LMFDB - Embedded newform 741.2.d.a.740.5

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			740.5
Character	$\chi$	$=$	741.740
Dual form			741.2.d.a.740.82

$q$-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} +(5.79960 - 2.31616i) 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} +(-6.07272 - 15.2059i) 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	$-0.380122\pi$
$5$	1.64471			0.735538			0.367769	+	0.929917i	$0.380122\pi$
$6$	−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	$-0.509604\pi$
$11$	−0.200098			−0.0603319			−0.0301659	+	0.999545i	$0.509604\pi$
$12$	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	$0.210602\pi$
$17$			5.06647i			1.22880i	−0.788995	+	0.614400i	$0.789398\pi$
$18$	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	$0.138579\pi$
$23$			4.04516i			0.843474i	−0.906718	+	0.421737i	$0.861421\pi$
$24$	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	$-0.663266\pi$
$31$	−5.46443			−0.981441			−0.490720	+	0.871317i	$0.663266\pi$
$32$		−	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	$-0.778152\pi$
$37$	−9.32852			−1.53360			−0.766800	+	0.641887i	$0.778152\pi$
$38$	−9.93575	+	5.64737i	−1.61179	+	0.916124i
$39$	5.79960	−	2.31616i	0.928680	−	0.370882i
$40$			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	$-0.575021\pi$
$47$	−3.20171			−0.467017			−0.233508	+	0.972355i	$0.575021\pi$
$48$	−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	$-0.518640\pi$
$67$	−0.958106			−0.117051			−0.0585256	+	0.998286i	$0.518640\pi$
$68$		−	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
$78$	−6.07272	−	15.2059i	−0.687600	−	1.72173i
$79$			6.77157i			0.761861i	0.924604	+	0.380930i	$0.124396\pi$
$79$			6.77157i			0.761861i	−0.924604	+	0.380930i	$0.875604\pi$
$80$	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	$-0.241775\pi$
$83$	13.2127			1.45028			0.725141	+	0.688601i	$0.241775\pi$
$84$	−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	$-0.472234\pi$
$97$	1.71606			0.174239			0.0871196	+	0.996198i	$0.472234\pi$
$98$			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	$0.277961\pi$
$101$			15.4047i			1.53283i	−0.642347	+	0.766414i	$0.722039\pi$
$102$	−7.60834	−	21.7137i	−0.753338	−	2.14998i
$103$		−	3.96713i		−	0.390893i	−0.980714	−	0.195446i	$-0.937384\pi$
$103$		−	3.96713i		−	0.390893i	0.980714	−	0.195446i	$-0.0626156\pi$
$104$	−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	$-0.348913\pi$
$109$	9.54308			0.914061			0.457031	+	0.889451i	$0.348913\pi$
$110$			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
$117$	−7.10778	−	8.15350i	−0.657114	−	0.753791i
$118$	−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	$0.193287\pi$
$127$			12.8605i			1.14119i	−0.821232	+	0.570595i	$0.806713\pi$
$128$			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	$-0.750662\pi$
$131$		−	16.1527i		−	1.41127i	0.708577	−	0.705634i	$-0.249338\pi$
$132$	−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	$-0.492842\pi$
$137$	0.526348			0.0449689			0.0224845	+	0.999747i	$0.492842\pi$
$138$	−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	$-0.272595\pi$
$149$	15.9949			1.31035			0.655176	+	0.755476i	$0.272595\pi$
$150$	9.83548	−	3.44629i	0.803064	−	0.281388i
$151$	2.76186			0.224757			0.112378	−	0.993665i	$-0.464153\pi$
$151$	2.76186			0.224757			0.112378	+	0.993665i	$0.464153\pi$
$152$	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
$156$	−28.2691	+	11.2897i	−2.26334	+	0.903897i
$157$	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	$0.382937\pi$
$181$			25.1080i			1.86627i	−0.359531	+	0.933133i	$0.617063\pi$
$182$	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	$0.346346\pi$
$191$			24.4822i			1.77147i	−0.464189	+	0.885736i	$0.653654\pi$
$192$	5.31252	+	15.1616i	0.383398	+	1.09419i
$193$	4.03383			0.290362			0.145181	−	0.989405i	$-0.453624\pi$
$193$	4.03383			0.290362			0.145181	+	0.989405i	$0.453624\pi$
