LMFDB - Embedded newform 690.2.m.g.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.g.271.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 + 0.281733i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(0.841254 + 0.540641i) q^{6} +(1.68254 - 3.68425i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(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} +(1.68254 - 3.68425i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.415415 + 0.909632i) q^{10} +(-0.746018 - 0.219051i) q^{11} +(-0.959493 - 0.281733i) q^{12} +(-1.73977 - 3.80956i) q^{13} +(-0.576412 + 4.00903i) q^{14} +(-0.654861 + 0.755750i) q^{15} +(0.415415 - 0.909632i) q^{16} +(0.246954 + 0.158708i) q^{17} +(-0.142315 - 0.989821i) q^{18} +(1.50337 - 0.966158i) q^{19} +(-0.654861 - 0.755750i) q^{20} +(-3.88620 + 1.14109i) q^{21} +0.777512 q^{22} +(2.10059 + 4.31132i) q^{23} +1.00000 q^{24} +(-0.959493 + 0.281733i) q^{25} +(2.74258 + 3.16510i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-0.576412 - 4.00903i) q^{28} +(-2.37162 - 1.52415i) q^{29} +(0.415415 - 0.909632i) q^{30} +(-5.90838 + 6.81863i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(0.322990 + 0.707250i) q^{33} +(-0.281664 - 0.0827039i) q^{34} +(-3.88620 - 1.14109i) q^{35} +(0.415415 + 0.909632i) q^{36} +(1.01155 - 7.03551i) q^{37} +(-1.17028 + 1.35057i) q^{38} +(-1.73977 + 3.80956i) q^{39} +(0.841254 + 0.540641i) q^{40} +(0.298907 + 2.07895i) q^{41} +(3.40730 - 2.18974i) q^{42} +(-4.60514 - 5.31462i) q^{43} +(-0.746018 + 0.219051i) q^{44} +1.00000 q^{45} +(-3.23014 - 3.54488i) q^{46} -4.14235 q^{47} +(-0.959493 + 0.281733i) q^{48} +(-6.15871 - 7.10753i) q^{49} +(0.841254 - 0.540641i) q^{50} +(-0.0417772 - 0.290567i) q^{51} +(-3.52319 - 2.26422i) q^{52} +(1.69935 - 3.72107i) q^{53} +(-0.654861 + 0.755750i) q^{54} +(-0.110652 + 0.769598i) q^{55} +(1.68254 + 3.68425i) q^{56} +(-1.71467 - 0.503473i) q^{57} +(2.70495 + 0.794245i) q^{58} +(-3.75952 - 8.23221i) q^{59} +(-0.142315 + 0.989821i) q^{60} +(-0.280885 + 0.324158i) q^{61} +(3.74802 - 8.20701i) q^{62} +(3.40730 + 2.18974i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-3.52319 + 2.26422i) q^{65} +(-0.509162 - 0.587605i) q^{66} +(-3.59690 + 1.05614i) q^{67} +0.293555 q^{68} +(1.88269 - 4.41084i) q^{69} +4.05026 q^{70} +(-9.31938 + 2.73642i) q^{71} +(-0.654861 - 0.755750i) q^{72} +(13.1960 - 8.48054i) q^{73} +(1.01155 + 7.03551i) q^{74} +(0.841254 + 0.540641i) q^{75} +(0.742372 - 1.62557i) q^{76} +(-2.06224 + 2.37995i) q^{77} +(0.596019 - 4.14540i) q^{78} +(-1.41045 - 3.08845i) q^{79} +(-0.959493 - 0.281733i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-0.872506 - 1.91052i) q^{82} +(-0.601899 + 4.18630i) q^{83} +(-2.65236 + 3.06098i) q^{84} +(0.121947 - 0.267027i) q^{85} +(5.91590 + 3.80192i) q^{86} +(0.401206 + 2.79045i) q^{87} +(0.654085 - 0.420355i) q^{88} +(-4.76064 - 5.49407i) q^{89} +(-0.959493 + 0.281733i) q^{90} -16.9626 q^{91} +(4.09801 + 2.49125i) q^{92} +9.02235 q^{93} +(3.97456 - 1.16704i) q^{94} +(-1.17028 - 1.35057i) q^{95} +(0.841254 - 0.540641i) q^{96} +(0.102356 + 0.711900i) q^{97} +(7.91166 + 5.08452i) q^{98} +(0.322990 - 0.707250i) 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
$7$	1.68254	−	3.68425i	0.635940	−	1.39251i	−0.267399	−	0.963586i	$-0.586164\pi$
$7$	1.68254	−	3.68425i	0.635940	−	1.39251i	0.903339	−	0.428928i	$-0.141109\pi$
$8$	−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
$11$	−0.746018	−	0.219051i	−0.224933	−	0.0660462i	0.167324	−	0.985902i	$-0.446487\pi$
$11$	−0.746018	−	0.219051i	−0.224933	−	0.0660462i	−0.392257	+	0.919856i	$0.628306\pi$
$12$	−0.959493	−	0.281733i	−0.276982	−	0.0813292i
$13$	−1.73977	−	3.80956i	−0.482525	−	1.05658i	−0.981761	−	0.190117i	$-0.939113\pi$
$13$	−1.73977	−	3.80956i	−0.482525	−	1.05658i	0.499236	−	0.866466i	$-0.333614\pi$
$14$	−0.576412	+	4.00903i	−0.154053	+	1.07146i
$15$	−0.654861	+	0.755750i	−0.169084	+	0.195134i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	0.246954	+	0.158708i	0.0598951	+	0.0384923i	0.570246	−	0.821474i	$-0.306848\pi$
$17$	0.246954	+	0.158708i	0.0598951	+	0.0384923i	−0.510351	+	0.859966i	$0.670484\pi$
$18$	−0.142315	−	0.989821i	−0.0335439	−	0.233303i
$19$	1.50337	−	0.966158i	0.344897	−	0.221652i	−0.356711	−	0.934215i	$-0.616102\pi$
$19$	1.50337	−	0.966158i	0.344897	−	0.221652i	0.701608	+	0.712563i	$0.252466\pi$
$20$	−0.654861	−	0.755750i	−0.146431	−	0.168991i
$21$	−3.88620	+	1.14109i	−0.848038	+	0.249006i
$22$	0.777512			0.165766
$23$	2.10059	+	4.31132i	0.438004	+	0.898973i
$23$	2.10059	+	4.31132i	0.438004	+	0.898973i
$24$	1.00000			0.204124
$25$	−0.959493	+	0.281733i	−0.191899	+	0.0563465i
$26$	2.74258	+	3.16510i	0.537863	+	0.620727i
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$	−0.576412	−	4.00903i	−0.108932	−	0.757636i
$29$	−2.37162	−	1.52415i	−0.440398	−	0.283027i	0.301593	−	0.953437i	$-0.402482\pi$
$29$	−2.37162	−	1.52415i	−0.440398	−	0.283027i	−0.741991	+	0.670410i	$0.766118\pi$
$30$	0.415415	−	0.909632i	0.0758441	−	0.166075i
$31$	−5.90838	+	6.81863i	−1.06118	+	1.22466i	−0.0876348	+	0.996153i	$0.527931\pi$
$31$	−5.90838	+	6.81863i	−1.06118	+	1.22466i	−0.973542	+	0.228510i	$0.926615\pi$
$32$	−0.142315	+	0.989821i	−0.0251579	+	0.174977i
$33$	0.322990	+	0.707250i	0.0562254	+	0.123116i
$34$	−0.281664	−	0.0827039i	−0.0483049	−	0.0141836i
$35$	−3.88620	−	1.14109i	−0.656887	−	0.192879i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	1.01155	−	7.03551i	0.166298	−	1.15663i	−0.720155	−	0.693813i	$-0.755929\pi$
$37$	1.01155	−	7.03551i	0.166298	−	1.15663i	0.886453	−	0.462818i	$-0.153162\pi$
$38$	−1.17028	+	1.35057i	−0.189844	+	0.219092i
$39$	−1.73977	+	3.80956i	−0.278586	+	0.610018i
$40$	0.841254	+	0.540641i	0.133014	+	0.0854828i
$41$	0.298907	+	2.07895i	0.0466815	+	0.324677i	0.999759	+	0.0219507i	$0.00698767\pi$
$41$	0.298907	+	2.07895i	0.0466815	+	0.324677i	−0.953078	+	0.302726i	$0.902103\pi$
$42$	3.40730	−	2.18974i	0.525757	−	0.337884i
$43$	−4.60514	−	5.31462i	−0.702277	−	0.810471i	0.286781	−	0.957996i	$-0.407415\pi$
$43$	−4.60514	−	5.31462i	−0.702277	−	0.810471i	−0.989058	+	0.147525i	$0.952869\pi$
$44$	−0.746018	+	0.219051i	−0.112466	+	0.0330231i
$45$	1.00000			0.149071
$46$	−3.23014	−	3.54488i	−0.476259	−	0.522664i
$47$	−4.14235			−0.604224			−0.302112	−	0.953272i	$-0.597692\pi$
$47$	−4.14235			−0.604224			−0.302112	+	0.953272i	$0.597692\pi$
$48$	−0.959493	+	0.281733i	−0.138491	+	0.0406646i
$49$	−6.15871	−	7.10753i	−0.879816	−	1.01536i
$50$	0.841254	−	0.540641i	0.118971	−	0.0764582i
$51$	−0.0417772	−	0.290567i	−0.00584998	−	0.0406875i
$52$	−3.52319	−	2.26422i	−0.488579	−	0.313991i
$53$	1.69935	−	3.72107i	0.233424	−	0.511128i	−0.756281	−	0.654247i	$-0.772986\pi$
$53$	1.69935	−	3.72107i	0.233424	−	0.511128i	0.989706	+	0.143119i	$0.0457131\pi$
$54$	−0.654861	+	0.755750i	−0.0891153	+	0.102844i
$55$	−0.110652	+	0.769598i	−0.0149202	+	0.103773i
$56$	1.68254	+	3.68425i	0.224839	+	0.492328i
$57$	−1.71467	−	0.503473i	−0.227114	−	0.0666867i
$58$	2.70495	+	0.794245i	0.355177	+	0.104289i
$59$	−3.75952	−	8.23221i	−0.489448	−	1.07174i	−0.979756	−	0.200193i	$-0.935843\pi$
$59$	−3.75952	−	8.23221i	−0.489448	−	1.07174i	0.490308	−	0.871549i	$-0.336884\pi$
$60$	−0.142315	+	0.989821i	−0.0183728	+	0.127785i
$61$	−0.280885	+	0.324158i	−0.0359636	+	0.0415042i	−0.773446	−	0.633862i	$-0.781469\pi$
$61$	−0.280885	+	0.324158i	−0.0359636	+	0.0415042i	0.737483	+	0.675366i	$0.236014\pi$
$62$	3.74802	−	8.20701i	0.475999	−	1.04229i
$63$	3.40730	+	2.18974i	0.429279	+	0.275881i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	−3.52319	+	2.26422i	−0.436998	+	0.280842i
$66$	−0.509162	−	0.587605i	−0.0626735	−	0.0723291i
$67$	−3.59690	+	1.05614i	−0.439431	+	0.129029i	−0.493962	−	0.869484i	$-0.664452\pi$
$67$	−3.59690	+	1.05614i	−0.439431	+	0.129029i	0.0545311	+	0.998512i	$0.482634\pi$
$68$	0.293555			0.0355987
$69$	1.88269	−	4.41084i	0.226649	−	0.531002i
$70$	4.05026			0.484099
$71$	−9.31938	+	2.73642i	−1.10601	+	0.324753i	−0.783236	−	0.621724i	$-0.786433\pi$
$71$	−9.31938	+	2.73642i	−1.10601	+	0.324753i	−0.322771	+	0.946477i	$0.604614\pi$
$72$	−0.654861	−	0.755750i	−0.0771761	−	0.0890659i
$73$	13.1960	−	8.48054i	1.54447	−	0.992572i	0.557777	−	0.829991i	$-0.311655\pi$
$73$	13.1960	−	8.48054i	1.54447	−	0.992572i	0.986695	−	0.162581i	$-0.0519818\pi$
$74$	1.01155	+	7.03551i	0.117591	+	0.817862i
$75$	0.841254	+	0.540641i	0.0971396	+	0.0624278i
$76$	0.742372	−	1.62557i	0.0851559	−	0.186465i
$77$	−2.06224	+	2.37995i	−0.235014	+	0.271221i
$78$	0.596019	−	4.14540i	0.0674858	−	0.469374i
$79$	−1.41045	−	3.08845i	−0.158688	−	0.347478i	0.813542	−	0.581506i	$-0.197536\pi$
$79$	−1.41045	−	3.08845i	−0.158688	−	0.347478i	−0.972230	+	0.234028i	$0.924809\pi$
$80$	−0.959493	−	0.281733i	−0.107275	−	0.0314987i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−0.872506	−	1.91052i	−0.0963522	−	0.210982i
$83$	−0.601899	+	4.18630i	−0.0660670	+	0.459506i	0.929754	+	0.368181i	$0.120019\pi$
$83$	−0.601899	+	4.18630i	−0.0660670	+	0.459506i	−0.995821	+	0.0913251i	$0.970890\pi$
$84$	−2.65236	+	3.06098i	−0.289396	+	0.333981i
