LMFDB - Embedded newform 690.2.m.g.331.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 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("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			331.1
Character	$\chi$	$=$	690.331
Dual form			690.2.m.g.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 + 0.281733i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-1.37681 + 3.01480i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.959493 + 0.281733i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-1.37681 + 3.01480i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.415415 + 0.909632i) q^{10} +(4.09562 + 1.20258i) q^{11} +(-0.959493 - 0.281733i) q^{12} +(-1.47014 - 3.21916i) q^{13} +(0.471675 - 3.28057i) q^{14} +(-0.654861 + 0.755750i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-1.63053 - 1.04787i) q^{17} +(-0.142315 - 0.989821i) q^{18} +(-5.63886 + 3.62388i) q^{19} +(-0.654861 - 0.755750i) q^{20} +(3.18005 - 0.933748i) q^{21} -4.26852 q^{22} +(-4.79377 - 0.140475i) q^{23} +1.00000 q^{24} +(-0.959493 + 0.281733i) q^{25} +(2.31753 + 2.67458i) q^{26} +(0.841254 - 0.540641i) q^{27} +(0.471675 + 3.28057i) q^{28} +(5.55566 + 3.57041i) q^{29} +(0.415415 - 0.909632i) q^{30} +(-3.67482 + 4.24096i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(-1.77321 - 3.88279i) q^{33} +(1.85970 + 0.546057i) q^{34} +(3.18005 + 0.933748i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-1.32433 + 9.21089i) q^{37} +(4.38949 - 5.06574i) q^{38} +(-1.47014 + 3.21916i) q^{39} +(0.841254 + 0.540641i) q^{40} +(0.502543 + 3.49527i) q^{41} +(-2.78817 + 1.79185i) q^{42} +(2.71793 + 3.13666i) q^{43} +(4.09562 - 1.20258i) q^{44} +1.00000 q^{45} +(4.63917 - 1.21578i) q^{46} +11.1457 q^{47} +(-0.959493 + 0.281733i) q^{48} +(-2.60938 - 3.01138i) q^{49} +(0.841254 - 0.540641i) q^{50} +(0.275836 + 1.91848i) q^{51} +(-2.97717 - 1.91331i) q^{52} +(-1.98060 + 4.33692i) q^{53} +(-0.654861 + 0.755750i) q^{54} +(0.607474 - 4.22508i) q^{55} +(-1.37681 - 3.01480i) q^{56} +(6.43142 + 1.88843i) q^{57} +(-6.33652 - 1.86057i) q^{58} +(2.90537 + 6.36187i) q^{59} +(-0.142315 + 0.989821i) q^{60} +(1.09537 - 1.26412i) q^{61} +(2.33114 - 5.10449i) q^{62} +(-2.78817 - 1.79185i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-2.97717 + 1.91331i) q^{65} +(2.79529 + 3.22594i) q^{66} +(-15.0956 + 4.43247i) q^{67} -1.93821 q^{68} +(3.03309 + 3.71488i) q^{69} -3.31431 q^{70} +(4.06919 - 1.19482i) q^{71} +(-0.654861 - 0.755750i) q^{72} +(-8.31387 + 5.34300i) q^{73} +(-1.32433 - 9.21089i) q^{74} +(0.841254 + 0.540641i) q^{75} +(-2.78450 + 6.09720i) q^{76} +(-9.26445 + 10.6917i) q^{77} +(0.503648 - 3.50295i) q^{78} +(2.80003 + 6.13120i) q^{79} +(-0.959493 - 0.281733i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-1.46692 - 3.21210i) q^{82} +(-1.30743 + 9.09336i) q^{83} +(2.17041 - 2.50479i) q^{84} +(-0.805161 + 1.76306i) q^{85} +(-3.49153 - 2.24387i) q^{86} +(-0.939852 - 6.53681i) q^{87} +(-3.59091 + 2.30774i) q^{88} +(-9.44270 - 10.8975i) q^{89} +(-0.959493 + 0.281733i) q^{90} +11.7292 q^{91} +(-4.10873 + 2.47353i) q^{92} +5.61160 q^{93} +(-10.6942 + 3.14010i) q^{94} +(4.38949 + 5.06574i) q^{95} +(0.841254 - 0.540641i) q^{96} +(-2.63607 - 18.3343i) q^{97} +(3.35209 + 2.15425i) q^{98} +(-1.77321 + 3.88279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{11}\right)$

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 $

$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$4$	0.841254	−	0.540641i	0.420627	−	0.270320i
$5$	−0.142315	−	0.989821i	−0.0636451	−	0.442662i
$5$	−0.142315	−	0.989821i	−0.0636451	−	0.442662i
$6$	0.841254	+	0.540641i	0.343440	+	0.220716i
$7$	−1.37681	+	3.01480i	−0.520386	+	1.13949i	0.448907	+	0.893579i	$0.351814\pi$
$7$	−1.37681	+	3.01480i	−0.520386	+	1.13949i	−0.969293	+	0.245909i	$0.920914\pi$
$8$	−0.654861	+	0.755750i	−0.231528	+	0.267198i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	0.415415	+	0.909632i	0.131366	+	0.287651i
$11$	4.09562	+	1.20258i	1.23488	+	0.362592i	0.833088	−	0.553141i	$-0.186571\pi$
$11$	4.09562	+	1.20258i	1.23488	+	0.362592i	0.401788	+	0.915733i	$0.368389\pi$
$12$	−0.959493	−	0.281733i	−0.276982	−	0.0813292i
$13$	−1.47014	−	3.21916i	−0.407744	−	0.892835i	−0.996426	−	0.0844704i	$-0.973080\pi$
$13$	−1.47014	−	3.21916i	−0.407744	−	0.892835i	0.588682	−	0.808365i	$-0.299647\pi$
$14$	0.471675	−	3.28057i	0.126060	−	0.876770i
$15$	−0.654861	+	0.755750i	−0.169084	+	0.195134i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	−1.63053	−	1.04787i	−0.395460	−	0.254147i	0.327765	−	0.944759i	$-0.393705\pi$
$17$	−1.63053	−	1.04787i	−0.395460	−	0.254147i	−0.723225	+	0.690612i	$0.757341\pi$
$18$	−0.142315	−	0.989821i	−0.0335439	−	0.233303i
$19$	−5.63886	+	3.62388i	−1.29364	+	0.831375i	−0.992505	−	0.122205i	$-0.961003\pi$
$19$	−5.63886	+	3.62388i	−1.29364	+	0.831375i	−0.301139	+	0.953580i	$0.597367\pi$
$20$	−0.654861	−	0.755750i	−0.146431	−	0.168991i
$21$	3.18005	−	0.933748i	0.693945	−	0.203761i
$22$	−4.26852			−0.910053
$23$	−4.79377	−	0.140475i	−0.999571	−	0.0292910i
$23$	−4.79377	−	0.140475i	−0.999571	−	0.0292910i
$24$	1.00000			0.204124
$25$	−0.959493	+	0.281733i	−0.191899	+	0.0563465i
$26$	2.31753	+	2.67458i	0.454506	+	0.524528i
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$	0.471675	+	3.28057i	0.0891382	+	0.619970i
$29$	5.55566	+	3.57041i	1.03166	+	0.663008i	0.942911	−	0.333046i	$-0.108076\pi$
$29$	5.55566	+	3.57041i	1.03166	+	0.663008i	0.0887502	+	0.996054i	$0.471713\pi$
$30$	0.415415	−	0.909632i	0.0758441	−	0.166075i
$31$	−3.67482	+	4.24096i	−0.660017	+	0.761700i	−0.982780	−	0.184780i	$-0.940843\pi$
$31$	−3.67482	+	4.24096i	−0.660017	+	0.761700i	0.322763	+	0.946480i	$0.395388\pi$
$32$	−0.142315	+	0.989821i	−0.0251579	+	0.174977i
$33$	−1.77321	−	3.88279i	−0.308676	−	0.675906i
$34$	1.85970	+	0.546057i	0.318936	+	0.0936479i
$35$	3.18005	+	0.933748i	0.537527	+	0.157832i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	−1.32433	+	9.21089i	−0.217718	+	1.51426i	0.528715	+	0.848800i	$0.322674\pi$
$37$	−1.32433	+	9.21089i	−0.217718	+	1.51426i	−0.746432	+	0.665461i	$0.768235\pi$
$38$	4.38949	−	5.06574i	0.712069	−	0.821771i
$39$	−1.47014	+	3.21916i	−0.235411	+	0.515479i
$40$	0.841254	+	0.540641i	0.133014	+	0.0854828i
$41$	0.502543	+	3.49527i	0.0784841	+	0.545869i	0.990690	+	0.136137i	$0.0434687\pi$
$41$	0.502543	+	3.49527i	0.0784841	+	0.545869i	−0.912206	+	0.409732i	$0.865622\pi$
$42$	−2.78817	+	1.79185i	−0.430224	+	0.276488i
$43$	2.71793	+	3.13666i	0.414480	+	0.478336i	0.924148	−	0.382036i	$-0.124777\pi$
$43$	2.71793	+	3.13666i	0.414480	+	0.478336i	−0.509667	+	0.860372i	$0.670231\pi$
$44$	4.09562	−	1.20258i	0.617438	−	0.181296i
$45$	1.00000			0.149071
$46$	4.63917	−	1.21578i	0.684008	−	0.179257i
$47$	11.1457			1.62577			0.812883	−	0.582427i	$-0.197897\pi$
$47$	11.1457			1.62577			0.812883	+	0.582427i	$0.197897\pi$
$48$	−0.959493	+	0.281733i	−0.138491	+	0.0406646i
$49$	−2.60938	−	3.01138i	−0.372768	−	0.430198i
$50$	0.841254	−	0.540641i	0.118971	−	0.0764582i
$51$	0.275836	+	1.91848i	0.0386248	+	0.268641i
$52$	−2.97717	−	1.91331i	−0.412860	−	0.265329i
$53$	−1.98060	+	4.33692i	−0.272057	+	0.595722i	−0.995510	−	0.0946515i	$-0.969826\pi$
$53$	−1.98060	+	4.33692i	−0.272057	+	0.595722i	0.723454	+	0.690373i	$0.242554\pi$
$54$	−0.654861	+	0.755750i	−0.0891153	+	0.102844i
$55$	0.607474	−	4.22508i	0.0819118	−	0.569709i
$56$	−1.37681	−	3.01480i	−0.183984	−	0.402870i
$57$	6.43142	+	1.88843i	0.851862	+	0.250129i
$58$	−6.33652	−	1.86057i	−0.832026	−	0.244305i
$59$	2.90537	+	6.36187i	0.378247	+	0.828245i	0.999020	+	0.0442548i	$0.0140914\pi$
$59$	2.90537	+	6.36187i	0.378247	+	0.828245i	−0.620774	+	0.783990i	$0.713181\pi$
$60$	−0.142315	+	0.989821i	−0.0183728	+	0.127785i
$61$	1.09537	−	1.26412i	0.140247	−	0.161854i	−0.681281	−	0.732022i	$-0.738577\pi$
$61$	1.09537	−	1.26412i	0.140247	−	0.161854i	0.821528	+	0.570168i	$0.193122\pi$
$62$	2.33114	−	5.10449i	0.296055	−	0.648271i
$63$	−2.78817	−	1.79185i	−0.351277	−	0.225752i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	−2.97717	+	1.91331i	−0.369273	+	0.237317i
$66$	2.79529	+	3.22594i	0.344076	+	0.397085i
$67$	−15.0956	+	4.43247i	−1.84422	+	0.541512i	−0.844235	+	0.535973i	$0.819945\pi$
$67$	−15.0956	+	4.43247i	−1.84422	+	0.541512i	−0.999985	+	0.00553908i	$0.998237\pi$
$68$	−1.93821			−0.235042
$69$	3.03309	+	3.71488i	0.365141	+	0.447219i
$70$	−3.31431			−0.396135
$71$	4.06919	−	1.19482i	0.482924	−	0.141799i	−0.0312032	−	0.999513i	$-0.509934\pi$
$71$	4.06919	−	1.19482i	0.482924	−	0.141799i	0.514128	+	0.857714i	$0.328116\pi$
$72$	−0.654861	−	0.755750i	−0.0771761	−	0.0890659i
$73$	−8.31387	+	5.34300i	−0.973065	+	0.625351i	−0.927584	−	0.373614i	$-0.878118\pi$
$73$	−8.31387	+	5.34300i	−0.973065	+	0.625351i	−0.0454808	+	0.998965i	$0.514482\pi$
$74$	−1.32433	−	9.21089i	−0.153950	−	1.07074i
$75$	0.841254	+	0.540641i	0.0971396	+	0.0624278i
$76$	−2.78450	+	6.09720i	−0.319404	+	0.699397i
$77$	−9.26445	+	10.6917i	−1.05578	+	1.21844i
$78$	0.503648	−	3.50295i	0.0570270	−	0.396631i
$79$	2.80003	+	6.13120i	0.315028	+	0.689814i	0.999220	−	0.0394874i	$-0.0125725\pi$
