LMFDB - Embedded newform 605.2.g.q.511.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(81,605)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("605.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			511.1
Character	$\chi$	$=$	605.511
Dual form			605.2.g.q.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.810808 - 2.49541i) q^{2} +(-1.08398 - 0.787560i) q^{3} +(-3.95163 + 2.87103i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-1.08638 + 3.34354i) q^{6} +(-2.12272 + 1.54225i) q^{7} +(6.12296 + 4.44859i) q^{8} +(-0.372282 - 1.14577i) q^{9} +O(q^{10})$	\(q+(-0.810808 - 2.49541i) q^{2} +(-1.08398 - 0.787560i) q^{3} +(-3.95163 + 2.87103i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-1.08638 + 3.34354i) q^{6} +(-2.12272 + 1.54225i) q^{7} +(6.12296 + 4.44859i) q^{8} +(-0.372282 - 1.14577i) q^{9} -2.62383 q^{10} +6.54461 q^{12} +(2.07910 + 6.39883i) q^{13} +(5.56966 + 4.04660i) q^{14} +(-1.08398 + 0.787560i) q^{15} +(3.11774 - 9.59541i) q^{16} +(-0.551150 + 1.69626i) q^{17} +(-2.55731 + 1.85799i) q^{18} +(-1.19772 - 0.870194i) q^{19} +(1.50939 + 4.64542i) q^{20} +3.51561 q^{21} +5.20473 q^{23} +(-3.13365 - 9.64440i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(14.2819 - 10.3764i) q^{26} +(-1.74095 + 5.35808i) q^{27} +(3.96038 - 12.1888i) q^{28} +(0.952511 - 0.692040i) q^{29} +(2.84419 + 2.06642i) q^{30} +(-1.41043 - 4.34085i) q^{31} -11.3356 q^{32} +4.67975 q^{34} +(0.810808 + 2.49541i) q^{35} +(4.76065 + 3.45881i) q^{36} +(0.549932 - 0.399549i) q^{37} +(-1.20037 + 3.69436i) q^{38} +(2.78574 - 8.57364i) q^{39} +(6.12296 - 4.44859i) q^{40} +(4.44898 + 3.23238i) q^{41} +(-2.85048 - 8.77289i) q^{42} -3.80120 q^{43} -1.20473 q^{45} +(-4.22004 - 12.9879i) q^{46} +(-5.38815 - 3.91472i) q^{47} +(-10.9365 + 7.94586i) q^{48} +(-0.0356965 + 0.109863i) q^{49} +(-0.810808 + 2.49541i) q^{50} +(1.93335 - 1.40466i) q^{51} +(-26.5871 - 19.3166i) q^{52} +(4.41707 + 13.5943i) q^{53} +14.7822 q^{54} -19.8582 q^{56} +(0.612978 + 1.88655i) q^{57} +(-2.49923 - 1.81579i) q^{58} +(3.14261 - 2.28324i) q^{59} +(2.02239 - 6.22429i) q^{60} +(-0.992721 + 3.05528i) q^{61} +(-9.68861 + 7.03919i) q^{62} +(2.55731 + 1.85799i) q^{63} +(2.95551 + 9.09613i) q^{64} +6.72812 q^{65} +4.66012 q^{67} +(-2.69208 - 8.28538i) q^{68} +(-5.64184 - 4.09904i) q^{69} +(5.56966 - 4.04660i) q^{70} +(1.20037 - 3.69436i) q^{71} +(2.81758 - 8.67161i) q^{72} +(-2.88586 + 2.09670i) q^{73} +(-1.44293 - 1.04835i) q^{74} +(0.414045 + 1.27430i) q^{75} +7.23130 q^{76} -23.6535 q^{78} +(4.67753 + 14.3959i) q^{79} +(-8.16235 - 5.93029i) q^{80} +(3.18303 - 2.31260i) q^{81} +(4.45883 - 13.7229i) q^{82} +(-2.26643 + 6.97535i) q^{83} +(-13.8924 + 10.0934i) q^{84} +(1.44293 + 1.04835i) q^{85} +(3.08204 + 9.48555i) q^{86} -1.57753 q^{87} +3.44872 q^{89} +(0.976805 + 3.00630i) q^{90} +(-14.2819 - 10.3764i) q^{91} +(-20.5672 + 14.9429i) q^{92} +(-1.88980 + 5.81620i) q^{93} +(-5.40008 + 16.6197i) q^{94} +(-1.19772 + 0.870194i) q^{95} +(12.2876 + 8.92746i) q^{96} +(0.455807 + 1.40283i) q^{97} +0.303095 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9}+O(q^{10}) $ 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9	$ 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9} + 72 q^{12} + 18 q^{14} - 6 q^{15} - 18 q^{16} - 6 q^{20} + 48 q^{23} - 6 q^{25} + 36 q^{26} - 30 q^{27} + 96 q^{34} + 12 q^{36} + 30 q^{42} + 48 q^{45} - 42 q^{47} + 6 q^{48} + 24 q^{49} - 24 q^{53} - 120 q^{56} + 24 q^{58} - 18 q^{60} - 30 q^{64} + 120 q^{67} + 24 q^{69} + 18 q^{70} - 6 q^{75} - 288 q^{78} - 18 q^{80} - 30 q^{81} - 42 q^{82} + 6 q^{86} - 120 q^{89} - 36 q^{91} - 36 q^{92} + 60 q^{93} - 24 q^{97}+O(q^{100}) $ 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9 + 72 * q^12 + 18 * q^14 - 6 * q^15 - 18 * q^16 - 6 * q^20 + 48 * q^23 - 6 * q^25 + 36 * q^26 - 30 * q^27 + 96 * q^34 + 12 * q^36 + 30 * q^42 + 48 * q^45 - 42 * q^47 + 6 * q^48 + 24 * q^49 - 24 * q^53 - 120 * q^56 + 24 * q^58 - 18 * q^60 - 30 * q^64 + 120 * q^67 + 24 * q^69 + 18 * q^70 - 6 * q^75 - 288 * q^78 - 18 * q^80 - 30 * q^81 - 42 * q^82 + 6 * q^86 - 120 * q^89 - 36 * q^91 - 36 * q^92 + 60 * q^93 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.810808	−	2.49541i	−0.573328	−	1.76452i	−0.641804	−	0.766869i	$-0.721814\pi$
$2$	−0.810808	−	2.49541i	−0.573328	−	1.76452i	0.0684758	−	0.997653i	$-0.478186\pi$
$3$	−1.08398	−	0.787560i	−0.625838	−	0.454698i	0.229118	−	0.973399i	$-0.426416\pi$
$3$	−1.08398	−	0.787560i	−0.625838	−	0.454698i	−0.854956	+	0.518701i	$0.826416\pi$
$4$	−3.95163	+	2.87103i	−1.97582	+	1.43551i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$6$	−1.08638	+	3.34354i	−0.443514	+	1.36500i
$7$	−2.12272	+	1.54225i	−0.802314	+	0.582915i	−0.911592	−	0.411096i	$-0.865146\pi$
$7$	−2.12272	+	1.54225i	−0.802314	+	0.582915i	0.109278	+	0.994011i	$0.465146\pi$
$8$	6.12296	+	4.44859i	2.16479	+	1.57281i
$9$	−0.372282	−	1.14577i	−0.124094	−	0.381922i
$10$	−2.62383			−0.829728
$11$		0			0
$11$		0			0
$12$	6.54461			1.88927
$13$	2.07910	+	6.39883i	0.576640	+	1.77471i	0.630526	+	0.776168i	$0.282839\pi$
$13$	2.07910	+	6.39883i	0.576640	+	1.77471i	−0.0538866	+	0.998547i	$0.517161\pi$
$14$	5.56966	+	4.04660i	1.48856	+	1.08150i
$15$	−1.08398	+	0.787560i	−0.279883	+	0.203347i
$16$	3.11774	−	9.59541i	0.779435	−	2.39885i
$17$	−0.551150	+	1.69626i	−0.133673	+	0.411405i	−0.995381	−	0.0960001i	$-0.969395\pi$
$17$	−0.551150	+	1.69626i	−0.133673	+	0.411405i	0.861708	+	0.507405i	$0.169395\pi$
$18$	−2.55731	+	1.85799i	−0.602763	+	0.437933i
$19$	−1.19772	−	0.870194i	−0.274776	−	0.199636i	0.441860	−	0.897084i	$-0.354319\pi$
$19$	−1.19772	−	0.870194i	−0.274776	−	0.199636i	−0.716636	+	0.697448i	$0.754319\pi$
$20$	1.50939	+	4.64542i	0.337510	+	1.03875i
$21$	3.51561			0.767169
$22$		0			0
$23$	5.20473			1.08526			0.542631	−	0.839971i	$-0.317428\pi$
$23$	5.20473			1.08526			0.542631	+	0.839971i	$0.317428\pi$
$24$	−3.13365	−	9.64440i	−0.639654	−	1.96865i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	14.2819	−	10.3764i	2.80092	−	2.03499i
$27$	−1.74095	+	5.35808i	−0.335045	+	1.03116i
$28$	3.96038	−	12.1888i	0.748441	−	2.30347i
$29$	0.952511	−	0.692040i	0.176877	−	0.128509i	−0.495824	−	0.868423i	$-0.665134\pi$
$29$	0.952511	−	0.692040i	0.176877	−	0.128509i	0.672701	+	0.739914i	$0.265134\pi$
$30$	2.84419	+	2.06642i	0.519275	+	0.377276i
$31$	−1.41043	−	4.34085i	−0.253320	−	0.779639i	−0.994156	−	0.107953i	$-0.965570\pi$
$31$	−1.41043	−	4.34085i	−0.253320	−	0.779639i	0.740836	−	0.671686i	$-0.234430\pi$
$32$	−11.3356			−2.00387
$33$		0			0
$34$	4.67975			0.802571
$35$	0.810808	+	2.49541i	0.137052	+	0.421801i
$36$	4.76065	+	3.45881i	0.793441	+	0.576469i
$37$	0.549932	−	0.399549i	0.0904083	−	0.0656855i	−0.541663	−	0.840596i	$-0.682205\pi$
$37$	0.549932	−	0.399549i	0.0904083	−	0.0656855i	0.632071	+	0.774910i	$0.282205\pi$
$38$	−1.20037	+	3.69436i	−0.194726	+	0.599305i
$39$	2.78574	−	8.57364i	0.446076	−	1.37288i
$40$	6.12296	−	4.44859i	0.968125	−	0.703384i
$41$	4.44898	+	3.23238i	0.694815	+	0.504812i	0.878239	−	0.478221i	$-0.158718\pi$
$41$	4.44898	+	3.23238i	0.694815	+	0.504812i	−0.183425	+	0.983034i	$0.558718\pi$
$42$	−2.85048	−	8.77289i	−0.439839	−	1.35369i
$43$	−3.80120			−0.579677			−0.289839	−	0.957076i	$-0.593602\pi$
$43$	−3.80120			−0.579677			−0.289839	+	0.957076i	$0.593602\pi$
$44$		0			0
$45$	−1.20473			−0.179591
$46$	−4.22004	−	12.9879i	−0.622210	−	1.91497i
$47$	−5.38815	−	3.91472i	−0.785943	−	0.571021i	0.120814	−	0.992675i	$-0.461450\pi$
$47$	−5.38815	−	3.91472i	−0.785943	−	0.571021i	−0.906757	+	0.421654i	$0.861450\pi$
$48$	−10.9365	+	7.94586i	−1.57855	+	1.14689i
$49$	−0.0356965	+	0.109863i	−0.00509950	+	0.0156946i
$50$	−0.810808	+	2.49541i	−0.114666	+	0.352904i
$51$	1.93335	−	1.40466i	0.270723	−	0.196692i
$52$	−26.5871	−	19.3166i	−3.68696	−	2.67873i
$53$	4.41707	+	13.5943i	0.606731	+	1.86733i	0.484420	+	0.874836i	$0.339031\pi$
$53$	4.41707	+	13.5943i	0.606731	+	1.86733i	0.122311	+	0.992492i	$0.460969\pi$
$54$	14.7822			2.01160
$55$		0			0
$56$	−19.8582			−2.65366
$57$	0.612978	+	1.88655i	0.0811909	+	0.249880i
$58$	−2.49923	−	1.81579i	−0.328164	−	0.238425i
$59$	3.14261	−	2.28324i	0.409133	−	0.297253i	−0.364117	−	0.931353i	$-0.618629\pi$
$59$	3.14261	−	2.28324i	0.409133	−	0.297253i	0.773251	+	0.634100i	$0.218629\pi$
$60$	2.02239	−	6.22429i	0.261090	−	0.803553i
$61$	−0.992721	+	3.05528i	−0.127105	+	0.391189i	−0.994279	−	0.106817i	$-0.965934\pi$
$61$	−0.992721	+	3.05528i	−0.127105	+	0.391189i	0.867174	+	0.498006i	$0.165934\pi$
$62$	−9.68861	+	7.03919i	−1.23045	+	0.893978i
$63$	2.55731	+	1.85799i	0.322191	+	0.234085i
$64$	2.95551	+	9.09613i	0.369439	+	1.13702i
$65$	6.72812			0.834521
