LMFDB - Embedded newform 690.2.m.h.331.3

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			331.3
Character	$\chi$	$=$	690.331
Dual form			690.2.m.h.271.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 - 0.281733i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.142315 + 0.989821i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(1.63201 - 3.57361i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(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} +(1.63201 - 3.57361i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.415415 + 0.909632i) q^{10} +(-6.13770 - 1.80219i) q^{11} +(-0.959493 - 0.281733i) q^{12} +(-0.723107 - 1.58338i) q^{13} +(0.559102 - 3.88864i) q^{14} +(0.654861 - 0.755750i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-0.131904 - 0.0847692i) q^{17} +(0.142315 + 0.989821i) q^{18} +(6.10613 - 3.92417i) q^{19} +(0.654861 + 0.755750i) q^{20} +(-3.76949 + 1.10682i) q^{21} -6.39682 q^{22} +(4.11665 + 2.46032i) q^{23} -1.00000 q^{24} +(-0.959493 + 0.281733i) q^{25} +(-1.13991 - 1.31552i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-0.559102 - 3.88864i) q^{28} +(-5.92269 - 3.80628i) q^{29} +(0.415415 - 0.909632i) q^{30} +(3.21133 - 3.70607i) q^{31} +(0.142315 - 0.989821i) q^{32} +(2.65733 + 5.81875i) q^{33} +(-0.150443 - 0.0441740i) q^{34} +(3.76949 + 1.10682i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-1.18509 + 8.24248i) q^{37} +(4.75322 - 5.48551i) q^{38} +(-0.723107 + 1.58338i) q^{39} +(0.841254 + 0.540641i) q^{40} +(-0.548601 - 3.81561i) q^{41} +(-3.30497 + 2.12398i) q^{42} +(0.521265 + 0.601572i) q^{43} +(-6.13770 + 1.80219i) q^{44} -1.00000 q^{45} +(4.64305 + 1.20086i) q^{46} -4.44479 q^{47} +(-0.959493 + 0.281733i) q^{48} +(-5.52318 - 6.37409i) q^{49} +(-0.841254 + 0.540641i) q^{50} +(0.0223141 + 0.155198i) q^{51} +(-1.46436 - 0.941085i) q^{52} +(3.34250 - 7.31906i) q^{53} +(0.654861 - 0.755750i) q^{54} +(0.910362 - 6.33171i) q^{55} +(-1.63201 - 3.57361i) q^{56} +(-6.96435 - 2.04492i) q^{57} +(-6.75513 - 1.98348i) q^{58} +(2.41963 + 5.29825i) q^{59} +(0.142315 - 0.989821i) q^{60} +(-1.01059 + 1.16628i) q^{61} +(2.03713 - 4.46069i) q^{62} +(3.30497 + 2.12398i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(1.46436 - 0.941085i) q^{65} +(4.18902 + 4.83439i) q^{66} +(1.51830 - 0.445814i) q^{67} -0.156794 q^{68} +(-0.836450 - 4.72232i) q^{69} +3.92863 q^{70} +(14.1577 - 4.15706i) q^{71} +(0.654861 + 0.755750i) q^{72} +(1.67555 - 1.07681i) q^{73} +(1.18509 + 8.24248i) q^{74} +(0.841254 + 0.540641i) q^{75} +(3.01523 - 6.60244i) q^{76} +(-16.4571 + 18.9925i) q^{77} +(-0.247725 + 1.72297i) q^{78} +(1.30733 + 2.86265i) q^{79} +(0.959493 + 0.281733i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-1.60136 - 3.50649i) q^{82} +(-1.35884 + 9.45094i) q^{83} +(-2.57271 + 2.96906i) q^{84} +(0.0651346 - 0.142625i) q^{85} +(0.669633 + 0.430347i) q^{86} +(1.00194 + 6.96865i) q^{87} +(-5.38134 + 3.45838i) q^{88} +(11.8388 + 13.6627i) q^{89} +(-0.959493 + 0.281733i) q^{90} -6.83851 q^{91} +(4.79330 - 0.155879i) q^{92} -4.90384 q^{93} +(-4.26474 + 1.25224i) q^{94} +(4.75322 + 5.48551i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(0.522476 + 3.63390i) q^{97} +(-7.09524 - 4.55983i) q^{98} +(2.65733 - 5.81875i) 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	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 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 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * 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
$7$	1.63201	−	3.57361i	0.616842	−	1.35070i	−0.300952	−	0.953639i	$-0.597304\pi$
$7$	1.63201	−	3.57361i	0.616842	−	1.35070i	0.917794	−	0.397057i	$-0.129968\pi$
$8$	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
$11$	−6.13770	−	1.80219i	−1.85059	−	0.543381i	−0.999842	−	0.0178024i	$-0.994333\pi$
$11$	−6.13770	−	1.80219i	−1.85059	−	0.543381i	−0.850745	−	0.525579i	$-0.823849\pi$
$12$	−0.959493	−	0.281733i	−0.276982	−	0.0813292i
$13$	−0.723107	−	1.58338i	−0.200554	−	0.439151i	0.782456	−	0.622706i	$-0.213967\pi$
$13$	−0.723107	−	1.58338i	−0.200554	−	0.439151i	−0.983009	+	0.183555i	$0.941240\pi$
$14$	0.559102	−	3.88864i	0.149426	−	1.03928i
$15$	0.654861	−	0.755750i	0.169084	−	0.195134i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	−0.131904	−	0.0847692i	−0.0319913	−	0.0205596i	0.524547	−	0.851381i	$-0.324235\pi$
$17$	−0.131904	−	0.0847692i	−0.0319913	−	0.0205596i	−0.556539	+	0.830822i	$0.687871\pi$
$18$	0.142315	+	0.989821i	0.0335439	+	0.233303i
$19$	6.10613	−	3.92417i	1.40084	−	0.900266i	0.400967	−	0.916093i	$-0.368674\pi$
$19$	6.10613	−	3.92417i	1.40084	−	0.900266i	0.999875	+	0.0158262i	$0.00503784\pi$
$20$	0.654861	+	0.755750i	0.146431	+	0.168991i
$21$	−3.76949	+	1.10682i	−0.822571	+	0.241529i
$22$	−6.39682			−1.36381
$23$	4.11665	+	2.46032i	0.858382	+	0.513012i
$23$	4.11665	+	2.46032i	0.858382	+	0.513012i
$24$	−1.00000			−0.204124
$25$	−0.959493	+	0.281733i	−0.191899	+	0.0563465i
$26$	−1.13991	−	1.31552i	−0.223554	−	0.257995i
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$	−0.559102	−	3.88864i	−0.105660	−	0.734884i
$29$	−5.92269	−	3.80628i	−1.09982	−	0.706808i	−0.140765	−	0.990043i	$-0.544956\pi$
$29$	−5.92269	−	3.80628i	−1.09982	−	0.706808i	−0.959051	+	0.283235i	$0.908592\pi$
$30$	0.415415	−	0.909632i	0.0758441	−	0.166075i
$31$	3.21133	−	3.70607i	0.576772	−	0.665631i	−0.390135	−	0.920758i	$-0.627572\pi$
$31$	3.21133	−	3.70607i	0.576772	−	0.665631i	0.966908	+	0.255127i	$0.0821172\pi$
$32$	0.142315	−	0.989821i	0.0251579	−	0.174977i
$33$	2.65733	+	5.81875i	0.462582	+	1.01291i
$34$	−0.150443	−	0.0441740i	−0.0258007	−	0.00757577i
$35$	3.76949	+	1.10682i	0.637160	+	0.187087i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	−1.18509	+	8.24248i	−0.194828	+	1.35506i	0.624183	+	0.781278i	$0.285432\pi$
$37$	−1.18509	+	8.24248i	−0.194828	+	1.35506i	−0.819011	+	0.573778i	$0.805477\pi$
$38$	4.75322	−	5.48551i	0.771074	−	0.889867i
$39$	−0.723107	+	1.58338i	−0.115790	+	0.253544i
$40$	0.841254	+	0.540641i	0.133014	+	0.0854828i
$41$	−0.548601	−	3.81561i	−0.0856772	−	0.595898i	−0.986752	−	0.162235i	$-0.948130\pi$
$41$	−0.548601	−	3.81561i	−0.0856772	−	0.595898i	0.901075	−	0.433663i	$-0.142779\pi$
$42$	−3.30497	+	2.12398i	−0.509968	+	0.327737i
$43$	0.521265	+	0.601572i	0.0794922	+	0.0917389i	0.794102	−	0.607784i	$-0.207941\pi$
$43$	0.521265	+	0.601572i	0.0794922	+	0.0917389i	−0.714610	+	0.699523i	$0.753396\pi$
$44$	−6.13770	+	1.80219i	−0.925293	+	0.271691i
$45$	−1.00000			−0.149071
$46$	4.64305	+	1.20086i	0.684581	+	0.177058i
$47$	−4.44479			−0.648339			−0.324170	−	0.945999i	$-0.605085\pi$
$47$	−4.44479			−0.648339			−0.324170	+	0.945999i	$0.605085\pi$
$48$	−0.959493	+	0.281733i	−0.138491	+	0.0406646i
$49$	−5.52318	−	6.37409i	−0.789026	−	0.910584i
$50$	−0.841254	+	0.540641i	−0.118971	+	0.0764582i
$51$	0.0223141	+	0.155198i	0.00312460	+	0.0217321i
$52$	−1.46436	−	0.941085i	−0.203070	−	0.130505i
$53$	3.34250	−	7.31906i	0.459128	−	1.00535i	−0.528558	−	0.848897i	$-0.677267\pi$
$53$	3.34250	−	7.31906i	0.459128	−	1.00535i	0.987685	−	0.156452i	$-0.0500058\pi$
$54$	0.654861	−	0.755750i	0.0891153	−	0.102844i
$55$	0.910362	−	6.33171i	0.122753	−	0.853767i
$56$	−1.63201	−	3.57361i	−0.218087	−	0.477543i
$57$	−6.96435	−	2.04492i	−0.922451	−	0.270856i
$58$	−6.75513	−	1.98348i	−0.886992	−	0.260444i
$59$	2.41963	+	5.29825i	0.315009	+	0.689773i	0.999219	−	0.0395118i	$-0.0125803\pi$
$59$	2.41963	+	5.29825i	0.315009	+	0.689773i	−0.684210	+	0.729285i	$0.739853\pi$
$60$	0.142315	−	0.989821i	0.0183728	−	0.127785i
$61$	−1.01059	+	1.16628i	−0.129392	+	0.149327i	−0.816749	−	0.576994i	$-0.804226\pi$
$61$	−1.01059	+	1.16628i	−0.129392	+	0.149327i	0.687356	+	0.726320i	$0.258771\pi$
$62$	2.03713	−	4.46069i	0.258716	−	0.566508i
$63$	3.30497	+	2.12398i	0.416387	+	0.267596i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	1.46436	−	0.941085i	0.181631	−	0.116727i
$66$	4.18902	+	4.83439i	0.515633	+	0.595072i
$67$	1.51830	−	0.445814i	0.185490	−	0.0544648i	−0.187668	−	0.982232i	$-0.560093\pi$
$67$	1.51830	−	0.445814i	0.185490	−	0.0544648i	0.373158	+	0.927768i	$0.378275\pi$
$68$	−0.156794			−0.0190141
$69$	−0.836450	−	4.72232i	−0.100697	−	0.568501i
$70$	3.92863			0.469561
$71$	14.1577	−	4.15706i	1.68021	−	0.493353i	0.704000	−	0.710200i	$-0.251396\pi$
$71$	14.1577	−	4.15706i	1.68021	−	0.493353i	0.976205	+	0.216847i	$0.0695774\pi$
$72$	0.654861	+	0.755750i	0.0771761	+	0.0890659i
$73$	1.67555	−	1.07681i	0.196109	−	0.126031i	−0.438901	−	0.898535i	$-0.644632\pi$
$73$	1.67555	−	1.07681i	0.196109	−	0.126031i	0.635010	+	0.772504i	$0.280996\pi$
$74$	1.18509	+	8.24248i	0.137764	+	0.958169i
$75$	0.841254	+	0.540641i	0.0971396	+	0.0624278i
$76$	3.01523	−	6.60244i	0.345871	−	0.757352i
$77$	−16.4571	+	18.9925i	−1.87546	+	2.16440i
$78$	−0.247725	+	1.72297i	−0.0280494	+	0.195088i
$79$	1.30733	+	2.86265i	0.147086	+	0.322073i	0.968807	−	0.247817i	$-0.0797131\pi$
$79$	1.30733	+	2.86265i	0.147086	+	0.322073i	−0.821721	+	0.569890i	$0.806986\pi$
$80$	0.959493	+	0.281733i	0.107275	+	0.0314987i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−1.60136	−	3.50649i	−0.176841	−	0.387227i
