LMFDB - Embedded newform 63.3.r.a.29.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,3,Mod(29,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("63.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.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:	$1.71662566547$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.8
Character	$\chi$	$=$	63.29
Dual form			63.3.r.a.50.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.744550 + 0.429866i) q^{2} +(-2.65028 - 1.40570i) q^{3} +(-1.63043 - 2.82399i) q^{4} +(5.58239 - 3.22299i) q^{5} +(-1.36900 - 2.18588i) q^{6} +(1.32288 - 2.29129i) q^{7} -6.24239i q^{8} +(5.04801 + 7.45102i) q^{9} +O(q^{10})$	\(q+(0.744550 + 0.429866i) q^{2} +(-2.65028 - 1.40570i) q^{3} +(-1.63043 - 2.82399i) q^{4} +(5.58239 - 3.22299i) q^{5} +(-1.36900 - 2.18588i) q^{6} +(1.32288 - 2.29129i) q^{7} -6.24239i q^{8} +(5.04801 + 7.45102i) q^{9} +5.54182 q^{10} +(-11.7915 - 6.80780i) q^{11} +(0.351418 + 9.77627i) q^{12} +(9.13554 + 15.8232i) q^{13} +(1.96989 - 1.13732i) q^{14} +(-19.3255 + 0.694673i) q^{15} +(-3.83833 + 6.64818i) q^{16} +4.81189i q^{17} +(0.555553 + 7.71762i) q^{18} +14.3999 q^{19} +(-18.2034 - 10.5097i) q^{20} +(-6.72686 + 4.21299i) q^{21} +(-5.85288 - 10.1375i) q^{22} +(21.4911 - 12.4079i) q^{23} +(-8.77494 + 16.5441i) q^{24} +(8.27536 - 14.3333i) q^{25} +15.7082i q^{26} +(-2.90474 - 26.8433i) q^{27} -8.62743 q^{28} +(3.66899 + 2.11829i) q^{29} +(-14.6874 - 7.79014i) q^{30} +(28.8686 + 50.0019i) q^{31} +(-27.3399 + 15.7847i) q^{32} +(21.6810 + 34.6179i) q^{33} +(-2.06847 + 3.58269i) q^{34} -17.0545i q^{35} +(12.8112 - 26.4039i) q^{36} -27.0684 q^{37} +(10.7214 + 6.19001i) q^{38} +(-1.96905 - 54.7779i) q^{39} +(-20.1192 - 34.8475i) q^{40} +(42.9502 - 24.7973i) q^{41} +(-6.81950 + 0.245134i) q^{42} +(0.0645211 - 0.111754i) q^{43} +44.3986i q^{44} +(52.1945 + 25.3248i) q^{45} +21.3349 q^{46} +(-49.3157 - 28.4725i) q^{47} +(19.5180 - 12.2240i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(12.3228 - 7.11459i) q^{50} +(6.76408 - 12.7529i) q^{51} +(29.7897 - 51.5973i) q^{52} -5.32385i q^{53} +(9.37629 - 21.2348i) q^{54} -87.7660 q^{55} +(-14.3031 - 8.25791i) q^{56} +(-38.1637 - 20.2419i) q^{57} +(1.82116 + 3.15435i) q^{58} +(-23.1276 + 13.3527i) q^{59} +(33.4706 + 53.4423i) q^{60} +(-14.6922 + 25.4477i) q^{61} +49.6385i q^{62} +(23.7503 - 1.70967i) q^{63} +3.56540 q^{64} +(101.996 + 58.8876i) q^{65} +(1.26151 + 35.0946i) q^{66} +(-47.5501 - 82.3592i) q^{67} +(13.5887 - 7.84545i) q^{68} +(-74.3994 + 2.67436i) q^{69} +(7.33114 - 12.6979i) q^{70} +94.1213i q^{71} +(46.5122 - 31.5116i) q^{72} +5.12556 q^{73} +(-20.1538 - 11.6358i) q^{74} +(-42.0805 + 26.3547i) q^{75} +(-23.4780 - 40.6651i) q^{76} +(-31.1973 + 18.0117i) q^{77} +(22.0811 - 41.6313i) q^{78} +(-73.3067 + 126.971i) q^{79} +49.4836i q^{80} +(-30.0353 + 75.2255i) q^{81} +42.6381 q^{82} +(35.8068 + 20.6731i) q^{83} +(22.8651 + 12.1276i) q^{84} +(15.5087 + 26.8618i) q^{85} +(0.0960783 - 0.0554708i) q^{86} +(-6.74618 - 10.7716i) q^{87} +(-42.4970 + 73.6069i) q^{88} -25.7267i q^{89} +(27.9751 + 41.2922i) q^{90} +48.3407 q^{91} +(-70.0796 - 40.4605i) q^{92} +(-6.22224 - 173.100i) q^{93} +(-24.4787 - 42.3983i) q^{94} +(80.3857 - 46.4107i) q^{95} +(94.6472 - 3.40219i) q^{96} +(6.86238 - 11.8860i) q^{97} -6.01812i q^{98} +(-8.79831 - 122.224i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{3} + 24 q^{4} - 18 q^{5} - 14 q^{6} + 26 q^{9}+O(q^{10}) $ 24 * q + 2 * q^3 + 24 * q^4 - 18 * q^5 - 14 * q^6 + 26 * q^9	$ 24 q + 2 q^{3} + 24 q^{4} - 18 q^{5} - 14 q^{6} + 26 q^{9} - 18 q^{11} + 4 q^{12} - 10 q^{15} - 48 q^{16} - 62 q^{18} - 24 q^{19} - 18 q^{20} - 14 q^{21} - 24 q^{22} + 72 q^{23} + 54 q^{24} + 54 q^{25} - 124 q^{27} + 54 q^{29} - 212 q^{30} + 30 q^{31} + 126 q^{32} - 178 q^{33} + 60 q^{34} + 124 q^{36} + 84 q^{37} - 144 q^{38} + 92 q^{39} - 60 q^{40} + 180 q^{41} + 140 q^{42} - 60 q^{43} - 118 q^{45} - 168 q^{46} + 378 q^{47} + 436 q^{48} - 84 q^{49} - 378 q^{50} + 168 q^{51} - 18 q^{52} + 514 q^{54} - 132 q^{55} - 232 q^{57} + 90 q^{58} - 90 q^{59} + 76 q^{60} + 28 q^{63} + 324 q^{64} + 126 q^{65} + 202 q^{66} + 6 q^{67} - 738 q^{68} - 432 q^{69} - 246 q^{72} - 72 q^{73} - 792 q^{74} + 40 q^{75} + 84 q^{76} + 28 q^{78} - 6 q^{79} - 34 q^{81} - 108 q^{82} - 558 q^{83} - 322 q^{84} + 126 q^{85} + 90 q^{86} + 428 q^{87} + 168 q^{88} - 488 q^{90} + 84 q^{91} + 774 q^{92} - 738 q^{93} - 354 q^{94} + 648 q^{95} - 280 q^{96} - 270 q^{97} + 296 q^{99}+O(q^{100}) $ 24 * q + 2 * q^3 + 24 * q^4 - 18 * q^5 - 14 * q^6 + 26 * q^9 - 18 * q^11 + 4 * q^12 - 10 * q^15 - 48 * q^16 - 62 * q^18 - 24 * q^19 - 18 * q^20 - 14 * q^21 - 24 * q^22 + 72 * q^23 + 54 * q^24 + 54 * q^25 - 124 * q^27 + 54 * q^29 - 212 * q^30 + 30 * q^31 + 126 * q^32 - 178 * q^33 + 60 * q^34 + 124 * q^36 + 84 * q^37 - 144 * q^38 + 92 * q^39 - 60 * q^40 + 180 * q^41 + 140 * q^42 - 60 * q^43 - 118 * q^45 - 168 * q^46 + 378 * q^47 + 436 * q^48 - 84 * q^49 - 378 * q^50 + 168 * q^51 - 18 * q^52 + 514 * q^54 - 132 * q^55 - 232 * q^57 + 90 * q^58 - 90 * q^59 + 76 * q^60 + 28 * q^63 + 324 * q^64 + 126 * q^65 + 202 * q^66 + 6 * q^67 - 738 * q^68 - 432 * q^69 - 246 * q^72 - 72 * q^73 - 792 * q^74 + 40 * q^75 + 84 * q^76 + 28 * q^78 - 6 * q^79 - 34 * q^81 - 108 * q^82 - 558 * q^83 - 322 * q^84 + 126 * q^85 + 90 * q^86 + 428 * q^87 + 168 * q^88 - 488 * q^90 + 84 * q^91 + 774 * q^92 - 738 * q^93 - 354 * q^94 + 648 * q^95 - 280 * q^96 - 270 * q^97 + 296 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.744550	+	0.429866i	0.372275	+	0.214933i	0.674452	−	0.738319i	$-0.264380\pi$
$2$	0.744550	+	0.429866i	0.372275	+	0.214933i	−0.302177	+	0.953252i	$0.597713\pi$
$3$	−2.65028	−	1.40570i	−0.883428	−	0.468567i
$3$	−2.65028	−	1.40570i	−0.883428	−	0.468567i
$4$	−1.63043	−	2.82399i	−0.407608	−	0.705997i
$5$	5.58239	−	3.22299i	1.11648	−	0.644598i	0.175978	−	0.984394i	$-0.443691\pi$
$5$	5.58239	−	3.22299i	1.11648	−	0.644598i	0.940499	+	0.339796i	$0.110358\pi$
$6$	−1.36900	−	2.18588i	−0.228167	−	0.364313i
$7$	1.32288	−	2.29129i	0.188982	−	0.327327i
$7$	1.32288	−	2.29129i	0.188982	−	0.327327i
$8$		−	6.24239i		−	0.780299i
$9$	5.04801	+	7.45102i	0.560890	+	0.827891i
$10$	5.54182			0.554182
$11$	−11.7915	−	6.80780i	−1.07195	−	0.618891i	−0.143237	−	0.989688i	$-0.545751\pi$
$11$	−11.7915	−	6.80780i	−1.07195	−	0.618891i	−0.928714	+	0.370797i	$0.879084\pi$
$12$	0.351418	+	9.77627i	0.0292848	+	0.814689i
$13$	9.13554	+	15.8232i	0.702734	+	1.21717i	0.967503	+	0.252859i	$0.0813709\pi$
$13$	9.13554	+	15.8232i	0.702734	+	1.21717i	−0.264769	+	0.964312i	$0.585296\pi$
$14$	1.96989	−	1.13732i	0.140707	−	0.0812370i
$15$	−19.3255	+	0.694673i	−1.28836	+	0.0463116i
$16$	−3.83833	+	6.64818i	−0.239896	+	0.415512i
$17$			4.81189i			0.283052i	0.989935	+	0.141526i	$0.0452009\pi$
$17$			4.81189i			0.283052i	−0.989935	+	0.141526i	$0.954799\pi$
$18$	0.555553	+	7.71762i	0.0308640	+	0.428756i
$19$	14.3999			0.757888			0.378944	−	0.925420i	$-0.376287\pi$
$19$	14.3999			0.757888			0.378944	+	0.925420i	$0.376287\pi$
$20$	−18.2034	−	10.5097i	−0.910169	−	0.525487i
$21$	−6.72686	+	4.21299i	−0.320327	+	0.200619i
$22$	−5.85288	−	10.1375i	−0.266040	−	0.460795i
$23$	21.4911	−	12.4079i	0.934397	−	0.539474i	0.0461975	−	0.998932i	$-0.485290\pi$
$23$	21.4911	−	12.4079i	0.934397	−	0.539474i	0.888200	+	0.459458i	$0.151956\pi$
$24$	−8.77494	+	16.5441i	−0.365623	+	0.689338i
$25$	8.27536	−	14.3333i	0.331014	−	0.573334i
$26$			15.7082i			0.604163i
$27$	−2.90474	−	26.8433i	−0.107583	−	0.994196i
$28$	−8.62743			−0.308122
$29$	3.66899	+	2.11829i	0.126517	+	0.0730446i	0.561923	−	0.827190i	$-0.310062\pi$
$29$	3.66899	+	2.11829i	0.126517	+	0.0730446i	−0.435406	+	0.900234i	$0.643395\pi$
$30$	−14.6874	−	7.79014i	−0.489580	−	0.259671i
$31$	28.8686	+	50.0019i	0.931245	+	1.61296i	0.781197	+	0.624285i	$0.214609\pi$
$31$	28.8686	+	50.0019i	0.931245	+	1.61296i	0.150048	+	0.988679i	$0.452057\pi$
$32$	−27.3399	+	15.7847i	−0.854373	+	0.493273i
$33$	21.6810	+	34.6179i	0.656999	+	1.04903i
$34$	−2.06847	+	3.58269i	−0.0608372	+	0.105373i
$35$		−	17.0545i		−	0.487271i
$36$	12.8112	−	26.4039i	0.355866	−	0.733441i
$37$	−27.0684			−0.731579			−0.365790	−	0.930698i	$-0.619201\pi$
$37$	−27.0684			−0.731579			−0.365790	+	0.930698i	$0.619201\pi$
$38$	10.7214	+	6.19001i	0.282143	+	0.162895i
$39$	−1.96905	−	54.7779i	−0.0504883	−	1.40456i
$40$	−20.1192	−	34.8475i	−0.502980	−	0.871186i
$41$	42.9502	−	24.7973i	1.04757	−	0.604813i	0.125600	−	0.992081i	$-0.459915\pi$
$41$	42.9502	−	24.7973i	1.04757	−	0.604813i	0.921967	+	0.387268i	$0.126581\pi$
$42$	−6.81950	+	0.245134i	−0.162369	+	0.00583652i
$43$	0.0645211	−	0.111754i	0.00150049	−	0.00259893i	−0.865274	−	0.501299i	$-0.832856\pi$
$43$	0.0645211	−	0.111754i	0.00150049	−	0.00259893i	0.866775	+	0.498700i	$0.166189\pi$
$44$			44.3986i			1.00906i
$45$	52.1945	+	25.3248i	1.15988	+	0.562773i
$46$	21.3349			0.463803
$47$	−49.3157	−	28.4725i	−1.04927	−	0.605797i	−0.126826	−	0.991925i	$-0.540479\pi$
$47$	−49.3157	−	28.4725i	−1.04927	−	0.605797i	−0.922445	+	0.386128i	$0.873812\pi$
$48$	19.5180	−	12.2240i	0.406626	−	0.254667i
$49$	−3.50000	−	6.06218i	−0.0714286	−	0.123718i
$50$	12.3228	−	7.11459i	0.246457	−	0.142292i
$51$	6.76408	−	12.7529i	0.132629	−	0.250056i
$52$	29.7897	−	51.5973i	0.572880	−	0.992256i
