LMFDB - Embedded newform 740.2.u.a.191.42

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			191.42
Character	$\chi$	$=$	740.191
Dual form			740.2.u.a.31.42

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.124456 + 1.40873i) q^{2} -3.04334 q^{3} +(-1.96902 + 0.350649i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.378763 - 4.28724i) q^{6} +3.54875i q^{7} +(-0.739026 - 2.73017i) 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} +(-4.99921 + 0.441663i) q^{14} +(-2.15197 - 2.15197i) q^{15} +(3.75409 - 1.38087i) q^{16} +(0.288821 + 0.288821i) q^{17} +(0.779336 + 8.82135i) q^{18} +(-4.90665 + 4.90665i) q^{19} +(-1.64025 - 1.14436i) q^{20} -10.8001i q^{21} +(0.685168 + 7.75546i) q^{22} +(0.251261 - 0.251261i) q^{23} +(2.24911 + 8.30885i) 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} +(2.41249 + 5.11663i) 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} +(15.2143 - 1.34413i) 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} +(-1.40873 + 0.124456i) q^{50} +(-0.878981 - 0.878981i) q^{51} +(-8.54825 - 5.96389i) q^{52} -10.2797 q^{53} +(-1.23550 - 13.9847i) q^{54} +(3.89283 + 3.89283i) q^{55} +(9.68869 - 2.62262i) q^{56} +(14.9326 - 14.9326i) q^{57} +(9.60094 + 8.04223i) q^{58} +(1.97286 - 1.97286i) q^{59} +(4.99186 + 3.48269i) 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} +(-2.08520 - 23.6025i) q^{66} +14.2853 q^{67} +(-0.669969 - 0.467420i) q^{68} +(-0.764674 + 0.764674i) q^{69} +(-3.84728 - 3.22268i) q^{70} -5.67025i q^{71} +(-4.62773 - 17.0962i) q^{72} -7.92218i q^{73} +(-8.59685 - 0.306970i) q^{74} -3.04334i q^{75} +(7.94078 - 11.3818i) q^{76} +19.5369i q^{77} +(14.4032 - 17.1947i) q^{78} +(2.51765 - 2.51765i) q^{79} +(3.63097 + 1.67812i) q^{80} +11.4260 q^{81} +(-2.55936 + 0.226111i) 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} +(-4.06856 - 15.0304i) q^{88} +(5.47671 - 5.47671i) q^{89} +(-5.68657 + 6.78871i) q^{90} +(-13.0775 + 13.0775i) q^{91} +(-0.406634 + 0.582843i) q^{92} +(6.63068 + 6.63068i) q^{93} +(-2.86576 + 0.253180i) q^{94} -6.93905 q^{95} +(-7.34204 - 15.5717i) q^{96} +(-3.75385 - 3.75385i) q^{97} +(-0.696159 - 7.87986i) 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 $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	0.124456	+	1.40873i	0.0880038	+	0.996120i
$2$	0.124456	+	1.40873i	0.0880038	+	0.996120i
$3$	−3.04334			−1.75707			−0.878537	−	0.477674i	$-0.841480\pi$
$3$	−3.04334			−1.75707			−0.878537	+	0.477674i	$0.841480\pi$
$4$	−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
$6$	−0.378763	−	4.28724i	−0.154629	−	1.75026i
$7$			3.54875i			1.34130i	0.741774	+	0.670650i	$0.233985\pi$
$7$			3.54875i			1.34130i	−0.741774	+	0.670650i	$0.766015\pi$
$8$	−0.739026	−	2.73017i	−0.261285	−	0.965262i
$9$	6.26194			2.08731
$10$	−0.908116	+	1.08412i	−0.287172	+	0.342830i
$11$	5.50530			1.65991			0.829955	−	0.557830i	$-0.188366\pi$
$11$	5.50530			1.65991			0.829955	+	0.557830i	$0.188366\pi$
$12$	5.99241	−	1.06715i	1.72986	−	0.308059i
$13$	3.68511	+	3.68511i	1.02207	+	1.02207i	0.999751	+	0.0223157i	$0.00710390\pi$
$13$	3.68511	+	3.68511i	1.02207	+	1.02207i	0.0223157	+	0.999751i	$0.492896\pi$
$14$	−4.99921	+	0.441663i	−1.33610	+	0.118040i
$15$	−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	0.741264	−	0.671214i	$-0.234227\pi$
$17$	0.288821	+	0.288821i	0.0700494	+	0.0700494i	−0.671214	+	0.741264i	$0.734227\pi$
$18$	0.779336	+	8.82135i	0.183691	+	2.07921i
$19$	−4.90665	+	4.90665i	−1.12566	+	1.12566i	−0.134788	+	0.990874i	$0.543035\pi$
$19$	−4.90665	+	4.90665i	−1.12566	+	1.12566i	−0.990874	+	0.134788i	$0.956965\pi$
$20$	−1.64025	−	1.14436i	−0.366772	−	0.255887i
$21$		−	10.8001i		−	2.35677i
$22$	0.685168	+	7.75546i	0.146078	+	1.65347i
$23$	0.251261	−	0.251261i	0.0523916	−	0.0523916i	−0.680426	−	0.732817i	$-0.738205\pi$
$23$	0.251261	−	0.251261i	0.0523916	−	0.0523916i	0.732817	+	0.680426i	$0.238205\pi$
$24$	2.24911	+	8.30885i	0.459097	+	1.69604i
$25$			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	0.178992	−	0.983850i	$-0.442716\pi$
$29$	6.26210	−	6.26210i	1.16284	−	1.16284i	0.983850	−	0.178992i	$-0.0572837\pi$
$30$	2.76371	−	3.29936i	0.504582	−	0.602378i
$31$	−2.17875	−	2.17875i	−0.391315	−	0.391315i	0.483841	−	0.875156i	$-0.339241\pi$
$31$	−2.17875	−	2.17875i	−0.391315	−	0.391315i	−0.875156	+	0.483841i	$0.839241\pi$
$32$	2.41249	+	5.11663i	0.426472	+	0.904501i
$33$	−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	$0.0453107\pi$
$41$			1.81679i			0.283735i	−0.989886	+	0.141867i	$0.954689\pi$
$42$	15.2143	−	1.34413i	2.34762	−	0.207404i
$43$	−1.37483	+	1.37483i	−0.209660	+	0.209660i	−0.804123	−	0.594463i	$-0.797365\pi$
$43$	−1.37483	+	1.37483i	−0.209660	+	0.209660i	0.594463	+	0.804123i	$0.297365\pi$
$44$	−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
$50$	−1.40873	+	0.124456i	−0.199224	+	0.0176008i
$51$	−0.878981	−	0.878981i	−0.123082	−	0.123082i
$52$	−8.54825	−	5.96389i	−1.18543	−	0.827042i
$53$	−10.2797			−1.41202			−0.706012	−	0.708200i	$-0.749507\pi$
$53$	−10.2797			−1.41202			−0.706012	+	0.708200i	$0.749507\pi$
$54$	−1.23550	−	13.9847i	−0.168130	−	1.90308i
$55$	3.89283	+	3.89283i	0.524910	+	0.524910i
$56$	9.68869	−	2.62262i	1.29471	−	0.350462i
$57$	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	$-0.691867\pi$
$59$	1.97286	−	1.97286i	0.256844	−	0.256844i	0.823769	+	0.566925i	$0.191867\pi$
$60$	4.99186	+	3.48269i	0.644446	+	0.449613i
$61$	−7.95581	+	7.95581i	−1.01864	+	1.01864i	−0.0188138	+	0.999823i	$0.505989\pi$
$61$	−7.95581	+	7.95581i	−1.01864	+	1.01864i	−0.999823	+	0.0188138i	$0.994011\pi$
$62$	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
$66$	−2.08520	−	23.6025i	−0.256671	−	2.90527i
$67$	14.2853			1.74522			0.872612	−	0.488414i	$-0.162424\pi$
$67$	14.2853			1.74522			0.872612	+	0.488414i	$0.162424\pi$
$68$	−0.669969	−	0.467420i	−0.0812457	−	0.0566830i
$69$	−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	$-0.109232\pi$
$72$	−4.62773	−	17.0962i	−0.545383	−	2.01480i
$73$		−	7.92218i		−	0.927221i	−0.886039	−	0.463610i	$-0.846554\pi$
$73$		−	7.92218i		−	0.927221i	0.886039	−	0.463610i	$-0.153446\pi$
$74$	−8.59685	−	0.306970i	−0.999363	−	0.0356846i
$75$		−	3.04334i		−	0.351415i
$76$	7.94078	−	11.3818i	0.910870	−	1.30558i
