LMFDB - Embedded newform 725.2.k.a.581.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(146,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([6, 0]))

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

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

chi := DirichletCharacter("725.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.k (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.78915414654$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			581.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	725.581
Dual form			725.2.k.a.146.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.11803 + 1.53884i) q^{3} +(1.61803 - 1.17557i) q^{4} +(-1.80902 - 1.31433i) q^{5} -3.00000 q^{7} +(1.19098 - 3.66547i) q^{9} +(-0.118034 - 0.363271i) q^{11} +(-1.61803 + 4.97980i) q^{12} +(-0.309017 + 0.951057i) q^{13} +5.85410 q^{15} +(1.23607 - 3.80423i) q^{16} +(1.00000 + 0.726543i) q^{17} +(5.92705 + 4.30625i) q^{19} -4.47214 q^{20} +(6.35410 - 4.61653i) q^{21} +(2.26393 + 6.96767i) q^{23} +(1.54508 + 4.75528i) q^{25} +(0.690983 + 2.12663i) q^{27} +(-4.85410 + 3.52671i) q^{28} +(-0.809017 + 0.587785i) q^{29} +(1.69098 + 1.22857i) q^{31} +(0.809017 + 0.587785i) q^{33} +(5.42705 + 3.94298i) q^{35} +(-2.38197 - 7.33094i) q^{36} +(2.14590 - 6.60440i) q^{37} +(-0.809017 - 2.48990i) q^{39} +(-0.500000 + 1.53884i) q^{41} +6.70820 q^{43} +(-0.618034 - 0.449028i) q^{44} +(-6.97214 + 5.06555i) q^{45} +(1.50000 - 1.08981i) q^{47} +(3.23607 + 9.95959i) q^{48} +2.00000 q^{49} -3.23607 q^{51} +(0.618034 + 1.90211i) q^{52} +(-3.00000 + 2.17963i) q^{53} +(-0.263932 + 0.812299i) q^{55} -19.1803 q^{57} +(-3.78115 + 11.6372i) q^{59} +(9.47214 - 6.88191i) q^{60} +(4.57295 + 14.0741i) q^{61} +(-3.57295 + 10.9964i) q^{63} +(-2.47214 - 7.60845i) q^{64} +(1.80902 - 1.31433i) q^{65} +(6.28115 + 4.56352i) q^{67} +2.47214 q^{68} +(-15.5172 - 11.2739i) q^{69} +(7.54508 - 5.48183i) q^{71} +(0.354102 + 1.08981i) q^{73} +(-10.5902 - 7.69421i) q^{75} +14.6525 q^{76} +(0.354102 + 1.08981i) q^{77} +(-3.19098 + 2.31838i) q^{79} +(-7.23607 + 5.25731i) q^{80} +(4.61803 + 3.35520i) q^{81} +(7.28115 + 5.29007i) q^{83} +(4.85410 - 14.9394i) q^{84} +(-0.854102 - 2.62866i) q^{85} +(0.809017 - 2.48990i) q^{87} +(-1.38197 - 4.25325i) q^{89} +(0.927051 - 2.85317i) q^{91} +(11.8541 + 8.61251i) q^{92} -5.47214 q^{93} +(-5.06231 - 15.5802i) q^{95} +(-2.42705 + 1.76336i) q^{97} -1.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 2 q^{4} - 5 q^{5} - 12 q^{7} + 7 q^{9} + 4 q^{11} - 2 q^{12} + q^{13} + 10 q^{15} - 4 q^{16} + 4 q^{17} + 17 q^{19} + 12 q^{21} + 18 q^{23} - 5 q^{25} + 5 q^{27} - 6 q^{28} - q^{29} + 9 q^{31}+ \cdots + 12 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + 2 * q^4 - 5 * q^5 - 12 * q^7 + 7 * q^9 + 4 * q^11 - 2 * q^12 + q^13 + 10 * q^15 - 4 * q^16 + 4 * q^17 + 17 * q^19 + 12 * q^21 + 18 * q^23 - 5 * q^25 + 5 * q^27 - 6 * q^28 - q^29 + 9 * q^31 + q^33 + 15 * q^35 - 14 * q^36 + 22 * q^37 - q^39 - 2 * q^41 + 2 * q^44 - 10 * q^45 + 6 * q^47 + 4 * q^48 + 8 * q^49 - 4 * q^51 - 2 * q^52 - 12 * q^53 - 10 * q^55 - 32 * q^57 + 5 * q^59 + 20 * q^60 + 25 * q^61 - 21 * q^63 + 8 * q^64 + 5 * q^65 + 5 * q^67 - 8 * q^68 - 33 * q^69 + 19 * q^71 - 12 * q^73 - 20 * q^75 - 4 * q^76 - 12 * q^77 - 15 * q^79 - 20 * q^80 + 14 * q^81 + 9 * q^83 + 6 * q^84 + 10 * q^85 + q^87 - 10 * q^89 - 3 * q^91 + 34 * q^92 - 4 * q^93 + 20 * q^95 - 3 * q^97 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$2$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$3$	−2.11803	+	1.53884i	−1.22285	+	0.888451i	−0.996333	−	0.0855571i	$-0.972733\pi$
$3$	−2.11803	+	1.53884i	−1.22285	+	0.888451i	−0.226514	+	0.974008i	$0.572733\pi$
$4$	1.61803	−	1.17557i	0.809017	−	0.587785i
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$6$		0			0
$7$	−3.00000			−1.13389			−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000			−1.13389			−0.566947	+	0.823754i	$0.691875\pi$
$8$		0			0
$9$	1.19098	−	3.66547i	0.396994	−	1.22182i
$10$		0			0
$11$	−0.118034	−	0.363271i	−0.0355886	−	0.109530i	0.931684	−	0.363269i	$-0.118340\pi$
$11$	−0.118034	−	0.363271i	−0.0355886	−	0.109530i	−0.967273	+	0.253739i	$0.918340\pi$
$12$	−1.61803	+	4.97980i	−0.467086	+	1.43754i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i	−0.984720	−	0.174143i	$-0.944284\pi$
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i	0.899014	+	0.437919i	$0.144284\pi$
$14$		0			0
$15$	5.85410			1.51152
$16$	1.23607	−	3.80423i	0.309017	−	0.951057i
$17$	1.00000	+	0.726543i	0.242536	+	0.176212i	0.702412	−	0.711770i	$-0.252106\pi$
$17$	1.00000	+	0.726543i	0.242536	+	0.176212i	−0.459877	+	0.887983i	$0.652106\pi$
$18$		0			0
$19$	5.92705	+	4.30625i	1.35976	+	0.987923i	0.998460	+	0.0554724i	$0.0176665\pi$
$19$	5.92705	+	4.30625i	1.35976	+	0.987923i	0.361299	+	0.932450i	$0.382334\pi$
$20$	−4.47214			−1.00000
$21$	6.35410	−	4.61653i	1.38658	−	1.00741i
$22$		0			0
$23$	2.26393	+	6.96767i	0.472062	+	1.45286i	0.849879	+	0.526978i	$0.176675\pi$
$23$	2.26393	+	6.96767i	0.472062	+	1.45286i	−0.377816	+	0.925881i	$0.623325\pi$
$24$		0			0
$25$	1.54508	+	4.75528i	0.309017	+	0.951057i
$26$		0			0
$27$	0.690983	+	2.12663i	0.132980	+	0.409270i
$28$	−4.85410	+	3.52671i	−0.917339	+	0.666486i
$29$	−0.809017	+	0.587785i	−0.150231	+	0.109149i
$29$	−0.809017	+	0.587785i	−0.150231	+	0.109149i
$30$		0			0
$31$	1.69098	+	1.22857i	0.303710	+	0.220658i	0.729193	−	0.684308i	$-0.239896\pi$
$31$	1.69098	+	1.22857i	0.303710	+	0.220658i	−0.425483	+	0.904966i	$0.639896\pi$
$32$		0			0
$33$	0.809017	+	0.587785i	0.140832	+	0.102320i
$34$		0			0
$35$	5.42705	+	3.94298i	0.917339	+	0.666486i
$36$	−2.38197	−	7.33094i	−0.396994	−	1.22182i
$37$	2.14590	−	6.60440i	0.352783	−	1.08576i	−0.604500	−	0.796605i	$-0.706627\pi$
$37$	2.14590	−	6.60440i	0.352783	−	1.08576i	0.957284	−	0.289151i	$-0.0933729\pi$
$38$		0			0
$39$	−0.809017	−	2.48990i	−0.129546	−	0.398703i
$40$		0			0
$41$	−0.500000	+	1.53884i	−0.0780869	+	0.240327i	−0.982478	−	0.186377i	$-0.940325\pi$
$41$	−0.500000	+	1.53884i	−0.0780869	+	0.240327i	0.904391	+	0.426704i	$0.140325\pi$
$42$		0			0
$43$	6.70820			1.02299			0.511496	−	0.859286i	$-0.329092\pi$
$43$	6.70820			1.02299			0.511496	+	0.859286i	$0.329092\pi$
$44$	−0.618034	−	0.449028i	−0.0931721	−	0.0676935i
$45$	−6.97214	+	5.06555i	−1.03934	+	0.755128i
$46$		0			0
$47$	1.50000	−	1.08981i	0.218797	−	0.158966i	−0.472988	−	0.881069i	$-0.656825\pi$
$47$	1.50000	−	1.08981i	0.218797	−	0.158966i	0.691785	+	0.722103i	$0.256825\pi$
$48$	3.23607	+	9.95959i	0.467086	+	1.43754i
$49$	2.00000			0.285714
$50$		0			0
$51$	−3.23607			−0.453140
$52$	0.618034	+	1.90211i	0.0857059	+	0.263776i
$53$	−3.00000	+	2.17963i	−0.412082	+	0.299395i	−0.774444	−	0.632642i	$-0.781970\pi$
$53$	−3.00000	+	2.17963i	−0.412082	+	0.299395i	0.362362	+	0.932037i	$0.381970\pi$
$54$		0			0
$55$	−0.263932	+	0.812299i	−0.0355886	+	0.109530i
$56$		0			0
$57$	−19.1803			−2.54050
$58$		0			0
$59$	−3.78115	+	11.6372i	−0.492264	+	1.51503i	0.328913	+	0.944360i	$0.393318\pi$
$59$	−3.78115	+	11.6372i	−0.492264	+	1.51503i	−0.821177	+	0.570673i	$0.806682\pi$
$60$	9.47214	−	6.88191i	1.22285	−	0.888451i
$61$	4.57295	+	14.0741i	0.585506	+	1.80200i	0.597228	+	0.802071i	$0.296269\pi$
$61$	4.57295	+	14.0741i	0.585506	+	1.80200i	−0.0117222	+	0.999931i	$0.503731\pi$
$62$		0			0
$63$	−3.57295	+	10.9964i	−0.450149	+	1.38542i
$64$	−2.47214	−	7.60845i	−0.309017	−	0.951057i
