LMFDB - Embedded newform 400.2.u.b.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(81,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("400.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.u (of order $5$, degree $4$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	400.81
Dual form			400.2.u.b.321.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{3} +(-0.690983 + 2.12663i) q^{5} -0.618034 q^{7} +(-0.618034 + 1.90211i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{3} +(-0.690983 + 2.12663i) q^{5} -0.618034 q^{7} +(-0.618034 + 1.90211i) q^{9} +(1.61803 + 4.97980i) q^{11} +(0.572949 - 1.76336i) q^{13} +(0.690983 + 2.12663i) q^{15} +(4.23607 + 3.07768i) q^{17} +(0.690983 + 0.502029i) q^{19} +(-0.500000 + 0.363271i) q^{21} +(-1.16312 - 3.57971i) q^{23} +(-4.04508 - 2.93893i) q^{25} +(1.54508 + 4.75528i) q^{27} +(2.92705 - 2.12663i) q^{29} +(-2.42705 - 1.76336i) q^{31} +(4.23607 + 3.07768i) q^{33} +(0.427051 - 1.31433i) q^{35} +(-0.0729490 + 0.224514i) q^{37} +(-0.572949 - 1.76336i) q^{39} +(-0.236068 + 0.726543i) q^{41} +4.85410 q^{43} +(-3.61803 - 2.62866i) q^{45} +(0.500000 - 0.363271i) q^{47} -6.61803 q^{49} +5.23607 q^{51} +(2.80902 - 2.04087i) q^{53} -11.7082 q^{55} +0.854102 q^{57} +(3.35410 - 10.3229i) q^{59} +(2.69098 + 8.28199i) q^{61} +(0.381966 - 1.17557i) q^{63} +(3.35410 + 2.43690i) q^{65} +(3.85410 + 2.80017i) q^{67} +(-3.04508 - 2.21238i) q^{69} +(-5.35410 + 3.88998i) q^{71} +(-2.78115 - 8.55951i) q^{73} -5.00000 q^{75} +(-1.00000 - 3.07768i) q^{77} +(-6.54508 + 4.75528i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-5.04508 - 3.66547i) q^{83} +(-9.47214 + 6.88191i) q^{85} +(1.11803 - 3.44095i) q^{87} +(-2.76393 - 8.50651i) q^{89} +(-0.354102 + 1.08981i) q^{91} -3.00000 q^{93} +(-1.54508 + 1.12257i) q^{95} +(3.11803 - 2.26538i) q^{97} -10.4721 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} - 5 q^{5} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 4 * q + q^3 - 5 * q^5 + 2 * q^7 + 2 * q^9	$ 4 q + q^{3} - 5 q^{5} + 2 q^{7} + 2 q^{9} + 2 q^{11} + 9 q^{13} + 5 q^{15} + 8 q^{17} + 5 q^{19} - 2 q^{21} + 11 q^{23} - 5 q^{25} - 5 q^{27} + 5 q^{29} - 3 q^{31} + 8 q^{33} - 5 q^{35} - 7 q^{37} - 9 q^{39} + 8 q^{41} + 6 q^{43} - 10 q^{45} + 2 q^{47} - 22 q^{49} + 12 q^{51} + 9 q^{53} - 20 q^{55} - 10 q^{57} + 13 q^{61} + 6 q^{63} + 2 q^{67} - q^{69} - 8 q^{71} + 9 q^{73} - 20 q^{75} - 4 q^{77} - 15 q^{79} - q^{81} - 9 q^{83} - 20 q^{85} - 20 q^{89} + 12 q^{91} - 12 q^{93} + 5 q^{95} + 8 q^{97} - 24 q^{99}+O(q^{100}) $ 4 * q + q^3 - 5 * q^5 + 2 * q^7 + 2 * q^9 + 2 * q^11 + 9 * q^13 + 5 * q^15 + 8 * q^17 + 5 * q^19 - 2 * q^21 + 11 * q^23 - 5 * q^25 - 5 * q^27 + 5 * q^29 - 3 * q^31 + 8 * q^33 - 5 * q^35 - 7 * q^37 - 9 * q^39 + 8 * q^41 + 6 * q^43 - 10 * q^45 + 2 * q^47 - 22 * q^49 + 12 * q^51 + 9 * q^53 - 20 * q^55 - 10 * q^57 + 13 * q^61 + 6 * q^63 + 2 * q^67 - q^69 - 8 * q^71 + 9 * q^73 - 20 * q^75 - 4 * q^77 - 15 * q^79 - q^81 - 9 * q^83 - 20 * q^85 - 20 * q^89 + 12 * q^91 - 12 * q^93 + 5 * q^95 + 8 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

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			0
$2$		0			0
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i	−0.329218	−	0.944254i	$-0.606785\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i	0.796305	+	0.604896i	$0.206785\pi$
$4$		0			0
$5$	−0.690983	+	2.12663i	−0.309017	+	0.951057i
$5$	−0.690983	+	2.12663i	−0.309017	+	0.951057i
$6$		0			0
$7$	−0.618034			−0.233595			−0.116797	−	0.993156i	$-0.537263\pi$
$7$	−0.618034			−0.233595			−0.116797	+	0.993156i	$0.537263\pi$
$8$		0			0
$9$	−0.618034	+	1.90211i	−0.206011	+	0.634038i
$10$		0			0
$11$	1.61803	+	4.97980i	0.487856	+	1.50147i	0.827802	+	0.561020i	$0.189591\pi$
$11$	1.61803	+	4.97980i	0.487856	+	1.50147i	−0.339946	+	0.940445i	$0.610409\pi$
$12$		0			0
$13$	0.572949	−	1.76336i	0.158907	−	0.489067i	−0.839628	−	0.543161i	$-0.817227\pi$
$13$	0.572949	−	1.76336i	0.158907	−	0.489067i	0.998536	+	0.0540944i	$0.0172272\pi$
$14$		0			0
$15$	0.690983	+	2.12663i	0.178411	+	0.549093i
$16$		0			0
$17$	4.23607	+	3.07768i	1.02740	+	0.746448i	0.967786	−	0.251774i	$-0.0810139\pi$
$17$	4.23607	+	3.07768i	1.02740	+	0.746448i	0.0596113	+	0.998222i	$0.481014\pi$
$18$		0			0
$19$	0.690983	+	0.502029i	0.158522	+	0.115173i	0.664219	−	0.747538i	$-0.268764\pi$
$19$	0.690983	+	0.502029i	0.158522	+	0.115173i	−0.505696	+	0.862712i	$0.668764\pi$
$20$		0			0
$21$	−0.500000	+	0.363271i	−0.109109	+	0.0792723i
$22$		0			0
$23$	−1.16312	−	3.57971i	−0.242527	−	0.746422i	−0.996033	−	0.0889808i	$-0.971639\pi$
$23$	−1.16312	−	3.57971i	−0.242527	−	0.746422i	0.753506	−	0.657441i	$-0.228361\pi$
$24$		0			0
$25$	−4.04508	−	2.93893i	−0.809017	−	0.587785i
$26$		0			0
$27$	1.54508	+	4.75528i	0.297352	+	0.915155i
$28$		0			0
$29$	2.92705	−	2.12663i	0.543540	−	0.394905i	−0.281858	−	0.959456i	$-0.590951\pi$
$29$	2.92705	−	2.12663i	0.543540	−	0.394905i	0.825398	+	0.564551i	$0.190951\pi$
$30$		0			0
$31$	−2.42705	−	1.76336i	−0.435911	−	0.316708i	0.348097	−	0.937459i	$-0.386828\pi$
$31$	−2.42705	−	1.76336i	−0.435911	−	0.316708i	−0.784008	+	0.620750i	$0.786828\pi$
$32$		0			0
$33$	4.23607	+	3.07768i	0.737405	+	0.535756i
$34$		0			0
$35$	0.427051	−	1.31433i	0.0721848	−	0.222162i
$36$		0			0
$37$	−0.0729490	+	0.224514i	−0.0119927	+	0.0369099i	−0.956874	−	0.290504i	$-0.906177\pi$
$37$	−0.0729490	+	0.224514i	−0.0119927	+	0.0369099i	0.944881	+	0.327414i	$0.106177\pi$
$38$		0			0
$39$	−0.572949	−	1.76336i	−0.0917453	−	0.282363i
$40$		0			0
$41$	−0.236068	+	0.726543i	−0.0368676	+	0.113467i	−0.967797	−	0.251733i	$-0.918999\pi$
$41$	−0.236068	+	0.726543i	−0.0368676	+	0.113467i	0.930929	+	0.365200i	$0.118999\pi$
$42$		0			0
$43$	4.85410			0.740244			0.370122	−	0.928983i	$-0.379316\pi$
$43$	4.85410			0.740244			0.370122	+	0.928983i	$0.379316\pi$
$44$		0			0
$45$	−3.61803	−	2.62866i	−0.539345	−	0.391857i
$46$		0			0
$47$	0.500000	−	0.363271i	0.0729325	−	0.0529886i	−0.550722	−	0.834689i	$-0.685647\pi$
$47$	0.500000	−	0.363271i	0.0729325	−	0.0529886i	0.623654	+	0.781700i	$0.285647\pi$
$48$		0			0
$49$	−6.61803			−0.945433
$50$		0			0
$51$	5.23607			0.733196
$52$		0			0
$53$	2.80902	−	2.04087i	0.385848	−	0.280335i	−0.377904	−	0.925845i	$-0.623355\pi$
$53$	2.80902	−	2.04087i	0.385848	−	0.280335i	0.763752	+	0.645510i	$0.223355\pi$
$54$		0			0
$55$	−11.7082			−1.57873
$56$		0			0
$57$	0.854102			0.113129
$58$		0			0
$59$	3.35410	−	10.3229i	0.436667	−	1.34392i	−0.454702	−	0.890644i	$-0.650254\pi$
$59$	3.35410	−	10.3229i	0.436667	−	1.34392i	0.891369	−	0.453279i	$-0.149746\pi$
$60$		0			0
$61$	2.69098	+	8.28199i	0.344545	+	1.06040i	0.961827	+	0.273659i	$0.0882338\pi$
$61$	2.69098	+	8.28199i	0.344545	+	1.06040i	−0.617282	+	0.786742i	$0.711766\pi$
$62$		0			0
$63$	0.381966	−	1.17557i	0.0481232	−	0.148108i
$64$		0			0
$65$	3.35410	+	2.43690i	0.416025	+	0.302260i
$66$		0			0
$67$	3.85410	+	2.80017i	0.470853	+	0.342095i	0.797774	−	0.602957i	$-0.206011\pi$