$66$		0			0
$67$	4.66012			0.569325			0.284662	−	0.958628i	$-0.408119\pi$
$67$	4.66012			0.569325			0.284662	+	0.958628i	$0.408119\pi$
$68$	−2.69208	−	8.28538i	−0.326463	−	1.00475i
$69$	−5.64184	−	4.09904i	−0.679198	−	0.493466i
$70$	5.56966	−	4.04660i	0.665702	−	0.483661i
$71$	1.20037	−	3.69436i	0.142458	−	0.438440i	−0.854217	−	0.519916i	$-0.825963\pi$
$71$	1.20037	−	3.69436i	0.142458	−	0.438440i	0.996675	+	0.0814756i	$0.0259633\pi$
$72$	2.81758	−	8.67161i	0.332055	−	1.02196i
$73$	−2.88586	+	2.09670i	−0.337764	+	0.245400i	−0.743718	−	0.668494i	$-0.766939\pi$
$73$	−2.88586	+	2.09670i	−0.337764	+	0.245400i	0.405954	+	0.913894i	$0.366939\pi$
$74$	−1.44293	−	1.04835i	−0.167737	−	0.121868i
$75$	0.414045	+	1.27430i	0.0478098	+	0.147143i
$76$	7.23130			0.829487
$77$		0			0
$78$	−23.6535			−2.67823
$79$	4.67753	+	14.3959i	0.526263	+	1.61967i	0.761805	+	0.647806i	$0.224313\pi$
$79$	4.67753	+	14.3959i	0.526263	+	1.61967i	−0.235543	+	0.971864i	$0.575687\pi$
$80$	−8.16235	−	5.93029i	−0.912578	−	0.663027i
$81$	3.18303	−	2.31260i	0.353670	−	0.256956i
$82$	4.45883	−	13.7229i	0.492396	−	1.51544i
$83$	−2.26643	+	6.97535i	−0.248773	+	0.765644i	0.746220	+	0.665699i	$0.231867\pi$
$83$	−2.26643	+	6.97535i	−0.248773	+	0.765644i	−0.994993	+	0.0999446i	$0.968133\pi$
$84$	−13.8924	+	10.0934i	−1.51578	+	1.10128i
$85$	1.44293	+	1.04835i	0.156508	+	0.113709i
$86$	3.08204	+	9.48555i	0.332345	+	1.02285i
$87$	−1.57753			−0.169129
$88$		0			0
$89$	3.44872			0.365564			0.182782	−	0.983153i	$-0.441490\pi$
$89$	3.44872			0.365564			0.182782	+	0.983153i	$0.441490\pi$
$90$	0.976805	+	3.00630i	0.102964	+	0.316891i
$91$	−14.2819	−	10.3764i	−1.49715	−	1.08775i
$92$	−20.5672	+	14.9429i	−2.14428	+	1.55791i
$93$	−1.88980	+	5.81620i	−0.195963	+	0.603112i
$94$	−5.40008	+	16.6197i	−0.556976	+	1.71420i
$95$	−1.19772	+	0.870194i	−0.122883	+	0.0892801i
$96$	12.2876	+	8.92746i	1.25410	+	0.911155i
$97$	0.455807	+	1.40283i	0.0462802	+	0.142436i	0.971526	−	0.236931i	$-0.0761417\pi$
$97$	0.455807	+	1.40283i	0.0462802	+	0.142436i	−0.925246	+	0.379367i	$0.876142\pi$
$98$	0.303095			0.0306172
$99$		0			0
$100$	4.88448			0.488448
$101$	1.05455	+	3.24557i	0.104932	+	0.322946i	0.989714	−	0.143057i	$-0.0456934\pi$
$101$	1.05455	+	3.24557i	0.104932	+	0.322946i	−0.884783	+	0.466004i	$0.845693\pi$
$102$	−5.07277	−	3.68559i	−0.502280	−	0.364927i
$103$	4.02381	−	2.92347i	0.396477	−	0.288058i	−0.371627	−	0.928382i	$-0.621200\pi$
$103$	4.02381	−	2.92347i	0.396477	−	0.288058i	0.768105	+	0.640324i	$0.221200\pi$
$104$	−15.7355	+	48.4288i	−1.54299	+	4.74884i
$105$	1.08638	−	3.34354i	0.106020	−	0.326296i
$106$	30.3421	−	22.0448i	2.94708	−	2.14118i
$107$	5.71588	+	4.15283i	0.552575	+	0.401469i	0.828734	−	0.559643i	$-0.189062\pi$
$107$	5.71588	+	4.15283i	0.552575	+	0.401469i	−0.276159	+	0.961112i	$0.589062\pi$
$108$	−8.50362	−	26.1715i	−0.818262	−	2.51835i
$109$	10.6439			1.01950			0.509750	−	0.860323i	$-0.329738\pi$
$109$	10.6439			1.01950			0.509750	+	0.860323i	$0.329738\pi$
$110$		0			0
$111$	−0.910786			−0.0864480
$112$	8.18042	+	25.1767i	0.772977	+	2.37898i
$113$	11.1393	+	8.09320i	1.04790	+	0.761344i	0.971812	−	0.235757i	$-0.0757570\pi$
$113$	11.1393	+	8.09320i	1.04790	+	0.761344i	0.0760879	+	0.997101i	$0.475757\pi$
$114$	4.21071	−	3.05926i	0.394370	−	0.286526i
$115$	1.60835	−	4.94999i	0.149979	−	0.461589i
$116$	−1.77711	+	5.46937i	−0.165000	+	0.507818i
$117$	6.55754	−	4.76434i	0.606245	−	0.440463i
$118$	−8.24568	−	5.99084i	−0.759077	−	0.551501i
$119$	−1.44612	−	4.45071i	−0.132566	−	0.407996i
$120$	−10.1407			−0.925717
$121$		0			0
$122$	8.42909			0.763134
$123$	−2.27693	−	7.00768i	−0.205304	−	0.631862i
$124$	18.0362	+	13.1041i	1.61970	+	1.17678i
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$	2.56297	−	7.88801i	0.228327	−	0.702720i
$127$	3.80489	−	11.7102i	0.337629	−	1.03912i	−0.627783	−	0.778388i	$-0.716037\pi$
$127$	3.80489	−	11.7102i	0.337629	−	1.03912i	0.965412	−	0.260728i	$-0.0839625\pi$
$128$	1.96085	−	1.42464i	0.173317	−	0.125922i
$129$	4.12043	+	2.99367i	0.362784	+	0.263578i
$130$	−5.45522	−	16.7894i	−0.478454	−	1.47253i
$131$	−19.5102			−1.70461			−0.852306	−	0.523043i	$-0.824797\pi$
$131$	−19.5102			−1.70461			−0.852306	+	0.523043i	$0.824797\pi$
$132$		0			0
$133$	3.88448			0.336827
$134$	−3.77847	−	11.6289i	−0.326410	−	1.00459i
$135$	4.55786	+	3.31148i	0.392278	+	0.285007i
$136$	−10.9207	+	7.93432i	−0.936439	+	0.680362i
$137$	−2.64649	+	8.14507i	−0.226105	+	0.695881i	0.772072	+	0.635535i	$0.219220\pi$
$137$	−2.64649	+	8.14507i	−0.226105	+	0.695881i	−0.998178	+	0.0603458i	$0.980780\pi$
$138$	−5.65433	+	17.4022i	−0.481329	+	1.48138i
$139$	1.60480	−	1.16595i	0.136117	−	0.0988949i	−0.517643	−	0.855597i	$-0.673190\pi$
$139$	1.60480	−	1.16595i	0.136117	−	0.0988949i	0.653760	+	0.756702i	$0.273190\pi$
$140$	−10.3684	−	7.53309i	−0.876290	−	0.636662i
$141$	2.75759	+	8.48699i	0.232231	+	0.714733i
$142$	−10.1922			−0.855313
$143$		0			0
$144$	−12.1548			−1.01290
$145$	−0.363827	−	1.11974i	−0.0302142	−	0.0929896i
$146$	7.57200	+	5.50138i	0.626663	+	0.455297i
$147$	0.125218	−	0.0909760i	0.0103278	−	0.00750357i
$148$	−1.02601	+	3.15774i	−0.0843377	+	0.259565i
$149$	5.67025	−	17.4512i	0.464525	−	1.42966i	−0.395055	−	0.918658i	$-0.629274\pi$
$149$	5.67025	−	17.4512i	0.464525	−	1.42966i	0.859579	−	0.511002i	$-0.170726\pi$
$150$	2.84419	−	2.06642i	0.232227	−	0.168723i
$151$	13.9341	+	10.1237i	1.13394	+	0.823854i	0.986263	−	0.165182i	$-0.0528212\pi$
$151$	13.9341	+	10.1237i	1.13394	+	0.823854i	0.147674	+	0.989036i	$0.452821\pi$
$152$	−3.46245	−	10.6563i	−0.280842	−	0.864343i
$153$	2.14871			0.173713
$154$		0			0
$155$	−4.56424			−0.366608
$156$	13.6069	+	41.8778i	1.08943	+	3.35291i
$157$	16.9064	+	12.2832i	1.34928	+	0.980307i	0.999047	+	0.0436428i	$0.0138963\pi$
$157$	16.9064	+	12.2832i	1.34928	+	0.980307i	0.350229	+	0.936664i	$0.386104\pi$
$158$	32.1312	−	23.3447i	2.55622	−	1.85720i
$159$	5.91833	−	18.2148i	0.469354	−	1.44452i
$160$	−3.50289	+	10.7808i	−0.276928	+	0.852296i
$161$	−11.0482	+	8.02699i	−0.870720	+	0.632615i
$162$	−8.35172	−	6.06788i	−0.656173	−	0.476738i
$163$	2.92188	+	8.99261i	0.228859	+	0.704356i	0.997877	+	0.0651285i	$0.0207457\pi$
$163$	2.92188	+	8.99261i	0.228859	+	0.704356i	−0.769018	+	0.639227i	$0.779254\pi$
$164$	−26.8610			−2.09749
$165$		0			0
$166$	19.2440			1.49362
$167$	2.91991	+	8.98655i	0.225949	+	0.695400i	0.998194	+	0.0600749i	$0.0191340\pi$
$167$	2.91991	+	8.98655i	0.225949	+	0.695400i	−0.772245	+	0.635325i	$0.780866\pi$
$168$	21.5259	+	15.6395i	1.66076	+	1.20661i
$169$	−26.1051	+	18.9664i	−2.00808	+	1.45896i
$170$	1.44612	−	4.45071i	0.110913	−	0.341354i
$171$	−0.551150	+	1.69626i	−0.0421475	+	0.129717i
$172$	15.0209	−	10.9133i	1.14534	−	0.832135i
$173$	−7.34819	−	5.33877i	−0.558672	−	0.405899i	0.272300	−	0.962212i	$-0.412216\pi$
$173$	−7.34819	−	5.33877i	−0.558672	−	0.405899i	−0.830973	+	0.556313i	$0.812216\pi$
$174$	1.27907	+	3.93658i	0.0969662	+	0.298431i
$175$	2.62383			0.198343
$176$		0			0
$177$	−5.20473			−0.391211
$178$	−2.79625	−	8.60598i	−0.209588	−	0.645045i
$179$	11.1393	+	8.09320i	0.832593	+	0.604914i	0.920292	−	0.391233i	$-0.127951\pi$
$179$	11.1393	+	8.09320i	0.832593	+	0.604914i	−0.0876991	+	0.996147i	$0.527951\pi$
$180$	4.76065	−	3.45881i	0.354838	−	0.257805i
$181$	−7.37258	+	22.6905i	−0.548000	+	1.68657i	0.165749	+	0.986168i	$0.446996\pi$
$181$	−7.37258	+	22.6905i	−0.548000	+	1.68657i	−0.713749	+	0.700402i	$0.753004\pi$
$182$	−14.3136	+	44.0526i	−1.06099	+	3.26540i
$183$	3.48231	−	2.53005i	0.257420	−	0.187026i
$184$	31.8684	+	23.1537i	2.34937	+	1.70691i
$185$	−0.210055	−	0.646484i	−0.0154436	−	0.0475305i
$186$	16.0461			1.17656
$187$		0			0
$188$	32.5313			2.37259
$189$	−4.56795	−	14.0587i	−0.332269	−	1.02262i
$190$	3.14261	+	2.28324i	0.227989	+	0.165644i
$191$	−12.9952	+	9.44154i	−0.940297	+	0.683166i	−0.948492	−	0.316800i	$-0.897391\pi$
$191$	−12.9952	+	9.44154i	−0.940297	+	0.683166i	0.00819487	+	0.999966i	$0.497391\pi$
$192$	3.96002	−	12.1877i	0.285790	−	0.879571i
$193$	−6.63113	+	20.4085i	−0.477320	+	1.46904i	0.365484	+	0.930818i	$0.380903\pi$
$193$	−6.63113	+	20.4085i	−0.477320	+	1.46904i	−0.842804	+	0.538221i	$0.819097\pi$
$194$	3.13107	−	2.27485i	0.224798	−	0.163325i
$195$	−7.29317	−	5.29880i	−0.522275	−	0.379455i
$196$	−0.174359	−	0.536622i	−0.0124542	−	0.0383301i
$197$	−9.21494			−0.656537			−0.328269	−	0.944584i	$-0.606465\pi$
$197$	−9.21494			−0.656537			−0.328269	+	0.944584i	$0.606465\pi$
$198$		0			0
$199$	−16.4880			−1.16880			−0.584401	−	0.811465i	$-0.698670\pi$
$199$	−16.4880			−1.16880			−0.584401	+	0.811465i	$0.698670\pi$
$200$	−2.33876	−	7.19797i	−0.165375	−	0.508973i
