LMFDB - Embedded newform 690.2.m.h.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			271.1
Character	$\chi$	$=$	690.271
Dual form			690.2.m.h.331.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 + 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(-1.89055 - 4.13973i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(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} +(-1.89055 - 4.13973i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.415415 - 0.909632i) q^{10} +(-5.69717 + 1.67284i) q^{11} +(-0.959493 + 0.281733i) q^{12} +(2.66114 - 5.82708i) q^{13} +(-0.647674 - 4.50467i) q^{14} +(0.654861 + 0.755750i) q^{15} +(0.415415 + 0.909632i) q^{16} +(1.63381 - 1.04999i) q^{17} +(0.142315 - 0.989821i) q^{18} +(-4.19949 - 2.69885i) q^{19} +(0.654861 - 0.755750i) q^{20} +(4.36665 + 1.28216i) q^{21} -5.93769 q^{22} +(-4.53841 + 1.55010i) q^{23} -1.00000 q^{24} +(-0.959493 - 0.281733i) q^{25} +(4.19502 - 4.84131i) q^{26} +(0.841254 + 0.540641i) q^{27} +(0.647674 - 4.50467i) q^{28} +(4.82554 - 3.10118i) q^{29} +(0.415415 + 0.909632i) q^{30} +(1.95199 + 2.25272i) q^{31} +(0.142315 + 0.989821i) q^{32} +(2.46661 - 5.40111i) q^{33} +(1.86345 - 0.547157i) q^{34} +(-4.36665 + 1.28216i) q^{35} +(0.415415 - 0.909632i) q^{36} +(0.612262 + 4.25838i) q^{37} +(-3.26903 - 3.77266i) q^{38} +(2.66114 + 5.82708i) q^{39} +(0.841254 - 0.540641i) q^{40} +(0.242109 - 1.68390i) q^{41} +(3.82854 + 2.46045i) q^{42} +(2.38869 - 2.75670i) q^{43} +(-5.69717 - 1.67284i) q^{44} -1.00000 q^{45} +(-4.79129 + 0.208693i) q^{46} +7.68917 q^{47} +(-0.959493 - 0.281733i) q^{48} +(-8.97916 + 10.3625i) q^{49} +(-0.841254 - 0.540641i) q^{50} +(-0.276392 + 1.92235i) q^{51} +(5.38905 - 3.46333i) q^{52} +(3.24074 + 7.09623i) q^{53} +(0.654861 + 0.755750i) q^{54} +(0.845021 + 5.87725i) q^{55} +(1.89055 - 4.13973i) q^{56} +(4.78973 - 1.40639i) q^{57} +(5.50377 - 1.61605i) q^{58} +(5.34869 - 11.7120i) q^{59} +(0.142315 + 0.989821i) q^{60} +(-7.80181 - 9.00377i) q^{61} +(1.23826 + 2.71141i) q^{62} +(-3.82854 + 2.46045i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-5.38905 - 3.46333i) q^{65} +(3.88836 - 4.48741i) q^{66} +(9.62355 + 2.82573i) q^{67} +1.94211 q^{68} +(1.80054 - 4.44500i) q^{69} -4.55100 q^{70} +(-3.97507 - 1.16719i) q^{71} +(0.654861 - 0.755750i) q^{72} +(-4.73896 - 3.04555i) q^{73} +(-0.612262 + 4.25838i) q^{74} +(0.841254 - 0.540641i) q^{75} +(-2.07373 - 4.54083i) q^{76} +(17.6959 + 20.4222i) q^{77} +(0.911665 + 6.34077i) q^{78} +(2.82179 - 6.17886i) q^{79} +(0.959493 - 0.281733i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(0.706713 - 1.54748i) q^{82} +(1.06972 + 7.44010i) q^{83} +(2.98027 + 3.43941i) q^{84} +(-0.806784 - 1.76661i) q^{85} +(3.06859 - 1.97206i) q^{86} +(-0.816336 + 5.67774i) q^{87} +(-4.99510 - 3.21016i) q^{88} +(-1.61061 + 1.85874i) q^{89} +(-0.959493 - 0.281733i) q^{90} -29.1536 q^{91} +(-4.65600 - 1.14962i) q^{92} -2.98078 q^{93} +(7.37771 + 2.16629i) q^{94} +(-3.26903 + 3.77266i) q^{95} +(-0.841254 - 0.540641i) q^{96} +(1.14642 - 7.97352i) q^{97} +(-11.5349 + 7.41303i) q^{98} +(2.46661 + 5.40111i) 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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
$7$	−1.89055	−	4.13973i	−0.714561	−	1.56467i	−0.821373	−	0.570392i	$-0.806791\pi$
$7$	−1.89055	−	4.13973i	−0.714561	−	1.56467i	0.106811	−	0.994279i	$-0.465936\pi$
$8$	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
$11$	−5.69717	+	1.67284i	−1.71776	+	0.504380i	−0.984473	−	0.175537i	$-0.943834\pi$
$11$	−5.69717	+	1.67284i	−1.71776	+	0.504380i	−0.733289	+	0.679917i	$0.762016\pi$
$12$	−0.959493	+	0.281733i	−0.276982	+	0.0813292i
$13$	2.66114	−	5.82708i	0.738067	−	1.61614i	−0.0486416	−	0.998816i	$-0.515489\pi$
$13$	2.66114	−	5.82708i	0.738067	−	1.61614i	0.786708	−	0.617325i	$-0.211784\pi$
$14$	−0.647674	−	4.50467i	−0.173098	−	1.20392i
$15$	0.654861	+	0.755750i	0.169084	+	0.195134i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	1.63381	−	1.04999i	0.396257	−	0.254659i	−0.327304	−	0.944919i	$-0.606140\pi$
$17$	1.63381	−	1.04999i	0.396257	−	0.254659i	0.723562	+	0.690260i	$0.242504\pi$
$18$	0.142315	−	0.989821i	0.0335439	−	0.233303i
$19$	−4.19949	−	2.69885i	−0.963429	−	0.619158i	−0.0384837	−	0.999259i	$-0.512253\pi$
$19$	−4.19949	−	2.69885i	−0.963429	−	0.619158i	−0.924945	+	0.380101i	$0.875889\pi$
$20$	0.654861	−	0.755750i	0.146431	−	0.168991i
$21$	4.36665	+	1.28216i	0.952881	+	0.279791i
$22$	−5.93769			−1.26592
$23$	−4.53841	+	1.55010i	−0.946324	+	0.323218i
$23$	−4.53841	+	1.55010i	−0.946324	+	0.323218i
$24$	−1.00000			−0.204124
$25$	−0.959493	−	0.281733i	−0.191899	−	0.0563465i
$26$	4.19502	−	4.84131i	0.822711	−	0.949459i
$27$	0.841254	+	0.540641i	0.161899	+	0.104046i
$28$	0.647674	−	4.50467i	0.122399	−	0.851303i
$29$	4.82554	−	3.10118i	0.896079	−	0.575875i	−0.00954565	−	0.999954i	$-0.503039\pi$
$29$	4.82554	−	3.10118i	0.896079	−	0.575875i	0.905625	+	0.424079i	$0.139402\pi$
$30$	0.415415	+	0.909632i	0.0758441	+	0.166075i
$31$	1.95199	+	2.25272i	0.350588	+	0.404601i	0.903465	−	0.428663i	$-0.141015\pi$
$31$	1.95199	+	2.25272i	0.350588	+	0.404601i	−0.552876	+	0.833263i	$0.686470\pi$
$32$	0.142315	+	0.989821i	0.0251579	+	0.174977i
$33$	2.46661	−	5.40111i	0.429381	−	0.940213i
$34$	1.86345	−	0.547157i	0.319578	−	0.0938367i
$35$	−4.36665	+	1.28216i	−0.738098	+	0.216725i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	0.612262	+	4.25838i	0.100655	+	0.700073i	0.976190	+	0.216918i	$0.0696003\pi$
$37$	0.612262	+	4.25838i	0.100655	+	0.700073i	−0.875535	+	0.483155i	$0.839491\pi$
$38$	−3.26903	−	3.77266i	−0.530306	−	0.612006i
$39$	2.66114	+	5.82708i	0.426123	+	0.933079i
$40$	0.841254	−	0.540641i	0.133014	−	0.0854828i
$41$	0.242109	−	1.68390i	0.0378111	−	0.262982i	−0.962143	−	0.272544i	$-0.912135\pi$
$41$	0.242109	−	1.68390i	0.0378111	−	0.262982i	0.999954	+	0.00956266i	$0.00304394\pi$
$42$	3.82854	+	2.46045i	0.590757	+	0.379656i
$43$	2.38869	−	2.75670i	0.364272	−	0.420393i	−0.543794	−	0.839219i	$-0.683013\pi$
$43$	2.38869	−	2.75670i	0.364272	−	0.420393i	0.908067	+	0.418826i	$0.137558\pi$
$44$	−5.69717	−	1.67284i	−0.858881	−	0.252190i
$45$	−1.00000			−0.149071
$46$	−4.79129	+	0.208693i	−0.706437	+	0.0307701i
$47$	7.68917			1.12158			0.560790	−	0.827958i	$-0.310497\pi$
$47$	7.68917			1.12158			0.560790	+	0.827958i	$0.310497\pi$
$48$	−0.959493	−	0.281733i	−0.138491	−	0.0406646i
$49$	−8.97916	+	10.3625i	−1.28274	+	1.48036i
$50$	−0.841254	−	0.540641i	−0.118971	−	0.0764582i
$51$	−0.276392	+	1.92235i	−0.0387026	+	0.269182i
$52$	5.38905	−	3.46333i	0.747327	−	0.480278i
$53$	3.24074	+	7.09623i	0.445150	+	0.974742i	0.990624	+	0.136614i	$0.0436221\pi$
$53$	3.24074	+	7.09623i	0.445150	+	0.974742i	−0.545475	+	0.838127i	$0.683651\pi$
$54$	0.654861	+	0.755750i	0.0891153	+	0.102844i
$55$	0.845021	+	5.87725i	0.113943	+	0.792489i
$56$	1.89055	−	4.13973i	0.252636	−	0.553195i
$57$	4.78973	−	1.40639i	0.634416	−	0.186281i
$58$	5.50377	−	1.61605i	0.722681	−	0.212198i
$59$	5.34869	−	11.7120i	0.696340	−	1.52477i	−0.148013	−	0.988985i	$-0.547288\pi$
$59$	5.34869	−	11.7120i	0.696340	−	1.52477i	0.844353	−	0.535787i	$-0.179985\pi$
$60$	0.142315	+	0.989821i	0.0183728	+	0.127785i
$61$	−7.80181	−	9.00377i	−0.998919	−	1.15281i	−0.988246	−	0.152871i	$-0.951148\pi$
$61$	−7.80181	−	9.00377i	−0.998919	−	1.15281i	−0.0106734	−	0.999943i	$-0.503398\pi$
$62$	1.23826	+	2.71141i	0.157259	+	0.344349i
$63$	−3.82854	+	2.46045i	−0.482351	+	0.309988i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	−5.38905	−	3.46333i	−0.668429	−	0.429573i
$66$	3.88836	−	4.48741i	0.478624	−	0.552362i
$67$	9.62355	+	2.82573i	1.17570	+	0.345218i	0.810516	−	0.585716i	$-0.199187\pi$
$67$	9.62355	+	2.82573i	1.17570	+	0.345218i	0.365187	+	0.930934i	$0.381005\pi$
$68$	1.94211			0.235516
$69$	1.80054	−	4.44500i	0.216759	−	0.535116i
$70$	−4.55100			−0.543948
$71$	−3.97507	−	1.16719i	−0.471754	−	0.138520i	0.0372095	−	0.999307i	$-0.488153\pi$
$71$	−3.97507	−	1.16719i	−0.471754	−	0.138520i	−0.508964	+	0.860788i	$0.669971\pi$
$72$	0.654861	−	0.755750i	0.0771761	−	0.0890659i
$73$	−4.73896	−	3.04555i	−0.554654	−	0.356454i	0.233092	−	0.972455i	$-0.425116\pi$
$73$	−4.73896	−	3.04555i	−0.554654	−	0.356454i	−0.787746	+	0.616000i	$0.788752\pi$
$74$	−0.612262	+	4.25838i	−0.0711741	+	0.495026i
$75$	0.841254	−	0.540641i	0.0971396	−	0.0624278i
$76$	−2.07373	−	4.54083i	−0.237873	−	0.520869i
$77$	17.6959	+	20.4222i	2.01664	+	2.32732i
$78$	0.911665	+	6.34077i	0.103226	+	0.717951i
$79$	2.82179	−	6.17886i	0.317476	−	0.695177i	−0.681864	−	0.731479i	$-0.738831\pi$
$79$	2.82179	−	6.17886i	0.317476	−	0.695177i	0.999341	+	0.0363021i	$0.0115578\pi$
$80$	0.959493	−	0.281733i	0.107275	−	0.0314987i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	0.706713	−	1.54748i	0.0780433	−	0.170891i
$83$	1.06972	+	7.44010i	0.117417	+	0.816657i	0.960382	+	0.278687i	$0.0898993\pi$
$83$	1.06972	+	7.44010i	0.117417	+	0.816657i	−0.842964	+	0.537969i	$0.819192\pi$
$84$	2.98027	+	3.43941i	0.325174	+	0.375271i
