LMFDB - Embedded newform 275.3.bk.c.207.13

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			207.13
Character	$\chi$	$=$	275.207
Dual form			275.3.bk.c.93.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.18572 - 1.11368i) q^{2} +(-0.493690 + 3.11704i) q^{3} +(1.18596 - 1.63233i) q^{4} +(2.39232 + 7.36280i) q^{6} +(-0.245682 - 1.55118i) q^{7} +(-0.760714 + 4.80296i) q^{8} +(-0.912687 - 0.296550i) q^{9} +(4.19559 + 10.1684i) q^{11} +(4.50255 + 4.50255i) q^{12} +(2.11052 + 4.14212i) q^{13} +(-2.26451 - 3.11683i) q^{14} +(6.18024 + 19.0208i) q^{16} +(-4.99857 + 9.81025i) q^{17} +(-2.32514 + 0.368267i) q^{18} +(-2.44564 - 3.36614i) q^{19} +4.95637 q^{21} +(20.4948 + 17.5528i) q^{22} +(-4.08642 + 4.08642i) q^{23} +(-14.5955 - 4.74235i) q^{24} +(9.22601 + 6.70309i) q^{26} +(-11.5198 + 22.6088i) q^{27} +(-2.82341 - 1.43860i) q^{28} +(9.31687 - 12.8236i) q^{29} +(16.8361 - 51.8163i) q^{31} +(20.9373 + 20.9373i) q^{32} +(-33.7667 + 8.05774i) q^{33} +27.0093i q^{34} +(-1.56648 + 1.13811i) q^{36} +(3.88071 + 24.5018i) q^{37} +(-9.09431 - 4.63378i) q^{38} +(-13.9531 + 4.53363i) q^{39} +(34.9390 - 25.3846i) q^{41} +(10.8333 - 5.51982i) q^{42} +(33.7901 - 33.7901i) q^{43} +(21.5741 + 5.21076i) q^{44} +(-4.38082 + 13.4828i) q^{46} +(-75.2645 - 11.9207i) q^{47} +(-62.3398 + 9.87365i) q^{48} +(44.2560 - 14.3796i) q^{49} +(-28.1112 - 20.4240i) q^{51} +(9.26431 + 1.46732i) q^{52} +(-12.5467 - 24.6242i) q^{53} +62.2460i q^{54} +7.63714 q^{56} +(11.6998 - 5.96133i) q^{57} +(6.08273 - 38.4048i) q^{58} +(59.8804 - 82.4183i) q^{59} +(-8.72078 - 26.8398i) q^{61} +(-20.9077 - 132.006i) q^{62} +(-0.235771 + 1.48860i) q^{63} +(-7.00270 - 2.27532i) q^{64} +(-64.8310 + 55.2174i) q^{66} +(-1.02357 - 1.02357i) q^{67} +(10.0855 + 19.7939i) q^{68} +(-10.7201 - 14.7550i) q^{69} +(23.0126 + 70.8254i) q^{71} +(2.11861 - 4.15801i) q^{72} +(97.0924 - 15.3779i) q^{73} +(35.7694 + 49.2323i) q^{74} -8.39510 q^{76} +(14.7423 - 9.00630i) q^{77} +(-25.4486 + 25.4486i) q^{78} +(-107.275 - 34.8559i) q^{79} +(-71.7727 - 52.1459i) q^{81} +(48.0965 - 94.3947i) q^{82} +(96.8777 + 49.3617i) q^{83} +(5.87806 - 8.09045i) q^{84} +(36.2243 - 111.487i) q^{86} +(35.3719 + 35.3719i) q^{87} +(-52.0302 + 12.4160i) q^{88} -21.2775i q^{89} +(5.90665 - 4.29143i) q^{91} +(1.82407 + 11.5167i) q^{92} +(153.202 + 78.0601i) q^{93} +(-177.783 + 57.7653i) q^{94} +(-75.5989 + 54.9258i) q^{96} +(18.7565 - 9.55693i) 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 $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	2.18572	−	1.11368i	1.09286	−	0.556841i	0.187837	−	0.982200i	$-0.439852\pi$
$2$	2.18572	−	1.11368i	1.09286	−	0.556841i	0.905025	+	0.425359i	$0.139852\pi$
$3$	−0.493690	+	3.11704i	−0.164563	+	1.03901i	0.757743	+	0.652553i	$0.226302\pi$
$3$	−0.493690	+	3.11704i	−0.164563	+	1.03901i	−0.922306	+	0.386459i	$0.873698\pi$
$4$	1.18596	−	1.63233i	0.296490	−	0.408083i
$5$		0			0
$5$		0			0
$6$	2.39232	+	7.36280i	0.398720	+	1.22713i
$7$	−0.245682	−	1.55118i	−0.0350975	−	0.221597i	0.963905	−	0.266245i	$-0.0857832\pi$
$7$	−0.245682	−	1.55118i	−0.0350975	−	0.221597i	−0.999003	+	0.0446486i	$0.985783\pi$
$8$	−0.760714	+	4.80296i	−0.0950893	+	0.600370i
$9$	−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
$13$	2.11052	+	4.14212i	0.162347	+	0.318625i	0.957822	−	0.287362i	$-0.0927784\pi$
$13$	2.11052	+	4.14212i	0.162347	+	0.318625i	−0.795475	+	0.605987i	$0.792778\pi$
$14$	−2.26451	−	3.11683i	−0.161751	−	0.222631i
$15$		0			0
$16$	6.18024	+	19.0208i	0.386265	+	1.18880i
$17$	−4.99857	+	9.81025i	−0.294034	+	0.577074i	−0.990011	−	0.140990i	$-0.954971\pi$
$17$	−4.99857	+	9.81025i	−0.294034	+	0.577074i	0.695977	+	0.718064i	$0.254971\pi$
$18$	−2.32514	+	0.368267i	−0.129175	+	0.0204593i
$19$	−2.44564	−	3.36614i	−0.128718	−	0.177165i	0.739794	−	0.672834i	$-0.234923\pi$
$19$	−2.44564	−	3.36614i	−0.128718	−	0.177165i	−0.868512	+	0.495669i	$0.834923\pi$
$20$		0			0
$21$	4.95637			0.236018
$22$	20.4948	+	17.5528i	0.931581	+	0.797856i
$23$	−4.08642	+	4.08642i	−0.177671	+	0.177671i	−0.790340	−	0.612669i	$-0.790096\pi$
$23$	−4.08642	+	4.08642i	−0.177671	+	0.177671i	0.612669	+	0.790340i	$0.290096\pi$
$24$	−14.5955	−	4.74235i	−0.608144	−	0.197598i
$25$		0			0
$26$	9.22601	+	6.70309i	0.354846	+	0.257811i
$27$	−11.5198	+	22.6088i	−0.426658	+	0.837363i
$28$	−2.82341	−	1.43860i	−0.100836	−	0.0513785i
$29$	9.31687	−	12.8236i	0.321271	−	0.442192i	−0.617583	−	0.786505i	$-0.711888\pi$
$29$	9.31687	−	12.8236i	0.321271	−	0.442192i	0.938855	+	0.344313i	$0.111888\pi$
$30$		0			0
$31$	16.8361	−	51.8163i	0.543101	−	1.67149i	−0.182360	−	0.983232i	$-0.558374\pi$
$31$	16.8361	−	51.8163i	0.543101	−	1.67149i	0.725462	−	0.688263i	$-0.241626\pi$
$32$	20.9373	+	20.9373i	0.654291	+	0.654291i
$33$	−33.7667	+	8.05774i	−1.02323	+	0.244174i
$34$			27.0093i			0.794392i
$35$		0			0
$36$	−1.56648	+	1.13811i	−0.0435133	+	0.0316143i
$37$	3.88071	+	24.5018i	0.104884	+	0.662211i	0.982978	+	0.183723i	$0.0588150\pi$
$37$	3.88071	+	24.5018i	0.104884	+	0.662211i	−0.878094	+	0.478488i	$0.841185\pi$
$38$	−9.09431	−	4.63378i	−0.239324	−	0.121942i
$39$	−13.9531	+	4.53363i	−0.357771	+	0.116247i
$40$		0			0
$41$	34.9390	−	25.3846i	0.852170	−	0.619138i	−0.0735735	−	0.997290i	$-0.523440\pi$
$41$	34.9390	−	25.3846i	0.852170	−	0.619138i	0.925743	+	0.378152i	$0.123440\pi$
$42$	10.8333	−	5.51982i	0.257935	−	0.131424i
$43$	33.7901	−	33.7901i	0.785815	−	0.785815i	−0.194990	−	0.980805i	$-0.562467\pi$
$43$	33.7901	−	33.7901i	0.785815	−	0.785815i	0.980805	+	0.194990i	$0.0624675\pi$
$44$	21.5741	+	5.21076i	0.490320	+	0.118426i
$45$		0			0
$46$	−4.38082	+	13.4828i	−0.0952351	+	0.293104i
$47$	−75.2645	−	11.9207i	−1.60137	−	0.253632i	−0.709092	−	0.705116i	$-0.750895\pi$
$47$	−75.2645	−	11.9207i	−1.60137	−	0.253632i	−0.892279	+	0.451484i	$0.850895\pi$
$48$	−62.3398	+	9.87365i	−1.29875	+	0.205701i
$49$	44.2560	−	14.3796i	0.903183	−	0.293462i
$50$		0			0
$51$	−28.1112	−	20.4240i	−0.551199	−	0.400470i
$52$	9.26431	+	1.46732i	0.178160	+	0.0282177i
$53$	−12.5467	−	24.6242i	−0.236730	−	0.464608i	0.741826	−	0.670593i	$-0.233960\pi$
$53$	−12.5467	−	24.6242i	−0.236730	−	0.464608i	−0.978555	+	0.205985i	$0.933960\pi$
$54$			62.2460i			1.15270i
$55$		0			0
$56$	7.63714			0.136378
$57$	11.6998	−	5.96133i	0.205259	−	0.104585i
$58$	6.08273	−	38.4048i	0.104875	−	0.662152i
$59$	59.8804	−	82.4183i	1.01492	−	1.39692i	0.0992186	−	0.995066i	$-0.468366\pi$
$59$	59.8804	−	82.4183i	1.01492	−	1.39692i	0.915703	−	0.401855i	$-0.131634\pi$
$60$		0			0
$61$	−8.72078	−	26.8398i	−0.142964	−	0.439997i	0.853780	−	0.520634i	$-0.174304\pi$
$61$	−8.72078	−	26.8398i	−0.142964	−	0.439997i	−0.996744	+	0.0806373i	$0.974304\pi$
$62$	−20.9077	−	132.006i	−0.337222	−	2.12913i
$63$	−0.235771	+	1.48860i	−0.00374239	+	0.0236285i
$64$	−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	0.699427	−	0.714704i	$-0.253439\pi$
$67$	−1.02357	−	1.02357i	−0.0152771	−	0.0152771i	−0.714704	+	0.699427i	$0.753439\pi$
$68$	10.0855	+	19.7939i	0.148316	+	0.291087i
$69$	−10.7201	−	14.7550i	−0.155364	−	0.213840i
$70$		0			0
$71$	23.0126	+	70.8254i	0.324121	+	0.997540i	0.971836	+	0.235658i	$0.0757245\pi$
$71$	23.0126	+	70.8254i	0.324121	+	0.997540i	−0.647716	+	0.761882i	$0.724275\pi$
$72$	2.11861	−	4.15801i	0.0294252	−	0.0577502i