$67$	3.85410	+	2.80017i	0.470853	+	0.342095i	−0.326920	+	0.945052i	$0.606011\pi$
$68$		0			0
$69$	−3.04508	−	2.21238i	−0.366585	−	0.266340i
$70$		0			0
$71$	−5.35410	+	3.88998i	−0.635415	+	0.461656i	−0.858272	−	0.513195i	$-0.828462\pi$
$71$	−5.35410	+	3.88998i	−0.635415	+	0.461656i	0.222857	+	0.974851i	$0.428462\pi$
$72$		0			0
$73$	−2.78115	−	8.55951i	−0.325509	−	1.00181i	−0.971210	−	0.238224i	$-0.923435\pi$
$73$	−2.78115	−	8.55951i	−0.325509	−	1.00181i	0.645701	−	0.763590i	$-0.276565\pi$
$74$		0			0
$75$	−5.00000			−0.577350
$76$		0			0
$77$	−1.00000	−	3.07768i	−0.113961	−	0.350735i
$78$		0			0
$79$	−6.54508	+	4.75528i	−0.736380	+	0.535011i	−0.891575	−	0.452873i	$-0.850399\pi$
$79$	−6.54508	+	4.75528i	−0.736380	+	0.535011i	0.155196	+	0.987884i	$0.450399\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	−5.04508	−	3.66547i	−0.553770	−	0.402337i	0.275404	−	0.961329i	$-0.411189\pi$
$83$	−5.04508	−	3.66547i	−0.553770	−	0.402337i	−0.829174	+	0.558991i	$0.811189\pi$
$84$		0			0
$85$	−9.47214	+	6.88191i	−1.02740	+	0.746448i
$86$		0			0
$87$	1.11803	−	3.44095i	0.119866	−	0.368909i
$88$		0			0
$89$	−2.76393	−	8.50651i	−0.292976	−	0.901688i	−0.983894	−	0.178754i	$-0.942793\pi$
$89$	−2.76393	−	8.50651i	−0.292976	−	0.901688i	0.690918	−	0.722934i	$-0.257207\pi$
$90$		0			0
$91$	−0.354102	+	1.08981i	−0.0371200	+	0.114244i
$92$		0			0
$93$	−3.00000			−0.311086
$94$		0			0
$95$	−1.54508	+	1.12257i	−0.158522	+	0.115173i
$96$		0			0
$97$	3.11803	−	2.26538i	0.316588	−	0.230015i	−0.418130	−	0.908387i	$-0.637314\pi$
$97$	3.11803	−	2.26538i	0.316588	−	0.230015i	0.734718	+	0.678372i	$0.237314\pi$
$98$		0			0
$99$	−10.4721			−1.05249
$100$		0			0
$101$	1.47214			0.146483			0.0732415	−	0.997314i	$-0.476666\pi$
$101$	1.47214			0.146483			0.0732415	+	0.997314i	$0.476666\pi$
$102$		0			0
$103$	6.92705	−	5.03280i	0.682543	−	0.495896i	−0.191658	−	0.981462i	$-0.561386\pi$
$103$	6.92705	−	5.03280i	0.682543	−	0.495896i	0.874200	+	0.485566i	$0.161386\pi$
$104$		0			0
$105$	−0.427051	−	1.31433i	−0.0416759	−	0.128265i
$106$		0			0
$107$	16.4164			1.58703			0.793517	−	0.608548i	$-0.208248\pi$
$107$	16.4164			1.58703			0.793517	+	0.608548i	$0.208248\pi$
$108$		0			0
$109$	3.09017	−	9.51057i	0.295985	−	0.910947i	−0.686904	−	0.726748i	$-0.741031\pi$
$109$	3.09017	−	9.51057i	0.295985	−	0.910947i	0.982889	−	0.184199i	$-0.0589691\pi$
$110$		0			0
$111$	0.0729490	+	0.224514i	0.00692401	+	0.0213099i
$112$		0			0
$113$	5.20820	−	16.0292i	0.489947	−	1.50790i	−0.334740	−	0.942311i	$-0.608648\pi$
$113$	5.20820	−	16.0292i	0.489947	−	1.50790i	0.824687	−	0.565590i	$-0.191352\pi$
$114$		0			0
$115$	8.41641			0.784834
$116$		0			0
$117$	3.00000	+	2.17963i	0.277350	+	0.201507i
$118$		0			0
$119$	−2.61803	−	1.90211i	−0.239995	−	0.174366i
$120$		0			0
$121$	−13.2812	+	9.64932i	−1.20738	+	0.877211i
$122$		0			0
$123$	0.236068	+	0.726543i	0.0212855	+	0.0655101i
$124$		0			0
$125$	9.04508	−	6.57164i	0.809017	−	0.587785i
$126$		0			0
$127$	−6.14590	−	18.9151i	−0.545360	−	1.67845i	−0.720132	−	0.693837i	$-0.755919\pi$
$127$	−6.14590	−	18.9151i	−0.545360	−	1.67845i	0.174772	−	0.984609i	$-0.444081\pi$
$128$		0			0
$129$	3.92705	−	2.85317i	0.345758	−	0.251208i
$130$		0			0
$131$	5.50000	+	3.99598i	0.480537	+	0.349131i	0.801534	−	0.597950i	$-0.204018\pi$
$131$	5.50000	+	3.99598i	0.480537	+	0.349131i	−0.320996	+	0.947080i	$0.604018\pi$
$132$		0			0
$133$	−0.427051	−	0.310271i	−0.0370300	−	0.0269039i
$134$		0			0
$135$	−11.1803			−0.962250
$136$		0			0
$137$	−3.69098	+	11.3597i	−0.315342	+	0.970523i	0.660271	+	0.751027i	$0.270441\pi$
$137$	−3.69098	+	11.3597i	−0.315342	+	0.970523i	−0.975613	+	0.219496i	$0.929559\pi$
$138$		0			0
$139$	−1.54508	−	4.75528i	−0.131052	−	0.403338i	0.863903	−	0.503659i	$-0.168013\pi$
$139$	−1.54508	−	4.75528i	−0.131052	−	0.403338i	−0.994955	+	0.100321i	$0.968013\pi$
$140$		0			0
$141$	0.190983	−	0.587785i	0.0160837	−	0.0495004i
$142$		0			0
$143$	9.70820			0.811841
$144$		0			0
$145$	2.50000	+	7.69421i	0.207614	+	0.638969i
$146$		0			0
$147$	−5.35410	+	3.88998i	−0.441599	+	0.320840i
$148$		0			0
$149$	−3.94427			−0.323127			−0.161564	−	0.986862i	$-0.551654\pi$
$149$	−3.94427			−0.323127			−0.161564	+	0.986862i	$0.551654\pi$
$150$		0			0
$151$	−14.5623			−1.18506			−0.592532	−	0.805547i	$-0.701872\pi$
$151$	−14.5623			−1.18506			−0.592532	+	0.805547i	$0.701872\pi$
$152$		0			0
$153$	−8.47214	+	6.15537i	−0.684932	+	0.497632i
$154$		0			0
$155$	5.42705	−	3.94298i	0.435911	−	0.316708i
$156$		0			0
$157$	13.1803			1.05191			0.525953	−	0.850514i	$-0.323709\pi$
$157$	13.1803			1.05191			0.525953	+	0.850514i	$0.323709\pi$
$158$		0			0
$159$	1.07295	−	3.30220i	0.0850904	−	0.261881i
$160$		0			0
$161$	0.718847	+	2.21238i	0.0566531	+	0.174360i
$162$		0			0
$163$	−3.39919	+	10.4616i	−0.266245	+	0.819417i	0.725159	+	0.688581i	$0.241766\pi$
$163$	−3.39919	+	10.4616i	−0.266245	+	0.819417i	−0.991404	+	0.130836i	$0.958234\pi$
$164$		0			0
$165$	−9.47214	+	6.88191i	−0.737405	+	0.535756i
$166$		0			0
$167$	11.7812	+	8.55951i	0.911653	+	0.662355i	0.941432	−	0.337202i	$-0.109480\pi$
$167$	11.7812	+	8.55951i	0.911653	+	0.662355i	−0.0297794	+	0.999556i	$0.509480\pi$
$168$		0			0
$169$	7.73607	+	5.62058i	0.595082	+	0.432352i
$170$		0			0
$171$	−1.38197	+	1.00406i	−0.105682	+	0.0767822i
$172$		0			0
$173$	5.83688	+	17.9641i	0.443770	+	1.36578i	0.883827	+	0.467813i	$0.154958\pi$
$173$	5.83688	+	17.9641i	0.443770	+	1.36578i	−0.440057	+	0.897970i	$0.645042\pi$
$174$		0			0
$175$	2.50000	+	1.81636i	0.188982	+	0.137304i
$176$		0			0
$177$	−3.35410	−	10.3229i	−0.252110	−	0.775914i
$178$		0			0
$179$	−0.427051	+	0.310271i	−0.0319193	+	0.0231907i	−0.603631	−	0.797264i	$-0.706280\pi$
$179$	−0.427051	+	0.310271i	−0.0319193	+	0.0231907i	0.571711	+	0.820455i	$0.306280\pi$
$180$		0			0
$181$	−0.236068	−	0.171513i	−0.0175468	−	0.0127485i	0.578977	−	0.815344i	$-0.303452\pi$
$181$	−0.236068	−	0.171513i	−0.0175468	−	0.0127485i	−0.596524	+	0.802595i	$0.703452\pi$
$182$		0			0
$183$	7.04508	+	5.11855i	0.520788	+	0.378374i
$184$		0			0
$185$	−0.427051	−	0.310271i	−0.0313974	−	0.0228116i
$186$		0			0
$187$	−8.47214	+	26.0746i	−0.619544	+	1.90676i
$188$		0			0
$189$	−0.954915	−	2.93893i	−0.0694598	−	0.213775i
$190$		0			0
$191$	0.562306	−	1.73060i	0.0406870	−	0.125222i	−0.928650	−	0.370958i	$-0.879030\pi$
$191$	0.562306	−	1.73060i	0.0406870	−	0.125222i	0.969337	+	0.245736i	$0.0790295\pi$
$192$		0			0
$193$	7.70820			0.554849			0.277424	−	0.960747i	$-0.410519\pi$
$193$	7.70820			0.554849			0.277424	+	0.960747i	$0.410519\pi$
$194$		0			0
$195$	4.14590			0.296894
$196$		0			0
$197$	−3.00000	+	2.17963i	−0.213741	+	0.155292i	−0.689505	−	0.724281i	$-0.742172\pi$
$197$	−3.00000	+	2.17963i	−0.213741	+	0.155292i	0.475764	+	0.879573i	$0.342172\pi$
$198$		0			0
$199$	17.5623			1.24496			0.622479	−	0.782636i	$-0.286125\pi$
$199$	17.5623			1.24496			0.622479	+	0.782636i	$0.286125\pi$
$200$		0			0
$201$	4.76393			0.336022
$202$		0			0
$203$	−1.80902	+	1.31433i	−0.126968	+	0.0922477i