$83$	−1.35884	+	9.45094i	−0.149152	+	1.03738i	0.768460	+	0.639898i	$0.221023\pi$
$83$	−1.35884	+	9.45094i	−0.149152	+	1.03738i	−0.917612	+	0.397478i	$0.869886\pi$
$84$	−2.57271	+	2.96906i	−0.280705	+	0.323951i
$85$	0.0651346	−	0.142625i	0.00706484	−	0.0154698i
$86$	0.669633	+	0.430347i	0.0722084	+	0.0464055i
$87$	1.00194	+	6.96865i	0.107419	+	0.747118i
$88$	−5.38134	+	3.45838i	−0.573653	+	0.368665i
$89$	11.8388	+	13.6627i	1.25491	+	1.44824i	0.843803	+	0.536654i	$0.180312\pi$
$89$	11.8388	+	13.6627i	1.25491	+	1.44824i	0.411106	+	0.911588i	$0.365143\pi$
$90$	−0.959493	+	0.281733i	−0.101139	+	0.0296972i
$91$	−6.83851			−0.716870
$92$	4.79330	−	0.155879i	0.499736	−	0.0162515i
$93$	−4.90384			−0.508504
$94$	−4.26474	+	1.25224i	−0.439875	+	0.129159i
$95$	4.75322	+	5.48551i	0.487670	+	0.562801i
$96$	−0.841254	+	0.540641i	−0.0858601	+	0.0551789i
$97$	0.522476	+	3.63390i	0.0530494	+	0.368966i	0.999002	+	0.0446620i	$0.0142211\pi$
$97$	0.522476	+	3.63390i	0.0530494	+	0.368966i	−0.945953	+	0.324304i	$0.894870\pi$
$98$	−7.09524	−	4.55983i	−0.716727	−	0.460613i
$99$	2.65733	−	5.81875i	0.267072	−	0.584806i
$100$	−0.654861	+	0.755750i	−0.0654861	+	0.0755750i
$101$	−1.48805	+	10.3496i	−0.148067	+	1.02983i	0.771313	+	0.636456i	$0.219600\pi$
$101$	−1.48805	+	10.3496i	−0.148067	+	1.02983i	−0.919380	+	0.393371i	$0.871309\pi$
$102$	0.0651346	+	0.142625i	0.00644928	+	0.0141220i
$103$	−6.32596	−	1.85747i	−0.623315	−	0.183022i	−0.0452013	−	0.998978i	$-0.514393\pi$
$103$	−6.32596	−	1.85747i	−0.623315	−	0.183022i	−0.578114	+	0.815956i	$0.696211\pi$
$104$	−1.67018	−	0.490408i	−0.163774	−	0.0480884i
$105$	−1.63201	−	3.57361i	−0.159268	−	0.348748i
$106$	1.14509	−	7.96428i	0.111221	−	0.773559i
$107$	−8.87272	+	10.2397i	−0.857759	+	0.989906i	0.142241	+	0.989832i	$0.454569\pi$
$107$	−8.87272	+	10.2397i	−0.857759	+	0.989906i	−1.00000		7.41018e-5i	$0.999976\pi$
$108$	0.415415	−	0.909632i	0.0399733	−	0.0875294i
$109$	10.2535	+	6.58955i	0.982112	+	0.631165i	0.930032	−	0.367478i	$-0.119779\pi$
$109$	10.2535	+	6.58955i	0.982112	+	0.631165i	0.0520795	+	0.998643i	$0.483415\pi$
$110$	−0.910362	−	6.33171i	−0.0867996	−	0.603705i
$111$	7.00532	−	4.50205i	0.664916	−	0.427315i
$112$	−2.57271	−	2.96906i	−0.243098	−	0.280550i
$113$	12.6482	−	3.71385i	1.18984	−	0.349370i	0.373883	−	0.927476i	$-0.378026\pi$
$113$	12.6482	−	3.71385i	1.18984	−	0.349370i	0.815962	+	0.578106i	$0.196208\pi$
$114$	−7.25837			−0.679808
$115$	−1.84941	+	4.42489i	−0.172459	+	0.412623i
$116$	−7.04031			−0.653676
$117$	1.67018	−	0.490408i	0.154408	−	0.0453382i
$118$	3.81430	+	4.40194i	0.351135	+	0.405232i
$119$	−0.518200	+	0.333027i	−0.0475033	+	0.0305285i
$120$	−0.142315	−	0.989821i	−0.0129915	−	0.0903579i
$121$	25.1697	+	16.1756i	2.28815	+	1.47051i
$122$	−0.641072	+	1.40375i	−0.0580399	+	0.127090i
$123$	−2.52439	+	2.91330i	−0.227616	+	0.262683i
$124$	0.697889	−	4.85393i	0.0626723	−	0.435895i
$125$	−0.415415	−	0.909632i	−0.0371558	−	0.0813600i
$126$	3.76949	+	1.10682i	0.335813	+	0.0986036i
$127$	−1.52579	−	0.448011i	−0.135392	−	0.0397546i	0.213335	−	0.976979i	$-0.431568\pi$
$127$	−1.52579	−	0.448011i	−0.135392	−	0.0397546i	−0.348726	+	0.937225i	$0.613386\pi$
$128$	−0.415415	−	0.909632i	−0.0367178	−	0.0804009i
$129$	0.113282	−	0.787892i	0.00997390	−	0.0693700i
$130$	1.13991	−	1.31552i	0.0999764	−	0.115379i
$131$	2.26236	−	4.95387i	0.197663	−	0.432822i	−0.784682	−	0.619898i	$-0.787174\pi$
$131$	2.26236	−	4.95387i	0.197663	−	0.432822i	0.982345	+	0.187077i	$0.0599012\pi$
$132$	5.38134	+	3.45838i	0.468386	+	0.301013i
$133$	−4.05817	−	28.2252i	−0.351888	−	2.44743i
$134$	1.33120	−	0.855511i	0.114998	−	0.0739049i
$135$	0.654861	+	0.755750i	0.0563614	+	0.0650446i
$136$	−0.150443	+	0.0441740i	−0.0129004	+	0.00378789i
$137$	−9.30058			−0.794602			−0.397301	−	0.917688i	$-0.630053\pi$
$137$	−9.30058			−0.794602			−0.397301	+	0.917688i	$0.630053\pi$
$138$	−2.13300	−	4.29538i	−0.181573	−	0.365647i
$139$	8.55577			0.725691			0.362846	−	0.931849i	$-0.381805\pi$
$139$	8.55577			0.725691			0.362846	+	0.931849i	$0.381805\pi$
$140$	3.76949	−	1.10682i	0.318580	−	0.0935436i
$141$	2.91072	+	3.35915i	0.245127	+	0.282891i
$142$	12.4130	−	7.97735i	1.04168	−	0.669444i
$143$	1.58465	+	11.0215i	0.132515	+	0.921665i
$144$	0.841254	+	0.540641i	0.0701045	+	0.0450534i
$145$	2.92465	−	6.40409i	0.242879	−	0.531831i
$146$	1.30431	−	1.50525i	0.107945	−	0.124575i
$147$	−1.20030	+	8.34828i	−0.0989992	+	0.688555i
$148$	3.45926	+	7.57473i	0.284350	+	0.622639i
$149$	−15.5770	−	4.57382i	−1.27612	−	0.374702i	−0.427647	−	0.903946i	$-0.640657\pi$
$149$	−15.5770	−	4.57382i	−1.27612	−	0.374702i	−0.848470	+	0.529244i	$0.822476\pi$
$150$	0.959493	+	0.281733i	0.0783423	+	0.0230034i
$151$	1.39447	+	3.05346i	0.113480	+	0.248487i	0.957847	−	0.287278i	$-0.0927504\pi$
$151$	1.39447	+	3.05346i	0.113480	+	0.248487i	−0.844367	+	0.535766i	$0.820023\pi$
$152$	1.03297	−	7.18449i	0.0837852	−	0.582739i
$153$	0.102678	−	0.118497i	0.00830104	−	0.00957991i
$154$	−10.4397	+	22.8597i	−0.841253	+	1.84209i
$155$	4.12537	+	2.65122i	0.331358	+	0.212951i
$156$	0.247725	+	1.72297i	0.0198339	+	0.137948i
$157$	−10.7647	+	6.91806i	−0.859118	+	0.552121i	−0.894406	−	0.447256i	$-0.852401\pi$
$157$	−10.7647	+	6.91806i	−0.859118	+	0.552121i	0.0352885	+	0.999377i	$0.488765\pi$
$158$	2.06087	+	2.37838i	0.163954	+	0.189213i
$159$	−7.72025	+	2.26687i	−0.612256	+	0.179774i
$160$	1.00000			0.0790569
$161$	15.5106	−	10.6960i	1.22241	−	0.842965i
$162$	−1.00000			−0.0785674
$163$	18.2602	−	5.36169i	1.43025	−	0.419960i	0.527292	−	0.849684i	$-0.323207\pi$
$163$	18.2602	−	5.36169i	1.43025	−	0.419960i	0.902960	+	0.429724i	$0.141389\pi$
$164$	−2.52439	−	2.91330i	−0.197121	−	0.227490i
$165$	−5.38134	+	3.45838i	−0.418937	+	0.269235i
$166$	1.35884	+	9.45094i	0.105466	+	0.733535i
$167$	9.21745	+	5.92370i	0.713268	+	0.458389i	0.846289	−	0.532724i	$-0.178832\pi$
$167$	9.21745	+	5.92370i	0.713268	+	0.458389i	−0.133021	+	0.991113i	$0.542468\pi$
$168$	−1.63201	+	3.57361i	−0.125912	+	0.275710i
$169$	6.52897	−	7.53483i	0.502229	−	0.579603i
$170$	0.0223141	−	0.155198i	0.00171141	−	0.0119031i
$171$	3.01523	+	6.60244i	0.230581	+	0.504901i
$172$	0.763751	+	0.224257i	0.0582354	+	0.0170995i
$173$	16.0139	+	4.70211i	1.21752	+	0.357495i	0.826525	−	0.562900i	$-0.190314\pi$
$173$	16.0139	+	4.70211i	1.21752	+	0.357495i	0.390991	+	0.920395i	$0.372132\pi$
$174$	2.92465	+	6.40409i	0.221717	+	0.485493i
$175$	−0.559102	+	3.88864i	−0.0422642	+	0.293954i
$176$	−4.18902	+	4.83439i	−0.315760	+	0.364406i
$177$	2.41963	−	5.29825i	0.181870	−	0.398241i
$178$	15.2085	+	9.77388i	1.13992	+	0.732583i
$179$	−2.26621	−	15.7618i	−0.169384	−	1.17809i	−0.880160	−	0.474676i	$-0.842565\pi$
$179$	−2.26621	−	15.7618i	−0.169384	−	1.17809i	0.710776	−	0.703418i	$-0.248344\pi$
$180$	−0.841254	+	0.540641i	−0.0627033	+	0.0402970i
$181$	−14.6165	−	16.8684i	−1.08644	−	1.25382i	−0.965290	−	0.261181i	$-0.915888\pi$
$181$	−14.6165	−	16.8684i	−1.08644	−	1.25382i	−0.121147	−	0.992635i	$-0.538657\pi$
$182$	−6.56150	+	1.92663i	−0.486371	+	0.142811i
$183$	1.54321			0.114077
$184$	4.55522	−	1.49999i	0.335815	−	0.110581i
$185$	−8.32724			−0.612231
$186$	−4.70520	+	1.38157i	−0.345002	+	0.101302i
$187$	0.656814	+	0.758004i	0.0480310	+	0.0554307i
$188$	−3.73920	+	2.40303i	−0.272709	+	0.175259i
$189$	−0.559102	−	3.88864i	−0.0406687	−	0.282857i
$190$	6.10613	+	3.92417i	0.442985	+	0.284689i
$191$	−5.34789	+	11.7102i	−0.386959	+	0.847323i	0.611468	+	0.791269i	$0.290579\pi$
$191$	−5.34789	+	11.7102i	−0.386959	+	0.847323i	−0.998428	+	0.0560540i	$0.982148\pi$
$192$	−0.654861	+	0.755750i	−0.0472605	+	0.0545415i
$193$	−0.949111	+	6.60121i	−0.0683185	+	0.475166i	0.926726	+	0.375737i	$0.122611\pi$
$193$	−0.949111	+	6.60121i	−0.0683185	+	0.475166i	−0.995045	+	0.0994284i	$0.968299\pi$
$194$	1.52510	+	3.33950i	0.109496	+	0.239762i
$195$	−1.67018	−	0.490408i	−0.119604	−	0.0351188i
$196$	−8.09249	−	2.37617i	−0.578035	−	0.169726i
$197$	−2.55373	−	5.59189i	−0.181946	−	0.398406i	0.796579	−	0.604534i	$-0.206641\pi$
$197$	−2.55373	−	5.59189i	−0.181946	−	0.398406i	−0.978525	+	0.206128i	$0.933914\pi$
$198$	0.910362	−	6.33171i	0.0646966	−	0.449975i
$199$	−0.677702	+	0.782109i	−0.0480410	+	0.0554423i	−0.779261	−	0.626699i	$-0.784406\pi$
$199$	−0.677702	+	0.782109i	−0.0480410	+	0.0554423i	0.731220	+	0.682141i	$0.238951\pi$
$200$	−0.415415	+	0.909632i	−0.0293743	+	0.0643207i
$201$	−1.33120	−	0.855511i	−0.0938957	−	0.0603431i
$202$	1.48805	+	10.3496i	0.104699	+	0.728198i
$203$	−23.2680	+	14.9535i	−1.63310	+	1.04953i
$204$	0.102678	+	0.118497i	0.00718891	+	0.00829645i
$205$	3.69870	−	1.08603i	0.258328	−	0.0758520i
$206$	−6.59302			−0.459358
$207$	−3.02114	+	3.72461i	−0.209984	+	0.258878i
$208$	−1.74069			−0.120695
$209$	−44.5497	+	13.0810i	−3.08157	+	0.904830i
$210$	−2.57271	−	2.96906i	−0.177534	−	0.204885i
$211$	20.2463	−	13.0115i	1.39381	−	0.895747i	0.394082	−	0.919075i	$-0.371062\pi$
$211$	20.2463	−	13.0115i	1.39381	−	0.895747i	0.999728	+	0.0233276i	$0.00742608\pi$
$212$	−1.14509	−	7.96428i	−0.0786451	−	0.546989i
$213$	−12.4130	−	7.97735i	−0.850524	−	0.546599i
$214$	−5.62847	+	12.3246i	−0.384754	+	0.842494i