$73$	97.0924	−	15.3779i	1.33003	−	0.210656i	0.549354	−	0.835590i	$-0.314874\pi$
$73$	97.0924	−	15.3779i	1.33003	−	0.210656i	0.780678	+	0.624933i	$0.214874\pi$
$74$	35.7694	+	49.2323i	0.483370	+	0.665302i
$75$		0			0
$76$	−8.39510			−0.110462
$77$	14.7423	−	9.00630i	0.191458	−	0.116965i
$78$	−25.4486	+	25.4486i	−0.326264	+	0.326264i
$79$	−107.275	−	34.8559i	−1.35792	−	0.441213i	−0.462569	−	0.886583i	$-0.653072\pi$
$79$	−107.275	−	34.8559i	−1.35792	−	0.441213i	−0.895347	+	0.445370i	$0.853072\pi$
$80$		0			0
$81$	−71.7727	−	52.1459i	−0.886083	−	0.643777i
$82$	48.0965	−	94.3947i	0.586543	−	1.15116i
$83$	96.8777	+	49.3617i	1.16720	+	0.594719i	0.926653	−	0.375918i	$-0.122673\pi$
$83$	96.8777	+	49.3617i	1.16720	+	0.594719i	0.240549	+	0.970637i	$0.422673\pi$
$84$	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
$88$	−52.0302	+	12.4160i	−0.591253	+	0.141090i
$89$		−	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
$92$	1.82407	+	11.5167i	0.0198269	+	0.125182i
$93$	153.202	+	78.0601i	1.64733	+	0.839356i
$94$	−177.783	+	57.7653i	−1.89131	+	0.614524i
$95$		0			0
$96$	−75.5989	+	54.9258i	−0.787488	+	0.572144i
$97$	18.7565	−	9.55693i	0.193366	−	0.0985250i	−0.354627	−	0.935008i	$-0.615392\pi$
$97$	18.7565	−	9.55693i	0.193366	−	0.0985250i	0.547993	+	0.836483i	$0.315392\pi$
$98$	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	0.395940	+	0.918276i	$0.370419\pi$
$101$	−46.8773	+	144.273i	−0.464132	+	1.42845i	−0.860071	+	0.510174i	$0.829581\pi$
$102$	−84.1891	−	13.3342i	−0.825383	−	0.130728i
$103$	−83.4524	+	13.2176i	−0.810218	+	0.128326i	−0.547779	−	0.836623i	$-0.684527\pi$
$103$	−83.4524	+	13.2176i	−0.810218	+	0.128326i	−0.262438	+	0.964949i	$0.584527\pi$
$104$	−21.4999	+	6.98575i	−0.206730	+	0.0671707i
$105$		0			0
$106$	−54.8471	−	39.8488i	−0.517426	−	0.375932i
$107$	−168.284	−	26.6535i	−1.57274	−	0.249098i	−0.691718	−	0.722167i	$-0.743146\pi$
$107$	−168.284	−	26.6535i	−1.57274	−	0.249098i	−0.881025	+	0.473069i	$0.843146\pi$
$108$	23.2431	+	45.6172i	0.215214	+	0.422382i
$109$			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
$112$	27.9863	−	14.2597i	0.249878	−	0.127319i
$113$	−8.78415	+	55.4609i	−0.0777358	+	0.490805i	0.917848	+	0.396931i	$0.129925\pi$
$113$	−8.78415	+	55.4609i	−0.0777358	+	0.490805i	−0.995584	+	0.0938734i	$0.970075\pi$
$114$	18.9334	−	26.0596i	0.166083	−	0.228593i
$115$		0			0
$116$	−9.88292	−	30.4165i	−0.0851976	−	0.262211i
$117$	−0.697894	−	4.40633i	−0.00596491	−	0.0376610i
$118$	39.0942	−	246.831i	0.331307	−	2.09179i
$119$	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
$123$	61.8759	+	121.438i	0.503056	+	0.987303i
$124$	−64.6145	−	88.9343i	−0.521085	−	0.717212i
$125$		0			0
$126$	1.14249	+	3.51623i	0.00906741	+	0.0279066i
$127$	−50.8561	+	99.8107i	−0.400441	+	0.785911i	−0.999895	−	0.0144990i	$-0.995385\pi$
$127$	−50.8561	+	99.8107i	−0.400441	+	0.785911i	0.599453	+	0.800410i	$0.295385\pi$
$128$	−134.821	+	21.3535i	−1.05329	+	0.166825i
$129$	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	$0.216274\pi$
$132$	−26.8930	+	64.6747i	−0.203735	+	0.489960i
$133$	−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
$137$	118.092	−	231.768i	0.861984	−	1.69174i	0.150995	−	0.988535i	$-0.451752\pi$
$137$	118.092	−	231.768i	0.861984	−	1.69174i	0.710989	−	0.703204i	$-0.248248\pi$
$138$	−39.8635	−	20.3115i	−0.288866	−	0.147185i
$139$	24.0521	−	33.1048i	0.173037	−	0.238164i	−0.713687	−	0.700465i	$-0.752976\pi$
$139$	24.0521	−	33.1048i	0.173037	−	0.238164i	0.886723	+	0.462301i	$0.152976\pi$
$140$		0			0
$141$	74.3147	−	228.717i	0.527054	−	1.62211i
$142$	129.176	+	129.176i	0.909690	+	0.909690i
$143$	−33.2640	+	38.8393i	−0.232616	+	0.271603i
$144$		−	19.1928i		−	0.133283i
$145$		0			0
$146$	195.091	−	141.742i	1.33624	−	0.970835i
$147$	22.9731	+	145.047i	0.156280	+	0.986712i
$148$	44.5975	+	22.7236i	0.301334	+	0.153538i
$149$	104.012	−	33.7955i	0.698066	−	0.226816i	0.0615785	−	0.998102i	$-0.480387\pi$
$149$	104.012	−	33.7955i	0.698066	−	0.226816i	0.636488	+	0.771287i	$0.280387\pi$
$150$		0			0
$151$	−99.2813	+	72.1321i	−0.657492	+	0.477696i	−0.865815	−	0.500364i	$-0.833199\pi$
$151$	−99.2813	+	72.1321i	−0.657492	+	0.477696i	0.208323	+	0.978060i	$0.433199\pi$
$152$	18.0279	−	9.18566i	0.118604	−	0.0604320i
$153$	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
$157$	193.032	+	30.5733i	1.22950	+	0.194734i	0.737191	−	0.675685i	$-0.236152\pi$
$157$	193.032	+	30.5733i	1.22950	+	0.194734i	0.492312	+	0.870419i	$0.336152\pi$
$158$	−273.293	+	43.2853i	−1.72970	+	0.273958i
$159$	82.9488	−	26.9517i	0.521691	−	0.169508i
$160$		0			0
$161$	7.34273	+	5.33481i	0.0456070	+	0.0331354i
$162$	−214.949	−	34.0446i	−1.32685	−	0.210152i
$163$	−142.717	−	280.098i	−0.875566	−	1.71840i	−0.673732	−	0.738975i	$-0.735310\pi$
$163$	−142.717	−	280.098i	−0.875566	−	1.71840i	−0.201834	−	0.979420i	$-0.564690\pi$
$164$		−	87.1372i		−	0.531324i
$165$		0			0
$166$	266.721			1.60675
$167$	−26.7496	+	13.6296i	−0.160177	+	0.0816143i	−0.532241	−	0.846593i	$-0.678650\pi$
$167$	−26.7496	+	13.6296i	−0.160177	+	0.0816143i	0.372064	+	0.928207i	$0.378650\pi$
$168$	−3.77038	+	23.8053i	−0.0224428	+	0.141698i
$169$	86.6328	−	119.240i	0.512620	−	0.705561i
$170$		0			0
$171$	1.23388	+	3.79749i	0.00721566	+	0.0222075i
$172$	−15.0830	−	95.2303i	−0.0876918	−	0.553664i
$173$	20.0520	−	126.603i	0.115907	−	0.731811i	−0.859457	−	0.511209i	$-0.829198\pi$
$173$	20.0520	−	126.603i	0.115907	−	0.731811i	0.975364	−	0.220602i	$-0.0708021\pi$
$174$	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
$178$	−23.6964	−	46.5068i	−0.133126	−	0.261274i
$179$	68.7567	+	94.6354i	0.384115	+	0.528690i	0.956669	−	0.291178i	$-0.0940471\pi$
$179$	68.7567	+	94.6354i	0.384115	+	0.528690i	−0.572554	+	0.819867i	$0.694047\pi$
$180$		0			0
$181$	−18.9964	−	58.4650i	−0.104953	−	0.323011i	0.884767	−	0.466034i	$-0.154318\pi$
$181$	−18.9964	−	58.4650i	−0.104953	−	0.323011i	−0.989719	+	0.143023i	$0.954318\pi$
$182$	8.13101	−	15.9580i	0.0446759	−	0.0876813i
$183$	87.9661	−	13.9325i	0.480689	−	0.0761336i
$184$	−16.5183	−	22.7355i	−0.0897735	−	0.123563i
$185$		0			0
$186$	421.791			2.26769
$187$	−120.727	−	9.66791i	−0.645598	−	0.0517001i
$188$	−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	0.809852	−	0.586634i	$-0.199547\pi$
$191$	95.9178	+	69.6884i	0.502187	+	0.364860i	−0.307664	+	0.951495i	$0.599547\pi$
$192$	10.5494	−	20.7044i	0.0549449	−	0.107835i
$193$	39.0672	+	19.9057i	0.202421	+	0.103139i	0.552262	−	0.833670i	$-0.313765\pi$
$193$	39.0672	+	19.9057i	0.202421	+	0.103139i	−0.349842	+	0.936809i	$0.613765\pi$
$194$	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	0.812118	−	0.583493i	$-0.198314\pi$
$197$	45.0392	+	45.0392i	0.228626	+	0.228626i	−0.583493	+	0.812118i	$0.698314\pi$
$198$	−13.5000	−	22.0980i	−0.0681820	−	0.111606i
$199$		−	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
$202$	58.2139	+	367.548i	0.288188	+	1.81955i
$203$	−22.1806	−	11.3016i	−0.109264	−	0.0556729i
$204$	−66.6774	+	21.6648i	−0.326850	+	0.106200i
$205$		0			0
$206$	−167.684	+	121.829i	−0.813999	+	0.591405i
$207$	4.94145	−	2.51780i	0.0238718	−	0.0121633i
$208$	−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	0.539329	+	0.842095i	$0.318678\pi$
$211$	−82.7053	+	254.541i	−0.391968	+	1.20635i	−0.931298	+	0.364259i	$0.881322\pi$
