LMFDB - Embedded newform 400.2.u.c.241.1

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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			241.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	400.241
Dual form			400.2.u.c.161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 2.48990i) q^{3} +(0.690983 + 2.12663i) q^{5} +3.00000 q^{7} +(-3.11803 + 2.26538i) q^{9} +O(q^{10})$	\(q+(0.809017 + 2.48990i) q^{3} +(0.690983 + 2.12663i) q^{5} +3.00000 q^{7} +(-3.11803 + 2.26538i) q^{9} +(-0.190983 - 0.138757i) q^{11} +(-0.809017 + 0.587785i) q^{13} +(-4.73607 + 3.44095i) q^{15} +(2.42705 - 7.46969i) q^{17} +(0.263932 - 0.812299i) q^{19} +(2.42705 + 7.46969i) q^{21} +(-5.04508 - 3.66547i) q^{23} +(-4.04508 + 2.93893i) q^{25} +(-1.80902 - 1.31433i) q^{27} +(-0.163119 - 0.502029i) q^{29} +(-1.30902 + 4.02874i) q^{31} +(0.190983 - 0.587785i) q^{33} +(2.07295 + 6.37988i) q^{35} +(-5.92705 + 4.30625i) q^{37} +(-2.11803 - 1.53884i) q^{39} +(6.04508 - 4.39201i) q^{41} +1.76393 q^{43} +(-6.97214 - 5.06555i) q^{45} +(-1.83688 - 5.65334i) q^{47} +2.00000 q^{49} +20.5623 q^{51} +(0.472136 + 1.45309i) q^{53} +(0.163119 - 0.502029i) q^{55} +2.23607 q^{57} +(3.61803 - 2.62866i) q^{59} +(1.73607 + 1.26133i) q^{61} +(-9.35410 + 6.79615i) q^{63} +(-1.80902 - 1.31433i) q^{65} +(1.78115 - 5.48183i) q^{67} +(5.04508 - 15.5272i) q^{69} +(0.927051 + 2.85317i) q^{71} +(4.61803 + 3.35520i) q^{73} +(-10.5902 - 7.69421i) q^{75} +(-0.572949 - 0.416272i) q^{77} +(0.854102 + 2.62866i) q^{79} +(-1.76393 + 5.42882i) q^{81} +(4.16312 - 12.8128i) q^{83} +17.5623 q^{85} +(1.11803 - 0.812299i) q^{87} +(3.61803 + 2.62866i) q^{89} +(-2.42705 + 1.76336i) q^{91} -11.0902 q^{93} +1.90983 q^{95} +(-3.26393 - 10.0453i) q^{97} +0.909830 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} + 5 q^{5} + 12 q^{7} - 8 q^{9}+O(q^{10}) $ 4 * q + q^3 + 5 * q^5 + 12 * q^7 - 8 * q^9	$ 4 q + q^{3} + 5 q^{5} + 12 q^{7} - 8 q^{9} - 3 q^{11} - q^{13} - 10 q^{15} + 3 q^{17} + 10 q^{19} + 3 q^{21} - 9 q^{23} - 5 q^{25} - 5 q^{27} + 15 q^{29} - 3 q^{31} + 3 q^{33} + 15 q^{35} - 17 q^{37} - 4 q^{39} + 13 q^{41} + 16 q^{43} - 10 q^{45} - 23 q^{47} + 8 q^{49} + 42 q^{51} - 16 q^{53} - 15 q^{55} + 10 q^{59} - 2 q^{61} - 24 q^{63} - 5 q^{65} - 13 q^{67} + 9 q^{69} - 3 q^{71} + 14 q^{73} - 20 q^{75} - 9 q^{77} - 10 q^{79} - 16 q^{81} + q^{83} + 30 q^{85} + 10 q^{89} - 3 q^{91} - 22 q^{93} + 30 q^{95} - 22 q^{97} + 26 q^{99}+O(q^{100}) $ 4 * q + q^3 + 5 * q^5 + 12 * q^7 - 8 * q^9 - 3 * q^11 - q^13 - 10 * q^15 + 3 * q^17 + 10 * q^19 + 3 * q^21 - 9 * q^23 - 5 * q^25 - 5 * q^27 + 15 * q^29 - 3 * q^31 + 3 * q^33 + 15 * q^35 - 17 * q^37 - 4 * q^39 + 13 * q^41 + 16 * q^43 - 10 * q^45 - 23 * q^47 + 8 * q^49 + 42 * q^51 - 16 * q^53 - 15 * q^55 + 10 * q^59 - 2 * q^61 - 24 * q^63 - 5 * q^65 - 13 * q^67 + 9 * q^69 - 3 * q^71 + 14 * q^73 - 20 * q^75 - 9 * q^77 - 10 * q^79 - 16 * q^81 + q^83 + 30 * q^85 + 10 * q^89 - 3 * q^91 - 22 * q^93 + 30 * q^95 - 22 * q^97 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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	+	2.48990i	0.467086	+	1.43754i	0.856340	+	0.516413i	$0.172733\pi$
$3$	0.809017	+	2.48990i	0.467086	+	1.43754i	−0.389254	+	0.921131i	$0.627267\pi$
$4$		0			0
$5$	0.690983	+	2.12663i	0.309017	+	0.951057i
$5$	0.690983	+	2.12663i	0.309017	+	0.951057i
$6$		0			0
$7$	3.00000			1.13389			0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000			1.13389			0.566947	+	0.823754i	$0.308125\pi$
$8$		0			0
$9$	−3.11803	+	2.26538i	−1.03934	+	0.755128i
$10$		0			0
$11$	−0.190983	−	0.138757i	−0.0575835	−	0.0418369i	0.558621	−	0.829423i	$-0.311331\pi$
$11$	−0.190983	−	0.138757i	−0.0575835	−	0.0418369i	−0.616205	+	0.787586i	$0.711331\pi$
$12$		0			0
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i	−0.694297	−	0.719689i	$-0.744284\pi$
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i	0.469916	+	0.882711i	$0.344284\pi$
$14$		0			0
$15$	−4.73607	+	3.44095i	−1.22285	+	0.888451i
$16$		0			0
$17$	2.42705	−	7.46969i	0.588646	−	1.81167i	0.00454037	−	0.999990i	$-0.498555\pi$
$17$	2.42705	−	7.46969i	0.588646	−	1.81167i	0.584106	−	0.811677i	$-0.301445\pi$
$18$		0			0
$19$	0.263932	−	0.812299i	0.0605502	−	0.186354i	−0.916206	−	0.400707i	$-0.868764\pi$
$19$	0.263932	−	0.812299i	0.0605502	−	0.186354i	0.976756	+	0.214353i	$0.0687644\pi$
$20$		0			0
$21$	2.42705	+	7.46969i	0.529626	+	1.63002i
$22$		0			0
$23$	−5.04508	−	3.66547i	−1.05197	−	0.764303i	−0.0793863	−	0.996844i	$-0.525296\pi$
$23$	−5.04508	−	3.66547i	−1.05197	−	0.764303i	−0.972587	+	0.232541i	$0.925296\pi$
$24$		0			0
$25$	−4.04508	+	2.93893i	−0.809017	+	0.587785i
$26$		0			0
$27$	−1.80902	−	1.31433i	−0.348145	−	0.252942i
$28$		0			0
$29$	−0.163119	−	0.502029i	−0.0302904	−	0.0932244i	0.934768	−	0.355258i	$-0.115607\pi$
$29$	−0.163119	−	0.502029i	−0.0302904	−	0.0932244i	−0.965059	+	0.262033i	$0.915607\pi$
$30$		0			0
$31$	−1.30902	+	4.02874i	−0.235106	+	0.723583i	0.762001	+	0.647576i	$0.224217\pi$
$31$	−1.30902	+	4.02874i	−0.235106	+	0.723583i	−0.997107	+	0.0760071i	$0.975783\pi$
$32$		0			0
$33$	0.190983	−	0.587785i	0.0332459	−	0.102320i
$34$		0			0
$35$	2.07295	+	6.37988i	0.350392	+	1.07840i
$36$		0			0
$37$	−5.92705	+	4.30625i	−0.974401	+	0.707944i	−0.956450	−	0.291895i	$-0.905714\pi$
$37$	−5.92705	+	4.30625i	−0.974401	+	0.707944i	−0.0179508	+	0.999839i	$0.505714\pi$
$38$		0			0
$39$	−2.11803	−	1.53884i	−0.339157	−	0.246412i
$40$		0			0
$41$	6.04508	−	4.39201i	0.944084	−	0.685917i	−0.00531652	−	0.999986i	$-0.501692\pi$
$41$	6.04508	−	4.39201i	0.944084	−	0.685917i	0.949400	+	0.314069i	$0.101692\pi$
$42$		0			0
$43$	1.76393			0.268997			0.134499	−	0.990914i	$-0.457058\pi$
$43$	1.76393			0.268997			0.134499	+	0.990914i	$0.457058\pi$
$44$		0			0
$45$	−6.97214	−	5.06555i	−1.03934	−	0.755128i
$46$		0			0
$47$	−1.83688	−	5.65334i	−0.267937	−	0.824624i	−0.991002	−	0.133845i	$-0.957268\pi$
$47$	−1.83688	−	5.65334i	−0.267937	−	0.824624i	0.723066	−	0.690779i	$-0.242732\pi$
$48$		0			0
$49$	2.00000			0.285714
$50$		0			0
$51$	20.5623			2.87930
$52$		0			0
$53$	0.472136	+	1.45309i	0.0648529	+	0.199597i	0.978232	−	0.207513i	$-0.0665368\pi$
$53$	0.472136	+	1.45309i	0.0648529	+	0.199597i	−0.913379	+	0.407109i	$0.866537\pi$
$54$		0			0
$55$	0.163119	−	0.502029i	0.0219950	−	0.0676935i
$56$		0			0
$57$	2.23607			0.296174
$58$		0			0
$59$	3.61803	−	2.62866i	0.471028	−	0.342222i	−0.326814	−	0.945089i	$-0.605975\pi$
$59$	3.61803	−	2.62866i	0.471028	−	0.342222i	0.797842	+	0.602867i	$0.205975\pi$
$60$		0			0
$61$	1.73607	+	1.26133i	0.222281	+	0.161496i	0.693353	−	0.720598i	$-0.256133\pi$
$61$	1.73607	+	1.26133i	0.222281	+	0.161496i	−0.471072	+	0.882095i	$0.656133\pi$
$62$		0			0
$63$	−9.35410	+	6.79615i	−1.17851	+	0.856235i
$64$		0			0
$65$	−1.80902	−	1.31433i	−0.224381	−	0.163022i
$66$		0			0