$215$	−0.521265	+	0.601572i	−0.0355500	+	0.0410269i
$216$	0.142315	−	0.989821i	0.00968330	−	0.0673488i
$217$	−8.00312	−	17.5244i	−0.543287	−	1.18963i
$218$	11.6947	+	3.43387i	0.792065	+	0.232571i
$219$	−1.91105	−	0.561136i	−0.129137	−	0.0379181i
$220$	−2.65733	−	5.81875i	−0.179157	−	0.392300i
$221$	−0.0388418	+	0.270151i	−0.00261279	+	0.0181723i
$222$	5.45318	−	6.29331i	0.365994	−	0.422379i
$223$	−6.55894	+	14.3621i	−0.439219	+	0.961755i	0.552522	+	0.833498i	$0.313666\pi$
$223$	−6.55894	+	14.3621i	−0.439219	+	0.961755i	−0.991741	+	0.128257i	$0.959062\pi$
$224$	−3.30497	−	2.12398i	−0.220823	−	0.141914i
$225$	−0.142315	−	0.989821i	−0.00948766	−	0.0659881i
$226$	11.0896	−	7.12683i	0.737667	−	0.474070i
$227$	−5.00940	−	5.78115i	−0.332485	−	0.383709i	0.564749	−	0.825263i	$-0.308973\pi$
$227$	−5.00940	−	5.78115i	−0.332485	−	0.383709i	−0.897235	+	0.441554i	$0.854427\pi$
$228$	−6.96435	+	2.04492i	−0.461226	+	0.135428i
$229$	−16.9131			−1.11765			−0.558824	−	0.829286i	$-0.688747\pi$
$229$	−16.9131			−1.11765			−0.558824	+	0.829286i	$0.688747\pi$
$230$	−0.527865	+	4.76669i	−0.0348064	+	0.314306i
$231$	25.1307			1.65348
$232$	−6.75513	+	1.98348i	−0.443496	+	0.130222i
$233$	10.3688	+	11.9663i	0.679284	+	0.783936i	0.985799	−	0.167930i	$-0.0537083\pi$
$233$	10.3688	+	11.9663i	0.679284	+	0.783936i	−0.306515	+	0.951866i	$0.599163\pi$
$234$	1.46436	−	0.941085i	0.0957280	−	0.0615207i
$235$	−0.632560	−	4.39955i	−0.0412636	−	0.286995i
$236$	4.89997	+	3.14902i	0.318961	+	0.204984i
$237$	1.30733	−	2.86265i	0.0849201	−	0.185949i
$238$	−0.403385	+	0.465531i	−0.0261475	+	0.0301759i
$239$	3.69699	−	25.7131i	0.239139	−	1.66325i	−0.417227	−	0.908802i	$-0.636998\pi$
$239$	3.69699	−	25.7131i	0.239139	−	1.66325i	0.656366	−	0.754443i	$-0.272093\pi$
$240$	−0.415415	−	0.909632i	−0.0268149	−	0.0587165i
$241$	−18.3583	−	5.39047i	−1.18256	−	0.347231i	−0.369399	−	0.929271i	$-0.620436\pi$
$241$	−18.3583	−	5.39047i	−1.18256	−	0.347231i	−0.813160	+	0.582040i	$0.802255\pi$
$242$	28.7073	+	8.42923i	1.84538	+	0.541852i
$243$	0.415415	+	0.909632i	0.0266489	+	0.0583529i
$244$	−0.219621	+	1.52750i	−0.0140598	+	0.0977882i
$245$	5.52318	−	6.37409i	0.352863	−	0.407226i
$246$	−1.60136	+	3.50649i	−0.102099	+	0.223566i
$247$	−10.6288	−	6.83074i	−0.676297	−	0.434630i
$248$	−0.697889	−	4.85393i	−0.0443160	−	0.308225i
$249$	8.03240	−	5.16211i	0.509032	−	0.327135i
$250$	−0.654861	−	0.755750i	−0.0414170	−	0.0477978i
$251$	−3.38386	+	0.993591i	−0.213587	+	0.0627149i	−0.386776	−	0.922174i	$-0.626411\pi$
$251$	−3.38386	+	0.993591i	−0.213587	+	0.0627149i	0.173188	+	0.984889i	$0.444593\pi$
$252$	3.92863			0.247480
$253$	−20.8328	−	22.5197i	−1.30975	−	1.41580i
$254$	−1.59020			−0.0997781
$255$	−0.150443	+	0.0441740i	−0.00942109	+	0.00276628i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	−13.9953	+	8.99426i	−0.873005	+	0.561046i	−0.898671	−	0.438624i	$-0.855466\pi$
$257$	−13.9953	+	8.99426i	−0.873005	+	0.561046i	0.0256653	+	0.999671i	$0.491830\pi$
$258$	−0.113282	−	0.787892i	−0.00705261	−	0.0490520i
$259$	27.5213	+	17.6869i	1.71009	+	1.09901i
$260$	0.723107	−	1.58338i	0.0448452	−	0.0981972i
$261$	4.61042	−	5.32071i	0.285378	−	0.329344i
$262$	0.775049	−	5.39058i	0.0478827	−	0.333031i
$263$	4.29105	+	9.39610i	0.264598	+	0.579388i	0.994568	−	0.104091i	$-0.0331933\pi$
$263$	4.29105	+	9.39610i	0.264598	+	0.579388i	−0.729970	+	0.683479i	$0.760466\pi$
$264$	6.13770	+	1.80219i	0.377749	+	0.110917i
$265$	7.72025	+	2.26687i	0.474251	+	0.139253i
$266$	−11.8457	−	25.9386i	−0.726309	−	1.59039i
$267$	2.57281	−	17.8943i	0.157454	−	1.09511i
$268$	1.03625	−	1.19590i	0.0632992	−	0.0730512i
$269$	2.80456	−	6.14113i	0.170997	−	0.374431i	−0.804659	−	0.593737i	$-0.797652\pi$
$269$	2.80456	−	6.14113i	0.170997	−	0.374431i	0.975656	+	0.219306i	$0.0703792\pi$
$270$	0.841254	+	0.540641i	0.0511971	+	0.0329024i
$271$	−1.08370	−	7.53729i	−0.0658300	−	0.457858i	−0.995899	−	0.0904727i	$-0.971162\pi$
$271$	−1.08370	−	7.53729i	−0.0658300	−	0.457858i	0.930069	−	0.367385i	$-0.119747\pi$
$272$	−0.131904	+	0.0847692i	−0.00799782	+	0.00513989i
$273$	4.47827	+	5.16820i	0.271037	+	0.312794i
$274$	−8.92384	+	2.62028i	−0.539109	+	0.158297i
$275$	6.39682			0.385743
$276$	−3.25675	−	3.52045i	−0.196033	−	0.211906i
$277$	6.09489			0.366207			0.183103	−	0.983094i	$-0.441386\pi$
$277$	6.09489			0.366207			0.183103	+	0.983094i	$0.441386\pi$
$278$	8.20920	−	2.41044i	0.492355	−	0.144569i
$279$	3.21133	+	3.70607i	0.192257	+	0.221877i
$280$	3.30497	−	2.12398i	0.197510	−	0.126932i
$281$	−0.423554	−	2.94589i	−0.0252671	−	0.175737i	0.973280	−	0.229621i	$-0.0737488\pi$
$281$	−0.423554	−	2.94589i	−0.0252671	−	0.175737i	−0.998547	+	0.0538846i	$0.982840\pi$
$282$	3.73920	+	2.40303i	0.222666	+	0.143099i
$283$	−5.31686	+	11.6423i	−0.316054	+	0.692062i	−0.999272	−	0.0381524i	$-0.987853\pi$
$283$	−5.31686	+	11.6423i	−0.316054	+	0.692062i	0.683218	+	0.730215i	$0.260580\pi$
$284$	9.66270	−	11.1514i	0.573376	−	0.661711i
$285$	1.03297	−	7.18449i	0.0611881	−	0.425572i
$286$	4.62558	+	10.1286i	0.273516	+	0.598917i
$287$	−14.5308	−	4.26663i	−0.857726	−	0.251851i
$288$	0.959493	+	0.281733i	0.0565387	+	0.0166013i
$289$	−7.05184	−	15.4414i	−0.414814	−	0.908317i
$290$	1.00194	−	6.96865i	0.0588360	−	0.409213i
$291$	2.40417	−	2.77456i	0.140935	−	0.162647i
$292$	0.827396	−	1.81174i	0.0484197	−	0.106024i
$293$	9.37893	+	6.02747i	0.547923	+	0.352129i	0.785131	−	0.619330i	$-0.212596\pi$
$293$	9.37893	+	6.02747i	0.547923	+	0.352129i	−0.237208	+	0.971459i	$0.576232\pi$
$294$	1.20030	+	8.34828i	0.0700030	+	0.486882i
$295$	−4.89997	+	3.14902i	−0.285287	+	0.183343i
$296$	5.45318	+	6.29331i	0.316960	+	0.365791i
$297$	−6.13770	+	1.80219i	−0.356146	+	0.104574i
$298$	−16.2346			−0.940445
$299$	0.918846	−	8.29731i	0.0531382	−	0.479846i
$300$	1.00000			0.0577350
$301$	3.00049	−	0.881024i	0.172946	−	0.0507814i
$302$	2.19825	+	2.53691i	0.126495	+	0.145983i
$303$	8.79620	−	5.65298i	0.505329	−	0.324755i
$304$	−1.03297	−	7.18449i	−0.0592451	−	0.412059i
$305$	−1.29823	−	0.834321i	−0.0743364	−	0.0477731i
$306$	0.0651346	−	0.142625i	0.00372350	−	0.00815332i
$307$	−10.1111	+	11.6689i	−0.577072	+	0.665977i	−0.966973	−	0.254880i	$-0.917964\pi$
$307$	−10.1111	+	11.6689i	−0.577072	+	0.665977i	0.389900	+	0.920857i	$0.372509\pi$
$308$	−3.57647	+	24.8749i	−0.203789	+	1.41738i
$309$	2.73884	+	5.99722i	0.155807	+	0.341170i
$310$	4.70520	+	1.38157i	0.267237	+	0.0784680i
$311$	11.4648	+	3.36638i	0.650112	+	0.190890i	0.590129	−	0.807309i	$-0.299077\pi$
$311$	11.4648	+	3.36638i	0.650112	+	0.190890i	0.0599833	+	0.998199i	$0.480895\pi$
$312$	0.723107	+	1.58338i	0.0409379	+	0.0896414i
$313$	3.08538	−	21.4593i	0.174396	−	1.21295i	−0.695064	−	0.718948i	$-0.744624\pi$
$313$	3.08538	−	21.4593i	0.174396	−	1.21295i	0.869460	−	0.494003i	$-0.164467\pi$
$314$	−8.37962	+	9.67060i	−0.472889	+	0.545744i
$315$	−1.63201	+	3.57361i	−0.0919534	+	0.201350i
$316$	2.64746	+	1.70142i	0.148931	+	0.0957123i
$317$	−0.758593	−	5.27613i	−0.0426068	−	0.296337i	−0.999972	−	0.00745708i	$-0.997626\pi$
$317$	−0.758593	−	5.27613i	−0.0426068	−	0.296337i	0.957365	−	0.288880i	$-0.0932828\pi$
$318$	−6.76887	+	4.35009i	−0.379580	+	0.243941i
$319$	29.4920	+	34.0356i	1.65124	+	1.90563i
$320$	0.959493	−	0.281733i	0.0536373	−	0.0157493i
$321$	13.5490			0.756233
$322$	11.8689	−	14.6326i	0.661429	−	0.815444i
$323$	−1.13807			−0.0633238
$324$	−0.959493	+	0.281733i	−0.0533052	+	0.0156518i
$325$	1.13991	+	1.31552i	0.0632306	+	0.0729720i
$326$	16.0100	−	10.2890i	0.886713	−	0.569856i
$327$	−1.73459	−	12.0644i	−0.0959232	−	0.667160i
$328$	−3.24290	−	2.08409i	−0.179059	−	0.115074i
$329$	−7.25395	+	15.8839i	−0.399923	+	0.875710i
$330$	−4.18902	+	4.83439i	−0.230598	+	0.266124i
$331$	−0.447783	+	3.11440i	−0.0246124	+	0.171183i	−0.998420	−	0.0561903i	$-0.982105\pi$
$331$	−0.447783	+	3.11440i	−0.0246124	+	0.171183i	0.973808	+	0.227373i	$0.0730137\pi$
$332$	3.96644	+	8.68528i	0.217686	+	0.476667i
$333$	−7.98993	−	2.34606i	−0.437845	−	0.128563i
$334$	10.5130	+	3.08689i	0.575245	+	0.168907i
$335$	0.657353	+	1.43940i	0.0359150	+	0.0786430i
$336$	−0.559102	+	3.88864i	−0.0305015	+	0.212143i
$337$	−5.77089	+	6.65997i	−0.314361	+	0.362791i	−0.890838	−	0.454322i	$-0.849882\pi$
$337$	−5.77089	+	6.65997i	−0.314361	+	0.362791i	0.576477	+	0.817113i	$0.304427\pi$
$338$	4.14169	−	9.06904i	0.225278	−	0.493291i
$339$	−11.0896	−	7.12683i	−0.602303	−	0.387076i
$340$	−0.0223141	−	0.155198i	−0.00121015	−	0.00841680i
$341$	−26.3892	+	16.9593i	−1.42906	+	0.918400i
$342$	4.75322	+	5.48551i	0.257025	+	0.296622i
$343$	−5.40593	+	1.58733i	−0.291893	+	0.0857075i
$344$	0.795994			0.0429171
$345$	4.55522	−	1.49999i	0.245245	−	0.0807569i
$346$	16.6900			0.897259
$347$	−22.4091	+	6.57991i	−1.20298	+	0.353228i	−0.820993	−	0.570938i	$-0.806580\pi$
$347$	−22.4091	+	6.57991i	−1.20298	+	0.353228i	−0.381991	+	0.924166i	$0.624761\pi$
$348$	4.61042	+	5.32071i	0.247145	+	0.285220i
$349$	−12.1042	+	7.77892i	−0.647925	+	0.416396i	−0.822907	−	0.568176i	$-0.807649\pi$
$349$	−12.1042	+	7.77892i	−0.647925	+	0.416396i	0.174983	+	0.984572i	$0.444013\pi$
$350$	0.559102	+	3.88864i	0.0298853	+	0.207857i