$79$	2.80003	+	6.13120i	0.315028	+	0.689814i	−0.684193	+	0.729301i	$0.739845\pi$
$80$	−0.959493	−	0.281733i	−0.107275	−	0.0314987i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−1.46692	−	3.21210i	−0.161994	−	0.354717i
$83$	−1.30743	+	9.09336i	−0.143509	+	0.998125i	0.783046	+	0.621964i	$0.213665\pi$
$83$	−1.30743	+	9.09336i	−0.143509	+	0.998125i	−0.926554	+	0.376161i	$0.877244\pi$
$84$	2.17041	−	2.50479i	0.236811	−	0.273295i
$85$	−0.805161	+	1.76306i	−0.0873320	+	0.191230i
$86$	−3.49153	−	2.24387i	−0.376502	−	0.241963i
$87$	−0.939852	−	6.53681i	−0.100763	−	0.700820i
$88$	−3.59091	+	2.30774i	−0.382792	+	0.246006i
$89$	−9.44270	−	10.8975i	−1.00092	−	1.15513i	−0.987881	−	0.155213i	$-0.950393\pi$
$89$	−9.44270	−	10.8975i	−1.00092	−	1.15513i	−0.0130434	−	0.999915i	$-0.504152\pi$
$90$	−0.959493	+	0.281733i	−0.101139	+	0.0296972i
$91$	11.7292			1.22956
$92$	−4.10873	+	2.47353i	−0.428364	+	0.257884i
$93$	5.61160			0.581896
$94$	−10.6942	+	3.14010i	−1.10302	+	0.323877i
$95$	4.38949	+	5.06574i	0.450352	+	0.519734i
$96$	0.841254	−	0.540641i	0.0858601	−	0.0551789i
$97$	−2.63607	−	18.3343i	−0.267653	−	1.86156i	−0.470562	−	0.882367i	$-0.655949\pi$
$97$	−2.63607	−	18.3343i	−0.267653	−	1.86156i	0.202909	−	0.979198i	$-0.434960\pi$
$98$	3.35209	+	2.15425i	0.338612	+	0.217613i
$99$	−1.77321	+	3.88279i	−0.178214	+	0.390235i
$100$	−0.654861	+	0.755750i	−0.0654861	+	0.0755750i
$101$	0.122363	−	0.851052i	0.0121756	−	0.0846829i	−0.982828	−	0.184526i	$-0.940925\pi$
$101$	0.122363	−	0.851052i	0.0121756	−	0.0846829i	0.995003	+	0.0998431i	$0.0318341\pi$
$102$	−0.805161	−	1.76306i	−0.0797228	−	0.174569i
$103$	7.37177	+	2.16455i	0.726362	+	0.213279i	0.623952	−	0.781463i	$-0.285526\pi$
$103$	7.37177	+	2.16455i	0.726362	+	0.213279i	0.102411	+	0.994742i	$0.467344\pi$
$104$	3.39562	+	0.997044i	0.332968	+	0.0977682i
$105$	−1.37681	−	3.01480i	−0.134363	−	0.294214i
$106$	0.678525	−	4.71924i	0.0659042	−	0.458373i
$107$	0.147621	−	0.170364i	0.0142710	−	0.0164697i	−0.748569	−	0.663057i	$-0.769259\pi$
$107$	0.147621	−	0.170364i	0.0142710	−	0.0164697i	0.762840	+	0.646587i	$0.223804\pi$
$108$	0.415415	−	0.909632i	0.0399733	−	0.0875294i
$109$	−12.6043	−	8.10026i	−1.20727	−	0.775865i	−0.227070	−	0.973879i	$-0.572914\pi$
$109$	−12.6043	−	8.10026i	−1.20727	−	0.775865i	−0.980199	+	0.198014i	$0.936551\pi$
$110$	0.607474	+	4.22508i	0.0579204	+	0.402845i
$111$	7.82837	−	5.03099i	0.743036	−	0.477521i
$112$	2.17041	+	2.50479i	0.205084	+	0.236680i
$113$	2.74248	−	0.805266i	0.257991	−	0.0757531i	−0.150179	−	0.988659i	$-0.547985\pi$
$113$	2.74248	−	0.805266i	0.257991	−	0.0757531i	0.408170	+	0.912906i	$0.366167\pi$
$114$	−6.70293			−0.627787
$115$	0.543180	+	4.76497i	0.0506518	+	0.444336i
$116$	6.60403			0.613169
$117$	3.39562	−	0.997044i	0.313925	−	0.0921767i
$118$	−4.58003	−	5.28563i	−0.421626	−	0.486582i
$119$	5.40406	−	3.47298i	0.495389	−	0.318367i
$120$	−0.142315	−	0.989821i	−0.0129915	−	0.0903579i
$121$	6.07410	+	3.90359i	0.552191	+	0.354872i
$122$	−0.694852	+	1.52151i	−0.0629090	+	0.137751i
$123$	2.31245	−	2.66871i	0.208507	−	0.240629i
$124$	−0.798614	+	5.55448i	−0.0717176	+	0.498807i
$125$	0.415415	+	0.909632i	0.0371558	+	0.0813600i
$126$	3.18005	+	0.933748i	0.283302	+	0.0831849i
$127$	14.8763	+	4.36808i	1.32006	+	0.387604i	0.864514	−	0.502608i	$-0.167626\pi$
$127$	14.8763	+	4.36808i	1.32006	+	0.387604i	0.455545	+	0.890213i	$0.349444\pi$
$128$	0.415415	+	0.909632i	0.0367178	+	0.0804009i
$129$	0.590663	−	4.10815i	0.0520049	−	0.361702i
$130$	2.31753	−	2.67458i	0.203261	−	0.234576i
$131$	4.14112	−	9.06779i	0.361811	−	0.792256i	−0.637943	−	0.770084i	$-0.720214\pi$
$131$	4.14112	−	9.06779i	0.361811	−	0.792256i	0.999754	−	0.0221725i	$-0.00705831\pi$
$132$	−3.59091	−	2.30774i	−0.312549	−	0.200863i
$133$	−3.16161	−	21.9895i	−0.274146	−	1.90673i
$134$	13.2353	−	8.50584i	1.14336	−	0.734793i
$135$	−0.654861	−	0.755750i	−0.0563614	−	0.0650446i
$136$	1.85970	−	0.546057i	0.159468	−	0.0468240i
$137$	−12.0986			−1.03365			−0.516826	−	0.856090i	$-0.672887\pi$
$137$	−12.0986			−1.03365			−0.516826	+	0.856090i	$0.672887\pi$
$138$	−3.95683	−	2.70988i	−0.336828	−	0.230681i
$139$	3.44900			0.292541			0.146270	−	0.989245i	$-0.453273\pi$
$139$	3.44900			0.292541			0.146270	+	0.989245i	$0.453273\pi$
$140$	3.18005	−	0.933748i	0.268764	−	0.0789161i
$141$	−7.29887	−	8.42335i	−0.614676	−	0.709374i
$142$	−3.56774	+	2.29285i	−0.299398	+	0.192412i
$143$	−2.14984	−	14.9524i	−0.179778	−	1.25039i
$144$	0.841254	+	0.540641i	0.0701045	+	0.0450534i
$145$	2.74341	−	6.00724i	0.227828	−	0.498874i
$146$	6.47180	−	7.46886i	0.535610	−	0.618127i
$147$	−0.567072	+	3.94407i	−0.0467713	+	0.325302i
$148$	3.86569	+	8.46468i	0.317758	+	0.695792i
$149$	−20.9690	−	6.15706i	−1.71785	−	0.504406i	−0.733359	−	0.679841i	$-0.762049\pi$
$149$	−20.9690	−	6.15706i	−1.71785	−	0.504406i	−0.984491	+	0.175435i	$0.943867\pi$
$150$	−0.959493	−	0.281733i	−0.0783423	−	0.0230034i
$151$	7.33850	+	16.0691i	0.597199	+	1.30768i	0.930993	+	0.365037i	$0.118944\pi$
$151$	7.33850	+	16.0691i	0.597199	+	1.30768i	−0.333794	+	0.942646i	$0.608329\pi$
$152$	0.953927	−	6.63471i	0.0773737	−	0.538146i
$153$	1.26926	−	1.46480i	0.102613	−	0.118422i
$154$	5.87696	−	12.8687i	0.473579	−	1.03699i
$155$	4.72078	+	3.03386i	0.379182	+	0.243685i
$156$	0.503648	+	3.50295i	0.0403241	+	0.280461i
$157$	4.45741	−	2.86460i	0.355740	−	0.228620i	−0.350548	−	0.936545i	$-0.614005\pi$
$157$	4.45741	−	2.86460i	0.355740	−	0.228620i	0.706288	+	0.707924i	$0.250368\pi$
$158$	−4.41396	−	5.09399i	−0.351156	−	0.405256i
$159$	4.57464	−	1.34324i	0.362793	−	0.106526i
$160$	1.00000			0.0790569
$161$	7.02363	−	14.2589i	0.553540	−	1.12376i
$162$	1.00000			0.0785674
$163$	−14.4322	+	4.23769i	−1.13042	+	0.331921i	−0.792873	−	0.609387i	$-0.791416\pi$
$163$	−14.4322	+	4.23769i	−1.13042	+	0.331921i	−0.337548	+	0.941308i	$0.609597\pi$
$164$	2.31245	+	2.66871i	0.180572	+	0.208391i
$165$	−3.59091	+	2.30774i	−0.279552	+	0.179657i
$166$	−1.30743	−	9.09336i	−0.101476	−	0.705781i
$167$	−7.52328	−	4.83492i	−0.582169	−	0.374137i	0.216161	−	0.976358i	$-0.430646\pi$
$167$	−7.52328	−	4.83492i	−0.582169	−	0.374137i	−0.798330	+	0.602221i	$0.794283\pi$
$168$	−1.37681	+	3.01480i	−0.106223	+	0.232597i
$169$	0.311497	−	0.359487i	0.0239613	−	0.0276528i
$170$	0.275836	−	1.91848i	0.0211556	−	0.147141i
$171$	−2.78450	−	6.09720i	−0.212936	−	0.466265i
$172$	3.98227	+	1.16930i	0.303646	+	0.0891584i
$173$	15.5942	+	4.57887i	1.18560	+	0.348125i	0.814332	−	0.580399i	$-0.197103\pi$
$173$	15.5942	+	4.57887i	1.18560	+	0.348125i	0.371273	+	0.928524i	$0.378922\pi$
$174$	2.74341	+	6.00724i	0.207978	+	0.455408i
$175$	0.471675	−	3.28057i	0.0356553	−	0.247988i
$176$	2.79529	−	3.22594i	0.210703	−	0.243164i
$177$	2.90537	−	6.36187i	0.218381	−	0.478187i
$178$	12.1304	+	7.79572i	0.909210	+	0.584314i
$179$	−1.41262	−	9.82497i	−0.105584	−	0.734352i	−0.971992	−	0.235015i	$-0.924486\pi$
$179$	−1.41262	−	9.82497i	−0.105584	−	0.734352i	0.866408	−	0.499337i	$-0.166423\pi$
$180$	0.841254	−	0.540641i	0.0627033	−	0.0402970i
$181$	12.8709	+	14.8538i	0.956687	+	1.10408i	0.994494	+	0.104790i	$0.0334171\pi$
$181$	12.8709	+	14.8538i	0.956687	+	1.10408i	−0.0378076	+	0.999285i	$0.512037\pi$
$182$	−11.2541	+	3.30451i	−0.834211	+	0.244947i
$183$	−1.67267			−0.123647
$184$	3.24542	−	3.53090i	0.239255	−	0.260301i
$185$	9.30561			0.684162
$186$	−5.38429	+	1.58097i	−0.394795	+	0.115922i
$187$	−5.41785	−	6.25254i	−0.396193	−	0.457231i
$188$	9.37635	−	6.02582i	0.683841	−	0.439478i
$189$	0.471675	+	3.28057i	0.0343093	+	0.238627i
$190$	−5.63886	−	3.62388i	−0.409086	−	0.262904i
$191$	2.28035	−	4.99327i	0.165000	−	0.361300i	−0.809013	−	0.587791i	$-0.799998\pi$
$191$	2.28035	−	4.99327i	0.165000	−	0.361300i	0.974013	+	0.226490i	$0.0727252\pi$
$192$	−0.654861	+	0.755750i	−0.0472605	+	0.0545415i
$193$	−2.21096	+	15.3775i	−0.159148	+	1.10690i	0.741060	+	0.671439i	$0.234323\pi$
$193$	−2.21096	+	15.3775i	−0.159148	+	1.10690i	−0.900208	+	0.435460i	$0.856586\pi$
$194$	7.69466	+	16.8489i	0.552444	+	1.20968i
$195$	3.39562	+	0.997044i	0.243165	+	0.0713998i
$196$	−3.82323	−	1.12260i	−0.273088	−	0.0801858i
$197$	−2.49780	−	5.46942i	−0.177961	−	0.389680i	0.799539	−	0.600614i	$-0.205077\pi$
$197$	−2.49780	−	5.46942i	−0.177961	−	0.389680i	−0.977500	+	0.210933i	$0.932350\pi$
$198$	0.607474	−	4.22508i	0.0431713	−	0.300263i
$199$	−0.193573	+	0.223396i	−0.0137221	+	0.0158361i	−0.762569	−	0.646907i	$-0.776062\pi$
$199$	−0.193573	+	0.223396i	−0.0137221	+	0.0158361i	0.748847	+	0.662743i	$0.230608\pi$
$200$	0.415415	−	0.909632i	0.0293743	−	0.0643207i
$201$	13.2353	+	8.50584i	0.933549	+	0.599956i
$202$	0.122363	+	0.851052i	0.00860942	+	0.0598798i
$203$	−18.4132	+	11.8334i	−1.29235	+	0.830544i
$204$	1.26926	+	1.46480i	0.0888658	+	0.102557i
$205$	3.38817	−	0.994856i	0.236640	−	0.0694838i
$206$	−7.68299			−0.535299
$207$	0.821270	−	4.72499i	0.0570822	−	0.328409i
$208$	−3.53897			−0.245384
$209$	−27.4527	+	8.06083i	−1.89894	+	0.557579i
$210$	2.17041	+	2.50479i	0.149772	+	0.172847i
$211$	1.24580	−	0.800630i	0.0857647	−	0.0551176i	−0.497056	−	0.867719i	$-0.665586\pi$
