LMFDB - Embedded newform 740.2.u.a.31.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(31,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.u (of order $4$, degree $2$, 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:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$76$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.1
Character	$\chi$	$=$	740.31
Dual form			740.2.u.a.191.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40873 + 0.124456i) q^{2} +3.04334 q^{3} +(1.96902 - 0.350649i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-4.28724 + 0.378763i) q^{6} +3.54875i q^{7} +(-2.73017 + 0.739026i) q^{8} +6.26194 q^{9} +(-0.908116 + 1.08412i) q^{10} -5.50530 q^{11} +(5.99241 - 1.06715i) q^{12} +(3.68511 - 3.68511i) q^{13} +(-0.441663 - 4.99921i) q^{14} +(2.15197 - 2.15197i) q^{15} +(3.75409 - 1.38087i) q^{16} +(0.288821 - 0.288821i) q^{17} +(-8.82135 + 0.779336i) q^{18} +(4.90665 + 4.90665i) q^{19} +(1.14436 - 1.64025i) q^{20} +10.8001i q^{21} +(7.75546 - 0.685168i) q^{22} +(-0.251261 - 0.251261i) q^{23} +(-8.30885 + 2.24911i) q^{24} -1.00000i q^{25} +(-4.73268 + 5.64995i) q^{26} +9.92719 q^{27} +(1.24437 + 6.98756i) q^{28} +(6.26210 + 6.26210i) q^{29} +(-2.76371 + 3.29936i) q^{30} +(2.17875 - 2.17875i) q^{31} +(-5.11663 + 2.41249i) q^{32} -16.7545 q^{33} +(-0.370924 + 0.442815i) q^{34} +(2.50934 + 2.50934i) q^{35} +(12.3299 - 2.19574i) q^{36} +(-0.751184 - 6.03620i) q^{37} +(-7.52279 - 6.30146i) q^{38} +(11.2151 - 11.2151i) q^{39} +(-1.40795 + 2.45309i) q^{40} -1.81679i q^{41} +(-1.34413 - 15.2143i) q^{42} +(1.37483 + 1.37483i) q^{43} +(-10.8401 + 1.93043i) q^{44} +(4.42786 - 4.42786i) q^{45} +(0.385229 + 0.322687i) q^{46} +2.03429i q^{47} +(11.4250 - 4.20247i) q^{48} -5.59361 q^{49} +(0.124456 + 1.40873i) q^{50} +(0.878981 - 0.878981i) q^{51} +(5.96389 - 8.54825i) q^{52} -10.2797 q^{53} +(-13.9847 + 1.23550i) q^{54} +(-3.89283 + 3.89283i) q^{55} +(-2.62262 - 9.68869i) q^{56} +(14.9326 + 14.9326i) q^{57} +(-9.60094 - 8.04223i) q^{58} +(-1.97286 - 1.97286i) q^{59} +(3.48269 - 4.99186i) q^{60} +(-7.95581 - 7.95581i) q^{61} +(-2.79810 + 3.34042i) q^{62} +22.2220i q^{63} +(6.90768 - 4.03534i) q^{64} -5.21154i q^{65} +(23.6025 - 2.08520i) q^{66} -14.2853 q^{67} +(0.467420 - 0.669969i) q^{68} +(-0.764674 - 0.764674i) q^{69} +(-3.84728 - 3.22268i) q^{70} -5.67025i q^{71} +(-17.0962 + 4.62773i) q^{72} +7.92218i q^{73} +(1.80945 + 8.40987i) q^{74} -3.04334i q^{75} +(11.3818 + 7.94078i) q^{76} -19.5369i q^{77} +(-14.4032 + 17.1947i) q^{78} +(-2.51765 - 2.51765i) q^{79} +(1.67812 - 3.63097i) q^{80} +11.4260 q^{81} +(0.226111 + 2.55936i) q^{82} +2.88336i q^{83} +(3.78703 + 21.2655i) q^{84} -0.408454i q^{85} +(-2.10787 - 1.76566i) q^{86} +(19.0577 + 19.0577i) q^{87} +(15.0304 - 4.06856i) q^{88} +(5.47671 + 5.47671i) q^{89} +(-5.68657 + 6.78871i) q^{90} +(13.0775 + 13.0775i) q^{91} +(-0.582843 - 0.406634i) q^{92} +(6.63068 - 6.63068i) q^{93} +(-0.253180 - 2.86576i) q^{94} +6.93905 q^{95} +(-15.5717 + 7.34204i) q^{96} +(-3.75385 + 3.75385i) q^{97} +(7.87986 - 0.696159i) q^{98} -34.4738 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 4 q^{2} - 4 q^{8} + 152 q^{9} - 16 q^{13} + 24 q^{14} + 40 q^{16} + 16 q^{22} - 36 q^{24} + 32 q^{29} - 4 q^{32} - 16 q^{37} - 40 q^{38} - 20 q^{42} - 72 q^{44} + 8 q^{46} - 248 q^{49} - 4 q^{50}+ \cdots + 24 q^{98}+O(q^{100}) $ 152 * q - 4 * q^2 - 4 * q^8 + 152 * q^9 - 16 * q^13 + 24 * q^14 + 40 * q^16 + 16 * q^22 - 36 * q^24 + 32 * q^29 - 4 * q^32 - 16 * q^37 - 40 * q^38 - 20 * q^42 - 72 * q^44 + 8 * q^46 - 248 * q^49 - 4 * q^50 - 20 * q^52 + 8 * q^54 - 4 * q^56 + 48 * q^57 + 28 * q^60 + 16 * q^61 + 16 * q^66 - 28 * q^68 - 128 * q^72 - 80 * q^74 + 76 * q^76 + 152 * q^81 + 16 * q^82 - 56 * q^84 - 96 * q^86 - 72 * q^88 + 8 * q^89 - 152 * q^92 + 16 * q^93 + 28 * q^94 + 48 * q^96 - 48 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.40873	+	0.124456i	−0.996120	+	0.0880038i
$2$	−1.40873	+	0.124456i	−0.996120	+	0.0880038i
$3$	3.04334			1.75707			0.878537	−	0.477674i	$-0.158520\pi$
$3$	3.04334			1.75707			0.878537	+	0.477674i	$0.158520\pi$
$4$	1.96902	−	0.350649i	0.984511	−	0.175325i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−4.28724	+	0.378763i	−1.75026	+	0.154629i
$7$			3.54875i			1.34130i	0.741774	+	0.670650i	$0.233985\pi$
$7$			3.54875i			1.34130i	−0.741774	+	0.670650i	$0.766015\pi$
$8$	−2.73017	+	0.739026i	−0.965262	+	0.261285i
$9$	6.26194			2.08731
$10$	−0.908116	+	1.08412i	−0.287172	+	0.342830i
$11$	−5.50530			−1.65991			−0.829955	−	0.557830i	$-0.811634\pi$
$11$	−5.50530			−1.65991			−0.829955	+	0.557830i	$0.811634\pi$
$12$	5.99241	−	1.06715i	1.72986	−	0.308059i
$13$	3.68511	−	3.68511i	1.02207	−	1.02207i	0.0223157	−	0.999751i	$-0.492896\pi$
$13$	3.68511	−	3.68511i	1.02207	−	1.02207i	0.999751	−	0.0223157i	$-0.00710390\pi$
$14$	−0.441663	−	4.99921i	−0.118040	−	1.33610i
$15$	2.15197	−	2.15197i	0.555636	−	0.555636i
$16$	3.75409	−	1.38087i	0.938523	−	0.345218i
$17$	0.288821	−	0.288821i	0.0700494	−	0.0700494i	−0.671214	−	0.741264i	$-0.734227\pi$
$17$	0.288821	−	0.288821i	0.0700494	−	0.0700494i	0.741264	+	0.671214i	$0.234227\pi$
$18$	−8.82135	+	0.779336i	−2.07921	+	0.183691i
$19$	4.90665	+	4.90665i	1.12566	+	1.12566i	0.990874	+	0.134788i	$0.0430354\pi$
$19$	4.90665	+	4.90665i	1.12566	+	1.12566i	0.134788	+	0.990874i	$0.456965\pi$
$20$	1.14436	−	1.64025i	0.255887	−	0.366772i
$21$			10.8001i			2.35677i
$22$	7.75546	−	0.685168i	1.65347	−	0.146078i
$23$	−0.251261	−	0.251261i	−0.0523916	−	0.0523916i	0.680426	−	0.732817i	$-0.261795\pi$
$23$	−0.251261	−	0.251261i	−0.0523916	−	0.0523916i	−0.732817	+	0.680426i	$0.761795\pi$
$24$	−8.30885	+	2.24911i	−1.69604	+	0.459097i
$25$		−	1.00000i		−	0.200000i
$26$	−4.73268	+	5.64995i	−0.928155	+	1.10805i
$27$	9.92719			1.91049
$28$	1.24437	+	6.98756i	0.235163	+	1.32052i
$29$	6.26210	+	6.26210i	1.16284	+	1.16284i	0.983850	+	0.178992i	$0.0572837\pi$
$29$	6.26210	+	6.26210i	1.16284	+	1.16284i	0.178992	+	0.983850i	$0.442716\pi$
$30$	−2.76371	+	3.29936i	−0.504582	+	0.602378i
$31$	2.17875	−	2.17875i	0.391315	−	0.391315i	−0.483841	−	0.875156i	$-0.660759\pi$
$31$	2.17875	−	2.17875i	0.391315	−	0.391315i	0.875156	+	0.483841i	$0.160759\pi$
$32$	−5.11663	+	2.41249i	−0.904501	+	0.426472i
$33$	−16.7545			−2.91659
$34$	−0.370924	+	0.442815i	−0.0636130	+	0.0759422i
$35$	2.50934	+	2.50934i	0.424156	+	0.424156i
$36$	12.3299	−	2.19574i	2.05498	−	0.365957i
$37$	−0.751184	−	6.03620i	−0.123494	−	0.992345i
$37$	−0.751184	−	6.03620i	−0.123494	−	0.992345i
$38$	−7.52279	−	6.30146i	−1.22036	−	1.02223i
$39$	11.2151	−	11.2151i	1.79585	−	1.79585i
$40$	−1.40795	+	2.45309i	−0.222617	+	0.387868i
$41$		−	1.81679i		−	0.283735i	−0.989886	−	0.141867i	$-0.954689\pi$
$41$		−	1.81679i		−	0.283735i	0.989886	−	0.141867i	$-0.0453107\pi$
$42$	−1.34413	−	15.2143i	−0.207404	−	2.34762i
$43$	1.37483	+	1.37483i	0.209660	+	0.209660i	0.804123	−	0.594463i	$-0.202635\pi$
$43$	1.37483	+	1.37483i	0.209660	+	0.209660i	−0.594463	+	0.804123i	$0.702635\pi$
$44$	−10.8401	+	1.93043i	−1.63420	+	0.291023i
$45$	4.42786	−	4.42786i	0.660066	−	0.660066i
$46$	0.385229	+	0.322687i	0.0567990	+	0.0475777i
$47$			2.03429i			0.296732i	0.988933	+	0.148366i	$0.0474013\pi$
$47$			2.03429i			0.296732i	−0.988933	+	0.148366i	$0.952599\pi$
$48$	11.4250	−	4.20247i	1.64905	−	0.606574i
$49$	−5.59361			−0.799087
$50$	0.124456	+	1.40873i	0.0176008	+	0.199224i
$51$	0.878981	−	0.878981i	0.123082	−	0.123082i
$52$	5.96389	−	8.54825i	0.827042	−	1.18543i
$53$	−10.2797			−1.41202			−0.706012	−	0.708200i	$-0.749507\pi$
$53$	−10.2797			−1.41202			−0.706012	+	0.708200i	$0.749507\pi$
$54$	−13.9847	+	1.23550i	−1.90308	+	0.168130i
$55$	−3.89283	+	3.89283i	−0.524910	+	0.524910i
$56$	−2.62262	−	9.68869i	−0.350462	−	1.29471i
$57$	14.9326	+	14.9326i	1.97787	+	1.97787i
$58$	−9.60094	−	8.04223i	−1.26067	−	1.05600i
$59$	−1.97286	−	1.97286i	−0.256844	−	0.256844i	0.566925	−	0.823769i	$-0.308133\pi$
$59$	−1.97286	−	1.97286i	−0.256844	−	0.256844i	−0.823769	+	0.566925i	$0.808133\pi$
$60$	3.48269	−	4.99186i	0.449613	−	0.644446i
$61$	−7.95581	−	7.95581i	−1.01864	−	1.01864i	−0.999823	−	0.0188138i	$-0.994011\pi$
$61$	−7.95581	−	7.95581i	−1.01864	−	1.01864i	−0.0188138	−	0.999823i	$-0.505989\pi$
$62$	−2.79810	+	3.34042i	−0.355360	+	0.424234i
$63$			22.2220i			2.79971i
$64$	6.90768	−	4.03534i	0.863460	−	0.504417i
$65$		−	5.21154i		−	0.646412i
$66$	23.6025	−	2.08520i	2.90527	−	0.256671i
$67$	−14.2853			−1.74522			−0.872612	−	0.488414i	$-0.837576\pi$
$67$	−14.2853			−1.74522			−0.872612	+	0.488414i	$0.837576\pi$
$68$	0.467420	−	0.669969i	0.0566830	−	0.0812457i
$69$	−0.764674	−	0.764674i	−0.0920559	−	0.0920559i
