LMFDB - Embedded newform 750.2.l.b.107.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(107,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("750.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.l (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			107.8
Character	$\chi$	$=$	750.107
Dual form			750.2.l.b.743.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.891007 + 0.453990i) q^{2} +(0.322239 + 1.70181i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-0.485490 + 1.66262i) q^{6} +(-0.0556476 - 0.0556476i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-2.79232 + 1.09678i) q^{9} +O(q^{10})$	\(q+(0.891007 + 0.453990i) q^{2} +(0.322239 + 1.70181i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-0.485490 + 1.66262i) q^{6} +(-0.0556476 - 0.0556476i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-2.79232 + 1.09678i) q^{9} +(-1.04749 + 0.340351i) q^{11} +(-1.18739 + 1.26100i) q^{12} +(2.31368 + 4.54086i) q^{13} +(-0.0243189 - 0.0748459i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-3.10226 + 0.491350i) q^{17} +(-2.98591 - 0.290452i) q^{18} +(-0.824223 + 1.13445i) q^{19} +(0.0767699 - 0.112634i) q^{21} +(-1.08784 - 0.172297i) q^{22} +(-1.13408 + 2.22575i) q^{23} +(-1.63045 + 0.584493i) q^{24} +5.09632i q^{26} +(-2.76630 - 4.39859i) q^{27} +(0.0123110 - 0.0777287i) q^{28} +(5.66803 - 4.11807i) q^{29} +(7.72991 + 5.61611i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.916756 - 1.67296i) q^{33} +(-2.98720 - 0.970601i) q^{34} +(-2.52860 - 1.61437i) q^{36} +(-9.23065 + 4.70325i) q^{37} +(-1.24942 + 0.636609i) q^{38} +(-6.98213 + 5.40069i) q^{39} +(3.55210 + 1.15415i) q^{41} +(0.119537 - 0.0655044i) q^{42} +(1.00563 - 1.00563i) q^{43} +(-0.891050 - 0.647386i) q^{44} +(-2.02094 + 1.46830i) q^{46} +(1.98797 - 12.5515i) q^{47} +(-1.71810 - 0.219422i) q^{48} -6.99381i q^{49} +(-1.83585 - 5.12113i) q^{51} +(-2.31368 + 4.54086i) q^{52} +(6.70559 + 1.06206i) q^{53} +(-0.467880 - 5.17504i) q^{54} +(0.0462573 - 0.0636677i) q^{56} +(-2.19621 - 1.03711i) q^{57} +(6.91981 - 1.09599i) q^{58} +(2.03647 - 6.26761i) q^{59} +(1.23324 + 3.79553i) q^{61} +(4.33774 + 8.51329i) q^{62} +(0.216419 + 0.0943531i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-0.0573270 - 1.90682i) q^{66} +(1.04169 + 6.57696i) q^{67} +(-2.22097 - 2.22097i) q^{68} +(-4.15326 - 1.21276i) q^{69} +(-7.51096 - 10.3379i) q^{71} +(-1.52009 - 2.58637i) q^{72} +(-1.18329 - 0.602914i) q^{73} -10.3598 q^{74} -1.40225 q^{76} +(0.0772302 + 0.0393507i) q^{77} +(-8.67298 + 1.64223i) q^{78} +(5.85354 + 8.05671i) q^{79} +(6.59415 - 6.12512i) q^{81} +(2.64098 + 2.64098i) q^{82} +(0.137997 + 0.871279i) q^{83} +(0.136247 - 0.00409615i) q^{84} +(1.35257 - 0.439477i) q^{86} +(8.83463 + 8.31892i) q^{87} +(-0.500025 - 0.981353i) q^{88} +(1.01326 + 3.11850i) q^{89} +(0.123937 - 0.381439i) q^{91} +(-2.46727 + 0.390777i) q^{92} +(-7.06668 + 14.9646i) q^{93} +(7.46957 - 10.2810i) q^{94} +(-1.43122 - 0.975505i) q^{96} +(10.2531 + 1.62393i) q^{97} +(3.17512 - 6.23153i) q^{98} +(2.55165 - 2.09924i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) $ 80 * q - 4 * q^3 - 4 * q^7	$ 80 q - 4 q^{3} - 4 q^{7} + 4 q^{12} + 20 q^{16} + 8 q^{18} - 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} - 40 q^{34} + 24 q^{37} - 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} + 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} + 80 q^{79} - 40 q^{81} - 96 q^{82} + 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97}+O(q^{100}) $ 80 * q - 4 * q^3 - 4 * q^7 + 4 * q^12 + 20 * q^16 + 8 * q^18 - 40 * q^19 + 36 * q^22 - 4 * q^27 + 16 * q^28 - 4 * q^33 - 40 * q^34 + 24 * q^37 - 40 * q^39 + 4 * q^42 + 24 * q^43 + 4 * q^48 + 64 * q^57 - 20 * q^58 - 64 * q^63 - 96 * q^67 + 140 * q^69 - 8 * q^72 - 100 * q^73 - 100 * q^78 + 80 * q^79 - 40 * q^81 - 96 * q^82 + 60 * q^84 - 80 * q^87 - 4 * q^88 - 12 * q^93 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$-1$

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 $

$2$	0.891007	+	0.453990i	0.630037	+	0.321020i
$2$	0.891007	+	0.453990i	0.630037	+	0.321020i
$3$	0.322239	+	1.70181i	0.186045	+	0.982541i
$3$	0.322239	+	1.70181i	0.186045	+	0.982541i
$4$	0.587785	+	0.809017i	0.293893	+	0.404508i
$5$		0			0
$5$		0			0
$6$	−0.485490	+	1.66262i	−0.198200	+	0.678761i
$7$	−0.0556476	−	0.0556476i	−0.0210328	−	0.0210328i	0.696512	−	0.717545i	$-0.254734\pi$
$7$	−0.0556476	−	0.0556476i	−0.0210328	−	0.0210328i	−0.717545	+	0.696512i	$0.754734\pi$
$8$	0.156434	+	0.987688i	0.0553079	+	0.349201i
$9$	−2.79232	+	1.09678i	−0.930775	+	0.365593i
$10$		0			0
$11$	−1.04749	+	0.340351i	−0.315831	+	0.102620i	−0.462643	−	0.886545i	$-0.653099\pi$
$11$	−1.04749	+	0.340351i	−0.315831	+	0.102620i	0.146812	+	0.989164i	$0.453099\pi$
$12$	−1.18739	+	1.26100i	−0.342769	+	0.364018i
$13$	2.31368	+	4.54086i	0.641700	+	1.25941i	0.951220	+	0.308514i	$0.0998317\pi$
$13$	2.31368	+	4.54086i	0.641700	+	1.25941i	−0.309520	+	0.950893i	$0.600168\pi$
$14$	−0.0243189	−	0.0748459i	−0.00649950	−	0.0200034i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−3.10226	+	0.491350i	−0.752408	+	0.119170i	−0.520846	−	0.853650i	$-0.674384\pi$
$17$	−3.10226	+	0.491350i	−0.752408	+	0.119170i	−0.231562	+	0.972820i	$0.574384\pi$
$18$	−2.98591	−	0.290452i	−0.703785	−	0.0684602i
$19$	−0.824223	+	1.13445i	−0.189090	+	0.260260i	−0.893028	−	0.450002i	$-0.851423\pi$
$19$	−0.824223	+	1.13445i	−0.189090	+	0.260260i	0.703938	+	0.710262i	$0.251423\pi$
$20$		0			0
$21$	0.0767699	−	0.112634i	0.0167526	−	0.0245787i
$22$	−1.08784	−	0.172297i	−0.231928	−	0.0367338i
$23$	−1.13408	+	2.22575i	−0.236472	+	0.464102i	−0.978495	−	0.206273i	$-0.933867\pi$
$23$	−1.13408	+	2.22575i	−0.236472	+	0.464102i	0.742023	+	0.670375i	$0.233867\pi$
$24$	−1.63045	+	0.584493i	−0.332814	+	0.119309i
$25$		0			0
$26$			5.09632i			0.999471i
$27$	−2.76630	−	4.39859i	−0.532376	−	0.846508i
$28$	0.0123110	−	0.0777287i	0.00232656	−	0.0146893i
$29$	5.66803	−	4.11807i	1.05253	−	0.764705i	0.0798355	−	0.996808i	$-0.474560\pi$
$29$	5.66803	−	4.11807i	1.05253	−	0.764705i	0.972691	+	0.232103i	$0.0745605\pi$
$30$		0			0
$31$	7.72991	+	5.61611i	1.38833	+	1.00868i	0.996046	+	0.0888399i	$0.0283160\pi$
$31$	7.72991	+	5.61611i	1.38833	+	1.00868i	0.392287	+	0.919843i	$0.371684\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−0.916756	−	1.67296i	−0.159587	−	0.291225i
$34$	−2.98720	−	0.970601i	−0.512301	−	0.166457i
$35$		0			0
$36$	−2.52860	−	1.61437i	−0.421433	−	0.269061i
$37$	−9.23065	+	4.70325i	−1.51751	+	0.773210i	−0.996755	−	0.0804961i	$-0.974350\pi$
$37$	−9.23065	+	4.70325i	−1.51751	+	0.773210i	−0.520755	+	0.853706i	$0.674350\pi$
$38$	−1.24942	+	0.636609i	−0.202682	+	0.103272i
$39$	−6.98213	+	5.40069i	−1.11803	+	0.864803i
$40$		0			0
$41$	3.55210	+	1.15415i	0.554745	+	0.180248i	0.572956	−	0.819586i	$-0.305797\pi$
$41$	3.55210	+	1.15415i	0.554745	+	0.180248i	−0.0182101	+	0.999834i	$0.505797\pi$
$42$	0.119537	−	0.0655044i	0.0184450	−	0.0101075i
$43$	1.00563	−	1.00563i	0.153357	−	0.153357i	−0.626258	−	0.779616i	$-0.715414\pi$
$43$	1.00563	−	1.00563i	0.153357	−	0.153357i	0.779616	+	0.626258i	$0.215414\pi$
$44$	−0.891050	−	0.647386i	−0.134331	−	0.0975971i
$45$		0			0
$46$	−2.02094	+	1.46830i	−0.297972	+	0.216489i
$47$	1.98797	−	12.5515i	0.289975	−	1.83083i	−0.225883	−	0.974154i	$-0.572527\pi$
$47$	1.98797	−	12.5515i	0.289975	−	1.83083i	0.515858	−	0.856674i	$-0.327473\pi$
$48$	−1.71810	−	0.219422i	−0.247986	−	0.0316708i
$49$		−	6.99381i		−	0.999115i
$50$		0			0
$51$	−1.83585	−	5.12113i	−0.257071	−	0.717101i
$52$	−2.31368	+	4.54086i	−0.320850	+	0.629704i
$53$	6.70559	+	1.06206i	0.921083	+	0.145885i	0.598929	−	0.800802i	$-0.295593\pi$
$53$	6.70559	+	1.06206i	0.921083	+	0.145885i	0.322154	+	0.946687i	$0.395593\pi$
$54$	−0.467880	−	5.17504i	−0.0636704	−	0.704234i
$55$		0			0
$56$	0.0462573	−	0.0636677i	0.00618139	−	0.00850795i
$57$	−2.19621	−	1.03711i	−0.290895	−	0.137369i
$58$	6.91981	−	1.09599i	0.908616	−	0.143911i
$59$	2.03647	−	6.26761i	0.265126	−	0.815974i	−0.726538	−	0.687126i	$-0.758872\pi$
$59$	2.03647	−	6.26761i	0.265126	−	0.815974i	0.991664	−	0.128848i	$-0.0411279\pi$
$60$		0			0
$61$	1.23324	+	3.79553i	0.157901	+	0.485968i	0.998443	−	0.0557774i	$-0.0177637\pi$
$61$	1.23324	+	3.79553i	0.157901	+	0.485968i	−0.840543	+	0.541745i	$0.817764\pi$
$62$	4.33774	+	8.51329i	0.550894	+	1.08119i
$63$	0.216419	+	0.0943531i	0.0272663	+	0.0118874i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$		0			0
$66$	−0.0573270	−	1.90682i	−0.00705647	−	0.234713i
$67$	1.04169	+	6.57696i	0.127263	+	0.803504i	0.965919	+	0.258844i	$0.0833414\pi$
$67$	1.04169	+	6.57696i	0.127263	+	0.803504i	−0.838657	+	0.544660i	$0.816659\pi$
