LMFDB - Embedded newform 608.2.bf.a.529.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [608,2,Mod(17,608)]

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

lf = mfeigenbasis(mf)

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")

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

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			529.13
Character	$\chi$	$=$	608.529
Dual form			608.2.bf.a.177.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.467226 + 1.28369i) q^{3} +(1.73333 + 0.305632i) q^{5} +(-1.91364 - 3.31452i) q^{7} +(0.868569 - 0.728816i) q^{9} +O(q^{10})$	\(q+(0.467226 + 1.28369i) q^{3} +(1.73333 + 0.305632i) q^{5} +(-1.91364 - 3.31452i) q^{7} +(0.868569 - 0.728816i) q^{9} +(2.26499 + 1.30769i) q^{11} +(2.03996 - 5.60474i) q^{13} +(0.417517 + 2.36785i) q^{15} +(2.13151 + 1.78855i) q^{17} +(-0.713969 - 4.30003i) q^{19} +(3.36072 - 4.00515i) q^{21} +(1.10686 + 6.27729i) q^{23} +(-1.78746 - 0.650581i) q^{25} +(4.89056 + 2.82357i) q^{27} +(2.78015 + 3.31326i) q^{29} +(-2.41499 - 4.18289i) q^{31} +(-0.620412 + 3.51853i) q^{33} +(-2.30393 - 6.33001i) q^{35} +7.50278i q^{37} +8.14787 q^{39} +(-6.78504 + 2.46955i) q^{41} +(3.24204 + 0.571659i) q^{43} +(1.72826 - 0.997812i) q^{45} +(-3.73496 + 3.13400i) q^{47} +(-3.82402 + 6.62340i) q^{49} +(-1.30005 + 3.57186i) q^{51} +(-1.49917 + 0.264344i) q^{53} +(3.52629 + 2.95890i) q^{55} +(5.18633 - 2.92560i) q^{57} +(4.81703 - 5.74071i) q^{59} +(-5.64385 + 0.995163i) q^{61} +(-4.07780 - 1.48420i) q^{63} +(5.24890 - 9.09135i) q^{65} +(2.11430 + 2.51972i) q^{67} +(-7.54096 + 4.35377i) q^{69} +(-0.236392 + 1.34065i) q^{71} +(10.5450 - 3.83807i) q^{73} -2.59851i q^{75} -10.0098i q^{77} +(6.51619 - 2.37170i) q^{79} +(-0.748928 + 4.24738i) q^{81} +(5.89196 - 3.40173i) q^{83} +(3.14796 + 3.75160i) q^{85} +(-2.95424 + 5.11690i) q^{87} +(-6.91135 - 2.51553i) q^{89} +(-22.4807 + 3.96396i) q^{91} +(4.24120 - 5.05446i) q^{93} +(0.0766864 - 7.67156i) q^{95} +(-9.33891 - 7.83628i) q^{97} +(2.92036 - 0.514939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 108 * q + 6 * q^7 - 12 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$0.0179199\pi$
$3$	0.467226	+	1.28369i	0.269753	+	0.741140i	−0.728663	+	0.684872i	$0.759858\pi$
$4$		0			0
$5$	1.73333	+	0.305632i	0.775167	+	0.136683i	0.547218	−	0.836990i	$-0.315687\pi$
$5$	1.73333	+	0.305632i	0.775167	+	0.136683i	0.227949	+	0.973673i	$0.426798\pi$
$6$		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	0.800954	−	0.598726i	$-0.204326\pi$
$11$	2.26499	+	1.30769i	0.682919	+	0.394283i	−0.118035	+	0.993009i	$0.537659\pi$
$12$		0			0
$13$	2.03996	−	5.60474i	0.565782	−	1.55447i	−0.245242	−	0.969462i	$-0.578867\pi$
$13$	2.03996	−	5.60474i	0.565782	−	1.55447i	0.811024	−	0.585012i	$-0.198910\pi$
$14$		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	0.959693	−	0.281052i	$-0.0906833\pi$
$29$	2.78015	+	3.31326i	0.516261	+	0.615256i	−0.443431	+	0.896308i	$0.646239\pi$
$30$		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	$0.211541\pi$
$37$			7.50278i			1.23345i	−0.787179	+	0.616725i	$0.788459\pi$
$38$		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	0.415292	−	0.909688i	$-0.363679\pi$
$43$	3.24204	+	0.571659i	0.494407	+	0.0871772i	0.0791149	+	0.996866i	$0.474791\pi$