$53$		−	5.32385i		−	0.100450i	−0.998738	−	0.0502250i	$-0.984006\pi$
$53$		−	5.32385i		−	0.100450i	0.998738	−	0.0502250i	$-0.0159938\pi$
$54$	9.37629	−	21.2348i	0.173635	−	0.393237i
$55$	−87.7660			−1.59574
$56$	−14.3031	−	8.25791i	−0.255413	−	0.147463i
$57$	−38.1637	−	20.2419i	−0.669539	−	0.355121i
$58$	1.82116	+	3.15435i	0.0313994	+	0.0543853i
$59$	−23.1276	+	13.3527i	−0.391993	+	0.226317i	−0.683023	−	0.730397i	$-0.739335\pi$
$59$	−23.1276	+	13.3527i	−0.391993	+	0.226317i	0.291030	+	0.956714i	$0.406002\pi$
$60$	33.4706	+	53.4423i	0.557843	+	0.890705i
$61$	−14.6922	+	25.4477i	−0.240856	+	0.417175i	−0.960958	−	0.276693i	$-0.910762\pi$
$61$	−14.6922	+	25.4477i	−0.240856	+	0.417175i	0.720102	+	0.693868i	$0.244095\pi$
$62$			49.6385i			0.800621i
$63$	23.7503	−	1.70967i	0.376989	−	0.0271376i
$64$	3.56540			0.0557093
$65$	101.996	+	58.8876i	1.56917	+	0.905963i
$66$	1.26151	+	35.0946i	0.0191138	+	0.531737i
$67$	−47.5501	−	82.3592i	−0.709703	−	1.22924i	−0.964967	−	0.262371i	$-0.915496\pi$
$67$	−47.5501	−	82.3592i	−0.709703	−	1.22924i	0.255264	−	0.966871i	$-0.417838\pi$
$68$	13.5887	−	7.84545i	0.199834	−	0.115374i
$69$	−74.3994	+	2.67436i	−1.07825	+	0.0387589i
$70$	7.33114	−	12.6979i	0.104731	−	0.181399i
$71$			94.1213i			1.32565i	0.748774	+	0.662826i	$0.230643\pi$
$71$			94.1213i			1.32565i	−0.748774	+	0.662826i	$0.769357\pi$
$72$	46.5122	−	31.5116i	0.646002	−	0.437662i
$73$	5.12556			0.0702132			0.0351066	−	0.999384i	$-0.488823\pi$
$73$	5.12556			0.0702132			0.0351066	+	0.999384i	$0.488823\pi$
$74$	−20.1538	−	11.6358i	−0.272348	−	0.157240i
$75$	−42.0805	+	26.3547i	−0.561073	+	0.351397i
$76$	−23.4780	−	40.6651i	−0.308921	−	0.535067i
$77$	−31.1973	+	18.0117i	−0.405159	+	0.233919i
$78$	22.0811	−	41.6313i	0.283091	−	0.533734i
$79$	−73.3067	+	126.971i	−0.927933	+	1.60723i	−0.141158	+	0.989987i	$0.545083\pi$
$79$	−73.3067	+	126.971i	−0.927933	+	1.60723i	−0.786775	+	0.617240i	$0.788251\pi$
$80$			49.4836i			0.618546i
$81$	−30.0353	+	75.2255i	−0.370806	+	0.928710i
$82$	42.6381			0.519977
$83$	35.8068	+	20.6731i	0.431408	+	0.249073i	0.699946	−	0.714196i	$-0.253207\pi$
$83$	35.8068	+	20.6731i	0.431408	+	0.249073i	−0.268539	+	0.963269i	$0.586541\pi$
$84$	22.8651	+	12.1276i	0.272204	+	0.144376i
$85$	15.5087	+	26.8618i	0.182455	+	0.316021i
$86$	0.0960783	−	0.0554708i	0.00111719	−	0.000645010i
$87$	−6.74618	−	10.7716i	−0.0775423	−	0.123811i
$88$	−42.4970	+	73.6069i	−0.482920	+	0.836442i
$89$		−	25.7267i		−	0.289064i	−0.989500	−	0.144532i	$-0.953832\pi$
$89$		−	25.7267i		−	0.289064i	0.989500	−	0.144532i	$-0.0461677\pi$
$90$	27.9751	+	41.2922i	0.310835	+	0.458802i
$91$	48.3407			0.531217
$92$	−70.0796	−	40.4605i	−0.761735	−	0.439788i
$93$	−6.22224	−	173.100i	−0.0669058	−	1.86129i
$94$	−24.4787	−	42.3983i	−0.260411	−	0.451046i
$95$	80.3857	−	46.4107i	0.846165	−	0.488533i
$96$	94.6472	−	3.40219i	0.985908	−	0.0354395i
$97$	6.86238	−	11.8860i	0.0707462	−	0.122536i	−0.828482	−	0.560015i	$-0.810795\pi$
$97$	6.86238	−	11.8860i	0.0707462	−	0.122536i	0.899229	+	0.437479i	$0.144129\pi$
$98$		−	6.01812i		−	0.0614094i
$99$	−8.79831	−	122.224i	−0.0888718	−	1.23459i
$100$	−53.9696			−0.539696
$101$	−135.293	−	78.1117i	−1.33954	−	0.773383i	−0.352800	−	0.935699i	$-0.614770\pi$
$101$	−135.293	−	78.1117i	−1.33954	−	0.773383i	−0.986739	+	0.162315i	$0.948104\pi$
$102$	10.5182	−	6.58749i	0.103120	−	0.0645833i
$103$	28.6359	+	49.5988i	0.278018	+	0.481542i	0.970892	−	0.239517i	$-0.0769891\pi$
$103$	28.6359	+	49.5988i	0.278018	+	0.481542i	−0.692874	+	0.721059i	$0.743656\pi$
$104$	98.7748	−	57.0276i	0.949757	−	0.548343i
$105$	−23.9735	+	45.1992i	−0.228319	+	0.430468i
$106$	2.28854	−	3.96387i	0.0215900	−	0.0373950i
$107$		−	138.727i		−	1.29651i	−0.761423	−	0.648256i	$-0.775499\pi$
$107$		−	138.727i		−	1.29651i	0.761423	−	0.648256i	$-0.224501\pi$
$108$	−71.0692	+	51.9691i	−0.658048	+	0.481195i
$109$	188.067			1.72539			0.862694	−	0.505727i	$-0.168776\pi$
$109$	188.067			1.72539			0.862694	+	0.505727i	$0.168776\pi$
$110$	−65.3461	−	37.7276i	−0.594056	−	0.342978i
$111$	71.7390	+	38.0501i	0.646297	+	0.342794i
$112$	10.1553	+	17.5894i	0.0906720	+	0.157049i
$113$	−38.1000	+	21.9971i	−0.337168	+	0.194664i	−0.659019	−	0.752126i	$-0.729028\pi$
$113$	−38.1000	+	21.9971i	−0.337168	+	0.194664i	0.321851	+	0.946790i	$0.395695\pi$
$114$	−19.7135	−	31.4764i	−0.172925	−	0.276109i
$115$	79.9812	−	138.532i	0.695489	−	1.20462i
$116$		−	13.8149i		−	0.119094i
$117$	−71.7828	+	147.945i	−0.613528	+	1.26449i
$118$	−22.9595			−0.194572
$119$	11.0254	+	6.36553i	0.0926506	+	0.0534918i
$120$	4.33642	+	120.637i	0.0361369	+	1.00531i
$121$	32.1923	+	55.7587i	0.266052	+	0.460816i
$122$	−21.8782	+	12.6314i	−0.179329	+	0.103536i
$123$	−148.688	+	5.34474i	−1.20885	+	0.0434532i
$124$	94.1365	−	163.049i	0.759165	−	1.31491i
$125$			54.4639i			0.435711i
$126$	18.4182	+	8.93651i	0.146176	+	0.0709247i
$127$	−31.6314			−0.249066			−0.124533	−	0.992215i	$-0.539743\pi$
$127$	−31.6314			−0.249066			−0.124533	+	0.992215i	$0.539743\pi$
$128$	112.014	+	64.6715i	0.875112	+	0.505246i
$129$	−0.328092	+	0.205482i	−0.00254335	+	0.00159288i
$130$	50.6275	+	87.6894i	0.389442	+	0.674534i
$131$	−73.0257	+	42.1614i	−0.557448	+	0.321843i	−0.752121	−	0.659025i	$-0.770969\pi$
$131$	−73.0257	+	42.1614i	−0.557448	+	0.321843i	0.194672	+	0.980868i	$0.437636\pi$
$132$	62.4112	−	117.669i	0.472812	−	0.891431i
$133$	19.0492	−	32.9943i	0.143227	−	0.248077i
$134$		−	81.7607i		−	0.610154i
$135$	−102.731	−	140.488i	−0.760971	−	1.04065i
$136$	30.0377			0.220865
$137$	−7.91257	−	4.56832i	−0.0577560	−	0.0333454i	0.470844	−	0.882217i	$-0.343949\pi$
$137$	−7.91257	−	4.56832i	−0.0577560	−	0.0333454i	−0.528600	+	0.848871i	$0.677283\pi$
$138$	−56.5437	−	29.9906i	−0.409737	−	0.217323i
$139$	62.2334	+	107.791i	0.447723	+	0.775478i	0.998237	−	0.0593472i	$-0.0189019\pi$
$139$	62.2334	+	107.791i	0.447723	+	0.775478i	−0.550515	+	0.834825i	$0.685569\pi$
$140$	−48.1616	+	27.8061i	−0.344012	+	0.198615i
$141$	90.6769	+	144.783i	0.643099	+	1.02683i
$142$	−40.4595	+	70.0779i	−0.284926	+	0.493507i
$143$		−	248.772i		−	1.73966i
$144$	−68.9116	+	4.96061i	−0.478553	+	0.0344487i
$145$	27.3090			0.188338
$146$	3.81624	+	2.20330i	0.0261386	+	0.0150911i
$147$	0.754379	+	20.9864i	0.00513183	+	0.142765i
$148$	44.1332	+	76.4409i	0.298197	+	0.516493i
$149$	−12.5407	+	7.24040i	−0.0841660	+	0.0485933i	−0.541492	−	0.840706i	$-0.682140\pi$
$149$	−12.5407	+	7.24040i	−0.0841660	+	0.0485933i	0.457326	+	0.889299i	$0.348807\pi$
$150$	−42.6600	+	1.53346i	−0.284400	+	0.0102230i
$151$	8.04005	−	13.9258i	0.0532453	−	0.0922236i	−0.838174	−	0.545403i	$-0.816377\pi$
$151$	8.04005	−	13.9258i	0.0532453	−	0.0922236i	0.891420	+	0.453179i	$0.149710\pi$
$152$		−	89.8897i		−	0.591379i
$153$	−35.8534	+	24.2904i	−0.234336	+	0.158761i
$154$	−30.9705			−0.201107
$155$	322.311	+	186.086i	2.07943	+	1.20056i
$156$	−151.482	+	94.8721i	−0.971037	+	0.608154i
$157$	−59.9669	−	103.866i	−0.381954	−	0.661565i	0.609387	−	0.792873i	$-0.291416\pi$
$157$	−59.9669	−	103.866i	−0.381954	−	0.661565i	−0.991342	+	0.131308i	$0.958082\pi$
$158$	−109.161	+	63.0241i	−0.690892	+	0.398887i
$159$	−7.48374	+	14.1097i	−0.0470676	+	0.0887403i
$160$	−101.748	+	176.233i	−0.635925	+	1.10146i
$161$		−	65.6565i		−	0.407804i
$162$	−54.6996	+	43.0980i	−0.337652	+	0.266037i
$163$	−246.955			−1.51506			−0.757530	−	0.652800i	$-0.773594\pi$
$163$	−246.955			−1.51506			−0.757530	+	0.652800i	$0.773594\pi$
$164$	−140.055	−	80.8607i	−0.853993	−	0.493053i
$165$	232.605	+	123.373i	1.40973	+	0.747714i
$166$	17.7733	+	30.7843i	0.107068	+	0.185447i
$167$	−55.6660	+	32.1388i	−0.333329	+	0.192448i	−0.657318	−	0.753613i	$-0.728309\pi$
$167$	−55.6660	+	32.1388i	−0.333329	+	0.192448i	0.323989	+	0.946061i	$0.394976\pi$
$168$	26.2992	+	41.9917i	0.156543	+	0.249951i
$169$	−82.4163	+	142.749i	−0.487670	+	0.844670i
$170$			26.6666i			0.156862i
$171$	72.6906	+	107.294i	0.425091	+	0.627448i
$172$	−0.420789			−0.00244645
$173$	19.0774	+	11.0143i	0.110274	+	0.0636666i	0.554123	−	0.832435i	$-0.313054\pi$
$173$	19.0774	+	11.0143i	0.110274	+	0.0636666i	−0.443849	+	0.896102i	$0.646387\pi$
$174$	−0.392528	−	10.9199i	−0.00225591	−	0.0627582i
$175$	−21.8945	−	37.9225i	−0.125112	−	0.216700i
$176$	90.5190	−	52.2612i	0.514313	−	0.296939i
$177$	80.0646	−	2.87800i	0.452342	−	0.0162599i
$178$	11.0590	−	19.1548i	0.0621294	−	0.107611i
$179$			37.3305i			0.208550i	0.994548	+	0.104275i	$0.0332523\pi$
$179$			37.3305i			0.208550i	−0.994548	+	0.104275i	$0.966748\pi$
$180$	−13.5826	−	188.687i	−0.0754591	−	1.04826i
$181$	208.749			1.15331			0.576655	−	0.816988i	$-0.304358\pi$
$181$	208.749			1.15331			0.576655	+	0.816988i	$0.304358\pi$
$182$	35.9921	+	20.7800i	0.197759	+	0.114176i
$183$	74.7104	−	46.7907i	0.408253	−	0.255687i
$184$	−77.4551	−	134.156i	−0.420951	−	0.729109i
$185$	−151.106	+	87.2413i	−0.816792	+	0.471575i
$186$	69.7769	−	131.556i	0.375145	−	0.707291i
$187$	32.7584	−	56.7391i	0.175178	−	0.303418i
$188$			185.689i			0.987710i
$189$	−65.3483	−	28.8547i	−0.345758	−	0.152671i
$190$	79.8015			0.420008
$191$	249.245	+	143.902i	1.30495	+	0.753411i	0.981248	−	0.192749i	$-0.0617404\pi$
$191$	249.245	+	143.902i	1.30495	+	0.753411i	0.323698	+	0.946160i	$0.395074\pi$
$192$	−9.44931	−	5.01189i	−0.0492152	−	0.0261036i
$193$	−31.8888	−	55.2330i	−0.165227	−	0.286181i	0.771509	−	0.636219i	$-0.219502\pi$