$211$	1.24580	−	0.800630i	0.0857647	−	0.0551176i	0.582820	+	0.812601i	$0.301949\pi$
$212$	0.678525	+	4.71924i	0.0466013	+	0.324119i
$213$	−3.56774	−	2.29285i	−0.244458	−	0.157103i
$214$	−0.0936442	+	0.205052i	−0.00640139	+	0.0140171i
$215$	2.71793	−	3.13666i	0.185361	−	0.213918i
$216$	−0.142315	+	0.989821i	−0.00968330	+	0.0673488i
$217$	−7.72612	−	16.9179i	−0.524483	−	1.14846i
$218$	14.3758	+	4.22112i	0.973652	+	0.285890i
$219$	9.48240	+	2.78428i	0.640761	+	0.188144i
$220$	−1.77321	−	3.88279i	−0.119550	−	0.261777i
$221$	−0.976176	+	6.78945i	−0.0656647	+	0.456708i
$222$	−6.09388	+	7.03271i	−0.408994	+	0.472004i
$223$	7.09048	−	15.5260i	0.474813	−	1.03970i	−0.509044	−	0.860741i	$-0.670001\pi$
$223$	7.09048	−	15.5260i	0.474813	−	1.03970i	0.983857	−	0.178956i	$-0.0572719\pi$
$224$	−2.78817	−	1.79185i	−0.186293	−	0.119723i
$225$	−0.142315	−	0.989821i	−0.00948766	−	0.0659881i
$226$	−2.40452	+	1.54529i	−0.159947	+	0.102791i
$227$	−9.09106	−	10.4916i	−0.603395	−	0.696355i	0.369071	−	0.929401i	$-0.379676\pi$
$227$	−9.09106	−	10.4916i	−0.603395	−	0.696355i	−0.972466	+	0.233046i	$0.925131\pi$
$228$	6.43142	−	1.88843i	0.425931	−	0.125065i
$229$	−17.2511			−1.13999			−0.569993	−	0.821650i	$-0.693054\pi$
$229$	−17.2511			−1.13999			−0.569993	+	0.821650i	$0.693054\pi$
$230$	−1.86363	−	4.41893i	−0.122884	−	0.291375i
$231$	14.1472			0.930818
$232$	−6.33652	+	1.86057i	−0.416013	+	0.122152i
$233$	−2.94776	−	3.40189i	−0.193114	−	0.222865i	0.650932	−	0.759136i	$-0.274378\pi$
$233$	−2.94776	−	3.40189i	−0.193114	−	0.222865i	−0.844046	+	0.536270i	$0.819833\pi$
$234$	−2.97717	+	1.91331i	−0.194624	+	0.125077i
$235$	−1.58620	−	11.0322i	−0.103472	−	0.719664i
$236$	5.88364	+	3.78118i	0.382992	+	0.246134i
$237$	2.80003	−	6.13120i	0.181881	−	0.398264i
$238$	−4.20671	+	4.85480i	−0.272680	+	0.314690i
$239$	−0.438586	+	3.05044i	−0.0283698	+	0.197316i	−0.999077	−	0.0429480i	$-0.986325\pi$
$239$	−0.438586	+	3.05044i	−0.0283698	+	0.197316i	0.970708	+	0.240264i	$0.0772341\pi$
$240$	0.415415	+	0.909632i	0.0268149	+	0.0587165i
$241$	19.1215	+	5.61459i	1.23173	+	0.361668i	0.831901	−	0.554924i	$-0.187253\pi$
$241$	19.1215	+	5.61459i	1.23173	+	0.361668i	0.399825	+	0.916591i	$0.369071\pi$
$242$	−6.92783	−	2.03419i	−0.445338	−	0.130763i
$243$	0.415415	+	0.909632i	0.0266489	+	0.0583529i
$244$	0.238046	−	1.65564i	0.0152393	−	0.105992i
$245$	−2.60938	+	3.01138i	−0.166707	+	0.192390i
$246$	−1.46692	+	3.21210i	−0.0935272	+	0.204796i
$247$	19.9558	+	12.8248i	1.26976	+	0.816023i
$248$	−0.798614	−	5.55448i	−0.0507120	−	0.352710i
$249$	7.72848	−	4.96679i	0.489773	−	0.314758i
$250$	−0.654861	−	0.755750i	−0.0414170	−	0.0477978i
$251$	−6.19845	+	1.82003i	−0.391243	+	0.114879i	−0.471436	−	0.881900i	$-0.656264\pi$
$251$	−6.19845	+	1.82003i	−0.391243	+	0.114879i	0.0801937	+	0.996779i	$0.474446\pi$
$252$	−3.31431			−0.208782
$253$	−19.4645	−	6.34024i	−1.22373	−	0.398607i
$254$	−15.5043			−0.972829
$255$	1.85970	−	0.546057i	0.116459	−	0.0341954i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	16.1965	−	10.4088i	1.01031	−	0.649286i	0.0728353	−	0.997344i	$-0.476795\pi$
$257$	16.1965	−	10.4088i	1.01031	−	0.649286i	0.937473	+	0.348058i	$0.113159\pi$
$258$	0.590663	+	4.10815i	0.0367731	+	0.255762i
$259$	−25.9456	−	16.6742i	−1.61218	−	1.03609i
$260$	−1.47014	+	3.21916i	−0.0911744	+	0.199644i
$261$	−4.32472	+	4.99099i	−0.267693	+	0.308935i
$262$	−1.41868	+	9.86717i	−0.0876466	+	0.609596i
$263$	9.26861	+	20.2954i	0.571527	+	1.25147i	0.945981	+	0.324223i	$0.105103\pi$
$263$	9.26861	+	20.2954i	0.571527	+	1.25147i	−0.374454	+	0.927246i	$0.622170\pi$
$264$	4.09562	+	1.20258i	0.252068	+	0.0740138i
$265$	4.57464	+	1.34324i	0.281018	+	0.0825144i
$266$	9.22868	+	20.2080i	0.565847	+	1.23903i
$267$	−2.05210	+	14.2726i	−0.125586	+	0.873471i
$268$	−10.3028	+	11.8901i	−0.629347	+	0.726305i
$269$	−4.93070	+	10.7967i	−0.300630	+	0.658288i	−0.998309	−	0.0581223i	$-0.981489\pi$
$269$	−4.93070	+	10.7967i	−0.300630	+	0.658288i	0.697680	+	0.716410i	$0.254216\pi$
$270$	0.841254	+	0.540641i	0.0511971	+	0.0329024i
$271$	0.126793	+	0.881862i	0.00770210	+	0.0535693i	0.993310	−	0.115478i	$-0.0368400\pi$
$271$	0.126793	+	0.881862i	0.00770210	+	0.0535693i	−0.985608	+	0.169047i	$0.945931\pi$
$272$	−1.63053	+	1.04787i	−0.0988651	+	0.0635367i
$273$	−7.68102	−	8.86437i	−0.464877	−	0.536496i
$274$	11.6085	−	3.40857i	0.701296	−	0.205919i
$275$	−4.26852			−0.257402
$276$	4.56002	+	1.48535i	0.274481	+	0.0894074i
$277$	11.0736			0.665351			0.332676	−	0.943041i	$-0.392049\pi$
$277$	11.0736			0.665351			0.332676	+	0.943041i	$0.392049\pi$
$278$	−3.30929	+	0.971696i	−0.198478	+	0.0582785i
$279$	−3.67482	−	4.24096i	−0.220006	−	0.253900i
$280$	−2.78817	+	1.79185i	−0.166625	+	0.107084i
$281$	−1.93387	−	13.4503i	−0.115365	−	0.802380i	−0.962554	−	0.271089i	$-0.912616\pi$
$281$	−1.93387	−	13.4503i	−0.115365	−	0.802380i	0.847189	−	0.531291i	$-0.178293\pi$
$282$	9.37635	+	6.02582i	0.558354	+	0.358832i
$283$	11.1431	−	24.4000i	0.662389	−	1.45043i	−0.217891	−	0.975973i	$-0.569918\pi$
$283$	11.1431	−	24.4000i	0.662389	−	1.45043i	0.880279	−	0.474456i	$-0.157355\pi$
$284$	2.77725	−	3.20512i	0.164800	−	0.190189i
$285$	0.953927	−	6.63471i	0.0565057	−	0.393006i
$286$	6.27534	+	13.7411i	0.371069	+	0.812527i
$287$	−11.2294	−	3.29726i	−0.662853	−	0.194631i
$288$	−0.959493	−	0.281733i	−0.0565387	−	0.0166013i
$289$	−5.50148	−	12.0466i	−0.323617	−	0.708622i
$290$	−0.939852	+	6.53681i	−0.0551900	+	0.383855i
$291$	−12.1299	+	13.9986i	−0.711065	+	0.820613i
$292$	−4.10543	+	8.98964i	−0.240252	+	0.526079i
$293$	25.1311	+	16.1508i	1.46818	+	0.943540i	0.998144	+	0.0608913i	$0.0193943\pi$
$293$	25.1311	+	16.1508i	1.46818	+	0.943540i	0.470033	+	0.882649i	$0.344242\pi$
$294$	−0.567072	−	3.94407i	−0.0330723	−	0.230023i
$295$	5.88364	−	3.78118i	0.342559	−	0.220149i
$296$	−6.09388	−	7.03271i	−0.354199	−	0.408768i
$297$	4.09562	−	1.20258i	0.237652	−	0.0697809i
$298$	21.8543			1.26598
$299$	6.59532	+	15.6385i	0.381417	+	0.904395i
$300$	1.00000			0.0577350
$301$	−13.1985	+	3.87542i	−0.760748	+	0.223376i
$302$	−11.5684	−	13.3507i	−0.665688	−	0.768245i
$303$	−0.723313	+	0.464845i	−0.0415533	+	0.0267047i
$304$	0.953927	+	6.63471i	0.0547114	+	0.380526i
$305$	−1.40714	−	0.904314i	−0.0805726	−	0.0517809i
$306$	−0.805161	+	1.76306i	−0.0460280	+	0.100787i
$307$	9.90948	−	11.4361i	0.565564	−	0.652695i	−0.398874	−	0.917006i	$-0.630599\pi$
$307$	9.90948	−	11.4361i	0.565564	−	0.652695i	0.964438	+	0.264310i	$0.0851443\pi$
$308$	−2.01336	+	14.0032i	−0.114722	+	0.797907i
$309$	−3.19163	−	6.98869i	−0.181565	−	0.397573i
$310$	−5.38429	−	1.58097i	−0.305807	−	0.0897931i
$311$	−30.2337	−	8.87742i	−1.71440	−	0.503392i	−0.730619	−	0.682785i	$-0.760769\pi$
$311$	−30.2337	−	8.87742i	−1.71440	−	0.503392i	−0.983778	+	0.179393i	$0.942587\pi$
$312$	−1.47014	−	3.21916i	−0.0832304	−	0.182249i
$313$	0.115527	−	0.803511i	0.00652999	−	0.0454171i	−0.986296	−	0.164986i	$-0.947242\pi$
$313$	0.115527	−	0.803511i	0.00652999	−	0.0454171i	0.992826	+	0.119569i	$0.0381512\pi$
$314$	−3.46980	+	4.00437i	−0.195812	+	0.225979i
$315$	−1.37681	+	3.01480i	−0.0775746	+	0.169865i
$316$	5.67031	+	3.64409i	0.318980	+	0.204996i
$317$	1.69785	+	11.8088i	0.0953608	+	0.663249i	0.980296	+	0.197535i	$0.0632935\pi$
$317$	1.69785	+	11.8088i	0.0953608	+	0.663249i	−0.884935	+	0.465714i	$0.845797\pi$
$318$	−4.01091	+	2.57765i	−0.224920	+	0.144548i
$319$	18.4602	+	21.3042i	1.03357	+	1.19280i
$320$	−0.959493	+	0.281733i	−0.0536373	+	0.0157493i
$321$	−0.225423			−0.0125819
$322$	−2.72194	+	15.6601i	−0.151688	+	0.872701i
$323$	12.9917			0.722877
$324$	−0.959493	+	0.281733i	−0.0533052	+	0.0156518i
$325$	2.31753	+	2.67458i	0.128554	+	0.148359i
$326$	12.6537	−	8.13206i	0.700826	−	0.450393i
$327$	2.13226	+	14.8302i	0.117914	+	0.820112i
$328$	−2.97064	−	1.90912i	−0.164026	−	0.105413i
$329$	−15.3455	+	33.6020i	−0.846027	+	1.85254i
$330$	2.79529	−	3.22594i	0.153876	−	0.177582i
$331$	−2.44124	+	16.9792i	−0.134183	+	0.933263i	0.805836	+	0.592139i	$0.201716\pi$
$331$	−2.44124	+	16.9792i	−0.134183	+	0.933263i	−0.940019	+	0.341123i	$0.889193\pi$
$332$	3.81636	+	8.35667i	0.209450	+	0.458632i
$333$	−8.92866	−	2.62169i	−0.489288	−	0.143668i
$334$	8.58068	+	2.51952i	0.469514	+	0.137862i
$335$	6.53568	+	14.3111i	0.357082	+	0.781901i
$336$	0.471675	−	3.28057i	0.0257320	−	0.178970i
$337$	−4.55753	+	5.25967i	−0.248264	+	0.286512i	−0.866180	−	0.499732i	$-0.833432\pi$
$337$	−4.55753	+	5.25967i	−0.248264	+	0.286512i	0.617916	+	0.786244i	$0.287977\pi$
$338$	−0.197600	+	0.432684i	−0.0107480	+	0.0235349i
$339$	−2.40452	−	1.54529i	−0.130596	−	0.0839289i
$340$	0.275836	+	1.91848i	0.0149593	+	0.104044i
$341$	−20.1508	+	12.9501i	−1.09122	+	0.701288i
$342$	4.38949	+	5.06574i	0.237356	+	0.273924i
$343$	−9.58903	+	2.81559i	−0.517759	+	0.152028i
$344$	−4.15039			−0.223774
$345$	3.24542	−	3.53090i	0.174727	−	0.190097i
$346$	−16.2525			−0.873742
$347$	30.6347	−	8.99515i	1.64455	−	0.482885i	0.677092	−	0.735898i	$-0.263240\pi$
$347$	30.6347	−	8.99515i	1.64455	−	0.482885i	0.967463	+	0.253014i	$0.0814217\pi$
$348$	−4.32472	−	4.99099i	−0.231829	−	0.267545i
