LMFDB - Embedded newform 273.2.r.b.68.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(68,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 2]))

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

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

chi := DirichletCharacter("273.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.r (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.12
Character	$\chi$	$=$	273.68
Dual form			273.2.r.b.269.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.883413i q^{2} +(1.41202 + 1.00309i) q^{3} +1.21958 q^{4} +(-1.72131 + 2.98140i) q^{5} +(0.886146 - 1.24740i) q^{6} +(-2.26618 + 1.36544i) q^{7} -2.84422i q^{8} +(0.987606 + 2.83278i) q^{9} +(2.63381 + 1.52063i) q^{10} +(3.32619 + 1.92038i) q^{11} +(1.72207 + 1.22335i) q^{12} +(0.144185 - 3.60267i) q^{13} +(1.20624 + 2.00198i) q^{14} +(-5.42115 + 2.48316i) q^{15} -0.0734612 q^{16} -0.161995 q^{17} +(2.50251 - 0.872465i) q^{18} +(-1.41529 + 0.817116i) q^{19} +(-2.09928 + 3.63606i) q^{20} +(-4.56956 - 0.345169i) q^{21} +(1.69649 - 2.93840i) q^{22} -4.54399i q^{23} +(2.85302 - 4.01610i) q^{24} +(-3.42582 - 5.93370i) q^{25} +(-3.18264 - 0.127375i) q^{26} +(-1.44702 + 4.99060i) q^{27} +(-2.76379 + 1.66526i) q^{28} +(8.21721 - 4.74421i) q^{29} +(2.19366 + 4.78911i) q^{30} +(0.139734 - 0.0806754i) q^{31} -5.62354i q^{32} +(2.77034 + 6.04810i) q^{33} +0.143108i q^{34} +(-0.170104 - 9.10673i) q^{35} +(1.20447 + 3.45480i) q^{36} -3.98455 q^{37} +(0.721851 + 1.25028i) q^{38} +(3.81740 - 4.94241i) q^{39} +(8.47975 + 4.89579i) q^{40} +(2.41336 + 4.18006i) q^{41} +(-0.304927 + 4.03681i) q^{42} +(4.32913 - 7.49828i) q^{43} +(4.05656 + 2.34206i) q^{44} +(-10.1456 - 1.93164i) q^{45} -4.01422 q^{46} +(3.42471 - 5.93177i) q^{47} +(-0.103729 - 0.0736885i) q^{48} +(3.27117 - 6.18866i) q^{49} +(-5.24191 + 3.02642i) q^{50} +(-0.228740 - 0.162496i) q^{51} +(0.175845 - 4.39374i) q^{52} +(-11.2686 + 6.50591i) q^{53} +(4.40877 + 1.27832i) q^{54} +(-11.4508 + 6.61114i) q^{55} +(3.88360 + 6.44552i) q^{56} +(-2.81806 - 0.265880i) q^{57} +(-4.19110 - 7.25920i) q^{58} -8.91725 q^{59} +(-6.61153 + 3.02841i) q^{60} +(-5.63535 + 3.25357i) q^{61} +(-0.0712698 - 0.123443i) q^{62} +(-6.10608 - 5.07108i) q^{63} -5.11484 q^{64} +(10.4928 + 6.63118i) q^{65} +(5.34297 - 2.44735i) q^{66} +(0.472730 - 0.818793i) q^{67} -0.197566 q^{68} +(4.55805 - 6.41621i) q^{69} +(-8.04501 + 0.150272i) q^{70} +(4.33350 + 2.50195i) q^{71} +(8.05705 - 2.80897i) q^{72} +(8.62581 - 4.98012i) q^{73} +3.52001i q^{74} +(1.11472 - 11.8149i) q^{75} +(-1.72606 + 0.996539i) q^{76} +(-10.1599 + 0.189777i) q^{77} +(-4.36619 - 3.37235i) q^{78} +(-5.23295 + 9.06373i) q^{79} +(0.126450 - 0.219017i) q^{80} +(-7.04927 + 5.59534i) q^{81} +(3.69272 - 2.13200i) q^{82} -1.04892 q^{83} +(-5.57294 - 0.420961i) q^{84} +(0.278843 - 0.482971i) q^{85} +(-6.62408 - 3.82441i) q^{86} +(16.3618 + 1.54371i) q^{87} +(5.46198 - 9.46043i) q^{88} -6.88870 q^{89} +(-1.70644 + 8.96277i) q^{90} +(4.59246 + 8.36118i) q^{91} -5.54177i q^{92} +(0.278232 + 0.0262508i) q^{93} +(-5.24021 - 3.02543i) q^{94} -5.62604i q^{95} +(5.64094 - 7.94056i) q^{96} +(6.97520 + 4.02713i) q^{97} +(-5.46714 - 2.88979i) q^{98} +(-2.15504 + 11.3189i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 64 q^{4} + 12 q^{6} - 10 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{12} + 12 q^{13} - 9 q^{15} + 32 q^{16} + 2 q^{18} - 36 q^{19} + 10 q^{21} + 10 q^{22} - 18 q^{24} - 24 q^{25} - 14 q^{28} + 8 q^{30} - 24 q^{31}+ \cdots + 22 q^{99}+O(q^{100}) $ 64 * q - 64 * q^4 + 12 * q^6 - 10 * q^7 - 4 * q^9 - 6 * q^10 + 6 * q^12 + 12 * q^13 - 9 * q^15 + 32 * q^16 + 2 * q^18 - 36 * q^19 + 10 * q^21 + 10 * q^22 - 18 * q^24 - 24 * q^25 - 14 * q^28 + 8 * q^30 - 24 * q^31 - 45 * q^33 + 33 * q^39 + 90 * q^40 + 3 * q^42 - 20 * q^43 - 6 * q^48 - 6 * q^49 - 10 * q^51 - 48 * q^52 - 18 * q^55 + 4 * q^57 + 30 * q^58 + 55 * q^60 - 18 * q^61 + 31 * q^63 - 84 * q^64 + 75 * q^66 + 44 * q^67 + 33 * q^69 + 20 * q^70 + 17 * q^72 + 84 * q^73 - 18 * q^76 - 71 * q^78 + 20 * q^79 + 16 * q^81 - 18 * q^82 - 135 * q^84 - 2 * q^85 - 46 * q^88 - 10 * q^91 - 56 * q^93 + 36 * q^94 + 30 * q^96 - 24 * q^97 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	0.883413i		−	0.624668i	−0.949972	−	0.312334i	$-0.898889\pi$
$2$		−	0.883413i		−	0.624668i	0.949972	−	0.312334i	$-0.101111\pi$
$3$	1.41202	+	1.00309i	0.815231	+	0.579136i
$3$	1.41202	+	1.00309i	0.815231	+	0.579136i
$4$	1.21958			0.609790
$5$	−1.72131	+	2.98140i	−0.769794	+	1.33332i	0.167881	+	0.985807i	$0.446308\pi$
$5$	−1.72131	+	2.98140i	−0.769794	+	1.33332i	−0.937675	+	0.347514i	$0.887026\pi$
$6$	0.886146	−	1.24740i	0.361768	−	0.509248i
$7$	−2.26618	+	1.36544i	−0.856537	+	0.516086i
$7$	−2.26618	+	1.36544i	−0.856537	+	0.516086i
$8$		−	2.84422i		−	1.00558i
$9$	0.987606	+	2.83278i	0.329202	+	0.944259i
$10$	2.63381	+	1.52063i	0.832883	+	0.480865i
$11$	3.32619	+	1.92038i	1.00289	+	0.579016i	0.909101	−	0.416576i	$-0.136770\pi$
$11$	3.32619	+	1.92038i	1.00289	+	0.579016i	0.0937846	+	0.995593i	$0.470104\pi$
$12$	1.72207	+	1.22335i	0.497120	+	0.353152i
$13$	0.144185	−	3.60267i	0.0399897	−	0.999200i
$13$	0.144185	−	3.60267i	0.0399897	−	0.999200i
$14$	1.20624	+	2.00198i	0.322382	+	0.535051i
$15$	−5.42115	+	2.48316i	−1.39973	+	0.641149i
$16$	−0.0734612			−0.0183653
$17$	−0.161995			−0.0392895			−0.0196448	−	0.999807i	$-0.506254\pi$
$17$	−0.161995			−0.0392895			−0.0196448	+	0.999807i	$0.506254\pi$
$18$	2.50251	−	0.872465i	0.589848	−	0.205642i
$19$	−1.41529	+	0.817116i	−0.324689	+	0.187459i	−0.653481	−	0.756943i	$-0.726692\pi$
$19$	−1.41529	+	0.817116i	−0.324689	+	0.187459i	0.328792	+	0.944402i	$0.393359\pi$
$20$	−2.09928	+	3.63606i	−0.469413	+	0.813047i
$21$	−4.56956	−	0.345169i	−0.997159	−	0.0753220i
$22$	1.69649	−	2.93840i	0.361693	−	0.626470i
$23$		−	4.54399i		−	0.947488i	−0.880663	−	0.473744i	$-0.842902\pi$
$23$		−	4.54399i		−	0.947488i	0.880663	−	0.473744i	$-0.157098\pi$
$24$	2.85302	−	4.01610i	0.582370	−	0.819783i
$25$	−3.42582	−	5.93370i	−0.685164	−	1.18674i
$26$	−3.18264	−	0.127375i	−0.624168	−	0.0249803i
$27$	−1.44702	+	4.99060i	−0.278479	+	0.960442i
$28$	−2.76379	+	1.66526i	−0.522308	+	0.314705i
$29$	8.21721	−	4.74421i	1.52590	−	0.880978i	0.526370	−	0.850255i	$-0.323553\pi$
$29$	8.21721	−	4.74421i	1.52590	−	0.880978i	0.999528	−	0.0307223i	$-0.00978076\pi$
$30$	2.19366	+	4.78911i	0.400505	+	0.874369i
$31$	0.139734	−	0.0806754i	0.0250970	−	0.0144897i	−0.487399	−	0.873179i	$-0.662054\pi$
$31$	0.139734	−	0.0806754i	0.0250970	−	0.0144897i	0.512496	+	0.858690i	$0.328721\pi$
$32$		−	5.62354i		−	0.994112i
$33$	2.77034	+	6.04810i	0.482254	+	1.05284i
$34$			0.143108i			0.0245429i
$35$	−0.170104	−	9.10673i	−0.0287528	−	1.53932i
$36$	1.20447	+	3.45480i	0.200744	+	0.575800i
$37$	−3.98455			−0.655056			−0.327528	−	0.944841i	$-0.606216\pi$
$37$	−3.98455			−0.655056			−0.327528	+	0.944841i	$0.606216\pi$
$38$	0.721851	+	1.25028i	0.117100	+	0.202823i
$39$	3.81740	−	4.94241i	0.611274	−	0.791419i
$40$	8.47975	+	4.89579i	1.34077	+	0.774092i
$41$	2.41336	+	4.18006i	0.376904	+	0.652816i	0.990610	−	0.136718i	$-0.0436555\pi$
$41$	2.41336	+	4.18006i	0.376904	+	0.652816i	−0.613706	+	0.789534i	$0.710322\pi$
$42$	−0.304927	+	4.03681i	−0.0470512	+	0.622893i
$43$	4.32913	−	7.49828i	0.660186	−	1.14348i	−0.320380	−	0.947289i	$-0.603811\pi$
$43$	4.32913	−	7.49828i	0.660186	−	1.14348i	0.980566	−	0.196187i	$-0.0628561\pi$
$44$	4.05656	+	2.34206i	0.611550	+	0.353078i
$45$	−10.1456	−	1.93164i	−1.51242	−	0.287953i
$46$	−4.01422			−0.591865
$47$	3.42471	−	5.93177i	0.499545	−	0.865238i	−0.500455	−	0.865763i	$-0.666834\pi$
$47$	3.42471	−	5.93177i	0.499545	−	0.865238i	1.00000		0.000525066i	$0.000167134\pi$
$48$	−0.103729	−	0.0736885i	−0.0149720	−	0.0106360i
$49$	3.27117	−	6.18866i	0.467310	−	0.884094i
$50$	−5.24191	+	3.02642i	−0.741317	+	0.428000i
$51$	−0.228740	−	0.162496i	−0.0320300	−	0.0227540i
$52$	0.175845	−	4.39374i	0.0243853	−	0.609303i
$53$	−11.2686	+	6.50591i	−1.54786	+	0.893656i	−0.549552	+	0.835459i	$0.685202\pi$
$53$	−11.2686	+	6.50591i	−1.54786	+	0.893656i	−0.998305	+	0.0581968i	$0.981465\pi$
$54$	4.40877	+	1.27832i	0.599957	+	0.173957i
$55$	−11.4508	+	6.61114i	−1.54403	+	0.891446i
$56$	3.88360	+	6.44552i	0.518968	+	0.861319i
$57$	−2.81806	−	0.265880i	−0.373261	−	0.0352166i
$58$	−4.19110	−	7.25920i	−0.550318	−	0.953179i
$59$	−8.91725			−1.16093			−0.580464	−	0.814286i	$-0.697129\pi$
$59$	−8.91725			−1.16093			−0.580464	+	0.814286i	$0.697129\pi$
$60$	−6.61153	+	3.02841i	−0.853544	+	0.390967i
$61$	−5.63535	+	3.25357i	−0.721533	+	0.416577i	−0.815317	−	0.579015i	$-0.803437\pi$
$61$	−5.63535	+	3.25357i	−0.721533	+	0.416577i	0.0937835	+	0.995593i	$0.470104\pi$
$62$	−0.0712698	−	0.123443i	−0.00905127	−	0.0156773i
$63$	−6.10608	−	5.07108i	−0.769293	−	0.638896i
$64$	−5.11484			−0.639355
$65$	10.4928	+	6.63118i	1.30147	+	0.822497i
$66$	5.34297	−	2.44735i	0.657674	−	0.301248i
$67$	0.472730	−	0.818793i	0.0577532	−	0.100031i	−0.835703	−	0.549181i	$-0.814940\pi$
$67$	0.472730	−	0.818793i	0.0577532	−	0.100031i	0.893457	+	0.449150i	$0.148273\pi$
