LMFDB - Embedded newform 275.3.bk.c.82.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(82,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.82"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.bk (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [128] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			82.13
Character	$\chi$	$=$	275.82
Dual form			275.3.bk.c.218.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.11368 - 2.18572i) q^{2} +(3.11704 - 0.493690i) q^{3} +(-1.18596 - 1.63233i) q^{4} +(2.39232 - 7.36280i) q^{6} +(1.55118 + 0.245682i) q^{7} +(4.80296 - 0.760714i) q^{8} +(0.912687 - 0.296550i) q^{9} +(4.19559 - 10.1684i) q^{11} +(-4.50255 - 4.50255i) q^{12} +(4.14212 + 2.11052i) q^{13} +(2.26451 - 3.11683i) q^{14} +(6.18024 - 19.0208i) q^{16} +(-9.81025 + 4.99857i) q^{17} +(0.368267 - 2.32514i) q^{18} +(2.44564 - 3.36614i) q^{19} +4.95637 q^{21} +(-17.5528 - 20.4948i) q^{22} +(4.08642 - 4.08642i) q^{23} +(14.5955 - 4.74235i) q^{24} +(9.22601 - 6.70309i) q^{26} +(-22.6088 + 11.5198i) q^{27} +(-1.43860 - 2.82341i) q^{28} +(-9.31687 - 12.8236i) q^{29} +(16.8361 + 51.8163i) q^{31} +(-20.9373 - 20.9373i) q^{32} +(8.05774 - 33.7667i) q^{33} +27.0093i q^{34} +(-1.56648 - 1.13811i) q^{36} +(-24.5018 - 3.88071i) q^{37} +(-4.63378 - 9.09431i) q^{38} +(13.9531 + 4.53363i) q^{39} +(34.9390 + 25.3846i) q^{41} +(5.51982 - 10.8333i) q^{42} +(-33.7901 + 33.7901i) q^{43} +(-21.5741 + 5.21076i) q^{44} +(-4.38082 - 13.4828i) q^{46} +(11.9207 + 75.2645i) q^{47} +(9.87365 - 62.3398i) q^{48} +(-44.2560 - 14.3796i) q^{49} +(-28.1112 + 20.4240i) q^{51} +(-1.46732 - 9.26431i) q^{52} +(-24.6242 - 12.5467i) q^{53} +62.2460i q^{54} +7.63714 q^{56} +(5.96133 - 11.6998i) q^{57} +(-38.4048 + 6.08273i) q^{58} +(-59.8804 - 82.4183i) q^{59} +(-8.72078 + 26.8398i) q^{61} +(132.006 + 20.9077i) q^{62} +(1.48860 - 0.235771i) q^{63} +(7.00270 - 2.27532i) q^{64} +(-64.8310 - 55.2174i) q^{66} +(1.02357 + 1.02357i) q^{67} +(19.7939 + 10.0855i) q^{68} +(10.7201 - 14.7550i) q^{69} +(23.0126 - 70.8254i) q^{71} +(4.15801 - 2.11861i) q^{72} +(-15.3779 + 97.0924i) q^{73} +(-35.7694 + 49.2323i) q^{74} -8.39510 q^{76} +(9.00630 - 14.7423i) q^{77} +(25.4486 - 25.4486i) q^{78} +(107.275 - 34.8559i) q^{79} +(-71.7727 + 52.1459i) q^{81} +(94.3947 - 48.0965i) q^{82} +(49.3617 + 96.8777i) q^{83} +(-5.87806 - 8.09045i) q^{84} +(36.2243 + 111.487i) q^{86} +(-35.3719 - 35.3719i) q^{87} +(12.4160 - 52.0302i) q^{88} -21.2775i q^{89} +(5.90665 + 4.29143i) q^{91} +(-11.5167 - 1.82407i) q^{92} +(78.0601 + 153.202i) q^{93} +(177.783 + 57.7653i) q^{94} +(-75.5989 - 54.9258i) q^{96} +(9.55693 - 18.7565i) q^{97} +(-80.7170 + 80.7170i) q^{98} +(0.813807 - 10.5248i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 48 q^{6} + 32 q^{11} + 280 q^{16} - 8 q^{21} + 528 q^{26} - 16 q^{31} + 336 q^{36} - 604 q^{41} - 1152 q^{46} - 1024 q^{51} - 992 q^{56} - 320 q^{61} + 1624 q^{66} + 536 q^{71} + 1776 q^{76} + 3680 q^{81}+ \cdots - 6584 q^{96}+O(q^{100}) $ 128 * q - 48 * q^6 + 32 * q^11 + 280 * q^16 - 8 * q^21 + 528 * q^26 - 16 * q^31 + 336 * q^36 - 604 * q^41 - 1152 * q^46 - 1024 * q^51 - 992 * q^56 - 320 * q^61 + 1624 * q^66 + 536 * q^71 + 1776 * q^76 + 3680 * q^81 + 872 * q^86 - 448 * q^91 - 6584 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.11368	−	2.18572i	0.556841	−	1.09286i	−0.425359	−	0.905025i	$-0.639852\pi$
$2$	1.11368	−	2.18572i	0.556841	−	1.09286i	0.982200	−	0.187837i	$-0.0601477\pi$
$3$	3.11704	−	0.493690i	1.03901	−	0.164563i	0.386459	−	0.922306i	$-0.373698\pi$
$3$	3.11704	−	0.493690i	1.03901	−	0.164563i	0.652553	+	0.757743i	$0.273698\pi$
$4$	−1.18596	−	1.63233i	−0.296490	−	0.408083i
$5$		0			0
$5$		0			0
$6$	2.39232	−	7.36280i	0.398720	−	1.22713i
$7$	1.55118	+	0.245682i	0.221597	+	0.0350975i	0.266245	−	0.963905i	$-0.414217\pi$
$7$	1.55118	+	0.245682i	0.221597	+	0.0350975i	−0.0446486	+	0.999003i	$0.514217\pi$
$8$	4.80296	−	0.760714i	0.600370	−	0.0950893i
$9$	0.912687	−	0.296550i	0.101410	−	0.0329500i
$10$		0			0
$11$	4.19559	−	10.1684i	0.381417	−	0.924403i
$11$	4.19559	−	10.1684i	0.381417	−	0.924403i
$12$	−4.50255	−	4.50255i	−0.375212	−	0.375212i
$13$	4.14212	+	2.11052i	0.318625	+	0.162347i	0.605987	−	0.795475i	$-0.292778\pi$
$13$	4.14212	+	2.11052i	0.318625	+	0.162347i	−0.287362	+	0.957822i	$0.592778\pi$
$14$	2.26451	−	3.11683i	0.161751	−	0.222631i
$15$		0			0
$16$	6.18024	−	19.0208i	0.386265	−	1.18880i
$17$	−9.81025	+	4.99857i	−0.577074	+	0.294034i	−0.718064	−	0.695977i	$-0.754971\pi$
$17$	−9.81025	+	4.99857i	−0.577074	+	0.294034i	0.140990	+	0.990011i	$0.454971\pi$
$18$	0.368267	−	2.32514i	0.0204593	−	0.129175i
$19$	2.44564	−	3.36614i	0.128718	−	0.177165i	−0.739794	−	0.672834i	$-0.765077\pi$
$19$	2.44564	−	3.36614i	0.128718	−	0.177165i	0.868512	+	0.495669i	$0.165077\pi$
$20$		0			0
$21$	4.95637			0.236018
$22$	−17.5528	−	20.4948i	−0.797856	−	0.931581i
$23$	4.08642	−	4.08642i	0.177671	−	0.177671i	−0.612669	−	0.790340i	$-0.709904\pi$
$23$	4.08642	−	4.08642i	0.177671	−	0.177671i	0.790340	+	0.612669i	$0.209904\pi$
$24$	14.5955	−	4.74235i	0.608144	−	0.197598i
$25$		0			0
$26$	9.22601	−	6.70309i	0.354846	−	0.257811i
$27$	−22.6088	+	11.5198i	−0.837363	+	0.426658i
$28$	−1.43860	−	2.82341i	−0.0513785	−	0.100836i
$29$	−9.31687	−	12.8236i	−0.321271	−	0.442192i	0.617583	−	0.786505i	$-0.288112\pi$
$29$	−9.31687	−	12.8236i	−0.321271	−	0.442192i	−0.938855	+	0.344313i	$0.888112\pi$
$30$		0			0
$31$	16.8361	+	51.8163i	0.543101	+	1.67149i	0.725462	+	0.688263i	$0.241626\pi$
$31$	16.8361	+	51.8163i	0.543101	+	1.67149i	−0.182360	+	0.983232i	$0.558374\pi$
$32$	−20.9373	−	20.9373i	−0.654291	−	0.654291i
$33$	8.05774	−	33.7667i	0.244174	−	1.02323i
$34$			27.0093i			0.794392i
$35$		0			0
$36$	−1.56648	−	1.13811i	−0.0435133	−	0.0316143i
$37$	−24.5018	−	3.88071i	−0.662211	−	0.104884i	−0.183723	−	0.982978i	$-0.558815\pi$
$37$	−24.5018	−	3.88071i	−0.662211	−	0.104884i	−0.478488	+	0.878094i	$0.658815\pi$
$38$	−4.63378	−	9.09431i	−0.121942	−	0.239324i
$39$	13.9531	+	4.53363i	0.357771	+	0.116247i
$40$		0			0
$41$	34.9390	+	25.3846i	0.852170	+	0.619138i	0.925743	−	0.378152i	$-0.123440\pi$
$41$	34.9390	+	25.3846i	0.852170	+	0.619138i	−0.0735735	+	0.997290i	$0.523440\pi$
$42$	5.51982	−	10.8333i	0.131424	−	0.257935i
$43$	−33.7901	+	33.7901i	−0.785815	+	0.785815i	−0.980805	−	0.194990i	$-0.937533\pi$
$43$	−33.7901	+	33.7901i	−0.785815	+	0.785815i	0.194990	+	0.980805i	$0.437533\pi$
$44$	−21.5741	+	5.21076i	−0.490320	+	0.118426i
$45$		0			0
$46$	−4.38082	−	13.4828i	−0.0952351	−	0.293104i
$47$	11.9207	+	75.2645i	0.253632	+	1.60137i	0.705116	+	0.709092i	$0.250895\pi$
$47$	11.9207	+	75.2645i	0.253632	+	1.60137i	−0.451484	+	0.892279i	$0.649105\pi$
$48$	9.87365	−	62.3398i	0.205701	−	1.29875i
$49$	−44.2560	−	14.3796i	−0.903183	−	0.293462i
$50$		0			0
$51$	−28.1112	+	20.4240i	−0.551199	+	0.400470i
$52$	−1.46732	−	9.26431i	−0.0282177	−	0.178160i
$53$	−24.6242	−	12.5467i	−0.464608	−	0.236730i	0.205985	−	0.978555i	$-0.433960\pi$
$53$	−24.6242	−	12.5467i	−0.464608	−	0.236730i	−0.670593	+	0.741826i	$0.733960\pi$
$54$			62.2460i			1.15270i
$55$		0			0
$56$	7.63714			0.136378
$57$	5.96133	−	11.6998i	0.104585	−	0.205259i
$58$	−38.4048	+	6.08273i	−0.662152	+	0.104875i
$59$	−59.8804	−	82.4183i	−1.01492	−	1.39692i	−0.915703	−	0.401855i	$-0.868366\pi$
$59$	−59.8804	−	82.4183i	−1.01492	−	1.39692i	−0.0992186	−	0.995066i	$-0.531634\pi$
$60$		0			0
$61$	−8.72078	+	26.8398i	−0.142964	+	0.439997i	−0.996744	−	0.0806373i	$-0.974304\pi$
$61$	−8.72078	+	26.8398i	−0.142964	+	0.439997i	0.853780	+	0.520634i	$0.174304\pi$
$62$	132.006	+	20.9077i	2.12913	+	0.337222i
$63$	1.48860	−	0.235771i	0.0236285	−	0.00374239i
$64$	7.00270	−	2.27532i	0.109417	−	0.0355518i
$65$		0			0
$66$	−64.8310	−	55.2174i	−0.982287	−	0.836627i
$67$	1.02357	+	1.02357i	0.0152771	+	0.0152771i	0.714704	−	0.699427i	$-0.246561\pi$
$67$	1.02357	+	1.02357i	0.0152771	+	0.0152771i	−0.699427	+	0.714704i	$0.746561\pi$
$68$	19.7939	+	10.0855i	0.291087	+	0.148316i
$69$	10.7201	−	14.7550i	0.155364	−	0.213840i
$70$		0			0
$71$	23.0126	−	70.8254i	0.324121	−	0.997540i	−0.647716	−	0.761882i	$-0.724275\pi$
$71$	23.0126	−	70.8254i	0.324121	−	0.997540i	0.971836	−	0.235658i	$-0.0757245\pi$
$72$	4.15801	−	2.11861i	0.0577502	−	0.0294252i
