LMFDB - Embedded newform 936.2.w.j.307.7

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			307.7
Character	$\chi$	$=$	936.307
Dual form			936.2.w.j.811.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.140104 + 1.40726i) q^{2} +(-1.96074 + 0.394325i) q^{4} +(-3.08779 + 3.08779i) q^{5} +(2.85816 + 2.85816i) q^{7} +(-0.829624 - 2.70402i) q^{8} +(-4.77792 - 3.91270i) q^{10} +(-2.57668 + 2.57668i) q^{11} +(-3.51077 - 0.821294i) q^{13} +(-3.62173 + 4.42261i) q^{14} +(3.68902 - 1.54634i) q^{16} +1.07196i q^{17} +(1.46161 + 1.46161i) q^{19} +(4.83676 - 7.27194i) q^{20} +(-3.98706 - 3.26505i) q^{22} +5.52786 q^{23} -14.0688i q^{25} +(0.663899 - 5.05561i) q^{26} +(-6.73116 - 4.47707i) q^{28} +0.512377i q^{29} +(-2.85816 + 2.85816i) q^{31} +(2.69294 + 4.97474i) q^{32} +(-1.50852 + 0.150186i) q^{34} -17.6508 q^{35} +(1.97885 + 1.97885i) q^{37} +(-1.85209 + 2.26164i) q^{38} +(10.9111 + 5.78773i) q^{40} +(0.0336607 + 0.0336607i) q^{41} -3.49466i q^{43} +(4.03616 - 6.06826i) q^{44} +(0.774476 + 7.77911i) q^{46} +(-6.45565 - 6.45565i) q^{47} +9.33817i q^{49} +(19.7985 - 1.97110i) q^{50} +(7.20756 + 0.225963i) q^{52} -8.04121i q^{53} -15.9125i q^{55} +(5.35733 - 10.0997i) q^{56} +(-0.721046 + 0.0717861i) q^{58} +(-1.23075 + 1.23075i) q^{59} -4.66832i q^{61} +(-4.42261 - 3.62173i) q^{62} +(-6.62345 + 4.48664i) q^{64} +(13.3765 - 8.30451i) q^{65} +(2.03305 + 2.03305i) q^{67} +(-0.422701 - 2.10184i) q^{68} +(-2.47295 - 24.8392i) q^{70} +(5.60969 - 5.60969i) q^{71} +(-5.73067 + 5.73067i) q^{73} +(-2.50750 + 3.06199i) q^{74} +(-3.44220 - 2.28950i) q^{76} -14.7292 q^{77} +6.65963i q^{79} +(-6.61613 + 16.1657i) q^{80} +(-0.0426532 + 0.0520852i) q^{82} +(-0.153984 - 0.153984i) q^{83} +(-3.30998 - 3.30998i) q^{85} +(4.91788 - 0.489616i) q^{86} +(9.10509 + 4.82973i) q^{88} +(-11.3765 + 11.3765i) q^{89} +(-7.68694 - 12.3817i) q^{91} +(-10.8387 + 2.17977i) q^{92} +(8.18029 - 9.98921i) q^{94} -9.02631 q^{95} +(8.80263 + 8.80263i) q^{97} +(-13.1412 + 1.30832i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.140104	+	1.40726i	0.0990686	+	0.995081i
$2$	0.140104	+	1.40726i	0.0990686	+	0.995081i
$3$		0			0
$3$		0			0
$4$	−1.96074	+	0.394325i	−0.980371	+	0.197162i
$5$	−3.08779	+	3.08779i	−1.38090	+	1.38090i	−0.537875	+	0.843024i	$0.680773\pi$
$5$	−3.08779	+	3.08779i	−1.38090	+	1.38090i	−0.843024	+	0.537875i	$0.819227\pi$
$6$		0			0
$7$	2.85816	+	2.85816i	1.08028	+	1.08028i	0.996483	+	0.0838010i	$0.0267060\pi$
$7$	2.85816	+	2.85816i	1.08028	+	1.08028i	0.0838010	+	0.996483i	$0.473294\pi$
$8$	−0.829624	−	2.70402i	−0.293316	−	0.956015i
$9$		0			0
$10$	−4.77792	−	3.91270i	−1.51091	−	1.23730i
$11$	−2.57668	+	2.57668i	−0.776900	+	0.776900i	−0.979302	−	0.202403i	$-0.935125\pi$
$11$	−2.57668	+	2.57668i	−0.776900	+	0.776900i	0.202403	+	0.979302i	$0.435125\pi$
$12$		0			0
$13$	−3.51077	−	0.821294i	−0.973711	−	0.227786i
$13$	−3.51077	−	0.821294i	−0.973711	−	0.227786i
$14$	−3.62173	+	4.42261i	−0.967947	+	1.18199i
$15$		0			0
$16$	3.68902	−	1.54634i	0.922254	−	0.386585i
$17$			1.07196i			0.259989i	0.991515	+	0.129994i	$0.0414959\pi$
$17$			1.07196i			0.259989i	−0.991515	+	0.129994i	$0.958504\pi$
$18$		0			0
$19$	1.46161	+	1.46161i	0.335317	+	0.335317i	0.854602	−	0.519284i	$-0.173801\pi$
$19$	1.46161	+	1.46161i	0.335317	+	0.335317i	−0.519284	+	0.854602i	$0.673801\pi$
$20$	4.83676	−	7.27194i	1.08153	−	1.62606i
$21$		0			0
$22$	−3.98706	−	3.26505i	−0.850044	−	0.696111i
$23$	5.52786			1.15264			0.576319	−	0.817225i	$-0.304489\pi$
$23$	5.52786			1.15264			0.576319	+	0.817225i	$0.304489\pi$
$24$		0			0
$25$		−	14.0688i		−	2.81377i
$26$	0.663899	−	5.05561i	0.130201	−	0.991488i
$27$		0			0
$28$	−6.73116	−	4.47707i	−1.27207	−	0.846087i
$29$			0.512377i			0.0951460i	0.998868	+	0.0475730i	$0.0151487\pi$
$29$			0.512377i			0.0951460i	−0.998868	+	0.0475730i	$0.984851\pi$
$30$		0			0
$31$	−2.85816	+	2.85816i	−0.513341	+	0.513341i	−0.915549	−	0.402208i	$-0.868243\pi$
$31$	−2.85816	+	2.85816i	−0.513341	+	0.513341i	0.402208	+	0.915549i	$0.368243\pi$
$32$	2.69294	+	4.97474i	0.476049	+	0.879419i
$33$		0			0
$34$	−1.50852	+	0.150186i	−0.258710	+	0.0257567i
$35$	−17.6508			−2.98353
$36$		0			0
$37$	1.97885	+	1.97885i	0.325321	+	0.325321i	0.850804	−	0.525483i	$-0.176115\pi$
$37$	1.97885	+	1.97885i	0.325321	+	0.325321i	−0.525483	+	0.850804i	$0.676115\pi$
$38$	−1.85209	+	2.26164i	−0.300448	+	0.366887i
$39$		0			0
$40$	10.9111	+	5.78773i	1.72520	+	0.915121i
$41$	0.0336607	+	0.0336607i	0.00525692	+	0.00525692i	0.709730	−	0.704473i	$-0.248817\pi$
$41$	0.0336607	+	0.0336607i	0.00525692	+	0.00525692i	−0.704473	+	0.709730i	$0.748817\pi$
$42$		0			0
$43$		−	3.49466i		−	0.532931i	−0.963844	−	0.266465i	$-0.914144\pi$
$43$		−	3.49466i		−	0.532931i	0.963844	−	0.266465i	$-0.0858558\pi$
$44$	4.03616	−	6.06826i	0.608474	−	0.914825i
$45$		0			0
$46$	0.774476	+	7.77911i	0.114190	+	1.14697i
$47$	−6.45565	−	6.45565i	−0.941653	−	0.941653i	0.0567363	−	0.998389i	$-0.481931\pi$
$47$	−6.45565	−	6.45565i	−0.941653	−	0.941653i	−0.998389	+	0.0567363i	$0.981931\pi$
$48$		0			0
$49$			9.33817i			1.33402i
$50$	19.7985	−	1.97110i	2.79993	−	0.278756i
$51$		0			0
$52$	7.20756	+	0.225963i	0.999509	+	0.0313355i
$53$		−	8.04121i		−	1.10455i	−0.833663	−	0.552273i	$-0.813761\pi$
$53$		−	8.04121i		−	1.10455i	0.833663	−	0.552273i	$-0.186239\pi$
$54$		0			0
$55$		−	15.9125i		−	2.14564i
$56$	5.35733	−	10.0997i	0.715903	−	1.34963i
$57$		0			0
$58$	−0.721046	+	0.0717861i	−0.0946779	+	0.00942598i
$59$	−1.23075	+	1.23075i	−0.160231	+	0.160231i	−0.782669	−	0.622438i	$-0.786142\pi$
$59$	−1.23075	+	1.23075i	−0.160231	+	0.160231i	0.622438	+	0.782669i	$0.286142\pi$
$60$		0			0
$61$		−	4.66832i		−	0.597717i	−0.954297	−	0.298859i	$-0.903394\pi$
$61$		−	4.66832i		−	0.597717i	0.954297	−	0.298859i	$-0.0966059\pi$
$62$	−4.42261	−	3.62173i	−0.561672	−	0.459960i
$63$		0			0
$64$	−6.62345	+	4.48664i	−0.827931	+	0.560830i
$65$	13.3765	−	8.30451i	1.65915	−	1.03005i
$66$		0			0
$67$	2.03305	+	2.03305i	0.248376	+	0.248376i	0.820304	−	0.571928i	$-0.193804\pi$
$67$	2.03305	+	2.03305i	0.248376	+	0.248376i	−0.571928	+	0.820304i	$0.693804\pi$
$68$	−0.422701	−	2.10184i	−0.0512600	−	0.254885i
$69$		0			0
$70$	−2.47295	−	24.8392i	−0.295574	−	2.96885i
$71$	5.60969	−	5.60969i	0.665747	−	0.665747i	−0.290981	−	0.956729i	$-0.593982\pi$
$71$	5.60969	−	5.60969i	0.665747	−	0.665747i	0.956729	+	0.290981i	$0.0939818\pi$
$72$		0			0
$73$	−5.73067	+	5.73067i	−0.670724	+	0.670724i	−0.957883	−	0.287159i	$-0.907289\pi$
$73$	−5.73067	+	5.73067i	−0.670724	+	0.670724i	0.287159	+	0.957883i	$0.407289\pi$
$74$	−2.50750	+	3.06199i	−0.291491	+	0.355949i
$75$		0			0
$76$	−3.44220	−	2.28950i	−0.394847	−	0.262623i
$77$	−14.7292			−1.67854
$78$		0			0
$79$			6.65963i			0.749267i	0.927173	+	0.374633i	$0.122231\pi$
$79$			6.65963i			0.749267i	−0.927173	+	0.374633i	$0.877769\pi$
$80$	−6.61613	+	16.1657i	−0.739706	+	1.80737i
$81$		0			0
$82$	−0.0426532	+	0.0520852i	−0.00471026	+	0.00575185i
$83$	−0.153984	−	0.153984i	−0.0169020	−	0.0169020i	0.698605	−	0.715507i	$-0.253804\pi$
$83$	−0.153984	−	0.153984i	−0.0169020	−	0.0169020i	−0.715507	+	0.698605i	$0.753804\pi$