$85$	−0.806784	−	1.76661i	−0.0875080	−	0.191616i
$86$	3.06859	−	1.97206i	0.330894	−	0.212653i
$87$	−0.816336	+	5.67774i	−0.0875204	+	0.608718i
$88$	−4.99510	−	3.21016i	−0.532480	−	0.342204i
$89$	−1.61061	+	1.85874i	−0.170724	+	0.197026i	−0.834663	−	0.550761i	$-0.814338\pi$
$89$	−1.61061	+	1.85874i	−0.170724	+	0.197026i	0.663940	+	0.747786i	$0.268883\pi$
$90$	−0.959493	−	0.281733i	−0.101139	−	0.0296972i
$91$	−29.1536			−3.05612
$92$	−4.65600	−	1.14962i	−0.485422	−	0.119856i
$93$	−2.98078			−0.309092
$94$	7.37771	+	2.16629i	0.760952	+	0.223436i
$95$	−3.26903	+	3.77266i	−0.335395	+	0.387066i
$96$	−0.841254	−	0.540641i	−0.0858601	−	0.0551789i
$97$	1.14642	−	7.97352i	0.116401	−	0.809588i	−0.845065	−	0.534664i	$-0.820438\pi$
$97$	1.14642	−	7.97352i	0.116401	−	0.809588i	0.961466	−	0.274924i	$-0.0886528\pi$
$98$	−11.5349	+	7.41303i	−1.16520	+	0.748829i
$99$	2.46661	+	5.40111i	0.247903	+	0.542832i
$100$	−0.654861	−	0.755750i	−0.0654861	−	0.0755750i
$101$	1.80977	+	12.5872i	0.180079	+	1.25248i	0.856572	+	0.516027i	$0.172590\pi$
$101$	1.80977	+	12.5872i	0.180079	+	1.25248i	−0.676493	+	0.736449i	$0.736501\pi$
$102$	−0.806784	+	1.76661i	−0.0798835	+	0.174920i
$103$	−11.9106	+	3.49728i	−1.17359	+	0.344597i	−0.809700	−	0.586845i	$-0.800370\pi$
$103$	−11.9106	+	3.49728i	−1.17359	+	0.344597i	−0.363890	+	0.931442i	$0.618552\pi$
$104$	6.14649	−	1.80477i	0.602713	−	0.176972i
$105$	1.89055	−	4.13973i	0.184499	−	0.403996i
$106$	1.11023	+	7.72180i	0.107835	+	0.750007i
$107$	4.64167	+	5.35677i	0.448727	+	0.517859i	0.934373	−	0.356297i	$-0.115961\pi$
$107$	4.64167	+	5.35677i	0.448727	+	0.517859i	−0.485646	+	0.874156i	$0.661415\pi$
$108$	0.415415	+	0.909632i	0.0399733	+	0.0875294i
$109$	−5.51311	+	3.54306i	−0.528060	+	0.339364i	−0.777353	−	0.629064i	$-0.783438\pi$
$109$	−5.51311	+	3.54306i	−0.528060	+	0.339364i	0.249293	+	0.968428i	$0.419802\pi$
$110$	−0.845021	+	5.87725i	−0.0805696	+	0.560374i
$111$	−3.61921	−	2.32593i	−0.343521	−	0.220767i
$112$	2.98027	−	3.43941i	0.281609	−	0.324994i
$113$	−16.1049	−	4.72883i	−1.51502	−	0.444851i	−0.584596	−	0.811325i	$-0.698747\pi$
$113$	−16.1049	−	4.72883i	−1.51502	−	0.444851i	−0.930428	+	0.366474i	$0.880565\pi$
$114$	4.99194			0.467538
$115$	0.888440	+	4.71282i	0.0828475	+	0.439473i
$116$	5.73613			0.532586
$117$	−6.14649	−	1.80477i	−0.568243	−	0.166851i
$118$	8.43168	−	9.73068i	0.776199	−	0.895782i
$119$	−7.43547	−	4.77848i	−0.681608	−	0.438043i
$120$	−0.142315	+	0.989821i	−0.0129915	+	0.0903579i
$121$	20.4056	−	13.1139i	1.85505	−	1.19217i
$122$	−4.94913	−	10.8371i	−0.448073	−	0.981143i
$123$	1.11406	+	1.28570i	0.100452	+	0.115927i
$124$	0.424209	+	2.95044i	0.0380951	+	0.264957i
$125$	−0.415415	+	0.909632i	−0.0371558	+	0.0813600i
$126$	−4.36665	+	1.28216i	−0.389012	+	0.114224i
$127$	4.78273	−	1.40433i	0.424398	−	0.124615i	−0.0625572	−	0.998041i	$-0.519926\pi$
$127$	4.78273	−	1.40433i	0.424398	−	0.124615i	0.486955	+	0.873427i	$0.338107\pi$
$128$	−0.415415	+	0.909632i	−0.0367178	+	0.0804009i
$129$	0.519113	+	3.61051i	0.0457053	+	0.317887i
$130$	−4.19502	−	4.84131i	−0.367928	−	0.424611i
$131$	−1.62719	−	3.56305i	−0.142168	−	0.311305i	0.825132	−	0.564941i	$-0.191101\pi$
$131$	−1.62719	−	3.56305i	−0.142168	−	0.311305i	−0.967300	+	0.253635i	$0.918374\pi$
$132$	4.99510	−	3.21016i	0.434768	−	0.279408i
$133$	−3.23315	+	22.4871i	−0.280350	+	1.94988i
$134$	8.43763	+	5.42253i	0.728900	+	0.468435i
$135$	0.654861	−	0.755750i	0.0563614	−	0.0650446i
$136$	1.86345	+	0.547157i	0.159789	+	0.0469183i
$137$	−1.43020			−0.122190			−0.0610952	−	0.998132i	$-0.519459\pi$
$137$	−1.43020			−0.122190			−0.0610952	+	0.998132i	$0.519459\pi$
$138$	2.97991	−	3.75768i	0.253667	−	0.319875i
$139$	6.63271			0.562579			0.281290	−	0.959623i	$-0.409238\pi$
$139$	6.63271			0.562579			0.281290	+	0.959623i	$0.409238\pi$
$140$	−4.36665	−	1.28216i	−0.369049	−	0.108363i
$141$	−5.03534	+	5.81109i	−0.424052	+	0.489382i
$142$	−3.48522	−	2.23981i	−0.292473	−	0.187961i
$143$	−5.41318	+	37.6495i	−0.452673	+	3.14841i
$144$	0.841254	−	0.540641i	0.0701045	−	0.0450534i
$145$	−2.38287	−	5.21776i	−0.197887	−	0.433312i
$146$	−3.68897	−	4.25730i	−0.305302	−	0.352337i
$147$	−1.95136	−	13.5720i	−0.160945	−	1.11940i
$148$	−1.78719	+	3.91339i	−0.146906	+	0.321679i
$149$	0.953265	−	0.279904i	0.0780945	−	0.0229306i	−0.242452	−	0.970163i	$-0.577952\pi$
$149$	0.953265	−	0.279904i	0.0780945	−	0.0229306i	0.320546	+	0.947233i	$0.396133\pi$
$150$	0.959493	−	0.281733i	0.0783423	−	0.0230034i
$151$	1.28686	−	2.81783i	0.104723	−	0.229311i	−0.850016	−	0.526758i	$-0.823408\pi$
$151$	1.28686	−	2.81783i	0.104723	−	0.229311i	0.954739	+	0.297446i	$0.0961349\pi$
$152$	−0.710427	−	4.94113i	−0.0576233	−	0.400779i
$153$	−1.27181	−	1.46775i	−0.102820	−	0.118661i
$154$	11.2255	+	24.5804i	0.904577	+	1.98075i
$155$	2.50759	−	1.61153i	0.201414	−	0.129441i
$156$	−0.911665	+	6.34077i	−0.0729916	+	0.507668i
$157$	16.5840	+	10.6579i	1.32355	+	0.850593i	0.995564	−	0.0940901i	$-0.0299942\pi$
$157$	16.5840	+	10.6579i	1.32355	+	0.850593i	0.327985	+	0.944683i	$0.393631\pi$
$158$	4.44828	−	5.13359i	0.353886	−	0.408406i
$159$	−7.48520	−	2.19785i	−0.593615	−	0.174301i
$160$	1.00000			0.0790569
$161$	14.9971	+	15.8573i	1.18194	+	1.24973i
$162$	−1.00000			−0.0785674
$163$	1.07416	+	0.315403i	0.0841349	+	0.0247042i	0.323529	−	0.946218i	$-0.395131\pi$
$163$	1.07416	+	0.315403i	0.0841349	+	0.0247042i	−0.239394	+	0.970922i	$0.576949\pi$
$164$	1.11406	−	1.28570i	0.0869937	−	0.100396i
$165$	−4.99510	−	3.21016i	−0.388868	−	0.249910i
$166$	−1.06972	+	7.44010i	−0.0830267	+	0.577463i
$167$	1.75940	−	1.13070i	0.136146	−	0.0874960i	−0.470795	−	0.882243i	$-0.656033\pi$
$167$	1.75940	−	1.13070i	0.136146	−	0.0874960i	0.606941	+	0.794747i	$0.292396\pi$
$168$	1.89055	+	4.13973i	0.145859	+	0.319387i
$169$	−18.3600	−	21.1886i	−1.41231	−	1.62989i
$170$	−0.276392	−	1.92235i	−0.0211983	−	0.147437i
$171$	−2.07373	+	4.54083i	−0.158582	+	0.347246i
$172$	3.49988	−	1.02766i	0.266863	−	0.0783582i
$173$	22.6881	−	6.66182i	1.72494	−	0.506489i	0.739019	−	0.673684i	$-0.235289\pi$
$173$	22.6881	−	6.66182i	1.72494	−	0.506489i	0.985924	+	0.167196i	$0.0534711\pi$
$174$	−2.38287	+	5.21776i	−0.180645	+	0.395558i
$175$	0.647674	+	4.50467i	0.0489596	+	0.340521i
$176$	−3.88836	−	4.48741i	−0.293096	−	0.338251i
$177$	5.34869	+	11.7120i	0.402032	+	0.880328i
$178$	−2.06903	+	1.32969i	−0.155080	+	0.0996641i
$179$	−0.562626	+	3.91315i	−0.0420527	+	0.292483i	0.957932	+	0.286994i	$0.0926561\pi$
$179$	−0.562626	+	3.91315i	−0.0420527	+	0.292483i	−0.999985	+	0.00548837i	$0.998253\pi$
$180$	−0.841254	−	0.540641i	−0.0627033	−	0.0402970i
$181$	4.80735	−	5.54797i	0.357327	−	0.412378i	−0.548415	−	0.836206i	$-0.684769\pi$
$181$	4.80735	−	5.54797i	0.357327	−	0.412378i	0.905742	+	0.423829i	$0.139314\pi$
$182$	−27.9726	−	8.21351i	−2.07347	−	0.608826i
$183$	11.9137			0.880686
$184$	−4.14352	−	2.41480i	−0.305464	−	0.178022i
$185$	4.30217			0.316302
$186$	−2.86003	−	0.839782i	−0.209708	−	0.0615758i
$187$	−7.55164	+	8.71506i	−0.552231	+	0.637308i
$188$	6.46854	+	4.15708i	0.471767	+	0.303186i
$189$	0.647674	−	4.50467i	0.0471114	−	0.327667i
$190$	−4.19949	+	2.69885i	−0.304663	+	0.195795i
$191$	−1.49763	−	3.27935i	−0.108365	−	0.237286i	0.847679	−	0.530509i	$-0.177999\pi$
$191$	−1.49763	−	3.27935i	−0.108365	−	0.237286i	−0.956044	+	0.293224i	$0.905272\pi$
$192$	−0.654861	−	0.755750i	−0.0472605	−	0.0545415i
$193$	−2.19477	−	15.2650i	−0.157983	−	1.09880i	−0.902343	−	0.431019i	$-0.858154\pi$
$193$	−2.19477	−	15.2650i	−0.157983	−	1.09880i	0.744360	−	0.667779i	$-0.232755\pi$
$194$	3.34638	−	7.32755i	0.240256	−	0.526088i
$195$	6.14649	−	1.80477i	0.440159	−	0.129242i
$196$	−13.1561	+	3.86299i	−0.939725	+	0.275928i
$197$	−4.57369	+	10.0150i	−0.325862	+	0.713538i	−0.999678	−	0.0253608i	$-0.991927\pi$
$197$	−4.57369	+	10.0150i	−0.325862	+	0.713538i	0.673817	+	0.738899i	$0.264654\pi$
$198$	0.845021	+	5.87725i	0.0600531	+	0.417678i
$199$	6.00922	+	6.93501i	0.425982	+	0.491610i	0.927650	−	0.373451i	$-0.121826\pi$
$199$	6.00922	+	6.93501i	0.425982	+	0.491610i	−0.501668	+	0.865060i	$0.667280\pi$
$200$	−0.415415	−	0.909632i	−0.0293743	−	0.0643207i
$201$	−8.43763	+	5.42253i	−0.595144	+	0.382476i
$202$	−1.80977	+	12.5872i	−0.127335	+	0.885635i
$203$	−21.9610	−	14.1135i	−1.54136	−	0.990572i
$204$	−1.27181	+	1.46775i	−0.0890448	+	0.102763i
$205$	−1.63231	−	0.479289i	−0.114005	−	0.0334750i
$206$	−12.4135			−0.864887
$207$	2.18021	+	4.27162i	0.151535	+	0.296898i
$208$	6.40597			0.444174
$209$	28.4399	+	8.35072i	1.96723	+	0.577631i
$210$	2.98027	−	3.43941i	0.205658	−	0.237342i
$211$	−0.826227	−	0.530984i	−0.0568798	−	0.0365544i	0.511892	−	0.859050i	$-0.328945\pi$
$211$	−0.826227	−	0.530984i	−0.0568798	−	0.0365544i	−0.568772	+	0.822495i	$0.692581\pi$
$212$	−1.11023	+	7.72180i	−0.0762507	+	0.530335i
$213$	3.48522	−	2.23981i	0.238803	−	0.153470i
$214$	2.94447	+	6.44749i	0.201280	+	0.440742i
$215$	−2.38869	−	2.75670i	−0.162908	−	0.188005i
$216$	0.142315	+	0.989821i	0.00968330	+	0.0673488i