$68$	−2.22097	−	2.22097i	−0.269332	−	0.269332i
$69$	−4.15326	−	1.21276i	−0.499993	−	0.146000i
$70$		0			0
$71$	−7.51096	−	10.3379i	−0.891387	−	1.22689i	−0.973135	−	0.230236i	$-0.926050\pi$
$71$	−7.51096	−	10.3379i	−0.891387	−	1.22689i	0.0817481	−	0.996653i	$-0.473950\pi$
$72$	−1.52009	−	2.58637i	−0.179144	−	0.304807i
$73$	−1.18329	−	0.602914i	−0.138493	−	0.0705658i	0.383371	−	0.923595i	$-0.374763\pi$
$73$	−1.18329	−	0.602914i	−0.138493	−	0.0705658i	−0.521864	+	0.853029i	$0.674763\pi$
$74$	−10.3598			−1.20430
$75$		0			0
$76$	−1.40225			−0.160849
$77$	0.0772302	+	0.0393507i	0.00880119	+	0.00448443i
$78$	−8.67298	+	1.64223i	−0.982022	+	0.185946i
$79$	5.85354	+	8.05671i	0.658575	+	0.906451i	0.999433	−	0.0336639i	$-0.0107176\pi$
$79$	5.85354	+	8.05671i	0.658575	+	0.906451i	−0.340858	+	0.940115i	$0.610718\pi$
$80$		0			0
$81$	6.59415	−	6.12512i	0.732684	−	0.680569i
$82$	2.64098	+	2.64098i	0.291647	+	0.291647i
$83$	0.137997	+	0.871279i	0.0151471	+	0.0956353i	0.994104	−	0.108433i	$-0.0345834\pi$
$83$	0.137997	+	0.871279i	0.0151471	+	0.0956353i	−0.978957	+	0.204069i	$0.934583\pi$
$84$	0.136247	−	0.00409615i	0.0148657	−	0.000446927i
$85$		0			0
$86$	1.35257	−	0.439477i	0.145851	−	0.0473900i
$87$	8.83463	+	8.31892i	0.947172	+	0.891882i
$88$	−0.500025	−	0.981353i	−0.0533028	−	0.104613i
$89$	1.01326	+	3.11850i	0.107406	+	0.330560i	0.990288	−	0.139035i	$-0.0444000\pi$
$89$	1.01326	+	3.11850i	0.107406	+	0.330560i	−0.882882	+	0.469595i	$0.844400\pi$
$90$		0			0
$91$	0.123937	−	0.381439i	0.0129921	−	0.0399856i
$92$	−2.46727	+	0.390777i	−0.257230	+	0.0407413i
$93$	−7.06668	+	14.9646i	−0.732781	+	1.55175i
$94$	7.46957	−	10.2810i	0.770427	−	1.06040i
$95$		0			0
$96$	−1.43122	−	0.975505i	−0.146073	−	0.0995621i
$97$	10.2531	+	1.62393i	1.04104	+	0.164885i	0.653469	−	0.756953i	$-0.273313\pi$
$97$	10.2531	+	1.62393i	1.04104	+	0.164885i	0.387575	+	0.921838i	$0.373313\pi$
$98$	3.17512	−	6.23153i	0.320736	−	0.629479i
$99$	2.55165	−	2.09924i	0.256450	−	0.210981i
$100$		0			0
$101$			14.0377i			1.39680i	0.715708	+	0.698399i	$0.246104\pi$
$101$			14.0377i			1.39680i	−0.715708	+	0.698399i	$0.753896\pi$
$102$	0.689188	−	5.39642i	0.0682398	−	0.534325i
$103$	2.06559	−	13.0416i	0.203529	−	1.28503i	−0.648371	−	0.761324i	$-0.724549\pi$
$103$	2.06559	−	13.0416i	0.203529	−	1.28503i	0.851900	−	0.523705i	$-0.175451\pi$
$104$	−4.12301	+	2.99554i	−0.404295	+	0.293737i
$105$		0			0
$106$	5.49256	+	3.99058i	0.533484	+	0.387599i
$107$	13.7619	−	13.7619i	1.33041	−	1.33041i	0.425413	−	0.904999i	$-0.360129\pi$
$107$	13.7619	−	13.7619i	1.33041	−	1.33041i	0.904999	−	0.425413i	$-0.139871\pi$
$108$	1.93254	−	4.82341i	0.185958	−	0.464133i
$109$	11.7044	+	3.80299i	1.12108	+	0.364260i	0.810178	−	0.586183i	$-0.199370\pi$
$109$	11.7044	+	3.80299i	1.12108	+	0.364260i	0.310898	+	0.950443i	$0.399370\pi$
$110$		0			0
$111$	−10.9785	−	14.1933i	−1.04204	−	1.34716i
$112$	0.0701201	−	0.0357280i	0.00662572	−	0.00337598i
$113$	−6.80204	+	3.46581i	−0.639882	+	0.326036i	−0.743654	−	0.668565i	$-0.766909\pi$
$113$	−6.80204	+	3.46581i	−0.639882	+	0.326036i	0.103771	+	0.994601i	$0.466909\pi$
$114$	−1.48600	−	1.92113i	−0.139177	−	0.179930i
$115$		0			0
$116$	6.66317	+	2.16499i	0.618660	+	0.201015i
$117$	−11.4409	−	10.1420i	−1.05771	−	0.937624i
$118$	4.65995	−	4.65995i	0.428983	−	0.428983i
$119$	0.199976	+	0.145291i	0.0183317	+	0.0133188i
$120$		0			0
$121$	−7.91779	+	5.75261i	−0.719799	+	0.522964i
$122$	−0.624308	+	3.94172i	−0.0565222	+	0.356867i
$123$	−0.819518	+	6.41692i	−0.0738935	+	0.578594i
$124$			9.55469i			0.858037i
$125$		0			0
$126$	0.149996	+	0.182322i	0.0133627	+	0.0162425i
$127$	1.46280	−	2.87091i	0.129803	−	0.254752i	−0.816954	−	0.576703i	$-0.804339\pi$
$127$	1.46280	−	2.87091i	0.129803	−	0.254752i	0.946756	+	0.321952i	$0.104339\pi$
$128$	−0.987688	−	0.156434i	−0.0873001	−	0.0138270i
$129$	2.03545	+	1.38734i	0.179211	+	0.122149i
$130$		0			0
$131$	3.12598	−	4.30255i	0.273118	−	0.375915i	−0.650321	−	0.759660i	$-0.725366\pi$
$131$	3.12598	−	4.30255i	0.273118	−	0.375915i	0.923439	+	0.383744i	$0.125366\pi$
$132$	0.814598	−	1.72501i	0.0709017	−	0.150143i
$133$	0.108995	−	0.0172632i	0.00945109	−	0.00149690i
$134$	−2.05773	+	6.33303i	−0.177761	+	0.547091i
$135$		0			0
$136$	−0.970601	−	2.98720i	−0.0832283	−	0.256150i
$137$	5.21451	+	10.2341i	0.445506	+	0.874354i	0.999135	+	0.0415907i	$0.0132426\pi$
$137$	5.21451	+	10.2341i	0.445506	+	0.874354i	−0.553629	+	0.832763i	$0.686757\pi$
$138$	−3.15000	−	2.96612i	−0.268146	−	0.252493i
$139$	10.3684	−	3.36891i	0.879440	−	0.285747i	0.165715	−	0.986174i	$-0.447007\pi$
$139$	10.3684	−	3.36891i	0.879440	−	0.285747i	0.713725	+	0.700426i	$0.247007\pi$
$140$		0			0
$141$	22.0009	−	0.661442i	1.85281	−	0.0557034i
$142$	−1.99898	−	12.6211i	−0.167751	−	1.05914i
$143$	−3.96905	−	3.96905i	−0.331909	−	0.331909i
$144$	−0.180223	−	2.99458i	−0.0150186	−	0.249548i
$145$		0			0
$146$	−0.780598	−	1.07440i	−0.0646028	−	0.0889181i
$147$	11.9021	−	2.25367i	0.981672	−	0.185880i
$148$	−9.23065	−	4.70325i	−0.758755	−	0.386605i
$149$	14.3679			1.17707			0.588534	−	0.808472i	$-0.299705\pi$
$149$	14.3679			1.17707			0.588534	+	0.808472i	$0.299705\pi$
$150$		0			0
$151$	−0.326435			−0.0265649			−0.0132824	−	0.999912i	$-0.504228\pi$
$151$	−0.326435			−0.0265649			−0.0132824	+	0.999912i	$0.504228\pi$
$152$	−1.24942	−	0.636609i	−0.101341	−	0.0516358i
$153$	8.12361	−	4.77450i	0.656755	−	0.385995i
$154$	0.0509477	+	0.0701235i	0.00410548	+	0.00565071i
$155$		0			0
$156$	−8.47324	−	2.47421i	−0.678402	−	0.198096i
$157$	3.47556	+	3.47556i	0.277380	+	0.277380i	0.832062	−	0.554682i	$-0.187160\pi$
$157$	3.47556	+	3.47556i	0.277380	+	0.277380i	−0.554682	+	0.832062i	$0.687160\pi$
$158$	1.55788	+	9.83604i	0.123938	+	0.782513i
$159$	0.353372	+	11.7539i	0.0280242	+	0.932144i
$160$		0			0
$161$	0.186967	−	0.0607491i	0.0147350	−	0.00478770i
$162$	8.65618	−	2.46384i	0.680094	−	0.193578i
$163$	0.695961	+	1.36590i	0.0545119	+	0.106986i	0.916655	−	0.399679i	$-0.130878\pi$
$163$	0.695961	+	1.36590i	0.0545119	+	0.106986i	−0.862143	+	0.506664i	$0.830878\pi$
$164$	1.15415	+	3.55210i	0.0901239	+	0.277373i
$165$		0			0
$166$	−0.272596	+	0.838964i	−0.0211576	+	0.0651163i
$167$	−22.1072	+	3.50144i	−1.71071	+	0.270949i	−0.933573	−	0.358387i	$-0.883327\pi$
$167$	−22.1072	+	3.50144i	−1.71071	+	0.270949i	−0.777133	+	0.629336i	$0.783327\pi$
$168$	0.123256	+	0.0582050i	0.00950943	+	0.00449061i
$169$	−7.62505	+	10.4950i	−0.586542	+	0.807306i
$170$		0			0
$171$	1.05726	−	4.07173i	0.0808509	−	0.311373i
$172$	1.40467	+	0.222477i	0.107105	+	0.0169637i
$173$	6.43491	−	12.6292i	0.489237	−	0.960182i	−0.505985	−	0.862542i	$-0.668871\pi$
$173$	6.43491	−	12.6292i	0.489237	−	0.960182i	0.995222	−	0.0976395i	$-0.0311292\pi$
$174$	4.09500	+	11.4230i	0.310441	+	0.865979i
$175$		0			0
$176$		−	1.10140i		−	0.0830211i
$177$	11.3225	+	1.44602i	0.851053	+	0.108690i
$178$	−0.512946	+	3.23861i	−0.0384469	+	0.242744i
$179$	−12.2896	+	8.92889i	−0.918565	+	0.667377i	−0.943167	−	0.332320i	$-0.892168\pi$
$179$	−12.2896	+	8.92889i	−0.918565	+	0.667377i	0.0246011	+	0.999697i	$0.492168\pi$
$180$		0			0
$181$	−8.30933	−	6.03708i	−0.617627	−	0.448733i	0.234465	−	0.972125i	$-0.424666\pi$
$181$	−8.30933	−	6.03708i	−0.617627	−	0.448733i	−0.852092	+	0.523392i	$0.824666\pi$
$182$	0.283598	−	0.283598i	0.0210217	−	0.0210217i
$183$	−6.06188	+	3.32181i	−0.448107	+	0.245556i
$184$	−2.37576	−	0.771931i	−0.175143	−	0.0569075i
$185$		0			0
$186$	−13.0902	+	10.1253i	−0.959823	+	0.742425i
$187$	3.08236	−	1.57054i	0.225405	−	0.114849i
$188$	11.3229	−	5.76930i	0.825807	−	0.420770i
$189$	−0.0908325	+	0.398709i	−0.00660709	+	0.0290018i
$190$		0			0
$191$	−10.3303	−	3.35652i	−0.747475	−	0.242869i	−0.0895805	−	0.995980i	$-0.528553\pi$
$191$	−10.3303	−	3.35652i	−0.747475	−	0.242869i	−0.657894	+	0.753110i	$0.728553\pi$
$192$	−0.832356	−	1.51894i	−0.0600701	−	0.109620i
$193$	13.7241	−	13.7241i	0.987880	−	0.987880i	−0.0120476	−	0.999927i	$-0.503835\pi$
$193$	13.7241	−	13.7241i	0.987880	−	0.987880i	0.999927	+	0.0120476i	$0.00383498\pi$
$194$	8.39833	+	6.10174i	0.602965	+	0.438080i
$195$		0			0
$196$	5.65811	−	4.11086i	0.404151	−	0.293633i
$197$	−1.91320	+	12.0795i	−0.136310	+	0.860625i	0.820867	+	0.571120i	$0.193491\pi$
$197$	−1.91320	+	12.0795i	−0.136310	+	0.860625i	−0.957176	+	0.289506i	$0.906509\pi$
$198$	3.22657	−	0.712010i	0.229302	−	0.0506003i
$199$		−	15.9356i		−	1.12965i	−0.825212	−	0.564823i	$-0.808944\pi$
$199$		−	15.9356i		−	1.12965i	0.825212	−	0.564823i	$-0.191056\pi$
$200$		0			0
$201$	−10.8571	+	3.89211i	−0.765799	+	0.274528i
$202$	−6.37296	+	12.5076i	−0.448400	+	0.880034i