$212$	−55.0748	−	8.72299i	−0.259787	−	0.0411462i
$213$	−232.126	+	36.7652i	−1.08980	+	0.172607i
$214$	−397.505	+	129.157i	−1.85750	+	0.603538i
$215$		0			0
$216$	−99.8260	−	72.5278i	−0.462157	−	0.335777i
$217$	−84.5127	−	13.3855i	−0.389459	−	0.0616843i
$218$	161.457	+	316.877i	0.740628	+	1.45356i
$219$			310.233i			1.41659i
$220$		0			0
$221$	−51.1848			−0.231605
$222$	−171.118	+	87.1890i	−0.770802	+	0.392743i
$223$	18.6057	−	117.472i	0.0834335	−	0.526778i	−0.910205	−	0.414159i	$-0.864076\pi$
$223$	18.6057	−	117.472i	0.0834335	−	0.526778i	0.993638	−	0.112620i	$-0.0359242\pi$
$224$	27.3335	−	37.6214i	0.122025	−	0.167953i
$225$		0			0
$226$	42.5661	+	131.005i	0.188346	+	0.579668i
$227$	26.6968	+	168.557i	0.117607	+	0.742543i	0.974055	+	0.226310i	$0.0726662\pi$
$227$	26.6968	+	168.557i	0.117607	+	0.742543i	−0.856448	+	0.516233i	$0.827334\pi$
$228$	4.14458	−	26.1678i	0.0181780	−	0.114771i
$229$	−121.738	−	39.5550i	−0.531606	−	0.172729i	0.0309000	−	0.999522i	$-0.490163\pi$
$229$	−121.738	−	39.5550i	−0.531606	−	0.172729i	−0.562506	+	0.826793i	$0.690163\pi$
$230$		0			0
$231$	20.7949	+	50.3985i	0.0900211	+	0.218175i
$232$	54.5037	+	54.5037i	0.234930	+	0.234930i
$233$	120.805	+	237.093i	0.518477	+	1.01757i	0.990697	+	0.136087i	$0.0434527\pi$
$233$	120.805	+	237.093i	0.518477	+	1.01757i	−0.472220	+	0.881481i	$0.656547\pi$
$234$	−6.43266	−	8.85379i	−0.0274900	−	0.0378367i
$235$		0			0
$236$	−63.5184	−	195.490i	−0.269146	−	0.828346i
$237$	161.608	−	317.173i	0.681890	−	1.33828i
$238$	41.8962	−	6.63571i	0.176035	−	0.0278811i
$239$	−106.692	−	146.849i	−0.446411	−	0.614432i	0.525211	−	0.850972i	$-0.323987\pi$
$239$	−106.692	−	146.849i	−0.446411	−	0.614432i	−0.971622	+	0.236540i	$0.923987\pi$
$240$		0			0
$241$	114.219			0.473937			0.236968	−	0.971517i	$-0.423846\pi$
$241$	114.219			0.473937			0.236968	+	0.971517i	$0.423846\pi$
$242$	−92.4973	+	282.044i	−0.382220	+	1.16547i
$243$	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
$247$	8.78138	−	17.2344i	0.0355522	−	0.0697750i
$248$	236.064	+	120.281i	0.951872	+	0.485003i
$249$	−201.690	+	277.602i	−0.809999	+	1.11487i
$250$		0			0
$251$	58.3065	−	179.449i	0.232297	−	0.714936i	−0.765172	−	0.643826i	$-0.777346\pi$
$251$	58.3065	−	179.449i	0.232297	−	0.714936i	0.997469	−	0.0711096i	$-0.0226540\pi$
$252$	2.15027	+	2.15027i	0.00853282	+	0.00853282i
$253$	−58.6975	−	24.4076i	−0.232006	−	0.0964727i
$254$			274.796i			1.08187i
$255$		0			0
$256$	−247.073	+	179.509i	−0.965129	+	0.701207i
$257$	5.02657	+	31.7365i	0.0195587	+	0.123488i	0.995536	−	0.0943842i	$-0.0300882\pi$
$257$	5.02657	+	31.7365i	0.0195587	+	0.123488i	−0.975977	+	0.217873i	$0.930088\pi$
$258$	329.626	+	167.953i	1.27762	+	0.650980i
$259$	37.0532	−	12.0393i	0.143063	−	0.0464839i
$260$		0			0
$261$	−12.3062	+	8.94099i	−0.0471503	+	0.0342567i
$262$	445.485	−	226.986i	1.70032	−	0.866358i
$263$	−265.068	+	265.068i	−1.00786	+	1.00786i	−0.00789398	+	0.999969i	$0.502513\pi$
$263$	−265.068	+	265.068i	−1.00786	+	1.00786i	−0.999969	+	0.00789398i	$0.997487\pi$
$264$	−13.0142	−	168.310i	−0.0492962	−	0.637537i
$265$		0			0
$266$	−4.95351	+	15.2453i	−0.0186222	+	0.0573132i
$267$	66.3228	+	10.5045i	0.248400	+	0.0393427i
$268$	−2.88471	+	0.456893i	−0.0107638	+	0.00170482i
$269$	−99.1773	+	32.2247i	−0.368689	+	0.119794i	−0.487501	−	0.873122i	$-0.662091\pi$
$269$	−99.1773	+	32.2247i	−0.368689	+	0.119794i	0.118812	+	0.992917i	$0.462091\pi$
$270$		0			0
$271$	−137.306	−	99.7586i	−0.506664	−	0.368113i	0.304892	−	0.952387i	$-0.401379\pi$
$271$	−137.306	−	99.7586i	−0.506664	−	0.368113i	−0.811557	+	0.584274i	$0.801379\pi$
$272$	−217.492	−	34.4473i	−0.799601	−	0.126644i
$273$	10.4605	+	20.5299i	0.0383168	+	0.0752010i
$274$		−	638.098i		−	2.32882i
$275$		0			0
$276$	−36.7986			−0.133328
$277$	30.3745	−	15.4766i	0.109655	−	0.0558722i	−0.398302	−	0.917254i	$-0.630401\pi$
$277$	30.3745	−	15.4766i	0.109655	−	0.0558722i	0.507958	+	0.861382i	$0.330401\pi$
$278$	15.7029	−	99.1444i	0.0564854	−	0.356635i
$279$	−30.7323	+	42.2993i	−0.110151	+	0.151610i
$280$		0			0
$281$	−15.6934	−	48.2993i	−0.0558484	−	0.171884i	0.919241	−	0.393695i	$-0.128803\pi$
$281$	−15.6934	−	48.2993i	−0.0558484	−	0.171884i	−0.975090	+	0.221811i	$0.928803\pi$
$282$	−92.2867	−	582.675i	−0.327258	−	2.06622i
$283$	35.0423	−	221.248i	0.123824	−	0.781797i	−0.845131	−	0.534560i	$-0.820477\pi$
$283$	35.0423	−	221.248i	0.123824	−	0.781797i	0.968955	−	0.247237i	$-0.0795226\pi$
$284$	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
$288$	−12.9002	−	25.3182i	−0.0447925	−	0.0879103i
$289$	98.6147	+	135.731i	0.341227	+	0.469659i
$290$		0			0
$291$	20.5294	+	63.1830i	0.0705477	+	0.217124i
$292$	90.0457	−	176.725i	0.308376	−	0.605222i
$293$	482.899	−	76.4836i	1.64812	−	0.261036i	0.737822	−	0.674995i	$-0.235854\pi$
$293$	482.899	−	76.4836i	1.64812	−	0.261036i	0.910296	+	0.413959i	$0.135854\pi$
$294$	211.749	+	291.447i	0.720234	+	0.991317i
$295$		0			0
$296$	−120.633			−0.407545
$297$	−278.228	−	22.2808i	−0.936796	−	0.0750194i
$298$	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
$302$	−136.669	+	268.228i	−0.452547	+	0.888174i
$303$	−426.563	−	217.345i	−1.40780	−	0.717309i
$304$	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	0.206119	−	0.978527i	$-0.433917\pi$
$307$	−237.129	−	237.129i	−0.772408	−	0.772408i	−0.978527	+	0.206119i	$0.933917\pi$
$308$	2.78244	−	34.7454i	0.00903391	−	0.112810i
$309$		−	266.650i		−	0.862944i
$310$		0			0
$311$	−369.314	+	268.322i	−1.18751	+	0.862773i	−0.992998	−	0.118128i	$-0.962311\pi$
$311$	−369.314	+	268.322i	−1.18751	+	0.862773i	−0.194507	+	0.980901i	$0.562311\pi$
$312$	−11.1605	−	70.4649i	−0.0357710	−	0.225849i
$313$	−339.470	−	172.969i	−1.08457	−	0.552616i	−0.182061	−	0.983287i	$-0.558277\pi$
$313$	−339.470	−	172.969i	−1.08457	−	0.552616i	−0.902509	+	0.430671i	$0.858277\pi$
$314$	455.963	−	148.152i	1.45211	−	0.471820i
$315$		0			0
$316$	−184.121	+	133.771i	−0.582660	+	0.423327i
$317$	321.390	−	163.756i	1.01385	−	0.516582i	0.133571	−	0.991039i	$-0.457356\pi$
$317$	321.390	−	163.756i	1.01385	−	0.516582i	0.880278	+	0.474457i	$0.157356\pi$
$318$	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
$322$	21.9905	+	3.48295i	0.0682933	+	0.0108166i
$323$	45.2474	−	7.16648i	0.140085	−	0.0221873i
$324$	−170.239	+	55.3140i	−0.525429	+	0.170722i
$325$		0			0
$326$	−623.881	−	453.276i	−1.91375	−	1.39042i
$327$	−451.895	−	71.5731i	−1.38194	−	0.218878i
$328$	95.3429	+	187.121i	0.290680	+	0.570491i
$329$			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	$0.517620\pi$
$332$	195.468	−	99.5958i	0.588758	−	0.299987i
$333$	3.72414	−	23.5133i	0.0111836	−	0.0706105i
$334$	−43.2882	+	59.5810i	−0.129605	+	0.178386i
$335$		0			0
$336$	30.6316	+	94.2743i	0.0911654	+	0.280578i
$337$	−79.7500	−	503.522i	−0.236647	−	1.49413i	−0.764406	−	0.644736i	$-0.776967\pi$
$337$	−79.7500	−	503.522i	−0.236647	−	1.49413i	0.527759	−	0.849394i	$-0.323033\pi$
$338$	56.5602	−	357.107i	0.167338	−	1.05653i
$339$	−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
$343$	−68.1152	−	133.684i	−0.198587	−	0.389748i
$344$	136.588	+	187.997i	0.397057	+	0.546503i
$345$		0			0
$346$	−97.1676	−	299.051i	−0.280831	−	0.864310i
$347$	−26.4729	+	51.9560i	−0.0762908	+	0.149729i	−0.926001	−	0.377521i	$-0.876777\pi$
