LMFDB - Embedded newform 950.2.bb.e.193.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			193.5
Character	$\chi$	$=$	950.193
Dual form			950.2.bb.e.507.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0871557 - 0.996195i) q^{2} +(1.36202 - 2.92085i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-3.02844 - 1.10226i) q^{6} +(-1.04490 - 0.279979i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-4.74793 - 5.65836i) q^{9} +O(q^{10})$	\(q+(-0.0871557 - 0.996195i) q^{2} +(1.36202 - 2.92085i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-3.02844 - 1.10226i) q^{6} +(-1.04490 - 0.279979i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-4.74793 - 5.65836i) q^{9} +(-0.276688 + 0.479237i) q^{11} +(-0.834123 + 3.11299i) q^{12} +(-5.99214 + 2.79418i) q^{13} +(-0.187845 + 1.06532i) q^{14} +(0.939693 - 0.342020i) q^{16} +(0.798807 - 0.0698866i) q^{17} +(-5.22302 + 5.22302i) q^{18} +(-4.04714 + 1.61883i) q^{19} +(-2.24094 + 2.67065i) q^{21} +(0.501528 + 0.233867i) q^{22} +(2.47314 - 3.53200i) q^{23} +(3.17384 + 0.559634i) q^{24} +(3.30580 + 5.72581i) q^{26} +(-13.6550 + 3.65885i) q^{27} +(1.07764 + 0.0942813i) q^{28} +(0.676108 - 0.567322i) q^{29} +(6.22083 - 3.59160i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(1.02293 + 1.46089i) q^{33} +(-0.139241 - 0.789676i) q^{34} +(5.65836 + 4.74793i) q^{36} +(-4.18017 - 4.18017i) q^{37} +(1.96540 + 3.89065i) q^{38} +21.3079i q^{39} +(-1.28804 - 3.53886i) q^{41} +(2.85580 + 1.99965i) q^{42} +(-2.98989 + 2.09354i) q^{43} +(0.189266 - 0.520003i) q^{44} +(-3.73411 - 2.15589i) q^{46} +(0.945489 - 10.8070i) q^{47} +(0.280886 - 3.21054i) q^{48} +(-5.04876 - 2.91490i) q^{49} +(0.883859 - 2.42838i) q^{51} +(5.41590 - 3.79226i) q^{52} +(-4.39113 - 3.07471i) q^{53} +(4.83504 + 13.2842i) q^{54} -1.08176i q^{56} +(-0.783903 + 14.0260i) q^{57} +(-0.624090 - 0.624090i) q^{58} +(0.957472 + 0.803415i) q^{59} +(-1.55079 - 8.79498i) q^{61} +(-4.12011 - 5.88413i) q^{62} +(3.37687 + 7.24172i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(1.36618 - 1.14636i) q^{66} +(4.81807 + 0.421526i) q^{67} +(-0.774536 + 0.207536i) q^{68} +(-6.94801 - 12.0343i) q^{69} +(-0.661243 - 0.116595i) q^{71} +(4.23670 - 6.05064i) q^{72} +(11.2621 + 5.25162i) q^{73} +(-3.79994 + 4.52859i) q^{74} +(3.70455 - 2.29702i) q^{76} +(0.423286 - 0.423286i) q^{77} +(21.2268 - 1.85710i) q^{78} +(8.16910 - 2.97331i) q^{79} +(-4.06344 + 23.0449i) q^{81} +(-3.41314 + 1.59157i) q^{82} +(-2.55303 + 9.52805i) q^{83} +(1.74314 - 3.01921i) q^{84} +(2.34616 + 2.79605i) q^{86} +(-0.736194 - 2.74751i) q^{87} +(-0.534520 - 0.143224i) q^{88} +(7.77234 + 2.82890i) q^{89} +(7.04348 - 1.24196i) q^{91} +(-1.82224 + 3.90780i) q^{92} +(-2.01766 - 23.0619i) q^{93} -10.8483 q^{94} -3.22280 q^{96} +(-0.115548 - 1.32071i) q^{97} +(-2.46378 + 5.28360i) q^{98} +(4.02539 - 0.709785i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^7	$ 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) $ 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$3$	1.36202	−	2.92085i	0.786360	−	1.68635i	0.0608462	−	0.998147i	$-0.480620\pi$
$3$	1.36202	−	2.92085i	0.786360	−	1.68635i	0.725514	−	0.688208i	$-0.241602\pi$
$4$	−0.984808	+	0.173648i	−0.492404	+	0.0868241i
$5$		0			0
$5$		0			0
$6$	−3.02844	−	1.10226i	−1.23636	−	0.449997i
$7$	−1.04490	−	0.279979i	−0.394934	−	0.105822i	0.0558861	−	0.998437i	$-0.482202\pi$
$7$	−1.04490	−	0.279979i	−0.394934	−	0.105822i	−0.450820	+	0.892615i	$0.648868\pi$
$8$	0.258819	+	0.965926i	0.0915064	+	0.341506i
$9$	−4.74793	−	5.65836i	−1.58264	−	1.88612i
$10$		0			0
$11$	−0.276688	+	0.479237i	−0.0834245	+	0.144495i	−0.904719	−	0.426009i	$-0.859919\pi$
$11$	−0.276688	+	0.479237i	−0.0834245	+	0.144495i	0.821294	+	0.570505i	$0.193252\pi$
$12$	−0.834123	+	3.11299i	−0.240791	+	0.898643i
$13$	−5.99214	+	2.79418i	−1.66192	+	0.774967i	−0.662251	+	0.749282i	$0.730399\pi$
$13$	−5.99214	+	2.79418i	−1.66192	+	0.774967i	−0.999670	+	0.0256845i	$0.991823\pi$
$14$	−0.187845	+	1.06532i	−0.0502037	+	0.284719i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	0.798807	−	0.0698866i	0.193739	−	0.0169500i	0.0101269	−	0.999949i	$-0.496776\pi$
$17$	0.798807	−	0.0698866i	0.193739	−	0.0169500i	0.183612	+	0.982999i	$0.441221\pi$
$18$	−5.22302	+	5.22302i	−1.23108	+	1.23108i
$19$	−4.04714	+	1.61883i	−0.928479	+	0.371386i
$19$	−4.04714	+	1.61883i	−0.928479	+	0.371386i
$20$		0			0
$21$	−2.24094	+	2.67065i	−0.489014	+	0.582784i
$22$	0.501528	+	0.233867i	0.106926	+	0.0498605i
$23$	2.47314	−	3.53200i	0.515685	−	0.736474i	−0.473876	−	0.880592i	$-0.657146\pi$
$23$	2.47314	−	3.53200i	0.515685	−	0.736474i	0.989561	+	0.144118i	$0.0460344\pi$
$24$	3.17384	+	0.559634i	0.647858	+	0.114235i
$25$		0			0
$26$	3.30580	+	5.72581i	0.648320	+	1.12292i
$27$	−13.6550	+	3.65885i	−2.62791	+	0.704146i
$28$	1.07764	+	0.0942813i	0.203655	+	0.0178175i
$29$	0.676108	−	0.567322i	0.125550	−	0.105349i	−0.577851	−	0.816143i	$-0.696108\pi$
$29$	0.676108	−	0.567322i	0.125550	−	0.105349i	0.703401	+	0.710793i	$0.251664\pi$
$30$		0			0
$31$	6.22083	−	3.59160i	1.11729	−	0.645070i	0.176585	−	0.984285i	$-0.443495\pi$
$31$	6.22083	−	3.59160i	1.11729	−	0.645070i	0.940709	+	0.339216i	$0.110162\pi$
$32$	−0.422618	−	0.906308i	−0.0747091	−	0.160214i
$33$	1.02293	+	1.46089i	0.178069	+	0.254309i
$34$	−0.139241	−	0.789676i	−0.0238797	−	0.135428i
$35$		0			0
$36$	5.65836	+	4.74793i	0.943060	+	0.791321i
$37$	−4.18017	−	4.18017i	−0.687216	−	0.687216i	0.274399	−	0.961616i	$-0.411521\pi$
$37$	−4.18017	−	4.18017i	−0.687216	−	0.687216i	−0.961616	+	0.274399i	$0.911521\pi$
$38$	1.96540	+	3.89065i	0.318831	+	0.631147i
$39$			21.3079i			3.41199i
$40$		0			0
$41$	−1.28804	−	3.53886i	−0.201158	−	0.552677i	0.797563	−	0.603236i	$-0.206122\pi$
$41$	−1.28804	−	3.53886i	−0.201158	−	0.552677i	−0.998721	+	0.0505583i	$0.983900\pi$
$42$	2.85580	+	1.99965i	0.440660	+	0.308553i
$43$	−2.98989	+	2.09354i	−0.455954	+	0.319262i	−0.778892	−	0.627158i	$-0.784218\pi$
$43$	−2.98989	+	2.09354i	−0.455954	+	0.319262i	0.322938	+	0.946420i	$0.395329\pi$
$44$	0.189266	−	0.520003i	0.0285329	−	0.0783934i
$45$		0			0
$46$	−3.73411	−	2.15589i	−0.550565	−	0.317869i
$47$	0.945489	−	10.8070i	0.137914	−	1.57636i	−0.540284	−	0.841483i	$-0.681683\pi$
$47$	0.945489	−	10.8070i	0.137914	−	1.57636i	0.678198	−	0.734879i	$-0.262761\pi$
$48$	0.280886	−	3.21054i	0.0405424	−	0.463402i
$49$	−5.04876	−	2.91490i	−0.721251	−	0.416414i
$50$		0			0
$51$	0.883859	−	2.42838i	0.123765	−	0.340042i
$52$	5.41590	−	3.79226i	0.751051	−	0.525891i
$53$	−4.39113	−	3.07471i	−0.603169	−	0.422343i	0.231704	−	0.972786i	$-0.425570\pi$
$53$	−4.39113	−	3.07471i	−0.603169	−	0.422343i	−0.834873	+	0.550443i	$0.814459\pi$
$54$	4.83504	+	13.2842i	0.657965	+	1.80775i
$55$		0			0
$56$		−	1.08176i		−	0.144556i
$57$	−0.783903	+	14.0260i	−0.103830	+	1.85779i
$58$	−0.624090	−	0.624090i	−0.0819470	−	0.0819470i
$59$	0.957472	+	0.803415i	0.124652	+	0.104596i	0.702983	−	0.711207i	$-0.251851\pi$
$59$	0.957472	+	0.803415i	0.124652	+	0.104596i	−0.578330	+	0.815803i	$0.696296\pi$
$60$		0			0
$61$	−1.55079	−	8.79498i	−0.198559	−	1.12608i	−0.907259	−	0.420572i	$-0.861829\pi$
$61$	−1.55079	−	8.79498i	−0.198559	−	1.12608i	0.708700	−	0.705510i	$-0.249282\pi$
$62$	−4.12011	−	5.88413i	−0.523254	−	0.747285i
$63$	3.37687	+	7.24172i	0.425446	+	0.912371i
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$		0			0
$66$	1.36618	−	1.14636i	0.168165	−	0.141107i
$67$	4.81807	+	0.421526i	0.588621	+	0.0514977i	0.377576	−	0.925979i	$-0.376758\pi$
$67$	4.81807	+	0.421526i	0.588621	+	0.0514977i	0.211045	+	0.977476i	$0.432313\pi$
$68$	−0.774536	+	0.207536i	−0.0939263	+	0.0251675i
$69$	−6.94801	−	12.0343i	−0.836442	−	1.44876i
$70$		0			0
$71$	−0.661243	−	0.116595i	−0.0784751	−	0.0138373i	0.134273	−	0.990944i	$-0.457130\pi$
$71$	−0.661243	−	0.116595i	−0.0784751	−	0.0138373i	−0.212748	+	0.977107i	$0.568241\pi$
$72$	4.23670	−	6.05064i	0.499300	−	0.713074i
$73$	11.2621	+	5.25162i	1.31813	+	0.614655i	0.949163	−	0.314786i	$-0.101933\pi$
$73$	11.2621	+	5.25162i	1.31813	+	0.614655i	0.368970	+	0.929441i	$0.379711\pi$
$74$	−3.79994	+	4.52859i	−0.441734	+	0.526438i
$75$		0			0
$76$	3.70455	−	2.29702i	0.424941	−	0.263486i
$77$	0.423286	−	0.423286i	0.0482380	−	0.0482380i
$78$	21.2268	−	1.85710i	2.40346	−	0.210276i
$79$	8.16910	−	2.97331i	0.919096	−	0.334524i	0.161217	−	0.986919i	$-0.448458\pi$
