LMFDB - Embedded newform 741.2.d.a.740.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [741,2,Mod(740,741)] 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("741.740"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(741, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 741 = 3 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	741.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.91691478978$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			740.6
Character	$\chi$	$=$	741.740
Dual form			741.2.d.a.740.81

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.62189i q^{2} +(-0.572756 + 1.63461i) q^{3} -4.87431 q^{4} -1.64471 q^{5} +(4.28577 + 1.50170i) q^{6} +4.37710i q^{7} +7.53612i q^{8} +(-2.34390 - 1.87247i) q^{9} +4.31226i q^{10} +0.200098 q^{11} +(2.79179 - 7.96759i) q^{12} +(-0.154753 - 3.60223i) q^{13} +11.4763 q^{14} +(0.942020 - 2.68847i) q^{15} +10.0103 q^{16} -5.06647i q^{17} +(-4.90940 + 6.14545i) q^{18} +(2.15393 - 3.78954i) q^{19} +8.01684 q^{20} +(-7.15486 - 2.50701i) q^{21} -0.524635i q^{22} -4.04516i q^{23} +(-12.3186 - 4.31636i) q^{24} -2.29492 q^{25} +(-9.44465 + 0.405744i) q^{26} +(4.40324 - 2.75890i) q^{27} -21.3353i q^{28} +4.80265 q^{29} +(-7.04886 - 2.46987i) q^{30} +5.46443 q^{31} -11.1736i q^{32} +(-0.114607 + 0.327082i) q^{33} -13.2837 q^{34} -7.19908i q^{35} +(11.4249 + 9.12698i) q^{36} +9.32852 q^{37} +(-9.93575 - 5.64737i) q^{38} +(5.97687 + 1.81024i) q^{39} -12.3948i q^{40} +7.17304i q^{41} +(-6.57311 + 18.7592i) q^{42} +4.54412 q^{43} -0.975340 q^{44} +(3.85505 + 3.07967i) q^{45} -10.6060 q^{46} +3.20171 q^{47} +(-5.73344 + 16.3629i) q^{48} -12.1590 q^{49} +6.01702i q^{50} +(8.28170 + 2.90185i) q^{51} +(0.754312 + 17.5584i) q^{52} -7.48265 q^{53} +(-7.23352 - 11.5448i) q^{54} -0.329104 q^{55} -32.9864 q^{56} +(4.96074 + 5.69132i) q^{57} -12.5920i q^{58} -6.13368i q^{59} +(-4.59170 + 13.1044i) q^{60} -2.92010 q^{61} -14.3271i q^{62} +(8.19598 - 10.2595i) q^{63} -9.27536 q^{64} +(0.254524 + 5.92464i) q^{65} +(0.857574 + 0.300488i) q^{66} +0.958106 q^{67} +24.6955i q^{68} +(6.61225 + 2.31689i) q^{69} -18.8752 q^{70} -8.64301i q^{71} +(14.1111 - 17.6639i) q^{72} +4.64417i q^{73} -24.4584i q^{74} +(1.31443 - 3.75129i) q^{75} +(-10.4989 + 18.4714i) q^{76} +0.875850i q^{77} +(4.74625 - 15.6707i) q^{78} -6.77157i q^{79} -16.4640 q^{80} +(1.98774 + 8.77775i) q^{81} +18.8069 q^{82} -13.2127 q^{83} +(34.8750 + 12.2200i) q^{84} +8.33289i q^{85} -11.9142i q^{86} +(-2.75075 + 7.85047i) q^{87} +1.50796i q^{88} -14.5724i q^{89} +(8.07456 - 10.1075i) q^{90} +(15.7673 - 0.677368i) q^{91} +19.7173i q^{92} +(-3.12979 + 8.93222i) q^{93} -8.39452i q^{94} +(-3.54260 + 6.23270i) q^{95} +(18.2644 + 6.39974i) q^{96} -1.71606 q^{97} +31.8796i q^{98} +(-0.469010 - 0.374677i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 88 q^{4} - 4 q^{9} + 72 q^{16} + 64 q^{25} - 60 q^{30} - 48 q^{36} + 20 q^{39} + 48 q^{42} - 64 q^{43} - 112 q^{49} - 24 q^{55} - 64 q^{61} - 104 q^{64} + 12 q^{66} + 60 q^{81} + 56 q^{82} - 32 q^{87}+O(q^{100}) $ 88 * q - 88 * q^4 - 4 * q^9 + 72 * q^16 + 64 * q^25 - 60 * q^30 - 48 * q^36 + 20 * q^39 + 48 * q^42 - 64 * q^43 - 112 * q^49 - 24 * q^55 - 64 * q^61 - 104 * q^64 + 12 * q^66 + 60 * q^81 + 56 * q^82 - 32 * q^87

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/741\mathbb{Z}\right)^\times$.

$n$	$40$	$248$	$457$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$		−	2.62189i		−	1.85396i	−0.375115	−	0.926978i	$-0.622397\pi$
$2$		−	2.62189i		−	1.85396i	0.375115	−	0.926978i	$-0.377603\pi$
$3$	−0.572756	+	1.63461i	−0.330681	+	0.943743i
$3$	−0.572756	+	1.63461i	−0.330681	+	0.943743i
$4$	−4.87431			−2.43715
$5$	−1.64471			−0.735538			−0.367769	−	0.929917i	$-0.619878\pi$
$5$	−1.64471			−0.735538			−0.367769	+	0.929917i	$0.619878\pi$
$6$	4.28577	+	1.50170i	1.74966	+	0.613068i
$7$			4.37710i			1.65439i	0.561916	+	0.827195i	$0.310065\pi$
$7$			4.37710i			1.65439i	−0.561916	+	0.827195i	$0.689935\pi$
$8$			7.53612i			2.66442i
$9$	−2.34390	−	1.87247i	−0.781300	−	0.624156i
$10$			4.31226i			1.36366i
$11$	0.200098			0.0603319			0.0301659	−	0.999545i	$-0.490396\pi$
$11$	0.200098			0.0603319			0.0301659	+	0.999545i	$0.490396\pi$
$12$	2.79179	−	7.96759i	0.805921	−	2.30005i
$13$	−0.154753	−	3.60223i	−0.0429206	−	0.999078i
$13$	−0.154753	−	3.60223i	−0.0429206	−	0.999078i
$14$	11.4763			3.06717
$15$	0.942020	−	2.68847i	0.243229	−	0.694159i
$16$	10.0103			2.50257
$17$		−	5.06647i		−	1.22880i	−0.788995	−	0.614400i	$-0.789398\pi$
$17$		−	5.06647i		−	1.22880i	0.788995	−	0.614400i	$-0.210602\pi$
$18$	−4.90940	+	6.14545i	−1.15716	+	1.44850i
$19$	2.15393	−	3.78954i	0.494146	−	0.869379i
$19$	2.15393	−	3.78954i	0.494146	−	0.869379i
$20$	8.01684			1.79262
$21$	−7.15486	−	2.50701i	−1.56132	−	0.547075i
$22$		−	0.524635i		−	0.111853i
$23$		−	4.04516i		−	0.843474i	−0.906718	−	0.421737i	$-0.861421\pi$
$23$		−	4.04516i		−	0.843474i	0.906718	−	0.421737i	$-0.138579\pi$
$24$	−12.3186	−	4.31636i	−2.51453	−	0.881074i
$25$	−2.29492			−0.458983
$26$	−9.44465	+	0.405744i	−1.85225	+	0.0795730i
$27$	4.40324	−	2.75890i	0.847403	−	0.530950i
$28$		−	21.3353i		−	4.03200i
$29$	4.80265			0.891830			0.445915	−	0.895075i	$-0.352878\pi$
$29$	4.80265			0.891830			0.445915	+	0.895075i	$0.352878\pi$
$30$	−7.04886	−	2.46987i	−1.28694	−	0.450935i
$31$	5.46443			0.981441			0.490720	−	0.871317i	$-0.336734\pi$
$31$	5.46443			0.981441			0.490720	+	0.871317i	$0.336734\pi$
$32$		−	11.1736i		−	1.97523i
$33$	−0.114607	+	0.327082i	−0.0199506	+	0.0569377i
$34$	−13.2837			−2.27814
$35$		−	7.19908i		−	1.21687i
$36$	11.4249	+	9.12698i	1.90415	+	1.52116i
$37$	9.32852			1.53360			0.766800	−	0.641887i	$-0.221848\pi$
$37$	9.32852			1.53360			0.766800	+	0.641887i	$0.221848\pi$
$38$	−9.93575	−	5.64737i	−1.61179	−	0.916124i
$39$	5.97687	+	1.81024i	0.957066	+	0.289870i
$40$		−	12.3948i		−	1.95978i
$41$			7.17304i			1.12024i	0.828411	+	0.560120i	$0.189245\pi$
$41$			7.17304i			1.12024i	−0.828411	+	0.560120i	$0.810755\pi$
$42$	−6.57311	+	18.7592i	−1.01425	+	2.89461i
$43$	4.54412			0.692971			0.346486	−	0.938055i	$-0.387375\pi$
$43$	4.54412			0.692971			0.346486	+	0.938055i	$0.387375\pi$
$44$	−0.975340			−0.147038
$45$	3.85505	+	3.07967i	0.574676	+	0.459090i
$46$	−10.6060			−1.56376
$47$	3.20171			0.467017			0.233508	−	0.972355i	$-0.424979\pi$
$47$	3.20171			0.467017			0.233508	+	0.972355i	$0.424979\pi$
$48$	−5.73344	+	16.3629i	−0.827551	+	2.36178i
$49$	−12.1590			−1.73700
$50$			6.01702i			0.850935i
$51$	8.28170	+	2.90185i	1.15967	+	0.406341i
$52$	0.754312	+	17.5584i	0.104604	+	2.43491i
$53$	−7.48265			−1.02782			−0.513911	−	0.857844i	$-0.671804\pi$
$53$	−7.48265			−1.02782			−0.513911	+	0.857844i	$0.671804\pi$
$54$	−7.23352	−	11.5448i	−0.984358	−	1.57105i
$55$	−0.329104			−0.0443764
$56$	−32.9864			−4.40799
$57$	4.96074	+	5.69132i	0.657066	+	0.753833i
$58$		−	12.5920i		−	1.65341i
$59$		−	6.13368i		−	0.798537i	−0.916834	−	0.399269i	$-0.869264\pi$
$59$		−	6.13368i		−	0.798537i	0.916834	−	0.399269i	$-0.130736\pi$
$60$	−4.59170	+	13.1044i	−0.592786	+	1.69177i
$61$	−2.92010			−0.373880			−0.186940	−	0.982371i	$-0.559857\pi$
$61$	−2.92010			−0.373880			−0.186940	+	0.982371i	$0.559857\pi$
$62$		−	14.3271i		−	1.81955i
$63$	8.19598	−	10.2595i	1.03260	−	1.29257i
$64$	−9.27536			−1.15942
$65$	0.254524	+	5.92464i	0.0315698	+	0.734861i
$66$	0.857574	+	0.300488i	0.105560	+	0.0369875i
$67$	0.958106			0.117051			0.0585256	−	0.998286i	$-0.481360\pi$
$67$	0.958106			0.117051			0.0585256	+	0.998286i	$0.481360\pi$