$201$	−5.05150	−	3.67013i	−0.356305	−	0.258871i
$202$	7.24399	−	5.26307i	0.509686	−	0.370308i
$203$	−0.954620	+	2.93802i	−0.0670012	+	0.206208i
$204$	−3.60706	+	11.1014i	−0.252545	+	0.777252i
$205$	4.44898	−	3.23238i	0.310731	−	0.225759i
$206$	−10.5578	−	7.67068i	−0.735596	−	0.534441i
$207$	−1.93763	−	5.96340i	−0.134674	−	0.414485i
$208$	67.8815			4.70673
$209$		0			0
$210$	−9.22436			−0.636541
$211$	−4.58386	−	14.1077i	−0.315566	−	0.971213i	−0.975521	−	0.219907i	$-0.929424\pi$
$211$	−4.58386	−	14.1077i	−0.315566	−	0.971213i	0.659955	−	0.751306i	$-0.270576\pi$
$212$	−56.4844	−	41.0383i	−3.87936	−	2.81852i
$213$	−4.21071	+	3.05926i	−0.288513	+	0.209617i
$214$	5.72854	−	17.6306i	0.391595	−	1.20520i
$215$	−1.17463	+	3.61515i	−0.0801094	+	0.246551i
$216$	−34.4957	+	25.0626i	−2.34713	+	1.70529i
$217$	9.68861	+	7.03919i	0.657706	+	0.477851i
$218$	−8.63015	−	26.5609i	−0.584508	−	1.79893i
$219$	4.77950			0.322968
$220$		0			0
$221$	−12.0000			−0.807207
$222$	0.738473	+	2.27279i	0.0495631	+	0.152539i
$223$	−18.9333	−	13.7558i	−1.26786	−	0.921157i	−0.268749	−	0.963210i	$-0.586610\pi$
$223$	−18.9333	−	13.7558i	−1.26786	−	0.921157i	−0.999115	+	0.0420528i	$0.986610\pi$
$224$	24.0623	−	17.4823i	1.60773	−	1.16809i
$225$	−0.372282	+	1.14577i	−0.0248188	+	0.0763844i
$226$	11.1640	−	34.3592i	0.742618	−	2.28554i
$227$	−2.12272	+	1.54225i	−0.140890	+	0.102363i	−0.655998	−	0.754763i	$-0.727752\pi$
$227$	−2.12272	+	1.54225i	−0.140890	+	0.102363i	0.515108	+	0.857125i	$0.327752\pi$
$228$	−7.83861	−	5.69508i	−0.519124	−	0.377166i
$229$	−6.80969	−	20.9581i	−0.449997	−	1.38495i	−0.876910	−	0.480655i	$-0.840399\pi$
$229$	−6.80969	−	20.9581i	−0.449997	−	1.38495i	0.426913	−	0.904293i	$-0.359601\pi$
$230$	−13.6563			−0.900471
$231$		0			0
$232$	8.91079			0.585022
$233$	−1.65161	−	5.08314i	−0.108201	−	0.333007i	0.882268	−	0.470748i	$-0.156016\pi$
$233$	−1.65161	−	5.08314i	−0.108201	−	0.333007i	−0.990468	+	0.137741i	$0.956016\pi$
$234$	−17.2059	−	12.5008i	−1.12478	−	0.817203i
$235$	−5.38815	+	3.91472i	−0.351484	+	0.255368i
$236$	−5.86319	+	18.0451i	−0.381661	+	1.17463i
$237$	6.26731	−	19.2888i	0.407105	−	1.25294i
$238$	−9.93382	+	7.21734i	−0.643914	+	0.467831i
$239$	−10.1790	−	7.39550i	−0.658427	−	0.478375i	0.207705	−	0.978192i	$-0.433401\pi$
$239$	−10.1790	−	7.39550i	−0.658427	−	0.478375i	−0.866131	+	0.499817i	$0.833401\pi$
$240$	4.17739	+	12.8567i	0.269649	+	0.829895i
$241$	4.28687			0.276141			0.138071	−	0.990422i	$-0.455910\pi$
$241$	4.28687			0.276141			0.138071	+	0.990422i	$0.455910\pi$
$242$		0			0
$243$	11.6298			0.746052
$244$	−4.84893	−	14.9235i	−0.310421	−	0.955378i
$245$	0.0934546	+	0.0678988i	0.00597060	+	0.00433789i
$246$	−15.6409	+	11.3638i	−0.997227	+	0.724528i
$247$	3.07804	−	9.47323i	0.195851	−	0.602767i
$248$	10.6747	−	32.8532i	0.677842	−	2.08618i
$249$	7.95027	−	5.77621i	0.503828	−	0.366052i
$250$	2.12272	+	1.54225i	0.134253	+	0.0975404i
$251$	3.10961	+	9.57040i	0.196277	+	0.604078i	0.999959	+	0.00901968i	$0.00287109\pi$
$251$	3.10961	+	9.57040i	0.196277	+	0.604078i	−0.803682	+	0.595058i	$0.797129\pi$
$252$	−15.4399			−0.972621
$253$		0			0
$254$	−32.3069			−2.02712
$255$	−0.738473	−	2.27279i	−0.0462450	−	0.142327i
$256$	10.3303	+	7.50541i	0.645644	+	0.469088i
$257$	2.56092	−	1.86062i	0.159746	−	0.116062i	−0.505041	−	0.863095i	$-0.668523\pi$
$257$	2.56092	−	1.86062i	0.159746	−	0.116062i	0.664786	+	0.747033i	$0.268523\pi$
$258$	4.12956	−	12.7095i	0.257095	−	0.791257i
$259$	−0.551150	+	1.69626i	−0.0342468	+	0.105401i
$260$	−26.5871	+	19.3166i	−1.64886	+	1.19797i
$261$	−1.14752	−	0.833721i	−0.0710296	−	0.0516060i
$262$	15.8190	+	48.6859i	0.977302	+	3.00783i
$263$	−22.3681			−1.37928			−0.689638	−	0.724155i	$-0.742230\pi$
$263$	−22.3681			−1.37928			−0.689638	+	0.724155i	$0.742230\pi$
$264$		0			0
$265$	14.2939			0.878070
$266$	−3.14957	−	9.69338i	−0.193113	−	0.594339i
$267$	−3.73836	−	2.71607i	−0.228784	−	0.166221i
$268$	−18.4151	+	13.3793i	−1.12488	+	0.817273i
$269$	4.93614	−	15.1919i	0.300962	−	0.926266i	−0.680191	−	0.733035i	$-0.738103\pi$
$269$	4.93614	−	15.1919i	0.300962	−	0.926266i	0.981153	−	0.193231i	$-0.0618967\pi$
$270$	4.56795	−	14.0587i	0.277996	−	0.855585i
$271$	−12.6530	+	9.19294i	−0.768615	+	0.558431i	−0.901541	−	0.432695i	$-0.857563\pi$
$271$	−12.6530	+	9.19294i	−0.768615	+	0.558431i	0.132926	+	0.991126i	$0.457563\pi$
$272$	14.5580	+	10.5770i	0.882710	+	0.641326i
$273$	7.30932	+	22.4958i	0.442380	+	1.36151i
$274$	22.4711			1.35753
$275$		0			0
$276$	34.0629			2.05035
$277$	−7.38043	−	22.7146i	−0.443447	−	1.36479i	−0.884178	−	0.467150i	$-0.845281\pi$
$277$	−7.38043	−	22.7146i	−0.443447	−	1.36479i	0.440731	−	0.897639i	$-0.354719\pi$
$278$	−4.21071	−	3.05926i	−0.252542	−	0.183482i
$279$	−4.44852	+	3.23204i	−0.266326	+	0.193497i
$280$	−6.13652	+	18.8863i	−0.366727	+	1.12867i
$281$	−3.78356	+	11.6446i	−0.225708	+	0.694659i	0.772511	+	0.635002i	$0.219001\pi$
$281$	−3.78356	+	11.6446i	−0.225708	+	0.694659i	−0.998219	+	0.0596571i	$0.980999\pi$
$282$	18.9426	−	13.7626i	1.12802	−	0.819553i
$283$	−16.8709	−	12.2575i	−1.00287	−	0.728630i	−0.0401707	−	0.999193i	$-0.512790\pi$
$283$	−16.8709	−	12.2575i	−1.00287	−	0.728630i	−0.962702	+	0.270563i	$0.912790\pi$
$284$	5.86319	+	18.0451i	0.347917	+	1.07078i
$285$	1.98364			0.117501
$286$		0			0
$287$	−14.4291			−0.851722
$288$	4.22004	+	12.9879i	0.248668	+	0.765322i
$289$	11.1797	+	8.12256i	0.657632	+	0.477797i
$290$	−2.49923	+	1.81579i	−0.146760	+	0.106627i
$291$	0.610726	−	1.87962i	0.0358014	−	0.110185i
$292$	5.38416	−	16.5708i	0.315084	−	0.969730i
$293$	11.5936	−	8.42327i	0.677307	−	0.492093i	−0.195156	−	0.980772i	$-0.562521\pi$
$293$	11.5936	−	8.42327i	0.677307	−	0.492093i	0.872463	+	0.488680i	$0.162521\pi$
$294$	−0.328550	−	0.238706i	−0.0191614	−	0.0139216i
$295$	−1.20037	−	3.69436i	−0.0698883	−	0.215094i
$296$	5.14464			0.299026
$297$		0			0
$298$	−48.1455			−2.78899
$299$	10.8212	+	33.3042i	0.625805	+	1.92603i
$300$	−5.29470	−	3.84682i	−0.305690	−	0.222096i
$301$	8.06889	−	5.86239i	0.465083	−	0.337903i
$302$	13.9649	−	42.9796i	0.803590	−	2.47320i
$303$	1.41297	−	4.34866i	0.0811728	−	0.249824i
$304$	−12.0841	+	8.77958i	−0.693068	+	0.503543i
$305$	2.59898	+	1.88827i	0.148817	+	0.108122i
$306$	−1.74219	−	5.36190i	−0.0995943	−	0.306520i
$307$	−10.2952			−0.587580			−0.293790	−	0.955870i	$-0.594917\pi$
$307$	−10.2952			−0.587580			−0.293790	+	0.955870i	$0.594917\pi$
$308$		0			0
$309$	−6.66414			−0.379110
$310$	3.70072	+	11.3896i	0.210187	+	0.646888i
$311$	15.4944	+	11.2573i	0.878606	+	0.638345i	0.932882	−	0.360181i	$-0.117285\pi$
$311$	15.4944	+	11.2573i	0.878606	+	0.638345i	−0.0542760	+	0.998526i	$0.517285\pi$
$312$	55.1976	−	40.1034i	3.12495	−	2.27041i
$313$	−4.62713	+	14.2408i	−0.261541	+	0.804939i	0.730930	+	0.682453i	$0.239087\pi$
$313$	−4.62713	+	14.2408i	−0.261541	+	0.804939i	−0.992470	+	0.122486i	$0.960913\pi$
$314$	16.9438	−	52.1477i	0.956195	−	2.94286i
$315$	2.55731	−	1.85799i	0.144088	−	0.104686i
$316$	−59.8150	−	43.4581i	−3.36486	−	2.44471i
$317$	3.76334	+	11.5824i	0.211370	+	0.650531i	0.999391	+	0.0348827i	$0.0111057\pi$
$317$	3.76334	+	11.5824i	0.211370	+	0.650531i	−0.788021	+	0.615648i	$0.788894\pi$
$318$	−50.2519			−2.81799
$319$		0			0
$320$	9.56424			0.534657
$321$	−2.92532	−	9.00320i	−0.163275	−	0.502510i
$322$	28.9886	+	21.0614i	1.61547	+	1.17371i
$323$	2.13620	−	1.55204i	0.118862	−	0.0863580i
$324$	−5.93859	+	18.2771i	−0.329922	+	1.01539i
$325$	2.07910	−	6.39883i	0.115328	−	0.354943i
$326$	20.0712	−	14.5826i	1.11164	−	0.807654i
$327$	−11.5378	−	8.38270i	−0.638042	−	0.463565i
$328$	12.8614	+	39.5834i	0.710154	+	2.18563i
$329$	17.4750			0.963430
$330$		0			0
$331$	−15.8319			−0.870199			−0.435099	−	0.900382i	$-0.643287\pi$
$331$	−15.8319			−0.870199			−0.435099	+	0.900382i	$0.643287\pi$
$332$	−11.0703	−	34.0710i	−0.607563	−	1.86989i
$333$	−0.662520	−	0.481349i	−0.0363059	−	0.0263778i
$334$	20.0576	−	14.5727i	1.09751	−	0.797385i
$335$	1.44006	−	4.43204i	0.0786787	−	0.242148i
$336$	10.9607	−	33.7337i	0.597958	−	1.84033i
$337$	5.44317	−	3.95469i	0.296508	−	0.215426i	−0.429578	−	0.903030i	$-0.641338\pi$
$337$	5.44317	−	3.95469i	0.296508	−	0.215426i	0.726086	+	0.687604i	$0.241338\pi$
$338$	68.4953	+	49.7647i	3.72565	+	2.70684i
$339$	−5.70097	−	17.5458i	−0.309634	−	0.952956i
$340$	−8.71176			−0.472462
$341$		0			0
$342$	4.67975			0.253052
$343$	−5.76932	−	17.7561i	−0.311514	−	0.958741i
$344$	−23.2746	−	16.9100i	−1.25488	−	0.911725i
$345$	−5.64184	+	4.09904i	−0.303746	+	0.220685i
$346$	−7.36446	+	22.6655i	−0.395916	+	1.21850i
$347$	−10.3532	+	31.8638i	−0.555788	+	1.71054i	0.138066	+	0.990423i	$0.455912\pi$