$77$			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	$-0.685810\pi$
$79$	2.51765	−	2.51765i	0.283258	−	0.283258i	0.834407	+	0.551149i	$0.185810\pi$
$80$	3.63097	+	1.67812i	0.405954	+	0.187619i
$81$	11.4260			1.26956
$82$	−2.55936	+	0.226111i	−0.282634	+	0.0249697i
$83$			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
$88$	−4.06856	−	15.0304i	−0.433710	−	1.60225i
$89$	5.47671	−	5.47671i	0.580530	−	0.580530i	−0.354519	−	0.935049i	$-0.615355\pi$
$89$	5.47671	−	5.47671i	0.580530	−	0.580530i	0.935049	+	0.354519i	$0.115355\pi$
$90$	−5.68657	+	6.78871i	−0.599417	+	0.715593i
$91$	−13.0775	+	13.0775i	−1.37090	+	1.37090i
$92$	−0.406634	+	0.582843i	−0.0423945	+	0.0607656i
$93$	6.63068	+	6.63068i	0.687570	+	0.687570i
$94$	−2.86576	+	0.253180i	−0.295580	+	0.0261135i
$95$	−6.93905			−0.711932
$96$	−7.34204	−	15.5717i	−0.749343	−	1.58928i
$97$	−3.75385	−	3.75385i	−0.381146	−	0.381146i	0.490369	−	0.871515i	$-0.336862\pi$
$97$	−3.75385	−	3.75385i	−0.381146	−	0.381146i	−0.871515	+	0.490369i	$0.836862\pi$
$98$	−0.696159	−	7.87986i	−0.0703227	−	0.795987i
$99$	34.4738			3.46475
$100$	−0.350649	−	1.96902i	−0.0350649	−	0.196902i
$101$			17.9080i			1.78191i	0.454092	+	0.890955i	$0.349964\pi$
$101$			17.9080i			1.78191i	−0.454092	+	0.890955i	$0.650036\pi$
$102$	1.12885	−	1.34764i	0.111773	−	0.133436i
$103$	−5.17895	−	5.17895i	−0.510298	−	0.510298i	0.404320	−	0.914618i	$-0.367508\pi$
$103$	−5.17895	−	5.17895i	−0.510298	−	0.510298i	−0.914618	+	0.404320i	$0.867508\pi$
$104$	7.33760	−	12.7844i	0.719511	−	1.25361i
$105$	7.63679	−	7.63679i	0.745275	−	0.745275i
$106$	−1.27937	−	14.4813i	−0.124263	−	1.40654i
$107$			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	0.436434	−	0.899737i	$-0.356241\pi$
$109$	−4.83703	−	4.83703i	−0.463303	−	0.463303i	−0.899737	+	0.436434i	$0.856241\pi$
$110$	−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	−0.904403	−	0.426680i	$-0.859683\pi$
$113$	−5.07826	+	5.07826i	−0.477722	+	0.477722i	0.426680	+	0.904403i	$0.359683\pi$
$114$	22.8944	+	19.1775i	2.14426	+	1.79614i
$115$	0.355337			0.0331354
$116$	−10.1344	+	14.5260i	−0.940956	+	1.34871i
$117$	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
$124$	5.05398	+	3.52603i	0.453861	+	0.316647i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	−31.3048	+	2.76567i	−2.78885	+	0.246385i
$127$		−	12.5825i		−	1.11652i	−0.829666	−	0.558259i	$-0.811469\pi$
$127$		−	12.5825i		−	1.11652i	0.829666	−	0.558259i	$-0.188531\pi$
$128$	−6.54439	−	9.22881i	−0.578448	−	0.815720i
$129$	4.18409	−	4.18409i	0.368389	−	0.368389i
$130$	−7.34163	+	0.648608i	−0.643904	+	0.0568867i
$131$	0.202539	+	0.202539i	0.0176959	+	0.0176959i	0.715899	−	0.698203i	$-0.246017\pi$
$131$	0.202539	+	0.202539i	0.0176959	+	0.0176959i	−0.698203	+	0.715899i	$0.746017\pi$
$132$	32.9900	−	5.87496i	2.87141	−	0.511350i
$133$	−17.4125	−	17.4125i	−1.50985	−	1.50985i
$134$	1.77789	+	20.1240i	0.153586	+	1.73845i
$135$	−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	$-0.343618\pi$
$139$	11.1240			0.943526			0.471763	+	0.881725i	$0.343618\pi$
$140$	4.06105	−	5.82085i	0.343221	−	0.491952i
$141$		−	6.19104i		−	0.521380i
$142$	7.98783	−	0.705697i	0.670324	−	0.0592208i
$143$	20.2877	+	20.2877i	1.69654	+	1.69654i
$144$	23.5079	−	8.64693i	1.95899	−	0.720578i
$145$	8.85595			0.735446
$146$	11.1602	−	0.985964i	0.923623	−	0.0815989i
$147$	17.0233			1.40406
$148$	−0.637493	−	12.1488i	−0.0524016	−	0.998626i
$149$	11.1188			0.910884			0.455442	−	0.890265i	$-0.349481\pi$
$149$	11.1188			0.910884			0.455442	+	0.890265i	$0.349481\pi$
$150$	4.28724	−	0.378763i	0.350052	−	0.0309258i
$151$	−8.39398			−0.683092			−0.341546	−	0.939865i	$-0.610951\pi$
$151$	−8.39398			−0.683092			−0.341546	+	0.939865i	$0.610951\pi$
$152$	17.0221	+	9.76986i	1.38068	+	0.792440i
$153$	1.80858	+	1.80858i	0.146215	+	0.146215i
$154$	−27.5222	+	2.43149i	−2.21780	+	0.195935i
$155$		−	3.08122i		−	0.247489i
$156$	26.0153	+	18.1501i	2.08289	+	1.45317i
$157$	−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
$162$	1.42204	+	16.0961i	0.111726	+	1.26463i
$163$	8.13382	+	8.13382i	0.637090	+	0.637090i	0.949837	−	0.312746i	$-0.101249\pi$
$163$	8.13382	+	8.13382i	0.637090	+	0.637090i	−0.312746	+	0.949837i	$0.601249\pi$
$164$	−0.637056	−	3.57730i	−0.0497457	−	0.279340i
$165$	−11.8472	−	11.8472i	−0.922306	−	0.922306i
$166$	−4.06187	+	0.358852i	−0.315262	+	0.0278523i
$167$	5.33364	−	5.33364i	0.412730	−	0.412730i	−0.469959	−	0.882688i	$-0.655731\pi$
$167$	5.33364	−	5.33364i	0.412730	−	0.412730i	0.882688	+	0.469959i	$0.155731\pi$
$168$	−29.4860	+	7.98152i	−2.27490	+	0.615788i
$169$			14.1601i			1.08924i
$170$	−0.575401	+	0.0508347i	−0.0441312	+	0.00389884i
$171$	−30.7251	+	30.7251i	−2.34961	+	2.34961i
$172$	2.22499	−	3.18916i	0.169654	−	0.243171i
$173$			9.08143i			0.690449i	0.938520	+	0.345224i	$0.112197\pi$
$173$			9.08143i			0.690449i	−0.938520	+	0.345224i	$0.887803\pi$
$174$	−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	$-0.425513\pi$
$179$	−9.91212	−	9.91212i	−0.740867	−	0.740867i	−0.972745	+	0.231878i	$0.925513\pi$
$180$	−10.2712	−	7.16592i	−0.765568	−	0.534116i
$181$	−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
$190$	−0.863607	−	9.77522i	−0.0626527	−	0.709169i
$191$	−0.289059	+	0.289059i	−0.0209155	+	0.0209155i	−0.717487	−	0.696572i	$-0.754708\pi$
$191$	−0.289059	+	0.289059i	−0.0209155	+	0.0209155i	0.696572	+	0.717487i	$0.254708\pi$
$192$	21.0224	−	12.2809i	1.51716	−	0.886298i
$193$	5.02910	+	5.02910i	0.362003	+	0.362003i	0.864550	−	0.502547i	$-0.167604\pi$
$193$	5.02910	+	5.02910i	0.362003	+	0.362003i	−0.502547	+	0.864550i	$0.667604\pi$
$194$	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	$0.546860\pi$
$198$	4.29048	+	48.5642i	0.304911	+	3.45131i
$199$	−16.6558	−	16.6558i	−1.18070	−	1.18070i	−0.979564	−	0.201135i	$-0.935537\pi$
$199$	−16.6558	−	16.6558i	−1.18070	−	1.18070i	−0.201135	−	0.979564i	$-0.564463\pi$
$200$	2.73017	−	0.739026i	0.193052	−	0.0522570i
$201$	−43.4750			−3.06649
$202$	−25.2274	+	2.22876i	−1.77500	+	0.156815i
$203$	22.2226	+	22.2226i	1.55972	+	1.55972i
$204$	2.03895	+	1.42252i	0.142755	+	0.0995962i
$205$	−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
$208$	18.9229	+	8.74558i	1.31207	+	0.606397i
$209$	−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