$70$	−3.84728	−	3.22268i	−0.459838	−	0.385183i
$71$		−	5.67025i		−	0.672935i	−0.941695	−	0.336467i	$-0.890768\pi$
$71$		−	5.67025i		−	0.672935i	0.941695	−	0.336467i	$-0.109232\pi$
$72$	−17.0962	+	4.62773i	−2.01480	+	0.545383i
$73$			7.92218i			0.927221i	0.886039	+	0.463610i	$0.153446\pi$
$73$			7.92218i			0.927221i	−0.886039	+	0.463610i	$0.846554\pi$
$74$	1.80945	+	8.40987i	0.210345	+	0.977627i
$75$		−	3.04334i		−	0.351415i
$76$	11.3818	+	7.94078i	1.30558	+	0.910870i
$77$		−	19.5369i		−	2.22644i
$78$	−14.4032	+	17.1947i	−1.63084	+	1.94692i
$79$	−2.51765	−	2.51765i	−0.283258	−	0.283258i	0.551149	−	0.834407i	$-0.314190\pi$
$79$	−2.51765	−	2.51765i	−0.283258	−	0.283258i	−0.834407	+	0.551149i	$0.814190\pi$
$80$	1.67812	−	3.63097i	0.187619	−	0.405954i
$81$	11.4260			1.26956
$82$	0.226111	+	2.55936i	0.0249697	+	0.282634i
$83$			2.88336i			0.316490i	0.987400	+	0.158245i	$0.0505836\pi$
$83$			2.88336i			0.316490i	−0.987400	+	0.158245i	$0.949416\pi$
$84$	3.78703	+	21.2655i	0.413199	+	2.32026i
$85$		−	0.408454i		−	0.0443031i
$86$	−2.10787	−	1.76566i	−0.227298	−	0.190396i
$87$	19.0577	+	19.0577i	2.04320	+	2.04320i
$88$	15.0304	−	4.06856i	1.60225	−	0.433710i
$89$	5.47671	+	5.47671i	0.580530	+	0.580530i	0.935049	−	0.354519i	$-0.115355\pi$
$89$	5.47671	+	5.47671i	0.580530	+	0.580530i	−0.354519	+	0.935049i	$0.615355\pi$
$90$	−5.68657	+	6.78871i	−0.599417	+	0.715593i
$91$	13.0775	+	13.0775i	1.37090	+	1.37090i
$92$	−0.582843	−	0.406634i	−0.0607656	−	0.0423945i
$93$	6.63068	−	6.63068i	0.687570	−	0.687570i
$94$	−0.253180	−	2.86576i	−0.0261135	−	0.295580i
$95$	6.93905			0.711932
$96$	−15.5717	+	7.34204i	−1.58928	+	0.749343i
$97$	−3.75385	+	3.75385i	−0.381146	+	0.381146i	−0.871515	−	0.490369i	$-0.836862\pi$
$97$	−3.75385	+	3.75385i	−0.381146	+	0.381146i	0.490369	+	0.871515i	$0.336862\pi$
$98$	7.87986	−	0.696159i	0.795987	−	0.0703227i
$99$	−34.4738			−3.46475
$100$	−0.350649	−	1.96902i	−0.0350649	−	0.196902i
$101$		−	17.9080i		−	1.78191i	−0.454092	−	0.890955i	$-0.650036\pi$
$101$		−	17.9080i		−	1.78191i	0.454092	−	0.890955i	$-0.349964\pi$
$102$	−1.12885	+	1.34764i	−0.111773	+	0.133436i
$103$	5.17895	−	5.17895i	0.510298	−	0.510298i	−0.404320	−	0.914618i	$-0.632492\pi$
$103$	5.17895	−	5.17895i	0.510298	−	0.510298i	0.914618	+	0.404320i	$0.132492\pi$
$104$	−7.33760	+	12.7844i	−0.719511	+	1.25361i
$105$	7.63679	+	7.63679i	0.745275	+	0.745275i
$106$	14.4813	−	1.27937i	1.40654	−	0.124263i
$107$			6.62299i			0.640269i	0.947372	+	0.320134i	$0.103728\pi$
$107$			6.62299i			0.640269i	−0.947372	+	0.320134i	$0.896272\pi$
$108$	19.5468	−	3.48096i	1.88090	−	0.334956i
$109$	−4.83703	+	4.83703i	−0.463303	+	0.463303i	−0.899737	−	0.436434i	$-0.856241\pi$
$109$	−4.83703	+	4.83703i	−0.463303	+	0.463303i	0.436434	+	0.899737i	$0.356241\pi$
$110$	4.99945	−	5.96843i	0.476679	−	0.569067i
$111$	−2.28611	−	18.3702i	−0.216988	−	1.74362i
$112$	4.90037	+	13.3223i	0.463041	+	1.25884i
$113$	−5.07826	−	5.07826i	−0.477722	−	0.477722i	0.426680	−	0.904403i	$-0.359683\pi$
$113$	−5.07826	−	5.07826i	−0.477722	−	0.477722i	−0.904403	+	0.426680i	$0.859683\pi$
$114$	−22.8944	−	19.1775i	−2.14426	−	1.79614i
$115$	−0.355337			−0.0331354
$116$	14.5260	+	10.1344i	1.34871	+	0.940956i
$117$	23.0759	−	23.0759i	2.13337	−	2.13337i
$118$	3.02475	+	2.53368i	0.278451	+	0.233244i
$119$	1.02495	+	1.02495i	0.0939572	+	0.0939572i
$120$	−4.28488	+	7.46560i	−0.391155	+	0.681513i
$121$	19.3083			1.75530
$122$	12.1977	+	10.2174i	1.10433	+	0.925041i
$123$		−	5.52911i		−	0.498543i
$124$	3.52603	−	5.05398i	0.316647	−	0.453861i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−2.76567	−	31.3048i	−0.246385	−	2.78885i
$127$		−	12.5825i		−	1.11652i	−0.829666	−	0.558259i	$-0.811469\pi$
$127$		−	12.5825i		−	1.11652i	0.829666	−	0.558259i	$-0.188531\pi$
$128$	−9.22881	+	6.54439i	−0.815720	+	0.578448i
$129$	4.18409	+	4.18409i	0.368389	+	0.368389i
$130$	0.648608	+	7.34163i	0.0568867	+	0.643904i
$131$	−0.202539	+	0.202539i	−0.0176959	+	0.0176959i	−0.715899	−	0.698203i	$-0.753983\pi$
$131$	−0.202539	+	0.202539i	−0.0176959	+	0.0176959i	0.698203	+	0.715899i	$0.253983\pi$
$132$	−32.9900	+	5.87496i	−2.87141	+	0.511350i
$133$	−17.4125	+	17.4125i	−1.50985	+	1.50985i
$134$	20.1240	−	1.77789i	1.73845	−	0.153586i
$135$	7.01958	−	7.01958i	0.604149	−	0.604149i
$136$	−0.575085	+	1.00198i	−0.0493131	+	0.0859188i
$137$	−14.3714			−1.22783			−0.613915	−	0.789372i	$-0.710406\pi$
$137$	−14.3714			−1.22783			−0.613915	+	0.789372i	$0.710406\pi$
$138$	1.17239	+	0.982048i	0.0998000	+	0.0835975i
$139$	−11.1240			−0.943526			−0.471763	−	0.881725i	$-0.656382\pi$
$139$	−11.1240			−0.943526			−0.471763	+	0.881725i	$0.656382\pi$
$140$	5.82085	+	4.06105i	0.491952	+	0.343221i
$141$			6.19104i			0.521380i
$142$	0.705697	+	7.98783i	0.0592208	+	0.670324i
$143$	−20.2877	+	20.2877i	−1.69654	+	1.69654i
$144$	23.5079	−	8.64693i	1.95899	−	0.720578i
$145$	8.85595			0.735446
$146$	−0.985964	−	11.1602i	−0.0815989	−	0.923623i
$147$	−17.0233			−1.40406
$148$	−3.59569	−	11.6220i	−0.295564	−	0.955323i
$149$	11.1188			0.910884			0.455442	−	0.890265i	$-0.349481\pi$
$149$	11.1188			0.910884			0.455442	+	0.890265i	$0.349481\pi$
$150$	0.378763	+	4.28724i	0.0309258	+	0.350052i
$151$	8.39398			0.683092			0.341546	−	0.939865i	$-0.389049\pi$
$151$	8.39398			0.683092			0.341546	+	0.939865i	$0.389049\pi$
$152$	−17.0221	−	9.76986i	−1.38068	−	0.792440i
$153$	1.80858	−	1.80858i	0.146215	−	0.146215i
$154$	2.43149	+	27.5222i	0.195935	+	2.21780i
$155$		−	3.08122i		−	0.247489i
$156$	18.1501	−	26.0153i	1.45317	−	2.08289i
$157$	−3.26809			−0.260822			−0.130411	−	0.991460i	$-0.541630\pi$
$157$	−3.26809			−0.260822			−0.130411	+	0.991460i	$0.541630\pi$
$158$	3.86002	+	3.23334i	0.307086	+	0.257231i
$159$	−31.2846			−2.48103
$160$	−1.91211	+	5.32389i	−0.151166	+	0.420891i
$161$	0.891663	−	0.891663i	0.0702729	−	0.0702729i
$162$	−16.0961	+	1.42204i	−1.26463	+	0.111726i
$163$	−8.13382	+	8.13382i	−0.637090	+	0.637090i	−0.949837	−	0.312746i	$-0.898751\pi$
$163$	−8.13382	+	8.13382i	−0.637090	+	0.637090i	0.312746	+	0.949837i	$0.398751\pi$
$164$	−0.637056	−	3.57730i	−0.0497457	−	0.279340i
$165$	−11.8472	+	11.8472i	−0.922306	+	0.922306i
$166$	−0.358852	−	4.06187i	−0.0278523	−	0.315262i
$167$	−5.33364	−	5.33364i	−0.412730	−	0.412730i	0.469959	−	0.882688i	$-0.344269\pi$
$167$	−5.33364	−	5.33364i	−0.412730	−	0.412730i	−0.882688	+	0.469959i	$0.844269\pi$
$168$	−7.98152	−	29.4860i	−0.615788	−	2.27490i
$169$		−	14.1601i		−	1.08924i
$170$	0.0508347	+	0.575401i	0.00389884	+	0.0441312i
$171$	30.7251	+	30.7251i	2.34961	+	2.34961i
$172$	3.18916	+	2.22499i	0.243171	+	0.169654i
$173$		−	9.08143i		−	0.690449i	−0.938520	−	0.345224i	$-0.887803\pi$
$173$		−	9.08143i		−	0.690449i	0.938520	−	0.345224i	$-0.112197\pi$
$174$	−29.2190	−	24.4753i	−2.21508	−	1.85546i
$175$	3.54875			0.268260
$176$	−20.6674	+	7.60211i	−1.55786	+	0.573031i
$177$	−6.00408	−	6.00408i	−0.451294	−	0.451294i
$178$	−8.39680	−	7.03358i	−0.629367	−	0.527189i
$179$	9.91212	−	9.91212i	0.740867	−	0.740867i	−0.231878	−	0.972745i	$-0.574487\pi$
$179$	9.91212	−	9.91212i	0.740867	−	0.740867i	0.972745	+	0.231878i	$0.0744871\pi$
$180$	7.16592	−	10.2712i	0.534116	−	0.765568i
$181$	−14.7304			−1.09490			−0.547450	−	0.836838i	$-0.684402\pi$
$181$	−14.7304			−1.09490			−0.547450	+	0.836838i	$0.684402\pi$
$182$	−20.0503	−	16.7951i	−1.48622	−	1.24494i
$183$	−24.2122	−	24.2122i	−1.78982	−	1.78982i
$184$	0.871675	+	0.500298i	0.0642607	+	0.0368825i
$185$	−4.79941	−	3.73707i	−0.352859	−	0.274755i
$186$	−8.51559	+	10.1660i	−0.624393	+	0.745411i
$187$	−1.59005	+	1.59005i	−0.116276	+	0.116276i
$188$	0.713322	+	4.00556i	0.0520244	+	0.292136i
$189$			35.2291i			2.56254i
$190$	−9.77522	+	0.863607i	−0.709169	+	0.0626527i
$191$	0.289059	+	0.289059i	0.0209155	+	0.0209155i	0.717487	−	0.696572i	$-0.245292\pi$
$191$	0.289059	+	0.289059i	0.0209155	+	0.0209155i	−0.696572	+	0.717487i	$0.745292\pi$
$192$	21.0224	−	12.2809i	1.51716	−	0.886298i
$193$	5.02910	−	5.02910i	0.362003	−	0.362003i	−0.502547	−	0.864550i	$-0.667604\pi$
$193$	5.02910	−	5.02910i	0.362003	−	0.362003i	0.864550	+	0.502547i	$0.167604\pi$
$194$	4.82096	−	5.75534i	0.346125	−	0.413209i
$195$		−	15.8605i		−	1.13579i
$196$	−11.0139	+	1.96139i	−0.786710	+	0.140100i
$197$	−4.11766			−0.293371			−0.146685	−	0.989183i	$-0.546860\pi$
$197$	−4.11766			−0.293371			−0.146685	+	0.989183i	$0.546860\pi$
$198$	48.5642	−	4.29048i	3.45131	−	0.304911i
$199$	16.6558	−	16.6558i	1.18070	−	1.18070i	0.201135	−	0.979564i	$-0.435537\pi$
$199$	16.6558	−	16.6558i	1.18070	−	1.18070i	0.979564	−	0.201135i	$-0.0644629\pi$
$200$	0.739026	+	2.73017i	0.0522570	+	0.193052i
$201$	−43.4750			−3.06649
$202$	2.22876	+	25.2274i	0.156815	+	1.77500i