$217$	5.63531	−	12.3396i	0.382550	−	0.837668i
$218$	−6.28799	+	1.84632i	−0.425876	+	0.125049i
$219$	5.40503	−	1.58706i	0.365238	−	0.107244i
$220$	−2.46661	+	5.40111i	−0.166299	+	0.364143i
$221$	−1.77056	−	12.3145i	−0.119101	−	0.828363i
$222$	−2.81732	−	3.25136i	−0.189086	−	0.218217i
$223$	−11.4278	−	25.0234i	−0.765262	−	1.67569i	−0.736814	−	0.676096i	$-0.763671\pi$
$223$	−11.4278	−	25.0234i	−0.765262	−	1.67569i	−0.0284486	−	0.999595i	$-0.509057\pi$
$224$	3.82854	−	2.46045i	0.255805	−	0.164396i
$225$	−0.142315	+	0.989821i	−0.00948766	+	0.0659881i
$226$	−14.1203	−	9.07456i	−0.939268	−	0.603631i
$227$	19.0681	−	22.0057i	1.26559	−	1.46057i	0.438272	−	0.898843i	$-0.355591\pi$
$227$	19.0681	−	22.0057i	1.26559	−	1.46057i	0.827321	−	0.561729i	$-0.189864\pi$
$228$	4.78973	+	1.40639i	0.317208	+	0.0931406i
$229$	−13.3632			−0.883062			−0.441531	−	0.897246i	$-0.645564\pi$
$229$	−13.3632			−0.883062			−0.441531	+	0.897246i	$0.645564\pi$
$230$	−0.475303	+	4.77222i	−0.0313405	+	0.314671i
$231$	−27.0224			−1.77794
$232$	5.50377	+	1.61605i	0.361340	+	0.106099i
$233$	7.67165	−	8.85356i	0.502587	−	0.580016i	−0.446598	−	0.894735i	$-0.647365\pi$
$233$	7.67165	−	8.85356i	0.502587	−	0.580016i	0.949185	+	0.314719i	$0.101910\pi$
$234$	−5.38905	−	3.46333i	−0.352293	−	0.226405i
$235$	1.09428	−	7.61091i	0.0713832	−	0.496481i
$236$	10.8316	−	6.96104i	0.705076	−	0.453125i
$237$	2.82179	+	6.17886i	0.183295	+	0.401360i
$238$	−5.78802	−	6.67973i	−0.375182	−	0.432983i
$239$	−0.431374	−	3.00027i	−0.0279033	−	0.194071i	0.971102	−	0.238665i	$-0.0767098\pi$
$239$	−0.431374	−	3.00027i	−0.0279033	−	0.194071i	−0.999005	+	0.0445936i	$0.985801\pi$
$240$	−0.415415	+	0.909632i	−0.0268149	+	0.0587165i
$241$	−1.73094	+	0.508249i	−0.111499	+	0.0327392i	−0.337006	−	0.941502i	$-0.609414\pi$
$241$	−1.73094	+	0.508249i	−0.111499	+	0.0327392i	0.225507	+	0.974242i	$0.427596\pi$
$242$	23.2736	−	6.83375i	1.49608	−	0.439290i
$243$	0.415415	−	0.909632i	0.0266489	−	0.0583529i
$244$	−1.69550	−	11.7924i	−0.108543	−	0.754933i
$245$	8.97916	+	10.3625i	0.573658	+	0.662036i
$246$	0.706713	+	1.54748i	0.0450583	+	0.0986640i
$247$	−26.9018	+	17.2887i	−1.71172	+	1.10006i
$248$	−0.424209	+	2.95044i	−0.0269373	+	0.187353i
$249$	−6.32337	−	4.06378i	−0.400727	−	0.257532i
$250$	−0.654861	+	0.755750i	−0.0414170	+	0.0477978i
$251$	−0.569867	−	0.167328i	−0.0359697	−	0.0105616i	0.263698	−	0.964605i	$-0.415058\pi$
$251$	−0.569867	−	0.167328i	−0.0359697	−	0.0105616i	−0.299668	+	0.954044i	$0.596876\pi$
$252$	−4.55100			−0.286686
$253$	23.2630	−	16.4232i	1.46253	−	1.03252i
$254$	4.98464			0.312764
$255$	1.86345	+	0.547157i	0.116693	+	0.0342643i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	23.5728	+	15.1493i	1.47043	+	0.944990i	0.997973	+	0.0636382i	$0.0202704\pi$
$257$	23.5728	+	15.1493i	1.47043	+	0.944990i	0.472460	+	0.881352i	$0.343366\pi$
$258$	−0.519113	+	3.61051i	−0.0323185	+	0.224780i
$259$	16.4710	−	10.5853i	1.02346	−	0.657738i
$260$	−2.66114	−	5.82708i	−0.165037	−	0.361380i
$261$	−3.75636	−	4.33507i	−0.232513	−	0.268334i
$262$	−0.557451	−	3.87715i	−0.0344394	−	0.239531i
$263$	5.13078	−	11.2348i	0.316377	−	0.692770i	−0.682911	−	0.730502i	$-0.739286\pi$
$263$	5.13078	−	11.2348i	0.316377	−	0.692770i	0.999288	+	0.0377322i	$0.0120134\pi$
$264$	5.69717	−	1.67284i	0.350637	−	0.102956i
$265$	7.48520	−	2.19785i	0.459812	−	0.135013i
$266$	−9.43752	+	20.6653i	−0.578652	+	1.26707i
$267$	−0.350018	−	2.43443i	−0.0214207	−	0.148985i
$268$	6.56814	+	7.58004i	0.401213	+	0.463024i
$269$	4.60590	+	10.0855i	0.280827	+	0.614925i	0.996508	−	0.0835028i	$-0.0266107\pi$
$269$	4.60590	+	10.0855i	0.280827	+	0.614925i	−0.715681	+	0.698427i	$0.753883\pi$
$270$	0.841254	−	0.540641i	0.0511971	−	0.0329024i
$271$	3.10224	−	21.5765i	0.188448	−	1.31068i	−0.647581	−	0.761996i	$-0.724219\pi$
$271$	3.10224	−	21.5765i	0.188448	−	1.31068i	0.836029	−	0.548685i	$-0.184872\pi$
$272$	1.63381	+	1.04999i	0.0990643	+	0.0636648i
$273$	19.0915	−	22.0328i	1.15547	−	1.33349i
$274$	−1.37227	−	0.402935i	−0.0829018	−	0.0243422i
$275$	5.93769			0.358056
$276$	3.91786	−	2.76593i	0.235828	−	0.166489i
$277$	1.59642			0.0959196			0.0479598	−	0.998849i	$-0.484728\pi$
$277$	1.59642			0.0959196			0.0479598	+	0.998849i	$0.484728\pi$
$278$	6.36404	+	1.86865i	0.381690	+	0.112074i
$279$	1.95199	−	2.25272i	0.116863	−	0.134867i
$280$	−3.82854	−	2.46045i	−0.228799	−	0.147040i
$281$	0.921450	−	6.40882i	0.0549691	−	0.382318i	−0.943703	−	0.330795i	$-0.892683\pi$
$281$	0.921450	−	6.40882i	0.0549691	−	0.382318i	0.998672	−	0.0515236i	$-0.0164077\pi$
$282$	−6.46854	+	4.15708i	−0.385196	+	0.247551i
$283$	8.13464	+	17.8124i	0.483554	+	1.05884i	0.981471	+	0.191611i	$0.0613711\pi$
$283$	8.13464	+	17.8124i	0.483554	+	1.05884i	−0.497917	+	0.867225i	$0.665902\pi$
$284$	−2.71301	−	3.13099i	−0.160988	−	0.185790i
$285$	−0.710427	−	4.94113i	−0.0420821	−	0.292687i
$286$	−15.8010	+	34.5994i	−0.934333	+	2.04590i
$287$	−7.42863	+	2.18124i	−0.438498	+	0.128755i
$288$	0.959493	−	0.281733i	0.0565387	−	0.0166013i
$289$	−5.49519	+	12.0328i	−0.323246	+	0.707811i
$290$	−0.816336	−	5.67774i	−0.0479369	−	0.333408i
$291$	5.27524	+	6.08795i	0.309240	+	0.356882i
$292$	−2.34012	−	5.12415i	−0.136945	−	0.299868i
$293$	−4.65107	+	2.98906i	−0.271719	+	0.174623i	−0.669403	−	0.742899i	$-0.733450\pi$
$293$	−4.65107	+	2.98906i	−0.271719	+	0.174623i	0.397685	+	0.917522i	$0.369814\pi$
$294$	1.95136	−	13.5720i	0.113806	−	0.791535i
$295$	−10.8316	−	6.96104i	−0.630640	−	0.405287i
$296$	−2.81732	+	3.25136i	−0.163753	+	0.188982i
$297$	−5.69717	−	1.67284i	−0.330583	−	0.0970680i
$298$	0.993509			0.0575524
$299$	−3.04478	+	30.5707i	−0.176084	+	1.76795i
$300$	1.00000			0.0577350
$301$	−15.9279	−	4.67686i	−0.918071	−	0.269570i
$302$	2.02860	−	2.34113i	0.116733	−	0.134717i
$303$	−10.6979	−	6.87515i	−0.614581	−	0.394967i
$304$	0.710427	−	4.94113i	0.0407458	−	0.283393i
$305$	−10.0224	+	6.44103i	−0.573883	+	0.368812i
$306$	−0.806784	−	1.76661i	−0.0461208	−	0.100990i
$307$	−4.83611	−	5.58117i	−0.276011	−	0.318534i	0.600771	−	0.799421i	$-0.294860\pi$
$307$	−4.83611	−	5.58117i	−0.276011	−	0.318534i	−0.876783	+	0.480887i	$0.840315\pi$
$308$	3.84569	+	26.7473i	0.219128	+	1.52407i
$309$	5.15674	−	11.2917i	0.293357	−	0.642362i
$310$	2.86003	−	0.839782i	0.162439	−	0.0476964i
$311$	−19.2911	+	5.66437i	−1.09390	+	0.321197i	−0.778425	−	0.627738i	$-0.783981\pi$
$311$	−19.2911	+	5.66437i	−1.09390	+	0.321197i	−0.315472	+	0.948935i	$0.602163\pi$
$312$	−2.66114	+	5.82708i	−0.150657	+	0.329893i
$313$	1.61337	+	11.2212i	0.0911931	+	0.634262i	0.983240	+	0.182318i	$0.0583601\pi$
$313$	1.61337	+	11.2212i	0.0911931	+	0.634262i	−0.892047	+	0.451944i	$0.850731\pi$
$314$	12.9096	+	14.8984i	0.728529	+	0.840767i
$315$	1.89055	+	4.13973i	0.106521	+	0.233247i
$316$	5.71439	−	3.67242i	0.321460	−	0.206589i
$317$	0.943543	−	6.56248i	0.0529946	−	0.368586i	−0.946016	−	0.324119i	$-0.894932\pi$
$317$	0.943543	−	6.56248i	0.0529946	−	0.368586i	0.999011	−	0.0444665i	$-0.0141588\pi$
$318$	−6.56279	−	4.21765i	−0.368023	−	0.236514i
$319$	−22.3041	+	25.7403i	−1.24879	+	1.44118i
$320$	0.959493	+	0.281733i	0.0536373	+	0.0157493i
$321$	−7.08802			−0.395615
$322$	9.92211	+	19.4401i	0.552938	+	1.08335i
$323$	−9.69492			−0.539440
$324$	−0.959493	−	0.281733i	−0.0533052	−	0.0156518i
$325$	−4.19502	+	4.84131i	−0.232698	+	0.268548i
$326$	0.941792	+	0.605253i	0.0521611	+	0.0335219i
$327$	0.932653	−	6.48674i	0.0515758	−	0.358718i
$328$	1.43116	−	0.919749i	0.0790225	−	0.0507847i
$329$	−14.5368	−	31.8311i	−0.801438	−	1.75491i
$330$	−3.88836	−	4.48741i	−0.214047	−	0.247024i
$331$	3.73700	+	25.9914i	0.205404	+	1.42862i	0.787911	+	0.615789i	$0.211163\pi$
$331$	3.73700	+	25.9914i	0.205404	+	1.42862i	−0.582507	+	0.812826i	$0.697928\pi$
$332$	−3.12251	+	6.83734i	−0.171370	+	0.375248i
$333$	4.12790	−	1.21206i	0.226208	−	0.0664205i
$334$	2.00669	−	0.589216i	0.109801	−	0.0322405i
$335$	4.16654	−	9.12345i	0.227642	−	0.498467i
$336$	0.647674	+	4.50467i	0.0353335	+	0.245750i
$337$	−21.7500	−	25.1008i	−1.18480	−	1.36733i	−0.914518	−	0.404546i	$-0.867430\pi$
$337$	−21.7500	−	25.1008i	−1.18480	−	1.36733i	−0.270279	−	0.962782i	$-0.587116\pi$
$338$	−11.6468	−	25.5029i	−0.633502	−	1.38718i
$339$	14.1203	−	9.07456i	0.766909	−	0.492863i
$340$	0.276392	−	1.92235i	0.0149894	−	0.104254i
$341$	−14.8893	−	9.56876i	−0.806300	−	0.518178i
$342$	−3.26903	+	3.77266i	−0.176769	+	0.204002i
$343$	29.3070	+	8.60531i	1.58243	+	0.464643i
$344$	3.64764			0.196667
$345$	−4.14352	−	2.41480i	−0.223079	−	0.130009i
$346$	23.6459			1.27121
$347$	−4.35767	−	1.27953i	−0.233932	−	0.0686887i	0.162665	−	0.986681i	$-0.447991\pi$
$347$	−4.35767	−	1.27953i	−0.233932	−	0.0686887i	−0.396597	+	0.917993i	$0.629809\pi$
$348$	−3.75636	+	4.33507i	−0.201362	+	0.232384i
$349$	19.6961	+	12.6579i	1.05431	+	0.677563i	0.948485	−	0.316822i	$-0.102616\pi$
$349$	19.6961	+	12.6579i	1.05431	+	0.677563i	0.105823	+	0.994385i	$0.466252\pi$
$350$	−0.647674	+	4.50467i	−0.0346196	+	0.240785i
$351$	5.38905	−	3.46333i	0.287646	−	0.184859i