$349$	14.0680	−	9.04093i	0.753041	−	0.483950i	−0.106947	−	0.994265i	$-0.534107\pi$
$349$	14.0680	−	9.04093i	0.753041	−	0.483950i	0.859988	+	0.510315i	$0.170471\pi$
$350$	0.471675	+	3.28057i	0.0252121	+	0.175354i
$351$	−2.97717	−	1.91331i	−0.158910	−	0.102125i
$352$	−1.77321	+	3.88279i	−0.0945124	+	0.206953i
$353$	−10.9733	+	12.6639i	−0.584051	+	0.674031i	−0.968471	−	0.249128i	$-0.919856\pi$
$353$	−10.9733	+	12.6639i	−0.584051	+	0.674031i	0.384420	+	0.923158i	$0.374402\pi$
$354$	−0.995335	+	6.92270i	−0.0529014	+	0.367938i
$355$	−1.76177	−	3.85773i	−0.0935050	−	0.204747i
$356$	−13.8353	−	4.06242i	−0.733270	−	0.215308i
$357$	−6.16361	−	1.80980i	−0.326213	−	0.0957847i
$358$	4.12341	+	9.02901i	0.217929	+	0.477198i
$359$	−3.69844	+	25.7232i	−0.195196	+	1.35762i	0.622794	+	0.782386i	$0.285998\pi$
$359$	−3.69844	+	25.7232i	−0.195196	+	1.35762i	−0.817990	+	0.575233i	$0.804912\pi$
$360$	−0.654861	+	0.755750i	−0.0345142	+	0.0398315i
$361$	10.7714	−	23.5861i	0.566917	−	1.24137i
$362$	−16.5343	−	10.6260i	−0.869026	−	0.558489i
$363$	−1.02756	−	7.14681i	−0.0539327	−	0.375110i
$364$	9.86727	−	6.34131i	0.517185	−	0.332375i
$365$	6.47180	+	7.46886i	0.338750	+	0.390938i
$366$	1.60492	−	0.471246i	0.0838903	−	0.0246324i
$367$	−32.6264			−1.70309			−0.851543	−	0.524285i	$-0.824333\pi$
$367$	−32.6264			−1.70309			−0.851543	+	0.524285i	$0.824333\pi$
$368$	−2.11919	+	4.30221i	−0.110470	+	0.224268i
$369$	−3.53121			−0.183827
$370$	−8.92866	+	2.62169i	−0.464179	+	0.136295i
$371$	−10.3480	−	11.9423i	−0.537242	−	0.620011i
$372$	4.72078	−	3.03386i	0.244761	−	0.157298i
$373$	2.65996	+	18.5004i	0.137728	+	0.957916i	0.935089	+	0.354414i	$0.115319\pi$
$373$	2.65996	+	18.5004i	0.137728	+	0.957916i	−0.797361	+	0.603502i	$0.793771\pi$
$374$	6.95994	+	4.47288i	0.359890	+	0.231287i
$375$	0.415415	−	0.909632i	0.0214519	−	0.0469732i
$376$	−7.29887	+	8.42335i	−0.376411	+	0.434401i
$377$	3.32611	−	23.1336i	0.171303	−	1.19144i
$378$	−1.37681	−	3.01480i	−0.0708156	−	0.155065i
$379$	−9.25596	−	2.71779i	−0.475446	−	0.139604i	0.0352253	−	0.999379i	$-0.488785\pi$
$379$	−9.25596	−	2.71779i	−0.475446	−	0.139604i	−0.510672	+	0.859776i	$0.670603\pi$
$380$	6.43142	+	1.88843i	0.329925	+	0.0968746i
$381$	−6.44074	−	14.1033i	−0.329969	−	0.722531i
$382$	−0.781213	+	5.43345i	−0.0399703	+	0.278000i
$383$	10.9349	−	12.6196i	0.558748	−	0.644830i	−0.404151	−	0.914692i	$-0.632433\pi$
$383$	10.9349	−	12.6196i	0.558748	−	0.644830i	0.962899	+	0.269863i	$0.0869783\pi$
$384$	0.415415	−	0.909632i	0.0211991	−	0.0464195i
$385$	11.9014	+	7.64855i	0.606551	+	0.389806i
$386$	−2.21096	−	15.3775i	−0.112535	−	0.782696i
$387$	−3.49153	+	2.24387i	−0.177485	+	0.114062i
$388$	−12.1299	−	13.9986i	−0.615801	−	0.710672i
$389$	13.1831	−	3.87090i	0.668408	−	0.196262i	0.0701141	−	0.997539i	$-0.477664\pi$
$389$	13.1831	−	3.87090i	0.668408	−	0.196262i	0.598294	+	0.801277i	$0.295845\pi$
$390$	−3.53897			−0.179203
$391$	7.66917	+	5.25232i	0.387847	+	0.265621i
$392$	3.98463			0.201254
$393$	−9.56483	+	2.80849i	−0.482482	+	0.141669i
$394$	3.93754	+	4.54416i	0.198370	+	0.228932i
$395$	5.67031	−	3.64409i	0.285304	−	0.183354i
$396$	0.607474	+	4.22508i	0.0305267	+	0.212318i
$397$	−16.6176	−	10.6795i	−0.834015	−	0.535989i	0.0525365	−	0.998619i	$-0.483269\pi$
$397$	−16.6176	−	10.6795i	−0.834015	−	0.535989i	−0.886551	+	0.462630i	$0.846906\pi$
$398$	0.122794	−	0.268882i	0.00615513	−	0.0134779i
$399$	−14.5481	+	16.7894i	−0.728316	+	0.840522i
$400$	−0.142315	+	0.989821i	−0.00711574	+	0.0494911i
$401$	−12.8432	−	28.1226i	−0.641357	−	1.40438i	−0.898919	−	0.438114i	$-0.855647\pi$
$401$	−12.8432	−	28.1226i	−0.641357	−	1.40438i	0.257563	−	0.966262i	$-0.417081\pi$
$402$	−15.0956	−	4.43247i	−0.752900	−	0.221071i
$403$	19.0549	+	5.59501i	0.949190	+	0.278707i
$404$	−0.357176	−	0.782105i	−0.0177701	−	0.0389112i
$405$	−0.142315	+	0.989821i	−0.00707168	+	0.0491846i
$406$	14.3335	−	16.5417i	0.711357	−	0.820950i
$407$	−16.5008	+	36.1317i	−0.817914	+	1.79098i
$408$	−1.63053	−	1.04787i	−0.0807230	−	0.0518775i
$409$	−2.55859	−	17.7954i	−0.126514	−	0.879925i	−0.949925	−	0.312479i	$-0.898841\pi$
$409$	−2.55859	−	17.7954i	−0.126514	−	0.879925i	0.823410	−	0.567446i	$-0.192069\pi$
$410$	−2.97064	+	1.90912i	−0.146710	+	0.0942845i
$411$	7.92289	+	9.14351i	0.390808	+	0.451016i
$412$	7.37177	−	2.16455i	0.363181	−	0.106640i
$413$	−23.1799			−1.14061
$414$	0.543180	+	4.76497i	0.0266958	+	0.234186i
$415$	9.18686			0.450965
$416$	3.39562	−	0.997044i	0.166484	−	0.0488841i
$417$	−2.25862	−	2.60658i	−0.110605	−	0.127645i
$418$	24.0696	−	15.4686i	1.17728	−	0.756595i
$419$	−2.65205	−	18.4454i	−0.129561	−	0.901116i	−0.946111	−	0.323842i	$-0.895025\pi$
$419$	−2.65205	−	18.4454i	−0.129561	−	0.901116i	0.816550	−	0.577274i	$-0.195884\pi$
$420$	−2.78817	−	1.79185i	−0.136049	−	0.0874333i
$421$	−2.28600	+	5.00564i	−0.111413	+	0.243960i	−0.957123	−	0.289683i	$-0.906450\pi$
$421$	−2.28600	+	5.00564i	−0.111413	+	0.243960i	0.845710	+	0.533643i	$0.179177\pi$
$422$	−0.969777	+	1.11918i	−0.0472080	+	0.0544810i
$423$	−1.58620	+	11.0322i	−0.0771235	+	0.536406i
$424$	−1.98060	−	4.33692i	−0.0961867	−	0.210619i
$425$	1.85970	+	0.546057i	0.0902086	+	0.0264876i
$426$	4.06919	+	1.19482i	0.197153	+	0.0578894i
$427$	2.30295	+	5.04277i	0.111448	+	0.244037i
$428$	0.0320811	−	0.223129i	0.00155070	−	0.0107853i
$429$	−9.89245	+	11.4165i	−0.477612	+	0.551194i
$430$	−1.72414	+	3.77533i	−0.0831452	+	0.182063i
$431$	−3.89628	−	2.50399i	−0.187677	−	0.120613i	0.443428	−	0.896310i	$-0.353762\pi$
$431$	−3.89628	−	2.50399i	−0.187677	−	0.120613i	−0.631105	+	0.775697i	$0.717399\pi$
$432$	−0.142315	−	0.989821i	−0.00684713	−	0.0476228i
$433$	−7.40979	+	4.76198i	−0.356092	+	0.228846i	−0.706439	−	0.707774i	$-0.749700\pi$
$433$	−7.40979	+	4.76198i	−0.356092	+	0.228846i	0.350348	+	0.936620i	$0.386063\pi$
$434$	12.1795	+	14.0559i	0.584633	+	0.674703i
$435$	−6.33652	+	1.86057i	−0.303813	+	0.0892075i
$436$	−14.9827			−0.717542
$437$	27.5405	−	16.5799i	1.31744	−	0.793126i
$438$	−9.88272			−0.472214
$439$	−0.680280	+	0.199748i	−0.0324680	+	0.00953346i	−0.297926	−	0.954589i	$-0.596295\pi$
$439$	−0.680280	+	0.199748i	−0.0324680	+	0.00953346i	0.265458	+	0.964122i	$0.414477\pi$
$440$	2.79529	+	3.22594i	0.133260	+	0.153790i
$441$	3.35209	−	2.15425i	0.159623	−	0.102584i
$442$	−0.976176	−	6.78945i	−0.0464319	−	0.322941i
$443$	−5.29152	−	3.40065i	−0.251407	−	0.161570i	0.408867	−	0.912594i	$-0.365924\pi$
$443$	−5.29152	−	3.40065i	−0.251407	−	0.161570i	−0.660275	+	0.751024i	$0.729560\pi$
$444$	3.86569	−	8.46468i	0.183457	−	0.401716i
$445$	−9.44270	+	10.8975i	−0.447627	+	0.516589i
$446$	−2.42909	+	16.8947i	−0.115021	+	0.799987i
$447$	9.07860	+	19.8794i	0.429403	+	0.940261i
$448$	3.18005	+	0.933748i	0.150243	+	0.0441155i
$449$	16.9314	+	4.97152i	0.799044	+	0.234620i	0.655669	−	0.755048i	$-0.272387\pi$
$449$	16.9314	+	4.97152i	0.799044	+	0.234620i	0.143374	+	0.989669i	$0.454205\pi$
$450$	0.415415	+	0.909632i	0.0195829	+	0.0428805i
$451$	−2.14512	+	14.9196i	−0.101010	+	0.702538i
$452$	1.87176	−	2.16013i	0.0880404	−	0.101604i
$453$	7.33850	−	16.0691i	0.344793	−	0.754991i
$454$	11.6787	+	7.50541i	0.548106	+	0.352246i
$455$	−1.66925	−	11.6099i	−0.0782554	−	0.544279i
$456$	−5.63886	+	3.62388i	−0.264064	+	0.169704i
$457$	6.93567	+	8.00419i	0.324437	+	0.374420i	0.894414	−	0.447241i	$-0.147593\pi$
$457$	6.93567	+	8.00419i	0.324437	+	0.374420i	−0.569977	+	0.821661i	$0.693048\pi$
$458$	16.5523	−	4.86020i	0.773439	−	0.227102i
$459$	−1.93821			−0.0904678
$460$	3.03309	+	3.71488i	0.141419	+	0.173207i
$461$	−14.8143			−0.689969			−0.344984	−	0.938608i	$-0.612116\pi$
$461$	−14.8143			−0.689969			−0.344984	+	0.938608i	$0.612116\pi$
$462$	−13.5741	+	3.98573i	−0.631526	+	0.185433i
$463$	22.8239	+	26.3402i	1.06072	+	1.22413i	0.973678	+	0.227926i	$0.0731945\pi$
$463$	22.8239	+	26.3402i	1.06072	+	1.22413i	0.0870375	+	0.996205i	$0.472260\pi$
$464$	5.55566	−	3.57041i	0.257915	−	0.165752i
$465$	−0.798614	−	5.55448i	−0.0370348	−	0.257583i
$466$	3.78677	+	2.43361i	0.175419	+	0.112735i
$467$	−12.0725	+	26.4350i	−0.558647	+	1.22327i	0.393978	+	0.919120i	$0.371099\pi$
$467$	−12.0725	+	26.4350i	−0.558647	+	1.22327i	−0.952625	+	0.304147i	$0.901629\pi$
$468$	2.31753	−	2.67458i	0.107128	−	0.123632i
$469$	7.42081	−	51.6129i	0.342661	−	2.38326i
$470$	4.63009	+	10.1385i	0.213570	+	0.467653i
$471$	−5.08391	−	1.49277i	−0.234254	−	0.0687832i
$472$	−6.71059	−	1.97041i	−0.308880	−	0.0906953i
$473$	7.35952	+	16.1151i	0.338391	+	0.740973i
$474$	−0.959246	+	6.67170i	−0.0440596	+	0.306441i
$475$	4.38949	−	5.06574i	0.201403	−	0.232432i
$476$	2.66855	−	5.84331i	0.122313	−	0.267828i
$477$	−4.01091	−	2.57765i	−0.183647	−	0.118023i
$478$	−0.438586	−	3.05044i	−0.0200605	−	0.139524i
$479$	23.6497	−	15.1987i	1.08058	−	0.694447i	0.125889	−	0.992044i	$-0.459822\pi$
$479$	23.6497	−	15.1987i	1.08058	−	0.694447i	0.954692	+	0.297597i	$0.0961852\pi$
$480$	−0.654861	−	0.755750i	−0.0298902	−	0.0344951i
$481$	31.5983	−	9.27810i	1.44076	−	0.423045i
$482$	−19.9288			−0.907732
$483$	−15.3756	+	4.02946i	−0.699615	+	0.183347i
$484$	7.22030			0.328196
