LMFDB - Embedded newform 936.2.w.j.307.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(307,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.307"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.11
Character	$\chi$	$=$	936.307
Dual form			936.2.w.j.811.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.35425 + 0.407446i) q^{2} +(1.66797 + 1.10357i) q^{4} +(-0.273741 + 0.273741i) q^{5} +(1.75949 + 1.75949i) q^{7} +(1.80921 + 2.17411i) q^{8} +(-0.482247 + 0.259178i) q^{10} +(3.22801 - 3.22801i) q^{11} +(-1.42905 - 3.31026i) q^{13} +(1.66589 + 3.09968i) q^{14} +(1.56428 + 3.68144i) q^{16} -2.18769i q^{17} +(5.33373 + 5.33373i) q^{19} +(-0.758684 + 0.154501i) q^{20} +(5.68676 - 3.05628i) q^{22} -6.75871 q^{23} +4.85013i q^{25} +(-0.586533 - 5.06517i) q^{26} +(0.993070 + 4.87650i) q^{28} -0.239304i q^{29} +(-1.75949 + 1.75949i) q^{31} +(0.618432 + 5.62295i) q^{32} +(0.891368 - 2.96268i) q^{34} -0.963288 q^{35} +(3.35366 + 3.35366i) q^{37} +(5.04999 + 9.39641i) q^{38} +(-1.09040 - 0.0998898i) q^{40} +(-1.29342 - 1.29342i) q^{41} +2.60196i q^{43} +(8.94655 - 1.82191i) q^{44} +(-9.15296 - 2.75381i) q^{46} +(-7.61070 - 7.61070i) q^{47} -0.808387i q^{49} +(-1.97617 + 6.56828i) q^{50} +(1.26948 - 7.09848i) q^{52} +11.6675i q^{53} +1.76727i q^{55} +(-0.642050 + 7.00861i) q^{56} +(0.0975034 - 0.324076i) q^{58} +(9.48121 - 9.48121i) q^{59} -1.47245i q^{61} +(-3.09968 + 1.66589i) q^{62} +(-1.45354 + 7.86684i) q^{64} +(1.29734 + 0.514964i) q^{65} +(-7.93570 - 7.93570i) q^{67} +(2.41427 - 3.64902i) q^{68} +(-1.30453 - 0.392488i) q^{70} +(5.30009 - 5.30009i) q^{71} +(3.04174 - 3.04174i) q^{73} +(3.17525 + 5.90813i) q^{74} +(3.01040 + 14.7827i) q^{76} +11.3593 q^{77} -16.2639i q^{79} +(-1.43597 - 0.579554i) q^{80} +(-1.22462 - 2.27862i) q^{82} +(2.81374 + 2.81374i) q^{83} +(0.598861 + 0.598861i) q^{85} +(-1.06016 + 3.52370i) q^{86} +(12.8582 + 1.17792i) q^{88} +(0.702659 - 0.702659i) q^{89} +(3.30997 - 8.33877i) q^{91} +(-11.2734 - 7.45868i) q^{92} +(-7.20583 - 13.4077i) q^{94} -2.92012 q^{95} +(-3.22944 - 3.22944i) q^{97} +(0.329375 - 1.09476i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{8} - 8 q^{11} - 36 q^{14} + 28 q^{16} + 20 q^{19} + 20 q^{20} + 20 q^{22} - 12 q^{26} - 16 q^{28} + 30 q^{32} + 16 q^{34} - 16 q^{35} + 36 q^{40} + 12 q^{41} + 32 q^{44} - 44 q^{46} + 36 q^{50}+ \cdots - 68 q^{98}+O(q^{100}) $ 24 * q + 6 * q^8 - 8 * q^11 - 36 * q^14 + 28 * q^16 + 20 * q^19 + 20 * q^20 + 20 * q^22 - 12 * q^26 - 16 * q^28 + 30 * q^32 + 16 * q^34 - 16 * q^35 + 36 * q^40 + 12 * q^41 + 32 * q^44 - 44 * q^46 + 36 * q^50 + 4 * q^52 + 32 * q^58 + 16 * q^59 + 76 * q^65 + 28 * q^67 - 32 * q^68 - 40 * q^70 - 8 * q^73 + 32 * q^74 - 36 * q^76 + 32 * q^80 + 72 * q^83 - 4 * q^86 - 28 * q^89 - 4 * q^91 - 32 * q^92 + 28 * q^94 + 24 * q^97 - 68 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$-1$

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 $

$2$	1.35425	+	0.407446i	0.957598	+	0.288108i
$2$	1.35425	+	0.407446i	0.957598	+	0.288108i
$3$		0			0
$3$		0			0
$4$	1.66797	+	1.10357i	0.833987	+	0.551783i
$5$	−0.273741	+	0.273741i	−0.122421	+	0.122421i	−0.765663	−	0.643242i	$-0.777589\pi$
$5$	−0.273741	+	0.273741i	−0.122421	+	0.122421i	0.643242	+	0.765663i	$0.277589\pi$
$6$		0			0
$7$	1.75949	+	1.75949i	0.665025	+	0.665025i	0.956560	−	0.291535i	$-0.0941661\pi$
$7$	1.75949	+	1.75949i	0.665025	+	0.665025i	−0.291535	+	0.956560i	$0.594166\pi$
$8$	1.80921	+	2.17411i	0.639651	+	0.768665i
$9$		0			0
$10$	−0.482247	+	0.259178i	−0.152500	+	0.0819593i
$11$	3.22801	−	3.22801i	0.973281	−	0.973281i	−0.0263717	−	0.999652i	$-0.508395\pi$
$11$	3.22801	−	3.22801i	0.973281	−	0.973281i	0.999652	+	0.0263717i	$0.00839534\pi$
$12$		0			0
$13$	−1.42905	−	3.31026i	−0.396347	−	0.918101i
$13$	−1.42905	−	3.31026i	−0.396347	−	0.918101i
$14$	1.66589	+	3.09968i	0.445227	+	0.828425i
$15$		0			0
$16$	1.56428	+	3.68144i	0.391070	+	0.920361i
$17$		−	2.18769i		−	0.530594i	−0.964167	−	0.265297i	$-0.914530\pi$
$17$		−	2.18769i		−	0.530594i	0.964167	−	0.265297i	$-0.0854700\pi$
$18$		0			0
$19$	5.33373	+	5.33373i	1.22364	+	1.22364i	0.966328	+	0.257315i	$0.0828379\pi$
$19$	5.33373	+	5.33373i	1.22364	+	1.22364i	0.257315	+	0.966328i	$0.417162\pi$
$20$	−0.758684	+	0.154501i	−0.169647	+	0.0345476i
$21$		0			0
$22$	5.68676	−	3.05628i	1.21242	−	0.651601i
$23$	−6.75871			−1.40929			−0.704644	−	0.709561i	$-0.748893\pi$
$23$	−6.75871			−1.40929			−0.704644	+	0.709561i	$0.748893\pi$
$24$		0			0
$25$			4.85013i			0.970026i
$26$	−0.586533	−	5.06517i	−0.115029	−	0.993362i
$27$		0			0
$28$	0.993070	+	4.87650i	0.187673	+	0.921572i
$29$		−	0.239304i		−	0.0444375i	−0.999753	−	0.0222188i	$-0.992927\pi$
$29$		−	0.239304i		−	0.0444375i	0.999753	−	0.0222188i	$-0.00707304\pi$
$30$		0			0
$31$	−1.75949	+	1.75949i	−0.316014	+	0.316014i	−0.847234	−	0.531220i	$-0.821734\pi$
$31$	−1.75949	+	1.75949i	−0.316014	+	0.316014i	0.531220	+	0.847234i	$0.321734\pi$
$32$	0.618432	+	5.62295i	0.109324	+	0.994006i
$33$		0			0
$34$	0.891368	−	2.96268i	0.152868	−	0.508096i
$35$	−0.963288			−0.162825
$36$		0			0
$37$	3.35366	+	3.35366i	0.551339	+	0.551339i	0.926827	−	0.375488i	$-0.122525\pi$
$37$	3.35366	+	3.35366i	0.551339	+	0.551339i	−0.375488	+	0.926827i	$0.622525\pi$
$38$	5.04999	+	9.39641i	0.819216	+	1.52430i
$39$		0			0
$40$	−1.09040	−	0.0998898i	−0.172407	−	0.0157940i
$41$	−1.29342	−	1.29342i	−0.201999	−	0.201999i	0.598857	−	0.800856i	$-0.295622\pi$
$41$	−1.29342	−	1.29342i	−0.201999	−	0.201999i	−0.800856	+	0.598857i	$0.795622\pi$
$42$		0			0
$43$			2.60196i			0.396796i	0.980122	+	0.198398i	$0.0635738\pi$
$43$			2.60196i			0.396796i	−0.980122	+	0.198398i	$0.936426\pi$
$44$	8.94655	−	1.82191i	1.34874	−	0.274664i
$45$		0			0
$46$	−9.15296	−	2.75381i	−1.34953	−	0.406027i
$47$	−7.61070	−	7.61070i	−1.11014	−	1.11014i	−0.993131	−	0.117004i	$-0.962671\pi$
$47$	−7.61070	−	7.61070i	−1.11014	−	1.11014i	−0.117004	−	0.993131i	$-0.537329\pi$
$48$		0			0
$49$		−	0.808387i		−	0.115484i
$50$	−1.97617	+	6.56828i	−0.279473	+	0.928895i
$51$		0			0
$52$	1.26948	−	7.09848i	0.176045	−	0.984382i
$53$			11.6675i			1.60265i	0.598229	+	0.801325i	$0.295871\pi$
$53$			11.6675i			1.60265i	−0.598229	+	0.801325i	$0.704129\pi$
$54$		0			0
$55$			1.76727i			0.238299i
$56$	−0.642050	+	7.00861i	−0.0857975	+	0.936565i
$57$		0			0
$58$	0.0975034	−	0.324076i	0.0128028	−	0.0425533i
$59$	9.48121	−	9.48121i	1.23435	−	1.23435i	0.272071	−	0.962277i	$-0.412291\pi$
$59$	9.48121	−	9.48121i	1.23435	−	1.23435i	0.962277	−	0.272071i	$-0.0877086\pi$
$60$		0			0
$61$		−	1.47245i		−	0.188528i	−0.995547	−	0.0942641i	$-0.969950\pi$
$61$		−	1.47245i		−	0.188528i	0.995547	−	0.0942641i	$-0.0300498\pi$
$62$	−3.09968	+	1.66589i	−0.393660	+	0.211568i
$63$		0			0
$64$	−1.45354	+	7.86684i	−0.181693	+	0.983355i
$65$	1.29734	+	0.514964i	0.160915	+	0.0638734i
$66$		0			0
$67$	−7.93570	−	7.93570i	−0.969500	−	0.969500i	0.0300487	−	0.999548i	$-0.490434\pi$
$67$	−7.93570	−	7.93570i	−0.969500	−	0.969500i	−0.999548	+	0.0300487i	$0.990434\pi$
$68$	2.41427	−	3.64902i	0.292773	−	0.442509i
$69$		0			0
$70$	−1.30453	−	0.392488i	−0.155921	−	0.0469113i
$71$	5.30009	−	5.30009i	0.629005	−	0.629005i	−0.318813	−	0.947818i	$-0.603284\pi$
$71$	5.30009	−	5.30009i	0.629005	−	0.629005i	0.947818	+	0.318813i	$0.103284\pi$
$72$		0			0