$352$	−2.46661	−	5.40111i	−0.131471	−	0.287880i
$353$	−17.2619	−	19.9213i	−0.918757	−	1.06030i	−0.997985	−	0.0634457i	$-0.979791\pi$
$353$	−17.2619	−	19.9213i	−0.918757	−	1.06030i	0.0792282	−	0.996857i	$-0.474754\pi$
$354$	1.83238	+	12.7445i	0.0973899	+	0.677362i
$355$	−1.72102	+	3.76850i	−0.0913421	+	0.200011i
$356$	−2.35984	+	0.692910i	−0.125071	+	0.0367242i
$357$	8.48053	−	2.49011i	0.448837	−	0.131791i
$358$	−1.64230	+	3.59613i	−0.0867982	+	0.190061i
$359$	0.301256	+	2.09528i	0.0158997	+	0.110585i	0.996226	−	0.0868003i	$-0.0276642\pi$
$359$	0.301256	+	2.09528i	0.0158997	+	0.110585i	−0.980326	+	0.197385i	$0.936755\pi$
$360$	−0.654861	−	0.755750i	−0.0345142	−	0.0398315i
$361$	2.45904	+	5.38454i	0.129423	+	0.283397i
$362$	6.17566	−	3.96885i	0.324585	−	0.208598i
$363$	−3.45201	+	24.0093i	−0.181184	+	1.26016i
$364$	−24.5255	−	15.7616i	−1.28549	−	0.826133i
$365$	−3.68897	+	4.25730i	−0.193090	+	0.222837i
$366$	11.4311	+	3.35648i	0.597513	+	0.175446i
$367$	30.7746			1.60642			0.803210	−	0.595696i	$-0.203124\pi$
$367$	30.7746			1.60642			0.803210	+	0.595696i	$0.203124\pi$
$368$	−3.29535	−	3.48435i	−0.171782	−	0.181634i
$369$	−1.70122			−0.0885620
$370$	4.12790	+	1.21206i	0.214599	+	0.0630120i
$371$	23.2497	−	26.8316i	1.20706	−	1.39303i
$372$	−2.50759	−	1.61153i	−0.130012	−	0.0835539i
$373$	3.22322	−	22.4180i	0.166892	−	1.16076i	−0.718368	−	0.695663i	$-0.755111\pi$
$373$	3.22322	−	22.4180i	0.166892	−	1.16076i	0.885260	−	0.465096i	$-0.153980\pi$
$374$	−9.70106	+	6.23449i	−0.501630	+	0.322378i
$375$	−0.415415	−	0.909632i	−0.0214519	−	0.0469732i
$376$	5.03534	+	5.81109i	0.259678	+	0.299684i
$377$	−5.22943	−	36.3715i	−0.269329	−	1.87323i
$378$	1.89055	−	4.13973i	0.0972395	−	0.212925i
$379$	9.35445	−	2.74672i	0.480506	−	0.141089i	−0.0325045	−	0.999472i	$-0.510348\pi$
$379$	9.35445	−	2.74672i	0.480506	−	0.141089i	0.513011	+	0.858382i	$0.328530\pi$
$380$	−4.78973	+	1.40639i	−0.245708	+	0.0721464i
$381$	−2.07069	+	4.53419i	−0.106085	+	0.232293i
$382$	−0.513065	−	3.56845i	−0.0262507	−	0.182578i
$383$	22.5092	+	25.9770i	1.15017	+	1.32736i	0.936585	+	0.350439i	$0.113968\pi$
$383$	22.5092	+	25.9770i	1.15017	+	1.32736i	0.213582	+	0.976925i	$0.431487\pi$
$384$	−0.415415	−	0.909632i	−0.0211991	−	0.0464195i
$385$	22.7327	−	14.6094i	1.15857	−	0.744565i
$386$	2.19477	−	15.2650i	0.111711	−	0.776967i
$387$	−3.06859	−	1.97206i	−0.155985	−	0.100245i
$388$	5.27524	−	6.08795i	0.267810	−	0.309069i
$389$	10.0861	+	2.96156i	0.511388	+	0.150157i	0.527239	−	0.849717i	$-0.323227\pi$
$389$	10.0861	+	2.96156i	0.511388	+	0.150157i	−0.0158505	+	0.999874i	$0.505046\pi$
$390$	6.40597			0.324379
$391$	−5.78732	+	7.29784i	−0.292677	+	0.369068i
$392$	−13.7116			−0.692538
$393$	3.75836	+	1.10355i	0.189584	+	0.0556669i
$394$	−7.20997	+	8.32075i	−0.363233	+	0.419193i
$395$	−5.71439	−	3.67242i	−0.287522	−	0.184779i
$396$	−0.845021	+	5.87725i	−0.0424639	+	0.295343i
$397$	13.4419	−	8.63856i	0.674628	−	0.433557i	−0.157963	−	0.987445i	$-0.550493\pi$
$397$	13.4419	−	8.63856i	0.674628	−	0.433557i	0.832591	+	0.553888i	$0.186856\pi$
$398$	3.81198	+	8.34708i	0.191078	+	0.418401i
$399$	−14.8773	−	17.1693i	−0.744798	−	0.859542i
$400$	−0.142315	−	0.989821i	−0.00711574	−	0.0494911i
$401$	8.96039	−	19.6205i	0.447461	−	0.979802i	−0.542708	−	0.839922i	$-0.682601\pi$
$401$	8.96039	−	19.6205i	0.447461	−	0.979802i	0.990168	−	0.139881i	$-0.0446719\pi$
$402$	−9.62355	+	2.82573i	−0.479979	+	0.140935i
$403$	18.3213	−	5.37962i	0.912649	−	0.267978i
$404$	−5.28270	+	11.5675i	−0.262824	+	0.575504i
$405$	0.142315	+	0.989821i	0.00707168	+	0.0491846i
$406$	−17.0952	−	19.7289i	−0.848420	−	0.979129i
$407$	−10.6118	−	23.2365i	−0.526005	−	1.15179i
$408$	−1.63381	+	1.04999i	−0.0808857	+	0.0519821i
$409$	−4.09235	+	28.4629i	−0.202354	+	1.40740i	0.594921	+	0.803784i	$0.297183\pi$
$409$	−4.09235	+	28.4629i	−0.202354	+	1.40740i	−0.797275	+	0.603616i	$0.793726\pi$
$410$	−1.43116	−	0.919749i	−0.0706798	−	0.0454232i
$411$	0.936583	−	1.08087i	0.0461983	−	0.0533156i
$412$	−11.9106	−	3.49728i	−0.586795	−	0.172299i
$413$	−58.5965			−2.88335
$414$	0.888440	+	4.71282i	0.0436644	+	0.231622i
$415$	7.51660			0.368976
$416$	6.14649	+	1.80477i	0.301356	+	0.0884862i
$417$	−4.34350	+	5.01267i	−0.212702	+	0.245471i
$418$	24.9353	+	16.0249i	1.21962	+	0.783804i
$419$	1.50850	−	10.4919i	0.0736951	−	0.512561i	−0.919221	−	0.393742i	$-0.871180\pi$
$419$	1.50850	−	10.4919i	0.0736951	−	0.512561i	0.992916	−	0.118818i	$-0.0379106\pi$
$420$	3.82854	−	2.46045i	0.186814	−	0.120058i
$421$	−7.53415	−	16.4975i	−0.367192	−	0.804038i	−0.999568	−	0.0293769i	$-0.990648\pi$
$421$	−7.53415	−	16.4975i	−0.367192	−	0.804038i	0.632377	−	0.774661i	$-0.282080\pi$
$422$	−0.643164	−	0.742251i	−0.0313087	−	0.0361322i
$423$	−1.09428	−	7.61091i	−0.0532059	−	0.370055i
$424$	−3.24074	+	7.09623i	−0.157384	+	0.344623i
$425$	−1.86345	+	0.547157i	−0.0903904	+	0.0265410i
$426$	3.97507	−	1.16719i	0.192593	−	0.0565504i
$427$	−22.5235	+	49.3195i	−1.08999	+	2.38674i
$428$	1.00873	+	7.01588i	0.0487589	+	0.339125i
$429$	−24.9087	−	28.7462i	−1.20260	−	1.38788i
$430$	−1.51528	−	3.31801i	−0.0730734	−	0.160008i
$431$	19.6177	−	12.6075i	0.944951	−	0.607283i	0.0251565	−	0.999684i	$-0.491992\pi$
$431$	19.6177	−	12.6075i	0.944951	−	0.607283i	0.919795	+	0.392400i	$0.128355\pi$
$432$	−0.142315	+	0.989821i	−0.00684713	+	0.0476228i
$433$	34.0821	+	21.9033i	1.63788	+	1.05260i	0.942631	+	0.333837i	$0.108344\pi$
$433$	34.0821	+	21.9033i	1.63788	+	1.05260i	0.695252	+	0.718766i	$0.255293\pi$
$434$	8.88351	−	10.2521i	0.426422	−	0.492118i
$435$	5.50377	+	1.61605i	0.263886	+	0.0774838i
$436$	−6.55345			−0.313853
$437$	23.2425	+	5.73885i	1.11184	+	0.274526i
$438$	5.63322			0.269166
$439$	−17.1899	−	5.04740i	−0.820428	−	0.240899i	−0.155528	−	0.987832i	$-0.549708\pi$
$439$	−17.1899	−	5.04740i	−0.820428	−	0.240899i	−0.664900	+	0.746932i	$0.731526\pi$
$440$	−3.88836	+	4.48741i	−0.185370	+	0.213929i
$441$	11.5349	+	7.41303i	0.549281	+	0.353001i
$442$	1.77056	−	12.3145i	0.0842169	−	0.585741i
$443$	−1.65428	+	1.06314i	−0.0785970	+	0.0505112i	−0.579349	−	0.815080i	$-0.696693\pi$
$443$	−1.65428	+	1.06314i	−0.0785970	+	0.0505112i	0.500752	+	0.865591i	$0.333057\pi$
$444$	−1.78719	−	3.91339i	−0.0848161	−	0.185721i
$445$	1.61061	+	1.85874i	0.0763500	+	0.0881126i
$446$	−3.91499	−	27.2294i	−0.185380	−	1.28935i
$447$	−0.412719	+	0.903728i	−0.0195209	+	0.0427449i
$448$	4.36665	−	1.28216i	0.206305	−	0.0605765i
$449$	−39.0169	+	11.4564i	−1.84132	+	0.540660i	−0.841320	+	0.540538i	$0.818221\pi$
$449$	−39.0169	+	11.4564i	−1.84132	+	0.540660i	−1.00000		0.000122726i	$0.999961\pi$
$450$	−0.415415	+	0.909632i	−0.0195829	+	0.0428805i
$451$	1.43757	+	9.99850i	0.0676924	+	0.470811i
$452$	−10.9917	−	12.6851i	−0.517007	−	0.596658i
$453$	1.28686	+	2.81783i	0.0604619	+	0.132393i
$454$	24.4954	−	15.7422i	1.14963	−	0.738820i
$455$	−4.14898	+	28.8568i	−0.194507	+	1.35283i
$456$	4.19949	+	2.69885i	0.196659	+	0.126385i
$457$	21.1225	−	24.3766i	0.988067	−	1.14029i	−0.00204265	−	0.999998i	$-0.500650\pi$
$457$	21.1225	−	24.3766i	0.988067	−	1.14029i	0.990110	−	0.140293i	$-0.0448044\pi$
$458$	−12.8218	−	3.76483i	−0.599126	−	0.175919i
$459$	1.94211			0.0906502
$460$	−1.80054	+	4.44500i	−0.0839506	+	0.207249i
$461$	−3.75318			−0.174803			−0.0874016	−	0.996173i	$-0.527856\pi$
$461$	−3.75318			−0.174803			−0.0874016	+	0.996173i	$0.527856\pi$
$462$	−25.9278	−	7.61309i	−1.20627	−	0.354193i
$463$	5.21854	−	6.02252i	0.242526	−	0.279890i	−0.621416	−	0.783480i	$-0.713442\pi$
$463$	5.21854	−	6.02252i	0.242526	−	0.279890i	0.863943	+	0.503590i	$0.167988\pi$
$464$	4.82554	+	3.10118i	0.224020	+	0.143969i
$465$	−0.424209	+	2.95044i	−0.0196722	+	0.136823i
$466$	9.85523	−	6.33357i	0.456535	−	0.293397i
$467$	2.07108	+	4.53503i	0.0958382	+	0.209856i	0.951479	−	0.307714i	$-0.0995639\pi$
$467$	2.07108	+	4.53503i	0.0958382	+	0.209856i	−0.855641	+	0.517570i	$0.826837\pi$
$468$	−4.19502	−	4.84131i	−0.193915	−	0.223790i
$469$	−6.49606	−	45.1811i	−0.299960	−	2.08627i
$470$	3.19420	−	6.99432i	0.147337	−	0.322624i
$471$	−18.9149	+	5.55392i	−0.871554	+	0.255911i
$472$	12.3540	−	3.62746i	0.568638	−	0.166967i
$473$	−8.99728	+	19.7013i	−0.413695	+	0.905866i
$474$	0.966703	+	6.72357i	0.0444021	+	0.308824i
$475$	3.26903	+	3.77266i	0.149993	+	0.173101i
$476$	−3.67167	−	8.03983i	−0.168291	−	0.368505i
$477$	6.56279	−	4.21765i	0.300490	−	0.193113i
$478$	0.431374	−	3.00027i	0.0197306	−	0.137229i
$479$	−3.98716	−	2.56239i	−0.182178	−	0.117079i	0.446373	−	0.894847i	$-0.352715\pi$
$479$	−3.98716	−	2.56239i	−0.182178	−	0.117079i	−0.628551	+	0.777768i	$0.716352\pi$
$480$	−0.654861	+	0.755750i	−0.0298902	+	0.0344951i
$481$	26.4432	+	7.76443i	1.20571	+	0.354028i
$482$	−1.80401			−0.0821705
$483$	−21.8051	+	0.949760i	−0.992168	+	0.0432156i
$484$	24.2562			1.10255
$485$	−7.72921	−	2.26950i	−0.350965	−	0.103053i
$486$	0.654861	−	0.755750i	0.0297051	−	0.0342815i
$487$	−6.35967	−	4.08711i	−0.288184	−	0.185205i	0.388559	−	0.921424i	$-0.372973\pi$