$347$	−10.3532	+	31.8638i	−0.555788	+	1.71054i	−0.693853	+	0.720116i	$0.744088\pi$
$348$	6.23381	−	4.52913i	0.334167	−	0.242787i
$349$	18.4247	+	13.3863i	0.986252	+	0.716554i	0.959097	−	0.283077i	$-0.0913552\pi$
$349$	18.4247	+	13.3863i	0.986252	+	0.716554i	0.0271551	+	0.999631i	$0.491355\pi$
$350$	−2.12742	−	6.54753i	−0.113716	−	0.349980i
$351$	−37.9050			−2.02322
$352$		0			0
$353$	−15.4617			−0.822942			−0.411471	−	0.911423i	$-0.634985\pi$
$353$	−15.4617			−0.822942			−0.411471	+	0.911423i	$0.634985\pi$
$354$	4.22004	+	12.9879i	0.224292	+	0.690301i
$355$	−3.14261	−	2.28324i	−0.166793	−	0.121182i
$356$	−13.6281	+	9.90137i	−0.722286	+	0.524772i
$357$	−1.93763	+	5.96340i	−0.102550	+	0.315617i
$358$	11.1640	−	34.3592i	0.590035	−	1.81594i
$359$	7.75526	−	5.63453i	0.409307	−	0.297379i	−0.364014	−	0.931393i	$-0.618594\pi$
$359$	7.75526	−	5.63453i	0.409307	−	0.297379i	0.773321	+	0.634014i	$0.218594\pi$
$360$	−7.37651	−	5.35935i	−0.388776	−	0.282463i
$361$	−5.19403	−	15.9856i	−0.273370	−	0.841346i
$362$	62.5998			3.29017
$363$		0			0
$364$	86.2280			4.51957
$365$	1.10230	+	3.39253i	0.0576970	+	0.177573i
$366$	−9.13699	−	6.63841i	−0.477598	−	0.346995i
$367$	8.76857	−	6.37074i	0.457716	−	0.332550i	−0.334919	−	0.942247i	$-0.608709\pi$
$367$	8.76857	−	6.37074i	0.457716	−	0.332550i	0.792635	+	0.609697i	$0.208709\pi$
$368$	16.2270	−	49.9415i	0.845890	−	2.60338i
$369$	2.04727	−	6.30085i	0.106577	−	0.328009i
$370$	−1.44293	+	1.04835i	−0.0750143	+	0.0545011i
$371$	−30.3421	−	22.0448i	−1.57528	−	1.14451i
$372$	−9.23069	−	28.4091i	−0.478589	−	1.47295i
$373$	10.0212			0.518878			0.259439	−	0.965759i	$-0.416462\pi$
$373$	10.0212			0.518878			0.259439	+	0.965759i	$0.416462\pi$
$374$		0			0
$375$	1.33988			0.0691909
$376$	−15.5764	−	47.9394i	−0.803294	−	2.47228i
$377$	6.40861	+	4.65613i	0.330060	+	0.239803i
$378$	−31.3785	+	22.7978i	−1.61394	+	1.17259i
$379$	1.29533	−	3.98661i	0.0665366	−	0.204778i	−0.912261	−	0.409610i	$-0.865665\pi$
$379$	1.29533	−	3.98661i	0.0665366	−	0.204778i	0.978797	+	0.204832i	$0.0656647\pi$
$380$	2.23459	−	6.87737i	0.114632	−	0.352802i
$381$	−13.3470	+	9.69713i	−0.683785	+	0.496799i
$382$	34.0971	+	24.7730i	1.74456	+	1.26750i
$383$	5.94672	+	18.3021i	0.303863	+	0.935195i	0.980099	+	0.198510i	$0.0636101\pi$
$383$	5.94672	+	18.3021i	0.303863	+	0.935195i	−0.676236	+	0.736685i	$0.736390\pi$
$384$	−3.24753			−0.165725
$385$		0			0
$386$	56.3042			2.86581
$387$	1.41512	+	4.35528i	0.0719345	+	0.221392i
$388$	−5.82875	−	4.23483i	−0.295910	−	0.214991i
$389$	22.9942	−	16.7063i	1.16585	−	0.847042i	0.175347	−	0.984507i	$-0.443895\pi$
$389$	22.9942	−	16.7063i	1.16585	−	0.847042i	0.990507	+	0.137465i	$0.0438954\pi$
$390$	−7.30932	+	22.4958i	−0.370122	+	1.13912i
$391$	−2.86859	+	8.82860i	−0.145071	+	0.446481i
$392$	−0.707302	+	0.513885i	−0.0357241	+	0.0259551i
$393$	21.1487	+	15.3654i	1.06681	+	0.775084i
$394$	7.47154	+	22.9951i	0.376411	+	1.15847i
$395$	15.1368			0.761615
$396$		0			0
$397$	−22.1784			−1.11310			−0.556552	−	0.830813i	$-0.687876\pi$
$397$	−22.1784			−1.11310			−0.556552	+	0.830813i	$0.687876\pi$
$398$	13.3686	+	41.1443i	0.670107	+	2.06238i
$399$	−4.21071	−	3.05926i	−0.210799	−	0.153155i
$400$	−8.16235	+	5.93029i	−0.408117	+	0.296515i
$401$	6.82182	−	20.9954i	0.340665	−	1.04846i	−0.623198	−	0.782064i	$-0.714167\pi$
$401$	6.82182	−	20.9954i	0.340665	−	1.04846i	0.963864	−	0.266396i	$-0.0858330\pi$
$402$	−5.06268	+	15.5813i	−0.252503	+	0.777126i
$403$	24.8439	−	18.0502i	1.23756	−	0.899142i
$404$	−13.4853	−	9.79765i	−0.670919	−	0.487451i
$405$	−1.21581	−	3.74187i	−0.0604140	−	0.185935i
$406$	8.10557			0.402273
$407$		0			0
$408$	18.0866			0.895418
$409$	−7.62386	−	23.4638i	−0.376975	−	1.16021i	−0.942136	−	0.335230i	$-0.891186\pi$
$409$	−7.62386	−	23.4638i	−0.376975	−	1.16021i	0.565161	−	0.824981i	$-0.308814\pi$
$410$	−11.6734	−	8.48121i	−0.576507	−	0.418857i
$411$	9.28349	−	6.74485i	0.457921	−	0.332699i
$412$	−7.50724	+	23.1049i	−0.369855	+	1.13830i
$413$	−3.14957	+	9.69338i	−0.154980	+	0.476980i
$414$	−13.3101	+	9.67035i	−0.654156	+	0.475272i
$415$	5.93358	+	4.31100i	0.291268	+	0.211619i
$416$	−23.5679	−	72.5345i	−1.15551	−	3.55629i
$417$	−2.65783			−0.130155
$418$		0			0
$419$	17.6535			0.862428			0.431214	−	0.902250i	$-0.358085\pi$
$419$	17.6535			0.862428			0.431214	+	0.902250i	$0.358085\pi$
$420$	5.30642	+	16.3315i	0.258927	+	0.796895i
$421$	−1.23373	−	0.896358i	−0.0601284	−	0.0436858i	0.557315	−	0.830301i	$-0.311832\pi$
$421$	−1.23373	−	0.896358i	−0.0601284	−	0.0436858i	−0.617443	+	0.786615i	$0.711832\pi$
$422$	−31.4878	+	22.8772i	−1.53280	+	1.11365i
$423$	−2.47944	+	7.63094i	−0.120555	+	0.371029i
$424$	−33.4301	+	102.887i	−1.62351	+	4.99665i
$425$	1.44293	−	1.04835i	0.0699923	−	0.0508524i
$426$	11.0482	+	8.02699i	0.535287	+	0.388909i
$427$	−2.60473	−	8.01654i	−0.126052	−	0.387948i
$428$	−34.5099			−1.66810
$429$		0			0
$430$	9.97370			0.480974
$431$	5.17583	+	15.9296i	0.249311	+	0.767300i	0.994897	+	0.100891i	$0.0321694\pi$
$431$	5.17583	+	15.9296i	0.249311	+	0.767300i	−0.745587	+	0.666409i	$0.767831\pi$
$432$	45.9852	+	33.4102i	2.21246	+	1.60745i
$433$	−6.04742	+	4.39371i	−0.290621	+	0.211148i	−0.723537	−	0.690286i	$-0.757485\pi$
$433$	−6.04742	+	4.39371i	−0.290621	+	0.211148i	0.432916	+	0.901434i	$0.357485\pi$
$434$	9.71006	−	29.8845i	0.466098	−	1.43450i
$435$	−0.487483	+	1.50032i	−0.0233730	+	0.0719348i
$436$	−42.0607	+	30.5589i	−2.01434	+	1.46351i
$437$	−6.23381	−	4.52913i	−0.298204	−	0.216658i
$438$	−3.87525	−	11.9268i	−0.185167	−	0.569885i
$439$	−17.4585			−0.833250			−0.416625	−	0.909078i	$-0.636787\pi$
$439$	−17.4585			−0.833250			−0.416625	+	0.909078i	$0.636787\pi$
$440$		0			0
$441$	0.139166			0.00662695
$442$	9.72970	+	29.9449i	0.462794	+	1.42433i
$443$	11.8794	+	8.63091i	0.564408	+	0.410067i	0.833070	−	0.553168i	$-0.186581\pi$
$443$	11.8794	+	8.63091i	0.564408	+	0.410067i	−0.268661	+	0.963235i	$0.586581\pi$
$444$	3.59909	−	2.61489i	0.170805	−	0.124097i
$445$	1.06571	−	3.27993i	0.0505197	−	0.155484i
$446$	−18.9752	+	58.3996i	−0.898500	+	2.76530i
$447$	−19.8903	+	14.4512i	−0.940781	+	0.683517i
$448$	−20.3022	−	14.7504i	−0.959190	−	0.696892i
$449$	−0.403974	−	1.24330i	−0.0190647	−	0.0586752i	0.941072	−	0.338208i	$-0.109821\pi$
$449$	−0.403974	−	1.24330i	−0.0190647	−	0.0586752i	−0.960136	+	0.279532i	$0.909821\pi$
$450$	3.16101			0.149011
$451$		0			0
$452$	−67.2543			−3.16338
$453$	−7.13128	−	21.9478i	−0.335057	−	1.03120i
$454$	5.56966	+	4.04660i	0.261397	+	0.189916i
$455$	−14.2819	+	10.3764i	−0.669548	+	0.486455i
$456$	−4.63926	+	14.2782i	−0.217253	+	0.668637i
$457$	−3.14957	+	9.69338i	−0.147331	+	0.453437i	−0.997303	−	0.0733895i	$-0.976618\pi$
$457$	−3.14957	+	9.69338i	−0.147331	+	0.453437i	0.849973	+	0.526827i	$0.176618\pi$
$458$	−46.7776	+	33.9859i	−2.18577	+	1.58806i
$459$	−8.12920	−	5.90621i	−0.379439	−	0.275678i
$460$	7.85596	+	24.1782i	0.366286	+	1.12731i
$461$	4.12180			0.191971			0.0959857	−	0.995383i	$-0.469400\pi$
$461$	4.12180			0.191971			0.0959857	+	0.995383i	$0.469400\pi$
$462$		0			0
$463$	32.7623			1.52259			0.761296	−	0.648404i	$-0.224563\pi$
$463$	32.7623			1.52259			0.761296	+	0.648404i	$0.224563\pi$
$464$	−3.67073	−	11.2973i	−0.170409	−	0.524465i
$465$	4.94756	+	3.59461i	0.229437	+	0.166696i
$466$	−11.3454	+	8.24289i	−0.525564	+	0.381845i
$467$	11.7162	−	36.0588i	0.542161	−	1.66860i	−0.185485	−	0.982647i	$-0.559386\pi$
$467$	11.7162	−	36.0588i	0.542161	−	1.66860i	0.727646	−	0.685953i	$-0.240614\pi$
$468$	−12.2345	+	37.6538i	−0.565538	+	1.74055i
$469$	−9.89215	+	7.18707i	−0.456777	+	0.331868i
$470$	14.1376	+	10.2716i	0.652119	+	0.473792i
$471$	−8.65248	−	26.6296i	−0.398685	−	1.22703i
$472$	29.3993			1.35321
$473$		0			0
$474$	−53.2150			−2.44425
$475$	0.457488	+	1.40800i	0.0209910	+	0.0646037i
$476$	18.4927	+	13.4357i	0.847610	+	0.615824i
$477$	13.9315	−	10.1219i	0.637882	−	0.463448i
$478$	−10.2016	+	31.3972i	−0.466609	+	1.43607i
$479$	1.99626	−	6.14386i	0.0912116	−	0.280720i	−0.895036	−	0.445993i	$-0.852851\pi$
$479$	1.99626	−	6.14386i	0.0912116	−	0.280720i	0.986248	+	0.165273i	$0.0528505\pi$
$480$	12.2876	−	8.92746i	0.560849	−	0.407481i
$481$	3.70001	+	2.68822i	0.168706	+	0.122572i
$482$	−3.47583	−	10.6975i	−0.158320	−	0.487257i
$483$	18.2978			0.832579
$484$		0			0
$485$	1.47502			0.0669774
$486$	−9.42954	−	29.0211i	−0.427732	−	1.31643i
$487$	−35.1612	−	25.5461i	−1.59331	−	1.15761i	−0.899019	−	0.437909i	$-0.855719\pi$
$487$	−35.1612	−	25.5461i	−1.59331	−	1.15761i	−0.694288	−	0.719697i	$-0.744281\pi$
$488$	−19.6701	+	14.2912i	−0.890423	+	0.646930i
$489$	3.91496	−	12.0490i	0.177040	−	0.544874i
$490$	0.0936615	−	0.288261i	0.00423120	−	0.0130223i
