LMFDB - Embedded newform 483.2.r.a.181.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(34,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 9]))

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

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

chi := DirichletCharacter("483.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.r (of order $22$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$32$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			181.28
Character	$\chi$	$=$	483.181
Dual form			483.2.r.a.475.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.308578 + 2.14621i) q^{2} +(0.909632 + 0.415415i) q^{3} +(-2.59201 + 0.761082i) q^{4} +(-1.43859 + 1.66022i) q^{5} +(-0.610875 + 2.08045i) q^{6} +(-1.37803 - 2.25855i) q^{7} +(-0.631807 - 1.38346i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(0.308578 + 2.14621i) q^{2} +(0.909632 + 0.415415i) q^{3} +(-2.59201 + 0.761082i) q^{4} +(-1.43859 + 1.66022i) q^{5} +(-0.610875 + 2.08045i) q^{6} +(-1.37803 - 2.25855i) q^{7} +(-0.631807 - 1.38346i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-4.00709 - 2.57520i) q^{10} +(-0.255739 - 0.0367698i) q^{11} +(-2.67394 - 0.384454i) q^{12} +(-3.68666 + 5.73656i) q^{13} +(4.42209 - 3.65447i) q^{14} +(-1.99826 + 0.912577i) q^{15} +(-1.77094 + 1.13811i) q^{16} +(-2.19190 - 0.643600i) q^{17} +(-1.41992 + 1.63868i) q^{18} +(-3.39559 + 0.997034i) q^{19} +(2.46527 - 5.39818i) q^{20} +(-0.315263 - 2.62690i) q^{21} -0.560217i q^{22} +(3.53937 - 3.23618i) q^{23} -1.52090i q^{24} +(0.0247828 + 0.172368i) q^{25} +(-13.4495 - 6.14218i) q^{26} +(0.281733 + 0.959493i) q^{27} +(5.29080 + 4.80538i) q^{28} +(9.53259 + 2.79902i) q^{29} +(-2.57520 - 4.00709i) q^{30} +(6.00587 - 2.74279i) q^{31} +(-4.98107 - 5.74846i) q^{32} +(-0.217354 - 0.139685i) q^{33} +(0.704927 - 4.90288i) q^{34} +(5.73210 + 0.961294i) q^{35} +(-2.27259 - 1.46051i) q^{36} +(-0.438038 + 0.379562i) q^{37} +(-3.18765 - 6.97998i) q^{38} +(-5.73656 + 3.68666i) q^{39} +(3.20576 + 0.941296i) q^{40} +(7.48371 + 6.48467i) q^{41} +(5.54060 - 1.48722i) q^{42} +(-5.35293 - 2.44460i) q^{43} +(0.690863 - 0.0993311i) q^{44} -2.19678 q^{45} +(8.03769 + 6.59762i) q^{46} +3.99142i q^{47} +(-2.08370 + 0.299590i) q^{48} +(-3.20208 + 6.22468i) q^{49} +(-0.362291 + 0.106378i) q^{50} +(-1.72646 - 1.49599i) q^{51} +(5.18987 - 17.6751i) q^{52} +(3.89450 + 6.05996i) q^{53} +(-1.97234 + 0.900736i) q^{54} +(0.428949 - 0.371687i) q^{55} +(-2.25397 + 3.33342i) q^{56} +(-3.50292 - 0.503644i) q^{57} +(-3.06573 + 21.3226i) q^{58} +(0.106189 - 0.165233i) q^{59} +(4.48497 - 3.88625i) q^{60} +(1.60888 + 3.52295i) q^{61} +(7.73988 + 12.0435i) q^{62} +(0.804481 - 2.52048i) q^{63} +(8.04322 - 9.28237i) q^{64} +(-4.22036 - 14.3732i) q^{65} +(0.232722 - 0.509591i) q^{66} +(10.7587 - 1.54687i) q^{67} +6.17125 q^{68} +(4.56388 - 1.47342i) q^{69} +(-0.294337 + 12.5989i) q^{70} +(-1.25392 - 8.72118i) q^{71} +(0.631807 - 1.38346i) q^{72} +(-1.68819 - 5.74945i) q^{73} +(-0.949788 - 0.822996i) q^{74} +(-0.0490612 + 0.167087i) q^{75} +(8.04256 - 5.16864i) q^{76} +(0.269370 + 0.628270i) q^{77} +(-9.68253 - 11.1742i) q^{78} +(-5.82232 + 9.05970i) q^{79} +(0.658135 - 4.57743i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-11.6081 + 18.0626i) q^{82} +(-2.69802 - 3.11368i) q^{83} +(2.81645 + 6.56901i) q^{84} +(4.22176 - 2.71316i) q^{85} +(3.59483 - 12.2429i) q^{86} +(7.50839 + 6.50606i) q^{87} +(0.110708 + 0.377038i) q^{88} +(-4.46618 + 9.77956i) q^{89} +(-0.677880 - 4.71476i) q^{90} +(18.0366 + 0.421373i) q^{91} +(-6.71108 + 11.0819i) q^{92} +6.60253 q^{93} +(-8.56641 + 1.23166i) q^{94} +(3.22955 - 7.07174i) q^{95} +(-2.14294 - 7.29819i) q^{96} +(-3.35789 + 3.87521i) q^{97} +(-14.3476 - 4.95154i) q^{98} +(-0.139685 - 0.217354i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{22}\right)$

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 $

$2$	0.308578	+	2.14621i	0.218198	+	1.51760i	0.744685	+	0.667416i	$0.232600\pi$
$2$	0.308578	+	2.14621i	0.218198	+	1.51760i	−0.526487	+	0.850183i	$0.676491\pi$
$3$	0.909632	+	0.415415i	0.525176	+	0.239840i
$3$	0.909632	+	0.415415i	0.525176	+	0.239840i
$4$	−2.59201	+	0.761082i	−1.29600	+	0.380541i
$5$	−1.43859	+	1.66022i	−0.643356	+	0.742472i	−0.979964	−	0.199172i	$-0.936175\pi$
$5$	−1.43859	+	1.66022i	−0.643356	+	0.742472i	0.336609	+	0.941645i	$0.390720\pi$
$6$	−0.610875	+	2.08045i	−0.249389	+	0.849340i
$7$	−1.37803	−	2.25855i	−0.520845	−	0.853651i
$7$	−1.37803	−	2.25855i	−0.520845	−	0.853651i
$8$	−0.631807	−	1.38346i	−0.223377	−	0.489128i
$9$	0.654861	+	0.755750i	0.218287	+	0.251917i
$10$	−4.00709	−	2.57520i	−1.26715	−	0.814350i
$11$	−0.255739	−	0.0367698i	−0.0771083	−	0.0110865i	0.103653	−	0.994614i	$-0.466947\pi$
$11$	−0.255739	−	0.0367698i	−0.0771083	−	0.0110865i	−0.180761	+	0.983527i	$0.557856\pi$
$12$	−2.67394	−	0.384454i	−0.771899	−	0.110982i
$13$	−3.68666	+	5.73656i	−1.02250	+	1.59104i	−0.237646	+	0.971352i	$0.576376\pi$
$13$	−3.68666	+	5.73656i	−1.02250	+	1.59104i	−0.784851	+	0.619684i	$0.787261\pi$
$14$	4.42209	−	3.65447i	1.18185	−	0.976699i
$15$	−1.99826	+	0.912577i	−0.515950	+	0.235626i
$16$	−1.77094	+	1.13811i	−0.442735	+	0.284529i
$17$	−2.19190	−	0.643600i	−0.531614	−	0.156096i	0.00489913	−	0.999988i	$-0.498441\pi$
$17$	−2.19190	−	0.643600i	−0.531614	−	0.156096i	−0.536513	+	0.843892i	$0.680259\pi$
$18$	−1.41992	+	1.63868i	−0.334679	+	0.386240i
$19$	−3.39559	+	0.997034i	−0.779001	+	0.228735i	−0.646975	−	0.762511i	$-0.723966\pi$
$19$	−3.39559	+	0.997034i	−0.779001	+	0.228735i	−0.132026	+	0.991246i	$0.542148\pi$
$20$	2.46527	−	5.39818i	0.551250	−	1.20707i
$21$	−0.315263	−	2.62690i	−0.0687959	−	0.573237i
$22$		−	0.560217i		−	0.119439i
$23$	3.53937	−	3.23618i	0.738010	−	0.674790i
$23$	3.53937	−	3.23618i	0.738010	−	0.674790i
$24$		−	1.52090i		−	0.310453i
$25$	0.0247828	+	0.172368i	0.00495657	+	0.0344737i
$26$	−13.4495	−	6.14218i	−2.63766	−	1.20458i
$27$	0.281733	+	0.959493i	0.0542195	+	0.184655i
$28$	5.29080	+	4.80538i	0.999867	+	0.908132i
$29$	9.53259	+	2.79902i	1.77016	+	0.519765i	0.993864	−	0.110608i	$-0.0352798\pi$
$29$	9.53259	+	2.79902i	1.77016	+	0.519765i	0.776293	+	0.630373i	$0.217098\pi$
$30$	−2.57520	−	4.00709i	−0.470165	−	0.731592i
$31$	6.00587	−	2.74279i	1.07869	−	0.492620i	0.204827	−	0.978798i	$-0.434337\pi$
$31$	6.00587	−	2.74279i	1.07869	−	0.492620i	0.873859	+	0.486179i	$0.161610\pi$
$32$	−4.98107	−	5.74846i	−0.880537	−	1.01619i
$33$	−0.217354	−	0.139685i	−0.0378365	−	0.0243160i
$34$	0.704927	−	4.90288i	0.120894	−	0.840836i
$35$	5.73210	+	0.961294i	0.968901	+	0.162488i
$36$	−2.27259	−	1.46051i	−0.378765	−	0.243418i
$37$	−0.438038	+	0.379562i	−0.0720129	+	0.0623996i	−0.690124	−	0.723692i	$-0.742444\pi$
$37$	−0.438038	+	0.379562i	−0.0720129	+	0.0623996i	0.618111	+	0.786091i	$0.287898\pi$
$38$	−3.18765	−	6.97998i	−0.517105	−	1.13230i
$39$	−5.73656	+	3.68666i	−0.918585	+	0.590339i
$40$	3.20576	+	0.941296i	0.506875	+	0.148832i
$41$	7.48371	+	6.48467i	1.16876	+	1.01274i	0.999632	+	0.0271411i	$0.00864033\pi$
$41$	7.48371	+	6.48467i	1.16876	+	1.01274i	0.169127	+	0.985594i	$0.445905\pi$
$42$	5.54060	−	1.48722i	0.854933	−	0.229484i
$43$	−5.35293	−	2.44460i	−0.816315	−	0.372798i	−0.0369096	−	0.999319i	$-0.511751\pi$
$43$	−5.35293	−	2.44460i	−0.816315	−	0.372798i	−0.779405	+	0.626520i	$0.784479\pi$
$44$	0.690863	−	0.0993311i	0.104152	−	0.0149747i
$45$	−2.19678			−0.327477
$46$	8.03769	+	6.59762i	1.18509	+	0.972766i
$47$			3.99142i			0.582208i	0.956691	+	0.291104i	$0.0940225\pi$
$47$			3.99142i			0.582208i	−0.956691	+	0.291104i	$0.905977\pi$
$48$	−2.08370	+	0.299590i	−0.300755	+	0.0432421i
$49$	−3.20208	+	6.22468i	−0.457440	+	0.889240i
$50$	−0.362291	+	0.106378i	−0.0512357	+	0.0150442i
$51$	−1.72646	−	1.49599i	−0.241753	−	0.209480i
$52$	5.18987	−	17.6751i	0.719705	−	2.45109i
$53$	3.89450	+	6.05996i	0.534951	+	0.832400i	0.998560	−	0.0536400i	$-0.0170823\pi$
$53$	3.89450	+	6.05996i	0.534951	+	0.832400i	−0.463610	+	0.886040i	$0.653446\pi$
$54$	−1.97234	+	0.900736i	−0.268401	+	0.122575i
$55$	0.428949	−	0.371687i	0.0578395	−	0.0501182i
$56$	−2.25397	+	3.33342i	−0.301200	+	0.445446i
$57$	−3.50292	−	0.503644i	−0.463973	−	0.0667092i
$58$	−3.06573	+	21.3226i	−0.402550	+	2.79980i
$59$	0.106189	−	0.165233i	0.0138246	−	0.0215115i	−0.834272	−	0.551352i	$-0.814112\pi$
$59$	0.106189	−	0.165233i	0.0138246	−	0.0215115i	0.848097	+	0.529841i	$0.177748\pi$
$60$	4.48497	−	3.88625i	0.579007	−	0.501713i
$61$	1.60888	+	3.52295i	0.205996	+	0.451068i	0.984227	−	0.176910i	$-0.0566102\pi$
$61$	1.60888	+	3.52295i	0.205996	+	0.451068i	−0.778231	+	0.627978i	$0.783883\pi$
$62$	7.73988	+	12.0435i	0.982966	+	1.52953i
$63$	0.804481	−	2.52048i	0.101355	−	0.317550i
$64$	8.04322	−	9.28237i	1.00540	−	1.16030i
$65$	−4.22036	−	14.3732i	−0.523471	−	1.78278i
$66$	0.232722	−	0.509591i	0.0286461	−	0.0627263i
$67$	10.7587	−	1.54687i	1.31438	−	0.188980i	0.550772	−	0.834656i	$-0.314333\pi$
$67$	10.7587	−	1.54687i	1.31438	−	0.188980i	0.763611	+	0.645676i	$0.223424\pi$
$68$	6.17125			0.748374
$69$	4.56388	−	1.47342i	0.549427	−	0.177379i
$70$	−0.294337	+	12.5989i	−0.0351800	+	1.50586i
$71$	−1.25392	−	8.72118i	−0.148812	−	1.03501i	−0.918168	−	0.396192i	$-0.870331\pi$
$71$	−1.25392	−	8.72118i	−0.148812	−	1.03501i	0.769355	−	0.638821i	$-0.220578\pi$