$203$	−0.544573	−	0.0862519i	−0.0382215	−	0.00605369i
$204$	3.06399	−	4.49536i	0.214522	−	0.314738i
$205$		0			0
$206$	7.76123	−	10.6824i	0.540750	−	0.744279i
$207$	0.725556	−	7.45886i	0.0504296	−	0.518427i
$208$	−5.03358	+	0.797241i	−0.349016	+	0.0552787i
$209$	0.477258	−	1.46885i	0.0330126	−	0.101602i
$210$		0			0
$211$	−3.41758	−	10.5182i	−0.235276	−	0.724104i	−0.997085	−	0.0763026i	$-0.975689\pi$
$211$	−3.41758	−	10.5182i	−0.235276	−	0.724104i	0.761809	−	0.647802i	$-0.224311\pi$
$212$	3.08222	+	6.04920i	0.211688	+	0.415461i
$213$	15.1729	−	16.1135i	1.03963	−	1.10408i
$214$	18.5097	−	6.01417i	1.26530	−	0.411120i
$215$		0			0
$216$	3.91169	−	3.42034i	0.266157	−	0.232724i
$217$	−0.117628	−	0.742674i	−0.00798511	−	0.0504160i
$218$	8.70216	+	8.70216i	0.589385	+	0.589385i
$219$	0.644746	−	2.20801i	0.0435679	−	0.149204i
$220$		0			0
$221$	−9.40879	−	12.9501i	−0.632904	−	0.871117i
$222$	−3.33833	−	17.6304i	−0.224054	−	1.18328i
$223$	−4.89460	−	2.49393i	−0.327767	−	0.167006i	0.282362	−	0.959308i	$-0.408882\pi$
$223$	−4.89460	−	2.49393i	−0.327767	−	0.167006i	−0.610129	+	0.792302i	$0.708882\pi$
$224$	0.0786976			0.00525820
$225$		0			0
$226$	−7.63411			−0.507814
$227$	−6.02606	−	3.07043i	−0.399964	−	0.203792i	0.242426	−	0.970170i	$-0.422057\pi$
$227$	−6.02606	−	3.07043i	−0.399964	−	0.203792i	−0.642390	+	0.766378i	$0.722057\pi$
$228$	−0.451860	−	2.38637i	−0.0299251	−	0.158041i
$229$	−1.78525	−	2.45719i	−0.117973	−	0.162376i	0.745947	−	0.666006i	$-0.231997\pi$
$229$	−1.78525	−	2.45719i	−0.117973	−	0.162376i	−0.863919	+	0.503630i	$0.831997\pi$
$230$		0			0
$231$	−0.0420810	+	0.144111i	−0.00276873	+	0.00948184i
$232$	4.95404	+	4.95404i	0.325249	+	0.325249i
$233$	0.216297	+	1.36565i	0.0141701	+	0.0894666i	0.993760	−	0.111541i	$-0.0355785\pi$
$233$	0.216297	+	1.36565i	0.0141701	+	0.0894666i	−0.979590	+	0.201007i	$0.935579\pi$
$234$	−5.58954	−	14.2306i	−0.365400	−	0.930283i
$235$		0			0
$236$	6.26761	−	2.03647i	0.407987	−	0.132563i
$237$	−11.8248	+	12.5578i	−0.768101	+	0.815717i
$238$	0.112219	+	0.220242i	0.00727408	+	0.0142762i
$239$	−3.51376	−	10.8143i	−0.227287	−	0.699516i	−0.998051	−	0.0623963i	$-0.980126\pi$
$239$	−3.51376	−	10.8143i	−0.227287	−	0.699516i	0.770765	−	0.637120i	$-0.219874\pi$
$240$		0			0
$241$	−2.72661	+	8.39163i	−0.175636	+	0.540552i	−0.999662	−	0.0259998i	$-0.991723\pi$
$241$	−2.72661	+	8.39163i	−0.175636	+	0.540552i	0.824026	+	0.566552i	$0.191723\pi$
$242$	−9.66643	+	1.53101i	−0.621382	+	0.0984172i
$243$	12.5487	+	9.24826i	0.804999	+	0.593276i
$244$	−2.34577	+	3.22867i	−0.150172	+	0.206695i
$245$		0			0
$246$	−3.64342	+	5.34547i	−0.232296	+	0.340814i
$247$	−7.05835	−	1.11793i	−0.449112	−	0.0711323i
$248$	−4.33774	+	8.51329i	−0.275447	+	0.540595i
$249$	−1.43828	+	0.515604i	−0.0911475	+	0.0326751i
$250$		0			0
$251$			14.6104i			0.922197i	0.887349	+	0.461099i	$0.152545\pi$
$251$			14.6104i			0.922197i	−0.887349	+	0.461099i	$0.847455\pi$
$252$	0.0508748	+	0.230546i	0.00320481	+	0.0145230i
$253$	0.430401	−	2.71745i	0.0270591	−	0.170844i
$254$	2.60673	−	1.89390i	0.163561	−	0.118834i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	1.57229	−	1.57229i	0.0980767	−	0.0980767i	−0.656366	−	0.754443i	$-0.727907\pi$
$257$	1.57229	−	1.57229i	0.0980767	−	0.0980767i	0.754443	+	0.656366i	$0.227907\pi$
$258$	1.18376	+	2.16020i	0.0736975	+	0.134488i
$259$	0.775389	+	0.251939i	0.0481803	+	0.0156547i
$260$		0			0
$261$	−11.3104	+	17.7155i	−0.700095	+	1.09656i
$262$	4.73859	−	2.41443i	0.292751	−	0.149164i
$263$	−17.2650	+	8.79695i	−1.06460	+	0.542443i	−0.896371	−	0.443304i	$-0.853806\pi$
$263$	−17.2650	+	8.79695i	−1.06460	+	0.542443i	−0.168233	+	0.985747i	$0.553806\pi$
$264$	1.50895	−	1.16718i	0.0928695	−	0.0718348i
$265$		0			0
$266$	0.104953	+	0.0341012i	0.00643507	+	0.00209088i
$267$	−4.98058	+	2.72928i	−0.304807	+	0.167029i
$268$	−4.70859	+	4.70859i	−0.287623	+	0.287623i
$269$	4.44596	+	3.23018i	0.271075	+	0.196948i	0.715015	−	0.699109i	$-0.246420\pi$
$269$	4.44596	+	3.23018i	0.271075	+	0.196948i	−0.443940	+	0.896056i	$0.646420\pi$
$270$		0			0
$271$	6.02194	−	4.37520i	0.365807	−	0.265774i	−0.389663	−	0.920957i	$-0.627409\pi$
$271$	6.02194	−	4.37520i	0.365807	−	0.265774i	0.755470	+	0.655183i	$0.227409\pi$
$272$	0.491350	−	3.10226i	0.0297924	−	0.188102i
$273$	0.689074	+	0.0880031i	0.0417047	+	0.00532619i
$274$			11.4859i			0.693891i
$275$		0			0
$276$	−1.46008	−	4.07290i	−0.0878863	−	0.245160i
$277$	8.66928	−	17.0144i	0.520886	−	1.02230i	−0.469365	−	0.883004i	$-0.655517\pi$
$277$	8.66928	−	17.0144i	0.520886	−	1.02230i	0.990251	−	0.139293i	$-0.0444830\pi$
$278$	10.7678	+	1.70545i	0.645810	+	0.102286i
$279$	−27.7440	−	7.20400i	−1.66099	−	0.431292i
$280$		0			0
$281$	0.827936	−	1.13956i	0.0493905	−	0.0679802i	−0.783607	−	0.621256i	$-0.786623\pi$
$281$	0.827936	−	1.13956i	0.0493905	−	0.0679802i	0.832998	+	0.553276i	$0.186623\pi$
$282$	19.9033	+	9.39887i	1.18522	+	0.559694i
$283$	−9.41786	+	1.49164i	−0.559834	+	0.0886689i	−0.429937	−	0.902859i	$-0.641464\pi$
$283$	−9.41786	+	1.49164i	−0.559834	+	0.0886689i	−0.129896	+	0.991528i	$0.541464\pi$
$284$	3.94874	−	12.1530i	0.234315	−	0.721147i
$285$		0			0
$286$	−1.73454	−	5.33836i	−0.102565	−	0.315664i
$287$	−0.133440	−	0.261892i	−0.00787674	−	0.0154590i
$288$	1.19893	−	2.75001i	0.0706478	−	0.162046i
$289$	−6.78537	+	2.20470i	−0.399139	+	0.129688i
$290$		0			0
$291$	0.540319	+	17.9721i	0.0316740	+	1.05355i
$292$	−0.207750	−	1.31168i	−0.0121577	−	0.0767604i
$293$	−22.0266	−	22.0266i	−1.28681	−	1.28681i	−0.936716	−	0.350091i	$-0.886151\pi$
$293$	−22.0266	−	22.0266i	−1.28681	−	1.28681i	−0.350091	−	0.936716i	$-0.613849\pi$
$294$	11.6280	+	3.39542i	0.678161	+	0.198025i
$295$		0			0
$296$	−6.08934	−	8.38126i	−0.353936	−	0.487151i
$297$	4.39475	+	3.66597i	0.255009	+	0.212721i
$298$	12.8019	+	6.52291i	0.741596	+	0.377862i
$299$	−12.7307			−0.736237
$300$		0			0
$301$	−0.111922			−0.00645107
$302$	−0.290856	−	0.148198i	−0.0167369	−	0.00852785i
$303$	−23.8894	+	4.52347i	−1.37241	+	0.259867i
$304$	−0.824223	−	1.13445i	−0.0472724	−	0.0650649i
$305$		0			0
$306$	9.40577	−	0.566067i	0.537692	−	0.0323599i
$307$	−1.56450	−	1.56450i	−0.0892910	−	0.0892910i	0.661050	−	0.750341i	$-0.270111\pi$
$307$	−1.56450	−	1.56450i	−0.0892910	−	0.0892910i	−0.750341	+	0.661050i	$0.770111\pi$
$308$	0.0135593	+	0.0856103i	0.000772615	+	0.00487810i
$309$	22.8600	−	0.687269i	1.30046	−	0.0390974i
$310$		0			0
$311$	12.9644	−	4.21240i	0.735145	−	0.238863i	0.0825681	−	0.996585i	$-0.473688\pi$
$311$	12.9644	−	4.21240i	0.735145	−	0.238863i	0.652577	+	0.757722i	$0.273688\pi$
$312$	−6.42644	−	6.05131i	−0.363826	−	0.342588i
$313$	8.67043	+	17.0167i	0.490082	+	0.961839i	0.995113	+	0.0987386i	$0.0314808\pi$
$313$	8.67043	+	17.0167i	0.490082	+	0.961839i	−0.505032	+	0.863101i	$0.668519\pi$
$314$	1.51888	+	4.67462i	0.0857152	+	0.263804i
$315$		0			0
$316$	−3.07739	+	9.47123i	−0.173117	+	0.532798i
$317$	−8.97408	+	1.42135i	−0.504034	+	0.0798312i	−0.403274	−	0.915079i	$-0.632128\pi$
$317$	−8.97408	+	1.42135i	−0.504034	+	0.0798312i	−0.100761	+	0.994911i	$0.532128\pi$
$318$	−5.02130	+	10.6332i	−0.281580	+	0.596281i
$319$	−4.53563	+	6.24276i	−0.253947	+	0.349528i
$320$		0			0
$321$	27.8548	+	18.9855i	1.55470	+	1.05967i
$322$	0.194168	+	0.0307532i	0.0108206	+	0.00171381i
$323$	1.99954	−	3.92433i	0.111258	−	0.218355i
$324$	8.83128	+	1.73453i	0.490626	+	0.0963625i
$325$		0			0
$326$			1.53299i			0.0849043i
$327$	−2.70036	+	21.1441i	−0.149330	+	1.16927i
$328$	−0.584268	+	3.68892i	−0.0322608	+	0.203687i
$329$	−0.809088	+	0.587837i	−0.0446065	+	0.0324085i
$330$		0			0
$331$	8.94485	+	6.49882i	0.491654	+	0.357207i	0.805820	−	0.592161i	$-0.201725\pi$
$331$	8.94485	+	6.49882i	0.491654	+	0.357207i	−0.314166	+	0.949368i	$0.601725\pi$
$332$	−0.623767	+	0.623767i	−0.0342336	+	0.0342336i
$333$	20.6166	−	23.2570i	1.12978	−	1.27448i
$334$	−21.2873	−	6.91666i	−1.16479	−	0.378463i
$335$		0			0
$336$	0.0833977	+	0.107818i	0.00454971	+	0.00588197i
$337$	−15.4169	+	7.85531i	−0.839813	+	0.427906i	−0.820321	−	0.571904i	$-0.806205\pi$
$337$	−15.4169	+	7.85531i	−0.839813	+	0.427906i	−0.0194923	+	0.999810i	$0.506205\pi$
$338$	−11.5586	+	5.88940i	−0.628705	+	0.320341i
$339$	−8.09004	−	10.4590i	−0.439391	−	0.568054i
$340$		0			0
$341$	−10.0085	−	3.25195i	−0.541989	−	0.176103i
$342$	2.79056	−	3.14795i	0.150896	−	0.170222i
$343$	−0.778722	+	0.778722i	−0.0420470	+	0.0420470i
$344$	1.15057	+	0.835934i	0.0620343	+	0.0450706i
$345$		0			0
$346$	11.4671	−	8.33133i	0.616475	−	0.447895i
$347$	2.33923	−	14.7693i	0.125576	−	0.792857i	−0.841851	−	0.539709i	$-0.818534\pi$
$347$	2.33923	−	14.7693i	0.125576	−	0.792857i	0.967428	−	0.253148i	$-0.0814658\pi$