$67$	1.78115	−	5.48183i	0.217602	−	0.669712i	−0.781356	−	0.624085i	$-0.785472\pi$
$67$	1.78115	−	5.48183i	0.217602	−	0.669712i	0.998959	−	0.0456261i	$-0.0145283\pi$
$68$		0			0
$69$	5.04508	−	15.5272i	0.607357	−	1.86925i
$70$		0			0
$71$	0.927051	+	2.85317i	0.110021	+	0.338609i	0.990876	−	0.134777i	$-0.0430317\pi$
$71$	0.927051	+	2.85317i	0.110021	+	0.338609i	−0.880855	+	0.473386i	$0.843032\pi$
$72$		0			0
$73$	4.61803	+	3.35520i	0.540500	+	0.392696i	0.824271	−	0.566196i	$-0.191585\pi$
$73$	4.61803	+	3.35520i	0.540500	+	0.392696i	−0.283771	+	0.958892i	$0.591585\pi$
$74$		0			0
$75$	−10.5902	−	7.69421i	−1.22285	−	0.888451i
$76$		0			0
$77$	−0.572949	−	0.416272i	−0.0652936	−	0.0474386i
$78$		0			0
$79$	0.854102	+	2.62866i	0.0960940	+	0.295747i	0.987537	−	0.157385i	$-0.0503065\pi$
$79$	0.854102	+	2.62866i	0.0960940	+	0.295747i	−0.891443	+	0.453132i	$0.850307\pi$
$80$		0			0
$81$	−1.76393	+	5.42882i	−0.195992	+	0.603203i
$82$		0			0
$83$	4.16312	−	12.8128i	0.456962	−	1.40638i	−0.411855	−	0.911249i	$-0.635119\pi$
$83$	4.16312	−	12.8128i	0.456962	−	1.40638i	0.868817	−	0.495134i	$-0.164881\pi$
$84$		0			0
$85$	17.5623			1.90490
$86$		0			0
$87$	1.11803	−	0.812299i	0.119866	−	0.0870876i
$88$		0			0
$89$	3.61803	+	2.62866i	0.383511	+	0.278637i	0.762791	−	0.646645i	$-0.223828\pi$
$89$	3.61803	+	2.62866i	0.383511	+	0.278637i	−0.379280	+	0.925282i	$0.623828\pi$
$90$		0			0
$91$	−2.42705	+	1.76336i	−0.254424	+	0.184850i
$92$		0			0
$93$	−11.0902			−1.15000
$94$		0			0
$95$	1.90983			0.195944
$96$		0			0
$97$	−3.26393	−	10.0453i	−0.331402	−	1.01995i	−0.968467	−	0.249141i	$-0.919852\pi$
$97$	−3.26393	−	10.0453i	−0.331402	−	1.01995i	0.637065	−	0.770810i	$-0.280148\pi$
$98$		0			0
$99$	0.909830			0.0914414
$100$		0			0
$101$	−1.61803			−0.161000			−0.0805002	−	0.996755i	$-0.525652\pi$
$101$	−1.61803			−0.161000			−0.0805002	+	0.996755i	$0.525652\pi$
$102$		0			0
$103$	6.13525	+	18.8824i	0.604525	+	1.86054i	0.500026	+	0.866010i	$0.333324\pi$
$103$	6.13525	+	18.8824i	0.604525	+	1.86054i	0.104499	+	0.994525i	$0.466676\pi$
$104$		0			0
$105$	−14.2082	+	10.3229i	−1.38658	+	1.00741i
$106$		0			0
$107$	−10.0902			−0.975454			−0.487727	−	0.872996i	$-0.662174\pi$
$107$	−10.0902			−0.975454			−0.487727	+	0.872996i	$0.662174\pi$
$108$		0			0
$109$	12.1353	−	8.81678i	1.16235	−	0.844494i	0.172274	−	0.985049i	$-0.444889\pi$
$109$	12.1353	−	8.81678i	1.16235	−	0.844494i	0.990073	+	0.140555i	$0.0448886\pi$
$110$		0			0
$111$	−15.5172	−	11.2739i	−1.47283	−	1.07007i
$112$		0			0
$113$	−6.66312	+	4.84104i	−0.626814	+	0.455407i	−0.855295	−	0.518142i	$-0.826624\pi$
$113$	−6.66312	+	4.84104i	−0.626814	+	0.455407i	0.228481	+	0.973548i	$0.426624\pi$
$114$		0			0
$115$	4.30902	−	13.2618i	0.401818	−	1.23667i
$116$		0			0
$117$	1.19098	−	3.66547i	0.110106	−	0.338873i
$118$		0			0
$119$	7.28115	−	22.4091i	0.667462	−	2.05424i
$120$		0			0
$121$	−3.38197	−	10.4086i	−0.307451	−	0.946238i
$122$		0			0
$123$	15.8262	+	11.4984i	1.42700	+	1.03678i
$124$		0			0
$125$	−9.04508	−	6.57164i	−0.809017	−	0.587785i
$126$		0			0
$127$	−10.0902	−	7.33094i	−0.895358	−	0.650516i	0.0419116	−	0.999121i	$-0.486655\pi$
$127$	−10.0902	−	7.33094i	−0.895358	−	0.650516i	−0.937269	+	0.348606i	$0.886655\pi$
$128$		0			0
$129$	1.42705	+	4.39201i	0.125645	+	0.386695i
$130$		0			0
$131$	−3.21885	+	9.90659i	−0.281232	+	0.865543i	0.706271	+	0.707942i	$0.250376\pi$
$131$	−3.21885	+	9.90659i	−0.281232	+	0.865543i	−0.987503	+	0.157601i	$0.949624\pi$
$132$		0			0
$133$	0.791796	−	2.43690i	0.0686574	−	0.211306i
$134$		0			0
$135$	1.54508	−	4.75528i	0.132980	−	0.409270i
$136$		0			0
$137$	4.92705	−	3.57971i	0.420946	−	0.305835i	−0.357072	−	0.934077i	$-0.616225\pi$
$137$	4.92705	−	3.57971i	0.420946	−	0.305835i	0.778018	+	0.628241i	$0.216225\pi$
$138$		0			0
$139$	8.35410	+	6.06961i	0.708586	+	0.514818i	0.882717	−	0.469905i	$-0.155712\pi$
$139$	8.35410	+	6.06961i	0.708586	+	0.514818i	−0.174131	+	0.984722i	$0.555712\pi$
$140$		0			0
$141$	12.5902	−	9.14729i	1.06028	−	0.770341i
$142$		0			0
$143$	0.236068			0.0197410
$144$		0			0
$145$	0.954915	−	0.693786i	0.0793014	−	0.0576158i
$146$		0			0
$147$	1.61803	+	4.97980i	0.133453	+	0.410727i
$148$		0			0
$149$	−2.23607			−0.183186			−0.0915929	−	0.995797i	$-0.529196\pi$
$149$	−2.23607			−0.183186			−0.0915929	+	0.995797i	$0.529196\pi$
$150$		0			0
$151$	−3.70820			−0.301769			−0.150885	−	0.988551i	$-0.548212\pi$
$151$	−3.70820			−0.301769			−0.150885	+	0.988551i	$0.548212\pi$
$152$		0			0
$153$	9.35410	+	28.7890i	0.756234	+	2.32745i
$154$		0			0
$155$	−9.47214			−0.760820
$156$		0			0
$157$	−15.5623			−1.24201			−0.621004	−	0.783808i	$-0.713275\pi$
$157$	−15.5623			−1.24201			−0.621004	+	0.783808i	$0.713275\pi$
$158$		0			0
$159$	−3.23607	+	2.35114i	−0.256637	+	0.186458i
$160$		0			0
$161$	−15.1353	−	10.9964i	−1.19283	−	0.866638i
$162$		0			0
$163$	−3.92705	+	2.85317i	−0.307590	+	0.223477i	−0.730862	−	0.682525i	$-0.760882\pi$
$163$	−3.92705	+	2.85317i	−0.307590	+	0.223477i	0.423271	+	0.906003i	$0.360882\pi$
$164$		0			0
$165$	1.38197			0.107586
$166$		0			0
$167$	−4.82624	+	14.8536i	−0.373466	+	1.14941i	0.571043	+	0.820920i	$0.306539\pi$
$167$	−4.82624	+	14.8536i	−0.373466	+	1.14941i	−0.944508	+	0.328488i	$0.893461\pi$
$168$		0			0
$169$	−3.70820	+	11.4127i	−0.285246	+	0.877898i
$170$		0			0
$171$	1.01722	+	3.13068i	0.0777888	+	0.239409i
$172$		0			0
$173$	−2.61803	−	1.90211i	−0.199045	−	0.144615i	0.483798	−	0.875180i	$-0.339257\pi$
$173$	−2.61803	−	1.90211i	−0.199045	−	0.144615i	−0.682843	+	0.730565i	$0.739257\pi$
$174$		0			0
$175$	−12.1353	+	8.81678i	−0.917339	+	0.666486i
$176$		0			0
$177$	9.47214	+	6.88191i	0.711969	+	0.517276i
$178$		0			0
$179$	3.45492	+	10.6331i	0.258232	+	0.794758i	0.993176	+	0.116629i	$0.0372089\pi$
$179$	3.45492	+	10.6331i	0.258232	+	0.794758i	−0.734943	+	0.678129i	$0.762791\pi$
$180$		0			0
$181$	−6.61803	+	20.3682i	−0.491915	+	1.51396i	0.329796	+	0.944052i	$0.393020\pi$
$181$	−6.61803	+	20.3682i	−0.491915	+	1.51396i	−0.821710	+	0.569905i	$0.806980\pi$
$182$		0			0
$183$	−1.73607	+	5.34307i	−0.128334	+	0.394971i
$184$		0			0
$185$	−13.2533	−	9.62908i	−0.974401	−	0.707944i
$186$		0			0
$187$	−1.50000	+	1.08981i	−0.109691	+	0.0796951i
$188$		0			0
$189$	−5.42705	−	3.94298i	−0.394760	−	0.286810i
$190$		0			0
$191$	14.2812	−	10.3759i	1.03335	−	0.750771i	0.0643719	−	0.997926i	$-0.479496\pi$
$191$	14.2812	−	10.3759i	1.03335	−	0.750771i	0.968976	+	0.247155i	$0.0794956\pi$
$192$		0			0
$193$	16.6525			1.19867			0.599336	−	0.800498i	$-0.295431\pi$
$193$	16.6525			1.19867			0.599336	+	0.800498i	$0.295431\pi$
$194$		0			0
$195$	1.80902	−	5.56758i	0.129546	−	0.398703i
$196$		0			0
$197$	3.70820	+	11.4127i	0.264199	+	0.813120i	0.991877	+	0.127201i	$0.0405994\pi$
$197$	3.70820	+	11.4127i	0.264199	+	0.813120i	−0.727678	+	0.685919i	$0.759401\pi$
$198$		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