$485$	−17.7725	+	5.21848i	−0.807008	+	0.236959i
$486$	−0.654861	−	0.755750i	−0.0297051	−	0.0342815i
$487$	24.8323	−	15.9587i	1.12526	−	0.723160i	0.160694	−	0.987004i	$-0.448627\pi$
$487$	24.8323	−	15.9587i	1.12526	−	0.723160i	0.964565	+	0.263844i	$0.0849906\pi$
$488$	0.238046	+	1.65564i	0.0107758	+	0.0749475i
$489$	12.6537	+	8.13206i	0.572222	+	0.367745i
$490$	1.65528	−	3.62455i	0.0747777	−	0.163740i
$491$	−6.75516	+	7.79587i	−0.304856	+	0.351823i	−0.887420	−	0.460962i	$-0.847504\pi$
$491$	−6.75516	+	7.79587i	−0.304856	+	0.351823i	0.582564	+	0.812785i	$0.302050\pi$
$492$	0.502543	−	3.49527i	0.0226564	−	0.157579i
$493$	−5.31731	−	11.6433i	−0.239480	−	0.524387i
$494$	−22.7606	−	6.68312i	−1.02405	−	0.300688i
$495$	4.09562	+	1.20258i	0.184084	+	0.0540521i
$496$	2.33114	+	5.10449i	0.104671	+	0.229198i
$497$	−2.00037	+	13.9129i	−0.0897287	+	0.624077i
$498$	−6.01612	+	6.94297i	−0.269589	+	0.311122i
$499$	−16.2638	+	35.6127i	−0.728067	+	1.59424i	0.0741757	+	0.997245i	$0.476367\pi$
$499$	−16.2638	+	35.6127i	−0.728067	+	1.59424i	−0.802242	+	0.596998i	$0.796360\pi$
$500$	0.841254	+	0.540641i	0.0376220	+	0.0241782i
$501$	1.27271	+	8.85191i	0.0568606	+	0.395474i
$502$	5.43461	−	3.49261i	0.242558	−	0.155883i
$503$	1.96368	+	2.26621i	0.0875562	+	0.101045i	0.797837	−	0.602873i	$-0.205978\pi$
$503$	1.96368	+	2.26621i	0.0875562	+	0.101045i	−0.710281	+	0.703918i	$0.751432\pi$
$504$	3.18005	−	0.933748i	0.141651	−	0.0415925i
$505$	−0.859804			−0.0382608
$506$	20.4623	+	0.599620i	0.909662	+	0.0266564i
$507$	−0.475669			−0.0211252
$508$	14.8763	−	4.36808i	0.660030	−	0.193802i
$509$	−7.48385	−	8.63682i	−0.331716	−	0.382820i	0.565251	−	0.824919i	$-0.308779\pi$
$509$	−7.48385	−	8.63682i	−0.331716	−	0.382820i	−0.896966	+	0.442099i	$0.854234\pi$
$510$	−1.63053	+	1.04787i	−0.0722009	+	0.0464007i
$511$	−4.66143	−	32.4210i	−0.206210	−	1.43422i
$512$	0.841254	+	0.540641i	0.0371785	+	0.0238932i
$513$	−2.78450	+	6.09720i	−0.122939	+	0.269198i
$514$	−12.6079	+	14.5503i	−0.556110	+	0.641785i
$515$	1.09340	−	7.60478i	0.0481811	−	0.335107i
$516$	−1.72414	−	3.77533i	−0.0759009	−	0.166200i
$517$	45.6485	+	13.4036i	2.00762	+	0.589490i
$518$	29.5923	+	8.68909i	1.30021	+	0.381777i
$519$	−6.75155	−	14.7838i	−0.296360	−	0.648938i
$520$	0.503648	−	3.50295i	0.0220864	−	0.153615i
$521$	9.55233	−	11.0240i	0.418495	−	0.482969i	−0.506883	−	0.862015i	$-0.669202\pi$
$521$	9.55233	−	11.0240i	0.418495	−	0.482969i	0.925378	+	0.379046i	$0.123748\pi$
$522$	2.74341	−	6.00724i	0.120076	−	0.262930i
$523$	32.8485	+	21.1104i	1.43636	+	0.923095i	0.999725	+	0.0234575i	$0.00746745\pi$
$523$	32.8485	+	21.1104i	1.43636	+	0.923095i	0.436638	+	0.899637i	$0.356169\pi$
$524$	−1.41868	−	9.86717i	−0.0619755	−	0.431049i
$525$	−2.78817	+	1.79185i	−0.121686	+	0.0782027i
$526$	−14.6110	−	16.8620i	−0.637072	−	0.735220i
$527$	10.4359	−	3.06425i	0.454594	−	0.133481i
$528$	−4.26852			−0.185764
$529$	22.9605	+	1.34681i	0.998284	+	0.0585569i
$530$	−4.76777			−0.207099
$531$	−6.71059	+	1.97041i	−0.291215	+	0.0855084i
$532$	−14.5481	−	16.7894i	−0.630740	−	0.727913i
$533$	10.5130	−	6.75631i	0.455369	−	0.292648i
$534$	−2.05210	−	14.2726i	−0.0888028	−	0.617637i
$535$	−0.189638	−	0.121873i	−0.00819877	−	0.00526903i
$536$	6.53568	−	14.3111i	0.282298	−	0.618147i
$537$	−6.50015	+	7.50157i	−0.280502	+	0.323717i
$538$	1.68918	−	11.7485i	0.0728258	−	0.506514i
$539$	−7.06559	−	15.4715i	−0.304336	−	0.666404i
$540$	−0.959493	−	0.281733i	−0.0412900	−	0.0121238i
$541$	9.01585	+	2.64729i	0.387622	+	0.113816i	0.469736	−	0.882807i	$-0.344349\pi$
$541$	9.01585	+	2.64729i	0.387622	+	0.113816i	−0.0821143	+	0.996623i	$0.526167\pi$
$542$	−0.370106	−	0.810419i	−0.0158974	−	0.0348105i
$543$	2.79711	−	19.4544i	0.120036	−	0.834867i
$544$	1.26926	−	1.46480i	0.0544189	−	0.0628028i
$545$	−6.22404	+	13.6288i	−0.266609	+	0.583792i
$546$	9.86727	+	6.34131i	0.422280	+	0.271383i
$547$	−3.47911	−	24.1977i	−0.148756	−	1.03462i	−0.918260	−	0.395978i	$-0.870406\pi$
$547$	−3.47911	−	24.1977i	−0.148756	−	1.03462i	0.769504	−	0.638642i	$-0.220504\pi$
$548$	−10.1780	+	6.54099i	−0.434782	+	0.279417i
$549$	1.09537	+	1.26412i	0.0467491	+	0.0539513i
$550$	4.09562	−	1.20258i	0.174638	−	0.0512783i
$551$	−44.2664			−1.88581
$552$	−4.79377	−	0.140475i	−0.204037	−	0.00597901i
$553$	−22.3395			−0.949970
$554$	−10.6251	+	3.11981i	−0.451417	+	0.132548i
$555$	−6.09388	−	7.03271i	−0.258671	−	0.298522i
$556$	2.90149	−	1.86467i	0.123050	−	0.0790797i
$557$	−3.51429	−	24.4424i	−0.148905	−	1.03566i	−0.918016	−	0.396544i	$-0.870210\pi$
$557$	−3.51429	−	24.4424i	−0.148905	−	1.03566i	0.769111	−	0.639116i	$-0.220700\pi$
$558$	4.72078	+	3.03386i	0.199846	+	0.128434i
$559$	6.10167	−	13.3608i	0.258073	−	0.565101i
$560$	2.17041	−	2.50479i	0.0917165	−	0.105847i
$561$	−1.17741	+	8.18908i	−0.0497104	+	0.345743i
$562$	5.64493	+	12.3607i	0.238117	+	0.521404i
$563$	−6.35603	−	1.86630i	−0.267875	−	0.0786551i	0.145037	−	0.989426i	$-0.453670\pi$
$563$	−6.35603	−	1.86630i	−0.267875	−	0.0786551i	−0.412912	+	0.910771i	$0.635488\pi$
$564$	−10.6942	−	3.14010i	−0.450308	−	0.132222i
$565$	−1.18737	−	2.59997i	−0.0499529	−	0.109381i
$566$	−3.81746	+	26.5510i	−0.160460	+	1.11602i
$567$	2.17041	−	2.50479i	0.0911486	−	0.105191i
$568$	−1.76177	+	3.85773i	−0.0739222	+	0.161867i
$569$	20.5874	+	13.2307i	0.863070	+	0.554661i	0.895626	−	0.444809i	$-0.146728\pi$
$569$	20.5874	+	13.2307i	0.863070	+	0.554661i	−0.0325558	+	0.999470i	$0.510365\pi$
$570$	0.953927	+	6.63471i	0.0399556	+	0.277897i
$571$	−14.4526	+	9.28815i	−0.604824	+	0.388697i	−0.806913	−	0.590670i	$-0.798863\pi$
$571$	−14.4526	+	9.28815i	−0.604824	+	0.388697i	0.202089	+	0.979367i	$0.435227\pi$
$572$	−9.89245	−	11.4165i	−0.413624	−	0.477348i
$573$	−5.26697	+	1.54652i	−0.220031	+	0.0646069i
$574$	11.7035			0.488495
$575$	4.63917	−	1.21578i	0.193467	−	0.0507014i
$576$	1.00000			0.0416667
$577$	7.24920	−	2.12856i	0.301788	−	0.0886130i	−0.127333	−	0.991860i	$-0.540642\pi$
$577$	7.24920	−	2.12856i	0.301788	−	0.0886130i	0.429121	+	0.903247i	$0.358823\pi$
$578$	8.67255	+	10.0087i	0.360730	+	0.416305i
$579$	13.0694	−	8.39921i	0.543147	−	0.349059i
$580$	−0.939852	−	6.53681i	−0.0390252	−	0.271426i
$581$	−25.6146	−	16.4615i	−1.06267	−	0.682937i
$582$	7.69466	−	16.8489i	0.318954	−	0.698411i
$583$	−13.3273	+	15.3805i	−0.551961	+	0.636996i
$584$	1.40646	−	9.78212i	0.0581996	−	0.404787i
$585$	−1.47014	−	3.21916i	−0.0607829	−	0.133096i
$586$	−28.6634	−	8.41632i	−1.18407	−	0.347675i
$587$	8.32196	+	2.44355i	0.343484	+	0.100856i	0.448925	−	0.893570i	$-0.351807\pi$
$587$	8.32196	+	2.44355i	0.343484	+	0.100856i	−0.105441	+	0.994426i	$0.533625\pi$
$588$	1.65528	+	3.62455i	0.0682624	+	0.149474i
$589$	5.35305	−	37.2313i	0.220569	−	1.53409i
$590$	−4.58003	+	5.28563i	−0.188557	+	0.217606i
$591$	−2.49780	+	5.46942i	−0.102746	+	0.224982i
$592$	7.82837	+	5.03099i	0.321744	+	0.206772i
$593$	5.18234	+	36.0439i	0.212813	+	1.48015i	0.763702	+	0.645569i	$0.223380\pi$
$593$	5.18234	+	36.0439i	0.212813	+	1.48015i	−0.550889	+	0.834578i	$0.685711\pi$
$594$	−3.59091	+	2.30774i	−0.147337	+	0.0946877i
$595$	−4.20671	−	4.85480i	−0.172458	−	0.199027i
$596$	−20.9690	+	6.15706i	−0.858925	+	0.252203i
$597$	0.295595			0.0120979
$598$	−10.7340	−	13.1469i	−0.438947	−	0.537616i
$599$	7.14771			0.292048			0.146024	−	0.989281i	$-0.453352\pi$
$599$	7.14771			0.292048			0.146024	+	0.989281i	$0.453352\pi$
$600$	−0.959493	+	0.281733i	−0.0391711	+	0.0115017i
$601$	−8.96900	−	10.3508i	−0.365853	−	0.422217i	0.542739	−	0.839901i	$-0.317387\pi$
$601$	−8.96900	−	10.3508i	−0.365853	−	0.422217i	−0.908592	+	0.417684i	$0.862842\pi$
$602$	11.5720	−	7.43688i	0.471640	−	0.303105i
$603$	−2.23902	−	15.5727i	−0.0911801	−	0.634171i
$604$	14.8611	+	9.55067i	0.604691	+	0.388611i
$605$	2.99942	−	6.56782i	0.121944	−	0.267020i
$606$	0.563052	−	0.649797i	0.0228724	−	0.0263962i
$607$	−3.56487	+	24.7942i	−0.144694	+	1.00637i	0.780034	+	0.625737i	$0.215202\pi$
$607$	−3.56487	+	24.7942i	−0.144694	+	1.00637i	−0.924728	+	0.380629i	$0.875707\pi$
$608$	−2.78450	−	6.09720i	−0.112926	−	0.247274i
$609$	21.0012	+	6.16650i	0.851011	+	0.249879i
$610$	1.60492	+	0.471246i	0.0649811	+	0.0190802i
$611$	−16.3858	−	35.8798i	−0.662897	−	1.45154i
$612$	0.275836	−	1.91848i	0.0111500	−	0.0775500i
$613$	0.636851	−	0.734965i	0.0257222	−	0.0296850i	−0.742743	−	0.669577i	$-0.766475\pi$
$613$	0.636851	−	0.734965i	0.0257222	−	0.0296850i	0.768465	+	0.639892i	$0.221021\pi$
$614$	−6.28614	+	13.7647i	−0.253688	+	0.555499i
$615$	−2.97064	−	1.90912i	−0.119788	−	0.0769830i
$616$	−2.01336	−	14.0032i	−0.0811205	−	0.564205i
$617$	36.6268	−	23.5386i	1.47454	−	0.947629i	0.476901	−	0.878957i	$-0.341760\pi$
$617$	36.6268	−	23.5386i	1.47454	−	0.947629i	0.997639	−	0.0686721i	$-0.0218762\pi$
$618$	5.03129	+	5.80641i	0.202388	+	0.233568i
$619$	−30.2163	+	8.87231i	−1.21450	+	0.356608i	−0.825379	−	0.564580i	$-0.809038\pi$
$619$	−30.2163	+	8.87231i	−1.21450	+	0.356608i	−0.389118	+	0.921188i	$0.627220\pi$
$620$	5.61160			0.225367
$621$	−4.10873	+	2.47353i	−0.164877	+	0.0992595i
$622$	31.5101			1.26344
$623$	45.8545	−	13.4641i	1.83712	−	0.539428i
