LMFDB - Embedded newform 2380.2.cb.b.781.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2380,2,Mod(781,2380)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2380.781"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2380, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2380 = 2^{2} \cdot 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2380.cb (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [92] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$19.0043956811$
Analytic rank:	$0$
Dimension:	$92$
Relative dimension:	$46$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			781.6
Character	$\chi$	$=$	2380.781
Dual form			2380.2.cb.b.1801.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.29941 - 1.32756i) q^{3} +(-0.866025 + 0.500000i) q^{5} +(2.54913 - 0.708459i) q^{7} +(2.02485 + 3.50715i) q^{9} +(1.96280 + 1.13322i) q^{11} +5.19317 q^{13} +2.65513 q^{15} +(-2.10957 + 3.54256i) q^{17} +(2.74671 + 4.75744i) q^{19} +(-6.80202 - 1.75510i) q^{21} +(-7.41926 + 4.28351i) q^{23} +(0.500000 - 0.866025i) q^{25} -2.78710i q^{27} -6.77457i q^{29} +(-1.99915 - 1.15421i) q^{31} +(-3.00885 - 5.21148i) q^{33} +(-1.85339 + 1.88811i) q^{35} +(-1.84700 + 1.06637i) q^{37} +(-11.9412 - 6.89426i) q^{39} -1.68589i q^{41} -9.33371 q^{43} +(-3.50715 - 2.02485i) q^{45} +(1.83350 + 3.17572i) q^{47} +(5.99617 - 3.61191i) q^{49} +(9.55373 - 5.34520i) q^{51} +(-4.19617 + 7.26798i) q^{53} -2.26644 q^{55} -14.5857i q^{57} +(-3.70533 + 6.41782i) q^{59} +(-3.20135 + 1.84830i) q^{61} +(7.64629 + 7.50566i) q^{63} +(-4.49742 + 2.59658i) q^{65} +(1.60521 - 2.78030i) q^{67} +22.7466 q^{69} +6.38209i q^{71} +(-7.06719 - 4.08025i) q^{73} +(-2.29941 + 1.32756i) q^{75} +(5.80628 + 1.49817i) q^{77} +(3.93995 - 2.27473i) q^{79} +(2.37450 - 4.11276i) q^{81} -10.1819 q^{83} +(0.0556607 - 4.12273i) q^{85} +(-8.99368 + 15.5775i) q^{87} +(5.39421 + 9.34304i) q^{89} +(13.2381 - 3.67914i) q^{91} +(3.06458 + 5.30800i) q^{93} +(-4.75744 - 2.74671i) q^{95} +2.95814i q^{97} +9.17843i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 56 q^{9} - 24 q^{13} + 12 q^{15} + 4 q^{17} - 24 q^{21} + 46 q^{25} - 24 q^{33} + 14 q^{35} - 64 q^{43} + 16 q^{47} + 38 q^{49} - 22 q^{51} - 8 q^{53} + 18 q^{59} + 16 q^{67} - 36 q^{69} - 12 q^{77}+ \cdots + 44 q^{93}+O(q^{100}) $ 92 * q + 56 * q^9 - 24 * q^13 + 12 * q^15 + 4 * q^17 - 24 * q^21 + 46 * q^25 - 24 * q^33 + 14 * q^35 - 64 * q^43 + 16 * q^47 + 38 * q^49 - 22 * q^51 - 8 * q^53 + 18 * q^59 + 16 * q^67 - 36 * q^69 - 12 * q^77 - 86 * q^81 + 8 * q^83 - 20 * q^85 + 20 * q^87 + 2 * q^89 + 44 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2380\mathbb{Z}\right)^\times$.

$n$	$477$	$1191$	$1261$	$1361$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.29941	−	1.32756i	−1.32756	−	0.766469i	−0.342642	−	0.939466i	$-0.611322\pi$
$3$	−2.29941	−	1.32756i	−1.32756	−	0.766469i	−0.984922	+	0.172997i	$0.944655\pi$
$4$		0			0
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$		0			0
$7$	2.54913	−	0.708459i	0.963482	−	0.267772i
$7$	2.54913	−	0.708459i	0.963482	−	0.267772i
$8$		0			0
$9$	2.02485	+	3.50715i	0.674951	+	1.16905i
$10$		0			0
$11$	1.96280	+	1.13322i	0.591806	+	0.341679i	0.765811	−	0.643065i	$-0.222338\pi$
$11$	1.96280	+	1.13322i	0.591806	+	0.341679i	−0.174005	+	0.984745i	$0.555671\pi$
$12$		0			0
$13$	5.19317			1.44033			0.720163	−	0.693805i	$-0.244067\pi$
$13$	5.19317			1.44033			0.720163	+	0.693805i	$0.244067\pi$
$14$		0			0
$15$	2.65513			0.685551
$16$		0			0
$17$	−2.10957	+	3.54256i	−0.511646	+	0.859197i
$17$	−2.10957	+	3.54256i	−0.511646	+	0.859197i
$18$		0			0
$19$	2.74671	+	4.75744i	0.630139	+	1.09143i	0.987523	+	0.157475i	$0.0503353\pi$
$19$	2.74671	+	4.75744i	0.630139	+	1.09143i	−0.357384	+	0.933957i	$0.616331\pi$
$20$		0			0
$21$	−6.80202	−	1.75510i	−1.48432	−	0.382995i
$22$		0			0
$23$	−7.41926	+	4.28351i	−1.54702	+	0.893174i	−0.548657	+	0.836048i	$0.684861\pi$
$23$	−7.41926	+	4.28351i	−1.54702	+	0.893174i	−0.998367	+	0.0571267i	$0.981806\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		0			0
$27$		−	2.78710i		−	0.536377i
$28$		0			0
$29$		−	6.77457i		−	1.25801i	−0.777403	−	0.629003i	$-0.783463\pi$
$29$		−	6.77457i		−	1.25801i	0.777403	−	0.629003i	$-0.216537\pi$
$30$		0			0
$31$	−1.99915	−	1.15421i	−0.359058	−	0.207302i	0.309609	−	0.950864i	$-0.399802\pi$
$31$	−1.99915	−	1.15421i	−0.359058	−	0.207302i	−0.668668	+	0.743561i	$0.733135\pi$
$32$		0			0
$33$	−3.00885	−	5.21148i	−0.523774	−	0.907203i
$34$		0			0
$35$	−1.85339	+	1.88811i	−0.313279	+	0.319149i
$36$		0			0
$37$	−1.84700	+	1.06637i	−0.303645	+	0.175310i	−0.644079	−	0.764959i	$-0.722759\pi$
$37$	−1.84700	+	1.06637i	−0.303645	+	0.175310i	0.340434	+	0.940268i	$0.389426\pi$
$38$		0			0
$39$	−11.9412	−	6.89426i	−1.91212	−	1.10397i
$40$		0			0
$41$		−	1.68589i		−	0.263291i	−0.991297	−	0.131646i	$-0.957974\pi$
$41$		−	1.68589i		−	0.263291i	0.991297	−	0.131646i	$-0.0420261\pi$
$42$		0			0
$43$	−9.33371			−1.42338			−0.711688	−	0.702495i	$-0.752069\pi$
$43$	−9.33371			−1.42338			−0.711688	+	0.702495i	$0.752069\pi$
$44$		0			0
$45$	−3.50715	−	2.02485i	−0.522815	−	0.301847i
$46$		0			0
$47$	1.83350	+	3.17572i	0.267444	+	0.463226i	0.968201	−	0.250174i	$-0.0804877\pi$
$47$	1.83350	+	3.17572i	0.267444	+	0.463226i	−0.700757	+	0.713400i	$0.747154\pi$
$48$		0			0
$49$	5.99617	−	3.61191i	0.856596	−	0.515987i
$50$		0			0
$51$	9.55373	−	5.34520i	1.33779	−	0.748478i
$52$		0			0
$53$	−4.19617	+	7.26798i	−0.576389	+	0.998334i	0.419501	+	0.907755i	$0.362205\pi$
$53$	−4.19617	+	7.26798i	−0.576389	+	0.998334i	−0.995889	+	0.0905792i	$0.971128\pi$
$54$		0			0
$55$	−2.26644			−0.305607
$56$		0			0
$57$		−	14.5857i		−	1.93193i
$58$		0			0
$59$	−3.70533	+	6.41782i	−0.482393	+	0.835529i	−0.999796	−	0.0202129i	$-0.993566\pi$
$59$	−3.70533	+	6.41782i	−0.482393	+	0.835529i	0.517403	+	0.855742i	$0.326899\pi$
$60$		0			0
$61$	−3.20135	+	1.84830i	−0.409891	+	0.236651i	−0.690743	−	0.723100i	$-0.742716\pi$
$61$	−3.20135	+	1.84830i	−0.409891	+	0.236651i	0.280852	+	0.959751i	$0.409383\pi$
$62$		0			0
$63$	7.64629	+	7.50566i	0.963342	+	0.945625i
$64$		0			0
$65$	−4.49742	+	2.59658i	−0.557836	+	0.322067i
$66$		0			0
$67$	1.60521	−	2.78030i	0.196107	−	0.339668i	−0.751156	−	0.660125i	$-0.770503\pi$
$67$	1.60521	−	2.78030i	0.196107	−	0.339668i	0.947263	+	0.320457i	$0.103837\pi$
$68$		0			0
$69$	22.7466			2.73836
$70$		0			0
$71$			6.38209i			0.757415i	0.925516	+	0.378707i	$0.123631\pi$
$71$			6.38209i			0.757415i	−0.925516	+	0.378707i	$0.876369\pi$