$79$	8.16910	−	2.97331i	0.919096	−	0.334524i	0.757879	+	0.652395i	$0.226236\pi$
$80$		0			0
$81$	−4.06344	+	23.0449i	−0.451494	+	2.56055i
$82$	−3.41314	+	1.59157i	−0.376918	+	0.175760i
$83$	−2.55303	+	9.52805i	−0.280232	+	1.04584i	0.672022	+	0.740531i	$0.265426\pi$
$83$	−2.55303	+	9.52805i	−0.280232	+	1.04584i	−0.952254	+	0.305308i	$0.901241\pi$
$84$	1.74314	−	3.01921i	0.190193	−	0.329423i
$85$		0			0
$86$	2.34616	+	2.79605i	0.252993	+	0.301506i
$87$	−0.736194	−	2.74751i	−0.0789283	−	0.294564i
$88$	−0.534520	−	0.143224i	−0.0569800	−	0.0152677i
$89$	7.77234	+	2.82890i	0.823867	+	0.299863i	0.719339	−	0.694659i	$-0.244445\pi$
$89$	7.77234	+	2.82890i	0.823867	+	0.299863i	0.104528	+	0.994522i	$0.466667\pi$
$90$		0			0
$91$	7.04348	−	1.24196i	0.738357	−	0.130192i
$92$	−1.82224	+	3.90780i	−0.189981	+	0.407416i
$93$	−2.01766	−	23.0619i	−0.209221	−	2.39141i
$94$	−10.8483			−1.11891
$95$		0			0
$96$	−3.22280			−0.328926
$97$	−0.115548	−	1.32071i	−0.0117321	−	0.134098i	0.988070	−	0.154007i	$-0.0492179\pi$
$97$	−0.115548	−	1.32071i	−0.0117321	−	0.134098i	−0.999802	+	0.0199090i	$0.993662\pi$
$98$	−2.46378	+	5.28360i	−0.248879	+	0.533724i
$99$	4.02539	−	0.709785i	0.404567	−	0.0713360i
$100$		0			0
$101$	12.1010	+	4.40440i	1.20409	+	0.438254i	0.864651	−	0.502373i	$-0.167540\pi$
$101$	12.1010	+	4.40440i	1.20409	+	0.438254i	0.339442	+	0.940627i	$0.389762\pi$
$102$	−2.49618	−	0.668849i	−0.247158	−	0.0662259i
$103$	−0.000877574	−	0.00327515i	−8.64700e−5	−	0.000322710i	0.965883	−	0.258980i	$-0.0833865\pi$
$103$	−0.000877574	−	0.00327515i	−8.64700e−5	−	0.000322710i	−0.965969	+	0.258658i	$0.916720\pi$
$104$	−4.24985	−	5.06478i	−0.416732	−	0.496642i
$105$		0			0
$106$	−2.68029	+	4.64240i	−0.260333	+	0.450910i
$107$	−0.347852	+	1.29820i	−0.0336281	+	0.125502i	−0.980699	−	0.195521i	$-0.937360\pi$
$107$	−0.347852	+	1.29820i	−0.0336281	+	0.125502i	0.947071	+	0.321023i	$0.104027\pi$
$108$	12.8122	−	5.97443i	1.23286	−	0.574890i
$109$	2.34699	−	13.3105i	0.224801	−	1.27491i	−0.638263	−	0.769818i	$-0.720347\pi$
$109$	2.34699	−	13.3105i	0.224801	−	1.27491i	0.863065	−	0.505093i	$-0.168542\pi$
$110$		0			0
$111$	−17.9031	+	6.51621i	−1.69929	+	0.618491i
$112$	−1.07764	+	0.0942813i	−0.101827	+	0.00890874i
$113$	0.949939	−	0.949939i	0.0893627	−	0.0893627i	−0.661012	−	0.750375i	$-0.729873\pi$
$113$	0.949939	−	0.949939i	0.0893627	−	0.0893627i	0.750375	+	0.661012i	$0.229873\pi$
$114$	14.0409	−	0.441525i	1.31505	−	0.0413526i
$115$		0			0
$116$	−0.567322	+	0.676108i	−0.0526745	+	0.0627751i
$117$	44.2607	+	20.6391i	4.09191	+	1.90809i
$118$	0.716908	−	1.02385i	0.0659967	−	0.0942531i
$119$	−0.854238	−	0.150625i	−0.0783078	−	0.0138078i
$120$		0			0
$121$	5.34689	+	9.26108i	0.486081	+	0.841916i
$122$	−8.62635	+	2.31142i	−0.780993	+	0.209267i
$123$	−12.0908	−	1.05781i	−1.09019	−	0.0953795i
$124$	−5.50264	+	4.61727i	−0.494152	+	0.414643i
$125$		0			0
$126$	6.91985	−	3.99518i	0.616469	−	0.355919i
$127$	1.78723	+	3.83273i	0.158591	+	0.340100i	0.969507	−	0.245062i	$-0.0788085\pi$
$127$	1.78723	+	3.83273i	0.158591	+	0.340100i	−0.810916	+	0.585163i	$0.801031\pi$
$128$	0.573576	+	0.819152i	0.0506975	+	0.0724035i
$129$	2.04265	+	11.5845i	0.179846	+	1.01996i
$130$		0			0
$131$	−3.15713	−	2.64915i	−0.275840	−	0.231457i	0.494364	−	0.869255i	$-0.335401\pi$
$131$	−3.15713	−	2.64915i	−0.275840	−	0.231457i	−0.770204	+	0.637798i	$0.779846\pi$
$132$	−1.26107	−	1.26107i	−0.109762	−	0.109762i
$133$	4.68209	−	0.558397i	0.405988	−	0.0484191i
$134$		−	4.83647i		−	0.417808i
$135$		0			0
$136$	0.274252	+	0.753500i	0.0235169	+	0.0646121i
$137$	−14.6431	−	10.2532i	−1.25104	−	0.875991i	−0.255185	−	0.966892i	$-0.582136\pi$
$137$	−14.6431	−	10.2532i	−1.25104	−	0.875991i	−0.995860	+	0.0909017i	$0.971025\pi$
$138$	−11.3830	+	7.97043i	−0.968982	+	0.678488i
$139$	1.17949	−	3.24061i	0.100043	−	0.274865i	−0.879567	−	0.475775i	$-0.842168\pi$
$139$	1.17949	−	3.24061i	0.100043	−	0.274865i	0.979610	+	0.200910i	$0.0643899\pi$
$140$		0			0
$141$	−30.2779	−	17.4809i	−2.54986	−	1.47216i
$142$	−0.0585202	+	0.668889i	−0.00491091	+	0.0561319i
$143$	0.318876	−	3.64477i	0.0266658	−	0.304791i
$144$	−6.39686	−	3.69323i	−0.533072	−	0.307769i
$145$		0			0
$146$	4.25007	−	11.6770i	0.351739	−	0.966394i
$147$	−15.3905	+	10.7765i	−1.26939	+	0.888833i
$148$	4.84255	+	3.39079i	0.398055	+	0.278721i
$149$	−2.68288	−	7.37114i	−0.219790	−	0.603867i	0.779969	−	0.625818i	$-0.215235\pi$
$149$	−2.68288	−	7.37114i	−0.219790	−	0.603867i	−0.999759	+	0.0219503i	$0.993012\pi$
$150$		0			0
$151$		−	10.6027i		−	0.862835i	−0.902152	−	0.431418i	$-0.858014\pi$
$151$		−	10.6027i		−	0.862835i	0.902152	−	0.431418i	$-0.141986\pi$
$152$	−2.61115	−	3.49026i	−0.211792	−	0.283097i
$153$	−4.18812	−	4.18812i	−0.338590	−	0.338590i
$154$	−0.458568	−	0.384784i	−0.0369524	−	0.0310068i
$155$		0			0
$156$	−3.70007	−	20.9842i	−0.296243	−	1.68008i
$157$	−6.17741	−	8.82225i	−0.493011	−	0.704092i	0.493139	−	0.869951i	$-0.335849\pi$
$157$	−6.17741	−	8.82225i	−0.493011	−	0.704092i	−0.986150	+	0.165858i	$0.946961\pi$
$158$	−3.67398	−	7.87888i	−0.292286	−	0.626810i
$159$	−14.9616	+	8.63806i	−1.18653	+	0.685043i
$160$		0			0
$161$	−3.57306	+	2.99815i	−0.281597	+	0.236288i
$162$	23.3114	+	2.03948i	1.83152	+	0.160237i
$163$	−17.7704	+	4.76157i	−1.39189	+	0.372955i	−0.875425	−	0.483354i	$-0.839418\pi$
$163$	−17.7704	+	4.76157i	−1.39189	+	0.372955i	−0.516463	+	0.856309i	$0.672752\pi$
$164$	1.88299	+	3.26143i	0.147037	+	0.254675i
$165$		0			0
$166$	9.71431	+	1.71289i	0.753976	+	0.132946i
$167$	−6.89103	+	9.84141i	−0.533244	+	0.761551i	−0.991894	−	0.127066i	$-0.959444\pi$
$167$	−6.89103	+	9.84141i	−0.533244	+	0.761551i	0.458650	+	0.888617i	$0.348333\pi$
$168$	−3.15965	−	1.47337i	−0.243772	−	0.113673i
$169$	19.7421	−	23.5277i	1.51862	−	1.80982i
$170$		0			0
$171$	28.3755	+	15.2141i	2.16993	+	1.16345i
$172$	2.58093	−	2.58093i	0.196794	−	0.196794i
$173$	−6.75802	+	0.591250i	−0.513803	+	0.0449519i	−0.341109	−	0.940024i	$-0.610803\pi$
$173$	−6.75802	+	0.591250i	−0.513803	+	0.0449519i	−0.172693	+	0.984976i	$0.555247\pi$
$174$	−2.67289	+	0.972854i	−0.202632	+	0.0737519i
$175$		0			0
$176$	−0.0960926	+	0.544968i	−0.00724325	+	0.0410785i
$177$	3.65075	−	1.70237i	0.274407	−	0.127958i
$178$	2.14073	−	7.98932i	0.160455	−	0.598825i
$179$	−7.43804	+	12.8831i	−0.555945	+	0.962925i	0.441884	+	0.897072i	$0.354310\pi$
$179$	−7.43804	+	12.8831i	−0.555945	+	0.962925i	−0.997829	+	0.0658528i	$0.979023\pi$
$180$		0			0
$181$	6.46102	+	7.69994i	0.480244	+	0.572332i	0.950708	−	0.310087i	$-0.100358\pi$
$181$	6.46102	+	7.69994i	0.480244	+	0.572332i	−0.470465	+	0.882419i	$0.655914\pi$
$182$	−1.85111	−	6.90844i	−0.137213	−	0.512087i
$183$	−27.8010	−	7.44927i	−2.05511	−	0.550666i
$184$	4.05175	+	1.47472i	0.298699	+	0.108718i
$185$		0			0
$186$	−22.7983	+	4.01996i	−1.67165	+	0.294758i
$187$	−0.187528	+	0.402155i	−0.0137134	+	0.0294085i
$188$	0.945489	+	10.8070i	0.0689569	+	0.788181i
$189$	15.2925			1.11236
$190$		0			0
$191$	−20.3068			−1.46935			−0.734674	−	0.678420i	$-0.762665\pi$
$191$	−20.3068			−1.46935			−0.734674	+	0.678420i	$0.762665\pi$
$192$	0.280886	+	3.21054i	0.0202712	+	0.231701i
$193$	7.98203	−	17.1175i	0.574559	−	1.23215i	−0.377436	−	0.926035i	$-0.623194\pi$
$193$	7.98203	−	17.1175i	0.574559	−	1.23215i	0.951996	−	0.306111i	$-0.0990279\pi$
$194$	−1.30562	+	0.230216i	−0.0937379	+	0.0165285i
$195$		0			0
$196$	5.47822	+	1.99391i	0.391302	+	0.142422i
$197$	13.2536	+	3.55129i	0.944279	+	0.253019i	0.697933	−	0.716163i	$-0.254103\pi$
$197$	13.2536	+	3.55129i	0.944279	+	0.253019i	0.246346	+	0.969182i	$0.420770\pi$
$198$	−1.05792	−	3.94821i	−0.0751831	−	0.280587i
$199$	−13.3099	−	15.8621i	−0.943511	−	1.12443i	−0.992079	−	0.125613i	$-0.959910\pi$
$199$	−13.3099	−	15.8621i	−0.943511	−	1.12443i	0.0485685	−	0.998820i	$-0.484534\pi$
$200$		0			0
$201$	7.79350	−	13.4987i	0.549711	−	0.952128i
$202$	3.33297	−	12.4388i	0.234507	−	0.875191i
$203$	−0.865301	+	0.403497i	−0.0607322	+	0.0283199i
$204$	−0.448747	+	2.54497i	−0.0314186	+	0.178184i
$205$		0			0
$206$	−0.00318620	+	0.00115968i	−0.000221993	+	8.07990e-5i
$207$	−31.7276	+	2.77581i	−2.20522	+	0.192932i
$208$	−4.67511	+	4.67511i	−0.324160	+	0.324160i
$209$	0.343990	−	2.38745i	0.0237943	−	0.165144i
$210$		0			0
$211$	−8.16782	+	9.73403i	−0.562296	+	0.670118i	−0.970031	−	0.242982i	$-0.921874\pi$