$487$	−6.35967	−	4.08711i	−0.288184	−	0.185205i	−0.676743	+	0.736219i	$0.736609\pi$
$488$	1.69550	−	11.7924i	0.0767515	−	0.533818i
$489$	−0.941792	+	0.605253i	−0.0425893	+	0.0273705i
$490$	5.69599	+	12.4725i	0.257318	+	0.563449i
$491$	−3.18022	−	3.67017i	−0.143521	−	0.165633i	0.679438	−	0.733733i	$-0.262224\pi$
$491$	−3.18022	−	3.67017i	−0.143521	−	0.165633i	−0.822959	+	0.568101i	$0.807678\pi$
$492$	0.242109	+	1.68390i	0.0109151	+	0.0759163i
$493$	4.62781	−	10.1335i	0.208426	−	0.456390i
$494$	−30.6829	+	9.00931i	−1.38049	+	0.405348i
$495$	5.69717	−	1.67284i	0.256069	−	0.0751886i
$496$	−1.23826	+	2.71141i	−0.0555995	+	0.121746i
$497$	2.68324	+	18.6624i	0.120360	+	0.837121i
$498$	−4.92233	−	5.68067i	−0.220575	−	0.254557i
$499$	10.3140	+	22.5845i	0.461719	+	1.01102i	0.987092	+	0.160151i	$0.0511982\pi$
$499$	10.3140	+	22.5845i	0.461719	+	1.01102i	−0.525374	+	0.850872i	$0.676075\pi$
$500$	−0.841254	+	0.540641i	−0.0376220	+	0.0241782i
$501$	−0.297638	+	2.07011i	−0.0132975	+	0.0924859i
$502$	−0.499641	−	0.321100i	−0.0223001	−	0.0143314i
$503$	9.78571	−	11.2933i	0.436323	−	0.503544i	−0.494417	−	0.869225i	$-0.664618\pi$
$503$	9.78571	−	11.2933i	0.436323	−	0.503544i	0.930740	+	0.365681i	$0.119164\pi$
$504$	−4.36665	−	1.28216i	−0.194506	−	0.0571121i
$505$	12.7167			0.565884
$506$	26.9477	−	9.20402i	1.19797	−	0.409169i
$507$	28.0365			1.24514
$508$	4.78273	+	1.40433i	0.212199	+	0.0623073i
$509$	−18.8341	+	21.7357i	−0.834807	+	0.963419i	−0.999738	−	0.0228861i	$-0.992714\pi$
$509$	−18.8341	+	21.7357i	−0.834807	+	0.963419i	0.164931	+	0.986305i	$0.447260\pi$
$510$	1.63381	+	1.04999i	0.0723464	+	0.0464942i
$511$	−3.64849	+	25.3758i	−0.161400	+	1.12256i
$512$	−0.841254	+	0.540641i	−0.0371785	+	0.0238932i
$513$	−2.07373	−	4.54083i	−0.0915573	−	0.200483i
$514$	18.3499	+	21.1769i	0.809380	+	0.934074i
$515$	1.76662	+	12.2871i	0.0778466	+	0.541435i
$516$	−1.51528	+	3.31801i	−0.0667066	+	0.146067i
$517$	−43.8065	+	12.8628i	−1.92661	+	0.565703i
$518$	18.7861	−	5.51608i	0.825412	−	0.242363i
$519$	−9.82286	+	21.5091i	−0.431176	+	0.944143i
$520$	−0.911665	−	6.34077i	−0.0399792	−	0.278061i
$521$	8.70916	+	10.0509i	0.381555	+	0.440338i	0.913746	−	0.406286i	$-0.133176\pi$
$521$	8.70916	+	10.0509i	0.381555	+	0.440338i	−0.532190	+	0.846625i	$0.678631\pi$
$522$	−2.38287	−	5.21776i	−0.104296	−	0.228375i
$523$	23.3930	−	15.0338i	1.02290	−	0.657381i	0.0822030	−	0.996616i	$-0.473804\pi$
$523$	23.3930	−	15.0338i	1.02290	−	0.657381i	0.940702	+	0.339235i	$0.110168\pi$
$524$	0.557451	−	3.87715i	0.0243523	−	0.169374i
$525$	−3.82854	−	2.46045i	−0.167091	−	0.107383i
$526$	8.08817	−	9.33424i	0.352661	−	0.406992i
$527$	5.55452	+	1.63095i	0.241958	+	0.0710454i
$528$	5.93769			0.258405
$529$	18.1944	−	14.0700i	0.791060	−	0.611739i
$530$	7.80120			0.338863
$531$	−12.3540	−	3.62746i	−0.536117	−	0.157418i
$532$	−14.8773	+	17.1693i	−0.645014	+	0.744385i
$533$	−9.16796	−	5.89189i	−0.397108	−	0.255206i
$534$	0.350018	−	2.43443i	0.0151468	−	0.105348i
$535$	5.96283	−	3.83208i	0.257795	−	0.165675i
$536$	4.16654	+	9.12345i	0.179967	+	0.394073i
$537$	−2.58892	−	2.98777i	−0.111720	−	0.128932i
$538$	1.57791	+	10.9746i	0.0680286	+	0.473149i
$539$	33.8210	−	74.0577i	1.45677	−	3.18989i
$540$	0.959493	−	0.281733i	0.0412900	−	0.0121238i
$541$	12.6101	−	3.70265i	0.542150	−	0.159190i	0.000819644	−	1.00000i	$-0.499739\pi$
$541$	12.6101	−	3.70265i	0.542150	−	0.159190i	0.541330	+	0.840810i	$0.317921\pi$
$542$	9.05539	−	19.8285i	0.388962	−	0.851709i
$543$	1.04474	+	7.26630i	0.0448339	+	0.311827i
$544$	1.27181	+	1.46775i	0.0545286	+	0.0629294i
$545$	2.72240	+	5.96123i	0.116615	+	0.255351i
$546$	24.5255	−	15.7616i	1.04960	−	0.674534i
$547$	3.08035	−	21.4243i	0.131706	−	0.916036i	−0.811624	−	0.584180i	$-0.801416\pi$
$547$	3.08035	−	21.4243i	0.131706	−	0.916036i	0.943330	−	0.331856i	$-0.107675\pi$
$548$	−1.20316	−	0.773226i	−0.0513966	−	0.0330306i
$549$	−7.80181	+	9.00377i	−0.332973	+	0.384272i
$550$	5.69717	+	1.67284i	0.242928	+	0.0713302i
$551$	−28.6344			−1.21987
$552$	4.53841	−	1.55010i	0.193168	−	0.0659767i
$553$	−30.9136			−1.31458
$554$	1.53175	+	0.449764i	0.0650780	+	0.0191086i
$555$	−2.81732	+	3.25136i	−0.119589	+	0.138013i
$556$	5.57979	+	3.58591i	0.236636	+	0.152077i
$557$	−1.83833	+	12.7859i	−0.0778927	+	0.541756i	0.913089	+	0.407760i	$0.133690\pi$
$557$	−1.83833	+	12.7859i	−0.0778927	+	0.541756i	−0.990982	+	0.133996i	$0.957219\pi$
$558$	2.50759	−	1.61153i	0.106155	−	0.0682215i
$559$	−9.70686	−	21.2551i	−0.410556	−	0.898993i
$560$	−2.98027	−	3.43941i	−0.125939	−	0.145342i
$561$	−1.64113	−	11.4143i	−0.0692885	−	0.481912i
$562$	2.68970	−	5.88962i	0.113458	−	0.248439i
$563$	−36.7370	+	10.7870i	−1.54828	+	0.454616i	−0.940586	−	0.339556i	$-0.889723\pi$
$563$	−36.7370	+	10.7870i	−1.54828	+	0.454616i	−0.607694	+	0.794172i	$0.707905\pi$
$564$	−7.37771	+	2.16629i	−0.310657	+	0.0912173i
$565$	−6.97267	+	15.2680i	−0.293342	+	0.642330i
$566$	2.78680	+	19.3826i	0.117138	+	0.814713i
$567$	2.98027	+	3.43941i	0.125159	+	0.144442i
$568$	−1.72102	−	3.76850i	−0.0722123	−	0.158123i
$569$	3.08480	−	1.98248i	0.129322	−	0.0831099i	−0.474381	−	0.880320i	$-0.657328\pi$
$569$	3.08480	−	1.98248i	0.129322	−	0.0831099i	0.603702	+	0.797210i	$0.293692\pi$
$570$	0.710427	−	4.94113i	0.0297565	−	0.206961i
$571$	32.5487	+	20.9178i	1.36212	+	0.875382i	0.998423	−	0.0561355i	$-0.0178779\pi$
$571$	32.5487	+	20.9178i	1.36212	+	0.875382i	0.363697	+	0.931517i	$0.381514\pi$
$572$	−24.9087	+	28.7462i	−1.04149	+	1.20194i
$573$	3.45911	+	1.01569i	0.144506	+	0.0424309i
$574$	−7.74225			−0.323155
$575$	4.79129	−	0.208693i	0.199811	−	0.00870309i
$576$	1.00000			0.0416667
$577$	−6.87781	−	2.01951i	−0.286327	−	0.0840732i	0.135415	−	0.990789i	$-0.456763\pi$
$577$	−6.87781	−	2.01951i	−0.286327	−	0.0840732i	−0.421742	+	0.906716i	$0.638581\pi$
$578$	−8.66262	+	9.99720i	−0.360318	+	0.415829i
$579$	12.9738	+	8.33774i	0.539172	+	0.346505i
$580$	0.816336	−	5.67774i	0.0338965	−	0.235755i
$581$	28.7776	−	18.4943i	1.19390	−	0.767271i
$582$	3.34638	+	7.32755i	0.138712	+	0.303737i
$583$	−30.3339	−	35.0072i	−1.25630	−	1.44985i
$584$	−0.801690	−	5.57588i	−0.0331742	−	0.230732i
$585$	−2.66114	+	5.82708i	−0.110025	+	0.240920i
$586$	−5.30479	+	1.55763i	−0.219139	+	0.0643450i
$587$	18.8936	−	5.54766i	0.779822	−	0.228976i	0.132490	−	0.991184i	$-0.457703\pi$
$587$	18.8936	−	5.54766i	0.779822	−	0.228976i	0.647332	+	0.762208i	$0.275885\pi$
$588$	5.69599	−	12.4725i	0.234899	−	0.514356i
$589$	−2.11763	−	14.7284i	−0.0872552	−	0.606873i
$590$	−8.43168	−	9.73068i	−0.347127	−	0.400606i
$591$	−4.57369	−	10.0150i	−0.188136	−	0.411961i
$592$	−3.61921	+	2.32593i	−0.148749	+	0.0955950i
$593$	−3.26656	+	22.7195i	−0.134142	+	0.932976i	0.805933	+	0.592007i	$0.201664\pi$
$593$	−3.26656	+	22.7195i	−0.134142	+	0.932976i	−0.940075	+	0.340969i	$0.889245\pi$
$594$	−4.99510	−	3.21016i	−0.204952	−	0.131714i
$595$	−5.78802	+	6.67973i	−0.237286	+	0.273842i
$596$	0.953265	+	0.279904i	0.0390473	+	0.0114653i
$597$	−9.17633			−0.375562
$598$	−11.5342	+	28.4746i	−0.471669	+	1.16441i
$599$	−42.9487			−1.75484			−0.877418	−	0.479727i	$-0.840736\pi$
$599$	−42.9487			−1.75484			−0.877418	+	0.479727i	$0.840736\pi$
$600$	0.959493	+	0.281733i	0.0391711	+	0.0115017i
$601$	−30.6822	+	35.4091i	−1.25155	+	1.44437i	−0.403048	+	0.915179i	$0.632049\pi$
$601$	−30.6822	+	35.4091i	−1.25155	+	1.44437i	−0.848504	+	0.529189i	$0.822496\pi$
$602$	−13.9651	−	8.97484i	−0.569176	−	0.365787i
$603$	1.42739	−	9.92774i	0.0581279	−	0.404289i
$604$	2.60601	−	1.67478i	0.106037	−	0.0681457i
$605$	−10.0764	−	22.0642i	−0.409663	−	0.897036i
$606$	−8.32765	−	9.61062i	−0.338288	−	0.390405i
$607$	4.83373	+	33.6193i	0.196195	+	1.36457i	0.815200	+	0.579179i	$0.196627\pi$
$607$	4.83373	+	33.6193i	0.196195	+	1.36457i	−0.619005	+	0.785387i	$0.712464\pi$
$608$	2.07373	−	4.54083i	0.0841007	−	0.184155i
$609$	25.0476	−	7.35465i	1.01498	−	0.298025i
$610$	−11.4311	+	3.35648i	−0.462832	+	0.135900i
$611$	20.4619	−	44.8054i	0.827802	−	1.81263i
$612$	−0.276392	−	1.92235i	−0.0111725	−	0.0777063i
$613$	−2.99099	−	3.45179i	−0.120805	−	0.139416i	0.692125	−	0.721777i	$-0.256675\pi$
$613$	−2.99099	−	3.45179i	−0.120805	−	0.139416i	−0.812930	+	0.582361i	$0.802129\pi$
$614$	−3.06782	−	6.71758i	−0.123807	−	0.271100i
$615$	1.43116	−	0.919749i	0.0577099	−	0.0370879i
$616$	−3.84569	+	26.7473i	−0.154947	+	1.07768i
$617$	−1.45844	−	0.937285i	−0.0587147	−	0.0377337i	0.510954	−	0.859608i	$-0.329292\pi$
$617$	−1.45844	−	0.937285i	−0.0587147	−	0.0377337i	−0.569669	+	0.821874i	$0.692929\pi$
$618$	8.12909	−	9.38147i	0.327000	−	0.377378i
$619$	−38.4836	−	11.2998i	−1.54679	−	0.454177i	−0.606648	−	0.794971i	$-0.707486\pi$
$619$	−38.4836	−	11.2998i	−1.54679	−	0.454177i	−0.940138	+	0.340793i	$0.889304\pi$
$620$	2.98078			0.119711
$621$	−4.65600	−	1.14962i	−0.186839	−	0.0461328i
$622$	−20.1055			−0.806157
$623$	10.7396	+	3.15343i	0.430273	+	0.126340i
$624$	−4.19502	+	4.84131i	−0.167935	+	0.193808i
$625$	0.841254	+	0.540641i	0.0336501	+	0.0216256i