$201$	15.0902			1.06438
$202$		0			0
$203$	−0.489357	−	1.50609i	−0.0343461	−	0.105706i
$204$		0			0
$205$	13.5172	+	9.82084i	0.944084	+	0.685917i
$206$		0			0
$207$	24.0344			1.67051
$208$		0			0
$209$	−0.163119	+	0.118513i	−0.0112832	+	0.00819771i
$210$		0			0
$211$	9.11803	+	6.62464i	0.627711	+	0.456059i	0.855607	−	0.517627i	$-0.173184\pi$
$211$	9.11803	+	6.62464i	0.627711	+	0.456059i	−0.227895	+	0.973686i	$0.573184\pi$
$212$		0			0
$213$	−6.35410	+	4.61653i	−0.435376	+	0.316319i
$214$		0			0
$215$	1.21885	+	3.75123i	0.0831247	+	0.255831i
$216$		0			0
$217$	−3.92705	+	12.0862i	−0.266586	+	0.820466i
$218$		0			0
$219$	−4.61803	+	14.2128i	−0.312058	+	0.960415i
$220$		0			0
$221$	2.42705	+	7.46969i	0.163261	+	0.502466i
$222$		0			0
$223$	−7.28115	−	5.29007i	−0.487582	−	0.354249i	0.316672	−	0.948535i	$-0.397435\pi$
$223$	−7.28115	−	5.29007i	−0.487582	−	0.354249i	−0.804254	+	0.594286i	$0.797435\pi$
$224$		0			0
$225$	5.95492	−	18.3273i	0.396994	−	1.22182i
$226$		0			0
$227$	−12.4271	−	9.02878i	−0.824812	−	0.599261i	0.0932746	−	0.995640i	$-0.470267\pi$
$227$	−12.4271	−	9.02878i	−0.824812	−	0.599261i	−0.918087	+	0.396379i	$0.870267\pi$
$228$		0			0
$229$	5.42705	+	16.7027i	0.358630	+	1.10375i	0.953875	+	0.300204i	$0.0970549\pi$
$229$	5.42705	+	16.7027i	0.358630	+	1.10375i	−0.595245	+	0.803544i	$0.702945\pi$
$230$		0			0
$231$	0.572949	−	1.76336i	0.0376973	−	0.116020i
$232$		0			0
$233$	8.56231	−	26.3521i	0.560935	−	1.72638i	−0.118795	−	0.992919i	$-0.537903\pi$
$233$	8.56231	−	26.3521i	0.560935	−	1.72638i	0.679730	−	0.733463i	$-0.262097\pi$
$234$		0			0
$235$	10.7533	−	7.81272i	0.701467	−	0.509646i
$236$		0			0
$237$	−5.85410	+	4.25325i	−0.380265	+	0.276279i
$238$		0			0
$239$	−14.6353	−	10.6331i	−0.946676	−	0.687800i	0.00334240	−	0.999994i	$-0.498936\pi$
$239$	−14.6353	−	10.6331i	−0.946676	−	0.687800i	−0.950018	+	0.312194i	$0.898936\pi$
$240$		0			0
$241$	−10.8262	+	7.86572i	−0.697379	+	0.506676i	−0.879078	−	0.476679i	$-0.841841\pi$
$241$	−10.8262	+	7.86572i	−0.697379	+	0.506676i	0.181698	+	0.983354i	$0.441841\pi$
$242$		0			0
$243$	−21.6525			−1.38901
$244$		0			0
$245$	1.38197	+	4.25325i	0.0882906	+	0.271730i
$246$		0			0
$247$	0.263932	+	0.812299i	0.0167936	+	0.0516854i
$248$		0			0
$249$	35.2705			2.23518
$250$		0			0
$251$	−23.1803			−1.46313			−0.731565	−	0.681772i	$-0.761210\pi$
$251$	−23.1803			−1.46313			−0.731565	+	0.681772i	$0.761210\pi$
$252$		0			0
$253$	0.454915	+	1.40008i	0.0286003	+	0.0880226i
$254$		0			0
$255$	14.2082	+	43.7284i	0.889752	+	2.73838i
$256$		0			0
$257$	−16.7426			−1.04438			−0.522189	−	0.852830i	$-0.674884\pi$
$257$	−16.7426			−1.04438			−0.522189	+	0.852830i	$0.674884\pi$
$258$		0			0
$259$	−17.7812	+	12.9188i	−1.10487	+	0.802733i
$260$		0			0
$261$	1.64590	+	1.19581i	0.101879	+	0.0740191i
$262$		0			0
$263$	1.92705	−	1.40008i	0.118827	−	0.0863329i	−0.526785	−	0.849999i	$-0.676603\pi$
$263$	1.92705	−	1.40008i	0.118827	−	0.0863329i	0.645612	+	0.763666i	$0.276603\pi$
$264$		0			0
$265$	−2.76393	+	2.00811i	−0.169787	+	0.123357i
$266$		0			0
$267$	−3.61803	+	11.1352i	−0.221420	+	0.681461i
$268$		0			0
$269$	4.04508	−	12.4495i	0.246633	−	0.759059i	−0.748730	−	0.662875i	$-0.769336\pi$
$269$	4.04508	−	12.4495i	0.246633	−	0.759059i	0.995364	−	0.0961842i	$-0.0306638\pi$
$270$		0			0
$271$	2.93769	+	9.04129i	0.178452	+	0.549219i	0.999774	−	0.0212453i	$-0.00676311\pi$
$271$	2.93769	+	9.04129i	0.178452	+	0.549219i	−0.821322	+	0.570465i	$0.806763\pi$
$272$		0			0
$273$	−6.35410	−	4.61653i	−0.384568	−	0.279405i
$274$		0			0
$275$	1.18034			0.0711772
$276$		0			0
$277$	−11.0902	−	8.05748i	−0.666344	−	0.484127i	0.202456	−	0.979291i	$-0.435108\pi$
$277$	−11.0902	−	8.05748i	−0.666344	−	0.484127i	−0.868799	+	0.495164i	$0.835108\pi$
$278$		0			0
$279$	−5.04508	−	15.5272i	−0.302041	−	0.929588i
$280$		0			0
$281$	−5.92705	+	18.2416i	−0.353578	+	1.08820i	0.603251	+	0.797551i	$0.293872\pi$
$281$	−5.92705	+	18.2416i	−0.353578	+	1.08820i	−0.956829	+	0.290651i	$0.906128\pi$
$282$		0			0
$283$	7.94427	−	24.4500i	0.472238	−	1.45340i	−0.377409	−	0.926047i	$-0.623185\pi$
$283$	7.94427	−	24.4500i	0.472238	−	1.45340i	0.849647	−	0.527352i	$-0.176815\pi$
$284$		0			0
$285$	1.54508	+	4.75528i	0.0915229	+	0.281679i
$286$		0			0
$287$	18.1353	−	13.1760i	1.07049	−	0.777757i
$288$		0			0
$289$	−36.1525	−	26.2663i	−2.12662	−	1.54508i
$290$		0			0
$291$	22.3713	−	16.2537i	1.31143	−	0.952810i
$292$		0			0
$293$	−11.5623			−0.675477			−0.337739	−	0.941240i	$-0.609662\pi$
$293$	−11.5623			−0.675477			−0.337739	+	0.941240i	$0.609662\pi$
$294$		0			0
$295$	8.09017	+	5.87785i	0.471028	+	0.342222i
$296$		0			0
$297$	0.163119	+	0.502029i	0.00946512	+	0.0291307i
$298$		0			0
$299$	6.23607			0.360641
$300$		0			0
$301$	5.29180			0.305014
$302$		0			0
$303$	−1.30902	−	4.02874i	−0.0752011	−	0.231445i
$304$		0			0
$305$	−1.48278	+	4.56352i	−0.0849037	+	0.261307i
$306$		0			0
$307$	−17.1246			−0.977353			−0.488677	−	0.872465i	$-0.662520\pi$
$307$	−17.1246			−0.977353			−0.488677	+	0.872465i	$0.662520\pi$
$308$		0			0
$309$	−42.0517	+	30.5523i	−2.39224	+	1.73806i
$310$		0			0
$311$	−17.0623	−	12.3965i	−0.967515	−	0.702941i	−0.0126308	−	0.999920i	$-0.504021\pi$
$311$	−17.0623	−	12.3965i	−0.967515	−	0.702941i	−0.954884	+	0.296980i	$0.904021\pi$
$312$		0			0
$313$	−2.88197	+	2.09387i	−0.162898	+	0.118353i	−0.666248	−	0.745730i	$-0.732101\pi$
$313$	−2.88197	+	2.09387i	−0.162898	+	0.118353i	0.503350	+	0.864083i	$0.332101\pi$
$314$		0			0
$315$	−20.9164	−	15.1967i	−1.17851	−	0.856235i
$316$		0			0
$317$	3.28115	−	10.0984i	0.184288	−	0.567180i	−0.815647	−	0.578549i	$-0.803619\pi$
$317$	3.28115	−	10.0984i	0.184288	−	0.567180i	0.999935	+	0.0113694i	$0.00361906\pi$
$318$		0			0
$319$	−0.0385072	+	0.118513i	−0.00215599	+	0.00663545i
$320$		0			0
$321$	−8.16312	−	25.1235i	−0.455621	−	1.40226i
$322$		0			0
$323$	−5.42705	−	3.94298i	−0.301969	−	0.219393i
$324$		0			0
$325$	1.54508	−	4.75528i	0.0857059	−	0.263776i
$326$		0			0
$327$	31.7705	+	23.0826i	1.75691	+	1.27647i
$328$		0			0
$329$	−5.51064	−	16.9600i	−0.303812	−	0.935036i
$330$		0			0
$331$	−1.40983	+	4.33901i	−0.0774913	+	0.238494i	−0.982297	−	0.187332i	$-0.940016\pi$
$331$	−1.40983	+	4.33901i	−0.0774913	+	0.238494i	0.904805	+	0.425825i	$0.140016\pi$
$332$		0			0
$333$	8.72542	−	26.8541i	0.478150	−	1.47160i
$334$		0			0
$335$	12.8885			0.704176
$336$		0			0
$337$	25.4164	−	18.4661i	1.38452	−	1.00591i	0.388078	−	0.921626i	$-0.373139\pi$
$337$	25.4164	−	18.4661i	1.38452	−	1.00591i	0.996442	−	0.0842863i	$-0.0268610\pi$
$338$		0			0
$339$	−17.4443	−	12.6740i	−0.947443	−	0.688357i
$340$		0			0
$341$	0.809017	−	0.587785i	0.0438107	−	0.0318304i
$342$		0			0
$343$	−15.0000			−0.809924
$344$		0			0
$345$	36.5066			1.96545
$346$		0			0
$347$	3.06231	+	9.42481i	0.164393	+	0.505950i	0.998991	−	0.0449095i	$-0.0142999\pi$