$44$		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	−0.275660	−	0.961255i	$-0.588896\pi$
$53$	−1.49917	+	0.264344i	−0.205927	+	0.0363104i	0.0697332	+	0.997566i	$0.477785\pi$
$54$		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	−0.355154	−	0.934808i	$-0.615572\pi$
$59$	4.81703	−	5.74071i	0.627124	−	0.747377i	0.982278	+	0.187431i	$0.0600161\pi$
$60$		0			0
$61$	−5.64385	+	0.995163i	−0.722621	+	0.127418i	−0.522850	−	0.852425i	$-0.675131\pi$
$61$	−5.64385	+	0.995163i	−0.722621	+	0.127418i	−0.199771	+	0.979843i	$0.564020\pi$
$62$		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	0.879574	−	0.475763i	$-0.157828\pi$
$67$	2.11430	+	2.51972i	0.258302	+	0.307833i	−0.621271	+	0.783596i	$0.713383\pi$
$68$		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	−0.140474	−	0.990084i	$-0.544863\pi$
$83$	5.89196	−	3.40173i	0.646727	−	0.373388i	0.787201	+	0.616696i	$0.211529\pi$
$84$		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	$0.330183\pi$
$101$	−4.36652	+	11.9969i	−0.434485	+	1.19374i	−0.943031	+	0.332704i	$0.892039\pi$
$102$		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	−0.445820	−	0.895122i	$-0.647088\pi$
$107$	1.10131	−	0.635844i	0.106468	−	0.0614693i	0.552288	+	0.833653i	$0.313755\pi$
$108$		0			0
$109$	3.33109	+	0.587360i	0.319060	+	0.0562589i	0.330885	−	0.943671i	$-0.392653\pi$
$109$	3.33109	+	0.587360i	0.319060	+	0.0562589i	−0.0118246	+	0.999930i	$0.503764\pi$
$110$		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	−0.980303	−	0.197497i	$-0.936719\pi$
$131$	−7.04562	+	8.39664i	−0.615579	+	0.733618i	0.364725	+	0.931115i	$0.381163\pi$
$132$		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	$0.358245\pi$
$139$	−5.65104	+	15.5261i	−0.479315	+	1.31691i	−0.910076	+	0.414441i	$0.863977\pi$
$140$		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	$0.159896\pi$
$149$	6.28070	+	17.2561i	0.514535	+	1.41367i	−0.361929	+	0.932206i	$0.617882\pi$
$150$		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	0.213114	−	0.977027i	$-0.431639\pi$
$157$	0.992527	+	0.175009i	0.0792123	+	0.0139673i	−0.133902	+	0.990995i	$0.542751\pi$
$158$		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	0.913270	−	0.407356i	$-0.133549\pi$
$163$	12.9858	+	7.49734i	1.01712	+	0.587237i	0.103854	+	0.994593i	$0.466882\pi$
$164$		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	$-0.539353\pi$
$173$	11.5139	−	13.7218i	0.875388	−	1.04325i	0.998705	−	0.0508794i	$-0.0162024\pi$
$174$		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	−0.476745	−	0.879042i	$-0.658184\pi$
$179$	−19.7528	−	11.4043i	−1.47639	−	0.852394i	−0.999645	+	0.0266474i	$0.991517\pi$
$180$		0			0
$181$	−3.56113	−	4.24399i	−0.264696	−	0.315453i	0.617283	−	0.786741i	$-0.288233\pi$
$181$	−3.56113	−	4.24399i	−0.264696	−	0.315453i	−0.881979	+	0.471289i	$0.843789\pi$
$182$		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	−0.303871	−	0.952713i	$-0.598279\pi$
$197$	5.18292	−	2.99236i	0.369268	−	0.213197i	0.673138	+	0.739517i	$0.264946\pi$
$198$		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	$0.497984\pi$
$211$	−14.2288	+	16.9573i	−0.979553	+	1.16739i	−0.985888	+	0.167406i	$0.946461\pi$
$212$		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	$-0.982172\pi$