$73$	3.04174	−	3.04174i	0.356009	−	0.356009i	−0.506330	−	0.862340i	$-0.668998\pi$
$73$	3.04174	−	3.04174i	0.356009	−	0.356009i	0.862340	+	0.506330i	$0.168998\pi$
$74$	3.17525	+	5.90813i	0.369116	+	0.686806i
$75$		0			0
$76$	3.01040	+	14.7827i	0.345317	+	1.69569i
$77$	11.3593			1.29451
$78$		0			0
$79$		−	16.2639i		−	1.82983i	−0.403642	−	0.914917i	$-0.632256\pi$
$79$		−	16.2639i		−	1.82983i	0.403642	−	0.914917i	$-0.367744\pi$
$80$	−1.43597	−	0.579554i	−0.160546	−	0.0647961i
$81$		0			0
$82$	−1.22462	−	2.27862i	−0.135236	−	0.251631i
$83$	2.81374	+	2.81374i	0.308848	+	0.308848i	0.844463	−	0.535615i	$-0.179920\pi$
$83$	2.81374	+	2.81374i	0.308848	+	0.308848i	−0.535615	+	0.844463i	$0.679920\pi$
$84$		0			0
$85$	0.598861	+	0.598861i	0.0649556	+	0.0649556i
$86$	−1.06016	+	3.52370i	−0.114320	+	0.379971i
$87$		0			0
$88$	12.8582	+	1.17792i	1.37069	+	0.125567i
$89$	0.702659	−	0.702659i	0.0744817	−	0.0744817i	−0.668885	−	0.743366i	$-0.733228\pi$
$89$	0.702659	−	0.702659i	0.0744817	−	0.0744817i	0.743366	+	0.668885i	$0.233228\pi$
$90$		0			0
$91$	3.30997	−	8.33877i	0.346979	−	0.874140i
$92$	−11.2734	−	7.45868i	−1.17533	−	0.777622i
$93$		0			0
$94$	−7.20583	−	13.4077i	−0.743224	−	1.38290i
$95$	−2.92012			−0.299598
$96$		0			0
$97$	−3.22944	−	3.22944i	−0.327900	−	0.327900i	0.523888	−	0.851787i	$-0.324481\pi$
$97$	−3.22944	−	3.22944i	−0.327900	−	0.327900i	−0.851787	+	0.523888i	$0.824481\pi$
$98$	0.329375	−	1.09476i	0.0332719	−	0.110587i
$99$		0			0
$100$	−5.35245	+	8.08990i	−0.535245	+	0.808990i
$101$	−12.6936			−1.26306			−0.631528	−	0.775353i	$-0.717572\pi$
$101$	−12.6936			−1.26306			−0.631528	+	0.775353i	$0.717572\pi$
$102$		0			0
$103$	−10.4036			−1.02510			−0.512548	−	0.858659i	$-0.671298\pi$
$103$	−10.4036			−1.02510			−0.512548	+	0.858659i	$0.671298\pi$
$104$	4.61144	−	9.09586i	0.452188	−	0.891922i
$105$		0			0
$106$	−4.75387	+	15.8006i	−0.461737	+	1.53469i
$107$	−9.91564			−0.958581			−0.479291	−	0.877656i	$-0.659106\pi$
$107$	−9.91564			−0.958581			−0.479291	+	0.877656i	$0.659106\pi$
$108$		0			0
$109$	−8.34923	+	8.34923i	−0.799711	+	0.799711i	−0.983050	−	0.183338i	$-0.941310\pi$
$109$	−8.34923	+	8.34923i	−0.799711	+	0.799711i	0.183338	+	0.983050i	$0.441310\pi$
$110$	−0.720069	+	2.39333i	−0.0686559	+	0.228195i
$111$		0			0
$112$	−3.72513	+	9.22980i	−0.351992	+	0.872134i
$113$	−3.60085			−0.338739			−0.169370	−	0.985553i	$-0.554173\pi$
$113$	−3.60085			−0.338739			−0.169370	+	0.985553i	$0.554173\pi$
$114$		0			0
$115$	1.85013	−	1.85013i	0.172526	−	0.172526i
$116$	0.264087	−	0.399152i	0.0245199	−	0.0370604i
$117$		0			0
$118$	16.7030	−	8.97682i	1.53763	−	0.826383i
$119$	3.84923	−	3.84923i	0.352858	−	0.352858i
$120$		0			0
$121$		−	9.84005i		−	0.894550i
$122$	0.599945	−	1.99406i	0.0543165	−	0.180534i
$123$		0			0
$124$	−4.87650	+	0.993070i	−0.437923	+	0.0891803i
$125$	−2.69638	−	2.69638i	−0.241172	−	0.241172i
$126$		0			0
$127$	4.03065			0.357662			0.178831	−	0.983880i	$-0.442768\pi$
$127$	4.03065			0.357662			0.178831	+	0.983880i	$0.442768\pi$
$128$	−5.17377	+	10.0614i	−0.457301	+	0.889312i
$129$		0			0
$130$	1.54710	+	1.22599i	0.135690	+	0.107526i
$131$	−6.67425			−0.583132			−0.291566	−	0.956551i	$-0.594176\pi$
$131$	−6.67425			−0.583132			−0.291566	+	0.956551i	$0.594176\pi$
$132$		0			0
$133$			18.7693i			1.62751i
$134$	−7.51353	−	13.9803i	−0.649070	−	1.20771i
$135$		0			0
$136$	4.75630	−	3.95799i	0.407849	−	0.339395i
$137$	−8.50127	+	8.50127i	−0.726312	+	0.726312i	−0.969883	−	0.243571i	$-0.921681\pi$
$137$	−8.50127	+	8.50127i	−0.726312	+	0.726312i	0.243571	+	0.969883i	$0.421681\pi$
$138$		0			0
$139$	−0.357408			−0.0303149			−0.0151575	−	0.999885i	$-0.504825\pi$
$139$	−0.357408			−0.0303149			−0.0151575	+	0.999885i	$0.504825\pi$
$140$	−1.60674	−	1.06305i	−0.135794	−	0.0898444i
$141$		0			0
$142$	9.33713	−	5.01813i	0.783555	−	0.421112i
$143$	−15.2985	−	6.07256i	−1.27933	−	0.507813i
$144$		0			0
$145$	0.0655071	+	0.0655071i	0.00544007	+	0.00544007i
$146$	5.35862	−	2.87993i	0.443483	−	0.238345i
$147$		0			0
$148$	1.89283	+	9.29482i	0.155590	+	0.764029i
$149$	0.325120	−	0.325120i	0.0266349	−	0.0266349i	−0.693664	−	0.720299i	$-0.744005\pi$
$149$	0.325120	−	0.325120i	0.0266349	−	0.0266349i	0.720299	+	0.693664i	$0.244005\pi$
$150$		0			0
$151$	−11.3804	−	11.3804i	−0.926126	−	0.926126i	0.0713267	−	0.997453i	$-0.477277\pi$
$151$	−11.3804	−	11.3804i	−0.926126	−	0.926126i	−0.997453	+	0.0713267i	$0.977277\pi$
$152$	−1.94632	+	21.2460i	−0.157867	+	1.72328i
$153$		0			0
$154$	15.3833	+	4.62830i	1.23962	+	0.372959i
$155$		−	0.963288i		−	0.0773731i
$156$		0			0
$157$		−	16.2487i		−	1.29679i	−0.761303	−	0.648396i	$-0.775440\pi$
$157$		−	16.2487i		−	1.29679i	0.761303	−	0.648396i	$-0.224560\pi$
$158$	6.62668	−	22.0254i	0.527190	−	1.75224i
$159$		0			0
$160$	−1.70852	−	1.36994i	−0.135070	−	0.108303i
$161$	−11.8919	−	11.8919i	−0.937211	−	0.937211i
$162$		0			0
$163$	11.3489	−	11.3489i	0.888911	−	0.888911i	−0.105508	−	0.994418i	$-0.533647\pi$
$163$	11.3489	−	11.3489i	0.888911	−	0.888911i	0.994418	+	0.105508i	$0.0336468\pi$
$164$	−0.730018	−	3.58478i	−0.0570049	−	0.279924i
$165$		0			0
$166$	2.66405	+	4.95695i	0.206771	+	0.384734i
$167$	10.8504	+	10.8504i	0.839631	+	0.839631i	0.988810	−	0.149179i	$-0.0476630\pi$
$167$	10.8504	+	10.8504i	0.839631	+	0.839631i	−0.149179	+	0.988810i	$0.547663\pi$
$168$		0			0
$169$	−8.91564	+	9.46105i	−0.685818	+	0.727773i
$170$	0.567002	+	1.05501i	0.0434871	+	0.0809156i
$171$		0			0
$172$	−2.87144	+	4.34001i	−0.218945	+	0.330923i
$173$	15.4648			1.17577			0.587885	−	0.808944i	$-0.299961\pi$
$173$	15.4648			1.17577			0.587885	+	0.808944i	$0.299961\pi$
$174$		0			0
$175$	−8.53376	+	8.53376i	−0.645092	+	0.645092i
$176$	16.9332	+	6.83422i	1.27639	+	0.515149i
$177$		0			0
$178$	1.23787	−	0.665278i	0.0927823	−	0.0498647i
$179$		−	11.8652i		−	0.886850i	−0.896311	−	0.443425i	$-0.853763\pi$
$179$		−	11.8652i		−	0.886850i	0.896311	−	0.443425i	$-0.146237\pi$
$180$		0			0
$181$	23.5146			1.74783			0.873913	−	0.486083i	$-0.161575\pi$
$181$	23.5146			1.74783			0.873913	+	0.486083i	$0.161575\pi$
$182$	7.88012	−	9.94412i	0.584114	−	0.737107i
$183$		0			0
$184$	−12.2279	−	14.6942i	−0.901453	−	1.08327i
$185$	−1.83607			−0.134990
$186$		0			0
$187$	−7.06189	−	7.06189i	−0.516417	−	0.516417i
$188$	−4.29554	−	21.0934i	−0.313285	−	1.53839i
$189$		0			0
$190$	−3.95457	−	1.18979i	−0.286894	−	0.0863166i
$191$			4.77834i			0.345748i	0.984944	+	0.172874i	$0.0553054\pi$
$191$			4.77834i			0.345748i	−0.984944	+	0.172874i	$0.944695\pi$
$192$		0			0
$193$	−8.23161	+	8.23161i	−0.592524	+	0.592524i	−0.938312	−	0.345789i	$-0.887611\pi$
$193$	−8.23161	+	8.23161i	−0.592524	+	0.592524i	0.345789	+	0.938312i	$0.387611\pi$
$194$	−3.05764	−	5.68929i	−0.219526	−	0.408467i
$195$		0			0
$196$	0.892110	−	1.34837i	0.0637221	−	0.0963121i
$197$	2.67116	−	2.67116i	0.190312	−	0.190312i	−0.605519	−	0.795831i	$-0.707034\pi$
$197$	2.67116	−	2.67116i	0.190312	−	0.190312i	0.795831	+	0.605519i	$0.207034\pi$
$198$		0			0
$199$	−6.54186			−0.463740			−0.231870	−	0.972747i	$-0.574484\pi$
$199$	−6.54186			−0.463740			−0.231870	+	0.972747i	$0.574484\pi$
$200$	−10.5447	+	8.77489i	−0.745626	+	0.620479i
$201$		0			0
$202$	−17.1902	−	5.17194i	−1.20950	−	0.363897i
$203$	0.421052	−	0.421052i	0.0295521	−	0.0295521i
$204$		0			0