$68$			24.6955i			2.99477i
$69$	6.61225	+	2.31689i	0.796022	+	0.278921i
$70$	−18.8752			−2.25602
$71$		−	8.64301i		−	1.02574i	−0.858467	−	0.512868i	$-0.828583\pi$
$71$		−	8.64301i		−	1.02574i	0.858467	−	0.512868i	$-0.171417\pi$
$72$	14.1111	−	17.6639i	1.66301	−	2.08171i
$73$			4.64417i			0.543559i	0.962360	+	0.271779i	$0.0876121\pi$
$73$			4.64417i			0.543559i	−0.962360	+	0.271779i	$0.912388\pi$
$74$		−	24.4584i		−	2.84323i
$75$	1.31443	−	3.75129i	0.151777	−	0.433162i
$76$	−10.4989	+	18.4714i	−1.20431	+	2.11881i
$77$			0.875850i			0.0998124i
$78$	4.74625	−	15.6707i	0.537407	−	1.77436i
$79$		−	6.77157i		−	0.761861i	−0.924604	−	0.380930i	$-0.875604\pi$
$79$		−	6.77157i		−	0.761861i	0.924604	−	0.380930i	$-0.124396\pi$
$80$	−16.4640			−1.84073
$81$	1.98774	+	8.77775i	0.220860	+	0.975306i
$82$	18.8069			2.07688
$83$	−13.2127			−1.45028			−0.725141	−	0.688601i	$-0.758225\pi$
$83$	−13.2127			−1.45028			−0.725141	+	0.688601i	$0.758225\pi$
$84$	34.8750	+	12.2200i	3.80517	+	1.33331i
$85$			8.33289i			0.903829i
$86$		−	11.9142i		−	1.28474i
$87$	−2.75075	+	7.85047i	−0.294911	+	0.841658i
$88$			1.50796i			0.160750i
$89$		−	14.5724i		−	1.54467i	−0.635217	−	0.772334i	$-0.719089\pi$
$89$		−	14.5724i		−	1.54467i	0.635217	−	0.772334i	$-0.280911\pi$
$90$	8.07456	−	10.1075i	0.851134	−	1.06542i
$91$	15.7673	−	0.677368i	1.65286	−	0.0710074i
$92$			19.7173i			2.05568i
$93$	−3.12979	+	8.93222i	−0.324544	+	0.926228i
$94$		−	8.39452i		−	0.865829i
$95$	−3.54260	+	6.23270i	−0.363463	+	0.639462i
$96$	18.2644	+	6.39974i	1.86411	+	0.653171i
$97$	−1.71606			−0.174239			−0.0871196	−	0.996198i	$-0.527766\pi$
$97$	−1.71606			−0.174239			−0.0871196	+	0.996198i	$0.527766\pi$
$98$			31.8796i			3.22033i
$99$	−0.469010	−	0.374677i	−0.0471373	−	0.0376565i
$100$	11.1861			1.11861
$101$		−	15.4047i		−	1.53283i	−0.642347	−	0.766414i	$-0.722039\pi$
$101$		−	15.4047i		−	1.53283i	0.642347	−	0.766414i	$-0.277961\pi$
$102$	7.60834	−	21.7137i	0.753338	−	2.14998i
$103$			3.96713i			0.390893i	0.980714	+	0.195446i	$0.0626156\pi$
$103$			3.96713i			0.390893i	−0.980714	+	0.195446i	$0.937384\pi$
$104$	27.1468	−	1.16623i	2.66197	−	0.114359i
$105$	11.7677	+	4.12332i	1.14841	+	0.402395i
$106$			19.6187i			1.90554i
$107$	2.00525			0.193855			0.0969276	−	0.995291i	$-0.469098\pi$
$107$	2.00525			0.193855			0.0969276	+	0.995291i	$0.469098\pi$
$108$	−21.4627	+	13.4477i	−2.06525	+	1.29401i
$109$	−9.54308			−0.914061			−0.457031	−	0.889451i	$-0.651087\pi$
$109$	−9.54308			−0.914061			−0.457031	+	0.889451i	$0.651087\pi$
$110$			0.862875i			0.0822719i
$111$	−5.34297	+	15.2485i	−0.507132	+	1.44732i
$112$			43.8160i			4.14022i
$113$	16.6865			1.56973			0.784865	−	0.619667i	$-0.212732\pi$
$113$	16.6865			1.56973			0.784865	+	0.619667i	$0.212732\pi$
$114$	14.9220	−	13.0065i	1.39757	−	1.21817i
$115$			6.65313i			0.620407i
$116$	−23.4096			−2.17353
$117$	−6.38233	+	8.73303i	−0.590046	+	0.807369i
$118$	−16.0818			−1.48045
$119$	22.1764			2.03291
$120$	20.2606	+	7.09918i	1.84953	+	0.648063i
$121$	−10.9600			−0.996360
$122$			7.65617i			0.693157i
$123$	−11.7251	−	4.10840i	−1.05722	−	0.370442i
$124$	−26.6353			−2.39192
$125$	11.9981			1.07314
$126$	−26.8993	−	21.4890i	−2.39638	−	1.91439i
$127$		−	12.8605i		−	1.14119i	−0.821232	−	0.570595i	$-0.806713\pi$
$127$		−	12.8605i		−	1.14119i	0.821232	−	0.570595i	$-0.193287\pi$
$128$			1.97183i			0.174287i
$129$	−2.60267	+	7.42786i	−0.229152	+	0.653987i
$130$	15.5337	−	0.667333i	1.36240	−	0.0585290i
$131$			16.1527i			1.41127i	0.708577	+	0.705634i	$0.249338\pi$
$131$			16.1527i			1.41127i	−0.708577	+	0.705634i	$0.750662\pi$
$132$	0.558632	−	1.59430i	0.0486227	−	0.138766i
$133$	16.5872	+	9.42798i	1.43829	+	0.817509i
$134$		−	2.51205i		−	0.217008i
$135$	−7.24206	+	4.53759i	−0.623298	+	0.390534i
$136$	38.1815			3.27404
$137$	−0.526348			−0.0449689			−0.0224845	−	0.999747i	$-0.507158\pi$
$137$	−0.526348			−0.0449689			−0.0224845	+	0.999747i	$0.507158\pi$
$138$	6.07463	−	17.3366i	0.517107	−	1.47579i
$139$	13.7784			1.16867			0.584335	−	0.811513i	$-0.301355\pi$
$139$	13.7784			1.16867			0.584335	+	0.811513i	$0.301355\pi$
$140$			35.0905i			2.96569i
$141$	−1.83380	+	5.23354i	−0.154434	+	0.440744i
$142$	−22.6610			−1.90167
$143$	−0.0309657	−	0.720799i	−0.00258948	−	0.0602763i
$144$	−23.4631	−	18.7439i	−1.95526	−	1.56199i
$145$	−7.89899			−0.655975
$146$	12.1765			1.00773
$147$	6.96416	−	19.8753i	0.574394	−	1.63928i
$148$	−45.4701			−3.73762
$149$	−15.9949			−1.31035			−0.655176	−	0.755476i	$-0.727405\pi$
$149$	−15.9949			−1.31035			−0.655176	+	0.755476i	$0.727405\pi$
$150$	−9.83548	−	3.44629i	−0.803064	−	0.281388i
$151$	−2.76186			−0.224757			−0.112378	−	0.993665i	$-0.535847\pi$
$151$	−2.76186			−0.224757			−0.112378	+	0.993665i	$0.535847\pi$
$152$	28.5584	+	16.2323i	2.31639	+	1.31661i
$153$	−9.48679	+	11.8753i	−0.766962	+	0.960061i
$154$	2.29638			0.185048
$155$	−8.98743			−0.721888
$156$	−29.1331	−	8.82366i	−2.33252	−	0.706459i
$157$	11.4583			0.914471			0.457236	−	0.889346i	$-0.348840\pi$
$157$	11.4583			0.914471			0.457236	+	0.889346i	$0.348840\pi$
$158$	−17.7543			−1.41246
$159$	4.28574	−	12.2312i	0.339881	−	0.969999i
$160$			18.3773i			1.45286i
$161$	17.7061			1.39543
$162$	23.0143	−	5.21163i	1.80817	−	0.409464i
$163$		−	15.9254i		−	1.24737i	−0.781676	−	0.623685i	$-0.785635\pi$
$163$		−	15.9254i		−	1.24737i	0.781676	−	0.623685i	$-0.214365\pi$
$164$		−	34.9636i		−	2.73020i
$165$	0.188497	−	0.537957i	0.0146744	−	0.0418799i
$166$			34.6422i			2.68876i
$167$			2.70200i			0.209087i	0.994520	+	0.104543i	$0.0333381\pi$
$167$			2.70200i			0.209087i	−0.994520	+	0.104543i	$0.966662\pi$
$168$	18.8932	−	53.9199i	1.45764	−	4.16001i
$169$	−12.9521	+	1.11491i	−0.996316	+	0.0857622i
$170$	21.8479			1.67566
$171$	−12.1444	+	4.84913i	−0.928704	+	0.370822i
$172$	−22.1494			−1.68888
$173$	6.45272			0.490591			0.245295	−	0.969448i	$-0.421115\pi$
$173$	6.45272			0.490591			0.245295	+	0.969448i	$0.421115\pi$
$174$	20.5831	+	7.21216i	1.56040	+	0.546753i
$175$		−	10.0451i		−	0.759337i
$176$	2.00304			0.150985
$177$	10.0262	+	3.51310i	0.753613	+	0.264061i
$178$	−38.2072			−2.86375
$179$	11.0181			0.823533			0.411767	−	0.911289i	$-0.364912\pi$
$179$	11.0181			0.823533			0.411767	+	0.911289i	$0.364912\pi$
$180$	−18.7907	−	15.0113i	−1.40057	−	1.11887i
$181$		−	25.1080i		−	1.86627i	−0.359531	−	0.933133i	$-0.617063\pi$
$181$		−	25.1080i		−	1.86627i	0.359531	−	0.933133i	$-0.382937\pi$
$182$	−1.77598	−	41.3402i	−0.131645	−	3.06434i
$183$	1.67250	−	4.77322i	0.123635	−	0.352846i
$184$	30.4848			2.24737
$185$	−15.3427			−1.12802
$186$	23.4193	+	8.20596i	1.71719	+	0.601690i
$187$		−	1.01379i		−	0.0741357i
$188$	−15.6061			−1.13819
$189$	12.0760	+	19.2734i	0.878398	+	1.40193i
$190$	16.3415	+	9.28831i	1.18553	+	0.673845i
$191$		−	24.4822i		−	1.77147i	−0.464189	−	0.885736i	$-0.653654\pi$
$191$		−	24.4822i		−	1.77147i	0.464189	−	0.885736i	$-0.346346\pi$
$192$	5.31252	−	15.1616i	0.383398	−	1.09419i
$193$	−4.03383			−0.290362			−0.145181	−	0.989405i	$-0.546376\pi$
$193$	−4.03383			−0.290362			−0.145181	+	0.989405i	$0.546376\pi$
$194$			4.49932i			0.323032i
$195$	−9.83025	−	2.97733i	−0.703959	−	0.213211i
$196$	59.2668			4.23335
$197$	6.59858			0.470129			0.235065	−	0.971980i	$-0.424470\pi$
$197$	6.59858			0.470129			0.235065	+	0.971980i	$0.424470\pi$
$198$	−0.982362	+	1.22969i	−0.0698134	+	0.0873905i
$199$	−7.51677			−0.532850			−0.266425	−	0.963856i	$-0.585842\pi$
$199$	−7.51677			−0.532850			−0.266425	+	0.963856i	$0.585842\pi$
$200$		−	17.2948i		−	1.22292i
