LMFDB - Embedded newform 495.2.u.b.364.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(34,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3, 0]))

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

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

chi := DirichletCharacter("495.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.u (of order $6$, degree $2$, 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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			364.30
Character	$\chi$	$=$	495.364
Dual form			495.2.u.b.34.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.85631 - 1.07174i) q^{2} +(-0.637067 - 1.61064i) q^{3} +(1.29725 - 2.24690i) q^{4} +(1.72303 - 1.42519i) q^{5} +(-2.90877 - 2.30706i) q^{6} +(2.53525 - 1.46372i) q^{7} -1.27429i q^{8} +(-2.18829 + 2.05216i) q^{9} +O(q^{10})$	\(q+(1.85631 - 1.07174i) q^{2} +(-0.637067 - 1.61064i) q^{3} +(1.29725 - 2.24690i) q^{4} +(1.72303 - 1.42519i) q^{5} +(-2.90877 - 2.30706i) q^{6} +(2.53525 - 1.46372i) q^{7} -1.27429i q^{8} +(-2.18829 + 2.05216i) q^{9} +(1.67104 - 4.49223i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-4.44537 - 0.657969i) q^{12} +(1.15477 + 0.666707i) q^{13} +(3.13746 - 5.43424i) q^{14} +(-3.39315 - 1.86723i) q^{15} +(1.22879 + 2.12833i) q^{16} +7.10247i q^{17} +(-1.86276 + 6.15472i) q^{18} -8.57612 q^{19} +(-0.967063 - 5.72030i) q^{20} +(-3.97265 - 3.15087i) q^{21} +(1.85631 + 1.07174i) q^{22} +(-2.26009 - 1.30486i) q^{23} +(-2.05241 + 0.811806i) q^{24} +(0.937663 - 4.91129i) q^{25} +2.85814 q^{26} +(4.69938 + 2.21718i) q^{27} -7.59525i q^{28} +(-2.32609 - 4.02891i) q^{29} +(-8.29990 + 0.170415i) q^{30} +(-0.273415 + 0.473569i) q^{31} +(6.76916 + 3.90818i) q^{32} +(1.07632 - 1.35703i) q^{33} +(7.61199 + 13.1843i) q^{34} +(2.28222 - 6.13525i) q^{35} +(1.77225 + 7.57904i) q^{36} +5.16561i q^{37} +(-15.9199 + 9.19136i) q^{38} +(0.338156 - 2.28465i) q^{39} +(-1.81610 - 2.19564i) q^{40} +(1.36211 - 2.35924i) q^{41} +(-10.7514 - 1.59133i) q^{42} +(-6.67079 + 3.85138i) q^{43} +2.59450 q^{44} +(-0.845768 + 6.65467i) q^{45} -5.59389 q^{46} +(7.63697 - 4.40921i) q^{47} +(2.64514 - 3.33502i) q^{48} +(0.784980 - 1.35962i) q^{49} +(-3.52303 - 10.1218i) q^{50} +(11.4395 - 4.52474i) q^{51} +(2.99605 - 1.72977i) q^{52} +3.90137i q^{53} +(11.0997 - 0.920745i) q^{54} +(2.09577 + 0.779592i) q^{55} +(-1.86521 - 3.23063i) q^{56} +(5.46356 + 13.8130i) q^{57} +(-8.63588 - 4.98593i) q^{58} +(3.42152 - 5.92624i) q^{59} +(-8.59723 + 5.20180i) q^{60} +(2.03932 + 3.53221i) q^{61} +1.17212i q^{62} +(-2.54406 + 8.40580i) q^{63} +11.8390 q^{64} +(2.93989 - 0.497012i) q^{65} +(0.543590 - 3.67260i) q^{66} +(-1.70302 - 0.983237i) q^{67} +(15.9585 + 9.21366i) q^{68} +(-0.661832 + 4.47147i) q^{69} +(-2.33889 - 13.8348i) q^{70} -10.9996 q^{71} +(2.61505 + 2.78851i) q^{72} -11.8252i q^{73} +(5.53618 + 9.58895i) q^{74} +(-8.50765 + 1.61859i) q^{75} +(-11.1254 + 19.2697i) q^{76} +(2.53525 + 1.46372i) q^{77} +(-1.82083 - 4.60343i) q^{78} +(0.576774 + 0.999001i) q^{79} +(5.15052 + 1.91591i) q^{80} +(0.577248 - 8.98147i) q^{81} -5.83930i q^{82} +(8.64355 - 4.99036i) q^{83} +(-12.2332 + 4.83868i) q^{84} +(10.1224 + 12.2378i) q^{85} +(-8.25535 + 14.2987i) q^{86} +(-5.00723 + 6.31317i) q^{87} +(1.10357 - 0.637144i) q^{88} +17.0187 q^{89} +(5.56207 + 13.2596i) q^{90} +3.90350 q^{91} +(-5.86380 + 3.38546i) q^{92} +(0.936931 + 0.138677i) q^{93} +(9.45104 - 16.3697i) q^{94} +(-14.7769 + 12.2226i) q^{95} +(1.98224 - 13.3924i) q^{96} +(-9.35583 + 5.40159i) q^{97} -3.36517i q^{98} +(-2.87137 - 0.869035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 40 q^{4} - 2 q^{5} + 4 q^{6} - 4 q^{9}+O(q^{10}) $ 68 * q + 40 * q^4 - 2 * q^5 + 4 * q^6 - 4 * q^9	$ 68 q + 40 q^{4} - 2 q^{5} + 4 q^{6} - 4 q^{9} + 34 q^{11} - 10 q^{14} - 28 q^{15} - 52 q^{16} - 40 q^{19} + q^{20} - 14 q^{21} + 20 q^{24} + 2 q^{25} - 24 q^{26} - 6 q^{29} + 22 q^{30} - 36 q^{31} + 34 q^{34} - 16 q^{36} - 12 q^{39} + 15 q^{40} + 6 q^{41} + 80 q^{44} + 50 q^{45} + 84 q^{46} + 60 q^{49} - 19 q^{50} + 48 q^{51} - 50 q^{54} - 4 q^{55} + 30 q^{56} - 103 q^{60} - 62 q^{61} - 164 q^{64} - 17 q^{65} + 2 q^{66} - 20 q^{69} + 28 q^{70} - 60 q^{71} + 14 q^{74} + 11 q^{75} - 86 q^{76} + 32 q^{79} + 50 q^{80} - 112 q^{81} - 36 q^{84} + q^{85} + 14 q^{86} + 20 q^{89} + 101 q^{90} + 104 q^{91} + 38 q^{94} + 6 q^{95} + 40 q^{96} + 4 q^{99}+O(q^{100}) $ 68 * q + 40 * q^4 - 2 * q^5 + 4 * q^6 - 4 * q^9 + 34 * q^11 - 10 * q^14 - 28 * q^15 - 52 * q^16 - 40 * q^19 + q^20 - 14 * q^21 + 20 * q^24 + 2 * q^25 - 24 * q^26 - 6 * q^29 + 22 * q^30 - 36 * q^31 + 34 * q^34 - 16 * q^36 - 12 * q^39 + 15 * q^40 + 6 * q^41 + 80 * q^44 + 50 * q^45 + 84 * q^46 + 60 * q^49 - 19 * q^50 + 48 * q^51 - 50 * q^54 - 4 * q^55 + 30 * q^56 - 103 * q^60 - 62 * q^61 - 164 * q^64 - 17 * q^65 + 2 * q^66 - 20 * q^69 + 28 * q^70 - 60 * q^71 + 14 * q^74 + 11 * q^75 - 86 * q^76 + 32 * q^79 + 50 * q^80 - 112 * q^81 - 36 * q^84 + q^85 + 14 * q^86 + 20 * q^89 + 101 * q^90 + 104 * q^91 + 38 * q^94 + 6 * q^95 + 40 * q^96 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.85631	−	1.07174i	1.31261	−	0.757834i	0.330079	−	0.943953i	$-0.392924\pi$
$2$	1.85631	−	1.07174i	1.31261	−	0.757834i	0.982527	+	0.186119i	$0.0595912\pi$
$3$	−0.637067	−	1.61064i	−0.367811	−	0.929901i
$3$	−0.637067	−	1.61064i	−0.367811	−	0.929901i
$4$	1.29725	−	2.24690i	0.648624	−	1.12345i
$5$	1.72303	−	1.42519i	0.770562	−	0.637365i
$5$	1.72303	−	1.42519i	0.770562	−	0.637365i
$6$	−2.90877	−	2.30706i	−1.18750	−	0.941855i
$7$	2.53525	−	1.46372i	0.958233	−	0.553236i	0.0626041	−	0.998038i	$-0.480059\pi$
$7$	2.53525	−	1.46372i	0.958233	−	0.553236i	0.895629	+	0.444803i	$0.146726\pi$
$8$		−	1.27429i		−	0.450529i
$9$	−2.18829	+	2.05216i	−0.729431	+	0.684055i
$10$	1.67104	−	4.49223i	0.528429	−	1.42057i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−4.44537	−	0.657969i	−1.28327	−	0.189939i
$13$	1.15477	+	0.666707i	0.320276	+	0.184911i	0.651516	−	0.758635i	$-0.274134\pi$
$13$	1.15477	+	0.666707i	0.320276	+	0.184911i	−0.331240	+	0.943547i	$0.607467\pi$
$14$	3.13746	−	5.43424i	0.838522	−	1.45236i
$15$	−3.39315	−	1.86723i	−0.876107	−	0.482117i
$16$	1.22879	+	2.12833i	0.307198	+	0.532083i
$17$			7.10247i			1.72260i	0.508096	+	0.861301i	$0.330350\pi$
$17$			7.10247i			1.72260i	−0.508096	+	0.861301i	$0.669650\pi$
$18$	−1.86276	+	6.15472i	−0.439056	+	1.45068i
$19$	−8.57612			−1.96750			−0.983749	−	0.179549i	$-0.942536\pi$
$19$	−8.57612			−1.96750			−0.983749	+	0.179549i	$0.942536\pi$
$20$	−0.967063	−	5.72030i	−0.216242	−	1.27910i
$21$	−3.97265	−	3.15087i	−0.866903	−	0.687575i
$22$	1.85631	+	1.07174i	0.395766	+	0.228495i
$23$	−2.26009	−	1.30486i	−0.471262	−	0.272083i	0.245506	−	0.969395i	$-0.421046\pi$
$23$	−2.26009	−	1.30486i	−0.471262	−	0.272083i	−0.716768	+	0.697312i	$0.754379\pi$
$24$	−2.05241	+	0.811806i	−0.418947	+	0.165709i
$25$	0.937663	−	4.91129i	0.187533	−	0.982258i
$26$	2.85814			0.560528
$27$	4.69938	+	2.21718i	0.904395	+	0.426696i
$28$		−	7.59525i		−	1.43537i
$29$	−2.32609	−	4.02891i	−0.431944	−	0.748150i	0.565096	−	0.825025i	$-0.308839\pi$
$29$	−2.32609	−	4.02891i	−0.431944	−	0.748150i	−0.997041	+	0.0768753i	$0.975506\pi$
$30$	−8.29990	+	0.170415i	−1.51535	+	0.0311134i
$31$	−0.273415	+	0.473569i	−0.0491068	+	0.0850556i	−0.889534	−	0.456869i	$-0.848971\pi$
$31$	−0.273415	+	0.473569i	−0.0491068	+	0.0850556i	0.840427	+	0.541925i	$0.182304\pi$
$32$	6.76916	+	3.90818i	1.19663	+	0.690874i
$33$	1.07632	−	1.35703i	0.187363	−	0.236229i
$34$	7.61199	+	13.1843i	1.30545	+	2.26110i
$35$	2.28222	−	6.13525i	0.385765	−	1.03705i
$36$	1.77225	+	7.57904i	0.295375	+	1.26317i
$37$			5.16561i			0.849220i	0.905376	+	0.424610i	$0.139589\pi$
$37$			5.16561i			0.849220i	−0.905376	+	0.424610i	$0.860411\pi$
$38$	−15.9199	+	9.19136i	−2.58255	+	1.49104i
$39$	0.338156	−	2.28465i	0.0541484	−	0.365837i
$40$	−1.81610	−	2.19564i	−0.287151	−	0.347160i
$41$	1.36211	−	2.35924i	0.212726	−	0.368452i	−0.739841	−	0.672782i	$-0.765099\pi$
$41$	1.36211	−	2.35924i	0.212726	−	0.368452i	0.952567	+	0.304330i	$0.0984326\pi$
$42$	−10.7514	−	1.59133i	−1.65897	−	0.245548i
$43$	−6.67079	+	3.85138i	−1.01729	+	0.587330i	−0.913317	−	0.407250i	$-0.866488\pi$
$43$	−6.67079	+	3.85138i	−1.01729	+	0.587330i	−0.103969	+	0.994581i	$0.533154\pi$
$44$	2.59450			0.391135
$45$	−0.845768	+	6.65467i	−0.126080	+	0.992020i
$46$	−5.59389			−0.824775
$47$	7.63697	−	4.40921i	1.11397	−	0.643149i	0.174113	−	0.984726i	$-0.444294\pi$
$47$	7.63697	−	4.40921i	1.11397	−	0.643149i	0.939854	+	0.341576i	$0.110961\pi$
$48$	2.64514	−	3.33502i	0.381793	−	0.481369i
$49$	0.784980	−	1.35962i	0.112140	−	0.194232i
$50$	−3.52303	−	10.1218i	−0.498232	−	1.43144i
$51$	11.4395	−	4.52474i	1.60185	−	0.633591i
$52$	2.99605	−	1.72977i	0.415477	−	0.239876i
$53$			3.90137i			0.535894i	0.963434	+	0.267947i	$0.0863452\pi$
$53$			3.90137i			0.535894i	−0.963434	+	0.267947i	$0.913655\pi$
$54$	11.0997	−	0.920745i	1.51048	−	0.125298i
$55$	2.09577	+	0.779592i	0.282593	+	0.105120i
$56$	−1.86521	−	3.23063i	−0.249249	−	0.431711i
$57$	5.46356	+	13.8130i	0.723666	+	1.82958i
$58$	−8.63588	−	4.98593i	−1.13395	−	0.654684i