$72$		0			0
$73$	−7.06719	−	4.08025i	−0.827153	−	0.477557i	0.0257242	−	0.999669i	$-0.491811\pi$
$73$	−7.06719	−	4.08025i	−0.827153	−	0.477557i	−0.852877	+	0.522112i	$0.825144\pi$
$74$		0			0
$75$	−2.29941	+	1.32756i	−0.265513	+	0.153294i
$76$		0			0
$77$	5.80628	+	1.49817i	0.661687	+	0.170733i
$78$		0			0
$79$	3.93995	−	2.27473i	0.443279	−	0.255927i	−0.261708	−	0.965147i	$-0.584286\pi$
$79$	3.93995	−	2.27473i	0.443279	−	0.255927i	0.704988	+	0.709220i	$0.250953\pi$
$80$		0			0
$81$	2.37450	−	4.11276i	0.263834	−	0.456974i
$82$		0			0
$83$	−10.1819			−1.11761			−0.558805	−	0.829299i	$-0.688740\pi$
$83$	−10.1819			−1.11761			−0.558805	+	0.829299i	$0.688740\pi$
$84$		0			0
$85$	0.0556607	−	4.12273i	0.00603725	−	0.447173i
$86$		0			0
$87$	−8.99368	+	15.5775i	−0.964224	+	1.67008i
$88$		0			0
$89$	5.39421	+	9.34304i	0.571785	+	0.990360i	0.996383	+	0.0849782i	$0.0270821\pi$
$89$	5.39421	+	9.34304i	0.571785	+	0.990360i	−0.424598	+	0.905382i	$0.639585\pi$
$90$		0			0
$91$	13.2381	−	3.67914i	1.38773	−	0.385679i
$92$		0			0
$93$	3.06458	+	5.30800i	0.317782	+	0.550414i
$94$		0			0
$95$	−4.75744	−	2.74671i	−0.488103	−	0.281807i
$96$		0			0
$97$			2.95814i			0.300353i	0.988659	+	0.150177i	$0.0479843\pi$
$97$			2.95814i			0.300353i	−0.988659	+	0.150177i	$0.952016\pi$
$98$		0			0
$99$			9.17843i			0.922467i
$100$		0			0
$101$	−6.85443	+	11.8722i	−0.682041	+	1.18133i	0.292316	+	0.956322i	$0.405574\pi$
$101$	−6.85443	+	11.8722i	−0.682041	+	1.18133i	−0.974357	+	0.225008i	$0.927759\pi$
$102$		0			0
$103$	8.94692	+	15.4965i	0.881566	+	1.52692i	0.849600	+	0.527428i	$0.176843\pi$
$103$	8.94692	+	15.4965i	0.881566	+	1.52692i	0.0319659	+	0.999489i	$0.489823\pi$
$104$		0			0
$105$	6.76828	−	1.88105i	0.660516	−	0.183571i
$106$		0			0
$107$	−11.9643	+	6.90759i	−1.15663	+	0.667782i	−0.950495	−	0.310741i	$-0.899423\pi$
$107$	−11.9643	+	6.90759i	−1.15663	+	0.667782i	−0.206138	+	0.978523i	$0.566090\pi$
$108$		0			0
$109$	10.4322	+	6.02304i	0.999225	+	0.576903i	0.908019	−	0.418929i	$-0.137595\pi$
$109$	10.4322	+	6.02304i	0.999225	+	0.576903i	0.0912059	+	0.995832i	$0.470928\pi$
$110$		0			0
$111$	5.66268			0.537478
$112$		0			0
$113$		−	5.36234i		−	0.504447i	−0.967669	−	0.252223i	$-0.918838\pi$
$113$		−	5.36234i		−	0.504447i	0.967669	−	0.252223i	$-0.0811618\pi$
$114$		0			0
$115$	4.28351	−	7.41926i	0.399440	−	0.691850i
$116$		0			0
$117$	10.5154	+	18.2132i	0.972149	+	1.68381i
$118$		0			0
$119$	−2.86782	+	10.5250i	−0.262892	+	0.964825i
$120$		0			0
$121$	−2.93161	−	5.07770i	−0.266510	−	0.461609i
$122$		0			0
$123$	−2.23812	+	3.87654i	−0.201805	+	0.349536i
$124$		0			0
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	−11.6950			−1.03776			−0.518880	−	0.854847i	$-0.673651\pi$
$127$	−11.6950			−1.03776			−0.518880	+	0.854847i	$0.673651\pi$
$128$		0			0
$129$	21.4620	+	12.3911i	1.88962	+	1.09097i
$130$		0			0
$131$	−13.7140	+	7.91779i	−1.19820	+	0.691780i	−0.960153	−	0.279473i	$-0.909840\pi$
$131$	−13.7140	+	7.91779i	−1.19820	+	0.691780i	−0.238046	+	0.971254i	$0.576507\pi$
$132$		0			0
$133$	10.3722	+	10.1814i	0.899382	+	0.882842i
$134$		0			0
$135$	1.39355	+	2.41370i	0.119938	+	0.207738i
$136$		0			0
$137$	8.82606	−	15.2872i	0.754061	−	1.30607i	−0.191779	−	0.981438i	$-0.561426\pi$
$137$	8.82606	−	15.2872i	0.754061	−	1.30607i	0.945840	−	0.324634i	$-0.105241\pi$
$138$		0			0
$139$			17.8871i			1.51717i	0.651577	+	0.758583i	$0.274108\pi$
$139$			17.8871i			1.51717i	−0.651577	+	0.758583i	$0.725892\pi$
$140$		0			0
$141$		−	9.73636i		−	0.819949i
$142$		0			0
$143$	10.1931	+	5.88501i	0.852394	+	0.492130i
$144$		0			0
$145$	3.38729	+	5.86695i	0.281299	+	0.487224i
$146$		0			0
$147$	−18.5827	+	0.344957i	−1.53267	+	0.0284516i
$148$		0			0
$149$	6.71665	+	11.6336i	0.550249	+	0.953060i	0.998256	+	0.0590299i	$0.0188007\pi$
$149$	6.71665	+	11.6336i	0.550249	+	0.953060i	−0.448007	+	0.894030i	$0.647866\pi$
$150$		0			0
$151$	9.70439	−	16.8085i	0.789732	−	1.36786i	−0.136399	−	0.990654i	$-0.543553\pi$
$151$	9.70439	−	16.8085i	0.789732	−	1.36786i	0.926131	−	0.377202i	$-0.123114\pi$
$152$		0			0
$153$	−16.6958	−	0.225410i	−1.34978	−	0.0182233i
$154$		0			0
$155$	2.30842			0.185417
$156$		0			0
$157$	5.08009	−	8.79897i	0.405435	−	0.702235i	−0.588937	−	0.808179i	$-0.700453\pi$
$157$	5.08009	−	8.79897i	0.405435	−	0.702235i	0.994372	+	0.105945i	$0.0337866\pi$
$158$		0			0
$159$	19.2974	−	11.1414i	1.53039	−	0.883568i
$160$		0			0
$161$	−15.8780	+	16.1755i	−1.25136	+	1.27481i
$162$		0			0
$163$	−5.21254	+	3.00946i	−0.408278	+	0.235719i	−0.690050	−	0.723762i	$-0.742411\pi$
$163$	−5.21254	+	3.00946i	−0.408278	+	0.235719i	0.281772	+	0.959481i	$0.409078\pi$
$164$		0			0
$165$	5.21148	+	3.00885i	0.405713	+	0.234239i
$166$		0			0
$167$		−	9.19627i		−	0.711629i	−0.934557	−	0.355814i	$-0.884204\pi$
$167$		−	9.19627i		−	0.711629i	0.934557	−	0.355814i	$-0.115796\pi$
$168$		0			0
$169$	13.9690			1.07454
$170$		0			0
$171$	−11.1234	+	19.2662i	−0.850625	+	1.47333i
$172$		0			0
$173$	18.7923	−	10.8497i	1.42875	−	0.824890i	0.431729	−	0.902004i	$-0.357904\pi$
$173$	18.7923	−	10.8497i	1.42875	−	0.824890i	0.997022	+	0.0771138i	$0.0245705\pi$
$174$		0			0
$175$	0.661024	−	2.56184i	0.0499687	−	0.193657i
$176$		0			0
$177$	17.0401	−	9.83813i	1.28082	−	0.739479i
$178$		0			0
$179$	10.0329	−	17.3774i	0.749891	−	1.29885i	−0.197983	−	0.980205i	$-0.563439\pi$
$179$	10.0329	−	17.3774i	0.749891	−	1.29885i	0.947874	−	0.318644i	$-0.103227\pi$
$180$		0			0
$181$			7.37876i			0.548459i	0.961664	+	0.274230i	$0.0884228\pi$
$181$			7.37876i			0.548459i	−0.961664	+	0.274230i	$0.911577\pi$
$182$		0			0
$183$	9.81496			0.725543
$184$		0			0
$185$	1.06637	−	1.84700i	0.0784008	−	0.135794i
$186$		0			0
$187$	−8.15517	+	4.56272i	−0.596365	+	0.333659i
$188$		0			0
$189$	−1.97454	−	7.10469i	−0.143627	−	0.516790i
$190$		0			0
$191$	−11.8913	−	20.5964i	−0.860427	−	1.49030i	−0.871517	−	0.490365i	$-0.836864\pi$
$191$	−11.8913	−	20.5964i	−0.860427	−	1.49030i	0.0110905	−	0.999938i	$-0.496470\pi$
$192$		0			0
$193$	2.74549	+	1.58511i	0.197625	+	0.114099i	0.595547	−	0.803320i	$-0.296935\pi$
$193$	2.74549	+	1.58511i	0.197625	+	0.114099i	−0.397922	+	0.917419i	$0.630269\pi$
$194$		0			0
$195$	13.7885			0.987417
$196$		0			0
$197$			24.3208i			1.73278i	0.499366	+	0.866391i	$0.333566\pi$
$197$			24.3208i			1.73278i	−0.499366	+	0.866391i	$0.666434\pi$
$198$		0			0
$199$	13.2113	+	7.62752i	0.936521	+	0.540701i	0.888868	−	0.458163i	$-0.151492\pi$