$68$	−0.197566			−0.0239584
$69$	4.55805	−	6.41621i	0.548725	−	0.772421i
$70$	−8.04501	+	0.150272i	−0.961562	+	0.0179610i
$71$	4.33350	+	2.50195i	0.514292	+	0.296927i	0.734596	−	0.678505i	$-0.237372\pi$
$71$	4.33350	+	2.50195i	0.514292	+	0.296927i	−0.220304	+	0.975431i	$0.570705\pi$
$72$	8.05705	−	2.80897i	0.949532	−	0.331040i
$73$	8.62581	−	4.98012i	1.00958	−	0.582878i	0.0985078	−	0.995136i	$-0.468593\pi$
$73$	8.62581	−	4.98012i	1.00958	−	0.582878i	0.911067	+	0.412258i	$0.135260\pi$
$74$			3.52001i			0.409193i
$75$	1.11472	−	11.8149i	0.128717	−	1.36427i
$76$	−1.72606	+	0.996539i	−0.197992	+	0.114311i
$77$	−10.1599	+	0.189777i	−1.15783	+	0.0216270i
$78$	−4.36619	−	3.37235i	−0.494374	−	0.381843i
$79$	−5.23295	+	9.06373i	−0.588753	+	1.01975i	0.405644	+	0.914031i	$0.367047\pi$
$79$	−5.23295	+	9.06373i	−0.588753	+	1.01975i	−0.994396	+	0.105718i	$0.966286\pi$
$80$	0.126450	−	0.219017i	0.0141375	−	0.0244868i
$81$	−7.04927	+	5.59534i	−0.783252	+	0.621705i
$82$	3.69272	−	2.13200i	0.407793	−	0.235439i
$83$	−1.04892			−0.115134			−0.0575672	−	0.998342i	$-0.518334\pi$
$83$	−1.04892			−0.115134			−0.0575672	+	0.998342i	$0.518334\pi$
$84$	−5.57294	−	0.420961i	−0.608058	−	0.0459306i
$85$	0.278843	−	0.482971i	0.0302448	−	0.0523856i
$86$	−6.62408	−	3.82441i	−0.714293	−	0.412397i
$87$	16.3618	+	1.54371i	1.75417	+	0.165503i
$88$	5.46198	−	9.46043i	0.582249	−	1.00849i
$89$	−6.88870			−0.730200			−0.365100	−	0.930968i	$-0.618965\pi$
$89$	−6.88870			−0.730200			−0.365100	+	0.930968i	$0.618965\pi$
$90$	−1.70644	+	8.96277i	−0.179875	+	0.944759i
$91$	4.59246	+	8.36118i	0.481421	+	0.876490i
$92$		−	5.54177i		−	0.577769i
$93$	0.278232	+	0.0262508i	0.0288513	+	0.00272208i
$94$	−5.24021	−	3.02543i	−0.540486	−	0.312050i
$95$		−	5.62604i		−	0.577220i
$96$	5.64094	−	7.94056i	0.575726	−	0.810430i
$97$	6.97520	+	4.02713i	0.708224	+	0.408893i	0.810403	−	0.585873i	$-0.199248\pi$
$97$	6.97520	+	4.02713i	0.708224	+	0.408893i	−0.102179	+	0.994766i	$0.532581\pi$
$98$	−5.46714	−	2.88979i	−0.552265	−	0.291913i
$99$	−2.15504	+	11.3189i	−0.216589	+	1.13760i
$100$	−4.17807	−	7.23662i	−0.417807	−	0.723662i
$101$	−2.54956	+	4.41597i	−0.253691	+	0.439405i	−0.964539	−	0.263940i	$-0.914978\pi$
$101$	−2.54956	+	4.41597i	−0.253691	+	0.439405i	0.710848	+	0.703345i	$0.248311\pi$
$102$	−0.143551	+	0.202072i	−0.0142137	+	0.0200081i
$103$	−0.996557	−	0.575362i	−0.0981937	−	0.0566921i	0.450099	−	0.892979i	$-0.351389\pi$
$103$	−0.996557	−	0.575362i	−0.0981937	−	0.0566921i	−0.548293	+	0.836287i	$0.684722\pi$
$104$	−10.2468	−	0.410094i	−1.00478	−	0.0402130i
$105$	8.89471	−	13.0295i	0.868035	−	1.27155i
$106$	5.74741	+	9.95481i	0.558238	+	0.966897i
$107$			19.1301i			1.84938i	0.380720	+	0.924690i	$0.375676\pi$
$107$			19.1301i			1.84938i	−0.380720	+	0.924690i	$0.624324\pi$
$108$	−1.76476	+	6.08644i	−0.169814	+	0.585668i
$109$	−9.89648	−	17.1412i	−0.947911	−	1.64183i	−0.749815	−	0.661647i	$-0.769858\pi$
$109$	−9.89648	−	17.1412i	−0.947911	−	1.64183i	−0.198096	−	0.980183i	$-0.563476\pi$
$110$	5.84037	+	10.1158i	0.556857	+	0.964505i
$111$	−5.62627	−	3.99688i	−0.534022	−	0.379367i
$112$	0.166476	−	0.100307i	0.0157305	−	0.00947808i
$113$	−0.613946	−	0.354462i	−0.0577552	−	0.0333450i	0.470844	−	0.882216i	$-0.343949\pi$
$113$	−0.613946	−	0.354462i	−0.0577552	−	0.0333450i	−0.528600	+	0.848871i	$0.677283\pi$
$114$	−0.234882	+	2.48951i	−0.0219987	+	0.233164i
$115$	13.5475	+	7.82162i	1.26331	+	0.729370i
$116$	10.0216	−	5.78595i	0.930478	−	0.537212i
$117$	10.3480	−	3.14957i	0.956669	−	0.291178i
$118$			7.87762i			0.725194i
$119$	0.367110	−	0.221194i	0.0336529	−	0.0202768i
$120$	7.06266	+	15.4189i	0.644729	+	1.40755i
$121$	1.87571	+	3.24883i	0.170519	+	0.295348i
$122$	2.87425	+	4.97835i	0.260222	+	0.450718i
$123$	−0.785279	+	8.32316i	−0.0708062	+	0.750474i
$124$	0.170417	−	0.0983902i	0.0153039	−	0.00883570i
$125$	6.37450			0.570153
$126$	−4.47986	+	5.39419i	−0.399098	+	0.480553i
$127$	3.35273	+	5.80710i	0.297507	+	0.515297i	0.975565	−	0.219711i	$-0.0705116\pi$
$127$	3.35273	+	5.80710i	0.297507	+	0.515297i	−0.678058	+	0.735008i	$0.737178\pi$
$128$		−	6.72857i		−	0.594728i
$129$	13.6343	−	6.24520i	1.20043	−	0.549859i
$130$	5.85808	−	9.26948i	0.513787	−	0.812987i
$131$	5.07994	−	8.79871i	0.443836	−	0.768747i	−0.554134	−	0.832427i	$-0.686951\pi$
$131$	5.07994	−	8.79871i	0.443836	−	0.768747i	0.997970	+	0.0636806i	$0.0202839\pi$
$132$	3.37865	+	7.37615i	0.294074	+	0.642011i
$133$	2.09158	−	3.78422i	0.181363	−	0.328133i
$134$	−0.723332	−	0.417616i	−0.0624864	−	0.0360765i
$135$	−12.3882	−	12.9045i	−1.06621	−	1.11064i
$136$			0.460749i			0.0395089i
$137$		−	9.23159i		−	0.788708i	−0.918959	−	0.394354i	$-0.870968\pi$
$137$		−	9.23159i		−	0.788708i	0.918959	−	0.394354i	$-0.129032\pi$
$138$	−5.66817	−	4.02664i	−0.482507	−	0.342771i
$139$	8.92213	+	5.15119i	0.756765	+	0.436919i	0.828133	−	0.560532i	$-0.189403\pi$
$139$	8.92213	+	5.15119i	0.756765	+	0.436919i	−0.0713680	+	0.997450i	$0.522736\pi$
$140$	−0.207456	−	11.1064i	−0.0175332	−	0.938662i
$141$	10.7859	−	4.94048i	0.908335	−	0.416064i
$142$	2.21026	−	3.82827i	0.185481	−	0.321262i
$143$	7.39807	−	11.7063i	0.618658	−	0.978928i
$144$	−0.0725507	−	0.208099i	−0.00604590	−	0.0173416i
$145$			32.6650i			2.71268i
$146$	−4.39950	−	7.62016i	−0.364105	−	0.630649i
$147$	10.8268	−	5.45723i	0.892976	−	0.450104i
$148$	−4.85948			−0.399447
$149$	2.60371	−	1.50326i	0.213305	−	0.123151i	−0.389542	−	0.921009i	$-0.627367\pi$
$149$	2.60371	−	1.50326i	0.213305	−	0.123151i	0.602846	+	0.797857i	$0.294033\pi$
$150$	−10.4375	−	0.984760i	−0.852215	−	0.0804053i
$151$	1.79991	+	3.11753i	0.146475	+	0.253701i	0.929922	−	0.367757i	$-0.119874\pi$
$151$	1.79991	+	3.11753i	0.146475	+	0.253701i	−0.783448	+	0.621458i	$0.786541\pi$
$152$	2.32406	+	4.02539i	0.188506	+	0.326502i
$153$	−0.159987	−	0.458895i	−0.0129342	−	0.0370995i
$154$	0.167651	+	8.97541i	0.0135097	+	0.723259i
$155$			0.555470i			0.0446164i
$156$	4.65563	−	6.02767i	0.372749	−	0.482600i
$157$	4.18032	−	2.41351i	0.333626	−	0.192619i	−0.323824	−	0.946117i	$-0.604968\pi$
$157$	4.18032	−	2.41351i	0.333626	−	0.192619i	0.657450	+	0.753498i	$0.271635\pi$
$158$	8.00702	+	4.62286i	0.637004	+	0.367775i
$159$	−22.4375	−	2.11695i	−1.77941	−	0.167885i
$160$	16.7660	+	9.67987i	1.32547	+	0.765261i
$161$	6.20453	+	10.2975i	0.488986	+	0.811558i
$162$	4.94300	+	6.22742i	0.388359	+	0.489272i
$163$	4.21441	+	7.29957i	0.330098	+	0.571746i	0.982531	−	0.186100i	$-0.0595849\pi$
$163$	4.21441	+	7.29957i	0.330098	+	0.571746i	−0.652433	+	0.757847i	$0.726252\pi$
$164$	2.94329	+	5.09792i	0.229832	+	0.398081i
$165$	−22.8004	−	2.15119i	−1.77501	−	0.167470i
$166$			0.926634i			0.0719207i
$167$	−0.713480	−	1.23578i	−0.0552108	−	0.0956279i	0.837099	−	0.547051i	$-0.184250\pi$
$167$	−0.713480	−	1.23578i	−0.0552108	−	0.0956279i	−0.892310	+	0.451423i	$0.850916\pi$
$168$	−0.981736	+	12.9968i	−0.0757425	+	1.00273i
$169$	−12.9584	−	1.03890i	−0.996802	−	0.0799155i
$170$	−0.426663	−	0.246334i	−0.0327236	−	0.0188930i
$171$	−3.71245	−	3.20220i	−0.283899	−	0.244879i
$172$	5.27973	−	9.14475i	0.402575	−	0.697281i
$173$	−8.35447	−	14.4704i	−0.635179	−	1.10016i	−0.986477	−	0.163898i	$-0.947593\pi$
$173$	−8.35447	−	14.4704i	−0.635179	−	1.10016i	0.351299	−	0.936263i	$-0.385740\pi$
$174$	1.36373	−	14.4542i	0.103384	−	1.09577i
$175$	15.8656	+	8.76910i	1.19933	+	0.662881i
$176$	−0.244346	−	0.141073i	−0.0184183	−	0.0106338i
$177$	−12.5913	−	8.94484i	−0.946423	−	0.672335i
$178$			6.08557i			0.456133i
$179$	9.53071	+	5.50256i	0.712359	+	0.411281i	0.811934	−	0.583749i	$-0.198415\pi$
$179$	9.53071	+	5.50256i	0.712359	+	0.411281i	−0.0995749	+	0.995030i	$0.531748\pi$
$180$	−12.3734	−	2.35580i	−0.922259	−	0.175591i
$181$			2.82101i			0.209684i	0.994489	+	0.104842i	$0.0334337\pi$
$181$			2.82101i			0.209684i	−0.994489	+	0.104842i	$0.966566\pi$
$182$	7.38638	−	4.05704i	0.547515	−	0.300728i
$183$	−11.2209	−	1.05867i	−0.829471	−	0.0782594i
$184$	−12.9241			−0.952779
$185$	6.85865	−	11.8795i	0.504258	−	0.873401i
$186$	0.0231903	−	0.245794i	0.00170040	−	0.0180225i
$187$	−0.538826	−	0.311091i	−0.0394029	−	0.0227493i
$188$	4.17671	−	7.23427i	0.304618	−	0.527614i
$189$	−3.53514	−	13.2854i	−0.257144	−	0.966373i
$190$	−4.97012			−0.360570
$191$	−2.19950	+	1.26988i	−0.159150	+	0.0918854i	−0.577460	−	0.816419i	$-0.695956\pi$
$191$	−2.19950	+	1.26988i	−0.159150	+	0.0918854i	0.418310	+	0.908304i	$0.362623\pi$
$192$	−7.22226	−	5.13066i	−0.521222	−	0.370274i
$193$	−5.35745	+	9.27937i	−0.385638	+	0.667944i	−0.991857	−	0.127353i	$-0.959352\pi$
$193$	−5.35745	+	9.27937i	−0.385638	+	0.667944i	0.606220	+	0.795297i	$0.292685\pi$
$194$	3.55762	−	6.16198i	0.255422	−	0.442405i
$195$	8.16435	+	19.8886i	0.584661	+	1.42425i
$196$	3.98945	−	7.54757i	0.284961	−	0.539112i
$197$	−4.30705	+	2.48668i	−0.306865	+	0.177168i	−0.645523	−	0.763741i	$-0.723360\pi$
$197$	−4.30705	+	2.48668i	−0.306865	+	0.177168i	0.338658	+	0.940910i	$0.390027\pi$
$198$	9.99931	+	1.90379i	0.710620	+	0.135296i
$199$		−	9.82186i		−	0.696253i	−0.937448	−	0.348127i	$-0.886818\pi$