$347$	3.06231	+	9.42481i	0.164393	+	0.505950i	−0.834598	+	0.550860i	$0.814300\pi$
$348$		0			0
$349$	−22.2361			−1.19027			−0.595135	−	0.803626i	$-0.702901\pi$
$349$	−22.2361			−1.19027			−0.595135	+	0.803626i	$0.702901\pi$
$350$		0			0
$351$	2.23607			0.119352
$352$		0			0
$353$	−5.18034	−	15.9434i	−0.275722	−	0.848584i	−0.989028	−	0.147731i	$-0.952803\pi$
$353$	−5.18034	−	15.9434i	−0.275722	−	0.848584i	0.713306	−	0.700853i	$-0.247197\pi$
$354$		0			0
$355$	−5.42705	+	3.94298i	−0.288038	+	0.209272i
$356$		0			0
$357$	61.6869			3.26482
$358$		0			0
$359$	2.50000	−	1.81636i	0.131945	−	0.0958636i	−0.519855	−	0.854254i	$-0.674014\pi$
$359$	2.50000	−	1.81636i	0.131945	−	0.0958636i	0.651800	+	0.758391i	$0.274014\pi$
$360$		0			0
$361$	14.7812	+	10.7391i	0.777955	+	0.565218i
$362$		0			0
$363$	23.1803	−	16.8415i	1.21665	−	0.883950i
$364$		0			0
$365$	−3.94427	+	12.1392i	−0.206453	+	0.635396i
$366$		0			0
$367$	9.74671	−	29.9973i	0.508774	−	1.56585i	−0.285557	−	0.958362i	$-0.592179\pi$
$367$	9.74671	−	29.9973i	0.508774	−	1.56585i	0.794332	−	0.607484i	$-0.207821\pi$
$368$		0			0
$369$	−8.89919	+	27.3889i	−0.463273	+	1.42581i
$370$		0			0
$371$	1.41641	+	4.35926i	0.0735362	+	0.226321i
$372$		0			0
$373$	13.1353	+	9.54332i	0.680118	+	0.494134i	0.873397	−	0.487009i	$-0.161912\pi$
$373$	13.1353	+	9.54332i	0.680118	+	0.494134i	−0.193279	+	0.981144i	$0.561912\pi$
$374$		0			0
$375$	9.04508	−	27.8379i	0.467086	−	1.43754i
$376$		0			0
$377$	0.427051	+	0.310271i	0.0219942	+	0.0159798i
$378$		0			0
$379$	−0.163119	−	0.502029i	−0.00837886	−	0.0257875i	0.946780	−	0.321882i	$-0.104316\pi$
$379$	−0.163119	−	0.502029i	−0.00837886	−	0.0257875i	−0.955159	+	0.296095i	$0.904316\pi$
$380$		0			0
$381$	10.0902	−	31.0543i	0.516935	−	1.59096i
$382$		0			0
$383$	1.33688	−	4.11450i	0.0683114	−	0.210241i	−0.911073	−	0.412244i	$-0.864745\pi$
$383$	1.33688	−	4.11450i	0.0683114	−	0.210241i	0.979385	+	0.202003i	$0.0647451\pi$
$384$		0			0
$385$	0.489357	−	1.50609i	0.0249399	−	0.0767572i
$386$		0			0
$387$	−5.50000	+	3.99598i	−0.279581	+	0.203127i
$388$		0			0
$389$	26.8713	+	19.5232i	1.36243	+	0.989863i	0.998286	+	0.0585208i	$0.0186384\pi$
$389$	26.8713	+	19.5232i	1.36243	+	0.989863i	0.364144	+	0.931343i	$0.381362\pi$
$390$		0			0
$391$	−39.6246	+	28.7890i	−2.00390	+	1.45592i
$392$		0			0
$393$	−27.2705			−1.37562
$394$		0			0
$395$	−5.00000	+	3.63271i	−0.251577	+	0.182782i
$396$		0			0
$397$	−1.78115	−	5.48183i	−0.0893935	−	0.275125i	0.896359	−	0.443330i	$-0.146203\pi$
$397$	−1.78115	−	5.48183i	−0.0893935	−	0.275125i	−0.985752	+	0.168205i	$0.946203\pi$
$398$		0			0
$399$	6.70820			0.335830
$400$		0			0
$401$	8.18034			0.408507			0.204253	−	0.978918i	$-0.434523\pi$
$401$	8.18034			0.408507			0.204253	+	0.978918i	$0.434523\pi$
$402$		0			0
$403$	−1.30902	−	4.02874i	−0.0652068	−	0.200686i
$404$		0			0
$405$	−12.7639			−0.634245
$406$		0			0
$407$	1.72949			0.0857276
$408$		0			0
$409$	−5.42705	+	3.94298i	−0.268350	+	0.194968i	−0.713820	−	0.700329i	$-0.753037\pi$
$409$	−5.42705	+	3.94298i	−0.268350	+	0.194968i	0.445470	+	0.895297i	$0.353037\pi$
$410$		0			0
$411$	12.8992	+	9.37181i	0.636270	+	0.462277i
$412$		0			0
$413$	10.8541	−	7.88597i	0.534095	−	0.388043i
$414$		0			0
$415$	30.1246			1.47876
$416$		0			0
$417$	−8.35410	+	25.7113i	−0.409102	+	1.25909i
$418$		0			0
$419$	−8.41641	+	25.9030i	−0.411168	+	1.26545i	0.504465	+	0.863432i	$0.331690\pi$
$419$	−8.41641	+	25.9030i	−0.411168	+	1.26545i	−0.915633	+	0.402014i	$0.868310\pi$
$420$		0			0
$421$	−3.79180	−	11.6699i	−0.184801	−	0.568758i	0.815144	−	0.579258i	$-0.196658\pi$
$421$	−3.79180	−	11.6699i	−0.184801	−	0.568758i	−0.999945	+	0.0104998i	$0.996658\pi$
$422$		0			0
$423$	18.5344	+	13.4661i	0.901175	+	0.654742i
$424$		0			0
$425$	12.1353	+	37.3485i	0.588646	+	1.81167i
$426$		0			0
$427$	5.20820	+	3.78398i	0.252043	+	0.183120i
$428$		0			0
$429$	0.190983	+	0.587785i	0.00922075	+	0.0283785i
$430$		0			0
$431$	9.90983	−	30.4993i	0.477340	−	1.46910i	−0.365436	−	0.930836i	$-0.619080\pi$
$431$	9.90983	−	30.4993i	0.477340	−	1.46910i	0.842776	−	0.538264i	$-0.180920\pi$
$432$		0			0
$433$	7.21885	−	22.2173i	0.346916	−	1.06770i	−0.613635	−	0.789590i	$-0.710293\pi$
$433$	7.21885	−	22.2173i	0.346916	−	1.06770i	0.960550	−	0.278106i	$-0.0897068\pi$
$434$		0			0
$435$	2.50000	+	1.81636i	0.119866	+	0.0870876i
$436$		0			0
$437$	−4.30902	+	3.13068i	−0.206128	+	0.149761i
$438$		0			0
$439$	−4.57295	−	3.32244i	−0.218255	−	0.158572i	0.473286	−	0.880909i	$-0.343068\pi$
$439$	−4.57295	−	3.32244i	−0.218255	−	0.158572i	−0.691541	+	0.722337i	$0.743068\pi$
$440$		0			0
$441$	−6.23607	+	4.53077i	−0.296956	+	0.215751i
$442$		0			0
$443$	7.41641			0.352364			0.176182	−	0.984358i	$-0.443625\pi$
$443$	7.41641			0.352364			0.176182	+	0.984358i	$0.443625\pi$
$444$		0			0
$445$	−3.09017	+	9.51057i	−0.146488	+	0.450844i
$446$		0			0
$447$	−1.80902	−	5.56758i	−0.0855636	−	0.263338i
$448$		0			0
$449$	13.9443			0.658071			0.329035	−	0.944318i	$-0.393276\pi$
$449$	13.9443			0.658071			0.329035	+	0.944318i	$0.393276\pi$
$450$		0			0
$451$	−1.76393			−0.0830603
$452$		0			0
$453$	−3.00000	−	9.23305i	−0.140952	−	0.433807i
$454$		0			0
$455$	−5.42705	−	3.94298i	−0.254424	−	0.184850i
$456$		0			0
$457$	−11.2148			−0.524605			−0.262303	−	0.964986i	$-0.584482\pi$
$457$	−11.2148			−0.524605			−0.262303	+	0.964986i	$0.584482\pi$
$458$		0			0
$459$	−14.2082	+	10.3229i	−0.663182	+	0.481830i
$460$		0			0
$461$	−22.7984	−	16.5640i	−1.06183	−	0.771462i	−0.0874008	−	0.996173i	$-0.527856\pi$
$461$	−22.7984	−	16.5640i	−1.06183	−	0.771462i	−0.974425	+	0.224711i	$0.927856\pi$
$462$		0			0
$463$	9.69098	−	7.04091i	0.450378	−	0.327219i	−0.339367	−	0.940654i	$-0.610213\pi$
$463$	9.69098	−	7.04091i	0.450378	−	0.327219i	0.789745	+	0.613435i	$0.210213\pi$
$464$		0			0
$465$	−7.66312	−	23.5847i	−0.355369	−	1.09371i
$466$		0			0
$467$	−0.982779	+	3.02468i	−0.0454776	+	0.139966i	−0.971217	−	0.238196i	$-0.923444\pi$
$467$	−0.982779	+	3.02468i	−0.0454776	+	0.139966i	0.925739	+	0.378162i	$0.123444\pi$
$468$		0			0
$469$	5.34346	−	16.4455i	0.246738	−	0.759381i
$470$		0			0
$471$	−12.5902	−	38.7486i	−0.580124	−	1.78544i
$472$		0			0
$473$	−0.336881	−	0.244758i	−0.0154898	−	0.0112540i
$474$		0			0
$475$	1.31966	+	4.06150i	0.0605502	+	0.186354i
$476$		0			0
$477$	−4.76393	−	3.46120i	−0.218125	−	0.158477i
$478$		0			0
$479$	12.2984	+	37.8505i	0.561927	+	1.72943i	0.676910	+	0.736066i	$0.263319\pi$
$479$	12.2984	+	37.8505i	0.561927	+	1.72943i	−0.114983	+	0.993368i	$0.536681\pi$
$480$		0			0
$481$	2.26393	−	6.96767i	0.103226	−	0.317698i
$482$		0			0
$483$	15.1353	−	46.5815i	0.688678	−	2.11953i
$484$		0			0
$485$	19.1074	−	13.8823i	0.867622	−	0.630364i
$486$		0			0
$487$	−14.6631	+	10.6534i	−0.664449	+	0.482751i	−0.868163	−	0.496280i	$-0.834699\pi$
$487$	−14.6631	+	10.6534i	−0.664449	+	0.482751i	0.203713	+	0.979031i	$0.434699\pi$