$348$	−1.53728	+	12.0371i	−0.0824070	+	0.645256i
$349$		−	0.345103i		−	0.0184729i	−0.999957	−	0.00923647i	$-0.997060\pi$
$349$		−	0.345103i		−	0.0184729i	0.999957	−	0.00923647i	$-0.00294010\pi$
$350$		0			0
$351$	13.5730	−	22.7383i	0.724473	−	1.21368i
$352$	0.500025	−	0.981353i	0.0266514	−	0.0523063i
$353$	−19.7879	−	3.13409i	−1.05320	−	0.166811i	−0.394256	−	0.919001i	$-0.628998\pi$
$353$	−19.7879	−	3.13409i	−1.05320	−	0.166811i	−0.658947	+	0.752190i	$0.728998\pi$
$354$	9.43196	+	6.42874i	0.501303	+	0.341683i
$355$		0			0
$356$	−1.92734	+	2.65275i	−0.102149	+	0.140596i
$357$	−0.182818	+	0.387139i	−0.00967574	+	0.0204896i
$358$	−15.0037	+	2.37636i	−0.792971	+	0.125594i
$359$	−5.66877	+	17.4467i	−0.299186	+	0.920800i	0.682597	+	0.730795i	$0.260850\pi$
$359$	−5.66877	+	17.4467i	−0.299186	+	0.920800i	−0.981783	+	0.190005i	$0.939150\pi$
$360$		0			0
$361$	5.26370	+	16.2000i	0.277037	+	0.852632i
$362$	−4.66289	−	9.15143i	−0.245076	−	0.480989i
$363$	−12.3413	−	11.6209i	−0.647749	−	0.609937i
$364$	0.381439	−	0.123937i	0.0199928	−	0.00649606i
$365$		0			0
$366$	−6.90925	+	0.207721i	−0.361152	+	0.0108578i
$367$	−0.00304877	−	0.0192492i	−0.000159144	−	0.00100480i	0.987609	−	0.156937i	$-0.0501619\pi$
$367$	−0.00304877	−	0.0192492i	−0.000159144	−	0.00100480i	−0.987768	+	0.155932i	$0.950162\pi$
$368$	−1.76637	−	1.76637i	−0.0920783	−	0.0920783i
$369$	−11.1845	+	0.673114i	−0.582240	+	0.0350409i
$370$		0			0
$371$	−0.314049	−	0.432251i	−0.0163046	−	0.0224414i
$372$	−16.2603	+	3.07889i	−0.843057	+	0.159633i
$373$	6.23329	+	3.17602i	0.322748	+	0.164448i	0.607856	−	0.794047i	$-0.292030\pi$
$373$	6.23329	+	3.17602i	0.322748	+	0.164448i	−0.285109	+	0.958495i	$0.592030\pi$
$374$	3.45942			0.178882
$375$		0			0
$376$	12.7080			0.655364
$377$	31.8136	+	16.2098i	1.63848	+	0.834848i
$378$	−0.261942	+	0.314015i	−0.0134729	+	0.0161512i
$379$	−7.15293	−	9.84516i	−0.367421	−	0.505712i	0.584776	−	0.811194i	$-0.301182\pi$
$379$	−7.15293	−	9.84516i	−0.367421	−	0.505712i	−0.952198	+	0.305483i	$0.901182\pi$
$380$		0			0
$381$	5.35711	+	1.56429i	0.274453	+	0.0801412i
$382$	−7.68054	−	7.68054i	−0.392971	−	0.392971i
$383$	0.148258	+	0.936062i	0.00757561	+	0.0478305i	0.991187	−	0.132473i	$-0.0422919\pi$
$383$	0.148258	+	0.936062i	0.00757561	+	0.0478305i	−0.983611	+	0.180304i	$0.942292\pi$
$384$	−0.0520493	−	1.73127i	−0.00265613	−	0.0883484i
$385$		0			0
$386$	18.4588	−	5.99764i	0.939530	−	0.305272i
$387$	−1.70509	+	3.91100i	−0.0866748	+	0.198807i
$388$	4.71283	+	9.24945i	0.239258	+	0.469570i
$389$	−6.14102	−	18.9001i	−0.311362	−	0.958273i	−0.977226	−	0.212200i	$-0.931937\pi$
$389$	−6.14102	−	18.9001i	−0.311362	−	0.958273i	0.665864	−	0.746073i	$-0.268063\pi$
$390$		0			0
$391$	2.42458	−	7.46210i	0.122616	−	0.377374i
$392$	6.90770	−	1.09407i	0.348892	−	0.0552590i
$393$	8.32944	+	3.93339i	0.420164	+	0.198413i
$394$	−7.18863	+	9.89430i	−0.362158	+	0.498468i
$395$		0			0
$396$	3.19814	+	0.830427i	0.160713	+	0.0417305i
$397$	−26.6394	−	4.21926i	−1.33699	−	0.211759i	−0.553338	−	0.832957i	$-0.686646\pi$
$397$	−26.6394	−	4.21926i	−1.33699	−	0.211759i	−0.783654	+	0.621198i	$0.786646\pi$
$398$	7.23462	−	14.1987i	0.362639	−	0.711719i
$399$	0.0645011	+	0.179927i	0.00322909	+	0.00900759i
$400$		0			0
$401$			33.9394i			1.69485i	0.530912	+	0.847427i	$0.321849\pi$
$401$			33.9394i			1.69485i	−0.530912	+	0.847427i	$0.678151\pi$
$402$	−11.4407	−	1.46112i	−0.570611	−	0.0728739i
$403$	−7.61739	+	48.0943i	−0.379449	+	2.39575i
$404$	−11.3567	+	8.25112i	−0.565017	+	0.410509i
$405$		0			0
$406$	−0.446060	−	0.324082i	−0.0221376	−	0.0160839i
$407$	8.06828	−	8.06828i	0.399930	−	0.399930i
$408$	4.77089	−	2.61437i	0.236194	−	0.129431i
$409$	−15.1218	−	4.91338i	−0.747726	−	0.242951i	−0.0897236	−	0.995967i	$-0.528598\pi$
$409$	−15.1218	−	4.91338i	−0.747726	−	0.242951i	−0.658002	+	0.753016i	$0.728598\pi$
$410$		0			0
$411$	−15.7361	+	12.1719i	−0.776205	+	0.600396i
$412$	11.7650	−	5.99458i	0.579621	−	0.295332i
$413$	−0.462102	+	0.235453i	−0.0227386	+	0.0115859i
$414$	4.03273	−	6.31650i	0.198198	−	0.310439i
$415$		0			0
$416$	−4.84689	−	1.57485i	−0.237638	−	0.0772134i
$417$	9.07436	+	16.5595i	0.444373	+	0.810924i
$418$	1.09208	−	1.09208i	0.0534155	−	0.0534155i
$419$	−22.2455	−	16.1623i	−1.08677	−	0.789582i	−0.107916	−	0.994160i	$-0.534418\pi$
$419$	−22.2455	−	16.1623i	−1.08677	−	0.789582i	−0.978850	+	0.204578i	$0.934418\pi$
$420$		0			0
$421$	25.8507	−	18.7816i	1.25988	−	0.915359i	0.261132	−	0.965303i	$-0.415904\pi$
$421$	25.8507	−	18.7816i	1.25988	−	0.915359i	0.998752	+	0.0499438i	$0.0159042\pi$
$422$	1.73009	−	10.9234i	0.0842194	−	0.531741i
$423$	8.21520	+	37.2283i	0.399437	+	1.81010i
$424$			6.78917i			0.329711i
$425$		0			0
$426$	20.8346	−	7.46889i	1.00944	−	0.361869i
$427$	0.142585	−	0.279839i	0.00690018	−	0.0135424i
$428$	19.2226	+	3.04457i	0.929162	+	0.147165i
$429$	5.47559	−	8.03356i	0.264364	−	0.387864i
$430$		0			0
$431$	−5.09101	+	7.00718i	−0.245225	+	0.337524i	−0.913832	−	0.406093i	$-0.866891\pi$
$431$	−5.09101	+	7.00718i	−0.245225	+	0.337524i	0.668607	+	0.743616i	$0.266891\pi$
$432$	5.03814	−	1.27167i	0.242398	−	0.0611835i
$433$	−10.6490	+	1.68664i	−0.511760	+	0.0810548i	−0.406974	−	0.913440i	$-0.633416\pi$
$433$	−10.6490	+	1.68664i	−0.511760	+	0.0810548i	−0.104786	+	0.994495i	$0.533416\pi$
$434$	0.232360	−	0.715129i	0.0111536	−	0.0343273i
$435$		0			0
$436$	3.80299	+	11.7044i	0.182130	+	0.560538i
$437$	−1.59026	−	3.12107i	−0.0760726	−	0.149301i
$438$	1.57689	−	1.67464i	0.0753467	−	0.0800176i
$439$	−32.6251	+	10.6006i	−1.55711	+	0.505937i	−0.956035	−	0.293253i	$-0.905262\pi$
$439$	−32.6251	+	10.6006i	−1.55711	+	0.505937i	−0.601078	+	0.799190i	$0.705262\pi$
$440$		0			0
$441$	7.67066	+	19.5290i	0.365269	+	0.929951i
$442$	−2.50408	−	15.8101i	−0.119107	−	0.752011i
$443$	4.58214	+	4.58214i	0.217704	+	0.217704i	0.807530	−	0.589826i	$-0.200804\pi$
$443$	4.58214	+	4.58214i	0.217704	+	0.217704i	−0.589826	+	0.807530i	$0.700804\pi$
$444$	5.02958	−	17.2244i	0.238693	−	0.817434i
$445$		0			0
$446$	−3.22891	−	4.44421i	−0.152893	−	0.210439i
$447$	4.62991	+	24.4515i	0.218987	+	1.15652i
$448$	0.0701201	+	0.0357280i	0.00331286	+	0.00168799i
$449$	22.7460			1.07345			0.536726	−	0.843756i	$-0.319661\pi$
$449$	22.7460			1.07345			0.536726	+	0.843756i	$0.319661\pi$
$450$		0			0
$451$	−4.11362			−0.193703
$452$	−6.80204	−	3.46581i	−0.319941	−	0.163018i
$453$	−0.105190	−	0.555530i	−0.00494225	−	0.0261011i
$454$	−3.97531	−	5.47155i	−0.186571	−	0.256792i
$455$		0			0
$456$	0.680779	−	2.33141i	0.0318804	−	0.109178i
$457$	6.28077	+	6.28077i	0.293802	+	0.293802i	0.838580	−	0.544778i	$-0.183386\pi$
$457$	6.28077	+	6.28077i	0.293802	+	0.293802i	−0.544778	+	0.838580i	$0.683386\pi$
$458$	−0.475131	−	2.99986i	−0.0222014	−	0.140174i
$459$	10.7430	+	12.2863i	0.501442	+	0.573477i
$460$		0			0
$461$	−21.3397	+	6.93369i	−0.993889	+	0.322934i	−0.760421	−	0.649430i	$-0.775007\pi$
$461$	−21.3397	+	6.93369i	−0.993889	+	0.322934i	−0.233468	+	0.972364i	$0.575007\pi$
$462$	−0.102920	+	0.109300i	−0.00478826	+	0.00508509i
$463$	−10.9916	−	21.5722i	−0.510823	−	1.00255i	−0.992037	−	0.125944i	$-0.959804\pi$
$463$	−10.9916	−	21.5722i	−0.510823	−	1.00255i	0.481214	−	0.876603i	$-0.340196\pi$
$464$	2.16499	+	6.66317i	0.100507	+	0.309330i
$465$		0			0
$466$	−0.427269	+	1.31500i	−0.0197929	+	0.0609161i
$467$	13.3049	−	2.10730i	0.615679	−	0.0975140i	0.159197	−	0.987247i	$-0.449109\pi$
$467$	13.3049	−	2.10730i	0.615679	−	0.0975140i	0.456482	+	0.889733i	$0.349109\pi$
$468$	1.48024	−	15.2171i	0.0684240	−	0.703413i
$469$	0.308025	−	0.423960i	0.0142233	−	0.0195766i
$470$		0			0
$471$	−4.79479	+	7.03472i	−0.220932	+	0.324143i
$472$	6.50902	+	1.03093i	0.299602	+	0.0474523i
$473$	−0.711123	+	1.39566i	−0.0326975	+	0.0641724i
$474$	−16.2371	+	5.82076i	−0.745793	+	0.267356i
$475$		0			0
$476$			0.247184i			0.0113296i
$477$	−19.8890	+	4.38893i	−0.910656	+	0.200955i
$478$	1.77878	−	11.2308i	0.0813596	−	0.513684i
$479$	13.9808	−	10.1576i	0.638797	−	0.464113i	−0.220639	−	0.975355i	$-0.570814\pi$
$479$	13.9808	−	10.1576i	0.638797	−	0.464113i	0.859437	+	0.511242i	$0.170814\pi$
$480$		0			0
$481$	−42.7136	−	31.0332i	−1.94757	−	1.41499i
$482$	−6.23914	+	6.23914i	−0.284185	+	0.284185i
$483$	0.163631	+	0.298606i	0.00744549	+	0.0135871i
$484$	−9.30791	−	3.02432i	−0.423087	−	0.137469i
$485$		0			0
$486$	6.98235	+	13.9372i	0.316726	+	0.632206i
$487$	−3.22789	+	1.64469i	−0.146270	+	0.0745281i	−0.525593	−	0.850736i	$-0.676157\pi$
$487$	−3.22789	+	1.64469i	−0.146270	+	0.0745281i	0.379324	+	0.925264i	$0.376157\pi$
$488$	−3.55588	+	1.81181i	−0.160967	+	0.0820169i
$489$	−2.10024	+	1.62454i	−0.0949761	+	0.0734643i