$201$	−0.548761	+	1.56613i	−0.0387066	+	0.110466i
$202$	−40.3895			−2.84180
$203$			21.0217i			1.47543i
$204$	−40.3676	−	14.1445i	−2.82629	−	0.990315i
$205$		−	11.7976i		−	0.823980i
$206$	10.4014			0.724699
$207$	−7.57442	+	9.48145i	−0.526459	+	0.659006i
$208$	−1.54911	−	36.0593i	−0.107412	−	2.50026i
$209$	0.430998	−	0.758279i	0.0298127	−	0.0524513i
$210$	10.8109	−	30.8536i	0.746022	−	2.12910i
$211$			18.8866i			1.30021i	0.759845	+	0.650104i	$0.225275\pi$
$211$			18.8866i			1.30021i	−0.759845	+	0.650104i	$0.774725\pi$
$212$	36.4728			2.50496
$213$	14.1280	+	4.95034i	0.968032	+	0.339192i
$214$		−	5.25755i		−	0.359399i
$215$	−7.47377			−0.509707
$216$	20.7914	+	33.1833i	1.41467	+	2.25784i
$217$			23.9184i			1.62369i
$218$			25.0209i			1.69463i
$219$	−7.59141	−	2.65998i	−0.512980	−	0.179745i
$220$	1.60416			0.108152
$221$	−18.2506	+	0.784049i	−1.22767	+	0.0527408i
$222$	39.9799	+	14.0087i	2.68327	+	0.940201i
$223$	8.96039			0.600032			0.300016	−	0.953934i	$-0.403008\pi$
$223$	8.96039			0.600032			0.300016	+	0.953934i	$0.403008\pi$
$224$	48.9079			3.26780
$225$	5.37905	+	4.29715i	0.358604	+	0.286477i
$226$		−	43.7501i		−	2.91021i
$227$			10.0174i			0.664875i	0.943125	+	0.332437i	$0.107871\pi$
$227$			10.0174i			0.664875i	−0.943125	+	0.332437i	$0.892129\pi$
$228$	−24.1802	−	27.7412i	−1.60137	−	1.83721i
$229$			17.2301i			1.13860i	0.822131	+	0.569298i	$0.192785\pi$
$229$			17.2301i			1.13860i	−0.822131	+	0.569298i	$0.807215\pi$
$230$	17.4438			1.15021
$231$	−1.43167	−	0.501649i	−0.0941972	−	0.0330061i
$232$			36.1934i			2.37621i
$233$		−	17.3799i		−	1.13860i	−0.822131	−	0.569299i	$-0.807215\pi$
$233$		−	17.3799i		−	1.13860i	0.822131	−	0.569299i	$-0.192785\pi$
$234$	22.8971	+	16.7338i	1.49683	+	1.09392i
$235$	−5.26589			−0.343509
$236$			29.8974i			1.94616i
$237$	11.0689	+	3.87846i	0.719000	+	0.251933i
$238$		−	58.1442i		−	3.76893i
$239$	−26.8615			−1.73752			−0.868762	−	0.495229i	$-0.835084\pi$
$239$	−26.8615			−1.73752			−0.868762	+	0.495229i	$0.835084\pi$
$240$	9.42988	−	26.9123i	0.608696	−	1.73718i
$241$	21.3885			1.37775			0.688876	−	0.724879i	$-0.258104\pi$
$241$	21.3885			1.37775			0.688876	+	0.724879i	$0.258104\pi$
$242$			28.7358i			1.84721i
$243$	−15.4867	−	1.77834i	−0.993472	−	0.114080i
$244$	14.2335			0.911203
$245$	19.9981			1.27763
$246$	−10.7718	+	30.7420i	−0.686784	+	1.96004i
$247$	−13.9841	−	7.17251i	−0.889787	−	0.456376i
$248$			41.1806i			2.61497i
$249$	7.56765	−	21.5976i	0.479581	−	1.36869i
$250$		−	31.4576i		−	1.98955i
$251$			1.58597i			0.100105i	0.998747	+	0.0500527i	$0.0159389\pi$
$251$			1.58597i			0.100105i	−0.998747	+	0.0500527i	$0.984061\pi$
$252$	−39.9497	+	50.0079i	−2.51660	+	3.15020i
$253$		−	0.809428i		−	0.0508883i
$254$	−33.7189			−2.11571
$255$	−13.6210	−	4.77272i	−0.852982	−	0.298879i
$256$	−13.3808			−0.836301
$257$	−0.288137			−0.0179735			−0.00898674	−	0.999960i	$-0.502861\pi$
$257$	−0.288137			−0.0179735			−0.00898674	+	0.999960i	$0.502861\pi$
$258$	19.4750	+	6.82392i	1.21246	+	0.424839i
$259$			40.8319i			2.53717i
$260$	−1.24063	−	28.8785i	−0.0769404	−	1.79097i
$261$	−11.2569	−	8.99281i	−0.696787	−	0.556641i
$262$	42.3506			2.61643
$263$		−	5.21374i		−	0.321493i	−0.986996	−	0.160746i	$-0.948610\pi$
$263$		−	5.21374i		−	0.321493i	0.986996	−	0.160746i	$-0.0513901\pi$
$264$	−2.46493	−	0.863696i	−0.151706	−	0.0531568i
$265$	12.3068			0.756002
$266$	24.7191	−	43.4898i	1.51563	−	2.66653i
$267$	23.8201	+	8.34642i	1.45777	+	0.510792i
$268$	−4.67010			−0.285272
$269$	−22.1875			−1.35280			−0.676398	−	0.736536i	$-0.736460\pi$
$269$	−22.1875			−1.35280			−0.676398	+	0.736536i	$0.736460\pi$
$270$	11.8971	+	18.9879i	0.724033	+	1.15557i
$271$		−	8.34280i		−	0.506789i	−0.967363	−	0.253394i	$-0.918453\pi$
$271$		−	8.34280i		−	0.506789i	0.967363	−	0.253394i	$-0.0815471\pi$
$272$		−	50.7167i		−	3.07515i
$273$	−7.92360	+	26.1614i	−0.479558	+	1.58336i
$274$			1.38003i			0.0833704i
$275$	−0.459208			−0.0276913
$276$	−32.2302	−	11.2932i	−1.94003	−	0.679773i
$277$	7.78002			0.467456			0.233728	−	0.972302i	$-0.424907\pi$
$277$	7.78002			0.467456			0.233728	+	0.972302i	$0.424907\pi$
$278$		−	36.1255i		−	2.16666i
$279$	−12.8081	−	10.2320i	−0.766800	−	0.612572i
$280$	54.2532			3.24225
$281$		−	1.69764i		−	0.101273i	−0.998717	−	0.0506363i	$-0.983875\pi$
$281$		−	1.69764i		−	0.101273i	0.998717	−	0.0506363i	$-0.0161249\pi$
$282$	13.7218	+	4.80802i	0.817120	+	0.286313i
$283$	16.7129			0.993476			0.496738	−	0.867900i	$-0.334531\pi$
$283$	16.7129			0.993476			0.496738	+	0.867900i	$0.334531\pi$
$284$			42.1287i			2.49988i
$285$	−8.15899	−	9.36059i	−0.483297	−	0.554473i
$286$	−1.88986	+	0.0811887i	−0.111750	+	0.00480079i
$287$	−31.3971			−1.85331
$288$	−20.9222	+	26.1898i	−1.23285	+	1.54325i
$289$	−8.66910			−0.509947
$290$			20.7103i			1.21615i
$291$	0.982883	−	2.80509i	0.0576176	−	0.164437i
$292$		−	22.6371i		−	1.32474i
$293$		−	17.7530i		−	1.03714i	−0.855034	−	0.518571i	$-0.826464\pi$
$293$		−	17.7530i		−	1.03714i	0.855034	−	0.518571i	$-0.173536\pi$
$294$	−52.1108	−	18.2593i	−3.03916	−	1.06490i
$295$			10.0881i			0.587355i
$296$			70.3009i			4.08615i
$297$	0.881079	−	0.552050i	0.0511254	−	0.0320332i
$298$			41.9368i			2.42934i
$299$	−14.5716	+	0.625998i	−0.842696	+	0.0362024i
$300$	−6.40693	+	18.2850i	−0.369904	+	1.05568i
$301$			19.8901i			1.14644i
$302$			7.24128i			0.416689i
$303$	25.1807	+	8.82316i	1.44660	+	0.506877i
$304$	21.5614	−	37.9343i	1.23663	−	2.17568i
$305$	4.80272			0.275003
$306$	31.1357	+	24.8733i	1.77991	+	1.42191i
$307$	29.1887			1.66589			0.832945	−	0.553356i	$-0.186653\pi$
$307$	29.1887			1.66589			0.832945	+	0.553356i	$0.186653\pi$
$308$		−	4.26916i		−	0.243258i
$309$	−6.48471	−	2.27220i	−0.368902	−	0.129261i
$310$			23.5640i			1.33835i
$311$			15.5326i			0.880775i	0.897808	+	0.440388i	$0.145159\pi$
$311$			15.5326i			0.880775i	−0.897808	+	0.440388i	$0.854841\pi$
$312$	−13.6422	+	45.0425i	−0.772337	+	2.55003i
$313$	16.3701			0.925291			0.462646	−	0.886543i	$-0.346900\pi$
$313$	16.3701			0.925291			0.462646	+	0.886543i	$0.346900\pi$
$314$		−	30.0424i		−	1.69539i
$315$	−13.4800	+	16.8739i	−0.759514	+	0.950738i
$316$			33.0067i			1.85677i
$317$			14.0146i			0.787138i	0.919295	+	0.393569i	$0.128760\pi$
$317$			14.0146i			0.787138i	−0.919295	+	0.393569i	$0.871240\pi$
$318$	−32.0689	−	11.2367i	−1.79834	−	0.630124i
$319$	0.961002			0.0538058
$320$	15.2553			0.852798
$321$	−1.14852	+	3.27781i	−0.0641042	+	0.182949i
$322$		−	46.4234i		−	2.58707i
$323$	−19.1996	−	10.9128i	−1.06829	−	0.607206i
$324$	−9.68885	−	42.7855i	−0.538269	−	2.37697i
$325$	0.355144	+	8.26681i	0.0196999	+	0.458560i
$326$	−41.7545			−2.31257
$327$	5.46586	−	15.5992i	0.302263	−	0.862638i
$328$	−54.0569			−2.98479
$329$			14.0142i			0.772628i
$330$	−1.41046	−	0.494217i	−0.0776435	−	0.0272058i
$331$	11.2817			0.620099			0.310050	−	0.950720i	$-0.399654\pi$
$331$	11.2817			0.620099			0.310050	+	0.950720i	$0.399654\pi$
$332$	64.4028			3.53456
$333$	−21.8651	−	17.4673i	−1.19820	−	0.957204i
$334$	7.08434			0.387638
$335$	−1.57581			−0.0860957
$336$	−71.6220	−	25.0959i	−3.90730	−	1.36909i
$337$		−	9.68227i		−	0.527427i	−0.964601	−	0.263713i	$-0.915053\pi$
$337$		−	9.68227i		−	0.527427i	0.964601	−	0.263713i	$-0.0849473\pi$
$338$	2.92317	+	33.9590i	0.158999	+	1.84713i
$339$	−9.55728	+	27.2759i	−0.519080	+	1.48142i
$340$		−	40.6171i		−	2.20277i
$341$	1.09342			0.0592122
$342$	12.7139	+	31.8412i	0.687488	+	1.72178i
$343$		−	22.5816i		−	1.21929i
$344$			34.2450i			1.84637i
$345$	−10.8753	−	3.81062i	−0.585505	−	0.205157i
