LMFDB - Embedded newform 740.2.u.a.31.13

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			31.13
Character	$\chi$	$=$	740.31
Dual form			740.2.u.a.191.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.29954 + 0.557859i) q^{2} -2.62771 q^{3} +(1.37759 - 1.44991i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(3.41481 - 1.46589i) q^{6} +5.20761i q^{7} +(-0.981377 + 2.65272i) q^{8} +3.90487 q^{9} +(0.524445 - 1.31338i) q^{10} +4.49242 q^{11} +(-3.61990 + 3.80996i) q^{12} +(-0.442487 + 0.442487i) q^{13} +(-2.90511 - 6.76748i) q^{14} +(1.85807 - 1.85807i) q^{15} +(-0.204505 - 3.99477i) q^{16} +(3.94888 - 3.94888i) q^{17} +(-5.07452 + 2.17837i) q^{18} +(1.95846 + 1.95846i) q^{19} +(0.0511429 + 1.99935i) q^{20} -13.6841i q^{21} +(-5.83807 + 2.50614i) q^{22} +(-3.11281 - 3.11281i) q^{23} +(2.57878 - 6.97057i) q^{24} -1.00000i q^{25} +(0.328183 - 0.821873i) q^{26} -2.37774 q^{27} +(7.55059 + 7.17394i) q^{28} +(6.40099 + 6.40099i) q^{29} +(-1.37809 + 3.45118i) q^{30} +(-4.23759 + 4.23759i) q^{31} +(2.49428 + 5.07726i) q^{32} -11.8048 q^{33} +(-2.92879 + 7.33462i) q^{34} +(-3.68234 - 3.68234i) q^{35} +(5.37930 - 5.66173i) q^{36} +(6.07636 + 0.279018i) q^{37} +(-3.63763 - 1.45255i) q^{38} +(1.16273 - 1.16273i) q^{39} +(-1.18181 - 2.56969i) q^{40} +7.95524i q^{41} +(7.63379 + 17.7830i) q^{42} +(-2.88460 - 2.88460i) q^{43} +(6.18871 - 6.51363i) q^{44} +(-2.76116 + 2.76116i) q^{45} +(5.78172 + 2.30870i) q^{46} +8.87735i q^{47} +(0.537379 + 10.4971i) q^{48} -20.1192 q^{49} +(0.557859 + 1.29954i) q^{50} +(-10.3765 + 10.3765i) q^{51} +(0.0320037 + 1.25113i) q^{52} +12.0521 q^{53} +(3.08996 - 1.32644i) q^{54} +(-3.17662 + 3.17662i) q^{55} +(-13.8143 - 5.11063i) q^{56} +(-5.14627 - 5.14627i) q^{57} +(-11.8892 - 4.74747i) q^{58} +(3.35411 + 3.35411i) q^{59} +(-0.134389 - 5.25371i) q^{60} +(-5.46979 - 5.46979i) q^{61} +(3.14292 - 7.87087i) q^{62} +20.3350i q^{63} +(-6.07380 - 5.20663i) q^{64} -0.625771i q^{65} +(15.3408 - 6.58541i) q^{66} -4.17514 q^{67} +(-0.285610 - 11.1655i) q^{68} +(8.17957 + 8.17957i) q^{69} +(6.83955 + 2.73111i) q^{70} -6.13360i q^{71} +(-3.83215 + 10.3585i) q^{72} +5.49958i q^{73} +(-8.05210 + 3.02715i) q^{74} +2.62771i q^{75} +(5.53755 - 0.141649i) q^{76} +23.3948i q^{77} +(-0.862369 + 2.15965i) q^{78} +(-1.29005 - 1.29005i) q^{79} +(2.96933 + 2.68012i) q^{80} -5.46659 q^{81} +(-4.43790 - 10.3381i) q^{82} -2.48336i q^{83} +(-19.8408 - 18.8510i) q^{84} +5.58456i q^{85} +(5.35784 + 2.13944i) q^{86} +(-16.8200 - 16.8200i) q^{87} +(-4.40876 + 11.9171i) q^{88} +(-3.60454 - 3.60454i) q^{89} +(2.04789 - 5.12857i) q^{90} +(-2.30430 - 2.30430i) q^{91} +(-8.80148 + 0.225140i) q^{92} +(11.1352 - 11.1352i) q^{93} +(-4.95231 - 11.5364i) q^{94} -2.76968 q^{95} +(-6.55424 - 13.3416i) q^{96} +(-4.10744 + 4.10744i) q^{97} +(26.1456 - 11.2237i) q^{98} +17.5423 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 $

$2$	−1.29954	+	0.557859i	−0.918911	+	0.394466i
$2$	−1.29954	+	0.557859i	−0.918911	+	0.394466i
$3$	−2.62771			−1.51711			−0.758555	−	0.651609i	$-0.774094\pi$
$3$	−2.62771			−1.51711			−0.758555	+	0.651609i	$0.774094\pi$
$4$	1.37759	−	1.44991i	0.688794	−	0.724957i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	3.41481	−	1.46589i	1.39409	−	0.598448i
$7$			5.20761i			1.96829i	0.177363	+	0.984146i	$0.443243\pi$
$7$			5.20761i			1.96829i	−0.177363	+	0.984146i	$0.556757\pi$
$8$	−0.981377	+	2.65272i	−0.346969	+	0.937876i
$9$	3.90487			1.30162
$10$	0.524445	−	1.31338i	0.165844	−	0.415326i
$11$	4.49242			1.35452			0.677258	−	0.735745i	$-0.263168\pi$
$11$	4.49242			1.35452			0.677258	+	0.735745i	$0.263168\pi$
$12$	−3.61990	+	3.80996i	−1.04498	+	1.09984i
$13$	−0.442487	+	0.442487i	−0.122724	+	0.122724i	−0.765801	−	0.643077i	$-0.777657\pi$
$13$	−0.442487	+	0.442487i	−0.122724	+	0.122724i	0.643077	+	0.765801i	$0.277657\pi$
$14$	−2.90511	−	6.76748i	−0.776423	−	1.80868i
$15$	1.85807	−	1.85807i	0.479752	−	0.479752i
$16$	−0.204505	−	3.99477i	−0.0511261	−	0.998692i
$17$	3.94888	−	3.94888i	0.957743	−	0.957743i	−0.0413992	−	0.999143i	$-0.513182\pi$
$17$	3.94888	−	3.94888i	0.957743	−	0.957743i	0.999143	+	0.0413992i	$0.0131816\pi$
$18$	−5.07452	+	2.17837i	−1.19608	+	0.513446i
$19$	1.95846	+	1.95846i	0.449302	+	0.449302i	0.895122	−	0.445821i	$-0.147088\pi$
$19$	1.95846	+	1.95846i	0.449302	+	0.449302i	−0.445821	+	0.895122i	$0.647088\pi$
$20$	0.0511429	+	1.99935i	0.0114359	+	0.447067i
$21$		−	13.6841i		−	2.98612i
$22$	−5.83807	+	2.50614i	−1.24468	+	0.534310i
$23$	−3.11281	−	3.11281i	−0.649066	−	0.649066i	0.303701	−	0.952767i	$-0.401777\pi$
$23$	−3.11281	−	3.11281i	−0.649066	−	0.649066i	−0.952767	+	0.303701i	$0.901777\pi$
$24$	2.57878	−	6.97057i	0.526391	−	1.42286i
$25$		−	1.00000i		−	0.200000i
$26$	0.328183	−	0.821873i	0.0643619	−	0.161183i
$27$	−2.37774			−0.457597
$28$	7.55059	+	7.17394i	1.42693	+	1.35575i
$29$	6.40099	+	6.40099i	1.18863	+	1.18863i	0.977445	+	0.211189i	$0.0677335\pi$
$29$	6.40099	+	6.40099i	1.18863	+	1.18863i	0.211189	+	0.977445i	$0.432267\pi$
$30$	−1.37809	+	3.45118i	−0.251604	+	0.630095i
$31$	−4.23759	+	4.23759i	−0.761093	+	0.761093i	−0.976520	−	0.215427i	$-0.930886\pi$
$31$	−4.23759	+	4.23759i	−0.761093	+	0.761093i	0.215427	+	0.976520i	$0.430886\pi$
$32$	2.49428	+	5.07726i	0.440930	+	0.897541i
$33$	−11.8048			−2.05495
$34$	−2.92879	+	7.33462i	−0.502284	+	1.25788i
$35$	−3.68234	−	3.68234i	−0.622428	−	0.622428i
$36$	5.37930	−	5.66173i	0.896551	−	0.943622i
$37$	6.07636	+	0.279018i	0.998947	+	0.0458704i
$37$	6.07636	+	0.279018i	0.998947	+	0.0458704i
$38$	−3.63763	−	1.45255i	−0.590102	−	0.235634i
$39$	1.16273	−	1.16273i	0.186186	−	0.186186i
$40$	−1.18181	−	2.56969i	−0.186861	−	0.406304i
$41$			7.95524i			1.24240i	0.783652	+	0.621200i	$0.213355\pi$
$41$			7.95524i			1.24240i	−0.783652	+	0.621200i	$0.786645\pi$
$42$	7.63379	+	17.7830i	1.17792	+	2.74397i
$43$	−2.88460	−	2.88460i	−0.439897	−	0.439897i	0.452080	−	0.891977i	$-0.350682\pi$
$43$	−2.88460	−	2.88460i	−0.439897	−	0.439897i	−0.891977	+	0.452080i	$0.850682\pi$
$44$	6.18871	−	6.51363i	0.932983	−	0.981967i
$45$	−2.76116	+	2.76116i	−0.411610	+	0.411610i
$46$	5.78172	+	2.30870i	0.852468	+	0.340399i
$47$			8.87735i			1.29489i	0.762110	+	0.647447i	$0.224163\pi$
$47$			8.87735i			1.29489i	−0.762110	+	0.647447i	$0.775837\pi$
$48$	0.537379	+	10.4971i	0.0775640	+	1.51513i
$49$	−20.1192			−2.87417
$50$	0.557859	+	1.29954i	0.0788931	+	0.183782i
$51$	−10.3765	+	10.3765i	−1.45300	+	1.45300i
$52$	0.0320037	+	1.25113i	0.00443812	+	0.173501i
$53$	12.0521			1.65549			0.827744	−	0.561106i	$-0.189624\pi$
$53$	12.0521			1.65549			0.827744	+	0.561106i	$0.189624\pi$
$54$	3.08996	−	1.32644i	0.420491	−	0.180506i
$55$	−3.17662	+	3.17662i	−0.428336	+	0.428336i
$56$	−13.8143	−	5.11063i	−1.84601	−	0.682937i
$57$	−5.14627	−	5.14627i	−0.681640	−	0.681640i
$58$	−11.8892	−	4.74747i	−1.56112	−	0.623373i
$59$	3.35411	+	3.35411i	0.436668	+	0.436668i	0.890889	−	0.454221i	$-0.150082\pi$
$59$	3.35411	+	3.35411i	0.436668	+	0.436668i	−0.454221	+	0.890889i	$0.650082\pi$
$60$	−0.134389	−	5.25371i	−0.0173495	−	0.678251i
$61$	−5.46979	−	5.46979i	−0.700335	−	0.700335i	0.264148	−	0.964482i	$-0.414909\pi$
$61$	−5.46979	−	5.46979i	−0.700335	−	0.700335i	−0.964482	+	0.264148i	$0.914909\pi$
$62$	3.14292	−	7.87087i	0.399151	−	0.999601i
$63$			20.3350i			2.56198i
$64$	−6.07380	−	5.20663i	−0.759225	−	0.650829i
$65$		−	0.625771i		−	0.0776173i
$66$	15.3408	−	6.58541i	1.88832	−	0.810608i
$67$	−4.17514			−0.510075			−0.255037	−	0.966931i	$-0.582088\pi$
$67$	−4.17514			−0.510075			−0.255037	+	0.966931i	$0.582088\pi$
$68$	−0.285610	−	11.1655i	−0.0346353	−	1.35401i
$69$	8.17957	+	8.17957i	0.984705	+	0.984705i
$70$	6.83955	+	2.73111i	0.817483	+	0.326430i
$71$		−	6.13360i		−	0.727925i	−0.931414	−	0.363962i	$-0.881424\pi$
$71$		−	6.13360i		−	0.727925i	0.931414	−	0.363962i	$-0.118576\pi$
$72$	−3.83215	+	10.3585i	−0.451624	+	1.22076i
$73$			5.49958i			0.643677i	0.946795	+	0.321839i	$0.104301\pi$
$73$			5.49958i			0.643677i	−0.946795	+	0.321839i	$0.895699\pi$
$74$	−8.05210	+	3.02715i	−0.936038	+	0.351900i
$75$			2.62771i			0.303422i
$76$	5.53755	−	0.141649i	0.635201	−	0.0162483i
$77$			23.3948i			2.66608i
$78$	−0.862369	+	2.15965i	−0.0976441	+	0.244532i
$79$	−1.29005	−	1.29005i	−0.145142	−	0.145142i	0.630802	−	0.775944i	$-0.282726\pi$
$79$	−1.29005	−	1.29005i	−0.145142	−	0.145142i	−0.775944	+	0.630802i	$0.782726\pi$
$80$	2.96933	+	2.68012i	0.331982	+	0.299647i