$73$	−15.3779	+	97.0924i	−0.210656	+	1.33003i	0.624933	+	0.780678i	$0.285126\pi$
$73$	−15.3779	+	97.0924i	−0.210656	+	1.33003i	−0.835590	+	0.549354i	$0.814874\pi$
$74$	−35.7694	+	49.2323i	−0.483370	+	0.665302i
$75$		0			0
$76$	−8.39510			−0.110462
$77$	9.00630	−	14.7423i	0.116965	−	0.191458i
$78$	25.4486	−	25.4486i	0.326264	−	0.326264i
$79$	107.275	−	34.8559i	1.35792	−	0.441213i	0.462569	−	0.886583i	$-0.346928\pi$
$79$	107.275	−	34.8559i	1.35792	−	0.441213i	0.895347	+	0.445370i	$0.146928\pi$
$80$		0			0
$81$	−71.7727	+	52.1459i	−0.886083	+	0.643777i
$82$	94.3947	−	48.0965i	1.15116	−	0.586543i
$83$	49.3617	+	96.8777i	0.594719	+	1.16720i	0.970637	+	0.240549i	$0.0773273\pi$
$83$	49.3617	+	96.8777i	0.594719	+	1.16720i	−0.375918	+	0.926653i	$0.622673\pi$
$84$	−5.87806	−	8.09045i	−0.0699768	−	0.0963149i
$85$		0			0
$86$	36.2243	+	111.487i	0.421213	+	1.29636i
$87$	−35.3719	−	35.3719i	−0.406574	−	0.406574i
$88$	12.4160	−	52.0302i	0.141090	−	0.591253i
$89$		−	21.2775i		−	0.239073i	−0.992830	−	0.119537i	$-0.961859\pi$
$89$		−	21.2775i		−	0.239073i	0.992830	−	0.119537i	$-0.0381409\pi$
$90$		0			0
$91$	5.90665	+	4.29143i	0.0649082	+	0.0471586i
$92$	−11.5167	−	1.82407i	−0.125182	−	0.0198269i
$93$	78.0601	+	153.202i	0.839356	+	1.64733i
$94$	177.783	+	57.7653i	1.89131	+	0.614524i
$95$		0			0
$96$	−75.5989	−	54.9258i	−0.787488	−	0.572144i
$97$	9.55693	−	18.7565i	0.0985250	−	0.193366i	−0.836483	−	0.547993i	$-0.815392\pi$
$97$	9.55693	−	18.7565i	0.0985250	−	0.193366i	0.935008	+	0.354627i	$0.115392\pi$
$98$	−80.7170	+	80.7170i	−0.823643	+	0.823643i
$99$	0.813807	−	10.5248i	0.00822027	−	0.106311i
$100$		0			0
$101$	−46.8773	−	144.273i	−0.464132	−	1.42845i	−0.860071	−	0.510174i	$-0.829581\pi$
$101$	−46.8773	−	144.273i	−0.464132	−	1.42845i	0.395940	−	0.918276i	$-0.370419\pi$
$102$	13.3342	+	84.1891i	0.130728	+	0.825383i
$103$	13.2176	−	83.4524i	0.128326	−	0.810218i	−0.836623	−	0.547779i	$-0.815473\pi$
$103$	13.2176	−	83.4524i	0.128326	−	0.810218i	0.964949	−	0.262438i	$-0.0845267\pi$
$104$	21.4999	+	6.98575i	0.206730	+	0.0671707i
$105$		0			0
$106$	−54.8471	+	39.8488i	−0.517426	+	0.375932i
$107$	26.6535	+	168.284i	0.249098	+	1.57274i	0.722167	+	0.691718i	$0.243146\pi$
$107$	26.6535	+	168.284i	0.249098	+	1.57274i	−0.473069	+	0.881025i	$0.656854\pi$
$108$	45.6172	+	23.2431i	0.422382	+	0.215214i
$109$			144.976i			1.33005i	0.746820	+	0.665026i	$0.231580\pi$
$109$			144.976i			1.33005i	−0.746820	+	0.665026i	$0.768420\pi$
$110$		0			0
$111$	−78.2889			−0.705306
$112$	14.2597	−	27.9863i	0.127319	−	0.249878i
$113$	55.4609	−	8.78415i	0.490805	−	0.0777358i	0.0938734	−	0.995584i	$-0.470075\pi$
$113$	55.4609	−	8.78415i	0.490805	−	0.0777358i	0.396931	+	0.917848i	$0.370075\pi$
$114$	−18.9334	−	26.0596i	−0.166083	−	0.228593i
$115$		0			0
$116$	−9.88292	+	30.4165i	−0.0851976	+	0.262211i
$117$	4.40633	+	0.697894i	0.0376610	+	0.00596491i
$118$	−246.831	+	39.0942i	−2.09179	+	0.331307i
$119$	−16.4455	+	5.34347i	−0.138197	+	0.0449031i
$120$		0			0
$121$	−85.7941	−	85.3251i	−0.709042	−	0.705166i
$122$	48.9522	+	48.9522i	0.401248	+	0.401248i
$123$	121.438	+	61.8759i	0.987303	+	0.503056i
$124$	64.6145	−	88.9343i	0.521085	−	0.717212i
$125$		0			0
$126$	1.14249	−	3.51623i	0.00906741	−	0.0279066i
$127$	−99.8107	+	50.8561i	−0.785911	+	0.400441i	−0.800410	−	0.599453i	$-0.795385\pi$
$127$	−99.8107	+	50.8561i	−0.785911	+	0.400441i	0.0144990	+	0.999895i	$0.495385\pi$
$128$	21.3535	−	134.821i	0.166825	−	1.05329i
$129$	−88.6431	+	122.007i	−0.687155	+	0.945788i
$130$		0			0
$131$	203.816			1.55585			0.777923	−	0.628360i	$-0.216274\pi$
$131$	203.816			1.55585			0.777923	+	0.628360i	$0.216274\pi$
$132$	−64.6747	+	26.8930i	−0.489960	+	0.203735i
$133$	4.62063	−	4.62063i	0.0347416	−	0.0347416i
$134$	3.37716	−	1.09730i	0.0252027	−	0.00818884i
$135$		0			0
$136$	−43.3158	+	31.4707i	−0.318498	+	0.231403i
$137$	231.768	−	118.092i	1.69174	−	0.861984i	0.703204	−	0.710989i	$-0.251752\pi$
$137$	231.768	−	118.092i	1.69174	−	0.861984i	0.988535	−	0.150995i	$-0.0482478\pi$
$138$	−20.3115	−	39.8635i	−0.147185	−	0.288866i
$139$	−24.0521	−	33.1048i	−0.173037	−	0.238164i	0.713687	−	0.700465i	$-0.247024\pi$
$139$	−24.0521	−	33.1048i	−0.173037	−	0.238164i	−0.886723	+	0.462301i	$0.847024\pi$
$140$		0			0
$141$	74.3147	+	228.717i	0.527054	+	1.62211i
$142$	−129.176	−	129.176i	−0.909690	−	0.909690i
$143$	38.8393	−	33.2640i	0.271603	−	0.232616i
$144$		−	19.1928i		−	0.133283i
$145$		0			0
$146$	195.091	+	141.742i	1.33624	+	0.970835i
$147$	−145.047	−	22.9731i	−0.986712	−	0.156280i
$148$	22.7236	+	44.5975i	0.153538	+	0.301334i
$149$	−104.012	−	33.7955i	−0.698066	−	0.226816i	−0.0615785	−	0.998102i	$-0.519613\pi$
$149$	−104.012	−	33.7955i	−0.698066	−	0.226816i	−0.636488	+	0.771287i	$0.719613\pi$
$150$		0			0
$151$	−99.2813	−	72.1321i	−0.657492	−	0.477696i	0.208323	−	0.978060i	$-0.433199\pi$
$151$	−99.2813	−	72.1321i	−0.657492	−	0.477696i	−0.865815	+	0.500364i	$0.833199\pi$
$152$	9.18566	−	18.0279i	0.0604320	−	0.118604i
$153$	−7.47136	+	7.47136i	−0.0488324	+	0.0488324i
$154$	−22.1924	−	36.1035i	−0.144106	−	0.234438i
$155$		0			0
$156$	−9.14740	−	28.1528i	−0.0586372	−	0.180467i
$157$	−30.5733	−	193.032i	−0.194734	−	1.22950i	−0.870419	−	0.492312i	$-0.836152\pi$
$157$	−30.5733	−	193.032i	−0.194734	−	1.22950i	0.675685	−	0.737191i	$-0.263848\pi$
$158$	43.2853	−	273.293i	0.273958	−	1.72970i
$159$	−82.9488	−	26.9517i	−0.521691	−	0.169508i
$160$		0			0
$161$	7.34273	−	5.33481i	0.0456070	−	0.0331354i
$162$	34.0446	+	214.949i	0.210152	+	1.32685i
$163$	−280.098	−	142.717i	−1.71840	−	0.875566i	−0.979420	−	0.201834i	$-0.935310\pi$
$163$	−280.098	−	142.717i	−1.71840	−	0.875566i	−0.738975	−	0.673732i	$-0.764690\pi$
$164$		−	87.1372i		−	0.531324i
$165$		0			0
$166$	266.721			1.60675
$167$	−13.6296	+	26.7496i	−0.0816143	+	0.160177i	−0.928207	−	0.372064i	$-0.878650\pi$
$167$	−13.6296	+	26.7496i	−0.0816143	+	0.160177i	0.846593	+	0.532241i	$0.178650\pi$
$168$	23.8053	−	3.77038i	0.141698	−	0.0224428i
$169$	−86.6328	−	119.240i	−0.512620	−	0.705561i
$170$		0			0
$171$	1.23388	−	3.79749i	0.00721566	−	0.0222075i
$172$	95.2303	+	15.0830i	0.553664	+	0.0876918i
$173$	−126.603	+	20.0520i	−0.731811	+	0.115907i	−0.511209	−	0.859457i	$-0.670802\pi$
$173$	−126.603	+	20.0520i	−0.731811	+	0.115907i	−0.220602	+	0.975364i	$0.570802\pi$
$174$	−116.706	+	37.9202i	−0.670726	+	0.217932i
$175$		0			0
$176$	−167.482	−	142.647i	−0.951604	−	0.810494i
$177$	−227.339	−	227.339i	−1.28440	−	1.28440i
$178$	−46.5068	−	23.6964i	−0.261274	−	0.133126i
$179$	−68.7567	+	94.6354i	−0.384115	+	0.528690i	−0.956669	−	0.291178i	$-0.905953\pi$
$179$	−68.7567	+	94.6354i	−0.384115	+	0.528690i	0.572554	+	0.819867i	$0.305953\pi$
$180$		0			0
$181$	−18.9964	+	58.4650i	−0.104953	+	0.323011i	−0.989719	−	0.143023i	$-0.954318\pi$
$181$	−18.9964	+	58.4650i	−0.104953	+	0.323011i	0.884767	+	0.466034i	$0.154318\pi$
$182$	15.9580	−	8.13101i	0.0876813	−	0.0446759i
$183$	−13.9325	+	87.9661i	−0.0761336	+	0.480689i
$184$	16.5183	−	22.7355i	0.0897735	−	0.123563i
$185$		0			0
$186$	421.791			2.26769
$187$	9.66791	+	120.727i	0.0517001	+	0.645598i
$188$	108.719	−	108.719i	0.578294	−	0.578294i
$189$	−37.9005	+	12.3146i	−0.200532	+	0.0651567i
$190$		0			0
$191$	95.9178	−	69.6884i	0.502187	−	0.364860i	−0.307664	−	0.951495i	$-0.599547\pi$
$191$	95.9178	−	69.6884i	0.502187	−	0.364860i	0.809852	+	0.586634i	$0.199547\pi$
$192$	20.7044	−	10.5494i	0.107835	−	0.0549449i
$193$	19.9057	+	39.0672i	0.103139	+	0.202421i	0.936809	−	0.349842i	$-0.113765\pi$
$193$	19.9057	+	39.0672i	0.103139	+	0.202421i	−0.833670	+	0.552262i	$0.813765\pi$
$194$	−30.3532	−	41.7776i	−0.156460	−	0.215349i
$195$		0			0
$196$	29.0134	+	89.2942i	0.148028	+	0.455583i
$197$	−45.0392	−	45.0392i	−0.228626	−	0.228626i	0.583493	−	0.812118i	$-0.301686\pi$
$197$	−45.0392	−	45.0392i	−0.228626	−	0.228626i	−0.812118	+	0.583493i	$0.801686\pi$
$198$	−22.0980	−	13.5000i	−0.111606	−	0.0681820i
$199$		−	185.939i		−	0.934367i	−0.884160	−	0.467184i	$-0.845269\pi$
$199$		−	185.939i		−	0.934367i	0.884160	−	0.467184i	$-0.154731\pi$
$200$		0			0
$201$	3.69582	+	2.68517i	0.0183871	+	0.0133590i
$202$	−367.548	−	58.2139i	−1.81955	−	0.288188i
$203$	−11.3016	−	22.1806i	−0.0556729	−	0.109264i
$204$	66.6774	+	21.6648i	0.326850	+	0.106200i
$205$		0			0
$206$	−167.684	−	121.829i	−0.813999	−	0.591405i