$203$	−22.2226	+	22.2226i	−1.55972	+	1.55972i
$204$	1.42252	−	2.03895i	0.0995962	−	0.142755i
$205$	−1.28466	−	1.28466i	−0.0897249	−	0.0897249i
$206$	−6.65118	+	7.94028i	−0.463410	+	0.553226i
$207$	−1.57338	−	1.57338i	−0.109358	−	0.109358i
$208$	8.74558	−	18.9229i	0.606397	−	1.31207i
$209$	−27.0126	−	27.0126i	−1.86850	−	1.86850i
$210$	−11.7086	−	9.80771i	−0.807970	−	0.676796i
$211$			10.5551i			0.726646i	0.931663	+	0.363323i	$0.118358\pi$
$211$			10.5551i			0.726646i	−0.931663	+	0.363323i	$0.881642\pi$
$212$	−20.2409	+	3.60456i	−1.39015	+	0.247563i
$213$		−	17.2565i		−	1.18240i
$214$	−0.824272	−	9.32999i	−0.0563461	−	0.637785i
$215$	1.94431			0.132601
$216$	−27.1029	+	7.33645i	−1.84412	+	0.499182i
$217$	7.73183	+	7.73183i	0.524871	+	0.524871i
$218$	6.21205	−	7.41604i	0.420733	−	0.502278i
$219$			24.1099i			1.62920i
$220$	−6.30005	+	9.03009i	−0.424750	+	0.608809i
$221$		−	2.12868i		−	0.143190i
$222$	5.50679	+	25.5941i	0.369592	+	1.71776i
$223$			0.212350i			0.0142200i	0.999975	+	0.00711002i	$0.00226321\pi$
$223$			0.212350i			0.0142200i	−0.999975	+	0.00711002i	$0.997737\pi$
$224$	−8.56132	−	18.1576i	−0.572027	−	1.21321i
$225$		−	6.26194i		−	0.417462i
$226$	7.78590	+	6.52186i	0.517910	+	0.433827i
$227$	−15.1309	−	15.1309i	−1.00427	−	1.00427i	−0.999991	−	0.00428348i	$-0.998637\pi$
$227$	−15.1309	−	15.1309i	−1.00427	−	1.00427i	−0.00428348	−	0.999991i	$-0.501363\pi$
$228$	34.6388	+	24.1665i	2.29401	+	1.60047i
$229$	10.8143			0.714627			0.357314	−	0.933985i	$-0.383693\pi$
$229$	10.8143			0.714627			0.357314	+	0.933985i	$0.383693\pi$
$230$	0.500573	−	0.0442239i	0.0330068	−	0.00291604i
$231$		−	59.4575i		−	3.91202i
$232$	−21.7245	−	12.4688i	−1.42628	−	0.818614i
$233$			19.5713i			1.28216i	0.767475	+	0.641079i	$0.221513\pi$
$233$			19.5713i			1.28216i	−0.767475	+	0.641079i	$0.778487\pi$
$234$	−29.6358	+	35.3796i	−1.93735	+	2.31284i
$235$	1.43846	+	1.43846i	0.0938348	+	0.0938348i
$236$	−4.57637	−	3.19281i	−0.297897	−	0.207834i
$237$	−7.66207	−	7.66207i	−0.497705	−	0.497705i
$238$	−1.57144	−	1.31632i	−0.101861	−	0.0853241i
$239$	5.55672	+	5.55672i	0.359434	+	0.359434i	0.863604	−	0.504170i	$-0.168202\pi$
$239$	5.55672	+	5.55672i	0.359434	+	0.359434i	−0.504170	+	0.863604i	$0.668202\pi$
$240$	5.10709	−	11.0503i	0.329661	−	0.713292i
$241$	−9.57502	+	9.57502i	−0.616781	+	0.616781i	−0.944704	−	0.327923i	$-0.893651\pi$
$241$	−9.57502	+	9.57502i	−0.616781	+	0.616781i	0.327923	+	0.944704i	$0.393651\pi$
$242$	−27.2001	+	2.40304i	−1.74849	+	0.154473i
$243$	4.99175			0.320221
$244$	−18.4549	−	12.8755i	−1.18145	−	0.824267i
$245$	−3.95528	+	3.95528i	−0.252693	+	0.252693i
$246$	0.688132	+	7.78901i	0.0438737	+	0.496609i
$247$	36.1631			2.30100
$248$	−4.33821	+	7.55851i	−0.275477	+	0.479966i
$249$			8.77507i			0.556097i
$250$	1.08412	+	0.908116i	0.0685660	+	0.0574343i
$251$	−2.85748	+	2.85748i	−0.180363	+	0.180363i	−0.791514	−	0.611151i	$-0.790707\pi$
$251$	−2.85748	+	2.85748i	−0.180363	+	0.180363i	0.611151	+	0.791514i	$0.290707\pi$
$252$	7.79214	+	43.7556i	0.490859	+	2.75635i
$253$	1.38327	+	1.38327i	0.0869653	+	0.0869653i
$254$	1.56597	+	17.7253i	0.0982579	+	1.11219i
$255$		−	1.24307i		−	0.0778439i
$256$	12.1864	−	10.3678i	0.761649	−	0.647990i
$257$	3.89695	−	3.89695i	0.243085	−	0.243085i	−0.575040	−	0.818125i	$-0.695014\pi$
$257$	3.89695	−	3.89695i	0.243085	−	0.243085i	0.818125	+	0.575040i	$0.195014\pi$
$258$	−6.41498	−	5.37351i	−0.399379	−	0.334540i
$259$	21.4210	−	2.66576i	1.33103	−	0.165642i
$260$	−1.82742	−	10.2616i	−0.113332	−	0.636399i
$261$	39.2129	+	39.2129i	2.42722	+	2.42722i
$262$	0.260114	−	0.310529i	0.0160699	−	0.0191845i
$263$	3.96155			0.244279			0.122140	−	0.992513i	$-0.461024\pi$
$263$	3.96155			0.244279			0.122140	+	0.992513i	$0.461024\pi$
$264$	45.7427	−	12.3820i	2.81527	−	0.762061i
$265$	−7.26884	+	7.26884i	−0.446521	+	0.446521i
$266$	22.3623	−	26.6965i	1.37112	−	1.63687i
$267$	16.6675	+	16.6675i	1.02004	+	1.02004i
$268$	−28.1280	+	5.00912i	−1.71819	+	0.305981i
$269$	28.6408			1.74626			0.873129	−	0.487489i	$-0.162087\pi$
$269$	28.6408			1.74626			0.873129	+	0.487489i	$0.162087\pi$
$270$	−9.01504	+	10.7623i	−0.548638	+	0.654973i
$271$			18.4627i			1.12153i	0.827976	+	0.560764i	$0.189492\pi$
$271$			18.4627i			1.12153i	−0.827976	+	0.560764i	$0.810508\pi$
$272$	0.685435	−	1.48308i	0.0415606	−	0.0899252i
$273$	39.7994	+	39.7994i	2.40877	+	2.40877i
$274$	20.2453	−	1.78861i	1.22307	−	0.108054i
$275$			5.50530i			0.331982i
$276$	−1.77379	−	1.23753i	−0.106770	−	0.0744904i
$277$	−5.39405	−	5.39405i	−0.324097	−	0.324097i	0.526239	−	0.850337i	$-0.323602\pi$
$277$	−5.39405	−	5.39405i	−0.324097	−	0.324097i	−0.850337	+	0.526239i	$0.823602\pi$
$278$	15.6707	−	1.38445i	0.939865	−	0.0830338i
$279$	13.6432	−	13.6432i	0.816796	−	0.816796i
$280$	−8.70541	−	4.99647i	−0.520248	−	0.298596i
$281$	20.7317	−	20.7317i	1.23675	−	1.23675i	0.275425	−	0.961323i	$-0.411181\pi$
$281$	20.7317	−	20.7317i	1.23675	−	1.23675i	0.961323	−	0.275425i	$-0.0888185\pi$
$282$	−0.770513	−	8.72149i	−0.0458834	−	0.519357i
$283$	12.6105	−	12.6105i	0.749618	−	0.749618i	−0.224789	−	0.974407i	$-0.572169\pi$
$283$	12.6105	−	12.6105i	0.749618	−	0.749618i	0.974407	+	0.224789i	$0.0721693\pi$
$284$	−1.98827	−	11.1648i	−0.117982	−	0.662512i
$285$	21.1179			1.25092
$286$	26.0548	−	31.1047i	1.54065	−	1.83926i
$287$	6.44733			0.380574
$288$	−32.0400	+	15.1069i	−1.88797	+	0.890180i
$289$			16.8332i			0.990186i
$290$	−12.4756	+	1.10218i	−0.732593	+	0.0647221i
$291$	−11.4243	+	11.4243i	−0.669702	+	0.669702i
$292$	2.77791	+	15.5989i	0.162565	+	0.912859i
$293$	−20.8147			−1.21601			−0.608003	−	0.793935i	$-0.708029\pi$
$293$	−20.8147			−1.21601			−0.608003	+	0.793935i	$0.708029\pi$
$294$	23.9811	−	2.11865i	1.39861	−	0.123562i
$295$	−2.79004			−0.162442
$296$	6.51177	+	15.9247i	0.378489	+	0.925606i
$297$	−54.6521			−3.17124
$298$	−15.6633	+	1.38380i	−0.907350	+	0.0801612i
$299$	−1.85185			−0.107095
$300$	−1.06715	−	5.99241i	−0.0616117	−	0.345972i
$301$	−4.87894	+	4.87894i	−0.281217	+	0.281217i
$302$	−11.8248	+	1.04468i	−0.680442	+	0.0601147i
$303$		−	54.5001i		−	3.13095i
$304$	25.1955	+	11.6445i	1.44506	+	0.667861i
$305$	−11.2512			−0.644242
$306$	−2.32270	+	2.77288i	−0.132780	+	0.158515i
$307$	−25.4539			−1.45273			−0.726364	−	0.687310i	$-0.758791\pi$
$307$	−25.4539			−1.45273			−0.726364	+	0.687310i	$0.758791\pi$
$308$	−6.85061	−	38.4686i	−0.390350	−	2.19195i
$309$	15.7613	−	15.7613i	0.896631	−	0.896631i
$310$	0.383476	+	4.34059i	0.0217800	+	0.246529i
$311$	−5.20773	+	5.20773i	−0.295304	+	0.295304i	−0.839171	−	0.543868i	$-0.816959\pi$
$311$	−5.20773	+	5.20773i	−0.295304	+	0.295304i	0.543868	+	0.839171i	$0.316959\pi$
$312$	−22.3308	+	38.9073i	−1.26423	+	2.20269i
$313$	5.92624	−	5.92624i	0.334971	−	0.334971i	−0.519500	−	0.854471i	$-0.673882\pi$
$313$	5.92624	−	5.92624i	0.334971	−	0.334971i	0.854471	+	0.519500i	$0.173882\pi$
$314$	4.60384	−	0.406734i	0.259810	−	0.0229533i
$315$	15.7133	+	15.7133i	0.885347	+	0.885347i
$316$	−5.84012	−	4.07449i	−0.328532	−	0.229208i
$317$		−	1.36380i		−	0.0765986i	−0.999266	−	0.0382993i	$-0.987806\pi$
$317$		−	1.36380i		−	0.0765986i	0.999266	−	0.0382993i	$-0.0121940\pi$
$318$	44.0715	−	3.89356i	2.47140	−	0.218340i
$319$	−34.4747	−	34.4747i	−1.93021	−	1.93021i
$320$	2.03106	−	7.73788i	0.113539	−	0.432561i
$321$			20.1560i			1.12500i
$322$	−1.14514	+	1.36708i	−0.0638159	+	0.0761845i
$323$	2.83429			0.157704
$324$	22.4981	−	4.00653i	1.24989	−	0.222585i
$325$	−3.68511	−	3.68511i	−0.204413	−	0.204413i
$326$	10.4460	−	12.4706i	0.578552	−	0.690685i
$327$	−14.7207	+	14.7207i	−0.814058	+	0.814058i
$328$	1.34265	+	4.96015i	0.0741357	+	0.273878i
$329$	−7.21918			−0.398006
$330$	15.2150	−	18.1640i	0.837561	−	0.999894i
$331$	−9.83223	−	9.83223i	−0.540428	−	0.540428i	0.383226	−	0.923655i	$-0.374813\pi$
$331$	−9.83223	−	9.83223i	−0.540428	−	0.540428i	−0.923655	+	0.383226i	$0.874813\pi$
$332$	1.01105	+	5.67741i	0.0554886	+	0.311588i
$333$	−4.70386	−	37.7983i	−0.257770	−	2.07133i
$334$	8.17745	+	6.84984i	0.447450	+	0.374807i
$335$	−10.1012	+	10.1012i	−0.551888	+	0.551888i
$336$	14.9135	+	40.5444i	0.813598	+	2.21188i
$337$			19.1986i			1.04582i	0.852389	+	0.522908i	$0.175153\pi$
$337$			19.1986i			1.04582i	−0.852389	+	0.522908i	$0.824847\pi$
$338$	1.76231	+	19.9477i	0.0958573	+	1.08501i
$339$	−15.4549	−	15.4549i	−0.839394	−	0.839394i
$340$	−0.143224	−	0.804256i	−0.00776743	−	0.0436169i
$341$	−11.9947	+	11.9947i	−0.649548	+	0.649548i
$342$	−47.1072	−	39.4594i	−2.54727	−	2.13372i
$343$			4.99093i			0.269485i
$344$	−4.76957	−	2.73750i	−0.257158	−	0.147596i
$345$	−1.08141			−0.0582213
$346$	1.13024	+	12.7933i	0.0607621	+	0.687770i