$346$		−	16.9183i		−	0.909534i
$347$		−	22.6659i		−	1.21677i	−0.793643	−	0.608384i	$-0.791818\pi$
$347$		−	22.6659i		−	1.21677i	0.793643	−	0.608384i	$-0.208182\pi$
$348$	13.4080	−	38.2656i	0.718745	−	2.05125i
$349$			21.3254i			1.14152i	0.821115	+	0.570762i	$0.193352\pi$
$349$			21.3254i			1.14152i	−0.821115	+	0.570762i	$0.806648\pi$
$350$	−26.3371			−1.40778
$351$	−10.6196	−	15.4345i	−0.566832	−	0.823834i
$352$		−	2.23581i		−	0.119169i
$353$	−16.8994			−0.899465			−0.449732	−	0.893163i	$-0.648481\pi$
$353$	−16.8994			−0.899465			−0.449732	+	0.893163i	$0.648481\pi$
$354$	9.21097	−	26.2875i	0.489558	−	1.39717i
$355$			14.2153i			0.754469i
$356$			71.0302i			3.76459i
$357$	−12.7017	+	36.2498i	−0.672245	+	1.91855i
$358$		−	28.8883i		−	1.52679i
$359$	19.8463			1.04745			0.523724	−	0.851888i	$-0.324542\pi$
$359$	19.8463			1.04745			0.523724	+	0.851888i	$0.324542\pi$
$360$	−23.2088	+	29.0521i	−1.22321	+	1.53118i
$361$	−9.72116	−	16.3248i	−0.511640	−	0.859200i
$362$	−65.8306			−3.45998
$363$	6.27739	−	17.9153i	0.329477	−	0.940307i
$364$	−76.8548	+	3.30170i	−4.02829	+	0.173056i
$365$		−	7.63833i		−	0.399808i
$366$	−12.5149	−	4.38512i	−0.654162	−	0.229214i
$367$	−1.33453			−0.0696622			−0.0348311	−	0.999393i	$-0.511089\pi$
$367$	−1.33453			−0.0696622			−0.0348311	+	0.999393i	$0.511089\pi$
$368$		−	40.4931i		−	2.11085i
$369$	13.4313	−	16.8129i	0.699204	−	0.875244i
$370$			40.2270i			2.09130i
$371$		−	32.7523i		−	1.70042i
$372$	15.2556	−	43.5384i	0.790964	−	2.25736i
$373$		−	27.4206i		−	1.41978i	−0.704310	−	0.709892i	$-0.748744\pi$
$373$		−	27.4206i		−	1.41978i	0.704310	−	0.709892i	$-0.251256\pi$
$374$	−2.65805			−0.137444
$375$	−6.87196	+	19.6121i	−0.354866	+	1.01277i
$376$			24.1285i			1.24433i
$377$	−0.743223	−	17.3003i	−0.0382779	−	0.891008i
$378$	50.5328	−	31.6619i	2.59913	−	1.62851i
$379$	−27.0397			−1.38894			−0.694469	−	0.719523i	$-0.744360\pi$
$379$	−27.0397			−1.38894			−0.694469	+	0.719523i	$0.744360\pi$
$380$	17.2677	−	30.3801i	0.885816	−	1.55847i
$381$	21.0220	+	7.36596i	1.07699	+	0.377370i
$382$	−64.1897			−3.28423
$383$			3.31429i			0.169352i	0.996409	+	0.0846762i	$0.0269856\pi$
$383$			3.31429i			0.169352i	−0.996409	+	0.0846762i	$0.973014\pi$
$384$	−3.22317	−	1.12938i	−0.164482	−	0.0576333i
$385$		−	1.44052i		−	0.0734158i
$386$			10.5763i			0.538318i
$387$	−10.6510	−	8.50871i	−0.541419	−	0.432522i
$388$	8.36460			0.424648
$389$			29.4262i			1.49197i	0.665963	+	0.745985i	$0.268021\pi$
$389$			29.4262i			1.49197i	−0.665963	+	0.745985i	$0.731979\pi$
$390$	−7.80622	+	25.7738i	−0.395283	+	1.30511i
$391$	−20.4947			−1.03646
$392$		−	91.6319i		−	4.62811i
$393$	−26.4034	−	9.25156i	−1.33187	−	0.466679i
$394$		−	17.3007i		−	0.871599i
$395$			11.1373i			0.560378i
$396$	2.28610	+	1.82629i	0.114881	+	0.0917746i
$397$			9.27167i			0.465332i	0.972557	+	0.232666i	$0.0747449\pi$
$397$			9.27167i			0.465332i	−0.972557	+	0.232666i	$0.925255\pi$
$398$			19.7081i			0.987880i
$399$	−24.9115	+	21.7136i	−1.24713	+	1.08704i
$400$	−22.9727			−1.14864
$401$			2.27972i			0.113844i	0.998379	+	0.0569219i	$0.0181286\pi$
$401$			2.27972i			0.113844i	−0.998379	+	0.0569219i	$0.981871\pi$
$402$	4.10622	+	1.43879i	0.204800	+	0.0717604i
$403$	−0.845635	−	19.6841i	−0.0421241	−	0.980537i
$404$			75.0874i			3.73574i
$405$	−3.26926	−	14.4369i	−0.162451	−	0.717375i
$406$	55.1166			2.73539
$407$	1.86662			0.0925249
$408$	−21.8687	+	62.4119i	−1.08266	+	3.08985i
$409$	3.10323			0.153445			0.0767225	−	0.997052i	$-0.475554\pi$
$409$	3.10323			0.153445			0.0767225	+	0.997052i	$0.475554\pi$
$410$	−30.9320			−1.52762
$411$	0.301469	−	0.860373i	0.0148704	−	0.0424391i
$412$		−	19.3370i		−	0.952666i
$413$	26.8477			1.32109
$414$	24.8593	+	19.8593i	1.22177	+	0.976031i
$415$	21.7311			1.06674
$416$	−40.2498	+	1.72914i	−1.97341	+	0.0847781i
$417$	−7.89168	+	22.5223i	−0.386457	+	1.10292i
$418$	−1.98812	−	1.13003i	−0.0972424	−	0.0552715i
$419$			11.6328i			0.568300i	0.958780	+	0.284150i	$0.0917114\pi$
$419$			11.6328i			0.568300i	−0.958780	+	0.284150i	$0.908289\pi$
$420$	−57.3594	−	20.0983i	−2.79885	−	0.980698i
$421$	6.89214			0.335902			0.167951	−	0.985795i	$-0.446285\pi$
$421$	6.89214			0.335902			0.167951	+	0.985795i	$0.446285\pi$
$422$	49.5186			2.41053
$423$	−7.50448	−	5.99509i	−0.364880	−	0.291491i
$424$		−	56.3902i		−	2.73855i
$425$			11.6271i			0.563998i
$426$	12.9792	−	37.0420i	0.628847	−	1.79469i
$427$		−	12.7816i		−	0.618543i
$428$	−9.77422			−0.472455
$429$	1.19596	+	0.362226i	0.0577416	+	0.0174884i
$430$			19.5954i			0.944975i
$431$			23.9948i			1.15579i	0.816112	+	0.577893i	$0.196125\pi$
$431$			23.9948i			1.15579i	−0.816112	+	0.577893i	$0.803875\pi$
$432$	44.0776	−	27.6173i	2.12068	−	1.32874i
$433$			7.41439i			0.356313i	0.984002	+	0.178156i	$0.0570133\pi$
$433$			7.41439i			0.356313i	−0.984002	+	0.178156i	$0.942987\pi$
$434$	62.7114			3.01024
$435$	4.52420	−	12.9118i	0.216919	−	0.619072i
$436$	46.5159			2.22771
$437$	−15.3293	−	8.71299i	−0.733298	−	0.416799i
$438$	−6.97417	+	19.9038i	−0.333239	+	0.951042i
$439$			6.20188i			0.296000i	0.988987	+	0.148000i	$0.0472835\pi$
$439$			6.20188i			0.296000i	−0.988987	+	0.148000i	$0.952716\pi$
$440$		−	2.48017i		−	0.118237i
$441$	28.4995	+	22.7674i	1.35712	+	1.08416i
$442$	2.05569	+	47.8510i	0.0977792	+	2.27604i
$443$			30.7339i			1.46021i	0.683334	+	0.730106i	$0.260530\pi$
$443$			30.7339i			1.46021i	−0.683334	+	0.730106i	$0.739470\pi$
$444$	26.0433	−	74.3259i	1.23596	−	3.52735i
$445$			23.9674i			1.13616i
$446$		−	23.4932i		−	1.11243i
$447$	9.16117	−	26.1454i	0.433308	−	1.23663i
$448$		−	40.5992i		−	1.91813i
$449$			11.6278i			0.548751i	0.961623	+	0.274376i	$0.0884712\pi$
$449$			11.6278i			0.548751i	−0.961623	+	0.274376i	$0.911529\pi$
$450$	11.2667	−	14.1033i	0.531116	−	0.664836i
$451$			1.43531i			0.0675862i
$452$	−81.3350			−3.82567
$453$	1.58187	−	4.51456i	0.0743228	−	0.212112i
$454$	26.2644			1.23265
$455$	−25.9327	+	1.11408i	−1.21575	+	0.0522287i
$456$	−42.8905	+	37.3847i	−2.00853	+	1.75070i
$457$			11.4081i			0.533648i	0.963745	+	0.266824i	$0.0859743\pi$
$457$			11.4081i			0.533648i	−0.963745	+	0.266824i	$0.914026\pi$
$458$	45.1754			2.11091
$459$	−13.9779	−	22.3089i	−0.652431	−	1.04129i
$460$		−	32.4294i		−	1.51203i
$461$	16.4845			0.767761			0.383881	−	0.923383i	$-0.374587\pi$
$461$	16.4845			0.767761			0.383881	+	0.923383i	$0.374587\pi$
$462$	−1.31527	+	3.75369i	−0.0611918	+	0.174637i
$463$		−	25.5864i		−	1.18910i	−0.804059	−	0.594550i	$-0.797330\pi$
$463$		−	25.5864i		−	1.18910i	0.804059	−	0.594550i	$-0.202670\pi$
$464$	48.0758			2.23187
$465$	5.14761	−	14.6909i	0.238715	−	0.681276i
$466$	−45.5683			−2.11091
$467$			14.0957i			0.652271i	0.945323	+	0.326135i	$0.105747\pi$
$467$			14.0957i			0.652271i	−0.945323	+	0.326135i	$0.894253\pi$
$468$	31.1094	−	42.5675i	1.43803	−	1.96768i
$469$			4.19373i			0.193648i
$470$			13.8066i			0.636850i
$471$	−6.56281	+	18.7298i	−0.302398	+	0.863026i
$472$	46.2242			2.12764
$473$	0.909269			0.0418082
$474$	10.1689	−	29.0214i	0.467073	−	1.33300i
$475$	−4.94309	+	8.69667i	−0.226805	+	0.399030i
$476$	−108.095			−4.95452
$477$	17.5386	+	14.0110i	0.803037	+	0.641520i
$478$			70.4279i			3.22130i
$479$	−36.3199			−1.65950			−0.829750	−	0.558135i	$-0.811517\pi$
$479$	−36.3199			−1.65950			−0.829750	+	0.558135i	$0.811517\pi$
$480$	−30.0398	−	10.5257i	−1.37112	−	0.480432i
$481$	−1.44361	−	33.6035i	−0.0658231	−	1.53219i
$482$		−	56.0782i		−	2.55429i
$483$	−10.1413	+	28.9425i	−0.461443	+	1.31693i
$484$	53.4222			2.42828
$485$	2.82242			0.128160
