^{68} +(0.246696 - 0.309347i) q^{69} +(0.0641262 - 0.0804117i) q^{70} +(12.3613 - 5.95287i) q^{71} +(-1.51165 - 6.62298i) q^{72} +(-2.17710 - 2.72999i) q^{73} +(1.20932 + 5.29839i) q^{74} +(-2.37563 - 1.14404i) q^{75} +(-4.16500 + 5.22274i) q^{76} +(-2.44915 - 1.17945i) q^{77} +(-1.43800 - 1.80319i) q^{78} +14.5104 q^{79} -0.337855 q^{80} +(4.04860 + 5.07678i) q^{81} +(-5.33438 + 2.56890i) q^{82} +(3.07128 - 13.4562i) q^{83} +(0.0872480 + 0.382258i) q^{84} -0.290122 q^{85} +(3.39668 - 3.27111i) q^{86} -1.71809 q^{87} +(-3.07329 - 13.4650i) q^{88} +(2.63557 - 11.5472i) q^{89} +(-0.509843 + 0.245528i) q^{90} +(-1.83778 - 2.30450i) q^{91} +1.09385 q^{92} -0.584268 q^{93} +(0.141237 + 0.177106i) q^{94} +(1.17755 + 0.567077i) q^{95} +(-1.95530 + 2.45187i) q^{96} +(-9.81356 - 4.72596i) q^{97} +(1.08127 + 4.73735i) q^{98} +(9.32515 + 11.6934i) 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 $

$2$	−0.160022	−	0.701103i	−0.113153	−	0.495755i	−0.999466	−	0.0326690i	$-0.989599\pi$
$2$	−0.160022	−	0.701103i	−0.113153	−	0.495755i	0.886313	−	0.463086i	$-0.153258\pi$
$3$	0.119356	−	0.522931i	0.0689100	−	0.301914i	−0.928715	−	0.370794i	$-0.879085\pi$
$3$	0.119356	−	0.522931i	0.0689100	−	0.301914i	0.997625	+	0.0688801i	$0.0219426\pi$
$4$	1.33600	−	0.643383i	0.667999	−	0.321692i
$5$	−0.180888	−	0.226826i	−0.0808955	−	0.101440i	0.739737	−	0.672896i	$-0.234950\pi$
$5$	−0.180888	−	0.226826i	−0.0808955	−	0.101440i	−0.820632	+	0.571457i	$0.806379\pi$
$6$	−0.385728			−0.157473
$7$	−0.492965			−0.186323			−0.0931617	−	0.995651i	$-0.529697\pi$
$7$	−0.492965			−0.186323			−0.0931617	+	0.995651i	$0.529697\pi$
$8$	−1.56161	−	1.95820i	−0.552113	−	0.692328i
$9$	2.44370	+	1.17682i	0.814565	+	0.392274i
$10$	−0.130083	+	0.163118i	−0.0411357	+	0.0515826i
$11$	4.96820	+	2.39256i	1.49797	+	0.721384i	0.990141	−	0.140075i	$-0.0447344\pi$
$11$	4.96820	+	2.39256i	1.49797	+	0.721384i	0.507828	+	0.861459i	$0.330449\pi$
$12$	−0.176986	−	0.775427i	−0.0510915	−	0.223846i
$13$	3.72800	+	4.67477i	1.03396	+	1.29655i	0.954018	+	0.299749i	$0.0969028\pi$
$13$	3.72800	+	4.67477i	1.03396	+	1.29655i	0.0799443	+	0.996799i	$0.474526\pi$
$14$	0.0788854	+	0.345620i	0.0210830	+	0.0923707i
$15$	−0.140204	+	0.0675189i	−0.0362006	+	0.0174333i
$16$	0.726072	−	0.910465i	0.181518	−	0.227616i
$17$	0.623490	−	0.781831i	0.151218	−	0.189622i
$17$	0.623490	−	0.781831i	0.151218	−	0.189622i
$18$	0.434028	−	1.90160i	0.102301	−	0.448212i
$19$	−4.05881	+	1.95462i	−0.931155	+	0.448421i	−0.837041	−	0.547141i	$-0.815716\pi$
$19$	−4.05881	+	1.95462i	−0.931155	+	0.448421i	−0.0941144	+	0.995561i	$0.530002\pi$
$20$	−0.387602	−	0.186659i	−0.0866705	−	0.0417383i
$21$	−0.0588382	+	0.257787i	−0.0128395	+	0.0562537i
$22$	0.882409	−	3.86608i	0.188130	−	0.824252i
$23$	0.664616	+	0.320062i	0.138582	+	0.0667375i	0.501890	−	0.864932i	$-0.332638\pi$
$23$	0.664616	+	0.320062i	0.138582	+	0.0667375i	−0.363308	+	0.931669i	$0.618353\pi$
$24$	−1.21039	+	0.582894i	−0.247070	+	0.118983i
$25$	1.09387	−	4.79258i	0.218775	−	0.958516i
$26$	2.68093	−	3.36178i	0.525774	−	0.659300i
$27$	1.91035	−	2.39550i	0.367646	−	0.461014i
$28$	−0.658601	+	0.317166i	−0.124464	+	0.0599387i
$29$	−0.712761	−	3.12281i	−0.132356	−	0.579891i	−0.996993	−	0.0774931i	$-0.975308\pi$
$29$	−0.712761	−	3.12281i	−0.132356	−	0.579891i	0.864637	−	0.502398i	$-0.167549\pi$
$30$	0.0697736	+	0.0874933i	0.0127389	+	0.0159740i
$31$	−0.242388	−	1.06197i	−0.0435342	−	0.190736i	0.948485	−	0.316822i	$-0.102616\pi$
$31$	−0.242388	−	1.06197i	−0.0435342	−	0.190736i	−0.992019	+	0.126086i	$0.959758\pi$
$32$	−5.26771	−	2.53680i	−0.931208	−	0.448446i
$33$	1.84413	−	2.31246i	0.321021	−	0.402548i
$34$	−0.647917	−	0.312020i	−0.111117	−	0.0535111i
$35$	0.0891714	+	0.111817i	0.0150727	+	0.0189006i
$36$	4.02192			0.670320
$37$	−7.55722			−1.24240			−0.621199	−	0.783653i	$-0.713354\pi$
$37$	−7.55722			−1.24240			−0.621199	+	0.783653i	$0.713354\pi$
$38$	2.01989	+	2.53286i	0.327670	+	0.410885i
$39$	2.88954	−	1.39153i	0.462697	−	0.222823i
$40$	−0.161694	+	0.708429i	−0.0255661	+	0.112013i
$41$	−1.83204	−	8.02670i	−0.286117	−	1.25356i	−0.889806	−	0.456340i	$-0.849160\pi$
$41$	−1.83204	−	8.02670i	−0.286117	−	1.25356i	0.603689	−	0.797220i	$-0.293697\pi$
$42$	0.190151			0.0293409
$43$	3.38360	+	5.61705i	0.515995	+	0.856592i
$43$	3.38360	+	5.61705i	0.515995	+	0.856592i
$44$	8.17684			1.23271
$45$	−0.175101	−	0.767167i	−0.0261025	−	0.114362i
$46$	0.118043	−	0.517181i	0.0174045	−	0.0762542i
$47$	−0.283805	+	0.136673i	−0.0413973	+	0.0199359i	−0.454468	−	0.890763i	$-0.650171\pi$
$47$	−0.283805	+	0.136673i	−0.0413973	+	0.0199359i	0.413071	+	0.910699i	$0.364456\pi$
$48$	−0.389450	−	0.488355i	−0.0562122	−	0.0704879i
$49$	−6.75699			−0.965284
$50$	−3.53514			−0.499944
$51$	−0.334427	−	0.419358i	−0.0468291	−	0.0587219i
$52$	7.98828	+	3.84695i	1.10777	+	0.533476i
$53$	−1.11831	+	1.40231i	−0.153611	+	0.192623i	−0.852682	−	0.522430i	$-0.825026\pi$
$53$	−1.11831	+	1.40231i	−0.153611	+	0.192623i	0.699071	+	0.715052i	$0.253597\pi$
$54$	−1.98519	−	0.956017i	−0.270150	−	0.130097i
$55$	−0.355992	−	1.55970i	−0.0480020	−	0.210310i
$56$	0.769821	+	0.965325i	0.102872	+	0.128997i
$57$	0.537690	+	2.35577i	0.0712187	+	0.312030i
$58$	−2.07535	+	0.999438i	−0.272507	+	0.131233i
$59$	−5.74421	+	7.20301i	−0.747832	+	0.937752i	−0.999548	−	0.0300490i	$-0.990434\pi$
$59$	−5.74421	+	7.20301i	−0.747832	+	0.937752i	0.251716	+	0.967801i	$0.419005\pi$
$60$	−0.143872	+	0.180410i	−0.0185739	+	0.0232909i
$61$	−0.991234	+	4.34288i	−0.126915	+	0.556049i	0.870987	+	0.491305i	$0.163480\pi$
$61$	−0.991234	+	4.34288i	−0.126915	+	0.556049i	−0.997902	+	0.0647435i	$0.979377\pi$
$62$	−0.705764	+	0.339878i	−0.0896321	+	0.0431646i
$63$	−1.20466	−	0.580132i	−0.151773	−	0.0730898i
$64$	−0.417341	+	1.82849i	−0.0521676	+	0.228561i
$65$	0.386010	−	1.69122i	0.0478786	−	0.209770i
$66$	−1.91638	−	0.922878i	−0.235889	−	0.113598i
$67$	−7.56704	+	3.64410i	−0.924461	+	0.445197i	−0.834662	−	0.550763i	$-0.814337\pi$
$67$	−7.56704	+	3.64410i	−0.924461	+	0.445197i	−0.0897995	+	0.995960i	$0.528623\pi$
$68$	0.329964	−	1.44567i	0.0400141	−	0.175313i
$69$	0.246696	−	0.309347i	0.0296987	−	0.0372410i
$70$	0.0641262	−	0.0804117i	0.00766455	−	0.00961104i
$71$	12.3613	−	5.95287i	1.46701	−	0.706476i	0.481557	−	0.876415i	$-0.340071\pi$
$71$	12.3613	−	5.95287i	1.46701	−	0.706476i	0.985455	+	0.169939i	$0.0543571\pi$
$72$	−1.51165	−	6.62298i	−0.178150	−	0.780526i
$73$	−2.17710	−	2.72999i	−0.254810	−	0.319521i	0.637930	−	0.770095i	$-0.279791\pi$
$73$	−2.17710	−	2.72999i	−0.254810	−	0.319521i	−0.892739	+	0.450573i	$0.851220\pi$
$74$	1.20932	+	5.29839i	0.140581	+	0.615925i
$75$	−2.37563	−	1.14404i	−0.274314	−	0.132103i
$76$	−4.16500	+	5.22274i	−0.477758	+	0.599089i
$77$	−2.44915	−	1.17945i	−0.279107	−	0.134411i
$78$	−1.43800	−	1.80319i	−0.162821	−	0.204171i
$79$	14.5104			1.63254			0.816272	−	0.577668i	$-0.196037\pi$
$79$	14.5104			1.63254			0.816272	+	0.577668i	$0.196037\pi$
$80$	−0.337855			−0.0377733
$81$	4.04860	+	5.07678i	0.449844	+	0.564087i
$82$	−5.33438	+	2.56890i	−0.589084	+	0.283688i
$83$	3.07128	−	13.4562i	0.337117	−	1.47700i	−0.467915	−	0.883773i	$-0.654995\pi$
$83$	3.07128	−	13.4562i	0.337117	−	1.47700i	0.805032	−	0.593231i	$-0.202148\pi$
$84$	0.0872480	+	0.382258i	0.00951954	+	0.0417078i
$85$	−0.290122			−0.0314681
$86$	3.39668	−	3.27111i	0.366273	−	0.352733i
$87$	−1.71809			−0.184198
$88$	−3.07329	−	13.4650i	−0.327614	−	1.43537i
$89$	2.63557	−	11.5472i	0.279370	−	1.22400i	−0.619222	−	0.785216i	$-0.712552\pi$
$89$	2.63557	−	11.5472i	0.279370	−	1.22400i	0.898592	−	0.438785i	$-0.144591\pi$
$90$	−0.509843	+	0.245528i	−0.0537422	+	0.0258809i
$91$	−1.83778	−	2.30450i	−0.192651	−	0.241577i
$92$	1.09385			0.114042
$93$	−0.584268			−0.0605858
$94$	0.141237	+	0.177106i	0.0145675	+	0.0182671i
$95$	1.17755	+	0.567077i	0.120814	+	0.0581809i
$96$	−1.95530	+	2.45187i	−0.199562	+	0.250243i
$97$	−9.81356	−	4.72596i	−0.996416	−	0.479849i	−0.136695	−	0.990613i	$-0.543648\pi$
$97$	−9.81356	−	4.72596i	−0.996416	−	0.479849i	−0.859721	+	0.510765i	$0.829362\pi$
$98$	1.08127	+	4.73735i	0.109225	+	0.478544i
$99$	9.32515	+	11.6934i	0.937213	+	1.17523i
$100$	−1.62205	−	7.10666i	−0.162205	−	0.710666i
$101$	−2.04165	+	0.983207i	−0.203152	+	0.0978327i	−0.532693	−	0.846308i	$-0.678820\pi$
$101$	−2.04165	+	0.983207i	−0.203152	+	0.0978327i	0.329542	+	0.944141i	$0.393106\pi$
$102$	−0.240498	+	0.301575i	−0.0238128	+	0.0298603i
$103$	−6.82601	+	8.55954i	−0.672587	+	0.843397i	−0.994648	−	0.103322i	$-0.967053\pi$
$103$	−6.82601	+	8.55954i	−0.672587	+	0.843397i	0.322061	+	0.946719i	$0.395624\pi$
$104$	3.33244	−	14.6004i	0.326772	−	1.43168i
$105$	0.0691159	−	0.0332845i	0.00674502	−	0.00324823i
$106$	1.16212	+	0.559648i	0.112875	+	0.0543578i