$65$	1.80902	−	1.31433i	0.224381	−	0.163022i
$66$		0			0
$67$	6.28115	+	4.56352i	0.767365	+	0.557523i	0.901160	−	0.433486i	$-0.142717\pi$
$67$	6.28115	+	4.56352i	0.767365	+	0.557523i	−0.133795	+	0.991009i	$0.542717\pi$
$68$	2.47214			0.299791
$69$	−15.5172	−	11.2739i	−1.86805	−	1.35722i
$70$		0			0
$71$	7.54508	−	5.48183i	0.895437	−	0.650573i	−0.0418530	−	0.999124i	$-0.513326\pi$
$71$	7.54508	−	5.48183i	0.895437	−	0.650573i	0.937290	+	0.348551i	$0.113326\pi$
$72$		0			0
$73$	0.354102	+	1.08981i	0.0414445	+	0.127553i	0.969638	−	0.244545i	$-0.0786386\pi$
$73$	0.354102	+	1.08981i	0.0414445	+	0.127553i	−0.928193	+	0.372098i	$0.878639\pi$
$74$		0			0
$75$	−10.5902	−	7.69421i	−1.22285	−	0.888451i
$76$	14.6525			1.68075
$77$	0.354102	+	1.08981i	0.0403537	+	0.124196i
$78$		0			0
$79$	−3.19098	+	2.31838i	−0.359014	+	0.260839i	−0.752641	−	0.658432i	$-0.771220\pi$
$79$	−3.19098	+	2.31838i	−0.359014	+	0.260839i	0.393627	+	0.919270i	$0.371220\pi$
$80$	−7.23607	+	5.25731i	−0.809017	+	0.587785i
$81$	4.61803	+	3.35520i	0.513115	+	0.372800i
$82$		0			0
$83$	7.28115	+	5.29007i	0.799210	+	0.580660i	0.910682	−	0.413107i	$-0.135557\pi$
$83$	7.28115	+	5.29007i	0.799210	+	0.580660i	−0.111472	+	0.993768i	$0.535557\pi$
$84$	4.85410	−	14.9394i	0.529626	−	1.63002i
$85$	−0.854102	−	2.62866i	−0.0926404	−	0.285118i
$86$		0			0
$87$	0.809017	−	2.48990i	0.0867357	−	0.266945i
$88$		0			0
$89$	−1.38197	−	4.25325i	−0.146488	−	0.450844i	0.850711	−	0.525633i	$-0.176172\pi$
$89$	−1.38197	−	4.25325i	−0.146488	−	0.450844i	−0.997199	+	0.0747893i	$0.976172\pi$
$90$		0			0
$91$	0.927051	−	2.85317i	0.0971813	−	0.299093i
$92$	11.8541	+	8.61251i	1.23588	+	0.897916i
$93$	−5.47214			−0.567434
$94$		0			0
$95$	−5.06231	−	15.5802i	−0.519382	−	1.59849i
$96$		0			0
$97$	−2.42705	+	1.76336i	−0.246430	+	0.179042i	−0.704143	−	0.710058i	$-0.748669\pi$
$97$	−2.42705	+	1.76336i	−0.246430	+	0.179042i	0.457713	+	0.889100i	$0.348669\pi$
$98$		0			0
$99$	−1.47214			−0.147955
$100$	8.09017	+	5.87785i	0.809017	+	0.587785i
$101$	−9.70820			−0.966002			−0.483001	−	0.875620i	$-0.660453\pi$
$101$	−9.70820			−0.966002			−0.483001	+	0.875620i	$0.660453\pi$
$102$		0			0
$103$	1.69098	−	1.22857i	0.166618	−	0.121055i	−0.501352	−	0.865244i	$-0.667164\pi$
$103$	1.69098	−	1.22857i	0.166618	−	0.121055i	0.667969	+	0.744189i	$0.267164\pi$
$104$		0			0
$105$	−17.5623			−1.71391
$106$		0			0
$107$	−6.47214			−0.625685			−0.312842	−	0.949805i	$-0.601281\pi$
$107$	−6.47214			−0.625685			−0.312842	+	0.949805i	$0.601281\pi$
$108$	3.61803	+	2.62866i	0.348145	+	0.252942i
$109$	2.80902	−	8.64527i	0.269055	−	0.828066i	−0.721676	−	0.692231i	$-0.756628\pi$
$109$	2.80902	−	8.64527i	0.269055	−	0.828066i	0.990731	−	0.135836i	$-0.0433719\pi$
$110$		0			0
$111$	5.61803	+	17.2905i	0.533240	+	1.64114i
$112$	−3.70820	+	11.4127i	−0.350392	+	1.07840i
$113$	1.57295	−	4.84104i	0.147971	−	0.455407i	−0.849410	−	0.527733i	$-0.823042\pi$
$113$	1.57295	−	4.84104i	0.147971	−	0.455407i	0.997381	+	0.0723261i	$0.0230422\pi$
$114$		0			0
$115$	5.06231	−	15.5802i	0.472062	−	1.45286i
$116$	−0.618034	+	1.90211i	−0.0573830	+	0.176607i
$117$	3.11803	+	2.26538i	0.288262	+	0.209435i
$118$		0			0
$119$	−3.00000	−	2.17963i	−0.275010	−	0.199806i
$120$		0			0
$121$	8.78115	−	6.37988i	0.798287	−	0.579989i
$122$		0			0
$123$	−1.30902	−	4.02874i	−0.118030	−	0.363259i
$124$	4.18034			0.375406
$125$	3.45492	−	10.6331i	0.309017	−	0.951057i
$126$		0			0
$127$	−3.97214	−	12.2250i	−0.352470	−	1.08479i	−0.957462	−	0.288560i	$-0.906824\pi$
$127$	−3.97214	−	12.2250i	−0.352470	−	1.08479i	0.604992	−	0.796232i	$-0.293176\pi$
$128$		0			0
$129$	−14.2082	+	10.3229i	−1.25096	+	0.908878i
$130$		0			0
$131$	−6.61803	−	4.80828i	−0.578220	−	0.420102i	0.259862	−	0.965646i	$-0.416323\pi$
$131$	−6.61803	−	4.80828i	−0.578220	−	0.420102i	−0.838082	+	0.545544i	$0.816323\pi$
$132$	2.00000			0.174078
$133$	−17.7812	−	12.9188i	−1.54182	−	1.12020i
$134$		0			0
$135$	1.54508	−	4.75528i	0.132980	−	0.409270i
$136$		0			0
$137$	−1.00000	+	3.07768i	−0.0854358	+	0.262944i	−0.984643	−	0.174578i	$-0.944144\pi$
$137$	−1.00000	+	3.07768i	−0.0854358	+	0.262944i	0.899208	+	0.437522i	$0.144144\pi$
$138$		0			0
$139$	2.80902	+	8.64527i	0.238258	+	0.733282i	0.996673	+	0.0815097i	$0.0259742\pi$
$139$	2.80902	+	8.64527i	0.238258	+	0.733282i	−0.758415	+	0.651772i	$0.774026\pi$
$140$	13.4164			1.13389
$141$	−1.50000	+	4.61653i	−0.126323	+	0.388782i
$142$		0			0
$143$	0.381966			0.0319416
$144$	−12.4721	−	9.06154i	−1.03934	−	0.755128i
$145$	2.23607			0.185695
$146$		0			0
$147$	−4.23607	+	3.07768i	−0.349385	+	0.253843i
$148$	−4.29180	−	13.2088i	−0.352783	−	1.08576i
$149$	−19.2361			−1.57588			−0.787940	−	0.615752i	$-0.788852\pi$
$149$	−19.2361			−1.57588			−0.787940	+	0.615752i	$0.788852\pi$
$150$		0			0
$151$	22.4164			1.82422			0.912111	−	0.409944i	$-0.134452\pi$
$151$	22.4164			1.82422			0.912111	+	0.409944i	$0.134452\pi$
$152$		0			0
$153$	3.85410	−	2.80017i	0.311586	−	0.226380i
$154$		0			0
$155$	−1.44427	−	4.44501i	−0.116007	−	0.357032i
$156$	−4.23607	−	3.07768i	−0.339157	−	0.246412i
$157$	16.6180			1.32626			0.663132	−	0.748503i	$-0.269227\pi$
$157$	16.6180			1.32626			0.663132	+	0.748503i	$0.269227\pi$
$158$		0			0
$159$	3.00000	−	9.23305i	0.237915	−	0.732229i
$160$		0			0
$161$	−6.79180	−	20.9030i	−0.535269	−	1.64739i
$162$		0			0
$163$	0.163119	−	0.502029i	0.0127765	−	0.0393219i	−0.944465	−	0.328612i	$-0.893419\pi$
$163$	0.163119	−	0.502029i	0.0127765	−	0.0393219i	0.957242	+	0.289290i	$0.0934192\pi$
$164$	1.00000	+	3.07768i	0.0780869	+	0.240327i
$165$	−0.690983	−	2.12663i	−0.0537930	−	0.165558i
$166$		0			0
$167$	4.66312	+	3.38795i	0.360843	+	0.262168i	0.753404	−	0.657558i	$-0.228411\pi$
$167$	4.66312	+	3.38795i	0.360843	+	0.262168i	−0.392561	+	0.919726i	$0.628411\pi$
$168$		0			0
$169$	9.70820	+	7.05342i	0.746785	+	0.542571i
$170$		0			0
$171$	22.8435	−	16.5967i	1.74688	−	1.26918i
$172$	10.8541	−	7.88597i	0.827618	−	0.601299i
$173$	−0.427051	−	1.31433i	−0.0324681	−	0.0999265i	0.933509	−	0.358554i	$-0.116730\pi$
$173$	−0.427051	−	1.31433i	−0.0324681	−	0.0999265i	−0.965977	+	0.258627i	$0.916730\pi$
$174$		0			0
$175$	−4.63525	−	14.2658i	−0.350392	−	1.07840i
$176$	−1.52786			−0.115167
$177$	−9.89919	−	30.4666i	−0.744068	−	2.29001i
$178$		0			0
$179$	−8.00000	+	5.81234i	−0.597948	+	0.434435i	−0.845150	−	0.534529i	$-0.820489\pi$
$179$	−8.00000	+	5.81234i	−0.597948	+	0.434435i	0.247202	+	0.968964i	$0.420489\pi$
$180$	−5.32624	+	16.3925i	−0.396994	+	1.22182i
$181$	−8.09017	−	5.87785i	−0.601338	−	0.436897i	0.245016	−	0.969519i	$-0.421207\pi$
$181$	−8.09017	−	5.87785i	−0.601338	−	0.436897i	−0.846353	+	0.532622i	$0.821207\pi$
$182$		0			0
$183$	−31.3435	−	22.7724i	−2.31698	−	1.68338i
$184$		0			0
$185$	−12.5623	+	9.12705i	−0.923599	+	0.671034i
$186$		0			0
$187$	0.145898	−	0.449028i	0.0106691	−	0.0328362i
$188$	1.14590	−	3.52671i	0.0835732	−	0.257212i
$189$	−2.07295	−	6.37988i	−0.150785	−	0.464068i
$190$		0			0
$191$	2.79837	−	8.61251i	0.202483	−	0.623179i	−0.797324	−	0.603551i	$-0.793752\pi$
$191$	2.79837	−	8.61251i	0.202483	−	0.623179i	0.999807	−	0.0196279i	$-0.00624817\pi$
$192$	16.9443	+	12.3107i	1.22285	+	0.888451i
$193$	13.2705			0.955232			0.477616	−	0.878569i	$-0.341501\pi$
$193$	13.2705			0.955232			0.477616	+	0.878569i	$0.341501\pi$
$194$		0			0
$195$	−1.80902	+	5.56758i	−0.129546	+	0.398703i