$81$	−5.46659			−0.607399
$82$	−4.43790	−	10.3381i	−0.490084	−	1.14165i
$83$		−	2.48336i		−	0.272584i	−0.990669	−	0.136292i	$-0.956481\pi$
$83$		−	2.48336i		−	0.272584i	0.990669	−	0.136292i	$-0.0435186\pi$
$84$	−19.8408	−	18.8510i	−2.16481	−	2.05682i
$85$			5.58456i			0.605730i
$86$	5.35784	+	2.13944i	0.577751	+	0.230702i
$87$	−16.8200	−	16.8200i	−1.80329	−	1.80329i
$88$	−4.40876	+	11.9171i	−0.469976	+	1.27037i
$89$	−3.60454	−	3.60454i	−0.382081	−	0.382081i	0.489771	−	0.871851i	$-0.337081\pi$
$89$	−3.60454	−	3.60454i	−0.382081	−	0.382081i	−0.871851	+	0.489771i	$0.837081\pi$
$90$	2.04789	−	5.12857i	0.215867	−	0.540598i
$91$	−2.30430	−	2.30430i	−0.241556	−	0.241556i
$92$	−8.80148	+	0.225140i	−0.917618	+	0.0234725i
$93$	11.1352	−	11.1352i	1.15466	−	1.15466i
$94$	−4.95231	−	11.5364i	−0.510791	−	1.18989i
$95$	−2.76968			−0.284163
$96$	−6.55424	−	13.3416i	−0.668940	−	1.36167i
$97$	−4.10744	+	4.10744i	−0.417048	+	0.417048i	−0.884185	−	0.467137i	$-0.845285\pi$
$97$	−4.10744	+	4.10744i	−0.417048	+	0.417048i	0.467137	+	0.884185i	$0.345285\pi$
$98$	26.1456	−	11.2237i	2.64111	−	1.13376i
$99$	17.5423			1.76307
$100$	−1.44991	−	1.37759i	−0.144991	−	0.137759i
$101$			3.60331i			0.358542i	0.983800	+	0.179271i	$0.0573740\pi$
$101$			3.60331i			0.358542i	−0.983800	+	0.179271i	$0.942626\pi$
$102$	7.69603	−	19.2733i	0.762020	−	1.90834i
$103$	−5.99273	+	5.99273i	−0.590481	+	0.590481i	−0.937761	−	0.347280i	$-0.887105\pi$
$103$	−5.99273	+	5.99273i	−0.590481	+	0.590481i	0.347280	+	0.937761i	$0.387105\pi$
$104$	−0.739545	−	1.60804i	−0.0725184	−	0.157681i
$105$	9.67612	+	9.67612i	0.944292	+	0.944292i
$106$	−15.6622	+	6.72339i	−1.52125	+	0.653033i
$107$		−	9.89603i		−	0.956685i	−0.878173	−	0.478343i	$-0.841238\pi$
$107$		−	9.89603i		−	0.956685i	0.878173	−	0.478343i	$-0.158762\pi$
$108$	−3.27555	+	3.44752i	−0.315190	+	0.331738i
$109$	−10.0578	+	10.0578i	−0.963364	+	0.963364i	−0.999352	−	0.0359882i	$-0.988542\pi$
$109$	−10.0578	+	10.0578i	−0.963364	+	0.963364i	0.0359882	+	0.999352i	$0.488542\pi$
$110$	2.35603	−	5.90024i	0.224639	−	0.562566i
$111$	−15.9669	−	0.733180i	−1.51551	−	0.0695904i
$112$	20.8032	−	1.06498i	1.96572	−	0.100631i
$113$	−6.25489	−	6.25489i	−0.588411	−	0.588411i	0.348790	−	0.937201i	$-0.386593\pi$
$113$	−6.25489	−	6.25489i	−0.588411	−	0.588411i	−0.937201	+	0.348790i	$0.886593\pi$
$114$	9.55865	+	3.81687i	0.895250	+	0.357483i
$115$	4.40218			0.410505
$116$	18.0988	−	0.462964i	1.68043	−	0.0429851i
$117$	−1.72785	+	1.72785i	−0.159740	+	0.159740i
$118$	−6.22991	−	2.48767i	−0.573510	−	0.229009i
$119$	20.5642	+	20.5642i	1.88512	+	1.88512i
$120$	3.10547	+	6.75241i	0.283489	+	0.616408i
$121$	9.18188			0.834716
$122$	10.1596	+	4.05682i	0.919803	+	0.367287i
$123$		−	20.9041i		−	1.88486i
$124$	0.306492	+	11.9818i	0.0275238	+	1.07600i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−11.3441	−	26.4261i	−1.01061	−	2.35423i
$127$			4.99694i			0.443407i	0.975114	+	0.221704i	$0.0711617\pi$
$127$			4.99694i			0.443407i	−0.975114	+	0.221704i	$0.928838\pi$
$128$	10.7977	+	3.37788i	0.954389	+	0.298566i
$129$	7.57990	+	7.57990i	0.667373	+	0.667373i
$130$	0.349092	+	0.813212i	0.0306174	+	0.0713234i
$131$	3.09591	−	3.09591i	0.270491	−	0.270491i	−0.558807	−	0.829298i	$-0.688741\pi$
$131$	3.09591	−	3.09591i	0.270491	−	0.270491i	0.829298	+	0.558807i	$0.188741\pi$
$132$	−16.2621	+	17.1159i	−1.41544	+	1.48975i
$133$	−10.1989	+	10.1989i	−0.884356	+	0.884356i
$134$	5.42575	−	2.32914i	0.468713	−	0.201207i
$135$	1.68132	−	1.68132i	0.144705	−	0.144705i
$136$	6.59991	+	14.3506i	0.565937	+	1.23055i
$137$	−3.30372			−0.282256			−0.141128	−	0.989991i	$-0.545073\pi$
$137$	−3.30372			−0.282256			−0.141128	+	0.989991i	$0.545073\pi$
$138$	−15.1927	−	6.06660i	−1.29329	−	0.516424i
$139$	−4.13746			−0.350934			−0.175467	−	0.984485i	$-0.556144\pi$
$139$	−4.13746			−0.350934			−0.175467	+	0.984485i	$0.556144\pi$
$140$	−10.4118	+	0.266332i	−0.879959	+	0.0225092i
$141$		−	23.3271i		−	1.96450i
$142$	3.42168	+	7.97084i	0.287141	+	0.668898i
$143$	−1.98784	+	1.98784i	−0.166231	+	0.166231i
$144$	−0.798564	−	15.5991i	−0.0665470	−	1.29992i
$145$	−9.05237			−0.751758
$146$	−3.06799	−	7.14690i	−0.253908	−	0.591482i
$147$	52.8674			4.36043
$148$	8.77527	−	8.42583i	0.721323	−	0.692599i
$149$	15.0664			1.23429			0.617145	−	0.786849i	$-0.288289\pi$
$149$	15.0664			1.23429			0.617145	+	0.786849i	$0.288289\pi$
$150$	−1.46589	−	3.41481i	−0.119690	−	0.278818i
$151$	12.3997			1.00908			0.504538	−	0.863390i	$-0.331663\pi$
$151$	12.3997			1.00908			0.504538	+	0.863390i	$0.331663\pi$
$152$	−7.11723	+	3.27325i	−0.577283	+	0.265496i
$153$	15.4199	−	15.4199i	1.24662	−	1.24662i
$154$	−13.0510	−	30.4024i	−1.05168	−	2.44989i
$155$		−	5.99285i		−	0.481357i
$156$	−0.0840966	−	3.28762i	−0.00673311	−	0.263220i
$157$	6.84164			0.546022			0.273011	−	0.962011i	$-0.411980\pi$
$157$	6.84164			0.546022			0.273011	+	0.962011i	$0.411980\pi$
$158$	2.39613	+	0.956801i	0.190626	+	0.0761190i
$159$	−31.6695			−2.51156
$160$	−5.35389	−	1.82645i	−0.423262	−	0.144393i
$161$	16.2103	−	16.2103i	1.27755	−	1.27755i
$162$	7.10403	−	3.04958i	0.558145	−	0.239598i
$163$	2.23351	−	2.23351i	0.174942	−	0.174942i	−0.614205	−	0.789147i	$-0.710523\pi$
$163$	2.23351	−	2.23351i	0.174942	−	0.174942i	0.789147	+	0.614205i	$0.210523\pi$
$164$	11.5344	+	10.9590i	0.900687	+	0.855757i
$165$	8.34725	−	8.34725i	0.649833	−	0.649833i
$166$	1.38536	+	3.22722i	0.107525	+	0.250481i
$167$	−3.77219	−	3.77219i	−0.291901	−	0.291901i	0.545930	−	0.837831i	$-0.316176\pi$
$167$	−3.77219	−	3.77219i	−0.291901	−	0.291901i	−0.837831	+	0.545930i	$0.816176\pi$
$168$	36.3000	+	13.4293i	2.80061	+	1.03609i
$169$			12.6084i			0.969878i
$170$	−3.11539	−	7.25733i	−0.238940	−	0.556612i
$171$	7.64754	+	7.64754i	0.584822	+	0.584822i
$172$	−8.15621	+	0.208634i	−0.621905	+	0.0159082i
$173$		−	4.24993i		−	0.323116i	−0.986863	−	0.161558i	$-0.948348\pi$
$173$		−	4.24993i		−	0.323116i	0.986863	−	0.161558i	$-0.0516519\pi$
$174$	31.2413	+	12.4750i	2.36840	+	0.945726i
$175$	5.20761			0.393658
$176$	−0.918721	−	17.9462i	−0.0692512	−	1.35275i
$177$	−8.81364	−	8.81364i	−0.662474	−	0.662474i
$178$	6.69506	+	2.67341i	0.501816	+	0.200380i
$179$	−13.1456	+	13.1456i	−0.982550	+	0.982550i	−0.999850	−	0.0173001i	$-0.994493\pi$
$179$	−13.1456	+	13.1456i	−0.982550	+	0.982550i	0.0173001	+	0.999850i	$0.494493\pi$
$180$	0.199706	+	7.80719i	0.0148852	+	0.581914i
$181$	1.15313			0.0857118			0.0428559	−	0.999081i	$-0.486354\pi$
$181$	1.15313			0.0857118			0.0428559	+	0.999081i	$0.486354\pi$
$182$	4.27999	+	1.70905i	0.317254	+	0.126683i
$183$	14.3730	+	14.3730i	1.06249	+	1.06249i
$184$	11.3122	−	5.20256i	0.833950	−	0.383538i
$185$	−4.49393	+	4.09934i	−0.330400	+	0.301389i
$186$	−8.25869	+	20.6824i	−0.605557	+	1.51651i
$187$	17.7400	−	17.7400i	1.29728	−	1.29728i
$188$	12.8714	+	12.2293i	0.938743	+	0.891916i
$189$		−	12.3824i		−	0.900684i
$190$	3.59930	−	1.54509i	0.261121	−	0.112093i
$191$	−7.34387	−	7.34387i	−0.531384	−	0.531384i	0.389600	−	0.920984i	$-0.372613\pi$
$191$	−7.34387	−	7.34387i	−0.531384	−	0.531384i	−0.920984	+	0.389600i	$0.872613\pi$
$192$	15.9602	+	13.6815i	1.15183	+	0.987379i
$193$	4.21937	−	4.21937i	0.303717	−	0.303717i	−0.538749	−	0.842466i	$-0.681103\pi$
$193$	4.21937	−	4.21937i	0.303717	−	0.303717i	0.842466	+	0.538749i	$0.181103\pi$
$194$	3.04640	−	7.62914i	0.218719	−	0.547740i
$195$			1.64435i			0.117754i
$196$	−27.7159	+	29.1711i	−1.97971	+	2.08365i
$197$	−22.2109			−1.58246			−0.791229	−	0.611520i	$-0.790558\pi$
$197$	−22.2109			−1.58246			−0.791229	+	0.611520i	$0.790558\pi$
$198$	−22.7969	+	9.78615i	−1.62011	+	0.695471i
$199$	−0.798323	+	0.798323i	−0.0565916	+	0.0565916i	−0.734836	−	0.678245i	$-0.762741\pi$
$199$	−0.798323	+	0.798323i	−0.0565916	+	0.0565916i	0.678245	+	0.734836i	$0.262741\pi$
$200$	2.65272	+	0.981377i	0.187575	+	0.0693939i
$201$	10.9711			0.773840
$202$	−2.01014	−	4.68263i	−0.141433	−	0.329468i
$203$	−33.3339	+	33.3339i	−2.33958	+	2.33958i
$204$	0.750501	+	29.3396i	0.0525456	+	2.05418i
$205$	−5.62520	−	5.62520i	−0.392881	−	0.392881i
$206$	4.44467	−	11.1309i	0.309675	−	0.775524i
$207$	−12.1551	−	12.1551i	−0.844840	−	0.844840i
$208$	1.85812	+	1.67714i	0.128838	+	0.116289i
$209$	8.79823	+	8.79823i	0.608587	+	0.608587i
$210$	−17.9724	−	7.17656i	−1.24021	−	0.495230i
$211$		−	19.7107i		−	1.35694i	−0.734626	−	0.678472i	$-0.762643\pi$
$211$		−	19.7107i		−	1.35694i	0.734626	−	0.678472i	$-0.237357\pi$