$491$	−4.41213	+	3.20560i	−0.199117	+	0.144667i	−0.682876	−	0.730534i	$-0.739271\pi$
$491$	−4.41213	+	3.20560i	−0.199117	+	0.144667i	0.483759	+	0.875201i	$0.339271\pi$
$492$	29.1169	+	21.1546i	1.31269	+	0.953725i
$493$	0.648906	+	1.99713i	0.0292253	+	0.0899461i
$494$	−26.1353			−1.17588
$495$		0			0
$496$	−46.0496			−2.06769
$497$	3.14957	+	9.69338i	0.141278	+	0.434808i
$498$	−20.8602	−	15.1558i	−0.934766	−	0.679147i
$499$	−10.1030	+	7.34025i	−0.452272	+	0.328595i	−0.790492	−	0.612472i	$-0.790175\pi$
$499$	−10.1030	+	7.34025i	−0.452272	+	0.328595i	0.338220	+	0.941067i	$0.390175\pi$
$500$	1.50939	−	4.64542i	0.0675019	−	0.207750i
$501$	3.91232	−	12.0409i	0.174789	−	0.537946i
$502$	21.3608	−	15.5195i	0.953378	−	0.692670i
$503$	−16.8709	−	12.2575i	−0.752238	−	0.546533i	0.144282	−	0.989537i	$-0.453913\pi$
$503$	−16.8709	−	12.2575i	−0.752238	−	0.546533i	−0.896520	+	0.443004i	$0.853913\pi$
$504$	7.39284	+	22.7528i	0.329303	+	1.01349i
$505$	3.41259			0.151858
$506$		0			0
$507$	43.2347			1.92012
$508$	18.5849	+	57.1985i	0.824572	+	2.53777i
$509$	21.5014	+	15.6217i	0.953033	+	0.692419i	0.951522	−	0.307580i	$-0.0995191\pi$
$509$	21.5014	+	15.6217i	0.953033	+	0.692419i	0.00151069	+	0.999999i	$0.499519\pi$
$510$	−5.07277	+	3.68559i	−0.224626	+	0.163201i
$511$	2.89225	−	8.90142i	0.127945	−	0.393776i
$512$	11.8511	−	36.4741i	0.523751	−	1.61194i
$513$	6.74774	−	4.90252i	0.297920	−	0.216452i
$514$	−6.71941	−	4.88194i	−0.296381	−	0.215333i
$515$	−1.53696	−	4.73027i	−0.0677264	−	0.208440i
$516$	−24.8773			−1.09516
$517$		0			0
$518$	4.67975			0.205617
$519$	3.76071	+	11.5743i	0.165077	+	0.508054i
$520$	41.1960	+	29.9307i	1.80657	+	1.31255i
$521$	18.6392	−	13.5421i	0.816596	−	0.593292i	−0.0991393	−	0.995074i	$-0.531609\pi$
$521$	18.6392	−	13.5421i	0.816596	−	0.593292i	0.915735	+	0.401782i	$0.131609\pi$
$522$	−1.15006	+	3.53952i	−0.0503367	+	0.154920i
$523$	0.365665	−	1.12540i	0.0159894	−	0.0492104i	−0.942743	−	0.333519i	$-0.891764\pi$
$523$	0.365665	−	1.12540i	0.0159894	−	0.0492104i	0.958733	+	0.284308i	$0.0917639\pi$
$524$	77.0970	−	56.0143i	3.36800	−	2.44699i
$525$	−2.84419	−	2.06642i	−0.124131	−	0.0901861i
$526$	18.1362	+	55.8176i	0.790777	+	2.43376i
$527$	8.14058			0.354609
$528$		0			0
$529$	4.08921			0.177792
$530$	−11.5896	−	35.6693i	−0.503422	−	1.54937i
$531$	−3.78600	−	2.75069i	−0.164298	−	0.119370i
$532$	−15.3500	+	11.1525i	−0.665509	+	0.483520i
$533$	−11.4335	+	35.1887i	−0.495240	+	1.52419i
$534$	−3.74663	+	11.5309i	−0.162133	+	0.498993i
$535$	5.71588	−	4.15283i	0.247119	−	0.179543i
$536$	28.5337	+	20.7310i	1.23247	+	0.895442i
$537$	−5.70097	−	17.5458i	−0.246015	−	0.757156i
$538$	−41.9123			−1.80697
$539$		0			0
$540$	−27.5183			−1.18420
$541$	9.76663	+	30.0586i	0.419900	+	1.29232i	0.907794	+	0.419417i	$0.137765\pi$
$541$	9.76663	+	30.0586i	0.419900	+	1.29232i	−0.487894	+	0.872903i	$0.662235\pi$
$542$	33.1993	+	24.1207i	1.42603	+	1.03607i
$543$	25.8619	−	18.7897i	1.10984	−	0.806345i
$544$	6.24761	−	19.2282i	0.267864	−	0.824401i
$545$	3.28914	−	10.1229i	0.140891	−	0.433619i
$546$	50.2097	−	36.4795i	2.14878	−	1.56118i
$547$	−4.02856	−	2.92692i	−0.172249	−	0.125146i	0.498321	−	0.866993i	$-0.333950\pi$
$547$	−4.02856	−	2.92692i	−0.172249	−	0.125146i	−0.670570	+	0.741847i	$0.733950\pi$
$548$	−12.9268	−	39.7845i	−0.552204	−	1.69951i
$549$	3.87021			0.165177
$550$		0			0
$551$	−1.74305			−0.0742564
$552$	−16.3098	−	50.1965i	−0.694192	−	2.13650i
$553$	−32.1312	−	23.3447i	−1.36636	−	0.992717i
$554$	−50.6982	+	36.8344i	−2.15396	+	1.56494i
$555$	−0.281448	+	0.866209i	−0.0119468	+	0.0367685i
$556$	−2.99408	+	9.21483i	−0.126977	+	0.390796i
$557$	−20.3297	+	14.7704i	−0.861399	+	0.625843i	−0.928265	−	0.371919i	$-0.878700\pi$
$557$	−20.3297	+	14.7704i	−0.861399	+	0.625843i	0.0668666	+	0.997762i	$0.478700\pi$
$558$	11.6722	+	8.48032i	0.494122	+	0.359001i
$559$	−7.90309	−	24.3232i	−0.334265	−	1.02876i
$560$	26.4724			1.11866
$561$		0			0
$562$	32.1258			1.35515
$563$	3.50289	+	10.7808i	0.147629	+	0.454356i	0.997340	−	0.0728935i	$-0.0232233\pi$
$563$	3.50289	+	10.7808i	0.147629	+	0.454356i	−0.849711	+	0.527250i	$0.823223\pi$
$564$	−35.2633	−	25.6203i	−1.48485	−	1.07881i
$565$	11.1393	−	8.09320i	0.468635	−	0.340483i
$566$	−16.9083	+	52.0384i	−0.710708	+	2.18734i
$567$	−3.19007	+	9.81803i	−0.133970	+	0.412319i
$568$	23.7845	−	17.2805i	0.997977	−	0.725073i
$569$	−9.67527	−	7.02949i	−0.405608	−	0.294692i	0.366213	−	0.930531i	$-0.380654\pi$
$569$	−9.67527	−	7.02949i	−0.405608	−	0.294692i	−0.771821	+	0.635839i	$0.780654\pi$
$570$	−1.60835	−	4.94999i	−0.0673664	−	0.207332i
$571$	29.8054			1.24732			0.623659	−	0.781697i	$-0.285645\pi$
$571$	29.8054			1.24732			0.623659	+	0.781697i	$0.285645\pi$
$572$		0			0
$573$	21.5223			0.899108
$574$	11.6992	+	36.0065i	0.488316	+	1.50288i
$575$	−4.21071	−	3.05926i	−0.175599	−	0.127580i
$576$	9.32176	−	6.77265i	0.388406	−	0.282194i
$577$	−5.71240	+	17.5810i	−0.237810	+	0.731905i	0.758926	+	0.651177i	$0.225724\pi$
$577$	−5.71240	+	17.5810i	−0.237810	+	0.731905i	−0.996736	+	0.0807279i	$0.974276\pi$
$578$	11.2045	−	34.4839i	0.466045	−	1.43434i
$579$	23.2610	−	16.9001i	0.966693	−	0.702344i
$580$	4.65252	+	3.38026i	0.193186	+	0.140357i
$581$	−5.94672	−	18.3021i	−0.246712	−	0.759300i
$582$	−5.18561			−0.214950
$583$		0			0
$584$	−26.9973			−1.11716
$585$	−2.50476	−	7.70886i	−0.103559	−	0.318722i
$586$	−30.4197	−	22.1012i	−1.25663	−	0.912993i
$587$	2.17122	−	1.57748i	0.0896157	−	0.0651097i	−0.542075	−	0.840330i	$-0.682361\pi$
$587$	2.17122	−	1.57748i	0.0896157	−	0.0651097i	0.631691	+	0.775220i	$0.282361\pi$
$588$	−0.233620	+	0.719007i	−0.00963431	+	0.0296514i
$589$	−2.08809	+	6.42647i	−0.0860381	+	0.264798i
$590$	−8.24568	+	5.99084i	−0.339469	+	0.246639i
$591$	9.98884	+	7.25731i	0.410886	+	0.298526i
$592$	−2.11929	−	6.52252i	−0.0871025	−	0.268074i
$593$	28.7251			1.17960			0.589800	−	0.807550i	$-0.299207\pi$
$593$	28.7251			1.17960			0.589800	+	0.807550i	$0.299207\pi$
$594$		0			0
$595$	−4.67975			−0.191851
$596$	27.6962	+	85.2402i	1.13448	+	3.49158i
$597$	17.8727	+	12.9853i	0.731481	+	0.531452i
$598$	74.3337	−	54.0066i	3.03973	−	2.20849i
$599$	−10.5624	+	32.5078i	−0.431569	+	1.32823i	0.464994	+	0.885314i	$0.346057\pi$
$599$	−10.5624	+	32.5078i	−0.431569	+	1.32823i	−0.896562	+	0.442918i	$0.853943\pi$
$600$	−3.13365	+	9.64440i	−0.127931	+	0.393731i
$601$	−26.2585	+	19.0779i	−1.07111	+	0.778205i	−0.976111	−	0.217273i	$-0.930284\pi$
$601$	−26.2585	+	19.0779i	−1.07111	+	0.778205i	−0.0949959	+	0.995478i	$0.530284\pi$
$602$	−21.1714	−	15.3819i	−0.862882	−	0.626920i
$603$	−1.73488	−	5.33941i	−0.0706498	−	0.217438i
$604$	−84.1276			−3.42310
$605$		0			0
$606$	−11.9973			−0.487359
$607$	−1.65161	−	5.08314i	−0.0670368	−	0.206318i	0.911927	−	0.410353i	$-0.134594\pi$
$607$	−1.65161	−	5.08314i	−0.0670368	−	0.206318i	−0.978964	+	0.204035i	$0.934594\pi$
$608$	13.5769	+	9.86417i	0.550615	+	0.400045i
$609$	3.34866	−	2.43294i	0.135694	−	0.0985877i
$610$	2.60473	−	8.01654i	0.105463	−	0.324580i
$611$	13.8471	−	42.6170i	0.560193	−	1.72410i
$612$	−8.49089	+	6.16899i	−0.343224	+	0.249367i
$613$	−24.4368	−	17.7544i	−0.986994	−	0.717093i	−0.0277333	−	0.999615i	$-0.508829\pi$
$613$	−24.4368	−	17.7544i	−0.986994	−	0.717093i	−0.959261	+	0.282522i	$0.908829\pi$
$614$	8.34746	+	25.6909i	0.336876	+	1.03680i
$615$	−7.36831			−0.297119
$616$		0			0
$617$	0.973697			0.0391996			0.0195998	−	0.999808i	$-0.493761\pi$
$617$	0.973697			0.0391996			0.0195998	+	0.999808i	$0.493761\pi$
$618$	5.40334	+	16.6298i	0.217354	+	0.668947i
$619$	−1.47368	−	1.07069i	−0.0592323	−	0.0430348i	0.557775	−	0.829992i	$-0.311655\pi$
$619$	−1.47368	−	1.07069i	−0.0592323	−	0.0430348i	−0.617007	+	0.786957i	$0.711655\pi$
$620$	18.0362	−	13.1041i	0.724350	−	0.526271i
$621$	−9.06116	+	27.8874i	−0.363612	+	1.11908i
$622$	15.5287	−	47.7924i	0.622644	−	1.91630i
$623$	−7.32068	+	5.31879i	−0.293297	+	0.213093i
$624$	−73.5824	−	53.4607i	−2.94565	−	2.14014i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	39.2884			1.57028
$627$		0			0
$628$	−102.073			−4.07316
$629$	0.374646	+	1.15304i	0.0149381	+	0.0459748i
$630$	−6.70994	−	4.87506i	−0.267330	−	0.194227i
$631$	26.1772	−	19.0189i	1.04210	−	0.757130i	0.0714054	−	0.997447i	$-0.477252\pi$
$631$	26.1772	−	19.0189i	1.04210	−	0.757130i	0.970694	+	0.240318i	$0.0772516\pi$
$632$	−35.4014	+	108.954i	−1.40819	+	4.33396i
$633$	−6.14181	+	18.9026i	−0.244115	+	0.751309i
$634$	25.8514	−	18.7822i	1.02669	−	0.745935i
$635$	−9.96133	−	7.23733i	−0.395303	−	0.287205i
$636$	28.9080	+	88.9697i	1.14628	+	3.52788i
$637$	−0.777208			−0.0307941
$638$		0			0
$639$	−4.67975			−0.185128
$640$	−0.748980	−	2.30512i	−0.0296060	−	0.0911180i