$214$	−9.32999	+	0.824272i	−0.637785	+	0.0563461i
$215$	−1.94431			−0.132601
$216$	7.33645	+	27.1029i	0.499182	+	1.84412i
$217$	7.73183	−	7.73183i	0.524871	−	0.524871i
$218$	6.21205	−	7.41604i	0.420733	−	0.502278i
$219$			24.1099i			1.62920i
$220$	−9.03009	−	6.30005i	−0.608809	−	0.424750i
$221$			2.12868i			0.143190i
$222$	26.1632	+	0.934216i	1.75596	+	0.0627005i
$223$			0.212350i			0.0142200i	0.999975	+	0.00711002i	$0.00226321\pi$
$223$			0.212350i			0.0142200i	−0.999975	+	0.00711002i	$0.997737\pi$
$224$	−18.1576	+	8.56132i	−1.21321	+	0.572027i
$225$			6.26194i			0.417462i
$226$	−7.78590	−	6.52186i	−0.517910	−	0.433827i
$227$	15.1309	−	15.1309i	1.00427	−	1.00427i	0.00428348	−	0.999991i	$-0.498637\pi$
$227$	15.1309	−	15.1309i	1.00427	−	1.00427i	0.999991	−	0.00428348i	$-0.00136348\pi$
$228$	−24.1665	+	34.6388i	−1.60047	+	2.29401i
$229$	10.8143			0.714627			0.357314	−	0.933985i	$-0.383693\pi$
$229$	10.8143			0.714627			0.357314	+	0.933985i	$0.383693\pi$
$230$	0.0442239	+	0.500573i	0.00291604	+	0.0330068i
$231$		−	59.4575i		−	3.91202i
$232$	−21.7245	−	12.4688i	−1.42628	−	0.818614i
$233$		−	19.5713i		−	1.28216i	−0.767475	−	0.641079i	$-0.778487\pi$
$233$		−	19.5713i		−	1.28216i	0.767475	−	0.641079i	$-0.221513\pi$
$234$	−29.6358	+	35.3796i	−1.93735	+	2.31284i
$235$	−1.43846	+	1.43846i	−0.0938348	+	0.0938348i
$236$	−3.19281	+	4.57637i	−0.207834	+	0.297897i
$237$	−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	$-0.831798\pi$
$239$	−5.55672	+	5.55672i	−0.359434	+	0.359434i	0.504170	+	0.863604i	$0.331798\pi$
$240$	−11.0503	−	5.10709i	−0.713292	−	0.329661i
$241$	−9.57502	−	9.57502i	−0.616781	−	0.616781i	0.327923	−	0.944704i	$-0.393651\pi$
$241$	−9.57502	−	9.57502i	−0.616781	−	0.616781i	−0.944704	+	0.327923i	$0.893651\pi$
$242$	2.40304	+	27.2001i	0.154473	+	1.74849i
$243$	−4.99175			−0.320221
$244$	12.8755	−	18.4549i	0.824267	−	1.18145i
$245$	−3.95528	−	3.95528i	−0.252693	−	0.252693i
$246$	7.78901	−	0.688132i	0.496609	−	0.0438737i
$247$	−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	$-0.209293\pi$
$251$	2.85748	+	2.85748i	0.180363	+	0.180363i	−0.611151	+	0.791514i	$0.709293\pi$
$252$	−7.79214	−	43.7556i	−0.490859	−	2.75635i
$253$	1.38327	−	1.38327i	0.0869653	−	0.0869653i
$254$	17.7253	−	1.56597i	1.11219	−	0.0982579i
$255$		−	1.24307i		−	0.0778439i
$256$	12.1864	−	10.3678i	0.761649	−	0.647990i
$257$	3.89695	+	3.89695i	0.243085	+	0.243085i	0.818125	−	0.575040i	$-0.195014\pi$
$257$	3.89695	+	3.89695i	0.243085	+	0.243085i	−0.575040	+	0.818125i	$0.695014\pi$
$258$	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	$-0.538976\pi$
$263$	−3.96155			−0.244279			−0.122140	+	0.992513i	$0.538976\pi$
$264$	12.3820	+	45.7427i	0.762061	+	2.81527i
$265$	−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	$0.810508\pi$
$272$	1.48308	+	0.685435i	0.0899252	+	0.0415606i
$273$	39.7994	−	39.7994i	2.40877	−	2.40877i
$274$	−1.78861	−	20.2453i	−0.108054	−	1.22307i
$275$			5.50530i			0.331982i
$276$	1.23753	−	1.77379i	0.0744904	−	0.106770i
$277$	−5.39405	+	5.39405i	−0.324097	+	0.324097i	−0.850337	−	0.526239i	$-0.823602\pi$
$277$	−5.39405	+	5.39405i	−0.324097	+	0.324097i	0.526239	+	0.850337i	$0.323602\pi$
$278$	1.38445	+	15.6707i	0.0830338	+	0.939865i
$279$	−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	0.961323	+	0.275425i	$0.0888185\pi$
$281$	20.7317	+	20.7317i	1.23675	+	1.23675i	0.275425	+	0.961323i	$0.411181\pi$
$282$	8.72149	−	0.770513i	0.519357	−	0.0458834i
$283$	−12.6105	−	12.6105i	−0.749618	−	0.749618i	0.224789	−	0.974407i	$-0.427831\pi$
$283$	−12.6105	−	12.6105i	−0.749618	−	0.749618i	−0.974407	+	0.224789i	$0.927831\pi$
$284$	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
$288$	15.1069	+	32.0400i	0.890180	+	1.88797i
$289$		−	16.8332i		−	0.990186i
$290$	1.10218	+	12.4756i	0.0647221	+	0.732593i
$291$	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	$0.708029\pi$
$294$	2.11865	+	23.9811i	0.123562	+	1.39861i
$295$	2.79004			0.162442
$296$	17.0350	−	2.41005i	0.990140	−	0.140081i
$297$	−54.6521			−3.17124
$298$	1.38380	+	15.6633i	0.0801612	+	0.907350i
$299$	1.85185			0.107095
$300$	1.06715	+	5.99241i	0.0616117	+	0.345972i
$301$	−4.87894	−	4.87894i	−0.281217	−	0.281217i
$302$	−1.04468	−	11.8248i	−0.0601147	−	0.680442i
$303$		−	54.5001i		−	3.13095i
$304$	−11.6445	+	25.1955i	−0.667861	+	1.44506i
$305$	−11.2512			−0.644242
$306$	−2.32270	+	2.77288i	−0.132780	+	0.158515i
$307$	25.4539			1.45273			0.726364	−	0.687310i	$-0.241209\pi$
$307$	25.4539			1.45273			0.726364	+	0.687310i	$0.241209\pi$
$308$	−6.85061	−	38.4686i	−0.390350	−	2.19195i
$309$	15.7613	+	15.7613i	0.896631	+	0.896631i
$310$	4.34059	−	0.383476i	0.246529	−	0.0217800i
$311$	5.20773	+	5.20773i	0.295304	+	0.295304i	0.839171	−	0.543868i	$-0.183041\pi$
$311$	5.20773	+	5.20773i	0.295304	+	0.295304i	−0.543868	+	0.839171i	$0.683041\pi$
$312$	−22.3308	+	38.9073i	−1.26423	+	2.20269i
$313$	5.92624	+	5.92624i	0.334971	+	0.334971i	0.854471	−	0.519500i	$-0.173882\pi$
$313$	5.92624	+	5.92624i	0.334971	+	0.334971i	−0.519500	+	0.854471i	$0.673882\pi$
$314$	−0.406734	−	4.60384i	−0.0229533	−	0.259810i
$315$	−15.7133	+	15.7133i	−0.885347	+	0.885347i
$316$	−4.07449	+	5.84012i	−0.229208	+	0.328532i
$317$			1.36380i			0.0765986i	0.999266	+	0.0382993i	$0.0121940\pi$
$317$			1.36380i			0.0765986i	−0.999266	+	0.0382993i	$0.987806\pi$
$318$	3.89356	+	44.0715i	0.218340	+	2.47140i
$319$	34.4747	−	34.4747i	1.93021	−	1.93021i
$320$	−7.73788	−	2.03106i	−0.432561	−	0.113539i
$321$		−	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
$328$	4.96015	−	1.34265i	0.273878	−	0.0741357i
$329$	−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	$-0.625187\pi$
$331$	9.83223	−	9.83223i	0.540428	−	0.540428i	0.923655	+	0.383226i	$0.125187\pi$
$332$	−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	$-0.824847\pi$
$337$		−	19.1986i		−	1.04582i	0.852389	−	0.522908i	$-0.175153\pi$
$338$	−19.9477	+	1.76231i	−1.08501	+	0.0958573i
$339$	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
$346$	−12.7933	+	1.13024i	−0.687770	+	0.0607621i
$347$	−10.1689	−	10.1689i	−0.545896	−	0.545896i	0.379355	−	0.925251i	$-0.376146\pi$
$347$	−10.1689	−	10.1689i	−0.545896	−	0.545896i	−0.925251	+	0.379355i	$0.876146\pi$