$211$	−8.16782	+	9.73403i	−0.562296	+	0.670118i	0.407735	+	0.913100i	$0.366319\pi$
$212$	4.85834	+	2.26548i	0.333672	+	0.155594i
$213$	−1.24118	+	1.77259i	−0.0850443	+	0.121456i
$214$	1.32358	+	0.233383i	0.0904780	+	0.0159537i
$215$		0			0
$216$	−7.06835	−	12.2427i	−0.480941	−	0.833013i
$217$	−7.50569	+	2.01114i	−0.509520	+	0.136525i
$218$	−13.4644	−	1.17798i	−0.911922	−	0.0797828i
$219$	30.6784	−	25.7422i	2.07305	−	1.73950i
$220$		0			0
$221$	−4.59129	+	2.65078i	−0.308844	+	0.178311i
$222$	8.05177	+	17.2671i	0.540399	+	1.15889i
$223$	6.12215	+	8.74334i	0.409970	+	0.585497i	0.970039	−	0.242948i	$-0.0781145\pi$
$223$	6.12215	+	8.74334i	0.409970	+	0.585497i	−0.560070	+	0.828446i	$0.689226\pi$
$224$	0.187845	+	1.06532i	0.0125509	+	0.0711798i
$225$		0			0
$226$	−1.02912	−	0.863531i	−0.0684558	−	0.0574412i
$227$	18.4975	+	18.4975i	1.22772	+	1.22772i	0.964824	+	0.262897i	$0.0846781\pi$
$227$	18.4975	+	18.4975i	1.22772	+	1.22772i	0.262897	+	0.964824i	$0.415322\pi$
$228$	−1.66359	−	13.9490i	−0.110174	−	0.923797i
$229$			3.53960i			0.233903i	0.993138	+	0.116952i	$0.0373122\pi$
$229$			3.53960i			0.233903i	−0.993138	+	0.116952i	$0.962688\pi$
$230$		0			0
$231$	−0.659834	−	1.81288i	−0.0434139	−	0.119279i
$232$	0.722981	+	0.506236i	0.0474660	+	0.0332361i
$233$	−10.3890	+	7.27446i	−0.680606	+	0.476566i	−0.862042	−	0.506837i	$-0.830815\pi$
$233$	−10.3890	+	7.27446i	−0.680606	+	0.476566i	0.181436	+	0.983403i	$0.441926\pi$
$234$	16.7030	−	45.8911i	1.09191	−	3.00000i
$235$		0			0
$236$	−1.08244	−	0.624946i	−0.0704607	−	0.0406805i
$237$	2.44185	−	27.9104i	0.158615	−	1.81298i
$238$	−0.0756002	+	0.864115i	−0.00490044	+	0.0560122i
$239$	0.798776	+	0.461173i	0.0516685	+	0.0298308i	0.525612	−	0.850725i	$-0.323836\pi$
$239$	0.798776	+	0.461173i	0.0516685	+	0.0298308i	−0.473943	+	0.880555i	$0.657170\pi$
$240$		0			0
$241$	1.55729	−	4.27862i	0.100314	−	0.275610i	−0.879376	−	0.476127i	$-0.842040\pi$
$241$	1.55729	−	4.27862i	0.100314	−	0.275610i	0.979690	+	0.200517i	$0.0642623\pi$
$242$	8.75983	−	6.13370i	0.563103	−	0.394289i
$243$	27.0360	+	18.9308i	1.73436	+	1.21441i
$244$	3.05447	+	8.39207i	0.195542	+	0.537247i
$245$		0			0
$246$			12.1370i			0.773827i
$247$	19.7278	−	21.0087i	1.25525	−	1.33675i
$248$	5.07928	+	5.07928i	0.322535	+	0.322535i
$249$	24.3528	+	20.4344i	1.54329	+	1.29498i
$250$		0			0
$251$	−1.60384	−	9.09581i	−0.101233	−	0.574122i	−0.992658	−	0.120954i	$-0.961405\pi$
$251$	−1.60384	−	9.09581i	−0.101233	−	0.574122i	0.891425	−	0.453168i	$-0.149706\pi$
$252$	−4.58308	−	6.54532i	−0.288707	−	0.412316i
$253$	1.00838	+	2.16248i	0.0633964	+	0.135954i
$254$	3.66238	−	2.11448i	0.229798	−	0.132674i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	13.2081	+	1.15556i	0.823901	+	0.0720820i	0.491305	−	0.870988i	$-0.336520\pi$
$257$	13.2081	+	1.15556i	0.823901	+	0.0720820i	0.332596	+	0.943070i	$0.392076\pi$
$258$	11.3624	−	3.04453i	0.707389	−	0.189544i
$259$	3.19749	+	5.53821i	0.198682	+	0.344128i
$260$		0			0
$261$	−6.42022	−	1.13206i	−0.397402	−	0.0700727i
$262$	−2.36391	+	3.37601i	−0.146043	+	0.208570i
$263$	21.7197	+	10.1281i	1.33929	+	0.624523i	0.954426	−	0.298448i	$-0.0964689\pi$
$263$	21.7197	+	10.1281i	1.33929	+	0.624523i	0.384869	+	0.922971i	$0.374247\pi$
$264$	−1.14636	+	1.36618i	−0.0705536	+	0.0840825i
$265$		0			0
$266$	−0.964343	−	4.61560i	−0.0591276	−	0.283001i
$267$	18.8489	−	18.8489i	1.15353	−	1.15353i
$268$	−4.81807	+	0.421526i	−0.294310	+	0.0257488i
$269$	−7.76263	+	2.82537i	−0.473296	+	0.172266i	−0.567645	−	0.823274i	$-0.692145\pi$
$269$	−7.76263	+	2.82537i	−0.473296	+	0.172266i	0.0943489	+	0.995539i	$0.469923\pi$
$270$		0			0
$271$	3.37614	−	19.1470i	0.205086	−	1.16310i	−0.692219	−	0.721687i	$-0.743367\pi$
$271$	3.37614	−	19.1470i	0.205086	−	1.16310i	0.897305	−	0.441411i	$-0.145522\pi$
$272$	0.726731	−	0.338880i	0.0440645	−	0.0205476i
$273$	5.96576	−	22.2645i	0.361064	−	1.34751i
$274$	−8.93796	+	15.4810i	−0.539962	+	0.935242i
$275$		0			0
$276$	8.93219	+	10.6450i	0.537655	+	0.640752i
$277$	−5.03003	−	18.7723i	−0.302225	−	1.12792i	−0.935308	−	0.353836i	$-0.884877\pi$
$277$	−5.03003	−	18.7723i	−0.302225	−	1.12792i	0.633082	−	0.774085i	$-0.281790\pi$
$278$	−3.33108	−	0.892559i	−0.199785	−	0.0535321i
$279$	−49.8586	−	18.1470i	−2.98495	−	1.08643i
$280$		0			0
$281$	−5.67733	+	1.00107i	−0.338681	+	0.0597186i	−0.340402	−	0.940280i	$-0.610563\pi$
$281$	−5.67733	+	1.00107i	−0.338681	+	0.0597186i	0.00172130	+	0.999999i	$0.499452\pi$
$282$	−14.7755	+	31.6862i	−0.879869	+	1.88689i
$283$	−0.652833	−	7.46191i	−0.0388069	−	0.443565i	−0.990597	−	0.136814i	$-0.956314\pi$
$283$	−0.652833	−	7.46191i	−0.0388069	−	0.443565i	0.951790	−	0.306751i	$-0.0992418\pi$
$284$	0.671444			0.0398429
$285$		0			0
$286$	−3.65870			−0.216343
$287$	0.355061	+	4.05837i	0.0209586	+	0.239558i
$288$	−3.12165	+	6.69441i	−0.183945	+	0.394472i
$289$	−16.1085	+	2.84037i	−0.947560	+	0.167080i
$290$		0			0
$291$	−4.01499	−	1.46134i	−0.235363	−	0.0856651i
$292$	−12.0030	−	3.21619i	−0.702421	−	0.188213i
$293$	−2.69775	−	10.0682i	−0.157605	−	0.588188i	−0.998868	−	0.0475631i	$-0.984854\pi$
$293$	−2.69775	−	10.0682i	−0.157605	−	0.588188i	0.841264	−	0.540625i	$-0.181812\pi$
$294$	12.0769	+	14.3927i	0.704339	+	0.839398i
$295$		0			0
$296$	2.95583	−	5.11965i	0.171804	−	0.297573i
$297$	2.02472	−	7.55635i	0.117486	−	0.438464i
$298$	−7.10926	+	3.31510i	−0.411829	+	0.192039i
$299$	−4.95032	+	28.0747i	−0.286284	+	1.62360i
$300$		0			0
$301$	3.71028	−	1.35043i	0.213857	−	0.0778375i
$302$	−10.5623	+	0.924086i	−0.607795	+	0.0531752i
$303$	29.3463	−	29.3463i	1.68590	−	1.68590i
$304$	−3.24940	+	2.90541i	−0.186366	+	0.166637i
$305$		0			0
$306$	−3.80717	+	4.53720i	−0.217641	+	0.259375i
$307$	−7.45242	−	3.47512i	−0.425332	−	0.198336i	0.198153	−	0.980171i	$-0.436506\pi$
$307$	−7.45242	−	3.47512i	−0.425332	−	0.198336i	−0.623485	+	0.781836i	$0.714284\pi$
$308$	−0.343353	+	0.490359i	−0.0195643	+	0.0279408i
$309$	−0.0107615	−	0.00189754i	−0.000612201	−	0.000107947i
$310$		0			0
$311$	−5.55405	−	9.61990i	−0.314941	−	0.545495i	0.664484	−	0.747303i	$-0.268652\pi$
$311$	−5.55405	−	9.61990i	−0.314941	−	0.545495i	−0.979425	+	0.201808i	$0.935318\pi$
$312$	−20.5818	+	5.51488i	−1.16522	+	0.312219i
$313$	27.7731	+	2.42983i	1.56983	+	0.137342i	0.838584	−	0.544773i	$-0.183384\pi$
$313$	27.7731	+	2.42983i	1.56983	+	0.137342i	0.731245	+	0.682115i	$0.238940\pi$
$314$	−8.25028	+	6.92281i	−0.465590	+	0.390677i
$315$		0			0
$316$	−7.52869	+	4.34669i	−0.423522	+	0.244520i
$317$	10.5185	+	22.5570i	0.590779	+	1.26693i	0.943553	+	0.331221i	$0.107461\pi$
$317$	10.5185	+	22.5570i	0.590779	+	1.26693i	−0.352774	+	0.935708i	$0.614762\pi$
$318$	9.90917	+	14.1518i	0.555679	+	0.793592i
$319$	0.0848110	+	0.480987i	0.00474850	+	0.0269301i
$320$		0			0
$321$	3.31808	+	2.78420i	0.185197	+	0.155399i
$322$	3.29816	+	3.29816i	0.183799	+	0.183799i
$323$	−3.11975	+	1.57598i	−0.173588	+	0.0876897i
$324$		−	23.4004i		−	1.30002i
$325$		0			0
$326$	6.29225	+	17.2878i	0.348496	+	0.957484i
$327$	−35.6813	−	24.9843i	−1.97318	−	1.38163i
$328$	3.08491	−	2.16008i	0.170336	−	0.119270i
$329$	−4.01367	+	11.0275i	−0.221281	+	0.607964i
$330$		0			0
$331$	4.19603	+	2.42258i	0.230635	+	0.133157i	0.610865	−	0.791735i	$-0.290822\pi$
$331$	4.19603	+	2.42258i	0.230635	+	0.133157i	−0.380230	+	0.924892i	$0.624155\pi$
$332$	0.859719	−	9.82663i	0.0471832	−	0.539306i
$333$	−3.80576	+	43.5001i	−0.208555	+	2.38379i
$334$	10.4046	+	6.00707i	0.569312	+	0.328692i
$335$		0			0
$336$	−1.19238	+	3.27604i	−0.0650497	+	0.178723i
$337$	2.04884	−	1.43461i	0.111607	−	0.0781484i	−0.516440	−	0.856323i	$-0.672743\pi$
$337$	2.04884	−	1.43461i	0.111607	−	0.0781484i	0.628048	+	0.778175i	$0.283854\pi$
$338$	−25.1588	−	17.6164i	−1.36846	−	0.958205i
$339$	−1.48080	−	4.06846i	−0.0804259	−	0.220968i
$340$		0			0
$341$			3.97500i			0.215258i
$342$	12.6831	−	29.5935i	0.685824	−	1.60023i
$343$	9.81374	+	9.81374i	0.529892	+	0.529892i
$344$	−2.79605	−	2.34616i	−0.150753	−	0.126497i
$345$		0			0
$346$	1.17800	+	6.68077i	0.0633297	+	0.359160i
$347$	0.478594	+	0.683503i	0.0256923	+	0.0366924i	0.831793	−	0.555086i	$-0.187315\pi$
$347$	0.478594	+	0.683503i	0.0256923	+	0.0366924i	−0.806100	+	0.591779i	$0.798426\pi$
$348$	1.20211	+	2.57793i	0.0644399	+	0.138192i
$349$	22.4999	−	12.9903i	1.20439	−	0.695355i	0.242862	−	0.970061i	$-0.421914\pi$