$641$	11.1393	+	8.09320i	0.439977	+	0.319662i	0.785626	−	0.618702i	$-0.212341\pi$
$641$	11.1393	+	8.09320i	0.439977	+	0.319662i	−0.345649	+	0.938364i	$0.612341\pi$
$642$	−20.0948	+	14.5997i	−0.793079	+	0.576206i
$643$	9.93832	−	30.5870i	0.391929	−	1.20623i	−0.539399	−	0.842051i	$-0.681348\pi$
$643$	9.93832	−	30.5870i	0.391929	−	1.20623i	0.931328	−	0.364183i	$-0.118652\pi$
$644$	20.6127	−	63.4394i	0.812254	−	2.49986i
$645$	4.12043	−	2.99367i	0.162242	−	0.117876i
$646$	−5.60503	−	4.07230i	−0.220527	−	0.160222i
$647$	6.02006	+	18.5278i	0.236673	+	0.728404i	0.996895	+	0.0787410i	$0.0250900\pi$
$647$	6.02006	+	18.5278i	0.236673	+	0.728404i	−0.760222	+	0.649663i	$0.774910\pi$
$648$	29.7774			1.16977
$649$		0			0
$650$	−17.6535			−0.692425
$651$	−4.95851	−	15.2607i	−0.194339	−	0.598115i
$652$	−37.3642	−	27.1467i	−1.46330	−	1.06315i
$653$	−0.630757	+	0.458272i	−0.0246834	+	0.0179336i	−0.600059	−	0.799956i	$-0.704856\pi$
$653$	−0.630757	+	0.458272i	−0.0246834	+	0.0179336i	0.575375	+	0.817890i	$0.304856\pi$
$654$	−11.5633	+	35.5883i	−0.452163	+	1.39161i
$655$	−6.02898	+	18.5553i	−0.235572	+	0.725015i
$656$	44.8868	−	32.6121i	1.75253	−	1.27329i
$657$	3.47668	+	2.52596i	0.135638	+	0.0985469i
$658$	−14.1689	−	43.6074i	−0.552361	−	1.69999i
$659$	28.1929			1.09824			0.549119	−	0.835744i	$-0.314963\pi$
$659$	28.1929			1.09824			0.549119	+	0.835744i	$0.314963\pi$
$660$		0			0
$661$	1.70340			0.0662547			0.0331274	−	0.999451i	$-0.489453\pi$
$661$	1.70340			0.0662547			0.0331274	+	0.999451i	$0.489453\pi$
$662$	12.8366	+	39.5070i	0.498909	+	1.53548i
$663$	13.0078	+	9.45072i	0.505181	+	0.367035i
$664$	−44.9077	+	32.6274i	−1.74276	+	1.26619i
$665$	1.20037	−	3.69436i	0.0465484	−	0.143261i
$666$	−0.663987	+	2.04354i	−0.0257290	+	0.0791856i
$667$	4.95756	−	3.60188i	0.191958	−	0.139465i
$668$	−37.3390	−	27.1284i	−1.44469	−	1.04963i
$669$	9.68980	+	29.8221i	0.374629	+	1.15299i
$670$	−12.2274			−0.472385
$671$		0			0
$672$	−39.8515			−1.53731
$673$	−3.40056	−	10.4658i	−0.131082	−	0.403429i	0.863878	−	0.503701i	$-0.168029\pi$
$673$	−3.40056	−	10.4658i	−0.131082	−	0.403429i	−0.994960	+	0.100272i	$0.968029\pi$
$674$	−14.2819	−	10.3764i	−0.550120	−	0.399685i
$675$	4.55786	−	3.31148i	0.175432	−	0.127459i
$676$	48.7044	−	149.897i	1.87325	−	5.76526i
$677$	6.61012	−	20.3439i	0.254048	−	0.781878i	−0.739968	−	0.672642i	$-0.765160\pi$
$677$	6.61012	−	20.3439i	0.254048	−	0.781878i	0.994016	−	0.109236i	$-0.0348405\pi$
$678$	−39.1615	+	28.4525i	−1.50399	+	1.09271i
$679$	−3.13107	−	2.27485i	−0.120159	−	0.0873009i
$680$	4.17132	+	12.8380i	0.159963	+	0.492315i
$681$	3.51561			0.134718
$682$		0			0
$683$	34.0959			1.30464			0.652321	−	0.757942i	$-0.273795\pi$
$683$	34.0959			1.30464			0.652321	+	0.757942i	$0.273795\pi$
$684$	−2.69208	−	8.28538i	−0.102934	−	0.316799i
$685$	6.92861	+	5.03393i	0.264729	+	0.192337i
$686$	−39.6310	+	28.7936i	−1.51312	+	1.09935i
$687$	−9.12414	+	28.0812i	−0.348108	+	1.07137i
$688$	−11.8511	+	36.4741i	−0.451821	+	1.39056i
$689$	−77.8043	+	56.5281i	−2.96411	+	2.15355i
$690$	14.8032	+	10.7552i	0.563549	+	0.409443i
$691$	14.3136	+	44.0528i	0.544516	+	1.67585i	0.722138	+	0.691749i	$0.243160\pi$
$691$	14.3136	+	44.0528i	0.544516	+	1.67585i	−0.177622	+	0.984099i	$0.556840\pi$
$692$	44.3651			1.68651
$693$		0			0
$694$	87.9077			3.33693
$695$	−0.612978	−	1.88655i	−0.0232516	−	0.0715610i
$696$	−9.65914	−	7.01778i	−0.366129	−	0.266008i
$697$	−7.93502	+	5.76513i	−0.300560	+	0.218370i
$698$	18.4655	−	56.8310i	0.698930	−	2.15108i
$699$	−2.21296	+	6.81078i	−0.0837017	+	0.257607i
$700$	−10.3684	+	7.53309i	−0.391889	+	0.284724i
$701$	35.0828	+	25.4891i	1.32506	+	0.962711i	0.999854	+	0.0170666i	$0.00543272\pi$
$701$	35.0828	+	25.4891i	1.32506	+	0.962711i	0.325203	+	0.945644i	$0.394567\pi$
$702$	30.7337	+	94.5886i	1.15997	+	3.57002i
$703$	−1.00635			−0.0379552
$704$		0			0
$705$	8.92375			0.336088
$706$	12.5365	+	38.5832i	0.471816	+	1.45210i
$707$	−7.24399	−	5.26307i	−0.272438	−	0.197938i
$708$	20.5672	−	14.9429i	0.772962	−	0.561589i
$709$	5.92646	−	18.2398i	0.222573	−	0.685009i	−0.775956	−	0.630787i	$-0.782732\pi$
$709$	5.92646	−	18.2398i	0.222573	−	0.685009i	0.998529	−	0.0542219i	$-0.0172678\pi$
$710$	−3.14957	+	9.69338i	−0.118201	+	0.363786i
$711$	14.7530	−	10.7187i	0.553282	−	0.401983i
$712$	21.1164	+	15.3419i	0.791370	+	0.574964i
$713$	−7.34089	−	22.5929i	−0.274919	−	0.846112i
$714$	16.4522			0.615708
$715$		0			0
$716$	−67.2543			−2.51341
$717$	5.20950	+	16.0332i	0.194552	+	0.598771i
$718$	−20.3485	−	14.7840i	−0.759399	−	0.551736i
$719$	26.1263	−	18.9819i	0.974348	−	0.707906i	0.0179100	−	0.999840i	$-0.494299\pi$
$719$	26.1263	−	18.9819i	0.974348	−	0.707906i	0.956438	+	0.291934i	$0.0942988\pi$
$720$	−3.75603	+	11.5599i	−0.139979	+	0.430811i
$721$	−4.03271	+	12.4114i	−0.150186	+	0.462225i
$722$	−35.6792	+	25.9225i	−1.32784	+	0.964734i
$723$	−4.64689	−	3.37616i	−0.172820	−	0.125561i
$724$	−36.0113	−	110.831i	−1.33835	−	4.11901i
$725$	−1.17737			−0.0437264
$726$		0			0
$727$	−40.8622			−1.51550			−0.757748	−	0.652548i	$-0.773700\pi$
$727$	−40.8622			−1.51550			−0.757748	+	0.652548i	$0.773700\pi$
$728$	−41.2872	−	127.069i	−1.53021	−	4.70949i
$729$	−22.1556	−	16.0970i	−0.820577	−	0.596184i
$730$	7.57200	−	5.50138i	0.280252	−	0.203615i
$731$	2.09503	−	6.44784i	0.0774875	−	0.238482i
$732$	−6.49697	+	19.9956i	−0.240135	+	0.739059i
$733$	−8.02880	+	5.83326i	−0.296550	+	0.215457i	−0.726104	−	0.687585i	$-0.758671\pi$
$733$	−8.02880	+	5.83326i	−0.296550	+	0.215457i	0.429554	+	0.903041i	$0.358671\pi$
$734$	−23.0072	−	16.7157i	−0.849213	−	0.616989i
$735$	−0.0478289	−	0.147202i	−0.00176420	−	0.00542964i
$736$	−58.9987			−2.17472
$737$		0			0
$738$	−17.3832			−0.639883
$739$	−10.3127	−	31.7392i	−0.379358	−	1.16754i	−0.940491	−	0.339818i	$-0.889634\pi$
$739$	−10.3127	−	31.7392i	−0.379358	−	1.16754i	0.561133	−	0.827726i	$-0.310366\pi$
$740$	2.68614	+	1.95159i	0.0987443	+	0.0717419i
$741$	−10.7973	+	7.84468i	−0.396648	+	0.288181i
$742$	−30.4093	+	93.5901i	−1.11636	+	3.43580i
$743$	−1.17647	+	3.62081i	−0.0431606	+	0.132835i	−0.970315	−	0.241845i	$-0.922247\pi$
$743$	−1.17647	+	3.62081i	−0.0431606	+	0.132835i	0.927154	+	0.374680i	$0.122247\pi$
$744$	−37.4451	+	27.2054i	−1.37280	+	0.997399i
$745$	−14.8449	−	10.7855i	−0.543875	−	0.395148i
$746$	−8.12528	−	25.0070i	−0.297487	−	0.915572i
$747$	8.83587			0.323287
$748$		0			0
$749$	−18.5379			−0.677361
$750$	−1.08638	−	3.34354i	−0.0396691	−	0.122089i
$751$	−18.2105	−	13.2307i	−0.664509	−	0.482794i	0.203674	−	0.979039i	$-0.434712\pi$
$751$	−18.2105	−	13.2307i	−0.664509	−	0.482794i	−0.868183	+	0.496245i	$0.834712\pi$
$752$	−54.3622	+	39.4965i	−1.98239	+	1.44029i
$753$	4.16650	−	12.8232i	0.151836	−	0.467302i
$754$	6.42280	−	19.7673i	0.233904	−	0.719884i
$755$	13.9341	−	10.1237i	0.507112	−	0.368439i
$756$	58.4137	+	42.4401i	2.12449	+	1.54353i
$757$	−10.4116	−	32.0437i	−0.378417	−	1.16465i	−0.941144	−	0.338005i	$-0.890248\pi$
$757$	−10.4116	−	32.0437i	−0.378417	−	1.16465i	0.562728	−	0.826642i	$-0.309752\pi$
$758$	−10.9985			−0.399483
$759$		0			0
$760$	−11.2047			−0.406438
$761$	−5.80084	−	17.8531i	−0.210280	−	0.647176i	−0.999455	−	0.0330075i	$-0.989491\pi$
$761$	−5.80084	−	17.8531i	−0.210280	−	0.647176i	0.789175	−	0.614169i	$-0.210509\pi$
$762$	35.0201	+	25.4436i	1.26865	+	0.921725i
$763$	−22.5940	+	16.4155i	−0.817959	+	0.594282i
$764$	24.2452	−	74.6190i	0.877160	−	2.69962i
$765$	0.663987	−	2.04354i	0.0240065	−	0.0738844i
$766$	40.8497	−	29.6790i	1.47596	−	1.07235i
$767$	21.1439	+	15.3619i	0.763462	+	0.554687i
$768$	−5.28692	−	16.2715i	−0.190775	−	0.587146i
$769$	21.5618			0.777539			0.388770	−	0.921335i	$-0.372900\pi$
$769$	21.5618			0.777539			0.388770	+	0.921335i	$0.372900\pi$
$770$		0			0
$771$	−4.24134			−0.152748
$772$	−32.3897	−	99.6852i	−1.16573	−	3.58775i
$773$	18.9174	+	13.7443i	0.680411	+	0.494347i	0.873494	−	0.486835i	$-0.161849\pi$
$773$	18.9174	+	13.7443i	0.680411	+	0.494347i	−0.193083	+	0.981182i	$0.561849\pi$
$774$	9.72083	−	7.06260i	0.349408	−	0.253860i
$775$	−1.41043	+	4.34085i	−0.0506640	+	0.155928i
$776$	−3.44973	+	10.6172i	−0.123838	+	0.381135i
$777$	1.93335	−	1.40466i	0.0693584	−	0.0503919i
$778$	−60.3329	−	43.8344i	−2.16304	−	1.57154i
$779$	−2.51584	−	7.74296i	−0.0901394	−	0.277420i
$780$	44.0329			1.57663
$781$		0			0
$782$	24.3569			0.870999
$783$	2.04973	+	6.30843i	0.0732515	+	0.225445i
$784$	0.942884	+	0.685045i	0.0336744	+	0.0244659i
$785$	16.9064	−	12.2832i	0.603415	−	0.438407i
$786$	21.1955	−	65.2331i	0.756019	−	2.32679i
$787$	−7.75476	+	23.8667i	−0.276427	+	0.850756i	0.712411	+	0.701763i	$0.247603\pi$
$787$	−7.75476	+	23.8667i	−0.276427	+	0.850756i	−0.988838	+	0.148993i	$0.952397\pi$