$347$	10.1689	−	10.1689i	0.545896	−	0.545896i	−0.379355	−	0.925251i	$-0.623854\pi$
$347$	10.1689	−	10.1689i	0.545896	−	0.545896i	0.925251	+	0.379355i	$0.123854\pi$
$348$	44.2076	+	30.8425i	2.36978	+	1.65333i
$349$	3.54294			0.189649			0.0948245	−	0.995494i	$-0.469771\pi$
$349$	3.54294			0.189649			0.0948245	+	0.995494i	$0.469771\pi$
$350$	−4.99921	+	0.441663i	−0.267219	+	0.0236079i
$351$	36.5828	−	36.5828i	1.95265	−	1.95265i
$352$	28.1686	−	13.2815i	1.50139	−	0.707905i
$353$	1.57576	+	1.57576i	0.0838694	+	0.0838694i	0.747797	−	0.663927i	$-0.231112\pi$
$353$	1.57576	+	1.57576i	0.0838694	+	0.0838694i	−0.663927	+	0.747797i	$0.731112\pi$
$354$	9.20534	+	7.71086i	0.489259	+	0.409827i
$355$	−4.00947	−	4.00947i	−0.212801	−	0.212801i
$356$	12.7042	+	8.86336i	0.673320	+	0.469757i
$357$	3.11928	+	3.11928i	0.165090	+	0.165090i
$358$	−12.7298	+	15.1971i	−0.672793	+	0.803191i
$359$		−	6.39655i		−	0.337597i	−0.985651	−	0.168798i	$-0.946011\pi$
$359$		−	6.39655i		−	0.337597i	0.985651	−	0.168798i	$-0.0539887\pi$
$360$	−8.81651	+	15.3611i	−0.464671	+	0.809602i
$361$			29.1504i			1.53423i
$362$	20.7511	−	1.83329i	1.09065	−	0.0963554i
$363$	58.7618			3.08420
$364$	30.3356	+	21.1643i	1.59002	+	1.10931i
$365$	5.60183	+	5.60183i	0.293213	+	0.293213i
$366$	37.1218	+	31.0951i	1.94039	+	1.62537i
$367$			4.13353i			0.215769i	0.994163	+	0.107884i	$0.0344076\pi$
$367$			4.13353i			0.215769i	−0.994163	+	0.107884i	$0.965592\pi$
$368$	−1.29022	−	0.596298i	−0.0672572	−	0.0310842i
$369$		−	11.3766i		−	0.592243i
$370$	7.22615	+	4.66720i	0.375670	+	0.242636i
$371$		−	36.4800i		−	1.89395i
$372$	10.7309	−	15.3810i	0.556372	−	0.797468i
$373$			26.3503i			1.36437i	0.731182	+	0.682183i	$0.238969\pi$
$373$			26.3503i			1.36437i	−0.731182	+	0.682183i	$0.761031\pi$
$374$	2.04205	−	2.43783i	0.105592	−	0.126057i
$375$	−2.15197	−	2.15197i	−0.111127	−	0.111127i
$376$	−1.50339	−	5.55396i	−0.0775316	−	0.286424i
$377$	46.1531			2.37701
$378$	−4.38447	−	49.6281i	−0.225513	−	2.55260i
$379$			19.2939i			0.991063i	0.868590	+	0.495531i	$0.165027\pi$
$379$			19.2939i			0.991063i	−0.868590	+	0.495531i	$0.834973\pi$
$380$	13.6631	−	2.43317i	0.700904	−	0.124819i
$381$		−	38.2929i		−	1.96181i
$382$	−0.443180	−	0.371229i	−0.0226750	−	0.0189937i
$383$	−18.4674	−	18.4674i	−0.943641	−	0.943641i	0.0548537	−	0.998494i	$-0.482531\pi$
$383$	−18.4674	−	18.4674i	−0.943641	−	0.943641i	−0.998494	+	0.0548537i	$0.982531\pi$
$384$	−28.0864	+	19.9168i	−1.43328	+	1.01638i
$385$	−13.8147	−	13.8147i	−0.704062	−	0.704062i
$386$	−6.45872	+	7.71053i	−0.328740	+	0.392456i
$387$	8.60913	+	8.60913i	0.437626	+	0.437626i
$388$	−6.07513	+	8.70770i	−0.308418	+	0.442067i
$389$	−18.6478	+	18.6478i	−0.945482	+	0.945482i	−0.998589	−	0.0531070i	$-0.983088\pi$
$389$	−18.6478	+	18.6478i	−0.945482	+	0.945482i	0.0531070	+	0.998589i	$0.483088\pi$
$390$	1.97394	+	22.3431i	0.0999541	+	1.13139i
$391$	−0.145139			−0.00733999
$392$	15.2715	−	4.13382i	0.771328	−	0.208789i
$393$	−0.616394	+	0.616394i	−0.0310930	+	0.0310930i
$394$	5.80065	−	0.512467i	0.292233	−	0.0258177i
$395$	−3.56049			−0.179148
$396$	−67.8797	+	12.0882i	−3.41108	+	0.607456i
$397$		−	15.0013i		−	0.752894i	−0.926438	−	0.376447i	$-0.877146\pi$
$397$		−	15.0013i		−	0.752894i	0.926438	−	0.376447i	$-0.122854\pi$
$398$	−21.3906	+	25.5364i	−1.07221	+	1.28002i
$399$	−52.9921	+	52.9921i	−2.65292	+	2.65292i
$400$	−1.38087	−	3.75409i	−0.0690436	−	0.187705i
$401$	23.3639	+	23.3639i	1.16674	+	1.16674i	0.982970	+	0.183767i	$0.0588291\pi$
$401$	23.3639	+	23.3639i	1.16674	+	1.16674i	0.183767	+	0.982970i	$0.441171\pi$
$402$	61.2444	−	5.41073i	3.05459	−	0.269863i
$403$		−	16.0579i		−	0.799900i
$404$	−6.27942	−	35.2612i	−0.312413	−	1.75431i
$405$	8.07942	−	8.07942i	0.401470	−	0.401470i
$406$	28.5398	−	34.0713i	1.41641	−	1.69093i
$407$	4.13549	+	33.2311i	0.204989	+	1.64720i
$408$	−1.75018	+	3.04936i	−0.0866468	+	0.150966i
$409$	0.461293	+	0.461293i	0.0228095	+	0.0228095i	0.718420	−	0.695610i	$-0.244866\pi$
$409$	0.461293	+	0.461293i	0.0228095	+	0.0228095i	−0.695610	+	0.718420i	$0.744866\pi$
$410$	1.96963	+	1.64986i	0.0972729	+	0.0814806i
$411$	−43.7370			−2.15739
$412$	8.38147	−	12.0135i	0.412926	−	0.591861i
$413$	7.00117	−	7.00117i	0.344505	−	0.344505i
$414$	2.41228	+	2.02065i	0.118557	+	0.0993094i
$415$	2.03885	+	2.03885i	0.100083	+	0.100083i
$416$	−9.96506	+	27.7457i	−0.488577	+	1.36034i
$417$	−33.8542			−1.65785
$418$	41.4152	+	34.6915i	2.02568	+	1.69681i
$419$			23.0170i			1.12446i	0.826982	+	0.562228i	$0.190056\pi$
$419$			23.0170i			1.12446i	−0.826982	+	0.562228i	$0.809944\pi$
$420$	17.7148	+	12.3592i	0.864396	+	0.603066i
$421$	−11.4273	−	11.4273i	−0.556932	−	0.556932i	0.371501	−	0.928433i	$-0.378843\pi$
$421$	−11.4273	−	11.4273i	−0.556932	−	0.556932i	−0.928433	+	0.371501i	$0.878843\pi$
$422$	−1.31365	−	14.8693i	−0.0639476	−	0.723827i
$423$			12.7386i			0.619372i
$424$	28.0653	−	7.59695i	1.36297	−	0.368941i
$425$	−0.288821	−	0.288821i	−0.0140099	−	0.0140099i
$426$	2.14768	+	24.3097i	0.104055	+	1.17781i
$427$	28.2332	−	28.2332i	1.36630	−	1.36630i
$428$	2.32235	+	13.0408i	0.112255	+	0.630352i
$429$	−61.7423	+	61.7423i	−2.98095	+	2.98095i
$430$	−2.73900	+	0.241981i	−0.132086	+	0.0116694i
$431$	−23.4348	+	23.4348i	−1.12882	+	1.12882i	−0.138445	+	0.990370i	$0.544210\pi$
$431$	−23.4348	+	23.4348i	−1.12882	+	1.12882i	−0.990370	+	0.138445i	$0.955790\pi$
$432$	37.2676	−	13.7082i	1.79304	−	0.659535i
$433$	4.29979			0.206635			0.103317	−	0.994648i	$-0.467054\pi$
$433$	4.29979			0.206635			0.103317	+	0.994648i	$0.467054\pi$
$434$	−11.8543	−	9.92976i	−0.569025	−	0.476644i
$435$	26.9517			1.29223
$436$	−7.82811	+	11.2203i	−0.374898	+	0.537355i
$437$		−	2.46570i		−	0.117951i
$438$	−3.00063	−	33.9643i	−0.143375	−	1.62288i
$439$	−19.8868	+	19.8868i	−0.949145	+	0.949145i	−0.998768	−	0.0496231i	$-0.984198\pi$
$439$	−19.8868	+	19.8868i	−0.949145	+	0.949145i	0.0496231	+	0.998768i	$0.484198\pi$
$440$	7.75120	−	13.5050i	0.369524	−	0.643826i
$441$	−35.0268			−1.66794
$442$	0.264927	+	2.99872i	0.0126013	+	0.142635i
$443$	25.7261			1.22229			0.611143	−	0.791520i	$-0.290710\pi$
$443$	25.7261			1.22229			0.611143	+	0.791520i	$0.290710\pi$
$444$	−10.9429	−	35.3697i	−0.519327	−	1.67857i
$445$	7.74524			0.367160
$446$	−0.0264283	−	0.299144i	−0.00125142	−	0.0141649i
$447$	33.8382			1.60049
$448$	14.3204	+	24.5136i	0.676575	+	1.15816i
$449$	12.3689	−	12.3689i	0.583726	−	0.583726i	−0.352199	−	0.935925i	$-0.614566\pi$
$449$	12.3689	−	12.3689i	0.583726	−	0.583726i	0.935925	+	0.352199i	$0.114566\pi$
$450$	0.779336	+	8.82135i	0.0367383	+	0.415843i
$451$			10.0020i			0.470975i
$452$	−11.7799	−	8.21851i	−0.554079	−	0.386566i
$453$	25.5458			1.20024
$454$	23.1985	+	19.4322i	1.08876	+	0.911998i
$455$	18.4944			0.867032
$456$	−51.8042	−	29.7330i	−2.42595	−	1.39238i
$457$	11.6738	−	11.6738i	0.546079	−	0.546079i	−0.379225	−	0.925304i	$-0.623809\pi$
$457$	11.6738	−	11.6738i	0.546079	−	0.546079i	0.925304	+	0.379225i	$0.123809\pi$
$458$	−15.2343	+	1.34590i	−0.711854	+	0.0628899i
$459$	2.86718	−	2.86718i	0.133828	−	0.133828i
$460$	−0.699666	+	0.124599i	−0.0326221	+	0.00580944i
$461$	4.98508	−	4.98508i	0.232178	−	0.232178i	−0.581423	−	0.813601i	$-0.697504\pi$
$461$	4.98508	−	4.98508i	0.232178	−	0.232178i	0.813601	+	0.581423i	$0.197504\pi$
$462$	7.39985	+	83.7594i	0.344272	+	3.89684i
$463$	−17.5521	−	17.5521i	−0.815717	−	0.815717i	0.169767	−	0.985484i	$-0.445698\pi$
$463$	−17.5521	−	17.5521i	−0.815717	−	0.815717i	−0.985484	+	0.169767i	$0.945698\pi$
$464$	32.1556	+	14.8613i	1.49279	+	0.689920i
$465$		−	9.37720i		−	0.434857i
$466$	−2.43577	−	27.5706i	−0.112835	−	1.27718i
$467$	2.77467	+	2.77467i	0.128397	+	0.128397i	0.768385	−	0.639988i	$-0.221061\pi$
$467$	2.77467	+	2.77467i	0.128397	+	0.128397i	−0.639988	+	0.768385i	$0.721061\pi$
$468$	37.3455	−	53.5286i	1.72629	−	2.47436i
$469$		−	50.6948i		−	2.34087i
$470$	−2.20542	−	1.84737i	−0.101729	−	0.0852129i
$471$	−9.94591			−0.458284
$472$	6.84423	+	3.92824i	0.315031	+	0.180812i
$473$	−7.56888	−	7.56888i	−0.348017	−	0.348017i
$474$	11.7474	+	9.84017i	0.539574	+	0.451974i
$475$	4.90665	−	4.90665i	0.225133	−	0.225133i
$476$	2.37755	+	1.65875i	0.108975	+	0.0760289i
$477$	−64.3707			−2.94733
$478$	−8.51947	−	7.13633i	−0.389671	−	0.326408i
$479$	20.0930	+	20.0930i	0.918074	+	0.918074i	0.996889	−	0.0788157i	$-0.0251139\pi$
$479$	20.0930	+	20.0930i	0.918074	+	0.918074i	−0.0788157	+	0.996889i	$0.525114\pi$
$480$	−5.81922	+	16.2024i	−0.265610	+	0.739536i
$481$	−25.0123	−	19.4759i	−1.14046	−	0.888024i
$482$	12.2969	−	14.6803i	0.560109	−	0.668667i
$483$	2.71364	−	2.71364i	0.123475	−	0.123475i
$484$	38.0185	−	6.77045i	1.72811	−	0.307748i
$485$			5.30875i			0.241058i
