LMFDB - Embedded newform 275.3.bk.c.82.4

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			82.4
Character	$\chi$	$=$	275.82
Dual form			275.3.bk.c.218.4

$q$-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	$0.360148\pi$
$2$	−1.11368	+	2.18572i	−0.556841	+	1.09286i	−0.982200	+	0.187837i	$0.939852\pi$
$3$	−3.11704	+	0.493690i	−1.03901	+	0.164563i	−0.652553	−	0.757743i	$-0.726302\pi$
$3$	−3.11704	+	0.493690i	−1.03901	+	0.164563i	−0.386459	+	0.922306i	$0.626302\pi$
$4$	−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	0.0446486	−	0.999003i	$-0.485783\pi$
$7$	−1.55118	−	0.245682i	−0.221597	−	0.0350975i	−0.266245	+	0.963905i	$0.585783\pi$
$8$	−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	0.287362	−	0.957822i	$-0.407222\pi$
$13$	−4.14212	−	2.11052i	−0.318625	−	0.162347i	−0.605987	+	0.795475i	$0.707222\pi$
$14$	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	−0.140990	−	0.990011i	$-0.545029\pi$
$17$	9.81025	−	4.99857i	0.577074	−	0.294034i	0.718064	+	0.695977i	$0.245029\pi$
$18$	−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	−0.790340	−	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
$27$	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	0.478488	−	0.878094i	$-0.341185\pi$
$37$	24.5018	+	3.88071i	0.662211	+	0.104884i	0.183723	+	0.982978i	$0.441185\pi$
$38$	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	−0.194990	−	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
$47$	−11.9207	−	75.2645i	−0.253632	−	1.60137i	−0.705116	−	0.709092i	$-0.749105\pi$
$47$	−11.9207	−	75.2645i	−0.253632	−	1.60137i	0.451484	−	0.892279i	$-0.350895\pi$
$48$	−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	0.670593	−	0.741826i	$-0.266040\pi$
$53$	24.6242	+	12.5467i	0.464608	+	0.236730i	−0.205985	+	0.978555i	$0.566040\pi$
$54$			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	0.699427	−	0.714704i	$-0.253439\pi$
$67$	−1.02357	−	1.02357i	−0.0152771	−	0.0152771i	−0.714704	+	0.699427i	$0.753439\pi$
$68$	−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	$-0.714874\pi$
$73$	15.3779	−	97.0924i	0.210656	−	1.33003i	0.835590	−	0.549354i	$-0.185126\pi$
$74$	−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	$-0.922673\pi$
$83$	−49.3617	−	96.8777i	−0.594719	−	1.16720i	0.375918	−	0.926653i	$-0.377327\pi$
$84$	−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	−0.935008	−	0.354627i	$-0.884608\pi$
$97$	−9.55693	+	18.7565i	−0.0985250	+	0.193366i	0.836483	+	0.547993i	$0.184608\pi$
$98$	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	$0.184527\pi$
$103$	−13.2176	+	83.4524i	−0.128326	+	0.810218i	−0.964949	+	0.262438i	$0.915473\pi$
$104$	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	$-0.756854\pi$
$107$	−26.6535	−	168.284i	−0.249098	−	1.57274i	0.473069	−	0.881025i	$-0.343146\pi$
$108$	−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	−0.396931	−	0.917848i	$-0.629925\pi$
$113$	−55.4609	+	8.78415i	−0.490805	+	0.0777358i	−0.0938734	+	0.995584i	$0.529925\pi$
$114$	−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	−0.0144990	−	0.999895i	$-0.504615\pi$
$127$	99.8107	−	50.8561i	0.785911	−	0.400441i	0.800410	+	0.599453i	$0.204615\pi$
$128$	−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	$0.748248\pi$
$137$	−231.768	+	118.092i	−1.69174	+	0.861984i	−0.988535	+	0.150995i	$0.951752\pi$
$138$	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	$0.163848\pi$
$157$	30.5733	+	193.032i	0.194734	+	1.22950i	−0.675685	+	0.737191i	$0.736152\pi$
$158$	−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	$0.0646900\pi$
$163$	280.098	+	142.717i	1.71840	+	0.875566i	0.738975	+	0.673732i	$0.235310\pi$
$164$		−	87.1372i		−	0.531324i
$165$		0			0
$166$	266.721			1.60675
$167$	13.6296	−	26.7496i	0.0816143	−	0.160177i	−0.846593	−	0.532241i	$-0.821350\pi$
$167$	13.6296	−	26.7496i	0.0816143	−	0.160177i	0.928207	+	0.372064i	$0.121350\pi$