$349$	22.4999	−	12.9903i	1.20439	−	0.695355i	0.961528	+	0.274706i	$0.0885805\pi$
$350$		0			0
$351$	71.5993	−	60.0789i	3.82169	−	3.20678i
$352$	0.551270	+	0.0482298i	0.0293828	+	0.00257066i
$353$	−3.34216	+	0.895528i	−0.177885	+	0.0476642i	−0.346662	−	0.937990i	$-0.612685\pi$
$353$	−3.34216	+	0.895528i	−0.177885	+	0.0476642i	0.168777	+	0.985654i	$0.446018\pi$
$354$	−2.01408	−	3.48848i	−0.107047	−	0.185411i
$355$		0			0
$356$	−8.14550	−	1.43627i	−0.431711	−	0.0761222i
$357$	−1.60344	+	2.28995i	−0.0848630	+	0.121197i
$358$	13.4823	+	6.28690i	0.712562	+	0.332273i
$359$	−7.08260	+	8.44071i	−0.373805	+	0.445484i	−0.919849	−	0.392273i	$-0.871689\pi$
$359$	−7.08260	+	8.44071i	−0.373805	+	0.445484i	0.546044	+	0.837757i	$0.316133\pi$
$360$		0			0
$361$	13.7588	−	13.1033i	0.724145	−	0.689647i
$362$	7.10753	−	7.10753i	0.373563	−	0.373563i
$363$	34.3328	−	3.00373i	1.80200	−	0.157655i
$364$	−6.72081	+	2.44618i	−0.352266	+	0.128214i
$365$		0			0
$366$	−4.99790	+	28.3445i	−0.261244	+	1.48159i
$367$	−13.7895	+	6.43014i	−0.719805	+	0.335650i	−0.747769	−	0.663958i	$-0.768875\pi$
$367$	−13.7895	+	6.43014i	−0.719805	+	0.335650i	0.0279647	+	0.999609i	$0.491097\pi$
$368$	1.11597	−	4.16486i	0.0581740	−	0.217108i
$369$	−13.9086	+	24.0904i	−0.724054	+	1.25410i
$370$		0			0
$371$	3.72743	+	4.44218i	0.193518	+	0.230626i
$372$	5.99167	+	22.3612i	0.310653	+	1.15937i
$373$	6.18361	+	1.65689i	0.320175	+	0.0857907i	0.415327	−	0.909672i	$-0.363667\pi$
$373$	6.18361	+	1.65689i	0.320175	+	0.0857907i	−0.0951520	+	0.995463i	$0.530334\pi$
$374$	0.416969	+	0.151764i	0.0215609	+	0.00784754i
$375$		0			0
$376$	10.6835	−	1.88378i	0.550958	−	0.0971487i
$377$	−2.46613	+	5.28864i	−0.127012	+	0.272379i
$378$	−1.33283	−	15.2343i	−0.0685532	−	0.783567i
$379$	33.1465			1.70262			0.851311	−	0.524661i	$-0.175808\pi$
$379$	33.1465			1.70262			0.851311	+	0.524661i	$0.175808\pi$
$380$		0			0
$381$	13.6291			0.698239
$382$	1.76985	+	20.2295i	0.0905536	+	1.03503i
$383$	11.0677	−	23.7347i	0.565532	−	1.21279i	−0.390793	−	0.920479i	$-0.627799\pi$
$383$	11.0677	−	23.7347i	0.565532	−	1.21279i	0.956324	−	0.292308i	$-0.0944232\pi$
$384$	3.17384	−	0.559634i	0.161964	−	0.0285587i
$385$		0			0
$386$	−17.7481	−	6.45977i	−0.903353	−	0.328794i
$387$	26.0418	+	6.97788i	1.32378	+	0.354706i
$388$	0.343132	+	1.28059i	0.0174199	+	0.0650119i
$389$	18.8381	+	22.4504i	0.955129	+	1.13828i	0.990307	+	0.138897i	$0.0443558\pi$
$389$	18.8381	+	22.4504i	0.955129	+	1.13828i	−0.0351777	+	0.999381i	$0.511200\pi$
$390$		0			0
$391$	1.72872	−	2.99423i	0.0874251	−	0.151425i
$392$	1.50886	−	5.63116i	0.0762091	−	0.284416i
$393$	−12.0378	+	5.61334i	−0.607229	+	0.283155i
$394$	2.38265	−	13.5127i	0.120036	−	0.680758i
$395$		0			0
$396$	−3.84098	+	1.39800i	−0.193017	+	0.0702523i
$397$	23.0558	−	2.01712i	1.15714	−	0.101236i	0.507619	−	0.861582i	$-0.330526\pi$
$397$	23.0558	−	2.01712i	1.15714	−	0.101236i	0.649519	+	0.760345i	$0.274970\pi$
$398$	−14.6417	+	14.6417i	−0.733921	+	0.733921i
$399$	4.74608	−	14.4362i	0.237601	−	0.722715i
$400$		0			0
$401$	−8.71693	+	10.3884i	−0.435303	+	0.518774i	−0.938444	−	0.345430i	$-0.887733\pi$
$401$	−8.71693	+	10.3884i	−0.435303	+	0.518774i	0.503142	+	0.864204i	$0.332177\pi$
$402$	−14.1266	−	6.58735i	−0.704572	−	0.328547i
$403$	−27.2405	+	38.9035i	−1.35695	+	1.93792i
$404$	−12.6820	−	2.23617i	−0.630951	−	0.111254i
$405$		0			0
$406$	0.477377	+	0.826842i	0.0236918	+	0.0410355i
$407$	3.15990	−	0.846692i	0.156630	−	0.0419690i
$408$	2.57440	+	0.225231i	0.127452	+	0.0111506i
$409$	−13.2107	+	11.0851i	−0.653225	+	0.548121i	−0.908048	−	0.418867i	$-0.862427\pi$
$409$	−13.2107	+	11.0851i	−0.653225	+	0.548121i	0.254822	+	0.966988i	$0.417983\pi$
$410$		0			0
$411$	−49.8922	+	28.8053i	−2.46100	+	1.42086i
$412$	0.00143297	+	0.00307301i	7.05972e−5	+	0.000151396i
$413$	−0.775520	−	1.10756i	−0.0381608	−	0.0544993i
$414$	5.53049	+	31.3650i	0.271809	+	1.54150i
$415$		0			0
$416$	5.06478	+	4.24985i	0.248321	+	0.208366i
$417$	−7.85886	−	7.85886i	−0.384850	−	0.384850i
$418$	−2.40835	−	0.134601i	−0.117796	−	0.00658355i
$419$		−	9.05564i		−	0.442397i	−0.975229	−	0.221198i	$-0.929003\pi$
$419$		−	9.05564i		−	0.442397i	0.975229	−	0.221198i	$-0.0709968\pi$
$420$		0			0
$421$	3.29739	+	9.05951i	0.160705	+	0.441534i	0.993744	−	0.111680i	$-0.0356233\pi$
$421$	3.29739	+	9.05951i	0.160705	+	0.441534i	−0.833039	+	0.553214i	$0.813401\pi$
$422$	10.4089	+	7.28836i	0.506695	+	0.354792i
$423$	−65.6390	+	45.9609i	−3.19148	+	2.23470i
$424$	1.83343	−	5.03730i	0.0890391	−	0.244633i
$425$		0			0
$426$	1.87402	+	1.08197i	0.0907966	+	0.0524214i
$427$	−0.841994	+	9.62404i	−0.0407469	+	0.465740i
$428$	0.117137	−	1.33888i	0.00566204	−	0.0647174i
$429$	−10.2115	−	5.89563i	−0.493017	−	0.284644i
$430$		0			0
$431$	2.38004	−	6.53911i	0.114643	−	0.314978i	−0.869080	−	0.494672i	$-0.835288\pi$
$431$	2.38004	−	6.53911i	0.114643	−	0.314978i	0.983723	+	0.179694i	$0.0575106\pi$
$432$	−11.5801	+	8.10848i	−0.557148	+	0.390120i
$433$	−5.77435	−	4.04324i	−0.277497	−	0.194306i	0.426540	−	0.904469i	$-0.359732\pi$
$433$	−5.77435	−	4.04324i	−0.277497	−	0.194306i	−0.704037	+	0.710163i	$0.748621\pi$
$434$	2.65766	+	7.30185i	0.127572	+	0.350500i
$435$		0			0
$436$			13.5158i			0.647289i
$437$	−4.29141	+	18.2981i	−0.205286	+	0.875318i
$438$	−28.3181	−	28.3181i	−1.35309	−	1.35309i
$439$	0.810135	+	0.679784i	0.0386656	+	0.0324443i	0.661916	−	0.749578i	$-0.269744\pi$
$439$	0.810135	+	0.679784i	0.0386656	+	0.0324443i	−0.623250	+	0.782023i	$0.714188\pi$
$440$		0			0
$441$	7.47757	+	42.4074i	0.356075	+	2.01940i
$442$	3.04085	+	4.34279i	0.144639	+	0.206565i
$443$	2.06266	+	4.42340i	0.0980001	+	0.210162i	0.949195	−	0.314687i	$-0.101900\pi$
$443$	2.06266	+	4.42340i	0.0980001	+	0.210162i	−0.851195	+	0.524849i	$0.824122\pi$
$444$	16.4996	−	9.52606i	0.783037	−	0.452087i
$445$		0			0
$446$	8.17649	−	6.86089i	0.387168	−	0.324872i
$447$	−25.1841	−	2.20333i	−1.19117	−	0.104214i
$448$	1.04490	−	0.279979i	0.0493667	−	0.0132278i
$449$	−15.7973	−	27.3616i	−0.745518	−	1.29128i	−0.949952	−	0.312395i	$-0.898869\pi$
$449$	−15.7973	−	27.3616i	−0.745518	−	1.29128i	0.204434	−	0.978880i	$-0.434465\pi$
$450$		0			0
$451$	2.05234	+	0.361883i	0.0966409	+	0.0170404i
$452$	−0.770552	+	1.10046i	−0.0362437	+	0.0517614i
$453$	−30.9689	−	14.4410i	−1.45505	−	0.678499i
$454$	16.8149	−	20.0393i	0.789164	−	0.940489i
$455$		0			0
$456$	−13.7510	+	2.87300i	−0.643947	+	0.134541i
$457$	−0.198343	+	0.198343i	−0.00927808	+	0.00927808i	−0.711731	−	0.702453i	$-0.752088\pi$
$457$	−0.198343	+	0.198343i	−0.00927808	+	0.00927808i	0.702453	+	0.711731i	$0.252088\pi$
$458$	3.52613	−	0.308496i	0.164765	−	0.0144151i
$459$	−10.6520	+	3.87702i	−0.497194	+	0.180964i
$460$		0			0
$461$	2.61725	−	14.8432i	0.121897	−	0.691315i	−0.861205	−	0.508258i	$-0.830290\pi$
$461$	2.61725	−	14.8432i	0.121897	−	0.691315i	0.983102	−	0.183057i	$-0.0585993\pi$
$462$	−1.74847	+	0.815326i	−0.0813463	+	0.0379324i
$463$	9.46242	−	35.3142i	0.439756	−	1.64119i	−0.289666	−	0.957128i	$-0.593544\pi$
$463$	9.46242	−	35.3142i	0.439756	−	1.64119i	0.729422	−	0.684064i	$-0.239789\pi$
$464$	0.441298	−	0.764351i	0.0204868	−	0.0354841i
$465$		0			0
$466$	8.15224	+	9.71546i	0.377645	+	0.450060i
$467$	3.82337	+	14.2690i	0.176924	+	0.660291i	0.996216	+	0.0869137i	$0.0277004\pi$
$467$	3.82337	+	14.2690i	0.176924	+	0.660291i	−0.819291	+	0.573377i	$0.805633\pi$
$468$	−47.1723	−	12.6398i	−2.18054	−	0.584274i
$469$	−4.91637	−	1.78941i	−0.227017	−	0.0826273i
$470$		0			0
$471$	−34.1822	+	6.02725i	−1.57503	+	0.277721i
$472$	−0.528227	+	1.13279i	−0.0243136	+	0.0521407i
$473$	−0.176038	−	2.01212i	−0.00809424	−	0.0925176i
$474$	−28.0171			−1.28687
$475$		0			0
$476$	0.867416			0.0397579
$477$	3.45100	+	39.4451i	0.158010	+	1.80607i
$478$	0.389801	−	0.835930i	0.0178291	−	0.0382346i
$479$	2.55341	−	0.450235i	0.116668	−	0.0205717i	−0.115009	−	0.993364i	$-0.536690\pi$
$479$	2.55341	−	0.450235i	0.116668	−	0.0205717i	0.231677	+	0.972793i	$0.425579\pi$
$480$		0			0
$481$	36.7284	+	13.3680i	1.67467	+	0.609530i
$482$	−4.39806	−	1.17846i	−0.200326	−	0.0536772i
$483$	3.89060	+	14.5199i	0.177028	+	0.660679i
$484$	−6.87383	−	8.19191i	−0.312447	−	0.372359i
$485$		0			0
$486$	16.5025	−	28.5831i	0.748567	−	1.29656i
$487$	−3.48724	+	13.0145i	−0.158022	+	0.589745i	0.840806	+	0.541337i	$0.182082\pi$