$107$	−0.361111	+	1.58213i	−0.0349099	+	0.152950i	−0.989379	−	0.145360i	$-0.953566\pi$
$107$	−0.361111	+	1.58213i	−0.0349099	+	0.152950i	0.954469	+	0.298310i	$0.0964231\pi$
$108$	1.01100	−	4.42947i	0.0972832	−	0.426226i
$109$	−2.13757	−	1.02940i	−0.204742	−	0.0985987i	0.328703	−	0.944433i	$-0.393389\pi$
$109$	−2.13757	−	1.02940i	−0.204742	−	0.0985987i	−0.533445	+	0.845835i	$0.679103\pi$
$110$	−1.03655	+	0.499174i	−0.0988308	+	0.0475944i
$111$	−0.901996	+	3.95190i	−0.0856137	+	0.375098i
$112$	−0.357928	+	0.448828i	−0.0338210	+	0.0424102i
$113$	−6.66459	+	8.35713i	−0.626952	+	0.786173i	−0.989304	−	0.145869i	$-0.953402\pi$
$113$	−6.66459	+	8.35713i	−0.626952	+	0.786173i	0.362352	+	0.932041i	$0.381974\pi$
$114$	1.56560	−	0.753952i	0.146632	−	0.0706141i
$115$	−0.0476224	−	0.208648i	−0.00444082	−	0.0194565i
$116$	−2.96141	−	3.71349i	−0.274960	−	0.344789i
$117$	3.60874	+	15.8109i	0.333628	+	1.46172i
$118$	5.96926	+	2.87464i	0.549515	+	0.264632i
$119$	−0.307359	+	0.385416i	−0.0281755	+	0.0353310i
$120$	0.351161	+	0.169110i	0.0320564	+	0.0154376i
$121$	12.1003	+	15.1733i	1.10003	+	1.37939i
$122$	3.20343			0.290025
$123$	−4.41608			−0.398184
$124$	−1.00708	−	1.26284i	−0.0904388	−	0.113407i
$125$	−2.59190	+	1.24820i	−0.231827	+	0.111642i
$126$	−0.213961	+	0.937423i	−0.0190611	+	0.0835123i
$127$	0.535265	+	2.34515i	0.0474971	+	0.208098i	0.993108	−	0.117201i	$-0.0373921\pi$
$127$	0.535265	+	2.34515i	0.0474971	+	0.208098i	−0.945611	+	0.325299i	$0.894535\pi$
$128$	−10.3447			−0.914350
$129$	3.34118	−	1.09896i	0.294175	−	0.0967584i
$130$	−1.24749			−0.109412
$131$	0.312581	+	1.36951i	0.0273104	+	0.119654i	0.986746	−	0.162274i	$-0.0518829\pi$
$131$	0.312581	+	1.36951i	0.0273104	+	0.119654i	−0.959435	+	0.281929i	$0.909026\pi$
$132$	0.975952	−	4.27592i	0.0849457	−	0.372171i
$133$	2.00085	−	0.963560i	0.173496	−	0.0835512i
$134$	3.76578	+	4.72214i	0.325314	+	0.407931i
$135$	−0.888920			−0.0765061
$136$	−2.50463			−0.214770
$137$	−2.91112	−	3.65043i	−0.248714	−	0.311877i	0.641766	−	0.766901i	$-0.278202\pi$
$137$	−2.91112	−	3.65043i	−0.248714	−	0.311877i	−0.890479	+	0.455024i	$0.849631\pi$
$138$	−0.256361	−	0.123457i	−0.0218229	−	0.0105094i
$139$	1.15684	−	1.45064i	0.0981222	−	0.123041i	−0.730346	−	0.683077i	$-0.760641\pi$
$139$	1.15684	−	1.45064i	0.0981222	−	0.123041i	0.828468	+	0.560036i	$0.189213\pi$
$140$	0.191074	+	0.0920166i	0.0161487	+	0.00777682i
$141$	0.0375970	+	0.164723i	0.00316624	+	0.0138722i
$142$	−6.15165	−	7.71393i	−0.516235	−	0.647339i
$143$	7.33681	+	32.1447i	0.613535	+	2.68807i
$144$	2.84575	−	1.37044i	0.237146	−	0.114204i
$145$	−0.579405	+	0.726551i	−0.0481170	+	0.0603368i
$146$	−1.56562	+	1.96323i	−0.129572	+	0.162478i
$147$	−0.806484	+	3.53344i	−0.0665177	+	0.291433i
$148$	−10.0964	+	4.86219i	−0.829922	+	0.399669i
$149$	19.6670	+	9.47113i	1.61118	+	0.775905i	0.999880	−	0.0154903i	$-0.00493092\pi$
$149$	19.6670	+	9.47113i	1.61118	+	0.775905i	0.611304	+	0.791396i	$0.290645\pi$
$150$	−0.421939	+	1.84863i	−0.0344511	+	0.150940i
$151$	−3.02668	+	13.2608i	−0.246308	+	1.07914i	0.688847	+	0.724906i	$0.258117\pi$
$151$	−3.02668	+	13.2608i	−0.246308	+	1.07914i	−0.935155	+	0.354238i	$0.884740\pi$
$152$	10.1658	+	4.89560i	0.824557	+	0.397086i
$153$	2.44370	−	1.17682i	0.197561	−	0.0951404i
$154$	−0.434997	+	1.90585i	−0.0350530	+	0.153577i
$155$	−0.197038	+	0.247078i	−0.0158265	+	0.0198458i
$156$	2.96514	−	3.71816i	0.237401	−	0.297691i
$157$	−21.5634	+	10.3844i	−1.72095	+	0.828764i	−0.731854	+	0.681462i	$0.761345\pi$
$157$	−21.5634	+	10.3844i	−1.72095	+	0.828764i	−0.989092	+	0.147302i	$0.952941\pi$
$158$	−2.32198	−	10.1733i	−0.184727	−	0.809341i
$159$	0.599837	+	0.752172i	0.0475702	+	0.0596511i
$160$	0.377453	+	1.65373i	0.0298403	+	0.130739i
$161$	−0.327632	−	0.157779i	−0.0258211	−	0.0124348i
$162$	2.91148	−	3.65089i	0.228748	−	0.286841i
$163$	−19.7378	−	9.50523i	−1.54599	−	0.744507i	−0.550097	−	0.835101i	$-0.685409\pi$
$163$	−19.7378	−	9.50523i	−1.54599	−	0.744507i	−0.995888	+	0.0905933i	$0.971124\pi$
$164$	−7.61185	−	9.54496i	−0.594386	−	0.745336i
$165$	−0.858107			−0.0668035
$166$	−9.92563			−0.770378
$167$	−4.14114	−	5.19283i	−0.320451	−	0.401833i	0.595349	−	0.803467i	$-0.297014\pi$
$167$	−4.14114	−	5.19283i	−0.320451	−	0.401833i	−0.915800	+	0.401634i	$0.868442\pi$
$168$	0.596681	−	0.287346i	0.0460349	−	0.0221693i
$169$	−5.06268	+	22.1811i	−0.389437	+	1.70624i
$170$	0.0464259	+	0.203405i	0.00356071	+	0.0156005i
$171$	−12.2187			−0.934390
$172$	8.13440	+	5.32742i	0.620242	+	0.406212i
$173$	−2.62117			−0.199284			−0.0996419	−	0.995023i	$-0.531770\pi$
$173$	−2.62117			−0.199284			−0.0996419	+	0.995023i	$0.531770\pi$
$174$	0.274932	+	1.20456i	0.0208425	+	0.0913171i
$175$	−0.539242	+	2.36258i	−0.0407629	+	0.178594i
$176$	5.78561	−	2.78620i	0.436107	−	0.210018i
$177$	3.08107	+	3.86355i	0.231588	+	0.290402i
$178$	−8.51754			−0.638416
$179$	1.60003			0.119592			0.0597959	−	0.998211i	$-0.480955\pi$
$179$	1.60003			0.119592			0.0597959	+	0.998211i	$0.480955\pi$
$180$	−0.727517	−	0.912277i	−0.0542259	−	0.0679971i
$181$	11.4804	+	5.52866i	0.853330	+	0.410942i	0.808813	−	0.588067i	$-0.200111\pi$
$181$	11.4804	+	5.52866i	0.853330	+	0.410942i	0.0445174	+	0.999009i	$0.485825\pi$
$182$	−1.32161	+	1.65724i	−0.0979641	+	0.122843i
$183$	2.15272	+	1.03669i	0.159133	+	0.0766346i
$184$	−0.411127	−	1.80126i	−0.0303087	−	0.132791i
$185$	1.36701	+	1.71417i	0.100504	+	0.126029i
$186$	0.0934959	+	0.409632i	0.00685545	+	0.0300357i
$187$	4.96820	−	2.39256i	0.363311	−	0.174961i
$188$	−0.291230	+	0.365191i	−0.0212401	+	0.0266343i
$189$	−0.941734	+	1.18090i	−0.0685011	+	0.0858977i
$190$	0.209146	−	0.916328i	0.0151730	−	0.0664774i
$191$	−5.12274	+	2.46698i	−0.370668	+	0.178504i	−0.609939	−	0.792449i	$-0.708806\pi$
$191$	−5.12274	+	2.46698i	−0.370668	+	0.178504i	0.239271	+	0.970953i	$0.423092\pi$
$192$	0.906362	+	0.436481i	0.0654111	+	0.0315003i
$193$	2.69825	−	11.8218i	0.194224	−	0.850952i	−0.780074	−	0.625688i	$-0.784818\pi$
$193$	2.69825	−	11.8218i	0.194224	−	0.850952i	0.974298	−	0.225264i	$-0.0723245\pi$
$194$	−1.74300	+	7.63658i	−0.125140	+	0.548274i
$195$	−0.838318	−	0.403713i	−0.0600332	−	0.0289105i
$196$	−9.02732	+	4.34733i	−0.644809	+	0.310524i
$197$	2.30809	−	10.1124i	0.164445	−	0.720479i	−0.823709	−	0.567013i	$-0.808099\pi$
$197$	2.30809	−	10.1124i	0.164445	−	0.720479i	0.988154	−	0.153467i	$-0.0490438\pi$
$198$	6.70603	−	8.40910i	0.476577	−	0.597608i
$199$	−4.44983	+	5.57991i	−0.315440	+	0.395550i	−0.914123	−	0.405437i	$-0.867120\pi$
$199$	−4.44983	+	5.57991i	−0.315440	+	0.395550i	0.598683	+	0.800986i	$0.295691\pi$
$200$	−11.0930	+	5.34213i	−0.784396	+	0.377745i
$201$	1.00244	+	4.39198i	0.0707068	+	0.309787i
$202$	1.01604	+	1.27407i	0.0714883	+	0.0896434i
$203$	0.351366	+	1.53944i	0.0246611	+	0.108047i
$204$	−0.716602	−	0.345097i	−0.0501722	−	0.0241616i
$205$	−1.48927	+	1.86749i	−0.104015	+	0.130431i
$206$	7.09344	+	3.41602i	0.494223	+	0.238005i
$207$	1.24746	+	1.56427i	0.0867046	+	0.108724i
$208$	6.96301			0.482798
$209$	−24.8415			−1.71832
$210$	−0.0343960	−	0.0431312i	−0.00237355	−	0.00297633i
$211$	17.0233	−	8.19798i	1.17193	−	0.564372i	0.256381	−	0.966576i	$-0.417470\pi$
$211$	17.0233	−	8.19798i	1.17193	−	0.564372i	0.915550	+	0.402203i	$0.131756\pi$
$212$	−0.591833	+	2.59299i	−0.0406473	+	0.178087i
$213$	−1.63755	−	7.17460i	−0.112203	−	0.491595i
$214$	1.16702			0.0797760
$215$	0.662041	−	1.78355i	0.0451508	−	0.121637i
$216$	−7.67409			−0.522155
$217$	0.119489	+	0.523515i	0.00811143	+	0.0355385i
$218$	−0.379657	+	1.66339i	−0.0257136	+	0.112659i
$219$	−1.68745	+	0.812631i	−0.114027	+	0.0549125i
$220$	−1.47909	−	1.85472i	−0.0997203	−	0.125045i
$221$	5.97926			0.402208
$222$	2.91503			0.195644
$223$	−0.481565	−	0.603863i	−0.0322480	−	0.0404377i	0.765446	−	0.643500i	$-0.222518\pi$
$223$	−0.481565	−	0.603863i	−0.0322480	−	0.0404377i	−0.797694	+	0.603062i	$0.793947\pi$
$224$	2.59680	+	1.25055i	0.173506	+	0.0835560i
$225$	8.31311	−	10.4243i	0.554207	−	0.694954i
$226$	6.92569	+	3.33524i	0.460690	+	0.221857i
$227$	4.21287	+	18.4578i	0.279618	+	1.22509i	0.898278	+	0.439428i	$0.144819\pi$
$227$	4.21287	+	18.4578i	0.279618	+	1.22509i	−0.618660	+	0.785659i	$0.712324\pi$
$228$	2.23402	+	2.80137i	0.147951	+	0.185525i
$229$	1.78320	+	7.81273i	0.117837	+	0.516279i	0.999051	+	0.0435607i	$0.0138702\pi$
$229$	1.78320	+	7.81273i	0.117837	+	0.516279i	−0.881213	+	0.472719i	$0.843273\pi$
$230$	−0.138663	+	0.0667765i	−0.00914316	+	0.00440311i
$231$	−0.909090	+	1.13996i	−0.0598137	+	0.0750041i
$232$	−5.00203	+	6.27234i	−0.328399	+	0.411800i
$233$	6.17245	−	27.0433i	0.404370	−	1.77166i	−0.204985	−	0.978765i	$-0.565714\pi$
$233$	6.17245	−	27.0433i	0.404370	−	1.77166i	0.609355	−	0.792897i	$-0.291428\pi$