$205$	0.708125			0.0494576
$206$	−14.0890	−	4.23890i	−0.981630	−	0.295338i
$207$		0			0
$208$	9.95110	−	10.4391i	0.689985	−	0.723824i
$209$	34.4347			2.38190
$210$		0			0
$211$	3.19386			0.219874			0.109937	−	0.993939i	$-0.464935\pi$
$211$	3.19386			0.219874			0.109937	+	0.993939i	$0.464935\pi$
$212$	−12.8758	+	19.4610i	−0.884316	+	1.33659i
$213$		0			0
$214$	−13.4282	−	4.04009i	−0.917935	−	0.276175i
$215$	−0.712263	−	0.712263i	−0.0485759	−	0.0485759i
$216$		0			0
$217$	−6.19161			−0.420314
$218$	−14.7088	+	7.90507i	−0.996205	+	0.535399i
$219$		0			0
$220$	−1.95030	+	2.94777i	−0.131489	+	0.198738i
$221$	−7.24184	+	3.12632i	−0.487139	+	0.210299i
$222$		0			0
$223$	−2.23810	+	2.23810i	−0.149874	+	0.149874i	−0.778062	−	0.628188i	$-0.783797\pi$
$223$	−2.23810	+	2.23810i	−0.149874	+	0.149874i	0.628188	+	0.778062i	$0.283797\pi$
$224$	−8.80540	+	10.9816i	−0.588335	+	0.733742i
$225$		0			0
$226$	−4.87644	−	1.46715i	−0.324376	−	0.0975935i
$227$	0.434431	+	0.434431i	0.0288342	+	0.0288342i	0.721377	−	0.692543i	$-0.243510\pi$
$227$	0.434431	+	0.434431i	0.0288342	+	0.0288342i	−0.692543	+	0.721377i	$0.743510\pi$
$228$		0			0
$229$	12.0455	+	12.0455i	0.795989	+	0.795989i	0.982460	−	0.186472i	$-0.0597052\pi$
$229$	12.0455	+	12.0455i	0.795989	+	0.795989i	−0.186472	+	0.982460i	$0.559705\pi$
$230$	3.25937	−	1.75171i	0.214916	−	0.115504i
$231$		0			0
$232$	0.520273	−	0.432950i	0.0341576	−	0.0284245i
$233$			8.29495i			0.543420i	0.962379	+	0.271710i	$0.0875892\pi$
$233$			8.29495i			0.543420i	−0.962379	+	0.271710i	$0.912411\pi$
$234$		0			0
$235$	4.16672			0.271807
$236$	26.2776	−	5.35127i	1.71052	−	0.348338i
$237$		0			0
$238$	6.78116	−	3.64445i	0.439558	−	0.236235i
$239$	−6.22920	+	6.22920i	−0.402933	+	0.402933i	−0.879265	−	0.476332i	$-0.841966\pi$
$239$	−6.22920	+	6.22920i	−0.402933	+	0.402933i	0.476332	+	0.879265i	$0.341966\pi$
$240$		0			0
$241$	2.37756	−	2.37756i	0.153152	−	0.153152i	−0.626372	−	0.779524i	$-0.715461\pi$
$241$	2.37756	−	2.37756i	0.153152	−	0.153152i	0.779524	+	0.626372i	$0.215461\pi$
$242$	4.00929	−	13.3259i	0.257727	−	0.856619i
$243$		0			0
$244$	1.62495	−	2.45601i	0.104027	−	0.157230i
$245$	0.221288	+	0.221288i	0.0141376	+	0.0141376i
$246$		0			0
$247$	10.0339	−	25.2782i	0.638441	−	1.60841i
$248$	−7.00861	−	0.642050i	−0.445047	−	0.0407702i
$249$		0			0
$250$	−2.55294	−	4.75020i	−0.161462	−	0.300429i
$251$		−	6.08062i		−	0.383806i	−0.981414	−	0.191903i	$-0.938534\pi$
$251$		−	6.08062i		−	0.383806i	0.981414	−	0.191903i	$-0.0614658\pi$
$252$		0			0
$253$	−21.8171	+	21.8171i	−1.37163	+	1.37163i
$254$	5.45850	+	1.64227i	0.342496	+	0.103045i
$255$		0			0
$256$	−11.1061	+	11.5176i	−0.694129	+	0.719851i
$257$		−	10.6271i		−	0.662903i	−0.943472	−	0.331452i	$-0.892462\pi$
$257$		−	10.6271i		−	0.662903i	0.943472	−	0.331452i	$-0.107538\pi$
$258$		0			0
$259$			11.8015i			0.733308i
$260$	1.59564	+	2.29065i	0.0989571	+	0.142060i
$261$		0			0
$262$	−9.03859	−	2.71940i	−0.558406	−	0.168005i
$263$			7.34200i			0.452727i	0.974043	+	0.226364i	$0.0726838\pi$
$263$			7.34200i			0.452727i	−0.974043	+	0.226364i	$0.927316\pi$
$264$		0			0
$265$	−3.19386	−	3.19386i	−0.196197	−	0.196197i
$266$	−7.64749	+	25.4183i	−0.468898	+	1.55850i
$267$		0			0
$268$	−4.47897	−	21.9941i	−0.273597	−	1.34350i
$269$			7.05046i			0.429874i	0.976628	+	0.214937i	$0.0689547\pi$
$269$			7.05046i			0.429874i	−0.976628	+	0.214937i	$0.931045\pi$
$270$		0			0
$271$	−10.1872	−	10.1872i	−0.618830	−	0.618830i	0.326401	−	0.945231i	$-0.394164\pi$
$271$	−10.1872	−	10.1872i	−0.618830	−	0.618830i	−0.945231	+	0.326401i	$0.894164\pi$
$272$	8.05388	−	3.42217i	0.488338	−	0.207499i
$273$		0			0
$274$	−14.9766	+	8.04901i	−0.904772	+	0.486259i
$275$	15.6563	+	15.6563i	0.944108	+	0.944108i
$276$		0			0
$277$	17.5316			1.05337			0.526687	−	0.850059i	$-0.323434\pi$
$277$	17.5316			1.05337			0.526687	+	0.850059i	$0.323434\pi$
$278$	−0.484018	−	0.145624i	−0.0290295	−	0.00873397i
$279$		0			0
$280$	−1.74279	−	2.09430i	−0.104151	−	0.125158i
$281$	−14.4169	+	14.4169i	−0.860041	+	0.860041i	−0.991342	−	0.131302i	$-0.958084\pi$
$281$	−14.4169	+	14.4169i	−0.860041	+	0.860041i	0.131302	+	0.991342i	$0.458084\pi$
$282$		0			0
$283$		−	32.4691i		−	1.93009i	−0.262086	−	0.965045i	$-0.584410\pi$
$283$		−	32.4691i		−	1.93009i	0.262086	−	0.965045i	$-0.415590\pi$
$284$	14.6894	−	2.99141i	0.871656	−	0.177508i
$285$		0			0
$286$	−18.2437	−	14.4571i	−1.07878	−	0.854865i
$287$		−	4.55153i		−	0.268668i
$288$		0			0
$289$	12.2140			0.718470
$290$	0.0620222	+	0.115403i	0.00364207	+	0.00677673i
$291$		0			0
$292$	8.43032	−	1.71678i	0.493347	−	0.100467i
$293$	−16.5624	−	16.5624i	−0.967588	−	0.967588i	0.0319027	−	0.999491i	$-0.489843\pi$
$293$	−16.5624	−	16.5624i	−0.967588	−	0.967588i	−0.999491	+	0.0319027i	$0.989843\pi$
$294$		0			0
$295$			5.19078i			0.302219i
$296$	−1.22377	+	13.3587i	−0.0711304	+	0.776459i
$297$		0			0
$298$	0.572763	−	0.307824i	0.0331793	−	0.0178318i
$299$	9.65852	+	22.3731i	0.558567	+	1.29387i
$300$		0			0
$301$	−4.57813	+	4.57813i	−0.263879	+	0.263879i
$302$	−10.7750	−	20.0488i	−0.620032	−	1.15368i
$303$		0			0
$304$	−11.2924	+	27.9793i	−0.647663	+	1.60472i
$305$	0.403070	+	0.403070i	0.0230797	+	0.0230797i
$306$		0			0
$307$	−12.1539	+	12.1539i	−0.693662	+	0.693662i	−0.963036	−	0.269374i	$-0.913183\pi$
$307$	−12.1539	+	12.1539i	−0.693662	+	0.693662i	0.269374	+	0.963036i	$0.413183\pi$
$308$	18.9470	+	12.5357i	1.07961	+	0.714290i
$309$		0			0
$310$	0.392488	−	1.30453i	0.0222918	−	0.0740924i
$311$	31.7700			1.80151			0.900755	−	0.434328i	$-0.143014\pi$
$311$	31.7700			1.80151			0.900755	+	0.434328i	$0.143014\pi$
$312$		0			0
$313$	−31.0473			−1.75490			−0.877449	−	0.479669i	$-0.840757\pi$
$313$	−31.0473			−1.75490			−0.877449	+	0.479669i	$0.840757\pi$
$314$	6.62050	−	22.0048i	0.373616	−	1.24180i
$315$		0			0
$316$	17.9483	−	27.1278i	1.00967	−	1.52606i
$317$	−1.06867	+	1.06867i	−0.0600226	+	0.0600226i	−0.736481	−	0.676458i	$-0.763514\pi$
$317$	−1.06867	+	1.06867i	−0.0600226	+	0.0600226i	0.676458	+	0.736481i	$0.263514\pi$
$318$		0			0
$319$	−0.772473	−	0.772473i	−0.0432502	−	0.0432502i
$320$	−1.75558	−	2.55137i	−0.0981400	−	0.142626i
$321$		0			0
$322$	−11.2592	−	20.9499i	−0.627453	−	1.16749i
$323$	11.6686	−	11.6686i	0.649257	−	0.649257i
$324$		0			0
$325$	16.0552	−	6.93108i	0.890582	−	0.384467i
$326$	19.9932	−	10.7451i	1.10732	−	0.595117i
$327$		0			0
$328$	0.471979	−	5.15212i	0.0260607	−	0.284478i
$329$		−	26.7819i		−	1.47654i
$330$		0			0
$331$	23.2735	+	23.2735i	1.27923	+	1.27923i	0.941100	+	0.338127i	$0.109793\pi$
$331$	23.2735	+	23.2735i	1.27923	+	1.27923i	0.338127	+	0.941100i	$0.390207\pi$
$332$	1.58810	+	7.79839i	0.0871581	+	0.427992i
$333$		0			0
$334$	10.2732	+	19.1151i	0.562125	+	1.04593i
$335$	4.34465			0.237373
$336$		0			0
$337$		−	7.22327i		−	0.393477i	−0.980456	−	0.196738i	$-0.936965\pi$
$337$		−	7.22327i		−	0.393477i	0.980456	−	0.196738i	$-0.0630350\pi$
$338$	−15.9289	+	9.17996i	−0.866415	+	0.499324i
$339$		0			0
$340$	0.338002	+	1.65977i	0.0183307	+	0.0900136i
$341$			11.3593i			0.615140i
$342$		0			0
$343$	13.7388	−	13.7388i	0.741825	−	0.741825i
$344$	−5.65696	+	4.70749i	−0.305003	+	0.253811i
$345$		0			0
$346$	20.9432	+	6.30110i	1.12592	+	0.338749i
$347$	−22.1160			−1.18725			−0.593623	−	0.804743i	$-0.702303\pi$