$351$	−1.46436	−	0.941085i	−0.0781616	−	0.0502314i
$352$	−2.65733	+	5.81875i	−0.141636	+	0.310140i
$353$	−6.04352	+	6.97459i	−0.321664	+	0.371220i	−0.893434	−	0.449193i	$-0.851711\pi$
$353$	−6.04352	+	6.97459i	−0.321664	+	0.371220i	0.571770	+	0.820414i	$0.306257\pi$
$354$	0.828928	−	5.76532i	0.0440570	−	0.306423i
$355$	6.12960	+	13.4219i	0.325325	+	0.712363i
$356$	17.3460	+	5.09325i	0.919337	+	0.269942i
$357$	0.591034	+	0.173543i	0.0312808	+	0.00918488i
$358$	−6.61503	−	14.4849i	−0.349615	−	0.765551i
$359$	1.18738	−	8.25838i	0.0626673	−	0.435861i	−0.934199	−	0.356753i	$-0.883884\pi$
$359$	1.18738	−	8.25838i	0.0626673	−	0.435861i	0.996866	−	0.0791077i	$-0.0252071\pi$
$360$	−0.654861	+	0.755750i	−0.0345142	+	0.0398315i
$361$	13.9928	−	30.6400i	0.736463	−	1.61263i
$362$	−18.7768	−	12.0671i	−0.986887	−	0.634234i
$363$	−4.25796	−	29.6147i	−0.223485	−	1.55437i
$364$	−5.75292	+	3.69718i	−0.301535	+	0.193785i
$365$	1.30431	+	1.50525i	0.0682706	+	0.0787885i
$366$	1.48070	−	0.434772i	0.0773973	−	0.0227259i
$367$	5.49808			0.286997			0.143499	−	0.989650i	$-0.454165\pi$
$367$	5.49808			0.286997			0.143499	+	0.989650i	$0.454165\pi$
$368$	3.94810	−	2.72259i	0.205809	−	0.141925i
$369$	3.85484			0.200675
$370$	−7.98993	+	2.34606i	−0.415377	+	0.121966i
$371$	−20.7004	−	23.8896i	−1.07471	−	1.24028i
$372$	−4.12537	+	2.65122i	−0.213891	+	0.137459i
$373$	−1.57611	−	10.9621i	−0.0816078	−	0.567595i	−0.989068	−	0.147458i	$-0.952891\pi$
$373$	−1.57611	−	10.9621i	−0.0816078	−	0.567595i	0.907461	−	0.420137i	$-0.138018\pi$
$374$	0.843763	+	0.542253i	0.0436299	+	0.0280392i
$375$	−0.415415	+	0.909632i	−0.0214519	+	0.0469732i
$376$	−2.91072	+	3.35915i	−0.150109	+	0.173235i
$377$	−1.74406	+	12.1302i	−0.0898238	+	0.624738i
$378$	−1.63201	−	3.57361i	−0.0839416	−	0.183807i
$379$	−30.9947	−	9.10085i	−1.59209	−	0.467480i	−0.638758	−	0.769407i	$-0.720552\pi$
$379$	−30.9947	−	9.10085i	−1.59209	−	0.467480i	−0.953331	+	0.301928i	$0.902370\pi$
$380$	6.96435	+	2.04492i	0.357264	+	0.104902i
$381$	0.660593	+	1.44650i	0.0338432	+	0.0741063i
$382$	−1.83210	+	12.7426i	−0.0937386	+	0.651966i
$383$	14.3373	−	16.5461i	0.732600	−	0.845466i	−0.260161	−	0.965565i	$-0.583776\pi$
$383$	14.3373	−	16.5461i	0.732600	−	0.845466i	0.992762	+	0.120099i	$0.0383212\pi$
$384$	−0.415415	+	0.909632i	−0.0211991	+	0.0464195i
$385$	−21.1413	−	13.5867i	−1.07746	−	0.692442i
$386$	0.949111	+	6.60121i	0.0483085	+	0.335993i
$387$	−0.669633	+	0.430347i	−0.0340393	+	0.0218758i
$388$	2.40417	+	2.77456i	0.122053	+	0.140857i
$389$	34.4931	−	10.1281i	1.74887	−	0.513514i	0.758464	−	0.651715i	$-0.225950\pi$
$389$	34.4931	−	10.1281i	1.74887	−	0.513514i	0.990404	+	0.138201i	$0.0441321\pi$
$390$	−1.74069			−0.0881430
$391$	−0.334442	−	0.673490i	−0.0169134	−	0.0340599i
$392$	−8.43413			−0.425988
$393$	−5.22541	+	1.53432i	−0.263587	+	0.0773962i
$394$	−4.02571	−	4.64591i	−0.202812	−	0.234058i
$395$	−2.64746	+	1.70142i	−0.133208	+	0.0856077i
$396$	−0.910362	−	6.33171i	−0.0457474	−	0.318180i
$397$	15.4181	+	9.90860i	0.773811	+	0.497298i	0.866974	−	0.498353i	$-0.166061\pi$
$397$	15.4181	+	9.90860i	0.773811	+	0.497298i	−0.0931632	+	0.995651i	$0.529698\pi$
$398$	−0.429904	+	0.941359i	−0.0215492	+	0.0471861i
$399$	−18.6736	+	21.5505i	−0.934851	+	1.07888i
$400$	−0.142315	+	0.989821i	−0.00711574	+	0.0494911i
$401$	−11.0921	−	24.2883i	−0.553913	−	1.21290i	−0.954930	−	0.296830i	$-0.904071\pi$
$401$	−11.0921	−	24.2883i	−0.553913	−	1.21290i	0.401017	−	0.916070i	$-0.368657\pi$
$402$	−1.51830	−	0.445814i	−0.0757261	−	0.0222352i
$403$	−8.19027	−	2.40488i	−0.407986	−	0.119796i
$404$	4.34361	+	9.51117i	0.216103	+	0.473199i
$405$	0.142315	−	0.989821i	0.00707168	−	0.0491846i
$406$	−18.1126	+	20.9031i	−0.898915	+	1.03740i
$407$	22.1283	−	48.4541i	1.09686	−	2.40178i
$408$	0.131904	+	0.0847692i	0.00653020	+	0.00419670i
$409$	1.75458	+	12.2034i	0.0867584	+	0.603418i	0.986098	+	0.166167i	$0.0531390\pi$
$409$	1.75458	+	12.2034i	0.0867584	+	0.603418i	−0.899339	+	0.437252i	$0.855952\pi$
$410$	3.24290	−	2.08409i	0.160155	−	0.102926i
$411$	6.09059	+	7.02891i	0.300426	+	0.346711i
$412$	−6.32596	+	1.85747i	−0.311658	+	0.0915109i
$413$	22.8827			1.12598
$414$	−1.84941	+	4.42489i	−0.0908938	+	0.217472i
$415$	−9.54813			−0.468699
$416$	−1.67018	+	0.490408i	−0.0818871	+	0.0240442i
$417$	−5.60284	−	6.46602i	−0.274372	−	0.316642i
$418$	−39.0598	+	25.1022i	−1.91048	+	1.22779i
$419$	−4.86983	−	33.8704i	−0.237907	−	1.65468i	−0.662330	−	0.749212i	$-0.730432\pi$
$419$	−4.86983	−	33.8704i	−0.237907	−	1.65468i	0.424423	−	0.905464i	$-0.360477\pi$
$420$	−3.30497	−	2.12398i	−0.161266	−	0.103639i
$421$	−14.9865	+	32.8158i	−0.730396	+	1.59935i	0.0683386	+	0.997662i	$0.478230\pi$
$421$	−14.9865	+	32.8158i	−0.730396	+	1.59935i	−0.798735	+	0.601683i	$0.794497\pi$
$422$	15.7604	−	18.1885i	0.767204	−	0.885400i
$423$	0.632560	−	4.39955i	0.0307561	−	0.213913i
$424$	−3.34250	−	7.31906i	−0.162326	−	0.355445i
$425$	0.150443	+	0.0441740i	0.00729754	+	0.00214275i
$426$	−14.1577	−	4.15706i	−0.685941	−	0.201410i
$427$	2.51853	+	5.51482i	0.121880	+	0.266881i
$428$	−1.92823	+	13.4111i	−0.0932044	+	0.648251i
$429$	7.29177	−	8.41515i	0.352050	−	0.406287i
$430$	−0.330668	+	0.724062i	−0.0159462	+	0.0349174i
$431$	16.3281	+	10.4934i	0.786496	+	0.505450i	0.871184	−	0.490957i	$-0.163353\pi$
$431$	16.3281	+	10.4934i	0.786496	+	0.505450i	−0.0846877	+	0.996408i	$0.526989\pi$
$432$	−0.142315	−	0.989821i	−0.00684713	−	0.0476228i
$433$	−23.6105	+	15.1735i	−1.13465	+	0.729194i	−0.966525	−	0.256573i	$-0.917407\pi$
$433$	−23.6105	+	15.1735i	−1.13465	+	0.729194i	−0.168122	+	0.985766i	$0.553770\pi$
$434$	−12.6161	−	14.5598i	−0.605594	−	0.698892i
$435$	−6.75513	+	1.98348i	−0.323884	+	0.0951008i
$436$	12.1884			0.583719
$437$	34.7915	−	1.13143i	1.66430	−	0.0541236i
$438$	−1.99173			−0.0951687
$439$	35.3435	−	10.3778i	1.68685	−	0.495304i	0.709106	−	0.705102i	$-0.249099\pi$
$439$	35.3435	−	10.3778i	1.68685	−	0.495304i	0.977745	+	0.209797i	$0.0672805\pi$
$440$	−4.18902	−	4.83439i	−0.199704	−	0.230471i
$441$	7.09524	−	4.55983i	0.337869	−	0.217135i
$442$	0.0388418	+	0.270151i	0.00184752	+	0.0128498i
$443$	−18.5955	−	11.9506i	−0.883500	−	0.567791i	0.0183541	−	0.999832i	$-0.494157\pi$
$443$	−18.5955	−	11.9506i	−0.883500	−	0.567791i	−0.901854	+	0.432040i	$0.857794\pi$
$444$	3.45926	−	7.57473i	0.164169	−	0.359481i
$445$	−11.8388	+	13.6627i	−0.561212	+	0.647673i
$446$	−2.24699	+	15.6282i	−0.106398	+	0.740015i
$447$	6.74410	+	14.7675i	0.318985	+	0.698479i
$448$	−3.76949	−	1.10682i	−0.178092	−	0.0522925i
$449$	27.1550	+	7.97342i	1.28152	+	0.376289i	0.850463	−	0.526035i	$-0.176322\pi$
$449$	27.1550	+	7.97342i	1.28152	+	0.376289i	0.431059	+	0.902324i	$0.358140\pi$
$450$	−0.415415	−	0.909632i	−0.0195829	−	0.0428805i
$451$	−3.50930	+	24.4077i	−0.165247	+	1.14932i
$452$	8.63250	−	9.96244i	0.406039	−	0.468594i
$453$	1.39447	−	3.05346i	0.0655179	−	0.143464i
$454$	−6.43522	−	4.13567i	−0.302020	−	0.194096i
$455$	−0.973221	−	6.76890i	−0.0456253	−	0.317331i
$456$	−6.10613	+	3.92417i	−0.285946	+	0.183766i
$457$	22.7185	+	26.2185i	1.06272	+	1.22645i	0.973078	+	0.230476i	$0.0740283\pi$
$457$	22.7185	+	26.2185i	1.06272	+	1.22645i	0.0896464	+	0.995974i	$0.471426\pi$
$458$	−16.2280	+	4.76497i	−0.758285	+	0.222652i
$459$	−0.156794			−0.00731852
$460$	0.836450	+	4.72232i	0.0389997	+	0.220180i
$461$	−32.5043			−1.51387			−0.756937	−	0.653487i	$-0.773305\pi$
$461$	−32.5043			−1.51387			−0.756937	+	0.653487i	$0.773305\pi$
$462$	24.1128	−	7.08014i	1.12183	−	0.329398i
$463$	−25.3333	−	29.2362i	−1.17734	−	1.35872i	−0.919768	−	0.392464i	$-0.871623\pi$
$463$	−25.3333	−	29.2362i	−1.17734	−	1.35872i	−0.257572	−	0.966259i	$-0.582923\pi$
$464$	−5.92269	+	3.80628i	−0.274954	+	0.176702i
$465$	−0.697889	−	4.85393i	−0.0323638	−	0.225095i
$466$	13.3201	+	8.56031i	0.617042	+	0.396549i
$467$	−4.35728	+	9.54110i	−0.201631	+	0.441510i	−0.983254	−	0.182241i	$-0.941665\pi$
$467$	−4.35728	+	9.54110i	−0.201631	+	0.441510i	0.781623	+	0.623751i	$0.214392\pi$
$468$	1.13991	−	1.31552i	0.0526922	−	0.0608100i
$469$	0.884724	−	6.15339i	0.0408528	−	0.284137i
$470$	−1.84643	−	4.04312i	−0.0851696	−	0.186495i
$471$	12.2777	+	3.60506i	0.565727	+	0.166112i
$472$	5.58867	+	1.64098i	0.257239	+	0.0755323i
$473$	−2.11522	−	4.63169i	−0.0972580	−	0.212965i
$474$	0.447871	−	3.11501i	0.0205714	−	0.143077i
$475$	−4.75322	+	5.48551i	−0.218093	+	0.251692i
$476$	−0.255890	+	0.560320i	−0.0117287	+	0.0256822i
$477$	6.76887	+	4.35009i	0.309925	+	0.199177i
$478$	−3.69699	−	25.7131i	−0.169096	−	1.17609i
$479$	32.2619	−	20.7335i	1.47408	−	0.947336i	0.476405	−	0.879226i	$-0.341939\pi$
$479$	32.2619	−	20.7335i	1.47408	−	0.947336i	0.997678	−	0.0681100i	$-0.0216969\pi$
$480$	−0.654861	−	0.755750i	−0.0298902	−	0.0344951i
$481$	13.9080	−	4.08374i	0.634148	−	0.186203i
$482$	−19.1333			−0.871497
$483$	−18.2408	−	4.71774i	−0.829986	−	0.214665i
$484$	29.9193			1.35997
$485$	−3.52255	+	1.03431i	−0.159951	+	0.0469658i
$486$	0.654861	+	0.755750i	0.0297051	+	0.0342815i
$487$	14.5843	−	9.37273i	0.660876	−	0.424719i	−0.166750	−	0.985999i	$-0.553327\pi$
$487$	14.5843	−	9.37273i	0.660876	−	0.424719i	0.827626	+	0.561280i	$0.189691\pi$
