LMFDB - Embedded newform 608.2.bf.a.529.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [608,2,Mod(17,608)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(608, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("608.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 608 = 2^{5} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	608.bf (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.85490444289$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			529.6
Character	$\chi$	$=$	608.529
Dual form			608.2.bf.a.177.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.467226 - 1.28369i) q^{3} +(-1.73333 - 0.305632i) q^{5} +(-1.91364 - 3.31452i) q^{7} +(0.868569 - 0.728816i) q^{9} +(-2.26499 - 1.30769i) q^{11} +(-2.03996 + 5.60474i) q^{13} +(0.417517 + 2.36785i) q^{15} +(2.13151 + 1.78855i) q^{17} +(0.713969 + 4.30003i) q^{19} +(-3.36072 + 4.00515i) q^{21} +(1.10686 + 6.27729i) q^{23} +(-1.78746 - 0.650581i) q^{25} +(-4.89056 - 2.82357i) q^{27} +(-2.78015 - 3.31326i) q^{29} +(-2.41499 - 4.18289i) q^{31} +(-0.620412 + 3.51853i) q^{33} +(2.30393 + 6.33001i) q^{35} -7.50278i q^{37} +8.14787 q^{39} +(-6.78504 + 2.46955i) q^{41} +(-3.24204 - 0.571659i) q^{43} +(-1.72826 + 0.997812i) q^{45} +(-3.73496 + 3.13400i) q^{47} +(-3.82402 + 6.62340i) q^{49} +(1.30005 - 3.57186i) q^{51} +(1.49917 - 0.264344i) q^{53} +(3.52629 + 2.95890i) q^{55} +(5.18633 - 2.92560i) q^{57} +(-4.81703 + 5.74071i) q^{59} +(5.64385 - 0.995163i) q^{61} +(-4.07780 - 1.48420i) q^{63} +(5.24890 - 9.09135i) q^{65} +(-2.11430 - 2.51972i) q^{67} +(7.54096 - 4.35377i) q^{69} +(-0.236392 + 1.34065i) q^{71} +(10.5450 - 3.83807i) q^{73} +2.59851i q^{75} +10.0098i q^{77} +(6.51619 - 2.37170i) q^{79} +(-0.748928 + 4.24738i) q^{81} +(-5.89196 + 3.40173i) q^{83} +(-3.14796 - 3.75160i) q^{85} +(-2.95424 + 5.11690i) q^{87} +(-6.91135 - 2.51553i) q^{89} +(22.4807 - 3.96396i) q^{91} +(-4.24120 + 5.05446i) q^{93} +(0.0766864 - 7.67156i) q^{95} +(-9.33891 - 7.83628i) q^{97} +(-2.92036 + 0.514939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 6 q^{7} - 12 q^{9} + 12 q^{15} - 12 q^{17} + 12 q^{23} - 12 q^{25} - 30 q^{31} - 30 q^{33} + 24 q^{39} - 24 q^{41} + 48 q^{47} - 24 q^{49} + 42 q^{55} - 12 q^{57} - 30 q^{63} - 6 q^{65} + 12 q^{71}+ \cdots - 12 q^{97}+O(q^{100}) $ 108 * q + 6 * q^7 - 12 * q^9 + 12 * q^15 - 12 * q^17 + 12 * q^23 - 12 * q^25 - 30 * q^31 - 30 * q^33 + 24 * q^39 - 24 * q^41 + 48 * q^47 - 24 * q^49 + 42 * q^55 - 12 * q^57 - 30 * q^63 - 6 * q^65 + 12 * q^71 + 12 * q^73 + 12 * q^79 - 18 * q^81 + 6 * q^87 - 12 * q^89 + 72 * q^95 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/608\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$	$-1$

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
$3$	−0.467226	−	1.28369i	−0.269753	−	0.741140i	−0.998416	−	0.0562672i	$-0.982080\pi$
$3$	−0.467226	−	1.28369i	−0.269753	−	0.741140i	0.728663	−	0.684872i	$-0.240142\pi$
$4$		0			0
$5$	−1.73333	−	0.305632i	−0.775167	−	0.136683i	−0.227949	−	0.973673i	$-0.573202\pi$
$5$	−1.73333	−	0.305632i	−0.775167	−	0.136683i	−0.547218	+	0.836990i	$0.684313\pi$
$6$		0			0
$7$	−1.91364	−	3.31452i	−0.723287	−	1.25277i	−0.959675	−	0.281112i	$-0.909297\pi$
$7$	−1.91364	−	3.31452i	−0.723287	−	1.25277i	0.236388	−	0.971659i	$-0.424036\pi$
$8$		0			0
$9$	0.868569	−	0.728816i	0.289523	−	0.242939i
$10$		0			0
$11$	−2.26499	−	1.30769i	−0.682919	−	0.394283i	0.118035	−	0.993009i	$-0.462341\pi$
$11$	−2.26499	−	1.30769i	−0.682919	−	0.394283i	−0.800954	+	0.598726i	$0.795674\pi$
$12$		0			0
$13$	−2.03996	+	5.60474i	−0.565782	+	1.55447i	0.245242	+	0.969462i	$0.421133\pi$
$13$	−2.03996	+	5.60474i	−0.565782	+	1.55447i	−0.811024	+	0.585012i	$0.801090\pi$
$14$		0			0
$15$	0.417517	+	2.36785i	0.107802	+	0.611377i
$16$		0			0
$17$	2.13151	+	1.78855i	0.516967	+	0.433787i	0.863573	−	0.504224i	$-0.168221\pi$
$17$	2.13151	+	1.78855i	0.516967	+	0.433787i	−0.346606	+	0.938011i	$0.612666\pi$
$18$		0			0
$19$	0.713969	+	4.30003i	0.163796	+	0.986494i
$19$	0.713969	+	4.30003i	0.163796	+	0.986494i
$20$		0			0
$21$	−3.36072	+	4.00515i	−0.733369	+	0.873995i
$22$		0			0
$23$	1.10686	+	6.27729i	0.230796	+	1.30891i	0.851290	+	0.524696i	$0.175821\pi$
$23$	1.10686	+	6.27729i	0.230796	+	1.30891i	−0.620494	+	0.784211i	$0.713068\pi$
$24$		0			0
$25$	−1.78746	−	0.650581i	−0.357492	−	0.130116i
$26$		0			0
$27$	−4.89056	−	2.82357i	−0.941189	−	0.543396i
$28$		0			0
$29$	−2.78015	−	3.31326i	−0.516261	−	0.615256i	0.443431	−	0.896308i	$-0.353761\pi$
$29$	−2.78015	−	3.31326i	−0.516261	−	0.615256i	−0.959693	+	0.281052i	$0.909317\pi$
$30$		0			0
$31$	−2.41499	−	4.18289i	−0.433746	−	0.751270i	0.563447	−	0.826153i	$-0.309475\pi$
$31$	−2.41499	−	4.18289i	−0.433746	−	0.751270i	−0.997192	+	0.0748828i	$0.976142\pi$
$32$		0			0
$33$	−0.620412	+	3.51853i	−0.108000	+	0.612497i
$34$		0			0
$35$	2.30393	+	6.33001i	0.389436	+	1.06997i
$36$		0			0
$37$		−	7.50278i		−	1.23345i	−0.787179	−	0.616725i	$-0.788459\pi$
$37$		−	7.50278i		−	1.23345i	0.787179	−	0.616725i	$-0.211541\pi$
$38$		0			0
$39$	8.14787			1.30470
$40$		0			0
$41$	−6.78504	+	2.46955i	−1.05964	+	0.385679i	−0.812295	−	0.583247i	$-0.801782\pi$
$41$	−6.78504	+	2.46955i	−1.05964	+	0.385679i	−0.247350	+	0.968926i	$0.579560\pi$
$42$		0			0
$43$	−3.24204	−	0.571659i	−0.494407	−	0.0871772i	−0.0791149	−	0.996866i	$-0.525209\pi$
$43$	−3.24204	−	0.571659i	−0.494407	−	0.0871772i	−0.415292	+	0.909688i	$0.636321\pi$
$44$		0			0
$45$	−1.72826	+	0.997812i	−0.257634	+	0.148745i
$46$		0			0
$47$	−3.73496	+	3.13400i	−0.544800	+	0.457141i	−0.873175	−	0.487406i	$-0.837943\pi$
$47$	−3.73496	+	3.13400i	−0.544800	+	0.457141i	0.328376	+	0.944547i	$0.393499\pi$
$48$		0			0
$49$	−3.82402	+	6.62340i	−0.546289	+	0.946200i
$50$		0			0
$51$	1.30005	−	3.57186i	0.182043	−	0.500160i
$52$		0			0
$53$	1.49917	−	0.264344i	0.205927	−	0.0363104i	−0.0697332	−	0.997566i	$-0.522215\pi$
$53$	1.49917	−	0.264344i	0.205927	−	0.0363104i	0.275660	+	0.961255i	$0.411104\pi$
$54$		0			0
$55$	3.52629	+	2.95890i	0.475484	+	0.398979i
$56$		0			0
$57$	5.18633	−	2.92560i	0.686946	−	0.387505i
$58$		0			0
$59$	−4.81703	+	5.74071i	−0.627124	+	0.747377i	−0.982278	−	0.187431i	$-0.939984\pi$
$59$	−4.81703	+	5.74071i	−0.627124	+	0.747377i	0.355154	+	0.934808i	$0.384428\pi$
$60$		0			0
$61$	5.64385	−	0.995163i	0.722621	−	0.127418i	0.199771	−	0.979843i	$-0.435980\pi$
$61$	5.64385	−	0.995163i	0.722621	−	0.127418i	0.522850	+	0.852425i	$0.324869\pi$
$62$		0			0
$63$	−4.07780	−	1.48420i	−0.513755	−	0.186991i
$64$		0			0
$65$	5.24890	−	9.09135i	0.651045	−	1.12764i
$66$		0			0
$67$	−2.11430	−	2.51972i	−0.258302	−	0.307833i	0.621271	−	0.783596i	$-0.286617\pi$
$67$	−2.11430	−	2.51972i	−0.258302	−	0.307833i	−0.879574	+	0.475763i	$0.842172\pi$
$68$		0			0
$69$	7.54096	−	4.35377i	0.907825	−	0.524133i
$70$		0			0
$71$	−0.236392	+	1.34065i	−0.0280546	+	0.159106i	−0.995617	−	0.0935279i	$-0.970186\pi$