$490$		0			0
$491$	−5.48953	−	1.78366i	−0.247739	−	0.0804953i	0.182515	−	0.983203i	$-0.441576\pi$
$491$	−5.48953	−	1.78366i	−0.247739	−	0.0804953i	−0.430254	+	0.902708i	$0.641576\pi$
$492$	−5.67310	+	3.10877i	−0.255763	+	0.140154i
$493$	−15.5603	+	15.5603i	−0.700800	+	0.700800i
$494$	−5.78150	−	4.20051i	−0.260122	−	0.188990i
$495$		0			0
$496$	−7.72991	+	5.61611i	−0.347083	+	0.252171i
$497$	−0.157315	+	0.993249i	−0.00705655	+	0.0445533i
$498$	−1.51560	−	0.193560i	−0.0679157	−	0.00867365i
$499$		−	28.5582i		−	1.27844i	−0.769024	−	0.639220i	$-0.779257\pi$
$499$		−	28.5582i		−	1.27844i	0.769024	−	0.639220i	$-0.220743\pi$
$500$		0			0
$501$	−13.0826	−	36.4940i	−0.584486	−	1.63043i
$502$	−6.63296	+	13.0179i	−0.296044	+	0.581018i
$503$	23.7938	+	3.76856i	1.06091	+	0.168032i	0.662414	−	0.749138i	$-0.269532\pi$
$503$	23.7938	+	3.76856i	1.06091	+	0.168032i	0.398497	+	0.917170i	$0.369532\pi$
$504$	−0.0593360	+	0.228515i	−0.00264304	+	0.0101789i
$505$		0			0
$506$	1.61718	−	2.22586i	0.0718926	−	0.0989517i
$507$	−20.3176	−	9.59451i	−0.902335	−	0.426107i
$508$	3.18243	−	0.504047i	0.141197	−	0.0223635i
$509$	−1.35722	+	4.17708i	−0.0601576	+	0.185146i	−0.976619	−	0.214977i	$-0.931032\pi$
$509$	−1.35722	+	4.17708i	−0.0601576	+	0.185146i	0.916462	+	0.400123i	$0.131032\pi$
$510$		0			0
$511$	0.0322963	+	0.0993978i	0.00142870	+	0.00439710i
$512$	−0.453990	−	0.891007i	−0.0200637	−	0.0393773i
$513$	7.27001	+	0.487193i	0.320979	+	0.0215101i
$514$	2.11472	−	0.687116i	0.0932765	−	0.0303074i
$515$		0			0
$516$	0.0740233	+	2.46217i	0.00325869	+	0.108391i
$517$	2.18954	+	13.8242i	0.0962960	+	0.607989i
$518$	0.576498	+	0.576498i	0.0253299	+	0.0253299i
$519$	23.5661	+	6.88138i	1.03444	+	0.302059i
$520$		0			0
$521$	3.85216	+	5.30205i	0.168766	+	0.232287i	0.885020	−	0.465553i	$-0.154145\pi$
$521$	3.85216	+	5.30205i	0.168766	+	0.232287i	−0.716254	+	0.697840i	$0.754145\pi$
$522$	−18.1203	+	10.6499i	−0.793104	+	0.466132i
$523$	−7.96973	−	4.06078i	−0.348492	−	0.177566i	0.270979	−	0.962585i	$-0.412653\pi$
$523$	−7.96973	−	4.06078i	−0.348492	−	0.177566i	−0.619471	+	0.785020i	$0.712653\pi$
$524$	5.31824			0.232328
$525$		0			0
$526$	−19.3769			−0.844875
$527$	−26.7397	−	13.6245i	−1.16480	−	0.593494i
$528$	1.87437	−	0.354913i	0.0815716	−	0.0154456i
$529$	9.85121	+	13.5590i	0.428314	+	0.589523i
$530$		0			0
$531$	1.18770	+	19.7348i	0.0515416	+	0.856416i
$532$	0.0780320	+	0.0780320i	0.00338312	+	0.00338312i
$533$	2.97762	+	18.7999i	0.128975	+	0.814315i
$534$	−5.67680	+	0.170669i	−0.245659	+	0.00738556i
$535$		0			0
$536$	−6.33303	+	2.05773i	−0.273545	+	0.0888803i
$537$	−19.1555	−	18.0373i	−0.826619	−	0.778367i
$538$	2.49491	+	4.89653i	0.107563	+	0.211105i
$539$	2.38035	+	7.32596i	0.102529	+	0.315551i
$540$		0			0
$541$	4.98127	−	15.3308i	0.214161	−	0.659121i	−0.785051	−	0.619432i	$-0.787363\pi$
$541$	4.98127	−	15.3308i	0.214161	−	0.659121i	0.999212	−	0.0396896i	$-0.0126369\pi$
$542$	7.35189	−	1.16442i	0.315791	−	0.0500163i
$543$	7.59639	−	16.0863i	0.325992	−	0.690329i
$544$	1.84619	−	2.54107i	0.0791548	−	0.108947i
$545$		0			0
$546$	0.574017	+	0.391244i	0.0245657	+	0.0167437i
$547$	23.3625	+	3.70025i	0.998907	+	0.158211i	0.634413	−	0.772994i	$-0.281242\pi$
$547$	23.3625	+	3.70025i	0.998907	+	0.158211i	0.364494	+	0.931206i	$0.381242\pi$
$548$	−5.21451	+	10.2341i	−0.222753	+	0.437177i
$549$	−7.60647	−	9.24576i	−0.324636	−	0.394599i
$550$		0			0
$551$			9.82428i			0.418528i
$552$	0.548120	−	4.29184i	0.0233295	−	0.182673i
$553$	0.122601	−	0.774072i	0.00521353	−	0.0329169i
$554$	15.4488	−	11.2242i	0.656355	−	0.476870i
$555$		0			0
$556$	8.81992	+	6.40805i	0.374048	+	0.271762i
$557$	−27.5142	+	27.5142i	−1.16581	+	1.16581i	−0.182634	+	0.983181i	$0.558462\pi$
$557$	−27.5142	+	27.5142i	−1.16581	+	1.16581i	−0.983181	+	0.182634i	$0.941538\pi$
$558$	−21.4496	−	19.0143i	−0.908033	−	0.804941i
$559$	6.89314	+	2.23972i	0.291549	+	0.0947299i
$560$		0			0
$561$	3.66602	+	4.73951i	0.154780	+	0.200102i
$562$	1.25504	−	0.639477i	0.0529408	−	0.0269747i
$563$	22.1789	−	11.3007i	0.934728	−	0.476267i	0.0808412	−	0.996727i	$-0.474239\pi$
$563$	22.1789	−	11.3007i	0.934728	−	0.476267i	0.853886	+	0.520460i	$0.174239\pi$
$564$	13.4669	+	17.4103i	0.567061	+	0.733108i
$565$		0			0
$566$	−9.06857	−	2.94656i	−0.381180	−	0.123853i
$567$	−0.707797	−	0.0261004i	−0.0297247	−	0.00109611i
$568$	9.03570	−	9.03570i	0.379129	−	0.379129i
$569$	25.9540	+	18.8567i	1.08805	+	0.790515i	0.979069	−	0.203529i	$-0.0652412\pi$
$569$	25.9540	+	18.8567i	1.08805	+	0.790515i	0.108981	+	0.994044i	$0.465241\pi$
$570$		0			0
$571$	−34.1170	+	24.7874i	−1.42775	+	1.03732i	−0.437322	+	0.899305i	$0.644073\pi$
$571$	−34.1170	+	24.7874i	−1.42775	+	1.03732i	−0.990430	+	0.138017i	$0.955927\pi$
$572$	0.878080	−	5.54398i	0.0367144	−	0.231805i
$573$	2.38334	−	18.6618i	0.0995655	−	0.779609i
$574$		−	0.293928i		−	0.0122683i
$575$		0			0
$576$	2.31674	−	1.90597i	0.0965306	−	0.0794156i
$577$	10.0150	−	19.6556i	0.416931	−	0.818274i	−0.583052	−	0.812435i	$-0.698141\pi$
$577$	10.0150	−	19.6556i	0.416931	−	0.818274i	0.999983	−	0.00583873i	$-0.00185853\pi$
$578$	−7.04672	−	1.11609i	−0.293105	−	0.0464233i
$579$	27.7782	+	18.9333i	1.15442	+	0.786843i
$580$		0			0
$581$	0.0408054	−	0.0561638i	0.00169289	−	0.00233007i
$582$	−7.67775	+	16.2586i	−0.318253	+	0.673940i
$583$	−7.38553	+	1.16975i	−0.305877	+	0.0484462i
$584$	0.410385	−	1.26303i	0.0169818	−	0.0522647i
$585$		0			0
$586$	−9.62597	−	29.6257i	−0.397645	−	1.22383i
$587$	−5.85750	−	11.4960i	−0.241765	−	0.474490i	0.737958	−	0.674846i	$-0.235790\pi$
$587$	−5.85750	−	11.4960i	−0.241765	−	0.474490i	−0.979723	+	0.200356i	$0.935790\pi$
$588$	8.81916	+	8.30436i	0.363696	+	0.342466i
$589$	−12.7423	+	4.14024i	−0.525039	+	0.170596i
$590$		0			0
$591$	−21.1735	+	0.636564i	−0.870960	+	0.0261848i
$592$	−1.62063	−	10.2323i	−0.0666075	−	0.420543i
$593$	3.75033	+	3.75033i	0.154007	+	0.154007i	0.779905	−	0.625898i	$-0.215267\pi$
$593$	3.75033	+	3.75033i	0.154007	+	0.154007i	−0.625898	+	0.779905i	$0.715267\pi$
$594$	2.25143	+	5.26158i	0.0923774	+	0.215885i
$595$		0			0
$596$	8.44527	+	11.6239i	0.345932	+	0.476134i
$597$	27.1194	−	5.13507i	1.10992	−	0.210165i
$598$	−11.3432	−	5.77963i	−0.463856	−	0.236347i
$599$	−29.8620			−1.22013			−0.610065	−	0.792352i	$-0.708857\pi$
$599$	−29.8620			−1.22013			−0.610065	+	0.792352i	$0.708857\pi$
$600$		0			0
$601$	19.0008			0.775058			0.387529	−	0.921858i	$-0.373329\pi$
$601$	19.0008			0.775058			0.387529	+	0.921858i	$0.373329\pi$
$602$	−0.0997231	−	0.0508115i	−0.00406441	−	0.00207092i
$603$	−10.1222	−	17.2225i	−0.412208	−	0.701355i
$604$	−0.191874	−	0.264091i	−0.00780722	−	0.0107457i
$605$		0			0
$606$	−23.3393	−	6.81513i	−0.948092	−	0.276846i
$607$	−29.8007	−	29.8007i	−1.20957	−	1.20957i	−0.971165	−	0.238406i	$-0.923375\pi$
$607$	−29.8007	−	29.8007i	−1.20957	−	1.20957i	−0.238406	−	0.971165i	$-0.576625\pi$
$608$	−0.219361	−	1.38499i	−0.00889625	−	0.0561687i
$609$	−0.0286980	−	0.954554i	−0.00116290	−	0.0386805i
$610$		0			0
$611$	61.5942	−	20.0132i	2.49184	−	0.809646i
$612$	8.63759	+	3.76576i	0.349154	+	0.152222i
$613$	−0.600877	−	1.17929i	−0.0242692	−	0.0476310i	0.878554	−	0.477644i	$-0.158509\pi$
$613$	−0.600877	−	1.17929i	−0.0242692	−	0.0476310i	−0.902823	+	0.430013i	$0.858509\pi$
$614$	−0.683714	−	2.10425i	−0.0275924	−	0.0849208i
$615$		0			0
$616$	−0.0267848	+	0.0824351i	−0.00107919	+	0.00332141i
$617$	41.5066	−	6.57400i	1.67099	−	0.264659i	0.752067	−	0.659087i	$-0.229057\pi$
$617$	41.5066	−	6.57400i	1.67099	−	0.264659i	0.918927	+	0.394428i	$0.129057\pi$
$618$	20.6804	+	9.76586i	0.831889	+	0.392841i
$619$	−9.51877	+	13.1015i	−0.382592	+	0.526592i	−0.956269	−	0.292489i	$-0.905516\pi$
$619$	−9.51877	+	13.1015i	−0.382592	+	0.526592i	0.573677	+	0.819082i	$0.305516\pi$
$620$		0			0
$621$	12.9274	−	1.16877i	0.518758	−	0.0469013i
$622$	13.4638	+	2.13245i	0.539848	+	0.0855036i
$623$	0.117151	−	0.229923i	0.00469357	−	0.00921165i
$624$	−2.97877	−	8.30930i	−0.119246	−	0.332638i
$625$		0			0
$626$			19.0983i			0.763320i
$627$	2.65349	+	0.338883i	0.105970	+	0.0135337i
$628$	−0.768905	+	4.85468i	−0.0306827	+	0.193723i
$629$	26.3249	−	19.1262i	1.04964	−	0.762611i
$630$		0			0
$631$	−9.33690	−	6.78365i	−0.371696	−	0.270053i	0.386218	−	0.922408i	$-0.373781\pi$
$631$	−9.33690	−	6.78365i	−0.371696	−	0.270053i	−0.757914	+	0.652355i	$0.773781\pi$
$632$	−7.04182	+	7.04182i	−0.280109	+	0.280109i
$633$	16.7988	−	9.20545i	0.667691	−	0.365884i
$634$	−8.64124	−	2.80771i	−0.343188	−	0.111508i
$635$		0			0
$636$	−9.30139	+	7.19464i	−0.368824	+	0.285286i
$637$	31.7579	−	16.1814i	1.25829	−	0.641132i