$212$	16.6029	−	17.4746i	1.14029	−	1.20016i
$213$			16.1173i			1.10434i
$214$	5.52058	+	12.8602i	0.377379	+	0.879108i
$215$	4.07944			0.278216
$216$	2.33346	−	6.30748i	0.158772	−	0.429169i
$217$	−22.0677	−	22.0677i	−1.49805	−	1.49805i
$218$	7.45966	−	18.6813i	0.505232	−	1.26526i
$219$		−	14.4513i		−	0.976529i
$220$	0.229755	+	8.98191i	0.0154901	+	0.605560i
$221$			3.49465i			0.235076i
$222$	21.1586	−	7.95449i	1.42007	−	0.533871i
$223$			6.92510i			0.463739i	0.972747	+	0.231870i	$0.0744842\pi$
$223$			6.92510i			0.463739i	−0.972747	+	0.231870i	$0.925516\pi$
$224$	−26.4404	+	12.9892i	−1.76662	+	0.867879i
$225$		−	3.90487i		−	0.260325i
$226$	11.6178	+	4.63911i	0.772805	+	0.308589i
$227$	−0.379069	−	0.379069i	−0.0251597	−	0.0251597i	0.694415	−	0.719575i	$-0.255663\pi$
$227$	−0.379069	−	0.379069i	−0.0251597	−	0.0251597i	−0.719575	+	0.694415i	$0.755663\pi$
$228$	−14.5511	+	0.372214i	−0.963670	+	0.0246505i
$229$	−10.2755			−0.679027			−0.339514	−	0.940601i	$-0.610262\pi$
$229$	−10.2755			−0.679027			−0.339514	+	0.940601i	$0.610262\pi$
$230$	−5.72079	+	2.45579i	−0.377218	+	0.161930i
$231$		−	61.4748i		−	4.04474i
$232$	−23.2618	+	10.6982i	−1.52721	+	0.702372i
$233$			9.28981i			0.608595i	0.952577	+	0.304298i	$0.0984218\pi$
$233$			9.28981i			0.608595i	−0.952577	+	0.304298i	$0.901578\pi$
$234$	1.28151	−	3.20931i	0.0837750	−	0.209799i
$235$	−6.27724	−	6.27724i	−0.409482	−	0.409482i
$236$	9.48376	−	0.242593i	0.617340	−	0.0157914i
$237$	3.38988	+	3.38988i	0.220196	+	0.220196i
$238$	−38.1959	−	15.2520i	−2.47587	−	0.988641i
$239$	−5.70017	−	5.70017i	−0.368713	−	0.368713i	0.498295	−	0.867008i	$-0.333960\pi$
$239$	−5.70017	−	5.70017i	−0.368713	−	0.368713i	−0.867008	+	0.498295i	$0.833960\pi$
$240$	−7.80256	−	7.04259i	−0.503653	−	0.454597i
$241$	5.85341	−	5.85341i	0.377051	−	0.377051i	−0.492986	−	0.870037i	$-0.664095\pi$
$241$	5.85341	−	5.85341i	0.377051	−	0.377051i	0.870037	+	0.492986i	$0.164095\pi$
$242$	−11.9322	+	5.12219i	−0.767029	+	0.329267i
$243$	21.4979			1.37909
$244$	−15.4658	+	0.395613i	−0.990099	+	0.0253265i
$245$	14.2264	−	14.2264i	0.908892	−	0.908892i
$246$	11.6615	+	27.1656i	0.743511	+	1.73202i
$247$	−1.73319			−0.110280
$248$	−7.08244	−	15.3998i	−0.449735	−	0.977887i
$249$			6.52556i			0.413540i
$250$	−1.31338	−	0.524445i	−0.0830652	−	0.0331688i
$251$	−10.8985	+	10.8985i	−0.687908	+	0.687908i	−0.961769	−	0.273861i	$-0.911699\pi$
$251$	−10.8985	+	10.8985i	−0.687908	+	0.687908i	0.273861	+	0.961769i	$0.411699\pi$
$252$	29.4841	+	28.0133i	1.85732	+	1.76467i
$253$	−13.9841	−	13.9841i	−0.879171	−	0.879171i
$254$	−2.78759	−	6.49371i	−0.174909	−	0.407452i
$255$		−	14.6746i		−	0.918959i
$256$	−15.9164	+	1.63390i	−0.994772	+	0.102119i
$257$	−8.31752	+	8.31752i	−0.518832	+	0.518832i	−0.917218	−	0.398386i	$-0.869571\pi$
$257$	−8.31752	+	8.31752i	−0.518832	+	0.518832i	0.398386	+	0.917218i	$0.369571\pi$
$258$	−14.0789	−	5.62184i	−0.876512	−	0.350000i
$259$	−1.45302	+	31.6433i	−0.0902862	+	1.96622i
$260$	−0.907314	−	0.862054i	−0.0562693	−	0.0534623i
$261$	24.9950	+	24.9950i	1.54715	+	1.54715i
$262$	−2.29617	+	5.75033i	−0.141858	+	0.355257i
$263$	−1.34290			−0.0828068			−0.0414034	−	0.999143i	$-0.513183\pi$
$263$	−1.34290			−0.0828068			−0.0414034	+	0.999143i	$0.513183\pi$
$264$	11.5850	−	31.3148i	0.713005	−	1.92729i
$265$	−8.52214	+	8.52214i	−0.523511	+	0.523511i
$266$	7.56429	−	18.9434i	0.463796	−	1.16149i
$267$	9.47170	+	9.47170i	0.579659	+	0.579659i
$268$	−5.75163	+	6.05360i	−0.351336	+	0.369783i
$269$	32.2025			1.96342			0.981709	−	0.190387i	$-0.0609743\pi$
$269$	32.2025			1.96342			0.981709	+	0.190387i	$0.0609743\pi$
$270$	−1.24700	+	3.12287i	−0.0758898	+	0.190052i
$271$			22.7417i			1.38146i	0.723114	+	0.690729i	$0.242710\pi$
$271$			22.7417i			1.38146i	−0.723114	+	0.690729i	$0.757290\pi$
$272$	−16.5824	−	14.9673i	−1.00546	−	0.907525i
$273$	6.05503	+	6.05503i	0.366467	+	0.366467i
$274$	4.29330	−	1.84301i	0.259368	−	0.111340i
$275$		−	4.49242i		−	0.270903i
$276$	23.1278	−	0.591603i	1.39213	−	0.0356103i
$277$	−1.79552	−	1.79552i	−0.107882	−	0.107882i	0.651105	−	0.758987i	$-0.274306\pi$
$277$	−1.79552	−	1.79552i	−0.107882	−	0.107882i	−0.758987	+	0.651105i	$0.774306\pi$
$278$	5.37677	−	2.30812i	0.322477	−	0.138432i
$279$	−16.5472	+	16.5472i	−0.990657	+	0.990657i
$280$	13.3819	−	6.15443i	0.799724	−	0.367797i
$281$	9.42583	−	9.42583i	0.562298	−	0.562298i	−0.367662	−	0.929960i	$-0.619842\pi$
$281$	9.42583	−	9.42583i	0.562298	−	0.562298i	0.929960	+	0.367662i	$0.119842\pi$
$282$	13.0132	+	30.3144i	0.774927	+	1.80520i
$283$	15.9179	−	15.9179i	0.946224	−	0.946224i	−0.0524023	−	0.998626i	$-0.516688\pi$
$283$	15.9179	−	15.9179i	0.946224	−	0.946224i	0.998626	+	0.0524023i	$0.0166878\pi$
$284$	−8.89320	−	8.44958i	−0.527714	−	0.501390i
$285$	7.27793			0.431107
$286$	1.47434	−	3.69220i	0.0871793	−	0.218324i
$287$	−41.4278			−2.44540
$288$	9.73983	+	19.8261i	0.573925	+	1.16826i
$289$		−	14.1873i		−	0.834545i
$290$	11.7639	−	5.04994i	0.690799	−	0.296543i
$291$	10.7932	−	10.7932i	0.632707	−	0.632707i
$292$	7.97392	+	7.57615i	0.466638	+	0.443361i
$293$	−1.33683			−0.0780982			−0.0390491	−	0.999237i	$-0.512433\pi$
$293$	−1.33683			−0.0780982			−0.0390491	+	0.999237i	$0.512433\pi$
$294$	−68.7031	+	29.4926i	−4.00685	+	1.72004i
$295$	−4.74343			−0.276173
$296$	−6.70336	+	15.8450i	−0.389625	+	0.920974i
$297$	−10.6818			−0.619823
$298$	−19.5794	+	8.40494i	−1.13420	+	0.486885i
$299$	2.75476			0.159312
$300$	3.80996	+	3.61990i	0.219968	+	0.208995i
$301$	15.0219	−	15.0219i	0.865846	−	0.865846i
$302$	−16.1139	+	6.91729i	−0.927250	+	0.398045i
$303$		−	9.46845i		−	0.543948i
$304$	7.42308	−	8.22411i	0.425743	−	0.471685i
$305$	7.73545			0.442931
$306$	−11.4366	+	28.6408i	−0.653785	+	1.63728i
$307$	−0.208746			−0.0119137			−0.00595687	−	0.999982i	$-0.501896\pi$
$307$	−0.208746			−0.0119137			−0.00595687	+	0.999982i	$0.501896\pi$
$308$	33.9204	+	32.2284i	1.93280	+	1.83638i
$309$	15.7472	−	15.7472i	0.895825	−	0.895825i
$310$	3.34316	+	7.78793i	0.189879	+	0.442324i
$311$	11.0726	−	11.0726i	0.627869	−	0.627869i	−0.319663	−	0.947531i	$-0.603570\pi$
$311$	11.0726	−	11.0726i	0.627869	−	0.627869i	0.947531	+	0.319663i	$0.103570\pi$
$312$	1.94331	+	4.22546i	0.110018	+	0.239220i
$313$	14.2920	−	14.2920i	0.807832	−	0.807832i	−0.176473	−	0.984305i	$-0.556469\pi$
$313$	14.2920	−	14.2920i	0.807832	−	0.807832i	0.984305	+	0.176473i	$0.0564690\pi$
$314$	−8.89096	+	3.81667i	−0.501746	+	0.215387i
$315$	−14.3790	−	14.3790i	−0.810168	−	0.810168i
$316$	−3.64762	+	0.0933054i	−0.205195	+	0.00524884i
$317$		−	7.21584i		−	0.405282i	−0.979253	−	0.202641i	$-0.935048\pi$
$317$		−	7.21584i		−	0.405282i	0.979253	−	0.202641i	$-0.0649524\pi$
$318$	41.1557	−	17.6671i	2.30790	−	0.990723i
$319$	28.7560	+	28.7560i	1.61002	+	1.61002i
$320$	7.97647	−	0.613179i	0.445898	−	0.0342778i
$321$			26.0039i			1.45140i
$322$	−12.0228	+	30.1089i	−0.670005	+	1.67790i
$323$	15.4674			0.860631
$324$	−7.53071	+	7.92609i	−0.418373	+	0.440338i
$325$	0.442487	+	0.442487i	0.0245448	+	0.0245448i
$326$	−1.65654	+	4.14851i	−0.0917475	+	0.229765i
$327$	26.4290	−	26.4290i	1.46153	−	1.46153i
$328$	−21.1030	−	7.80709i	−1.16522	−	0.431075i
$329$	−46.2298			−2.54873
$330$	−6.19097	+	15.5041i	−0.340802	+	0.853475i
$331$	2.69271	+	2.69271i	0.148005	+	0.148005i	0.777226	−	0.629221i	$-0.216626\pi$
$331$	2.69271	+	2.69271i	0.148005	+	0.148005i	−0.629221	+	0.777226i	$0.716626\pi$
$332$	−3.60066	−	3.42105i	−0.197612	−	0.187754i
$333$	23.7274	+	1.08953i	1.30025	+	0.0597059i
$334$	7.00645	+	2.79775i	0.383376	+	0.153086i
$335$	2.95227	−	2.95227i	0.161300	−	0.161300i
$336$	−54.6648	+	2.79846i	−2.98221	+	0.152669i
$337$			34.5195i			1.88039i	0.340630	+	0.940197i	$0.389360\pi$
$337$			34.5195i			1.88039i	−0.340630	+	0.940197i	$0.610640\pi$
$338$	−7.03371	−	16.3851i	−0.382583	−	0.891231i
$339$	16.4361	+	16.4361i	0.892684	+	0.892684i
$340$	8.09713	+	7.69322i	0.439128	+	0.417223i
$341$	−19.0370	+	19.0370i	−1.03091	+	1.03091i
$342$	−14.2045	−	5.67201i	−0.768091	−	0.306707i
$343$		−	68.3196i		−	3.68891i
$344$	10.4829	−	4.82114i	0.565200	−	0.259939i
$345$	−11.5677			−0.622782
$346$	2.37086	+	5.52294i	0.127458	+	0.296915i
$347$	11.3167	−	11.3167i	0.607513	−	0.607513i	−0.334783	−	0.942295i	$-0.608663\pi$
$347$	11.3167	−	11.3167i	0.607513	−	0.607513i	0.942295	+	0.334783i	$0.108663\pi$
$348$	−47.5585	+	1.21654i	−2.54940	+	0.0652132i
$349$	−21.0345			−1.12595			−0.562975	−	0.826474i	$-0.690343\pi$