$193$	−31.8888	−	55.2330i	−0.165227	−	0.286181i	−0.936736	+	0.350037i	$0.886169\pi$
$194$	10.2188	−	5.89981i	0.0526741	−	0.0304114i
$195$	−187.541	−	299.445i	−0.961747	−	1.53562i
$196$	−11.4130	+	19.7679i	−0.0582297	+	0.100857i
$197$		−	147.465i		−	0.748554i	−0.927317	−	0.374277i	$-0.877891\pi$
$197$		−	147.465i		−	0.748554i	0.927317	−	0.374277i	$-0.122109\pi$
$198$	45.9892	−	94.7840i	0.232269	−	0.478707i
$199$	−83.2087			−0.418134			−0.209067	−	0.977901i	$-0.567043\pi$
$199$	−83.2087			−0.418134			−0.209067	+	0.977901i	$0.567043\pi$
$200$	−89.4744	−	51.6581i	−0.447372	−	0.258290i
$201$	10.2488	+	285.117i	0.0509891	+	1.41849i
$202$	−67.1551	−	116.316i	−0.332451	−	0.575822i
$203$	9.70724	−	5.60448i	0.0478189	−	0.0276083i
$204$	−47.0423	+	1.69098i	−0.230599	+	0.00828913i
$205$	159.843	−	276.857i	0.779723	−	1.35052i
$206$			49.2383i			0.239021i
$207$	200.939	+	97.4956i	0.970719	+	0.470993i
$208$	−140.261			−0.674331
$209$	−169.795	−	98.0315i	−0.812419	−	0.469050i
$210$	−37.2790	+	23.3476i	−0.177519	+	0.111179i
$211$	−136.631	−	236.652i	−0.647542	−	1.12158i	−0.983708	−	0.179773i	$-0.942464\pi$
$211$	−136.631	−	236.652i	−0.647542	−	1.12158i	0.336166	−	0.941803i	$-0.390870\pi$
$212$	−15.0345	+	8.68017i	−0.0709174	+	0.0409442i
$213$	132.306	−	249.448i	0.621157	−	1.17112i
$214$	59.6339	−	103.289i	0.278663	−	0.482659i
$215$		−	0.831804i		−	0.00386886i
$216$	−167.566	+	18.1325i	−0.775770	+	0.0839469i
$217$	152.758			0.703955
$218$	140.025	+	80.8437i	0.642318	+	0.370843i
$219$	−13.5842	−	7.20501i	−0.0620283	−	0.0328996i
$220$	143.096	+	247.850i	0.650438	+	1.12659i
$221$	−76.1395	+	43.9592i	−0.344523	+	0.198910i
$222$	37.0568	+	59.1684i	0.166922	+	0.266524i
$223$	−71.0061	+	122.986i	−0.318413	+	0.551508i	−0.980157	−	0.198222i	$-0.936483\pi$
$223$	−71.0061	+	122.986i	−0.318413	+	0.551508i	0.661744	+	0.749730i	$0.269817\pi$
$224$			83.5249i			0.372879i
$225$	148.572	−	10.6950i	0.660320	−	0.0475332i
$226$	−37.8231			−0.167359
$227$	190.845	+	110.184i	0.840725	+	0.485393i	0.857511	−	0.514466i	$-0.172010\pi$
$227$	190.845	+	110.184i	0.840725	+	0.485393i	−0.0167853	+	0.999859i	$0.505343\pi$
$228$	5.06037	+	140.777i	0.0221946	+	0.617443i
$229$	−63.8364	−	110.568i	−0.278762	−	0.482830i	0.692316	−	0.721595i	$-0.256591\pi$
$229$	−63.8364	−	110.568i	−0.278762	−	0.482830i	−0.971077	+	0.238765i	$0.923257\pi$
$230$	119.100	−	68.7624i	0.517826	−	0.298967i
$231$	108.001	−	3.88219i	0.467536	−	0.0168060i
$232$	13.2232	−	22.9033i	0.0569966	−	0.0987210i
$233$		−	42.4347i		−	0.182123i	−0.995845	−	0.0910615i	$-0.970974\pi$
$233$		−	42.4347i		−	0.182123i	0.995845	−	0.0910615i	$-0.0290260\pi$
$234$	−117.042	+	79.2952i	−0.500181	+	0.338869i
$235$	−367.066			−1.56198
$236$	75.4159	+	43.5414i	0.319559	+	0.184497i
$237$	372.767	−	233.462i	1.57286	−	0.985070i
$238$	5.47265	+	9.47890i	0.0229943	+	0.0398273i
$239$	−315.183	+	181.971i	−1.31876	+	0.761384i	−0.983529	−	0.180753i	$-0.942147\pi$
$239$	−315.183	+	181.971i	−1.31876	+	0.761384i	−0.335228	+	0.942137i	$0.608813\pi$
$240$	69.5592	−	131.146i	0.289830	−	0.546440i
$241$	−60.8005	+	105.310i	−0.252284	+	0.436969i	−0.964154	−	0.265342i	$-0.914515\pi$
$241$	−60.8005	+	105.310i	−0.252284	+	0.436969i	0.711870	+	0.702311i	$0.247848\pi$
$242$			55.3535i			0.228733i
$243$	185.347	−	157.148i	0.762744	−	0.646701i
$244$	95.8186			0.392699
$245$	−39.0767	−	22.5609i	−0.159497	−	0.0920855i
$246$	−113.003	−	59.9365i	−0.459362	−	0.243644i
$247$	131.551	+	227.852i	0.532594	+	0.922479i
$248$	312.131	−	180.209i	1.25859	−	0.726650i
$249$	−65.8381	−	105.123i	−0.264410	−	0.422182i
$250$	−23.4122	+	40.5511i	−0.0936487	+	0.162204i
$251$			212.435i			0.846355i	0.906047	+	0.423177i	$0.139085\pi$
$251$			212.435i			0.846355i	−0.906047	+	0.423177i	$0.860915\pi$
$252$	−43.5513	−	64.2831i	−0.172823	−	0.255092i
$253$	−337.882			−1.33550
$254$	−23.5511	−	13.5973i	−0.0927210	−	0.0535325i
$255$	−3.34269	−	92.9920i	−0.0131086	−	0.364674i
$256$	48.4694	+	83.9514i	0.189333	+	0.327935i
$257$	−418.319	+	241.517i	−1.62770	+	0.939753i	−0.642924	+	0.765930i	$0.722279\pi$
$257$	−418.319	+	241.517i	−1.62770	+	0.939753i	−0.984777	+	0.173823i	$0.944388\pi$
$258$	−0.332610	+	0.0119560i	−0.00128919	+	4.63411e-5i
$259$	−35.8082	+	62.0216i	−0.138255	+	0.239465i
$260$		−	384.048i		−	1.47711i
$261$	2.73765	+	38.0309i	0.0104891	+	0.145712i
$262$	−72.4950			−0.276699
$263$	−42.2204	−	24.3760i	−0.160534	−	0.0926843i	0.417581	−	0.908640i	$-0.362878\pi$
$263$	−42.2204	−	24.3760i	−0.160534	−	0.0926843i	−0.578115	+	0.815955i	$0.696211\pi$
$264$	216.098	−	135.341i	0.818554	−	0.512656i
$265$	−17.1587	−	29.7198i	−0.0647499	−	0.112150i
$266$	28.3662	−	16.3772i	0.106640	−	0.0615686i
$267$	−36.1641	+	68.1831i	−0.135446	+	0.255367i
$268$	−155.054	+	268.562i	−0.578561	+	1.00210i
$269$			311.246i			1.15705i	0.815666	+	0.578523i	$0.196371\pi$
$269$			311.246i			1.15705i	−0.815666	+	0.578523i	$0.803629\pi$
$270$	−16.0975	−	148.761i	−0.0596205	−	0.550965i
$271$	244.797			0.903311			0.451655	−	0.892192i	$-0.350834\pi$
$271$	244.797			0.903311			0.451655	+	0.892192i	$0.350834\pi$
$272$	−31.9903	−	18.4696i	−0.117611	−	0.0679030i
$273$	−128.117	−	67.9527i	−0.469292	−	0.248911i
$274$	−3.92753	−	6.80268i	−0.0143341	−	0.0248273i
$275$	−195.157	+	112.674i	−0.709662	+	0.409724i
$276$	128.855	+	205.743i	0.466868	+	0.745445i
$277$	146.486	−	253.720i	0.528829	−	0.915958i	−0.470606	−	0.882343i	$-0.655965\pi$
$277$	146.486	−	253.720i	0.528829	−	0.915958i	0.999435	−	0.0336147i	$-0.0107019\pi$
$278$			107.008i			0.384921i
$279$	−226.836	+	467.510i	−0.813032	+	1.67566i
$280$	−106.461			−0.380217
$281$	−357.671	−	206.502i	−1.27285	−	0.734881i	−0.297328	−	0.954775i	$-0.596096\pi$
$281$	−357.671	−	206.502i	−1.27285	−	0.734881i	−0.975524	+	0.219894i	$0.929429\pi$
$282$	5.27606	+	146.777i	0.0187094	+	0.520487i
$283$	−28.9243	−	50.0983i	−0.102206	−	0.177026i	0.810387	−	0.585895i	$-0.199257\pi$
$283$	−28.9243	−	50.0983i	−0.102206	−	0.177026i	−0.912593	+	0.408869i	$0.865923\pi$
$284$	265.797	−	153.458i	0.935906	−	0.540346i
$285$	−278.284	+	10.0032i	−0.976436	+	0.0350990i
$286$	106.939	−	185.223i	0.373911	−	0.647633i
$287$		−	131.215i		−	0.457196i
$288$	−255.624	−	124.029i	−0.887585	−	0.430656i
$289$	265.846			0.919881
$290$	20.3329	+	11.7392i	0.0701134	+	0.0404800i
$291$	−34.8954	+	21.8548i	−0.119916	+	0.0751024i
$292$	−8.35687	−	14.4745i	−0.0286194	−	0.0495703i
$293$	488.834	−	282.229i	1.66838	−	0.963238i	0.699863	−	0.714278i	$-0.253245\pi$
$293$	488.834	−	282.229i	1.66838	−	0.963238i	0.968514	−	0.248960i	$-0.0800888\pi$
$294$	−8.45968	+	15.9497i	−0.0287744	+	0.0542508i
$295$	−86.0714	+	149.080i	−0.291768	+	0.505356i
$296$			168.972i			0.570851i
$297$	−148.493	+	336.296i	−0.499975	+	1.13231i
$298$	−12.4496			−0.0417772
$299$	392.666	+	226.706i	1.31327	+	0.758214i
$300$	143.035	+	75.8652i	0.476783	+	0.252884i
$301$	−0.170707	−	0.295673i	−0.000567132	−	0.000982302i
$302$	11.9724	−	6.91228i	0.0396438	−	0.0228884i
$303$	248.764	+	397.200i	0.821004	+	1.31089i
$304$	−55.2715	+	95.7330i	−0.181814	+	0.314911i
$305$			189.412i			0.621022i
$306$	−37.1363	+	2.67326i	−0.121360	+	0.00873613i
$307$	−176.336			−0.574385			−0.287192	−	0.957873i	$-0.592722\pi$
$307$	−176.336			−0.574385			−0.287192	+	0.957873i	$0.592722\pi$
$308$	101.730	+	58.7338i	0.330292	+	0.190694i
$309$	−6.17209	−	171.704i	−0.0199744	−	0.555678i
$310$	159.984	+	277.101i	0.516079	+	0.893875i
$311$	106.277	−	61.3589i	0.341726	−	0.197296i	−0.319309	−	0.947651i	$-0.603451\pi$
$311$	106.277	−	61.3589i	0.341726	−	0.197296i	0.661035	+	0.750355i	$0.270117\pi$
$312$	−341.945	+	12.2916i	−1.09598	+	0.0393960i
$313$	−43.6863	+	75.6669i	−0.139573	+	0.241747i	−0.927335	−	0.374232i	$-0.877906\pi$
$313$	−43.6863	+	75.6669i	−0.139573	+	0.241747i	0.787762	+	0.615980i	$0.211240\pi$
$314$		−	103.111i		−	0.328378i
$315$	127.073	−	86.0911i	0.403407	−	0.273305i
$316$	478.086			1.51293
$317$	−367.545	−	212.202i	−1.15945	−	0.669407i	−0.208276	−	0.978070i	$-0.566785\pi$
$317$	−367.545	−	212.202i	−1.15945	−	0.669407i	−0.951172	+	0.308663i	$0.900119\pi$
$318$	−11.6373	+	7.28837i	−0.0365953	+	0.0229194i
$319$	−28.8418	−	49.9555i	−0.0904133	−	0.156600i
$320$	19.9034	−	11.4912i	0.0621982	−	0.0359102i
$321$	−195.008	+	367.665i	−0.607503	+	1.14537i
$322$	28.2235	−	48.8845i	0.0876506	−	0.151815i
$323$			69.2905i			0.214522i
$324$	261.407	−	37.8307i	0.806810	−	0.116762i
$325$	302.400			0.930460
$326$	−183.870	−	106.157i	−0.564019	−	0.325636i
$327$	−498.431	−	264.366i	−1.52426	−	0.808460i
$328$	−154.795	−	268.112i	−0.471935	−	0.817415i
$329$	−130.477	+	75.3310i	−0.396587	+	0.228970i
$330$	120.152	+	191.846i	0.364097	+	0.581351i
$331$	232.410	−	402.546i	0.702146	−	1.21615i	−0.265566	−	0.964093i	$-0.585559\pi$
$331$	232.410	−	402.546i	0.702146	−	1.21615i	0.967712	−	0.252060i	$-0.0811079\pi$
$332$		−	134.824i		−	0.406097i
$333$	−136.642	−	201.687i	−0.410335	−	0.605668i
$334$	−55.2615			−0.165454
$335$	−530.886	−	306.507i	−1.58474	−	0.914947i
$336$	−2.18883	−	60.8923i	−0.00651439	−	0.181227i
$337$	−80.8275	−	139.997i	−0.239844	−	0.415422i	0.720825	−	0.693117i	$-0.243763\pi$
$337$	−80.8275	−	139.997i	−0.239844	−	0.415422i	−0.960669	+	0.277694i	$0.910430\pi$
$338$	−122.726	+	70.8559i	−0.363095	+	0.209633i
$339$	131.897	−	4.74118i	0.389077	−	0.0139858i
$340$	50.5716	−	87.5926i	0.148740	−	0.257625i
