LMFDB - Embedded newform 740.2.u.a.31.52

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			31.52
Character	$\chi$	$=$	740.31
Dual form			740.2.u.a.191.52

$q$-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 $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

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

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 $

$2$	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	$-0.556757\pi$
$7$		−	5.20761i		−	1.96829i	0.177363	−	0.984146i	$-0.443243\pi$
$8$	−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	−0.765801	−	0.643077i	$-0.777657\pi$
$13$	−0.442487	+	0.442487i	−0.122724	+	0.122724i	0.643077	+	0.765801i	$0.277657\pi$
$14$	−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	−0.0413992	−	0.999143i	$-0.513182\pi$
$17$	3.94888	−	3.94888i	0.957743	−	0.957743i	0.999143	+	0.0413992i	$0.0131816\pi$
$18$	2.17837	−	5.07452i	0.513446	−	1.19608i
$19$	−1.95846	−	1.95846i	−0.449302	−	0.449302i	0.445821	−	0.895122i	$-0.352912\pi$
$19$	−1.95846	−	1.95846i	−0.449302	−	0.449302i	−0.895122	+	0.445821i	$0.852912\pi$
$20$	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	0.952767	−	0.303701i	$-0.0982225\pi$
$23$	3.11281	+	3.11281i	0.649066	+	0.649066i	−0.303701	+	0.952767i	$0.598223\pi$
$24$	−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	0.977445	+	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	−0.215427	−	0.976520i	$-0.569114\pi$
$31$	4.23759	−	4.23759i	0.761093	−	0.761093i	0.976520	+	0.215427i	$0.0691144\pi$
$32$	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	$0.213355\pi$
$41$			7.95524i			1.24240i	−0.783652	+	0.621200i	$0.786645\pi$
$42$	−17.7830	−	7.63379i	−2.74397	−	1.17792i
$43$	2.88460	+	2.88460i	0.439897	+	0.439897i	0.891977	−	0.452080i	$-0.149318\pi$
$43$	2.88460	+	2.88460i	0.439897	+	0.439897i	−0.452080	+	0.891977i	$0.649318\pi$
$44$	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	$-0.775837\pi$
$47$		−	8.87735i		−	1.29489i	0.762110	−	0.647447i	$-0.224163\pi$
$48$	−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	0.454221	−	0.890889i	$-0.349918\pi$
$59$	−3.35411	−	3.35411i	−0.436668	−	0.436668i	−0.890889	+	0.454221i	$0.849918\pi$
$60$	5.25371	+	0.134389i	0.678251	+	0.0173495i
$61$	−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
$66$	−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	$0.118576\pi$
$71$			6.13360i			0.727925i	−0.931414	+	0.363962i	$0.881424\pi$
$72$	−10.3585	+	3.83215i	−1.22076	+	0.451624i
$73$			5.49958i			0.643677i	0.946795	+	0.321839i	$0.104301\pi$
$73$			5.49958i			0.643677i	−0.946795	+	0.321839i	$0.895699\pi$
$74$	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	0.775944	−	0.630802i	$-0.217274\pi$
$79$	1.29005	+	1.29005i	0.145142	+	0.145142i	−0.630802	+	0.775944i	$0.717274\pi$
$80$	−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	$0.0435186\pi$
$83$			2.48336i			0.272584i	−0.990669	+	0.136292i	$0.956481\pi$
$84$	−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	0.489771	−	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
$92$	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	−0.884185	−	0.467137i	$-0.845285\pi$
$97$	−4.10744	+	4.10744i	−0.417048	+	0.417048i	0.467137	+	0.884185i	$0.345285\pi$
$98$	−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	$0.0573740\pi$
$101$			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	−0.347280	−	0.937761i	$-0.612895\pi$
$103$	5.99273	−	5.99273i	0.590481	−	0.590481i	0.937761	+	0.347280i	$0.112895\pi$
$104$	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	$0.158762\pi$
$107$			9.89603i			0.956685i	−0.878173	+	0.478343i	$0.841238\pi$
$108$	−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
$116$	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	$-0.928838\pi$
$127$		−	4.99694i		−	0.443407i	0.975114	−	0.221704i	$-0.0711617\pi$
$128$	−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	−0.829298	−	0.558807i	$-0.811259\pi$
$131$	−3.09591	+	3.09591i	−0.270491	+	0.270491i	0.558807	+	0.829298i	$0.311259\pi$
