LMFDB - Embedded newform 483.2.u.a.113.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(113,483)]

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([11, 0, 13]))

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

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

chi := DirichletCharacter("483.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.u (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:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			113.3
Character	$\chi$	$=$	483.113
Dual form			483.2.u.a.218.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39817 + 2.17560i) q^{2} +(1.72494 + 0.156831i) q^{3} +(-1.94751 - 4.26445i) q^{4} +(1.23964 + 0.363993i) q^{5} +(-2.75296 + 3.53349i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(6.88105 + 0.989346i) q^{8} +(2.95081 + 0.541047i) q^{9} +(-2.52514 + 2.18804i) q^{10} +(3.71546 - 2.38778i) q^{11} +(-2.69053 - 7.66133i) q^{12} +(-0.344957 - 0.398101i) q^{13} +(2.48138 - 0.728599i) q^{14} +(2.08122 + 0.822278i) q^{15} +(-5.63319 + 6.50105i) q^{16} +(2.16923 - 4.74995i) q^{17} +(-5.30283 + 5.66329i) q^{18} +(1.34429 - 0.613919i) q^{19} +(-0.861991 - 5.99528i) q^{20} +(-1.20092 - 1.24812i) q^{21} +11.4219i q^{22} +(-1.94152 + 4.38526i) q^{23} +(11.7142 + 2.78572i) q^{24} +(-2.80204 - 1.80076i) q^{25} +(1.34842 - 0.193873i) q^{26} +(5.00510 + 1.39605i) q^{27} +(-1.32079 + 4.49820i) q^{28} +(6.92796 + 3.16389i) q^{29} +(-4.69885 + 3.37821i) q^{30} +(-0.577752 + 4.01835i) q^{31} +(-2.35040 - 8.00471i) q^{32} +(6.78341 - 3.53607i) q^{33} +(7.30102 + 11.3606i) q^{34} +(-0.698497 - 1.08688i) q^{35} +(-3.43946 - 13.6373i) q^{36} +(-1.17478 - 4.00094i) q^{37} +(-0.543914 + 3.78301i) q^{38} +(-0.532593 - 0.740799i) q^{39} +(8.16994 + 3.73109i) q^{40} +(-2.78436 + 9.48267i) q^{41} +(4.39449 - 0.867629i) q^{42} +(-0.283316 + 0.0407347i) q^{43} +(-17.4185 - 11.1942i) q^{44} +(3.46102 + 1.74478i) q^{45} +(-6.82599 - 10.3553i) q^{46} -3.99331i q^{47} +(-10.7365 + 10.3304i) q^{48} +(0.142315 + 0.989821i) q^{49} +(7.83546 - 3.57834i) q^{50} +(4.48672 - 7.85315i) q^{51} +(-1.02588 + 2.24636i) q^{52} +(-5.13750 + 5.92899i) q^{53} +(-10.0352 + 8.93717i) q^{54} +(5.47499 - 1.60760i) q^{55} +(-4.55247 - 5.25383i) q^{56} +(2.41510 - 0.848144i) q^{57} +(-16.5698 + 10.6488i) q^{58} +(-2.48304 + 2.15157i) q^{59} +(-0.546634 - 10.4767i) q^{60} +(-7.73502 - 1.11213i) q^{61} +(-7.93452 - 6.87530i) q^{62} +(-1.87576 - 2.34126i) q^{63} +(4.19393 + 1.23145i) q^{64} +(-0.282718 - 0.619065i) q^{65} +(-1.79130 + 19.7020i) q^{66} +(3.01381 - 4.68957i) q^{67} -24.4805 q^{68} +(-4.03674 + 7.25980i) q^{69} +3.34123 q^{70} +(-3.85240 + 5.99446i) q^{71} +(19.7694 + 6.64234i) q^{72} +(-6.10000 - 13.3571i) q^{73} +(10.3470 + 3.03815i) q^{74} +(-4.55092 - 3.54564i) q^{75} +(-5.23605 - 4.53707i) q^{76} +(-4.37162 - 0.628544i) q^{77} +(2.35634 - 0.122945i) q^{78} +(-4.18417 + 3.62560i) q^{79} +(-9.34949 + 6.00855i) q^{80} +(8.41454 + 3.19305i) q^{81} +(-16.7374 - 19.3160i) q^{82} +(11.8076 - 3.46701i) q^{83} +(-2.98374 + 7.55197i) q^{84} +(4.41802 - 5.09866i) q^{85} +(0.307502 - 0.673335i) q^{86} +(11.4541 + 6.54403i) q^{87} +(27.9286 - 12.7546i) q^{88} +(2.24892 + 15.6415i) q^{89} +(-8.63503 + 5.09028i) q^{90} +0.526763i q^{91} +(22.4819 - 0.260832i) q^{92} +(-1.62679 + 6.84080i) q^{93} +(8.68782 + 5.58333i) q^{94} +(1.88991 - 0.271728i) q^{95} +(-2.79889 - 14.1762i) q^{96} +(-0.730490 + 2.48782i) q^{97} +(-2.35243 - 1.07432i) q^{98} +(12.2555 - 5.03565i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9} - 22 q^{12} + 8 q^{13} - 22 q^{15} - 24 q^{16} - 30 q^{18} - 120 q^{24} - 88 q^{25} + 16 q^{27} - 44 q^{30} + 8 q^{31} - 22 q^{33} - 44 q^{34} + 10 q^{36}+ \cdots - 132 q^{97}+O(q^{100}) $ 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

Character values

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

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−1.39817	+	2.17560i	−0.988656	+	1.53838i	−0.153660	+	0.988124i	$0.549106\pi$
$2$	−1.39817	+	2.17560i	−0.988656	+	1.53838i	−0.834996	+	0.550256i	$0.814530\pi$
$3$	1.72494	+	0.156831i	0.995892	+	0.0905464i
$3$	1.72494	+	0.156831i	0.995892	+	0.0905464i
$4$	−1.94751	−	4.26445i	−0.973755	−	2.13223i
$5$	1.23964	+	0.363993i	0.554386	+	0.162782i	0.546913	−	0.837190i	$-0.315803\pi$
$5$	1.23964	+	0.363993i	0.554386	+	0.162782i	0.00747329	+	0.999972i	$0.497621\pi$
$6$	−2.75296	+	3.53349i	−1.12389	+	1.44254i
$7$	−0.755750	−	0.654861i	−0.285646	−	0.247514i
$7$	−0.755750	−	0.654861i	−0.285646	−	0.247514i
$8$	6.88105	+	0.989346i	2.43282	+	0.349786i
$9$	2.95081	+	0.541047i	0.983603	+	0.180349i
$10$	−2.52514	+	2.18804i	−0.798518	+	0.691920i
$11$	3.71546	−	2.38778i	1.12025	−	0.719943i	0.156750	−	0.987638i	$-0.449898\pi$
$11$	3.71546	−	2.38778i	1.12025	−	0.719943i	0.963504	+	0.267695i	$0.0862620\pi$
$12$	−2.69053	−	7.66133i	−0.776689	−	2.21164i
$13$	−0.344957	−	0.398101i	−0.0956737	−	0.110413i	0.705894	−	0.708318i	$-0.250546\pi$
$13$	−0.344957	−	0.398101i	−0.0956737	−	0.110413i	−0.801567	+	0.597904i	$0.796000\pi$
$14$	2.48138	−	0.728599i	0.663177	−	0.194726i
$15$	2.08122	+	0.822278i	0.537369	+	0.212311i
$16$	−5.63319	+	6.50105i	−1.40830	+	1.62526i
$17$	2.16923	−	4.74995i	0.526115	−	1.15203i	−0.440957	−	0.897528i	$-0.645361\pi$
$17$	2.16923	−	4.74995i	0.526115	−	1.15203i	0.967072	−	0.254503i	$-0.0819120\pi$
$18$	−5.30283	+	5.66329i	−1.24989	+	1.33485i
$19$	1.34429	−	0.613919i	0.308402	−	0.140843i	−0.255201	−	0.966888i	$-0.582142\pi$
$19$	1.34429	−	0.613919i	0.308402	−	0.140843i	0.563604	+	0.826045i	$0.309415\pi$
$20$	−0.861991	−	5.99528i	−0.192747	−	1.34059i
$21$	−1.20092	−	1.24812i	−0.262062	−	0.272362i
$22$			11.4219i			2.43515i
$23$	−1.94152	+	4.38526i	−0.404834	+	0.914390i
$23$	−1.94152	+	4.38526i	−0.404834	+	0.914390i
$24$	11.7142	+	2.78572i	2.39115	+	0.568633i
$25$	−2.80204	−	1.80076i	−0.560408	−	0.360152i
$26$	1.34842	−	0.193873i	0.264446	−	0.0380216i
$27$	5.00510	+	1.39605i	0.963232	+	0.268670i
$28$	−1.32079	+	4.49820i	−0.249606	+	0.850081i
$29$	6.92796	+	3.16389i	1.28649	+	0.587520i	0.936970	−	0.349409i	$-0.113618\pi$
$29$	6.92796	+	3.16389i	1.28649	+	0.587520i	0.349519	+	0.936929i	$0.386345\pi$
$30$	−4.69885	+	3.37821i	−0.857889	+	0.616775i
$31$	−0.577752	+	4.01835i	−0.103767	+	0.721718i	0.869814	+	0.493379i	$0.164238\pi$
$31$	−0.577752	+	4.01835i	−0.103767	+	0.721718i	−0.973582	+	0.228339i	$0.926671\pi$
$32$	−2.35040	−	8.00471i	−0.415495	−	1.41505i
$33$	6.78341	−	3.53607i	1.18084	−	0.615551i
$34$	7.30102	+	11.3606i	1.25211	+	1.94833i
$35$	−0.698497	−	1.08688i	−0.118067	−	0.183717i
$36$	−3.43946	−	13.6373i	−0.573243	−	2.27288i
$37$	−1.17478	−	4.00094i	−0.193133	−	0.657750i	−0.997936	−	0.0642089i	$-0.979548\pi$
$37$	−1.17478	−	4.00094i	−0.193133	−	0.657750i	0.804804	−	0.593541i	$-0.202271\pi$
$38$	−0.543914	+	3.78301i	−0.0882345	+	0.613685i
$39$	−0.532593	−	0.740799i	−0.0852832	−	0.118623i
$40$	8.16994	+	3.73109i	1.29178	+	0.589937i
$41$	−2.78436	+	9.48267i	−0.434844	+	1.48094i	0.392765	+	0.919639i	$0.371519\pi$
$41$	−2.78436	+	9.48267i	−0.434844	+	1.48094i	−0.827609	+	0.561305i	$0.810300\pi$
$42$	4.39449	−	0.867629i	0.678084	−	0.133878i
$43$	−0.283316	+	0.0407347i	−0.0432053	+	0.00621198i	−0.163884	−	0.986480i	$-0.552402\pi$
$43$	−0.283316	+	0.0407347i	−0.0432053	+	0.00621198i	0.120678	+	0.992692i	$0.461493\pi$
$44$	−17.4185	−	11.1942i	−2.62593	−	1.68758i
$45$	3.46102	+	1.74478i	0.515938	+	0.260096i
$46$	−6.82599	−	10.3553i	−1.00644	−	1.52681i
$47$		−	3.99331i		−	0.582483i	−0.956649	−	0.291242i	$-0.905932\pi$
$47$		−	3.99331i		−	0.582483i	0.956649	−	0.291242i	$-0.0940684\pi$
$48$	−10.7365	+	10.3304i	−1.54967	+	1.49107i
$49$	0.142315	+	0.989821i	0.0203307	+	0.141403i
$50$	7.83546	−	3.57834i	1.10810	−	0.506053i
$51$	4.48672	−	7.85315i	0.628266	−	1.09966i
$52$	−1.02588	+	2.24636i	−0.142263	+	0.311513i
$53$	−5.13750	+	5.92899i	−0.705689	+	0.814409i	−0.989509	−	0.144469i	$-0.953853\pi$
$53$	−5.13750	+	5.92899i	−0.705689	+	0.814409i	0.283820	+	0.958878i	$0.408398\pi$
$54$	−10.0352	+	8.93717i	−1.36562	+	1.21619i
$55$	5.47499	−	1.60760i	0.738247	−	0.216769i
$56$	−4.55247	−	5.25383i	−0.608349	−	0.702072i
$57$	2.41510	−	0.848144i	0.319888	−	0.112339i
$58$	−16.5698	+	10.6488i	−2.17573	+	1.39825i
$59$	−2.48304	+	2.15157i	−0.323264	+	0.280110i	−0.801341	−	0.598208i	$-0.795880\pi$
$59$	−2.48304	+	2.15157i	−0.323264	+	0.280110i	0.478076	+	0.878318i	$0.341334\pi$
$60$	−0.546634	−	10.4767i	−0.0705702	−	1.35253i
$61$	−7.73502	−	1.11213i	−0.990368	−	0.142393i	−0.371959	−	0.928249i	$-0.621314\pi$
$61$	−7.73502	−	1.11213i	−0.990368	−	0.142393i	−0.618410	+	0.785856i	$0.712223\pi$
$62$	−7.93452	−	6.87530i	−1.00769	−	0.873165i
$63$	−1.87576	−	2.34126i	−0.236324	−	0.294972i
$64$	4.19393	+	1.23145i	0.524241	+	0.153931i
$65$	−0.282718	−	0.619065i	−0.0350668	−	0.0767856i
$66$	−1.79130	+	19.7020i	−0.220494	+	2.42515i
$67$	3.01381	−	4.68957i	0.368195	−	0.572923i	−0.606881	−	0.794793i	$-0.707580\pi$
$67$	3.01381	−	4.68957i	0.368195	−	0.572923i	0.975076	+	0.221870i	$0.0712160\pi$
$68$	−24.4805			−2.96870
$69$	−4.03674	+	7.25980i	−0.485966	+	0.873978i
$70$	3.34123			0.399354
$71$	−3.85240	+	5.99446i	−0.457196	+	0.711411i	−0.990950	−	0.134229i	$-0.957144\pi$