$341$		−	786.126i		−	2.30536i
$342$	7.99989	+	111.133i	0.0233915	+	0.324949i
$343$	−18.5203			−0.0539949
$344$	−0.697611	−	0.402766i	−0.00202794	−	0.00117083i
$345$	−406.707	+	254.718i	−1.17886	+	0.738313i
$346$	9.46936	+	16.4014i	0.0273681	+	0.0474029i
$347$	486.794	−	281.050i	1.40286	−	0.809943i	0.408178	−	0.912902i	$-0.366164\pi$
$347$	486.794	−	281.050i	1.40286	−	0.809943i	0.994686	+	0.102959i	$0.0328310\pi$
$348$	−19.4197	+	36.6134i	−0.0558036	+	0.105211i
$349$	118.447	−	205.156i	0.339389	−	0.587839i	−0.644929	−	0.764243i	$-0.723113\pi$
$349$	118.447	−	205.156i	0.339389	−	0.587839i	0.984318	+	0.176403i	$0.0564463\pi$
$350$		−	37.6469i		−	0.107562i
$351$	398.211	−	291.190i	1.13450	−	0.829602i
$352$	429.837			1.22113
$353$	292.226	+	168.717i	0.827837	+	0.477952i	0.853111	−	0.521729i	$-0.174713\pi$
$353$	292.226	+	168.717i	0.827837	+	0.477952i	−0.0252745	+	0.999681i	$0.508046\pi$
$354$	60.8492	+	32.2742i	0.171890	+	0.0911701i
$355$	303.352	+	525.421i	0.854513	+	1.48006i
$356$	−72.6519	+	41.9456i	−0.204078	+	0.117825i
$357$	−20.2724	−	32.3689i	−0.0567856	−	0.0906692i
$358$	−16.0471	+	27.7944i	−0.0448243	+	0.0776380i
$359$		−	523.877i		−	1.45927i	−0.683838	−	0.729634i	$-0.739691\pi$
$359$		−	523.877i		−	1.45927i	0.683838	−	0.729634i	$-0.260309\pi$
$360$	158.087	−	325.819i	0.439131	−	0.905051i
$361$	−153.644			−0.425606
$362$	155.424	+	89.7341i	0.429348	+	0.247884i
$363$	−6.93863	−	193.029i	−0.0191147	−	0.531761i
$364$	−78.8162	−	136.514i	−0.216528	−	0.375038i
$365$	28.6129	−	16.5196i	0.0783914	−	0.0452593i
$366$	75.7393	−	2.72252i	0.206938	−	0.00743859i
$367$	−140.875	+	244.003i	−0.383856	+	0.664858i	−0.991610	−	0.129268i	$-0.958737\pi$
$367$	−140.875	+	244.003i	−0.383856	+	0.664858i	0.607754	+	0.794125i	$0.292071\pi$
$368$			190.503i			0.517670i
$369$	401.578	+	194.846i	1.08829	+	0.528038i
$370$	−150.008			−0.405428
$371$	−12.1985	−	7.04279i	−0.0328800	−	0.0189833i
$372$	−478.687	+	299.799i	−1.28679	+	0.805910i
$373$	−182.906	−	316.803i	−0.490366	−	0.849338i	0.509573	−	0.860428i	$-0.329803\pi$
$373$	−182.906	−	316.803i	−0.490366	−	0.849338i	−0.999939	+	0.0110892i	$0.996470\pi$
$374$	48.7804	−	28.1634i	0.130429	−	0.0753032i
$375$	76.5600	−	144.345i	0.204160	−	0.384920i
$376$	−177.736	+	307.848i	−0.472703	+	0.818745i
$377$			77.4070i			0.205324i
$378$	−36.2514	−	49.5748i	−0.0959032	−	0.131150i
$379$	348.614			0.919825			0.459913	−	0.887964i	$-0.347881\pi$
$379$	348.614			0.919825			0.459913	+	0.887964i	$0.347881\pi$
$380$	−262.126	−	151.339i	−0.689807	−	0.398260i
$381$	83.8322	+	44.4643i	0.220032	+	0.116704i
$382$	123.717	+	214.284i	0.323866	+	0.560952i
$383$	342.311	−	197.634i	0.893763	−	0.516014i	0.0185917	−	0.999827i	$-0.494082\pi$
$383$	342.311	−	197.634i	0.893763	−	0.516014i	0.875172	+	0.483813i	$0.160748\pi$
$384$	−205.961	−	328.857i	−0.536357	−	0.856398i
$385$	−116.103	+	201.097i	−0.301567	+	0.522330i
$386$		−	54.8316i		−	0.142051i
$387$	1.15838	−	0.0833862i	0.00299324	−	0.000215468i
$388$	−44.7546			−0.115347
$389$	−201.874	−	116.552i	−0.518957	−	0.299620i	0.217551	−	0.976049i	$-0.430193\pi$
$389$	−201.874	−	116.552i	−0.518957	−	0.299620i	−0.736508	+	0.676429i	$0.763526\pi$
$390$	−10.9121	−	303.569i	−0.0279797	−	0.778382i
$391$	59.7055	+	103.413i	0.152699	+	0.264483i
$392$	−37.8425	+	21.8484i	−0.0965370	+	0.0557357i
$393$	252.805	−	9.08734i	0.643271	−	0.0231230i
$394$	63.3902	−	109.795i	0.160889	−	0.278668i
$395$			945.068i			2.39258i
$396$	−330.815	+	224.124i	−0.835390	+	0.565971i
$397$	−433.882			−1.09290			−0.546451	−	0.837491i	$-0.684022\pi$
$397$	−433.882			−1.09290			−0.546451	+	0.837491i	$0.684022\pi$
$398$	−61.9530	−	35.7686i	−0.155661	−	0.0898708i
$399$	−96.8660	+	60.6666i	−0.242772	+	0.152047i
$400$	63.5271	+	110.032i	0.158818	+	0.275081i
$401$	−238.433	+	137.659i	−0.594596	+	0.343290i	−0.766913	−	0.641751i	$-0.778208\pi$
$401$	−238.433	+	137.659i	−0.594596	+	0.343290i	0.172317	+	0.985042i	$0.444875\pi$
$402$	−114.931	+	216.689i	−0.285898	+	0.539027i
$403$	−527.460	+	913.588i	−1.30883	+	2.26697i
$404$			509.423i			1.26095i
$405$	74.7828	+	516.742i	0.184649	+	1.27591i
$406$	9.63669			0.0237357
$407$	319.176	+	184.276i	0.784217	+	0.452768i
$408$	−79.6084	−	42.2240i	−0.195119	−	0.103490i
$409$	−0.296429	−	0.513430i	−0.000724766	−	0.00125533i	0.865663	−	0.500628i	$-0.166897\pi$
$409$	−0.296429	−	0.513430i	−0.000724766	−	0.00125533i	−0.866388	+	0.499372i	$0.833564\pi$
$410$	238.022	−	137.422i	0.580542	−	0.335176i
$411$	14.5488	+	23.2301i	0.0353987	+	0.0565208i
$412$	93.3776	−	161.735i	0.226645	−	0.392560i
$413$			70.6560i			0.171080i
$414$	107.699	+	158.967i	0.260142	+	0.383978i
$415$	266.517			0.642209
$416$	−499.530	−	288.404i	−1.20079	−	0.693279i
$417$	−13.4136	−	373.160i	−0.0321669	−	0.894867i
$418$	−84.2808	−	145.979i	−0.201629	−	0.349231i
$419$	−236.644	+	136.627i	−0.564783	+	0.326078i	−0.755063	−	0.655652i	$-0.772394\pi$
$419$	−236.644	+	136.627i	−0.564783	+	0.326078i	0.190280	+	0.981730i	$0.439060\pi$
$420$	166.729	−	5.99325i	0.396974	−	0.0142696i
$421$	346.217	−	599.666i	0.822369	−	1.42439i	−0.0815442	−	0.996670i	$-0.525985\pi$
$421$	346.217	−	599.666i	0.822369	−	1.42439i	0.903913	−	0.427716i	$-0.140681\pi$
$422$		−	234.933i		−	0.556712i
$423$	−36.7974	−	511.181i	−0.0869915	−	1.20847i
$424$	−33.2336			−0.0783810
$425$	68.9704	+	39.8201i	0.162283	+	0.0936943i
$426$	205.738	−	128.852i	0.482953	−	0.302470i
$427$	38.8720	+	67.3282i	0.0910350	+	0.157677i
$428$	−391.763	+	226.184i	−0.915334	+	0.528468i
$429$	−349.699	+	659.316i	−0.815149	+	1.53687i
$430$	0.357564	−	0.619319i	0.000831545	−	0.00144028i
$431$			72.4993i			0.168212i	0.996457	+	0.0841059i	$0.0268034\pi$
$431$			72.4993i			0.168212i	−0.996457	+	0.0841059i	$0.973197\pi$
$432$	189.609	+	83.7222i	0.438909	+	0.193801i
$433$	631.250			1.45785			0.728926	−	0.684593i	$-0.240020\pi$
$433$	631.250			1.45785			0.728926	+	0.684593i	$0.240020\pi$
$434$	113.736	+	65.6655i	0.262065	+	0.151303i
$435$	−72.3765	−	38.3883i	−0.166383	−	0.0882489i
$436$	−306.631	−	531.100i	−0.703281	−	1.21812i
$437$	309.470	−	178.672i	0.708168	−	0.408861i
$438$	−7.01692	−	11.2039i	−0.0160204	−	0.0255796i
$439$	51.1350	−	88.5683i	0.116481	−	0.201750i	−0.801890	−	0.597472i	$-0.796172\pi$
$439$	51.1350	−	88.5683i	0.116481	−	0.201750i	0.918371	+	0.395721i	$0.129505\pi$
$440$			547.870i			1.24516i
$441$	27.5014	−	56.6805i	0.0623614	−	0.128527i
$442$	−75.5862			−0.171010
$443$	351.260	+	202.800i	0.792912	+	0.457788i	0.840987	−	0.541056i	$-0.181975\pi$
$443$	351.260	+	202.800i	0.792912	+	0.457788i	−0.0480746	+	0.998844i	$0.515309\pi$
$444$	−9.51233	−	264.628i	−0.0214242	−	0.596010i
$445$	−82.9170	−	143.616i	−0.186330	−	0.322733i
$446$	−105.735	+	61.0462i	−0.237074	+	0.136875i
$447$	43.4143	−	1.56057i	0.0971238	−	0.00349121i
$448$	4.71658	−	8.16935i	0.0105281	−	0.0182352i
$449$			540.146i			1.20300i	0.798874	+	0.601499i	$0.205430\pi$
$449$			540.146i			1.20300i	−0.798874	+	0.601499i	$0.794570\pi$
$450$	115.217	+	55.9031i	0.256037	+	0.124229i
$451$	−675.261			−1.49725
$452$	124.239	+	71.7294i	0.274865	+	0.158693i
$453$	−40.8839	+	25.6053i	−0.0902514	+	0.0565239i
$454$	94.7289	+	164.075i	0.208654	+	0.361399i
$455$	269.857	−	155.802i	0.593092	−	0.342422i
$456$	−126.358	+	238.233i	−0.277101	+	0.522441i
$457$	−50.5988	+	87.6397i	−0.110719	+	0.191772i	−0.916061	−	0.401040i	$-0.868649\pi$
$457$	−50.5988	+	87.6397i	−0.110719	+	0.191772i	0.805341	+	0.592812i	$0.201982\pi$
$458$		−	109.764i		−	0.239660i
$459$	129.167	−	13.9773i	0.281409	−	0.0304516i
$460$	−521.615			−1.13395
$461$	−630.815	−	364.201i	−1.36836	−	0.790024i	−0.377642	−	0.925951i	$-0.623265\pi$
$461$	−630.815	−	364.201i	−1.36836	−	0.790024i	−0.990719	+	0.135928i	$0.956598\pi$
$462$	82.0807	+	43.5353i	0.177664	+	0.0942323i
$463$	113.194	+	196.057i	0.244479	+	0.423450i	0.961985	−	0.273102i	$-0.0880497\pi$
$463$	113.194	+	196.057i	0.244479	+	0.423450i	−0.717506	+	0.696552i	$0.754716\pi$
$464$	−28.1656	+	16.2614i	−0.0607017	+	0.0350462i
$465$	−592.634	−	946.255i	−1.27448	−	2.03496i
$466$	18.2412	−	31.5947i	0.0391442	−	0.0677998i
$467$			67.6972i			0.144962i	0.997370	+	0.0724810i	$0.0230917\pi$
$467$			67.6972i			0.144962i	−0.997370	+	0.0724810i	$0.976908\pi$
$468$	534.831	−	38.4998i	1.14280	−	0.0822646i
$469$	−251.612			−0.536485
$470$	−273.299	−	157.789i	−0.581487	−	0.335722i
$471$	12.9251	+	359.569i	0.0274417	+	0.763416i
$472$	83.3529	+	144.372i	0.176595	+	0.305872i
$473$	−1.52160	+	0.878494i	−0.00321690	+	0.00185728i
$474$	377.901	−	13.5840i	0.797259	−	0.0286583i
$475$	119.164	−	206.398i	0.250872	−	0.434523i
$476$		−	41.5142i		−	0.0872147i
$477$	39.6681	−	26.8748i	0.0831616	−	0.0563413i
$478$	−312.892			−0.654586
$479$	−37.6979	−	21.7649i	−0.0787013	−	0.0454382i	0.460133	−	0.887850i	$-0.347802\pi$
$479$	−37.6979	−	21.7649i	−0.0787013	−	0.0454382i	−0.538834	+	0.842412i	$0.681135\pi$
$480$	517.392	−	324.040i	1.07790	−	0.675082i
$481$	−247.285	−	428.310i	−0.514106	−	0.890457i
$482$	−90.5380	+	52.2721i	−0.187838	+	0.108448i
$483$	−92.2934	+	174.008i	−0.191084	+	0.360266i
$484$	104.975	−	181.821i	0.216890	−	0.375664i
$485$		−	88.4697i		−	0.182412i
$486$	205.552	−	37.3305i	0.422948	−	0.0768118i
$487$	760.496			1.56159			0.780797	−	0.624785i	$-0.214813\pi$
$487$	760.496			1.56159			0.780797	+	0.624785i	$0.214813\pi$
$488$	158.854	+	91.7146i	0.325521	+	0.187940i