$199$		−	9.82186i		−	0.696253i	0.937448	−	0.348127i	$-0.113182\pi$
$200$	−16.8767	+	9.74379i	−1.19337	+	0.688990i
$201$	1.48883	−	0.681960i	0.105014	−	0.0481017i
$202$	3.90112	+	2.25231i	0.274482	+	0.158472i
$203$	−12.1438	+	21.9713i	−0.852327	+	1.54208i
$204$	−0.278967	−	0.198177i	−0.0195316	−	0.0138752i
$205$	−16.6166			−1.16055
$206$	−0.508283	+	0.880372i	−0.0354137	+	0.0613384i
$207$	12.8721	−	4.48768i	0.894675	−	0.311915i
$208$	−0.0105920	+	0.264656i	−0.000734423	+	0.0183506i
$209$	−6.27669			−0.434168
$210$	−11.5105	−	7.85771i	−0.794297	−	0.542233i
$211$	7.89735	+	13.6786i	0.543676	+	0.941675i	0.998689	+	0.0511899i	$0.0163014\pi$
$211$	7.89735	+	13.6786i	0.543676	+	0.941675i	−0.455013	+	0.890485i	$0.650365\pi$
$212$	−13.7429	+	7.93449i	−0.943869	+	0.544943i
$213$	3.60931	+	7.87971i	0.247306	+	0.539909i
$214$	16.8998			1.15525
$215$	14.9036	+	25.8137i	1.01641	+	1.76048i
$216$	14.1944	+	4.11565i	0.965805	+	0.280034i
$217$	−0.206505	+	0.373623i	−0.0140185	+	0.0253632i
$218$	−15.1428	+	8.74268i	−1.02560	+	0.592129i
$219$	17.1754	+	1.62047i	1.16060	+	0.109501i
$220$	−13.9652	+	8.06282i	−0.941534	+	0.543595i
$221$	−0.0233572	+	0.583613i	−0.00157118	+	0.0392581i
$222$	−3.53090	+	4.97032i	−0.236978	+	0.333586i
$223$	0.772875	−	0.446219i	0.0517555	−	0.0298811i	−0.473899	−	0.880579i	$-0.657154\pi$
$223$	0.772875	−	0.446219i	0.0517555	−	0.0298811i	0.525654	+	0.850698i	$0.323820\pi$
$224$	7.67859	+	12.7440i	0.513048	+	0.851493i
$225$	13.4255	−	15.5647i	0.895032	−	1.03765i
$226$	−0.313136	+	0.542368i	−0.0208295	+	0.0360778i
$227$	−2.82097			−0.187234			−0.0936171	−	0.995608i	$-0.529843\pi$
$227$	−2.82097			−0.187234			−0.0936171	+	0.995608i	$0.529843\pi$
$228$	−3.43685	−	0.324262i	−0.227611	−	0.0214748i
$229$	−15.0847	−	8.70916i	−0.996826	−	0.575518i	−0.0895184	−	0.995985i	$-0.528533\pi$
$229$	−15.0847	−	8.70916i	−0.996826	−	0.575518i	−0.907308	+	0.420467i	$0.861866\pi$
$230$	6.90973	−	11.9680i	0.455614	−	0.789146i
$231$	−14.5364	−	9.92338i	−0.956424	−	0.652911i
$232$	−13.4936	−	23.3716i	−0.885897	−	1.53442i
$233$	−17.8552	−	10.3087i	−1.16973	−	0.675345i	−0.216115	−	0.976368i	$-0.569338\pi$
$233$	−17.8552	−	10.3087i	−1.16973	−	0.675345i	−0.953617	+	0.301023i	$0.902672\pi$
$234$	−2.78238	−	9.14152i	−0.181890	−	0.597600i
$235$	11.7900	+	20.4208i	0.769093	+	1.33211i
$236$	−10.8753			−0.707922
$237$	−16.4808	+	7.54904i	−1.07054	+	0.490363i
$238$	−0.195405	−	0.324310i	−0.0126662	−	0.0210219i
$239$		−	17.5634i		−	1.13608i	−0.823000	−	0.568042i	$-0.807701\pi$
$239$		−	17.5634i		−	1.13608i	0.823000	−	0.568042i	$-0.192299\pi$
$240$	0.398244	−	0.182416i	0.0257065	−	0.0117749i
$241$		−	1.97278i		−	0.127078i	−0.997979	−	0.0635389i	$-0.979761\pi$
$241$		−	1.97278i		−	0.127078i	0.997979	−	0.0635389i	$-0.0202387\pi$
$242$	2.87006	−	1.65703i	0.184494	−	0.106518i
$243$	−15.5664	+	0.829664i	−0.998583	+	0.0532229i
$244$	−6.87277	+	3.96800i	−0.439984	+	0.254025i
$245$	12.8201	+	20.4052i	0.819049	+	1.30364i
$246$	7.35279	+	0.693726i	0.468797	+	0.0442303i
$247$	2.73973	+	5.21662i	0.174325	+	0.331926i
$248$	−0.229459	−	0.397434i	−0.0145706	−	0.0252371i
$249$	−1.48110	−	1.05217i	−0.0938611	−	0.0666785i
$250$		−	5.63132i		−	0.356156i
$251$	0.542545	−	0.939716i	0.0342452	−	0.0593144i	−0.848395	−	0.529364i	$-0.822431\pi$
$251$	0.542545	−	0.939716i	0.0342452	−	0.0593144i	0.882640	+	0.470050i	$0.155764\pi$
$252$	−7.44685	−	6.18459i	−0.469108	−	0.389593i
$253$	8.72619	−	15.1142i	0.548611	−	0.950222i
$254$	5.13007	−	2.96185i	0.321889	−	0.185843i
$255$	0.878198	−	0.402259i	0.0549949	−	0.0251904i
$256$	−16.1738			−1.01086
$257$	13.9742			0.871688			0.435844	−	0.900022i	$-0.356450\pi$
$257$	13.9742			0.871688			0.435844	+	0.900022i	$0.356450\pi$
$258$	−5.51709	−	12.0447i	−0.343479	−	0.749872i
$259$	9.02973	−	5.44065i	0.561080	−	0.338066i
$260$	12.7968	+	8.08726i	0.793625	+	0.501551i
$261$	21.5547	+	18.5921i	1.33420	+	1.15082i
$262$	−7.77290	−	4.48768i	−0.480211	−	0.277250i
$263$	−5.41212	−	3.12469i	−0.333726	−	0.192677i	0.323768	−	0.946136i	$-0.395050\pi$
$263$	−5.41212	−	3.12469i	−0.333726	−	0.192677i	−0.657494	+	0.753460i	$0.728383\pi$
$264$	17.2021	−	7.87945i	1.05872	−	0.484946i
$265$		−	44.7948i		−	2.75172i
$266$	−3.34303	−	1.84773i	−0.204974	−	0.113291i
$267$	−9.72699	−	6.91001i	−0.595282	−	0.422886i
$268$	0.576533	−	0.998584i	0.0352173	−	0.0609982i
$269$	−10.0437			−0.612376			−0.306188	−	0.951971i	$-0.599054\pi$
$269$	−10.0437			−0.612376			−0.306188	+	0.951971i	$0.599054\pi$
$270$	−11.4000	+	10.9439i	−0.693784	+	0.666025i
$271$			15.3416i			0.931936i	0.884802	+	0.465968i	$0.154294\pi$
$271$			15.3416i			0.931936i	−0.884802	+	0.465968i	$0.845706\pi$
$272$	0.0119003			0.000721564
$273$	−1.90239	+	16.4128i	−0.115138	+	0.993350i
$274$	−8.15531			−0.492680
$275$		−	26.3155i		−	1.58688i
$276$	5.55891	−	7.82509i	0.334607	−	0.471015i
$277$	9.45069			0.567837			0.283919	−	0.958848i	$-0.408365\pi$
$277$	9.45069			0.567837			0.283919	+	0.958848i	$0.408365\pi$
$278$	4.55063	−	7.88193i	0.272929	−	0.472727i
$279$	0.366538	+	0.316160i	0.0219440	+	0.0189280i
$280$	−25.9016	+	0.483814i	−1.54791	+	0.0289134i
$281$		−	11.6272i		−	0.693622i	−0.937935	−	0.346811i	$-0.887265\pi$
$281$		−	11.6272i		−	0.693622i	0.937935	−	0.346811i	$-0.112735\pi$
$282$	−4.36449	−	9.52839i	−0.259901	−	0.567408i
$283$	1.40991	+	0.814013i	0.0838106	+	0.0483881i	0.541320	−	0.840817i	$-0.317925\pi$
$283$	1.40991	+	0.814013i	0.0838106	+	0.0483881i	−0.457509	+	0.889205i	$0.651258\pi$
$284$	5.28506	+	3.05133i	0.313610	+	0.181063i
$285$	5.64345	−	7.94409i	0.334289	−	0.470567i
$286$	−10.3415	−	6.53556i	−0.611505	−	0.386456i
$287$	−11.1767	−	6.17750i	−0.659741	−	0.364646i
$288$	15.9303	−	5.55385i	0.938699	−	0.327264i
$289$	−16.9738			−0.998456
$290$	28.8567			1.69453
$291$	5.80954	+	12.6832i	0.340561	+	0.743501i
$292$	10.5199	−	6.07365i	0.615629	−	0.355434i
$293$	−2.80580	+	4.85979i	−0.163917	+	0.283912i	−0.936270	−	0.351281i	$-0.885746\pi$
$293$	−2.80580	+	4.85979i	−0.163917	+	0.283912i	0.772353	+	0.635193i	$0.219079\pi$
$294$	−4.82099	−	9.56450i	−0.281166	−	0.557813i
$295$	15.3494	−	26.5859i	0.893674	−	1.54789i
$296$			11.3329i			0.658714i
$297$	−14.3969	+	13.8209i	−0.835394	+	0.801969i
$298$	−1.32800	−	2.30016i	−0.0769287	−	0.133244i
$299$	−16.3705	−	0.655176i	−0.946730	−	0.0378898i
$300$	1.35949	−	14.4093i	0.0784903	−	0.831918i
$301$	0.427815	+	22.9036i	0.0246589	+	1.32014i
$302$	2.75407	−	1.59006i	0.158479	−	0.0914979i
$303$	−8.02966	+	3.67799i	−0.461292	+	0.211295i
$304$	0.103969	−	0.0600263i	0.00596301	−	0.00344275i
$305$		−	22.4016i		−	1.28271i
$306$	−0.405394	+	0.141335i	−0.0231749	+	0.00807957i
$307$		−	8.81390i		−	0.503036i	−0.967853	−	0.251518i	$-0.919070\pi$
$307$		−	8.81390i		−	0.503036i	0.967853	−	0.251518i	$-0.0809297\pi$
$308$	−12.3908	+	0.231448i	−0.706034	+	0.0131880i
$309$	−0.830017	−	1.81206i	−0.0472180	−	0.103085i
$310$	0.490710			0.0278704
$311$	11.9788	+	20.7478i	0.679254	+	1.17650i	0.975206	+	0.221299i	$0.0710297\pi$
$311$	11.9788	+	20.7478i	0.679254	+	1.17650i	−0.295952	+	0.955203i	$0.595637\pi$
$312$	−14.0573	−	10.8575i	−0.795838	−	0.614687i
$313$	5.88550	+	3.39799i	0.332668	+	0.192066i	0.657025	−	0.753869i	$-0.271815\pi$
$313$	5.88550	+	3.39799i	0.332668	+	0.192066i	−0.324357	+	0.945935i	$0.605148\pi$
$314$	−2.13213	−	3.69295i	−0.120323	−	0.208405i
$315$	25.6294	−	9.47573i	1.44405	−	0.533897i
$316$	−6.38200	+	11.0540i	−0.359016	+	0.621833i
$317$	6.84769	+	3.95352i	0.384605	+	0.222052i	0.679820	−	0.733379i	$-0.262058\pi$
$317$	6.84769	+	3.95352i	0.384605	+	0.222052i	−0.295215	+	0.955431i	$0.595391\pi$
$318$	−1.87014	+	19.8216i	−0.104872	+	1.11154i
$319$	36.4427			2.04040
$320$	8.80422	−	15.2494i	0.492171	−	0.852465i
$321$	−19.1893	+	27.0122i	−1.07104	+	1.50767i
$322$	9.09697	−	5.48117i	0.506954	−	0.305454i
$323$	0.229269	−	0.132369i	0.0127569	−	0.00736518i
$324$	−8.59715	+	6.82397i	−0.477619	+	0.379109i
$325$	−21.8711	+	11.4865i	−1.21319	+	0.637159i
$326$	6.44854	−	3.72307i	0.357151	−	0.206202i
$327$	3.22020	−	34.1308i	0.178077	−	1.88744i
$328$	11.8890	−	6.86413i	0.656461	−	0.379008i
$329$	0.338438	+	18.1187i	0.0186587	+	0.998916i
$330$	−1.90039	+	20.1422i	−0.104613	+	1.10879i
$331$	4.41316	+	7.64382i	0.242569	+	0.420143i	0.961445	−	0.274996i	$-0.0886764\pi$
$331$	4.41316	+	7.64382i	0.242569	+	0.420143i	−0.718876	+	0.695138i	$0.755343\pi$
$332$	−1.27925			−0.0702078
$333$	−3.93517	−	11.2874i	−0.215646	−	0.618543i
$334$	−1.09171	+	0.630298i	−0.0597356	+	0.0344884i
$335$	1.62743	+	2.81879i	0.0889161	+	0.154007i
$336$	0.335685	+	0.0253565i	0.0183131	+	0.00138331i
$337$	−11.5765			−0.630611			−0.315306	−	0.948990i	$-0.602107\pi$
$337$	−11.5765			−0.630611			−0.315306	+	0.948990i	$0.602107\pi$
$338$	−0.917779	+	11.4476i	−0.0499206	+	0.622670i
$339$	−0.511346	−	1.11635i	−0.0277725	−	0.0606320i
$340$	0.340072	−	0.589022i	0.0184430	−	0.0319442i
$341$	0.619710			0.0335592
$342$	−2.82887	+	3.27963i	−0.152968	+	0.177342i
$343$	1.03715	+	18.4912i	0.0560010	+	0.998431i
$344$	−21.3268	−	12.3130i	−1.14986	−	0.663873i
$345$	11.2835	+	24.6337i	0.607481	+	1.32623i
