LMFDB - Embedded newform 690.2.m.g.361.1

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			361.1
Character	$\chi$	$=$	690.361
Dual form			690.2.m.g.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 + 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-2.83591 + 0.832699i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.654861 + 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-2.83591 + 0.832699i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-0.959493 - 0.281733i) q^{10} +(-1.08040 - 1.24684i) q^{11} +(-0.654861 - 0.755750i) q^{12} +(6.41701 + 1.88420i) q^{13} +(1.22782 - 2.68854i) q^{14} +(0.841254 + 0.540641i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-1.04227 + 7.24915i) q^{17} +(0.415415 + 0.909632i) q^{18} +(0.0331744 + 0.230733i) q^{19} +(0.841254 - 0.540641i) q^{20} +(-1.93553 + 2.23372i) q^{21} +1.64981 q^{22} +(4.77970 - 0.393012i) q^{23} +1.00000 q^{24} +(-0.654861 + 0.755750i) q^{25} +(-5.62623 + 3.61576i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(1.22782 + 2.68854i) q^{28} +(-1.22302 + 8.50631i) q^{29} +(-0.959493 + 0.281733i) q^{30} +(0.547910 + 0.352120i) q^{31} +(0.415415 - 0.909632i) q^{32} +(-1.58298 - 0.464805i) q^{33} +(-4.79600 - 5.53488i) q^{34} +(-1.93553 - 2.23372i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(2.22961 - 4.88215i) q^{37} +(-0.196101 - 0.126026i) q^{38} +(6.41701 - 1.88420i) q^{39} +(-0.142315 + 0.989821i) q^{40} +(3.35643 + 7.34956i) q^{41} +(-0.420631 - 2.92555i) q^{42} +(2.11612 - 1.35995i) q^{43} +(-1.08040 + 1.24684i) q^{44} +1.00000 q^{45} +(-2.83302 + 3.86962i) q^{46} +3.80565 q^{47} +(-0.654861 + 0.755750i) q^{48} +(1.46023 - 0.938434i) q^{49} +(-0.142315 - 0.989821i) q^{50} +(3.04237 + 6.66187i) q^{51} +(0.951790 - 6.61984i) q^{52} +(-0.0131435 + 0.00385927i) q^{53} +(0.841254 + 0.540641i) q^{54} +(0.685355 - 1.50072i) q^{55} +(-2.83591 - 0.832699i) q^{56} +(0.152652 + 0.176170i) q^{57} +(-5.62773 - 6.49475i) q^{58} +(6.55130 + 1.92363i) q^{59} +(0.415415 - 0.909632i) q^{60} +(-9.37563 - 6.02535i) q^{61} +(-0.624919 + 0.183493i) q^{62} +(-0.420631 + 2.92555i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.951790 + 6.61984i) q^{65} +(1.38791 - 0.891954i) q^{66} +(0.687452 - 0.793361i) q^{67} +7.32370 q^{68} +(3.80846 - 2.91472i) q^{69} +2.95564 q^{70} +(1.76802 - 2.04040i) q^{71} +(0.841254 - 0.540641i) q^{72} +(1.13271 + 7.87819i) q^{73} +(2.22961 + 4.88215i) q^{74} +(-0.142315 + 0.989821i) q^{75} +(0.223663 - 0.0656735i) q^{76} +(4.10215 + 2.63629i) q^{77} +(-2.77826 + 6.08354i) q^{78} +(-6.77960 - 1.99067i) q^{79} +(-0.654861 - 0.755750i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-7.75242 - 2.27632i) q^{82} +(-1.45295 + 3.18151i) q^{83} +(2.48644 + 1.59794i) q^{84} +(-7.02704 + 2.06332i) q^{85} +(-0.357984 + 2.48983i) q^{86} +(3.56999 + 7.81718i) q^{87} +(-0.234792 - 1.63302i) q^{88} +(-5.25139 + 3.37487i) q^{89} +(-0.654861 + 0.755750i) q^{90} -19.7670 q^{91} +(-1.06923 - 4.67512i) q^{92} +0.651301 q^{93} +(-2.49217 + 2.87612i) q^{94} +(-0.196101 + 0.126026i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(-2.63137 - 5.76190i) q^{97} +(-0.247027 + 1.71811i) q^{98} +(-1.58298 + 0.464805i) 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	0.415415	+	0.909632i	0.185779	+	0.406800i
$5$	0.415415	+	0.909632i	0.185779	+	0.406800i
$6$	−0.142315	+	0.989821i	−0.0580998	+	0.404093i
$7$	−2.83591	+	0.832699i	−1.07187	+	0.314731i	−0.769623	−	0.638498i	$-0.779556\pi$
$7$	−2.83591	+	0.832699i	−1.07187	+	0.314731i	−0.302250	+	0.953229i	$0.597738\pi$
$8$	0.841254	+	0.540641i	0.297428	+	0.191145i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	−0.959493	−	0.281733i	−0.303418	−	0.0890917i
$11$	−1.08040	−	1.24684i	−0.325751	−	0.375937i	0.569125	−	0.822251i	$-0.307282\pi$
$11$	−1.08040	−	1.24684i	−0.325751	−	0.375937i	−0.894877	+	0.446314i	$0.852737\pi$
$12$	−0.654861	−	0.755750i	−0.189042	−	0.218166i
$13$	6.41701	+	1.88420i	1.77976	+	0.522584i	0.995234	−	0.0975138i	$-0.0310890\pi$
$13$	6.41701	+	1.88420i	1.77976	+	0.522584i	0.784524	+	0.620098i	$0.212907\pi$
$14$	1.22782	−	2.68854i	0.328147	−	0.718543i
$15$	0.841254	+	0.540641i	0.217211	+	0.139593i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	−1.04227	+	7.24915i	−0.252788	+	1.75818i	0.328523	+	0.944496i	$0.393449\pi$
$17$	−1.04227	+	7.24915i	−0.252788	+	1.75818i	−0.581310	+	0.813682i	$0.697460\pi$
$18$	0.415415	+	0.909632i	0.0979143	+	0.214402i
$19$	0.0331744	+	0.230733i	0.00761073	+	0.0529338i	0.993273	−	0.115797i	$-0.0369422\pi$
$19$	0.0331744	+	0.230733i	0.00761073	+	0.0529338i	−0.985662	+	0.168731i	$0.946033\pi$
$20$	0.841254	−	0.540641i	0.188110	−	0.120891i
$21$	−1.93553	+	2.23372i	−0.422367	+	0.487438i
$22$	1.64981			0.351740
$23$	4.77970	−	0.393012i	0.996637	−	0.0819486i
$23$	4.77970	−	0.393012i	0.996637	−	0.0819486i
$24$	1.00000			0.204124
$25$	−0.654861	+	0.755750i	−0.130972	+	0.151150i
$26$	−5.62623	+	3.61576i	−1.10340	+	0.709109i
$27$	−0.142315	−	0.989821i	−0.0273885	−	0.190491i
$28$	1.22782	+	2.68854i	0.232035	+	0.508086i
$29$	−1.22302	+	8.50631i	−0.227110	+	1.57958i	0.483083	+	0.875575i	$0.339517\pi$
$29$	−1.22302	+	8.50631i	−0.227110	+	1.57958i	−0.710192	+	0.704008i	$0.751392\pi$
$30$	−0.959493	+	0.281733i	−0.175179	+	0.0514371i
$31$	0.547910	+	0.352120i	0.0984075	+	0.0632426i	0.588919	−	0.808192i	$-0.299554\pi$
$31$	0.547910	+	0.352120i	0.0984075	+	0.0632426i	−0.490512	+	0.871435i	$0.663190\pi$
$32$	0.415415	−	0.909632i	0.0734357	−	0.160802i
$33$	−1.58298	−	0.464805i	−0.275561	−	0.0809121i
$34$	−4.79600	−	5.53488i	−0.822508	−	0.949224i
$35$	−1.93553	−	2.23372i	−0.327164	−	0.377568i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	2.22961	−	4.88215i	0.366545	−	0.802621i	−0.633049	−	0.774112i	$-0.718197\pi$
$37$	2.22961	−	4.88215i	0.366545	−	0.802621i	0.999594	−	0.0285092i	$-0.00907600\pi$
$38$	−0.196101	−	0.126026i	−0.0318118	−	0.0204442i
$39$	6.41701	−	1.88420i	1.02754	−	0.301714i
$40$	−0.142315	+	0.989821i	−0.0225020	+	0.156505i
$41$	3.35643	+	7.34956i	0.524187	+	1.14781i	0.967830	+	0.251605i	$0.0809584\pi$
$41$	3.35643	+	7.34956i	0.524187	+	1.14781i	−0.443643	+	0.896203i	$0.646314\pi$
$42$	−0.420631	−	2.92555i	−0.0649047	−	0.451422i
$43$	2.11612	−	1.35995i	0.322705	−	0.207390i	−0.369251	−	0.929330i	$-0.620386\pi$
$43$	2.11612	−	1.35995i	0.322705	−	0.207390i	0.691956	+	0.721940i	$0.256749\pi$
$44$	−1.08040	+	1.24684i	−0.162876	+	0.187969i
$45$	1.00000			0.149071
$46$	−2.83302	+	3.86962i	−0.417706	+	0.570545i
$47$	3.80565			0.555111			0.277555	−	0.960710i	$-0.410476\pi$
$47$	3.80565			0.555111			0.277555	+	0.960710i	$0.410476\pi$
$48$	−0.654861	+	0.755750i	−0.0945210	+	0.109083i
$49$	1.46023	−	0.938434i	0.208605	−	0.134062i
$50$	−0.142315	−	0.989821i	−0.0201264	−	0.139982i
$51$	3.04237	+	6.66187i	0.426018	+	0.932848i
$52$	0.951790	−	6.61984i	0.131990	−	0.918007i
$53$	−0.0131435	+	0.00385927i	−0.00180540	+	0.000530112i	−0.282635	−	0.959227i	$-0.591209\pi$
$53$	−0.0131435	+	0.00385927i	−0.00180540	+	0.000530112i	0.280830	+	0.959758i	$0.409390\pi$
$54$	0.841254	+	0.540641i	0.114480	+	0.0735719i
$55$	0.685355	−	1.50072i	0.0924133	−	0.202357i
$56$	−2.83591	−	0.832699i	−0.378965	−	0.111274i
$57$	0.152652	+	0.176170i	0.0202192	+	0.0233342i
$58$	−5.62773	−	6.49475i	−0.738957	−	0.852802i
$59$	6.55130	+	1.92363i	0.852906	+	0.250436i	0.678829	−	0.734296i	$-0.262488\pi$
$59$	6.55130	+	1.92363i	0.852906	+	0.250436i	0.174077	+	0.984732i	$0.444306\pi$
$60$	0.415415	−	0.909632i	0.0536298	−	0.117433i
$61$	−9.37563	−	6.02535i	−1.20043	−	0.771467i	−0.221396	−	0.975184i	$-0.571061\pi$
$61$	−9.37563	−	6.02535i	−1.20043	−	0.771467i	−0.979030	+	0.203717i	$0.934698\pi$
$62$	−0.624919	+	0.183493i	−0.0793648	+	0.0233036i
$63$	−0.420631	+	2.92555i	−0.0529945	+	0.368585i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	0.951790	+	6.61984i	0.118055	+	0.821091i
$66$	1.38791	−	0.891954i	0.170840	−	0.109792i
$67$	0.687452	−	0.793361i	0.0839856	−	0.0969245i	−0.712201	−	0.701975i	$-0.752302\pi$
$67$	0.687452	−	0.793361i	0.0839856	−	0.0969245i	0.796187	+	0.605051i	$0.206847\pi$
$68$	7.32370			0.888129
$69$	3.80846	−	2.91472i	0.458485	−	0.350892i
$70$	2.95564			0.353266
$71$	1.76802	−	2.04040i	0.209825	−	0.242151i	−0.641075	−	0.767478i	$-0.721511\pi$
$71$	1.76802	−	2.04040i	0.209825	−	0.242151i	0.850901	+	0.525327i	$0.176057\pi$
$72$	0.841254	−	0.540641i	0.0991427	−	0.0637151i
$73$	1.13271	+	7.87819i	0.132574	+	0.922072i	0.942182	+	0.335101i	$0.108771\pi$
$73$	1.13271	+	7.87819i	0.132574	+	0.922072i	−0.809608	+	0.586971i	$0.800320\pi$
$74$	2.22961	+	4.88215i	0.259186	+	0.567539i
$75$	−0.142315	+	0.989821i	−0.0164331	+	0.114295i
$76$	0.223663	−	0.0656735i	0.0256559	−	0.00753326i
$77$	4.10215	+	2.63629i	0.467483	+	0.300433i
$78$	−2.77826	+	6.08354i	−0.314576	+	0.688826i
$79$	−6.77960	−	1.99067i	−0.762764	−	0.223968i	−0.122862	−	0.992424i	$-0.539207\pi$
$79$	−6.77960	−	1.99067i	−0.762764	−	0.223968i	−0.639903	+	0.768456i	$0.721025\pi$
$80$	−0.654861	−	0.755750i	−0.0732157	−	0.0844954i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−7.75242	−	2.27632i	−0.856112	−	0.251377i