$196$	3.23607	−	2.35114i	0.231148	−	0.167939i
$197$	−17.2082	+	12.5025i	−1.22603	+	0.890766i	−0.996586	−	0.0825554i	$-0.973692\pi$
$197$	−17.2082	+	12.5025i	−1.22603	+	0.890766i	−0.229447	+	0.973321i	$0.573692\pi$
$198$		0			0
$199$	4.14590			0.293895			0.146947	−	0.989144i	$-0.453055\pi$
$199$	4.14590			0.293895			0.146947	+	0.989144i	$0.453055\pi$
$200$		0			0
$201$	−20.3262			−1.43370
$202$		0			0
$203$	2.42705	−	1.76336i	0.170346	−	0.123763i
$204$	−5.23607	+	3.80423i	−0.366598	+	0.266349i
$205$	2.92705	−	2.12663i	0.204434	−	0.148530i
$206$		0			0
$207$	28.2361			1.96254
$208$	3.23607	+	2.35114i	0.224381	+	0.163022i
$209$	0.864745	−	2.66141i	0.0598157	−	0.184094i
$210$		0			0
$211$	3.85410	+	11.8617i	0.265327	+	0.816594i	0.991618	+	0.129206i	$0.0412427\pi$
$211$	3.85410	+	11.8617i	0.265327	+	0.816594i	−0.726290	+	0.687388i	$0.758757\pi$
$212$	−2.29180	+	7.05342i	−0.157401	+	0.484431i
$213$	−7.54508	+	23.2214i	−0.516981	+	1.59110i
$214$		0			0
$215$	−12.1353	−	8.81678i	−0.827618	−	0.601299i
$216$		0			0
$217$	−5.07295	−	3.68571i	−0.344374	−	0.250203i
$218$		0			0
$219$	−2.42705	−	1.76336i	−0.164005	−	0.119157i
$220$	0.527864	+	1.62460i	0.0355886	+	0.109530i
$221$	−1.00000	+	0.726543i	−0.0672673	+	0.0488725i
$222$		0			0
$223$	7.50000	+	23.0826i	0.502237	+	1.54573i	0.805366	+	0.592778i	$0.201969\pi$
$223$	7.50000	+	23.0826i	0.502237	+	1.54573i	−0.303129	+	0.952949i	$0.598031\pi$
$224$		0			0
$225$	19.2705			1.28470
$226$		0			0
$227$	7.41641	+	22.8254i	0.492244	+	1.51497i	0.821208	+	0.570629i	$0.193301\pi$
$227$	7.41641	+	22.8254i	0.492244	+	1.51497i	−0.328963	+	0.944343i	$0.606699\pi$
$228$	−31.0344	+	22.5478i	−2.05531	+	1.49327i
$229$	−13.5172	+	9.82084i	−0.893243	+	0.648979i	−0.936722	−	0.350075i	$-0.886156\pi$
$229$	−13.5172	+	9.82084i	−0.893243	+	0.648979i	0.0434785	+	0.999054i	$0.486156\pi$
$230$		0			0
$231$	−2.42705	−	1.76336i	−0.159688	−	0.116020i
$232$		0			0
$233$	−21.1353	−	15.3557i	−1.38462	−	1.00598i	−0.996432	−	0.0844013i	$-0.973102\pi$
$233$	−21.1353	−	15.3557i	−1.38462	−	1.00598i	−0.388185	−	0.921582i	$-0.626898\pi$
$234$		0			0
$235$	−4.14590			−0.270449
$236$	7.56231	+	23.2744i	0.492264	+	1.51503i
$237$	3.19098	−	9.82084i	0.207277	−	0.637932i
$238$		0			0
$239$	8.57295	+	26.3848i	0.554538	+	1.70669i	0.697160	+	0.716915i	$0.254447\pi$
$239$	8.57295	+	26.3848i	0.554538	+	1.70669i	−0.142622	+	0.989777i	$0.545553\pi$
$240$	7.23607	−	22.2703i	0.467086	−	1.43754i
$241$	−8.00000	+	24.6215i	−0.515325	+	1.58601i	0.267364	+	0.963596i	$0.413847\pi$
$241$	−8.00000	+	24.6215i	−0.515325	+	1.58601i	−0.782689	+	0.622413i	$0.786153\pi$
$242$		0			0
$243$	−21.6525			−1.38901
$244$	23.9443	+	17.3965i	1.53287	+	1.11370i
$245$	−3.61803	−	2.62866i	−0.231148	−	0.167939i
$246$		0			0
$247$	−5.92705	+	4.30625i	−0.377129	+	0.274000i
$248$		0			0
$249$	−23.5623			−1.49320
$250$		0			0
$251$	9.61803			0.607085			0.303542	−	0.952818i	$-0.401831\pi$
$251$	9.61803			0.607085			0.303542	+	0.952818i	$0.401831\pi$
$252$	7.14590	+	21.9928i	0.450149	+	1.38542i
$253$	2.26393	−	1.64484i	0.142332	−	0.103410i
$254$		0			0
$255$	5.85410	+	4.25325i	0.366598	+	0.266349i
$256$	−12.9443	−	9.40456i	−0.809017	−	0.587785i
$257$	19.9443			1.24409			0.622045	−	0.782982i	$-0.286302\pi$
$257$	19.9443			1.24409			0.622045	+	0.782982i	$0.286302\pi$
$258$		0			0
$259$	−6.43769	+	19.8132i	−0.400019	+	1.23113i
$260$	1.38197	−	4.25325i	0.0857059	−	0.263776i
$261$	1.19098	+	3.66547i	0.0737200	+	0.226887i
$262$		0			0
$263$	0.100813	−	0.310271i	0.00621640	−	0.0191321i	−0.947900	−	0.318567i	$-0.896798\pi$
$263$	0.100813	−	0.310271i	0.00621640	−	0.0191321i	0.954117	+	0.299435i	$0.0967983\pi$
$264$		0			0
$265$	8.29180			0.509361
$266$		0			0
$267$	9.47214	+	6.88191i	0.579685	+	0.421166i
$268$	15.5279			0.948515
$269$	−25.8435	−	18.7764i	−1.57570	−	1.14482i	−0.921421	−	0.388565i	$-0.872971\pi$
$269$	−25.8435	−	18.7764i	−1.57570	−	1.14482i	−0.654282	−	0.756250i	$-0.727029\pi$
$270$		0			0
$271$	1.95492	−	1.42033i	0.118753	−	0.0862788i	−0.526824	−	0.849975i	$-0.676617\pi$
$271$	1.95492	−	1.42033i	0.118753	−	0.0862788i	0.645576	+	0.763696i	$0.276617\pi$
$272$	4.00000	−	2.90617i	0.242536	−	0.176212i
$273$	2.42705	+	7.46969i	0.146892	+	0.452086i
$274$		0			0
$275$	1.54508	−	1.12257i	0.0931721	−	0.0676935i
$276$	−38.3607			−2.30904
$277$	−1.07295	−	3.30220i	−0.0644673	−	0.198410i	0.913635	−	0.406536i	$-0.133263\pi$
$277$	−1.07295	−	3.30220i	−0.0644673	−	0.198410i	−0.978102	+	0.208126i	$0.933263\pi$
$278$		0			0
$279$	6.51722	−	4.73504i	0.390176	−	0.283479i
$280$		0			0
$281$	13.8992	+	10.0984i	0.829156	+	0.602417i	0.919320	−	0.393510i	$-0.128739\pi$
$281$	13.8992	+	10.0984i	0.829156	+	0.602417i	−0.0901644	+	0.995927i	$0.528739\pi$
$282$		0			0
$283$	−16.3992	−	11.9147i	−0.974830	−	0.708256i	−0.0182831	−	0.999833i	$-0.505820\pi$
$283$	−16.3992	−	11.9147i	−0.974830	−	0.708256i	−0.956547	+	0.291577i	$0.905820\pi$
$284$	5.76393	−	17.7396i	0.342026	−	1.05265i
$285$	34.6976	+	25.2093i	2.05531	+	1.49327i
$286$		0			0
$287$	1.50000	−	4.61653i	0.0885422	−	0.272505i
$288$		0			0
$289$	−4.78115	−	14.7149i	−0.281244	−	0.865581i
$290$		0			0
$291$	2.42705	−	7.46969i	0.142276	−	0.437881i
$292$	1.85410	+	1.34708i	0.108503	+	0.0788321i
$293$	16.4164			0.959057			0.479528	−	0.877526i	$-0.340808\pi$
$293$	16.4164			0.959057			0.479528	+	0.877526i	$0.340808\pi$
$294$		0			0
$295$	22.1353	−	16.0822i	1.28876	−	0.936342i
$296$		0			0
$297$	0.690983	−	0.502029i	0.0400949	−	0.0291307i
$298$		0			0
$299$	−7.32624			−0.423687
$300$	−26.1803			−1.51152
$301$	−20.1246			−1.15996
$302$		0			0
$303$	20.5623	−	14.9394i	1.18127	−	0.858246i
$304$	23.7082	−	17.2250i	1.35976	−	0.987923i
$305$	10.2254	−	31.4706i	0.585506	−	1.80200i
$306$		0			0
$307$	11.0000			0.627803			0.313902	−	0.949456i	$-0.398364\pi$
$307$	11.0000			0.627803			0.313902	+	0.949456i	$0.398364\pi$
$308$	1.85410	+	1.34708i	0.105647	+	0.0767572i
$309$	−1.69098	+	5.20431i	−0.0961967	+	0.296063i
$310$		0			0
$311$	7.42705	+	22.8581i	0.421149	+	1.29616i	0.906633	+	0.421919i	$0.138643\pi$
$311$	7.42705	+	22.8581i	0.421149	+	1.29616i	−0.485484	+	0.874246i	$0.661357\pi$
$312$		0			0
$313$	−1.41641	+	4.35926i	−0.0800601	+	0.246400i	−0.983073	−	0.183213i	$-0.941350\pi$
$313$	−1.41641	+	4.35926i	−0.0800601	+	0.246400i	0.903013	+	0.429613i	$0.141350\pi$
$314$		0			0
$315$	20.9164	−	15.1967i	1.17851	−	0.856235i
$316$	−2.43769	+	7.50245i	−0.137131	+	0.422046i
$317$	15.6631	+	11.3799i	0.879728	+	0.639160i	0.933180	−	0.359410i	$-0.117022\pi$
$317$	15.6631	+	11.3799i	0.879728	+	0.639160i	−0.0534512	+	0.998570i	$0.517022\pi$
$318$		0			0
$319$	0.309017	+	0.224514i	0.0173016	+	0.0125704i
$320$	−5.52786	+	17.0130i	−0.309017	+	0.951057i
$321$	13.7082	−	9.95959i	0.765117	−	0.555890i
$322$		0			0
$323$	2.79837	+	8.61251i	0.155706	+	0.479213i
$324$	11.4164			0.634245
$325$	−5.00000			−0.277350
$326$		0			0
$327$	7.35410	+	22.6336i	0.406683	+	1.25164i
$328$		0			0
$329$	−4.50000	+	3.26944i	−0.248093	+	0.180250i
$330$		0			0
$331$	−20.9164	−	15.1967i	−1.14967	−	0.835284i	−0.161233	−	0.986916i	$-0.551547\pi$
$331$	−20.9164	−	15.1967i	−1.14967	−	0.835284i	−0.988437	+	0.151632i	$0.951547\pi$
$332$	18.0000			0.987878
$333$	−21.6525	−	15.7314i	−1.18655	−	0.862078i
$334$		0			0
$335$	−5.36475	−	16.5110i	−0.293107	−	0.902092i
$336$	−9.70820	−	29.8788i	−0.529626	−	1.63002i
$337$	0.309017	−	0.951057i	0.0168332	−	0.0518073i	−0.942287	−	0.334806i	$-0.891329\pi$