$346$	−12.7833	+	7.38045i	−0.687235	+	0.396776i
$347$			18.6275i			0.999976i	0.866032	+	0.499988i	$0.166662\pi$
$347$			18.6275i			0.999976i	−0.866032	+	0.499988i	$0.833338\pi$
$348$	19.9545	+	1.88268i	1.06967	+	0.100922i
$349$	9.48259	−	5.47477i	0.507591	−	0.293058i	−0.224252	−	0.974531i	$-0.571994\pi$
$349$	9.48259	−	5.47477i	0.507591	−	0.293058i	0.731843	+	0.681473i	$0.238660\pi$
$350$	7.74674	−	14.0159i	0.414081	−	0.749181i
$351$	17.7708	+	5.93270i	0.948538	+	0.316664i
$352$	10.7993	−	18.7050i	0.575607	−	0.996980i
$353$	−11.4363	+	19.8082i	−0.608691	+	1.05428i	0.382766	+	0.923845i	$0.374972\pi$
$353$	−11.4363	+	19.8082i	−0.608691	+	1.05428i	−0.991457	+	0.130438i	$0.958362\pi$
$354$	−7.90199	+	11.1234i	−0.419986	+	0.591200i
$355$	−14.9186	+	8.61326i	−0.791798	+	0.457145i
$356$	−8.40132			−0.445269
$357$	0.740245	+	0.0559155i	0.0391779	+	0.00295936i
$358$	4.86104	−	8.41956i	0.256914	−	0.444988i
$359$	29.3954	+	16.9714i	1.55143	+	0.895719i	0.998026	+	0.0628057i	$0.0200048\pi$
$359$	29.3954	+	16.9714i	1.55143	+	0.895719i	0.553404	+	0.832913i	$0.313328\pi$
$360$	−5.49402	+	28.8564i	−0.289560	+	1.52086i
$361$	−8.16464	+	14.1416i	−0.429718	+	0.744293i
$362$	2.49212			0.130983
$363$	−0.610334	+	6.46893i	−0.0320342	+	0.339531i
$364$	5.60088	+	10.1971i	0.293566	+	0.534475i
$365$			34.2893i			1.79478i
$366$	−0.935247	+	9.91267i	−0.0488861	+	0.518144i
$367$	−24.4916	−	14.1402i	−1.27845	−	0.738115i	−0.301889	−	0.953343i	$-0.597617\pi$
$367$	−24.4916	−	14.1402i	−1.27845	−	0.738115i	−0.976564	+	0.215228i	$0.930950\pi$
$368$			0.333807i			0.0174009i
$369$	−9.45774	+	10.9648i	−0.492350	+	0.570803i
$370$	−10.4945	−	6.05903i	−0.545585	−	0.314994i
$371$	16.6532	−	30.1301i	0.864593	−	1.56428i
$372$	0.339327	+	0.0320150i	0.0175933	+	0.00165990i
$373$	−2.11110	−	3.65653i	−0.109309	−	0.189328i	0.806182	−	0.591668i	$-0.201530\pi$
$373$	−2.11110	−	3.65653i	−0.109309	−	0.189328i	−0.915490	+	0.402340i	$0.868197\pi$
$374$	−0.274822	+	0.476006i	−0.0142107	+	0.0246137i
$375$	9.00093	+	6.39422i	0.464806	+	0.330196i
$376$	−16.8713	−	9.74063i	−0.870069	−	0.502335i
$377$	−15.9070	−	30.2879i	−0.819253	−	1.55991i
$378$	−11.7365	+	3.12299i	−0.603662	+	0.160629i
$379$	16.6762	+	28.8840i	0.856599	+	1.48367i	0.875153	+	0.483846i	$0.160760\pi$
$379$	16.6762	+	28.8840i	0.856599	+	1.48367i	−0.0185539	+	0.999828i	$0.505906\pi$
$380$		−	6.86141i		−	0.351983i
$381$	−1.09094	+	11.5629i	−0.0558905	+	0.592383i
$382$	1.12183	+	1.94307i	0.0573978	+	0.0994159i
$383$	−8.93585	−	15.4774i	−0.456601	−	0.790856i	0.542178	−	0.840264i	$-0.317600\pi$
$383$	−8.93585	−	15.4774i	−0.456601	−	0.790856i	−0.998779	+	0.0494080i	$0.984267\pi$
$384$	6.74939	−	9.50089i	0.344428	−	0.484840i
$385$	16.9226	−	30.6174i	0.862454	−	1.56041i
$386$	8.19752	+	4.73284i	0.417243	+	0.240895i
$387$	25.5164	+	4.85813i	1.29707	+	0.246952i
$388$	8.50682	+	4.91141i	0.431868	+	0.249339i
$389$	−21.4374	+	12.3769i	−1.08692	+	0.627533i	−0.932755	−	0.360512i	$-0.882602\pi$
$389$	−21.4374	+	12.3769i	−1.08692	+	0.627533i	−0.154165	+	0.988045i	$0.549269\pi$
$390$	17.5699	−	7.21250i	0.889685	−	0.365219i
$391$			0.736103i			0.0372263i
$392$	−17.6019	−	9.30392i	−0.889030	−	0.469919i
$393$	15.9989	−	7.32831i	0.807038	−	0.369664i
$394$	2.19676	+	3.80491i	0.110671	+	0.191688i
$395$	−18.0151	−	31.2030i	−0.906436	−	1.56999i
$396$	−2.62824	+	13.8044i	−0.132074	+	0.693696i
$397$	−19.5919	+	11.3114i	−0.983292	+	0.567704i	−0.903262	−	0.429089i	$-0.858835\pi$
$397$	−19.5919	+	11.3114i	−0.983292	+	0.567704i	−0.0800293	+	0.996793i	$0.525501\pi$
$398$	−8.67676			−0.434927
$399$	6.74928	−	3.24535i	0.337886	−	0.162471i
$400$	0.251665	+	0.435896i	0.0125832	+	0.0217948i
$401$		−	24.4083i		−	1.21889i	−0.792827	−	0.609446i	$-0.791392\pi$
$401$		−	24.4083i		−	1.21889i	0.792827	−	0.609446i	$-0.208608\pi$
$402$	−0.602452	−	1.31525i	−0.0300476	−	0.0655989i
$403$	−0.270499	−	0.515047i	−0.0134745	−	0.0256563i
$404$	−3.10939	+	5.38563i	−0.154698	+	0.267945i
$405$	−4.54796	−	30.6480i	−0.225990	−	1.52291i
$406$	19.4098	+	10.7280i	0.963291	+	0.532421i
$407$	−13.2534	−	7.65185i	−0.656947	−	0.379288i
$408$	−0.462174	+	0.650587i	−0.0228810	+	0.0322089i
$409$		−	31.7712i		−	1.57098i	−0.618872	−	0.785492i	$-0.712410\pi$
$409$		−	31.7712i		−	1.57098i	0.618872	−	0.785492i	$-0.287590\pi$
$410$			14.6793i			0.724959i
$411$	9.26014	−	13.0352i	0.456769	−	0.642979i
$412$	−1.21538	−	0.701701i	−0.0598775	−	0.0345703i
$413$	20.2081	−	12.1759i	0.994377	−	0.599139i
$414$	−3.96447	−	11.3714i	−0.194843	−	0.558874i
$415$	1.80552	−	3.12726i	0.0886297	−	0.153511i
$416$	−20.2598	−	0.810831i	−0.993316	−	0.0397542i
$417$	7.43110	+	16.2233i	0.363903	+	0.794460i
$418$			5.54491i			0.271211i
$419$	9.86318	+	17.0835i	0.481848	+	0.834585i	0.999783	−	0.0208352i	$-0.00663253\pi$
$419$	9.86318	+	17.0835i	0.481848	+	0.834585i	−0.517935	+	0.855420i	$0.673299\pi$
$420$	10.8478	−	15.8906i	0.529319	−	0.775380i
$421$	−14.3999			−0.701807			−0.350903	−	0.936412i	$-0.614125\pi$
$421$	−14.3999			−0.701807			−0.350903	+	0.936412i	$0.614125\pi$
$422$	12.0839	−	6.97663i	0.588234	−	0.339617i
$423$	20.1857	+	3.84319i	0.981460	+	0.186862i
$424$	18.5043	+	32.0503i	0.898646	+	1.55650i
$425$	0.554965	+	0.961228i	0.0269198	+	0.0466264i
$426$	6.96105	−	3.18851i	0.337264	−	0.154484i
$427$	8.32820	−	15.0679i	0.403030	−	0.729187i
$428$			23.3308i			1.12773i
$429$	22.1887	−	9.10855i	1.07128	−	0.439765i
$430$	22.8042	−	13.1660i	1.09972	−	0.634921i
$431$	−4.36109	−	2.51788i	−0.210066	−	0.121282i	0.391276	−	0.920273i	$-0.372034\pi$
$431$	−4.36109	−	2.51788i	−0.210066	−	0.121282i	−0.601342	+	0.798992i	$0.705367\pi$
$432$	0.106300	−	0.366616i	0.00511436	−	0.0176388i
$433$	−27.2316	−	15.7222i	−1.30867	−	0.755561i	−0.326795	−	0.945095i	$-0.605969\pi$
$433$	−27.2316	−	15.7222i	−1.30867	−	0.755561i	−0.981874	+	0.189535i	$0.939302\pi$
$434$	0.330064	+	0.182430i	0.0158436	+	0.00875691i
$435$	−32.7661	+	46.1237i	−1.57101	+	2.21146i
$436$	−12.0696	−	20.9051i	−0.578027	−	1.00117i
$437$	3.71297	+	6.43105i	0.177615	+	0.307639i
$438$	1.43155	−	15.1729i	0.0684019	−	0.724991i
$439$		−	8.15183i		−	0.389066i	−0.980896	−	0.194533i	$-0.937681\pi$
$439$		−	8.15183i		−	0.389066i	0.980896	−	0.194533i	$-0.0623191\pi$
$440$	18.8035	+	32.5687i	0.896423	+	1.55265i
$441$	20.7617	+	3.15454i	0.988653	+	0.150216i
$442$	0.515572	+	0.0206341i	0.0245233	+	0.000981463i
$443$	18.0400	+	10.4154i	0.857106	+	0.494850i	0.863042	−	0.505132i	$-0.168556\pi$
$443$	18.0400	+	10.4154i	0.857106	+	0.494850i	−0.00593636	+	0.999982i	$0.501890\pi$
$444$	−6.86169	−	4.87452i	−0.325642	−	0.231334i
$445$	11.8576	−	20.5379i	0.562104	−	0.973592i
$446$	−0.394196	−	0.682768i	−0.0186657	−	0.0323300i
$447$	5.18440	+	0.489141i	0.245214	+	0.0231356i
$448$	11.5912	−	6.98398i	0.547631	−	0.329962i
$449$	−2.96108	−	1.70958i	−0.139742	−	0.0806801i	0.428499	−	0.903542i	$-0.359043\pi$
$449$	−2.96108	−	1.70958i	−0.139742	−	0.0806801i	−0.568241	+	0.822862i	$0.692376\pi$
$450$	−13.7501	−	11.8603i	−0.648186	−	0.559098i
$451$			18.5383i			0.872933i
$452$	−0.748757	−	0.432295i	−0.0352186	−	0.0203334i
$453$	−0.585669	+	6.20750i	−0.0275171	+	0.291654i
$454$			2.49208i			0.116959i
$455$	−32.8330	−	0.700225i	−1.53924	−	0.0328271i
$456$	−0.756221	+	8.01518i	−0.0354133	+	0.375345i
$457$	32.5714			1.52362			0.761812	−	0.647798i	$-0.224310\pi$
$457$	32.5714			1.52362			0.761812	+	0.647798i	$0.224310\pi$
$458$	−7.69379	+	13.3260i	−0.359507	+	0.622685i
$459$	0.234410	−	0.808452i	0.0109413	−	0.0377353i
$460$	16.5222	+	9.53910i	0.770352	+	0.444763i
$461$	−17.7020	+	30.6608i	−0.824467	+	1.42802i	0.0778597	+	0.996964i	$0.475191\pi$
$461$	−17.7020	+	30.6608i	−0.824467	+	1.42802i	−0.902326	+	0.431054i	$0.858142\pi$
$462$	−8.76645	+	12.8416i	−0.407852	+	0.597447i
$463$	17.8630			0.830164			0.415082	−	0.909784i	$-0.363753\pi$
$463$	17.8630			0.830164			0.415082	+	0.909784i	$0.363753\pi$
$464$	−0.603646	+	0.348515i	−0.0280236	+	0.0161794i
$465$	−0.557188	+	0.784335i	−0.0258390	+	0.0363727i
$466$	−9.10683	+	15.7735i	−0.421866	+	0.730693i
$467$	−20.0513	+	34.7299i	−0.927864	+	1.60711i	−0.140976	+	0.990013i	$0.545024\pi$
$467$	−20.0513	+	34.7299i	−0.927864	+	1.60711i	−0.786888	+	0.617095i	$0.788309\pi$
$468$	12.6202	−	3.84116i	0.583367	−	0.177558i
$469$	0.0467164	+	2.50102i	0.00215716	+	0.115486i
$470$	18.0400	−	10.4154i	0.832125	−	0.480428i
$471$	8.32368	+	0.785328i	0.383535	+	0.0361860i
$472$			25.3626i			1.16741i
$473$	28.7991	−	16.6271i	1.32418	−	0.764517i
$474$	6.66892	+	14.5594i	0.306314	+	0.668734i
$475$	9.69704	+	5.59859i	0.444930	+	0.256881i
$476$	0.447720	−	0.269763i	0.0205212	−	0.0123646i
$477$	−29.5587	−	25.4961i	−1.35340	−	1.16739i
$478$	−15.5158			−0.709675
$479$	12.9793	−	22.4808i	0.593039	−	1.02717i	−0.400782	−	0.916174i	$-0.631261\pi$
$479$	12.9793	−	22.4808i	0.593039	−	1.02717i	0.993820	−	0.111000i	$-0.0354052\pi$
$480$	13.9642	+	30.4861i	0.637374	+	1.39149i
$481$	−0.574513	+	14.3550i	−0.0261955	+	0.654533i
$482$	−1.74278			−0.0793813
$483$	−1.56844	+	20.7640i	−0.0713667	+	0.944797i
$484$	2.28758	+	3.96221i	0.103981	+	0.180100i