$487$	−3.48724	+	13.0145i	−0.158022	+	0.589745i	−0.998828	+	0.0484085i	$0.984585\pi$
$488$	8.09393	−	3.77426i	0.366395	−	0.170853i
$489$	−10.2958	+	58.3902i	−0.465590	+	2.64049i
$490$		0			0
$491$	−40.0446	+	14.5750i	−1.80719	+	0.657762i	−0.809704	+	0.586838i	$0.800373\pi$
$491$	−40.0446	+	14.5750i	−1.80719	+	0.657762i	−0.997482	+	0.0709238i	$0.977405\pi$
$492$	12.0908	−	1.05781i	0.545096	−	0.0476898i
$493$	0.500432	−	0.500432i	0.0225383	−	0.0225383i
$494$	−22.6482	−	17.8216i	−1.01899	−	0.801834i
$495$		0			0
$496$	4.61727	−	5.50264i	0.207321	−	0.247076i
$497$	0.658287	+	0.306964i	0.0295282	+	0.0137692i
$498$	18.2342	−	26.0411i	0.817092	−	1.16693i
$499$	18.0296	+	3.17910i	0.807115	+	0.142316i	0.561956	−	0.827167i	$-0.310049\pi$
$499$	18.0296	+	3.17910i	0.807115	+	0.142316i	0.245159	+	0.969483i	$0.421160\pi$
$500$		0			0
$501$	19.3596	+	33.5318i	0.864924	+	1.49809i
$502$	−8.92141	+	2.39048i	−0.398182	+	0.106693i
$503$	−6.06025	−	0.530203i	−0.270213	−	0.0236406i	−0.0487561	−	0.998811i	$-0.515526\pi$
$503$	−6.06025	−	0.530203i	−0.270213	−	0.0236406i	−0.221457	+	0.975170i	$0.571081\pi$
$504$	−6.12097	+	5.13610i	−0.272650	+	0.228780i
$505$		0			0
$506$	2.06637	−	1.19302i	0.0918612	−	0.0530361i
$507$	−41.8319	−	89.7088i	−1.85782	−	3.98411i
$508$	−2.42563	−	3.46416i	−0.107620	−	0.153697i
$509$	−4.08090	−	23.1439i	−0.180883	−	1.02584i	−0.931132	−	0.364681i	$-0.881178\pi$
$509$	−4.08090	−	23.1439i	−0.180883	−	1.02584i	0.750250	−	0.661154i	$-0.229933\pi$
$510$		0			0
$511$	−10.2974	−	8.64056i	−0.455531	−	0.382236i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	49.3407	−	36.9131i	2.17845	−	1.62975i
$514$		−	13.2586i		−	0.584811i
$515$		0			0
$516$	−4.02324	−	11.0538i	−0.177113	−	0.486615i
$517$	4.91751	+	3.44328i	0.216272	+	0.151435i
$518$	5.23846	−	3.66801i	0.230165	−	0.161163i
$519$	−7.47757	+	20.5445i	−0.328229	+	0.901802i
$520$		0			0
$521$	−16.3905	−	9.46308i	−0.718083	−	0.414585i	0.0959639	−	0.995385i	$-0.469407\pi$
$521$	−16.3905	−	9.46308i	−0.718083	−	0.414585i	−0.814047	+	0.580800i	$0.802740\pi$
$522$	−0.568191	+	6.49446i	−0.0248691	+	0.284255i
$523$	−0.492426	+	5.62845i	−0.0215323	+	0.246115i	0.977799	+	0.209546i	$0.0671985\pi$
$523$	−0.492426	+	5.62845i	−0.0215323	+	0.246115i	−0.999331	+	0.0365693i	$0.988357\pi$
$524$	3.56919	+	2.06067i	0.155921	+	0.0900209i
$525$		0			0
$526$	8.19653	−	22.5198i	0.357386	−	0.981909i
$527$	4.71824	−	3.30374i	0.205530	−	0.143913i
$528$	1.46089	+	1.02293i	0.0635772	+	0.0445172i
$529$	1.50781	+	4.14267i	0.0655570	+	0.180116i
$530$		0			0
$531$		−	9.23227i		−	0.400647i
$532$	−4.51399	+	1.36295i	−0.195706	+	0.0590913i
$533$	17.6063	+	17.6063i	0.762615	+	0.762615i
$534$	−20.4199	−	17.1343i	−0.883656	−	0.741476i
$535$		0			0
$536$	0.839845	+	4.76300i	0.0362758	+	0.205730i
$537$	27.4988	+	39.2723i	1.18666	+	1.69473i
$538$	3.49117	+	7.48685i	0.150515	+	0.322781i
$539$	2.79386	−	1.61303i	0.120340	−	0.0694783i
$540$		0			0
$541$	−15.6928	+	13.1678i	−0.674687	+	0.566130i	−0.914449	−	0.404702i	$-0.867375\pi$
$541$	−15.6928	+	13.1678i	−0.674687	+	0.566130i	0.239762	+	0.970832i	$0.422931\pi$
$542$	−19.3684	−	1.69452i	−0.831944	−	0.0727857i
$543$	31.2904	−	8.38424i	1.34280	−	0.359802i
$544$	−0.400929	−	0.694430i	−0.0171897	−	0.0297734i
$545$		0			0
$546$	−22.6998	−	4.00258i	−0.971460	−	0.171295i
$547$	−4.71867	+	6.73895i	−0.201756	+	0.288137i	−0.907261	−	0.420567i	$-0.861831\pi$
$547$	−4.71867	+	6.73895i	−0.201756	+	0.288137i	0.705506	+	0.708704i	$0.250720\pi$
$548$	16.2011	+	7.55469i	0.692076	+	0.322720i
$549$	−42.4021	+	50.5329i	−1.80968	+	2.15669i
$550$		0			0
$551$	−1.81791	+	3.39054i	−0.0774455	+	0.144442i
$552$	9.82597	−	9.82597i	0.418221	−	0.418221i
$553$	−9.36833	+	0.819623i	−0.398382	+	0.0348539i
$554$	−18.2625	+	6.64701i	−0.775900	+	0.282404i
$555$		0			0
$556$	−0.598840	+	3.39619i	−0.0253965	+	0.144031i
$557$	−26.6386	+	12.4218i	−1.12871	+	0.526328i	−0.895039	−	0.445987i	$-0.852853\pi$
$557$	−26.6386	+	12.4218i	−1.12871	+	0.526328i	−0.233674	+	0.972315i	$0.575075\pi$
$558$	−13.7325	+	51.2505i	−0.581344	+	2.16961i
$559$	12.0661	−	20.8991i	0.510342	−	0.883938i
$560$		0			0
$561$	0.919219	+	1.09548i	0.0388094	+	0.0462513i
$562$	1.49207	+	5.56847i	0.0629391	+	0.234892i
$563$	1.16978	+	0.313442i	0.0493005	+	0.0132100i	0.283385	−	0.959006i	$-0.408543\pi$
$563$	1.16978	+	0.313442i	0.0493005	+	0.0132100i	−0.234085	+	0.972216i	$0.575209\pi$
$564$	32.8534	+	11.9577i	1.38338	+	0.503508i
$565$		0			0
$566$	−7.37662	+	1.30070i	−0.310062	+	0.0546724i
$567$	10.6980	−	22.9419i	0.449273	−	0.963469i
$568$	−0.0585202	−	0.668889i	−0.00245545	−	0.0280660i
$569$	45.0467			1.88846			0.944229	−	0.329291i	$-0.106810\pi$
$569$	45.0467			1.88846			0.944229	+	0.329291i	$0.106810\pi$
$570$		0			0
$571$	13.3014			0.556646			0.278323	−	0.960488i	$-0.410221\pi$
$571$	13.3014			0.556646			0.278323	+	0.960488i	$0.410221\pi$
$572$	0.318876	+	3.64477i	0.0133329	+	0.152396i
$573$	−27.6582	+	59.3131i	−1.15544	+	2.47784i
$574$	4.01198	−	0.707420i	0.167457	−	0.0295272i
$575$		0			0
$576$	6.94100	+	2.52632i	0.289209	+	0.105263i
$577$	1.27169	+	0.340748i	0.0529411	+	0.0141855i	0.285192	−	0.958470i	$-0.407943\pi$
$577$	1.27169	+	0.340748i	0.0529411	+	0.0141855i	−0.232251	+	0.972656i	$0.574609\pi$
$578$	4.23351	+	15.7997i	0.176091	+	0.657180i
$579$	−39.1261	−	46.6287i	−1.62603	−	1.93782i
$580$		0			0
$581$	5.33531	−	9.24103i	0.221346	−	0.383383i
$582$	−1.10585	+	4.12708i	−0.0458388	+	0.171073i
$583$	2.68849	−	1.25366i	0.111346	−	0.0519214i
$584$	−2.15782	+	12.2376i	−0.0892912	+	0.506396i
$585$		0			0
$586$	−9.79472	+	3.56499i	−0.404616	+	0.147268i
$587$	14.3253	−	1.25330i	0.591268	−	0.0517292i	0.212404	−	0.977182i	$-0.431871\pi$
$587$	14.3253	−	1.25330i	0.591268	−	0.0517292i	0.378863	+	0.925453i	$0.376315\pi$
$588$	13.2853	−	13.2853i	0.547878	−	0.547878i
$589$	−19.3624	+	24.6062i	−0.797814	+	1.01388i
$590$		0			0
$591$	28.4244	−	33.8749i	1.16922	−	1.39343i
$592$	−5.35778	−	2.49837i	−0.220203	−	0.102683i
$593$	16.0863	−	22.9736i	0.660584	−	0.943411i	−0.339413	−	0.940638i	$-0.610228\pi$
$593$	16.0863	−	22.9736i	0.660584	−	0.943411i	0.999996	−	0.00277351i	$-0.000882837\pi$
$594$	−7.70406	−	1.35843i	−0.316101	−	0.0557372i
$595$		0			0
$596$	3.92210	+	6.79328i	0.160656	+	0.278264i
$597$	−64.4590	+	17.2717i	−2.63813	+	0.706885i
$598$	28.3993	+	2.48462i	1.16133	+	0.101603i
$599$	4.78623	−	4.01612i	0.195560	−	0.164094i	−0.539750	−	0.841826i	$-0.681481\pi$
$599$	4.78623	−	4.01612i	0.195560	−	0.164094i	0.735310	+	0.677731i	$0.237037\pi$
$600$		0			0
$601$	5.40209	−	3.11890i	0.220356	−	0.127222i	−0.385759	−	0.922599i	$-0.626060\pi$
$601$	5.40209	−	3.11890i	0.220356	−	0.127222i	0.606115	+	0.795377i	$0.292727\pi$
$602$	−1.66866	−	3.57846i	−0.0680096	−	0.145847i
$603$	−20.4907	−	29.2637i	−0.834446	−	1.19171i
$604$	1.84114	+	10.4416i	0.0749149	+	0.424863i
$605$		0			0
$606$	−31.7924	−	26.6770i	−1.29148	−	1.08368i
$607$	27.2734	+	27.2734i	1.10699	+	1.10699i	0.993544	+	0.113448i	$0.0361895\pi$
$607$	27.2734	+	27.2734i	1.10699	+	1.10699i	0.113448	+	0.993544i	$0.463811\pi$
$608$	3.17756	+	2.98381i	0.128867	+	0.121009i
$609$			3.07699i			0.124686i
$610$		0			0
$611$	24.5312	+	67.3989i	0.992426	+	2.72667i
$612$	4.85175	+	3.39723i	0.196121	+	0.137325i
$613$	28.4882	−	19.9477i	1.15063	−	0.805679i	0.167013	−	0.985955i	$-0.446588\pi$
$613$	28.4882	−	19.9477i	1.15063	−	0.805679i	0.983616	+	0.180275i	$0.0576989\pi$
$614$	−2.81238	+	7.72694i	−0.113498	+	0.311834i
$615$		0			0
$616$	0.518418	+	0.299309i	0.0208877	+	0.0120595i
$617$	0.881335	−	10.0737i	0.0354812	−	0.405552i	−0.957598	−	0.288107i	$-0.906974\pi$
$617$	0.881335	−	10.0737i	0.0354812	−	0.405552i	0.993079	−	0.117445i	$-0.0374704\pi$
$618$	−0.000952396		0.0108859i	−3.83110e−5		0.000437897i
$619$	−21.9825	−	12.6916i	−0.883551	−	0.510119i	−0.0117236	−	0.999931i	$-0.503732\pi$
$619$	−21.9825	−	12.6916i	−0.883551	−	0.510119i	−0.871828	+	0.489813i	$0.837065\pi$
$620$		0			0
$621$	−20.8476	+	57.2784i	−0.836587	+	2.29850i
$622$	−9.09923	+	6.37135i	−0.364846	+	0.255468i
$623$	−7.32926	−	5.13200i	−0.293641	−	0.205609i
$624$	7.28772	+	20.0229i	0.291742	+	0.801556i
$625$		0			0
$626$		−	27.8792i		−	1.11428i
$627$	−6.50488	−	4.25649i	−0.259780	−	0.169988i
$628$	7.61553	+	7.61553i	0.303893	+	0.303893i
$629$	−3.63129	−	3.04701i	−0.144789	−	0.121492i
$630$		0			0