$349$	−21.0345			−1.12595			−0.562975	+	0.826474i	$0.690343\pi$
$350$	−6.76748	+	2.90511i	−0.361737	+	0.155285i
$351$	1.05212	−	1.05212i	0.0561580	−	0.0561580i
$352$	11.2054	+	22.8092i	0.597247	+	1.21574i
$353$	−18.1744	−	18.1744i	−0.967327	−	0.967327i	0.0321554	−	0.999483i	$-0.489763\pi$
$353$	−18.1744	−	18.1744i	−0.967327	−	0.967327i	−0.999483	+	0.0321554i	$0.989763\pi$
$354$	16.3704	+	6.53688i	0.870077	+	0.347431i
$355$	4.33711	+	4.33711i	0.230190	+	0.230190i
$356$	−10.1919	+	0.260706i	−0.540167	+	0.0138174i
$357$	−54.0368	−	54.0368i	−2.85993	−	2.85993i
$358$	9.74981	−	24.4166i	0.515294	−	1.29046i
$359$		−	20.9802i		−	1.10729i	−0.832752	−	0.553647i	$-0.813236\pi$
$359$		−	20.9802i		−	1.10729i	0.832752	−	0.553647i	$-0.186764\pi$
$360$	−4.61483	−	10.0343i	−0.243223	−	0.528855i
$361$		−	11.3289i		−	0.596256i
$362$	−1.49854	+	0.643286i	−0.0787615	+	0.0338104i
$363$	−24.1273			−1.26636
$364$	−6.51541	+	0.166663i	−0.341500	+	0.00873551i
$365$	−3.88879	−	3.88879i	−0.203549	−	0.203549i
$366$	−26.6964	−	10.6602i	−1.39544	−	0.557215i
$367$			12.6396i			0.659781i	0.944019	+	0.329890i	$0.107012\pi$
$367$			12.6396i			0.659781i	−0.944019	+	0.329890i	$0.892988\pi$
$368$	−11.7984	+	13.0715i	−0.615033	+	0.681401i
$369$			31.0642i			1.61714i
$370$	3.55317	−	7.83422i	0.184721	−	0.407282i
$371$			62.7628i			3.25848i
$372$	−0.805372	−	31.4847i	−0.0417566	−	1.63240i
$373$			23.5852i			1.22119i	0.791942	+	0.610597i	$0.209070\pi$
$373$			23.5852i			1.22119i	−0.791942	+	0.610597i	$0.790930\pi$
$374$	−13.1574	+	32.9502i	−0.680352	+	1.70382i
$375$	−1.85807	−	1.85807i	−0.0959505	−	0.0959505i
$376$	−23.5491	−	8.71203i	−1.21445	−	0.449289i
$377$	−5.66471			−0.291747
$378$	6.90760	+	16.0913i	0.355289	+	0.827648i
$379$			30.7075i			1.57734i	0.614818	+	0.788669i	$0.289230\pi$
$379$			30.7075i			1.57734i	−0.614818	+	0.788669i	$0.710770\pi$
$380$	−3.81548	+	4.01580i	−0.195730	+	0.206006i
$381$		−	13.1305i		−	0.672698i
$382$	13.6405	+	5.44678i	0.697907	+	0.278682i
$383$	22.7595	+	22.7595i	1.16295	+	1.16295i	0.983826	+	0.179129i	$0.0573279\pi$
$383$	22.7595	+	22.7595i	1.16295	+	1.16295i	0.179129	+	0.983826i	$0.442672\pi$
$384$	−28.3732	−	8.87611i	−1.44791	−	0.452957i
$385$	−16.5426	−	16.5426i	−0.843090	−	0.843090i
$386$	−3.12941	+	7.83703i	−0.159283	+	0.398895i
$387$	−11.2640	−	11.2640i	−0.572581	−	0.572581i
$388$	0.297079	+	11.6138i	0.0150819	+	0.589601i
$389$	2.98939	−	2.98939i	0.151568	−	0.151568i	−0.627250	−	0.778818i	$-0.715820\pi$
$389$	2.98939	−	2.98939i	0.151568	−	0.151568i	0.778818	+	0.627250i	$0.215820\pi$
$390$	−0.917313	−	2.13689i	−0.0464499	−	0.108205i
$391$	−24.5842			−1.24328
$392$	19.7445	−	53.3705i	0.997249	−	2.69562i
$393$	−8.13517	+	8.13517i	−0.410365	+	0.410365i
$394$	28.8638	−	12.3905i	1.45414	−	0.624225i
$395$	1.82441			0.0917959
$396$	24.1661	−	25.4349i	1.21439	−	1.27815i
$397$			20.8140i			1.04462i	0.852754	+	0.522312i	$0.174931\pi$
$397$			20.8140i			1.04462i	−0.852754	+	0.522312i	$0.825069\pi$
$398$	0.592098	−	1.48280i	0.0296792	−	0.0743261i
$399$	26.7998	−	26.7998i	1.34167	−	1.34167i
$400$	−3.99477	+	0.204505i	−0.199738	+	0.0102252i
$401$	−1.44115	−	1.44115i	−0.0719675	−	0.0719675i	0.670207	−	0.742174i	$-0.266205\pi$
$401$	−1.44115	−	1.44115i	−0.0719675	−	0.0719675i	−0.742174	+	0.670207i	$0.766205\pi$
$402$	−14.2573	+	6.12031i	−0.711090	+	0.305253i
$403$		−	3.75015i		−	0.186808i
$404$	5.22449	+	4.96387i	0.259928	+	0.246962i
$405$	3.86546	−	3.86546i	0.192076	−	0.192076i
$406$	24.7230	−	61.9141i	1.22698	−	3.07275i
$407$	27.2976	+	1.25347i	1.35309	+	0.0621322i
$408$	−17.3427	−	37.7092i	−0.858590	−	1.86688i
$409$	−2.25122	−	2.25122i	−0.111316	−	0.111316i	0.649255	−	0.760571i	$-0.275081\pi$
$409$	−2.25122	−	2.25122i	−0.111316	−	0.111316i	−0.760571	+	0.649255i	$0.775081\pi$
$410$	10.4482	+	4.17209i	0.516001	+	0.206045i
$411$	8.68122			0.428213
$412$	0.433436	+	16.9445i	0.0213539	+	0.834794i
$413$	−17.4669	+	17.4669i	−0.859490	+	0.859490i
$414$	22.5769	+	9.01518i	1.10959	+	0.443072i
$415$	1.75600	+	1.75600i	0.0861987	+	0.0861987i
$416$	−3.35031	−	1.14294i	−0.164262	−	0.0560371i
$417$	10.8720			0.532406
$418$	−16.3418	−	6.52545i	−0.799303	−	0.319170i
$419$			11.9297i			0.582804i	0.956601	+	0.291402i	$0.0941217\pi$
$419$			11.9297i			0.582804i	−0.956601	+	0.291402i	$0.905878\pi$
$420$	27.3592	−	0.699844i	1.33499	−	0.0341489i
$421$	17.8543	+	17.8543i	0.870165	+	0.870165i	0.992490	−	0.122325i	$-0.0390351\pi$
$421$	17.8543	+	17.8543i	0.870165	+	0.870165i	−0.122325	+	0.992490i	$0.539035\pi$
$422$	10.9958	+	25.6148i	0.535268	+	1.24691i
$423$			34.6649i			1.68547i
$424$	−11.8277	+	31.9709i	−0.574403	+	1.55264i
$425$	−3.94888	−	3.94888i	−0.191549	−	0.191549i
$426$	−8.99120	−	20.9451i	−0.435625	−	1.01479i
$427$	28.4845	−	28.4845i	1.37846	−	1.37846i
$428$	−14.3484	−	13.6326i	−0.693556	−	0.658959i
$429$	5.22347	−	5.22347i	0.252191	−	0.252191i
$430$	−5.30138	+	2.27575i	−0.255655	+	0.109746i
$431$	6.15948	−	6.15948i	0.296692	−	0.296692i	−0.543025	−	0.839717i	$-0.682721\pi$
$431$	6.15948	−	6.15948i	0.296692	−	0.296692i	0.839717	+	0.543025i	$0.182721\pi$
$432$	0.486259	+	9.49853i	0.0233952	+	0.456998i
$433$	−19.9184			−0.957216			−0.478608	−	0.878029i	$-0.658859\pi$
$433$	−19.9184			−0.957216			−0.478608	+	0.878029i	$0.658859\pi$
$434$	40.9884	+	16.3671i	1.96751	+	0.785646i
$435$	23.7870			1.14050
$436$	0.727451	+	28.4385i	0.0348386	+	1.36196i
$437$		−	12.1926i		−	0.583253i
$438$	8.06179	+	18.7800i	0.385207	+	0.897343i
$439$	19.6697	−	19.6697i	0.938785	−	0.938785i	−0.0594464	−	0.998232i	$-0.518934\pi$
$439$	19.6697	−	19.6697i	0.938785	−	0.938785i	0.998232	+	0.0594464i	$0.0189335\pi$
$440$	−5.30921	−	11.5441i	−0.253107	−	0.550346i
$441$	−78.5629			−3.74109
$442$	−1.94952	−	4.54143i	−0.0927293	−	0.216014i
$443$	17.6544			0.838784			0.419392	−	0.907805i	$-0.362243\pi$
$443$	17.6544			0.838784			0.419392	+	0.907805i	$0.362243\pi$
$444$	−23.0589	+	22.1407i	−1.09433	+	1.05075i
$445$	5.09759			0.241649
$446$	−3.86323	−	8.99942i	−0.182929	−	0.426135i
$447$	−39.5903			−1.87256
$448$	27.1141	−	31.6300i	1.28102	−	1.49438i
$449$	26.6185	−	26.6185i	1.25621	−	1.25621i	0.303315	−	0.952890i	$-0.401907\pi$
$449$	26.6185	−	26.6185i	1.25621	−	1.25621i	0.952890	−	0.303315i	$-0.0980934\pi$
$450$	2.17837	+	5.07452i	0.102689	+	0.239215i
$451$			35.7383i			1.68285i
$452$	−17.6857	+	0.452397i	−0.831867	+	0.0212790i
$453$	−32.5829			−1.53088
$454$	0.704081	+	0.281147i	0.0330442	+	0.0131949i
$455$	3.25877			0.152774
$456$	18.7020	−	8.60116i	0.875802	−	0.402786i
$457$	−2.04963	+	2.04963i	−0.0958775	+	0.0958775i	−0.753419	−	0.657541i	$-0.771597\pi$
$457$	−2.04963	+	2.04963i	−0.0958775	+	0.0958775i	0.657541	+	0.753419i	$0.271597\pi$
$458$	13.3534	−	5.73230i	0.623965	−	0.267853i
$459$	−9.38942	+	9.38942i	−0.438260	+	0.438260i
$460$	6.06439	−	6.38278i	0.282754	−	0.297599i
$461$	−26.7058	+	26.7058i	−1.24381	+	1.24381i	−0.285407	+	0.958406i	$0.592129\pi$
$461$	−26.7058	+	26.7058i	−1.24381	+	1.24381i	−0.958406	+	0.285407i	$0.907871\pi$
$462$	34.2942	+	79.8887i	1.59551	+	3.71676i
$463$	19.3976	+	19.3976i	0.901484	+	0.901484i	0.995565	−	0.0940802i	$-0.0299910\pi$
$463$	19.3976	+	19.3976i	0.901484	+	0.901484i	−0.0940802	+	0.995565i	$0.529991\pi$
$464$	24.2614	−	26.8795i	1.12631	−	1.24785i
$465$			15.7475i			0.730272i
$466$	−5.18240	−	12.0724i	−0.240070	−	0.559245i
$467$	−7.84731	−	7.84731i	−0.363130	−	0.363130i	0.501834	−	0.864964i	$-0.332659\pi$
$467$	−7.84731	−	7.84731i	−0.363130	−	0.363130i	−0.864964	+	0.501834i	$0.832659\pi$
$468$	0.124970	+	4.88551i	0.00577676	+	0.225833i
$469$		−	21.7425i		−	1.00398i
$470$	11.6593	+	4.65568i	0.537804	+	0.214751i
$471$	−17.9779			−0.828376
$472$	−12.1892	+	5.60585i	−0.561051	+	0.258030i
$473$	−12.9588	−	12.9588i	−0.595848	−	0.595848i
$474$	−6.29635	−	2.51420i	−0.289201	−	0.115481i
$475$	1.95846	−	1.95846i	0.0898603	−	0.0898603i
$476$	58.1453	−	1.48735i	2.66509	−	0.0681724i
$477$	47.0620			2.15482
$478$	10.5875	+	4.22769i	0.484259	+	0.193370i
$479$	−22.1306	−	22.1306i	−1.01117	−	1.01117i	−0.999937	−	0.0112359i	$-0.996423\pi$
$479$	−22.1306	−	22.1306i	−1.01117	−	1.01117i	−0.0112359	−	0.999937i	$-0.503577\pi$
$480$	14.0685	+	4.79937i	0.642135	+	0.219060i
$481$	−2.81217	+	2.56525i	−0.128224	+	0.116965i
$482$	−4.34134	+	10.8721i	−0.197743	+	0.495210i
$483$	−42.5960	+	42.5960i	−1.93819	+	1.93819i
$484$	12.6488	−	13.3129i	0.574947	−	0.605133i
$485$		−	5.80880i		−	0.263764i
$486$	−27.9372	+	11.9928i	−1.26726	+	0.544003i