$207$	2.51780	−	4.94145i	0.0121633	−	0.0238718i
$208$	65.7431	−	65.7431i	0.316072	−	0.316072i
$209$	−23.9675	−	38.9913i	−0.114677	−	0.186561i
$210$		0			0
$211$	−82.7053	−	254.541i	−0.391968	−	1.20635i	−0.931298	−	0.364259i	$-0.881322\pi$
$211$	−82.7053	−	254.541i	−0.391968	−	1.20635i	0.539329	−	0.842095i	$-0.318678\pi$
$212$	8.72299	+	55.0748i	0.0411462	+	0.259787i
$213$	36.7652	−	232.126i	0.172607	−	1.08980i
$214$	397.505	+	129.157i	1.85750	+	0.603538i
$215$		0			0
$216$	−99.8260	+	72.5278i	−0.462157	+	0.335777i
$217$	13.3855	+	84.5127i	0.0616843	+	0.389459i
$218$	316.877	+	161.457i	1.45356	+	0.740628i
$219$			310.233i			1.41659i
$220$		0			0
$221$	−51.1848			−0.231605
$222$	−87.1890	+	171.118i	−0.392743	+	0.770802i
$223$	−117.472	+	18.6057i	−0.526778	+	0.0834335i	−0.414159	−	0.910205i	$-0.635924\pi$
$223$	−117.472	+	18.6057i	−0.526778	+	0.0834335i	−0.112620	+	0.993638i	$0.535924\pi$
$224$	−27.3335	−	37.6214i	−0.122025	−	0.167953i
$225$		0			0
$226$	42.5661	−	131.005i	0.188346	−	0.579668i
$227$	−168.557	−	26.6968i	−0.742543	−	0.117607i	−0.226310	−	0.974055i	$-0.572666\pi$
$227$	−168.557	−	26.6968i	−0.742543	−	0.117607i	−0.516233	+	0.856448i	$0.672666\pi$
$228$	−26.1678	+	4.14458i	−0.114771	+	0.0181780i
$229$	121.738	−	39.5550i	0.531606	−	0.172729i	−0.0309000	−	0.999522i	$-0.509837\pi$
$229$	121.738	−	39.5550i	0.531606	−	0.172729i	0.562506	+	0.826793i	$0.309837\pi$
$230$		0			0
$231$	20.7949	−	50.3985i	0.0900211	−	0.218175i
$232$	−54.5037	−	54.5037i	−0.234930	−	0.234930i
$233$	237.093	+	120.805i	1.01757	+	0.518477i	0.881481	−	0.472220i	$-0.156547\pi$
$233$	237.093	+	120.805i	1.01757	+	0.518477i	0.136087	+	0.990697i	$0.456547\pi$
$234$	6.43266	−	8.85379i	0.0274900	−	0.0378367i
$235$		0			0
$236$	−63.5184	+	195.490i	−0.269146	+	0.828346i
$237$	317.173	−	161.608i	1.33828	−	0.681890i
$238$	−6.63571	+	41.8962i	−0.0278811	+	0.176035i
$239$	106.692	−	146.849i	0.446411	−	0.614432i	−0.525211	−	0.850972i	$-0.676013\pi$
$239$	106.692	−	146.849i	0.446411	−	0.614432i	0.971622	+	0.236540i	$0.0760135\pi$
$240$		0			0
$241$	114.219			0.473937			0.236968	−	0.971517i	$-0.423846\pi$
$241$	114.219			0.473937			0.236968	+	0.971517i	$0.423846\pi$
$242$	−282.044	+	92.4973i	−1.16547	+	0.382220i
$243$	−36.4923	+	36.4923i	−0.150174	+	0.150174i
$244$	54.1540	−	17.5957i	0.221943	−	0.0721135i
$245$		0			0
$246$	270.487	−	196.520i	1.09954	−	0.798863i
$247$	17.2344	−	8.78138i	0.0697750	−	0.0355522i
$248$	120.281	+	236.064i	0.485003	+	0.951872i
$249$	201.690	+	277.602i	0.809999	+	1.11487i
$250$		0			0
$251$	58.3065	+	179.449i	0.232297	+	0.714936i	0.997469	+	0.0711096i	$0.0226540\pi$
$251$	58.3065	+	179.449i	0.232297	+	0.714936i	−0.765172	+	0.643826i	$0.777346\pi$
$252$	−2.15027	−	2.15027i	−0.00853282	−	0.00853282i
$253$	−24.4076	−	58.6975i	−0.0964727	−	0.232006i
$254$			274.796i			1.08187i
$255$		0			0
$256$	−247.073	−	179.509i	−0.965129	−	0.701207i
$257$	−31.7365	−	5.02657i	−0.123488	−	0.0195587i	0.0943842	−	0.995536i	$-0.469912\pi$
$257$	−31.7365	−	5.02657i	−0.123488	−	0.0195587i	−0.217873	+	0.975977i	$0.569912\pi$
$258$	167.953	+	329.626i	0.650980	+	1.27762i
$259$	−37.0532	−	12.0393i	−0.143063	−	0.0464839i
$260$		0			0
$261$	−12.3062	−	8.94099i	−0.0471503	−	0.0342567i
$262$	226.986	−	445.485i	0.866358	−	1.70032i
$263$	265.068	−	265.068i	1.00786	−	1.00786i	0.00789398	−	0.999969i	$-0.497487\pi$
$263$	265.068	−	265.068i	1.00786	−	1.00786i	0.999969	−	0.00789398i	$-0.00251276\pi$
$264$	13.0142	−	168.310i	0.0492962	−	0.637537i
$265$		0			0
$266$	−4.95351	−	15.2453i	−0.0186222	−	0.0573132i
$267$	−10.5045	−	66.3228i	−0.0393427	−	0.248400i
$268$	0.456893	−	2.88471i	0.00170482	−	0.0107638i
$269$	99.1773	+	32.2247i	0.368689	+	0.119794i	0.487501	−	0.873122i	$-0.337909\pi$
$269$	99.1773	+	32.2247i	0.368689	+	0.119794i	−0.118812	+	0.992917i	$0.537909\pi$
$270$		0			0
$271$	−137.306	+	99.7586i	−0.506664	+	0.368113i	−0.811557	−	0.584274i	$-0.801379\pi$
$271$	−137.306	+	99.7586i	−0.506664	+	0.368113i	0.304892	+	0.952387i	$0.401379\pi$
$272$	34.4473	+	217.492i	0.126644	+	0.799601i
$273$	20.5299	+	10.4605i	0.0752010	+	0.0383168i
$274$		−	638.098i		−	2.32882i
$275$		0			0
$276$	−36.7986			−0.133328
$277$	15.4766	−	30.3745i	0.0558722	−	0.109655i	−0.861382	−	0.507958i	$-0.830401\pi$
$277$	15.4766	−	30.3745i	0.0558722	−	0.109655i	0.917254	+	0.398302i	$0.130401\pi$
$278$	−99.1444	+	15.7029i	−0.356635	+	0.0564854i
$279$	30.7323	+	42.2993i	0.110151	+	0.151610i
$280$		0			0
$281$	−15.6934	+	48.2993i	−0.0558484	+	0.171884i	−0.975090	−	0.221811i	$-0.928803\pi$
$281$	−15.6934	+	48.2993i	−0.0558484	+	0.171884i	0.919241	+	0.393695i	$0.128803\pi$
$282$	582.675	+	92.2867i	2.06622	+	0.327258i
$283$	−221.248	+	35.0423i	−0.781797	+	0.123824i	−0.534560	−	0.845131i	$-0.679523\pi$
$283$	−221.248	+	35.0423i	−0.781797	+	0.123824i	−0.247237	+	0.968955i	$0.579523\pi$
$284$	−142.903	+	46.4319i	−0.503178	+	0.163492i
$285$		0			0
$286$	−29.4514	−	121.937i	−0.102977	−	0.426355i
$287$	47.9600	+	47.9600i	0.167108	+	0.167108i
$288$	−25.3182	−	12.9002i	−0.0879103	−	0.0447925i
$289$	−98.6147	+	135.731i	−0.341227	+	0.469659i
$290$		0			0
$291$	20.5294	−	63.1830i	0.0705477	−	0.217124i
$292$	176.725	−	90.0457i	0.605222	−	0.308376i
$293$	−76.4836	+	482.899i	−0.261036	+	1.64812i	0.413959	+	0.910296i	$0.364146\pi$
$293$	−76.4836	+	482.899i	−0.261036	+	1.64812i	−0.674995	+	0.737822i	$0.735854\pi$
$294$	−211.749	+	291.447i	−0.720234	+	0.991317i
$295$		0			0
$296$	−120.633			−0.407545
$297$	22.2808	+	278.228i	0.0750194	+	0.936796i
$298$	−189.704	+	189.704i	−0.636590	+	0.636590i
$299$	25.5509	−	8.30199i	0.0854545	−	0.0277659i
$300$		0			0
$301$	−60.7160	+	44.1127i	−0.201714	+	0.146554i
$302$	−268.228	+	136.669i	−0.888174	+	0.452547i
$303$	−217.345	−	426.563i	−0.717309	−	1.40780i
$304$	−48.9121	−	67.3217i	−0.160895	−	0.221453i
$305$		0			0
$306$	8.00961	+	24.6511i	0.0261752	+	0.0805590i
$307$	237.129	+	237.129i	0.772408	+	0.772408i	0.978527	−	0.206119i	$-0.0660833\pi$
$307$	237.129	+	237.129i	0.772408	+	0.772408i	−0.206119	+	0.978527i	$0.566083\pi$
$308$	−34.7454	+	2.78244i	−0.112810	+	0.00903391i
$309$		−	266.650i		−	0.862944i
$310$		0			0
$311$	−369.314	−	268.322i	−1.18751	−	0.862773i	−0.194507	−	0.980901i	$-0.562311\pi$
$311$	−369.314	−	268.322i	−1.18751	−	0.862773i	−0.992998	+	0.118128i	$0.962311\pi$
$312$	70.4649	+	11.1605i	0.225849	+	0.0357710i
$313$	−172.969	−	339.470i	−0.552616	−	1.08457i	−0.983287	−	0.182061i	$-0.941723\pi$
$313$	−172.969	−	339.470i	−0.552616	−	1.08457i	0.430671	−	0.902509i	$-0.358277\pi$
$314$	−455.963	−	148.152i	−1.45211	−	0.471820i
$315$		0			0
$316$	−184.121	−	133.771i	−0.582660	−	0.423327i
$317$	163.756	−	321.390i	0.516582	−	1.01385i	−0.474457	−	0.880278i	$-0.657356\pi$
$317$	163.756	−	321.390i	0.516582	−	1.01385i	0.991039	−	0.133571i	$-0.0426443\pi$
$318$	−151.288	+	151.288i	−0.475747	+	0.475747i
$319$	−169.485	+	40.9356i	−0.531302	+	0.128325i
$320$		0			0
$321$	166.160	+	511.388i	0.517632	+	1.59311i
$322$	−3.48295	−	21.9905i	−0.0108166	−	0.0682933i
$323$	−7.16648	+	45.2474i	−0.0221873	+	0.140085i
$324$	170.239	+	55.3140i	0.525429	+	0.170722i
$325$		0			0
$326$	−623.881	+	453.276i	−1.91375	+	1.39042i
$327$	71.5731	+	451.895i	0.218878	+	1.38194i
$328$	187.121	+	95.3429i	0.570491	+	0.290680i
$329$			119.677i			0.363761i
$330$		0			0
$331$	−36.6252			−0.110650			−0.0553250	−	0.998468i	$-0.517620\pi$
$331$	−36.6252			−0.110650			−0.0553250	+	0.998468i	$0.517620\pi$
$332$	99.5958	−	195.468i	0.299987	−	0.588758i
$333$	−23.5133	+	3.72414i	−0.0706105	+	0.0111836i
$334$	43.2882	+	59.5810i	0.129605	+	0.178386i
$335$		0			0
$336$	30.6316	−	94.2743i	0.0911654	−	0.280578i
$337$	503.522	+	79.7500i	1.49413	+	0.236647i	0.849394	−	0.527759i	$-0.176967\pi$
$337$	503.522	+	79.7500i	1.49413	+	0.236647i	0.644736	+	0.764406i	$0.276967\pi$
$338$	−357.107	+	56.5602i	−1.05653	+	0.167338i
$339$	168.537	−	54.7611i	0.497160	−	0.161537i
$340$		0			0
$341$	597.528	+	46.2026i	1.75228	+	0.135491i
$342$	−6.92611	−	6.92611i	−0.0202518	−	0.0202518i
$343$	−133.684	−	68.1152i	−0.389748	−	0.198587i
$344$	−136.588	+	187.997i	−0.397057	+	0.546503i
$345$		0			0
$346$	−97.1676	+	299.051i	−0.280831	+	0.864310i
$347$	−51.9560	+	26.4729i	−0.149729	+	0.0762908i	−0.527250	−	0.849710i	$-0.676777\pi$