$83$	−1.45295	+	3.18151i	−0.159482	+	0.349216i	−0.972457	−	0.233082i	$-0.925119\pi$
$83$	−1.45295	+	3.18151i	−0.159482	+	0.349216i	0.812976	+	0.582298i	$0.197846\pi$
$84$	2.48644	+	1.59794i	0.271293	+	0.174349i
$85$	−7.02704	+	2.06332i	−0.762189	+	0.223799i
$86$	−0.357984	+	2.48983i	−0.0386024	+	0.268485i
$87$	3.56999	+	7.81718i	0.382743	+	0.838090i
$88$	−0.234792	−	1.63302i	−0.0250289	−	0.174080i
$89$	−5.25139	+	3.37487i	−0.556647	+	0.357735i	−0.788518	−	0.615011i	$-0.789151\pi$
$89$	−5.25139	+	3.37487i	−0.556647	+	0.357735i	0.231872	+	0.972746i	$0.425515\pi$
$90$	−0.654861	+	0.755750i	−0.0690284	+	0.0796630i
$91$	−19.7670			−2.07215
$92$	−1.06923	−	4.67512i	−0.111475	−	0.487415i
$93$	0.651301			0.0675368
$94$	−2.49217	+	2.87612i	−0.257048	+	0.296649i
$95$	−0.196101	+	0.126026i	−0.0201195	+	0.0129300i
$96$	−0.142315	−	0.989821i	−0.0145249	−	0.101023i
$97$	−2.63137	−	5.76190i	−0.267175	−	0.585032i	0.727728	−	0.685866i	$-0.240576\pi$
$97$	−2.63137	−	5.76190i	−0.267175	−	0.585032i	−0.994903	+	0.100834i	$0.967849\pi$
$98$	−0.247027	+	1.71811i	−0.0249535	+	0.173556i
$99$	−1.58298	+	0.464805i	−0.159095	+	0.0467146i
$100$	0.841254	+	0.540641i	0.0841254	+	0.0540641i
$101$	−3.50145	+	7.66710i	−0.348407	+	0.762905i	0.651584	+	0.758577i	$0.274105\pi$
$101$	−3.50145	+	7.66710i	−0.348407	+	0.762905i	−0.999991	+	0.00432828i	$0.998622\pi$
$102$	−7.02704	−	2.06332i	−0.695780	−	0.204300i
$103$	0.629476	+	0.726454i	0.0620241	+	0.0715796i	0.785914	−	0.618336i	$-0.212193\pi$
$103$	0.629476	+	0.726454i	0.0620241	+	0.0715796i	−0.723890	+	0.689916i	$0.757648\pi$
$104$	4.37966	+	5.05439i	0.429461	+	0.495624i
$105$	−2.83591	−	0.832699i	−0.276757	−	0.0812631i
$106$	0.00569050	−	0.0124605i	0.000552711	−	0.00121027i
$107$	−9.12882	−	5.86674i	−0.882517	−	0.567159i	0.0190407	−	0.999819i	$-0.493939\pi$
$107$	−9.12882	−	5.86674i	−0.882517	−	0.567159i	−0.901557	+	0.432660i	$0.857575\pi$
$108$	−0.959493	+	0.281733i	−0.0923273	+	0.0271097i
$109$	1.60511	−	11.1638i	0.153742	−	1.06930i	−0.756134	−	0.654417i	$-0.772914\pi$
$109$	1.60511	−	11.1638i	0.153742	−	1.06930i	0.909876	−	0.414881i	$-0.136177\pi$
$110$	0.685355	+	1.50072i	0.0653461	+	0.143088i
$111$	−0.763829	−	5.31255i	−0.0724994	−	0.504244i
$112$	2.48644	−	1.59794i	0.234946	−	0.150991i
$113$	9.61853	−	11.1004i	0.904835	−	1.04424i	−0.0939804	−	0.995574i	$-0.529959\pi$
$113$	9.61853	−	11.1004i	0.904835	−	1.04424i	0.998815	−	0.0486611i	$-0.0154954\pi$
$114$	−0.233106			−0.0218323
$115$	2.34306	+	4.18451i	0.218491	+	0.390207i
$116$	8.59378			0.797913
$117$	4.37966	−	5.05439i	0.404899	−	0.467279i
$118$	−5.74397	+	3.69143i	−0.528776	+	0.339823i
$119$	−3.08057	−	21.4259i	−0.282396	−	1.96410i
$120$	0.415415	+	0.909632i	0.0379220	+	0.0830377i
$121$	1.17810	−	8.19387i	0.107100	−	0.744897i
$122$	10.6934	−	3.13986i	0.968134	−	0.284270i
$123$	6.79708	+	4.36822i	0.612872	+	0.393869i
$124$	0.270560	−	0.592445i	0.0242970	−	0.0532031i
$125$	−0.959493	−	0.281733i	−0.0858197	−	0.0251989i
$126$	−1.93553	−	2.23372i	−0.172431	−	0.198996i
$127$	3.05101	+	3.52105i	0.270733	+	0.312443i	0.874794	−	0.484496i	$-0.160997\pi$
$127$	3.05101	+	3.52105i	0.270733	+	0.312443i	−0.604060	+	0.796938i	$0.706451\pi$
$128$	−0.959493	−	0.281733i	−0.0848080	−	0.0249019i
$129$	1.04495	−	2.28812i	0.0920027	−	0.201458i
$130$	−5.62623	−	3.61576i	−0.493453	−	0.317123i
$131$	−19.2773	+	5.66031i	−1.68426	+	0.494544i	−0.977149	−	0.212556i	$-0.931821\pi$
$131$	−19.2773	+	5.66031i	−1.68426	+	0.494544i	−0.707113	+	0.707100i	$0.750003\pi$
$132$	−0.234792	+	1.63302i	−0.0204360	+	0.142136i
$133$	−0.286211	−	0.626714i	−0.0248176	−	0.0543430i
$134$	0.149398	+	1.03908i	0.0129060	+	0.0897631i
$135$	0.841254	−	0.540641i	0.0724036	−	0.0465310i
$136$	−4.79600	+	5.53488i	−0.411254	+	0.474612i
$137$	18.6726			1.59531			0.797654	−	0.603115i	$-0.206074\pi$
$137$	18.6726			1.59531			0.797654	+	0.603115i	$0.206074\pi$
$138$	−0.291211	+	4.78698i	−0.0247895	+	0.407495i
$139$	13.3244			1.13016			0.565080	−	0.825036i	$-0.308845\pi$
$139$	13.3244			1.13016			0.565080	+	0.825036i	$0.308845\pi$
$140$	−1.93553	+	2.23372i	−0.163582	+	0.188784i
$141$	3.20152	−	2.05749i	0.269616	−	0.173272i
$142$	0.384227	+	2.67236i	0.0322436	+	0.224259i
$143$	−4.58360	−	10.0367i	−0.383300	−	0.839310i
$144$	−0.142315	+	0.989821i	−0.0118596	+	0.0824851i
$145$	−8.24567	+	2.42115i	−0.684766	+	0.201065i
$146$	−6.69571	−	4.30307i	−0.554141	−	0.356125i
$147$	0.721069	−	1.57892i	0.0594728	−	0.130227i
$148$	−5.14977	−	1.51211i	−0.423308	−	0.124295i
$149$	−11.6603	−	13.4567i	−0.955252	−	1.10242i	−0.994661	−	0.103197i	$-0.967093\pi$
$149$	−11.6603	−	13.4567i	−0.955252	−	1.10242i	0.0394088	−	0.999223i	$-0.487453\pi$
$150$	−0.654861	−	0.755750i	−0.0534692	−	0.0617067i
$151$	6.36320	+	1.86840i	0.517830	+	0.152049i	0.530196	−	0.847875i	$-0.322118\pi$
$151$	6.36320	+	1.86840i	0.517830	+	0.152049i	−0.0123665	+	0.999924i	$0.503936\pi$
$152$	−0.0968356	+	0.212040i	−0.00785440	+	0.0171987i
$153$	6.16109	+	3.95949i	0.498094	+	0.320106i
$154$	−4.67871	+	1.37379i	−0.377021	+	0.110703i
$155$	−0.0926899	+	0.644672i	−0.00744503	+	0.0517813i
$156$	−2.77826	−	6.08354i	−0.222439	−	0.487073i
$157$	−0.358502	−	2.49343i	−0.0286115	−	0.198998i	0.970502	−	0.241093i	$-0.0775058\pi$
$157$	−0.358502	−	2.49343i	−0.0286115	−	0.198998i	−0.999114	+	0.0420952i	$0.986597\pi$
$158$	5.94414	−	3.82007i	0.472890	−	0.303908i
$159$	−0.00897052	+	0.0103525i	−0.000711408	+	0.000821009i
$160$	1.00000			0.0790569
$161$	−13.2275	+	5.09460i	−1.04248	+	0.401511i
$162$	1.00000			0.0785674
$163$	15.2960	−	17.6525i	1.19808	−	1.38265i	0.293712	−	0.955894i	$-0.405109\pi$
$163$	15.2960	−	17.6525i	1.19808	−	1.38265i	0.904365	−	0.426760i	$-0.140345\pi$
$164$	6.79708	−	4.36822i	0.530763	−	0.341101i
$165$	−0.234792	−	1.63302i	−0.0182786	−	0.127130i
$166$	−1.45295	−	3.18151i	−0.112771	−	0.246933i
$167$	−2.13301	+	14.8354i	−0.165057	+	1.14800i	0.723866	+	0.689940i	$0.242363\pi$
$167$	−2.13301	+	14.8354i	−0.165057	+	1.14800i	−0.888923	+	0.458056i	$0.848546\pi$
$168$	−2.83591	+	0.832699i	−0.218795	+	0.0642441i
$169$	26.6915	+	17.1536i	2.05319	+	1.31951i
$170$	3.04237	−	6.66187i	0.233339	−	0.510942i
$171$	0.223663	+	0.0656735i	0.0171040	+	0.00502218i
$172$	−1.64726	−	1.90104i	−0.125602	−	0.144953i
$173$	−11.2582	−	12.9927i	−0.855945	−	0.987813i	0.144054	−	0.989570i	$-0.453986\pi$
$173$	−11.2582	−	12.9927i	−0.855945	−	0.987813i	−0.999998	+	0.00175677i	$0.999441\pi$
$174$	−8.24567	−	2.42115i	−0.625103	−	0.183547i
$175$	1.22782	−	2.68854i	0.0928141	−	0.203235i
$176$	1.38791	+	0.891954i	0.104617	+	0.0672336i
$177$	6.55130	−	1.92363i	0.492426	−	0.144589i
$178$	0.888378	−	6.17880i	0.0665867	−	0.463121i
$179$	−0.177830	−	0.389394i	−0.0132917	−	0.0291047i	0.902870	−	0.429914i	$-0.141456\pi$
$179$	−0.177830	−	0.389394i	−0.0132917	−	0.0291047i	−0.916161	+	0.400810i	$0.868729\pi$
$180$	−0.142315	−	0.989821i	−0.0106075	−	0.0737769i
$181$	13.4236	−	8.62682i	0.997767	−	0.641226i	0.0635680	−	0.997978i	$-0.479752\pi$
$181$	13.4236	−	8.62682i	0.997767	−	0.641226i	0.934199	+	0.356751i	$0.116116\pi$
$182$	12.9447	−	14.9389i	0.959522	−	1.10735i
$183$	−11.1448			−0.823850
$184$	4.23342	+	2.25348i	0.312092	+	0.166129i
$185$	5.36718			0.394603
$186$	−0.426512	+	0.492221i	−0.0312734	+	0.0360914i
$187$	10.1646	−	6.53240i	0.743310	−	0.477697i
$188$	−0.541600	−	3.76691i	−0.0395003	−	0.274730i
$189$	1.22782	+	2.68854i	0.0893104	+	0.195563i
$190$	0.0331744	−	0.230733i	0.00240672	−	0.0167391i
$191$	8.45427	−	2.48240i	0.611730	−	0.179620i	0.0388304	−	0.999246i	$-0.487637\pi$
$191$	8.45427	−	2.48240i	0.611730	−	0.179620i	0.572899	+	0.819626i	$0.305819\pi$
$192$	0.841254	+	0.540641i	0.0607122	+	0.0390174i
$193$	−2.05626	+	4.50258i	−0.148013	+	0.324103i	−0.969087	−	0.246718i	$-0.920648\pi$
$193$	−2.05626	+	4.50258i	−0.148013	+	0.324103i	0.821074	+	0.570821i	$0.193375\pi$
$194$	6.07774	+	1.78458i	0.436356	+	0.128126i
$195$	4.37966	+	5.05439i	0.313634	+	0.361952i
$196$	−1.13669	−	1.31182i	−0.0811925	−	0.0937011i
$197$	−10.2033	−	2.99597i	−0.726958	−	0.213454i	−0.102744	−	0.994708i	$-0.532762\pi$
$197$	−10.2033	−	2.99597i	−0.726958	−	0.213454i	−0.624214	+	0.781254i	$0.714581\pi$
$198$	0.685355	−	1.50072i	0.0487061	−	0.106651i
$199$	−22.3584	−	14.3688i	−1.58494	−	1.01858i	−0.973899	−	0.226984i	$-0.927114\pi$
$199$	−22.3584	−	14.3688i	−1.58494	−	1.01858i	−0.611044	−	0.791597i	$-0.709250\pi$
$200$	−0.959493	+	0.281733i	−0.0678464	+	0.0199215i
$201$	0.149398	−	1.03908i	0.0105377	−	0.0732912i
$202$	−3.50145	−	7.66710i	−0.246361	−	0.539455i
$203$	−3.61481	−	25.1416i	−0.253710	−	1.76459i
$204$	6.16109	−	3.95949i	0.431362	−	0.277220i
$205$	−5.29108	+	6.10623i	−0.369545	+	0.426478i
$206$	−0.961236			−0.0669725
$207$	1.62806	−	4.51103i	0.113158	−	0.313538i
$208$	−6.68792			−0.463724
$209$	0.251846	−	0.290646i	0.0174206	−	0.0201044i
$210$	2.48644	−	1.59794i	0.171581	−	0.110268i
$211$	−3.18286	−	22.1373i	−0.219117	−	1.52399i	−0.741309	−	0.671164i	$-0.765794\pi$
$211$	−3.18286	−	22.1373i	−0.219117	−	1.52399i	0.522191	−	0.852828i	$-0.325115\pi$
$212$	0.00569050	+	0.0124605i	0.000390825	+	0.000855788i
$213$	0.384227	−	2.67236i	0.0263268	−	0.183107i