$347$	−26.4729	+	51.9560i	−0.0762908	+	0.149729i	0.849710	+	0.527250i	$0.176777\pi$
$348$	99.6884	−	15.7891i	0.286461	−	0.0453710i
$349$	−260.442	−	358.468i	−0.746253	−	1.02713i	−0.998234	−	0.0593967i	$-0.981082\pi$
$349$	−260.442	−	358.468i	−0.746253	−	1.02713i	0.251982	−	0.967732i	$-0.418918\pi$
$350$		0			0
$351$	−117.961			−0.336071
$352$	−125.055	+	300.744i	−0.355271	+	0.854386i
$353$	−124.571	+	124.571i	−0.352892	+	0.352892i	−0.861184	−	0.508293i	$-0.830277\pi$
$353$	−124.571	+	124.571i	−0.352892	+	0.352892i	0.508293	+	0.861184i	$0.330277\pi$
$354$	750.082	+	243.716i	2.11888	+	0.688465i
$355$		0			0
$356$	−34.7320	−	25.2343i	−0.0975618	−	0.0708828i
$357$	−24.7748	+	48.6232i	−0.0693971	+	0.136200i
$358$	255.677	+	130.274i	0.714181	+	0.363893i
$359$	−290.091	+	399.276i	−0.808053	+	1.11219i	0.183568	+	0.983007i	$0.441235\pi$
$359$	−290.091	+	399.276i	−0.808053	+	1.11219i	−0.991621	+	0.129183i	$0.958765\pi$
$360$		0			0
$361$	106.205	−	326.867i	0.294198	−	0.905448i
$362$	−106.632	−	106.632i	−0.294565	−	0.294565i
$363$	−223.606	−	309.548i	−0.615994	−	0.852749i
$364$		−	14.7311i		−	0.0404700i
$365$		0			0
$366$	176.753	−	128.419i	0.482932	−	0.350871i
$367$	14.6008	+	92.1861i	0.0397843	+	0.251188i	0.999563	−	0.0295704i	$-0.00941392\pi$
$367$	14.6008	+	92.1861i	0.0397843	+	0.251188i	−0.959778	+	0.280759i	$0.909414\pi$
$368$	−102.982	−	52.4721i	−0.279843	−	0.142587i
$369$	−39.4162	+	12.8071i	−0.106819	+	0.0347076i
$370$		0			0
$371$	−35.1141	+	25.5119i	−0.0946470	+	0.0687651i
$372$	309.111	−	157.500i	0.830944	−	0.423387i
$373$	−278.202	+	278.202i	−0.745850	+	0.745850i	−0.973697	−	0.227847i	$-0.926831\pi$
$373$	−278.202	+	278.202i	−0.745850	+	0.745850i	0.227847	+	0.973697i	$0.426831\pi$
$374$	−274.642	+	113.320i	−0.734338	+	0.302994i
$375$		0			0
$376$	114.510	−	352.424i	0.304547	−	0.937298i
$377$	72.7802	+	11.5272i	0.193051	+	0.0305763i
$378$	96.5545	−	15.2927i	0.255435	−	0.0404570i
$379$	267.869	−	87.0358i	0.706777	−	0.229646i	0.0664964	−	0.997787i	$-0.478818\pi$
$379$	267.869	−	87.0358i	0.706777	−	0.229646i	0.640281	+	0.768141i	$0.278818\pi$
$380$		0			0
$381$	−286.006	−	207.796i	−0.750673	−	0.545396i
$382$	287.260	+	45.4976i	0.751991	+	0.119104i
$383$	105.002	+	206.078i	0.274156	+	0.538062i	0.986499	−	0.163770i	$-0.0523656\pi$
$383$	105.002	+	206.078i	0.274156	+	0.538062i	−0.712342	+	0.701832i	$0.752366\pi$
$384$		−	430.784i		−	1.12183i
$385$		0			0
$386$	107.559			0.278650
$387$	−40.8602	+	20.8193i	−0.105582	+	0.0537966i
$388$	6.64439	−	41.9510i	0.0171247	−	0.108121i
$389$	−238.146	+	327.780i	−0.612200	+	0.842621i	−0.996756	−	0.0804803i	$-0.974355\pi$
$389$	−238.146	+	327.780i	−0.612200	+	0.842621i	0.384556	+	0.923102i	$0.374355\pi$
$390$		0			0
$391$	−19.6625	−	60.5151i	−0.0502879	−	0.154770i
$392$	35.3987	+	223.499i	0.0903028	+	0.570149i
$393$	−100.622	+	635.301i	−0.256035	+	1.61654i
$394$	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	0.416706	−	0.909041i	$-0.363184\pi$
$397$	−195.457	−	195.457i	−0.492335	−	0.492335i	−0.909041	+	0.416706i	$0.863184\pi$
$398$	−207.077	−	406.411i	−0.520294	−	1.02113i
$399$	−12.1215	−	16.6838i	−0.0303797	−	0.0418141i
$400$		0			0
$401$	−83.1565	−	255.929i	−0.207373	−	0.638228i	−0.999608	−	0.0280116i	$-0.991082\pi$
$401$	−83.1565	−	255.929i	−0.207373	−	0.638228i	0.792235	−	0.610216i	$-0.208918\pi$
$402$	5.08761	−	9.98500i	0.0126557	−	0.0248383i
$403$	250.162	−	39.6218i	0.620750	−	0.0983172i
$404$	179.908	+	247.622i	0.445316	+	0.612925i
$405$		0			0
$406$	−61.0671			−0.150412
$407$	−232.863	+	142.260i	−0.572146	+	0.349534i
$408$	119.480	−	119.480i	0.292843	−	0.292843i
$409$	−646.708	−	210.128i	−1.58119	−	0.513761i	−0.618830	−	0.785525i	$-0.712393\pi$
$409$	−646.708	−	210.128i	−1.58119	−	0.513761i	−0.962364	+	0.271764i	$0.912393\pi$
$410$		0			0
$411$	664.129	+	482.518i	1.61589	+	1.17401i
$412$	−77.3957	+	151.898i	−0.187854	+	0.368684i
$413$	−142.557	−	72.6364i	−0.345174	−	0.175875i
$414$	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
$418$	8.96236	−	111.916i	0.0214410	−	0.267742i
$419$			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	−0.883795	−	0.467875i	$-0.845020\pi$
$421$	−299.721	+	217.760i	−0.711926	+	0.517245i	0.171868	+	0.985120i	$0.445020\pi$
$422$	102.706	+	648.463i	0.243380	+	1.53664i
$423$	65.1578	+	33.1996i	0.154037	+	0.0784860i
$424$	127.814	−	41.5292i	0.301447	−	0.0979462i
$425$		0			0
$426$	−466.419	+	338.874i	−1.09488	+	0.795478i
$427$	−39.4908	+	20.1215i	−0.0924842	+	0.0471231i
$428$	−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	0.421538	+	0.906811i	$0.361490\pi$
$431$	−195.029	+	600.237i	−0.452503	+	1.39266i	−0.874041	+	0.485851i	$0.838510\pi$
$432$	−501.233	−	79.3876i	−1.16026	−	0.183768i
$433$	537.926	−	85.1992i	1.24232	−	0.196765i	0.499537	−	0.866293i	$-0.333503\pi$
$433$	537.926	−	85.1992i	1.24232	−	0.196765i	0.742787	+	0.669528i	$0.233503\pi$
$434$	−199.629	+	64.8632i	−0.459974	+	0.149454i
$435$		0			0
$436$	236.649	+	171.935i	0.542772	+	0.394347i
$437$	23.7494	+	3.76154i	0.0543464	+	0.00860763i
$438$	345.500	+	678.083i	0.788814	+	1.54813i
$439$		−	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
$442$	−111.876	+	57.0036i	−0.253113	+	0.128967i
$443$	52.9881	−	334.553i	0.119612	−	0.755200i	−0.852853	−	0.522151i	$-0.825130\pi$
$443$	52.9881	−	334.553i	0.119612	−	0.755200i	0.972465	−	0.233049i	$-0.0748702\pi$
$444$	−92.8475	+	127.794i	−0.209116	+	0.287824i
$445$		0			0
$446$	−90.1591	−	277.481i	−0.202150	−	0.622155i
$447$	53.9922	+	340.894i	0.120788	+	0.762625i
$448$	−1.80898	+	11.4214i	−0.00403790	+	0.0254943i
$449$	−666.170	−	216.452i	−1.48368	−	0.482075i	−0.548467	−	0.836173i	$-0.684788\pi$
$449$	−666.170	−	216.452i	−1.48368	−	0.482075i	−0.935209	+	0.354097i	$0.884788\pi$
$450$		0			0
$451$	404.712	+	248.771i	0.897365	+	0.551599i
$452$	80.1131	+	80.1131i	0.177241	+	0.177241i
$453$	−175.824	−	345.074i	−0.388133	−	0.761753i
$454$	246.071	+	338.688i	0.542007	+	0.746008i
$455$		0			0
$456$	19.7319	+	60.7284i	0.0432716	+	0.133176i
$457$	69.6387	−	136.674i	0.152382	−	0.299067i	−0.802178	−	0.597085i	$-0.796325\pi$
$457$	69.6387	−	136.674i	0.152382	−	0.299067i	0.954560	+	0.298018i	$0.0963255\pi$
$458$	−310.137	+	49.1208i	−0.677154	+	0.107251i
$459$	−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	$0.490642\pi$
$462$	101.580	+	86.9984i	0.219870	+	0.188308i
$463$	−422.021	+	422.021i	−0.911492	+	0.911492i	−0.996390	−	0.0848979i	$-0.972944\pi$
$463$	−422.021	+	422.021i	−0.911492	+	0.911492i	0.0848979	+	0.996390i	$0.472944\pi$
$464$	301.496	+	97.9619i	0.649775	+	0.211125i
$465$		0			0
$466$	528.093	+	383.682i	1.13325	+	0.823352i
$467$	63.4768	−	124.580i	0.135925	−	0.266767i	−0.813004	−	0.582258i	$-0.802169\pi$
$467$	63.4768	−	124.580i	0.135925	−	0.266767i	0.948929	+	0.315491i	$0.102169\pi$
$468$	−8.02028	−	4.08654i	−0.0171373	−	0.00873191i
$469$	−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
$473$	485.361	+	201.823i	1.02613	+	0.426687i
$474$		−	873.233i		−	1.84226i
$475$		0			0
$476$	28.2260	−	20.5074i	0.0592984	−	0.0430828i
$477$	4.14887	+	26.1949i	0.00869784	+	0.0549160i
$478$	−396.743	−	202.151i	−0.830007	−	0.422909i
$479$	−250.078	+	81.2552i	−0.522083	+	0.169635i	−0.558190	−	0.829713i	$-0.688504\pi$