$59$	3.42152	−	5.92624i	0.445444	−	0.771531i	−0.552639	−	0.833421i	$-0.686379\pi$
$59$	3.42152	−	5.92624i	0.445444	−	0.771531i	0.998083	+	0.0618893i	$0.0197126\pi$
$60$	−8.59723	+	5.20180i	−1.10990	+	0.671549i
$61$	2.03932	+	3.53221i	0.261108	+	0.452253i	0.966537	−	0.256528i	$-0.0825787\pi$
$61$	2.03932	+	3.53221i	0.261108	+	0.452253i	−0.705428	+	0.708781i	$0.749245\pi$
$62$			1.17212i			0.148859i
$63$	−2.54406	+	8.40580i	−0.320521	+	1.05903i
$64$	11.8390			1.47988
$65$	2.93989	−	0.497012i	0.364648	−	0.0616468i
$66$	0.543590	−	3.67260i	0.0669113	−	0.452066i
$67$	−1.70302	−	0.983237i	−0.208057	−	0.120122i	0.392351	−	0.919815i	$-0.371662\pi$
$67$	−1.70302	−	0.983237i	−0.208057	−	0.120122i	−0.600408	+	0.799694i	$0.704995\pi$
$68$	15.9585	+	9.21366i	1.93526	+	1.11732i
$69$	−0.661832	+	4.47147i	−0.0796752	+	0.538302i
$70$	−2.33889	−	13.8348i	−0.279551	−	1.65358i
$71$	−10.9996			−1.30542			−0.652708	−	0.757610i	$-0.726367\pi$
$71$	−10.9996			−1.30542			−0.652708	+	0.757610i	$0.726367\pi$
$72$	2.61505	+	2.78851i	0.308186	+	0.328629i
$73$		−	11.8252i		−	1.38404i	−0.721879	−	0.692019i	$-0.756721\pi$
$73$		−	11.8252i		−	1.38404i	0.721879	−	0.692019i	$-0.243279\pi$
$74$	5.53618	+	9.58895i	0.643568	+	1.11469i
$75$	−8.50765	+	1.61859i	−0.982379	+	0.186898i
$76$	−11.1254	+	19.2697i	−1.27617	+	2.21038i
$77$	2.53525	+	1.46372i	0.288918	+	0.166807i
$78$	−1.82083	−	4.60343i	−0.206168	−	0.521236i
$79$	0.576774	+	0.999001i	0.0648921	+	0.112396i	0.896646	−	0.442748i	$-0.145996\pi$
$79$	0.576774	+	0.999001i	0.0648921	+	0.112396i	−0.831754	+	0.555144i	$0.812663\pi$
$80$	5.15052	+	1.91591i	0.575846	+	0.214206i
$81$	0.577248	−	8.98147i	0.0641386	−	0.997941i
$82$		−	5.83930i		−	0.644843i
$83$	8.64355	−	4.99036i	0.948753	−	0.547763i	0.0560596	−	0.998427i	$-0.482146\pi$
$83$	8.64355	−	4.99036i	0.948753	−	0.547763i	0.892693	+	0.450665i	$0.148813\pi$
$84$	−12.2332	+	4.83868i	−1.33475	+	0.527943i
$85$	10.1224	+	12.2378i	1.09793	+	1.32737i
$86$	−8.25535	+	14.2987i	−0.890197	+	1.54187i
$87$	−5.00723	+	6.31317i	−0.536831	+	0.676843i
$88$	1.10357	−	0.637144i	0.117640	−	0.0679198i
$89$	17.0187			1.80398			0.901988	−	0.431760i	$-0.142107\pi$
$89$	17.0187			1.80398			0.901988	+	0.431760i	$0.142107\pi$
$90$	5.56207	+	13.2596i	0.586293	+	1.39768i
$91$	3.90350			0.409198
$92$	−5.86380	+	3.38546i	−0.611343	+	0.352959i
$93$	0.936931	+	0.138677i	0.0971552	+	0.0143802i
$94$	9.45104	−	16.3697i	0.974800	−	1.68840i
$95$	−14.7769	+	12.2226i	−1.51608	+	1.25401i
$96$	1.98224	−	13.3924i	0.202312	−	1.36686i
$97$	−9.35583	+	5.40159i	−0.949941	+	0.548449i	−0.893063	−	0.449932i	$-0.851448\pi$
$97$	−9.35583	+	5.40159i	−0.949941	+	0.548449i	−0.0568783	+	0.998381i	$0.518115\pi$
$98$		−	3.36517i		−	0.339934i
$99$	−2.87137	−	0.869035i	−0.288584	−	0.0873413i
$100$	−9.81880	−	8.47800i	−0.981880	−	0.847800i
$101$	−3.55260	−	6.15328i	−0.353497	−	0.612274i	0.633363	−	0.773855i	$-0.281674\pi$
$101$	−3.55260	−	6.15328i	−0.353497	−	0.612274i	−0.986859	+	0.161581i	$0.948341\pi$
$102$	16.3858	−	20.6594i	1.62244	−	2.04559i
$103$	3.75768	+	2.16949i	0.370255	+	0.213767i	0.673570	−	0.739124i	$-0.264760\pi$
$103$	3.75768	+	2.16949i	0.370255	+	0.213767i	−0.303315	+	0.952890i	$0.598093\pi$
$104$	0.849577	−	1.47151i	0.0833079	−	0.144293i
$105$	−11.3356	+	0.232744i	−1.10624	+	0.0227135i
$106$	4.18125	+	7.24213i	0.406119	+	0.703418i
$107$		−	6.22273i		−	0.601574i	−0.953691	−	0.300787i	$-0.902751\pi$
$107$		−	6.22273i		−	0.601574i	0.953691	−	0.300787i	$-0.0972493\pi$
$108$	11.0780	−	7.68279i	1.06598	−	0.739277i
$109$	−19.2812			−1.84681			−0.923404	−	0.383829i	$-0.874605\pi$
$109$	−19.2812			−1.84681			−0.923404	+	0.383829i	$0.874605\pi$
$110$	4.72590	−	0.798952i	0.450597	−	0.0761771i
$111$	8.31991	−	3.29083i	0.789691	−	0.312352i
$112$	6.23058	+	3.59723i	0.588734	+	0.339906i
$113$	12.6548	+	7.30627i	1.19047	+	0.687316i	0.958412	−	0.285387i	$-0.0921222\pi$
$113$	12.6548	+	7.30627i	1.19047	+	0.687316i	0.232054	+	0.972703i	$0.425456\pi$
$114$	24.9460	+	19.7857i	2.33641	+	1.85310i
$115$	−5.75388	+	0.972741i	−0.536553	+	0.0907086i
$116$	−12.0701			−1.12068
$117$	−3.89517	+	0.910829i	−0.360109	+	0.0842061i
$118$		−	14.6679i		−	1.35029i
$119$	10.3961	+	18.0065i	0.953005	+	1.65065i
$120$	−2.37939	+	4.32384i	−0.217208	+	0.394711i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	7.57121	+	4.37124i	0.685465	+	0.395753i
$123$	−4.66763	−	0.690867i	−0.420866	−	0.0622934i
$124$	0.709375	+	1.22867i	0.0637037	+	0.110338i
$125$	−5.38391	−	9.79865i	−0.481551	−	0.876418i
$126$	4.28627	+	18.3303i	0.381851	+	1.63299i
$127$		−	12.1554i		−	1.07862i	−0.842108	−	0.539308i	$-0.818686\pi$
$127$		−	12.1554i		−	1.07862i	0.842108	−	0.539308i	$-0.181314\pi$
$128$	8.43850	−	4.87197i	0.745865	−	0.430625i
$129$	10.4529	+	8.29062i	0.920327	+	0.729948i
$130$	4.92467	−	4.07340i	0.431922	−	0.357261i
$131$	−1.29559	+	2.24403i	−0.113196	+	0.196062i	−0.917057	−	0.398756i	$-0.869442\pi$
$131$	−1.29559	+	2.24403i	−0.113196	+	0.196062i	0.803861	+	0.594817i	$0.202776\pi$
$132$	−1.65287	−	4.17879i	−0.143864	−	0.363717i
$133$	−21.7426	+	12.5531i	−1.88532	+	1.08849i
$134$	−4.21509			−0.364129
$135$	11.2571	−	2.87725i	0.968854	−	0.247634i
$136$	9.05058			0.776081
$137$	11.5754	−	6.68304i	0.988951	−	0.570971i	0.0839903	−	0.996467i	$-0.473234\pi$
$137$	11.5754	−	6.68304i	0.988951	−	0.570971i	0.904961	+	0.425496i	$0.139900\pi$
$138$	3.56368	+	9.00972i	0.303361	+	0.766959i
$139$	1.11569	−	1.93243i	0.0946313	−	0.163906i	−0.814823	−	0.579709i	$-0.803166\pi$
$139$	1.11569	−	1.93243i	0.0946313	−	0.163906i	0.909455	+	0.415803i	$0.136499\pi$
$140$	−10.8247	−	13.0868i	−0.914853	−	1.10604i
$141$	−11.9669	−	9.49142i	−1.00779	−	0.799322i
$142$	−20.4187	+	11.7887i	−1.71350	+	0.989288i
$143$			1.33341i			0.111506i
$144$	−7.05664	−	2.13573i	−0.588053	−	0.177977i
$145$	−9.74989	−	3.62681i	−0.809684	−	0.301190i
$146$	−12.6736	−	21.9512i	−1.04887	−	1.81670i
$147$	−2.68994	−	0.398145i	−0.221863	−	0.0328384i
$148$	11.6066	+	6.70107i	0.954056	+	0.550825i
$149$	−9.75873	+	16.9026i	−0.799467	+	1.38472i	0.120497	+	0.992714i	$0.461551\pi$
$149$	−9.75873	+	16.9026i	−0.799467	+	1.38472i	−0.919964	+	0.392003i	$0.871782\pi$
$150$	−14.0581	+	12.1226i	−1.14784	+	0.989804i
$151$	−6.76648	−	11.7199i	−0.550648	−	0.953751i	−0.998228	−	0.0595069i	$-0.981047\pi$
$151$	−6.76648	−	11.7199i	−0.550648	−	0.953751i	0.447579	−	0.894244i	$-0.352286\pi$
$152$			10.9284i			0.886414i
$153$	−14.5754	−	15.5423i	−1.17835	−	1.25652i
$154$	6.27492			0.505648
$155$	0.203824	+	1.20564i	0.0163715	+	0.0968396i
$156$	−4.69471	−	3.72356i	−0.375878	−	0.298124i
$157$	8.15431	+	4.70789i	0.650785	+	0.375731i	0.788757	−	0.614705i	$-0.210725\pi$
$157$	8.15431	+	4.70789i	0.650785	+	0.375731i	−0.137972	+	0.990436i	$0.544058\pi$
$158$	2.14134	+	1.23630i	0.170356	+	0.0983549i
$159$	6.28368	−	2.48543i	0.498328	−	0.197108i
$160$	17.2334	−	2.91344i	1.36242	−	0.230328i
$161$	−7.63985			−0.602104
$162$	−8.55424	−	17.2910i	−0.672085	−	1.35851i
$163$		−	10.6611i		−	0.835038i	−0.908668	−	0.417519i	$-0.862900\pi$
$163$		−	10.6611i		−	0.835038i	0.908668	−	0.417519i	$-0.137100\pi$
$164$	−3.53399	−	6.12104i	−0.275958	−	0.477973i
$165$	−0.0795039	−	3.87217i	−0.00618937	−	0.301448i
$166$	10.6967	−	18.5273i	0.830226	−	1.43799i
$167$	0.408443	+	0.235815i	0.0316063	+	0.0182479i	0.515720	−	0.856757i	$-0.327525\pi$
$167$	0.408443	+	0.235815i	0.0316063	+	0.0182479i	−0.484114	+	0.875005i	$0.660858\pi$
$168$	−4.01511	+	5.06229i	−0.309772	+	0.390564i
$169$	−5.61100	−	9.71854i	−0.431616	−	0.747580i
$170$	31.9059	+	11.8685i	2.44707	+	0.910272i
$171$	18.7671	−	17.5996i	1.43515	−	1.34588i
$172$			19.9848i			1.52383i
$173$	−14.1170	+	8.15044i	−1.07329	+	0.619667i	−0.929080	−	0.369880i	$-0.879399\pi$
$173$	−14.1170	+	8.15044i	−1.07329	+	0.619667i	−0.144215	+	0.989546i	$0.546066\pi$
$174$	−2.52888	+	17.0856i	−0.191714	+	1.29526i
$175$	−4.81157	−	13.8238i	−0.363721	−	1.04498i
$176$	−1.22879	+	2.12833i	−0.0926237	+	0.160429i
$177$	−11.7248	−	1.73541i	−0.881286	−	0.130441i
$178$	31.5919	−	18.2396i	2.36791	−	1.36711i
$179$	−0.437477			−0.0326986			−0.0163493	−	0.999866i	$-0.505204\pi$
$179$	−0.437477			−0.0326986			−0.0163493	+	0.999866i	$0.505204\pi$
$180$	13.8552	+	10.5331i	1.03271	+	0.785092i
$181$	−10.7760			−0.800970			−0.400485	−	0.916303i	$-0.631158\pi$
$181$	−10.7760			−0.800970			−0.400485	+	0.916303i	$0.631158\pi$
$182$	7.24610	−	4.18354i	0.537117	−	0.310104i
$183$	4.38992	−	5.53485i	0.324512	−	0.409148i
$184$	−1.66277	+	2.88001i	−0.122581	+	0.212317i
$185$	7.36197	+	8.90049i	0.541263	+	0.654377i
$186$	1.88786	−	0.746718i	0.138424	−	0.0547520i
$187$	−6.15092	+	3.55123i	−0.449800	+	0.259692i
$188$		−	22.8793i		−	1.66865i
$189$	15.1594	−	1.25751i	1.10268	−	0.0914701i
$190$	−14.3310	+	38.5259i	−1.03968	+	2.79496i
$191$	−1.31978	−	2.28593i	−0.0954963	−	0.165404i	0.814319	−	0.580417i	$-0.197110\pi$
$191$	−1.31978	−	2.28593i	−0.0954963	−	0.165404i	−0.909816	+	0.415013i	$0.863777\pi$
$192$	−7.54223	−	19.0683i	−0.544314	−	1.37614i
$193$	−11.0154	−	6.35974i	−0.792905	−	0.457784i	0.0480790	−	0.998844i	$-0.484690\pi$
$193$	−11.0154	−	6.35974i	−0.792905	−	0.457784i	−0.840984	+	0.541059i	$0.818023\pi$
