LMFDB - Embedded newform 605.2.g.q.251.6

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			251.6
Character	$\chi$	$=$	605.251
Dual form			605.2.g.q.511.6

$q$-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 $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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	−0.0684758	−	0.997653i	$-0.521814\pi$
$2$	0.810808	−	2.49541i	0.573328	−	1.76452i	0.641804	−	0.766869i	$-0.278186\pi$
$3$	−1.08398	+	0.787560i	−0.625838	+	0.454698i	−0.854956	−	0.518701i	$-0.826416\pi$
$3$	−1.08398	+	0.787560i	−0.625838	+	0.454698i	0.229118	+	0.973399i	$0.426416\pi$
$4$	−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	$-0.134854\pi$
$7$	2.12272	+	1.54225i	0.802314	+	0.582915i	−0.109278	+	0.994011i	$0.534854\pi$
$8$	−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	0.0538866	+	0.998547i	$0.482839\pi$
$13$	−2.07910	+	6.39883i	−0.576640	+	1.77471i	−0.630526	+	0.776168i	$0.717161\pi$
$14$	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	$-0.0306049\pi$
$17$	0.551150	+	1.69626i	0.133673	+	0.411405i	−0.861708	+	0.507405i	$0.830605\pi$
$18$	2.55731	+	1.85799i	0.602763	+	0.437933i
$19$	1.19772	−	0.870194i	0.274776	−	0.199636i	−0.441860	−	0.897084i	$-0.645681\pi$
$19$	1.19772	−	0.870194i	0.274776	−	0.199636i	0.716636	+	0.697448i	$0.245681\pi$
$20$	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	$-0.334866\pi$
$29$	−0.952511	−	0.692040i	−0.176877	−	0.128509i	−0.672701	+	0.739914i	$0.734866\pi$
$30$	−2.84419	+	2.06642i	−0.519275	+	0.377276i
$31$	−1.41043	+	4.34085i	−0.253320	+	0.779639i	0.740836	+	0.671686i	$0.234430\pi$
$31$	−1.41043	+	4.34085i	−0.253320	+	0.779639i	−0.994156	+	0.107953i	$0.965570\pi$
$32$	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	0.632071	−	0.774910i	$-0.282205\pi$
$37$	0.549932	+	0.399549i	0.0904083	+	0.0656855i	−0.541663	+	0.840596i	$0.682205\pi$
$38$	−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	$-0.841282\pi$
$41$	−4.44898	+	3.23238i	−0.694815	+	0.504812i	0.183425	+	0.983034i	$0.441282\pi$
$42$	−2.85048	+	8.77289i	−0.439839	+	1.35369i
$43$	3.80120			0.579677			0.289839	−	0.957076i	$-0.406398\pi$
$43$	3.80120			0.579677			0.289839	+	0.957076i	$0.406398\pi$
$44$		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	−0.906757	−	0.421654i	$-0.861450\pi$
$47$	−5.38815	+	3.91472i	−0.785943	+	0.571021i	0.120814	+	0.992675i	$0.461450\pi$
$48$	−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	0.122311	−	0.992492i	$-0.460969\pi$
$53$	4.41707	−	13.5943i	0.606731	−	1.86733i	0.484420	−	0.874836i	$-0.339031\pi$
$54$	−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	0.773251	−	0.634100i	$-0.218629\pi$
$59$	3.14261	+	2.28324i	0.409133	+	0.297253i	−0.364117	+	0.931353i	$0.618629\pi$
$60$	2.02239	+	6.22429i	0.261090	+	0.803553i
$61$	0.992721	+	3.05528i	0.127105	+	0.391189i	0.994279	−	0.106817i	$-0.0340659\pi$
$61$	0.992721	+	3.05528i	0.127105	+	0.391189i	−0.867174	+	0.498006i	$0.834066\pi$
$62$	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	0.996675	−	0.0814756i	$-0.0259633\pi$
$71$	1.20037	+	3.69436i	0.142458	+	0.438440i	−0.854217	+	0.519916i	$0.825963\pi$
$72$	−2.81758	−	8.67161i	−0.332055	−	1.02196i
$73$	2.88586	+	2.09670i	0.337764	+	0.245400i	0.743718	−	0.668494i	$-0.233061\pi$
$73$	2.88586	+	2.09670i	0.337764	+	0.245400i	−0.405954	+	0.913894i	$0.633061\pi$
$74$	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	0.235543	+	0.971864i	$0.424313\pi$
$79$	−4.67753	+	14.3959i	−0.526263	+	1.61967i	−0.761805	+	0.647806i	$0.775687\pi$