$626$	−1.61337	+	11.2212i	−0.0644832	+	0.448491i
$627$	−24.9353	+	16.0249i	−0.995818	+	0.639973i
$628$	8.18927	+	17.9320i	0.326787	+	0.715564i
$629$	5.47156	+	6.31452i	0.218165	+	0.251776i
$630$	0.647674	+	4.50467i	0.0258040	+	0.179470i
$631$	2.89020	−	6.32866i	0.115057	−	0.251940i	−0.843339	−	0.537382i	$-0.819413\pi$
$631$	2.89020	−	6.32866i	0.115057	−	0.251940i	0.958396	+	0.285442i	$0.0921405\pi$
$632$	6.51756	−	1.91373i	0.259254	−	0.0761240i
$633$	0.942355	−	0.276700i	0.0374552	−	0.0109978i
$634$	2.75419	−	6.03083i	0.109383	−	0.239515i
$635$	−0.709388	−	4.93390i	−0.0281512	−	0.195796i
$636$	−5.10870	−	5.89576i	−0.202573	−	0.233782i
$637$	36.4883	+	79.8983i	1.44572	+	3.16569i
$638$	−28.6525	+	18.4139i	−1.13436	+	0.729012i
$639$	−0.589594	+	4.10072i	−0.0233240	+	0.162222i
$640$	0.841254	+	0.540641i	0.0332535	+	0.0213707i
$641$	−29.2175	+	33.7188i	−1.15402	+	1.33181i	−0.219623	+	0.975585i	$0.570483\pi$
$641$	−29.2175	+	33.7188i	−1.15402	+	1.33181i	−0.934399	+	0.356228i	$0.884063\pi$
$642$	−6.80091	−	1.99693i	−0.268411	−	0.0788124i
$643$	−12.3957			−0.488837			−0.244419	−	0.969670i	$-0.578597\pi$
$643$	−12.3957			−0.488837			−0.244419	+	0.969670i	$0.578597\pi$
$644$	4.04329	+	21.4480i	0.159328	+	0.845170i
$645$	3.64764			0.143626
$646$	−9.30221	−	2.73138i	−0.365991	−	0.107465i
$647$	−6.03490	+	6.96465i	−0.237257	+	0.273809i	−0.861874	−	0.507122i	$-0.830709\pi$
$647$	−6.03490	+	6.96465i	−0.237257	+	0.273809i	0.624618	+	0.780931i	$0.285255\pi$
$648$	−0.841254	−	0.540641i	−0.0330476	−	0.0212384i
$649$	−10.8801	+	75.6728i	−0.427081	+	2.97042i
$650$	−5.38905	+	3.46333i	−0.211376	+	0.135843i
$651$	5.63531	+	12.3396i	0.220865	+	0.483628i
$652$	0.733124	+	0.846070i	0.0287113	+	0.0331347i
$653$	3.82815	+	26.6254i	0.149807	+	1.04193i	0.916534	+	0.399957i	$0.130975\pi$
$653$	3.82815	+	26.6254i	0.149807	+	1.04193i	−0.766727	+	0.641973i	$0.778116\pi$
$654$	2.72240	−	5.96123i	0.106454	−	0.233102i
$655$	−3.75836	+	1.10355i	−0.146851	+	0.0431194i
$656$	1.63231	−	0.479289i	0.0637310	−	0.0187131i
$657$	−2.34012	+	5.12415i	−0.0912969	+	0.199912i
$658$	−4.98008	−	34.6372i	−0.194144	−	1.35030i
$659$	−9.67453	−	11.1650i	−0.376866	−	0.434927i	0.535354	−	0.844628i	$-0.320178\pi$
$659$	−9.67453	−	11.1650i	−0.376866	−	0.434927i	−0.912220	+	0.409701i	$0.865633\pi$
$660$	−2.46661	−	5.40111i	−0.0960125	−	0.210238i
$661$	5.31680	−	3.41690i	0.206799	−	0.132902i	−0.433142	−	0.901326i	$-0.642595\pi$
$661$	5.31680	−	3.41690i	0.206799	−	0.132902i	0.639941	+	0.768424i	$0.278959\pi$
$662$	−3.73700	+	25.9914i	−0.145242	+	1.01018i
$663$	10.4662	+	6.72619i	0.406472	+	0.261223i
$664$	−4.92233	+	5.68067i	−0.191023	+	0.220453i
$665$	21.7980	+	6.40048i	0.845292	+	0.248200i
$666$	4.30217			0.166706
$667$	−17.0931	+	21.5545i	−0.661848	+	0.834594i
$668$	2.09140			0.0809188
$669$	26.3950	+	7.75028i	1.02049	+	0.299643i
$670$	6.56814	−	7.58004i	0.253749	−	0.292842i
$671$	59.5101	+	38.2448i	2.29736	+	1.47643i
$672$	−0.647674	+	4.50467i	−0.0249846	+	0.173772i
$673$	−12.6473	+	8.12793i	−0.487518	+	0.313309i	−0.761206	−	0.648510i	$-0.775393\pi$
$673$	−12.6473	+	8.12793i	−0.487518	+	0.313309i	0.273689	+	0.961818i	$0.411756\pi$
$674$	−13.7972	−	30.2117i	−0.531449	−	1.16371i
$675$	−0.654861	−	0.755750i	−0.0252056	−	0.0290888i
$676$	−3.99001	−	27.7511i	−0.153462	−	1.06735i
$677$	−3.12895	+	6.85144i	−0.120255	+	0.263322i	−0.960181	−	0.279379i	$-0.909871\pi$
$677$	−3.12895	+	6.85144i	−0.120255	+	0.263322i	0.839926	+	0.542702i	$0.182599\pi$
$678$	16.1049	−	4.72883i	0.618506	−	0.181610i
$679$	−35.1756	+	10.3285i	−1.34992	+	0.396371i
$680$	0.806784	−	1.76661i	0.0309387	−	0.0677464i
$681$	4.14389	+	28.8214i	0.158794	+	1.10444i
$682$	−11.5903	−	13.3760i	−0.443817	−	0.512192i
$683$	4.24399	+	9.29305i	0.162392	+	0.355589i	0.973283	−	0.229608i	$-0.0737445\pi$
$683$	4.24399	+	9.29305i	0.162392	+	0.355589i	−0.810891	+	0.585197i	$0.801017\pi$
$684$	−4.19949	+	2.69885i	−0.160571	+	0.103193i
$685$	−0.203539	+	1.41565i	−0.00777683	+	0.0540890i
$686$	25.6955	+	16.5135i	0.981058	+	0.630487i
$687$	8.75100	−	10.0992i	0.333872	−	0.385308i
$688$	3.49988	+	1.02766i	0.133432	+	0.0391791i
$689$	49.9743			1.90387
$690$	−3.29535	−	3.48435i	−0.125452	−	0.132647i
$691$	−16.3151			−0.620656			−0.310328	−	0.950630i	$-0.600439\pi$
$691$	−16.3151			−0.620656			−0.310328	+	0.950630i	$0.600439\pi$
$692$	22.6881	+	6.66182i	0.862471	+	0.253244i
$693$	17.6959	−	20.4222i	0.672212	−	0.775774i
$694$	−3.82067	−	2.45540i	−0.145031	−	0.0932056i
$695$	0.943933	−	6.56520i	0.0358054	−	0.249032i
$696$	−4.82554	+	3.10118i	−0.182911	+	0.117550i
$697$	−1.37252	−	3.00539i	−0.0519878	−	0.113837i
$698$	15.3321	+	17.6942i	0.580330	+	0.669736i
$699$	1.66721	+	11.5957i	0.0630597	+	0.438590i
$700$	−1.89055	+	4.13973i	−0.0714561	+	0.156467i
$701$	−13.0232	+	3.82396i	−0.491880	+	0.144429i	−0.518260	−	0.855223i	$-0.673420\pi$
$701$	−13.0232	+	3.82396i	−0.491880	+	0.144429i	0.0263803	+	0.999652i	$0.491602\pi$
$702$	6.14649	−	1.80477i	0.231984	−	0.0681167i
$703$	8.92152	−	19.5354i	0.336482	−	0.736792i
$704$	−0.845021	−	5.87725i	−0.0318479	−	0.221507i
$705$	5.03534	+	5.81109i	0.189642	+	0.218858i
$706$	−10.9502	−	23.9776i	−0.412115	−	0.902407i
$707$	48.6863	−	31.2888i	1.83104	−	1.17674i
$708$	−1.83238	+	12.7445i	−0.0688651	+	0.478967i
$709$	33.4608	+	21.5039i	1.25665	+	0.807598i	0.987822	−	0.155591i	$-0.0497283\pi$
$709$	33.4608	+	21.5039i	1.25665	+	0.807598i	0.268825	+	0.963189i	$0.413365\pi$
$710$	−2.71301	+	3.13099i	−0.101818	+	0.117504i
$711$	−6.51756	−	1.91373i	−0.244427	−	0.0717704i
$712$	−2.45946			−0.0921722
$713$	−12.3509	−	7.19799i	−0.462545	−	0.269567i
$714$	8.83856			0.330775
$715$	36.4959	+	10.7162i	1.36487	+	0.400762i
$716$	−2.58892	+	2.98777i	−0.0967525	+	0.111658i
$717$	2.54994	+	1.63875i	0.0952294	+	0.0612002i
$718$	−0.301256	+	2.09528i	−0.0112428	+	0.0781951i
$719$	−33.6430	+	21.6210i	−1.25467	+	0.806329i	−0.987546	−	0.157333i	$-0.949710\pi$
$719$	−33.6430	+	21.6210i	−1.25467	+	0.806329i	−0.267126	+	0.963662i	$0.586074\pi$
$720$	−0.415415	−	0.909632i	−0.0154816	−	0.0339000i
$721$	36.9955	+	42.6950i	1.37778	+	1.59005i
$722$	0.842429	+	5.85922i	0.0313520	+	0.218058i
$723$	0.749414	−	1.64099i	0.0278710	−	0.0610290i
$724$	7.04366	−	2.06820i	0.261775	−	0.0768642i
$725$	−5.50377	+	1.61605i	−0.204405	+	0.0600187i
$726$	−10.0764	+	22.0642i	−0.373969	+	0.818878i
$727$	5.98687	+	41.6396i	0.222041	+	1.54433i	0.730302	+	0.683125i	$0.239379\pi$
$727$	5.98687	+	41.6396i	0.222041	+	1.54433i	−0.508261	+	0.861203i	$0.669711\pi$
$728$	−19.0915	−	22.0328i	−0.707579	−	0.816590i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	−4.73896	+	3.04555i	−0.175397	+	0.112721i
$731$	1.00818	−	7.01202i	0.0372888	−	0.259349i
$732$	10.0224	+	6.44103i	0.370440	+	0.238067i
$733$	27.4166	−	31.6404i	1.01266	−	1.16867i	0.0270445	−	0.999634i	$-0.491390\pi$
$733$	27.4166	−	31.6404i	1.01266	−	1.16867i	0.985611	−	0.169032i	$-0.0540641\pi$
$734$	29.5280	+	8.67020i	1.08990	+	0.320023i
$735$	−13.7116			−0.505758
$736$	−2.18021	−	4.27162i	−0.0803635	−	0.157454i
$737$	−59.5540			−2.19370
$738$	−1.63231	−	0.479289i	−0.0600861	−	0.0176429i
$739$	−15.6844	+	18.1007i	−0.576959	+	0.665847i	−0.966948	−	0.254973i	$-0.917933\pi$
$739$	−15.6844	+	18.1007i	−0.576959	+	0.665847i	0.389989	+	0.920820i	$0.372479\pi$
$740$	3.61921	+	2.32593i	0.133045	+	0.0855028i
$741$	4.55098	−	31.6528i	0.167184	−	1.16279i
$742$	29.8672	−	19.1945i	1.09646	−	0.704652i
$743$	6.02264	+	13.1877i	0.220949	+	0.483811i	0.987351	−	0.158550i	$-0.0506820\pi$
$743$	6.02264	+	13.1877i	0.220949	+	0.483811i	−0.766402	+	0.642362i	$0.777955\pi$
$744$	−1.95199	−	2.25272i	−0.0715636	−	0.0825887i
$745$	−0.141391	−	0.983397i	−0.00518017	−	0.0360289i
$746$	9.40853	−	20.6018i	0.344471	−	0.754286i
$747$	7.21213	−	2.11767i	0.263878	−	0.0774816i
$748$	−11.0646	+	3.24885i	−0.404560	+	0.118790i
$749$	13.4003	−	29.3425i	0.489635	−	1.07215i
$750$	−0.142315	−	0.989821i	−0.00519660	−	0.0361432i
$751$	−17.6770	−	20.4003i	−0.645042	−	0.744418i	0.335216	−	0.942141i	$-0.391191\pi$
$751$	−17.6770	−	20.4003i	−0.645042	−	0.744418i	−0.980258	+	0.197723i	$0.936645\pi$
$752$	3.19420	+	6.99432i	0.116480	+	0.255056i
$753$	0.499641	−	0.321100i	0.0182079	−	0.0117015i
$754$	5.22943	−	36.3715i	0.190444	−	1.32457i
$755$	−2.60601	−	1.67478i	−0.0948422	−	0.0609514i
$756$	2.98027	−	3.43941i	0.108391	−	0.125090i
$757$	7.44330	+	2.18555i	0.270532	+	0.0794352i	0.414185	−	0.910193i	$-0.364067\pi$
$757$	7.44330	+	2.18555i	0.270532	+	0.0794352i	−0.143653	+	0.989628i	$0.545885\pi$
$758$	9.74937			0.354113
$759$	−2.82220	+	28.3360i	−0.102439	+	1.02853i
$760$	−4.99194			−0.181077
$761$	−15.1912	−	4.46053i	−0.550680	−	0.161694i	−0.00545672	−	0.999985i	$-0.501737\pi$
$761$	−15.1912	−	4.46053i	−0.550680	−	0.161694i	−0.545223	+	0.838291i	$0.683555\pi$
$762$	−3.26424	+	3.76714i	−0.118251	+	0.136469i
$763$	25.0901	+	16.1245i	0.908324	+	0.583745i
$764$	0.513065	−	3.56845i	0.0185621	−	0.129102i
$765$	−1.63381	+	1.04999i	−0.0590706	+	0.0379623i