$199$	13.2113	+	7.62752i	0.936521	+	0.540701i	0.0476531	+	0.998864i	$0.484826\pi$
$200$		0			0
$201$	−7.38205	+	4.26203i	−0.520690	+	0.300620i
$202$		0			0
$203$	−4.79950	−	17.2693i	−0.336859	−	1.21207i
$204$		0			0
$205$	0.842943	+	1.46002i	0.0588737	+	0.101972i
$206$		0			0
$207$	−30.0458	−	17.3470i	−2.08833	−	1.20570i
$208$		0			0
$209$			12.4505i			0.861222i
$210$		0			0
$211$			13.9799i			0.962418i	0.876606	+	0.481209i	$0.159802\pi$
$211$			13.9799i			0.962418i	−0.876606	+	0.481209i	$0.840198\pi$
$212$		0			0
$213$	8.47263	−	14.6750i	0.580535	−	1.00552i
$214$		0			0
$215$	8.08323	−	4.66685i	0.551271	−	0.318277i
$216$		0			0
$217$	−5.91382	−	1.52592i	−0.401456	−	0.103586i
$218$		0			0
$219$	10.8336	+	18.7643i	0.732065	+	1.26797i
$220$		0			0
$221$	−10.9553	+	18.3971i	−0.736936	+	1.23752i
$222$		0			0
$223$	−18.5025			−1.23902			−0.619508	−	0.784990i	$-0.712668\pi$
$223$	−18.5025			−1.23902			−0.619508	+	0.784990i	$0.712668\pi$
$224$		0			0
$225$	4.04970			0.269980
$226$		0			0
$227$	19.0454	+	10.9959i	1.26409	+	0.729822i	0.973863	−	0.227137i	$-0.0729364\pi$
$227$	19.0454	+	10.9959i	1.26409	+	0.729822i	0.290225	+	0.956958i	$0.406270\pi$
$228$		0			0
$229$	11.7307	+	20.3181i	0.775184	+	1.34266i	0.934691	+	0.355461i	$0.115676\pi$
$229$	11.7307	+	20.3181i	0.775184	+	1.34266i	−0.159507	+	0.987197i	$0.550990\pi$
$230$		0			0
$231$	−11.3621	−	11.1531i	−0.747570	−	0.733822i
$232$		0			0
$233$	−6.22393	+	3.59339i	−0.407743	+	0.235411i	−0.689820	−	0.723981i	$-0.742310\pi$
$233$	−6.22393	+	3.59339i	−0.407743	+	0.235411i	0.282076	+	0.959392i	$0.408977\pi$
$234$		0			0
$235$	−3.17572	−	1.83350i	−0.207161	−	0.119604i
$236$		0			0
$237$	−12.0794			−0.784642
$238$		0			0
$239$	−16.3353			−1.05664			−0.528320	−	0.849045i	$-0.677178\pi$
$239$	−16.3353			−1.05664			−0.528320	+	0.849045i	$0.677178\pi$
$240$		0			0
$241$	5.48166	+	3.16484i	0.353105	+	0.203865i	0.666052	−	0.745905i	$-0.267983\pi$
$241$	5.48166	+	3.16484i	0.353105	+	0.203865i	−0.312947	+	0.949771i	$0.601316\pi$
$242$		0			0
$243$	−18.1610	+	10.4853i	−1.16503	+	0.672630i
$244$		0			0
$245$	−3.38688	+	6.12609i	−0.216380	+	0.391382i
$246$		0			0
$247$	14.2641	+	24.7062i	0.907605	+	1.57202i
$248$		0			0
$249$	23.4124	+	13.5171i	1.48370	+	0.856613i
$250$		0			0
$251$	25.9339			1.63693			0.818465	−	0.574556i	$-0.194825\pi$
$251$	25.9339			1.63693			0.818465	+	0.574556i	$0.194825\pi$
$252$		0			0
$253$	−19.4167			−1.22072
$254$		0			0
$255$	−5.60117	+	9.40595i	−0.350759	+	0.589023i
$256$		0			0
$257$	6.18454	+	10.7119i	0.385781	+	0.668192i	0.991877	−	0.127199i	$-0.0405987\pi$
$257$	6.18454	+	10.7119i	0.385781	+	0.668192i	−0.606096	+	0.795391i	$0.707265\pi$
$258$		0			0
$259$	−3.95278	+	4.02683i	−0.245614	+	0.250215i
$260$		0			0
$261$	23.7594	−	13.7175i	1.47067	−	0.849092i
$262$		0			0
$263$	3.07046	−	5.31819i	0.189333	−	0.327934i	−0.755695	−	0.654923i	$-0.772701\pi$
$263$	3.07046	−	5.31819i	0.189333	−	0.327934i	0.945028	+	0.326990i	$0.106034\pi$
$264$		0			0
$265$		−	8.39234i		−	0.515538i
$266$		0			0
$267$		−	28.6446i		−	1.75302i
$268$		0			0
$269$	−8.28619	−	4.78403i	−0.505218	−	0.291688i	0.225648	−	0.974209i	$-0.427550\pi$
$269$	−8.28619	−	4.78403i	−0.505218	−	0.291688i	−0.730866	+	0.682521i	$0.760883\pi$
$270$		0			0
$271$	−1.40631	−	2.43580i	−0.0854272	−	0.147964i	0.820146	−	0.572154i	$-0.193892\pi$
$271$	−1.40631	−	2.43580i	−0.0854272	−	0.147964i	−0.905573	+	0.424190i	$0.860559\pi$
$272$		0			0
$273$	−35.3241	−	9.11455i	−2.13791	−	0.551638i
$274$		0			0
$275$	1.96280	−	1.13322i	0.118361	−	0.0683359i
$276$		0			0
$277$	−15.6812	−	9.05357i	−0.942195	−	0.543976i	−0.0515472	−	0.998671i	$-0.516415\pi$
$277$	−15.6812	−	9.05357i	−0.942195	−	0.543976i	−0.890648	+	0.454694i	$0.849749\pi$
$278$		0			0
$279$		−	9.34842i		−	0.559675i
$280$		0			0
$281$	−9.69058			−0.578092			−0.289046	−	0.957315i	$-0.593338\pi$
$281$	−9.69058			−0.578092			−0.289046	+	0.957315i	$0.593338\pi$
$282$		0			0
$283$	0.0630133	+	0.0363808i	0.00374575	+	0.00216261i	0.501872	−	0.864942i	$-0.332645\pi$
$283$	0.0630133	+	0.0363808i	0.00374575	+	0.00216261i	−0.498126	+	0.867105i	$0.665978\pi$
$284$		0			0
$285$	7.29287	+	12.6316i	0.431992	+	0.748232i
$286$		0			0
$287$	−1.19438	−	4.29755i	−0.0705021	−	0.253676i
$288$		0			0
$289$	−8.09944	−	14.9465i	−0.476438	−	0.879208i
$290$		0			0
$291$	3.92712	−	6.80197i	0.230212	−	0.398738i
$292$		0			0
$293$	9.79142			0.572021			0.286010	−	0.958227i	$-0.407671\pi$
$293$	9.79142			0.572021			0.286010	+	0.958227i	$0.407671\pi$
$294$		0			0
$295$		−	7.41066i		−	0.431465i
$296$		0			0
$297$	3.15840	−	5.47051i	0.183269	−	0.317431i
$298$		0			0
$299$	−38.5295	+	22.2450i	−2.22822	+	1.28646i
$300$		0			0
$301$	−23.7929	+	6.61254i	−1.37140	+	0.381141i
$302$		0			0
$303$	31.5223	−	18.1994i	1.81091	−	1.04553i
$304$		0			0
$305$	1.84830	−	3.20135i	0.105834	−	0.183309i
$306$		0			0
$307$	−20.6621			−1.17925			−0.589624	−	0.807678i	$-0.700724\pi$
$307$	−20.6621			−1.17925			−0.589624	+	0.807678i	$0.700724\pi$
$308$		0			0
$309$		−	47.5104i		−	2.70277i
$310$		0			0
$311$	−1.77694	−	1.02592i	−0.100761	−	0.0581745i	0.448773	−	0.893646i	$-0.351861\pi$
$311$	−1.77694	−	1.02592i	−0.100761	−	0.0581745i	−0.549534	+	0.835471i	$0.685195\pi$
$312$		0			0
$313$	15.4073	−	8.89542i	0.870873	−	0.502799i	0.00323490	−	0.999995i	$-0.498970\pi$
$313$	15.4073	−	8.89542i	0.870873	−	0.502799i	0.867638	+	0.497196i	$0.165637\pi$
$314$		0			0
$315$	−10.3747	−	2.67695i	−0.584549	−	0.150829i
$316$		0			0
$317$	11.1022	−	6.40988i	0.623564	−	0.360015i	−0.154691	−	0.987963i	$-0.549438\pi$
$317$	11.1022	−	6.40988i	0.623564	−	0.360015i	0.778255	+	0.627948i	$0.216105\pi$
$318$		0			0
$319$	7.67710	−	13.2971i	0.429835	−	0.744496i
$320$		0			0
$321$	36.6811			2.04734
$322$		0			0
$323$	−22.6479	−	0.305768i	−1.26016	−	0.0170134i
$324$		0			0
$325$	2.59658	−	4.49742i	0.144033	−	0.249472i
$326$		0			0
$327$	−15.9919	−	27.6989i	−0.884356	−	1.53175i
$328$		0			0
$329$	6.92371	+	6.79637i	0.381716	+	0.374696i
$330$		0			0
$331$	−7.95698	−	13.7819i	−0.437355	−	0.757522i	0.560129	−	0.828405i	$-0.310751\pi$
$331$	−7.95698	−	13.7819i	−0.437355	−	0.757522i	−0.997485	+	0.0708836i	$0.977418\pi$
$332$		0			0
$333$	−7.47981	−	4.31847i	−0.409891	−	0.236651i
$334$		0			0
$335$			3.21041i			0.175404i
$336$		0			0
$337$		−	0.705077i		−	0.0384080i	−0.999816	−	0.0192040i	$-0.993887\pi$
$337$		−	0.705077i		−	0.0384080i	0.999816	−	0.0192040i	$-0.00611319\pi$
$338$		0			0
$339$	−7.11885	+	12.3302i	−0.386643	+	0.669685i