$132$	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	−0.789147	−	0.614205i	$-0.789477\pi$
$163$	−2.23351	+	2.23351i	−0.174942	+	0.174942i	0.614205	+	0.789147i	$0.289477\pi$
$164$	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	0.837831	−	0.545930i	$-0.183824\pi$
$167$	3.77219	+	3.77219i	0.291901	+	0.291901i	−0.545930	+	0.837831i	$0.683824\pi$
$168$	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	$-0.948348\pi$
$173$		−	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	−0.0173001	−	0.999850i	$-0.505507\pi$
$179$	13.1456	−	13.1456i	0.982550	−	0.982550i	0.999850	+	0.0173001i	$0.00550706\pi$
$180$	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	0.920984	−	0.389600i	$-0.127387\pi$
$191$	7.34387	+	7.34387i	0.531384	+	0.531384i	−0.389600	+	0.920984i	$0.627387\pi$
$192$	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	$0.790558\pi$
$198$	−9.78615	+	22.7969i	−0.695471	+	1.62011i
$199$	0.798323	−	0.798323i	0.0565916	−	0.0565916i	−0.678245	−	0.734836i	$-0.737259\pi$
$199$	0.798323	−	0.798323i	0.0565916	−	0.0565916i	0.734836	+	0.678245i	$0.237259\pi$
$200$	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	$0.237357\pi$
$211$			19.7107i			1.35694i	−0.734626	+	0.678472i	$0.762643\pi$
$212$	−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	$-0.925516\pi$
$223$		−	6.92510i		−	0.463739i	0.972747	−	0.231870i	$-0.0744842\pi$
$224$	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	0.719575	−	0.694415i	$-0.244337\pi$
$227$	0.379069	+	0.379069i	0.0251597	+	0.0251597i	−0.694415	+	0.719575i	$0.744337\pi$
$228$	−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	$0.0984218\pi$
$233$			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
$236$	−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	0.867008	−	0.498295i	$-0.166040\pi$
$239$	5.70017	+	5.70017i	0.368713	+	0.368713i	−0.498295	+	0.867008i	$0.666040\pi$
$240$	−7.04259	−	7.80256i	−0.454597	−	0.503653i
$241$	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	$0.164095\pi$
$242$	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	−0.273861	−	0.961769i	$-0.588301\pi$
$251$	10.8985	−	10.8985i	0.687908	−	0.687908i	0.961769	+	0.273861i	$0.0883010\pi$
$252$	−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	−0.917218	−	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	$-0.486817\pi$
$263$	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	$-0.757290\pi$
$271$		−	22.7417i		−	1.38146i	0.723114	−	0.690729i	$-0.242710\pi$
$272$	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	0.651105	−	0.758987i	$-0.274306\pi$
$277$	−1.79552	−	1.79552i	−0.107882	−	0.107882i	−0.758987	+	0.651105i	$0.774306\pi$
$278$	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	−0.367662	−	0.929960i	$-0.619842\pi$
$281$	9.42583	−	9.42583i	0.562298	−	0.562298i	0.929960	+	0.367662i	$0.119842\pi$
$282$	−30.3144	−	13.0132i	−1.80520	−	0.774927i
$283$	−15.9179	+	15.9179i	−0.946224	+	0.946224i	−0.998626	−	0.0524023i	$-0.983312\pi$
$283$	−15.9179	+	15.9179i	−0.946224	+	0.946224i	0.0524023	+	0.998626i	$0.483312\pi$
$284$	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	−0.947531	−	0.319663i	$-0.896430\pi$
$311$	−11.0726	+	11.0726i	−0.627869	+	0.627869i	0.319663	+	0.947531i	$0.396430\pi$
$312$	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	$0.0564690\pi$
$314$	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	$-0.935048\pi$
$317$		−	7.21584i		−	0.405282i	0.979253	−	0.202641i	$-0.0649524\pi$
$318$	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	0.629221	−	0.777226i	$-0.283374\pi$
$331$	−2.69271	−	2.69271i	−0.148005	−	0.148005i	−0.777226	+	0.629221i	$0.783374\pi$
$332$	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	$0.610640\pi$
$338$	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	−0.942295	−	0.334783i	$-0.891337\pi$
$347$	−11.3167	+	11.3167i	−0.607513	+	0.607513i	0.334783	+	0.942295i	$0.391337\pi$
$348$	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	0.0321554	−	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