$214$	10.4119	−	3.05721i	0.711742	−	0.208986i
$215$	2.11612	+	1.35995i	0.144318	+	0.0927476i
$216$	0.415415	−	0.909632i	0.0282654	−	0.0618926i
$217$	−1.84703	−	0.542338i	−0.125385	−	0.0368163i
$218$	7.38592	+	8.52380i	0.500237	+	0.577305i
$219$	5.21217	+	6.01516i	0.352206	+	0.406467i
$220$	−1.58298	−	0.464805i	−0.106724	−	0.0313371i
$221$	−20.3472	+	44.5540i	−1.36870	+	2.99703i
$222$	4.51516	+	2.90171i	0.303037	+	0.194750i
$223$	−12.9498	+	3.80240i	−0.867183	+	0.254628i	−0.684917	−	0.728621i	$-0.740161\pi$
$223$	−12.9498	+	3.80240i	−0.867183	+	0.254628i	−0.182266	+	0.983249i	$0.558343\pi$
$224$	−0.420631	+	2.92555i	−0.0281046	+	0.195472i
$225$	0.415415	+	0.909632i	0.0276943	+	0.0606421i
$226$	2.09031	+	14.5384i	0.139045	+	0.967080i
$227$	15.9410	−	10.2446i	1.05804	−	0.679961i	0.108656	−	0.994079i	$-0.465345\pi$
$227$	15.9410	−	10.2446i	1.05804	−	0.679961i	0.949384	+	0.314119i	$0.101709\pi$
$228$	0.152652	−	0.176170i	0.0101096	−	0.0116671i
$229$	−21.2220			−1.40239			−0.701195	−	0.712969i	$-0.747350\pi$
$229$	−21.2220			−1.40239			−0.701195	+	0.712969i	$0.747350\pi$
$230$	−4.69681	−	0.969505i	−0.309699	−	0.0639273i
$231$	4.87623			0.320833
$232$	−5.62773	+	6.49475i	−0.369479	+	0.426401i
$233$	4.74290	−	3.04808i	0.310718	−	0.199686i	−0.375983	−	0.926627i	$-0.622695\pi$
$233$	4.74290	−	3.04808i	0.310718	−	0.199686i	0.686701	+	0.726940i	$0.259058\pi$
$234$	0.951790	+	6.61984i	0.0622205	+	0.432753i
$235$	1.58092	+	3.46174i	0.103128	+	0.225819i
$236$	0.971708	−	6.75838i	0.0632528	−	0.439933i
$237$	−6.77960	+	1.99067i	−0.440382	+	0.129308i
$238$	18.2099	+	11.7028i	1.18037	+	0.758580i
$239$	7.90267	−	17.3044i	0.511181	−	1.11933i	−0.461490	−	0.887145i	$-0.652685\pi$
$239$	7.90267	−	17.3044i	0.511181	−	1.11933i	0.972672	−	0.232186i	$-0.0745877\pi$
$240$	−0.959493	−	0.281733i	−0.0619350	−	0.0181858i
$241$	7.80766	+	9.01052i	0.502935	+	0.580418i	0.949276	−	0.314445i	$-0.101818\pi$
$241$	7.80766	+	9.01052i	0.502935	+	0.580418i	−0.446340	+	0.894863i	$0.647273\pi$
$242$	5.42102	+	6.25619i	0.348477	+	0.402163i
$243$	−0.959493	−	0.281733i	−0.0615515	−	0.0180732i
$244$	−4.62973	+	10.1377i	−0.296388	+	0.648999i
$245$	1.46023	+	0.938434i	0.0932908	+	0.0599543i
$246$	−7.75242	+	2.27632i	−0.494276	+	0.145133i
$247$	−0.221868	+	1.54312i	−0.0141171	+	0.0981866i
$248$	0.270560	+	0.592445i	0.0171806	+	0.0376203i
$249$	0.497757	+	3.46198i	0.0315441	+	0.219394i
$250$	0.841254	−	0.540641i	0.0532055	−	0.0341931i
$251$	−13.3841	+	15.4461i	−0.844799	+	0.974950i	−0.999916	−	0.0129465i	$-0.995879\pi$
$251$	−13.3841	+	15.4461i	−0.844799	+	0.974950i	0.155118	+	0.987896i	$0.450424\pi$
$252$	2.95564			0.186188
$253$	−5.65399	−	5.53493i	−0.355463	−	0.347978i
$254$	−4.65902			−0.292333
$255$	−4.79600	+	5.53488i	−0.300337	+	0.346608i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	0.134123	+	0.932843i	0.00836634	+	0.0581892i	0.993577	−	0.113159i	$-0.0360969\pi$
$257$	0.134123	+	0.932843i	0.00836634	+	0.0581892i	−0.985211	+	0.171348i	$0.945188\pi$
$258$	1.04495	+	2.28812i	0.0650557	+	0.142452i
$259$	−2.25760	+	15.7019i	−0.140280	+	0.975671i
$260$	6.41701	−	1.88420i	0.397966	−	0.116853i
$261$	7.22955	+	4.64615i	0.447498	+	0.287589i
$262$	8.34614	−	18.2755i	0.515626	−	1.12906i
$263$	3.18758	+	0.935958i	0.196555	+	0.0577136i	0.378528	−	0.925590i	$-0.376430\pi$
$263$	3.18758	+	0.935958i	0.196555	+	0.0577136i	−0.181974	+	0.983303i	$0.558249\pi$
$264$	−1.08040	−	1.24684i	−0.0664937	−	0.0767378i
$265$	−0.00897052	−	0.0103525i	−0.000551054	−	0.000635951i
$266$	0.661067	+	0.194107i	0.0405326	+	0.0119015i
$267$	−2.59316	+	5.67823i	−0.158699	+	0.347502i
$268$	−0.883121	−	0.567547i	−0.0539452	−	0.0346685i
$269$	−0.524005	+	0.153862i	−0.0319491	+	0.00938111i	−0.297668	−	0.954669i	$-0.596209\pi$
$269$	−0.524005	+	0.153862i	−0.0319491	+	0.00938111i	0.265719	+	0.964051i	$0.414391\pi$
$270$	−0.142315	+	0.989821i	−0.00866101	+	0.0602386i
$271$	−7.88564	−	17.2671i	−0.479019	−	1.04890i	−0.982732	−	0.185034i	$-0.940761\pi$
$271$	−7.88564	−	17.2671i	−0.479019	−	1.04890i	0.503714	−	0.863871i	$-0.331967\pi$
$272$	−1.04227	−	7.24915i	−0.0631970	−	0.439545i
$273$	−16.6291	+	10.6869i	−1.00644	+	0.646799i
$274$	−12.2280	+	14.1118i	−0.738718	+	0.852526i
$275$	1.64981			0.0994872
$276$	−3.42706	−	3.35489i	−0.206285	−	0.201941i
$277$	4.15170			0.249451			0.124726	−	0.992191i	$-0.460195\pi$
$277$	4.15170			0.249451			0.124726	+	0.992191i	$0.460195\pi$
$278$	−8.72562	+	10.0699i	−0.523328	+	0.603952i
$279$	0.547910	−	0.352120i	0.0328025	−	0.0210809i
$280$	−0.420631	−	2.92555i	−0.0251375	−	0.174835i
$281$	0.821390	+	1.79859i	0.0490000	+	0.107295i	0.932549	−	0.361044i	$-0.117580\pi$
$281$	0.821390	+	1.79859i	0.0490000	+	0.107295i	−0.883549	+	0.468339i	$0.844852\pi$
$282$	−0.541600	+	3.76691i	−0.0322518	+	0.224316i
$283$	13.9758	−	4.10365i	0.830773	−	0.243937i	0.161424	−	0.986885i	$-0.448391\pi$
$283$	13.9758	−	4.10365i	0.830773	−	0.243937i	0.669349	+	0.742948i	$0.266573\pi$
$284$	−2.27125	−	1.45964i	−0.134774	−	0.0866139i
$285$	−0.0968356	+	0.212040i	−0.00573605	+	0.0125602i
$286$	10.5868	+	3.10858i	0.626013	+	0.183814i
$287$	−15.6385	−	18.0478i	−0.923112	−	1.06533i
$288$	−0.654861	−	0.755750i	−0.0385880	−	0.0445330i
$289$	−35.1525	−	10.3217i	−2.06780	−	0.607160i
$290$	3.56999	−	7.81718i	0.209637	−	0.459041i
$291$	−5.32877	−	3.42459i	−0.312378	−	0.200753i
$292$	7.63680	−	2.24237i	0.446910	−	0.131225i
$293$	−1.50731	+	10.4836i	−0.0880582	+	0.612458i	0.897231	+	0.441562i	$0.145575\pi$
$293$	−1.50731	+	10.4836i	−0.0880582	+	0.612458i	−0.985289	+	0.170896i	$0.945334\pi$
$294$	0.721069	+	1.57892i	0.0420536	+	0.0920846i
$295$	0.971708	+	6.75838i	0.0565750	+	0.393488i
$296$	4.51516	−	2.90171i	0.262438	−	0.168659i
$297$	−1.08040	+	1.24684i	−0.0626909	+	0.0723491i
$298$	17.8058			1.03146
$299$	31.4119	+	6.48397i	1.81660	+	0.374978i
$300$	1.00000			0.0577350
$301$	−4.86870	+	5.61878i	−0.280627	+	0.323861i
$302$	−5.57905	+	3.58544i	−0.321038	+	0.206319i
$303$	1.19954	+	8.34300i	0.0689119	+	0.479293i
$304$	−0.0968356	−	0.212040i	−0.00555390	−	0.0121614i
$305$	1.58607	−	11.0314i	0.0908184	−	0.631656i
$306$	−7.02704	+	2.06332i	−0.401709	+	0.117952i
$307$	27.1876	+	17.4724i	1.55168	+	0.997202i	0.984859	+	0.173358i	$0.0554617\pi$
$307$	27.1876	+	17.4724i	1.55168	+	0.997202i	0.566817	+	0.823844i	$0.308175\pi$
$308$	2.02566	−	4.43558i	0.115423	−	0.252741i
$309$	0.922299	+	0.270811i	0.0524678	+	0.0154059i
$310$	−0.426512	−	0.492221i	−0.0242242	−	0.0279563i
$311$	−12.2669	−	14.1567i	−0.695590	−	0.802754i	0.292560	−	0.956247i	$-0.405493\pi$
$311$	−12.2669	−	14.1567i	−0.695590	−	0.802754i	−0.988150	+	0.153494i	$0.950948\pi$
$312$	6.41701	+	1.88420i	0.363292	+	0.106672i
$313$	−9.46193	+	20.7187i	−0.534820	+	1.17109i	0.428698	+	0.903448i	$0.358972\pi$
$313$	−9.46193	+	20.7187i	−0.534820	+	1.17109i	−0.963518	+	0.267644i	$0.913755\pi$
$314$	2.11918	+	1.36191i	0.119592	+	0.0768572i
$315$	−2.83591	+	0.832699i	−0.159786	+	0.0469173i
$316$	−1.00557	+	6.99389i	−0.0565677	+	0.393437i
$317$	0.256202	+	0.561004i	0.0143897	+	0.0315091i	0.916690	−	0.399598i	$-0.130850\pi$
$317$	0.256202	+	0.561004i	0.0143897	+	0.0315091i	−0.902301	+	0.431107i	$0.858123\pi$
$318$	−0.00194948	−	0.0135589i	−0.000109321	−	0.000760347i
$319$	11.9274	−	7.66526i	0.667805	−	0.429172i
$320$	−0.654861	+	0.755750i	−0.0366078	+	0.0422477i
$321$	−10.8515			−0.605669
$322$	4.81196	−	13.3330i	0.268160	−	0.743017i
$323$	−1.70720			−0.0949909
$324$	−0.654861	+	0.755750i	−0.0363812	+	0.0419861i
$325$	−5.62623	+	3.61576i	−0.312087	+	0.200566i
$326$	3.32414	+	23.1199i	0.184107	+	1.28049i
$327$	−4.68530	−	10.2594i	−0.259098	−	0.567345i
$328$	−1.14986	+	7.99747i	−0.0634905	+	0.441586i
$329$	−10.7925	+	3.16896i	−0.595009	+	0.174710i
$330$	1.38791	+	0.891954i	0.0764018	+	0.0491005i
$331$	−14.6668	+	32.1159i	−0.806162	+	1.76525i	−0.183071	+	0.983100i	$0.558604\pi$
$331$	−14.6668	+	32.1159i	−0.806162	+	1.76525i	−0.623091	+	0.782149i	$0.714124\pi$
$332$	3.35590	+	0.985382i	0.184179	+	0.0540798i
$333$	−3.51475	−	4.05624i	−0.192607	−	0.222281i
$334$	−9.81501	−	11.3271i	−0.537053	−	0.619793i
$335$	1.00724	+	0.295754i	0.0550317	+	0.0161588i
$336$	1.22782	−	2.68854i	0.0669828	−	0.146672i
$337$	20.0876	+	12.9095i	1.09424	+	0.703226i	0.957804	−	0.287423i	$-0.0927985\pi$
$337$	20.0876	+	12.9095i	1.09424	+	0.703226i	0.136437	+	0.990649i	$0.456435\pi$
$338$	−30.4430	+	8.93888i	−1.65588	+	0.486211i
$339$	2.09031	−	14.5384i	0.113530	−	0.789617i
$340$	3.04237	+	6.66187i	0.164996	+	0.361291i
$341$	−0.152921	−	1.06359i	−0.00828111	−	0.0575964i
$342$	−0.196101	+	0.126026i	−0.0106039	+	0.00681473i
$343$	10.1891	−	11.7588i	0.550157	−	0.634915i
$344$	2.51544			0.135623
$345$	4.23342	+	2.25348i	0.227920	+	0.121323i
$346$	17.1917			0.924234
$347$	−10.8750	+	12.5504i	−0.583799	+	0.673740i	−0.968417	−	0.249336i	$-0.919788\pi$
$347$	−10.8750	+	12.5504i	−0.583799	+	0.673740i	0.384618	+	0.923076i	$0.374333\pi$
$348$	7.22955	−	4.64615i	0.387545	−	0.249060i
$349$	0.566452	+	3.93976i	0.0303215	+	0.210891i	0.999350	−	0.0360597i	$-0.0114806\pi$
$349$	0.566452	+	3.93976i	0.0303215	+	0.210891i	−0.969028	+	0.246950i	$0.920572\pi$