$204$		0			0
$205$	−1.38197	−	1.00406i	−0.0965207	−	0.0701264i
$206$		0			0
$207$	7.52786			0.523223
$208$		0			0
$209$	−1.38197	+	4.25325i	−0.0955926	+	0.294204i
$210$		0			0
$211$	2.83688	+	8.73102i	0.195299	+	0.601068i	0.999973	+	0.00735149i	$0.00234007\pi$
$211$	2.83688	+	8.73102i	0.195299	+	0.601068i	−0.804674	+	0.593717i	$0.797660\pi$
$212$		0			0
$213$	−2.04508	+	6.29412i	−0.140127	+	0.431266i
$214$		0			0
$215$	−3.35410	+	10.3229i	−0.228748	+	0.704014i
$216$		0			0
$217$	1.50000	+	1.08981i	0.101827	+	0.0739814i
$218$		0			0
$219$	−7.28115	−	5.29007i	−0.492015	−	0.357470i
$220$		0			0
$221$	7.85410	−	5.70634i	0.528324	−	0.383850i
$222$		0			0
$223$	0.0557281	+	0.171513i	0.00373183	+	0.0114854i	0.952905	−	0.303269i	$-0.0980780\pi$
$223$	0.0557281	+	0.171513i	0.00373183	+	0.0114854i	−0.949173	+	0.314754i	$0.898078\pi$
$224$		0			0
$225$	8.09017	−	5.87785i	0.539345	−	0.391857i
$226$		0			0
$227$	−4.56231	−	14.0413i	−0.302811	−	0.931956i	−0.980485	−	0.196594i	$-0.937012\pi$
$227$	−4.56231	−	14.0413i	−0.302811	−	0.931956i	0.677674	−	0.735362i	$-0.262988\pi$
$228$		0			0
$229$	−17.5623	+	12.7598i	−1.16055	+	0.843189i	−0.989847	−	0.142134i	$-0.954604\pi$
$229$	−17.5623	+	12.7598i	−1.16055	+	0.843189i	−0.170702	+	0.985323i	$0.554604\pi$
$230$		0			0
$231$	−2.61803	−	1.90211i	−0.172254	−	0.125150i
$232$		0			0
$233$	2.38197	+	1.73060i	0.156048	+	0.113375i	0.663069	−	0.748558i	$-0.269254\pi$
$233$	2.38197	+	1.73060i	0.156048	+	0.113375i	−0.507021	+	0.861933i	$0.669254\pi$
$234$		0			0
$235$	0.427051	+	1.31433i	0.0278577	+	0.0857373i
$236$		0			0
$237$	−2.50000	+	7.69421i	−0.162392	+	0.499793i
$238$		0			0
$239$	6.34346	+	19.5232i	0.410324	+	1.26285i	0.916367	+	0.400340i	$0.131108\pi$
$239$	6.34346	+	19.5232i	0.410324	+	1.26285i	−0.506043	+	0.862508i	$0.668892\pi$
$240$		0			0
$241$	0.781153	−	2.40414i	0.0503185	−	0.154864i	−0.922740	−	0.385423i	$-0.874055\pi$
$241$	0.781153	−	2.40414i	0.0503185	−	0.154864i	0.973058	+	0.230559i	$0.0740554\pi$
$242$		0			0
$243$	−16.0000			−1.02640
$244$		0			0
$245$	4.57295	−	14.0741i	0.292155	−	0.899161i
$246$		0			0
$247$	1.28115	−	0.930812i	0.0815178	−	0.0592262i
$248$		0			0
$249$	−6.23607			−0.395195
$250$		0			0
$251$	29.1803			1.84185			0.920923	−	0.389744i	$-0.127436\pi$
$251$	29.1803			1.84185			0.920923	+	0.389744i	$0.127436\pi$
$252$		0			0
$253$	15.9443	−	11.5842i	1.00241	−	0.728292i
$254$		0			0
$255$	−3.61803	+	11.1352i	−0.226570	+	0.697311i
$256$		0			0
$257$	22.8541			1.42560			0.712800	−	0.701367i	$-0.247427\pi$
$257$	22.8541			1.42560			0.712800	+	0.701367i	$0.247427\pi$
$258$		0			0
$259$	0.0450850	−	0.138757i	0.00280144	−	0.00862196i
$260$		0			0
$261$	2.23607	+	6.88191i	0.138409	+	0.425980i
$262$		0			0
$263$	3.37132	−	10.3759i	0.207885	−	0.639803i	−0.791698	−	0.610913i	$-0.790803\pi$
$263$	3.37132	−	10.3759i	0.207885	−	0.639803i	0.999583	−	0.0288905i	$-0.00919740\pi$
$264$		0			0
$265$	2.39919	+	7.38394i	0.147381	+	0.453592i
$266$		0			0
$267$	−7.23607	−	5.25731i	−0.442840	−	0.321742i
$268$		0			0
$269$	10.3262	+	7.50245i	0.629602	+	0.457433i	0.856262	−	0.516541i	$-0.172781\pi$
$269$	10.3262	+	7.50245i	0.629602	+	0.457433i	−0.226660	+	0.973974i	$0.572781\pi$
$270$		0			0
$271$	−6.47214	+	4.70228i	−0.393154	+	0.285643i	−0.766747	−	0.641950i	$-0.778126\pi$
$271$	−6.47214	+	4.70228i	−0.393154	+	0.285643i	0.373593	+	0.927593i	$0.378126\pi$
$272$		0			0
$273$	0.354102	+	1.08981i	0.0214312	+	0.0659585i
$274$		0			0
$275$	8.09017	−	24.8990i	0.487856	−	1.50147i
$276$		0			0
$277$	−7.63525	−	23.4989i	−0.458758	−	1.41191i	−0.866666	−	0.498889i	$-0.833742\pi$
$277$	−7.63525	−	23.4989i	−0.458758	−	1.41191i	0.407908	−	0.913023i	$-0.366258\pi$
$278$		0			0
$279$	4.85410	−	3.52671i	0.290607	−	0.211139i
$280$		0			0
$281$	−8.16312	−	5.93085i	−0.486971	−	0.353805i	0.317047	−	0.948410i	$-0.397309\pi$
$281$	−8.16312	−	5.93085i	−0.486971	−	0.353805i	−0.804018	+	0.594605i	$0.797309\pi$
$282$		0			0
$283$	−24.1525	−	17.5478i	−1.43572	−	1.04311i	−0.988916	−	0.148474i	$-0.952564\pi$
$283$	−24.1525	−	17.5478i	−1.43572	−	1.04311i	−0.446799	−	0.894634i	$-0.647436\pi$
$284$		0			0
$285$	−0.590170	+	1.81636i	−0.0349587	+	0.107592i
$286$		0			0
$287$	0.145898	−	0.449028i	0.00861209	−	0.0265053i
$288$		0			0
$289$	3.21885	+	9.90659i	0.189344	+	0.582741i
$290$		0			0
$291$	1.19098	−	3.66547i	0.0698167	−	0.214874i
$292$		0			0
$293$	−19.5279			−1.14083			−0.570415	−	0.821357i	$-0.693218\pi$
$293$	−19.5279			−1.14083			−0.570415	+	0.821357i	$0.693218\pi$
$294$		0			0
$295$	19.6353	+	14.2658i	1.14321	+	0.830590i
$296$		0			0
$297$	−21.1803	+	15.3884i	−1.22901	+	0.892927i
$298$		0			0
$299$	−6.97871			−0.403589
$300$		0			0
$301$	−3.00000			−0.172917
$302$		0			0
$303$	1.19098	−	0.865300i	0.0684202	−	0.0497102i
$304$		0			0
$305$	−19.4721			−1.11497
$306$		0			0
$307$	−9.23607			−0.527130			−0.263565	−	0.964642i	$-0.584898\pi$
$307$	−9.23607			−0.527130			−0.263565	+	0.964642i	$0.584898\pi$
$308$		0			0
$309$	2.64590	−	8.14324i	0.150520	−	0.463253i
$310$		0			0
$311$	−2.62868	−	8.09024i	−0.149059	−	0.458755i	0.848452	−	0.529272i	$-0.177535\pi$
$311$	−2.62868	−	8.09024i	−0.149059	−	0.458755i	−0.997511	+	0.0705172i	$0.977535\pi$
$312$		0			0
$313$	−5.18034	+	15.9434i	−0.292810	+	0.901177i	0.691138	+	0.722723i	$0.257110\pi$
$313$	−5.18034	+	15.9434i	−0.292810	+	0.901177i	−0.983948	+	0.178454i	$0.942890\pi$
$314$		0			0
$315$	2.23607	+	1.62460i	0.125988	+	0.0915358i
$316$		0			0
$317$	−6.19098	−	4.49801i	−0.347720	−	0.252634i	0.400192	−	0.916431i	$-0.368944\pi$
$317$	−6.19098	−	4.49801i	−0.347720	−	0.252634i	−0.747912	+	0.663798i	$0.768944\pi$
$318$		0			0
$319$	15.3262	+	11.1352i	0.858105	+	0.623449i
$320$		0			0
$321$	13.2812	−	9.64932i	0.741282	−	0.538573i
$322$		0			0
$323$	1.38197	+	4.25325i	0.0768946	+	0.236657i
$324$		0			0
$325$	−7.50000	+	5.44907i	−0.416025	+	0.302260i
$326$		0			0
$327$	−3.09017	−	9.51057i	−0.170887	−	0.525935i
$328$		0			0
$329$	−0.309017	+	0.224514i	−0.0170367	+	0.0123779i
$330$		0			0
$331$	−18.7082	−	13.5923i	−1.02830	−	0.747101i	−0.0603290	−	0.998179i	$-0.519215\pi$
$331$	−18.7082	−	13.5923i	−1.02830	−	0.747101i	−0.967967	+	0.251078i	$0.919215\pi$
$332$		0			0
$333$	−0.381966	−	0.277515i	−0.0209316	−	0.0152077i
$334$		0			0
$335$	−8.61803	+	6.26137i	−0.470853	+	0.342095i
$336$		0			0
$337$	2.42705	−	7.46969i	0.132210	−	0.406900i	−0.862936	−	0.505314i	$-0.831377\pi$
$337$	2.42705	−	7.46969i	0.132210	−	0.406900i	0.995146	+	0.0984135i	$0.0313768\pi$
$338$		0			0
$339$	−5.20820	−	16.0292i	−0.282871	−	0.870587i
$340$		0			0
$341$	4.85410	−	14.9394i	0.262864	−	0.809013i
$342$		0			0
$343$	8.41641			0.454443
$344$		0			0
$345$	6.80902	−	4.94704i	0.366585	−	0.266340i
$346$		0			0
$347$	−16.1074	+	11.7027i	−0.864690	+	0.628234i	−0.929157	−	0.369686i	$-0.879465\pi$
$347$	−16.1074	+	11.7027i	−0.864690	+	0.628234i	0.0644668	+	0.997920i	$0.479465\pi$
$348$		0			0
$349$	21.7082			1.16201			0.581007	−	0.813899i	$-0.302659\pi$
