LMFDB - Embedded newform 136.3.t.a.41.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,3,Mod(41,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 0, 11]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("136.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	136.t (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.70573159530$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			41.4
Character	$\chi$	$=$	136.41
Dual form			136.3.t.a.73.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.24344 - 3.35755i) q^{3} +(-0.109963 - 0.552824i) q^{5} +(1.03372 - 5.19685i) q^{7} +(-2.79594 - 6.74999i) q^{9} +O(q^{10})$	\(q+(2.24344 - 3.35755i) q^{3} +(-0.109963 - 0.552824i) q^{5} +(1.03372 - 5.19685i) q^{7} +(-2.79594 - 6.74999i) q^{9} +(4.88551 - 3.26439i) q^{11} +(-4.17282 + 4.17282i) q^{13} +(-2.10283 - 0.871019i) q^{15} +(-11.8901 - 12.1502i) q^{17} +(-0.379535 + 0.916277i) q^{19} +(-15.1296 - 15.1296i) q^{21} +(12.9011 + 19.3078i) q^{23} +(22.8035 - 9.44551i) q^{25} +(6.70854 + 1.33441i) q^{27} +(-13.8685 + 2.75862i) q^{29} +(39.4846 + 26.3828i) q^{31} -23.7268i q^{33} -2.98661 q^{35} +(-15.6389 + 23.4053i) q^{37} +(4.64896 + 23.3719i) q^{39} +(-2.15298 + 10.8238i) q^{41} +(2.23584 + 5.39780i) q^{43} +(-3.42410 + 2.28791i) q^{45} +(-32.6850 + 32.6850i) q^{47} +(19.3315 + 8.00735i) q^{49} +(-67.4694 + 12.6632i) q^{51} +(-37.6680 + 90.9385i) q^{53} +(-2.34186 - 2.34186i) q^{55} +(2.22498 + 3.32992i) q^{57} +(45.2268 - 18.7336i) q^{59} +(-20.7230 - 4.12205i) q^{61} +(-37.9689 + 7.55248i) q^{63} +(2.76569 + 1.84797i) q^{65} -122.406i q^{67} +93.7697 q^{69} +(-19.8317 + 29.6802i) q^{71} +(19.1521 + 96.2843i) q^{73} +(19.4445 - 97.7541i) q^{75} +(-11.9143 - 28.7637i) q^{77} +(100.384 - 67.0746i) q^{79} +(66.0265 - 66.0265i) q^{81} +(-91.2068 - 37.7791i) q^{83} +(-5.40943 + 7.90918i) q^{85} +(-21.8510 + 52.7529i) q^{87} +(-50.1935 - 50.1935i) q^{89} +(17.3720 + 25.9990i) q^{91} +(177.163 - 73.3831i) q^{93} +(0.548275 + 0.109059i) q^{95} +(12.2786 - 2.44236i) q^{97} +(-35.6942 - 23.8501i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9}+O(q^{10}) $ 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9	$ 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9} - 24 q^{11} + 48 q^{13} + 96 q^{15} + 40 q^{19} - 80 q^{21} - 48 q^{23} + 112 q^{25} - 80 q^{27} + 56 q^{29} - 24 q^{31} - 96 q^{35} + 48 q^{37} - 72 q^{39} - 160 q^{41} + 112 q^{43} - 504 q^{45} + 48 q^{47} + 208 q^{49} - 400 q^{51} + 304 q^{53} - 368 q^{55} - 264 q^{57} + 192 q^{59} - 288 q^{61} + 56 q^{63} + 8 q^{65} + 32 q^{69} + 352 q^{71} - 184 q^{73} + 24 q^{75} + 688 q^{77} - 424 q^{79} + 312 q^{81} + 600 q^{83} - 512 q^{85} + 1336 q^{87} - 144 q^{89} - 24 q^{91} + 944 q^{93} - 256 q^{95} + 416 q^{97} + 128 q^{99}+O(q^{100}) $ 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9 - 24 * q^11 + 48 * q^13 + 96 * q^15 + 40 * q^19 - 80 * q^21 - 48 * q^23 + 112 * q^25 - 80 * q^27 + 56 * q^29 - 24 * q^31 - 96 * q^35 + 48 * q^37 - 72 * q^39 - 160 * q^41 + 112 * q^43 - 504 * q^45 + 48 * q^47 + 208 * q^49 - 400 * q^51 + 304 * q^53 - 368 * q^55 - 264 * q^57 + 192 * q^59 - 288 * q^61 + 56 * q^63 + 8 * q^65 + 32 * q^69 + 352 * q^71 - 184 * q^73 + 24 * q^75 + 688 * q^77 - 424 * q^79 + 312 * q^81 + 600 * q^83 - 512 * q^85 + 1336 * q^87 - 144 * q^89 - 24 * q^91 + 944 * q^93 - 256 * q^95 + 416 * q^97 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{16}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.24344	−	3.35755i	0.747813	−	1.11918i	−0.241073	−	0.970507i	$-0.577499\pi$
$3$	2.24344	−	3.35755i	0.747813	−	1.11918i	0.988886	−	0.148675i	$-0.0475008\pi$
$4$		0			0
$5$	−0.109963	−	0.552824i	−0.0219927	−	0.110565i	0.968230	−	0.250063i	$-0.0804512\pi$
$5$	−0.109963	−	0.552824i	−0.0219927	−	0.110565i	−0.990222	+	0.139498i	$0.955451\pi$
$6$		0			0
$7$	1.03372	−	5.19685i	0.147674	−	0.742407i	−0.833989	−	0.551781i	$-0.813948\pi$
$7$	1.03372	−	5.19685i	0.147674	−	0.742407i	0.981663	−	0.190626i	$-0.0610516\pi$
$8$		0			0
$9$	−2.79594	−	6.74999i	−0.310660	−	0.749999i
$10$		0			0
$11$	4.88551	−	3.26439i	0.444137	−	0.296763i	−0.313320	−	0.949647i	$-0.601441\pi$
$11$	4.88551	−	3.26439i	0.444137	−	0.296763i	0.757457	+	0.652885i	$0.226441\pi$
$12$		0			0
$13$	−4.17282	+	4.17282i	−0.320986	+	0.320986i	−0.849145	−	0.528159i	$-0.822882\pi$
$13$	−4.17282	+	4.17282i	−0.320986	+	0.320986i	0.528159	+	0.849145i	$0.322882\pi$
$14$		0			0
$15$	−2.10283	−	0.871019i	−0.140188	−	0.0580680i
$16$		0			0
$17$	−11.8901	−	12.1502i	−0.699415	−	0.714716i
$17$	−11.8901	−	12.1502i	−0.699415	−	0.714716i
$18$		0			0
$19$	−0.379535	+	0.916277i	−0.0199755	+	0.0482251i	−0.933553	−	0.358441i	$-0.883309\pi$
$19$	−0.379535	+	0.916277i	−0.0199755	+	0.0482251i	0.913577	+	0.406666i	$0.133309\pi$
$20$		0			0
$21$	−15.1296	−	15.1296i	−0.720455	−	0.720455i
$22$		0			0
$23$	12.9011	+	19.3078i	0.560917	+	0.839471i	0.998207	−	0.0598492i	$-0.0190620\pi$
$23$	12.9011	+	19.3078i	0.560917	+	0.839471i	−0.437291	+	0.899320i	$0.644062\pi$
$24$		0			0
$25$	22.8035	−	9.44551i	0.912139	−	0.377820i
$26$		0			0
$27$	6.70854	+	1.33441i	0.248465	+	0.0494227i
$28$		0			0
$29$	−13.8685	+	2.75862i	−0.478224	+	0.0951247i	−0.428316	−	0.903629i	$-0.640893\pi$
$29$	−13.8685	+	2.75862i	−0.478224	+	0.0951247i	−0.0499083	+	0.998754i	$0.515893\pi$
$30$		0			0
$31$	39.4846	+	26.3828i	1.27370	+	0.851057i	0.994037	−	0.109043i	$-0.0347785\pi$
$31$	39.4846	+	26.3828i	1.27370	+	0.851057i	0.279659	+	0.960099i	$0.409779\pi$
$32$		0			0
$33$		−	23.7268i		−	0.718993i
$34$		0			0
$35$	−2.98661			−0.0853317
$36$		0			0
$37$	−15.6389	+	23.4053i	−0.422674	+	0.632576i	−0.980300	−	0.197516i	$-0.936712\pi$
$37$	−15.6389	+	23.4053i	−0.422674	+	0.632576i	0.557626	+	0.830093i	$0.311712\pi$
$38$		0			0
$39$	4.64896	+	23.3719i	0.119204	+	0.599279i
$40$		0			0
$41$	−2.15298	+	10.8238i	−0.0525117	+	0.263994i	−0.998118	−	0.0613184i	$-0.980469\pi$
$41$	−2.15298	+	10.8238i	−0.0525117	+	0.263994i	0.945607	+	0.325313i	$0.105469\pi$
$42$		0			0
$43$	2.23584	+	5.39780i	0.0519963	+	0.125530i	0.947743	−	0.319034i	$-0.103358\pi$
$43$	2.23584	+	5.39780i	0.0519963	+	0.125530i	−0.895747	+	0.444564i	$0.853358\pi$
$44$		0			0
$45$	−3.42410	+	2.28791i	−0.0760912	+	0.0508425i
$46$		0			0
$47$	−32.6850	+	32.6850i	−0.695425	+	0.695425i	−0.963420	−	0.267995i	$-0.913639\pi$
$47$	−32.6850	+	32.6850i	−0.695425	+	0.695425i	0.267995	+	0.963420i	$0.413639\pi$
$48$		0			0
$49$	19.3315	+	8.00735i	0.394520	+	0.163415i
$50$		0			0
$51$	−67.4694	+	12.6632i	−1.32293	+	0.248298i
$52$		0			0
$53$	−37.6680	+	90.9385i	−0.710716	+	1.71582i	−0.0125133	+	0.999922i	$0.503983\pi$
$53$	−37.6680	+	90.9385i	−0.710716	+	1.71582i	−0.698203	+	0.715900i	$0.746017\pi$
$54$		0			0
$55$	−2.34186	−	2.34186i	−0.0425793	−	0.0425793i
$56$		0			0
$57$	2.22498	+	3.32992i	0.0390347	+	0.0584196i
$58$		0			0
$59$	45.2268	−	18.7336i	0.766556	−	0.317518i	0.0350798	−	0.999385i	$-0.488831\pi$
$59$	45.2268	−	18.7336i	0.766556	−	0.317518i	0.731477	+	0.681866i	$0.238831\pi$
$60$		0			0