$85$	0.121947	−	0.267027i	0.0132270	−	0.0289631i
$86$	5.91590	+	3.80192i	0.637928	+	0.409971i
$87$	0.401206	+	2.79045i	0.0430138	+	0.299168i
$88$	0.654085	−	0.420355i	0.0697257	−	0.0448100i
$89$	−4.76064	−	5.49407i	−0.504626	−	0.582370i	0.445088	−	0.895487i	$-0.353172\pi$
$89$	−4.76064	−	5.49407i	−0.504626	−	0.582370i	−0.949715	+	0.313117i	$0.898627\pi$
$90$	−0.959493	+	0.281733i	−0.101139	+	0.0296972i
$91$	−16.9626			−1.77816
$92$	4.09801	+	2.49125i	0.427247	+	0.259731i
$93$	9.02235			0.935574
$94$	3.97456	−	1.16704i	0.409944	−	0.120370i
$95$	−1.17028	−	1.35057i	−0.120068	−	0.138566i
$96$	0.841254	−	0.540641i	0.0858601	−	0.0551789i
$97$	0.102356	+	0.711900i	0.0103926	+	0.0722825i	0.994358	−	0.106079i	$-0.0338296\pi$
$97$	0.102356	+	0.711900i	0.0103926	+	0.0722825i	−0.983965	+	0.178361i	$0.942920\pi$
$98$	7.91166	+	5.08452i	0.799198	+	0.513614i
$99$	0.322990	−	0.707250i	0.0324617	−	0.0710813i
$100$	−0.654861	+	0.755750i	−0.0654861	+	0.0755750i
$101$	−1.53454	+	10.6729i	−0.152692	+	1.06200i	0.758990	+	0.651102i	$0.225693\pi$
$101$	−1.53454	+	10.6729i	−0.152692	+	1.06200i	−0.911683	+	0.410895i	$0.865216\pi$
$102$	0.121947	+	0.267027i	0.0120746	+	0.0264396i
$103$	−0.393736	−	0.115611i	−0.0387959	−	0.0113915i	0.262277	−	0.964993i	$-0.415527\pi$
$103$	−0.393736	−	0.115611i	−0.0387959	−	0.0113915i	−0.301073	+	0.953601i	$0.597345\pi$
$104$	4.01838	+	1.17990i	0.394035	+	0.115699i
$105$	1.68254	+	3.68425i	0.164199	+	0.359546i
$106$	−0.582173	+	4.04910i	−0.0565456	+	0.393283i
$107$	7.38778	−	8.52595i	0.714203	−	0.824235i	−0.276394	−	0.961044i	$-0.589139\pi$
$107$	7.38778	−	8.52595i	0.714203	−	0.824235i	0.990597	+	0.136810i	$0.0436849\pi$
$108$	0.415415	−	0.909632i	0.0399733	−	0.0875294i
$109$	14.4807	+	9.30618i	1.38700	+	0.891370i	0.999534	−	0.0305148i	$-0.00971467\pi$
$109$	14.4807	+	9.30618i	1.38700	+	0.891370i	0.387464	+	0.921885i	$0.373351\pi$
$110$	−0.110652	−	0.769598i	−0.0105502	−	0.0733783i
$111$	−5.97951	+	3.84280i	−0.567550	+	0.364742i
$112$	−2.65236	−	3.06098i	−0.250624	−	0.289236i
$113$	1.43358	−	0.420937i	0.134860	−	0.0395984i	−0.213606	−	0.976920i	$-0.568521\pi$
$113$	1.43358	−	0.420937i	0.134860	−	0.0395984i	0.348466	+	0.937321i	$0.386703\pi$
$114$	1.78706			0.167374
$115$	3.96850	−	2.69278i	0.370064	−	0.251103i
$116$	−2.81915			−0.261751
$117$	4.01838	−	1.17990i	0.371500	−	0.109082i
$118$	5.92652	+	6.83957i	0.545580	+	0.629633i
$119$	1.00023	−	0.642807i	0.0916907	−	0.0589260i
$120$	−0.142315	−	0.989821i	−0.0129915	−	0.0903579i
$121$	−8.74523	−	5.62022i	−0.795021	−	0.510929i
$122$	0.178181	−	0.390162i	0.0161317	−	0.0353236i
$123$	1.37542	−	1.58732i	0.124017	−	0.143124i
$124$	−1.28401	+	8.93051i	−0.115308	+	0.801984i
$125$	0.415415	+	0.909632i	0.0371558	+	0.0813600i
$126$	−3.88620	−	1.14109i	−0.346210	−	0.101656i
$127$	−2.03730	−	0.598205i	−0.180781	−	0.0530821i	0.190089	−	0.981767i	$-0.439122\pi$
$127$	−2.03730	−	0.598205i	−0.180781	−	0.0530821i	−0.370870	+	0.928685i	$0.620941\pi$
$128$	0.415415	+	0.909632i	0.0367178	+	0.0804009i
$129$	−1.00079	+	6.96067i	−0.0881149	+	0.612853i
$130$	2.74258	−	3.16510i	0.240540	−	0.277598i
$131$	−0.578105	+	1.26587i	−0.0505093	+	0.110600i	−0.933204	−	0.359347i	$-0.883000\pi$
$131$	−0.578105	+	1.26587i	−0.0505093	+	0.110600i	0.882695	+	0.469947i	$0.155727\pi$
$132$	0.654085	+	0.420355i	0.0569308	+	0.0365872i
$133$	−1.03008	−	7.16439i	−0.0893196	−	0.621231i
$134$	3.15365	−	2.02673i	0.272434	−	0.175082i
$135$	−0.654861	−	0.755750i	−0.0563614	−	0.0650446i
$136$	−0.281664	+	0.0827039i	−0.0241525	+	0.00709180i
$137$	−8.01169			−0.684485			−0.342242	−	0.939612i	$-0.611186\pi$
$137$	−8.01169			−0.684485			−0.342242	+	0.939612i	$0.611186\pi$
$138$	−0.563748	+	4.76258i	−0.0479894	+	0.405418i
$139$	22.5693			1.91430			0.957151	−	0.289590i	$-0.0935190\pi$
$139$	22.5693			1.91430			0.957151	+	0.289590i	$0.0935190\pi$
$140$	−3.88620	+	1.14109i	−0.328444	+	0.0964397i
$141$	2.71266	+	3.13058i	0.228447	+	0.263642i
$142$	8.17094	−	5.25115i	0.685690	−	0.440666i
$143$	0.463412	+	3.22310i	0.0387524	+	0.269529i
$144$	0.841254	+	0.540641i	0.0701045	+	0.0450534i
$145$	−1.17112	+	2.56438i	−0.0972558	+	0.212961i
$146$	−10.2722	+	11.8548i	−0.850133	+	0.981106i
$147$	−1.33842	+	9.30888i	−0.110391	+	0.767784i
$148$	−2.95271	−	6.46554i	−0.242711	−	0.531464i
$149$	12.8431	+	3.77108i	1.05215	+	0.308939i	0.761685	−	0.647947i	$-0.224372\pi$
$149$	12.8431	+	3.77108i	1.05215	+	0.308939i	0.290463	+	0.956886i	$0.406191\pi$
$150$	−0.959493	−	0.281733i	−0.0783423	−	0.0230034i
$151$	3.78765	+	8.29379i	0.308234	+	0.674939i	0.998833	−	0.0482991i	$-0.0153801\pi$
$151$	3.78765	+	8.29379i	0.308234	+	0.674939i	−0.690598	+	0.723238i	$0.742653\pi$
$152$	−0.254325	+	1.76887i	−0.0206285	+	0.143474i
$153$	−0.192237	+	0.221854i	−0.0155415	+	0.0179358i
$154$	1.30819	−	2.86455i	0.105417	−	0.230832i
$155$	7.59008	+	4.87785i	0.609650	+	0.391798i
$156$	0.596019	+	4.14540i	0.0477197	+	0.331898i
$157$	12.9304	−	8.30988i	1.03196	−	0.663201i	0.0889748	−	0.996034i	$-0.471641\pi$
$157$	12.9304	−	8.30988i	1.03196	−	0.663201i	0.942986	+	0.332833i	$0.108005\pi$
$158$	2.22343	+	2.56598i	0.176887	+	0.204138i
$159$	−3.92503	+	1.15249i	−0.311275	+	0.0913987i
$160$	1.00000			0.0790569
$161$	19.4183	−	0.485125i	1.53038	−	0.0382332i
$162$	1.00000			0.0785674
$163$	−10.4642	+	3.07257i	−0.819620	+	0.240662i	−0.664552	−	0.747242i	$-0.731378\pi$
$163$	−10.4642	+	3.07257i	−0.819620	+	0.240662i	−0.155068	+	0.987904i	$0.549560\pi$
$164$	1.37542	+	1.58732i	0.107402	+	0.123949i
$165$	0.654085	−	0.420355i	0.0509204	−	0.0327246i
$166$	−0.601899	−	4.18630i	−0.0467164	−	0.324920i
$167$	1.54438	+	0.992513i	0.119508	+	0.0768030i	0.599029	−	0.800727i	$-0.295553\pi$
$167$	1.54438	+	0.992513i	0.119508	+	0.0768030i	−0.479521	+	0.877530i	$0.659190\pi$
$168$	1.68254	−	3.68425i	0.129811	−	0.284246i
$169$	−2.97279	+	3.43078i	−0.228676	+	0.263906i
$170$	−0.0417772	+	0.290567i	−0.00320416	+	0.0222854i
$171$	0.742372	+	1.62557i	0.0567706	+	0.124310i
$172$	−6.74739	−	1.98121i	−0.514484	−	0.151066i
$173$	11.1622	+	3.27752i	0.848647	+	0.249185i	0.677009	−	0.735975i	$-0.263276\pi$
$173$	11.1622	+	3.27752i	0.848647	+	0.249185i	0.171638	+	0.985160i	$0.445094\pi$
$174$	−1.17112	−	2.56438i	−0.0887820	−	0.194406i
$175$	−0.576412	+	4.00903i	−0.0435727	+	0.303055i
$176$	−0.509162	+	0.587605i	−0.0383795	+	0.0442924i
$177$	−3.75952	+	8.23221i	−0.282583	+	0.618771i
$178$	6.11565	+	3.93029i	0.458388	+	0.294588i
$179$	−2.42001	−	16.8315i	−0.180880	−	1.25805i	−0.854688	−	0.519142i	$-0.826252\pi$
$179$	−2.42001	−	16.8315i	−0.180880	−	1.25805i	0.673808	−	0.738906i	$-0.264657\pi$
$180$	0.841254	−	0.540641i	0.0627033	−	0.0402970i
$181$	15.4585	+	17.8401i	1.14902	+	1.32604i	0.937223	+	0.348730i	$0.113387\pi$
$181$	15.4585	+	17.8401i	1.14902	+	1.32604i	0.211800	+	0.977313i	$0.432068\pi$
$182$	16.2755	−	4.77892i	1.20642	−	0.354237i
$183$	0.428923			0.0317069
$184$	−4.63388	−	1.23580i	−0.341614	−	0.0911041i
$185$	−7.10786			−0.522580
$186$	−8.65688	+	2.54189i	−0.634753	+	0.186380i
$187$	−0.149467	−	0.172494i	−0.0109301	−	0.0126140i
$188$	−3.48477	+	2.23952i	−0.254153	+	0.163334i
$189$	−0.576412	−	4.00903i	−0.0419278	−	0.291614i
$190$	1.50337	+	0.966158i	0.109066	+	0.0700925i
$191$	−1.24849	+	2.73381i	−0.0903377	+	0.197812i	−0.949408	−	0.314046i	$-0.898315\pi$
$191$	−1.24849	+	2.73381i	−0.0903377	+	0.197812i	0.859070	+	0.511858i	$0.171043\pi$
$192$	−0.654861	+	0.755750i	−0.0472605	+	0.0545415i
$193$	0.641449	−	4.46138i	0.0461725	−	0.321137i	−0.953625	−	0.300998i	$-0.902680\pi$
$193$	0.641449	−	4.46138i	0.0461725	−	0.321137i	0.999797	−	0.0201387i	$-0.00641077\pi$
$194$	−0.298775	−	0.654226i	−0.0214508	−	0.0469707i
$195$	4.01838	+	1.17990i	0.287762	+	0.0844947i
$196$	−9.02366	−	2.64958i	−0.644547	−	0.189256i
$197$	3.88442	+	8.50570i	0.276754	+	0.606006i	0.996060	−	0.0886874i	$-0.0282672\pi$
$197$	3.88442	+	8.50570i	0.276754	+	0.606006i	−0.719306	+	0.694694i	$0.755540\pi$
$198$	−0.110652	+	0.769598i	−0.00786366	+	0.0546930i
$199$	14.1670	−	16.3496i	1.00427	−	1.15899i	0.0170145	−	0.999855i	$-0.494584\pi$
$199$	14.1670	−	16.3496i	1.00427	−	1.15899i	0.987257	−	0.159136i	$-0.0508707\pi$
$200$	0.415415	−	0.909632i	0.0293743	−	0.0643207i
$201$	3.15365	+	2.02673i	0.222441	+	0.142954i
$202$	−1.53454	−	10.6729i	−0.107970	−	0.750945i
$203$	−9.60566	+	6.17318i	−0.674185	+	0.433273i
$204$	−0.192237	−	0.221854i	−0.0134593	−	0.0155329i
$205$	2.01525	−	0.591730i	0.140751	−	0.0413282i
$206$	0.410358			0.0285910
$207$	−4.56639	+	1.46564i	−0.317386	+	0.101869i
$208$	−4.18803			−0.290387
$209$	−1.33318	+	0.391457i	−0.0922179	+	0.0270776i
$210$	−2.65236	−	3.06098i	−0.183030	−	0.211228i
$211$	−18.8611	+	12.1213i	−1.29845	+	0.834465i	−0.993043	−	0.117756i	$-0.962430\pi$
$211$	−18.8611	+	12.1213i	−1.29845	+	0.834465i	−0.305411	+	0.952221i	$0.598794\pi$
$212$	−0.582173	−	4.04910i	−0.0399838	−	0.278093i
$213$	8.17094	+	5.25115i	0.559864	+	0.359803i
$214$	−4.68648	+	10.2620i	−0.320361	+	0.701494i
$215$	−4.60514	+	5.31462i	−0.314068	+	0.362454i
$216$	−0.142315	+	0.989821i	−0.00968330	+	0.0673488i