$347$	−22.1160			−1.18725			−0.593623	+	0.804743i	$0.702303\pi$
$348$		0			0
$349$	7.54495	+	7.54495i	0.403872	+	0.403872i	0.879595	−	0.475723i	$-0.157814\pi$
$349$	7.54495	+	7.54495i	0.403872	+	0.403872i	−0.475723	+	0.879595i	$0.657814\pi$
$350$	−15.0339	+	8.07978i	−0.803595	+	0.431882i
$351$		0			0
$352$	20.1472	+	16.1546i	1.07385	+	0.861044i
$353$	8.70266	+	8.70266i	0.463196	+	0.463196i	0.899701	−	0.436506i	$-0.143784\pi$
$353$	8.70266	+	8.70266i	0.463196	+	0.463196i	−0.436506	+	0.899701i	$0.643784\pi$
$354$		0			0
$355$			2.90170i			0.154006i
$356$	1.94745	−	0.396586i	0.103215	−	0.0210190i
$357$		0			0
$358$	4.83445	−	16.0685i	0.255509	−	0.849246i
$359$	−15.0569	−	15.0569i	−0.794672	−	0.794672i	0.187578	−	0.982250i	$-0.439936\pi$
$359$	−15.0569	−	15.0569i	−0.794672	−	0.794672i	−0.982250	+	0.187578i	$0.939936\pi$
$360$		0			0
$361$			37.8975i			1.99460i
$362$	31.8446	+	9.58093i	1.67371	+	0.503563i
$363$		0			0
$364$	14.7233	−	10.2561i	0.771713	−	0.537565i
$365$			1.66530i			0.0871657i
$366$		0			0
$367$			9.34625i			0.487870i	0.969792	+	0.243935i	$0.0784384\pi$
$367$			9.34625i			0.487870i	−0.969792	+	0.243935i	$0.921562\pi$
$368$	−10.5725	−	24.8818i	−0.551130	−	1.29705i
$369$		0			0
$370$	−2.48649	−	0.748099i	−0.129266	−	0.0388918i
$371$	−20.5288	+	20.5288i	−1.06580	+	1.06580i
$372$		0			0
$373$			13.7080i			0.709776i	0.934909	+	0.354888i	$0.115481\pi$
$373$			13.7080i			0.709776i	−0.934909	+	0.354888i	$0.884519\pi$
$374$	−6.68621	−	12.4409i	−0.345736	−	0.643303i
$375$		0			0
$376$	2.77720	−	30.3159i	0.143223	−	1.56342i
$377$	−0.792157	+	0.341976i	−0.0407982	+	0.0176127i
$378$		0			0
$379$	12.8046	+	12.8046i	0.657726	+	0.657726i	0.954842	−	0.297116i	$-0.0960246\pi$
$379$	12.8046	+	12.8046i	0.657726	+	0.657726i	−0.297116	+	0.954842i	$0.596025\pi$
$380$	−4.87069	−	3.22255i	−0.249861	−	0.165313i
$381$		0			0
$382$	−1.94692	+	6.47105i	−0.0996129	+	0.331088i
$383$	3.65583	−	3.65583i	0.186804	−	0.186804i	−0.607509	−	0.794313i	$-0.707831\pi$
$383$	3.65583	−	3.65583i	0.186804	−	0.186804i	0.794313	+	0.607509i	$0.207831\pi$
$384$		0			0
$385$	−3.10950	+	3.10950i	−0.158475	+	0.158475i
$386$	−14.5016	+	7.79370i	−0.738111	+	0.396689i
$387$		0			0
$388$	−1.82272	−	8.95053i	−0.0925346	−	0.454394i
$389$	17.1554			0.869813			0.434906	−	0.900476i	$-0.356781\pi$
$389$	17.1554			0.869813			0.434906	+	0.900476i	$0.356781\pi$
$390$		0			0
$391$			14.7860i			0.747759i
$392$	1.75753	−	1.46254i	0.0887685	−	0.0738694i
$393$		0			0
$394$	4.70577	−	2.52906i	0.237073	−	0.127412i
$395$	4.45209	+	4.45209i	0.224009	+	0.224009i
$396$		0			0
$397$	7.76633	+	7.76633i	0.389781	+	0.389781i	0.874609	−	0.484829i	$-0.161118\pi$
$397$	7.76633	+	7.76633i	0.389781	+	0.389781i	−0.484829	+	0.874609i	$0.661118\pi$
$398$	−8.85930	−	2.66546i	−0.444077	−	0.133607i
$399$		0			0
$400$	−17.8555	+	7.58696i	−0.892774	+	0.379348i
$401$	−26.6147	+	26.6147i	−1.32907	+	1.32907i	−0.422894	+	0.906179i	$0.638986\pi$
$401$	−26.6147	+	26.6147i	−1.32907	+	1.32907i	−0.906179	+	0.422894i	$0.861014\pi$
$402$		0			0
$403$	8.33877	+	3.30997i	0.415384	+	0.164881i
$404$	−21.1725	−	14.0082i	−1.05337	−	0.696934i
$405$		0			0
$406$	0.741765	−	0.398653i	0.0368132	−	0.0197848i
$407$	21.6513			1.07321
$408$		0			0
$409$	−5.43112	−	5.43112i	−0.268551	−	0.268551i	0.559965	−	0.828516i	$-0.310815\pi$
$409$	−5.43112	−	5.43112i	−0.268551	−	0.268551i	−0.828516	+	0.559965i	$0.810815\pi$
$410$	0.958977	+	0.288523i	0.0473605	+	0.0142491i
$411$		0			0
$412$	−17.3529	−	11.4811i	−0.854917	−	0.565631i
$413$	33.3642			1.64174
$414$		0			0
$415$	−1.54047			−0.0756186
$416$	17.7296	−	10.0826i	0.869268	−	0.494342i
$417$		0			0
$418$	46.6331	+	14.0303i	2.28090	+	0.686243i
$419$	1.40140			0.0684629			0.0342314	−	0.999414i	$-0.489102\pi$
$419$	1.40140			0.0684629			0.0342314	+	0.999414i	$0.489102\pi$
$420$		0			0
$421$	20.5866	−	20.5866i	1.00333	−	1.00333i	0.00333710	−	0.999994i	$-0.498938\pi$
$421$	20.5866	−	20.5866i	1.00333	−	1.00333i	0.999994	−	0.00333710i	$-0.00106223\pi$
$422$	4.32528	+	1.30133i	0.210551	+	0.0633476i
$423$		0			0
$424$	−25.3664	+	21.1089i	−1.23190	+	1.02514i
$425$	10.6106			0.514690
$426$		0			0
$427$	2.59076	−	2.59076i	0.125376	−	0.125376i
$428$	−16.5390	−	10.9426i	−0.799445	−	0.528929i
$429$		0			0
$430$	−0.674372	−	1.25479i	−0.0325211	−	0.0605113i
$431$	−25.8032	+	25.8032i	−1.24290	+	1.24290i	−0.284104	+	0.958793i	$0.591696\pi$
$431$	−25.8032	+	25.8032i	−1.24290	+	1.24290i	−0.958793	+	0.284104i	$0.908304\pi$
$432$		0			0
$433$			24.9806i			1.20049i	0.799815	+	0.600246i	$0.204931\pi$
$433$			24.9806i			1.20049i	−0.799815	+	0.600246i	$0.795069\pi$
$434$	−8.38498	−	2.52275i	−0.402492	−	0.121096i
$435$		0			0
$436$	−23.1402	+	4.71237i	−1.10822	+	0.225682i
$437$	−36.0491	−	36.0491i	−1.72446	−	1.72446i
$438$		0			0
$439$	24.4346			1.16620			0.583100	−	0.812401i	$-0.301840\pi$
$439$	24.4346			1.16620			0.583100	+	0.812401i	$0.301840\pi$
$440$	−3.84225	+	3.19736i	−0.183172	+	0.152428i
$441$		0			0
$442$	−11.0811	+	1.28315i	−0.527072	+	0.0610334i
$443$	−18.3745			−0.873000			−0.436500	−	0.899704i	$-0.643782\pi$
$443$	−18.3745			−0.873000			−0.436500	+	0.899704i	$0.643782\pi$
$444$		0			0
$445$			0.384692i			0.0182362i
$446$	−3.94284	+	2.11903i	−0.186699	+	0.100339i
$447$		0			0
$448$	−16.3991	+	11.2841i	−0.774786	+	0.533126i
$449$	−2.60237	+	2.60237i	−0.122813	+	0.122813i	−0.765842	−	0.643029i	$-0.777678\pi$
$449$	−2.60237	+	2.60237i	−0.122813	+	0.122813i	0.643029	+	0.765842i	$0.277678\pi$
$450$		0			0
$451$	−8.35036			−0.393203
$452$	−6.00612	−	3.97378i	−0.282504	−	0.186911i
$453$		0			0
$454$	0.411320	+	0.765335i	0.0193042	+	0.0359189i
$455$	1.37659	+	3.18873i	0.0645353	+	0.149490i
$456$		0			0
$457$	25.2812	+	25.2812i	1.18261	+	1.18261i	0.979067	+	0.203540i	$0.0652448\pi$
$457$	25.2812	+	25.2812i	1.18261	+	1.18261i	0.203540	+	0.979067i	$0.434755\pi$
$458$	11.4047	+	21.2205i	0.532906	+	0.991568i
$459$		0			0
$460$	5.12772	−	1.04423i	0.239081	−	0.0486874i
$461$	−6.82810	+	6.82810i	−0.318016	+	0.318016i	−0.848005	−	0.529989i	$-0.822196\pi$
$461$	−6.82810	+	6.82810i	−0.318016	+	0.318016i	0.529989	+	0.848005i	$0.322196\pi$
$462$		0			0
$463$	−22.9626	−	22.9626i	−1.06716	−	1.06716i	−0.997576	−	0.0695868i	$-0.977832\pi$
$463$	−22.9626	−	22.9626i	−1.06716	−	1.06716i	−0.0695868	−	0.997576i	$-0.522168\pi$
$464$	0.880982	−	0.374338i	0.0408986	−	0.0173782i
$465$		0			0
$466$	−3.37975	+	11.2334i	−0.156564	+	0.520378i
$467$		−	31.5214i		−	1.45864i	−0.684173	−	0.729319i	$-0.739837\pi$
$467$		−	31.5214i		−	1.45864i	0.684173	−	0.729319i	$-0.260163\pi$
$468$		0			0
$469$		−	27.9256i		−	1.28948i
$470$	5.64277	+	1.69771i	0.260282	+	0.0783097i
$471$		0			0
$472$	37.7667	+	3.45976i	1.73835	+	0.159248i
$473$	8.39915	+	8.39915i	0.386193	+	0.386193i
$474$		0			0
$475$	−25.8693	+	25.8693i	−1.18697	+	1.18697i
$476$	10.6683	−	2.17253i	0.488981	−	0.0995780i
$477$		0			0
$478$	−10.9739	+	5.89781i	−0.501936	+	0.269760i
$479$	5.14345	+	5.14345i	0.235010	+	0.235010i	0.814780	−	0.579770i	$-0.196858\pi$
$479$	5.14345	+	5.14345i	0.235010	+	0.235010i	−0.579770	+	0.814780i	$0.696858\pi$
$480$		0			0
$481$	6.30895	−	15.8940i	0.287663	−	0.724706i
$482$	4.18853	−	2.25107i	0.190782	−	0.102534i
$483$		0			0
$484$	10.8592	−	16.4130i	0.493598	−	0.746043i
$485$	1.76806			0.0802834