$350$	1.22782	+	2.68854i	0.0656295	+	0.143709i
$351$	0.951790	−	6.61984i	0.0508028	−	0.353341i
$352$	−1.58298	+	0.464805i	−0.0843731	+	0.0247742i
$353$	−18.7243	−	12.0334i	−0.996594	−	0.640472i	−0.0627038	−	0.998032i	$-0.519972\pi$
$353$	−18.7243	−	12.0334i	−0.996594	−	0.640472i	−0.933890	+	0.357560i	$0.883609\pi$
$354$	−2.83640	+	6.21085i	−0.150753	+	0.330103i
$355$	2.59048	+	0.760632i	0.137488	+	0.0403702i
$356$	4.08787	+	4.71765i	0.216656	+	0.250035i
$357$	−14.1752	−	16.3591i	−0.750233	−	0.865815i
$358$	0.410738	+	0.120604i	0.0217082	+	0.00637410i
$359$	−8.50807	+	18.6301i	−0.449039	+	0.983257i	0.540812	+	0.841144i	$0.318117\pi$
$359$	−8.50807	+	18.6301i	−0.449039	+	0.983257i	−0.989850	+	0.142114i	$0.954610\pi$
$360$	0.841254	+	0.540641i	0.0443380	+	0.0284943i
$361$	18.1782	−	5.33761i	0.956749	−	0.280927i
$362$	−2.27087	+	15.7942i	−0.119354	+	0.830126i
$363$	−3.43886	−	7.53005i	−0.180493	−	0.395225i
$364$	2.81314	+	19.5658i	0.147449	+	1.02553i
$365$	−6.69571	+	4.30307i	−0.350469	+	0.225233i
$366$	7.29831	−	8.42270i	0.381489	−	0.440262i
$367$	−0.851290			−0.0444370			−0.0222185	−	0.999753i	$-0.507073\pi$
$367$	−0.851290			−0.0444370			−0.0222185	+	0.999753i	$0.507073\pi$
$368$	−4.47537	+	1.72369i	−0.233295	+	0.0898535i
$369$	8.07971			0.420613
$370$	−3.51475	+	4.05624i	−0.182723	+	0.210874i
$371$	0.0340601	−	0.0218891i	0.00176831	−	0.00113643i
$372$	−0.0926899	−	0.644672i	−0.00480574	−	0.0334247i
$373$	8.08300	+	17.6993i	0.418522	+	0.916435i	0.995052	+	0.0993592i	$0.0316793\pi$
$373$	8.08300	+	17.6993i	0.418522	+	0.916435i	−0.576530	+	0.817076i	$0.695593\pi$
$374$	−1.71955	+	11.9597i	−0.0889157	+	0.618422i
$375$	−0.959493	+	0.281733i	−0.0495480	+	0.0145486i
$376$	3.20152	+	2.05749i	0.165106	+	0.106107i
$377$	−23.8758	+	52.2807i	−1.22967	+	2.69259i
$378$	−2.83591	−	0.832699i	−0.145864	−	0.0428294i
$379$	0.510397	+	0.589030i	0.0262174	+	0.0302564i	0.768707	−	0.639601i	$-0.220901\pi$
$379$	0.510397	+	0.589030i	0.0262174	+	0.0302564i	−0.742489	+	0.669858i	$0.766355\pi$
$380$	0.152652	+	0.176170i	0.00783087	+	0.00903731i
$381$	4.47029	+	1.31260i	0.229020	+	0.0672464i
$382$	−3.66030	+	8.01494i	−0.187277	+	0.410080i
$383$	9.92301	+	6.37713i	0.507042	+	0.325856i	0.769028	−	0.639216i	$-0.220741\pi$
$383$	9.92301	+	6.37713i	0.507042	+	0.325856i	−0.261985	+	0.965072i	$0.584377\pi$
$384$	−0.959493	+	0.281733i	−0.0489639	+	0.0143771i
$385$	−0.693960	+	4.82660i	−0.0353675	+	0.245986i
$386$	−2.05626	−	4.50258i	−0.104661	−	0.229175i
$387$	−0.357984	−	2.48983i	−0.0181973	−	0.126565i
$388$	−5.32877	+	3.42459i	−0.270527	+	0.173857i
$389$	21.2935	−	24.5740i	1.07962	−	1.24595i	0.111958	−	0.993713i	$-0.464288\pi$
$389$	21.2935	−	24.5740i	1.07962	−	1.24595i	0.967665	−	0.252238i	$-0.0811667\pi$
$390$	−6.68792			−0.338656
$391$	−2.13274	+	35.0584i	−0.107857	+	1.77298i
$392$	1.73578			0.0876702
$393$	−13.1569	+	15.1838i	−0.663676	+	0.765923i
$394$	8.94597	−	5.74923i	0.450692	−	0.289642i
$395$	−1.00557	−	6.99389i	−0.0505957	−	0.351901i
$396$	0.685355	+	1.50072i	0.0344404	+	0.0754140i
$397$	−4.42000	+	30.7418i	−0.221833	+	1.54288i	0.509263	+	0.860611i	$0.329918\pi$
$397$	−4.42000	+	30.7418i	−0.221833	+	1.54288i	−0.731097	+	0.682274i	$0.760991\pi$
$398$	25.5009	−	7.48773i	1.27824	−	0.375326i
$399$	−0.579603	−	0.372488i	−0.0290164	−	0.0186477i
$400$	0.415415	−	0.909632i	0.0207708	−	0.0454816i
$401$	22.2668	+	6.53812i	1.11195	+	0.326498i	0.785590	−	0.618747i	$-0.212359\pi$
$401$	22.2668	+	6.53812i	1.11195	+	0.326498i	0.326360	+	0.945245i	$0.394178\pi$
$402$	0.687452	+	0.793361i	0.0342870	+	0.0395693i
$403$	2.85248	+	3.29193i	0.142092	+	0.163983i
$404$	8.08737	+	2.37467i	0.402362	+	0.118144i
$405$	0.415415	−	0.909632i	0.0206421	−	0.0452000i
$406$	21.3679	+	13.7323i	1.06047	+	0.681524i
$407$	−8.49613	+	2.49469i	−0.421138	+	0.123657i
$408$	−1.04227	+	7.24915i	−0.0516001	+	0.358887i
$409$	−2.73022	−	5.97836i	−0.135001	−	0.295611i	0.830043	−	0.557700i	$-0.188316\pi$
$409$	−2.73022	−	5.97836i	−0.135001	−	0.295611i	−0.965044	+	0.262089i	$0.915589\pi$
$410$	−1.14986	−	7.99747i	−0.0567876	−	0.394967i
$411$	15.7084	−	10.0952i	0.774838	−	0.497958i
$412$	0.629476	−	0.726454i	0.0310120	−	0.0357898i
$413$	−20.1807			−0.993028
$414$	2.34306	+	4.18451i	0.115155	+	0.205657i
$415$	−3.49758			−0.171689
$416$	4.37966	−	5.05439i	0.214730	−	0.247812i
$417$	11.2092	−	7.20371i	0.548916	−	0.352767i
$418$	0.0547314	+	0.380665i	0.00267700	+	0.0186190i
$419$	12.7252	+	27.8643i	0.621667	+	1.36126i	0.914301	+	0.405036i	$0.132741\pi$
$419$	12.7252	+	27.8643i	0.621667	+	1.36126i	−0.292633	+	0.956225i	$0.594532\pi$
$420$	−0.420631	+	2.92555i	−0.0205247	+	0.142752i
$421$	27.3653	−	8.03518i	1.33370	−	0.391611i	0.464285	−	0.885686i	$-0.346311\pi$
$421$	27.3653	−	8.03518i	1.33370	−	0.391611i	0.869419	+	0.494075i	$0.164493\pi$
$422$	18.8146	+	12.0914i	0.915879	+	0.588599i
$423$	1.58092	−	3.46174i	0.0768671	−	0.168316i
$424$	−0.0131435	−	0.00385927i	−0.000638304	−	0.000187423i
$425$	−4.79600	−	5.53488i	−0.232640	−	0.268481i
$426$	1.76802	+	2.04040i	0.0856608	+	0.0988578i
$427$	31.6057	+	9.28029i	1.52951	+	0.449104i
$428$	−4.50786	+	9.87083i	−0.217895	+	0.477124i
$429$	−9.28221	−	5.96532i	−0.448149	−	0.288008i
$430$	−2.41354	+	0.708680i	−0.116391	+	0.0341756i
$431$	1.15571	−	8.03815i	0.0556687	−	0.387184i	−0.942871	−	0.333158i	$-0.891886\pi$
$431$	1.15571	−	8.03815i	0.0556687	−	0.387184i	0.998540	−	0.0540257i	$-0.0172053\pi$
$432$	0.415415	+	0.909632i	0.0199867	+	0.0437647i
$433$	0.241134	+	1.67712i	0.0115882	+	0.0805974i	0.994795	−	0.101898i	$-0.0324916\pi$
$433$	0.241134	+	1.67712i	0.0115882	+	0.0805974i	−0.983207	+	0.182496i	$0.941582\pi$
$434$	1.61942	−	1.04074i	0.0777347	−	0.0499571i
$435$	−5.62773	+	6.49475i	−0.269829	+	0.311399i
$436$	−11.2786			−0.540147
$437$	0.249245	+	1.08980i	0.0119230	+	0.0521321i
$438$	−7.95920			−0.380305
$439$	−4.91735	+	5.67493i	−0.234692	+	0.270849i	−0.860863	−	0.508836i	$-0.830076\pi$
$439$	−4.91735	+	5.67493i	−0.234692	+	0.270849i	0.626171	+	0.779686i	$0.284621\pi$
$440$	1.38791	−	0.891954i	0.0661659	−	0.0425222i
$441$	−0.247027	−	1.71811i	−0.0117632	−	0.0818149i
$442$	−20.3472	−	44.5540i	−0.967815	−	2.11922i
$443$	5.94970	−	41.3810i	0.282679	−	1.96607i	0.0256402	−	0.999671i	$-0.491838\pi$
$443$	5.94970	−	41.3810i	0.282679	−	1.96607i	0.257038	−	0.966401i	$-0.417253\pi$
$444$	−5.14977	+	1.51211i	−0.244397	+	0.0717615i
$445$	−5.25139	−	3.37487i	−0.248940	−	0.159984i
$446$	5.60665	−	12.2769i	0.265483	−	0.581326i
$447$	−17.0846	−	5.01648i	−0.808072	−	0.237271i
$448$	−1.93553	−	2.23372i	−0.0914452	−	0.105533i
$449$	−19.2190	−	22.1799i	−0.907000	−	1.04673i	−0.998701	−	0.0509469i	$-0.983776\pi$
$449$	−19.2190	−	22.1799i	−0.907000	−	1.04673i	0.0917017	−	0.995787i	$-0.470769\pi$
$450$	−0.959493	−	0.281733i	−0.0452309	−	0.0132810i
$451$	5.53747	−	12.1254i	0.260749	−	0.570961i
$452$	−12.3562	−	7.94088i	−0.581189	−	0.373507i
$453$	6.36320	−	1.86840i	0.298969	−	0.0877852i
$454$	−2.69673	+	18.7562i	−0.126564	+	0.880272i
$455$	−8.21153	−	17.9807i	−0.384962	−	0.842950i
$456$	0.0331744	+	0.230733i	0.00155353	+	0.0108051i
$457$	−12.9653	+	8.33231i	−0.606492	+	0.389769i	−0.807540	−	0.589812i	$-0.799202\pi$
$457$	−12.9653	+	8.33231i	−0.606492	+	0.389769i	0.201048	+	0.979581i	$0.435565\pi$
$458$	13.8975	−	16.0385i	0.649386	−	0.749432i
$459$	7.32370			0.341841
$460$	3.80846	−	2.91472i	0.177570	−	0.135900i
$461$	33.7344			1.57117			0.785585	−	0.618754i	$-0.212362\pi$
$461$	33.7344			1.57117			0.785585	+	0.618754i	$0.212362\pi$
$462$	−3.19325	+	3.68521i	−0.148564	+	0.171452i
$463$	−3.96382	+	2.54739i	−0.184215	+	0.118387i	−0.629498	−	0.777002i	$-0.716739\pi$
$463$	−3.96382	+	2.54739i	−0.184215	+	0.118387i	0.445283	+	0.895390i	$0.353103\pi$
$464$	−1.22302	−	8.50631i	−0.0567774	−	0.394896i
$465$	0.270560	+	0.592445i	0.0125469	+	0.0274740i
$466$	−0.802357	+	5.58052i	−0.0371685	+	0.258512i
$467$	15.0653	−	4.42358i	0.697141	−	0.204699i	0.0860866	−	0.996288i	$-0.472564\pi$
$467$	15.0653	−	4.42358i	0.697141	−	0.204699i	0.611054	+	0.791589i	$0.290746\pi$
$468$	−5.62623	−	3.61576i	−0.260073	−	0.167139i
$469$	−1.28892	+	2.82234i	−0.0595168	+	0.130324i
$470$	−3.65149	−	1.07218i	−0.168431	−	0.0494557i
$471$	−1.64964	−	1.90379i	−0.0760115	−	0.0877219i
$472$	4.47131	+	5.16016i	0.205809	+	0.237516i
$473$	−3.98188	−	1.16919i	−0.183087	−	0.0537593i
$474$	2.93524	−	6.42729i	0.134820	−	0.295215i
$475$	−0.196101	−	0.126026i	−0.00899773	−	0.00578249i
$476$	−20.7694	+	6.09843i	−0.951962	+	0.279521i
$477$	−0.00194948	+	0.0135589i	−8.92605e−5	+	0.000620821i
$478$	7.90267	+	17.3044i	0.361460	+	0.791486i
$479$	−5.24382	−	36.4716i	−0.239596	−	1.66643i	−0.654121	−	0.756390i	$-0.726961\pi$
$479$	−5.24382	−	36.4716i	−0.239596	−	1.66643i	0.414524	−	0.910038i	$-0.363948\pi$
$480$	0.841254	−	0.540641i	0.0383978	−	0.0246768i
$481$	23.5064	−	27.1278i	1.07180	−	1.23692i
$482$	−11.9226			−0.543061
$483$	−8.37337	+	11.4372i	−0.381002	+	0.520411i
$484$	−8.27813			−0.376279
$485$	4.14810	−	4.78716i	0.188355	−	0.217374i
$486$	0.841254	−	0.540641i	0.0381600	−	0.0245240i