$217$	15.1804	+	33.2405i	1.03052	+	2.25652i
$218$	−16.5160	−	4.84953i	−1.11860	−	0.328451i
$219$	−15.0507	−	4.41928i	−1.01703	−	0.298627i
$220$	0.322990	+	0.707250i	0.0217760	+	0.0476828i
$221$	0.174964	−	1.21690i	0.0117694	−	0.0818576i
$222$	4.65466	−	5.37176i	0.312400	−	0.360529i
$223$	−9.56806	+	20.9511i	−0.640725	+	1.40299i	0.258718	+	0.965953i	$0.416700\pi$
$223$	−9.56806	+	20.9511i	−0.640725	+	1.40299i	−0.899443	+	0.437038i	$0.856027\pi$
$224$	3.40730	+	2.18974i	0.227660	+	0.146308i
$225$	−0.142315	−	0.989821i	−0.00948766	−	0.0659881i
$226$	−1.25692	+	0.807772i	−0.0836089	+	0.0537322i
$227$	−3.27545	−	3.78007i	−0.217399	−	0.250892i	0.636566	−	0.771222i	$-0.280354\pi$
$227$	−3.27545	−	3.78007i	−0.217399	−	0.250892i	−0.853965	+	0.520330i	$0.825809\pi$
$228$	−1.71467	+	0.503473i	−0.113557	+	0.0333433i
$229$	1.69592			0.112069			0.0560347	−	0.998429i	$-0.482154\pi$
$229$	1.69592			0.112069			0.0560347	+	0.998429i	$0.482154\pi$
$230$	−3.04910	+	3.70175i	−0.201052	+	0.244086i
$231$	3.14913			0.207197
$232$	2.70495	−	0.794245i	0.177589	−	0.0521447i
$233$	−12.7354	−	14.6974i	−0.834323	−	0.962860i	0.165404	−	0.986226i	$-0.447107\pi$
$233$	−12.7354	−	14.6974i	−0.834323	−	0.962860i	−0.999727	+	0.0233657i	$0.992562\pi$
$234$	−3.52319	+	2.26422i	−0.230318	+	0.148017i
$235$	0.589518	+	4.10019i	0.0384559	+	0.267467i
$236$	−7.61338	−	4.89282i	−0.495589	−	0.318496i
$237$	−1.41045	+	3.08845i	−0.0916185	+	0.200617i
$238$	−0.778612	+	0.898566i	−0.0504699	+	0.0582454i
$239$	−1.48422	+	10.3230i	−0.0960061	+	0.667737i	0.883811	+	0.467843i	$0.154969\pi$
$239$	−1.48422	+	10.3230i	−0.0960061	+	0.667737i	−0.979818	+	0.199894i	$0.935940\pi$
$240$	0.415415	+	0.909632i	0.0268149	+	0.0587165i
$241$	16.8684	+	4.95301i	1.08659	+	0.319051i	0.775512	−	0.631333i	$-0.217492\pi$
$241$	16.8684	+	4.95301i	1.08659	+	0.319051i	0.311078	+	0.950385i	$0.399310\pi$
$242$	9.97438	+	2.92874i	0.641178	+	0.188267i
$243$	0.415415	+	0.909632i	0.0266489	+	0.0583529i
$244$	−0.0610420	+	0.424557i	−0.00390782	+	0.0271795i
$245$	−6.15871	+	7.10753i	−0.393466	+	0.454083i
$246$	−0.872506	+	1.91052i	−0.0556290	+	0.121810i
$247$	−6.29616	−	4.04630i	−0.400615	−	0.257460i
$248$	−1.28401	−	8.93051i	−0.0815349	−	0.567088i
$249$	3.55795	−	2.28656i	0.225476	−	0.144905i
$250$	−0.654861	−	0.755750i	−0.0414170	−	0.0477978i
$251$	28.8648	−	8.47548i	1.82193	−	0.534967i	0.822503	−	0.568761i	$-0.192577\pi$
$251$	28.8648	−	8.47548i	1.82193	−	0.534967i	0.999429	+	0.0337932i	$0.0107588\pi$
$252$	4.05026			0.255142
$253$	−0.622680	−	3.67646i	−0.0391476	−	0.231137i
$254$	2.12331			0.133228
$255$	−0.281664	+	0.0827039i	−0.0176385	+	0.00517912i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	18.4803	−	11.8765i	1.15277	−	0.740838i	0.182579	−	0.983191i	$-0.441556\pi$
$257$	18.4803	−	11.8765i	1.15277	−	0.740838i	0.970188	+	0.242353i	$0.0779193\pi$
$258$	−1.00079	−	6.96067i	−0.0623066	−	0.433352i
$259$	−24.2186	−	15.5643i	−1.50487	−	0.967121i
$260$	−1.73977	+	3.80956i	−0.107896	+	0.236259i
$261$	1.84615	−	2.13057i	0.114274	−	0.131879i
$262$	0.198050	−	1.37747i	0.0122356	−	0.0851002i
$263$	−8.84525	−	19.3684i	−0.545421	−	1.19431i	−0.958887	−	0.283787i	$-0.908409\pi$
$263$	−8.84525	−	19.3684i	−0.545421	−	1.19431i	0.413466	−	0.910519i	$-0.364318\pi$
$264$	−0.746018	−	0.219051i	−0.0459142	−	0.0134816i
$265$	−3.92503	−	1.15249i	−0.241113	−	0.0707971i
$266$	3.00680	+	6.58397i	0.184359	+	0.403689i
$267$	−1.03458	+	7.19570i	−0.0633156	+	0.440369i
$268$	−2.45491	+	2.83311i	−0.149957	+	0.173060i
$269$	11.1174	−	24.3438i	0.677841	−	1.48427i	−0.187073	−	0.982346i	$-0.559900\pi$
$269$	11.1174	−	24.3438i	0.677841	−	1.48427i	0.864914	−	0.501920i	$-0.167373\pi$
$270$	0.841254	+	0.540641i	0.0511971	+	0.0329024i
$271$	−2.02076	−	14.0547i	−0.122753	−	0.853762i	−0.954415	−	0.298482i	$-0.903520\pi$
$271$	−2.02076	−	14.0547i	−0.122753	−	0.853762i	0.831663	−	0.555281i	$-0.187389\pi$
$272$	0.246954	−	0.158708i	0.0149738	−	0.00962306i
$273$	11.1081	+	12.8195i	0.672295	+	0.775870i
$274$	7.68716	−	2.25715i	0.464398	−	0.136360i
$275$	0.777512			0.0468858
$276$	−0.800862	−	4.72849i	−0.0482062	−	0.284622i
$277$	16.9832			1.02042			0.510211	−	0.860049i	$-0.329567\pi$
$277$	16.9832			1.02042			0.510211	+	0.860049i	$0.329567\pi$
$278$	−21.6551	+	6.35850i	−1.29878	+	0.381358i
$279$	−5.90838	−	6.81863i	−0.353725	−	0.408221i
$280$	3.40730	−	2.18974i	0.203625	−	0.130862i
$281$	−2.58120	−	17.9526i	−0.153981	−	1.07096i	−0.909460	−	0.415791i	$-0.863505\pi$
$281$	−2.58120	−	17.9526i	−0.153981	−	1.07096i	0.755479	−	0.655173i	$-0.227404\pi$
$282$	−3.48477	−	2.23952i	−0.207515	−	0.133362i
$283$	0.781211	−	1.71061i	0.0464382	−	0.101685i	−0.884991	−	0.465608i	$-0.845836\pi$
$283$	0.781211	−	1.71061i	0.0464382	−	0.101685i	0.931429	+	0.363923i	$0.118563\pi$
$284$	−6.36054	+	7.34046i	−0.377429	+	0.435576i
$285$	−0.254325	+	1.76887i	−0.0150649	+	0.104779i
$286$	−1.35269	−	2.96198i	−0.0799864	−	0.175146i
$287$	8.16227	+	2.39666i	0.481804	+	0.141470i
$288$	−0.959493	−	0.281733i	−0.0565387	−	0.0166013i
$289$	−7.02626	−	15.3854i	−0.413309	−	0.905021i
$290$	0.401206	−	2.79045i	0.0235596	−	0.163861i
$291$	0.470989	−	0.543550i	0.0276099	−	0.0318635i
$292$	6.51623	−	14.2686i	0.381334	−	0.835005i
$293$	−23.5717	−	15.1486i	−1.37707	−	0.884992i	−0.377909	−	0.925843i	$-0.623357\pi$
$293$	−23.5717	−	15.1486i	−1.37707	−	0.884992i	−0.999165	+	0.0408512i	$0.986993\pi$
$294$	−1.33842	−	9.30888i	−0.0780580	−	0.542905i
$295$	−7.61338	+	4.89282i	−0.443268	+	0.284871i
$296$	4.65466	+	5.37176i	0.270547	+	0.312227i
$297$	−0.746018	+	0.219051i	−0.0432883	+	0.0127106i
$298$	−13.3853			−0.775390
$299$	12.7697	−	15.5030i	0.738492	−	0.896564i
$300$	1.00000			0.0577350
$301$	−27.3287	+	8.02443i	−1.57520	+	0.462520i
$302$	−5.97085	−	6.89073i	−0.343584	−	0.396517i
$303$	9.07098	−	5.82956i	0.521114	−	0.334900i
$304$	−0.254325	−	1.76887i	−0.0145866	−	0.101452i
$305$	0.360833	+	0.231893i	0.0206612	+	0.0132782i
$306$	0.121947	−	0.267027i	0.00697125	−	0.0152649i
$307$	−8.52960	+	9.84369i	−0.486810	+	0.561809i	−0.945010	−	0.327040i	$-0.893949\pi$
$307$	−8.52960	+	9.84369i	−0.486810	+	0.561809i	0.458200	+	0.888849i	$0.348494\pi$
$308$	−0.448168	+	3.11707i	−0.0255367	+	0.177612i
$309$	0.170469	+	0.373275i	0.00969763	+	0.0212349i
$310$	−8.65688	−	2.54189i	−0.491678	−	0.144370i
$311$	28.6369	+	8.40856i	1.62385	+	0.476806i	0.962050	−	0.272873i	$-0.0879739\pi$
$311$	28.6369	+	8.40856i	1.62385	+	0.476806i	0.661802	+	0.749679i	$0.269792\pi$
$312$	−1.73977	−	3.80956i	−0.0984951	−	0.215674i
$313$	−0.571095	+	3.97205i	−0.0322802	+	0.224514i	−0.999575	−	0.0291397i	$-0.990723\pi$
$313$	−0.571095	+	3.97205i	−0.0322802	+	0.224514i	0.967295	+	0.253654i	$0.0816323\pi$
$314$	−10.0655	+	11.6162i	−0.568029	+	0.655540i
$315$	1.68254	−	3.68425i	0.0948003	−	0.207584i
$316$	−2.85629	−	1.83562i	−0.160679	−	0.103262i
$317$	−4.05714	−	28.2180i	−0.227871	−	1.58488i	−0.707050	−	0.707164i	$-0.749974\pi$
$317$	−4.05714	−	28.2180i	−0.227871	−	1.58488i	0.479179	−	0.877717i	$-0.340935\pi$
$318$	3.44135	−	2.21162i	0.192981	−	0.124021i
$319$	1.43540	+	1.65654i	0.0803671	+	0.0927486i
$320$	−0.959493	+	0.281733i	−0.0536373	+	0.0157493i
$321$	−11.2814			−0.629669
$322$	−18.4951	+	5.93624i	−1.03069	+	0.330814i
$323$	0.524600			0.0291895
$324$	−0.959493	+	0.281733i	−0.0533052	+	0.0156518i
$325$	2.74258	+	3.16510i	0.152131	+	0.175568i
$326$	9.17469	−	5.89622i	0.508139	−	0.326561i
$327$	−2.44970	−	17.0380i	−0.135469	−	0.942205i
$328$	−1.76691	−	1.13552i	−0.0975610	−	0.0626987i
$329$	−6.96967	+	15.2614i	−0.384250	+	0.841391i
$330$	−0.509162	+	0.587605i	−0.0280285	+	0.0323466i
$331$	1.08707	−	7.56074i	0.0597508	−	0.415576i	−0.937890	−	0.346932i	$-0.887224\pi$
$331$	1.08707	−	7.56074i	0.0597508	−	0.415576i	0.997641	−	0.0686443i	$-0.0218673\pi$
$332$	1.75693	+	3.84715i	0.0964243	+	0.211140i
$333$	6.81994	+	2.00252i	0.373730	+	0.109737i
$334$	−1.76145	−	0.517207i	−0.0963820	−	0.0283003i
$335$	1.55729	+	3.40998i	0.0850836	+	0.186307i
$336$	−0.576412	+	4.00903i	−0.0314459	+	0.218711i
$337$	−1.41217	+	1.62973i	−0.0769259	+	0.0887773i	−0.792908	−	0.609342i	$-0.791434\pi$
$337$	−1.41217	+	1.62973i	−0.0769259	+	0.0887773i	0.715982	+	0.698119i	$0.245979\pi$
$338$	1.88581	−	4.12935i	0.102574	−	0.224607i
$339$	−1.25692	−	0.807772i	−0.0682664	−	0.0438721i
$340$	−0.0417772	−	0.290567i	−0.00226569	−	0.0157582i
$341$	5.90138	−	3.79259i	0.319578	−	0.205380i
$342$	−1.17028	−	1.35057i	−0.0632813	−	0.0730305i
$343$	−9.34479	+	2.74388i	−0.504571	+	0.148155i
$344$	7.03225			0.379153
$345$	−4.63388	−	1.23580i	−0.249480	−	0.0665330i
$346$	−11.6334			−0.625418
$347$	−5.53220	+	1.62440i	−0.296984	+	0.0872024i	−0.426830	−	0.904332i	$-0.640370\pi$
$347$	−5.53220	+	1.62440i	−0.296984	+	0.0872024i	0.129846	+	0.991534i	$0.458552\pi$
$348$	1.84615	+	2.13057i	0.0989639	+	0.114210i
$349$	16.0806	−	10.3344i	0.860777	−	0.553188i	−0.0341416	−	0.999417i	$-0.510870\pi$
$349$	16.0806	−	10.3344i	0.860777	−	0.553188i	0.894919	+	0.446229i	$0.147233\pi$
$350$	−0.576412	−	4.00903i	−0.0308105	−	0.214292i