$234$	10.5076	−	5.06020i	0.686904	−	0.330795i
$235$	0.0823381	+	0.0396519i	0.00537114	+	0.00258661i
$236$	−3.03996	+	13.3189i	−0.197885	+	0.866989i
$237$	1.73189	−	7.58792i	0.112499	−	0.492888i
$238$	0.319401	+	0.153815i	0.0207037	+	0.00997036i
$239$	11.1960	−	5.39173i	0.724212	−	0.348762i	−0.0351929	−	0.999381i	$-0.511205\pi$
$239$	11.1960	−	5.39173i	0.724212	−	0.348762i	0.759405	+	0.650618i	$0.225490\pi$
$240$	−0.0403249	+	0.176675i	−0.00260296	+	0.0114043i
$241$	−3.48148	+	4.36563i	−0.224262	+	0.281215i	−0.881215	−	0.472716i	$-0.843274\pi$
$241$	−3.48148	+	4.36563i	−0.224262	+	0.281215i	0.656953	+	0.753932i	$0.271845\pi$
$242$	8.70172	−	10.9116i	0.559368	−	0.701425i
$243$	11.4196	−	5.49940i	0.732569	−	0.352787i
$244$	1.46985	+	6.43983i	0.0940974	+	0.412268i
$245$	1.22226	+	1.53266i	0.0780871	+	0.0979181i
$246$	0.706671	+	3.09613i	0.0450557	+	0.197402i
$247$	−24.2687	−	11.6872i	−1.54418	−	0.743637i
$248$	−1.70104	+	2.13303i	−0.108016	+	0.135448i
$249$	−6.67006	−	3.21213i	−0.422698	−	0.203561i
$250$	1.28988	+	1.61745i	0.0815789	+	0.102297i
$251$	−23.7349			−1.49813			−0.749065	−	0.662496i	$-0.769497\pi$
$251$	−23.7349			−1.49813			−0.749065	+	0.662496i	$0.769497\pi$
$252$	−1.98267			−0.124896
$253$	2.53618	+	3.18026i	0.159448	+	0.199941i
$254$	1.55854	−	0.750553i	0.0977914	−	0.0470939i
$255$	−0.0346276	+	0.151714i	−0.00216847	+	0.00950067i
$256$	2.49006	+	10.9097i	0.155629	+	0.681855i
$257$	−1.40924			−0.0879062			−0.0439531	−	0.999034i	$-0.513995\pi$
$257$	−1.40924			−0.0879062			−0.0439531	+	0.999034i	$0.513995\pi$
$258$	−1.30515	−	2.16665i	−0.0812552	−	0.134890i
$259$	3.72545			0.231488
$260$	−0.572393	−	2.50782i	−0.0354983	−	0.155528i
$261$	1.93322	−	8.46998i	0.119663	−	0.524279i
$262$	0.910147	−	0.438304i	0.0562291	−	0.0270785i
$263$	14.4636	+	18.1368i	0.891865	+	1.11836i	0.992354	+	0.123425i	$0.0393879\pi$
$263$	14.4636	+	18.1368i	0.891865	+	1.11836i	−0.100489	+	0.994938i	$0.532041\pi$
$264$	−7.40807			−0.455935
$265$	0.520370			0.0319661
$266$	−0.995736	−	1.24861i	−0.0610525	−	0.0765574i
$267$	−5.72382	−	2.75645i	−0.350292	−	0.168692i
$268$	−7.76501	+	9.73701i	−0.474323	+	0.594783i
$269$	−15.1920	−	7.31606i	−0.926270	−	0.446068i	−0.0909645	−	0.995854i	$-0.528995\pi$
$269$	−15.1920	−	7.31606i	−0.926270	−	0.446068i	−0.835306	+	0.549786i	$0.814709\pi$
$270$	0.142247	+	0.623225i	0.00865688	+	0.0379283i
$271$	13.6523	+	17.1194i	0.829316	+	1.03993i	0.998522	+	0.0543483i	$0.0173081\pi$
$271$	13.6523	+	17.1194i	0.829316	+	1.03993i	−0.169206	+	0.985581i	$0.554120\pi$
$272$	−0.259132	−	1.13533i	−0.0157122	−	0.0688396i
$273$	−1.42444	+	0.685976i	−0.0862112	+	0.0415171i
$274$	−2.09348	+	2.62514i	−0.126472	+	0.158591i
$275$	16.9011	−	21.1933i	1.01918	−	1.27801i
$276$	0.130557	−	0.572007i	0.00785860	−	0.0344308i
$277$	5.90617	−	2.84426i	0.354867	−	0.170895i	−0.247953	−	0.968772i	$-0.579758\pi$
$277$	5.90617	−	2.84426i	0.354867	−	0.170895i	0.602820	+	0.797877i	$0.294044\pi$
$278$	−1.20217	−	0.578933i	−0.0721012	−	0.0347221i
$279$	0.657428	−	2.88038i	0.0393592	−	0.172444i
$280$	0.0797097	−	0.349231i	0.00476357	−	0.0208706i
$281$	−16.9143	−	8.14552i	−1.00903	−	0.485921i	−0.145033	−	0.989427i	$-0.546329\pi$
$281$	−16.9143	−	8.14552i	−1.00903	−	0.485921i	−0.863992	+	0.503506i	$0.832043\pi$
$282$	0.109472	−	0.0527188i	0.00651895	−	0.00313936i
$283$	−4.32163	+	18.9343i	−0.256894	+	1.12553i	0.667657	+	0.744469i	$0.267297\pi$
$283$	−4.32163	+	18.9343i	−0.256894	+	1.12553i	−0.924551	+	0.381058i	$0.875560\pi$
$284$	12.6847	−	15.9061i	0.752696	−	0.943851i
$285$	0.437089	−	0.548093i	0.0258909	−	0.0324662i
$286$	21.3627	−	10.2877i	1.26320	−	0.608326i
$287$	0.903133	+	3.95689i	0.0533103	+	0.233568i
$288$	−9.88732	−	12.3983i	−0.582616	−	0.730577i
$289$	−0.222521	−	0.974928i	−0.0130895	−	0.0573487i
$290$	0.602105	+	0.289958i	0.0353568	+	0.0170269i
$291$	−3.64265	+	4.56774i	−0.213536	+	0.267766i
$292$	−4.66503	−	2.24656i	−0.273000	−	0.131470i
$293$	−20.6404	−	25.8823i	−1.20583	−	1.51206i	−0.802113	−	0.597172i	$-0.796291\pi$
$293$	−20.6404	−	25.8823i	−1.20583	−	1.51206i	−0.403712	−	0.914886i	$-0.632280\pi$
$294$	2.60636			0.152006
$295$	2.67289			0.155622
$296$	11.8014	+	14.7985i	0.685945	+	0.860148i
$297$	15.2224	−	7.33070i	0.883291	−	0.425370i
$298$	3.49308	−	15.3042i	0.202349	−	0.886548i
$299$	0.981474	+	4.30012i	0.0567601	+	0.248682i
$300$	−3.90989			−0.225738
$301$	−1.66800	−	2.76901i	−0.0961419	−	0.159603i
$302$	9.78150			0.562862
$303$	0.270467	+	1.18499i	0.0155379	+	0.0680761i
$304$	−1.16737	+	5.11460i	−0.0669535	+	0.293342i
$305$	1.16438	−	0.560736i	0.0666723	−	0.0321077i
$306$	−1.21612	−	1.52497i	−0.0695209	−	0.0871765i
$307$	−0.677228			−0.0386514			−0.0193257	−	0.999813i	$-0.506152\pi$
$307$	−0.677228			−0.0386514			−0.0193257	+	0.999813i	$0.506152\pi$
$308$	−4.03090			−0.229682
$309$	3.66133	+	4.59116i	0.208286	+	0.261182i
$310$	0.204757	+	0.0986060i	0.0116294	+	0.00560044i
$311$	3.92738	−	4.92478i	0.222701	−	0.279259i	−0.657911	−	0.753095i	$-0.728560\pi$
$311$	3.92738	−	4.92478i	0.222701	−	0.279259i	0.880613	+	0.473837i	$0.157131\pi$
$312$	−7.23724	−	3.48527i	−0.409728	−	0.197315i
$313$	−1.08886	−	4.77062i	−0.0615461	−	0.269651i	0.934787	−	0.355208i	$-0.115590\pi$
$313$	−1.08886	−	4.77062i	−0.0615461	−	0.269651i	−0.996333	+	0.0855572i	$0.972733\pi$
$314$	10.7311	+	13.4564i	0.605594	+	0.759390i
$315$	0.0863187	+	0.378187i	0.00486351	+	0.0213084i
$316$	19.3858	−	9.33572i	1.09054	−	0.525175i
$317$	−1.84034	+	2.30772i	−0.103364	+	0.129614i	−0.830823	−	0.556537i	$-0.812130\pi$
$317$	−1.84034	+	2.30772i	−0.103364	+	0.129614i	0.727459	+	0.686151i	$0.240701\pi$
$318$	0.431363	−	0.540912i	0.0241896	−	0.0303329i
$319$	3.93037	−	17.2201i	0.220058	−	0.964138i
$320$	0.490241	−	0.236088i	0.0274053	−	0.0131977i
$321$	0.784244	+	0.377672i	0.0437722	+	0.0210796i
$322$	−0.0581912	+	0.254952i	−0.00324287	+	0.0142079i
$323$	−1.00244	+	4.39199i	−0.0557774	+	0.244377i
$324$	8.67524	+	4.17778i	0.481958	+	0.232099i
$325$	26.4822	−	12.7531i	1.46897	−	0.707417i
$326$	−3.50566	+	15.3593i	−0.194161	+	0.850673i
$327$	−0.793437	+	0.994938i	−0.0438771	+	0.0550202i
$328$	−12.8569	+	16.1221i	−0.709906	+	0.890194i
$329$	0.139906	−	0.0673753i	0.00771328	−	0.00371452i
$330$	0.137316	+	0.601622i	0.00755901	+	0.0331182i
$331$	−7.09083	−	8.89162i	−0.389747	−	0.488728i	0.547788	−	0.836617i	$-0.315470\pi$
$331$	−7.09083	−	8.89162i	−0.389747	−	0.488728i	−0.937536	+	0.347889i	$0.886899\pi$
$332$	−4.55424	−	19.9534i	−0.249946	−	1.09509i
$333$	−18.4675	−	8.89350i	−1.01201	−	0.487361i
$334$	−2.97804	+	3.73434i	−0.162951	+	0.204334i
$335$	2.19536	+	1.05723i	0.119945	+	0.0577627i
$336$	0.191985	+	0.240742i	0.0104737	+	0.0131335i
$337$	−26.9887			−1.47017			−0.735085	−	0.677975i	$-0.762858\pi$
$337$	−26.9887			−1.47017			−0.735085	+	0.677975i	$0.762858\pi$
$338$	16.3614			0.889941
$339$	3.57475	+	4.48259i	0.194154	+	0.243461i
$340$	−0.387602	+	0.186659i	−0.0210207	+	0.0101230i
$341$	1.33660	−	5.85601i	0.0723808	−	0.317121i
$342$	1.95527	+	8.56660i	0.105729	+	0.463229i
$343$	6.78172			0.366178
$344$	5.71543	−	15.3974i	0.308155	−	0.830174i
$345$	−0.114792			−0.00618021
$346$	0.419445	+	1.83771i	0.0225495	+	0.0987959i
$347$	−4.82123	+	21.1232i	−0.258817	+	1.13395i	0.663701	+	0.747998i	$0.268985\pi$
$347$	−4.82123	+	21.1232i	−0.258817	+	1.13395i	−0.922518	+	0.385954i	$0.873872\pi$
$348$	−2.29536	+	1.10539i	−0.123044	+	0.0592550i
$349$	−3.40971	−	4.27564i	−0.182518	−	0.228870i	0.682153	−	0.731210i	$-0.261044\pi$
$349$	−3.40971	−	4.27564i	−0.182518	−	0.228870i	−0.864670	+	0.502340i	$0.832473\pi$
$350$	1.74270			0.0931513
$351$	18.3202			0.977859
$352$	−20.1016	−	25.2066i	−1.07142	−	1.34352i
$353$	6.23137	+	3.00087i	0.331662	+	0.159720i	0.592302	−	0.805716i	$-0.298219\pi$
$353$	6.23137	+	3.00087i	0.331662	+	0.159720i	−0.260640	+	0.965436i	$0.583934\pi$
$354$	2.21570	−	2.77841i	0.117763	−	0.147671i
$355$	−3.58627	−	1.72706i	−0.190339	−	0.0916626i
$356$	−3.90815	−	17.1227i	−0.207132	−	0.907503i
$357$	0.164861	+	0.206729i	0.00872536	+	0.0109413i
$358$	−0.256040	−	1.12179i	−0.0135322	−	0.0592883i
$359$	−0.490614	+	0.236267i	−0.0258936	+	0.0124697i	−0.446786	−	0.894641i	$-0.647431\pi$
$359$	−0.490614	+	0.236267i	−0.0258936	+	0.0124697i	0.420892	+	0.907111i	$0.361717\pi$
$360$	−1.22883	+	1.54090i	−0.0647649	+	0.0812126i
$361$	0.807095	−	1.01207i	0.0424787	−	0.0532666i
$362$	2.03905	−	8.93364i	0.107170	−	0.469542i
$363$	9.37881	−	4.51660i	0.492260	−	0.237060i
$364$	−3.93794	−	1.89641i	−0.206404	−	0.0993991i
$365$	−0.225423	+	0.987645i	−0.0117992	+	0.0516957i
$366$	0.382347	−	1.67517i	0.0199856	−	0.0875626i
$367$	−7.20527	−	3.46988i	−0.376112	−	0.181126i	0.236271	−	0.971687i	$-0.424075\pi$
$367$	−7.20527	−	3.46988i	−0.376112	−	0.181126i	−0.612383	+	0.790561i	$0.709789\pi$