$72$	0.631807	−	1.38346i	0.0744591	−	0.163043i
$73$	−1.68819	−	5.74945i	−0.197588	−	0.672922i	−0.997360	−	0.0726183i	$-0.976864\pi$
$73$	−1.68819	−	5.74945i	−0.197588	−	0.672922i	0.799772	−	0.600304i	$-0.204954\pi$
$74$	−0.949788	−	0.822996i	−0.110411	−	0.0956713i
$75$	−0.0490612	+	0.167087i	−0.00566509	+	0.0192935i
$76$	8.04256	−	5.16864i	0.922545	−	0.592884i
$77$	0.269370	+	0.628270i	0.0306975	+	0.0715980i
$78$	−9.68253	−	11.1742i	−1.09633	−	1.26523i
$79$	−5.82232	+	9.05970i	−0.655062	+	1.01930i	0.341772	+	0.939783i	$0.388973\pi$
$79$	−5.82232	+	9.05970i	−0.655062	+	1.01930i	−0.996834	+	0.0795132i	$0.974663\pi$
$80$	0.658135	−	4.57743i	0.0735817	−	0.511772i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−11.6081	+	18.0626i	−1.28191	+	1.99468i
$83$	−2.69802	−	3.11368i	−0.296146	−	0.341771i	0.588103	−	0.808786i	$-0.299875\pi$
$83$	−2.69802	−	3.11368i	−0.296146	−	0.341771i	−0.884249	+	0.467015i	$0.845329\pi$
$84$	2.81645	+	6.56901i	0.307300	+	0.716737i
$85$	4.22176	−	2.71316i	0.457914	−	0.294283i
$86$	3.59483	−	12.2429i	0.387641	−	1.32018i
$87$	7.50839	+	6.50606i	0.804984	+	0.697523i
$88$	0.110708	+	0.377038i	0.0118015	+	0.0401923i
$89$	−4.46618	+	9.77956i	−0.473414	+	1.03663i	0.510808	+	0.859695i	$0.329346\pi$
$89$	−4.46618	+	9.77956i	−0.473414	+	1.03663i	−0.984222	+	0.176937i	$0.943381\pi$
$90$	−0.677880	−	4.71476i	−0.0714548	−	0.496979i
$91$	18.0366	+	0.421373i	1.89075	+	0.0441719i
$92$	−6.71108	+	11.0819i	−0.699679	+	1.15537i
$93$	6.60253			0.684650
$94$	−8.56641	+	1.23166i	−0.883558	+	0.127036i
$95$	3.22955	−	7.07174i	0.331345	−	0.725545i
$96$	−2.14294	−	7.29819i	−0.218713	−	0.744869i
$97$	−3.35789	+	3.87521i	−0.340942	+	0.393468i	−0.900165	−	0.435550i	$-0.856554\pi$
$97$	−3.35789	+	3.87521i	−0.340942	+	0.393468i	0.559223	+	0.829017i	$0.311100\pi$
$98$	−14.3476	−	4.95154i	−1.44932	−	0.500181i
$99$	−0.139685	−	0.217354i	−0.0140389	−	0.0218449i
$100$	−0.195424	−	0.427918i	−0.0195424	−	0.0427918i
$101$	0.985853	−	0.854247i	0.0980961	−	0.0850007i	−0.604432	−	0.796657i	$-0.706600\pi$
$101$	0.985853	−	0.854247i	0.0980961	−	0.0850007i	0.702528	+	0.711656i	$0.252054\pi$
$102$	2.67795	−	4.16698i	0.265157	−	0.412592i
$103$	2.78396	−	19.3629i	0.274312	−	1.90788i	−0.126938	−	0.991911i	$-0.540515\pi$
$103$	2.78396	−	19.3629i	0.274312	−	1.90788i	0.401249	−	0.915969i	$-0.368576\pi$
$104$	10.2656	+	1.47597i	1.00662	+	0.144731i
$105$	4.81476	+	3.25562i	0.469873	+	0.317716i
$106$	−11.8042	+	10.2284i	−1.14652	+	0.993468i
$107$	−9.21850	+	4.20995i	−0.891186	+	0.406991i	−0.807752	−	0.589522i	$-0.799316\pi$
$107$	−9.21850	+	4.20995i	−0.891186	+	0.406991i	−0.0834342	+	0.996513i	$0.526589\pi$
$108$	−1.46051	−	2.27259i	−0.140537	−	0.218680i
$109$	−3.00360	+	10.2293i	−0.287692	+	0.979790i	0.681156	+	0.732138i	$0.261477\pi$
$109$	−3.00360	+	10.2293i	−0.287692	+	0.979790i	−0.968849	+	0.247653i	$0.920341\pi$
$110$	0.930082	+	0.805921i	0.0886798	+	0.0768415i
$111$	−0.556129	+	0.163294i	−0.0527854	+	0.0154992i
$112$	5.01089	+	2.43140i	0.473485	+	0.229746i
$113$	15.0308	−	2.16111i	1.41398	−	0.203300i	0.607387	−	0.794406i	$-0.292218\pi$
$113$	15.0308	−	2.16111i	1.41398	−	0.203300i	0.806594	+	0.591106i	$0.201309\pi$
$114$		−	7.67341i		−	0.718680i
$115$	0.281063	+	10.5317i	0.0262093	+	0.982082i
$116$	−26.8388			−2.49192
$117$	−6.74966	+	0.970454i	−0.624006	+	0.0897185i
$118$	0.387392	+	0.176916i	0.0356624	+	0.0162865i
$119$	1.56690	+	5.83741i	0.143637	+	0.535115i
$120$	2.52503	+	2.18795i	0.230503	+	0.199732i
$121$	−10.4904	−	3.08025i	−0.953670	−	0.280023i
$122$	−7.06452	+	4.54009i	−0.639592	+	0.411041i
$123$	4.11359	+	9.00751i	0.370910	+	0.812180i
$124$	−13.4798	+	11.6803i	−1.21052	+	1.04892i
$125$	−9.56208	−	6.14518i	−0.855259	−	0.549641i
$126$	5.65772	+	0.948820i	0.504030	+	0.0845276i
$127$	−0.330123	+	2.29606i	−0.0292937	+	0.203742i	−0.999212	−	0.0396880i	$-0.987364\pi$
$127$	−0.330123	+	2.29606i	−0.0292937	+	0.203742i	0.969918	+	0.243430i	$0.0782727\pi$
$128$	9.60622	+	6.17354i	0.849078	+	0.545669i
$129$	−3.85368	−	4.44738i	−0.339297	−	0.391570i
$130$	29.5456	−	13.4930i	2.59132	−	1.18342i
$131$	3.26499	+	5.08043i	0.285264	+	0.443879i	0.954081	−	0.299547i	$-0.0968356\pi$
$131$	3.26499	+	5.08043i	0.285264	+	0.443879i	−0.668818	+	0.743427i	$0.733199\pi$
$132$	0.669695	+	0.196640i	0.0582895	+	0.0171153i
$133$	6.93106	+	6.29516i	0.600999	+	0.545859i
$134$	6.63980	+	22.6131i	0.573591	+	1.95347i
$135$	−1.99826	−	0.912577i	−0.171983	−	0.0785421i
$136$	0.494460	+	3.43904i	0.0423996	+	0.294896i
$137$			3.32826i			0.284352i	0.989841	+	0.142176i	$0.0454099\pi$
$137$			3.32826i			0.284352i	−0.989841	+	0.142176i	$0.954590\pi$
$138$	4.57059	+	9.34038i	0.389074	+	0.795106i
$139$			13.4467i			1.14054i	0.821458	+	0.570269i	$0.193161\pi$
$139$			13.4467i			1.14054i	−0.821458	+	0.570269i	$0.806839\pi$
$140$	−15.5893	+	1.87092i	−1.31753	+	0.158121i
$141$	−1.65809	+	3.63072i	−0.139637	+	0.305762i
$142$	18.3305	−	5.38233i	1.53827	−	0.451675i
$143$	1.15376	−	1.33151i	0.0964821	−	0.111346i
$144$	−2.01985	−	0.593081i	−0.168321	−	0.0494235i
$145$	−18.3604	+	11.7995i	−1.52475	+	0.979898i
$146$	11.8186	−	5.39737i	0.978113	−	0.446689i
$147$	−5.49854	+	4.33198i	−0.453512	+	0.357295i
$148$	0.846519	−	1.31721i	0.0695834	−	0.108274i
$149$	9.25712	+	1.33097i	0.758372	+	0.109037i	0.510644	−	0.859792i	$-0.329407\pi$
$149$	9.25712	+	1.33097i	0.758372	+	0.109037i	0.247728	+	0.968830i	$0.420316\pi$
$150$	−0.373743	−	0.0537361i	−0.0305160	−	0.00438753i
$151$	−7.00659	−	4.50286i	−0.570188	−	0.366438i	0.223555	−	0.974691i	$-0.428234\pi$
$151$	−7.00659	−	4.50286i	−0.570188	−	0.366438i	−0.793743	+	0.608254i	$0.791870\pi$
$152$	3.52472	+	4.06774i	0.285892	+	0.329937i
$153$	−0.948989	−	2.07800i	−0.0767212	−	0.167996i
$154$	−1.26528	+	0.771994i	−0.101959	+	0.0622090i
$155$	−4.08634	+	13.9168i	−0.328223	+	1.11782i
$156$	12.0634	−	13.9219i	0.965841	−	1.11464i
$157$	18.4886	−	5.42874i	1.47555	−	0.433261i	0.557652	−	0.830075i	$-0.311703\pi$
$157$	18.4886	−	5.42874i	1.47555	−	0.433261i	0.917899	+	0.396814i	$0.129884\pi$
$158$	−21.2407	−	9.70028i	−1.68982	−	0.771713i
$159$	1.02516	+	7.13017i	0.0813007	+	0.565459i
$160$	16.7094			1.32099
$161$	−12.1864	−	3.53431i	−0.960424	−	0.278542i
$162$	−2.16828			−0.170356
$163$	0.223975	+	1.55778i	0.0175431	+	0.122015i	0.996711	−	0.0810369i	$-0.0258232\pi$
$163$	0.223975	+	1.55778i	0.0175431	+	0.122015i	−0.979168	+	0.203052i	$0.934914\pi$
$164$	−24.3332	−	11.1126i	−1.90010	−	0.867748i
$165$	0.544590	−	0.159906i	0.0423963	−	0.0124487i
$166$	5.85006	−	6.75133i	0.454053	−	0.524005i
$167$	6.36621	−	21.6813i	0.492632	−	1.67775i	−0.219426	−	0.975629i	$-0.570419\pi$
$167$	6.36621	−	21.6813i	0.492632	−	1.67775i	0.712058	−	0.702121i	$-0.247763\pi$
$168$	−3.43504	+	2.09585i	−0.265019	+	0.161698i
$169$	−13.9163	−	30.4724i	−1.07048	−	2.34403i
$170$	7.12575	+	8.22355i	0.546520	+	0.630717i
$171$	−2.97714	−	1.91329i	−0.227668	−	0.146313i
$172$	15.7354	+	2.26241i	1.19981	+	0.172507i
$173$	11.7359	+	1.68737i	0.892264	+	0.128288i	0.573172	−	0.819435i	$-0.305713\pi$
$173$	11.7359	+	1.68737i	0.892264	+	0.128288i	0.319093	+	0.947724i	$0.396622\pi$
$174$	−11.6464	+	18.1222i	−0.882914	+	1.37384i
$175$	0.355151	−	0.293502i	0.0268469	−	0.0221866i
$176$	0.494748	−	0.225944i	0.0372930	−	0.0170312i
$177$	0.165233	−	0.106189i	0.0124197	−	0.00798165i
$178$	−22.3671	−	6.56759i	−1.67649	−	0.492261i
$179$	−9.07754	+	10.4760i	−0.678487	+	0.783016i	−0.985679	−	0.168632i	$-0.946065\pi$
$179$	−9.07754	+	10.4760i	−0.678487	+	0.783016i	0.307192	+	0.951648i	$0.400611\pi$
$180$	5.69408	−	1.67193i	0.424412	−	0.124618i
$181$	9.36452	−	20.5054i	0.696060	−	1.52416i	−0.148625	−	0.988894i	$-0.547485\pi$
$181$	9.36452	−	20.5054i	0.696060	−	1.52416i	0.844685	−	0.535264i	$-0.179788\pi$
$182$	4.66136	+	38.8404i	0.345523	+	2.87904i
$183$			3.87294i			0.286296i
$184$	−6.71333	−	2.85196i	−0.494913	−	0.210249i
$185$		−	1.27327i		−	0.0936127i
$186$	2.03740	+	14.1704i	0.149389	+	1.03902i
$187$	0.536890	+	0.245190i	0.0392613	+	0.0179300i
$188$	−3.03779	−	10.3458i	−0.221554	−	0.754543i
$189$	1.77883	−	1.95851i	0.129391	−	0.142461i
$190$	16.1740	+	4.74911i	1.17339	+	0.344537i
$191$	11.4836	+	17.8688i	0.830922	+	1.29294i	0.953777	+	0.300515i	$0.0971587\pi$
$191$	11.4836	+	17.8688i	0.830922	+	1.29294i	−0.122855	+	0.992425i	$0.539205\pi$
$192$	11.1724	−	5.10227i	0.806299	−	0.368225i
$193$	−3.67102	−	4.23659i	−0.264246	−	0.304956i	0.608085	−	0.793872i	$-0.291938\pi$
$193$	−3.67102	−	4.23659i	−0.264246	−	0.304956i	−0.872331	+	0.488916i	$0.837393\pi$
$194$	−9.35317	−	6.01092i	−0.671519	−	0.431559i
$195$	2.13188	−	14.8275i	0.152667	−	1.06182i
$196$	3.56233	−	18.5715i	0.254452	−	1.32653i
$197$	8.18943	+	5.26303i	0.583473	+	0.374975i	0.798827	−	0.601561i	$-0.205454\pi$
$197$	8.18943	+	5.26303i	0.583473	+	0.374975i	−0.215354	+	0.976536i	$0.569091\pi$
$198$	0.423384	−	0.366864i	0.0300886	−	0.0260719i
$199$	3.84018	+	8.40883i	0.272223	+	0.596086i	0.995531	−	0.0944404i	$-0.0301062\pi$
$199$	3.84018	+	8.40883i	0.272223	+	0.596086i	−0.723307	+	0.690526i	$0.757379\pi$
$200$	0.222807	−	0.143190i	0.0157549	−	0.0101250i
$201$	10.4290	+	3.06224i	0.735608	+	0.215994i
$202$	2.13760	+	1.85225i	0.150401	+	0.130324i
$203$	−6.81444	−	25.3869i	−0.478280	−	1.78181i