$71$	−0.236392	+	1.34065i	−0.0280546	+	0.159106i	0.967562	+	0.252633i	$0.0812967\pi$
$72$		0			0
$73$	10.5450	−	3.83807i	1.23420	−	0.449212i	0.359166	−	0.933274i	$-0.383061\pi$
$73$	10.5450	−	3.83807i	1.23420	−	0.449212i	0.875034	+	0.484062i	$0.160839\pi$
$74$		0			0
$75$			2.59851i			0.300050i
$76$		0			0
$77$			10.0098i			1.14072i
$78$		0			0
$79$	6.51619	−	2.37170i	0.733128	−	0.266837i	0.0516399	−	0.998666i	$-0.483555\pi$
$79$	6.51619	−	2.37170i	0.733128	−	0.266837i	0.681488	+	0.731829i	$0.261333\pi$
$80$		0			0
$81$	−0.748928	+	4.24738i	−0.0832143	+	0.471932i
$82$		0			0
$83$	−5.89196	+	3.40173i	−0.646727	+	0.373388i	−0.787201	−	0.616696i	$-0.788471\pi$
$83$	−5.89196	+	3.40173i	−0.646727	+	0.373388i	0.140474	+	0.990084i	$0.455137\pi$
$84$		0			0
$85$	−3.14796	−	3.75160i	−0.341444	−	0.406918i
$86$		0			0
$87$	−2.95424	+	5.11690i	−0.316728	+	0.548589i
$88$		0			0
$89$	−6.91135	−	2.51553i	−0.732602	−	0.266645i	−0.0513361	−	0.998681i	$-0.516348\pi$
$89$	−6.91135	−	2.51553i	−0.732602	−	0.266645i	−0.681266	+	0.732036i	$0.738570\pi$
$90$		0			0
$91$	22.4807	−	3.96396i	2.35662	−	0.415536i
$92$		0			0
$93$	−4.24120	+	5.05446i	−0.439792	+	0.524123i
$94$		0			0
$95$	0.0766864	−	7.67156i	0.00786786	−	0.787085i
$96$		0			0
$97$	−9.33891	−	7.83628i	−0.948223	−	0.795653i	0.0307745	−	0.999526i	$-0.490203\pi$
$97$	−9.33891	−	7.83628i	−0.948223	−	0.795653i	−0.978997	+	0.203873i	$0.934647\pi$
$98$		0			0
$99$	−2.92036	+	0.514939i	−0.293507	+	0.0517533i
$100$		0			0
$101$	4.36652	−	11.9969i	0.434485	−	1.19374i	−0.508546	−	0.861035i	$-0.669817\pi$
$101$	4.36652	−	11.9969i	0.434485	−	1.19374i	0.943031	−	0.332704i	$-0.107961\pi$
$102$		0			0
$103$	2.02806	−	3.51270i	0.199831	−	0.346117i	−0.748643	−	0.662974i	$-0.769294\pi$
$103$	2.02806	−	3.51270i	0.199831	−	0.346117i	0.948473	+	0.316857i	$0.102627\pi$
$104$		0			0
$105$	7.04932	−	5.91508i	0.687943	−	0.577253i
$106$		0			0
$107$	−1.10131	+	0.635844i	−0.106468	+	0.0614693i	−0.552288	−	0.833653i	$-0.686245\pi$
$107$	−1.10131	+	0.635844i	−0.106468	+	0.0614693i	0.445820	+	0.895122i	$0.352912\pi$
$108$		0			0
$109$	−3.33109	−	0.587360i	−0.319060	−	0.0562589i	0.0118246	−	0.999930i	$-0.496236\pi$
$109$	−3.33109	−	0.587360i	−0.319060	−	0.0562589i	−0.330885	+	0.943671i	$0.607347\pi$
$110$		0			0
$111$	−9.63126	+	3.50549i	−0.914159	+	0.332727i
$112$		0			0
$113$	−15.3010			−1.43939			−0.719697	−	0.694288i	$-0.755719\pi$
$113$	−15.3010			−1.43939			−0.719697	+	0.694288i	$0.755719\pi$
$114$		0			0
$115$		−	11.2189i		−	1.04617i
$116$		0			0
$117$	2.31298	+	6.35485i	0.213835	+	0.587506i
$118$		0			0
$119$	1.84924	−	10.4876i	0.169520	−	0.961394i
$120$		0			0
$121$	−2.07989	−	3.60248i	−0.189081	−	0.327498i
$122$		0			0
$123$	6.34028	+	7.55606i	0.571684	+	0.681307i
$124$		0			0
$125$	10.5207	+	6.07413i	0.941001	+	0.543287i
$126$		0			0
$127$	−10.6056	−	3.86013i	−0.941097	−	0.342531i	−0.174498	−	0.984657i	$-0.555830\pi$
$127$	−10.6056	−	3.86013i	−0.941097	−	0.342531i	−0.766599	+	0.642126i	$0.778053\pi$
$128$		0			0
$129$	0.780930	+	4.42887i	0.0687571	+	0.389941i
$130$		0			0
$131$	7.04562	−	8.39664i	0.615579	−	0.733618i	−0.364725	−	0.931115i	$-0.618837\pi$
$131$	7.04562	−	8.39664i	0.615579	−	0.733618i	0.980303	+	0.197497i	$0.0632813\pi$
$132$		0			0
$133$	12.8862	−	10.5952i	1.11738	−	0.918717i
$134$		0			0
$135$	7.61396	+	6.38887i	0.655305	+	0.549867i
$136$		0			0
$137$	3.48972	+	19.7912i	0.298147	+	1.69087i	0.654130	+	0.756382i	$0.273035\pi$
$137$	3.48972	+	19.7912i	0.298147	+	1.69087i	−0.355984	+	0.934492i	$0.615854\pi$
$138$		0			0
$139$	5.65104	−	15.5261i	0.479315	−	1.31691i	−0.430761	−	0.902466i	$-0.641755\pi$
$139$	5.65104	−	15.5261i	0.479315	−	1.31691i	0.910076	−	0.414441i	$-0.136023\pi$
$140$		0			0
$141$	5.76816	+	3.33025i	0.485767	+	0.280458i
$142$		0			0
$143$	11.9497	−	10.0270i	0.999287	−	0.838501i
$144$		0			0
$145$	3.80627	+	6.59266i	0.316094	+	0.547490i
$146$		0			0
$147$	10.2891	+	1.81424i	0.848630	+	0.149636i
$148$		0			0
$149$	−6.28070	−	17.2561i	−0.514535	−	1.41367i	−0.876464	−	0.481468i	$-0.840104\pi$
$149$	−6.28070	−	17.2561i	−0.514535	−	1.41367i	0.361929	−	0.932206i	$-0.382118\pi$
$150$		0			0
$151$	−13.2947			−1.08191			−0.540954	−	0.841052i	$-0.681937\pi$
$151$	−13.2947			−1.08191			−0.540954	+	0.841052i	$0.681937\pi$
$152$		0			0
$153$	3.15489			0.255057
$154$		0			0
$155$	2.90754	+	7.98841i	0.233540	+	0.641645i
$156$		0			0
$157$	−0.992527	−	0.175009i	−0.0792123	−	0.0139673i	0.133902	−	0.990995i	$-0.457249\pi$
$157$	−0.992527	−	0.175009i	−0.0792123	−	0.0139673i	−0.213114	+	0.977027i	$0.568361\pi$
$158$		0			0
$159$	−1.03979	−	1.80096i	−0.0824604	−	0.142826i
$160$		0			0
$161$	18.6881	−	15.6812i	1.47283	−	1.23585i
$162$		0			0
$163$	−12.9858	−	7.49734i	−1.01712	−	0.587237i	−0.103854	−	0.994593i	$-0.533118\pi$
$163$	−12.9858	−	7.49734i	−1.01712	−	0.587237i	−0.913270	+	0.407356i	$0.866451\pi$
$164$		0			0
$165$	2.15075	−	5.90914i	0.167436	−	0.460026i
$166$		0			0
$167$	0.413879	+	2.34722i	0.0320269	+	0.181634i	0.996625	−	0.0820914i	$-0.0261600\pi$
$167$	0.413879	+	2.34722i	0.0320269	+	0.181634i	−0.964598	+	0.263725i	$0.915049\pi$
$168$		0			0
$169$	−17.2931	−	14.5106i	−1.33024	−	1.11620i
$170$		0			0
$171$	3.75406	+	3.21452i	0.287080	+	0.245820i
$172$		0			0
$173$	−11.5139	+	13.7218i	−0.875388	+	1.04325i	0.123317	+	0.992367i	$0.460647\pi$
$173$	−11.5139	+	13.7218i	−0.875388	+	1.04325i	−0.998705	+	0.0508794i	$0.983798\pi$
$174$		0			0
$175$	1.26418	+	7.16954i	0.0955633	+	0.541966i
$176$		0			0
$177$	9.61994	+	3.50137i	0.723079	+	0.263179i
$178$		0			0
$179$	19.7528	+	11.4043i	1.47639	+	0.852394i	0.999645	−	0.0266474i	$-0.00848313\pi$
$179$	19.7528	+	11.4043i	1.47639	+	0.852394i	0.476745	+	0.879042i	$0.341816\pi$
$180$		0			0
$181$	3.56113	+	4.24399i	0.264696	+	0.315453i	0.881979	−	0.471289i	$-0.156211\pi$
$181$	3.56113	+	4.24399i	0.264696	+	0.315453i	−0.617283	+	0.786741i	$0.711767\pi$
$182$		0			0
$183$	−3.91443	−	6.78000i	−0.289363	−	0.501192i
$184$		0			0
$185$	−2.29309	+	13.0048i	−0.168591	+	0.956129i
$186$		0			0
$187$	−2.48897	−	6.83839i	−0.182012	−	0.500073i
$188$		0			0
$189$			21.6131i			1.57213i
$190$		0			0
$191$	1.52320			0.110215			0.0551073	−	0.998480i	$-0.482450\pi$
$191$	1.52320			0.110215			0.0551073	+	0.998480i	$0.482450\pi$
$192$		0			0
$193$	9.17926	−	3.34098i	0.660738	−	0.240489i	0.0101828	−	0.999948i	$-0.496759\pi$
$193$	9.17926	−	3.34098i	0.660738	−	0.240489i	0.650555	+	0.759459i	$0.274536\pi$
$194$		0			0
$195$	−14.1229	−	2.49025i	−1.01136	−	0.178331i
$196$		0			0
$197$	−5.18292	+	2.99236i	−0.369268	+	0.213197i	−0.673138	−	0.739517i	$-0.735054\pi$
$197$	−5.18292	+	2.99236i	−0.369268	+	0.213197i	0.303871	+	0.952713i	$0.401721\pi$
$198$		0			0
$199$	−3.61157	+	3.03047i	−0.256017	+	0.214824i	−0.761758	−	0.647861i	$-0.775664\pi$