$84$		0			0
$85$	−3.30998	−	3.30998i	−0.359018	−	0.359018i
$86$	4.91788	−	0.489616i	0.530309	−	0.0527967i
$87$		0			0
$88$	9.10509	+	4.82973i	0.970606	+	0.514851i
$89$	−11.3765	+	11.3765i	−1.20590	+	1.20590i	−0.233562	+	0.972342i	$0.575038\pi$
$89$	−11.3765	+	11.3765i	−1.20590	+	1.20590i	−0.972342	+	0.233562i	$0.924962\pi$
$90$		0			0
$91$	−7.68694	−	12.3817i	−0.805811	−	1.29796i
$92$	−10.8387	+	2.17977i	−1.13001	+	0.227257i
$93$		0			0
$94$	8.18029	−	9.98921i	0.843732	−	1.03031i
$95$	−9.02631			−0.926079
$96$		0			0
$97$	8.80263	+	8.80263i	0.893772	+	0.893772i	0.994876	−	0.101104i	$-0.0322376\pi$
$97$	8.80263	+	8.80263i	0.893772	+	0.893772i	−0.101104	+	0.994876i	$0.532238\pi$
$98$	−13.1412	+	1.30832i	−1.32746	+	0.132160i
$99$		0			0
$100$	5.54769	+	27.5854i	0.554769	+	2.75854i
$101$	2.89040			0.287605			0.143803	−	0.989606i	$-0.454067\pi$
$101$	2.89040			0.287605			0.143803	+	0.989606i	$0.454067\pi$
$102$		0			0
$103$	−7.15687			−0.705187			−0.352594	−	0.935777i	$-0.614700\pi$
$103$	−7.15687			−0.705187			−0.352594	+	0.935777i	$0.614700\pi$
$104$	0.691821	+	10.1745i	0.0678386	+	0.997696i
$105$		0			0
$106$	11.3160	−	1.12661i	1.09911	−	0.109426i
$107$	10.6510			1.02967			0.514833	−	0.857290i	$-0.327854\pi$
$107$	10.6510			1.02967			0.514833	+	0.857290i	$0.327854\pi$
$108$		0			0
$109$	−1.78060	+	1.78060i	−0.170551	+	0.170551i	−0.787221	−	0.616671i	$-0.788481\pi$
$109$	−1.78060	+	1.78060i	−0.170551	+	0.170551i	0.616671	+	0.787221i	$0.288481\pi$
$110$	22.3930	−	2.22941i	2.13509	−	0.212566i
$111$		0			0
$112$	14.9635	+	6.12412i	1.41392	+	0.578675i
$113$	−2.99536			−0.281780			−0.140890	−	0.990025i	$-0.544996\pi$
$113$	−2.99536			−0.281780			−0.140890	+	0.990025i	$0.544996\pi$
$114$		0			0
$115$	−17.0688	+	17.0688i	−1.59168	+	1.59168i
$116$	−0.202043	−	1.00464i	−0.0187592	−	0.0932784i
$117$		0			0
$118$	−1.90442	−	1.55955i	−0.175316	−	0.143569i
$119$	−3.06383	+	3.06383i	−0.280861	+	0.280861i
$120$		0			0
$121$		−	2.27861i		−	0.207146i
$122$	6.56952	−	0.654051i	0.594777	−	0.0592150i
$123$		0			0
$124$	4.47707	−	6.73116i	0.402053	−	0.604476i
$125$	28.0026	+	28.0026i	2.50463	+	2.50463i
$126$		0			0
$127$	−16.1639			−1.43431			−0.717156	−	0.696913i	$-0.754557\pi$
$127$	−16.1639			−1.43431			−0.717156	+	0.696913i	$0.754557\pi$
$128$	−7.24183	−	8.69229i	−0.640093	−	0.768297i
$129$		0			0
$130$	13.5607	+	17.6606i	1.18935	+	1.54894i
$131$	0.118526			0.0103557			0.00517783	−	0.999987i	$-0.498352\pi$
$131$	0.118526			0.0103557			0.00517783	+	0.999987i	$0.498352\pi$
$132$		0			0
$133$			8.35506i			0.724476i
$134$	−2.57618	+	3.14586i	−0.222548	+	0.271761i
$135$		0			0
$136$	2.89860	−	0.889324i	0.248553	−	0.0762589i
$137$	−8.38715	+	8.38715i	−0.716563	+	0.716563i	−0.967900	−	0.251337i	$-0.919130\pi$
$137$	−8.38715	+	8.38715i	−0.716563	+	0.716563i	0.251337	+	0.967900i	$0.419130\pi$
$138$		0			0
$139$	−9.73531			−0.825738			−0.412869	−	0.910790i	$-0.635473\pi$
$139$	−9.73531			−0.825738			−0.412869	+	0.910790i	$0.635473\pi$
$140$	34.6086	−	6.96014i	2.92496	−	0.588239i
$141$		0			0
$142$	8.68021	+	7.10833i	0.728427	+	0.596518i
$143$	11.1624	−	6.92992i	0.933443	−	0.579509i
$144$		0			0
$145$	−1.58211	−	1.58211i	−0.131387	−	0.131387i
$146$	−8.86741	−	7.26163i	−0.733872	−	0.600977i
$147$		0			0
$148$	−4.66032	−	3.09970i	−0.383076	−	0.254794i
$149$	−6.39777	+	6.39777i	−0.524126	+	0.524126i	−0.918815	−	0.394689i	$-0.870852\pi$
$149$	−6.39777	+	6.39777i	−0.524126	+	0.524126i	0.394689	+	0.918815i	$0.370852\pi$
$150$		0			0
$151$	6.23105	+	6.23105i	0.507076	+	0.507076i	0.913628	−	0.406552i	$-0.133269\pi$
$151$	6.23105	+	6.23105i	0.507076	+	0.507076i	−0.406552	+	0.913628i	$0.633269\pi$
$152$	2.73964	−	5.16483i	0.222214	−	0.418923i
$153$		0			0
$154$	−2.06362	−	20.7277i	−0.166291	−	1.67029i
$155$		−	17.6508i		−	1.41774i
$156$		0			0
$157$			23.8222i			1.90122i	0.310393	+	0.950608i	$0.399539\pi$
$157$			23.8222i			1.90122i	−0.310393	+	0.950608i	$0.600461\pi$
$158$	−9.37180	+	0.933041i	−0.745581	+	0.0742288i
$159$		0			0
$160$	−23.6762	−	7.04572i	−1.87177	−	0.557013i
$161$	15.7995	+	15.7995i	1.24518	+	1.24518i
$162$		0			0
$163$	4.03428	−	4.03428i	0.315989	−	0.315989i	−0.531235	−	0.847224i	$-0.678272\pi$
$163$	4.03428	−	4.03428i	0.315989	−	0.315989i	0.847224	+	0.531235i	$0.178272\pi$
$164$	−0.0792732	−	0.0527267i	−0.00619020	−	0.00411726i
$165$		0			0
$166$	0.195121	−	0.238269i	0.0151444	−	0.0184933i
$167$	−4.78853	−	4.78853i	−0.370548	−	0.370548i	0.497129	−	0.867677i	$-0.334388\pi$
$167$	−4.78853	−	4.78853i	−0.370548	−	0.370548i	−0.867677	+	0.497129i	$0.834388\pi$
$168$		0			0
$169$	11.6510	+	5.76674i	0.896227	+	0.443596i
$170$	4.19425	−	5.12174i	0.321685	−	0.392819i
$171$		0			0
$172$	1.37803	+	6.85213i	0.105074	+	0.522470i
$173$	1.81603			0.138070			0.0690350	−	0.997614i	$-0.478008\pi$
$173$	1.81603			0.138070			0.0690350	+	0.997614i	$0.478008\pi$
$174$		0			0
$175$	40.2110	−	40.2110i	3.03967	−	3.03967i
$176$	−5.52100	+	13.4899i	−0.416161	+	1.01684i
$177$		0			0
$178$	−17.6035	−	14.4157i	−1.31944	−	1.08050i
$179$			10.4962i			0.784521i	0.919854	+	0.392261i	$0.128307\pi$
$179$			10.4962i			0.784521i	−0.919854	+	0.392261i	$0.871693\pi$
$180$		0			0
$181$	14.0565			1.04481			0.522407	−	0.852696i	$-0.325034\pi$
$181$	14.0565			1.04481			0.522407	+	0.852696i	$0.325034\pi$
$182$	16.3473	−	12.5522i	1.21174	−	0.930433i
$183$		0			0
$184$	−4.58605	−	14.9474i	−0.338088	−	1.10194i
$185$	−12.2205			−0.898470
$186$		0			0
$187$	−2.76210	−	2.76210i	−0.201985	−	0.201985i
$188$	15.2035	+	10.1122i	1.10883	+	0.737510i
$189$		0			0
$190$	−1.26462	−	12.7023i	−0.0917454	−	0.921524i
$191$		−	15.1540i		−	1.09650i	−0.836313	−	0.548252i	$-0.815294\pi$
$191$		−	15.1540i		−	1.09650i	0.836313	−	0.548252i	$-0.184706\pi$
$192$		0			0
$193$	−16.5694	+	16.5694i	−1.19269	+	1.19269i	−0.216380	+	0.976309i	$0.569425\pi$
$193$	−16.5694	+	16.5694i	−1.19269	+	1.19269i	−0.976309	+	0.216380i	$0.930575\pi$
$194$	−11.1543	+	13.6208i	−0.800830	+	0.977919i
$195$		0			0
$196$	−3.68227	−	18.3097i	−0.263020	−	1.30784i
$197$	6.24885	−	6.24885i	0.445212	−	0.445212i	−0.448547	−	0.893759i	$-0.648058\pi$
$197$	6.24885	−	6.24885i	0.445212	−	0.445212i	0.893759	+	0.448547i	$0.148058\pi$
$198$		0			0
$199$	4.22848			0.299749			0.149875	−	0.988705i	$-0.452113\pi$
$199$	4.22848			0.299749			0.149875	+	0.988705i	$0.452113\pi$
$200$	−38.0424	+	11.6719i	−2.69001	+	0.825325i
$201$		0			0
$202$	0.404956	+	4.06753i	0.0284926	+	0.286190i
$203$	−1.46446	+	1.46446i	−0.102785	+	0.102785i
$204$		0			0
$205$	−0.207874			−0.0145186
$206$	−1.00271	−	10.0715i	−0.0698619	−	0.701718i
$207$		0			0
$208$	−14.2213	+	2.39907i	−0.986068	+	0.166345i
$209$	−7.53224			−0.521016
$210$		0			0
$211$	−24.8295			−1.70934			−0.854668	−	0.519175i	$-0.826239\pi$
$211$	−24.8295			−1.70934			−0.854668	+	0.519175i	$0.826239\pi$
$212$	3.17085	+	15.7667i	0.217775	+	1.08286i
$213$		0			0
$214$	1.49224	+	14.9886i	0.102008	+	1.02460i
$215$	10.7908	+	10.7908i	0.735924	+	0.735924i
$216$		0			0
$217$	−16.3382			−1.10911
$218$	−2.75523	−	2.25629i	−0.186608	−	0.152815i
$219$		0			0