$204$	5.61357	+	2.56363i	0.393028	+	0.179490i
$205$	−21.5319	+	3.09583i	−1.50386	+	0.216222i
$206$	42.4158			2.95525
$207$	4.76354	+	0.555634i	0.331089	+	0.0386193i
$208$		−	14.3550i		−	0.995338i
$209$	0.905046	−	0.130126i	0.0626034	−	0.00900100i
$210$	−5.50152	+	11.3381i	−0.379641	+	0.782403i
$211$	8.64199	−	2.53752i	0.594939	−	0.174690i	0.0296186	−	0.999561i	$-0.490571\pi$
$211$	8.64199	−	2.53752i	0.594939	−	0.174690i	0.565320	+	0.824871i	$0.308753\pi$
$212$	−14.7067	−	12.7434i	−1.01006	−	0.875222i
$213$	2.48231	−	8.45396i	0.170085	−	0.579256i
$214$	−11.8801	−	18.4857i	−0.812104	−	1.26366i
$215$	11.7592	−	5.37026i	0.801973	−	0.366249i
$216$	1.14942	−	0.995981i	0.0782083	−	0.0677679i
$217$	−14.4710	−	9.78492i	−0.982354	−	0.664243i
$218$	−22.8811	−	3.28980i	−1.54970	−	0.222814i
$219$	0.852775	−	5.93118i	0.0576252	−	0.400792i
$220$	−0.828956	+	1.28988i	−0.0558882	+	0.0869637i
$221$	11.7729	−	10.2012i	0.791928	−	0.686209i
$222$	−0.522072	−	1.14318i	−0.0350392	−	0.0767252i
$223$	−7.27592	−	11.3216i	−0.487232	−	0.758148i	0.507390	−	0.861716i	$-0.330610\pi$
$223$	−7.27592	−	11.3216i	−0.487232	−	0.758148i	−0.994622	+	0.103569i	$0.966974\pi$
$224$	−6.11913	+	19.1715i	−0.408851	+	1.28095i
$225$	−0.114038	+	0.131607i	−0.00760254	+	0.00877379i
$226$	9.27637	+	31.5924i	0.617055	+	2.10150i
$227$	−0.737962	+	1.61591i	−0.0489802	+	0.107252i	−0.932540	−	0.361067i	$-0.882413\pi$
$227$	−0.737962	+	1.61591i	−0.0489802	+	0.107252i	0.883560	+	0.468318i	$0.155140\pi$
$228$	9.46290	−	1.36056i	0.626696	−	0.0901053i
$229$	−7.53659			−0.498032			−0.249016	−	0.968499i	$-0.580107\pi$
$229$	−7.53659			−0.498032			−0.249016	+	0.968499i	$0.580107\pi$
$230$	−22.5164	+	3.85306i	−1.48469	+	0.254063i
$231$	−0.0159655	+	0.683394i	−0.00105045	+	0.0449640i
$232$	−2.15041	−	14.9564i	−0.141181	−	0.981937i
$233$	0.429478	−	0.940425i	0.0281360	−	0.0616093i	−0.895042	−	0.445981i	$-0.852855\pi$
$233$	0.429478	−	0.940425i	0.0281360	−	0.0616093i	0.923178	+	0.384372i	$0.125582\pi$
$234$	−4.16559	−	14.1867i	−0.272313	−	0.927414i
$235$	−6.62662	−	5.74200i	−0.432273	−	0.374567i
$236$	−0.149486	+	0.509104i	−0.00973074	+	0.0331398i
$237$	−9.05970	+	5.82232i	−0.588491	+	0.378200i
$238$	−12.0448	+	5.16418i	−0.780748	+	0.334744i
$239$	9.47601	+	10.9359i	0.612952	+	0.707385i	0.974353	−	0.225026i	$-0.0722467\pi$
$239$	9.47601	+	10.9359i	0.612952	+	0.707385i	−0.361400	+	0.932411i	$0.617701\pi$
$240$	2.50019	−	3.89038i	0.161387	−	0.251123i
$241$	1.14287	−	7.94885i	0.0736189	−	0.512030i	−0.919330	−	0.393487i	$-0.871269\pi$
$241$	1.14287	−	7.94885i	0.0736189	−	0.512030i	0.992949	−	0.118543i	$-0.0378224\pi$
$242$	3.37376	−	23.4650i	0.216874	−	1.50839i
$243$	−0.540641	+	0.841254i	−0.0346821	+	0.0539664i
$244$	−6.85148	−	7.90702i	−0.438621	−	0.506195i
$245$	−5.72786	−	14.2709i	−0.365939	−	0.911735i
$246$	−18.0626	+	11.6081i	−1.15163	+	0.740108i
$247$	6.79884	−	23.1547i	0.432600	−	1.47330i
$248$	−7.58910	−	6.57599i	−0.481908	−	0.417576i
$249$	−1.16074	−	3.95310i	−0.0735586	−	0.250518i
$250$	10.2382	−	22.4185i	0.647520	−	1.41787i
$251$	−2.85766	−	19.8754i	−0.180374	−	1.25453i	−0.855881	−	0.517173i	$-0.826984\pi$
$251$	−2.85766	−	19.8754i	−0.180374	−	1.25453i	0.675507	−	0.737353i	$-0.263925\pi$
$252$	−0.166931	+	7.14537i	−0.0105156	+	0.450116i
$253$	−1.02415	+	0.697476i	−0.0643878	+	0.0438499i
$254$	−5.02969			−0.315591
$255$	4.96733	−	0.714194i	0.311066	−	0.0447246i
$256$	−0.0809075	+	0.177163i	−0.00505672	+	0.0110727i
$257$	−7.02989	−	23.9416i	−0.438513	−	1.49344i	−0.821783	−	0.569800i	$-0.807021\pi$
$257$	−7.02989	−	23.9416i	−0.438513	−	1.49344i	0.383271	−	0.923636i	$-0.374798\pi$
$258$	8.35584	−	9.64316i	0.520212	−	0.600357i
$259$	1.46089	+	0.466283i	0.0907750	+	0.0289734i
$260$	21.8784	+	34.0434i	1.35684	+	2.11128i
$261$	4.12716	+	9.03722i	0.255465	+	0.559390i
$262$	−9.89616	+	8.57507i	−0.611387	+	0.529770i
$263$	−0.943150	+	1.46757i	−0.0581571	+	0.0904943i	−0.869114	−	0.494611i	$-0.835310\pi$
$263$	−0.943150	+	1.46757i	−0.0581571	+	0.0904943i	0.810957	+	0.585105i	$0.198947\pi$
$264$	−0.0559233	+	0.388955i	−0.00344184	+	0.0239385i
$265$	−15.6634	−	2.25206i	−0.962197	−	0.138343i
$266$	−11.3719	+	16.8181i	−0.697259	+	1.03118i
$267$	−8.12515	+	7.04049i	−0.497251	+	0.430871i
$268$	−26.7093	+	12.1977i	−1.63153	+	0.745095i
$269$	6.97051	+	10.8463i	0.425000	+	0.661312i	0.986046	−	0.166472i	$-0.0532375\pi$
$269$	6.97051	+	10.8463i	0.425000	+	0.661312i	−0.561047	+	0.827784i	$0.689601\pi$
$270$	1.34196	−	4.57030i	0.0816691	−	0.278139i
$271$	12.9165	+	11.1922i	0.784620	+	0.679877i	0.952028	−	0.306010i	$-0.0989942\pi$
$271$	12.9165	+	11.1922i	0.784620	+	0.679877i	−0.167408	+	0.985888i	$0.553540\pi$
$272$	4.61422	−	1.35486i	0.279778	−	0.0821502i
$273$	16.2316	+	7.87598i	0.982384	+	0.476676i
$274$	−7.14313	+	1.02703i	−0.431532	+	0.0620450i
$275$		−	0.0449927i		−	0.00271316i
$276$	−10.7082	+	7.29261i	−0.644559	+	0.438963i
$277$	−6.63150			−0.398448			−0.199224	−	0.979954i	$-0.563842\pi$
$277$	−6.63150			−0.398448			−0.199224	+	0.979954i	$0.563842\pi$
$278$	−28.8595	+	4.14937i	−1.73088	+	0.248863i
$279$	6.00587	+	2.74279i	0.359562	+	0.164207i
$280$	−2.29166	−	8.53750i	−0.136953	−	0.510213i
$281$	5.23020	+	4.53199i	0.312008	+	0.270356i	0.796761	−	0.604295i	$-0.206545\pi$
$281$	5.23020	+	4.53199i	0.312008	+	0.270356i	−0.484753	+	0.874651i	$0.661091\pi$
$282$	−8.30393	−	2.43826i	−0.494492	−	0.145196i
$283$	10.2151	−	6.56483i	0.607223	−	0.390239i	−0.200592	−	0.979675i	$-0.564286\pi$
$283$	10.2151	−	6.56483i	0.607223	−	0.390239i	0.807815	+	0.589436i	$0.200650\pi$
$284$	9.88769	+	21.6510i	0.586727	+	1.28475i
$285$	5.87541	−	5.09107i	0.348029	−	0.301569i
$286$	3.21372	+	2.06533i	0.190031	+	0.122126i
$287$	4.33319	−	25.8384i	0.255780	−	1.52519i
$288$	1.08249	−	7.52888i	0.0637863	−	0.443644i
$289$	−9.91111	−	6.36948i	−0.583006	−	0.374675i
$290$	−30.9899	−	35.7643i	−1.81979	−	2.10015i
$291$	−4.66426	+	2.13010i	−0.273424	+	0.124868i
$292$	8.75160	+	13.6178i	0.512149	+	0.796919i
$293$	−15.6519	−	4.59582i	−0.914395	−	0.268491i	−0.209505	−	0.977808i	$-0.567185\pi$
$293$	−15.6519	−	4.59582i	−0.914395	−	0.268491i	−0.704890	+	0.709317i	$0.749004\pi$
$294$	−10.9941	−	10.4643i	−0.641187	−	0.610289i
$295$	0.121561	+	0.413999i	0.00707756	+	0.0241040i
$296$	0.801865	+	0.366199i	0.0466074	+	0.0212849i
$297$	−0.0367698	−	0.255739i	−0.00213360	−	0.0148395i
$298$			20.2784i			1.17470i
$299$	5.51605	+	32.2345i	0.319001	+	1.86417i
$300$		−	0.470430i		−	0.0271603i
$301$	1.85523	+	15.4586i	0.106934	+	0.891018i
$302$	7.50200	−	16.4271i	0.431692	−	0.945273i
$303$	1.25163	−	0.367512i	0.0719043	−	0.0211130i
$304$	4.87865	−	5.63026i	0.279810	−	0.322917i
$305$	−8.16338	−	2.39698i	−0.467434	−	0.137251i
$306$	4.16698	−	2.67795i	0.238210	−	0.153088i
$307$	−26.3739	+	12.0445i	−1.50524	+	0.687418i	−0.985928	−	0.167169i	$-0.946537\pi$
$307$	−26.3739	+	12.0445i	−1.50524	+	0.687418i	−0.519307	+	0.854587i	$0.673810\pi$
$308$	−1.17637	−	1.42347i	−0.0670300	−	0.0811096i
$309$	10.5760	−	16.4566i	0.601648	−	0.936182i
$310$	−31.1293	−	4.47572i	−1.76803	−	0.254204i
$311$	17.5430	+	2.52231i	0.994774	+	0.143027i	0.620429	−	0.784263i	$-0.286959\pi$
$311$	17.5430	+	2.52231i	0.994774	+	0.143027i	0.374345	+	0.927290i	$0.377868\pi$
$312$	8.72477	+	5.60707i	0.493943	+	0.317438i
$313$	−2.30342	−	2.65829i	−0.130197	−	0.150255i	0.686908	−	0.726745i	$-0.258968\pi$
$313$	−2.30342	−	2.65829i	−0.130197	−	0.150255i	−0.817105	+	0.576489i	$0.804422\pi$
$314$	17.3564	+	38.0052i	0.979478	+	2.14476i
$315$	3.02723	+	4.96154i	0.170565	+	0.279551i
$316$	8.19631	−	27.9141i	0.461079	−	1.57029i
$317$	−1.06135	+	1.22486i	−0.0596112	+	0.0687949i	−0.784772	−	0.619785i	$-0.787220\pi$
$317$	−1.06135	+	1.22486i	−0.0596112	+	0.0687949i	0.725161	+	0.688580i	$0.241765\pi$
$318$	−14.9865	+	4.40043i	−0.840401	+	0.246764i
$319$	−2.33494	−	1.06633i	−0.130731	−	0.0597031i
$320$	3.83989	+	26.7070i	0.214656	+	1.49297i
$321$	−10.1343			−0.565643
$322$	3.82490	−	27.2452i	0.213153	−	1.51832i
$323$	8.08448			0.449832
$324$	−0.384454	−	2.67394i	−0.0213586	−	0.148552i
$325$	−1.08017	−	0.493296i	−0.0599169	−	0.0273632i
$326$	−3.27421	+	0.961395i	−0.181342	+	0.0532467i
$327$	−6.98158	+	8.05717i	−0.386082	+	0.445563i
$328$	4.24305	−	14.4505i	0.234283	−	0.797895i
$329$	9.01481	−	5.50028i	0.497002	−	0.303240i
$330$	0.511241	+	1.11946i	0.0281429	+	0.0616243i
$331$	11.5153	+	13.2893i	0.632936	+	0.730447i	0.978109	−	0.208092i	$-0.0667254\pi$
$331$	11.5153	+	13.2893i	0.632936	+	0.730447i	−0.345174	+	0.938539i	$0.612180\pi$
$332$	9.36305	+	6.01727i	0.513864	+	0.330241i
$333$	−0.573707	−	0.0824866i	−0.0314390	−	0.00452024i
$334$	48.4971	+	6.97283i	2.65364	+	0.381536i
$335$	−12.9092	+	20.0871i	−0.705304	+	1.09747i
$336$	3.54803	+	4.29328i	0.193561	+	0.234218i
$337$	2.72937	−	1.24646i	0.148678	−	0.0678990i	−0.339686	−	0.940539i	$-0.610321\pi$
$337$	2.72937	−	1.24646i	0.148678	−	0.0678990i	0.488365	+	0.872640i	$0.337594\pi$
$338$	61.1058	−	39.2703i	3.32372	−	2.13602i
$339$	14.5703	+	4.27822i	0.791348	+	0.232361i
$340$	−8.87789	+	10.2456i	−0.481471	+	0.555647i
$341$	−1.63679	+	0.480605i	−0.0886372	+	0.0260262i
$342$	3.18765	−	6.97998i	0.172368	−	0.377434i
$343$	18.4713	−	1.34572i	0.997357	−	0.0726621i
$344$			8.95011i			0.482557i