$348$	30.8425	−	44.2076i	1.65333	−	2.36978i
$349$	3.54294			0.189649			0.0948245	−	0.995494i	$-0.469771\pi$
$349$	3.54294			0.189649			0.0948245	+	0.995494i	$0.469771\pi$
$350$	−0.441663	−	4.99921i	−0.0236079	−	0.267219i
$351$	−36.5828	−	36.5828i	−1.95265	−	1.95265i
$352$	13.2815	+	28.1686i	0.707905	+	1.50139i
$353$	1.57576	−	1.57576i	0.0838694	−	0.0838694i	−0.663927	−	0.747797i	$-0.731112\pi$
$353$	1.57576	−	1.57576i	0.0838694	−	0.0838694i	0.747797	+	0.663927i	$0.231112\pi$
$354$	−9.20534	−	7.71086i	−0.489259	−	0.409827i
$355$	4.00947	−	4.00947i	0.212801	−	0.212801i
$356$	−8.86336	+	12.7042i	−0.469757	+	0.673320i
$357$	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
$362$	−1.83329	−	20.7511i	−0.0963554	−	1.09065i
$363$	−58.7618			−3.08420
$364$	21.1643	−	30.3356i	1.10931	−	1.59002i
$365$	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	$0.965592\pi$
$368$	0.596298	−	1.29022i	0.0310842	−	0.0672572i
$369$			11.3766i			0.592243i
$370$	−5.86183	−	6.29595i	−0.304742	−	0.327311i
$371$		−	36.4800i		−	1.89395i
$372$	−15.3810	−	10.7309i	−0.797468	−	0.556372i
$373$		−	26.3503i		−	1.36437i	−0.731182	−	0.682183i	$-0.761031\pi$
$373$		−	26.3503i		−	1.36437i	0.731182	−	0.682183i	$-0.238969\pi$
$374$	−2.04205	+	2.43783i	−0.105592	+	0.126057i
$375$	2.15197	−	2.15197i	0.111127	−	0.111127i
$376$	5.55396	−	1.50339i	0.286424	−	0.0775316i
$377$	46.1531			2.37701
$378$	49.6281	−	4.38447i	2.55260	−	0.225513i
$379$			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	$-0.517469\pi$
$383$	18.4674	−	18.4674i	0.943641	−	0.943641i	0.998494	+	0.0548537i	$0.0174692\pi$
$384$	19.9168	+	28.0864i	1.01638	+	1.43328i
$385$	−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
$388$	8.70770	+	6.07513i	0.442067	+	0.308418i
$389$	−18.6478	−	18.6478i	−0.945482	−	0.945482i	0.0531070	−	0.998589i	$-0.483088\pi$
$389$	−18.6478	−	18.6478i	−0.945482	−	0.945482i	−0.998589	+	0.0531070i	$0.983088\pi$
$390$	22.3431	−	1.97394i	1.13139	−	0.0999541i
$391$	0.145139			0.00733999
$392$	4.13382	+	15.2715i	0.208789	+	0.771328i
$393$	−0.616394	−	0.616394i	−0.0310930	−	0.0310930i
$394$	−0.512467	−	5.80065i	−0.0258177	−	0.292233i
$395$	3.56049			0.179148
$396$	−67.8797	+	12.0882i	−3.41108	+	0.607456i
$397$			15.0013i			0.752894i	0.926438	+	0.376447i	$0.122854\pi$
$397$			15.0013i			0.752894i	−0.926438	+	0.376447i	$0.877146\pi$
$398$	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	0.183767	−	0.982970i	$-0.441171\pi$
$401$	23.3639	−	23.3639i	1.16674	−	1.16674i	0.982970	−	0.183767i	$-0.0588291\pi$
$402$	−5.41073	−	61.2444i	−0.269863	−	3.05459i
$403$		−	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	−0.695610	−	0.718420i	$-0.744866\pi$
$409$	0.461293	−	0.461293i	0.0228095	−	0.0228095i	0.718420	+	0.695610i	$0.244866\pi$
$410$	−1.96963	−	1.64986i	−0.0972729	−	0.0814806i
$411$	43.7370			2.15739
$412$	12.0135	+	8.38147i	0.591861	+	0.412926i
$413$	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	$0.809944\pi$
$420$	−12.3592	+	17.7148i	−0.603066	+	0.864396i
$421$	−11.4273	+	11.4273i	−0.556932	+	0.556932i	−0.928433	−	0.371501i	$-0.878843\pi$
$421$	−11.4273	+	11.4273i	−0.556932	+	0.556932i	0.371501	+	0.928433i	$0.378843\pi$
$422$	−14.8693	+	1.31365i	−0.723827	+	0.0639476i
$423$			12.7386i			0.619372i
$424$	7.59695	+	28.0653i	0.368941	+	1.36297i
$425$	−0.288821	+	0.288821i	−0.0140099	+	0.0140099i
$426$	−24.3097	+	2.14768i	−1.17781	+	0.104055i
$427$	−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
$430$	−0.241981	−	2.73900i	−0.0116694	−	0.132086i
$431$	23.4348	+	23.4348i	1.12882	+	1.12882i	0.990370	+	0.138445i	$0.0442104\pi$
$431$	23.4348	+	23.4348i	1.12882	+	1.12882i	0.138445	+	0.990370i	$0.455790\pi$
$432$	−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
$436$	11.2203	+	7.82811i	0.537355	+	0.374898i
$437$			2.46570i			0.117951i
$438$	−33.9643	+	3.00063i	−1.62288	+	0.143375i
$439$	19.8868	+	19.8868i	0.949145	+	0.949145i	0.998768	−	0.0496231i	$-0.0158020\pi$
$439$	19.8868	+	19.8868i	0.949145	+	0.949145i	−0.0496231	+	0.998768i	$0.515802\pi$
$440$	7.75120	−	13.5050i	0.369524	−	0.643826i
$441$	−35.0268			−1.66794
$442$	−2.99872	+	0.264927i	−0.142635	+	0.0126013i
$443$	−25.7261			−1.22229			−0.611143	−	0.791520i	$-0.709290\pi$
$443$	−25.7261			−1.22229			−0.611143	+	0.791520i	$0.709290\pi$
$444$	1.94011	+	36.9730i	0.0920735	+	1.75466i
$445$	7.74524			0.367160
$446$	−0.299144	+	0.0264283i	−0.0141649	+	0.00125142i
$447$	−33.8382			−1.60049
$448$	−14.3204	−	24.5136i	−0.676575	−	1.15816i
$449$	12.3689	+	12.3689i	0.583726	+	0.583726i	0.935925	−	0.352199i	$-0.114566\pi$
$449$	12.3689	+	12.3689i	0.583726	+	0.583726i	−0.352199	+	0.935925i	$0.614566\pi$
$450$	−8.82135	+	0.779336i	−0.415843	+	0.0367383i
$451$			10.0020i			0.470975i
$452$	8.21851	−	11.7799i	0.386566	−	0.554079i
$453$	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	0.925304	−	0.379225i	$-0.123809\pi$
$457$	11.6738	+	11.6738i	0.546079	+	0.546079i	−0.379225	+	0.925304i	$0.623809\pi$
$458$	1.34590	+	15.2343i	0.0628899	+	0.711854i
$459$	−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	0.813601	−	0.581423i	$-0.197504\pi$
$461$	4.98508	+	4.98508i	0.232178	+	0.232178i	−0.581423	+	0.813601i	$0.697504\pi$
$462$	83.7594	−	7.39985i	3.89684	−	0.344272i
$463$	17.5521	−	17.5521i	0.815717	−	0.815717i	−0.169767	−	0.985484i	$-0.554302\pi$
$463$	17.5521	−	17.5521i	0.815717	−	0.815717i	0.985484	+	0.169767i	$0.0543017\pi$
$464$	14.8613	−	32.1556i	0.689920	−	1.49279i
$465$			9.37720i			0.434857i
$466$	27.5706	−	2.43577i	1.27718	−	0.112835i
$467$	−2.77467	+	2.77467i	−0.128397	+	0.128397i	−0.768385	−	0.639988i	$-0.778939\pi$
$467$	−2.77467	+	2.77467i	−0.128397	+	0.128397i	0.639988	+	0.768385i	$0.278939\pi$
$468$	−53.5286	−	37.3455i	−2.47436	−	1.72629i
$469$			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
$476$	1.65875	−	2.37755i	0.0760289	−	0.108975i
$477$	−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	$-0.974886\pi$
$479$	−20.0930	+	20.0930i	−0.918074	+	0.918074i	0.0788157	+	0.996889i	$0.474886\pi$
$480$	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
$486$	−0.621254	−	7.03202i	−0.0281807	−	0.318979i
$487$	−18.5020	+	18.5020i	−0.838405	+	0.838405i	−0.988649	−	0.150244i	$-0.951994\pi$