$227$		−	1.68680i		−	0.111957i	0.998432	−	0.0559784i	$-0.0178278\pi$
$228$		0			0
$229$			3.60123i			0.237976i	0.992896	+	0.118988i	$0.0379650\pi$
$229$			3.60123i			0.237976i	−0.992896	+	0.118988i	$0.962035\pi$
$230$		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	−0.342584	−	0.939487i	$-0.611302\pi$
$251$	−5.43707	+	0.958702i	−0.343185	+	0.0605127i	−0.000600364		1.00000i	$0.500191\pi$
$252$		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	0.786135	−	0.618055i	$-0.212079\pi$
$269$	−3.49933	−	9.61432i	−0.213358	−	0.586195i	−0.999492	+	0.0318599i	$0.989857\pi$
$270$		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	0.827448	−	0.561543i	$-0.189792\pi$
$277$	12.5634	+	7.25348i	0.754862	+	0.435820i	−0.0725863	+	0.997362i	$0.523125\pi$
$278$		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	−0.513179	−	0.858282i	$-0.671532\pi$
$283$	7.08527	−	8.44390i	0.421176	−	0.501938i	0.934355	+	0.356344i	$0.115977\pi$
$284$		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	0.744955	−	0.667115i	$-0.232471\pi$
$293$	9.23806	+	5.33360i	0.539693	+	0.311592i	−0.205261	+	0.978707i	$0.565804\pi$
$294$		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	0.980512	−	0.196457i	$-0.0629436\pi$
$307$	1.80674	+	4.96398i	0.103116	+	0.283309i	−0.877396	+	0.479766i	$0.840721\pi$
$308$		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	−0.950248	−	0.311493i	$-0.899171\pi$
$317$	−0.393337	+	1.08068i	−0.0220920	+	0.0606973i	0.928156	+	0.372190i	$0.121393\pi$
$318$		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	0.395227	−	0.918583i	$-0.370666\pi$
$331$	−3.68736	−	2.12890i	−0.202676	−	0.117015i	−0.597903	+	0.801568i	$0.703999\pi$
$332$		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	0.626143	−	0.779708i	$-0.284633\pi$
$347$	17.6565	+	3.11331i	0.947849	+	0.167131i	0.321706	+	0.946840i	$0.395744\pi$
$348$		0			0
$349$	17.4551	−	10.0777i	0.934352	−	0.539449i	0.0461670	−	0.998934i	$-0.485299\pi$
$349$	17.4551	−	10.0777i	0.934352	−	0.539449i	0.888185	+	0.459485i	$0.151966\pi$
$350$		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	−0.997846	−	0.0655941i	$-0.979106\pi$
$373$	−27.8103	+	16.0563i	−1.43996	+	0.831363i	−0.442117	+	0.896957i	$0.645772\pi$
$374$		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	$-0.959788\pi$
$379$		−	4.90569i		−	0.251989i	0.992031	−	0.125994i	$-0.0402121\pi$
$380$		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	0.978158	−	0.207863i	$-0.0666507\pi$
$389$	11.9048	+	14.1876i	0.603598	+	0.719340i	−0.374560	+	0.927203i	$0.622206\pi$
$390$		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	−0.492629	−	0.870240i	$-0.663964\pi$
$397$	8.96487	−	10.6839i	0.449934	−	0.536210i	0.942563	+	0.334029i	$0.108408\pi$
$398$		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	$0.128659\pi$
$419$			16.1004i			0.786557i	−0.919419	+	0.393279i	$0.871341\pi$
$420$		0			0
$421$	−0.928735	−	2.55168i	−0.0452638	−	0.124361i	0.915001	−	0.403451i	$-0.132189\pi$
$421$	−0.928735	−	2.55168i	−0.0452638	−	0.124361i	−0.960265	+	0.279090i	$0.909967\pi$
$422$		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	$0.402728\pi$
$443$	−11.4208	+	31.3785i	−0.542620	+	1.49084i	−0.843476	+	0.537167i	$0.819494\pi$
$444$		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	−0.899445	−	0.437035i	$-0.856029\pi$