$486$	−7.03202	+	0.621254i	−0.318979	+	0.0281807i
$487$	18.5020	+	18.5020i	0.838405	+	0.838405i	0.988649	−	0.150244i	$-0.0480060\pi$
$487$	18.5020	+	18.5020i	0.838405	+	0.838405i	−0.150244	+	0.988649i	$0.548006\pi$
$488$	27.6003	+	15.8412i	1.24941	+	0.717096i
$489$	−24.7540	+	24.7540i	−1.11942	+	1.11942i
$490$	5.07965	−	6.06416i	0.229475	−	0.273951i
$491$			26.8160i			1.21019i	0.796153	+	0.605095i	$0.206865\pi$
$491$			26.8160i			1.21019i	−0.796153	+	0.605095i	$0.793135\pi$
$492$	−1.93878	−	10.8869i	−0.0874070	−	0.490821i
$493$	3.61725			0.162913
$494$	−50.9440	+	4.50072i	−2.29208	+	0.202497i
$495$	−24.3767	+	24.3767i	−1.09565	+	1.09565i
$496$	5.17065	−	11.1878i	0.232169	−	0.502347i
$497$	20.1223			0.902608
$498$	−1.09211	−	12.3617i	−0.0489387	−	0.553940i
$499$	−9.70913	+	9.70913i	−0.434640	+	0.434640i	−0.890203	−	0.455563i	$-0.849438\pi$
$499$	−9.70913	+	9.70913i	−0.434640	+	0.434640i	0.455563	+	0.890203i	$0.349438\pi$
$500$	−1.64025	−	1.14436i	−0.0733544	−	0.0511774i
$501$	−16.2321	−	16.2321i	−0.725197	−	0.725197i
$502$	3.66978	−	4.38104i	0.163790	−	0.195535i
$503$	0.00277987	+	0.00277987i	0.000123948	+	0.000123948i	0.707169	−	0.707045i	$-0.249972\pi$
$503$	0.00277987	+	0.00277987i	0.000123948	+	0.000123948i	−0.707045	+	0.707169i	$0.749972\pi$
$504$	−16.4227	−	60.6700i	−0.731523	−	2.70245i
$505$	−12.6628	−	12.6628i	−0.563489	−	0.563489i
$506$	−2.12080	−	1.77649i	−0.0942812	−	0.0789746i
$507$		−	43.0941i		−	1.91388i
$508$	−4.41205	−	24.7753i	−0.195753	−	1.09922i
$509$		−	7.23471i		−	0.320673i	−0.987062	−	0.160337i	$-0.948742\pi$
$509$		−	7.23471i		−	0.320673i	0.987062	−	0.160337i	$-0.0512579\pi$
$510$	0.154707	+	1.75114i	0.00685055	+	0.0775418i
$511$	−28.1138			−1.24368
$512$	−15.8769	+	16.1221i	−0.701668	+	0.712504i
$513$	48.7092	+	48.7092i	2.15056	+	2.15056i
$514$	−5.00473	+	5.97473i	−0.220749	+	0.263534i
$515$		−	7.32415i		−	0.322740i
$516$	9.70572	+	6.77142i	0.427270	+	0.298095i
$517$		−	11.1994i		−	0.492548i
$518$	−29.8445	+	6.42130i	−1.31129	+	0.282136i
$519$		−	27.6379i		−	1.21317i
$520$	3.85146	+	14.2284i	0.168898	+	0.623956i
$521$		−	14.1908i		−	0.621711i	−0.950457	−	0.310856i	$-0.899384\pi$
$521$		−	14.1908i		−	0.621711i	0.950457	−	0.310856i	$-0.100616\pi$
$522$	−60.1205	−	50.3599i	−2.63140	−	2.20419i
$523$	20.3978	+	20.3978i	0.891932	+	0.891932i	0.994705	−	0.102773i	$-0.0327714\pi$
$523$	20.3978	+	20.3978i	0.891932	+	0.891932i	−0.102773	+	0.994705i	$0.532771\pi$
$524$	−0.327783	+	0.469823i	−0.0143193	+	0.0205243i
$525$	10.8001			0.471353
$526$	−5.58073	+	0.493039i	−0.243332	+	0.0214975i
$527$		−	1.25854i		−	0.0548227i
$528$	−62.8980	+	23.1358i	−2.73728	+	1.00686i
$529$		−	22.8737i		−	0.994510i
$530$	9.33515	−	11.1445i	0.405493	−	0.484084i
$531$	−12.3539	−	12.3539i	−0.536113	−	0.536113i
$532$	−28.1798	+	40.3912i	−1.22175	+	1.75118i
$533$	−6.69508	−	6.69508i	−0.289996	−	0.289996i
$534$	−25.5543	−	21.4056i	−1.10584	−	0.926311i
$535$	4.68316	+	4.68316i	0.202471	+	0.202471i
$536$	39.0013	−	10.5572i	1.68460	−	0.456001i
$537$	30.1660	−	30.1660i	1.30176	−	1.30176i
$538$	−40.3470	+	3.56452i	−1.73948	+	0.153677i
$539$	30.7945			1.32641
$540$	11.3603	−	16.2831i	0.488869	−	0.700714i
$541$	15.6275	−	15.6275i	0.671877	−	0.671877i	−0.286271	−	0.958149i	$-0.592416\pi$
$541$	15.6275	−	15.6275i	0.671877	−	0.671877i	0.958149	+	0.286271i	$0.0924158\pi$
$542$	−2.29779	−	26.0088i	−0.0986986	−	1.11718i
$543$	−44.8296			−1.92382
$544$	−0.781012	+	2.17457i	−0.0334856	+	0.0932338i
$545$			6.84059i			0.293019i
$546$	−61.0198	−	51.1132i	−2.61141	−	2.18744i
$547$	−22.6313	+	22.6313i	−0.967644	+	0.967644i	−0.999493	−	0.0318485i	$-0.989861\pi$
$547$	−22.6313	+	22.6313i	−0.967644	+	0.967644i	0.0318485	+	0.999493i	$0.489861\pi$
$548$	−28.2975	+	5.03931i	−1.20881	+	0.215269i
$549$	−49.8188	−	49.8188i	−2.12621	−	2.12621i
$550$	−0.685168	−	7.75546i	−0.0292157	−	0.330694i
$551$			61.4519i			2.61794i
$552$	2.65281	+	1.52258i	0.112911	+	0.0648052i
$553$	8.93450	−	8.93450i	0.379934	−	0.379934i
$554$	8.27007	+	6.92742i	0.351362	+	0.294318i
$555$	−14.6062	−	11.3732i	−0.620000	−	0.482765i
$556$	−21.9034	+	3.90063i	−0.928911	+	0.165423i
$557$	26.6304	+	26.6304i	1.12836	+	1.12836i	0.990443	+	0.137922i	$0.0440422\pi$
$557$	26.6304	+	26.6304i	1.12836	+	1.12836i	0.137922	+	0.990443i	$0.455958\pi$
$558$	−17.5215	+	20.9175i	−0.741746	+	0.885508i
$559$	10.1328			0.428574
$560$	12.8854	+	5.95522i	0.544507	+	0.251654i
$561$	−4.83905	+	4.83905i	−0.204305	+	0.204305i
$562$	−26.6251	+	31.7854i	−1.12311	+	1.34079i
$563$	−1.70293	−	1.70293i	−0.0717699	−	0.0717699i	0.670311	−	0.742081i	$-0.266161\pi$
$563$	−1.70293	−	1.70293i	−0.0717699	−	0.0717699i	−0.742081	+	0.670311i	$0.766161\pi$
$564$	2.17088	+	12.1903i	0.0914107	+	0.513304i
$565$	−7.18174			−0.302138
$566$	−16.1953	+	19.3343i	−0.680741	+	0.812679i
$567$			40.5481i			1.70286i
$568$	4.19046	+	15.4808i	0.175828	+	0.649558i
$569$	27.6253	+	27.6253i	1.15811	+	1.15811i	0.984881	+	0.173234i	$0.0554215\pi$
$569$	27.6253	+	27.6253i	1.15811	+	1.15811i	0.173234	+	0.984881i	$0.444578\pi$
$570$	−29.7494	+	2.62825i	−1.24606	+	0.110085i
$571$		−	41.6395i		−	1.74256i	−0.490788	−	0.871279i	$-0.663291\pi$
$571$		−	41.6395i		−	1.74256i	0.490788	−	0.871279i	$-0.336709\pi$
$572$	−32.8330	+	47.0607i	−1.37282	+	1.96771i
$573$	0.879704	+	0.879704i	0.0367502	+	0.0367502i
$574$	−9.08252	+	0.802410i	−0.379097	+	0.0334919i
$575$	−0.251261	+	0.251261i	−0.0104783	+	0.0104783i
$576$	43.2555	−	25.2690i	1.80231	−	1.05288i
$577$	−3.70088	+	3.70088i	−0.154070	+	0.154070i	−0.779933	−	0.625863i	$-0.784747\pi$
$577$	−3.70088	+	3.70088i	−0.154070	+	0.154070i	0.625863	+	0.779933i	$0.284747\pi$
$578$	−2.09499	−	23.7133i	−0.0871401	−	0.986344i
$579$	15.3053	−	15.3053i	0.636065	−	0.636065i
$580$	17.4375	−	3.10533i	0.724055	−	0.128942i
$581$	−10.2323			−0.424509
$582$	14.6718	−	17.5155i	0.608167	−	0.726040i
$583$	56.5927			2.34383
$584$	−5.85469	−	21.6289i	−0.242269	−	0.895011i
$585$		−	32.6343i		−	1.34926i
$586$	29.3222	−	2.59051i	1.21129	−	0.107013i
$587$	25.6983	−	25.6983i	1.06068	−	1.06068i	0.0626456	−	0.998036i	$-0.480046\pi$
$587$	25.6983	−	25.6983i	1.06068	−	1.06068i	0.998036	−	0.0626456i	$-0.0199538\pi$
$588$	−33.5192	+	5.96920i	−1.38231	+	0.246166i
$589$	21.3807			0.880977
$590$	3.93040	−	0.347237i	0.161812	−	0.0142955i
$591$	−12.5314			−0.515474
$592$	−11.1552	−	21.6232i	−0.458477	−	0.888706i
$593$	3.32519			0.136549			0.0682746	−	0.997667i	$-0.478251\pi$
$593$	3.32519			0.136549			0.0682746	+	0.997667i	$0.478251\pi$
$594$	76.9899	−	6.80179i	3.15893	−	0.279081i
$595$	1.44950			0.0594238
$596$	21.8931	−	3.89878i	0.896775	−	0.159700i
$597$	50.6893	−	50.6893i	2.07458	−	2.07458i
$598$	2.60875	−	0.230474i	0.106680	−	0.00942480i
$599$			14.0840i			0.575457i	0.957712	+	0.287728i	$0.0929000\pi$
$599$			14.0840i			0.575457i	−0.957712	+	0.287728i	$0.907100\pi$
$600$	2.24911	+	8.30885i	0.0918195	+	0.339207i
$601$	4.48402			0.182907			0.0914534	−	0.995809i	$-0.470849\pi$
$601$	4.48402			0.182907			0.0914534	+	0.995809i	$0.470849\pi$
$602$	6.26588	−	7.48031i	0.255378	−	0.304875i
$603$	−89.4535			−3.64283
$604$	16.5279	−	2.94334i	0.672512	−	0.119763i
$605$	13.6530	−	13.6530i	0.555075	−	0.555075i
$606$	6.78287	+	76.7757i	0.275535	+	3.11880i
$607$	10.5943	−	10.5943i	0.430007	−	0.430007i	−0.458623	−	0.888631i	$-0.651657\pi$
$607$	10.5943	−	10.5943i	0.430007	−	0.430007i	0.888631	+	0.458623i	$0.151657\pi$
$608$	−36.9427	−	13.2683i	−1.49823	−	0.538099i
$609$	−67.6310	+	67.6310i	−2.74055	+	2.74055i
$610$	15.8499	−	1.40028i	0.641743	−	0.0566958i
$611$	7.49659	+	7.49659i	0.303280	+	0.303280i
$612$	2.92695	−	4.19531i	0.118315	−	0.169585i
$613$			34.8028i			1.40567i	0.711351	+	0.702837i	$0.248084\pi$
$613$			34.8028i			1.40567i	−0.711351	+	0.702837i	$0.751916\pi$
$614$	35.8575	−	3.16789i	1.44709	−	0.127846i
$615$	−3.90967	−	3.90967i	−0.157653	−	0.157653i
$616$	14.4383	+	53.3392i	0.581735	+	2.14910i
$617$		−	15.9571i		−	0.642410i	−0.947010	−	0.321205i	$-0.895912\pi$
$617$		−	15.9571i		−	0.642410i	0.947010	−	0.321205i	$-0.104088\pi$
$618$	−20.2418	+	24.1650i	−0.814245	+	0.972059i
$619$	−43.2205			−1.73718			−0.868589	−	0.495533i	$-0.834973\pi$
$619$	−43.2205			−1.73718			−0.868589	+	0.495533i	$0.834973\pi$
$620$	−1.08043	−	6.06698i	−0.0433910	−	0.243656i
$621$	−2.49432	−	2.49432i	−0.100093	−	0.100093i
$622$	6.68814	−	7.98441i	0.268170	−	0.320146i
$623$	−19.4355	+	19.4355i	−0.778666	+	0.778666i
$624$	26.6158	−	57.5889i	1.06548	−	2.30540i
$625$	−1.00000			−0.0400000
$626$	−7.61090	+	9.08601i	−0.304193	+	0.363150i
$627$	−82.2085	−	82.2085i	−3.28309	−	3.28309i
$628$	−6.43494	+	1.14595i	−0.256782	+	0.0457285i
$629$	−1.96034	−	1.52642i	−0.0781638	−	0.0608625i