$351$	−3.52319	−	2.26422i	−0.188054	−	0.120855i
$352$	0.322990	−	0.707250i	0.0172154	−	0.0376966i
$353$	10.5755	−	12.2048i	0.562877	−	0.649594i	−0.400958	−	0.916097i	$-0.631323\pi$
$353$	10.5755	−	12.2048i	0.562877	−	0.649594i	0.963834	+	0.266502i	$0.0858680\pi$
$354$	1.28796	−	8.95793i	0.0684541	−	0.476108i
$355$	4.03485	+	8.83509i	0.214148	+	0.468918i
$356$	−6.97522	−	2.04811i	−0.369686	−	0.108550i
$357$	−1.14081	−	0.334972i	−0.0603781	−	0.0177286i
$358$	7.06397	+	15.4679i	0.373343	+	0.817506i
$359$	−1.31708	+	9.16049i	−0.0695128	+	0.483472i	0.925093	+	0.379742i	$0.123987\pi$
$359$	−1.31708	+	9.16049i	−0.0695128	+	0.483472i	−0.994605	+	0.103731i	$0.966922\pi$
$360$	−0.654861	+	0.755750i	−0.0345142	+	0.0398315i
$361$	−6.56622	+	14.3780i	−0.345591	+	0.756738i
$362$	−19.8585	−	12.7623i	−1.04374	−	0.670770i
$363$	1.47943	+	10.2897i	0.0776500	+	0.540067i
$364$	−14.2699	+	9.17068i	−0.747943	+	0.480674i
$365$	−10.2722	−	11.8548i	−0.537672	−	0.620506i
$366$	−0.411548	+	0.120841i	−0.0215120	+	0.00631648i
$367$	−34.2323			−1.78691			−0.893455	−	0.449153i	$-0.851726\pi$
$367$	−34.2323			−1.78691			−0.893455	+	0.449153i	$0.851726\pi$
$368$	4.79434	−	0.119776i	0.249922	−	0.00624377i
$369$	−2.10032			−0.109339
$370$	6.81994	−	2.00252i	0.354552	−	0.104106i
$371$	−10.8501	−	12.5217i	−0.563309	−	0.650093i
$372$	7.59008	−	4.87785i	0.393527	−	0.252905i
$373$	−3.30591	−	22.9931i	−0.171173	−	1.19054i	−0.876410	−	0.481565i	$-0.840069\pi$
$373$	−3.30591	−	22.9931i	−0.171173	−	1.19054i	0.705237	−	0.708972i	$-0.250841\pi$
$374$	0.192010	+	0.123397i	0.00992858	+	0.00638071i
$375$	0.415415	−	0.909632i	0.0214519	−	0.0469732i
$376$	2.71266	−	3.13058i	0.139895	−	0.161447i
$377$	−1.68026	+	11.6865i	−0.0865379	+	0.601885i
$378$	1.68254	+	3.68425i	0.0865405	+	0.189497i
$379$	30.8601	+	9.06133i	1.58518	+	0.465449i	0.951372	−	0.308045i	$-0.0996747\pi$
$379$	30.8601	+	9.06133i	1.58518	+	0.465449i	0.633803	+	0.773494i	$0.281493\pi$
$380$	−1.71467	−	0.503473i	−0.0879609	−	0.0258276i
$381$	0.882054	+	1.93143i	0.0451890	+	0.0989501i
$382$	0.427714	−	2.97482i	0.0218838	−	0.152205i
$383$	−19.8013	+	22.8520i	−1.01180	+	1.16768i	−0.0260178	+	0.999661i	$0.508283\pi$
$383$	−19.8013	+	22.8520i	−1.01180	+	1.16768i	−0.985784	+	0.168020i	$0.946263\pi$
$384$	0.415415	−	0.909632i	0.0211991	−	0.0464195i
$385$	2.64921	+	1.70255i	0.135016	+	0.0867698i
$386$	0.641449	+	4.46138i	0.0326489	+	0.227078i
$387$	5.91590	−	3.80192i	0.300722	−	0.193262i
$388$	0.470989	+	0.543550i	0.0239109	+	0.0275946i
$389$	−15.5167	+	4.55612i	−0.786728	+	0.231004i	−0.650332	−	0.759650i	$-0.725370\pi$
$389$	−15.5167	+	4.55612i	−0.786728	+	0.231004i	−0.136396	+	0.990654i	$0.543552\pi$
$390$	−4.18803			−0.212069
$391$	−0.165491	+	1.39808i	−0.00836923	+	0.0707039i
$392$	9.40461			0.475005
$393$	1.33526	−	0.392068i	0.0673550	−	0.0197772i
$394$	−6.12341	−	7.06679i	−0.308493	−	0.356020i
$395$	−2.85629	+	1.83562i	−0.143715	+	0.0923603i
$396$	−0.110652	−	0.769598i	−0.00556045	−	0.0386738i
$397$	19.0274	+	12.2282i	0.954957	+	0.613713i	0.922598	−	0.385763i	$-0.126062\pi$
$397$	19.0274	+	12.2282i	0.954957	+	0.613713i	0.0323586	+	0.999476i	$0.489698\pi$
$398$	−8.98692	+	19.6786i	−0.450474	+	0.986399i
$399$	−4.73992	+	5.47016i	−0.237293	+	0.273851i
$400$	−0.142315	+	0.989821i	−0.00711574	+	0.0494911i
$401$	−11.5664	−	25.3269i	−0.577598	−	1.26476i	−0.942652	−	0.333777i	$-0.891677\pi$
$401$	−11.5664	−	25.3269i	−0.577598	−	1.26476i	0.365054	−	0.930986i	$-0.381051\pi$
$402$	−3.59690	−	1.05614i	−0.179397	−	0.0526757i
$403$	36.2552	+	10.6455i	1.80600	+	0.530290i
$404$	4.47929	+	9.80828i	0.222853	+	0.487980i
$405$	−0.142315	+	0.989821i	−0.00707168	+	0.0491846i
$406$	7.47738	−	8.62936i	0.371096	−	0.428268i
$407$	−2.29577	+	5.02703i	−0.113797	+	0.249181i
$408$	0.246954	+	0.158708i	0.0122260	+	0.00785720i
$409$	1.31801	+	9.16699i	0.0651716	+	0.453278i	0.996111	+	0.0881051i	$0.0280811\pi$
$409$	1.31801	+	9.16699i	0.0651716	+	0.453278i	−0.930940	+	0.365173i	$0.881010\pi$
$410$	−1.76691	+	1.13552i	−0.0872612	+	0.0560794i
$411$	5.24654	+	6.05483i	0.258793	+	0.298663i
$412$	−0.393736	+	0.115611i	−0.0193980	+	0.00569575i
$413$	−36.6550			−1.80368
$414$	3.96850	−	2.69278i	0.195041	−	0.132343i
$415$	4.22935			0.207611
$416$	4.01838	−	1.17990i	0.197017	−	0.0578495i
$417$	−14.7797	−	17.0567i	−0.723767	−	0.835271i
$418$	1.16889	−	0.751200i	0.0571723	−	0.0367424i
$419$	−0.395685	−	2.75205i	−0.0193305	−	0.134446i	0.977871	−	0.209209i	$-0.0670891\pi$
$419$	−0.395685	−	2.75205i	−0.0193305	−	0.134446i	−0.997201	+	0.0747630i	$0.976180\pi$
$420$	3.40730	+	2.18974i	0.166259	+	0.106848i
$421$	−2.68536	+	5.88011i	−0.130876	+	0.286579i	−0.963713	−	0.266939i	$-0.913988\pi$
$421$	−2.68536	+	5.88011i	−0.130876	+	0.286579i	0.832837	+	0.553518i	$0.186715\pi$
$422$	14.6821	−	16.9441i	0.714716	−	0.824826i
$423$	0.589518	−	4.10019i	0.0286633	−	0.199358i
$424$	1.69935	+	3.72107i	0.0825279	+	0.180711i
$425$	−0.281664	−	0.0827039i	−0.0136627	−	0.00401173i
$426$	−9.31938	−	2.73642i	−0.451526	−	0.132580i
$427$	0.721679	+	1.58026i	0.0349245	+	0.0764740i
$428$	1.60552	−	11.1666i	0.0776056	−	0.539759i
$429$	2.13239	−	2.46090i	0.102953	−	0.118814i
$430$	2.92130	−	6.39676i	0.140878	−	0.308479i
$431$	16.3674	+	10.5187i	0.788388	+	0.506666i	0.871808	−	0.489848i	$-0.162948\pi$
$431$	16.3674	+	10.5187i	0.788388	+	0.506666i	−0.0834197	+	0.996515i	$0.526584\pi$
$432$	−0.142315	−	0.989821i	−0.00684713	−	0.0476228i
$433$	20.7724	−	13.3496i	0.998256	−	0.641540i	0.0639281	−	0.997955i	$-0.479637\pi$
$433$	20.7724	−	13.3496i	0.998256	−	0.641540i	0.934328	+	0.356414i	$0.116001\pi$
$434$	−23.9305	−	27.6172i	−1.14870	−	1.32567i
$435$	2.70495	−	0.794245i	0.129692	−	0.0380811i
$436$	17.2132			0.824364
$437$	7.32339	+	4.45202i	0.350325	+	0.212969i
$438$	15.6861			0.749510
$439$	−11.4425	+	3.35983i	−0.546122	+	0.160356i	−0.543144	−	0.839640i	$-0.682766\pi$
$439$	−11.4425	+	3.35983i	−0.546122	+	0.160356i	−0.00297839	+	0.999996i	$0.500948\pi$
$440$	−0.509162	−	0.587605i	−0.0242734	−	0.0280129i
$441$	7.91166	−	5.08452i	0.376746	−	0.242120i
$442$	0.174964	+	1.21690i	0.00832219	+	0.0578821i
$443$	−18.0120	−	11.5756i	−0.855775	−	0.549973i	0.0375959	−	0.999293i	$-0.488030\pi$
$443$	−18.0120	−	11.5756i	−0.855775	−	0.549973i	−0.893371	+	0.449320i	$0.851666\pi$
$444$	−2.95271	+	6.46554i	−0.140129	+	0.306841i
$445$	−4.76064	+	5.49407i	−0.225676	+	0.260444i
$446$	3.27787	−	22.7981i	0.155212	−	1.07952i
$447$	−5.56046	−	12.1757i	−0.263001	−	0.575891i
$448$	−3.88620	−	1.14109i	−0.183606	−	0.0539114i
$449$	35.9807	+	10.5649i	1.69804	+	0.498588i	0.980265	−	0.197690i	$-0.0633440\pi$
$449$	35.9807	+	10.5649i	1.69804	+	0.498588i	0.717772	+	0.696279i	$0.245162\pi$
$450$	0.415415	+	0.909632i	0.0195829	+	0.0428805i
$451$	0.232404	−	1.61641i	0.0109435	−	0.0761136i
$452$	0.978428	−	1.12917i	0.0460214	−	0.0531115i
$453$	3.78765	−	8.29379i	0.177959	−	0.389676i
$454$	4.20774	+	2.70415i	0.197479	+	0.126912i
$455$	2.41403	+	16.7899i	0.113171	+	0.787125i
$456$	1.50337	−	0.966158i	0.0704018	−	0.0452445i
$457$	7.68966	+	8.87434i	0.359707	+	0.415124i	0.906542	−	0.422117i	$-0.138713\pi$
$457$	7.68966	+	8.87434i	0.359707	+	0.415124i	−0.546834	+	0.837241i	$0.684167\pi$
$458$	−1.62722	+	0.477795i	−0.0760350	+	0.0223259i
$459$	0.293555			0.0137020
$460$	1.88269	−	4.41084i	0.0877807	−	0.205656i
$461$	−25.2443			−1.17575			−0.587873	−	0.808953i	$-0.700034\pi$
$461$	−25.2443			−1.17575			−0.587873	+	0.808953i	$0.700034\pi$
$462$	−3.02157	+	0.887212i	−0.140576	+	0.0412768i
$463$	19.2732	+	22.2425i	0.895704	+	1.03370i	0.999236	+	0.0390712i	$0.0124399\pi$
$463$	19.2732	+	22.2425i	0.895704	+	1.03370i	−0.103533	+	0.994626i	$0.533015\pi$
$464$	−2.37162	+	1.52415i	−0.110100	+	0.0707567i
$465$	−1.28401	−	8.93051i	−0.0595447	−	0.414143i
$466$	16.3603	+	10.5141i	0.757874	+	0.487056i
$467$	−3.93063	+	8.60687i	−0.181888	+	0.398279i	−0.978510	−	0.206199i	$-0.933891\pi$
$467$	−3.93063	+	8.60687i	−0.181888	+	0.398279i	0.796622	+	0.604477i	$0.206618\pi$
$468$	2.74258	−	3.16510i	0.126776	−	0.146307i
$469$	−2.16082	+	15.0289i	−0.0997776	+	0.693968i
$470$	−1.72079	−	3.76802i	−0.0793743	−	0.173806i
$471$	−14.7478	−	4.33035i	−0.679544	−	0.199532i
$472$	8.68345	+	2.54969i	0.399688	+	0.117359i
$473$	2.27135	+	4.97356i	0.104437	+	0.228684i
$474$	0.483198	−	3.36072i	0.0221940	−	0.154363i
$475$	−1.17028	+	1.35057i	−0.0536960	+	0.0619684i
$476$	0.493917	−	1.08153i	0.0226387	−	0.0495717i
$477$	3.44135	+	2.21162i	0.157568	+	0.101263i
$478$	−1.48422	−	10.3230i	−0.0678866	−	0.472162i
$479$	−28.9976	+	18.6356i	−1.32493	+	0.851484i	−0.995688	−	0.0927604i	$-0.970431\pi$
$479$	−28.9976	+	18.6356i	−1.32493	+	0.851484i	−0.329246	+	0.944244i	$0.606795\pi$
$480$	−0.654861	−	0.755750i	−0.0298902	−	0.0344951i
$481$	−28.5621	+	8.38659i	−1.30232	+	0.382396i
$482$	−17.5805			−0.800772
$483$	−13.0829	−	14.3577i	−0.595293	−	0.653297i
$484$	−10.3955			−0.472522
$485$	0.690087	−	0.202628i	0.0313352	−	0.00920085i
$486$	−0.654861	−	0.755750i	−0.0297051	−	0.0342815i
$487$	−22.2993	+	14.3309i	−1.01048	+	0.649393i	−0.937516	−	0.347942i	$-0.886881\pi$