$71$	−3.85240	+	5.99446i	−0.457196	+	0.711411i	0.533754	+	0.845640i	$0.320781\pi$
$72$	19.7694	+	6.64234i	2.32984	+	0.782807i
$73$	−6.10000	−	13.3571i	−0.713951	−	1.56333i	−0.822192	−	0.569210i	$-0.807249\pi$
$73$	−6.10000	−	13.3571i	−0.713951	−	1.56333i	0.108241	−	0.994125i	$-0.465478\pi$
$74$	10.3470	+	3.03815i	1.20281	+	0.353177i
$75$	−4.55092	−	3.54564i	−0.525495	−	0.409416i
$76$	−5.23605	−	4.53707i	−0.600616	−	0.520437i
$77$	−4.37162	−	0.628544i	−0.498193	−	0.0716293i
$78$	2.35634	−	0.122945i	0.266803	−	0.0139208i
$79$	−4.18417	+	3.62560i	−0.470756	+	0.407912i	−0.857668	−	0.514205i	$-0.828087\pi$
$79$	−4.18417	+	3.62560i	−0.470756	+	0.407912i	0.386912	+	0.922117i	$0.373542\pi$
$80$	−9.34949	+	6.00855i	−1.04530	+	0.671776i
$81$	8.41454	+	3.19305i	0.934949	+	0.354783i
$82$	−16.7374	−	19.3160i	−1.84834	−	2.13310i
$83$	11.8076	−	3.46701i	1.29605	−	0.380554i	0.440255	−	0.897873i	$-0.354888\pi$
$83$	11.8076	−	3.46701i	1.29605	−	0.380554i	0.855793	+	0.517319i	$0.173070\pi$
$84$	−2.98374	+	7.55197i	−0.325553	+	0.823988i
$85$	4.41802	−	5.09866i	0.479201	−	0.553028i
$86$	0.307502	−	0.673335i	0.0331588	−	0.0726076i
$87$	11.4541	+	6.54403i	1.22801	+	0.701594i
$88$	27.9286	−	12.7546i	2.97720	−	1.35964i
$89$	2.24892	+	15.6415i	0.238385	+	1.65800i	0.660029	+	0.751240i	$0.270544\pi$
$89$	2.24892	+	15.6415i	0.238385	+	1.65800i	−0.421645	+	0.906761i	$0.638547\pi$
$90$	−8.63503	+	5.09028i	−0.910212	+	0.536563i
$91$			0.526763i			0.0552198i
$92$	22.4819	−	0.260832i	2.34389	−	0.0271936i
$93$	−1.62679	+	6.84080i	−0.168690	+	0.709357i
$94$	8.68782	+	5.58333i	0.896081	+	0.575876i
$95$	1.88991	−	0.271728i	0.193901	−	0.0278787i
$96$	−2.79889	−	14.1762i	−0.285661	−	1.44686i
$97$	−0.730490	+	2.48782i	−0.0741700	+	0.252600i	−0.988229	−	0.152981i	$-0.951113\pi$
$97$	−0.730490	+	2.48782i	−0.0741700	+	0.252600i	0.914059	+	0.405581i	$0.132931\pi$
$98$	−2.35243	−	1.07432i	−0.237632	−	0.108523i
$99$	12.2555	−	5.03565i	1.23173	−	0.506102i
$100$	−2.22226	+	15.4562i	−0.222226	+	1.54562i
$101$	−2.55419	−	8.69878i	−0.254152	−	0.865561i	−0.983421	−	0.181335i	$-0.941958\pi$
$101$	−2.55419	−	8.69878i	−0.254152	−	0.865561i	0.729270	−	0.684226i	$-0.239860\pi$
$102$	10.8121	+	20.7413i	1.07056	+	2.05370i
$103$	3.51040	+	5.46229i	0.345890	+	0.538216i	0.969995	−	0.243125i	$-0.0781725\pi$
$103$	3.51040	+	5.46229i	0.345890	+	0.538216i	−0.624105	+	0.781341i	$0.714536\pi$
$104$	−1.97980	−	3.08063i	−0.194136	−	0.302081i
$105$	−1.03441	−	1.98435i	−0.100948	−	0.193652i
$106$	−5.71599	−	19.4669i	−0.555186	−	1.89079i
$107$	2.89908	−	20.1636i	0.280265	−	1.94929i	−0.0325434	−	0.999470i	$-0.510361\pi$
$107$	2.89908	−	20.1636i	0.280265	−	1.94929i	0.312808	−	0.949816i	$-0.398730\pi$
$108$	−3.79410	−	24.0628i	−0.365088	−	2.31545i
$109$	12.7548	+	5.82491i	1.22168	+	0.557925i	0.918657	−	0.395057i	$-0.129275\pi$
$109$	12.7548	+	5.82491i	1.22168	+	0.557925i	0.303028	+	0.952982i	$0.402002\pi$
$110$	−4.15748	+	14.1591i	−0.396400	+	1.35001i
$111$	−1.39895	−	7.08560i	−0.132783	−	0.672536i
$112$	8.51456	−	1.22421i	0.804551	−	0.115677i
$113$	−13.8258	−	8.88531i	−1.30062	−	0.835859i	−0.307343	−	0.951599i	$-0.599440\pi$
$113$	−13.8258	−	8.88531i	−1.30062	−	0.835859i	−0.993280	+	0.115740i	$0.963076\pi$
$114$	−1.53151	+	6.44014i	−0.143439	+	0.603175i
$115$	−4.00299	+	4.72947i	−0.373281	+	0.441025i
$116$		−	35.7056i		−	3.31519i
$117$	−0.802509	−	1.36136i	−0.0741920	−	0.125858i
$118$	−1.20923	−	8.41036i	−0.111318	−	0.774236i
$119$	−4.74995	+	2.16923i	−0.435427	+	0.198853i
$120$	13.5075	+	7.71719i	1.23306	+	0.704480i
$121$	3.53358	−	7.73746i	0.321235	−	0.703406i
$122$	13.2344	−	15.2733i	1.19819	−	1.38278i
$123$	−6.29002	+	15.9203i	−0.567152	+	1.43549i
$124$	18.2613	−	5.36199i	1.63991	−	0.481521i
$125$	−7.04840	−	8.13429i	−0.630428	−	0.727553i
$126$	7.71628	−	0.807413i	0.687421	−	0.0719301i
$127$	7.10771	−	4.56785i	0.630707	−	0.405331i	−0.185864	−	0.982575i	$-0.559508\pi$
$127$	7.10771	−	4.56785i	0.630707	−	0.405331i	0.816571	+	0.577244i	$0.195872\pi$
$128$	4.06693	−	3.52402i	0.359469	−	0.311482i
$129$	−0.495090	+	0.0258320i	−0.0435903	+	0.00227438i
$130$	1.74212	+	0.250480i	0.152794	+	0.0219685i
$131$	9.01733	+	7.81356i	0.787848	+	0.682674i	0.952790	−	0.303629i	$-0.0981984\pi$
$131$	9.01733	+	7.81356i	0.787848	+	0.682674i	−0.164942	+	0.986303i	$0.552744\pi$
$132$	−28.2902	−	22.0410i	−2.46234	−	1.91842i
$133$	−1.41798	−	0.416357i	−0.122955	−	0.0361027i
$134$	5.98881	+	13.1137i	0.517354	+	1.13285i
$135$	5.69640	+	3.55242i	0.490268	+	0.305744i
$136$	19.6259	−	30.5385i	1.68291	−	2.61866i
$137$	−4.57560			−0.390920			−0.195460	−	0.980712i	$-0.562620\pi$
$137$	−4.57560			−0.390920			−0.195460	+	0.980712i	$0.562620\pi$
$138$	−10.1504	−	18.9328i	−0.864056	−	1.61166i
$139$	−16.6325			−1.41075			−0.705376	−	0.708834i	$-0.749222\pi$
$139$	−16.6325			−1.41075			−0.705376	+	0.708834i	$0.749222\pi$
$140$	−3.27463	+	5.09542i	−0.276756	+	0.430641i
$141$	0.626274	−	6.88820i	0.0527418	−	0.580091i
$142$	−7.65520	−	16.7626i	−0.642410	−	1.40668i
$143$	−2.23225	−	0.655448i	−0.186670	−	0.0548113i
$144$	−20.1398	+	16.1355i	−1.67832	+	1.34463i
$145$	7.43657	+	6.44383i	0.617574	+	0.535131i
$146$	37.5886	+	5.40442i	3.11085	+	0.447273i
$147$	0.0902493	+	1.72970i	0.00744364	+	0.142663i
$148$	−14.7739	+	12.8017i	−1.21441	+	1.05229i
$149$	−4.12160	+	2.64879i	−0.337655	+	0.216998i	−0.698469	−	0.715640i	$-0.746135\pi$
$149$	−4.12160	+	2.64879i	−0.337655	+	0.216998i	0.360814	+	0.932638i	$0.382499\pi$
$150$	14.0769	−	4.94356i	1.14937	−	0.403640i
$151$	12.0633	+	13.9218i	0.981699	+	1.13294i	0.991118	+	0.132986i	$0.0424564\pi$
$151$	12.0633	+	13.9218i	0.981699	+	1.13294i	−0.00941881	+	0.999956i	$0.502998\pi$
$152$	9.85754	−	2.89443i	0.799552	−	0.234770i
$153$	8.97092	−	12.8425i	0.725256	−	1.03826i
$154$	7.47974	−	8.63207i	0.602734	−	0.695592i
$155$	−2.17886	+	4.77103i	−0.175010	+	0.383219i
$156$	−2.12187	+	3.71393i	−0.169885	+	0.297352i
$157$	−0.552181	+	0.252172i	−0.0440688	+	0.0201255i	−0.437328	−	0.899302i	$-0.644075\pi$
$157$	−0.552181	+	0.252172i	−0.0440688	+	0.0201255i	0.393259	+	0.919428i	$0.371348\pi$
$158$	−2.03767	−	14.1723i	−0.162108	−	1.12749i
$159$	−9.79170	+	9.42141i	−0.776532	+	0.747166i
$160$		−	10.7785i		−	0.852117i
$161$	4.33904	−	2.04274i	0.341964	−	0.160990i
$162$	−18.7118	+	13.8422i	−1.47013	+	1.08755i
$163$	4.43943	+	2.85305i	0.347723	+	0.223468i	0.702830	−	0.711358i	$-0.251919\pi$
$163$	4.43943	+	2.85305i	0.347723	+	0.223468i	−0.355108	+	0.934825i	$0.615556\pi$
$164$	45.8609	−	6.59381i	3.58114	−	0.514890i
$165$	9.69612	−	1.91436i	0.754842	−	0.149033i
$166$	−8.96616	+	30.5359i	−0.695909	+	2.37005i
$167$	−11.7765	−	5.37815i	−0.911293	−	0.416173i	−0.0961057	−	0.995371i	$-0.530639\pi$
$167$	−11.7765	−	5.37815i	−0.911293	−	0.416173i	−0.815187	+	0.579198i	$0.803366\pi$
$168$	−7.02875	−	9.77648i	−0.542280	−	0.754272i
$169$	1.81060	−	12.5930i	0.139277	−	0.968694i
$170$	4.91549	+	16.7406i	0.377001	+	1.28395i
$171$	4.29891	−	1.08423i	0.328746	−	0.0829132i
$172$	0.725471	+	1.12886i	0.0553167	+	0.0860744i
$173$	7.00240	+	10.8960i	0.532383	+	0.828404i	0.998410	−	0.0563665i	$-0.0179515\pi$
$173$	7.00240	+	10.8960i	0.532383	+	0.828404i	−0.466027	+	0.884770i	$0.654315\pi$
$174$	−30.2520	+	15.7698i	−2.29339	+	1.19551i
$175$	0.938392	+	3.19587i	0.0709358	+	0.241585i
$176$	−5.40681	+	37.6052i	−0.407554	+	2.83460i
$177$	−4.62052	+	3.32190i	−0.347299	+	0.249689i
$178$	−37.1741	−	16.9768i	−2.78631	−	1.27247i
$179$	−5.04260	+	17.1735i	−0.376902	+	1.28361i	0.524791	+	0.851231i	$0.324144\pi$
$179$	−5.04260	+	17.1735i	−0.376902	+	1.28361i	−0.901692	+	0.432378i	$0.857675\pi$
$180$	0.700156	−	18.1573i	0.0521866	−	1.35337i
$181$	−10.4545	+	1.50313i	−0.777079	+	0.111727i	−0.519432	−	0.854512i	$-0.673856\pi$
$181$	−10.4545	+	1.50313i	−0.777079	+	0.111727i	−0.257647	+	0.966239i	$0.582947\pi$
$182$	−1.14602	−	0.736505i	−0.0849490	−	0.0545934i
$183$	−13.1680	−	3.13144i	−0.973407	−	0.231483i
$184$	−17.6982	+	28.2544i	−1.30473	+	2.08294i
$185$		−	5.38735i		−	0.396086i
$186$	−12.6083	−	13.1038i	−0.924484	−	0.960820i
$187$	−3.28215	−	22.8279i	−0.240015	−	1.66934i
$188$	−17.0293	+	7.77700i	−1.24199	+	0.567196i
$189$	−2.86839	−	4.33271i	−0.208644	−	0.315158i
$190$	−2.05125	+	4.49160i	−0.148813	+	0.325855i
$191$	−14.5904	+	16.8382i	−1.05572	+	1.21837i	−0.0805902	+	0.996747i	$0.525680\pi$
$191$	−14.5904	+	16.8382i	−1.05572	+	1.21837i	−0.975133	+	0.221622i	$0.928865\pi$
$192$	7.04113	+	2.78191i	0.508150	+	0.200767i
$193$	−17.5093	+	5.14121i	−1.26035	+	0.370072i	−0.842625	−	0.538501i	$-0.818991\pi$
$193$	−17.5093	+	5.14121i	−1.26035	+	0.370072i	−0.417725	+	0.908573i	$0.637172\pi$
$194$	−4.39114	−	5.06765i	−0.315266	−	0.363836i
$195$	−0.390581	−	1.11219i	−0.0279701	−	0.0796454i
$196$	3.94389	−	2.53458i	0.281706	−	0.181042i
$197$	8.21351	−	7.11705i	0.585188	−	0.507069i	−0.311196	−	0.950346i	$-0.600730\pi$
$197$	8.21351	−	7.11705i	0.585188	−	0.507069i	0.896385	+	0.443277i	$0.146184\pi$
$198$	−6.17977	+	33.7038i	−0.439177	+	2.39522i
$199$	−0.122054	−	0.0175487i	−0.00865219	−	0.00124400i	0.137987	−	0.990434i	$-0.455937\pi$
$199$	−0.122054	−	0.0175487i	−0.00865219	−	0.00124400i	−0.146640	+	0.989190i	$0.546846\pi$
$200$	−17.4994	−	15.1633i	−1.23739	−	1.07221i
$201$	5.93409	−	7.61656i	0.418559	−	0.537231i