$61$	−20.7230	−	4.12205i	−0.339721	−	0.0675747i	0.0222819	−	0.999752i	$-0.492907\pi$
$61$	−20.7230	−	4.12205i	−0.339721	−	0.0675747i	−0.362003	+	0.932177i	$0.617907\pi$
$62$		0			0
$63$	−37.9689	+	7.55248i	−0.602680	+	0.119881i
$64$		0			0
$65$	2.76569	+	1.84797i	0.0425491	+	0.0284304i
$66$		0			0
$67$		−	122.406i		−	1.82695i	−0.406889	−	0.913477i	$-0.633387\pi$
$67$		−	122.406i		−	1.82695i	0.406889	−	0.913477i	$-0.366613\pi$
$68$		0			0
$69$	93.7697			1.35898
$70$		0			0
$71$	−19.8317	+	29.6802i	−0.279320	+	0.418032i	−0.944429	−	0.328714i	$-0.893385\pi$
$71$	−19.8317	+	29.6802i	−0.279320	+	0.418032i	0.665110	+	0.746746i	$0.268385\pi$
$72$		0			0
$73$	19.1521	+	96.2843i	0.262358	+	1.31896i	0.857143	+	0.515078i	$0.172237\pi$
$73$	19.1521	+	96.2843i	0.262358	+	1.31896i	−0.594785	+	0.803885i	$0.702763\pi$
$74$		0			0
$75$	19.4445	−	97.7541i	0.259260	−	1.30339i
$76$		0			0
$77$	−11.9143	−	28.7637i	−0.154731	−	0.373554i
$78$		0			0
$79$	100.384	−	67.0746i	1.27069	−	0.849046i	0.276961	−	0.960881i	$-0.410673\pi$
$79$	100.384	−	67.0746i	1.27069	−	0.849046i	0.993727	+	0.111835i	$0.0356729\pi$
$80$		0			0
$81$	66.0265	−	66.0265i	0.815142	−	0.815142i
$82$		0			0
$83$	−91.2068	−	37.7791i	−1.09888	−	0.455170i	−0.241783	−	0.970330i	$-0.577732\pi$
$83$	−91.2068	−	37.7791i	−1.09888	−	0.455170i	−0.857094	+	0.515161i	$0.827732\pi$
$84$		0			0
$85$	−5.40943	+	7.90918i	−0.0636404	+	0.0930491i
$86$		0			0
$87$	−21.8510	+	52.7529i	−0.251161	+	0.606355i
$88$		0			0
$89$	−50.1935	−	50.1935i	−0.563972	−	0.563972i	0.366461	−	0.930433i	$-0.380569\pi$
$89$	−50.1935	−	50.1935i	−0.563972	−	0.563972i	−0.930433	+	0.366461i	$0.880569\pi$
$90$		0			0
$91$	17.3720	+	25.9990i	0.190901	+	0.285703i
$92$		0			0
$93$	177.163	−	73.3831i	1.90497	−	0.789066i
$94$		0			0
$95$	0.548275	+	0.109059i	0.00577131	+	0.00114799i
$96$		0			0
$97$	12.2786	−	2.44236i	0.126583	−	0.0251790i	−0.131392	−	0.991330i	$-0.541945\pi$
$97$	12.2786	−	2.44236i	0.126583	−	0.0251790i	0.257975	+	0.966152i	$0.416945\pi$
$98$		0			0
$99$	−35.6942	−	23.8501i	−0.360547	−	0.240910i
$100$		0			0
$101$		−	132.456i		−	1.31145i	−0.755000	−	0.655725i	$-0.772363\pi$
$101$		−	132.456i		−	1.31145i	0.755000	−	0.655725i	$-0.227637\pi$
$102$		0			0
$103$	−125.077			−1.21434			−0.607168	−	0.794574i	$-0.707694\pi$
$103$	−125.077			−1.21434			−0.607168	+	0.794574i	$0.707694\pi$
$104$		0			0
$105$	−6.70028	+	10.0277i	−0.0638122	+	0.0955017i
$106$		0			0
$107$	−9.26618	−	46.5842i	−0.0865998	−	0.435367i	−0.999623	−	0.0274588i	$-0.991259\pi$
$107$	−9.26618	−	46.5842i	−0.0865998	−	0.435367i	0.913023	−	0.407908i	$-0.133741\pi$
$108$		0			0
$109$	17.5038	−	87.9978i	0.160586	−	0.807319i	−0.813574	−	0.581461i	$-0.802481\pi$
$109$	17.5038	−	87.9978i	0.160586	−	0.807319i	0.974160	−	0.225858i	$-0.0725187\pi$
$110$		0			0
$111$	43.4994	+	105.017i	0.391887	+	0.946098i
$112$		0			0
$113$	−160.821	+	107.457i	−1.42320	+	0.950951i	−0.424229	+	0.905555i	$0.639455\pi$
$113$	−160.821	+	107.457i	−1.42320	+	0.950951i	−0.998969	+	0.0453959i	$0.985545\pi$
$114$		0			0
$115$	9.25518	−	9.25518i	0.0804798	−	0.0804798i
$116$		0			0
$117$	39.8334	+	16.4995i	0.340456	+	0.141022i
$118$		0			0
$119$	−75.4335	+	49.2309i	−0.633895	+	0.413705i
$120$		0			0
$121$	−33.0928	+	79.8930i	−0.273494	+	0.660273i
$122$		0			0
$123$	31.5112	+	31.5112i	0.256188	+	0.256188i
$124$		0			0
$125$	−15.5580	−	23.2842i	−0.124464	−	0.186273i
$126$		0			0
$127$	107.226	−	44.4143i	0.844296	−	0.349719i	0.0817498	−	0.996653i	$-0.473949\pi$
$127$	107.226	−	44.4143i	0.844296	−	0.349719i	0.762546	+	0.646934i	$0.223949\pi$
$128$		0			0
$129$	23.1393	+	4.60270i	0.179375	+	0.0356798i
$130$		0			0
$131$	−192.407	+	38.2722i	−1.46876	+	0.292154i	−0.863691	−	0.504022i	$-0.831853\pi$
$131$	−192.407	+	38.2722i	−1.46876	+	0.292154i	−0.605066	+	0.796176i	$0.706853\pi$
$132$		0			0
$133$	4.36942	+	2.91955i	0.0328528	+	0.0219515i
$134$		0			0
$135$		−	3.85538i		−	0.0285584i
$136$		0			0
$137$	−60.0914			−0.438623			−0.219312	−	0.975655i	$-0.570381\pi$
$137$	−60.0914			−0.438623			−0.219312	+	0.975655i	$0.570381\pi$
$138$		0			0
$139$	96.9713	−	145.128i	0.697635	−	1.04408i	−0.298341	−	0.954459i	$-0.596433\pi$
$139$	96.9713	−	145.128i	0.697635	−	1.04408i	0.995976	−	0.0896250i	$-0.0285669\pi$
$140$		0			0
$141$	36.4145	+	183.068i	0.258259	+	1.29836i
$142$		0			0
$143$	−6.76462	+	34.0080i	−0.0473050	+	0.237818i
$144$		0			0
$145$	3.05006	+	7.36349i	0.0210349	+	0.0507827i
$146$		0			0
$147$	70.2540	−	46.9422i	0.477918	−	0.319335i
$148$		0			0
$149$	20.1219	−	20.1219i	0.135047	−	0.135047i	−0.636352	−	0.771399i	$-0.719557\pi$
$149$	20.1219	−	20.1219i	0.135047	−	0.135047i	0.771399	+	0.636352i	$0.219557\pi$
$150$		0			0
$151$	156.650	+	64.8865i	1.03742	+	0.429712i	0.835384	−	0.549667i	$-0.185245\pi$
$151$	156.650	+	64.8865i	1.03742	+	0.429712i	0.202033	+	0.979379i	$0.435245\pi$
$152$		0			0
$153$	−48.7697	+	114.229i	−0.318756	+	0.746594i
$154$		0			0
$155$	10.2431	−	24.7291i	0.0660848	−	0.159543i
$156$		0			0
$157$	−38.8419	−	38.8419i	−0.247401	−	0.247401i	0.572502	−	0.819903i	$-0.305973\pi$
$157$	−38.8419	−	38.8419i	−0.247401	−	0.247401i	−0.819903	+	0.572502i	$0.805973\pi$
$158$		0			0
$159$	220.824	+	330.487i	1.38883	+	2.07854i
$160$		0			0
$161$	113.676	−	47.0861i	0.706061	−	0.292460i
$162$		0			0
$163$	−78.3648	−	15.5877i	−0.480766	−	0.0956302i	−0.0512428	−	0.998686i	$-0.516318\pi$
$163$	−78.3648	−	15.5877i	−0.480766	−	0.0956302i	−0.429523	+	0.903056i	$0.641318\pi$
$164$		0			0
$165$	−13.1167	+	2.60908i	−0.0794953	+	0.0158126i
$166$		0			0
$167$	−117.388	−	78.4365i	−0.702925	−	0.469679i	0.152034	−	0.988375i	$-0.451418\pi$
$167$	−117.388	−	78.4365i	−0.702925	−	0.469679i	−0.854959	+	0.518696i	$0.826418\pi$
$168$		0			0
$169$			134.175i			0.793936i
$170$		0			0
$171$	7.24602			0.0423744
$172$		0			0
$173$	−20.9128	+	31.2982i	−0.120883	+	0.180914i	−0.886976	−	0.461816i	$-0.847198\pi$
$173$	−20.9128	+	31.2982i	−0.120883	+	0.180914i	0.766093	+	0.642730i	$0.222198\pi$
$174$		0			0
$175$	−25.5145	−	128.270i	−0.145797	−	0.732972i
$176$		0			0
$177$	38.5649	−	193.879i	0.217881	−	1.09536i
$178$		0			0
$179$	95.5245	+	230.617i	0.533656	+	1.28836i	0.929086	+	0.369864i	$0.120596\pi$
$179$	95.5245	+	230.617i	0.533656	+	1.28836i	−0.395430	+	0.918496i	$0.629404\pi$
$180$		0			0
$181$	−243.295	+	162.564i	−1.34417	+	0.898146i	−0.999181	−	0.0404610i	$-0.987117\pi$
$181$	−243.295	+	162.564i	−1.34417	+	0.898146i	−0.344989	+	0.938607i	$0.612117\pi$
$182$		0			0
$183$	−60.3307	+	60.3307i	−0.329676	+	0.329676i
$184$		0			0
$185$	14.6587	+	6.07184i	0.0792364	+	0.0328208i
$186$		0			0
$187$	−97.7518	−	20.5460i	−0.522737	−	0.109871i
$188$		0			0
$189$	13.8695	−	33.4839i	0.0733834	−	0.177163i
$190$		0			0
$191$	79.9107	+	79.9107i	0.418381	+	0.418381i	0.884645	−	0.466265i	$-0.154401\pi$
$191$	79.9107	+	79.9107i	0.418381	+	0.418381i	−0.466265	+	0.884645i	$0.654401\pi$
$192$		0			0
$193$	97.9794	+	146.637i	0.507665	+	0.759775i	0.993446	−	0.114306i	$-0.0364644\pi$