$630$	−24.0914	−	20.1802i	−0.959826	−	0.803998i
$631$	19.4219	−	19.4219i	0.773173	−	0.773173i	−0.205487	−	0.978660i	$-0.565878\pi$
$631$	19.4219	−	19.4219i	0.773173	−	0.773173i	0.978660	+	0.205487i	$0.0658778\pi$
$632$	8.73422	+	5.01301i	0.347429	+	0.199407i
$633$			32.1229i			1.27677i
$634$	0.169733	+	1.92122i	0.00674097	+	0.0763014i
$635$	−8.89719	−	8.89719i	−0.353074	−	0.353074i
$636$	−61.6001	+	10.9699i	−2.44260	+	0.434986i
$637$	−20.6131	+	20.6131i	−0.816720	+	0.816720i
$638$	52.8561	+	44.2749i	2.09259	+	1.75286i
$639$		−	35.5067i		−	1.40463i
$640$	−1.89817	+	11.1533i	−0.0750320	+	0.440874i
$641$	25.8888			1.02255			0.511273	−	0.859419i	$-0.329174\pi$
$641$	25.8888			1.02255			0.511273	+	0.859419i	$0.329174\pi$
$642$	−2.50854	−	28.3943i	−0.0990043	−	1.12064i
$643$	19.1649	−	19.1649i	0.755791	−	0.755791i	−0.219762	−	0.975553i	$-0.570528\pi$
$643$	19.1649	−	19.1649i	0.755791	−	0.755791i	0.975553	+	0.219762i	$0.0705282\pi$
$644$	1.44304	−	2.06836i	0.0568638	−	0.0815049i
$645$	5.91720			0.232990
$646$	−3.99273	+	0.352744i	−0.157092	+	0.0138785i
$647$	1.55532	−	1.55532i	0.0611461	−	0.0611461i	−0.675873	−	0.737019i	$-0.736233\pi$
$647$	1.55532	−	1.55532i	0.0611461	−	0.0611461i	0.737019	+	0.675873i	$0.236233\pi$
$648$	−31.1950	+	8.44413i	−1.22546	+	0.331717i
$649$	10.8612	+	10.8612i	0.426338	+	0.426338i
$650$	5.64995	+	4.73268i	0.221609	+	0.185631i
$651$	23.5306	+	23.5306i	0.922238	+	0.922238i
$652$	−13.1636	+	18.8678i	−0.515525	+	0.738920i
$653$	13.8307	+	13.8307i	0.541236	+	0.541236i	0.923891	−	0.382655i	$-0.124990\pi$
$653$	13.8307	+	13.8307i	0.541236	+	0.541236i	−0.382655	+	0.923891i	$0.624990\pi$
$654$	18.9054	−	22.5696i	0.739259	−	0.882540i
$655$			0.286433i			0.0111919i
$656$	−2.50875	−	6.82039i	−0.0979504	−	0.266292i
$657$			49.6082i			1.93540i
$658$	10.1699	−	0.898471i	0.396462	−	0.0350261i
$659$	0.389577			0.0151758			0.00758789	−	0.999971i	$-0.497585\pi$
$659$	0.389577			0.0151758			0.00758789	+	0.999971i	$0.497585\pi$
$660$	−19.1732	+	27.4817i	−0.746317	+	1.06972i
$661$	−8.61627	−	8.61627i	−0.335134	−	0.335134i	0.519398	−	0.854532i	$-0.326156\pi$
$661$	−8.61627	−	8.61627i	−0.335134	−	0.335134i	−0.854532	+	0.519398i	$0.826156\pi$
$662$	15.0746	+	12.6272i	0.585891	+	0.490772i
$663$		−	6.47829i		−	0.251596i
$664$	−2.13088	−	7.87208i	−0.0826942	−	0.305496i
$665$			24.6249i			0.954914i
$666$	11.3307	+	52.6620i	0.439055	+	2.04061i
$667$		−	3.14685i		−	0.121846i
$668$	−12.3723	−	8.63182i	−0.478699	−	0.333975i
$669$			0.646255i			0.0249857i
$670$	12.9727	−	15.4870i	0.501179	−	0.598315i
$671$	43.7991	+	43.7991i	1.69085	+	1.69085i
$672$	−26.0550	−	55.2599i	−1.00509	−	2.13170i
$673$	−27.8608			−1.07395			−0.536977	−	0.843597i	$-0.680434\pi$
$673$	−27.8608			−1.07395			−0.536977	+	0.843597i	$0.680434\pi$
$674$	−2.38939	−	27.0456i	−0.0920357	−	1.04176i
$675$		−	9.92719i		−	0.382098i
$676$	−4.96524	−	27.8816i	−0.190971	−	1.07237i
$677$			5.81128i			0.223346i	0.993745	+	0.111673i	$0.0356209\pi$
$677$			5.81128i			0.223346i	−0.993745	+	0.111673i	$0.964379\pi$
$678$	23.6952	+	19.8482i	0.910007	+	0.762267i
$679$	−13.3215	−	13.3215i	−0.511231	−	0.511231i
$680$	0.301858	+	1.11515i	0.0115757	+	0.0427641i
$681$	−46.0486	−	46.0486i	−1.76459	−	1.76459i
$682$	15.4044	−	18.3900i	0.589865	−	0.704190i
$683$	−5.50713	−	5.50713i	−0.210724	−	0.210724i	0.593851	−	0.804575i	$-0.297607\pi$
$683$	−5.50713	−	5.50713i	−0.210724	−	0.210724i	−0.804575	+	0.593851i	$0.797607\pi$
$684$	71.2722	+	49.7247i	2.72516	+	1.90127i
$685$	−10.1621	+	10.1621i	−0.388274	+	0.388274i
$686$	−0.621152	−	7.03085i	−0.0237157	−	0.268439i
$687$	32.9115			1.25565
$688$	7.05972	+	3.26278i	0.269149	+	0.124392i
$689$	−37.8818	+	37.8818i	−1.44318	+	1.44318i
$690$	1.52341	−	0.134588i	0.0579954	−	0.00512369i
$691$	−20.1854			−0.767890			−0.383945	−	0.923356i	$-0.625435\pi$
$691$	−20.1854			−0.767890			−0.383945	+	0.923356i	$0.625435\pi$
$692$	−3.18440	−	17.8815i	−0.121053	−	0.679754i
$693$		−	122.339i		−	4.64727i
$694$	−13.0596	+	15.5908i	−0.495737	+	0.591819i
$695$	−7.86586	+	7.86586i	−0.298369	+	0.298369i
$696$	−66.1150	−	37.9467i	−2.50608	−	1.43837i
$697$	−0.524727	−	0.524727i	−0.0198755	−	0.0198755i
$698$	−4.99103	+	0.440940i	−0.188913	+	0.0166898i
$699$			59.5622i			2.25285i
$700$	6.98756	−	1.24437i	0.264105	−	0.0470326i
$701$	30.6020	−	30.6020i	1.15582	−	1.15582i	0.170456	−	0.985365i	$-0.445476\pi$
$701$	30.6020	−	30.6020i	1.15582	−	1.15582i	0.985365	−	0.170456i	$-0.0545241\pi$
$702$	−46.9822	+	56.0881i	−1.77323	+	2.11691i
$703$	25.9317	−	33.3033i	0.978034	−	1.25606i
$704$	−38.0289	+	22.2157i	−1.43327	+	0.837287i
$705$	4.37773	+	4.37773i	0.164875	+	0.164875i
$706$	−2.41593	−	2.02371i	−0.0909249	−	0.0761632i
$707$	63.5509			2.39008
$708$	−13.9275	−	9.71683i	−0.523427	−	0.365181i
$709$	10.3275	−	10.3275i	0.387856	−	0.387856i	−0.486066	−	0.873922i	$-0.661569\pi$
$709$	10.3275	−	10.3275i	0.387856	−	0.387856i	0.873922	+	0.486066i	$0.161569\pi$
$710$	6.14725	+	5.14925i	0.230702	+	0.193248i
$711$	−15.7654	−	15.7654i	−0.591247	−	0.591247i
$712$	−18.9998	−	10.9049i	−0.712048	−	0.408680i
$713$	−1.09487			−0.0410032
$714$	−4.78243	−	4.00600i	−0.178978	−	0.149921i
$715$			28.6911i			1.07299i
$716$	16.0415	−	22.9929i	0.599499	−	0.859283i
$717$	16.9110	+	16.9110i	0.631553	+	0.631553i
$718$	0.796089	+	9.01098i	0.0297098	+	0.336287i
$719$		−	28.4515i		−	1.06106i	−0.847665	−	0.530532i	$-0.821992\pi$
$719$		−	28.4515i		−	1.06106i	0.847665	−	0.530532i	$-0.178008\pi$
$720$	10.5083	−	22.7369i	0.391620	−	0.847353i
$721$	18.3788	+	18.3788i	0.684462	+	0.684462i
$722$	−3.62795	−	41.0650i	−0.135018	−	1.52828i
$723$	−29.1401	+	29.1401i	−1.08373	+	1.08373i
$724$	−29.0044	+	5.16520i	−1.07794	+	0.191963i
$725$	6.26210	−	6.26210i	0.232569	−	0.232569i
$726$	−82.7794	+	7.31327i	−3.07223	+	0.271421i
$727$	−9.33076	+	9.33076i	−0.346059	+	0.346059i	−0.858639	−	0.512580i	$-0.828690\pi$
$727$	−9.33076	+	9.33076i	−0.346059	+	0.346059i	0.512580	+	0.858639i	$0.328690\pi$
$728$	−45.3686	−	26.0393i	−1.68147	−	0.965080i
$729$	−19.0865			−0.706906
$730$	−8.58862	−	7.19426i	−0.317879	−	0.266271i
$731$	0.794162			0.0293731
$732$	−56.1644	−	39.1844i	−2.07590	−	1.44830i
$733$		−	14.3359i		−	0.529510i	−0.964316	−	0.264755i	$-0.914709\pi$
$733$		−	14.3359i		−	0.529510i	0.964316	−	0.264755i	$-0.0852910\pi$
$734$	−0.514443	−	5.82302i	−0.0189885	−	0.214931i
$735$	−12.0373	+	12.0373i	−0.444001	+	0.444001i
$736$	1.89178	+	0.679445i	0.0697318	+	0.0250447i
$737$	78.6447			2.89692
$738$	1.41589	+	16.0265i	0.0521196	+	0.589945i
$739$	25.1747			0.926066			0.463033	−	0.886341i	$-0.346761\pi$
$739$	25.1747			0.926066			0.463033	+	0.886341i	$0.346761\pi$
$740$	−10.7605	−	5.67547i	−0.395565	−	0.208634i
$741$	110.057			4.04304
$742$	4.54016	+	51.3904i	0.166675	+	1.88660i
$743$	−41.7006			−1.52985			−0.764923	−	0.644122i	$-0.777223\pi$
$743$	−41.7006			−1.52985			−0.764923	+	0.644122i	$0.777223\pi$
$744$	−13.2027	+	23.0032i	−0.484033	+	0.843336i
$745$	7.86215	−	7.86215i	0.288047	−	0.288047i
$746$	−3.27945	−	37.1203i	−0.120069	−	1.35907i
$747$			18.0554i			0.660614i
$748$	−2.57329	+	3.68838i	−0.0940886	+	0.134861i
$749$	−23.5033			−0.858793
$750$	3.29936	+	2.76371i	0.120476	+	0.100916i
$751$	12.5103			0.456509			0.228254	−	0.973602i	$-0.426698\pi$
$751$	12.5103			0.456509			0.228254	+	0.973602i	$0.426698\pi$
$752$	2.80909	+	7.63691i	0.102437	+	0.278489i
$753$	−8.69629	+	8.69629i	−0.316910	+	0.316910i
$754$	−65.0171	+	5.74404i	−2.36778	+	0.209185i
$755$	5.93544	−	5.93544i	0.216013	−	0.216013i
$756$	12.3531	+	69.3668i	0.449276	+	2.52285i
$757$	10.8024	−	10.8024i	0.392620	−	0.392620i	−0.483000	−	0.875620i	$-0.660453\pi$
$757$	10.8024	−	10.8024i	0.392620	−	0.392620i	0.875620	+	0.483000i	$0.160453\pi$
$758$	−2.40125	−	27.1799i	−0.0872173	−	0.987218i
$759$	4.20976	+	4.20976i	0.152805	+	0.152805i
$760$	−18.9448	+	5.12814i	−0.687200	+	0.186017i
$761$			19.3432i			0.701189i	0.936527	+	0.350595i	$0.114021\pi$
$761$			19.3432i			0.701189i	−0.936527	+	0.350595i	$0.885979\pi$
$762$	4.76579	+	53.9443i	0.172646	+	1.95420i
$763$	−17.1654	−	17.1654i	−0.621429	−	0.621429i
$764$	0.670521	+	0.467804i	0.0242586	+	0.0169246i
$765$		−	2.55772i		−	0.0924744i
$766$	28.3139	+	23.7172i	1.02302	+	0.856936i
$767$	−14.5404			−0.525023
$768$	37.0873	−	31.5529i	1.33827	−	1.13857i
$769$	7.29639	+	7.29639i	0.263114	+	0.263114i	0.826318	−	0.563204i	$-0.190431\pi$
$769$	7.29639	+	7.29639i	0.263114	+	0.263114i	−0.563204	+	0.826318i	$0.690431\pi$
$770$	21.1804	+	17.7418i	0.763290	+	0.639370i
$771$	11.8597	−	11.8597i	0.427118	−	0.427118i
$772$	8.13895	−	11.6659i	0.292927	−	0.419863i
$773$	16.5755			0.596178			0.298089	−	0.954538i	$-0.403651\pi$