$631$	5.54247	+	31.4329i	0.220642	+	1.25133i	0.870842	+	0.491562i	$0.163574\pi$
$631$	5.54247	+	31.4329i	0.220642	+	1.25133i	−0.650200	+	0.759763i	$0.725315\pi$
$632$	4.98632	+	7.12120i	0.198345	+	0.283266i
$633$	17.3070	+	37.1149i	0.687890	+	1.47518i
$634$	21.5545	−	12.4445i	0.856037	−	0.494233i
$635$		0			0
$636$	13.2343	−	11.1049i	0.524773	−	0.440337i
$637$	38.3976	+	3.35936i	1.52137	+	0.133103i
$638$	0.471765	−	0.126409i	0.0186774	−	0.00500458i
$639$	2.47980	+	4.29514i	0.0980993	+	0.169913i
$640$		0			0
$641$	24.9736	+	4.40352i	0.986399	+	0.173929i	0.643502	−	0.765444i	$-0.277481\pi$
$641$	24.9736	+	4.40352i	0.986399	+	0.173929i	0.342897	+	0.939373i	$0.388592\pi$
$642$	2.48441	−	3.54811i	0.0980519	−	0.140033i
$643$	−44.0880	−	20.5586i	−1.73866	−	0.810752i	−0.988816	−	0.149139i	$-0.952350\pi$
$643$	−44.0880	−	20.5586i	−1.73866	−	0.810752i	−0.749846	−	0.661612i	$-0.769872\pi$
$644$	2.99815	−	3.57306i	0.118144	−	0.140798i
$645$		0			0
$646$	1.84188	+	2.97053i	0.0724679	+	0.116874i
$647$	1.04795	−	1.04795i	0.0411993	−	0.0411993i	−0.686207	−	0.727406i	$-0.740726\pi$
$647$	1.04795	−	1.04795i	0.0411993	−	0.0411993i	0.727406	+	0.686207i	$0.240726\pi$
$648$	−23.3114	+	2.03948i	−0.915758	+	0.0801185i
$649$	−0.649947	+	0.236561i	−0.0255126	+	0.00928584i
$650$		0			0
$651$	−4.34862	+	24.6622i	−0.170436	+	0.966589i
$652$	16.6736	−	7.77504i	0.652990	−	0.304494i
$653$	−1.79509	+	6.69936i	−0.0702473	+	0.262166i	−0.992114	−	0.125342i	$-0.959997\pi$
$653$	−1.79509	+	6.69936i	−0.0702473	+	0.262166i	0.921866	+	0.387508i	$0.126664\pi$
$654$	−21.7794	+	37.7230i	−0.851641	+	1.47509i
$655$		0			0
$656$	−2.42072	−	2.88491i	−0.0945134	−	0.112637i
$657$	−23.7562	−	88.6595i	−0.926819	−	3.45894i
$658$	11.3353	+	3.03729i	0.441897	+	0.118406i
$659$	23.5139	+	8.55836i	0.915972	+	0.333386i	0.756635	−	0.653838i	$-0.226842\pi$
$659$	23.5139	+	8.55836i	0.915972	+	0.333386i	0.159337	+	0.987224i	$0.449064\pi$
$660$		0			0
$661$	30.6131	−	5.39792i	1.19071	−	0.209955i	0.457033	−	0.889450i	$-0.348912\pi$
$661$	30.6131	−	5.39792i	1.19071	−	0.209955i	0.733680	+	0.679495i	$0.237801\pi$
$662$	2.04765	−	4.39120i	0.0795842	−	0.170669i
$663$	1.48913	+	17.0209i	0.0578332	+	0.661036i
$664$	−9.86417			−0.382804
$665$		0			0
$666$	43.6662			1.69203
$667$	−0.331677	−	3.79108i	−0.0128426	−	0.146791i
$668$	5.07740	−	10.8885i	0.196450	−	0.421289i
$669$	33.8765	−	5.97334i	1.30974	−	0.230942i
$670$		0			0
$671$	4.64397	+	1.69027i	0.179278	+	0.0652520i
$672$	3.36750	+	0.902318i	0.129904	+	0.0348077i
$673$	10.5573	+	39.4002i	0.406953	+	1.51877i	0.800426	+	0.599432i	$0.204607\pi$
$673$	10.5573	+	39.4002i	0.406953	+	1.51877i	−0.393473	+	0.919336i	$0.628727\pi$
$674$	−1.60772	−	1.91601i	−0.0619272	−	0.0738019i
$675$		0			0
$676$	−15.3566	+	26.5984i	−0.590639	+	1.02302i
$677$	−7.83958	+	29.2577i	−0.301300	+	1.12447i	0.634784	+	0.772689i	$0.281089\pi$
$677$	−7.83958	+	29.2577i	−0.301300	+	1.12447i	−0.936084	+	0.351776i	$0.885578\pi$
$678$	−3.92392	+	1.82975i	−0.150697	+	0.0702713i
$679$	−0.249037	+	1.41236i	−0.00955718	+	0.0542015i
$680$		0			0
$681$	79.2223	−	28.8346i	3.03580	−	1.10494i
$682$	3.95988	−	0.346444i	0.151631	−	0.0132660i
$683$	−25.6883	+	25.6883i	−0.982934	+	0.982934i	−0.999857	−	0.0169224i	$-0.994613\pi$
$683$	−25.6883	+	25.6883i	−0.982934	+	0.982934i	0.0169224	+	0.999857i	$0.494613\pi$
$684$	−30.5863	−	10.0556i	−1.16950	−	0.384486i
$685$		0			0
$686$	8.92107	−	10.6317i	0.340608	−	0.405921i
$687$	10.3386	+	4.82099i	0.394444	+	0.183932i
$688$	−2.09354	+	2.98989i	−0.0798156	+	0.113989i
$689$	34.9036	+	6.15444i	1.32972	+	0.234466i
$690$		0			0
$691$	−9.52340	−	16.4950i	−0.362287	−	0.627500i	0.626050	−	0.779783i	$-0.284671\pi$
$691$	−9.52340	−	16.4950i	−0.362287	−	0.627500i	−0.988337	+	0.152283i	$0.951337\pi$
$692$	6.55268	−	1.75578i	0.249095	−	0.0667449i
$693$	−4.40484	−	0.385374i	−0.167326	−	0.0146391i
$694$	0.639190	−	0.536344i	0.0242633	−	0.0203593i
$695$		0			0
$696$	2.46335	−	1.42222i	0.0933731	−	0.0539090i
$697$	−1.27621	−	2.73685i	−0.0483401	−	0.103666i
$698$	−14.9019	−	21.2821i	−0.564044	−	0.805538i
$699$	7.09763	+	40.2527i	0.268457	+	1.52250i
$700$		0			0
$701$	−18.5814	−	15.5917i	−0.701810	−	0.588889i	0.220478	−	0.975392i	$-0.429238\pi$
$701$	−18.5814	−	15.5917i	−0.701810	−	0.588889i	−0.922288	+	0.386503i	$0.873683\pi$
$702$	−66.0906	−	66.0906i	−2.49443	−	2.49443i
$703$	23.6848	+	10.1508i	0.893288	+	0.382843i
$704$		−	0.553375i		−	0.0208561i
$705$		0			0
$706$	1.18341	+	3.25139i	0.0445382	+	0.122368i
$707$	−11.4111	−	7.99017i	−0.429160	−	0.300501i
$708$	−3.29967	+	2.31045i	−0.124009	+	0.0868322i
$709$	−0.0939030	+	0.257996i	−0.00352660	+	0.00968926i	−0.941443	−	0.337171i	$-0.890530\pi$
$709$	−0.0939030	+	0.257996i	−0.00352660	+	0.00968926i	0.937917	+	0.346860i	$0.112752\pi$
$710$		0			0
$711$	−55.6104	−	32.1067i	−2.08555	−	1.20409i
$712$	−0.720879	+	8.23968i	−0.0270161	+	0.308795i
$713$	2.69942	−	30.8545i	0.101094	−	1.15551i
$714$	2.42098	+	1.39776i	0.0906030	+	0.0523097i
$715$		0			0
$716$	5.08792	−	13.9789i	0.190144	−	0.522417i
$717$	2.43496	−	1.70498i	0.0909354	−	0.0636737i
$718$	9.02588	+	6.31999i	0.336843	+	0.235860i
$719$	1.33451	+	3.66653i	0.0497688	+	0.136739i	0.962087	−	0.272744i	$-0.0879313\pi$
$719$	1.33451	+	3.66653i	0.0497688	+	0.136739i	−0.912318	+	0.409483i	$0.865709\pi$
$720$		0			0
$721$			0.00366790i			0.000136600i
$722$	−14.2526	−	12.5644i	−0.530427	−	0.467598i
$723$	−10.3762	−	10.3762i	−0.385893	−	0.385893i
$724$	−7.69994	−	6.46102i	−0.286166	−	0.240122i
$725$		0			0
$726$	−5.98460	−	33.9404i	−0.222109	−	1.25964i
$727$	−1.68203	−	2.40218i	−0.0623829	−	0.0890920i	0.786749	−	0.617274i	$-0.211763\pi$
$727$	−1.68203	−	2.40218i	−0.0623829	−	0.0890920i	−0.849131	+	0.528182i	$0.822874\pi$
$728$	3.02262	+	6.48204i	0.112026	+	0.240240i
$729$	31.3216	−	18.0835i	1.16006	−	0.669759i
$730$		0			0
$731$	−2.24204	+	1.88129i	−0.0829247	+	0.0695821i
$732$	28.6722	+	2.50850i	1.05976	+	0.0927167i
$733$	7.39993	−	1.98280i	0.273322	−	0.0732365i	−0.119554	−	0.992828i	$-0.538147\pi$
$733$	7.39993	−	1.98280i	0.273322	−	0.0732365i	0.392877	+	0.919591i	$0.371480\pi$
$734$	7.60750	+	13.1766i	0.280798	+	0.486356i
$735$		0			0
$736$	−4.24628	−	0.748733i	−0.156520	−	0.0275987i
$737$	−1.53511	+	2.19237i	−0.0565466	+	0.0807569i
$738$	25.2110	+	11.7561i	0.928030	+	0.432747i
$739$	−18.5636	+	22.1232i	−0.682872	+	0.813815i	−0.990474	−	0.137700i	$-0.956029\pi$
$739$	−18.5636	+	22.1232i	−0.682872	+	0.813815i	0.307602	+	0.951515i	$0.400473\pi$
$740$		0			0
$741$	−34.4939	−	86.2361i	−1.26716	−	3.16796i
$742$	4.10041	−	4.10041i	0.150531	−	0.150531i
$743$	17.3020	−	1.51373i	0.634749	−	0.0555334i	0.234760	−	0.972053i	$-0.424569\pi$
$743$	17.3020	−	1.51373i	0.634749	−	0.0555334i	0.399989	+	0.916520i	$0.369014\pi$
$744$	21.7539	−	7.91777i	0.797537	−	0.290280i
$745$		0			0
$746$	1.11165	−	6.30449i	0.0407005	−	0.230824i
$747$	66.0348	−	30.7925i	2.41609	−	1.12664i
$748$	0.114845	−	0.428609i	0.00419917	−	0.0156715i
$749$	0.726939	−	1.25910i	0.0265618	−	0.0460063i
$750$		0			0
$751$	−0.788580	−	0.939792i	−0.0287757	−	0.0342935i	0.751465	−	0.659773i	$-0.229348\pi$
$751$	−0.788580	−	0.939792i	−0.0287757	−	0.0342935i	−0.780240	+	0.625480i	$0.784903\pi$
$752$	−2.80774	−	10.4786i	−0.102388	−	0.382116i
$753$	−28.7520	−	7.70406i	−1.04778	−	0.280752i
$754$	5.48346	+	1.99581i	0.199696	+	0.0726833i
$755$		0			0
$756$	−15.0601	+	2.65551i	−0.547732	+	0.0965800i
$757$	9.40023	−	20.1588i	0.341657	−	0.732686i	−0.658139	−	0.752897i	$-0.728656\pi$
$757$	9.40023	−	20.1588i	0.341657	−	0.732686i	0.999796	+	0.0202109i	$0.00643375\pi$
$758$	−2.88891	−	33.0204i	−0.104930	−	1.19935i
$759$	7.68972			0.279119
$760$		0			0
$761$	−28.7440			−1.04197			−0.520985	−	0.853566i	$-0.674435\pi$
$761$	−28.7440			−1.04197			−0.520985	+	0.853566i	$0.674435\pi$
$762$	−1.18785	−	13.5772i	−0.0430314	−	0.491851i
$763$	−6.17902	+	13.2509i	−0.223696	+	0.479717i
$764$	19.9983	−	3.52624i	0.723513	−	0.127575i
$765$		0			0
$766$	−24.6090	−	8.95694i	−0.889159	−	0.323627i
$767$	−7.98220	−	2.13882i	−0.288220	−	0.0772284i
$768$	−0.834123	−	3.11299i	−0.0300988	−	0.112330i
$769$	−11.7488	−	14.0016i	−0.423671	−	0.504912i	0.511414	−	0.859334i	$-0.329122\pi$
$769$	−11.7488	−	14.0016i	−0.423671	−	0.504912i	−0.935085	+	0.354423i	$0.884677\pi$
$770$		0			0
$771$	21.3649	−	37.0051i	0.769438	−	1.33271i
$772$	−4.88834	+	18.2435i	−0.175935	+	0.656599i