$488$		0			0
$489$	−10.2812	−	7.46969i	−0.464930	−	0.337791i
$490$		0			0
$491$	11.9443	−	8.67802i	0.539037	−	0.391634i	−0.284690	−	0.958620i	$-0.591891\pi$
$491$	11.9443	−	8.67802i	0.539037	−	0.391634i	0.823727	+	0.566986i	$0.191891\pi$
$492$		0			0
$493$	−4.14590			−0.186722
$494$		0			0
$495$	0.628677	+	1.93487i	0.0282569	+	0.0869659i
$496$		0			0
$497$	2.78115	+	8.55951i	0.124752	+	0.383946i
$498$		0			0
$499$	−40.8541			−1.82888			−0.914440	−	0.404721i	$-0.867369\pi$
$499$	−40.8541			−1.82888			−0.914440	+	0.404721i	$0.867369\pi$
$500$		0			0
$501$	−40.8885			−1.82677
$502$		0			0
$503$	−2.31966	−	7.13918i	−0.103429	−	0.318320i	0.885930	−	0.463819i	$-0.153521\pi$
$503$	−2.31966	−	7.13918i	−0.103429	−	0.318320i	−0.989358	+	0.145499i	$0.953521\pi$
$504$		0			0
$505$	−1.11803	−	3.44095i	−0.0497519	−	0.153120i
$506$		0			0
$507$	−31.4164			−1.39525
$508$		0			0
$509$	10.5902	−	7.69421i	0.469401	−	0.341040i	−0.327807	−	0.944745i	$-0.606310\pi$
$509$	10.5902	−	7.69421i	0.469401	−	0.341040i	0.797208	+	0.603705i	$0.206310\pi$
$510$		0			0
$511$	13.8541	+	10.0656i	0.612869	+	0.445276i
$512$		0			0
$513$	−1.54508	+	1.12257i	−0.0682172	+	0.0495627i
$514$		0			0
$515$	−35.9164	+	26.0948i	−1.58267	+	1.14987i
$516$		0			0
$517$	−0.433629	+	1.33457i	−0.0190710	+	0.0586944i
$518$		0			0
$519$	2.61803	−	8.05748i	0.114919	−	0.353684i
$520$		0			0
$521$	10.0279	+	30.8626i	0.439329	+	1.35211i	0.888585	+	0.458712i	$0.151689\pi$
$521$	10.0279	+	30.8626i	0.439329	+	1.35211i	−0.449256	+	0.893403i	$0.648311\pi$
$522$		0			0
$523$	21.5623	+	15.6659i	0.942854	+	0.685023i	0.949106	−	0.314957i	$-0.101990\pi$
$523$	21.5623	+	15.6659i	0.942854	+	0.685023i	−0.00625211	+	0.999980i	$0.501990\pi$
$524$		0			0
$525$	−31.7705	−	23.0826i	−1.38658	−	1.00741i
$526$		0			0
$527$	26.9164	+	19.5559i	1.17250	+	0.851869i
$528$		0			0
$529$	4.90983	+	15.1109i	0.213471	+	0.656996i
$530$		0			0
$531$	−5.32624	+	16.3925i	−0.231139	+	0.711373i
$532$		0			0
$533$	−2.30902	+	7.10642i	−0.100015	+	0.307813i
$534$		0			0
$535$	−6.97214	−	21.4580i	−0.301432	−	0.927711i
$536$		0			0
$537$	−23.6803	+	17.2048i	−1.02188	+	0.742441i
$538$		0			0
$539$	−0.381966	−	0.277515i	−0.0164524	−	0.0119534i
$540$		0			0
$541$	−23.2254	+	16.8743i	−0.998539	+	0.725481i	−0.961774	−	0.273843i	$-0.911705\pi$
$541$	−23.2254	+	16.8743i	−0.998539	+	0.725481i	−0.0367646	+	0.999324i	$0.511705\pi$
$542$		0			0
$543$	−56.0689			−2.40615
$544$		0			0
$545$	27.1353	+	19.7149i	1.16235	+	0.844494i
$546$		0			0
$547$	−3.28115	−	10.0984i	−0.140292	−	0.431774i	0.856084	−	0.516837i	$-0.172891\pi$
$547$	−3.28115	−	10.0984i	−0.140292	−	0.431774i	−0.996376	+	0.0850631i	$0.972891\pi$
$548$		0			0
$549$	−8.27051			−0.352977
$550$		0			0
$551$	−0.450850			−0.0192068
$552$		0			0
$553$	2.56231	+	7.88597i	0.108960	+	0.335345i
$554$		0			0
$555$	13.2533	−	40.7894i	0.562571	−	1.73141i
$556$		0			0
$557$	−10.8885			−0.461362			−0.230681	−	0.973029i	$-0.574095\pi$
$557$	−10.8885			−0.461362			−0.230681	+	0.973029i	$0.574095\pi$
$558$		0			0
$559$	−1.42705	+	1.03681i	−0.0603578	+	0.0438525i
$560$		0			0
$561$	−3.92705	−	2.85317i	−0.165800	−	0.120461i
$562$		0			0
$563$	−28.1976	+	20.4867i	−1.18839	+	0.863413i	−0.993093	−	0.117332i	$-0.962566\pi$
$563$	−28.1976	+	20.4867i	−1.18839	+	0.863413i	−0.195293	+	0.980745i	$0.562566\pi$
$564$		0			0
$565$	−14.8992	−	10.8249i	−0.626814	−	0.455407i
$566$		0			0
$567$	−5.29180	+	16.2865i	−0.222235	+	0.683968i
$568$		0			0
$569$	6.87132	−	21.1478i	0.288061	−	0.886560i	−0.697404	−	0.716679i	$-0.745661\pi$
$569$	6.87132	−	21.1478i	0.288061	−	0.886560i	0.985464	−	0.169882i	$-0.0543385\pi$
$570$		0			0
$571$	−0.517221	−	1.59184i	−0.0216450	−	0.0666165i	0.939651	−	0.342136i	$-0.111150\pi$
$571$	−0.517221	−	1.59184i	−0.0216450	−	0.0666165i	−0.961296	+	0.275519i	$0.911150\pi$
$572$		0			0
$573$	37.3885	+	27.1644i	1.56193	+	1.13481i
$574$		0			0
$575$	31.1803			1.30031
$576$		0			0
$577$	34.7877	+	25.2748i	1.44823	+	1.05220i	0.986240	+	0.165318i	$0.0528651\pi$
$577$	34.7877	+	25.2748i	1.44823	+	1.05220i	0.461992	+	0.886884i	$0.347135\pi$
$578$		0			0
$579$	13.4721	+	41.4630i	0.559883	+	1.72314i
$580$		0			0
$581$	12.4894	−	38.4383i	0.518146	−	1.59469i
$582$		0			0
$583$	0.111456	−	0.343027i	0.00461604	−	0.0142067i
$584$		0			0
$585$	8.61803			0.356312
$586$		0			0
$587$	−9.56231	+	6.94742i	−0.394679	+	0.286751i	−0.767370	−	0.641205i	$-0.778435\pi$
$587$	−9.56231	+	6.94742i	−0.394679	+	0.286751i	0.372691	+	0.927955i	$0.378435\pi$
$588$		0			0
$589$	2.92705	+	2.12663i	0.120607	+	0.0876261i
$590$		0			0
$591$	−25.4164	+	18.4661i	−1.04549	+	0.759594i
$592$		0			0
$593$	−47.0132			−1.93060			−0.965299	−	0.261145i	$-0.915900\pi$
$593$	−47.0132			−1.93060			−0.965299	+	0.261145i	$0.915900\pi$
$594$		0			0
$595$	52.6869			2.15995
$596$		0			0
$597$	14.2082	+	43.7284i	0.581503	+	1.78968i
$598$		0			0
$599$	8.94427			0.365453			0.182727	−	0.983164i	$-0.441508\pi$
$599$	8.94427			0.365453			0.182727	+	0.983164i	$0.441508\pi$
$600$		0			0
$601$	−14.8328			−0.605043			−0.302522	−	0.953143i	$-0.597828\pi$
$601$	−14.8328			−0.605043			−0.302522	+	0.953143i	$0.597828\pi$
$602$		0			0
$603$	6.86475	+	21.1275i	0.279554	+	0.860379i
$604$		0			0
$605$	19.7984	−	14.3844i	0.804918	−	0.584807i
$606$		0			0
$607$	27.1459			1.10182			0.550909	−	0.834565i	$-0.314281\pi$
$607$	27.1459			1.10182			0.550909	+	0.834565i	$0.314281\pi$
$608$		0			0
$609$	3.35410	−	2.43690i	0.135915	−	0.0987481i
$610$		0			0
$611$	4.80902	+	3.49396i	0.194552	+	0.141350i
$612$		0			0
$613$	33.6246	−	24.4297i	1.35809	−	0.986707i	0.359521	−	0.933137i	$-0.382940\pi$
$613$	33.6246	−	24.4297i	1.35809	−	0.986707i	0.998564	−	0.0535698i	$-0.0170600\pi$
$614$		0			0
$615$	−13.5172	+	41.6017i	−0.545067	+	1.67754i
$616$		0			0
$617$	−9.38197	+	28.8747i	−0.377704	+	1.16245i	0.563933	+	0.825821i	$0.309288\pi$
$617$	−9.38197	+	28.8747i	−0.377704	+	1.16245i	−0.941636	+	0.336632i	$0.890712\pi$
$618$		0			0
$619$	14.5106	−	44.6592i	0.583232	−	1.79500i	−0.0230252	−	0.999735i	$-0.507330\pi$
$619$	14.5106	−	44.6592i	0.583232	−	1.79500i	0.606257	−	0.795269i	$-0.292670\pi$
$620$		0			0
$621$	4.30902	+	13.2618i	0.172915	+	0.532177i
$622$		0			0
$623$	10.8541	+	7.88597i	0.434860	+	0.315945i
$624$		0			0
$625$	7.72542	−	23.7764i	0.309017	−	0.951057i
$626$		0			0
$627$	−0.427051	−	0.310271i	−0.0170548	−	0.0123910i
$628$		0			0
$629$	17.7812	+	54.7248i	0.708981	+	2.18202i
$630$		0			0
$631$	−2.72949	+	8.40051i	−0.108659	+	0.334419i	−0.990572	−	0.136994i	$-0.956256\pi$
$631$	−2.72949	+	8.40051i	−0.108659	+	0.334419i	0.881913	+	0.471413i	$0.156256\pi$
$632$		0			0
$633$	−9.11803	+	28.0624i	−0.362409	+	1.11538i
$634$		0			0
$635$	8.61803	−	26.5236i	0.341996	−	1.05256i
$636$		0			0
$637$	−1.61803	+	1.17557i	−0.0641088	+	0.0465778i
$638$		0			0
$639$	−9.35410	−	6.79615i	−0.370043	−	0.268852i
$640$		0			0