$194$		−	4.49932i		−	0.323032i
$195$	9.53869	−	3.80942i	0.683080	−	0.272798i
$196$	59.2668			4.23335
$197$	−6.59858			−0.470129			−0.235065	−	0.971980i	$-0.575530\pi$
$197$	−6.59858			−0.470129			−0.235065	+	0.971980i	$0.575530\pi$
$198$	−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	$-0.774725\pi$
$211$		−	18.8866i		−	1.30021i	0.759845	−	0.650104i	$-0.225275\pi$
$212$	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	$-0.596992\pi$
$223$	−8.96039			−0.600032			−0.300016	+	0.953934i	$0.596992\pi$
$224$	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	$0.192785\pi$
$233$			17.3799i			1.13860i	−0.822131	+	0.569299i	$0.807215\pi$
$234$	−21.3776	+	18.6358i	−1.39750	+	1.21826i
$235$	−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	$-0.164916\pi$
$239$	26.8615			1.73752			0.868762	+	0.495229i	$0.164916\pi$
$240$	−9.42988	−	26.9123i	−0.608696	−	1.73718i
$241$	−21.3885			−1.37775			−0.688876	−	0.724879i	$-0.741896\pi$
$241$	−21.3885			−1.37775			−0.688876	+	0.724879i	$0.741896\pi$
$242$			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
$247$	13.3174	−	8.34539i	0.847369	−	0.531005i
$248$		−	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	$-0.984061\pi$
$251$		−	1.58597i		−	0.100105i	0.998747	−	0.0500527i	$-0.0159389\pi$
$252$	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	$0.0513901\pi$
$263$			5.21374i			0.321493i	−0.986996	+	0.160746i	$0.948610\pi$
$264$	−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
$273$	10.1381	+	25.3855i	0.613584	+	1.53640i
$274$		−	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	$-0.813347\pi$
$307$	−29.1887			−1.66589			−0.832945	+	0.553356i	$0.813347\pi$
$308$			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	$-0.854841\pi$
$311$		−	15.5326i		−	0.880775i	0.897808	−	0.440388i	$-0.145159\pi$
$312$	17.4549	+	43.7065i	0.988187	+	2.47439i
$313$	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	$-0.600346\pi$
$331$	−11.2817			−0.620099			−0.310050	+	0.950720i	$0.600346\pi$
$332$	−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	$0.0849473\pi$
$337$			9.68227i			0.527427i	−0.964601	+	0.263713i	$0.915053\pi$
$338$	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	$0.208182\pi$
$347$			22.6659i			1.21677i	−0.793643	+	0.608384i	$0.791818\pi$
$348$	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
$351$	−9.25676	+	16.2884i	−0.494089	+	0.869411i
$352$			2.23581i			0.119169i
$353$	16.8994			0.899465			0.449732	−	0.893163i	$-0.351519\pi$
$353$	16.8994			0.899465			0.449732	+	0.893163i	$0.351519\pi$
$354$	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	$-0.675458\pi$
$359$	−19.8463			−1.04745			−0.523724	+	0.851888i	$0.675458\pi$
$360$	−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	$0.251256\pi$
$373$			27.4206i			1.41978i	−0.704310	+	0.709892i	$0.748744\pi$
$374$	−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	$-0.255640\pi$
$379$	27.0397			1.38894			0.694469	+	0.719523i	$0.255640\pi$
$380$	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	$-0.731979\pi$
$389$		−	29.4262i		−	1.49197i	0.665963	−	0.745985i	$-0.268021\pi$
$390$	−9.98788	−	25.0094i	−0.505756	−	1.26640i
$391$	−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	$-0.524446\pi$
$409$	−3.10323			−0.153445			−0.0767225	+	0.997052i	$0.524446\pi$
$410$	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	$-0.908289\pi$
$419$		−	11.6328i		−	0.568300i	0.958780	−	0.284150i	$-0.0917114\pi$
$420$	−57.3594	+	20.0983i	−2.79885	+	0.980698i
$421$	−6.89214			−0.335902			−0.167951	−	0.985795i	$-0.553715\pi$
$421$	−6.89214			−0.335902			−0.167951	+	0.985795i	$0.553715\pi$
$422$	−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
$429$	−1.16049	+	0.463459i	−0.0560290	+	0.0223760i
$430$		−	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	$-0.942987\pi$
$433$		−	7.41439i		−	0.356313i	0.984002	−	0.178156i	$-0.0570133\pi$