$345$	−4.11934	+	9.69669i	−0.221778	+	0.522052i
$346$			25.7084i			1.38209i
$347$	−0.828281	−	5.76082i	−0.0444645	−	0.309257i	−0.999901	−	0.0140610i	$-0.995524\pi$
$347$	−0.828281	−	5.76082i	−0.0444645	−	0.309257i	0.955437	−	0.295196i	$-0.0953850\pi$
$348$	−24.4134	−	11.1492i	−1.30870	−	0.597662i
$349$	−4.14067	−	14.1018i	−0.221645	−	0.754853i	−0.992965	−	0.118406i	$-0.962221\pi$
$349$	−4.14067	−	14.1018i	−0.221645	−	0.754853i	0.771320	−	0.636447i	$-0.219597\pi$
$350$	0.739508	+	0.671660i	0.0395283	+	0.0359017i
$351$	−6.54284	−	1.92115i	−0.349231	−	0.102544i
$352$	1.06249	+	1.65326i	0.0566307	+	0.0881191i
$353$	−14.8399	+	6.77713i	−0.789846	+	0.360710i	−0.769144	−	0.639075i	$-0.779317\pi$
$353$	−14.8399	+	6.77713i	−0.789846	+	0.360710i	−0.0207014	+	0.999786i	$0.506590\pi$
$354$	0.278891	+	0.321857i	0.0148229	+	0.0171065i
$355$	16.2829	+	10.4644i	0.864208	+	0.555393i
$356$	4.13331	−	28.7478i	0.219065	−	1.52363i
$357$	−0.999649	+	5.96081i	−0.0529070	+	0.315479i
$358$	−25.2849	−	16.2496i	−1.33635	−	0.858819i
$359$	13.5769	−	11.7644i	0.716559	−	0.620902i	−0.218316	−	0.975878i	$-0.570056\pi$
$359$	13.5769	−	11.7644i	0.716559	−	0.620902i	0.934875	+	0.354976i	$0.115511\pi$
$360$	1.38794	+	3.03917i	0.0731510	+	0.160178i
$361$	−5.44788	+	3.50114i	−0.286731	+	0.184271i
$362$	46.8987	+	13.7707i	2.46494	+	0.723771i
$363$	−8.26280	−	7.15975i	−0.433684	−	0.375790i
$364$	−47.0718	+	12.6352i	−2.46723	+	0.662262i
$365$	11.9740	+	5.46832i	0.626745	+	0.286225i
$366$	−8.31214	+	1.19511i	−0.434482	+	0.0624692i
$367$	−2.86465			−0.149533			−0.0747667	−	0.997201i	$-0.523821\pi$
$367$	−2.86465			−0.149533			−0.0747667	+	0.997201i	$0.523821\pi$
$368$	−2.58488	+	9.75929i	−0.134746	+	0.508738i
$369$			9.90236i			0.515497i
$370$	2.73270	−	0.392904i	0.142067	−	0.0204261i
$371$	8.31999	−	17.1467i	0.431952	−	0.890213i
$372$	−17.1138	+	5.02507i	−0.887309	+	0.260538i
$373$	17.1393	+	14.8513i	0.887440	+	0.768971i	0.973827	−	0.227291i	$-0.0729867\pi$
$373$	17.1393	+	14.8513i	0.887440	+	0.768971i	−0.0863870	+	0.996262i	$0.527532\pi$
$374$	−0.360555	+	1.22794i	−0.0186439	+	0.0634952i
$375$	−6.14518	−	9.56208i	−0.317336	−	0.493784i
$376$	5.52198	−	2.52180i	0.284774	−	0.130052i
$377$	−51.2002	+	44.3652i	−2.63694	+	2.28493i
$378$	4.75229	+	3.21338i	0.244431	+	0.165278i
$379$	−22.6955	−	3.26312i	−1.16579	−	0.167615i	−0.467873	−	0.883796i	$-0.654980\pi$
$379$	−22.6955	−	3.26312i	−1.16579	−	0.167615i	−0.697915	+	0.716181i	$0.745889\pi$
$380$	−2.98886	+	20.7879i	−0.153325	+	1.06640i
$381$	−1.25411	+	1.95143i	−0.0642499	+	0.0999748i
$382$	−34.8066	+	30.1601i	−1.78086	+	1.54312i
$383$	−3.50251	−	7.66944i	−0.178970	−	0.391890i	0.798792	−	0.601607i	$-0.205473\pi$
$383$	−3.50251	−	7.66944i	−0.178970	−	0.391890i	−0.977762	+	0.209718i	$0.932746\pi$
$384$	6.17354	+	9.60622i	0.315042	+	0.490215i
$385$	−1.43058	−	0.456609i	−0.0729089	−	0.0232709i
$386$	7.95980	−	9.18610i	0.405143	−	0.467560i
$387$	−1.65792	−	5.64635i	−0.0842767	−	0.287020i
$388$	5.75431	−	12.6002i	0.292131	−	0.639678i
$389$	21.0003	−	3.01938i	1.06476	−	0.153089i	0.412401	−	0.911002i	$-0.364690\pi$
$389$	21.0003	−	3.01938i	1.06476	−	0.153089i	0.652355	+	0.757914i	$0.273781\pi$
$390$	32.4808			1.64473
$391$	−9.84075	+	4.81544i	−0.497668	+	0.243527i
$392$	10.6347	+	0.497169i	0.537134	+	0.0251108i
$393$	0.859456	+	5.97765i	0.0433538	+	0.301533i
$394$	−8.76848	+	19.2003i	−0.441750	+	0.967297i
$395$	−6.66517	−	22.6995i	−0.335361	−	1.14214i
$396$	0.527489	+	0.457072i	0.0265073	+	0.0229687i
$397$	−5.44418	+	18.5412i	−0.273235	+	0.930555i	0.702515	+	0.711669i	$0.252060\pi$
$397$	−5.44418	+	18.5412i	−0.273235	+	0.930555i	−0.975751	+	0.218886i	$0.929758\pi$
$398$	−16.8621	+	10.8366i	−0.845221	+	0.543191i
$399$	3.68961	+	8.60554i	0.184712	+	0.430816i
$400$	−0.240064	−	0.277049i	−0.0120032	−	0.0138524i
$401$	−8.15589	+	12.6908i	−0.407286	+	0.633749i	−0.982936	−	0.183947i	$-0.941113\pi$
$401$	−8.15589	+	12.6908i	−0.407286	+	0.633749i	0.575650	+	0.817696i	$0.304749\pi$
$402$	−3.35404	+	23.3278i	−0.167284	+	1.16349i
$403$	−6.40745	+	44.5648i	−0.319178	+	2.21993i
$404$	−1.90519	+	2.96453i	−0.0947866	+	0.147491i
$405$	−1.43859	−	1.66022i	−0.0714840	−	0.0824969i
$406$	52.3829	−	22.4591i	2.59972	−	1.11462i
$407$	0.125980	−	0.0809623i	0.00624459	−	0.00401315i
$408$	−0.978854	+	3.33367i	−0.0484605	+	0.165041i
$409$	−5.63195	−	4.88011i	−0.278482	−	0.241306i	0.504409	−	0.863465i	$-0.331710\pi$
$409$	−5.63195	−	4.88011i	−0.278482	−	0.241306i	−0.782891	+	0.622159i	$0.786256\pi$
$410$	−13.2886	−	45.2567i	−0.656276	−	2.23507i
$411$	−1.38261	+	3.02749i	−0.0681990	+	0.149335i
$412$	7.52068	+	52.3075i	0.370517	+	2.57701i
$413$	−0.519518	−	0.0121370i	−0.0255638	−	0.000597224i
$414$	0.277416	+	10.3950i	0.0136343	+	0.510886i
$415$	9.05073			0.444283
$416$	51.3399	−	7.38157i	2.51715	−	0.361911i
$417$	−5.58598	+	12.2316i	−0.273547	+	0.598984i
$418$	0.558555	+	1.90226i	0.0273198	+	0.0930428i
$419$	3.05734	−	3.52836i	0.149361	−	0.172372i	−0.676139	−	0.736774i	$-0.736348\pi$
$419$	3.05734	−	3.52836i	0.149361	−	0.172372i	0.825500	+	0.564403i	$0.190893\pi$
$420$	−14.9577	−	4.77417i	−0.729861	−	0.232956i
$421$	−16.8449	−	26.2111i	−0.820969	−	1.27745i	−0.957966	−	0.286881i	$-0.907382\pi$
$421$	−16.8449	−	26.2111i	−0.820969	−	1.27745i	0.136997	−	0.990571i	$-0.456255\pi$
$422$	8.11277	+	17.7645i	0.394924	+	0.864762i
$423$	−3.01651	+	2.61382i	−0.146668	+	0.127088i
$424$	5.92316	−	9.21662i	0.287654	−	0.447599i
$425$	0.0566148	−	0.393764i	0.00274622	−	0.0191004i
$426$	18.9100	+	2.71884i	0.916190	+	0.131728i
$427$	5.73968	−	8.48845i	0.277762	−	0.410785i
$428$	20.6903	−	17.9283i	1.00010	−	0.866595i
$429$	1.60262	−	0.731893i	0.0773754	−	0.0353362i
$430$	15.1544	+	23.5806i	0.730808	+	1.13716i
$431$	6.62273	−	22.5549i	0.319006	−	1.08643i	−0.631410	−	0.775450i	$-0.717523\pi$
$431$	6.62273	−	22.5549i	0.319006	−	1.08643i	0.950415	−	0.310984i	$-0.100659\pi$
$432$	−1.59095	−	1.37856i	−0.0765444	−	0.0663261i
$433$	−16.6422	+	4.88660i	−0.799774	+	0.234835i	−0.655986	−	0.754773i	$-0.727747\pi$
$433$	−16.6422	+	4.88660i	−0.799774	+	0.234835i	−0.143789	+	0.989608i	$0.545929\pi$
$434$	16.5350	−	34.0772i	0.793708	−	1.63576i
$435$	−21.6030	+	3.10604i	−1.03578	+	0.148923i
$436$		−	28.8004i		−	1.37929i
$437$	−8.79167	+	14.5176i	−0.420563	+	0.694471i
$438$	12.9927			0.620816
$439$	−12.3533	+	1.77613i	−0.589589	+	0.0847701i	−0.430651	−	0.902518i	$-0.641716\pi$
$439$	−12.3533	+	1.77613i	−0.589589	+	0.0847701i	−0.158938	+	0.987289i	$0.550807\pi$
$440$	−0.785228	−	0.358602i	−0.0374343	−	0.0170957i
$441$	−6.80122	+	1.65633i	−0.323868	+	0.0788727i
$442$	25.5268	+	22.1191i	1.21419	+	1.05210i
$443$	−8.97443	−	2.63513i	−0.426388	−	0.125199i	0.0614959	−	0.998107i	$-0.480413\pi$
$443$	−8.97443	−	2.63513i	−0.426388	−	0.125199i	−0.487884	+	0.872909i	$0.662231\pi$
$444$	1.31721	−	0.846519i	0.0625120	−	0.0401740i
$445$	−9.81122	−	21.4836i	−0.465097	−	1.01842i
$446$	22.0532	−	19.1092i	1.04425	−	0.904849i
$447$	7.86766	+	5.05624i	0.372128	+	0.239152i
$448$	−32.0485	−	5.37465i	−1.51415	−	0.253928i
$449$	−1.32239	+	9.19742i	−0.0624074	+	0.434053i	0.934532	+	0.355878i	$0.115818\pi$
$449$	−1.32239	+	9.19742i	−0.0624074	+	0.434053i	−0.996940	+	0.0781747i	$0.975091\pi$
$450$	−0.317646	−	0.204138i	−0.0149740	−	0.00962318i
$451$	−1.67544	−	1.93356i	−0.0788934	−	0.0910478i
$452$	−37.3152	+	17.0413i	−1.75516	+	0.801555i
$453$	−4.50286	−	7.00659i	−0.211563	−	0.329198i
$454$	−3.69580	−	1.08518i	−0.173453	−	0.0509302i
$455$	−26.6468	+	29.3386i	−1.24922	+	1.37541i
$456$	1.51639	+	5.16436i	0.0710117	+	0.241844i
$457$	−9.13242	−	4.17064i	−0.427196	−	0.195094i	0.190201	−	0.981745i	$-0.439086\pi$
$457$	−9.13242	−	4.17064i	−0.427196	−	0.195094i	−0.617398	+	0.786651i	$0.711813\pi$
$458$	−2.32563	−	16.1751i	−0.108670	−	0.755813i
$459$		−	2.28444i		−	0.106628i
$460$	−8.74397	−	27.0842i	−0.407690	−	1.26281i
$461$		−	2.26484i		−	0.105484i	−0.998608	−	0.0527422i	$-0.983204\pi$
$461$		−	2.26484i		−	0.105484i	0.998608	−	0.0527422i	$-0.0167961\pi$
$462$	−1.47163	+	0.176615i	−0.0684666	+	0.00821689i
$463$	−1.01788	+	2.22884i	−0.0473047	+	0.103583i	−0.931809	−	0.362950i	$-0.881770\pi$
$463$	−1.01788	+	2.22884i	−0.0473047	+	0.103583i	0.884504	+	0.466533i	$0.154497\pi$
$464$	−20.0673	+	5.89228i	−0.931599	+	0.273542i
$465$	−9.49832	+	10.9616i	−0.440474	+	0.508334i
$466$	2.15088	+	0.631554i	0.0996374	+	0.0292562i
$467$	10.9117	−	7.01253i	0.504934	−	0.324501i	−0.263253	−	0.964727i	$-0.584795\pi$
$467$	10.9117	−	7.01253i	0.504934	−	0.324501i	0.768187	+	0.640226i	$0.221159\pi$
$468$	16.7566	−	7.65247i	0.774572	−	0.353735i
$469$	−18.3194	−	22.1674i	−0.845913	−	1.02360i
$470$	10.2787	−	15.9940i	0.474121	−	0.737747i
$471$	19.0730	+	2.74228i	0.878837	+	0.126358i
$472$	−0.295685	−	0.0425131i	−0.0136100	−	0.00195682i
$473$	1.27907	+	0.822008i	0.0588117	+	0.0377960i
$474$	−15.2915	−	17.6474i	−0.702364	−	0.810571i
$475$	−0.256009	−	0.560583i	−0.0117465	−	0.0257213i
$476$	−8.50415	−	13.9381i	−0.389787	−	0.638850i
$477$	−2.02946	+	6.91170i	−0.0929225	+	0.316465i
$478$	−20.5466	+	23.7121i	−0.939782	+	1.08457i
$479$	14.8145	−	4.34994i	0.676893	−	0.198754i	0.0748226	−	0.997197i	$-0.476161\pi$
$479$	14.8145	−	4.34994i	0.676893	−	0.198754i	0.602070	+	0.798443i	$0.294343\pi$
