LMFDB - Embedded newform 740.2.u.a.191.52

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			191.52
Character	$\chi$	$=$	740.191
Dual form			740.2.u.a.31.52

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.557859 + 1.29954i) q^{2} +2.62771 q^{3} +(-1.37759 + 1.44991i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(1.46589 + 3.41481i) q^{6} +5.20761i q^{7} +(-2.65272 - 0.981377i) 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} +(-6.76748 + 2.90511i) q^{14} +(-1.85807 - 1.85807i) q^{15} +(-0.204505 - 3.99477i) q^{16} +(3.94888 + 3.94888i) q^{17} +(2.17837 + 5.07452i) q^{18} +(-1.95846 + 1.95846i) q^{19} +(1.99935 - 0.0511429i) q^{20} +13.6841i q^{21} +(-2.50614 - 5.83807i) q^{22} +(3.11281 - 3.11281i) q^{23} +(-6.97057 - 2.57878i) 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} +(5.07726 - 2.49428i) 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} +(-17.7830 + 7.63379i) 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} +(-1.29954 + 0.557859i) q^{50} +(10.3765 + 10.3765i) q^{51} +(1.25113 - 0.0320037i) q^{52} +12.0521 q^{53} +(1.32644 + 3.08996i) q^{54} +(3.17662 + 3.17662i) q^{55} +(5.11063 - 13.8143i) q^{56} +(-5.14627 + 5.14627i) q^{57} +(11.8892 + 4.74747i) q^{58} +(-3.35411 + 3.35411i) q^{59} +(5.25371 - 0.134389i) 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} +(-6.58541 - 15.3408i) q^{66} +4.17514 q^{67} +(-11.1655 + 0.285610i) q^{68} +(8.17957 - 8.17957i) q^{69} +(6.83955 + 2.73111i) q^{70} -6.13360i q^{71} +(-10.3585 - 3.83215i) q^{72} -5.49958i q^{73} +(3.75234 + 7.74080i) q^{74} +2.62771i q^{75} +(-0.141649 - 5.53755i) q^{76} -23.3948i q^{77} +(0.862369 - 2.15965i) q^{78} +(1.29005 - 1.29005i) q^{79} +(-2.68012 + 2.96933i) q^{80} -5.46659 q^{81} +(10.3381 - 4.43790i) 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} +(11.9171 + 4.40876i) q^{88} +(-3.60454 + 3.60454i) q^{89} +(2.04789 - 5.12857i) q^{90} +(2.30430 - 2.30430i) q^{91} +(0.225140 + 8.80148i) q^{92} +(11.1352 + 11.1352i) q^{93} +(-11.5364 + 4.95231i) q^{94} +2.76968 q^{95} +(13.3416 - 6.55424i) q^{96} +(-4.10744 - 4.10744i) q^{97} +(-11.2237 - 26.1456i) 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 $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.557859	+	1.29954i	0.394466	+	0.918911i
$2$	0.557859	+	1.29954i	0.394466	+	0.918911i
$3$	2.62771			1.51711			0.758555	−	0.651609i	$-0.225906\pi$
$3$	2.62771			1.51711			0.758555	+	0.651609i	$0.225906\pi$
$4$	−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
$6$	1.46589	+	3.41481i	0.598448	+	1.39409i
$7$			5.20761i			1.96829i	0.177363	+	0.984146i	$0.443243\pi$
$7$			5.20761i			1.96829i	−0.177363	+	0.984146i	$0.556757\pi$
$8$	−2.65272	−	0.981377i	−0.937876	−	0.346969i
$9$	3.90487			1.30162
$10$	0.524445	−	1.31338i	0.165844	−	0.415326i
$11$	−4.49242			−1.35452			−0.677258	−	0.735745i	$-0.736832\pi$
$11$	−4.49242			−1.35452			−0.677258	+	0.735745i	$0.736832\pi$
$12$	−3.61990	+	3.80996i	−1.04498	+	1.09984i
$13$	−0.442487	−	0.442487i	−0.122724	−	0.122724i	0.643077	−	0.765801i	$-0.277657\pi$
$13$	−0.442487	−	0.442487i	−0.122724	−	0.122724i	−0.765801	+	0.643077i	$0.777657\pi$
$14$	−6.76748	+	2.90511i	−1.80868	+	0.776423i
$15$	−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	0.999143	−	0.0413992i	$-0.0131816\pi$
$17$	3.94888	+	3.94888i	0.957743	+	0.957743i	−0.0413992	+	0.999143i	$0.513182\pi$
$18$	2.17837	+	5.07452i	0.513446	+	1.19608i
$19$	−1.95846	+	1.95846i	−0.449302	+	0.449302i	−0.895122	−	0.445821i	$-0.852912\pi$
$19$	−1.95846	+	1.95846i	−0.449302	+	0.449302i	0.445821	+	0.895122i	$0.352912\pi$
$20$	1.99935	−	0.0511429i	0.447067	−	0.0114359i
$21$			13.6841i			2.98612i
$22$	−2.50614	−	5.83807i	−0.534310	−	1.24468i
$23$	3.11281	−	3.11281i	0.649066	−	0.649066i	−0.303701	−	0.952767i	$-0.598223\pi$
$23$	3.11281	−	3.11281i	0.649066	−	0.649066i	0.952767	+	0.303701i	$0.0982225\pi$
$24$	−6.97057	−	2.57878i	−1.42286	−	0.526391i
$25$			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	0.211189	−	0.977445i	$-0.432267\pi$
$29$	6.40099	−	6.40099i	1.18863	−	1.18863i	0.977445	−	0.211189i	$-0.0677335\pi$
$30$	1.37809	−	3.45118i	0.251604	−	0.630095i
$31$	4.23759	+	4.23759i	0.761093	+	0.761093i	0.976520	−	0.215427i	$-0.0691144\pi$
$31$	4.23759	+	4.23759i	0.761093	+	0.761093i	−0.215427	+	0.976520i	$0.569114\pi$
$32$	5.07726	−	2.49428i	0.897541	−	0.440930i
$33$	−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	$-0.786645\pi$
$41$		−	7.95524i		−	1.24240i	0.783652	−	0.621200i	$-0.213355\pi$
$42$	−17.7830	+	7.63379i	−2.74397	+	1.17792i
$43$	2.88460	−	2.88460i	0.439897	−	0.439897i	−0.452080	−	0.891977i	$-0.649318\pi$
$43$	2.88460	−	2.88460i	0.439897	−	0.439897i	0.891977	+	0.452080i	$0.149318\pi$
$44$	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
$50$	−1.29954	+	0.557859i	−0.183782	+	0.0788931i
$51$	10.3765	+	10.3765i	1.45300	+	1.45300i
$52$	1.25113	−	0.0320037i	0.173501	−	0.00443812i
$53$	12.0521			1.65549			0.827744	−	0.561106i	$-0.189624\pi$
$53$	12.0521			1.65549			0.827744	+	0.561106i	$0.189624\pi$
$54$	1.32644	+	3.08996i	0.180506	+	0.420491i
$55$	3.17662	+	3.17662i	0.428336	+	0.428336i
$56$	5.11063	−	13.8143i	0.682937	−	1.84601i
$57$	−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	$-0.849918\pi$
$59$	−3.35411	+	3.35411i	−0.436668	+	0.436668i	0.454221	+	0.890889i	$0.349918\pi$
$60$	5.25371	−	0.134389i	0.678251	−	0.0173495i
$61$	−5.46979	+	5.46979i	−0.700335	+	0.700335i	−0.964482	−	0.264148i	$-0.914909\pi$
$61$	−5.46979	+	5.46979i	−0.700335	+	0.700335i	0.264148	+	0.964482i	$0.414909\pi$
$62$	−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
$66$	−6.58541	−	15.3408i	−0.810608	−	1.88832i
$67$	4.17514			0.510075			0.255037	−	0.966931i	$-0.417912\pi$
$67$	4.17514			0.510075			0.255037	+	0.966931i	$0.417912\pi$
$68$	−11.1655	+	0.285610i	−1.35401	+	0.0346353i
$69$	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	$-0.118576\pi$
$72$	−10.3585	−	3.83215i	−1.22076	−	0.451624i
$73$		−	5.49958i		−	0.643677i	−0.946795	−	0.321839i	$-0.895699\pi$
$73$		−	5.49958i		−	0.643677i	0.946795	−	0.321839i	$-0.104301\pi$
$74$	3.75234	+	7.74080i	0.436201	+	0.899849i
$75$			2.62771i			0.303422i
$76$	−0.141649	−	5.53755i	−0.0162483	−	0.635201i