$487$	−18.5020	+	18.5020i	−0.838405	+	0.838405i	0.150244	+	0.988649i	$0.451994\pi$
$488$	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
$494$	−4.50072	−	50.9440i	−0.202497	−	2.29208i
$495$	24.3767	+	24.3767i	1.09565	+	1.09565i
$496$	−11.1878	−	5.17065i	−0.502347	−	0.232169i
$497$	20.1223			0.902608
$498$	12.3617	−	1.09211i	0.553940	−	0.0489387i
$499$	9.70913	+	9.70913i	0.434640	+	0.434640i	0.890203	−	0.455563i	$-0.150562\pi$
$499$	9.70913	+	9.70913i	0.434640	+	0.434640i	−0.455563	+	0.890203i	$0.650562\pi$
$500$	1.14436	−	1.64025i	0.0511774	−	0.0733544i
$501$	−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	$-0.750028\pi$
$503$	−0.00277987	+	0.00277987i	−0.000123948	+	0.000123948i	0.707045	+	0.707169i	$0.250028\pi$
$504$	60.6700	−	16.4227i	2.70245	−	0.731523i
$505$	−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	$0.0512579\pi$
$509$			7.23471i			0.320673i	−0.987062	+	0.160337i	$0.948742\pi$
$510$	1.75114	−	0.154707i	0.0775418	−	0.00685055i
$511$	28.1138			1.24368
$512$	16.1221	+	15.8769i	0.712504	+	0.701668i
$513$	48.7092	−	48.7092i	2.15056	−	2.15056i
$514$	−5.00473	+	5.97473i	−0.220749	+	0.263534i
$515$		−	7.32415i		−	0.322740i
$516$	−6.77142	+	9.70572i	−0.298095	+	0.427270i
$517$			11.1994i			0.492548i
$518$	1.08936	−	30.5080i	0.0478637	−	1.34045i
$519$		−	27.6379i		−	1.21317i
$520$	14.2284	−	3.85146i	0.623956	−	0.168898i
$521$			14.1908i			0.621711i	0.950457	+	0.310856i	$0.100616\pi$
$521$			14.1908i			0.621711i	−0.950457	+	0.310856i	$0.899384\pi$
$522$	60.1205	+	50.3599i	2.63140	+	2.20419i
$523$	−20.3978	+	20.3978i	−0.891932	+	0.891932i	−0.994705	−	0.102773i	$-0.967229\pi$
$523$	−20.3978	+	20.3978i	−0.891932	+	0.891932i	0.102773	+	0.994705i	$0.467229\pi$
$524$	−0.469823	−	0.327783i	−0.0205243	−	0.0143193i
$525$	10.8001			0.471353
$526$	−0.493039	−	5.58073i	−0.0214975	−	0.243332i
$527$		−	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
$532$	40.3912	+	28.1798i	1.75118	+	1.22175i
$533$	−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
$536$	−10.5572	−	39.0013i	−0.456001	−	1.68460i
$537$	30.1660	+	30.1660i	1.30176	+	1.30176i
$538$	3.56452	+	40.3470i	0.153677	+	1.73948i
$539$	−30.7945			−1.32641
$540$	16.2831	+	11.3603i	0.700714	+	0.488869i
$541$	15.6275	+	15.6275i	0.671877	+	0.671877i	0.958149	−	0.286271i	$-0.0924158\pi$
$541$	15.6275	+	15.6275i	0.671877	+	0.671877i	−0.286271	+	0.958149i	$0.592416\pi$
$542$	−26.0088	+	2.29779i	−1.11718	+	0.0986986i
$543$	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	$-0.0101394\pi$
$547$	22.6313	+	22.6313i	0.967644	+	0.967644i	−0.0318485	+	0.999493i	$0.510139\pi$
$548$	28.2975	−	5.03931i	1.20881	−	0.215269i
$549$	−49.8188	+	49.8188i	−2.12621	+	2.12621i
$550$	−7.75546	+	0.685168i	−0.330694	+	0.0292157i
$551$			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	0.137922	−	0.990443i	$-0.455958\pi$
$557$	26.6304	−	26.6304i	1.12836	−	1.12836i	0.990443	−	0.137922i	$-0.0440422\pi$
$558$	17.5215	−	20.9175i	0.741746	−	0.885508i
$559$	−10.1328			−0.428574
$560$	−5.95522	+	12.8854i	−0.251654	+	0.544507i
$561$	−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	$-0.733839\pi$
$563$	1.70293	−	1.70293i	0.0717699	−	0.0717699i	0.742081	+	0.670311i	$0.233839\pi$
$564$	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
$568$	−15.4808	+	4.19046i	−0.649558	+	0.175828i
$569$	27.6253	−	27.6253i	1.15811	−	1.15811i	0.173234	−	0.984881i	$-0.444578\pi$
$569$	27.6253	−	27.6253i	1.15811	−	1.15811i	0.984881	−	0.173234i	$-0.0554215\pi$
$570$	2.62825	+	29.7494i	0.110085	+	1.24606i
$571$		−	41.6395i		−	1.74256i	−0.490788	−	0.871279i	$-0.663291\pi$
$571$		−	41.6395i		−	1.74256i	0.490788	−	0.871279i	$-0.336709\pi$
$572$	−47.0607	−	32.8330i	−1.96771	−	1.37282i
$573$	0.879704	−	0.879704i	0.0367502	−	0.0367502i
$574$	−0.802410	−	9.08252i	−0.0334919	−	0.379097i
$575$	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	0.625863	−	0.779933i	$-0.284747\pi$
$577$	−3.70088	−	3.70088i	−0.154070	−	0.154070i	−0.779933	+	0.625863i	$0.784747\pi$
$578$	23.7133	−	2.09499i	0.986344	−	0.0871401i
$579$	−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
$584$	−21.6289	+	5.85469i	−0.895011	+	0.242269i
$585$			32.6343i			1.34926i
$586$	−2.59051	−	29.3222i	−0.107013	−	1.21129i
$587$	−25.6983	−	25.6983i	−1.06068	−	1.06068i	−0.998036	−	0.0626456i	$-0.980046\pi$
$587$	−25.6983	−	25.6983i	−1.06068	−	1.06068i	−0.0626456	−	0.998036i	$-0.519954\pi$
$588$	−33.5192	+	5.96920i	−1.38231	+	0.246166i
$589$	21.3807			0.880977
$590$	0.347237	+	3.93040i	0.0142955	+	0.161812i
$591$	12.5314			0.515474
$592$	5.51521	+	23.6977i	0.226674	+	0.973971i
$593$	3.32519			0.136549			0.0682746	−	0.997667i	$-0.478251\pi$
$593$	3.32519			0.136549			0.0682746	+	0.997667i	$0.478251\pi$
$594$	−6.80179	−	76.9899i	−0.279081	−	3.15893i
$595$	−1.44950			−0.0594238
$596$	−21.8931	+	3.89878i	−0.896775	+	0.159700i
$597$	50.6893	+	50.6893i	2.07458	+	2.07458i
$598$	0.230474	+	2.60875i	0.00942480	+	0.106680i
$599$			14.0840i			0.575457i	0.957712	+	0.287728i	$0.0929000\pi$
$599$			14.0840i			0.575457i	−0.957712	+	0.287728i	$0.907100\pi$
$600$	−8.30885	+	2.24911i	−0.339207	+	0.0918195i
$601$	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
$606$	76.7757	−	6.78287i	3.11880	−	0.275535i
$607$	−10.5943	−	10.5943i	−0.430007	−	0.430007i	0.458623	−	0.888631i	$-0.348343\pi$
$607$	−10.5943	−	10.5943i	−0.430007	−	0.430007i	−0.888631	+	0.458623i	$0.848343\pi$
$608$	−36.9427	−	13.2683i	−1.49823	−	0.538099i
$609$	−67.6310	−	67.6310i	−2.74055	−	2.74055i
$610$	−1.40028	−	15.8499i	−0.0566958	−	0.641743i
$611$	−7.49659	+	7.49659i	−0.303280	+	0.303280i
$612$	−4.19531	−	2.92695i	−0.169585	−	0.118315i
$613$		−	34.8028i		−	1.40567i	−0.711351	−	0.702837i	$-0.751916\pi$
$613$		−	34.8028i		−	1.40567i	0.711351	−	0.702837i	$-0.248084\pi$
$614$	3.16789	+	35.8575i	0.127846	+	1.44709i
$615$	3.90967	−	3.90967i	0.157653	−	0.157653i
$616$	53.3392	−	14.4383i	2.14910	−	0.581735i
$617$			15.9571i			0.642410i	0.947010	+	0.321205i	$0.104088\pi$
$617$			15.9571i			0.642410i	−0.947010	+	0.321205i	$0.895912\pi$
$618$	−20.2418	+	24.1650i	−0.814245	+	0.972059i
$619$	43.2205			1.73718			0.868589	−	0.495533i	$-0.165027\pi$
$619$	43.2205			1.73718			0.868589	+	0.495533i	$0.165027\pi$
$620$	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