$194$	−11.5782	+	20.0540i	−0.831266	+	1.43979i
$195$	−2.67341	−	4.41846i	−0.191447	−	0.316413i
$196$	−2.03663	−	3.52754i	−0.145473	−	0.251967i
$197$			17.8489i			1.27168i	0.771821	+	0.635840i	$0.219346\pi$
$197$			17.8489i			1.27168i	−0.771821	+	0.635840i	$0.780654\pi$
$198$	−6.26152	+	1.46417i	−0.444987	+	0.104054i
$199$	−3.26066			−0.231142			−0.115571	−	0.993299i	$-0.536870\pi$
$199$	−3.26066			−0.231142			−0.115571	+	0.993299i	$0.536870\pi$
$200$	−6.25840	−	1.19485i	−0.442536	−	0.0844888i
$201$	−0.498702	+	3.36933i	−0.0351757	+	0.237654i
$202$	−13.1894	−	7.61491i	−0.928004	−	0.535783i
$203$	−11.7944	−	6.80952i	−0.827807	−	0.477934i
$204$	4.67320	−	31.5731i	0.327190	−	2.21056i
$205$	−1.01542	−	6.00631i	−0.0709197	−	0.419499i
$206$	9.30053			0.647998
$207$	7.62354	−	1.78265i	0.529872	−	0.123903i
$208$			3.27698i			0.227218i
$209$	−4.28806	−	7.42714i	−0.296611	−	0.513746i
$210$	−20.7929	+	12.5808i	−1.43484	+	0.868159i
$211$	−5.63414	+	9.75862i	−0.387870	+	0.671811i	−0.992163	−	0.124951i	$-0.960122\pi$
$211$	−5.63414	+	9.75862i	−0.387870	+	0.671811i	0.604293	+	0.796762i	$0.293456\pi$
$212$	8.76598	+	5.06104i	0.602050	+	0.347594i
$213$	7.00750	+	17.7164i	0.480146	+	1.21391i
$214$	−6.66914	−	11.5513i	−0.455893	−	0.789630i
$215$	−6.00501	+	16.1432i	−0.409538	+	1.10096i
$216$	2.82532	−	5.98836i	0.192239	−	0.407456i
$217$			1.60082i			0.108671i
$218$	−35.7919	+	20.6645i	−2.42413	+	1.39957i
$219$	−19.0461	+	7.53346i	−1.28702	+	0.509064i
$220$	4.47039	−	3.69765i	0.301394	−	0.249296i
$221$	−4.73527	+	8.20172i	−0.318529	+	0.551708i
$222$	11.9174	−	15.0256i	0.799842	−	1.00845i
$223$	−2.92808	+	1.69053i	−0.196079	+	0.113206i	−0.594825	−	0.803855i	$-0.702779\pi$
$223$	−2.92808	+	1.69053i	−0.196079	+	0.113206i	0.398746	+	0.917061i	$0.369445\pi$
$224$	22.8820			1.52887
$225$	8.02690	+	12.6716i	0.535126	+	0.844772i
$226$	31.3216			2.08348
$227$	4.05679	−	2.34219i	0.269259	−	0.155457i	−0.359292	−	0.933225i	$-0.616982\pi$
$227$	4.05679	−	2.34219i	0.269259	−	0.155457i	0.628551	+	0.777769i	$0.283648\pi$
$228$	38.1240	+	5.64282i	2.52483	+	0.373705i
$229$	−6.42968	+	11.1365i	−0.424885	+	0.735923i	−0.996410	−	0.0846620i	$-0.973019\pi$
$229$	−6.42968	+	11.1365i	−0.424885	+	0.735923i	0.571524	+	0.820585i	$0.306352\pi$
$230$	−9.63845	+	7.97237i	−0.635540	+	0.525682i
$231$	0.742407	−	5.01585i	0.0488468	−	0.330018i
$232$	−5.13399	+	2.96411i	−0.337063	+	0.194603i
$233$			2.75352i			0.180389i	0.995924	+	0.0901944i	$0.0287488\pi$
$233$			2.75352i			0.180389i	−0.995924	+	0.0901944i	$0.971251\pi$
$234$	−6.25446	+	5.86538i	−0.408867	+	0.383432i
$235$	6.87477	−	18.4813i	0.448461	−	1.20559i
$236$	−8.87711	−	15.3756i	−0.577851	−	1.00087i
$237$	1.24158	−	1.56540i	0.0806495	−	0.101684i
$238$	38.5965	+	22.2837i	2.50184	+	1.44444i
$239$	7.92403	−	13.7248i	0.512563	−	0.887785i	−0.487331	−	0.873217i	$-0.662029\pi$
$239$	7.92403	−	13.7248i	0.512563	−	0.887785i	0.999894	−	0.0145679i	$-0.00463726\pi$
$240$	−0.195388	−	9.51618i	−0.0126122	−	0.614267i
$241$	9.66100	+	16.7333i	0.622320	+	1.07789i	0.989053	+	0.147563i	$0.0471430\pi$
$241$	9.66100	+	16.7333i	0.622320	+	1.07789i	−0.366733	+	0.930326i	$0.619524\pi$
$242$			2.14348i			0.137788i
$243$	−14.8336	+	4.79206i	−0.951577	+	0.307411i
$244$	10.5820			0.677444
$245$	−0.585181	−	3.46142i	−0.0373859	−	0.221142i
$246$	−9.40498	+	3.72002i	−0.599640	+	0.237180i
$247$	−9.90346	−	5.71777i	−0.630142	−	0.363813i
$248$	0.603463	+	0.348410i	0.0383200	+	0.0221240i
$249$	−13.5442	−	10.7424i	−0.858326	−	0.680773i
$250$	−20.4958	−	12.4191i	−1.29627	−	0.785456i
$251$	−4.66295			−0.294323			−0.147161	−	0.989112i	$-0.547014\pi$
$251$	−4.66295			−0.294323			−0.147161	+	0.989112i	$0.547014\pi$
$252$	15.5867	+	16.6206i	0.981870	+	1.04700i
$253$		−	2.60973i		−	0.164072i
$254$	−13.0274	−	22.5641i	−0.817412	−	1.41580i
$255$	13.2619	−	24.0997i	0.830495	−	1.50918i
$256$	−1.39605	+	2.41803i	−0.0872532	+	0.151127i
$257$	−4.40733	−	2.54458i	−0.274922	−	0.158726i	0.356200	−	0.934410i	$-0.384072\pi$
$257$	−4.40733	−	2.54458i	−0.274922	−	0.158726i	−0.631122	+	0.775683i	$0.717405\pi$
$258$	28.2892	+	4.18714i	1.76121	+	0.260680i
$259$	7.56103	+	13.0961i	0.469819	+	0.813751i
$260$	2.69703	−	7.25038i	0.167263	−	0.449650i
$261$	13.3582	+	4.04291i	0.826849	+	0.250250i
$262$			5.55414i			0.343136i
$263$	−1.95001	+	1.12584i	−0.120243	+	0.0694221i	−0.558915	−	0.829225i	$-0.688782\pi$
$263$	−1.95001	+	1.12584i	−0.120243	+	0.0694221i	0.438672	+	0.898647i	$0.355449\pi$
$264$	−1.72925	−	1.37154i	−0.106428	−	0.0844124i
$265$	5.56019	+	6.72217i	0.341560	+	0.412940i
$266$	−26.9073	+	46.6047i	−1.64979	+	2.85752i
$267$	−10.8420	−	27.4109i	−0.663522	−	1.67752i
$268$	−4.41847	+	2.55101i	−0.269901	+	0.155827i
$269$	20.5811			1.25485			0.627426	−	0.778676i	$-0.284108\pi$
$269$	20.5811			1.25485			0.627426	+	0.778676i	$0.284108\pi$
$270$	17.8129	−	17.4057i	1.08406	−	1.05928i
$271$	23.3736			1.41984			0.709921	−	0.704281i	$-0.248730\pi$
$271$	23.3736			1.41984			0.709921	+	0.704281i	$0.248730\pi$
$272$	−15.1164	+	8.72746i	−0.916566	+	0.529180i
$273$	−2.48679	−	6.28712i	−0.150507	−	0.380514i
$274$	14.3250	−	24.8116i	0.865402	−	1.49892i
$275$	4.72213	−	1.64361i	0.284755	−	0.0991132i
$276$	9.18838	+	7.28767i	0.553075	+	0.438666i
$277$	−9.20882	+	5.31671i	−0.553304	+	0.319450i	−0.750454	−	0.660923i	$-0.770165\pi$
$277$	−9.20882	+	5.31671i	−0.553304	+	0.319450i	0.197149	+	0.980373i	$0.436832\pi$
$278$		−	4.78290i		−	0.286859i
$279$	−0.373529	−	1.59740i	−0.0223626	−	0.0956339i
$280$	−7.81807	−	2.90820i	−0.467219	−	0.173798i
$281$	9.77821	+	16.9364i	0.583319	+	1.01034i	0.995083	+	0.0990476i	$0.0315796\pi$
$281$	9.77821	+	16.9364i	0.583319	+	1.01034i	−0.411764	+	0.911291i	$0.635087\pi$
$282$	−32.3865	−	4.79360i	−1.92859	−	0.285455i
$283$	12.1586	+	7.01977i	0.722754	+	0.417282i	0.815765	−	0.578383i	$-0.196316\pi$
$283$	12.1586	+	7.01977i	0.722754	+	0.417282i	−0.0930115	+	0.995665i	$0.529649\pi$
$284$	−14.2692	+	24.7151i	−0.846724	+	1.46657i
$285$	29.1001	+	16.0136i	1.72374	+	0.948564i
$286$	1.42907	+	2.47523i	0.0845028	+	0.146363i
$287$		−	7.97501i		−	0.470750i
$288$	−22.8331	+	5.33919i	−1.34545	+	0.314615i
$289$	−33.4450			−1.96735
$290$	−21.9858	+	3.71687i	−1.29105	+	0.218262i
$291$	14.6603	+	11.6277i	0.859401	+	0.681626i
$292$	−26.5701	−	15.3403i	−1.55490	−	0.897720i
$293$	−2.40153	−	1.38653i	−0.140299	−	0.0810017i	0.428207	−	0.903680i	$-0.359145\pi$
$293$	−2.40153	−	1.38653i	−0.140299	−	0.0810017i	−0.568506	+	0.822679i	$0.692479\pi$
$294$	−5.42007	+	2.14384i	−0.316105	+	0.125031i
$295$	−2.55065	−	15.0874i	−0.148505	−	0.878423i
$296$	6.58247			0.382598
$297$	0.429557	+	5.17837i	0.0249254	+	0.300479i
$298$			41.8353i			2.42345i
$299$	−1.73993	−	3.01364i	−0.100622	−	0.174283i
$300$	−7.39973	+	21.2155i	−0.427224	+	1.22488i
$301$	−11.2747	+	19.5284i	−0.649864	+	1.12560i
$302$	−25.1213	−	14.5038i	−1.44557	−	0.834600i
$303$	−7.64745	+	9.64199i	−0.439335	+	0.553918i
$304$	−10.5383	−	18.2528i	−0.604412	−	1.04687i
$305$	8.54788	+	3.17968i	0.489450	+	0.182068i
$306$	−43.7137	−	13.2302i	−2.49895	−	0.756318i
$307$		−	1.65546i		−	0.0944819i	−0.998884	−	0.0472409i	$-0.984957\pi$
$307$		−	1.65546i		−	0.0944819i	0.998884	−	0.0472409i	$-0.0150429\pi$
$308$	6.57768	−	3.79763i	0.374798	−	0.216390i
$309$	1.10038	−	7.43436i	0.0625982	−	0.422926i
$310$	1.67049	+	2.01960i	0.0948777	+	0.114705i
$311$	15.5068	−	26.8586i	0.879312	−	1.52301i	0.0272154	−	0.999630i	$-0.491336\pi$
$311$	15.5068	−	26.8586i	0.879312	−	1.52301i	0.852097	−	0.523384i	$-0.175331\pi$
$312$	−2.91130	−	0.430909i	−0.164820	−	0.0243954i
$313$	−10.4016	+	6.00534i	−0.587931	+	0.339442i	−0.764279	−	0.644886i	$-0.776905\pi$
$313$	−10.4016	+	6.00534i	−0.587931	+	0.339442i	0.176348	+	0.984328i	$0.443572\pi$
$314$	20.1825			1.13897
$315$	7.59638	+	18.1092i	0.428008	+	1.02034i
$316$	2.99287			0.168362
$317$	15.1879	−	8.76871i	0.853035	−	0.492500i	−0.00863890	−	0.999963i	$-0.502750\pi$
$317$	15.1879	−	8.76871i	0.853035	−	0.492500i	0.861674	+	0.507463i	$0.169417\pi$
$318$	9.00070	−	11.3482i	0.504734	−	0.636375i
$319$	2.32609	−	4.02891i	0.130236	−	0.225576i
$320$	20.3990	−	16.8728i	1.14034	−	0.943220i
$321$	−10.0225	+	3.96429i	−0.559404	+	0.221265i
$322$	−14.1819	+	8.18792i	−0.790326	+	0.456295i
$323$		−	60.9116i		−	3.38921i
$324$	−19.4316	−	12.9482i	−1.07953	−	0.719345i
$325$	4.35718	−	5.04627i	0.241693	−	0.279917i
$326$	−11.4259	−	19.7902i	−0.632820	−	1.09608i
$327$	12.2834	+	31.0551i	0.679276	+	1.71735i
$328$	−3.00635	−	1.73572i	−0.165998	−	0.0958390i
$329$	12.9077	−	22.3569i	0.711627	−	1.23257i
$330$	−4.29754	−	7.10272i	−0.236572	−	0.390992i
$331$	−0.632417	−	1.09538i	−0.0347608	−	0.0602074i	0.848122	−	0.529802i	$-0.177734\pi$
$331$	−0.632417	−	1.09538i	−0.0347608	−	0.0602074i	−0.882882	+	0.469594i	$0.844400\pi$
$332$		−	25.8949i		−	1.42117i
$333$	−10.6007	−	11.3039i	−0.580913	−	0.619448i
$334$	1.01093			0.0553155
$335$	−4.33565	+	0.732977i	−0.236882	+	0.0400468i
$336$	1.82453	−	12.3269i	0.0995361	−	0.672486i
$337$	−16.2827	−	9.40083i	−0.886976	−	0.512096i	−0.0140239	−	0.999902i	$-0.504464\pi$
$337$	−16.2827	−	9.40083i	−0.886976	−	0.512096i	−0.872952	+	0.487806i	$0.837797\pi$