$486$	−4.66260	+	40.6044i	−0.211500	+	1.84185i
$487$	6.99334			0.316898			0.158449	−	0.987367i	$-0.449351\pi$
$487$	6.99334			0.316898			0.158449	+	0.987367i	$0.449351\pi$
$488$		−	22.0062i		−	0.996174i
$489$	26.0318	+	9.12135i	1.17720	+	0.412482i
$490$		−	52.4329i		−	2.36868i
$491$		−	20.8013i		−	0.938750i	−0.882999	−	0.469375i	$-0.844479\pi$
$491$		−	20.8013i		−	0.938750i	0.882999	−	0.469375i	$-0.155521\pi$
$492$	57.1519	+	20.0256i	2.57661	+	0.902825i
$493$		−	24.3325i		−	1.09588i
$494$	−18.8055	+	36.6648i	−0.846101	+	1.64963i
$495$	0.771387	+	0.616237i	0.0346713	+	0.0276978i
$496$	54.7004			2.45612
$497$	37.8314			1.69697
$498$	−56.6266	−	19.8416i	−2.53750	−	0.889122i
$499$		−	2.13525i		−	0.0955871i	−0.998857	−	0.0477936i	$-0.984781\pi$
$499$		−	2.13525i		−	0.0955871i	0.998857	−	0.0477936i	$-0.0152190\pi$
$500$	−58.4822			−2.61540
$501$	−4.41671	−	1.54759i	−0.197324	−	0.0691410i
$502$	4.15824			0.185591
$503$		−	2.93733i		−	0.130969i	−0.997854	−	0.0654846i	$-0.979141\pi$
$503$		−	2.93733i		−	0.130969i	0.997854	−	0.0654846i	$-0.0208593\pi$
$504$	77.3168	+	61.7659i	3.44396	+	2.75127i
$505$			25.3364i			1.12745i
$506$	−2.12223			−0.0943447
$507$	5.59596	−	21.8102i	0.248525	−	0.968625i
$508$			62.6863i			2.78125i
$509$			32.7089i			1.44980i	0.688855	+	0.724899i	$0.258114\pi$
$509$			32.7089i			1.44980i	−0.688855	+	0.724899i	$0.741886\pi$
$510$	−12.5135	+	35.7128i	−0.554109	+	1.58139i
$511$	−20.3280			−0.899258
$512$			39.0267i			1.72475i
$513$	−0.970669	−	22.6287i	−0.0428561	−	0.999081i
$514$			0.755463i			0.0333221i
$515$		−	6.52479i		−	0.287517i
$516$	12.6862	−	36.2057i	0.558480	−	1.59387i
$517$	0.640656			0.0281760
$518$	107.057			4.70380
$519$	−3.69583	+	10.5477i	−0.162229	+	0.462992i
$520$	−44.6488	+	1.91812i	−1.95798	+	0.0841152i
$521$	16.3337			0.715592			0.357796	−	0.933800i	$-0.383528\pi$
$521$	16.3337			0.715592			0.357796	+	0.933800i	$0.383528\pi$
$522$	−23.5782	+	29.5145i	−1.03199	+	1.29181i
$523$		−	24.5557i		−	1.07374i	−0.843664	−	0.536872i	$-0.819606\pi$
$523$		−	24.5557i		−	1.07374i	0.843664	−	0.536872i	$-0.180394\pi$
$524$		−	78.7332i		−	3.43948i
$525$	16.4198	+	5.75338i	0.716619	+	0.251098i
$526$	−13.6698			−0.596034
$527$		−	27.6854i		−	1.20599i
$528$	−1.14725	+	3.27418i	−0.0499277	+	0.142491i
$529$	6.63670			0.288552
$530$		−	32.2671i		−	1.40159i
$531$	−11.4851	+	14.3767i	−0.498411	+	0.623897i
$532$	−80.8511	−	45.9549i	−3.50534	−	1.99240i
$533$	25.8389	−	1.11005i	1.11921	−	0.0480814i
$534$	21.8834	−	62.4538i	0.946987	−	2.70264i
$535$	−3.29807			−0.142588
$536$			7.22040i			0.311874i
$537$	−6.31070	+	18.0103i	−0.272327	+	0.777204i
$538$			58.1732i			2.50803i
$539$	−2.43300			−0.104797
$540$	35.3001	−	22.1176i	1.51907	−	0.951792i
$541$			38.7880i			1.66763i	0.552046	+	0.833814i	$0.313847\pi$
$541$			38.7880i			1.66763i	−0.552046	+	0.833814i	$0.686153\pi$
$542$	−21.8739			−0.939565
$543$	41.0419	+	14.3808i	1.76128	+	0.617139i
$544$	−56.6106			−2.42716
$545$	15.6956			0.672327
$546$	68.5923	+	20.7748i	2.93548	+	0.889080i
$547$			2.43017i			0.103907i	0.998650	+	0.0519533i	$0.0165447\pi$
$547$			2.43017i			0.103907i	−0.998650	+	0.0519533i	$0.983455\pi$
$548$	2.56558			0.109596
$549$	6.84441	+	5.46778i	0.292113	+	0.233359i
$550$			1.20399i			0.0513385i
$551$	10.3446	−	18.1998i	0.440694	−	0.775339i
$552$	−17.4604	+	49.8308i	−0.743162	+	2.12094i
$553$	29.6398			1.26041
$554$		−	20.3984i		−	0.866643i
$555$	8.78765	−	25.0794i	0.373015	−	1.06456i
$556$	−67.1603			−2.84823
$557$	−13.0977			−0.554967			−0.277483	−	0.960730i	$-0.589500\pi$
$557$	−13.0977			−0.554967			−0.277483	+	0.960730i	$0.589500\pi$
$558$	−26.8271	+	33.5814i	−1.13568	+	1.42161i
$559$	−0.703214	−	16.3689i	−0.0297428	−	0.692333i
$560$		−	72.0647i		−	3.04529i
$561$	1.65715	+	0.580655i	0.0699650	+	0.0245153i
$562$	−4.45102			−0.187755
$563$	26.9813			1.13712			0.568562	−	0.822640i	$-0.307500\pi$
$563$	26.9813			1.13712			0.568562	+	0.822640i	$0.307500\pi$
$564$	8.93850	−	25.5099i	0.376379	−	1.07416i
$565$	−27.4445			−1.15460
$566$		−	43.8193i		−	1.84186i
$567$	−38.4211	+	8.70053i	−1.61353	+	0.365388i
$568$	65.1348			2.73300
$569$	−38.0361			−1.59455			−0.797277	−	0.603613i	$-0.793727\pi$
$569$	−38.0361			−1.59455			−0.797277	+	0.603613i	$0.793727\pi$
$570$	−24.5424	+	21.3920i	−1.02797	+	0.896011i
$571$	35.2111			1.47354			0.736769	−	0.676145i	$-0.236351\pi$
$571$	35.2111			1.47354			0.736769	+	0.676145i	$0.236351\pi$
$572$	0.150936	+	3.51340i	0.00631097	+	0.146903i
$573$	40.0189	+	14.0224i	1.67181	+	0.585792i
$574$			82.3198i			3.43596i
$575$			9.28330i			0.387140i
$576$	21.7405	+	17.3678i	0.905855	+	0.723659i
$577$		−	3.21463i		−	0.133827i	−0.997759	−	0.0669134i	$-0.978685\pi$
$577$		−	3.21463i		−	0.133827i	0.997759	−	0.0669134i	$-0.0213151\pi$
$578$			22.7294i			0.945420i
$579$	2.31040	−	6.59374i	0.0960171	−	0.274027i
$580$	38.5021			1.59871
$581$		−	57.8333i		−	2.39933i
$582$	−7.35463	−	2.57701i	−0.304859	−	0.106821i
$583$	−1.49726			−0.0620104
$584$	−34.9990			−1.44827
$585$	10.4971	−	14.3633i	0.434002	−	0.593851i
$586$	−46.5465			−1.92282
$587$	6.15086			0.253873			0.126937	−	0.991911i	$-0.459485\pi$
$587$	6.15086			0.253873			0.126937	+	0.991911i	$0.459485\pi$
$588$	−33.9455	+	96.8782i	−1.39989	+	3.99519i
$589$	11.7700	−	20.7077i	0.484975	−	0.853244i
$590$	26.4500			1.08893
$591$	−3.77938	+	10.7861i	−0.155463	+	0.443681i
$592$	93.3810			3.83793
$593$	−1.72928			−0.0710129			−0.0355065	−	0.999369i	$-0.511304\pi$
$593$	−1.72928			−0.0710129			−0.0355065	+	0.999369i	$0.511304\pi$
$594$	−1.44741	−	2.31009i	−0.0593881	−	0.0947843i
$595$	−36.4739			−1.49528
$596$	77.9640			3.19353
$597$	4.30528	−	12.2870i	0.176203	−	0.502873i
$598$	1.64130	+	38.2051i	0.0671177	+	1.56232i
$599$	2.01370			0.0822776			0.0411388	−	0.999153i	$-0.486901\pi$
$599$	2.01370			0.0822776			0.0411388	+	0.999153i	$0.486901\pi$
$600$	28.2702	+	9.90569i	1.15413	+	0.404398i
$601$		−	0.225873i		−	0.00921354i	−0.999989	−	0.00460677i	$-0.998534\pi$
$601$		−	0.225873i		−	0.00921354i	0.999989	−	0.00460677i	$-0.00146639\pi$
$602$	52.1496			2.12546
$603$	−2.24570	−	1.79402i	−0.0914521	−	0.0730582i
$604$	13.4621			0.547767
$605$	18.0260			0.732861
$606$	23.1334	−	66.0211i	0.939728	−	2.68192i
$607$		−	6.43634i		−	0.261243i	−0.991432	−	0.130621i	$-0.958303\pi$
$607$		−	6.43634i		−	0.261243i	0.991432	−	0.130621i	$-0.0416973\pi$
$608$	−42.3427	−	24.0671i	−1.71722	−	0.976051i
$609$	−34.3623	−	12.0403i	−1.39243	−	0.487898i
$610$		−	12.5922i		−	0.509844i
$611$	−0.495472	−	11.5333i	−0.0200447	−	0.466587i
$612$	46.2416	−	57.8839i	1.86920	−	2.33982i
$613$		−	35.2282i		−	1.42285i	−0.702761	−	0.711426i	$-0.748050\pi$
$613$		−	35.2282i		−	1.42285i	0.702761	−	0.711426i	$-0.251950\pi$
$614$		−	76.5297i		−	3.08849i
$615$	19.2845	+	6.75715i	0.777625	+	0.272475i
$616$	−6.60051			−0.265942
$617$	−17.4585			−0.702851			−0.351425	−	0.936216i	$-0.614303\pi$
$617$	−17.4585			−0.702851			−0.351425	+	0.936216i	$0.614303\pi$
$618$	−5.95746	+	17.0022i	−0.239644	+	0.683929i
$619$		−	26.9285i		−	1.08235i	−0.840910	−	0.541174i	$-0.817980\pi$
$619$		−	26.9285i		−	1.08235i	0.840910	−	0.541174i	$-0.182020\pi$
$620$	43.8075			1.75935
$621$	−11.1602	−	17.8118i	−0.447842	−	0.714762i
$622$	40.7249			1.63292
$623$	63.7847			2.55548
$624$	59.8301	+	18.1210i	2.39512	+	0.725420i
$625$	−8.25878			−0.330351
$626$		−	42.9205i		−	1.71545i
$627$	0.992634	+	1.13882i	0.0396420	+	0.0454802i
$628$	−55.8513			−2.22871
$629$		−	47.2626i		−	1.88449i
$630$	44.2416	+	35.3432i	1.76263	+	1.40811i
$631$		−	41.6501i		−	1.65807i	−0.559200	−	0.829033i	$-0.688892\pi$