$479$	−250.078	+	81.2552i	−0.522083	+	0.169635i	0.0361074	+	0.999348i	$0.488504\pi$
$480$		0			0
$481$	−93.2991	+	67.7858i	−0.193969	+	0.140927i
$482$	249.651	−	127.203i	0.517947	−	0.263907i
$483$	−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
$487$	750.146	+	118.812i	1.54034	+	0.243966i	0.868109	−	0.496374i	$-0.165335\pi$
$487$	750.146	+	118.812i	1.54034	+	0.243966i	0.672233	+	0.740340i	$0.265335\pi$
$488$	135.545	−	21.4682i	0.277755	−	0.0439921i
$489$	943.536	−	306.573i	1.92952	−	0.626939i
$490$		0			0
$491$	433.696	+	315.098i	0.883290	+	0.641748i	0.934120	−	0.356959i	$-0.116187\pi$
$491$	433.696	+	315.098i	0.883290	+	0.641748i	−0.0508295	+	0.998707i	$0.516187\pi$
$492$	271.610	+	43.0188i	0.552053	+	0.0874366i
$493$	79.2314	+	155.500i	0.160713	+	0.315417i
$494$		−	47.4494i		−	0.0960514i
$495$		0			0
$496$	1089.64			2.19686
$497$	104.209	−	53.0971i	0.209676	−	0.106835i
$498$	−131.678	+	831.380i	−0.264413	+	1.66944i
$499$	−33.5801	+	46.2190i	−0.0672947	+	0.0926233i	−0.841338	−	0.540510i	$-0.818231\pi$
$499$	−33.5801	+	46.2190i	−0.0672947	+	0.0926233i	0.774043	+	0.633133i	$0.218231\pi$
$500$		0			0
$501$	−29.2779	−	90.1082i	−0.0584390	−	0.179857i
$502$	−72.4071	−	457.161i	−0.144237	−	0.910678i
$503$	−58.9680	+	372.309i	−0.117233	+	0.740177i	0.857114	+	0.515126i	$0.172255\pi$
$503$	−58.9680	+	372.309i	−0.117233	+	0.740177i	−0.974347	+	0.225051i	$0.927745\pi$
$504$	−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
$508$	102.611	+	201.385i	0.201990	+	0.396428i
$509$	−453.233	−	623.822i	−0.890438	−	1.22558i	−0.973419	−	0.229032i	$-0.926444\pi$
$509$	−453.233	−	623.822i	−0.890438	−	1.22558i	0.0829808	−	0.996551i	$-0.473556\pi$
$510$		0			0
$511$	−47.7078	−	146.829i	−0.0933616	−	0.287337i
$512$	−92.2357	+	181.023i	−0.180148	+	0.353560i
$513$	104.278	−	16.5160i	0.203270	−	0.0321948i
$514$	46.3311	+	63.7693i	0.0901384	+	0.124065i
$515$		0			0
$516$	304.283			0.589695
$517$	−194.563	−	815.336i	−0.376332	−	1.57705i
$518$	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	0.928441	−	0.371480i	$-0.121149\pi$
$521$	449.127	+	326.310i	0.862047	+	0.626314i	−0.0663939	+	0.997793i	$0.521149\pi$
$522$	−16.9406	+	33.2478i	−0.0324532	+	0.0636930i
$523$	−467.329	−	238.116i	−0.893555	−	0.455289i	−0.0539855	−	0.998542i	$-0.517192\pi$
$523$	−467.329	−	238.116i	−0.893555	−	0.455289i	−0.839569	+	0.543253i	$0.817192\pi$
$524$	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
$528$	−361.951	−	592.472i	−0.685514	−	1.12211i
$529$			495.602i			0.936866i
$530$		0			0
$531$	−79.0932	+	57.4646i	−0.148951	+	0.108220i
$532$	2.06253	+	13.0223i	0.00387693	+	0.0244780i
$533$	178.885	+	91.1467i	0.335620	+	0.171007i
$534$	156.662	−	50.9026i	0.293375	−	0.0953232i
$535$		0			0
$536$	5.69478	−	4.13750i	0.0106246	−	0.00771922i
$537$	−328.927	+	167.597i	−0.612527	+	0.312098i
$538$	−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	−0.373039	−	0.927815i	$-0.621684\pi$
$541$	256.495	−	789.409i	0.474112	−	1.45917i	0.847151	−	0.531351i	$-0.178316\pi$
$542$	−411.212	−	65.1296i	−0.758694	−	0.120165i
$543$	191.616	−	30.3490i	0.352884	−	0.0558914i
$544$	−310.057	+	100.744i	−0.569957	+	0.185190i
$545$		0			0
$546$	45.7275	+	33.2230i	0.0837500	+	0.0608479i
$547$	−553.032	−	87.5917i	−1.01103	−	0.160131i	−0.371122	−	0.928584i	$-0.621027\pi$
$547$	−553.032	−	87.5917i	−1.01103	−	0.160131i	−0.639906	+	0.768453i	$0.721027\pi$
$548$	−238.271	−	467.633i	−0.434801	−	0.853344i
$549$			27.0825i			0.0493306i
$550$		0			0
$551$	−65.9517			−0.119695
$552$	79.0225	−	40.2640i	0.143157	−	0.0729419i
$553$	−27.7120	+	174.967i	−0.0501121	+	0.316395i
$554$	49.1543	−	67.6551i	0.0887262	−	0.122121i
$555$		0			0
$556$	−25.5134	−	78.5220i	−0.0458873	−	0.141227i
$557$	135.902	+	858.051i	0.243989	+	1.54049i	0.740261	+	0.672320i	$0.234702\pi$
$557$	135.902	+	858.051i	0.243989	+	1.54049i	−0.496272	+	0.868167i	$0.665298\pi$
$558$	−20.0642	+	126.681i	−0.0359574	+	0.227026i
$559$	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
$563$	−416.009	−	816.464i	−0.738915	−	1.45020i	−0.887262	−	0.461267i	$-0.847395\pi$
$563$	−416.009	−	816.464i	−0.738915	−	1.45020i	0.148347	−	0.988935i	$-0.452605\pi$
$564$	−285.208	−	392.555i	−0.505688	−	0.696020i
$565$		0			0
$566$	−169.808	−	522.614i	−0.300013	−	0.923346i
$567$	−63.2543	+	124.144i	−0.111560	+	0.218948i
$568$	−357.678	+	56.6506i	−0.629714	+	0.0997369i
$569$	229.953	+	316.504i	0.404136	+	0.556245i	0.961776	−	0.273838i	$-0.0882931\pi$
$569$	229.953	+	316.504i	0.404136	+	0.556245i	−0.557640	+	0.830083i	$0.688293\pi$
$570$		0			0
$571$	−768.261			−1.34547			−0.672733	−	0.739886i	$-0.734880\pi$
$571$	−768.261			−1.34547			−0.672733	+	0.739886i	$0.734880\pi$
$572$	23.9488	+	100.360i	0.0418686	+	0.175454i
$573$	−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
$577$	114.260	−	224.247i	0.198023	−	0.388643i	−0.770547	−	0.637384i	$-0.780017\pi$
$577$	114.260	−	224.247i	0.198023	−	0.388643i	0.968570	+	0.248741i	$0.0800167\pi$
$578$	366.706	+	186.846i	0.634439	+	0.323263i
$579$	−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
$583$	197.749	−	230.893i	0.339193	−	0.396043i
$584$			478.029i			0.818543i
$585$		0			0
$586$	970.304	−	704.967i	1.65581	−	1.20302i
$587$	−71.3761	−	450.651i	−0.121595	−	0.767719i	−0.970841	−	0.239722i	$-0.922944\pi$
$587$	−71.3761	−	450.651i	−0.121595	−	0.767719i	0.849247	−	0.527996i	$-0.177056\pi$
$588$	264.010	+	134.520i	0.448996	+	0.228775i
$589$	−215.596	+	70.0514i	−0.366038	+	0.118933i
$590$		0			0
$591$	−162.624	+	118.154i	−0.275168	+	0.199921i
$592$	−442.061	+	225.241i	−0.746725	+	0.380475i
$593$	−237.348	+	237.348i	−0.400250	+	0.400250i	−0.878321	−	0.478071i	$-0.841336\pi$
$593$	−237.348	+	237.348i	−0.400250	+	0.400250i	0.478071	+	0.878321i	$0.341336\pi$
$594$	−632.944	+	261.158i	−1.06556	+	0.439660i
$595$		0			0
$596$	68.1884	−	209.862i	0.114410	−	0.352118i
$597$	579.579	+	91.7963i	0.970820	+	0.153763i
$598$	−65.0930	+	10.3097i	−0.108851	+	0.0172403i
$599$	984.287	−	319.814i	1.64322	−	0.533913i	0.665962	−	0.745985i	$-0.268021\pi$
$599$	984.287	−	319.814i	1.64322	−	0.533913i	0.977254	+	0.212072i	$0.0680212\pi$
$600$		0			0
$601$	45.7081	+	33.2089i	0.0760534	+	0.0552560i	0.625162	−	0.780495i	$-0.285033\pi$
$601$	45.7081	+	33.2089i	0.0760534	+	0.0552560i	−0.549109	+	0.835751i	$0.685033\pi$
$602$	−181.836	−	28.8000i	−0.302053	−	0.0478405i
$603$	0.630656	+	1.23773i	0.00104586	+	0.00205262i
$604$			247.606i			0.409943i
$605$		0			0
$606$	−1174.40			−1.93796
$607$	−725.590	+	369.707i	−1.19537	+	0.609072i	−0.934383	−	0.356270i	$-0.884048\pi$
$607$	−725.590	+	369.707i	−1.19537	+	0.609072i	−0.260988	+	0.965342i	$0.584048\pi$
$608$	19.2727	−	121.683i	0.0316985	−	0.200137i
$609$	46.1779	−	63.5584i	0.0758257	−	0.104365i
$610$		0			0
$611$	−109.470	−	336.913i	−0.179165	−	0.551413i
$612$	−3.33502	−	21.0565i	−0.00544938	−	0.0344060i
$613$	127.102	−	802.492i	0.207345	−	1.30912i	−0.635975	−	0.771710i	$-0.719402\pi$
$613$	127.102	−	802.492i	0.207345	−	1.30912i	0.843320	−	0.537412i	$-0.180598\pi$
$614$	−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	0.511955	−	0.859012i	$-0.328921\pi$
$617$	−214.134	−	214.134i	−0.347057	−	0.347057i	−0.859012	+	0.511955i	$0.828921\pi$
$618$	−296.963	−	582.823i	−0.480523	−	0.943079i
$619$	589.455	+	811.316i	0.952270	+	1.31069i	0.950512	+	0.310689i	$0.100560\pi$