$638$	−6.87543	+	3.50321i	−0.272201	+	0.138693i
$639$	32.3115	+	20.6290i	1.27822	+	0.816073i
$640$		0			0
$641$	−15.5088	−	5.03912i	−0.612561	−	0.199033i	−0.0137264	−	0.999906i	$-0.504369\pi$
$641$	−15.5088	−	5.03912i	−0.612561	−	0.199033i	−0.598835	+	0.800873i	$0.704369\pi$
$642$	16.1995	+	29.5620i	0.639344	+	1.16672i
$643$	12.8296	−	12.8296i	0.505952	−	0.505952i	−0.407330	−	0.913281i	$-0.633540\pi$
$643$	12.8296	−	12.8296i	0.505952	−	0.505952i	0.913281	+	0.407330i	$0.133540\pi$
$644$	0.159043	+	0.115552i	0.00626719	+	0.00455338i
$645$		0			0
$646$	3.56321	−	2.58883i	0.140193	−	0.101856i
$647$	−3.97829	+	25.1179i	−0.156403	+	0.987488i	0.777220	+	0.629229i	$0.216629\pi$
$647$	−3.97829	+	25.1179i	−0.156403	+	0.987488i	−0.933622	+	0.358259i	$0.883371\pi$
$648$	7.08127	+	5.55479i	0.278178	+	0.218213i
$649$			7.25839i			0.284917i
$650$		0			0
$651$	1.22599	−	0.439499i	0.0480502	−	0.0172253i
$652$	−0.695961	+	1.36590i	−0.0272559	+	0.0534928i
$653$	30.0615	+	4.76127i	1.17640	+	0.186323i	0.713867	−	0.700281i	$-0.246942\pi$
$653$	30.0615	+	4.76127i	1.17640	+	0.186323i	0.462529	+	0.886604i	$0.346942\pi$
$654$	−12.0053	+	17.6136i	−0.469443	+	0.688747i
$655$		0			0
$656$	−2.19532	+	3.02160i	−0.0857129	+	0.117974i
$657$	3.96538	+	0.385730i	0.154704	+	0.0150488i
$658$	−0.987775	+	0.156448i	−0.0385075	+	0.00609899i
$659$	3.19473	−	9.83236i	0.124449	−	0.383014i	−0.869351	−	0.494195i	$-0.835463\pi$
$659$	3.19473	−	9.83236i	0.124449	−	0.383014i	0.993800	+	0.111180i	$0.0354631\pi$
$660$		0			0
$661$	3.97825	+	12.2438i	0.154736	+	0.476229i	0.998134	−	0.0610606i	$-0.0194483\pi$
$661$	3.97825	+	12.2438i	0.154736	+	0.476229i	−0.843398	+	0.537289i	$0.819448\pi$
$662$	5.01952	+	9.85137i	0.195089	+	0.382884i
$663$	19.0067	−	20.1850i	0.738161	−	0.783921i
$664$	−0.838964	+	0.272596i	−0.0325581	+	0.0105788i
$665$		0			0
$666$	28.9279	−	11.3624i	1.12093	−	0.440284i
$667$	2.73781	+	17.2859i	0.106008	+	0.669311i
$668$	−15.8270	−	15.8270i	−0.612365	−	0.612365i
$669$	2.66696	−	9.13333i	0.103111	−	0.353115i
$670$		0			0
$671$	−2.58363	−	3.55605i	−0.0997397	−	0.137280i
$672$	0.0253594	+	0.133928i	0.000978260	+	0.00516640i
$673$	−30.0291	−	15.3006i	−1.15754	−	0.589794i	−0.233596	−	0.972334i	$-0.575049\pi$
$673$	−30.0291	−	15.3006i	−1.15754	−	0.589794i	−0.923939	+	0.382540i	$0.875049\pi$
$674$	−17.3028			−0.666479
$675$		0			0
$676$	−12.9725			−0.498943
$677$	−13.8891	−	7.07682i	−0.533800	−	0.271984i	0.166244	−	0.986085i	$-0.446836\pi$
$677$	−13.8891	−	7.07682i	−0.533800	−	0.271984i	−0.700044	+	0.714100i	$0.746836\pi$
$678$	−2.46001	−	12.9918i	−0.0944759	−	0.498948i
$679$	−0.480192	−	0.660928i	−0.0184281	−	0.0253641i
$680$		0			0
$681$	3.28346	−	11.2446i	0.125823	−	0.430895i
$682$	−7.44126	−	7.44126i	−0.284940	−	0.284940i
$683$	4.20549	+	26.5524i	0.160919	+	1.01600i	0.927492	+	0.373844i	$0.121960\pi$
$683$	4.20549	+	26.5524i	0.160919	+	1.01600i	−0.766573	+	0.642157i	$0.778040\pi$
$684$	3.91554	−	1.53796i	0.149715	−	0.0588054i
$685$		0			0
$686$	−1.04738	+	0.340314i	−0.0399891	+	0.0129932i
$687$	3.60640	−	3.82996i	0.137593	−	0.146122i
$688$	0.645655	+	1.26717i	0.0246154	+	0.0483104i
$689$	10.6919	+	32.9064i	0.407330	+	1.25363i
$690$		0			0
$691$	7.00128	−	21.5477i	0.266341	−	0.819714i	−0.725040	−	0.688707i	$-0.758179\pi$
$691$	7.00128	−	21.5477i	0.266341	−	0.819714i	0.991381	−	0.131007i	$-0.0418212\pi$
$692$	13.9996	−	2.21732i	0.532185	−	0.0842898i
$693$	−0.258811	−	0.0251756i	−0.00983141	−	0.000956343i
$694$	8.78938	−	12.0975i	0.333640	−	0.459217i
$695$		0			0
$696$	−6.83446	+	10.0272i	−0.259060	+	0.380081i
$697$	−11.5866	−	1.83514i	−0.438875	−	0.0695110i
$698$	0.156673	−	0.307489i	0.00593018	−	0.0116386i
$699$	−2.25438	+	0.808162i	−0.0852684	+	0.0305675i
$700$		0			0
$701$		−	37.8133i		−	1.42819i	−0.700049	−	0.714095i	$-0.746839\pi$
$701$		−	37.8133i		−	1.42819i	0.700049	−	0.714095i	$-0.253161\pi$
$702$	22.4166	−	14.0980i	0.846061	−	0.532094i
$703$	2.27253	−	14.3482i	0.0857102	−	0.541153i
$704$	0.891050	−	0.647386i	0.0335827	−	0.0243993i
$705$		0			0
$706$	−16.2083	−	11.7760i	−0.610007	−	0.443196i
$707$	0.781162	−	0.781162i	0.0293786	−	0.0293786i
$708$	5.48536	+	10.0101i	0.206152	+	0.376201i
$709$	37.7779	+	12.2748i	1.41878	+	0.460989i	0.915214	−	0.402968i	$-0.132022\pi$
$709$	37.7779	+	12.2748i	1.41878	+	0.460989i	0.503565	+	0.863958i	$0.332022\pi$
$710$		0			0
$711$	−25.1814	−	16.0769i	−0.944377	−	0.602931i
$712$	−2.92160	+	1.48863i	−0.109491	+	0.0557887i
$713$	−21.2664	+	10.8358i	−0.796433	+	0.405803i
$714$	−0.338649	+	0.261946i	−0.0126736	+	0.00980309i
$715$		0			0
$716$	−14.4473	−	4.69420i	−0.539919	−	0.175430i
$717$	17.2716	−	9.46453i	0.645018	−	0.353459i
$718$	−12.9715	+	12.9715i	−0.484093	+	0.484093i
$719$	−25.6075	−	18.6049i	−0.954998	−	0.693847i	−0.00301445	−	0.999995i	$-0.500960\pi$
$719$	−25.6075	−	18.6049i	−0.954998	−	0.693847i	−0.951984	+	0.306149i	$0.900960\pi$
$720$		0			0
$721$	−0.840680	+	0.610790i	−0.0313086	+	0.0227470i
$722$	−2.66466	+	16.8240i	−0.0991682	+	0.626124i
$723$	−15.1596	−	1.93606i	−0.563791	−	0.0720029i
$724$		−	10.2709i		−	0.381715i
$725$		0			0
$726$	−5.72039	−	15.9571i	−0.212304	−	0.592223i
$727$	23.4214	−	45.9671i	0.868652	−	1.70483i	0.174934	−	0.984580i	$-0.444029\pi$
$727$	23.4214	−	45.9671i	0.868652	−	1.70483i	0.693719	−	0.720246i	$-0.255971\pi$
$728$	0.396131	+	0.0627409i	0.0146816	+	0.00232533i
$729$	−11.6951	+	24.3357i	−0.433152	+	0.901321i
$730$		0			0
$731$	−2.62561	+	3.61384i	−0.0971117	+	0.133663i
$732$	−6.25049	−	2.95165i	−0.231025	−	0.109096i
$733$	20.9008	−	3.31036i	0.771988	−	0.122271i	0.242000	−	0.970276i	$-0.422197\pi$
$733$	20.9008	−	3.31036i	0.771988	−	0.122271i	0.529988	+	0.848005i	$0.322197\pi$
$734$	0.00602247	−	0.0185352i	0.000222293	−	0.000684148i
$735$		0			0
$736$	−0.771931	−	2.37576i	−0.0284538	−	0.0875717i
$737$	−3.32964	−	6.53478i	−0.122649	−	0.240712i
$738$	−10.2710	−	4.47789i	−0.378082	−	0.164834i
$739$	11.8537	−	3.85150i	0.436046	−	0.141680i	−0.0827648	−	0.996569i	$-0.526375\pi$
$739$	11.8537	−	3.85150i	0.436046	−	0.141680i	0.518811	+	0.854889i	$0.326375\pi$
$740$		0			0
$741$	−0.371961	−	12.3722i	−0.0136643	−	0.454505i
$742$	−0.0835816	−	0.527714i	−0.00306838	−	0.0193730i
$743$	2.30237	+	2.30237i	0.0844658	+	0.0844658i	0.748077	−	0.663612i	$-0.230977\pi$
$743$	2.30237	+	2.30237i	0.0844658	+	0.0844658i	−0.663612	+	0.748077i	$0.730977\pi$
$744$	−15.8858	−	4.63870i	−0.582402	−	0.170063i
$745$		0			0
$746$	4.11202	+	5.65971i	0.150552	+	0.207217i
$747$	−1.34093	−	2.28154i	−0.0490621	−	0.0834772i
$748$	3.08236	+	1.57054i	0.112702	+	0.0574247i
$749$	−1.53163			−0.0559646
$750$		0			0
$751$	18.7652			0.684751			0.342375	−	0.939563i	$-0.388769\pi$
$751$	18.7652			0.684751			0.342375	+	0.939563i	$0.388769\pi$
$752$	11.3229	+	5.76930i	0.412904	+	0.210385i
$753$	−24.8641	+	4.70802i	−0.906097	+	0.171570i
$754$	20.9870	+	28.8861i	0.764301	+	1.05197i
$755$		0			0
$756$	−0.375952	+	0.160870i	−0.0136733	+	0.00585079i
$757$	7.02667	+	7.02667i	0.255389	+	0.255389i	0.823176	−	0.567787i	$-0.192200\pi$
$757$	7.02667	+	7.02667i	0.255389	+	0.255389i	−0.567787	+	0.823176i	$0.692200\pi$
$758$	−1.90370	−	12.0195i	−0.0691453	−	0.436567i
$759$	4.76327	−	0.143204i	0.172896	−	0.00519798i
$760$		0			0
$761$	48.1462	−	15.6436i	1.74530	−	0.567081i	0.749782	−	0.661685i	$-0.230158\pi$
$761$	48.1462	−	15.6436i	1.74530	−	0.567081i	0.995515	+	0.0946038i	$0.0301584\pi$
$762$	4.06305	+	3.82587i	0.147189	+	0.138597i
$763$	−0.439694	−	0.862948i	−0.0159180	−	0.0312408i
$764$	−3.35652	−	10.3303i	−0.121435	−	0.373737i
$765$		0			0
$766$	−0.292865	+	0.901344i	−0.0105816	+	0.0325669i
$767$	33.1721	−	5.25394i	1.19777	−	0.189709i
$768$	0.739603	−	1.56620i	0.0266881	−	0.0565154i
$769$	21.2813	−	29.2912i	0.767422	−	1.05627i	−0.229138	−	0.973394i	$-0.573591\pi$
$769$	21.2813	−	29.2912i	0.767422	−	1.05627i	0.996560	−	0.0828721i	$-0.0264093\pi$
$770$		0			0
$771$	3.18239	+	2.16909i	0.114611	+	0.0781178i
$772$	19.1698	+	3.03620i	0.689936	+	0.109275i
$773$	10.6768	−	20.9544i	0.384019	−	0.753679i	−0.615384	−	0.788227i	$-0.710999\pi$
$773$	10.6768	−	20.9544i	0.384019	−	0.753679i	0.999403	+	0.0345481i	$0.0109992\pi$
$774$	−3.29481	+	2.71063i	−0.118429	+	0.0974317i
$775$		0			0
$776$			10.3809i			0.372653i
$777$	−0.178893	+	1.40075i	−0.00641774	+	0.0502516i
$778$	3.10878	−	19.6281i	0.111455	−	0.703701i
$779$	−4.23704	+	3.07839i	−0.151808	+	0.110295i
$780$		0			0
$781$	11.3862	+	8.27256i	0.407430	+	0.296015i
$782$	5.54804	−	5.54804i	0.198397	−	0.198397i
$783$	−33.7932	−	13.5395i	−1.20767	−	0.483862i
$784$	6.65151	+	2.16121i	0.237554	+	0.0771859i
$785$		0			0
$786$	5.63586	+	7.28616i	0.201025	+	0.259889i