$368$	0.773964	−	0.372721i	0.0403456	−	0.0194294i
$369$	4.96904	−	21.7708i	0.258678	−	1.13334i
$370$	0.983062	−	1.23272i	0.0511070	−	0.0640861i
$371$	0.551287	−	0.691292i	0.0286214	−	0.0358901i
$372$	−0.780581	+	0.375908i	−0.0404713	+	0.0194899i
$373$	2.24433	+	9.83306i	0.116207	+	0.509136i	0.999209	+	0.0397671i	$0.0126616\pi$
$373$	2.24433	+	9.83306i	0.116207	+	0.509136i	−0.883002	+	0.469369i	$0.844481\pi$
$374$	−2.47245	−	3.10036i	−0.127848	−	0.160316i
$375$	0.343362	+	1.50437i	0.0177311	+	0.0776851i
$376$	0.710828	+	0.342317i	0.0366582	+	0.0176536i
$377$	11.9412	−	14.9738i	0.615005	−	0.771192i
$378$	0.978630	+	0.471283i	0.0503353	+	0.0242402i
$379$	−18.1624	−	22.7749i	−0.932941	−	1.16987i	−0.985230	−	0.171238i	$-0.945223\pi$
$379$	−18.1624	−	22.7749i	−0.932941	−	1.16987i	0.0522891	−	0.998632i	$-0.483348\pi$
$380$	1.93805			0.0994200
$381$	1.29024			0.0661009
$382$	2.54936	+	3.19680i	0.130437	+	0.163562i
$383$	1.12049	−	0.539598i	0.0572542	−	0.0275722i	−0.405038	−	0.914300i	$-0.632742\pi$
$383$	1.12049	−	0.539598i	0.0572542	−	0.0275722i	0.462292	+	0.886728i	$0.347027\pi$
$384$	−1.23470	+	5.40956i	−0.0630078	+	0.276055i
$385$	0.175492	+	0.768879i	0.00894389	+	0.0391857i
$386$	−8.72009			−0.443841
$387$	1.65823	+	17.7083i	0.0842926	+	0.900161i
$388$	−16.1515			−0.819968
$389$	1.79632	+	7.87021i	0.0910773	+	0.399036i	0.999833	−	0.0182936i	$-0.00582335\pi$
$389$	1.79632	+	7.87021i	0.0910773	+	0.399036i	−0.908755	+	0.417329i	$0.862966\pi$
$390$	−0.148895	+	0.652351i	−0.00753958	+	0.0330331i
$391$	0.664616	−	0.320062i	0.0336111	−	0.0161862i
$392$	10.5518	+	13.2315i	0.532946	+	0.668293i
$393$	0.753467			0.0380074
$394$	−7.45919			−0.375789
$395$	−2.62475	−	3.29133i	−0.132065	−	0.165605i
$396$	19.9817	+	9.62268i	1.00412	+	0.483558i
$397$	8.88677	−	11.1437i	0.446014	−	0.559284i	−0.507103	−	0.861885i	$-0.669284\pi$
$397$	8.88677	−	11.1437i	0.446014	−	0.559284i	0.953117	+	0.302601i	$0.0978551\pi$
$398$	4.62417	+	2.22688i	0.231789	+	0.111624i
$399$	−0.265062	−	1.16131i	−0.0132697	−	0.0581384i
$400$	−3.56924	−	4.47569i	−0.178462	−	0.223785i
$401$	−4.19958	−	18.3996i	−0.209717	−	0.918830i	−0.964755	−	0.263149i	$-0.915239\pi$
$401$	−4.19958	−	18.3996i	−0.209717	−	0.918830i	0.755038	−	0.655681i	$-0.227618\pi$
$402$	2.91882	−	1.40563i	0.145578	−	0.0701065i
$403$	4.06085	−	5.09214i	0.202285	−	0.253658i
$404$	−2.09506	+	2.62713i	−0.104233	+	0.130704i
$405$	0.419205	−	1.83666i	0.0208305	−	0.0912642i
$406$	1.02308	−	0.492688i	0.0507745	−	0.0244517i
$407$	−37.5458	−	18.0811i	−1.86107	−	0.896246i
$408$	−0.298942	+	1.30975i	−0.0147998	+	0.0648423i
$409$	−7.19976	+	31.5442i	−0.356005	+	1.55976i	0.407036	+	0.913412i	$0.366562\pi$
$409$	−7.19976	+	31.5442i	−0.356005	+	1.55976i	−0.763042	+	0.646349i	$0.776295\pi$
$410$	1.54762	+	0.745294i	0.0764315	+	0.0368074i
$411$	−2.25638	+	1.08662i	−0.111299	+	0.0535988i
$412$	−3.61247	+	15.8273i	−0.177974	+	0.779754i
$413$	2.83170	−	3.55083i	0.139339	−	0.174725i
$414$	0.897092	−	1.12492i	0.0440897	−	0.0552867i
$415$	−3.60776	+	1.73741i	−0.177098	+	0.0852860i
$416$	−7.77911	−	34.0825i	−0.381402	−	1.67103i
$417$	−0.620507	−	0.778091i	−0.0303864	−	0.0381033i
$418$	3.97520	+	17.4165i	0.194433	+	0.851868i
$419$	26.7535	+	12.8838i	1.30699	+	0.629414i	0.952184	−	0.305525i	$-0.0988318\pi$
$419$	26.7535	+	12.8838i	1.30699	+	0.629414i	0.354808	+	0.934939i	$0.384546\pi$
$420$	0.0709241	−	0.0889361i	0.00346074	−	0.00433963i
$421$	18.7743	+	9.04121i	0.915001	+	0.440641i	0.831284	−	0.555848i	$-0.187606\pi$
$421$	18.7743	+	9.04121i	0.915001	+	0.440641i	0.0837175	+	0.996490i	$0.473321\pi$
$422$	−8.47174	−	10.6232i	−0.412398	−	0.517130i
$423$	−0.854374			−0.0415411
$424$	4.49238			0.218169
$425$	−3.06497	−	3.84335i	−0.148673	−	0.186430i
$426$	−4.76809	+	2.29619i	−0.231015	+	0.111251i
$427$	0.488644	−	2.14089i	0.0236471	−	0.103605i
$428$	0.535472	+	2.34606i	0.0258830	+	0.113401i
$429$	17.6851			0.853846
$430$	−1.35639	−	0.178752i	−0.0654110	−	0.00862020i
$431$	−20.1669			−0.971407			−0.485703	−	0.874124i	$-0.661436\pi$
$431$	−20.1669			−0.971407			−0.485703	+	0.874124i	$0.661436\pi$
$432$	−0.793969	−	3.47861i	−0.0381999	−	0.167365i
$433$	−3.77602	+	16.5438i	−0.181464	+	0.795045i	0.799471	+	0.600705i	$0.205113\pi$
$433$	−3.77602	+	16.5438i	−0.181464	+	0.795045i	−0.980934	+	0.194339i	$0.937744\pi$
$434$	0.347917	−	0.167548i	0.0167006	−	0.00804257i
$435$	0.310781	+	0.389707i	0.0149008	+	0.0186850i
$436$	−3.51809			−0.168486
$437$	−3.32315			−0.158968
$438$	0.839767	+	1.05304i	0.0401256	+	0.0503160i
$439$	0.150746	+	0.0725956i	0.00719473	+	0.00346480i	0.437478	−	0.899229i	$-0.355872\pi$
$439$	0.150746	+	0.0725956i	0.00719473	+	0.00346480i	−0.430283	+	0.902694i	$0.641586\pi$
$440$	−2.49829	+	3.13276i	−0.119101	+	0.149348i
$441$	−16.5120	−	7.95177i	−0.786286	−	0.378656i
$442$	−0.956814	−	4.19208i	−0.0455110	−	0.199397i
$443$	20.7452	+	26.0136i	0.985632	+	1.23594i	0.971743	+	0.236040i	$0.0758498\pi$
$443$	20.7452	+	26.0136i	0.985632	+	1.23594i	0.0138892	+	0.999904i	$0.495579\pi$
$444$	1.33752	+	5.86007i	0.0634760	+	0.278106i
$445$	−3.09595	+	1.49093i	−0.146762	+	0.0706770i
$446$	−0.346309	+	0.434258i	−0.0163982	+	0.0205627i
$447$	7.30012	−	9.15406i	0.345284	−	0.432972i
$448$	0.205735	−	0.901382i	0.00972005	−	0.0425863i
$449$	−1.99723	+	0.961816i	−0.0942552	+	0.0453909i	−0.480417	−	0.877040i	$-0.659515\pi$
$449$	−1.99723	+	0.961816i	−0.0942552	+	0.0453909i	0.386162	+	0.922431i	$0.373801\pi$
$450$	−8.63880	−	4.16023i	−0.407237	−	0.196115i
$451$	10.1024	−	44.2615i	0.475704	−	2.08419i
$452$	−3.52705	+	15.4530i	−0.165898	+	0.726848i
$453$	6.57321	+	3.16549i	0.308836	+	0.148728i
$454$	12.2667	−	5.90732i	0.575704	−	0.277244i
$455$	−0.190289	+	0.833712i	−0.00892090	+	0.0390850i
$456$	3.77341	−	4.73171i	0.176706	−	0.221583i
$457$	14.3318	−	17.9715i	0.670414	−	0.840673i	−0.324018	−	0.946051i	$-0.605034\pi$
$457$	14.3318	−	17.9715i	0.670414	−	0.840673i	0.994432	+	0.105378i	$0.0336052\pi$
$458$	5.19218	−	2.50042i	0.242614	−	0.116837i
$459$	−0.681795	−	2.98714i	−0.0318234	−	0.139428i
$460$	−0.197864	−	0.248113i	−0.00922545	−	0.0115683i
$461$	−4.24364	−	18.5926i	−0.197646	−	0.865944i	−0.972333	−	0.233599i	$-0.924950\pi$
$461$	−4.24364	−	18.5926i	−0.197646	−	0.865944i	0.774687	−	0.632345i	$-0.217908\pi$
$462$	0.944707	+	0.454947i	0.0439517	+	0.0211660i
$463$	24.5472	−	30.7812i	1.14081	−	1.43053i	0.254714	−	0.967017i	$-0.418019\pi$
$463$	24.5472	−	30.7812i	1.14081	−	1.43053i	0.886092	−	0.463509i	$-0.153410\pi$
$464$	−3.36072	−	1.61844i	−0.156018	−	0.0751341i
$465$	0.105687	+	0.132527i	0.00490112	+	0.00614581i
$466$	−19.9478			−0.924066
$467$	1.73921			0.0804813			0.0402406	−	0.999190i	$-0.487188\pi$
$467$	1.73921			0.0804813			0.0402406	+	0.999190i	$0.487188\pi$
$468$	14.9937	+	18.8016i	0.693086	+	0.869102i
$469$	3.73029	−	1.79641i	0.172249	−	0.0829506i
$470$	0.0146242	−	0.0640727i	0.000674563	−	0.00295545i
$471$	2.85660	+	12.5156i	0.131625	+	0.576688i
$472$	23.0752			1.06212
$473$	3.37129	+	36.0021i	0.155012	+	1.65538i
$474$	−5.59706			−0.257081
$475$	4.92784	+	21.5903i	0.226105	+	0.990630i
$476$	−0.162661	+	0.712665i	−0.00745556	+	0.0326649i
$477$	−4.38308	+	2.11078i	−0.200687	+	0.0966460i
$478$	−5.57178	−	6.98679i	−0.254847	−	0.319568i
$479$	12.0499			0.550575			0.275288	−	0.961362i	$-0.411227\pi$
$479$	12.0499			0.550575			0.275288	+	0.961362i	$0.411227\pi$
$480$	0.909838			0.0415282
$481$	−28.1733	−	35.3282i	−1.28459	−	1.61083i
$482$	3.61788	+	1.74228i	0.164790	+	0.0793585i
$483$	−0.121613	+	0.152497i	−0.00553356	+	0.00693887i
$484$	25.9282	+	12.4864i	1.17855	+	0.567562i
$485$	0.703182	+	3.08084i	0.0319298	+	0.139894i
$486$	−5.68304	−	7.12631i	−0.257788	−	0.323256i
$487$	1.31484	+	5.76069i	0.0595811	+	0.261042i	0.995942	−	0.0899969i	$-0.0286857\pi$
$487$	1.31484	+	5.76069i	0.0595811	+	0.261042i	−0.936361	+	0.351039i	$0.885829\pi$
$488$	10.0522	−	4.84086i	0.455040	−	0.219135i
$489$	−7.32640	+	9.18702i	−0.331311	+	0.415451i
$490$	0.878966	−	1.10219i	0.0397076	−	0.0497918i
$491$	1.32279	−	5.79551i	0.0596966	−	0.261548i	−0.936269	−	0.351284i	$-0.885745\pi$
$491$	1.32279	−	5.79551i	0.0596966	−	0.261548i	0.995966	+	0.0897360i	$0.0286023\pi$
$492$	−5.89987	+	2.84123i	−0.265987	+	0.128092i
$493$	−2.88591	−	1.38978i	−0.129975	−	0.0625926i
$494$	−4.31039	+	18.8851i	−0.193934	+	0.849679i
$495$	0.965556	−	4.23038i	0.0433985	−	0.190141i
$496$	−1.14288	−	0.550381i	−0.0513168	−	0.0247129i
$497$	−6.09367	+	2.93456i	−0.273339	+	0.131633i
$498$	−1.18468	+	5.19042i	−0.0530867	+	0.232588i
$499$	−2.79825	+	3.50889i	−0.125267	+	0.157080i	−0.840510	−	0.541796i	$-0.817745\pi$
$499$	−2.79825	+	3.50889i	−0.125267	+	0.157080i	0.715243	+	0.698876i	$0.246316\pi$
$500$	−2.65971	+	3.33517i	−0.118946	+	0.149154i