$337$	0.309017	−	0.951057i	0.0168332	−	0.0518073i	0.959120	+	0.282999i	$0.0913292\pi$
$338$		0			0
$339$	4.11803	+	12.6740i	0.223661	+	0.688357i
$340$	−4.47214	−	3.24920i	−0.242536	−	0.176212i
$341$	0.246711	−	0.759299i	0.0133602	−	0.0411183i
$342$		0			0
$343$	15.0000			0.809924
$344$		0			0
$345$	13.2533	+	40.7894i	0.713533	+	2.19603i
$346$		0			0
$347$	−17.3992	+	12.6412i	−0.934037	+	0.678618i	−0.946978	−	0.321298i	$-0.895881\pi$
$347$	−17.3992	+	12.6412i	−0.934037	+	0.678618i	0.0129407	+	0.999916i	$0.495881\pi$
$348$	−1.61803	−	4.97980i	−0.0867357	−	0.266945i
$349$	−21.3607			−1.14341			−0.571705	−	0.820459i	$-0.693718\pi$
$349$	−21.3607			−1.14341			−0.571705	+	0.820459i	$0.693718\pi$
$350$		0			0
$351$	−2.23607			−0.119352
$352$		0			0
$353$	2.45492	−	1.78360i	0.130662	−	0.0949315i	−0.520535	−	0.853841i	$-0.674267\pi$
$353$	2.45492	−	1.78360i	0.130662	−	0.0949315i	0.651197	+	0.758909i	$0.274267\pi$
$354$		0			0
$355$	−20.8541			−1.10682
$356$	−7.23607	−	5.25731i	−0.383511	−	0.278637i
$357$	9.70820			0.513813
$358$		0			0
$359$	5.26393	−	16.2007i	0.277820	−	0.855041i	−0.710640	−	0.703556i	$-0.751594\pi$
$359$	5.26393	−	16.2007i	0.277820	−	0.855041i	0.988460	−	0.151485i	$-0.0484056\pi$
$360$		0			0
$361$	10.7148	+	32.9767i	0.563936	+	1.73562i
$362$		0			0
$363$	−8.78115	+	27.0256i	−0.460891	+	1.41848i
$364$	−1.85410	−	5.70634i	−0.0971813	−	0.299093i
$365$	0.791796	−	2.43690i	0.0414445	−	0.127553i
$366$		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	$0.932495\pi$
$368$	29.3050			1.52763
$369$	5.04508	+	3.66547i	0.262637	+	0.190817i
$370$		0			0
$371$	9.00000	−	6.53888i	0.467257	−	0.339482i
$372$	−8.85410	+	6.43288i	−0.459064	+	0.333529i
$373$	−10.0172	−	30.8298i	−0.518672	−	1.59631i	−0.776500	−	0.630117i	$-0.783007\pi$
$373$	−10.0172	−	30.8298i	−0.518672	−	1.59631i	0.257828	−	0.966191i	$-0.416993\pi$
$374$		0			0
$375$	9.04508	+	27.8379i	0.467086	+	1.43754i
$376$		0			0
$377$	−0.309017	−	0.951057i	−0.0159152	−	0.0489819i
$378$		0			0
$379$	−11.1353	+	8.09024i	−0.571980	+	0.415568i	−0.835824	−	0.548998i	$-0.815010\pi$
$379$	−11.1353	+	8.09024i	−0.571980	+	0.415568i	0.263844	+	0.964565i	$0.415010\pi$
$380$	−26.5066	−	19.2582i	−1.35976	−	0.987923i
$381$	27.2254	+	19.7804i	1.39480	+	1.01338i
$382$		0			0
$383$	−7.59017	−	5.51458i	−0.387840	−	0.281782i	0.376730	−	0.926323i	$-0.377048\pi$
$383$	−7.59017	−	5.51458i	−0.387840	−	0.281782i	−0.764570	+	0.644541i	$0.777048\pi$
$384$		0			0
$385$	0.791796	−	2.43690i	0.0403537	−	0.124196i
$386$		0			0
$387$	7.98936	−	24.5887i	0.406122	−	1.24991i
$388$	−1.85410	+	5.70634i	−0.0941278	+	0.289695i
$389$	9.59017	+	29.5155i	0.486241	+	1.49650i	0.830176	+	0.557502i	$0.188240\pi$
$389$	9.59017	+	29.5155i	0.486241	+	1.49650i	−0.343935	+	0.938994i	$0.611760\pi$
$390$		0			0
$391$	−2.79837	+	8.61251i	−0.141520	+	0.435553i
$392$		0			0
$393$	21.4164			1.08031
$394$		0			0
$395$	8.81966			0.443765
$396$	−2.38197	+	1.73060i	−0.119698	+	0.0869659i
$397$	−13.7082	+	9.95959i	−0.687995	+	0.499858i	−0.876000	−	0.482310i	$-0.839798\pi$
$397$	−13.7082	+	9.95959i	−0.687995	+	0.499858i	0.188005	+	0.982168i	$0.439798\pi$
$398$		0			0
$399$	57.5410			2.88065
$400$	20.0000			1.00000
$401$	7.76393			0.387712			0.193856	−	0.981030i	$-0.437901\pi$
$401$	7.76393			0.387712			0.193856	+	0.981030i	$0.437901\pi$
$402$		0			0
$403$	−1.69098	+	1.22857i	−0.0842339	+	0.0611995i
$404$	−15.7082	+	11.4127i	−0.781512	+	0.567802i
$405$	−3.94427	−	12.1392i	−0.195992	−	0.603203i
$406$		0			0
$407$	−2.65248			−0.131478
$408$		0			0
$409$	−3.70820	+	11.4127i	−0.183359	+	0.564321i	−0.999916	−	0.0129437i	$-0.995880\pi$
$409$	−3.70820	+	11.4127i	−0.183359	+	0.564321i	0.816557	+	0.577264i	$0.195880\pi$
$410$		0			0
$411$	−2.61803	−	8.05748i	−0.129138	−	0.397446i
$412$	1.29180	−	3.97574i	0.0636422	−	0.195871i
$413$	11.3435	−	34.9116i	0.558175	−	1.71789i
$414$		0			0
$415$	−6.21885	−	19.1396i	−0.305271	−	0.939528i
$416$		0			0
$417$	−19.2533	−	13.9883i	−0.942838	−	0.685012i
$418$		0			0
$419$	−19.1353	−	13.9026i	−0.934818	−	0.679185i	0.0123494	−	0.999924i	$-0.496069\pi$
$419$	−19.1353	−	13.9026i	−0.934818	−	0.679185i	−0.947168	+	0.320738i	$0.896069\pi$
$420$	−28.4164	+	20.6457i	−1.38658	+	1.00741i
$421$	33.1525	−	24.0867i	1.61575	−	1.17391i	0.776676	−	0.629901i	$-0.216904\pi$
$421$	33.1525	−	24.0867i	1.61575	−	1.17391i	0.839077	−	0.544012i	$-0.183096\pi$
$422$		0			0
$423$	−2.20820	−	6.79615i	−0.107367	−	0.330440i
$424$		0			0
$425$	−1.90983	+	5.87785i	−0.0926404	+	0.285118i
$426$		0			0
$427$	−13.7188	−	42.2223i	−0.663902	−	2.04328i
$428$	−10.4721	+	7.60845i	−0.506190	+	0.367768i
$429$	−0.809017	+	0.587785i	−0.0390597	+	0.0283785i
$430$		0			0
$431$	2.20820	+	1.60435i	0.106365	+	0.0772790i	0.639697	−	0.768628i	$-0.279060\pi$
$431$	2.20820	+	1.60435i	0.106365	+	0.0772790i	−0.533331	+	0.845907i	$0.679060\pi$
$432$	8.94427			0.430331
$433$	21.0172	+	15.2699i	1.01002	+	0.733825i	0.964214	−	0.265125i	$-0.0854134\pi$
$433$	21.0172	+	15.2699i	1.01002	+	0.733825i	0.0458092	+	0.998950i	$0.485413\pi$
$434$		0			0
$435$	−4.73607	+	3.44095i	−0.227077	+	0.164981i
$436$	−5.61803	−	17.2905i	−0.269055	−	0.828066i
$437$	−16.5861	+	51.0468i	−0.793421	+	2.44190i
$438$		0			0
$439$	4.47214	+	13.7638i	0.213443	+	0.656911i	0.999260	+	0.0384522i	$0.0122427\pi$
$439$	4.47214	+	13.7638i	0.213443	+	0.656911i	−0.785817	+	0.618459i	$0.787757\pi$
$440$		0			0
$441$	2.38197	−	7.33094i	0.113427	−	0.349092i
$442$		0			0
$443$	−13.4721			−0.640080			−0.320040	−	0.947404i	$-0.603696\pi$
$443$	−13.4721			−0.640080			−0.320040	+	0.947404i	$0.603696\pi$
$444$	29.4164	+	21.3723i	1.39604	+	1.01428i
$445$	−3.09017	+	9.51057i	−0.146488	+	0.450844i
$446$		0			0
$447$	40.7426	−	29.6013i	1.92706	−	1.40009i
$448$	7.41641	+	22.8254i	0.350392	+	1.07840i
$449$	−3.76393			−0.177631			−0.0888155	−	0.996048i	$-0.528308\pi$
$449$	−3.76393			−0.177631			−0.0888155	+	0.996048i	$0.528308\pi$
$450$		0			0
$451$	0.618034			0.0291021
$452$	−3.14590	−	9.68208i	−0.147971	−	0.455407i
$453$	−47.4787	+	34.4953i	−2.23074	+	1.62073i
$454$		0			0
$455$	−5.42705	+	3.94298i	−0.254424	+	0.184850i
$456$		0			0
$457$	5.36068			0.250762			0.125381	−	0.992109i	$-0.459985\pi$
$457$	5.36068			0.250762			0.125381	+	0.992109i	$0.459985\pi$
$458$		0			0
$459$	−0.854102	+	2.62866i	−0.0398661	+	0.122695i
$460$	−10.1246	−	31.1604i	−0.472062	−	1.45286i
$461$	−5.04508	−	15.5272i	−0.234973	−	0.723173i	−0.997125	−	0.0757745i	$-0.975857\pi$
$461$	−5.04508	−	15.5272i	−0.234973	−	0.723173i	0.762152	−	0.647398i	$-0.224143\pi$
$462$		0			0
$463$	9.18034	−	28.2542i	0.426647	−	1.31308i	−0.474762	−	0.880114i	$-0.657466\pi$
$463$	9.18034	−	28.2542i	0.426647	−	1.31308i	0.901409	−	0.432969i	$-0.142534\pi$
$464$	1.23607	+	3.80423i	0.0573830	+	0.176607i
$465$	9.89919	+	7.19218i	0.459064	+	0.333529i
$466$		0			0
$467$	−9.00000	−	6.53888i	−0.416470	−	0.302583i	0.359746	−	0.933050i	$-0.382863\pi$
$467$	−9.00000	−	6.53888i	−0.416470	−	0.302583i	−0.776216	+	0.630467i	$0.782863\pi$
$468$	7.70820			0.356312
$469$	−18.8435	−	13.6906i	−0.870110	−	0.632172i
$470$		0			0
$471$	−35.1976	+	25.5725i	−1.62182	+	1.17832i
$472$		0			0
$473$	−0.791796	−	2.43690i	−0.0364068	−	0.112049i
$474$		0			0
$475$	−11.3197	+	34.8383i	−0.519382	+	1.59849i
$476$	−7.41641			−0.339930
$477$	4.41641	+	13.5923i	0.202213	+	0.622349i
$478$		0			0