$624$	2.31753	+	2.67458i	0.0927756	+	0.107069i
$625$	0.841254	−	0.540641i	0.0336501	−	0.0216256i
$626$	0.115527	+	0.803511i	0.00461740	+	0.0321147i
$627$	24.0696	+	15.4686i	0.961249	+	0.617757i
$628$	2.20109	−	4.81972i	0.0878331	−	0.192328i
$629$	11.8112	−	13.6309i	0.470944	−	0.543498i
$630$	0.471675	−	3.28057i	0.0187920	−	0.130701i
$631$	6.05183	+	13.2517i	0.240920	+	0.527540i	0.991009	−	0.133796i	$-0.0427168\pi$
$631$	6.05183	+	13.2517i	0.240920	+	0.527540i	−0.750089	+	0.661337i	$0.769990\pi$
$632$	−6.46728	−	1.89896i	−0.257255	−	0.0755368i
$633$	−1.42090	−	0.417215i	−0.0564759	−	0.0165828i
$634$	−4.95600	−	10.8521i	−0.196828	−	0.430993i
$635$	2.20650	−	15.3465i	0.0875622	−	0.609009i
$636$	3.12223	−	3.60324i	0.123804	−	0.142878i
$637$	−5.85798	+	12.8272i	−0.232102	+	0.508231i
$638$	−23.7145	−	15.2404i	−0.938866	−	0.603372i
$639$	0.603555	+	4.19782i	0.0238763	+	0.166063i
$640$	0.841254	−	0.540641i	0.0332535	−	0.0213707i
$641$	26.8708	+	31.0105i	1.06133	+	1.22484i	0.973496	+	0.228706i	$0.0734495\pi$
$641$	26.8708	+	31.0105i	1.06133	+	1.22484i	0.0878354	+	0.996135i	$0.472005\pi$
$642$	0.216292	−	0.0635091i	0.00853637	−	0.00250650i
$643$	−13.0456			−0.514470			−0.257235	−	0.966349i	$-0.582811\pi$
$643$	−13.0456			−0.514470			−0.257235	+	0.966349i	$0.582811\pi$
$644$	−1.80027	−	15.7926i	−0.0709404	−	0.622315i
$645$	−4.15039			−0.163422
$646$	−12.4654	+	3.66018i	−0.490446	+	0.144008i
$647$	2.19122	+	2.52880i	0.0861456	+	0.0994174i	0.797186	−	0.603734i	$-0.206321\pi$
$647$	2.19122	+	2.52880i	0.0861456	+	0.0994174i	−0.711040	+	0.703151i	$0.751776\pi$
$648$	0.841254	−	0.540641i	0.0330476	−	0.0212384i
$649$	4.24861	+	29.5497i	0.166773	+	1.15993i
$650$	−2.97717	−	1.91331i	−0.116774	−	0.0750463i
$651$	−7.72612	+	16.9179i	−0.302811	+	0.663063i
$652$	−9.85011	+	11.3676i	−0.385760	+	0.445191i
$653$	−3.24450	+	22.5660i	−0.126967	+	0.883076i	0.822400	+	0.568909i	$0.192634\pi$
$653$	−3.24450	+	22.5660i	−0.126967	+	0.883076i	−0.949368	+	0.314167i	$0.898275\pi$
$654$	−6.22404	−	13.6288i	−0.243379	−	0.532926i
$655$	−9.56483	−	2.80849i	−0.373729	−	0.109737i
$656$	3.38817	+	0.994856i	0.132286	+	0.0388426i
$657$	−4.10543	−	8.98964i	−0.160168	−	0.350719i
$658$	5.25714	−	36.5642i	0.204945	−	1.42542i
$659$	9.48701	−	10.9486i	0.369562	−	0.426497i	−0.540259	−	0.841499i	$-0.681674\pi$
$659$	9.48701	−	10.9486i	0.369562	−	0.426497i	0.909820	+	0.415002i	$0.136219\pi$
$660$	−1.77321	+	3.88279i	−0.0690221	+	0.151137i
$661$	−26.9491	−	17.3191i	−1.04820	−	0.673635i	−0.101196	−	0.994866i	$-0.532267\pi$
$661$	−26.9491	−	17.3191i	−1.04820	−	0.673635i	−0.947001	+	0.321231i	$0.895903\pi$
$662$	−2.44124	−	16.9792i	−0.0948816	−	0.659916i
$663$	5.77038	−	3.70840i	0.224103	−	0.144022i
$664$	−6.01612	−	6.94297i	−0.233471	−	0.269439i
$665$	−21.3157	+	6.25885i	−0.826587	+	0.242708i
$666$	9.30561			0.360585
$667$	−26.1310	−	17.8962i	−1.01180	−	0.692942i
$668$	−8.94294			−0.346013
$669$	−16.3770	+	4.80873i	−0.633172	+	0.185916i
$670$	−10.3028	−	11.8901i	−0.398034	−	0.459355i
$671$	6.00641	−	3.86009i	0.231875	−	0.149017i
$672$	0.471675	+	3.28057i	0.0181953	+	0.126551i
$673$	−15.4238	−	9.91224i	−0.594542	−	0.382089i	0.208490	−	0.978024i	$-0.433145\pi$
$673$	−15.4238	−	9.91224i	−0.594542	−	0.382089i	−0.803032	+	0.595935i	$0.796781\pi$
$674$	2.89110	−	6.33062i	0.111361	−	0.243846i
$675$	−0.654861	+	0.755750i	−0.0252056	+	0.0290888i
$676$	0.0676948	−	0.470827i	0.00260364	−	0.0181087i
$677$	2.99201	+	6.55159i	0.114992	+	0.251798i	0.958373	−	0.285518i	$-0.0921655\pi$
$677$	2.99201	+	6.55159i	0.114992	+	0.251798i	−0.843381	+	0.537316i	$0.819438\pi$
$678$	2.74248	+	0.805266i	0.105324	+	0.0309261i
$679$	58.9036	+	17.2956i	2.26051	+	0.663746i
$680$	−0.805161	−	1.76306i	−0.0308765	−	0.0676101i
$681$	−1.97568	+	13.7411i	−0.0757081	+	0.526561i
$682$	15.6860	−	18.1027i	0.600650	−	0.693187i
$683$	16.3449	−	35.7904i	0.625421	−	1.36948i	−0.286089	−	0.958203i	$-0.592355\pi$
$683$	16.3449	−	35.7904i	0.625421	−	1.36948i	0.911510	−	0.411278i	$-0.134917\pi$
$684$	−5.63886	−	3.62388i	−0.215607	−	0.138562i
$685$	1.72181	+	11.9754i	0.0657870	+	0.457558i
$686$	8.40737	−	5.40309i	0.320995	−	0.206291i
$687$	11.2971	+	13.0375i	0.431010	+	0.497413i
$688$	3.98227	−	1.16930i	0.151823	−	0.0445792i
$689$	16.8730			0.642811
$690$	−2.11919	+	4.30221i	−0.0806760	+	0.163783i
$691$	−30.1405			−1.14660			−0.573300	−	0.819346i	$-0.694337\pi$
$691$	−30.1405			−1.14660			−0.573300	+	0.819346i	$0.694337\pi$
$692$	15.5942	−	4.57887i	0.592802	−	0.174063i
$693$	−9.26445	−	10.6917i	−0.351927	−	0.406146i
$694$	−26.8595	+	17.2616i	−1.01957	+	0.655240i
$695$	−0.490844	−	3.41390i	−0.0186188	−	0.129496i
$696$	5.55566	+	3.57041i	0.210587	+	0.135336i
$697$	2.84319	−	6.22572i	0.107694	−	0.235816i
$698$	−10.9510	+	12.6381i	−0.414501	+	0.478360i
$699$	−0.640609	+	4.45553i	−0.0242300	+	0.168524i
$700$	−1.37681	−	3.01480i	−0.0520386	−	0.113949i
$701$	31.9238	+	9.37366i	1.20574	+	0.354038i	0.822046	−	0.569421i	$-0.192832\pi$
$701$	31.9238	+	9.37366i	1.20574	+	0.354038i	0.383697	+	0.923459i	$0.374651\pi$
$702$	3.39562	+	0.997044i	0.128159	+	0.0376310i
$703$	−25.9114	−	56.7382i	−0.977269	−	2.13992i
$704$	0.607474	−	4.22508i	0.0228951	−	0.159239i
$705$	−7.29887	+	8.42335i	−0.274892	+	0.317242i
$706$	6.96099	−	15.2424i	0.261980	−	0.573657i
$707$	2.39728	+	1.54064i	0.0901591	+	0.0579417i
$708$	−0.995335	−	6.92270i	−0.0374070	−	0.260171i
$709$	−4.10606	+	2.63880i	−0.154206	+	0.0991023i	−0.615468	−	0.788162i	$-0.711033\pi$
$709$	−4.10606	+	2.63880i	−0.154206	+	0.0991023i	0.461262	+	0.887264i	$0.347397\pi$
$710$	2.77725	+	3.20512i	0.104228	+	0.120286i
$711$	−6.46728	+	1.89896i	−0.242542	+	0.0712167i
$712$	14.4194			0.540390
$713$	18.2120	−	19.8140i	0.682044	−	0.742040i
$714$	6.42382			0.240405
$715$	−14.4943	+	4.25591i	−0.542056	+	0.159162i
$716$	−6.50015	−	7.50157i	−0.242922	−	0.280347i
$717$	2.59258	−	1.66615i	0.0968216	−	0.0622235i
$718$	−3.69844	−	25.7232i	−0.138024	−	0.959981i
$719$	−25.3218	−	16.2734i	−0.944346	−	0.606894i	−0.0247218	−	0.999694i	$-0.507870\pi$
$719$	−25.3218	−	16.2734i	−0.944346	−	0.606894i	−0.919624	+	0.392800i	$0.871506\pi$
$720$	0.415415	−	0.909632i	0.0154816	−	0.0339000i
$721$	−16.6752	+	19.2442i	−0.621018	+	0.716693i
$722$	−3.69012	+	25.6654i	−0.137332	+	0.955166i
$723$	−8.27872	−	18.1279i	−0.307889	−	0.674183i
$724$	18.8583	+	5.53729i	0.700862	+	0.205792i
$725$	−6.33652	−	1.86057i	−0.235332	−	0.0690999i
$726$	2.99942	+	6.56782i	0.111319	+	0.243755i
$727$	−1.53688	+	10.6892i	−0.0569997	+	0.396442i	0.941271	+	0.337653i	$0.109633\pi$
$727$	−1.53688	+	10.6892i	−0.0569997	+	0.396442i	−0.998270	+	0.0587889i	$0.981276\pi$
$728$	−7.68102	+	8.86437i	−0.284678	+	0.328535i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−8.31387	−	5.34300i	−0.307710	−	0.197753i
$731$	−1.14483	−	7.96245i	−0.0423430	−	0.294502i
$732$	−1.40714	+	0.904314i	−0.0520094	+	0.0334244i
$733$	−4.83042	−	5.57460i	−0.178416	−	0.205903i	0.659497	−	0.751707i	$-0.270769\pi$
$733$	−4.83042	−	5.57460i	−0.178416	−	0.205903i	−0.837912	+	0.545805i	$0.816224\pi$
$734$	31.3048	−	9.19193i	1.15548	−	0.339280i
$735$	3.98463			0.146975
$736$	0.821270	−	4.72499i	0.0302724	−	0.174165i
$737$	−67.1562			−2.47373
$738$	3.38817	−	0.994856i	0.124720	−	0.0366212i
$739$	0.204970	+	0.236548i	0.00753995	+	0.00870157i	0.759507	−	0.650499i	$-0.225440\pi$
$739$	0.204970	+	0.236548i	0.00753995	+	0.00870157i	−0.751967	+	0.659201i	$0.770895\pi$
$740$	7.82837	−	5.03099i	0.287777	−	0.184943i
$741$	−3.37592	−	23.4800i	−0.124018	−	0.862561i
$742$	13.2934	+	8.54313i	0.488015	+	0.313628i
$743$	−7.62234	+	16.6906i	−0.279636	+	0.612318i	−0.996379	−	0.0850192i	$-0.972905\pi$
$743$	−7.62234	+	16.6906i	−0.279636	+	0.612318i	0.716743	+	0.697337i	$0.245632\pi$
$744$	−3.67482	+	4.24096i	−0.134725	+	0.155481i
$745$	−3.11019	+	21.6318i	−0.113949	+	0.792529i
$746$	−7.76439	−	17.0016i	−0.284274	−	0.622474i
$747$	−8.81473	−	2.58824i	−0.322514	−	0.0946987i
$748$	−7.93817	−	2.33086i	−0.290248	−	0.0852245i
$749$	0.310366	+	0.679606i	0.0113405	+	0.0248323i
$750$	−0.142315	+	0.989821i	−0.00519660	+	0.0361432i
$751$	−10.1717	+	11.7388i	−0.371171	+	0.428354i	−0.910351	−	0.413836i	$-0.864189\pi$
$751$	−10.1717	+	11.7388i	−0.371171	+	0.428354i	0.539181	+	0.842190i	$0.318734\pi$
$752$	4.63009	−	10.1385i	0.168842	−	0.369712i
$753$	5.43461	+	3.49261i	0.198048	+	0.127278i
$754$	3.32611	+	23.1336i	0.121130	+	0.842476i
$755$	14.8611	−	9.55067i	0.540852	−	0.347585i
$756$	2.17041	+	2.50479i	0.0789370	+	0.0910982i
$757$	22.3284	−	6.55621i	0.811540	−	0.238290i	0.150471	−	0.988614i	$-0.451921\pi$
$757$	22.3284	−	6.55621i	0.811540	−	0.238290i	0.661069	+	0.750325i	$0.270103\pi$
$758$	9.64672			0.350384
$759$	7.95493	+	18.8623i	0.288746	+	0.684658i
$760$	−6.70293			−0.243141
$761$	−10.7811	+	3.16560i	−0.390813	+	0.114753i	−0.471235	−	0.882008i	$-0.656192\pi$
$761$	−10.7811	+	3.16560i	−0.390813	+	0.114753i	0.0804216	+	0.996761i	$0.474373\pi$
$762$	10.1532	+	11.7174i	0.367811	+	0.424477i
$763$	41.7744	−	26.8468i	1.51233	−	0.971918i
$764$	−0.781213	−	5.43345i	−0.0282633	−	0.196575i
$765$	−1.63053	−	1.04787i	−0.0589518	−	0.0378860i