$619$	589.455	+	811.316i	0.952270	+	1.31069i	0.00175860	+	0.999998i	$0.499440\pi$
$620$		0			0
$621$	−45.3145	−	139.464i	−0.0729703	−	0.224579i
$622$	−508.393	+	997.777i	−0.817352	+	1.60414i
$623$	−33.0052	+	5.22751i	−0.0529778	+	0.00839087i
$624$	−172.467	−	237.380i	−0.276389	−	0.380417i
$625$		0			0
$626$	−934.621			−1.49300
$627$	109.705	+	93.9571i	0.174968	+	0.149852i
$628$	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	−0.141130	−	0.989991i	$-0.545073\pi$
$631$	−710.682	−	516.341i	−1.12628	−	0.818289i	−0.985149	+	0.171702i	$0.945073\pi$
$632$	249.017	−	488.724i	0.394015	−	0.773297i
$633$	−752.582	−	383.460i	−1.18891	−	0.605782i
$634$	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
$638$	416.038	−	99.2789i	0.652096	−	0.155610i
$639$		−	71.4658i		−	0.111840i
$640$		0			0
$641$	398.231	−	289.331i	0.621265	−	0.451375i	−0.232098	−	0.972692i	$-0.574559\pi$
$641$	398.231	−	289.331i	0.621265	−	0.451375i	0.853363	+	0.521317i	$0.174559\pi$
$642$	−206.343	−	1302.80i	−0.321407	−	2.02929i
$643$	319.165	+	162.623i	0.496369	+	0.252913i	0.684208	−	0.729287i	$-0.260148\pi$
$643$	319.165	+	162.623i	0.496369	+	0.252913i	−0.187839	+	0.982200i	$0.560148\pi$
$644$	17.4164	−	5.65892i	0.0270440	−	0.00878714i
$645$		0			0
$646$	90.9171	−	66.0551i	0.140739	−	0.102253i
$647$	19.7726	−	10.0746i	0.0305604	−	0.0155713i	−0.438644	−	0.898661i	$-0.644541\pi$
$647$	19.7726	−	10.0746i	0.0305604	−	0.0155713i	0.469204	+	0.883090i	$0.344541\pi$
$648$	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
$652$	−626.471	−	99.2233i	−0.960845	−	0.152183i
$653$	630.349	−	99.8375i	0.965313	−	0.152891i	0.346173	−	0.938171i	$-0.387481\pi$
$653$	630.349	−	99.8375i	0.965313	−	0.152891i	0.619140	+	0.785280i	$0.287481\pi$
$654$	−1067.43	+	346.828i	−1.63215	+	0.530318i
$655$		0			0
$656$	698.768	+	507.685i	1.06520	+	0.773910i
$657$	−93.1753	−	14.7575i	−0.141819	−	0.0224620i
$658$	133.282	+	261.581i	0.202557	+	0.397540i
$659$			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	$0.548137\pi$
$662$	−80.0525	+	40.7888i	−0.120925	+	0.0616145i
$663$	25.2694	−	159.545i	0.0381138	−	0.240641i
$664$	−310.778	+	427.750i	−0.468040	+	0.644202i
$665$		0			0
$666$	−18.0464	−	55.5411i	−0.0270967	−	0.0833951i
$667$	14.3299	+	90.4752i	0.0214841	+	0.135645i
$668$	−9.47588	+	59.8284i	−0.0141855	+	0.0895634i
$669$	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
$673$	433.104	+	850.014i	0.643542	+	1.26302i	0.950330	+	0.311244i	$0.100746\pi$
$673$	433.104	+	850.014i	0.643542	+	1.26302i	−0.306788	+	0.951778i	$0.599254\pi$
$674$	−735.075	−	1011.74i	−1.09062	−	1.50110i
$675$		0			0
$676$	−91.8962	−	282.827i	−0.135941	−	0.418384i
$677$	375.286	−	736.540i	0.554337	−	1.08795i	−0.428512	−	0.903536i	$-0.640962\pi$
$677$	375.286	−	736.540i	0.554337	−	1.08795i	0.982849	−	0.184411i	$-0.0590378\pi$
$678$	−429.362	+	68.0043i	−0.633278	+	0.100301i
$679$	−19.4326	−	26.7467i	−0.0286195	−	0.0393914i
$680$		0			0
$681$	−538.579			−0.790865
$682$	1254.58	−	766.443i	1.83956	−	1.12382i
$683$	398.457	−	398.457i	0.583392	−	0.583392i	−0.352442	−	0.935834i	$-0.614649\pi$
$683$	398.457	−	398.457i	0.583392	−	0.583392i	0.935834	+	0.352442i	$0.114649\pi$
$684$	7.66209	+	2.48957i	0.0112019	+	0.00363972i
$685$		0			0
$686$	−297.762	−	216.337i	−0.434055	−	0.315360i
$687$	183.395	−	359.933i	0.266951	−	0.523920i
$688$	851.546	+	433.884i	1.23771	+	0.630646i
$689$	75.5166	−	103.940i	0.109603	−	0.150856i
$690$		0			0
$691$	−26.9603	+	82.9754i	−0.0390164	+	0.120080i	−0.968668	−	0.248361i	$-0.920108\pi$
$691$	−26.9603	+	82.9754i	−0.0390164	+	0.120080i	0.929651	+	0.368441i	$0.120108\pi$
$692$	−182.878	−	182.878i	−0.264274	−	0.264274i
$693$	−16.1259	+	3.84812i	−0.0232697	+	0.00555284i
$694$			143.044i			0.206115i
$695$		0			0
$696$	−196.798	+	142.982i	−0.282756	+	0.205434i
$697$	74.3848	+	469.647i	0.106721	+	0.673812i
$698$	−968.474	−	493.462i	−1.38750	−	0.706966i
$699$	−798.669	+	259.503i	−1.14259	+	0.371249i
$700$		0			0
$701$	48.2784	−	35.0763i	0.0688707	−	0.0500375i	−0.552817	−	0.833303i	$-0.686447\pi$
$701$	48.2784	−	35.0763i	0.0688707	−	0.0500375i	0.621688	+	0.783265i	$0.286447\pi$
$702$	−257.830	+	131.371i	−0.367279	+	0.187138i
$703$	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
$707$	235.311	+	37.2695i	0.332830	+	0.0527151i
$708$	640.707	−	101.478i	0.904953	−	0.143330i
$709$	590.657	−	191.916i	0.833085	−	0.270686i	0.138740	−	0.990329i	$-0.455695\pi$
$709$	590.657	−	191.916i	0.833085	−	0.270686i	0.694344	+	0.719643i	$0.255695\pi$
$710$		0			0
$711$	87.5723	+	63.6250i	0.123168	+	0.0894866i
$712$	102.195	+	16.1861i	0.143532	+	0.0227333i
$713$	142.944	+	280.543i	0.200482	+	0.393468i
$714$			133.868i			0.187490i
$715$		0			0
$716$	236.019			0.329636
$717$	510.408	−	260.066i	0.711866	−	0.362714i
$718$	−189.392	+	1195.78i	−0.263778	+	1.66543i
$719$	629.901	−	866.984i	0.876079	−	1.20582i	−0.101412	−	0.994844i	$-0.532336\pi$
$719$	629.901	−	866.984i	0.876079	−	1.20582i	0.977491	−	0.210975i	$-0.0676639\pi$
$720$		0			0
$721$	41.0056	+	126.202i	0.0568732	+	0.175038i
$722$	−131.890	−	832.719i	−0.182673	−	1.15335i
$723$	−56.3887	+	356.024i	−0.0779926	+	0.492426i
$724$	−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	0.234910	−	0.972017i	$-0.424521\pi$
$727$	−535.877	−	535.877i	−0.737107	−	0.737107i	−0.972017	+	0.234910i	$0.924521\pi$
$728$	16.1183	+	31.6339i	0.0221405	+	0.0434532i
$729$	−373.581	−	514.191i	−0.512457	−	0.705337i
$730$		0			0
$731$	162.587	+	500.391i	0.222417	+	0.684529i
$732$	81.5818	−	160.113i	0.111451	−	0.218734i
$733$	234.969	−	37.2155i	0.320558	−	0.0507714i	0.00591819	−	0.999982i	$-0.498116\pi$
$733$	234.969	−	37.2155i	0.320558	−	0.0507714i	0.314640	+	0.949211i	$0.398116\pi$
$734$	134.579	+	185.233i	0.183351	+	0.252361i
$735$		0			0
$736$	−171.117			−0.232496
$737$	6.11360	−	14.7025i	0.00829525	−	0.0199491i
$738$	−71.8898	+	71.8898i	−0.0974117	+	0.0974117i
$739$	143.146	+	46.5111i	0.193703	+	0.0629378i	0.404262	−	0.914643i	$-0.367528\pi$
$739$	143.146	+	46.5111i	0.193703	+	0.0629378i	−0.210559	+	0.977581i	$0.567528\pi$
$740$		0			0
$741$	49.3851	+	35.8804i	0.0666466	+	0.0484216i
$742$	−48.3375	+	94.8677i	−0.0651449	+	0.127854i
$743$	212.210	+	108.126i	0.285612	+	0.145526i	0.590927	−	0.806725i	$-0.298762\pi$
$743$	212.210	+	108.126i	0.285612	+	0.145526i	−0.305316	+	0.952251i	$0.598762\pi$
$744$	−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
$748$	−158.958	+	185.601i	−0.212511	+	0.248129i
$749$			267.586i			0.357258i
$750$		0			0
$751$	−930.748	+	676.228i	−1.23935	+	0.900437i	−0.997555	−	0.0698916i	$-0.977735\pi$
$751$	−930.748	+	676.228i	−1.23935	+	0.900437i	−0.241790	+	0.970328i	$0.577735\pi$
$752$	−238.411	−	1505.27i	−0.317035	−	2.00168i
$753$	530.564	+	270.336i	0.704600	+	0.359012i
$754$	171.915	−	55.8586i	0.228004	−	0.0740830i
$755$		0			0
$756$	65.0500	−	47.2616i	0.0860450	−	0.0625153i
$757$	−1091.88	+	556.341i	−1.44238	+	0.734929i	−0.987793	−	0.155774i	$-0.950213\pi$
$757$	−1091.88	+	556.341i	−1.44238	+	0.734929i	−0.454586	+	0.890703i	$0.650213\pi$
$758$	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	0.762311	+	0.647211i	$0.224065\pi$
$761$	−178.708	+	550.005i	−0.234833	+	0.722740i	−0.997144	+	0.0755295i	$0.975935\pi$