$788$	36.4140	−	26.4563i	1.29720	−	0.942468i
$789$	24.2466	+	17.6162i	0.863203	+	0.627154i
$790$	−12.2730	−	37.7725i	−0.436655	−	1.34389i
$791$	−36.1274			−1.28454
$792$		0			0
$793$	−21.6142			−0.767542
$794$	17.9824	+	55.3443i	0.638173	+	1.96410i
$795$	−15.4944	−	11.2573i	−0.549530	−	0.399257i
$796$	65.1544	−	47.3375i	2.30934	−	1.67783i
$797$	−3.73177	+	11.4852i	−0.132186	+	0.406827i	−0.995142	−	0.0984529i	$-0.968611\pi$
$797$	−3.73177	+	11.4852i	−0.132186	+	0.406827i	0.862956	+	0.505280i	$0.168611\pi$
$798$	−4.22004	+	12.9879i	−0.149388	+	0.459768i
$799$	9.61008	−	6.98214i	0.339980	−	0.247010i
$800$	9.17069	+	6.66289i	0.324233	+	0.235569i
$801$	−1.28390	−	3.95143i	−0.0453643	−	0.139617i
$802$	−57.9233			−2.04534
$803$		0			0
$804$	30.4987			1.07561
$805$	4.22004	+	12.9879i	0.148737	+	0.457765i
$806$	−65.1862	−	47.3605i	−2.29609	−	1.66820i
$807$	−17.3152	+	12.5802i	−0.609525	+	0.442846i
$808$	−7.98125	+	24.5638i	−0.280779	+	0.864150i
$809$	−2.81574	+	8.66595i	−0.0989961	+	0.304679i	−0.988275	−	0.152688i	$-0.951207\pi$
$809$	−2.81574	+	8.66595i	−0.0989961	+	0.304679i	0.889278	+	0.457366i	$0.151207\pi$
$810$	−8.35172	+	6.06788i	−0.293449	+	0.213204i
$811$	2.41895	+	1.75747i	0.0849409	+	0.0617132i	0.629445	−	0.777045i	$-0.283282\pi$
$811$	2.41895	+	1.75747i	0.0849409	+	0.0617132i	−0.544504	+	0.838758i	$0.683282\pi$
$812$	−4.66282	−	14.3507i	−0.163633	−	0.503611i
$813$	20.9556			0.734946
$814$		0			0
$815$	9.45539			0.331208
$816$	−7.45061	−	22.9306i	−0.260824	−	0.802732i
$817$	4.55277	+	3.30778i	0.159281	+	0.115725i
$818$	−52.3704	+	38.0493i	−1.83109	+	1.33036i
$819$	−6.57206	+	20.2267i	−0.229646	+	0.706779i
$820$	−8.30050	+	25.5463i	−0.289866	+	0.892116i
$821$	28.5337	−	20.7310i	0.995835	−	0.723516i	0.0346436	−	0.999400i	$-0.488970\pi$
$821$	28.5337	−	20.7310i	0.995835	−	0.723516i	0.961191	+	0.275884i	$0.0889704\pi$
$822$	−24.3583	−	17.6973i	−0.849593	−	0.617266i
$823$	4.80755	+	14.7961i	0.167581	+	0.515760i	0.999217	−	0.0395600i	$-0.0125956\pi$
$823$	4.80755	+	14.7961i	0.167581	+	0.515760i	−0.831636	+	0.555320i	$0.812596\pi$
$824$	37.6429			1.31135
$825$		0			0
$826$	26.7427			0.930496
$827$	3.25374	+	10.0140i	0.113144	+	0.348220i	0.991555	−	0.129684i	$-0.0413964\pi$
$827$	3.25374	+	10.0140i	0.113144	+	0.348220i	−0.878412	+	0.477905i	$0.841396\pi$
$828$	24.7779	+	18.0022i	0.861091	+	0.625619i
$829$	−20.7310	+	15.0619i	−0.720016	+	0.523122i	−0.886389	−	0.462941i	$-0.846794\pi$
$829$	−20.7310	+	15.0619i	−0.720016	+	0.523122i	0.166373	+	0.986063i	$0.446794\pi$
$830$	5.94672	−	18.3021i	0.206414	−	0.635276i
$831$	−9.88886	+	30.4348i	−0.343041	+	1.05577i
$832$	−52.0597	+	37.8236i	−1.80485	+	1.31130i
$833$	−0.166682	−	0.121101i	−0.00577518	−	0.00419592i
$834$	2.15499	+	6.63238i	0.0746212	+	0.229661i
$835$	9.44902			0.326997
$836$		0			0
$837$	25.7141			0.888809
$838$	−14.3136	−	44.0526i	−0.494454	−	1.52177i
$839$	−21.1362	−	15.3564i	−0.729704	−	0.530161i	0.159766	−	0.987155i	$-0.448926\pi$
$839$	−21.1362	−	15.3564i	−0.729704	−	0.530161i	−0.889470	+	0.456994i	$0.848926\pi$
$840$	21.5259	−	15.6395i	0.742715	−	0.539614i
$841$	−8.53313	+	26.2623i	−0.294246	+	0.905596i
$842$	−1.23646	+	3.80544i	−0.0426113	+	0.131144i
$843$	13.2721	−	9.64278i	0.457117	−	0.332115i
$844$	58.6173	+	42.5879i	2.01769	+	1.46594i
$845$	9.97125	+	30.6884i	0.343021	+	1.05571i
$846$	21.0527			0.723806
$847$		0			0
$848$	144.215			4.95235
$849$	8.63433	+	26.5737i	0.296330	+	0.912009i
$850$	−3.78600	−	2.75069i	−0.129859	−	0.0943479i
$851$	2.86225	−	2.07955i	0.0981166	−	0.0712859i
$852$	7.85596	−	24.1782i	0.269141	−	0.828330i
$853$	−0.851310	+	2.62006i	−0.0291483	+	0.0897092i	−0.964572	−	0.263819i	$-0.915018\pi$
$853$	−0.851310	+	2.62006i	−0.0291483	+	0.0897092i	0.935424	+	0.353528i	$0.115018\pi$
$854$	−17.8926	+	12.9998i	−0.612273	+	0.444842i
$855$	1.44293	+	1.04835i	0.0493471	+	0.0358528i
$856$	16.5239	+	50.8552i	0.564774	+	1.73820i
$857$	−20.3164			−0.693997			−0.346998	−	0.937866i	$-0.612799\pi$
$857$	−20.3164			−0.693997			−0.346998	+	0.937866i	$0.612799\pi$
$858$		0			0
$859$	22.6249			0.771951			0.385975	−	0.922509i	$-0.373865\pi$
$859$	22.6249			0.771951			0.385975	+	0.922509i	$0.373865\pi$
$860$	−5.73748	−	17.6582i	−0.195647	−	0.602138i
$861$	15.6409	+	11.3638i	0.533040	+	0.387276i
$862$	35.5542	−	25.8316i	1.21098	−	0.879829i
$863$	13.3214	−	40.9989i	0.453465	−	1.39562i	−0.419464	−	0.907772i	$-0.637782\pi$
$863$	13.3214	−	40.9989i	0.453465	−	1.39562i	0.872928	−	0.487848i	$-0.162218\pi$
$864$	19.7347	−	60.7370i	0.671387	−	2.06632i
$865$	−7.34819	+	5.33877i	−0.249846	+	0.181524i
$866$	15.8674	+	11.5283i	0.539196	+	0.391749i
$867$	−5.72165	−	17.6094i	−0.194317	−	0.598048i
$868$	−58.4955			−1.98547
$869$		0			0
$870$	4.13917			0.140331
$871$	9.68888	+	29.8193i	0.328295	+	1.01039i
$872$	65.1721	+	47.3503i	2.20701	+	1.60348i
$873$	1.43763	−	1.04450i	0.0486563	−	0.0353509i
$874$	−6.24761	+	19.2282i	−0.211329	+	0.650402i
$875$	0.810808	−	2.49541i	0.0274103	−	0.0843603i
$876$	−18.8868	+	13.7221i	−0.638126	+	0.463626i
$877$	−13.4987	−	9.80735i	−0.455817	−	0.331171i	0.336071	−	0.941837i	$-0.390902\pi$
$877$	−13.4987	−	9.80735i	−0.455817	−	0.331171i	−0.791888	+	0.610666i	$0.790902\pi$
$878$	14.1555	+	43.5662i	0.477726	+	1.47029i
$879$	−19.2011			−0.647638
$880$		0			0
$881$	−43.5116			−1.46594			−0.732972	−	0.680259i	$-0.761867\pi$
$881$	−43.5116			−1.46594			−0.732972	+	0.680259i	$0.761867\pi$
$882$	−0.112837	−	0.347276i	−0.00379941	−	0.0116934i
$883$	21.8431	+	15.8700i	0.735080	+	0.534067i	0.891167	−	0.453676i	$-0.149888\pi$
$883$	21.8431	+	15.8700i	0.735080	+	0.534067i	−0.156086	+	0.987743i	$0.549888\pi$
$884$	47.4196	−	34.4523i	1.59489	−	1.15876i
$885$	−1.60835	+	4.94999i	−0.0540641	+	0.166392i
$886$	11.9057	−	36.6420i	0.399981	−	1.23101i
$887$	−18.5591	+	13.4840i	−0.623153	+	0.452747i	−0.854021	−	0.520238i	$-0.825843\pi$
$887$	−18.5591	+	13.4840i	−0.623153	+	0.452747i	0.230869	+	0.972985i	$0.425843\pi$
$888$	−5.57671	−	4.05172i	−0.187142	−	0.135967i
$889$	9.98338	+	30.7257i	0.334832	+	1.03051i
$890$	−9.04886			−0.303318
$891$		0			0
$892$	114.311			3.82740
$893$	3.04693	+	9.37748i	0.101962	+	0.313805i
$894$	52.1889	+	37.9174i	1.74546	+	1.26815i
$895$	11.1393	−	8.09320i	0.372347	−	0.270526i
$896$	−1.96520	+	6.04825i	−0.0656526	+	0.202058i
$897$	14.4990	−	44.6235i	0.484109	−	1.48993i
$898$	−2.77501	+	2.01616i	−0.0926033	+	0.0672802i
$899$	−4.34749	−	3.15863i	−0.144997	−	0.105346i
$900$	−1.81841	−	5.59648i	−0.0606135	−	0.186549i
$901$	−25.4941			−0.849331
$902$		0			0
$903$	−13.3635			−0.444710
$904$	32.2023	+	99.1086i	1.07103	+	3.29630i
$905$	19.3017	+	14.0235i	0.641609	+	0.466156i
$906$	−48.9867	+	35.5909i	−1.62747	+	1.18243i
$907$	12.8964	−	39.6911i	0.428219	−	1.31792i	−0.471659	−	0.881781i	$-0.656345\pi$
$907$	12.8964	−	39.6911i	0.428219	−	1.31792i	0.899878	−	0.436141i	$-0.143655\pi$
$908$	3.96038	−	12.1888i	0.131430	−	0.404499i
$909$	3.32607	−	2.41653i	0.110319	−	0.0801514i
$910$	37.4734	+	27.2260i	1.24223	+	0.902533i
$911$	−11.9673	−	36.8316i	−0.396495	−	1.22029i	−0.927791	−	0.373100i	$-0.878295\pi$
$911$	−11.9673	−	36.8316i	−0.396495	−	1.22029i	0.531296	−	0.847186i	$-0.321705\pi$
$912$	20.0134			0.662708
$913$		0			0
$914$	26.7427			0.884569
$915$	−1.33012	−	4.09370i	−0.0439726	−	0.135334i
$916$	87.0805	+	63.2677i	2.87722	+	2.09042i
$917$	41.4147	−	30.0895i	1.36763	−	0.993644i
$918$	−8.14720	+	25.0745i	−0.268898	+	0.827582i
$919$	0.881305	−	2.71238i	0.0290716	−	0.0894730i	−0.935468	−	0.353411i	$-0.885022\pi$
$919$	0.881305	−	2.71238i	0.0290716	−	0.0894730i	0.964540	+	0.263938i	$0.0850216\pi$
$920$	31.8684	−	23.1537i	1.05067	−	0.763355i
$921$	11.1599	+	8.10812i	0.367730	+	0.267172i
$922$	−3.34199	−	10.2856i	−0.110063	−	0.338738i
$923$	26.1353			0.860253
$924$		0			0
$925$	−0.679754			−0.0223502
$926$	−26.5639	−	81.7554i	−0.872945	−	2.68665i
$927$	−4.84760	−	3.52199i	−0.159216	−	0.115677i
$928$	−10.7973	+	7.84468i	−0.354438	+	0.257514i
$929$	−4.08779	+	12.5809i	−0.134116	+	0.412767i	−0.995451	−	0.0952697i	$-0.969629\pi$
$929$	−4.08779	+	12.5809i	−0.134116	+	0.412767i	0.861335	+	0.508037i	$0.169629\pi$
$930$	4.95851	−	15.2607i	0.162596	−	0.500419i
$931$	0.138356	−	0.100522i	0.00453444	−	0.00329446i
$932$	21.1204	+	15.3449i	0.691821	+	0.502637i
$933$	−7.92984	−	24.4055i	−0.259611	−	0.799001i
$934$	−99.4810			−3.25512
$935$		0			0
$936$	61.3462			2.00516
$937$	−0.519316	−	1.59829i	−0.0169653	−	0.0522139i	0.942215	−	0.335008i	$-0.108739\pi$
$937$	−0.519316	−	1.59829i	−0.0169653	−	0.0522139i	−0.959181	+	0.282794i	$0.908739\pi$
$938$	25.9553	+	18.8576i	0.847471	+	0.615724i
$939$	16.2312	−	11.7927i	0.529686	−	0.384840i