$487$	−22.2993	+	14.3309i	−1.01048	+	0.649393i	−0.0729595	+	0.997335i	$0.523244\pi$
$488$	−0.0610420	−	0.424557i	−0.00276324	−	0.0192188i
$489$	9.17469	+	5.89622i	0.414894	+	0.266636i
$490$	3.90682	−	8.55473i	0.176492	−	0.386463i
$491$	26.4467	−	30.5211i	1.19352	−	1.37740i	0.285552	−	0.958363i	$-0.407823\pi$
$491$	26.4467	−	30.5211i	1.19352	−	1.37740i	0.907970	−	0.419035i	$-0.137632\pi$
$492$	0.298907	−	2.07895i	0.0134758	−	0.0937261i
$493$	−0.343786	−	0.752787i	−0.0154834	−	0.0339038i
$494$	7.18110	+	2.10856i	0.323093	+	0.0948686i
$495$	−0.746018	−	0.219051i	−0.0335310	−	0.00984559i
$496$	3.74802	+	8.20701i	0.168291	+	0.368506i
$497$	−5.59859	+	38.9390i	−0.251131	+	1.74665i
$498$	−2.76963	+	3.19633i	−0.124110	+	0.143231i
$499$	9.54541	−	20.9015i	0.427311	−	0.935681i	−0.566444	−	0.824100i	$-0.691681\pi$
$499$	9.54541	−	20.9015i	0.427311	−	0.935681i	0.993755	−	0.111581i	$-0.0355913\pi$
$500$	0.841254	+	0.540641i	0.0376220	+	0.0241782i
$501$	−0.261263	−	1.81712i	−0.0116724	−	0.0811831i
$502$	−25.3078	+	16.2643i	−1.12954	+	0.725912i
$503$	18.8691	+	21.7761i	0.841330	+	0.970947i	0.999865	−	0.0164067i	$-0.00522264\pi$
$503$	18.8691	+	21.7761i	0.841330	+	0.970947i	−0.158535	+	0.987353i	$0.550677\pi$
$504$	−3.88620	+	1.14109i	−0.173105	+	0.0508282i
$505$	10.7827			0.479823
$506$	1.63324	+	3.35211i	0.0726062	+	0.149019i
$507$	4.53958			0.201610
$508$	−2.03730	+	0.598205i	−0.0903906	+	0.0265411i
$509$	−22.3329	−	25.7736i	−0.989890	−	1.14239i	−0.989810	−	0.142393i	$-0.954520\pi$
$509$	−22.3329	−	25.7736i	−0.989890	−	1.14239i	−7.94231e−5	−	1.00000i	$-0.500025\pi$
$510$	0.246954	−	0.158708i	0.0109353	−	0.00702769i
$511$	−9.04165	−	62.8861i	−0.399979	−	2.78192i
$512$	0.841254	+	0.540641i	0.0371785	+	0.0238932i
$513$	0.742372	−	1.62557i	0.0327765	−	0.0717706i
$514$	−14.3857	+	16.6019i	−0.634525	+	0.732280i
$515$	−0.0584000	+	0.406181i	−0.00257341	+	0.0178985i
$516$	2.92130	+	6.39676i	0.128603	+	0.281601i
$517$	3.09027	+	0.907384i	0.135910	+	0.0399067i
$518$	27.6225	+	8.11071i	1.21366	+	0.356364i
$519$	−4.83271	−	10.5822i	−0.212132	−	0.464505i
$520$	0.596019	−	4.14540i	0.0261371	−	0.181788i
$521$	18.4772	−	21.3239i	0.809502	−	0.934215i	−0.189360	−	0.981908i	$-0.560641\pi$
$521$	18.4772	−	21.3239i	0.809502	−	0.934215i	0.998862	+	0.0476927i	$0.0151868\pi$
$522$	−1.17112	+	2.56438i	−0.0512583	+	0.112240i
$523$	27.9055	+	17.9338i	1.22022	+	0.784190i	0.982340	−	0.187103i	$-0.0599099\pi$
$523$	27.9055	+	17.9338i	1.22022	+	0.784190i	0.237884	+	0.971294i	$0.423546\pi$
$524$	0.198050	+	1.37747i	0.00865185	+	0.0601750i
$525$	3.40730	−	2.18974i	0.148707	−	0.0955679i
$526$	13.9437	+	16.0918i	0.607972	+	0.701638i
$527$	−2.54127	+	0.746183i	−0.110699	+	0.0325043i
$528$	0.777512			0.0338369
$529$	−14.1750	+	18.1127i	−0.616306	+	0.787507i
$530$	4.09074			0.177690
$531$	8.68345	−	2.54969i	0.376830	−	0.110647i
$532$	−4.73992	−	5.47016i	−0.205502	−	0.237162i
$533$	7.39985	−	4.75559i	0.320523	−	0.205988i
$534$	−1.03458	−	7.19570i	−0.0447709	−	0.311388i
$535$	−9.49056	−	6.09921i	−0.410313	−	0.263692i
$536$	1.55729	−	3.40998i	0.0672645	−	0.147289i
$537$	−11.1357	+	12.8512i	−0.480539	+	0.554571i
$538$	−3.80866	+	26.4898i	−0.164203	+	1.14206i
$539$	3.03760	+	6.65141i	0.130839	+	0.286497i
$540$	−0.959493	−	0.281733i	−0.0412900	−	0.0121238i
$541$	6.31082	+	1.85302i	0.271323	+	0.0796677i	0.414564	−	0.910020i	$-0.363934\pi$
$541$	6.31082	+	1.85302i	0.271323	+	0.0796677i	−0.143241	+	0.989688i	$0.545752\pi$
$542$	5.89857	+	12.9161i	0.253365	+	0.554793i
$543$	3.35946	−	23.3655i	0.144168	−	1.00271i
$544$	−0.192237	+	0.221854i	−0.00824211	+	0.00951190i
$545$	7.15063	−	15.6577i	0.306300	−	0.670702i
$546$	−14.2699	−	9.17068i	−0.610693	−	0.392469i
$547$	−2.50549	−	17.4260i	−0.107127	−	0.745084i	−0.970602	−	0.240692i	$-0.922626\pi$
$547$	−2.50549	−	17.4260i	−0.107127	−	0.745084i	0.863475	−	0.504392i	$-0.168283\pi$
$548$	−6.73986	+	4.33145i	−0.287913	+	0.185030i
$549$	−0.280885	−	0.324158i	−0.0119879	−	0.0138347i
$550$	−0.746018	+	0.219051i	−0.0318103	+	0.00934035i
$551$	−5.03799			−0.214625
$552$	2.10059	+	4.31132i	0.0894071	+	0.183502i
$553$	−13.7518			−0.584784
$554$	−16.2953	+	4.78472i	−0.692320	+	0.203283i
$555$	4.65466	+	5.37176i	0.197579	+	0.228019i
$556$	18.9865	−	12.2019i	0.805206	−	0.517475i
$557$	−0.00888742	−	0.0618133i	−0.000376572	−	0.00261912i	0.989632	−	0.143624i	$-0.0458757\pi$
$557$	−0.00888742	−	0.0618133i	−0.000376572	−	0.00261912i	−0.990009	+	0.141005i	$0.954967\pi$
$558$	7.59008	+	4.87785i	0.321314	+	0.206496i
$559$	−12.2345	+	26.7898i	−0.517464	+	1.13309i
$560$	−2.65236	+	3.06098i	−0.112083	+	0.129350i
$561$	−0.0324823	+	0.225919i	−0.00137140	+	0.00953832i
$562$	7.53448	+	16.4982i	0.317823	+	0.695935i
$563$	−13.9264	−	4.08916i	−0.586927	−	0.172337i	−0.0252321	−	0.999682i	$-0.508032\pi$
$563$	−13.9264	−	4.08916i	−0.586927	−	0.172337i	−0.561695	+	0.827344i	$0.689851\pi$
$564$	3.97456	+	1.16704i	0.167359	+	0.0491410i
$565$	−0.620672	−	1.35908i	−0.0261119	−	0.0571770i
$566$	−0.267631	+	1.86142i	−0.0112494	+	0.0782411i
$567$	−2.65236	+	3.06098i	−0.111389	+	0.128549i
$568$	4.03485	−	8.83509i	0.169299	−	0.370712i
$569$	18.0938	+	11.6282i	0.758530	+	0.487478i	0.861845	−	0.507171i	$-0.169309\pi$
$569$	18.0938	+	11.6282i	0.758530	+	0.487478i	−0.103315	+	0.994649i	$0.532945\pi$
$570$	−0.254325	−	1.76887i	−0.0106525	−	0.0740899i
$571$	−36.1179	+	23.2116i	−1.51149	+	0.971375i	−0.518257	+	0.855225i	$0.673419\pi$
$571$	−36.1179	+	23.2116i	−1.51149	+	0.971375i	−0.993232	+	0.116150i	$0.962945\pi$
$572$	2.13239	+	2.46090i	0.0891595	+	0.102896i
$573$	2.88367	−	0.846721i	0.120467	−	0.0353723i
$574$	−8.50686			−0.355070
$575$	−3.23014	−	3.54488i	−0.134706	−	0.147832i
$576$	1.00000			0.0416667
$577$	22.4720	−	6.59836i	0.935520	−	0.274693i	0.221774	−	0.975098i	$-0.428815\pi$
$577$	22.4720	−	6.59836i	0.935520	−	0.274693i	0.713746	+	0.700405i	$0.246997\pi$
$578$	11.0762	+	12.7826i	0.460709	+	0.531687i
$579$	−3.79174	+	2.43681i	−0.157580	+	0.101270i
$580$	0.401206	+	2.79045i	0.0166592	+	0.115867i
$581$	14.4106	+	9.26116i	0.597854	+	0.384217i
$582$	−0.298775	+	0.654226i	−0.0123846	+	0.0271185i
$583$	−2.08285	+	2.40374i	−0.0862628	+	0.0995526i
$584$	−2.23236	+	15.5264i	−0.0923758	+	0.642488i
$585$	−1.73977	−	3.80956i	−0.0719306	−	0.157506i
$586$	26.8847	+	7.89407i	1.11060	+	0.326101i
$587$	19.9340	+	5.85315i	0.822765	+	0.241585i	0.665906	−	0.746036i	$-0.268045\pi$
$587$	19.9340	+	5.85315i	0.822765	+	0.241585i	0.156859	+	0.987621i	$0.449863\pi$
$588$	3.90682	+	8.55473i	0.161114	+	0.352791i
$589$	−2.29461	+	15.9594i	−0.0945478	+	0.657594i
$590$	5.92652	−	6.83957i	0.243991	−	0.281580i
$591$	3.88442	−	8.50570i	0.159784	−	0.349878i
$592$	−5.97951	−	3.84280i	−0.245756	−	0.157938i
$593$	4.61579	+	32.1035i	0.189548	+	1.31833i	0.833182	+	0.553000i	$0.186517\pi$
$593$	4.61579	+	32.1035i	0.189548	+	1.31833i	−0.643634	+	0.765334i	$0.722574\pi$
$594$	0.654085	−	0.420355i	0.0268374	−	0.0172474i
$595$	−0.778612	−	0.898566i	−0.0319200	−	0.0368376i
$596$	12.8431	−	3.77108i	0.526074	−	0.154469i
$597$	−21.6336			−0.885404
$598$	−7.88474	+	18.4727i	−0.322431	+	0.755405i
$599$	8.60216			0.351475			0.175737	−	0.984437i	$-0.443769\pi$
$599$	8.60216			0.351475			0.175737	+	0.984437i	$0.443769\pi$
$600$	−0.959493	+	0.281733i	−0.0391711	+	0.0115017i
$601$	2.22864	+	2.57198i	0.0909079	+	0.104913i	0.799381	−	0.600825i	$-0.205161\pi$
$601$	2.22864	+	2.57198i	0.0909079	+	0.104913i	−0.708473	+	0.705738i	$0.750616\pi$
$602$	23.9609	−	15.3988i	0.976575	−	0.627607i
$603$	−0.533502	−	3.71059i	−0.0217259	−	0.151107i
$604$	7.67034	+	4.92943i	0.312102	+	0.200575i
$605$	−4.31844	+	9.45606i	−0.175569	+	0.384443i
$606$	−7.06116	+	8.14901i	−0.286840	+	0.331031i
$607$	4.31417	−	30.0057i	0.175107	−	1.21790i	−0.692786	−	0.721144i	$-0.743617\pi$
$607$	4.31417	−	30.0057i	0.175107	−	1.21790i	0.867893	−	0.496752i	$-0.165474\pi$
$608$	0.742372	+	1.62557i	0.0301072	+	0.0659255i
$609$	10.9558	+	3.21690i	0.443950	+	0.130355i
$610$	−0.411548	−	0.120841i	−0.0166631	−	0.00489273i
$611$	7.20674	+	15.7806i	0.291553	+	0.638413i
$612$	−0.0417772	+	0.290567i	−0.00168874	+	0.0117455i
$613$	−18.9354	+	21.8527i	−0.764795	+	0.882620i	−0.995914	−	0.0903050i	$-0.971216\pi$
$613$	−18.9354	+	21.8527i	−0.764795	+	0.882620i	0.231119	+	0.972925i	$0.425761\pi$
$614$	5.41081	−	11.8480i	0.218362	−	0.478147i
$615$	−1.76691	−	1.13552i	−0.0712485	−	0.0457886i
$616$	−0.448168	−	3.11707i	−0.0180572	−	0.125590i
$617$	−3.09089	+	1.98639i	−0.124435	+	0.0799693i	−0.601377	−	0.798965i	$-0.705381\pi$
$617$	−3.09089	+	1.98639i	−0.124435	+	0.0799693i	0.476943	+	0.878934i	$0.341745\pi$
$618$	−0.268727	−	0.310128i	−0.0108098	−	0.0124752i
$619$	32.6007	−	9.57244i	1.31033	−	0.384749i	0.449338	−	0.893362i	$-0.351660\pi$
$619$	32.6007	−	9.57244i	1.31033	−	0.384749i	0.860995	+	0.508613i	$0.169842\pi$
$620$	9.02235			0.362346
$621$	4.09801	+	2.49125i	0.164447	+	0.0999705i
$622$	−29.8459			−1.19671
$623$	−28.2514	+	8.29537i	−1.13187	+	0.332347i
$624$	2.74258	+	3.16510i	0.109791	+	0.126705i