$501$	−3.20976	+	1.54574i	−0.143402	+	0.0690585i
$502$	3.79811	+	16.6406i	0.169518	+	0.742706i
$503$	19.7102	+	24.7158i	0.878834	+	1.10202i	0.994076	+	0.108685i	$0.0346641\pi$
$503$	19.7102	+	24.7158i	0.878834	+	1.10202i	−0.115242	+	0.993337i	$0.536764\pi$
$504$	0.745193	+	3.26490i	0.0331935	+	0.145430i
$505$	0.592327	+	0.285249i	0.0263582	+	0.0126934i
$506$	1.82385	−	2.28703i	0.0810800	−	0.101671i
$507$	10.9949	+	5.29487i	0.488301	+	0.235153i
$508$	2.22394	+	2.78874i	0.0986716	+	0.123730i
$509$	−13.0094			−0.576630			−0.288315	−	0.957536i	$-0.593095\pi$
$509$	−13.0094			−0.576630			−0.288315	+	0.957536i	$0.593095\pi$
$510$	0.111908			0.00495537
$511$	1.07323	+	1.34579i	0.0474770	+	0.0595343i
$512$	−11.3901	+	5.48520i	−0.503378	+	0.242414i
$513$	−3.07144	+	13.4569i	−0.135608	+	0.594136i
$514$	0.225510	+	0.988025i	0.00994684	+	0.0435799i
$515$	3.17627			0.139963
$516$	3.75676	−	3.61788i	0.165382	−	0.159268i
$517$	−1.73700			−0.0763932
$518$	−0.596154	−	2.61192i	−0.0261935	−	0.114761i
$519$	−0.312851	+	1.37069i	−0.0137326	+	0.0601666i
$520$	−3.91454	+	1.88514i	−0.171664	+	0.0826690i
$521$	−19.4925	−	24.4428i	−0.853981	−	1.07086i	−0.996706	−	0.0810963i	$-0.974158\pi$
$521$	−19.4925	−	24.4428i	−0.853981	−	1.07086i	0.142725	−	0.989762i	$-0.454414\pi$
$522$	−6.24769			−0.273454
$523$	29.4371			1.28719			0.643597	−	0.765365i	$-0.277441\pi$
$523$	29.4371			1.28719			0.643597	+	0.765365i	$0.277441\pi$
$524$	1.29873	+	1.62855i	0.0567351	+	0.0711436i
$525$	1.17110	+	0.563973i	0.0511111	+	0.0246138i
$526$	10.4013	−	13.0428i	0.453517	−	0.568692i
$527$	−0.981409	−	0.472622i	−0.0427508	−	0.0205877i
$528$	−0.766447	−	3.35802i	−0.0333553	−	0.146139i
$529$	−14.0010	−	17.5567i	−0.608739	−	0.763334i
$530$	−0.0832708	−	0.364833i	−0.00361705	−	0.0158473i
$531$	−22.5138	+	10.8421i	−0.977014	+	0.470505i
$532$	2.05320	−	2.57463i	0.0890175	−	0.111624i
$533$	30.6931	−	38.4880i	1.32947	−	1.66710i
$534$	−1.01662	+	4.45408i	−0.0439933	+	0.192747i
$535$	0.424189	−	0.204279i	0.0183393	−	0.00883174i
$536$	18.9527	+	9.12712i	0.818630	+	0.394231i
$537$	0.190973	−	0.836705i	0.00824107	−	0.0361065i
$538$	−2.69826	+	11.8219i	−0.116330	+	0.509677i
$539$	−33.5701	−	16.1665i	−1.44596	−	0.696340i
$540$	−1.18760	+	0.571916i	−0.0511060	+	0.0246114i
$541$	−8.90076	+	38.9968i	−0.382674	+	1.67660i	0.306394	+	0.951905i	$0.400878\pi$
$541$	−8.90076	+	38.9968i	−0.382674	+	1.67660i	−0.689067	+	0.724697i	$0.741980\pi$
$542$	9.81780	−	12.3111i	0.421711	−	0.528808i
$543$	4.26136	−	5.34357i	0.182872	−	0.229315i
$544$	−5.26771	+	2.53680i	−0.225851	+	0.108764i
$545$	0.153166	+	0.671063i	0.00656090	+	0.0287452i
$546$	0.708883	+	0.888911i	0.0303374	+	0.0380419i
$547$	−5.29804	−	23.2122i	−0.226528	−	0.992483i	−0.952447	−	0.304703i	$-0.901443\pi$
$547$	−5.29804	−	23.2122i	−0.226528	−	0.992483i	0.725920	−	0.687780i	$-0.241414\pi$
$548$	−6.23787	−	3.00400i	−0.266469	−	0.128325i
$549$	−7.53307	+	9.44617i	−0.321504	+	0.403153i
$550$	−17.5633	−	8.45803i	−0.748900	−	0.360651i
$551$	8.99686	+	11.2817i	0.383279	+	0.480617i
$552$	−0.991007			−0.0421800
$553$	−7.15311			−0.304181
$554$	−2.93924	−	3.68569i	−0.124876	−	0.156590i
$555$	1.05956	−	0.510255i	0.0449756	−	0.0216591i
$556$	0.612227	−	2.68234i	0.0259642	−	0.113757i
$557$	−7.00813	−	30.7046i	−0.296944	−	1.30100i	−0.874651	−	0.484753i	$-0.838910\pi$
$557$	−7.00813	−	30.7046i	−0.296944	−	1.30100i	0.577707	−	0.816244i	$-0.303948\pi$
$558$	−2.12465			−0.0899435
$559$	−13.6443	+	36.7579i	−0.577093	+	1.55470i
$560$	0.166551			0.00703805
$561$	−0.658161	−	2.88359i	−0.0277876	−	0.121745i
$562$	−3.00418	+	13.1622i	−0.126724	+	0.555213i
$563$	−7.53312	+	3.62776i	−0.317483	+	0.152892i	−0.585838	−	0.810428i	$-0.699234\pi$
$563$	−7.53312	+	3.62776i	−0.317483	+	0.152892i	0.268355	+	0.963320i	$0.413520\pi$
$564$	0.156210	+	0.195881i	0.00657762	+	0.00824808i
$565$	3.10116			0.130467
$566$	13.9665			0.587054
$567$	−1.99582	−	2.50268i	−0.0838165	−	0.105103i
$568$	−30.9604	−	14.9097i	−1.29907	−	0.625599i
$569$	17.9197	−	22.4706i	0.751233	−	0.942017i	−0.248412	−	0.968655i	$-0.579909\pi$
$569$	17.9197	−	22.4706i	0.751233	−	0.942017i	0.999645	+	0.0266377i	$0.00848004\pi$
$570$	−0.454214	−	0.218738i	−0.0190249	−	0.00916192i
$571$	−6.16374	−	27.0051i	−0.257944	−	1.13013i	−0.923445	−	0.383731i	$-0.874639\pi$
$571$	−6.16374	−	27.0051i	−0.257944	−	1.13013i	0.665501	−	0.746397i	$-0.268218\pi$
$572$	30.4833	+	38.2249i	1.27457	+	1.59826i
$573$	0.678633	+	2.97329i	0.0283503	+	0.124211i
$574$	2.62966	−	1.26638i	0.109760	−	0.0528577i
$575$	2.26093	−	2.83511i	0.0942872	−	0.118232i
$576$	−3.17166	+	3.97714i	−0.132153	+	0.165714i
$577$	−0.293577	+	1.28625i	−0.0122218	+	0.0535472i	−0.980671	−	0.195663i	$-0.937314\pi$
$577$	−0.293577	+	1.28625i	−0.0122218	+	0.0535472i	0.968449	+	0.249211i	$0.0801711\pi$
$578$	−0.647917	+	0.312020i	−0.0269498	+	0.0129783i
$579$	−5.85994	−	2.82200i	−0.243531	−	0.117278i
$580$	−0.306634	+	1.34345i	−0.0127323	+	0.0557837i
$581$	−1.51403	+	6.63342i	−0.0628127	+	0.275200i
$582$	3.78537	+	1.82294i	0.156908	+	0.0755631i
$583$	−8.91110	+	4.29136i	−0.369060	+	0.177730i
$584$	−1.94609	+	8.52638i	−0.0805298	+	0.352824i
$585$	2.93355	−	3.67856i	0.121287	−	0.152090i
$586$	−14.8432	+	18.6128i	−0.613168	+	0.768888i
$587$	−13.1331	+	6.32458i	−0.542062	+	0.261043i	−0.684817	−	0.728715i	$-0.740118\pi$
$587$	−13.1331	+	6.32458i	−0.542062	+	0.261043i	0.142756	+	0.989758i	$0.454404\pi$
$588$	1.19589	+	5.23955i	0.0493178	+	0.216075i
$589$	3.05956	+	3.83656i	0.126067	+	0.158083i
$590$	−0.427722	−	1.87397i	−0.0176090	−	0.0771502i
$591$	−5.01261	−	2.41395i	−0.206191	−	0.0992964i
$592$	−5.48708	+	6.88058i	−0.225518	+	0.282790i
$593$	−8.63901	−	4.16033i	−0.354762	−	0.170844i	0.248011	−	0.968757i	$-0.420223\pi$
$593$	−8.63901	−	4.16033i	−0.354762	−	0.170844i	−0.602773	+	0.797913i	$0.705937\pi$
$594$	−7.57549	−	9.49937i	−0.310826	−	0.389764i
$595$	0.143020			0.00586324
$596$	32.3687			1.32587
$597$	2.38680	+	2.99295i	0.0976851	+	0.122493i
$598$	2.85777	−	1.37623i	0.116863	−	0.0562782i
$599$	−1.67980	+	7.35969i	−0.0686349	+	0.300709i	−0.997582	−	0.0695043i	$-0.977858\pi$
$599$	−1.67980	+	7.35969i	−0.0686349	+	0.300709i	0.928947	+	0.370213i	$0.120715\pi$
$600$	1.46955	+	6.43851i	0.0599940	+	0.262851i
$601$	47.9946			1.95774			0.978871	−	0.204478i	$-0.0655498\pi$
$601$	47.9946			1.95774			0.978871	+	0.204478i	$0.0655498\pi$
$602$	−1.67445	+	1.61254i	−0.0682453	+	0.0657223i
$603$	−22.7800			−0.927673
$604$	4.48810	+	19.6637i	0.182618	+	0.800103i
$605$	1.25290	−	5.48932i	0.0509377	−	0.223173i
$606$	0.787522	−	0.379251i	0.0319909	−	0.0154060i
$607$	−10.4366	−	13.0871i	−0.423608	−	0.531187i	0.523533	−	0.852005i	$-0.324614\pi$
$607$	−10.4366	−	13.0871i	−0.423608	−	0.531187i	−0.947141	+	0.320818i	$0.896042\pi$
$608$	26.3391			1.06819
$609$	0.846956			0.0343204
$610$	−0.579461	−	0.726621i	−0.0234617	−	0.0294200i
$611$	−1.69694	−	0.817206i	−0.0686510	−	0.0330606i
$612$	2.50763	−	3.14446i	0.101365	−	0.127107i
$613$	38.0366	+	18.3175i	1.53629	+	0.739836i	0.994893	−	0.100934i	$-0.0321831\pi$
$613$	38.0366	+	18.3175i	1.53629	+	0.739836i	0.541392	+	0.840770i	$0.317897\pi$
$614$	0.108372	+	0.474807i	0.00437352	+	0.0191616i
$615$	0.798815	+	1.00168i	0.0322113	+	0.0403917i
$616$	1.51503	+	6.63777i	0.0610422	+	0.267443i
$617$	14.9041	−	7.17746i	0.600018	−	0.288954i	−0.109114	−	0.994029i	$-0.534801\pi$
$617$	14.9041	−	7.17746i	0.600018	−	0.288954i	0.709132	+	0.705076i	$0.249087\pi$
$618$	2.63298	−	3.30166i	0.105914	−	0.132812i
$619$	25.4578	−	31.9231i	1.02324	−	1.28310i	0.0647684	−	0.997900i	$-0.479369\pi$
$619$	25.4578	−	31.9231i	1.02324	−	1.28310i	0.958469	−	0.285198i	$-0.0920594\pi$
$620$	−0.104277	+	0.456866i	−0.00418785	+	0.0183482i
$621$	2.03635	−	0.980656i	0.0817161	−	0.0393524i
$622$	−4.08125	−	1.96543i	−0.163643	−	0.0788064i
$623$	−1.29925	+	5.69237i	−0.0520532	+	0.228060i
$624$	0.831075	−	3.64118i	0.0332696	−	0.145764i
$625$	−21.3931	−	10.3024i	−0.855723	−	0.412095i
$626$	−3.17045	+	1.52681i	−0.126717	+	0.0610236i
$627$	−2.96498	+	12.9904i	−0.118410	+	0.518787i
$628$	−22.1275	+	27.7470i	−0.882984	+	1.10723i
$629$	−4.71185	+	5.90847i	−0.187874	+	0.235586i
$630$	0.251335	−	0.121037i	0.0100134	−	0.00482221i
$631$	5.89418	+	25.8241i	0.234644	+	1.02804i	0.945734	+	0.324940i	$0.105344\pi$
$631$	5.89418	+	25.8241i	0.234644	+	1.02804i	−0.711091	+	0.703100i	$0.751799\pi$
$632$	−22.6596	−	28.4142i	−0.901349	−	1.13026i
$633$	−2.25516	−	9.88048i	−0.0896344	−	0.392714i
$634$	1.91244	+	0.920984i	0.0759528	+	0.0365769i
$635$	0.435119	−	0.545621i	0.0172672	−	0.0216523i
$636$	1.28532	+	0.618976i	0.0509661	+	0.0245440i
$637$	−25.1901	−	31.5874i	−0.998067	−	1.25154i
$638$	−12.7020			−0.502876
$639$	37.2126			1.47211