$199$	−3.61157	+	3.03047i	−0.256017	+	0.214824i	0.505741	+	0.862685i	$0.331219\pi$
$200$		0			0
$201$	−2.24669	+	3.89138i	−0.158469	+	0.274477i
$202$		0			0
$203$	−5.66165	+	15.5552i	−0.397370	+	1.09176i
$204$		0			0
$205$	12.5154	−	2.20681i	0.874117	−	0.154130i
$206$		0			0
$207$	5.53637	+	4.64557i	0.384805	+	0.322889i
$208$		0			0
$209$	4.00598	−	10.6732i	0.277099	−	0.738278i
$210$		0			0
$211$	14.2288	−	16.9573i	0.979553	−	1.16739i	−0.00633485	−	0.999980i	$-0.502016\pi$
$211$	14.2288	−	16.9573i	0.979553	−	1.16739i	0.985888	−	0.167406i	$-0.0535391\pi$
$212$		0			0
$213$	1.83143	−	0.322930i	0.125487	−	0.0221268i
$214$		0			0
$215$	5.44479	+	1.98174i	0.371332	+	0.135154i
$216$		0			0
$217$	−9.24285	+	16.0091i	−0.627446	+	1.08677i
$218$		0			0
$219$	−9.85379	−	11.7433i	−0.665857	−	0.793538i
$220$		0			0
$221$	−14.3725	+	8.29799i	−0.966801	+	0.558183i
$222$		0			0
$223$	−4.15766	+	23.5792i	−0.278417	+	1.57898i	0.449476	+	0.893292i	$0.351611\pi$
$223$	−4.15766	+	23.5792i	−0.278417	+	1.57898i	−0.727894	+	0.685690i	$0.759500\pi$
$224$		0			0
$225$	−2.02668	+	0.737653i	−0.135112	+	0.0491769i
$226$		0			0
$227$			1.68680i			0.111957i	0.998432	+	0.0559784i	$0.0178278\pi$
$227$			1.68680i			0.111957i	−0.998432	+	0.0559784i	$0.982172\pi$
$228$		0			0
$229$		−	3.60123i		−	0.237976i	−0.992896	−	0.118988i	$-0.962035\pi$
$229$		−	3.60123i		−	0.237976i	0.992896	−	0.118988i	$-0.0379650\pi$
$230$		0			0
$231$	12.8495	−	4.67683i	0.845433	−	0.307713i
$232$		0			0
$233$	−0.677514	+	3.84237i	−0.0443854	+	0.251722i	−0.998925	−	0.0463631i	$-0.985237\pi$
$233$	−0.677514	+	3.84237i	−0.0443854	+	0.251722i	0.954539	+	0.298085i	$0.0963480\pi$
$234$		0			0
$235$	7.43175	−	4.29072i	0.484794	−	0.279896i
$236$		0			0
$237$	−6.08906	−	7.25666i	−0.395527	−	0.471371i
$238$		0			0
$239$	1.71193	−	2.96514i	0.110735	−	0.191799i	−0.805332	−	0.592825i	$-0.798013\pi$
$239$	1.71193	−	2.96514i	0.110735	−	0.191799i	0.916067	+	0.401025i	$0.131346\pi$
$240$		0			0
$241$	8.46332	+	3.08040i	0.545171	+	0.198426i	0.599900	−	0.800075i	$-0.295207\pi$
$241$	8.46332	+	3.08040i	0.545171	+	0.198426i	−0.0547288	+	0.998501i	$0.517429\pi$
$242$		0			0
$243$	−10.8818	+	1.91875i	−0.698066	+	0.123088i
$244$		0			0
$245$	8.65260	−	10.3118i	0.552794	−	0.658795i
$246$		0			0
$247$	−25.5570	−	4.77027i	−1.62615	−	0.303525i
$248$		0			0
$249$	7.11964	+	5.97409i	0.451189	+	0.378593i
$250$		0			0
$251$	5.43707	−	0.958702i	0.343185	−	0.0605127i	0.000600364	−	1.00000i	$-0.499809\pi$
$251$	5.43707	−	0.958702i	0.343185	−	0.0605127i	0.342584	+	0.939487i	$0.388698\pi$
$252$		0			0
$253$	5.70174	−	15.6654i	0.358466	−	0.984876i
$254$		0			0
$255$	−3.34508	+	5.79385i	−0.209477	+	0.362825i
$256$		0			0
$257$	−16.0217	+	13.4438i	−0.999404	+	0.838600i	−0.986902	−	0.161322i	$-0.948424\pi$
$257$	−16.0217	+	13.4438i	−0.999404	+	0.838600i	−0.0125022	+	0.999922i	$0.503980\pi$
$258$		0			0
$259$	−24.8681	+	14.3576i	−1.54523	+	0.892139i
$260$		0			0
$261$	−4.82951	−	0.851573i	−0.298939	−	0.0527110i
$262$		0			0
$263$	1.63905	−	0.596565i	0.101068	−	0.0367857i	−0.290991	−	0.956726i	$-0.593985\pi$
$263$	1.63905	−	0.596565i	0.101068	−	0.0367857i	0.392059	+	0.919940i	$0.371763\pi$
$264$		0			0
$265$	−2.67934			−0.164590
$266$		0			0
$267$			10.0474i			0.614889i
$268$		0			0
$269$	3.49933	+	9.61432i	0.213358	+	0.586195i	0.999492	−	0.0318599i	$-0.0101430\pi$
$269$	3.49933	+	9.61432i	0.213358	+	0.586195i	−0.786135	+	0.618055i	$0.787921\pi$
$270$		0			0
$271$	3.72486	−	21.1247i	0.226269	−	1.28323i	−0.633976	−	0.773353i	$-0.718578\pi$
$271$	3.72486	−	21.1247i	0.226269	−	1.28323i	0.860244	−	0.509882i	$-0.170311\pi$
$272$		0			0
$273$	−15.5921	−	27.0063i	−0.943676	−	1.63449i
$274$		0			0
$275$	3.19781	+	3.81100i	0.192835	+	0.229812i
$276$		0			0
$277$	−12.5634	−	7.25348i	−0.754862	−	0.435820i	0.0725863	−	0.997362i	$-0.476875\pi$
$277$	−12.5634	−	7.25348i	−0.754862	−	0.435820i	−0.827448	+	0.561543i	$0.810208\pi$
$278$		0			0
$279$	−5.14615	−	1.87304i	−0.308092	−	0.112136i
$280$		0			0
$281$	−4.40069	−	24.9576i	−0.262523	−	1.48884i	−0.775996	−	0.630738i	$-0.782752\pi$
$281$	−4.40069	−	24.9576i	−0.262523	−	1.48884i	0.513473	−	0.858106i	$-0.328359\pi$
$282$		0			0
$283$	−7.08527	+	8.44390i	−0.421176	+	0.501938i	−0.934355	−	0.356344i	$-0.884023\pi$
$283$	−7.08527	+	8.44390i	−0.421176	+	0.501938i	0.513179	+	0.858282i	$0.328468\pi$
$284$		0			0
$285$	−9.88375	+	3.48591i	−0.585463	+	0.206487i
$286$		0			0
$287$	21.1695	+	17.7633i	1.24959	+	1.04853i
$288$		0			0
$289$	−1.60759	−	9.11711i	−0.0945643	−	0.536301i
$290$		0			0
$291$	−5.69599	+	15.6496i	−0.333905	+	0.917395i
$292$		0			0
$293$	−9.23806	−	5.33360i	−0.539693	−	0.311592i	0.205261	−	0.978707i	$-0.434196\pi$
$293$	−9.23806	−	5.33360i	−0.539693	−	0.311592i	−0.744955	+	0.667115i	$0.767529\pi$
$294$		0			0
$295$	10.1040	−	8.47828i	0.588279	−	0.493624i
$296$		0			0
$297$	7.38470	+	12.7907i	0.428504	+	0.742191i
$298$		0			0
$299$	−37.4405	−	6.60177i	−2.16524	−	0.381790i
$300$		0			0
$301$	4.30932	+	11.8398i	0.248385	+	0.682432i
$302$		0			0
$303$	−17.4405			−1.00193
$304$		0			0
$305$	−10.0868			−0.577567
$306$		0			0
$307$	−1.80674	−	4.96398i	−0.103116	−	0.283309i	0.877396	−	0.479766i	$-0.159279\pi$
$307$	−1.80674	−	4.96398i	−0.103116	−	0.283309i	−0.980512	+	0.196457i	$0.937056\pi$
$308$		0			0
$309$	−5.45679	−	0.962179i	−0.310426	−	0.0547365i
$310$		0			0
$311$	3.54816	+	6.14559i	0.201197	+	0.348484i	0.948915	−	0.315533i	$-0.102183\pi$
$311$	3.54816	+	6.14559i	0.201197	+	0.348484i	−0.747717	+	0.664017i	$0.768850\pi$
$312$		0			0
$313$	19.4806	−	16.3462i	1.10111	−	0.923942i	0.103612	−	0.994618i	$-0.466960\pi$
$313$	19.4806	−	16.3462i	1.10111	−	0.923942i	0.997499	+	0.0706759i	$0.0225156\pi$
$314$		0			0
$315$	6.61454	+	3.81890i	0.372687	+	0.215171i
$316$		0			0
$317$	0.393337	−	1.08068i	0.0220920	−	0.0606973i	−0.928156	−	0.372190i	$-0.878607\pi$
$317$	0.393337	−	1.08068i	0.0220920	−	0.0606973i	0.950248	+	0.311493i	$0.100829\pi$
$318$		0			0
$319$	1.96429	+	11.1401i	0.109979	+	0.623724i
$320$		0			0
$321$	1.33079	+	1.11666i	0.0742774	+	0.0623261i
$322$		0			0
$323$	−6.16898	+	10.4425i	−0.343251	+	0.581038i
$324$		0			0
$325$	7.29267	−	8.69107i	0.404525	−	0.482094i
$326$		0			0
$327$	0.802379	+	4.55052i	0.0443716	+	0.251644i
$328$		0			0
$329$	17.5351	+	6.38224i	0.966740	+	0.351864i
$330$		0			0
$331$	3.68736	+	2.12890i	0.202676	+	0.117015i	0.597903	−	0.801568i	$-0.296001\pi$
$331$	3.68736	+	2.12890i	0.202676	+	0.117015i	−0.395227	+	0.918583i	$0.629334\pi$
$332$		0			0
$333$	−5.46815	−	6.51668i	−0.299653	−	0.357112i
$334$		0			0
$335$	2.89466	+	5.01369i	0.158152	+	0.273927i
$336$		0			0
$337$	−4.68326	+	26.5601i	−0.255114	+	1.44682i	0.540667	+	0.841237i	$0.318172\pi$
$337$	−4.68326	+	26.5601i	−0.255114	+	1.44682i	−0.795781	+	0.605585i	$0.792939\pi$
$338$		0			0
$339$	7.14900	+	19.6417i	0.388281	+	1.06679i