$624$	−57.5889	−	26.6158i	−2.30540	−	1.06548i
$625$	−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	$-0.434122\pi$
$631$	−19.4219	−	19.4219i	−0.773173	−	0.773173i	−0.978660	+	0.205487i	$0.934122\pi$
$632$	−8.73422	−	5.01301i	−0.347429	−	0.199407i
$633$		−	32.1229i		−	1.27677i
$634$	−1.92122	+	0.169733i	−0.0763014	+	0.00674097i
$635$	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	$0.329174\pi$
$642$	28.3943	−	2.50854i	1.12064	−	0.0990043i
$643$	−19.1649	−	19.1649i	−0.755791	−	0.755791i	0.219762	−	0.975553i	$-0.429472\pi$
$643$	−19.1649	−	19.1649i	−0.755791	−	0.755791i	−0.975553	+	0.219762i	$0.929472\pi$
$644$	−2.06836	−	1.44304i	−0.0815049	−	0.0568638i
$645$	5.91720			0.232990
$646$	−0.352744	−	3.99273i	−0.0138785	−	0.157092i
$647$	−1.55532	−	1.55532i	−0.0611461	−	0.0611461i	0.675873	−	0.737019i	$-0.263767\pi$
$647$	−1.55532	−	1.55532i	−0.0611461	−	0.0611461i	−0.737019	+	0.675873i	$0.763767\pi$
$648$	−8.44413	−	31.1950i	−0.331717	−	1.22546i
$649$	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
$652$	−18.8678	−	13.1636i	−0.738920	−	0.515525i
$653$	13.8307	−	13.8307i	0.541236	−	0.541236i	−0.382655	−	0.923891i	$-0.624990\pi$
$653$	13.8307	−	13.8307i	0.541236	−	0.541236i	0.923891	+	0.382655i	$0.124990\pi$
$654$	−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
$658$	−0.898471	−	10.1699i	−0.0350261	−	0.396462i
$659$	−0.389577			−0.0151758			−0.00758789	−	0.999971i	$-0.502415\pi$
$659$	−0.389577			−0.0151758			−0.00758789	+	0.999971i	$0.502415\pi$
$660$	27.4817	+	19.1732i	1.06972	+	0.746317i
$661$	−8.61627	+	8.61627i	−0.335134	+	0.335134i	−0.854532	−	0.519398i	$-0.826156\pi$
$661$	−8.61627	+	8.61627i	−0.335134	+	0.335134i	0.519398	+	0.854532i	$0.326156\pi$
$662$	15.0746	+	12.6272i	0.585891	+	0.490772i
$663$		−	6.47829i		−	0.251596i
$664$	7.87208	−	2.13088i	0.305496	−	0.0826942i
$665$		−	24.6249i		−	0.954914i
$666$	−53.8329	−	1.92223i	−2.08598	−	0.0744848i
$667$		−	3.14685i		−	0.121846i
$668$	−8.63182	+	12.3723i	−0.333975	+	0.478699i
$669$		−	0.646255i		−	0.0249857i
$670$	−12.9727	+	15.4870i	−0.501179	+	0.598315i
$671$	−43.7991	+	43.7991i	−1.69085	+	1.69085i
$672$	55.2599	−	26.0550i	2.13170	−	1.00509i
$673$	−27.8608			−1.07395			−0.536977	−	0.843597i	$-0.680434\pi$
$673$	−27.8608			−1.07395			−0.536977	+	0.843597i	$0.680434\pi$
$674$	27.0456	−	2.38939i	1.04176	−	0.0920357i
$675$		−	9.92719i		−	0.382098i
$676$	−4.96524	−	27.8816i	−0.190971	−	1.07237i
$677$		−	5.81128i		−	0.223346i	−0.993745	−	0.111673i	$-0.964379\pi$
$677$		−	5.81128i		−	0.223346i	0.993745	−	0.111673i	$-0.0356209\pi$
$678$	23.6952	+	19.8482i	0.910007	+	0.762267i
$679$	13.3215	−	13.3215i	0.511231	−	0.511231i
$680$	1.11515	−	0.301858i	0.0427641	−	0.0115757i
$681$	−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	$-0.702393\pi$
$683$	5.50713	−	5.50713i	0.210724	−	0.210724i	0.804575	+	0.593851i	$0.202393\pi$
$684$	49.7247	−	71.2722i	1.90127	−	2.72516i
$685$	−10.1621	−	10.1621i	−0.388274	−	0.388274i
$686$	−7.03085	+	0.621152i	−0.268439	+	0.0237157i
$687$	−32.9115			−1.25565
$688$	−3.26278	+	7.05972i	−0.124392	+	0.269149i
$689$	−37.8818	−	37.8818i	−1.44318	−	1.44318i
$690$	−0.134588	−	1.52341i	−0.00512369	−	0.0579954i
$691$	20.1854			0.767890			0.383945	−	0.923356i	$-0.374565\pi$
$691$	20.1854			0.767890			0.383945	+	0.923356i	$0.374565\pi$
$692$	−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
$698$	0.440940	+	4.99103i	0.0166898	+	0.188913i
$699$			59.5622i			2.25285i
$700$	6.98756	−	1.24437i	0.264105	−	0.0470326i
$701$	30.6020	+	30.6020i	1.15582	+	1.15582i	0.985365	+	0.170456i	$0.0545241\pi$
$701$	30.6020	+	30.6020i	1.15582	+	1.15582i	0.170456	+	0.985365i	$0.445476\pi$
$702$	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
$708$	9.71683	−	13.9275i	0.365181	−	0.523427i
$709$	10.3275	+	10.3275i	0.387856	+	0.387856i	0.873922	−	0.486066i	$-0.161569\pi$
$709$	10.3275	+	10.3275i	0.387856	+	0.387856i	−0.486066	+	0.873922i	$0.661569\pi$
$710$	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
$716$	22.9929	+	16.0415i	0.859283	+	0.599499i
$717$	16.9110	−	16.9110i	0.631553	−	0.631553i
$718$	9.01098	−	0.796089i	0.336287	−	0.0297098i
$719$		−	28.4515i		−	1.06106i	−0.847665	−	0.530532i	$-0.821992\pi$
$719$		−	28.4515i		−	1.06106i	0.847665	−	0.530532i	$-0.178008\pi$
$720$	22.7369	+	10.5083i	0.847353	+	0.391620i
$721$	18.3788	−	18.3788i	0.684462	−	0.684462i
$722$	41.0650	−	3.62795i	1.52828	−	0.135018i
$723$	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
$726$	−7.31327	−	82.7794i	−0.271421	−	3.07223i
$727$	9.33076	+	9.33076i	0.346059	+	0.346059i	0.858639	−	0.512580i	$-0.171310\pi$
$727$	9.33076	+	9.33076i	0.346059	+	0.346059i	−0.512580	+	0.858639i	$0.671310\pi$
$728$	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
$732$	−39.1844	+	56.1644i	−1.44830	+	2.07590i
$733$			14.3359i			0.529510i	0.964316	+	0.264755i	$0.0852910\pi$
$733$			14.3359i			0.529510i	−0.964316	+	0.264755i	$0.914709\pi$
$734$	−5.82302	+	0.514443i	−0.214931	+	0.0189885i
$735$	12.0373	+	12.0373i	0.444001	+	0.444001i
$736$	1.89178	+	0.679445i	0.0697318	+	0.0250447i
$737$	78.6447			2.89692
$738$	−16.0265	+	1.41589i	−0.589945	+	0.0521196i
$739$	−25.1747			−0.926066			−0.463033	−	0.886341i	$-0.653239\pi$
$739$	−25.1747			−0.926066			−0.463033	+	0.886341i	$0.653239\pi$
$740$	8.13973	−	9.04128i	0.299222	−	0.332364i
$741$	110.057			4.04304
$742$	51.3904	−	4.54016i	1.88660	−	0.166675i
$743$	41.7006			1.52985			0.764923	−	0.644122i	$-0.222777\pi$
$743$	41.7006			1.52985			0.764923	+	0.644122i	$0.222777\pi$
$744$	13.2027	−	23.0032i	0.484033	−	0.843336i
$745$	7.86215	+	7.86215i	0.288047	+	0.288047i
$746$	37.1203	−	3.27945i	1.35907	−	0.120069i
$747$			18.0554i			0.660614i
$748$	−3.68838	−	2.57329i	−0.134861	−	0.0940886i
$749$	−23.5033			−0.858793
$750$	3.29936	+	2.76371i	0.120476	+	0.100916i
$751$	−12.5103			−0.456509			−0.228254	−	0.973602i	$-0.573302\pi$
$751$	−12.5103			−0.456509			−0.228254	+	0.973602i	$0.573302\pi$
$752$	2.80909	+	7.63691i	0.102437	+	0.278489i
$753$	−8.69629	−	8.69629i	−0.316910	−	0.316910i
$754$	5.74404	+	65.0171i	0.209185	+	2.36778i
$755$	−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	0.875620	−	0.483000i	$-0.160453\pi$