$461$	−40.6685	−	7.17095i	−1.89412	−	0.333985i	−0.994676	+	0.103050i	$0.967140\pi$
$462$		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	0.00152700	−	0.999999i	$-0.499514\pi$
$467$	−18.6654	−	10.7765i	−0.863734	−	0.498677i	−0.865261	+	0.501322i	$0.832847\pi$
$468$		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	0.825042	−	0.565071i	$-0.191151\pi$
$491$	−3.77132	−	10.3616i	−0.170197	−	0.467613i	−0.995240	+	0.0974577i	$0.968929\pi$
$492$		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	−0.477474	−	0.878646i	$-0.658448\pi$
$499$	−27.4017	−	4.83166i	−1.22667	−	0.216295i	−0.749193	+	0.662351i	$0.769559\pi$
$500$		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	0.0999901	−	0.994988i	$-0.468119\pi$
$509$	12.0534	−	2.12533i	0.534256	−	0.0942038i	0.434266	+	0.900785i	$0.357008\pi$
$510$		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	0.604109	−	0.796902i	$-0.293529\pi$
$523$	−6.53118	−	7.78356i	−0.285589	−	0.340351i	−0.889697	+	0.456551i	$0.849085\pi$
$524$		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	0.983982	−	0.178267i	$-0.0570490\pi$
$541$	14.8292	+	17.6728i	0.637557	+	0.759811i	−0.346425	+	0.938078i	$0.612605\pi$
$542$		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	0.119457	−	0.992839i	$-0.461885\pi$
$547$	13.3611	−	2.35593i	0.571281	−	0.100732i	0.451824	+	0.892107i	$0.350773\pi$
$548$		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	$-0.591816\pi$
$557$	12.9729	−	35.6427i	0.549679	−	1.51023i	0.834145	−	0.551545i	$-0.185961\pi$
$558$		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	−0.922233	−	0.386635i	$-0.873637\pi$
$563$	−24.8787	+	14.3637i	−1.04851	+	0.605360i	−0.126281	+	0.991995i	$0.540304\pi$
$564$		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	$-0.699094\pi$
$571$		−	38.7437i		−	1.62137i	0.585480	−	0.810687i	$-0.300906\pi$
$572$		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	−0.952840	−	0.303474i	$-0.901853\pi$
$587$	−11.8358	+	14.1054i	−0.488517	+	0.582192i	0.464323	+	0.885666i	$0.346298\pi$
$588$		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	0.705650	−	0.708561i	$-0.250655\pi$
$613$	27.8884	+	4.91748i	1.12640	+	0.198615i	0.420752	+	0.907176i	$0.361766\pi$
$614$		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	0.314826	−	0.949149i	$-0.398054\pi$
$619$	−8.70164	−	5.02389i	−0.349748	−	0.201927i	−0.664574	+	0.747222i	$0.731387\pi$
$620$		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	$0.113235\pi$
$643$	11.2379	+	30.8759i	0.443180	+	1.21763i	−0.494209	+	0.869343i	$0.664542\pi$
$644$		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	−0.876826	−	0.480809i	$-0.840343\pi$
$653$	−22.9690	+	13.2611i	−0.898846	+	0.518949i	−0.0220202	+	0.999758i	$0.507010\pi$
$654$		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	−0.966026	−	0.258444i	$-0.916790\pi$
$659$	−1.53725	+	4.22355i	−0.0598827	+	0.164526i	0.906144	+	0.422970i	$0.139013\pi$
$660$		0			0
$661$	−14.3356	+	2.52775i	−0.557589	+	0.0983179i	−0.445339	−	0.895362i	$-0.646917\pi$
$661$	−14.3356	+	2.52775i	−0.557589	+	0.0983179i	−0.112250	+	0.993680i	$0.535806\pi$
$662$		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	0.114825	−	0.993386i	$-0.463369\pi$