$202$	22.4962	+	6.60549i	1.58283	+	0.464761i
$203$	−3.16389	−	6.92796i	−0.222062	−	0.486247i
$204$	−42.2273	−	3.83930i	−2.95650	−	0.268805i
$205$	−6.90324	+	10.7417i	−0.482143	+	0.750229i
$206$	−16.7919			−1.16995
$207$	−8.10168	+	11.8896i	−0.563105	+	0.826385i
$208$	4.53128			0.314188
$209$	3.52877	−	5.49087i	0.244090	−	0.379812i
$210$	5.76342	+	0.524009i	0.397713	+	0.0361601i
$211$	−2.51377	−	5.50439i	−0.173055	−	0.378938i	0.803153	−	0.595772i	$-0.203154\pi$
$211$	−2.51377	−	5.50439i	−0.173055	−	0.378938i	−0.976208	+	0.216835i	$0.930427\pi$
$212$	35.2892	+	10.3618i	2.42367	+	0.711654i
$213$	−7.58526	+	9.73588i	−0.519734	+	0.667091i
$214$	39.8144	+	34.4994i	2.72166	+	2.35833i
$215$	−0.366038	−	0.0526283i	−0.0249636	−	0.00358922i
$216$	33.0592	+	14.5581i	2.24939	+	0.990550i
$217$	3.06810	−	2.65852i	0.208276	−	0.180472i
$218$	−30.5060	+	19.6050i	−2.06613	+	1.32782i
$219$	−8.42730	−	23.9969i	−0.569464	−	1.62156i
$220$	−17.5181	−	20.2170i	−1.18107	−	1.36303i
$221$	−2.63925	+	0.774953i	−0.177535	+	0.0521290i
$222$	17.3714	+	6.86333i	1.16589	+	0.460637i
$223$	3.39355	−	3.91637i	0.227249	−	0.262259i	−0.630662	−	0.776058i	$-0.717217\pi$
$223$	3.39355	−	3.91637i	0.227249	−	0.262259i	0.857911	+	0.513798i	$0.171762\pi$
$224$	−3.46566	+	7.58874i	−0.231559	+	0.507044i
$225$	−7.29398	−	6.82974i	−0.486266	−	0.455316i
$226$	38.6617	−	17.6562i	2.57174	−	1.17447i
$227$	−2.38547	−	16.5913i	−0.158329	−	1.10120i	−0.901712	−	0.432337i	$-0.857689\pi$
$227$	−2.38547	−	16.5913i	−0.158329	−	1.10120i	0.743383	−	0.668866i	$-0.233220\pi$
$228$	−8.32030	−	8.64732i	−0.551026	−	0.572683i
$229$		−	18.9924i		−	1.25505i	−0.778596	−	0.627525i	$-0.784068\pi$
$229$		−	18.9924i		−	1.25505i	0.778596	−	0.627525i	$-0.215932\pi$
$230$	−4.69254	−	15.3215i	−0.309417	−	1.01027i
$231$	−7.44219	−	1.76980i	−0.489660	−	0.116445i
$232$	44.5414	+	28.6250i	2.92429	+	1.87933i
$233$	−8.46696	+	1.21737i	−0.554689	+	0.0797523i	−0.413959	−	0.910296i	$-0.635854\pi$
$233$	−8.46696	+	1.21737i	−0.554689	+	0.0797523i	−0.140731	+	0.990048i	$0.544945\pi$
$234$	4.08381	+	0.157474i	0.266967	+	0.0102944i
$235$	1.45353	−	4.95028i	0.0948181	−	0.322921i
$236$	14.0110	+	6.39861i	0.912038	+	0.416514i
$237$	−7.78603	+	5.59772i	−0.505757	+	0.363611i
$238$	1.92187	−	13.3669i	0.124577	−	0.866449i
$239$	−5.94724	−	20.2544i	−0.384695	−	1.31015i	−0.893420	−	0.449222i	$-0.851701\pi$
$239$	−5.94724	−	20.2544i	−0.384695	−	1.31015i	0.508726	−	0.860929i	$-0.330117\pi$
$240$	−17.0696	+	8.89808i	−1.10184	+	0.574368i
$241$	1.11011	+	1.72736i	0.0715083	+	0.111269i	0.875166	−	0.483823i	$-0.160752\pi$
$241$	1.11011	+	1.72736i	0.0715083	+	0.111269i	−0.803658	+	0.595092i	$0.797116\pi$
$242$	11.8930	+	18.5059i	0.764514	+	1.18961i
$243$	14.0138	+	6.82747i	0.898984	+	0.437982i
$244$	10.3214	+	35.1515i	0.660761	+	2.25034i
$245$	−0.183868	+	1.27883i	−0.0117469	+	0.0817013i
$246$	−25.8417	−	35.9439i	−1.64760	−	2.29170i
$247$	−0.708125	−	0.323390i	−0.0450569	−	0.0205768i
$248$	−7.95108	+	27.0789i	−0.504894	+	1.71951i
$249$	20.9110	−	4.12858i	1.32518	−	0.261638i
$250$	27.5518	−	3.96135i	1.74253	−	0.250538i
$251$	1.07214	+	0.689026i	0.0676732	+	0.0434909i	0.574040	−	0.818827i	$-0.305375\pi$
$251$	1.07214	+	0.689026i	0.0676732	+	0.0434909i	−0.506367	+	0.862318i	$0.669012\pi$
$252$	−6.33114	+	12.5587i	−0.398824	+	0.791125i
$253$	3.25741	+	20.9292i	0.204792	+	1.31581i
$254$			21.8502i			1.37100i
$255$	8.42043	−	8.10199i	0.527308	−	0.507366i
$256$	3.22469	+	22.4282i	0.201543	+	1.40176i
$257$	−17.9092	+	8.17884i	−1.11714	+	0.510182i	−0.886441	−	0.462842i	$-0.846830\pi$
$257$	−17.9092	+	8.17884i	−1.11714	+	0.510182i	−0.230702	+	0.973024i	$0.574102\pi$
$258$	0.636021	−	1.11323i	0.0395969	−	0.0693069i
$259$	−1.73222	+	3.79302i	−0.107635	+	0.235687i
$260$	−2.08938	+	2.41127i	−0.129578	+	0.149541i
$261$	18.7313	+	13.0844i	1.15944	+	0.809903i
$262$	−29.6069	+	8.69338i	−1.82912	+	0.537079i
$263$	12.7978	+	14.7694i	0.789146	+	0.910723i	0.997734	−	0.0672808i	$-0.0214323\pi$
$263$	12.7978	+	14.7694i	0.789146	+	0.910723i	−0.208588	+	0.978004i	$0.566887\pi$
$264$	50.1754	−	17.6207i	3.08808	−	1.08448i
$265$	−8.52678	+	5.47983i	−0.523796	+	0.336623i
$266$	2.88841	−	2.50282i	0.177100	−	0.153458i
$267$	1.42616	+	27.3334i	0.0872793	+	1.67278i
$268$	−25.8679	−	3.71924i	−1.58013	−	0.227189i
$269$	−14.2269	−	12.3277i	−0.867429	−	0.751632i	0.102574	−	0.994725i	$-0.467292\pi$
$269$	−14.2269	−	12.3277i	−0.867429	−	0.751632i	−0.970003	+	0.243094i	$0.921838\pi$
$270$	−15.6932	+	7.42617i	−0.955057	+	0.451942i
$271$	−10.6230	−	3.11921i	−0.645304	−	0.189478i	−0.0573264	−	0.998355i	$-0.518258\pi$
$271$	−10.6230	−	3.11921i	−0.645304	−	0.189478i	−0.587978	+	0.808877i	$0.700076\pi$
$272$	18.6600	+	40.8596i	1.13143	+	2.47748i
$273$	−0.0826128	+	0.908633i	−0.00499995	+	0.0549930i
$274$	6.39747	−	9.95466i	0.386485	−	0.601383i
$275$	−14.7107			−0.887088
$276$	38.8207	+	3.07593i	2.33673	+	0.185149i
$277$	−15.7272			−0.944957			−0.472479	−	0.881342i	$-0.656641\pi$
$277$	−15.7272			−0.944957			−0.472479	+	0.881342i	$0.656641\pi$
$278$	23.2551	−	36.1856i	1.39475	−	2.17027i
$279$	−3.87895	+	11.5448i	−0.232227	+	0.691169i
$280$	−3.73109	−	8.16994i	−0.222975	−	0.488247i
$281$	14.3714	+	4.21981i	0.857323	+	0.251733i	0.680715	−	0.732548i	$-0.261669\pi$
$281$	14.3714	+	4.21981i	0.857323	+	0.251733i	0.176608	+	0.984281i	$0.443487\pi$
$282$	14.1103	+	10.9934i	0.840256	+	0.654647i
$283$	11.0229	+	9.55138i	0.655242	+	0.567771i	0.917750	−	0.397159i	$-0.130004\pi$
$283$	11.0229	+	9.55138i	0.655242	+	0.567771i	−0.262507	+	0.964930i	$0.584549\pi$
$284$	33.0657	+	4.75412i	1.96209	+	0.282105i
$285$	3.30259	−	0.172317i	0.195628	−	0.0102072i
$286$	4.54706	−	3.94005i	0.268873	−	0.232980i
$287$	8.31411	−	5.34315i	0.490766	−	0.315396i
$288$	−2.60464	−	24.8920i	−0.153480	−	1.46678i
$289$	−6.72382	−	7.75971i	−0.395519	−	0.456453i
$290$	−24.4168	+	7.16941i	−1.43380	+	0.421002i
$291$	−1.65022	+	4.17677i	−0.0967373	+	0.244846i
$292$	−45.0811	+	52.0263i	−2.63817	+	3.04461i
$293$	−2.13862	+	4.68293i	−0.124940	+	0.273580i	−0.961758	−	0.273901i	$-0.911686\pi$
$293$	−2.13862	+	4.68293i	−0.124940	+	0.273580i	0.836818	+	0.547481i	$0.184413\pi$
$294$	−3.88931	−	2.22207i	−0.226829	−	0.129594i
$295$	−3.86124	+	1.76337i	−0.224810	+	0.102667i
$296$	−4.12542	−	28.6929i	−0.239785	−	1.66774i
$297$	21.9297	−	6.76413i	1.27249	−	0.392494i
$298$		−	12.6704i		−	0.733978i
$299$	2.41552	−	0.739804i	0.139693	−	0.0427840i
$300$	−6.25726	+	26.3124i	−0.361263	+	1.51915i
$301$	0.240791	+	0.154747i	0.0138790	+	0.00891948i
$302$	−47.1548	+	6.77984i	−2.71346	+	0.390136i
$303$	−3.04158	−	15.4054i	−0.174734	−	0.885018i
$304$	−3.58155	+	12.1976i	−0.205416	+	0.699583i
$305$	−9.18388	−	4.19414i	−0.525867	−	0.240155i
$306$	15.3973	+	37.4732i	0.880204	+	2.14220i
$307$	1.62125	−	11.2760i	0.0925294	−	0.643556i	−0.889794	−	0.456363i	$-0.849152\pi$
$307$	1.62125	−	11.2760i	0.0925294	−	0.643556i	0.982323	−	0.187193i	$-0.0599390\pi$
$308$	5.83338	+	19.8667i	0.332388	+	1.13201i
$309$	5.19856	+	9.97265i	0.295736	+	0.567324i
$310$	−7.33343	−	11.4110i	−0.416511	−	0.648104i
$311$	12.6635	+	19.7047i	0.718079	+	1.11735i	0.987998	+	0.154470i	$0.0493669\pi$
$311$	12.6635	+	19.7047i	0.718079	+	1.11735i	−0.269918	+	0.962883i	$0.586997\pi$
$312$	−2.93190	−	5.62439i	−0.165986	−	0.318418i
$313$	−8.28669	−	28.2219i	−0.468391	−	1.59519i	−0.767548	−	0.640991i	$-0.778524\pi$
$313$	−8.28669	−	28.2219i	−0.468391	−	1.59519i	0.299157	−	0.954204i	$-0.403295\pi$
$314$	0.223417	−	1.55390i	0.0126082	−	0.0876918i
$315$	−1.47308	−	3.58510i	−0.0829984	−	0.201997i
$316$	23.6099	+	10.7823i	1.32816	+	0.606551i
$317$	0.271611	−	0.925021i	0.0152552	−	0.0519543i	−0.951514	−	0.307606i	$-0.900472\pi$
$317$	0.271611	−	0.925021i	0.0152552	−	0.0519543i	0.966769	+	0.255652i	$0.0822902\pi$
$318$	−6.80670	−	34.4755i	−0.381701	−	1.93329i
$319$	33.2952	−	4.78713i	1.86418	−	0.268028i
$320$	4.75075	+	3.05312i	0.265575	+	0.170675i
$321$	8.16301	−	34.3262i	0.455615	−	1.91590i
$322$	−1.62255	+	12.2961i	−0.0904210	+	0.685234i
$323$		−	7.71706i		−	0.429389i
$324$	−2.77079	−	42.1019i	−0.153933	−	2.33899i
$325$	0.249697	+	1.73668i	0.0138507	+	0.0963336i
$326$	−12.4142	+	5.66935i	−0.687556	+	0.313996i
$327$	21.0876	+	12.0479i	1.16615	+	0.666252i
$328$	−28.5410	+	62.4960i	−1.57591	+	3.45076i
$329$	−2.61506	+	3.01794i	−0.144173	+	0.166384i
$330$	−9.39196	+	23.7715i	−0.517010	+	1.30858i
$331$	−22.7628	+	6.68377i	−1.25116	+	0.367373i	−0.839197	−	0.543828i	$-0.816974\pi$
$331$	−22.7628	+	6.68377i	−1.25116	+	0.367373i	−0.411962	+	0.911201i	$0.635156\pi$
$332$	−37.7802	−	43.6007i	−2.07346	−	2.39290i
$333$	−1.30186	−	12.4416i	−0.0713415	−	0.681796i
$334$	28.1662	−	18.1013i	1.54119	−	0.990461i
$335$	5.44302	−	4.71640i	0.297384	−	0.257685i
$336$	14.8791	−	0.776336i	0.811720	−	0.0423526i
$337$	11.4844	+	1.65121i	0.625596	+	0.0899472i	0.447820	−	0.894124i	$-0.352201\pi$
$337$	11.4844	+	1.65121i	0.625596	+	0.0899472i	0.177776	+	0.984071i	$0.443110\pi$
$338$	24.8658	+	21.5463i	1.35252	+	1.17197i
$339$	−22.4551	−	17.4949i	−1.21960	−	0.950192i
$340$	−30.3471	−	8.91072i	−1.64580	−	0.483252i
$341$	7.44834	+	16.3096i	0.403350	+	0.883213i
$342$	−3.65177	+	10.8686i	−0.197465	+	0.587709i
$343$	0.540641	−	0.841254i	0.0291919	−	0.0454234i