$479$	32.9894	−	23.9682i	1.50732	−	1.09513i	0.539974	−	0.841682i	$-0.318434\pi$
$479$	32.9894	−	23.9682i	1.50732	−	1.09513i	0.967348	−	0.253452i	$-0.0815660\pi$
$480$		0			0
$481$	5.61803	+	4.08174i	0.256160	+	0.186111i
$482$		0			0
$483$	46.5517	+	33.8218i	2.11817	+	1.53894i
$484$	6.70820	−	20.6457i	0.304918	−	0.938442i
$485$	6.70820			0.304604
$486$		0			0
$487$	−12.1631	+	37.4342i	−0.551164	+	1.69631i	0.154702	+	0.987961i	$0.450558\pi$
$487$	−12.1631	+	37.4342i	−0.551164	+	1.69631i	−0.705866	+	0.708346i	$0.749442\pi$
$488$		0			0
$489$	0.427051	+	1.31433i	0.0193119	+	0.0594360i
$490$		0			0
$491$	−6.01722	+	18.5191i	−0.271553	+	0.835755i	0.718557	+	0.695468i	$0.244803\pi$
$491$	−6.01722	+	18.5191i	−0.271553	+	0.835755i	−0.990111	+	0.140288i	$0.955197\pi$
$492$	−6.85410	−	4.97980i	−0.309007	−	0.224507i
$493$	−1.23607			−0.0556697
$494$		0			0
$495$	2.66312	+	1.93487i	0.119698	+	0.0869659i
$496$	6.76393	−	4.91428i	0.303710	−	0.220658i
$497$	−22.6353	+	16.4455i	−1.01533	+	0.737680i
$498$		0			0
$499$	23.2148			1.03924			0.519618	−	0.854399i	$-0.326074\pi$
$499$	23.2148			1.03924			0.519618	+	0.854399i	$0.326074\pi$
$500$	−6.90983	−	21.2663i	−0.309017	−	0.951057i
$501$	−15.0902			−0.674179
$502$		0			0
$503$	1.21885	−	0.885544i	0.0543457	−	0.0394845i	−0.560281	−	0.828303i	$-0.689307\pi$
$503$	1.21885	−	0.885544i	0.0543457	−	0.0394845i	0.614626	+	0.788818i	$0.289307\pi$
$504$		0			0
$505$	17.5623	+	12.7598i	0.781512	+	0.567802i
$506$		0			0
$507$	−31.4164			−1.39525
$508$	−20.7984	−	15.1109i	−0.922779	−	0.670438i
$509$	−0.673762	+	2.07363i	−0.0298640	+	0.0919119i	−0.964878	−	0.262700i	$-0.915387\pi$
$509$	−0.673762	+	2.07363i	−0.0298640	+	0.0919119i	0.935014	+	0.354612i	$0.115387\pi$
$510$		0			0
$511$	−1.06231	−	3.26944i	−0.0469936	−	0.144632i
$512$		0			0
$513$	−5.06231	+	15.5802i	−0.223506	+	0.687882i
$514$		0			0
$515$	−4.67376			−0.205951
$516$	−10.8541	+	33.4055i	−0.477825	+	1.47059i
$517$	−0.572949	−	0.416272i	−0.0251983	−	0.0183076i
$518$		0			0
$519$	2.92705	+	2.12663i	0.128483	+	0.0933486i
$520$		0			0
$521$	24.1353	−	17.5353i	1.05738	−	0.768235i	0.0837820	−	0.996484i	$-0.473300\pi$
$521$	24.1353	−	17.5353i	1.05738	−	0.768235i	0.973603	+	0.228249i	$0.0733001\pi$
$522$		0			0
$523$	1.86475	+	5.73910i	0.0815396	+	0.250953i	0.983513	−	0.180839i	$-0.0578814\pi$
$523$	1.86475	+	5.73910i	0.0815396	+	0.250953i	−0.901973	+	0.431792i	$0.857881\pi$
$524$	−16.3607			−0.714720
$525$	31.7705	+	23.0826i	1.38658	+	1.00741i
$526$		0			0
$527$	0.798374	+	2.45714i	0.0347777	+	0.107035i
$528$	3.23607	−	2.35114i	0.140832	−	0.102320i
$529$	−24.8156	+	18.0296i	−1.07894	+	0.783895i
$530$		0			0
$531$	38.1525	+	27.7194i	1.65568	+	1.20292i
$532$	−43.9574			−1.90580
$533$	−1.30902	−	0.951057i	−0.0566998	−	0.0411948i
$534$		0			0
$535$	11.7082	+	8.50651i	0.506190	+	0.367768i
$536$		0			0
$537$	8.00000	−	24.6215i	0.345225	−	1.06249i
$538$		0			0
$539$	−0.236068	−	0.726543i	−0.0101682	−	0.0312944i
$540$	−3.09017	−	9.51057i	−0.132980	−	0.409270i
$541$	3.16312	−	9.73508i	0.135993	−	0.418544i	−0.859750	−	0.510715i	$-0.829381\pi$
$541$	3.16312	−	9.73508i	0.135993	−	0.418544i	0.995743	+	0.0921713i	$0.0293807\pi$
$542$		0			0
$543$	26.1803			1.12351
$544$		0			0
$545$	−16.4443	+	11.9475i	−0.704395	+	0.511773i
$546$		0			0
$547$	−12.9894	+	9.43732i	−0.555385	+	0.403511i	−0.829767	−	0.558110i	$-0.811527\pi$
$547$	−12.9894	+	9.43732i	−0.555385	+	0.403511i	0.274382	+	0.961621i	$0.411527\pi$
$548$	2.00000	+	6.15537i	0.0854358	+	0.262944i
$549$	57.0344			2.43417
$550$		0			0
$551$	−7.32624			−0.312108
$552$		0			0
$553$	9.57295	−	6.95515i	0.407083	−	0.295763i
$554$		0			0
$555$	12.5623	−	38.6628i	0.533240	−	1.64114i
$556$	14.7082	+	10.6861i	0.623767	+	0.453193i
$557$	−29.5623			−1.25260			−0.626298	−	0.779584i	$-0.715430\pi$
$557$	−29.5623			−1.25260			−0.626298	+	0.779584i	$0.715430\pi$
$558$		0			0
$559$	−2.07295	+	6.37988i	−0.0876764	+	0.269840i
$560$	21.7082	−	15.7719i	0.917339	−	0.666486i
$561$	0.381966	+	1.17557i	0.0161266	+	0.0496326i
$562$		0			0
$563$	−9.20163	+	28.3197i	−0.387802	+	1.19353i	0.546625	+	0.837378i	$0.315912\pi$
$563$	−9.20163	+	28.3197i	−0.387802	+	1.19353i	−0.934427	+	0.356155i	$0.884088\pi$
$564$	3.00000	+	9.23305i	0.126323	+	0.388782i
$565$	−9.20820	+	6.69015i	−0.387392	+	0.281457i
$566$		0			0
$567$	−13.8541	−	10.0656i	−0.581818	−	0.422715i
$568$		0			0
$569$	−8.59017	−	6.24112i	−0.360119	−	0.261642i	0.392983	−	0.919546i	$-0.371443\pi$
$569$	−8.59017	−	6.24112i	−0.360119	−	0.261642i	−0.753102	+	0.657904i	$0.771443\pi$
$570$		0			0
$571$	18.8435	−	13.6906i	0.788574	−	0.572933i	−0.118966	−	0.992898i	$-0.537958\pi$
$571$	18.8435	−	13.6906i	0.788574	−	0.572933i	0.907540	+	0.419966i	$0.137958\pi$
$572$	0.618034	−	0.449028i	0.0258413	−	0.0187748i
$573$	7.32624	+	22.5478i	0.306058	+	0.941950i
$574$		0			0
$575$	−29.6353	+	21.5313i	−1.23588	+	0.897916i
$576$	−30.8328			−1.28470
$577$	3.00658	+	9.25330i	0.125165	+	0.385220i	0.993931	−	0.110004i	$-0.0350862\pi$
$577$	3.00658	+	9.25330i	0.125165	+	0.385220i	−0.868766	+	0.495223i	$0.835086\pi$
$578$		0			0
$579$	−28.1074	+	20.4212i	−1.16810	+	0.848677i
$580$	3.61803	−	2.62866i	0.150231	−	0.109149i
$581$	−21.8435	−	15.8702i	−0.906219	−	0.658407i
$582$		0			0
$583$	1.14590	+	0.832544i	0.0474582	+	0.0344804i
$584$		0			0
$585$	−2.66312	−	8.19624i	−0.110106	−	0.338873i
$586$		0			0
$587$	11.2361	−	34.5811i	0.463762	−	1.42731i	−0.396770	−	0.917918i	$-0.629869\pi$
$587$	11.2361	−	34.5811i	0.463762	−	1.42731i	0.860533	−	0.509395i	$-0.170131\pi$
$588$	−3.23607	+	9.95959i	−0.133453	+	0.410727i
$589$	4.73200	+	14.5636i	0.194979	+	0.600083i
$590$		0			0
$591$	17.2082	−	52.9614i	0.707851	−	2.17854i
$592$	−22.4721	−	16.3270i	−0.923599	−	0.671034i
$593$	40.3262			1.65600			0.828000	−	0.560728i	$-0.189479\pi$
$593$	40.3262			1.65600			0.828000	+	0.560728i	$0.189479\pi$
$594$		0			0
$595$	2.56231	+	7.88597i	0.105044	+	0.323293i
$596$	−31.1246	+	22.6134i	−1.27491	+	0.926279i
$597$	−8.78115	+	6.37988i	−0.359389	+	0.261111i
$598$		0			0
$599$	19.0902			0.780003			0.390002	−	0.920814i	$-0.372474\pi$
$599$	19.0902			0.780003			0.390002	+	0.920814i	$0.372474\pi$
$600$		0			0
$601$	11.5836			0.472505			0.236252	−	0.971692i	$-0.424081\pi$
$601$	11.5836			0.472505			0.236252	+	0.971692i	$0.424081\pi$
$602$		0			0
$603$	24.2082	−	17.5883i	0.985834	−	0.716251i
$604$	36.2705	−	26.3521i	1.47583	−	1.07225i
$605$	−24.2705			−0.986737
$606$		0			0
$607$	−0.965558			−0.0391908			−0.0195954	−	0.999808i	$-0.506238\pi$
$607$	−0.965558			−0.0391908			−0.0195954	+	0.999808i	$0.506238\pi$
$608$		0			0
$609$	−2.42705	+	7.46969i	−0.0983491	+	0.302687i
$610$		0			0
$611$	0.572949	+	1.76336i	0.0231790	+	0.0713377i
$612$	2.94427	−	9.06154i	0.119015	−	0.366291i
$613$	−12.0279	+	37.0180i	−0.485801	+	1.49514i	0.345017	+	0.938597i	$0.387873\pi$
$613$	−12.0279	+	37.0180i	−0.485801	+	1.49514i	−0.830818	+	0.556545i	$0.812127\pi$
$614$		0			0
$615$	−2.92705	+	9.00854i	−0.118030	+	0.363259i
$616$		0			0
$617$	−16.2812	−	11.8290i	−0.655455	−	0.476216i	0.209670	−	0.977772i	$-0.432761\pi$
$617$	−16.2812	−	11.8290i	−0.655455	−	0.476216i	−0.865125	+	0.501557i	$0.832761\pi$
$618$		0			0
$619$	13.2812	+	9.64932i	0.533815	+	0.387839i	0.821783	−	0.569801i	$-0.192980\pi$
$619$	13.2812	+	9.64932i	0.533815	+	0.387839i	−0.287968	+	0.957640i	$0.592980\pi$
$620$	−7.56231	−	5.49434i	−0.303710	−	0.220658i