$488$	0.219621	+	1.52750i	0.00994180	+	0.0691467i
$489$	−16.0100	−	10.2890i	−0.723998	−	0.465285i
$490$	3.50366	−	7.67195i	0.158279	−	0.346583i
$491$	21.0443	−	24.2864i	0.949715	−	1.09603i	−0.0455630	−	0.998961i	$-0.514508\pi$
$491$	21.0443	−	24.2864i	0.949715	−	1.09603i	0.995278	−	0.0970678i	$-0.0309464\pi$
$492$	−0.548601	+	3.81561i	−0.0247329	+	0.172021i
$493$	0.458568	+	1.00412i	0.0206528	+	0.0452234i
$494$	−12.1227	−	3.55956i	−0.545428	−	0.160152i
$495$	6.13770	+	1.80219i	0.275869	+	0.0810025i
$496$	−2.03713	−	4.46069i	−0.0914698	−	0.200291i
$497$	8.24975	−	57.3783i	0.370052	−	2.57377i
$498$	6.25269	−	7.21599i	0.280190	−	0.323356i
$499$	5.11092	−	11.1913i	0.228796	−	0.500993i	−0.760063	−	0.649850i	$-0.774832\pi$
$499$	5.11092	−	11.1913i	0.228796	−	0.500993i	0.988859	+	0.148856i	$0.0475591\pi$
$500$	−0.841254	−	0.540641i	−0.0376220	−	0.0241782i
$501$	−1.55932	−	10.8453i	−0.0696651	−	0.484531i
$502$	−2.96686	+	1.90669i	−0.132418	+	0.0850997i
$503$	3.51474	+	4.05623i	0.156715	+	0.180858i	0.828677	−	0.559727i	$-0.189094\pi$
$503$	3.51474	+	4.05623i	0.156715	+	0.180858i	−0.671963	+	0.740585i	$0.734548\pi$
$504$	3.76949	−	1.10682i	0.167907	−	0.0493018i
$505$	−10.4561			−0.465289
$506$	−26.3335	−	15.7382i	−1.17067	−	0.699649i
$507$	−9.97002			−0.442784
$508$	−1.52579	+	0.448011i	−0.0676958	+	0.0198773i
$509$	11.7800	+	13.5949i	0.522140	+	0.602581i	0.954165	−	0.299280i	$-0.0967465\pi$
$509$	11.7800	+	13.5949i	0.522140	+	0.602581i	−0.432026	+	0.901861i	$0.642201\pi$
$510$	−0.131904	+	0.0847692i	−0.00584079	+	0.00375364i
$511$	−1.11358	−	7.74514i	−0.0492620	−	0.342625i
$512$	−0.841254	−	0.540641i	−0.0371785	−	0.0238932i
$513$	3.01523	−	6.60244i	0.133126	−	0.291505i
$514$	−10.8945	+	12.5729i	−0.480534	+	0.554566i
$515$	0.938285	−	6.52592i	0.0413458	−	0.287566i
$516$	−0.330668	−	0.724062i	−0.0145568	−	0.0318750i
$517$	27.2808	+	8.01036i	1.19981	+	0.352295i
$518$	31.3895	+	9.21678i	1.37917	+	0.404962i
$519$	−6.93327	−	15.1817i	−0.304337	−	0.666405i
$520$	0.247725	−	1.72297i	0.0108635	−	0.0755571i
$521$	−10.2318	+	11.8081i	−0.448261	+	0.517321i	−0.934238	−	0.356651i	$-0.883919\pi$
$521$	−10.2318	+	11.8081i	−0.448261	+	0.517321i	0.485977	+	0.873972i	$0.338464\pi$
$522$	2.92465	−	6.40409i	0.128008	−	0.280299i
$523$	−14.3189	−	9.20219i	−0.626122	−	0.402384i	0.188750	−	0.982025i	$-0.439556\pi$
$523$	−14.3189	−	9.20219i	−0.626122	−	0.402384i	−0.814872	+	0.579641i	$0.803193\pi$
$524$	−0.775049	−	5.39058i	−0.0338582	−	0.235489i
$525$	3.30497	−	2.12398i	0.144241	−	0.0926980i
$526$	6.76442	+	7.80656i	0.294943	+	0.340382i
$527$	−0.737747	+	0.216622i	−0.0321368	+	0.00943621i
$528$	6.39682			0.278386
$529$	10.8937	+	20.2566i	0.473638	+	0.880720i
$530$	8.04617			0.349504
$531$	−5.58867	+	1.64098i	−0.242527	+	0.0712125i
$532$	−18.6736	−	21.5505i	−0.809605	−	0.934334i
$533$	−5.64487	+	3.62774i	−0.244506	+	0.157135i
$534$	−2.57281	−	17.8943i	−0.111337	−	0.774362i
$535$	−11.3982	−	7.32515i	−0.492786	−	0.316694i
$536$	0.657353	−	1.43940i	0.0283933	−	0.0621727i
$537$	−10.4279	+	12.0345i	−0.449999	+	0.519327i
$538$	0.960799	−	6.68251i	0.0414230	−	0.288103i
$539$	22.4123	+	49.0761i	0.965366	+	2.11386i
$540$	0.959493	+	0.281733i	0.0412900	+	0.0121238i
$541$	−13.7757	−	4.04491i	−0.592264	−	0.173904i	−0.0281534	−	0.999604i	$-0.508963\pi$
$541$	−13.7757	−	4.04491i	−0.592264	−	0.173904i	−0.564111	+	0.825699i	$0.690781\pi$
$542$	−3.16330	−	6.92666i	−0.135875	−	0.297526i
$543$	−3.17647	+	22.0929i	−0.136315	+	0.948095i
$544$	−0.102678	+	0.118497i	−0.00440229	+	0.00508052i
$545$	−5.06325	+	11.0870i	−0.216886	+	0.474914i
$546$	5.75292	+	3.69718i	0.246202	+	0.158225i
$547$	1.79202	+	12.4637i	0.0766211	+	0.532911i	0.991593	+	0.129394i	$0.0413033\pi$
$547$	1.79202	+	12.4637i	0.0766211	+	0.532911i	−0.914972	+	0.403517i	$0.867788\pi$
$548$	−7.82415	+	5.02827i	−0.334231	+	0.214797i
$549$	−1.01059	−	1.16628i	−0.0431308	−	0.0497756i
$550$	6.13770	−	1.80219i	0.261712	−	0.0768457i
$551$	−51.1012			−2.17698
$552$	−4.11665	−	2.46032i	−0.175216	−	0.104718i
$553$	12.3636			0.525752
$554$	5.84801	−	1.71713i	0.248458	−	0.0729539i
$555$	5.45318	+	6.29331i	0.231475	+	0.267136i
$556$	7.19757	−	4.62560i	0.305245	−	0.196169i
$557$	2.77839	+	19.3242i	0.117724	+	0.818791i	0.960051	+	0.279824i	$0.0902761\pi$
$557$	2.77839	+	19.3242i	0.117724	+	0.818791i	−0.842327	+	0.538967i	$0.818815\pi$
$558$	4.12537	+	2.65122i	0.174641	+	0.112235i
$559$	0.575589	−	1.26036i	0.0243448	−	0.0533077i
$560$	2.57271	−	2.96906i	0.108717	−	0.125466i
$561$	0.142739	−	0.992774i	0.00602646	−	0.0419149i
$562$	−1.23635	−	2.70723i	−0.0521522	−	0.114197i
$563$	38.9300	+	11.4309i	1.64070	+	0.481754i	0.966473	−	0.256769i	$-0.0826578\pi$
$563$	38.9300	+	11.4309i	1.64070	+	0.481754i	0.674229	+	0.738522i	$0.264476\pi$
$564$	4.26474	+	1.25224i	0.179578	+	0.0527289i
$565$	5.47608	+	11.9909i	0.230380	+	0.504463i
$566$	−1.82147	+	12.6686i	−0.0765623	+	0.532502i
$567$	−2.57271	+	2.96906i	−0.108043	+	0.124689i
$568$	6.12960	−	13.4219i	0.257192	−	0.563172i
$569$	−9.91017	−	6.36888i	−0.415456	−	0.266997i	0.316171	−	0.948702i	$-0.397603\pi$
$569$	−9.91017	−	6.36888i	−0.415456	−	0.266997i	−0.731627	+	0.681705i	$0.761239\pi$
$570$	−1.03297	−	7.18449i	−0.0432665	−	0.300925i
$571$	−10.1008	+	6.49140i	−0.422706	+	0.271657i	−0.734653	−	0.678443i	$-0.762655\pi$
$571$	−10.1008	+	6.49140i	−0.422706	+	0.271657i	0.311947	+	0.950099i	$0.399019\pi$
$572$	7.29177	+	8.41515i	0.304884	+	0.351855i
$573$	12.3521	−	3.62691i	0.516017	−	0.151516i
$574$	−15.1443			−0.632109
$575$	−4.64305	−	1.20086i	−0.193629	−	0.0500794i
$576$	1.00000			0.0416667
$577$	−13.8679	+	4.07198i	−0.577327	+	0.169519i	−0.557344	−	0.830282i	$-0.688180\pi$
$577$	−13.8679	+	4.07198i	−0.577327	+	0.169519i	−0.0199834	+	0.999800i	$0.506361\pi$
$578$	−11.1165	−	12.8292i	−0.462387	−	0.533623i
$579$	5.61040	−	3.60559i	0.233160	−	0.149843i
$580$	−1.00194	−	6.96865i	−0.0416033	−	0.289357i
$581$	31.5563	+	20.2800i	1.30918	+	0.841356i
$582$	1.52510	−	3.33950i	0.0632174	−	0.138427i
$583$	−33.7056	+	38.8984i	−1.39594	+	1.61101i
$584$	0.283453	−	1.97146i	0.0117294	−	0.0815796i
$585$	0.723107	+	1.58338i	0.0298968	+	0.0654648i
$586$	10.6972	+	3.14097i	0.441895	+	0.129752i
$587$	−22.5099	−	6.60949i	−0.929082	−	0.272803i	−0.218029	−	0.975942i	$-0.569963\pi$
$587$	−22.5099	−	6.60949i	−0.929082	−	0.272803i	−0.711052	+	0.703139i	$0.751781\pi$
$588$	3.50366	+	7.67195i	0.144489	+	0.316386i
$589$	5.06554	−	35.2316i	0.208722	−	1.45169i
$590$	−3.81430	+	4.40194i	−0.157032	+	0.181225i
$591$	−2.55373	+	5.59189i	−0.105047	+	0.230020i
$592$	7.00532	+	4.50205i	0.287917	+	0.185033i
$593$	−0.0489645	−	0.340556i	−0.00201073	−	0.0139849i	0.988791	−	0.149304i	$-0.0477032\pi$
$593$	−0.0489645	−	0.340556i	−0.00201073	−	0.0139849i	−0.990802	+	0.135319i	$0.956794\pi$
$594$	−5.38134	+	3.45838i	−0.220799	+	0.141899i
$595$	−0.403385	−	0.465531i	−0.0165372	−	0.0190849i
$596$	−15.5770	+	4.57382i	−0.638058	+	0.187351i
$597$	1.03488			0.0423548
$598$	−1.45600	−	8.22008i	−0.0595401	−	0.336144i
$599$	0.195297			0.00797964			0.00398982	−	0.999992i	$-0.498730\pi$
$599$	0.195297			0.00797964			0.00398982	+	0.999992i	$0.498730\pi$
$600$	0.959493	−	0.281733i	0.0391711	−	0.0115017i
$601$	−12.5246	−	14.4542i	−0.510891	−	0.589599i	0.440436	−	0.897784i	$-0.354824\pi$
$601$	−12.5246	−	14.4542i	−0.510891	−	0.589599i	−0.951327	+	0.308185i	$0.900279\pi$
$602$	2.63074	−	1.69067i	0.107221	−	0.0689067i
$603$	0.225199	+	1.56629i	0.00917082	+	0.0637845i
$604$	2.82393	+	1.81483i	0.114904	+	0.0738444i
$605$	−12.4289	+	27.2155i	−0.505307	+	1.10647i
$606$	6.84727	−	7.90217i	0.278151	−	0.321004i
$607$	−6.27046	+	43.6120i	−0.254510	+	1.77016i	0.315897	+	0.948793i	$0.397695\pi$
$607$	−6.27046	+	43.6120i	−0.254510	+	1.77016i	−0.570407	+	0.821362i	$0.693215\pi$
$608$	−3.01523	−	6.60244i	−0.122284	−	0.267764i
$609$	26.5384	+	7.79238i	1.07539	+	0.315763i
$610$	−1.48070	−	0.434772i	−0.0599517	−	0.0176034i
$611$	3.21406	+	7.03780i	0.130027	+	0.284719i
$612$	0.0223141	−	0.155198i	0.000901995	−	0.00627351i
$613$	−20.4628	+	23.6154i	−0.826486	+	0.953816i	−0.999516	−	0.0311005i	$-0.990099\pi$
$613$	−20.4628	+	23.6154i	−0.826486	+	0.953816i	0.173030	+	0.984917i	$0.444644\pi$
$614$	−6.41405	+	14.0448i	−0.258850	+	0.566803i
$615$	−3.24290	−	2.08409i	−0.130766	−	0.0840385i
$616$	3.57647	+	24.8749i	0.144100	+	1.00224i
$617$	−41.5128	+	26.6787i	−1.67124	+	1.07404i	−0.773169	+	0.634200i	$0.781330\pi$
$617$	−41.5128	+	26.6787i	−1.67124	+	1.07404i	−0.898074	+	0.439843i	$0.855034\pi$
$618$	4.31751	+	4.98267i	0.173676	+	0.200433i
$619$	−44.8761	+	13.1768i	−1.80372	+	0.529621i	−0.998032	−	0.0627129i	$-0.980025\pi$
$619$	−44.8761	+	13.1768i	−1.80372	+	0.529621i	−0.805692	+	0.592334i	$0.798207\pi$
$620$	4.90384			0.196943
$621$	4.79330	−	0.155879i	0.192348	−	0.00625522i
$622$	11.9489			0.479106
$623$	68.1461	−	20.0095i	2.73022	−	0.801664i
$624$	1.13991	+	1.31552i	0.0456328	+	0.0526630i
$625$	0.841254	−	0.540641i	0.0336501	−	0.0216256i
$626$	−3.08538	−	21.4593i	−0.123317	−	0.857686i
$627$	39.0598	+	25.1022i	1.55990	+	1.00249i
$628$	−5.31567	+	11.6397i	−0.212118	+	0.464474i