$485$	−24.0130	+	13.8639i	−1.09037	+	0.629527i
$486$	0.732936	+	13.7515i	0.0332467	+	0.623782i
$487$	−25.7565			−1.16714			−0.583570	−	0.812063i	$-0.698345\pi$
$487$	−25.7565			−1.16714			−0.583570	+	0.812063i	$0.698345\pi$
$488$	9.25388	+	16.0282i	0.418904	+	0.725562i
$489$	−1.37132	+	14.5346i	−0.0620132	+	0.657277i
$490$	18.0263	−	11.3255i	0.814344	−	0.511634i
$491$	3.64975	−	2.10719i	0.164711	−	0.0950959i	−0.415379	−	0.909649i	$-0.636351\pi$
$491$	3.64975	−	2.10719i	0.164711	−	0.0950959i	0.580090	+	0.814553i	$0.303018\pi$
$492$	−0.957711	+	10.1508i	−0.0431769	+	0.457632i
$493$	−1.33115	+	0.768537i	−0.0599518	+	0.0346132i
$494$	4.60843	−	2.42032i	0.207343	−	0.108895i
$495$	−30.0368	−	25.9085i	−1.35005	−	1.16450i
$496$	−0.0102650	+	0.00592651i	−0.000460913	+	0.000266108i
$497$	−13.2368	+	0.247249i	−0.593750	+	0.0110906i
$498$	−0.929500	+	1.30843i	−0.0416519	+	0.0586320i
$499$	4.79919	−	8.31244i	0.214841	−	0.372116i	−0.738382	−	0.674383i	$-0.764410\pi$
$499$	4.79919	−	8.31244i	0.214841	−	0.372116i	0.953223	+	0.302266i	$0.0977432\pi$
$500$	7.77422			0.347674
$501$	0.232158	−	2.46064i	0.0103721	−	0.109933i
$502$	−0.830158	−	0.479292i	−0.0370518	−	0.0213918i
$503$	2.79256	−	4.83685i	0.124514	−	0.215664i	−0.797029	−	0.603941i	$-0.793596\pi$
$503$	2.79256	−	4.83685i	0.124514	−	0.215664i	0.921543	+	0.388277i	$0.126930\pi$
$504$	−14.4233	+	17.3670i	−0.642463	+	0.773589i
$505$	−8.77717	−	15.2025i	−0.390579	−	0.676502i
$506$	−13.3521	−	7.70883i	−0.593573	−	0.342699i
$507$	−17.2554	−	14.4655i	−0.766341	−	0.642434i
$508$	4.08893	+	7.08223i	0.181417	+	0.314223i
$509$	32.6652			1.44786			0.723929	−	0.689875i	$-0.242334\pi$
$509$	32.6652			1.44786			0.723929	+	0.689875i	$0.242334\pi$
$510$	−0.355361	−	0.775812i	−0.0157357	−	0.0343535i
$511$	−12.7476	+	23.0638i	−0.563922	+	1.02028i
$512$			0.830992i			0.0367250i
$513$	−2.02995	−	8.24552i	−0.0896246	−	0.364049i
$514$		−	12.3450i		−	0.544515i
$515$	3.43077	−	1.98075i	0.151178	−	0.0872825i
$516$	16.6281	−	7.61652i	0.732013	−	0.335299i
$517$	22.7825	−	13.1535i	1.00197	−	0.578489i
$518$	−4.80635	−	7.97698i	−0.211179	−	0.350488i
$519$	2.71845	−	28.8128i	0.119327	−	1.26474i
$520$	18.8605	−	29.8438i	0.827090	−	1.30874i
$521$	−11.5944	−	20.0821i	−0.507961	−	0.879815i	−0.999958	−	0.00921756i	$-0.997066\pi$
$521$	−11.5944	−	20.0821i	−0.507961	−	0.879815i	0.491996	−	0.870597i	$-0.336267\pi$
$522$	16.4245	−	19.0417i	0.718883	−	0.833432i
$523$		−	25.6088i		−	1.11979i	−0.828562	−	0.559897i	$-0.810841\pi$
$523$		−	25.6088i		−	1.11979i	0.828562	−	0.559897i	$-0.189159\pi$
$524$	6.19539	−	10.7307i	0.270647	−	0.468774i
$525$	13.6064	+	28.2969i	0.593830	+	1.23498i
$526$	−2.76039	+	4.78114i	−0.120359	+	0.208468i
$527$	−0.0226362	+	0.0130690i	−0.000986047	+	0.000569295i
$528$	−0.203512	−	0.444301i	−0.00885673	−	0.0193357i
$529$	2.35213			0.102266
$530$	−39.5723			−1.71891
$531$	−8.80673	−	25.2606i	−0.382180	−	1.09622i
$532$	2.55085	−	4.61516i	0.110593	−	0.200093i
$533$	15.4073	−	8.09183i	0.667366	−	0.350496i
$534$	−6.10439	+	8.59295i	−0.264163	+	0.371853i
$535$	−57.0346	−	32.9289i	−2.46582	−	1.42364i
$536$	−2.32883	−	1.34455i	−0.100590	−	0.0580757i
$537$	7.93798	+	17.3299i	0.342549	+	0.747842i
$538$			8.87275i			0.382531i
$539$	22.7651	−	14.3028i	0.980562	−	0.616065i
$540$	−15.1084	−	15.7381i	−0.650163	−	0.677260i
$541$	−20.3485	+	35.2447i	−0.874851	+	1.51529i	−0.0179303	+	0.999839i	$0.505708\pi$
$541$	−20.3485	+	35.2447i	−0.874851	+	1.51529i	−0.856921	+	0.515448i	$0.827626\pi$
$542$	13.5530			0.582150
$543$	−2.82974	+	3.98333i	−0.121436	+	0.170941i
$544$			0.910985i			0.0390582i
$545$	68.1397			2.91878
$546$	14.4993	+	1.68060i	0.620513	+	0.0719229i
$547$	−24.1727			−1.03355			−0.516776	−	0.856121i	$-0.672868\pi$
$547$	−24.1727			−1.03355			−0.516776	+	0.856121i	$0.672868\pi$
$548$		−	11.2587i		−	0.480946i
$549$	−14.7822	−	12.7505i	−0.630887	−	0.544176i
$550$	−23.2475			−0.991275
$551$	−7.75314	+	13.4288i	−0.330295	+	0.572088i
$552$	−18.2491	−	12.9641i	−0.776734	−	0.551789i
$553$	−0.517133	−	27.6853i	−0.0219907	−	1.17730i
$554$		−	8.34887i		−	0.354709i
$555$	21.6009	−	9.89428i	0.916905	−	0.419989i
$556$	10.8813	+	6.28230i	0.461468	+	0.266429i
$557$	−5.80067	−	3.34902i	−0.245782	−	0.141903i	0.372049	−	0.928213i	$-0.378655\pi$
$557$	−5.80067	−	3.34902i	−0.245782	−	0.141903i	−0.617832	+	0.786310i	$0.711989\pi$
$558$	0.279300	−	0.323804i	0.0118237	−	0.0137077i
$559$	−26.3896	−	16.6776i	−1.11616	−	0.705386i
$560$	0.0124961	+	0.668991i	0.000528055	+	0.0282700i
$561$	−0.448780	−	0.979761i	−0.0189475	−	0.0413655i
$562$	−10.2716			−0.433283
$563$	−12.0846			−0.509306			−0.254653	−	0.967033i	$-0.581961\pi$
$563$	−12.0846			−0.509306			−0.254653	+	0.967033i	$0.581961\pi$
$564$	13.1543	−	6.02532i	0.553894	−	0.253712i
$565$	2.11358	−	1.22028i	0.0889191	−	0.0513375i
$566$	0.719110	−	1.24554i	0.0302265	−	0.0523538i
$567$	8.33485	−	22.3054i	0.350031	−	0.936738i
$568$	7.11610	−	12.3254i	0.298585	−	0.517164i
$569$		−	11.7276i		−	0.491646i	−0.969315	−	0.245823i	$-0.920942\pi$
$569$		−	11.7276i		−	0.491646i	0.969315	−	0.245823i	$-0.0790582\pi$
$570$	−7.01791	−	4.98550i	−0.293948	−	0.208819i
$571$	−15.1381	−	26.2200i	−0.633511	−	1.09727i	−0.986829	−	0.161770i	$-0.948280\pi$
$571$	−15.1381	−	26.2200i	−0.633511	−	1.09727i	0.353318	−	0.935503i	$-0.385053\pi$
$572$	9.02255	−	14.2768i	0.377252	−	0.596941i
$573$	−4.37955	−	0.413204i	−0.182958	−	0.0172619i
$574$	−5.45728	+	9.87367i	−0.227783	+	0.412119i
$575$	−26.9627	+	15.5669i	−1.12442	+	0.649185i
$576$	−5.05145	−	14.4892i	−0.210477	−	0.603717i
$577$	−27.0888	+	15.6397i	−1.12772	+	0.651089i	−0.943360	−	0.331770i	$-0.892354\pi$
$577$	−27.0888	+	15.6397i	−1.12772	+	0.651089i	−0.184359	+	0.982859i	$0.559021\pi$
$578$			14.9948i			0.623703i
$579$	−16.8729	+	7.72865i	−0.701214	+	0.321192i
$580$			39.8377i			1.65417i
$581$	2.37705	−	1.43224i	0.0986168	−	0.0594193i
$582$	11.2045	−	5.13222i	0.464441	−	0.212737i
$583$	−49.9753			−2.06976
$584$	−14.1645	−	24.5337i	−0.586133	−	1.01521i
$585$	−8.42192	+	36.2728i	−0.348203	+	1.49969i
$586$	4.29320	+	2.47868i	0.177351	+	0.102393i
$587$	0.348443	+	0.603522i	0.0143818	+	0.0249100i	0.873127	−	0.487493i	$-0.162089\pi$
$587$	0.348443	+	0.603522i	0.0143818	+	0.0249100i	−0.858745	+	0.512403i	$0.828755\pi$
$588$	13.2041	−	6.65553i	0.544528	−	0.274469i
$589$	−0.131842	+	0.228358i	−0.00543247	+	0.00940931i
$590$	−23.4863	−	13.5598i	−0.966916	−	0.558249i
$591$	−8.57602	−	0.809135i	−0.352770	−	0.0332834i
$592$	0.292710			0.0120303
$593$	−14.0745	+	24.3778i	−0.577972	+	1.00108i	0.417740	+	0.908567i	$0.362822\pi$
$593$	−14.0745	+	24.3778i	−0.577972	+	1.00108i	−0.995712	+	0.0925098i	$0.970511\pi$
$594$	12.2096	+	12.7184i	0.500964	+	0.521844i
$595$	0.0275560	+	1.47524i	0.00112969	+	0.0604791i
$596$	3.17544	−	1.83334i	0.130071	−	0.0750966i
$597$	9.85224	−	13.8687i	0.403225	−	0.567607i
$598$	−0.578791	+	14.4619i	−0.0236685	+	0.591392i
$599$	5.29808	−	3.05885i	0.216474	−	0.124981i	−0.387843	−	0.921726i	$-0.626780\pi$
$599$	5.29808	−	3.05885i	0.216474	−	0.124981i	0.604316	+	0.796744i	$0.293446\pi$
$600$	−33.6042	−	3.17051i	−1.37189	−	0.129436i
$601$	4.63482	−	2.67591i	0.189058	−	0.109153i	−0.402483	−	0.915427i	$-0.631853\pi$
$601$	4.63482	−	2.67591i	0.189058	−	0.109153i	0.591542	+	0.806275i	$0.298520\pi$
$602$	20.2334	−	0.377938i	0.824650	−	0.0154036i
$603$	2.78633	+	0.530495i	0.113468	+	0.0216034i
$604$	2.19514	+	3.80209i	0.0893188	+	0.154705i
$605$	−12.9147			−0.525058
$606$	3.24919	+	7.09351i	0.131989	+	0.288154i
$607$	18.8484	−	10.8822i	0.765035	−	0.441693i	−0.0660657	−	0.997815i	$-0.521045\pi$
$607$	18.8484	−	10.8822i	0.765035	−	0.441693i	0.831101	+	0.556122i	$0.187711\pi$
$608$	4.59509	+	7.95893i	0.186355	+	0.322777i
$609$	−39.1866	+	18.8426i	−1.58792	+	0.763542i
$610$	−19.7899			−0.801270
$611$	−20.8764	−	13.1934i	−0.844569	−	0.533746i
$612$	−0.195117	−	0.559660i	−0.00788715	−	0.0226229i
$613$	10.3604	−	17.9448i	0.418454	−	0.724783i	−0.577330	−	0.816511i	$-0.695905\pi$
$613$	10.3604	−	17.9448i	0.418454	−	0.724783i	0.995784	+	0.0917273i	$0.0292388\pi$
$614$	−7.78632			−0.314230
$615$	−23.4629	−	16.6680i	−0.946117	−	0.672118i
$616$	0.539767	+	28.8971i	0.0217478	+	1.16430i
$617$	23.0797	+	13.3251i	0.929153	+	0.536447i	0.886544	−	0.462645i	$-0.153100\pi$
$617$	23.0797	+	13.3251i	0.929153	+	0.536447i	0.0426095	+	0.999092i	$0.486433\pi$
$618$	−1.60080	+	0.733248i	−0.0643937	+	0.0294956i
$619$	29.5414	−	17.0557i	1.18737	−	0.685527i	0.229660	−	0.973271i	$-0.426239\pi$
$619$	29.5414	−	17.0557i	1.18737	−	0.685527i	0.957707	+	0.287744i	$0.0929052\pi$
$620$			0.677440i			0.0272067i
$621$	22.6773	+	6.57525i	0.910008	+	0.263856i
$622$	18.3289	−	10.5822i	0.734923	−	0.424308i
$623$	15.6110	−	9.40608i	0.625443	−	0.376847i
$624$	−0.280431	+	0.363075i	−0.0112262	+	0.0145346i
$625$	6.15661	−	10.6636i	0.246264	−	0.426542i
$626$	3.00183	−	5.19933i	0.119977	−	0.207807i
$627$	−8.86282	−	6.29611i	−0.353947	−	0.251442i
$628$	5.09824	−	2.94347i	0.203442	−	0.117457i
$629$	0.645477			0.0257368
$630$	−8.37099	−	22.6413i	−0.333508	−	0.902052i