$193$	97.9794	+	146.637i	0.507665	+	0.759775i	−0.485780	+	0.874081i	$0.661464\pi$
$194$		0			0
$195$	12.4093	−	5.14011i	0.0636375	−	0.0263595i
$196$		0			0
$197$	−319.291	−	63.5109i	−1.62077	−	0.322391i	−0.700491	−	0.713661i	$-0.747036\pi$
$197$	−319.291	−	63.5109i	−1.62077	−	0.322391i	−0.920276	+	0.391271i	$0.872036\pi$
$198$		0			0
$199$	−123.884	+	24.6420i	−0.622531	+	0.123829i	−0.496270	−	0.868168i	$-0.665298\pi$
$199$	−123.884	+	24.6420i	−0.622531	+	0.123829i	−0.126261	+	0.991997i	$0.540298\pi$
$200$		0			0
$201$	−410.984	−	274.610i	−2.04469	−	1.36622i
$202$		0			0
$203$			74.9241i			0.369084i
$204$		0			0
$205$	6.22038			0.0303433
$206$		0			0
$207$	94.2570	−	141.066i	0.455348	−	0.681476i
$208$		0			0
$209$	1.13687	+	5.71543i	0.00543957	+	0.0273465i
$210$		0			0
$211$	9.20754	−	46.2894i	0.0436376	−	0.219381i	−0.952813	−	0.303557i	$-0.901826\pi$
$211$	9.20754	−	46.2894i	0.0436376	−	0.219381i	0.996451	+	0.0841758i	$0.0268257\pi$
$212$		0			0
$213$	55.1615	+	133.172i	0.258974	+	0.625219i
$214$		0			0
$215$	2.73817	−	1.82959i	0.0127357	−	0.00850971i
$216$		0			0
$217$	177.923	−	177.923i	0.819922	−	0.819922i
$218$		0			0
$219$	366.246	+	151.704i	1.67235	+	0.692712i
$220$		0			0
$221$	100.315	+	1.08542i	0.453916	+	0.00491140i
$222$		0			0
$223$	78.3405	−	189.131i	0.351303	−	0.848120i	−0.645157	−	0.764050i	$-0.723208\pi$
$223$	78.3405	−	189.131i	0.351303	−	0.848120i	0.996460	−	0.0840698i	$-0.0267919\pi$
$224$		0			0
$225$	−127.514	−	127.514i	−0.566729	−	0.566729i
$226$		0			0
$227$	118.982	+	178.070i	0.524152	+	0.784448i	0.995221	−	0.0976478i	$-0.0311319\pi$
$227$	118.982	+	178.070i	0.524152	+	0.784448i	−0.471069	+	0.882096i	$0.656132\pi$
$228$		0			0
$229$	−68.3678	+	28.3189i	−0.298550	+	0.123663i	−0.526930	−	0.849909i	$-0.676657\pi$
$229$	−68.3678	+	28.3189i	−0.298550	+	0.123663i	0.228380	+	0.973572i	$0.426657\pi$
$230$		0			0
$231$	−123.304	−	24.5268i	−0.533785	−	0.106176i
$232$		0			0
$233$	382.165	−	76.0174i	1.64019	−	0.326255i	0.713094	−	0.701069i	$-0.247293\pi$
$233$	382.165	−	76.0174i	1.64019	−	0.326255i	0.927100	+	0.374814i	$0.122293\pi$
$234$		0			0
$235$	21.6632	+	14.4749i	0.0921838	+	0.0615952i
$236$		0			0
$237$		−	487.523i		−	2.05706i
$238$		0			0
$239$	−237.465			−0.993578			−0.496789	−	0.867871i	$-0.665488\pi$
$239$	−237.465			−0.993578			−0.496789	+	0.867871i	$0.665488\pi$
$240$		0			0
$241$	200.362	−	299.863i	0.831379	−	1.24425i	−0.135948	−	0.990716i	$-0.543408\pi$
$241$	200.362	−	299.863i	0.831379	−	1.24425i	0.967327	−	0.253531i	$-0.0815918\pi$
$242$		0			0
$243$	−61.5508	−	309.437i	−0.253295	−	1.27340i
$244$		0			0
$245$	2.30090	−	11.5674i	0.00939143	−	0.0472139i
$246$		0			0
$247$	−2.23973	−	5.40719i	−0.00906773	−	0.0218914i
$248$		0			0
$249$	−331.462	+	221.476i	−1.33117	+	0.889461i
$250$		0			0
$251$	36.8585	−	36.8585i	0.146847	−	0.146847i	−0.629861	−	0.776708i	$-0.716888\pi$
$251$	36.8585	−	36.8585i	0.146847	−	0.146847i	0.776708	+	0.629861i	$0.216888\pi$
$252$		0			0
$253$	126.057	+	52.2144i	0.498248	+	0.206381i
$254$		0			0
$255$	14.4197	+	35.9062i	0.0565478	+	0.140809i
$256$		0			0
$257$	142.481	−	343.979i	0.554400	−	1.33844i	−0.359744	−	0.933051i	$-0.617136\pi$
$257$	142.481	−	343.979i	0.554400	−	1.33844i	0.914144	−	0.405390i	$-0.132864\pi$
$258$		0			0
$259$	105.468	+	105.468i	0.407211	+	0.407211i
$260$		0			0
$261$	57.3961	+	85.8993i	0.219908	+	0.329116i
$262$		0			0
$263$	217.738	−	90.1899i	0.827900	−	0.342927i	0.0718290	−	0.997417i	$-0.477116\pi$
$263$	217.738	−	90.1899i	0.827900	−	0.342927i	0.756071	+	0.654490i	$0.227116\pi$
$264$		0			0
$265$	54.4151	+	10.8238i	0.205340	+	0.0408446i
$266$		0			0
$267$	−281.133	+	55.9209i	−1.05293	+	0.209442i
$268$		0			0
$269$	−217.593	−	145.391i	−0.808898	−	0.540488i	0.0809649	−	0.996717i	$-0.474200\pi$
$269$	−217.593	−	145.391i	−0.808898	−	0.540488i	−0.889862	+	0.456229i	$0.849200\pi$
$270$		0			0
$271$		−	143.692i		−	0.530228i	−0.964217	−	0.265114i	$-0.914590\pi$
$271$		−	143.692i		−	0.530228i	0.964217	−	0.265114i	$-0.0854095\pi$
$272$		0			0
$273$	126.266			0.462512
$274$		0			0
$275$	80.5727	−	120.586i	0.292991	−	0.438493i
$276$		0			0
$277$	52.3324	+	263.093i	0.188926	+	0.949794i	0.952608	+	0.304201i	$0.0983896\pi$
$277$	52.3324	+	263.093i	0.188926	+	0.949794i	−0.763682	+	0.645593i	$0.776610\pi$
$278$		0			0
$279$	67.6869	−	340.285i	0.242605	−	1.21966i
$280$		0			0
$281$	74.9569	+	180.962i	0.266750	+	0.643993i	0.999327	−	0.0366925i	$-0.0116822\pi$
$281$	74.9569	+	180.962i	0.266750	+	0.643993i	−0.732576	+	0.680685i	$0.761682\pi$
$282$		0			0
$283$	−270.968	+	181.055i	−0.957485	+	0.639771i	−0.932980	−	0.359929i	$-0.882801\pi$
$283$	−270.968	+	181.055i	−0.957485	+	0.639771i	−0.0245054	+	0.999700i	$0.507801\pi$
$284$		0			0
$285$	1.59619	−	1.59619i	0.00560067	−	0.00560067i
$286$		0			0
$287$	54.0238	+	22.3774i	0.188236	+	0.0779701i
$288$		0			0
$289$	−6.25326	+	288.932i	−0.0216376	+	0.999766i
$290$		0			0
$291$	19.3459	−	46.7052i	0.0664808	−	0.160499i
$292$		0			0
$293$	219.099	+	219.099i	0.747780	+	0.747780i	0.974062	−	0.226282i	$-0.0726571\pi$
$293$	219.099	+	219.099i	0.747780	+	0.747780i	−0.226282	+	0.974062i	$0.572657\pi$
$294$		0			0
$295$	−15.3297	−	22.9425i	−0.0519649	−	0.0777710i
$296$		0			0
$297$	37.1307	−	15.3800i	0.125019	−	0.0517846i
$298$		0			0
$299$	−134.402	−	26.7342i	−0.449505	−	0.0894120i
$300$		0			0
$301$	30.3628	−	6.03953i	0.100873	−	0.0200649i
$302$		0			0
$303$	−444.729	−	297.158i	−1.46775	−	0.980720i
$304$		0			0
$305$			11.9094i			0.0390473i
$306$		0			0
$307$	−208.356			−0.678684			−0.339342	−	0.940663i	$-0.610204\pi$
$307$	−208.356			−0.678684			−0.339342	+	0.940663i	$0.610204\pi$
$308$		0			0
$309$	−280.602	+	419.950i	−0.908096	+	1.35906i
$310$		0			0
$311$	43.0871	+	216.614i	0.138544	+	0.696507i	0.986147	+	0.165876i	$0.0530451\pi$
$311$	43.0871	+	216.614i	0.138544	+	0.696507i	−0.847603	+	0.530631i	$0.821955\pi$
$312$		0			0
$313$	−101.383	+	509.685i	−0.323906	+	1.62839i	0.384883	+	0.922965i	$0.374242\pi$
$313$	−101.383	+	509.685i	−0.323906	+	1.62839i	−0.708789	+	0.705421i	$0.750758\pi$
$314$		0			0
$315$	8.35037	+	20.1596i	0.0265091	+	0.0639987i
$316$		0			0
$317$	48.4489	−	32.3725i	0.152836	−	0.102121i	−0.476801	−	0.879011i	$-0.658204\pi$
$317$	48.4489	−	32.3725i	0.152836	−	0.102121i	0.629637	+	0.776890i	$0.283204\pi$
$318$		0			0
$319$	−58.7494	+	58.7494i	−0.184168	+	0.184168i
$320$		0			0
$321$	−177.197	−	73.3973i	−0.552015	−	0.228652i
$322$		0			0
$323$	15.6456	−	6.28318i	0.0484384	−	0.0194526i
$324$		0			0
$325$	−55.7403	+	134.569i	−0.171509	+	0.414059i
$326$		0			0
$327$	−256.188	−	256.188i	−0.783449	−	0.783449i
$328$		0			0
$329$	136.072	+	203.646i	0.413592	+	0.618984i
$330$		0			0
$331$	−94.0466	+	38.9554i	−0.284129	+	0.117690i	−0.520196	−	0.854047i	$-0.674141\pi$
$331$	−94.0466	+	38.9554i	−0.284129	+	0.117690i	0.236068	+	0.971737i	$0.424141\pi$
$332$		0			0
$333$	201.711	+	40.1228i	0.605739	+	0.120489i
$334$		0			0
$335$	−67.6689	+	13.4602i	−0.201997	+	0.0401797i
$336$		0			0