$220$	6.27469	+	31.2003i	0.423040	+	2.10352i
$221$	0.880394	−	3.76340i	0.0592217	−	0.253154i
$222$		0			0
$223$	−1.83341	+	1.83341i	−0.122774	+	0.122774i	−0.765824	−	0.643050i	$-0.777669\pi$
$223$	−1.83341	+	1.83341i	−0.122774	+	0.122774i	0.643050	+	0.765824i	$0.277669\pi$
$224$	−6.52176	+	21.9155i	−0.435753	+	1.46429i
$225$		0			0
$226$	−0.419662	−	4.21524i	−0.0279155	−	0.280394i
$227$	−9.42020	−	9.42020i	−0.625240	−	0.625240i	0.321626	−	0.946867i	$-0.395771\pi$
$227$	−9.42020	−	9.42020i	−0.625240	−	0.625240i	−0.946867	+	0.321626i	$0.895771\pi$
$228$		0			0
$229$	4.97977	+	4.97977i	0.329073	+	0.329073i	0.852234	−	0.523161i	$-0.175247\pi$
$229$	4.97977	+	4.97977i	0.329073	+	0.329073i	−0.523161	+	0.852234i	$0.675247\pi$
$230$	−26.4117	−	21.6288i	−1.74153	−	1.42616i
$231$		0			0
$232$	1.38548	−	0.425080i	0.0909610	−	0.0279079i
$233$		−	5.38474i		−	0.352766i	−0.984322	−	0.176383i	$-0.943560\pi$
$233$		−	5.38474i		−	0.352766i	0.984322	−	0.176383i	$-0.0564397\pi$
$234$		0			0
$235$	39.8673			2.60066
$236$	1.92788	−	2.89851i	0.125494	−	0.188677i
$237$		0			0
$238$	−4.74086	−	3.88235i	−0.307304	−	0.251655i
$239$	6.48045	−	6.48045i	0.419186	−	0.419186i	−0.465737	−	0.884923i	$-0.654211\pi$
$239$	6.48045	−	6.48045i	0.419186	−	0.419186i	0.884923	+	0.465737i	$0.154211\pi$
$240$		0			0
$241$	16.2281	−	16.2281i	1.04534	−	1.04534i	0.0464205	−	0.998922i	$-0.485219\pi$
$241$	16.2281	−	16.2281i	1.04534	−	1.04534i	0.998922	−	0.0464205i	$-0.0147814\pi$
$242$	3.20659	−	0.319242i	0.206127	−	0.0205217i
$243$		0			0
$244$	1.84083	+	9.15337i	0.117847	+	0.585984i
$245$	−28.8343	−	28.8343i	−1.84215	−	1.84215i
$246$		0			0
$247$	−3.93097	−	6.33180i	−0.250122	−	0.402883i
$248$	10.0997	+	5.35733i	0.641333	+	0.340191i
$249$		0			0
$250$	−35.4836	+	43.3302i	−2.24418	+	2.74044i
$251$		−	0.990551i		−	0.0625230i	−0.999511	−	0.0312615i	$-0.990048\pi$
$251$		−	0.990551i		−	0.0625230i	0.999511	−	0.0312615i	$-0.00995247\pi$
$252$		0			0
$253$	−14.2435	+	14.2435i	−0.895484	+	0.895484i
$254$	−2.26463	−	22.7467i	−0.142095	−	1.42726i
$255$		0			0
$256$	11.2177	−	11.4089i	0.701105	−	0.713058i
$257$		−	16.9182i		−	1.05533i	−0.849453	−	0.527665i	$-0.823068\pi$
$257$		−	16.9182i		−	1.05533i	0.849453	−	0.527665i	$-0.176932\pi$
$258$		0			0
$259$			11.3117i			0.702877i
$260$	−22.9531	+	21.5577i	−1.42349	+	1.33695i
$261$		0			0
$262$	0.0166060	+	0.166796i	0.00102592	+	0.0103047i
$263$			28.7035i			1.76993i	0.465655	+	0.884966i	$0.345819\pi$
$263$			28.7035i			1.76993i	−0.465655	+	0.884966i	$0.654181\pi$
$264$		0			0
$265$	24.8295	+	24.8295i	1.52527	+	1.52527i
$266$	−11.7577	+	1.17058i	−0.720912	+	0.0717728i
$267$		0			0
$268$	−4.78796	−	3.18460i	−0.292471	−	0.194530i
$269$			25.8818i			1.57804i	0.614366	+	0.789021i	$0.289412\pi$
$269$			25.8818i			1.57804i	−0.614366	+	0.789021i	$0.710588\pi$
$270$		0			0
$271$	−6.06113	−	6.06113i	−0.368187	−	0.368187i	0.498628	−	0.866816i	$-0.333837\pi$
$271$	−6.06113	−	6.06113i	−0.368187	−	0.368187i	−0.866816	+	0.498628i	$0.833837\pi$
$272$	1.65761	+	3.95448i	0.100508	+	0.239775i
$273$		0			0
$274$	−12.9779	−	10.6278i	−0.784026	−	0.642049i
$275$	36.2510	+	36.2510i	2.18602	+	2.18602i
$276$		0			0
$277$	−2.49785			−0.150081			−0.0750407	−	0.997180i	$-0.523909\pi$
$277$	−2.49785			−0.150081			−0.0750407	+	0.997180i	$0.523909\pi$
$278$	−1.36396	−	13.7001i	−0.0818047	−	0.821676i
$279$		0			0
$280$	14.6435	+	47.7281i	0.875117	+	2.85230i
$281$	6.26380	−	6.26380i	0.373667	−	0.373667i	−0.495144	−	0.868811i	$-0.664885\pi$
$281$	6.26380	−	6.26380i	0.373667	−	0.373667i	0.868811	+	0.495144i	$0.164885\pi$
$282$		0			0
$283$		−	11.9847i		−	0.712416i	−0.934407	−	0.356208i	$-0.884069\pi$
$283$		−	11.9847i		−	0.712416i	0.934407	−	0.356208i	$-0.115931\pi$
$284$	−8.78711	+	13.2112i	−0.521419	+	0.783940i
$285$		0			0
$286$	11.3161	+	14.7374i	0.669133	+	0.871440i
$287$			0.192415i			0.0113579i
$288$		0			0
$289$	15.8509			0.932406
$290$	2.00477	−	2.44809i	0.117724	−	0.143757i
$291$		0			0
$292$	8.97662	−	13.4961i	0.525317	−	0.789800i
$293$	3.26151	+	3.26151i	0.190539	+	0.190539i	0.795929	−	0.605390i	$-0.206983\pi$
$293$	3.26151	+	3.26151i	0.190539	+	0.190539i	−0.605390	+	0.795929i	$0.706983\pi$
$294$		0			0
$295$		−	7.60061i		−	0.442525i
$296$	3.70914	−	6.99255i	0.215590	−	0.406433i
$297$		0			0
$298$	−9.89966	−	8.10695i	−0.573472	−	0.469623i
$299$	−19.4070	−	4.54000i	−1.12234	−	0.262555i
$300$		0			0
$301$	9.98830	−	9.98830i	0.575716	−	0.575716i
$302$	−7.89570	+	9.64169i	−0.454346	+	0.554817i
$303$		0			0
$304$	7.65207	+	3.13177i	0.438876	+	0.179619i
$305$	14.4148	+	14.4148i	0.825387	+	0.825387i
$306$		0			0
$307$	−7.00180	+	7.00180i	−0.399614	+	0.399614i	−0.878097	−	0.478483i	$-0.841187\pi$
$307$	−7.00180	+	7.00180i	−0.399614	+	0.399614i	0.478483	+	0.878097i	$0.341187\pi$
$308$	28.8801	−	5.80807i	1.64560	−	0.330946i
$309$		0			0
$310$	24.8392	−	2.47295i	1.41077	−	0.140454i
$311$	−29.2550			−1.65890			−0.829450	−	0.558582i	$-0.811346\pi$
$311$	−29.2550			−1.65890			−0.829450	+	0.558582i	$0.811346\pi$
$312$		0			0
$313$	2.65852			0.150269			0.0751343	−	0.997173i	$-0.476061\pi$
$313$	2.65852			0.150269			0.0751343	+	0.997173i	$0.476061\pi$
$314$	−33.5239	+	3.33758i	−1.89186	+	0.188351i
$315$		0			0
$316$	−2.62606	−	13.0578i	−0.147727	−	0.734559i
$317$	−5.19502	+	5.19502i	−0.291781	+	0.291781i	−0.837784	−	0.546002i	$-0.816149\pi$
$317$	−5.19502	+	5.19502i	−0.291781	+	0.291781i	0.546002	+	0.837784i	$0.316149\pi$
$318$		0			0
$319$	−1.32023	−	1.32023i	−0.0739189	−	0.0739189i
$320$	6.59800	−	34.3056i	0.368839	−	1.91774i
$321$		0			0
$322$	−20.0204	+	24.4475i	−1.11569	+	1.36241i
$323$	−1.56679	+	1.56679i	−0.0871787	+	0.0871787i
$324$		0			0
$325$	−11.5547	+	49.3924i	−0.640937	+	2.73980i
$326$	6.24248	+	5.11204i	0.345739	+	0.283130i
$327$		0			0
$328$	0.0630935	−	0.118945i	0.00348375	−	0.00656764i
$329$		−	36.9026i		−	2.03450i
$330$		0			0
$331$	−14.6385	−	14.6385i	−0.804603	−	0.804603i	0.179208	−	0.983811i	$-0.442647\pi$
$331$	−14.6385	−	14.6385i	−0.804603	−	0.804603i	−0.983811	+	0.179208i	$0.942647\pi$
$332$	0.362643	+	0.241203i	0.0199026	+	0.0132378i
$333$		0			0
$334$	6.06780	−	7.40959i	0.332015	−	0.405435i
$335$	−12.5552			−0.685965
$336$		0			0
$337$		−	19.9550i		−	1.08702i	−0.839404	−	0.543508i	$-0.817096\pi$
$337$		−	19.9550i		−	1.08702i	0.839404	−	0.543508i	$-0.182904\pi$
$338$	−6.48294	+	17.2038i	−0.352625	+	0.935765i
$339$		0			0
$340$	7.79523	+	5.18481i	0.422756	+	0.281186i
$341$		−	14.7292i		−	0.797629i
$342$		0			0
$343$	−6.68288	+	6.68288i	−0.360841	+	0.360841i
$344$	−9.44963	+	2.89926i	−0.509490	+	0.156317i
$345$		0			0
$346$	0.254433	+	2.55562i	0.0136784	+	0.137391i
$347$	13.2961			0.713770			0.356885	−	0.934148i	$-0.383839\pi$
$347$	13.2961			0.713770			0.356885	+	0.934148i	$0.383839\pi$
$348$		0			0
$349$	−20.5685	−	20.5685i	−1.10101	−	1.10101i	−0.994290	−	0.106716i	$-0.965967\pi$
$349$	−20.5685	−	20.5685i	−1.10101	−	1.10101i	−0.106716	−	0.994290i	$-0.534033\pi$
$350$	62.2210	+	50.9535i	3.32585	+	2.72358i
$351$		0			0
$352$	−19.7572	−	5.87948i	−1.05306	−	0.313378i