$434$	−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	$-0.952716\pi$
$439$		−	6.20188i		−	0.296000i	0.988987	−	0.148000i	$-0.0472835\pi$
$440$		−	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	$-0.739470\pi$
$443$		−	30.7339i		−	1.46021i	0.683334	−	0.730106i	$-0.260530\pi$
$444$	−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	$-0.625413\pi$
$461$	−16.4845			−0.767761			−0.383881	+	0.923383i	$0.625413\pi$
$462$	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	$-0.894253\pi$
$467$		−	14.0957i		−	0.652271i	0.945323	−	0.326135i	$-0.105747\pi$
$468$	34.6455	+	39.7427i	1.60149	+	1.83710i
$469$		−	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	$-0.188483\pi$
$479$	36.3199			1.65950			0.829750	+	0.558135i	$0.188483\pi$
$480$	−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	$-0.550649\pi$
$487$	−6.99334			−0.316898			−0.158449	+	0.987367i	$0.550649\pi$
$488$		−	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	$0.155521\pi$
$491$			20.8013i			0.938750i	−0.882999	+	0.469375i	$0.844479\pi$
$492$	−57.1519	+	20.0256i	−2.57661	+	0.902825i
$493$			24.3325i			1.09588i
$494$	−21.8807	−	34.9169i	−0.984459	−	1.57099i
$495$	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	$0.0208593\pi$
$503$			2.93733i			0.130969i	−0.997854	+	0.0654846i	$0.979141\pi$
$504$	77.3168	−	61.7659i	3.44396	−	2.75127i
$505$			25.3364i			1.12745i
$506$	−2.12223			−0.0943447
$507$	9.24084	+	20.5331i	0.410400	+	0.911906i
$508$		−	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	$0.180394\pi$
$523$			24.5557i			1.07374i	−0.843664	+	0.536872i	$0.819606\pi$
$524$			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
$546$	66.5579	−	26.5809i	2.84841	−	1.13756i
$547$		−	2.43017i		−	0.103907i	−0.998650	−	0.0519533i	$-0.983455\pi$
$547$		−	2.43017i		−	0.103907i	0.998650	−	0.0519533i	$-0.0165447\pi$
$548$	−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	$-0.410500\pi$
$557$	13.0977			0.554967			0.277483	+	0.960730i	$0.410500\pi$
$558$	−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
$585$	−11.6903	−	13.4102i	−0.483333	−	0.554442i
$586$	−46.5465			−1.92282
$587$	−6.15086			−0.253873			−0.126937	−	0.991911i	$-0.540515\pi$
$587$	−6.15086			−0.253873			−0.126937	+	0.991911i	$0.540515\pi$
$588$	−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	$-0.488696\pi$
$593$	1.72928			0.0710129			0.0355065	+	0.999369i	$0.488696\pi$
$594$	−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	$0.00146639\pi$
$601$			0.225873i			0.00921354i	−0.999989	+	0.00460677i	$0.998534\pi$
$602$	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	$0.0416973\pi$
$607$			6.43634i			0.261243i	−0.991432	+	0.130621i	$0.958303\pi$
$608$	−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	$-0.385697\pi$
$617$	17.4585			0.702851			0.351425	+	0.936216i	$0.385697\pi$
$618$	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
$624$	58.0556	−	23.1854i	2.32408	−	0.928158i
$625$	−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	$0.304159\pi$
$647$			41.5438i			1.63325i	−0.577165	+	0.816627i	$0.695841\pi$
$648$	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	$-0.859088\pi$
$653$		−	21.8931i		−	0.856743i	0.903603	−	0.428371i	$-0.140912\pi$
$654$	−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	$-0.237827\pi$
$661$	37.7229			1.46725			0.733625	+	0.679554i	$0.237827\pi$
$662$			29.5794i			1.14964i
$663$	11.7347	+	29.3835i	0.455740	+	1.14116i
$664$			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	$0.0484490\pi$
$673$			7.86672i			0.303240i	−0.988439	+	0.151620i	$0.951551\pi$
$674$	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	$-0.872496\pi$
$701$		−	20.6484i		−	0.779880i	0.920840	−	0.389940i	$-0.127504\pi$
$702$	42.7064	+	24.2702i	1.61185	+	0.916020i
$703$	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	$0.262430\pi$
$719$			39.3725i			1.46835i	−0.678962	+	0.734173i	$0.737570\pi$