$677$	26.8658	−	15.5109i	1.03253	−	0.596134i	0.917710	+	0.397252i	$0.130036\pi$
$678$		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	$-0.730113\pi$
$683$		−	39.1949i		−	1.49975i	0.661578	−	0.749876i	$-0.269887\pi$
$684$		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	−0.493187	−	0.869923i	$-0.664168\pi$
$691$	0.357391	−	0.206340i	0.0135958	−	0.00784954i	0.506782	+	0.862074i	$0.330835\pi$
$692$		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	−0.779132	−	0.626860i	$-0.784340\pi$
$701$	−0.701629	+	0.836169i	−0.0265002	+	0.0315817i	0.752632	+	0.658442i	$0.228784\pi$
$702$		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	$-0.564445\pi$
$709$	15.5133	−	42.6225i	0.582615	−	1.60072i	0.783695	−	0.621146i	$-0.213333\pi$
$710$		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	−0.0230105	−	0.999735i	$-0.507325\pi$
$733$	−24.3750	−	14.0729i	−0.900312	−	0.519795i	−0.877301	+	0.479940i	$0.840658\pi$
$734$		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	$-0.544284\pi$
$739$	23.3977	−	27.8843i	0.860699	−	1.02574i	0.999373	−	0.0354033i	$-0.0112716\pi$
$740$		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	$0.0522378\pi$
$757$	9.23982	+	25.3862i	0.335827	+	0.922677i	−0.650737	+	0.759303i	$0.725540\pi$
$758$		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	$-0.776159\pi$
$773$	6.59542	−	18.1208i	0.237221	−	0.651759i	0.999987	−	0.00508474i	$-0.00161853\pi$
$774$		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	0.799169	−	0.601107i	$-0.205273\pi$
$787$	19.0253	+	10.9843i	0.678179	+	0.391547i	−0.120990	+	0.992654i	$0.538607\pi$
$788$		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	$0.00400599\pi$
$797$			0.710570i			0.0251697i	−0.999921	+	0.0125848i	$0.995994\pi$
$798$		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	−0.994067	−	0.108769i	$-0.965309\pi$
$811$	−4.63202	+	12.7264i	−0.162652	+	0.446883i	0.831415	+	0.555652i	$0.187531\pi$
$812$		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	−0.537697	−	0.843138i	$-0.680706\pi$
$821$	−21.6215	+	3.81246i	−0.754597	+	0.133056i	−0.216900	+	0.976194i	$0.569594\pi$
$822$		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	0.605439	−	0.795891i	$-0.292997\pi$
$827$	−8.15261	−	9.71590i	−0.283494	−	0.337855i	−0.888933	+	0.458036i	$0.848553\pi$
$828$		0			0
$829$	38.1089	−	22.0022i	1.32358	−	0.764168i	0.339280	−	0.940686i	$-0.389817\pi$
$829$	38.1089	−	22.0022i	1.32358	−	0.764168i	0.984297	+	0.176518i	$0.0564834\pi$
$830$		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	−0.542885	−	0.839807i	$-0.682668\pi$
$853$	11.0526	−	13.1720i	0.378434	−	0.451000i	0.921319	+	0.388807i	$0.127113\pi$
$854$		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	0.194394	−	0.980924i	$-0.437726\pi$
$859$	20.8842	−	3.68245i	0.712559	−	0.125643i	0.518166	+	0.855280i	$0.326615\pi$
$860$		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	$0.256819\pi$
$877$	18.5385	+	50.9342i	0.626001	+	1.71992i	−0.0657963	+	0.997833i	$0.520959\pi$
$878$		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	$-0.943557\pi$
$883$	−29.3322	−	34.9568i	−0.987108	−	1.17639i	−0.00278783	−	0.999996i	$-0.500887\pi$
$884$		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	0.339030	−	0.940775i	$-0.389901\pi$