$349$	21.7082			1.16201			0.581007	+	0.813899i	$0.302659\pi$
$350$		0			0
$351$	9.27051			0.494823
$352$		0			0
$353$	−10.4443	+	7.58821i	−0.555893	+	0.403880i	−0.829953	−	0.557833i	$-0.811633\pi$
$353$	−10.4443	+	7.58821i	−0.555893	+	0.403880i	0.274061	+	0.961712i	$0.411633\pi$
$354$		0			0
$355$	−4.57295	−	14.0741i	−0.242707	−	0.746975i
$356$		0			0
$357$	−3.23607			−0.171271
$358$		0			0
$359$	−4.24671	+	13.0700i	−0.224133	+	0.689810i	0.774246	+	0.632885i	$0.218130\pi$
$359$	−4.24671	+	13.0700i	−0.224133	+	0.689810i	−0.998378	+	0.0569247i	$0.981870\pi$
$360$		0			0
$361$	−5.64590	−	17.3763i	−0.297153	−	0.914541i
$362$		0			0
$363$	−5.07295	+	15.6129i	−0.266261	+	0.819466i
$364$		0			0
$365$	20.1246			1.05337
$366$		0			0
$367$	−20.6803	−	15.0251i	−1.07950	−	0.784306i	−0.101908	−	0.994794i	$-0.532495\pi$
$367$	−20.6803	−	15.0251i	−1.07950	−	0.784306i	−0.977597	+	0.210488i	$0.932495\pi$
$368$		0			0
$369$	−1.23607	−	0.898056i	−0.0643471	−	0.0467509i
$370$		0			0
$371$	−1.73607	+	1.26133i	−0.0901322	+	0.0654848i
$372$		0			0
$373$	−8.73607	−	26.8869i	−0.452336	−	1.39215i	−0.874234	−	0.485505i	$-0.838636\pi$
$373$	−8.73607	−	26.8869i	−0.452336	−	1.39215i	0.421897	−	0.906644i	$-0.361364\pi$
$374$		0			0
$375$	3.45492	−	10.6331i	0.178411	−	0.549093i
$376$		0			0
$377$	−2.07295	−	6.37988i	−0.106762	−	0.328581i
$378$		0			0
$379$	11.8090	−	8.57975i	0.606588	−	0.440712i	−0.241623	−	0.970370i	$-0.577680\pi$
$379$	11.8090	−	8.57975i	0.606588	−	0.440712i	0.848211	+	0.529658i	$0.177680\pi$
$380$		0			0
$381$	−16.0902	−	11.6902i	−0.824324	−	0.598907i
$382$		0			0
$383$	26.9894	+	19.6089i	1.37909	+	1.00197i	0.996964	+	0.0778591i	$0.0248084\pi$
$383$	26.9894	+	19.6089i	1.37909	+	1.00197i	0.382127	+	0.924110i	$0.375192\pi$
$384$		0			0
$385$	7.23607			0.368784
$386$		0			0
$387$	−3.00000	+	9.23305i	−0.152499	+	0.469342i
$388$		0			0
$389$	4.63525	+	14.2658i	0.235017	+	0.723307i	0.997119	+	0.0758507i	$0.0241672\pi$
$389$	4.63525	+	14.2658i	0.235017	+	0.723307i	−0.762102	+	0.647456i	$0.775833\pi$
$390$		0			0
$391$	6.09017	−	18.7436i	0.307993	−	0.947905i
$392$		0			0
$393$	6.79837			0.342933
$394$		0			0
$395$	−5.59017	−	17.2048i	−0.281272	−	0.865666i
$396$		0			0
$397$	−23.4894	+	17.0660i	−1.17890	+	0.856519i	−0.992047	−	0.125870i	$-0.959828\pi$
$397$	−23.4894	+	17.0660i	−1.17890	+	0.856519i	−0.186850	+	0.982388i	$0.559828\pi$
$398$		0			0
$399$	−0.527864			−0.0264263
$400$		0			0
$401$	26.5967			1.32818			0.664089	−	0.747653i	$-0.268820\pi$
$401$	26.5967			1.32818			0.664089	+	0.747653i	$0.268820\pi$
$402$		0			0
$403$	−4.50000	+	3.26944i	−0.224161	+	0.162862i
$404$		0			0
$405$	1.80902	−	1.31433i	0.0898908	−	0.0653095i
$406$		0			0
$407$	−1.23607			−0.0612696
$408$		0			0
$409$	0.489357	−	1.50609i	0.0241971	−	0.0744711i	−0.938229	−	0.346016i	$-0.887534\pi$
$409$	0.489357	−	1.50609i	0.0241971	−	0.0744711i	0.962426	+	0.271544i	$0.0875344\pi$
$410$		0			0
$411$	3.69098	+	11.3597i	0.182063	+	0.560332i
$412$		0			0
$413$	−2.07295	+	6.37988i	−0.102003	+	0.313933i
$414$		0			0
$415$	11.2812	−	8.19624i	0.553770	−	0.402337i
$416$		0			0
$417$	−4.04508	−	2.93893i	−0.198089	−	0.143920i
$418$		0			0
$419$	−7.66312	−	5.56758i	−0.374368	−	0.271994i	0.384652	−	0.923062i	$-0.374321\pi$
$419$	−7.66312	−	5.56758i	−0.374368	−	0.271994i	−0.759020	+	0.651068i	$0.774321\pi$
$420$		0			0
$421$	−25.8885	+	18.8091i	−1.26173	+	0.916701i	−0.998841	−	0.0481252i	$-0.984675\pi$
$421$	−25.8885	+	18.8091i	−1.26173	+	0.916701i	−0.262889	+	0.964826i	$0.584675\pi$
$422$		0			0
$423$	0.381966	+	1.17557i	0.0185718	+	0.0571582i
$424$		0			0
$425$	−8.09017	−	24.8990i	−0.392431	−	1.20778i
$426$		0			0
$427$	−1.66312	−	5.11855i	−0.0804840	−	0.247704i
$428$		0			0
$429$	7.85410	−	5.70634i	0.379200	−	0.275505i
$430$		0			0
$431$	−24.1353	−	17.5353i	−1.16255	−	0.844645i	−0.172456	−	0.985017i	$-0.555170\pi$
$431$	−24.1353	−	17.5353i	−1.16255	−	0.844645i	−0.990099	+	0.140372i	$0.955170\pi$
$432$		0			0
$433$	−21.7254	−	15.7844i	−1.04406	−	0.758552i	−0.0729839	−	0.997333i	$-0.523252\pi$
$433$	−21.7254	−	15.7844i	−1.04406	−	0.758552i	−0.971073	+	0.238781i	$0.923252\pi$
$434$		0			0
$435$	6.54508	+	4.75528i	0.313813	+	0.227998i
$436$		0			0
$437$	0.993422	−	3.05744i	0.0475218	−	0.146257i
$438$		0			0
$439$	12.6631	+	38.9731i	0.604378	+	1.86008i	0.501013	+	0.865440i	$0.332961\pi$
$439$	12.6631	+	38.9731i	0.604378	+	1.86008i	0.103365	+	0.994644i	$0.467039\pi$
$440$		0			0
$441$	4.09017	−	12.5882i	0.194770	−	0.599440i
$442$		0			0
$443$	−29.9443			−1.42270			−0.711348	−	0.702840i	$-0.751915\pi$
$443$	−29.9443			−1.42270			−0.711348	+	0.702840i	$0.751915\pi$
$444$		0			0
$445$	20.0000			0.948091
$446$		0			0
$447$	−3.19098	+	2.31838i	−0.150928	+	0.109656i
$448$		0			0
$449$	4.67376			0.220568			0.110284	−	0.993900i	$-0.464824\pi$
$449$	4.67376			0.220568			0.110284	+	0.993900i	$0.464824\pi$
$450$		0			0
$451$	−4.00000			−0.188353
$452$		0			0
$453$	−11.7812	+	8.55951i	−0.553527	+	0.402161i
$454$		0			0
$455$	−2.07295	−	1.50609i	−0.0971813	−	0.0706064i
$456$		0			0
$457$	−21.4164			−1.00182			−0.500909	−	0.865500i	$-0.667001\pi$
$457$	−21.4164			−1.00182			−0.500909	+	0.865500i	$0.667001\pi$
$458$		0			0
$459$	−8.09017	+	24.8990i	−0.377617	+	1.16218i
$460$		0			0
$461$	0.253289	+	0.779543i	0.0117968	+	0.0363069i	0.956782	−	0.290807i	$-0.0939238\pi$
$461$	0.253289	+	0.779543i	0.0117968	+	0.0363069i	−0.944985	+	0.327114i	$0.893924\pi$
$462$		0			0
$463$	7.45492	−	22.9439i	0.346459	−	1.06629i	−0.614339	−	0.789042i	$-0.710577\pi$
$463$	7.45492	−	22.9439i	0.346459	−	1.06629i	0.960798	−	0.277250i	$-0.0894229\pi$
$464$		0			0
$465$	2.07295	−	6.37988i	0.0961307	−	0.295860i
$466$		0			0
$467$	22.2082	+	16.1352i	1.02767	+	0.746648i	0.967842	−	0.251560i	$-0.0809437\pi$
$467$	22.2082	+	16.1352i	1.02767	+	0.746648i	0.0598315	+	0.998208i	$0.480944\pi$
$468$		0			0
$469$	−2.38197	−	1.73060i	−0.109989	−	0.0799117i
$470$		0			0
$471$	10.6631	−	7.74721i	0.491331	−	0.356973i
$472$		0			0
$473$	7.85410	+	24.1724i	0.361132	+	1.11145i
$474$		0			0
$475$	−1.31966	−	4.06150i	−0.0605502	−	0.186354i
$476$		0			0
$477$	2.14590	+	6.60440i	0.0982539	+	0.302394i
$478$		0			0
$479$	−8.78115	+	6.37988i	−0.401221	+	0.291504i	−0.770038	−	0.637998i	$-0.779763\pi$
$479$	−8.78115	+	6.37988i	−0.401221	+	0.291504i	0.368817	+	0.929502i	$0.379763\pi$
$480$		0			0
$481$	0.354102	+	0.257270i	0.0161457	+	0.0117305i
$482$		0			0
$483$	1.88197	+	1.36733i	0.0856324	+	0.0622156i
$484$		0			0
$485$	2.66312	+	8.19624i	0.120926	+	0.372172i
$486$		0			0
$487$	11.2533	−	34.6341i	0.509935	−	1.56942i	−0.282377	−	0.959303i	$-0.591123\pi$
$487$	11.2533	−	34.6341i	0.509935	−	1.56942i	0.792312	−	0.610116i	$-0.208877\pi$
$488$		0			0
$489$	3.39919	+	10.4616i	0.153717	+	0.473091i
$490$		0			0
$491$	13.3647	−	41.1325i	0.603143	−	1.85628i	0.0940550	−	0.995567i	$-0.470017\pi$
$491$	13.3647	−	41.1325i	0.603143	−	1.85628i	0.509088	−	0.860715i	$-0.329983\pi$
$492$		0			0
$493$	18.9443			0.853207
$494$		0			0