$486$		0			0
$487$	−16.3140	+	16.3140i	−0.739257	+	0.739257i	−0.972434	−	0.233177i	$-0.925088\pi$
$487$	−16.3140	+	16.3140i	−0.739257	+	0.739257i	0.233177	+	0.972434i	$0.425088\pi$
$488$	3.20128	−	2.66397i	0.144915	−	0.120592i
$489$		0			0
$490$	0.209516	+	0.389843i	0.00946498	+	0.0176113i
$491$			28.9725i			1.30751i	0.756706	+	0.653755i	$0.226807\pi$
$491$			28.9725i			1.30751i	−0.756706	+	0.653755i	$0.773193\pi$
$492$		0			0
$493$	−0.523523			−0.0235783
$494$	23.8879	−	30.1447i	1.07477	−	1.35627i
$495$		0			0
$496$	−9.22980	−	3.72513i	−0.414430	−	0.167263i
$497$	18.6509			0.836607
$498$		0			0
$499$	−6.81836	−	6.81836i	−0.305232	−	0.305232i	0.537825	−	0.843057i	$-0.319246\pi$
$499$	−6.81836	−	6.81836i	−0.305232	−	0.305232i	−0.843057	+	0.537825i	$0.819246\pi$
$500$	−1.52186	−	7.47313i	−0.0680596	−	0.334209i
$501$		0			0
$502$	2.47753	−	8.23467i	0.110577	−	0.367531i
$503$		−	10.1216i		−	0.451298i	−0.974209	−	0.225649i	$-0.927550\pi$
$503$		−	10.1216i		−	0.451298i	0.974209	−	0.225649i	$-0.0724503\pi$
$504$		0			0
$505$	3.47474	−	3.47474i	0.154624	−	0.154624i
$506$	−38.4351	+	20.6565i	−1.70865	+	0.918294i
$507$		0			0
$508$	6.72302	+	4.44809i	0.298286	+	0.197352i
$509$	16.1690	−	16.1690i	0.716678	−	0.716678i	−0.251245	−	0.967923i	$-0.580840\pi$
$509$	16.1690	−	16.1690i	0.716678	−	0.716678i	0.967923	+	0.251245i	$0.0808400\pi$
$510$		0			0
$511$	10.7038			0.473510
$512$	−19.7332	+	11.0726i	−0.872091	+	0.489344i
$513$		0			0
$514$	4.32999	−	14.3918i	0.190988	−	0.634795i
$515$	2.84788	−	2.84788i	0.125493	−	0.125493i
$516$		0			0
$517$	−49.1348			−2.16095
$518$	−4.80847	+	15.9821i	−0.211272	+	0.702214i
$519$		0			0
$520$	1.22757	+	3.75224i	0.0538325	+	0.164547i
$521$	−10.5425			−0.461875			−0.230938	−	0.972969i	$-0.574179\pi$
$521$	−10.5425			−0.461875			−0.230938	+	0.972969i	$0.574179\pi$
$522$		0			0
$523$	−25.4062			−1.11093			−0.555467	−	0.831538i	$-0.687461\pi$
$523$	−25.4062			−1.11093			−0.555467	+	0.831538i	$0.687461\pi$
$524$	−11.1325	−	7.36549i	−0.486325	−	0.321763i
$525$		0			0
$526$	−2.99147	+	9.94289i	−0.130434	+	0.433531i
$527$	3.84923	+	3.84923i	0.167675	+	0.167675i
$528$		0			0
$529$	22.6801			0.986091
$530$	−3.02395	−	5.62661i	−0.131352	−	0.244404i
$531$		0			0
$532$	−20.7132	+	31.3067i	−0.898031	+	1.35732i
$533$	−2.43320	+	6.12993i	−0.105394	+	0.265517i
$534$		0			0
$535$	2.71431	−	2.71431i	0.117350	−	0.117350i
$536$	2.89579	−	31.6104i	0.125079	−	1.36536i
$537$		0			0
$538$	−2.87269	+	9.54807i	−0.123850	+	0.411647i
$539$	−2.60948	−	2.60948i	−0.112398	−	0.112398i
$540$		0			0
$541$	−29.5292	−	29.5292i	−1.26956	−	1.26956i	−0.946316	−	0.323244i	$-0.895227\pi$
$541$	−29.5292	−	29.5292i	−1.26956	−	1.26956i	−0.323244	−	0.946316i	$-0.604773\pi$
$542$	−9.64529	−	17.9468i	−0.414301	−	0.770881i
$543$		0			0
$544$	12.3013	−	1.35294i	0.527414	−	0.0580068i
$545$		−	4.57105i		−	0.195802i
$546$		0			0
$547$	15.7462			0.673259			0.336630	−	0.941637i	$-0.390713\pi$
$547$	15.7462			0.673259			0.336630	+	0.941637i	$0.390713\pi$
$548$	−23.5616	+	4.79818i	−1.00650	+	0.204968i
$549$		0			0
$550$	14.8234	+	27.5815i	0.632071	+	1.17608i
$551$	1.27638	−	1.27638i	0.0543757	−	0.0543757i
$552$		0			0
$553$	28.6162	−	28.6162i	1.21688	−	1.21688i
$554$	23.7422	+	7.14320i	1.00871	+	0.303486i
$555$		0			0
$556$	−0.596147	−	0.394423i	−0.0252823	−	0.0167273i
$557$	28.9539	+	28.9539i	1.22682	+	1.22682i	0.965162	+	0.261654i	$0.0842679\pi$
$557$	28.9539	+	28.9539i	1.22682	+	1.22682i	0.261654	+	0.965162i	$0.415732\pi$
$558$		0			0
$559$	8.61317	−	3.71833i	0.364298	−	0.157269i
$560$	−1.50685	−	3.54629i	−0.0636761	−	0.149858i
$561$		0			0
$562$	−25.3982	+	13.6499i	−1.07136	+	0.575788i
$563$			14.4177i			0.607633i	0.952731	+	0.303816i	$0.0982610\pi$
$563$			14.4177i			0.607633i	−0.952731	+	0.303816i	$0.901739\pi$
$564$		0			0
$565$	0.985698	−	0.985698i	0.0414686	−	0.0414686i
$566$	13.2294	−	43.9712i	0.556074	−	1.84825i
$567$		0			0
$568$	21.1119	+	1.93404i	0.885838	+	0.0811504i
$569$			15.1969i			0.637087i	0.947908	+	0.318544i	$0.103194\pi$
$569$			15.1969i			0.637087i	−0.947908	+	0.318544i	$0.896806\pi$
$570$		0			0
$571$			2.38340i			0.0997424i	0.998756	+	0.0498712i	$0.0158811\pi$
$571$			2.38340i			0.0997424i	−0.998756	+	0.0498712i	$0.984119\pi$
$572$	−18.8161	−	27.0118i	−0.786739	−	1.12942i
$573$		0			0
$574$	1.85451	−	6.16390i	0.0774056	−	0.257276i
$575$		−	32.7806i		−	1.36705i
$576$		0			0
$577$	0.400904	+	0.400904i	0.0166898	+	0.0166898i	0.715402	−	0.698713i	$-0.246243\pi$
$577$	0.400904	+	0.400904i	0.0166898	+	0.0166898i	−0.698713	+	0.715402i	$0.746243\pi$
$578$	16.5408	+	4.97655i	0.688005	+	0.206997i
$579$		0			0
$580$	0.0369727	+	0.181556i	0.00153521	+	0.00753869i
$581$			9.90149i			0.410783i
$582$		0			0
$583$	37.6627	+	37.6627i	1.55983	+	1.55983i
$584$	12.1162	+	1.10995i	0.501374	+	0.0459302i
$585$		0			0
$586$	−15.6813	−	29.1780i	−0.647790	−	1.20533i
$587$	14.4823	+	14.4823i	0.597749	+	0.597749i	0.939713	−	0.341964i	$-0.111092\pi$
$587$	14.4823	+	14.4823i	0.597749	+	0.597749i	−0.341964	+	0.939713i	$0.611092\pi$
$588$		0			0
$589$	−18.7693			−0.773376
$590$	−2.11497	+	7.02961i	−0.0870718	+	0.289404i
$591$		0			0
$592$	−7.10025	+	17.5924i	−0.291819	+	0.723043i
$593$	−23.4172	+	23.4172i	−0.961630	+	0.961630i	−0.999291	−	0.0376610i	$-0.988009\pi$
$593$	−23.4172	+	23.4172i	−0.961630	+	0.961630i	0.0376610	+	0.999291i	$0.488009\pi$
$594$		0			0
$595$			2.10738i			0.0863942i
$596$	0.901085	−	0.183500i	0.0369099	−	0.00751647i
$597$		0			0
$598$	3.96420	+	34.2340i	0.162108	+	1.39993i
$599$			13.3632i			0.546005i	0.962013	+	0.273003i	$0.0880168\pi$
$599$			13.3632i			0.546005i	−0.962013	+	0.273003i	$0.911983\pi$
$600$		0			0
$601$	37.8658			1.54458			0.772289	−	0.635271i	$-0.219112\pi$
$601$	37.8658			1.54458			0.772289	+	0.635271i	$0.219112\pi$
$602$	−8.06526	+	4.33458i	−0.328716	+	0.176664i
$603$		0			0
$604$	−6.42320	−	31.5413i	−0.261356	−	1.28340i
$605$	2.69362	+	2.69362i	0.109511	+	0.109511i
$606$		0			0
$607$			26.8173i			1.08848i	0.838929	+	0.544241i	$0.183182\pi$
$607$			26.8173i			1.08848i	−0.838929	+	0.544241i	$0.816818\pi$
$608$	−26.6928	+	33.2899i	−1.08253	+	1.35008i
$609$		0			0
$610$	0.381627	+	0.710086i	0.0154516	+	0.0287505i
$611$	−14.3173	+	36.0695i	−0.579218	+	1.45921i
$612$		0			0
$613$	2.02228	−	2.02228i	0.0816792	−	0.0816792i	−0.665087	−	0.746766i	$-0.731605\pi$
$613$	2.02228	−	2.02228i	0.0816792	−	0.0816792i	0.746766	+	0.665087i	$0.231605\pi$
$614$	−21.4115	+	11.5074i	−0.864099	+	0.464400i
$615$		0			0
$616$	20.5513	+	24.6964i	0.828036	+	0.995046i
$617$	16.8200	+	16.8200i	0.677147	+	0.677147i	0.959354	−	0.282207i	$-0.0910664\pi$
$617$	16.8200	+	16.8200i	0.677147	+	0.677147i	−0.282207	+	0.959354i	$0.591066\pi$
$618$		0			0
$619$	−8.23170	+	8.23170i	−0.330860	+	0.330860i	−0.852913	−	0.522053i	$-0.825166\pi$
$619$	−8.23170	+	8.23170i	−0.330860	+	0.330860i	0.522053	+	0.852913i	$0.325166\pi$
$620$	1.06305	−	1.60674i	0.0426932	−	0.0645282i
$621$		0			0
$622$	43.0244	+	12.9446i	1.72512	+	0.519030i
$623$	2.47264			0.0990643
$624$		0			0
$625$	−22.7744			−0.910978
$626$	−42.0458	−	12.6501i	−1.68049	−	0.505601i
$627$		0			0
$628$	17.9316	−	27.1025i	0.715548	−	1.08151i
$629$	7.33679	−	7.33679i	0.292537	−	0.292537i
$630$		0			0
$631$	25.0108	+	25.0108i	0.995663	+	0.995663i	0.999991	−	0.00432741i	$-0.00137746\pi$