$80$	−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	0.994993	+	0.0999446i	$0.0318666\pi$
$83$	2.26643	+	6.97535i	0.248773	+	0.765644i	−0.746220	+	0.665699i	$0.768133\pi$
$84$	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	−0.925246	−	0.379367i	$-0.876142\pi$
$97$	0.455807	−	1.40283i	0.0462802	−	0.142436i	0.971526	+	0.236931i	$0.0761417\pi$
$98$	−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	$-0.954307\pi$
$101$	−1.05455	+	3.24557i	−0.104932	+	0.322946i	0.884783	+	0.466004i	$0.154307\pi$
$102$	−5.07277	+	3.68559i	−0.502280	+	0.364927i
$103$	4.02381	+	2.92347i	0.396477	+	0.288058i	0.768105	−	0.640324i	$-0.221200\pi$
$103$	4.02381	+	2.92347i	0.396477	+	0.288058i	−0.371627	+	0.928382i	$0.621200\pi$
$104$	−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	$-0.810938\pi$
$107$	−5.71588	+	4.15283i	−0.552575	+	0.401469i	0.276159	+	0.961112i	$0.410938\pi$
$108$	−8.50362	+	26.1715i	−0.818262	+	2.51835i
$109$	−10.6439			−1.01950			−0.509750	−	0.860323i	$-0.670262\pi$
$109$	−10.6439			−1.01950			−0.509750	+	0.860323i	$0.670262\pi$
$110$		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	0.0760879	−	0.997101i	$-0.475757\pi$
$113$	11.1393	−	8.09320i	1.04790	−	0.761344i	0.971812	+	0.235757i	$0.0757570\pi$
$114$	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	−0.965412	−	0.260728i	$-0.916037\pi$
$127$	−3.80489	−	11.7102i	−0.337629	−	1.03912i	0.627783	−	0.778388i	$-0.283963\pi$
$128$	−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	$-0.175203\pi$
$131$	19.5102			1.70461			0.852306	+	0.523043i	$0.175203\pi$
$132$		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	−0.998178	−	0.0603458i	$-0.980780\pi$
$137$	−2.64649	−	8.14507i	−0.226105	−	0.695881i	0.772072	−	0.635535i	$-0.219220\pi$
$138$	5.65433	+	17.4022i	0.481329	+	1.48138i
$139$	−1.60480	−	1.16595i	−0.136117	−	0.0988949i	0.517643	−	0.855597i	$-0.326810\pi$
$139$	−1.60480	−	1.16595i	−0.136117	−	0.0988949i	−0.653760	+	0.756702i	$0.726810\pi$
$140$	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	−0.859579	−	0.511002i	$-0.829274\pi$
$149$	−5.67025	−	17.4512i	−0.464525	−	1.42966i	0.395055	−	0.918658i	$-0.370726\pi$
$150$	−2.84419	−	2.06642i	−0.232227	−	0.168723i
$151$	−13.9341	+	10.1237i	−1.13394	+	0.823854i	−0.986263	−	0.165182i	$-0.947179\pi$
$151$	−13.9341	+	10.1237i	−1.13394	+	0.823854i	−0.147674	+	0.989036i	$0.547179\pi$
$152$	−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	0.350229	−	0.936664i	$-0.386104\pi$
$157$	16.9064	−	12.2832i	1.34928	−	0.980307i	0.999047	−	0.0436428i	$-0.0138963\pi$
$158$	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	−0.769018	−	0.639227i	$-0.779254\pi$
$163$	2.92188	−	8.99261i	0.228859	−	0.704356i	0.997877	−	0.0651285i	$-0.0207457\pi$
$164$	26.8610			2.09749
$165$		0			0
$166$	19.2440			1.49362
$167$	−2.91991	+	8.98655i	−0.225949	+	0.695400i	0.772245	+	0.635325i	$0.219134\pi$
$167$	−2.91991	+	8.98655i	−0.225949	+	0.695400i	−0.998194	+	0.0600749i	$0.980866\pi$
$168$	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	$-0.587784\pi$
$173$	7.34819	−	5.33877i	0.558672	−	0.405899i	0.830973	+	0.556313i	$0.187784\pi$
$174$	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	−0.0876991	−	0.996147i	$-0.527951\pi$
$179$	11.1393	−	8.09320i	0.832593	−	0.604914i	0.920292	+	0.391233i	$0.127951\pi$
$180$	4.76065	+	3.45881i	0.354838	+	0.257805i
$181$	−7.37258	−	22.6905i	−0.548000	−	1.68657i	−0.713749	−	0.700402i	$-0.753004\pi$
$181$	−7.37258	−	22.6905i	−0.548000	−	1.68657i	0.165749	−	0.986168i	$-0.446996\pi$