$495$	7.23607	−	22.2703i	0.325237	−	1.00098i
$496$		0			0
$497$	3.30902	−	2.40414i	0.148430	−	0.107840i
$498$		0			0
$499$	−7.56231			−0.338535			−0.169268	−	0.985570i	$-0.554140\pi$
$499$	−7.56231			−0.338535			−0.169268	+	0.985570i	$0.554140\pi$
$500$		0			0
$501$	14.5623			0.650596
$502$		0			0
$503$	−30.2705	+	21.9928i	−1.34970	+	0.980611i	−0.350669	+	0.936500i	$0.614046\pi$
$503$	−30.2705	+	21.9928i	−1.34970	+	0.980611i	−0.999027	+	0.0441115i	$0.985954\pi$
$504$		0			0
$505$	−1.01722	+	3.13068i	−0.0452657	+	0.139314i
$506$		0			0
$507$	9.56231			0.424677
$508$		0			0
$509$	−6.28115	+	19.3314i	−0.278407	+	0.856849i	0.709891	+	0.704312i	$0.248744\pi$
$509$	−6.28115	+	19.3314i	−0.278407	+	0.856849i	−0.988298	+	0.152537i	$0.951256\pi$
$510$		0			0
$511$	1.71885	+	5.29007i	0.0760373	+	0.234019i
$512$		0			0
$513$	−1.31966	+	4.06150i	−0.0582644	+	0.179319i
$514$		0			0
$515$	5.91641	+	18.2088i	0.260708	+	0.802377i
$516$		0			0
$517$	2.61803	+	1.90211i	0.115141	+	0.0836548i
$518$		0			0
$519$	15.2812	+	11.1024i	0.670768	+	0.487342i
$520$		0			0
$521$	−23.7533	+	17.2578i	−1.04065	+	0.756077i	−0.970412	−	0.241453i	$-0.922376\pi$
$521$	−23.7533	+	17.2578i	−1.04065	+	0.756077i	−0.0702381	+	0.997530i	$0.522376\pi$
$522$		0			0
$523$	4.06231	+	12.5025i	0.177632	+	0.546696i	0.999744	−	0.0226305i	$-0.00720412\pi$
$523$	4.06231	+	12.5025i	0.177632	+	0.546696i	−0.822112	+	0.569326i	$0.807204\pi$
$524$		0			0
$525$	3.09017			0.134866
$526$		0			0
$527$	−4.85410	−	14.9394i	−0.211448	−	0.650770i
$528$		0			0
$529$	7.14590	−	5.19180i	0.310691	−	0.225730i
$530$		0			0
$531$	17.5623	+	12.7598i	0.762139	+	0.553727i
$532$		0			0
$533$	1.14590	+	0.832544i	0.0496344	+	0.0360615i
$534$		0			0
$535$	−11.3435	+	34.9116i	−0.490420	+	1.50936i
$536$		0			0
$537$	−0.163119	+	0.502029i	−0.00703910	+	0.0216641i
$538$		0			0
$539$	−10.7082	−	32.9565i	−0.461235	−	1.41954i
$540$		0			0
$541$	8.38197	−	25.7970i	0.360369	−	1.10910i	−0.592462	−	0.805599i	$-0.701844\pi$
$541$	8.38197	−	25.7970i	0.360369	−	1.10910i	0.952831	−	0.303503i	$-0.0981561\pi$
$542$		0			0
$543$	−0.291796			−0.0125222
$544$		0			0
$545$	18.0902	+	13.1433i	0.774898	+	0.562996i
$546$		0			0
$547$	−17.2254	+	12.5150i	−0.736506	+	0.535103i	−0.891615	−	0.452794i	$-0.850427\pi$
$547$	−17.2254	+	12.5150i	−0.736506	+	0.535103i	0.155109	+	0.987897i	$0.450427\pi$
$548$		0			0
$549$	−17.4164			−0.743314
$550$		0			0
$551$	3.09017			0.131646
$552$		0			0
$553$	4.04508	−	2.93893i	0.172015	−	0.124976i
$554$		0			0
$555$	−0.527864			−0.0224066
$556$		0			0
$557$	4.76393			0.201854			0.100927	−	0.994894i	$-0.467819\pi$
$557$	4.76393			0.201854			0.100927	+	0.994894i	$0.467819\pi$
$558$		0			0
$559$	2.78115	−	8.55951i	0.117630	−	0.362029i
$560$		0			0
$561$	8.47214	+	26.0746i	0.357694	+	1.10087i
$562$		0			0
$563$	−2.28115	+	7.02067i	−0.0961391	+	0.295886i	−0.987549	−	0.157312i	$-0.949717\pi$
$563$	−2.28115	+	7.02067i	−0.0961391	+	0.295886i	0.891410	+	0.453198i	$0.149717\pi$
$564$		0			0
$565$	30.4894	+	22.1518i	1.28270	+	0.931934i
$566$		0			0
$567$	0.500000	+	0.363271i	0.0209980	+	0.0152560i
$568$		0			0
$569$	−16.6074	−	12.0660i	−0.696218	−	0.505832i	0.182480	−	0.983210i	$-0.441587\pi$
$569$	−16.6074	−	12.0660i	−0.696218	−	0.505832i	−0.878698	+	0.477377i	$0.841587\pi$
$570$		0			0
$571$	−6.57295	+	4.77553i	−0.275069	+	0.199850i	−0.716764	−	0.697316i	$-0.754377\pi$
$571$	−6.57295	+	4.77553i	−0.275069	+	0.199850i	0.441695	+	0.897165i	$0.354377\pi$
$572$		0			0
$573$	−0.562306	−	1.73060i	−0.0234907	−	0.0722968i
$574$		0			0
$575$	−5.81559	+	17.8986i	−0.242527	+	0.746422i
$576$		0			0
$577$	−10.4377	−	32.1239i	−0.434527	−	1.33734i	−0.893571	−	0.448923i	$-0.851808\pi$
$577$	−10.4377	−	32.1239i	−0.434527	−	1.33734i	0.459044	−	0.888414i	$-0.348192\pi$
$578$		0			0
$579$	6.23607	−	4.53077i	0.259162	−	0.188292i
$580$		0			0
$581$	3.11803	+	2.26538i	0.129358	+	0.0939840i
$582$		0			0
$583$	14.7082	+	10.6861i	0.609152	+	0.442575i
$584$		0			0
$585$	−6.70820	+	4.87380i	−0.277350	+	0.201507i
$586$		0			0
$587$	−1.63525	+	5.03280i	−0.0674942	+	0.207726i	−0.979115	−	0.203306i	$-0.934831\pi$
$587$	−1.63525	+	5.03280i	−0.0674942	+	0.207726i	0.911621	+	0.411032i	$0.134831\pi$
$588$		0			0
$589$	−0.791796	−	2.43690i	−0.0326254	−	0.100411i
$590$		0			0
$591$	−1.14590	+	3.52671i	−0.0471359	+	0.145070i
$592$		0			0
$593$	−10.9098			−0.448013			−0.224007	−	0.974588i	$-0.571914\pi$
$593$	−10.9098			−0.448013			−0.224007	+	0.974588i	$0.571914\pi$
$594$		0			0
$595$	5.85410	−	4.25325i	0.239995	−	0.174366i
$596$		0			0
$597$	14.2082	−	10.3229i	0.581503	−	0.422487i
$598$		0			0
$599$	9.47214			0.387021			0.193510	−	0.981098i	$-0.438013\pi$
$599$	9.47214			0.387021			0.193510	+	0.981098i	$0.438013\pi$
$600$		0			0
$601$	2.72949			0.111338			0.0556691	−	0.998449i	$-0.482271\pi$
$601$	2.72949			0.111338			0.0556691	+	0.998449i	$0.482271\pi$
$602$		0			0
$603$	−7.70820	+	5.60034i	−0.313902	+	0.228063i
$604$		0			0
$605$	−11.3435	−	34.9116i	−0.461177	−	1.41936i
$606$		0			0
$607$	35.5623			1.44343			0.721715	−	0.692191i	$-0.243354\pi$
$607$	35.5623			1.44343			0.721715	+	0.692191i	$0.243354\pi$
$608$		0			0
$609$	−0.690983	+	2.12663i	−0.0280000	+	0.0861753i
$610$		0			0
$611$	−0.354102	−	1.08981i	−0.0143254	−	0.0440891i
$612$		0			0
$613$	−4.62868	+	14.2456i	−0.186951	+	0.575374i	−0.999977	−	0.00685287i	$-0.997819\pi$
$613$	−4.62868	+	14.2456i	−0.186951	+	0.575374i	0.813026	+	0.582227i	$0.197819\pi$
$614$		0			0
$615$	−1.70820			−0.0688814
$616$		0			0
$617$	−11.5172	−	8.36775i	−0.463666	−	0.336873i	0.331302	−	0.943525i	$-0.392512\pi$
$617$	−11.5172	−	8.36775i	−0.463666	−	0.336873i	−0.794968	+	0.606652i	$0.792512\pi$
$618$		0			0
$619$	24.6976	+	17.9438i	0.992679	+	0.721223i	0.960506	−	0.278259i	$-0.0897573\pi$
$619$	24.6976	+	17.9438i	0.992679	+	0.721223i	0.0321727	+	0.999482i	$0.489757\pi$
$620$		0			0
$621$	15.2254	−	11.0619i	0.610975	−	0.443900i
$622$		0			0
$623$	1.70820	+	5.25731i	0.0684377	+	0.210630i
$624$		0			0
$625$	7.72542	+	23.7764i	0.309017	+	0.951057i
$626$		0			0
$627$	1.38197	+	4.25325i	0.0551904	+	0.169859i
$628$		0			0
$629$	−1.00000	+	0.726543i	−0.0398726	+	0.0289691i
$630$		0			0
$631$	−8.28115	−	6.01661i	−0.329667	−	0.239517i	0.410622	−	0.911806i	$-0.365312\pi$
$631$	−8.28115	−	6.01661i	−0.329667	−	0.239517i	−0.740290	+	0.672288i	$0.765312\pi$
$632$		0			0
$633$	7.42705	+	5.39607i	0.295199	+	0.214474i
$634$		0			0
$635$	44.4721			1.76482
$636$		0			0
$637$	−3.79180	+	11.6699i	−0.150236	+	0.462380i
$638$		0			0
$639$	−4.09017	−	12.5882i	−0.161805	−	0.497983i
$640$		0			0
$641$	−0.336881	+	1.03681i	−0.0133060	+	0.0409517i	−0.957489	−	0.288470i	$-0.906854\pi$
$641$	−0.336881	+	1.03681i	−0.0133060	+	0.0409517i	0.944183	+	0.329421i	$0.106854\pi$
$642$		0			0
$643$	30.8328			1.21593			0.607964	−	0.793965i	$-0.291987\pi$
$643$	30.8328			1.21593			0.607964	+	0.793965i	$0.291987\pi$
$644$		0			0
$645$	3.35410	+	10.3229i	0.132068	+	0.406462i
$646$		0			0