$344$	−1.98981			−0.107283
$345$	−7.64663	+	7.53023i	−0.411681	+	0.405414i
$346$	−33.4958			−1.80074
$347$	−6.99122	+	10.8786i	−0.375308	+	0.583991i	−0.976607	−	0.215033i	$-0.931014\pi$
$347$	−6.99122	+	10.8786i	−0.375308	+	0.583991i	0.601298	+	0.799025i	$0.294650\pi$
$348$	5.59975	−	61.5900i	0.300178	−	3.30157i
$349$	−15.3264	−	33.5601i	−0.820401	−	1.79643i	−0.553873	−	0.832601i	$-0.686851\pi$
$349$	−15.3264	−	33.5601i	−0.820401	−	1.79643i	−0.266528	−	0.963827i	$-0.585877\pi$
$350$	−8.26496	−	2.42681i	−0.441781	−	0.129718i
$351$	−1.17077	−	2.47411i	−0.0624913	−	0.132058i
$352$	−27.8463	−	24.1290i	−1.48421	−	1.28608i
$353$	−34.5509	−	4.96767i	−1.83896	−	0.264403i	−0.866789	−	0.498675i	$-0.833820\pi$
$353$	−34.5509	−	4.96767i	−1.83896	−	0.264403i	−0.972171	+	0.234272i	$0.924729\pi$
$354$	−0.766834	−	14.6970i	−0.0407568	−	0.781135i
$355$	−6.95755	+	6.02875i	−0.369268	+	0.319973i
$356$	62.3228	−	40.0525i	3.30310	−	2.12278i
$357$	−8.53356	+	2.99684i	−0.451644	+	0.158610i
$358$	−30.3122	−	34.9822i	−1.60205	−	1.84887i
$359$	19.6488	−	5.76940i	1.03702	−	0.304497i	0.281459	−	0.959573i	$-0.409182\pi$
$359$	19.6488	−	5.76940i	1.03702	−	0.304497i	0.755563	+	0.655076i	$0.227363\pi$
$360$	22.0892	+	15.4300i	1.16421	+	0.813235i
$361$	−11.0121	+	12.7087i	−0.579585	+	0.668877i
$362$	11.3470	−	24.8465i	0.596385	−	1.30590i
$363$	7.30867	−	12.7925i	0.383606	−	0.671430i
$364$	2.24636	−	1.02588i	0.117741	−	0.0537705i
$365$	−2.69994	−	18.7785i	−0.141321	−	0.982910i
$366$	25.2239	−	24.2700i	1.31847	−	1.26861i
$367$			30.5290i			1.59360i	0.604243	+	0.796800i	$0.293476\pi$
$367$			30.5290i			1.59360i	−0.604243	+	0.796800i	$0.706524\pi$
$368$	−17.5719	−	37.3249i	−0.915996	−	1.94570i
$369$	−13.3467	+	26.4751i	−0.694801	+	1.37824i
$370$	11.7207	+	7.53244i	0.609331	+	0.391593i
$371$	7.76532	−	1.11648i	0.403155	−	0.0579650i
$372$	32.3404	−	6.38516i	1.67677	−	0.331055i
$373$	−4.78660	+	16.3017i	−0.247841	+	0.844069i	0.737772	+	0.675050i	$0.235878\pi$
$373$	−4.78660	+	16.3017i	−0.247841	+	0.844069i	−0.985613	+	0.169019i	$0.945940\pi$
$374$	54.2533	+	24.7767i	2.80537	+	1.28117i
$375$	−10.8823	−	15.1365i	−0.561961	−	0.781647i
$376$	3.95076	−	27.4781i	0.203745	−	1.41708i
$377$	−1.13030	−	3.84943i	−0.0582132	−	0.198256i
$378$	13.4367	−	0.182584i	0.691110	−	0.00939111i
$379$	1.52711	+	2.37623i	0.0784424	+	0.122059i	0.878258	−	0.478187i	$-0.158706\pi$
$379$	1.52711	+	2.37623i	0.0784424	+	0.122059i	−0.799816	+	0.600246i	$0.795069\pi$
$380$	−4.83939	−	7.53023i	−0.248255	−	0.386293i
$381$	12.9767	−	6.76454i	0.664818	−	0.346558i
$382$	−16.2333	−	55.2855i	−0.830567	−	2.82865i
$383$	−0.327432	+	2.27734i	−0.0167310	+	0.116367i	−0.996475	−	0.0838854i	$-0.973267\pi$
$383$	−0.327432	+	2.27734i	−0.0167310	+	0.116367i	0.979744	+	0.200252i	$0.0641761\pi$
$384$	7.56787	−	5.44088i	0.386196	−	0.277654i
$385$	−5.19047	−	2.37041i	−0.264531	−	0.120807i
$386$	13.2959	−	45.2815i	0.676742	−	2.30477i
$387$	−0.858050	−	0.0330869i	−0.0436171	−	0.00168190i
$388$	12.0318	−	1.72991i	0.610823	−	0.0878231i
$389$	4.97637	+	3.19812i	0.252312	+	0.162151i	0.660683	−	0.750665i	$-0.270267\pi$
$389$	4.97637	+	3.19812i	0.252312	+	0.162151i	−0.408371	+	0.912816i	$0.633903\pi$
$390$	2.96577	+	0.705281i	0.150178	+	0.0357133i
$391$	16.6182	+	18.7347i	0.840417	+	0.947457i
$392$			6.95181i			0.351119i
$393$	14.3289	+	14.8921i	0.722798	+	0.751207i
$394$	3.99993	+	27.8201i	0.201514	+	1.40156i
$395$	−6.50657	+	2.97145i	−0.327381	+	0.149510i
$396$	−45.3420	−	42.4561i	−2.27852	−	2.13350i
$397$	1.60640	−	3.51753i	0.0806229	−	0.176540i	−0.865028	−	0.501724i	$-0.832699\pi$
$397$	1.60640	−	3.51753i	0.0806229	−	0.176540i	0.945651	+	0.325185i	$0.105426\pi$
$398$	0.208832	−	0.241004i	0.0104678	−	0.0120805i
$399$	−2.38063	−	0.940572i	−0.119181	−	0.0470875i
$400$	27.4913	−	8.07216i	1.37456	−	0.403608i
$401$	8.94651	+	10.3248i	0.446767	+	0.515597i	0.933804	−	0.357785i	$-0.116468\pi$
$401$	8.94651	+	10.3248i	0.446767	+	0.515597i	−0.487037	+	0.873381i	$0.661922\pi$
$402$	8.27368	+	23.5595i	0.412654	+	1.17504i
$403$	1.79901	−	1.15615i	0.0896151	−	0.0575921i
$404$	−32.1212	+	27.8332i	−1.59809	+	1.38475i
$405$	9.26879	+	7.02108i	0.460570	+	0.348880i
$406$	19.4961	+	2.80312i	0.967576	+	0.139116i
$407$	−13.9182	−	12.0602i	−0.689900	−	0.597802i
$408$	38.6428	−	49.5990i	1.91310	−	2.45552i
$409$	−22.6458	−	6.64940i	−1.11976	−	0.328792i	−0.331086	−	0.943601i	$-0.607415\pi$
$409$	−22.6458	−	6.64940i	−1.11976	−	0.328792i	−0.788676	+	0.614809i	$0.789233\pi$
$410$	−13.7176	−	30.0373i	−0.677464	−	1.48344i
$411$	−7.89261	−	0.717595i	−0.389314	−	0.0353964i
$412$	16.4571	−	25.6078i	0.810785	−	1.26161i
$413$	3.28553			0.161671
$414$	−14.5395	−	34.2497i	−0.714576	−	1.68328i
$415$	15.8991			0.780458
$416$	−2.37590	+	3.69697i	−0.116488	+	0.181259i
$417$	−28.6900	−	2.60849i	−1.40496	−	0.127738i
$418$	7.01210	+	15.3544i	0.342973	+	0.751006i
$419$	−4.00437	−	1.17579i	−0.195626	−	0.0574410i	0.182452	−	0.983215i	$-0.441597\pi$
$419$	−4.00437	−	1.17579i	−0.195626	−	0.0574410i	−0.378078	+	0.925774i	$0.623415\pi$
$420$	−6.44764	+	8.27570i	−0.314613	+	0.403813i
$421$	0.126089	+	0.109257i	0.00614522	+	0.00532486i	0.657928	−	0.753081i	$-0.271433\pi$
$421$	0.126089	+	0.109257i	0.00614522	+	0.00532486i	−0.651783	+	0.758406i	$0.725979\pi$
$422$	15.4900	+	2.22713i	0.754042	+	0.108415i
$423$	2.16056	−	11.7835i	0.105050	−	0.572932i
$424$	−41.2172	+	35.7149i	−2.00168	+	1.73447i
$425$	−14.6318	+	9.40328i	−0.709746	+	0.456126i
$426$	−10.5758	−	30.1149i	−0.512401	−	1.45907i
$427$	5.11745	+	5.90585i	0.247651	+	0.285804i
$428$	−91.6326	+	26.9058i	−4.42923	+	1.30054i
$429$	−3.74769	−	1.48069i	−0.180940	−	0.0714885i
$430$	0.626282	−	0.722768i	0.0302020	−	0.0348550i
$431$	−4.37974	+	9.59029i	−0.210965	+	0.461948i	−0.985301	−	0.170826i	$-0.945356\pi$
$431$	−4.37974	+	9.59029i	−0.210965	+	0.461948i	0.774337	+	0.632774i	$0.218084\pi$
$432$	−37.2705	+	24.6742i	−1.79318	+	1.18714i
$433$	−12.0252	+	5.49172i	−0.577893	+	0.263915i	−0.682846	−	0.730562i	$-0.739258\pi$
$433$	−12.0252	+	5.49172i	−0.577893	+	0.263915i	0.104953	+	0.994477i	$0.466531\pi$
$434$	1.49415	+	10.3920i	0.0717213	+	0.498833i
$435$	11.8170	+	12.2815i	0.566583	+	0.588852i
$436$		−	65.7361i		−	3.14819i
$437$	0.0822227	+	7.08702i	0.00393324	+	0.339018i
$438$	63.9903	+	15.2173i	3.05758	+	0.727113i
$439$	−15.2464	−	9.79826i	−0.727670	−	0.467645i	0.123627	−	0.992329i	$-0.460547\pi$
$439$	−15.2464	−	9.79826i	−0.727670	−	0.467645i	−0.851297	+	0.524684i	$0.824184\pi$
$440$	39.2641	−	5.64533i	1.87184	−	0.269130i
$441$	−0.115596	+	2.99777i	−0.00550456	+	0.142751i
$442$	2.00414	−	6.82546i	0.0953270	−	0.324654i
$443$	21.8712	+	9.98824i	1.03913	+	0.474556i	0.860548	−	0.509369i	$-0.170121\pi$
$443$	21.8712	+	9.98824i	1.03913	+	0.474556i	0.178584	+	0.983925i	$0.442848\pi$
$444$	−27.4917	+	19.7650i	−1.30470	+	0.938007i
$445$	−2.90555	+	20.2086i	−0.137736	+	0.957977i
$446$	3.77567	+	12.8587i	0.178783	+	0.608879i
$447$	−7.52492	+	3.92261i	−0.355916	+	0.185533i
$448$	−2.36313	−	3.67711i	−0.111648	−	0.173727i
$449$	9.51557	+	14.8065i	0.449067	+	0.698763i	0.989805	−	0.142429i	$-0.0454912\pi$
$449$	9.51557	+	14.8065i	0.449067	+	0.698763i	−0.540738	+	0.841191i	$0.681855\pi$
$450$	25.0570	−	6.31963i	1.18120	−	0.297910i
$451$	12.2973	+	41.8809i	0.579060	+	1.97210i
$452$	−10.9651	+	76.2637i	−0.515753	+	3.58714i
$453$	18.6251	+	25.9061i	0.875083	+	1.21718i
$454$	39.4313	+	18.0077i	1.85060	+	0.845141i
$455$	−0.191738	+	0.652999i	−0.00898881	+	0.0306131i
$456$	17.4576	−	3.44675i	0.817525	−	0.161409i
$457$	15.3585	−	2.20822i	0.718440	−	0.103296i	0.226608	−	0.973986i	$-0.427236\pi$
$457$	15.3585	−	2.20822i	0.718440	−	0.103296i	0.491832	+	0.870690i	$0.336327\pi$
$458$	41.3197	+	26.5546i	1.93074	+	1.24081i
$459$	17.4884	−	20.7456i	0.816287	−	0.968323i
$460$	27.9644	+	7.85989i	1.30385	+	0.366469i
$461$		−	32.7446i		−	1.52507i	−0.646948	−	0.762534i	$-0.723955\pi$
$461$		−	32.7446i		−	1.52507i	0.646948	−	0.762534i	$-0.276045\pi$
$462$	14.2558	−	13.7167i	0.663242	−	0.638160i
$463$	5.43744	+	37.8182i	0.252699	+	1.75756i	0.581860	+	0.813289i	$0.302325\pi$
$463$	5.43744	+	37.8182i	0.252699	+	1.75756i	−0.329160	+	0.944274i	$0.606766\pi$
$464$	−59.5951	+	27.2162i	−2.76664	+	1.26348i
$465$	−4.50664	+	7.88802i	−0.208990	+	0.365798i
$466$	9.18977	−	20.1228i	0.425708	−	0.932170i
$467$	15.0713	−	17.3932i	0.697418	−	0.804863i	−0.290983	−	0.956728i	$-0.593982\pi$
$467$	15.0713	−	17.3932i	0.697418	−	0.804863i	0.988401	+	0.151865i	$0.0485279\pi$
$468$	−4.24255	+	6.07352i	−0.196112	+	0.280748i
$469$	−5.34870	+	1.57052i	−0.246980	+	0.0725199i
$470$	8.73753	+	10.0836i	0.403032	+	0.465124i
$471$	−0.992025	+	0.348382i	−0.0457101	+	0.0160526i
$472$	−19.2146	+	12.3485i	−0.884422	+	0.568384i
$473$	−0.955383	+	0.827844i	−0.0439286	+	0.0380643i
$474$	−1.29219	−	24.7658i	−0.0593523	−	1.13753i
$475$	−4.87229	−	0.700529i	−0.223556	−	0.0321425i
$476$	18.5011	+	16.0313i	0.847998	+	0.734795i
$477$	−18.3676	+	14.7157i	−0.840996	+	0.673785i
$478$	52.3807	+	15.3804i	2.39584	+	0.703482i
$479$	0.152764	+	0.334507i	0.00697998	+	0.0152840i	0.913090	−	0.407758i	$-0.133689\pi$
$479$	0.152764	+	0.334507i	0.00697998	+	0.0152840i	−0.906110	+	0.423042i	$0.860962\pi$