$621$	−13.2533	+	9.62908i	−0.531836	+	0.386402i
$622$		0			0
$623$	4.14590	+	12.7598i	0.166102	+	0.511209i
$624$	−10.4721			−0.419221
$625$	−20.2254	+	14.6946i	−0.809017	+	0.587785i
$626$		0			0
$627$	2.26393	+	6.96767i	0.0904127	+	0.278262i
$628$	26.8885	−	19.5357i	1.07297	−	0.779558i
$629$	6.94427	−	5.04531i	0.276886	−	0.201170i
$630$		0			0
$631$	−34.6074	−	25.1437i	−1.37770	−	1.00096i	−0.997091	−	0.0762198i	$-0.975715\pi$
$631$	−34.6074	−	25.1437i	−1.37770	−	1.00096i	−0.380607	−	0.924737i	$-0.624285\pi$
$632$		0			0
$633$	−26.4164	−	19.1926i	−1.04996	−	0.762839i
$634$		0			0
$635$	−8.88197	+	27.3359i	−0.352470	+	1.08479i
$636$	−6.00000	−	18.4661i	−0.237915	−	0.732229i
$637$	−0.618034	+	1.90211i	−0.0244874	+	0.0753645i
$638$		0			0
$639$	−11.1074	−	34.1850i	−0.439402	−	1.35234i
$640$		0			0
$641$	−9.03444	+	27.8052i	−0.356839	+	1.09824i	0.598096	+	0.801424i	$0.295924\pi$
$641$	−9.03444	+	27.8052i	−0.356839	+	1.09824i	−0.954935	+	0.296813i	$0.904076\pi$
$642$		0			0
$643$	−34.2148			−1.34930			−0.674650	−	0.738138i	$-0.735705\pi$
$643$	−34.2148			−1.34930			−0.674650	+	0.738138i	$0.735705\pi$
$644$	−35.5623	−	25.8375i	−1.40135	−	1.01814i
$645$	39.2705			1.54627
$646$		0			0
$647$	18.2254	−	13.2415i	0.716515	−	0.520579i	−0.168754	−	0.985658i	$-0.553974\pi$
$647$	18.2254	−	13.2415i	0.716515	−	0.520579i	0.885269	+	0.465079i	$0.153974\pi$
$648$		0			0
$649$	4.67376			0.183461
$650$		0			0
$651$	16.4164			0.643410
$652$	−0.326238	−	1.00406i	−0.0127765	−	0.0393219i
$653$	30.4894	−	22.1518i	1.19314	−	0.866867i	0.199548	−	0.979888i	$-0.436053\pi$
$653$	30.4894	−	22.1518i	1.19314	−	0.866867i	0.993593	+	0.113021i	$0.0360526\pi$
$654$		0			0
$655$	5.65248	+	17.3965i	0.220861	+	0.679739i
$656$	5.23607	+	3.80423i	0.204434	+	0.148530i
$657$	4.41641			0.172300
$658$		0			0
$659$	−4.60081	+	14.1598i	−0.179222	+	0.551589i	−0.999801	−	0.0199440i	$-0.993651\pi$
$659$	−4.60081	+	14.1598i	−0.179222	+	0.551589i	0.820579	+	0.571533i	$0.193651\pi$
$660$	−3.61803	−	2.62866i	−0.140832	−	0.102320i
$661$	−5.20820	−	16.0292i	−0.202576	−	0.623464i	−0.999804	−	0.0197862i	$-0.993701\pi$
$661$	−5.20820	−	16.0292i	−0.202576	−	0.623464i	0.797229	−	0.603678i	$-0.206299\pi$
$662$		0			0
$663$	1.00000	−	3.07768i	0.0388368	−	0.119527i
$664$		0			0
$665$	15.1869	+	46.7405i	0.588923	+	1.81252i
$666$		0			0
$667$	−5.92705	−	4.30625i	−0.229496	−	0.166739i
$668$	11.5279			0.446026
$669$	−51.4058	−	37.3485i	−1.98746	−	1.44398i
$670$		0			0
$671$	4.57295	−	3.32244i	0.176537	−	0.128261i
$672$		0			0
$673$	3.30902	+	10.1841i	0.127553	+	0.392568i	0.994358	−	0.106080i	$-0.0338299\pi$
$673$	3.30902	+	10.1841i	0.127553	+	0.392568i	−0.866804	+	0.498648i	$0.833830\pi$
$674$		0			0
$675$	−9.04508	+	6.57164i	−0.348145	+	0.252942i
$676$	24.0000			0.923077
$677$	−6.51064	−	20.0377i	−0.250224	−	0.770111i	−0.994733	−	0.102499i	$-0.967316\pi$
$677$	−6.51064	−	20.0377i	−0.250224	−	0.770111i	0.744509	−	0.667613i	$-0.232684\pi$
$678$		0			0
$679$	7.28115	−	5.29007i	0.279425	−	0.203014i
$680$		0			0
$681$	−50.8328	−	36.9322i	−1.94792	−	1.41525i
$682$		0			0
$683$	15.9271	+	11.5717i	0.609432	+	0.442778i	0.849214	−	0.528049i	$-0.177076\pi$
$683$	15.9271	+	11.5717i	0.609432	+	0.442778i	−0.239782	+	0.970827i	$0.577076\pi$
$684$	17.4508	−	53.7082i	0.667250	−	2.05358i
$685$	5.85410	−	4.25325i	0.223674	−	0.162508i
$686$		0			0
$687$	13.5172	−	41.6017i	0.515714	−	1.58720i
$688$	8.29180	−	25.5195i	0.316122	−	0.972923i
$689$	−1.14590	−	3.52671i	−0.0436552	−	0.134357i
$690$		0			0
$691$	11.5238	−	35.4666i	0.438386	−	1.34921i	−0.451191	−	0.892428i	$-0.649001\pi$
$691$	11.5238	−	35.4666i	0.438386	−	1.34921i	0.889577	−	0.456786i	$-0.150999\pi$
$692$	−2.23607	−	1.62460i	−0.0850026	−	0.0617580i
$693$	4.41641			0.167765
$694$		0			0
$695$	6.28115	−	19.3314i	0.238258	−	0.733282i
$696$		0			0
$697$	−1.61803	+	1.17557i	−0.0612874	+	0.0445279i
$698$		0			0
$699$	68.3951			2.58694
$700$	−24.2705	−	17.6336i	−0.917339	−	0.666486i
$701$	25.5066			0.963370			0.481685	−	0.876344i	$-0.340025\pi$
$701$	25.5066			0.963370			0.481685	+	0.876344i	$0.340025\pi$
$702$		0			0
$703$	41.1591	−	29.9038i	1.55234	−	1.12784i
$704$	−2.47214	+	1.79611i	−0.0931721	+	0.0676935i
$705$	8.78115	−	6.37988i	0.330717	−	0.240280i
$706$		0			0
$707$	29.1246			1.09534
$708$	−51.8328	−	37.6587i	−1.94800	−	1.41530i
$709$	−10.1008	+	31.0871i	−0.379344	+	1.16750i	0.561157	+	0.827709i	$0.310356\pi$
$709$	−10.1008	+	31.0871i	−0.379344	+	1.16750i	−0.940501	+	0.339791i	$0.889644\pi$
$710$		0			0
$711$	4.69756	+	14.4576i	0.176172	+	0.542203i
$712$		0			0
$713$	−4.73200	+	14.5636i	−0.177215	+	0.545411i
$714$		0			0
$715$	−0.690983	−	0.502029i	−0.0258413	−	0.0187748i
$716$	−6.11146	+	18.8091i	−0.228396	+	0.702930i
$717$	−58.7599	−	42.6915i	−2.19443	−	1.59434i
$718$		0			0
$719$	−18.0451	−	13.1105i	−0.672968	−	0.488940i	0.198049	−	0.980192i	$-0.436539\pi$
$719$	−18.0451	−	13.1105i	−0.672968	−	0.488940i	−0.871017	+	0.491252i	$0.836539\pi$
$720$	10.6525	+	32.7849i	0.396994	+	1.22182i
$721$	−5.07295	+	3.68571i	−0.188926	+	0.137263i
$722$		0			0
$723$	−20.9443	−	64.4598i	−0.778926	−	2.39729i
$724$	−20.0000			−0.743294
$725$	−4.04508	−	2.93893i	−0.150231	−	0.109149i
$726$		0			0
$727$	−15.1803	−	46.7203i	−0.563008	−	1.73276i	−0.673798	−	0.738916i	$-0.735338\pi$
$727$	−15.1803	−	46.7203i	−0.563008	−	1.73276i	0.110790	−	0.993844i	$-0.464662\pi$
$728$		0			0
$729$	32.0066	−	23.2541i	1.18543	−	0.861264i
$730$		0			0
$731$	6.70820	+	4.87380i	0.248112	+	0.180264i
$732$	−77.4853			−2.86394
$733$	−25.1353	−	18.2618i	−0.928392	−	0.674516i	0.0172067	−	0.999852i	$-0.494523\pi$
$733$	−25.1353	−	18.2618i	−0.928392	−	0.674516i	−0.945599	+	0.325336i	$0.894523\pi$
$734$		0			0
$735$	11.7082			0.431864
$736$		0			0
$737$	0.916408	−	2.82041i	0.0337563	−	0.103891i
$738$		0			0
$739$	−1.01722	−	3.13068i	−0.0374191	−	0.115164i	0.930602	−	0.366032i	$-0.119284\pi$
$739$	−1.01722	−	3.13068i	−0.0374191	−	0.115164i	−0.968021	+	0.250868i	$0.919284\pi$
$740$	−9.59675	+	29.5358i	−0.352783	+	1.08576i
$741$	5.92705	−	18.2416i	0.217736	−	0.670121i
$742$		0			0
$743$	−12.0557			−0.442282			−0.221141	−	0.975242i	$-0.570978\pi$
$743$	−12.0557			−0.442282			−0.221141	+	0.975242i	$0.570978\pi$
$744$		0			0
$745$	34.7984	+	25.2825i	1.27491	+	0.926279i
$746$		0			0
$747$	28.0623	−	20.3885i	1.02675	−	0.745975i
$748$	−0.291796	−	0.898056i	−0.0106691	−	0.0328362i
$749$	19.4164			0.709460
$750$		0			0
$751$	8.00000			0.291924			0.145962	−	0.989290i	$-0.453372\pi$
$751$	8.00000			0.291924			0.145962	+	0.989290i	$0.453372\pi$
$752$	−2.29180	−	7.05342i	−0.0835732	−	0.257212i
$753$	−20.3713	+	14.8006i	−0.742372	+	0.539365i
$754$		0			0
$755$	−40.5517	−	29.4625i	−1.47583	−	1.07225i
$756$	−10.8541	−	7.88597i	−0.394760	−	0.286810i
$757$	−23.5279			−0.855135			−0.427567	−	0.903983i	$-0.640629\pi$
$757$	−23.5279			−0.855135			−0.427567	+	0.903983i	$0.640629\pi$
$758$		0			0
$759$	−2.26393	+	6.96767i	−0.0821755	+	0.252910i
$760$		0			0
$761$	−0.916408	−	2.82041i	−0.0332198	−	0.102240i	0.933072	−	0.359690i	$-0.117118\pi$
$761$	−0.916408	−	2.82041i	−0.0332198	−	0.102240i	−0.966292	+	0.257450i	$0.917118\pi$
$762$		0			0
$763$	−8.42705	+	25.9358i	−0.305080	+	0.938939i
$764$	−5.59675	−	17.2250i	−0.202483	−	0.623179i
$765$	−10.6525			−0.385141
$766$		0			0
$767$	−9.89919	−	7.19218i	−0.357439	−	0.259695i
$768$	41.8885			1.51152