$641$	−11.6180	+	8.44100i	−0.458885	+	0.333399i	−0.793094	−	0.609100i	$-0.791531\pi$
$641$	−11.6180	+	8.44100i	−0.458885	+	0.333399i	0.334209	+	0.942499i	$0.391531\pi$
$642$		0			0
$643$	36.2361			1.42901			0.714506	−	0.699630i	$-0.246652\pi$
$643$	36.2361			1.42901			0.714506	+	0.699630i	$0.246652\pi$
$644$		0			0
$645$	−8.35410	+	6.06961i	−0.328942	+	0.238991i
$646$		0			0
$647$	−2.36475	−	7.27794i	−0.0929677	−	0.286125i	0.893751	−	0.448563i	$-0.148064\pi$
$647$	−2.36475	−	7.27794i	−0.0929677	−	0.286125i	−0.986719	+	0.162438i	$0.948064\pi$
$648$		0			0
$649$	−1.05573			−0.0414410
$650$		0			0
$651$	−33.2705			−1.30397
$652$		0			0
$653$	12.5451	+	38.6098i	0.490927	+	1.51092i	0.823209	+	0.567738i	$0.192181\pi$
$653$	12.5451	+	38.6098i	0.490927	+	1.51092i	−0.332282	+	0.943180i	$0.607819\pi$
$654$		0			0
$655$	−23.2918			−0.910086
$656$		0			0
$657$	−22.0000			−0.858302
$658$		0			0
$659$	4.57295	−	3.32244i	0.178137	−	0.129424i	−0.495144	−	0.868811i	$-0.664885\pi$
$659$	4.57295	−	3.32244i	0.178137	−	0.129424i	0.673281	+	0.739387i	$0.264885\pi$
$660$		0			0
$661$	−5.07295	−	3.68571i	−0.197315	−	0.143358i	0.484741	−	0.874658i	$-0.338914\pi$
$661$	−5.07295	−	3.68571i	−0.197315	−	0.143358i	−0.682056	+	0.731300i	$0.738914\pi$
$662$		0			0
$663$	−16.6353	+	12.0862i	−0.646060	+	0.469390i
$664$		0			0
$665$	5.72949			0.222180
$666$		0			0
$667$	−1.01722	+	3.13068i	−0.0393870	+	0.121221i
$668$		0			0
$669$	7.28115	−	22.4091i	0.281506	−	0.866385i
$670$		0			0
$671$	−0.156541	−	0.481784i	−0.00604320	−	0.0185991i
$672$		0			0
$673$	1.00000	+	0.726543i	0.0385472	+	0.0280062i	0.606892	−	0.794784i	$-0.292416\pi$
$673$	1.00000	+	0.726543i	0.0385472	+	0.0280062i	−0.568345	+	0.822790i	$0.692416\pi$
$674$		0			0
$675$	11.1803			0.430331
$676$		0			0
$677$	−8.59017	−	6.24112i	−0.330147	−	0.239866i	0.410346	−	0.911930i	$-0.365408\pi$
$677$	−8.59017	−	6.24112i	−0.330147	−	0.239866i	−0.740493	+	0.672064i	$0.765408\pi$
$678$		0			0
$679$	−9.79180	−	30.1360i	−0.375775	−	1.15652i
$680$		0			0
$681$	12.4271	−	38.2465i	0.476206	−	1.46561i
$682$		0			0
$683$	−10.3090	+	31.7279i	−0.394464	+	1.21403i	0.534915	+	0.844906i	$0.320344\pi$
$683$	−10.3090	+	31.7279i	−0.394464	+	1.21403i	−0.929379	+	0.369128i	$0.879656\pi$
$684$		0			0
$685$	11.0172	+	8.00448i	0.420946	+	0.305835i
$686$		0			0
$687$	−37.1976	+	27.0256i	−1.41918	+	1.03109i
$688$		0			0
$689$	−1.23607	−	0.898056i	−0.0470904	−	0.0342132i
$690$		0			0
$691$	1.02786	−	0.746787i	0.0391018	−	0.0284091i	−0.568063	−	0.822985i	$-0.692307\pi$
$691$	1.02786	−	0.746787i	0.0391018	−	0.0284091i	0.607164	+	0.794576i	$0.292307\pi$
$692$		0			0
$693$	2.72949			0.103685
$694$		0			0
$695$	−7.13525	+	21.9601i	−0.270656	+	0.832992i
$696$		0			0
$697$	−18.1353	−	55.8146i	−0.686922	−	2.11413i
$698$		0			0
$699$	72.5410			2.74375
$700$		0			0
$701$	−4.18034			−0.157889			−0.0789446	−	0.996879i	$-0.525155\pi$
$701$	−4.18034			−0.157889			−0.0789446	+	0.996879i	$0.525155\pi$
$702$		0			0
$703$	1.93363	+	5.95110i	0.0729282	+	0.224450i
$704$		0			0
$705$	28.1525	+	20.4540i	1.06028	+	0.770341i
$706$		0			0
$707$	−4.85410			−0.182557
$708$		0			0
$709$	−6.28115	+	4.56352i	−0.235894	+	0.171387i	−0.699452	−	0.714680i	$-0.746572\pi$
$709$	−6.28115	+	4.56352i	−0.235894	+	0.171387i	0.463558	+	0.886066i	$0.346572\pi$
$710$		0			0
$711$	−8.61803	−	6.26137i	−0.323202	−	0.234820i
$712$		0			0
$713$	21.3713	−	15.5272i	0.800362	−	0.581497i
$714$		0			0
$715$	0.163119	+	0.502029i	0.00610030	+	0.0187748i
$716$		0			0
$717$	14.6353	−	45.0427i	0.546564	−	1.68215i
$718$		0			0
$719$	8.19098	−	25.2093i	0.305472	−	0.940147i	−0.674028	−	0.738705i	$-0.735438\pi$
$719$	8.19098	−	25.2093i	0.305472	−	0.940147i	0.979501	−	0.201441i	$-0.0645625\pi$
$720$		0			0
$721$	18.4058	+	56.6471i	0.685466	+	2.10965i
$722$		0			0
$723$	−28.3435	−	20.5927i	−1.05410	−	0.765852i
$724$		0			0
$725$	2.13525	+	1.55135i	0.0793014	+	0.0576158i
$726$		0			0
$727$	−23.1803	−	16.8415i	−0.859711	−	0.624617i	0.0680952	−	0.997679i	$-0.478308\pi$
$727$	−23.1803	−	16.8415i	−0.859711	−	0.624617i	−0.927806	+	0.373062i	$0.878308\pi$
$728$		0			0
$729$	−12.2254	−	37.6260i	−0.452794	−	1.39356i
$730$		0			0
$731$	4.28115	−	13.1760i	0.158344	−	0.487333i
$732$		0			0
$733$	−12.2918	+	37.8303i	−0.454008	+	1.39729i	0.418288	+	0.908314i	$0.362630\pi$
$733$	−12.2918	+	37.8303i	−0.454008	+	1.39729i	−0.872296	+	0.488978i	$0.837370\pi$
$734$		0			0
$735$	−9.47214	+	6.88191i	−0.349385	+	0.253843i
$736$		0			0
$737$	−1.10081	+	0.799788i	−0.0405490	+	0.0294606i
$738$		0			0
$739$	24.2705	+	17.6336i	0.892805	+	0.648661i	0.936608	−	0.350379i	$-0.113947\pi$
$739$	24.2705	+	17.6336i	0.892805	+	0.648661i	−0.0438028	+	0.999040i	$0.513947\pi$
$740$		0			0
$741$	−1.80902	+	1.31433i	−0.0664559	+	0.0482830i
$742$		0			0
$743$	18.2705			0.670280			0.335140	−	0.942168i	$-0.391216\pi$
$743$	18.2705			0.670280			0.335140	+	0.942168i	$0.391216\pi$
$744$		0			0
$745$	−1.54508	−	4.75528i	−0.0566075	−	0.174220i
$746$		0			0
$747$	16.0451	+	49.3817i	0.587059	+	1.80678i
$748$		0			0
$749$	−30.2705			−1.10606
$750$		0			0
$751$	−1.14590			−0.0418144			−0.0209072	−	0.999781i	$-0.506655\pi$
$751$	−1.14590			−0.0418144			−0.0209072	+	0.999781i	$0.506655\pi$
$752$		0			0
$753$	−18.7533	−	57.7167i	−0.683408	−	2.10331i
$754$		0			0
$755$	−2.56231	−	7.88597i	−0.0932519	−	0.287000i
$756$		0			0
$757$	10.4164			0.378591			0.189295	−	0.981920i	$-0.439380\pi$
$757$	10.4164			0.378591			0.189295	+	0.981920i	$0.439380\pi$
$758$		0			0
$759$	−3.11803	+	2.26538i	−0.113177	+	0.0822282i
$760$		0			0
$761$	30.6803	+	22.2906i	1.11216	+	0.808033i	0.983003	−	0.183591i	$-0.0587723\pi$
$761$	30.6803	+	22.2906i	1.11216	+	0.808033i	0.129159	+	0.991624i	$0.458772\pi$
$762$		0			0
$763$	36.4058	−	26.4503i	1.31798	−	0.957566i
$764$		0			0
$765$	−54.7599	+	39.7854i	−1.97985	+	1.43844i
$766$		0			0
$767$	−1.38197	+	4.25325i	−0.0498999	+	0.153576i
$768$		0			0
$769$	−7.23607	+	22.2703i	−0.260939	+	0.803089i	0.731662	+	0.681668i	$0.238745\pi$
$769$	−7.23607	+	22.2703i	−0.260939	+	0.803089i	−0.992601	+	0.121421i	$0.961255\pi$
$770$		0			0
$771$	−13.5451	−	41.6875i	−0.487814	−	1.50134i
$772$		0			0
$773$	−5.01722	−	3.64522i	−0.180457	−	0.131110i	0.493890	−	0.869525i	$-0.335575\pi$
$773$	−5.01722	−	3.64522i	−0.180457	−	0.131110i	−0.674347	+	0.738415i	$0.735575\pi$
$774$		0			0
$775$	−6.54508	−	20.1437i	−0.235106	−	0.723583i
$776$		0			0
$777$	−46.5517	−	33.8218i	−1.67003	−	1.21335i
$778$		0			0
$779$	−1.97214	−	6.06961i	−0.0706591	−	0.217466i
$780$		0			0
$781$	0.218847	−	0.673542i	0.00783096	−	0.0241012i
$782$		0			0
$783$	−0.364745	+	1.12257i	−0.0130349	+	0.0401174i
$784$		0			0
$785$	−10.7533	−	33.0952i	−0.383801	−	1.18122i
$786$		0			0
$787$	12.4721	−	9.06154i	0.444584	−	0.323009i	−0.342870	−	0.939383i	$-0.611399\pi$
$787$	12.4721	−	9.06154i	0.444584	−	0.323009i	0.787454	+	0.616374i	$0.211399\pi$