$480$	1.69041	−	18.5923i	0.0771561	−	0.848617i
$481$	−1.18753	+	1.84783i	−0.0541467	+	0.0842538i
$482$	−5.31016			−0.241871
$483$	7.80492	−	2.84309i	0.355136	−	0.129365i
$484$	−39.8777			−1.81262
$485$	−1.81110	+	2.81812i	−0.0822376	+	0.127964i
$486$	−34.4475	+	20.9423i	−1.56257	+	0.949964i
$487$	−0.820268	−	1.79614i	−0.0371699	−	0.0813907i	0.890136	−	0.455694i	$-0.150609\pi$
$487$	−0.820268	−	1.79614i	−0.0371699	−	0.0813907i	−0.927306	+	0.374304i	$0.877882\pi$
$488$	−52.1248	−	15.3052i	−2.35958	−	0.692835i
$489$	7.21028	+	5.61756i	0.326060	+	0.254035i
$490$	−2.52514	−	2.18804i	−0.114074	−	0.0988457i
$491$	19.5975	+	2.81770i	0.884423	+	0.127161i	0.569534	−	0.821968i	$-0.307124\pi$
$491$	19.5975	+	2.81770i	0.884423	+	0.127161i	0.314889	+	0.949128i	$0.398033\pi$
$492$	80.1413	−	4.18148i	3.61305	−	0.188516i
$493$	30.0567	−	26.0442i	1.35368	−	1.17297i
$494$	1.69365	−	1.08844i	0.0762007	−	0.0489712i
$495$	17.0254	−	1.78150i	0.765236	−	0.0800724i
$496$	−22.8689	−	26.3922i	−1.02685	−	1.18504i
$497$	6.83699	−	2.00752i	0.306681	−	0.0900496i
$498$	−20.2550	+	51.2664i	−0.907650	+	2.29730i
$499$	12.7793	−	14.7481i	0.572079	−	0.660215i	−0.393803	−	0.919195i	$-0.628841\pi$
$499$	12.7793	−	14.7481i	0.572079	−	0.660215i	0.965883	+	0.258980i	$0.0833864\pi$
$500$	−20.9614	+	45.8992i	−0.937424	+	2.05267i
$501$	−19.4702	−	11.1239i	−0.869866	−	0.496978i
$502$	−2.99808	+	1.36918i	−0.133811	+	0.0611095i
$503$	5.50302	+	38.2743i	0.245368	+	1.70657i	0.624333	+	0.781158i	$0.285371\pi$
$503$	5.50302	+	38.2743i	0.245368	+	1.70657i	−0.378966	+	0.925411i	$0.623720\pi$
$504$	−10.5909	−	17.9661i	−0.471756	−	0.800275i
$505$		−	11.7131i		−	0.521226i
$506$	−50.0879	−	22.1758i	−2.22668	−	0.985833i
$507$	5.09815	−	21.4382i	0.226417	−	0.952104i
$508$	−33.3217	−	21.4146i	−1.47841	−	0.950117i
$509$	0.814459	−	0.117102i	0.0361003	−	0.00519043i	−0.124241	−	0.992252i	$-0.539650\pi$
$509$	0.814459	−	0.117102i	0.0361003	−	0.00519043i	0.160341	+	0.987062i	$0.448741\pi$
$510$	5.85346	+	29.6474i	0.259196	+	1.31281i
$511$	−4.13699	+	14.0893i	−0.183010	+	0.623274i
$512$	−43.5133	−	19.8719i	−1.92303	−	0.878220i
$513$	7.58539	−	1.19603i	0.334903	−	0.0528058i
$514$	7.24622	−	50.3985i	0.319617	−	2.22298i
$515$	2.36342	+	8.04906i	0.104145	+	0.354684i
$516$	1.07435	+	2.06098i	0.0472957	+	0.0907296i
$517$	−9.53514	−	14.8370i	−0.419355	−	0.652529i
$518$	−5.83016	−	9.07190i	−0.256162	−	0.398597i
$519$	10.3699	+	19.8930i	0.455187	+	0.873206i
$520$	−1.33292	−	4.53953i	−0.0584526	−	0.199071i
$521$	0.845516	−	5.88069i	0.0370427	−	0.257638i	−0.962882	−	0.269923i	$-0.913002\pi$
$521$	0.845516	−	5.88069i	0.0370427	−	0.257638i	0.999925	+	0.0122856i	$0.00391071\pi$
$522$	−54.6559	+	22.4575i	−2.39222	+	0.982936i
$523$	8.86234	+	4.04729i	0.387523	+	0.176976i	0.599643	−	0.800268i	$-0.295309\pi$
$523$	8.86234	+	4.04729i	0.387523	+	0.176976i	−0.212120	+	0.977244i	$0.568037\pi$
$524$	15.7592	−	53.6710i	0.688444	−	2.34463i
$525$	1.11746	+	5.65984i	0.0487697	+	0.247016i
$526$	−50.0259	+	7.19263i	−2.18123	+	0.313614i
$527$	17.8337	+	11.4610i	0.776848	+	0.499250i
$528$	−15.2241	+	64.0186i	−0.662543	+	2.78605i
$529$	−15.4610	−	17.0281i	−0.672218	−	0.740353i
$530$		−	26.2126i		−	1.13860i
$531$	−8.49108	+	5.00542i	−0.368481	+	0.217217i
$532$	0.985999	+	6.85777i	0.0427485	+	0.297322i
$533$	4.73554	−	2.16265i	0.205119	−	0.0936748i
$534$	−61.4604	−	35.1140i	−2.65965	−	1.51953i
$535$	10.9332	−	23.9404i	0.472685	−	1.03503i
$536$	25.3778	−	29.2875i	1.09615	−	1.26503i
$537$	−11.3915	+	28.8324i	−0.491580	+	1.24421i
$538$	46.7117	−	13.7158i	2.01388	−	0.591330i
$539$	2.89224	+	3.33783i	0.124578	+	0.143770i
$540$	4.05535	−	31.2104i	0.174515	−	1.34308i
$541$	−10.6837	+	6.86602i	−0.459329	+	0.295193i	−0.749768	−	0.661700i	$-0.769835\pi$
$541$	−10.6837	+	6.86602i	−0.459329	+	0.295193i	0.290439	+	0.956894i	$0.406199\pi$
$542$	21.6390	−	18.7503i	0.929474	−	0.805394i
$543$	−18.2691	+	0.953216i	−0.784003	+	0.0409064i
$544$	−43.1205	−	6.19979i	−1.84878	−	0.265814i
$545$	13.6912	+	11.8635i	0.586465	+	0.508174i
$546$	−1.86131	−	1.45016i	−0.0796568	−	0.0620610i
$547$	14.4348	+	4.23845i	0.617189	+	0.181223i	0.575358	−	0.817902i	$-0.304863\pi$
$547$	14.4348	+	4.23845i	0.617189	+	0.181223i	0.0418308	+	0.999125i	$0.486681\pi$
$548$	8.91102	+	19.5124i	0.380660	+	0.833529i
$549$	−22.2229	−	7.46669i	−0.948449	−	0.318670i
$550$	20.5681	−	32.0045i	0.877025	−	1.36468i
$551$	11.2556			0.479504
$552$	−34.9594	+	45.9613i	−1.48797	+	1.95624i
$553$	5.53645			0.235434
$554$	21.9894	−	34.2161i	0.934238	−	1.45370i
$555$	0.844904	−	9.29284i	0.0358642	−	0.394459i
$556$	32.3920	+	70.9285i	1.37373	+	3.00804i
$557$	37.2592	+	10.9403i	1.57872	+	0.463555i	0.949525	−	0.313691i	$-0.101566\pi$
$557$	37.2592	+	10.9403i	1.57872	+	0.463555i	0.629197	+	0.777246i	$0.283384\pi$
$558$	−19.6934	−	24.5807i	−0.833688	−	1.04058i
$559$	0.113948	+	0.0987366i	0.00481949	+	0.00417611i
$560$	11.0006	+	1.58165i	0.464862	+	0.0668370i
$561$	−2.08139	−	39.8914i	−0.0878763	−	1.68422i
$562$	−29.2742	+	25.3663i	−1.23486	+	1.07001i
$563$	−11.9746	+	7.69562i	−0.504670	+	0.324332i	−0.768082	−	0.640352i	$-0.778789\pi$
$563$	−11.9746	+	7.69562i	−0.504670	+	0.324332i	0.263412	+	0.964683i	$0.415152\pi$
$564$	−30.5940	+	10.7441i	−1.28824	+	0.452409i
$565$	−13.9049	−	16.0471i	−0.584984	−	0.675107i
$566$	−36.1918	+	10.6269i	−1.52126	+	0.446681i
$567$	−4.26828	−	7.92350i	−0.179251	−	0.332756i
$568$	−32.4392	+	37.4368i	−1.36112	+	1.57081i
$569$	−13.3800	+	29.2982i	−0.560920	+	1.22824i	0.390572	+	0.920572i	$0.372277\pi$
$569$	−13.3800	+	29.2982i	−0.560920	+	1.22824i	−0.951492	+	0.307672i	$0.900450\pi$
$570$	−4.24269	+	7.42603i	−0.177707	+	0.311042i
$571$	26.9477	−	12.3066i	1.12773	−	0.515015i	0.237889	−	0.971292i	$-0.423545\pi$
$571$	26.9477	−	12.3066i	1.12773	−	0.515015i	0.889838	+	0.456277i	$0.150817\pi$
$572$	1.55220	+	10.7958i	0.0649009	+	0.451396i
$573$	−27.8082	+	26.7566i	−1.16171	+	1.11777i
$574$			25.5588i			1.06680i
$575$	13.3370	−	8.79146i	0.556192	−	0.366629i
$576$	11.7092	+	5.90288i	0.487884	+	0.245953i
$577$	8.64071	+	5.55305i	0.359718	+	0.231177i	0.707999	−	0.706214i	$-0.249598\pi$
$577$	8.64071	+	5.55305i	0.359718	+	0.231177i	−0.348281	+	0.937390i	$0.613235\pi$
$578$	26.2830	−	3.77893i	1.09323	−	0.157183i
$579$	−31.0088	+	6.12224i	−1.28868	+	0.254432i
$580$	12.9966	−	44.2623i	0.539654	−	1.83789i
$581$	−11.1940	−	5.11211i	−0.464404	−	0.212086i
$582$	−6.77968	−	9.43004i	−0.281027	−	0.390888i
$583$	−4.93104	+	34.2961i	−0.204223	+	1.42040i
$584$	−28.7596	−	97.9461i	−1.19008	−	4.05304i
$585$	−0.499302	−	1.97971i	−0.0206436	−	0.0818508i
$586$	−7.19801	−	11.2003i	−0.297347	−	0.462681i
$587$	−1.69841	−	2.64277i	−0.0701008	−	0.109079i	0.804433	−	0.594043i	$-0.202469\pi$
$587$	−1.69841	−	2.64277i	−0.0701008	−	0.109079i	−0.874534	+	0.484964i	$0.838833\pi$
$588$	7.20045	−	3.75347i	0.296942	−	0.154790i
$589$	1.69027	+	5.75655i	0.0696465	+	0.237194i
$590$	1.56230	−	10.8660i	0.0643187	−	0.447346i
$591$	15.2840	−	10.9883i	0.628698	−	0.451999i
$592$	32.6281	+	14.9007i	1.34101	+	0.612416i
$593$	−0.932200	+	3.17478i	−0.0382809	+	0.130373i	−0.976417	−	0.215895i	$-0.930733\pi$
$593$	−0.932200	+	3.17478i	−0.0382809	+	0.130373i	0.938136	+	0.346268i	$0.112551\pi$
$594$	−15.9455	+	57.1676i	−0.654251	+	2.34562i
$595$	−6.67783	+	0.960127i	−0.273764	+	0.0393614i
$596$	19.3225	+	12.4178i	0.791481	+	0.508654i
$597$	−0.207783	−	0.0494123i	−0.00850401	−	0.00202231i
$598$	−1.76779	+	6.28956i	−0.0722903	+	0.257199i
$599$			28.6295i			1.16977i	0.811116	+	0.584885i	$0.198860\pi$
$599$			28.6295i			1.16977i	−0.811116	+	0.584885i	$0.801140\pi$
$600$	−27.8073	−	28.9002i	−1.13523	−	1.17985i
$601$	−3.38063	−	23.5128i	−0.137899	−	0.959106i	−0.934845	−	0.355056i	$-0.884462\pi$
$601$	−3.38063	−	23.5128i	−0.137899	−	0.959106i	0.796946	−	0.604050i	$-0.206447\pi$
$602$	−0.673335	+	0.307502i	−0.0274431	+	0.0125328i
$603$	11.4304	−	12.2074i	0.465484	−	0.497125i
$604$	35.8755	−	78.5563i	1.45975	−	3.19641i
$605$	7.19676	−	8.30551i	0.292590	−	0.337667i
$606$	37.7686	+	14.9222i	1.53425	+	0.606171i
$607$	−19.1375	+	5.61928i	−0.776768	+	0.228080i	−0.646004	−	0.763334i	$-0.723561\pi$
$607$	−19.1375	+	5.61928i	−0.776768	+	0.228080i	−0.130764	+	0.991414i	$0.541743\pi$
$608$	−8.07387	−	9.31774i	−0.327439	−	0.377884i
$609$	−4.37099	−	12.4465i	−0.177122	−	0.504357i
$610$	21.9654	−	14.1163i	0.889352	−	0.571552i
$611$	−1.58974	+	1.37752i	−0.0643140	+	0.0557284i
$612$	−72.2373	−	13.2451i	−2.92002	−	0.535401i
$613$	33.4279	+	4.80621i	1.35014	+	0.194121i	0.779152	−	0.626836i	$-0.215650\pi$
$613$	33.4279	+	4.80621i	1.35014	+	0.194121i	0.570990	+	0.820957i	$0.306559\pi$
$614$	22.2653	+	19.2930i	0.898553	+	0.778601i
$615$	−13.5923	+	17.4460i	−0.548093	+	0.703491i
$616$	−29.4595	−	8.65009i	−1.18696	−	0.348522i
$617$	−2.43478	−	5.33143i	−0.0980206	−	0.214635i	0.854269	−	0.519831i	$-0.174005\pi$
$617$	−2.43478	−	5.33143i	−0.0980206	−	0.214635i	−0.952290	+	0.305196i	$0.901278\pi$
$618$	−28.9649	−	2.63349i	−1.16514	−	0.105934i
$619$	−6.96296	+	10.8346i	−0.279865	+	0.435478i	−0.952519	−	0.304479i	$-0.901518\pi$
$619$	−6.96296	+	10.8346i	−0.279865	+	0.435478i	0.672654	+	0.739957i	$0.265154\pi$
$620$	24.5892			0.987526
$621$	−15.8395	+	19.2382i	−0.635618	+	0.772003i
$622$	−60.5753			−2.42885