$631$		−	41.6501i		−	1.65807i	0.559200	−	0.829033i	$-0.311108\pi$
$632$	51.0313			2.02992
$633$	−30.8722	−	10.8174i	−1.22706	−	0.429954i
$634$	36.7447			1.45932
$635$			21.1519i			0.839388i
$636$	−20.8900	+	59.6187i	−0.828342	+	2.36404i
$637$	1.88164	+	43.7996i	0.0745533	+	1.73540i
$638$		−	2.51964i		−	0.0997536i
$639$	−16.1838	+	20.2584i	−0.640219	+	0.801408i
$640$		−	3.24310i		−	0.128195i
$641$	−6.93322			−0.273846			−0.136923	−	0.990582i	$-0.543721\pi$
$641$	−6.93322			−0.273846			−0.136923	+	0.990582i	$0.543721\pi$
$642$	8.59405	+	3.01130i	0.339180	+	0.118846i
$643$		−	12.0718i		−	0.476065i	−0.971257	−	0.238033i	$-0.923497\pi$
$643$		−	12.0718i		−	0.476065i	0.971257	−	0.238033i	$-0.0765025\pi$
$644$	−86.3048			−3.40089
$645$	4.28065	−	12.2167i	0.168550	−	0.481032i
$646$	−28.6122	+	50.3391i	−1.12573	+	1.98057i
$647$		−	41.5438i		−	1.63325i	−0.577165	−	0.816627i	$-0.695841\pi$
$647$		−	41.5438i		−	1.63325i	0.577165	−	0.816627i	$-0.304159\pi$
$648$	−66.1502	+	14.9798i	−2.59863	+	0.588464i
$649$		−	1.22734i		−	0.0481772i
$650$	21.6747	−	0.931149i	0.850151	−	0.0365227i
$651$	−39.0972	−	13.6994i	−1.53234	−	0.536922i
$652$			77.6251i			3.04003i
$653$			21.8931i			0.856743i	0.903603	+	0.428371i	$0.140912\pi$
$653$			21.8931i			0.856743i	−0.903603	+	0.428371i	$0.859088\pi$
$654$	−40.8994	−	14.3309i	−1.59929	−	0.560382i
$655$		−	26.5666i		−	1.03804i
$656$			71.8040i			2.80348i
$657$	8.69605	−	10.8855i	0.339265	−	0.424683i
$658$	36.7437			1.43242
$659$	−45.4897			−1.77203			−0.886013	−	0.463661i	$-0.846536\pi$
$659$	−45.4897			−1.77203			−0.886013	+	0.463661i	$0.846536\pi$
$660$	−0.918790	+	2.62217i	−0.0357639	+	0.102068i
$661$	−37.7229			−1.46725			−0.733625	−	0.679554i	$-0.762173\pi$
$661$	−37.7229			−1.46725			−0.733625	+	0.679554i	$0.762173\pi$
$662$		−	29.5794i		−	1.14964i
$663$	9.17152	−	30.2816i	0.356192	−	1.17604i
$664$		−	99.5725i		−	3.86416i
$665$	−27.2812	−	15.5063i	−1.05792	−	0.601309i
$666$	−45.7975	+	57.3279i	−1.77462	+	2.22141i
$667$		−	19.4275i		−	0.752235i
$668$		−	13.1704i		−	0.509577i
$669$	−5.13212	+	14.6467i	−0.198419	+	0.566276i
$670$			4.13160i			0.159618i
$671$	−0.584306			−0.0225569
$672$	−28.0123	+	79.9454i	−1.08060	+	3.08396i
$673$		−	7.86672i		−	0.303240i	−0.988439	−	0.151620i	$-0.951551\pi$
$673$		−	7.86672i		−	0.303240i	0.988439	−	0.151620i	$-0.0484490\pi$
$674$	−25.3858			−0.977826
$675$	−10.1051	+	6.33144i	−0.388944	+	0.243697i
$676$	63.1325	−	5.43441i	2.42817	−	0.209016i
$677$	−2.06920			−0.0795258			−0.0397629	−	0.999209i	$-0.512660\pi$
$677$	−2.06920			−0.0795258			−0.0397629	+	0.999209i	$0.512660\pi$
$678$	71.5143	+	25.0581i	2.74649	+	0.962352i
$679$		−	7.51136i		−	0.288260i
$680$	−62.7977			−2.40818
$681$	−16.3745	−	5.73750i	−0.627471	−	0.219862i
$682$		−	2.86683i		−	0.109777i
$683$		−	0.698532i		−	0.0267286i	−0.999911	−	0.0133643i	$-0.995746\pi$
$683$		−	0.698532i		−	0.0267286i	0.999911	−	0.0133643i	$-0.00425411\pi$
$684$	59.1954	−	23.6362i	2.26339	−	0.903751i
$685$	0.865692			0.0330764
$686$	−59.2064			−2.26051
$687$	−28.1645	−	9.86865i	−1.07454	−	0.376512i
$688$	45.4878			1.73421
$689$	1.15796	+	26.9542i	0.0441147	+	1.02687i
$690$	−9.99103	+	28.5138i	−0.380352	+	1.08550i
$691$			39.4568i			1.50101i	0.660865	+	0.750505i	$0.270189\pi$
$691$			39.4568i			1.50101i	−0.660865	+	0.750505i	$0.729811\pi$
$692$	−31.4525			−1.19565
$693$	1.64000	−	2.05291i	0.0622984	−	0.0779834i
$694$	−59.4274			−2.25583
$695$	−22.6616			−0.859602
$696$	−59.1621	−	20.7300i	−2.24253	−	0.785768i
$697$	36.3420			1.37655
$698$	55.9130			2.11634
$699$	28.4094	+	9.95447i	1.07454	+	0.376513i
$700$			48.9628i			1.85062i
$701$			20.6484i			0.779880i	0.920840	+	0.389940i	$0.127504\pi$
$701$			20.6484i			0.779880i	−0.920840	+	0.389940i	$0.872496\pi$
$702$	−40.4676	+	27.8434i	−1.52735	+	1.05088i
$703$	20.0930	−	35.3508i	0.757821	−	1.33328i
$704$	−1.85598			−0.0699500
$705$	3.01607	−	8.60768i	0.113592	−	0.324184i
$706$			44.3084i			1.66757i
$707$	67.4281			2.53589
$708$	−48.8707	−	17.1240i	−1.83667	−	0.643557i
$709$		−	18.6287i		−	0.699615i	−0.936822	−	0.349807i	$-0.886247\pi$
$709$		−	18.6287i		−	0.699615i	0.936822	−	0.349807i	$-0.113753\pi$
$710$	37.2709			1.39875
$711$	−12.6795	+	15.8719i	−0.475520	+	0.595242i
$712$	109.819			4.11565
$713$		−	22.1045i		−	0.827820i
$714$	95.0431	+	33.3025i	3.55690	+	1.24631i
$715$	0.0509297	+	1.18551i	0.00190466	+	0.0443355i
$716$	−53.7057			−2.00708
$717$	15.3851	−	43.9080i	0.574566	−	1.63978i
$718$		−	52.0348i		−	1.94192i
$719$		−	39.3725i		−	1.46835i	−0.678962	−	0.734173i	$-0.737570\pi$
$719$		−	39.3725i		−	1.46835i	0.678962	−	0.734173i	$-0.262430\pi$
$720$	38.5900	+	30.8283i	1.43817	+	1.14890i
$721$	−17.3645			−0.646689
$722$	−42.8018	+	25.4878i	−1.59292	+	0.948559i
$723$	−12.2504	+	34.9618i	−0.455597	+	1.30024i
$724$			122.384i			4.54838i
$725$	−11.0217			−0.409335
$726$	−46.9719	−	16.4586i	−1.74329	−	0.610837i
$727$	−4.04586			−0.150053			−0.0750263	−	0.997182i	$-0.523904\pi$
$727$	−4.04586			−0.150053			−0.0750263	+	0.997182i	$0.523904\pi$
$728$	5.10473	+	118.824i	0.189194	+	4.40393i
$729$	11.7770	−	24.2961i	0.436185	−	0.899857i
$730$	−20.0269			−0.741227
$731$		−	23.0226i		−	0.851522i
$732$	−8.15230	+	23.2661i	−0.301318	+	0.859941i
$733$			27.6392i			1.02088i	0.859914	+	0.510439i	$0.170517\pi$
$733$			27.6392i			1.02088i	−0.859914	+	0.510439i	$0.829483\pi$
$734$			3.49900i			0.129151i
$735$	−11.4540	+	32.6891i	−0.422489	+	1.20576i
$736$	−45.1989			−1.66605
$737$	0.191715			0.00706192
$738$	−44.0816	−	35.2153i	−1.62266	−	1.29629i
$739$		−	13.5031i		−	0.496718i	−0.968668	−	0.248359i	$-0.920109\pi$
$739$		−	13.5031i		−	0.496718i	0.968668	−	0.248359i	$-0.0798913\pi$
$740$	74.7853			2.74916
$741$	19.7337	−	18.7505i	0.724937	−	0.688815i
$742$	−85.8730			−3.15250
$743$			6.28226i			0.230474i	0.993338	+	0.115237i	$0.0367627\pi$
$743$			6.28226i			0.230474i	−0.993338	+	0.115237i	$0.963237\pi$
$744$	−67.3143	−	23.5865i	−2.46786	−	0.864722i
$745$	26.3070			0.963814
$746$	−71.8938			−2.63222
$747$	30.9692	+	24.7403i	1.13311	+	0.905201i
$748$			4.94153i			0.180680i
$749$			8.77720i			0.320712i
$750$	51.4209	+	18.0175i	1.87762	+	0.657907i
$751$			37.9476i			1.38473i	0.721548	+	0.692364i	$0.243431\pi$
$751$			37.9476i			1.38473i	−0.721548	+	0.692364i	$0.756569\pi$
$752$	32.0499			1.16874
$753$	−2.59244	−	0.908374i	−0.0944738	−	0.0331030i
$754$	−45.3594	+	1.94865i	−1.65189	+	0.0709656i
$755$	4.54246			0.165317
$756$	−58.8620	−	93.9446i	−2.14079	−	3.41673i
$757$	−42.3041			−1.53757			−0.768784	−	0.639509i	$-0.779138\pi$
$757$	−42.3041			−1.53757			−0.768784	+	0.639509i	$0.779138\pi$
$758$			70.8952i			2.57503i
$759$	1.32310	+	0.463605i	0.0480255	+	0.0168278i
$760$	−46.9704	−	26.6975i	−1.70380	−	0.968419i
$761$	37.0723			1.34387			0.671934	−	0.740611i	$-0.265464\pi$
$761$	37.0723			1.34387			0.671934	+	0.740611i	$0.265464\pi$
$762$	19.3127	−	55.1173i	0.699627	−	1.99669i
$763$		−	41.7710i		−	1.51221i
$764$			119.334i			4.31735i
$765$	15.6031	−	19.5315i	0.564130	−	0.706162i
$766$	8.68971			0.313972
$767$	−22.0949	+	0.949203i	−0.797801	+	0.0342737i
$768$	7.66394	−	21.8724i	0.276549	−	0.789252i
$769$		−	27.4962i		−	0.991539i	−0.868454	−	0.495769i	$-0.834886\pi$
$769$		−	27.4962i		−	0.991539i	0.868454	−	0.495769i	$-0.165114\pi$
$770$	−3.77689			−0.136110
$771$	0.165032	−	0.470991i	0.00594349	−	0.0169623i
$772$	19.6621			0.707656
$773$			44.4041i			1.59710i	0.601926	+	0.798552i	$0.294400\pi$
$773$			44.4041i			1.59710i	−0.601926	+	0.798552i	$0.705600\pi$