$337$	−212.251	−	141.822i	−0.629825	−	0.420836i	0.199269	−	0.979945i	$-0.436143\pi$
$337$	−212.251	−	141.822i	−0.629825	−	0.420836i	−0.829094	+	0.559109i	$0.811143\pi$
$338$		0			0
$339$			781.040i			2.30395i
$340$		0			0
$341$	279.026			0.818257
$342$		0			0
$343$	205.841	−	308.063i	0.600120	−	0.898144i
$344$		0			0
$345$	−10.3112	−	51.8381i	−0.0298877	−	0.150255i
$346$		0			0
$347$	48.4441	−	243.545i	0.139608	−	0.701859i	−0.846050	−	0.533104i	$-0.821025\pi$
$347$	48.4441	−	243.545i	0.139608	−	0.701859i	0.985658	−	0.168755i	$-0.0539747\pi$
$348$		0			0
$349$	104.651	+	252.649i	0.299859	+	0.723922i	0.999951	+	0.00987059i	$0.00314196\pi$
$349$	104.651	+	252.649i	0.299859	+	0.723922i	−0.700093	+	0.714052i	$0.746858\pi$
$350$		0			0
$351$	−33.5618	+	22.4253i	−0.0956176	+	0.0638896i
$352$		0			0
$353$	315.756	−	315.756i	0.894492	−	0.894492i	−0.100450	−	0.994942i	$-0.532028\pi$
$353$	315.756	−	315.756i	0.894492	−	0.894492i	0.994942	+	0.100450i	$0.0320282\pi$
$354$		0			0
$355$	18.5887	+	7.69969i	0.0523625	+	0.0216893i
$356$		0			0
$357$	−3.93545	+	363.718i	−0.0110237	+	1.01882i
$358$		0			0
$359$	−6.00534	+	14.4982i	−0.0167280	+	0.0403849i	−0.932023	−	0.362400i	$-0.881958\pi$
$359$	−6.00534	+	14.4982i	−0.0167280	+	0.0403849i	0.915295	+	0.402784i	$0.131958\pi$
$360$		0			0
$361$	254.570	+	254.570i	0.705180	+	0.705180i
$362$		0			0
$363$	194.003	+	290.346i	0.534443	+	0.799850i
$364$		0			0
$365$	51.1222	−	21.1755i	0.140061	−	0.0580151i
$366$		0			0
$367$	−256.880	−	51.0966i	−0.699945	−	0.139228i	−0.167725	−	0.985834i	$-0.553642\pi$
$367$	−256.880	−	51.0966i	−0.699945	−	0.139228i	−0.532220	+	0.846606i	$0.678642\pi$
$368$		0			0
$369$	79.0798	−	15.7300i	0.214309	−	0.0426286i
$370$		0			0
$371$	433.656	+	289.759i	1.16888	+	0.781023i
$372$		0			0
$373$		−	605.650i		−	1.62373i	−0.583848	−	0.811863i	$-0.698453\pi$
$373$		−	605.650i		−	1.62373i	0.583848	−	0.811863i	$-0.301547\pi$
$374$		0			0
$375$	−113.081			−0.301549
$376$		0			0
$377$	46.3595	−	69.3819i	0.122970	−	0.184037i
$378$		0			0
$379$	55.7064	+	280.055i	0.146983	+	0.738932i	0.982026	+	0.188747i	$0.0604427\pi$
$379$	55.7064	+	280.055i	0.146983	+	0.738932i	−0.835043	+	0.550185i	$0.814557\pi$
$380$		0			0
$381$	91.4311	−	459.655i	0.239977	−	1.20644i
$382$		0			0
$383$	38.9101	+	93.9374i	0.101593	+	0.245267i	0.966501	−	0.256663i	$-0.0826232\pi$
$383$	38.9101	+	93.9374i	0.101593	+	0.245267i	−0.864908	+	0.501931i	$0.832623\pi$
$384$		0			0
$385$	−14.5911	+	9.74946i	−0.0378990	+	0.0253233i
$386$		0			0
$387$	30.1838	−	30.1838i	0.0779944	−	0.0779944i
$388$		0			0
$389$	−96.0858	−	39.8000i	−0.247007	−	0.102314i	0.255745	−	0.966744i	$-0.417679\pi$
$389$	−96.0858	−	39.8000i	−0.247007	−	0.102314i	−0.502752	+	0.864431i	$0.667679\pi$
$390$		0			0
$391$	81.1989	−	386.321i	0.207670	−	0.988034i
$392$		0			0
$393$	−303.153	+	731.877i	−0.771383	+	1.86228i
$394$		0			0
$395$	−48.1191	−	48.1191i	−0.121820	−	0.121820i
$396$		0			0
$397$	−232.267	−	347.612i	−0.585055	−	0.875597i	0.414349	−	0.910118i	$-0.364009\pi$
$397$	−232.267	−	347.612i	−0.585055	−	0.875597i	−0.999404	+	0.0345214i	$0.989009\pi$
$398$		0			0
$399$	19.6051	−	8.12069i	0.0491355	−	0.0203526i
$400$		0			0
$401$	467.261	+	92.9440i	1.16524	+	0.231781i	0.739558	−	0.673092i	$-0.235034\pi$
$401$	467.261	+	92.9440i	1.16524	+	0.231781i	0.425682	+	0.904873i	$0.360034\pi$
$402$		0			0
$403$	−274.852	+	54.6715i	−0.682016	+	0.135661i
$404$		0			0
$405$	−43.7615	−	29.2405i	−0.108053	−	0.0721988i
$406$		0			0
$407$			165.398i			0.406384i
$408$		0			0
$409$	−506.938			−1.23946			−0.619728	−	0.784817i	$-0.712757\pi$
$409$	−506.938			−1.23946			−0.619728	+	0.784817i	$0.712757\pi$
$410$		0			0
$411$	−134.811	+	201.760i	−0.328008	+	0.490899i
$412$		0			0
$413$	−50.6037	−	254.402i	−0.122527	−	0.615986i
$414$		0			0
$415$	−10.8558	+	54.5756i	−0.0261585	+	0.131507i
$416$		0			0
$417$	−269.724	−	651.171i	−0.646820	−	1.56156i
$418$		0			0
$419$	193.148	−	129.058i	0.460975	−	0.308013i	−0.303311	−	0.952892i	$-0.598092\pi$
$419$	193.148	−	129.058i	0.460975	−	0.308013i	0.764285	+	0.644878i	$0.223092\pi$
$420$		0			0
$421$	−101.890	+	101.890i	−0.242019	+	0.242019i	−0.817685	−	0.575666i	$-0.804743\pi$
$421$	−101.890	+	101.890i	−0.242019	+	0.242019i	0.575666	+	0.817685i	$0.304743\pi$
$422$		0			0
$423$	312.008	+	129.238i	0.737608	+	0.305527i
$424$		0			0
$425$	−385.899	−	164.758i	−0.907997	−	0.387667i
$426$		0			0
$427$	−42.8434	+	103.433i	−0.100336	+	0.242232i
$428$		0			0
$429$	99.0075	+	99.0075i	0.230787	+	0.230787i
$430$		0			0
$431$	−275.294	−	412.006i	−0.638733	−	0.955931i	−0.999727	−	0.0233633i	$-0.992563\pi$
$431$	−275.294	−	412.006i	−0.638733	−	0.955931i	0.360994	−	0.932568i	$-0.382437\pi$
$432$		0			0
$433$	145.697	−	60.3498i	0.336483	−	0.139376i	−0.208043	−	0.978120i	$-0.566709\pi$
$433$	145.697	−	60.3498i	0.336483	−	0.139376i	0.544526	+	0.838744i	$0.316709\pi$
$434$		0			0
$435$	31.5659	+	6.27884i	0.0725652	+	0.0144341i
$436$		0			0
$437$	−22.5877	+	4.49298i	−0.0516882	+	0.0102814i
$438$		0			0
$439$	587.813	+	392.764i	1.33898	+	0.894678i	0.998954	−	0.0457373i	$-0.0145637\pi$
$439$	587.813	+	392.764i	1.33898	+	0.894678i	0.340027	+	0.940416i	$0.389564\pi$
$440$		0			0
$441$		−	152.875i		−	0.346656i
$442$		0			0
$443$	−222.267			−0.501730			−0.250865	−	0.968022i	$-0.580715\pi$
$443$	−222.267			−0.501730			−0.250865	+	0.968022i	$0.580715\pi$
$444$		0			0
$445$	−22.2287	+	33.2676i	−0.0499522	+	0.0747587i
$446$		0			0
$447$	−22.4180	−	112.703i	−0.0501521	−	0.252131i
$448$		0			0
$449$	−121.386	+	610.248i	−0.270347	+	1.35913i	0.572027	+	0.820235i	$0.306157\pi$
$449$	−121.386	+	610.248i	−0.270347	+	1.35913i	−0.842374	+	0.538893i	$0.818843\pi$
$450$		0			0
$451$	24.8146	+	59.9077i	0.0550213	+	0.132833i
$452$		0			0
$453$	569.294	−	380.390i	1.25672	−	0.839713i
$454$		0			0
$455$	12.4626	−	12.4626i	0.0273903	−	0.0273903i
$456$		0			0
$457$	−565.132	−	234.085i	−1.23661	−	0.512221i	−0.333958	−	0.942588i	$-0.608384\pi$
$457$	−565.132	−	234.085i	−1.23661	−	0.512221i	−0.902654	+	0.430367i	$0.858384\pi$
$458$		0			0
$459$	−63.5516	−	97.3762i	−0.138457	−	0.212149i
$460$		0			0
$461$	167.918	−	405.389i	0.364246	−	0.879368i	−0.630423	−	0.776252i	$-0.717119\pi$
$461$	167.918	−	405.389i	0.364246	−	0.879368i	0.994669	−	0.103117i	$-0.0328815\pi$
$462$		0			0
$463$	−630.279	−	630.279i	−1.36129	−	1.36129i	−0.872272	−	0.489020i	$-0.837354\pi$
$463$	−630.279	−	630.279i	−1.36129	−	1.36129i	−0.489020	−	0.872272i	$-0.662646\pi$
$464$		0			0
$465$	−60.0494	−	89.8702i	−0.129138	−	0.193269i
$466$		0			0
$467$	777.730	−	322.146i	1.66538	−	0.689821i	0.666907	−	0.745141i	$-0.267618\pi$
$467$	777.730	−	322.146i	1.66538	−	0.689821i	0.998469	+	0.0553199i	$0.0176179\pi$
$468$		0			0
$469$	−636.125	−	126.533i	−1.35634	−	0.269793i
$470$		0			0
$471$	−217.553	+	43.2739i	−0.461896	+	0.0918767i
$472$		0			0
$473$	28.5438	+	19.0723i	0.0603462	+	0.0403220i
$474$		0			0
$475$			24.4792i			0.0515351i
$476$		0			0
$477$	719.151			1.50765
$478$		0			0