$766$	14.2789	+	31.2664i	0.515917	+	1.12970i
$767$	−54.0131	−	62.3345i	−1.95030	−	2.25077i
$768$	−0.142315	−	0.989821i	−0.00513534	−	0.0357171i
$769$	11.5480	−	25.2867i	0.416433	−	0.911861i	−0.578904	−	0.815396i	$-0.696519\pi$
$769$	11.5480	−	25.2867i	0.416433	−	0.911861i	0.995336	−	0.0964646i	$-0.0307535\pi$
$770$	25.9278	−	7.61309i	0.934373	−	0.274357i
$771$	−26.8860	+	7.89445i	−0.968277	+	0.284312i
$772$	6.40651	−	14.0283i	0.230575	−	0.504890i
$773$	−2.78889	−	19.3971i	−0.100309	−	0.697667i	−0.976471	−	0.215649i	$-0.930813\pi$
$773$	−2.78889	−	19.3971i	−0.100309	−	0.697667i	0.876162	−	0.482018i	$-0.160096\pi$
$774$	−2.38869	−	2.75670i	−0.0858598	−	0.0990875i
$775$	−1.23826	−	2.71141i	−0.0444796	−	0.0973967i
$776$	6.77673	−	4.35514i	0.243270	−	0.156340i
$777$	−2.78640	+	19.3799i	−0.0999617	+	0.695249i
$778$	8.84322	+	5.68319i	0.317045	+	0.203752i
$779$	−5.56133	+	6.41812i	−0.199255	+	0.229953i
$780$	6.14649	+	1.80477i	0.220080	+	0.0646212i
$781$	24.5992			0.880228
$782$	−7.60894	+	5.37175i	−0.272095	+	0.192094i
$783$	5.73613			0.204992
$784$	−13.1561	−	3.86299i	−0.469862	−	0.137964i
$785$	12.9096	−	14.8984i	0.460762	−	0.531748i
$786$	3.29521	+	2.11770i	0.117536	+	0.0755360i
$787$	−2.13119	+	14.8228i	−0.0759688	+	0.528375i	0.915929	+	0.401339i	$0.131455\pi$
$787$	−2.13119	+	14.8228i	−0.0759688	+	0.528375i	−0.991898	+	0.127035i	$0.959454\pi$
$788$	−9.26214	+	5.95242i	−0.329950	+	0.212046i
$789$	5.13078	+	11.2348i	0.182661	+	0.399971i
$790$	−4.44828	−	5.13359i	−0.158263	−	0.182645i
$791$	10.8711	+	75.6102i	0.386532	+	2.68839i
$792$	−2.46661	+	5.40111i	−0.0876470	+	0.191920i
$793$	−73.2274	+	21.5015i	−2.60038	+	0.763540i
$794$	15.3311	−	4.50163i	0.544082	−	0.159757i
$795$	−3.24074	+	7.09623i	−0.114937	+	0.251677i
$796$	1.30593	+	9.08293i	0.0462874	+	0.321936i
$797$	−1.67004	−	1.92733i	−0.0591557	−	0.0682694i	0.725400	−	0.688327i	$-0.241655\pi$
$797$	−1.67004	−	1.92733i	−0.0591557	−	0.0682694i	−0.784556	+	0.620058i	$0.787109\pi$
$798$	−9.43752	−	20.6653i	−0.334085	−	0.731543i
$799$	12.5627	−	8.07353i	0.444435	−	0.285621i
$800$	0.142315	−	0.989821i	0.00503159	−	0.0349955i
$801$	2.06903	+	1.32969i	0.0731056	+	0.0469821i
$802$	14.1252	−	16.3013i	0.498777	−	0.575620i
$803$	32.0934	+	9.42347i	1.13255	+	0.332547i
$804$	−10.0298			−0.353725
$805$	17.8302	−	12.5877i	0.628431	−	0.443659i
$806$	19.0948			0.672585
$807$	−10.6383	−	3.12370i	−0.374488	−	0.109959i
$808$	−8.32765	+	9.61062i	−0.292966	+	0.338100i
$809$	0.307314	+	0.197499i	0.0108046	+	0.00694369i	0.546032	−	0.837764i	$-0.316138\pi$
$809$	0.307314	+	0.197499i	0.0108046	+	0.00694369i	−0.535227	+	0.844708i	$0.679774\pi$
$810$	−0.142315	+	0.989821i	−0.00500043	+	0.0347788i
$811$	6.38075	−	4.10066i	0.224059	−	0.143994i	−0.423796	−	0.905758i	$-0.639303\pi$
$811$	6.38075	−	4.10066i	0.224059	−	0.143994i	0.647855	+	0.761764i	$0.275666\pi$
$812$	−10.8444	−	23.7460i	−0.380565	−	0.833322i
$813$	14.2749	+	16.4741i	0.500644	+	0.577774i
$814$	−3.63542	−	25.2849i	−0.127422	−	0.886236i
$815$	0.465062	−	1.01834i	0.0162904	−	0.0356710i
$816$	−1.86345	+	0.547157i	−0.0652336	+	0.0191543i
$817$	−17.4712	+	5.13001i	−0.611240	+	0.179476i
$818$	−11.9455	+	26.1570i	−0.417665	+	0.914559i
$819$	4.14898	+	28.8568i	0.144977	+	1.00834i
$820$	−1.11406	−	1.28570i	−0.0389048	−	0.0448985i
$821$	18.0425	+	39.5076i	0.629688	+	1.37882i	0.908259	+	0.418408i	$0.137412\pi$
$821$	18.0425	+	39.5076i	0.629688	+	1.37882i	−0.278571	+	0.960416i	$0.589861\pi$
$822$	1.20316	−	0.773226i	0.0419651	−	0.0269693i
$823$	−5.16830	+	35.9463i	−0.180155	+	1.25301i	0.676237	+	0.736684i	$0.263609\pi$
$823$	−5.16830	+	35.9463i	−0.180155	+	1.25301i	−0.856393	+	0.516325i	$0.827300\pi$
$824$	−10.4429	−	6.71123i	−0.363795	−	0.233797i
$825$	−3.88836	+	4.48741i	−0.135375	+	0.156231i
$826$	−56.2229	−	16.5085i	−1.95625	−	0.574406i
$827$	−30.3856			−1.05661			−0.528306	−	0.849054i	$-0.677172\pi$
$827$	−30.3856			−1.05661			−0.528306	+	0.849054i	$0.677172\pi$
$828$	−0.475303	+	4.77222i	−0.0165179	+	0.165846i
$829$	29.7157			1.03207			0.516034	−	0.856568i	$-0.327408\pi$
$829$	29.7157			1.03207			0.516034	+	0.856568i	$0.327408\pi$
$830$	7.21213	+	2.11767i	0.250337	+	0.0735055i
$831$	−1.04543	+	1.20649i	−0.0362657	+	0.0418528i
$832$	5.38905	+	3.46333i	0.186832	+	0.120069i
$833$	−3.78976	+	26.3584i	−0.131307	+	0.913263i
$834$	−5.57979	+	3.58591i	−0.193212	+	0.124170i
$835$	−0.868800	−	1.90241i	−0.0300661	−	0.0658355i
$836$	19.4105	+	22.4009i	0.671325	+	0.774750i
$837$	0.424209	+	2.95044i	0.0146628	+	0.101982i
$838$	4.40329	−	9.64186i	0.152109	−	0.333073i
$839$	−35.1276	+	10.3144i	−1.21274	+	0.356093i	−0.824711	−	0.565554i	$-0.808662\pi$
$839$	−35.1276	+	10.3144i	−1.21274	+	0.356093i	−0.388030	+	0.921647i	$0.626844\pi$
$840$	4.36665	−	1.28216i	0.150664	−	0.0442388i
$841$	1.62142	−	3.55042i	0.0559111	−	0.122428i
$842$	−2.58108	−	17.9518i	−0.0889500	−	0.618661i
$843$	4.24005	+	4.89327i	0.146035	+	0.168533i
$844$	−0.407995	−	0.893384i	−0.0140438	−	0.0307516i
$845$	−23.5858	+	15.1577i	−0.811377	+	0.521440i
$846$	1.09428	−	7.61091i	0.0376222	−	0.261668i
$847$	−92.8657	−	59.6812i	−3.19090	−	2.05067i
$848$	−5.10870	+	5.89576i	−0.175434	+	0.202461i
$849$	−18.7887	−	5.51687i	−0.644828	−	0.189339i
$850$	−1.94211			−0.0666140
$851$	−9.37962	−	18.3772i	−0.321529	−	0.629963i
$852$	4.14289			0.141933
$853$	−15.9155	−	4.67322i	−0.544937	−	0.160008i	−0.00233419	−	0.999997i	$-0.500743\pi$
$853$	−15.9155	−	4.67322i	−0.544937	−	0.160008i	−0.542603	+	0.839989i	$0.682561\pi$
$854$	−35.5060	+	40.9761i	−1.21499	+	1.40217i
$855$	4.19949	+	2.69885i	0.143619	+	0.0922986i
$856$	−1.00873	+	7.01588i	−0.0344777	+	0.239798i
$857$	−30.0873	+	19.3360i	−1.02776	+	0.660504i	−0.941931	−	0.335806i	$-0.890991\pi$
$857$	−30.0873	+	19.3360i	−1.02776	+	0.660504i	−0.0858329	+	0.996310i	$0.527355\pi$
$858$	−15.8010	−	34.5994i	−0.539438	−	1.18120i
$859$	−28.1246	−	32.4576i	−0.959600	−	1.10744i	−0.994147	−	0.108034i	$-0.965544\pi$
$859$	−28.1246	−	32.4576i	−0.959600	−	1.10744i	0.0345472	−	0.999403i	$-0.489001\pi$
$860$	−0.519113	−	3.61051i	−0.0177016	−	0.123117i
$861$	3.21625	−	7.04260i	0.109609	−	0.240011i
$862$	22.3750	−	6.56989i	0.762095	−	0.223771i
$863$	17.7396	−	5.20882i	0.603863	−	0.177310i	0.0345115	−	0.999404i	$-0.489012\pi$
$863$	17.7396	−	5.20882i	0.603863	−	0.177310i	0.569352	+	0.822094i	$0.307194\pi$
$864$	−0.415415	+	0.909632i	−0.0141327	+	0.0309463i
$865$	−3.36516	−	23.4052i	−0.114419	−	0.795802i
$866$	26.5307	+	30.6181i	0.901550	+	1.04044i
$867$	−5.49519	−	12.0328i	−0.186626	−	0.408655i
$868$	11.4120	−	7.33406i	0.387349	−	0.248934i
$869$	−5.73998	+	39.9225i	−0.194716	+	1.35428i
$870$	4.82554	+	3.10118i	0.163601	+	0.105140i
$871$	42.0753	−	48.5575i	1.42567	−	1.64531i
$872$	−6.28799	−	1.84632i	−0.212938	−	0.0625243i
$873$	−8.05551			−0.272638
$874$	20.6842	+	12.0546i	0.699653	+	0.407751i
$875$	4.55100			0.153852
$876$	5.40503	+	1.58706i	0.182619	+	0.0536218i
$877$	2.21541	−	2.55672i	0.0748091	−	0.0863344i	−0.717111	−	0.696959i	$-0.754536\pi$
$877$	2.21541	−	2.55672i	0.0748091	−	0.0863344i	0.791920	+	0.610624i	$0.209081\pi$
$878$	−15.0715	−	9.68589i	−0.508640	−	0.326883i
$879$	0.786822	−	5.47247i	0.0265388	−	0.184582i
$880$	−4.99510	+	3.21016i	−0.168385	+	0.108214i
$881$	9.90493	+	21.6888i	0.333706	+	0.730713i	0.999886	−	0.0150771i	$-0.00479937\pi$
$881$	9.90493	+	21.6888i	0.333706	+	0.730713i	−0.666181	+	0.745790i	$0.732072\pi$
$882$	8.97916	+	10.3625i	0.302344	+	0.348924i
$883$	−0.833982	−	5.80047i	−0.0280657	−	0.195201i	0.970965	−	0.239222i	$-0.0768924\pi$
$883$	−0.833982	−	5.80047i	−0.0280657	−	0.195201i	−0.999031	+	0.0440206i	$0.985983\pi$
$884$	5.16824	−	11.3169i	0.173827	−	0.380627i
$885$	12.3540	−	3.62746i	0.415275	−	0.121936i
$886$	−1.88679	+	0.554011i	−0.0633879	+	0.0186124i
$887$	21.0448	−	46.0816i	0.706614	−	1.54727i	−0.125148	−	0.992138i	$-0.539941\pi$
$887$	21.0448	−	46.0816i	0.706614	−	1.54727i	0.831762	−	0.555132i	$-0.187332\pi$
$888$	−0.612262	−	4.25838i	−0.0205462	−	0.142902i
$889$	−14.8556	−	17.1442i	−0.498239	−	0.574999i
$890$	1.02170	+	2.23721i	0.0342474	+	0.0749913i
$891$	4.99510	−	3.21016i	0.167342	−	0.107544i
$892$	3.91499	−	27.2294i	0.131084	−	0.911707i
$893$	−32.2906	−	20.7519i	−1.08056	−	0.694436i
$894$	−0.650610	+	0.750844i	−0.0217597	+	0.0251120i
$895$	3.79325	+	1.11380i	0.126794	+	0.0372302i
$896$	4.55100			0.152038
$897$	−21.1099	−	22.3207i	−0.704839	−	0.745265i
$898$	−40.6640			−1.35698
$899$	16.4055	+	4.81709i	0.547155	+	0.160659i
$900$	−0.654861	+	0.755750i	−0.0218287	+	0.0251917i
$901$	12.7457	+	8.19116i	0.424621	+	0.272887i
$902$	−1.43757	+	9.99850i	−0.0478658	+	0.332914i
$903$	13.9651	−	8.97484i	0.464730	−	0.298664i
$904$	−6.97267	−	15.2680i	−0.231908	−	0.507807i
$905$	−4.80735	−	5.54797i	−0.159802	−	0.184421i
$906$	0.440858	+	3.06623i	0.0146465	+	0.101869i
$907$	15.1173	−	33.1023i	0.501962	−	1.09914i	−0.473865	−	0.880598i	$-0.657142\pi$
$907$	15.1173	−	33.1023i	0.501962	−	1.09914i	0.975827	−	0.218546i	$-0.0701312\pi$