$338$	−20.8315	−	12.0271i	−1.13308	−	0.654186i
$339$	3.70577	−	25.0369i	0.201270	−	1.35982i
$340$	40.6282	−	6.86853i	2.20338	−	0.372499i
$341$	−0.546831			−0.0296125
$342$	15.9752	−	52.7837i	0.863842	−	2.85421i
$343$			15.8962i			0.858312i
$344$	4.90777	+	8.50050i	0.264609	+	0.458316i
$345$	5.23234	+	8.64771i	0.281700	+	0.465577i
$346$	−17.4703	+	30.2594i	−0.939209	+	1.62676i
$347$	2.11282	+	1.21984i	0.113422	+	0.0654844i	0.555638	−	0.831424i	$-0.312474\pi$
$347$	2.11282	+	1.21984i	0.113422	+	0.0654844i	−0.442216	+	0.896909i	$0.645807\pi$
$348$	7.68944	+	19.4405i	0.412197	+	1.04212i
$349$	12.4405	+	21.5476i	0.665925	+	1.15342i	0.979034	+	0.203699i	$0.0652963\pi$
$349$	12.4405	+	21.5476i	0.665925	+	1.15342i	−0.313108	+	0.949717i	$0.601370\pi$
$350$	−23.7473	−	20.5045i	−1.26934	−	1.09601i
$351$	3.94850	+	5.69344i	0.210755	+	0.303893i
$352$			7.81635i			0.416613i
$353$	11.8537	−	6.84374i	0.630909	−	0.364256i	−0.150195	−	0.988656i	$-0.547990\pi$
$353$	11.8537	−	6.84374i	0.630909	−	0.364256i	0.781104	+	0.624401i	$0.214657\pi$
$354$	−23.6246	+	9.34443i	−1.25564	+	0.496651i
$355$	−18.9527	+	15.6766i	−1.00590	+	0.832026i
$356$	22.0774	−	38.2393i	1.17010	−	2.02668i
$357$	22.3789	−	28.2156i	1.18442	−	1.49333i
$358$	−0.812091	+	0.468861i	−0.0429203	+	0.0247801i
$359$	−8.30156			−0.438140			−0.219070	−	0.975709i	$-0.570302\pi$
$359$	−8.30156			−0.438140			−0.219070	+	0.975709i	$0.570302\pi$
$360$	8.47997	+	1.07775i	0.446933	+	0.0568025i
$361$	54.5499			2.87105
$362$	−20.0035	+	11.5490i	−1.05136	+	0.607002i
$363$	1.71338	+	0.253602i	0.0899294	+	0.0133106i
$364$	5.06381	−	8.77078i	0.265416	−	0.459714i
$365$	−16.8532	−	20.3752i	−0.882137	−	1.06649i
$366$	2.21711	−	14.9792i	0.115890	−	0.782977i
$367$	4.43187	−	2.55874i	0.231342	−	0.133565i	−0.379849	−	0.925048i	$-0.624024\pi$
$367$	4.43187	−	2.55874i	0.231342	−	0.133565i	0.611191	+	0.791483i	$0.290691\pi$
$368$		−	6.41363i		−	0.334333i
$369$	1.86086	+	7.95798i	0.0968724	+	0.414276i
$370$	23.2051	+	8.63192i	1.20637	+	0.448752i
$371$	5.71053	+	9.89093i	0.296476	+	0.513511i
$372$	1.52703	−	1.92529i	0.0791726	−	0.0998217i
$373$	−3.97429	−	2.29456i	−0.205781	−	0.118808i	0.393568	−	0.919295i	$-0.371241\pi$
$373$	−3.97429	−	2.29456i	−0.205781	−	0.118808i	−0.599349	+	0.800488i	$0.704574\pi$
$374$	−7.61199	+	13.1843i	−0.393607	+	0.681747i
$375$	−12.3521	+	14.9139i	−0.637862	+	0.770151i
$376$	−5.61860	−	9.73170i	−0.289757	−	0.501874i
$377$		−	6.20329i		−	0.319486i
$378$	26.7928	−	18.5812i	1.37807	−	0.955716i
$379$	−2.21194			−0.113620			−0.0568099	−	0.998385i	$-0.518093\pi$
$379$	−2.21194			−0.113620			−0.0568099	+	0.998385i	$0.518093\pi$
$380$	8.29366	+	49.0580i	0.425456	+	2.51662i
$381$	−19.5779	+	7.74379i	−1.00301	+	0.396727i
$382$	−4.89985	−	2.82893i	−0.250698	−	0.144741i
$383$	15.2897	+	8.82752i	0.781268	+	0.451065i	0.836879	−	0.547387i	$-0.184378\pi$
$383$	15.2897	+	8.82752i	0.781268	+	0.451065i	−0.0556117	+	0.998452i	$0.517711\pi$
$384$	−13.2228	−	10.4876i	−0.674776	−	0.535192i
$385$	6.45439	−	1.09117i	0.328946	−	0.0556110i
$386$	−27.2639			−1.38770
$387$	6.69397	−	22.1175i	0.340274	−	1.12430i
$388$			28.0288i			1.42295i
$389$	−13.3684	−	23.1548i	−0.677807	−	1.17400i	−0.975640	−	0.219378i	$-0.929597\pi$
$389$	−13.3684	−	23.1548i	−0.677807	−	1.17400i	0.297833	−	0.954618i	$-0.403736\pi$
$390$	−9.69811	−	5.33682i	−0.491083	−	0.270240i
$391$	9.26775	−	16.0522i	0.468690	−	0.811796i
$392$	−1.73255	−	1.00029i	−0.0875071	−	0.0505223i
$393$	4.43969	+	0.657128i	0.223953	+	0.0331477i
$394$	19.1293	+	33.1330i	0.963723	+	1.66922i
$395$	2.41757	+	0.899296i	0.121641	+	0.0452485i
$396$	−5.67751	+	5.32433i	−0.285306	+	0.267558i
$397$		−	8.07833i		−	0.405440i	−0.979237	−	0.202720i	$-0.935022\pi$
$397$		−	8.07833i		−	0.405440i	0.979237	−	0.202720i	$-0.0649781\pi$
$398$	−6.05279	+	3.49458i	−0.303399	+	0.175167i
$399$	34.0699	+	27.0222i	1.70563	+	1.35280i
$400$	11.6050	−	4.03930i	0.580252	−	0.201965i
$401$	−11.6565	+	20.1897i	−0.582098	+	1.00822i	0.413132	+	0.910671i	$0.364435\pi$
$401$	−11.6565	+	20.1897i	−0.582098	+	1.00822i	−0.995230	+	0.0975523i	$0.968899\pi$
$402$	2.68530	+	6.78898i	0.133930	+	0.338604i
$403$	−0.631464	+	0.364576i	−0.0314555	+	0.0181608i
$404$	−18.4344			−0.917146
$405$	−11.8057	−	16.2980i	−0.586630	−	0.809855i
$406$	−29.1921			−1.44878
$407$	−4.47355	+	2.58280i	−0.221745	+	0.128025i
$408$	−5.76582	−	14.5772i	−0.285451	−	0.721678i
$409$	−1.53261	+	2.65456i	−0.0757827	+	0.131260i	−0.901426	−	0.432932i	$-0.857479\pi$
$409$	−1.53261	+	2.65456i	−0.0757827	+	0.131260i	0.825644	+	0.564192i	$0.190812\pi$
$410$	−8.32211	−	10.0613i	−0.411000	−	0.496891i
$411$	−18.1382	−	14.3862i	−0.894693	−	0.709617i
$412$	9.74927	−	5.62874i	0.480312	−	0.277308i
$413$		−	20.0326i		−	0.985742i
$414$	12.2411	−	11.4796i	0.601616	−	0.564191i
$415$	7.78089	−	20.9172i	0.381949	−	1.02679i
$416$	5.21122	+	9.02610i	0.255501	+	0.442541i
$417$	−3.82320	−	0.565881i	−0.187223	−	0.0277113i
$418$	−15.9199	−	9.19136i	−0.778668	−	0.449564i
$419$	−2.92425	+	5.06495i	−0.142859	+	0.247439i	−0.928572	−	0.371152i	$-0.878963\pi$
$419$	−2.92425	+	5.06495i	−0.142859	+	0.247439i	0.785713	+	0.618591i	$0.212296\pi$
$420$	−14.1821	+	25.7718i	−0.692015	+	1.25754i
$421$	0.346802	+	0.600679i	0.0169021	+	0.0292753i	0.874353	−	0.485291i	$-0.161286\pi$
$421$	0.346802	+	0.600679i	0.0169021	+	0.0292753i	−0.857451	+	0.514566i	$0.827953\pi$
$422$			24.1533i			1.17576i
$423$	−7.66351	+	25.3210i	−0.372613	+	1.23115i
$424$	4.97146			0.241436
$425$	34.8823	+	6.65972i	1.69204	+	0.323044i
$426$	31.9954	+	25.3768i	1.55018	+	1.22951i
$427$	10.3404	+	5.97001i	0.500405	+	0.288909i
$428$	−13.9818	−	8.07242i	−0.675838	−	0.390195i
$429$	2.14765	−	0.849474i	0.103689	−	0.0410130i
$430$	6.15414	+	36.4025i	0.296779	+	1.75548i
$431$	−15.2816			−0.736091			−0.368045	−	0.929808i	$-0.619973\pi$
$431$	−15.2816			−0.736091			−0.368045	+	0.929808i	$0.619973\pi$
$432$	1.05567	+	12.7263i	0.0507910	+	0.612293i
$433$			3.33946i			0.160484i	0.996775	+	0.0802422i	$0.0255694\pi$
$433$			3.33946i			0.160484i	−0.996775	+	0.0802422i	$0.974431\pi$
$434$	1.71566	+	2.97161i	0.0823543	+	0.142642i
$435$	0.369867	+	18.0140i	0.0177338	+	0.863707i
$436$	−25.0126	+	43.3230i	−1.19788	+	2.07480i
$437$	19.3828	+	11.1907i	0.927206	+	0.535323i
$438$	−27.2815	+	34.3969i	−1.30356	+	1.64355i
$439$	12.7675	+	22.1140i	0.609362	+	1.05545i	0.991346	+	0.131276i	$0.0419076\pi$
$439$	12.7675	+	22.1140i	0.609362	+	1.05545i	−0.381984	+	0.924169i	$0.624759\pi$
$440$	0.993424	−	2.67061i	0.0473597	−	0.127316i
$441$	1.07241	+	4.58616i	0.0510670	+	0.218389i
$442$			20.2999i			0.965567i
$443$	−22.5168	+	13.0001i	−1.06981	+	0.617652i	−0.928128	−	0.372260i	$-0.878583\pi$
$443$	−22.5168	+	13.0001i	−1.06981	+	0.617652i	−0.141677	+	0.989913i	$0.545249\pi$
$444$	3.39881	−	22.9630i	0.161300	−	1.08978i
$445$	29.3237	−	24.2549i	1.39008	−	1.14979i
$446$	−3.62361	+	6.27627i	−0.171583	+	0.297190i
$447$	33.4409	+	4.94967i	1.58170	+	0.234111i
$448$	30.0148	−	17.3290i	1.41807	−	0.818720i
$449$	−10.4205			−0.491775			−0.245887	−	0.969298i	$-0.579079\pi$
$449$	−10.4205			−0.491775			−0.245887	+	0.969298i	$0.579079\pi$
$450$	28.4810	+	14.9196i	1.34261	+	0.703316i
$451$	2.72422			0.128278
$452$	32.8329	−	18.9561i	1.54433	−	0.891619i
$453$	−14.5658	+	18.3647i	−0.684360	+	0.862848i
$454$	5.02043	−	8.69564i	0.235620	−	0.408106i
$455$	6.72585	−	5.56324i	0.315313	−	0.260809i
$456$	17.6017	−	6.96215i	0.824277	−	0.326032i
$457$	35.9618	−	20.7626i	1.68222	−	0.971232i	0.722044	−	0.691847i	$-0.243203\pi$
$457$	35.9618	−	20.7626i	1.68222	−	0.971232i	0.960179	−	0.279385i	$-0.0901305\pi$
$458$			27.5638i			1.28797i
$459$	−15.7474	+	33.3772i	−0.735027	+	1.55791i
$460$	−5.27856	+	14.1903i	−0.246114	+	0.661625i
$461$	−1.76713	−	3.06076i	−0.0823036	−	0.142554i	0.821935	−	0.569581i	$-0.192894\pi$
$461$	−1.76713	−	3.06076i	−0.0823036	−	0.142554i	−0.904239	+	0.427027i	$0.859561\pi$
$462$	−3.99754	−	10.1066i	−0.185983	−	0.470202i
$463$	16.0665	+	9.27602i	0.746676	+	0.431093i	0.824492	−	0.565874i	$-0.191461\pi$
$463$	16.0665	+	9.27602i	0.746676	+	0.431093i	−0.0778158	+	0.996968i	$0.524795\pi$
$464$	5.71657	−	9.90139i	0.265385	−	0.459660i
$465$	1.81200	−	1.09636i	0.0840296	−	0.0508425i
$466$	2.95105	+	5.11137i	0.136705	+	0.236779i
$467$		−	12.9754i		−	0.600431i	−0.953871	−	0.300216i	$-0.902941\pi$
$467$		−	12.9754i		−	0.600431i	0.953871	−	0.300216i	$-0.0970587\pi$
$468$	−3.00646	+	9.93362i	−0.138974	+	0.459182i
$469$	−5.75676			−0.265822
$470$	−7.04550	−	41.6750i	−0.324985	−	1.92232i
$471$	2.38786	−	16.1329i	0.110027	−	0.743363i
$472$	−7.55174	−	4.36000i	−0.347597	−	0.200685i
$473$	−6.67079	−	3.85138i	−0.306723	−	0.177087i
$474$	0.627057	−	4.23652i	0.0288017	−	0.194590i
$475$	−8.04151	+	42.1199i	−0.368970	+	1.93259i
$476$	53.9450			2.47257
$477$	−8.00625	−	8.53734i	−0.366581	−	0.390898i
$478$		−	33.9700i		−	1.55375i
$479$	−11.7779	−	20.3999i	−0.538146	−	0.932096i	−0.999004	−	0.0446221i	$-0.985792\pi$
$479$	−11.7779	−	20.3999i	−0.538146	−	0.932096i	0.460858	−	0.887474i	$-0.347542\pi$
$480$	−15.6713	−	25.9006i	−0.715293	−	1.18220i