$340$		0			0
$341$			12.6323i			0.684075i
$342$		0			0
$343$	2.48025			0.133921
$344$		0			0
$345$	−14.4016	+	5.24175i	−0.775355	+	0.282206i
$346$		0			0
$347$	−17.6565	−	3.11331i	−0.947849	−	0.167131i	−0.321706	−	0.946840i	$-0.604256\pi$
$347$	−17.6565	−	3.11331i	−0.947849	−	0.167131i	−0.626143	+	0.779708i	$0.715367\pi$
$348$		0			0
$349$	−17.4551	+	10.0777i	−0.934352	+	0.539449i	−0.888185	−	0.459485i	$-0.848034\pi$
$349$	−17.4551	+	10.0777i	−0.934352	+	0.539449i	−0.0461670	+	0.998934i	$0.514701\pi$
$350$		0			0
$351$	25.8019	−	21.6504i	1.37720	−	1.15561i
$352$		0			0
$353$	−5.89589	+	10.2120i	−0.313806	+	0.543529i	−0.979183	−	0.202979i	$-0.934938\pi$
$353$	−5.89589	+	10.2120i	−0.313806	+	0.543529i	0.665377	+	0.746508i	$0.268271\pi$
$354$		0			0
$355$	0.819490	−	2.25153i	0.0434940	−	0.119499i
$356$		0			0
$357$	−14.3268	+	2.52620i	−0.758255	+	0.133701i
$358$		0			0
$359$	−9.80756	−	8.22952i	−0.517623	−	0.434338i	0.346179	−	0.938169i	$-0.387479\pi$
$359$	−9.80756	−	8.22952i	−0.517623	−	0.434338i	−0.863802	+	0.503831i	$0.831923\pi$
$360$		0			0
$361$	−17.9805	+	6.14017i	−0.946342	+	0.323167i
$362$		0			0
$363$	−3.65269	+	4.35311i	−0.191717	+	0.228479i
$364$		0			0
$365$	−19.4510	+	3.42973i	−1.01811	+	0.179520i
$366$		0			0
$367$	31.4886	+	11.4609i	1.64369	+	0.598256i	0.987679	−	0.156492i	$-0.0500187\pi$
$367$	31.4886	+	11.4609i	1.64369	+	0.598256i	0.656015	+	0.754748i	$0.272241\pi$
$368$		0			0
$369$	−4.09342	+	7.09002i	−0.213095	+	0.369092i
$370$		0			0
$371$	−3.74504	−	4.46316i	−0.194433	−	0.231716i
$372$		0			0
$373$	27.8103	−	16.0563i	1.43996	−	0.831363i	0.442117	−	0.896957i	$-0.354228\pi$
$373$	27.8103	−	16.0563i	1.43996	−	0.831363i	0.997846	+	0.0655941i	$0.0208942\pi$
$374$		0			0
$375$	2.88177	−	16.3433i	0.148814	−	0.843966i
$376$		0			0
$377$	24.2413	−	8.82312i	1.24849	−	0.454414i
$378$		0			0
$379$			4.90569i			0.251989i	0.992031	+	0.125994i	$0.0402121\pi$
$379$			4.90569i			0.251989i	−0.992031	+	0.125994i	$0.959788\pi$
$380$		0			0
$381$			15.4179i			0.789883i
$382$		0			0
$383$	3.08105	−	1.12141i	0.157434	−	0.0573015i	−0.262101	−	0.965041i	$-0.584415\pi$
$383$	3.08105	−	1.12141i	0.157434	−	0.0573015i	0.419535	+	0.907739i	$0.362193\pi$
$384$		0			0
$385$	3.05931	−	17.3502i	0.155917	−	0.884249i
$386$		0			0
$387$	−3.23257	+	1.86633i	−0.164321	+	0.0948707i
$388$		0			0
$389$	−11.9048	−	14.1876i	−0.603598	−	0.719340i	0.374560	−	0.927203i	$-0.377794\pi$
$389$	−11.9048	−	14.1876i	−0.603598	−	0.719340i	−0.978158	+	0.207863i	$0.933349\pi$
$390$		0			0
$391$	−8.86798	+	15.3598i	−0.448473	+	0.776778i
$392$		0			0
$393$	−14.0706	−	5.12128i	−0.709768	−	0.258334i
$394$		0			0
$395$	−12.0195	+	2.11937i	−0.604769	+	0.106637i
$396$		0			0
$397$	−8.96487	+	10.6839i	−0.449934	+	0.536210i	−0.942563	−	0.334029i	$-0.891592\pi$
$397$	−8.96487	+	10.6839i	−0.449934	+	0.536210i	0.492629	+	0.870240i	$0.336036\pi$
$398$		0			0
$399$	−19.6217	−	11.5916i	−0.982314	−	0.580308i
$400$		0			0
$401$	18.4067	+	15.4451i	0.919188	+	0.771291i	0.973845	−	0.227215i	$-0.0729619\pi$
$401$	18.4067	+	15.4451i	0.919188	+	0.771291i	−0.0546563	+	0.998505i	$0.517406\pi$
$402$		0			0
$403$	28.3705	−	5.00248i	1.41323	−	0.249191i
$404$		0			0
$405$	2.59627	−	7.13320i	0.129010	−	0.354452i
$406$		0			0
$407$	−9.81132	+	16.9937i	−0.486329	+	0.842346i
$408$		0			0
$409$	27.4590	−	23.0409i	1.35776	−	1.13930i	0.381095	−	0.924536i	$-0.375547\pi$
$409$	27.4590	−	23.0409i	1.35776	−	1.13930i	0.976667	−	0.214762i	$-0.0688974\pi$
$410$		0			0
$411$	23.7753	−	13.7267i	1.17275	−	0.677086i
$412$		0			0
$413$	28.2457	+	4.98049i	1.38988	+	0.245074i
$414$		0			0
$415$	11.2524	−	4.09553i	0.552357	−	0.201041i
$416$		0			0
$417$	−22.5710			−1.10531
$418$		0			0
$419$		−	16.1004i		−	0.786557i	−0.919419	−	0.393279i	$-0.871341\pi$
$419$		−	16.1004i		−	0.786557i	0.919419	−	0.393279i	$-0.128659\pi$
$420$		0			0
$421$	0.928735	+	2.55168i	0.0452638	+	0.124361i	0.960265	−	0.279090i	$-0.0900328\pi$
$421$	0.928735	+	2.55168i	0.0452638	+	0.124361i	−0.915001	+	0.403451i	$0.867811\pi$
$422$		0			0
$423$	−0.959958	+	5.44419i	−0.0466748	+	0.264706i
$424$		0			0
$425$	−2.64639	−	4.58368i	−0.128369	−	0.222341i
$426$		0			0
$427$	−14.0988	−	16.8023i	−0.682288	−	0.813119i
$428$		0			0
$429$	−18.4548	−	10.6549i	−0.891007	−	0.514423i
$430$		0			0
$431$	−27.2647	−	9.92353i	−1.31329	−	0.478000i	−0.411990	−	0.911188i	$-0.635166\pi$
$431$	−27.2647	−	9.92353i	−1.31329	−	0.478000i	−0.901303	+	0.433189i	$0.857388\pi$
$432$		0			0
$433$	4.76510	+	27.0242i	0.228996	+	1.29870i	0.854897	+	0.518798i	$0.173620\pi$
$433$	4.76510	+	27.0242i	0.228996	+	1.29870i	−0.625901	+	0.779903i	$0.715269\pi$
$434$		0			0
$435$	6.68455	−	7.96634i	0.320500	−	0.381957i
$436$		0			0
$437$	−26.2023	+	9.24131i	−1.25343	+	0.442072i
$438$		0			0
$439$	2.72236	+	2.28433i	0.129931	+	0.109025i	0.705437	−	0.708772i	$-0.250751\pi$
$439$	2.72236	+	2.28433i	0.129931	+	0.109025i	−0.575506	+	0.817797i	$0.695195\pi$
$440$		0			0
$441$	1.50581	+	8.53989i	0.0717054	+	0.406661i
$442$		0			0
$443$	11.4208	−	31.3785i	0.542620	−	1.49084i	−0.300856	−	0.953670i	$-0.597272\pi$
$443$	11.4208	−	31.3785i	0.542620	−	1.49084i	0.843476	−	0.537167i	$-0.180506\pi$
$444$		0			0
$445$	11.2108	+	6.47256i	0.531443	+	0.306829i
$446$		0			0
$447$	−19.2170	+	16.1250i	−0.908932	+	0.762685i
$448$		0			0
$449$	−5.75115	−	9.96129i	−0.271414	−	0.470102i	0.697810	−	0.716283i	$-0.254158\pi$
$449$	−5.75115	−	9.96129i	−0.271414	−	0.470102i	−0.969224	+	0.246180i	$0.920825\pi$
$450$		0			0
$451$	18.5974	+	3.27923i	0.875718	+	0.154413i
$452$		0			0
$453$	6.21162	+	17.0663i	0.291847	+	0.801844i
$454$		0			0
$455$	−40.1779			−1.88357
$456$		0			0
$457$	−10.9250			−0.511048			−0.255524	−	0.966803i	$-0.582248\pi$
$457$	−10.9250			−0.511048			−0.255524	+	0.966803i	$0.582248\pi$
$458$		0			0
$459$	−5.37419	−	14.7655i	−0.250846	−	0.689193i
$460$		0			0
$461$	40.6685	+	7.17095i	1.89412	+	0.333985i	0.994676	−	0.103050i	$-0.0328602\pi$
$461$	40.6685	+	7.17095i	1.89412	+	0.333985i	0.899445	+	0.437035i	$0.143971\pi$
$462$		0			0
$463$	5.45960	+	9.45631i	0.253729	+	0.439472i	0.964550	−	0.263902i	$-0.0850095\pi$
$463$	5.45960	+	9.45631i	0.253729	+	0.439472i	−0.710820	+	0.703374i	$0.751676\pi$
$464$		0			0
$465$	8.89618	−	7.46478i	0.412550	−	0.346171i
$466$		0			0
$467$	18.6654	+	10.7765i	0.863734	+	0.498677i	0.865261	−	0.501322i	$-0.167153\pi$
$467$	18.6654	+	10.7765i	0.863734	+	0.498677i	−0.00152700	+	0.999999i	$0.500486\pi$
$468$		0			0
$469$	−4.30566	+	11.8297i	−0.198817	+	0.546245i
$470$		0			0
$471$	0.239076	+	1.35587i	0.0110160	+	0.0624751i
$472$		0			0
$473$	6.59562	+	5.53439i	0.303267	+	0.254471i
$474$		0			0
$475$	1.52133	−	8.15062i	0.0698034	−	0.373976i
$476$		0			0
$477$	1.10947	−	1.32222i	0.0507993	−	0.0605402i
$478$		0			0
$479$	5.48301	+	31.0957i	0.250525	+	1.42080i	0.807303	+	0.590137i	$0.200926\pi$