$629$	0.855027	−	0.986753i	0.0340921	−	0.0393444i
$630$	−0.559102	+	3.88864i	−0.0222752	+	0.154927i
$631$	18.0240	+	39.4670i	0.717523	+	1.57116i	0.817343	+	0.576151i	$0.195446\pi$
$631$	18.0240	+	39.4670i	0.717523	+	1.57116i	−0.0998200	+	0.995006i	$0.531827\pi$
$632$	3.01957	+	0.886624i	0.120112	+	0.0352680i
$633$	−23.0919	−	6.78040i	−0.917821	−	0.269497i
$634$	−2.21432	−	4.84869i	−0.0879419	−	0.192566i
$635$	0.226309	−	1.57402i	0.00898081	−	0.0624629i
$636$	−5.26912	+	6.08089i	−0.208934	+	0.241123i
$637$	−6.09877	+	13.3545i	−0.241642	+	0.529123i
$638$	37.8863	+	24.3481i	1.49993	+	0.963949i
$639$	2.09991	+	14.6052i	0.0830710	+	0.577772i
$640$	0.841254	−	0.540641i	0.0332535	−	0.0213707i
$641$	−19.3844	−	22.3708i	−0.765637	−	0.883592i	0.230349	−	0.973108i	$-0.426013\pi$
$641$	−19.3844	−	22.3708i	−0.765637	−	0.883592i	−0.995985	+	0.0895165i	$0.971468\pi$
$642$	13.0002	−	3.81720i	0.513077	−	0.150653i
$643$	31.6087			1.24653			0.623264	−	0.782012i	$-0.285806\pi$
$643$	31.6087			1.24653			0.623264	+	0.782012i	$0.285806\pi$
$644$	7.26567	−	17.3838i	0.286307	−	0.685016i
$645$	0.795994			0.0313422
$646$	−1.09197	+	0.320631i	−0.0429629	+	0.0126151i
$647$	−2.26119	−	2.60955i	−0.0888966	−	0.102592i	0.709558	−	0.704647i	$-0.248894\pi$
$647$	−2.26119	−	2.60955i	−0.0888966	−	0.102592i	−0.798455	+	0.602054i	$0.794349\pi$
$648$	−0.841254	+	0.540641i	−0.0330476	+	0.0212384i
$649$	−5.30250	−	36.8797i	−0.208141	−	1.44765i
$650$	1.46436	+	0.941085i	0.0574368	+	0.0369124i
$651$	−8.00312	+	17.5244i	−0.313667	+	0.686835i
$652$	12.4627	−	14.3828i	0.488079	−	0.563273i
$653$	5.81738	−	40.4608i	0.227652	−	1.58335i	−0.480308	−	0.877100i	$-0.659475\pi$
$653$	5.81738	−	40.4608i	0.227652	−	1.58335i	0.707960	−	0.706253i	$-0.249616\pi$
$654$	−5.06325	−	11.0870i	−0.197989	−	0.433535i
$655$	5.22541	+	1.53432i	0.204174	+	0.0599508i
$656$	−3.69870	−	1.08603i	−0.144410	−	0.0424025i
$657$	0.827396	+	1.81174i	0.0322798	+	0.0706829i
$658$	−2.48509	+	17.2842i	−0.0968790	+	0.673808i
$659$	−22.7375	+	26.2404i	−0.885726	+	1.02218i	0.113862	+	0.993497i	$0.463678\pi$
$659$	−22.7375	+	26.2404i	−0.885726	+	1.02218i	−0.999588	+	0.0286858i	$0.990868\pi$
$660$	−2.65733	+	5.81875i	−0.103437	+	0.226495i
$661$	9.56460	+	6.14679i	0.372020	+	0.239083i	0.713269	−	0.700890i	$-0.247214\pi$
$661$	9.56460	+	6.14679i	0.372020	+	0.239083i	−0.341249	+	0.939973i	$0.610850\pi$
$662$	0.447783	+	3.11440i	0.0174036	+	0.121045i
$663$	0.229602	−	0.147557i	0.00891702	−	0.00573062i
$664$	6.25269	+	7.21599i	0.242652	+	0.280035i
$665$	27.3604	−	8.03373i	1.06099	−	0.311535i
$666$	−8.32724			−0.322674
$667$	−15.0170	−	30.2408i	−0.581460	−	1.17093i
$668$	10.9568			0.423932
$669$	15.1493	−	4.44824i	0.585706	−	0.171979i
$670$	1.03625	+	1.19590i	0.0400339	+	0.0462016i
$671$	8.30454	−	5.33700i	0.320593	−	0.206033i
$672$	0.559102	+	3.88864i	0.0215678	+	0.150008i
$673$	4.78124	+	3.07272i	0.184303	+	0.118445i	0.629539	−	0.776969i	$-0.283244\pi$
$673$	4.78124	+	3.07272i	0.184303	+	0.118445i	−0.445236	+	0.895413i	$0.646880\pi$
$674$	−3.66080	+	8.01604i	−0.141009	+	0.308766i
$675$	−0.654861	+	0.755750i	−0.0252056	+	0.0290888i
$676$	1.41888	−	9.86853i	0.0545724	−	0.379559i
$677$	16.4721	+	36.0689i	0.633075	+	1.38624i	0.905617	+	0.424097i	$0.139408\pi$
$677$	16.4721	+	36.0689i	0.633075	+	1.38624i	−0.272542	+	0.962144i	$0.587864\pi$
$678$	−12.6482	−	3.71385i	−0.485752	−	0.142630i
$679$	13.8388	+	4.06344i	0.531085	+	0.155941i
$680$	−0.0651346	−	0.142625i	−0.00249780	−	0.00546941i
$681$	−1.08865	+	7.57170i	−0.0417170	+	0.290148i
$682$	−20.5423	+	23.7071i	−0.786605	+	0.907791i
$683$	0.0304378	−	0.0666494i	0.00116467	−	0.00255027i	−0.909049	−	0.416690i	$-0.863190\pi$
$683$	0.0304378	−	0.0666494i	0.00116467	−	0.00255027i	0.910213	+	0.414139i	$0.135917\pi$
$684$	6.10613	+	3.92417i	0.233474	+	0.150044i
$685$	−1.32361	−	9.20592i	−0.0505726	−	0.351740i
$686$	−4.73975	+	3.04605i	−0.180965	+	0.116299i
$687$	11.0757	+	12.7821i	0.422565	+	0.487666i
$688$	0.763751	−	0.224257i	0.0291177	−	0.00854973i
$689$	−14.0059			−0.533581
$690$	3.94810	−	2.72259i	0.150302	−	0.103647i
$691$	−41.0195			−1.56046			−0.780228	−	0.625495i	$-0.784897\pi$
$691$	−41.0195			−1.56046			−0.780228	+	0.625495i	$0.784897\pi$
$692$	16.0139	−	4.70211i	0.608758	−	0.178747i
$693$	−16.4571	−	18.9925i	−0.625154	−	0.721467i
$694$	−19.6476	+	12.6268i	−0.745813	+	0.479305i
$695$	1.21761	+	8.46869i	0.0461867	+	0.321236i
$696$	5.92269	+	3.80628i	0.224499	+	0.144277i
$697$	−0.251084	+	0.549796i	−0.00951047	+	0.0208250i
$698$	−9.42235	+	10.8740i	−0.356641	+	0.411586i
$699$	2.25336	−	15.6725i	0.0852300	−	0.592787i
$700$	1.63201	+	3.57361i	0.0616842	+	0.135070i
$701$	18.6792	+	5.48472i	0.705505	+	0.207155i	0.614754	−	0.788719i	$-0.289255\pi$
$701$	18.6792	+	5.48472i	0.705505	+	0.207155i	0.0907509	+	0.995874i	$0.471073\pi$
$702$	−1.67018	−	0.490408i	−0.0630367	−	0.0185092i
$703$	25.1086	+	54.9801i	0.946988	+	2.07362i
$704$	−0.910362	+	6.33171i	−0.0343106	+	0.238635i
$705$	−2.91072	+	3.35915i	−0.109624	+	0.126513i
$706$	−3.83375	+	8.39473i	−0.144285	+	0.315940i
$707$	34.5570	+	22.2084i	1.29965	+	0.835235i
$708$	−0.828928	−	5.76532i	−0.0311530	−	0.216674i
$709$	6.67953	−	4.29267i	0.250855	−	0.161215i	−0.409170	−	0.912458i	$-0.634182\pi$
$709$	6.67953	−	4.29267i	0.250855	−	0.161215i	0.660025	+	0.751243i	$0.270545\pi$
$710$	9.66270	+	11.1514i	0.362635	+	0.418503i
$711$	−3.01957	+	0.886624i	−0.113243	+	0.0332510i
$712$	18.0783			0.677514
$713$	22.3381	−	7.35573i	0.836567	−	0.275474i
$714$	0.615985			0.0230527
$715$	−10.6838	+	3.13705i	−0.399552	+	0.117319i
$716$	−10.4279	−	12.0345i	−0.389711	−	0.449750i
$717$	−21.8537	+	14.0445i	−0.816142	+	0.524503i
$718$	−1.18738	−	8.25838i	−0.0443125	−	0.308200i
$719$	−14.3446	−	9.21870i	−0.534962	−	0.343799i	0.245103	−	0.969497i	$-0.421178\pi$
$719$	−14.3446	−	9.21870i	−0.534962	−	0.343799i	−0.780066	+	0.625698i	$0.784814\pi$
$720$	−0.415415	+	0.909632i	−0.0154816	+	0.0339000i
$721$	−16.9619	+	19.5751i	−0.631694	+	0.729014i
$722$	4.79372	−	33.3411i	0.178404	−	1.24083i
$723$	7.94825	+	17.4042i	0.295599	+	0.647271i
$724$	−21.4159	−	6.28828i	−0.795916	−	0.233702i
$725$	6.75513	+	1.98348i	0.250879	+	0.0736648i
$726$	−12.4289	−	27.2155i	−0.461280	−	1.01006i
$727$	−0.563899	+	3.92200i	−0.0209139	+	0.145459i	−0.997603	−	0.0692006i	$-0.977955\pi$
$727$	−0.563899	+	3.92200i	−0.0209139	+	0.145459i	0.976689	+	0.214660i	$0.0688642\pi$
$728$	−4.47827	+	5.16820i	−0.165976	+	0.191546i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	1.67555	+	1.07681i	0.0620150	+	0.0398546i
$731$	−0.0177619	−	0.123537i	−0.000656948	−	0.00456917i
$732$	1.29823	−	0.834321i	0.0479839	−	0.0308374i
$733$	28.7894	+	33.2248i	1.06336	+	1.22718i	0.972886	+	0.231286i	$0.0742933\pi$
$733$	28.7894	+	33.2248i	1.06336	+	1.22718i	0.0904757	+	0.995899i	$0.471161\pi$
$734$	5.27537	−	1.54899i	0.194717	−	0.0571742i
$735$	−8.43413			−0.311097
$736$	3.02114	−	3.72461i	0.111361	−	0.137291i
$737$	−10.1223			−0.372861
$738$	3.69870	−	1.08603i	0.136151	−	0.0399775i
$739$	9.46891	+	10.9277i	0.348319	+	0.401982i	0.902693	−	0.430286i	$-0.141587\pi$
$739$	9.46891	+	10.9277i	0.348319	+	0.401982i	−0.554373	+	0.832268i	$0.687042\pi$
$740$	−7.00532	+	4.50205i	−0.257521	+	0.165499i
$741$	1.79808	+	12.5059i	0.0660542	+	0.459417i
$742$	−26.5924	−	17.0899i	−0.976237	−	0.627390i
$743$	7.97768	−	17.4687i	0.292673	−	0.640864i	−0.704988	−	0.709219i	$-0.749048\pi$
$743$	7.97768	−	17.4687i	0.292673	−	0.640864i	0.997661	+	0.0683551i	$0.0217751\pi$
$744$	−3.21133	+	3.70607i	−0.117733	+	0.135871i
$745$	2.31043	−	16.0694i	0.0846474	−	0.588736i
$746$	−4.60064	−	10.0740i	−0.168441	−	0.368835i
$747$	−9.16136	−	2.69002i	−0.335197	−	0.0984226i
$748$	0.962355	+	0.282573i	0.0351872	+	0.0103319i
$749$	22.1122	+	48.4189i	0.807961	+	1.76919i
$750$	−0.142315	+	0.989821i	−0.00519660	+	0.0361432i
$751$	12.6040	−	14.5458i	0.459926	−	0.530782i	−0.477656	−	0.878547i	$-0.658514\pi$
$751$	12.6040	−	14.5458i	0.459926	−	0.530782i	0.937582	+	0.347764i	$0.113059\pi$
$752$	−1.84643	+	4.04312i	−0.0673325	+	0.147438i
$753$	2.96686	+	1.90669i	0.108119	+	0.0694836i
$754$	1.74406	+	12.1302i	0.0635150	+	0.441757i
$755$	−2.82393	+	1.81483i	−0.102773	+	0.0660484i
$756$	−2.57271	−	2.96906i	−0.0935684	−	0.107984i
$757$	45.9855	−	13.5026i	1.67137	−	0.490759i	0.697259	−	0.716819i	$-0.254403\pi$
$757$	45.9855	−	13.5026i	1.67137	−	0.490759i	0.974113	+	0.226060i	$0.0725845\pi$
$758$	−32.3032			−1.17330
$759$	−3.37665	+	30.4917i	−0.122565	+	1.10678i
$760$	7.25837			0.263289
$761$	−10.3535	+	3.04005i	−0.375313	+	0.110202i	−0.463948	−	0.885862i	$-0.653568\pi$
$761$	−10.3535	+	3.04005i	−0.375313	+	0.110202i	0.0886352	+	0.996064i	$0.471749\pi$
$762$	1.04136	+	1.20179i	0.0377245	+	0.0435364i
$763$	40.2824	−	25.8879i	1.45832	−	0.937206i
$764$	1.83210	+	12.7426i	0.0662832	+	0.461010i
$765$	0.131904	+	0.0847692i	0.00476898	+	0.00306484i
$766$	9.09494	−	19.9151i	0.328614	−	0.719563i
$767$	6.63950	−	7.66240i	0.239739	−	0.276673i
$768$	−0.142315	+	0.989821i	−0.00513534	+	0.0357171i
$769$	17.2234	+	37.7140i	0.621093	+	1.36000i	0.914722	+	0.404084i	$0.132410\pi$