$773$	16.5755			0.596178			0.298089	+	0.954538i	$0.403651\pi$
$774$	−13.1994	−	11.0564i	−0.474441	−	0.397416i
$775$	−2.17875	−	2.17875i	−0.0782630	−	0.0782630i
$776$	7.47447	−	13.0229i	0.268318	−	0.467493i
$777$	65.1913	−	8.11283i	2.33872	−	0.291046i
$778$	23.9488	−	28.5905i	0.858607	−	1.02502i
$779$	8.91435	−	8.91435i	0.319390	−	0.319390i
$780$	−5.56147	−	31.2297i	−0.199133	−	1.11820i
$781$			31.2164i			1.11701i
$782$	0.204461	−	0.0180634i	0.00731152	−	0.000645947i
$783$	62.1650	+	62.1650i	2.22160	+	2.22160i
$784$	−20.9989	+	7.72406i	−0.749961	+	0.275859i
$785$	−2.31089	+	2.31089i	−0.0824791	+	0.0824791i
$786$	0.791617	−	0.945045i	0.0282360	−	0.0337087i
$787$		−	17.9684i		−	0.640503i	−0.947333	−	0.320252i	$-0.896233\pi$
$787$		−	17.9684i		−	0.640503i	0.947333	−	0.320252i	$-0.103767\pi$
$788$	−8.10775	+	1.44385i	−0.288827	+	0.0514351i
$789$	12.0563			0.429217
$790$	5.01576	−	0.443125i	0.178453	−	0.0157657i
$791$	18.0215	−	18.0215i	0.640769	−	0.640769i
$792$	94.1195	−	25.4770i	3.34439	−	0.905288i
$793$	−58.6361			−2.08223
$794$	1.86701	+	21.1328i	0.0662575	+	0.749973i
$795$	−22.1216	+	22.1216i	−0.784571	+	0.784571i
$796$	26.9553	−	38.6360i	0.955405	−	1.36942i
$797$	−5.16043	−	5.16043i	−0.182792	−	0.182792i	0.609779	−	0.792571i	$-0.291258\pi$
$797$	−5.16043	−	5.16043i	−0.182792	−	0.182792i	−0.792571	+	0.609779i	$0.791258\pi$
$798$	68.0562	−	81.2465i	2.40916	−	2.87610i
$799$	0.587546	+	0.587546i	0.0207859	+	0.0207859i
$800$	2.41249	+	5.11663i	0.0852944	+	0.180900i
$801$	34.2948	+	34.2948i	1.21175	+	1.21175i
$802$	−35.8211	−	30.0055i	−1.26489	−	1.05953i
$803$		−	43.6140i		−	1.53910i
$804$	−85.6032	+	15.2445i	−3.01899	+	0.537631i
$805$		−	1.26100i		−	0.0444445i
$806$	1.99850	+	22.6212i	0.0703942	+	0.796797i
$807$	87.1637			3.06831
$808$	13.2345	+	48.8919i	0.465586	+	1.72001i
$809$	−11.4336	−	11.4336i	−0.401985	−	0.401985i	0.476947	−	0.878932i	$-0.341743\pi$
$809$	−11.4336	−	11.4336i	−0.401985	−	0.401985i	−0.878932	+	0.476947i	$0.841743\pi$
$810$	−10.3762	+	12.3872i	−0.364581	+	0.435243i
$811$		−	15.3487i		−	0.538964i	−0.963005	−	0.269482i	$-0.913147\pi$
$811$		−	15.3487i		−	0.538964i	0.963005	−	0.269482i	$-0.0868525\pi$
$812$	−35.9645	+	51.5491i	−1.26210	+	1.80902i
$813$			56.1882i			1.97061i
$814$	−9.96159	−	46.2988i	−0.349154	−	1.62277i
$815$			11.5030i			0.402931i
$816$	2.08601	−	4.51353i	0.0730251	−	0.158005i
$817$			13.4917i			0.472014i
$818$	−0.707246	−	0.592425i	−0.0247283	−	0.0207136i
$819$	81.8907	+	81.8907i	2.86149	+	2.86149i
$820$	−2.98000	−	2.07907i	−0.104066	−	0.0726041i
$821$	48.9359			1.70788			0.853938	−	0.520375i	$-0.174208\pi$
$821$	48.9359			1.70788			0.853938	+	0.520375i	$0.174208\pi$
$822$	61.6135	−	5.44334i	2.14902	−	0.189858i
$823$			38.8266i			1.35341i	0.736254	+	0.676705i	$0.236593\pi$
$823$			38.8266i			1.35341i	−0.736254	+	0.676705i	$0.763407\pi$
$824$	−10.3121	+	17.9668i	−0.359238	+	0.625904i
$825$			16.7545i			0.583317i
$826$	−8.99139	+	10.7341i	−0.312850	+	0.373486i
$827$	9.26744	+	9.26744i	0.322260	+	0.322260i	0.849634	−	0.527373i	$-0.176823\pi$
$827$	9.26744	+	9.26744i	0.322260	+	0.322260i	−0.527373	+	0.849634i	$0.676823\pi$
$828$	−3.64973	−	2.54632i	−0.126837	−	0.0884906i
$829$	11.0440	+	11.0440i	0.383572	+	0.383572i	0.872387	−	0.488815i	$-0.162571\pi$
$829$	11.0440	+	11.0440i	0.383572	+	0.383572i	−0.488815	+	0.872387i	$0.662571\pi$
$830$	−3.12592	−	2.61843i	−0.108502	−	0.0908871i
$831$	−16.4160	−	16.4160i	−0.569463	−	0.569463i
$832$	10.5849	−	40.3263i	0.366966	−	1.39806i
$833$	−1.61555	+	1.61555i	−0.0559755	+	0.0559755i
$834$	47.6913	−	4.21336i	1.65141	−	0.145897i
$835$	−7.54291			−0.261033
$836$	−62.6603	−	43.7164i	−2.16715	−	1.51196i
$837$	21.6289	−	21.6289i	0.747603	−	0.747603i
$838$	−2.86461	−	32.4247i	−0.0989564	−	1.12009i
$839$	9.29548			0.320916			0.160458	−	0.987043i	$-0.448703\pi$
$839$	9.29548			0.320916			0.160458	+	0.987043i	$0.448703\pi$
$840$	−26.4935	−	15.2060i	−0.914114	−	0.524656i
$841$			49.4278i			1.70441i
$842$	17.5201	+	14.6757i	0.603783	+	0.505759i
$843$	63.0936	−	63.0936i	2.17306	−	2.17306i
$844$	3.70115	+	20.7833i	0.127399	+	0.715391i
$845$	−10.0127	−	10.0127i	−0.344448	−	0.344448i
$846$	−1.58540	−	17.9452i	−0.0545070	−	0.616968i
$847$			68.5204i			2.35439i
$848$	−38.5909	+	14.1949i	−1.32522	+	0.487456i
$849$	38.3782	−	38.3782i	1.31714	−	1.31714i
$850$	0.442815	+	0.370924i	0.0151884	+	0.0127226i
$851$	−1.32792	+	1.70541i	−0.0455205	+	0.0584606i
$852$	−6.05099	−	33.9784i	−0.207303	−	1.16408i
$853$	25.7372	+	25.7372i	0.881224	+	0.881224i	0.993659	−	0.112435i	$-0.0358651\pi$
$853$	25.7372	+	25.7372i	0.881224	+	0.881224i	−0.112435	+	0.993659i	$0.535865\pi$
$854$	−36.2590	+	43.2866i	−1.24076	+	1.48124i
$855$	43.4519			1.48602
$856$	−4.89456	−	18.0819i	−0.167293	−	0.618027i
$857$	−26.9222	+	26.9222i	−0.919646	+	0.919646i	−0.997003	−	0.0773577i	$-0.975352\pi$
$857$	−26.9222	+	26.9222i	−0.919646	+	0.919646i	0.0773577	+	0.997003i	$0.475352\pi$
$858$	79.2938	−	94.6622i	2.70705	−	3.23171i
$859$	3.03404	+	3.03404i	0.103520	+	0.103520i	0.756970	−	0.653450i	$-0.226679\pi$
$859$	3.03404	+	3.03404i	0.103520	+	0.103520i	−0.653450	+	0.756970i	$0.726679\pi$
$860$	3.82839	−	0.681771i	0.130547	−	0.0232482i
$861$	19.6214			0.668697
$862$	30.0966	−	35.9298i	1.02510	−	1.22378i
$863$			20.8201i			0.708724i	0.935108	+	0.354362i	$0.115302\pi$
$863$			20.8201i			0.708724i	−0.935108	+	0.354362i	$0.884698\pi$
$864$	−50.7937	+	23.9492i	−1.72804	+	0.814770i
$865$	−6.42154	−	6.42154i	−0.218339	−	0.218339i
$866$	−6.05722	+	0.535135i	−0.205833	+	0.0181846i
$867$			51.2291i			1.73983i
$868$	17.9353	+	12.5130i	0.608764	+	0.424718i
$869$	13.8604	+	13.8604i	0.470182	+	0.470182i
$870$	−37.9676	+	3.35430i	−1.28722	+	0.113721i
$871$	−52.6429	+	52.6429i	−1.78374	+	1.78374i
$872$	9.63123	−	16.7806i	0.326154	−	0.568263i
$873$	−23.5064	+	23.5064i	−0.795570	+	0.795570i
$874$	0.306872	+	3.47350i	0.0103801	+	0.117493i
$875$	2.50934	−	2.50934i	0.0848313	−	0.0848313i
$876$	8.45412	+	47.4729i	0.285638	+	1.60396i
$877$	17.5169			0.591503			0.295752	−	0.955265i	$-0.404430\pi$
$877$	17.5169			0.591503			0.295752	+	0.955265i	$0.404430\pi$
$878$	25.5400	−	30.4901i	0.861934	−	1.02899i
$879$	−63.3461			−2.13661
$880$	−9.23855	+	19.9896i	−0.311431	+	0.673848i
$881$		−	53.2166i		−	1.79291i	−0.443132	−	0.896457i	$-0.646133\pi$
$881$		−	53.2166i		−	1.79291i	0.443132	−	0.896457i	$-0.353867\pi$
$882$	49.3432	−	4.35930i	1.66147	−	0.146785i
$883$	28.6806	−	28.6806i	0.965181	−	0.965181i	−0.0342332	−	0.999414i	$-0.510899\pi$
$883$	28.6806	−	28.6806i	0.965181	−	0.965181i	0.999414	+	0.0342332i	$0.0108989\pi$
$884$	−0.746419	−	4.19141i	−0.0251048	−	0.140972i
$885$	−8.49104			−0.285423
$886$	−36.2411	+	3.20178i	−1.21754	+	0.107566i
$887$	−8.29465			−0.278507			−0.139254	−	0.990257i	$-0.544470\pi$
$887$	−8.29465			−0.278507			−0.139254	+	0.990257i	$0.544470\pi$
$888$	19.8175	+	48.4644i	0.665033	+	1.62636i
$889$	44.6522			1.49759
$890$	−10.9109	+	0.963943i	−0.365735	+	0.0323114i
$891$	−62.9037			−2.10735
$892$	0.0744606	+	0.418123i	0.00249312	+	0.0139998i
$893$	−9.98155	+	9.98155i	−0.334020	+	0.334020i
$894$	−47.6688	+	4.21137i	−1.59428	+	0.140849i
$895$		−	14.0179i		−	0.468565i
$896$	−23.2244	−	32.7507i	−0.775872	−	1.09412i
$897$	−5.63582			−0.188175
$898$	−15.8851	+	18.9638i	−0.530091	+	0.632831i
$899$	27.2871			0.910076
$900$	−2.19574	−	12.3299i	−0.0731914	−	0.410996i
$901$	−2.96899	+	2.96899i	−0.0989113	+	0.0989113i
$902$	−1.24481	−	14.0900i	−0.0414475	−	0.469147i
$903$	−14.8483	+	14.8483i	−0.494120	+	0.494120i
$904$	17.6175	+	10.1116i	0.585949	+	0.336305i
$905$	−10.4160	+	10.4160i	−0.346238	+	0.346238i
$906$	−35.9870	+	3.17933i	−1.19559	+	0.105626i
$907$	−23.2515	−	23.2515i	−0.772055	−	0.772055i	0.206411	−	0.978465i	$-0.433822\pi$
$907$	−23.2515	−	23.2515i	−0.772055	−	0.772055i	−0.978465	+	0.206411i	$0.933822\pi$
$908$	−35.0987	−	24.4875i	−1.16479	−	0.812645i
$909$		−	112.139i		−	3.71940i
$910$	−26.0536	+	2.30175i	−0.863668	+	0.0763021i
$911$	29.5003	+	29.5003i	0.977389	+	0.977389i	0.999750	−	0.0223608i	$-0.00711825\pi$
$911$	29.5003	+	29.5003i	0.977389	+	0.977389i	−0.0223608	+	0.999750i	$0.507118\pi$
$912$	76.6784	+	35.4384i	2.53908	+	1.17348i
$913$		−	15.8738i		−	0.525346i
$914$	−14.9924	+	17.8981i	−0.495903	+	0.592017i
$915$	−34.2413			−1.13198
$916$	21.2935	−	3.79202i	0.703558	−	0.125292i
$917$	−0.718758	−	0.718758i	−0.0237355	−	0.0237355i
$918$	−3.68223	+	4.39591i	−0.121532	+	0.145087i
$919$	−31.2700	+	31.2700i	−1.03150	+	1.03150i	−0.0320162	+	0.999487i	$0.510193\pi$
$919$	−31.2700	+	31.2700i	−1.03150	+	1.03150i	−0.999487	+	0.0320162i	$0.989807\pi$
$920$	0.970131	−	0.262603i	0.0319843	−	0.00865777i