$77$		−	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	$-0.717274\pi$
$79$	1.29005	−	1.29005i	0.145142	−	0.145142i	0.775944	+	0.630802i	$0.217274\pi$
$80$	−2.68012	+	2.96933i	−0.299647	+	0.331982i
$81$	−5.46659			−0.607399
$82$	10.3381	−	4.43790i	1.14165	−	0.490084i
$83$		−	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
$88$	11.9171	+	4.40876i	1.27037	+	0.469976i
$89$	−3.60454	+	3.60454i	−0.382081	+	0.382081i	−0.871851	−	0.489771i	$-0.837081\pi$
$89$	−3.60454	+	3.60454i	−0.382081	+	0.382081i	0.489771	+	0.871851i	$0.337081\pi$
$90$	2.04789	−	5.12857i	0.215867	−	0.540598i
$91$	2.30430	−	2.30430i	0.241556	−	0.241556i
$92$	0.225140	+	8.80148i	0.0234725	+	0.917618i
$93$	11.1352	+	11.1352i	1.15466	+	1.15466i
$94$	−11.5364	+	4.95231i	−1.18989	+	0.510791i
$95$	2.76968			0.284163
$96$	13.3416	−	6.55424i	1.36167	−	0.668940i
$97$	−4.10744	−	4.10744i	−0.417048	−	0.417048i	0.467137	−	0.884185i	$-0.345285\pi$
$97$	−4.10744	−	4.10744i	−0.417048	−	0.417048i	−0.884185	+	0.467137i	$0.845285\pi$
$98$	−11.2237	−	26.1456i	−1.13376	−	2.64111i
$99$	−17.5423			−1.76307
$100$	−1.44991	−	1.37759i	−0.144991	−	0.137759i
$101$		−	3.60331i		−	0.358542i	−0.983800	−	0.179271i	$-0.942626\pi$
$101$		−	3.60331i		−	0.358542i	0.983800	−	0.179271i	$-0.0573740\pi$
$102$	−7.69603	+	19.2733i	−0.762020	+	1.90834i
$103$	5.99273	+	5.99273i	0.590481	+	0.590481i	0.937761	−	0.347280i	$-0.112895\pi$
$103$	5.99273	+	5.99273i	0.590481	+	0.590481i	−0.347280	+	0.937761i	$0.612895\pi$
$104$	0.739545	+	1.60804i	0.0725184	+	0.157681i
$105$	9.67612	−	9.67612i	0.944292	−	0.944292i
$106$	6.72339	+	15.6622i	0.653033	+	1.52125i
$107$		−	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	0.0359882	−	0.999352i	$-0.488542\pi$
$109$	−10.0578	−	10.0578i	−0.963364	−	0.963364i	−0.999352	+	0.0359882i	$0.988542\pi$
$110$	−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	−0.937201	−	0.348790i	$-0.886593\pi$
$113$	−6.25489	+	6.25489i	−0.588411	+	0.588411i	0.348790	+	0.937201i	$0.386593\pi$
$114$	−9.55865	−	3.81687i	−0.895250	−	0.357483i
$115$	−4.40218			−0.410505
$116$	0.462964	+	18.0988i	0.0429851	+	1.68043i
$117$	−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
$124$	−11.9818	+	0.306492i	−1.07600	+	0.0275238i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	−26.4261	+	11.3441i	−2.35423	+	1.01061i
$127$			4.99694i			0.443407i	0.975114	+	0.221704i	$0.0711617\pi$
$127$			4.99694i			0.443407i	−0.975114	+	0.221704i	$0.928838\pi$
$128$	−3.37788	+	10.7977i	−0.298566	+	0.954389i
$129$	7.57990	−	7.57990i	0.667373	−	0.667373i
$130$	−0.813212	+	0.349092i	−0.0713234	+	0.0306174i
$131$	−3.09591	−	3.09591i	−0.270491	−	0.270491i	0.558807	−	0.829298i	$-0.311259\pi$
$131$	−3.09591	−	3.09591i	−0.270491	−	0.270491i	−0.829298	+	0.558807i	$0.811259\pi$
$132$	16.2621	−	17.1159i	1.41544	−	1.48975i
$133$	−10.1989	−	10.1989i	−0.884356	−	0.884356i
$134$	2.32914	+	5.42575i	0.201207	+	0.468713i
$135$	−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	$-0.443856\pi$
$139$	4.13746			0.350934			0.175467	+	0.984485i	$0.443856\pi$
$140$	0.266332	+	10.4118i	0.0225092	+	0.879959i
$141$			23.3271i			1.96450i
$142$	7.97084	−	3.42168i	0.668898	−	0.287141i
$143$	1.98784	+	1.98784i	0.166231	+	0.166231i
$144$	−0.798564	−	15.5991i	−0.0665470	−	1.29992i
$145$	−9.05237			−0.751758
$146$	7.14690	−	3.06799i	0.591482	−	0.253908i
$147$	−52.8674			−4.36043
$148$	−7.96617	+	9.19458i	−0.654815	+	0.755789i
$149$	15.0664			1.23429			0.617145	−	0.786849i	$-0.288289\pi$
$149$	15.0664			1.23429			0.617145	+	0.786849i	$0.288289\pi$
$150$	−3.41481	+	1.46589i	−0.278818	+	0.119690i
$151$	−12.3997			−1.00908			−0.504538	−	0.863390i	$-0.668337\pi$
$151$	−12.3997			−1.00908			−0.504538	+	0.863390i	$0.668337\pi$
$152$	7.11723	−	3.27325i	0.577283	−	0.265496i
$153$	15.4199	+	15.4199i	1.24662	+	1.24662i
$154$	30.4024	−	13.0510i	2.44989	−	1.05168i
$155$		−	5.99285i		−	0.481357i
$156$	3.28762	−	0.0840966i	0.263220	−	0.00673311i
$157$	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
$162$	−3.04958	−	7.10403i	−0.239598	−	0.558145i
$163$	−2.23351	−	2.23351i	−0.174942	−	0.174942i	0.614205	−	0.789147i	$-0.289477\pi$
$163$	−2.23351	−	2.23351i	−0.174942	−	0.174942i	−0.789147	+	0.614205i	$0.789477\pi$
$164$	11.5344	+	10.9590i	0.900687	+	0.855757i
$165$	8.34725	+	8.34725i	0.649833	+	0.649833i
$166$	3.22722	−	1.38536i	0.250481	−	0.107525i
$167$	3.77219	−	3.77219i	0.291901	−	0.291901i	−0.545930	−	0.837831i	$-0.683824\pi$
$167$	3.77219	−	3.77219i	0.291901	−	0.291901i	0.837831	+	0.545930i	$0.183824\pi$
$168$	13.4293	−	36.3000i	1.03609	−	2.80061i
$169$		−	12.6084i		−	0.969878i
$170$	7.25733	−	3.11539i	0.556612	−	0.238940i
$171$	−7.64754	+	7.64754i	−0.584822	+	0.584822i
$172$	0.208634	+	8.15621i	0.0159082	+	0.621905i
$173$			4.24993i			0.323116i	0.986863	+	0.161558i	$0.0516519\pi$
$173$			4.24993i			0.323116i	−0.986863	+	0.161558i	$0.948348\pi$
$174$	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	$-0.00550706\pi$
$179$	13.1456	+	13.1456i	0.982550	+	0.982550i	−0.0173001	+	0.999850i	$0.505507\pi$
$180$	7.80719	−	0.199706i	0.581914	−	0.0148852i
$181$	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
$190$	1.54509	+	3.59930i	0.112093	+	0.261121i
$191$	7.34387	−	7.34387i	0.531384	−	0.531384i	−0.389600	−	0.920984i	$-0.627387\pi$
$191$	7.34387	−	7.34387i	0.531384	−	0.531384i	0.920984	+	0.389600i	$0.127387\pi$
$192$	15.9602	+	13.6815i	1.15183	+	0.987379i
$193$	4.21937	+	4.21937i	0.303717	+	0.303717i	0.842466	−	0.538749i	$-0.181103\pi$
$193$	4.21937	+	4.21937i	0.303717	+	0.303717i	−0.538749	+	0.842466i	$0.681103\pi$
$194$	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	$0.790558\pi$
$198$	−9.78615	−	22.7969i	−0.695471	−	1.62011i
$199$	0.798323	+	0.798323i	0.0565916	+	0.0565916i	0.734836	−	0.678245i	$-0.237259\pi$
$199$	0.798323	+	0.798323i	0.0565916	+	0.0565916i	−0.678245	+	0.734836i	$0.737259\pi$
$200$	0.981377	−	2.65272i	0.0693939	−	0.187575i
$201$	10.9711			0.773840
$202$	4.68263	−	2.01014i	0.329468	−	0.141433i
$203$	33.3339	+	33.3339i	2.33958	+	2.33958i
$204$	−29.3396	+	0.750501i	−2.05418	+	0.0525456i
$205$	−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
$208$	−1.67714	+	1.85812i	−0.116289	+	0.128838i
$209$	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