$481$	−3.44395	+	5.96509i	−0.157031	+	0.271985i
$482$	35.8676	+	20.7081i	1.63372	+	0.943230i
$483$	4.86709	+	12.3050i	0.221460	+	0.559897i
$484$	1.29725	+	2.24690i	0.0589658	+	0.102132i
$485$	−8.42208	+	22.6410i	−0.382427	+	1.02807i
$486$	−22.3999	+	24.7933i	−1.01608	+	1.12465i
$487$			16.1533i			0.731978i	0.930619	+	0.365989i	$0.119269\pi$
$487$			16.1533i			0.731978i	−0.930619	+	0.365989i	$0.880731\pi$
$488$	4.50105	−	2.59868i	0.203753	−	0.117637i
$489$	−17.1711	+	6.79180i	−0.776503	+	0.307136i
$490$	−4.79601	−	5.79829i	−0.216662	−	0.261940i
$491$	10.6388	−	18.4269i	0.480122	−	0.831595i	−0.519618	−	0.854399i	$-0.673926\pi$
$491$	10.6388	−	18.4269i	0.480122	−	0.831595i	0.999740	+	0.0228033i	$0.00725914\pi$
$492$	−7.60738	+	9.59147i	−0.342967	+	0.432417i
$493$	28.6152	−	16.5210i	1.28876	−	0.744068i
$494$	−24.5118			−1.10284
$495$	−6.18600	+	2.59488i	−0.278040	+	0.116631i
$496$	−1.34388			−0.0603421
$497$	−27.8868	+	16.1004i	−1.25089	+	0.722203i
$498$	−36.6552	−	5.42541i	−1.64256	−	0.243119i
$499$	6.89669	−	11.9454i	0.308738	−	0.534750i	−0.669348	−	0.742949i	$-0.733427\pi$
$499$	6.89669	−	11.9454i	0.308738	−	0.534750i	0.978087	+	0.208198i	$0.0667599\pi$
$500$	−29.0008	−	0.614181i	−1.29696	−	0.0274670i
$501$	0.119606	−	0.808083i	0.00534361	−	0.0361025i
$502$	−8.65587	+	4.99747i	−0.386330	+	0.223048i
$503$			13.2258i			0.589708i	0.955542	+	0.294854i	$0.0952710\pi$
$503$			13.2258i			0.589708i	−0.955542	+	0.294854i	$0.904729\pi$
$504$	10.7114	+	3.24186i	0.477124	+	0.144404i
$505$	−14.8908	−	5.53916i	−0.662633	−	0.246489i
$506$	−2.79695	−	4.84445i	−0.124339	−	0.215362i
$507$	−12.0784	+	15.2286i	−0.536423	+	0.676327i
$508$	−27.3119	−	15.7686i	−1.21177	−	0.699616i
$509$	12.2170	−	21.1604i	0.541508	−	0.937920i	−0.457309	−	0.889308i	$-0.651187\pi$
$509$	12.2170	−	21.1604i	0.541508	−	0.937920i	0.998818	−	0.0486123i	$-0.0154799\pi$
$510$	−1.21037	−	58.9498i	−0.0535959	−	2.61034i
$511$	−17.3089	−	29.9799i	−0.765700	−	1.32623i
$512$			25.4727i			1.12574i
$513$	−40.3024	−	19.0148i	−1.77940	−	0.839523i
$514$	−10.9085			−0.481152
$515$	9.56653	−	1.61730i	0.421552	−	0.0712667i
$516$	32.1882	−	12.7316i	1.41701	−	0.560479i
$517$	7.63697	+	4.40921i	0.335874	+	0.193917i
$518$	28.0712	+	16.2069i	1.23338	+	0.712090i
$519$	22.1208	+	17.5449i	0.970998	+	0.770137i
$520$	−0.633337	−	3.74627i	−0.0277737	−	0.164285i
$521$	23.8170			1.04344			0.521722	−	0.853116i	$-0.325290\pi$
$521$	23.8170			1.04344			0.521722	+	0.853116i	$0.325290\pi$
$522$	29.1298	−	6.81157i	1.27497	−	0.298134i
$523$			29.9922i			1.31147i	0.754993	+	0.655733i	$0.227640\pi$
$523$			29.9922i			1.31147i	−0.754993	+	0.655733i	$0.772360\pi$
$524$	3.36140	+	5.82212i	0.146844	+	0.254341i
$525$	−19.1998	+	16.5564i	−0.837949	+	0.722580i
$526$	−2.41321	+	4.17979i	−0.105221	+	0.182248i
$527$	−3.36351	−	1.94192i	−0.146517	−	0.0845915i
$528$	4.21079	+	0.623248i	0.183251	+	0.0271234i
$529$	−8.09466	−	14.0204i	−0.351942	−	0.609581i
$530$	17.5258	+	6.51934i	0.761274	+	0.283182i
$531$	4.67434	+	19.9899i	0.202849	+	0.867487i
$532$			65.1378i			2.82408i
$533$	3.14585	−	1.81626i	0.136262	−	0.0786708i
$534$	−49.5034	−	39.2632i	−2.14222	−	1.69908i
$535$	−8.86858	−	10.7219i	−0.383422	−	0.463550i
$536$	−1.25293	+	2.17013i	−0.0541182	+	0.0937355i
$537$	0.278702	+	0.704616i	0.0120269	+	0.0304064i
$538$	38.2048	−	22.0576i	1.64713	−	0.950970i
$539$	1.56996			0.0676229
$540$	8.13832	−	29.0260i	0.350217	−	1.24908i
$541$	−3.48759			−0.149943			−0.0749716	−	0.997186i	$-0.523887\pi$
$541$	−3.48759			−0.149943			−0.0749716	+	0.997186i	$0.523887\pi$
$542$	43.3885	−	25.0504i	1.86370	−	1.07600i
$543$	6.86500	+	17.3561i	0.294605	+	0.744823i
$544$	−27.7577	+	48.0777i	−1.19010	+	2.06132i
$545$	−33.2222	+	27.4795i	−1.42308	+	1.17709i
$546$	−11.3544	−	9.00563i	−0.485923	−	0.385405i
$547$	−38.1700	+	22.0375i	−1.63203	+	0.942255i	−0.648568	+	0.761157i	$0.724632\pi$
$547$	−38.1700	+	22.0375i	−1.63203	+	0.942255i	−0.983465	+	0.181098i	$0.942035\pi$
$548$		−	34.6783i		−	1.48138i
$549$	−11.7113	−	3.54448i	−0.499826	−	0.151275i
$550$	7.00421	−	8.11193i	0.298661	−	0.345894i
$551$	19.9489	+	34.5524i	0.849850	+	1.47198i
$552$	5.69794	+	0.843364i	0.242520	+	0.0358960i
$553$	2.92453	+	1.68848i	0.124363	+	0.0718013i
$554$	−11.3963	+	19.7389i	−0.484181	+	0.838625i
$555$	9.64538	−	17.5277i	0.409424	−	0.744008i
$556$	−2.89465	−	5.01367i	−0.122760	−	0.212627i
$557$			35.9042i			1.52131i	0.649156	+	0.760655i	$0.275122\pi$
$557$			35.9042i			1.52131i	−0.649156	+	0.760655i	$0.724878\pi$
$558$	−2.40538	−	2.56494i	−0.101828	−	0.108583i
$559$	−10.2710			−0.434416
$560$	15.8622	−	2.68164i	0.670301	−	0.113320i
$561$	9.63828	+	7.64451i	0.406929	+	0.322752i
$562$	36.3027	+	20.9594i	1.53134	+	0.884118i
$563$	39.3566	+	22.7226i	1.65868	+	0.957641i	0.973323	+	0.229437i	$0.0736886\pi$
$563$	39.3566	+	22.7226i	1.65868	+	0.957641i	0.685360	+	0.728204i	$0.259645\pi$
$564$	−36.8503	+	14.5757i	−1.55168	+	0.613746i
$565$	32.2175	−	5.44663i	1.35540	−	0.229141i
$566$	30.0935			1.26492
$567$	−11.6829	−	23.6152i	−0.490637	−	0.991744i
$568$			14.0167i			0.588127i
$569$	4.66447	+	8.07910i	0.195545	+	0.338694i	0.947079	−	0.321001i	$-0.104019\pi$
$569$	4.66447	+	8.07910i	0.195545	+	0.338694i	−0.751534	+	0.659694i	$0.770686\pi$
$570$	71.1810	−	1.46150i	2.98144	−	0.0612155i
$571$	22.1856	−	38.4266i	0.928439	−	1.60810i	0.142503	−	0.989794i	$-0.454485\pi$
$571$	22.1856	−	38.4266i	0.928439	−	1.60810i	0.785936	−	0.618308i	$-0.212182\pi$
$572$	2.99605	+	1.72977i	0.125271	+	0.0723253i
$573$	−2.84102	+	3.58198i	−0.118685	+	0.149640i
$574$	−8.54713	−	14.8041i	−0.356750	−	0.617909i
$575$	−8.52777	+	9.87645i	−0.355633	+	0.411876i
$576$	−25.9072	+	24.2956i	−1.07947	+	1.01232i
$577$			0.997162i			0.0415124i	0.999785	+	0.0207562i	$0.00660738\pi$
$577$			0.997162i			0.0415124i	−0.999785	+	0.0207562i	$0.993393\pi$
$578$	−62.0842	+	35.8443i	−2.58236	+	1.49093i
$579$	−3.22568	+	21.7934i	−0.134055	+	0.905701i
$580$	−20.7971	+	17.2022i	−0.863552	+	0.714280i
$581$	14.6090	−	25.3036i	0.606084	−	1.04977i
$582$	39.6758	+	5.87250i	1.64461	+	0.243423i
$583$	−3.37868	+	1.95068i	−0.139931	+	0.0807891i
$584$	−15.0687			−0.623549
$585$	−5.41339	+	7.12074i	−0.223816	+	0.294407i
$586$	−5.94397			−0.245543
$587$	−30.7696	+	17.7649i	−1.27000	+	0.733234i	−0.974987	−	0.222260i	$-0.928657\pi$
$587$	−30.7696	+	17.7649i	−1.27000	+	0.733234i	−0.295011	+	0.955494i	$0.595323\pi$
$588$	−4.38411	+	5.52754i	−0.180798	+	0.227952i
$589$	2.34484	−	4.06139i	0.0966176	−	0.167347i
$590$	−20.9046	−	25.2732i	−0.860627	−	1.04048i
$591$	28.7481	−	11.3709i	1.18254	−	0.467738i
$592$	−10.9941	+	6.34746i	−0.451855	+	0.260879i
$593$			10.2210i			0.419727i	0.977731	+	0.209863i	$0.0673019\pi$
$593$			10.2210i			0.419727i	−0.977731	+	0.209863i	$0.932698\pi$
$594$	6.34724	+	9.15226i	0.260431	+	0.375522i
$595$	43.5754	+	16.2094i	1.78642	+	0.664519i
$596$	25.3190	+	43.8538i	1.03711	+	1.79632i
$597$	2.07726	+	5.25174i	0.0850166	+	0.214939i
$598$	−6.45967	−	3.72949i	−0.264155	−	0.152510i
$599$	16.1828	−	28.0294i	0.661209	−	1.14525i	−0.319089	−	0.947725i	$-0.603377\pi$
$599$	16.1828	−	28.0294i	0.661209	−	1.14525i	0.980298	−	0.197523i	$-0.0632899\pi$
$600$	2.06255	+	10.8412i	0.0842031	+	0.442590i
$601$	6.54913	+	11.3434i	0.267144	+	0.462708i	0.968123	−	0.250474i	$-0.0805866\pi$
$601$	6.54913	+	11.3434i	0.267144	+	0.462708i	−0.700979	+	0.713182i	$0.747253\pi$
$602$			48.3342i			1.96996i
$603$	5.74446	−	1.34326i	0.233933	−	0.0547017i
$604$	−35.1112			−1.42865
$605$	0.372737	+	2.20478i	0.0151539	+	0.0896372i
$606$	−3.86231	+	26.0946i	−0.156896	+	1.06002i
$607$	−36.5277	−	21.0893i	−1.48261	−	0.855986i	−0.482807	−	0.875727i	$-0.660383\pi$
$607$	−36.5277	−	21.0893i	−1.48261	−	0.855986i	−0.999805	+	0.0197404i	$0.993716\pi$
$608$	−58.0532	−	33.5170i	−2.35437	−	1.35929i
$609$	−3.45381	+	23.3346i	−0.139956	+	0.945567i
$610$	19.2753	−	3.25864i	0.780433	−	0.131939i
$611$	11.7586			0.475702
$612$	−53.8299	+	12.5873i	−2.17594	+	0.508812i
$613$			22.8483i			0.922833i	0.887184	+	0.461417i	$0.152659\pi$
$613$			22.8483i			0.922833i	−0.887184	+	0.461417i	$0.847341\pi$
$614$	−1.77422	−	3.07303i	−0.0716016	−	0.124018i
$615$	−9.02709	+	5.46188i	−0.364007	+	0.220244i
$616$	1.86521	−	3.23063i	0.0751513	−	0.130166i
$617$	27.3736	+	15.8041i	1.10202	+	0.636251i	0.936751	−	0.349998i	$-0.113818\pi$
$617$	27.3736	+	15.8041i	1.10202	+	0.636251i	0.165268	+	0.986249i	$0.447151\pi$
$618$	−5.92505	−	14.9798i	−0.238341	−	0.602574i
$619$	−7.98122	−	13.8239i	−0.320792	−	0.555629i	0.659859	−	0.751389i	$-0.270616\pi$
$619$	−7.98122	−	13.8239i	−0.320792	−	0.555629i	−0.980652	+	0.195760i	$0.937283\pi$
$620$	2.97337	+	1.10605i	0.119413	+	0.0444199i
$621$	−7.72790	−	11.1431i	−0.310110	−	0.447156i
$622$		−	66.4771i		−	2.66549i
$623$	43.1465	−	24.9107i	1.72863	−	0.998025i
$624$	5.27802	−	2.08765i	0.211290	−	0.0835730i
$625$	−23.2416	−	9.21027i	−0.929663	−	0.368411i
$626$	−12.8723	+	22.2955i	−0.514481	+	0.891107i
$627$	−9.23064	+	11.6381i	−0.368636	+	0.464780i
$628$	21.1563	−	12.2146i	0.844229	−	0.487416i
$629$	−36.6885			−1.46287
$630$	33.5095	+	25.4749i	1.33505	+	1.01494i
$631$	−11.9102			−0.474137			−0.237069	−	0.971493i	$-0.576187\pi$