$356$	−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	$0.186764\pi$
$359$			20.9802i			1.10729i	−0.832752	+	0.553647i	$0.813236\pi$
$360$	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	$-0.892988\pi$
$367$		−	12.6396i		−	0.659781i	0.944019	−	0.329890i	$-0.107012\pi$
$368$	−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	$0.209070\pi$
$373$			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
$376$	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	$-0.710770\pi$
$379$		−	30.7075i		−	1.57734i	0.614818	−	0.788669i	$-0.289230\pi$
$380$	−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	$-0.942672\pi$
$383$	−22.7595	−	22.7595i	−1.16295	−	1.16295i	−0.179129	−	0.983826i	$-0.557328\pi$
$384$	−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	−0.627250	−	0.778818i	$-0.715820\pi$
$389$	2.98939	−	2.98939i	0.151568	−	0.151568i	0.778818	+	0.627250i	$0.215820\pi$
$390$	−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	$0.174931\pi$
$397$			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	$0.766205\pi$
$402$	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	0.649255	−	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
$412$	−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	$-0.905878\pi$
$419$		−	11.9297i		−	0.582804i	0.956601	−	0.291402i	$-0.0941217\pi$
$420$	0.699844	−	27.3592i	0.0341489	−	1.33499i
$421$	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	$0.539035\pi$
$422$	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	−0.839717	−	0.543025i	$-0.817279\pi$
$431$	−6.15948	+	6.15948i	−0.296692	+	0.296692i	0.543025	+	0.839717i	$0.317279\pi$
$432$	−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	−0.998232	−	0.0594464i	$-0.981066\pi$
$439$	−19.6697	+	19.6697i	−0.938785	+	0.938785i	0.0594464	+	0.998232i	$0.481066\pi$
$440$	−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	0.303315	−	0.952890i	$-0.401907\pi$
$449$	26.6185	−	26.6185i	1.25621	−	1.25621i	0.952890	−	0.303315i	$-0.0980934\pi$
$450$	−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	−0.753419	−	0.657541i	$-0.771597\pi$
$457$	−2.04963	+	2.04963i	−0.0958775	+	0.0958775i	0.657541	+	0.753419i	$0.271597\pi$
$458$	−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	−0.285407	+	0.958406i	$0.592129\pi$
$461$	−26.7058	+	26.7058i	−1.24381	+	1.24381i	−0.958406	+	0.285407i	$0.907871\pi$
$462$	79.8887	+	34.2942i	3.71676	+	1.59551i
$463$	−19.3976	−	19.3976i	−0.901484	−	0.901484i	0.0940802	−	0.995565i	$-0.470009\pi$
$463$	−19.3976	−	19.3976i	−0.901484	−	0.901484i	−0.995565	+	0.0940802i	$0.970009\pi$
$464$	−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	0.864964	−	0.501834i	$-0.167341\pi$
$467$	7.84731	+	7.84731i	0.363130	+	0.363130i	−0.501834	+	0.864964i	$0.667341\pi$
$468$	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	0.999937	+	0.0112359i	$0.00357659\pi$
$479$	22.1306	+	22.1306i	1.01117	+	1.01117i	0.0112359	+	0.999937i	$0.496423\pi$
$480$	−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	0.635305	−	0.772261i	$-0.280874\pi$
$487$	−3.02235	−	3.02235i	−0.136956	−	0.136956i	−0.772261	+	0.635305i	$0.780874\pi$
$488$	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	$0.181196\pi$
$491$			23.8867i			1.07799i	−0.842308	+	0.538996i	$0.818804\pi$
$492$	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	−0.991882	−	0.127163i	$-0.959413\pi$
$499$	−19.3164	+	19.3164i	−0.864719	+	0.864719i	0.127163	+	0.991882i	$0.459413\pi$
$500$	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	0.437818	−	0.899063i	$-0.355751\pi$
$503$	−10.3447	−	10.3447i	−0.461245	−	0.461245i	−0.899063	+	0.437818i	$0.855751\pi$
$504$	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	$0.214024\pi$
$509$			28.1041i			1.24569i	−0.782344	+	0.622846i	$0.785976\pi$
$510$	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	$0.0407113\pi$
$521$			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	0.773539	−	0.633748i	$-0.218484\pi$
$523$	3.19692	+	3.19692i	0.139791	+	0.139791i	−0.633748	+	0.773539i	$0.718484\pi$