$214$	12.8602	−	5.52058i	0.879108	−	0.377379i
$215$	−4.07944			−0.278216
$216$	−6.30748	−	2.33346i	−0.429169	−	0.158772i
$217$	−22.0677	+	22.0677i	−1.49805	+	1.49805i
$218$	7.45966	−	18.6813i	0.505232	−	1.26526i
$219$		−	14.4513i		−	0.976529i
$220$	−8.98191	+	0.229755i	−0.605560	+	0.0154901i
$221$		−	3.49465i		−	0.235076i
$222$	9.86008	+	20.3406i	0.661765	+	1.36517i
$223$			6.92510i			0.463739i	0.972747	+	0.231870i	$0.0744842\pi$
$223$			6.92510i			0.463739i	−0.972747	+	0.231870i	$0.925516\pi$
$224$	12.9892	+	26.4404i	0.867879	+	1.76662i
$225$			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	$-0.744337\pi$
$227$	0.379069	−	0.379069i	0.0251597	−	0.0251597i	0.719575	+	0.694415i	$0.244337\pi$
$228$	−0.372214	−	14.5511i	−0.0246505	−	0.963670i
$229$	−10.2755			−0.679027			−0.339514	−	0.940601i	$-0.610262\pi$
$229$	−10.2755			−0.679027			−0.339514	+	0.940601i	$0.610262\pi$
$230$	−2.45579	−	5.72079i	−0.161930	−	0.377218i
$231$		−	61.4748i		−	4.04474i
$232$	−23.2618	+	10.6982i	−1.52721	+	0.702372i
$233$		−	9.28981i		−	0.608595i	−0.952577	−	0.304298i	$-0.901578\pi$
$233$		−	9.28981i		−	0.608595i	0.952577	−	0.304298i	$-0.0984218\pi$
$234$	1.28151	−	3.20931i	0.0837750	−	0.209799i
$235$	6.27724	−	6.27724i	0.409482	−	0.409482i
$236$	−0.242593	−	9.48376i	−0.0157914	−	0.617340i
$237$	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	$-0.666040\pi$
$239$	5.70017	−	5.70017i	0.368713	−	0.368713i	0.867008	+	0.498295i	$0.166040\pi$
$240$	−7.04259	+	7.80256i	−0.454597	+	0.503653i
$241$	5.85341	+	5.85341i	0.377051	+	0.377051i	0.870037	−	0.492986i	$-0.164095\pi$
$241$	5.85341	+	5.85341i	0.377051	+	0.377051i	−0.492986	+	0.870037i	$0.664095\pi$
$242$	5.12219	+	11.9322i	0.329267	+	0.767029i
$243$	−21.4979			−1.37909
$244$	−0.395613	−	15.4658i	−0.0253265	−	0.990099i
$245$	14.2264	+	14.2264i	0.908892	+	0.908892i
$246$	27.1656	−	11.6615i	1.73202	−	0.743511i
$247$	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	$-0.0883010\pi$
$251$	10.8985	+	10.8985i	0.687908	+	0.687908i	−0.273861	+	0.961769i	$0.588301\pi$
$252$	−29.4841	−	28.0133i	−1.85732	−	1.76467i
$253$	−13.9841	+	13.9841i	−0.879171	+	0.879171i
$254$	−6.49371	+	2.78759i	−0.407452	+	0.174909i
$255$		−	14.6746i		−	0.918959i
$256$	−15.9164	+	1.63390i	−0.994772	+	0.102119i
$257$	−8.31752	−	8.31752i	−0.518832	−	0.518832i	0.398386	−	0.917218i	$-0.369571\pi$
$257$	−8.31752	−	8.31752i	−0.518832	−	0.518832i	−0.917218	+	0.398386i	$0.869571\pi$
$258$	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	$-0.486817\pi$
$263$	1.34290			0.0828068			0.0414034	+	0.999143i	$0.486817\pi$
$264$	31.3148	+	11.5850i	1.92729	+	0.713005i
$265$	−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	$0.757290\pi$
$272$	14.9673	−	16.5824i	0.907525	−	1.00546i
$273$	6.05503	−	6.05503i	0.366467	−	0.366467i
$274$	−1.84301	−	4.29330i	−0.111340	−	0.259368i
$275$		−	4.49242i		−	0.270903i
$276$	0.591603	+	23.1278i	0.0356103	+	1.39213i
$277$	−1.79552	+	1.79552i	−0.107882	+	0.107882i	−0.758987	−	0.651105i	$-0.774306\pi$
$277$	−1.79552	+	1.79552i	−0.107882	+	0.107882i	0.651105	+	0.758987i	$0.274306\pi$
$278$	2.30812	+	5.37677i	0.138432	+	0.322477i
$279$	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	0.929960	−	0.367662i	$-0.119842\pi$
$281$	9.42583	+	9.42583i	0.562298	+	0.562298i	−0.367662	+	0.929960i	$0.619842\pi$
$282$	−30.3144	+	13.0132i	−1.80520	+	0.774927i
$283$	−15.9179	−	15.9179i	−0.946224	−	0.946224i	0.0524023	−	0.998626i	$-0.483312\pi$
$283$	−15.9179	−	15.9179i	−0.946224	−	0.946224i	−0.998626	+	0.0524023i	$0.983312\pi$
$284$	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
$288$	19.8261	−	9.73983i	1.16826	−	0.573925i
$289$			14.1873i			0.834545i
$290$	−5.04994	−	11.7639i	−0.296543	−	0.690799i
$291$	−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	$0.512433\pi$
$294$	−29.4926	−	68.7031i	−1.72004	−	4.00685i
$295$	4.74343			0.276173
$296$	−16.3927	−	5.22305i	−0.952805	−	0.303583i
$297$	−10.6818			−0.619823
$298$	8.40494	+	19.5794i	0.486885	+	1.13420i
$299$	−2.75476			−0.159312
$300$	−3.80996	−	3.61990i	−0.219968	−	0.208995i
$301$	15.0219	+	15.0219i	0.865846	+	0.865846i
$302$	−6.91729	−	16.1139i	−0.398045	−	0.927250i
$303$		−	9.46845i		−	0.543948i
$304$	8.22411	+	7.42308i	0.471685	+	0.425743i
$305$	7.73545			0.442931
$306$	−11.4366	+	28.6408i	−0.653785	+	1.63728i
$307$	0.208746			0.0119137			0.00595687	−	0.999982i	$-0.498104\pi$
$307$	0.208746			0.0119137			0.00595687	+	0.999982i	$0.498104\pi$
$308$	33.9204	+	32.2284i	1.93280	+	1.83638i
$309$	15.7472	+	15.7472i	0.895825	+	0.895825i
$310$	7.78793	−	3.34316i	0.442324	−	0.189879i
$311$	−11.0726	−	11.0726i	−0.627869	−	0.627869i	0.319663	−	0.947531i	$-0.396430\pi$
$311$	−11.0726	−	11.0726i	−0.627869	−	0.627869i	−0.947531	+	0.319663i	$0.896430\pi$
$312$	1.94331	+	4.22546i	0.110018	+	0.239220i
$313$	14.2920	+	14.2920i	0.807832	+	0.807832i	0.984305	−	0.176473i	$-0.0564690\pi$
$313$	14.2920	+	14.2920i	0.807832	+	0.807832i	−0.176473	+	0.984305i	$0.556469\pi$
$314$	3.81667	+	8.89096i	0.215387	+	0.501746i
$315$	14.3790	−	14.3790i	0.810168	−	0.810168i
$316$	0.0933054	+	3.64762i	0.00524884	+	0.205195i
$317$			7.21584i			0.405282i	0.979253	+	0.202641i	$0.0649524\pi$
$317$			7.21584i			0.405282i	−0.979253	+	0.202641i	$0.935048\pi$
$318$	17.6671	+	41.1557i	0.990723	+	2.30790i
$319$	−28.7560	+	28.7560i	−1.61002	+	1.61002i
$320$	−0.613179	−	7.97647i	−0.0342778	−	0.445898i
$321$		−	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
$328$	−7.80709	+	21.1030i	−0.431075	+	1.16522i
$329$	−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	$-0.783374\pi$
$331$	−2.69271	+	2.69271i	−0.148005	+	0.148005i	0.629221	+	0.777226i	$0.283374\pi$
$332$	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	$-0.610640\pi$
$337$		−	34.5195i		−	1.88039i	0.340630	−	0.940197i	$-0.389360\pi$
$338$	16.3851	−	7.03371i	0.891231	−	0.382583i
$339$	−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
$346$	−5.52294	+	2.37086i	−0.296915	+	0.127458i
$347$	−11.3167	−	11.3167i	−0.607513	−	0.607513i	0.334783	−	0.942295i	$-0.391337\pi$
$347$	−11.3167	−	11.3167i	−0.607513	−	0.607513i	−0.942295	+	0.334783i	$0.891337\pi$
$348$	1.21654	+	47.5585i	0.0652132	+	2.54940i
$349$	−21.0345			−1.12595			−0.562975	−	0.826474i	$-0.690343\pi$