$353$	−3.37647	−	3.37647i	−0.179712	−	0.179712i	0.611519	−	0.791230i	$-0.290559\pi$
$353$	−3.37647	−	3.37647i	−0.179712	−	0.179712i	−0.791230	+	0.611519i	$0.790559\pi$
$354$		0			0
$355$			34.6430i			1.83866i
$356$	17.8203	−	26.7924i	0.944474	−	1.41999i
$357$		0			0
$358$	−14.7708	+	1.47056i	−0.780662	+	0.0777214i
$359$	10.1733	+	10.1733i	0.536927	+	0.536927i	0.922625	−	0.385698i	$-0.126039\pi$
$359$	10.1733	+	10.1733i	0.536927	+	0.536927i	−0.385698	+	0.922625i	$0.626039\pi$
$360$		0			0
$361$		−	14.7274i		−	0.775124i
$362$	1.96938	+	19.7811i	0.103508	+	1.03967i
$363$		0			0
$364$	19.9545	+	21.2462i	1.04590	+	1.11360i
$365$		−	35.3902i		−	1.85241i
$366$		0			0
$367$			12.7553i			0.665820i	0.942959	+	0.332910i	$0.108030\pi$
$367$			12.7553i			0.665820i	−0.942959	+	0.332910i	$0.891970\pi$
$368$	20.3924	−	8.54794i	1.06303	−	0.445592i
$369$		0			0
$370$	−1.71215	−	17.1974i	−0.0890102	−	0.894050i
$371$	22.9831	−	22.9831i	1.19322	−	1.19322i
$372$		0			0
$373$			13.6959i			0.709147i	0.935028	+	0.354573i	$0.115374\pi$
$373$			13.6959i			0.709147i	−0.935028	+	0.354573i	$0.884626\pi$
$374$	3.50001	−	4.27397i	0.180981	−	0.221002i
$375$		0			0
$376$	−12.1004	+	22.8120i	−0.624032	+	1.17644i
$377$	0.420812	−	1.79884i	0.0216729	−	0.0926447i
$378$		0			0
$379$	−16.8734	−	16.8734i	−0.866730	−	0.866730i	0.125379	−	0.992109i	$-0.459985\pi$
$379$	−16.8734	−	16.8734i	−0.866730	−	0.866730i	−0.992109	+	0.125379i	$0.959985\pi$
$380$	17.6983	−	3.55930i	0.907901	−	0.182588i
$381$		0			0
$382$	21.3255	−	2.12313i	1.09111	−	0.108629i
$383$	−2.81081	+	2.81081i	−0.143625	+	0.143625i	−0.775263	−	0.631638i	$-0.782383\pi$
$383$	−2.81081	+	2.81081i	−0.143625	+	0.143625i	0.631638	+	0.775263i	$0.282383\pi$
$384$		0			0
$385$	45.4805	−	45.4805i	2.31790	−	2.31790i
$386$	−25.6388	−	20.9959i	−1.30498	−	1.06866i
$387$		0			0
$388$	−20.7308	−	13.7886i	−1.05245	−	0.700009i
$389$	34.2597			1.73703			0.868517	−	0.495660i	$-0.165074\pi$
$389$	34.2597			1.73703			0.868517	+	0.495660i	$0.165074\pi$
$390$		0			0
$391$			5.92564i			0.299673i
$392$	25.2506	−	7.74717i	1.27535	−	0.391291i
$393$		0			0
$394$	9.66923	+	7.91825i	0.487129	+	0.398916i
$395$	−20.5635	−	20.5635i	−1.03466	−	1.03466i
$396$		0			0
$397$	−16.1956	−	16.1956i	−0.812836	−	0.812836i	0.172223	−	0.985058i	$-0.444905\pi$
$397$	−16.1956	−	16.1956i	−0.812836	−	0.812836i	−0.985058	+	0.172223i	$0.944905\pi$
$398$	0.592428	+	5.95056i	0.0296957	+	0.298274i
$399$		0			0
$400$	−21.7552	−	51.9002i	−1.08776	−	2.59501i
$401$	−18.5045	+	18.5045i	−0.924069	+	0.924069i	−0.997314	−	0.0732452i	$-0.976664\pi$
$401$	−18.5045	+	18.5045i	−0.924069	+	0.924069i	0.0732452	+	0.997314i	$0.476664\pi$
$402$		0			0
$403$	12.3817	−	7.68694i	0.616778	−	0.382914i
$404$	−5.66732	+	1.13975i	−0.281960	+	0.0567049i
$405$		0			0
$406$	−2.26604	−	1.85569i	−0.112462	−	0.0920963i
$407$	−10.1977			−0.505483
$408$		0			0
$409$	−19.3758	−	19.3758i	−0.958070	−	0.958070i	0.0410856	−	0.999156i	$-0.486918\pi$
$409$	−19.3758	−	19.3758i	−0.958070	−	0.958070i	−0.999156	+	0.0410856i	$0.986918\pi$
$410$	−0.0291240	−	0.292532i	−0.00143833	−	0.0144471i
$411$		0			0
$412$	14.0328	−	2.82213i	0.691345	−	0.139036i
$413$	−7.03539			−0.346189
$414$		0			0
$415$	0.950941			0.0466798
$416$	−5.36856	−	19.6769i	−0.263215	−	0.964737i
$417$		0			0
$418$	−1.05530	−	10.5998i	−0.0516163	−	0.518453i
$419$	−36.1631			−1.76668			−0.883341	−	0.468731i	$-0.844711\pi$
$419$	−36.1631			−1.76668			−0.883341	+	0.468731i	$0.844711\pi$
$420$		0			0
$421$	0.701961	−	0.701961i	0.0342115	−	0.0342115i	−0.689794	−	0.724006i	$-0.742299\pi$
$421$	0.701961	−	0.701961i	0.0342115	−	0.0342115i	0.724006	+	0.689794i	$0.242299\pi$
$422$	−3.47872	−	34.9415i	−0.169342	−	1.70093i
$423$		0			0
$424$	−21.7436	+	6.67119i	−1.05596	+	0.323981i
$425$	15.0812			0.731547
$426$		0			0
$427$	13.3428	−	13.3428i	0.645704	−	0.645704i
$428$	−20.8838	+	4.19994i	−1.00945	+	0.203012i
$429$		0			0
$430$	−13.6735	+	16.6972i	−0.659397	+	0.805211i
$431$	−2.65259	+	2.65259i	−0.127771	+	0.127771i	−0.768100	−	0.640330i	$-0.778798\pi$
$431$	−2.65259	+	2.65259i	−0.127771	+	0.127771i	0.640330	+	0.768100i	$0.278798\pi$
$432$		0			0
$433$			27.2434i			1.30923i	0.755961	+	0.654617i	$0.227170\pi$
$433$			27.2434i			1.30923i	−0.755961	+	0.654617i	$0.772830\pi$
$434$	−2.28905	−	22.9920i	−0.109878	−	1.10365i
$435$		0			0
$436$	2.78916	−	4.19344i	0.133577	−	0.200829i
$437$	8.07960	+	8.07960i	0.386500	+	0.386500i
$438$		0			0
$439$	28.4482			1.35776			0.678878	−	0.734251i	$-0.262466\pi$
$439$	28.4482			1.35776			0.678878	+	0.734251i	$0.262466\pi$
$440$	−43.0277	+	13.2014i	−2.05127	+	0.629352i
$441$		0			0
$442$	5.41942	+	0.711673i	0.257775	+	0.0338508i
$443$	26.2562			1.24747			0.623735	−	0.781636i	$-0.285614\pi$
$443$	26.2562			1.24747			0.623735	+	0.781636i	$0.285614\pi$
$444$		0			0
$445$		−	70.2562i		−	3.33046i
$446$	−2.83694	−	2.32321i	−0.134333	−	0.110007i
$447$		0			0
$448$	−31.7544	−	6.10734i	−1.50026	−	0.288545i
$449$	10.3557	−	10.3557i	0.488717	−	0.488717i	−0.419185	−	0.907901i	$-0.637684\pi$
$449$	10.3557	−	10.3557i	0.488717	−	0.488717i	0.907901	+	0.419185i	$0.137684\pi$
$450$		0			0
$451$	−0.173466			−0.00816820
$452$	5.87313	−	1.18115i	0.276249	−	0.0555564i
$453$		0			0
$454$	11.9368	−	14.5764i	0.560223	−	0.684106i
$455$	61.9678	+	14.4965i	2.90509	+	0.679605i
$456$		0			0
$457$	20.3069	+	20.3069i	0.949918	+	0.949918i	0.998804	−	0.0488865i	$-0.0155673\pi$
$457$	20.3069	+	20.3069i	0.949918	+	0.949918i	−0.0488865	+	0.998804i	$0.515567\pi$
$458$	−6.31013	+	7.70550i	−0.294853	+	0.360055i
$459$		0			0
$460$	26.7369	−	40.1983i	1.24662	−	1.87425i
$461$	−13.3085	+	13.3085i	−0.619838	+	0.619838i	−0.945490	−	0.325652i	$-0.894416\pi$
$461$	−13.3085	+	13.3085i	−0.619838	+	0.619838i	0.325652	+	0.945490i	$0.394416\pi$
$462$		0			0
$463$	−3.24915	−	3.24915i	−0.151001	−	0.151001i	0.627564	−	0.778565i	$-0.284052\pi$
$463$	−3.24915	−	3.24915i	−0.151001	−	0.151001i	−0.778565	+	0.627564i	$0.784052\pi$
$464$	0.792308	+	1.89017i	0.0367820	+	0.0877488i
$465$		0			0
$466$	7.57771	−	0.754424i	0.351031	−	0.0349480i
$467$			40.2993i			1.86483i	0.361392	+	0.932414i	$0.382302\pi$
$467$			40.2993i			1.86483i	−0.361392	+	0.932414i	$0.617698\pi$
$468$		0			0
$469$			11.6215i			0.536633i
$470$	5.58557	+	56.1035i	0.257643	+	2.58786i
$471$		0			0
$472$	4.34905	+	2.30692i	0.200181	+	0.106185i
$473$	9.00464	+	9.00464i	0.414034	+	0.414034i
$474$		0			0
$475$	20.5632	−	20.5632i	0.943506	−	0.943506i
$476$	4.79924	−	7.21554i	0.219973	−	0.330724i
$477$		0			0
$478$	10.0276	+	8.21172i	0.458652	+	0.375595i
$479$	19.0201	+	19.0201i	0.869049	+	0.869049i	0.992367	−	0.123318i	$-0.0393536\pi$
$479$	19.0201	+	19.0201i	0.869049	+	0.869049i	−0.123318	+	0.992367i	$0.539354\pi$
$480$		0			0
$481$	−5.32206	−	8.57249i	−0.242665	−	0.390872i
$482$	25.1107	+	20.5634i	1.14376	+	0.936639i
$483$		0			0
$484$	0.898512	+	4.46776i	0.0408415	+	0.203080i
$485$	−54.3613			−2.46842
$486$		0			0
$487$	8.43408	−	8.43408i	0.382184	−	0.382184i	−0.489704	−	0.871889i	$-0.662895\pi$
$487$	8.43408	−	8.43408i	0.382184	−	0.382184i	0.871889	+	0.489704i	$0.162895\pi$
$488$	−12.6232	+	3.87295i	−0.571427	+	0.175320i