$766$	−6.93663	+	15.1891i	−0.250631	+	0.548805i
$767$	16.2086	−	18.7057i	0.585258	−	0.675424i
$768$	−0.142315	+	0.989821i	−0.00513534	+	0.0357171i
$769$	7.11398	+	15.5774i	0.256537	+	0.561737i	0.993452	−	0.114248i	$-0.0364458\pi$
$769$	7.11398	+	15.5774i	0.256537	+	0.561737i	−0.736916	+	0.675985i	$0.763719\pi$
$770$	−13.5741	−	3.98573i	−0.489178	−	0.143636i
$771$	−18.4729	−	5.42414i	−0.665286	−	0.195345i
$772$	6.45375	+	14.1317i	0.232275	+	0.508612i
$773$	−6.21607	+	43.2337i	−0.223576	+	1.55501i	0.500775	+	0.865577i	$0.333048\pi$
$773$	−6.21607	+	43.2337i	−0.223576	+	1.55501i	−0.724352	+	0.689431i	$0.757861\pi$
$774$	2.71793	−	3.13666i	0.0976940	−	0.112745i
$775$	2.33114	−	5.10449i	0.0837371	−	0.183359i
$776$	15.5824	+	10.0142i	0.559375	+	0.359489i
$777$	4.38922	+	30.5277i	0.157462	+	1.09518i
$778$	−11.5585	+	7.42820i	−0.414392	+	0.266314i
$779$	−15.5002	−	17.8882i	−0.555352	−	0.640910i
$780$	3.39562	−	0.997044i	0.121583	−	0.0356999i
$781$	18.1027			0.647767
$782$	−8.83826	−	2.87891i	−0.316056	−	0.102950i
$783$	6.60403			0.236009
$784$	−3.82323	+	1.12260i	−0.136544	+	0.0400929i
$785$	−3.46980	−	4.00437i	−0.123843	−	0.142922i
$786$	8.38615	−	5.38945i	0.299124	−	0.192235i
$787$	2.32865	+	16.1961i	0.0830074	+	0.577329i	0.988298	+	0.152536i	$0.0487440\pi$
$787$	2.32865	+	16.1961i	0.0830074	+	0.577329i	−0.905291	+	0.424793i	$0.860347\pi$
$788$	−5.05828	−	3.25076i	−0.180194	−	0.115803i
$789$	9.26861	−	20.2954i	0.329971	−	0.722536i
$790$	−4.41396	+	5.09399i	−0.157042	+	0.181236i
$791$	−1.34817	+	9.37674i	−0.0479355	+	0.333399i
$792$	−1.77321	−	3.88279i	−0.0630082	−	0.137969i
$793$	−5.67975	−	1.66773i	−0.201694	−	0.0592227i
$794$	18.9533	+	5.56518i	0.672626	+	0.197501i
$795$	−1.98060	−	4.33692i	−0.0702448	−	0.153815i
$796$	−0.0420675	+	0.292586i	−0.00149104	+	0.0103704i
$797$	9.23099	−	10.6531i	0.326978	−	0.377353i	−0.568329	−	0.822801i	$-0.692410\pi$
$797$	9.23099	−	10.6531i	0.326978	−	0.377353i	0.895308	+	0.445448i	$0.146956\pi$
$798$	9.22868	−	20.2080i	0.326692	−	0.715355i
$799$	−18.1733	−	11.6793i	−0.642926	−	0.413184i
$800$	−0.142315	−	0.989821i	−0.00503159	−	0.0349955i
$801$	12.1304	−	7.79572i	0.428606	−	0.275448i
$802$	20.2460	+	23.3651i	0.714910	+	0.825050i
$803$	−40.4758	+	11.8848i	−1.42836	+	0.419405i
$804$	15.7329			0.554856
$805$	−15.1133	−	4.92290i	−0.532674	−	0.173509i
$806$	−19.8593			−0.699514
$807$	11.3885	−	3.34398i	0.400895	−	0.117714i
$808$	0.563052	+	0.649797i	0.0198081	+	0.0228598i
$809$	6.37773	−	4.09872i	0.224229	−	0.144103i	−0.423704	−	0.905801i	$-0.639270\pi$
$809$	6.37773	−	4.09872i	0.224229	−	0.144103i	0.647933	+	0.761698i	$0.275634\pi$
$810$	−0.142315	−	0.989821i	−0.00500043	−	0.0347788i
$811$	19.6622	+	12.6361i	0.690433	+	0.443714i	0.838240	−	0.545302i	$-0.183585\pi$
$811$	19.6622	+	12.6361i	0.690433	+	0.443714i	−0.147807	+	0.989016i	$0.547221\pi$
$812$	−9.09252	+	19.9098i	−0.319085	+	0.698698i
$813$	0.583435	−	0.673320i	0.0204620	−	0.0236144i
$814$	5.65292	−	39.3169i	0.198135	−	1.37806i
$815$	6.24848	+	13.6823i	0.218875	+	0.479269i
$816$	1.85970	+	0.546057i	0.0651024	+	0.0191158i
$817$	−26.6929	−	7.83775i	−0.933867	−	0.274208i
$818$	7.46849	+	16.3537i	0.261130	+	0.571794i
$819$	−1.66925	+	11.6099i	−0.0583282	+	0.405681i
$820$	2.31245	−	2.66871i	0.0807542	−	0.0931954i
$821$	−16.6536	+	36.4663i	−0.581215	+	1.27268i	0.359392	+	0.933187i	$0.382984\pi$
$821$	−16.6536	+	36.4663i	−0.581215	+	1.27268i	−0.940607	+	0.339497i	$0.889743\pi$
$822$	−10.1780	−	6.54099i	−0.354998	−	0.228143i
$823$	−6.44030	−	44.7932i	−0.224495	−	1.56139i	−0.720736	−	0.693210i	$-0.756196\pi$
$823$	−6.44030	−	44.7932i	−0.224495	−	1.56139i	0.496241	−	0.868185i	$-0.334713\pi$
$824$	−6.46334	+	4.15374i	−0.225161	+	0.144702i
$825$	2.79529	+	3.22594i	0.0973195	+	0.112313i
$826$	22.2410	−	6.53053i	0.773862	−	0.227226i
$827$	12.2699			0.426666			0.213333	−	0.976980i	$-0.431568\pi$
$827$	12.2699			0.426666			0.213333	+	0.976980i	$0.431568\pi$
$828$	−1.86363	−	4.41893i	−0.0647655	−	0.153568i
$829$	28.3016			0.982957			0.491478	−	0.870890i	$-0.336457\pi$
$829$	28.3016			0.982957			0.491478	+	0.870890i	$0.336457\pi$
$830$	−8.81473	+	2.58824i	−0.305964	+	0.0898391i
$831$	−7.25170	−	8.36891i	−0.251559	−	0.290314i
$832$	−2.97717	+	1.91331i	−0.103215	+	0.0663322i
$833$	1.09910	+	7.64444i	0.0380817	+	0.264864i
$834$	2.90149	+	1.86467i	0.100470	+	0.0645683i
$835$	−3.71503	+	8.13478i	−0.128564	+	0.281516i
$836$	−18.7366	+	21.6232i	−0.648020	+	0.747855i
$837$	−0.798614	+	5.55448i	−0.0276041	+	0.191991i
$838$	7.74128	+	16.9510i	0.267418	+	0.585564i
$839$	21.7156	+	6.37626i	0.749705	+	0.220133i	0.634195	−	0.773173i	$-0.281332\pi$
$839$	21.7156	+	6.37626i	0.749705	+	0.220133i	0.115510	+	0.993306i	$0.463150\pi$
$840$	3.18005	+	0.933748i	0.109722	+	0.0322174i
$841$	6.07055	+	13.2927i	0.209329	+	0.458367i
$842$	0.783148	−	5.44691i	0.0269891	−	0.187713i
$843$	−8.89868	+	10.2696i	−0.306487	+	0.353704i
$844$	0.615184	−	1.34707i	0.0211755	−	0.0463679i
$845$	−0.400158	−	0.257166i	−0.0137659	−	0.00884678i
$846$	−1.58620	−	11.0322i	−0.0545346	−	0.379296i
$847$	−20.1314	+	12.9377i	−0.691725	+	0.444545i
$848$	3.12223	+	3.60324i	0.107218	+	0.123736i
$849$	−25.7375	+	7.55720i	−0.883307	+	0.259362i
$850$	−1.93821			−0.0664800
$851$	7.64242	−	43.9689i	0.261979	−	1.50723i
$852$	−4.24098			−0.145294
$853$	−20.6878	+	6.07450i	−0.708338	+	0.207987i	−0.616006	−	0.787741i	$-0.711250\pi$
$853$	−20.6878	+	6.07450i	−0.708338	+	0.207987i	−0.0923322	+	0.995728i	$0.529432\pi$
$854$	−3.63038	−	4.18968i	−0.124229	−	0.143368i
$855$	−5.63886	+	3.62388i	−0.192845	+	0.123934i
$856$	0.0320811	+	0.223129i	0.00109651	+	0.00762638i
$857$	32.2003	+	20.6939i	1.09994	+	0.706890i	0.959079	−	0.283139i	$-0.0913756\pi$
$857$	32.2003	+	20.6939i	1.09994	+	0.706890i	0.140864	+	0.990029i	$0.455012\pi$
$858$	6.27534	−	13.7411i	0.214237	−	0.469113i
$859$	−32.6956	+	37.7328i	−1.11556	+	1.28743i	−0.161811	+	0.986822i	$0.551734\pi$
$859$	−32.6956	+	37.7328i	−1.11556	+	1.28743i	−0.953749	+	0.300604i	$0.902812\pi$
$860$	0.590663	−	4.10815i	0.0201414	−	0.140087i
$861$	4.86181	+	10.6459i	0.165690	+	0.362811i
$862$	4.44391	+	1.30485i	0.151360	+	0.0444434i
$863$	52.3532	+	15.3723i	1.78212	+	0.523279i	0.995551	−	0.0942198i	$-0.0300357\pi$
$863$	52.3532	+	15.3723i	1.78212	+	0.523279i	0.786572	+	0.617498i	$0.211854\pi$
$864$	0.415415	+	0.909632i	0.0141327	+	0.0309463i
$865$	2.31298	−	16.0871i	0.0786436	−	0.546978i
$866$	5.76803	−	6.65666i	0.196006	−	0.226203i
$867$	−5.50148	+	12.0466i	−0.186840	+	0.409123i
$868$	−15.6461	−	10.0551i	−0.531064	−	0.341294i
$869$	4.09457	+	28.4783i	0.138899	+	0.966061i
$870$	5.55566	−	3.57041i	0.188355	−	0.121048i
$871$	36.4615	+	42.0788i	1.23545	+	1.42579i
$872$	14.3758	−	4.22112i	0.486826	−	0.142945i
$873$	18.5228			0.626902
$874$	−21.7538	+	23.6674i	−0.735834	+	0.800561i
$875$	−3.31431			−0.112044
$876$	9.48240	−	2.78428i	0.320381	−	0.0940722i
$877$	−0.0538351	−	0.0621290i	−0.00181788	−	0.00209795i	0.754840	−	0.655909i	$-0.227715\pi$
$877$	−0.0538351	−	0.0621290i	−0.00181788	−	0.00209795i	−0.756658	+	0.653811i	$0.773169\pi$
$878$	0.596448	−	0.383314i	0.0201292	−	0.0129362i
$879$	−4.25144	−	29.5694i	−0.143397	−	0.997351i
$880$	−3.59091	−	2.30774i	−0.121050	−	0.0777939i
$881$	5.11880	−	11.2086i	0.172457	−	0.377628i	−0.803592	−	0.595181i	$-0.797080\pi$
$881$	5.11880	−	11.2086i	0.172457	−	0.377628i	0.976048	+	0.217553i	$0.0698076\pi$
$882$	−2.60938	+	3.01138i	−0.0878624	+	0.101399i
$883$	−4.92927	+	34.2838i	−0.165883	+	1.15374i	0.721400	+	0.692518i	$0.243499\pi$
$883$	−4.92927	+	34.2838i	−0.165883	+	1.15374i	−0.887283	+	0.461225i	$0.847410\pi$
$884$	2.84944	+	6.23941i	0.0958372	+	0.209854i
$885$	−6.71059	−	1.97041i	−0.225574	−	0.0662345i
$886$	6.03525	+	1.77211i	0.202758	+	0.0595351i
$887$	13.7709	+	30.1540i	0.462381	+	1.01247i	0.986938	+	0.161098i	$0.0515037\pi$
$887$	13.7709	+	30.1540i	0.462381	+	1.01247i	−0.524557	+	0.851375i	$0.675769\pi$
$888$	−1.32433	+	9.21089i	−0.0444415	+	0.309097i
$889$	−33.6508	+	38.8351i	−1.12861	+	1.30249i
$890$	5.99004	−	13.1164i	0.200786	−	0.439661i
$891$	−3.59091	−	2.30774i	−0.120300	−	0.0773122i
$892$	−2.42909	−	16.8947i	−0.0813319	−	0.565676i
$893$	−62.8490	+	40.3906i	−2.10316	+	1.35162i
$894$	−14.3115	−	16.5164i	−0.478649	−	0.552390i
$895$	−9.52393	+	2.79648i	−0.318350	+	0.0934759i
$896$	−3.31431			−0.110723
$897$	7.49974	−	15.2254i	0.250409	−	0.508362i
$898$	−17.6462			−0.588862
$899$	−35.5580	+	10.4408i	−1.18593	+	0.348219i
$900$	−0.654861	−	0.755750i	−0.0218287	−	0.0251917i
$901$	7.77397	−	4.99603i	0.258989	−	0.166442i
$902$	−2.14512	−	14.9196i	−0.0714246	−	0.496769i
$903$	11.5720	+	7.43688i	0.385093	+	0.247484i
$904$	−1.18737	+	2.59997i	−0.0394912	+	0.0864737i
$905$	12.8709	−	14.8538i	0.427843	−	0.493758i
$906$	−2.51406	+	17.4857i	−0.0835240	+	0.580922i
$907$	6.20721	+	13.5919i	0.206107	+	0.451312i	0.984252	−	0.176774i	$-0.0565661\pi$
$907$	6.20721	+	13.5919i	0.206107	+	0.451312i	−0.778144	+	0.628085i	$0.783839\pi$
$908$	−13.3201	−	3.91113i	−0.442043	−	0.129796i
$909$	0.824976	+	0.242235i	0.0273627	+	0.00803442i