$489$	654.500	+	347.145i	1.33845	+	0.709908i
$490$	−19.3964	−	33.5955i	−0.0395844	−	0.0685622i
$491$	−225.908	+	130.428i	−0.460098	+	0.265637i	−0.712085	−	0.702093i	$-0.752249\pi$
$491$	−225.908	+	130.428i	−0.460098	+	0.265637i	0.251988	+	0.967730i	$0.418916\pi$
$492$	257.519	+	411.179i	0.523412	+	0.835730i
$493$	−10.1930	+	17.6548i	−0.0206754	+	0.0358109i
$494$			226.197i			0.457888i
$495$	−443.043	−	653.946i	−0.895037	−	1.32110i
$496$	−443.229			−0.893606
$497$	215.659	+	124.511i	0.433921	+	0.250525i
$498$	−3.83080	−	106.571i	−0.00769237	−	0.213998i
$499$	42.8559	+	74.2287i	0.0858836	+	0.148755i	0.905767	−	0.423775i	$-0.139295\pi$
$499$	42.8559	+	74.2287i	0.0858836	+	0.148755i	−0.819884	+	0.572530i	$0.805962\pi$
$500$	153.805	−	88.7996i	0.307611	−	0.177599i
$501$	192.708	−	6.92709i	0.384647	−	0.0138265i
$502$	−91.3186	+	158.168i	−0.181910	+	0.315077i
$503$			120.281i			0.239127i	0.992827	+	0.119564i	$0.0381495\pi$
$503$			120.281i			0.239127i	−0.992827	+	0.119564i	$0.961850\pi$
$504$	−10.6724	−	148.259i	−0.0211754	−	0.294164i
$505$	−1007.01			−1.99409
$506$	−251.570	−	145.244i	−0.497174	−	0.287044i
$507$	419.089	−	262.473i	0.826606	−	0.517698i
$508$	51.5728	+	89.3267i	0.101521	+	0.175840i
$509$	719.180	−	415.219i	1.41293	−	0.815754i	0.417265	−	0.908785i	$-0.362989\pi$
$509$	719.180	−	415.219i	1.41293	−	0.815754i	0.995663	+	0.0930306i	$0.0296554\pi$
$510$	37.4853	−	70.6740i	0.0735005	−	0.138577i
$511$	6.78048	−	11.7441i	0.0132690	−	0.0229827i
$512$		−	434.031i		−	0.847717i
$513$	−41.8279	−	386.540i	−0.0815358	−	0.753489i
$514$	−415.279			−0.807936
$515$	319.713	+	184.586i	0.620802	+	0.358420i
$516$	1.11521	+	0.591503i	0.00216126	+	0.00114632i
$517$	387.670	+	671.463i	0.749845	+	1.29877i
$518$	−53.3219	+	30.7854i	−0.102938	+	0.0594313i
$519$	−35.0776	−	56.0082i	−0.0675868	−	0.107916i
$520$	367.599	−	636.701i	0.706922	−	1.22442i
$521$		−	453.371i		−	0.870194i	−0.900384	−	0.435097i	$-0.856714\pi$
$521$		−	453.371i		−	0.870194i	0.900384	−	0.435097i	$-0.143286\pi$
$522$	−14.3099	+	29.4927i	−0.0274135	+	0.0564994i
$523$	154.051			0.294553			0.147277	−	0.989095i	$-0.452949\pi$
$523$	154.051			0.294553			0.147277	+	0.989095i	$0.452949\pi$
$524$	238.127	+	137.483i	0.454441	+	0.262371i
$525$	4.71908	+	131.282i	0.00898873	+	0.250062i
$526$	−20.9568	−	36.2982i	−0.0398418	−	0.0690080i
$527$	−240.603	+	138.912i	−0.456553	+	0.263591i
$528$	−313.365	+	11.2642i	−0.593494	+	0.0213337i
$529$	43.4125	−	75.1926i	0.0820652	−	0.142141i
$530$		−	29.5038i		−	0.0556676i
$531$	−216.240	−	104.919i	−0.407231	−	0.197588i
$532$	−124.234			−0.233522
$533$	784.747	+	453.074i	1.47232	+	0.850045i
$534$	−56.2355	+	35.2200i	−0.105310	+	0.0659550i
$535$	−447.115	−	774.426i	−0.835730	−	1.44753i
$536$	−514.119	+	296.827i	−0.959177	+	0.553781i
$537$	52.4756	−	98.9364i	0.0977199	−	0.184239i
$538$	−133.794	+	231.738i	−0.248687	+	0.430739i
$539$			95.3092i			0.176826i
$540$	−229.240	+	519.167i	−0.424518	+	0.961420i
$541$	375.368			0.693842			0.346921	−	0.937894i	$-0.387227\pi$
$541$	375.368			0.693842			0.346921	+	0.937894i	$0.387227\pi$
$542$	182.264	+	105.230i	0.336280	+	0.194151i
$543$	−553.244	−	293.439i	−1.01887	−	0.540403i
$544$	−75.9543	−	131.557i	−0.139622	−	0.241832i
$545$	1049.86	−	606.139i	1.92636	−	1.11218i
$546$	−66.1787	−	105.667i	−0.121206	−	0.193530i
$547$	−11.7034	+	20.2709i	−0.0213957	+	0.0370584i	−0.876525	−	0.481356i	$-0.840144\pi$
$547$	−11.7034	+	20.2709i	−0.0213957	+	0.0370584i	0.855129	+	0.518415i	$0.173478\pi$
$548$			29.7933i			0.0543674i
$549$	−263.777	+	18.9880i	−0.480469	+	0.0345866i
$550$	−193.739			−0.352252
$551$	52.8330	+	30.5031i	0.0958856	+	0.0553596i
$552$	16.6944	+	464.430i	0.0302435	+	0.841359i
$553$	193.951	+	335.934i	0.350726	+	0.607475i
$554$	218.131	−	125.938i	0.393739	−	0.227325i
$555$	523.110	−	18.8037i	0.942541	−	0.0338806i
$556$	202.935	−	351.493i	0.364990	−	0.632182i
$557$			1073.51i			1.92731i	0.267147	+	0.963656i	$0.413919\pi$
$557$			1073.51i			1.92731i	−0.267147	+	0.963656i	$0.586081\pi$
$558$	−369.857	+	250.575i	−0.662826	+	0.449060i
$559$	2.35774			0.00421778
$560$	113.381	+	65.4607i	0.202467	+	0.116894i
$561$	−166.577	+	104.326i	−0.296929	+	0.185965i
$562$	−177.536	−	307.501i	−0.315900	−	0.547156i
$563$	−428.903	+	247.627i	−0.761817	+	0.439835i	−0.829948	−	0.557841i	$-0.811630\pi$
$563$	−428.903	+	247.627i	−0.761817	+	0.439835i	0.0681310	+	0.997676i	$0.478296\pi$
$564$	261.024	−	492.130i	0.462808	−	0.872570i
$565$	−141.793	+	245.592i	−0.250961	+	0.434676i
$566$		−	49.7342i		−	0.0878697i
$567$	132.630	+	168.334i	0.233916	+	0.296884i
$568$	587.542			1.03440
$569$	−831.331	−	479.969i	−1.46104	−	0.843531i	−0.461979	−	0.886891i	$-0.652861\pi$
$569$	−831.331	−	479.969i	−1.46104	−	0.843531i	−0.999060	+	0.0433594i	$0.986194\pi$
$570$	−211.497	−	112.177i	−0.371047	−	0.196802i
$571$	−145.853	−	252.625i	−0.255434	−	0.442425i	0.709579	−	0.704626i	$-0.248885\pi$
$571$	−145.853	−	252.625i	−0.255434	−	0.442425i	−0.965013	+	0.262200i	$0.915552\pi$
$572$	−702.529	+	405.605i	−1.22820	+	0.709100i
$573$	−458.287	−	731.744i	−0.799802	−	1.27704i
$574$	56.4049	−	97.6962i	0.0982664	−	0.170202i
$575$		−	410.720i		−	0.714295i
$576$	17.9981	+	26.5658i	0.0312468	+	0.0461212i
$577$	347.015			0.601413			0.300706	−	0.953717i	$-0.402778\pi$
$577$	347.015			0.601413			0.300706	+	0.953717i	$0.402778\pi$
$578$	197.935	+	114.278i	0.342449	+	0.197713i
$579$	6.87321	+	191.209i	0.0118708	+	0.330241i
$580$	−44.5254	−	77.1202i	−0.0767679	−	0.132966i
$581$	94.7360	−	54.6958i	0.163057	−	0.0941408i
$582$	−35.3760	+	1.27163i	−0.0607835	+	0.00218492i
$583$	−36.2437	+	62.7759i	−0.0621676	+	0.107677i
$584$		−	31.9958i		−	0.0547873i
$585$	76.1055	+	1057.24i	0.130095	+	1.80725i
$586$	485.282			0.828126
$587$	−623.671	−	360.076i	−1.06247	−	0.613418i	−0.136357	−	0.990660i	$-0.543539\pi$
$587$	−623.671	−	360.076i	−1.06247	−	0.613418i	−0.926115	+	0.377242i	$0.876873\pi$
$588$	58.0355	−	36.3473i	0.0986999	−	0.0618151i
$589$	415.704	+	720.020i	0.705779	+	1.22245i
$590$	−128.169	+	73.9983i	−0.217235	+	0.125421i
$591$	−207.292	+	390.825i	−0.350748	+	0.661294i
$592$	103.898	−	179.956i	0.175503	−	0.303980i
$593$		−	294.452i		−	0.496546i	−0.968690	−	0.248273i	$-0.920137\pi$
$593$		−	294.452i		−	0.496546i	0.968690	−	0.248273i	$-0.0798631\pi$
$594$	−255.123	+	186.557i	−0.429499	+	0.314070i
$595$	82.0642			0.137923
$596$	40.8936	+	23.6099i	0.0686134	+	0.0396140i
$597$	220.527	+	116.967i	0.369391	+	0.195924i
$598$	194.906	+	337.588i	0.325930	+	0.564528i
$599$	−211.271	+	121.977i	−0.352706	+	0.203635i	−0.665877	−	0.746062i	$-0.731942\pi$
$599$	−211.271	+	121.977i	−0.352706	+	0.203635i	0.313170	+	0.949697i	$0.398609\pi$
$600$	164.517	+	262.683i	0.274194	+	0.437805i
$601$	−117.398	+	203.339i	−0.195337	+	0.338334i	−0.947011	−	0.321201i	$-0.895913\pi$
$601$	−117.398	+	203.339i	−0.195337	+	0.338334i	0.751674	+	0.659535i	$0.229247\pi$
$602$		−	0.293524i		−	0.000487582i
$603$	373.627	−	770.047i	0.619613	−	1.27703i
$604$	−52.4350			−0.0868128
$605$	359.420	+	207.511i	0.594082	+	0.342994i
$606$	14.4744	+	402.671i	0.0238851	+	0.664473i
$607$	−41.8661	−	72.5141i	−0.0689721	−	0.119463i	0.829477	−	0.558541i	$-0.188639\pi$
$607$	−41.8661	−	72.5141i	−0.0689721	−	0.119463i	−0.898449	+	0.439078i	$0.855305\pi$
$608$	−393.692	+	227.298i	−0.647519	+	0.373845i
$609$	−33.6051	+	1.20797i	−0.0551809	+	0.00198353i
$610$	−81.4216	+	141.026i	−0.133478	+	0.231191i
$611$		−	1040.45i		−	1.70286i
$612$	127.052	+	61.6459i	0.207602	+	0.100729i
$613$	−195.300			−0.318596			−0.159298	−	0.987231i	$-0.550923\pi$
$613$	−195.300			−0.318596			−0.159298	+	0.987231i	$0.550923\pi$
$614$	−131.291	−	75.8008i	−0.213829	−	0.123454i
$615$	−812.808	+	509.057i	−1.32164	+	0.827734i
$616$	112.436	+	194.746i	0.182527	+	0.316145i
$617$	−398.406	+	230.020i	−0.645715	+	0.372804i	−0.786813	−	0.617192i	$-0.788270\pi$
$617$	−398.406	+	230.020i	−0.645715	+	0.372804i	0.141098	+	0.989996i	$0.454937\pi$
$618$	69.2144	−	130.496i	0.111997	−	0.211158i
$619$	−507.446	+	878.921i	−0.819783	+	1.41991i	0.0860595	+	0.996290i	$0.472572\pi$
$619$	−507.446	+	878.921i	−0.819783	+	1.41991i	−0.905842	+	0.423615i	$0.860761\pi$
$620$		−	1213.60i		−	1.95743i
$621$	−395.495	−	540.851i	−0.636869	−	0.870936i
$622$	105.504			0.169621
$623$	−58.9473	−	34.0332i	−0.0946184	−	0.0546280i
$624$	371.731	+	197.165i	0.595723	+	0.315970i
$625$	382.421	+	662.372i	0.611873	+	1.05980i
$626$	−65.0532	+	37.5585i	−0.103919	+	0.0599976i
$627$	312.203	+	498.493i	0.497932	+	0.795045i
$628$	−195.544	+	338.691i	−0.311375	+	0.539318i
$629$		−	130.250i		−	0.207075i
$630$	131.620	−	9.47466i	0.208920	−	0.0150391i
$631$	250.996			0.397775			0.198887	−	0.980022i	$-0.436267\pi$
$631$	250.996			0.397775			0.198887	+	0.980022i	$0.436267\pi$
$632$	792.603	+	457.609i	1.25412	+	0.724065i
$633$	29.4491	+	819.259i	0.0465230	+	1.29425i
$634$	−182.437	−	315.990i	−0.287755	−	0.498407i
$635$	−176.579	+	101.948i	−0.278077	+	0.160548i
$636$	52.0474	−	1.87090i	0.0818355	−	0.00294166i
$637$	63.9488	−	110.763i	0.100391	−	0.173882i
$638$		−	49.5925i		−	0.0777311i
$639$	−701.299	+	475.125i	−1.09749	+	0.743544i
$640$	833.743			1.30272
$641$	4.46525	+	2.57802i	0.00696607	+	0.00402187i	0.503479	−	0.864007i	$-0.332053\pi$
$641$	4.46525	+	2.57802i	0.00696607	+	0.00402187i	−0.496513	+	0.868029i	$0.665386\pi$