$631$	−11.9102			−0.474137			−0.237069	+	0.971493i	$0.576187\pi$
$632$	1.27301	−	0.734975i	0.0506378	−	0.0292358i
$633$	19.3069	+	2.85766i	0.767380	+	0.113582i
$634$	18.7955	−	32.5548i	0.746466	−	1.29292i
$635$	−17.3238	−	20.9441i	−0.687472	−	0.831141i
$636$	2.56698	−	17.3430i	0.101787	−	0.687695i
$637$	1.81294	−	1.04670i	0.0718315	−	0.0414719i
$638$		−	9.97185i		−	0.394789i
$639$	24.0704	−	22.5730i	0.952211	−	0.892976i
$640$	7.59629	−	20.4210i	0.300270	−	0.807211i
$641$	5.78367	+	10.0176i	0.228441	+	0.395672i	0.957346	−	0.288943i	$-0.0933038\pi$
$641$	5.78367	+	10.0176i	0.228441	+	0.395672i	−0.728905	+	0.684615i	$0.759971\pi$
$642$	−14.3562	+	18.1005i	−0.566595	+	0.714370i
$643$	−23.8786	−	13.7863i	−0.941681	−	0.543680i	−0.0511944	−	0.998689i	$-0.516303\pi$
$643$	−23.8786	−	13.7863i	−0.941681	−	0.543680i	−0.890487	+	0.455009i	$0.849636\pi$
$644$	−9.91078	+	17.1660i	−0.390539	+	0.676434i
$645$	29.8264	−	0.612400i	1.17441	−	0.0241132i
$646$	−65.2814	−	113.071i	−2.56846	−	4.44870i
$647$		−	19.9539i		−	0.784467i	−0.919866	−	0.392234i	$-0.871703\pi$
$647$		−	19.9539i		−	0.784467i	0.919866	−	0.392234i	$-0.128297\pi$
$648$	−11.4450	−	0.735580i	−0.449601	−	0.0288963i
$649$	6.84304			0.268613
$650$	2.67998	−	14.0372i	0.105117	−	0.550584i
$651$	2.57834	−	1.01983i	0.101053	−	0.0399702i
$652$	−23.9543	−	13.8300i	−0.938124	−	0.541626i
$653$	8.25073	+	4.76356i	0.322876	+	0.186413i	0.652674	−	0.757639i	$-0.273647\pi$
$653$	8.25073	+	4.76356i	0.322876	+	0.186413i	−0.329798	+	0.944052i	$0.606981\pi$
$654$	56.0847	+	44.4831i	2.19309	+	1.73943i
$655$	0.965828	+	5.71299i	0.0377380	+	0.223225i
$656$	6.69499			0.261396
$657$	24.2673	+	25.8771i	0.946758	+	1.00956i
$658$		−	55.3349i		−	2.15718i
$659$	13.9315	+	24.1300i	0.542693	+	0.939972i	0.998748	+	0.0500206i	$0.0159287\pi$
$659$	13.9315	+	24.1300i	0.542693	+	0.939972i	−0.456055	+	0.889952i	$0.650738\pi$
$660$	−8.80350	−	4.84452i	−0.342676	−	0.188573i
$661$	24.0289	−	41.6193i	0.934617	−	1.61880i	0.159301	−	0.987230i	$-0.449076\pi$
$661$	24.0289	−	41.6193i	0.934617	−	1.61880i	0.775316	−	0.631574i	$-0.217591\pi$
$662$	−2.34792	−	1.35557i	−0.0912544	−	0.0526858i
$663$	16.2267	+	2.40175i	0.630191	+	0.0932760i
$664$	−6.35915	−	11.0144i	−0.246783	−	0.427440i
$665$	−19.5726	+	52.6167i	−0.758992	+	2.04039i
$666$	−31.7929	−	9.62227i	−1.23195	−	0.372855i
$667$			12.1409i			0.470099i
$668$	1.05970	−	0.611821i	0.0410012	−	0.0236720i
$669$	4.58820	+	3.63909i	0.177390	+	0.140695i
$670$	−7.26273	+	6.00731i	−0.280584	+	0.232083i
$671$	−2.03932	+	3.53221i	−0.0787271	+	0.136359i
$672$	−14.5773	−	36.8545i	−0.562333	−	1.42169i
$673$	23.5807	−	13.6143i	0.908968	−	0.524793i	0.0288694	−	0.999583i	$-0.490809\pi$
$673$	23.5807	−	13.6143i	0.908968	−	0.524793i	0.880099	+	0.474790i	$0.157476\pi$
$674$	−40.3009			−1.55233
$675$	15.2956	−	21.0010i	0.588729	−	0.808330i
$676$	−29.1154			−1.11982
$677$	−2.42546	+	1.40034i	−0.0932181	+	0.0538195i	−0.545884	−	0.837861i	$-0.683806\pi$
$677$	−2.42546	+	1.40034i	−0.0932181	+	0.0538195i	0.452666	+	0.891680i	$0.350473\pi$
$678$	−19.9540	−	50.4477i	−0.766327	−	1.93743i
$679$	−15.8129	+	27.3887i	−0.606843	+	1.05108i
$680$	15.5944	−	12.8988i	0.598019	−	0.494647i
$681$	−6.35686	−	5.04188i	−0.243595	−	0.193205i
$682$	−1.01509	+	0.586060i	−0.0388696	+	0.0224414i
$683$		−	30.3400i		−	1.16093i	−0.814286	−	0.580464i	$-0.802871\pi$
$683$		−	30.3400i		−	1.16093i	0.814286	−	0.580464i	$-0.197129\pi$
$684$	−15.1990	−	64.9988i	−0.581149	−	2.48529i
$685$	10.4201	−	28.0122i	0.398131	−	1.07029i
$686$	17.0365	+	29.5082i	0.650458	+	1.12663i
$687$	22.0330	+	3.26116i	0.840613	+	0.124421i
$688$	−16.3940	−	9.46509i	−0.625016	−	0.360853i
$689$	−2.60107	+	4.50519i	−0.0990929	+	0.171634i
$690$	18.9809	+	10.4451i	0.722591	+	0.397638i
$691$	−7.84530	−	13.5885i	−0.298449	−	0.516929i	0.677332	−	0.735677i	$-0.263136\pi$
$691$	−7.84530	−	13.5885i	−0.298449	−	0.516929i	−0.975781	+	0.218748i	$0.929803\pi$
$692$			42.2926i			1.60772i
$693$	−8.55166	+	1.99968i	−0.324851	+	0.0759616i
$694$	5.22940			0.198505
$695$	−0.831715	−	4.91970i	−0.0315487	−	0.186615i
$696$	8.04479	+	6.38065i	0.304937	+	0.241858i
$697$	16.7564	+	9.67433i	0.634695	+	0.366441i
$698$	46.1868	+	26.6659i	1.74820	+	1.00932i
$699$	4.43491	−	1.75417i	0.167744	−	0.0663489i
$700$	−37.3025	−	7.12179i	−1.40990	−	0.269178i
$701$	−29.9940			−1.13286			−0.566429	−	0.824111i	$-0.691675\pi$
$701$	−29.9940			−1.13286			−0.566429	+	0.824111i	$0.691675\pi$
$702$	13.4315	+	6.33701i	0.506939	+	0.239175i
$703$		−	44.3009i		−	1.67084i
$704$	5.91950	+	10.2529i	0.223100	+	0.386420i
$705$	−34.1464	+	0.701099i	−1.28603	+	0.0264049i
$706$	14.6694	−	25.4082i	0.552091	−	0.956249i
$707$	−18.0134	−	10.4001i	−0.677464	−	0.391134i
$708$	−19.1092	+	24.0931i	−0.718168	+	0.905474i
$709$	−19.2325	−	33.3117i	−0.722293	−	1.25105i	−0.960079	−	0.279730i	$-0.909755\pi$
$709$	−19.2325	−	33.3117i	−0.722293	−	1.25105i	0.237786	−	0.971318i	$-0.423578\pi$
$710$	−18.3808	+	49.4128i	−0.689819	+	1.85443i
$711$	−3.31226	−	1.00247i	−0.124220	−	0.0375957i
$712$		−	21.6867i		−	0.812743i
$713$	1.23589	−	0.713540i	0.0462843	−	0.0267223i
$714$	11.3024	−	76.3611i	0.422981	−	2.85774i
$715$	1.90037	+	2.29751i	0.0710698	+	0.0859221i
$716$	−0.567516	+	0.982967i	−0.0212091	+	0.0367352i
$717$	−27.1538	−	4.01910i	−1.01408	−	0.150096i
$718$	−15.4102	+	8.89711i	−0.575105	+	0.332037i
$719$	−18.8148			−0.701674			−0.350837	−	0.936437i	$-0.614103\pi$
$719$	−18.8148			−0.701674			−0.350837	+	0.936437i	$0.614103\pi$
$720$	−15.2026	+	6.37714i	−0.566568	+	0.237662i
$721$	12.7022			0.473054
$722$	101.261	−	58.4633i	3.76856	−	2.17578i
$723$	20.7966	−	26.2206i	0.773435	−	0.975155i
$724$	−13.9791	+	24.2125i	−0.519528	+	0.899850i
$725$	−21.9682	+	7.64636i	−0.815880	+	0.283979i
$726$	3.45236	−	1.36554i	0.128129	−	0.0506799i
$727$	3.54926	−	2.04917i	0.131635	−	0.0759995i	−0.432736	−	0.901520i	$-0.642452\pi$
$727$	3.54926	−	2.04917i	0.131635	−	0.0759995i	0.564371	+	0.825521i	$0.309119\pi$
$728$		−	4.97419i		−	0.184356i
$729$	17.1683	+	20.8387i	0.635861	+	0.771803i
$730$	−53.1216	−	19.7604i	−1.96612	−	0.731366i
$731$	−27.3543	−	47.3790i	−1.01174	−	1.75238i
$732$	−6.74145	−	17.0438i	−0.249171	−	0.629956i
$733$	9.25389	+	5.34273i	0.341800	+	0.197338i	0.661068	−	0.750326i	$-0.270104\pi$
$733$	9.25389	+	5.34273i	0.341800	+	0.197338i	−0.319268	+	0.947665i	$0.603437\pi$
$734$	5.48461	−	9.49962i	0.202441	−	0.350637i
$735$	−5.20229	+	3.14767i	−0.191889	+	0.116104i
$736$	−10.1993	−	17.6657i	−0.375950	−	0.651165i
$737$		−	1.96647i		−	0.0724360i
$738$	11.9832	+	12.7781i	0.441108	+	0.470368i
$739$	−5.02556			−0.184868			−0.0924341	−	0.995719i	$-0.529465\pi$
$739$	−5.02556			−0.184868			−0.0924341	+	0.995719i	$0.529465\pi$
$740$	29.5488	−	4.99547i	1.08624	−	0.183637i
$741$	−2.90007	+	19.5935i	−0.106537	+	0.719784i
$742$	21.2010	+	12.2404i	0.778312	+	0.449359i
$743$	−13.2205	−	7.63287i	−0.485014	−	0.280023i	0.237490	−	0.971390i	$-0.423675\pi$
$743$	−13.2205	−	7.63287i	−0.485014	−	0.280023i	−0.722504	+	0.691367i	$0.757009\pi$
$744$	0.176715	−	1.19392i	0.00647868	−	0.0437712i
$745$	7.27487	+	43.0318i	0.266531	+	1.57656i
$746$	−9.83666			−0.360146
$747$	−8.67359	+	28.6583i	−0.317350	+	1.04855i
$748$			18.4273i			0.673769i
$749$	−9.10836	−	15.7761i	−0.332812	−	0.576448i
$750$	−6.94555	+	40.9230i	−0.253616	+	1.49430i
$751$	−24.2082	+	41.9299i	−0.883370	+	1.53004i	−0.0358003	+	0.999359i	$0.511398\pi$
$751$	−24.2082	+	41.9299i	−0.883370	+	1.53004i	−0.847570	+	0.530683i	$0.821935\pi$
$752$	18.7685	+	10.8360i	0.684417	+	0.395148i
$753$	2.97061	+	7.51032i	0.108255	+	0.273691i
$754$	−6.64831	−	11.5152i	−0.242117	−	0.419359i
$755$	−28.3619	−	10.5502i	−1.03220	−	0.383961i
$756$	16.8400	−	35.6929i	0.612465	−	1.29814i
$757$		−	44.1392i		−	1.60427i	−0.597145	−	0.802133i	$-0.703698\pi$
$757$		−	44.1392i		−	1.60427i	0.597145	−	0.802133i	$-0.296302\pi$
$758$	−4.10604	+	2.37062i	−0.149138	+	0.0861049i
$759$	−4.20332	+	1.66257i	−0.152571	+	0.0603475i
$760$	15.5751	+	18.8300i	0.564969	+	0.683037i
$761$	18.4236	−	31.9106i	0.667856	−	1.15676i	−0.310647	−	0.950525i	$-0.600546\pi$
$761$	18.4236	−	31.9106i	0.667856	−	1.15676i	0.978503	−	0.206234i	$-0.0661209\pi$
$762$	−28.0433	+	35.3572i	−1.01590	+	1.28086i
$763$	−48.8827	+	28.2224i	−1.76967	+	1.02172i
$764$	−6.84835			−0.247765
$765$	−47.2646	−	6.00704i	−1.70885	−	0.217185i
$766$	37.8432			1.36733
$767$	7.90214	−	4.56230i	0.285330	−	0.164735i
$768$	4.78395	+	0.708083i	0.172626	+	0.0255507i
$769$	18.8544	−	32.6568i	0.679906	−	1.17763i	−0.295102	−	0.955466i	$-0.595354\pi$
$769$	18.8544	−	32.6568i	0.679906	−	1.17763i	0.975009	−	0.222167i	$-0.0713130\pi$
$770$	10.8119	−	8.94296i	0.389633	−	0.322282i
$771$	−1.29062	+	8.71967i	−0.0464805	+	0.314031i
$772$	−28.5794	+	16.5003i	−1.02859	+	0.593859i
$773$		−	10.2370i		−	0.368201i	−0.982907	−	0.184100i	$-0.941063\pi$
$773$		−	10.2370i		−	0.368201i	0.982907	−	0.184100i	$-0.0589372\pi$
$774$	−11.2781	−	48.2310i	−0.405384	−	1.73363i
$775$	2.06947	+	1.78687i	0.0743374	+	0.0641863i
$776$	6.88318	+	11.9220i	0.247092	+	0.427976i
$777$	16.2761	−	20.5211i	0.583903	−	0.736191i