$487$	3.02235	+	3.02235i	0.136956	+	0.136956i	0.772261	−	0.635305i	$-0.219126\pi$
$487$	3.02235	+	3.02235i	0.136956	+	0.136956i	−0.635305	+	0.772261i	$0.719126\pi$
$488$	19.8777	−	9.14187i	0.899822	−	0.413833i
$489$	−5.86902	+	5.86902i	−0.265406	+	0.265406i
$490$	−10.5514	+	26.4241i	−0.476664	+	1.19372i
$491$		−	23.8867i		−	1.07799i	−0.842308	−	0.538996i	$-0.818804\pi$
$491$		−	23.8867i		−	1.07799i	0.842308	−	0.538996i	$-0.181196\pi$
$492$	−30.3091	−	28.7972i	−1.36644	−	1.29828i
$493$	50.5534			2.27681
$494$	2.25234	−	0.966873i	0.101337	−	0.0435017i
$495$	−12.4043	+	12.4043i	−0.557532	+	0.557532i
$496$	17.7948	+	16.0616i	0.799009	+	0.721186i
$497$	31.9414			1.43277
$498$	−3.64034	−	8.48020i	−0.163127	−	0.380007i
$499$	19.3164	−	19.3164i	0.864719	−	0.864719i	−0.127163	−	0.991882i	$-0.540587\pi$
$499$	19.3164	−	19.3164i	0.864719	−	0.864719i	0.991882	+	0.127163i	$0.0405871\pi$
$500$	1.99935	−	0.0511429i	0.0894135	−	0.00228718i
$501$	9.91223	+	9.91223i	0.442846	+	0.442846i
$502$	8.08318	−	20.2428i	0.360770	−	0.903482i
$503$	10.3447	+	10.3447i	0.461245	+	0.461245i	0.899063	−	0.437818i	$-0.144249\pi$
$503$	10.3447	+	10.3447i	0.461245	+	0.461245i	−0.437818	+	0.899063i	$0.644249\pi$
$504$	−53.9431	−	19.9564i	−2.40282	−	0.888927i
$505$	−2.54792	−	2.54792i	−0.113381	−	0.113381i
$506$	25.9739	+	10.3717i	1.15468	+	0.461077i
$507$		−	33.1313i		−	1.47141i
$508$	7.24514	+	6.88373i	0.321451	+	0.305416i
$509$			28.1041i			1.24569i	0.782344	+	0.622846i	$0.214024\pi$
$509$			28.1041i			1.24569i	−0.782344	+	0.622846i	$0.785976\pi$
$510$	8.18635	+	19.0702i	0.362498	+	0.844442i
$511$	−28.6397			−1.26694
$512$	19.7724	−	11.0024i	0.873825	−	0.486241i
$513$	−4.65672	−	4.65672i	−0.205599	−	0.205599i
$514$	6.16891	−	15.4489i	0.272099	−	0.681422i
$515$		−	8.47500i		−	0.373453i
$516$	21.4322	−	0.548231i	0.943499	−	0.0241345i
$517$			39.8808i			1.75396i
$518$	−15.7642	−	41.9322i	−0.692641	−	1.84239i
$519$			11.1676i			0.490203i
$520$	1.65999	+	0.614118i	0.0727955	+	0.0269308i
$521$			5.82277i			0.255100i	0.991832	+	0.127550i	$0.0407113\pi$
$521$			5.82277i			0.255100i	−0.991832	+	0.127550i	$0.959289\pi$
$522$	−46.4257	−	18.5383i	−2.03200	−	0.811398i
$523$	−3.19692	−	3.19692i	−0.139791	−	0.139791i	0.633748	−	0.773539i	$-0.281516\pi$
$523$	−3.19692	−	3.19692i	−0.139791	−	0.139791i	−0.773539	+	0.633748i	$0.781516\pi$
$524$	−0.223918	−	8.75370i	−0.00978190	−	0.382407i
$525$	−13.6841			−0.597223
$526$	1.74515	−	0.749149i	0.0760921	−	0.0326645i
$527$			33.4674i			1.45786i
$528$	2.41414	+	47.1574i	0.105062	+	2.05226i
$529$		−	3.62082i		−	0.157427i
$530$	6.32068	−	15.8290i	0.274553	−	0.687567i
$531$	13.0974	+	13.0974i	0.568378	+	0.568378i
$532$	0.737655	+	28.8374i	0.0319814	+	1.25026i
$533$	−3.52009	−	3.52009i	−0.152472	−	0.152472i
$534$	−17.5927	−	7.02495i	−0.761310	−	0.303999i
$535$	6.99755	+	6.99755i	0.302530	+	0.302530i
$536$	4.09739	−	11.0755i	0.176980	−	0.478387i
$537$	34.5429	−	34.5429i	1.49064	−	1.49064i
$538$	−41.8482	+	17.9644i	−1.80421	+	0.774501i
$539$	−90.3839			−3.89311
$540$	−0.121605	−	4.75393i	−0.00523303	−	0.204577i
$541$	7.19827	−	7.19827i	0.309478	−	0.309478i	−0.535229	−	0.844707i	$-0.679775\pi$
$541$	7.19827	−	7.19827i	0.309478	−	0.309478i	0.844707	+	0.535229i	$0.179775\pi$
$542$	−12.6866	−	29.5536i	−0.544938	−	1.26944i
$543$	−3.03011			−0.130034
$544$	29.8991	+	10.1999i	1.28191	+	0.437317i
$545$		−	14.2239i		−	0.609285i
$546$	−11.2466	−	4.49088i	−0.481310	−	0.192192i
$547$	−11.7275	+	11.7275i	−0.501432	+	0.501432i	−0.911883	−	0.410451i	$-0.865371\pi$
$547$	−11.7275	+	11.7275i	−0.501432	+	0.501432i	0.410451	+	0.911883i	$0.365371\pi$
$548$	−4.55116	+	4.79011i	−0.194416	+	0.204623i
$549$	−21.3588	−	21.3588i	−0.911573	−	0.911573i
$550$	2.50614	+	5.83807i	0.106862	+	0.248936i
$551$			25.0722i			1.06811i
$552$	−29.7253	+	13.6708i	−1.26519	+	0.581869i
$553$	6.71808	−	6.71808i	0.285682	−	0.285682i
$554$	3.33498	+	1.33169i	0.141690	+	0.0565782i
$555$	11.8088	−	10.7719i	0.501254	−	0.457241i
$556$	−5.69971	+	5.99896i	−0.241721	+	0.254412i
$557$	24.7106	+	24.7106i	1.04702	+	1.04702i	0.998839	+	0.0481832i	$0.0153431\pi$
$557$	24.7106	+	24.7106i	1.04702	+	1.04702i	0.0481832	+	0.998839i	$0.484657\pi$
$558$	12.2727	−	30.7347i	0.519545	−	1.30111i
$559$	2.55280			0.107972
$560$	−13.9570	+	15.4631i	−0.589792	+	0.653437i
$561$	−46.6157	+	46.6157i	−1.96812	+	1.96812i
$562$	−6.99092	+	17.5075i	−0.294894	+	0.738508i
$563$	−11.9347	−	11.9347i	−0.502987	−	0.502987i	0.409378	−	0.912365i	$-0.365746\pi$
$563$	−11.9347	−	11.9347i	−0.502987	−	0.502987i	−0.912365	+	0.409378i	$0.865746\pi$
$564$	−33.8223	−	32.1352i	−1.42418	−	1.35313i
$565$	8.84576			0.372144
$566$	−11.8060	+	29.5659i	−0.496242	+	1.24275i
$567$		−	28.4679i		−	1.19554i
$568$	16.2707	+	6.01938i	0.682703	+	0.252568i
$569$	−6.08324	−	6.08324i	−0.255023	−	0.255023i	0.568003	−	0.823026i	$-0.307716\pi$
$569$	−6.08324	−	6.08324i	−0.255023	−	0.255023i	−0.823026	+	0.568003i	$0.807716\pi$
$570$	−9.45793	+	4.06005i	−0.396149	+	0.170057i
$571$		−	19.4564i		−	0.814224i	−0.913378	−	0.407112i	$-0.866536\pi$
$571$		−	19.4564i		−	0.814224i	0.913378	−	0.407112i	$-0.133464\pi$
$572$	0.143774	+	5.62062i	0.00601151	+	0.235010i
$573$	19.2976	+	19.2976i	0.806168	+	0.806168i
$574$	53.8369	−	23.1108i	2.24711	−	0.964628i
$575$	−3.11281	+	3.11281i	−0.129813	+	0.129813i
$576$	−23.7174	−	20.3312i	−0.988225	−	0.847134i
$577$	−15.9205	+	15.9205i	−0.662778	+	0.662778i	−0.956034	−	0.293256i	$-0.905261\pi$
$577$	−15.9205	+	15.9205i	−0.662778	+	0.662778i	0.293256	+	0.956034i	$0.405261\pi$
$578$	7.91449	+	18.4369i	0.329199	+	0.766872i
$579$	−11.0873	+	11.0873i	−0.460772	+	0.460772i
$580$	−12.4704	+	13.1252i	−0.517806	+	0.544993i
$581$	12.9324			0.536525
$582$	−8.00506	+	20.0472i	−0.331820	+	0.830983i
$583$	54.1433			2.24239
$584$	−14.5888	−	5.39716i	−0.603690	−	0.223336i
$585$		−	2.44356i		−	0.101029i
$586$	1.73725	−	0.745760i	0.0717653	−	0.0308071i
$587$	−14.3495	+	14.3495i	−0.592269	+	0.592269i	−0.938244	−	0.345975i	$-0.887548\pi$
$587$	−14.3495	+	14.3495i	−0.592269	+	0.592269i	0.345975	+	0.938244i	$0.387548\pi$
$588$	72.8295	−	76.6533i	3.00344	−	3.16113i
$589$	−16.5983			−0.683920
$590$	6.16426	−	2.64616i	0.253779	−	0.108941i
$591$	58.3637			2.40076
$592$	−0.128029	−	24.3307i	−0.00526197	−	0.999986i
$593$	33.0042			1.35532			0.677660	−	0.735376i	$-0.262994\pi$
$593$	33.0042			1.35532			0.677660	+	0.735376i	$0.262994\pi$
$594$	13.8814	−	5.95895i	0.569562	−	0.244499i
$595$	−29.0822			−1.19225
$596$	20.7553	−	21.8451i	0.850172	−	0.894808i
$597$	2.09776	−	2.09776i	0.0858557	−	0.0858557i
$598$	−3.57990	+	1.53676i	−0.146393	+	0.0628430i
$599$			3.17263i			0.129630i	0.997897	+	0.0648150i	$0.0206457\pi$
$599$			3.17263i			0.129630i	−0.997897	+	0.0648150i	$0.979354\pi$
$600$	−6.97057	−	2.57878i	−0.284572	−	0.105278i
$601$	−28.5702			−1.16540			−0.582702	−	0.812686i	$-0.698005\pi$
$601$	−28.5702			−1.16540			−0.582702	+	0.812686i	$0.698005\pi$
$602$	−11.1414	+	27.9015i	−0.454089	+	1.13718i
$603$	−16.3034			−0.663926
$604$	17.0817	−	17.9785i	0.695045	−	0.731537i
$605$	−6.49257	+	6.49257i	−0.263960	+	0.263960i
$606$	5.28206	+	12.3046i	0.214569	+	0.499840i
$607$	−18.2312	+	18.2312i	−0.739980	+	0.739980i	−0.972574	−	0.232594i	$-0.925279\pi$
$607$	−18.2312	+	18.2312i	−0.739980	+	0.739980i	0.232594	+	0.972574i	$0.425279\pi$
$608$	−5.05867	+	14.8286i	−0.205156	+	0.601377i
$609$	87.5918	−	87.5918i	3.54940	−	3.54940i
$610$	−10.0525	+	4.31529i	−0.407014	+	0.174721i
$611$	−3.92811	−	3.92811i	−0.158914	−	0.158914i
$612$	−1.11527	−	43.5997i	−0.0450822	−	1.76241i
$613$		−	28.3812i		−	1.14631i	−0.819449	−	0.573153i	$-0.805720\pi$
$613$		−	28.3812i		−	1.14631i	0.819449	−	0.573153i	$-0.194280\pi$
$614$	0.271272	−	0.116451i	0.0109477	−	0.00469956i
$615$	14.7814	+	14.7814i	0.596044	+	0.596044i
$616$	−62.0597	−	22.9591i	−2.50046	−	0.925049i
$617$			21.2344i			0.854866i	0.904047	+	0.427433i	$0.140582\pi$
$617$			21.2344i			0.854866i	−0.904047	+	0.427433i	$0.859418\pi$
$618$	−11.6793	+	29.2487i	−0.469811	+	1.17656i
$619$	−15.0854			−0.606332			−0.303166	−	0.952938i	$-0.598044\pi$
$619$	−15.0854			−0.606332			−0.303166	+	0.952938i	$0.598044\pi$
$620$	−8.68912	−	8.25568i	−0.348964	−	0.331556i
$621$	7.40146	+	7.40146i	0.297011	+	0.297011i
$622$	−8.21229	+	20.5662i	−0.329283	+	0.824628i
$623$	18.7711	−	18.7711i	0.752046	−	0.752046i
$624$	−4.88261	−	4.40705i	−0.195461	−	0.176423i
$625$	−1.00000			−0.0400000