$640$	1.87123	+	2.34645i	0.0739668	+	0.0927514i
$641$	2.08217	−	1.00272i	0.0822406	−	0.0396050i	−0.392311	−	0.919833i	$-0.628324\pi$
$641$	2.08217	−	1.00272i	0.0822406	−	0.0396050i	0.474552	+	0.880228i	$0.342610\pi$
$642$	0.139291	−	0.610272i	0.00549736	−	0.0240855i
$643$	4.42059	+	19.3679i	0.174331	+	0.763794i	0.984182	+	0.177159i	$0.0566906\pi$
$643$	4.42059	+	19.3679i	0.174331	+	0.763794i	−0.809851	+	0.586635i	$0.800452\pi$
$644$	−0.539229			−0.0212486
$645$	−0.853653	−	0.559078i	−0.0336126	−	0.0220137i
$646$	3.23965			0.127462
$647$	7.13087	+	31.2424i	0.280343	+	1.22826i	0.897355	+	0.441310i	$0.145486\pi$
$647$	7.13087	+	31.2424i	0.280343	+	1.22826i	−0.617011	+	0.786954i	$0.711657\pi$
$648$	3.61901	−	15.8559i	0.142168	−	0.622880i
$649$	−45.7720	+	22.0426i	−1.79671	+	0.865249i
$650$	−13.1790	−	16.5260i	−0.516923	−	0.648201i
$651$	0.288024			0.0112885
$652$	−32.4852			−1.27222
$653$	23.5633	+	29.5475i	0.922105	+	1.15628i	0.987373	+	0.158415i	$0.0506385\pi$
$653$	23.5633	+	29.5475i	0.922105	+	1.15628i	−0.0652675	+	0.997868i	$0.520790\pi$
$654$	0.824522	+	0.397069i	0.0322414	+	0.0155266i
$655$	0.254098	−	0.318629i	0.00992844	−	0.0124499i
$656$	−8.63823	−	4.15995i	−0.337266	−	0.162419i
$657$	−2.10745	−	9.23332i	−0.0822193	−	0.360226i
$658$	−0.0696251	−	0.0873072i	−0.00271427	−	0.00340359i
$659$	8.03352	+	35.1972i	0.312942	+	1.37109i	0.849663	+	0.527327i	$0.176806\pi$
$659$	8.03352	+	35.1972i	0.312942	+	1.37109i	−0.536721	+	0.843760i	$0.680337\pi$
$660$	−1.14643	+	0.552091i	−0.0446247	+	0.0214901i
$661$	1.25401	−	1.57248i	0.0487755	−	0.0611625i	−0.756845	−	0.653594i	$-0.773260\pi$
$661$	1.25401	−	1.57248i	0.0487755	−	0.0611625i	0.805621	+	0.592431i	$0.201832\pi$
$662$	−5.09926	+	6.39426i	−0.198188	+	0.248520i
$663$	0.713658	−	3.12674i	0.0277162	−	0.121432i
$664$	−31.1460	+	14.9991i	−1.20870	+	0.582079i
$665$	−0.580491	−	0.279550i	−0.0225105	−	0.0108405i
$666$	−3.28004	+	14.3708i	−0.127099	+	0.556858i
$667$	0.525780	−	2.30359i	0.0203583	−	0.0891955i
$668$	−8.87354	−	4.27327i	−0.343328	−	0.165338i
$669$	−0.373256	+	0.179751i	−0.0144309	+	0.00694956i
$670$	0.389921	−	1.70836i	0.0150640	−	0.0659996i
$671$	−15.3152	+	19.2047i	−0.591238	+	0.741390i
$672$	0.963895	−	1.20869i	0.0371831	−	0.0466261i
$673$	−10.5256	+	5.06885i	−0.405731	+	0.195390i	−0.625608	−	0.780138i	$-0.715149\pi$
$673$	−10.5256	+	5.06885i	−0.405731	+	0.195390i	0.219876	+	0.975528i	$0.429435\pi$
$674$	4.31880	+	18.9219i	0.166354	+	0.728844i
$675$	−9.39094	−	11.7759i	−0.361457	−	0.453253i
$676$	7.50719	+	32.8911i	0.288738	+	1.26504i
$677$	10.9441	+	5.27041i	0.420617	+	0.202558i	0.632206	−	0.774800i	$-0.282150\pi$
$677$	10.9441	+	5.27041i	0.420617	+	0.202558i	−0.211589	+	0.977359i	$0.567864\pi$
$678$	2.57072	−	3.22358i	0.0987279	−	0.123801i
$679$	4.83774	+	2.32973i	0.185656	+	0.0894070i
$680$	0.453058	+	0.568116i	0.0173740	+	0.0217863i
$681$	10.1550			0.389140
$682$	−4.31956			−0.165404
$683$	13.1828	+	16.5307i	0.504426	+	0.632530i	0.967221	−	0.253935i	$-0.0817250\pi$
$683$	13.1828	+	16.5307i	0.504426	+	0.632530i	−0.462796	+	0.886465i	$0.653154\pi$
$684$	−16.3242	+	7.86133i	−0.624172	+	0.300585i
$685$	−0.301427	+	1.32064i	−0.0115169	+	0.0504589i
$686$	−1.08523	−	4.75468i	−0.0414341	−	0.181535i
$687$	4.29835			0.163992
$688$	7.57086	+	0.997728i	0.288637	+	0.0380380i
$689$	−10.7246			−0.408573
$690$	0.0183693	+	0.0804813i	0.000699308	+	0.00306387i
$691$	−4.83573	+	21.1867i	−0.183960	+	0.805981i	0.795760	+	0.605612i	$0.207071\pi$
$691$	−4.83573	+	21.1867i	−0.183960	+	0.805981i	−0.979720	+	0.200370i	$0.935786\pi$
$692$	−3.50188	+	1.68642i	−0.133121	+	0.0641079i
$693$	−4.59698	−	5.76443i	−0.174625	−	0.218972i
$694$	15.5810			0.591448
$695$	−0.538301			−0.0204189
$696$	2.68298	+	3.36436i	0.101698	+	0.127526i
$697$	−7.41779	−	3.57222i	−0.280969	−	0.135307i
$698$	−2.45204	+	3.07476i	−0.0928109	+	0.116381i
$699$	−13.4050	−	6.45553i	−0.507025	−	0.244170i
$700$	0.799614	+	3.50334i	0.0302226	+	0.132414i
$701$	−14.4648	−	18.1382i	−0.546327	−	0.685072i	0.429638	−	0.903001i	$-0.358641\pi$
$701$	−14.4648	−	18.1382i	−0.546327	−	0.685072i	−0.975965	+	0.217929i	$0.930070\pi$
$702$	−2.93164	−	12.8443i	−0.110648	−	0.484779i
$703$	30.6733	−	14.7715i	1.15687	−	0.557117i
$704$	−6.44820	+	8.08579i	−0.243026	+	0.304745i
$705$	0.0305627	−	0.0383245i	0.00115106	−	0.00144338i
$706$	1.10676	−	4.84904i	0.0416535	−	0.182496i
$707$	1.00646	−	0.484687i	0.0378519	−	0.0182285i
$708$	6.60205	+	3.17938i	0.248120	+	0.119488i
$709$	−3.37043	+	14.7668i	−0.126579	+	0.554579i	0.871373	+	0.490620i	$0.163230\pi$
$709$	−3.37043	+	14.7668i	−0.126579	+	0.554579i	−0.997953	+	0.0639589i	$0.979627\pi$
$710$	−0.636962	+	2.79071i	−0.0239048	+	0.104734i
$711$	35.4589	+	17.0761i	1.32981	+	0.640404i
$712$	−26.7275	+	12.8713i	−1.00165	+	0.482372i
$713$	0.178802	−	0.783382i	0.00669618	−	0.0293379i
$714$	0.118557	−	0.148666i	0.00443688	−	0.00556368i
$715$	5.96411	−	7.47876i	0.223045	−	0.279690i
$716$	2.13764	−	1.02943i	0.0798873	−	0.0384717i
$717$	−1.48319	−	6.49829i	−0.0553908	−	0.242683i
$718$	0.244157	+	0.306163i	0.00911186	+	0.0114259i
$719$	−1.27444	−	5.58370i	−0.0475287	−	0.208237i	0.945588	−	0.325367i	$-0.105488\pi$
$719$	−1.27444	−	5.58370i	−0.0475287	−	0.208237i	−0.993117	+	0.117130i	$0.962631\pi$
$720$	−0.825614	−	0.397595i	−0.0307688	−	0.0148175i
$721$	3.36499	−	4.21956i	0.125319	−	0.157145i
$722$	−0.838716	−	0.403904i	−0.0312138	−	0.0150318i
$723$	1.86739	+	2.34164i	0.0694491	+	0.0870864i
$724$	18.8948			0.702221
$725$	−15.7460			−0.584791
$726$	−4.66742	−	5.85276i	−0.173224	−	0.217216i
$727$	−44.1112	+	21.2429i	−1.63600	+	0.787854i	−0.636128	+	0.771584i	$0.719465\pi$
$727$	−44.1112	+	21.2429i	−1.63600	+	0.787854i	−0.999868	+	0.0162703i	$0.994821\pi$
$728$	−1.64278	+	7.19747i	−0.0608853	+	0.266756i
$729$	2.82197	+	12.3639i	0.104518	+	0.457921i
$730$	0.728514			0.0269635
$731$	6.50123	+	0.856765i	0.240457	+	0.0316886i
$732$	3.54302			0.130954
$733$	10.3361	+	45.2855i	0.381774	+	1.67266i	0.691923	+	0.721972i	$0.256764\pi$
$733$	10.3361	+	45.2855i	0.381774	+	1.67266i	−0.310149	+	0.950688i	$0.600379\pi$
$734$	−1.27974	+	5.60690i	−0.0472360	+	0.206954i
$735$	0.947359	−	0.456224i	0.0349439	−	0.0168281i
$736$	−2.68907	−	3.37199i	−0.0991204	−	0.124293i
$737$	−46.3133			−1.70597
$738$	−16.0587			−0.591130
$739$	−15.4143	−	19.3289i	−0.567023	−	0.711025i	0.412816	−	0.910815i	$-0.364545\pi$
$739$	−15.4143	−	19.3289i	−0.567023	−	0.711025i	−0.979839	+	0.199790i	$0.935974\pi$
$740$	2.92919	+	1.41063i	0.107679	+	0.0518556i
$741$	−9.00819	+	11.2959i	−0.330924	+	0.414966i
$742$	−0.572886	−	0.275887i	−0.0210313	−	0.0101281i
$743$	−8.57724	−	37.5794i	−0.314668	−	1.37865i	−0.846764	−	0.531968i	$-0.821452\pi$
$743$	−8.57724	−	37.5794i	−0.314668	−	1.37865i	0.532096	−	0.846684i	$-0.321405\pi$
$744$	0.912400	+	1.14411i	0.0334502	+	0.0419452i
$745$	−1.40922	−	6.17421i	−0.0516299	−	0.226205i
$746$	6.53485	−	3.14702i	0.239258	−	0.115220i
$747$	23.3408	−	29.2684i	0.853994	−	1.07087i
$748$	5.09818	−	6.39291i	0.186408	−	0.233748i
$749$	0.178015	−	0.779935i	0.00650453	−	0.0284982i
$750$	0.999771	−	0.481464i	0.0365065	−	0.0175806i
$751$	7.58516	+	3.65282i	0.276786	+	0.133293i	0.567128	−	0.823630i	$-0.308055\pi$
$751$	7.58516	+	3.65282i	0.276786	+	0.133293i	−0.290341	+	0.956923i	$0.593769\pi$
$752$	−0.0816266	+	0.357630i	−0.00297662	+	0.0130414i
$753$	−2.83289	+	12.4117i	−0.103236	+	0.452307i
$754$	−12.4091	−	5.97589i	−0.451912	−	0.217629i
$755$	3.55538	−	1.71218i	0.129393	−	0.0623126i
$756$	−0.498387	+	2.18357i	−0.0181261	+	0.0794158i
$757$	14.7693	−	18.5201i	0.536800	−	0.673126i	−0.437281	−	0.899325i	$-0.644059\pi$
$757$	14.7693	−	18.5201i	0.536800	−	0.673126i	0.974081	+	0.226199i	$0.0726300\pi$
$758$	−13.0612	+	16.3782i	−0.474404	+	0.594884i
$759$	1.96577	−	0.946663i	0.0713528	−	0.0343617i
$760$	−0.728423	−	3.19143i	−0.0264227	−	0.115765i
$761$	9.31420	+	11.6796i	0.337639	+	0.423387i	0.921446	−	0.388506i	$-0.127009\pi$
$761$	9.31420	+	11.6796i	0.337639	+	0.423387i	−0.583807	+	0.811893i	$0.698437\pi$
$762$	−0.206467	−	0.904591i	−0.00747951	−	0.0327699i
$763$	1.05375	+	0.507459i	0.0381483	+	0.0183712i
$764$	−5.25676	+	6.59177i	−0.190183	+	0.238482i
$765$	−0.708969	−	0.341421i	−0.0256328	−	0.0123441i
$766$	−0.557617	−	0.699229i	−0.0201475	−	0.0252642i
$767$	−55.0869			−1.98907
$768$	6.00221			0.216586
$769$	−24.1361	−	30.2657i	−0.870370	−	1.09141i	−0.995066	−	0.0992148i	$-0.968367\pi$
$769$	−24.1361	−	30.2657i	−0.870370	−	1.09141i	0.124696	−	0.992195i	$-0.460205\pi$
$770$	0.510981	−	0.246076i	0.0184145	−	0.00886795i
$771$	−0.168201	+	0.736937i	−0.00605761	+	0.0265401i
$772$	−4.00109	−	17.5299i	−0.144002	−	0.630916i
$773$	15.4039			0.554039			0.277019	−	0.960864i	$-0.410653\pi$