$642$	−303.240	+	189.918i	−0.472337	+	0.295822i
$643$	−426.952	−	739.502i	−0.664000	−	1.15008i	−0.979555	−	0.201174i	$-0.935524\pi$
$643$	−426.952	−	739.502i	−0.664000	−	1.15008i	0.315556	−	0.948907i	$-0.397809\pi$
$644$	−185.413	+	107.048i	−0.287909	+	0.166224i
$645$	−1.16927	+	2.20452i	−0.00181282	+	0.00341786i
$646$	−29.7856	+	51.5902i	−0.0461078	+	0.0798611i
$647$		−	1008.87i		−	1.55930i	−0.626217	−	0.779649i	$-0.715398\pi$
$647$		−	1008.87i		−	1.55930i	0.626217	−	0.779649i	$-0.284602\pi$
$648$	469.587	+	187.492i	0.724672	+	0.289340i
$649$	363.611			0.560263
$650$	225.152	+	129.991i	0.346387	+	0.199987i
$651$	−404.853	−	214.732i	−0.621893	−	0.329850i
$652$	402.643	+	697.398i	0.617550	+	1.06963i
$653$	−689.028	+	397.810i	−1.05517	+	0.609204i	−0.924093	−	0.382168i	$-0.875178\pi$
$653$	−689.028	+	397.810i	−1.05517	+	0.609204i	−0.131080	+	0.991372i	$0.541844\pi$
$654$	−257.465	−	411.093i	−0.393677	−	0.628582i
$655$	−271.772	+	470.723i	−0.414919	+	0.718661i
$656$			380.721i			0.580368i
$657$	25.8739	+	38.1906i	0.0393818	+	0.0581288i
$658$	−129.529			−0.196853
$659$	−446.049	−	257.526i	−0.676857	−	0.390784i	0.121813	−	0.992553i	$-0.461129\pi$
$659$	−446.049	−	257.526i	−0.676857	−	0.390784i	−0.798670	+	0.601769i	$0.794463\pi$
$660$	−30.8425	−	858.024i	−0.0467311	−	1.30004i
$661$	302.407	+	523.784i	0.457499	+	0.792411i	0.998828	−	0.0483995i	$-0.0154120\pi$
$661$	302.407	+	523.784i	0.457499	+	0.792411i	−0.541329	+	0.840811i	$0.682079\pi$
$662$	346.082	−	199.810i	0.522782	−	0.301829i
$663$	263.585	−	9.47482i	0.397564	−	0.0142908i
$664$	129.049	−	223.520i	0.194352	−	0.336627i
$665$		−	245.582i		−	0.369297i
$666$	−15.0379	−	208.904i	−0.0225795	−	0.313669i
$667$	105.134			0.157623
$668$	181.519	+	104.800i	0.271735	+	0.156886i
$669$	361.068	−	226.135i	0.539713	−	0.338019i
$670$	−263.514	−	456.420i	−0.393305	−	0.681224i
$671$	346.485	−	200.043i	0.516372	−	0.298127i
$672$	117.411	−	221.365i	0.174719	−	0.329412i
$673$	112.242	−	194.409i	0.166779	−	0.288869i	−0.770507	−	0.637432i	$-0.779997\pi$
$673$	112.242	−	194.409i	0.166779	−	0.288869i	0.937286	+	0.348563i	$0.113330\pi$
$674$		−	138.980i		−	0.206202i
$675$	−408.792	−	180.503i	−0.605618	−	0.267412i
$676$	537.496			0.795112
$677$	−892.200	−	515.112i	−1.31787	−	0.760874i	−0.334487	−	0.942400i	$-0.608563\pi$
$677$	−892.200	−	515.112i	−1.31787	−	0.760874i	−0.983386	+	0.181526i	$0.941896\pi$
$678$	100.242	+	53.1681i	0.147850	+	0.0784190i
$679$	−18.1562	−	31.4474i	−0.0267396	−	0.0463143i
$680$	167.682	−	96.8112i	0.246591	−	0.142369i
$681$	−350.906	−	560.290i	−0.515281	−	0.822746i
$682$	337.929	−	585.310i	0.495497	−	0.858226i
$683$		−	785.892i		−	1.15065i	−0.817926	−	0.575323i	$-0.804876\pi$
$683$		−	785.892i		−	1.15065i	0.817926	−	0.575323i	$-0.195124\pi$
$684$	184.479	−	380.212i	0.269706	−	0.555866i
$685$	−58.8947			−0.0859776
$686$	−13.7893	−	7.96123i	−0.0201009	−	0.0116053i
$687$	13.7591	+	382.771i	0.0200278	+	0.557164i
$688$	0.495307	+	0.857896i	0.000719923	+	0.00124694i
$689$	84.2405	−	48.6363i	0.122265	−	0.0705896i
$690$	−412.308	+	14.8208i	−0.597548	+	0.0214795i
$691$	355.528	−	615.792i	0.514512	−	0.891161i	−0.485346	−	0.874322i	$-0.661306\pi$
$691$	355.528	−	615.792i	0.514512	−	0.891161i	0.999858	−	0.0168390i	$-0.00536029\pi$
$692$		−	71.8323i		−	0.103804i
$693$	−291.690	−	141.528i	−0.420909	−	0.204225i
$694$	483.256			0.696334
$695$	694.822	+	401.156i	0.999744	+	0.577203i
$696$	−67.2404	+	42.1123i	−0.0966098	+	0.0605062i
$697$	119.322	+	206.672i	0.171194	+	0.296516i
$698$	176.379	−	101.832i	0.252692	−	0.145892i
$699$	−59.6505	+	112.464i	−0.0853369	+	0.160893i
$700$	−71.3951	+	123.660i	−0.101993	+	0.176657i
$701$			563.991i			0.804552i	0.915518	+	0.402276i	$0.131781\pi$
$701$			563.991i			0.804552i	−0.915518	+	0.402276i	$0.868219\pi$
$702$	421.661	−	45.6283i	0.600656	−	0.0649976i
$703$	−389.782			−0.554455
$704$	−42.0412	−	24.2725i	−0.0597177	−	0.0344780i
$705$	972.829	+	515.985i	1.37990	+	0.731894i
$706$	145.051	+	251.236i	0.205455	+	0.355859i
$707$	−357.953	+	206.664i	−0.506298	+	0.292311i
$708$	−138.667	−	221.409i	−0.195858	−	0.312725i
$709$	−405.913	+	703.063i	−0.572515	+	0.991626i	0.423791	+	0.905760i	$0.360699\pi$
$709$	−405.913	+	703.063i	−0.572515	+	0.991626i	−0.996307	+	0.0858659i	$0.972634\pi$
$710$			521.603i			0.734652i
$711$	−1316.12	+	94.7406i	−1.85108	+	0.133250i
$712$	−160.596			−0.225556
$713$	1240.84	+	716.398i	1.74030	+	1.00477i
$714$	−1.17956	−	32.8147i	−0.00165204	−	0.0459589i
$715$	−801.790	−	1388.74i	−1.12138	−	1.94229i
$716$	105.421	−	60.8648i	0.147236	−	0.0850067i
$717$	1091.12	−	39.2214i	1.52179	−	0.0547021i
$718$	225.197	−	390.052i	0.313645	−	0.543248i
$719$		−	143.068i		−	0.198983i	−0.995038	−	0.0994913i	$-0.968278\pi$
$719$		−	143.068i		−	0.198983i	0.995038	−	0.0994913i	$-0.0317215\pi$
$720$	−368.703	+	249.794i	−0.512088	+	0.346936i
$721$	151.527			0.210162
$722$	−114.395	−	66.0462i	−0.158442	−	0.0914767i
$723$	309.172	−	193.633i	0.427624	−	0.267819i
$724$	−340.351	−	589.505i	−0.470098	−	0.814234i
$725$	60.7244	−	35.0593i	0.0837578	−	0.0483576i
$726$	77.8105	−	146.702i	0.107177	−	0.202069i
$727$	413.878	−	716.857i	0.569295	−	0.986049i	−0.427340	−	0.904091i	$-0.640549\pi$
$727$	413.878	−	716.857i	0.569295	−	0.986049i	0.996636	−	0.0819578i	$-0.0261173\pi$
$728$		−	301.762i		−	0.414508i
$729$	−712.125	+	155.946i	−0.976852	+	0.213917i
$730$	28.4049			0.0389109
$731$	0.537747	+	0.310468i	0.000735632	+	0.000424717i
$732$	−253.946	−	134.692i	−0.346921	−	0.184006i
$733$	479.236	+	830.062i	0.653801	+	1.13242i	0.982193	+	0.187875i	$0.0601601\pi$
$733$	479.236	+	830.062i	0.653801	+	1.13242i	−0.328392	+	0.944542i	$0.606507\pi$
$734$	−209.777	+	121.115i	−0.285800	+	0.165007i
$735$	71.8504	+	114.723i	0.0977556	+	0.156086i
$736$	−391.711	+	678.463i	−0.532216	+	0.921825i
$737$			1294.85i			1.75692i
$738$	215.237	+	317.697i	0.291650	+	0.430484i
$739$	−912.717			−1.23507			−0.617535	−	0.786543i	$-0.711869\pi$
$739$	−912.717			−1.23507			−0.617535	+	0.786543i	$0.711869\pi$
$740$	492.737	+	284.482i	0.665861	+	0.384435i
$741$	−28.3540	−	788.794i	−0.0382645	−	1.06450i
$742$	−6.05491	−	10.4874i	−0.00816026	−	0.0141340i
$743$	841.128	−	485.625i	1.13207	−	0.653601i	0.187615	−	0.982243i	$-0.439924\pi$
$743$	841.128	−	485.625i	1.13207	−	0.653601i	0.944455	+	0.328642i	$0.106591\pi$
$744$	−1080.56	+	38.8417i	−1.45236	+	0.0522066i
$745$	−46.6715	+	80.8374i	−0.0626463	+	0.108507i
$746$		−	314.501i		−	0.421583i
$747$	26.7176	+	371.155i	0.0357665	+	0.496861i
$748$	−213.641			−0.285616
$749$	−317.863	−	183.518i	−0.424383	−	0.245018i
$750$	119.052	−	74.5613i	0.158736	−	0.0994151i
$751$	125.398	+	217.196i	0.166975	+	0.289210i	0.937355	−	0.348376i	$-0.113267\pi$
$751$	125.398	+	217.196i	0.166975	+	0.289210i	−0.770380	+	0.637585i	$0.779933\pi$
$752$	378.580	−	218.573i	0.503431	−	0.290656i
$753$	298.620	−	563.013i	0.396574	−	0.747693i
$754$	−33.2746	+	57.6333i	−0.0441308	+	0.0764368i
$755$		−	103.652i		−	0.137287i
$756$	25.0604	+	231.589i	0.0331487	+	0.306334i
$757$	−1180.28			−1.55916			−0.779580	−	0.626302i	$-0.784568\pi$
$757$	−1180.28			−1.55916			−0.779580	+	0.626302i	$0.784568\pi$
$758$	259.560	+	149.857i	0.342428	+	0.197701i
$759$	895.484	+	474.962i	1.17982	+	0.625773i
$760$	−289.714	−	501.799i	−0.381202	−	0.660262i
$761$	−194.712	+	112.417i	−0.255863	+	0.147723i	−0.622446	−	0.782663i	$-0.713861\pi$
$761$	−194.712	+	112.417i	−0.255863	+	0.147723i	0.366583	+	0.930385i	$0.380528\pi$
$762$	43.3035	+	69.1425i	0.0568288	+	0.0907382i
$763$	248.790	−	430.916i	0.326068	−	0.564766i
$764$		−	938.486i		−	1.22838i
$765$	−121.860	+	251.154i	−0.159294	+	0.328306i
$766$	339.824			0.443634
$767$	−422.566	−	243.969i	−0.550934	−	0.318082i
$768$	−10.4469	−	290.629i	−0.0136028	−	0.378423i
$769$	−138.770	−	240.357i	−0.180455	−	0.312557i	0.761581	−	0.648070i	$-0.224424\pi$
$769$	−138.770	−	240.357i	−0.180455	−	0.312557i	−0.942036	+	0.335513i	$0.891090\pi$
$770$	−172.890	+	99.8178i	−0.224532	+	0.129634i
$771$	1448.16	−	52.0557i	1.87829	−	0.0675171i
$772$	−103.985	+	180.107i	−0.134696	+	0.233300i
$773$		−	34.8511i		−	0.0450855i	−0.999746	−	0.0225428i	$-0.992824\pi$
$773$		−	34.8511i		−	0.0450855i	0.999746	−	0.0225428i	$-0.00717619\pi$
$774$	0.898318	+	0.435864i	0.00116062	+	0.000563132i
$775$	955.592			1.23302
$776$	−74.1971	−	42.8377i	−0.0956148	−	0.0552032i
$777$	182.086	−	114.039i	0.234344	−	0.146769i
$778$	−100.204	−	173.558i	−0.128796	−	0.223082i
$779$	618.478	−	357.078i	0.793938	−	0.458381i
$780$	−539.857	+	1017.84i	−0.692125	+	1.30492i
$781$	640.759	−	1109.83i	0.820434	−	1.42103i
$782$			102.661i			0.131280i
$783$	46.2045	−	104.641i	0.0590096	−	0.133641i
$784$	53.7366			0.0685416
$785$	−669.516	−	386.545i	−0.852887	−	0.492415i
$786$	192.132	+	101.906i	0.244443	+	0.129652i
$787$	97.1676	+	168.299i	0.123466	+	0.213849i	0.921132	−	0.389250i	$-0.127266\pi$
$787$	97.1676	+	168.299i	0.123466	+	0.213849i	−0.797666	+	0.603099i	$0.793932\pi$
$788$	−416.440	+	240.432i	−0.528477	+	0.305116i
$789$	77.6307	+	123.953i	0.0983913	+	0.157101i
$790$	−406.252	+	703.650i	−0.514244	+	0.890696i
$791$			116.398i			0.147152i
$792$	−762.971	+	54.9225i	−0.963347	+	0.0693466i
$793$	−536.886			−0.677031
$794$	−323.047	−	186.511i	−0.406860	−	0.234901i
$795$	3.69834	+	102.886i	0.00465200	+	0.129416i