$349$	−21.0345			−1.12595			−0.562975	+	0.826474i	$0.690343\pi$
$350$	−2.90511	−	6.76748i	−0.155285	−	0.361737i
$351$	−1.05212	−	1.05212i	−0.0561580	−	0.0561580i
$352$	−22.8092	+	11.2054i	−1.21574	+	0.597247i
$353$	−18.1744	+	18.1744i	−0.967327	+	0.967327i	−0.999483	−	0.0321554i	$-0.989763\pi$
$353$	−18.1744	+	18.1744i	−0.967327	+	0.967327i	0.0321554	+	0.999483i	$0.489763\pi$
$354$	−16.3704	−	6.53688i	−0.870077	−	0.347431i
$355$	−4.33711	+	4.33711i	−0.230190	+	0.230190i
$356$	−0.260706	−	10.1919i	−0.0138174	−	0.540167i
$357$	−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
$362$	0.643286	+	1.49854i	0.0338104	+	0.0787615i
$363$	24.1273			1.26636
$364$	0.166663	+	6.51541i	0.00873551	+	0.341500i
$365$	−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	$0.892988\pi$
$368$	−13.0715	−	11.7984i	−0.681401	−	0.615033i
$369$		−	31.0642i		−	1.61714i
$370$	2.82026	−	8.12688i	0.146618	−	0.422496i
$371$			62.7628i			3.25848i
$372$	−31.4847	+	0.805372i	−1.63240	+	0.0417566i
$373$		−	23.5852i		−	1.22119i	−0.791942	−	0.610597i	$-0.790930\pi$
$373$		−	23.5852i		−	1.22119i	0.791942	−	0.610597i	$-0.209070\pi$
$374$	13.1574	−	32.9502i	0.680352	−	1.70382i
$375$	1.85807	−	1.85807i	0.0959505	−	0.0959505i
$376$	8.71203	−	23.5491i	0.449289	−	1.21445i
$377$	−5.66471			−0.291747
$378$	−16.0913	+	6.90760i	−0.827648	+	0.355289i
$379$			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	−0.179129	+	0.983826i	$0.557328\pi$
$383$	−22.7595	+	22.7595i	−1.16295	+	1.16295i	−0.983826	+	0.179129i	$0.942672\pi$
$384$	−8.87611	+	28.3732i	−0.452957	+	1.44791i
$385$	−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
$388$	11.6138	−	0.297079i	0.589601	−	0.0150819i
$389$	2.98939	+	2.98939i	0.151568	+	0.151568i	0.778818	−	0.627250i	$-0.215820\pi$
$389$	2.98939	+	2.98939i	0.151568	+	0.151568i	−0.627250	+	0.778818i	$0.715820\pi$
$390$	−2.13689	+	0.917313i	−0.108205	+	0.0464499i
$391$	24.5842			1.24328
$392$	53.3705	+	19.7445i	2.69562	+	0.997249i
$393$	−8.13517	−	8.13517i	−0.410365	−	0.410365i
$394$	−12.3905	−	28.8638i	−0.624225	−	1.45414i
$395$	−1.82441			−0.0917959
$396$	24.1661	−	25.4349i	1.21439	−	1.27815i
$397$		−	20.8140i		−	1.04462i	−0.852754	−	0.522312i	$-0.825069\pi$
$397$		−	20.8140i		−	1.04462i	0.852754	−	0.522312i	$-0.174931\pi$
$398$	−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	−0.742174	−	0.670207i	$-0.766205\pi$
$401$	−1.44115	+	1.44115i	−0.0719675	+	0.0719675i	0.670207	+	0.742174i	$0.266205\pi$
$402$	6.12031	+	14.2573i	0.305253	+	0.711090i
$403$		−	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	−0.760571	−	0.649255i	$-0.775081\pi$
$409$	−2.25122	+	2.25122i	−0.111316	+	0.111316i	0.649255	+	0.760571i	$0.275081\pi$
$410$	−10.4482	−	4.17209i	−0.516001	−	0.206045i
$411$	−8.68122			−0.428213
$412$	−16.9445	+	0.433436i	−0.834794	+	0.0213539i
$413$	−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	$0.905878\pi$
$420$	0.699844	+	27.3592i	0.0341489	+	1.33499i
$421$	17.8543	−	17.8543i	0.870165	−	0.870165i	−0.122325	−	0.992490i	$-0.539035\pi$
$421$	17.8543	−	17.8543i	0.870165	−	0.870165i	0.992490	+	0.122325i	$0.0390351\pi$
$422$	25.6148	−	10.9958i	1.24691	−	0.535268i
$423$			34.6649i			1.68547i
$424$	−31.9709	−	11.8277i	−1.55264	−	0.574403i
$425$	−3.94888	+	3.94888i	−0.191549	+	0.191549i
$426$	20.9451	−	8.99120i	1.01479	−	0.435625i
$427$	−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
$430$	−2.27575	−	5.30138i	−0.109746	−	0.255655i
$431$	−6.15948	−	6.15948i	−0.296692	−	0.296692i	0.543025	−	0.839717i	$-0.317279\pi$
$431$	−6.15948	−	6.15948i	−0.296692	−	0.296692i	−0.839717	+	0.543025i	$0.817279\pi$
$432$	−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
$436$	28.4385	−	0.727451i	1.36196	−	0.0348386i
$437$			12.1926i			0.583253i
$438$	18.7800	−	8.06179i	0.897343	−	0.385207i
$439$	−19.6697	−	19.6697i	−0.938785	−	0.938785i	0.0594464	−	0.998232i	$-0.481066\pi$
$439$	−19.6697	−	19.6697i	−0.938785	−	0.938785i	−0.998232	+	0.0594464i	$0.981066\pi$
$440$	−5.30921	−	11.5441i	−0.253107	−	0.550346i
$441$	−78.5629			−3.74109
$442$	4.54143	−	1.94952i	0.216014	−	0.0927293i
$443$	−17.6544			−0.838784			−0.419392	−	0.907805i	$-0.637757\pi$
$443$	−17.6544			−0.838784			−0.419392	+	0.907805i	$0.637757\pi$
$444$	−20.9328	+	24.1607i	−0.993426	+	1.14662i
$445$	5.09759			0.241649
$446$	−8.99942	+	3.86323i	−0.426135	+	0.182929i
$447$	39.5903			1.87256
$448$	−27.1141	+	31.6300i	−1.28102	+	1.49438i
$449$	26.6185	+	26.6185i	1.25621	+	1.25621i	0.952890	+	0.303315i	$0.0980934\pi$
$449$	26.6185	+	26.6185i	1.25621	+	1.25621i	0.303315	+	0.952890i	$0.401907\pi$
$450$	−5.07452	+	2.17837i	−0.239215	+	0.102689i
$451$			35.7383i			1.68285i
$452$	−0.452397	−	17.6857i	−0.0212790	−	0.831867i
$453$	−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	0.657541	−	0.753419i	$-0.271597\pi$
$457$	−2.04963	−	2.04963i	−0.0958775	−	0.0958775i	−0.753419	+	0.657541i	$0.771597\pi$
$458$	−5.73230	−	13.3534i	−0.267853	−	0.623965i
$459$	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	−0.958406	−	0.285407i	$-0.907871\pi$
$461$	−26.7058	−	26.7058i	−1.24381	−	1.24381i	−0.285407	−	0.958406i	$-0.592129\pi$
$462$	79.8887	−	34.2942i	3.71676	−	1.59551i
$463$	−19.3976	+	19.3976i	−0.901484	+	0.901484i	−0.995565	−	0.0940802i	$-0.970009\pi$
$463$	−19.3976	+	19.3976i	−0.901484	+	0.901484i	0.0940802	+	0.995565i	$0.470009\pi$
$464$	−26.8795	−	24.2614i	−1.24785	−	1.12631i
$465$		−	15.7475i		−	0.730272i
$466$	12.0724	−	5.18240i	0.559245	−	0.240070i
$467$	7.84731	−	7.84731i	0.363130	−	0.363130i	−0.501834	−	0.864964i	$-0.667341\pi$
$467$	7.84731	−	7.84731i	0.363130	−	0.363130i	0.864964	+	0.501834i	$0.167341\pi$
$468$	4.88551	−	0.124970i	0.225833	−	0.00577676i
$469$			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
$476$	−1.48735	−	58.1453i	−0.0681724	−	2.66509i
$477$	47.0620			2.15482
$478$	10.5875	+	4.22769i	0.484259	+	0.193370i
$479$	22.1306	−	22.1306i	1.01117	−	1.01117i	0.0112359	−	0.999937i	$-0.496423\pi$
$479$	22.1306	−	22.1306i	1.01117	−	1.01117i	0.999937	−	0.0112359i	$-0.00357659\pi$
$480$	−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
$486$	−11.9928	−	27.9372i	−0.544003	−	1.26726i
$487$	−3.02235	+	3.02235i	−0.136956	+	0.136956i	−0.772261	−	0.635305i	$-0.780874\pi$