$182$	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	0.00819487	−	0.999966i	$-0.497391\pi$
$191$	−12.9952	−	9.44154i	−0.940297	−	0.683166i	−0.948492	+	0.316800i	$0.897391\pi$
$192$	3.96002	+	12.1877i	0.285790	+	0.879571i
$193$	6.63113	+	20.4085i	0.477320	+	1.46904i	0.842804	+	0.538221i	$0.180903\pi$
$193$	6.63113	+	20.4085i	0.477320	+	1.46904i	−0.365484	+	0.930818i	$0.619097\pi$
$194$	−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	$-0.393535\pi$
$197$	9.21494			0.656537			0.328269	+	0.944584i	$0.393535\pi$
$198$		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	−0.659955	−	0.751306i	$-0.729424\pi$
$211$	4.58386	−	14.1077i	0.315566	−	0.971213i	0.975521	−	0.219907i	$-0.0705755\pi$
$212$	−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	−0.999115	−	0.0420528i	$-0.986610\pi$
$223$	−18.9333	+	13.7558i	−1.26786	+	0.921157i	−0.268749	+	0.963210i	$0.586610\pi$
$224$	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	$-0.272248\pi$
$227$	2.12272	+	1.54225i	0.140890	+	0.102363i	−0.515108	+	0.857125i	$0.672248\pi$
$228$	7.83861	−	5.69508i	0.519124	−	0.377166i
$229$	−6.80969	+	20.9581i	−0.449997	+	1.38495i	0.426913	+	0.904293i	$0.359601\pi$
$229$	−6.80969	+	20.9581i	−0.449997	+	1.38495i	−0.876910	+	0.480655i	$0.840399\pi$
$230$	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	$-0.843984\pi$
$233$	1.65161	−	5.08314i	0.108201	−	0.333007i	0.990468	+	0.137741i	$0.0439841\pi$
$234$	−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	$-0.566599\pi$
$239$	10.1790	−	7.39550i	0.658427	−	0.478375i	0.866131	+	0.499817i	$0.166599\pi$
$240$	4.17739	−	12.8567i	0.269649	−	0.829895i
$241$	−4.28687			−0.276141			−0.138071	−	0.990422i	$-0.544090\pi$
$241$	−4.28687			−0.276141			−0.138071	+	0.990422i	$0.544090\pi$
$242$		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	−0.803682	−	0.595058i	$-0.797129\pi$
$251$	3.10961	−	9.57040i	0.196277	−	0.604078i	0.999959	−	0.00901968i	$-0.00287109\pi$
$252$	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	0.664786	−	0.747033i	$-0.268523\pi$
$257$	2.56092	+	1.86062i	0.159746	+	0.116062i	−0.505041	+	0.863095i	$0.668523\pi$
$258$	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	$-0.257770\pi$
$263$	22.3681			1.37928			0.689638	+	0.724155i	$0.257770\pi$
$264$		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	0.981153	+	0.193231i	$0.0618967\pi$
$269$	4.93614	+	15.1919i	0.300962	+	0.926266i	−0.680191	+	0.733035i	$0.738103\pi$
$270$	−4.56795	−	14.0587i	−0.277996	−	0.855585i
$271$	12.6530	+	9.19294i	0.768615	+	0.558431i	0.901541	−	0.432695i	$-0.142437\pi$
$271$	12.6530	+	9.19294i	0.768615	+	0.558431i	−0.132926	+	0.991126i	$0.542437\pi$
$272$	−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	−0.440731	−	0.897639i	$-0.645281\pi$
$277$	7.38043	−	22.7146i	0.443447	−	1.36479i	0.884178	−	0.467150i	$-0.154719\pi$
$278$	−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	0.998219	+	0.0596571i	$0.0190007\pi$
$281$	3.78356	+	11.6446i	0.225708	+	0.694659i	−0.772511	+	0.635002i	$0.780999\pi$
$282$	−18.9426	−	13.7626i	−1.12802	−	0.819553i
$283$	16.8709	−	12.2575i	1.00287	−	0.728630i	0.0401707	−	0.999193i	$-0.487210\pi$
$283$	16.8709	−	12.2575i	1.00287	−	0.728630i	0.962702	+	0.270563i	$0.0872098\pi$
$284$	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	$-0.437479\pi$
$293$	−11.5936	−	8.42327i	−0.677307	−	0.492093i	−0.872463	+	0.488680i	$0.837479\pi$
$294$	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	$-0.405083\pi$