$631$	25.0108	+	25.0108i	0.995663	+	0.995663i	−0.00432741	+	0.999991i	$0.501377\pi$
$632$	35.3596	−	29.4248i	1.40653	−	1.17046i
$633$		0			0
$634$	−1.88267	+	1.01182i	−0.0747705	+	0.0401845i
$635$	−1.10335	+	1.10335i	−0.0437852	+	0.0437852i
$636$		0			0
$637$	−2.67597	+	1.15523i	−0.106026	+	0.0457717i
$638$	−0.731379	−	1.36086i	−0.0289556	−	0.0538770i
$639$		0			0
$640$	−1.33795	−	4.17049i	−0.0528870	−	0.164853i
$641$			6.52712i			0.257806i	0.991657	+	0.128903i	$0.0411455\pi$
$641$			6.52712i			0.257806i	−0.991657	+	0.128903i	$0.958854\pi$
$642$		0			0
$643$	10.6765	+	10.6765i	0.421040	+	0.421040i	0.885562	−	0.464521i	$-0.153774\pi$
$643$	10.6765	+	10.6765i	0.421040	+	0.421040i	−0.464521	+	0.885562i	$0.653774\pi$
$644$	−6.71187	−	32.9588i	−0.264485	−	1.29876i
$645$		0			0
$646$	20.5565	−	11.0478i	0.808784	−	0.434671i
$647$	38.6860			1.52090			0.760452	−	0.649394i	$-0.224978\pi$
$647$	38.6860			1.52090			0.760452	+	0.649394i	$0.224978\pi$
$648$		0			0
$649$		−	61.2108i		−	2.40273i
$650$	24.5668	−	2.84476i	0.963588	−	0.111581i
$651$		0			0
$652$	31.4538	−	6.40538i	1.23183	−	0.250854i
$653$			20.5679i			0.804883i	0.915446	+	0.402442i	$0.131838\pi$
$653$			20.5679i			0.804883i	−0.915446	+	0.402442i	$0.868162\pi$
$654$		0			0
$655$	1.82701	−	1.82701i	0.0713874	−	0.0713874i
$656$	2.73839	−	6.78494i	0.106916	−	0.264908i
$657$		0			0
$658$	10.9122	−	36.2694i	0.425402	−	1.41393i
$659$	43.3731			1.68958			0.844789	−	0.535100i	$-0.179726\pi$
$659$	43.3731			1.68958			0.844789	+	0.535100i	$0.179726\pi$
$660$		0			0
$661$	−16.4842	−	16.4842i	−0.641162	−	0.641162i	0.309679	−	0.950841i	$-0.399778\pi$
$661$	−16.4842	−	16.4842i	−0.641162	−	0.641162i	−0.950841	+	0.309679i	$0.899778\pi$
$662$	22.0354	+	41.0008i	0.856430	+	1.59354i
$663$		0			0
$664$	−1.02675	+	11.2080i	−0.0398457	+	0.434956i
$665$	−5.13792	−	5.13792i	−0.199240	−	0.199240i
$666$		0			0
$667$			1.61738i			0.0626253i
$668$	6.12407	+	30.0724i	0.236947	+	1.16354i
$669$		0			0
$670$	5.88373	+	1.77021i	0.227308	+	0.0683892i
$671$	−4.75308	−	4.75308i	−0.183491	−	0.183491i
$672$		0			0
$673$			2.17145i			0.0837031i	0.999124	+	0.0418516i	$0.0133257\pi$
$673$			2.17145i			0.0837031i	−0.999124	+	0.0418516i	$0.986674\pi$
$674$	2.94310	−	9.78210i	0.113364	−	0.376793i
$675$		0			0
$676$	−25.3120	+	5.94178i	−0.973537	+	0.228530i
$677$			8.31481i			0.319564i	0.987152	+	0.159782i	$0.0510792\pi$
$677$			8.31481i			0.319564i	−0.987152	+	0.159782i	$0.948921\pi$
$678$		0			0
$679$		−	11.3643i		−	0.436123i
$680$	−0.218528	+	2.38546i	−0.00838018	+	0.0914780i
$681$		0			0
$682$	−4.62830	+	15.3833i	−0.177227	+	0.589057i
$683$	20.4776	−	20.4776i	0.783553	−	0.783553i	−0.196875	−	0.980429i	$-0.563079\pi$
$683$	20.4776	−	20.4776i	0.783553	−	0.783553i	0.980429	+	0.196875i	$0.0630794\pi$
$684$		0			0
$685$		−	4.65428i		−	0.177831i
$686$	24.2035	−	13.0079i	0.924095	−	0.496644i
$687$		0			0
$688$	−9.57898	+	4.07020i	−0.365195	+	0.155175i
$689$	38.6224	−	16.6734i	1.47139	−	0.635205i
$690$		0			0
$691$	−24.6029	−	24.6029i	−0.935940	−	0.935940i	0.0621285	−	0.998068i	$-0.480211\pi$
$691$	−24.6029	−	24.6029i	−0.935940	−	0.935940i	−0.998068	+	0.0621285i	$0.980211\pi$
$692$	25.7950	+	17.0665i	0.980578	+	0.648771i
$693$		0			0
$694$	−29.9505	−	9.01107i	−1.13690	−	0.342055i
$695$	0.0978370	−	0.0978370i	0.00371117	−	0.00371117i
$696$		0			0
$697$	−2.82962	+	2.82962i	−0.107179	+	0.107179i
$698$	7.14357	+	13.2919i	0.270388	+	0.503106i
$699$		0			0
$700$	−23.6517	+	4.81652i	−0.893949	+	0.182047i
$701$	4.72081			0.178302			0.0891512	−	0.996018i	$-0.471585\pi$
$701$	4.72081			0.178302			0.0891512	+	0.996018i	$0.471585\pi$
$702$		0			0
$703$			35.7751i			1.34928i
$704$	20.7022	+	30.0863i	0.780243	+	1.13392i
$705$		0			0
$706$	8.23969	+	15.3314i	0.310105	+	0.577006i
$707$	−22.3342	−	22.3342i	−0.839964	−	0.839964i
$708$		0			0
$709$	0.847414	+	0.847414i	0.0318253	+	0.0318253i	0.722840	−	0.691015i	$-0.242836\pi$
$709$	0.847414	+	0.847414i	0.0318253	+	0.0318253i	−0.691015	+	0.722840i	$0.742836\pi$
$710$	−1.18229	+	3.92962i	−0.0443704	+	0.147476i
$711$		0			0
$712$	2.79892	+	0.256405i	0.104894	+	0.00960918i
$713$	11.8919	−	11.8919i	0.445354	−	0.445354i
$714$		0			0
$715$	5.85013	−	2.52552i	0.218783	−	0.0944491i
$716$	13.0941	−	19.7909i	0.489349	−	0.739622i
$717$		0			0
$718$	−14.2559	−	26.5256i	−0.532025	−	0.989928i
$719$	−16.0362			−0.598048			−0.299024	−	0.954246i	$-0.596661\pi$
$719$	−16.0362			−0.598048			−0.299024	+	0.954246i	$0.596661\pi$
$720$		0			0
$721$	−18.3050	−	18.3050i	−0.681714	−	0.681714i
$722$	−15.4412	+	51.3226i	−0.574661	+	1.91003i
$723$		0			0
$724$	39.2217	+	25.9499i	1.45766	+	0.964421i
$725$	1.16065			0.0431056
$726$		0			0
$727$	16.4293			0.609329			0.304665	−	0.952460i	$-0.401456\pi$
$727$	16.4293			0.609329			0.304665	+	0.952460i	$0.401456\pi$
$728$	24.1179	−	7.89030i	0.893867	−	0.292434i
$729$		0			0
$730$	−0.678520	+	2.25523i	−0.0251131	+	0.0834697i
$731$	5.69230			0.210537
$732$		0			0
$733$	−2.39796	+	2.39796i	−0.0885706	+	0.0885706i	−0.750004	−	0.661433i	$-0.769948\pi$
$733$	−2.39796	+	2.39796i	−0.0885706	+	0.0885706i	0.661433	+	0.750004i	$0.269948\pi$
$734$	−3.80810	+	12.6571i	−0.140559	+	0.467184i
$735$		0			0
$736$	−4.17980	−	38.0038i	−0.154069	−	1.40084i
$737$	−51.2330			−1.88719
$738$		0			0
$739$	1.09924	−	1.09924i	0.0404364	−	0.0404364i	−0.686599	−	0.727036i	$-0.740897\pi$
$739$	1.09924	−	1.09924i	0.0404364	−	0.0404364i	0.727036	+	0.686599i	$0.240897\pi$
$740$	−3.06251	−	2.02622i	−0.112580	−	0.0744855i
$741$		0			0
$742$	−36.1655	+	19.4367i	−1.32768	+	0.713544i
$743$	−15.6356	+	15.6356i	−0.573615	+	0.573615i	−0.933137	−	0.359522i	$-0.882940\pi$
$743$	−15.6356	+	15.6356i	−0.573615	+	0.573615i	0.359522	+	0.933137i	$0.382940\pi$
$744$		0			0
$745$			0.177997i			0.00652132i
$746$	−5.58530	+	18.5641i	−0.204492	+	0.679680i
$747$		0			0
$748$	−3.98579	−	19.5723i	−0.145735	−	0.715635i
$749$	−17.4465	−	17.4465i	−0.637480	−	0.637480i
$750$		0			0
$751$	−28.2017			−1.02910			−0.514548	−	0.857462i	$-0.672040\pi$
$751$	−28.2017			−1.02910			−0.514548	+	0.857462i	$0.672040\pi$
$752$	16.1131	−	39.9237i	0.587585	−	1.45587i
$753$		0			0
$754$	−1.21211	+	0.140359i	−0.0441426	+	0.00511159i
$755$	6.23057			0.226754
$756$		0			0
$757$		−	8.46085i		−	0.307515i	−0.988109	−	0.153757i	$-0.950863\pi$
$757$		−	8.46085i		−	0.307515i	0.988109	−	0.153757i	$-0.0491374\pi$
$758$	12.1234	+	22.5577i	0.440341	+	0.819333i
$759$		0			0
$760$	−5.28310	−	6.34867i	−0.191638	−	0.230291i
$761$	9.80630	−	9.80630i	0.355478	−	0.355478i	−0.506665	−	0.862143i	$-0.669122\pi$
$761$	9.80630	−	9.80630i	0.355478	−	0.355478i	0.862143	+	0.506665i	$0.169122\pi$
$762$		0			0
$763$	−29.3808			−1.06366
$764$	−5.27321	+	7.97014i	−0.190778	+	0.288350i
$765$		0			0
$766$	6.44046	−	3.46135i	0.232703	−	0.125064i
$767$	−44.9344	−	17.8362i	−1.62249	−	0.644026i
$768$		0			0
$769$	−13.5147	−	13.5147i	−0.487354	−	0.487354i	0.420116	−	0.907470i	$-0.361989\pi$
$769$	−13.5147	−	13.5147i	−0.487354	−	0.487354i	−0.907470	+	0.420116i	$0.861989\pi$
$770$	−5.47799	+	2.94408i	−0.197413	+	0.106097i
$771$		0			0
$772$	−22.8142	+	4.64598i	−0.821102	+	0.167213i
$773$	−30.1630	+	30.1630i	−1.08489	+	1.08489i	−0.0888435	+	0.996046i	$0.528317\pi$
$773$	−30.1630	+	30.1630i	−1.08489	+	1.08489i	−0.996046	+	0.0888435i	$0.971683\pi$