$487$	−3.02235	+	3.02235i	−0.136956	+	0.136956i	0.635305	+	0.772261i	$0.280874\pi$
$488$	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
$494$	0.966873	+	2.25234i	0.0435017	+	0.101337i
$495$	12.4043	+	12.4043i	0.557532	+	0.557532i
$496$	16.0616	−	17.7948i	0.721186	−	0.799009i
$497$	31.9414			1.43277
$498$	8.48020	−	3.64034i	0.380007	−	0.163127i
$499$	−19.3164	−	19.3164i	−0.864719	−	0.864719i	0.127163	−	0.991882i	$-0.459413\pi$
$499$	−19.3164	−	19.3164i	−0.864719	−	0.864719i	−0.991882	+	0.127163i	$0.959413\pi$
$500$	0.0511429	+	1.99935i	0.00228718	+	0.0894135i
$501$	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	$-0.855751\pi$
$503$	−10.3447	+	10.3447i	−0.461245	+	0.461245i	0.437818	+	0.899063i	$0.355751\pi$
$504$	19.9564	−	53.9431i	0.888927	−	2.40282i
$505$	−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	$-0.785976\pi$
$509$		−	28.1041i		−	1.24569i	0.782344	−	0.622846i	$-0.214024\pi$
$510$	19.0702	−	8.18635i	0.844442	−	0.362498i
$511$	28.6397			1.26694
$512$	−11.0024	−	19.7724i	−0.486241	−	0.873825i
$513$	−4.65672	+	4.65672i	−0.205599	+	0.205599i
$514$	6.16891	−	15.4489i	0.272099	−	0.681422i
$515$		−	8.47500i		−	0.373453i
$516$	0.548231	+	21.4322i	0.0241345	+	0.943499i
$517$		−	39.8808i		−	1.75396i
$518$	−40.3110	+	19.5407i	−1.77117	+	0.858571i
$519$			11.1676i			0.490203i
$520$	0.614118	−	1.65999i	0.0269308	−	0.0727955i
$521$		−	5.82277i		−	0.255100i	−0.991832	−	0.127550i	$-0.959289\pi$
$521$		−	5.82277i		−	0.255100i	0.991832	−	0.127550i	$-0.0407113\pi$
$522$	46.4257	+	18.5383i	2.03200	+	0.811398i
$523$	3.19692	−	3.19692i	0.139791	−	0.139791i	−0.633748	−	0.773539i	$-0.718484\pi$
$523$	3.19692	−	3.19692i	0.139791	−	0.139791i	0.773539	+	0.633748i	$0.218484\pi$
$524$	8.75370	−	0.223918i	0.382407	−	0.00978190i
$525$	−13.6841			−0.597223
$526$	0.749149	+	1.74515i	0.0326645	+	0.0760921i
$527$			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
$532$	28.8374	−	0.737655i	1.25026	−	0.0319814i
$533$	−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
$536$	−11.0755	−	4.09739i	−0.478387	−	0.176980i
$537$	34.5429	+	34.5429i	1.49064	+	1.49064i
$538$	17.9644	+	41.8482i	0.774501	+	1.80421i
$539$	90.3839			3.89311
$540$	4.75393	−	0.121605i	0.204577	−	0.00523303i
$541$	7.19827	+	7.19827i	0.309478	+	0.309478i	0.844707	−	0.535229i	$-0.179775\pi$
$541$	7.19827	+	7.19827i	0.309478	+	0.309478i	−0.535229	+	0.844707i	$0.679775\pi$
$542$	−29.5536	+	12.6866i	−1.26944	+	0.544938i
$543$	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	$-0.134629\pi$
$547$	11.7275	+	11.7275i	0.501432	+	0.501432i	−0.410451	+	0.911883i	$0.634629\pi$
$548$	4.55116	−	4.79011i	0.194416	−	0.204623i
$549$	−21.3588	+	21.3588i	−0.911573	+	0.911573i
$550$	5.83807	−	2.50614i	0.248936	−	0.106862i
$551$			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	0.0481832	−	0.998839i	$-0.484657\pi$
$557$	24.7106	−	24.7106i	1.04702	−	1.04702i	0.998839	−	0.0481832i	$-0.0153431\pi$
$558$	−12.2727	+	30.7347i	−0.519545	+	1.30111i
$559$	−2.55280			−0.107972
$560$	−15.4631	−	13.9570i	−0.653437	−	0.589792i
$561$	−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	$-0.634254\pi$
$563$	11.9347	−	11.9347i	0.502987	−	0.502987i	0.912365	+	0.409378i	$0.134254\pi$
$564$	−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
$568$	−6.01938	+	16.2707i	−0.252568	+	0.682703i
$569$	−6.08324	+	6.08324i	−0.255023	+	0.255023i	−0.823026	−	0.568003i	$-0.807716\pi$
$569$	−6.08324	+	6.08324i	−0.255023	+	0.255023i	0.568003	+	0.823026i	$0.307716\pi$
$570$	4.06005	+	9.45793i	0.170057	+	0.396149i
$571$		−	19.4564i		−	0.814224i	−0.913378	−	0.407112i	$-0.866536\pi$
$571$		−	19.4564i		−	0.814224i	0.913378	−	0.407112i	$-0.133464\pi$
$572$	−5.62062	+	0.143774i	−0.235010	+	0.00601151i
$573$	19.2976	−	19.2976i	0.806168	−	0.806168i
$574$	23.1108	+	53.8369i	0.964628	+	2.24711i
$575$	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	0.293256	−	0.956034i	$-0.405261\pi$
$577$	−15.9205	−	15.9205i	−0.662778	−	0.662778i	−0.956034	+	0.293256i	$0.905261\pi$
$578$	−18.4369	+	7.91449i	−0.766872	+	0.329199i
$579$	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
$584$	−5.39716	+	14.5888i	−0.223336	+	0.603690i
$585$			2.44356i			0.101029i
$586$	−0.745760	−	1.73725i	−0.0308071	−	0.0717653i
$587$	14.3495	+	14.3495i	0.592269	+	0.592269i	0.938244	−	0.345975i	$-0.112452\pi$
$587$	14.3495	+	14.3495i	0.592269	+	0.592269i	−0.345975	+	0.938244i	$0.612452\pi$
$588$	72.8295	−	76.6533i	3.00344	−	3.16113i
$589$	−16.5983			−0.683920
$590$	2.64616	+	6.16426i	0.108941	+	0.253779i
$591$	−58.3637			−2.40076
$592$	−2.35726	−	24.2166i	−0.0968827	−	0.995296i
$593$	33.0042			1.35532			0.677660	−	0.735376i	$-0.262994\pi$
$593$	33.0042			1.35532			0.677660	+	0.735376i	$0.262994\pi$
$594$	−5.95895	−	13.8814i	−0.244499	−	0.569562i
$595$	29.0822			1.19225
$596$	−20.7553	+	21.8451i	−0.850172	+	0.894808i
$597$	2.09776	+	2.09776i	0.0858557	+	0.0858557i
$598$	−1.53676	−	3.57990i	−0.0628430	−	0.146393i
$599$			3.17263i			0.129630i	0.997897	+	0.0648150i	$0.0206457\pi$
$599$			3.17263i			0.129630i	−0.997897	+	0.0648150i	$0.979354\pi$
$600$	2.57878	−	6.97057i	0.105278	−	0.284572i
$601$	−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
$606$	12.3046	−	5.28206i	0.499840	−	0.214569i
$607$	18.2312	+	18.2312i	0.739980	+	0.739980i	0.972574	−	0.232594i	$-0.0747212\pi$
$607$	18.2312	+	18.2312i	0.739980	+	0.739980i	−0.232594	+	0.972574i	$0.574721\pi$
$608$	−5.05867	+	14.8286i	−0.205156	+	0.601377i
$609$	87.5918	+	87.5918i	3.54940	+	3.54940i
$610$	4.31529	+	10.0525i	0.174721	+	0.407014i
$611$	3.92811	−	3.92811i	0.158914	−	0.158914i
$612$	−43.5997	+	1.11527i	−1.76241	+	0.0450822i
$613$			28.3812i			1.14631i	0.819449	+	0.573153i	$0.194280\pi$
$613$			28.3812i			1.14631i	−0.819449	+	0.573153i	$0.805720\pi$
$614$	0.116451	+	0.271272i	0.00469956	+	0.0109477i
$615$	−14.7814	+	14.7814i	−0.596044	+	0.596044i
$616$	−22.9591	+	62.0597i	−0.925049	+	2.50046i
$617$		−	21.2344i		−	0.854866i	−0.904047	−	0.427433i	$-0.859418\pi$
$617$		−	21.2344i		−	0.854866i	0.904047	−	0.427433i	$-0.140582\pi$
$618$	−11.6793	+	29.2487i	−0.469811	+	1.17656i
$619$	15.0854			0.606332			0.303166	−	0.952938i	$-0.401956\pi$
$619$	15.0854			0.606332			0.303166	+	0.952938i	$0.401956\pi$
$620$	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