$626$	−10.6001	+	26.5459i	−0.423664	+	1.06099i
$627$	−23.1192	−	23.1192i	−0.923293	−	0.923293i
$628$	9.42496	−	9.91979i	0.376097	−	0.395843i
$629$	25.0966	−	22.8930i	1.00067	−	0.912803i
$630$	26.7076	+	10.6646i	1.06405	+	0.424888i
$631$	−27.4359	+	27.4359i	−1.09221	+	1.09221i	−0.0969133	+	0.995293i	$0.530897\pi$
$631$	−27.4359	+	27.4359i	−1.09221	+	1.09221i	−0.995293	+	0.0969133i	$0.969103\pi$
$632$	4.68816	−	2.15611i	0.186485	−	0.0857654i
$633$			51.7942i			2.05863i
$634$	4.02542	+	9.37724i	0.159870	+	0.372418i
$635$	−3.53337	−	3.53337i	−0.140218	−	0.140218i
$636$	−43.6276	+	45.9181i	−1.72995	+	1.82077i
$637$	8.90248	−	8.90248i	0.352729	−	0.352729i
$638$	−53.4112	−	21.3276i	−2.11457	−	0.844370i
$639$		−	23.9509i		−	0.947484i
$640$	−10.0236	+	5.24659i	−0.396219	+	0.207390i
$641$	−18.5886			−0.734204			−0.367102	−	0.930181i	$-0.619650\pi$
$641$	−18.5886			−0.734204			−0.367102	+	0.930181i	$0.619650\pi$
$642$	−14.5065	−	33.7930i	−0.572526	−	1.33370i
$643$	11.4860	−	11.4860i	0.452964	−	0.452964i	−0.443373	−	0.896337i	$-0.646218\pi$
$643$	11.4860	−	11.4860i	0.452964	−	0.452964i	0.896337	+	0.443373i	$0.146218\pi$
$644$	−1.17244	−	45.8347i	−0.0462007	−	1.80614i
$645$	−10.7196			−0.422084
$646$	−20.1005	+	8.62864i	−0.790843	+	0.339489i
$647$	10.0235	−	10.0235i	0.394065	−	0.394065i	−0.482068	−	0.876134i	$-0.660114\pi$
$647$	10.0235	−	10.0235i	0.394065	−	0.394065i	0.876134	+	0.482068i	$0.160114\pi$
$648$	5.36479	−	14.5013i	0.210749	−	0.569665i
$649$	15.0681	+	15.0681i	0.591474	+	0.591474i
$650$	−0.821873	−	0.328183i	−0.0322365	−	0.0128724i
$651$	57.9875	+	57.9875i	2.27271	+	2.27271i
$652$	−0.161543	−	6.31525i	−0.00632651	−	0.247324i
$653$	−29.0696	−	29.0696i	−1.13758	−	1.13758i	−0.988883	−	0.148698i	$-0.952492\pi$
$653$	−29.0696	−	29.0696i	−1.13758	−	1.13758i	−0.148698	−	0.988883i	$-0.547508\pi$
$654$	−19.6018	+	49.0892i	−0.766492	+	1.91954i
$655$			4.37828i			0.171074i
$656$	31.7793	−	1.62688i	1.24078	−	0.0635191i
$657$			21.4752i			0.837826i
$658$	60.0773	−	25.7897i	2.34206	−	1.00539i
$659$	16.9936			0.661976			0.330988	−	0.943635i	$-0.392618\pi$
$659$	16.9936			0.661976			0.330988	+	0.943635i	$0.392618\pi$
$660$	−0.603731	−	23.6019i	−0.0235002	−	0.918702i
$661$	15.3725	+	15.3725i	0.597919	+	0.597919i	0.939758	−	0.341839i	$-0.111050\pi$
$661$	15.3725	+	15.3725i	0.597919	+	0.597919i	−0.341839	+	0.939758i	$0.611050\pi$
$662$	−5.00143	−	1.99713i	−0.194386	−	0.0776205i
$663$		−	9.18294i		−	0.356636i
$664$	6.58765	+	2.43711i	0.255650	+	0.0945784i
$665$		−	14.4234i		−	0.559316i
$666$	−31.4424	+	11.8207i	−1.21837	+	0.458041i
$667$		−	39.8501i		−	1.54300i
$668$	−10.6659	+	0.272831i	−0.412675	+	0.0105562i
$669$		−	18.1972i		−	0.703543i
$670$	−2.18963	+	5.48353i	−0.0845929	+	0.211847i
$671$	−24.5726	−	24.5726i	−0.948615	−	0.948615i
$672$	69.4777	−	34.1319i	2.68016	−	1.31667i
$673$	15.2875			0.589288			0.294644	−	0.955607i	$-0.404799\pi$
$673$	15.2875			0.589288			0.294644	+	0.955607i	$0.404799\pi$
$674$	−19.2570	−	44.8593i	−0.741751	−	1.72792i
$675$			2.37774i			0.0915194i
$676$	18.2811	+	17.3692i	0.703120	+	0.668046i
$677$			16.6306i			0.639166i	0.947558	+	0.319583i	$0.103543\pi$
$677$			16.6306i			0.639166i	−0.947558	+	0.319583i	$0.896457\pi$
$678$	−30.5283	−	12.1903i	−1.17243	−	0.468164i
$679$	−21.3900	−	21.3900i	−0.820871	−	0.820871i
$680$	−14.8142	−	5.48056i	−0.568100	−	0.210170i
$681$	0.996085	+	0.996085i	0.0381701	+	0.0381701i
$682$	14.1193	−	35.3593i	0.540657	−	1.35398i
$683$	−8.88079	−	8.88079i	−0.339814	−	0.339814i	0.516483	−	0.856297i	$-0.327241\pi$
$683$	−8.88079	−	8.88079i	−0.339814	−	0.339814i	−0.856297	+	0.516483i	$0.827241\pi$
$684$	21.6234	−	0.553123i	0.826792	−	0.0211492i
$685$	2.33608	−	2.33608i	0.0892571	−	0.0892571i
$686$	38.1127	+	88.7838i	1.45515	+	3.38978i
$687$	27.0012			1.03016
$688$	−10.9334	+	12.1132i	−0.416832	+	0.461812i
$689$	−5.33291	+	5.33291i	−0.203168	+	0.203168i
$690$	15.0326	−	6.45312i	0.572281	−	0.245666i
$691$	−17.2128			−0.654804			−0.327402	−	0.944885i	$-0.606173\pi$
$691$	−17.2128			−0.654804			−0.327402	+	0.944885i	$0.606173\pi$
$692$	−6.16204	−	5.85465i	−0.234245	−	0.222560i
$693$			91.3537i			3.47024i
$694$	−8.39335	+	21.0196i	−0.318607	+	0.797893i
$695$	2.92562	−	2.92562i	0.110975	−	0.110975i
$696$	61.1253	−	28.1118i	2.31695	−	1.06558i
$697$	31.4143	+	31.4143i	1.18990	+	1.18990i
$698$	27.3351	−	11.7343i	1.03465	−	0.444148i
$699$		−	24.4109i		−	0.923306i
$700$	7.17394	−	7.55059i	0.271149	−	0.285385i
$701$	18.9413	−	18.9413i	0.715405	−	0.715405i	−0.252256	−	0.967661i	$-0.581172\pi$
$701$	18.9413	−	18.9413i	0.715405	−	0.715405i	0.967661	+	0.252256i	$0.0811725\pi$
$702$	−0.780334	+	1.95420i	−0.0294518	+	0.0737566i
$703$	11.3539	+	12.4468i	0.428219	+	0.469438i
$704$	−27.2861	−	23.3904i	−1.02838	−	0.881559i
$705$	16.4948	+	16.4948i	0.621229	+	0.621229i
$706$	33.7571	+	13.4796i	1.27046	+	0.507310i
$707$	−18.7646			−0.705716
$708$	−24.9206	+	0.637464i	−0.936573	+	0.0239574i
$709$	24.3086	−	24.3086i	0.912928	−	0.912928i	−0.0835733	−	0.996502i	$-0.526633\pi$
$709$	24.3086	−	24.3086i	0.912928	−	0.912928i	0.996502	+	0.0835733i	$0.0266333\pi$
$710$	−8.05573	−	3.21674i	−0.302326	−	0.120722i
$711$	−5.03748	−	5.03748i	−0.188920	−	0.188920i
$712$	13.0992	−	6.02441i	0.490915	−	0.225774i
$713$	26.3816			0.987999
$714$	100.368	+	40.0779i	3.75617	+	1.49988i
$715$		−	2.81123i		−	0.105134i
$716$	0.950783	+	37.1693i	0.0355324	+	1.38908i
$717$	14.9784	+	14.9784i	0.559379	+	0.559379i
$718$	11.7040	+	27.2646i	0.436789	+	1.01750i
$719$		−	20.5144i		−	0.765056i	−0.923944	−	0.382528i	$-0.875054\pi$
$719$		−	20.5144i		−	0.765056i	0.923944	−	0.382528i	$-0.124946\pi$
$720$	11.5949	+	10.4655i	0.432115	+	0.390027i
$721$	−31.2078	−	31.2078i	−1.16224	−	1.16224i
$722$	6.31991	+	14.7223i	0.235203	+	0.547906i
$723$	−15.3811	+	15.3811i	−0.572028	+	0.572028i
$724$	1.58854	−	1.67195i	0.0590378	−	0.0621374i
$725$	6.40099	−	6.40099i	0.237727	−	0.237727i
$726$	31.3543	−	13.4596i	1.16367	−	0.499534i
$727$	−5.05004	+	5.05004i	−0.187296	+	0.187296i	−0.794526	−	0.607230i	$-0.792281\pi$
$727$	−5.05004	+	5.05004i	−0.187296	+	0.187296i	0.607230	+	0.794526i	$0.292281\pi$
$728$	8.37404	−	3.85126i	0.310362	−	0.142737i
$729$	−40.0904			−1.48483
$730$	7.22302	+	2.88423i	0.267336	+	0.106750i
$731$	−22.7819			−0.842618
$732$	40.6398	−	1.03956i	1.50209	−	0.0384232i
$733$		−	32.4328i		−	1.19793i	−0.800775	−	0.598966i	$-0.795579\pi$
$733$		−	32.4328i		−	1.19793i	0.800775	−	0.598966i	$-0.204421\pi$
$734$	−7.05110	−	16.4256i	−0.260261	−	0.606280i
$735$	−37.3829	+	37.3829i	−1.37889	+	1.37889i
$736$	8.04034	−	23.5688i	0.296371	−	0.868756i
$737$	−18.7565			−0.690905
$738$	−17.3294	−	40.3690i	−0.637905	−	1.48600i
$739$	21.7908			0.801588			0.400794	−	0.916168i	$-0.368734\pi$
$739$	21.7908			0.801588			0.400794	+	0.916168i	$0.368734\pi$
$740$	−0.247092	+	12.1630i	−0.00908328	+	0.447121i
$741$	4.55431			0.167307
$742$	−35.0128	−	81.5625i	−1.28536	−	2.99425i
$743$	−8.31087			−0.304896			−0.152448	−	0.988311i	$-0.548716\pi$
$743$	−8.31087			−0.304896			−0.152448	+	0.988311i	$0.548716\pi$
$744$	18.6106	+	40.4662i	0.682298	+	1.48356i
$745$	−10.6536	+	10.6536i	−0.390317	+	0.390317i
$746$	−13.1572	−	30.6498i	−0.481719	−	1.12217i
$747$		−	9.69720i		−	0.354802i
$748$	−1.28308	−	50.1600i	−0.0469141	−	1.83403i
$749$	51.5346			1.88304
$750$	3.45118	+	1.37809i	0.126019	+	0.0503208i
$751$	44.4891			1.62343			0.811715	−	0.584054i	$-0.198534\pi$
$751$	44.4891			1.62343			0.811715	+	0.584054i	$0.198534\pi$
$752$	35.4630	−	1.81546i	1.29320	−	0.0662030i
$753$	28.6381	−	28.6381i	1.04363	−	1.04363i
$754$	7.36149	−	3.16011i	0.268090	−	0.115084i
$755$	−8.76793	+	8.76793i	−0.319098	+	0.319098i
$756$	−17.9534	−	17.0578i	−0.652957	−	0.620386i
$757$	−1.61375	+	1.61375i	−0.0586529	+	0.0586529i	−0.735825	−	0.677172i	$-0.763205\pi$
$757$	−1.61375	+	1.61375i	−0.0586529	+	0.0586529i	0.677172	+	0.735825i	$0.263205\pi$
$758$	−17.1304	−	39.9055i	−0.622206	−	1.44943i
$759$	36.7461	+	36.7461i	1.33380	+	1.33380i
$760$	2.71810	−	7.34718i	0.0985959	−	0.266510i
$761$		−	3.44597i		−	0.124916i	−0.998048	−	0.0624581i	$-0.980106\pi$
$761$		−	3.44597i		−	0.124916i	0.998048	−	0.0624581i	$-0.0198940\pi$
$762$	7.32498	+	17.0636i	0.265356	+	0.618149i
$763$	−52.3772	−	52.3772i	−1.89618	−	1.89618i
$764$	−20.7648	+	0.531160i	−0.751245	+	0.0192167i
$765$			21.8070i			0.788433i
$766$	−42.2733	−	16.8802i	−1.52740	−	0.609906i
$767$	−2.96830			−0.107179