$480$	15.1994	+	6.94134i	0.693755	+	0.316827i
$481$	−0.562482	−	3.91215i	−0.0256470	−	0.178379i
$482$	17.4126			0.793120
$483$	−9.61695	−	8.27734i	−0.437586	−	0.376632i
$484$	29.5354			1.34252
$485$	−1.60308	−	11.1496i	−0.0727920	−	0.506279i
$486$	−1.97234	−	0.900736i	−0.0894670	−	0.0408582i
$487$	25.7071	−	7.54829i	1.16490	−	0.342046i	0.358565	−	0.933505i	$-0.383266\pi$
$487$	25.7071	−	7.54829i	1.16490	−	0.342046i	0.806335	+	0.591459i	$0.201448\pi$
$488$	3.85737	−	4.45165i	0.174615	−	0.201517i
$489$	−0.443391	+	1.51005i	−0.0200508	+	0.0682868i
$490$	28.8609	−	16.6969i	1.30380	−	0.754288i
$491$	7.07751	+	15.4976i	0.319403	+	0.699396i	0.999429	−	0.0337927i	$-0.0107586\pi$
$491$	7.07751	+	15.4976i	0.319403	+	0.699396i	−0.680026	+	0.733188i	$0.738031\pi$
$492$	−17.5179	−	20.2167i	−0.789768	−	0.911441i
$493$	−19.0930	−	12.2703i	−0.859907	−	0.552628i
$494$	51.7929	+	7.44669i	2.33027	+	0.335042i
$495$	0.561804	+	0.0807753i	0.0252512	+	0.00363058i
$496$	−7.51444	+	11.6927i	−0.337408	+	0.525017i
$497$	−17.9693	+	14.8501i	−0.806032	+	0.666116i
$498$	8.12601	−	3.71102i	0.364135	−	0.166295i
$499$	8.60423	−	5.52961i	0.385178	−	0.247539i	−0.333694	−	0.942682i	$-0.608295\pi$
$499$	8.60423	−	5.52961i	0.385178	−	0.247539i	0.718872	+	0.695142i	$0.244659\pi$
$500$	29.4620	+	8.65081i	1.31758	+	0.386876i
$501$	14.7976	−	17.0774i	0.661110	−	0.762962i
$502$	41.7750	−	12.2663i	1.86451	−	0.547470i
$503$	−0.642178	+	1.40617i	−0.0286333	+	0.0626982i	−0.923408	−	0.383819i	$-0.874609\pi$
$503$	−0.642178	+	1.40617i	−0.0286333	+	0.0626982i	0.894775	+	0.446517i	$0.147336\pi$
$504$	−3.99527	+	0.479484i	−0.177963	+	0.0213579i
$505$			2.86564i			0.127519i
$506$	−1.81296	−	1.98282i	−0.0805959	−	0.0881469i
$507$		−	33.4996i		−	1.48777i
$508$	−0.891806	−	6.20265i	−0.0395675	−	0.275198i
$509$	30.9458	+	14.1325i	1.37165	+	0.626411i	0.958720	−	0.284352i	$-0.0917784\pi$
$509$	30.9458	+	14.1325i	1.37165	+	0.626411i	0.412929	+	0.910763i	$0.364506\pi$
$510$	3.06562	+	10.4405i	0.135748	+	0.462315i
$511$	−10.6590	+	11.7358i	−0.471528	+	0.519159i
$512$	21.5076	+	6.31520i	0.950510	+	0.279095i
$513$	−1.91329	−	2.97714i	−0.0844740	−	0.131444i
$514$	49.2144	−	22.4755i	2.17076	−	0.991351i
$515$	28.1416	+	32.4772i	1.24007	+	1.43111i
$516$	13.3736	+	8.59467i	0.588739	+	0.378359i
$517$	0.146763	−	1.02076i	0.00645465	−	0.0448931i
$518$	−0.549943	+	3.27925i	−0.0241631	+	0.144082i
$519$	9.97440	+	6.41016i	0.437827	+	0.281375i
$520$	−17.2184	+	14.9198i	−0.755076	+	0.654277i
$521$	12.3372	+	27.0148i	0.540505	+	1.18354i	0.961077	+	0.276281i	$0.0891021\pi$
$521$	12.3372	+	27.0148i	0.540505	+	1.18354i	−0.420572	+	0.907259i	$0.638171\pi$
$522$	−18.1222	+	11.6464i	−0.793187	+	0.509751i
$523$	41.2856	+	12.1226i	1.80529	+	0.530082i	0.998180	−	0.0603125i	$-0.0192097\pi$
$523$	41.2856	+	12.1226i	1.80529	+	0.530082i	0.807115	+	0.590395i	$0.201028\pi$
$524$	−12.3295	−	10.6836i	−0.538617	−	0.466715i
$525$	0.444982	−	0.119443i	0.0194206	−	0.00521294i
$526$	−3.44075	−	1.57134i	−0.150024	−	0.0685135i
$527$	−14.9295	+	2.14654i	−0.650341	+	0.0935049i
$528$	0.543899			0.0236702
$529$	2.05432	−	22.9081i	0.0893183	−	0.996003i
$530$		−	34.3119i		−	1.49042i
$531$	0.194414	−	0.0279525i	0.00843684	−	0.00121303i
$532$	−22.7565	−	11.0420i	−0.986619	−	0.478731i
$533$	−64.7896	+	19.0240i	−2.80635	+	0.824019i
$534$	−17.6176	−	15.2657i	−0.762388	−	0.660613i
$535$	6.27219	−	21.3611i	0.271170	−	0.923521i
$536$	−8.93744	−	13.9069i	−0.386039	−	0.600688i
$537$	−12.6091	+	5.75839i	−0.544124	+	0.248493i
$538$	−21.1275	+	18.3071i	−0.910873	+	0.789276i
$539$	1.04778	−	1.47416i	0.0451310	−	0.0634964i
$540$	5.87406	+	0.844563i	0.252779	+	0.0363442i
$541$	3.35267	−	23.3183i	0.144142	−	1.00253i	−0.781438	−	0.623982i	$-0.785514\pi$
$541$	3.35267	−	23.3183i	0.144142	−	1.00253i	0.925581	−	0.378550i	$-0.123577\pi$
$542$	−20.0350	+	31.1751i	−0.860579	+	1.33909i
$543$	17.0365	−	14.7622i	0.731108	−	0.633509i
$544$	7.21830	+	15.8059i	0.309482	+	0.677671i
$545$	−12.6620	−	19.7024i	−0.542379	−	0.843958i
$546$	−11.8948	+	37.2669i	−0.509049	+	1.59487i
$547$	26.7014	−	30.8151i	1.14167	−	1.31756i	0.200474	−	0.979699i	$-0.435752\pi$
$547$	26.7014	−	30.8151i	1.14167	−	1.31756i	0.941197	−	0.337859i	$-0.109703\pi$
$548$	−2.53307	−	8.62686i	−0.108208	−	0.368521i
$549$	−1.60888	+	3.52295i	−0.0686652	+	0.150356i
$550$	0.0965636	−	0.0138838i	0.00411749	−	0.000592005i
$551$	−35.1594			−1.49784
$552$	−4.92192	−	5.38305i	−0.209491	−	0.229118i
$553$	28.4851	+	0.665471i	1.21131	+	0.0282987i
$554$	−2.04634	−	14.2326i	−0.0869405	−	0.604685i
$555$	0.528936	−	1.15821i	0.0224521	−	0.0491632i
$556$	−10.2341	−	34.8541i	−0.434022	−	1.47814i
$557$	−5.48191	−	4.75010i	−0.232276	−	0.201268i	0.530944	−	0.847407i	$-0.321837\pi$
$557$	−5.48191	−	4.75010i	−0.232276	−	0.201268i	−0.763220	+	0.646139i	$0.776383\pi$
$558$	−4.03332	+	13.7362i	−0.170744	+	0.581501i
$559$	33.7581	−	21.6950i	1.42782	−	0.917601i
$560$	−11.2453	+	4.82139i	−0.475199	+	0.203741i
$561$	0.386517	+	0.446065i	0.0163188	+	0.0188329i
$562$	−8.11268	+	12.6236i	−0.342213	+	0.532493i
$563$	−6.54639	+	45.5311i	−0.275897	+	1.91891i	0.105352	+	0.994435i	$0.466403\pi$
$563$	−6.54639	+	45.5311i	−0.275897	+	1.91891i	−0.381249	+	0.924472i	$0.624506\pi$
$564$	1.53452	−	10.6728i	0.0646148	−	0.449406i
$565$	−18.0352	+	28.0634i	−0.758748	+	1.18064i
$566$	17.2416	+	19.8979i	0.724720	+	0.836372i
$567$	2.43167	−	1.04258i	0.102121	−	0.0437841i
$568$	−11.2732	+	7.24485i	−0.473013	+	0.303987i
$569$	−3.52545	+	12.0066i	−0.147794	+	0.503342i	−0.999796	−	0.0201975i	$-0.993571\pi$
$569$	−3.52545	+	12.0066i	−0.147794	+	0.503342i	0.852002	+	0.523539i	$0.175389\pi$
$570$	12.7395	+	11.0389i	0.533600	+	0.462367i
$571$	7.38572	+	25.1535i	0.309083	+	1.05264i	0.956797	+	0.290756i	$0.0939069\pi$
$571$	7.38572	+	25.1535i	0.309083	+	1.05264i	−0.647714	+	0.761883i	$0.724275\pi$
$572$	−1.97716	+	4.32938i	−0.0826693	+	0.181021i
$573$	3.02286	+	21.0245i	0.126282	+	0.878310i
$574$	56.7917	+	1.32677i	2.37044	+	0.0553784i
$575$	0.645530	+	0.529874i	0.0269205	+	0.0220973i
$576$	12.2823			0.511764
$577$	16.2231	−	2.33252i	0.675375	−	0.0971042i	0.203911	−	0.978989i	$-0.434635\pi$
$577$	16.2231	−	2.33252i	0.675375	−	0.0971042i	0.471464	+	0.881885i	$0.343726\pi$
$578$	10.6119	−	23.2368i	0.441396	−	0.966523i
$579$	−1.57934	−	5.37873i	−0.0656351	−	0.223533i
$580$	38.6100	−	44.5583i	1.60319	−	1.85018i
$581$	−3.31446	+	10.3843i	−0.137507	+	0.430815i
$582$	−6.01092	−	9.35317i	−0.249161	−	0.387702i
$583$	−0.773154	−	1.69297i	−0.0320208	−	0.0701157i
$584$	−6.88754	+	5.96809i	−0.285009	+	0.246961i
$585$	8.09881	−	12.6020i	0.334844	−	0.521028i
$586$	5.03374	−	35.0105i	0.207942	−	1.44627i
$587$	−12.3436	−	1.77473i	−0.509473	−	0.0732511i	−0.117215	−	0.993107i	$-0.537397\pi$
$587$	−12.3436	−	1.77473i	−0.509473	−	0.0732511i	−0.392258	+	0.919855i	$0.628306\pi$
$588$	10.9553	−	15.4134i	0.451788	−	0.635636i
$589$	−17.6588	+	15.3014i	−0.727618	+	0.630485i
$590$	−0.851018	+	0.388647i	−0.0350358	+	0.0160003i
$591$	5.26303	+	8.18943i	0.216492	+	0.336868i
$592$	0.343754	−	1.17072i	0.0141282	−	0.0481162i
$593$	−9.86323	−	8.54653i	−0.405034	−	0.350964i	0.428394	−	0.903592i	$-0.359080\pi$
$593$	−9.86323	−	8.54653i	−0.405034	−	0.350964i	−0.833428	+	0.552628i	$0.813625\pi$
$594$	0.537524	−	0.157831i	0.0220549	−	0.00647590i
$595$	−11.9455	−	5.79624i	−0.489717	−	0.237622i
$596$	−25.0075	+	3.59553i	−1.02435	+	0.147279i
$597$			9.24421i			0.378340i
$598$	−67.4799	+	21.7855i	−2.75946	+	0.890874i
$599$	3.99213			0.163114			0.0815570	−	0.996669i	$-0.474011\pi$
$599$	3.99213			0.163114			0.0815570	+	0.996669i	$0.474011\pi$
$600$	0.262156	−	0.0376923i	0.0107025	−	0.00153878i
$601$	18.2703	+	8.34375i	0.745260	+	0.340349i	0.751589	−	0.659631i	$-0.229288\pi$
$601$	18.2703	+	8.34375i	0.745260	+	0.340349i	−0.00632957	+	0.999980i	$0.502015\pi$
$602$	−32.6049	+	8.75190i	−1.32888	+	0.356701i
$603$	8.21449	+	7.11789i	0.334520	+	0.289863i
$604$	21.5882	+	6.33886i	0.878410	+	0.257925i
$605$	20.2052	−	12.9851i	0.821458	−	0.527919i
$606$	1.17498	+	2.57285i	0.0477304	+	0.104515i
$607$	−14.7460	+	12.7775i	−0.598523	+	0.518623i	−0.900594	−	0.434662i	$-0.856868\pi$
$607$	−14.7460	+	12.7775i	−0.598523	+	0.518623i	0.302070	+	0.953286i	$0.402322\pi$
$608$	22.6451	+	14.5531i	0.918379	+	0.590206i
$609$	4.34748	−	25.9236i	0.176169	−	1.05048i
$610$	2.62539	−	18.2600i	0.106299	−	0.739325i
$611$	−22.8970	−	14.7150i	−0.926314	−	0.595306i
$612$	4.04131	+	4.66392i	0.163360	+	0.188528i
$613$	−31.1052	+	14.2053i	−1.25633	+	0.573746i	−0.928620	−	0.371033i	$-0.879004\pi$
$613$	−31.1052	+	14.2053i	−1.25633	+	0.573746i	−0.327709	+	0.944779i	$0.606276\pi$
$614$	−33.9885	−	52.8871i	−1.37166	−	2.13435i
$615$	−20.8722	−	6.12863i	−0.841648	−	0.247130i
$616$	0.698999	−	0.769608i	0.0281635	−	0.0310084i
$617$	−0.561620	−	1.91270i	−0.0226100	−	0.0770024i	0.947415	−	0.320007i	$-0.103685\pi$
$617$	−0.561620	−	1.91270i	−0.0226100	−	0.0770024i	−0.970025	+	0.243004i	$0.921867\pi$
$618$	38.5828	+	17.6202i	1.55203	+	0.708787i
$619$	6.32455	+	43.9882i	0.254205	+	1.76804i	0.572366	+	0.819998i	$0.306026\pi$
$619$	6.32455	+	43.9882i	0.254205	+	1.76804i	−0.318161	+	0.948037i	$0.603065\pi$
$620$		−	39.1825i		−	1.57361i
$621$	4.10225	+	2.48427i	0.164617	+	0.0996902i