$787$	28.0403	−	14.2872i	0.999529	−	0.509285i	0.123913	−	0.992293i	$-0.460456\pi$
$787$	28.0403	−	14.2872i	0.999529	−	0.509285i	0.875616	+	0.483008i	$0.160456\pi$
$788$	−10.8970	+	5.55232i	−0.388191	+	0.197793i
$789$	−20.5342	−	26.5470i	−0.731036	−	0.945099i
$790$		0			0
$791$	0.571382	+	0.185653i	0.0203160	+	0.00660107i
$792$	2.47256	+	2.19184i	0.0878585	+	0.0778837i
$793$	−14.3816	+	14.3816i	−0.510707	+	0.510707i
$794$	−21.8203	−	15.8534i	−0.774375	−	0.562616i
$795$		0			0
$796$	12.8922	−	9.36672i	0.456952	−	0.331995i
$797$	−0.989635	+	6.24831i	−0.0350547	+	0.221326i	−0.998997	−	0.0447862i	$-0.985739\pi$
$797$	−0.989635	+	6.24831i	−0.0350547	+	0.221326i	0.963942	+	0.266113i	$0.0857393\pi$
$798$	−0.0242140	+	0.189599i	−0.000857167	+	0.00671172i
$799$			39.9149i			1.41209i
$800$		0			0
$801$	−6.24966	−	7.59654i	−0.220821	−	0.268410i
$802$	−15.4082	+	30.2402i	−0.544081	+	1.06782i
$803$	1.44469	+	0.228816i	0.0509818	+	0.00807473i
$804$	−9.53041	−	6.49584i	−0.336112	−	0.229091i
$805$		0			0
$806$	−28.6215	+	39.3941i	−1.00815	+	1.38760i
$807$	−4.06450	+	8.60707i	−0.143077	+	0.302983i
$808$	−13.8648	+	2.19597i	−0.487763	+	0.0772540i
$809$	−10.4456	+	32.1483i	−0.367249	+	1.13028i	0.581312	+	0.813681i	$0.302539\pi$
$809$	−10.4456	+	32.1483i	−0.367249	+	1.13028i	−0.948561	+	0.316595i	$0.897461\pi$
$810$		0			0
$811$	−11.3720	−	34.9993i	−0.399324	−	1.22899i	−0.925543	−	0.378643i	$-0.876391\pi$
$811$	−11.3720	−	34.9993i	−0.399324	−	1.22899i	0.526219	−	0.850349i	$-0.323609\pi$
$812$	−0.250313	−	0.491266i	−0.00878425	−	0.0172401i
$813$	9.38626	+	8.83835i	0.329191	+	0.309975i
$814$	10.8518	−	3.52597i	0.380356	−	0.123585i
$815$		0			0
$816$	5.43779	−	0.163483i	0.190361	−	0.00572306i
$817$	0.311969	+	1.96970i	0.0109144	+	0.0689110i
$818$	−11.2430	−	11.2430i	−0.393103	−	0.393103i
$819$	0.0722816	+	1.20103i	0.00252572	+	0.0419675i
$820$		0			0
$821$	−1.94467	−	2.67661i	−0.0678695	−	0.0934144i	0.773733	−	0.633512i	$-0.218387\pi$
$821$	−1.94467	−	2.67661i	−0.0678695	−	0.0934144i	−0.841602	+	0.540098i	$0.818387\pi$
$822$	−19.5469	+	3.70121i	−0.681777	+	0.129095i
$823$	31.6727	+	16.1380i	1.10404	+	0.562537i	0.908385	−	0.418136i	$-0.137316\pi$
$823$	31.6727	+	16.1380i	1.10404	+	0.562537i	0.195656	+	0.980673i	$0.437316\pi$
$824$	13.2042			0.459990
$825$		0			0
$826$	−0.518630			−0.0180454
$827$	7.96567	+	4.05871i	0.276993	+	0.141135i	0.586969	−	0.809609i	$-0.300321\pi$
$827$	7.96567	+	4.05871i	0.276993	+	0.141135i	−0.309976	+	0.950744i	$0.600321\pi$
$828$	6.46082	−	3.79722i	0.224529	−	0.131963i
$829$	−6.82593	−	9.39508i	−0.237074	−	0.326305i	0.673858	−	0.738861i	$-0.264636\pi$
$829$	−6.82593	−	9.39508i	−0.237074	−	0.326305i	−0.910932	+	0.412556i	$0.864636\pi$
$830$		0			0
$831$	31.7489	+	9.27078i	1.10136	+	0.321600i
$832$	−3.60364	−	3.60364i	−0.124934	−	0.124934i
$833$	3.43640	+	21.6966i	0.119064	+	0.751743i
$834$	0.567443	+	18.8743i	0.0196489	+	0.653565i
$835$		0			0
$836$	1.46885	−	0.477258i	0.0508012	−	0.0165063i
$837$	3.31965	−	49.5365i	0.114744	−	1.71223i
$838$	−12.4834	−	24.5000i	−0.431231	−	0.846339i
$839$	−1.99464	−	6.13888i	−0.0688628	−	0.211938i	0.910703	−	0.413062i	$-0.135541\pi$
$839$	−1.99464	−	6.13888i	−0.0688628	−	0.211938i	−0.979566	+	0.201124i	$0.935541\pi$
$840$		0			0
$841$	6.20662	−	19.1020i	0.214021	−	0.658690i
$842$	31.5598	−	4.99858i	1.08762	−	0.172262i
$843$	2.20610	+	1.04178i	0.0759822	+	0.0358809i
$844$	6.50062	−	8.94734i	0.223761	−	0.307980i
$845$		0			0
$846$	−9.58150	+	36.9003i	−0.329419	+	1.26866i
$847$	0.760725	+	0.120487i	0.0261388	+	0.00413998i
$848$	−3.08222	+	6.04920i	−0.105844	+	0.207730i
$849$	−5.57329	−	15.5468i	−0.191275	−	0.533563i
$850$		0			0
$851$		−	25.8790i		−	0.887121i
$852$	21.9545	+	2.80386i	0.752150	+	0.0960586i
$853$	4.13209	−	26.0890i	0.141480	−	0.893271i	−0.810194	−	0.586162i	$-0.800638\pi$
$853$	4.13209	−	26.0890i	0.141480	−	0.893271i	0.951674	−	0.307109i	$-0.0993616\pi$
$854$	0.254089	−	0.184606i	0.00869474	−	0.00631710i
$855$		0			0
$856$	15.7453	+	11.4396i	0.538163	+	0.390998i
$857$	−21.7170	+	21.7170i	−0.741840	+	0.741840i	−0.972932	−	0.231092i	$-0.925770\pi$
$857$	−21.7170	+	21.7170i	−0.741840	+	0.741840i	0.231092	+	0.972932i	$0.425770\pi$
$858$	8.52595	−	4.67208i	0.291071	−	0.159502i
$859$	−2.16755	−	0.704281i	−0.0739560	−	0.0240298i	0.271805	−	0.962352i	$-0.412379\pi$
$859$	−2.16755	−	0.704281i	−0.0739560	−	0.0240298i	−0.345761	+	0.938322i	$0.612379\pi$
$860$		0			0
$861$	0.402691	−	0.311482i	0.0137237	−	0.0106153i
$862$	−7.71732	+	3.93217i	−0.262853	+	0.133930i
$863$	−1.81350	+	0.924026i	−0.0617324	+	0.0314542i	−0.484584	−	0.874745i	$-0.661029\pi$
$863$	−1.81350	+	0.924026i	−0.0617324	+	0.0314542i	0.422852	+	0.906199i	$0.361029\pi$
$864$	5.06634	+	1.15420i	0.172360	+	0.0392666i
$865$		0			0
$866$	−10.2541	−	3.33175i	−0.348448	−	0.113218i
$867$	−5.93849	−	10.8370i	−0.201682	−	0.368043i
$868$	0.531696	−	0.531696i	0.0180469	−	0.0180469i
$869$	−8.87365	−	6.44709i	−0.301018	−	0.218702i
$870$		0			0
$871$	−27.4549	+	19.9472i	−0.930274	+	0.675884i
$872$	−1.92520	+	12.1552i	−0.0651953	+	0.411627i
$873$	−30.4111	+	6.71083i	−1.02926	+	0.227127i
$874$		−	3.50286i		−	0.118486i
$875$		0			0
$876$	2.16529	−	0.776226i	0.0731584	−	0.0262263i
$877$	2.88829	−	5.66858i	0.0975305	−	0.191414i	−0.837086	−	0.547071i	$-0.815743\pi$
$877$	2.88829	−	5.66858i	0.0975305	−	0.191414i	0.934617	+	0.355657i	$0.115743\pi$
$878$	−33.8818	−	5.36634i	−1.14345	−	0.181105i
$879$	30.3873	−	44.5829i	1.02494	−	1.50374i
$880$		0			0
$881$	−3.61099	+	4.97010i	−0.121657	+	0.167447i	−0.865502	−	0.500906i	$-0.833000\pi$
$881$	−3.61099	+	4.97010i	−0.121657	+	0.167447i	0.743844	+	0.668353i	$0.233000\pi$
$882$	−2.03137	+	20.8829i	−0.0683996	+	0.703162i
$883$	39.1067	−	6.19390i	1.31605	−	0.208441i	0.541362	−	0.840789i	$-0.317909\pi$
$883$	39.1067	−	6.19390i	1.31605	−	0.208441i	0.774684	+	0.632348i	$0.217909\pi$
$884$	4.94649	−	15.2237i	0.166369	−	0.512030i
$885$		0			0
$886$	2.00247	+	6.16296i	0.0672742	+	0.207049i
$887$	−21.9363	−	43.0525i	−0.736550	−	1.44556i	−0.889313	−	0.457299i	$-0.848817\pi$
$887$	−21.9363	−	43.0525i	−0.736550	−	1.44556i	0.152763	−	0.988263i	$-0.451183\pi$
$888$	12.3011	−	13.0637i	0.412798	−	0.438388i
$889$	−0.241160	+	0.0783578i	−0.00808826	+	0.00262804i
$890$		0			0
$891$	−4.82263	+	8.66035i	−0.161564	+	0.290133i
$892$	−0.859348	−	5.42571i	−0.0287731	−	0.181666i
$893$	12.6005	+	12.6005i	0.421660	+	0.421660i
$894$	−6.97549	+	23.8884i	−0.233295	+	0.798948i
$895$		0			0
$896$	0.0462573	+	0.0636677i	0.00154535	+	0.00212699i
$897$	−4.10233	−	21.6653i	−0.136973	−	0.723383i
$898$	20.2669	+	10.3265i	0.676314	+	0.344599i
$899$	66.9409			2.23260
$900$		0			0
$901$	−21.3243			−0.710416
$902$	−3.66526	−	1.86754i	−0.122040	−	0.0621824i
$903$	−0.0360655	−	0.190470i	−0.00120019	−	0.00633844i
$904$	−4.48722	−	6.17613i	−0.149243	−	0.205415i
$905$		0			0
$906$	0.158481	−	0.542736i	0.00526517	−	0.0180312i
$907$	24.7561	+	24.7561i	0.822014	+	0.822014i	0.986397	−	0.164383i	$-0.0525632\pi$
$907$	24.7561	+	24.7561i	0.822014	+	0.822014i	−0.164383	+	0.986397i	$0.552563\pi$
$908$	−1.05800	−	6.67994i	−0.0351109	−	0.221682i
$909$	−15.3962	−	39.1977i	−0.510660	−	1.30010i
$910$		0			0
$911$	48.5335	−	15.7695i	1.60799	−	0.522466i	0.638921	−	0.769272i	$-0.279381\pi$
$911$	48.5335	−	15.7695i	1.60799	−	0.522466i	0.969065	+	0.246806i	$0.0793810\pi$
$912$	1.66502	−	1.76823i	0.0551342	−	0.0585521i
$913$	−0.441091	−	0.865690i	−0.0145980	−	0.0286502i
$914$	2.74480	+	8.44762i	0.0907898	+	0.279422i
$915$		0			0
$916$	0.938563	−	2.88860i	0.0310110	−	0.0954420i
$917$	−0.413380	+	0.0654729i	−0.0136510	+	0.00216211i
$918$	3.99424	+	15.8244i	0.131830	+	0.522284i
$919$	6.34757	−	8.73668i	0.209387	−	0.288196i	−0.691387	−	0.722485i	$-0.743000\pi$
$919$	6.34757	−	8.73668i	0.209387	−	0.288196i	0.900774	+	0.434288i	$0.143000\pi$
$920$		0			0
$921$	2.15835	−	3.16664i	0.0711200	−	0.104344i
$922$	−22.1617	−	3.51006i	−0.729855	−	0.115598i
$923$	29.5652	−	58.0249i	0.973150	−	1.90991i
$924$	−0.141323	+	0.0506624i	−0.00464919	+	0.00166667i
$925$		0			0
$926$		−	24.2111i		−	0.795626i
$927$	8.53597	+	38.6819i	0.280358	+	1.27048i
$928$	−1.09599	+	6.91981i	−0.0359777	+	0.227154i
$929$	−38.0194	+	27.6227i	−1.24738	+	0.906272i	−0.998067	−	0.0621513i	$-0.980204\pi$
$929$	−38.0194	+	27.6227i	−1.24738	+	0.906272i	−0.249310	+	0.968424i	$0.580204\pi$
$930$		0			0
$931$	7.93409	+	5.76446i	0.260029	+	0.188922i
$932$	−0.977696	+	0.977696i	−0.0320255	+	0.0320255i
$933$	11.3463	+	20.7056i	0.371463	+	0.677871i
$934$	12.8115	+	4.16270i	0.419204	+	0.136208i
$935$		0			0
$936$	8.22734	−	12.8866i	0.268919	−	0.421210i