$307$	10.2952			0.587580			0.293790	+	0.955870i	$0.405083\pi$
$308$		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	−0.0542760	−	0.998526i	$-0.517285\pi$
$311$	15.4944	−	11.2573i	0.878606	−	0.638345i	0.932882	+	0.360181i	$0.117285\pi$
$312$	55.1976	+	40.1034i	3.12495	+	2.27041i
$313$	−4.62713	−	14.2408i	−0.261541	−	0.804939i	−0.992470	−	0.122486i	$-0.960913\pi$
$313$	−4.62713	−	14.2408i	−0.261541	−	0.804939i	0.730930	−	0.682453i	$-0.239087\pi$
$314$	−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	−0.788021	−	0.615648i	$-0.788894\pi$
$317$	3.76334	−	11.5824i	0.211370	−	0.650531i	0.999391	−	0.0348827i	$-0.0111057\pi$
$318$	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	$-0.358662\pi$
$337$	−5.44317	−	3.95469i	−0.296508	−	0.215426i	−0.726086	+	0.687604i	$0.758662\pi$
$338$	−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	0.693853	+	0.720116i	$0.255912\pi$
$347$	10.3532	+	31.8638i	0.555788	+	1.71054i	−0.138066	+	0.990423i	$0.544088\pi$
$348$	−6.23381	−	4.52913i	−0.334167	−	0.242787i
$349$	−18.4247	+	13.3863i	−0.986252	+	0.716554i	−0.959097	−	0.283077i	$-0.908645\pi$
$349$	−18.4247	+	13.3863i	−0.986252	+	0.716554i	−0.0271551	+	0.999631i	$0.508645\pi$
$350$	−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	$-0.381406\pi$
$359$	−7.75526	−	5.63453i	−0.409307	−	0.297379i	−0.773321	+	0.634014i	$0.781406\pi$
$360$	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	0.792635	−	0.609697i	$-0.208709\pi$
$367$	8.76857	+	6.37074i	0.457716	+	0.332550i	−0.334919	+	0.942247i	$0.608709\pi$
$368$	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	$-0.583538\pi$
$373$	−10.0212			−0.518878			−0.259439	+	0.965759i	$0.583538\pi$
$374$		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	0.978797	−	0.204832i	$-0.0656647\pi$
$379$	1.29533	+	3.98661i	0.0665366	+	0.204778i	−0.912261	+	0.409610i	$0.865665\pi$
$380$	−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	−0.676236	−	0.736685i	$-0.736390\pi$
$383$	5.94672	−	18.3021i	0.303863	−	0.935195i	0.980099	−	0.198510i	$-0.0636101\pi$
$384$	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	0.990507	−	0.137465i	$-0.0438954\pi$
$389$	22.9942	+	16.7063i	1.16585	+	0.847042i	0.175347	+	0.984507i	$0.443895\pi$
$390$	−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	0.963864	+	0.266396i	$0.0858330\pi$
$401$	6.82182	+	20.9954i	0.340665	+	1.04846i	−0.623198	+	0.782064i	$0.714167\pi$
$402$	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	−0.565161	−	0.824981i	$-0.691186\pi$
$409$	7.62386	−	23.4638i	0.376975	−	1.16021i	0.942136	−	0.335230i	$-0.108814\pi$
$410$	−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	−0.617443	−	0.786615i	$-0.711832\pi$
$421$	−1.23373	+	0.896358i	−0.0601284	+	0.0436858i	0.557315	+	0.830301i	$0.311832\pi$
$422$	−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	0.745587	+	0.666409i	$0.232169\pi$
$431$	−5.17583	+	15.9296i	−0.249311	+	0.767300i	−0.994897	+	0.100891i	$0.967831\pi$
$432$	45.9852	−	33.4102i	2.21246	−	1.60745i
$433$	−6.04742	−	4.39371i	−0.290621	−	0.211148i	0.432916	−	0.901434i	$-0.357485\pi$
$433$	−6.04742	−	4.39371i	−0.290621	−	0.211148i	−0.723537	+	0.690286i	$0.757485\pi$
$434$	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	$-0.363213\pi$
$439$	17.4585			0.833250			0.416625	+	0.909078i	$0.363213\pi$
$440$		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	−0.268661	−	0.963235i	$-0.586581\pi$
$443$	11.8794	−	8.63091i	0.564408	−	0.410067i	0.833070	+	0.553168i	$0.186581\pi$