$773$	15.4039			0.554039			0.277019	+	0.960864i	$0.410653\pi$
$774$	12.1500	−	3.99631i	0.436721	−	0.143644i
$775$	−5.35472			−0.192347
$776$	6.07060	+	26.5970i	0.217922	+	0.954778i
$777$	0.444653	−	1.94815i	0.0159518	−	0.0698895i
$778$	5.23038	−	2.51882i	0.187518	−	0.0903040i
$779$	23.1251	+	28.9979i	0.828541	+	1.03896i
$780$	−1.37973			−0.0494024
$781$	75.6558			2.70718
$782$	−0.330750	−	0.414747i	−0.0118276	−	0.0148313i
$783$	−8.84230	−	4.25823i	−0.315998	−	0.152177i
$784$	−4.90606	+	6.15200i	−0.175216	+	0.219714i
$785$	6.25600	+	3.01273i	0.223286	+	0.107529i
$786$	−0.120571	−	0.528258i	−0.00430064	−	0.0188423i
$787$	5.39241	+	6.76186i	0.192219	+	0.241034i	0.868596	−	0.495521i	$-0.165023\pi$
$787$	5.39241	+	6.76186i	0.192219	+	0.241034i	−0.676378	+	0.736555i	$0.736451\pi$
$788$	−3.42255	−	14.9952i	−0.121923	−	0.534180i
$789$	11.2106	−	5.39875i	0.399108	−	0.192200i
$790$	−1.88754	+	2.36691i	−0.0671558	+	0.0842107i
$791$	3.28541	−	4.11977i	0.116816	−	0.146482i
$792$	8.33569	−	36.5210i	0.296196	−	1.29772i
$793$	−23.9973	+	11.5565i	−0.852169	+	0.410383i
$794$	−9.23494	−	4.44731i	−0.327736	−	0.157829i
$795$	0.0621091	−	0.272118i	0.00220278	−	0.00965102i
$796$	−2.35495	+	10.3177i	−0.0834689	+	0.365701i
$797$	−15.1998	−	7.31985i	−0.538406	−	0.259282i	0.144860	−	0.989452i	$-0.453727\pi$
$797$	−15.1998	−	7.31985i	−0.538406	−	0.259282i	−0.683266	+	0.730170i	$0.739441\pi$
$798$	−0.771786	+	0.371672i	−0.0273209	+	0.0131571i
$799$	−0.0700941	+	0.307102i	−0.00247975	+	0.0108645i
$800$	−17.9200	+	22.4710i	−0.633568	+	0.794469i
$801$	20.0295	−	25.1163i	0.707709	−	0.887439i
$802$	−12.2280	+	5.88868i	−0.431785	+	0.207936i
$803$	−4.28458	−	18.7720i	−0.151200	−	0.662449i
$804$	4.16499	+	5.22273i	0.146888	+	0.184192i
$805$	0.0234762	+	0.102856i	0.000827428	+	0.00362520i
$806$	−4.21994	−	2.03222i	−0.148641	−	0.0715818i
$807$	−5.63904	+	7.07113i	−0.198504	+	0.248916i
$808$	5.11358	+	2.46257i	0.179895	+	0.0866329i
$809$	21.9249	+	27.4929i	0.770837	+	0.966599i	0.999977	−	0.00679418i	$-0.00216267\pi$
$809$	21.9249	+	27.4929i	0.770837	+	0.966599i	−0.229140	+	0.973394i	$0.573591\pi$
$810$	−1.35477			−0.0476017
$811$	−31.5383			−1.10746			−0.553730	−	0.832697i	$-0.686796\pi$
$811$	−31.5383			−1.10746			−0.553730	+	0.832697i	$0.686796\pi$
$812$	1.45987	+	1.83062i	0.0512315	+	0.0642422i
$813$	10.5817	−	5.09589i	0.371118	−	0.178721i
$814$	−6.66855	+	29.2168i	−0.233733	+	1.02405i
$815$	1.41430	+	6.19644i	0.0495406	+	0.217052i
$816$	−0.624629			−0.0218664
$817$	−24.7126	−	16.1849i	−0.864584	−	0.566237i
$818$	23.2679			0.813542
$819$	−1.77898	−	7.79423i	−0.0621627	−	0.272352i
$820$	−0.788155	+	3.45313i	−0.0275236	+	0.120589i
$821$	−37.4786	+	18.0487i	−1.30801	+	0.629905i	−0.952435	−	0.304743i	$-0.901430\pi$
$821$	−37.4786	+	18.0487i	−1.30801	+	0.629905i	−0.355576	+	0.934647i	$0.615715\pi$
$822$	1.12290	+	1.40807i	0.0391657	+	0.0491122i
$823$	−43.7799			−1.52607			−0.763035	−	0.646357i	$-0.776292\pi$
$823$	−43.7799			−1.52607			−0.763035	+	0.646357i	$0.776292\pi$
$824$	27.4209			0.955252
$825$	−9.06541	−	11.3677i	−0.315617	−	0.395771i
$826$	−2.94264	−	1.41710i	−0.102387	−	0.0493072i
$827$	14.0977	−	17.6779i	0.490224	−	0.614722i	−0.473769	−	0.880649i	$-0.657107\pi$
$827$	14.0977	−	17.6779i	0.490224	−	0.614722i	0.963993	+	0.265927i	$0.0856781\pi$
$828$	2.67303	+	1.28726i	0.0928943	+	0.0447355i
$829$	−8.81887	−	38.6380i	−0.306292	−	1.34195i	−0.860447	−	0.509540i	$-0.829816\pi$
$829$	−8.81887	−	38.6380i	−0.306292	−	1.34195i	0.554155	−	0.832413i	$-0.313041\pi$
$830$	1.79543	+	2.25139i	0.0623201	+	0.0781470i
$831$	−0.782418	−	3.42800i	−0.0271418	−	0.118916i
$832$	−10.1036	+	4.86565i	−0.350280	+	0.168686i
$833$	−4.21291	+	5.28282i	−0.145969	+	0.183039i
$834$	−0.446227	+	0.559551i	−0.0154516	+	0.0193757i
$835$	−0.428787	+	1.87864i	−0.0148388	+	0.0650130i
$836$	−33.1882	+	15.9826i	−1.14784	+	0.552770i
$837$	−3.00700	−	1.44809i	−0.103937	−	0.0500534i
$838$	4.75172	−	20.8186i	0.164145	−	0.719168i
$839$	−2.80488	+	12.2890i	−0.0968352	+	0.424263i	−0.999987	−	0.00505817i	$-0.998390\pi$
$839$	−2.80488	+	12.2890i	−0.0968352	+	0.424263i	0.903152	+	0.429321i	$0.141247\pi$
$840$	−0.173110	−	0.0833654i	−0.00597286	−	0.00287638i
$841$	16.8842	−	8.13100i	0.582214	−	0.280379i
$842$	3.33452	−	14.6095i	0.114915	−	0.503476i
$843$	−6.27837	+	7.87282i	−0.216238	+	0.271154i
$844$	17.4686	−	21.9050i	0.601296	−	0.754001i
$845$	5.94703	−	2.86394i	0.204584	−	0.0985224i
$846$	0.136719	+	0.599005i	0.00470049	+	0.0205942i
$847$	−5.96502	−	7.47990i	−0.204961	−	0.257012i
$848$	0.464786	+	2.03636i	0.0159608	+	0.0699289i
$849$	9.38552	+	4.51983i	0.322110	+	0.155120i
$850$	−2.20412	+	2.76388i	−0.0756008	+	0.0948004i
$851$	−5.02264	−	2.41878i	−0.172174	−	0.0829146i
$852$	−6.80379	−	8.53168i	−0.233094	−	0.292290i
$853$	11.3026			0.386995			0.193497	−	0.981101i	$-0.438017\pi$
$853$	11.3026			0.386995			0.193497	+	0.981101i	$0.438017\pi$
$854$	−1.57918			−0.0540384
$855$	2.21022	+	2.77153i	0.0755880	+	0.0947843i
$856$	3.66204	−	1.76355i	0.125166	−	0.0602768i
$857$	10.8125	−	47.3727i	0.369348	−	1.61822i	−0.359225	−	0.933251i	$-0.616959\pi$
$857$	10.8125	−	47.3727i	0.369348	−	1.61822i	0.728573	−	0.684968i	$-0.240184\pi$
$858$	−2.83002	−	12.3991i	−0.0966151	−	0.423299i
$859$	−0.221304			−0.00755080			−0.00377540	−	0.999993i	$-0.501202\pi$
$859$	−0.221304			−0.00755080			−0.00377540	+	0.999993i	$0.501202\pi$
$860$	−0.263017	−	2.80876i	−0.00896881	−	0.0957780i
$861$	2.17697			0.0741910
$862$	3.22716	+	14.1391i	0.109917	+	0.481580i
$863$	−8.15276	+	35.7196i	−0.277523	+	1.21591i	0.623390	+	0.781911i	$0.285755\pi$
$863$	−8.15276	+	35.7196i	−0.277523	+	1.21591i	−0.900914	+	0.433998i	$0.857102\pi$
$864$	−16.1400	+	7.77263i	−0.549095	+	0.264430i
$865$	0.474138	+	0.594550i	0.0161212	+	0.0202153i
$866$	12.2032			0.414680
$867$	−0.536379			−0.0182164
$868$	0.496458	+	0.622538i	0.0168509	+	0.0211303i
$869$	72.0904	+	34.7169i	2.44550	+	1.17769i
$870$	0.223493	−	0.280251i	0.00757712	−	0.00950141i
$871$	−45.2453	−	21.7890i	−1.53308	−	0.738291i
$872$	1.32229	+	5.79332i	0.0447783	+	0.196187i
$873$	−18.4197	−	23.0976i	−0.623413	−	0.781736i
$874$	0.531778	+	2.32987i	0.0179876	+	0.0788090i
$875$	1.27772	−	0.615317i	0.0431948	−	0.0208015i
$876$	−1.73159	+	2.17135i	−0.0585051	+	0.0733631i
$877$	22.8099	−	28.6028i	0.770237	−	0.965846i	−0.229736	−	0.973253i	$-0.573786\pi$
$877$	22.8099	−	28.6028i	0.770237	−	0.965846i	0.999973	+	0.00740658i	$0.00235761\pi$
$878$	0.0267743	−	0.117306i	0.000903588	−	0.00395888i
$879$	−15.9982	+	7.70432i	−0.539605	+	0.259860i
$880$	−1.67853	−	0.808338i	−0.0565833	−	0.0272491i
$881$	5.28236	−	23.1435i	0.177967	−	0.779725i	−0.804600	−	0.593817i	$-0.797620\pi$
$881$	5.28236	−	23.1435i	0.177967	−	0.779725i	0.982567	−	0.185908i	$-0.0595226\pi$
$882$	−2.93272	+	12.8491i	−0.0987498	+	0.432651i
$883$	21.7653	+	10.4816i	0.732462	+	0.352735i	0.762652	−	0.646809i	$-0.223897\pi$
$883$	21.7653	+	10.4816i	0.732462	+	0.352735i	−0.0301898	+	0.999544i	$0.509611\pi$
$884$	7.98828	−	3.84695i	0.268675	−	0.129387i
$885$	0.319024	−	1.39774i	0.0107239	−	0.0469844i
$886$	14.9185	−	18.7073i	0.501198	−	0.628483i
$887$	−13.8398	+	17.3545i	−0.464694	+	0.582708i	−0.957863	−	0.287226i	$-0.907267\pi$
$887$	−13.8398	+	17.3545i	−0.464694	+	0.582708i	0.493169	+	0.869934i	$0.335839\pi$
$888$	9.14719	−	4.40505i	0.306959	−	0.147824i
$889$	−0.263867	−	1.15608i	−0.00884982	−	0.0387736i
$890$	1.54072	+	1.93200i	0.0516450	+	0.0647608i
$891$	7.96775	+	34.9090i	0.266930	+	1.16950i
$892$	−1.03189	−	0.496930i	−0.0345501	−	0.0166384i
$893$	0.884767	−	1.10946i	0.0296076	−	0.0371268i
$894$	−7.58612	−	3.65328i	−0.253718	−	0.122184i
$895$	−0.289426	−	0.362929i	−0.00967444	−	0.0121314i
$896$	5.09957			0.170365
$897$	2.36581			0.0789921
$898$	0.993934	+	1.24635i	0.0331680	+	0.0415914i
$899$	−3.14357	+	1.51386i	−0.104844	+	0.0504901i
$900$	4.39948	−	19.2754i	0.146649	−	0.642513i
$901$	0.399120	+	1.74866i	0.0132966	+	0.0582562i
$902$	−32.6485			−1.08708
$903$	−1.64709	+	0.541752i	−0.0548116	+	0.0180284i
$904$	26.7724			0.890438
$905$	−0.822617	−	3.60412i	−0.0273447	−	0.119805i
$906$	1.16748	−	5.11505i	0.0387868	−	0.169936i
$907$	1.76297	−	0.849003i	0.0585385	−	0.0281907i	−0.404385	−	0.914589i	$-0.632515\pi$
$907$	1.76297	−	0.849003i	0.0585385	−	0.0281907i	0.462924	+	0.886398i	$0.346800\pi$
$908$	17.5038	+	21.9491i	0.580885	+	0.728407i
$909$	−6.14623			−0.203858
$910$	0.614969			0.0203860
$911$	−17.2014	−	21.5698i	−0.569907	−	0.714641i	0.410448	−	0.911884i	$-0.365372\pi$
$911$	−17.2014	−	21.5698i	−0.569907	−	0.714641i	−0.980355	+	0.197244i	$0.936801\pi$
$912$	2.53525	+	1.22091i	0.0839505	+	0.0404284i
$913$	47.4534	−	59.5046i	1.57048	−	1.96932i
$914$	−14.8933	−	7.17224i	−0.492627	−	0.237237i