$631$	−2.85221	+	4.94018i	−0.113545	+	0.196665i	−0.917197	−	0.398434i	$-0.869554\pi$
$631$	−2.85221	+	4.94018i	−0.113545	+	0.196665i	0.803652	+	0.595099i	$0.202887\pi$
$632$	25.7793	+	14.8837i	1.02544	+	0.592040i
$633$	−2.56971	+	27.2363i	−0.102137	+	1.08254i
$634$	3.49259	−	6.04934i	0.138708	−	0.240250i
$635$	−23.0844			−0.916075
$636$	−27.3643	−	2.58179i	−1.08507	−	0.102375i
$637$	−21.8240	−	12.6772i	−0.864699	−	0.502290i
$638$		−	32.1940i		−	1.27457i
$639$	−2.80767	+	14.7468i	−0.111070	+	0.583374i
$640$	20.0606	+	11.5820i	0.792963	+	0.457817i
$641$			2.73353i			0.107968i	0.998542	+	0.0539839i	$0.0171920\pi$
$641$			2.73353i			0.107968i	−0.998542	+	0.0539839i	$0.982808\pi$
$642$	23.8629	+	16.9521i	0.941794	+	0.669046i
$643$	−1.97815	−	1.14209i	−0.0780108	−	0.0450395i	0.460487	−	0.887666i	$-0.347675\pi$
$643$	−1.97815	−	1.14209i	−0.0780108	−	0.0450395i	−0.538498	+	0.842627i	$0.681008\pi$
$644$	7.56693	+	12.5587i	0.298179	+	0.494880i
$645$	−4.84944	+	51.3992i	−0.190947	+	2.02384i
$646$	−0.116936	−	0.202539i	−0.00460079	−	0.00796880i
$647$	−17.1874	+	29.7695i	−0.675707	+	1.17036i	0.300554	+	0.953765i	$0.402828\pi$
$647$	−17.1874	+	29.7695i	−0.675707	+	1.17036i	−0.976262	+	0.216595i	$0.930505\pi$
$648$	15.9144	+	20.0497i	0.625176	+	0.787625i
$649$	−29.6605	−	17.1245i	−1.16428	−	0.672196i
$650$	10.1474	+	19.3212i	0.398012	+	0.757840i
$651$	−0.666369	+	0.320419i	−0.0261171	+	0.0125582i
$652$	5.13981	+	8.90242i	0.201291	+	0.348645i
$653$		−	4.40548i		−	0.172400i	−0.996278	−	0.0861998i	$-0.972528\pi$
$653$		−	4.40548i		−	0.172400i	0.996278	−	0.0861998i	$-0.0274723\pi$
$654$	−30.1516	−	2.84477i	−1.17902	−	0.111239i
$655$	17.4883	+	30.2906i	0.683324	+	1.18355i
$656$	−0.177288	−	0.307072i	−0.00692195	−	0.0119892i
$657$	22.6265	+	19.5166i	0.882743	+	0.761416i
$658$	16.0063	−	0.298981i	0.623991	−	0.0116555i
$659$	40.5474	+	23.4100i	1.57950	+	0.911926i	0.994928	+	0.100585i	$0.0320714\pi$
$659$	40.5474	+	23.4100i	1.57950	+	0.911926i	0.584573	+	0.811341i	$0.301262\pi$
$660$	−27.8069	−	2.62354i	−1.08238	−	0.102121i
$661$	23.3517	+	13.4821i	0.908276	+	0.524393i	0.879876	−	0.475203i	$-0.157625\pi$
$661$	23.3517	+	13.4821i	0.908276	+	0.524393i	0.0284000	+	0.999597i	$0.490959\pi$
$662$	6.75266	−	3.89865i	0.262449	−	0.151525i
$663$	−0.618400	+	0.800645i	−0.0240167	+	0.0310945i
$664$			2.98337i			0.115777i
$665$	7.68200	+	12.7496i	0.297895	+	0.494410i
$666$	−9.97140	+	3.47638i	−0.386384	+	0.134707i
$667$	−21.5577	−	37.3390i	−0.834716	−	1.44577i
$668$	−0.870147	−	1.50714i	−0.0336670	−	0.0583129i
$669$	1.53892	+	0.145195i	0.0594979	+	0.00561354i
$670$	2.49016	−	1.43769i	0.0962033	−	0.0555430i
$671$	−24.9924			−0.964820
$672$	−1.94107	+	25.6971i	−0.0748784	+	0.991288i
$673$	−7.16313	−	12.4069i	−0.276118	−	0.478251i	0.694298	−	0.719687i	$-0.255715\pi$
$673$	−7.16313	−	12.4069i	−0.276118	−	0.478251i	−0.970417	+	0.241436i	$0.922381\pi$
$674$			10.2268i			0.393922i
$675$	34.5700	−	8.51073i	1.33060	−	0.327578i
$676$	−15.8038	−	1.26702i	−0.607840	−	0.0487317i
$677$	19.8879	−	34.4468i	0.764353	−	1.32390i	−0.176235	−	0.984348i	$-0.556392\pi$
$677$	19.8879	−	34.4468i	0.764353	−	1.32390i	0.940588	−	0.339550i	$-0.110275\pi$
$678$	−0.986201	+	0.451730i	−0.0378748	+	0.0173486i
$679$	−21.3059	+	0.397971i	−0.817644	+	0.0152727i
$680$	−1.37368	−	0.793092i	−0.0526781	−	0.0304137i
$681$	−3.98326	−	2.82969i	−0.152639	−	0.108434i
$682$		−	0.547460i		−	0.0209633i
$683$		−	24.9682i		−	0.955383i	−0.878528	−	0.477692i	$-0.841474\pi$
$683$		−	24.9682i		−	0.955383i	0.878528	−	0.477692i	$-0.158526\pi$
$684$	−4.52764	−	3.90535i	−0.173119	−	0.149325i
$685$	27.5230	+	15.8904i	1.05160	+	0.607142i
$686$	16.3354	−	0.916235i	0.623687	−	0.0349820i
$687$	−12.5638	−	27.4289i	−0.479340	−	1.04648i
$688$	−0.318023	+	0.550832i	−0.0121245	+	0.0210003i
$689$	21.8139	+	41.5350i	0.831043	+	1.58236i
$690$	21.7617	−	9.96796i	0.828454	−	0.379474i
$691$		−	22.9567i		−	0.873315i	−0.899628	−	0.436657i	$-0.856162\pi$
$691$		−	22.9567i		−	0.873315i	0.899628	−	0.436657i	$-0.143838\pi$
$692$	−10.1890	−	17.6478i	−0.387326	−	0.670868i
$693$	−10.5716	−	28.5934i	−0.401582	−	1.08617i
$694$	16.4558			0.624653
$695$	−30.7155	+	17.7336i	−1.16511	+	0.672674i
$696$	4.39065	−	46.5365i	0.166427	−	1.76396i
$697$	−0.390952	−	0.677149i	−0.0148084	−	0.0256488i
$698$	−4.83649	−	8.37705i	−0.183064	−	0.317076i
$699$	−14.8713	−	32.4665i	−0.562484	−	1.22800i
$700$	19.3494	+	10.6946i	0.731339	+	0.404219i
$701$		−	12.8742i		−	0.486253i	−0.969995	−	0.243126i	$-0.921827\pi$
$701$		−	12.8742i		−	0.486253i	0.969995	−	0.243126i	$-0.0781730\pi$
$702$	5.24103	−	15.6990i	0.197810	−	0.592521i
$703$	5.63928	−	3.25584i	0.212690	−	0.122796i
$704$	−17.0129	−	9.82243i	−0.641199	−	0.370197i
$705$	−3.83632	+	40.6611i	−0.144484	+	1.53139i
$706$	17.4988	+	10.1029i	0.658576	+	0.380229i
$707$	−0.251954	−	13.4886i	−0.00947569	−	0.507293i
$708$	−15.3562	−	10.9090i	−0.577120	−	0.409984i
$709$	18.6136	+	32.2398i	0.699050	+	1.21079i	0.968796	+	0.247858i	$0.0797268\pi$
$709$	18.6136	+	32.2398i	0.699050	+	1.21079i	−0.269747	+	0.962931i	$0.586940\pi$
$710$	7.60907	+	13.1793i	0.285563	+	0.494610i
$711$	−30.8436	−	5.87238i	−1.15673	−	0.220231i
$712$			19.5930i			0.734278i
$713$	−0.366589	−	0.634950i	−0.0137289	−	0.0237791i
$714$	0.0493965	−	0.653942i	0.00184862	−	0.0244732i
$715$	22.1667	+	42.2067i	0.828987	+	1.57844i
$716$	11.6235	+	6.71082i	0.434390	+	0.250795i
$717$	17.6178	−	24.7999i	0.657947	−	0.926170i
$718$	14.9928	−	25.9683i	0.559526	−	0.969128i
$719$	23.9349	+	41.4564i	0.892619	+	1.54606i	0.836724	+	0.547625i	$0.184468\pi$
$719$	23.9349	+	41.4564i	0.892619	+	1.54606i	0.0558957	+	0.998437i	$0.482199\pi$
$720$	0.745309	+	0.141901i	0.0277760	+	0.00528833i
$721$	3.04400	−	0.0568587i	0.113364	−	0.00211753i
$722$	12.4929	+	7.21275i	0.464936	+	0.268431i
$723$	1.97888	−	2.78560i	0.0735953	−	0.103598i
$724$			3.44045i			0.127863i
$725$	−56.3014	−	32.5056i	−2.09098	−	1.20723i
$726$	5.71474	+	0.539177i	0.212094	+	0.0200108i
$727$			10.2075i			0.378574i	0.981922	+	0.189287i	$0.0606176\pi$
$727$			10.2075i			0.378574i	−0.981922	+	0.189287i	$0.939382\pi$
$728$	23.7810	−	13.0620i	0.881384	−	0.484109i
$729$	−22.8123	−	14.4430i	−0.844899	−	0.534927i
$730$	30.2916			1.12114
$731$	−0.701297	+	1.21468i	−0.0259384	+	0.0449266i
$732$	−13.6848	−	1.29114i	−0.505804	−	0.0477219i
$733$	36.4929	+	21.0692i	1.34789	+	0.778208i	0.987951	−	0.154766i	$-0.0494625\pi$
$733$	36.4929	+	21.0692i	1.34789	+	0.778208i	0.359944	+	0.932974i	$0.382796\pi$
$734$	−12.4917	+	21.6362i	−0.461076	+	0.798608i
$735$	−2.36606	+	41.6724i	−0.0872733	+	1.53711i
$736$	−25.5534			−0.941909
$737$	3.14478	−	1.81564i	0.115840	−	0.0668800i
$738$	9.68643	+	8.35510i	0.356562	+	0.307555i
$739$	−3.56007	+	6.16622i	−0.130959	+	0.226828i	−0.924047	−	0.382280i	$-0.875139\pi$
$739$	−3.56007	+	6.16622i	−0.130959	+	0.226828i	0.793087	+	0.609108i	$0.208472\pi$
$740$	8.36468	−	14.4881i	0.307492	−	0.532591i
$741$	−1.36420	+	10.1142i	−0.0501151	+	0.371554i
$742$	−26.6173	−	14.7117i	−0.977153	−	0.540083i
$743$	−19.3136	+	11.1507i	−0.708546	+	0.409079i	−0.810522	−	0.585708i	$-0.800817\pi$
$743$	−19.3136	+	11.1507i	−0.708546	+	0.409079i	0.101976	+	0.994787i	$0.467483\pi$
$744$	0.0746631	−	0.791354i	0.00273728	−	0.0290124i
$745$			10.3503i			0.379205i
$746$	−3.23023	+	1.86497i	−0.118267	+	0.0682815i
$747$	−1.03592	−	2.97137i	−0.0379025	−	0.108717i
$748$	−0.657142	−	0.379401i	−0.0240275	−	0.0138723i
$749$	−26.1210	−	43.3524i	−0.954440	−	1.58406i
$750$	5.64874	−	7.95154i	0.206263	−	0.290349i
$751$	23.5627			0.859815			0.429908	−	0.902873i	$-0.358546\pi$
$751$	23.5627			0.859815			0.429908	+	0.902873i	$0.358546\pi$
$752$	−0.251583	+	0.435755i	−0.00917430	+	0.0158903i
$753$	1.70871	−	0.782675i	0.0622688	−	0.0285223i
$754$	−26.7568	+	14.0525i	−0.974424	+	0.511761i
$755$	−12.3928			−0.451021
$756$	−4.31139	−	16.2027i	−0.156804	−	0.589285i
$757$	−3.94895	−	6.83979i	−0.143527	−	0.248596i	0.785295	−	0.619121i	$-0.212511\pi$
$757$	−3.94895	−	6.83979i	−0.143527	−	0.248596i	−0.928822	+	0.370525i	$0.879178\pi$
$758$	25.5166	−	14.7320i	0.926803	−	0.535090i
$759$	27.4825	−	12.5884i	0.997552	−	0.456930i
$760$	−16.0017			−0.580443
$761$	−21.4232	−	37.1060i	−0.776590	−	1.34509i	−0.933897	−	0.357543i	$-0.883615\pi$
$761$	−21.4232	−	37.1060i	−0.776590	−	1.34509i	0.157307	−	0.987550i	$-0.449719\pi$
$762$	10.2148	+	0.963750i	0.370042	+	0.0349130i
$763$	45.8325	+	25.3321i	1.65925	+	0.917083i
$764$	−2.68247	+	1.54872i	−0.0970482	+	0.0560308i
$765$	1.64354	+	0.312916i	0.0594222	+	0.0113135i
$766$	−13.6729	+	7.89405i	−0.494022	+	0.285224i
$767$	−1.28573	+	32.1259i	−0.0464252	+	1.16000i
$768$	−22.8377	−	16.2238i	−0.824085	−	0.585427i
$769$	28.1847	−	16.2725i	1.01637	−	0.586800i	0.103318	−	0.994648i	$-0.467054\pi$
$769$	28.1847	−	16.2725i	1.01637	−	0.586800i	0.913050	+	0.407848i	$0.133721\pi$
$770$	−27.0478	−	14.9496i	−0.974736	−	0.538747i
$771$	19.7319	+	14.0174i	0.710627	+	0.504826i
$772$	−6.53384	+	11.3169i	−0.235158	+	0.407306i
$773$	45.7029			1.64382			0.821910	−	0.569618i	$-0.192909\pi$
$773$	45.7029			1.64382			0.821910	+	0.569618i	$0.192909\pi$