$487$	2.32553	+	16.1744i	0.105380	+	0.732932i	0.972173	+	0.234264i	$0.0752682\pi$
$487$	2.32553	+	16.1744i	0.105380	+	0.732932i	−0.866793	+	0.498668i	$0.833823\pi$
$488$	−4.62973	−	10.1377i	−0.209578	−	0.458912i
$489$	3.32414	−	23.1199i	0.150323	−	1.04552i
$490$	−1.66547	+	0.489026i	−0.0752382	+	0.0220919i
$491$	−17.6675	−	11.3542i	−0.797322	−	0.512408i	0.0774190	−	0.996999i	$-0.475332\pi$
$491$	−17.6675	−	11.3542i	−0.797322	−	0.512408i	−0.874741	+	0.484591i	$0.838968\pi$
$492$	3.35643	−	7.34956i	0.151320	−	0.331344i
$493$	−60.3888	−	17.7318i	−2.71978	−	0.798598i
$494$	−1.02092	−	1.17821i	−0.0459335	−	0.0530101i
$495$	−1.08040	−	1.24684i	−0.0485601	−	0.0560414i
$496$	−0.624919	−	0.183493i	−0.0280597	−	0.00823907i
$497$	−3.31490	+	7.25862i	−0.148694	+	0.325594i
$498$	−2.94235	−	1.89093i	−0.131850	−	0.0847348i
$499$	19.6796	−	5.77846i	0.880981	−	0.258679i	0.190202	−	0.981745i	$-0.439086\pi$
$499$	19.6796	−	5.77846i	0.880981	−	0.258679i	0.690779	+	0.723066i	$0.257268\pi$
$500$	−0.142315	+	0.989821i	−0.00636451	+	0.0442662i
$501$	6.22621	+	13.6335i	0.278167	+	0.609100i
$502$	−2.90865	−	20.2301i	−0.129819	−	0.902913i
$503$	−4.09119	+	2.62925i	−0.182417	+	0.117232i	−0.628662	−	0.777678i	$-0.716397\pi$
$503$	−4.09119	+	2.62925i	−0.182417	+	0.117232i	0.446245	+	0.894911i	$0.352761\pi$
$504$	−1.93553	+	2.23372i	−0.0862153	+	0.0994978i
$505$	−8.42880			−0.375076
$506$	7.88559	−	0.648394i	0.350557	−	0.0288246i
$507$	31.7282			1.40910
$508$	3.05101	−	3.52105i	0.135367	−	0.156221i
$509$	−0.440429	+	0.283047i	−0.0195217	+	0.0125458i	−0.550365	−	0.834924i	$-0.685512\pi$
$509$	−0.440429	+	0.283047i	−0.0195217	+	0.0125458i	0.530844	+	0.847470i	$0.321875\pi$
$510$	−1.04227	−	7.24915i	−0.0461525	−	0.320998i
$511$	−9.77243	−	21.3986i	−0.432307	−	0.946620i
$512$	−0.142315	+	0.989821i	−0.00628949	+	0.0437443i
$513$	0.223663	−	0.0656735i	0.00987498	−	0.00289955i
$514$	−0.792828	−	0.509519i	−0.0349701	−	0.0224739i
$515$	−0.399312	+	0.874371i	−0.0175958	+	0.0385294i
$516$	−2.41354	−	0.708680i	−0.106250	−	0.0311979i
$517$	−4.11160	−	4.74504i	−0.180828	−	0.208687i
$518$	−10.3883	−	11.9888i	−0.456437	−	0.526756i
$519$	−16.4954	−	4.84347i	−0.724066	−	0.212605i
$520$	−2.77826	+	6.08354i	−0.121835	+	0.266781i
$521$	12.1195	+	7.78875i	0.530967	+	0.341232i	0.778497	−	0.627649i	$-0.215983\pi$
$521$	12.1195	+	7.78875i	0.530967	+	0.341232i	−0.247530	+	0.968880i	$0.579619\pi$
$522$	−8.24567	+	2.42115i	−0.360903	+	0.105971i
$523$	−5.76917	+	40.1255i	−0.252268	+	1.75456i	0.332257	+	0.943189i	$0.392190\pi$
$523$	−5.76917	+	40.1255i	−0.252268	+	1.75456i	−0.584525	+	0.811376i	$0.698719\pi$
$524$	8.34614	+	18.2755i	0.364603	+	0.798369i
$525$	−0.420631	−	2.92555i	−0.0183578	−	0.127682i
$526$	−2.79477	+	1.79609i	−0.121858	+	0.0783132i
$527$	−3.12364	+	3.60488i	−0.136068	+	0.157031i
$528$	1.64981			0.0717987
$529$	22.6911	−	3.75696i	0.986569	−	0.163346i
$530$	0.0136984			0.000595019
$531$	4.47131	−	5.16016i	0.194038	−	0.223932i
$532$	−0.579603	+	0.372488i	−0.0251290	+	0.0161494i
$533$	7.69018	+	53.4864i	0.333099	+	2.31675i
$534$	−2.59316	−	5.67823i	−0.112217	−	0.245721i
$535$	1.54432	−	10.7410i	0.0667669	−	0.464374i
$536$	1.00724	−	0.295754i	0.0435063	−	0.0127746i
$537$	−0.360123	−	0.231437i	−0.0155404	−	0.00998723i
$538$	0.226869	−	0.496774i	0.00978103	−	0.0214175i
$539$	−2.74771	−	0.806799i	−0.118352	−	0.0347513i
$540$	−0.654861	−	0.755750i	−0.0281807	−	0.0325223i
$541$	−4.64461	−	5.36016i	−0.199687	−	0.230451i	0.647070	−	0.762430i	$-0.275994\pi$
$541$	−4.64461	−	5.36016i	−0.199687	−	0.230451i	−0.846758	+	0.531979i	$0.821449\pi$
$542$	18.2136	+	5.34801i	0.782343	+	0.229717i
$543$	6.62863	−	14.5147i	0.284462	−	0.622884i
$544$	6.16109	+	3.95949i	0.264154	+	0.169762i
$545$	10.8217	−	3.17755i	0.463553	−	0.136111i
$546$	2.81314	−	19.5658i	0.120391	−	0.837341i
$547$	−13.9912	−	30.6366i	−0.598223	−	1.30992i	−0.930344	−	0.366688i	$-0.880492\pi$
$547$	−13.9912	−	30.6366i	−0.598223	−	1.30992i	0.332121	−	0.943237i	$-0.392236\pi$
$548$	−2.65739	−	18.4826i	−0.113518	−	0.789535i
$549$	−9.37563	+	6.02535i	−0.400142	+	0.257156i
$550$	−1.08040	+	1.24684i	−0.0460682	+	0.0531655i
$551$	−2.00326			−0.0853417
$552$	4.77970	−	0.393012i	0.203438	−	0.0167277i
$553$	20.8840			0.888077
$554$	−2.71878	+	3.13764i	−0.115510	+	0.133306i
$555$	4.51516	−	2.90171i	0.191658	−	0.123171i
$556$	−1.89626	−	13.1888i	−0.0804192	−	0.559328i
$557$	−0.864454	−	1.89289i	−0.0366281	−	0.0802043i	0.890434	−	0.455113i	$-0.150401\pi$
$557$	−0.864454	−	1.89289i	−0.0366281	−	0.0802043i	−0.927062	+	0.374909i	$0.877674\pi$
$558$	−0.0926899	+	0.644672i	−0.00392387	+	0.0272911i
$559$	16.1416	−	4.73959i	0.682716	−	0.200463i
$560$	2.48644	+	1.59794i	0.105071	+	0.0675252i
$561$	5.01934	−	10.9908i	0.211917	−	0.464033i
$562$	−1.89718	−	0.557063i	−0.0800278	−	0.0234983i
$563$	12.4860	+	14.4096i	0.526220	+	0.607290i	0.955177	−	0.296034i	$-0.0956643\pi$
$563$	12.4860	+	14.4096i	0.526220	+	0.607290i	−0.428957	+	0.903325i	$0.641119\pi$
$564$	−2.49217	−	2.87612i	−0.104939	−	0.121106i
$565$	14.0929	+	4.13806i	0.592894	+	0.174089i
$566$	−6.05084	+	13.2495i	−0.254336	+	0.556918i
$567$	2.48644	+	1.59794i	0.104421	+	0.0671071i
$568$	2.59048	−	0.760632i	0.108694	−	0.0319154i
$569$	−6.21587	+	43.2323i	−0.260583	+	1.81239i	0.267897	+	0.963447i	$0.413671\pi$
$569$	−6.21587	+	43.2323i	−0.260583	+	1.81239i	−0.528480	+	0.848946i	$0.677238\pi$
$570$	−0.0968356	−	0.212040i	−0.00405600	−	0.00888140i
$571$	−6.09172	−	42.3688i	−0.254931	−	1.77308i	−0.567684	−	0.823247i	$-0.692160\pi$
$571$	−6.09172	−	42.3688i	−0.254931	−	1.77308i	0.312753	−	0.949834i	$-0.398749\pi$
$572$	−9.28221	+	5.96532i	−0.388109	+	0.249422i
$573$	5.77010	−	6.65905i	0.241049	−	0.278186i
$574$	23.8807			0.996760
$575$	−2.83302	+	3.86962i	−0.118145	+	0.161375i
$576$	1.00000			0.0416667
$577$	−4.46207	+	5.14951i	−0.185759	+	0.214377i	−0.840989	−	0.541052i	$-0.818026\pi$
$577$	−4.46207	+	5.14951i	−0.185759	+	0.214377i	0.655230	+	0.755429i	$0.272572\pi$
$578$	30.8206	−	19.8072i	1.28197	−	0.823872i
$579$	0.704443	+	4.89951i	0.0292756	+	0.203617i
$580$	3.56999	+	7.81718i	0.148236	+	0.324591i
$581$	1.47119	−	10.2323i	0.0610352	−	0.424509i
$582$	6.07774	−	1.78458i	0.251930	−	0.0739734i
$583$	0.0190121	+	0.0122183i	0.000787399	+	0.000506030i
$584$	−3.30637	+	7.23994i	−0.136819	+	0.299591i
$585$	6.41701	+	1.88420i	0.265311	+	0.0779023i
$586$	−6.93589	−	8.00445i	−0.286519	−	0.330661i
$587$	−27.3739	−	31.5911i	−1.12984	−	1.30391i	−0.947170	−	0.320732i	$-0.896071\pi$
$587$	−27.3739	−	31.5911i	−1.12984	−	1.30391i	−0.182671	−	0.983174i	$-0.558474\pi$
$588$	−1.66547	−	0.489026i	−0.0686828	−	0.0201671i
$589$	−0.0630692	+	0.138102i	−0.00259872	+	0.00569040i
$590$	−5.74397	−	3.69143i	−0.236476	−	0.151974i
$591$	−10.2033	+	2.99597i	−0.419709	+	0.123238i
$592$	−0.763829	+	5.31255i	−0.0313932	+	0.218344i
$593$	−11.5354	−	25.2591i	−0.473704	−	1.03727i	−0.984147	−	0.177355i	$-0.943246\pi$
$593$	−11.5354	−	25.2591i	−0.473704	−	1.03727i	0.510443	−	0.859912i	$-0.329481\pi$
$594$	−0.234792	−	1.63302i	−0.00963364	−	0.0670035i
$595$	18.2099	−	11.7028i	0.746534	−	0.479768i
$596$	−11.6603	+	13.4567i	−0.477626	+	0.551210i
$597$	−26.5774			−1.08774
$598$	−25.4707	+	19.4934i	−1.04157	+	0.797146i
$599$	−25.8304			−1.05540			−0.527701	−	0.849430i	$-0.676946\pi$
$599$	−25.8304			−1.05540			−0.527701	+	0.849430i	$0.676946\pi$
$600$	−0.654861	+	0.755750i	−0.0267346	+	0.0308533i
$601$	23.9714	−	15.4055i	0.977812	−	0.628402i	0.0489397	−	0.998802i	$-0.484416\pi$
$601$	23.9714	−	15.4055i	0.977812	−	0.628402i	0.928872	+	0.370400i	$0.120779\pi$
$602$	−1.05807	−	7.35904i	−0.0431237	−	0.299932i
$603$	−0.436089	−	0.954902i	−0.0177589	−	0.0388866i
$604$	0.943808	−	6.56433i	0.0384030	−	0.267099i
$605$	7.94281	−	2.33222i	0.322921	−	0.0948182i
$606$	−7.09075	−	4.55695i	−0.288042	−	0.185113i
$607$	−6.53336	+	14.3061i	−0.265181	+	0.580665i	−0.994645	−	0.103354i	$-0.967042\pi$
$607$	−6.53336	+	14.3061i	−0.265181	+	0.580665i	0.729464	+	0.684019i	$0.239770\pi$
$608$	0.223663	+	0.0656735i	0.00907074	+	0.00266341i
$609$	−16.6335	−	19.1961i	−0.674024	−	0.777865i
$610$	7.29831	+	8.42270i	0.295500	+	0.341025i
$611$	24.4209	+	7.17062i	0.987963	+	0.290092i
$612$	3.04237	−	6.66187i	0.122981	−	0.269290i
$613$	16.2031	+	10.4131i	0.654438	+	0.420582i	0.825286	−	0.564716i	$-0.191014\pi$
$613$	16.2031	+	10.4131i	0.654438	+	0.420582i	−0.170847	+	0.985298i	$0.554651\pi$
$614$	−31.0088	+	9.10501i	−1.25141	+	0.367448i
$615$	−1.14986	+	7.99747i	−0.0463669	+	0.322489i
$616$	2.02566	+	4.43558i	0.0816162	+	0.178715i
$617$	2.83713	+	19.7327i	0.114219	+	0.794409i	0.963738	+	0.266851i	$0.0859831\pi$
$617$	2.83713	+	19.7327i	0.114219	+	0.794409i	−0.849519	+	0.527558i	$0.823108\pi$
$618$	−0.808643	+	0.519683i	−0.0325284	+	0.0209047i
$619$	4.16549	−	4.80723i	0.167425	−	0.193219i	−0.665837	−	0.746098i	$-0.731925\pi$
$619$	4.16549	−	4.80723i	0.167425	−	0.193219i	0.833262	+	0.552879i	$0.186471\pi$
$620$	0.651301			0.0261569
$621$	−1.06923	−	4.67512i	−0.0429069	−	0.187606i
$622$	18.7320			0.751085
$623$	12.0822	−	13.9436i	0.484065	−	0.558640i
$624$	−5.62623	+	3.61576i	−0.225230	+	0.144746i