$489$		0			0
$490$	36.5374	−	44.6170i	1.65059	−	2.01559i
$491$			23.3787i			1.05507i	0.849534	+	0.527533i	$0.176883\pi$
$491$			23.3787i			1.05507i	−0.849534	+	0.527533i	$0.823117\pi$
$492$		0			0
$493$	−0.549248			−0.0247369
$494$	8.35972	−	6.41900i	0.376122	−	0.288804i
$495$		0			0
$496$	−6.12412	+	14.9635i	−0.274981	+	0.671880i
$497$	32.0668			1.43839
$498$		0			0
$499$	−18.6272	−	18.6272i	−0.833867	−	0.833867i	0.154176	−	0.988043i	$-0.450728\pi$
$499$	−18.6272	−	18.6272i	−0.833867	−	0.833867i	−0.988043	+	0.154176i	$0.950728\pi$
$500$	−65.9481	−	43.8638i	−2.94929	−	1.96165i
$501$		0			0
$502$	1.39396	−	0.138780i	0.0622154	−	0.00619407i
$503$		−	12.2441i		−	0.545939i	−0.962023	−	0.272969i	$-0.911994\pi$
$503$		−	12.2441i		−	0.545939i	0.962023	−	0.272969i	$-0.0880058\pi$
$504$		0			0
$505$	−8.92492	+	8.92492i	−0.397154	+	0.397154i
$506$	−22.0399	−	18.0487i	−0.979793	−	0.802365i
$507$		0			0
$508$	31.6932	−	6.37382i	1.40616	−	0.282792i
$509$	25.7075	−	25.7075i	1.13947	−	1.13947i	0.150920	−	0.988546i	$-0.451776\pi$
$509$	25.7075	−	25.7075i	1.13947	−	1.13947i	0.988546	−	0.150920i	$-0.0482237\pi$
$510$		0			0
$511$	−32.7584			−1.44914
$512$	17.6269	+	14.1877i	0.779008	+	0.627014i
$513$		0			0
$514$	23.8083	−	2.37031i	1.05014	−	0.104550i
$515$	22.0989	−	22.0989i	0.973793	−	0.973793i
$516$		0			0
$517$	33.2683			1.46314
$518$	−15.9185	+	1.58482i	−0.699419	+	0.0696330i
$519$		0			0
$520$	−33.5530	−	29.2806i	−1.47140	−	1.28404i
$521$	41.6747			1.82580			0.912902	−	0.408179i	$-0.133836\pi$
$521$	41.6747			1.82580			0.912902	+	0.408179i	$0.133836\pi$
$522$		0			0
$523$	16.6394			0.727591			0.363796	−	0.931479i	$-0.381481\pi$
$523$	16.6394			0.727591			0.363796	+	0.931479i	$0.381481\pi$
$524$	−0.232399	+	0.0467377i	−0.0101524	+	0.00204175i
$525$		0			0
$526$	−40.3932	+	4.02148i	−1.76123	+	0.175345i
$527$	−3.06383	−	3.06383i	−0.133463	−	0.133463i
$528$		0			0
$529$	7.55722			0.328575
$530$	−31.4628	+	38.4203i	−1.36666	+	1.66887i
$531$		0			0
$532$	−3.29461	−	16.3821i	−0.142839	−	0.710255i
$533$	−0.0905295	−	0.145820i	−0.00392127	−	0.00631617i
$534$		0			0
$535$	−32.8879	+	32.8879i	−1.42187	+	1.42187i
$536$	3.81073	−	7.18406i	0.164599	−	0.310304i
$537$		0			0
$538$	−36.4224	+	3.62615i	−1.57028	+	0.156334i
$539$	−24.0615	−	24.0615i	−1.03640	−	1.03640i
$540$		0			0
$541$	23.7679	+	23.7679i	1.02186	+	1.02186i	0.999756	+	0.0221074i	$0.00703757\pi$
$541$	23.7679	+	23.7679i	1.02186	+	1.02186i	0.0221074	+	0.999756i	$0.492962\pi$
$542$	7.68037	−	9.37875i	0.329900	−	0.402852i
$543$		0			0
$544$	−5.33273	+	2.88673i	−0.228639	+	0.123767i
$545$		−	10.9962i		−	0.471027i
$546$		0			0
$547$	20.4838			0.875824			0.437912	−	0.899018i	$-0.355718\pi$
$547$	20.4838			0.875824			0.437912	+	0.899018i	$0.355718\pi$
$548$	13.1378	−	19.7523i	0.561218	−	0.843776i
$549$		0			0
$550$	−45.9355	+	56.0933i	−1.95870	+	2.39183i
$551$	−0.748898	+	0.748898i	−0.0319041	+	0.0319041i
$552$		0			0
$553$	−19.0343	+	19.0343i	−0.809420	+	0.809420i
$554$	−0.349960	−	3.51512i	−0.0148684	−	0.149343i
$555$		0			0
$556$	19.0884	−	3.83887i	0.809529	−	0.162805i
$557$	30.8045	+	30.8045i	1.30523	+	1.30523i	0.924819	+	0.380408i	$0.124217\pi$
$557$	30.8045	+	30.8045i	1.30523	+	1.30523i	0.380408	+	0.924819i	$0.375783\pi$
$558$		0			0
$559$	−2.87014	+	12.2689i	−0.121394	+	0.518921i
$560$	−65.1140	+	27.2941i	−2.75157	+	1.15339i
$561$		0			0
$562$	9.69236	+	7.93719i	0.408847	+	0.334810i
$563$		−	33.7226i		−	1.42124i	−0.703578	−	0.710618i	$-0.748415\pi$
$563$		−	33.7226i		−	1.42124i	0.703578	−	0.710618i	$-0.251585\pi$
$564$		0			0
$565$	9.24903	−	9.24903i	0.389110	−	0.389110i
$566$	16.8655	−	1.67911i	0.708912	−	0.0705781i
$567$		0			0
$568$	−19.8226	−	10.5148i	−0.831739	−	0.441190i
$569$		−	37.5317i		−	1.57341i	−0.617329	−	0.786705i	$-0.711785\pi$
$569$		−	37.5317i		−	1.57341i	0.617329	−	0.786705i	$-0.288215\pi$
$570$		0			0
$571$			10.4261i			0.436318i	0.975913	+	0.218159i	$0.0700051\pi$
$571$			10.4261i			0.436318i	−0.975913	+	0.218159i	$0.929995\pi$
$572$	−19.1538	+	17.9894i	−0.800863	+	0.752174i
$573$		0			0
$574$	−0.270778	+	0.0269582i	−0.0113021	+	0.00112521i
$575$		−	77.7706i		−	3.24326i
$576$		0			0
$577$	−5.95723	−	5.95723i	−0.248003	−	0.248003i	0.572148	−	0.820150i	$-0.306110\pi$
$577$	−5.95723	−	5.95723i	−0.248003	−	0.248003i	−0.820150	+	0.572148i	$0.806110\pi$
$578$	2.22078	+	22.3063i	0.0923721	+	0.927819i
$579$		0			0
$580$	3.72597	+	2.47824i	0.154713	+	0.102903i
$581$		−	0.880223i		−	0.0365178i
$582$		0			0
$583$	20.7197	+	20.7197i	0.858121	+	0.858121i
$584$	20.2501	+	10.7415i	0.837957	+	0.444488i
$585$		0			0
$586$	−4.13283	+	5.04673i	−0.170726	+	0.208478i
$587$	−1.72078	−	1.72078i	−0.0710241	−	0.0710241i	0.670702	−	0.741727i	$-0.265993\pi$
$587$	−1.72078	−	1.72078i	−0.0710241	−	0.0710241i	−0.741727	+	0.670702i	$0.765993\pi$
$588$		0			0
$589$	−8.35506			−0.344264
$590$	10.6960	−	1.06488i	0.440348	−	0.0438403i
$591$		0			0
$592$	10.3600	+	4.24003i	0.425792	+	0.174264i
$593$	−13.4905	+	13.4905i	−0.553990	+	0.553990i	−0.927590	−	0.373600i	$-0.878123\pi$
$593$	−13.4905	+	13.4905i	−0.553990	+	0.553990i	0.373600	+	0.927590i	$0.378123\pi$
$594$		0			0
$595$		−	18.9209i		−	0.775683i
$596$	10.0216	−	15.0672i	0.410500	−	0.617175i
$597$		0			0
$598$	3.66994	−	27.9467i	0.150075	−	1.14283i
$599$			37.0916i			1.51552i	0.652533	+	0.757760i	$0.273706\pi$
$599$			37.0916i			1.51552i	−0.652533	+	0.757760i	$0.726294\pi$
$600$		0			0
$601$	−17.3441			−0.707483			−0.353741	−	0.935343i	$-0.615091\pi$
$601$	−17.3441			−0.707483			−0.353741	+	0.935343i	$0.615091\pi$
$602$	15.4555	+	12.6567i	0.629919	+	0.515849i
$603$		0			0
$604$	−14.6745	−	9.76043i	−0.597099	−	0.397146i
$605$	7.03585	+	7.03585i	0.286048	+	0.286048i
$606$		0			0
$607$			0.0268909i			0.00109147i	1.00000		0.000545735i	$0.000173713\pi$
$607$			0.0268909i			0.00109147i	−1.00000		0.000545735i	$0.999826\pi$
$608$	−3.33512	+	11.2072i	−0.135257	+	0.454512i
$609$		0			0
$610$	−18.2657	+	22.3049i	−0.739557	+	0.903097i
$611$	17.3623	+	27.9662i	0.702403	+	1.13139i
$612$		0			0
$613$	21.4415	−	21.4415i	0.866013	−	0.866013i	−0.126015	−	0.992028i	$-0.540219\pi$
$613$	21.4415	−	21.4415i	0.866013	−	0.866013i	0.992028	+	0.126015i	$0.0402188\pi$
$614$	−10.8343	−	8.87234i	−0.437237	−	0.358059i
$615$		0			0
$616$	12.2197	+	39.8279i	0.492345	+	1.60471i
$617$	10.1510	+	10.1510i	0.408663	+	0.408663i	0.881272	−	0.472609i	$-0.156688\pi$
$617$	10.1510	+	10.1510i	0.408663	+	0.408663i	−0.472609	+	0.881272i	$0.656688\pi$
$618$		0			0
$619$	−10.4442	+	10.4442i	−0.419789	+	0.419789i	−0.885131	−	0.465342i	$-0.845931\pi$
$619$	−10.4442	+	10.4442i	−0.419789	+	0.419789i	0.465342	+	0.885131i	$0.345931\pi$
$620$	6.96014	+	34.6086i	0.279526	+	1.38992i
$621$		0			0
$622$	−4.09875	−	41.1693i	−0.164345	−	1.65074i
$623$	−65.0316			−2.60544
$624$		0			0
$625$	−102.588			−4.10352
$626$	0.372470	+	3.74122i	0.0148869	+	0.149529i
$627$		0			0
$628$	−9.39368	−	46.7091i	−0.374848	−	1.86390i
$629$	−2.12125	+	2.12125i	−0.0845796	+	0.0845796i
$630$		0			0
$631$	−21.3320	−	21.3320i	−0.849215	−	0.849215i	0.140820	−	0.990035i	$-0.455026\pi$