$774$		0			0
$775$	−8.53376	−	8.53376i	−0.306542	−	0.306542i
$776$	1.17844	−	12.8639i	0.0423037	−	0.461787i
$777$		0			0
$778$	23.2327	+	6.98990i	0.832931	+	0.250600i
$779$		−	13.7976i		−	0.494349i
$780$		0			0
$781$		−	34.2174i		−	1.22440i
$782$	−6.02450	+	20.0239i	−0.215436	+	0.716053i
$783$		0			0
$784$	2.97603	−	1.26454i	0.106287	−	0.0451623i
$785$	4.44794	+	4.44794i	0.158754	+	0.158754i
$786$		0			0
$787$	14.9019	−	14.9019i	0.531194	−	0.531194i	−0.389734	−	0.920928i	$-0.627433\pi$
$787$	14.9019	−	14.9019i	0.531194	−	0.531194i	0.920928	+	0.389734i	$0.127433\pi$
$788$	7.40324	−	1.50763i	0.263730	−	0.0537069i
$789$		0			0
$790$	4.21525	+	7.84323i	0.149972	+	0.279050i
$791$	−6.33566	−	6.33566i	−0.225270	−	0.225270i
$792$		0			0
$793$	−4.87420	+	2.10421i	−0.173088	+	0.0747225i
$794$	7.35317	+	13.6819i	0.260954	+	0.485552i
$795$		0			0
$796$	−10.9117	−	7.21938i	−0.386753	−	0.255884i
$797$	30.6279			1.08490			0.542448	−	0.840090i	$-0.317498\pi$
$797$	30.6279			1.08490			0.542448	+	0.840090i	$0.317498\pi$
$798$		0			0
$799$	−16.6499	+	16.6499i	−0.589031	+	0.589031i
$800$	−27.2720	+	2.99948i	−0.964212	+	0.106047i
$801$		0			0
$802$	−46.8869	+	25.1988i	−1.65563	+	0.889801i
$803$		−	19.6375i		−	0.692994i
$804$		0			0
$805$	6.51058			0.229468
$806$	9.94412	+	7.88012i	0.350267	+	0.277566i
$807$		0			0
$808$	−22.9653	−	27.5972i	−0.807915	−	0.970867i
$809$	6.57046			0.231005			0.115503	−	0.993307i	$-0.463152\pi$
$809$	6.57046			0.231005			0.115503	+	0.993307i	$0.463152\pi$
$810$		0			0
$811$	−15.6438	−	15.6438i	−0.549328	−	0.549328i	0.376918	−	0.926246i	$-0.376984\pi$
$811$	−15.6438	−	15.6438i	−0.549328	−	0.549328i	−0.926246	+	0.376918i	$0.876984\pi$
$812$	1.16696	−	0.237645i	0.0409524	−	0.00833971i
$813$		0			0
$814$	29.3212	+	8.82174i	1.02771	+	0.309202i
$815$			6.21328i			0.217642i
$816$		0			0
$817$	−13.8782	+	13.8782i	−0.485536	+	0.485536i
$818$	−5.14219	−	9.56797i	−0.179792	−	0.334536i
$819$		0			0
$820$	1.18113	+	0.781463i	0.0412470	+	0.0272899i
$821$	−27.5507	+	27.5507i	−0.961528	+	0.961528i	−0.999287	−	0.0377591i	$-0.987978\pi$
$821$	−27.5507	+	27.5507i	−0.961528	+	0.961528i	0.0377591	+	0.999287i	$0.487978\pi$
$822$		0			0
$823$	34.2171			1.19273			0.596367	−	0.802712i	$-0.296610\pi$
$823$	34.2171			1.19273			0.596367	+	0.802712i	$0.296610\pi$
$824$	−18.8222	−	22.6186i	−0.655704	−	0.787956i
$825$		0			0
$826$	45.1834	+	13.5941i	1.57213	+	0.473000i
$827$	20.7423	−	20.7423i	0.721281	−	0.721281i	−0.247585	−	0.968866i	$-0.579637\pi$
$827$	20.7423	−	20.7423i	0.721281	−	0.721281i	0.968866	+	0.247585i	$0.0796371\pi$
$828$		0			0
$829$	−16.8224			−0.584267			−0.292134	−	0.956377i	$-0.594365\pi$
$829$	−16.8224			−0.584267			−0.292134	+	0.956377i	$0.594365\pi$
$830$	−2.08618	−	0.627659i	−0.0724123	−	0.0217863i
$831$		0			0
$832$	28.1185	−	6.43051i	0.974833	−	0.222938i
$833$	−1.76851			−0.0612751
$834$		0			0
$835$	−5.94041			−0.205576
$836$	57.4361	+	38.0010i	1.98647	+	1.31429i
$837$		0			0
$838$	1.89784	+	0.570995i	0.0655599	+	0.0197247i
$839$	4.33267	+	4.33267i	0.149580	+	0.149580i	0.777931	−	0.628350i	$-0.216270\pi$
$839$	4.33267	+	4.33267i	0.149580	+	0.149580i	−0.628350	+	0.777931i	$0.716270\pi$
$840$		0			0
$841$	28.9427			0.998025
$842$	36.2674	−	19.4915i	1.24986	−	0.671720i
$843$		0			0
$844$	5.32728	+	3.52464i	0.183372	+	0.121323i
$845$	−0.149300	−	5.03044i	−0.00513607	−	0.173053i
$846$		0			0
$847$	17.3135	−	17.3135i	0.594898	−	0.594898i
$848$	−42.9531	+	18.2512i	−1.47502	+	0.626748i
$849$		0			0
$850$	14.3694	+	4.32326i	0.492866	+	0.148286i
$851$	−22.6664	−	22.6664i	−0.776995	−	0.776995i
$852$		0			0
$853$	−31.1735	−	31.1735i	−1.06736	−	1.06736i	−0.997561	−	0.0697978i	$-0.977765\pi$
$853$	−31.1735	−	31.1735i	−1.06736	−	1.06736i	−0.0697978	−	0.997561i	$-0.522235\pi$
$854$	4.56414	−	2.45294i	0.156182	−	0.0839379i
$855$		0			0
$856$	−17.9394	−	21.5577i	−0.613158	−	0.736828i
$857$		−	35.6847i		−	1.21897i	−0.792799	−	0.609484i	$-0.791377\pi$
$857$		−	35.6847i		−	1.21897i	0.792799	−	0.609484i	$-0.208623\pi$
$858$		0			0
$859$	38.7058			1.32063			0.660313	−	0.750990i	$-0.270424\pi$
$859$	38.7058			1.32063			0.660313	+	0.750990i	$0.270424\pi$
$860$	−0.402007	−	1.97407i	−0.0137083	−	0.0673151i
$861$		0			0
$862$	−45.4574	+	24.4305i	−1.54828	+	0.832107i
$863$	29.2256	−	29.2256i	0.994851	−	0.994851i	−0.00513541	−	0.999987i	$-0.501635\pi$
$863$	29.2256	−	29.2256i	0.994851	−	0.994851i	0.999987	+	0.00513541i	$0.00163466\pi$
$864$		0			0
$865$	−4.23336	+	4.23336i	−0.143938	+	0.143938i
$866$	−10.1783	+	33.8300i	−0.345872	+	1.14959i
$867$		0			0
$868$	−10.3275	−	6.83286i	−0.350537	−	0.231922i
$869$	−52.5000	−	52.5000i	−1.78094	−	1.78094i
$870$		0			0
$871$	−14.9287	+	37.6097i	−0.505840	+	1.27436i
$872$	−33.2577	−	3.04669i	−1.12625	−	0.103174i
$873$		0			0
$874$	−34.1314	−	63.5076i	−1.15451	−	2.14818i
$875$		−	9.48851i		−	0.320770i
$876$		0			0
$877$	13.1005	−	13.1005i	0.442373	−	0.442373i	−0.450436	−	0.892809i	$-0.648731\pi$
$877$	13.1005	−	13.1005i	0.442373	−	0.442373i	0.892809	+	0.450436i	$0.148731\pi$
$878$	33.0905	+	9.95579i	1.11675	+	0.335992i
$879$		0			0
$880$	−6.50612	+	2.76451i	−0.219321	+	0.0931916i
$881$		−	28.4181i		−	0.957431i	−0.877970	−	0.478715i	$-0.841103\pi$
$881$		−	28.4181i		−	0.957431i	0.877970	−	0.478715i	$-0.158897\pi$
$882$		0			0
$883$			27.5297i			0.926448i	0.886241	+	0.463224i	$0.153308\pi$
$883$			27.5297i			0.926448i	−0.886241	+	0.463224i	$0.846692\pi$
$884$	−15.5293	−	2.77723i	−0.522307	−	0.0934082i
$885$		0			0
$886$	−24.8837	−	7.48663i	−0.835983	−	0.251518i
$887$			43.5367i			1.46182i	0.682473	+	0.730910i	$0.260904\pi$
$887$			43.5367i			1.46182i	−0.682473	+	0.730910i	$0.739096\pi$
$888$		0			0
$889$	7.09188	+	7.09188i	0.237854	+	0.237854i
$890$	−0.156742	+	0.520969i	−0.00525399	+	0.0174629i
$891$		0			0
$892$	−6.20298	+	1.26320i	−0.207691	+	0.0422951i
$893$		−	81.1870i		−	2.71682i
$894$		0			0
$895$	3.24800	+	3.24800i	0.108569	+	0.108569i
$896$	−26.8062	+	8.59976i	−0.895531	+	0.287298i
$897$		0			0
$898$	−4.58458	+	2.46393i	−0.152989	+	0.0822224i
$899$	0.421052	+	0.421052i	0.0140429	+	0.0140429i
$900$		0			0
$901$	25.5249			0.850357
$902$	−11.3085	−	3.40232i	−0.376530	−	0.113285i
$903$		0			0
$904$	−6.51468	−	7.82865i	−0.216675	−	0.260377i
$905$	−6.43690	+	6.43690i	−0.213970	+	0.213970i
$906$		0			0
$907$			27.6601i			0.918440i	0.888323	+	0.459220i	$0.151871\pi$
$907$			27.6601i			0.918440i	−0.888323	+	0.459220i	$0.848129\pi$
$908$	0.245196	+	1.20404i	0.00813712	+	0.0399576i
$909$		0			0
$910$	0.565000	+	4.87922i	0.0187296	+	0.161745i
$911$		−	7.25921i		−	0.240508i	−0.992743	−	0.120254i	$-0.961629\pi$
$911$		−	7.25921i		−	0.240508i	0.992743	−	0.120254i	$-0.0383710\pi$
$912$		0			0
$913$	18.1655			0.601191
$914$	23.9363	+	44.5378i	0.791743	+	1.47318i
$915$		0			0
$916$	6.79857	+	33.3846i	0.224631	+	1.10306i
$917$	−11.7433	−	11.7433i	−0.387797	−	0.387797i
$918$		0			0
$919$		−	18.1717i		−	0.599429i	−0.954029	−	0.299715i	$-0.903109\pi$
$919$		−	18.1717i		−	0.599429i	0.954029	−	0.299715i	$-0.0968915\pi$
$920$	7.36967	+	0.675126i	0.242971	+	0.0222582i
$921$		0			0
$922$	−12.0290	+	6.46486i	−0.396155	+	0.212909i
$923$	−25.1188	−	9.97058i	−0.826794	−	0.328186i
$924$		0			0
$925$	−16.2657	+	16.2657i	−0.534813	+	0.534813i