$762$	−856.550	−	135.664i	−1.12408	−	0.178037i
$763$	224.883	−	35.6180i	0.294735	−	0.0466815i
$764$	227.509	−	73.9222i	0.297787	−	0.0967569i
$765$		0			0
$766$	459.010	+	333.490i	0.599230	+	0.435366i
$767$	467.765	+	74.0867i	0.609863	+	0.0965928i
$768$	−437.559	−	858.758i	−0.569738	−	1.11817i
$769$			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
$772$	78.8249	−	40.1633i	0.102105	−	0.0520250i
$773$	135.591	−	856.088i	0.175409	−	1.10749i	−0.730156	−	0.683280i	$-0.760553\pi$
$773$	135.591	−	856.088i	0.175409	−	1.10749i	0.905565	−	0.424207i	$-0.139447\pi$
$774$	−66.1230	+	91.0105i	−0.0854302	+	0.117585i
$775$		0			0
$776$	31.6332	+	97.3570i	0.0407644	+	0.125460i
$777$	19.2342	+	121.440i	0.0247545	+	0.156293i
$778$	−155.479	+	981.655i	−0.199844	+	1.26177i
$779$	−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
$783$	182.598	+	358.368i	0.233203	+	0.457686i
$784$	547.025	+	752.916i	0.697737	+	0.960352i
$785$		0			0
$786$	487.592	+	1500.65i	0.620346	+	1.90923i
$787$	−153.220	+	300.712i	−0.194689	+	0.382099i	−0.967628	−	0.252382i	$-0.918786\pi$
$787$	−153.220	+	300.712i	−0.194689	+	0.382099i	0.772939	+	0.634481i	$0.218786\pi$
$788$	126.934	−	20.1043i	0.161084	−	0.0255131i
$789$	−695.365	−	957.088i	−0.881325	−	1.21304i
$790$		0			0
$791$	88.1879			0.111489
$792$	51.1693	+	4.09768i	0.0646077	+	0.00517384i
$793$	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
$797$	−31.7654	+	62.3432i	−0.0398562	+	0.0782223i	−0.910076	−	0.414442i	$-0.863977\pi$
$797$	−31.7654	+	62.3432i	−0.0398562	+	0.0782223i	0.870220	+	0.492664i	$0.163977\pi$
$798$	−45.0748	−	22.9667i	−0.0564847	−	0.0287804i
$799$	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
$803$	563.729	+	922.758i	0.702028	+	1.14914i
$804$		−	9.21730i		−	0.0114643i
$805$		0			0
$806$	502.660	−	365.204i	0.623647	−	0.453106i
$807$	−51.4826	−	325.048i	−0.0637951	−	0.402786i
$808$	−657.280	−	334.901i	−0.813465	−	0.414481i
$809$	577.635	−	187.685i	0.714011	−	0.231996i	0.0705865	−	0.997506i	$-0.477513\pi$
$809$	577.635	−	187.685i	0.714011	−	0.231996i	0.643425	+	0.765509i	$0.277513\pi$
$810$		0			0
$811$	1034.41	−	751.545i	1.27548	−	0.926689i	0.276071	−	0.961137i	$-0.410967\pi$
$811$	1034.41	−	751.545i	1.27548	−	0.926689i	0.999406	+	0.0344482i	$0.0109674\pi$
$812$	−44.7533	+	22.8030i	−0.0551149	+	0.0280825i
$813$	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
$817$	−196.380	−	31.1036i	−0.240368	−	0.0380705i
$818$	−1647.54	+	260.945i	−2.01411	+	0.319004i
$819$	−6.66354	+	2.16512i	−0.00813619	+	0.00264361i
$820$		0			0
$821$	−388.039	−	281.927i	−0.472641	−	0.343394i	0.325828	−	0.945429i	$-0.394357\pi$
$821$	−388.039	−	281.927i	−0.472641	−	0.343394i	−0.798470	+	0.602035i	$0.794357\pi$
$822$	1988.97	+	315.023i	2.41968	+	0.383239i
$823$	39.4376	+	77.4006i	0.0479193	+	0.0940469i	0.913724	−	0.406334i	$-0.133193\pi$
$823$	39.4376	+	77.4006i	0.0479193	+	0.0940469i	−0.865805	+	0.500381i	$0.833193\pi$
$824$		−	410.874i		−	0.498633i
$825$		0			0
$826$	−392.484			−0.475162
$827$	254.677	−	129.764i	0.307953	−	0.156910i	−0.293184	−	0.956056i	$-0.594715\pi$
$827$	254.677	−	129.764i	0.307953	−	0.156910i	0.601137	+	0.799146i	$0.294715\pi$
$828$	1.75048	−	11.0521i	0.00211411	−	0.0133480i
$829$	−561.476	+	772.805i	−0.677293	+	0.932214i	−0.999897	−	0.0143202i	$-0.995442\pi$
$829$	−561.476	+	772.805i	−0.677293	+	0.932214i	0.322605	+	0.946534i	$0.395442\pi$
$830$		0			0
$831$	33.2455	+	102.319i	0.0400067	+	0.123128i
$832$	−5.35468	−	33.8081i	−0.00643591	−	0.0406348i
$833$	−80.1488	+	506.040i	−0.0962171	+	0.607491i
$834$	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
$838$	503.267	+	987.718i	0.600558	+	1.17866i
$839$	−603.415	−	830.530i	−0.719208	−	0.989904i	−0.999550	−	0.0300042i	$-0.990448\pi$
$839$	−603.415	−	830.530i	−0.719208	−	0.989904i	0.280342	−	0.959900i	$-0.409552\pi$
$840$		0			0
$841$	182.243	+	560.887i	0.216698	+	0.666929i
$842$	−412.592	+	809.757i	−0.490014	+	0.961707i
$843$	158.298	−	25.0720i	0.187780	−	0.0297414i
$844$	317.410	+	436.878i	0.376078	+	0.517628i
$845$		0			0
$846$	179.391			0.212046
$847$	153.432	+	112.119i	0.181148	+	0.132372i
$848$	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
$852$	−215.279	+	422.510i	−0.252675	+	0.495904i
$853$	−51.5549	−	26.2685i	−0.0604395	−	0.0307955i	0.423510	−	0.905892i	$-0.360798\pi$
$853$	−51.5549	−	26.2685i	−0.0604395	−	0.0307955i	−0.483949	+	0.875096i	$0.660798\pi$
$854$	−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	0.559756	−	0.828658i	$-0.310895\pi$
$857$	−230.449	−	230.449i	−0.268902	−	0.268902i	−0.828658	+	0.559756i	$0.810895\pi$
$858$	−365.544	−	152.000i	−0.426042	−	0.177157i
$859$		−	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
$862$	242.194	+	1529.15i	0.280968	+	1.77396i
$863$	−177.097	−	90.2355i	−0.205211	−	0.104560i	0.348365	−	0.937359i	$-0.386737\pi$
$863$	−177.097	−	90.2355i	−0.205211	−	0.104560i	−0.553576	+	0.832799i	$0.686737\pi$
$864$	−714.560	+	232.175i	−0.827037	+	0.268721i
$865$		0			0
$866$	1080.87	−	785.301i	1.24812	−	0.906814i
$867$	−471.765	+	240.376i	−0.544135	+	0.277251i
$868$	−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
$872$	−696.313	−	110.285i	−0.798524	−	0.126474i
$873$	−19.9529	+	3.16024i	−0.0228556	+	0.00361997i
$874$	56.0988	−	18.2276i	0.0641862	−	0.0208554i
$875$		0			0
$876$	506.403	+	367.923i	0.578086	+	0.420004i
$877$	1373.24	+	217.500i	1.56584	+	0.248005i	0.878289	−	0.478130i	$-0.158685\pi$
$877$	1373.24	+	217.500i	1.56584	+	0.248005i	0.687552	+	0.726135i	$0.258685\pi$
$878$	−551.633	−	1082.64i	−0.628283	−	1.23308i
$879$			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	$0.463023\pi$
$882$	−97.6060	+	49.7327i	−0.110664	+	0.0563863i
$883$	194.461	−	1227.78i	0.220227	−	1.39046i	−0.591445	−	0.806346i	$-0.701442\pi$
$883$	194.461	−	1227.78i	0.220227	−	1.39046i	0.811672	−	0.584114i	$-0.198558\pi$
$884$	−60.7031	+	83.5506i	−0.0686687	+	0.0945143i
$885$		0			0
$886$	−256.769	−	790.253i	−0.289807	−	0.891934i
$887$	187.852	+	1186.05i	0.211784	+	1.33715i	0.832896	+	0.553430i	$0.186681\pi$
$887$	187.852	+	1186.05i	0.211784	+	1.33715i	−0.621112	+	0.783722i	$0.713319\pi$
$888$	59.5555	−	376.019i	0.0670670	−	0.423445i
$889$	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
$893$	143.943	+	282.504i	0.161191	+	0.316354i
$894$	497.659	+	684.969i	0.556666	+	0.766184i
$895$		0			0
$896$	66.2463	+	203.885i	0.0739356	+	0.227550i
$897$	38.4919	−	75.5445i	0.0429118	−	0.0842191i
$898$	−1697.12	+	268.798i	−1.88989	+	0.299329i
$899$	−507.610	−	698.666i	−0.564639	−	0.777159i
$900$		0			0
$901$	304.285			0.337719
$902$	1161.64	+	93.0251i	1.28785	+	0.103132i
$903$	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
$907$	−722.625	+	1418.23i	−0.796720	+	1.56365i	0.0290052	+	0.999579i	$0.490766\pi$
$907$	−722.625	+	1418.23i	−0.796720	+	1.56365i	−0.825725	+	0.564072i	$0.809234\pi$
$908$	306.803	+	156.324i	0.337889	+	0.172163i
$909$	85.5686	−	117.775i	0.0941349	−	0.129566i
$910$		0			0
$911$	409.334	−	1259.80i	0.449324	−	1.38288i	−0.428348	−	0.903614i	$-0.640904\pi$
$911$	409.334	−	1259.80i	0.449324	−	1.38288i	0.877672	−	0.479263i	$-0.159096\pi$
$912$	185.697	+	185.697i	0.203615	+	0.203615i
$913$	−95.4721	+	1192.20i	−0.104570	+	1.30580i
$914$		−	376.286i		−	0.411692i
$915$		0			0
$916$	−208.943	+	151.806i	−0.228104	+	0.165727i