$625$	−0.142315	−	0.989821i	−0.00569259	−	0.0395929i
$626$	−9.46193	−	20.7187i	−0.378175	−	0.828087i
$627$	0.0547314	−	0.380665i	0.00218576	−	0.0152023i
$628$	−2.41703	+	0.709705i	−0.0964501	+	0.0283203i
$629$	33.0676	+	21.2513i	1.31849	+	0.847344i
$630$	1.22782	−	2.68854i	0.0489173	−	0.107114i
$631$	−12.6522	−	3.71501i	−0.503675	−	0.147892i	0.0200178	−	0.999800i	$-0.493628\pi$
$631$	−12.6522	−	3.71501i	−0.503675	−	0.147892i	−0.523692	+	0.851907i	$0.675446\pi$
$632$	−4.62712	−	5.33998i	−0.184057	−	0.212413i
$633$	−14.6459	−	16.9023i	−0.582122	−	0.671805i
$634$	−0.591755	−	0.173755i	−0.0235016	−	0.00690069i
$635$	−1.93543	+	4.23799i	−0.0768050	+	0.168180i
$636$	0.0115238	+	0.00740589i	0.000456948	+	0.000293663i
$637$	11.1385	−	3.27057i	0.441324	−	0.129585i
$638$	−2.01775	+	14.0338i	−0.0798836	+	0.555603i
$639$	−1.12155	−	2.45586i	−0.0443680	−	0.0971523i
$640$	−0.142315	−	0.989821i	−0.00562549	−	0.0391261i
$641$	−19.9430	+	12.8166i	−0.787701	+	0.506225i	−0.871581	−	0.490251i	$-0.836905\pi$
$641$	−19.9430	+	12.8166i	−0.787701	+	0.506225i	0.0838803	+	0.996476i	$0.473269\pi$
$642$	7.10619	−	8.20098i	0.280459	−	0.323667i
$643$	−1.53887			−0.0606871			−0.0303436	−	0.999540i	$-0.509660\pi$
$643$	−1.53887			−0.0606871			−0.0303436	+	0.999540i	$0.509660\pi$
$644$	6.92522	+	12.3679i	0.272892	+	0.487363i
$645$	2.51544			0.0990452
$646$	1.11798	−	1.29021i	0.0439862	−	0.0507627i
$647$	−25.8876	+	16.6370i	−1.01775	+	0.654066i	−0.939387	−	0.342859i	$-0.888605\pi$
$647$	−25.8876	+	16.6370i	−1.01775	+	0.654066i	−0.0783602	+	0.996925i	$0.524968\pi$
$648$	−0.142315	−	0.989821i	−0.00559065	−	0.0388839i
$649$	−4.67952	−	10.2467i	−0.183687	−	0.402219i
$650$	0.951790	−	6.61984i	0.0373323	−	0.259652i
$651$	−1.84703	+	0.542338i	−0.0723909	+	0.0212559i
$652$	−19.6497	−	12.6281i	−0.769543	−	0.494555i
$653$	16.2720	−	35.6307i	0.636773	−	1.39434i	−0.265895	−	0.964002i	$-0.585668\pi$
$653$	16.2720	−	35.6307i	0.636773	−	1.39434i	0.902668	−	0.430337i	$-0.141605\pi$
$654$	10.8217	+	3.17755i	0.423164	+	0.124252i
$655$	−13.1569	−	15.1838i	−0.514081	−	0.593281i
$656$	−5.29108	−	6.10623i	−0.206582	−	0.238408i
$657$	7.63680	+	2.24237i	0.297940	+	0.0874830i
$658$	4.67263	−	10.2316i	0.182158	−	0.398871i
$659$	−31.4252	−	20.1958i	−1.22415	−	0.786716i	−0.241183	−	0.970480i	$-0.577535\pi$
$659$	−31.4252	−	20.1958i	−1.22415	−	0.786716i	−0.982970	+	0.183764i	$0.941172\pi$
$660$	−1.58298	+	0.464805i	−0.0616174	+	0.0180925i
$661$	−0.448287	+	3.11791i	−0.0174364	+	0.121272i	−0.996681	−	0.0814113i	$-0.974057\pi$
$661$	−0.448287	+	3.11791i	−0.0174364	+	0.121272i	0.979244	+	0.202684i	$0.0649664\pi$
$662$	−14.6668	−	32.1159i	−0.570043	−	1.24822i
$663$	6.97062	+	48.4817i	0.270717	+	1.88288i
$664$	−2.94235	+	1.89093i	−0.114185	+	0.0733825i
$665$	0.451183	−	0.520693i	0.0174961	−	0.0201916i
$666$	5.36718			0.207974
$667$	−2.50260	+	41.1383i	−0.0969012	+	1.59288i
$668$	14.9879			0.579901
$669$	−8.83833	+	10.2000i	−0.341710	+	0.394354i
$670$	−0.883121	+	0.567547i	−0.0341179	+	0.0219263i
$671$	2.61672	+	18.1997i	0.101017	+	0.702591i
$672$	1.22782	+	2.68854i	0.0473640	+	0.103713i
$673$	−0.222339	+	1.54640i	−0.00857055	+	0.0596095i	−0.993658	−	0.112446i	$-0.964132\pi$
$673$	−0.222339	+	1.54640i	−0.00857055	+	0.0596095i	0.985087	+	0.172055i	$0.0550407\pi$
$674$	−22.9109	+	6.72726i	−0.882496	+	0.259124i
$675$	0.841254	+	0.540641i	0.0323799	+	0.0208093i
$676$	13.1804	−	28.8610i	0.506938	−	1.11004i
$677$	−8.99713	−	2.64180i	−0.345788	−	0.101532i	0.104227	−	0.994554i	$-0.466763\pi$
$677$	−8.99713	−	2.64180i	−0.345788	−	0.101532i	−0.450015	+	0.893021i	$0.648581\pi$
$678$	9.61853	+	11.1004i	0.369397	+	0.426307i
$679$	12.2603	+	14.1491i	0.470506	+	0.542993i
$680$	−7.02704	−	2.06332i	−0.269475	−	0.0791249i
$681$	7.87173	−	17.2367i	0.301645	−	0.660511i
$682$	0.903946	+	0.580931i	0.0346139	+	0.0222450i
$683$	26.6419	−	7.82275i	1.01942	−	0.299329i	0.271019	−	0.962574i	$-0.412639\pi$
$683$	26.6419	−	7.82275i	1.01942	−	0.299329i	0.748403	+	0.663245i	$0.230821\pi$
$684$	0.0331744	−	0.230733i	0.00126845	−	0.00882230i
$685$	7.75688	+	16.9852i	0.296375	+	0.648971i
$686$	2.21429	+	15.4007i	0.0845421	+	0.588003i
$687$	−17.8531	+	11.4735i	−0.681138	+	0.437741i
$688$	−1.64726	+	1.90104i	−0.0628012	+	0.0724764i
$689$	−0.0916135			−0.00349020
$690$	−4.47537	+	1.72369i	−0.170374	+	0.0656197i
$691$	27.5794			1.04917			0.524584	−	0.851359i	$-0.324221\pi$
$691$	27.5794			1.04917			0.524584	+	0.851359i	$0.324221\pi$
$692$	−11.2582	+	12.9927i	−0.427972	+	0.493907i
$693$	4.10215	−	2.63629i	0.155828	−	0.100144i
$694$	−2.36336	−	16.4375i	−0.0897118	−	0.623959i
$695$	5.53515	+	12.1203i	0.209960	+	0.459749i
$696$	−1.22302	+	8.50631i	−0.0463586	+	0.322431i
$697$	−56.7764	+	16.6711i	−2.15056	+	0.631461i
$698$	−3.34842	−	2.15190i	−0.126740	−	0.0814506i
$699$	2.34207	−	5.12842i	0.0885852	−	0.193974i
$700$	−2.83591	−	0.832699i	−0.107187	−	0.0314731i
$701$	9.06539	+	10.4620i	0.342395	+	0.395145i	0.900665	−	0.434515i	$-0.143080\pi$
$701$	9.06539	+	10.4620i	0.342395	+	0.395145i	−0.558270	+	0.829659i	$0.688535\pi$
$702$	4.37966	+	5.05439i	0.165299	+	0.190766i
$703$	1.20044	+	0.352481i	0.0452755	+	0.0132941i
$704$	0.685355	−	1.50072i	0.0258303	−	0.0565605i
$705$	3.20152	+	2.05749i	0.120576	+	0.0774895i
$706$	21.3560	−	6.27070i	0.803745	−	0.236001i
$707$	3.54541	−	24.6589i	0.133339	−	0.927392i
$708$	−2.83640	−	6.21085i	−0.106598	−	0.233418i
$709$	0.0154681	+	0.107583i	0.000580916	+	0.00404036i	0.990110	−	0.140294i	$-0.0448049\pi$
$709$	0.0154681	+	0.107583i	0.000580916	+	0.00404036i	−0.989529	+	0.144335i	$0.953896\pi$
$710$	−2.27125	+	1.45964i	−0.0852384	+	0.0547794i
$711$	−4.62712	+	5.33998i	−0.173531	+	0.200265i
$712$	−6.24234			−0.233942
$713$	2.75723	+	1.46769i	0.103259	+	0.0549656i
$714$	21.6462			0.810088
$715$	7.22559	−	8.33878i	0.270222	−	0.311853i
$716$	−0.360123	+	0.231437i	−0.0134584	+	0.00864919i
$717$	−2.70733	−	18.8299i	−0.101107	−	0.703216i
$718$	−8.50807	−	18.6301i	−0.317518	−	0.695268i
$719$	6.17165	−	42.9248i	0.230164	−	1.60082i	−0.467230	−	0.884136i	$-0.654748\pi$
$719$	6.17165	−	42.9248i	0.230164	−	1.60082i	0.697393	−	0.716689i	$-0.254343\pi$
$720$	−0.959493	+	0.281733i	−0.0357582	+	0.0104996i
$721$	−2.39005	−	1.53599i	−0.0890103	−	0.0572034i
$722$	−7.87031	+	17.2336i	−0.292903	+	0.641367i
$723$	11.4397	+	3.35899i	0.425446	+	0.124922i
$724$	−10.4494	−	12.0592i	−0.388348	−	0.448178i
$725$	−5.62773	−	6.49475i	−0.209009	−	0.241209i
$726$	7.94281	+	2.33222i	0.294785	+	0.0865568i
$727$	−9.91690	+	21.7150i	−0.367797	+	0.805364i	0.631747	+	0.775175i	$0.282338\pi$
$727$	−9.91690	+	21.7150i	−0.367797	+	0.805364i	−0.999544	+	0.0301892i	$0.990389\pi$
$728$	−16.6291	−	10.6869i	−0.616315	−	0.396082i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	1.13271	−	7.87819i	0.0419236	−	0.291585i
$731$	7.65290	+	16.7575i	0.283053	+	0.619799i
$732$	1.58607	+	11.0314i	0.0586230	+	0.407732i
$733$	39.2620	−	25.2321i	1.45017	−	0.931970i	0.450951	−	0.892549i	$-0.351085\pi$
$733$	39.2620	−	25.2321i	1.45017	−	0.931970i	0.999223	−	0.0394214i	$-0.0125515\pi$
$734$	0.557476	−	0.643362i	0.0205768	−	0.0237469i
$735$	1.73578			0.0640252
$736$	1.62806	−	4.51103i	0.0600112	−	0.166279i
$737$	−1.73192			−0.0637959
$738$	−5.29108	+	6.10623i	−0.194767	+	0.224774i
$739$	−25.8218	+	16.5947i	−0.949871	+	0.610445i	−0.921177	−	0.389143i	$-0.872771\pi$
$739$	−25.8218	+	16.5947i	−0.949871	+	0.610445i	−0.0286939	+	0.999588i	$0.509135\pi$
$740$	−0.763829	−	5.31255i	−0.0280789	−	0.195293i
$741$	0.647629	+	1.41811i	0.0237912	+	0.0520955i
$742$	−0.00576195	+	0.0400752i	−0.000211528	+	0.00147121i
$743$	24.6126	−	7.22691i	0.902948	−	0.265129i	0.202878	−	0.979204i	$-0.434970\pi$
$743$	24.6126	−	7.22691i	0.902948	−	0.265129i	0.700070	+	0.714075i	$0.253152\pi$
$744$	0.547910	+	0.352120i	0.0200873	+	0.0129093i
$745$	7.39681	−	16.1968i	0.270998	−	0.593403i
$746$	−18.6695	−	5.48186i	−0.683538	−	0.200705i
$747$	2.29043	+	2.64329i	0.0838023	+	0.0967130i
$748$	−7.91249	−	9.13150i	−0.289309	−	0.333881i
$749$	30.7738	+	9.03599i	1.12445	+	0.330168i
$750$	0.415415	−	0.909632i	0.0151688	−	0.0332151i
$751$	−27.1561	−	17.4522i	−0.990941	−	0.636839i	−0.0585475	−	0.998285i	$-0.518647\pi$
$751$	−27.1561	−	17.4522i	−0.990941	−	0.636839i	−0.932393	+	0.361446i	$0.882283\pi$
$752$	−3.65149	+	1.07218i	−0.133156	+	0.0390982i
$753$	−2.90865	+	20.2301i	−0.105997	+	0.737226i
$754$	−23.8758	−	52.2807i	−0.869505	−	1.90395i
$755$	0.943808	+	6.56433i	0.0343487	+	0.238900i
$756$	2.48644	−	1.59794i	0.0904309	−	0.0581164i
$757$	−12.4854	+	14.4089i	−0.453789	+	0.523701i	−0.935832	−	0.352447i	$-0.885350\pi$
$757$	−12.4854	+	14.4089i	−0.453789	+	0.523701i	0.482042	+	0.876148i	$0.339895\pi$
$758$	−0.779398			−0.0283090
$759$	−7.74885	−	1.59950i	−0.281265	−	0.0580581i
$760$	−0.233106			−0.00845563
$761$	20.1923	−	23.3031i	0.731969	−	0.844737i	−0.260723	−	0.965414i	$-0.583961\pi$
$761$	20.1923	−	23.3031i	0.731969	−	0.844737i	0.992692	+	0.120676i	$0.0385064\pi$
$762$	−3.91941	+	2.51885i	−0.141985	+	0.0912485i
$763$	4.74413	+	32.9961i	0.171749	+	1.19454i
$764$	−3.66030	−	8.01494i	−0.132425	−	0.289970i
$765$	−1.04227	+	7.24915i	−0.0376834	+	0.262094i