$773$	31.7979	−	14.8276i	1.14369	−	0.533312i	0.243972	−	0.969782i	$-0.421549\pi$
$773$	31.7979	−	14.8276i	1.14369	−	0.533312i	0.899719	+	0.436470i	$0.143772\pi$
$774$	4.68164	−	26.5509i	0.168278	−	0.954351i
$775$		0			0
$776$	1.24581	−	0.453437i	0.0447219	−	0.0162774i
$777$	20.5313	−	1.79626i	0.736557	−	0.0644404i
$778$	20.7231	−	20.7231i	0.742959	−	0.742959i
$779$	10.9417	+	12.2372i	0.392027	+	0.438442i
$780$		0			0
$781$	0.238835	−	0.284632i	0.00854617	−	0.0101849i
$782$	−3.13350	−	1.46118i	−0.112054	−	0.0522516i
$783$	−7.15652	+	10.2206i	−0.255753	+	0.365253i
$784$	−5.74123	−	1.01233i	−0.205044	−	0.0361548i
$785$		0			0
$786$	6.64114	+	11.5028i	0.236882	+	0.410291i
$787$	45.1052	−	12.0859i	1.60783	−	0.430816i	0.660432	−	0.750886i	$-0.270373\pi$
$787$	45.1052	−	12.0859i	1.60783	−	0.430816i	0.947394	+	0.320070i	$0.103707\pi$
$788$	−13.6689	−	1.19587i	−0.486935	−	0.0426013i
$789$	59.1652	−	49.6455i	2.10634	−	1.76743i
$790$		0			0
$791$	−1.25855	+	0.726625i	−0.0447489	+	0.0258358i
$792$	1.72745	+	3.70452i	0.0613821	+	0.131634i
$793$	33.8673	+	48.3676i	1.20266	+	1.71758i
$794$	−4.01889	−	22.7923i	−0.142625	−	0.808868i
$795$		0			0
$796$	15.8621	+	13.3099i	0.562216	+	0.471755i
$797$	−7.75145	−	7.75145i	−0.274570	−	0.274570i	0.556367	−	0.830937i	$-0.312195\pi$
$797$	−7.75145	−	7.75145i	−0.274570	−	0.274570i	−0.830937	+	0.556367i	$0.812195\pi$
$798$	−14.7949	−	3.46982i	−0.523735	−	0.122830i
$799$		−	8.69878i		−	0.307741i
$800$		0			0
$801$	−20.8956	−	57.4101i	−0.738309	−	2.02849i
$802$	11.1086	+	7.77835i	0.392259	+	0.274663i
$803$	−5.63286	+	3.94417i	−0.198779	+	0.139187i
$804$	−5.33107	+	14.6470i	−0.188012	+	0.516560i
$805$		0			0
$806$	41.1296	+	23.7462i	1.44873	+	0.836424i
$807$	−2.32035	+	26.5217i	−0.0816801	+	0.933608i
$808$	−1.12236	+	12.8286i	−0.0394844	+	0.451309i
$809$	−31.3800	−	18.1173i	−1.10326	−	0.636969i	−0.166187	−	0.986094i	$-0.553145\pi$
$809$	−31.3800	−	18.1173i	−1.10326	−	0.636969i	−0.937076	+	0.349125i	$0.886479\pi$
$810$		0			0
$811$	7.95465	−	21.8552i	0.279326	−	0.767441i	−0.718114	−	0.695926i	$-0.754994\pi$
$811$	7.95465	−	21.8552i	0.279326	−	0.767441i	0.997440	−	0.0715151i	$-0.0227834\pi$
$812$	0.782089	−	0.547625i	0.0274459	−	0.0192179i
$813$	−51.3272	−	35.9397i	−1.80013	−	1.26046i
$814$	−1.11887	−	3.07408i	−0.0392165	−	0.107746i
$815$		0			0
$816$		−	2.58423i		−	0.0904662i
$817$	8.71142	−	13.3130i	0.304774	−	0.465763i
$818$	12.1943	+	12.1943i	0.426363	+	0.426363i
$819$	−40.4694	−	33.9578i	−1.41411	−	1.18658i
$820$		0			0
$821$	−0.0396201	−	0.224697i	−0.00138275	−	0.00784197i	0.984109	−	0.177568i	$-0.0568229\pi$
$821$	−0.0396201	−	0.224697i	−0.00138275	−	0.00784197i	−0.985491	+	0.169726i	$0.945712\pi$
$822$	33.0441	+	47.1918i	1.15254	+	1.64600i
$823$	−23.4587	−	50.3073i	−0.817718	−	1.75360i	−0.638237	−	0.769840i	$-0.720336\pi$
$823$	−23.4587	−	50.3073i	−0.817718	−	1.75360i	−0.179481	−	0.983761i	$-0.557442\pi$
$824$	0.00293642	−	0.00169534i	0.000102295	−	5.90601e-5i
$825$		0			0
$826$	−1.03575	+	0.869099i	−0.0360384	+	0.0302398i
$827$	−44.5958	−	3.90163i	−1.55075	−	0.135673i	−0.720654	−	0.693295i	$-0.756158\pi$
$827$	−44.5958	−	3.90163i	−1.55075	−	0.135673i	−0.830095	+	0.557622i	$0.811714\pi$
$828$	30.7636	−	8.24308i	1.06911	−	0.286467i
$829$	10.1012	+	17.4958i	0.350830	+	0.607655i	0.986395	−	0.164392i	$-0.0525662\pi$
$829$	10.1012	+	17.4958i	0.350830	+	0.607655i	−0.635565	+	0.772047i	$0.719233\pi$
$830$		0			0
$831$	−61.6822	−	10.8762i	−2.13973	−	0.377292i
$832$	3.79226	−	5.41590i	0.131473	−	0.187763i
$833$	−4.23670	−	1.97560i	−0.146793	−	0.0684506i
$834$	−7.14401	+	8.51390i	−0.247377	+	0.294812i
$835$		0			0
$836$	0.0758126	+	2.41092i	0.00262203	+	0.0833833i
$837$	−71.8044	+	71.8044i	−2.48192	+	2.48192i
$838$	−9.02118	+	0.789251i	−0.311631	+	0.0272642i
$839$	3.61774	−	1.31675i	0.124898	−	0.0454592i	−0.278815	−	0.960345i	$-0.589942\pi$
$839$	3.61774	−	1.31675i	0.124898	−	0.0454592i	0.403713	+	0.914886i	$0.367719\pi$
$840$		0			0
$841$	−4.90053	+	27.7923i	−0.168984	+	0.958355i
$842$	8.73765	−	4.07443i	0.301119	−	0.140414i
$843$	−4.80864	+	17.9461i	−0.165618	+	0.618096i
$844$	6.35344	−	11.0045i	0.218694	−	0.378790i
$845$		0			0
$846$	51.5068	+	61.3834i	1.77084	+	2.11041i
$847$	−2.99403	−	11.1739i	−0.102876	−	0.383939i
$848$	−5.17793	−	1.38742i	−0.177811	−	0.0476443i
$849$	−22.6843	−	8.25641i	−0.778524	−	0.283359i
$850$		0			0
$851$	−25.1025	+	4.42625i	−0.860504	+	0.151730i
$852$	0.914517	−	1.96119i	0.0313308	−	0.0671892i
$853$	−3.14093	−	35.9009i	−0.107543	−	1.22922i	−0.837771	−	0.546021i	$-0.816142\pi$
$853$	−3.14093	−	35.9009i	−0.107543	−	1.22922i	0.730228	−	0.683203i	$-0.239414\pi$
$854$	9.66080			0.330586
$855$		0			0
$856$	−1.34400			−0.0459369
$857$	−0.681293	−	7.78722i	−0.0232725	−	0.266006i	−0.998912	−	0.0466277i	$-0.985153\pi$
$857$	−0.681293	−	7.78722i	−0.0232725	−	0.266006i	0.975640	−	0.219379i	$-0.0704030\pi$
$858$	−4.98320	+	10.6865i	−0.170124	+	0.364831i
$859$	21.7191	−	3.82966i	0.741045	−	0.130666i	0.209633	−	0.977780i	$-0.432773\pi$
$859$	21.7191	−	3.82966i	0.741045	−	0.130666i	0.531411	+	0.847114i	$0.321662\pi$
$860$		0			0
$861$	12.3375	+	4.49048i	0.420461	+	0.153035i
$862$	−6.72166	−	1.80106i	−0.228941	−	0.0613445i
$863$	−12.7626	−	47.6306i	−0.434443	−	1.62136i	−0.742395	−	0.669963i	$-0.766310\pi$
$863$	−12.7626	−	47.6306i	−0.434443	−	1.62136i	0.307952	−	0.951402i	$-0.400357\pi$
$864$	9.08690	+	10.8293i	0.309143	+	0.368422i
$865$		0			0
$866$	−3.52459	+	6.10477i	−0.119770	+	0.207448i
$867$	−13.6438	+	50.9192i	−0.463367	+	1.72931i
$868$	7.04243	−	3.28394i	0.239036	−	0.111464i
$869$	−0.835370	+	4.73762i	−0.0283380	+	0.160713i
$870$		0			0
$871$	−30.0484	+	10.9367i	−1.01815	+	0.370576i
$872$	13.4644	−	1.17798i	0.455961	−	0.0398914i
$873$	−6.92447	+	6.92447i	−0.234358	+	0.234358i
$874$	18.6025	+	2.68030i	0.629240	+	0.0906624i
$875$		0			0
$876$	−25.7422	+	30.6784i	−0.869749	+	1.03653i
$877$	−27.5456	−	12.8447i	−0.930149	−	0.433735i	−0.102342	−	0.994749i	$-0.532634\pi$
$877$	−27.5456	−	12.8447i	−0.930149	−	0.433735i	−0.827806	+	0.561014i	$0.810411\pi$
$878$	0.606589	−	0.866299i	0.0204714	−	0.0292362i
$879$	−33.0820	−	5.83325i	−1.11583	−	0.196751i
$880$		0			0
$881$	−8.38881	−	14.5298i	−0.282626	−	0.489523i	0.689405	−	0.724376i	$-0.257872\pi$
$881$	−8.38881	−	14.5298i	−0.282626	−	0.489523i	−0.972031	+	0.234854i	$0.924539\pi$
$882$	41.5943	−	11.1452i	1.40055	−	0.375277i
$883$	9.12991	+	0.798763i	0.307246	+	0.0268805i	0.239736	−	0.970838i	$-0.422939\pi$
$883$	9.12991	+	0.798763i	0.307246	+	0.0268805i	0.0675097	+	0.997719i	$0.478495\pi$
$884$	4.06123	−	3.40778i	0.136594	−	0.114616i
$885$		0			0
$886$	4.22679	−	2.44034i	0.142002	−	0.0819848i
$887$	−2.05420	−	4.40525i	−0.0689734	−	0.147914i	0.868799	−	0.495166i	$-0.164893\pi$
$887$	−2.05420	−	4.40525i	−0.0689734	−	0.147914i	−0.937772	+	0.347252i	$0.887115\pi$
$888$	−10.9278	−	15.6066i	−0.366714	−	0.523722i
$889$	−0.794388	−	4.50520i	−0.0266429	−	0.151100i
$890$		0			0
$891$	−9.91969	−	8.32360i	−0.332322	−	0.278851i
$892$	−7.54741	−	7.54741i	−0.252706	−	0.252706i
$893$	13.6682	+	45.2681i	0.457388	+	1.51484i
$894$			25.2803i			0.845501i
$895$		0			0
$896$	−0.369983	−	1.01652i	−0.0123602	−	0.0339595i
$897$	75.2595	+	52.6973i	2.51284	+	1.75951i
$898$	−25.8807	+	18.1219i	−0.863650	+	0.604734i
$899$	2.16836	−	5.95752i	0.0723188	−	0.198694i
$900$		0			0
$901$	−3.72255	−	2.14922i	−0.124016	−	0.0716007i
$902$	0.181633	−	2.07607i	0.00604770	−	0.0691255i
$903$	1.10905	−	12.6765i	0.0369068	−	0.421847i
$904$	1.16343	+	0.671708i	0.0386952	+	0.0223407i
$905$		0			0
$906$	−11.6870	+	32.1097i	−0.388273	+	1.06677i
$907$	0.0211732	−	0.0148257i	0.000703046	−	0.000492278i	−0.573225	−	0.819398i	$-0.694308\pi$
$907$	0.0211732	−	0.0148257i	0.000703046	−	0.000492278i	0.573928	+	0.818906i	$0.305419\pi$
$908$	−21.4285	−	15.0044i	−0.711130	−	0.497939i
$909$	−32.5329	−	89.3835i	−1.07905	−	2.96466i
$910$		0			0
$911$			59.0698i			1.95707i	0.206084	+	0.978534i	$0.433928\pi$
$911$			59.0698i			1.95707i	−0.206084	+	0.978534i	$0.566072\pi$
$912$	4.06054	+	13.4482i	0.134458	+	0.445315i
$913$	−3.85980	−	3.85980i	−0.127741	−	0.127741i
$914$	0.214875	+	0.180301i	0.00710742	+	0.00596384i
$915$		0			0
$916$	−0.614645	−	3.48582i	−0.0203084	−	0.115175i
$917$	2.55717	+	3.65202i	0.0844452	+	0.120600i
$918$	4.79065	+	10.2736i	0.158115	+	0.339079i