$631$	−21.3320	−	21.3320i	−0.849215	−	0.849215i	−0.990035	+	0.140820i	$0.955026\pi$
$632$	18.0078	−	5.52499i	0.716310	−	0.219772i
$633$		0			0
$634$	−8.03857	−	6.58288i	−0.319252	−	0.261440i
$635$	49.9106	−	49.9106i	1.98064	−	1.98064i
$636$		0			0
$637$	7.66939	−	32.7841i	0.303872	−	1.29895i
$638$	1.67294	−	2.04288i	0.0662322	−	0.0808783i
$639$		0			0
$640$	49.2011	+	4.47873i	1.94485	+	0.177037i
$641$			28.5426i			1.12736i	0.825992	+	0.563682i	$0.190616\pi$
$641$			28.5426i			1.12736i	−0.825992	+	0.563682i	$0.809384\pi$
$642$		0			0
$643$	18.1283	+	18.1283i	0.714912	+	0.714912i	0.967559	−	0.252647i	$-0.0813010\pi$
$643$	18.1283	+	18.1283i	0.714912	+	0.714912i	−0.252647	+	0.967559i	$0.581301\pi$
$644$	−37.2089	−	24.7486i	−1.46624	−	0.975232i
$645$		0			0
$646$	−2.42439	−	1.98536i	−0.0953865	−	0.0781131i
$647$	−23.0407			−0.905824			−0.452912	−	0.891555i	$-0.649615\pi$
$647$	−23.0407			−0.905824			−0.452912	+	0.891555i	$0.649615\pi$
$648$		0			0
$649$		−	6.34253i		−	0.248966i
$650$	−71.1266	−	9.34028i	−2.78982	−	0.366356i
$651$		0			0
$652$	−6.31936	+	9.50099i	−0.247485	+	0.372087i
$653$			14.8261i			0.580191i	0.956998	+	0.290095i	$0.0936870\pi$
$653$			14.8261i			0.580191i	−0.956998	+	0.290095i	$0.906313\pi$
$654$		0			0
$655$	−0.365983	+	0.365983i	−0.0143001	+	0.0143001i
$656$	0.176226	+	0.0721240i	0.00688046	+	0.00281597i
$657$		0			0
$658$	51.9314	−	5.17020i	2.02450	−	0.201555i
$659$	−14.8920			−0.580112			−0.290056	−	0.957010i	$-0.593674\pi$
$659$	−14.8920			−0.580112			−0.290056	+	0.957010i	$0.593674\pi$
$660$		0			0
$661$	21.6359	+	21.6359i	0.841538	+	0.841538i	0.989059	−	0.147521i	$-0.0471293\pi$
$661$	21.6359	+	21.6359i	0.841538	+	0.841538i	−0.147521	+	0.989059i	$0.547129\pi$
$662$	18.5492	−	22.6510i	0.720934	−	0.880356i
$663$		0			0
$664$	−0.288627	+	0.544125i	−0.0112009	+	0.0211162i
$665$	−25.7986	−	25.7986i	−1.00043	−	1.00043i
$666$		0			0
$667$			2.83235i			0.109669i
$668$	11.2773	+	7.50084i	0.436332	+	0.290216i
$669$		0			0
$670$	−1.75904	−	17.6684i	−0.0679576	−	0.682590i
$671$	12.0288	+	12.0288i	0.464366	+	0.464366i
$672$		0			0
$673$			35.0331i			1.35043i	0.737623	+	0.675213i	$0.235948\pi$
$673$			35.0331i			1.35043i	−0.737623	+	0.675213i	$0.764052\pi$
$674$	28.0817	−	2.79577i	1.08167	−	0.107689i
$675$		0			0
$676$	−25.1185	−	6.71283i	−0.966095	−	0.258186i
$677$			7.24823i			0.278572i	0.990252	+	0.139286i	$0.0444807\pi$
$677$			7.24823i			0.278572i	−0.990252	+	0.139286i	$0.955519\pi$
$678$		0			0
$679$			50.3187i			1.93105i
$680$	−6.20422	+	11.6963i	−0.237921	+	0.448533i
$681$		0			0
$682$	20.7277	−	2.06362i	0.793705	−	0.0790200i
$683$	7.11346	−	7.11346i	0.272189	−	0.272189i	−0.557792	−	0.829981i	$-0.688351\pi$
$683$	7.11346	−	7.11346i	0.272189	−	0.272189i	0.829981	+	0.557792i	$0.188351\pi$
$684$		0			0
$685$		−	51.7955i		−	1.97900i
$686$	−10.3408	−	8.46822i	−0.394814	−	0.323318i
$687$		0			0
$688$	−5.40393	−	12.8919i	−0.206023	−	0.491497i
$689$	−6.60420	+	28.2308i	−0.251600	+	1.07551i
$690$		0			0
$691$	32.6940	+	32.6940i	1.24374	+	1.24374i	0.958439	+	0.285298i	$0.0920924\pi$
$691$	32.6940	+	32.6940i	1.24374	+	1.24374i	0.285298	+	0.958439i	$0.407908\pi$
$692$	−3.56076	+	0.716105i	−0.135360	+	0.0272222i
$693$		0			0
$694$	1.86283	+	18.7110i	0.0707122	+	0.710259i
$695$	30.0605	−	30.0605i	1.14026	−	1.14026i
$696$		0			0
$697$	−0.0360829	+	0.0360829i	−0.00136674	+	0.00136674i
$698$	26.0634	−	31.8268i	0.986514	−	1.20466i
$699$		0			0
$700$	−62.9872	+	94.6996i	−2.38069	+	3.57931i
$701$	−29.6221			−1.11881			−0.559406	−	0.828894i	$-0.688971\pi$
$701$	−29.6221			−1.11881			−0.559406	+	0.828894i	$0.688971\pi$
$702$		0			0
$703$			5.78463i			0.218171i
$704$	5.50588	−	28.6272i	0.207511	−	1.07893i
$705$		0			0
$706$	4.27851	−	5.22462i	0.161024	−	0.196631i
$707$	8.26122	+	8.26122i	0.310695	+	0.310695i
$708$		0			0
$709$	−25.8554	−	25.8554i	−0.971021	−	0.971021i	0.0285709	−	0.999592i	$-0.490904\pi$
$709$	−25.8554	−	25.8554i	−0.971021	−	0.971021i	−0.999592	+	0.0285709i	$0.990904\pi$
$710$	−48.7516	+	4.85363i	−1.82962	+	0.182154i
$711$		0			0
$712$	40.2004	+	21.3240i	1.50657	+	0.799151i
$713$	−15.7995	+	15.7995i	−0.591696	+	0.591696i
$714$		0			0
$715$	−13.0688	+	55.8651i	−0.488747	+	2.08923i
$716$	−4.13891	−	20.5803i	−0.154678	−	0.769122i
$717$		0			0
$718$	−12.8911	+	15.7418i	−0.481093	+	0.587478i
$719$	−31.2277			−1.16460			−0.582299	−	0.812975i	$-0.697847\pi$
$719$	−31.2277			−1.16460			−0.582299	+	0.812975i	$0.697847\pi$
$720$		0			0
$721$	−20.4555	−	20.4555i	−0.761802	−	0.761802i
$722$	20.7252	−	2.06336i	0.771311	−	0.0767905i
$723$		0			0
$724$	−27.5612	+	5.54284i	−1.02430	+	0.205998i
$725$	7.20855			0.267719
$726$		0			0
$727$	21.2172			0.786902			0.393451	−	0.919346i	$-0.371281\pi$
$727$	21.2172			0.786902			0.393451	+	0.919346i	$0.371281\pi$
$728$	−27.1032	+	31.0578i	−1.00451	+	1.15108i
$729$		0			0
$730$	49.8030	−	4.95831i	1.84329	−	0.183515i
$731$	3.74614			0.138556
$732$		0			0
$733$	−23.8649	+	23.8649i	−0.881469	+	0.881469i	−0.993684	−	0.112215i	$-0.964206\pi$
$733$	−23.8649	+	23.8649i	−0.881469	+	0.881469i	0.112215	+	0.993684i	$0.464206\pi$
$734$	−17.9499	+	1.78707i	−0.662544	+	0.0659618i
$735$		0			0
$736$	14.8862	+	27.4997i	0.548712	+	1.01365i
$737$	−10.4770			−0.385927
$738$		0			0
$739$	28.5318	−	28.5318i	1.04956	−	1.04956i	0.0508533	−	0.998706i	$-0.483806\pi$
$739$	28.5318	−	28.5318i	1.04956	−	1.04956i	0.998706	−	0.0508533i	$-0.0161941\pi$
$740$	23.9613	−	4.81885i	0.880834	−	0.177145i
$741$		0			0
$742$	35.5631	+	29.1231i	1.30556	+	1.06914i
$743$	14.7470	−	14.7470i	0.541013	−	0.541013i	−0.382813	−	0.923826i	$-0.625044\pi$
$743$	14.7470	−	14.7470i	0.541013	−	0.541013i	0.923826	+	0.382813i	$0.125044\pi$
$744$		0			0
$745$		−	39.5099i		−	1.44753i
$746$	−19.2736	+	1.91885i	−0.705658	+	0.0702542i
$747$		0			0
$748$	6.50494	+	4.32660i	0.237844	+	0.158196i
$749$	30.4421	+	30.4421i	1.11233	+	1.11233i
$750$		0			0
$751$	−44.2644			−1.61523			−0.807615	−	0.589710i	$-0.799242\pi$
$751$	−44.2644			−1.61523			−0.807615	+	0.589710i	$0.799242\pi$
$752$	−33.7976	−	13.8324i	−1.23247	−	0.504415i
$753$		0			0
$754$	2.59038	+	0.340166i	0.0943361	+	0.0123881i
$755$	−38.4803			−1.40044
$756$		0			0
$757$		−	15.4803i		−	0.562641i	−0.959614	−	0.281320i	$-0.909228\pi$
$757$		−	15.4803i		−	0.562641i	0.959614	−	0.281320i	$-0.0907724\pi$
$758$	21.3812	−	26.1093i	0.776601	−	0.948332i
$759$		0			0
$760$	7.48844	+	24.4073i	0.271634	+	0.885346i
$761$	−15.3450	+	15.3450i	−0.556257	+	0.556257i	−0.928240	−	0.371983i	$-0.878678\pi$
$761$	−15.3450	+	15.3450i	−0.556257	+	0.556257i	0.371983	+	0.928240i	$0.378678\pi$
$762$		0			0
$763$	−10.1785			−0.368486
$764$	5.97559	+	29.7130i	0.216189	+	1.07498i
$765$		0			0
$766$	−4.34933	−	3.56172i	−0.157148	−	0.128690i
$767$	5.33170	−	3.31008i	0.192517	−	0.119520i
$768$		0			0
$769$	0.693724	+	0.693724i	0.0250163	+	0.0250163i	0.719504	−	0.694488i	$-0.244369\pi$
$769$	0.693724	+	0.693724i	0.0250163	+	0.0250163i	−0.694488	+	0.719504i	$0.744369\pi$
$770$	70.3747	+	57.6307i	2.53613	+	2.07687i
$771$		0			0
$772$	25.9545	−	39.0220i	0.934124	−	1.40443i