$647$	−29.5623	+	21.4783i	−1.16221	+	0.844398i	−0.990056	−	0.140671i	$-0.955074\pi$
$647$	−29.5623	+	21.4783i	−1.16221	+	0.844398i	−0.172158	+	0.985069i	$0.555074\pi$
$648$		0			0
$649$	56.8328			2.23088
$650$		0			0
$651$	1.85410			0.0726680
$652$		0			0
$653$	−15.4443	+	11.2209i	−0.604381	+	0.439109i	−0.847431	−	0.530905i	$-0.821852\pi$
$653$	−15.4443	+	11.2209i	−0.604381	+	0.439109i	0.243050	+	0.970014i	$0.421852\pi$
$654$		0			0
$655$	−12.2984	+	8.93529i	−0.480537	+	0.349131i
$656$		0			0
$657$	18.0000			0.702247
$658$		0			0
$659$	−4.79837	+	14.7679i	−0.186918	+	0.575275i	−0.999976	−	0.00690786i	$-0.997801\pi$
$659$	−4.79837	+	14.7679i	−0.186918	+	0.575275i	0.813058	+	0.582183i	$0.197801\pi$
$660$		0			0
$661$	6.08359	+	18.7234i	0.236624	+	0.728255i	0.996902	+	0.0786563i	$0.0250630\pi$
$661$	6.08359	+	18.7234i	0.236624	+	0.728255i	−0.760277	+	0.649598i	$0.774937\pi$
$662$		0			0
$663$	3.00000	−	9.23305i	0.116510	−	0.358582i
$664$		0			0
$665$	0.954915	−	0.693786i	0.0370300	−	0.0269039i
$666$		0			0
$667$	−11.0172	−	8.00448i	−0.426588	−	0.309935i
$668$		0			0
$669$	0.145898	+	0.106001i	0.00564074	+	0.00409824i
$670$		0			0
$671$	−36.8885	+	26.8011i	−1.42407	+	1.03464i
$672$		0			0
$673$	3.76393	+	11.5842i	0.145089	+	0.446538i	0.997022	−	0.0771122i	$-0.0245700\pi$
$673$	3.76393	+	11.5842i	0.145089	+	0.446538i	−0.851934	+	0.523650i	$0.824570\pi$
$674$		0			0
$675$	7.72542	−	23.7764i	0.297352	−	0.915155i
$676$		0			0
$677$	3.28115	+	10.0984i	0.126105	+	0.388111i	0.994101	−	0.108460i	$-0.0345921\pi$
$677$	3.28115	+	10.0984i	0.126105	+	0.388111i	−0.867996	+	0.496571i	$0.834592\pi$
$678$		0			0
$679$	−1.92705	+	1.40008i	−0.0739534	+	0.0537303i
$680$		0			0
$681$	−11.9443	−	8.67802i	−0.457705	−	0.332543i
$682$		0			0
$683$	−10.8992	−	7.91872i	−0.417046	−	0.303002i	0.359402	−	0.933183i	$-0.382981\pi$
$683$	−10.8992	−	7.91872i	−0.417046	−	0.303002i	−0.776448	+	0.630181i	$0.782981\pi$
$684$		0			0
$685$	−21.6074	−	15.6987i	−0.825576	−	0.599816i
$686$		0			0
$687$	−6.70820	+	20.6457i	−0.255934	+	0.787684i
$688$		0			0
$689$	−1.98936	−	6.12261i	−0.0757885	−	0.233253i
$690$		0			0
$691$	−11.2082	+	34.4953i	−0.426380	+	1.31226i	0.475286	+	0.879831i	$0.342344\pi$
$691$	−11.2082	+	34.4953i	−0.426380	+	1.31226i	−0.901667	+	0.432432i	$0.857656\pi$
$692$		0			0
$693$	6.47214			0.245856
$694$		0			0
$695$	11.1803			0.424094
$696$		0			0
$697$	−3.23607	+	2.35114i	−0.122575	+	0.0890558i
$698$		0			0
$699$	2.94427			0.111363
$700$		0			0
$701$	−41.0132			−1.54905			−0.774523	−	0.632546i	$-0.782010\pi$
$701$	−41.0132			−1.54905			−0.774523	+	0.632546i	$0.782010\pi$
$702$		0			0
$703$	−0.163119	+	0.118513i	−0.00615215	+	0.00446980i
$704$		0			0
$705$	1.11803	+	0.812299i	0.0421076	+	0.0305930i
$706$		0			0
$707$	−0.909830			−0.0342177
$708$		0			0
$709$	−10.3647	+	31.8994i	−0.389256	+	1.19801i	0.544089	+	0.839027i	$0.316875\pi$
$709$	−10.3647	+	31.8994i	−0.389256	+	1.19801i	−0.933345	+	0.358980i	$0.883125\pi$
$710$		0			0
$711$	−5.00000	−	15.3884i	−0.187515	−	0.577111i
$712$		0			0
$713$	−3.48936	+	10.7391i	−0.130677	+	0.402184i
$714$		0			0
$715$	−6.70820	+	20.6457i	−0.250873	+	0.772106i
$716$		0			0
$717$	16.6074	+	12.0660i	0.620214	+	0.450612i
$718$		0			0
$719$	−18.8435	−	13.6906i	−0.702742	−	0.510572i	0.178082	−	0.984016i	$-0.443011\pi$
$719$	−18.8435	−	13.6906i	−0.702742	−	0.510572i	−0.880824	+	0.473443i	$0.843011\pi$
$720$		0			0
$721$	−4.28115	+	3.11044i	−0.159438	+	0.115839i
$722$		0			0
$723$	−0.781153	−	2.40414i	−0.0290514	−	0.0894110i
$724$		0			0
$725$	−18.0902			−0.671852
$726$		0			0
$727$	−7.59017	−	23.3601i	−0.281504	−	0.866380i	−0.987425	−	0.158089i	$-0.949467\pi$
$727$	−7.59017	−	23.3601i	−0.281504	−	0.866380i	0.705921	−	0.708291i	$-0.250533\pi$
$728$		0			0
$729$	−10.5172	+	7.64121i	−0.389527	+	0.283008i
$730$		0			0
$731$	20.5623	+	14.9394i	0.760524	+	0.552553i
$732$		0			0
$733$	16.1631	+	11.7432i	0.596998	+	0.433745i	0.844812	−	0.535063i	$-0.179712\pi$
$733$	16.1631	+	11.7432i	0.596998	+	0.433745i	−0.247814	+	0.968808i	$0.579712\pi$
$734$		0			0
$735$	−4.57295	−	14.0741i	−0.168676	−	0.519131i
$736$		0			0
$737$	−7.70820	+	23.7234i	−0.283935	+	0.873863i
$738$		0			0
$739$	−4.93769	−	15.1967i	−0.181636	−	0.559018i	0.818238	−	0.574879i	$-0.194951\pi$
$739$	−4.93769	−	15.1967i	−0.181636	−	0.559018i	−0.999874	+	0.0158612i	$0.994951\pi$
$740$		0			0
$741$	0.489357	−	1.50609i	0.0179770	−	0.0553274i
$742$		0			0
$743$	−28.3607			−1.04045			−0.520226	−	0.854029i	$-0.674152\pi$
$743$	−28.3607			−1.04045			−0.520226	+	0.854029i	$0.674152\pi$
$744$		0			0
$745$	2.72542	−	8.38800i	0.0998518	−	0.307312i
$746$		0			0
$747$	10.0902	−	7.33094i	0.369180	−	0.268225i
$748$		0			0
$749$	−10.1459			−0.370723
$750$		0			0
$751$	5.11146			0.186520			0.0932598	−	0.995642i	$-0.470271\pi$
$751$	5.11146			0.186520			0.0932598	+	0.995642i	$0.470271\pi$
$752$		0			0
$753$	23.6074	−	17.1518i	0.860301	−	0.625045i
$754$		0			0
$755$	10.0623	−	30.9686i	0.366205	−	1.12706i
$756$		0			0
$757$	30.4164			1.10550			0.552752	−	0.833346i	$-0.313578\pi$
$757$	30.4164			1.10550			0.552752	+	0.833346i	$0.313578\pi$
$758$		0			0
$759$	6.09017	−	18.7436i	0.221059	−	0.680350i
$760$		0			0
$761$	−5.70163	−	17.5478i	−0.206684	−	0.636107i	−0.999640	−	0.0268287i	$-0.991459\pi$
$761$	−5.70163	−	17.5478i	−0.206684	−	0.636107i	0.792956	−	0.609279i	$-0.208541\pi$
$762$		0			0
$763$	−1.90983	+	5.87785i	−0.0691405	+	0.212793i
$764$		0			0
$765$	−7.23607	−	22.2703i	−0.261621	−	0.805185i
$766$		0			0
$767$	−16.2812	−	11.8290i	−0.587878	−	0.427119i
$768$		0			0
$769$	−10.8541	−	7.88597i	−0.391409	−	0.284375i	0.374624	−	0.927177i	$-0.377772\pi$
$769$	−10.8541	−	7.88597i	−0.391409	−	0.284375i	−0.766033	+	0.642802i	$0.777772\pi$
$770$		0			0
$771$	18.4894	−	13.4333i	0.665878	−	0.483789i
$772$		0			0
$773$	−11.1738	−	34.3893i	−0.401892	−	1.23690i	−0.923462	−	0.383689i	$-0.874654\pi$
$773$	−11.1738	−	34.3893i	−0.401892	−	1.23690i	0.521570	−	0.853208i	$-0.325346\pi$
$774$		0			0
$775$	4.63525	+	14.2658i	0.166503	+	0.512444i
$776$		0			0
$777$	−0.0450850	−	0.138757i	−0.00161741	−	0.00497789i
$778$		0			0
$779$	−0.527864	+	0.383516i	−0.0189127	+	0.0137409i
$780$		0			0
$781$	−28.0344	−	20.3682i	−1.00315	−	0.728832i
$782$		0			0
$783$	14.6353	+	10.6331i	0.523021	+	0.379997i
$784$		0			0
$785$	−9.10739	+	28.0297i	−0.325057	+	1.00042i
$786$		0			0
$787$	3.65248	−	11.2412i	0.130197	−	0.400704i	−0.864615	−	0.502434i	$-0.832438\pi$
$787$	3.65248	−	11.2412i	0.130197	−	0.400704i	0.994812	+	0.101730i	$0.0324378\pi$
$788$		0			0
$789$	−3.37132	−	10.3759i	−0.120022	−	0.369391i
$790$		0			0
$791$	−3.21885	+	9.90659i	−0.114449	+	0.352238i
$792$		0			0
$793$	16.1459			0.573358
$794$		0			0
$795$	6.28115	+	4.56352i	0.222770	+	0.161852i
$796$		0			0
$797$	−7.89919	+	5.73910i	−0.279804	+	0.203289i	−0.718832	−	0.695184i	$-0.755323\pi$
$797$	−7.89919	+	5.73910i	−0.279804	+	0.203289i	0.439028	+	0.898473i	$0.355323\pi$
$798$		0			0
$799$	3.23607			0.114484