$774$	−22.3089	+	27.9256i	−0.801877	+	1.00377i
$775$	−12.5404			−0.450465
$776$		−	12.9324i		−	0.464247i
$777$	−66.7442	−	23.3867i	−2.39444	−	0.838994i
$778$	77.1524			2.76605
$779$	27.1825	+	15.4502i	0.973914	+	0.553562i
$780$	47.9157	+	14.5124i	1.71566	+	0.519627i
$781$		−	1.72945i		−	0.0618846i
$782$			53.7348i			1.92155i
$783$	21.1472	−	13.2500i	0.755740	−	0.473517i
$784$	−121.715			−4.34697
$785$	−18.8456			−0.672629
$786$	−24.2566	+	69.2267i	−0.865203	+	2.46924i
$787$	−0.272964			−0.00973010			−0.00486505	−	0.999988i	$-0.501549\pi$
$787$	−0.272964			−0.00973010			−0.00486505	+	0.999988i	$0.501549\pi$
$788$	−32.1635			−1.14578
$789$	8.52243	+	2.98620i	0.303406	+	0.106312i
$790$	29.2007			1.03892
$791$			73.0383i			2.59694i
$792$	2.82361	−	3.53452i	0.100333	−	0.125594i
$793$	0.451892	+	10.5189i	0.0160472	+	0.373535i
$794$	24.3093			0.862705
$795$	−7.04881	+	20.1169i	−0.249996	+	0.713471i
$796$	36.6391			1.29864
$797$	13.0454			0.462093			0.231046	−	0.972943i	$-0.425785\pi$
$797$	13.0454			0.462093			0.231046	+	0.972943i	$0.425785\pi$
$798$	56.9308	+	65.3152i	2.01533	+	2.31213i
$799$		−	16.2213i		−	0.573870i
$800$			25.6424i			0.906597i
$801$	−27.2863	+	34.1562i	−0.964113	+	1.20685i
$802$	5.97718			0.211061
$803$			0.929290i			0.0327939i
$804$	2.67483	−	7.63380i	0.0943340	−	0.269223i
$805$	−29.1214			−1.02639
$806$	−51.6096	+	2.21716i	−1.81787	+	0.0780962i
$807$	12.7080	−	36.2679i	0.447344	−	1.27669i
$808$	116.092			4.08410
$809$		−	7.28056i		−	0.255971i	−0.991776	−	0.127985i	$-0.959149\pi$
$809$		−	7.28056i		−	0.255971i	0.991776	−	0.127985i	$-0.0408511\pi$
$810$	−37.8519	+	8.57164i	−1.32998	+	0.301177i
$811$	−5.35557			−0.188059			−0.0940297	−	0.995569i	$-0.529975\pi$
$811$	−5.35557			−0.188059			−0.0940297	+	0.995569i	$0.529975\pi$
$812$		−	102.466i		−	3.59586i
$813$	13.6372	+	4.77839i	0.478278	+	0.167585i
$814$		−	4.89407i		−	0.171537i
$815$			26.1927i			0.917489i
$816$	82.9020	+	29.0483i	2.90215	+	1.01689i
$817$	9.78771	−	17.2201i	0.342429	−	0.602455i
$818$		−	8.13634i		−	0.284481i
$819$	−38.2254	−	27.9361i	−1.33570	−	0.976166i
$820$			57.5051i			2.00817i
$821$	−12.3157			−0.429821			−0.214910	−	0.976634i	$-0.568946\pi$
$821$	−12.3157			−0.429821			−0.214910	+	0.976634i	$0.568946\pi$
$822$	−2.25580	−	0.790419i	−0.0786802	−	0.0275690i
$823$	−35.6620			−1.24310			−0.621550	−	0.783374i	$-0.713497\pi$
$823$	−35.6620			−1.24310			−0.621550	+	0.783374i	$0.713497\pi$
$824$	−29.8968			−1.04150
$825$	0.263015	−	0.750627i	0.00915699	−	0.0261335i
$826$		−	70.3918i		−	2.44925i
$827$		−	3.53789i		−	0.123024i	−0.998106	−	0.0615122i	$-0.980408\pi$
$827$		−	3.53789i		−	0.123024i	0.998106	−	0.0615122i	$-0.0195923\pi$
$828$	36.9201	−	46.2155i	1.28306	−	1.60610i
$829$		−	1.90288i		−	0.0660897i	−0.999454	−	0.0330448i	$-0.989480\pi$
$829$		−	1.90288i		−	0.0660897i	0.999454	−	0.0330448i	$-0.0105204\pi$
$830$		−	56.9766i		−	1.97769i
$831$	−4.45606	+	12.7173i	−0.154579	+	0.441158i
$832$	1.43539	+	33.4120i	0.0497631	+	1.15835i
$833$			61.6033i			2.13443i
$834$	59.0511	+	20.6911i	2.04477	+	0.716474i
$835$		−	4.44401i		−	0.153791i
$836$	−2.10082	+	3.69609i	−0.0726582	+	0.127832i
$837$	24.0612	−	15.0758i	0.831676	−	0.521096i
$838$	30.5000			1.05360
$839$			48.0197i			1.65782i	0.559379	+	0.828912i	$0.311040\pi$
$839$			48.0197i			1.65782i	−0.559379	+	0.828912i	$0.688960\pi$
$840$	−31.0738	+	88.6828i	−1.07215	+	3.05985i
$841$	−5.93452			−0.204639
$842$		−	18.0704i		−	0.622748i
$843$	2.77498	+	0.972333i	0.0955753	+	0.0334889i
$844$		−	92.0591i		−	3.16881i
$845$	21.3025	−	1.83370i	0.732828	−	0.0630814i
$846$	−15.7185	+	19.6759i	−0.540412	+	0.676472i
$847$		−	47.9729i		−	1.64837i
$848$	−74.9033			−2.57219
$849$	−9.57239	+	27.3190i	−0.328524	+	0.937586i
$850$	30.4850			1.04563
$851$		−	37.7353i		−	1.29355i
$852$	−68.8640	−	24.1295i	−2.35924	−	0.826663i
$853$			10.7449i			0.367897i	0.982936	+	0.183949i	$0.0588880\pi$
$853$			10.7449i			0.367897i	−0.982936	+	0.183949i	$0.941112\pi$
$854$	−33.5118			−1.14675
$855$	19.9740	−	7.97543i	0.683097	−	0.272754i
$856$			15.1118i			0.516512i
$857$	46.8330			1.59979			0.799893	−	0.600143i	$-0.204890\pi$
$857$	46.8330			1.59979			0.799893	+	0.600143i	$0.204890\pi$
$858$	0.949716	−	3.13568i	0.0324228	−	0.107050i
$859$	26.4532			0.902571			0.451286	−	0.892380i	$-0.350966\pi$
$859$	26.4532			0.902571			0.451286	+	0.892380i	$0.350966\pi$
$860$	36.4295			1.24223
$861$	17.9829	−	51.3221i	0.612856	−	1.74905i
$862$	62.9116			2.14278
$863$		−	1.14474i		−	0.0389674i	−0.999810	−	0.0194837i	$-0.993798\pi$
$863$		−	1.14474i		−	0.0389674i	0.999810	−	0.0194837i	$-0.00620225\pi$
$864$	−30.8267	−	49.1999i	−1.04875	−	1.67382i
$865$	−10.6129			−0.360848
$866$	19.4397			0.660588
$867$	4.96528	−	14.1706i	0.168630	−	0.481259i
$868$		−	116.586i		−	3.95717i
$869$		−	1.35498i		−	0.0459645i
$870$	−33.8532	−	11.8619i	−1.14773	−	0.402158i
$871$	−0.148269	−	3.45132i	−0.00502391	−	0.116943i
$872$		−	71.9178i		−	2.43544i
$873$	4.02227	+	3.21326i	0.136133	+	0.108752i
$874$	−22.8445	+	40.1917i	−0.772727	+	1.35950i
$875$			52.5167i			1.77539i
$876$	37.0029	+	12.9655i	1.25021	+	0.438065i
$877$	2.43491			0.0822211			0.0411106	−	0.999155i	$-0.486910\pi$
$877$	2.43491			0.0822211			0.0411106	+	0.999155i	$0.486910\pi$
$878$	16.2607			0.548771
$879$	29.0193	+	10.1682i	0.978795	+	0.342963i
$880$	−3.29442			−0.111055
$881$		−	18.9422i		−	0.638180i	−0.947724	−	0.319090i	$-0.896623\pi$
$881$		−	18.9422i		−	0.638180i	0.947724	−	0.319090i	$-0.103377\pi$
$882$	59.6935	−	74.7227i	2.00999	−	2.51604i
$883$	19.6779			0.662215			0.331107	−	0.943593i	$-0.392578\pi$
$883$	19.6779			0.662215			0.331107	+	0.943593i	$0.392578\pi$
$884$	88.9589	−	3.82170i	2.99201	−	0.128538i
$885$	−16.4902	−	5.77805i	−0.554312	−	0.194227i
$886$	80.5810			2.70717
$887$	6.04610			0.203008			0.101504	−	0.994835i	$-0.467635\pi$
$887$	6.04610			0.203008			0.101504	+	0.994835i	$0.467635\pi$
$888$	−114.914	−	40.2653i	−3.85628	−	1.35121i
$889$	56.2919			1.88797
$890$	62.8398			2.10640
$891$	0.397743	+	1.75641i	0.0133249	+	0.0588420i
$892$	−43.6757			−1.46237
$893$	6.89625	−	12.1330i	0.230774	−	0.406015i
$894$	−68.5504	−	24.0196i	−2.29267	−	0.803335i
$895$	−18.1217			−0.605740
$896$	−8.63090			−0.288338
$897$	7.32270	−	24.1774i	0.244498	−	0.807260i
$898$	30.4869			1.01736
$899$	26.2438			0.875279
$900$	−26.2192	−	20.9457i	−0.873972	−	0.698188i
$901$			37.9106i			1.26299i
$902$	3.76323			0.125302
$903$	−32.5125	−	11.3922i	−1.08195	−	0.379107i
$904$			125.751i			4.18242i
$905$			41.2956i			1.37271i
$906$	−11.8367	−	4.14749i	−0.393247	−	0.137791i
$907$			49.4781i			1.64289i	0.570285	+	0.821447i	$0.306833\pi$
$907$			49.4781i			1.64289i	−0.570285	+	0.821447i	$0.693167\pi$
$908$		−	48.8277i		−	1.62040i
$909$	−28.8449	+	36.1072i	−0.956723	+	1.19760i
$910$	2.92099	+	67.9928i	0.0968297	+	2.25394i
$911$	−15.9225			−0.527537			−0.263769	−	0.964586i	$-0.584966\pi$
$911$	−15.9225			−0.527537			−0.263769	+	0.964586i	$0.584966\pi$
$912$	49.6583	+	56.9716i	1.64435	+	1.88652i
$913$	−2.64384			−0.0874982
$914$	29.9108			0.989360
$915$	−2.75079	+	7.85058i	−0.0909383	+	0.259532i
$916$		−	83.9848i		−	2.77494i
$917$	−70.7020			−2.33479
$918$	−58.4914	+	36.6484i	−1.93050	+	1.20958i
$919$	−37.1925			−1.22687			−0.613433	−	0.789746i	$-0.710212\pi$
$919$	−37.1925			−1.22687			−0.613433	+	0.789746i	$0.710212\pi$
$920$	−50.1388			−1.65303
$921$	−16.7180	+	47.7122i	−0.550878	+	1.57217i
$922$		−	43.2206i		−	1.42340i
$923$	−31.1341	+	1.33753i	−1.02479	+	0.0440253i