$774$	4.29173	−	22.5416i	0.154263	−	0.810240i
$775$	−0.957407	−	0.552759i	−0.0343911	−	0.0198557i
$776$	11.4541	−	19.8390i	0.411177	−	0.712179i
$777$	18.2076	+	1.37534i	0.653196	+	0.0493401i
$778$	10.9339	+	18.9381i	0.392000	+	0.678963i
$779$	−6.83119	−	3.94399i	−0.244753	−	0.141308i
$780$	9.95709	+	24.2558i	0.356521	+	0.868496i
$781$	9.60938	+	16.6439i	0.343851	+	0.595567i
$782$	0.650284			0.0232541
$783$	11.7860	+	47.8738i	0.421197	+	1.71087i
$784$	−0.240304	+	0.454626i	−0.00858228	+	0.0162366i
$785$			16.6176i			0.593108i
$786$	−6.47393	−	14.1336i	−0.230917	−	0.504131i
$787$			12.3889i			0.441616i	0.975317	+	0.220808i	$0.0708694\pi$
$787$			12.3889i			0.441616i	−0.975317	+	0.220808i	$0.929131\pi$
$788$	−5.25280	+	3.03270i	−0.187123	+	0.108036i
$789$	−4.50767	−	9.84099i	−0.160477	−	0.350349i
$790$	−27.5651	+	15.9147i	−0.980724	+	0.566221i
$791$	1.87531	−	0.0350288i	0.0666783	−	0.00124548i
$792$	32.1936	+	6.12940i	1.14395	+	0.217799i
$793$	10.9090	+	20.7714i	0.387390	+	0.737615i
$794$	9.99266	+	17.3078i	0.354626	+	0.614230i
$795$	44.9334	−	63.2512i	1.59362	−	2.24329i
$796$		−	11.9785i		−	0.424568i
$797$	10.3478	−	17.9229i	0.366537	−	0.634861i	−0.622484	−	0.782632i	$-0.713877\pi$
$797$	10.3478	−	17.9229i	0.366537	−	0.634861i	0.989022	+	0.147771i	$0.0472099\pi$
$798$	−2.86698	−	5.96240i	−0.101490	−	0.211067i
$799$	−0.554785	+	0.960916i	−0.0196269	+	0.0339948i
$800$	−33.3684	+	19.2653i	−1.17975	+	0.681130i
$801$	−6.80332	−	19.5142i	−0.240384	−	0.689499i
$802$	−21.5626			−0.761403
$803$	38.2548			1.34998
$804$	1.81575	−	0.831705i	0.0640365	−	0.0293320i
$805$	−41.3809	+	0.772952i	−1.45849	+	0.0272430i
$806$	−0.454999	+	0.238963i	−0.0160267	+	0.00841710i
$807$	−14.1819	−	10.0748i	−0.499227	−	0.354649i
$808$	12.5600	+	7.25151i	0.441859	+	0.255107i
$809$	32.8454	+	18.9633i	1.15478	+	0.666714i	0.950048	−	0.312104i	$-0.101034\pi$
$809$	32.8454	+	18.9633i	1.15478	+	0.666714i	0.204734	+	0.978818i	$0.434367\pi$
$810$	−27.0748	+	4.01773i	−0.951313	+	0.141168i
$811$			29.8342i			1.04762i	0.851835	+	0.523811i	$0.175490\pi$
$811$			29.8342i			1.04762i	−0.851835	+	0.523811i	$0.824510\pi$
$812$	−14.8103	+	26.7958i	−0.519741	+	0.940349i
$813$	−15.3891	+	21.6627i	−0.539718	+	0.759743i
$814$	−6.75975	+	11.7082i	−0.236929	+	0.410373i
$815$	−29.0172			−1.01643
$816$	0.0168035	+	0.0119371i	0.000588241	+	0.000417884i
$817$			14.1496i			0.495032i
$818$	−28.0671			−0.981342
$819$	−19.1498	+	21.2670i	−0.669149	+	0.743129i
$820$	−20.2653			−0.707693
$821$			21.3438i			0.744903i	0.928052	+	0.372452i	$0.121483\pi$
$821$			21.3438i			0.744903i	−0.928052	+	0.372452i	$0.878517\pi$
$822$	−11.5155	−	8.18054i	−0.401648	−	0.285329i
$823$	−49.4807			−1.72479			−0.862394	−	0.506238i	$-0.831036\pi$
$823$	−49.4807			−1.72479			−0.862394	+	0.506238i	$0.831036\pi$
$824$	−1.63646	+	2.83443i	−0.0570087	+	0.0987420i
$825$	26.3969	−	37.1580i	0.919022	−	1.29368i
$826$	−10.7564	−	17.8521i	−0.374263	−	0.621155i
$827$		−	32.7958i		−	1.14042i	−0.821498	−	0.570211i	$-0.806861\pi$
$827$		−	32.7958i		−	1.14042i	0.821498	−	0.570211i	$-0.193139\pi$
$828$	15.6986	−	5.47308i	0.545564	−	0.190203i
$829$	25.2173	+	14.5592i	0.875833	+	0.505662i	0.869282	−	0.494316i	$-0.164582\pi$
$829$	25.2173	+	14.5592i	0.875833	+	0.505662i	0.00655070	+	0.999979i	$0.497915\pi$
$830$	−2.76266	−	1.59502i	−0.0958934	−	0.0553641i
$831$	13.3446	+	9.47993i	0.462918	+	0.328855i
$832$	−0.737483	+	18.4271i	−0.0255676	+	0.638843i
$833$	−0.529912	+	1.00253i	−0.0183604	+	0.0347356i
$834$	14.3319	−	6.56474i	0.496273	−	0.227318i
$835$	4.91249			0.170004
$836$	−7.65493			−0.264751
$837$	0.200421	+	0.814096i	0.00692757	+	0.0281393i
$838$	15.0918	−	8.71326i	0.521338	−	0.300995i
$839$	5.75458	−	9.96723i	0.198670	−	0.344107i	−0.749427	−	0.662087i	$-0.769671\pi$
$839$	5.75458	−	9.96723i	0.198670	−	0.344107i	0.948098	+	0.317980i	$0.103004\pi$
$840$	−37.0588	−	25.2985i	−1.27865	−	0.872882i
$841$	30.5151	−	52.8536i	1.05224	−	1.82254i
$842$			12.7210i			0.438396i
$843$	11.6632	−	16.4179i	0.401702	−	0.565462i
$844$	9.63146	+	16.6822i	0.331529	+	0.574224i
$845$	25.4028	−	36.8459i	0.873884	−	1.26754i
$846$	3.39512	−	17.8323i	0.116727	−	0.613086i
$847$	−8.68677	−	4.80127i	−0.298481	−	0.164974i
$848$	0.827803	−	0.477932i	0.0284269	−	0.0164123i
$849$	1.17429	+	2.56368i	0.0403017	+	0.0879852i
$850$	0.849162	−	0.490264i	0.0291260	−	0.0168159i
$851$			18.1058i			0.620658i
$852$	4.40184	+	9.60995i	0.150805	+	0.329231i
$853$		−	29.7525i		−	1.01870i	−0.860558	−	0.509352i	$-0.829885\pi$
$853$		−	29.7525i		−	1.01870i	0.860558	−	0.509352i	$-0.170115\pi$
$854$	−13.3112	−	7.35724i	−0.455500	−	0.251760i
$855$	15.9373	−	5.55632i	0.545045	−	0.190022i
$856$	54.4103			1.85971
$857$	−19.5077	−	33.7884i	−0.666371	−	1.15419i	−0.978912	−	0.204285i	$-0.934513\pi$
$857$	−19.5077	−	33.7884i	−0.666371	−	1.15419i	0.312540	−	0.949905i	$-0.398820\pi$
$858$	−8.04662	−	19.6018i	−0.274707	−	0.669195i
$859$	−13.9082	−	8.02991i	−0.474542	−	0.273977i	0.243597	−	0.969877i	$-0.421673\pi$
$859$	−13.9082	−	8.02991i	−0.474542	−	0.273977i	−0.718139	+	0.695899i	$0.755006\pi$
$860$	18.1761	+	31.4819i	0.619800	+	1.07352i
$861$	−9.58516	−	19.9341i	−0.326662	−	0.679351i
$862$	−2.22433	+	3.85264i	−0.0757608	+	0.131222i
$863$	42.9178	+	24.7786i	1.46094	+	0.843474i	0.999055	−	0.0434667i	$-0.0138402\pi$
$863$	42.9178	+	24.7786i	1.46094	+	0.843474i	0.461884	+	0.886940i	$0.347174\pi$
$864$	28.0649	+	8.13739i	0.954787	+	0.276840i
$865$	57.5226			1.95583
$866$	−13.8892	+	24.0568i	−0.471974	+	0.817483i
$867$	−23.9673	−	17.0263i	−0.813972	−	0.578242i
$868$	−0.251850	+	0.455664i	−0.00854835	+	0.0154662i
$869$	−34.8116	+	20.0985i	−1.18090	+	0.681794i
$870$	40.7463	+	28.9460i	1.38143	+	0.981361i
$871$	−2.88168	−	1.82115i	−0.0976419	−	0.0617072i
$872$	−48.7534	+	28.1478i	−1.65100	+	0.953204i
$873$	−4.51922	+	23.7364i	−0.152953	+	0.803356i
$874$	5.68128	−	3.28009i	0.192172	−	0.110951i
$875$	−14.4458	+	8.70397i	−0.488357	+	0.294248i
$876$	20.9467	+	1.97629i	0.707724	+	0.0667728i
$877$	11.3479	+	19.6552i	0.383192	+	0.663708i	0.991517	−	0.129980i	$-0.0414914\pi$
$877$	11.3479	+	19.6552i	0.383192	+	0.663708i	−0.608324	+	0.793688i	$0.708158\pi$
$878$	−7.20144			−0.243037
$879$	−8.83667	+	4.04764i	−0.298054	+	0.136524i
$880$	0.841191	−	0.485662i	0.0283566	−	0.0163717i
$881$	4.12034	+	7.13665i	0.138818	+	0.240440i	0.927049	−	0.374939i	$-0.122336\pi$
$881$	4.12034	+	7.13665i	0.138818	+	0.240440i	−0.788232	+	0.615379i	$0.789003\pi$
$882$	2.78676	−	18.3412i	0.0938350	−	0.617580i
$883$	36.7826			1.23783			0.618917	−	0.785456i	$-0.287572\pi$
$883$	36.7826			1.23783			0.618917	+	0.785456i	$0.287572\pi$
$884$	−0.0284860	+	0.711764i	−0.000958088	+	0.0239392i
$885$	48.3417	−	22.1430i	1.62499	−	0.744328i
$886$	9.20110	−	15.9368i	0.309117	−	0.535406i
$887$	32.8788			1.10396			0.551981	−	0.833857i	$-0.313872\pi$
$887$	32.8788			1.10396			0.551981	+	0.833857i	$0.313872\pi$
$888$	−11.3680	+	16.0024i	−0.381485	+	0.537004i
$889$	−15.5271	−	8.58201i	−0.520763	−	0.287831i
$890$	−18.1435	−	10.4752i	−0.608171	−	0.351128i
$891$	−34.1924	+	5.07392i	−1.14549	+	0.169983i
$892$	0.942583	−	0.544201i	0.0315600	−	0.0182212i
$893$			11.1935i			0.374578i
$894$	0.432114	−	4.57997i	0.0144521	−	0.153177i
$895$	−32.8106	+	18.9432i	−1.09674	+	0.633202i
$896$	9.18744	+	15.2482i	0.306931	+	0.509406i
$897$	−22.4583	−	17.3463i	−0.749860	−	0.579175i
$898$	−1.51027	+	2.61586i	−0.0503982	+	0.0872923i
$899$	0.765482	−	1.32585i	0.0255303	−	0.0442197i
$900$	16.3735	−	18.9825i	0.545782	−	0.632749i
$901$	1.82545	−	1.05392i	0.0608146	−	0.0351113i
$902$	16.3770			0.545293
$903$	−22.3704	+	32.7695i	−0.744440	+	1.09050i
$904$	−1.00817	+	1.74620i	−0.0335312	+	0.0580777i
$905$	−8.41056	−	4.85584i	−0.279577	−	0.161414i
$906$	5.48379	+	0.517388i	0.182187	+	0.0171891i
$907$	−22.9658	+	39.7779i	−0.762567	+	1.32080i	0.178956	+	0.983857i	$0.442728\pi$
$907$	−22.9658	+	39.7779i	−0.762567	+	1.32080i	−0.941523	+	0.336948i	$0.890605\pi$
$908$	−3.44040			−0.114174
$909$	−15.0274	−	2.86110i	−0.498428	−	0.0948967i
$910$	−0.618588	+	29.0052i	−0.0205060	+	0.961512i
$911$			41.6510i			1.37996i	0.723829	+	0.689979i	$0.242380\pi$
$911$			41.6510i			1.37996i	−0.723829	+	0.689979i	$0.757620\pi$
$912$	0.207018	+	0.0195318i	0.00685505	+	0.000646764i
$913$	−3.48893	−	2.01433i	−0.115467	−	0.0666647i
$914$		−	28.7740i		−	0.951758i
$915$	22.4709	−	31.6316i	0.742867	−	1.04571i
$916$	−18.3970	−	10.6215i	−0.607855	−	0.350945i
$917$	0.502012	+	26.8758i	0.0165779	+	0.887518i
$918$	−0.714197	−	0.207081i	−0.0235720	−	0.00683469i
$919$	4.58336	+	7.93862i	0.151191	+	0.261871i	0.931666	−	0.363317i	$-0.118356\pi$
$919$	4.58336	+	7.93862i	0.151191	+	0.261871i	−0.780474	+	0.625188i	$0.785022\pi$
$920$	22.2464	−	38.5319i	0.733443	−	1.27036i
$921$	8.84117	−	12.4454i	0.291326	−	0.410090i
$922$	27.0862	+	15.6382i	0.892037	+	0.515018i
$923$	9.63852	−	15.2514i	0.317256	−	0.502007i
$924$	−17.7283	−	12.1024i	−0.583218	−	0.398139i
$925$	13.6504	+	23.6431i	0.448821	+	0.777381i
$926$		−	15.7804i		−	0.518577i
$927$	0.645668	−	3.39126i	0.0212065	−	0.111383i