$940$	10.0527	−	30.9391i	0.327883	−	1.00912i
$941$	4.53795	−	13.9664i	0.147933	−	0.455291i	−0.849443	−	0.527680i	$-0.823062\pi$
$941$	4.53795	−	13.9664i	0.147933	−	0.455291i	0.997377	+	0.0723886i	$0.0230622\pi$
$942$	−59.4362	+	43.1830i	−1.93654	+	1.40698i
$943$	23.1558	+	16.8236i	0.754055	+	0.547853i
$944$	−12.1108	−	37.2732i	−0.394173	−	1.21314i
$945$	−14.7822			−0.480865
$946$		0			0
$947$	17.6535			0.573660			0.286830	−	0.957981i	$-0.407399\pi$
$947$	17.6535			0.573660			0.286830	+	0.957981i	$0.407399\pi$
$948$	30.6126	+	94.2158i	0.994250	+	3.05999i
$949$	−19.4164	−	14.1068i	−0.630283	−	0.457928i
$950$	3.14261	−	2.28324i	0.101960	−	0.0740782i
$951$	5.04241	−	15.5190i	0.163511	−	0.503237i
$952$	10.9448	−	33.6847i	0.354724	−	1.09173i
$953$	17.6106	−	12.7948i	0.570462	−	0.414465i	−0.264811	−	0.964300i	$-0.585310\pi$
$953$	17.6106	−	12.7948i	0.570462	−	0.414465i	0.835273	+	0.549835i	$0.185310\pi$
$954$	−36.5540	−	26.5580i	−1.18348	−	0.859849i
$955$	4.96371	+	15.2767i	0.160622	+	0.494344i
$956$	61.4564			1.98764
$957$		0			0
$958$	−16.9500			−0.547631
$959$	−6.94395	−	21.3713i	−0.224232	−	0.690115i
$960$	−10.3675	−	7.53241i	−0.334609	−	0.243107i
$961$	8.22587	−	5.97645i	0.265351	−	0.192789i
$962$	3.70820	−	11.4127i	0.119557	−	0.367960i
$963$	2.63025	−	8.09509i	0.0847588	−	0.260861i
$964$	−16.9401	+	12.3077i	−0.545604	+	0.396405i
$965$	17.3605	+	12.6132i	0.558855	+	0.406032i
$966$	−14.8360	−	45.6605i	−0.477340	−	1.46910i
$967$	14.0684			0.452409			0.226204	−	0.974080i	$-0.427368\pi$
$967$	14.0684			0.452409			0.226204	+	0.974080i	$0.427368\pi$
$968$		0			0
$969$	−3.53793			−0.113655
$970$	−1.19596	−	3.68079i	−0.0384000	−	0.118183i
$971$	11.9187	+	8.65946i	0.382490	+	0.277895i	0.762371	−	0.647140i	$-0.224035\pi$
$971$	11.9187	+	8.65946i	0.382490	+	0.277895i	−0.379881	+	0.925035i	$0.624035\pi$
$972$	−45.9567	+	33.3895i	−1.47406	+	1.07097i
$973$	−1.60835	+	4.94999i	−0.0515613	+	0.158689i
$974$	−35.2391	+	108.455i	−1.12913	+	3.47511i
$975$	−7.29317	+	5.29880i	−0.233568	+	0.169697i
$976$	26.2216	+	19.0511i	0.839335	+	0.609812i
$977$	4.06105	+	12.4986i	0.129924	+	0.399866i	0.994766	−	0.102179i	$-0.0325813\pi$
$977$	4.06105	+	12.4986i	0.129924	+	0.399866i	−0.864842	+	0.502045i	$0.832581\pi$
$978$	−33.2415			−1.06294
$979$		0			0
$980$	−0.564237			−0.0180239
$981$	−3.96253	−	12.1954i	−0.126514	−	0.389370i
$982$	11.5767	+	8.41095i	0.369426	+	0.268404i
$983$	−14.8987	+	10.8245i	−0.475193	+	0.345248i	−0.799462	−	0.600717i	$-0.794882\pi$
$983$	−14.8987	+	10.8245i	−0.475193	+	0.345248i	0.324269	+	0.945965i	$0.394882\pi$
$984$	17.2327	−	53.0369i	0.549360	−	1.69076i
$985$	−2.84757	+	8.76393i	−0.0907312	+	0.279242i
$986$	4.45752	−	3.23857i	0.141956	−	0.103137i
$987$	−18.9426	−	13.7626i	−0.602951	−	0.438069i
$988$	15.0346	+	46.2718i	0.478315	+	1.47210i
$989$	−19.7842			−0.629101
$990$		0			0
$991$	44.3591			1.40911			0.704557	−	0.709647i	$-0.251146\pi$
$991$	44.3591			1.40911			0.704557	+	0.709647i	$0.251146\pi$
$992$	15.9880	+	49.2061i	0.507620	+	1.56229i
$993$	17.1615	+	12.4686i	0.544603	+	0.395678i
$994$	21.6353	−	15.7189i	0.686229	−	0.498575i
$995$	−5.09507	+	15.6810i	−0.161524	+	0.497121i
$996$	−14.8329	+	45.6509i	−0.469998	+	1.44650i
$997$	40.8497	−	29.6790i	1.29372	−	0.939944i	0.293848	−	0.955852i	$-0.405064\pi$
$997$	40.8497	−	29.6790i	1.29372	−	0.939944i	0.999873	+	0.0159081i	$0.00506393\pi$
$998$	26.5085	+	19.2596i	0.839113	+	0.609651i
$999$	1.18341	+	3.64218i	0.0374416	+	0.115233i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.q.511.1		24
11.2	odd	10	inner	605.2.g.q.251.6		24
11.3	even	5		605.2.a.m.1.1	✓	6
11.4	even	5	inner	605.2.g.q.366.6		24
11.5	even	5	inner	605.2.g.q.81.6		24
11.6	odd	10	inner	605.2.g.q.81.1		24
11.7	odd	10	inner	605.2.g.q.366.1		24
11.8	odd	10		605.2.a.m.1.6	yes	6
11.9	even	5	inner	605.2.g.q.251.1		24
11.10	odd	2	inner	605.2.g.q.511.6		24
33.8	even	10		5445.2.a.bx.1.1		6
33.14	odd	10		5445.2.a.bx.1.6		6
44.3	odd	10		9680.2.a.cw.1.3		6
44.19	even	10		9680.2.a.cw.1.4		6
55.14	even	10		3025.2.a.bg.1.6		6
55.19	odd	10		3025.2.a.bg.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.m.1.1	✓	6	11.3	even	5
605.2.a.m.1.6	yes	6	11.8	odd	10
605.2.g.q.81.1		24	11.6	odd	10	inner
605.2.g.q.81.6		24	11.5	even	5	inner
605.2.g.q.251.1		24	11.9	even	5	inner
605.2.g.q.251.6		24	11.2	odd	10	inner
605.2.g.q.366.1		24	11.7	odd	10	inner
605.2.g.q.366.6		24	11.4	even	5	inner
605.2.g.q.511.1		24	1.1	even	1	trivial
605.2.g.q.511.6		24	11.10	odd	2	inner
3025.2.a.bg.1.1		6	55.19	odd	10
3025.2.a.bg.1.6		6	55.14	even	10
5445.2.a.bx.1.1		6	33.8	even	10
5445.2.a.bx.1.6		6	33.14	odd	10
9680.2.a.cw.1.3		6	44.3	odd	10
9680.2.a.cw.1.4		6	44.19	even	10

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.810808 - 2.49541i) q^{2} +(-1.08398 - 0.787560i) q^{3} +(-3.95163 + 2.87103i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-1.08638 + 3.34354i) q^{6} +(-2.12272 + 1.54225i) q^{7} +(6.12296 + 4.44859i) q^{8} +(-0.372282 - 1.14577i) q^{9} +O(q^{10})\)	\(q+(-0.810808 - 2.49541i) q^{2} +(-1.08398 - 0.787560i) q^{3} +(-3.95163 + 2.87103i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-1.08638 + 3.34354i) q^{6} +(-2.12272 + 1.54225i) q^{7} +(6.12296 + 4.44859i) q^{8} +(-0.372282 - 1.14577i) q^{9} -2.62383 q^{10} +6.54461 q^{12} +(2.07910 + 6.39883i) q^{13} +(5.56966 + 4.04660i) q^{14} +(-1.08398 + 0.787560i) q^{15} +(3.11774 - 9.59541i) q^{16} +(-0.551150 + 1.69626i) q^{17} +(-2.55731 + 1.85799i) q^{18} +(-1.19772 - 0.870194i) q^{19} +(1.50939 + 4.64542i) q^{20} +3.51561 q^{21} +5.20473 q^{23} +(-3.13365 - 9.64440i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(14.2819 - 10.3764i) q^{26} +(-1.74095 + 5.35808i) q^{27} +(3.96038 - 12.1888i) q^{28} +(0.952511 - 0.692040i) q^{29} +(2.84419 + 2.06642i) q^{30} +(-1.41043 - 4.34085i) q^{31} -11.3356 q^{32} +4.67975 q^{34} +(0.810808 + 2.49541i) q^{35} +(4.76065 + 3.45881i) q^{36} +(0.549932 - 0.399549i) q^{37} +(-1.20037 + 3.69436i) q^{38} +(2.78574 - 8.57364i) q^{39} +(6.12296 - 4.44859i) q^{40} +(4.44898 + 3.23238i) q^{41} +(-2.85048 - 8.77289i) q^{42} -3.80120 q^{43} -1.20473 q^{45} +(-4.22004 - 12.9879i) q^{46} +(-5.38815 - 3.91472i) q^{47} +(-10.9365 + 7.94586i) q^{48} +(-0.0356965 + 0.109863i) q^{49} +(-0.810808 + 2.49541i) q^{50} +(1.93335 - 1.40466i) q^{51} +(-26.5871 - 19.3166i) q^{52} +(4.41707 + 13.5943i) q^{53} +14.7822 q^{54} -19.8582 q^{56} +(0.612978 + 1.88655i) q^{57} +(-2.49923 - 1.81579i) q^{58} +(3.14261 - 2.28324i) q^{59} +(2.02239 - 6.22429i) q^{60} +(-0.992721 + 3.05528i) q^{61} +(-9.68861 + 7.03919i) q^{62} +(2.55731 + 1.85799i) q^{63} +(2.95551 + 9.09613i) q^{64} +6.72812 q^{65} +4.66012 q^{67} +(-2.69208 - 8.28538i) q^{68} +(-5.64184 - 4.09904i) q^{69} +(5.56966 - 4.04660i) q^{70} +(1.20037 - 3.69436i) q^{71} +(2.81758 - 8.67161i) q^{72} +(-2.88586 + 2.09670i) q^{73} +(-1.44293 - 1.04835i) q^{74} +(0.414045 + 1.27430i) q^{75} +7.23130 q^{76} -23.6535 q^{78} +(4.67753 + 14.3959i) q^{79} +(-8.16235 - 5.93029i) q^{80} +(3.18303 - 2.31260i) q^{81} +(4.45883 - 13.7229i) q^{82} +(-2.26643 + 6.97535i) q^{83} +(-13.8924 + 10.0934i) q^{84} +(1.44293 + 1.04835i) q^{85} +(3.08204 + 9.48555i) q^{86} -1.57753 q^{87} +3.44872 q^{89} +(0.976805 + 3.00630i) q^{90} +(-14.2819 - 10.3764i) q^{91} +(-20.5672 + 14.9429i) q^{92} +(-1.88980 + 5.81620i) q^{93} +(-5.40008 + 16.6197i) q^{94} +(-1.19772 + 0.870194i) q^{95} +(12.2876 + 8.92746i) q^{96} +(0.455807 + 1.40283i) q^{97} +0.303095 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9}+O(q^{10}) \) 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9	\( 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9} + 72 q^{12} + 18 q^{14} - 6 q^{15} - 18 q^{16} - 6 q^{20} + 48 q^{23} - 6 q^{25} + 36 q^{26} - 30 q^{27} + 96 q^{34} + 12 q^{36} + 30 q^{42} + 48 q^{45} - 42 q^{47} + 6 q^{48} + 24 q^{49} - 24 q^{53} - 120 q^{56} + 24 q^{58} - 18 q^{60} - 30 q^{64} + 120 q^{67} + 24 q^{69} + 18 q^{70} - 6 q^{75} - 288 q^{78} - 18 q^{80} - 30 q^{81} - 42 q^{82} + 6 q^{86} - 120 q^{89} - 36 q^{91} - 36 q^{92} + 60 q^{93} - 24 q^{97}+O(q^{100}) \) 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9 + 72 * q^12 + 18 * q^14 - 6 * q^15 - 18 * q^16 - 6 * q^20 + 48 * q^23 - 6 * q^25 + 36 * q^26 - 30 * q^27 + 96 * q^34 + 12 * q^36 + 30 * q^42 + 48 * q^45 - 42 * q^47 + 6 * q^48 + 24 * q^49 - 24 * q^53 - 120 * q^56 + 24 * q^58 - 18 * q^60 - 30 * q^64 + 120 * q^67 + 24 * q^69 + 18 * q^70 - 6 * q^75 - 288 * q^78 - 18 * q^80 - 30 * q^81 - 42 * q^82 + 6 * q^86 - 120 * q^89 - 36 * q^91 - 36 * q^92 + 60 * q^93 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

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