$766$	−11.3177	+	3.32318i	−0.408925	+	0.120071i
$767$	38.4152	+	24.6880i	1.38709	+	0.891431i
$768$	0.415415	−	0.909632i	0.0149900	−	0.0328235i
$769$	45.4308	+	13.3397i	1.63828	+	0.481041i	0.965845	−	0.259119i	$-0.0834322\pi$
$769$	45.4308	+	13.3397i	1.63828	+	0.481041i	0.672430	+	0.740160i	$0.265250\pi$
$770$	−3.19325	−	3.68521i	−0.115077	−	0.132806i
$771$	0.617164	+	0.712246i	0.0222266	+	0.0256509i
$772$	4.74938	+	1.39455i	0.170934	+	0.0501908i
$773$	4.65862	−	10.2010i	0.167559	−	0.366903i	−0.807162	−	0.590331i	$-0.798997\pi$
$773$	4.65862	−	10.2010i	0.167559	−	0.366903i	0.974721	+	0.223428i	$0.0717246\pi$
$774$	2.11612	+	1.35995i	0.0760623	+	0.0488823i
$775$	−0.624919	+	0.183493i	−0.0224478	+	0.00659126i
$776$	0.901468	−	6.26985i	0.0323608	−	0.225074i
$777$	6.58990	+	14.4299i	0.236411	+	0.517669i
$778$	4.62752	+	32.1851i	0.165905	+	1.15389i
$779$	−1.58444	+	1.01826i	−0.0567684	+	0.0364828i
$780$	4.37966	−	5.05439i	0.156817	−	0.180976i
$781$	−4.45422			−0.159384
$782$	−25.0987	−	24.5702i	−0.897529	−	0.878628i
$783$	8.59378			0.307117
$784$	−1.13669	+	1.31182i	−0.0405962	+	0.0468506i
$785$	2.11918	−	1.36191i	0.0756368	−	0.0486088i
$786$	−2.85926	−	19.8866i	−0.101986	−	0.709331i
$787$	−8.48289	−	18.5749i	−0.302382	−	0.662125i	0.696056	−	0.717987i	$-0.254936\pi$
$787$	−8.48289	−	18.5749i	−0.302382	−	0.662125i	−0.998438	+	0.0558626i	$0.982209\pi$
$788$	−1.51339	+	10.5259i	−0.0539123	+	0.374968i
$789$	3.18758	−	0.935958i	0.113481	−	0.0333210i
$790$	5.94414	+	3.82007i	0.211483	+	0.135912i
$791$	−18.0340	+	39.4890i	−0.641216	+	1.40407i
$792$	−1.58298	−	0.464805i	−0.0562487	−	0.0165161i
$793$	−48.8105	−	56.3303i	−1.73331	−	2.00035i
$794$	−20.3386	−	23.4720i	−0.721789	−	0.832989i
$795$	−0.0131435	−	0.00385927i	−0.000466151	−	0.000136874i
$796$	−11.0407	+	24.1757i	−0.391326	+	0.856885i
$797$	−16.1384	−	10.3715i	−0.571652	−	0.367378i	0.222653	−	0.974898i	$-0.428528\pi$
$797$	−16.1384	−	10.3715i	−0.571652	−	0.367378i	−0.794305	+	0.607520i	$0.792165\pi$
$798$	0.661067	−	0.194107i	0.0234015	−	0.00687131i
$799$	−3.96652	+	27.5877i	−0.140325	+	0.975984i
$800$	0.415415	+	0.909632i	0.0146871	+	0.0321603i
$801$	0.888378	+	6.17880i	0.0313893	+	0.218317i
$802$	−19.5228	+	12.5466i	−0.689375	+	0.443034i
$803$	8.59908	−	9.92387i	0.303455	−	0.350206i
$804$	−1.04977			−0.0370225
$805$	−10.1291	−	9.91583i	−0.357005	−	0.349487i
$806$	−4.35585			−0.153428
$807$	−0.357637	+	0.412735i	−0.0125894	+	0.0145290i
$808$	−7.09075	+	4.55695i	−0.249452	+	0.160313i
$809$	5.80145	+	40.3499i	0.203968	+	1.41863i	0.792361	+	0.610053i	$0.208852\pi$
$809$	5.80145	+	40.3499i	0.203968	+	1.41863i	−0.588393	+	0.808575i	$0.700239\pi$
$810$	0.415415	+	0.909632i	0.0145962	+	0.0319612i
$811$	−1.13753	+	7.91167i	−0.0399440	+	0.277816i	−0.999998	−	0.00199827i	$-0.999364\pi$
$811$	−1.13753	+	7.91167i	−0.0399440	+	0.277816i	0.960054	+	0.279815i	$0.0902730\pi$
$812$	−24.3712	+	7.15603i	−0.855262	+	0.251127i
$813$	−15.9691	−	10.2627i	−0.560062	−	0.359930i
$814$	3.67842	−	8.05462i	0.128929	−	0.282314i
$815$	22.4115	+	6.58062i	0.785041	+	0.230509i
$816$	−4.79600	−	5.53488i	−0.167894	−	0.193760i
$817$	0.383986	+	0.443143i	0.0134340	+	0.0155036i
$818$	6.30606	+	1.85163i	0.220486	+	0.0647406i
$819$	−8.21153	+	17.9807i	−0.286934	+	0.628298i
$820$	6.79708	+	4.36822i	0.237364	+	0.152545i
$821$	52.5720	−	15.4365i	1.83478	−	0.538739i	0.834844	−	0.550486i	$-0.185558\pi$
$821$	52.5720	−	15.4365i	1.83478	−	0.538739i	0.999931	+	0.0117477i	$0.00373950\pi$
$822$	−2.65739	+	18.4826i	−0.0926871	+	0.644653i
$823$	2.09288	+	4.58277i	0.0729532	+	0.159745i	0.942595	−	0.333938i	$-0.108378\pi$
$823$	2.09288	+	4.58277i	0.0729532	+	0.159745i	−0.869642	+	0.493683i	$0.835650\pi$
$824$	0.136798	+	0.951452i	0.00476559	+	0.0331454i
$825$	1.38791	−	0.891954i	0.0483207	−	0.0310539i
$826$	13.2156	−	15.2516i	0.459828	−	0.530670i
$827$	−26.9719			−0.937905			−0.468952	−	0.883223i	$-0.655368\pi$
$827$	−26.9719			−0.937905			−0.468952	+	0.883223i	$0.655368\pi$
$828$	−4.69681	−	0.969505i	−0.163226	−	0.0336926i
$829$	4.44859			0.154506			0.0772529	−	0.997012i	$-0.475385\pi$
$829$	4.44859			0.154506			0.0772529	+	0.997012i	$0.475385\pi$
$830$	2.29043	−	2.64329i	0.0795019	−	0.0917501i
$831$	3.49263	−	2.24458i	0.121158	−	0.0778635i
$832$	0.951790	+	6.61984i	0.0329974	+	0.229502i
$833$	5.28089	+	11.5635i	0.182972	+	0.400653i
$834$	−1.89626	+	13.1888i	−0.0656620	+	0.456690i
$835$	−14.3808	+	4.22259i	−0.497669	+	0.146129i
$836$	−0.323529	−	0.207920i	−0.0111895	−	0.00719105i
$837$	0.270560	−	0.592445i	0.00935193	−	0.0204779i
$838$	−29.3917	−	8.63018i	−1.01532	−	0.298125i
$839$	9.05953	+	10.4553i	0.312770	+	0.360956i	0.890269	−	0.455436i	$-0.150517\pi$
$839$	9.05953	+	10.4553i	0.312770	+	0.360956i	−0.577499	+	0.816392i	$0.695971\pi$
$840$	−1.93553	−	2.23372i	−0.0667821	−	0.0770707i
$841$	−43.0362	−	12.6366i	−1.48401	−	0.435744i
$842$	−11.8479	+	25.9433i	−0.408305	+	0.894064i
$843$	1.66339	+	1.06900i	0.0572902	+	0.0368182i
$844$	−21.4590	+	6.30092i	−0.738648	+	0.216887i
$845$	−4.51540	+	31.4053i	−0.155335	+	1.08038i
$846$	1.58092	+	3.46174i	0.0543533	+	0.119017i
$847$	3.48204	+	24.2181i	0.119644	+	0.832144i
$848$	0.0115238	−	0.00740589i	0.000395729	−	0.000254319i
$849$	9.53856	−	11.0081i	0.327362	−	0.377796i
$850$	7.32370			0.251201
$851$	8.73810	−	24.2115i	0.299538	−	0.829959i
$852$	−2.69984			−0.0924949
$853$	−2.53246	+	2.92262i	−0.0867098	+	0.100068i	−0.797446	−	0.603390i	$-0.793816\pi$
$853$	−2.53246	+	2.92262i	−0.0867098	+	0.100068i	0.710737	+	0.703458i	$0.248362\pi$
$854$	−27.7109	+	17.8087i	−0.948249	+	0.609402i
$855$	0.0331744	+	0.230733i	0.00113454	+	0.00789090i
$856$	−4.50786	−	9.87083i	−0.154075	−	0.337378i
$857$	5.64611	−	39.2696i	0.192867	−	1.34142i	−0.631504	−	0.775373i	$-0.717562\pi$
$857$	5.64611	−	39.2696i	0.192867	−	1.34142i	0.824371	−	0.566050i	$-0.191529\pi$
$858$	10.5868	−	3.10858i	0.361429	−	0.106125i
$859$	11.2254	+	7.21413i	0.383006	+	0.246143i	0.717949	−	0.696095i	$-0.245081\pi$
$859$	11.2254	+	7.21413i	0.383006	+	0.246143i	−0.334944	+	0.942238i	$0.608717\pi$
$860$	1.04495	−	2.28812i	0.0356325	−	0.0780243i
$861$	−22.9133	−	6.72796i	−0.780884	−	0.229288i
$862$	5.31800	+	6.13730i	0.181132	+	0.209037i
$863$	−6.31623	−	7.28932i	−0.215007	−	0.248131i	0.637993	−	0.770042i	$-0.279765\pi$
$863$	−6.31623	−	7.28932i	−0.215007	−	0.248131i	−0.853000	+	0.521911i	$0.825219\pi$
$864$	−0.959493	−	0.281733i	−0.0326426	−	0.00958474i
$865$	7.14171	−	15.6382i	0.242825	−	0.531713i
$866$	−1.42539	−	0.916045i	−0.0484369	−	0.0311285i
$867$	−35.1525	+	10.3217i	−1.19384	+	0.350544i
$868$	−0.273957	+	1.90542i	−0.00929872	+	0.0646740i
$869$	4.84259	+	10.6038i	0.164274	+	0.359709i
$870$	−1.22302	−	8.50631i	−0.0414644	−	0.288391i
$871$	5.90624	−	3.79571i	0.200125	−	0.128613i
$872$	7.38592	−	8.52380i	0.250119	−	0.288652i
$873$	−6.33432			−0.214384
$874$	−0.986834	−	0.525299i	−0.0333802	−	0.0177685i
$875$	2.95564			0.0999187
$876$	5.21217	−	6.01516i	0.176103	−	0.203234i
$877$	28.2281	−	18.1411i	0.953195	−	0.612581i	0.0310879	−	0.999517i	$-0.490103\pi$
$877$	28.2281	−	18.1411i	0.953195	−	0.612581i	0.922107	+	0.386936i	$0.126466\pi$
$878$	−1.06864	−	7.43257i	−0.0360649	−	0.250837i
$879$	4.39983	+	9.63428i	0.148403	+	0.324956i
$880$	−0.234792	+	1.63302i	−0.00791485	+	0.0550490i
$881$	−33.6517	+	9.88104i	−1.13376	+	0.332901i	−0.794183	−	0.607679i	$-0.792101\pi$
$881$	−33.6517	+	9.88104i	−1.13376	+	0.332901i	−0.339573	+	0.940580i	$0.610283\pi$
$882$	1.46023	+	0.938434i	0.0491686	+	0.0315987i
$883$	20.2682	−	44.3813i	0.682081	−	1.49355i	−0.178343	−	0.983968i	$-0.557074\pi$
$883$	20.2682	−	44.3813i	0.682081	−	1.49355i	0.860423	−	0.509580i	$-0.170199\pi$
$884$	46.9963	+	13.7993i	1.58065	+	0.464122i
$885$	4.47131	+	5.16016i	0.150301	+	0.173457i
$886$	27.3775	+	31.5953i	0.919764	+	1.06146i
$887$	−31.5500	−	9.26390i	−1.05934	−	0.311051i	−0.294757	−	0.955572i	$-0.595239\pi$
$887$	−31.5500	−	9.26390i	−1.05934	−	0.311051i	−0.764587	+	0.644521i	$0.777057\pi$
$888$	2.22961	−	4.88215i	0.0748206	−	0.163834i
$889$	−11.5844	−	7.44482i	−0.388527	−	0.249691i
$890$	5.98948	−	1.75867i	0.200768	−	0.0589508i
$891$	−0.234792	+	1.63302i	−0.00786584	+	0.0547081i
$892$	5.60665	+	12.2769i	0.187725	+	0.411059i
$893$	0.126250	+	0.878089i	0.00422480	+	0.0293841i
$894$	14.9792	−	9.62656i	0.500980	−	0.321960i
$895$	0.280332	−	0.323520i	0.00937046	−	0.0108141i
$896$	2.95564			0.0987408
$897$	29.9309	−	11.5279i	0.999363	−	0.384905i
$898$	29.3482			0.979362
$899$	−3.66535	+	4.23004i	−0.122246	+	0.141080i
$900$	0.841254	−	0.540641i	0.0280418	−	0.0180214i
$901$	−0.0142774	−	0.0993015i	−0.000475649	−	0.00330821i
$902$	5.53747	+	12.1254i	0.184378	+	0.403731i
$903$	−1.05807	+	7.35904i	−0.0352104	+	0.244893i
$904$	14.0929	−	4.13806i	0.468724	−	0.137630i
$905$	13.4236	+	8.62682i	0.446215	+	0.286765i
$906$	−2.75496	+	6.03253i	−0.0915275	+	0.200417i
$907$	−4.35052	−	1.27743i	−0.144457	−	0.0424163i	0.208705	−	0.977979i	$-0.433075\pi$
$907$	−4.35052	−	1.27743i	−0.144457	−	0.0424163i	−0.353162	+	0.935562i	$0.614893\pi$
$908$	−12.4090	−	14.3207i	−0.411807	−	0.475251i