$757$	10.8024	+	10.8024i	0.392620	+	0.392620i	−0.483000	+	0.875620i	$0.660453\pi$
$758$	−27.1799	+	2.40125i	−0.987218	+	0.0872173i
$759$	−4.20976	+	4.20976i	−0.152805	+	0.152805i
$760$	5.12814	+	18.9448i	0.186017	+	0.687200i
$761$		−	19.3432i		−	0.701189i	−0.936527	−	0.350595i	$-0.885979\pi$
$761$		−	19.3432i		−	0.701189i	0.936527	−	0.350595i	$-0.114021\pi$
$762$	−53.9443	+	4.76579i	−1.95420	+	0.172646i
$763$	17.1654	−	17.1654i	0.621429	−	0.621429i
$764$	0.467804	−	0.670521i	0.0169246	−	0.0242586i
$765$			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	−0.563204	−	0.826318i	$-0.690431\pi$
$769$	7.29639	−	7.29639i	0.263114	−	0.263114i	0.826318	+	0.563204i	$0.190431\pi$
$770$	−21.1804	−	17.7418i	−0.763290	−	0.639370i
$771$	−11.8597	−	11.8597i	−0.427118	−	0.427118i
$772$	−11.6659	−	8.13895i	−0.419863	−	0.292927i
$773$	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
$782$	0.0180634	+	0.204461i	0.000645947	+	0.00731152i
$783$	−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
$790$	0.443125	+	5.01576i	0.0157657	+	0.178453i
$791$	−18.0215	−	18.0215i	−0.640769	−	0.640769i
$792$	−25.4770	−	94.1195i	−0.905288	−	3.34439i
$793$	−58.6361			−2.08223
$794$	−21.1328	+	1.86701i	−0.749973	+	0.0662575i
$795$	22.1216	+	22.1216i	0.784571	+	0.784571i
$796$	38.6360	+	26.9553i	1.36942	+	0.955405i
$797$	−5.16043	+	5.16043i	−0.182792	+	0.182792i	−0.792571	−	0.609779i	$-0.791258\pi$
$797$	−5.16043	+	5.16043i	−0.182792	+	0.182792i	0.609779	+	0.792571i	$0.291258\pi$
$798$	−68.0562	+	81.2465i	−2.40916	+	2.87610i
$799$	−0.587546	+	0.587546i	−0.0207859	+	0.0207859i
$800$	−5.11663	+	2.41249i	−0.180900	+	0.0852944i
$801$	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
$806$	22.6212	−	1.99850i	0.796797	−	0.0703942i
$807$	−87.1637			−3.06831
$808$	48.8919	−	13.2345i	1.72001	−	0.465586i
$809$	−11.4336	+	11.4336i	−0.401985	+	0.401985i	−0.878932	−	0.476947i	$-0.841743\pi$
$809$	−11.4336	+	11.4336i	−0.401985	+	0.401985i	0.476947	+	0.878932i	$0.341743\pi$
$810$	−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	$-0.0868525\pi$
$812$	−51.5491	−	35.9645i	−1.80902	−	1.26210i
$813$		−	56.1882i		−	1.97061i
$814$	−47.3282	−	1.68996i	−1.65885	−	0.0592332i
$815$			11.5030i			0.402931i
$816$	−4.51353	−	2.08601i	−0.158005	−	0.0730251i
$817$		−	13.4917i		−	0.472014i
$818$	0.707246	+	0.592425i	0.0247283	+	0.0207136i
$819$	−81.8907	+	81.8907i	−2.86149	+	2.86149i
$820$	2.07907	−	2.98000i	0.0726041	−	0.104066i
$821$	48.9359			1.70788			0.853938	−	0.520375i	$-0.174208\pi$
$821$	48.9359			1.70788			0.853938	+	0.520375i	$0.174208\pi$
$822$	5.44334	+	61.6135i	0.189858	+	2.14902i
$823$			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	$-0.823177\pi$
$827$	−9.26744	+	9.26744i	−0.322260	+	0.322260i	0.527373	+	0.849634i	$0.323177\pi$
$828$	−2.54632	+	3.64973i	−0.0884906	+	0.126837i
$829$	11.0440	−	11.0440i	0.383572	−	0.383572i	−0.488815	−	0.872387i	$-0.662571\pi$
$829$	11.0440	−	11.0440i	0.383572	−	0.383572i	0.872387	+	0.488815i	$0.162571\pi$
$830$	−3.12592	−	2.61843i	−0.108502	−	0.0908871i
$831$	16.4160	−	16.4160i	0.569463	−	0.569463i
$832$	−40.3263	−	10.5849i	−1.39806	−	0.366966i
$833$	−1.61555	−	1.61555i	−0.0559755	−	0.0559755i
$834$	−4.21336	−	47.6913i	−0.145897	−	1.65141i
$835$	7.54291			0.261033
$836$	43.7164	−	62.6603i	1.51196	−	2.16715i
$837$	21.6289	+	21.6289i	0.747603	+	0.747603i
$838$	−32.4247	+	2.86461i	−1.12009	+	0.0989564i
$839$	−9.29548			−0.320916			−0.160458	−	0.987043i	$-0.551297\pi$
$839$	−9.29548			−0.320916			−0.160458	+	0.987043i	$0.551297\pi$
$840$	−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
$846$	−17.9452	+	1.58540i	−0.616968	+	0.0545070i
$847$			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	−0.112435	−	0.993659i	$-0.535865\pi$
$853$	25.7372	−	25.7372i	0.881224	−	0.881224i	0.993659	+	0.112435i	$0.0358651\pi$
$854$	36.2590	−	43.2866i	1.24076	−	1.48124i
$855$	−43.4519			−1.48602
$856$	18.0819	−	4.89456i	0.618027	−	0.167293i
$857$	−26.9222	−	26.9222i	−0.919646	−	0.919646i	0.0773577	−	0.997003i	$-0.475352\pi$
$857$	−26.9222	−	26.9222i	−0.919646	−	0.919646i	−0.997003	+	0.0773577i	$0.975352\pi$
$858$	79.2938	−	94.6622i	2.70705	−	3.23171i
$859$	−3.03404	+	3.03404i	−0.103520	+	0.103520i	−0.756970	−	0.653450i	$-0.773321\pi$
$859$	−3.03404	+	3.03404i	−0.103520	+	0.103520i	0.653450	+	0.756970i	$0.273321\pi$
$860$	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	$0.884698\pi$
$864$	−23.9492	−	50.7937i	−0.814770	−	1.72804i
$865$	−6.42154	+	6.42154i	−0.218339	+	0.218339i
$866$	0.535135	+	6.05722i	0.0181846	+	0.205833i
$867$			51.2291i			1.73983i
$868$	−12.5130	+	17.9353i	−0.424718	+	0.608764i
$869$	13.8604	−	13.8604i	0.470182	−	0.470182i
$870$	−3.35430	−	37.9676i	−0.113721	−	1.28722i
$871$	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
$874$	−3.47350	+	0.306872i	−0.117493	+	0.0103801i
$875$	−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
$880$	19.9896	+	9.23855i	0.673848	+	0.311431i
$881$			53.2166i			1.79291i	0.443132	+	0.896457i	$0.353867\pi$
$881$			53.2166i			1.79291i	−0.443132	+	0.896457i	$0.646133\pi$
$882$	−4.35930	−	49.3432i	−0.146785	−	1.66147i
$883$	−28.6806	−	28.6806i	−0.965181	−	0.965181i	0.0342332	−	0.999414i	$-0.489101\pi$
$883$	−28.6806	−	28.6806i	−0.965181	−	0.965181i	−0.999414	+	0.0342332i	$0.989101\pi$
$884$	−0.746419	−	4.19141i	−0.0251048	−	0.140972i
$885$	−8.49104			−0.285423
$886$	−3.20178	−	36.2411i	−0.107566	−	1.21754i
$887$	8.29465			0.278507			0.139254	−	0.990257i	$-0.455530\pi$
$887$	8.29465			0.278507			0.139254	+	0.990257i	$0.455530\pi$
$888$	−51.8434	+	7.33460i	−1.73975	+	0.246133i
$889$	44.6522			1.49759
$890$	0.963943	+	10.9109i	0.0323114	+	0.365735i
$891$	62.9037			2.10735
$892$	−0.0744606	−	0.418123i	−0.00249312	−	0.0139998i
$893$	−9.98155	−	9.98155i	−0.334020	−	0.334020i
$894$	−4.21137	−	47.6688i	−0.140849	−	1.59428i
$895$		−	14.0179i		−	0.468565i
$896$	32.7507	−	23.2244i	1.09412	−	0.775872i
$897$	−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
$902$	−14.0900	+	1.24481i	−0.469147	+	0.0414475i
$903$	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
$906$	3.17933	+	35.9870i	0.105626	+	1.19559i
$907$	23.2515	−	23.2515i	0.772055	−	0.772055i	−0.206411	−	0.978465i	$-0.566178\pi$
$907$	23.2515	−	23.2515i	0.772055	−	0.772055i	0.978465	+	0.206411i	$0.0661783\pi$