$524$	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	−0.535229	−	0.844707i	$-0.679775\pi$
$541$	7.19827	−	7.19827i	0.309478	−	0.309478i	0.844707	+	0.535229i	$0.179775\pi$
$542$	−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	−0.410451	−	0.911883i	$-0.634629\pi$
$547$	11.7275	−	11.7275i	0.501432	−	0.501432i	0.911883	+	0.410451i	$0.134629\pi$
$548$	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	0.998839	+	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
$560$	−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	0.912365	−	0.409378i	$-0.134254\pi$
$563$	11.9347	+	11.9347i	0.502987	+	0.502987i	−0.409378	+	0.912365i	$0.634254\pi$
$564$	−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	0.568003	−	0.823026i	$-0.307716\pi$
$569$	−6.08324	−	6.08324i	−0.255023	−	0.255023i	−0.823026	+	0.568003i	$0.807716\pi$
$570$	4.06005	−	9.45793i	0.170057	−	0.396149i
$571$			19.4564i			0.814224i	0.913378	+	0.407112i	$0.133464\pi$
$571$			19.4564i			0.814224i	−0.913378	+	0.407112i	$0.866536\pi$
$572$	−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	−0.956034	−	0.293256i	$-0.905261\pi$
$577$	−15.9205	+	15.9205i	−0.662778	+	0.662778i	0.293256	+	0.956034i	$0.405261\pi$
$578$	−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	−0.345975	−	0.938244i	$-0.612452\pi$
$587$	14.3495	−	14.3495i	0.592269	−	0.592269i	0.938244	+	0.345975i	$0.112452\pi$
$588$	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	$-0.979354\pi$
$599$		−	3.17263i		−	0.129630i	0.997897	−	0.0648150i	$-0.0206457\pi$
$600$	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	−0.232594	−	0.972574i	$-0.574721\pi$
$607$	18.2312	−	18.2312i	0.739980	−	0.739980i	0.972574	+	0.232594i	$0.0747212\pi$
$608$	−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	$-0.805720\pi$
$613$		−	28.3812i		−	1.14631i	0.819449	−	0.573153i	$-0.194280\pi$
$614$	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	$0.140582\pi$
$617$			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	$-0.401956\pi$
$619$	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	0.0969133	−	0.995293i	$-0.469103\pi$
$631$	27.4359	−	27.4359i	1.09221	−	1.09221i	0.995293	−	0.0969133i	$-0.0308970\pi$
$632$	−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	−0.896337	−	0.443373i	$-0.853782\pi$
$643$	−11.4860	+	11.4860i	−0.452964	+	0.452964i	0.443373	+	0.896337i	$0.353782\pi$
$644$	−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	−0.876134	−	0.482068i	$-0.839886\pi$
$647$	−10.0235	+	10.0235i	−0.394065	+	0.394065i	0.482068	+	0.876134i	$0.339886\pi$
$648$	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	−0.988883	−	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
$658$	−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	0.939758	−	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
$664$	−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	$0.103543\pi$
$677$			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
$680$	−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	0.856297	−	0.516483i	$-0.172759\pi$
$683$	8.88079	+	8.88079i	0.339814	+	0.339814i	−0.516483	+	0.856297i	$0.672759\pi$
$684$	−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	−0.252256	−	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
$708$	−0.637464	+	24.9206i	−0.0239574	+	0.936573i
$709$	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
$716$	−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	$0.124946\pi$
$719$			20.5144i			0.765056i	−0.923944	+	0.382528i	$0.875054\pi$
$720$	−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	−0.607230	−	0.794526i	$-0.707719\pi$
$727$	5.05004	−	5.05004i	0.187296	−	0.187296i	0.794526	+	0.607230i	$0.207719\pi$
$728$	−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	$-0.795579\pi$
$733$		−	32.4328i		−	1.19793i	0.800775	−	0.598966i	$-0.204421\pi$
$734$	−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	−0.735825	−	0.677172i	$-0.763205\pi$
$757$	−1.61375	+	1.61375i	−0.0586529	+	0.0586529i	0.677172	+	0.735825i	$0.263205\pi$