$909$	5.51969	+	6.37006i	0.183076	+	0.211282i
$910$	18.9663	+	5.56902i	0.628728	+	0.184611i
$911$	−10.0620	+	22.0327i	−0.333369	+	0.729975i	−0.999880	−	0.0155199i	$-0.995060\pi$
$911$	−10.0620	+	22.0327i	−0.333369	+	0.729975i	0.666511	+	0.745495i	$0.267787\pi$
$912$	−0.196101	−	0.126026i	−0.00649355	−	0.00417315i
$913$	5.53660	−	1.62569i	0.183235	−	0.0538025i
$914$	2.19334	−	15.2550i	0.0725494	−	0.504592i
$915$	−4.62973	−	10.1377i	−0.153054	−	0.335142i
$916$	3.02021	+	21.0060i	0.0997905	+	0.694058i
$917$	49.9553	−	32.1043i	1.64967	−	1.06018i
$918$	−4.79600	+	5.53488i	−0.158292	+	0.182678i
$919$	−42.2352			−1.39321			−0.696605	−	0.717455i	$-0.745307\pi$
$919$	−42.2352			−1.39321			−0.696605	+	0.717455i	$0.745307\pi$
$920$	−0.291211	+	4.78698i	−0.00960094	+	0.157822i
$921$	32.3179			1.06491
$922$	−22.0914	+	25.4948i	−0.727540	+	0.839626i
$923$	15.1899	−	9.76197i	0.499982	−	0.321319i
$924$	−0.693960	−	4.82660i	−0.0228296	−	0.158784i
$925$	2.22961	+	4.88215i	0.0733090	+	0.160524i
$926$	0.670560	−	4.66385i	0.0220360	−	0.153264i
$927$	0.922299	−	0.270811i	0.0302923	−	0.00889461i
$928$	7.22955	+	4.64615i	0.237322	+	0.152517i
$929$	4.42402	−	9.68725i	0.145147	−	0.317828i	−0.823069	−	0.567941i	$-0.807740\pi$
$929$	4.42402	−	9.68725i	0.145147	−	0.317828i	0.968217	+	0.250112i	$0.0804676\pi$
$930$	−0.624919	−	0.183493i	−0.0204919	−	0.00601697i
$931$	0.264970	+	0.305792i	0.00868404	+	0.0100219i
$932$	−3.69204	−	4.26084i	−0.120937	−	0.139568i
$933$	−17.9732	−	5.27742i	−0.588417	−	0.172775i
$934$	−6.52258	+	14.2825i	−0.213425	+	0.467336i
$935$	10.1646	+	6.53240i	0.332419	+	0.213632i
$936$	6.41701	−	1.88420i	0.209747	−	0.0615871i
$937$	7.71996	−	53.6935i	0.252200	−	1.75409i	−0.332744	−	0.943017i	$-0.607975\pi$
$937$	7.71996	−	53.6935i	0.252200	−	1.75409i	0.584944	−	0.811073i	$-0.301116\pi$
$938$	−1.28892	−	2.82234i	−0.0420848	−	0.0921528i
$939$	3.24151	+	22.5452i	0.105783	+	0.735735i
$940$	3.20152	−	2.05749i	0.104422	−	0.0671079i
$941$	19.0663	−	22.0037i	0.621544	−	0.717301i	−0.354455	−	0.935073i	$-0.615334\pi$
$941$	19.0663	−	22.0037i	0.621544	−	0.717301i	0.976000	+	0.217772i	$0.0698791\pi$
$942$	2.51907			0.0820758
$943$	18.9312	+	33.8096i	0.616485	+	1.10099i
$944$	−6.82787			−0.222228
$945$	−1.93553	+	2.23372i	−0.0629628	+	0.0726629i
$946$	3.49119	−	2.24365i	0.113508	−	0.0729474i
$947$	7.86970	+	54.7350i	0.255731	+	1.77865i	0.562434	+	0.826842i	$0.309865\pi$
$947$	7.86970	+	54.7350i	0.255731	+	1.77865i	−0.306703	+	0.951805i	$0.599226\pi$
$948$	2.93524	+	6.42729i	0.0953323	+	0.208749i
$949$	−7.57549	+	52.6887i	−0.245911	+	1.71035i
$950$	0.223663	−	0.0656735i	0.00725660	−	0.00213073i
$951$	0.518832	+	0.333433i	0.0168243	+	0.0108123i
$952$	8.99215	−	19.6901i	0.291437	−	0.638159i
$953$	−14.4069	−	4.23026i	−0.466686	−	0.137032i	0.0399310	−	0.999202i	$-0.487286\pi$
$953$	−14.4069	−	4.23026i	−0.466686	−	0.137032i	−0.506618	+	0.862171i	$0.669104\pi$
$954$	−0.00897052	−	0.0103525i	−0.000290431	−	0.000335175i
$955$	5.77010	+	6.65905i	0.186716	+	0.215482i
$956$	−18.2530	−	5.35955i	−0.590343	−	0.173340i
$957$	5.88980	−	12.8969i	0.190390	−	0.416896i
$958$	30.9973	+	19.9208i	1.00148	+	0.643611i
$959$	−52.9539	+	15.5487i	−1.70997	+	0.502092i
$960$	−0.142315	+	0.989821i	−0.00459319	+	0.0319463i
$961$	−12.7016	−	27.8127i	−0.409731	−	0.897185i
$962$	5.10842	+	35.5299i	0.164702	+	1.14553i
$963$	−9.12882	+	5.86674i	−0.294172	+	0.189053i
$964$	7.80766	−	9.01052i	0.251468	−	0.290209i
$965$	−4.94989			−0.159343
$966$	−3.16027	−	13.8179i	−0.101680	−	0.444585i
$967$	3.91653			0.125947			0.0629736	−	0.998015i	$-0.479942\pi$
$967$	3.91653			0.125947			0.0629736	+	0.998015i	$0.479942\pi$
$968$	5.42102	−	6.25619i	0.174238	−	0.201082i
$969$	−1.43618	+	0.922980i	−0.0461369	+	0.0296504i
$970$	0.901468	+	6.26985i	0.0289444	+	0.201313i
$971$	−3.86283	−	8.45842i	−0.123964	−	0.271443i	0.837468	−	0.546487i	$-0.184035\pi$
$971$	−3.86283	−	8.45842i	−0.123964	−	0.271443i	−0.961432	+	0.275043i	$0.911308\pi$
$972$	−0.142315	+	0.989821i	−0.00456475	+	0.0317485i
$973$	−37.7868	+	11.0952i	−1.21139	+	0.355696i
$974$	−13.7467	−	8.83447i	−0.440473	−	0.283075i
$975$	−2.77826	+	6.08354i	−0.0889756	+	0.194829i
$976$	10.6934	+	3.13986i	0.342287	+	0.100505i
$977$	29.2296	+	33.7328i	0.935139	+	1.07921i	0.996706	+	0.0811046i	$0.0258448\pi$
$977$	29.2296	+	33.7328i	0.935139	+	1.07921i	−0.0615669	+	0.998103i	$0.519610\pi$
$978$	15.2960	+	17.6525i	0.489113	+	0.564466i
$979$	9.88150	+	2.90147i	0.315814	+	0.0927314i
$980$	0.721069	−	1.57892i	0.0230337	−	0.0504368i
$981$	−9.48817	−	6.09768i	−0.302934	−	0.194684i
$982$	20.1507	−	5.91677i	0.643033	−	0.188812i
$983$	3.96682	−	27.5899i	0.126522	−	0.879980i	−0.823393	−	0.567472i	$-0.807922\pi$
$983$	3.96682	−	27.5899i	0.126522	−	0.879980i	0.949915	−	0.312508i	$-0.101169\pi$
$984$	3.35643	+	7.34956i	0.106999	+	0.234295i
$985$	−1.51339	−	10.5259i	−0.0482206	−	0.335382i
$986$	52.9470	−	34.0270i	1.68618	−	1.08364i
$987$	−7.36595	+	8.50075i	−0.234461	+	0.270582i
$988$	1.55899			0.0495981
$989$	9.57994	−	7.33180i	0.304624	−	0.233138i
$990$	1.64981			0.0524344
$991$	−38.7484	+	44.7181i	−1.23088	+	1.42052i	−0.357196	+	0.934029i	$0.616267\pi$
$991$	−38.7484	+	44.7181i	−1.23088	+	1.42052i	−0.873688	+	0.486487i	$0.838278\pi$
$992$	0.547910	−	0.352120i	0.0173961	−	0.0111798i
$993$	5.02463	+	34.9471i	0.159452	+	1.10901i
$994$	−3.31490	−	7.25862i	−0.105142	−	0.230230i
$995$	3.78236	−	26.3069i	0.119909	−	0.833985i
$996$	3.35590	−	0.985382i	0.106336	−	0.0312230i
$997$	−4.39225	−	2.82273i	−0.139104	−	0.0893967i	0.469238	−	0.883072i	$-0.344529\pi$
$997$	−4.39225	−	2.82273i	−0.139104	−	0.0893967i	−0.608342	+	0.793675i	$0.708165\pi$
$998$	−8.52035	+	18.6570i	−0.269707	+	0.590576i
$999$	−5.14977	−	1.51211i	−0.162931	−	0.0478410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.g.361.1	yes	30
23.13	even	11	inner	690.2.m.g.151.1	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.g.151.1	✓	30	23.13	even	11	inner
690.2.m.g.361.1	yes	30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.654861 + 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-2.83591 + 0.832699i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.654861 + 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-2.83591 + 0.832699i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-0.959493 - 0.281733i) q^{10} +(-1.08040 - 1.24684i) q^{11} +(-0.654861 - 0.755750i) q^{12} +(6.41701 + 1.88420i) q^{13} +(1.22782 - 2.68854i) q^{14} +(0.841254 + 0.540641i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-1.04227 + 7.24915i) q^{17} +(0.415415 + 0.909632i) q^{18} +(0.0331744 + 0.230733i) q^{19} +(0.841254 - 0.540641i) q^{20} +(-1.93553 + 2.23372i) q^{21} +1.64981 q^{22} +(4.77970 - 0.393012i) q^{23} +1.00000 q^{24} +(-0.654861 + 0.755750i) q^{25} +(-5.62623 + 3.61576i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(1.22782 + 2.68854i) q^{28} +(-1.22302 + 8.50631i) q^{29} +(-0.959493 + 0.281733i) q^{30} +(0.547910 + 0.352120i) q^{31} +(0.415415 - 0.909632i) q^{32} +(-1.58298 - 0.464805i) q^{33} +(-4.79600 - 5.53488i) q^{34} +(-1.93553 - 2.23372i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(2.22961 - 4.88215i) q^{37} +(-0.196101 - 0.126026i) q^{38} +(6.41701 - 1.88420i) q^{39} +(-0.142315 + 0.989821i) q^{40} +(3.35643 + 7.34956i) q^{41} +(-0.420631 - 2.92555i) q^{42} +(2.11612 - 1.35995i) q^{43} +(-1.08040 + 1.24684i) q^{44} +1.00000 q^{45} +(-2.83302 + 3.86962i) q^{46} +3.80565 q^{47} +(-0.654861 + 0.755750i) q^{48} +(1.46023 - 0.938434i) q^{49} +(-0.142315 - 0.989821i) q^{50} +(3.04237 + 6.66187i) q^{51} +(0.951790 - 6.61984i) q^{52} +(-0.0131435 + 0.00385927i) q^{53} +(0.841254 + 0.540641i) q^{54} +(0.685355 - 1.50072i) q^{55} +(-2.83591 - 0.832699i) q^{56} +(0.152652 + 0.176170i) q^{57} +(-5.62773 - 6.49475i) q^{58} +(6.55130 + 1.92363i) q^{59} +(0.415415 - 0.909632i) q^{60} +(-9.37563 - 6.02535i) q^{61} +(-0.624919 + 0.183493i) q^{62} +(-0.420631 + 2.92555i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.951790 + 6.61984i) q^{65} +(1.38791 - 0.891954i) q^{66} +(0.687452 - 0.793361i) q^{67} +7.32370 q^{68} +(3.80846 - 2.91472i) q^{69} +2.95564 q^{70} +(1.76802 - 2.04040i) q^{71} +(0.841254 - 0.540641i) q^{72} +(1.13271 + 7.87819i) q^{73} +(2.22961 + 4.88215i) q^{74} +(-0.142315 + 0.989821i) q^{75} +(0.223663 - 0.0656735i) q^{76} +(4.10215 + 2.63629i) q^{77} +(-2.77826 + 6.08354i) q^{78} +(-6.77960 - 1.99067i) q^{79} +(-0.654861 - 0.755750i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-7.75242 - 2.27632i) q^{82} +(-1.45295 + 3.18151i) q^{83} +(2.48644 + 1.59794i) q^{84} +(-7.02704 + 2.06332i) q^{85} +(-0.357984 + 2.48983i) q^{86} +(3.56999 + 7.81718i) q^{87} +(-0.234792 - 1.63302i) q^{88} +(-5.25139 + 3.37487i) q^{89} +(-0.654861 + 0.755750i) q^{90} -19.7670 q^{91} +(-1.06923 - 4.67512i) q^{92} +0.651301 q^{93} +(-2.49217 + 2.87612i) q^{94} +(-0.196101 + 0.126026i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(-2.63137 - 5.76190i) q^{97} +(-0.247027 + 1.71811i) q^{98} +(-1.58298 + 0.464805i) 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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