$340$		0			0
$341$	−2.61595	−	4.53097i	−0.141662	−	0.245366i
$342$		0			0
$343$	12.7262	−	13.4553i	0.687148	−	0.726517i
$344$		0			0
$345$	−19.6991	+	11.3733i	−1.06056	+	0.612317i
$346$		0			0
$347$	−7.83467	−	4.52335i	−0.420587	−	0.242826i	0.274741	−	0.961518i	$-0.411408\pi$
$347$	−7.83467	−	4.52335i	−0.420587	−	0.242826i	−0.695328	+	0.718692i	$0.744741\pi$
$348$		0			0
$349$	14.6559			0.784511			0.392256	−	0.919856i	$-0.371695\pi$
$349$	14.6559			0.784511			0.392256	+	0.919856i	$0.371695\pi$
$350$		0			0
$351$		−	14.4739i		−	0.772558i
$352$		0			0
$353$	−0.182487	+	0.316077i	−0.00971280	+	0.0168231i	−0.870841	−	0.491565i	$-0.836425\pi$
$353$	−0.182487	+	0.316077i	−0.00971280	+	0.0168231i	0.861128	+	0.508388i	$0.169758\pi$
$354$		0			0
$355$	−3.19105	−	5.52705i	−0.169363	−	0.293346i
$356$		0			0
$357$	20.5669	−	20.3941i	1.08852	−	1.07937i
$358$		0			0
$359$	15.1685	+	26.2726i	0.800563	+	1.38662i	0.919246	+	0.393684i	$0.128800\pi$
$359$	15.1685	+	26.2726i	0.800563	+	1.38662i	−0.118682	+	0.992932i	$0.537867\pi$
$360$		0			0
$361$	−5.58884	+	9.68015i	−0.294149	+	0.509482i
$362$		0			0
$363$			15.5676i			0.817088i
$364$		0			0
$365$	8.16049			0.427140
$366$		0			0
$367$	−15.3092	−	8.83874i	−0.799131	−	0.461379i	0.0440360	−	0.999030i	$-0.485978\pi$
$367$	−15.3092	−	8.83874i	−0.799131	−	0.461379i	−0.843167	+	0.537651i	$0.819312\pi$
$368$		0			0
$369$	5.91265	−	3.41367i	0.307800	−	0.177709i
$370$		0			0
$371$	−5.54754	+	21.4999i	−0.288014	+	1.11622i
$372$		0			0
$373$	5.02179	+	8.69800i	0.260019	+	0.450366i	0.966247	−	0.257619i	$-0.0829379\pi$
$373$	5.02179	+	8.69800i	0.260019	+	0.450366i	−0.706228	+	0.707985i	$0.749605\pi$
$374$		0			0
$375$	1.32756	−	2.29941i	0.0685551	−	0.118741i
$376$		0			0
$377$		−	35.1815i		−	1.81194i
$378$		0			0
$379$			32.2693i			1.65756i	0.559572	+	0.828782i	$0.310965\pi$
$379$			32.2693i			1.65756i	−0.559572	+	0.828782i	$0.689035\pi$
$380$		0			0
$381$	26.8915	+	15.5258i	1.37769	+	0.795411i
$382$		0			0
$383$	−10.6946	−	18.5236i	−0.546469	−	0.946512i	−0.998513	−	0.0545160i	$-0.982638\pi$
$383$	−10.6946	−	18.5236i	−0.546469	−	0.946512i	0.452044	−	0.891996i	$-0.350695\pi$
$384$		0			0
$385$	−5.77747	+	1.60568i	−0.294447	+	0.0818331i
$386$		0			0
$387$	−18.8994	−	32.7347i	−0.960709	−	1.66400i
$388$		0			0
$389$	0.528754	−	0.915828i	0.0268089	−	0.0464343i	−0.852310	−	0.523037i	$-0.824799\pi$
$389$	0.528754	−	0.915828i	0.0268089	−	0.0464343i	0.879119	+	0.476603i	$0.158132\pi$
$390$		0			0
$391$	0.476847	−	35.3195i	0.0241152	−	1.78619i
$392$		0			0
$393$	42.0455			2.12091
$394$		0			0
$395$	−2.27473	+	3.93995i	−0.114454	+	0.198241i
$396$		0			0
$397$	−29.2258	+	16.8735i	−1.46680	+	0.846858i	−0.999310	−	0.0371399i	$-0.988175\pi$
$397$	−29.2258	+	16.8735i	−1.46680	+	0.846858i	−0.467491	+	0.883998i	$0.654842\pi$
$398$		0			0
$399$	−10.3334	−	37.1810i	−0.517316	−	1.86138i
$400$		0			0
$401$	−2.36176	+	1.36356i	−0.117941	+	0.0680931i	−0.557810	−	0.829969i	$-0.688358\pi$
$401$	−2.36176	+	1.36356i	−0.117941	+	0.0680931i	0.439869	+	0.898062i	$0.355025\pi$
$402$		0			0
$403$	−10.3819	−	5.99401i	−0.517161	−	0.298583i
$404$		0			0
$405$			4.74901i			0.235980i
$406$		0			0
$407$	−4.83372			−0.239599
$408$		0			0
$409$	10.8425	−	18.7797i	0.536126	−	0.928597i	−0.462982	−	0.886367i	$-0.653221\pi$
$409$	10.8425	−	18.7797i	0.536126	−	0.928597i	0.999108	−	0.0422292i	$-0.0134460\pi$
$410$		0			0
$411$	−40.5894	+	23.4343i	−2.00213	+	1.15593i
$412$		0			0
$413$	−4.89863	+	18.9850i	−0.241046	+	0.934189i
$414$		0			0
$415$	8.81779	−	5.09095i	0.432848	−	0.249905i
$416$		0			0
$417$	23.7463	−	41.1298i	1.16286	−	2.01413i
$418$		0			0
$419$		−	23.5890i		−	1.15240i	−0.817309	−	0.576199i	$-0.804535\pi$
$419$		−	23.5890i		−	1.15240i	0.817309	−	0.576199i	$-0.195465\pi$
$420$		0			0
$421$	−14.5795			−0.710560			−0.355280	−	0.934760i	$-0.615614\pi$
$421$	−14.5795			−0.710560			−0.355280	+	0.934760i	$0.615614\pi$
$422$		0			0
$423$	−7.42514	+	12.8607i	−0.361023	+	0.625309i
$424$		0			0
$425$	2.01316	+	3.59822i	0.0976527	+	0.174539i
$426$		0			0
$427$	−6.85124	+	6.97960i	−0.331555	+	0.337767i
$428$		0			0
$429$	−15.6255	−	27.0641i	−0.754405	−	1.30667i
$430$		0			0
$431$	8.35896	+	4.82605i	0.402637	+	0.232463i	0.687621	−	0.726070i	$-0.258655\pi$
$431$	8.35896	+	4.82605i	0.402637	+	0.232463i	−0.284984	+	0.958532i	$0.591988\pi$
$432$		0			0
$433$	14.4445			0.694161			0.347080	−	0.937835i	$-0.387173\pi$
$433$	14.4445			0.694161			0.347080	+	0.937835i	$0.387173\pi$
$434$		0			0
$435$		−	17.9874i		−	0.862428i
$436$		0			0
$437$	−40.7571	−	23.5311i	−1.94968	−	1.12565i
$438$		0			0
$439$	−15.2473	+	8.80304i	−0.727714	+	0.420146i	−0.817585	−	0.575807i	$-0.804688\pi$
$439$	−15.2473	+	8.80304i	−0.727714	+	0.420146i	0.0898711	+	0.995953i	$0.471354\pi$
$440$		0			0
$441$	24.8089	+	13.7159i	1.18137	+	0.653137i
$442$		0			0
$443$	4.28777	+	7.42664i	0.203718	+	0.352850i	0.949724	−	0.313090i	$-0.101364\pi$
$443$	4.28777	+	7.42664i	0.203718	+	0.352850i	−0.746005	+	0.665940i	$0.768031\pi$
$444$		0			0
$445$	−9.34304	−	5.39421i	−0.442902	−	0.255710i
$446$		0			0
$447$		−	35.6671i		−	1.68700i
$448$		0			0
$449$			14.2397i			0.672011i	0.941860	+	0.336006i	$0.109076\pi$
$449$			14.2397i			0.672011i	−0.941860	+	0.336006i	$0.890924\pi$
$450$		0			0
$451$	1.91048	−	3.30906i	0.0899612	−	0.155817i
$452$		0			0
$453$	−44.6287	+	25.7664i	−2.09684	+	1.21061i
$454$		0			0
$455$	−9.62494	+	9.80527i	−0.451224	+	0.459678i
$456$		0			0
$457$	2.93435	+	5.08245i	0.137263	+	0.237747i	0.926460	−	0.376394i	$-0.122836\pi$
$457$	2.93435	+	5.08245i	0.137263	+	0.237747i	−0.789197	+	0.614141i	$0.789503\pi$
$458$		0			0
$459$	9.87346	+	5.87958i	0.460854	+	0.274435i
$460$		0			0
$461$	−0.693346			−0.0322924			−0.0161462	−	0.999870i	$-0.505140\pi$
$461$	−0.693346			−0.0322924			−0.0161462	+	0.999870i	$0.505140\pi$
$462$		0			0
$463$	4.52755			0.210413			0.105207	−	0.994450i	$-0.466450\pi$
$463$	4.52755			0.210413			0.105207	+	0.994450i	$0.466450\pi$
$464$		0			0
$465$	−5.30800	−	3.06458i	−0.246153	−	0.142116i
$466$		0			0
$467$	8.26513	+	14.3156i	0.382465	+	0.662448i	0.991414	−	0.130761i	$-0.0417421\pi$
$467$	8.26513	+	14.3156i	0.382465	+	0.662448i	−0.608949	+	0.793209i	$0.708409\pi$
$468$		0			0
$469$	2.12216	−	8.22458i	0.0979922	−	0.379776i
$470$		0			0
$471$	−23.3624	+	13.4883i	−1.07648	+	0.621508i
$472$		0			0
$473$	−18.3202	−	10.5772i	−0.842363	−	0.486339i
$474$		0			0
$475$	5.49342			0.252055
$476$		0			0
$477$	−33.9865			−1.55614