$444$	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	−0.960136	−	0.279532i	$-0.909821\pi$
$449$	−0.403974	+	1.24330i	−0.0190647	+	0.0586752i	0.941072	+	0.338208i	$0.109821\pi$
$450$	−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	$-0.0233816\pi$
$457$	3.14957	+	9.69338i	0.147331	+	0.453437i	−0.849973	+	0.526827i	$0.823382\pi$
$458$	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	$-0.530600\pi$
$461$	−4.12180			−0.191971			−0.0959857	+	0.995383i	$0.530600\pi$
$462$		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	0.727646	+	0.685953i	$0.240614\pi$
$467$	11.7162	+	36.0588i	0.542161	+	1.66860i	−0.185485	+	0.982647i	$0.559386\pi$
$468$	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	$-0.147149\pi$
$479$	−1.99626	−	6.14386i	−0.0912116	−	0.280720i	−0.986248	+	0.165273i	$0.947149\pi$
$480$	−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	−0.694288	+	0.719697i	$0.744281\pi$
$487$	−35.1612	+	25.5461i	−1.59331	+	1.15761i	−0.899019	+	0.437909i	$0.855719\pi$
$488$	−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	$-0.260729\pi$
$491$	4.41213	+	3.20560i	0.199117	+	0.144667i	−0.483759	+	0.875201i	$0.660729\pi$
$492$	−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	0.338220	−	0.941067i	$-0.390175\pi$
$499$	−10.1030	−	7.34025i	−0.452272	−	0.328595i	−0.790492	+	0.612472i	$0.790175\pi$
$500$	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	$-0.546087\pi$
$503$	16.8709	−	12.2575i	0.752238	−	0.546533i	0.896520	+	0.443004i	$0.146087\pi$
$504$	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	0.00151069	−	0.999999i	$-0.499519\pi$
$509$	21.5014	−	15.6217i	0.953033	−	0.692419i	0.951522	+	0.307580i	$0.0995191\pi$
$510$	−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	0.915735	−	0.401782i	$-0.131609\pi$
$521$	18.6392	+	13.5421i	0.816596	+	0.593292i	−0.0991393	+	0.995074i	$0.531609\pi$
$522$	−1.15006	−	3.53952i	−0.0503367	−	0.154920i
$523$	−0.365665	−	1.12540i	−0.0159894	−	0.0492104i	0.942743	−	0.333519i	$-0.108236\pi$
$523$	−0.365665	−	1.12540i	−0.0159894	−	0.0492104i	−0.958733	+	0.284308i	$0.908236\pi$
$524$	−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	0.487894	+	0.872903i	$0.337765\pi$
$541$	−9.76663	+	30.0586i	−0.419900	+	1.29232i	−0.907794	+	0.419417i	$0.862235\pi$
$542$	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	$-0.666050\pi$
$547$	4.02856	−	2.92692i	0.172249	−	0.125146i	0.670570	+	0.741847i	$0.266050\pi$
$548$	−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	$-0.121300\pi$
$557$	20.3297	+	14.7704i	0.861399	+	0.625843i	−0.0668666	+	0.997762i	$0.521300\pi$
$558$	−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	$-0.976777\pi$
$563$	−3.50289	+	10.7808i	−0.147629	+	0.454356i	0.849711	+	0.527250i	$0.176777\pi$
$564$	−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	$-0.619346\pi$
$569$	9.67527	−	7.02949i	0.405608	−	0.294692i	0.771821	+	0.635839i	$0.219346\pi$
$570$	−1.60835	+	4.94999i	−0.0673664	+	0.207332i
$571$	−29.8054			−1.24732			−0.623659	−	0.781697i	$-0.714355\pi$
$571$	−29.8054			−1.24732			−0.623659	+	0.781697i	$0.714355\pi$
$572$		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	−0.996736	−	0.0807279i	$-0.974276\pi$
$577$	−5.71240	−	17.5810i	−0.237810	−	0.731905i	0.758926	−	0.651177i	$-0.225724\pi$
$578$	−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	0.631691	−	0.775220i	$-0.282361\pi$
$587$	2.17122	+	1.57748i	0.0896157	+	0.0651097i	−0.542075	+	0.840330i	$0.682361\pi$
$588$	−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	$-0.700793\pi$