$479$	−77.4278	+	115.879i	−0.161645	+	0.241918i	−0.903447	−	0.428701i	$-0.858971\pi$
$479$	−77.4278	+	115.879i	−0.161645	+	0.241918i	0.741802	+	0.670619i	$0.233971\pi$
$480$		0			0
$481$	−32.4077	−	162.925i	−0.0673757	−	0.338720i
$482$		0			0
$483$	96.9314	−	487.307i	0.200686	−	1.00892i
$484$		0			0
$485$	−2.70039	−	6.51932i	−0.00556782	−	0.0134419i
$486$		0			0
$487$	536.092	−	358.205i	1.10080	−	0.735534i	0.133982	−	0.990984i	$-0.457224\pi$
$487$	536.092	−	358.205i	1.10080	−	0.735534i	0.966822	+	0.255450i	$0.0822236\pi$
$488$		0			0
$489$	−228.143	+	228.143i	−0.466551	+	0.466551i
$490$		0			0
$491$	258.907	+	107.243i	0.527305	+	0.218417i	0.630422	−	0.776252i	$-0.282882\pi$
$491$	258.907	+	107.243i	0.527305	+	0.218417i	−0.103117	+	0.994669i	$0.532882\pi$
$492$		0			0
$493$	198.415	+	135.705i	0.402464	+	0.275263i
$494$		0			0
$495$	−9.25983	+	22.3552i	−0.0187067	+	0.0451621i
$496$		0			0
$497$	133.743	+	133.743i	0.269101	+	0.269101i
$498$		0			0
$499$	−103.674	−	155.160i	−0.207764	−	0.310941i	0.712923	−	0.701242i	$-0.247371\pi$
$499$	−103.674	−	155.160i	−0.207764	−	0.310941i	−0.920687	+	0.390301i	$0.872371\pi$
$500$		0			0
$501$	−526.708	+	218.170i	−1.05131	+	0.435468i
$502$		0			0
$503$	412.237	+	81.9990i	0.819557	+	0.163020i	0.587025	−	0.809569i	$-0.300299\pi$
$503$	412.237	+	81.9990i	0.819557	+	0.163020i	0.232532	+	0.972589i	$0.425299\pi$
$504$		0			0
$505$	−73.2251	+	14.5654i	−0.145000	+	0.0288423i
$506$		0			0
$507$	450.499	+	301.014i	0.888559	+	0.593716i
$508$		0			0
$509$		−	832.865i		−	1.63628i	−0.575021	−	0.818139i	$-0.695006\pi$
$509$		−	832.865i		−	1.63628i	0.575021	−	0.818139i	$-0.304994\pi$
$510$		0			0
$511$	520.173			1.01795
$512$		0			0
$513$	−3.76882	+	5.64043i	−0.00734662	+	0.0109950i
$514$		0			0
$515$	13.7538	+	69.1453i	0.0267065	+	0.134263i
$516$		0			0
$517$	−52.9861	+	266.379i	−0.102488	+	0.515240i
$518$		0			0
$519$	58.1685	+	140.431i	0.112078	+	0.270580i
$520$		0			0
$521$	38.9718	−	26.0402i	0.0748020	−	0.0499811i	−0.517607	−	0.855619i	$-0.673177\pi$
$521$	38.9718	−	26.0402i	0.0748020	−	0.0499811i	0.592409	+	0.805637i	$0.298177\pi$
$522$		0			0
$523$	93.2535	−	93.2535i	0.178305	−	0.178305i	−0.612312	−	0.790617i	$-0.709760\pi$
$523$	93.2535	−	93.2535i	0.178305	−	0.178305i	0.790617	+	0.612312i	$0.209760\pi$
$524$		0			0
$525$	−487.913	−	202.100i	−0.929358	−	0.384953i
$526$		0			0
$527$	−148.919	−	793.437i	−0.282578	−	1.50557i
$528$		0			0
$529$	−3.91494	+	9.45151i	−0.00740065	+	0.0178667i
$530$		0			0
$531$	−252.903	−	252.903i	−0.476276	−	0.476276i
$532$		0			0
$533$	−36.1816	−	54.1496i	−0.0678829	−	0.101594i
$534$		0			0
$535$	−24.7339	+	10.2451i	−0.0462316	+	0.0191498i
$536$		0			0
$537$	988.609	+	196.647i	1.84098	+	0.366195i
$538$		0			0
$539$	120.583	−	23.9855i	0.223716	−	0.0444999i
$540$		0			0
$541$	467.476	+	312.357i	0.864096	+	0.577370i	0.906726	−	0.421720i	$-0.138574\pi$
$541$	467.476	+	312.357i	0.864096	+	0.577370i	−0.0426299	+	0.999091i	$0.513574\pi$
$542$		0			0
$543$			1181.58i			2.17602i
$544$		0			0
$545$	−50.5720			−0.0927927
$546$		0			0
$547$	−444.766	+	665.640i	−0.813101	+	1.21689i	0.160138	+	0.987095i	$0.448806\pi$
$547$	−444.766	+	665.640i	−0.813101	+	1.21689i	−0.973239	+	0.229797i	$0.926194\pi$
$548$		0			0
$549$	30.1163	+	151.405i	0.0548566	+	0.275783i
$550$		0			0
$551$	2.73592	−	13.7544i	0.00496537	−	0.0249626i
$552$		0			0
$553$	−244.808	−	591.018i	−0.442690	−	1.06875i
$554$		0			0
$555$	53.2725	−	35.5955i	0.0959864	−	0.0641361i
$556$		0			0
$557$	−720.171	+	720.171i	−1.29295	+	1.29295i	−0.359990	+	0.932956i	$0.617220\pi$
$557$	−720.171	+	720.171i	−1.29295	+	1.29295i	−0.932956	+	0.359990i	$0.882780\pi$
$558$		0			0
$559$	−31.8538	−	13.1943i	−0.0569835	−	0.0236034i
$560$		0			0
$561$	−288.284	+	282.113i	−0.513876	+	0.502875i
$562$		0			0
$563$	−219.849	+	530.762i	−0.390495	+	0.942739i	0.599337	+	0.800497i	$0.295431\pi$
$563$	−219.849	+	530.762i	−0.390495	+	0.942739i	−0.989832	+	0.142242i	$0.954569\pi$
$564$		0			0
$565$	77.0895	+	77.0895i	0.136442	+	0.136442i
$566$		0			0
$567$	−274.877	−	411.382i	−0.484792	−	0.725542i
$568$		0			0
$569$	−316.680	+	131.173i	−0.556555	+	0.230533i	−0.643189	−	0.765708i	$-0.722389\pi$
$569$	−316.680	+	131.173i	−0.556555	+	0.230533i	0.0866340	+	0.996240i	$0.472389\pi$
$570$		0			0
$571$	−747.181	−	148.624i	−1.30855	−	0.260287i	−0.508937	−	0.860804i	$-0.669961\pi$
$571$	−747.181	−	148.624i	−1.30855	−	0.260287i	−0.799612	+	0.600517i	$0.794961\pi$
$572$		0			0
$573$	447.579	−	89.0289i	0.781114	−	0.155373i
$574$		0			0
$575$	476.562	+	318.428i	0.828803	+	0.553788i
$576$		0			0
$577$		−	368.362i		−	0.638409i	−0.947686	−	0.319205i	$-0.896584\pi$
$577$		−	368.362i		−	0.638409i	0.947686	−	0.319205i	$-0.103416\pi$
$578$		0			0
$579$	712.150			1.22997
$580$		0			0
$581$	−290.614	+	434.935i	−0.500196	+	0.748597i
$582$		0			0
$583$	112.832	+	567.244i	0.193537	+	0.972974i
$584$		0			0
$585$	4.74111	−	23.8352i	0.00810447	−	0.0407439i
$586$		0			0
$587$	−337.071	−	813.762i	−0.574227	−	1.38631i	−0.897926	−	0.440146i	$-0.854927\pi$
$587$	−337.071	−	813.762i	−0.574227	−	1.38631i	0.323700	−	0.946160i	$-0.395073\pi$
$588$		0			0
$589$	−39.1597	+	26.1657i	−0.0664850	+	0.0444239i
$590$		0			0
$591$	−929.551	+	929.551i	−1.57284	+	1.57284i
$592$		0			0
$593$	−559.217	−	231.635i	−0.943031	−	0.390616i	−0.142424	−	0.989806i	$-0.545490\pi$
$593$	−559.217	−	231.635i	−0.943031	−	0.390616i	−0.800607	+	0.599189i	$0.795490\pi$
$594$		0			0
$595$	35.5110	+	36.2878i	0.0596823	+	0.0609879i
$596$		0			0
$597$	−195.189	+	471.228i	−0.326950	+	0.789326i
$598$		0			0
$599$	251.045	+	251.045i	0.419107	+	0.419107i	0.884896	−	0.465789i	$-0.154229\pi$
$599$	251.045	+	251.045i	0.419107	+	0.419107i	−0.465789	+	0.884896i	$0.654229\pi$
$600$		0			0
$601$	177.023	+	264.934i	0.294547	+	0.440821i	0.948997	−	0.315284i	$-0.102100\pi$
$601$	177.023	+	264.934i	0.294547	+	0.440821i	−0.654450	+	0.756105i	$0.727100\pi$
$602$		0			0
$603$	−826.239	+	342.239i	−1.37021	+	0.567561i
$604$		0			0
$605$	47.8057	+	9.50915i	0.0790178	+	0.0157176i
$606$		0			0
$607$	354.964	−	70.6068i	0.584785	−	0.116321i	0.106173	−	0.994348i	$-0.466140\pi$
$607$	354.964	−	70.6068i	0.584785	−	0.116321i	0.478612	+	0.878027i	$0.341140\pi$
$608$		0			0
$609$	251.561	+	168.088i	0.413072	+	0.276006i
$610$		0			0
$611$		−	272.777i		−	0.446443i
$612$		0			0
$613$	−198.369			−0.323604			−0.161802	−	0.986823i	$-0.551731\pi$
$613$	−198.369			−0.323604			−0.161802	+	0.986823i	$0.551731\pi$
$614$		0			0
$615$	13.9550	−	20.8852i	0.0226911	−	0.0339597i
$616$		0			0
$617$	64.9055	+	326.302i	0.105195	+	0.528852i	0.997065	+	0.0765599i	$0.0243936\pi$
$617$	64.9055	+	326.302i	0.105195	+	0.528852i	−0.891870	+	0.452292i	$0.850606\pi$
$618$		0			0
$619$	−149.657	+	752.377i	−0.241772	+	1.21547i	0.648917	+	0.760859i	$0.275222\pi$
$619$	−149.657	+	752.377i	−0.241772	+	1.21547i	−0.890689	+	0.454613i	$0.849778\pi$
$620$		0			0
$621$	60.7829	+	146.743i	0.0978790	+	0.236301i
$622$		0			0
$623$	−312.734	+	208.962i	−0.501981	+	0.335413i
$624$		0			0