$624$	−4.40705	+	4.88261i	−0.176423	+	0.195461i
$625$	−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	0.995293	+	0.0969133i	$0.0308970\pi$
$631$	27.4359	+	27.4359i	1.09221	+	1.09221i	0.0969133	+	0.995293i	$0.469103\pi$
$632$	−4.68816	+	2.15611i	−0.186485	+	0.0857654i
$633$		−	51.7942i		−	2.05863i
$634$	−9.37724	+	4.02542i	−0.372418	+	0.159870i
$635$	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	$0.619650\pi$
$642$	33.7930	−	14.5065i	1.33370	−	0.572526i
$643$	−11.4860	−	11.4860i	−0.452964	−	0.452964i	0.443373	−	0.896337i	$-0.353782\pi$
$643$	−11.4860	−	11.4860i	−0.452964	−	0.452964i	−0.896337	+	0.443373i	$0.853782\pi$
$644$	−45.8347	+	1.17244i	−1.80614	+	0.0462007i
$645$	−10.7196			−0.422084
$646$	−8.62864	−	20.1005i	−0.339489	−	0.790843i
$647$	−10.0235	−	10.0235i	−0.394065	−	0.394065i	0.482068	−	0.876134i	$-0.339886\pi$
$647$	−10.0235	−	10.0235i	−0.394065	−	0.394065i	−0.876134	+	0.482068i	$0.839886\pi$
$648$	14.5013	+	5.36479i	0.569665	+	0.210749i
$649$	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
$652$	6.31525	−	0.161543i	0.247324	−	0.00632651i
$653$	−29.0696	+	29.0696i	−1.13758	+	1.13758i	−0.148698	+	0.988883i	$0.547508\pi$
$653$	−29.0696	+	29.0696i	−1.13758	+	1.13758i	−0.988883	+	0.148698i	$0.952492\pi$
$654$	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
$658$	−25.7897	−	60.0773i	−1.00539	−	2.34206i
$659$	−16.9936			−0.661976			−0.330988	−	0.943635i	$-0.607382\pi$
$659$	−16.9936			−0.661976			−0.330988	+	0.943635i	$0.607382\pi$
$660$	−23.6019	+	0.603731i	−0.918702	+	0.0235002i
$661$	15.3725	−	15.3725i	0.597919	−	0.597919i	−0.341839	−	0.939758i	$-0.611050\pi$
$661$	15.3725	−	15.3725i	0.597919	−	0.597919i	0.939758	+	0.341839i	$0.111050\pi$
$662$	−5.00143	−	1.99713i	−0.194386	−	0.0776205i
$663$		−	9.18294i		−	0.356636i
$664$	−2.43711	+	6.58765i	−0.0945784	+	0.255650i
$665$			14.4234i			0.559316i
$666$	14.6524	+	30.2268i	0.567770	+	1.17127i
$667$		−	39.8501i		−	1.54300i
$668$	0.272831	+	10.6659i	0.0105562	+	0.412675i
$669$			18.1972i			0.703543i
$670$	2.18963	−	5.48353i	0.0845929	−	0.211847i
$671$	24.5726	−	24.5726i	0.948615	−	0.948615i
$672$	34.1319	+	69.4777i	1.31667	+	2.68016i
$673$	15.2875			0.589288			0.294644	−	0.955607i	$-0.404799\pi$
$673$	15.2875			0.589288			0.294644	+	0.955607i	$0.404799\pi$
$674$	44.8593	−	19.2570i	1.72792	−	0.741751i
$675$			2.37774i			0.0915194i
$676$	18.2811	+	17.3692i	0.703120	+	0.668046i
$677$		−	16.6306i		−	0.639166i	−0.947558	−	0.319583i	$-0.896457\pi$
$677$		−	16.6306i		−	0.639166i	0.947558	−	0.319583i	$-0.103543\pi$
$678$	−30.5283	−	12.1903i	−1.17243	−	0.468164i
$679$	21.3900	−	21.3900i	0.820871	−	0.820871i
$680$	−5.48056	+	14.8142i	−0.210170	+	0.568100i
$681$	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	$-0.672759\pi$
$683$	8.88079	−	8.88079i	0.339814	−	0.339814i	0.856297	+	0.516483i	$0.172759\pi$
$684$	−0.553123	−	21.6234i	−0.0211492	−	0.826792i
$685$	2.33608	+	2.33608i	0.0892571	+	0.0892571i
$686$	88.7838	−	38.1127i	3.38978	−	1.45515i
$687$	−27.0012			−1.03016
$688$	−12.1132	−	10.9334i	−0.461812	−	0.416832i
$689$	−5.33291	−	5.33291i	−0.203168	−	0.203168i
$690$	−6.45312	−	15.0326i	−0.245666	−	0.572281i
$691$	17.2128			0.654804			0.327402	−	0.944885i	$-0.393827\pi$
$691$	17.2128			0.654804			0.327402	+	0.944885i	$0.393827\pi$
$692$	−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
$698$	−11.7343	−	27.3351i	−0.444148	−	1.03465i
$699$		−	24.4109i		−	0.923306i
$700$	7.17394	−	7.55059i	0.271149	−	0.285385i
$701$	18.9413	+	18.9413i	0.715405	+	0.715405i	0.967661	−	0.252256i	$-0.0811725\pi$
$701$	18.9413	+	18.9413i	0.715405	+	0.715405i	−0.252256	+	0.967661i	$0.581172\pi$
$702$	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
$708$	−0.637464	−	24.9206i	−0.0239574	−	0.936573i
$709$	24.3086	+	24.3086i	0.912928	+	0.912928i	0.996502	−	0.0835733i	$-0.0266333\pi$
$709$	24.3086	+	24.3086i	0.912928	+	0.912928i	−0.0835733	+	0.996502i	$0.526633\pi$
$710$	−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
$716$	−37.1693	+	0.950783i	−1.38908	+	0.0355324i
$717$	14.9784	−	14.9784i	0.559379	−	0.559379i
$718$	27.2646	−	11.7040i	1.01750	−	0.436789i
$719$		−	20.5144i		−	0.765056i	−0.923944	−	0.382528i	$-0.875054\pi$
$719$		−	20.5144i		−	0.765056i	0.923944	−	0.382528i	$-0.124946\pi$
$720$	−10.4655	+	11.5949i	−0.390027	+	0.432115i
$721$	−31.2078	+	31.2078i	−1.16224	+	1.16224i
$722$	−14.7223	+	6.31991i	−0.547906	+	0.235203i
$723$	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
$726$	13.4596	+	31.3543i	0.499534	+	1.16367i
$727$	5.05004	+	5.05004i	0.187296	+	0.187296i	0.794526	−	0.607230i	$-0.207719\pi$
$727$	5.05004	+	5.05004i	0.187296	+	0.187296i	−0.607230	+	0.794526i	$0.707719\pi$
$728$	−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
$732$	−1.03956	−	40.6398i	−0.0384232	−	1.50209i
$733$			32.4328i			1.19793i	0.800775	+	0.598966i	$0.204421\pi$
$733$			32.4328i			1.19793i	−0.800775	+	0.598966i	$0.795579\pi$
$734$	−16.4256	+	7.05110i	−0.606280	+	0.260261i
$735$	37.3829	+	37.3829i	1.37889	+	1.37889i
$736$	8.04034	−	23.5688i	0.296371	−	0.868756i
$737$	−18.7565			−0.690905
$738$	40.3690	−	17.3294i	1.48600	−	0.637905i
$739$	−21.7908			−0.801588			−0.400794	−	0.916168i	$-0.631266\pi$
$739$	−21.7908			−0.801588			−0.400794	+	0.916168i	$0.631266\pi$
$740$	12.1345	−	0.868617i	0.446072	−	0.0319310i
$741$	4.55431			0.167307
$742$	−81.5625	+	35.0128i	−2.99425	+	1.28536i
$743$	8.31087			0.304896			0.152448	−	0.988311i	$-0.451284\pi$
$743$	8.31087			0.304896			0.152448	+	0.988311i	$0.451284\pi$
$744$	−18.6106	−	40.4662i	−0.682298	−	1.48356i
$745$	−10.6536	−	10.6536i	−0.390317	−	0.390317i
$746$	30.6498	−	13.1572i	1.12217	−	0.481719i
$747$		−	9.69720i		−	0.354802i
$748$	50.1600	−	1.28308i	1.83403	−	0.0469141i
$749$	51.5346			1.88304
$750$	3.45118	+	1.37809i	0.126019	+	0.0503208i
$751$	−44.4891			−1.62343			−0.811715	−	0.584054i	$-0.801466\pi$
$751$	−44.4891			−1.62343			−0.811715	+	0.584054i	$0.801466\pi$
$752$	35.4630	−	1.81546i	1.29320	−	0.0662030i
$753$	28.6381	+	28.6381i	1.04363	+	1.04363i
$754$	−3.16011	−	7.36149i	−0.115084	−	0.268090i
$755$	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	0.677172	−	0.735825i	$-0.263205\pi$