$347$	−51.9560	+	26.4729i	−0.149729	+	0.0762908i	0.377521	+	0.926001i	$0.376777\pi$
$348$	−15.7891	+	99.6884i	−0.0453710	+	0.286461i
$349$	260.442	−	358.468i	0.746253	−	1.02713i	−0.251982	−	0.967732i	$-0.581082\pi$
$349$	260.442	−	358.468i	0.746253	−	1.02713i	0.998234	−	0.0593967i	$-0.0189177\pi$
$350$		0			0
$351$	−117.961			−0.336071
$352$	−300.744	+	125.055i	−0.854386	+	0.355271i
$353$	124.571	−	124.571i	0.352892	−	0.352892i	−0.508293	−	0.861184i	$-0.669723\pi$
$353$	124.571	−	124.571i	0.352892	−	0.352892i	0.861184	+	0.508293i	$0.169723\pi$
$354$	−750.082	+	243.716i	−2.11888	+	0.688465i
$355$		0			0
$356$	−34.7320	+	25.2343i	−0.0975618	+	0.0708828i
$357$	−48.6232	+	24.7748i	−0.136200	+	0.0693971i
$358$	130.274	+	255.677i	0.363893	+	0.714181i
$359$	290.091	+	399.276i	0.808053	+	1.11219i	0.991621	+	0.129183i	$0.0412353\pi$
$359$	290.091	+	399.276i	0.808053	+	1.11219i	−0.183568	+	0.983007i	$0.558765\pi$
$360$		0			0
$361$	106.205	+	326.867i	0.294198	+	0.905448i
$362$	106.632	+	106.632i	0.294565	+	0.294565i
$363$	−309.548	−	223.606i	−0.852749	−	0.615994i
$364$		−	14.7311i		−	0.0404700i
$365$		0			0
$366$	176.753	+	128.419i	0.482932	+	0.350871i
$367$	−92.1861	−	14.6008i	−0.251188	−	0.0397843i	0.0295704	−	0.999563i	$-0.490586\pi$
$367$	−92.1861	−	14.6008i	−0.251188	−	0.0397843i	−0.280759	+	0.959778i	$0.590586\pi$
$368$	−52.4721	−	102.982i	−0.142587	−	0.279843i
$369$	39.4162	+	12.8071i	0.106819	+	0.0347076i
$370$		0			0
$371$	−35.1141	−	25.5119i	−0.0946470	−	0.0687651i
$372$	157.500	−	309.111i	0.423387	−	0.830944i
$373$	278.202	−	278.202i	0.745850	−	0.745850i	−0.227847	−	0.973697i	$-0.573169\pi$
$373$	278.202	−	278.202i	0.745850	−	0.745850i	0.973697	+	0.227847i	$0.0731687\pi$
$374$	274.642	+	113.320i	0.734338	+	0.302994i
$375$		0			0
$376$	114.510	+	352.424i	0.304547	+	0.937298i
$377$	−11.5272	−	72.7802i	−0.0305763	−	0.193051i
$378$	−15.2927	+	96.5545i	−0.0404570	+	0.255435i
$379$	−267.869	−	87.0358i	−0.706777	−	0.229646i	−0.0664964	−	0.997787i	$-0.521182\pi$
$379$	−267.869	−	87.0358i	−0.706777	−	0.229646i	−0.640281	+	0.768141i	$0.721182\pi$
$380$		0			0
$381$	−286.006	+	207.796i	−0.750673	+	0.545396i
$382$	−45.4976	−	287.260i	−0.119104	−	0.751991i
$383$	206.078	+	105.002i	0.538062	+	0.274156i	0.701832	−	0.712342i	$-0.252366\pi$
$383$	206.078	+	105.002i	0.538062	+	0.274156i	−0.163770	+	0.986499i	$0.552366\pi$
$384$		−	430.784i		−	1.12183i
$385$		0			0
$386$	107.559			0.278650
$387$	−20.8193	+	40.8602i	−0.0537966	+	0.105582i
$388$	−41.9510	+	6.64439i	−0.108121	+	0.0171247i
$389$	238.146	+	327.780i	0.612200	+	0.842621i	0.996756	−	0.0804803i	$-0.0256454\pi$
$389$	238.146	+	327.780i	0.612200	+	0.842621i	−0.384556	+	0.923102i	$0.625645\pi$
$390$		0			0
$391$	−19.6625	+	60.5151i	−0.0502879	+	0.154770i
$392$	−223.499	−	35.3987i	−0.570149	−	0.0903028i
$393$	635.301	−	100.622i	1.61654	−	0.256035i
$394$	−148.603	+	48.2840i	−0.377164	+	0.122548i
$395$		0			0
$396$	−18.1451	+	11.1536i	−0.0458210	+	0.0281656i
$397$	195.457	+	195.457i	0.492335	+	0.492335i	0.909041	−	0.416706i	$-0.136816\pi$
$397$	195.457	+	195.457i	0.492335	+	0.492335i	−0.416706	+	0.909041i	$0.636816\pi$
$398$	−406.411	−	207.077i	−1.02113	−	0.520294i
$399$	12.1215	−	16.6838i	0.0303797	−	0.0418141i
$400$		0			0
$401$	−83.1565	+	255.929i	−0.207373	+	0.638228i	0.792235	+	0.610216i	$0.208918\pi$
$401$	−83.1565	+	255.929i	−0.207373	+	0.638228i	−0.999608	+	0.0280116i	$0.991082\pi$
$402$	9.98500	−	5.08761i	0.0248383	−	0.0126557i
$403$	−39.6218	+	250.162i	−0.0983172	+	0.620750i
$404$	−179.908	+	247.622i	−0.445316	+	0.612925i
$405$		0			0
$406$	−61.0671			−0.150412
$407$	−142.260	+	232.863i	−0.349534	+	0.572146i
$408$	−119.480	+	119.480i	−0.292843	+	0.292843i
$409$	646.708	−	210.128i	1.58119	−	0.513761i	0.618830	−	0.785525i	$-0.287607\pi$
$409$	646.708	−	210.128i	1.58119	−	0.513761i	0.962364	+	0.271764i	$0.0876069\pi$
$410$		0			0
$411$	664.129	−	482.518i	1.61589	−	1.17401i
$412$	−151.898	+	77.3957i	−0.368684	+	0.187854i
$413$	−72.6364	−	142.557i	−0.175875	−	0.345174i
$414$	−7.99663	−	11.0064i	−0.0193155	−	0.0265855i
$415$		0			0
$416$	−42.5363	−	130.913i	−0.102251	−	0.314695i
$417$	−91.3148	−	91.3148i	−0.218980	−	0.218980i
$418$	−111.916	+	8.96236i	−0.267742	+	0.0214410i
$419$			451.895i			1.07851i	0.842143	+	0.539254i	$0.181294\pi$
$419$			451.895i			1.07851i	−0.842143	+	0.539254i	$0.818706\pi$
$420$		0			0
$421$	−299.721	−	217.760i	−0.711926	−	0.517245i	0.171868	−	0.985120i	$-0.445020\pi$
$421$	−299.721	−	217.760i	−0.711926	−	0.517245i	−0.883795	+	0.467875i	$0.845020\pi$
$422$	−648.463	−	102.706i	−1.53664	−	0.243380i
$423$	33.1996	+	65.1578i	0.0784860	+	0.154037i
$424$	−127.814	−	41.5292i	−0.301447	−	0.0979462i
$425$		0			0
$426$	−466.419	−	338.874i	−1.09488	−	0.795478i
$427$	−20.1215	+	39.4908i	−0.0471231	+	0.0924842i
$428$	243.085	−	243.085i	0.567955	−	0.567955i
$429$	104.641	−	122.860i	0.243919	−	0.286386i
$430$		0			0
$431$	−195.029	−	600.237i	−0.452503	−	1.39266i	−0.874041	−	0.485851i	$-0.838510\pi$
$431$	−195.029	−	600.237i	−0.452503	−	1.39266i	0.421538	−	0.906811i	$-0.361490\pi$
$432$	79.3876	+	501.233i	0.183768	+	1.16026i
$433$	−85.1992	+	537.926i	−0.196765	+	1.24232i	0.669528	+	0.742787i	$0.266497\pi$
$433$	−85.1992	+	537.926i	−0.196765	+	1.24232i	−0.866293	+	0.499537i	$0.833503\pi$
$434$	199.629	+	64.8632i	0.459974	+	0.149454i
$435$		0			0
$436$	236.649	−	171.935i	0.542772	−	0.394347i
$437$	−3.76154	−	23.7494i	−0.00860763	−	0.0543464i
$438$	678.083	+	345.500i	1.54813	+	0.788814i
$439$		−	495.324i		−	1.12830i	−0.825672	−	0.564150i	$-0.809204\pi$
$439$		−	495.324i		−	1.12830i	0.825672	−	0.564150i	$-0.190796\pi$
$440$		0			0
$441$	−44.6561			−0.101261
$442$	−57.0036	+	111.876i	−0.128967	+	0.253113i
$443$	−334.553	+	52.9881i	−0.755200	+	0.119612i	−0.522151	−	0.852853i	$-0.674870\pi$
$443$	−334.553	+	52.9881i	−0.755200	+	0.119612i	−0.233049	+	0.972465i	$0.574870\pi$
$444$	92.8475	+	127.794i	0.209116	+	0.287824i
$445$		0			0
$446$	−90.1591	+	277.481i	−0.202150	+	0.622155i
$447$	−340.894	−	53.9922i	−0.762625	−	0.120788i
$448$	11.4214	−	1.80898i	0.0254943	−	0.00403790i
$449$	666.170	−	216.452i	1.48368	−	0.482075i	0.548467	−	0.836173i	$-0.315212\pi$
$449$	666.170	−	216.452i	1.48368	−	0.482075i	0.935209	+	0.354097i	$0.115212\pi$
$450$		0			0
$451$	404.712	−	248.771i	0.897365	−	0.551599i
$452$	−80.1131	−	80.1131i	−0.177241	−	0.177241i
$453$	−345.074	−	175.824i	−0.761753	−	0.388133i
$454$	−246.071	+	338.688i	−0.542007	+	0.746008i
$455$		0			0
$456$	19.7319	−	60.7284i	0.0432716	−	0.133176i
$457$	136.674	−	69.6387i	0.299067	−	0.152382i	−0.298018	−	0.954560i	$-0.596325\pi$
$457$	136.674	−	69.6387i	0.299067	−	0.152382i	0.597085	+	0.802178i	$0.296325\pi$
$458$	49.1208	−	310.137i	0.107251	−	0.677154i
$459$	164.216	−	226.024i	0.357768	−	0.492426i
$460$		0			0
$461$	27.1012			0.0587879			0.0293940	−	0.999568i	$-0.490642\pi$
$461$	27.1012			0.0587879			0.0293940	+	0.999568i	$0.490642\pi$
$462$	−86.9984	−	101.580i	−0.188308	−	0.219870i
$463$	422.021	−	422.021i	0.911492	−	0.911492i	−0.0848979	−	0.996390i	$-0.527056\pi$
$463$	422.021	−	422.021i	0.911492	−	0.911492i	0.996390	+	0.0848979i	$0.0270564\pi$
$464$	−301.496	+	97.9619i	−0.649775	+	0.211125i
$465$		0			0
$466$	528.093	−	383.682i	1.13325	−	0.823352i
$467$	124.580	−	63.4768i	0.266767	−	0.135925i	−0.315491	−	0.948929i	$-0.602169\pi$
$467$	124.580	−	63.4768i	0.266767	−	0.135925i	0.582258	+	0.813004i	$0.302169\pi$
$468$	−4.08654	−	8.02028i	−0.00873191	−	0.0171373i
$469$	1.33626	+	1.83920i	0.00284917	+	0.00392154i
$470$		0			0
$471$	−190.596	−	586.594i	−0.404663	−	1.24542i
$472$	−350.300	−	350.300i	−0.742161	−	0.742161i
$473$	201.823	+	485.361i	0.426687	+	1.02613i
$474$		−	873.233i		−	1.84226i
$475$		0			0
$476$	28.2260	+	20.5074i	0.0592984	+	0.0430828i
$477$	−26.1949	−	4.14887i	−0.0549160	−	0.00869784i
$478$	−202.151	−	396.743i	−0.422909	−	0.830007i
$479$	250.078	+	81.2552i	0.522083	+	0.169635i	0.558190	−	0.829713i	$-0.311496\pi$
$479$	250.078	+	81.2552i	0.522083	+	0.169635i	−0.0361074	+	0.999348i	$0.511496\pi$
$480$		0			0
$481$	−93.2991	−	67.7858i	−0.193969	−	0.140927i
$482$	127.203	−	249.651i	0.263907	−	0.517947i
$483$	20.2538	−	20.2538i	0.0419334	−	0.0419334i
$484$	−37.5306	+	241.237i	−0.0775426	+	0.498423i
$485$		0			0