$768$	41.8236	−	4.29341i	1.50918	−	0.154925i
$769$	−13.1569	−	13.1569i	−0.474449	−	0.474449i	0.428902	−	0.903351i	$-0.358901\pi$
$769$	−13.1569	−	13.1569i	−0.474449	−	0.474449i	−0.903351	+	0.428902i	$0.858901\pi$
$770$	30.7262	+	12.2693i	1.10729	+	0.442154i
$771$	21.8560	−	21.8560i	0.787126	−	0.787126i
$772$	−0.305174	−	11.9303i	−0.0109835	−	0.429380i
$773$	40.5838			1.45970			0.729849	−	0.683609i	$-0.239590\pi$
$773$	40.5838			1.45970			0.729849	+	0.683609i	$0.239590\pi$
$774$	20.9217	+	8.35425i	0.752014	+	0.300287i
$775$	4.23759	+	4.23759i	0.152219	+	0.152219i
$776$	−6.86492	−	14.9268i	−0.246436	−	0.535842i
$777$	3.81812	−	83.1495i	0.136974	−	2.98297i
$778$	−2.21716	+	5.55247i	−0.0794890	+	0.199066i
$779$	−15.5800	+	15.5800i	−0.558212	+	0.558212i
$780$	2.38416	+	2.26523i	0.0853667	+	0.0811083i
$781$		−	27.5547i		−	0.985986i
$782$	31.9481	−	13.7145i	1.14246	−	0.490430i
$783$	−15.2199	−	15.2199i	−0.543915	−	0.543915i
$784$	4.11447	+	80.3715i	0.146945	+	2.87041i
$785$	−4.83777	+	4.83777i	−0.172667	+	0.172667i
$786$	6.03367	−	15.1102i	0.215214	−	0.538964i
$787$			2.96153i			0.105567i	0.998606	+	0.0527836i	$0.0168094\pi$
$787$			2.96153i			0.105567i	−0.998606	+	0.0527836i	$0.983191\pi$
$788$	−30.5974	+	32.2038i	−1.08999	+	1.14721i
$789$	3.52876			0.125627
$790$	−2.37088	+	1.01776i	−0.0843522	+	0.0362103i
$791$	32.5730	−	32.5730i	1.15816	−	1.15816i
$792$	−17.2157	+	46.5348i	−0.611732	+	1.65354i
$793$	4.84062			0.171895
$794$	−11.6113	−	27.0485i	−0.412069	−	0.959917i
$795$	22.3937	−	22.3937i	0.794224	−	0.794224i
$796$	0.0577402	+	2.25726i	0.00204655	+	0.0800064i
$797$	−22.7310	−	22.7310i	−0.805174	−	0.805174i	0.178725	−	0.983899i	$-0.442803\pi$
$797$	−22.7310	−	22.7310i	−0.805174	−	0.805174i	−0.983899	+	0.178725i	$0.942803\pi$
$798$	−19.8768	+	49.7777i	−0.703630	+	1.76211i
$799$	35.0556	+	35.0556i	1.24018	+	1.24018i
$800$	5.07726	−	2.49428i	0.179508	−	0.0881860i
$801$	−14.0753	−	14.0753i	−0.497326	−	0.497326i
$802$	2.67678	+	1.06887i	0.0945204	+	0.0377430i
$803$			24.7064i			0.871872i
$804$	15.1136	−	15.9071i	0.533016	−	0.561001i
$805$			22.9248i			0.807994i
$806$	2.09205	+	4.87346i	0.0736895	+	0.171660i
$807$	−84.6188			−2.97872
$808$	−9.55855	−	3.53620i	−0.336269	−	0.124403i
$809$	7.94827	+	7.94827i	0.279446	+	0.279446i	0.832888	−	0.553442i	$-0.186686\pi$
$809$	7.94827	+	7.94827i	0.279446	+	0.279446i	−0.553442	+	0.832888i	$0.686686\pi$
$810$	−2.86693	+	7.17969i	−0.100734	+	0.252269i
$811$			31.8397i			1.11804i	0.829153	+	0.559022i	$0.188823\pi$
$811$			31.8397i			1.11804i	−0.829153	+	0.559022i	$0.811177\pi$
$812$	2.41094	+	94.2515i	0.0846073	+	3.30758i
$813$		−	59.7586i		−	2.09582i
$814$	−36.1735	+	13.5993i	−1.26788	+	0.476654i
$815$			3.15866i			0.110643i
$816$	43.5738	+	39.3297i	1.52539	+	1.37682i
$817$		−	11.2987i		−	0.395293i
$818$	4.18140	+	1.66968i	0.146199	+	0.0583789i
$819$	−8.99799	−	8.99799i	−0.314415	−	0.314415i
$820$	−15.9053	+	0.406854i	−0.555436	+	0.0142080i
$821$	25.7542			0.898829			0.449414	−	0.893323i	$-0.351633\pi$
$821$	25.7542			0.898829			0.449414	+	0.893323i	$0.351633\pi$
$822$	−11.2816	+	4.84289i	−0.393489	+	0.168915i
$823$			6.56492i			0.228839i	0.993433	+	0.114419i	$0.0365008\pi$
$823$			6.56492i			0.228839i	−0.993433	+	0.114419i	$0.963499\pi$
$824$	−10.0159	−	21.7781i	−0.348920	−	0.758677i
$825$			11.8048i			0.410990i
$826$	12.9548	−	32.4429i	0.450755	−	1.12883i
$827$	18.9814	+	18.9814i	0.660048	+	0.660048i	0.955391	−	0.295343i	$-0.0954340\pi$
$827$	18.9814	+	18.9814i	0.660048	+	0.660048i	−0.295343	+	0.955391i	$0.595434\pi$
$828$	−34.3687	+	0.879143i	−1.19439	+	0.0305523i
$829$	−30.2084	−	30.2084i	−1.04918	−	1.04918i	−0.998726	−	0.0504530i	$-0.983933\pi$
$829$	−30.2084	−	30.2084i	−1.04918	−	1.04918i	−0.0504530	−	0.998726i	$-0.516067\pi$
$830$	−3.26159	−	1.30239i	−0.113211	−	0.0452065i
$831$	4.71810	+	4.71810i	0.163669	+	0.163669i
$832$	4.99144	−	0.383710i	0.173047	−	0.0133027i
$833$	−79.4482	+	79.4482i	−2.75272	+	2.75272i
$834$	−14.1286	+	6.06506i	−0.489234	+	0.210016i
$835$	5.33468			0.184614
$836$	24.8770	−	0.636349i	0.860390	−	0.0220086i
$837$	10.0759	−	10.0759i	0.348274	−	0.348274i
$838$	−6.65509	−	15.5031i	−0.229896	−	0.535545i
$839$	38.9852			1.34592			0.672960	−	0.739679i	$-0.265023\pi$
$839$	38.9852			1.34592			0.672960	+	0.739679i	$0.265023\pi$
$840$	−35.1639	+	16.1721i	−1.21327	+	0.557989i
$841$			52.9453i			1.82570i
$842$	−33.1625	−	13.2421i	−1.14285	−	0.456354i
$843$	−24.7684	+	24.7684i	−0.853068	+	0.853068i
$844$	−28.5789	−	27.1533i	−0.983726	−	0.934654i
$845$	−8.91549	−	8.91549i	−0.306702	−	0.306702i
$846$	−19.3381	−	45.0483i	−0.664858	−	1.54879i
$847$			47.8156i			1.64296i
$848$	−2.46472	−	48.1455i	−0.0846387	−	1.65332i
$849$	−41.8278	+	41.8278i	−1.43553	+	1.43553i
$850$	7.33462	+	2.92879i	0.251576	+	0.100457i
$851$	−18.0460	−	19.7831i	−0.618610	−	0.678156i
$852$	23.3688	+	22.2031i	0.800601	+	0.760664i
$853$	−14.0025	−	14.0025i	−0.479437	−	0.479437i	0.425515	−	0.904951i	$-0.360093\pi$
$853$	−14.0025	−	14.0025i	−0.479437	−	0.479437i	−0.904951	+	0.425515i	$0.860093\pi$
$854$	−21.1263	+	52.9070i	−0.722928	+	1.81044i
$855$	−10.8153			−0.369874
$856$	26.2513	+	9.71174i	0.897253	+	0.331940i
$857$	30.7183	−	30.7183i	1.04932	−	1.04932i	0.0505976	−	0.998719i	$-0.483887\pi$
$857$	30.7183	−	30.7183i	1.04932	−	1.04932i	0.998719	−	0.0505976i	$-0.0161126\pi$
$858$	−3.87413	+	9.70204i	−0.132261	+	0.331222i
$859$	−18.6805	−	18.6805i	−0.637371	−	0.637371i	0.312535	−	0.949906i	$-0.398822\pi$
$859$	−18.6805	−	18.6805i	−0.637371	−	0.637371i	−0.949906	+	0.312535i	$0.898822\pi$
$860$	5.61979	−	5.91484i	0.191633	−	0.201694i
$861$	108.860			3.70995
$862$	−4.56834	+	11.4406i	−0.155598	+	0.389668i
$863$			14.6729i			0.499472i	0.968314	+	0.249736i	$0.0803439\pi$
$863$			14.6729i			0.499472i	−0.968314	+	0.249736i	$0.919656\pi$
$864$	−5.93075	−	12.0724i	−0.201768	−	0.410712i
$865$	3.00515	+	3.00515i	0.102178	+	0.102178i
$866$	25.8847	−	11.1116i	0.879596	−	0.377589i
$867$			37.2800i			1.26610i
$868$	−62.3964	+	1.59609i	−2.11787	+	0.0541748i
$869$	−5.79545	−	5.79545i	−0.196597	−	0.196597i
$870$	−30.9121	+	13.2698i	−1.04802	+	0.449888i
$871$	1.84745	−	1.84745i	0.0625983	−	0.0625983i
$872$	−16.8100	−	36.5510i	−0.569259	−	1.23777i
$873$	−16.0390	+	16.0390i	−0.542839	+	0.542839i
$874$	6.80176	+	15.8448i	0.230073	+	0.535957i
$875$	−3.68234	+	3.68234i	−0.124486	+	0.124486i
$876$	−20.9532	−	19.9080i	−0.707942	−	0.672627i
$877$	3.76989			0.127300			0.0636501	−	0.997972i	$-0.479726\pi$
$877$	3.76989			0.127300			0.0636501	+	0.997972i	$0.479726\pi$
$878$	−14.5886	+	36.5345i	−0.492341	+	1.23298i
$879$	3.51280			0.118484
$880$	13.3395	+	12.0402i	0.449675	+	0.405877i
$881$			11.9945i			0.404105i	0.979375	+	0.202053i	$0.0647612\pi$
$881$			11.9945i			0.404105i	−0.979375	+	0.202053i	$0.935239\pi$
$882$	102.095	−	43.8270i	3.43773	−	1.47573i
$883$	12.5586	−	12.5586i	0.422631	−	0.422631i	−0.463478	−	0.886109i	$-0.653399\pi$
$883$	12.5586	−	12.5586i	0.422631	−	0.422631i	0.886109	+	0.463478i	$0.153399\pi$
$884$	5.06695	+	4.81419i	0.170420	+	0.161919i
$885$	12.4644			0.418985
$886$	−22.9425	+	9.84863i	−0.770767	+	0.330871i
$887$	−16.0527			−0.538997			−0.269498	−	0.963001i	$-0.586858\pi$
$887$	−16.0527			−0.538997			−0.269498	+	0.963001i	$0.586858\pi$
$888$	17.6145	−	41.6362i	0.591104	−	1.39722i
$889$	−26.0221			−0.872754
$890$	−6.62451	+	2.84374i	−0.222054	+	0.0953223i
$891$	−24.5582			−0.822732
$892$	10.0408	+	9.53993i	0.336191	+	0.319421i
$893$	−17.3859	+	17.3859i	−0.581798	+	0.581798i
$894$	51.4490	−	22.0858i	1.72071	−	0.738659i
$895$		−	18.5907i		−	0.621419i
$896$	−17.5907	+	56.2301i	−0.587664	+	1.87852i
$897$	−7.23871			−0.241693
$898$	−19.7423	+	49.4411i	−0.658811	+	1.64987i
$899$	−54.2495			−1.80932
$900$	−5.66173	−	5.37930i	−0.188724	−	0.179310i
$901$	47.5924	−	47.5924i	1.58553	−	1.58553i
$902$	−19.9369	−	46.4432i	−0.663827	−	1.54639i
$903$	−39.4732	+	39.4732i	−1.31358	+	1.31358i
$904$	22.7309	−	10.4540i	0.756017	−	0.347696i
$905$	−0.815389	+	0.815389i	−0.0271045	+	0.0271045i
$906$	42.3427	−	18.1767i	1.40674	−	0.603879i
$907$	−12.0897	−	12.0897i	−0.401431	−	0.401431i	0.477306	−	0.878737i	$-0.341613\pi$
$907$	−12.0897	−	12.0897i	−0.401431	−	0.401431i	−0.878737	+	0.477306i	$0.841613\pi$
$908$	−1.07182	+	0.0274169i	−0.0355696	+	0.000909863i
$909$			14.0705i			0.466687i
$910$	−4.23489	+	1.81793i	−0.140385	+	0.0602639i
$911$	15.0273	+	15.0273i	0.497876	+	0.497876i	0.910776	−	0.412900i	$-0.135484\pi$