$478$		0			0
$479$	18.6809	+	10.7854i	0.853552	+	0.492798i	0.861848	−	0.507167i	$-0.169307\pi$
$479$	18.6809	+	10.7854i	0.853552	+	0.492798i	−0.00829605	+	0.999966i	$0.502641\pi$
$480$		0			0
$481$	−9.59178	+	5.53782i	−0.437348	+	0.252503i
$482$		0			0
$483$	57.9840	−	16.1150i	2.63836	−	0.733258i
$484$		0			0
$485$	−1.47907	−	2.56182i	−0.0671611	−	0.116326i
$486$		0			0
$487$	24.6661	+	14.2410i	1.11773	+	0.645320i	0.940820	−	0.338907i	$-0.110057\pi$
$487$	24.6661	+	14.2410i	1.11773	+	0.645320i	0.176908	+	0.984227i	$0.443391\pi$
$488$		0			0
$489$	15.9810			0.722687
$490$		0			0
$491$	−10.3393			−0.466608			−0.233304	−	0.972404i	$-0.574954\pi$
$491$	−10.3393			−0.466608			−0.233304	+	0.972404i	$0.574954\pi$
$492$		0			0
$493$	23.9993	+	14.2914i	1.08087	+	0.643653i
$494$		0			0
$495$	−4.58922	−	7.94875i	−0.206270	−	0.357270i
$496$		0			0
$497$	4.52145	+	16.2688i	0.202815	+	0.729756i
$498$		0			0
$499$	22.8635	−	13.2002i	1.02351	−	0.590923i	0.108391	−	0.994108i	$-0.465430\pi$
$499$	22.8635	−	13.2002i	1.02351	−	0.590923i	0.915118	+	0.403185i	$0.132097\pi$
$500$		0			0
$501$	−12.2086	+	21.1460i	−0.545442	+	0.944733i
$502$		0			0
$503$			17.4411i			0.777662i	0.921309	+	0.388831i	$0.127121\pi$
$503$			17.4411i			0.777662i	−0.921309	+	0.388831i	$0.872879\pi$
$504$		0			0
$505$		−	13.7089i		−	0.610036i
$506$		0			0
$507$	−32.1204	−	18.5447i	−1.42652	−	0.823600i
$508$		0			0
$509$	−11.7519	−	20.3549i	−0.520893	−	0.902214i	−0.999705	−	0.0242961i	$-0.992266\pi$
$509$	−11.7519	−	20.3549i	−0.520893	−	0.902214i	0.478811	−	0.877918i	$-0.341068\pi$
$510$		0			0
$511$	−20.9059	−	5.39428i	−0.924823	−	0.238629i
$512$		0			0
$513$	13.2595	−	7.65535i	0.585419	−	0.337992i
$514$		0			0
$515$	−15.4965	−	8.94692i	−0.682858	−	0.394248i
$516$		0			0
$517$			8.31106i			0.365520i
$518$		0			0
$519$	−57.6148			−2.52901
$520$		0			0
$521$	26.2021	+	15.1278i	1.14793	+	0.662759i	0.948383	−	0.317128i	$-0.102719\pi$
$521$	26.2021	+	15.1278i	1.14793	+	0.662759i	0.199550	+	0.979888i	$0.436052\pi$
$522$		0			0
$523$	0.277896	+	0.481330i	0.0121516	+	0.0210471i	0.872037	−	0.489440i	$-0.162799\pi$
$523$	0.277896	+	0.481330i	0.0121516	+	0.0210471i	−0.859886	+	0.510487i	$0.829465\pi$
$524$		0			0
$525$	−4.92098	+	5.01317i	−0.214769	+	0.218793i
$526$		0			0
$527$	8.30621	−	4.64722i	0.361824	−	0.202436i
$528$		0			0
$529$	25.1970	−	43.6425i	1.09552	−	1.89750i
$530$		0			0
$531$	−30.0110			−1.30237
$532$		0			0
$533$		−	8.75509i		−	0.379225i
$534$		0			0
$535$	6.90759	−	11.9643i	0.298641	−	0.517262i
$536$		0			0
$537$	−46.1393	+	26.6385i	−1.99106	+	1.14954i
$538$		0			0
$539$	15.8624	−	0.294459i	0.683241	−	0.0126833i
$540$		0			0
$541$	28.5680	−	16.4938i	1.22824	−	0.709122i	0.261575	−	0.965183i	$-0.415758\pi$
$541$	28.5680	−	16.4938i	1.22824	−	0.709122i	0.966661	+	0.256061i	$0.0824249\pi$
$542$		0			0
$543$	9.79578	−	16.9668i	0.420377	−	0.728115i
$544$		0			0
$545$	−12.0461			−0.515997
$546$		0			0
$547$			8.79966i			0.376246i	0.982145	+	0.188123i	$0.0602404\pi$
$547$			8.79966i			0.376246i	−0.982145	+	0.188123i	$0.939760\pi$
$548$		0			0
$549$	−12.9645	−	7.48508i	−0.553313	−	0.319455i
$550$		0			0
$551$	32.2296	−	18.6078i	1.37303	−	0.792718i
$552$		0			0
$553$	8.43191	−	8.58989i	0.358561	−	0.365279i
$554$		0			0
$555$	−4.90402	+	2.83134i	−0.208164	+	0.120184i
$556$		0			0
$557$	−13.4579	+	23.3098i	−0.570230	+	0.987668i	0.426312	+	0.904576i	$0.359813\pi$
$557$	−13.4579	+	23.3098i	−0.570230	+	0.987668i	−0.996542	+	0.0830915i	$0.973521\pi$
$558$		0			0
$559$	−48.4715			−2.05013
$560$		0			0
$561$	24.8094	+	0.334950i	1.04745	+	0.0141416i
$562$		0			0
$563$	−0.0997319	+	0.172741i	−0.00420320	+	0.00728015i	−0.868119	−	0.496356i	$-0.834671\pi$
$563$	−0.0997319	+	0.172741i	−0.00420320	+	0.00728015i	0.863916	+	0.503636i	$0.168005\pi$
$564$		0			0
$565$	2.68117	+	4.64393i	0.112798	+	0.195371i
$566$		0			0
$567$	3.13921	−	12.1662i	0.131834	−	0.510933i
$568$		0			0
$569$	−3.78163	−	6.54997i	−0.158534	−	0.274589i	0.775806	−	0.630971i	$-0.217343\pi$
$569$	−3.78163	−	6.54997i	−0.158534	−	0.274589i	−0.934340	+	0.356382i	$0.884010\pi$
$570$		0			0
$571$	9.94179	+	5.73989i	0.416051	+	0.240207i	0.693386	−	0.720566i	$-0.256118\pi$
$571$	9.94179	+	5.73989i	0.416051	+	0.240207i	−0.277335	+	0.960773i	$0.589451\pi$
$572$		0			0
$573$			63.1460i			2.63796i
$574$		0			0
$575$			8.56703i			0.357270i
$576$		0			0
$577$	4.14253	−	7.17507i	0.172456	−	0.298702i	−0.766822	−	0.641860i	$-0.778163\pi$
$577$	4.14253	−	7.17507i	0.172456	−	0.298702i	0.939278	+	0.343158i	$0.111497\pi$
$578$		0			0
$579$	−4.20867	−	7.28962i	−0.174906	−	0.302946i
$580$		0			0
$581$	−25.9550	+	7.21346i	−1.07680	+	0.299265i
$582$		0			0
$583$	−16.4725	+	9.51039i	−0.682221	+	0.393880i
$584$		0			0
$585$	−18.2132	−	10.5154i	−0.753023	−	0.434758i
$586$		0			0
$587$	−44.4591			−1.83502			−0.917512	−	0.397708i	$-0.869806\pi$
$587$	−44.4591			−1.83502			−0.917512	+	0.397708i	$0.869806\pi$
$588$		0			0
$589$		−	12.6811i		−	0.522517i
$590$		0			0
$591$	32.2874	−	55.9233i	1.32812	−	2.30038i
$592$		0			0
$593$	0.714808	+	1.23808i	0.0293536	+	0.0508420i	0.880329	−	0.474364i	$-0.157322\pi$
$593$	0.714808	+	1.23808i	0.0293536	+	0.0508420i	−0.850975	+	0.525206i	$0.823988\pi$
$594$		0			0
$595$	−2.77890	−	10.5488i	−0.113924	−	0.432460i
$596$		0			0
$597$	−20.2520	−	35.0776i	−0.828861	−	1.43563i
$598$		0			0
$599$	−17.0136	+	29.4685i	−0.695158	+	1.20405i	0.274969	+	0.961453i	$0.411332\pi$
$599$	−17.0136	+	29.4685i	−0.695158	+	1.20405i	−0.970127	+	0.242596i	$0.922001\pi$
$600$		0			0
$601$		−	44.9867i		−	1.83504i	−0.397685	−	0.917522i	$-0.630186\pi$
$601$		−	44.9867i		−	1.83504i	0.397685	−	0.917522i	$-0.369814\pi$
$602$		0			0
$603$	13.0012			0.529451
$604$		0			0
$605$	5.07770	+	2.93161i	0.206438	+	0.119187i
$606$		0			0
$607$	−31.6740	+	18.2870i	−1.28561	+	0.742246i	−0.977868	−	0.209224i	$-0.932906\pi$
$607$	−31.6740	+	18.2870i	−1.28561	+	0.742246i	−0.307741	+	0.951470i	$0.599573\pi$
$608$		0			0
$609$	−11.8901	+	46.0808i	−0.481810	+	1.86729i
$610$		0			0
$611$	9.52168	+	16.4920i	0.385206	+	0.667196i
$612$		0			0
$613$	−5.04168	+	8.73244i	−0.203631	+	0.352700i	−0.949696	−	0.313174i	$-0.898608\pi$
$613$	−5.04168	+	8.73244i	−0.203631	+	0.352700i	0.746064	+	0.665874i	$0.231941\pi$
$614$		0			0
$615$		−	4.47625i		−	0.180500i
$616$		0			0
$617$		−	7.17367i		−	0.288801i	−0.989519	−	0.144400i	$-0.953875\pi$
$617$		−	7.17367i		−	0.288801i	0.989519	−	0.144400i	$-0.0461254\pi$
$618$		0			0