$486$	39.1213	+	120.403i	0.0804964	+	0.247742i
$487$	−118.812	−	750.146i	−0.243966	−	1.54034i	−0.740340	−	0.672233i	$-0.765335\pi$
$487$	−118.812	−	750.146i	−0.243966	−	1.54034i	0.496374	−	0.868109i	$-0.334665\pi$
$488$	−21.4682	+	135.545i	−0.0439921	+	0.277755i
$489$	−943.536	−	306.573i	−1.92952	−	0.626939i
$490$		0			0
$491$	433.696	−	315.098i	0.883290	−	0.641748i	−0.0508295	−	0.998707i	$-0.516187\pi$
$491$	433.696	−	315.098i	0.883290	−	0.641748i	0.934120	+	0.356959i	$0.116187\pi$
$492$	−43.0188	−	271.610i	−0.0874366	−	0.552053i
$493$	155.500	+	79.2314i	0.315417	+	0.160713i
$494$		−	47.4494i		−	0.0960514i
$495$		0			0
$496$	1089.64			2.19686
$497$	53.0971	−	104.209i	0.106835	−	0.209676i
$498$	831.380	−	131.678i	1.66944	−	0.264413i
$499$	33.5801	+	46.2190i	0.0672947	+	0.0926233i	0.841338	−	0.540510i	$-0.181769\pi$
$499$	33.5801	+	46.2190i	0.0672947	+	0.0926233i	−0.774043	+	0.633133i	$0.781769\pi$
$500$		0			0
$501$	−29.2779	+	90.1082i	−0.0584390	+	0.179857i
$502$	457.161	+	72.4071i	0.910678	+	0.144237i
$503$	372.309	−	58.9680i	0.740177	−	0.117233i	0.225051	−	0.974347i	$-0.427745\pi$
$503$	372.309	−	58.9680i	0.740177	−	0.117233i	0.515126	+	0.857114i	$0.327745\pi$
$504$	6.97032	−	2.26479i	0.0138300	−	0.00449364i
$505$		0			0
$506$	−155.479	−	12.0221i	−0.307270	−	0.0237590i
$507$	−328.905	−	328.905i	−0.648729	−	0.648729i
$508$	201.385	+	102.611i	0.396428	+	0.201990i
$509$	453.233	−	623.822i	0.890438	−	1.22558i	−0.0829808	−	0.996551i	$-0.526444\pi$
$509$	453.233	−	623.822i	0.890438	−	1.22558i	0.973419	−	0.229032i	$-0.0735560\pi$
$510$		0			0
$511$	−47.7078	+	146.829i	−0.0933616	+	0.287337i
$512$	−181.023	+	92.2357i	−0.353560	+	0.180148i
$513$	−16.5160	+	104.278i	−0.0321948	+	0.203270i
$514$	−46.3311	+	63.7693i	−0.0901384	+	0.124065i
$515$		0			0
$516$	304.283			0.589695
$517$	815.336	+	194.563i	1.57705	+	0.376332i
$518$	−67.5802	+	67.5802i	−0.130464	+	0.130464i
$519$	−384.728	+	125.006i	−0.741286	+	0.240859i
$520$		0			0
$521$	449.127	−	326.310i	0.862047	−	0.626314i	−0.0663939	−	0.997793i	$-0.521149\pi$
$521$	449.127	−	326.310i	0.862047	−	0.626314i	0.928441	+	0.371480i	$0.121149\pi$
$522$	−33.2478	+	16.9406i	−0.0636930	+	0.0324532i
$523$	−238.116	−	467.329i	−0.455289	−	0.893555i	−0.998542	−	0.0539855i	$-0.982808\pi$
$523$	−238.116	−	467.329i	−0.455289	−	0.893555i	0.543253	−	0.839569i	$-0.317192\pi$
$524$	−241.717	−	332.695i	−0.461292	−	0.634915i
$525$		0			0
$526$	−284.164	−	874.567i	−0.540236	−	1.66267i
$527$	−424.174	−	424.174i	−0.804885	−	0.804885i
$528$	−592.472	−	361.951i	−1.12211	−	0.685514i
$529$			495.602i			0.936866i
$530$		0			0
$531$	−79.0932	−	57.4646i	−0.148951	−	0.108220i
$532$	−13.0223	−	2.06253i	−0.0244780	−	0.00387693i
$533$	91.1467	+	178.885i	0.171007	+	0.335620i
$534$	−156.662	−	50.9026i	−0.293375	−	0.0953232i
$535$		0			0
$536$	5.69478	+	4.13750i	0.0106246	+	0.00771922i
$537$	−167.597	+	328.927i	−0.312098	+	0.612527i
$538$	180.886	−	180.886i	0.336220	−	0.336220i
$539$	−331.898	+	389.683i	−0.615767	+	0.722974i
$540$		0			0
$541$	256.495	+	789.409i	0.474112	+	1.45917i	0.847151	+	0.531351i	$0.178316\pi$
$541$	256.495	+	789.409i	0.474112	+	1.45917i	−0.373039	+	0.927815i	$0.621684\pi$
$542$	65.1296	+	411.212i	0.120165	+	0.758694i
$543$	−30.3490	+	191.616i	−0.0558914	+	0.352884i
$544$	310.057	+	100.744i	0.569957	+	0.185190i
$545$		0			0
$546$	45.7275	−	33.2230i	0.0837500	−	0.0608479i
$547$	87.5917	+	553.032i	0.160131	+	1.01103i	0.928584	+	0.371122i	$0.121027\pi$
$547$	87.5917	+	553.032i	0.160131	+	1.01103i	−0.768453	+	0.639906i	$0.778973\pi$
$548$	−467.633	−	238.271i	−0.853344	−	0.434801i
$549$			27.0825i			0.0493306i
$550$		0			0
$551$	−65.9517			−0.119695
$552$	40.2640	−	79.0225i	0.0729419	−	0.143157i
$553$	174.967	−	27.7120i	0.316395	−	0.0501121i
$554$	−49.1543	−	67.6551i	−0.0887262	−	0.122121i
$555$		0			0
$556$	−25.5134	+	78.5220i	−0.0458873	+	0.141227i
$557$	−858.051	−	135.902i	−1.54049	−	0.243989i	−0.672320	−	0.740261i	$-0.734702\pi$
$557$	−858.051	−	135.902i	−1.54049	−	0.243989i	−0.868167	+	0.496272i	$0.834702\pi$
$558$	126.681	−	20.0642i	0.227026	−	0.0359574i
$559$	−211.277	+	68.6480i	−0.377955	+	0.122805i
$560$		0			0
$561$	89.7369	+	371.537i	0.159959	+	0.662277i
$562$	88.0915	+	88.0915i	0.156746	+	0.156746i
$563$	−816.464	−	416.009i	−1.45020	−	0.738915i	−0.461267	−	0.887262i	$-0.652605\pi$
$563$	−816.464	−	416.009i	−1.45020	−	0.738915i	−0.988935	+	0.148347i	$0.952605\pi$
$564$	285.208	−	392.555i	0.505688	−	0.696020i
$565$		0			0
$566$	−169.808	+	522.614i	−0.300013	+	0.923346i
$567$	−124.144	+	63.2543i	−0.218948	+	0.111560i
$568$	56.6506	−	357.678i	0.0997369	−	0.629714i
$569$	−229.953	+	316.504i	−0.404136	+	0.556245i	−0.961776	−	0.273838i	$-0.911707\pi$
$569$	−229.953	+	316.504i	−0.404136	+	0.556245i	0.557640	+	0.830083i	$0.311707\pi$
$570$		0			0
$571$	−768.261			−1.34547			−0.672733	−	0.739886i	$-0.734880\pi$
$571$	−768.261			−1.34547			−0.672733	+	0.739886i	$0.734880\pi$
$572$	−100.360	−	23.9488i	−0.175454	−	0.0418686i
$573$	264.575	−	264.575i	0.461736	−	0.461736i
$574$	158.239	−	51.4151i	0.275678	−	0.0895734i
$575$		0			0
$576$	5.71653	−	4.15330i	0.00992453	−	0.00721059i
$577$	224.247	−	114.260i	0.388643	−	0.198023i	−0.248741	−	0.968570i	$-0.580017\pi$
$577$	224.247	−	114.260i	0.388643	−	0.198023i	0.637384	+	0.770547i	$0.280017\pi$
$578$	186.846	+	366.706i	0.323263	+	0.634439i
$579$	81.3340	+	111.947i	0.140473	+	0.193345i
$580$		0			0
$581$	52.7676	+	162.402i	0.0908219	+	0.279521i
$582$	−115.237	−	115.237i	−0.198002	−	0.198002i
$583$	−230.893	+	197.749i	−0.396043	+	0.339193i
$584$			478.029i			0.818543i
$585$		0			0
$586$	970.304	+	704.967i	1.65581	+	1.20302i
$587$	450.651	+	71.3761i	0.767719	+	0.121595i	0.527996	−	0.849247i	$-0.322944\pi$
$587$	450.651	+	71.3761i	0.767719	+	0.121595i	0.239722	+	0.970841i	$0.422944\pi$
$588$	134.520	+	264.010i	0.228775	+	0.448996i
$589$	215.596	+	70.0514i	0.366038	+	0.118933i
$590$		0			0
$591$	−162.624	−	118.154i	−0.275168	−	0.199921i
$592$	−225.241	+	442.061i	−0.380475	+	0.746725i
$593$	237.348	−	237.348i	0.400250	−	0.400250i	−0.478071	−	0.878321i	$-0.658664\pi$
$593$	237.348	−	237.348i	0.400250	−	0.400250i	0.878321	+	0.478071i	$0.158664\pi$
$594$	632.944	+	261.158i	1.06556	+	0.439660i
$595$		0			0
$596$	68.1884	+	209.862i	0.114410	+	0.352118i
$597$	−91.7963	−	579.579i	−0.153763	−	0.970820i
$598$	10.3097	−	65.0930i	0.0172403	−	0.108851i
$599$	−984.287	−	319.814i	−1.64322	−	0.533913i	−0.665962	−	0.745985i	$-0.731979\pi$
$599$	−984.287	−	319.814i	−1.64322	−	0.533913i	−0.977254	+	0.212072i	$0.931979\pi$
$600$		0			0
$601$	45.7081	−	33.2089i	0.0760534	−	0.0552560i	−0.549109	−	0.835751i	$-0.685033\pi$
$601$	45.7081	−	33.2089i	0.0760534	−	0.0552560i	0.625162	+	0.780495i	$0.285033\pi$
$602$	28.8000	+	181.836i	0.0478405	+	0.302053i
$603$	1.23773	+	0.630656i	0.00205262	+	0.00104586i
$604$			247.606i			0.409943i
$605$		0			0
$606$	−1174.40			−1.93796
$607$	−369.707	+	725.590i	−0.609072	+	1.19537i	0.356270	+	0.934383i	$0.384048\pi$
$607$	−369.707	+	725.590i	−0.609072	+	1.19537i	−0.965342	+	0.260988i	$0.915952\pi$
$608$	−121.683	+	19.2727i	−0.200137	+	0.0316985i
$609$	−46.1779	−	63.5584i	−0.0758257	−	0.104365i
$610$		0			0
$611$	−109.470	+	336.913i	−0.179165	+	0.551413i
$612$	21.0565	+	3.33502i	0.0344060	+	0.00544938i
$613$	−802.492	+	127.102i	−1.30912	+	0.207345i	−0.771710	−	0.635975i	$-0.780598\pi$
$613$	−802.492	+	127.102i	−1.30912	+	0.207345i	−0.537412	+	0.843320i	$0.680598\pi$
$614$	782.386	−	254.213i	1.27424	−	0.414027i
$615$		0			0
$616$	32.0423	−	77.6578i	0.0520167	−	0.126068i
$617$	214.134	+	214.134i	0.347057	+	0.347057i	0.859012	−	0.511955i	$-0.171079\pi$
$617$	214.134	+	214.134i	0.347057	+	0.347057i	−0.511955	+	0.859012i	$0.671079\pi$
$618$	−582.823	−	296.963i	−0.943079	−	0.480523i
$619$	−589.455	+	811.316i	−0.952270	+	1.31069i	−0.00175860	+	0.999998i	$0.500560\pi$
$619$	−589.455	+	811.316i	−0.952270	+	1.31069i	−0.950512	+	0.310689i	$0.899440\pi$
$620$		0			0
$621$	−45.3145	+	139.464i	−0.0729703	+	0.224579i
$622$	−997.777	+	508.393i	−1.60414	+	0.817352i
$623$	5.22751	−	33.0052i	0.00839087	−	0.0529778i
$624$	172.467	−	237.380i	0.276389	−	0.380417i
$625$		0			0
$626$	−934.621			−1.49300
$627$	−93.9571	−	109.705i	−0.149852	−	0.174968i
$628$	−278.834	+	278.834i	−0.444003	+	0.444003i