$911$	15.0273	+	15.0273i	0.497876	+	0.497876i	−0.412900	+	0.910776i	$0.635484\pi$
$912$	−19.5057	+	21.6106i	−0.645899	+	0.715598i
$913$		−	11.1563i		−	0.369220i
$914$	1.52016	−	3.80697i	0.0502825	−	0.125923i
$915$	−20.3265			−0.671975
$916$	−14.1555	+	14.8987i	−0.467710	+	0.492266i
$917$	16.1223	+	16.1223i	0.532405	+	0.532405i
$918$	6.96392	−	17.4399i	0.229844	−	0.575601i
$919$	−36.5230	+	36.5230i	−1.20478	+	1.20478i	−0.232089	+	0.972694i	$0.574556\pi$
$919$	−36.5230	+	36.5230i	−1.20478	+	1.20478i	−0.972694	+	0.232089i	$0.925444\pi$
$920$	−4.32020	+	11.6777i	−0.142433	+	0.385003i
$921$	0.548523			0.0180745
$922$	19.8071	−	49.6032i	0.652312	−	1.63359i
$923$	2.71404	+	2.71404i	0.0893337	+	0.0893337i
$924$	−89.1332	−	84.6869i	−2.93227	−	2.78599i
$925$	0.279018	−	6.07636i	0.00917407	−	0.199789i
$926$	−36.0291	−	14.3868i	−1.18399	−	0.472779i
$927$	−23.4008	+	23.4008i	−0.768585	+	0.768585i
$928$	−16.5337	+	48.4653i	−0.542744	+	1.59095i
$929$			46.7744i			1.53462i	0.641276	+	0.767310i	$0.278405\pi$
$929$			46.7744i			1.53462i	−0.641276	+	0.767310i	$0.721595\pi$
$930$	−8.78487	−	20.4644i	−0.288067	−	0.671055i
$931$	−39.4026	−	39.4026i	−1.29137	−	1.29137i
$932$	13.4694	+	12.7975i	0.441206	+	0.419197i
$933$	−29.0956	+	29.0956i	−0.952546	+	0.952546i
$934$	14.5756	+	5.82018i	0.476927	+	0.190442i
$935$			25.0882i			0.820472i
$936$	−2.88783	−	6.27918i	−0.0943916	−	0.205242i
$937$	−10.2812			−0.335873			−0.167936	−	0.985798i	$-0.553710\pi$
$937$	−10.2812			−0.335873			−0.167936	+	0.985798i	$0.553710\pi$
$938$	12.1292	+	28.2552i	0.396034	+	0.922564i
$939$	−37.5553	+	37.5553i	−1.22557	+	1.22557i
$940$	−17.7489	+	0.454013i	−0.578905	+	0.0148083i
$941$	−28.0935			−0.915820			−0.457910	−	0.888998i	$-0.651402\pi$
$941$	−28.0935			−0.915820			−0.457910	+	0.888998i	$0.651402\pi$
$942$	23.3629	−	10.0291i	0.761204	−	0.326766i
$943$	24.7632	−	24.7632i	0.806399	−	0.806399i
$944$	12.7130	−	14.0848i	0.413772	−	0.458422i
$945$	8.75565	+	8.75565i	0.284821	+	0.284821i
$946$	24.0697	+	9.61128i	0.782573	+	0.312490i
$947$	−13.4049	−	13.4049i	−0.435600	−	0.435600i	0.454928	−	0.890528i	$-0.349665\pi$
$947$	−13.4049	−	13.4049i	−0.435600	−	0.435600i	−0.890528	+	0.454928i	$0.849665\pi$
$948$	9.58490	−	0.245180i	0.311303	−	0.00796307i
$949$	−2.43349	−	2.43349i	−0.0789945	−	0.0789945i
$950$	−1.45255	+	3.63763i	−0.0471268	+	0.118020i
$951$			18.9611i			0.614857i
$952$	−74.7322	+	34.3697i	−2.42209	+	1.11393i
$953$			44.1445i			1.42998i	0.699135	+	0.714990i	$0.253569\pi$
$953$			44.1445i			1.42998i	−0.699135	+	0.714990i	$0.746431\pi$
$954$	−61.1588	+	26.2540i	−1.98009	+	0.850003i
$955$	10.3858			0.336077
$956$	−16.1172	+	0.412276i	−0.521269	+	0.0133340i
$957$	−75.5624	−	75.5624i	−2.44259	−	2.44259i
$958$	41.1053	+	16.4138i	1.32805	+	0.530305i
$959$		−	17.2045i		−	0.555561i
$960$	−20.9599	+	1.61126i	−0.676477	+	0.0520032i
$961$		−	4.91426i		−	0.158525i
$962$	2.22347	−	4.90243i	0.0716876	−	0.158061i
$963$		−	38.6427i		−	1.24524i
$964$	−0.423359	−	16.5505i	−0.0136355	−	0.533057i
$965$			5.96709i			0.192087i
$966$	31.5925	−	79.1176i	1.01647	−	2.54557i
$967$	−36.1061	−	36.1061i	−1.16109	−	1.16109i	−0.984236	−	0.176858i	$-0.943407\pi$
$967$	−36.1061	−	36.1061i	−1.16109	−	1.16109i	−0.176858	−	0.984236i	$-0.556593\pi$
$968$	−9.01089	+	24.3569i	−0.289621	+	0.782860i
$969$	−40.6440			−1.30567
$970$	3.24049	+	7.54875i	0.104046	+	0.242376i
$971$			6.02587i			0.193379i	0.995315	+	0.0966897i	$0.0308254\pi$
$971$			6.02587i			0.193379i	−0.995315	+	0.0966897i	$0.969175\pi$
$972$	29.6152	−	31.1701i	0.949907	−	0.999780i
$973$		−	21.5463i		−	0.690741i
$974$	−5.61369	−	2.24161i	−0.179874	−	0.0718257i
$975$	−1.16273	−	1.16273i	−0.0372371	−	0.0372371i
$976$	−20.7319	+	22.9691i	−0.663613	+	0.735224i
$977$	−3.55871	−	3.55871i	−0.113853	−	0.113853i	0.647885	−	0.761738i	$-0.275654\pi$
$977$	−3.55871	−	3.55871i	−0.113853	−	0.113853i	−0.761738	+	0.647885i	$0.775654\pi$
$978$	4.35292	−	10.9011i	0.139191	−	0.348578i
$979$	−16.1931	−	16.1931i	−0.517535	−	0.517535i
$980$	−1.02895	−	40.2252i	−0.0328687	−	1.28495i
$981$	−39.2745	+	39.2745i	−1.25394	+	1.25394i
$982$	13.3254	+	31.0416i	0.425231	+	0.990578i
$983$	−5.73891			−0.183043			−0.0915215	−	0.995803i	$-0.529173\pi$
$983$	−5.73891			−0.183043			−0.0915215	+	0.995803i	$0.529173\pi$
$984$	55.4526	+	20.5148i	1.76776	+	0.653988i
$985$	15.7054	−	15.7054i	0.500417	−	0.500417i
$986$	−65.6960	+	28.2017i	−2.09219	+	0.898124i
$987$	121.479			3.86670
$988$	−2.38762	+	2.51297i	−0.0759602	+	0.0799483i
$989$			17.9584i			0.571045i
$990$	9.20000	−	23.0397i	0.292395	−	0.732250i
$991$	7.00298	−	7.00298i	0.222457	−	0.222457i	−0.587075	−	0.809532i	$-0.699721\pi$
$991$	7.00298	−	7.00298i	0.222457	−	0.222457i	0.809532	+	0.587075i	$0.199721\pi$
$992$	−32.0850	−	10.9456i	−1.01870	−	0.347524i
$993$	−7.07568	−	7.07568i	−0.224540	−	0.224540i
$994$	−41.5090	+	17.8188i	−1.31659	+	0.565178i
$995$		−	1.12900i		−	0.0357917i
$996$	9.46150	+	8.98953i	0.299799	+	0.284844i
$997$	20.8987	−	20.8987i	0.661869	−	0.661869i	−0.293951	−	0.955820i	$-0.594970\pi$
$997$	20.8987	−	20.8987i	0.661869	−	0.661869i	0.955820	+	0.293951i	$0.0949704\pi$
$998$	−14.3265	+	35.8781i	−0.453498	+	1.13570i
$999$	−14.4480	−	0.663434i	−0.457115	−	0.0209901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.u.a.31.13	✓	152
4.3	odd	2	inner	740.2.u.a.31.52	yes	152
37.6	odd	4	inner	740.2.u.a.191.52	yes	152
148.43	even	4	inner	740.2.u.a.191.13	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.u.a.31.13	✓	152	1.1	even	1	trivial
740.2.u.a.31.52	yes	152	4.3	odd	2	inner
740.2.u.a.191.13	yes	152	148.43	even	4	inner
740.2.u.a.191.52	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+(-1.29954 + 0.557859i) q^{2} -2.62771 q^{3} +(1.37759 - 1.44991i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(3.41481 - 1.46589i) q^{6} +5.20761i q^{7} +(-0.981377 + 2.65272i) q^{8} +3.90487 q^{9} +(0.524445 - 1.31338i) q^{10} +4.49242 q^{11} +(-3.61990 + 3.80996i) q^{12} +(-0.442487 + 0.442487i) q^{13} +(-2.90511 - 6.76748i) q^{14} +(1.85807 - 1.85807i) q^{15} +(-0.204505 - 3.99477i) q^{16} +(3.94888 - 3.94888i) q^{17} +(-5.07452 + 2.17837i) q^{18} +(1.95846 + 1.95846i) q^{19} +(0.0511429 + 1.99935i) q^{20} -13.6841i q^{21} +(-5.83807 + 2.50614i) q^{22} +(-3.11281 - 3.11281i) q^{23} +(2.57878 - 6.97057i) q^{24} -1.00000i q^{25} +(0.328183 - 0.821873i) q^{26} -2.37774 q^{27} +(7.55059 + 7.17394i) q^{28} +(6.40099 + 6.40099i) q^{29} +(-1.37809 + 3.45118i) q^{30} +(-4.23759 + 4.23759i) q^{31} +(2.49428 + 5.07726i) q^{32} -11.8048 q^{33} +(-2.92879 + 7.33462i) q^{34} +(-3.68234 - 3.68234i) q^{35} +(5.37930 - 5.66173i) q^{36} +(6.07636 + 0.279018i) q^{37} +(-3.63763 - 1.45255i) q^{38} +(1.16273 - 1.16273i) q^{39} +(-1.18181 - 2.56969i) q^{40} +7.95524i q^{41} +(7.63379 + 17.7830i) q^{42} +(-2.88460 - 2.88460i) q^{43} +(6.18871 - 6.51363i) q^{44} +(-2.76116 + 2.76116i) q^{45} +(5.78172 + 2.30870i) q^{46} +8.87735i q^{47} +(0.537379 + 10.4971i) q^{48} -20.1192 q^{49} +(0.557859 + 1.29954i) q^{50} +(-10.3765 + 10.3765i) q^{51} +(0.0320037 + 1.25113i) q^{52} +12.0521 q^{53} +(3.08996 - 1.32644i) q^{54} +(-3.17662 + 3.17662i) q^{55} +(-13.8143 - 5.11063i) q^{56} +(-5.14627 - 5.14627i) q^{57} +(-11.8892 - 4.74747i) q^{58} +(3.35411 + 3.35411i) q^{59} +(-0.134389 - 5.25371i) q^{60} +(-5.46979 - 5.46979i) q^{61} +(3.14292 - 7.87087i) q^{62} +20.3350i q^{63} +(-6.07380 - 5.20663i) q^{64} -0.625771i q^{65} +(15.3408 - 6.58541i) q^{66} -4.17514 q^{67} +(-0.285610 - 11.1655i) q^{68} +(8.17957 + 8.17957i) q^{69} +(6.83955 + 2.73111i) q^{70} -6.13360i q^{71} +(-3.83215 + 10.3585i) q^{72} +5.49958i q^{73} +(-8.05210 + 3.02715i) q^{74} +2.62771i q^{75} +(5.53755 - 0.141649i) q^{76} +23.3948i q^{77} +(-0.862369 + 2.15965i) q^{78} +(-1.29005 - 1.29005i) q^{79} +(2.96933 + 2.68012i) q^{80} -5.46659 q^{81} +(-4.43790 - 10.3381i) q^{82} -2.48336i q^{83} +(-19.8408 - 18.8510i) q^{84} +5.58456i q^{85} +(5.35784 + 2.13944i) q^{86} +(-16.8200 - 16.8200i) q^{87} +(-4.40876 + 11.9171i) q^{88} +(-3.60454 - 3.60454i) q^{89} +(2.04789 - 5.12857i) q^{90} +(-2.30430 - 2.30430i) q^{91} +(-8.80148 + 0.225140i) q^{92} +(11.1352 - 11.1352i) q^{93} +(-4.95231 - 11.5364i) q^{94} -2.76968 q^{95} +(-6.55424 - 13.3416i) q^{96} +(-4.10744 + 4.10744i) q^{97} +(26.1456 - 11.2237i) q^{98} +17.5423 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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