$479$	5.48301	+	31.0957i	0.250525	+	1.42080i	−0.556778	+	0.830661i	$0.687963\pi$
$480$		0			0
$481$	42.0511	+	15.3054i	1.91737	+	0.697864i
$482$		0			0
$483$	−28.8613	−	16.6631i	−1.31324	−	0.758197i
$484$		0			0
$485$	13.7924	+	16.4371i	0.626279	+	0.746370i
$486$		0			0
$487$	−8.73788	−	15.1345i	−0.395951	−	0.685808i	0.597271	−	0.802040i	$-0.296252\pi$
$487$	−8.73788	−	15.1345i	−0.395951	−	0.685808i	−0.993222	+	0.116232i	$0.962918\pi$
$488$		0			0
$489$	−3.55699	+	20.1727i	−0.160852	+	0.912240i
$490$		0			0
$491$	3.77132	+	10.3616i	0.170197	+	0.467613i	0.995240	−	0.0974577i	$-0.0310711\pi$
$491$	3.77132	+	10.3616i	0.170197	+	0.467613i	−0.825042	+	0.565071i	$0.808849\pi$
$492$		0			0
$493$		−	12.0347i		−	0.542015i
$494$		0			0
$495$	5.21932			0.234591
$496$		0			0
$497$	4.89597	−	1.78199i	0.219614	−	0.0799331i
$498$		0			0
$499$	27.4017	+	4.83166i	1.22667	+	0.216295i	0.749193	−	0.662351i	$-0.230441\pi$
$499$	27.4017	+	4.83166i	1.22667	+	0.216295i	0.477474	+	0.878646i	$0.341552\pi$
$500$		0			0
$501$	2.81974	−	1.62798i	0.125977	−	0.0727326i
$502$		0			0
$503$	5.06697	−	4.25169i	0.225925	−	0.189573i	−0.522798	−	0.852457i	$-0.675112\pi$
$503$	5.06697	−	4.25169i	0.225925	−	0.189573i	0.748723	+	0.662883i	$0.230667\pi$
$504$		0			0
$505$	−11.2352	+	19.4600i	−0.499962	+	0.865960i
$506$		0			0
$507$	−10.5474	+	28.9787i	−0.468425	+	1.28699i
$508$		0			0
$509$	−12.0534	+	2.12533i	−0.534256	+	0.0942038i	−0.434266	−	0.900785i	$-0.642992\pi$
$509$	−12.0534	+	2.12533i	−0.534256	+	0.0942038i	−0.0999901	+	0.994988i	$0.531881\pi$
$510$		0			0
$511$	−32.9007	−	27.6069i	−1.45544	−	1.22126i
$512$		0			0
$513$	8.64971	−	23.0455i	0.381894	−	1.01748i
$514$		0			0
$515$	−4.58888	+	5.46882i	−0.202210	+	0.240985i
$516$		0			0
$517$	12.5579	−	2.21430i	0.552297	−	0.0973849i
$518$		0			0
$519$	22.9941	+	8.36918i	1.00933	+	0.367366i
$520$		0			0
$521$	−6.12941	+	10.6165i	−0.268534	+	0.465115i	−0.968484	−	0.249077i	$-0.919873\pi$
$521$	−6.12941	+	10.6165i	−0.268534	+	0.465115i	0.699949	+	0.714193i	$0.253206\pi$
$522$		0			0
$523$	6.53118	+	7.78356i	0.285589	+	0.340351i	0.889697	−	0.456551i	$-0.150915\pi$
$523$	6.53118	+	7.78356i	0.285589	+	0.340351i	−0.604109	+	0.796902i	$0.706471\pi$
$524$		0			0
$525$	8.61282	−	4.97261i	0.375894	−	0.217023i
$526$		0			0
$527$	2.33373	−	13.2352i	0.101659	−	0.576535i
$528$		0			0
$529$	−16.5664	+	6.02967i	−0.720277	+	0.262159i
$530$		0			0
$531$			8.49693i			0.368735i
$532$		0			0
$533$		−	43.0661i		−	1.86540i
$534$		0			0
$535$	2.10327	−	0.765527i	0.0909322	−	0.0330966i
$536$		0			0
$537$	5.41056	−	30.6848i	0.233483	−	1.32415i
$538$		0			0
$539$	17.3227	−	10.0013i	0.746142	−	0.430785i
$540$		0			0
$541$	−14.8292	−	17.6728i	−0.637557	−	0.759811i	0.346425	−	0.938078i	$-0.387395\pi$
$541$	−14.8292	−	17.6728i	−0.637557	−	0.759811i	−0.983982	+	0.178267i	$0.942951\pi$
$542$		0			0
$543$	3.78412	−	6.55429i	0.162392	−	0.281271i
$544$		0			0
$545$	5.59434	+	2.03617i	0.239635	+	0.0872200i
$546$		0			0
$547$	−13.3611	+	2.35593i	−0.571281	+	0.100732i	−0.451824	−	0.892107i	$-0.649227\pi$
$547$	−13.3611	+	2.35593i	−0.571281	+	0.100732i	−0.119457	+	0.992839i	$0.538115\pi$
$548$		0			0
$549$	4.17678	−	4.97770i	0.178261	−	0.212443i
$550$		0			0
$551$	12.2622	−	14.3203i	0.522386	−	0.610065i
$552$		0			0
$553$	−20.3307	−	17.0595i	−0.864548	−	0.725442i
$554$		0			0
$555$	17.7655	−	3.13254i	0.754103	−	0.132969i
$556$		0			0
$557$	−12.9729	+	35.6427i	−0.549679	+	1.51023i	0.284466	+	0.958686i	$0.408184\pi$
$557$	−12.9729	+	35.6427i	−0.549679	+	1.51023i	−0.834145	+	0.551545i	$0.814039\pi$
$558$		0			0
$559$	9.81762	−	17.0046i	0.415241	−	0.719219i
$560$		0			0
$561$	−7.61548	+	6.39014i	−0.321526	+	0.269792i
$562$		0			0
$563$	24.8787	−	14.3637i	1.04851	−	0.605360i	0.126281	−	0.991995i	$-0.459696\pi$
$563$	24.8787	−	14.3637i	1.04851	−	0.605360i	0.922233	+	0.386635i	$0.126363\pi$
$564$		0			0
$565$	26.5216	+	4.67647i	1.11577	+	0.196740i
$566$		0			0
$567$	15.5112	−	5.64562i	0.651410	−	0.237094i
$568$		0			0
$569$	−14.4506			−0.605800			−0.302900	−	0.953022i	$-0.597955\pi$
$569$	−14.4506			−0.605800			−0.302900	+	0.953022i	$0.597955\pi$
$570$		0			0
$571$			38.7437i			1.62137i	0.585480	+	0.810687i	$0.300906\pi$
$571$			38.7437i			1.62137i	−0.585480	+	0.810687i	$0.699094\pi$
$572$		0			0
$573$	−0.711676	−	1.95531i	−0.0297307	−	0.0816844i
$574$		0			0
$575$	2.10543	−	11.9405i	0.0878026	−	0.497953i
$576$		0			0
$577$	−15.5793	−	26.9841i	−0.648575	−	1.12336i	−0.983463	−	0.181107i	$-0.942032\pi$
$577$	−15.5793	−	26.9841i	−0.648575	−	1.12336i	0.334889	−	0.942258i	$-0.391301\pi$
$578$		0			0
$579$	−8.57757	−	10.2223i	−0.356472	−	0.424826i
$580$		0			0
$581$	22.5502	+	13.0194i	0.935539	+	0.540134i
$582$		0			0
$583$	−3.74127	−	1.36171i	−0.154948	−	0.0563964i
$584$		0			0
$585$	−2.06690	−	11.7219i	−0.0854556	−	0.484643i
$586$		0			0
$587$	11.8358	−	14.1054i	0.488517	−	0.582192i	−0.464323	−	0.885666i	$-0.653702\pi$
$587$	11.8358	−	14.1054i	0.488517	−	0.582192i	0.952840	+	0.303474i	$0.0981467\pi$
$588$		0			0
$589$	16.2623	−	13.3710i	0.670078	−	0.550942i
$590$		0			0
$591$	6.26286	+	5.25516i	0.257619	+	0.216168i
$592$		0			0
$593$	1.95725	+	11.1001i	0.0803747	+	0.455828i	0.998259	+	0.0589799i	$0.0187848\pi$
$593$	1.95725	+	11.1001i	0.0803747	+	0.455828i	−0.917884	+	0.396848i	$0.870104\pi$
$594$		0			0
$595$	−6.41067	+	17.6132i	−0.262812	+	0.722070i
$596$		0			0
$597$	5.57760	+	3.22023i	0.228276	+	0.131795i
$598$		0			0
$599$	23.7426	−	19.9224i	0.970095	−	0.814007i	−0.0124703	−	0.999922i	$-0.503970\pi$
$599$	23.7426	−	19.9224i	0.970095	−	0.814007i	0.982566	+	0.185916i	$0.0595251\pi$
$600$		0			0
$601$	−11.2846	−	19.5455i	−0.460307	−	0.797276i	0.538669	−	0.842518i	$-0.318927\pi$
$601$	−11.2846	−	19.5455i	−0.460307	−	0.797276i	−0.998976	+	0.0452420i	$0.985594\pi$
$602$		0			0
$603$	−3.67282	−	0.647618i	−0.149569	−	0.0263730i
$604$		0			0
$605$	2.50410	+	6.87995i	0.101806	+	0.279710i
$606$		0			0
$607$	15.7003			0.637257			0.318628	−	0.947880i	$-0.396778\pi$
$607$	15.7003			0.637257			0.318628	+	0.947880i	$0.396778\pi$
$608$		0			0
$609$	22.6134			0.916341
$610$		0			0
$611$	−9.94610	−	27.3267i	−0.402376	−	1.10552i
$612$		0			0
$613$	−27.8884	−	4.91748i	−1.12640	−	0.198615i	−0.420752	−	0.907176i	$-0.638234\pi$
$613$	−27.8884	−	4.91748i	−1.12640	−	0.198615i	−0.705650	+	0.708561i	$0.749345\pi$
$614$		0			0
$615$	−8.68040	−	15.0349i	−0.350028	−	0.606266i
$616$		0			0
$617$	20.1984	−	16.9484i	0.813155	−	0.682318i	−0.138203	−	0.990404i	$-0.544133\pi$
$617$	20.1984	−	16.9484i	0.813155	−	0.682318i	0.951359	+	0.308086i	$0.0996883\pi$
$618$		0			0
$619$	8.70164	+	5.02389i	0.349748	+	0.201927i	0.664574	−	0.747222i	$-0.268613\pi$
$619$	8.70164	+	5.02389i	0.349748	+	0.201927i	−0.314826	+	0.949149i	$0.601946\pi$
$620$		0			0
$621$	12.3112	−	33.8248i	0.494032	−	1.35734i
$622$		0			0