$773$	2.77394	−	2.77394i	0.0997716	−	0.0997716i	−0.655459	−	0.755231i	$-0.727525\pi$
$773$	2.77394	−	2.77394i	0.0997716	−	0.0997716i	0.755231	+	0.655459i	$0.227525\pi$
$774$		0			0
$775$	40.2110	+	40.2110i	1.44442	+	1.44442i
$776$	16.4996	−	31.1054i	0.592301	−	1.11662i
$777$		0			0
$778$	4.79992	+	48.2121i	0.172085	+	1.72849i
$779$			0.0983980i			0.00352547i
$780$		0			0
$781$			28.9088i			1.03444i
$782$	−8.33890	+	0.830207i	−0.298198	+	0.0296881i
$783$		0			0
$784$	14.4400	+	34.4487i	0.515713	+	1.23031i
$785$	−73.5578	−	73.5578i	−2.62539	−	2.62539i
$786$		0			0
$787$	9.16585	−	9.16585i	0.326727	−	0.326727i	−0.524613	−	0.851341i	$-0.675790\pi$
$787$	9.16585	−	9.16585i	0.326727	−	0.326727i	0.851341	+	0.524613i	$0.175790\pi$
$788$	−9.78831	+	14.7165i	−0.348694	+	0.524252i
$789$		0			0
$790$	26.0571	−	31.8192i	0.927070	−	1.13207i
$791$	−8.56123	−	8.56123i	−0.304402	−	0.304402i
$792$		0			0
$793$	−3.83406	+	16.3894i	−0.136152	+	0.582004i
$794$	20.5223	−	25.0605i	0.728310	−	0.889363i
$795$		0			0
$796$	−8.29096	+	1.66740i	−0.293865	+	0.0590993i
$797$	21.6299			0.766172			0.383086	−	0.923713i	$-0.374861\pi$
$797$	21.6299			0.766172			0.383086	+	0.923713i	$0.374861\pi$
$798$		0			0
$799$	6.92020	−	6.92020i	0.244819	−	0.244819i
$800$	69.9889	−	37.8866i	2.47448	−	1.33949i
$801$		0			0
$802$	−28.6331	−	23.4480i	−1.01107	−	0.827977i
$803$		−	29.5323i		−	1.04217i
$804$		0			0
$805$	−97.5710			−3.43893
$806$	12.5522	+	16.3473i	0.442134	+	0.575809i
$807$		0			0
$808$	−2.39794	−	7.81569i	−0.0843593	−	0.274955i
$809$	12.8260			0.450937			0.225468	−	0.974250i	$-0.427609\pi$
$809$	12.8260			0.450937			0.225468	+	0.974250i	$0.427609\pi$
$810$		0			0
$811$	5.35046	+	5.35046i	0.187880	+	0.187880i	0.794779	−	0.606899i	$-0.207587\pi$
$811$	5.35046	+	5.35046i	0.187880	+	0.187880i	−0.606899	+	0.794779i	$0.707587\pi$
$812$	2.29395	−	3.44889i	0.0805018	−	0.121032i
$813$		0			0
$814$	−1.42874	−	14.3508i	−0.0500775	−	0.502996i
$815$			24.9140i			0.872698i
$816$		0			0
$817$	5.10785	−	5.10785i	0.178701	−	0.178701i
$818$	24.5520	−	29.9813i	0.858442	−	1.04827i
$819$		0			0
$820$	0.407587	−	0.0819699i	0.0142336	−	0.00286251i
$821$	−11.7654	+	11.7654i	−0.410614	+	0.410614i	−0.881953	−	0.471338i	$-0.843771\pi$
$821$	−11.7654	+	11.7654i	−0.410614	+	0.410614i	0.471338	+	0.881953i	$0.343771\pi$
$822$		0			0
$823$	−9.95031			−0.346846			−0.173423	−	0.984847i	$-0.555483\pi$
$823$	−9.95031			−0.346846			−0.173423	+	0.984847i	$0.555483\pi$
$824$	5.93751	+	19.3523i	0.206843	+	0.674170i
$825$		0			0
$826$	−0.985687	−	9.90060i	−0.0342965	−	0.344486i
$827$	0.583398	−	0.583398i	0.0202867	−	0.0202867i	−0.696891	−	0.717177i	$-0.745434\pi$
$827$	0.583398	−	0.583398i	0.0202867	−	0.0202867i	0.717177	+	0.696891i	$0.245434\pi$
$828$		0			0
$829$	43.6976			1.51768			0.758840	−	0.651277i	$-0.225766\pi$
$829$	43.6976			1.51768			0.758840	+	0.651277i	$0.225766\pi$
$830$	0.133231	+	1.33822i	0.00462450	+	0.0464502i
$831$		0			0
$832$	26.9382	−	10.3117i	0.933915	−	0.357496i
$833$	−10.0101			−0.346831
$834$		0			0
$835$	29.5719			1.02338
$836$	14.7688	−	2.97015i	0.510789	−	0.102725i
$837$		0			0
$838$	−5.06660	−	50.8907i	−0.175023	−	1.75799i
$839$	−25.4022	−	25.4022i	−0.876982	−	0.876982i	0.116239	−	0.993221i	$-0.462916\pi$
$839$	−25.4022	−	25.4022i	−0.876982	−	0.876982i	−0.993221	+	0.116239i	$0.962916\pi$
$840$		0			0
$841$	28.7375			0.990947
$842$	1.08619	+	0.889491i	0.0374325	+	0.0306539i
$843$		0			0
$844$	48.6843	−	9.79091i	1.67578	−	0.337017i
$845$	−53.7821	+	18.1692i	−1.85016	+	0.625039i
$846$		0			0
$847$	6.51263	−	6.51263i	0.223777	−	0.223777i
$848$	−12.4344	−	29.6642i	−0.427000	−	1.01867i
$849$		0			0
$850$	2.11294	+	21.2232i	0.0724734	+	0.727949i
$851$	10.9388	+	10.9388i	0.374977	+	0.374977i
$852$		0			0
$853$	15.3474	+	15.3474i	0.525486	+	0.525486i	0.919223	−	0.393737i	$-0.128818\pi$
$853$	15.3474	+	15.3474i	0.525486	+	0.525486i	−0.393737	+	0.919223i	$0.628818\pi$
$854$	20.6461	+	16.9074i	0.706496	+	0.578558i
$855$		0			0
$856$	−8.83629	−	28.8004i	−0.302018	−	0.984377i
$857$			45.0479i			1.53881i	0.638762	+	0.769404i	$0.279447\pi$
$857$			45.0479i			1.53881i	−0.638762	+	0.769404i	$0.720553\pi$
$858$		0			0
$859$	−24.0655			−0.821106			−0.410553	−	0.911837i	$-0.634664\pi$
$859$	−24.0655			−0.821106			−0.410553	+	0.911837i	$0.634664\pi$
$860$	−25.4130	−	16.9028i	−0.866575	−	0.576382i
$861$		0			0
$862$	−4.10451	−	3.36123i	−0.139800	−	0.114484i
$863$	7.38306	−	7.38306i	0.251322	−	0.251322i	−0.570190	−	0.821513i	$-0.693131\pi$
$863$	7.38306	−	7.38306i	0.251322	−	0.251322i	0.821513	+	0.570190i	$0.193131\pi$
$864$		0			0
$865$	−5.60750	+	5.60750i	−0.190661	+	0.190661i
$866$	−38.3384	+	3.81691i	−1.30279	+	0.129704i
$867$		0			0
$868$	32.0349	−	6.44255i	1.08734	−	0.218674i
$869$	−17.1598	−	17.1598i	−0.582105	−	0.582105i
$870$		0			0
$871$	−5.46782	−	8.80728i	−0.185270	−	0.298423i
$872$	6.29201	+	3.33755i	0.213074	+	0.113024i
$873$		0			0
$874$	−10.2381	+	12.5021i	−0.346308	+	0.422888i
$875$			160.072i			5.41143i
$876$		0			0
$877$	−0.141964	+	0.141964i	−0.00479380	+	0.00479380i	−0.709500	−	0.704706i	$-0.751079\pi$
$877$	−0.141964	+	0.141964i	−0.00479380	+	0.00479380i	0.704706	+	0.709500i	$0.251079\pi$
$878$	3.98570	+	40.0339i	0.134511	+	1.35108i
$879$		0			0
$880$	−24.6061	−	58.7015i	−0.829472	−	1.97883i
$881$			15.3692i			0.517802i	0.965904	+	0.258901i	$0.0833604\pi$
$881$			15.3692i			0.517802i	−0.965904	+	0.258901i	$0.916640\pi$
$882$		0			0
$883$			47.6748i			1.60438i	0.597066	+	0.802192i	$0.296333\pi$
$883$			47.6748i			1.60438i	−0.597066	+	0.802192i	$0.703667\pi$
$884$	−0.242224	+	7.72622i	−0.00814686	+	0.259861i
$885$		0			0
$886$	3.67860	+	36.9492i	0.123585	+	1.24133i
$887$			50.4271i			1.69317i	0.532250	+	0.846587i	$0.321347\pi$
$887$			50.4271i			1.69317i	−0.532250	+	0.846587i	$0.678653\pi$
$888$		0			0
$889$	−46.1990	−	46.1990i	−1.54946	−	1.54946i
$890$	98.8685	−	9.84319i	3.31408	−	0.329944i
$891$		0			0
$892$	2.87188	−	4.31780i	0.0961577	−	0.144571i
$893$		−	18.8713i		−	0.631505i
$894$		0			0
$895$	−32.4100	−	32.4100i	−1.08335	−	1.08335i
$896$	4.14567	−	45.5423i	0.138497	−	1.52146i
$897$		0			0
$898$	16.0240	+	13.1223i	0.534729	+	0.437896i
$899$	−1.46446	−	1.46446i	−0.0488423	−	0.0488423i
$900$		0			0
$901$	8.61986			0.287169
$902$	−0.0243033	−	0.244111i	−0.000809212	−	0.00812801i
$903$		0			0
$904$	2.48502	+	8.09952i	0.0826507	+	0.269386i
$905$	−43.4036	+	43.4036i	−1.44278	+	1.44278i
$906$		0			0
$907$		−	31.3735i		−	1.04174i	−0.853636	−	0.520870i	$-0.825608\pi$
$907$		−	31.3735i		−	1.04174i	0.853636	−	0.520870i	$-0.174392\pi$
$908$	22.1852	+	14.7560i	0.736241	+	0.489694i
$909$		0			0
$910$	−11.7183	+	89.2355i	−0.388459	+	2.95813i
$911$			37.5437i			1.24388i	0.783066	+	0.621939i	$0.213655\pi$
$911$			37.5437i			1.24388i	−0.783066	+	0.621939i	$0.786345\pi$
$912$		0			0
$913$	0.793538			0.0262623
$914$	−25.7320	+	31.4221i	−0.851138	+	1.03935i
$915$		0			0
$916$	−11.7277	−	7.80040i	−0.387494	−	0.257732i
$917$	0.338766	+	0.338766i	0.0111870	+	0.0111870i
$918$		0			0
$919$			30.2192i			0.996841i	0.866935	+	0.498420i	$0.166086\pi$