$796$	135.666	+	234.980i	0.170435	+	0.295202i
$797$	−386.180	+	222.961i	−0.484542	+	0.279750i	−0.722307	−	0.691572i	$-0.756918\pi$
$797$	−386.180	+	222.961i	−0.484542	+	0.279750i	0.237765	+	0.971323i	$0.423585\pi$
$798$	−98.2000	+	3.52990i	−0.123058	+	0.00442343i
$799$	137.006	−	237.302i	0.171472	−	0.296998i
$800$			522.497i			0.653121i
$801$	191.690	−	129.869i	0.239313	−	0.162133i
$802$	−236.700			−0.295138
$803$	−60.4379	−	34.8938i	−0.0752651	−	0.0434543i
$804$	788.456	−	493.805i	0.980667	−	0.614186i
$805$	−211.610	−	366.520i	−0.262870	−	0.455304i
$806$	−785.441	+	453.474i	−0.974492	+	0.562623i
$807$	437.518	−	824.889i	0.542154	−	1.02217i
$808$	−487.604	+	844.555i	−0.603470	+	1.04524i
$809$			1022.47i			1.26387i	0.775021	+	0.631935i	$0.217739\pi$
$809$			1022.47i			1.26387i	−0.775021	+	0.631935i	$0.782261\pi$
$810$	−166.450	+	416.886i	−0.205494	+	0.514674i
$811$	−452.827			−0.558357			−0.279178	−	0.960239i	$-0.590062\pi$
$811$	−452.827			−0.558357			−0.279178	+	0.960239i	$0.590062\pi$
$812$	−31.6540	−	18.2754i	−0.0389827	−	0.0225067i
$813$	−648.782	−	344.112i	−0.798010	−	0.423262i
$814$	158.428	+	274.406i	0.194629	+	0.337108i
$815$	−1378.60	+	795.934i	−1.69153	+	0.976606i
$816$	58.8206	+	93.9185i	0.0720841	+	0.115096i
$817$	0.929096	−	1.60924i	0.00113720	−	0.00196970i
$818$		−	0.509699i		−	0.000623104i
$819$	244.024	+	360.188i	0.297954	+	0.439790i
$820$	−1042.45			−1.27128
$821$	603.157	+	348.233i	0.734661	+	0.424157i	0.820125	−	0.572184i	$-0.193904\pi$
$821$	603.157	+	348.233i	0.734661	+	0.424157i	−0.0854637	+	0.996341i	$0.527237\pi$
$822$	0.846528	+	23.5500i	0.00102984	+	0.0286496i
$823$	534.992	+	926.634i	0.650051	+	1.12592i	0.983110	+	0.183016i	$0.0585860\pi$
$823$	534.992	+	926.634i	0.650051	+	1.12592i	−0.333058	+	0.942906i	$0.608081\pi$
$824$	309.615	−	178.756i	0.375747	−	0.216937i
$825$	675.608	−	24.2854i	0.818919	−	0.0294368i
$826$	−30.3726	+	52.6069i	−0.0367707	+	0.0636887i
$827$			1005.45i			1.21577i	0.794023	+	0.607887i	$0.207983\pi$
$827$			1005.45i			1.21577i	−0.794023	+	0.607887i	$0.792017\pi$
$828$	−52.2906	−	726.409i	−0.0631528	−	0.877305i
$829$	−16.7192			−0.0201679			−0.0100840	−	0.999949i	$-0.503210\pi$
$829$	−16.7192			−0.0201679			−0.0100840	+	0.999949i	$0.503210\pi$
$830$	198.435	+	114.566i	0.239078	+	0.138032i
$831$	−744.883	+	466.516i	−0.896370	+	0.561391i
$832$	32.5718	+	56.4161i	0.0391488	+	0.0678078i
$833$	29.1705	−	16.8416i	0.0350186	−	0.0202180i
$834$	150.421	−	283.602i	0.180362	−	0.340050i
$835$	−207.166	+	358.822i	−0.248103	+	0.429727i
$836$			639.334i			0.764754i
$837$	1258.36	−	920.170i	1.50342	−	1.09937i
$838$	−234.924			−0.280339
$839$	219.883	+	126.949i	0.262077	+	0.151310i	0.625282	−	0.780399i	$-0.284984\pi$
$839$	219.883	+	126.949i	0.262077	+	0.151310i	−0.363205	+	0.931709i	$0.618317\pi$
$840$	282.151	+	149.652i	0.335894	+	0.178157i
$841$	−411.526	−	712.783i	−0.489329	−	0.847543i
$842$	515.552	−	297.654i	0.612295	−	0.353508i
$843$	657.651	+	1050.07i	0.780132	+	1.24563i
$844$	−445.536	+	771.691i	−0.527886	+	0.914325i
$845$			1062.51i			1.25741i
$846$	192.342	−	396.418i	0.227355	−	0.468579i
$847$	170.346			0.201116
$848$	35.3939	+	20.4347i	0.0417381	+	0.0240975i
$849$	6.23425	+	173.434i	0.00734305	+	0.204280i
$850$	34.2346	+	59.2961i	0.0402760	+	0.0697601i
$851$	−581.731	+	335.863i	−0.683585	+	0.394668i
$852$	−920.155	+	33.0759i	−1.07999	+	0.0388215i
$853$	−178.211	+	308.670i	−0.208922	+	0.361864i	−0.951375	−	0.308034i	$-0.900329\pi$
$853$	−178.211	+	308.670i	−0.208922	+	0.361864i	0.742453	+	0.669898i	$0.233662\pi$
$854$			66.8389i			0.0782657i
$855$	751.594	+	364.673i	0.879057	+	0.426519i
$856$	−865.987			−1.01167
$857$	267.390	+	154.377i	0.312007	+	0.180137i	0.647824	−	0.761790i	$-0.275679\pi$
$857$	267.390	+	154.377i	0.312007	+	0.180137i	−0.335817	+	0.941927i	$0.609013\pi$
$858$	−543.786	+	340.570i	−0.633783	+	0.396934i
$859$	215.037	+	372.455i	0.250334	+	0.433591i	0.963618	−	0.267284i	$-0.0861262\pi$
$859$	215.037	+	372.455i	0.250334	+	0.433591i	−0.713284	+	0.700875i	$0.752793\pi$
$860$	−2.34901	+	1.35620i	−0.00273140	+	0.00157698i
$861$	−184.449	+	347.757i	−0.214227	+	0.403899i
$862$	−31.1650	+	53.9793i	−0.0361543	+	0.0626210i
$863$			299.454i			0.346992i	0.984835	+	0.173496i	$0.0555063\pi$
$863$			299.454i			0.346992i	−0.984835	+	0.173496i	$0.944494\pi$
$864$	503.129	+	688.044i	0.582326	+	0.796347i
$865$	141.996			0.164158
$866$	469.997	+	271.353i	0.542721	+	0.313340i
$867$	−704.567	−	373.700i	−0.812649	−	0.431026i
$868$	−249.062	−	431.387i	−0.286937	−	0.496990i
$869$	1728.79	−	998.115i	1.98940	−	1.14858i
$870$	−37.3861	−	59.6941i	−0.0429725	−	0.0686140i
$871$	868.792	−	1504.79i	0.997465	−	1.72766i
$872$		−	1173.99i		−	1.34632i
$873$	123.204	−	8.86885i	0.141127	−	0.0101591i
$874$	307.221			0.351511
$875$	124.793	+	72.0490i	0.142620	+	0.0823417i
$876$	1.80121	+	50.1089i	0.00205618	+	0.0572019i
$877$	−843.666	−	1461.27i	−0.961990	−	1.66622i	−0.717492	−	0.696566i	$-0.754710\pi$
$877$	−843.666	−	1461.27i	−0.961990	−	1.66622i	−0.244498	−	0.969650i	$-0.578623\pi$
$878$	76.1450	−	43.9623i	0.0867255	−	0.0500710i
$879$	−1692.28	+	60.8306i	−1.92523	+	0.0692044i
$880$	336.875	−	583.484i	0.382812	−	0.663050i
$881$			443.688i			0.503619i	0.967777	+	0.251809i	$0.0810256\pi$
$881$			443.688i			0.503619i	−0.967777	+	0.251809i	$0.918974\pi$
$882$	44.8411	−	30.3795i	0.0508403	−	0.0344439i
$883$	−77.3400			−0.0875877			−0.0437939	−	0.999041i	$-0.513944\pi$
$883$	−77.3400			−0.0875877			−0.0437939	+	0.999041i	$0.513944\pi$
$884$	248.281	+	143.345i	0.280860	+	0.162155i
$885$	437.676	−	274.114i	0.494549	−	0.309733i
$886$	174.354	+	301.989i	0.196787	+	0.340846i
$887$	−282.109	+	162.876i	−0.318048	+	0.183625i	−0.650522	−	0.759487i	$-0.725450\pi$
$887$	−282.109	+	162.876i	−0.318048	+	0.183625i	0.332474	+	0.943112i	$0.392117\pi$
$888$	237.524	−	447.823i	0.267482	−	0.504305i
$889$	−41.8444	+	72.4766i	−0.0470691	+	0.0815260i
$890$		−	142.573i		−	0.160194i
$891$	866.280	−	682.545i	0.972256	−	0.766043i
$892$	463.082			0.519150
$893$	−710.140	−	410.000i	−0.795230	−	0.459126i
$894$	32.9950	+	17.5004i	0.0369071	+	0.0195754i
$895$	120.316	+	208.393i	0.134431	+	0.232842i
$896$	296.362	−	171.105i	0.330761	−	0.190965i
$897$	−721.996	−	1152.81i	−0.804901	−	1.28518i
$898$	−232.190	+	402.165i	−0.258564	+	0.447846i
$899$			244.608i			0.272090i
$900$	−272.439	−	402.128i	−0.302710	−	0.446809i
$901$	25.6178			0.0284326
$902$	−502.765	−	290.272i	−0.557390	−	0.321809i
$903$	0.0367936	+	1.02358i	4.07460e−5	+	0.00113353i
$904$	137.314	+	237.835i	0.151896	+	0.263092i
$905$	1165.32	−	672.797i	1.28764	−	0.743422i
$906$	−41.4469	+	1.48985i	−0.0457472	+	0.00164443i
$907$	291.457	−	504.818i	0.321342	−	0.556580i	−0.659423	−	0.751772i	$-0.729200\pi$
$907$	291.457	−	504.818i	0.321342	−	0.556580i	0.980765	+	0.195192i	$0.0625329\pi$
$908$		−	718.591i		−	0.791400i
$909$	−100.950	−	1402.38i	−0.111057	−	1.54277i
$910$	267.896			0.294391
$911$	269.975	+	155.870i	0.296350	+	0.171098i	0.640802	−	0.767706i	$-0.278602\pi$
$911$	269.975	+	155.870i	0.296350	+	0.171098i	−0.344452	+	0.938804i	$0.611935\pi$
$912$	281.057	−	176.024i	0.308177	−	0.193009i
$913$	−281.476	−	487.531i	−0.308298	−	0.533988i
$914$	−75.3466	+	43.5014i	−0.0824361	+	0.0475945i
$915$	266.256	−	501.995i	0.290990	−	0.548628i
$916$	−208.162	+	360.547i	−0.227251	+	0.393610i
$917$			223.097i			0.243290i
$918$	102.179	+	45.1177i	0.111307	+	0.0491478i
$919$	471.826			0.513413			0.256706	−	0.966489i	$-0.417363\pi$
$919$	471.826			0.513413			0.256706	+	0.966489i	$0.417363\pi$
$920$	−864.768	−	499.274i	−0.939965	−	0.542689i
$921$	467.341	+	247.876i	0.507427	+	0.269138i
$922$	−313.115	−	542.331i	−0.339604	−	0.588212i
$923$	−1489.30	+	859.849i	−1.61354	+	0.931580i
$924$	−187.051	−	298.663i	−0.202436	−	0.323229i
$925$	−224.001	+	387.981i	−0.242163	+	0.419439i
$926$			194.633i			0.210186i
$927$	−225.007	+	463.741i	−0.242726	+	0.500260i
$928$	−133.747			−0.144124
$929$	−432.441	−	249.670i	−0.465491	−	0.268751i	0.248859	−	0.968540i	$-0.419944\pi$
$929$	−432.441	−	249.670i	−0.465491	−	0.268751i	−0.714350	+	0.699788i	$0.753278\pi$
$930$	−34.4825	−	959.287i	−0.0370780	−	1.03149i
$931$	−50.3996	−	87.2946i	−0.0541349	−	0.0937643i
$932$	−119.835	+	69.1868i	−0.128578	+	0.0742347i
$933$	−367.916	+	13.2251i	−0.394337	+	0.0141748i
$934$	−29.1007	+	50.4039i	−0.0311571	+	0.0539657i
$935$		−	422.320i		−	0.451679i
$936$	923.530	+	448.097i	0.986677	+	0.478736i
$937$	−407.714			−0.435127			−0.217563	−	0.976046i	$-0.569811\pi$
$937$	−407.714			−0.435127			−0.217563	+	0.976046i	$0.569811\pi$
$938$	−187.337	−	108.159i	−0.199720	−	0.115308i
$939$	222.146	−	139.129i	0.236577	−	0.148167i
$940$	598.476	+	1036.59i	0.636676	+	1.10276i
$941$	−49.2353	+	28.4260i	−0.0523223	+	0.0302083i	−0.525933	−	0.850526i	$-0.676284\pi$
$941$	−49.2353	+	28.4260i	−0.0523223	+	0.0302083i	0.473611	+	0.880734i	$0.342950\pi$
$942$	−144.943	+	273.273i	−0.153867	+	0.290099i
$943$	615.366	−	1065.85i	0.652562	−	1.13027i
$944$		−	205.009i		−	0.217170i
$945$	−457.798	+	49.5388i	−0.484443	+	0.0524220i
$946$	−1.51054			−0.00159676
$947$	659.563	+	380.799i	0.696477	+	0.402111i	0.806034	−	0.591870i	$-0.201610\pi$
$947$	659.563	+	380.799i	0.696477	+	0.402111i	−0.109557	+	0.993980i	$0.534943\pi$
$948$	−1267.06	−	672.046i	−1.33656	−	0.708910i