$623$	4.88807	+	27.7216i	0.195836	+	1.11064i
$624$		0			0
$625$	−9.09362	−	7.63045i	−0.363745	−	0.305218i
$626$		0			0
$627$	−15.5727	−	0.155668i	−0.621915	−	0.00621679i
$628$		0			0
$629$	13.4191	−	15.9923i	0.535054	−	0.637653i
$630$		0			0
$631$	−1.03255	−	5.85590i	−0.0411053	−	0.233120i	0.957333	−	0.288987i	$-0.0933186\pi$
$631$	−1.03255	−	5.85590i	−0.0411053	−	0.233120i	−0.998438	+	0.0558677i	$0.982207\pi$
$632$		0			0
$633$	−28.4160	−	10.3426i	−1.12943	−	0.411080i
$634$		0			0
$635$	17.2032	+	9.93228i	0.682689	+	0.394151i
$636$		0			0
$637$	−29.3216	−	34.9441i	−1.16176	−	1.38454i
$638$		0			0
$639$	0.771762	+	1.33673i	0.0305304	+	0.0528803i
$640$		0			0
$641$	−1.53945	+	8.73067i	−0.0608047	+	0.344841i	0.939194	+	0.343386i	$0.111574\pi$
$641$	−1.53945	+	8.73067i	−0.0608047	+	0.344841i	−0.999999	+	0.00145435i	$0.999537\pi$
$642$		0			0
$643$	−11.2379	−	30.8759i	−0.443180	−	1.21763i	−0.937389	−	0.348284i	$-0.886765\pi$
$643$	−11.2379	−	30.8759i	−0.443180	−	1.21763i	0.494209	−	0.869343i	$-0.335458\pi$
$644$		0			0
$645$		−	7.91536i		−	0.311667i
$646$		0			0
$647$	4.85643			0.190926			0.0954629	−	0.995433i	$-0.469567\pi$
$647$	4.85643			0.190926			0.0954629	+	0.995433i	$0.469567\pi$
$648$		0			0
$649$	18.4176	−	6.70345i	0.722953	−	0.263133i
$650$		0			0
$651$	24.8692	+	4.38512i	0.974702	+	0.171866i
$652$		0			0
$653$	22.9690	−	13.2611i	0.898846	−	0.518949i	0.0220202	−	0.999758i	$-0.492990\pi$
$653$	22.9690	−	13.2611i	0.898846	−	0.518949i	0.876826	+	0.480809i	$0.159657\pi$
$654$		0			0
$655$	−14.7786	+	12.4007i	−0.577449	+	0.484537i
$656$		0			0
$657$	6.36182	−	11.0190i	0.248198	−	0.429892i
$658$		0			0
$659$	1.53725	−	4.22355i	0.0598827	−	0.164526i	−0.906144	−	0.422970i	$-0.860987\pi$
$659$	1.53725	−	4.22355i	0.0598827	−	0.164526i	0.966026	+	0.258444i	$0.0832097\pi$
$660$		0			0
$661$	14.3356	−	2.52775i	0.557589	−	0.0983179i	0.112250	−	0.993680i	$-0.464194\pi$
$661$	14.3356	−	2.52775i	0.557589	−	0.0983179i	0.445339	+	0.895362i	$0.353083\pi$
$662$		0			0
$663$	17.3673	+	14.5729i	0.674489	+	0.565963i
$664$		0			0
$665$	−25.5743	+	14.4264i	−0.991728	+	0.559432i
$666$		0			0
$667$	17.7211	−	21.1191i	0.686162	−	0.817736i
$668$		0			0
$669$	32.2110	−	5.67967i	1.24535	−	0.219589i
$670$		0			0
$671$	−14.0846	−	5.12638i	−0.543730	−	0.197902i
$672$		0			0
$673$	−1.27655	+	2.21106i	−0.0492076	+	0.0852300i	−0.889580	−	0.456779i	$-0.849003\pi$
$673$	−1.27655	+	2.21106i	−0.0492076	+	0.0852300i	0.840372	+	0.542009i	$0.182336\pi$
$674$		0			0
$675$	6.90471	+	8.22872i	0.265763	+	0.316723i
$676$		0			0
$677$	−26.8658	+	15.5109i	−1.03253	+	0.596134i	−0.917710	−	0.397252i	$-0.869964\pi$
$677$	−26.8658	+	15.5109i	−1.03253	+	0.596134i	−0.114825	+	0.993386i	$0.536631\pi$
$678$		0			0
$679$	−8.10219	+	45.9498i	−0.310933	+	1.76339i
$680$		0			0
$681$	2.16533	−	0.788115i	0.0829756	−	0.0302006i
$682$		0			0
$683$			39.1949i			1.49975i	0.661578	+	0.749876i	$0.269887\pi$
$683$			39.1949i			1.49975i	−0.661578	+	0.749876i	$0.730113\pi$
$684$		0			0
$685$		−	35.3711i		−	1.35146i
$686$		0			0
$687$	−4.62287	+	1.68259i	−0.176374	+	0.0641947i
$688$		0			0
$689$	−1.57666	+	8.94169i	−0.0600660	+	0.340651i
$690$		0			0
$691$	−0.357391	+	0.206340i	−0.0135958	+	0.00784954i	−0.506782	−	0.862074i	$-0.669165\pi$
$691$	−0.357391	+	0.206340i	−0.0135958	+	0.00784954i	0.493187	+	0.869923i	$0.335832\pi$
$692$		0			0
$693$	7.29529	+	8.69419i	0.277125	+	0.330265i
$694$		0			0
$695$	−14.5404	+	25.1847i	−0.551548	+	0.955309i
$696$		0			0
$697$	−18.8793	−	6.87150i	−0.715104	−	0.260277i
$698$		0			0
$699$	5.24897	−	0.925536i	0.198534	−	0.0350070i
$700$		0			0
$701$	0.701629	−	0.836169i	0.0265002	−	0.0315817i	−0.752632	−	0.658442i	$-0.771216\pi$
$701$	0.701629	−	0.836169i	0.0265002	−	0.0315817i	0.779132	+	0.626860i	$0.215660\pi$
$702$		0			0
$703$	32.2622	−	5.35675i	1.21679	−	0.202034i
$704$		0			0
$705$	−8.98027	−	7.53534i	−0.338216	−	0.283797i
$706$		0			0
$707$	−48.1200	+	8.48485i	−1.80974	+	0.319106i
$708$		0			0
$709$	−15.5133	+	42.6225i	−0.582615	+	1.60072i	0.201080	+	0.979575i	$0.435555\pi$
$709$	−15.5133	+	42.6225i	−0.582615	+	1.60072i	−0.783695	+	0.621146i	$0.786667\pi$
$710$		0			0
$711$	3.93123	−	6.80908i	0.147433	−	0.255361i
$712$		0			0
$713$	23.5842	−	19.7895i	0.883235	−	0.741122i
$714$		0			0
$715$	−23.7773	+	13.7279i	−0.889222	+	0.513393i
$716$		0			0
$717$	−4.60619	−	0.812195i	−0.172021	−	0.0303320i
$718$		0			0
$719$	−27.5011	+	10.0096i	−1.02562	+	0.373295i	−0.799411	−	0.600785i	$-0.794855\pi$
$719$	−27.5011	+	10.0096i	−1.02562	+	0.373295i	−0.226207	+	0.974079i	$0.572633\pi$
$720$		0			0
$721$	−15.5239			−0.578140
$722$		0			0
$723$		−	12.3035i		−	0.457574i
$724$		0			0
$725$	2.81386	+	7.73102i	0.104504	+	0.287123i
$726$		0			0
$727$	4.42851	−	25.1153i	0.164244	−	0.931476i	−0.785596	−	0.618740i	$-0.787643\pi$
$727$	4.42851	−	25.1153i	0.164244	−	0.931476i	0.949840	−	0.312736i	$-0.101246\pi$
$728$		0			0
$729$	14.0167	+	24.2776i	0.519137	+	0.899171i
$730$		0			0
$731$	−5.88800	−	7.01705i	−0.217776	−	0.259535i
$732$		0			0
$733$	24.3750	+	14.0729i	0.900312	+	0.519795i	0.877301	−	0.479940i	$-0.159342\pi$
$733$	24.3750	+	14.0729i	0.900312	+	0.519795i	0.0230105	+	0.999735i	$0.492675\pi$
$734$		0			0
$735$	−17.2798	−	6.28935i	−0.637377	−	0.231986i
$736$		0			0
$737$	1.49384	+	8.47198i	0.0550262	+	0.312069i
$738$		0			0
$739$	−23.3977	+	27.8843i	−0.860699	+	1.02574i	0.138674	+	0.990338i	$0.455716\pi$
$739$	−23.3977	+	27.8843i	−0.860699	+	1.02574i	−0.999373	+	0.0354033i	$0.988728\pi$
$740$		0			0
$741$	5.81733	+	35.0361i	0.213705	+	1.28708i
$742$		0			0
$743$	−33.0844	−	27.7611i	−1.21375	−	1.01845i	−0.999128	−	0.0417571i	$-0.986704\pi$
$743$	−33.0844	−	27.7611i	−1.21375	−	1.01845i	−0.214619	−	0.976698i	$-0.568851\pi$
$744$		0			0
$745$	5.61248	+	31.8300i	0.205626	+	1.16616i
$746$		0			0
$747$	−2.63834	+	7.24879i	−0.0965320	+	0.265219i
$748$		0			0
$749$	4.21503	+	2.43355i	0.154014	+	0.0889199i
$750$		0			0
$751$	21.9887	−	18.4507i	0.802379	−	0.673276i	−0.146397	−	0.989226i	$-0.546768\pi$
$751$	21.9887	−	18.4507i	0.802379	−	0.673276i	0.948776	+	0.315950i	$0.102323\pi$
$752$		0			0
$753$	−3.77101	−	6.53159i	−0.137423	−	0.238024i
$754$		0			0
$755$	23.0440	+	4.06329i	0.838658	+	0.147878i
$756$		0			0
$757$	−9.23982	−	25.3862i	−0.335827	−	0.922677i	−0.986564	−	0.163374i	$-0.947762\pi$
$757$	−9.23982	−	25.3862i	−0.335827	−	0.922677i	0.650737	−	0.759303i	$-0.274460\pi$
$758$		0			0
$759$	−22.7736			−0.826628
$760$		0			0
$761$	42.3246			1.53427			0.767133	−	0.641488i	$-0.221682\pi$
$761$	42.3246			1.53427			0.767133	+	0.641488i	$0.221682\pi$
$762$		0			0
$763$	4.42768	+	12.1649i	0.160293	+	0.440400i
$764$		0			0
$765$	−5.46844	−	0.964234i	−0.197712	−	0.0348620i
$766$		0			0
$767$	−22.3486	−	38.7090i	−0.806962	−	1.39770i
$768$		0			0
$769$	−25.9294	+	21.7574i	−0.935038	+	0.784590i	−0.976715	−	0.214541i	$-0.931175\pi$