$593$	−28.7251			−1.17960			−0.589800	+	0.807550i	$0.700793\pi$
$594$		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	−0.896562	−	0.442918i	$-0.853943\pi$
$599$	−10.5624	−	32.5078i	−0.431569	−	1.32823i	0.464994	−	0.885314i	$-0.346057\pi$
$600$	3.13365	+	9.64440i	0.127931	+	0.393731i
$601$	26.2585	+	19.0779i	1.07111	+	0.778205i	0.976111	−	0.217273i	$-0.0697162\pi$
$601$	26.2585	+	19.0779i	1.07111	+	0.778205i	0.0949959	+	0.995478i	$0.469716\pi$
$602$	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	$-0.865406\pi$
$607$	1.65161	−	5.08314i	0.0670368	−	0.206318i	0.978964	+	0.204035i	$0.0654055\pi$
$608$	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	$-0.491171\pi$
$613$	24.4368	−	17.7544i	0.986994	−	0.717093i	0.959261	+	0.282522i	$0.0911711\pi$
$614$	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	−0.617007	−	0.786957i	$-0.711655\pi$
$619$	−1.47368	+	1.07069i	−0.0592323	+	0.0430348i	0.557775	+	0.829992i	$0.311655\pi$
$620$	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	0.970694	−	0.240318i	$-0.0772516\pi$
$631$	26.1772	+	19.0189i	1.04210	+	0.757130i	0.0714054	+	0.997447i	$0.477252\pi$
$632$	−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	−0.345649	−	0.938364i	$-0.612341\pi$
$641$	11.1393	−	8.09320i	0.439977	−	0.319662i	0.785626	+	0.618702i	$0.212341\pi$
$642$	−20.0948	−	14.5997i	−0.793079	−	0.576206i
$643$	9.93832	+	30.5870i	0.391929	+	1.20623i	0.931328	+	0.364183i	$0.118652\pi$
$643$	9.93832	+	30.5870i	0.391929	+	1.20623i	−0.539399	+	0.842051i	$0.681348\pi$
$644$	−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	−0.760222	−	0.649663i	$-0.774910\pi$
$647$	6.02006	−	18.5278i	0.236673	−	0.728404i	0.996895	−	0.0787410i	$-0.0250900\pi$
$648$	−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	0.575375	−	0.817890i	$-0.304856\pi$
$653$	−0.630757	−	0.458272i	−0.0246834	−	0.0179336i	−0.600059	+	0.799956i	$0.704856\pi$
$654$	−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	$-0.685037\pi$
$659$	−28.1929			−1.09824			−0.549119	+	0.835744i	$0.685037\pi$
$660$		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	$-0.831971\pi$
$673$	3.40056	−	10.4658i	0.131082	−	0.403429i	0.994960	+	0.100272i	$0.0319713\pi$
$674$	−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	−0.994016	−	0.109236i	$-0.965160\pi$
$677$	−6.61012	−	20.3439i	−0.254048	−	0.781878i	0.739968	−	0.672642i	$-0.234840\pi$
$678$	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	−0.177622	−	0.984099i	$-0.556840\pi$
$691$	14.3136	−	44.0528i	0.544516	−	1.67585i	0.722138	−	0.691749i	$-0.243160\pi$
$692$	−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	−0.325203	+	0.945644i	$0.605433\pi$
$701$	−35.0828	+	25.4891i	−1.32506	+	0.962711i	−0.999854	+	0.0170666i	$0.994567\pi$
$702$	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	0.998529	+	0.0542219i	$0.0172678\pi$
$709$	5.92646	+	18.2398i	0.222573	+	0.685009i	−0.775956	+	0.630787i	$0.782732\pi$
$710$	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	0.956438	−	0.291934i	$-0.0942988\pi$
$719$	26.1263	+	18.9819i	0.974348	+	0.707906i	0.0179100	+	0.999840i	$0.494299\pi$
$720$	−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	$-0.241329\pi$
$733$	8.02880	+	5.83326i	0.296550	+	0.215457i	−0.429554	+	0.903041i	$0.641329\pi$
$734$	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	−0.561133	−	0.827726i	$-0.689634\pi$
$739$	10.3127	−	31.7392i	0.379358	−	1.16754i	0.940491	−	0.339818i	$-0.110366\pi$
$740$	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	$-0.0777526\pi$