$622$			38.4293i			1.54088i
$623$	28.2421	−	3.38943i	1.13150	−	0.135794i
$624$	5.96327	−	13.0577i	0.238722	−	0.522728i
$625$	23.1228	−	6.78946i	0.924912	−	0.271579i
$626$	4.99446	−	5.76391i	0.199619	−	0.230372i
$627$	0.877315	+	0.257603i	0.0350366	+	0.0102877i
$628$	−43.7908	+	28.1427i	−1.74745	+	1.12301i
$629$	1.20442	−	0.550040i	0.0480234	−	0.0219315i
$630$	−9.71437	+	8.02809i	−0.387030	+	0.319847i
$631$	−9.89687	+	15.3998i	−0.393988	+	0.613057i	−0.980415	−	0.196945i	$-0.936898\pi$
$631$	−9.89687	+	15.3998i	−0.393988	+	0.613057i	0.586426	+	0.810002i	$0.300534\pi$
$632$	16.2123	+	2.33098i	0.644893	+	0.0927216i
$633$	8.91515	+	1.28181i	0.354345	+	0.0509472i
$634$	−2.95631	−	1.89991i	−0.117410	−	0.0754549i
$635$	−3.33705	−	3.85116i	−0.132427	−	0.152829i
$636$	−8.08387	−	17.7012i	−0.320546	−	0.701899i
$637$	−23.9033	−	41.3173i	−0.947082	−	1.63705i
$638$	1.56806	−	5.34031i	0.0620800	−	0.211425i
$639$	5.76989	−	6.65881i	0.228253	−	0.263418i
$640$	−24.0688	+	7.06724i	−0.951404	+	0.279357i
$641$	25.0320	+	11.4317i	0.988705	+	0.451526i	0.843065	−	0.537812i	$-0.180749\pi$
$641$	25.0320	+	11.4317i	0.988705	+	0.451526i	0.145639	+	0.989338i	$0.453476\pi$
$642$	−3.12723	−	21.7504i	−0.123422	−	0.858419i
$643$	−11.5113			−0.453959			−0.226980	−	0.973899i	$-0.572885\pi$
$643$	−11.5113			−0.453959			−0.226980	+	0.973899i	$0.572885\pi$
$644$	34.2772	−	0.113913i	1.35071	−	0.00448882i
$645$	12.9275			0.509019
$646$	2.49469	+	17.3510i	0.0981524	+	0.682665i
$647$	−1.23154	−	0.562423i	−0.0484167	−	0.0221111i	0.391060	−	0.920365i	$-0.372109\pi$
$647$	−1.23154	−	0.562423i	−0.0484167	−	0.0221111i	−0.439476	+	0.898254i	$0.644836\pi$
$648$	1.45930	−	0.428488i	0.0573266	−	0.0168326i
$649$	−0.0332323	+	0.0383521i	−0.00130448	+	0.00150545i
$650$	0.725400	−	2.47049i	0.0284525	−	0.0969005i
$651$	−9.09846	−	14.9121i	−0.356597	−	0.584453i
$652$	−1.76614	−	3.86731i	−0.0691675	−	0.151456i
$653$	−7.94273	−	9.16640i	−0.310823	−	0.358709i	0.578747	−	0.815507i	$-0.303542\pi$
$653$	−7.94273	−	9.16640i	−0.310823	−	0.358709i	−0.889571	+	0.456798i	$0.848996\pi$
$654$	−19.4467	−	12.4977i	−0.760428	−	0.488697i
$655$	−13.1316	−	1.88804i	−0.513094	−	0.0737718i
$656$	−20.6335	−	2.96665i	−0.805603	−	0.115828i
$657$	3.23961	−	5.04094i	0.126389	−	0.196666i
$658$	14.5865	+	17.6504i	0.568642	+	0.688084i
$659$	−35.7738	+	16.3373i	−1.39355	+	0.636412i	−0.963822	−	0.266547i	$-0.914117\pi$
$659$	−35.7738	+	16.3373i	−1.39355	+	0.636412i	−0.429727	+	0.902959i	$0.641390\pi$
$660$	−1.28988	+	0.828956i	−0.0502085	+	0.0322671i
$661$	18.5259	+	5.43970i	0.720574	+	0.211580i	0.621404	−	0.783491i	$-0.286563\pi$
$661$	18.5259	+	5.43970i	0.720574	+	0.211580i	0.0991709	+	0.995070i	$0.468381\pi$
$662$	−24.9683	+	28.8149i	−0.970420	+	1.11992i
$663$	14.9467	−	4.38875i	0.580482	−	0.170445i
$664$	−2.60304	+	5.69986i	−0.101017	+	0.221197i
$665$	−20.4223	+	2.45094i	−0.791942	+	0.0950434i
$666$		−	1.25675i		−	0.0486980i
$667$	42.7975	−	20.9424i	1.65713	−	0.810891i
$668$			61.0433i			2.36184i
$669$	−1.91527	−	13.3210i	−0.0740485	−	0.515019i
$670$	−47.0946	−	21.5074i	−1.81942	−	0.830902i
$671$	−0.281915	−	0.960115i	−0.0108832	−	0.0370648i
$672$	−13.5303	+	14.8970i	−0.521942	+	0.574666i
$673$	20.3893	+	5.98685i	0.785951	+	0.230776i	0.649995	−	0.759939i	$-0.274771\pi$
$673$	20.3893	+	5.98685i	0.785951	+	0.230776i	0.135956	+	0.990715i	$0.456589\pi$
$674$	3.51739	+	5.47316i	0.135485	+	0.210818i
$675$	−0.158404	+	0.0723407i	−0.00609698	+	0.00278440i
$676$	59.2630	+	68.3931i	2.27935	+	2.63051i
$677$	−1.73065	−	1.11222i	−0.0665142	−	0.0427461i	0.506961	−	0.861969i	$-0.330769\pi$
$677$	−1.73065	−	1.11222i	−0.0665142	−	0.0427461i	−0.573475	+	0.819223i	$0.694405\pi$
$678$	−4.68588	+	32.5910i	−0.179960	+	1.25165i
$679$	13.3796	+	2.24381i	0.513462	+	0.0861095i
$680$	−6.42089	−	4.12645i	−0.246230	−	0.158242i
$681$	−1.34255	+	1.16332i	−0.0514465	+	0.0445787i
$682$	−1.53656	−	3.36459i	−0.0588378	−	0.128837i
$683$	−7.63967	+	4.90972i	−0.292324	+	0.187865i	−0.678580	−	0.734526i	$-0.737404\pi$
$683$	−7.63967	+	4.90972i	−0.292324	+	0.187865i	0.386256	+	0.922392i	$0.373768\pi$
$684$	9.17295	+	2.69342i	0.350737	+	0.102986i
$685$	−5.52563	−	4.78799i	−0.211124	−	0.182940i
$686$	8.58804	+	39.2280i	0.327893	+	1.49773i
$687$	−6.85553	−	3.13081i	−0.261555	−	0.119448i
$688$	12.2620	−	1.76301i	0.467483	−	0.0672140i
$689$	−49.1211			−1.87136
$690$	−22.0823	−	5.84879i	−0.840657	−	0.222659i
$691$		−	46.7912i		−	1.78002i	−0.455938	−	0.890011i	$-0.650696\pi$
$691$		−	46.7912i		−	1.78002i	0.455938	−	0.890011i	$-0.349304\pi$
$692$	−31.7038	+	4.55832i	−1.20520	+	0.173281i
$693$	−0.298415	+	0.615005i	−0.0113358	+	0.0233621i
$694$	12.1083	−	3.55533i	0.459626	−	0.134958i
$695$	−22.3245	−	19.3443i	−0.846818	−	0.733772i
$696$	4.25704	−	14.4982i	0.161363	−	0.549551i
$697$	−12.2300	−	19.0303i	−0.463245	−	0.720823i
$698$	28.9877	−	13.2383i	1.09720	−	0.501076i
$699$	0.781333	−	0.677029i	0.0295527	−	0.0256076i
$700$	−0.697175	+	1.03106i	−0.0263507	+	0.0389703i
$701$	26.8713	+	3.86351i	1.01491	+	0.145923i	0.629646	−	0.776882i	$-0.283200\pi$
$701$	26.8713	+	3.86351i	1.01491	+	0.145923i	0.385268	+	0.922805i	$0.374109\pi$
$702$	2.10422	−	14.6351i	0.0794185	−	0.552368i
$703$	1.10896	−	1.72557i	0.0418252	−	0.0650812i
$704$	−2.39828	+	2.07812i	−0.0903886	+	0.0783222i
$705$	−3.64247	−	7.97591i	−0.137184	−	0.300390i
$706$	−19.1244	−	29.7581i	−0.719756	−	1.11996i
$707$	−3.28789	−	1.04942i	−0.123654	−	0.0394676i
$708$	−0.347467	+	0.400998i	−0.0130586	+	0.0150704i
$709$	2.60157	+	8.86013i	0.0977039	+	0.332749i	0.993810	−	0.111090i	$-0.0354343\pi$
$709$	2.60157	+	8.86013i	0.0977039	+	0.332749i	−0.896106	+	0.443839i	$0.853616\pi$
$710$	−17.4342	+	38.1757i	−0.654295	+	1.43271i
$711$	−10.6597	+	1.53263i	−0.399769	+	0.0574781i
$712$	16.3514			0.612796
$713$	12.3809	−	29.1438i	0.463667	−	1.09144i
$714$	−13.1016	−	0.306081i	−0.490315	−	0.0114548i
$715$	0.550812	+	3.83098i	0.0205992	+	0.143271i
$716$	15.5559	−	34.0627i	0.581352	−	1.27298i
$717$	4.07675	+	13.8841i	0.152249	+	0.518512i
$718$	29.4384	+	25.5085i	1.09863	+	0.951970i
$719$	−6.31287	+	21.4997i	−0.235430	+	0.801803i	0.754010	+	0.656863i	$0.228117\pi$
$719$	−6.31287	+	21.4997i	−0.235430	+	0.801803i	−0.989441	+	0.144940i	$0.953701\pi$
$720$	3.89038	−	2.50019i	0.144986	−	0.0931767i
$721$	−47.5683	+	20.3948i	−1.77154	+	0.759544i
$722$	−9.19528	−	10.6119i	−0.342213	−	0.394935i
$723$	4.34166	−	6.75576i	0.161468	−	0.251249i
$724$	−8.66659	+	60.2774i	−0.322091	+	2.24019i
$725$	−0.246218	+	1.71248i	−0.00914431	+	0.0636001i
$726$	12.8166	−	19.9430i	0.475669	−	0.740155i
$727$	−10.4820	−	12.0969i	−0.388755	−	0.448647i	0.527312	−	0.849672i	$-0.323200\pi$
$727$	−10.4820	−	12.0969i	−0.388755	−	0.448647i	−0.916067	+	0.401024i	$0.868654\pi$
$728$	−10.8127	−	25.2192i	−0.400746	−	0.934687i
$729$	−0.841254	+	0.540641i	−0.0311575	+	0.0200237i
$730$	−8.04126	+	27.3860i	−0.297620	+	1.01360i
$731$	10.1597	+	8.80347i	0.375772	+	0.325608i
$732$	−2.94762	−	10.0387i	−0.108947	−	0.371041i
$733$	−14.9691	+	32.7778i	−0.552897	+	1.21068i	0.402518	+	0.915412i	$0.368135\pi$
$733$	−14.9691	+	32.7778i	−0.552897	+	1.21068i	−0.955416	+	0.295264i	$0.904592\pi$
$734$	−0.883968	−	6.14813i	−0.0326279	−	0.226932i
$735$	0.718108	−	15.3607i	0.0264878	−	0.566588i
$736$	−36.2329	−	4.22632i	−1.33556	−	0.155784i
$737$	−2.80830			−0.103445
$738$	−21.2525	+	3.05565i	−0.782317	+	0.112480i
$739$	−15.1249	+	33.1189i	−0.556379	+	1.21830i	0.397360	+	0.917663i	$0.369926\pi$
$739$	−15.1249	+	33.1189i	−0.556379	+	1.21830i	−0.953739	+	0.300636i	$0.902801\pi$
$740$	0.969063	+	3.30033i	0.0356235	+	0.121322i
$741$	15.8033	−	18.2379i	0.580547	−	0.669988i
$742$	39.3678	+	12.5653i	1.44524	+	0.461288i
$743$	−9.97343	−	15.5190i	−0.365890	−	0.569335i	0.608681	−	0.793415i	$-0.291699\pi$
$743$	−9.97343	−	15.5190i	−0.365890	−	0.569335i	−0.974571	+	0.224079i	$0.928062\pi$
$744$	−4.17152	−	9.13436i	−0.152935	−	0.334882i
$745$	−15.5269	+	13.4541i	−0.568861	+	0.492921i
$746$	−26.5852	+	41.3673i	−0.973352	+	1.51457i
$747$	0.586336	−	4.07806i	0.0214529	−	0.149208i
$748$	−1.57823	−	0.226916i	−0.0577059	−	0.00829686i
$749$	22.2117	+	15.0190i	0.811599	+	0.548783i
$750$	18.6260	−	16.1395i	0.680124	−	0.589331i
$751$	5.08497	−	2.32223i	0.185553	−	0.0847393i	−0.320472	−	0.947258i	$-0.603842\pi$
$751$	5.08497	−	2.32223i	0.185553	−	0.0847393i	0.506025	+	0.862519i	$0.331114\pi$
$752$	−4.54269	−	7.06856i	−0.165655	−	0.257764i
$753$	5.65714	−	19.2664i	0.206158	−	0.702108i
$754$	−111.016	−	96.1962i	−4.04298	−	3.50326i
$755$	17.5553	−	5.15471i	0.638904	−	0.187599i
$756$	−3.12014	+	6.43031i	−0.113478	+	0.233868i
$757$	−10.1510	+	1.45949i	−0.368943	+	0.0530460i	−0.324293	−	0.945957i	$-0.605126\pi$
$757$	−10.1510	+	1.45949i	−0.368943	+	0.0530460i	−0.0446502	+	0.999003i	$0.514217\pi$
$758$		−	49.7162i		−	1.80577i
$759$	−1.22134	+	0.208999i	−0.0443319	+	0.00758618i
$760$	−11.8239			−0.428900
$761$	−41.4041	+	5.95301i	−1.50090	+	0.215796i	−0.843246	−	0.537527i	$-0.819359\pi$
$761$	−41.4041	+	5.95301i	−1.50090	+	0.215796i	−0.657650	+	0.753324i	$0.728449\pi$
$762$	−4.57517	−	2.08941i	−0.165741	−	0.0756913i
$763$	27.2424	−	7.31250i	0.986242	−	0.264730i
$764$	−43.3651	−	37.5761i	−1.56889	−	1.35945i
$765$	4.81513	+	1.41385i	0.174091	+	0.0511178i