$769$	−25.9294	+	21.7574i	−0.935038	+	0.784590i	0.0416766	+	0.999131i	$0.486730\pi$
$770$		0			0
$771$	24.7434	+	14.2856i	0.891111	+	0.514483i
$772$		0			0
$773$	−6.59542	+	18.1208i	−0.237221	+	0.651759i	0.762766	+	0.646674i	$0.223841\pi$
$773$	−6.59542	+	18.1208i	−0.237221	+	0.651759i	−0.999987	+	0.00508474i	$0.998381\pi$
$774$		0			0
$775$	1.59539	+	9.04790i	0.0573080	+	0.325010i
$776$		0			0
$777$	30.0498	+	25.2147i	1.07803	+	0.904574i
$778$		0			0
$779$	−15.4634	−	27.4127i	−0.554035	−	0.982161i
$780$		0			0
$781$	2.28858	−	2.72742i	0.0818917	−	0.0975948i
$782$		0			0
$783$	4.24131	+	24.0536i	0.151572	+	0.859607i
$784$		0			0
$785$	1.66688	+	0.606696i	0.0594937	+	0.0216539i
$786$		0			0
$787$	−19.0253	−	10.9843i	−0.678179	−	0.391547i	0.120990	−	0.992654i	$-0.461393\pi$
$787$	−19.0253	−	10.9843i	−0.678179	−	0.391547i	−0.799169	+	0.601107i	$0.794727\pi$
$788$		0			0
$789$	−1.53161	−	1.82530i	−0.0545267	−	0.0649824i
$790$		0			0
$791$	29.2805	+	50.7154i	1.04110	+	1.80323i
$792$		0			0
$793$	−5.93559	+	33.6624i	−0.210779	+	1.19539i
$794$		0			0
$795$	1.25186	+	3.43944i	0.0443987	+	0.121984i
$796$		0			0
$797$		−	0.710570i		−	0.0251697i	−0.999921	−	0.0125848i	$-0.995994\pi$
$797$		−	0.710570i		−	0.0251697i	0.999921	−	0.0125848i	$-0.00400599\pi$
$798$		0			0
$799$	−13.5664			−0.479945
$800$		0			0
$801$	−7.83634	+	2.85220i	−0.276884	+	0.100777i
$802$		0			0
$803$	−28.9033	−	5.09643i	−1.01997	−	0.179849i
$804$		0			0
$805$	−37.1852	+	21.4689i	−1.31061	+	0.756679i
$806$		0			0
$807$	10.7068	−	8.98411i	0.376899	−	0.316256i
$808$		0			0
$809$	7.13032	−	12.3501i	0.250689	−	0.434205i	−0.713027	−	0.701137i	$-0.752676\pi$
$809$	7.13032	−	12.3501i	0.250689	−	0.434205i	0.963716	+	0.266931i	$0.0860096\pi$
$810$		0			0
$811$	4.63202	−	12.7264i	0.162652	−	0.446883i	−0.831415	−	0.555652i	$-0.812469\pi$
$811$	4.63202	−	12.7264i	0.162652	−	0.446883i	0.994067	+	0.108769i	$0.0346909\pi$
$812$		0			0
$813$	−28.8580	+	5.08844i	−1.01209	+	0.178459i
$814$		0			0
$815$	20.2171	+	16.9642i	0.708175	+	0.594230i
$816$		0			0
$817$	0.143436	−	14.3490i	0.00501818	−	0.502009i
$818$		0			0
$819$	16.6371	−	19.8273i	0.581346	−	0.692822i
$820$		0			0
$821$	21.6215	−	3.81246i	0.754597	−	0.133056i	0.216900	−	0.976194i	$-0.430406\pi$
$821$	21.6215	−	3.81246i	0.754597	−	0.133056i	0.537697	+	0.843138i	$0.319294\pi$
$822$		0			0
$823$	37.4025	+	13.6134i	1.30377	+	0.474533i	0.898222	−	0.439541i	$-0.144859\pi$
$823$	37.4025	+	13.6134i	1.30377	+	0.474533i	0.405547	+	0.914074i	$0.367081\pi$
$824$		0			0
$825$	3.39805	−	5.88560i	0.118305	−	0.204910i
$826$		0			0
$827$	8.15261	+	9.71590i	0.283494	+	0.337855i	0.888933	−	0.458036i	$-0.151447\pi$
$827$	8.15261	+	9.71590i	0.283494	+	0.337855i	−0.605439	+	0.795891i	$0.707003\pi$
$828$		0			0
$829$	−38.1089	+	22.0022i	−1.32358	+	0.764168i	−0.984297	−	0.176518i	$-0.943517\pi$
$829$	−38.1089	+	22.0022i	−1.32358	+	0.764168i	−0.339280	+	0.940686i	$0.610183\pi$
$830$		0			0
$831$	−3.44129	+	19.5165i	−0.119377	+	0.677021i
$832$		0			0
$833$	−19.9972	+	7.27839i	−0.692863	+	0.252181i
$834$		0			0
$835$		−	4.19500i		−	0.145174i
$836$		0			0
$837$			27.2756i			0.942783i
$838$		0			0
$839$	−18.6755	+	6.79733i	−0.644750	+	0.234670i	−0.643639	−	0.765330i	$-0.722576\pi$
$839$	−18.6755	+	6.79733i	−0.644750	+	0.234670i	−0.00111150	+	0.999999i	$0.500354\pi$
$840$		0			0
$841$	1.78737	−	10.1367i	0.0616336	−	0.349541i
$842$		0			0
$843$	−29.9817	+	17.3099i	−1.03262	+	0.596186i
$844$		0			0
$845$	25.5396	+	30.4369i	0.878589	+	1.04706i
$846$		0			0
$847$	−7.96032	+	13.7877i	−0.273520	+	0.473750i
$848$		0			0
$849$	14.1498	+	5.15010i	0.485619	+	0.176751i
$850$		0			0
$851$	47.0972	−	8.30450i	1.61447	−	0.284675i
$852$		0			0
$853$	−11.0526	+	13.1720i	−0.378434	+	0.451000i	−0.921319	−	0.388807i	$-0.872887\pi$
$853$	−11.0526	+	13.1720i	−0.378434	+	0.451000i	0.542885	+	0.839807i	$0.317332\pi$
$854$		0			0
$855$	−5.52455	−	6.71917i	−0.188936	−	0.229791i
$856$		0			0
$857$	5.45272	+	4.57537i	0.186261	+	0.156292i	0.731150	−	0.682216i	$-0.238984\pi$
$857$	5.45272	+	4.57537i	0.186261	+	0.156292i	−0.544889	+	0.838508i	$0.683428\pi$
$858$		0			0
$859$	−20.8842	+	3.68245i	−0.712559	+	0.125643i	−0.518166	−	0.855280i	$-0.673385\pi$
$859$	−20.8842	+	3.68245i	−0.712559	+	0.125643i	−0.194394	+	0.980924i	$0.562274\pi$
$860$		0			0
$861$	12.9117	−	35.4746i	0.440029	−	1.20897i
$862$		0			0
$863$	−2.52232	+	4.36878i	−0.0858607	+	0.148715i	−0.905758	−	0.423796i	$-0.860697\pi$
$863$	−2.52232	+	4.36878i	−0.0858607	+	0.148715i	0.819897	+	0.572511i	$0.194031\pi$
$864$		0			0
$865$	24.1512	−	20.2653i	0.821165	−	0.689040i
$866$		0			0
$867$	−10.9524	+	6.32340i	−0.371965	+	0.214754i
$868$		0			0
$869$	−17.8605	−	3.14929i	−0.605877	−	0.106832i
$870$		0			0
$871$	18.4354	−	6.70995i	0.624661	−	0.227358i
$872$		0			0
$873$	−13.8227			−0.467827
$874$		0			0
$875$		−	46.4948i		−	1.57181i
$876$		0			0
$877$	−18.5385	−	50.9342i	−0.626001	−	1.71992i	−0.691798	−	0.722091i	$-0.743181\pi$
$877$	−18.5385	−	50.9342i	−0.626001	−	1.71992i	0.0657963	−	0.997833i	$-0.479041\pi$
$878$		0			0
$879$	−2.53044	+	14.3508i	−0.0853495	+	0.484041i
$880$		0			0
$881$	−21.6502	−	37.4992i	−0.729412	−	1.26338i	−0.957132	−	0.289653i	$-0.906460\pi$
$881$	−21.6502	−	37.4992i	−0.729412	−	1.26338i	0.227719	−	0.973727i	$-0.426873\pi$
$882$		0			0
$883$	29.3322	+	34.9568i	0.987108	+	1.17639i	0.984320	+	0.176393i	$0.0564430\pi$
$883$	29.3322	+	34.9568i	0.987108	+	1.17639i	0.00278783	+	0.999996i	$0.499113\pi$
$884$		0			0
$885$	−15.6044	−	9.00918i	−0.524535	−	0.302840i
$886$		0			0
$887$	9.47441	+	3.44840i	0.318120	+	0.115786i	0.496145	−	0.868240i	$-0.334749\pi$
$887$	9.47441	+	3.44840i	0.318120	+	0.115786i	−0.178025	+	0.984026i	$0.556971\pi$
$888$		0			0
$889$	7.50085	+	42.5394i	0.251570	+	1.42673i
$890$		0			0
$891$	7.25057	−	8.64090i	0.242903	−	0.289481i
$892$		0			0
$893$	−16.1429	−	13.8228i	−0.540203	−	0.462564i
$894$		0			0
$895$	−30.7524	−	25.8044i	−1.02794	−	0.862545i
$896$		0			0
$897$	9.01853	+	51.1466i	0.301120	+	1.70774i
$898$		0			0
$899$	−7.14495	+	19.6306i	−0.238297	+	0.654717i
$900$		0			0
$901$	3.66828	+	2.11788i	0.122208	+	0.0705570i
$902$		0			0
$903$	13.1852	−	11.0637i	0.438775	−	0.368176i
$904$		0			0
$905$	−4.87549	−	8.44460i	−0.162067	−	0.280708i
$906$		0			0
$907$	−10.1146	−	1.78348i	−0.335850	−	0.0592195i	0.00317994	−	0.999995i	$-0.498988\pi$
$907$	−10.1146	−	1.78348i	−0.335850	−	0.0592195i	−0.339030	+	0.940775i	$0.610099\pi$
$908$		0			0
$909$	−4.95092	−	13.6025i	−0.164212	−	0.451168i
$910$		0			0
$911$	−18.0080			−0.596631			−0.298316	−	0.954467i	$-0.596425\pi$
$911$	−18.0080			−0.596631			−0.298316	+	0.954467i	$0.596425\pi$
$912$		0			0
$913$	17.7936			0.588883
$914$		0			0
$915$	4.71280	+	12.9483i	0.155800	+	0.428058i
$916$		0			0
$917$	−41.3136	−	7.28470i	−1.36430	−	0.240562i