$625$	0.841254	−	0.540641i	0.0336501	−	0.0216256i
$626$	−0.571095	−	3.97205i	−0.0228256	−	0.158755i
$627$	1.16889	+	0.751200i	0.0466810	+	0.0300000i
$628$	6.38511	−	13.9814i	0.254794	−	0.557920i
$629$	1.36640	−	1.57691i	0.0544818	−	0.0628753i
$630$	−0.576412	+	4.00903i	−0.0229648	+	0.159724i
$631$	−0.532139	−	1.16522i	−0.0211841	−	0.0463868i	0.898744	−	0.438473i	$-0.144481\pi$
$631$	−0.532139	−	1.16522i	−0.0211841	−	0.0463868i	−0.919928	+	0.392087i	$0.871753\pi$
$632$	3.25774	+	0.956560i	0.129586	+	0.0380499i
$633$	21.5121	+	6.31652i	0.855028	+	0.251059i
$634$	11.8427	+	25.9319i	0.470335	+	1.02989i
$635$	−0.302178	+	2.10170i	−0.0119916	+	0.0834033i
$636$	−2.67886	+	3.09157i	−0.106224	+	0.122589i
$637$	−16.3619	+	35.8275i	−0.648280	+	1.41954i
$638$	−1.84396	−	1.18504i	−0.0730031	−	0.0469162i
$639$	−1.38228	−	9.61396i	−0.0546821	−	0.380322i
$640$	0.841254	−	0.540641i	0.0332535	−	0.0213707i
$641$	22.4504	+	25.9091i	0.886736	+	1.02335i	0.999558	+	0.0297329i	$0.00946568\pi$
$641$	22.4504	+	25.9091i	0.886736	+	1.02335i	−0.112822	+	0.993615i	$0.535989\pi$
$642$	10.8245	−	3.17835i	0.427208	−	0.125440i
$643$	−7.61631			−0.300358			−0.150179	−	0.988659i	$-0.547985\pi$
$643$	−7.61631			−0.300358			−0.150179	+	0.988659i	$0.547985\pi$
$644$	16.0734	−	10.9064i	0.633382	−	0.429774i
$645$	7.03225			0.276894
$646$	−0.503350	+	0.147797i	−0.0198040	+	0.00581499i
$647$	22.5600	+	26.0356i	0.886926	+	1.02357i	0.999552	+	0.0299294i	$0.00952826\pi$
$647$	22.5600	+	26.0356i	0.886926	+	1.02357i	−0.112626	+	0.993637i	$0.535926\pi$
$648$	0.841254	−	0.540641i	0.0330476	−	0.0212384i
$649$	1.00140	+	6.96490i	0.0393084	+	0.273396i
$650$	−3.52319	−	2.26422i	−0.138191	−	0.0888100i
$651$	15.1804	−	33.2405i	0.594969	−	1.30280i
$652$	−7.14190	+	8.24219i	−0.279698	+	0.322789i
$653$	4.81788	−	33.5091i	0.188538	−	1.31131i	−0.647257	−	0.762272i	$-0.724084\pi$
$653$	4.81788	−	33.5091i	0.188538	−	1.31131i	0.835796	−	0.549041i	$-0.185007\pi$
$654$	7.15063	+	15.6577i	0.279612	+	0.612265i
$655$	1.33526	+	0.392068i	0.0521730	+	0.0153194i
$656$	2.01525	+	0.591730i	0.0786822	+	0.0231032i
$657$	6.51623	+	14.2686i	0.254223	+	0.556670i
$658$	2.38770	−	16.6068i	0.0930823	−	0.647402i
$659$	−16.5623	+	19.1139i	−0.645176	+	0.744573i	−0.980281	−	0.197608i	$-0.936683\pi$
$659$	−16.5623	+	19.1139i	−0.645176	+	0.744573i	0.335105	+	0.942181i	$0.391228\pi$
$660$	0.322990	−	0.707250i	0.0125724	−	0.0275297i
$661$	−23.3071	−	14.9786i	−0.906542	−	0.582599i	0.00218129	−	0.999998i	$-0.499306\pi$
$661$	−23.3071	−	14.9786i	−0.906542	−	0.582599i	−0.908724	+	0.417398i	$0.862942\pi$
$662$	1.08707	+	7.56074i	0.0422502	+	0.293857i
$663$	−1.03425	+	0.664672i	−0.0401669	+	0.0258137i
$664$	−2.76963	−	3.19633i	−0.107483	−	0.124042i
$665$	−6.94487	+	2.03920i	−0.269311	+	0.0790767i
$666$	−7.10786			−0.275424
$667$	1.58929	−	13.4264i	0.0615375	−	0.519873i
$668$	1.83581			0.0710296
$669$	22.0996	−	6.48901i	0.854418	−	0.250880i
$670$	−2.45491	−	2.83311i	−0.0948413	−	0.109453i
$671$	0.280552	−	0.180300i	0.0108306	−	0.00696039i
$672$	−0.576412	−	4.00903i	−0.0222356	−	0.154652i
$673$	−4.79860	−	3.08387i	−0.184972	−	0.118875i	0.444877	−	0.895591i	$-0.353247\pi$
$673$	−4.79860	−	3.08387i	−0.184972	−	0.118875i	−0.629850	+	0.776717i	$0.716884\pi$
$674$	0.895821	−	1.96157i	0.0345057	−	0.0755570i
$675$	−0.654861	+	0.755750i	−0.0252056	+	0.0290888i
$676$	−0.646049	+	4.49337i	−0.0248480	+	0.172822i
$677$	−11.3646	−	24.8849i	−0.436775	−	0.956404i	−0.992179	−	0.124823i	$-0.960164\pi$
$677$	−11.3646	−	24.8849i	−0.436775	−	0.956404i	0.555404	−	0.831581i	$-0.312564\pi$
$678$	1.43358	+	0.420937i	0.0550563	+	0.0161660i
$679$	2.79503	+	0.820695i	0.107263	+	0.0314954i
$680$	0.121947	+	0.267027i	0.00467645	+	0.0102400i
$681$	−0.711823	+	4.95084i	−0.0272771	+	0.189717i
$682$	−4.59384	+	5.30157i	−0.175907	+	0.203008i
$683$	1.99302	−	4.36411i	0.0762610	−	0.166988i	−0.867661	−	0.497155i	$-0.834378\pi$
$683$	1.99302	−	4.36411i	0.0762610	−	0.166988i	0.943922	+	0.330167i	$0.107105\pi$
$684$	1.50337	+	0.966158i	0.0574829	+	0.0369420i
$685$	1.14018	+	7.93014i	0.0435641	+	0.302995i
$686$	8.19322	−	5.26546i	0.312818	−	0.201036i
$687$	−1.11059	−	1.28169i	−0.0423716	−	0.0488995i
$688$	−6.74739	+	1.98121i	−0.257242	+	0.0755330i
$689$	−17.1321			−0.652682
$690$	4.79434	−	0.119776i	0.182517	−	0.00455981i
$691$	32.2061			1.22518			0.612589	−	0.790402i	$-0.290128\pi$
$691$	32.2061			1.22518			0.612589	+	0.790402i	$0.290128\pi$
$692$	11.1622	−	3.27752i	0.424323	−	0.124593i
$693$	−2.06224	−	2.37995i	−0.0783380	−	0.0904069i
$694$	4.85046	−	3.11720i	0.184121	−	0.118327i
$695$	−3.21194	−	22.3396i	−0.121836	−	0.847388i
$696$	−2.37162	−	1.52415i	−0.0898959	−	0.0577726i
$697$	−0.256128	+	0.560843i	−0.00970155	+	0.0212434i
$698$	−12.5177	+	14.4462i	−0.473803	+	0.546798i
$699$	−2.76766	+	19.2495i	−0.104683	+	0.728084i
$700$	1.68254	+	3.68425i	0.0635940	+	0.139251i
$701$	18.6330	+	5.47115i	0.703759	+	0.206642i	0.613983	−	0.789320i	$-0.289567\pi$
$701$	18.6330	+	5.47115i	0.703759	+	0.206642i	0.0897766	+	0.995962i	$0.471385\pi$
$702$	4.01838	+	1.17990i	0.151664	+	0.0445326i
$703$	−5.27668	−	11.5543i	−0.199014	−	0.435779i
$704$	−0.110652	+	0.769598i	−0.00417034	+	0.0290053i
$705$	2.71266	−	3.13058i	0.102165	−	0.117904i
$706$	−6.70863	+	14.6898i	−0.252483	+	0.552860i
$707$	36.7398	+	23.6112i	1.38174	+	0.887992i
$708$	1.28796	+	8.95793i	0.0484043	+	0.336660i
$709$	7.32959	−	4.71044i	0.275269	−	0.176904i	−0.395722	−	0.918370i	$-0.629506\pi$
$709$	7.32959	−	4.71044i	0.275269	−	0.176904i	0.670990	+	0.741466i	$0.265869\pi$
$710$	−6.36054	−	7.34046i	−0.238707	−	0.275483i
$711$	3.25774	−	0.956560i	0.122175	−	0.0358738i
$712$	7.26969			0.272443
$713$	−41.8084	−	11.1498i	−1.56574	−	0.417562i
$714$	1.18897			0.0444962
$715$	3.12434	−	0.917390i	0.116844	−	0.0343084i
$716$	−11.1357	−	12.8512i	−0.416159	−	0.480273i
$717$	8.77354	−	5.63841i	0.327654	−	0.210570i
$718$	−1.31708	−	9.16049i	−0.0491530	−	0.341867i
$719$	17.6779	+	11.3609i	0.659275	+	0.423691i	0.827045	−	0.562136i	$-0.190020\pi$
$719$	17.6779	+	11.3609i	0.659275	+	0.423691i	−0.167770	+	0.985826i	$0.553656\pi$
$720$	0.415415	−	0.909632i	0.0154816	−	0.0339000i
$721$	−1.08842	+	1.25610i	−0.0405347	+	0.0467796i
$722$	2.24949	−	15.6455i	0.0837172	−	0.582266i
$723$	−7.30322	−	15.9918i	−0.271610	−	0.594742i
$724$	22.6496	+	6.65053i	0.841766	+	0.247165i
$725$	2.70495	+	0.794245i	0.100459	+	0.0294975i
$726$	−4.31844	−	9.45606i	−0.160272	−	0.350947i
$727$	1.15912	−	8.06182i	0.0429892	−	0.298996i	−0.956972	−	0.290180i	$-0.906285\pi$
$727$	1.15912	−	8.06182i	0.0429892	−	0.298996i	0.999961	−	0.00881597i	$-0.00280625\pi$
$728$	11.1081	−	12.8195i	0.411695	−	0.475122i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	13.1960	+	8.48054i	0.488405	+	0.313879i
$731$	−0.293787	−	2.04334i	−0.0108661	−	0.0755755i
$732$	0.360833	−	0.231893i	0.0133368	−	0.00857101i
$733$	13.3927	+	15.4560i	0.494670	+	0.570879i	0.947107	−	0.320917i	$-0.103991\pi$
$733$	13.3927	+	15.4560i	0.494670	+	0.570879i	−0.452438	+	0.891796i	$0.649446\pi$
$734$	32.8456	−	9.64434i	1.21235	−	0.355979i
$735$	9.40461			0.346894
$736$	−4.56639	+	1.46564i	−0.168319	+	0.0540244i
$737$	2.91470			0.107364
$738$	2.01525	−	0.591730i	0.0741822	−	0.0217819i
$739$	−26.9692	−	31.1241i	−0.992079	−	1.14492i	−0.989443	−	0.144924i	$-0.953706\pi$
$739$	−26.9692	−	31.1241i	−0.992079	−	1.14492i	−0.00263607	−	0.999997i	$-0.500839\pi$
$740$	−5.97951	+	3.84280i	−0.219811	+	0.141264i
$741$	1.06512	+	7.40808i	0.0391282	+	0.272143i
$742$	13.9384	+	8.95764i	0.511693	+	0.328845i
$743$	−4.72926	+	10.3556i	−0.173500	+	0.379911i	−0.976327	−	0.216301i	$-0.930601\pi$
$743$	−4.72926	+	10.3556i	−0.173500	+	0.379911i	0.802827	+	0.596212i	$0.203328\pi$
$744$	−5.90838	+	6.81863i	−0.216612	+	0.249983i
$745$	1.90493	−	13.2491i	0.0697912	−	0.485408i
$746$	9.64989	+	21.1303i	0.353308	+	0.773636i
$747$	−4.05803	−	1.19155i	−0.148476	−	0.0435964i
$748$	−0.218997	−	0.0643033i	−0.00800732	−	0.00235116i
$749$	−18.9815	−	41.5636i	−0.693568	−	1.51870i
$750$	−0.142315	+	0.989821i	−0.00519660	+	0.0361432i
$751$	5.73474	−	6.61824i	0.209264	−	0.241503i	−0.641409	−	0.767199i	$-0.721650\pi$
$751$	5.73474	−	6.61824i	0.209264	−	0.241503i	0.850672	+	0.525696i	$0.176195\pi$
$752$	−1.72079	+	3.76802i	−0.0627509	+	0.137405i
$753$	−25.3078	−	16.2643i	−0.922267	−	0.592705i
$754$	−1.68026	−	11.6865i	−0.0611916	−	0.425597i
$755$	7.67034	−	4.92943i	0.279152	−	0.179400i
$756$	−2.65236	−	3.06098i	−0.0964653	−	0.111327i
$757$	−0.706487	+	0.207443i	−0.0256777	+	0.00753965i	−0.294546	−	0.955637i	$-0.595168\pi$
$757$	−0.706487	+	0.207443i	−0.0256777	+	0.00753965i	0.268868	+	0.963177i	$0.413350\pi$
$758$	−32.1629			−1.16821
$759$	−2.37071	+	2.87816i	−0.0860515	+	0.104471i
$760$	1.78706			0.0648235
$761$	47.9202	−	14.0706i	1.73711	−	0.510060i	0.748833	−	0.662759i	$-0.230615\pi$
$761$	47.9202	−	14.0706i	1.73711	−	0.510060i	0.988273	+	0.152699i	$0.0487964\pi$
$762$	−1.39047	−	1.60469i	−0.0503715	−	0.0581318i
$763$	58.6506	−	37.6924i	2.12329	−	1.36456i
$764$	0.427714	+	2.97482i	0.0154742	+	0.107625i