$629$	259.767	−	84.4034i	0.412984	−	0.134187i
$630$		0			0
$631$	−710.682	+	516.341i	−1.12628	+	0.818289i	−0.985149	−	0.171702i	$-0.945073\pi$
$631$	−710.682	+	516.341i	−1.12628	+	0.818289i	−0.141130	+	0.989991i	$0.545073\pi$
$632$	488.724	−	249.017i	0.773297	−	0.394015i
$633$	−383.460	−	752.582i	−0.605782	−	1.18891i
$634$	−520.097	−	715.853i	−0.820343	−	1.12911i
$635$		0			0
$636$	54.3798	+	167.364i	0.0855028	+	0.263151i
$637$	−152.965	−	152.965i	−0.240134	−	0.240134i
$638$	−99.2789	+	416.038i	−0.155610	+	0.652096i
$639$		−	71.4658i		−	0.111840i
$640$		0			0
$641$	398.231	+	289.331i	0.621265	+	0.451375i	0.853363	−	0.521317i	$-0.174559\pi$
$641$	398.231	+	289.331i	0.621265	+	0.451375i	−0.232098	+	0.972692i	$0.574559\pi$
$642$	1302.80	+	206.343i	2.02929	+	0.321407i
$643$	162.623	+	319.165i	0.252913	+	0.496369i	0.982200	−	0.187839i	$-0.0601482\pi$
$643$	162.623	+	319.165i	0.252913	+	0.496369i	−0.729287	+	0.684208i	$0.760148\pi$
$644$	−17.4164	−	5.65892i	−0.0270440	−	0.00878714i
$645$		0			0
$646$	90.9171	+	66.0551i	0.140739	+	0.102253i
$647$	10.0746	−	19.7726i	0.0155713	−	0.0305604i	−0.883090	−	0.469204i	$-0.844541\pi$
$647$	10.0746	−	19.7726i	0.0155713	−	0.0305604i	0.898661	+	0.438644i	$0.144541\pi$
$648$	−305.053	+	305.053i	−0.470762	+	0.470762i
$649$	−1089.30	+	263.097i	−1.67843	+	0.405388i
$650$		0			0
$651$	83.4462	+	256.821i	0.128182	+	0.394502i
$652$	99.2233	+	626.471i	0.152183	+	0.960845i
$653$	−99.8375	+	630.349i	−0.152891	+	0.965313i	0.785280	+	0.619140i	$0.212519\pi$
$653$	−99.8375	+	630.349i	−0.152891	+	0.965313i	−0.938171	+	0.346173i	$0.887481\pi$
$654$	1067.43	+	346.828i	1.63215	+	0.530318i
$655$		0			0
$656$	698.768	−	507.685i	1.06520	−	0.773910i
$657$	14.7575	+	93.1753i	0.0224620	+	0.141819i
$658$	261.581	+	133.282i	0.397540	+	0.202557i
$659$			384.749i			0.583838i	0.956443	+	0.291919i	$0.0942938\pi$
$659$			384.749i			0.583838i	−0.956443	+	0.291919i	$0.905706\pi$
$660$		0			0
$661$	−199.159			−0.301300			−0.150650	−	0.988587i	$-0.548137\pi$
$661$	−199.159			−0.301300			−0.150650	+	0.988587i	$0.548137\pi$
$662$	−40.7888	+	80.0525i	−0.0616145	+	0.120925i
$663$	−159.545	+	25.2694i	−0.240641	+	0.0381138i
$664$	310.778	+	427.750i	0.468040	+	0.644202i
$665$		0			0
$666$	−18.0464	+	55.5411i	−0.0270967	+	0.0833951i
$667$	−90.4752	−	14.3299i	−0.135645	−	0.0214841i
$668$	59.8284	−	9.47588i	0.0895634	−	0.0141855i
$669$	−356.978	+	115.989i	−0.533599	+	0.173377i
$670$		0			0
$671$	236.330	+	201.285i	0.352206	+	0.299978i
$672$	−103.773	−	103.773i	−0.154424	−	0.154424i
$673$	850.014	+	433.104i	1.26302	+	0.643542i	0.951778	−	0.306788i	$-0.0992544\pi$
$673$	850.014	+	433.104i	1.26302	+	0.643542i	0.311244	+	0.950330i	$0.399254\pi$
$674$	735.075	−	1011.74i	1.09062	−	1.50110i
$675$		0			0
$676$	−91.8962	+	282.827i	−0.135941	+	0.418384i
$677$	736.540	−	375.286i	1.08795	−	0.554337i	0.184411	−	0.982849i	$-0.440962\pi$
$677$	736.540	−	375.286i	1.08795	−	0.554337i	0.903536	+	0.428512i	$0.140962\pi$
$678$	68.0043	−	429.362i	0.100301	−	0.633278i
$679$	19.4326	−	26.7467i	0.0286195	−	0.0393914i
$680$		0			0
$681$	−538.579			−0.790865
$682$	766.443	−	1254.58i	1.12382	−	1.83956i
$683$	−398.457	+	398.457i	−0.583392	+	0.583392i	−0.935834	−	0.352442i	$-0.885351\pi$
$683$	−398.457	+	398.457i	−0.583392	+	0.583392i	0.352442	+	0.935834i	$0.385351\pi$
$684$	−7.66209	+	2.48957i	−0.0112019	+	0.00363972i
$685$		0			0
$686$	−297.762	+	216.337i	−0.434055	+	0.315360i
$687$	359.933	−	183.395i	0.523920	−	0.266951i
$688$	433.884	+	851.546i	0.630646	+	1.23771i
$689$	−75.5166	−	103.940i	−0.109603	−	0.150856i
$690$		0			0
$691$	−26.9603	−	82.9754i	−0.0390164	−	0.120080i	0.929651	−	0.368441i	$-0.120108\pi$
$691$	−26.9603	−	82.9754i	−0.0390164	−	0.120080i	−0.968668	+	0.248361i	$0.920108\pi$
$692$	182.878	+	182.878i	0.264274	+	0.264274i
$693$	3.84812	−	16.1259i	0.00555284	−	0.0232697i
$694$			143.044i			0.206115i
$695$		0			0
$696$	−196.798	−	142.982i	−0.282756	−	0.205434i
$697$	−469.647	−	74.3848i	−0.673812	−	0.106721i
$698$	−493.462	−	968.474i	−0.706966	−	1.38750i
$699$	798.669	+	259.503i	1.14259	+	0.371249i
$700$		0			0
$701$	48.2784	+	35.0763i	0.0688707	+	0.0500375i	0.621688	−	0.783265i	$-0.286447\pi$
$701$	48.2784	+	35.0763i	0.0688707	+	0.0500375i	−0.552817	+	0.833303i	$0.686447\pi$
$702$	−131.371	+	257.830i	−0.187138	+	0.367279i
$703$	−72.9857	+	72.9857i	−0.103820	+	0.103820i
$704$	6.24403	−	80.7528i	0.00886937	−	0.114706i
$705$		0			0
$706$	−133.545	−	411.009i	−0.189157	−	0.582166i
$707$	−37.2695	−	235.311i	−0.0527151	−	0.332830i
$708$	−101.478	+	640.707i	−0.143330	+	0.904953i
$709$	−590.657	−	191.916i	−0.833085	−	0.270686i	−0.138740	−	0.990329i	$-0.544305\pi$
$709$	−590.657	−	191.916i	−0.833085	−	0.270686i	−0.694344	+	0.719643i	$0.744305\pi$
$710$		0			0
$711$	87.5723	−	63.6250i	0.123168	−	0.0894866i
$712$	−16.1861	−	102.195i	−0.0227333	−	0.143532i
$713$	280.543	+	142.944i	0.393468	+	0.200482i
$714$			133.868i			0.187490i
$715$		0			0
$716$	236.019			0.329636
$717$	260.066	−	510.408i	0.362714	−	0.711866i
$718$	1195.78	−	189.392i	1.66543	−	0.263778i
$719$	−629.901	−	866.984i	−0.876079	−	1.20582i	−0.977491	−	0.210975i	$-0.932336\pi$
$719$	−629.901	−	866.984i	−0.876079	−	1.20582i	0.101412	−	0.994844i	$-0.467664\pi$
$720$		0			0
$721$	41.0056	−	126.202i	0.0568732	−	0.175038i
$722$	832.719	+	131.890i	1.15335	+	0.182673i
$723$	356.024	−	56.3887i	0.492426	−	0.0779926i
$724$	117.963	−	38.3286i	0.162933	−	0.0529401i
$725$		0			0
$726$	−833.478	+	427.560i	−1.14804	+	0.588926i
$727$	535.877	+	535.877i	0.737107	+	0.737107i	0.972017	−	0.234910i	$-0.0754795\pi$
$727$	535.877	+	535.877i	0.737107	+	0.737107i	−0.234910	+	0.972017i	$0.575479\pi$
$728$	31.6339	+	16.1183i	0.0434532	+	0.0221405i
$729$	373.581	−	514.191i	0.512457	−	0.705337i
$730$		0			0
$731$	162.587	−	500.391i	0.222417	−	0.684529i
$732$	160.113	−	81.5818i	0.218734	−	0.111451i
$733$	−37.2155	+	234.969i	−0.0507714	+	0.320558i	0.949211	+	0.314640i	$0.101884\pi$
$733$	−37.2155	+	234.969i	−0.0507714	+	0.320558i	−0.999982	+	0.00591819i	$0.998116\pi$
$734$	−134.579	+	185.233i	−0.183351	+	0.252361i
$735$		0			0
$736$	−171.117			−0.232496
$737$	14.7025	−	6.11360i	0.0199491	−	0.00829525i
$738$	71.8898	−	71.8898i	0.0974117	−	0.0974117i
$739$	−143.146	+	46.5111i	−0.193703	+	0.0629378i	−0.404262	−	0.914643i	$-0.632472\pi$
$739$	−143.146	+	46.5111i	−0.193703	+	0.0629378i	0.210559	+	0.977581i	$0.432472\pi$
$740$		0			0
$741$	49.3851	−	35.8804i	0.0666466	−	0.0484216i
$742$	−94.8677	+	48.3375i	−0.127854	+	0.0651449i
$743$	108.126	+	212.210i	0.145526	+	0.285612i	0.952251	−	0.305316i	$-0.0987620\pi$
$743$	108.126	+	212.210i	0.145526	+	0.285612i	−0.806725	+	0.590927i	$0.798762\pi$
$744$	491.462	+	676.440i	0.660568	+	0.909194i
$745$		0			0
$746$	−298.244	−	917.901i	−0.399791	−	1.23043i
$747$	73.7808	+	73.7808i	0.0987695	+	0.0987695i
$748$	185.601	−	158.958i	0.248129	−	0.212511i
$749$			267.586i			0.357258i
$750$		0			0
$751$	−930.748	−	676.228i	−1.23935	−	0.900437i	−0.241790	−	0.970328i	$-0.577735\pi$
$751$	−930.748	−	676.228i	−1.23935	−	0.900437i	−0.997555	+	0.0698916i	$0.977735\pi$
$752$	1505.27	+	238.411i	2.00168	+	0.317035i
$753$	270.336	+	530.564i	0.359012	+	0.704600i
$754$	−171.915	−	55.8586i	−0.228004	−	0.0740830i
$755$		0			0
$756$	65.0500	+	47.2616i	0.0860450	+	0.0625153i
$757$	−556.341	+	1091.88i	−0.734929	+	1.44238i	0.155774	+	0.987793i	$0.450213\pi$
$757$	−556.341	+	1091.88i	−0.734929	+	1.44238i	−0.890703	+	0.454586i	$0.849787\pi$
$758$	−488.557	+	488.557i	−0.644534	+	0.644534i
$759$	−105.058	−	170.912i	−0.138416	−	0.225181i
$760$		0			0
$761$	−178.708	−	550.005i	−0.234833	−	0.722740i	−0.997144	−	0.0755295i	$-0.975935\pi$
$761$	−178.708	−	550.005i	−0.234833	−	0.722740i	0.762311	−	0.647211i	$-0.224065\pi$
$762$	135.664	+	856.550i	0.178037	+	1.12408i
$763$	−35.6180	+	224.883i	−0.0466815	+	0.294735i
$764$	−227.509	−	73.9222i	−0.297787	−	0.0967569i
$765$		0			0
$766$	459.010	−	333.490i	0.599230	−	0.435366i
$767$	−74.0867	−	467.765i	−0.0965928	−	0.609863i
$768$	−858.758	−	437.559i	−1.11817	−	0.569738i
$769$			1033.26i			1.34364i	0.740714	+	0.671821i	$0.234487\pi$
$769$			1033.26i			1.34364i	−0.740714	+	0.671821i	$0.765513\pi$
$770$		0			0
$771$	−101.406			−0.131525
$772$	40.1633	−	78.8249i	0.0520250	−	0.102105i