$168$	−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	0.220602	−	0.975364i	$-0.429198\pi$
$173$	126.603	−	20.0520i	0.731811	−	0.115907i	0.511209	+	0.859457i	$0.329198\pi$
$174$	−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	0.833670	−	0.552262i	$-0.186235\pi$
$193$	−19.9057	−	39.0672i	−0.103139	−	0.202421i	−0.936809	+	0.349842i	$0.886235\pi$
$194$	−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	$0.698314\pi$
$198$	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	0.112620	−	0.993638i	$-0.464076\pi$
$223$	117.472	−	18.6057i	0.526778	−	0.0834335i	0.414159	+	0.910205i	$0.364076\pi$
$224$	−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	0.516233	−	0.856448i	$-0.327334\pi$
$227$	168.557	+	26.6968i	0.742543	+	0.117607i	0.226310	+	0.974055i	$0.427334\pi$
$228$	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	−0.136087	−	0.990697i	$-0.543453\pi$
$233$	−237.093	−	120.805i	−1.01757	−	0.518477i	−0.881481	+	0.472220i	$0.843453\pi$
$234$	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	0.217873	−	0.975977i	$-0.430088\pi$
$257$	31.7365	+	5.02657i	0.123488	+	0.0195587i	−0.0943842	+	0.995536i	$0.530088\pi$
$258$	−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	$0.502513\pi$
$263$	−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
$267$	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	−0.917254	−	0.398302i	$-0.869599\pi$
$277$	−15.4766	+	30.3745i	−0.0558722	+	0.109655i	0.861382	+	0.507958i	$0.169599\pi$
$278$	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	0.247237	−	0.968955i	$-0.420477\pi$
$283$	221.248	−	35.0423i	0.781797	−	0.123824i	0.534560	+	0.845131i	$0.320477\pi$
$284$	−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	$-0.635854\pi$
$293$	76.4836	−	482.899i	0.261036	−	1.64812i	0.674995	−	0.737822i	$-0.264146\pi$
$294$	−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	0.206119	−	0.978527i	$-0.433917\pi$
$307$	−237.129	−	237.129i	−0.772408	−	0.772408i	−0.978527	+	0.206119i	$0.933917\pi$
$308$	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	$0.0582769\pi$
$313$	172.969	+	339.470i	0.552616	+	1.08457i	−0.430671	+	0.902509i	$0.641723\pi$
$314$	−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	$0.342644\pi$
$317$	−163.756	+	321.390i	−0.516582	+	1.01385i	−0.991039	+	0.133571i	$0.957356\pi$
$318$	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	−0.644736	−	0.764406i	$-0.723033\pi$
$337$	−503.522	−	79.7500i	−1.49413	−	0.236647i	−0.849394	+	0.527759i	$0.823033\pi$
$338$	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	−0.377521	−	0.926001i	$-0.623223\pi$
$347$	51.9560	−	26.4729i	0.149729	−	0.0762908i	0.527250	+	0.849710i	$0.323223\pi$
$348$	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	−0.861184	−	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
$357$	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	0.280759	−	0.959778i	$-0.409414\pi$
$367$	92.1861	+	14.6008i	0.251188	+	0.0397843i	−0.0295704	+	0.999563i	$0.509414\pi$
$368$	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	−0.973697	−	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
$377$	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	0.163770	−	0.986499i	$-0.447634\pi$
$383$	−206.078	−	105.002i	−0.538062	−	0.274156i	−0.701832	+	0.712342i	$0.747634\pi$
$384$		−	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	0.416706	−	0.909041i	$-0.363184\pi$
$397$	−195.457	−	195.457i	−0.492335	−	0.492335i	−0.909041	+	0.416706i	$0.863184\pi$
$398$	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	$-0.733503\pi$
$433$	85.1992	−	537.926i	0.196765	−	1.24232i	0.866293	−	0.499537i	$-0.166497\pi$
$434$	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	0.233049	−	0.972465i	$-0.425130\pi$
$443$	334.553	−	52.9881i	0.755200	−	0.119612i	0.522151	+	0.852853i	$0.325130\pi$
$444$	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	−0.597085	−	0.802178i	$-0.703675\pi$