$800$		0			0
$801$	17.8885			0.632061
$802$		0			0
$803$	38.1246	−	27.6992i	1.34539	−	0.977482i
$804$		0			0
$805$	−5.20163			−0.183333
$806$		0			0
$807$	12.7639			0.449312
$808$		0			0
$809$	9.57295	−	29.4625i	0.336567	−	1.03585i	−0.629378	−	0.777099i	$-0.716690\pi$
$809$	9.57295	−	29.4625i	0.336567	−	1.03585i	0.965945	−	0.258747i	$-0.0833097\pi$
$810$		0			0
$811$	4.54508	+	13.9883i	0.159600	+	0.491197i	0.998598	−	0.0529372i	$-0.0168583\pi$
$811$	4.54508	+	13.9883i	0.159600	+	0.491197i	−0.838998	+	0.544134i	$0.816858\pi$
$812$		0			0
$813$	−2.47214	+	7.60845i	−0.0867016	+	0.266840i
$814$		0			0
$815$	−19.8992	−	14.4576i	−0.697038	−	0.506428i
$816$		0			0
$817$	3.35410	+	2.43690i	0.117345	+	0.0852563i
$818$		0			0
$819$	−1.85410	−	1.34708i	−0.0647876	−	0.0470709i
$820$		0			0
$821$	32.9164	−	23.9152i	1.14879	−	0.834645i	0.160471	−	0.987041i	$-0.448699\pi$
$821$	32.9164	−	23.9152i	1.14879	−	0.834645i	0.988320	+	0.152395i	$0.0486987\pi$
$822$		0			0
$823$	−14.7426	−	45.3732i	−0.513896	−	1.58161i	−0.785281	−	0.619139i	$-0.787482\pi$
$823$	−14.7426	−	45.3732i	−0.513896	−	1.58161i	0.271385	−	0.962471i	$-0.412518\pi$
$824$		0			0
$825$	−8.09017	−	24.8990i	−0.281664	−	0.866871i
$826$		0			0
$827$	0.298374	+	0.918300i	0.0103755	+	0.0319324i	0.956110	−	0.293007i	$-0.0946560\pi$
$827$	0.298374	+	0.918300i	0.0103755	+	0.0319324i	−0.945735	+	0.324940i	$0.894656\pi$
$828$		0			0
$829$	29.0066	−	21.0745i	1.00744	−	0.731948i	0.0437695	−	0.999042i	$-0.486063\pi$
$829$	29.0066	−	21.0745i	1.00744	−	0.731948i	0.963671	+	0.267094i	$0.0860633\pi$
$830$		0			0
$831$	−19.9894	−	14.5231i	−0.693423	−	0.503801i
$832$		0			0
$833$	−28.0344	−	20.3682i	−0.971336	−	0.705717i
$834$		0			0
$835$	−26.3435	+	19.1396i	−0.911653	+	0.662355i
$836$		0			0
$837$	4.63525	−	14.2658i	0.160218	−	0.493100i
$838$		0			0
$839$	−3.35410	−	10.3229i	−0.115796	−	0.356385i	0.876316	−	0.481737i	$-0.159994\pi$
$839$	−3.35410	−	10.3229i	−0.115796	−	0.356385i	−0.992112	+	0.125352i	$0.959994\pi$
$840$		0			0
$841$	−4.91641	+	15.1311i	−0.169531	+	0.521764i
$842$		0			0
$843$	−10.0902			−0.347524
$844$		0			0
$845$	−17.2984	+	12.5680i	−0.595082	+	0.432352i
$846$		0			0
$847$	8.20820	−	5.96361i	0.282037	−	0.204912i
$848$		0			0
$849$	−29.8541			−1.02459
$850$		0			0
$851$	0.888544			0.0304589
$852$		0			0
$853$	12.3820	−	8.99602i	0.423950	−	0.308018i	−0.355275	−	0.934762i	$-0.615613\pi$
$853$	12.3820	−	8.99602i	0.423950	−	0.308018i	0.779225	+	0.626744i	$0.215613\pi$
$854$		0			0
$855$	−1.18034	−	3.63271i	−0.0403668	−	0.124236i
$856$		0			0
$857$	19.6869			0.672492			0.336246	−	0.941774i	$-0.390843\pi$
$857$	19.6869			0.672492			0.336246	+	0.941774i	$0.390843\pi$
$858$		0			0
$859$	0.489357	−	1.50609i	0.0166966	−	0.0513870i	−0.942361	−	0.334598i	$-0.891400\pi$
$859$	0.489357	−	1.50609i	0.0166966	−	0.0513870i	0.959058	+	0.283211i	$0.0913996\pi$
$860$		0			0
$861$	−0.145898	−	0.449028i	−0.00497219	−	0.0153028i
$862$		0			0
$863$	6.62461	−	20.3885i	0.225504	−	0.694031i	−0.772736	−	0.634728i	$-0.781112\pi$
$863$	6.62461	−	20.3885i	0.225504	−	0.694031i	0.998240	−	0.0593032i	$-0.0188879\pi$
$864$		0			0
$865$	−42.2361			−1.43607
$866$		0			0
$867$	8.42705	+	6.12261i	0.286198	+	0.207935i
$868$		0			0
$869$	−34.2705	−	24.8990i	−1.16255	−	0.844640i
$870$		0			0
$871$	7.14590	−	5.19180i	0.242130	−	0.175917i
$872$		0			0
$873$	2.38197	+	7.33094i	0.0806173	+	0.248115i
$874$		0			0
$875$	−5.59017	+	4.06150i	−0.188982	+	0.137304i
$876$		0			0
$877$	−11.2918	−	34.7526i	−0.381297	−	1.17351i	−0.939131	−	0.343559i	$-0.888368\pi$
$877$	−11.2918	−	34.7526i	−0.381297	−	1.17351i	0.557834	−	0.829952i	$-0.311632\pi$
$878$		0			0
$879$	−15.7984	+	11.4782i	−0.532866	+	0.387150i
$880$		0			0
$881$	32.6525	+	23.7234i	1.10009	+	0.799262i	0.981075	−	0.193630i	$-0.0620262\pi$
$881$	32.6525	+	23.7234i	1.10009	+	0.799262i	0.119015	+	0.992892i	$0.462026\pi$
$882$		0			0
$883$	−16.6525	−	12.0987i	−0.560400	−	0.407155i	0.271205	−	0.962522i	$-0.412578\pi$
$883$	−16.6525	−	12.0987i	−0.560400	−	0.407155i	−0.831605	+	0.555367i	$0.812578\pi$
$884$		0			0
$885$	24.2705			0.815844
$886$		0			0
$887$	−9.23607	+	28.4257i	−0.310117	+	0.954441i	0.667601	+	0.744519i	$0.267321\pi$
$887$	−9.23607	+	28.4257i	−0.310117	+	0.954441i	−0.977718	+	0.209922i	$0.932679\pi$
$888$		0			0
$889$	3.79837	+	11.6902i	0.127393	+	0.392076i
$890$		0			0
$891$	1.61803	−	4.97980i	0.0542062	−	0.166829i
$892$		0			0
$893$	0.527864			0.0176643
$894$		0			0
$895$	−0.364745	−	1.12257i	−0.0121921	−	0.0375234i
$896$		0			0
$897$	−5.64590	+	4.10199i	−0.188511	+	0.136961i
$898$		0			0
$899$	−10.8541			−0.362005
$900$		0			0
$901$	18.1803			0.605675
$902$		0			0
$903$	−2.42705	+	1.76336i	−0.0807672	+	0.0586808i
$904$		0			0
$905$	0.527864	−	0.383516i	0.0175468	−	0.0127485i
$906$		0			0
$907$	33.2492			1.10402			0.552011	−	0.833837i	$-0.313861\pi$
$907$	33.2492			1.10402			0.552011	+	0.833837i	$0.313861\pi$
$908$		0			0
$909$	−0.909830	+	2.80017i	−0.0301772	+	0.0928757i
$910$		0			0
$911$	12.4336	+	38.2668i	0.411944	+	1.26783i	0.914955	+	0.403555i	$0.132226\pi$
$911$	12.4336	+	38.2668i	0.411944	+	1.26783i	−0.503011	+	0.864280i	$0.667774\pi$
$912$		0			0
$913$	10.0902	−	31.0543i	0.333936	−	1.02775i
$914$		0			0
$915$	−15.7533	+	11.4454i	−0.520788	+	0.378374i
$916$		0			0
$917$	−3.39919	−	2.46965i	−0.112251	−	0.0815552i
$918$		0			0
$919$	−43.0517	−	31.2789i	−1.42014	−	1.03179i	−0.991748	−	0.128203i	$-0.959079\pi$
$919$	−43.0517	−	31.2789i	−1.42014	−	1.03179i	−0.428395	−	0.903591i	$-0.640921\pi$
$920$		0			0
$921$	−7.47214	+	5.42882i	−0.246215	+	0.178886i
$922$		0			0
$923$	3.79180	+	11.6699i	0.124808	+	0.384121i
$924$		0			0
$925$	0.954915	−	0.693786i	0.0313974	−	0.0228116i
$926$		0			0
$927$	5.29180	+	16.2865i	0.173805	+	0.534918i
$928$		0			0
$929$	−33.6803	+	24.4702i	−1.10502	+	0.802841i	−0.981872	−	0.189548i	$-0.939298\pi$
$929$	−33.6803	+	24.4702i	−1.10502	+	0.802841i	−0.123145	+	0.992389i	$0.539298\pi$
$930$		0			0
$931$	−4.57295	−	3.32244i	−0.149872	−	0.108889i
$932$		0			0
$933$	−6.88197	−	5.00004i	−0.225305	−	0.163694i
$934$		0			0
$935$	−49.5967	−	36.0341i	−1.62199	−	1.17844i
$936$		0			0
$937$	5.47871	−	16.8617i	0.178982	−	0.550849i	−0.820811	−	0.571200i	$-0.806478\pi$
$937$	5.47871	−	16.8617i	0.178982	−	0.550849i	0.999793	+	0.0203504i	$0.00647819\pi$
$938$		0			0
$939$	5.18034	+	15.9434i	0.169054	+	0.520295i
$940$		0			0
$941$	−14.3435	+	44.1446i	−0.467583	+	1.43907i	0.388121	+	0.921608i	$0.373124\pi$
$941$	−14.3435	+	44.1446i	−0.467583	+	1.43907i	−0.855704	+	0.517465i	$0.826876\pi$
$942$		0			0
$943$	2.87539			0.0936355
$944$		0			0
$945$	6.90983			0.224777
$946$		0			0
$947$	2.14590	−	1.55909i	0.0697323	−	0.0506635i	−0.552373	−	0.833597i	$-0.686278\pi$
$947$	2.14590	−	1.55909i	0.0697323	−	0.0506635i	0.622105	+	0.782934i	$0.286278\pi$
$948$		0			0
$949$	−16.6869			−0.541680
$950$		0			0
$951$	−7.65248			−0.248149
$952$		0			0
$953$	6.26393	−	4.55101i	0.202909	−	0.147422i	−0.481691	−	0.876341i	$-0.659977\pi$