$773$	−856.088	+	135.591i	−1.10749	+	0.175409i	−0.683280	−	0.730156i	$-0.739447\pi$
$773$	−856.088	+	135.591i	−1.10749	+	0.175409i	−0.424207	+	0.905565i	$0.639447\pi$
$774$	66.1230	+	91.0105i	0.0854302	+	0.117585i
$775$		0			0
$776$	31.6332	−	97.3570i	0.0407644	−	0.125460i
$777$	−121.440	−	19.2342i	−0.156293	−	0.0247545i
$778$	981.655	−	155.479i	1.26177	−	0.199844i
$779$	170.896	−	55.5276i	0.219379	−	0.0712807i
$780$		0			0
$781$	−623.632	−	531.156i	−0.798504	−	0.680097i
$782$	110.371	+	110.371i	0.141140	+	0.141140i
$783$	358.368	+	182.598i	0.457686	+	0.233203i
$784$	−547.025	+	752.916i	−0.697737	+	0.960352i
$785$		0			0
$786$	487.592	−	1500.65i	0.620346	−	1.90923i
$787$	−300.712	+	153.220i	−0.382099	+	0.194689i	−0.634481	−	0.772939i	$-0.718786\pi$
$787$	−300.712	+	153.220i	−0.382099	+	0.194689i	0.252382	+	0.967628i	$0.418786\pi$
$788$	−20.1043	+	126.934i	−0.0255131	+	0.161084i
$789$	695.365	−	957.088i	0.881325	−	1.21304i
$790$		0			0
$791$	88.1879			0.111489
$792$	−4.09768	−	51.1693i	−0.00517384	−	0.0646077i
$793$	−92.7683	+	92.7683i	−0.116984	+	0.116984i
$794$	644.892	−	209.538i	0.812207	−	0.263902i
$795$		0			0
$796$	−303.515	+	220.516i	−0.381300	+	0.277031i
$797$	−62.3432	+	31.7654i	−0.0782223	+	0.0398562i	−0.492664	−	0.870220i	$-0.663977\pi$
$797$	−62.3432	+	31.7654i	−0.0782223	+	0.0398562i	0.414442	+	0.910076i	$0.363977\pi$
$798$	−22.9667	−	45.0748i	−0.0287804	−	0.0564847i
$799$	−493.160	−	678.777i	−0.617222	−	0.849533i
$800$		0			0
$801$	−6.30985	−	19.4197i	−0.00787746	−	0.0242443i
$802$	466.781	+	466.781i	0.582021	+	0.582021i
$803$	922.758	+	563.729i	1.14914	+	0.702028i
$804$		−	9.21730i		−	0.0114643i
$805$		0			0
$806$	502.660	+	365.204i	0.623647	+	0.453106i
$807$	325.048	+	51.4826i	0.402786	+	0.0637951i
$808$	−334.901	−	657.280i	−0.414481	−	0.813465i
$809$	−577.635	−	187.685i	−0.714011	−	0.231996i	−0.0705865	−	0.997506i	$-0.522487\pi$
$809$	−577.635	−	187.685i	−0.714011	−	0.231996i	−0.643425	+	0.765509i	$0.722487\pi$
$810$		0			0
$811$	1034.41	+	751.545i	1.27548	+	0.926689i	0.999406	−	0.0344482i	$-0.0109674\pi$
$811$	1034.41	+	751.545i	1.27548	+	0.926689i	0.276071	+	0.961137i	$0.410967\pi$
$812$	−22.8030	+	44.7533i	−0.0280825	+	0.0551149i
$813$	−378.738	+	378.738i	−0.465853	+	0.465853i
$814$	350.542	+	570.277i	0.430641	+	0.700586i
$815$		0			0
$816$	214.747	+	660.923i	0.263170	+	0.809955i
$817$	31.1036	+	196.380i	0.0380705	+	0.240368i
$818$	260.945	−	1647.54i	0.319004	−	2.01411i
$819$	6.66354	+	2.16512i	0.00813619	+	0.00264361i
$820$		0			0
$821$	−388.039	+	281.927i	−0.472641	+	0.343394i	−0.798470	−	0.602035i	$-0.794357\pi$
$821$	−388.039	+	281.927i	−0.472641	+	0.343394i	0.325828	+	0.945429i	$0.394357\pi$
$822$	−315.023	−	1988.97i	−0.383239	−	2.41968i
$823$	77.4006	+	39.4376i	0.0940469	+	0.0479193i	0.500381	−	0.865805i	$-0.333193\pi$
$823$	77.4006	+	39.4376i	0.0940469	+	0.0479193i	−0.406334	+	0.913724i	$0.633193\pi$
$824$		−	410.874i		−	0.498633i
$825$		0			0
$826$	−392.484			−0.475162
$827$	129.764	−	254.677i	0.156910	−	0.307953i	−0.799146	−	0.601137i	$-0.794715\pi$
$827$	129.764	−	254.677i	0.156910	−	0.307953i	0.956056	+	0.293184i	$0.0947148\pi$
$828$	−11.0521	+	1.75048i	−0.0133480	+	0.00211411i
$829$	561.476	+	772.805i	0.677293	+	0.932214i	0.999897	−	0.0143202i	$-0.00455843\pi$
$829$	561.476	+	772.805i	0.677293	+	0.932214i	−0.322605	+	0.946534i	$0.604558\pi$
$830$		0			0
$831$	33.2455	−	102.319i	0.0400067	−	0.123128i
$832$	33.8081	+	5.35468i	0.0406348	+	0.00643591i
$833$	506.040	−	80.1488i	0.607491	−	0.0962171i
$834$	−301.285	+	97.8933i	−0.361252	+	0.117378i
$835$		0			0
$836$	−35.2223	+	85.3650i	−0.0421320	+	0.102111i
$837$	−977.557	−	977.557i	−1.16793	−	1.16793i
$838$	987.718	+	503.267i	1.17866	+	0.600558i
$839$	603.415	−	830.530i	0.719208	−	0.989904i	−0.280342	−	0.959900i	$-0.590448\pi$
$839$	603.415	−	830.530i	0.719208	−	0.989904i	0.999550	−	0.0300042i	$-0.00955205\pi$
$840$		0			0
$841$	182.243	−	560.887i	0.216698	−	0.666929i
$842$	−809.757	+	412.592i	−0.961707	+	0.490014i
$843$	−25.0720	+	158.298i	−0.0297414	+	0.187780i
$844$	−317.410	+	436.878i	−0.376078	+	0.517628i
$845$		0			0
$846$	179.391			0.212046
$847$	−112.119	−	153.432i	−0.132372	−	0.181148i
$848$	−390.832	+	390.832i	−0.460887	+	0.460887i
$849$	−672.340	+	218.456i	−0.791920	+	0.257310i
$850$		0			0
$851$	−115.983	+	84.2666i	−0.136290	+	0.0990206i
$852$	−422.510	+	215.279i	−0.495904	+	0.252675i
$853$	−26.2685	−	51.5549i	−0.0307955	−	0.0604395i	0.875096	−	0.483949i	$-0.160798\pi$
$853$	−26.2685	−	51.5549i	−0.0307955	−	0.0604395i	−0.905892	+	0.423510i	$0.860798\pi$
$854$	63.9069	+	87.9603i	0.0748324	+	0.102998i
$855$		0			0
$856$	256.031	+	787.984i	0.299102	+	0.920542i
$857$	230.449	+	230.449i	0.268902	+	0.268902i	0.828658	−	0.559756i	$-0.189105\pi$
$857$	230.449	+	230.449i	0.268902	+	0.268902i	−0.559756	+	0.828658i	$0.689105\pi$
$858$	−152.000	−	365.544i	−0.177157	−	0.426042i
$859$		−	768.251i		−	0.894355i	−0.894445	−	0.447177i	$-0.852429\pi$
$859$		−	768.251i		−	0.894355i	0.894445	−	0.447177i	$-0.147571\pi$
$860$		0			0
$861$	173.170	+	125.816i	0.201127	+	0.146127i
$862$	−1529.15	−	242.194i	−1.77396	−	0.280968i
$863$	−90.2355	−	177.097i	−0.104560	−	0.205211i	0.832799	−	0.553576i	$-0.186737\pi$
$863$	−90.2355	−	177.097i	−0.104560	−	0.205211i	−0.937359	+	0.348365i	$0.886737\pi$
$864$	714.560	+	232.175i	0.827037	+	0.268721i
$865$		0			0
$866$	1080.87	+	785.301i	1.24812	+	0.906814i
$867$	−240.376	+	471.765i	−0.277251	+	0.544135i
$868$	122.078	−	122.078i	0.140643	−	0.140643i
$869$	95.6532	−	1237.06i	0.110073	−	1.42355i
$870$		0			0
$871$	2.07948	+	6.39998i	0.00238746	+	0.00734785i
$872$	110.285	+	696.313i	0.126474	+	0.798524i
$873$	3.16024	−	19.9529i	0.00361997	−	0.0228556i
$874$	−56.0988	−	18.2276i	−0.0641862	−	0.0208554i
$875$		0			0
$876$	506.403	−	367.923i	0.578086	−	0.420004i
$877$	−217.500	−	1373.24i	−0.248005	−	1.56584i	−0.726135	−	0.687552i	$-0.758685\pi$
$877$	−217.500	−	1373.24i	−0.248005	−	1.56584i	0.478130	−	0.878289i	$-0.341315\pi$
$878$	−1082.64	−	551.633i	−1.23308	−	0.628283i
$879$			1542.97i			1.75537i
$880$		0			0
$881$	204.228			0.231813			0.115907	−	0.993260i	$-0.463023\pi$
$881$	204.228			0.231813			0.115907	+	0.993260i	$0.463023\pi$
$882$	−49.7327	+	97.6060i	−0.0563863	+	0.110664i
$883$	−1227.78	+	194.461i	−1.39046	+	0.220227i	−0.806346	−	0.591445i	$-0.798558\pi$
$883$	−1227.78	+	194.461i	−1.39046	+	0.220227i	−0.584114	+	0.811672i	$0.698558\pi$
$884$	60.7031	+	83.5506i	0.0686687	+	0.0945143i
$885$		0			0
$886$	−256.769	+	790.253i	−0.289807	+	0.891934i
$887$	−1186.05	−	187.852i	−1.33715	−	0.211784i	−0.553430	−	0.832896i	$-0.686681\pi$
$887$	−1186.05	−	187.852i	−1.33715	−	0.211784i	−0.783722	+	0.621112i	$0.786681\pi$
$888$	−376.019	+	59.5555i	−0.423445	+	0.0670670i
$889$	−167.318	+	54.3651i	−0.188210	+	0.0611531i
$890$		0			0
$891$	229.114	+	948.599i	0.257142	+	1.06465i
$892$	169.687	+	169.687i	0.190232	+	0.190232i
$893$	282.504	+	143.943i	0.316354	+	0.161191i
$894$	−497.659	+	684.969i	−0.556666	+	0.766184i
$895$		0			0
$896$	66.2463	−	203.885i	0.0739356	−	0.227550i
$897$	75.5445	−	38.4919i	0.0842191	−	0.0429118i
$898$	268.798	−	1697.12i	0.299329	−	1.88989i
$899$	507.610	−	698.666i	0.564639	−	0.777159i
$900$		0			0
$901$	304.285			0.337719
$902$	−93.0251	−	1161.64i	−0.103132	−	1.28785i
$903$	−167.476	+	167.476i	−0.185466	+	0.185466i
$904$	259.695	−	84.3799i	0.287273	−	0.0933406i
$905$		0			0
$906$	−768.606	+	558.425i	−0.848351	+	0.616363i
$907$	−1418.23	+	722.625i	−1.56365	+	0.796720i	−0.999579	−	0.0290052i	$-0.990766\pi$
$907$	−1418.23	+	722.625i	−1.56365	+	0.796720i	−0.564072	+	0.825725i	$0.690766\pi$
$908$	156.324	+	306.803i	0.172163	+	0.337889i
$909$	−85.5686	−	117.775i	−0.0941349	−	0.129566i
$910$		0			0
$911$	409.334	+	1259.80i	0.449324	+	1.38288i	0.877672	+	0.479263i	$0.159096\pi$
$911$	409.334	+	1259.80i	0.449324	+	1.38288i	−0.428348	+	0.903614i	$0.640904\pi$
$912$	−185.697	−	185.697i	−0.203615	−	0.203615i
$913$	1192.20	−	95.4721i	1.30580	−	0.104570i
$914$		−	376.286i		−	0.411692i
$915$		0			0
$916$	−208.943	−	151.806i	−0.228104	−	0.165727i
$917$	316.154	+	50.0739i	0.344770	+	0.0546063i
$918$	−311.141	−	610.648i	−0.338933	−	0.665194i
$919$	1470.30	+	477.730i	1.59989	+	0.519836i	0.967081	−	0.254470i	$-0.0819010\pi$