$765$	0.246954	+	0.158708i	0.00892864	+	0.00573809i
$766$	12.5611	−	27.5050i	0.453851	−	0.993796i
$767$	−24.8204	+	28.6443i	−0.896214	+	1.03429i
$768$	−0.142315	+	0.989821i	−0.00513534	+	0.0357171i
$769$	9.99779	+	21.8921i	0.360529	+	0.789449i	0.999791	+	0.0204598i	$0.00651301\pi$
$769$	9.99779	+	21.8921i	0.360529	+	0.789449i	−0.639261	+	0.768990i	$0.720760\pi$
$770$	−3.02157	−	0.887212i	−0.108890	−	0.0319729i
$771$	−21.0777	−	6.18897i	−0.759094	−	0.222890i
$772$	−1.87238	−	4.09994i	−0.0673885	−	0.147560i
$773$	−2.55329	+	17.7585i	−0.0918356	+	0.638730i	0.890967	+	0.454069i	$0.150028\pi$
$773$	−2.55329	+	17.7585i	−0.0918356	+	0.638730i	−0.982802	+	0.184662i	$0.940881\pi$
$774$	−4.60514	+	5.31462i	−0.165528	+	0.191030i
$775$	3.74802	−	8.20701i	0.134633	−	0.294805i
$776$	−0.605047	−	0.388840i	−0.0217199	−	0.0139585i
$777$	4.09706	+	28.4957i	0.146981	+	1.02228i
$778$	13.6046	−	8.74312i	0.487747	−	0.313456i
$779$	2.45796	+	2.83664i	0.0880656	+	0.101633i
$780$	4.01838	−	1.17990i	0.143881	−	0.0422473i
$781$	7.55184			0.270226
$782$	−0.235097	−	1.38807i	−0.00840705	−	0.0496373i
$783$	−2.81915			−0.100748
$784$	−9.02366	+	2.64958i	−0.322273	+	0.0946280i
$785$	−10.0655	−	11.6162i	−0.359253	−	0.414600i
$786$	−1.17072	+	0.752373i	−0.0417580	+	0.0268363i
$787$	−6.13129	−	42.6441i	−0.218557	−	1.52010i	−0.743370	−	0.668880i	$-0.766774\pi$
$787$	−6.13129	−	42.6441i	−0.218557	−	1.52010i	0.524813	−	0.851217i	$-0.324135\pi$
$788$	7.86632	+	5.05537i	0.280226	+	0.180090i
$789$	−8.84525	+	19.3684i	−0.314899	+	0.689533i
$790$	2.22343	−	2.56598i	0.0791062	−	0.0912934i
$791$	0.861218	−	5.98990i	0.0306214	−	0.212976i
$792$	0.322990	+	0.707250i	0.0114770	+	0.0251310i
$793$	1.72358	+	0.506087i	0.0612060	+	0.0179717i
$794$	−21.7017	−	6.37219i	−0.770165	−	0.226141i
$795$	1.69935	+	3.72107i	0.0602699	+	0.131973i
$796$	3.07878	−	21.4134i	0.109125	−	0.758978i
$797$	−12.1222	+	13.9897i	−0.429389	+	0.495541i	−0.928674	−	0.370897i	$-0.879050\pi$
$797$	−12.1222	+	13.9897i	−0.429389	+	0.495541i	0.499286	+	0.866438i	$0.333596\pi$
$798$	3.00680	−	6.58397i	0.106440	−	0.233070i
$799$	−1.02297	−	0.657423i	−0.0361901	−	0.0232579i
$800$	−0.142315	−	0.989821i	−0.00503159	−	0.0349955i
$801$	6.11565	−	3.93029i	0.216086	−	0.138870i
$802$	18.2333	+	21.0423i	0.643839	+	0.743030i
$803$	−11.7021	+	3.43604i	−0.412958	+	0.121255i
$804$	3.74875			0.132208
$805$	−3.24370	−	19.1516i	−0.114325	−	0.675006i
$806$	−37.7858			−1.33095
$807$	−25.6782	+	7.53979i	−0.903914	+	0.265413i
$808$	−7.06116	−	8.14901i	−0.248411	−	0.286681i
$809$	3.49006	−	2.24293i	0.122704	−	0.0788571i	−0.477849	−	0.878442i	$-0.658583\pi$
$809$	3.49006	−	2.24293i	0.122704	−	0.0788571i	0.600553	+	0.799585i	$0.294947\pi$
$810$	−0.142315	−	0.989821i	−0.00500043	−	0.0347788i
$811$	−8.29114	−	5.32839i	−0.291141	−	0.187105i	0.386915	−	0.922116i	$-0.373541\pi$
$811$	−8.29114	−	5.32839i	−0.291141	−	0.187105i	−0.678056	+	0.735011i	$0.737177\pi$
$812$	−4.74332	+	10.3864i	−0.166458	+	0.364492i
$813$	−9.29852	+	10.7311i	−0.326113	+	0.376355i
$814$	0.786496	−	5.47020i	0.0275667	−	0.191730i
$815$	4.53051	+	9.92043i	0.158697	+	0.347497i
$816$	−0.281664	−	0.0827039i	−0.00986020	−	0.00289522i
$817$	−12.0580	−	3.54055i	−0.421856	−	0.123868i
$818$	−3.84726	−	8.42433i	−0.134516	−	0.294550i
$819$	2.41403	−	16.7899i	0.0843530	−	0.586688i
$820$	1.37542	−	1.58732i	0.0480317	−	0.0554316i
$821$	−5.53334	+	12.1163i	−0.193115	+	0.422862i	−0.981276	−	0.192606i	$-0.938306\pi$
$821$	−5.53334	+	12.1163i	−0.193115	+	0.422862i	0.788161	+	0.615469i	$0.211033\pi$
$822$	−6.73986	−	4.33145i	−0.235080	−	0.151077i
$823$	1.32946	+	9.24661i	0.0463421	+	0.322316i	0.999785	+	0.0207424i	$0.00660297\pi$
$823$	1.32946	+	9.24661i	0.0463421	+	0.322316i	−0.953443	+	0.301574i	$0.902488\pi$
$824$	0.345215	−	0.221856i	0.0120261	−	0.00772873i
$825$	−0.509162	−	0.587605i	−0.0177268	−	0.0204578i
$826$	35.1702	−	10.3269i	1.22373	−	0.359319i
$827$	−46.9609			−1.63299			−0.816496	−	0.577351i	$-0.804086\pi$
$827$	−46.9609			−1.63299			−0.816496	+	0.577351i	$0.804086\pi$
$828$	−3.04910	+	3.70175i	−0.105964	+	0.128645i
$829$	18.1813			0.631464			0.315732	−	0.948848i	$-0.397750\pi$
$829$	18.1813			0.631464			0.315732	+	0.948848i	$0.397750\pi$
$830$	−4.05803	+	1.19155i	−0.140856	+	0.0413591i
$831$	−11.1216	−	12.8351i	−0.385805	−	0.445243i
$832$	−3.52319	+	2.26422i	−0.122145	+	0.0784977i
$833$	−0.392898	−	2.73267i	−0.0136131	−	0.0946813i
$834$	18.9865	+	12.2019i	0.657448	+	0.422516i
$835$	0.762623	−	1.66991i	0.0263916	−	0.0577896i
$836$	−0.909904	+	1.05009i	−0.0314697	+	0.0363180i
$837$	−1.28401	+	8.93051i	−0.0443820	+	0.308684i
$838$	1.15500	+	2.52910i	0.0398988	+	0.0873661i
$839$	−35.0957	−	10.3050i	−1.21164	−	0.355769i	−0.387347	−	0.921934i	$-0.626609\pi$
$839$	−35.0957	−	10.3050i	−1.21164	−	0.355769i	−0.824292	+	0.566164i	$0.808427\pi$
$840$	−3.88620	−	1.14109i	−0.134087	−	0.0393714i
$841$	−8.74549	−	19.1500i	−0.301569	−	0.660343i
$842$	0.919962	−	6.39848i	0.0317040	−	0.220506i
$843$	−11.8774	+	13.7072i	−0.409078	+	0.472101i
$844$	−9.31371	+	20.3942i	−0.320591	+	0.701997i
$845$	3.81894	+	2.45428i	0.131375	+	0.0844298i
$846$	0.589518	+	4.10019i	0.0202680	+	0.140967i
$847$	−35.4205	+	22.7633i	−1.21706	+	0.782158i
$848$	−2.67886	−	3.09157i	−0.0919926	−	0.106165i
$849$	−1.80438	+	0.529814i	−0.0619262	+	0.0181832i
$850$	0.293555			0.0100688
$851$	32.4572	−	10.4176i	1.11262	−	0.357111i
$852$	9.71282			0.332756
$853$	−34.4691	+	10.1210i	−1.18020	+	0.346538i	−0.812251	−	0.583308i	$-0.801758\pi$
$853$	−34.4691	+	10.1210i	−1.18020	+	0.346538i	−0.367949	+	0.929846i	$0.619940\pi$
$854$	−1.13766	−	1.31292i	−0.0389298	−	0.0449274i
$855$	1.50337	−	0.966158i	0.0514142	−	0.0330419i
$856$	1.60552	+	11.1666i	0.0548755	+	0.381667i
$857$	−35.3087	−	22.6915i	−1.20612	−	0.775128i	−0.226117	−	0.974100i	$-0.572603\pi$
$857$	−35.3087	−	22.6915i	−1.20612	−	0.775128i	−0.980005	+	0.198972i	$0.936240\pi$
$858$	−1.35269	+	2.96198i	−0.0461802	+	0.101120i
$859$	−33.0845	+	38.1816i	−1.12883	+	1.30274i	−0.181172	+	0.983451i	$0.557989\pi$
$859$	−33.0845	+	38.1816i	−1.12883	+	1.30274i	−0.947658	+	0.319288i	$0.896556\pi$
$860$	−1.00079	+	6.96067i	−0.0341268	+	0.237357i
$861$	−3.53388	−	7.73811i	−0.120434	−	0.263714i
$862$	−18.6678	−	5.48137i	−0.635828	−	0.186696i
$863$	26.3257	+	7.72991i	0.896136	+	0.263129i	0.697194	−	0.716882i	$-0.254431\pi$
$863$	26.3257	+	7.72991i	0.896136	+	0.263129i	0.198942	+	0.980011i	$0.436250\pi$
$864$	0.415415	+	0.909632i	0.0141327	+	0.0309463i
$865$	1.65561	−	11.5150i	0.0562925	−	0.391523i
$866$	−16.1699	+	18.6611i	−0.549476	+	0.634130i
$867$	−7.02626	+	15.3854i	−0.238624	+	0.522514i
$868$	30.7418	+	19.7566i	1.04344	+	0.670581i
$869$	0.375693	+	2.61300i	0.0127445	+	0.0886399i
$870$	−2.37162	+	1.52415i	−0.0804053	+	0.0516734i
$871$	10.2812	+	11.8652i	0.348366	+	0.402036i
$872$	−16.5160	+	4.84953i	−0.559301	+	0.164226i
$873$	−0.719220			−0.0243419
$874$	−8.28102	−	2.20844i	−0.280110	−	0.0747017i
$875$	4.05026			0.136924
$876$	−15.0507	+	4.41928i	−0.508516	+	0.149314i
$877$	−20.4102	−	23.5546i	−0.689202	−	0.795382i	0.298049	−	0.954551i	$-0.403664\pi$
$877$	−20.4102	−	23.5546i	−0.689202	−	0.795382i	−0.987251	+	0.159169i	$0.949119\pi$
$878$	10.0325	−	6.44747i	0.338579	−	0.217592i
$879$	3.98763	+	27.7345i	0.134499	+	0.935463i
$880$	0.654085	+	0.420355i	0.0220492	+	0.0141702i
$881$	−13.0936	+	28.6709i	−0.441134	+	0.965948i	0.550255	+	0.834997i	$0.314530\pi$
$881$	−13.0936	+	28.6709i	−0.441134	+	0.965948i	−0.991389	+	0.130951i	$0.958197\pi$
$882$	−6.15871	+	7.10753i	−0.207375	+	0.239323i
$883$	4.29496	−	29.8721i	0.144537	−	1.00528i	−0.780434	−	0.625239i	$-0.785002\pi$
$883$	4.29496	−	29.8721i	0.144537	−	1.00528i	0.924971	−	0.380039i	$-0.124089\pi$
$884$	−0.510717	−	1.11832i	−0.0171773	−	0.0376130i
$885$	8.68345	+	2.54969i	0.291891	+	0.0857070i
$886$	20.5436	+	6.03214i	0.690176	+	0.202654i
$887$	−1.27981	−	2.80239i	−0.0429718	−	0.0940951i	0.886929	−	0.461907i	$-0.152834\pi$
$887$	−1.27981	−	2.80239i	−0.0429718	−	0.0940951i	−0.929900	+	0.367811i	$0.880107\pi$
$888$	1.01155	−	7.03551i	0.0339455	−	0.236096i
$889$	−5.63177	+	6.49941i	−0.188884	+	0.217983i
$890$	3.01994	−	6.61274i	0.101229	−	0.221660i
$891$	0.654085	+	0.420355i	0.0219127	+	0.0140824i
$892$	3.27787	+	22.7981i	0.109751	+	0.763337i
$893$	−6.22749	+	4.00217i	−0.208395	+	0.133927i
$894$	8.76551	+	10.1159i	0.293163	+	0.338328i
$895$	−16.3158	+	4.79075i	−0.545377	+	0.160137i
$896$	4.05026			0.135310
$897$	−20.0788	+	0.501627i	−0.670412	+	0.0167488i
$898$	−37.4997			−1.25138
$899$	24.4050	−	7.16595i	0.813952	−	0.238998i
$900$	−0.654861	−	0.755750i	−0.0218287	−	0.0251917i
$901$	1.01022	−	0.649231i	0.0336554	−	0.0216290i
$902$	0.232404	+	1.61641i	0.00773821	+	0.0538204i
$903$	23.9609	+	15.3988i	0.797370	+	0.512439i
$904$	−0.620672	+	1.35908i	−0.0206432	+	0.0452024i
$905$	15.4585	−	17.8401i	0.513859	−	0.593025i
$906$	−1.29759	+	9.02494i	−0.0431096	+	0.299834i
$907$	−3.08377	−	6.75251i	−0.102395	−	0.224213i	0.851500	−	0.524355i	$-0.175693\pi$
$907$	−3.08377	−	6.75251i	−0.102395	−	0.224213i	−0.953895	+	0.300141i	$0.902966\pi$