$625$	425.164	−	425.164i	0.680263	−	0.680263i
$626$		0			0
$627$	21.7403	+	9.00513i	0.0346735	+	0.0143622i
$628$		0			0
$629$	470.326	−	88.2748i	0.747737	−	0.140341i
$630$		0			0
$631$	−196.546	+	474.505i	−0.311484	+	0.751989i	0.688167	+	0.725553i	$0.258416\pi$
$631$	−196.546	+	474.505i	−0.311484	+	0.751989i	−0.999651	+	0.0264359i	$0.991584\pi$
$632$		0			0
$633$	−134.762	−	134.762i	−0.212895	−	0.212895i
$634$		0			0
$635$	−36.3442	−	54.3929i	−0.0572349	−	0.0856581i
$636$		0			0
$637$	−114.080	+	47.2534i	−0.179089	+	0.0741812i
$638$		0			0
$639$	255.790	+	50.8797i	0.400297	+	0.0796239i
$640$		0			0
$641$	459.662	−	91.4325i	0.717102	−	0.142640i	0.176964	−	0.984217i	$-0.443372\pi$
$641$	459.662	−	91.4325i	0.717102	−	0.142640i	0.540137	+	0.841577i	$0.318372\pi$
$642$		0			0
$643$	536.780	+	358.665i	0.834805	+	0.557799i	0.897895	−	0.440209i	$-0.145096\pi$
$643$	536.780	+	358.665i	0.834805	+	0.557799i	−0.0630902	+	0.998008i	$0.520096\pi$
$644$		0			0
$645$		−	13.2981i		−	0.0206172i
$646$		0			0
$647$	−523.285			−0.808786			−0.404393	−	0.914585i	$-0.632517\pi$
$647$	−523.285			−0.808786			−0.404393	+	0.914585i	$0.632517\pi$
$648$		0			0
$649$	159.802	−	239.161i	0.246228	−	0.368507i
$650$		0			0
$651$	−198.225	−	996.544i	−0.304493	−	1.53079i
$652$		0			0
$653$	−118.139	+	593.924i	−0.180917	+	0.909532i	0.778522	+	0.627617i	$0.215970\pi$
$653$	−118.139	+	593.924i	−0.180917	+	0.909532i	−0.959439	+	0.281915i	$0.909030\pi$
$654$		0			0
$655$	42.3155	+	102.159i	0.0646038	+	0.155967i
$656$		0			0
$657$	596.370	−	398.482i	0.907716	−	0.606517i
$658$		0			0
$659$	606.682	−	606.682i	0.920610	−	0.920610i	−0.0764629	−	0.997072i	$-0.524363\pi$
$659$	606.682	−	606.682i	0.920610	−	0.920610i	0.997072	+	0.0764629i	$0.0243627\pi$
$660$		0			0
$661$	−521.354	−	215.952i	−0.788735	−	0.326705i	−0.0483000	−	0.998833i	$-0.515380\pi$
$661$	−521.354	−	215.952i	−0.788735	−	0.326705i	−0.740435	+	0.672128i	$0.765380\pi$
$662$		0			0
$663$	228.696	−	334.379i	0.344941	−	0.504342i
$664$		0			0
$665$	1.13352	−	2.73656i	0.00170454	−	0.00411513i
$666$		0			0
$667$	−232.182	−	232.182i	−0.348098	−	0.348098i
$668$		0			0
$669$	−459.263	−	687.335i	−0.686491	−	1.02741i
$670$		0			0
$671$	−114.698	+	47.5095i	−0.170936	+	0.0708041i
$672$		0			0
$673$	1238.00	+	246.253i	1.83952	+	0.365903i	0.987501	−	0.157611i	$-0.0503793\pi$
$673$	1238.00	+	246.253i	1.83952	+	0.365903i	0.852017	+	0.523514i	$0.175379\pi$
$674$		0			0
$675$	165.582	−	32.9364i	0.245307	−	0.0487946i
$676$		0			0
$677$	271.795	+	181.608i	0.401470	+	0.268254i	0.739872	−	0.672748i	$-0.234886\pi$
$677$	271.795	+	181.608i	0.401470	+	0.268254i	−0.338402	+	0.941002i	$0.609886\pi$
$678$		0			0
$679$		−	66.3346i		−	0.0976946i
$680$		0			0
$681$	864.807			1.26991
$682$		0			0
$683$	−24.7319	+	37.0139i	−0.0362107	+	0.0541932i	−0.849133	−	0.528179i	$-0.822875\pi$
$683$	−24.7319	+	37.0139i	−0.0362107	+	0.0541932i	0.812923	+	0.582372i	$0.197875\pi$
$684$		0			0
$685$	6.60786	+	33.2199i	0.00964651	+	0.0484963i
$686$		0			0
$687$	−58.2972	+	293.080i	−0.0848577	+	0.426608i
$688$		0			0
$689$	−222.288	−	536.651i	−0.322625	−	0.778884i
$690$		0			0
$691$	110.197	−	73.6313i	0.159475	−	0.106558i	−0.473272	−	0.880916i	$-0.656927\pi$
$691$	110.197	−	73.6313i	0.159475	−	0.106558i	0.632747	+	0.774359i	$0.281927\pi$
$692$		0			0
$693$	−160.843	+	160.843i	−0.232097	+	0.232097i
$694$		0			0
$695$	−90.8933	−	37.6493i	−0.130782	−	0.0541716i
$696$		0			0
$697$	157.110	−	102.536i	0.225408	−	0.147110i
$698$		0			0
$699$	602.133	−	1453.68i	0.861420	−	2.07965i
$700$		0			0
$701$	609.715	+	609.715i	0.869778	+	0.869778i	0.992448	−	0.122669i	$-0.0391454\pi$
$701$	609.715	+	609.715i	0.869778	+	0.869778i	−0.122669	+	0.992448i	$0.539145\pi$
$702$		0			0
$703$	−15.5103	−	23.2127i	−0.0220629	−	0.0330195i
$704$		0			0
$705$	97.2001	−	40.2616i	0.137872	−	0.0571087i
$706$		0			0
$707$	−688.356	−	136.923i	−0.973629	−	0.193667i
$708$		0			0
$709$	521.568	−	103.746i	0.735638	−	0.146328i	0.186968	−	0.982366i	$-0.440134\pi$
$709$	521.568	−	103.746i	0.735638	−	0.146328i	0.548671	+	0.836038i	$0.315134\pi$
$710$		0			0
$711$	−733.421	−	490.056i	−1.03153	−	0.689250i
$712$		0			0
$713$			1102.73i			1.54660i
$714$		0			0
$715$	19.5443			0.0273347
$716$		0			0
$717$	−532.739	+	797.300i	−0.743011	+	1.11199i
$718$		0			0
$719$	−68.0574	−	342.147i	−0.0946556	−	0.475866i	−0.998815	−	0.0486703i	$-0.984502\pi$
$719$	−68.0574	−	342.147i	−0.0946556	−	0.475866i	0.904159	−	0.427195i	$-0.140498\pi$
$720$		0			0
$721$	−129.294	+	650.003i	−0.179326	+	0.901530i
$722$		0			0
$723$	−557.304	−	1345.45i	−0.770822	−	1.86093i
$724$		0			0
$725$	−290.193	+	193.901i	−0.400267	+	0.267450i
$726$		0			0
$727$	23.2735	−	23.2735i	0.0320131	−	0.0320131i	−0.690919	−	0.722932i	$-0.742794\pi$
$727$	23.2735	−	23.2735i	0.0320131	−	0.0320131i	0.722932	+	0.690919i	$0.242794\pi$
$728$		0			0
$729$	−400.623	−	165.944i	−0.549552	−	0.227632i
$730$		0			0
$731$	38.9999	−	91.3460i	0.0533514	−	0.124960i
$732$		0			0
$733$	533.806	−	1288.72i	0.728248	−	1.75815i	0.0799007	−	0.996803i	$-0.474540\pi$
$733$	533.806	−	1288.72i	0.728248	−	1.75815i	0.648348	−	0.761344i	$-0.275460\pi$
$734$		0			0
$735$	−33.6761	−	33.6761i	−0.0458179	−	0.0458179i
$736$		0			0
$737$	−399.581	−	598.015i	−0.542172	−	0.811418i
$738$		0			0
$739$	−420.413	+	174.141i	−0.568894	+	0.235644i	−0.648541	−	0.761179i	$-0.724621\pi$
$739$	−420.413	+	174.141i	−0.568894	+	0.235644i	0.0796472	+	0.996823i	$0.474621\pi$
$740$		0			0
$741$	−23.1796	−	4.61070i	−0.0312815	−	0.00622227i
$742$		0			0
$743$	−567.191	+	112.821i	−0.763379	+	0.151846i	−0.561400	−	0.827544i	$-0.689737\pi$
$743$	−567.191	+	112.821i	−0.763379	+	0.151846i	−0.201979	+	0.979390i	$0.564737\pi$
$744$		0			0
$745$	−13.3366	−	8.91121i	−0.0179014	−	0.0119614i
$746$		0			0
$747$			721.273i			0.965559i
$748$		0			0
$749$	−251.670			−0.336007
$750$		0			0
$751$	489.153	−	732.069i	0.651335	−	0.974792i	−0.347969	−	0.937506i	$-0.613129\pi$
$751$	489.153	−	732.069i	0.651335	−	0.974792i	0.999305	−	0.0372861i	$-0.0118713\pi$
$752$		0			0
$753$	−41.0643	−	206.444i	−0.0545342	−	0.274162i
$754$		0			0
$755$	18.6450	−	93.7349i	0.0246954	−	0.124152i
$756$		0			0
$757$	342.701	+	827.354i	0.452710	+	1.09294i	0.971288	+	0.237908i	$0.0764617\pi$
$757$	342.701	+	827.354i	0.452710	+	1.09294i	−0.518578	+	0.855030i	$0.673538\pi$
$758$		0			0
$759$	458.113	−	306.101i	0.603574	−	0.403295i
$760$		0			0
$761$	33.2788	−	33.2788i	0.0437303	−	0.0437303i	−0.684903	−	0.728634i	$-0.740156\pi$
$761$	33.2788	−	33.2788i	0.0437303	−	0.0437303i	0.728634	+	0.684903i	$0.240156\pi$
$762$		0			0
$763$	−439.217	−	181.930i	−0.575645	−	0.238440i
$764$		0			0
$765$	68.5113	+	14.4000i	0.0895572	+	0.0188236i
$766$		0			0
$767$	−110.552	+	266.895i	−0.144135	+	0.347973i
$768$		0			0
$769$	−560.397	−	560.397i	−0.728734	−	0.728734i	0.241633	−	0.970368i	$-0.422317\pi$
$769$	−560.397	−	560.397i	−0.728734	−	0.728734i	−0.970368	+	0.241633i	$0.922317\pi$
$770$		0			0
$771$	−835.279	−	1250.08i	−1.08337	−	1.62138i