$919$	1470.30	+	477.730i	1.59989	+	0.519836i	0.632811	+	0.774306i	$0.281901\pi$
$920$		0			0
$921$	856.210	+	622.073i	0.929652	+	0.675432i
$922$	30.1821	−	59.2358i	0.0327355	−	0.0642471i
$923$	244.799	−	244.799i	0.265221	−	0.265221i
$924$	−106.929	+	25.8265i	−0.115724	+	0.0279507i
$925$		0			0
$926$	−452.424	−	1392.42i	−0.488579	−	1.50369i
$927$	−12.6843	−	80.0856i	−0.0136832	−	0.0863923i
$928$	−73.4209	+	463.561i	−0.0791173	+	0.499527i
$929$	−288.132	−	93.6196i	−0.310152	−	0.100775i	0.149805	−	0.988716i	$-0.452135\pi$
$929$	−288.132	−	93.6196i	−0.310152	−	0.100775i	−0.459958	+	0.887941i	$0.652135\pi$
$930$		0			0
$931$	−156.638	+	113.804i	−0.168247	+	0.122239i
$932$	−83.9889	−	530.285i	−0.0901169	−	0.568976i
$933$	−1283.63	−	654.044i	−1.37581	−	0.701012i
$934$		−	342.991i		−	0.367228i
$935$		0			0
$936$	21.6943			0.0231777
$937$	−666.244	+	1307.58i	−0.711039	+	1.39549i	0.198595	+	0.980082i	$0.436362\pi$
$937$	−666.244	+	1307.58i	−0.711039	+	1.39549i	−0.909634	+	0.415411i	$0.863638\pi$
$938$	5.50816	−	0.872406i	0.00587224	−	0.000930071i
$939$	−706.744	−	972.749i	−0.752656	−	1.03594i
$940$		0			0
$941$	503.470	−	1549.52i	0.535037	−	1.64667i	−0.208532	−	0.978015i	$-0.566869\pi$
$941$	503.470	−	1549.52i	0.535037	−	1.64667i	0.743569	−	0.668659i	$-0.233131\pi$
$942$	−1494.40	−	236.689i	−1.58641	−	0.251262i
$943$	246.508	−	39.0430i	0.261408	−	0.0414030i
$944$	−1937.74	+	629.610i	−2.05269	+	0.666960i
$945$		0			0
$946$	1285.63	+	99.4087i	1.35902	+	0.105083i
$947$	849.529	+	849.529i	0.897074	+	0.897074i	0.995176	−	0.0981026i	$-0.0312773\pi$
$947$	849.529	+	849.529i	0.897074	+	0.897074i	−0.0981026	+	0.995176i	$0.531277\pi$
$948$	−639.953	−	326.072i	−0.675055	−	0.343958i
$949$	−268.612	+	369.713i	−0.283048	+	0.389581i
$950$		0			0
$951$	351.768	−	1082.63i	0.369893	−	1.13841i
$952$	−74.9223	+	38.1748i	−0.0786998	+	0.0400996i
$953$	85.0162	−	536.771i	0.0892091	−	0.563244i	−0.902083	−	0.431563i	$-0.857962\pi$
$953$	85.0162	−	536.771i	0.0892091	−	0.563244i	0.991292	−	0.131681i	$-0.0420376\pi$
$954$	−38.2411	+	52.6344i	−0.0400850	+	0.0551723i
$955$		0			0
$956$	−366.240			−0.383096
$957$	−508.083	+	211.271i	−0.530912	+	0.220764i
$958$	456.108	−	456.108i	0.476105	−	0.476105i
$959$	388.527	−	126.240i	0.405137	−	0.131637i
$960$		0			0
$961$	−1624.01	+	1179.91i	−1.68992	+	1.22780i
$962$	−252.067	+	128.434i	−0.262023	+	0.133508i
$963$	74.2308	+	145.686i	0.0770829	+	0.151284i
$964$	−135.459	−	186.443i	−0.140517	−	0.193406i
$965$		0			0
$966$	−21.7129	−	66.8256i	−0.0224772	−	0.0691776i
$967$	1120.43	+	1120.43i	1.15867	+	1.15867i	0.984762	+	0.173909i	$0.0556400\pi$
$967$	1120.43	+	1120.43i	1.15867	+	1.15867i	0.173909	+	0.984762i	$0.444360\pi$
$968$	−476.974	−	344.548i	−0.492742	−	0.355938i
$969$			144.576i			0.149201i
$970$		0			0
$971$	−79.5621	−	57.8052i	−0.0819383	−	0.0595316i	0.546062	−	0.837745i	$-0.316126\pi$
$971$	−79.5621	−	57.8052i	−0.0819383	−	0.0595316i	−0.628000	+	0.778213i	$0.716126\pi$
$972$	102.846	+	16.2892i	0.105809	+	0.0167584i
$973$	−29.1758	−	57.2607i	−0.0299854	−	0.0588496i
$974$	−1771.93	−	575.735i	−1.81923	−	0.591104i
$975$		0			0
$976$	456.619	+	331.753i	0.467847	+	0.339911i
$977$	−84.4187	+	165.681i	−0.0864060	+	0.169581i	−0.930166	−	0.367140i	$-0.880337\pi$
$977$	−84.4187	+	165.681i	−0.0864060	+	0.169581i	0.843760	+	0.536721i	$0.180337\pi$
$978$	−1720.88	+	1720.88i	−1.75959	+	1.75959i
$979$	−216.359	−	89.2716i	−0.221000	−	0.0911865i
$980$		0			0
$981$	42.9925	+	132.317i	0.0438252	+	0.134880i
$982$	−205.719	−	1298.86i	−0.209490	−	1.32267i
$983$	288.673	−	1822.61i	0.293665	−	1.85413i	−0.193870	−	0.981027i	$-0.562104\pi$
$983$	288.673	−	1822.61i	0.293665	−	1.85413i	0.487535	−	0.873103i	$-0.337896\pi$
$984$	630.333	+	204.808i	0.640582	+	0.208138i
$985$		0			0
$986$	346.356	−	251.642i	0.351274	−	0.255215i
$987$	59.0835	+	373.038i	0.0598617	+	0.377952i
$988$	−34.7735	−	17.7180i	−0.0351958	−	0.0179332i
$989$			276.161i			0.279232i
$990$		0			0
$991$	340.674			0.343768			0.171884	−	0.985117i	$-0.445015\pi$
$991$	340.674			0.343768			0.171884	+	0.985117i	$0.445015\pi$
$992$	732.390	−	1437.40i	0.738297	−	1.44899i
$993$	−114.162	+	18.0815i	−0.114967	+	0.0182090i
$994$	−168.639	−	232.111i	−0.169657	−	0.233512i
$995$		0			0
$996$	213.943	−	658.450i	0.214803	−	0.661094i
$997$	735.280	+	116.457i	0.737492	+	0.116807i	0.513869	−	0.857868i	$-0.328212\pi$
$997$	735.280	+	116.457i	0.737492	+	0.116807i	0.223623	+	0.974676i	$0.428212\pi$
$998$	138.420	−	21.9235i	0.138697	−	0.0219674i
$999$	598.662	−	194.517i	0.599261	−	0.194712i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.bk.c.82.13	yes	128
5.2	odd	4	inner	275.3.bk.c.93.13	yes	128
5.3	odd	4	inner	275.3.bk.c.93.4	yes	128
5.4	even	2	inner	275.3.bk.c.82.4	✓	128
11.9	even	5	inner	275.3.bk.c.207.4	yes	128
55.9	even	10	inner	275.3.bk.c.207.13	yes	128
55.42	odd	20	inner	275.3.bk.c.218.4	yes	128
55.53	odd	20	inner	275.3.bk.c.218.13	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.bk.c.82.4	✓	128	5.4	even	2	inner
275.3.bk.c.82.13	yes	128	1.1	even	1	trivial
275.3.bk.c.93.4	yes	128	5.3	odd	4	inner
275.3.bk.c.93.13	yes	128	5.2	odd	4	inner
275.3.bk.c.207.4	yes	128	11.9	even	5	inner
275.3.bk.c.207.13	yes	128	55.9	even	10	inner
275.3.bk.c.218.4	yes	128	55.42	odd	20	inner
275.3.bk.c.218.13	yes	128	55.53	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11368 - 2.18572i) q^{2} +(3.11704 - 0.493690i) q^{3} +(-1.18596 - 1.63233i) q^{4} +(2.39232 - 7.36280i) q^{6} +(1.55118 + 0.245682i) q^{7} +(4.80296 - 0.760714i) q^{8} +(0.912687 - 0.296550i) q^{9} +(4.19559 - 10.1684i) q^{11} +(-4.50255 - 4.50255i) q^{12} +(4.14212 + 2.11052i) q^{13} +(2.26451 - 3.11683i) q^{14} +(6.18024 - 19.0208i) q^{16} +(-9.81025 + 4.99857i) q^{17} +(0.368267 - 2.32514i) q^{18} +(2.44564 - 3.36614i) q^{19} +4.95637 q^{21} +(-17.5528 - 20.4948i) q^{22} +(4.08642 - 4.08642i) q^{23} +(14.5955 - 4.74235i) q^{24} +(9.22601 - 6.70309i) q^{26} +(-22.6088 + 11.5198i) q^{27} +(-1.43860 - 2.82341i) q^{28} +(-9.31687 - 12.8236i) q^{29} +(16.8361 + 51.8163i) q^{31} +(-20.9373 - 20.9373i) q^{32} +(8.05774 - 33.7667i) q^{33} +27.0093i q^{34} +(-1.56648 - 1.13811i) q^{36} +(-24.5018 - 3.88071i) q^{37} +(-4.63378 - 9.09431i) q^{38} +(13.9531 + 4.53363i) q^{39} +(34.9390 + 25.3846i) q^{41} +(5.51982 - 10.8333i) q^{42} +(-33.7901 + 33.7901i) q^{43} +(-21.5741 + 5.21076i) q^{44} +(-4.38082 - 13.4828i) q^{46} +(11.9207 + 75.2645i) q^{47} +(9.87365 - 62.3398i) q^{48} +(-44.2560 - 14.3796i) q^{49} +(-28.1112 + 20.4240i) q^{51} +(-1.46732 - 9.26431i) q^{52} +(-24.6242 - 12.5467i) q^{53} +62.2460i q^{54} +7.63714 q^{56} +(5.96133 - 11.6998i) q^{57} +(-38.4048 + 6.08273i) q^{58} +(-59.8804 - 82.4183i) q^{59} +(-8.72078 + 26.8398i) q^{61} +(132.006 + 20.9077i) q^{62} +(1.48860 - 0.235771i) q^{63} +(7.00270 - 2.27532i) q^{64} +(-64.8310 - 55.2174i) q^{66} +(1.02357 + 1.02357i) q^{67} +(19.7939 + 10.0855i) q^{68} +(10.7201 - 14.7550i) q^{69} +(23.0126 - 70.8254i) q^{71} +(4.15801 - 2.11861i) q^{72} +(-15.3779 + 97.0924i) q^{73} +(-35.7694 + 49.2323i) q^{74} -8.39510 q^{76} +(9.00630 - 14.7423i) q^{77} +(25.4486 - 25.4486i) q^{78} +(107.275 - 34.8559i) q^{79} +(-71.7727 + 52.1459i) q^{81} +(94.3947 - 48.0965i) q^{82} +(49.3617 + 96.8777i) q^{83} +(-5.87806 - 8.09045i) q^{84} +(36.2243 + 111.487i) q^{86} +(-35.3719 - 35.3719i) q^{87} +(12.4160 - 52.0302i) q^{88} -21.2775i q^{89} +(5.90665 + 4.29143i) q^{91} +(-11.5167 - 1.82407i) q^{92} +(78.0601 + 153.202i) q^{93} +(177.783 + 57.7653i) q^{94} +(-75.5989 - 54.9258i) q^{96} +(9.55693 - 18.7565i) q^{97} +(-80.7170 + 80.7170i) q^{98} +(0.813807 - 10.5248i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 48 q^{6} + 32 q^{11} + 280 q^{16} - 8 q^{21} + 528 q^{26} - 16 q^{31} + 336 q^{36} - 604 q^{41} - 1152 q^{46} - 1024 q^{51} - 992 q^{56} - 320 q^{61} + 1624 q^{66} + 536 q^{71} + 1776 q^{76} + 3680 q^{81}+ \cdots - 6584 q^{96}+O(q^{100}) \) 128 * q - 48 * q^6 + 32 * q^11 + 280 * q^16 - 8 * q^21 + 528 * q^26 - 16 * q^31 + 336 * q^36 - 604 * q^41 - 1152 * q^46 - 1024 * q^51 - 992 * q^56 - 320 * q^61 + 1624 * q^66 + 536 * q^71 + 1776 * q^76 + 3680 * q^81 + 872 * q^86 - 448 * q^91 - 6584 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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