$921$	−77.4648			−2.55255
$922$	−6.40219	+	7.64304i	−0.210845	+	0.251710i
$923$	−20.8955	−	20.8955i	−0.687784	−	0.687784i
$924$	−20.8487	−	117.073i	−0.685873	−	3.85142i
$925$	−6.03620	+	0.751184i	−0.198469	+	0.0246988i
$926$	26.9106	+	22.5417i	0.884338	+	0.740766i
$927$	32.4303	−	32.4303i	1.06515	−	1.06515i
$928$	−47.1481	−	16.9336i	−1.54771	−	0.555872i
$929$		−	14.0453i		−	0.460810i	−0.973095	−	0.230405i	$-0.925995\pi$
$929$		−	14.0453i		−	0.460810i	0.973095	−	0.230405i	$-0.0740052\pi$
$930$	1.16705	+	13.2099i	0.0382691	+	0.433170i
$931$	−27.4459	−	27.4459i	−0.899502	−	0.899502i
$932$	6.86267	+	38.5363i	0.224794	+	1.26230i
$933$	−15.8489	+	15.8489i	−0.518870	+	0.518870i
$934$	−4.25408	−	3.56343i	−0.139198	−	0.116599i
$935$			2.24866i			0.0735392i
$936$	−45.9476	+	80.0550i	−1.50184	+	2.61668i
$937$	−45.2479			−1.47818			−0.739092	−	0.673605i	$-0.764745\pi$
$937$	−45.2479			−1.47818			−0.739092	+	0.673605i	$0.764745\pi$
$938$	6.30928	+	71.4152i	0.206005	+	2.33179i
$939$	18.0356	−	18.0356i	0.588569	−	0.588569i
$940$	3.33675	+	2.32796i	0.108833	+	0.0759298i
$941$	−26.8218			−0.874365			−0.437182	−	0.899373i	$-0.644024\pi$
$941$	−26.8218			−0.874365			−0.437182	+	0.899373i	$0.644024\pi$
$942$	14.0111	−	1.23783i	0.456505	−	0.0403307i
$943$	−0.456489	+	0.456489i	−0.0148653	+	0.0148653i
$944$	−10.1305	−	4.68202i	−0.329721	−	0.152387i
$945$	24.9107	+	24.9107i	0.810346	+	0.810346i
$946$	11.6045	+	9.72048i	0.377294	+	0.316040i
$947$	4.36152	+	4.36152i	0.141730	+	0.141730i	0.774412	−	0.632682i	$-0.218046\pi$
$947$	4.36152	+	4.36152i	0.141730	+	0.141730i	−0.632682	+	0.774412i	$0.718046\pi$
$948$	−17.7735	−	12.4001i	−0.577256	−	0.402736i
$949$	29.1941	+	29.1941i	0.947681	+	0.947681i
$950$	−6.30146	+	7.52279i	−0.204447	+	0.244072i
$951$		−	4.15051i		−	0.134589i
$952$	−3.55576	−	2.04083i	−0.115243	−	0.0661437i
$953$			47.3922i			1.53518i	0.640940	+	0.767591i	$0.278545\pi$
$953$			47.3922i			1.53518i	−0.640940	+	0.767591i	$0.721455\pi$
$954$	90.6807	−	8.01133i	2.93590	−	0.259376i
$955$	0.408791			0.0132282
$956$	12.8898	+	8.99284i	0.416885	+	0.290849i
$957$	−104.918	−	104.918i	−3.39153	−	3.39153i
$958$	−30.8063	−	25.8049i	−0.995305	−	0.833718i
$959$		−	51.0004i		−	1.64689i
$960$	6.18120	−	23.5490i	0.199497	−	0.760042i
$961$			21.5061i			0.693745i
$962$	37.6594	+	24.3233i	1.21419	+	0.784214i
$963$			41.4728i			1.33644i
$964$	−15.4959	+	22.2109i	−0.499091	+	0.715365i
$965$		−	7.11222i		−	0.228950i
$966$	−3.48504	+	4.16050i	−0.112129	+	0.133862i
$967$	−9.48475	−	9.48475i	−0.305009	−	0.305009i	0.537961	−	0.842970i	$-0.319195\pi$
$967$	−9.48475	−	9.48475i	−0.305009	−	0.305009i	−0.842970	+	0.537961i	$0.819195\pi$
$968$	−52.7150	+	14.2693i	−1.69433	+	0.458634i
$969$	8.62570			0.277098
$970$	−0.660706	−	7.47858i	−0.0212140	−	0.240123i
$971$		−	45.0472i		−	1.44563i	−0.691039	−	0.722817i	$-0.742847\pi$
$971$		−	45.0472i		−	1.44563i	0.691039	−	0.722817i	$-0.257153\pi$
$972$	9.82887	−	1.75035i	0.315261	−	0.0561427i
$973$		−	39.4763i		−	1.26555i
$974$	−28.3669	−	23.7615i	−0.908935	−	0.761369i
$975$	−11.2151	−	11.2151i	−0.359170	−	0.359170i
$976$	−40.8528	−	18.8809i	−1.30767	−	0.604362i
$977$	9.75590	+	9.75590i	0.312119	+	0.312119i	0.845730	−	0.533611i	$-0.179165\pi$
$977$	9.75590	+	9.75590i	0.312119	+	0.312119i	−0.533611	+	0.845730i	$0.679165\pi$
$978$	31.7908	−	37.9524i	1.01656	−	1.21358i
$979$	−30.1509	−	30.1509i	−0.963628	−	0.963628i
$980$	−6.40111	+	9.17494i	−0.204476	+	0.293083i
$981$	−30.2891	+	30.2891i	−0.967058	+	0.967058i
$982$	−3.33742	−	37.7764i	−0.106501	−	1.20549i
$983$	0.767711			0.0244862			0.0122431	−	0.999925i	$-0.496103\pi$
$983$	0.767711			0.0244862			0.0122431	+	0.999925i	$0.496103\pi$
$984$	4.08616	+	15.0954i	0.130262	+	0.481225i
$985$	−2.91162	+	2.91162i	−0.0927720	+	0.0927720i
$986$	−5.09572	+	0.450189i	−0.162281	+	0.0143369i
$987$	−21.9704			−0.699327
$988$	71.2060	−	12.6806i	2.26536	−	0.403423i
$989$		−	0.690885i		−	0.0219689i
$990$	31.3062	−	37.3739i	0.994978	−	1.18782i
$991$	1.98721	−	1.98721i	0.0631259	−	0.0631259i	−0.674839	−	0.737965i	$-0.735787\pi$
$991$	1.98721	−	1.98721i	0.0631259	−	0.0631259i	0.737965	+	0.674839i	$0.235787\pi$
$992$	−5.89164	+	16.4041i	−0.187060	+	0.520830i
$993$	−29.9229	−	29.9229i	−0.949573	−	0.949573i
$994$	−28.3468	+	2.50434i	−0.899106	+	0.0794329i
$995$		−	23.5549i		−	0.746739i
$996$	3.07697	+	17.2783i	0.0974976	+	0.547484i
$997$	−20.1252	+	20.1252i	−0.637370	+	0.637370i	−0.949906	−	0.312536i	$-0.898822\pi$
$997$	−20.1252	+	20.1252i	−0.637370	+	0.637370i	0.312536	+	0.949906i	$0.398822\pi$
$998$	12.4691	−	14.8859i	0.394704	−	0.471204i
$999$	−7.45714	−	59.9225i	−0.235934	−	1.89586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.u.a.31.1	✓	152
4.3	odd	2	inner	740.2.u.a.31.42	yes	152
37.6	odd	4	inner	740.2.u.a.191.42	yes	152
148.43	even	4	inner	740.2.u.a.191.1	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.u.a.31.1	✓	152	1.1	even	1	trivial
740.2.u.a.31.42	yes	152	4.3	odd	2	inner
740.2.u.a.191.1	yes	152	148.43	even	4	inner
740.2.u.a.191.42	yes	152	37.6	odd	4	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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40873 + 0.124456i) q^{2} +3.04334 q^{3} +(1.96902 - 0.350649i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-4.28724 + 0.378763i) q^{6} +3.54875i q^{7} +(-2.73017 + 0.739026i) q^{8} +6.26194 q^{9} +(-0.908116 + 1.08412i) q^{10} -5.50530 q^{11} +(5.99241 - 1.06715i) q^{12} +(3.68511 - 3.68511i) q^{13} +(-0.441663 - 4.99921i) q^{14} +(2.15197 - 2.15197i) q^{15} +(3.75409 - 1.38087i) q^{16} +(0.288821 - 0.288821i) q^{17} +(-8.82135 + 0.779336i) q^{18} +(4.90665 + 4.90665i) q^{19} +(1.14436 - 1.64025i) q^{20} +10.8001i q^{21} +(7.75546 - 0.685168i) q^{22} +(-0.251261 - 0.251261i) q^{23} +(-8.30885 + 2.24911i) q^{24} -1.00000i q^{25} +(-4.73268 + 5.64995i) q^{26} +9.92719 q^{27} +(1.24437 + 6.98756i) q^{28} +(6.26210 + 6.26210i) q^{29} +(-2.76371 + 3.29936i) q^{30} +(2.17875 - 2.17875i) q^{31} +(-5.11663 + 2.41249i) q^{32} -16.7545 q^{33} +(-0.370924 + 0.442815i) q^{34} +(2.50934 + 2.50934i) q^{35} +(12.3299 - 2.19574i) q^{36} +(-0.751184 - 6.03620i) q^{37} +(-7.52279 - 6.30146i) q^{38} +(11.2151 - 11.2151i) q^{39} +(-1.40795 + 2.45309i) q^{40} -1.81679i q^{41} +(-1.34413 - 15.2143i) q^{42} +(1.37483 + 1.37483i) q^{43} +(-10.8401 + 1.93043i) q^{44} +(4.42786 - 4.42786i) q^{45} +(0.385229 + 0.322687i) q^{46} +2.03429i q^{47} +(11.4250 - 4.20247i) q^{48} -5.59361 q^{49} +(0.124456 + 1.40873i) q^{50} +(0.878981 - 0.878981i) q^{51} +(5.96389 - 8.54825i) q^{52} -10.2797 q^{53} +(-13.9847 + 1.23550i) q^{54} +(-3.89283 + 3.89283i) q^{55} +(-2.62262 - 9.68869i) q^{56} +(14.9326 + 14.9326i) q^{57} +(-9.60094 - 8.04223i) q^{58} +(-1.97286 - 1.97286i) q^{59} +(3.48269 - 4.99186i) q^{60} +(-7.95581 - 7.95581i) q^{61} +(-2.79810 + 3.34042i) q^{62} +22.2220i q^{63} +(6.90768 - 4.03534i) q^{64} -5.21154i q^{65} +(23.6025 - 2.08520i) q^{66} -14.2853 q^{67} +(0.467420 - 0.669969i) q^{68} +(-0.764674 - 0.764674i) q^{69} +(-3.84728 - 3.22268i) q^{70} -5.67025i q^{71} +(-17.0962 + 4.62773i) q^{72} +7.92218i q^{73} +(1.80945 + 8.40987i) q^{74} -3.04334i q^{75} +(11.3818 + 7.94078i) q^{76} -19.5369i q^{77} +(-14.4032 + 17.1947i) q^{78} +(-2.51765 - 2.51765i) q^{79} +(1.67812 - 3.63097i) q^{80} +11.4260 q^{81} +(0.226111 + 2.55936i) q^{82} +2.88336i q^{83} +(3.78703 + 21.2655i) q^{84} -0.408454i q^{85} +(-2.10787 - 1.76566i) q^{86} +(19.0577 + 19.0577i) q^{87} +(15.0304 - 4.06856i) q^{88} +(5.47671 + 5.47671i) q^{89} +(-5.68657 + 6.78871i) q^{90} +(13.0775 + 13.0775i) q^{91} +(-0.582843 - 0.406634i) q^{92} +(6.63068 - 6.63068i) q^{93} +(-0.253180 - 2.86576i) q^{94} +6.93905 q^{95} +(-15.5717 + 7.34204i) q^{96} +(-3.75385 + 3.75385i) q^{97} +(7.87986 - 0.696159i) q^{98} -34.4738 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 4 q^{2} - 4 q^{8} + 152 q^{9} - 16 q^{13} + 24 q^{14} + 40 q^{16} + 16 q^{22} - 36 q^{24} + 32 q^{29} - 4 q^{32} - 16 q^{37} - 40 q^{38} - 20 q^{42} - 72 q^{44} + 8 q^{46} - 248 q^{49} - 4 q^{50}+ \cdots + 24 q^{98}+O(q^{100}) \) 152 * q - 4 * q^2 - 4 * q^8 + 152 * q^9 - 16 * q^13 + 24 * q^14 + 40 * q^16 + 16 * q^22 - 36 * q^24 + 32 * q^29 - 4 * q^32 - 16 * q^37 - 40 * q^38 - 20 * q^42 - 72 * q^44 + 8 * q^46 - 248 * q^49 - 4 * q^50 - 20 * q^52 + 8 * q^54 - 4 * q^56 + 48 * q^57 + 28 * q^60 + 16 * q^61 + 16 * q^66 - 28 * q^68 - 128 * q^72 - 80 * q^74 + 76 * q^76 + 152 * q^81 + 16 * q^82 - 56 * q^84 - 96 * q^86 - 72 * q^88 + 8 * q^89 - 152 * q^92 + 16 * q^93 + 28 * q^94 + 48 * q^96 - 48 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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