$769$	17.2234	+	37.7140i	0.621093	+	1.36000i	−0.293629	+	0.955919i	$0.594863\pi$
$770$	−24.1128	−	7.08014i	−0.868963	−	0.255151i
$771$	15.9624	+	4.68699i	0.574872	+	0.168798i
$772$	2.77044	+	6.06642i	0.0997104	+	0.218335i
$773$	−3.92479	+	27.2975i	−0.141165	+	0.981824i	0.788924	+	0.614490i	$0.210638\pi$
$773$	−3.92479	+	27.2975i	−0.141165	+	0.981824i	−0.930089	+	0.367333i	$0.880271\pi$
$774$	−0.521265	+	0.601572i	−0.0187365	+	0.0216231i
$775$	−2.03713	+	4.46069i	−0.0731758	+	0.160233i
$776$	3.08847	+	1.98484i	0.110869	+	0.0712515i
$777$	−4.65578	−	32.3817i	−0.167025	−	1.16169i
$778$	30.2424	−	19.4356i	1.08424	−	0.696801i
$779$	−18.3229	−	21.1458i	−0.656487	−	0.757626i
$780$	−1.67018	+	0.490408i	−0.0598019	+	0.0175594i
$781$	−94.3873			−3.37744
$782$	−0.510639	−	0.551986i	−0.0182604	−	0.0197390i
$783$	−7.04031			−0.251600
$784$	−8.09249	+	2.37617i	−0.289017	+	0.0848632i
$785$	−8.37962	−	9.67060i	−0.299082	−	0.345159i
$786$	−4.58148	+	2.94434i	−0.163416	+	0.105021i
$787$	−4.39158	−	30.5441i	−0.156543	−	1.08878i	−0.904943	−	0.425533i	$-0.860087\pi$
$787$	−4.39158	−	30.5441i	−0.156543	−	1.08878i	0.748400	−	0.663248i	$-0.230822\pi$
$788$	−5.17154	−	3.32355i	−0.184229	−	0.118397i
$789$	4.29105	−	9.39610i	0.152766	−	0.334510i
$790$	−2.06087	+	2.37838i	−0.0733226	+	0.0846188i
$791$	7.37019	−	51.2608i	0.262054	−	1.82262i
$792$	−2.65733	−	5.81875i	−0.0944242	−	0.206760i
$793$	2.57743	+	0.756801i	0.0915272	+	0.0268748i
$794$	17.5851	+	5.16346i	0.624072	+	0.183244i
$795$	−3.34250	−	7.31906i	−0.118546	−	0.259580i
$796$	−0.147279	+	1.02435i	−0.00522015	+	0.0363070i
$797$	5.74792	−	6.63345i	0.203602	−	0.234969i	−0.644761	−	0.764384i	$-0.723043\pi$
$797$	5.74792	−	6.63345i	0.203602	−	0.234969i	0.848363	+	0.529415i	$0.177589\pi$
$798$	−11.8457	+	25.9386i	−0.419335	+	0.918215i
$799$	0.586283	+	0.376781i	0.0207412	+	0.0133296i
$800$	0.142315	+	0.989821i	0.00503159	+	0.0349955i
$801$	−15.2085	+	9.77388i	−0.537364	+	0.345343i
$802$	−17.4856	−	20.1795i	−0.617438	−	0.712561i
$803$	−12.2247	+	3.58948i	−0.431399	+	0.126670i
$804$	−1.58240			−0.0558070
$805$	12.7946	+	13.8306i	0.450949	+	0.487463i
$806$	−8.53604			−0.300669
$807$	−6.47775	+	1.90204i	−0.228028	+	0.0669550i
$808$	6.84727	+	7.90217i	0.240886	+	0.277997i
$809$	38.1426	−	24.5128i	1.34102	−	0.861824i	0.344004	−	0.938968i	$-0.388217\pi$
$809$	38.1426	−	24.5128i	1.34102	−	0.861824i	0.997020	+	0.0771447i	$0.0245803\pi$
$810$	−0.142315	−	0.989821i	−0.00500043	−	0.0347788i
$811$	14.6376	+	9.40702i	0.513996	+	0.330325i	0.771793	−	0.635874i	$-0.219360\pi$
$811$	14.6376	+	9.40702i	0.513996	+	0.330325i	−0.257797	+	0.966199i	$0.582997\pi$
$812$	−11.4899	+	25.1593i	−0.403215	+	0.882918i
$813$	−4.98663	+	5.75488i	−0.174889	+	0.201832i
$814$	7.58080	−	52.7257i	0.265707	−	1.84803i
$815$	7.90582	+	17.3113i	0.276929	+	0.606390i
$816$	0.150443	+	0.0441740i	0.00526655	+	0.00154640i
$817$	5.54358	+	1.62774i	0.193945	+	0.0569475i
$818$	5.12160	+	11.2147i	0.179072	+	0.392114i
$819$	0.973221	−	6.76890i	0.0340071	−	0.236525i
$820$	2.52439	−	2.91330i	0.0881554	−	0.101737i
$821$	−3.70804	+	8.11948i	−0.129412	+	0.283372i	−0.963235	−	0.268659i	$-0.913420\pi$
$821$	−3.70804	+	8.11948i	−0.129412	+	0.283372i	0.833824	+	0.552031i	$0.186147\pi$
$822$	7.82415	+	5.02827i	0.272898	+	0.175381i
$823$	2.66179	+	18.5132i	0.0927843	+	0.645329i	0.982145	+	0.188123i	$0.0602405\pi$
$823$	2.66179	+	18.5132i	0.0927843	+	0.645329i	−0.889361	+	0.457205i	$0.848850\pi$
$824$	−5.54640	+	3.56446i	−0.193218	+	0.124174i
$825$	−4.18902	−	4.83439i	−0.145843	−	0.168312i
$826$	21.9558	−	6.44680i	0.763940	−	0.224313i
$827$	0.465944			0.0162024			0.00810122	−	0.999967i	$-0.497421\pi$
$827$	0.465944			0.0162024			0.00810122	+	0.999967i	$0.497421\pi$
$828$	−0.527865	+	4.76669i	−0.0183446	+	0.165654i
$829$	−8.55792			−0.297229			−0.148614	−	0.988895i	$-0.547481\pi$
$829$	−8.55792			−0.297229			−0.148614	+	0.988895i	$0.547481\pi$
$830$	−9.16136	+	2.69002i	−0.317995	+	0.0933719i
$831$	−3.99131	−	4.60621i	−0.138457	−	0.159788i
$832$	−1.46436	+	0.941085i	−0.0507675	+	0.0326263i
$833$	0.188200	+	1.30896i	0.00652075	+	0.0453528i
$834$	−7.19757	−	4.62560i	−0.249232	−	0.160171i
$835$	−4.55162	+	9.96666i	−0.157515	+	0.344911i
$836$	−30.4055	+	35.0898i	−1.05160	+	1.21361i
$837$	0.697889	−	4.85393i	0.0241226	−	0.167776i
$838$	−14.2150	−	31.1264i	−0.491047	−	1.07524i
$839$	−37.0541	−	10.8801i	−1.27925	−	0.375622i	−0.429624	−	0.903008i	$-0.641354\pi$
$839$	−37.0541	−	10.8801i	−1.27925	−	0.375622i	−0.849626	+	0.527386i	$0.823172\pi$
$840$	−3.76949	−	1.10682i	−0.130060	−	0.0381890i
$841$	8.54341	+	18.7075i	0.294600	+	0.645085i
$842$	−5.13414	+	35.7087i	−0.176934	+	1.23060i
$843$	−1.94898	+	2.24925i	−0.0671265	+	0.0774681i
$844$	9.99770	−	21.8919i	0.344135	−	0.753551i
$845$	8.38731	+	5.39020i	0.288532	+	0.185428i
$846$	−0.632560	−	4.39955i	−0.0217478	−	0.151260i
$847$	98.8824	−	63.5478i	3.39764	−	2.18353i
$848$	−5.26912	−	6.08089i	−0.180942	−	0.208819i
$849$	12.2805	−	3.60587i	0.421464	−	0.123753i
$850$	0.156794			0.00537799
$851$	−25.1577	+	31.0157i	−0.862396	+	1.06321i
$852$	−14.7554			−0.505510
$853$	43.4550	−	12.7595i	1.48787	−	0.436878i	0.566009	−	0.824399i	$-0.308487\pi$
$853$	43.4550	−	12.7595i	1.48787	−	0.436878i	0.921861	+	0.387521i	$0.126668\pi$
$854$	3.97022	+	4.58188i	0.135858	+	0.156789i
$855$	−6.10613	+	3.92417i	−0.208825	+	0.134204i
$856$	1.92823	+	13.4111i	0.0659054	+	0.458382i
$857$	−24.3417	−	15.6435i	−0.831497	−	0.534371i	0.0542562	−	0.998527i	$-0.482721\pi$
$857$	−24.3417	−	15.6435i	−0.831497	−	0.534371i	−0.885753	+	0.464156i	$0.846358\pi$
$858$	4.62558	−	10.1286i	0.157915	−	0.345785i
$859$	−6.65512	+	7.68041i	−0.227070	+	0.262052i	−0.857840	−	0.513918i	$-0.828194\pi$
$859$	−6.65512	+	7.68041i	−0.227070	+	0.262052i	0.630770	+	0.775970i	$0.282739\pi$
$860$	−0.113282	+	0.787892i	−0.00386288	+	0.0268669i
$861$	6.29115	+	13.7757i	0.214402	+	0.469474i
$862$	18.6230	+	5.46821i	0.634302	+	0.186248i
$863$	12.3947	+	3.63942i	0.421922	+	0.123887i	0.485799	−	0.874070i	$-0.338529\pi$
$863$	12.3947	+	3.63942i	0.421922	+	0.123887i	−0.0638775	+	0.997958i	$0.520347\pi$
$864$	−0.415415	−	0.909632i	−0.0141327	−	0.0309463i
$865$	−2.37523	+	16.5201i	−0.0807603	+	0.561700i
$866$	−18.3792	+	21.2107i	−0.624551	+	0.720770i
$867$	−7.05184	+	15.4414i	−0.239493	+	0.524417i
$868$	−16.2071	−	10.4156i	−0.550103	−	0.353530i
$869$	−2.86495	−	19.9262i	−0.0971867	−	0.675948i
$870$	−5.92269	+	3.80628i	−0.200798	+	0.129045i
$871$	−1.80379	−	2.08168i	−0.0611191	−	0.0705352i
$872$	11.6947	−	3.43387i	0.396032	−	0.116286i
$873$	−3.67127			−0.124254
$874$	33.0635	−	10.8875i	1.11839	−	0.368275i
$875$	−3.92863			−0.132812
$876$	−1.91105	+	0.561136i	−0.0645685	+	0.0189590i
$877$	−16.2986	−	18.8096i	−0.550364	−	0.635154i	0.410604	−	0.911814i	$-0.365318\pi$
$877$	−16.2986	−	18.8096i	−0.550364	−	0.635154i	−0.960968	+	0.276660i	$0.910773\pi$
$878$	30.9880	−	19.9148i	1.04580	−	0.672092i
$879$	−1.58663	−	11.0353i	−0.0535158	−	0.372211i
$880$	−5.38134	−	3.45838i	−0.181405	−	0.116582i
$881$	−14.8236	+	32.4591i	−0.499419	+	1.09358i	0.477238	+	0.878774i	$0.341638\pi$
$881$	−14.8236	+	32.4591i	−0.499419	+	1.09358i	−0.976658	+	0.214802i	$0.931089\pi$
$882$	5.52318	−	6.37409i	0.185975	−	0.214627i
$883$	−7.46830	+	51.9431i	−0.251328	+	1.74803i	0.338930	+	0.940811i	$0.389935\pi$
$883$	−7.46830	+	51.9431i	−0.251328	+	1.74803i	−0.590259	+	0.807214i	$0.700974\pi$
$884$	0.113379	+	0.248265i	0.00381334	+	0.00835005i
$885$	5.58867	+	1.64098i	0.187861	+	0.0551610i
$886$	−21.2092	−	6.22757i	−0.712536	−	0.209219i
$887$	−2.89392	−	6.33680i	−0.0971683	−	0.212769i	0.854805	−	0.518949i	$-0.173676\pi$
$887$	−2.89392	−	6.33680i	−0.0971683	−	0.212769i	−0.951974	+	0.306180i	$0.900949\pi$
$888$	1.18509	−	8.24248i	0.0397690	−	0.276600i
$889$	−4.09112	+	4.72140i	−0.137212	+	0.158351i
$890$	−7.51001	+	16.4446i	−0.251736	+	0.551225i
$891$	5.38134	+	3.45838i	0.180282	+	0.115860i
$892$	2.24699	+	15.6282i	0.0752348	+	0.523270i
$893$	−27.1405	+	17.4421i	−0.908221	+	0.583678i
$894$	10.6314	+	12.2693i	0.355567	+	0.410347i
$895$	15.2789	−	4.48629i	0.510717	−	0.149960i
$896$	−3.92863			−0.131246
$897$	−6.87241	+	4.73917i	−0.229463	+	0.158236i
$898$	28.3014			0.944429
$899$	−33.1261	+	9.72669i	−1.10482	+	0.324403i
$900$	−0.654861	−	0.755750i	−0.0218287	−	0.0251917i
$901$	−1.06132	+	0.682068i	−0.0353577	+	0.0227230i
$902$	3.50930	+	24.4077i	0.116847	+	0.812689i
$903$	−2.63074	−	1.69067i	−0.0875455	−	0.0562621i
$904$	5.47608	−	11.9909i	0.182132	−	0.398813i
$905$	14.6165	−	16.8684i	0.485869	−	0.560723i
$906$	0.477724	−	3.32265i	0.0158713	−	0.110388i
$907$	−9.97303	−	21.8379i	−0.331149	−	0.725115i	0.668681	−	0.743549i	$-0.266859\pi$
$907$	−9.97303	−	21.8379i	−0.331149	−	0.725115i	−0.999830	+	0.0184343i	$0.994132\pi$
$908$	−7.33970	−	2.15513i	−0.243577	−	0.0715205i
$909$	−10.0325	−	2.94581i	−0.332758	−	0.0977065i
$910$	−2.84082	−	6.22052i	−0.0941722	−	0.206208i
$911$	4.01033	−	27.8924i	0.132868	−	0.924118i	−0.808922	−	0.587916i	$-0.799948\pi$
$911$	4.01033	−	27.8924i	0.132868	−	0.924118i	0.941790	−	0.336202i	$-0.109142\pi$
$912$	−4.75322	+	5.48551i	−0.157395	+	0.181643i