$908$	−4.79914	−	1.40916i	−0.159265	−	0.0467645i
$909$	−10.3459	−	3.03783i	−0.343152	−	0.100759i
$910$	−7.04652	−	15.4297i	−0.233590	−	0.511490i
$911$	−1.84103	+	12.8046i	−0.0609960	+	0.424237i	0.936328	+	0.351127i	$0.114201\pi$
$911$	−1.84103	+	12.8046i	−0.0609960	+	0.424237i	−0.997324	+	0.0731097i	$0.976708\pi$
$912$	−1.17028	+	1.35057i	−0.0387517	+	0.0447219i
$913$	1.36604	−	2.99121i	0.0452093	−	0.0989945i
$914$	−9.87837	−	6.34844i	−0.326747	−	0.209988i
$915$	−0.0610420	−	0.424557i	−0.00201799	−	0.0140354i
$916$	1.42670	−	0.916882i	0.0471394	−	0.0302946i
$917$	3.69111	+	4.25976i	0.121891	+	0.140670i
$918$	−0.281664	+	0.0827039i	−0.00929629	+	0.00272964i
$919$	9.52152			0.314086			0.157043	−	0.987592i	$-0.449804\pi$
$919$	9.52152			0.314086			0.157043	+	0.987592i	$0.449804\pi$
$920$	−0.563748	+	4.76258i	−0.0185862	+	0.157018i
$921$	13.0251			0.429190
$922$	24.2218	−	7.11215i	0.797701	−	0.234226i
$923$	26.6381	+	30.7420i	0.876805	+	1.01189i
$924$	2.64921	−	1.70255i	0.0871528	−	0.0560097i
$925$	1.01155	+	7.03551i	0.0332597	+	0.231326i
$926$	−24.7590	−	15.9116i	−0.813631	−	0.522889i
$927$	0.170469	−	0.373275i	0.00559893	−	0.0122600i
$928$	1.84615	−	2.13057i	0.0606028	−	0.0699393i
$929$	5.58270	−	38.8285i	0.183163	−	1.27392i	−0.666064	−	0.745895i	$-0.732022\pi$
$929$	5.58270	−	38.8285i	0.183163	−	1.27392i	0.849227	−	0.528029i	$-0.177069\pi$
$930$	3.74802	+	8.20701i	0.122902	+	0.269119i
$931$	−16.1258	−	4.73497i	−0.528503	−	0.155182i
$932$	−18.6597	−	5.47899i	−0.611219	−	0.179470i
$933$	−12.3984	−	27.1488i	−0.405907	−	0.888812i
$934$	1.34657	−	9.36562i	0.0440612	−	0.306452i
$935$	−0.149467	+	0.172494i	−0.00488809	+	0.00564116i
$936$	−1.73977	+	3.80956i	−0.0568662	+	0.124520i
$937$	24.9371	+	16.0261i	0.814658	+	0.523549i	0.880369	−	0.474290i	$-0.157295\pi$
$937$	24.9371	+	16.0261i	0.814658	+	0.523549i	−0.0657105	+	0.997839i	$0.520931\pi$
$938$	−2.16082	−	15.0289i	−0.0705534	−	0.490710i
$939$	3.37587	−	2.16954i	0.110167	−	0.0708002i
$940$	2.71266	+	3.13058i	0.0884773	+	0.102108i
$941$	−27.5875	+	8.10042i	−0.899327	+	0.264066i	−0.698542	−	0.715569i	$-0.746167\pi$
$941$	−27.5875	+	8.10042i	−0.899327	+	0.264066i	−0.200785	+	0.979635i	$0.564349\pi$
$942$	15.3704			0.500796
$943$	−8.33513	+	5.65570i	−0.271429	+	0.184175i
$944$	−9.05004			−0.294554
$945$	−3.88620	+	1.14109i	−0.126418	+	0.0371197i
$946$	−3.58055	−	4.13218i	−0.116414	−	0.134349i
$947$	28.7705	−	18.4897i	0.934916	−	0.600834i	0.0179668	−	0.999839i	$-0.494281\pi$
$947$	28.7705	−	18.4897i	0.934916	−	0.600834i	0.916949	+	0.399005i	$0.130644\pi$
$948$	0.483198	+	3.36072i	0.0156935	+	0.109151i
$949$	−55.2651	−	35.5167i	−1.79398	−	1.15292i
$950$	0.742372	−	1.62557i	0.0240857	−	0.0527404i
$951$	−18.6689	+	21.5450i	−0.605380	+	0.698646i
$952$	−0.169208	+	1.17687i	−0.00548408	+	0.0381426i
$953$	1.65193	+	3.61723i	0.0535114	+	0.117174i	0.934499	−	0.355966i	$-0.115848\pi$
$953$	1.65193	+	3.61723i	0.0535114	+	0.117174i	−0.880988	+	0.473139i	$0.843121\pi$
$954$	−3.92503	−	1.15249i	−0.127078	−	0.0373134i
$955$	2.88367	+	0.846721i	0.0933133	+	0.0273993i
$956$	4.33241	+	9.48666i	0.140120	+	0.306821i
$957$	0.311943	−	2.16961i	0.0100837	−	0.0701335i
$958$	22.5727	−	26.0503i	0.729292	−	0.841648i
$959$	−13.4800	+	29.5170i	−0.435291	+	0.953155i
$960$	0.841254	+	0.540641i	0.0271513	+	0.0174491i
$961$	−7.17305	−	49.8897i	−0.231389	−	1.60934i
$962$	25.0424	−	16.0937i	0.807398	−	0.518883i
$963$	7.38778	+	8.52595i	0.238068	+	0.274745i
$964$	16.8684	−	4.95301i	0.543295	−	0.159526i
$965$	−4.50726			−0.145094
$966$	16.5980	+	10.0902i	0.534032	+	0.324647i
$967$	−3.05378			−0.0982030			−0.0491015	−	0.998794i	$-0.515636\pi$
$967$	−3.05378			−0.0982030			−0.0491015	+	0.998794i	$0.515636\pi$
$968$	9.97438	−	2.92874i	0.320589	−	0.0941334i
$969$	−0.343540	−	0.396466i	−0.0110361	−	0.0127363i
$970$	−0.605047	+	0.388840i	−0.0194269	+	0.0124849i
$971$	−2.35625	−	16.3881i	−0.0756157	−	0.525919i	−0.992061	−	0.125759i	$-0.959864\pi$
$971$	−2.35625	−	16.3881i	−0.0756157	−	0.525919i	0.916445	−	0.400160i	$-0.131046\pi$
$972$	0.841254	+	0.540641i	0.0269832	+	0.0173411i
$973$	37.9737	−	83.1508i	1.21738	−	2.66569i
$974$	17.3585	−	20.0328i	0.556202	−	0.641892i
$975$	0.596019	−	4.14540i	0.0190879	−	0.132759i
$976$	0.178181	+	0.390162i	0.00570343	+	0.0124888i
$977$	3.38157	+	0.992917i	0.108186	+	0.0317662i	0.335377	−	0.942084i	$-0.391136\pi$
$977$	3.38157	+	0.992917i	0.108186	+	0.0317662i	−0.227192	+	0.973850i	$0.572954\pi$
$978$	−10.4642	−	3.07257i	−0.334609	−	0.0982499i
$979$	2.34804	+	5.14149i	0.0750437	+	0.164323i
$980$	−1.33842	+	9.30888i	−0.0427541	+	0.297361i
$981$	−11.2723	+	13.0089i	−0.359896	+	0.415342i
$982$	−16.7766	+	36.7357i	−0.535364	+	1.17228i
$983$	27.7977	+	17.8645i	0.886610	+	0.569790i	0.902791	−	0.430079i	$-0.141514\pi$
$983$	27.7977	+	17.8645i	0.886610	+	0.569790i	−0.0161808	+	0.999869i	$0.505151\pi$
$984$	0.298907	+	2.07895i	0.00952882	+	0.0662744i
$985$	7.86632	−	5.05537i	0.250642	−	0.161078i
$986$	0.541945	+	0.625438i	0.0172591	+	0.0199180i
$987$	16.0980	−	4.72680i	0.512405	−	0.150456i
$988$	−7.48426			−0.238106
$989$	13.2395	−	31.0181i	0.420992	−	0.986318i
$990$	0.777512			0.0247110
$991$	−19.6667	+	5.77466i	−0.624733	+	0.183438i	−0.578751	−	0.815504i	$-0.696460\pi$
$991$	−19.6667	+	5.77466i	−0.624733	+	0.183438i	−0.0459815	+	0.998942i	$0.514642\pi$
$992$	−5.90838	−	6.81863i	−0.187591	−	0.216492i
$993$	−6.42591	+	4.12968i	−0.203920	+	0.131051i
$994$	−5.59859	−	38.9390i	−0.177576	−	1.23507i
$995$	−18.1993	−	11.6960i	−0.576958	−	0.370788i
$996$	1.75693	−	3.84715i	0.0556706	−	0.121902i
$997$	−4.64728	+	5.36325i	−0.147181	+	0.169856i	−0.824553	−	0.565785i	$-0.808573\pi$
$997$	−4.64728	+	5.36325i	−0.147181	+	0.169856i	0.677372	+	0.735641i	$0.263119\pi$
$998$	−3.27011	+	22.7441i	−0.103514	+	0.719952i
$999$	−2.95271	−	6.46554i	−0.0934197	−	0.204561i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.959493 + 0.281733i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(0.841254 + 0.540641i) q^{6} +(1.68254 - 3.68425i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(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} +(1.68254 - 3.68425i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.415415 + 0.909632i) q^{10} +(-0.746018 - 0.219051i) q^{11} +(-0.959493 - 0.281733i) q^{12} +(-1.73977 - 3.80956i) q^{13} +(-0.576412 + 4.00903i) q^{14} +(-0.654861 + 0.755750i) q^{15} +(0.415415 - 0.909632i) q^{16} +(0.246954 + 0.158708i) q^{17} +(-0.142315 - 0.989821i) q^{18} +(1.50337 - 0.966158i) q^{19} +(-0.654861 - 0.755750i) q^{20} +(-3.88620 + 1.14109i) q^{21} +0.777512 q^{22} +(2.10059 + 4.31132i) q^{23} +1.00000 q^{24} +(-0.959493 + 0.281733i) q^{25} +(2.74258 + 3.16510i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-0.576412 - 4.00903i) q^{28} +(-2.37162 - 1.52415i) q^{29} +(0.415415 - 0.909632i) q^{30} +(-5.90838 + 6.81863i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(0.322990 + 0.707250i) q^{33} +(-0.281664 - 0.0827039i) q^{34} +(-3.88620 - 1.14109i) q^{35} +(0.415415 + 0.909632i) q^{36} +(1.01155 - 7.03551i) q^{37} +(-1.17028 + 1.35057i) q^{38} +(-1.73977 + 3.80956i) q^{39} +(0.841254 + 0.540641i) q^{40} +(0.298907 + 2.07895i) q^{41} +(3.40730 - 2.18974i) q^{42} +(-4.60514 - 5.31462i) q^{43} +(-0.746018 + 0.219051i) q^{44} +1.00000 q^{45} +(-3.23014 - 3.54488i) q^{46} -4.14235 q^{47} +(-0.959493 + 0.281733i) q^{48} +(-6.15871 - 7.10753i) q^{49} +(0.841254 - 0.540641i) q^{50} +(-0.0417772 - 0.290567i) q^{51} +(-3.52319 - 2.26422i) q^{52} +(1.69935 - 3.72107i) q^{53} +(-0.654861 + 0.755750i) q^{54} +(-0.110652 + 0.769598i) q^{55} +(1.68254 + 3.68425i) q^{56} +(-1.71467 - 0.503473i) q^{57} +(2.70495 + 0.794245i) q^{58} +(-3.75952 - 8.23221i) q^{59} +(-0.142315 + 0.989821i) q^{60} +(-0.280885 + 0.324158i) q^{61} +(3.74802 - 8.20701i) q^{62} +(3.40730 + 2.18974i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-3.52319 + 2.26422i) q^{65} +(-0.509162 - 0.587605i) q^{66} +(-3.59690 + 1.05614i) q^{67} +0.293555 q^{68} +(1.88269 - 4.41084i) q^{69} +4.05026 q^{70} +(-9.31938 + 2.73642i) q^{71} +(-0.654861 - 0.755750i) q^{72} +(13.1960 - 8.48054i) q^{73} +(1.01155 + 7.03551i) q^{74} +(0.841254 + 0.540641i) q^{75} +(0.742372 - 1.62557i) q^{76} +(-2.06224 + 2.37995i) q^{77} +(0.596019 - 4.14540i) q^{78} +(-1.41045 - 3.08845i) q^{79} +(-0.959493 - 0.281733i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-0.872506 - 1.91052i) q^{82} +(-0.601899 + 4.18630i) q^{83} +(-2.65236 + 3.06098i) q^{84} +(0.121947 - 0.267027i) q^{85} +(5.91590 + 3.80192i) q^{86} +(0.401206 + 2.79045i) q^{87} +(0.654085 - 0.420355i) q^{88} +(-4.76064 - 5.49407i) q^{89} +(-0.959493 + 0.281733i) q^{90} -16.9626 q^{91} +(4.09801 + 2.49125i) q^{92} +9.02235 q^{93} +(3.97456 - 1.16704i) q^{94} +(-1.17028 - 1.35057i) q^{95} +(0.841254 - 0.540641i) q^{96} +(0.102356 + 0.711900i) q^{97} +(7.91166 + 5.08452i) q^{98} +(0.322990 - 0.707250i) 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

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