$953$	6.26393	−	4.55101i	0.202909	−	0.147422i	0.684599	+	0.728919i	$0.259977\pi$
$954$		0			0
$955$	3.29180	+	2.39163i	0.106520	+	0.0773913i
$956$		0			0
$957$	18.9443			0.612381
$958$		0			0
$959$	2.28115	−	7.02067i	0.0736623	−	0.226709i
$960$		0			0
$961$	−6.79837	−	20.9232i	−0.219302	−	0.674943i
$962$		0			0
$963$	−10.1459	+	31.2259i	−0.326947	+	1.00624i
$964$		0			0
$965$	−5.32624	+	16.3925i	−0.171458	+	0.527692i
$966$		0			0
$967$	3.32624	+	2.41665i	0.106965	+	0.0777143i	0.639982	−	0.768390i	$-0.278942\pi$
$967$	3.32624	+	2.41665i	0.106965	+	0.0777143i	−0.533017	+	0.846104i	$0.678942\pi$
$968$		0			0
$969$	3.61803	+	2.62866i	0.116228	+	0.0844446i
$970$		0			0
$971$	4.54508	−	3.30220i	0.145859	−	0.105973i	−0.512463	−	0.858709i	$-0.671267\pi$
$971$	4.54508	−	3.30220i	0.145859	−	0.105973i	0.658321	+	0.752737i	$0.271267\pi$
$972$		0			0
$973$	0.954915	+	2.93893i	0.0306132	+	0.0942177i
$974$		0			0
$975$	−2.86475	+	8.81678i	−0.0917453	+	0.282363i
$976$		0			0
$977$	−0.725425	−	2.23263i	−0.0232084	−	0.0714281i	0.938782	−	0.344513i	$-0.111956\pi$
$977$	−0.725425	−	2.23263i	−0.0232084	−	0.0714281i	−0.961990	+	0.273085i	$0.911956\pi$
$978$		0			0
$979$	37.8885	−	27.5276i	1.21092	−	0.879787i
$980$		0			0
$981$	16.1803	+	11.7557i	0.516598	+	0.375331i
$982$		0			0
$983$	7.78115	+	5.65334i	0.248180	+	0.180313i	0.704920	−	0.709287i	$-0.250983\pi$
$983$	7.78115	+	5.65334i	0.248180	+	0.180313i	−0.456740	+	0.889600i	$0.650983\pi$
$984$		0			0
$985$	−2.56231	−	7.88597i	−0.0816419	−	0.251268i
$986$		0			0
$987$	−0.118034	+	0.363271i	−0.00375706	+	0.0115631i
$988$		0			0
$989$	−5.64590	−	17.3763i	−0.179529	−	0.552534i
$990$		0			0
$991$	4.74671	−	14.6089i	0.150784	−	0.464066i	−0.846925	−	0.531712i	$-0.821549\pi$
$991$	4.74671	−	14.6089i	0.150784	−	0.464066i	0.997709	+	0.0676459i	$0.0215488\pi$
$992$		0			0
$993$	−23.1246			−0.733837
$994$		0			0
$995$	−12.1353	+	37.3485i	−0.384713	+	1.18403i
$996$		0			0
$997$	−20.1353	+	14.6291i	−0.637690	+	0.463309i	−0.859056	−	0.511882i	$-0.828949\pi$
$997$	−20.1353	+	14.6291i	−0.637690	+	0.463309i	0.221366	+	0.975191i	$0.428949\pi$
$998$		0			0
$999$	−1.18034			−0.0373443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.u.b.81.1		4
4.3	odd	2		25.2.d.a.6.1	✓	4
12.11	even	2		225.2.h.b.181.1		4
20.3	even	4		125.2.e.a.99.1		8
20.7	even	4		125.2.e.a.99.2		8
20.19	odd	2		125.2.d.a.26.1		4
25.11	even	5		10000.2.a.c.1.1		2
25.14	even	10		10000.2.a.l.1.2		2
25.21	even	5	inner	400.2.u.b.321.1		4
100.3	even	20		125.2.e.a.24.2		8
100.11	odd	10		625.2.a.b.1.1		2
100.19	odd	10		625.2.d.b.376.1		4
100.23	even	20		625.2.b.a.624.4		4
100.27	even	20		625.2.b.a.624.1		4
100.31	odd	10		625.2.d.h.376.1		4
100.39	odd	10		625.2.a.c.1.2		2
100.47	even	20		125.2.e.a.24.1		8
100.59	odd	10		625.2.d.b.251.1		4
100.63	even	20		625.2.e.c.374.1		8
100.67	even	20		625.2.e.c.249.1		8
100.71	odd	10		25.2.d.a.21.1	yes	4
100.79	odd	10		125.2.d.a.101.1		4
100.83	even	20		625.2.e.c.249.2		8
100.87	even	20		625.2.e.c.374.2		8
100.91	odd	10		625.2.d.h.251.1		4
300.11	even	10		5625.2.a.f.1.2		2
300.71	even	10		225.2.h.b.46.1		4
300.239	even	10		5625.2.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.d.a.6.1	✓	4	4.3	odd	2
25.2.d.a.21.1	yes	4	100.71	odd	10
125.2.d.a.26.1		4	20.19	odd	2
125.2.d.a.101.1		4	100.79	odd	10
125.2.e.a.24.1		8	100.47	even	20
125.2.e.a.24.2		8	100.3	even	20
125.2.e.a.99.1		8	20.3	even	4
125.2.e.a.99.2		8	20.7	even	4
225.2.h.b.46.1		4	300.71	even	10
225.2.h.b.181.1		4	12.11	even	2
400.2.u.b.81.1		4	1.1	even	1	trivial
400.2.u.b.321.1		4	25.21	even	5	inner
625.2.a.b.1.1		2	100.11	odd	10
625.2.a.c.1.2		2	100.39	odd	10
625.2.b.a.624.1		4	100.27	even	20
625.2.b.a.624.4		4	100.23	even	20
625.2.d.b.251.1		4	100.59	odd	10
625.2.d.b.376.1		4	100.19	odd	10
625.2.d.h.251.1		4	100.91	odd	10
625.2.d.h.376.1		4	100.31	odd	10
625.2.e.c.249.1		8	100.67	even	20
625.2.e.c.249.2		8	100.83	even	20
625.2.e.c.374.1		8	100.63	even	20
625.2.e.c.374.2		8	100.87	even	20
5625.2.a.d.1.1		2	300.239	even	10
5625.2.a.f.1.2		2	300.11	even	10
10000.2.a.c.1.1		2	25.11	even	5
10000.2.a.l.1.2		2	25.14	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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{3} +(-0.690983 + 2.12663i) q^{5} -0.618034 q^{7} +(-0.618034 + 1.90211i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{3} +(-0.690983 + 2.12663i) q^{5} -0.618034 q^{7} +(-0.618034 + 1.90211i) q^{9} +(1.61803 + 4.97980i) q^{11} +(0.572949 - 1.76336i) q^{13} +(0.690983 + 2.12663i) q^{15} +(4.23607 + 3.07768i) q^{17} +(0.690983 + 0.502029i) q^{19} +(-0.500000 + 0.363271i) q^{21} +(-1.16312 - 3.57971i) q^{23} +(-4.04508 - 2.93893i) q^{25} +(1.54508 + 4.75528i) q^{27} +(2.92705 - 2.12663i) q^{29} +(-2.42705 - 1.76336i) q^{31} +(4.23607 + 3.07768i) q^{33} +(0.427051 - 1.31433i) q^{35} +(-0.0729490 + 0.224514i) q^{37} +(-0.572949 - 1.76336i) q^{39} +(-0.236068 + 0.726543i) q^{41} +4.85410 q^{43} +(-3.61803 - 2.62866i) q^{45} +(0.500000 - 0.363271i) q^{47} -6.61803 q^{49} +5.23607 q^{51} +(2.80902 - 2.04087i) q^{53} -11.7082 q^{55} +0.854102 q^{57} +(3.35410 - 10.3229i) q^{59} +(2.69098 + 8.28199i) q^{61} +(0.381966 - 1.17557i) q^{63} +(3.35410 + 2.43690i) q^{65} +(3.85410 + 2.80017i) q^{67} +(-3.04508 - 2.21238i) q^{69} +(-5.35410 + 3.88998i) q^{71} +(-2.78115 - 8.55951i) q^{73} -5.00000 q^{75} +(-1.00000 - 3.07768i) q^{77} +(-6.54508 + 4.75528i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-5.04508 - 3.66547i) q^{83} +(-9.47214 + 6.88191i) q^{85} +(1.11803 - 3.44095i) q^{87} +(-2.76393 - 8.50651i) q^{89} +(-0.354102 + 1.08981i) q^{91} -3.00000 q^{93} +(-1.54508 + 1.12257i) q^{95} +(3.11803 - 2.26538i) q^{97} -10.4721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - 5 q^{5} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 4 * q + q^3 - 5 * q^5 + 2 * q^7 + 2 * q^9	\( 4 q + q^{3} - 5 q^{5} + 2 q^{7} + 2 q^{9} + 2 q^{11} + 9 q^{13} + 5 q^{15} + 8 q^{17} + 5 q^{19} - 2 q^{21} + 11 q^{23} - 5 q^{25} - 5 q^{27} + 5 q^{29} - 3 q^{31} + 8 q^{33} - 5 q^{35} - 7 q^{37} - 9 q^{39} + 8 q^{41} + 6 q^{43} - 10 q^{45} + 2 q^{47} - 22 q^{49} + 12 q^{51} + 9 q^{53} - 20 q^{55} - 10 q^{57} + 13 q^{61} + 6 q^{63} + 2 q^{67} - q^{69} - 8 q^{71} + 9 q^{73} - 20 q^{75} - 4 q^{77} - 15 q^{79} - q^{81} - 9 q^{83} - 20 q^{85} - 20 q^{89} + 12 q^{91} - 12 q^{93} + 5 q^{95} + 8 q^{97} - 24 q^{99}+O(q^{100}) \) 4 * q + q^3 - 5 * q^5 + 2 * q^7 + 2 * q^9 + 2 * q^11 + 9 * q^13 + 5 * q^15 + 8 * q^17 + 5 * q^19 - 2 * q^21 + 11 * q^23 - 5 * q^25 - 5 * q^27 + 5 * q^29 - 3 * q^31 + 8 * q^33 - 5 * q^35 - 7 * q^37 - 9 * q^39 + 8 * q^41 + 6 * q^43 - 10 * q^45 + 2 * q^47 - 22 * q^49 + 12 * q^51 + 9 * q^53 - 20 * q^55 - 10 * q^57 + 13 * q^61 + 6 * q^63 + 2 * q^67 - q^69 - 8 * q^71 + 9 * q^73 - 20 * q^75 - 4 * q^77 - 15 * q^79 - q^81 - 9 * q^83 - 20 * q^85 - 20 * q^89 + 12 * q^91 - 12 * q^93 + 5 * q^95 + 8 * q^97 - 24 * q^99

Introduction

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