$772$		0			0
$773$	−1020.58	+	422.736i	−1.32028	+	0.546878i	−0.927867	−	0.372912i	$-0.878359\pi$
$773$	−1020.58	+	422.736i	−1.32028	+	0.546878i	−0.392413	+	0.919789i	$0.628359\pi$
$774$		0			0
$775$	1149.58	+	228.666i	1.48333	+	0.295053i
$776$		0			0
$777$	590.723	−	117.502i	0.760261	−	0.151225i
$778$		0			0
$779$	−9.10044	−	6.08072i	−0.0116822	−	0.00780580i
$780$		0			0
$781$			209.741i			0.268555i
$782$		0			0
$783$	−96.7186			−0.123523
$784$		0			0
$785$	−17.2015	+	25.7439i	−0.0219128	+	0.0327948i
$786$		0			0
$787$	−72.5748	−	364.858i	−0.0922170	−	0.463606i	−0.999108	−	0.0422398i	$-0.986551\pi$
$787$	−72.5748	−	364.858i	−0.0922170	−	0.463606i	0.906891	−	0.421366i	$-0.138449\pi$
$788$		0			0
$789$	185.665	−	933.400i	0.235317	−	1.18302i
$790$		0			0
$791$	392.196	+	946.845i	0.495823	+	1.19702i
$792$		0			0
$793$	103.674	−	69.2726i	0.130736	−	0.0873551i
$794$		0			0
$795$	158.418	−	158.418i	0.199269	−	0.199269i
$796$		0			0
$797$	913.921	+	378.558i	1.14670	+	0.474979i	0.873426	−	0.486957i	$-0.161893\pi$
$797$	913.921	+	378.558i	1.14670	+	0.474979i	0.273275	+	0.961936i	$0.411893\pi$
$798$		0			0
$799$	785.754	+	8.50191i	0.983422	+	0.0106407i
$800$		0			0
$801$	−198.468	+	479.144i	−0.247775	+	0.598182i
$802$		0			0
$803$	407.877	+	407.877i	0.507942	+	0.507942i
$804$		0			0
$805$	−38.5305	−	57.6650i	−0.0478640	−	0.0716335i
$806$		0			0
$807$	−976.316	+	404.403i	−1.20981	+	0.501119i
$808$		0			0
$809$	−473.126	−	94.1105i	−0.584828	−	0.116329i	−0.106196	−	0.994345i	$-0.533867\pi$
$809$	−473.126	−	94.1105i	−0.584828	−	0.116329i	−0.478632	+	0.878016i	$0.658867\pi$
$810$		0			0
$811$	−642.627	+	127.827i	−0.792389	+	0.157616i	−0.574659	−	0.818393i	$-0.694865\pi$
$811$	−642.627	+	127.827i	−0.792389	+	0.157616i	−0.217730	+	0.976009i	$0.569865\pi$
$812$		0			0
$813$	−482.451	−	322.364i	−0.593421	−	0.396511i
$814$		0			0
$815$			45.0360i			0.0552589i
$816$		0			0
$817$	−5.79446			−0.00709236
$818$		0			0
$819$	126.922	−	189.952i	0.154972	−	0.231932i
$820$		0			0
$821$	−92.3790	−	464.421i	−0.112520	−	0.565677i	−0.995378	−	0.0960363i	$-0.969384\pi$
$821$	−92.3790	−	464.421i	−0.112520	−	0.565677i	0.882858	−	0.469641i	$-0.155616\pi$
$822$		0			0
$823$	−186.718	+	938.694i	−0.226875	+	1.14058i	0.684504	+	0.729009i	$0.260019\pi$
$823$	−186.718	+	938.694i	−0.226875	+	1.14058i	−0.911379	+	0.411568i	$0.864981\pi$
$824$		0			0
$825$	−224.111	−	541.053i	−0.271650	−	0.655821i
$826$		0			0
$827$	288.890	−	193.030i	0.349323	−	0.233410i	−0.368513	−	0.929623i	$-0.620133\pi$
$827$	288.890	−	193.030i	0.349323	−	0.233410i	0.717836	+	0.696213i	$0.245133\pi$
$828$		0			0
$829$	958.235	−	958.235i	1.15589	−	1.15589i	0.170542	−	0.985350i	$-0.445448\pi$
$829$	958.235	−	958.235i	1.15589	−	1.15589i	0.985350	−	0.170542i	$-0.0545518\pi$
$830$		0			0
$831$	1000.75	+	414.525i	1.20427	+	0.498826i
$832$		0			0
$833$	−132.561	−	330.088i	−0.159137	−	0.396264i
$834$		0			0
$835$	−30.4531	+	73.5203i	−0.0364708	+	0.0880482i
$836$		0			0
$837$	229.679	+	229.679i	0.274407	+	0.274407i
$838$		0			0
$839$	−236.082	−	353.322i	−0.281385	−	0.421123i	0.663674	−	0.748022i	$-0.268996\pi$
$839$	−236.082	−	353.322i	−0.281385	−	0.421123i	−0.945059	+	0.326899i	$0.893996\pi$
$840$		0			0
$841$	−592.257	+	245.321i	−0.704230	+	0.291702i
$842$		0			0
$843$	775.749	+	154.306i	0.920224	+	0.183044i
$844$		0			0
$845$	74.1752	−	14.7544i	0.0877813	−	0.0174608i
$846$		0			0
$847$	380.983	+	254.565i	0.449803	+	0.300549i
$848$		0			0
$849$			1315.98i			1.55003i
$850$		0			0
$851$	−653.665			−0.768114
$852$		0			0
$853$	654.682	−	979.801i	0.767505	−	1.14865i	−0.217488	−	0.976063i	$-0.569786\pi$
$853$	654.682	−	979.801i	0.767505	−	1.14865i	0.984994	−	0.172590i	$-0.0552136\pi$
$854$		0			0
$855$	−0.796797	−	4.00577i	−0.000931926	−	0.00468511i
$856$		0			0
$857$	−38.6709	+	194.412i	−0.0451236	+	0.226852i	−0.996766	−	0.0803554i	$-0.974394\pi$
$857$	−38.6709	+	194.412i	−0.0451236	+	0.226852i	0.951643	+	0.307207i	$0.0993945\pi$
$858$		0			0
$859$	−168.807	−	407.536i	−0.196515	−	0.474430i	0.794649	−	0.607069i	$-0.207655\pi$
$859$	−168.807	−	407.536i	−0.196515	−	0.474430i	−0.991164	+	0.132639i	$0.957655\pi$
$860$		0			0
$861$	196.332	−	131.185i	0.228028	−	0.152364i
$862$		0			0
$863$	−809.493	+	809.493i	−0.937999	+	0.937999i	−0.998187	−	0.0601880i	$-0.980830\pi$
$863$	−809.493	+	809.493i	−0.937999	+	0.937999i	0.0601880	+	0.998187i	$0.480830\pi$
$864$		0			0
$865$	19.6020	+	8.11942i	0.0226613	+	0.00938661i
$866$		0			0
$867$	956.075	+	669.198i	1.10274	+	0.771855i
$868$		0			0
$869$	271.470	−	655.387i	0.312394	−	0.754185i
$870$		0			0
$871$	510.778	+	510.778i	0.586427	+	0.586427i
$872$		0			0
$873$	−50.8160	−	76.0516i	−0.0582085	−	0.0871152i
$874$		0			0
$875$	−137.087	+	56.7832i	−0.156671	+	0.0648951i
$876$		0			0
$877$	−1540.44	−	306.413i	−1.75649	−	0.349388i	−0.791400	−	0.611299i	$-0.790647\pi$
$877$	−1540.44	−	306.413i	−1.75649	−	0.349388i	−0.965092	+	0.261911i	$0.915647\pi$
$878$		0			0
$879$	1227.17	−	244.100i	1.39610	−	0.277702i
$880$		0			0
$881$	−48.8787	−	32.6597i	−0.0554809	−	0.0370711i	0.527520	−	0.849542i	$-0.323122\pi$
$881$	−48.8787	−	32.6597i	−0.0554809	−	0.0370711i	−0.583001	+	0.812471i	$0.698122\pi$
$882$		0			0
$883$			1283.12i			1.45314i	0.687092	+	0.726571i	$0.258887\pi$
$883$			1283.12i			1.45314i	−0.687092	+	0.726571i	$0.741113\pi$
$884$		0			0
$885$	−111.422			−0.125900
$886$		0			0
$887$	−423.529	+	633.856i	−0.477485	+	0.714606i	−0.989526	−	0.144354i	$-0.953889\pi$
$887$	−423.529	+	633.856i	−0.477485	+	0.714606i	0.512041	+	0.858961i	$0.328889\pi$
$888$		0			0
$889$	−119.973	−	603.146i	−0.134953	−	0.678455i
$890$		0			0
$891$	107.037	−	538.109i	0.120131	−	0.603939i
$892$		0			0
$893$	−17.5434	−	42.3536i	−0.0196455	−	0.0474284i
$894$		0			0
$895$	116.986	−	78.1676i	0.130711	−	0.0873381i
$896$		0			0
$897$	−391.284	+	391.284i	−0.436214	+	0.436214i
$898$		0			0
$899$	−620.372	−	256.966i	−0.690069	−	0.285836i
$900$		0			0
$901$	1552.79	−	623.592i	1.72341	−	0.692111i
$902$		0			0
$903$	47.8391	−	115.494i	0.0529779	−	0.127900i
$904$		0			0
$905$	116.623	+	116.623i	0.128865	+	0.128865i
$906$		0			0
$907$	846.972	+	1267.58i	0.933817	+	1.39756i	0.917520	+	0.397689i	$0.130188\pi$
$907$	846.972	+	1267.58i	0.933817	+	1.39756i	0.0162965	+	0.999867i	$0.494812\pi$
$908$		0			0
$909$	−894.080	+	370.340i	−0.983586	+	0.407415i
$910$		0			0
$911$	−51.5057	−	10.2451i	−0.0565375	−	0.0112460i	0.166741	−	0.986001i	$-0.446676\pi$
$911$	−51.5057	−	10.2451i	−0.0565375	−	0.0112460i	−0.223278	+	0.974755i	$0.571676\pi$
$912$		0			0
$913$	−568.917	+	113.165i	−0.623129	+	0.123948i
$914$		0			0
$915$	39.9864	+	26.7181i	0.0437010	+	0.0292001i
$916$		0			0
$917$			1039.47i			1.13356i
$918$		0			0
$919$	−283.637			−0.308636			−0.154318	−	0.988021i	$-0.549318\pi$
$919$	−283.637			−0.308636			−0.154318	+	0.988021i	$0.549318\pi$
$920$		0			0
$921$	−467.434	+	699.564i	−0.507529	+	0.759571i
$922$		0			0
$923$	−41.0962	−	206.604i	−0.0445245	−	0.223840i
$924$		0			0