$778$	−49.6318	−	28.6550i	−1.77939	−	1.02733i
$779$	−11.6816	+	20.2332i	−0.418537	+	0.724928i
$780$	−13.3959	+	0.275047i	−0.479651	+	0.00984826i
$781$	−5.49982	−	9.52596i	−0.196799	−	0.340866i
$782$		−	39.7304i		−	1.42076i
$783$	−1.99838	−	24.0907i	−0.0714162	−	0.860932i
$784$	3.85831			0.137797
$785$	20.7598	−	3.50961i	0.740948	−	0.125263i
$786$	8.94569	−	3.53835i	0.319082	−	0.126209i
$787$	12.6552	+	7.30649i	0.451110	+	0.260448i	0.708299	−	0.705913i	$-0.249463\pi$
$787$	12.6552	+	7.30649i	0.451110	+	0.260448i	−0.257189	+	0.966361i	$0.582796\pi$
$788$	40.1047	+	23.1544i	1.42867	+	0.824842i
$789$	3.05560	+	2.42352i	0.108782	+	0.0862794i
$790$	5.45155	−	0.921629i	0.193958	−	0.0327901i
$791$	42.7775			1.52099
$792$	−1.10740	+	3.65895i	−0.0393498	+	0.130015i
$793$			5.43852i			0.193128i
$794$	−8.65786	−	14.9958i	−0.307256	−	0.532183i
$795$	7.28476	−	13.2379i	0.258364	−	0.469501i
$796$	−4.22989	+	7.32638i	−0.149924	+	0.259677i
$797$	−10.4253	−	6.01906i	−0.369283	−	0.213206i	0.303862	−	0.952716i	$-0.401724\pi$
$797$	−10.4253	−	6.01906i	−0.369283	−	0.213206i	−0.673145	+	0.739510i	$0.735057\pi$
$798$	92.2049	+	13.6475i	3.26402	+	0.483115i
$799$	31.3163	+	54.2414i	1.10789	+	1.91892i
$800$	25.5414	−	29.5808i	0.903024	−	1.04584i
$801$	−37.2419	+	34.9251i	−1.31588	+	1.23402i
$802$			49.9709i			1.76453i
$803$	10.2409	−	5.91261i	0.361395	−	0.208652i
$804$	6.92360	+	5.49138i	0.244176	+	0.193666i
$805$	−13.1637	+	10.8882i	−0.463959	+	0.383760i
$806$	−0.781461	+	1.35353i	−0.0275258	+	0.0476760i
$807$	−13.1115	−	33.1487i	−0.461548	−	1.16689i
$808$	−7.84105	+	4.52703i	−0.275847	+	0.159260i
$809$	−36.9537			−1.29922			−0.649611	−	0.760267i	$-0.725068\pi$
$809$	−36.9537			−1.29922			−0.649611	+	0.760267i	$0.725068\pi$
$810$	−39.3822	−	17.6015i	−1.38375	−	0.618454i
$811$	7.69946			0.270365			0.135182	−	0.990821i	$-0.456838\pi$
$811$	7.69946			0.270365			0.135182	+	0.990821i	$0.456838\pi$
$812$	−30.6006	+	17.6673i	−1.07387	+	0.619999i
$813$	−14.8905	−	37.6463i	−0.522233	−	1.32031i
$814$	−5.53618	+	9.58895i	−0.194043	+	0.336092i
$815$	−15.1940	−	18.3693i	−0.532224	−	0.643449i
$816$	23.6869	+	18.7870i	0.829207	+	0.657678i
$817$	57.2095	−	33.0299i	2.00151	−	1.15557i
$818$			6.57023i			0.229723i
$819$	−8.54201	+	8.01063i	−0.298482	+	0.279914i
$820$	−14.8128	−	5.51013i	−0.517286	−	0.192422i
$821$	−4.57702	−	7.92763i	−0.159739	−	0.276676i	0.775035	−	0.631918i	$-0.217732\pi$
$821$	−4.57702	−	7.92763i	−0.159739	−	0.276676i	−0.934775	+	0.355241i	$0.884399\pi$
$822$	−49.0883	−	7.26567i	−1.71215	−	0.253419i
$823$	17.2638	+	9.96727i	0.601779	+	0.347437i	0.769741	−	0.638356i	$-0.220385\pi$
$823$	17.2638	+	9.96727i	0.601779	+	0.347437i	−0.167962	+	0.985793i	$0.553719\pi$
$824$	2.76456	−	4.78836i	0.0963080	−	0.166810i
$825$	−5.65556	−	6.55855i	−0.196901	−	0.228339i
$826$	−21.4698	−	37.1867i	−0.747029	−	1.29389i
$827$		−	7.92306i		−	0.275512i	−0.990466	−	0.137756i	$-0.956011\pi$
$827$		−	7.92306i		−	0.275512i	0.990466	−	0.137756i	$-0.0439890\pi$
$828$	5.88417	−	19.4419i	0.204489	−	0.675651i
$829$	−15.0070			−0.521215			−0.260607	−	0.965445i	$-0.583923\pi$
$829$	−15.0070			−0.521215			−0.260607	+	0.965445i	$0.583923\pi$
$830$	−7.97411	−	47.1679i	−0.276786	−	1.63722i
$831$	14.4299	+	11.4449i	0.500568	+	0.397021i
$832$	13.6713	+	7.89315i	0.473968	+	0.273646i
$833$	9.65669	+	5.57529i	0.334584	+	0.193172i
$834$	−7.70351	+	3.04703i	−0.266751	+	0.105510i
$835$	1.03984	−	0.175794i	0.0359852	−	0.00608359i
$836$	−22.2507			−0.769557
$837$	−2.33487	+	1.61927i	−0.0807048	+	0.0559702i
$838$			12.5361i			0.433053i
$839$	−2.27387	−	3.93846i	−0.0785028	−	0.135971i	0.824101	−	0.566442i	$-0.191681\pi$
$839$	−2.27387	−	3.93846i	−0.0785028	−	0.135971i	−0.902604	+	0.430472i	$0.858347\pi$
$840$	0.296582	+	14.4448i	0.0102331	+	0.498392i
$841$	3.67859	−	6.37151i	0.126848	−	0.219707i
$842$	1.28754	+	0.743363i	0.0443716	+	0.0256180i
$843$	21.0489	−	26.5387i	0.724963	−	0.914042i
$844$	14.6178	+	25.3187i	0.503164	+	0.871505i
$845$	−23.5187	−	8.74859i	−0.809068	−	0.300961i
$846$	12.9116	+	55.2167i	0.443911	+	1.89839i
$847$			2.92745i			0.100588i
$848$	−8.30340	+	4.79397i	−0.285140	+	0.164626i
$849$	3.56046	−	24.0551i	0.122195	−	0.825570i
$850$	71.8897	−	25.0222i	2.46580	−	0.858255i
$851$	6.74041	−	11.6747i	0.231058	−	0.400205i
$852$	48.8974	+	7.23741i	1.67520	+	0.247950i
$853$	−14.4868	+	8.36398i	−0.496020	+	0.286377i	−0.727068	−	0.686565i	$-0.759118\pi$
$853$	−14.4868	+	8.36398i	−0.496020	+	0.286377i	0.231049	+	0.972942i	$0.425784\pi$
$854$	25.5932			0.875780
$855$	7.25341	−	57.0713i	0.248061	−	1.95180i
$856$	−7.92955			−0.271026
$857$	−9.13283	+	5.27284i	−0.311972	+	0.180117i	−0.647808	−	0.761803i	$-0.724314\pi$
$857$	−9.13283	+	5.27284i	−0.311972	+	0.180117i	0.335837	+	0.941920i	$0.390981\pi$
$858$	3.07627	−	3.87860i	0.105022	−	0.132413i
$859$	9.08417	−	15.7342i	0.309948	−	0.536846i	−0.668403	−	0.743800i	$-0.733022\pi$
$859$	9.08417	−	15.7342i	0.309948	−	0.536846i	0.978351	+	0.206954i	$0.0663550\pi$
$860$	28.4821	+	34.4344i	0.971232	+	1.17420i
$861$	−12.8448	+	5.08061i	−0.437751	+	0.173147i
$862$	−28.3674	+	16.3779i	−0.966197	+	0.557834i
$863$			22.9703i			0.781918i	0.920408	+	0.390959i	$0.127857\pi$
$863$			22.9703i			0.781918i	−0.920408	+	0.390959i	$0.872143\pi$
$864$	23.1457	+	33.3744i	0.787433	+	1.13542i
$865$	−12.7080	+	34.1628i	−0.432086	+	1.16157i
$866$	3.57903	+	6.19907i	0.121620	+	0.210653i
$867$	21.3067	+	53.8677i	0.723614	+	1.82944i
$868$	3.59688	+	2.07666i	0.122086	+	0.0704864i
$869$	−0.576774	+	0.999001i	−0.0195657	+	0.0338888i
$870$	19.9929	+	33.0432i	0.677824	+	1.12027i
$871$	−1.31106	−	2.27083i	−0.0444237	−	0.0769441i
$872$			24.5699i			0.832040i
$873$	9.38835	−	31.0200i	0.317747	−	1.04987i
$874$	47.9739			1.62274
$875$	−27.9921	−	16.9614i	−0.946304	−	0.573401i
$876$	−7.78063	+	52.5675i	−0.262883	+	1.77609i
$877$	−24.4760	−	14.1312i	−0.826497	−	0.477178i	0.0261550	−	0.999658i	$-0.491674\pi$
$877$	−24.4760	−	14.1312i	−0.826497	−	0.477178i	−0.852652	+	0.522480i	$0.825007\pi$
$878$	47.4009	+	27.3669i	1.59970	+	0.923590i
$879$	−0.703251	+	4.75130i	−0.0237201	+	0.160257i
$880$	0.916032	+	5.41844i	0.0308794	+	0.182656i
$881$	−11.8411			−0.398936			−0.199468	−	0.979904i	$-0.563921\pi$
$881$	−11.8411			−0.398936			−0.199468	+	0.979904i	$0.563921\pi$
$882$	6.90589	+	7.36398i	0.232533	+	0.247958i
$883$			12.5838i			0.423479i	0.977326	+	0.211740i	$0.0679129\pi$
$883$			12.5838i			0.423479i	−0.977326	+	0.211740i	$0.932087\pi$
$884$	12.2856	+	21.2793i	0.413210	+	0.715701i
$885$	−22.6754	+	13.7199i	−0.762225	+	0.461188i
$886$	−27.8654	+	48.2643i	−0.936156	+	1.62147i
$887$	−7.18600	−	4.14884i	−0.241282	−	0.139304i	0.374484	−	0.927234i	$-0.377820\pi$
$887$	−7.18600	−	4.14884i	−0.241282	−	0.139304i	−0.615766	+	0.787929i	$0.711153\pi$
$888$	−4.19347	−	10.6020i	−0.140724	−	0.355778i
$889$	−17.7921	−	30.8169i	−0.596729	−	1.03357i
$890$	28.4389	−	76.4518i	0.953273	−	2.56267i
$891$	8.06680	−	3.99082i	0.270248	−	0.133698i
$892$			8.77213i			0.293713i
$893$	−65.4956	+	37.8139i	−2.19173	+	1.26539i
$894$	67.3813	−	26.6518i	2.25357	−	0.891371i
$895$	−0.753786	+	0.623488i	−0.0251963	+	0.0208409i
$896$	14.2624	−	24.7033i	0.476475	−	0.825278i
$897$	−3.74543	+	4.72227i	−0.125056	+	0.157672i
$898$	−19.3437	+	11.1681i	−0.645507	+	0.372683i
$899$	2.54396			0.0848457
$900$	38.8846	−	1.59744i	1.29615	−	0.0532481i
$901$	−27.7093			−0.923132
$902$	5.05698	−	2.91965i	0.168379	−	0.0972137i
$903$	38.6359	+	5.71858i	1.28572	+	0.190302i
$904$	9.31028	−	16.1259i	0.309655	−	0.536339i
$905$	−18.5673	+	15.3578i	−0.617198	+	0.510510i
$906$	−7.35638	+	49.7012i	−0.244399	+	1.65121i
$907$	23.4187	−	13.5208i	0.777604	−	0.448950i	−0.0579763	−	0.998318i	$-0.518465\pi$
$907$	23.4187	−	13.5208i	0.777604	−	0.448950i	0.835581	+	0.549368i	$0.185131\pi$
$908$		−	12.1536i		−	0.403331i
$909$	20.4017	+	6.17466i	0.676680	+	0.204801i
$910$	6.52290	−	17.5354i	0.216232	−	0.581294i
$911$	12.8676	+	22.2873i	0.426321	+	0.738410i	0.996543	−	0.0830812i	$-0.0264761\pi$
$911$	12.8676	+	22.2873i	0.426321	+	0.738410i	−0.570222	+	0.821491i	$0.693143\pi$
$912$	−22.6851	+	28.6016i	−0.751178	+	0.947093i
$913$	8.64355	+	4.99036i	0.286060	+	0.165157i
$914$	44.5041	−	77.0834i	1.47206	−	2.54969i
$915$	−0.324268	−	15.7932i	−0.0107200	−	0.522107i
$916$	16.6818	+	28.8937i	0.551182	+	0.954675i
$917$			7.58555i			0.250497i
$918$	6.53956	+	78.8353i	0.215838	+	2.60195i
$919$	−37.9645			−1.25233			−0.626167	−	0.779689i	$-0.715377\pi$
$919$	−37.9645			−1.25233			−0.626167	+	0.779689i	$0.715377\pi$
$920$	1.23955	+	7.33210i	0.0408668	+	0.241732i
$921$	−2.66634	+	1.05464i	−0.0878588	+	0.0347514i
$922$	−6.56068	−	3.78781i	−0.216064	−	0.124745i
$923$	−12.7021	−	7.33354i	−0.418093	−	0.241386i
$924$	−10.3070	−	8.17491i	−0.339076	−	0.268935i
$925$	25.3698	+	4.84360i	0.834154	+	0.159256i
$926$	39.7659			1.30679
$927$	−12.6751	+	2.96388i	−0.416303	+	0.0973464i
$928$		−	36.3631i		−	1.19368i
$929$	21.3972	+	37.0611i	0.702020	+	1.21593i	0.967756	+	0.251888i	$0.0810515\pi$
$929$	21.3972	+	37.0611i	0.702020	+	1.21593i	−0.265737	+	0.964046i	$0.585615\pi$
$930$	2.18862	−	3.97717i	0.0717676	−	0.130417i