$788$		0			0
$789$	5.04508	+	3.66547i	0.179610	+	0.130494i
$790$		0			0
$791$	−19.9894	+	14.5231i	−0.710740	+	0.516383i
$792$		0			0
$793$	−2.14590			−0.0762031
$794$		0			0
$795$	−7.23607	−	5.25731i	−0.256637	−	0.186458i
$796$		0			0
$797$	1.04508	+	3.21644i	0.0370188	+	0.113932i	0.967858	−	0.251496i	$-0.0809226\pi$
$797$	1.04508	+	3.21644i	0.0370188	+	0.113932i	−0.930840	+	0.365428i	$0.880923\pi$
$798$		0			0
$799$	−46.6869			−1.65166
$800$		0			0
$801$	−17.2361			−0.609007
$802$		0			0
$803$	−0.416408	−	1.28157i	−0.0146947	−	0.0452257i
$804$		0			0
$805$	12.9271	−	39.7854i	0.455619	−	1.40225i
$806$		0			0
$807$	34.2705			1.20638
$808$		0			0
$809$	−1.80902	+	1.31433i	−0.0636017	+	0.0462093i	−0.619132	−	0.785287i	$-0.712515\pi$
$809$	−1.80902	+	1.31433i	−0.0636017	+	0.0462093i	0.555530	+	0.831496i	$0.312515\pi$
$810$		0			0
$811$	18.6525	+	13.5518i	0.654977	+	0.475869i	0.864963	−	0.501836i	$-0.167342\pi$
$811$	18.6525	+	13.5518i	0.654977	+	0.475869i	−0.209986	+	0.977704i	$0.567342\pi$
$812$		0			0
$813$	−20.1353	+	14.6291i	−0.706174	+	0.513066i
$814$		0			0
$815$	−8.78115	−	6.37988i	−0.307590	−	0.223477i
$816$		0			0
$817$	0.465558	−	1.43284i	0.0162878	−	0.0501287i
$818$		0			0
$819$	3.57295	−	10.9964i	0.124849	−	0.384246i
$820$		0			0
$821$	−9.31966	−	28.6830i	−0.325258	−	1.00104i	−0.971324	−	0.237760i	$-0.923587\pi$
$821$	−9.31966	−	28.6830i	−0.325258	−	1.00104i	0.646065	−	0.763282i	$-0.276413\pi$
$822$		0			0
$823$	26.5623	+	19.2986i	0.925904	+	0.672708i	0.944986	−	0.327109i	$-0.106075\pi$
$823$	26.5623	+	19.2986i	0.925904	+	0.672708i	−0.0190827	+	0.999818i	$0.506075\pi$
$824$		0			0
$825$	0.954915	+	2.93893i	0.0332459	+	0.102320i
$826$		0			0
$827$	19.4443	+	14.1271i	0.676144	+	0.491247i	0.872076	−	0.489370i	$-0.162773\pi$
$827$	19.4443	+	14.1271i	0.676144	+	0.491247i	−0.195932	+	0.980617i	$0.562773\pi$
$828$		0			0
$829$	8.21478	+	25.2825i	0.285311	+	0.878097i	0.986305	+	0.164930i	$0.0527399\pi$
$829$	8.21478	+	25.2825i	0.285311	+	0.878097i	−0.700994	+	0.713167i	$0.747260\pi$
$830$		0			0
$831$	11.0902	−	34.1320i	0.384714	−	1.18403i
$832$		0			0
$833$	4.85410	−	14.9394i	0.168185	−	0.517619i
$834$		0			0
$835$	−34.9230			−1.20856
$836$		0			0
$837$	7.66312	−	5.56758i	0.264876	−	0.192444i
$838$		0			0
$839$	20.4271	+	14.8411i	0.705220	+	0.512372i	0.881628	−	0.471945i	$-0.156448\pi$
$839$	20.4271	+	14.8411i	0.705220	+	0.512372i	−0.176408	+	0.984317i	$0.556448\pi$
$840$		0			0
$841$	23.2361	−	16.8820i	0.801244	−	0.582138i
$842$		0			0
$843$	−50.2148			−1.72949
$844$		0			0
$845$	−26.8328			−0.923077
$846$		0			0
$847$	−10.1459	−	31.2259i	−0.348617	−	1.07293i
$848$		0			0
$849$	67.3050			2.30990
$850$		0			0
$851$	45.6869			1.56613
$852$		0			0
$853$	−7.68034	−	23.6377i	−0.262970	−	0.809338i	−0.992154	−	0.125021i	$-0.960100\pi$
$853$	−7.68034	−	23.6377i	−0.262970	−	0.809338i	0.729184	−	0.684317i	$-0.239900\pi$
$854$		0			0
$855$	−5.95492	+	4.32650i	−0.203654	+	0.147963i
$856$		0			0
$857$	35.3394			1.20717			0.603585	−	0.797298i	$-0.293738\pi$
$857$	35.3394			1.20717			0.603585	+	0.797298i	$0.293738\pi$
$858$		0			0
$859$	−31.8713	+	23.1559i	−1.08744	+	0.790068i	−0.978964	−	0.204031i	$-0.934596\pi$
$859$	−31.8713	+	23.1559i	−1.08744	+	0.790068i	−0.108471	+	0.994100i	$0.534596\pi$
$860$		0			0
$861$	47.4787	+	34.4953i	1.61807	+	1.17560i
$862$		0			0
$863$	−5.47214	+	3.97574i	−0.186274	+	0.135336i	−0.677014	−	0.735970i	$-0.736726\pi$
$863$	−5.47214	+	3.97574i	−0.186274	+	0.135336i	0.490740	+	0.871306i	$0.336726\pi$
$864$		0			0
$865$	2.23607	−	6.88191i	0.0760286	−	0.233992i
$866$		0			0
$867$	36.1525	−	111.266i	1.22780	−	3.77879i
$868$		0			0
$869$	0.201626	−	0.620541i	0.00683970	−	0.0210504i
$870$		0			0
$871$	1.78115	+	5.48183i	0.0603521	+	0.185745i
$872$		0			0
$873$	32.9336	+	23.9277i	1.11463	+	0.809829i
$874$		0			0
$875$	−27.1353	−	19.7149i	−0.917339	−	0.666486i
$876$		0			0
$877$	−19.8713	−	14.4374i	−0.671007	−	0.487515i	0.199355	−	0.979927i	$-0.436115\pi$
$877$	−19.8713	−	14.4374i	−0.671007	−	0.487515i	−0.870362	+	0.492412i	$0.836115\pi$
$878$		0			0
$879$	−9.35410	−	28.7890i	−0.315506	−	0.971028i
$880$		0			0
$881$	4.88854	−	15.0454i	0.164699	−	0.506892i	−0.834315	−	0.551288i	$-0.814136\pi$
$881$	4.88854	−	15.0454i	0.164699	−	0.506892i	0.999014	+	0.0443963i	$0.0141364\pi$
$882$		0			0
$883$	−5.77458	+	17.7723i	−0.194330	+	0.598086i	0.805654	+	0.592387i	$0.201814\pi$
$883$	−5.77458	+	17.7723i	−0.194330	+	0.598086i	−0.999984	+	0.00569940i	$0.998186\pi$
$884$		0			0
$885$	−8.09017	+	24.8990i	−0.271948	+	0.836970i
$886$		0			0
$887$	8.75329	−	6.35964i	0.293907	−	0.213536i	−0.431054	−	0.902326i	$-0.641858\pi$
$887$	8.75329	−	6.35964i	0.293907	−	0.213536i	0.724960	+	0.688791i	$0.241858\pi$
$888$		0			0
$889$	−30.2705	−	21.9928i	−1.01524	−	0.737615i
$890$		0			0
$891$	1.09017	−	0.792055i	0.0365221	−	0.0265348i
$892$		0			0
$893$	−5.07701			−0.169896
$894$		0			0
$895$	−20.2254	+	14.6946i	−0.676061	+	0.491187i
$896$		0			0
$897$	5.04508	+	15.5272i	0.168450	+	0.518437i
$898$		0			0
$899$	2.23607			0.0745770
$900$		0			0
$901$	12.0000			0.399778
$902$		0			0
$903$	4.28115	+	13.1760i	0.142468	+	0.438471i
$904$		0			0
$905$	−47.8885			−1.59187
$906$		0			0
$907$	−23.3820			−0.776385			−0.388193	−	0.921578i	$-0.626901\pi$
$907$	−23.3820			−0.776385			−0.388193	+	0.921578i	$0.626901\pi$
$908$		0			0
$909$	5.04508	−	3.66547i	0.167335	−	0.121576i
$910$		0			0
$911$	8.42705	+	6.12261i	0.279201	+	0.202851i	0.718569	−	0.695456i	$-0.244798\pi$
$911$	8.42705	+	6.12261i	0.279201	+	0.202851i	−0.439368	+	0.898307i	$0.644798\pi$
$912$		0			0
$913$	−2.57295	+	1.86936i	−0.0851522	+	0.0618667i
$914$		0			0
$915$	−12.5623			−0.415297
$916$		0			0
$917$	−9.65654	+	29.7198i	−0.318887	+	0.981434i
$918$		0			0
$919$	−7.92705	+	24.3970i	−0.261489	+	0.804781i	0.730992	+	0.682386i	$0.239058\pi$
$919$	−7.92705	+	24.3970i	−0.261489	+	0.804781i	−0.992481	+	0.122395i	$0.960942\pi$
$920$		0			0
$921$	−13.8541	−	42.6385i	−0.456508	−	1.40499i
$922$		0			0
$923$	−2.42705	−	1.76336i	−0.0798874	−	0.0580416i
$924$		0			0
$925$	11.3197	−	34.8383i	0.372188	−	1.14548i
$926$		0			0
$927$	−61.9058	−	44.9772i	−2.03325	−	1.47724i
$928$		0			0
$929$	−5.28773	−	16.2740i	−0.173485	−	0.533931i	0.826076	−	0.563558i	$-0.190568\pi$
$929$	−5.28773	−	16.2740i	−0.173485	−	0.533931i	−0.999561	+	0.0296271i	$0.990568\pi$
$930$		0			0
$931$	0.527864	−	1.62460i	0.0173000	−	0.0532441i
$932$		0			0
$933$	17.0623	−	52.5124i	0.558595	−	1.71918i
$934$		0			0
$935$	−3.35410	−	2.43690i	−0.109691	−	0.0796951i
$936$		0			0
$937$	18.5451	−	13.4738i	0.605842	−	0.440170i	−0.242106	−	0.970250i	$-0.577838\pi$
$937$	18.5451	−	13.4738i	0.605842	−	0.440170i	0.847948	+	0.530080i	$0.177838\pi$
$938$		0			0
$939$	−7.54508	−	5.48183i	−0.246225	−	0.178893i
$940$		0			0