$926$	−21.7410	−	40.4531i	−0.714454	−	1.32937i
$927$		0			0
$928$	1.34559	−	0.147993i	0.0441712	−	0.00485810i
$929$	−20.8437	−	20.8437i	−0.683861	−	0.683861i	0.277007	−	0.960868i	$-0.410657\pi$
$929$	−20.8437	−	20.8437i	−0.683861	−	0.683861i	−0.960868	+	0.277007i	$0.910657\pi$
$930$		0			0
$931$	4.31172	−	4.31172i	0.141311	−	0.141311i
$932$	−9.15403	+	13.8358i	−0.299850	+	0.453205i
$933$		0			0
$934$	12.8433	−	42.6879i	0.420246	−	1.39679i
$935$	3.86625			0.126440
$936$		0			0
$937$	−60.3441			−1.97135			−0.985677	−	0.168642i	$-0.946062\pi$
$937$	−60.3441			−1.97135			−0.985677	+	0.168642i	$0.946062\pi$
$938$	11.3782	−	37.8181i	0.371511	−	1.23481i
$939$		0			0
$940$	6.94998	+	4.59825i	0.226683	+	0.149978i
$941$	−15.8804	+	15.8804i	−0.517686	+	0.517686i	−0.916871	−	0.399185i	$-0.869293\pi$
$941$	−15.8804	+	15.8804i	−0.517686	+	0.517686i	0.399185	+	0.916871i	$0.369293\pi$
$942$		0			0
$943$	8.74187	+	8.74187i	0.284674	+	0.284674i
$944$	49.7358	+	20.0733i	1.61876	+	0.653329i
$945$		0			0
$946$	7.95233	+	14.7967i	0.258553	+	0.481083i
$947$	−20.6366	+	20.6366i	−0.670600	+	0.670600i	−0.957854	−	0.287255i	$-0.907257\pi$
$947$	−20.6366	+	20.6366i	−0.670600	+	0.670600i	0.287255	+	0.957854i	$0.407257\pi$
$948$		0			0
$949$	−14.4158	−	5.72216i	−0.467956	−	0.185749i
$950$	−45.5738	+	24.4931i	−1.47861	+	0.794661i
$951$		0			0
$952$	15.3327	+	1.40461i	0.496936	+	0.0455236i
$953$		−	36.0075i		−	1.16640i	−0.812329	−	0.583199i	$-0.801801\pi$
$953$		−	36.0075i		−	1.16640i	0.812329	−	0.583199i	$-0.198199\pi$
$954$		0			0
$955$	−1.30802	−	1.30802i	−0.0423267	−	0.0423267i
$956$	−17.2645	+	3.51581i	−0.558373	+	0.113709i
$957$		0			0
$958$	4.86983	+	9.06119i	0.157337	+	0.292754i
$959$	−29.9158			−0.966031
$960$		0			0
$961$			24.8084i			0.800271i
$962$	15.0198	−	18.9539i	0.484259	−	0.611099i
$963$		0			0
$964$	6.58950	−	1.34191i	0.212233	−	0.0432200i
$965$		−	4.50665i		−	0.145074i
$966$		0			0
$967$	17.2077	−	17.2077i	0.553362	−	0.553362i	−0.374047	−	0.927410i	$-0.622030\pi$
$967$	17.2077	−	17.2077i	0.553362	−	0.553362i	0.927410	+	0.374047i	$0.122030\pi$
$968$	21.3934	−	17.8027i	0.687609	−	0.572200i
$969$		0			0
$970$	2.39439	+	0.720389i	0.0768792	+	0.0231303i
$971$	−15.5333			−0.498487			−0.249243	−	0.968441i	$-0.580182\pi$
$971$	−15.5333			−0.498487			−0.249243	+	0.968441i	$0.580182\pi$
$972$		0			0
$973$	−0.628855	−	0.628855i	−0.0201602	−	0.0201602i
$974$	−28.7402	+	15.4461i	−0.920897	+	0.494925i
$975$		0			0
$976$	5.42075	−	2.30333i	0.173514	−	0.0737277i
$977$	−38.0370	−	38.0370i	−1.21691	−	1.21691i	−0.968708	−	0.248204i	$-0.920160\pi$
$977$	−38.0370	−	38.0370i	−1.21691	−	1.21691i	−0.248204	−	0.968708i	$-0.579840\pi$
$978$		0			0
$979$		−	4.53637i		−	0.144983i
$980$	0.124897	+	0.613310i	0.00398969	+	0.0195915i
$981$		0			0
$982$	−11.8047	+	39.2359i	−0.376704	+	1.25207i
$983$	26.1000	+	26.1000i	0.832460	+	0.832460i	0.987853	−	0.155393i	$-0.0496643\pi$
$983$	26.1000	+	26.1000i	0.832460	+	0.832460i	−0.155393	+	0.987853i	$0.549664\pi$
$984$		0			0
$985$			1.46241i			0.0465963i
$986$	−0.708980	−	0.213308i	−0.0225785	−	0.00679310i
$987$		0			0
$988$	44.6325	−	31.0904i	1.41995	−	0.989116i
$989$		−	17.5859i		−	0.559199i
$990$		0			0
$991$		−	0.409809i		−	0.0130180i	−0.999979	−	0.00650901i	$-0.997928\pi$
$991$		−	0.409809i		−	0.0130180i	0.999979	−	0.00650901i	$-0.00207190\pi$
$992$	−10.9816	−	8.80540i	−0.348668	−	0.279572i
$993$		0			0
$994$	25.2580	+	7.59925i	0.801134	+	0.241033i
$995$	1.79077	−	1.79077i	0.0567713	−	0.0567713i
$996$		0			0
$997$			22.9475i			0.726756i	0.931642	+	0.363378i	$0.118377\pi$
$997$			22.9475i			0.726756i	−0.931642	+	0.363378i	$0.881623\pi$
$998$	−6.45564	−	12.0119i	−0.204350	−	0.380229i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.w.j.307.11		24
3.2	odd	2		312.2.t.e.307.2	yes	24
8.3	odd	2	inner	936.2.w.j.307.8		24
12.11	even	2		1248.2.bb.f.463.8		24
13.5	odd	4	inner	936.2.w.j.811.8		24
24.5	odd	2		1248.2.bb.f.463.5		24
24.11	even	2		312.2.t.e.307.5	yes	24
39.5	even	4		312.2.t.e.187.5	yes	24
104.83	even	4	inner	936.2.w.j.811.11		24
156.83	odd	4		1248.2.bb.f.655.5		24
312.5	even	4		1248.2.bb.f.655.8		24
312.83	odd	4		312.2.t.e.187.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.t.e.187.2	✓	24	312.83	odd	4
312.2.t.e.187.5	yes	24	39.5	even	4
312.2.t.e.307.2	yes	24	3.2	odd	2
312.2.t.e.307.5	yes	24	24.11	even	2
936.2.w.j.307.8		24	8.3	odd	2	inner
936.2.w.j.307.11		24	1.1	even	1	trivial
936.2.w.j.811.8		24	13.5	odd	4	inner
936.2.w.j.811.11		24	104.83	even	4	inner
1248.2.bb.f.463.5		24	24.5	odd	2
1248.2.bb.f.463.8		24	12.11	even	2
1248.2.bb.f.655.5		24	156.83	odd	4
1248.2.bb.f.655.8		24	312.5	even	4

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35425 + 0.407446i) q^{2} +(1.66797 + 1.10357i) q^{4} +(-0.273741 + 0.273741i) q^{5} +(1.75949 + 1.75949i) q^{7} +(1.80921 + 2.17411i) q^{8} +(-0.482247 + 0.259178i) q^{10} +(3.22801 - 3.22801i) q^{11} +(-1.42905 - 3.31026i) q^{13} +(1.66589 + 3.09968i) q^{14} +(1.56428 + 3.68144i) q^{16} -2.18769i q^{17} +(5.33373 + 5.33373i) q^{19} +(-0.758684 + 0.154501i) q^{20} +(5.68676 - 3.05628i) q^{22} -6.75871 q^{23} +4.85013i q^{25} +(-0.586533 - 5.06517i) q^{26} +(0.993070 + 4.87650i) q^{28} -0.239304i q^{29} +(-1.75949 + 1.75949i) q^{31} +(0.618432 + 5.62295i) q^{32} +(0.891368 - 2.96268i) q^{34} -0.963288 q^{35} +(3.35366 + 3.35366i) q^{37} +(5.04999 + 9.39641i) q^{38} +(-1.09040 - 0.0998898i) q^{40} +(-1.29342 - 1.29342i) q^{41} +2.60196i q^{43} +(8.94655 - 1.82191i) q^{44} +(-9.15296 - 2.75381i) q^{46} +(-7.61070 - 7.61070i) q^{47} -0.808387i q^{49} +(-1.97617 + 6.56828i) q^{50} +(1.26948 - 7.09848i) q^{52} +11.6675i q^{53} +1.76727i q^{55} +(-0.642050 + 7.00861i) q^{56} +(0.0975034 - 0.324076i) q^{58} +(9.48121 - 9.48121i) q^{59} -1.47245i q^{61} +(-3.09968 + 1.66589i) q^{62} +(-1.45354 + 7.86684i) q^{64} +(1.29734 + 0.514964i) q^{65} +(-7.93570 - 7.93570i) q^{67} +(2.41427 - 3.64902i) q^{68} +(-1.30453 - 0.392488i) q^{70} +(5.30009 - 5.30009i) q^{71} +(3.04174 - 3.04174i) q^{73} +(3.17525 + 5.90813i) q^{74} +(3.01040 + 14.7827i) q^{76} +11.3593 q^{77} -16.2639i q^{79} +(-1.43597 - 0.579554i) q^{80} +(-1.22462 - 2.27862i) q^{82} +(2.81374 + 2.81374i) q^{83} +(0.598861 + 0.598861i) q^{85} +(-1.06016 + 3.52370i) q^{86} +(12.8582 + 1.17792i) q^{88} +(0.702659 - 0.702659i) q^{89} +(3.30997 - 8.33877i) q^{91} +(-11.2734 - 7.45868i) q^{92} +(-7.20583 - 13.4077i) q^{94} -2.92012 q^{95} +(-3.22944 - 3.22944i) q^{97} +(0.329375 - 1.09476i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{8} - 8 q^{11} - 36 q^{14} + 28 q^{16} + 20 q^{19} + 20 q^{20} + 20 q^{22} - 12 q^{26} - 16 q^{28} + 30 q^{32} + 16 q^{34} - 16 q^{35} + 36 q^{40} + 12 q^{41} + 32 q^{44} - 44 q^{46} + 36 q^{50}+ \cdots - 68 q^{98}+O(q^{100}) \) 24 * q + 6 * q^8 - 8 * q^11 - 36 * q^14 + 28 * q^16 + 20 * q^19 + 20 * q^20 + 20 * q^22 - 12 * q^26 - 16 * q^28 + 30 * q^32 + 16 * q^34 - 16 * q^35 + 36 * q^40 + 12 * q^41 + 32 * q^44 - 44 * q^46 + 36 * q^50 + 4 * q^52 + 32 * q^58 + 16 * q^59 + 76 * q^65 + 28 * q^67 - 32 * q^68 - 40 * q^70 - 8 * q^73 + 32 * q^74 - 36 * q^76 + 32 * q^80 + 72 * q^83 - 4 * q^86 - 28 * q^89 - 4 * q^91 - 32 * q^92 + 28 * q^94 + 24 * q^97 - 68 * q^98

Introduction

L-functions

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