$758$	−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	$-0.980106\pi$
$761$		−	3.44597i		−	0.124916i	0.998048	−	0.0624581i	$-0.0198940\pi$
$762$	−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	0.428902	−	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
$772$	−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	$-0.983191\pi$
$787$		−	2.96153i		−	0.105567i	0.998606	−	0.0527836i	$-0.0168094\pi$
$788$	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	0.178725	−	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
$800$	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	0.832888	−	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	$-0.811177\pi$
$811$		−	31.8397i		−	1.11804i	0.829153	−	0.559022i	$-0.188823\pi$
$812$	−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	$-0.963499\pi$
$823$		−	6.56492i		−	0.228839i	0.993433	−	0.114419i	$-0.0365008\pi$
$824$	−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	0.295343	−	0.955391i	$-0.404566\pi$
$827$	−18.9814	−	18.9814i	−0.660048	−	0.660048i	−0.955391	+	0.295343i	$0.904566\pi$
$828$	0.879143	−	34.3687i	0.0305523	−	1.19439i
$829$	−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
$832$	−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	0.425515	−	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
$856$	−9.71174	−	26.2513i	−0.331940	−	0.897253i
$857$	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	0.949906	−	0.312535i	$-0.101178\pi$
$859$	18.6805	+	18.6805i	0.637371	+	0.637371i	−0.312535	+	0.949906i	$0.601178\pi$
$860$	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	$-0.919656\pi$
$863$		−	14.6729i		−	0.499472i	0.968314	−	0.249736i	$-0.0803439\pi$
$864$	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	$0.0647612\pi$
$881$			11.9945i			0.404105i	−0.979375	+	0.202053i	$0.935239\pi$
$882$	−43.8270	+	102.095i	−1.47573	+	3.43773i
$883$	−12.5586	+	12.5586i	−0.422631	+	0.422631i	−0.886109	−	0.463478i	$-0.846601\pi$
$883$	−12.5586	+	12.5586i	−0.422631	+	0.422631i	0.463478	+	0.886109i	$0.346601\pi$
$884$	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	0.878737	−	0.477306i	$-0.158387\pi$
$907$	12.0897	+	12.0897i	0.401431	+	0.401431i	−0.477306	+	0.878737i	$0.658387\pi$
$908$	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	0.412900	−	0.910776i	$-0.364516\pi$
$911$	−15.0273	−	15.0273i	−0.497876	−	0.497876i	−0.910776	+	0.412900i	$0.864516\pi$
$912$	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	0.232089	−	0.972694i	$-0.425444\pi$
$919$	36.5230	−	36.5230i	1.20478	−	1.20478i	0.972694	−	0.232089i	$-0.0745562\pi$
$920$	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	$0.278405\pi$
$929$			46.7744i			1.53462i	−0.641276	+	0.767310i	$0.721595\pi$
$930$	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	0.890528	−	0.454928i	$-0.150335\pi$
$947$	13.4049	+	13.4049i	0.435600	+	0.435600i	−0.454928	+	0.890528i	$0.650335\pi$
$948$	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	$0.253569\pi$
$953$			44.1445i			1.42998i	−0.699135	+	0.714990i	$0.746431\pi$
$954$	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	0.984236	+	0.176858i	$0.0565933\pi$
$967$	36.1061	+	36.1061i	1.16109	+	1.16109i	0.176858	+	0.984236i	$0.443407\pi$
$968$	−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	$-0.969175\pi$
$971$		−	6.02587i		−	0.193379i	0.995315	−	0.0966897i	$-0.0308254\pi$
$972$	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	0.647885	−	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
$980$	−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	−0.809532	−	0.587075i	$-0.800279\pi$
$991$	−7.00298	+	7.00298i	−0.222457	+	0.222457i	0.587075	+	0.809532i	$0.300279\pi$
$992$	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	−0.293951	−	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.31.52	yes	152
4.3	odd	2	inner	740.2.u.a.31.13	✓	152
37.6	odd	4	inner	740.2.u.a.191.13	yes	152
148.43	even	4	inner	740.2.u.a.191.52	yes	152

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