$720$	−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
$741$	−21.2691	−	16.9890i	−0.781340	−	0.624105i
$742$	−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	$-0.756569\pi$
$751$		−	37.9476i		−	1.38473i	0.721548	−	0.692364i	$-0.243431\pi$
$752$	−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	$-0.734536\pi$
$761$	−37.0723			−1.34387			−0.671934	+	0.740611i	$0.734536\pi$
$762$	−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
$780$	−46.4945	+	18.5683i	−1.66477	+	0.664851i
$781$			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	$-0.498451\pi$
$787$	0.272964			0.00973010			0.00486505	+	0.999988i	$0.498451\pi$
$788$	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	$0.0408511\pi$
$809$			7.28056i			0.255971i	−0.991776	+	0.127985i	$0.959149\pi$
$810$	−37.8519	−	8.57164i	−1.32998	−	0.301177i
$811$	5.35557			0.188059			0.0940297	−	0.995569i	$-0.470025\pi$
$811$	5.35557			0.188059			0.0940297	+	0.995569i	$0.470025\pi$
$812$		−	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
$819$	35.6887	−	31.1115i	1.24706	−	1.08712i
$820$		−	57.5051i		−	2.00817i
$821$	12.3157			0.429821			0.214910	−	0.976634i	$-0.431054\pi$
$821$	12.3157			0.429821			0.214910	+	0.976634i	$0.431054\pi$
$822$	−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	$0.0105204\pi$
$829$			1.90288i			0.0660897i	−0.999454	+	0.0330448i	$0.989480\pi$
$830$		−	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	$0.204890\pi$
$858$	1.21514	+	3.04268i	0.0414842	+	0.103875i
$859$	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	$-0.513090\pi$
$877$	−2.43491			−0.0822211			−0.0411106	+	0.999155i	$0.513090\pi$
$878$	−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	$0.103377\pi$
$881$			18.9422i			0.638180i	−0.947724	+	0.319090i	$0.896623\pi$
$882$	−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
$897$	9.36923	+	23.4603i	0.312829	+	0.783317i
$898$	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	$-0.693167\pi$
$907$		−	49.4781i		−	1.64289i	0.570285	−	0.821447i	$-0.306833\pi$
$908$		−	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	$-0.442491\pi$
$929$	10.9536			0.359376			0.179688	+	0.983724i	$0.442491\pi$
$930$	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
$936$	61.4457	−	53.5651i	2.00842	−	1.75083i
$937$	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	$-0.404632\pi$
$947$	18.1652			0.590289			0.295145	+	0.955453i	$0.404632\pi$
$948$	−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
$975$	−13.3096	+	5.31539i	−0.426248	+	0.170229i
$976$	−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
$988$	−64.9134	+	40.6780i	−2.06517	+	1.29414i
$989$			18.3817i			0.584503i
$990$	−1.61570	−	2.02249i	−0.0513505	−	0.0642791i
$991$			38.5600i			1.22490i	0.790509	+	0.612450i	$0.209816\pi$
$991$			38.5600i			1.22490i	−0.790509	+	0.612450i	$0.790184\pi$
$992$			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.740.5	✓	88
3.2	odd	2	inner	741.2.d.a.740.83	yes	88
13.12	even	2	inner	741.2.d.a.740.81	yes	88
19.18	odd	2	inner	741.2.d.a.740.84	yes	88
39.38	odd	2	inner	741.2.d.a.740.7	yes	88
57.56	even	2	inner	741.2.d.a.740.6	yes	88
247.246	odd	2	inner	741.2.d.a.740.8	yes	88
741.740	even	2	inner	741.2.d.a.740.82	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
741.2.d.a.740.5	✓	88	1.1	even	1	trivial
741.2.d.a.740.6	yes	88	57.56	even	2	inner
741.2.d.a.740.7	yes	88	39.38	odd	2	inner
741.2.d.a.740.8	yes	88	247.246	odd	2	inner
741.2.d.a.740.81	yes	88	13.12	even	2	inner
741.2.d.a.740.82	yes	88	741.740	even	2	inner
741.2.d.a.740.83	yes	88	3.2	odd	2	inner
741.2.d.a.740.84	yes	88	19.18	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} +(5.79960 - 2.31616i) 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} +(-6.07272 - 15.2059i) 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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