$915$	−0.154251	−	0.675818i	−0.00509938	−	0.0223419i
$916$	7.40893	+	9.29051i	0.244798	+	0.306967i
$917$	−0.154092	−	0.675120i	−0.00508856	−	0.0222944i
$918$	−1.98519	+	0.956017i	−0.0655210	+	0.0315533i
$919$	−5.62882	+	7.05832i	−0.185678	+	0.232833i	−0.865954	−	0.500123i	$-0.833288\pi$
$919$	−5.62882	+	7.05832i	−0.185678	+	0.232833i	0.680277	+	0.732955i	$0.261860\pi$
$920$	−0.334206	+	0.419081i	−0.0110184	+	0.0138167i
$921$	−0.0808310	+	0.354144i	−0.00266347	+	0.0116694i
$922$	−12.3563	+	5.95046i	−0.406932	+	0.195968i
$923$	73.9111	+	35.5937i	2.43281	+	1.17158i
$924$	−0.481110	+	2.10788i	−0.0158274	+	0.0693442i
$925$	−8.26665	+	36.2186i	−0.271806	+	1.19086i
$926$	−25.5089	−	12.2845i	−0.838275	−	0.403692i
$927$	−26.7537	+	12.8839i	−0.878708	+	0.423164i
$928$	−4.16731	+	18.2582i	−0.136799	+	0.599354i
$929$	−17.6310	+	22.1085i	−0.578453	+	0.725357i	−0.981848	−	0.189669i	$-0.939259\pi$
$929$	−17.6310	+	22.1085i	−0.578453	+	0.725357i	0.403395	+	0.915026i	$0.367830\pi$
$930$	0.0760031	−	0.0953048i	0.00249224	−	0.00312517i
$931$	27.4253	−	13.2073i	0.898829	−	0.432853i
$932$	−9.15279	−	40.1010i	−0.299810	−	1.31355i
$933$	−2.10657	−	2.64155i	−0.0689659	−	0.0864805i
$934$	−0.278313	−	1.21937i	−0.00910668	−	0.0398990i
$935$	−1.44138	−	0.694133i	−0.0471382	−	0.0227006i
$936$	25.3255	−	31.7572i	0.827789	−	1.03801i
$937$	−0.174322	−	0.0839490i	−0.00569485	−	0.00274249i	0.431034	−	0.902336i	$-0.358149\pi$
$937$	−0.174322	−	0.0839490i	−0.00569485	−	0.00274249i	−0.436729	+	0.899593i	$0.643863\pi$
$938$	−1.85640	−	2.32785i	−0.0606136	−	0.0760071i
$939$	−2.62467			−0.0856527
$940$	0.135515			0.00442001
$941$	16.6142	+	20.8336i	0.541609	+	0.679156i	0.975040	−	0.222031i	$-0.0712685\pi$
$941$	16.6142	+	20.8336i	0.541609	+	0.679156i	−0.433431	+	0.901187i	$0.642697\pi$
$942$	8.31761	−	4.00555i	0.271002	−	0.130508i
$943$	1.35144	−	5.92104i	0.0440089	−	0.192815i
$944$	2.38738	+	10.4598i	0.0777027	+	0.340438i
$945$	0.438207			0.0142549
$946$	24.7017	−	8.12476i	0.803122	−	0.264159i
$947$	20.5972			0.669320			0.334660	−	0.942339i	$-0.391379\pi$
$947$	20.5972			0.669320			0.334660	+	0.942339i	$0.391379\pi$
$948$	−2.56813	−	11.2517i	−0.0834091	−	0.365439i
$949$	4.64586	−	20.3548i	0.150811	−	0.660746i
$950$	14.3485	−	6.90985i	0.465525	−	0.224185i
$951$	0.987121	+	1.23781i	0.0320096	+	0.0401388i
$952$	1.23470			0.0400168
$953$	−12.5237			−0.405681			−0.202840	−	0.979212i	$-0.565017\pi$
$953$	−12.5237			−0.405681			−0.202840	+	0.979212i	$0.565017\pi$
$954$	2.18127	+	2.73522i	0.0706211	+	0.0885560i
$955$	1.48622	+	0.715724i	0.0480928	+	0.0231603i
$956$	11.4890	−	14.4067i	0.371579	−	0.465946i
$957$	−8.53579	−	4.11062i	−0.275923	−	0.132877i
$958$	−1.92826	−	8.44824i	−0.0622991	−	0.272950i
$959$	1.43508	+	1.79953i	0.0463412	+	0.0581100i
$960$	−0.0649446	−	0.284541i	−0.00209608	−	0.00918351i
$961$	26.8610	−	12.9356i	0.866484	−	0.417277i
$962$	−20.2604	+	25.4057i	−0.653221	+	0.819114i
$963$	−2.74433	+	3.44128i	−0.0884348	+	0.110894i
$964$	−1.84247	+	8.07241i	−0.0593421	+	0.259995i
$965$	−3.16957	+	1.52639i	−0.102032	+	0.0491361i
$966$	0.126377	+	0.0608600i	0.00406612	+	0.00195814i
$967$	7.77750	−	34.0755i	0.250108	−	1.09579i	−0.681354	−	0.731954i	$-0.738609\pi$
$967$	7.77750	−	34.0755i	0.250108	−	1.09579i	0.931462	−	0.363839i	$-0.118534\pi$
$968$	10.8164	−	47.3896i	0.347651	−	1.52316i
$969$	2.17706	+	1.04842i	0.0699373	+	0.0336800i
$970$	2.04746	−	0.986006i	0.0657401	−	0.0316588i
$971$	−10.5852	+	46.3770i	−0.339697	+	1.48831i	0.460008	+	0.887915i	$0.347847\pi$
$971$	−10.5852	+	46.3770i	−0.339697	+	1.48831i	−0.799705	+	0.600394i	$0.795011\pi$
$972$	11.7184	−	14.6944i	0.375867	−	0.471323i
$973$	−0.570284	+	0.715113i	−0.0182825	+	0.0229255i
$974$	3.82844	−	1.84368i	0.122671	−	0.0590752i
$975$	−3.50822	−	15.3705i	−0.112353	−	0.492250i
$976$	3.23433	+	4.05573i	0.103528	+	0.129821i
$977$	4.17608	+	18.2966i	0.133605	+	0.585360i	0.996761	+	0.0804230i	$0.0256271\pi$
$977$	4.17608	+	18.2966i	0.133605	+	0.585360i	−0.863156	+	0.504937i	$0.831516\pi$
$978$	7.61344	+	3.66644i	0.243451	+	0.117240i
$979$	40.7214	−	51.0631i	1.30146	−	1.63198i
$980$	2.61902	+	1.26125i	0.0836616	+	0.0402893i
$981$	−4.01215	−	5.03108i	−0.128098	−	0.160630i
$982$	−4.27493			−0.136418
$983$	39.2565			1.25209			0.626044	−	0.779788i	$-0.284673\pi$
$983$	39.2565			1.25209			0.626044	+	0.779788i	$0.284673\pi$
$984$	6.89620	+	8.64756i	0.219843	+	0.275674i
$985$	−2.71126	+	1.30568i	−0.0863881	+	0.0416023i
$986$	−0.512570	+	2.24572i	−0.0163236	+	0.0715182i
$987$	−0.0185340	−	0.0812029i	−0.000589945	−	0.00258472i
$988$	−39.9422			−1.27073
$989$	0.450991	+	4.81614i	0.0143407	+	0.153144i
$990$	−3.12044			−0.0991742
$991$	−5.49095	−	24.0574i	−0.174426	−	0.764210i	−0.984141	−	0.177387i	$-0.943236\pi$
$991$	−5.49095	−	24.0574i	−0.174426	−	0.764210i	0.809715	−	0.586823i	$-0.199622\pi$
$992$	−1.41717	+	6.20904i	−0.0449953	+	0.197137i
$993$	−5.49604	+	2.64675i	−0.174411	+	0.0839921i
$994$	3.03255	+	3.80270i	0.0961867	+	0.120614i
$995$	2.07059			0.0656422
$996$	−10.9778			−0.347846
$997$	−35.9494	−	45.0791i	−1.13853	−	1.42767i	−0.888168	−	0.459519i	$-0.848022\pi$
$997$	−35.9494	−	45.0791i	−1.13853	−	1.42767i	−0.250361	−	0.968152i	$-0.580549\pi$
$998$	2.90788	+	1.40036i	0.0920473	+	0.0443276i
$999$	−14.4369	+	18.1033i	−0.456763	+	0.572763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.k.a.188.13	yes	180
43.35	even	7	inner	731.2.k.a.35.13	✓	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.k.a.35.13	✓	180	43.35	even	7	inner
731.2.k.a.188.13	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)

\(f(q)\)	\(=\)	\(q+(-0.160022 - 0.701103i) q^{2} +(0.119356 - 0.522931i) q^{3} +(1.33600 - 0.643383i) q^{4} +(-0.180888 - 0.226826i) q^{5} -0.385728 q^{6} -0.492965 q^{7} +(-1.56161 - 1.95820i) q^{8} +(2.44370 + 1.17682i) q^{9} +O(q^{10})\)	\(q+(-0.160022 - 0.701103i) q^{2} +(0.119356 - 0.522931i) q^{3} +(1.33600 - 0.643383i) q^{4} +(-0.180888 - 0.226826i) q^{5} -0.385728 q^{6} -0.492965 q^{7} +(-1.56161 - 1.95820i) q^{8} +(2.44370 + 1.17682i) q^{9} +(-0.130083 + 0.163118i) q^{10} +(4.96820 + 2.39256i) q^{11} +(-0.176986 - 0.775427i) q^{12} +(3.72800 + 4.67477i) q^{13} +(0.0788854 + 0.345620i) q^{14} +(-0.140204 + 0.0675189i) q^{15} +(0.726072 - 0.910465i) q^{16} +(0.623490 - 0.781831i) q^{17} +(0.434028 - 1.90160i) q^{18} +(-4.05881 + 1.95462i) q^{19} +(-0.387602 - 0.186659i) q^{20} +(-0.0588382 + 0.257787i) q^{21} +(0.882409 - 3.86608i) q^{22} +(0.664616 + 0.320062i) q^{23} +(-1.21039 + 0.582894i) q^{24} +(1.09387 - 4.79258i) q^{25} +(2.68093 - 3.36178i) q^{26} +(1.91035 - 2.39550i) q^{27} +(-0.658601 + 0.317166i) q^{28} +(-0.712761 - 3.12281i) q^{29} +(0.0697736 + 0.0874933i) q^{30} +(-0.242388 - 1.06197i) q^{31} +(-5.26771 - 2.53680i) q^{32} +(1.84413 - 2.31246i) q^{33} +(-0.647917 - 0.312020i) q^{34} +(0.0891714 + 0.111817i) q^{35} +4.02192 q^{36} -7.55722 q^{37} +(2.01989 + 2.53286i) q^{38} +(2.88954 - 1.39153i) q^{39} +(-0.161694 + 0.708429i) q^{40} +(-1.83204 - 8.02670i) q^{41} +0.190151 q^{42} +(3.38360 + 5.61705i) q^{43} +8.17684 q^{44} +(-0.175101 - 0.767167i) q^{45} +(0.118043 - 0.517181i) q^{46} +(-0.283805 + 0.136673i) q^{47} +(-0.389450 - 0.488355i) q^{48} -6.75699 q^{49} -3.53514 q^{50} +(-0.334427 - 0.419358i) q^{51} +(7.98828 + 3.84695i) q^{52} +(-1.11831 + 1.40231i) q^{53} +(-1.98519 - 0.956017i) q^{54} +(-0.355992 - 1.55970i) q^{55} +(0.769821 + 0.965325i) q^{56} +(0.537690 + 2.35577i) q^{57} +(-2.07535 + 0.999438i) q^{58} +(-5.74421 + 7.20301i) q^{59} +(-0.143872 + 0.180410i) q^{60} +(-0.991234 + 4.34288i) q^{61} +(-0.705764 + 0.339878i) q^{62} +(-1.20466 - 0.580132i) q^{63} +(-0.417341 + 1.82849i) q^{64} +(0.386010 - 1.69122i) q^{65} +(-1.91638 - 0.922878i) q^{66} +(-7.56704 + 3.64410i) q^{67} +(0.329964 - 1.44567i) q^{68} +(0.246696 - 0.309347i) q^{69} +(0.0641262 - 0.0804117i) q^{70} +(12.3613 - 5.95287i) q^{71} +(-1.51165 - 6.62298i) q^{72} +(-2.17710 - 2.72999i) q^{73} +(1.20932 + 5.29839i) q^{74} +(-2.37563 - 1.14404i) q^{75} +(-4.16500 + 5.22274i) q^{76} +(-2.44915 - 1.17945i) q^{77} +(-1.43800 - 1.80319i) q^{78} +14.5104 q^{79} -0.337855 q^{80} +(4.04860 + 5.07678i) q^{81} +(-5.33438 + 2.56890i) q^{82} +(3.07128 - 13.4562i) q^{83} +(0.0872480 + 0.382258i) q^{84} -0.290122 q^{85} +(3.39668 - 3.27111i) q^{86} -1.71809 q^{87} +(-3.07329 - 13.4650i) q^{88} +(2.63557 - 11.5472i) q^{89} +(-0.509843 + 0.245528i) q^{90} +(-1.83778 - 2.30450i) q^{91} +1.09385 q^{92} -0.584268 q^{93} +(0.141237 + 0.177106i) q^{94} +(1.17755 + 0.567077i) q^{95} +(-1.95530 + 2.45187i) q^{96} +(-9.81356 - 4.72596i) q^{97} +(1.08127 + 4.73735i) q^{98} +(9.32515 + 11.6934i) 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

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