$743$	1.17647	+	3.62081i	0.0431606	+	0.132835i	−0.927154	+	0.374680i	$0.877753\pi$
$744$	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	−0.868183	−	0.496245i	$-0.834712\pi$
$751$	−18.2105	+	13.2307i	−0.664509	+	0.482794i	0.203674	+	0.979039i	$0.434712\pi$
$752$	−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	0.562728	+	0.826642i	$0.309752\pi$
$757$	−10.4116	+	32.0437i	−0.378417	+	1.16465i	−0.941144	+	0.338005i	$0.890248\pi$
$758$	10.9985			0.399483
$759$		0			0
$760$	−11.2047			−0.406438
$761$	5.80084	−	17.8531i	0.210280	−	0.647176i	−0.789175	−	0.614169i	$-0.789491\pi$
$761$	5.80084	−	17.8531i	0.210280	−	0.647176i	0.999455	−	0.0330075i	$-0.0105085\pi$
$762$	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	$-0.627100\pi$
$769$	−21.5618			−0.777539			−0.388770	+	0.921335i	$0.627100\pi$
$770$		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	−0.193083	−	0.981182i	$-0.561849\pi$
$773$	18.9174	−	13.7443i	0.680411	−	0.494347i	0.873494	+	0.486835i	$0.161849\pi$
$774$	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	0.988838	+	0.148993i	$0.0476033\pi$
$787$	7.75476	+	23.8667i	0.276427	+	0.850756i	−0.712411	+	0.701763i	$0.752397\pi$
$788$	−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	0.862956	−	0.505280i	$-0.168611\pi$
$797$	−3.73177	−	11.4852i	−0.132186	−	0.406827i	−0.995142	+	0.0984529i	$0.968611\pi$
$798$	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	$-0.0487928\pi$
$809$	2.81574	+	8.66595i	0.0989961	+	0.304679i	−0.889278	+	0.457366i	$0.848793\pi$
$810$	8.35172	+	6.06788i	0.293449	+	0.213204i
$811$	−2.41895	+	1.75747i	−0.0849409	+	0.0617132i	−0.629445	−	0.777045i	$-0.716718\pi$
$811$	−2.41895	+	1.75747i	−0.0849409	+	0.0617132i	0.544504	+	0.838758i	$0.316718\pi$
$812$	−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	$-0.511030\pi$
$821$	−28.5337	−	20.7310i	−0.995835	−	0.723516i	−0.961191	+	0.275884i	$0.911030\pi$
$822$	24.3583	−	17.6973i	0.849593	−	0.617266i
$823$	4.80755	−	14.7961i	0.167581	−	0.515760i	−0.831636	−	0.555320i	$-0.812596\pi$
$823$	4.80755	−	14.7961i	0.167581	−	0.515760i	0.999217	+	0.0395600i	$0.0125956\pi$
$824$	−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	$-0.958604\pi$
$827$	−3.25374	+	10.0140i	−0.113144	+	0.348220i	0.878412	+	0.477905i	$0.158604\pi$
$828$	24.7779	−	18.0022i	0.861091	−	0.625619i
$829$	−20.7310	−	15.0619i	−0.720016	−	0.523122i	0.166373	−	0.986063i	$-0.446794\pi$
$829$	−20.7310	−	15.0619i	−0.720016	−	0.523122i	−0.886389	+	0.462941i	$0.846794\pi$
$830$	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	−0.889470	−	0.456994i	$-0.848926\pi$
$839$	−21.1362	+	15.3564i	−0.729704	+	0.530161i	0.159766	+	0.987155i	$0.448926\pi$
$840$	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	$-0.0849820\pi$
$853$	0.851310	+	2.62006i	0.0291483	+	0.0897092i	−0.935424	+	0.353528i	$0.884982\pi$
$854$	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	$-0.387201\pi$
$857$	20.3164			0.693997			0.346998	+	0.937866i	$0.387201\pi$
$858$		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	0.872928	+	0.487848i	$0.162218\pi$
$863$	13.3214	+	40.9989i	0.453465	+	1.39562i	−0.419464	+	0.907772i	$0.637782\pi$
$864$	−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	$-0.609098\pi$
$877$	13.4987	−	9.80735i	0.455817	−	0.331171i	0.791888	+	0.610666i	$0.209098\pi$
$878$	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	−0.156086	−	0.987743i	$-0.549888\pi$
$883$	21.8431	−	15.8700i	0.735080	−	0.534067i	0.891167	+	0.453676i	$0.149888\pi$