$941$	9.39919	−	6.82891i	0.306405	−	0.222616i	−0.423948	−	0.905687i	$-0.639356\pi$
$941$	9.39919	−	6.82891i	0.306405	−	0.222616i	0.730352	+	0.683071i	$0.239356\pi$
$942$		0			0
$943$	−46.5967			−1.51740
$944$		0			0
$945$	4.63525	−	14.2658i	0.150785	−	0.464068i
$946$		0			0
$947$	12.8607	+	39.5811i	0.417916	+	1.28621i	0.909617	+	0.415449i	$0.136375\pi$
$947$	12.8607	+	39.5811i	0.417916	+	1.28621i	−0.491701	+	0.870764i	$0.663625\pi$
$948$		0			0
$949$	−5.70820			−0.185296
$950$		0			0
$951$	27.7984			0.901424
$952$		0			0
$953$	13.0967	+	40.3076i	0.424245	+	1.30569i	0.903715	+	0.428134i	$0.140829\pi$
$953$	13.0967	+	40.3076i	0.424245	+	1.30569i	−0.479470	+	0.877558i	$0.659171\pi$
$954$		0			0
$955$	31.9336	+	23.2011i	1.03335	+	0.750771i
$956$		0			0
$957$	−0.326238			−0.0105458
$958$		0			0
$959$	14.7812	−	10.7391i	0.477308	−	0.346785i
$960$		0			0
$961$	10.5623	+	7.67396i	0.340720	+	0.247547i
$962$		0			0
$963$	31.4615	−	22.8581i	1.01383	−	0.736592i
$964$		0			0
$965$	11.5066	+	35.4136i	0.370410	+	1.14000i
$966$		0			0
$967$	−8.38197	+	25.7970i	−0.269546	+	0.829577i	0.721065	+	0.692867i	$0.243653\pi$
$967$	−8.38197	+	25.7970i	−0.269546	+	0.829577i	−0.990611	+	0.136710i	$0.956347\pi$
$968$		0			0
$969$	5.42705	−	16.7027i	0.174342	−	0.536569i
$970$		0			0
$971$	16.0902	+	49.5205i	0.516358	+	1.58919i	0.780797	+	0.624785i	$0.214813\pi$
$971$	16.0902	+	49.5205i	0.516358	+	1.58919i	−0.264439	+	0.964402i	$0.585187\pi$
$972$		0			0
$973$	25.0623	+	18.2088i	0.803461	+	0.583748i
$974$		0			0
$975$	13.0902			0.419221
$976$		0			0
$977$	21.0451	+	15.2901i	0.673292	+	0.489175i	0.871126	−	0.491060i	$-0.163391\pi$
$977$	21.0451	+	15.2901i	0.673292	+	0.489175i	−0.197834	+	0.980236i	$0.563391\pi$
$978$		0			0
$979$	−0.326238	−	1.00406i	−0.0104266	−	0.0320898i
$980$		0			0
$981$	−17.8647	+	54.9820i	−0.570377	+	1.75544i
$982$		0			0
$983$	14.3647	−	44.2101i	0.458164	−	1.41008i	−0.409216	−	0.912438i	$-0.634198\pi$
$983$	14.3647	−	44.2101i	0.458164	−	1.41008i	0.867380	−	0.497647i	$-0.165802\pi$
$984$		0			0
$985$	−21.7082	+	15.7719i	−0.691681	+	0.502536i
$986$		0			0
$987$	37.7705	−	27.4419i	1.20225	−	0.873485i
$988$		0			0
$989$	−8.89919	−	6.46564i	−0.282978	−	0.205595i
$990$		0			0
$991$	42.4336	−	30.8298i	1.34795	−	0.979342i	0.348838	−	0.937183i	$-0.386576\pi$
$991$	42.4336	−	30.8298i	1.34795	−	0.979342i	0.999111	−	0.0421589i	$-0.0134236\pi$
$992$		0			0
$993$	−11.9443			−0.379040
$994$		0			0
$995$	12.1353	+	37.3485i	0.384713	+	1.18403i
$996$		0			0
$997$	−16.4549	−	50.6430i	−0.521132	−	1.60388i	−0.771839	−	0.635818i	$-0.780663\pi$
$997$	−16.4549	−	50.6430i	−0.521132	−	1.60388i	0.250707	−	0.968063i	$-0.419337\pi$
$998$		0			0
$999$	16.3820			0.518302

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.u.c.241.1		4
4.3	odd	2		50.2.d.a.41.1	yes	4
12.11	even	2		450.2.h.a.91.1		4
20.3	even	4		250.2.e.b.49.2		8
20.7	even	4		250.2.e.b.49.1		8
20.19	odd	2		250.2.d.a.201.1		4
25.6	even	5		10000.2.a.n.1.2		2
25.11	even	5	inner	400.2.u.c.161.1		4
25.19	even	10		10000.2.a.a.1.1		2
100.11	odd	10		50.2.d.a.11.1	✓	4
100.19	odd	10		1250.2.a.d.1.2		2
100.23	even	20		250.2.e.b.199.1		8
100.27	even	20		250.2.e.b.199.2		8
100.31	odd	10		1250.2.a.a.1.1		2
100.39	odd	10		250.2.d.a.51.1		4
100.67	even	20		1250.2.b.b.1249.2		4
100.83	even	20		1250.2.b.b.1249.3		4
300.11	even	10		450.2.h.a.361.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.a.11.1	✓	4	100.11	odd	10
50.2.d.a.41.1	yes	4	4.3	odd	2
250.2.d.a.51.1		4	100.39	odd	10
250.2.d.a.201.1		4	20.19	odd	2
250.2.e.b.49.1		8	20.7	even	4
250.2.e.b.49.2		8	20.3	even	4
250.2.e.b.199.1		8	100.23	even	20
250.2.e.b.199.2		8	100.27	even	20
400.2.u.c.161.1		4	25.11	even	5	inner
400.2.u.c.241.1		4	1.1	even	1	trivial
450.2.h.a.91.1		4	12.11	even	2
450.2.h.a.361.1		4	300.11	even	10
1250.2.a.a.1.1		2	100.31	odd	10
1250.2.a.d.1.2		2	100.19	odd	10
1250.2.b.b.1249.2		4	100.67	even	20
1250.2.b.b.1249.3		4	100.83	even	20
10000.2.a.a.1.1		2	25.19	even	10
10000.2.a.n.1.2		2	25.6	even	5

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)

\(f(q)\)	\(=\)	\(q+(0.809017 + 2.48990i) q^{3} +(0.690983 + 2.12663i) q^{5} +3.00000 q^{7} +(-3.11803 + 2.26538i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 2.48990i) q^{3} +(0.690983 + 2.12663i) q^{5} +3.00000 q^{7} +(-3.11803 + 2.26538i) q^{9} +(-0.190983 - 0.138757i) q^{11} +(-0.809017 + 0.587785i) q^{13} +(-4.73607 + 3.44095i) q^{15} +(2.42705 - 7.46969i) q^{17} +(0.263932 - 0.812299i) q^{19} +(2.42705 + 7.46969i) q^{21} +(-5.04508 - 3.66547i) q^{23} +(-4.04508 + 2.93893i) q^{25} +(-1.80902 - 1.31433i) q^{27} +(-0.163119 - 0.502029i) q^{29} +(-1.30902 + 4.02874i) q^{31} +(0.190983 - 0.587785i) q^{33} +(2.07295 + 6.37988i) q^{35} +(-5.92705 + 4.30625i) q^{37} +(-2.11803 - 1.53884i) q^{39} +(6.04508 - 4.39201i) q^{41} +1.76393 q^{43} +(-6.97214 - 5.06555i) q^{45} +(-1.83688 - 5.65334i) q^{47} +2.00000 q^{49} +20.5623 q^{51} +(0.472136 + 1.45309i) q^{53} +(0.163119 - 0.502029i) q^{55} +2.23607 q^{57} +(3.61803 - 2.62866i) q^{59} +(1.73607 + 1.26133i) q^{61} +(-9.35410 + 6.79615i) q^{63} +(-1.80902 - 1.31433i) q^{65} +(1.78115 - 5.48183i) q^{67} +(5.04508 - 15.5272i) q^{69} +(0.927051 + 2.85317i) q^{71} +(4.61803 + 3.35520i) q^{73} +(-10.5902 - 7.69421i) q^{75} +(-0.572949 - 0.416272i) q^{77} +(0.854102 + 2.62866i) q^{79} +(-1.76393 + 5.42882i) q^{81} +(4.16312 - 12.8128i) q^{83} +17.5623 q^{85} +(1.11803 - 0.812299i) q^{87} +(3.61803 + 2.62866i) q^{89} +(-2.42705 + 1.76336i) q^{91} -11.0902 q^{93} +1.90983 q^{95} +(-3.26393 - 10.0453i) q^{97} +0.909830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} + 5 q^{5} + 12 q^{7} - 8 q^{9}+O(q^{10}) \) 4 * q + q^3 + 5 * q^5 + 12 * q^7 - 8 * q^9	\( 4 q + q^{3} + 5 q^{5} + 12 q^{7} - 8 q^{9} - 3 q^{11} - q^{13} - 10 q^{15} + 3 q^{17} + 10 q^{19} + 3 q^{21} - 9 q^{23} - 5 q^{25} - 5 q^{27} + 15 q^{29} - 3 q^{31} + 3 q^{33} + 15 q^{35} - 17 q^{37} - 4 q^{39} + 13 q^{41} + 16 q^{43} - 10 q^{45} - 23 q^{47} + 8 q^{49} + 42 q^{51} - 16 q^{53} - 15 q^{55} + 10 q^{59} - 2 q^{61} - 24 q^{63} - 5 q^{65} - 13 q^{67} + 9 q^{69} - 3 q^{71} + 14 q^{73} - 20 q^{75} - 9 q^{77} - 10 q^{79} - 16 q^{81} + q^{83} + 30 q^{85} + 10 q^{89} - 3 q^{91} - 22 q^{93} + 30 q^{95} - 22 q^{97} + 26 q^{99}+O(q^{100}) \) 4 * q + q^3 + 5 * q^5 + 12 * q^7 - 8 * q^9 - 3 * q^11 - q^13 - 10 * q^15 + 3 * q^17 + 10 * q^19 + 3 * q^21 - 9 * q^23 - 5 * q^25 - 5 * q^27 + 15 * q^29 - 3 * q^31 + 3 * q^33 + 15 * q^35 - 17 * q^37 - 4 * q^39 + 13 * q^41 + 16 * q^43 - 10 * q^45 - 23 * q^47 + 8 * q^49 + 42 * q^51 - 16 * q^53 - 15 * q^55 + 10 * q^59 - 2 * q^61 - 24 * q^63 - 5 * q^65 - 13 * q^67 + 9 * q^69 - 3 * q^71 + 14 * q^73 - 20 * q^75 - 9 * q^77 - 10 * q^79 - 16 * q^81 + q^83 + 30 * q^85 + 10 * q^89 - 3 * q^91 - 22 * q^93 + 30 * q^95 - 22 * q^97 + 26 * q^99

Introduction

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