$766$	15.3794	−	9.88375i	0.555681	−	0.357114i
$767$	0.556387	+	1.21832i	0.0200900	+	0.0439909i
$768$	−0.147192	+	0.127543i	−0.00531134	+	0.00460230i
$769$	4.09277	+	2.63026i	0.147589	+	0.0948497i	0.612351	−	0.790586i	$-0.290224\pi$
$769$	4.09277	+	2.63026i	0.147589	+	0.0948497i	−0.464762	+	0.885436i	$0.653860\pi$
$770$	0.538533	−	3.21122i	0.0194074	−	0.115724i
$771$	3.55109	−	24.6984i	0.127889	−	0.889490i
$772$	12.7397	+	8.18731i	0.458512	+	0.294668i
$773$	−31.5067	−	36.3607i	−1.13322	−	1.30780i	−0.945515	−	0.325578i	$-0.894441\pi$
$773$	−31.5067	−	36.3607i	−1.13322	−	1.30780i	−0.187703	−	0.982226i	$-0.560104\pi$
$774$	11.6067	−	5.30058i	0.417193	−	0.190525i
$775$	0.621613	+	0.967248i	0.0223290	+	0.0347446i
$776$	7.48274	+	2.19713i	0.268615	+	0.0788724i
$777$	1.13517	+	1.03102i	0.0407239	+	0.0369876i
$778$	12.9605	+	44.1393i	0.464655	+	1.58247i
$779$	−31.8770	−	14.5577i	−1.14211	−	0.521585i
$780$	5.75913	+	40.0556i	0.206210	+	1.43422i
$781$			2.27646i			0.0814580i
$782$	−13.3716	−	19.6344i	−0.478167	−	0.702124i
$783$			9.93502i			0.355049i
$784$	−1.41370	−	14.6679i	−0.0504894	−	0.523853i
$785$	−17.5846	+	38.5048i	−0.627620	+	1.37430i
$786$	−12.5641	+	3.68915i	−0.448146	+	0.131587i
$787$	−4.69351	+	5.41660i	−0.167306	+	0.193081i	−0.833211	−	0.552955i	$-0.813500\pi$
$787$	−4.69351	+	5.41660i	−0.167306	+	0.193081i	0.665905	+	0.746036i	$0.268045\pi$
$788$	−25.2327	−	7.40898i	−0.898877	−	0.263934i
$789$	−1.46757	+	0.943150i	−0.0522469	+	0.0335770i
$790$	46.6611	−	21.3094i	1.66013	−	0.758155i
$791$	−25.5938	−	30.9698i	−0.910012	−	1.10116i
$792$	−0.212448	+	0.330575i	−0.00754899	+	0.0117465i
$793$	−26.1410	−	3.75851i	−0.928295	−	0.133469i
$794$	−41.4732	−	5.96294i	−1.47183	−	0.211617i
$795$	−13.3124	−	8.55538i	−0.472143	−	0.303428i
$796$	−16.3536	−	18.8731i	−0.579638	−	0.668938i
$797$	19.7596	+	43.2674i	0.699920	+	1.53261i	0.840068	+	0.542481i	$0.182515\pi$
$797$	19.7596	+	43.2674i	0.699920	+	1.53261i	−0.140148	+	0.990131i	$0.544758\pi$
$798$	−17.3308	+	10.5742i	−0.613502	+	0.374321i
$799$	2.56887	−	8.74878i	0.0908802	−	0.309510i
$800$	0.867408	−	1.00104i	0.0306675	−	0.0353922i
$801$	−10.3156	+	3.02894i	−0.364485	+	0.107022i
$802$	−29.7539	−	13.5881i	−1.05065	−	0.479814i
$803$	0.220331	+	1.53244i	0.00777531	+	0.0540785i
$804$	−29.3628			−1.03554
$805$	23.3989	−	15.1477i	0.824704	−	0.533886i
$806$	−97.6226			−3.43861
$807$	1.83487	+	12.7618i	0.0645906	+	0.449237i
$808$	−1.80469	−	0.824173i	−0.0634887	−	0.0289943i
$809$	40.8940	−	12.0076i	1.43776	−	0.422163i	0.532282	−	0.846567i	$-0.321334\pi$
$809$	40.8940	−	12.0076i	1.43776	−	0.422163i	0.905473	+	0.424404i	$0.139516\pi$
$810$	3.11926	−	3.59982i	0.109600	−	0.126485i
$811$	12.0146	−	40.9178i	0.421888	−	1.43682i	−0.425070	−	0.905161i	$-0.639750\pi$
$811$	12.0146	−	40.9178i	0.421888	−	1.43682i	0.846958	−	0.531659i	$-0.178431\pi$
$812$	36.9846	+	60.6168i	1.29791	+	2.12723i
$813$	7.09984	+	15.5465i	0.249002	+	0.545239i
$814$	0.212637	+	0.245396i	0.00745292	+	0.00860112i
$815$	−2.90846	−	1.86916i	−0.101879	−	0.0654737i
$816$	4.76007	+	0.684394i	0.166636	+	0.0239586i
$817$	20.6137	+	2.96380i	0.721182	+	0.103690i
$818$	8.73584	−	13.5932i	0.305442	−	0.475276i
$819$	11.4930	+	13.9071i	0.401599	+	0.485954i
$820$	53.4548	−	24.4120i	1.86672	−	0.852503i
$821$	−25.8340	+	16.6025i	−0.901611	+	0.579430i	−0.907268	−	0.420554i	$-0.861836\pi$
$821$	−25.8340	+	16.6025i	−0.901611	+	0.579430i	0.00565646	+	0.999984i	$0.498199\pi$
$822$	−6.92426	−	2.03315i	−0.241511	−	0.0709142i
$823$	−8.37455	+	9.66475i	−0.291919	+	0.336892i	−0.882698	−	0.469941i	$-0.844275\pi$
$823$	−8.37455	+	9.66475i	−0.291919	+	0.336892i	0.590779	+	0.806833i	$0.298820\pi$
$824$	−28.5467	+	8.38208i	−0.994473	+	0.292004i
$825$	0.0186906	−	0.0409268i	0.000650724	−	0.00142489i
$826$	−0.134263	−	1.11874i	−0.00467162	−	0.0389259i
$827$		−	25.0450i		−	0.870899i	−0.900213	−	0.435449i	$-0.856590\pi$
$827$		−	25.0450i		−	0.870899i	0.900213	−	0.435449i	$-0.143410\pi$
$828$	−12.7700	+	2.18523i	−0.443788	+	0.0759421i
$829$			5.88015i			0.204226i	0.994773	+	0.102113i	$0.0325604\pi$
$829$			5.88015i			0.204226i	−0.994773	+	0.102113i	$0.967440\pi$
$830$	2.79286	+	19.4248i	0.0969415	+	0.674243i
$831$	−6.03222	−	2.75482i	−0.209256	−	0.0955638i
$832$	23.5963	+	80.3615i	0.818053	+	2.78603i
$833$	11.0248	−	11.5830i	0.381988	−	0.401328i
$834$	−27.9753	−	8.21428i	−0.968704	−	0.284437i
$835$	26.8374	+	41.7597i	0.928745	+	1.44516i
$836$	−2.24685	+	1.02610i	−0.0777089	+	0.0354885i
$837$	4.32374	+	4.98986i	0.149450	+	0.172475i
$838$	8.51603	+	5.47292i	0.294181	+	0.189059i
$839$	4.75636	−	33.0812i	0.164208	−	1.14209i	−0.726385	−	0.687288i	$-0.758801\pi$
$839$	4.75636	−	33.0812i	0.164208	−	1.14209i	0.890593	−	0.454802i	$-0.150290\pi$
$840$	1.46204	−	8.71797i	0.0504450	−	0.300799i
$841$	58.6393	+	37.6852i	2.02205	+	1.29949i
$842$	51.0566	−	44.2408i	1.75953	−	1.52464i
$843$	2.87490	+	6.29515i	0.0990168	+	0.216816i
$844$	−20.4688	+	13.1545i	−0.704566	+	0.452797i
$845$	70.6105	+	20.7331i	2.42908	+	0.713241i
$846$	−6.54064	−	5.66749i	−0.224872	−	0.194852i
$847$	7.49912	+	27.9377i	0.257673	+	0.959950i
$848$	−13.7939	−	6.29945i	−0.473683	−	0.216324i
$849$	12.0191	−	1.72808i	0.412494	−	0.0593077i
$850$	0.862571			0.0295859
$851$	−0.322049	+	2.76098i	−0.0110397	+	0.0946451i
$852$			23.8020i			0.815442i
$853$	56.4275	−	8.11306i	1.93204	−	0.277786i	0.935001	−	0.354646i	$-0.115399\pi$
$853$	56.4275	−	8.11306i	1.93204	−	0.277786i	0.997042	+	0.0768604i	$0.0244896\pi$
$854$	19.9891	+	9.69920i	0.684014	+	0.331900i
$855$	7.45937	−	2.19027i	0.255105	−	0.0749056i
$856$	11.6486	+	10.0936i	0.398142	+	0.344992i
$857$	5.53065	−	18.8357i	0.188923	−	0.643414i	−0.809492	−	0.587132i	$-0.800257\pi$
$857$	5.53065	−	18.8357i	0.188923	−	0.643414i	0.998415	−	0.0562824i	$-0.0179247\pi$
$858$	2.06533	+	3.21372i	0.0705092	+	0.109715i
$859$	5.94849	−	2.71658i	0.202960	−	0.0926886i	−0.311342	−	0.950298i	$-0.600778\pi$
$859$	5.94849	−	2.71658i	0.202960	−	0.0926886i	0.514302	+	0.857609i	$0.328051\pi$
$860$	−26.3928	+	22.8695i	−0.899988	+	0.779844i
$861$	14.6753	−	21.7033i	0.500131	−	0.739648i
$862$	50.4513	+	7.25380i	1.71838	+	0.247065i
$863$	0.230270	−	1.60156i	0.00783849	−	0.0545179i	−0.985527	−	0.169520i	$-0.945778\pi$
$863$	0.230270	−	1.60156i	0.00783849	−	0.0545179i	0.993365	+	0.115002i	$0.0366874\pi$
$864$	4.11228	−	6.39883i	0.139903	−	0.217693i
$865$	−19.6845	+	17.0567i	−0.669294	+	0.579947i
$866$	−15.6231	−	34.2098i	−0.530894	−	1.16250i
$867$	−6.36948	−	9.91111i	−0.216319	−	0.336599i
$868$	44.9560	+	14.3490i	1.52591	+	0.487036i
$869$	1.82212	−	2.10284i	0.0618112	−	0.0713339i
$870$	−13.3324	−	45.4060i	−0.452011	−	1.53941i
$871$	−30.7900	+	67.4207i	−1.04328	+	2.28446i
$872$	16.0496	−	2.30758i	0.543507	−	0.0781445i
$873$	−5.12763			−0.173544
$874$	−33.8707	−	14.3889i	−1.14569	−	0.486713i
$875$	−0.702372	+	30.0646i	−0.0237445	+	1.01637i
$876$	2.30372	+	16.0227i	0.0778354	+	0.541357i
$877$	−11.6306	+	25.4674i	−0.392736	+	0.859972i	0.605219	+	0.796059i	$0.293085\pi$
$877$	−11.6306	+	25.4674i	−0.392736	+	0.859972i	−0.997955	+	0.0639135i	$0.979642\pi$
$878$	−7.62390	−	25.9646i	−0.257294	−	0.876263i
$879$	−12.3283	−	10.6825i	−0.415824	−	0.360313i
$880$	−0.336622	+	1.14643i	−0.0113475	+	0.0386461i
$881$	22.4839	−	14.4495i	0.757503	−	0.486817i	−0.103996	−	0.994578i	$-0.533163\pi$
$881$	22.4839	−	14.4495i	0.757503	−	0.486817i	0.861498	+	0.507760i	$0.169526\pi$
$882$	−5.65353	−	14.0857i	−0.190364	−	0.474291i
$883$	−21.0340	−	24.2745i	−0.707851	−	0.816903i	0.281940	−	0.959432i	$-0.409022\pi$
$883$	−21.0340	−	24.2745i	−0.707851	−	0.816903i	−0.989791	+	0.142529i	$0.954477\pi$
$884$	−22.7513	+	35.4018i	−0.765210	+	1.19069i
$885$	−0.0614056	+	0.427085i	−0.00206413	+	0.0143563i
$886$	2.88623	−	20.0741i	0.0969647	−	0.674404i
$887$	−19.5293	+	30.3882i	−0.655729	+	1.02033i	0.341043	+	0.940048i	$0.389220\pi$
$887$	−19.5293	+	30.3882i	−0.655729	+	1.02033i	−0.996772	+	0.0802868i	$0.974416\pi$
$888$	0.577277	+	0.666213i	0.0193722	+	0.0223567i
$889$	5.64068	−	2.41843i	0.189182	−	0.0811116i
$890$	43.0807	−	27.6863i	1.44407	−	0.928047i
$891$	0.0727910	−	0.247904i	0.00243859	−	0.00830508i
$892$	27.4759	+	23.8080i	0.919960	+	0.797150i
$893$	−3.97958	−	13.5532i	−0.133172	−	0.453540i
$894$	−8.42396	+	18.4459i	−0.281739	+	0.616923i
$895$	−4.33368	−	30.1414i	−0.144859	−	1.00752i
$896$	0.705615	−	30.2034i	0.0235729	−	1.00903i
$897$	−8.37313	+	31.6130i	−0.279571	+	1.05553i
$898$	−20.1476			−0.672336
$899$	64.9286	−	9.33533i	2.16549	−	0.311351i
$900$	0.195424	−	0.427918i	0.00651412	−	0.0142639i
$901$	−4.63616	−	15.7893i	−0.154453	−	0.526019i
$902$	3.63282	−	4.19250i	0.120960	−	0.139595i
$903$	−4.73415	+	14.8323i	−0.157543	+	0.493589i
$904$	−12.4864	−	19.4292i	−0.415291	−	0.646205i
$905$	20.5718	+	45.0460i	0.683831	+	1.49738i
$906$	13.6481	−	11.8262i	0.453428	−	0.392898i
$907$	2.38113	−	3.70511i	0.0790641	−	0.123026i	−0.799470	−	0.600707i	$-0.794886\pi$
$907$	2.38113	−	3.70511i	0.0790641	−	0.123026i	0.878534	+	0.477681i	$0.158522\pi$
$908$	0.682961	−	4.75010i	0.0226649	−	0.157638i
$909$	1.29119	+	0.185646i	0.0428262	+	0.00615747i
$910$	−71.1893	−	48.1364i	−2.35990	−	1.59571i
$911$	18.3586	−	15.9078i	0.608248	−	0.527050i	−0.295373	−	0.955382i	$-0.595444\pi$