$910$	4.87250	+	10.6693i	0.161522	+	0.353684i
$911$	−7.54641	+	52.4864i	−0.250024	+	1.73895i	0.348017	+	0.937488i	$0.386855\pi$
$911$	−7.54641	+	52.4864i	−0.250024	+	1.73895i	−0.598041	+	0.801465i	$0.704054\pi$
$912$	4.38949	−	5.06574i	0.145350	−	0.167743i
$913$	−16.2902	+	35.6706i	−0.539128	+	1.18053i
$914$	−8.90977	−	5.72596i	−0.294709	−	0.189398i
$915$	0.238046	+	1.65564i	0.00786955	+	0.0547339i
$916$	−14.5126	+	9.32666i	−0.479509	+	0.308161i
$917$	21.6360	+	24.9693i	0.714484	+	0.824559i
$918$	1.85970	−	0.546057i	0.0613792	−	0.0180226i
$919$	−47.6673			−1.57240			−0.786200	−	0.617973i	$-0.787954\pi$
$919$	−47.6673			−1.57240			−0.786200	+	0.617973i	$0.787954\pi$
$920$	−3.95683	−	2.70988i	−0.130453	−	0.0893423i
$921$	−15.1322			−0.498623
$922$	14.2142	−	4.17366i	0.468119	−	0.137452i
$923$	−9.82863	−	11.3428i	−0.323513	−	0.373354i
$924$	11.9014	−	7.64855i	0.391527	−	0.251619i
$925$	−1.32433	−	9.21089i	−0.0435436	−	0.302852i
$926$	−29.3202	−	18.8430i	−0.963523	−	0.619219i
$927$	−3.19163	+	6.98869i	−0.104827	+	0.229539i
$928$	−4.32472	+	4.99099i	−0.141966	+	0.163837i
$929$	2.31365	−	16.0918i	0.0759085	−	0.527955i	−0.916018	−	0.401138i	$-0.868615\pi$
$929$	2.31365	−	16.0918i	0.0759085	−	0.527955i	0.991926	−	0.126817i	$-0.0404762\pi$
$930$	2.33114	+	5.10449i	0.0764412	+	0.167383i
$931$	25.6268	+	7.52472i	0.839885	+	0.246613i
$932$	−4.31901	−	1.26818i	−0.141474	−	0.0415405i
$933$	13.0898	+	28.6626i	0.428540	+	0.938371i
$934$	4.13584	−	28.7654i	0.135329	−	0.941233i
$935$	−5.41785	+	6.25254i	−0.177183	+	0.204480i
$936$	−1.47014	+	3.21916i	−0.0480531	+	0.105222i
$937$	14.1970	+	9.12385i	0.463795	+	0.298063i	0.751592	−	0.659628i	$-0.229286\pi$
$937$	14.1970	+	9.12385i	0.463795	+	0.298063i	−0.287797	+	0.957692i	$0.592923\pi$
$938$	7.42081	+	51.6129i	0.242298	+	1.68522i
$939$	−0.682907	+	0.438878i	−0.0222858	+	0.0143222i
$940$	−7.29887	−	8.42335i	−0.238063	−	0.274739i
$941$	−7.57214	+	2.22338i	−0.246845	+	0.0724801i	−0.402814	−	0.915282i	$-0.631968\pi$
$941$	−7.57214	+	2.22338i	−0.246845	+	0.0724801i	0.155970	+	0.987762i	$0.450150\pi$
$942$	5.29854			0.172636
$943$	−1.91808	−	16.8261i	−0.0624613	−	0.547933i
$944$	6.99389			0.227632
$945$	3.18005	−	0.933748i	0.103447	−	0.0303748i
$946$	−11.6016	−	13.3889i	−0.377199	−	0.435311i
$947$	3.18239	−	2.04520i	0.103414	−	0.0664600i	−0.487912	−	0.872893i	$-0.662241\pi$
$947$	3.18239	−	2.04520i	0.103414	−	0.0664600i	0.591325	+	0.806433i	$0.298605\pi$
$948$	−0.959246	−	6.67170i	−0.0311549	−	0.216687i
$949$	29.4226	+	18.9087i	0.955097	+	0.613803i
$950$	−2.78450	+	6.09720i	−0.0903411	+	0.197819i
$951$	7.81265	−	9.01628i	0.253342	−	0.292373i
$952$	−0.914205	+	6.35843i	−0.0296296	+	0.206078i
$953$	−23.7652	−	52.0386i	−0.769831	−	1.68570i	−0.727024	−	0.686612i	$-0.759097\pi$
$953$	−23.7652	−	52.0386i	−0.769831	−	1.68570i	−0.0428072	−	0.999083i	$-0.513630\pi$
$954$	4.57464	+	1.34324i	0.148110	+	0.0434889i
$955$	−5.26697	−	1.54652i	−0.170435	−	0.0500443i
$956$	1.28023	+	2.80331i	0.0414055	+	0.0906654i
$957$	4.01178	−	27.9025i	0.129682	−	0.901961i
$958$	−18.4097	+	21.2459i	−0.594791	+	0.686425i
$959$	16.6575	−	36.4748i	0.537899	−	1.17783i
$960$	0.841254	+	0.540641i	0.0271513	+	0.0174491i
$961$	−0.0697419	−	0.485065i	−0.00224974	−	0.0156473i
$962$	−27.7044	+	17.8045i	−0.893226	+	0.574041i
$963$	0.147621	+	0.170364i	0.00475701	+	0.00548989i
$964$	19.1215	−	5.61459i	0.615863	−	0.180834i
$965$	15.5357			0.500111
$966$	13.6176	−	8.19805i	0.438138	−	0.263768i
$967$	35.4132			1.13881			0.569406	−	0.822056i	$-0.307173\pi$
$967$	35.4132			1.13881			0.569406	+	0.822056i	$0.307173\pi$
$968$	−6.92783	+	2.03419i	−0.222669	+	0.0653815i
$969$	−8.50774	−	9.81846i	−0.273308	−	0.315414i
$970$	15.5824	−	10.0142i	0.500320	−	0.321536i
$971$	−6.02151	−	41.8805i	−0.193239	−	1.34401i	−0.823363	−	0.567515i	$-0.807905\pi$
$971$	−6.02151	−	41.8805i	−0.193239	−	1.34401i	0.630124	−	0.776495i	$-0.283004\pi$
$972$	0.841254	+	0.540641i	0.0269832	+	0.0173411i
$973$	−4.74863	+	10.3981i	−0.152234	+	0.333346i
$974$	−19.3303	+	22.3084i	−0.619383	+	0.714806i
$975$	0.503648	−	3.50295i	0.0161297	−	0.112184i
$976$	−0.694852	−	1.52151i	−0.0222417	−	0.0487025i
$977$	−12.2967	−	3.61062i	−0.393405	−	0.115514i	0.0790462	−	0.996871i	$-0.474813\pi$
$977$	−12.2967	−	3.61062i	−0.393405	−	0.115514i	−0.472451	+	0.881357i	$0.656631\pi$
$978$	−14.4322	−	4.23769i	−0.461492	−	0.135506i
$979$	−25.5686	−	55.9875i	−0.817177	−	1.78937i
$980$	−0.567072	+	3.94407i	−0.0181145	+	0.125989i
$981$	9.81159	−	11.3232i	0.313260	−	0.361521i
$982$	4.28518	−	9.38323i	0.136746	−	0.299431i
$983$	41.8668	+	26.9062i	1.33534	+	0.858174i	0.996575	−	0.0826953i	$-0.0263528\pi$
$983$	41.8668	+	26.9062i	1.33534	+	0.858174i	0.338770	+	0.940869i	$0.389989\pi$
$984$	0.502543	+	3.49527i	0.0160205	+	0.111425i
$985$	−5.05828	+	3.25076i	−0.161170	+	0.103578i
$986$	8.38221	+	9.67359i	0.266944	+	0.308070i
$987$	35.4439	−	10.4073i	1.12819	−	0.331267i
$988$	23.7215			0.754681
$989$	−12.5885	−	15.4182i	−0.400292	−	0.490271i
$990$	−4.26852			−0.135663
$991$	43.9343	−	12.9003i	1.39562	−	0.409790i	0.504441	−	0.863446i	$-0.331699\pi$
$991$	43.9343	−	12.9003i	1.39562	−	0.409790i	0.891177	+	0.453656i	$0.149880\pi$
$992$	−3.67482	−	4.24096i	−0.116676	−	0.134651i
$993$	14.4307	−	9.27406i	0.457945	−	0.294303i
$994$	−2.00037	−	13.9129i	−0.0634478	−	0.441289i
$995$	0.248670	+	0.159811i	0.00788337	+	0.00506634i
$996$	3.81636	−	8.35667i	0.120926	−	0.264791i
$997$	−0.887210	+	1.02390i	−0.0280982	+	0.0324271i	−0.769625	−	0.638496i	$-0.779557\pi$
$997$	−0.887210	+	1.02390i	−0.0280982	+	0.0324271i	0.741527	+	0.670924i	$0.234102\pi$
$998$	5.57172	−	38.7522i	0.176370	−	1.22668i
$999$	3.86569	+	8.46468i	0.122305	+	0.267811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.g.331.1	yes	30
23.18	even	11	inner	690.2.m.g.271.1	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.g.271.1	✓	30	23.18	even	11	inner
690.2.m.g.331.1	yes	30	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 + 0.281733i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-1.37681 + 3.01480i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.959493 + 0.281733i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-1.37681 + 3.01480i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.415415 + 0.909632i) q^{10} +(4.09562 + 1.20258i) q^{11} +(-0.959493 - 0.281733i) q^{12} +(-1.47014 - 3.21916i) q^{13} +(0.471675 - 3.28057i) q^{14} +(-0.654861 + 0.755750i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-1.63053 - 1.04787i) q^{17} +(-0.142315 - 0.989821i) q^{18} +(-5.63886 + 3.62388i) q^{19} +(-0.654861 - 0.755750i) q^{20} +(3.18005 - 0.933748i) q^{21} -4.26852 q^{22} +(-4.79377 - 0.140475i) q^{23} +1.00000 q^{24} +(-0.959493 + 0.281733i) q^{25} +(2.31753 + 2.67458i) q^{26} +(0.841254 - 0.540641i) q^{27} +(0.471675 + 3.28057i) q^{28} +(5.55566 + 3.57041i) q^{29} +(0.415415 - 0.909632i) q^{30} +(-3.67482 + 4.24096i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(-1.77321 - 3.88279i) q^{33} +(1.85970 + 0.546057i) q^{34} +(3.18005 + 0.933748i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-1.32433 + 9.21089i) q^{37} +(4.38949 - 5.06574i) q^{38} +(-1.47014 + 3.21916i) q^{39} +(0.841254 + 0.540641i) q^{40} +(0.502543 + 3.49527i) q^{41} +(-2.78817 + 1.79185i) q^{42} +(2.71793 + 3.13666i) q^{43} +(4.09562 - 1.20258i) q^{44} +1.00000 q^{45} +(4.63917 - 1.21578i) q^{46} +11.1457 q^{47} +(-0.959493 + 0.281733i) q^{48} +(-2.60938 - 3.01138i) q^{49} +(0.841254 - 0.540641i) q^{50} +(0.275836 + 1.91848i) q^{51} +(-2.97717 - 1.91331i) q^{52} +(-1.98060 + 4.33692i) q^{53} +(-0.654861 + 0.755750i) q^{54} +(0.607474 - 4.22508i) q^{55} +(-1.37681 - 3.01480i) q^{56} +(6.43142 + 1.88843i) q^{57} +(-6.33652 - 1.86057i) q^{58} +(2.90537 + 6.36187i) q^{59} +(-0.142315 + 0.989821i) q^{60} +(1.09537 - 1.26412i) q^{61} +(2.33114 - 5.10449i) q^{62} +(-2.78817 - 1.79185i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-2.97717 + 1.91331i) q^{65} +(2.79529 + 3.22594i) q^{66} +(-15.0956 + 4.43247i) q^{67} -1.93821 q^{68} +(3.03309 + 3.71488i) q^{69} -3.31431 q^{70} +(4.06919 - 1.19482i) q^{71} +(-0.654861 - 0.755750i) q^{72} +(-8.31387 + 5.34300i) q^{73} +(-1.32433 - 9.21089i) q^{74} +(0.841254 + 0.540641i) q^{75} +(-2.78450 + 6.09720i) q^{76} +(-9.26445 + 10.6917i) q^{77} +(0.503648 - 3.50295i) q^{78} +(2.80003 + 6.13120i) q^{79} +(-0.959493 - 0.281733i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-1.46692 - 3.21210i) q^{82} +(-1.30743 + 9.09336i) q^{83} +(2.17041 - 2.50479i) q^{84} +(-0.805161 + 1.76306i) q^{85} +(-3.49153 - 2.24387i) q^{86} +(-0.939852 - 6.53681i) q^{87} +(-3.59091 + 2.30774i) q^{88} +(-9.44270 - 10.8975i) q^{89} +(-0.959493 + 0.281733i) q^{90} +11.7292 q^{91} +(-4.10873 + 2.47353i) q^{92} +5.61160 q^{93} +(-10.6942 + 3.14010i) q^{94} +(4.38949 + 5.06574i) q^{95} +(0.841254 - 0.540641i) q^{96} +(-2.63607 - 18.3343i) q^{97} +(3.35209 + 2.15425i) q^{98} +(-1.77321 + 3.88279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * q^99

Introduction

L-functions

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