$623$	8.54342	−	13.2938i	0.342285	−	0.532606i
$624$	7.81617	+	0.710645i	0.312897	+	0.0284486i
$625$	1.14161	+	2.49978i	0.0456644	+	0.0999911i
$626$	72.9857	+	21.4305i	2.91709	+	0.856536i
$627$	6.94804	−	8.91798i	0.277478	−	0.356150i
$628$	2.15075	+	1.86364i	0.0858244	+	0.0743673i
$629$	−21.5526	−	3.09880i	−0.859359	−	0.123557i
$630$	9.85934	+	1.80776i	0.392806	+	0.0720230i
$631$	35.5618	−	30.8145i	1.41569	−	1.22671i	0.478411	−	0.878136i	$-0.341213\pi$
$631$	35.5618	−	30.8145i	1.41569	−	1.22671i	0.937283	−	0.348569i	$-0.113332\pi$
$632$	−32.3784	+	20.8084i	−1.28795	+	0.827712i
$633$	−3.47283	−	9.88895i	−0.138033	−	0.393051i
$634$	1.63271	+	1.88425i	0.0648434	+	0.0748332i
$635$	10.4737	−	3.07536i	0.415636	−	0.122042i
$636$	59.2466	+	23.4080i	2.34928	+	0.928186i
$637$	0.344957	−	0.398101i	0.0136677	−	0.0157733i
$638$	−36.1376	+	79.1303i	−1.43070	+	3.13280i
$639$	−14.6110	+	15.6042i	−0.578002	+	0.617291i
$640$	6.32427	−	2.88820i	0.249989	−	0.114166i
$641$	−3.05946	−	21.2790i	−0.120841	−	0.840471i	−0.956606	−	0.291383i	$-0.905884\pi$
$641$	−3.05946	−	21.2790i	−0.120841	−	0.840471i	0.835765	−	0.549087i	$-0.185025\pi$
$642$	63.2667	+	65.7533i	2.49694	+	2.59508i
$643$			18.6711i			0.736318i	0.929763	+	0.368159i	$0.120012\pi$
$643$			18.6711i			0.736318i	−0.929763	+	0.368159i	$0.879988\pi$
$644$	−17.1615	−	14.5254i	−0.676256	−	0.572379i
$645$	−0.623138	−	0.148187i	−0.0245361	−	0.00583484i
$646$	16.7892	+	10.7898i	0.660563	+	0.424518i
$647$	14.9082	−	2.14347i	0.586101	−	0.0842685i	0.157116	−	0.987580i	$-0.449780\pi$
$647$	14.9082	−	2.14347i	0.586101	−	0.0842685i	0.428985	+	0.903312i	$0.358871\pi$
$648$	54.7418	+	30.2964i	2.15046	+	1.19016i
$649$	−4.08817	+	13.9230i	−0.160475	+	0.546526i
$650$	−4.12743	−	1.88494i	−0.161891	−	0.0739333i
$651$	5.70921	−	4.10461i	0.223762	−	0.160872i
$652$	3.52085	−	24.4880i	0.137887	−	0.959026i
$653$	−2.50841	−	8.54287i	−0.0981618	−	0.334308i	0.895740	−	0.444579i	$-0.146647\pi$
$653$	−2.50841	−	8.54287i	−0.0981618	−	0.334308i	−0.993902	+	0.110270i	$0.964828\pi$
$654$	−55.6956	+	29.0331i	−2.17787	+	1.13528i
$655$	8.33421	+	12.9683i	0.325644	+	0.506713i
$656$	−45.9624	−	71.5190i	−1.79453	−	2.79235i
$657$	−10.7731	−	42.7147i	−0.420299	−	1.66646i
$658$	−2.90952	−	9.90891i	−0.113425	−	0.386290i
$659$	−3.85790	+	26.8323i	−0.150282	+	1.04524i	0.765463	+	0.643479i	$0.222510\pi$
$659$	−3.85790	+	26.8323i	−0.150282	+	1.04524i	−0.915746	+	0.401758i	$0.868399\pi$
$660$	−27.0470	−	37.6204i	−1.05280	−	1.46437i
$661$	0.0415415	+	0.0189714i	0.00161578	+	0.000737900i	0.416223	−	0.909263i	$-0.363354\pi$
$661$	0.0415415	+	0.0189714i	0.00161578	+	0.000737900i	−0.414607	+	0.910001i	$0.636081\pi$
$662$	17.2852	−	58.8678i	0.671806	−	2.28796i
$663$	−4.67407	+	0.922829i	−0.181526	+	0.0358397i
$664$	84.6784	−	12.1749i	3.28616	−	0.472478i
$665$	−1.60624	−	1.03227i	−0.0622874	−	0.0400297i
$666$	28.8882	+	14.5632i	1.11939	+	0.564312i
$667$	−27.3252	+	24.2382i	−1.05804	+	0.938505i
$668$			60.6943i			2.34833i
$669$	6.46786	−	6.22327i	0.250062	−	0.240605i
$670$	2.65072	+	18.4362i	0.102406	+	0.712251i
$671$	−31.3947	+	14.3375i	−1.21198	+	0.553492i
$672$	−7.16819	+	12.5466i	−0.276519	+	0.483994i
$673$	1.39772	−	3.06058i	0.0538782	−	0.117977i	−0.880778	−	0.473529i	$-0.842980\pi$
$673$	1.39772	−	3.06058i	0.0538782	−	0.117977i	0.934656	+	0.355552i	$0.115707\pi$
$674$	−19.6496	+	22.6768i	−0.756873	+	0.873478i
$675$	−11.5105	−	12.9248i	−0.443041	−	0.497475i
$676$	−57.2285	+	16.8038i	−2.20110	+	0.646300i
$677$	−29.1808	−	33.6764i	−1.12151	−	1.29429i	−0.951089	−	0.308919i	$-0.900033\pi$
$677$	−29.1808	−	33.6764i	−1.12151	−	1.29429i	−0.170420	−	0.985371i	$-0.554512\pi$
$678$	69.4580	−	24.3925i	2.66752	−	0.936787i
$679$	2.18124	−	1.40180i	0.0837084	−	0.0537961i
$680$	35.4449	−	30.7132i	1.35925	−	1.17780i
$681$	−1.51275	−	28.9930i	−0.0579687	−	1.11102i
$682$	−45.8971	−	6.59901i	−1.75749	−	0.252689i
$683$	20.0131	+	17.3414i	0.765779	+	0.663552i	0.947485	−	0.319801i	$-0.103616\pi$
$683$	20.0131	+	17.3414i	0.765779	+	0.663552i	−0.181705	+	0.983353i	$0.558162\pi$
$684$	−12.9958	−	16.2210i	−0.496908	−	0.620224i
$685$	−5.67212	−	1.66548i	−0.216720	−	0.0636348i
$686$	1.07432	+	2.35243i	0.0410177	+	0.0898163i
$687$	2.97859	−	32.7606i	0.113640	−	1.24989i
$688$	1.33115	−	2.07132i	0.0507498	−	0.0789682i
$689$	4.13255			0.157438
$690$	−5.69145	−	27.1646i	−0.216670	−	1.03414i
$691$	27.4685			1.04495			0.522475	−	0.852655i	$-0.325009\pi$
$691$	27.4685			1.04495			0.522475	+	0.852655i	$0.325009\pi$
$692$	32.8280	−	51.0814i	1.24793	−	1.94182i
$693$	−12.5597	−	4.21997i	−0.477105	−	0.160303i
$694$	−13.8924	−	30.4202i	−0.527349	−	1.15473i
$695$	−20.6184	−	6.05411i	−0.782101	−	0.229645i
$696$	72.3418	+	56.3619i	2.74211	+	2.13639i
$697$	39.0023	+	33.7957i	1.47732	+	1.28010i
$698$	94.4420	+	13.5787i	3.57468	+	0.513962i
$699$	−14.7959	+	0.771996i	−0.559632	+	0.0291996i
$700$	11.8011	−	10.2257i	0.446040	−	0.386496i
$701$	−34.5236	+	22.1870i	−1.30394	+	0.837991i	−0.993635	−	0.112646i	$-0.964067\pi$
$701$	−34.5236	+	22.1870i	−1.30394	+	0.837991i	−0.310305	+	0.950637i	$0.600431\pi$
$702$	7.01961	+	0.912101i	0.264938	+	0.0344250i
$703$	−4.03550	−	4.65722i	−0.152202	−	0.175650i
$704$	18.5228	−	5.43879i	0.698105	−	0.204982i
$705$	3.28361	−	8.31096i	0.123668	−	0.313009i
$706$	59.1158	−	68.2232i	2.22485	−	2.56762i
$707$	−3.76616	+	8.24674i	−0.141641	+	0.310151i
$708$	23.1646	+	13.2345i	0.870578	+	0.497385i
$709$	−29.0037	+	13.2455i	−1.08926	+	0.497446i	−0.877353	−	0.479845i	$-0.840693\pi$
$709$	−29.0037	+	13.2455i	−1.08926	+	0.497446i	−0.211902	+	0.977291i	$0.567966\pi$
$710$	−3.38829	−	23.5660i	−0.127160	−	0.884418i
$711$	−14.3083	+	8.43463i	−0.536603	+	0.316323i
$712$			109.855i			4.11700i
$713$	−16.4998	−	10.3353i	−0.617923	−	0.387060i
$714$	5.41146	−	22.7557i	0.202519	−	0.851610i
$715$	−2.52862	−	1.62504i	−0.0945650	−	0.0607732i
$716$	83.0562	−	11.9417i	3.10395	−	0.446281i
$717$	−7.08208	−	35.8703i	−0.264485	−	1.33960i
$718$	−14.9205	+	50.8144i	−0.556826	+	1.89638i
$719$	−13.1484	−	6.00469i	−0.490354	−	0.223937i	0.154864	−	0.987936i	$-0.450506\pi$
$719$	−13.1484	−	6.00469i	−0.490354	−	0.223937i	−0.645218	+	0.763999i	$0.723233\pi$
$720$	−30.8395	+	12.6716i	−1.14932	+	0.472242i
$721$	0.924056	−	6.42695i	0.0344136	−	0.239352i
$722$	−12.2521	−	41.7268i	−0.455976	−	1.55291i
$723$	1.64396	+	3.15368i	0.0611395	+	0.117287i
$724$	26.7703	+	41.6554i	0.994911	+	1.54811i
$725$	−13.7150	−	21.3410i	−0.509362	−	0.792583i
$726$	17.6124	+	33.7868i	0.653659	+	1.25394i
$727$	−4.09259	−	13.9381i	−0.151786	−	0.516934i	0.848132	−	0.529785i	$-0.177728\pi$
$727$	−4.09259	−	13.9381i	−0.151786	−	0.516934i	−0.999917	+	0.0128509i	$0.995909\pi$
$728$	−0.521151	+	3.62468i	−0.0193151	+	0.134340i
$729$	23.1021	+	13.9747i	0.855633	+	0.517583i
$730$	44.6293	+	20.3815i	1.65181	+	0.754354i
$731$	−0.421089	+	1.43410i	−0.0155745	+	0.0530420i
$732$	12.2909	+	62.2528i	0.454286	+	2.30093i
$733$	−16.0370	+	2.30578i	−0.592341	+	0.0851658i	−0.431965	−	0.901890i	$-0.642180\pi$
$733$	−16.0370	+	2.30578i	−0.592341	+	0.0851658i	−0.160376	+	0.987056i	$0.551271\pi$
$734$	−66.4188	−	42.6848i	−2.45156	−	1.57552i
$735$	−0.517720	+	2.17706i	−0.0190964	+	0.0803021i
$736$	39.6661	+	5.23419i	1.46211	+	0.192935i
$737$		−	24.6202i		−	0.906898i
$738$	−38.9381	−	66.0537i	−1.43333	−	2.43147i
$739$	−5.43162	−	37.7777i	−0.199805	−	1.38968i	−0.804847	−	0.593482i	$-0.797753\pi$
$739$	−5.43162	−	37.7777i	−0.199805	−	1.38968i	0.605042	−	0.796194i	$-0.293156\pi$
$740$	−22.9741	+	10.4919i	−0.844545	+	0.385691i
$741$	−1.17075	−	0.668883i	−0.0430087	−	0.0245720i
$742$	−8.42823	+	18.4552i	−0.309410	+	0.677514i
$743$	29.3672	−	33.8915i	1.07738	−	1.24336i	0.108954	−	0.994047i	$-0.465250\pi$
$743$	29.3672	−	33.8915i	1.07738	−	1.24336i	0.968423	−	0.249313i	$-0.0802048\pi$
$744$	−17.9619	+	45.4624i	−0.658516	+	1.66673i
$745$	−6.07347	+	1.78333i	−0.222515	+	0.0653362i
$746$	−28.7734	−	33.2062i	−1.05347	−	1.21577i
$747$	36.7176	−	3.84204i	1.34343	−	0.140573i
$748$	−90.9564	+	58.4541i	−3.32569	+	2.13729i
$749$	−15.3953	+	13.3401i	−0.562533	+	0.487437i
$750$	48.1464	−	2.51210i	1.75806	−	0.0917290i
$751$	28.3314	+	4.07344i	1.03383	+	0.148642i	0.638281	−	0.769803i	$-0.279646\pi$
$751$	28.3314	+	4.07344i	1.03383	+	0.148642i	0.395547	+	0.918446i	$0.370555\pi$
$752$	25.9607	+	22.4951i	0.946688	+	0.820310i
$753$	1.74132	+	1.35667i	0.0634572	+	0.0494398i
$754$	9.95516	+	2.92310i	0.362546	+	0.106453i
$755$	9.88680	+	21.6491i	0.359817	+	0.787890i
$756$	−12.8904	+	20.6701i	−0.468820	+	0.751764i
$757$	−7.82748	+	12.1798i	−0.284495	+	0.442682i	−0.953860	−	0.300251i	$-0.902930\pi$
$757$	−7.82748	+	12.1798i	−0.284495	+	0.442682i	0.669366	+	0.742933i	$0.266566\pi$
$758$	−7.30488			−0.265325
$759$	2.33649	+	36.6124i	0.0848091	+	1.32894i
$760$	13.2734			0.481477
$761$	15.9225	−	24.7758i	0.577189	−	0.898123i	−0.422778	−	0.906233i	$-0.638945\pi$
$761$	15.9225	−	24.7758i	0.577189	−	0.898123i	0.999967	+	0.00810998i	$0.00258151\pi$
$762$	−3.42678	+	37.6901i	−0.124139	+	1.36537i
$763$	−5.82491	−	12.7548i	−0.210876	−	0.461754i
$764$	100.221	+	29.4274i	3.62585	+	1.06465i
$765$	15.7953	−	12.6548i	0.571082	−	0.457536i
$766$	−4.49677	−	3.89647i	−0.162475	−	0.140785i
$767$	1.71308	+	0.246304i	0.0618558	+	0.00889352i