$457$	−136.674	+	69.6387i	−0.299067	+	0.152382i	0.298018	+	0.954560i	$0.403675\pi$
$458$	−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	−0.996390	−	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
$467$	−124.580	+	63.4768i	−0.266767	+	0.135925i	−0.582258	−	0.813004i	$-0.697831\pi$
$467$	−124.580	+	63.4768i	−0.266767	+	0.135925i	0.315491	+	0.948929i	$0.397831\pi$
$468$	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	$0.234665\pi$
$487$	118.812	+	750.146i	0.243966	+	1.54034i	−0.496374	+	0.868109i	$0.665335\pi$
$488$	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	−0.515126	−	0.857114i	$-0.672255\pi$
$503$	−372.309	+	58.9680i	−0.740177	+	0.117233i	−0.225051	+	0.974347i	$0.572255\pi$
$504$	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	$0.0171925\pi$
$523$	238.116	+	467.329i	0.455289	+	0.893555i	−0.543253	+	0.839569i	$0.682808\pi$
$524$	−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	$-0.878973\pi$
$547$	−87.5917	−	553.032i	−0.160131	−	1.01103i	0.768453	−	0.639906i	$-0.221027\pi$
$548$	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	0.868167	−	0.496272i	$-0.165298\pi$
$557$	858.051	+	135.902i	1.54049	+	0.243989i	0.672320	+	0.740261i	$0.265298\pi$
$558$	−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	0.988935	−	0.148347i	$-0.0473952\pi$
$563$	816.464	+	416.009i	1.45020	+	0.738915i	0.461267	+	0.887262i	$0.347395\pi$
$564$	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	−0.637384	−	0.770547i	$-0.719983\pi$
$577$	−224.247	+	114.260i	−0.388643	+	0.198023i	0.248741	+	0.968570i	$0.419983\pi$
$578$	−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	−0.239722	−	0.970841i	$-0.577056\pi$
$587$	−450.651	−	71.3761i	−0.767719	−	0.121595i	−0.527996	+	0.849247i	$0.677056\pi$
$588$	−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	−0.878321	−	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
$597$	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	$-0.615952\pi$
$607$	369.707	−	725.590i	0.609072	−	1.19537i	0.965342	−	0.260988i	$-0.0840483\pi$
$608$	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	0.537412	−	0.843320i	$-0.319402\pi$
$613$	802.492	−	127.102i	1.30912	−	0.207345i	0.771710	+	0.635975i	$0.219402\pi$
$614$	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	$0.828921\pi$
$618$	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	0.729287	−	0.684208i	$-0.239852\pi$
$643$	−162.623	−	319.165i	−0.252913	−	0.496369i	−0.982200	+	0.187839i	$0.939852\pi$
$644$	−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	−0.898661	−	0.438644i	$-0.855459\pi$
$647$	−10.0746	+	19.7726i	−0.0155713	+	0.0305604i	0.883090	+	0.469204i	$0.155459\pi$
$648$	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	$-0.787481\pi$
$653$	99.8375	−	630.349i	0.152891	−	0.965313i	0.938171	−	0.346173i	$-0.112519\pi$
$654$	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	−0.311244	−	0.950330i	$-0.600746\pi$
$673$	−850.014	−	433.104i	−1.26302	−	0.643542i	−0.951778	+	0.306788i	$0.900746\pi$
$674$	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	−0.903536	−	0.428512i	$-0.859038\pi$
$677$	−736.540	+	375.286i	−1.08795	+	0.554337i	−0.184411	+	0.982849i	$0.559038\pi$
$678$	−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	−0.352442	−	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
$687$	−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	0.234910	−	0.972017i	$-0.424521\pi$
$727$	−535.877	−	535.877i	−0.737107	−	0.737107i	−0.972017	+	0.234910i	$0.924521\pi$
$728$	−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	$-0.898116\pi$
$733$	37.2155	−	234.969i	0.0507714	−	0.320558i	0.999982	−	0.00591819i	$-0.00188383\pi$
$734$	−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	0.806725	−	0.590927i	$-0.201238\pi$
$743$	−108.126	−	212.210i	−0.145526	−	0.285612i	−0.952251	+	0.305316i	$0.901238\pi$