$931$	−6.73208	+	11.6603i	−0.220635	+	0.382151i
$932$	6.18687	+	3.57199i	0.202658	+	0.117004i
$933$	−53.1384	−	7.86513i	−1.73967	−	0.257493i
$934$	−13.9063	−	24.0864i	−0.455027	−	0.788130i
$935$	−5.53703	+	14.8851i	−0.181080	+	0.486795i
$936$	1.16066	+	4.96357i	0.0379373	+	0.162239i
$937$		−	5.36895i		−	0.175396i	−0.996147	−	0.0876979i	$-0.972049\pi$
$937$		−	5.36895i		−	0.175396i	0.996147	−	0.0876979i	$-0.0279510\pi$
$938$	−10.6863	+	6.16974i	−0.348920	+	0.201449i
$939$	16.2989	+	12.9273i	0.531894	+	0.421867i
$940$	−32.6074	−	39.4218i	−1.06354	−	1.28580i
$941$	10.4632	−	18.1228i	0.341091	−	0.590786i	−0.643545	−	0.765408i	$-0.722537\pi$
$941$	10.4632	−	18.1228i	0.341091	−	0.590786i	0.984636	+	0.174622i	$0.0558703\pi$
$942$	−12.8576	−	32.5067i	−0.418924	−	1.05912i
$943$	−6.15698	+	3.55473i	−0.200499	+	0.115758i
$944$	16.8173			0.547358
$945$	24.3279	−	23.7718i	0.791387	−	0.773296i
$946$	−16.5107			−0.536809
$947$	3.61974	−	2.08986i	0.117626	−	0.0679113i	−0.440033	−	0.897982i	$-0.645033\pi$
$947$	3.61974	−	2.08986i	0.117626	−	0.0679113i	0.557659	+	0.830070i	$0.311700\pi$
$948$	−1.90666	−	4.82043i	−0.0619254	−	0.156560i
$949$	7.88397	−	13.6554i	0.255924	−	0.443274i
$950$	30.2140	+	86.8057i	0.980271	+	2.81635i
$951$	−23.7989	−	18.8758i	−0.771731	−	0.612091i
$952$	22.9455	−	13.2476i	0.743666	−	0.429356i
$953$			20.9281i			0.677929i	0.940799	+	0.338965i	$0.110077\pi$
$953$			20.9281i			0.677929i	−0.940799	+	0.338965i	$0.889923\pi$
$954$	−24.0118	−	7.26730i	−0.777412	−	0.235288i
$955$	−5.53192	−	2.05779i	−0.179009	−	0.0665884i
$956$	−20.5589	−	35.6090i	−0.664921	−	1.15168i
$957$	−7.97098	−	1.17980i	−0.257665	−	0.0381376i
$958$	−43.7268	−	25.2457i	−1.41275	−	0.815650i
$959$	19.5643	−	33.8863i	0.631763	−	1.09425i
$960$	−40.1715	−	22.1062i	−1.29653	−	0.713473i
$961$	15.3505	+	26.5878i	0.495177	+	0.857672i
$962$			14.7640i			0.476012i
$963$	12.7701	+	13.6172i	0.411509	+	0.438807i
$964$	50.1309			1.61461
$965$	−28.0437	+	4.74102i	−0.902758	+	0.152619i
$966$	22.2226	+	17.6256i	0.714999	+	0.567095i
$967$	28.4710	+	16.4377i	0.915564	+	0.528601i	0.882217	−	0.470843i	$-0.156050\pi$
$967$	28.4710	+	16.4377i	0.915564	+	0.528601i	0.0333471	+	0.999444i	$0.489383\pi$
$968$	1.10357	+	0.637144i	0.0354699	+	0.0204786i
$969$	−98.1064	+	38.8048i	−3.15163	+	1.24659i
$970$	8.63123	+	51.0548i	0.277132	+	1.63927i
$971$	−42.8909			−1.37644			−0.688218	−	0.725504i	$-0.741607\pi$
$971$	−42.8909			−1.37644			−0.688218	+	0.725504i	$0.741607\pi$
$972$	−8.47561	+	39.5461i	−0.271855	+	1.26844i
$973$		−	6.53223i		−	0.209414i
$974$	17.3122	+	29.9855i	0.554717	+	0.960799i
$975$	−10.9035	−	3.80302i	−0.349192	−	0.121794i
$976$	−5.01180	+	8.68070i	−0.160424	+	0.277862i
$977$	−41.6593	−	24.0520i	−1.33280	−	0.769491i	−0.347070	−	0.937839i	$-0.612823\pi$
$977$	−41.6593	−	24.0520i	−1.33280	−	0.769491i	−0.985728	+	0.168348i	$0.946157\pi$
$978$	−24.5957	+	31.0106i	−0.786485	+	0.991609i
$979$	8.50934	+	14.7386i	0.271960	+	0.471048i
$980$	−8.53659	−	3.17548i	−0.272691	−	0.101437i
$981$	42.1930	−	39.5683i	1.34712	−	1.26332i
$982$		−	45.6080i		−	1.45541i
$983$	48.2538	−	27.8594i	1.53906	−	0.888575i	0.540163	−	0.841560i	$-0.318362\pi$
$983$	48.2538	−	27.8594i	1.53906	−	0.888575i	0.998894	−	0.0470151i	$-0.0149709\pi$
$984$	−0.880363	+	5.94790i	−0.0280649	+	0.189612i
$985$	25.4381	+	30.7542i	0.810524	+	0.979909i
$986$	35.4124	−	61.3360i	1.12776	−	1.95334i
$987$	−44.2318	−	6.54685i	−1.40791	−	0.208389i
$988$	−25.6945	+	14.8347i	−0.817450	+	0.471955i
$989$	20.1021			0.639210
$990$	−8.70208	+	11.4467i	−0.276570	+	0.363799i
$991$	−6.82781			−0.216893			−0.108446	−	0.994102i	$-0.534588\pi$
$991$	−6.82781			−0.216893			−0.108446	+	0.994102i	$0.534588\pi$
$992$	−3.70158	+	2.13711i	−0.117525	+	0.0678533i
$993$	−1.36136	+	1.71642i	−0.0432016	+	0.0544690i
$994$	−34.5109	+	59.7747i	−1.09462	+	1.89594i
$995$	−5.61822	+	4.64707i	−0.178110	+	0.147322i
$996$	−41.7073	+	16.4968i	−1.32155	+	0.522721i
$997$	−47.2304	+	27.2685i	−1.49580	+	0.863602i	−0.999988	−	0.00482671i	$-0.998464\pi$
$997$	−47.2304	+	27.2685i	−1.49580	+	0.863602i	−0.495814	+	0.868429i	$0.665130\pi$
$998$		−	29.5658i		−	0.935889i
$999$	−11.4531	+	24.2751i	−0.362359	+	0.768031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.u.b.364.30	yes	68
5.4	even	2	inner	495.2.u.b.364.5	yes	68
9.7	even	3	inner	495.2.u.b.34.5	✓	68
45.34	even	6	inner	495.2.u.b.34.30	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.u.b.34.5	✓	68	9.7	even	3	inner
495.2.u.b.34.30	yes	68	45.34	even	6	inner
495.2.u.b.364.5	yes	68	5.4	even	2	inner
495.2.u.b.364.30	yes	68	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.85631 - 1.07174i) q^{2} +(-0.637067 - 1.61064i) q^{3} +(1.29725 - 2.24690i) q^{4} +(1.72303 - 1.42519i) q^{5} +(-2.90877 - 2.30706i) q^{6} +(2.53525 - 1.46372i) q^{7} -1.27429i q^{8} +(-2.18829 + 2.05216i) q^{9} +O(q^{10})\)	\(q+(1.85631 - 1.07174i) q^{2} +(-0.637067 - 1.61064i) q^{3} +(1.29725 - 2.24690i) q^{4} +(1.72303 - 1.42519i) q^{5} +(-2.90877 - 2.30706i) q^{6} +(2.53525 - 1.46372i) q^{7} -1.27429i q^{8} +(-2.18829 + 2.05216i) q^{9} +(1.67104 - 4.49223i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-4.44537 - 0.657969i) q^{12} +(1.15477 + 0.666707i) q^{13} +(3.13746 - 5.43424i) q^{14} +(-3.39315 - 1.86723i) q^{15} +(1.22879 + 2.12833i) q^{16} +7.10247i q^{17} +(-1.86276 + 6.15472i) q^{18} -8.57612 q^{19} +(-0.967063 - 5.72030i) q^{20} +(-3.97265 - 3.15087i) q^{21} +(1.85631 + 1.07174i) q^{22} +(-2.26009 - 1.30486i) q^{23} +(-2.05241 + 0.811806i) q^{24} +(0.937663 - 4.91129i) q^{25} +2.85814 q^{26} +(4.69938 + 2.21718i) q^{27} -7.59525i q^{28} +(-2.32609 - 4.02891i) q^{29} +(-8.29990 + 0.170415i) q^{30} +(-0.273415 + 0.473569i) q^{31} +(6.76916 + 3.90818i) q^{32} +(1.07632 - 1.35703i) q^{33} +(7.61199 + 13.1843i) q^{34} +(2.28222 - 6.13525i) q^{35} +(1.77225 + 7.57904i) q^{36} +5.16561i q^{37} +(-15.9199 + 9.19136i) q^{38} +(0.338156 - 2.28465i) q^{39} +(-1.81610 - 2.19564i) q^{40} +(1.36211 - 2.35924i) q^{41} +(-10.7514 - 1.59133i) q^{42} +(-6.67079 + 3.85138i) q^{43} +2.59450 q^{44} +(-0.845768 + 6.65467i) q^{45} -5.59389 q^{46} +(7.63697 - 4.40921i) q^{47} +(2.64514 - 3.33502i) q^{48} +(0.784980 - 1.35962i) q^{49} +(-3.52303 - 10.1218i) q^{50} +(11.4395 - 4.52474i) q^{51} +(2.99605 - 1.72977i) q^{52} +3.90137i q^{53} +(11.0997 - 0.920745i) q^{54} +(2.09577 + 0.779592i) q^{55} +(-1.86521 - 3.23063i) q^{56} +(5.46356 + 13.8130i) q^{57} +(-8.63588 - 4.98593i) q^{58} +(3.42152 - 5.92624i) q^{59} +(-8.59723 + 5.20180i) q^{60} +(2.03932 + 3.53221i) q^{61} +1.17212i q^{62} +(-2.54406 + 8.40580i) q^{63} +11.8390 q^{64} +(2.93989 - 0.497012i) q^{65} +(0.543590 - 3.67260i) q^{66} +(-1.70302 - 0.983237i) q^{67} +(15.9585 + 9.21366i) q^{68} +(-0.661832 + 4.47147i) q^{69} +(-2.33889 - 13.8348i) q^{70} -10.9996 q^{71} +(2.61505 + 2.78851i) q^{72} -11.8252i q^{73} +(5.53618 + 9.58895i) q^{74} +(-8.50765 + 1.61859i) q^{75} +(-11.1254 + 19.2697i) q^{76} +(2.53525 + 1.46372i) q^{77} +(-1.82083 - 4.60343i) q^{78} +(0.576774 + 0.999001i) q^{79} +(5.15052 + 1.91591i) q^{80} +(0.577248 - 8.98147i) q^{81} -5.83930i q^{82} +(8.64355 - 4.99036i) q^{83} +(-12.2332 + 4.83868i) q^{84} +(10.1224 + 12.2378i) q^{85} +(-8.25535 + 14.2987i) q^{86} +(-5.00723 + 6.31317i) q^{87} +(1.10357 - 0.637144i) q^{88} +17.0187 q^{89} +(5.56207 + 13.2596i) q^{90} +3.90350 q^{91} +(-5.86380 + 3.38546i) q^{92} +(0.936931 + 0.138677i) q^{93} +(9.45104 - 16.3697i) q^{94} +(-14.7769 + 12.2226i) q^{95} +(1.98224 - 13.3924i) q^{96} +(-9.35583 + 5.40159i) q^{97} -3.36517i q^{98} +(-2.87137 - 0.869035i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 40 q^{4} - 2 q^{5} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 68 * q + 40 * q^4 - 2 * q^5 + 4 * q^6 - 4 * q^9	\( 68 q + 40 q^{4} - 2 q^{5} + 4 q^{6} - 4 q^{9} + 34 q^{11} - 10 q^{14} - 28 q^{15} - 52 q^{16} - 40 q^{19} + q^{20} - 14 q^{21} + 20 q^{24} + 2 q^{25} - 24 q^{26} - 6 q^{29} + 22 q^{30} - 36 q^{31} + 34 q^{34} - 16 q^{36} - 12 q^{39} + 15 q^{40} + 6 q^{41} + 80 q^{44} + 50 q^{45} + 84 q^{46} + 60 q^{49} - 19 q^{50} + 48 q^{51} - 50 q^{54} - 4 q^{55} + 30 q^{56} - 103 q^{60} - 62 q^{61} - 164 q^{64} - 17 q^{65} + 2 q^{66} - 20 q^{69} + 28 q^{70} - 60 q^{71} + 14 q^{74} + 11 q^{75} - 86 q^{76} + 32 q^{79} + 50 q^{80} - 112 q^{81} - 36 q^{84} + q^{85} + 14 q^{86} + 20 q^{89} + 101 q^{90} + 104 q^{91} + 38 q^{94} + 6 q^{95} + 40 q^{96} + 4 q^{99}+O(q^{100}) \) 68 * q + 40 * q^4 - 2 * q^5 + 4 * q^6 - 4 * q^9 + 34 * q^11 - 10 * q^14 - 28 * q^15 - 52 * q^16 - 40 * q^19 + q^20 - 14 * q^21 + 20 * q^24 + 2 * q^25 - 24 * q^26 - 6 * q^29 + 22 * q^30 - 36 * q^31 + 34 * q^34 - 16 * q^36 - 12 * q^39 + 15 * q^40 + 6 * q^41 + 80 * q^44 + 50 * q^45 + 84 * q^46 + 60 * q^49 - 19 * q^50 + 48 * q^51 - 50 * q^54 - 4 * q^55 + 30 * q^56 - 103 * q^60 - 62 * q^61 - 164 * q^64 - 17 * q^65 + 2 * q^66 - 20 * q^69 + 28 * q^70 - 60 * q^71 + 14 * q^74 + 11 * q^75 - 86 * q^76 + 32 * q^79 + 50 * q^80 - 112 * q^81 - 36 * q^84 + q^85 + 14 * q^86 + 20 * q^89 + 101 * q^90 + 104 * q^91 + 38 * q^94 + 6 * q^95 + 40 * q^96 + 4 * q^99

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