$619$	35.8177	+	20.6793i	1.43963	+	0.831173i	0.997824	−	0.0659362i	$-0.0210034\pi$
$619$	35.8177	+	20.6793i	1.43963	+	0.831173i	0.441809	+	0.897109i	$0.354337\pi$
$620$		0			0
$621$	11.9386	+	20.6782i	0.479079	+	0.829788i
$622$		0			0
$623$	20.3697	+	19.9951i	0.816095	+	0.801086i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	16.5289	−	28.6289i	0.660100	−	1.14333i
$628$		0			0
$629$	0.118709	−	8.79268i	0.00473326	−	0.350587i
$630$		0			0
$631$	35.1276			1.39841			0.699204	−	0.714923i	$-0.253538\pi$
$631$	35.1276			1.39841			0.699204	+	0.714923i	$0.253538\pi$
$632$		0			0
$633$	18.5592	−	32.1456i	0.737664	−	1.27767i
$634$		0			0
$635$	10.1281	−	5.84748i	0.401922	−	0.232050i
$636$		0			0
$637$	31.1391	−	18.7573i	1.23378	−	0.743190i
$638$		0			0
$639$	−22.3829	+	12.9228i	−0.885455	+	0.511218i
$640$		0			0
$641$	17.1721	+	9.91433i	0.678258	+	0.391593i	0.799199	−	0.601067i	$-0.205258\pi$
$641$	17.1721	+	9.91433i	0.678258	+	0.391593i	−0.120940	+	0.992660i	$0.538591\pi$
$642$		0			0
$643$			7.76853i			0.306361i	0.988198	+	0.153180i	$0.0489516\pi$
$643$			7.76853i			0.306361i	−0.988198	+	0.153180i	$0.951048\pi$
$644$		0			0
$645$	−24.7822			−0.975798
$646$		0			0
$647$	−12.0714	+	20.9082i	−0.474574	+	0.821987i	−0.999576	−	0.0291143i	$-0.990731\pi$
$647$	−12.0714	+	20.9082i	−0.474574	+	0.821987i	0.525002	+	0.851101i	$0.324065\pi$
$648$		0			0
$649$	−14.5456	+	8.39793i	−0.570966	+	0.329648i
$650$		0			0
$651$	11.5725	+	11.3597i	0.453563	+	0.445221i
$652$		0			0
$653$	−18.8445	+	10.8799i	−0.737441	+	0.425762i	−0.821138	−	0.570730i	$-0.806660\pi$
$653$	−18.8445	+	10.8799i	−0.737441	+	0.425762i	0.0836974	+	0.996491i	$0.473327\pi$
$654$		0			0
$655$	7.91779	−	13.7140i	0.309374	−	0.535851i
$656$		0			0
$657$		−	33.0476i		−	1.28931i
$658$		0			0
$659$	−19.0502			−0.742091			−0.371045	−	0.928615i	$-0.621001\pi$
$659$	−19.0502			−0.742091			−0.371045	+	0.928615i	$0.621001\pi$
$660$		0			0
$661$	6.38718	−	11.0629i	0.248432	−	0.430298i	−0.714659	−	0.699473i	$-0.753418\pi$
$661$	6.38718	−	11.0629i	0.248432	−	0.430298i	0.963091	+	0.269176i	$0.0867513\pi$
$662$		0			0
$663$	49.6141	−	27.7585i	1.92685	−	1.07805i
$664$		0			0
$665$	−14.0733	−	3.63128i	−0.545739	−	0.140815i
$666$		0			0
$667$	29.0190	+	50.2623i	1.12362	+	1.94617i
$668$		0			0
$669$	42.5447	+	24.5632i	1.64487	+	0.949668i
$670$		0			0
$671$	−8.37815			−0.323435
$672$		0			0
$673$		−	1.43896i		−	0.0554678i	−0.999615	−	0.0277339i	$-0.991171\pi$
$673$		−	1.43896i		−	0.0554678i	0.999615	−	0.0277339i	$-0.00882911\pi$
$674$		0			0
$675$	−2.41370	−	1.39355i	−0.0929033	−	0.0536377i
$676$		0			0
$677$	10.7036	−	6.17972i	0.411372	−	0.237506i	−0.280007	−	0.959998i	$-0.590337\pi$
$677$	10.7036	−	6.17972i	0.411372	−	0.237506i	0.691379	+	0.722492i	$0.257003\pi$
$678$		0			0
$679$	2.09572	+	7.54069i	0.0804263	+	0.289385i
$680$		0			0
$681$	−29.1954	−	50.5680i	−1.11877	−	1.93777i
$682$		0			0
$683$	18.6703	+	10.7793i	0.714400	+	0.412459i	0.812688	−	0.582699i	$-0.198003\pi$
$683$	18.6703	+	10.7793i	0.714400	+	0.412459i	−0.0982881	+	0.995158i	$0.531337\pi$
$684$		0			0
$685$			17.6521i			0.674453i
$686$		0			0
$687$		−	62.2928i		−	2.37662i
$688$		0			0
$689$	−21.7914	+	37.7439i	−0.830187	+	1.43793i
$690$		0			0
$691$	−15.9270	+	9.19544i	−0.605891	+	0.349811i	−0.771355	−	0.636405i	$-0.780421\pi$
$691$	−15.9270	+	9.19544i	−0.605891	+	0.349811i	0.165465	+	0.986216i	$0.447088\pi$
$692$		0			0
$693$	6.50254	+	23.3971i	0.247011	+	0.888781i
$694$		0			0
$695$	−8.94356	−	15.4907i	−0.339249	−	0.587596i
$696$		0			0
$697$	5.97235	+	3.55649i	0.226219	+	0.134712i
$698$		0			0
$699$	19.0818			0.721740
$700$		0			0
$701$	−5.33558			−0.201522			−0.100761	−	0.994911i	$-0.532128\pi$
$701$	−5.33558			−0.201522			−0.100761	+	0.994911i	$0.532128\pi$
$702$		0			0
$703$	−10.1464	−	5.85800i	−0.382677	−	0.220939i
$704$		0			0
$705$	4.86818	+	8.43194i	0.183346	+	0.317565i
$706$		0			0
$707$	−9.06189	+	35.1200i	−0.340807	+	1.32082i
$708$		0			0
$709$	−1.27704	+	0.737301i	−0.0479603	+	0.0276899i	−0.523788	−	0.851848i	$-0.675482\pi$
$709$	−1.27704	+	0.737301i	−0.0479603	+	0.0276899i	0.475828	+	0.879538i	$0.342148\pi$
$710$		0			0
$711$	15.9556	+	9.21199i	0.598383	+	0.345477i
$712$		0			0
$713$	19.7763			0.740629
$714$		0			0
$715$	−11.7700			−0.440174
$716$		0			0
$717$	37.5614	+	21.6861i	1.40276	+	0.809882i
$718$		0			0
$719$	37.9996	−	21.9391i	1.41715	−	0.818189i	0.421098	−	0.907015i	$-0.361645\pi$
$719$	37.9996	−	21.9391i	1.41715	−	0.818189i	0.996047	+	0.0888256i	$0.0283114\pi$
$720$		0			0
$721$	33.7855	+	33.1642i	1.25824	+	1.23510i
$722$		0			0
$723$	−8.40306	−	14.5545i	−0.312513	−	0.541288i
$724$		0			0
$725$	−5.86695	−	3.38729i	−0.217893	−	0.125801i
$726$		0			0
$727$	32.1298			1.19163			0.595815	−	0.803122i	$-0.296829\pi$
$727$	32.1298			1.19163			0.595815	+	0.803122i	$0.296829\pi$
$728$		0			0
$729$	41.4324			1.53453
$730$		0			0
$731$	19.6901	−	33.0652i	0.728264	−	1.22296i
$732$		0			0
$733$	−16.6420	−	28.8248i	−0.614687	−	1.06467i	−0.990439	−	0.137949i	$-0.955949\pi$
$733$	−16.6420	−	28.8248i	−0.614687	−	1.06467i	0.375752	−	0.926720i	$-0.377384\pi$
$734$		0			0
$735$	15.9206	−	9.59009i	0.587240	−	0.353736i
$736$		0			0
$737$	6.30139	−	3.63811i	0.232115	−	0.134012i
$738$		0			0
$739$	17.7185	−	30.6894i	0.651787	−	1.12893i	−0.330902	−	0.943665i	$-0.607353\pi$
$739$	17.7185	−	30.6894i	0.651787	−	1.12893i	0.982689	−	0.185263i	$-0.0593138\pi$
$740$		0			0
$741$		−	75.7462i		−	2.78261i
$742$		0			0
$743$		−	41.1423i		−	1.50937i	−0.656090	−	0.754683i	$-0.727791\pi$
$743$		−	41.1423i		−	1.50937i	0.656090	−	0.754683i	$-0.272209\pi$
$744$		0			0
$745$	−11.6336	−	6.71665i	−0.426221	−	0.246079i
$746$		0			0
$747$	−20.6169	−	35.7094i	−0.754331	−	1.30654i
$748$		0			0
$749$	−25.6049	+	26.0846i	−0.935581	+	0.953110i
$750$		0			0
$751$	−19.1652	+	11.0650i	−0.699348	+	0.403769i	−0.807105	−	0.590408i	$-0.798967\pi$
$751$	−19.1652	+	11.0650i	−0.699348	+	0.403769i	0.107756	+	0.994177i	$0.465633\pi$
$752$		0			0
$753$	−59.6325	−	34.4289i	−2.17313	−	1.25466i
$754$		0			0
$755$			19.4088i			0.706358i
$756$		0			0
$757$	−22.1151			−0.803789			−0.401894	−	0.915686i	$-0.631648\pi$
$757$	−22.1151			−0.803789			−0.401894	+	0.915686i	$0.631648\pi$
$758$		0			0
$759$	44.6469	+	25.7769i	1.62058	+	0.935642i
$760$		0			0
$761$	−1.16722	−	2.02168i	−0.0423117	−	0.0732860i	0.844094	−	0.536195i	$-0.180139\pi$
$761$	−1.16722	−	2.02168i	−0.0423117	−	0.0732860i	−0.886406	+	0.462909i	$0.846806\pi$