$925$	−135.547	+	681.440i	−0.146537	+	0.736692i
$926$		0			0
$927$	349.706	+	844.265i	0.377245	+	0.910750i
$928$		0			0
$929$	−1185.90	+	792.393i	−1.27653	+	0.852952i	−0.994323	−	0.106400i	$-0.966067\pi$
$929$	−1185.90	+	792.393i	−1.27653	+	0.852952i	−0.282210	+	0.959353i	$0.591067\pi$
$930$		0			0
$931$	−14.6739	+	14.6739i	−0.0157615	+	0.0157615i
$932$		0			0
$933$	823.954	+	341.293i	0.883123	+	0.365801i
$934$		0			0
$935$	−0.609157	+	56.2988i	−0.000651505	+	0.0602127i
$936$		0			0
$937$	145.025	−	350.121i	0.154776	−	0.373662i	−0.827404	−	0.561608i	$-0.810183\pi$
$937$	145.025	−	350.121i	0.154776	−	0.373662i	0.982179	+	0.187946i	$0.0601830\pi$
$938$		0			0
$939$	1483.84	+	1483.84i	1.58024	+	1.58024i
$940$		0			0
$941$	−547.521	−	819.423i	−0.581850	−	0.870800i	0.417431	−	0.908709i	$-0.362930\pi$
$941$	−547.521	−	819.423i	−0.581850	−	0.870800i	−0.999281	+	0.0379085i	$0.987930\pi$
$942$		0			0
$943$	−236.759	+	98.0688i	−0.251070	+	0.103997i
$944$		0			0
$945$	−20.0358	−	3.98537i	−0.0212019	−	0.00421732i
$946$		0			0
$947$	−84.7442	+	16.8567i	−0.0894870	+	0.0178001i	−0.239631	−	0.970864i	$-0.577026\pi$
$947$	−84.7442	+	16.8567i	−0.0894870	+	0.0178001i	0.150144	+	0.988664i	$0.452026\pi$
$948$		0			0
$949$	−481.695	−	321.858i	−0.507582	−	0.339155i
$950$		0			0
$951$		−	235.295i		−	0.247419i
$952$		0			0
$953$	−1585.19			−1.66336			−0.831682	−	0.555252i	$-0.812622\pi$
$953$	−1585.19			−1.66336			−0.831682	+	0.555252i	$0.812622\pi$
$954$		0			0
$955$	35.3893	−	52.9638i	0.0370568	−	0.0554594i
$956$		0			0
$957$	65.4531	+	329.055i	0.0683940	+	0.343840i
$958$		0			0
$959$	−62.1175	+	312.286i	−0.0647732	+	0.325637i
$960$		0			0
$961$	495.224	+	1195.58i	0.515321	+	1.24410i
$962$		0			0
$963$	−288.535	+	192.793i	−0.299621	+	0.200201i
$964$		0			0
$965$	70.2900	−	70.2900i	0.0728394	−	0.0728394i
$966$		0			0
$967$	−1215.45	−	503.454i	−1.25692	−	0.520635i	−0.347960	−	0.937509i	$-0.613125\pi$
$967$	−1215.45	−	503.454i	−1.25692	−	0.520635i	−0.908964	+	0.416875i	$0.863125\pi$
$968$		0			0
$969$	14.0039	−	66.6268i	0.0144519	−	0.0687583i
$970$		0			0
$971$	608.139	−	1468.18i	0.626302	−	1.51203i	−0.217883	−	0.975975i	$-0.569915\pi$
$971$	608.139	−	1468.18i	0.626302	−	1.51203i	0.844185	−	0.536052i	$-0.180085\pi$
$972$		0			0
$973$	−653.966	−	653.966i	−0.672113	−	0.672113i
$974$		0			0
$975$	326.772	+	489.048i	0.335150	+	0.501588i
$976$		0			0
$977$	−76.2692	+	31.5917i	−0.0780647	+	0.0323355i	−0.421374	−	0.906887i	$-0.638452\pi$
$977$	−76.2692	+	31.5917i	−0.0780647	+	0.0323355i	0.343309	+	0.939222i	$0.388452\pi$
$978$		0			0
$979$	−409.072	−	81.3695i	−0.417847	−	0.0831149i
$980$		0			0
$981$	−642.924	+	127.885i	−0.655376	+	0.130362i
$982$		0			0
$983$	−1421.83	−	950.037i	−1.44642	−	0.966467i	−0.997334	−	0.0729784i	$-0.976750\pi$
$983$	−1421.83	−	950.037i	−1.44642	−	0.966467i	−0.449086	−	0.893488i	$-0.648250\pi$
$984$		0			0
$985$			183.496i			0.186290i
$986$		0			0
$987$	989.019			1.00205
$988$		0			0
$989$	−75.3750	+	112.807i	−0.0762134	+	0.114061i
$990$		0			0
$991$	96.5558	+	485.419i	0.0974327	+	0.489827i	0.998431	+	0.0560036i	$0.0178358\pi$
$991$	96.5558	+	485.419i	0.0974327	+	0.489827i	−0.900998	+	0.433823i	$0.857164\pi$
$992$		0			0
$993$	−80.1935	+	403.160i	−0.0807588	+	0.406002i
$994$		0			0
$995$	27.2454	+	65.7761i	0.0273823	+	0.0661066i
$996$		0			0
$997$	−225.480	+	150.661i	−0.226159	+	0.151114i	−0.663488	−	0.748187i	$-0.730925\pi$
$997$	−225.480	+	150.661i	−0.226159	+	0.151114i	0.437329	+	0.899302i	$0.355925\pi$
$998$		0			0
$999$	−136.147	+	136.147i	−0.136283	+	0.136283i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.3.t.a.41.4	✓	32
4.3	odd	2		272.3.bh.f.177.1		32
17.5	odd	16	inner	136.3.t.a.73.4	yes	32
68.39	even	16		272.3.bh.f.209.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.t.a.41.4	✓	32	1.1	even	1	trivial
136.3.t.a.73.4	yes	32	17.5	odd	16	inner
272.3.bh.f.177.1		32	4.3	odd	2
272.3.bh.f.209.1		32	68.39	even	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	136.t (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.24344 - 3.35755i) q^{3} +(-0.109963 - 0.552824i) q^{5} +(1.03372 - 5.19685i) q^{7} +(-2.79594 - 6.74999i) q^{9} +O(q^{10})\)	\(q+(2.24344 - 3.35755i) q^{3} +(-0.109963 - 0.552824i) q^{5} +(1.03372 - 5.19685i) q^{7} +(-2.79594 - 6.74999i) q^{9} +(4.88551 - 3.26439i) q^{11} +(-4.17282 + 4.17282i) q^{13} +(-2.10283 - 0.871019i) q^{15} +(-11.8901 - 12.1502i) q^{17} +(-0.379535 + 0.916277i) q^{19} +(-15.1296 - 15.1296i) q^{21} +(12.9011 + 19.3078i) q^{23} +(22.8035 - 9.44551i) q^{25} +(6.70854 + 1.33441i) q^{27} +(-13.8685 + 2.75862i) q^{29} +(39.4846 + 26.3828i) q^{31} -23.7268i q^{33} -2.98661 q^{35} +(-15.6389 + 23.4053i) q^{37} +(4.64896 + 23.3719i) q^{39} +(-2.15298 + 10.8238i) q^{41} +(2.23584 + 5.39780i) q^{43} +(-3.42410 + 2.28791i) q^{45} +(-32.6850 + 32.6850i) q^{47} +(19.3315 + 8.00735i) q^{49} +(-67.4694 + 12.6632i) q^{51} +(-37.6680 + 90.9385i) q^{53} +(-2.34186 - 2.34186i) q^{55} +(2.22498 + 3.32992i) q^{57} +(45.2268 - 18.7336i) q^{59} +(-20.7230 - 4.12205i) q^{61} +(-37.9689 + 7.55248i) q^{63} +(2.76569 + 1.84797i) q^{65} -122.406i q^{67} +93.7697 q^{69} +(-19.8317 + 29.6802i) q^{71} +(19.1521 + 96.2843i) q^{73} +(19.4445 - 97.7541i) q^{75} +(-11.9143 - 28.7637i) q^{77} +(100.384 - 67.0746i) q^{79} +(66.0265 - 66.0265i) q^{81} +(-91.2068 - 37.7791i) q^{83} +(-5.40943 + 7.90918i) q^{85} +(-21.8510 + 52.7529i) q^{87} +(-50.1935 - 50.1935i) q^{89} +(17.3720 + 25.9990i) q^{91} +(177.163 - 73.3831i) q^{93} +(0.548275 + 0.109059i) q^{95} +(12.2786 - 2.44236i) q^{97} +(-35.6942 - 23.8501i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9}+O(q^{10}) \) 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9	\( 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9} - 24 q^{11} + 48 q^{13} + 96 q^{15} + 40 q^{19} - 80 q^{21} - 48 q^{23} + 112 q^{25} - 80 q^{27} + 56 q^{29} - 24 q^{31} - 96 q^{35} + 48 q^{37} - 72 q^{39} - 160 q^{41} + 112 q^{43} - 504 q^{45} + 48 q^{47} + 208 q^{49} - 400 q^{51} + 304 q^{53} - 368 q^{55} - 264 q^{57} + 192 q^{59} - 288 q^{61} + 56 q^{63} + 8 q^{65} + 32 q^{69} + 352 q^{71} - 184 q^{73} + 24 q^{75} + 688 q^{77} - 424 q^{79} + 312 q^{81} + 600 q^{83} - 512 q^{85} + 1336 q^{87} - 144 q^{89} - 24 q^{91} + 944 q^{93} - 256 q^{95} + 416 q^{97} + 128 q^{99}+O(q^{100}) \) 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9 - 24 * q^11 + 48 * q^13 + 96 * q^15 + 40 * q^19 - 80 * q^21 - 48 * q^23 + 112 * q^25 - 80 * q^27 + 56 * q^29 - 24 * q^31 - 96 * q^35 + 48 * q^37 - 72 * q^39 - 160 * q^41 + 112 * q^43 - 504 * q^45 + 48 * q^47 + 208 * q^49 - 400 * q^51 + 304 * q^53 - 368 * q^55 - 264 * q^57 + 192 * q^59 - 288 * q^61 + 56 * q^63 + 8 * q^65 + 32 * q^69 + 352 * q^71 - 184 * q^73 + 24 * q^75 + 688 * q^77 - 424 * q^79 + 312 * q^81 + 600 * q^83 - 512 * q^85 + 1336 * q^87 - 144 * q^89 - 24 * q^91 + 944 * q^93 - 256 * q^95 + 416 * q^97 + 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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