$918$		0			0
$919$	−3.23798	−	5.60834i	−0.106811	−	0.185002i	0.807666	−	0.589641i	$-0.200731\pi$
$919$	−3.23798	−	5.60834i	−0.106811	−	0.185002i	−0.914477	+	0.404639i	$0.867397\pi$
$920$		0			0
$921$	−5.52806	+	4.63860i	−0.182156	+	0.152847i
$922$		0			0
$923$	−7.03175	−	4.05978i	−0.231453	−	0.133629i
$924$		0			0
$925$	−4.88117	+	13.4109i	−0.160492	+	0.440948i
$926$		0			0
$927$	−0.798604	−	4.52911i	−0.0262296	−	0.148755i
$928$		0			0
$929$	−5.56288	−	4.66781i	−0.182512	−	0.153146i	0.546954	−	0.837162i	$-0.315787\pi$
$929$	−5.56288	−	4.66781i	−0.182512	−	0.153146i	−0.729466	+	0.684017i	$0.760232\pi$
$930$		0			0
$931$	−31.2111	−	11.7145i	−1.02290	−	0.383927i
$932$		0			0
$933$	6.23125	−	7.42611i	0.204002	−	0.243120i
$934$		0			0
$935$	2.22417	+	12.6139i	0.0727380	+	0.412518i
$936$		0			0
$937$	−10.5825	−	3.85173i	−0.345717	−	0.125831i	0.163325	−	0.986572i	$-0.447778\pi$
$937$	−10.5825	−	3.85173i	−0.345717	−	0.125831i	−0.509042	+	0.860742i	$0.670000\pi$
$938$		0			0
$939$	−30.0853	−	17.3698i	−0.981798	−	0.566841i
$940$		0			0
$941$	11.4013	+	13.5876i	0.371673	+	0.442942i	0.919168	−	0.393867i	$-0.128863\pi$
$941$	11.4013	+	13.5876i	0.371673	+	0.442942i	−0.547495	+	0.836809i	$0.684418\pi$
$942$		0			0
$943$	−23.0122	−	39.8582i	−0.749379	−	1.29796i
$944$		0			0
$945$	6.60567	−	37.4626i	0.214882	−	1.21866i
$946$		0			0
$947$	−19.3370	−	53.1281i	−0.628370	−	1.72643i	−0.685508	−	0.728065i	$-0.740420\pi$
$947$	−19.3370	−	53.1281i	−0.628370	−	1.72643i	0.0571383	−	0.998366i	$-0.481802\pi$
$948$		0			0
$949$			66.9314i			2.17269i
$950$		0			0
$951$	−1.57104			−0.0509446
$952$		0			0
$953$	−14.6290	+	5.32453i	−0.473880	+	0.172478i	−0.567909	−	0.823091i	$-0.692248\pi$
$953$	−14.6290	+	5.32453i	−0.473880	+	0.172478i	0.0940291	+	0.995569i	$0.470025\pi$
$954$		0			0
$955$	−2.64019	−	0.465537i	−0.0854346	−	0.0150644i
$956$		0			0
$957$	13.3826	−	7.72647i	0.432599	−	0.249761i
$958$		0			0
$959$	58.9202	−	49.4399i	1.90263	−	1.59650i
$960$		0			0
$961$	3.83561	−	6.64346i	0.123729	−	0.214305i
$962$		0			0
$963$	−0.493154	+	1.35493i	−0.0158917	+	0.0436620i
$964$		0			0
$965$	−16.9318	+	2.98552i	−0.545052	+	0.0961074i
$966$		0			0
$967$	20.7509	+	17.4121i	0.667304	+	0.559935i	0.912266	−	0.409598i	$-0.134331\pi$
$967$	20.7509	+	17.4121i	0.667304	+	0.559935i	−0.244962	+	0.969533i	$0.578775\pi$
$968$		0			0
$969$	16.2873	+	3.04006i	0.523223	+	0.0976607i
$970$		0			0
$971$	−26.6891	+	31.8069i	−0.856495	+	1.02073i	0.143024	+	0.989719i	$0.454317\pi$
$971$	−26.6891	+	31.8069i	−0.856495	+	1.02073i	−0.999519	+	0.0310118i	$0.990127\pi$
$972$		0			0
$973$	−62.2756	+	10.9809i	−1.99647	+	0.352031i
$974$		0			0
$975$	−14.5640	−	5.30085i	−0.466421	−	0.169763i
$976$		0			0
$977$	22.2421	−	38.5244i	0.711587	−	1.23251i	−0.252674	−	0.967551i	$-0.581310\pi$
$977$	22.2421	−	38.5244i	0.711587	−	1.23251i	0.964261	−	0.264954i	$-0.0853567\pi$
$978$		0			0
$979$	12.3646	+	14.7355i	0.395174	+	0.470950i
$980$		0			0
$981$	−3.32135	+	1.91759i	−0.106043	+	0.0612238i
$982$		0			0
$983$	1.03224	−	5.85410i	0.0329232	−	0.186717i	−0.963911	−	0.266225i	$-0.914224\pi$
$983$	1.03224	−	5.85410i	0.0329232	−	0.186717i	0.996834	+	0.0795078i	$0.0253349\pi$
$984$		0			0
$985$	9.89824	−	3.60266i	0.315384	−	0.114790i
$986$		0			0
$987$		−	25.4916i		−	0.811405i
$988$		0			0
$989$		−	20.9840i		−	0.667252i
$990$		0			0
$991$	−8.99995	+	3.27572i	−0.285893	+	0.104057i	−0.480986	−	0.876728i	$-0.659721\pi$
$991$	−8.99995	+	3.27572i	−0.285893	+	0.104057i	0.195093	+	0.980785i	$0.437499\pi$
$992$		0			0
$993$	1.01002	−	5.72811i	0.0320520	−	0.181776i
$994$		0			0
$995$	7.18623	−	4.14897i	0.227819	−	0.131531i
$996$		0			0
$997$	19.6721	+	23.4443i	0.623021	+	0.742487i	0.981587	−	0.191017i	$-0.0611787\pi$
$997$	19.6721	+	23.4443i	0.623021	+	0.742487i	−0.358566	+	0.933504i	$0.616734\pi$
$998$		0			0
$999$	−21.1846	+	36.6928i	−0.670252	+	1.16091i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	608.2.bf.a.529.6		108
4.3	odd	2		152.2.t.a.149.6	yes	108
8.3	odd	2		152.2.t.a.149.4	yes	108
8.5	even	2	inner	608.2.bf.a.529.13		108
19.6	even	9	inner	608.2.bf.a.177.13		108
76.63	odd	18		152.2.t.a.101.4	✓	108
152.101	even	18	inner	608.2.bf.a.177.6		108
152.139	odd	18		152.2.t.a.101.6	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.t.a.101.4	✓	108	76.63	odd	18
152.2.t.a.101.6	yes	108	152.139	odd	18
152.2.t.a.149.4	yes	108	8.3	odd	2
152.2.t.a.149.6	yes	108	4.3	odd	2
608.2.bf.a.177.6		108	152.101	even	18	inner
608.2.bf.a.177.13		108	19.6	even	9	inner
608.2.bf.a.529.6		108	1.1	even	1	trivial
608.2.bf.a.529.13		108	8.5	even	2	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:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	608.bf (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.467226 - 1.28369i) q^{3} +(-1.73333 - 0.305632i) q^{5} +(-1.91364 - 3.31452i) q^{7} +(0.868569 - 0.728816i) q^{9} +(-2.26499 - 1.30769i) q^{11} +(-2.03996 + 5.60474i) q^{13} +(0.417517 + 2.36785i) q^{15} +(2.13151 + 1.78855i) q^{17} +(0.713969 + 4.30003i) q^{19} +(-3.36072 + 4.00515i) q^{21} +(1.10686 + 6.27729i) q^{23} +(-1.78746 - 0.650581i) q^{25} +(-4.89056 - 2.82357i) q^{27} +(-2.78015 - 3.31326i) q^{29} +(-2.41499 - 4.18289i) q^{31} +(-0.620412 + 3.51853i) q^{33} +(2.30393 + 6.33001i) q^{35} -7.50278i q^{37} +8.14787 q^{39} +(-6.78504 + 2.46955i) q^{41} +(-3.24204 - 0.571659i) q^{43} +(-1.72826 + 0.997812i) q^{45} +(-3.73496 + 3.13400i) q^{47} +(-3.82402 + 6.62340i) q^{49} +(1.30005 - 3.57186i) q^{51} +(1.49917 - 0.264344i) q^{53} +(3.52629 + 2.95890i) q^{55} +(5.18633 - 2.92560i) q^{57} +(-4.81703 + 5.74071i) q^{59} +(5.64385 - 0.995163i) q^{61} +(-4.07780 - 1.48420i) q^{63} +(5.24890 - 9.09135i) q^{65} +(-2.11430 - 2.51972i) q^{67} +(7.54096 - 4.35377i) q^{69} +(-0.236392 + 1.34065i) q^{71} +(10.5450 - 3.83807i) q^{73} +2.59851i q^{75} +10.0098i q^{77} +(6.51619 - 2.37170i) q^{79} +(-0.748928 + 4.24738i) q^{81} +(-5.89196 + 3.40173i) q^{83} +(-3.14796 - 3.75160i) q^{85} +(-2.95424 + 5.11690i) q^{87} +(-6.91135 - 2.51553i) q^{89} +(22.4807 - 3.96396i) q^{91} +(-4.24120 + 5.05446i) q^{93} +(0.0766864 - 7.67156i) q^{95} +(-9.33891 - 7.83628i) q^{97} +(-2.92036 + 0.514939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 6 q^{7} - 12 q^{9} + 12 q^{15} - 12 q^{17} + 12 q^{23} - 12 q^{25} - 30 q^{31} - 30 q^{33} + 24 q^{39} - 24 q^{41} + 48 q^{47} - 24 q^{49} + 42 q^{55} - 12 q^{57} - 30 q^{63} - 6 q^{65} + 12 q^{71}+ \cdots - 12 q^{97}+O(q^{100}) \) 108 * q + 6 * q^7 - 12 * q^9 + 12 * q^15 - 12 * q^17 + 12 * q^23 - 12 * q^25 - 30 * q^31 - 30 * q^33 + 24 * q^39 - 24 * q^41 + 48 * q^47 - 24 * q^49 + 42 * q^55 - 12 * q^57 - 30 * q^63 - 6 * q^65 + 12 * q^71 + 12 * q^73 + 12 * q^79 - 18 * q^81 + 6 * q^87 - 12 * q^89 + 72 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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