$907$	10.1146	+	1.78348i	0.335850	+	0.0592195i	−0.00317994	+	0.999995i	$0.501012\pi$
$908$		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	0.547495	−	0.836809i	$-0.315582\pi$
$941$	−11.4013	−	13.5876i	−0.371673	−	0.442942i	−0.919168	+	0.393867i	$0.871137\pi$
$942$		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	$0.259580\pi$
$947$	19.3370	+	53.1281i	0.628370	+	1.72643i	−0.0571383	+	0.998366i	$0.518198\pi$
$948$		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	$-0.545683\pi$
$971$	26.6891	−	31.8069i	0.856495	−	1.02073i	0.999519	−	0.0310118i	$-0.00987295\pi$
$972$		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	0.358566	−	0.933504i	$-0.383266\pi$
$997$	−19.6721	−	23.4443i	−0.623021	−	0.742487i	−0.981587	+	0.191017i	$0.938821\pi$
$998$		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.529.13		108
4.3	odd	2		152.2.t.a.149.4	yes	108
8.3	odd	2		152.2.t.a.149.6	yes	108
8.5	even	2	inner	608.2.bf.a.529.6		108
19.6	even	9	inner	608.2.bf.a.177.6		108
76.63	odd	18		152.2.t.a.101.6	yes	108
152.101	even	18	inner	608.2.bf.a.177.13		108
152.139	odd	18		152.2.t.a.101.4	✓	108

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

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

\(f(q)\)	\(=\)	\(q+(0.467226 + 1.28369i) q^{3} +(1.73333 + 0.305632i) q^{5} +(-1.91364 - 3.31452i) q^{7} +(0.868569 - 0.728816i) q^{9} +O(q^{10})\)	\(q+(0.467226 + 1.28369i) q^{3} +(1.73333 + 0.305632i) q^{5} +(-1.91364 - 3.31452i) q^{7} +(0.868569 - 0.728816i) q^{9} +(2.26499 + 1.30769i) q^{11} +(2.03996 - 5.60474i) q^{13} +(0.417517 + 2.36785i) q^{15} +(2.13151 + 1.78855i) q^{17} +(-0.713969 - 4.30003i) q^{19} +(3.36072 - 4.00515i) q^{21} +(1.10686 + 6.27729i) q^{23} +(-1.78746 - 0.650581i) q^{25} +(4.89056 + 2.82357i) q^{27} +(2.78015 + 3.31326i) q^{29} +(-2.41499 - 4.18289i) q^{31} +(-0.620412 + 3.51853i) q^{33} +(-2.30393 - 6.33001i) q^{35} +7.50278i q^{37} +8.14787 q^{39} +(-6.78504 + 2.46955i) q^{41} +(3.24204 + 0.571659i) q^{43} +(1.72826 - 0.997812i) q^{45} +(-3.73496 + 3.13400i) q^{47} +(-3.82402 + 6.62340i) q^{49} +(-1.30005 + 3.57186i) q^{51} +(-1.49917 + 0.264344i) q^{53} +(3.52629 + 2.95890i) q^{55} +(5.18633 - 2.92560i) q^{57} +(4.81703 - 5.74071i) q^{59} +(-5.64385 + 0.995163i) q^{61} +(-4.07780 - 1.48420i) q^{63} +(5.24890 - 9.09135i) q^{65} +(2.11430 + 2.51972i) q^{67} +(-7.54096 + 4.35377i) q^{69} +(-0.236392 + 1.34065i) q^{71} +(10.5450 - 3.83807i) q^{73} -2.59851i q^{75} -10.0098i q^{77} +(6.51619 - 2.37170i) q^{79} +(-0.748928 + 4.24738i) q^{81} +(5.89196 - 3.40173i) q^{83} +(3.14796 + 3.75160i) q^{85} +(-2.95424 + 5.11690i) q^{87} +(-6.91135 - 2.51553i) q^{89} +(-22.4807 + 3.96396i) q^{91} +(4.24120 - 5.05446i) q^{93} +(0.0766864 - 7.67156i) q^{95} +(-9.33891 - 7.83628i) q^{97} +(2.92036 - 0.514939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 108 * q + 6 * q^7 - 12 * q^9	\( 108 q + 6 q^{7} - 12 q^{9} + 12 q^{15} - 12 q^{17} + 12 q^{23} - 12 q^{25} - 30 q^{31} - 30 q^{33} + 24 q^{39} - 24 q^{41} + 48 q^{47} - 24 q^{49} + 42 q^{55} - 12 q^{57} - 30 q^{63} - 6 q^{65} + 12 q^{71} + 12 q^{73} + 12 q^{79} - 18 q^{81} + 6 q^{87} - 12 q^{89} + 72 q^{95} - 12 q^{97}+O(q^{100}) \) 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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