$937$	−40.7667	+	20.7717i	−1.33179	+	0.678581i	−0.967539	−	0.252721i	$-0.918675\pi$
$937$	−40.7667	+	20.7717i	−1.33179	+	0.678581i	−0.364250	+	0.931301i	$0.618675\pi$
$938$	0.466926	−	0.237911i	0.0152457	−	0.00776806i
$939$	−26.1652	+	20.2389i	−0.853870	+	0.660470i
$940$		0			0
$941$	−29.1364	−	9.46699i	−0.949820	−	0.308615i	−0.207177	−	0.978303i	$-0.566428\pi$
$941$	−29.1364	−	9.46699i	−0.949820	−	0.308615i	−0.742642	+	0.669688i	$0.766428\pi$
$942$	−7.46589	+	4.09119i	−0.243252	+	0.133298i
$943$	−6.59721	+	6.59721i	−0.214835	+	0.214835i
$944$	5.33155	+	3.87360i	0.173527	+	0.126075i
$945$		0			0
$946$	−1.26723	+	0.920697i	−0.0412012	+	0.0299344i
$947$	−2.25687	+	14.2493i	−0.0733384	+	0.463040i	0.923501	+	0.383596i	$0.125315\pi$
$947$	−2.25687	+	14.2493i	−0.0733384	+	0.463040i	−0.996839	+	0.0794442i	$0.974685\pi$
$948$	−17.1099	−	2.18514i	−0.555704	−	0.0709701i
$949$		−	6.76809i		−	0.219701i
$950$		0			0
$951$	−5.31067	−	14.8142i	−0.172210	−	0.480382i
$952$	−0.112219	+	0.220242i	−0.00363704	+	0.00713809i
$953$	−3.89283	−	0.616563i	−0.126101	−	0.0199724i	0.0930649	−	0.995660i	$-0.470334\pi$
$953$	−3.89283	−	0.616563i	−0.126101	−	0.0199724i	−0.219166	+	0.975688i	$0.570334\pi$
$954$	−19.7138	−	5.11887i	−0.638257	−	0.165729i
$955$		0			0
$956$	6.68358	−	9.19915i	0.216162	−	0.297522i
$957$	−12.0856	−	5.70713i	−0.390671	−	0.184485i
$958$	17.0684	−	2.70337i	0.551455	−	0.0873420i
$959$	0.279326	−	0.859676i	0.00901989	−	0.0277604i
$960$		0			0
$961$	18.6313	+	57.3413i	0.601010	+	1.84972i
$962$	−23.9693	−	47.0424i	−0.772801	−	1.51671i
$963$	−23.3339	+	53.5214i	−0.751925	+	1.72470i
$964$	−8.39163	+	2.72661i	−0.270276	+	0.0878181i
$965$		0			0
$966$	0.0102323	+	0.340347i	0.000329218	+	0.0109505i
$967$	8.16627	+	51.5598i	0.262610	+	1.65805i	0.668189	+	0.743992i	$0.267070\pi$
$967$	8.16627	+	51.5598i	0.262610	+	1.65805i	−0.405579	+	0.914060i	$0.632930\pi$
$968$	−6.92040	−	6.92040i	−0.222430	−	0.222430i
$969$	7.32280	+	2.13828i	0.235242	+	0.0686914i
$970$		0			0
$971$	2.69176	+	3.70489i	0.0863828	+	0.118896i	0.850021	−	0.526748i	$-0.176589\pi$
$971$	2.69176	+	3.70489i	0.0863828	+	0.118896i	−0.763638	+	0.645644i	$0.776589\pi$
$972$	−0.106057	+	15.5881i	−0.00340179	+	0.499988i
$973$	−0.764451	−	0.389507i	−0.0245072	−	0.0124870i
$974$	−3.62274			−0.116080
$975$		0			0
$976$	−3.99086			−0.127744
$977$	−3.68285	−	1.87651i	−0.117825	−	0.0600348i	0.394085	−	0.919074i	$-0.371062\pi$
$977$	−3.68285	−	1.87651i	−0.117825	−	0.0600348i	−0.511910	+	0.859039i	$0.671062\pi$
$978$	−2.60885	+	0.493987i	−0.0834219	+	0.0157960i
$979$	−2.12277	−	2.92174i	−0.0678439	−	0.0933792i
$980$		0			0
$981$	−36.8535	+	2.21795i	−1.17664	+	0.0708137i
$982$	−4.08144	−	4.08144i	−0.130244	−	0.130244i
$983$	−4.05781	−	25.6200i	−0.129424	−	0.817151i	−0.963931	−	0.266153i	$-0.914247\pi$
$983$	−4.05781	−	25.6200i	−0.129424	−	0.817151i	0.834507	−	0.550998i	$-0.185753\pi$
$984$	−6.46612	+	0.194399i	−0.206132	+	0.00619722i
$985$		0			0
$986$	−20.9285	+	6.80010i	−0.666501	+	0.216559i
$987$	−1.26111	−	1.18749i	−0.0401415	−	0.0377983i
$988$	−3.24437	−	6.36743i	−0.103217	−	0.202575i
$989$	1.09782	+	3.37875i	0.0349087	+	0.107438i
$990$		0			0
$991$	−7.36863	+	22.6783i	−0.234072	+	0.720400i	0.763171	+	0.646197i	$0.223641\pi$
$991$	−7.36863	+	22.6783i	−0.234072	+	0.720400i	−0.997243	+	0.0742035i	$0.976359\pi$
$992$	−9.43706	+	1.49468i	−0.299627	+	0.0474562i
$993$	−8.17738	+	17.3166i	−0.259501	+	0.549526i
$994$	−0.591094	+	0.813572i	−0.0187484	+	0.0258049i
$995$		0			0
$996$	−1.26253	−	0.860532i	−0.0400049	−	0.0272670i
$997$	−15.5032	−	2.45546i	−0.490990	−	0.0777652i	−0.0939699	−	0.995575i	$-0.529956\pi$
$997$	−15.5032	−	2.45546i	−0.490990	−	0.0777652i	−0.397020	+	0.917810i	$0.629956\pi$
$998$	12.9651	−	25.4455i	0.410404	−	0.805464i
$999$	46.2225	+	27.5912i	1.46241	+	0.872947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.b.107.8		80
3.2	odd	2	inner	750.2.l.b.107.2		80
5.2	odd	4		750.2.l.c.143.5		80
5.3	odd	4		750.2.l.a.143.6		80
5.4	even	2		150.2.l.a.17.3	✓	80
15.2	even	4		750.2.l.c.143.10		80
15.8	even	4		750.2.l.a.143.1		80
15.14	odd	2		150.2.l.a.17.9	yes	80
25.3	odd	20	inner	750.2.l.b.743.2		80
25.4	even	10		750.2.l.c.257.10		80
25.21	even	5		750.2.l.a.257.1		80
25.22	odd	20		150.2.l.a.53.9	yes	80
75.29	odd	10		750.2.l.c.257.5		80
75.47	even	20		150.2.l.a.53.3	yes	80
75.53	even	20	inner	750.2.l.b.743.8		80
75.71	odd	10		750.2.l.a.257.6		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.17.3	✓	80	5.4	even	2
150.2.l.a.17.9	yes	80	15.14	odd	2
150.2.l.a.53.3	yes	80	75.47	even	20
150.2.l.a.53.9	yes	80	25.22	odd	20
750.2.l.a.143.1		80	15.8	even	4
750.2.l.a.143.6		80	5.3	odd	4
750.2.l.a.257.1		80	25.21	even	5
750.2.l.a.257.6		80	75.71	odd	10
750.2.l.b.107.2		80	3.2	odd	2	inner
750.2.l.b.107.8		80	1.1	even	1	trivial
750.2.l.b.743.2		80	25.3	odd	20	inner
750.2.l.b.743.8		80	75.53	even	20	inner
750.2.l.c.143.5		80	5.2	odd	4
750.2.l.c.143.10		80	15.2	even	4
750.2.l.c.257.5		80	75.29	odd	10
750.2.l.c.257.10		80	25.4	even	10

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.891007 + 0.453990i) q^{2} +(0.322239 + 1.70181i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-0.485490 + 1.66262i) q^{6} +(-0.0556476 - 0.0556476i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-2.79232 + 1.09678i) q^{9} +O(q^{10})\)	\(q+(0.891007 + 0.453990i) q^{2} +(0.322239 + 1.70181i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-0.485490 + 1.66262i) q^{6} +(-0.0556476 - 0.0556476i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-2.79232 + 1.09678i) q^{9} +(-1.04749 + 0.340351i) q^{11} +(-1.18739 + 1.26100i) q^{12} +(2.31368 + 4.54086i) q^{13} +(-0.0243189 - 0.0748459i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-3.10226 + 0.491350i) q^{17} +(-2.98591 - 0.290452i) q^{18} +(-0.824223 + 1.13445i) q^{19} +(0.0767699 - 0.112634i) q^{21} +(-1.08784 - 0.172297i) q^{22} +(-1.13408 + 2.22575i) q^{23} +(-1.63045 + 0.584493i) q^{24} +5.09632i q^{26} +(-2.76630 - 4.39859i) q^{27} +(0.0123110 - 0.0777287i) q^{28} +(5.66803 - 4.11807i) q^{29} +(7.72991 + 5.61611i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.916756 - 1.67296i) q^{33} +(-2.98720 - 0.970601i) q^{34} +(-2.52860 - 1.61437i) q^{36} +(-9.23065 + 4.70325i) q^{37} +(-1.24942 + 0.636609i) q^{38} +(-6.98213 + 5.40069i) q^{39} +(3.55210 + 1.15415i) q^{41} +(0.119537 - 0.0655044i) q^{42} +(1.00563 - 1.00563i) q^{43} +(-0.891050 - 0.647386i) q^{44} +(-2.02094 + 1.46830i) q^{46} +(1.98797 - 12.5515i) q^{47} +(-1.71810 - 0.219422i) q^{48} -6.99381i q^{49} +(-1.83585 - 5.12113i) q^{51} +(-2.31368 + 4.54086i) q^{52} +(6.70559 + 1.06206i) q^{53} +(-0.467880 - 5.17504i) q^{54} +(0.0462573 - 0.0636677i) q^{56} +(-2.19621 - 1.03711i) q^{57} +(6.91981 - 1.09599i) q^{58} +(2.03647 - 6.26761i) q^{59} +(1.23324 + 3.79553i) q^{61} +(4.33774 + 8.51329i) q^{62} +(0.216419 + 0.0943531i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-0.0573270 - 1.90682i) q^{66} +(1.04169 + 6.57696i) q^{67} +(-2.22097 - 2.22097i) q^{68} +(-4.15326 - 1.21276i) q^{69} +(-7.51096 - 10.3379i) q^{71} +(-1.52009 - 2.58637i) q^{72} +(-1.18329 - 0.602914i) q^{73} -10.3598 q^{74} -1.40225 q^{76} +(0.0772302 + 0.0393507i) q^{77} +(-8.67298 + 1.64223i) q^{78} +(5.85354 + 8.05671i) q^{79} +(6.59415 - 6.12512i) q^{81} +(2.64098 + 2.64098i) q^{82} +(0.137997 + 0.871279i) q^{83} +(0.136247 - 0.00409615i) q^{84} +(1.35257 - 0.439477i) q^{86} +(8.83463 + 8.31892i) q^{87} +(-0.500025 - 0.981353i) q^{88} +(1.01326 + 3.11850i) q^{89} +(0.123937 - 0.381439i) q^{91} +(-2.46727 + 0.390777i) q^{92} +(-7.06668 + 14.9646i) q^{93} +(7.46957 - 10.2810i) q^{94} +(-1.43122 - 0.975505i) q^{96} +(10.2531 + 1.62393i) q^{97} +(3.17512 - 6.23153i) q^{98} +(2.55165 - 2.09924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) \) 80 * q - 4 * q^3 - 4 * q^7	\( 80 q - 4 q^{3} - 4 q^{7} + 4 q^{12} + 20 q^{16} + 8 q^{18} - 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} - 40 q^{34} + 24 q^{37} - 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} + 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} + 80 q^{79} - 40 q^{81} - 96 q^{82} + 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97}+O(q^{100}) \) 80 * q - 4 * q^3 - 4 * q^7 + 4 * q^12 + 20 * q^16 + 8 * q^18 - 40 * q^19 + 36 * q^22 - 4 * q^27 + 16 * q^28 - 4 * q^33 - 40 * q^34 + 24 * q^37 - 40 * q^39 + 4 * q^42 + 24 * q^43 + 4 * q^48 + 64 * q^57 - 20 * q^58 - 64 * q^63 - 96 * q^67 + 140 * q^69 - 8 * q^72 - 100 * q^73 - 100 * q^78 + 80 * q^79 - 40 * q^81 - 96 * q^82 + 60 * q^84 - 80 * q^87 - 4 * q^88 - 12 * q^93 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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