$768$	2.04494	+	39.1929i	0.0737905	+	1.41425i
$769$	25.0033	−	21.6655i	0.901644	−	0.781279i	−0.0747668	−	0.997201i	$-0.523821\pi$
$769$	25.0033	−	21.6655i	0.901644	−	0.781279i	0.976411	+	0.215922i	$0.0692758\pi$
$770$	12.4142	−	7.97814i	0.447378	−	0.287512i
$771$	−32.1749	+	11.2993i	−1.15875	+	0.406933i
$772$	56.0240	+	64.6552i	2.01635	+	2.32699i
$773$	−16.0042	+	4.69925i	−0.575631	+	0.169020i	−0.556574	−	0.830798i	$-0.687884\pi$
$773$	−16.0042	+	4.69925i	−0.575631	+	0.169020i	−0.0190565	+	0.999818i	$0.506066\pi$
$774$	1.27168	−	1.82051i	0.0457098	−	0.0654369i
$775$	8.85498	−	10.2192i	0.318080	−	0.367084i
$776$	−7.48785	+	16.3961i	−0.268798	+	0.588586i
$777$	−3.58283	+	6.27106i	−0.128533	+	0.224973i
$778$	−13.9156	+	6.35506i	−0.498900	+	0.227840i
$779$	2.07858	+	14.4569i	0.0744730	+	0.517971i
$780$	−3.98221	+	3.83161i	−0.142586	+	0.137194i
$781$			31.4709i			1.12612i
$782$	−63.9943	+	9.96006i	−2.28843	+	0.356171i
$783$	30.2582	+	25.5074i	1.08134	+	0.911559i
$784$	−7.23656	−	4.65066i	−0.258449	−	0.166095i
$785$	−0.776297	+	0.111615i	−0.0277072	+	0.00398370i
$786$	−52.4335	+	10.3522i	−1.87024	+	0.369252i
$787$	1.67261	−	5.69638i	0.0596221	−	0.203054i	−0.924295	−	0.381678i	$-0.875346\pi$
$787$	1.67261	−	5.69638i	0.0596221	−	0.203054i	0.983917	+	0.178624i	$0.0571645\pi$
$788$	−46.3462	−	21.1656i	−1.65101	−	0.753993i
$789$	19.7591	+	27.4834i	0.703441	+	0.978436i
$790$	2.63262	−	18.3103i	0.0936644	−	0.651451i
$791$	4.63021	+	15.7690i	0.164631	+	0.560683i
$792$	89.3128	−	22.5256i	3.17359	−	0.800412i
$793$	2.22551	+	3.46296i	0.0790301	+	0.122973i
$794$	5.40670	+	8.41298i	0.191876	+	0.298566i
$795$	−15.5676	+	8.11509i	−0.552124	+	0.287813i
$796$	0.162866	+	0.554670i	0.00577263	+	0.0196598i
$797$	2.79568	−	19.4444i	0.0990281	−	0.688756i	−0.878468	−	0.477802i	$-0.841434\pi$
$797$	2.79568	−	19.4444i	0.0990281	−	0.688756i	0.977496	−	0.210954i	$-0.0676571\pi$
$798$	5.37483	−	3.86421i	0.190267	−	0.136792i
$799$	−18.9680	−	8.66239i	−0.671039	−	0.306453i
$800$	−7.82867	+	26.6620i	−0.276785	+	0.942645i
$801$	−1.82669	+	47.3720i	−0.0645430	+	1.67381i
$802$	−34.9714	+	5.02813i	−1.23488	+	0.177549i
$803$	−54.5582	−	35.0625i	−1.92532	−	1.23733i
$804$	−44.0371	−	10.4723i	−1.55307	−	0.369331i
$805$	6.12240	−	0.952890i	0.215786	−	0.0335849i
$806$			5.53042i			0.194801i
$807$	−22.6071	−	23.4957i	−0.795809	−	0.827087i
$808$	−8.96943	−	62.3837i	−0.315543	−	2.19465i
$809$	18.7634	−	8.56896i	0.659686	−	0.301269i	−0.0572989	−	0.998357i	$-0.518249\pi$
$809$	18.7634	−	8.56896i	0.659686	−	0.301269i	0.716985	+	0.697088i	$0.245522\pi$
$810$	−28.2344	+	10.3485i	−0.992055	+	0.363609i
$811$	11.3427	−	24.8370i	0.398295	−	0.872144i	−0.599146	−	0.800640i	$-0.704493\pi$
$811$	11.3427	−	24.8370i	0.398295	−	0.872144i	0.997440	−	0.0715037i	$-0.0227798\pi$
$812$	−23.3822	+	26.9845i	−0.820555	+	0.946971i
$813$	−17.8349	−	7.04646i	−0.625497	−	0.247130i
$814$	45.6982	−	13.4182i	1.60172	−	0.470308i
$815$	4.46482	+	5.15268i	0.156396	+	0.180491i
$816$	25.7792	+	73.4067i	0.902452	+	2.56975i
$817$	−0.355852	+	0.228692i	−0.0124497	+	0.00800093i
$818$	46.1291	−	39.9711i	1.61287	−	1.39756i
$819$	−0.285003	+	1.55438i	−0.00995883	+	0.0543143i
$820$	59.2514	+	8.51906i	2.06915	+	0.297498i
$821$	−7.56413	−	6.55435i	−0.263990	−	0.228749i	0.512800	−	0.858508i	$-0.328608\pi$
$821$	−7.56413	−	6.55435i	−0.263990	−	0.228749i	−0.776790	+	0.629759i	$0.783154\pi$
$822$	12.5964	−	16.1678i	0.439351	−	0.563918i
$823$	3.30079	+	0.969199i	0.115058	+	0.0337842i	0.338755	−	0.940875i	$-0.389994\pi$
$823$	3.30079	+	0.969199i	0.115058	+	0.0337842i	−0.223697	+	0.974659i	$0.571812\pi$
$824$	18.7512	+	41.0593i	0.653228	+	1.43037i
$825$	−25.3750	−	2.30709i	−0.883444	−	0.0803226i
$826$	−4.59374	+	7.14800i	−0.159837	+	0.248711i
$827$	29.0973			1.01181			0.505906	−	0.862589i	$-0.331158\pi$
$827$	29.0973			1.01181			0.505906	+	0.862589i	$0.331158\pi$
$828$	66.4807	+	11.3941i	2.31037	+	0.395971i
$829$	31.6713			1.09999			0.549994	−	0.835169i	$-0.314630\pi$
$829$	31.6713			1.09999			0.549994	+	0.835169i	$0.314630\pi$
$830$	−22.2297	+	34.5901i	−0.771605	+	1.20064i
$831$	−27.1285	−	2.46652i	−0.941076	−	0.0855625i
$832$	−0.956483	−	2.09440i	−0.0331601	−	0.0726104i
$833$	5.01031	+	1.47116i	0.173597	+	0.0509727i
$834$	45.7886	−	58.7708i	1.58553	−	2.03507i
$835$	−12.6411	−	10.9535i	−0.437462	−	0.379063i
$836$	−30.2879	−	4.35474i	−1.04753	−	0.150612i
$837$	−8.50153	+	19.3057i	−0.293856	+	0.667303i
$838$	8.15683	−	7.06794i	0.281773	−	0.244158i
$839$	13.7363	−	8.82780i	0.474230	−	0.304769i	−0.281606	−	0.959530i	$-0.590867\pi$
$839$	13.7363	−	8.82780i	0.474230	−	0.304769i	0.755836	+	0.654761i	$0.227231\pi$
$840$	−5.15459	−	14.6778i	−0.177850	−	0.506431i
$841$	18.9954	+	21.9219i	0.655015	+	0.755928i
$842$	−0.413994	+	0.121560i	−0.0142672	+	0.00418922i
$843$	24.1279	+	9.53277i	0.831008	+	0.328326i
$844$	−18.5776	+	21.4397i	−0.639467	+	0.737985i
$845$	6.82827	−	14.9518i	0.234900	−	0.514359i
$846$	22.6153	+	21.1758i	0.777529	+	0.728040i
$847$	−7.73746	+	3.53358i	−0.265862	+	0.121415i
$848$	−9.60414	−	66.7982i	−0.329807	−	2.29386i
$849$	17.5158	+	18.2042i	0.601141	+	0.624768i
$850$		−	44.9803i		−	1.54281i
$851$	19.8260	+	2.61617i	0.679627	+	0.0896811i
$852$	56.2905	+	13.3863i	1.92848	+	0.458606i
$853$	17.3583	+	11.1555i	0.594337	+	0.381957i	0.802955	−	0.596040i	$-0.203260\pi$
$853$	17.3583	+	11.1555i	0.594337	+	0.381957i	−0.208618	+	0.977997i	$0.566896\pi$
$854$	−20.0038	+	2.87612i	−0.684517	+	0.0984187i
$855$	5.72378	+	0.220712i	0.195749	+	0.00754820i
$856$	39.8975	−	135.878i	1.36367	−	4.64423i
$857$	−50.7992	−	23.1992i	−1.73527	−	0.792470i	−0.992403	−	0.123027i	$-0.960740\pi$
$857$	−50.7992	−	23.1992i	−1.73527	−	0.792470i	−0.742864	−	0.669443i	$-0.766533\pi$
$858$	8.46131	−	6.08321i	0.288864	−	0.207677i
$859$	3.08477	−	21.4550i	0.105251	−	0.732036i	−0.867036	−	0.498245i	$-0.833978\pi$
$859$	3.08477	−	21.4550i	0.105251	−	0.732036i	0.972287	−	0.233791i	$-0.0751130\pi$
$860$	0.488432	+	1.66345i	0.0166554	+	0.0567230i
$861$	15.1793	−	7.91269i	0.517308	−	0.269664i
$862$	−14.7410	−	22.9374i	−0.502080	−	0.781252i
$863$	−9.09974	−	14.1595i	−0.309759	−	0.481994i	0.651116	−	0.758978i	$-0.274301\pi$
$863$	−9.09974	−	14.1595i	−0.309759	−	0.481994i	−0.960874	+	0.276985i	$0.910665\pi$
$864$	−0.589000	−	43.3457i	−0.0200382	−	1.47465i
$865$	4.71445	+	16.0559i	0.160296	+	0.545918i
$866$	4.86550	−	33.8403i	0.165337	−	1.14994i
$867$	−10.3812	−	14.4395i	−0.352564	−	0.490391i
$868$	−17.3123	−	7.90626i	−0.587617	−	0.268356i
$869$	−6.88896	+	23.4617i	−0.233692	+	0.795882i
$870$	−43.2418	+	8.53747i	−1.46603	+	0.289447i
$871$	−2.90656	+	0.417900i	−0.0984849	+	0.0141600i
$872$	82.0033	+	52.7003i	2.77698	+	1.78466i
$873$	−3.50156	+	6.94585i	−0.118510	+	0.235081i
$874$	−15.5335	−	9.72998i	−0.525427	−	0.329121i
$875$			10.7632i			0.363863i
$876$	−85.9213	+	82.6719i	−2.90301	+	2.79323i
$877$	−3.30875	−	23.0129i	−0.111729	−	0.777090i	−0.966238	−	0.257653i	$-0.917051\pi$
$877$	−3.30875	−	23.0129i	−0.111729	−	0.777090i	0.854509	−	0.519437i	$-0.173858\pi$
$878$	42.6341	−	19.4703i	1.43883	−	0.657092i
$879$	−4.42342	+	7.74235i	−0.149198	+	0.261143i
$880$	−20.3905	+	44.6491i	−0.687365	+	1.50512i
$881$	20.3238	−	23.4549i	0.684725	−	0.790215i	−0.301879	−	0.953346i	$-0.597614\pi$
$881$	20.3238	−	23.4549i	0.684725	−	0.790215i	0.986604	+	0.163131i	$0.0521594\pi$
$882$	−6.36032	−	4.44289i	−0.214163	−	0.149600i
$883$	−54.5336	+	16.0125i	−1.83520	+	0.538864i	−0.999940	−	0.0109874i	$-0.996503\pi$
$883$	−54.5336	+	16.0125i	−1.83520	+	0.538864i	−0.835263	+	0.549851i	$0.814684\pi$
$884$	8.44471	+	9.74572i	0.284026	+	0.327784i
$885$	−6.93695	+	2.43614i	−0.233183	+	0.0818899i
$886$	−52.3101	+	33.6177i	−1.75739	+	1.12941i
$887$	−16.4711	+	14.2723i	−0.553046	+	0.479217i	−0.885974	−	0.463735i	$-0.846509\pi$
$887$	−16.4711	+	14.2723i	−0.553046	+	0.479217i	0.332928	+	0.942952i	$0.391963\pi$
$888$	−2.61615	−	50.1404i	−0.0877921	−	1.68260i
$889$	−8.36296	−	1.20241i	−0.280485	−	0.0403276i
$890$	−39.9032	−	34.5763i	−1.33756	−	1.15900i
$891$	38.8882	−	8.22842i	1.30280	−	0.275663i
$892$	−23.3101	−	6.84447i	−0.780481	−	0.229170i
$893$	−2.45157	−	5.36818i	−0.0820385	−	0.179639i
$894$	1.98711	−	21.8557i	0.0664590	−	0.730963i
$895$	−12.5021	+	19.4536i	−0.417898	+	0.650262i
$896$	−5.38132			−0.179777
$897$	4.28263	−	0.897287i	0.142993	−	0.0299595i
$898$	−45.5174			−1.51894
$899$	−16.7163	+	26.0111i	−0.557519	+	0.867517i
$900$	−14.9200	+	44.4058i	−0.497332	+	1.48019i
$901$	17.0180	+	37.2642i	0.566951	+	1.24145i
$902$	−108.310	−	31.8026i	−3.60632	−	1.05891i
$903$	0.391081	+	0.304693i	0.0130143	+	0.0101395i
$904$	−86.3454	−	74.8187i	−2.87181	−	2.48843i
$905$	−13.5070	−	1.94202i	−0.448989	−	0.0645548i
$906$	−82.4024	+	4.29946i	−2.73764	+	0.142840i
$907$	3.57669	−	3.09922i	0.118762	−	0.102908i	−0.593455	−	0.804867i	$-0.702237\pi$
$907$	3.57669	−	3.09922i	0.118762	−	0.102908i	0.712217	+	0.701959i	$0.247691\pi$
$908$	−66.1070	+	42.4844i	−2.19384	+	1.40989i
$909$	−2.83049	−	27.0504i	−0.0938813	−	0.897204i
$910$	−1.15258	−	1.33015i	−0.0382077	−	0.0440940i
$911$	25.5398	−	7.49917i	0.846172	−	0.248459i	0.170222	−	0.985406i	$-0.445552\pi$
$911$	25.5398	−	7.49917i	0.846172	−	0.248459i	0.675950	+	0.736947i	$0.263733\pi$