$919$			30.2192i			0.996841i	−0.866935	+	0.498420i	$0.833914\pi$
$920$	60.3152	+	31.9938i	1.98853	+	1.05480i
$921$		0			0
$922$	−20.5930	−	16.8639i	−0.678195	−	0.555382i
$923$	−24.3015	+	15.0871i	−0.799894	+	0.496598i
$924$		0			0
$925$	27.8401	−	27.8401i	0.915377	−	0.915377i
$926$	4.11716	−	5.02760i	0.135298	−	0.165217i
$927$		0			0
$928$	−2.54894	+	1.37980i	−0.0836732	+	0.0452942i
$929$	−21.2995	−	21.2995i	−0.698815	−	0.698815i	0.265340	−	0.964155i	$-0.414516\pi$
$929$	−21.2995	−	21.2995i	−0.698815	−	0.698815i	−0.964155	+	0.265340i	$0.914516\pi$
$930$		0			0
$931$	−13.6488	+	13.6488i	−0.447322	+	0.447322i
$932$	2.12334	+	10.5581i	0.0695522	+	0.345841i
$933$		0			0
$934$	−56.7114	+	5.64609i	−1.85565	+	0.184746i
$935$	17.0576			0.557842
$936$		0			0
$937$	35.9894			1.17572			0.587861	−	0.808962i	$-0.299970\pi$
$937$	35.9894			1.17572			0.587861	+	0.808962i	$0.299970\pi$
$938$	−16.3545	+	1.62823i	−0.533993	+	0.0531635i
$939$		0			0
$940$	−78.1695	+	15.7207i	−2.54961	+	0.512752i
$941$	11.4948	−	11.4948i	0.374720	−	0.374720i	−0.494473	−	0.869193i	$-0.664639\pi$
$941$	11.4948	−	11.4948i	0.374720	−	0.374720i	0.869193	+	0.494473i	$0.164639\pi$
$942$		0			0
$943$	0.186072	+	0.186072i	0.00605932	+	0.00605932i
$944$	−2.63711	+	6.44344i	−0.0858306	+	0.209716i
$945$		0			0
$946$	−11.4102	+	13.9334i	−0.370979	+	0.453015i
$947$	−5.55235	+	5.55235i	−0.180427	+	0.180427i	−0.791542	−	0.611115i	$-0.790721\pi$
$947$	−5.55235	+	5.55235i	−0.180427	+	0.180427i	0.611115	+	0.791542i	$0.290721\pi$
$948$		0			0
$949$	24.8256	−	15.4125i	0.805873	−	0.500310i
$950$	31.8187	+	26.0567i	1.03234	+	0.845392i
$951$		0			0
$952$	10.8265	+	5.74284i	0.350889	+	0.186126i
$953$			10.6622i			0.345384i	0.984976	+	0.172692i	$0.0552465\pi$
$953$			10.6622i			0.345384i	−0.984976	+	0.172692i	$0.944753\pi$
$954$		0			0
$955$	46.7922	+	46.7922i	1.51416	+	1.51416i
$956$	−10.1511	+	15.2619i	−0.328310	+	0.493605i
$957$		0			0
$958$	−24.1013	+	29.4309i	−0.778678	+	0.950869i
$959$	−47.9437			−1.54818
$960$		0			0
$961$			14.6618i			0.472962i
$962$	11.3180	−	8.69054i	0.364909	−	0.280194i
$963$		0			0
$964$	−25.4199	+	38.2182i	−0.818721	+	1.23093i
$965$		−	102.325i		−	3.29397i
$966$		0			0
$967$	0.807895	−	0.807895i	0.0259801	−	0.0259801i	−0.693997	−	0.719978i	$-0.744152\pi$
$967$	0.807895	−	0.807895i	0.0259801	−	0.0259801i	0.719978	+	0.693997i	$0.244152\pi$
$968$	−6.16140	+	1.89039i	−0.198035	+	0.0607594i
$969$		0			0
$970$	−7.61624	−	76.5002i	−0.244543	−	2.45627i
$971$	−12.7850			−0.410290			−0.205145	−	0.978732i	$-0.565767\pi$
$971$	−12.7850			−0.410290			−0.205145	+	0.978732i	$0.565767\pi$
$972$		0			0
$973$	−27.8251	−	27.8251i	−0.892031	−	0.892031i
$974$	13.0506	+	10.6873i	0.418167	+	0.342442i
$975$		0			0
$976$	−7.21880	−	17.2215i	−0.231068	−	0.551247i
$977$	−10.2997	−	10.2997i	−0.329517	−	0.329517i	0.522886	−	0.852403i	$-0.324855\pi$
$977$	−10.2997	−	10.2997i	−0.329517	−	0.329517i	−0.852403	+	0.522886i	$0.824855\pi$
$978$		0			0
$979$		−	58.6272i		−	1.87373i
$980$	67.9066	+	45.1665i	2.16920	+	1.44279i
$981$		0			0
$982$	−32.8998	+	3.27545i	−1.04988	+	0.104524i
$983$	36.2990	+	36.2990i	1.15776	+	1.15776i	0.984957	+	0.172800i	$0.0552816\pi$
$983$	36.2990	+	36.2990i	1.15776	+	1.15776i	0.172800	+	0.984957i	$0.444718\pi$
$984$		0			0
$985$			38.5902i			1.22959i
$986$	−0.0769518	−	0.772932i	−0.00245065	−	0.0246152i
$987$		0			0
$988$	10.2044	+	10.8649i	0.324645	+	0.345660i
$989$		−	19.3180i		−	0.614276i
$990$		0			0
$991$		−	22.9756i		−	0.729843i	−0.931038	−	0.364922i	$-0.881096\pi$
$991$		−	22.9756i		−	0.729843i	0.931038	−	0.364922i	$-0.118904\pi$
$992$	−21.9155	−	6.52176i	−0.695817	−	0.207066i
$993$		0			0
$994$	4.49269	+	45.1262i	0.142499	+	1.43132i
$995$	−13.0566	+	13.0566i	−0.413923	+	0.413923i
$996$		0			0
$997$			38.3954i			1.21599i	0.793940	+	0.607997i	$0.208027\pi$
$997$			38.3954i			1.21599i	−0.793940	+	0.607997i	$0.791973\pi$
$998$	23.6035	−	28.8230i	0.747155	−	0.912375i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.w.j.307.7		24
3.2	odd	2		312.2.t.e.307.6	yes	24
8.3	odd	2	inner	936.2.w.j.307.12		24
12.11	even	2		1248.2.bb.f.463.12		24
13.5	odd	4	inner	936.2.w.j.811.12		24
24.5	odd	2		1248.2.bb.f.463.1		24
24.11	even	2		312.2.t.e.307.1	yes	24
39.5	even	4		312.2.t.e.187.1	✓	24
104.83	even	4	inner	936.2.w.j.811.7		24
156.83	odd	4		1248.2.bb.f.655.1		24
312.5	even	4		1248.2.bb.f.655.12		24
312.83	odd	4		312.2.t.e.187.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.t.e.187.1	✓	24	39.5	even	4
312.2.t.e.187.6	yes	24	312.83	odd	4
312.2.t.e.307.1	yes	24	24.11	even	2
312.2.t.e.307.6	yes	24	3.2	odd	2
936.2.w.j.307.7		24	1.1	even	1	trivial
936.2.w.j.307.12		24	8.3	odd	2	inner
936.2.w.j.811.7		24	104.83	even	4	inner
936.2.w.j.811.12		24	13.5	odd	4	inner
1248.2.bb.f.463.1		24	24.5	odd	2
1248.2.bb.f.463.12		24	12.11	even	2
1248.2.bb.f.655.1		24	156.83	odd	4
1248.2.bb.f.655.12		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)

\(f(q)\)	\(=\)	\(q+(0.140104 + 1.40726i) q^{2} +(-1.96074 + 0.394325i) q^{4} +(-3.08779 + 3.08779i) q^{5} +(2.85816 + 2.85816i) q^{7} +(-0.829624 - 2.70402i) q^{8} +(-4.77792 - 3.91270i) q^{10} +(-2.57668 + 2.57668i) q^{11} +(-3.51077 - 0.821294i) q^{13} +(-3.62173 + 4.42261i) q^{14} +(3.68902 - 1.54634i) q^{16} +1.07196i q^{17} +(1.46161 + 1.46161i) q^{19} +(4.83676 - 7.27194i) q^{20} +(-3.98706 - 3.26505i) q^{22} +5.52786 q^{23} -14.0688i q^{25} +(0.663899 - 5.05561i) q^{26} +(-6.73116 - 4.47707i) q^{28} +0.512377i q^{29} +(-2.85816 + 2.85816i) q^{31} +(2.69294 + 4.97474i) q^{32} +(-1.50852 + 0.150186i) q^{34} -17.6508 q^{35} +(1.97885 + 1.97885i) q^{37} +(-1.85209 + 2.26164i) q^{38} +(10.9111 + 5.78773i) q^{40} +(0.0336607 + 0.0336607i) q^{41} -3.49466i q^{43} +(4.03616 - 6.06826i) q^{44} +(0.774476 + 7.77911i) q^{46} +(-6.45565 - 6.45565i) q^{47} +9.33817i q^{49} +(19.7985 - 1.97110i) q^{50} +(7.20756 + 0.225963i) q^{52} -8.04121i q^{53} -15.9125i q^{55} +(5.35733 - 10.0997i) q^{56} +(-0.721046 + 0.0717861i) q^{58} +(-1.23075 + 1.23075i) q^{59} -4.66832i q^{61} +(-4.42261 - 3.62173i) q^{62} +(-6.62345 + 4.48664i) q^{64} +(13.3765 - 8.30451i) q^{65} +(2.03305 + 2.03305i) q^{67} +(-0.422701 - 2.10184i) q^{68} +(-2.47295 - 24.8392i) q^{70} +(5.60969 - 5.60969i) q^{71} +(-5.73067 + 5.73067i) q^{73} +(-2.50750 + 3.06199i) q^{74} +(-3.44220 - 2.28950i) q^{76} -14.7292 q^{77} +6.65963i q^{79} +(-6.61613 + 16.1657i) q^{80} +(-0.0426532 + 0.0520852i) q^{82} +(-0.153984 - 0.153984i) q^{83} +(-3.30998 - 3.30998i) q^{85} +(4.91788 - 0.489616i) q^{86} +(9.10509 + 4.82973i) q^{88} +(-11.3765 + 11.3765i) q^{89} +(-7.68694 - 12.3817i) q^{91} +(-10.8387 + 2.17977i) q^{92} +(8.18029 - 9.98921i) q^{94} -9.02631 q^{95} +(8.80263 + 8.80263i) q^{97} +(-13.1412 + 1.30832i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{8} - 8 q^{11} - 36 q^{14} + 28 q^{16} + 20 q^{19} + 20 q^{20} + 20 q^{22} - 12 q^{26} - 16 q^{28} + 30 q^{32} + 16 q^{34} - 16 q^{35} + 36 q^{40} + 12 q^{41} + 32 q^{44} - 44 q^{46} + 36 q^{50}+ \cdots - 68 q^{98}+O(q^{100}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more