$928$	−26.6793	−	46.2099i	−0.875790	−	1.51691i
$929$	−14.8882	−	25.7871i	−0.488466	−	0.846047i	0.511446	−	0.859315i	$-0.329110\pi$
$929$	−14.8882	−	25.7871i	−0.488466	−	0.846047i	−0.999912	+	0.0132680i	$0.995777\pi$
$930$	0.692892	+	0.492228i	0.0227208	+	0.0161408i
$931$	0.427211	+	11.4316i	0.0140013	+	0.374657i
$932$	−21.7758	−	12.5723i	−0.713291	−	0.411819i
$933$	−3.89775	+	41.3122i	−0.127607	+	1.35250i
$934$	30.6809	+	17.7136i	1.00391	+	0.579607i
$935$	1.85497	−	1.07097i	0.0606642	−	0.0350245i
$936$	−8.95808	−	29.4319i	−0.292804	−	0.962011i
$937$			13.4476i			0.439314i	0.975577	+	0.219657i	$0.0704939\pi$
$937$			13.4476i			0.439314i	−0.975577	+	0.219657i	$0.929506\pi$
$938$	2.20943	−	0.0412699i	0.0721405	−	0.00134751i
$939$	4.90194	+	10.7017i	0.159969	+	0.349238i
$940$	14.3788	+	24.9049i	0.468986	+	0.812307i
$941$	19.4524	+	33.6926i	0.634130	+	1.09835i	0.986699	+	0.162560i	$0.0519751\pi$
$941$	19.4524	+	33.6926i	0.634130	+	1.09835i	−0.352568	+	0.935786i	$0.614692\pi$
$942$	0.693769	−	7.35325i	0.0226042	−	0.239582i
$943$	18.9942	−	10.9663i	0.618536	−	0.357112i
$944$	0.655072			0.0213208
$945$	45.6942	+	12.3287i	1.48643	+	0.401053i
$946$	−14.6886	−	25.4415i	−0.477569	−	0.827174i
$947$		−	39.5781i		−	1.28611i	−0.765818	−	0.643057i	$-0.777666\pi$
$947$		−	39.5781i		−	1.28611i	0.765818	−	0.643057i	$-0.222334\pi$
$948$	−20.0997	+	9.20667i	−0.652807	+	0.299019i
$949$	−16.6980	−	31.7940i	−0.542040	−	1.03208i
$950$	4.94587	−	8.56649i	0.160465	−	0.277934i
$951$	5.70334	+	12.4513i	0.184943	+	0.403762i
$952$	−0.629123	−	1.04414i	−0.0203900	−	0.0338408i
$953$	−33.8841	−	19.5630i	−1.09761	−	0.633707i	−0.162020	−	0.986787i	$-0.551801\pi$
$953$	−33.8841	−	19.5630i	−1.09761	−	0.633707i	−0.935593	+	0.353080i	$0.885134\pi$
$954$	−22.5236	+	26.1126i	−0.729228	+	0.845426i
$955$		−	8.74344i		−	0.282931i
$956$		−	21.4200i		−	0.692773i
$957$	51.4579	+	36.5555i	1.66340	+	1.18167i
$958$	−19.8598	−	11.4661i	−0.641642	−	0.370452i
$959$	12.6051	+	20.9205i	0.407041	+	0.675557i
$960$	27.7283	−	12.7010i	0.894927	−	0.409922i
$961$	−15.4870	+	26.8242i	−0.499580	+	0.865298i
$962$	12.6814	+	0.507532i	0.408865	+	0.0163635i
$963$	−54.1915	+	18.8931i	−1.74630	+	0.608820i
$964$		−	2.40596i		−	0.0774908i
$965$	−18.4437	−	31.9454i	−0.593723	−	1.02836i
$966$	18.3432	+	1.38558i	0.590184	+	0.0445804i
$967$	32.9048			1.05815			0.529073	−	0.848576i	$-0.322540\pi$
$967$	32.9048			1.05815			0.529073	+	0.848576i	$0.322540\pi$
$968$	9.24038	−	5.33494i	0.296997	−	0.171471i
$969$	0.456511	+	0.0430712i	0.0146652	+	0.00138364i
$970$	12.2476	+	21.2134i	0.393245	+	0.681121i
$971$	−10.5908	−	18.3438i	−0.339875	−	0.588680i	0.644534	−	0.764576i	$-0.277051\pi$
$971$	−10.5908	−	18.3438i	−0.339875	−	0.588680i	−0.984409	+	0.175895i	$0.943718\pi$
$972$	−18.9844	+	1.01184i	−0.608926	+	0.0324548i
$973$	−27.2528	+	0.509054i	−0.873685	+	0.0163195i
$974$			22.7537i			0.729075i
$975$	−42.4045	−	5.71950i	−1.35803	−	0.183171i
$976$	0.413980	−	0.239011i	0.0132512	−	0.00765057i
$977$	17.6880	+	10.2122i	0.565888	+	0.326716i	0.755505	−	0.655142i	$-0.227391\pi$
$977$	17.6880	+	10.2122i	0.565888	+	0.326716i	−0.189617	+	0.981858i	$0.560725\pi$
$978$	12.8401	+	1.21144i	0.410580	+	0.0387376i
$979$	−22.9131	−	13.2289i	−0.732307	−	0.422798i
$980$	15.6352	+	24.8859i	0.499448	+	0.794949i
$981$	38.7834	−	44.9633i	1.23826	−	1.43557i
$982$	−1.86152	−	3.22424i	−0.0594034	−	0.102890i
$983$	−17.3835	−	30.1091i	−0.554448	−	0.960332i	−0.997946	−	0.0640565i	$-0.979596\pi$
$983$	−17.3835	−	30.1091i	−0.554448	−	0.960332i	0.443499	−	0.896275i	$-0.353737\pi$
$984$	23.6729	+	2.23351i	0.754665	+	0.0712016i
$985$		−	17.1214i		−	0.545533i
$986$	0.678936	+	1.17595i	0.0216217	+	0.0374499i
$987$	−17.6969	+	25.9235i	−0.563298	+	0.825153i
$988$	3.34133	+	6.36209i	0.106302	+	0.202405i
$989$	−34.0721	−	19.6715i	−1.08343	−	0.625519i
$990$	−22.8879	+	26.5349i	−0.727424	+	0.843335i
$991$	15.9297	−	27.5910i	0.506023	−	0.876458i	−0.493953	−	0.869489i	$-0.664448\pi$
$991$	15.9297	−	27.5910i	0.506023	−	0.876458i	0.999976	−	0.00696902i	$-0.00221833\pi$
$992$	−0.453682	−	0.785800i	−0.0144044	−	0.0249492i
$993$	−1.43599	+	15.2201i	−0.0455698	+	0.482994i
$994$	0.218423	+	11.6935i	0.00692795	+	0.370896i
$995$	29.2829	+	16.9065i	0.928329	+	0.535971i
$996$	−1.80632	−	1.28321i	−0.0572356	−	0.0406599i
$997$			24.0834i			0.762729i	0.924425	+	0.381365i	$0.124546\pi$
$997$			24.0834i			0.762729i	−0.924425	+	0.381365i	$0.875454\pi$
$998$	−7.34332	−	4.23967i	−0.232449	−	0.134204i
$999$	5.76573	−	19.8853i	0.182420	−	0.629144i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.r.b.68.12	✓	64
3.2	odd	2	inner	273.2.r.b.68.21	yes	64
7.3	odd	6		273.2.bf.b.185.21	yes	64
13.9	even	3		273.2.bf.b.152.12	yes	64
21.17	even	6		273.2.bf.b.185.12	yes	64
39.35	odd	6		273.2.bf.b.152.21	yes	64
91.87	odd	6	inner	273.2.r.b.269.12	yes	64
273.269	even	6	inner	273.2.r.b.269.21	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.r.b.68.12	✓	64	1.1	even	1	trivial
273.2.r.b.68.21	yes	64	3.2	odd	2	inner
273.2.r.b.269.12	yes	64	91.87	odd	6	inner
273.2.r.b.269.21	yes	64	273.269	even	6	inner
273.2.bf.b.152.12	yes	64	13.9	even	3
273.2.bf.b.152.21	yes	64	39.35	odd	6
273.2.bf.b.185.12	yes	64	21.17	even	6
273.2.bf.b.185.21	yes	64	7.3	odd	6

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.883413i q^{2} +(1.41202 + 1.00309i) q^{3} +1.21958 q^{4} +(-1.72131 + 2.98140i) q^{5} +(0.886146 - 1.24740i) q^{6} +(-2.26618 + 1.36544i) q^{7} -2.84422i q^{8} +(0.987606 + 2.83278i) q^{9} +(2.63381 + 1.52063i) q^{10} +(3.32619 + 1.92038i) q^{11} +(1.72207 + 1.22335i) q^{12} +(0.144185 - 3.60267i) q^{13} +(1.20624 + 2.00198i) q^{14} +(-5.42115 + 2.48316i) q^{15} -0.0734612 q^{16} -0.161995 q^{17} +(2.50251 - 0.872465i) q^{18} +(-1.41529 + 0.817116i) q^{19} +(-2.09928 + 3.63606i) q^{20} +(-4.56956 - 0.345169i) q^{21} +(1.69649 - 2.93840i) q^{22} -4.54399i q^{23} +(2.85302 - 4.01610i) q^{24} +(-3.42582 - 5.93370i) q^{25} +(-3.18264 - 0.127375i) q^{26} +(-1.44702 + 4.99060i) q^{27} +(-2.76379 + 1.66526i) q^{28} +(8.21721 - 4.74421i) q^{29} +(2.19366 + 4.78911i) q^{30} +(0.139734 - 0.0806754i) q^{31} -5.62354i q^{32} +(2.77034 + 6.04810i) q^{33} +0.143108i q^{34} +(-0.170104 - 9.10673i) q^{35} +(1.20447 + 3.45480i) q^{36} -3.98455 q^{37} +(0.721851 + 1.25028i) q^{38} +(3.81740 - 4.94241i) q^{39} +(8.47975 + 4.89579i) q^{40} +(2.41336 + 4.18006i) q^{41} +(-0.304927 + 4.03681i) q^{42} +(4.32913 - 7.49828i) q^{43} +(4.05656 + 2.34206i) q^{44} +(-10.1456 - 1.93164i) q^{45} -4.01422 q^{46} +(3.42471 - 5.93177i) q^{47} +(-0.103729 - 0.0736885i) q^{48} +(3.27117 - 6.18866i) q^{49} +(-5.24191 + 3.02642i) q^{50} +(-0.228740 - 0.162496i) q^{51} +(0.175845 - 4.39374i) q^{52} +(-11.2686 + 6.50591i) q^{53} +(4.40877 + 1.27832i) q^{54} +(-11.4508 + 6.61114i) q^{55} +(3.88360 + 6.44552i) q^{56} +(-2.81806 - 0.265880i) q^{57} +(-4.19110 - 7.25920i) q^{58} -8.91725 q^{59} +(-6.61153 + 3.02841i) q^{60} +(-5.63535 + 3.25357i) q^{61} +(-0.0712698 - 0.123443i) q^{62} +(-6.10608 - 5.07108i) q^{63} -5.11484 q^{64} +(10.4928 + 6.63118i) q^{65} +(5.34297 - 2.44735i) q^{66} +(0.472730 - 0.818793i) q^{67} -0.197566 q^{68} +(4.55805 - 6.41621i) q^{69} +(-8.04501 + 0.150272i) q^{70} +(4.33350 + 2.50195i) q^{71} +(8.05705 - 2.80897i) q^{72} +(8.62581 - 4.98012i) q^{73} +3.52001i q^{74} +(1.11472 - 11.8149i) q^{75} +(-1.72606 + 0.996539i) q^{76} +(-10.1599 + 0.189777i) q^{77} +(-4.36619 - 3.37235i) q^{78} +(-5.23295 + 9.06373i) q^{79} +(0.126450 - 0.219017i) q^{80} +(-7.04927 + 5.59534i) q^{81} +(3.69272 - 2.13200i) q^{82} -1.04892 q^{83} +(-5.57294 - 0.420961i) q^{84} +(0.278843 - 0.482971i) q^{85} +(-6.62408 - 3.82441i) q^{86} +(16.3618 + 1.54371i) q^{87} +(5.46198 - 9.46043i) q^{88} -6.88870 q^{89} +(-1.70644 + 8.96277i) q^{90} +(4.59246 + 8.36118i) q^{91} -5.54177i q^{92} +(0.278232 + 0.0262508i) q^{93} +(-5.24021 - 3.02543i) q^{94} -5.62604i q^{95} +(5.64094 - 7.94056i) q^{96} +(6.97520 + 4.02713i) q^{97} +(-5.46714 - 2.88979i) q^{98} +(-2.15504 + 11.3189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 64 q^{4} + 12 q^{6} - 10 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{12} + 12 q^{13} - 9 q^{15} + 32 q^{16} + 2 q^{18} - 36 q^{19} + 10 q^{21} + 10 q^{22} - 18 q^{24} - 24 q^{25} - 14 q^{28} + 8 q^{30} - 24 q^{31}+ \cdots + 22 q^{99}+O(q^{100}) \) 64 * q - 64 * q^4 + 12 * q^6 - 10 * q^7 - 4 * q^9 - 6 * q^10 + 6 * q^12 + 12 * q^13 - 9 * q^15 + 32 * q^16 + 2 * q^18 - 36 * q^19 + 10 * q^21 + 10 * q^22 - 18 * q^24 - 24 * q^25 - 14 * q^28 + 8 * q^30 - 24 * q^31 - 45 * q^33 + 33 * q^39 + 90 * q^40 + 3 * q^42 - 20 * q^43 - 6 * q^48 - 6 * q^49 - 10 * q^51 - 48 * q^52 - 18 * q^55 + 4 * q^57 + 30 * q^58 + 55 * q^60 - 18 * q^61 + 31 * q^63 - 84 * q^64 + 75 * q^66 + 44 * q^67 + 33 * q^69 + 20 * q^70 + 17 * q^72 + 84 * q^73 - 18 * q^76 - 71 * q^78 + 20 * q^79 + 16 * q^81 - 18 * q^82 - 135 * q^84 - 2 * q^85 - 46 * q^88 - 10 * q^91 - 56 * q^93 + 36 * q^94 + 30 * q^96 - 24 * q^97 + 22 * q^99

Introduction

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