$911$	18.3586	−	15.9078i	0.608248	−	0.527050i	0.903622	+	0.428332i	$0.140899\pi$
$912$	6.77667	−	3.09480i	0.224398	−	0.102479i
$913$	0.575501	+	0.895497i	0.0190463	+	0.0296366i
$914$	6.13299	−	20.8870i	0.202861	−	0.690882i
$915$	−6.42993	−	5.57156i	−0.212567	−	0.184190i
$916$	19.5349	−	5.73597i	0.645451	−	0.189522i
$917$	6.97515	−	14.3751i	0.230340	−	0.474708i
$918$	4.90288	−	0.704927i	0.161819	−	0.0232661i
$919$			35.4636i			1.16984i	0.811092	+	0.584919i	$0.198874\pi$
$919$			35.4636i			1.16984i	−0.811092	+	0.584919i	$0.801126\pi$
$920$	14.3926	−	7.04281i	0.474509	−	0.232195i
$921$	−28.9940			−0.955384
$922$	4.86083	−	0.698882i	0.160083	−	0.0230164i
$923$	54.6524	+	24.9589i	1.79890	+	0.821532i
$924$	−0.478736	−	1.78351i	−0.0157493	−	0.0586733i
$925$	−0.0762802	−	0.0660972i	−0.00250808	−	0.00217326i
$926$	−5.09765	−	1.49680i	−0.167519	−	0.0491880i
$927$	16.4566	−	10.5760i	0.540505	−	0.347362i
$928$	−31.3924	−	68.7398i	−1.03051	−	2.25649i
$929$	22.0949	−	19.1453i	0.724909	−	0.628137i	−0.212179	−	0.977231i	$-0.568056\pi$
$929$	22.0949	−	19.1453i	0.724909	−	0.628137i	0.937088	+	0.349094i	$0.113511\pi$
$930$	−26.4569	−	17.0028i	−0.867558	−	0.557545i
$931$	4.66673	−	24.3290i	0.152946	−	0.797352i
$932$	−0.397469	+	2.76446i	−0.0130195	+	0.0905527i
$933$	14.9099	+	9.58201i	0.488128	+	0.313701i
$934$	18.4175	+	21.2549i	0.602638	+	0.695482i
$935$	−1.17943	+	0.538628i	−0.0385715	+	0.0176150i
$936$	5.60707	+	8.72477i	0.183273	+	0.285178i
$937$	4.06823	+	1.19454i	0.132903	+	0.0390240i	0.347508	−	0.937677i	$-0.387028\pi$
$937$	4.06823	+	1.19454i	0.132903	+	0.0390240i	−0.214604	+	0.976701i	$0.568846\pi$
$938$	41.9229	−	46.1577i	1.36883	−	1.50710i
$939$	−0.990971	−	3.37494i	−0.0323391	−	0.110137i
$940$	21.5464	+	9.83990i	0.702765	+	0.320942i
$941$	−5.10308	−	35.4927i	−0.166356	−	1.15703i	−0.886339	−	0.463037i	$-0.846760\pi$
$941$	−5.10308	−	35.4927i	−0.166356	−	1.15703i	0.719983	−	0.693992i	$-0.244150\pi$
$942$			41.7808i			1.36129i
$943$	47.4732	−	1.26694i	1.54594	−	0.0412572i
$944$			0.413473i			0.0134574i
$945$	0.692564	+	5.77073i	0.0225291	+	0.187722i
$946$	−1.36951	+	2.99880i	−0.0445265	+	0.0974995i
$947$	11.1823	−	3.28342i	0.363376	−	0.106697i	−0.0949473	−	0.995482i	$-0.530268\pi$
$947$	11.1823	−	3.28342i	0.363376	−	0.106697i	0.458324	+	0.888785i	$0.348450\pi$
$948$	19.0516	−	21.9867i	0.618766	−	0.714094i
$949$	39.2059	+	11.5119i	1.27268	+	0.373692i
$950$	1.12413	−	0.722433i	0.0364715	−	0.0234388i
$951$	−1.47426	+	0.673272i	−0.0478061	+	0.0218323i
$952$	7.08587	−	5.85586i	0.229654	−	0.189789i
$953$	26.8477	−	41.7759i	0.869683	−	1.35325i	−0.0650422	−	0.997883i	$-0.520718\pi$
$953$	26.8477	−	41.7759i	0.869683	−	1.35325i	0.934725	−	0.355371i	$-0.115645\pi$
$954$	−15.4602	−	2.22284i	−0.500542	−	0.0719671i
$955$	−46.1862	−	6.64058i	−1.49455	−	0.214884i
$956$	−32.8850	−	21.1339i	−1.06358	−	0.683520i
$957$	−1.68097	−	1.93994i	−0.0543379	−	0.0627093i
$958$	13.9073	+	30.4528i	0.449325	+	0.983884i
$959$	7.51703	−	4.58643i	0.242737	−	0.148103i
$960$	−7.60161	+	25.8887i	−0.245341	+	0.835554i
$961$	8.24692	−	9.51746i	0.266030	−	0.307015i
$962$	8.22271	−	2.41441i	0.265111	−	0.0778436i
$963$	−9.21850	−	4.20995i	−0.297062	−	0.135664i
$964$	3.08739	+	21.4733i	0.0994382	+	0.691608i
$965$	12.3148			0.396426
$966$	14.7973	−	23.1942i	0.476096	−	0.746261i
$967$	33.7932			1.08672			0.543358	−	0.839501i	$-0.317153\pi$
$967$	33.7932			1.08672			0.543358	+	0.839501i	$0.317153\pi$
$968$	2.36647	+	16.4592i	0.0760613	+	0.529018i
$969$	7.35390	+	3.35841i	0.236241	+	0.107888i
$970$	23.4348	−	6.88108i	0.752446	−	0.220938i
$971$	−5.35331	+	6.17804i	−0.171796	+	0.198263i	−0.835118	−	0.550071i	$-0.814601\pi$
$971$	−5.35331	+	6.17804i	−0.171796	+	0.198263i	0.663322	+	0.748334i	$0.269146\pi$
$972$	0.761082	−	2.59201i	0.0244117	−	0.0831387i
$973$	30.3701	−	18.5300i	0.973622	−	0.594044i
$974$	24.1329	+	52.8436i	0.773267	+	1.69322i
$975$	−0.777633	−	0.897436i	−0.0249042	−	0.0287410i
$976$	−6.85875	−	4.40785i	−0.219543	−	0.141092i
$977$	3.16904	+	0.455639i	0.101387	+	0.0145772i	0.192821	−	0.981234i	$-0.438236\pi$
$977$	3.16904	+	0.455639i	0.101387	+	0.0145772i	−0.0914348	+	0.995811i	$0.529145\pi$
$978$	−3.37770	−	0.485640i	−0.108007	−	0.0155291i
$979$	1.50177	−	2.33680i	0.0479968	−	0.0746844i
$980$	25.7080	+	32.6309i	0.821211	+	1.04236i
$981$	−9.69774	+	4.42881i	−0.309625	+	0.141401i
$982$	−31.0771	+	19.9720i	−0.991709	+	0.637333i
$983$	−38.4455	−	11.2886i	−1.22622	−	0.360051i	−0.396399	−	0.918078i	$-0.629740\pi$
$983$	−38.4455	−	11.2886i	−1.22622	−	0.360051i	−0.829823	+	0.558027i	$0.811558\pi$
$984$	9.86257	−	11.3820i	0.314407	−	0.362845i
$985$	−20.5190	+	6.02492i	−0.653790	+	0.191970i
$986$	20.4430	−	44.7640i	0.651039	−	1.42558i
$987$	10.4851	−	1.25834i	0.333743	−	0.0400535i
$988$			65.1917i			2.07402i
$989$	−26.8572	+	8.67068i	−0.854009	+	0.275712i
$990$			1.23067i			0.0391134i
$991$	−5.13648	−	35.7250i	−0.163166	−	1.13484i	−0.892619	−	0.450811i	$-0.851135\pi$
$991$	−5.13648	−	35.7250i	−0.163166	−	1.13484i	0.729454	−	0.684030i	$-0.239774\pi$
$992$	−45.6825	−	20.8625i	−1.45042	−	0.662385i
$993$	4.95406	+	16.8720i	0.157212	+	0.535416i
$994$	−37.4162	−	33.9834i	−1.18677	−	1.07789i
$995$	−19.4849	−	5.72129i	−0.617714	−	0.181377i
$996$	6.01727	+	9.36305i	0.190664	+	0.296680i
$997$	18.2315	−	8.32605i	0.577397	−	0.263689i	−0.105239	−	0.994447i	$-0.533561\pi$
$997$	18.2315	−	8.32605i	0.577397	−	0.263689i	0.682636	+	0.730758i	$0.260833\pi$
$998$	14.5228	+	16.7602i	0.459710	+	0.530534i
$999$	−0.487596	−	0.313359i	−0.0154269	−	0.00991424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.r.a.181.28	yes	320
7.6	odd	2	inner	483.2.r.a.181.27	✓	320
23.15	odd	22	inner	483.2.r.a.475.27	yes	320
161.153	even	22	inner	483.2.r.a.475.28	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.r.a.181.27	✓	320	7.6	odd	2	inner
483.2.r.a.181.28	yes	320	1.1	even	1	trivial
483.2.r.a.475.27	yes	320	23.15	odd	22	inner
483.2.r.a.475.28	yes	320	161.153	even	22	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.308578 + 2.14621i) q^{2} +(0.909632 + 0.415415i) q^{3} +(-2.59201 + 0.761082i) q^{4} +(-1.43859 + 1.66022i) q^{5} +(-0.610875 + 2.08045i) q^{6} +(-1.37803 - 2.25855i) q^{7} +(-0.631807 - 1.38346i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.308578 + 2.14621i) q^{2} +(0.909632 + 0.415415i) q^{3} +(-2.59201 + 0.761082i) q^{4} +(-1.43859 + 1.66022i) q^{5} +(-0.610875 + 2.08045i) q^{6} +(-1.37803 - 2.25855i) q^{7} +(-0.631807 - 1.38346i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-4.00709 - 2.57520i) q^{10} +(-0.255739 - 0.0367698i) q^{11} +(-2.67394 - 0.384454i) q^{12} +(-3.68666 + 5.73656i) q^{13} +(4.42209 - 3.65447i) q^{14} +(-1.99826 + 0.912577i) q^{15} +(-1.77094 + 1.13811i) q^{16} +(-2.19190 - 0.643600i) q^{17} +(-1.41992 + 1.63868i) q^{18} +(-3.39559 + 0.997034i) q^{19} +(2.46527 - 5.39818i) q^{20} +(-0.315263 - 2.62690i) q^{21} -0.560217i q^{22} +(3.53937 - 3.23618i) q^{23} -1.52090i q^{24} +(0.0247828 + 0.172368i) q^{25} +(-13.4495 - 6.14218i) q^{26} +(0.281733 + 0.959493i) q^{27} +(5.29080 + 4.80538i) q^{28} +(9.53259 + 2.79902i) q^{29} +(-2.57520 - 4.00709i) q^{30} +(6.00587 - 2.74279i) q^{31} +(-4.98107 - 5.74846i) q^{32} +(-0.217354 - 0.139685i) q^{33} +(0.704927 - 4.90288i) q^{34} +(5.73210 + 0.961294i) q^{35} +(-2.27259 - 1.46051i) q^{36} +(-0.438038 + 0.379562i) q^{37} +(-3.18765 - 6.97998i) q^{38} +(-5.73656 + 3.68666i) q^{39} +(3.20576 + 0.941296i) q^{40} +(7.48371 + 6.48467i) q^{41} +(5.54060 - 1.48722i) q^{42} +(-5.35293 - 2.44460i) q^{43} +(0.690863 - 0.0993311i) q^{44} -2.19678 q^{45} +(8.03769 + 6.59762i) q^{46} +3.99142i q^{47} +(-2.08370 + 0.299590i) q^{48} +(-3.20208 + 6.22468i) q^{49} +(-0.362291 + 0.106378i) q^{50} +(-1.72646 - 1.49599i) q^{51} +(5.18987 - 17.6751i) q^{52} +(3.89450 + 6.05996i) q^{53} +(-1.97234 + 0.900736i) q^{54} +(0.428949 - 0.371687i) q^{55} +(-2.25397 + 3.33342i) q^{56} +(-3.50292 - 0.503644i) q^{57} +(-3.06573 + 21.3226i) q^{58} +(0.106189 - 0.165233i) q^{59} +(4.48497 - 3.88625i) q^{60} +(1.60888 + 3.52295i) q^{61} +(7.73988 + 12.0435i) q^{62} +(0.804481 - 2.52048i) q^{63} +(8.04322 - 9.28237i) q^{64} +(-4.22036 - 14.3732i) q^{65} +(0.232722 - 0.509591i) q^{66} +(10.7587 - 1.54687i) q^{67} +6.17125 q^{68} +(4.56388 - 1.47342i) q^{69} +(-0.294337 + 12.5989i) q^{70} +(-1.25392 - 8.72118i) q^{71} +(0.631807 - 1.38346i) q^{72} +(-1.68819 - 5.74945i) q^{73} +(-0.949788 - 0.822996i) q^{74} +(-0.0490612 + 0.167087i) q^{75} +(8.04256 - 5.16864i) q^{76} +(0.269370 + 0.628270i) q^{77} +(-9.68253 - 11.1742i) q^{78} +(-5.82232 + 9.05970i) q^{79} +(0.658135 - 4.57743i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-11.6081 + 18.0626i) q^{82} +(-2.69802 - 3.11368i) q^{83} +(2.81645 + 6.56901i) q^{84} +(4.22176 - 2.71316i) q^{85} +(3.59483 - 12.2429i) q^{86} +(7.50839 + 6.50606i) q^{87} +(0.110708 + 0.377038i) q^{88} +(-4.46618 + 9.77956i) q^{89} +(-0.677880 - 4.71476i) q^{90} +(18.0366 + 0.421373i) q^{91} +(-6.71108 + 11.0819i) q^{92} +6.60253 q^{93} +(-8.56641 + 1.23166i) q^{94} +(3.22955 - 7.07174i) q^{95} +(-2.14294 - 7.29819i) q^{96} +(-3.35789 + 3.87521i) q^{97} +(-14.3476 - 4.95154i) q^{98} +(-0.139685 - 0.217354i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more