$917$	−50.0739	−	316.154i	−0.0546063	−	0.344770i
$918$	−610.648	−	311.141i	−0.665194	−	0.338933i
$919$	−1470.30	+	477.730i	−1.59989	+	0.519836i	−0.967081	−	0.254470i	$-0.918099\pi$
$919$	−1470.30	+	477.730i	−1.59989	+	0.519836i	−0.632811	+	0.774306i	$0.718099\pi$
$920$		0			0
$921$	856.210	−	622.073i	0.929652	−	0.675432i
$922$	59.2358	−	30.1821i	0.0642471	−	0.0327355i
$923$	−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
$927$	80.0856	+	12.6843i	0.0863923	+	0.0136832i
$928$	463.561	−	73.4209i	0.499527	−	0.0791173i
$929$	288.132	−	93.6196i	0.310152	−	0.100775i	−0.149805	−	0.988716i	$-0.547865\pi$
$929$	288.132	−	93.6196i	0.310152	−	0.100775i	0.459958	+	0.887941i	$0.347865\pi$
$930$		0			0
$931$	−156.638	−	113.804i	−0.168247	−	0.122239i
$932$	530.285	+	83.9889i	0.568976	+	0.0901169i
$933$	−654.044	−	1283.63i	−0.701012	−	1.37581i
$934$		−	342.991i		−	0.367228i
$935$		0			0
$936$	21.6943			0.0231777
$937$	−1307.58	+	666.244i	−1.39549	+	0.711039i	−0.980082	−	0.198595i	$-0.936362\pi$
$937$	−1307.58	+	666.244i	−1.39549	+	0.711039i	−0.415411	+	0.909634i	$0.636362\pi$
$938$	−0.872406	+	5.50816i	−0.000930071	+	0.00587224i
$939$	706.744	−	972.749i	0.752656	−	1.03594i
$940$		0			0
$941$	503.470	+	1549.52i	0.535037	+	1.64667i	0.743569	+	0.668659i	$0.233131\pi$
$941$	503.470	+	1549.52i	0.535037	+	1.64667i	−0.208532	+	0.978015i	$0.566869\pi$
$942$	236.689	+	1494.40i	0.251262	+	1.58641i
$943$	−39.0430	+	246.508i	−0.0414030	+	0.261408i
$944$	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	0.0981026	−	0.995176i	$-0.468723\pi$
$947$	−849.529	−	849.529i	−0.897074	−	0.897074i	−0.995176	+	0.0981026i	$0.968723\pi$
$948$	−326.072	−	639.953i	−0.343958	−	0.675055i
$949$	268.612	+	369.713i	0.283048	+	0.389581i
$950$		0			0
$951$	351.768	+	1082.63i	0.369893	+	1.13841i
$952$	−38.1748	+	74.9223i	−0.0400996	+	0.0786998i
$953$	−536.771	+	85.0162i	−0.563244	+	0.0892091i	−0.431563	−	0.902083i	$-0.642038\pi$
$953$	−536.771	+	85.0162i	−0.563244	+	0.0892091i	−0.131681	+	0.991292i	$0.542038\pi$
$954$	38.2411	+	52.6344i	0.0400850	+	0.0551723i
$955$		0			0
$956$	−366.240			−0.383096
$957$	−211.271	+	508.083i	−0.220764	+	0.530912i
$958$	−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
$962$	−128.434	+	252.067i	−0.133508	+	0.262023i
$963$	145.686	+	74.2308i	0.151284	+	0.0770829i
$964$	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	$-0.944360\pi$
$967$	−1120.43	−	1120.43i	−1.15867	−	1.15867i	−0.173909	−	0.984762i	$-0.555640\pi$
$968$	−344.548	−	476.974i	−0.355938	−	0.492742i
$969$			144.576i			0.149201i
$970$		0			0
$971$	−79.5621	+	57.8052i	−0.0819383	+	0.0595316i	−0.628000	−	0.778213i	$-0.716126\pi$
$971$	−79.5621	+	57.8052i	−0.0819383	+	0.0595316i	0.546062	+	0.837745i	$0.316126\pi$
$972$	−16.2892	−	102.846i	−0.0167584	−	0.105809i
$973$	−57.2607	−	29.1758i	−0.0588496	−	0.0299854i
$974$	1771.93	−	575.735i	1.81923	−	0.591104i
$975$		0			0
$976$	456.619	−	331.753i	0.467847	−	0.339911i
$977$	−165.681	+	84.4187i	−0.169581	+	0.0864060i	−0.536721	−	0.843760i	$-0.680337\pi$
$977$	−165.681	+	84.4187i	−0.169581	+	0.0864060i	0.367140	+	0.930166i	$0.380337\pi$
$978$	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
$982$	1298.86	+	205.719i	1.32267	+	0.209490i
$983$	−1822.61	+	288.673i	−1.85413	+	0.293665i	−0.981027	−	0.193870i	$-0.937896\pi$
$983$	−1822.61	+	288.673i	−1.85413	+	0.293665i	−0.873103	+	0.487535i	$0.837896\pi$
$984$	−630.333	+	204.808i	−0.640582	+	0.208138i
$985$		0			0
$986$	346.356	+	251.642i	0.351274	+	0.255215i
$987$	−373.038	−	59.0835i	−0.377952	−	0.0598617i
$988$	−17.7180	−	34.7735i	−0.0179332	−	0.0351958i
$989$			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	$0.445015\pi$
$992$	1437.40	−	732.390i	1.44899	−	0.738297i
$993$	18.0815	−	114.162i	0.0182090	−	0.114967i
$994$	168.639	−	232.111i	0.169657	−	0.233512i
$995$		0			0
$996$	213.943	+	658.450i	0.214803	+	0.661094i
$997$	−116.457	−	735.280i	−0.116807	−	0.737492i	−0.974676	−	0.223623i	$-0.928212\pi$
$997$	−116.457	−	735.280i	−0.116807	−	0.737492i	0.857868	−	0.513869i	$-0.171788\pi$
$998$	−21.9235	+	138.420i	−0.0219674	+	0.138697i
$999$	−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.207.13	yes	128
5.2	odd	4	inner	275.3.bk.c.218.13	yes	128
5.3	odd	4	inner	275.3.bk.c.218.4	yes	128
5.4	even	2	inner	275.3.bk.c.207.4	yes	128
11.5	even	5	inner	275.3.bk.c.82.4	✓	128
55.27	odd	20	inner	275.3.bk.c.93.4	yes	128
55.38	odd	20	inner	275.3.bk.c.93.13	yes	128
55.49	even	10	inner	275.3.bk.c.82.13	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.bk.c.82.4	✓	128	11.5	even	5	inner
275.3.bk.c.82.13	yes	128	55.49	even	10	inner
275.3.bk.c.93.4	yes	128	55.27	odd	20	inner
275.3.bk.c.93.13	yes	128	55.38	odd	20	inner
275.3.bk.c.207.4	yes	128	5.4	even	2	inner
275.3.bk.c.207.13	yes	128	1.1	even	1	trivial
275.3.bk.c.218.4	yes	128	5.3	odd	4	inner
275.3.bk.c.218.13	yes	128	5.2	odd	4	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+(2.18572 - 1.11368i) q^{2} +(-0.493690 + 3.11704i) q^{3} +(1.18596 - 1.63233i) q^{4} +(2.39232 + 7.36280i) q^{6} +(-0.245682 - 1.55118i) q^{7} +(-0.760714 + 4.80296i) q^{8} +(-0.912687 - 0.296550i) q^{9} +(4.19559 + 10.1684i) q^{11} +(4.50255 + 4.50255i) q^{12} +(2.11052 + 4.14212i) q^{13} +(-2.26451 - 3.11683i) q^{14} +(6.18024 + 19.0208i) q^{16} +(-4.99857 + 9.81025i) q^{17} +(-2.32514 + 0.368267i) q^{18} +(-2.44564 - 3.36614i) q^{19} +4.95637 q^{21} +(20.4948 + 17.5528i) q^{22} +(-4.08642 + 4.08642i) q^{23} +(-14.5955 - 4.74235i) q^{24} +(9.22601 + 6.70309i) q^{26} +(-11.5198 + 22.6088i) q^{27} +(-2.82341 - 1.43860i) q^{28} +(9.31687 - 12.8236i) q^{29} +(16.8361 - 51.8163i) q^{31} +(20.9373 + 20.9373i) q^{32} +(-33.7667 + 8.05774i) q^{33} +27.0093i q^{34} +(-1.56648 + 1.13811i) q^{36} +(3.88071 + 24.5018i) q^{37} +(-9.09431 - 4.63378i) q^{38} +(-13.9531 + 4.53363i) q^{39} +(34.9390 - 25.3846i) q^{41} +(10.8333 - 5.51982i) q^{42} +(33.7901 - 33.7901i) q^{43} +(21.5741 + 5.21076i) q^{44} +(-4.38082 + 13.4828i) q^{46} +(-75.2645 - 11.9207i) q^{47} +(-62.3398 + 9.87365i) q^{48} +(44.2560 - 14.3796i) q^{49} +(-28.1112 - 20.4240i) q^{51} +(9.26431 + 1.46732i) q^{52} +(-12.5467 - 24.6242i) q^{53} +62.2460i q^{54} +7.63714 q^{56} +(11.6998 - 5.96133i) q^{57} +(6.08273 - 38.4048i) q^{58} +(59.8804 - 82.4183i) q^{59} +(-8.72078 - 26.8398i) q^{61} +(-20.9077 - 132.006i) q^{62} +(-0.235771 + 1.48860i) q^{63} +(-7.00270 - 2.27532i) q^{64} +(-64.8310 + 55.2174i) q^{66} +(-1.02357 - 1.02357i) q^{67} +(10.0855 + 19.7939i) q^{68} +(-10.7201 - 14.7550i) q^{69} +(23.0126 + 70.8254i) q^{71} +(2.11861 - 4.15801i) q^{72} +(97.0924 - 15.3779i) q^{73} +(35.7694 + 49.2323i) q^{74} -8.39510 q^{76} +(14.7423 - 9.00630i) q^{77} +(-25.4486 + 25.4486i) q^{78} +(-107.275 - 34.8559i) q^{79} +(-71.7727 - 52.1459i) q^{81} +(48.0965 - 94.3947i) q^{82} +(96.8777 + 49.3617i) q^{83} +(5.87806 - 8.09045i) q^{84} +(36.2243 - 111.487i) q^{86} +(35.3719 + 35.3719i) q^{87} +(-52.0302 + 12.4160i) q^{88} -21.2775i q^{89} +(5.90665 - 4.29143i) q^{91} +(1.82407 + 11.5167i) q^{92} +(153.202 + 78.0601i) q^{93} +(-177.783 + 57.7653i) q^{94} +(-75.5989 + 54.9258i) q^{96} +(18.7565 - 9.55693i) 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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