$913$	25.3726	−	55.5582i	0.839709	−	1.83871i
$914$	29.1848	+	18.7559i	0.965347	+	0.620391i
$915$	0.219621	+	1.52750i	0.00726046	+	0.0504976i
$916$	−14.2282	+	9.14391i	−0.470113	+	0.302123i
$917$	−14.0110	−	16.1695i	−0.462684	−	0.533965i
$918$	−0.150443	+	0.0441740i	−0.00496535	+	0.00145796i
$919$	42.3117			1.39574			0.697868	−	0.716227i	$-0.254132\pi$
$919$	42.3117			1.39574			0.697868	+	0.716227i	$0.254132\pi$
$920$	2.13300	+	4.29538i	0.0703229	+	0.141615i
$921$	15.4401			0.508769
$922$	−31.1876	+	9.15751i	−1.02711	+	0.301587i
$923$	−16.8197	−	19.4110i	−0.553628	−	0.638921i
$924$	21.1413	−	13.5867i	0.695498	−	0.446969i
$925$	−1.18509	−	8.24248i	−0.0389655	−	0.271011i
$926$	−32.5440	−	20.9147i	−1.06946	−	0.687301i
$927$	2.73884	−	5.99722i	0.0899553	−	0.196975i
$928$	−4.61042	+	5.32071i	−0.151345	+	0.174661i
$929$	−0.660690	+	4.59520i	−0.0216765	+	0.150764i	−0.997785	−	0.0665198i	$-0.978810\pi$
$929$	−0.660690	+	4.59520i	−0.0216765	+	0.150764i	0.976109	+	0.217283i	$0.0697195\pi$
$930$	−2.03713	−	4.46069i	−0.0668001	−	0.146272i
$931$	−58.7382	−	17.2471i	−1.92507	−	0.565251i
$932$	15.1923	+	4.46085i	0.497639	+	0.146120i
$933$	−4.96374	−	10.8691i	−0.162505	−	0.355837i
$934$	−1.49274	+	10.3822i	−0.0488438	+	0.339716i
$935$	−0.656814	+	0.758004i	−0.0214801	+	0.0247894i
$936$	0.723107	−	1.58338i	0.0236355	−	0.0517545i
$937$	42.0414	+	27.0184i	1.37343	+	0.882651i	0.999005	−	0.0446047i	$-0.0142028\pi$
$937$	42.0414	+	27.0184i	1.37343	+	0.882651i	0.374428	+	0.927256i	$0.377839\pi$
$938$	−0.884724	−	6.15339i	−0.0288873	−	0.200915i
$939$	−18.2384	+	11.7211i	−0.595186	+	0.382503i
$940$	−2.91072	−	3.35915i	−0.0949372	−	0.109563i
$941$	−35.6662	+	10.4725i	−1.16269	+	0.341395i	−0.805476	−	0.592629i	$-0.798090\pi$
$941$	−35.6662	+	10.4725i	−1.16269	+	0.341395i	−0.357210	+	0.934024i	$0.616272\pi$
$942$	12.7960			0.416917
$943$	7.12921	−	17.0573i	0.232159	−	0.555461i
$944$	5.82460			0.189575
$945$	3.76949	−	1.10682i	0.122622	−	0.0360049i
$946$	−3.33444	−	3.84815i	−0.108412	−	0.125114i
$947$	23.7839	−	15.2850i	0.772872	−	0.496695i	−0.0937887	−	0.995592i	$-0.529898\pi$
$947$	23.7839	−	15.2850i	0.772872	−	0.496695i	0.866661	+	0.498897i	$0.166261\pi$
$948$	−0.447871	−	3.11501i	−0.0145462	−	0.101171i
$949$	−2.91661	−	1.87439i	−0.0946771	−	0.0608453i
$950$	−3.01523	+	6.60244i	−0.0978271	+	0.214212i
$951$	−3.49066	+	4.02843i	−0.113192	+	0.130631i
$952$	−0.0876639	+	0.609716i	−0.00284120	+	0.0197610i
$953$	2.70879	+	5.93141i	0.0877462	+	0.192137i	0.948418	−	0.317023i	$-0.102683\pi$
$953$	2.70879	+	5.93141i	0.0877462	+	0.192137i	−0.860672	+	0.509160i	$0.829956\pi$
$954$	7.72025	+	2.26687i	0.249952	+	0.0733926i
$955$	−12.3521	−	3.62691i	−0.399705	−	0.117364i
$956$	−10.7915	−	23.6300i	−0.349021	−	0.764249i
$957$	6.40923	−	44.5772i	0.207181	−	1.44098i
$958$	25.1138	−	28.9828i	0.811389	−	0.936393i
$959$	−15.1787	+	33.2366i	−0.490144	+	1.07327i
$960$	−0.841254	−	0.540641i	−0.0271513	−	0.0174491i
$961$	0.989424	+	6.88160i	0.0319169	+	0.221987i
$962$	12.1941	−	7.83665i	0.393152	−	0.252664i
$963$	−8.87272	−	10.2397i	−0.285920	−	0.329969i
$964$	−18.3583	+	5.39047i	−0.591279	+	0.173615i
$965$	−6.66910			−0.214686
$966$	−18.8311	+	0.612392i	−0.605880	+	0.0197034i
$967$	−25.6035			−0.823352			−0.411676	−	0.911330i	$-0.635056\pi$
$967$	−25.6035			−0.823352			−0.411676	+	0.911330i	$0.635056\pi$
$968$	28.7073	−	8.42923i	0.922688	−	0.270926i
$969$	0.745276	+	0.860095i	0.0239417	+	0.0276302i
$970$	−3.08847	+	1.98484i	−0.0991646	+	0.0637292i
$971$	−1.80791	−	12.5743i	−0.0580187	−	0.403529i	−0.998049	−	0.0624375i	$-0.980113\pi$
$971$	−1.80791	−	12.5743i	−0.0580187	−	0.403529i	0.940030	−	0.341091i	$-0.110796\pi$
$972$	0.841254	+	0.540641i	0.0269832	+	0.0173411i
$973$	13.9631	−	30.5750i	0.447637	−	0.980188i
$974$	11.3529	−	13.1019i	0.363770	−	0.419813i
$975$	0.247725	−	1.72297i	0.00793356	−	0.0551791i
$976$	0.641072	+	1.40375i	0.0205202	+	0.0449330i
$977$	−8.59556	−	2.52388i	−0.274996	−	0.0807462i	0.141327	−	0.989963i	$-0.454863\pi$
$977$	−8.59556	−	2.52388i	−0.274996	−	0.0807462i	−0.416323	+	0.909217i	$0.636681\pi$
$978$	−18.2602	−	5.36169i	−0.583898	−	0.171448i
$979$	−48.0401	−	105.193i	−1.53537	−	3.36199i
$980$	1.20030	−	8.34828i	0.0383422	−	0.266676i
$981$	−7.98171	+	9.21139i	−0.254837	+	0.294097i
$982$	13.3496	−	29.2315i	0.426002	−	0.932814i
$983$	−48.3382	−	31.0651i	−1.54175	−	0.990822i	−0.987347	−	0.158572i	$-0.949311\pi$
$983$	−48.3382	−	31.0651i	−1.54175	−	0.990822i	−0.554401	−	0.832249i	$-0.687053\pi$
$984$	0.548601	+	3.81561i	0.0174888	+	0.121637i
$985$	5.17154	−	3.32355i	0.164779	−	0.105897i
$986$	0.722887	+	0.834256i	0.0230214	+	0.0265681i
$987$	16.7546	−	4.91959i	0.533305	−	0.156592i
$988$	−12.6345			−0.401958
$989$	0.665809	+	3.75894i	0.0211715	+	0.119527i
$990$	6.39682			0.203304
$991$	−15.3191	+	4.49809i	−0.486627	+	0.142887i	−0.515837	−	0.856687i	$-0.672519\pi$
$991$	−15.3191	+	4.49809i	−0.486627	+	0.142887i	0.0292099	+	0.999573i	$0.490701\pi$
$992$	−3.21133	−	3.70607i	−0.101960	−	0.117668i
$993$	2.64694	−	1.70109i	0.0839982	−	0.0539823i
$994$	−8.24975	−	57.3783i	−0.261666	−	1.81993i
$995$	−0.870596	−	0.559498i	−0.0275997	−	0.0177373i
$996$	3.96644	−	8.68528i	0.125681	−	0.275204i
$997$	10.1772	−	11.7451i	0.322315	−	0.371971i	−0.571350	−	0.820707i	$-0.693580\pi$
$997$	10.1772	−	11.7451i	0.322315	−	0.371971i	0.893665	+	0.448735i	$0.148125\pi$
$998$	1.75092	−	12.1779i	0.0554245	−	0.385486i
$999$	3.45926	+	7.57473i	0.109446	+	0.239654i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.h.331.3	yes	30
23.18	even	11	inner	690.2.m.h.271.3	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.h.271.3	✓	30	23.18	even	11	inner
690.2.m.h.331.3	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)

\(f(q)\)	\(=\)	\(q+(0.959493 - 0.281733i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.142315 + 0.989821i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(1.63201 - 3.57361i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(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} +(1.63201 - 3.57361i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.415415 + 0.909632i) q^{10} +(-6.13770 - 1.80219i) q^{11} +(-0.959493 - 0.281733i) q^{12} +(-0.723107 - 1.58338i) q^{13} +(0.559102 - 3.88864i) q^{14} +(0.654861 - 0.755750i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-0.131904 - 0.0847692i) q^{17} +(0.142315 + 0.989821i) q^{18} +(6.10613 - 3.92417i) q^{19} +(0.654861 + 0.755750i) q^{20} +(-3.76949 + 1.10682i) q^{21} -6.39682 q^{22} +(4.11665 + 2.46032i) q^{23} -1.00000 q^{24} +(-0.959493 + 0.281733i) q^{25} +(-1.13991 - 1.31552i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-0.559102 - 3.88864i) q^{28} +(-5.92269 - 3.80628i) q^{29} +(0.415415 - 0.909632i) q^{30} +(3.21133 - 3.70607i) q^{31} +(0.142315 - 0.989821i) q^{32} +(2.65733 + 5.81875i) q^{33} +(-0.150443 - 0.0441740i) q^{34} +(3.76949 + 1.10682i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-1.18509 + 8.24248i) q^{37} +(4.75322 - 5.48551i) q^{38} +(-0.723107 + 1.58338i) q^{39} +(0.841254 + 0.540641i) q^{40} +(-0.548601 - 3.81561i) q^{41} +(-3.30497 + 2.12398i) q^{42} +(0.521265 + 0.601572i) q^{43} +(-6.13770 + 1.80219i) q^{44} -1.00000 q^{45} +(4.64305 + 1.20086i) q^{46} -4.44479 q^{47} +(-0.959493 + 0.281733i) q^{48} +(-5.52318 - 6.37409i) q^{49} +(-0.841254 + 0.540641i) q^{50} +(0.0223141 + 0.155198i) q^{51} +(-1.46436 - 0.941085i) q^{52} +(3.34250 - 7.31906i) q^{53} +(0.654861 - 0.755750i) q^{54} +(0.910362 - 6.33171i) q^{55} +(-1.63201 - 3.57361i) q^{56} +(-6.96435 - 2.04492i) q^{57} +(-6.75513 - 1.98348i) q^{58} +(2.41963 + 5.29825i) q^{59} +(0.142315 - 0.989821i) q^{60} +(-1.01059 + 1.16628i) q^{61} +(2.03713 - 4.46069i) q^{62} +(3.30497 + 2.12398i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(1.46436 - 0.941085i) q^{65} +(4.18902 + 4.83439i) q^{66} +(1.51830 - 0.445814i) q^{67} -0.156794 q^{68} +(-0.836450 - 4.72232i) q^{69} +3.92863 q^{70} +(14.1577 - 4.15706i) q^{71} +(0.654861 + 0.755750i) q^{72} +(1.67555 - 1.07681i) q^{73} +(1.18509 + 8.24248i) q^{74} +(0.841254 + 0.540641i) q^{75} +(3.01523 - 6.60244i) q^{76} +(-16.4571 + 18.9925i) q^{77} +(-0.247725 + 1.72297i) q^{78} +(1.30733 + 2.86265i) q^{79} +(0.959493 + 0.281733i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-1.60136 - 3.50649i) q^{82} +(-1.35884 + 9.45094i) q^{83} +(-2.57271 + 2.96906i) q^{84} +(0.0651346 - 0.142625i) q^{85} +(0.669633 + 0.430347i) q^{86} +(1.00194 + 6.96865i) q^{87} +(-5.38134 + 3.45838i) q^{88} +(11.8388 + 13.6627i) q^{89} +(-0.959493 + 0.281733i) q^{90} -6.83851 q^{91} +(4.79330 - 0.155879i) q^{92} -4.90384 q^{93} +(-4.26474 + 1.25224i) q^{94} +(4.75322 + 5.48551i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(0.522476 + 3.63390i) q^{97} +(-7.09524 - 4.55983i) q^{98} +(2.65733 - 5.81875i) 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	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 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 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Introduction

L-functions

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