$919$	−28.1521	+	16.2536i	−0.928651	+	0.536157i	−0.886385	−	0.462950i	$-0.846791\pi$
$919$	−28.1521	+	16.2536i	−0.928651	+	0.536157i	−0.0422661	+	0.999106i	$0.513458\pi$
$920$		0			0
$921$	−20.3006	+	17.0342i	−0.668928	+	0.561297i
$922$	−15.0148	−	1.31362i	−0.494486	−	0.0432619i
$923$	4.28805	−	1.14898i	0.141143	−	0.0378191i
$924$	0.964613	+	1.67076i	0.0317334	+	0.0549639i
$925$		0			0
$926$	−36.0046	−	6.34858i	−1.18318	−	0.208627i
$927$	−0.0143653	+	0.0205158i	−0.000471819	+	0.000673828i
$928$	−0.799904	−	0.373001i	−0.0262581	−	0.0122444i
$929$	24.6735	−	29.4048i	0.809513	−	0.964740i	−0.190343	−	0.981718i	$-0.560960\pi$
$929$	24.6735	−	29.4048i	0.809513	−	0.964740i	0.999856	+	0.0169777i	$0.00540444\pi$
$930$		0			0
$931$	25.1518	+	3.62393i	0.824317	+	0.118770i
$932$	8.96797	−	8.96797i	0.293756	−	0.293756i
$933$	−35.6630	+	3.12011i	−1.16755	+	0.102148i
$934$	13.8815	−	5.05245i	0.454216	−	0.165321i
$935$		0			0
$936$	−8.48034	+	48.0944i	−0.277188	+	1.57201i
$937$	−7.54932	+	3.52031i	−0.246626	+	0.115003i	−0.542001	−	0.840378i	$-0.682333\pi$
$937$	−7.54932	+	3.52031i	−0.246626	+	0.115003i	0.295375	+	0.955381i	$0.404555\pi$
$938$	−1.35411	+	5.05361i	−0.0442133	+	0.165006i
$939$	44.9246	−	77.8116i	1.46606	−	2.53929i
$940$		0			0
$941$	9.88263	+	11.7777i	0.322164	+	0.383941i	0.902683	−	0.430306i	$-0.141595\pi$
$941$	9.88263	+	11.7777i	0.322164	+	0.383941i	−0.580518	+	0.814247i	$0.697150\pi$
$942$	8.98349	+	33.5268i	0.292698	+	1.09236i
$943$	−15.6848	−	4.20272i	−0.510767	−	0.136859i
$944$	1.17451	+	0.427488i	0.0382272	+	0.0139135i
$945$		0			0
$946$	−1.98913	+	0.350736i	−0.0646720	+	0.0114034i
$947$	−19.8478	+	42.5638i	−0.644967	+	1.38314i	0.263287	+	0.964718i	$0.415193\pi$
$947$	−19.8478	+	42.5638i	−0.644967	+	1.38314i	−0.908254	+	0.418419i	$0.862584\pi$
$948$	2.44185	+	27.9104i	0.0793075	+	0.906489i
$949$	−82.1583			−2.66697
$950$		0			0
$951$	80.2122			2.60106
$952$	−0.0756002	−	0.864115i	−0.00245022	−	0.0280061i
$953$	19.7865	−	42.4323i	0.640948	−	1.37452i	−0.270347	−	0.962763i	$-0.587138\pi$
$953$	19.7865	−	42.4323i	0.640948	−	1.37452i	0.911295	−	0.411754i	$-0.135084\pi$
$954$	38.9942	−	6.87573i	1.26248	−	0.222610i
$955$		0			0
$956$	−0.866723	−	0.315461i	−0.0280318	−	0.0102027i
$957$	1.52041	+	0.407392i	0.0491477	+	0.0131691i
$958$	−0.671065	−	2.50445i	−0.0216811	−	0.0809151i
$959$	12.4298	+	14.8133i	0.401380	+	0.478347i
$960$		0			0
$961$	10.2991	−	17.8386i	0.332230	−	0.575439i
$962$	10.1161	−	37.7537i	0.326155	−	1.21723i
$963$	8.99727	−	4.19550i	0.289933	−	0.135198i
$964$	−0.790656	+	4.48403i	−0.0254653	+	0.144421i
$965$		0			0
$966$	14.1256	−	5.14129i	0.454483	−	0.165418i
$967$	18.9628	−	1.65903i	0.609803	−	0.0533509i	0.221928	−	0.975063i	$-0.428765\pi$
$967$	18.9628	−	1.65903i	0.609803	−	0.0533509i	0.387875	+	0.921712i	$0.373209\pi$
$968$	−7.56164	+	7.56164i	−0.243040	+	0.243040i
$969$	0.354041	+	11.2588i	0.0113734	+	0.361686i
$970$		0			0
$971$	33.0438	−	39.3800i	1.06043	−	1.26377i	0.0971443	−	0.995270i	$-0.469029\pi$
$971$	33.0438	−	39.3800i	1.06043	−	1.26377i	0.963281	−	0.268495i	$-0.0865264\pi$
$972$	−29.9126	−	13.9485i	−0.959447	−	0.447398i
$973$	−2.13974	+	3.05587i	−0.0685970	+	0.0979667i
$974$	13.2690	+	2.33967i	0.425165	+	0.0749680i
$975$		0			0
$976$	−4.46533	−	7.73418i	−0.142932	−	0.247565i
$977$	35.1631	−	9.42193i	1.12497	−	0.301434i	0.352076	−	0.935971i	$-0.385476\pi$
$977$	35.1631	−	9.42193i	1.12497	−	0.301434i	0.772892	+	0.634537i	$0.218809\pi$
$978$	59.0653	+	5.16754i	1.88870	+	0.165240i
$979$	−3.50623	+	2.94207i	−0.112059	+	0.0940291i
$980$		0			0
$981$	−86.4587	+	49.9170i	−2.76042	+	1.59373i
$982$	18.0097	+	38.6219i	0.574712	+	1.23247i
$983$	−4.55582	−	6.50639i	−0.145308	−	0.207521i	0.739900	−	0.672717i	$-0.234873\pi$
$983$	−4.55582	−	6.50639i	−0.145308	−	0.207521i	−0.885208	+	0.465196i	$0.845984\pi$
$984$	−2.10757	−	11.9526i	−0.0671868	−	0.381036i
$985$		0			0
$986$	−0.542143	−	0.454912i	−0.0172653	−	0.0144873i
$987$	26.7429	+	26.7429i	0.851237	+	0.851237i
$988$	−15.7799	+	24.1153i	−0.502026	+	0.767208i
$989$			15.7379i			0.500437i
$990$		0			0
$991$	−9.78018	−	26.8708i	−0.310678	−	0.853580i	−0.992520	−	0.122081i	$-0.961043\pi$
$991$	−9.78018	−	26.8708i	−0.310678	−	0.853580i	0.681843	−	0.731499i	$-0.261179\pi$
$992$	−5.88413	−	4.12011i	−0.186821	−	0.130814i
$993$	12.7910	−	8.95639i	0.405912	−	0.284222i
$994$	0.248423	−	0.682535i	0.00787949	−	0.0216487i
$995$		0			0
$996$	−27.5312	−	15.8951i	−0.872359	−	0.503657i
$997$	3.01784	−	34.4941i	0.0955760	−	1.09244i	−0.785308	−	0.619106i	$-0.787495\pi$
$997$	3.01784	−	34.4941i	0.0955760	−	1.09244i	0.880884	−	0.473333i	$-0.156949\pi$
$998$	1.59562	−	18.2381i	0.0505086	−	0.577316i
$999$	72.3749	+	41.7857i	2.28984	+	1.32204i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.e.193.5		120
5.2	odd	4	inner	950.2.bb.e.307.6		120
5.3	odd	4		190.2.r.a.117.5	yes	120
5.4	even	2		190.2.r.a.3.6	✓	120
19.13	odd	18	inner	950.2.bb.e.393.6		120
95.13	even	36		190.2.r.a.127.6	yes	120
95.32	even	36	inner	950.2.bb.e.507.5		120
95.89	odd	18		190.2.r.a.13.5	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.r.a.3.6	✓	120	5.4	even	2
190.2.r.a.13.5	yes	120	95.89	odd	18
190.2.r.a.117.5	yes	120	5.3	odd	4
190.2.r.a.127.6	yes	120	95.13	even	36
950.2.bb.e.193.5		120	1.1	even	1	trivial
950.2.bb.e.307.6		120	5.2	odd	4	inner
950.2.bb.e.393.6		120	19.13	odd	18	inner
950.2.bb.e.507.5		120	95.32	even	36	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(1.36202 - 2.92085i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-3.02844 - 1.10226i) q^{6} +(-1.04490 - 0.279979i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-4.74793 - 5.65836i) q^{9} +O(q^{10})\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(1.36202 - 2.92085i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-3.02844 - 1.10226i) q^{6} +(-1.04490 - 0.279979i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-4.74793 - 5.65836i) q^{9} +(-0.276688 + 0.479237i) q^{11} +(-0.834123 + 3.11299i) q^{12} +(-5.99214 + 2.79418i) q^{13} +(-0.187845 + 1.06532i) q^{14} +(0.939693 - 0.342020i) q^{16} +(0.798807 - 0.0698866i) q^{17} +(-5.22302 + 5.22302i) q^{18} +(-4.04714 + 1.61883i) q^{19} +(-2.24094 + 2.67065i) q^{21} +(0.501528 + 0.233867i) q^{22} +(2.47314 - 3.53200i) q^{23} +(3.17384 + 0.559634i) q^{24} +(3.30580 + 5.72581i) q^{26} +(-13.6550 + 3.65885i) q^{27} +(1.07764 + 0.0942813i) q^{28} +(0.676108 - 0.567322i) q^{29} +(6.22083 - 3.59160i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(1.02293 + 1.46089i) q^{33} +(-0.139241 - 0.789676i) q^{34} +(5.65836 + 4.74793i) q^{36} +(-4.18017 - 4.18017i) q^{37} +(1.96540 + 3.89065i) q^{38} +21.3079i q^{39} +(-1.28804 - 3.53886i) q^{41} +(2.85580 + 1.99965i) q^{42} +(-2.98989 + 2.09354i) q^{43} +(0.189266 - 0.520003i) q^{44} +(-3.73411 - 2.15589i) q^{46} +(0.945489 - 10.8070i) q^{47} +(0.280886 - 3.21054i) q^{48} +(-5.04876 - 2.91490i) q^{49} +(0.883859 - 2.42838i) q^{51} +(5.41590 - 3.79226i) q^{52} +(-4.39113 - 3.07471i) q^{53} +(4.83504 + 13.2842i) q^{54} -1.08176i q^{56} +(-0.783903 + 14.0260i) q^{57} +(-0.624090 - 0.624090i) q^{58} +(0.957472 + 0.803415i) q^{59} +(-1.55079 - 8.79498i) q^{61} +(-4.12011 - 5.88413i) q^{62} +(3.37687 + 7.24172i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(1.36618 - 1.14636i) q^{66} +(4.81807 + 0.421526i) q^{67} +(-0.774536 + 0.207536i) q^{68} +(-6.94801 - 12.0343i) q^{69} +(-0.661243 - 0.116595i) q^{71} +(4.23670 - 6.05064i) q^{72} +(11.2621 + 5.25162i) q^{73} +(-3.79994 + 4.52859i) q^{74} +(3.70455 - 2.29702i) q^{76} +(0.423286 - 0.423286i) q^{77} +(21.2268 - 1.85710i) q^{78} +(8.16910 - 2.97331i) q^{79} +(-4.06344 + 23.0449i) q^{81} +(-3.41314 + 1.59157i) q^{82} +(-2.55303 + 9.52805i) q^{83} +(1.74314 - 3.01921i) q^{84} +(2.34616 + 2.79605i) q^{86} +(-0.736194 - 2.74751i) q^{87} +(-0.534520 - 0.143224i) q^{88} +(7.77234 + 2.82890i) q^{89} +(7.04348 - 1.24196i) q^{91} +(-1.82224 + 3.90780i) q^{92} +(-2.01766 - 23.0619i) q^{93} -10.8483 q^{94} -3.22280 q^{96} +(-0.115548 - 1.32071i) q^{97} +(-2.46378 + 5.28360i) q^{98} +(4.02539 - 0.709785i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^7	\( 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) \) 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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