$762$		0			0
$763$	30.8602	+	7.96275i	1.11721	+	0.288271i
$764$		0			0
$765$	14.5717	−	8.15271i	0.526842	−	0.294762i
$766$		0			0
$767$	−19.2424	+	33.3288i	−0.694803	+	1.20343i
$768$		0			0
$769$	−12.3981			−0.447089			−0.223544	−	0.974694i	$-0.571763\pi$
$769$	−12.3981			−0.447089			−0.223544	+	0.974694i	$0.571763\pi$
$770$		0			0
$771$		−	32.8415i		−	1.18276i
$772$		0			0
$773$	9.61898	−	16.6606i	0.345971	−	0.599239i	−0.639559	−	0.768742i	$-0.720883\pi$
$773$	9.61898	−	16.6606i	0.345971	−	0.599239i	0.985530	+	0.169503i	$0.0542163\pi$
$774$		0			0
$775$	−1.99915	+	1.15421i	−0.0718116	+	0.0414605i
$776$		0			0
$777$	14.4349	−	4.01177i	0.517850	−	0.143922i
$778$		0			0
$779$	8.02051	−	4.63064i	0.287365	−	0.165910i
$780$		0			0
$781$	−7.23233	+	12.5268i	−0.258793	+	0.448243i
$782$		0			0
$783$	−18.8814			−0.674766
$784$		0			0
$785$			10.1602i			0.362632i
$786$		0			0
$787$	28.6254	+	16.5269i	1.02038	+	0.589119i	0.914215	−	0.405229i	$-0.132808\pi$
$787$	28.6254	+	16.5269i	1.02038	+	0.589119i	0.106169	+	0.994348i	$0.466142\pi$
$788$		0			0
$789$	−14.1205	+	8.15247i	−0.502703	+	0.290235i
$790$		0			0
$791$	−3.79900	−	13.6693i	−0.135077	−	0.486026i
$792$		0			0
$793$	−16.6252	+	9.59855i	−0.590377	+	0.340854i
$794$		0			0
$795$	−11.1414	+	19.2974i	−0.395144	+	0.684409i
$796$		0			0
$797$	55.1647			1.95403			0.977016	−	0.213165i	$-0.0683771\pi$
$797$	55.1647			1.95403			0.977016	+	0.213165i	$0.0683771\pi$
$798$		0			0
$799$	−15.1181	−	0.204108i	−0.534839	−	0.00722082i
$800$		0			0
$801$	−21.8449	+	37.8365i	−0.771853	+	1.33689i
$802$		0			0
$803$	−9.24765	−	16.0174i	−0.326343	−	0.565242i
$804$		0			0
$805$	5.66301	−	21.9474i	0.199595	−	0.773544i
$806$		0			0
$807$	12.7022	+	22.0009i	0.447139	+	0.774468i
$808$		0			0
$809$	−7.35785	−	4.24806i	−0.258688	−	0.149354i	0.365048	−	0.930989i	$-0.381053\pi$
$809$	−7.35785	−	4.24806i	−0.258688	−	0.149354i	−0.623736	+	0.781635i	$0.714386\pi$
$810$		0			0
$811$			35.6068i			1.25032i	0.780495	+	0.625162i	$0.214967\pi$
$811$			35.6068i			1.25032i	−0.780495	+	0.625162i	$0.785033\pi$
$812$		0			0
$813$			7.46786i			0.261909i
$814$		0			0
$815$	3.00946	−	5.21254i	0.105417	−	0.182587i
$816$		0			0
$817$	−25.6370	−	44.4046i	−0.896925	−	1.55352i
$818$		0			0
$819$	39.7085	+	38.9782i	1.38753	+	1.36201i
$820$		0			0
$821$	14.6437	−	8.45455i	0.511069	−	0.295066i	−0.222204	−	0.975000i	$-0.571325\pi$
$821$	14.6437	−	8.45455i	0.511069	−	0.295066i	0.733273	+	0.679934i	$0.237992\pi$
$822$		0			0
$823$	−36.2795	−	20.9460i	−1.26462	−	0.730131i	−0.290658	−	0.956827i	$-0.593874\pi$
$823$	−36.2795	−	20.9460i	−1.26462	−	0.730131i	−0.973966	+	0.226696i	$0.927208\pi$
$824$		0			0
$825$	−6.01770			−0.209509
$826$		0			0
$827$		−	42.9221i		−	1.49255i	−0.665638	−	0.746274i	$-0.731841\pi$
$827$		−	42.9221i		−	1.49255i	0.665638	−	0.746274i	$-0.268159\pi$
$828$		0			0
$829$	−8.71323	+	15.0918i	−0.302623	+	0.524158i	−0.976729	−	0.214476i	$-0.931196\pi$
$829$	−8.71323	+	15.0918i	−0.302623	+	0.524158i	0.674106	+	0.738634i	$0.264529\pi$
$830$		0			0
$831$	24.0384	+	41.6357i	0.833883	+	1.44433i
$832$		0			0
$833$	0.146072	+	28.8614i	0.00506109	+	0.999987i
$834$		0			0
$835$	4.59814	+	7.96420i	0.159125	+	0.275613i
$836$		0			0
$837$	−3.21690	+	5.57183i	−0.111192	+	0.192591i
$838$		0			0
$839$			24.1800i			0.834788i	0.908726	+	0.417394i	$0.137056\pi$
$839$			24.1800i			0.834788i	−0.908726	+	0.417394i	$0.862944\pi$
$840$		0			0
$841$	−16.8948			−0.582580
$842$		0			0
$843$	22.2826	+	12.8649i	0.767454	+	0.443090i
$844$		0			0
$845$	−12.0975	+	6.98450i	−0.416167	+	0.240274i
$846$		0			0
$847$	−11.0704	−	10.8668i	−0.380384	−	0.373388i
$848$		0			0
$849$	−0.0965956	−	0.167308i	−0.00331515	−	0.00574201i
$850$		0			0
$851$	9.13559	−	15.8233i	0.313164	−	0.542416i
$852$		0			0
$853$			5.95768i			0.203987i	0.994785	+	0.101993i	$0.0325221\pi$
$853$			5.95768i			0.203987i	−0.994785	+	0.101993i	$0.967478\pi$
$854$		0			0
$855$		−	22.2467i		−	0.760822i
$856$		0			0
$857$	−9.98979	−	5.76761i	−0.341245	−	0.197018i	0.319578	−	0.947560i	$-0.396459\pi$
$857$	−9.98979	−	5.76761i	−0.341245	−	0.197018i	−0.660822	+	0.750542i	$0.729792\pi$
$858$		0			0
$859$	−0.822752	−	1.42505i	−0.0280719	−	0.0486220i	0.851648	−	0.524114i	$-0.175603\pi$
$859$	−0.822752	−	1.42505i	−0.0280719	−	0.0486220i	−0.879720	+	0.475492i	$0.842270\pi$
$860$		0			0
$861$	−2.95891	+	11.4674i	−0.100839	+	0.390809i
$862$		0			0
$863$	21.4495	+	37.1517i	0.730151	+	1.26466i	0.956818	+	0.290687i	$0.0938837\pi$
$863$	21.4495	+	37.1517i	0.730151	+	1.26466i	−0.226667	+	0.973972i	$0.572783\pi$
$864$		0			0
$865$	−10.8497	+	18.7923i	−0.368902	+	0.638957i
$866$		0			0
$867$	−1.21857	+	45.1207i	−0.0413847	+	1.53238i
$868$		0			0
$869$	10.3111			0.349780
$870$		0			0
$871$	8.33610	−	14.4386i	0.282458	−	0.489232i
$872$		0			0
$873$	−10.3746	+	5.98979i	−0.351128	+	0.202724i
$874$		0			0
$875$	0.708459	+	2.54913i	0.0239503	+	0.0861765i
$876$		0			0
$877$	−45.6353	+	26.3476i	−1.54100	+	0.889695i	−0.542220	+	0.840237i	$0.682416\pi$
$877$	−45.6353	+	26.3476i	−1.54100	+	0.889695i	−0.998776	+	0.0494579i	$0.984251\pi$
$878$		0			0
$879$	−22.5145	−	12.9987i	−0.759394	−	0.438436i
$880$		0			0
$881$		−	30.5581i		−	1.02953i	−0.857331	−	0.514765i	$-0.827879\pi$
$881$		−	30.5581i		−	1.02953i	0.857331	−	0.514765i	$-0.172121\pi$
$882$		0			0
$883$	54.0191			1.81789			0.908943	−	0.416920i	$-0.136890\pi$
$883$	54.0191			1.81789			0.908943	+	0.416920i	$0.136890\pi$
$884$		0			0
$885$	−9.83813	+	17.0401i	−0.330705	+	0.572798i
$886$		0			0
$887$	28.9204	−	16.6972i	0.971051	−	0.560637i	0.0714948	−	0.997441i	$-0.477223\pi$
$887$	28.9204	−	16.6972i	0.971051	−	0.560637i	0.899557	+	0.436804i	$0.143890\pi$
$888$		0			0
$889$	−29.8120	+	8.28539i	−0.999863	+	0.277883i
$890$		0			0
$891$	9.32135	−	5.38168i	0.312277	−	0.180293i
$892$		0			0
$893$	−10.0722	+	17.4456i	−0.337053	+	0.583793i
$894$		0			0
$895$			20.0657i			0.670723i
$896$		0			0
$897$	118.127			3.94414
$898$		0			0
$899$	−7.81928	+	13.5434i	−0.260788	+	0.451698i
$900$		0			0
$901$	−16.8951	−	30.1975i	−0.562859	−	1.00602i
$902$		0			0
$903$	63.4881	+	16.3816i	2.11275	+	0.545146i
$904$		0			0
$905$	−3.68938	−	6.39020i	−0.122639	−	0.212417i
$906$		0			0
$907$	31.2009	+	18.0138i	1.03601	+	0.598140i	0.918700	−	0.394956i	$-0.129240\pi$
$907$	31.2009	+	18.0138i	1.03601	+	0.598140i	0.117309	+	0.993096i	$0.462573\pi$
$908$		0			0
$909$	−55.5168			−1.84138
$910$		0			0
$911$		−	3.30503i		−	0.109500i	−0.998500	−	0.0547502i	$-0.982564\pi$