$884$	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	$-0.174157\pi$
$887$	18.5591	+	13.4840i	0.623153	+	0.452747i	−0.230869	+	0.972985i	$0.574157\pi$
$888$	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	0.899878	+	0.436141i	$0.143655\pi$
$907$	12.8964	+	39.6911i	0.428219	+	1.31792i	−0.471659	+	0.881781i	$0.656345\pi$
$908$	−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	0.531296	+	0.847186i	$0.321705\pi$
$911$	−11.9673	+	36.8316i	−0.396495	+	1.22029i	−0.927791	+	0.373100i	$0.878295\pi$
$912$	−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	$-0.114978\pi$
$919$	−0.881305	−	2.71238i	−0.0290716	−	0.0894730i	−0.964540	+	0.263938i	$0.914978\pi$
$920$	−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	0.861335	−	0.508037i	$-0.169629\pi$
$929$	−4.08779	−	12.5809i	−0.134116	−	0.412767i	−0.995451	+	0.0952697i	$0.969629\pi$
$930$	−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	$-0.891261\pi$
$937$	0.519316	−	1.59829i	0.0169653	−	0.0522139i	0.959181	+	0.282794i	$0.0912611\pi$
$938$	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	$-0.176938\pi$
$941$	−4.53795	−	13.9664i	−0.147933	−	0.455291i	−0.997377	+	0.0723886i	$0.976938\pi$
$942$	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	$-0.414690\pi$
$953$	−17.6106	−	12.7948i	−0.570462	−	0.414465i	−0.835273	+	0.549835i	$0.814690\pi$
$954$	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	$-0.572632\pi$
$967$	−14.0684			−0.452409			−0.226204	+	0.974080i	$0.572632\pi$
$968$		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	−0.379881	−	0.925035i	$-0.624035\pi$
$971$	11.9187	−	8.65946i	0.382490	−	0.277895i	0.762371	+	0.647140i	$0.224035\pi$
$972$	−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	−0.864842	−	0.502045i	$-0.832581\pi$
$977$	4.06105	−	12.4986i	0.129924	−	0.399866i	0.994766	+	0.102179i	$0.0325813\pi$
$978$	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	0.324269	−	0.945965i	$-0.394882\pi$
$983$	−14.8987	−	10.8245i	−0.475193	−	0.345248i	−0.799462	+	0.600717i	$0.794882\pi$
$984$	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	$-0.594936\pi$
$997$	−40.8497	−	29.6790i	−1.29372	−	0.939944i	−0.999873	+	0.0159081i	$0.994936\pi$
$998$	−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.251.6		24
11.2	odd	10	inner	605.2.g.q.366.6		24
11.3	even	5	inner	605.2.g.q.81.1		24
11.4	even	5		605.2.a.m.1.6	yes	6
11.5	even	5	inner	605.2.g.q.511.6		24
11.6	odd	10	inner	605.2.g.q.511.1		24
11.7	odd	10		605.2.a.m.1.1	✓	6
11.8	odd	10	inner	605.2.g.q.81.6		24
11.9	even	5	inner	605.2.g.q.366.1		24
11.10	odd	2	inner	605.2.g.q.251.1		24
33.26	odd	10		5445.2.a.bx.1.1		6
33.29	even	10		5445.2.a.bx.1.6		6
44.7	even	10		9680.2.a.cw.1.3		6
44.15	odd	10		9680.2.a.cw.1.4		6
55.4	even	10		3025.2.a.bg.1.1		6
55.29	odd	10		3025.2.a.bg.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.m.1.1	✓	6	11.7	odd	10
605.2.a.m.1.6	yes	6	11.4	even	5
605.2.g.q.81.1		24	11.3	even	5	inner
605.2.g.q.81.6		24	11.8	odd	10	inner
605.2.g.q.251.1		24	11.10	odd	2	inner
605.2.g.q.251.6		24	1.1	even	1	trivial
605.2.g.q.366.1		24	11.9	even	5	inner
605.2.g.q.366.6		24	11.2	odd	10	inner
605.2.g.q.511.1		24	11.6	odd	10	inner
605.2.g.q.511.6		24	11.5	even	5	inner
3025.2.a.bg.1.1		6	55.4	even	10
3025.2.a.bg.1.6		6	55.29	odd	10
5445.2.a.bx.1.1		6	33.26	odd	10
5445.2.a.bx.1.6		6	33.29	even	10
9680.2.a.cw.1.3		6	44.7	even	10
9680.2.a.cw.1.4		6	44.15	odd	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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more