$769$	−1.26393	−	0.918300i	−0.0455786	−	0.0331148i	0.564763	−	0.825253i	$-0.308968\pi$
$769$	−1.26393	−	0.918300i	−0.0455786	−	0.0331148i	−0.610341	+	0.792139i	$0.708968\pi$
$770$		0			0
$771$	−42.2426	+	30.6911i	−1.52133	+	1.10531i
$772$	21.4721	−	15.6004i	0.772799	−	0.561471i
$773$	−10.0623	−	30.9686i	−0.361916	−	1.11386i	−0.951890	−	0.306441i	$-0.900862\pi$
$773$	−10.0623	−	30.9686i	−0.361916	−	1.11386i	0.589974	−	0.807422i	$-0.299138\pi$
$774$		0			0
$775$	−3.22949	+	9.93935i	−0.116007	+	0.357032i
$776$		0			0
$777$	−16.8541	−	51.8716i	−0.604638	−	1.86088i
$778$		0			0
$779$	−9.59017	+	6.96767i	−0.343603	+	0.249643i
$780$	3.61803	+	11.1352i	0.129546	+	0.398703i
$781$	−2.88197	−	2.09387i	−0.103125	−	0.0749246i
$782$		0			0
$783$	−1.80902	−	1.31433i	−0.0646490	−	0.0469702i
$784$	2.47214	−	7.60845i	0.0882906	−	0.271730i
$785$	−30.0623	−	21.8415i	−1.07297	−	0.779558i
$786$		0			0
$787$	0.534442	−	1.64484i	0.0190508	−	0.0586323i	−0.941079	−	0.338186i	$-0.890187\pi$
$787$	0.534442	−	1.64484i	0.0190508	−	0.0586323i	0.960130	+	0.279554i	$0.0901866\pi$
$788$	−13.1459	+	40.4589i	−0.468303	+	1.44129i
$789$	0.263932	+	0.812299i	0.00939623	+	0.0289186i
$790$		0			0
$791$	−4.71885	+	14.5231i	−0.167783	+	0.516383i
$792$		0			0
$793$	−14.7984			−0.525506
$794$		0			0
$795$	−17.5623	+	12.7598i	−0.622871	+	0.452542i
$796$	6.70820	−	4.87380i	0.237766	−	0.172747i
$797$	19.7082	−	14.3188i	0.698100	−	0.507200i	−0.181213	−	0.983444i	$-0.558002\pi$
$797$	19.7082	−	14.3188i	0.698100	−	0.507200i	0.879313	+	0.476244i	$0.158002\pi$
$798$		0			0
$799$	2.29180			0.0810779
$800$		0			0
$801$	−17.2361			−0.609007
$802$		0			0
$803$	0.354102	−	0.257270i	0.0124960	−	0.00907887i
$804$	−32.8885	+	23.8949i	−1.15989	+	0.842709i
$805$	−15.1869	+	46.7405i	−0.535269	+	1.64739i
$806$		0			0
$807$	83.6312			2.94396
$808$		0			0
$809$	14.1287	−	43.4836i	0.496738	−	1.52880i	−0.317493	−	0.948261i	$-0.602841\pi$
$809$	14.1287	−	43.4836i	0.496738	−	1.52880i	0.814231	−	0.580541i	$-0.197159\pi$
$810$		0			0
$811$	11.5517	+	35.5524i	0.405634	+	1.24841i	0.920365	+	0.391061i	$0.127892\pi$
$811$	11.5517	+	35.5524i	0.405634	+	1.24841i	−0.514731	+	0.857352i	$0.672108\pi$
$812$	1.85410	−	5.70634i	0.0650662	−	0.200253i
$813$	−1.95492	+	6.01661i	−0.0685619	+	0.211012i
$814$		0			0
$815$	−0.954915	+	0.693786i	−0.0334492	+	0.0243023i
$816$	−4.00000	+	12.3107i	−0.140028	+	0.430962i
$817$	39.7599	+	28.8872i	1.39102	+	1.01064i
$818$		0			0
$819$	−9.35410	−	6.79615i	−0.326859	−	0.237477i
$820$	2.23607	−	6.88191i	0.0780869	−	0.240327i
$821$	3.00000	−	2.17963i	0.104701	−	0.0760695i	−0.534203	−	0.845356i	$-0.679388\pi$
$821$	3.00000	−	2.17963i	0.104701	−	0.0760695i	0.638904	+	0.769287i	$0.279388\pi$
$822$		0			0
$823$	−10.9615	−	33.7360i	−0.382094	−	1.17596i	−0.938567	−	0.345098i	$-0.887846\pi$
$823$	−10.9615	−	33.7360i	−0.382094	−	1.17596i	0.556473	−	0.830866i	$-0.312154\pi$
$824$		0			0
$825$	−1.54508	+	4.75528i	−0.0537930	+	0.165558i
$826$		0			0
$827$	11.3090	+	34.8056i	0.393253	+	1.21031i	0.930314	+	0.366765i	$0.119535\pi$
$827$	11.3090	+	34.8056i	0.393253	+	1.21031i	−0.537061	+	0.843544i	$0.680465\pi$
$828$	45.6869	−	33.1935i	1.58773	−	1.15355i
$829$	20.4443	−	14.8536i	0.710059	−	0.515888i	−0.173134	−	0.984898i	$-0.555389\pi$
$829$	20.4443	−	14.8536i	0.710059	−	0.515888i	0.883193	+	0.469010i	$0.155389\pi$
$830$		0			0
$831$	7.35410	+	5.34307i	0.255111	+	0.185349i
$832$	8.00000			0.277350
$833$	2.00000	+	1.45309i	0.0692959	+	0.0503464i
$834$		0			0
$835$	−3.98278	−	12.2577i	−0.137830	−	0.424196i
$836$	−1.72949	−	5.32282i	−0.0598157	−	0.184094i
$837$	−1.44427	+	4.44501i	−0.0499213	+	0.153642i
$838$		0			0
$839$	−2.22542	−	6.84915i	−0.0768302	−	0.236459i	0.905264	−	0.424849i	$-0.139673\pi$
$839$	−2.22542	−	6.84915i	−0.0768302	−	0.236459i	−0.982094	+	0.188390i	$0.939673\pi$
$840$		0			0
$841$	0.309017	−	0.951057i	0.0106558	−	0.0327951i
$842$		0			0
$843$	−44.9787			−1.54915
$844$	20.1803	+	14.6619i	0.694636	+	0.504683i
$845$	−8.29180	−	25.5195i	−0.285246	−	0.877898i
$846$		0			0
$847$	−26.3435	+	19.1396i	−0.905172	+	0.657646i
$848$	4.58359	+	14.1068i	0.157401	+	0.484431i
$849$	53.0689			1.82132
$850$		0			0
$851$	50.8754			1.74399
$852$	15.0902	+	46.4428i	0.516981	+	1.59110i
$853$	18.8435	−	13.6906i	0.645188	−	0.468756i	−0.216441	−	0.976296i	$-0.569445\pi$
$853$	18.8435	−	13.6906i	0.645188	−	0.468756i	0.861629	+	0.507539i	$0.169445\pi$
$854$		0			0
$855$	−63.1378			−2.15927
$856$		0			0
$857$	16.6738			0.569565			0.284782	−	0.958592i	$-0.408079\pi$
$857$	16.6738			0.569565			0.284782	+	0.958592i	$0.408079\pi$
$858$		0			0
$859$	4.45492	−	13.7108i	0.152000	−	0.467807i	−0.845845	−	0.533429i	$-0.820903\pi$
$859$	4.45492	−	13.7108i	0.152000	−	0.467807i	0.997845	+	0.0656219i	$0.0209031\pi$
$860$	−30.0000			−1.02299
$861$	3.92705	+	12.0862i	0.133834	+	0.411897i
$862$		0			0
$863$	6.13525	−	18.8824i	0.208847	−	0.642763i	−0.790687	−	0.612221i	$-0.790276\pi$
$863$	6.13525	−	18.8824i	0.208847	−	0.642763i	0.999533	−	0.0305428i	$-0.00972358\pi$
$864$		0			0
$865$	−0.954915	+	2.93893i	−0.0324681	+	0.0999265i
$866$		0			0
$867$	32.7705	+	23.8092i	1.11294	+	0.808602i
$868$	−12.5410			−0.425670
$869$	1.21885	+	0.885544i	0.0413466	+	0.0300400i
$870$		0			0
$871$	−6.28115	+	4.56352i	−0.212829	+	0.154629i
$872$		0			0
$873$	3.57295	+	10.9964i	0.120926	+	0.372172i
$874$		0			0
$875$	−10.3647	+	31.8994i	−0.350392	+	1.07840i
$876$	−6.00000			−0.202721
$877$	6.81559	+	20.9762i	0.230146	+	0.708317i	0.997728	+	0.0673667i	$0.0214597\pi$
$877$	6.81559	+	20.9762i	0.230146	+	0.708317i	−0.767582	+	0.640951i	$0.778540\pi$
$878$		0			0
$879$	−34.7705	+	25.2623i	−1.17278	+	0.852075i
$880$	2.76393	+	2.00811i	0.0931721	+	0.0676935i
$881$	−39.0066	−	28.3399i	−1.31416	−	0.954797i	−0.999985	−	0.00543325i	$-0.998271\pi$
$881$	−39.0066	−	28.3399i	−1.31416	−	0.954797i	−0.314180	−	0.949364i	$-0.601729\pi$
$882$		0			0
$883$	19.5172	+	14.1801i	0.656807	+	0.477198i	0.865583	−	0.500765i	$-0.166948\pi$
$883$	19.5172	+	14.1801i	0.656807	+	0.477198i	−0.208776	+	0.977963i	$0.566948\pi$
$884$	−0.763932	+	2.35114i	−0.0256938	+	0.0790774i
$885$	−22.1353	+	68.1253i	−0.744068	+	2.29001i
$886$		0			0
$887$	−7.07295	+	21.7683i	−0.237486	+	0.730908i	0.759295	+	0.650746i	$0.225544\pi$
$887$	−7.07295	+	21.7683i	−0.237486	+	0.730908i	−0.996782	+	0.0801619i	$0.974456\pi$
$888$		0			0
$889$	11.9164	+	36.6749i	0.399663	+	1.23004i
$890$		0			0
$891$	0.673762	−	2.07363i	0.0225719	−	0.0694691i
$892$	39.2705	+	28.5317i	1.31487	+	0.955312i
$893$	13.5836			0.454558
$894$		0			0
$895$	22.1115			0.739104
$896$		0			0
$897$	15.5172	−	11.2739i	0.518105	−	0.376425i
$898$		0			0
$899$	−2.09017			−0.0697111
$900$	31.1803	−	22.6538i	1.03934	−	0.755128i
$901$	−4.58359			−0.152702
$902$		0			0
$903$	42.6246	−	30.9686i	1.41846	−	1.03057i
$904$		0			0
$905$	6.90983	+	21.2663i	0.229691	+	0.706915i
$906$		0			0
$907$	39.5623			1.31364			0.656822	−	0.754045i	$-0.271900\pi$
$907$	39.5623			1.31364			0.656822	+	0.754045i	$0.271900\pi$
$908$	38.8328	+	28.2137i	1.28871	+	0.936304i
$909$	−11.5623	+	35.5851i	−0.383497	+	1.18028i
$910$		0			0
$911$	7.58359	+	23.3399i	0.251256	+	0.773285i	0.994544	+	0.104315i	$0.0332649\pi$
$911$	7.58359	+	23.3399i	0.251256	+	0.773285i	−0.743289	+	0.668971i	$0.766735\pi$
$912$	−23.7082	+	72.9663i	−0.785057	+	2.41616i
$913$	1.06231	−	3.26944i	0.0351572	−	0.108203i
$914$		0			0
$915$	26.7705	+	82.3912i	0.885006	+	2.72377i