$911$		−	3.30503i		−	0.109500i	0.998500	−	0.0547502i	$-0.0174362\pi$
$912$		0			0
$913$	−19.9850	−	11.5384i	−0.661408	−	0.381864i
$914$		0			0
$915$	−8.50001	+	4.90748i	−0.281002	+	0.162236i
$916$		0			0
$917$	−29.3494	+	29.8993i	−0.969204	+	0.987363i
$918$		0			0
$919$	−16.2089	−	28.0746i	−0.534682	−	0.926097i	−0.999179	−	0.0405221i	$-0.987098\pi$
$919$	−16.2089	−	28.0746i	−0.534682	−	0.926097i	0.464496	−	0.885575i	$-0.346235\pi$
$920$		0			0
$921$	47.5106	+	27.4302i	1.56553	+	0.903857i
$922$		0			0
$923$			33.1433i			1.09092i
$924$		0			0
$925$			2.13273i			0.0701238i
$926$		0			0
$927$	−36.2324	+	62.7563i	−1.19003	+	2.06119i
$928$		0			0
$929$	−22.2852	+	12.8664i	−0.731154	+	0.422132i	−0.818844	−	0.574016i	$-0.805385\pi$
$929$	−22.2852	+	12.8664i	−0.731154	+	0.422132i	0.0876899	+	0.996148i	$0.472052\pi$
$930$		0			0
$931$	33.6532	+	18.6056i	1.10294	+	0.609773i
$932$		0			0
$933$	2.72395	+	4.71801i	0.0891780	+	0.154461i
$934$		0			0
$935$	4.78122	−	8.02901i	0.156363	−	0.262577i
$936$		0			0
$937$	53.6320			1.75208			0.876040	−	0.482238i	$-0.160176\pi$
$937$	53.6320			1.75208			0.876040	+	0.482238i	$0.160176\pi$
$938$		0			0
$939$	−47.2370			−1.54152
$940$		0			0
$941$	3.63809	+	2.10045i	0.118598	+	0.0684727i	0.558126	−	0.829756i	$-0.311521\pi$
$941$	3.63809	+	2.10045i	0.118598	+	0.0684727i	−0.439527	+	0.898229i	$0.644854\pi$
$942$		0			0
$943$	7.22152	+	12.5080i	0.235165	+	0.407318i
$944$		0			0
$945$	5.26235	+	5.16557i	0.171184	+	0.168036i
$946$		0			0
$947$	0.438771	−	0.253324i	0.0142581	−	0.00823194i	−0.492854	−	0.870112i	$-0.664046\pi$
$947$	0.438771	−	0.253324i	0.0142581	−	0.00823194i	0.507112	+	0.861880i	$0.330713\pi$
$948$		0			0
$949$	−36.7011	−	21.1894i	−1.19137	−	0.687837i
$950$		0			0
$951$	−34.0381			−1.10376
$952$		0			0
$953$	7.68847			0.249054			0.124527	−	0.992216i	$-0.460259\pi$
$953$	7.68847			0.249054			0.124527	+	0.992216i	$0.460259\pi$
$954$		0			0
$955$	20.5964	+	11.8913i	0.666484	+	0.384795i
$956$		0			0
$957$	−35.3056	+	20.3837i	−1.14127	+	0.658911i
$958$		0			0
$959$	11.6685	−	45.2220i	0.376795	−	1.46029i
$960$		0			0
$961$	−12.8356	−	22.2319i	−0.414051	−	0.717158i
$962$		0			0
$963$	−48.4519	−	27.9737i	−1.56134	−	0.901440i
$964$		0			0
$965$	−3.17022			−0.102053
$966$		0			0
$967$	28.5744			0.918890			0.459445	−	0.888206i	$-0.348048\pi$
$967$	28.5744			0.918890			0.459445	+	0.888206i	$0.348048\pi$
$968$		0			0
$969$	51.6708	+	30.7696i	1.65991	+	0.988462i
$970$		0			0
$971$	−18.0778	−	31.3116i	−0.580144	−	1.00484i	−0.995462	−	0.0951620i	$-0.969663\pi$
$971$	−18.0778	−	31.3116i	−0.580144	−	1.00484i	0.415318	−	0.909676i	$-0.363670\pi$
$972$		0			0
$973$	12.6723	+	45.5967i	0.406255	+	1.46176i
$974$		0			0
$975$	−11.9412	+	6.89426i	−0.382425	+	0.220793i
$976$		0			0
$977$	−20.3621	+	35.2682i	−0.651441	+	1.12833i	0.331332	+	0.943514i	$0.392502\pi$
$977$	−20.3621	+	35.2682i	−0.651441	+	1.12833i	−0.982773	+	0.184815i	$0.940831\pi$
$978$		0			0
$979$			24.4513i			0.781468i
$980$		0			0
$981$			48.7831i			1.55752i
$982$		0			0
$983$	23.6425	+	13.6500i	0.754078	+	0.435367i	0.827166	−	0.561958i	$-0.189952\pi$
$983$	23.6425	+	13.6500i	0.754078	+	0.435367i	−0.0730872	+	0.997326i	$0.523285\pi$
$984$		0			0
$985$	−12.1604	−	21.0624i	−0.387462	−	0.671103i
$986$		0			0
$987$	−6.89781	−	24.8193i	−0.219560	−	0.790007i
$988$		0			0
$989$	69.2492	−	39.9811i	2.20200	−	1.27132i
$990$		0			0
$991$	−13.6834	−	7.90013i	−0.434669	−	0.250956i	0.266665	−	0.963789i	$-0.414078\pi$
$991$	−13.6834	−	7.90013i	−0.434669	−	0.250956i	−0.701334	+	0.712833i	$0.747412\pi$
$992$		0			0
$993$			42.2536i			1.34088i
$994$		0			0
$995$	−15.2550			−0.483617
$996$		0			0
$997$	−22.4152	−	12.9414i	−0.709895	−	0.409858i	0.101127	−	0.994874i	$-0.467755\pi$
$997$	−22.4152	−	12.9414i	−0.709895	−	0.409858i	−0.811022	+	0.585015i	$0.801088\pi$
$998$		0			0
$999$	2.97207	+	5.14777i	0.0940321	+	0.162868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2380.2.cb.b.781.6	✓	92
7.2	even	3	inner	2380.2.cb.b.1801.41	yes	92
17.16	even	2	inner	2380.2.cb.b.781.41	yes	92
119.16	even	6	inner	2380.2.cb.b.1801.6	yes	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2380.2.cb.b.781.6	✓	92	1.1	even	1	trivial
2380.2.cb.b.781.41	yes	92	17.16	even	2	inner
2380.2.cb.b.1801.6	yes	92	119.16	even	6	inner
2380.2.cb.b.1801.41	yes	92	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2380 = 2^{2} \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2380.cb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.29941 - 1.32756i) q^{3} +(-0.866025 + 0.500000i) q^{5} +(2.54913 - 0.708459i) q^{7} +(2.02485 + 3.50715i) q^{9} +(1.96280 + 1.13322i) q^{11} +5.19317 q^{13} +2.65513 q^{15} +(-2.10957 + 3.54256i) q^{17} +(2.74671 + 4.75744i) q^{19} +(-6.80202 - 1.75510i) q^{21} +(-7.41926 + 4.28351i) q^{23} +(0.500000 - 0.866025i) q^{25} -2.78710i q^{27} -6.77457i q^{29} +(-1.99915 - 1.15421i) q^{31} +(-3.00885 - 5.21148i) q^{33} +(-1.85339 + 1.88811i) q^{35} +(-1.84700 + 1.06637i) q^{37} +(-11.9412 - 6.89426i) q^{39} -1.68589i q^{41} -9.33371 q^{43} +(-3.50715 - 2.02485i) q^{45} +(1.83350 + 3.17572i) q^{47} +(5.99617 - 3.61191i) q^{49} +(9.55373 - 5.34520i) q^{51} +(-4.19617 + 7.26798i) q^{53} -2.26644 q^{55} -14.5857i q^{57} +(-3.70533 + 6.41782i) q^{59} +(-3.20135 + 1.84830i) q^{61} +(7.64629 + 7.50566i) q^{63} +(-4.49742 + 2.59658i) q^{65} +(1.60521 - 2.78030i) q^{67} +22.7466 q^{69} +6.38209i q^{71} +(-7.06719 - 4.08025i) q^{73} +(-2.29941 + 1.32756i) q^{75} +(5.80628 + 1.49817i) q^{77} +(3.93995 - 2.27473i) q^{79} +(2.37450 - 4.11276i) q^{81} -10.1819 q^{83} +(0.0556607 - 4.12273i) q^{85} +(-8.99368 + 15.5775i) q^{87} +(5.39421 + 9.34304i) q^{89} +(13.2381 - 3.67914i) q^{91} +(3.06458 + 5.30800i) q^{93} +(-4.75744 - 2.74671i) q^{95} +2.95814i q^{97} +9.17843i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 56 q^{9} - 24 q^{13} + 12 q^{15} + 4 q^{17} - 24 q^{21} + 46 q^{25} - 24 q^{33} + 14 q^{35} - 64 q^{43} + 16 q^{47} + 38 q^{49} - 22 q^{51} - 8 q^{53} + 18 q^{59} + 16 q^{67} - 36 q^{69} - 12 q^{77}+ \cdots + 44 q^{93}+O(q^{100}) \) 92 * q + 56 * q^9 - 24 * q^13 + 12 * q^15 + 4 * q^17 - 24 * q^21 + 46 * q^25 - 24 * q^33 + 14 * q^35 - 64 * q^43 + 16 * q^47 + 38 * q^49 - 22 * q^51 - 8 * q^53 + 18 * q^59 + 16 * q^67 - 36 * q^69 - 12 * q^77 - 86 * q^81 + 8 * q^83 - 20 * q^85 + 20 * q^87 + 2 * q^89 + 44 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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