$757$	−1.61375	−	1.61375i	−0.0586529	−	0.0586529i	−0.735825	+	0.677172i	$0.763205\pi$
$758$	−39.9055	+	17.1304i	−1.44943	+	0.622206i
$759$	−36.7461	+	36.7461i	−1.33380	+	1.33380i
$760$	−7.34718	−	2.71810i	−0.266510	−	0.0985959i
$761$			3.44597i			0.124916i	0.998048	+	0.0624581i	$0.0198940\pi$
$761$			3.44597i			0.124916i	−0.998048	+	0.0624581i	$0.980106\pi$
$762$	−17.0636	+	7.32498i	−0.618149	+	0.265356i
$763$	52.3772	−	52.3772i	1.89618	−	1.89618i
$764$	0.531160	+	20.7648i	0.0192167	+	0.751245i
$765$		−	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	−0.903351	−	0.428902i	$-0.858901\pi$
$769$	−13.1569	+	13.1569i	−0.474449	+	0.474449i	0.428902	+	0.903351i	$0.358901\pi$
$770$	−30.7262	−	12.2693i	−1.10729	−	0.442154i
$771$	−21.8560	−	21.8560i	−0.787126	−	0.787126i
$772$	−11.9303	+	0.305174i	−0.429380	+	0.0109835i
$773$	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
$782$	13.7145	+	31.9481i	0.490430	+	1.14246i
$783$	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
$790$	−1.01776	−	2.37088i	−0.0362103	−	0.0843522i
$791$	−32.5730	−	32.5730i	−1.15816	−	1.15816i
$792$	46.5348	+	17.2157i	1.65354	+	0.611732i
$793$	4.84062			0.171895
$794$	27.0485	−	11.6113i	0.959917	−	0.412069i
$795$	−22.3937	−	22.3937i	−0.794224	−	0.794224i
$796$	−2.25726	+	0.0577402i	−0.0800064	+	0.00204655i
$797$	−22.7310	+	22.7310i	−0.805174	+	0.805174i	−0.983899	−	0.178725i	$-0.942803\pi$
$797$	−22.7310	+	22.7310i	−0.805174	+	0.805174i	0.178725	+	0.983899i	$0.442803\pi$
$798$	19.8768	−	49.7777i	0.703630	−	1.76211i
$799$	−35.0556	+	35.0556i	−1.24018	+	1.24018i
$800$	2.49428	+	5.07726i	0.0881860	+	0.179508i
$801$	−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
$806$	4.87346	−	2.09205i	0.171660	−	0.0736895i
$807$	84.6188			2.97872
$808$	−3.53620	+	9.55855i	−0.124403	+	0.336269i
$809$	7.94827	−	7.94827i	0.279446	−	0.279446i	−0.553442	−	0.832888i	$-0.686686\pi$
$809$	7.94827	−	7.94827i	0.279446	−	0.279446i	0.832888	+	0.553442i	$0.186686\pi$
$810$	−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	$0.811177\pi$
$812$	−94.2515	+	2.41094i	−3.30758	+	0.0846073i
$813$			59.7586i			2.09582i
$814$	−16.8571	−	34.7749i	−0.590842	−	1.21886i
$815$			3.15866i			0.110643i
$816$	39.3297	−	43.5738i	1.37682	−	1.52539i
$817$			11.2987i			0.395293i
$818$	−4.18140	−	1.66968i	−0.146199	−	0.0583789i
$819$	8.99799	−	8.99799i	0.314415	−	0.314415i
$820$	−0.406854	−	15.9053i	−0.0142080	−	0.555436i
$821$	25.7542			0.898829			0.449414	−	0.893323i	$-0.351633\pi$
$821$	25.7542			0.898829			0.449414	+	0.893323i	$0.351633\pi$
$822$	−4.84289	−	11.2816i	−0.168915	−	0.393489i
$823$			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	$-0.904566\pi$
$827$	−18.9814	+	18.9814i	−0.660048	+	0.660048i	0.295343	+	0.955391i	$0.404566\pi$
$828$	0.879143	+	34.3687i	0.0305523	+	1.19439i
$829$	−30.2084	+	30.2084i	−1.04918	+	1.04918i	−0.0504530	+	0.998726i	$0.516067\pi$
$829$	−30.2084	+	30.2084i	−1.04918	+	1.04918i	−0.998726	+	0.0504530i	$0.983933\pi$
$830$	−3.26159	−	1.30239i	−0.113211	−	0.0452065i
$831$	−4.71810	+	4.71810i	−0.163669	+	0.163669i
$832$	−0.383710	−	4.99144i	−0.0133027	−	0.173047i
$833$	−79.4482	−	79.4482i	−2.75272	−	2.75272i
$834$	6.06506	+	14.1286i	0.210016	+	0.489234i
$835$	−5.33468			−0.184614
$836$	0.636349	+	24.8770i	0.0220086	+	0.860390i
$837$	10.0759	+	10.0759i	0.348274	+	0.348274i
$838$	−15.5031	+	6.65509i	−0.535545	+	0.229896i
$839$	−38.9852			−1.34592			−0.672960	−	0.739679i	$-0.734977\pi$
$839$	−38.9852			−1.34592			−0.672960	+	0.739679i	$0.734977\pi$
$840$	−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
$846$	−45.0483	+	19.3381i	−1.54879	+	0.664858i
$847$			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	−0.904951	−	0.425515i	$-0.860093\pi$
$853$	−14.0025	+	14.0025i	−0.479437	+	0.479437i	0.425515	+	0.904951i	$0.360093\pi$
$854$	21.1263	−	52.9070i	0.722928	−	1.81044i
$855$	10.8153			0.369874
$856$	−9.71174	+	26.2513i	−0.331940	+	0.897253i
$857$	30.7183	+	30.7183i	1.04932	+	1.04932i	0.998719	+	0.0505976i	$0.0161126\pi$
$857$	30.7183	+	30.7183i	1.04932	+	1.04932i	0.0505976	+	0.998719i	$0.483887\pi$
$858$	−3.87413	+	9.70204i	−0.132261	+	0.331222i
$859$	18.6805	−	18.6805i	0.637371	−	0.637371i	−0.312535	−	0.949906i	$-0.601178\pi$
$859$	18.6805	−	18.6805i	0.637371	−	0.637371i	0.949906	+	0.312535i	$0.101178\pi$
$860$	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	$0.919656\pi$
$864$	12.0724	−	5.93075i	0.410712	−	0.201768i
$865$	3.00515	−	3.00515i	0.102178	−	0.102178i
$866$	−11.1116	−	25.8847i	−0.377589	−	0.879596i
$867$			37.2800i			1.26610i
$868$	−1.59609	−	62.3964i	−0.0541748	−	2.11787i
$869$	−5.79545	+	5.79545i	−0.196597	+	0.196597i
$870$	−13.2698	−	30.9121i	−0.449888	−	1.04802i
$871$	−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
$874$	−15.8448	+	6.80176i	−0.535957	+	0.230073i
$875$	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
$880$	12.0402	−	13.3395i	0.405877	−	0.449675i
$881$		−	11.9945i		−	0.404105i	−0.979375	−	0.202053i	$-0.935239\pi$
$881$		−	11.9945i		−	0.404105i	0.979375	−	0.202053i	$-0.0647612\pi$
$882$	−43.8270	−	102.095i	−1.47573	−	3.43773i
$883$	−12.5586	−	12.5586i	−0.422631	−	0.422631i	0.463478	−	0.886109i	$-0.346601\pi$
$883$	−12.5586	−	12.5586i	−0.422631	−	0.422631i	−0.886109	+	0.463478i	$0.846601\pi$
$884$	5.06695	+	4.81419i	0.170420	+	0.161919i
$885$	12.4644			0.418985
$886$	−9.84863	−	22.9425i	−0.330871	−	0.770767i
$887$	16.0527			0.538997			0.269498	−	0.963001i	$-0.413142\pi$
$887$	16.0527			0.538997			0.269498	+	0.963001i	$0.413142\pi$
$888$	−43.0752	−	13.7247i	−1.44551	−	0.460570i
$889$	−26.0221			−0.872754
$890$	2.84374	+	6.62451i	0.0953223	+	0.222054i
$891$	24.5582			0.822732
$892$	−10.0408	−	9.53993i	−0.336191	−	0.319421i
$893$	−17.3859	−	17.3859i	−0.581798	−	0.581798i
$894$	22.0858	+	51.4490i	0.738659	+	1.72071i
$895$		−	18.5907i		−	0.621419i
$896$	−56.2301	−	17.5907i	−1.87852	−	0.587664i
$897$	−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
$902$	−46.4432	+	19.9369i	−1.54639	+	0.663827i
$903$	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
$906$	−18.1767	−	42.3427i	−0.603879	−	1.40674i
$907$	12.0897	−	12.0897i	0.401431	−	0.401431i	−0.477306	−	0.878737i	$-0.658387\pi$
$907$	12.0897	−	12.0897i	0.401431	−	0.401431i	0.878737	+	0.477306i	$0.158387\pi$