$908$	27.9383	−	8.20342i	0.927165	−	0.272240i
$909$	12.2016	−	3.58270i	0.404700	−	0.118831i
$910$	−12.1108	+	26.5190i	−0.401470	+	0.879097i
$911$	−5.56992	−	38.7397i	−0.184540	−	1.28350i	−0.845863	−	0.533401i	$-0.820914\pi$
$911$	−5.56992	−	38.7397i	−0.184540	−	1.28350i	0.661323	−	0.750101i	$-0.269995\pi$
$912$	3.26903	+	3.77266i	0.108248	+	0.124925i
$913$	−18.5405	−	40.5980i	−0.613601	−	1.34360i
$914$	27.1346	−	17.4383i	0.897531	−	0.576808i
$915$	1.69550	−	11.7924i	0.0560514	−	0.389846i
$916$	−11.2418	−	7.22466i	−0.371439	−	0.238710i
$917$	−11.6738	+	13.4723i	−0.385502	+	0.444893i
$918$	1.86345	+	0.547157i	0.0615029	+	0.0180589i
$919$	50.3931			1.66232			0.831158	−	0.556037i	$-0.187679\pi$
$919$	50.3931			1.66232			0.831158	+	0.556037i	$0.187679\pi$
$920$	−2.97991	+	3.75768i	−0.0982446	+	0.123887i
$921$	7.38495			0.243342
$922$	−3.60115	−	1.05739i	−0.118598	−	0.0348234i
$923$	−17.3795	+	20.0570i	−0.572053	+	0.660185i
$924$	−22.7327	−	14.6094i	−0.747850	−	0.480614i
$925$	0.612262	−	4.25838i	0.0201311	−	0.140015i
$926$	6.70389	−	4.30833i	0.220304	−	0.141580i
$927$	5.15674	+	11.2917i	0.169370	+	0.370868i
$928$	3.75636	+	4.33507i	0.123309	+	0.142306i
$929$	−4.77046	−	33.1793i	−0.156514	−	1.08858i	−0.904995	−	0.425421i	$-0.860126\pi$
$929$	−4.77046	−	33.1793i	−0.156514	−	1.08858i	0.748482	−	0.663155i	$-0.230783\pi$
$930$	−1.23826	+	2.71141i	−0.0406041	+	0.0889106i
$931$	65.6747	−	19.2838i	2.15240	−	0.632002i
$932$	11.2404	−	3.30048i	0.368192	−	0.108111i
$933$	8.35213	−	18.2886i	0.273436	−	0.598742i
$934$	0.709521	+	4.93482i	0.0232162	+	0.161472i
$935$	7.55164	+	8.71506i	0.246965	+	0.285013i
$936$	−2.66114	−	5.82708i	−0.0869820	−	0.190464i
$937$	−6.77982	+	4.35712i	−0.221487	+	0.142341i	−0.646679	−	0.762762i	$-0.723843\pi$
$937$	−6.77982	+	4.35712i	−0.221487	+	0.142341i	0.425192	+	0.905103i	$0.360206\pi$
$938$	6.49606	−	45.1811i	0.212104	−	1.47521i
$939$	−9.53698	−	6.12904i	−0.311227	−	0.200014i
$940$	5.03534	−	5.81109i	0.164235	−	0.189537i
$941$	−10.0361	−	2.94688i	−0.327169	−	0.0960654i	0.114023	−	0.993478i	$-0.463626\pi$
$941$	−10.0361	−	2.94688i	−0.327169	−	0.0960654i	−0.441192	+	0.897413i	$0.645444\pi$
$942$	−19.7135			−0.642299
$943$	1.51143	+	8.01755i	0.0492190	+	0.261087i
$944$	12.8755			0.419063
$945$	−4.36665	−	1.28216i	−0.142047	−	0.0417088i
$946$	−14.1833	+	16.3684i	−0.461139	+	0.532183i
$947$	47.5193	+	30.5388i	1.54417	+	0.992377i	0.986769	+	0.162134i	$0.0518376\pi$
$947$	47.5193	+	30.5388i	1.54417	+	0.992377i	0.557401	+	0.830244i	$0.311799\pi$
$948$	−0.966703	+	6.72357i	−0.0313971	+	0.218371i
$949$	−30.3577	+	19.5097i	−0.985452	+	0.633312i
$950$	2.07373	+	4.54083i	0.0672806	+	0.147324i
$951$	4.34170	+	5.01059i	0.140789	+	0.162480i
$952$	−1.25786	−	8.74859i	−0.0407674	−	0.283543i
$953$	−7.30212	+	15.9894i	−0.236539	+	0.517948i	−0.990257	−	0.139250i	$-0.955531\pi$
$953$	−7.30212	+	15.9894i	−0.236539	+	0.517948i	0.753719	+	0.657197i	$0.228258\pi$
$954$	7.48520	−	2.19785i	0.242342	−	0.0711581i
$955$	−3.45911	+	1.01569i	−0.111934	+	0.0328668i
$956$	1.25917	−	2.75721i	0.0407246	−	0.0891745i
$957$	−4.84715	−	33.7127i	−0.156686	−	1.08978i
$958$	−3.10374	−	3.58191i	−0.100277	−	0.115726i
$959$	2.70387	+	5.92065i	0.0873126	+	0.191188i
$960$	−0.841254	+	0.540641i	−0.0271513	+	0.0174491i
$961$	3.14729	−	21.8899i	0.101525	−	0.706125i
$962$	23.1846	+	14.8998i	0.747501	+	0.480390i
$963$	4.64167	−	5.35677i	0.149576	−	0.172620i
$964$	−1.73094	−	0.508249i	−0.0557497	−	0.0163696i
$965$	−15.4220			−0.496450
$966$	−21.1894	−	5.23193i	−0.681759	−	0.168335i
$967$	−24.5901			−0.790765			−0.395383	−	0.918516i	$-0.629388\pi$
$967$	−24.5901			−0.790765			−0.395383	+	0.918516i	$0.629388\pi$
$968$	23.2736	+	6.83375i	0.748042	+	0.219645i
$969$	6.34882	−	7.32693i	0.203954	−	0.235375i
$970$	−6.77673	−	4.35514i	−0.217588	−	0.139835i
$971$	5.02933	−	34.9797i	0.161399	−	1.12255i	−0.734601	−	0.678499i	$-0.762631\pi$
$971$	5.02933	−	34.9797i	0.161399	−	1.12255i	0.896000	−	0.444054i	$-0.146460\pi$
$972$	0.841254	−	0.540641i	0.0269832	−	0.0173411i
$973$	−12.5395	−	27.4576i	−0.401997	−	0.880251i
$974$	−4.95059	−	5.71328i	−0.158627	−	0.183065i
$975$	−0.911665	−	6.34077i	−0.0291967	−	0.203067i
$976$	4.94913	−	10.8371i	0.158418	−	0.346886i
$977$	25.8687	−	7.59573i	0.827612	−	0.243009i	0.159621	−	0.987178i	$-0.448973\pi$
$977$	25.8687	−	7.59573i	0.827612	−	0.243009i	0.667991	+	0.744169i	$0.267154\pi$
$978$	−1.07416	+	0.315403i	−0.0343479	+	0.0100855i
$979$	6.06652	−	13.2838i	0.193887	−	0.424553i
$980$	1.95136	+	13.5720i	0.0623338	+	0.433541i
$981$	4.29160	+	4.95277i	0.137020	+	0.158130i
$982$	−2.01739	−	4.41748i	−0.0643777	−	0.140967i
$983$	−12.1144	+	7.78547i	−0.386390	+	0.248318i	−0.719386	−	0.694610i	$-0.755577\pi$
$983$	−12.1144	+	7.78547i	−0.386390	+	0.248318i	0.332996	+	0.942928i	$0.391940\pi$
$984$	−0.242109	+	1.68390i	−0.00771815	+	0.0536809i
$985$	9.26214	+	5.95242i	0.295116	+	0.189660i
$986$	7.29529	−	8.41921i	0.232329	−	0.268122i
$987$	33.5759	+	9.85877i	1.06873	+	0.313808i
$988$	−31.9782			−1.01736
$989$	−6.56771	+	16.2138i	−0.208841	+	0.515567i
$990$	5.93769			0.188712
$991$	35.7697	+	10.5029i	1.13626	+	0.333637i	0.795166	−	0.606392i	$-0.207384\pi$
$991$	35.7697	+	10.5029i	1.13626	+	0.333637i	0.341096	+	0.940028i	$0.389202\pi$
$992$	−1.95199	+	2.25272i	−0.0619759	+	0.0715240i
$993$	−22.0902	−	14.1965i	−0.701011	−	0.450512i
$994$	−2.68324	+	18.6624i	−0.0851072	+	0.591934i
$995$	7.71962	−	4.96110i	0.244728	−	0.157277i
$996$	−3.12251	−	6.83734i	−0.0989405	−	0.216649i
$997$	−29.6711	−	34.2422i	−0.939692	−	1.08446i	−0.996289	−	0.0860657i	$-0.972570\pi$
$997$	−29.6711	−	34.2422i	−0.939692	−	1.08446i	0.0565971	−	0.998397i	$-0.481975\pi$
$998$	3.53342	+	24.5755i	0.111849	+	0.777924i
$999$	−1.78719	+	3.91339i	−0.0565440	+	0.123814i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.h.271.1	✓	30	1.1	even	1	trivial
690.2.m.h.331.1	yes	30	23.9	even	11	inner

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)

\(f(q)\)	\(=\)	\(q+(0.959493 + 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(-1.89055 - 4.13973i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(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} +(-1.89055 - 4.13973i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.415415 - 0.909632i) q^{10} +(-5.69717 + 1.67284i) q^{11} +(-0.959493 + 0.281733i) q^{12} +(2.66114 - 5.82708i) q^{13} +(-0.647674 - 4.50467i) q^{14} +(0.654861 + 0.755750i) q^{15} +(0.415415 + 0.909632i) q^{16} +(1.63381 - 1.04999i) q^{17} +(0.142315 - 0.989821i) q^{18} +(-4.19949 - 2.69885i) q^{19} +(0.654861 - 0.755750i) q^{20} +(4.36665 + 1.28216i) q^{21} -5.93769 q^{22} +(-4.53841 + 1.55010i) q^{23} -1.00000 q^{24} +(-0.959493 - 0.281733i) q^{25} +(4.19502 - 4.84131i) q^{26} +(0.841254 + 0.540641i) q^{27} +(0.647674 - 4.50467i) q^{28} +(4.82554 - 3.10118i) q^{29} +(0.415415 + 0.909632i) q^{30} +(1.95199 + 2.25272i) q^{31} +(0.142315 + 0.989821i) q^{32} +(2.46661 - 5.40111i) q^{33} +(1.86345 - 0.547157i) q^{34} +(-4.36665 + 1.28216i) q^{35} +(0.415415 - 0.909632i) q^{36} +(0.612262 + 4.25838i) q^{37} +(-3.26903 - 3.77266i) q^{38} +(2.66114 + 5.82708i) q^{39} +(0.841254 - 0.540641i) q^{40} +(0.242109 - 1.68390i) q^{41} +(3.82854 + 2.46045i) q^{42} +(2.38869 - 2.75670i) q^{43} +(-5.69717 - 1.67284i) q^{44} -1.00000 q^{45} +(-4.79129 + 0.208693i) q^{46} +7.68917 q^{47} +(-0.959493 - 0.281733i) q^{48} +(-8.97916 + 10.3625i) q^{49} +(-0.841254 - 0.540641i) q^{50} +(-0.276392 + 1.92235i) q^{51} +(5.38905 - 3.46333i) q^{52} +(3.24074 + 7.09623i) q^{53} +(0.654861 + 0.755750i) q^{54} +(0.845021 + 5.87725i) q^{55} +(1.89055 - 4.13973i) q^{56} +(4.78973 - 1.40639i) q^{57} +(5.50377 - 1.61605i) q^{58} +(5.34869 - 11.7120i) q^{59} +(0.142315 + 0.989821i) q^{60} +(-7.80181 - 9.00377i) q^{61} +(1.23826 + 2.71141i) q^{62} +(-3.82854 + 2.46045i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-5.38905 - 3.46333i) q^{65} +(3.88836 - 4.48741i) q^{66} +(9.62355 + 2.82573i) q^{67} +1.94211 q^{68} +(1.80054 - 4.44500i) q^{69} -4.55100 q^{70} +(-3.97507 - 1.16719i) q^{71} +(0.654861 - 0.755750i) q^{72} +(-4.73896 - 3.04555i) q^{73} +(-0.612262 + 4.25838i) q^{74} +(0.841254 - 0.540641i) q^{75} +(-2.07373 - 4.54083i) q^{76} +(17.6959 + 20.4222i) q^{77} +(0.911665 + 6.34077i) q^{78} +(2.82179 - 6.17886i) q^{79} +(0.959493 - 0.281733i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(0.706713 - 1.54748i) q^{82} +(1.06972 + 7.44010i) q^{83} +(2.98027 + 3.43941i) q^{84} +(-0.806784 - 1.76661i) q^{85} +(3.06859 - 1.97206i) q^{86} +(-0.816336 + 5.67774i) q^{87} +(-4.99510 - 3.21016i) q^{88} +(-1.61061 + 1.85874i) q^{89} +(-0.959493 - 0.281733i) q^{90} -29.1536 q^{91} +(-4.65600 - 1.14962i) q^{92} -2.98078 q^{93} +(7.37771 + 2.16629i) q^{94} +(-3.26903 + 3.77266i) q^{95} +(-0.841254 - 0.540641i) q^{96} +(1.14642 - 7.97352i) q^{97} +(-11.5349 + 7.41303i) q^{98} +(2.46661 + 5.40111i) 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

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