$744$	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	$-0.549787\pi$
$757$	556.341	−	1091.88i	0.734929	−	1.44238i	0.890703	−	0.454586i	$-0.150213\pi$
$758$	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	0.424207	−	0.905565i	$-0.360553\pi$
$773$	856.088	−	135.591i	1.10749	−	0.175409i	0.683280	+	0.730156i	$0.260553\pi$
$774$	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	−0.252382	−	0.967628i	$-0.581214\pi$
$787$	300.712	−	153.220i	0.382099	−	0.194689i	0.634481	+	0.772939i	$0.281214\pi$
$788$	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	−0.414442	−	0.910076i	$-0.636023\pi$
$797$	62.3432	−	31.7654i	0.0782223	−	0.0398562i	0.492664	+	0.870220i	$0.336023\pi$
$798$	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	0.406334	−	0.913724i	$-0.366807\pi$
$823$	−77.4006	−	39.4376i	−0.0940469	−	0.0479193i	−0.500381	+	0.865805i	$0.666807\pi$
$824$		−	410.874i		−	0.498633i
$825$		0			0
$826$	−392.484			−0.475162
$827$	−129.764	+	254.677i	−0.156910	+	0.307953i	−0.956056	−	0.293184i	$-0.905285\pi$
$827$	−129.764	+	254.677i	−0.156910	+	0.307953i	0.799146	+	0.601137i	$0.205285\pi$
$828$	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	0.905892	−	0.423510i	$-0.139202\pi$
$853$	26.2685	+	51.5549i	0.0307955	+	0.0604395i	−0.875096	+	0.483949i	$0.839202\pi$
$854$	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	$0.810895\pi$
$858$	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	0.937359	−	0.348365i	$-0.113263\pi$
$863$	90.2355	+	177.097i	0.104560	+	0.205211i	−0.832799	+	0.553576i	$0.813263\pi$
$864$	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	$0.241315\pi$
$877$	217.500	+	1373.24i	0.248005	+	1.56584i	−0.478130	+	0.878289i	$0.658685\pi$
$878$	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	0.584114	−	0.811672i	$-0.301442\pi$
$883$	1227.78	−	194.461i	1.39046	−	0.220227i	0.806346	+	0.591445i	$0.201442\pi$
$884$	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	0.783722	−	0.621112i	$-0.213319\pi$
$887$	1186.05	+	187.852i	1.33715	+	0.211784i	0.553430	+	0.832896i	$0.313319\pi$
$888$	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	0.564072	−	0.825725i	$-0.309234\pi$
$907$	1418.23	−	722.625i	1.56365	−	0.796720i	0.999579	+	0.0290052i	$0.00923393\pi$
$908$	−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	$-0.563638\pi$
$937$	666.244	−	1307.58i	0.711039	−	1.39549i	0.909634	−	0.415411i	$-0.136362\pi$
$938$	−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	0.0981026	−	0.995176i	$-0.468723\pi$
$947$	−849.529	−	849.529i	−0.897074	−	0.897074i	−0.995176	+	0.0981026i	$0.968723\pi$
$948$	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	$0.142038\pi$
$953$	−85.0162	+	536.771i	−0.0892091	+	0.563244i	−0.991292	+	0.131681i	$0.957962\pi$
$954$	−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	$-0.944360\pi$
$967$	−1120.43	−	1120.43i	−1.15867	−	1.15867i	−0.173909	−	0.984762i	$-0.555640\pi$
$968$	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	−0.843760	−	0.536721i	$-0.819663\pi$
$977$	84.4187	−	165.681i	0.0864060	−	0.169581i	0.930166	+	0.367140i	$0.119663\pi$
$978$	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	$0.437896\pi$
$983$	−288.673	+	1822.61i	−0.293665	+	1.85413i	−0.487535	+	0.873103i	$0.662104\pi$
$984$	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	−0.223623	−	0.974676i	$-0.571788\pi$
$997$	−735.280	−	116.457i	−0.737492	−	0.116807i	−0.513869	+	0.857868i	$0.671788\pi$
$998$	−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.82.4	✓	128
5.2	odd	4	inner	275.3.bk.c.93.4	yes	128
5.3	odd	4	inner	275.3.bk.c.93.13	yes	128
5.4	even	2	inner	275.3.bk.c.82.13	yes	128
11.9	even	5	inner	275.3.bk.c.207.13	yes	128
55.9	even	10	inner	275.3.bk.c.207.4	yes	128
55.42	odd	20	inner	275.3.bk.c.218.13	yes	128
55.53	odd	20	inner	275.3.bk.c.218.4	yes	128

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