$908$	−24.4875	+	35.0987i	−0.812645	+	1.16479i
$909$			112.139i			3.71940i
$910$	−2.30175	−	26.0536i	−0.0763021	−	0.863668i
$911$	−29.5003	+	29.5003i	−0.977389	+	0.977389i	−0.999750	−	0.0223608i	$-0.992882\pi$
$911$	−29.5003	+	29.5003i	−0.977389	+	0.977389i	0.0223608	+	0.999750i	$0.492882\pi$
$912$	35.4384	−	76.6784i	1.17348	−	2.53908i
$913$			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	0.999487	+	0.0320162i	$0.0101928\pi$
$919$	31.2700	+	31.2700i	1.03150	+	1.03150i	0.0320162	+	0.999487i	$0.489807\pi$
$920$	−0.262603	−	0.970131i	−0.00865777	−	0.0319843i
$921$	−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	$0.0740052\pi$
$929$			14.0453i			0.460810i	−0.973095	+	0.230405i	$0.925995\pi$
$930$	−13.2099	+	1.16705i	−0.433170	+	0.0382691i
$931$	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	$0.764745\pi$
$938$	−71.4152	+	6.30928i	−2.33179	+	0.206005i
$939$	−18.0356	−	18.0356i	−0.588569	−	0.588569i
$940$	2.32796	−	3.33675i	0.0759298	−	0.108833i
$941$	−26.8218			−0.874365			−0.437182	−	0.899373i	$-0.644024\pi$
$941$	−26.8218			−0.874365			−0.437182	+	0.899373i	$0.644024\pi$
$942$	1.23783	+	14.0111i	0.0403307	+	0.456505i
$943$	0.456489	+	0.456489i	0.0148653	+	0.0148653i
$944$	4.68202	−	10.1305i	0.152387	−	0.329721i
$945$	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	$-0.781954\pi$
$947$	−4.36152	+	4.36152i	−0.141730	+	0.141730i	0.632682	+	0.774412i	$0.281954\pi$
$948$	12.4001	−	17.7735i	0.402736	−	0.577256i
$949$	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	$-0.721455\pi$
$953$		−	47.3922i		−	1.53518i	0.640940	−	0.767591i	$-0.278545\pi$
$954$	−8.01133	−	90.6807i	−0.259376	−	2.93590i
$955$	−0.408791			−0.0132282
$956$	8.99284	−	12.8898i	0.290849	−	0.416885i
$957$	−104.918	+	104.918i	−3.39153	+	3.39153i
$958$	−30.8063	−	25.8049i	−0.995305	−	0.833718i
$959$		−	51.0004i		−	1.64689i
$960$	23.5490	+	6.18120i	0.760042	+	0.199497i
$961$		−	21.5061i		−	0.693745i
$962$	−30.5491	−	32.8116i	−0.984944	−	1.05789i
$963$			41.4728i			1.33644i
$964$	22.2109	+	15.4959i	0.715365	+	0.499091i
$965$			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	$-0.680805\pi$
$967$	9.48475	−	9.48475i	0.305009	−	0.305009i	0.842970	+	0.537961i	$0.180805\pi$
$968$	−14.2693	−	52.7150i	−0.458634	−	1.69433i
$969$	8.62570			0.277098
$970$	7.47858	−	0.660706i	0.240123	−	0.0212140i
$971$		−	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
$976$	−18.8809	+	40.8528i	−0.604362	+	1.30767i
$977$	9.75590	−	9.75590i	0.312119	−	0.312119i	−0.533611	−	0.845730i	$-0.679165\pi$
$977$	9.75590	−	9.75590i	0.312119	−	0.312119i	0.845730	+	0.533611i	$0.179165\pi$
$978$	31.7908	−	37.9524i	1.01656	−	1.21358i
$979$	30.1509	−	30.1509i	0.963628	−	0.963628i
$980$	9.17494	+	6.40111i	0.293083	+	0.204476i
$981$	−30.2891	−	30.2891i	−0.967058	−	0.967058i
$982$	−37.7764	+	3.33742i	−1.20549	+	0.106501i
$983$	−0.767711			−0.0244862			−0.0122431	−	0.999925i	$-0.503897\pi$
$983$	−0.767711			−0.0244862			−0.0122431	+	0.999925i	$0.503897\pi$
$984$	−15.0954	+	4.08616i	−0.481225	+	0.130262i
$985$	−2.91162	−	2.91162i	−0.0927720	−	0.0927720i
$986$	0.450189	+	5.09572i	0.0143369	+	0.162281i
$987$	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	$-0.264213\pi$
$991$	−1.98721	−	1.98721i	−0.0631259	−	0.0631259i	−0.737965	+	0.674839i	$0.764213\pi$
$992$	5.89164	−	16.4041i	0.187060	−	0.520830i
$993$	−29.9229	+	29.9229i	−0.949573	+	0.949573i
$994$	2.50434	+	28.3468i	0.0794329	+	0.899106i
$995$		−	23.5549i		−	0.746739i
$996$	3.07697	+	17.2783i	0.0974976	+	0.547484i
$997$	−20.1252	−	20.1252i	−0.637370	−	0.637370i	0.312536	−	0.949906i	$-0.398822\pi$
$997$	−20.1252	−	20.1252i	−0.637370	−	0.637370i	−0.949906	+	0.312536i	$0.898822\pi$
$998$	−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.191.42	yes	152
4.3	odd	2	inner	740.2.u.a.191.1	yes	152
37.31	odd	4	inner	740.2.u.a.31.1	✓	152
148.31	even	4	inner	740.2.u.a.31.42	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.u.a.31.1	✓	152	37.31	odd	4	inner
740.2.u.a.31.42	yes	152	148.31	even	4	inner
740.2.u.a.191.1	yes	152	4.3	odd	2	inner
740.2.u.a.191.42	yes	152	1.1	even	1	trivial

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+(0.124456 + 1.40873i) q^{2} -3.04334 q^{3} +(-1.96902 + 0.350649i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.378763 - 4.28724i) q^{6} +3.54875i q^{7} +(-0.739026 - 2.73017i) 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} +(-4.99921 + 0.441663i) q^{14} +(-2.15197 - 2.15197i) q^{15} +(3.75409 - 1.38087i) q^{16} +(0.288821 + 0.288821i) q^{17} +(0.779336 + 8.82135i) q^{18} +(-4.90665 + 4.90665i) q^{19} +(-1.64025 - 1.14436i) q^{20} -10.8001i q^{21} +(0.685168 + 7.75546i) q^{22} +(0.251261 - 0.251261i) q^{23} +(2.24911 + 8.30885i) 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} +(2.41249 + 5.11663i) 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} +(15.2143 - 1.34413i) 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} +(-1.40873 + 0.124456i) q^{50} +(-0.878981 - 0.878981i) q^{51} +(-8.54825 - 5.96389i) q^{52} -10.2797 q^{53} +(-1.23550 - 13.9847i) q^{54} +(3.89283 + 3.89283i) q^{55} +(9.68869 - 2.62262i) q^{56} +(14.9326 - 14.9326i) q^{57} +(9.60094 + 8.04223i) q^{58} +(1.97286 - 1.97286i) q^{59} +(4.99186 + 3.48269i) 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} +(-2.08520 - 23.6025i) q^{66} +14.2853 q^{67} +(-0.669969 - 0.467420i) q^{68} +(-0.764674 + 0.764674i) q^{69} +(-3.84728 - 3.22268i) q^{70} -5.67025i q^{71} +(-4.62773 - 17.0962i) q^{72} -7.92218i q^{73} +(-8.59685 - 0.306970i) q^{74} -3.04334i q^{75} +(7.94078 - 11.3818i) q^{76} +19.5369i q^{77} +(14.4032 - 17.1947i) q^{78} +(2.51765 - 2.51765i) q^{79} +(3.63097 + 1.67812i) q^{80} +11.4260 q^{81} +(-2.55936 + 0.226111i) 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} +(-4.06856 - 15.0304i) q^{88} +(5.47671 - 5.47671i) q^{89} +(-5.68657 + 6.78871i) q^{90} +(-13.0775 + 13.0775i) q^{91} +(-0.406634 + 0.582843i) q^{92} +(6.63068 + 6.63068i) q^{93} +(-2.86576 + 0.253180i) q^{94} -6.93905 q^{95} +(-7.34204 - 15.5717i) q^{96} +(-3.75385 - 3.75385i) q^{97} +(-0.696159 - 7.87986i) 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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