$912$	−8.09092	+	20.4785i	−0.267917	+	0.678110i
$913$	35.5920	−	41.0754i	1.17792	−	1.35940i
$914$	−16.6696	+	36.5014i	−0.551382	+	1.20736i
$915$	−15.1838	−	8.67493i	−0.501962	−	0.286784i
$916$	−80.9920	+	36.9878i	−2.67605	+	1.22211i
$917$	−1.69805	−	11.8102i	−0.0560745	−	0.390007i
$918$	20.6824	+	67.0536i	0.682620	+	2.21310i
$919$		−	46.7654i		−	1.54265i	−0.636444	−	0.771323i	$-0.719595\pi$
$919$		−	46.7654i		−	1.54265i	0.636444	−	0.771323i	$-0.280405\pi$
$920$	−32.2239	+	28.5834i	−1.06239	+	0.942365i
$921$	4.56497	−	19.1961i	0.150421	−	0.632534i
$922$	71.2390	+	45.7826i	2.34613	+	1.50777i
$923$	3.71531	−	0.534181i	0.122291	−	0.0175828i
$924$	6.94650	+	35.1836i	0.228523	+	1.15745i
$925$	−3.91295	+	13.3263i	−0.128657	+	0.438166i
$926$	−89.8797	−	41.0467i	−2.95363	−	1.34888i
$927$	7.40317	+	18.0175i	0.243152	+	0.591771i
$928$	9.04261	−	62.8927i	0.296838	−	2.06455i
$929$	11.8691	+	40.4225i	0.389413	+	1.32622i	0.888185	+	0.459485i	$0.151966\pi$
$929$	11.8691	+	40.4225i	0.389413	+	1.32622i	−0.498773	+	0.866733i	$0.666216\pi$
$930$	−10.8601	−	20.8334i	−0.356117	−	0.683155i
$931$	0.798983	+	1.24324i	0.0261856	+	0.0407456i
$932$	21.6809	+	33.7361i	0.710181	+	1.10506i
$933$	18.7534	+	35.9754i	0.613957	+	1.17778i
$934$	16.7684	+	57.1079i	0.548678	+	1.86863i
$935$	4.24047	−	29.4931i	0.138678	−	0.964529i
$936$	−4.17525	−	10.1615i	−0.136472	−	0.332140i
$937$	−32.2134	−	14.7114i	−1.05237	−	0.480599i	−0.187324	−	0.982298i	$-0.559981\pi$
$937$	−32.2134	−	14.7114i	−1.05237	−	0.480599i	−0.865042	+	0.501699i	$0.832709\pi$
$938$	4.06158	−	13.8325i	0.132615	−	0.451646i
$939$	−9.86795	−	49.9805i	−0.322028	−	1.63105i
$940$	−23.9410	+	3.44220i	−0.780869	+	0.112272i
$941$	0.688032	+	0.442172i	0.0224292	+	0.0144144i	0.551807	−	0.833972i	$-0.313938\pi$
$941$	0.688032	+	0.442172i	0.0224292	+	0.0144144i	−0.529378	+	0.848386i	$0.677575\pi$
$942$	0.629081	−	2.64534i	0.0204966	−	0.0861900i
$943$	−36.1781	−	30.6209i	−1.17812	−	0.997154i
$944$		−	28.2626i		−	0.919868i
$945$	−1.97871	−	6.41509i	−0.0643673	−	0.208683i
$946$	−0.465266	−	3.23600i	−0.0151271	−	0.105211i
$947$	8.36473	−	3.82004i	0.271817	−	0.124135i	−0.274844	−	0.961489i	$-0.588626\pi$
$947$	8.36473	−	3.82004i	0.271817	−	0.124135i	0.546661	+	0.837354i	$0.315899\pi$
$948$	39.0346	+	22.3015i	1.26778	+	0.724319i
$949$	−3.21326	+	7.03605i	−0.104307	+	0.228400i
$950$	8.33636	−	9.62067i	0.270467	−	0.312136i
$951$	0.613583	−	1.55300i	0.0198968	−	0.0503596i
$952$	−34.8307	+	10.2272i	−1.12887	+	0.331466i
$953$	12.7763	+	14.7446i	0.413864	+	0.477624i	0.923958	−	0.382494i	$-0.124935\pi$
$953$	12.7763	+	14.7446i	0.413864	+	0.477624i	−0.510094	+	0.860119i	$0.670389\pi$
$954$	−6.33430	−	60.5356i	−0.205080	−	1.95991i
$955$	−24.2159	+	15.5626i	−0.783607	+	0.503594i
$956$	−74.7917	+	64.8074i	−2.41894	+	2.09602i
$957$	58.1829	−	3.03577i	1.88079	−	0.0981326i
$958$	−0.941343	−	0.135345i	−0.0304134	−	0.00437279i
$959$	3.45801	+	2.99638i	0.111665	+	0.0967581i
$960$	7.71591	+	6.01150i	0.249030	+	0.194020i
$961$	13.9309	+	4.09048i	0.449384	+	0.131951i
$962$	−2.35977	−	5.16717i	−0.0760819	−	0.166596i
$963$	19.4641	−	57.9303i	0.627221	−	1.86678i
$964$	5.20430	−	8.09805i	0.167619	−	0.260820i
$965$	−23.5767			−0.758961
$966$	−4.72720	+	20.9555i	−0.152095	+	0.674232i
$967$	18.6843			0.600847			0.300424	−	0.953806i	$-0.402872\pi$
$967$	18.6843			0.600847			0.300424	+	0.953806i	$0.402872\pi$
$968$	31.9698	−	49.7459i	1.02755	−	1.59889i
$969$	1.21027	−	13.3114i	0.0388796	−	0.427625i
$970$	−3.59887	−	7.88043i	−0.115553	−	0.253025i
$971$	−46.3623	−	13.6132i	−1.48784	−	0.436868i	−0.565987	−	0.824414i	$-0.691505\pi$
$971$	−46.3623	−	13.6132i	−1.48784	−	0.436868i	−0.921850	+	0.387546i	$0.873323\pi$
$972$	1.82345	−	73.0576i	0.0584871	−	2.34332i
$973$	12.5700	+	10.8920i	0.402976	+	0.349181i
$974$	5.05455	+	0.726734i	0.161958	+	0.0232861i
$975$	0.158346	+	3.03482i	0.00507113	+	0.0971920i
$976$	50.8029	−	44.0209i	1.62616	−	1.40908i
$977$	7.15855	−	4.60052i	0.229022	−	0.147184i	−0.421098	−	0.907015i	$-0.638355\pi$
$977$	7.15855	−	4.60052i	0.229022	−	0.147184i	0.650120	+	0.759832i	$0.274719\pi$
$978$	−22.3028	+	7.83235i	−0.713163	+	0.250451i
$979$	45.7044	+	52.7456i	1.46072	+	1.68576i
$980$	5.81158	−	1.70644i	0.185644	−	0.0545101i
$981$	34.4853	+	24.0891i	1.10103	+	0.769106i
$982$	−33.5309	+	38.6967i	−1.07001	+	1.23486i
$983$	8.19442	−	17.9433i	0.261361	−	0.572301i	−0.732771	−	0.680476i	$-0.761773\pi$
$983$	8.19442	−	17.9433i	0.261361	−	0.572301i	0.994132	+	0.108174i	$0.0345004\pi$
$984$	−59.0327	+	103.326i	−1.88189	+	3.29390i
$985$	12.7724	−	5.83295i	0.406962	−	0.185853i
$986$	14.6374	+	101.805i	0.466150	+	3.24215i
$987$	−4.98412	+	4.79563i	−0.158646	+	0.152647i
$988$			3.64957i			0.116108i
$989$	0.371430	−	1.32150i	0.0118108	−	0.0420213i
$990$	−19.9286	+	39.5313i	−0.633373	+	1.25639i
$991$	−27.8581	−	17.9033i	−0.884942	−	0.568718i	0.0173469	−	0.999850i	$-0.494478\pi$
$991$	−27.8581	−	17.9033i	−0.884942	−	0.568718i	−0.902289	+	0.431132i	$0.858114\pi$
$992$	33.5237	−	4.81998i	1.06438	−	0.153035i
$993$	−40.3127	+	7.95916i	−1.27928	+	0.252576i
$994$	−5.19172	+	17.6814i	−0.164671	+	0.560819i
$995$	−0.144916	−	0.0661810i	−0.00459415	−	0.00209808i
$996$	−58.3305	−	81.1335i	−1.84827	−	2.57081i
$997$	−5.01669	+	34.8918i	−0.158880	+	1.10504i	0.741821	+	0.670598i	$0.233962\pi$
$997$	−5.01669	+	34.8918i	−0.158880	+	1.10504i	−0.900702	+	0.434438i	$0.856947\pi$
$998$	14.2182	+	48.4229i	0.450071	+	1.53280i
$999$	−0.294396	−	21.6652i	−0.00931427	−	0.685455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.u.a.113.3	✓	480
3.2	odd	2	inner	483.2.u.a.113.46	yes	480
23.11	odd	22	inner	483.2.u.a.218.46	yes	480
69.11	even	22	inner	483.2.u.a.218.3	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.u.a.113.3	✓	480	1.1	even	1	trivial
483.2.u.a.113.46	yes	480	3.2	odd	2	inner
483.2.u.a.218.3	yes	480	69.11	even	22	inner
483.2.u.a.218.46	yes	480	23.11	odd	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.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39817 + 2.17560i) q^{2} +(1.72494 + 0.156831i) q^{3} +(-1.94751 - 4.26445i) q^{4} +(1.23964 + 0.363993i) q^{5} +(-2.75296 + 3.53349i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(6.88105 + 0.989346i) q^{8} +(2.95081 + 0.541047i) q^{9} +(-2.52514 + 2.18804i) q^{10} +(3.71546 - 2.38778i) q^{11} +(-2.69053 - 7.66133i) q^{12} +(-0.344957 - 0.398101i) q^{13} +(2.48138 - 0.728599i) q^{14} +(2.08122 + 0.822278i) q^{15} +(-5.63319 + 6.50105i) q^{16} +(2.16923 - 4.74995i) q^{17} +(-5.30283 + 5.66329i) q^{18} +(1.34429 - 0.613919i) q^{19} +(-0.861991 - 5.99528i) q^{20} +(-1.20092 - 1.24812i) q^{21} +11.4219i q^{22} +(-1.94152 + 4.38526i) q^{23} +(11.7142 + 2.78572i) q^{24} +(-2.80204 - 1.80076i) q^{25} +(1.34842 - 0.193873i) q^{26} +(5.00510 + 1.39605i) q^{27} +(-1.32079 + 4.49820i) q^{28} +(6.92796 + 3.16389i) q^{29} +(-4.69885 + 3.37821i) q^{30} +(-0.577752 + 4.01835i) q^{31} +(-2.35040 - 8.00471i) q^{32} +(6.78341 - 3.53607i) q^{33} +(7.30102 + 11.3606i) q^{34} +(-0.698497 - 1.08688i) q^{35} +(-3.43946 - 13.6373i) q^{36} +(-1.17478 - 4.00094i) q^{37} +(-0.543914 + 3.78301i) q^{38} +(-0.532593 - 0.740799i) q^{39} +(8.16994 + 3.73109i) q^{40} +(-2.78436 + 9.48267i) q^{41} +(4.39449 - 0.867629i) q^{42} +(-0.283316 + 0.0407347i) q^{43} +(-17.4185 - 11.1942i) q^{44} +(3.46102 + 1.74478i) q^{45} +(-6.82599 - 10.3553i) q^{46} -3.99331i q^{47} +(-10.7365 + 10.3304i) q^{48} +(0.142315 + 0.989821i) q^{49} +(7.83546 - 3.57834i) q^{50} +(4.48672 - 7.85315i) q^{51} +(-1.02588 + 2.24636i) q^{52} +(-5.13750 + 5.92899i) q^{53} +(-10.0352 + 8.93717i) q^{54} +(5.47499 - 1.60760i) q^{55} +(-4.55247 - 5.25383i) q^{56} +(2.41510 - 0.848144i) q^{57} +(-16.5698 + 10.6488i) q^{58} +(-2.48304 + 2.15157i) q^{59} +(-0.546634 - 10.4767i) q^{60} +(-7.73502 - 1.11213i) q^{61} +(-7.93452 - 6.87530i) q^{62} +(-1.87576 - 2.34126i) q^{63} +(4.19393 + 1.23145i) q^{64} +(-0.282718 - 0.619065i) q^{65} +(-1.79130 + 19.7020i) q^{66} +(3.01381 - 4.68957i) q^{67} -24.4805 q^{68} +(-4.03674 + 7.25980i) q^{69} +3.34123 q^{70} +(-3.85240 + 5.99446i) q^{71} +(19.7694 + 6.64234i) q^{72} +(-6.10000 - 13.3571i) q^{73} +(10.3470 + 3.03815i) q^{74} +(-4.55092 - 3.54564i) q^{75} +(-5.23605 - 4.53707i) q^{76} +(-4.37162 - 0.628544i) q^{77} +(2.35634 - 0.122945i) q^{78} +(-4.18417 + 3.62560i) q^{79} +(-9.34949 + 6.00855i) q^{80} +(8.41454 + 3.19305i) q^{81} +(-16.7374 - 19.3160i) q^{82} +(11.8076 - 3.46701i) q^{83} +(-2.98374 + 7.55197i) q^{84} +(4.41802 - 5.09866i) q^{85} +(0.307502 - 0.673335i) q^{86} +(11.4541 + 6.54403i) q^{87} +(27.9286 - 12.7546i) q^{88} +(2.24892 + 15.6415i) q^{89} +(-8.63503 + 5.09028i) q^{90} +0.526763i q^{91} +(22.4819 - 0.260832i) q^{92} +(-1.62679 + 6.84080i) q^{93} +(8.68782 + 5.58333i) q^{94} +(1.88991 - 0.271728i) q^{95} +(-2.79889 - 14.1762i) q^{96} +(-0.730490 + 2.48782i) q^{97} +(-2.35243 - 1.07432i) q^{98} +(12.2555 - 5.03565i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9} - 22 q^{12} + 8 q^{13} - 22 q^{15} - 24 q^{16} - 30 q^{18} - 120 q^{24} - 88 q^{25} + 16 q^{27} - 44 q^{30} + 8 q^{31} - 22 q^{33} - 44 q^{34} + 10 q^{36}+ \cdots - 132 q^{97}+O(q^{100}) \) 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more