$924$	6.97842	+	2.44519i	0.229573	+	0.0804409i
$925$	−21.4082			−0.703896
$926$	−67.0847			−2.20454
$927$	7.42832	−	9.29856i	0.243978	−	0.305405i
$928$		−	53.6628i		−	1.76157i
$929$	−10.9536			−0.359376			−0.179688	−	0.983724i	$-0.557509\pi$
$929$	−10.9536			−0.359376			−0.179688	+	0.983724i	$0.557509\pi$
$930$	−38.5180	−	13.4965i	−1.26306	−	0.442566i
$931$	−26.1897	+	46.0771i	−0.858333	+	1.51011i
$932$			84.7152i			2.77494i
$933$	−25.3898	−	8.89642i	−0.831225	−	0.291256i
$934$	36.9574			1.20928
$935$			1.66740i			0.0545297i
$936$	−65.8132	−	48.0980i	−2.15117	−	1.57213i
$937$	53.4084			1.74478			0.872388	−	0.488814i	$-0.162570\pi$
$937$	53.4084			1.74478			0.872388	+	0.488814i	$0.162570\pi$
$938$	10.9955			0.359015
$939$	−9.37606	+	26.7587i	−0.305976	+	0.873237i
$940$	25.6676			0.837184
$941$			2.19490i			0.0715517i	0.999360	+	0.0357759i	$0.0113902\pi$
$941$			2.19490i			0.0715517i	−0.999360	+	0.0357759i	$0.988610\pi$
$942$	49.1076	+	17.2070i	1.60001	+	0.560633i
$943$	29.0161			0.944893
$944$		−	61.3998i		−	1.99839i
$945$	−19.8615	−	31.6993i	−0.646095	−	1.03118i
$946$		−	2.38400i		−	0.0775107i
$947$	−18.1652			−0.590289			−0.295145	−	0.955453i	$-0.595368\pi$
$947$	−18.1652			−0.590289			−0.295145	+	0.955453i	$0.595368\pi$
$948$	−53.9531	−	18.9048i	−1.75231	−	0.613999i
$949$	16.7294	−	0.718697i	0.543058	−	0.0233299i
$950$	22.8017	+	12.9602i	0.739785	+	0.420486i
$951$	−22.9084	−	8.02695i	−0.742856	−	0.260292i
$952$			167.124i			5.41653i
$953$	−0.828396			−0.0268344			−0.0134172	−	0.999910i	$-0.504271\pi$
$953$	−0.828396			−0.0268344			−0.0134172	+	0.999910i	$0.504271\pi$
$954$	36.7353	−	45.9843i	1.18935	−	1.48880i
$955$			40.2663i			1.30299i
$956$	130.931			4.23462
$957$	−0.550420	+	1.57086i	−0.0177926	+	0.0507788i
$958$			95.2269i			3.07664i
$959$		−	2.30388i		−	0.0743961i
$960$	−8.73758	+	24.9365i	−0.282004	+	0.804822i
$961$	−1.13998			−0.0367736
$962$	−88.1046	+	3.78499i	−2.84061	+	0.122033i
$963$	−4.70011	−	3.75477i	−0.151459	−	0.120996i
$964$	−104.254			−3.35780
$965$	6.63450			0.213572
$966$	75.8841	+	26.5893i	2.44153	+	0.855496i
$967$		−	10.0449i		−	0.323023i	−0.986871	−	0.161512i	$-0.948363\pi$
$967$		−	10.0449i		−	0.323023i	0.986871	−	0.161512i	$-0.0516369\pi$
$968$		−	82.5956i		−	2.65472i
$969$	28.8349	−	25.1334i	0.926310	−	0.807401i
$970$		−	7.40009i		−	0.237602i
$971$	46.4409			1.49036			0.745180	−	0.666863i	$-0.232363\pi$
$971$	46.4409			1.49036			0.745180	+	0.666863i	$0.232363\pi$
$972$	75.4869	+	8.66816i	2.42124	+	0.278031i
$973$			60.3095i			1.93344i
$974$		−	18.3358i		−	0.587516i
$975$	−13.7164	−	4.15435i	−0.439277	−	0.133046i
$976$	−29.2309			−0.935660
$977$		−	49.8562i		−	1.59504i	−0.603291	−	0.797521i	$-0.706144\pi$
$977$		−	49.8562i		−	1.59504i	0.603291	−	0.797521i	$-0.293856\pi$
$978$	23.9152	−	68.2524i	0.764723	−	2.18247i
$979$		−	2.91590i		−	0.0931927i
$980$	−97.4770			−3.11379
$981$	22.3680	+	17.8691i	0.714156	+	0.570516i
$982$	−54.5387			−1.74040
$983$		−	19.3921i		−	0.618512i	−0.950979	−	0.309256i	$-0.899920\pi$
$983$		−	19.3921i		−	0.618512i	0.950979	−	0.309256i	$-0.100080\pi$
$984$	30.9614	−	88.3620i	0.987014	−	2.81688i
$985$	−10.8528			−0.345798
$986$	−63.7971			−2.03171
$987$	−22.9077	−	8.02672i	−0.729162	−	0.255493i
$988$	68.1628	+	34.9610i	2.16855	+	1.11226i
$989$		−	18.3817i		−	0.584503i
$990$	1.61570	−	2.02249i	0.0513505	−	0.0642791i
$991$		−	38.5600i		−	1.22490i	−0.790509	−	0.612450i	$-0.790184\pi$
$991$		−	38.5600i		−	1.22490i	0.790509	−	0.612450i	$-0.209816\pi$
$992$		−	61.0573i		−	1.93857i
$993$	−6.46167	+	18.4412i	−0.205055	+	0.585214i
$994$		−	99.1897i		−	3.14610i
$995$	12.3629			0.391931
$996$	−36.8871	+	105.273i	−1.16881	+	3.33572i
$997$	−11.5470			−0.365699			−0.182849	−	0.983141i	$-0.558532\pi$
$997$	−11.5470			−0.365699			−0.182849	+	0.983141i	$0.558532\pi$
$998$	−5.59840			−0.177214
$999$	41.0757	−	25.7364i	1.29958	−	0.814264i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	741.2.d.a.740.6	yes	88
3.2	odd	2	inner	741.2.d.a.740.84	yes	88
13.12	even	2	inner	741.2.d.a.740.82	yes	88
19.18	odd	2	inner	741.2.d.a.740.83	yes	88
39.38	odd	2	inner	741.2.d.a.740.8	yes	88
57.56	even	2	inner	741.2.d.a.740.5	✓	88
247.246	odd	2	inner	741.2.d.a.740.7	yes	88
741.740	even	2	inner	741.2.d.a.740.81	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
741.2.d.a.740.5	✓	88	57.56	even	2	inner
741.2.d.a.740.6	yes	88	1.1	even	1	trivial
741.2.d.a.740.7	yes	88	247.246	odd	2	inner
741.2.d.a.740.8	yes	88	39.38	odd	2	inner
741.2.d.a.740.81	yes	88	741.740	even	2	inner
741.2.d.a.740.82	yes	88	13.12	even	2	inner
741.2.d.a.740.83	yes	88	19.18	odd	2	inner
741.2.d.a.740.84	yes	88	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 741 = 3 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	741.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.62189i q^{2} +(-0.572756 + 1.63461i) q^{3} -4.87431 q^{4} -1.64471 q^{5} +(4.28577 + 1.50170i) q^{6} +4.37710i q^{7} +7.53612i q^{8} +(-2.34390 - 1.87247i) q^{9} +4.31226i q^{10} +0.200098 q^{11} +(2.79179 - 7.96759i) q^{12} +(-0.154753 - 3.60223i) q^{13} +11.4763 q^{14} +(0.942020 - 2.68847i) q^{15} +10.0103 q^{16} -5.06647i q^{17} +(-4.90940 + 6.14545i) q^{18} +(2.15393 - 3.78954i) q^{19} +8.01684 q^{20} +(-7.15486 - 2.50701i) q^{21} -0.524635i q^{22} -4.04516i q^{23} +(-12.3186 - 4.31636i) q^{24} -2.29492 q^{25} +(-9.44465 + 0.405744i) q^{26} +(4.40324 - 2.75890i) q^{27} -21.3353i q^{28} +4.80265 q^{29} +(-7.04886 - 2.46987i) q^{30} +5.46443 q^{31} -11.1736i q^{32} +(-0.114607 + 0.327082i) q^{33} -13.2837 q^{34} -7.19908i q^{35} +(11.4249 + 9.12698i) q^{36} +9.32852 q^{37} +(-9.93575 - 5.64737i) q^{38} +(5.97687 + 1.81024i) q^{39} -12.3948i q^{40} +7.17304i q^{41} +(-6.57311 + 18.7592i) q^{42} +4.54412 q^{43} -0.975340 q^{44} +(3.85505 + 3.07967i) q^{45} -10.6060 q^{46} +3.20171 q^{47} +(-5.73344 + 16.3629i) q^{48} -12.1590 q^{49} +6.01702i q^{50} +(8.28170 + 2.90185i) q^{51} +(0.754312 + 17.5584i) q^{52} -7.48265 q^{53} +(-7.23352 - 11.5448i) q^{54} -0.329104 q^{55} -32.9864 q^{56} +(4.96074 + 5.69132i) q^{57} -12.5920i q^{58} -6.13368i q^{59} +(-4.59170 + 13.1044i) q^{60} -2.92010 q^{61} -14.3271i q^{62} +(8.19598 - 10.2595i) q^{63} -9.27536 q^{64} +(0.254524 + 5.92464i) q^{65} +(0.857574 + 0.300488i) q^{66} +0.958106 q^{67} +24.6955i q^{68} +(6.61225 + 2.31689i) q^{69} -18.8752 q^{70} -8.64301i q^{71} +(14.1111 - 17.6639i) q^{72} +4.64417i q^{73} -24.4584i q^{74} +(1.31443 - 3.75129i) q^{75} +(-10.4989 + 18.4714i) q^{76} +0.875850i q^{77} +(4.74625 - 15.6707i) q^{78} -6.77157i q^{79} -16.4640 q^{80} +(1.98774 + 8.77775i) q^{81} +18.8069 q^{82} -13.2127 q^{83} +(34.8750 + 12.2200i) q^{84} +8.33289i q^{85} -11.9142i q^{86} +(-2.75075 + 7.85047i) q^{87} +1.50796i q^{88} -14.5724i q^{89} +(8.07456 - 10.1075i) q^{90} +(15.7673 - 0.677368i) q^{91} +19.7173i q^{92} +(-3.12979 + 8.93222i) q^{93} -8.39452i q^{94} +(-3.54260 + 6.23270i) q^{95} +(18.2644 + 6.39974i) q^{96} -1.71606 q^{97} +31.8796i q^{98} +(-0.469010 - 0.374677i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 88 q^{4} - 4 q^{9} + 72 q^{16} + 64 q^{25} - 60 q^{30} - 48 q^{36} + 20 q^{39} + 48 q^{42} - 64 q^{43} - 112 q^{49} - 24 q^{55} - 64 q^{61} - 104 q^{64} + 12 q^{66} + 60 q^{81} + 56 q^{82} - 32 q^{87}+O(q^{100}) \) 88 * q - 88 * q^4 - 4 * q^9 + 72 * q^16 + 64 * q^25 - 60 * q^30 - 48 * q^36 + 20 * q^39 + 48 * q^42 - 64 * q^43 - 112 * q^49 - 24 * q^55 - 64 * q^61 - 104 * q^64 + 12 * q^66 + 60 * q^81 + 56 * q^82 - 32 * q^87

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