$949$	46.8248	+	81.1029i	0.0493412	+	0.0854615i
$950$	177.447	−	102.449i	0.186787	−	0.107841i
$951$	675.805	+	1079.05i	0.710626	+	1.13465i
$952$	39.7361	−	68.8250i	0.0417396	−	0.0722951i
$953$			91.0824i			0.0955744i	0.998858	+	0.0477872i	$0.0152169\pi$
$953$			91.0824i			0.0955744i	−0.998858	+	0.0477872i	$0.984783\pi$
$954$	41.0874	−	2.95768i	0.0430686	−	0.00310029i
$955$	1855.17			1.94259
$956$	1027.77	+	593.382i	1.07507	+	0.620692i
$957$	6.21648	+	172.939i	0.00649579	+	0.180710i
$958$	−18.7120	−	32.4101i	−0.0195323	−	0.0338310i
$959$	−20.9347	+	12.0866i	−0.0218297	+	0.0126034i
$960$	−68.9030	+	2.47679i	−0.0717740	+	0.00257999i
$961$	−1186.29	+	2054.72i	−1.23443	+	2.13810i
$962$		−	425.197i		−	0.441993i
$963$	1033.66	−	700.294i	1.07337	−	0.727200i
$964$	396.524			0.411332
$965$	−356.031	−	205.555i	−0.368944	−	0.213010i
$966$	−143.517	+	89.8840i	−0.148569	+	0.0930476i
$967$	227.566	+	394.155i	0.235331	+	0.407606i	0.959369	−	0.282155i	$-0.0910491\pi$
$967$	227.566	+	394.155i	0.235331	+	0.407606i	−0.724037	+	0.689761i	$0.757716\pi$
$968$	348.068	−	200.957i	0.359574	−	0.207600i
$969$	97.4018	−	183.640i	0.100518	−	0.189515i
$970$	38.0301	−	65.8700i	0.0392063	−	0.0679073i
$971$		−	962.944i		−	0.991704i	−0.868407	−	0.495852i	$-0.834856\pi$
$971$		−	962.944i		−	0.991704i	0.868407	−	0.495852i	$-0.165144\pi$
$972$	−745.980	−	267.197i	−0.767469	−	0.274894i
$973$	329.308			0.338446
$974$	566.227	+	326.911i	0.581342	+	0.335638i
$975$	−801.445	−	425.084i	−0.821995	−	0.435983i
$976$	−112.787	−	195.353i	−0.115561	−	0.200157i
$977$	1079.53	−	623.267i	1.10494	−	0.637940i	0.167429	−	0.985884i	$-0.446454\pi$
$977$	1079.53	−	623.267i	1.10494	−	0.637940i	0.937515	+	0.347945i	$0.113120\pi$
$978$	338.082	+	539.814i	0.345687	+	0.551957i
$979$	−175.142	+	303.355i	−0.178899	+	0.309862i
$980$			147.136i			0.150139i
$981$	949.364	+	1401.29i	0.967752	+	1.42843i
$982$	−224.266			−0.228377
$983$	−894.200	−	516.267i	−0.909664	−	0.525195i	−0.0293411	−	0.999569i	$-0.509341\pi$
$983$	−894.200	−	516.267i	−0.909664	−	0.525195i	−0.880323	+	0.474375i	$0.842674\pi$
$984$	33.3640	+	928.169i	0.0339065	+	0.943261i
$985$	−475.279	−	823.208i	−0.482517	−	0.835744i
$986$	−15.1784	+	8.76323i	−0.0153939	+	0.00888766i
$987$	451.695	−	16.2366i	0.457644	−	0.0164505i
$988$	428.968	−	742.995i	0.434179	−	0.752019i
$989$		−	3.20229i		−	0.00323791i
$990$	−48.7586	−	677.344i	−0.0492511	−	0.684186i
$991$	438.360			0.442341			0.221170	−	0.975235i	$-0.429012\pi$
$991$	438.360			0.442341			0.221170	+	0.975235i	$0.429012\pi$
$992$	−1578.53	−	911.365i	−1.59126	−	0.918715i
$993$	−1181.81	+	740.163i	−1.19014	+	0.745380i
$994$	107.046	+	185.409i	0.107692	+	0.186528i
$995$	−464.503	+	268.181i	−0.466837	+	0.269529i
$996$	−189.522	+	357.322i	−0.190284	+	0.358757i
$997$	−258.802	+	448.258i	−0.259581	+	0.449607i	−0.966130	−	0.258057i	$-0.916918\pi$
$997$	−258.802	+	448.258i	−0.259581	+	0.449607i	0.706549	+	0.707664i	$0.250251\pi$
$998$			73.6892i			0.0738369i
$999$	78.6268	+	726.606i	0.0787055	+	0.727333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.r.a.29.8	✓	24
3.2	odd	2		189.3.r.a.8.5		24
7.2	even	3		441.3.j.h.263.5		24
7.3	odd	6		441.3.n.h.128.5		24
7.4	even	3		441.3.n.g.128.5		24
7.5	odd	6		441.3.j.g.263.5		24
7.6	odd	2		441.3.r.h.344.8		24
9.2	odd	6		567.3.b.a.323.16		24
9.4	even	3		189.3.r.a.71.5		24
9.5	odd	6	inner	63.3.r.a.50.8	yes	24
9.7	even	3		567.3.b.a.323.9		24
63.5	even	6		441.3.n.h.410.5		24
63.23	odd	6		441.3.n.g.410.5		24
63.32	odd	6		441.3.j.h.275.8		24
63.41	even	6		441.3.r.h.50.8		24
63.59	even	6		441.3.j.g.275.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.r.a.29.8	✓	24	1.1	even	1	trivial
63.3.r.a.50.8	yes	24	9.5	odd	6	inner
189.3.r.a.8.5		24	3.2	odd	2
189.3.r.a.71.5		24	9.4	even	3
441.3.j.g.263.5		24	7.5	odd	6
441.3.j.g.275.8		24	63.59	even	6
441.3.j.h.263.5		24	7.2	even	3
441.3.j.h.275.8		24	63.32	odd	6
441.3.n.g.128.5		24	7.4	even	3
441.3.n.g.410.5		24	63.23	odd	6
441.3.n.h.128.5		24	7.3	odd	6
441.3.n.h.410.5		24	63.5	even	6
441.3.r.h.50.8		24	63.41	even	6
441.3.r.h.344.8		24	7.6	odd	2
567.3.b.a.323.9		24	9.7	even	3
567.3.b.a.323.16		24	9.2	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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.744550 + 0.429866i) q^{2} +(-2.65028 - 1.40570i) q^{3} +(-1.63043 - 2.82399i) q^{4} +(5.58239 - 3.22299i) q^{5} +(-1.36900 - 2.18588i) q^{6} +(1.32288 - 2.29129i) q^{7} -6.24239i q^{8} +(5.04801 + 7.45102i) q^{9} +O(q^{10})\)	\(q+(0.744550 + 0.429866i) q^{2} +(-2.65028 - 1.40570i) q^{3} +(-1.63043 - 2.82399i) q^{4} +(5.58239 - 3.22299i) q^{5} +(-1.36900 - 2.18588i) q^{6} +(1.32288 - 2.29129i) q^{7} -6.24239i q^{8} +(5.04801 + 7.45102i) q^{9} +5.54182 q^{10} +(-11.7915 - 6.80780i) q^{11} +(0.351418 + 9.77627i) q^{12} +(9.13554 + 15.8232i) q^{13} +(1.96989 - 1.13732i) q^{14} +(-19.3255 + 0.694673i) q^{15} +(-3.83833 + 6.64818i) q^{16} +4.81189i q^{17} +(0.555553 + 7.71762i) q^{18} +14.3999 q^{19} +(-18.2034 - 10.5097i) q^{20} +(-6.72686 + 4.21299i) q^{21} +(-5.85288 - 10.1375i) q^{22} +(21.4911 - 12.4079i) q^{23} +(-8.77494 + 16.5441i) q^{24} +(8.27536 - 14.3333i) q^{25} +15.7082i q^{26} +(-2.90474 - 26.8433i) q^{27} -8.62743 q^{28} +(3.66899 + 2.11829i) q^{29} +(-14.6874 - 7.79014i) q^{30} +(28.8686 + 50.0019i) q^{31} +(-27.3399 + 15.7847i) q^{32} +(21.6810 + 34.6179i) q^{33} +(-2.06847 + 3.58269i) q^{34} -17.0545i q^{35} +(12.8112 - 26.4039i) q^{36} -27.0684 q^{37} +(10.7214 + 6.19001i) q^{38} +(-1.96905 - 54.7779i) q^{39} +(-20.1192 - 34.8475i) q^{40} +(42.9502 - 24.7973i) q^{41} +(-6.81950 + 0.245134i) q^{42} +(0.0645211 - 0.111754i) q^{43} +44.3986i q^{44} +(52.1945 + 25.3248i) q^{45} +21.3349 q^{46} +(-49.3157 - 28.4725i) q^{47} +(19.5180 - 12.2240i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(12.3228 - 7.11459i) q^{50} +(6.76408 - 12.7529i) q^{51} +(29.7897 - 51.5973i) q^{52} -5.32385i q^{53} +(9.37629 - 21.2348i) q^{54} -87.7660 q^{55} +(-14.3031 - 8.25791i) q^{56} +(-38.1637 - 20.2419i) q^{57} +(1.82116 + 3.15435i) q^{58} +(-23.1276 + 13.3527i) q^{59} +(33.4706 + 53.4423i) q^{60} +(-14.6922 + 25.4477i) q^{61} +49.6385i q^{62} +(23.7503 - 1.70967i) q^{63} +3.56540 q^{64} +(101.996 + 58.8876i) q^{65} +(1.26151 + 35.0946i) q^{66} +(-47.5501 - 82.3592i) q^{67} +(13.5887 - 7.84545i) q^{68} +(-74.3994 + 2.67436i) q^{69} +(7.33114 - 12.6979i) q^{70} +94.1213i q^{71} +(46.5122 - 31.5116i) q^{72} +5.12556 q^{73} +(-20.1538 - 11.6358i) q^{74} +(-42.0805 + 26.3547i) q^{75} +(-23.4780 - 40.6651i) q^{76} +(-31.1973 + 18.0117i) q^{77} +(22.0811 - 41.6313i) q^{78} +(-73.3067 + 126.971i) q^{79} +49.4836i q^{80} +(-30.0353 + 75.2255i) q^{81} +42.6381 q^{82} +(35.8068 + 20.6731i) q^{83} +(22.8651 + 12.1276i) q^{84} +(15.5087 + 26.8618i) q^{85} +(0.0960783 - 0.0554708i) q^{86} +(-6.74618 - 10.7716i) q^{87} +(-42.4970 + 73.6069i) q^{88} -25.7267i q^{89} +(27.9751 + 41.2922i) q^{90} +48.3407 q^{91} +(-70.0796 - 40.4605i) q^{92} +(-6.22224 - 173.100i) q^{93} +(-24.4787 - 42.3983i) q^{94} +(80.3857 - 46.4107i) q^{95} +(94.6472 - 3.40219i) q^{96} +(6.86238 - 11.8860i) q^{97} -6.01812i q^{98} +(-8.79831 - 122.224i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} + 24 q^{4} - 18 q^{5} - 14 q^{6} + 26 q^{9}+O(q^{10}) \) 24 * q + 2 * q^3 + 24 * q^4 - 18 * q^5 - 14 * q^6 + 26 * q^9	\( 24 q + 2 q^{3} + 24 q^{4} - 18 q^{5} - 14 q^{6} + 26 q^{9} - 18 q^{11} + 4 q^{12} - 10 q^{15} - 48 q^{16} - 62 q^{18} - 24 q^{19} - 18 q^{20} - 14 q^{21} - 24 q^{22} + 72 q^{23} + 54 q^{24} + 54 q^{25} - 124 q^{27} + 54 q^{29} - 212 q^{30} + 30 q^{31} + 126 q^{32} - 178 q^{33} + 60 q^{34} + 124 q^{36} + 84 q^{37} - 144 q^{38} + 92 q^{39} - 60 q^{40} + 180 q^{41} + 140 q^{42} - 60 q^{43} - 118 q^{45} - 168 q^{46} + 378 q^{47} + 436 q^{48} - 84 q^{49} - 378 q^{50} + 168 q^{51} - 18 q^{52} + 514 q^{54} - 132 q^{55} - 232 q^{57} + 90 q^{58} - 90 q^{59} + 76 q^{60} + 28 q^{63} + 324 q^{64} + 126 q^{65} + 202 q^{66} + 6 q^{67} - 738 q^{68} - 432 q^{69} - 246 q^{72} - 72 q^{73} - 792 q^{74} + 40 q^{75} + 84 q^{76} + 28 q^{78} - 6 q^{79} - 34 q^{81} - 108 q^{82} - 558 q^{83} - 322 q^{84} + 126 q^{85} + 90 q^{86} + 428 q^{87} + 168 q^{88} - 488 q^{90} + 84 q^{91} + 774 q^{92} - 738 q^{93} - 354 q^{94} + 648 q^{95} - 280 q^{96} - 270 q^{97} + 296 q^{99}+O(q^{100}) \) 24 * q + 2 * q^3 + 24 * q^4 - 18 * q^5 - 14 * q^6 + 26 * q^9 - 18 * q^11 + 4 * q^12 - 10 * q^15 - 48 * q^16 - 62 * q^18 - 24 * q^19 - 18 * q^20 - 14 * q^21 - 24 * q^22 + 72 * q^23 + 54 * q^24 + 54 * q^25 - 124 * q^27 + 54 * q^29 - 212 * q^30 + 30 * q^31 + 126 * q^32 - 178 * q^33 + 60 * q^34 + 124 * q^36 + 84 * q^37 - 144 * q^38 + 92 * q^39 - 60 * q^40 + 180 * q^41 + 140 * q^42 - 60 * q^43 - 118 * q^45 - 168 * q^46 + 378 * q^47 + 436 * q^48 - 84 * q^49 - 378 * q^50 + 168 * q^51 - 18 * q^52 + 514 * q^54 - 132 * q^55 - 232 * q^57 + 90 * q^58 - 90 * q^59 + 76 * q^60 + 28 * q^63 + 324 * q^64 + 126 * q^65 + 202 * q^66 + 6 * q^67 - 738 * q^68 - 432 * q^69 - 246 * q^72 - 72 * q^73 - 792 * q^74 + 40 * q^75 + 84 * q^76 + 28 * q^78 - 6 * q^79 - 34 * q^81 - 108 * q^82 - 558 * q^83 - 322 * q^84 + 126 * q^85 + 90 * q^86 + 428 * q^87 + 168 * q^88 - 488 * q^90 + 84 * q^91 + 774 * q^92 - 738 * q^93 - 354 * q^94 + 648 * q^95 - 280 * q^96 - 270 * q^97 + 296 * q^99

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