$916$	−10.3262	+	31.7809i	−0.341189	+	1.05007i
$917$	19.8541	+	14.4248i	0.655640	+	0.476350i
$918$		0			0
$919$	−6.76393	−	4.91428i	−0.223122	−	0.162107i	0.470609	−	0.882342i	$-0.344034\pi$
$919$	−6.76393	−	4.91428i	−0.223122	−	0.162107i	−0.693731	+	0.720235i	$0.744034\pi$
$920$		0			0
$921$	−23.2984	+	16.9273i	−0.767708	+	0.557772i
$922$		0			0
$923$	2.88197	+	8.86978i	0.0948611	+	0.291952i
$924$	−6.00000			−0.197386
$925$	34.7214			1.14163
$926$		0			0
$927$	−2.48936	−	7.66145i	−0.0817612	−	0.251635i
$928$		0			0
$929$	−16.9164	+	12.2905i	−0.555009	+	0.403238i	−0.829629	−	0.558315i	$-0.811448\pi$
$929$	−16.9164	+	12.2905i	−0.555009	+	0.403238i	0.274620	+	0.961553i	$0.411448\pi$
$930$		0			0
$931$	11.8541	+	8.61251i	0.388503	+	0.282264i
$932$	−52.2492			−1.71148
$933$	−50.9058	−	36.9852i	−1.66658	−	1.21084i
$934$		0			0
$935$	−0.854102	+	0.620541i	−0.0279321	+	0.0202939i
$936$		0			0
$937$	7.22949	−	22.2501i	0.236177	−	0.726879i	−0.760786	−	0.649003i	$-0.775186\pi$
$937$	7.22949	−	22.2501i	0.236177	−	0.726879i	0.996963	−	0.0778756i	$-0.0248137\pi$
$938$		0			0
$939$	−3.70820	−	11.4127i	−0.121013	−	0.372439i
$940$	−6.70820	+	4.87380i	−0.218797	+	0.158966i
$941$	2.76393	−	8.50651i	0.0901016	−	0.277304i	−0.895845	−	0.444368i	$-0.853428\pi$
$941$	2.76393	−	8.50651i	0.0901016	−	0.277304i	0.985946	+	0.167063i	$0.0534284\pi$
$942$		0			0
$943$	−11.8541			−0.386023
$944$	39.5967	+	28.7687i	1.28876	+	0.936342i
$945$	−4.63525	+	14.2658i	−0.150785	+	0.464068i
$946$		0			0
$947$	18.9721	−	13.7841i	0.616512	−	0.447922i	−0.235190	−	0.971949i	$-0.575571\pi$
$947$	18.9721	−	13.7841i	0.616512	−	0.447922i	0.851701	+	0.524028i	$0.175571\pi$
$948$	−6.38197	−	19.6417i	−0.207277	−	0.637932i
$949$	−1.14590			−0.0371974
$950$		0			0
$951$	−50.6869			−1.64364
$952$		0			0
$953$	12.7533	−	9.26581i	0.413120	−	0.300149i	−0.361744	−	0.932277i	$-0.617819\pi$
$953$	12.7533	−	9.26581i	0.413120	−	0.300149i	0.774864	+	0.632129i	$0.217819\pi$
$954$		0			0
$955$	−16.3820	+	11.9022i	−0.530108	+	0.385146i
$956$	44.8885	+	32.6134i	1.45180	+	1.05479i
$957$	−1.00000			−0.0323254
$958$		0			0
$959$	3.00000	−	9.23305i	0.0968751	−	0.298151i
$960$	−14.4721	−	44.5407i	−0.467086	−	1.43754i
$961$	−8.22949	−	25.3278i	−0.265467	−	0.817025i
$962$		0			0
$963$	−7.70820	+	23.7234i	−0.248393	+	0.764476i
$964$	16.0000	+	49.2429i	0.515325	+	1.58601i
$965$	−24.0066	−	17.4418i	−0.772799	−	0.561471i
$966$		0			0
$967$	−41.5344	−	30.1765i	−1.33566	−	0.970412i	−0.999592	−	0.0285736i	$-0.990904\pi$
$967$	−41.5344	−	30.1765i	−1.33566	−	0.970412i	−0.336066	−	0.941838i	$-0.609096\pi$
$968$		0			0
$969$	−19.1803	−	13.9353i	−0.616161	−	0.447667i
$970$		0			0
$971$	−31.8607	+	23.1481i	−1.02246	+	0.742859i	−0.966785	−	0.255590i	$-0.917730\pi$
$971$	−31.8607	+	23.1481i	−1.02246	+	0.742859i	−0.0556726	+	0.998449i	$0.517730\pi$
$972$	−35.0344	+	25.4540i	−1.12373	+	0.816438i
$973$	−8.42705	−	25.9358i	−0.270159	−	0.831463i
$974$		0			0
$975$	10.5902	−	7.69421i	0.339157	−	0.246412i
$976$	59.1935			1.89474
$977$	2.94427	+	9.06154i	0.0941956	+	0.289904i	0.987043	−	0.160455i	$-0.0512960\pi$
$977$	2.94427	+	9.06154i	0.0941956	+	0.289904i	−0.892848	+	0.450359i	$0.851296\pi$
$978$		0			0
$979$	−1.38197	+	1.00406i	−0.0441678	+	0.0320898i
$980$	−8.94427			−0.285714
$981$	−28.3435	−	20.5927i	−0.904937	−	0.657475i
$982$		0			0
$983$	−29.9164	−	21.7355i	−0.954185	−	0.693256i	−0.00239220	−	0.999997i	$-0.500761\pi$
$983$	−29.9164	−	21.7355i	−0.954185	−	0.693256i	−0.951793	+	0.306741i	$0.900761\pi$
$984$		0			0
$985$	47.5623			1.51546
$986$		0			0
$987$	4.50000	−	13.8496i	0.143237	−	0.440837i
$988$	−4.52786	+	13.9353i	−0.144051	+	0.443342i
$989$	15.1869	+	46.7405i	0.482916	+	1.48626i
$990$		0			0
$991$	3.12868	−	9.62908i	0.0993857	−	0.305878i	−0.888986	−	0.457934i	$-0.848590\pi$
$991$	3.12868	−	9.62908i	0.0993857	−	0.305878i	0.988372	+	0.152056i	$0.0485895\pi$
$992$		0			0
$993$	67.6869			2.14798
$994$		0			0
$995$	−7.50000	−	5.44907i	−0.237766	−	0.172747i
$996$	−38.1246	+	27.6992i	−1.20802	+	0.877681i
$997$	4.73607	−	3.44095i	0.149993	−	0.108976i	−0.510258	−	0.860021i	$-0.670450\pi$
$997$	4.73607	−	3.44095i	0.149993	−	0.108976i	0.660251	+	0.751045i	$0.270450\pi$
$998$		0			0
$999$	15.5279			0.491280

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.k.a.581.1	yes	4
25.21	even	5	inner	725.2.k.a.146.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
725.2.k.a.146.1	✓	4	25.21	even	5	inner
725.2.k.a.581.1	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.11803 + 1.53884i) q^{3} +(1.61803 - 1.17557i) q^{4} +(-1.80902 - 1.31433i) q^{5} -3.00000 q^{7} +(1.19098 - 3.66547i) q^{9} +(-0.118034 - 0.363271i) q^{11} +(-1.61803 + 4.97980i) q^{12} +(-0.309017 + 0.951057i) q^{13} +5.85410 q^{15} +(1.23607 - 3.80423i) q^{16} +(1.00000 + 0.726543i) q^{17} +(5.92705 + 4.30625i) q^{19} -4.47214 q^{20} +(6.35410 - 4.61653i) q^{21} +(2.26393 + 6.96767i) q^{23} +(1.54508 + 4.75528i) q^{25} +(0.690983 + 2.12663i) q^{27} +(-4.85410 + 3.52671i) q^{28} +(-0.809017 + 0.587785i) q^{29} +(1.69098 + 1.22857i) q^{31} +(0.809017 + 0.587785i) q^{33} +(5.42705 + 3.94298i) q^{35} +(-2.38197 - 7.33094i) q^{36} +(2.14590 - 6.60440i) q^{37} +(-0.809017 - 2.48990i) q^{39} +(-0.500000 + 1.53884i) q^{41} +6.70820 q^{43} +(-0.618034 - 0.449028i) q^{44} +(-6.97214 + 5.06555i) q^{45} +(1.50000 - 1.08981i) q^{47} +(3.23607 + 9.95959i) q^{48} +2.00000 q^{49} -3.23607 q^{51} +(0.618034 + 1.90211i) q^{52} +(-3.00000 + 2.17963i) q^{53} +(-0.263932 + 0.812299i) q^{55} -19.1803 q^{57} +(-3.78115 + 11.6372i) q^{59} +(9.47214 - 6.88191i) q^{60} +(4.57295 + 14.0741i) q^{61} +(-3.57295 + 10.9964i) q^{63} +(-2.47214 - 7.60845i) q^{64} +(1.80902 - 1.31433i) q^{65} +(6.28115 + 4.56352i) q^{67} +2.47214 q^{68} +(-15.5172 - 11.2739i) q^{69} +(7.54508 - 5.48183i) q^{71} +(0.354102 + 1.08981i) q^{73} +(-10.5902 - 7.69421i) q^{75} +14.6525 q^{76} +(0.354102 + 1.08981i) q^{77} +(-3.19098 + 2.31838i) q^{79} +(-7.23607 + 5.25731i) q^{80} +(4.61803 + 3.35520i) q^{81} +(7.28115 + 5.29007i) q^{83} +(4.85410 - 14.9394i) q^{84} +(-0.854102 - 2.62866i) q^{85} +(0.809017 - 2.48990i) q^{87} +(-1.38197 - 4.25325i) q^{89} +(0.927051 - 2.85317i) q^{91} +(11.8541 + 8.61251i) q^{92} -5.47214 q^{93} +(-5.06231 - 15.5802i) q^{95} +(-2.42705 + 1.76336i) q^{97} -1.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 2 q^{4} - 5 q^{5} - 12 q^{7} + 7 q^{9} + 4 q^{11} - 2 q^{12} + q^{13} + 10 q^{15} - 4 q^{16} + 4 q^{17} + 17 q^{19} + 12 q^{21} + 18 q^{23} - 5 q^{25} + 5 q^{27} - 6 q^{28} - q^{29} + 9 q^{31}+ \cdots + 12 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 2 * q^4 - 5 * q^5 - 12 * q^7 + 7 * q^9 + 4 * q^11 - 2 * q^12 + q^13 + 10 * q^15 - 4 * q^16 + 4 * q^17 + 17 * q^19 + 12 * q^21 + 18 * q^23 - 5 * q^25 + 5 * q^27 - 6 * q^28 - q^29 + 9 * q^31 + q^33 + 15 * q^35 - 14 * q^36 + 22 * q^37 - q^39 - 2 * q^41 + 2 * q^44 - 10 * q^45 + 6 * q^47 + 4 * q^48 + 8 * q^49 - 4 * q^51 - 2 * q^52 - 12 * q^53 - 10 * q^55 - 32 * q^57 + 5 * q^59 + 20 * q^60 + 25 * q^61 - 21 * q^63 + 8 * q^64 + 5 * q^65 + 5 * q^67 - 8 * q^68 - 33 * q^69 + 19 * q^71 - 12 * q^73 - 20 * q^75 - 4 * q^76 - 12 * q^77 - 15 * q^79 - 20 * q^80 + 14 * q^81 + 9 * q^83 + 6 * q^84 + 10 * q^85 + q^87 - 10 * q^89 - 3 * q^91 + 34 * q^92 - 4 * q^93 + 20 * q^95 - 3 * q^97 + 12 * q^99

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