$908$	0.0274169	+	1.07182i	0.000909863	+	0.0355696i
$909$		−	14.0705i		−	0.466687i
$910$	−1.81793	−	4.23489i	−0.0602639	−	0.140385i
$911$	−15.0273	+	15.0273i	−0.497876	+	0.497876i	−0.910776	−	0.412900i	$-0.864516\pi$
$911$	−15.0273	+	15.0273i	−0.497876	+	0.497876i	0.412900	+	0.910776i	$0.364516\pi$
$912$	21.6106	+	19.5057i	0.715598	+	0.645899i
$913$			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	0.972694	+	0.232089i	$0.0745562\pi$
$919$	36.5230	+	36.5230i	1.20478	+	1.20478i	0.232089	+	0.972694i	$0.425444\pi$
$920$	11.6777	+	4.32020i	0.385003	+	0.142433i
$921$	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	$-0.721595\pi$
$929$		−	46.7744i		−	1.53462i	0.641276	−	0.767310i	$-0.278405\pi$
$930$	20.4644	−	8.78487i	0.671055	−	0.288067i
$931$	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	$0.553710\pi$
$938$	−28.2552	+	12.1292i	−0.922564	+	0.396034i
$939$	37.5553	+	37.5553i	1.22557	+	1.22557i
$940$	0.454013	+	17.7489i	0.0148083	+	0.578905i
$941$	−28.0935			−0.915820			−0.457910	−	0.888998i	$-0.651402\pi$
$941$	−28.0935			−0.915820			−0.457910	+	0.888998i	$0.651402\pi$
$942$	10.0291	+	23.3629i	0.326766	+	0.761204i
$943$	−24.7632	−	24.7632i	−0.806399	−	0.806399i
$944$	14.0848	+	12.7130i	0.458422	+	0.413772i
$945$	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	$-0.650335\pi$
$947$	13.4049	−	13.4049i	0.435600	−	0.435600i	0.890528	+	0.454928i	$0.150335\pi$
$948$	0.245180	+	9.58490i	0.00796307	+	0.311303i
$949$	−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	$-0.746431\pi$
$953$		−	44.1445i		−	1.42998i	0.699135	−	0.714990i	$-0.253569\pi$
$954$	26.2540	+	61.1588i	0.850003	+	1.98009i
$955$	−10.3858			−0.336077
$956$	0.412276	+	16.1172i	0.0133340	+	0.521269i
$957$	−75.5624	+	75.5624i	−2.44259	+	2.44259i
$958$	41.1053	+	16.4138i	1.32805	+	0.530305i
$959$		−	17.2045i		−	0.555561i
$960$	−1.61126	−	20.9599i	−0.0520032	−	0.676477i
$961$			4.91426i			0.158525i
$962$	1.76484	−	5.08556i	0.0569006	−	0.163965i
$963$		−	38.6427i		−	1.24524i
$964$	−16.5505	+	0.423359i	−0.533057	+	0.0136355i
$965$		−	5.96709i		−	0.192087i
$966$	−31.5925	+	79.1176i	−1.01647	+	2.54557i
$967$	36.1061	−	36.1061i	1.16109	−	1.16109i	0.176858	−	0.984236i	$-0.443407\pi$
$967$	36.1061	−	36.1061i	1.16109	−	1.16109i	0.984236	−	0.176858i	$-0.0565933\pi$
$968$	−24.3569	−	9.01089i	−0.782860	−	0.289621i
$969$	−40.6440			−1.30567
$970$	−7.54875	+	3.24049i	−0.242376	+	0.104046i
$971$			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
$976$	22.9691	+	20.7319i	0.735224	+	0.663613i
$977$	−3.55871	+	3.55871i	−0.113853	+	0.113853i	−0.761738	−	0.647885i	$-0.775654\pi$
$977$	−3.55871	+	3.55871i	−0.113853	+	0.113853i	0.647885	+	0.761738i	$0.275654\pi$
$978$	4.35292	−	10.9011i	0.139191	−	0.348578i
$979$	16.1931	−	16.1931i	0.517535	−	0.517535i
$980$	−40.2252	+	1.02895i	−1.28495	+	0.0328687i
$981$	−39.2745	−	39.2745i	−1.25394	−	1.25394i
$982$	31.0416	−	13.3254i	0.990578	−	0.425231i
$983$	5.73891			0.183043			0.0915215	−	0.995803i	$-0.470827\pi$
$983$	5.73891			0.183043			0.0915215	+	0.995803i	$0.470827\pi$
$984$	−20.5148	+	55.4526i	−0.653988	+	1.76776i
$985$	15.7054	+	15.7054i	0.500417	+	0.500417i
$986$	28.2017	+	65.6960i	0.898124	+	2.09219i
$987$	−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	$-0.300279\pi$
$991$	−7.00298	−	7.00298i	−0.222457	−	0.222457i	−0.809532	+	0.587075i	$0.800279\pi$
$992$	32.0850	+	10.9456i	1.01870	+	0.347524i
$993$	−7.07568	+	7.07568i	−0.224540	+	0.224540i
$994$	17.8188	+	41.5090i	0.565178	+	1.31659i
$995$		−	1.12900i		−	0.0357917i
$996$	9.46150	+	8.98953i	0.299799	+	0.284844i
$997$	20.8987	+	20.8987i	0.661869	+	0.661869i	0.955820	−	0.293951i	$-0.0949704\pi$
$997$	20.8987	+	20.8987i	0.661869	+	0.661869i	−0.293951	+	0.955820i	$0.594970\pi$
$998$	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.191.52	yes	152
4.3	odd	2	inner	740.2.u.a.191.13	yes	152
37.31	odd	4	inner	740.2.u.a.31.13	✓	152
148.31	even	4	inner	740.2.u.a.31.52	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.u.a.31.13	✓	152	37.31	odd	4	inner
740.2.u.a.31.52	yes	152	148.31	even	4	inner
740.2.u.a.191.13	yes	152	4.3	odd	2	inner
740.2.u.a.191.52	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+(0.557859 + 1.29954i) q^{2} +2.62771 q^{3} +(-1.37759 + 1.44991i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(1.46589 + 3.41481i) q^{6} +5.20761i q^{7} +(-2.65272 - 0.981377i) 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} +(-6.76748 + 2.90511i) q^{14} +(-1.85807 - 1.85807i) q^{15} +(-0.204505 - 3.99477i) q^{16} +(3.94888 + 3.94888i) q^{17} +(2.17837 + 5.07452i) q^{18} +(-1.95846 + 1.95846i) q^{19} +(1.99935 - 0.0511429i) q^{20} +13.6841i q^{21} +(-2.50614 - 5.83807i) q^{22} +(3.11281 - 3.11281i) q^{23} +(-6.97057 - 2.57878i) 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} +(5.07726 - 2.49428i) 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} +(-17.7830 + 7.63379i) 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} +(-1.29954 + 0.557859i) q^{50} +(10.3765 + 10.3765i) q^{51} +(1.25113 - 0.0320037i) q^{52} +12.0521 q^{53} +(1.32644 + 3.08996i) q^{54} +(3.17662 + 3.17662i) q^{55} +(5.11063 - 13.8143i) q^{56} +(-5.14627 + 5.14627i) q^{57} +(11.8892 + 4.74747i) q^{58} +(-3.35411 + 3.35411i) q^{59} +(5.25371 - 0.134389i) 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} +(-6.58541 - 15.3408i) q^{66} +4.17514 q^{67} +(-11.1655 + 0.285610i) q^{68} +(8.17957 - 8.17957i) q^{69} +(6.83955 + 2.73111i) q^{70} -6.13360i q^{71} +(-10.3585 - 3.83215i) q^{72} -5.49958i q^{73} +(3.75234 + 7.74080i) q^{74} +2.62771i q^{75} +(-0.141649 - 5.53755i) q^{76} -23.3948i q^{77} +(0.862369 - 2.15965i) q^{78} +(1.29005 - 1.29005i) q^{79} +(-2.68012 + 2.96933i) q^{80} -5.46659 q^{81} +(10.3381 - 4.43790i) 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} +(11.9171 + 4.40876i) q^{88} +(-3.60454 + 3.60454i) q^{89} +(2.04789 - 5.12857i) q^{90} +(2.30430 - 2.30430i) q^{91} +(0.225140 + 8.80148i) q^{92} +(11.1352 + 11.1352i) q^{93} +(-11.5364 + 4.95231i) q^{94} +2.76968 q^{95} +(13.3416 - 6.55424i) q^{96} +(-4.10744 - 4.10744i) q^{97} +(-11.2237 - 26.1456i) 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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