LMFDB - Embedded newform 140.3.x.a.103.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,3,Mod(3,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("140.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	140.x (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.81472370104$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.38
Character	$\chi$	$=$	140.103
Dual form			140.3.x.a.87.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.76148 + 0.947205i) q^{2} +(1.44098 - 5.37782i) q^{3} +(2.20561 + 3.33696i) q^{4} +(-0.743084 - 4.94447i) q^{5} +(7.63215 - 8.10800i) q^{6} +(0.760820 + 6.95853i) q^{7} +(0.724341 + 7.96714i) q^{8} +(-19.0503 - 10.9987i) q^{9} +O(q^{10})$	\(q+(1.76148 + 0.947205i) q^{2} +(1.44098 - 5.37782i) q^{3} +(2.20561 + 3.33696i) q^{4} +(-0.743084 - 4.94447i) q^{5} +(7.63215 - 8.10800i) q^{6} +(0.760820 + 6.95853i) q^{7} +(0.724341 + 7.96714i) q^{8} +(-19.0503 - 10.9987i) q^{9} +(3.37450 - 9.41343i) q^{10} +(7.37723 - 4.25924i) q^{11} +(21.1238 - 7.05285i) q^{12} +(-1.44303 + 1.44303i) q^{13} +(-5.25099 + 12.9779i) q^{14} +(-27.6612 - 3.12873i) q^{15} +(-6.27060 + 14.7200i) q^{16} +(1.06723 - 3.98297i) q^{17} +(-23.1386 - 37.4184i) q^{18} +(13.3982 + 7.73543i) q^{19} +(14.8606 - 13.3852i) q^{20} +(38.5180 + 5.93557i) q^{21} +(17.0292 - 0.514817i) q^{22} +(0.910087 + 3.39649i) q^{23} +(43.8896 + 7.58513i) q^{24} +(-23.8957 + 7.34832i) q^{25} +(-3.90871 + 1.17502i) q^{26} +(-51.1684 + 51.1684i) q^{27} +(-21.5423 + 17.8866i) q^{28} +18.6820i q^{29} +(-45.7611 - 31.7120i) q^{30} +(30.1165 + 52.1634i) q^{31} +(-24.9884 + 19.9895i) q^{32} +(-12.2750 - 45.8109i) q^{33} +(5.65259 - 6.00502i) q^{34} +(33.8409 - 8.93263i) q^{35} +(-5.31523 - 87.8287i) q^{36} +(1.66479 + 6.21307i) q^{37} +(16.2735 + 26.3166i) q^{38} +(5.68097 + 9.83973i) q^{39} +(38.8551 - 9.50174i) q^{40} -40.6046i q^{41} +(62.2264 + 46.9398i) q^{42} +(-3.57455 + 3.57455i) q^{43} +(30.4842 + 15.2233i) q^{44} +(-40.2267 + 102.366i) q^{45} +(-1.61408 + 6.84488i) q^{46} +(-20.4773 - 76.4223i) q^{47} +(70.1258 + 54.9335i) q^{48} +(-47.8423 + 10.5884i) q^{49} +(-49.0520 - 9.69017i) q^{50} +(-19.8818 - 11.4788i) q^{51} +(-7.99809 - 1.63258i) q^{52} +(-5.69408 + 21.2506i) q^{53} +(-138.599 + 41.6650i) q^{54} +(-26.5416 - 33.3115i) q^{55} +(-54.8885 + 11.1019i) q^{56} +(60.9062 - 60.9062i) q^{57} +(-17.6957 + 32.9079i) q^{58} +(-21.5785 + 12.4584i) q^{59} +(-50.5694 - 99.2052i) q^{60} +(-41.6775 - 24.0625i) q^{61} +(3.64020 + 120.411i) q^{62} +(62.0408 - 140.930i) q^{63} +(-62.9507 + 11.5418i) q^{64} +(8.20732 + 6.06273i) q^{65} +(21.7702 - 92.3217i) q^{66} +(15.8822 - 59.2733i) q^{67} +(15.6449 - 5.22354i) q^{68} +19.5771 q^{69} +(68.0711 + 16.3197i) q^{70} +73.0217i q^{71} +(73.8291 - 159.743i) q^{72} +(-103.355 - 27.6940i) q^{73} +(-2.95257 + 12.5211i) q^{74} +(5.08473 + 139.095i) q^{75} +(3.73824 + 61.7705i) q^{76} +(35.2508 + 48.0941i) q^{77} +(0.686662 + 22.7135i) q^{78} +(27.9522 - 48.4147i) q^{79} +(77.4424 + 20.0666i) q^{80} +(102.453 + 177.454i) q^{81} +(38.4609 - 71.5242i) q^{82} +(3.69632 + 3.69632i) q^{83} +(65.1488 + 141.625i) q^{84} +(-20.4867 - 2.31722i) q^{85} +(-9.68233 + 2.91066i) q^{86} +(100.468 + 26.9204i) q^{87} +(39.2776 + 55.6903i) q^{88} +(1.02734 - 1.77940i) q^{89} +(-167.820 + 142.213i) q^{90} +(-11.1393 - 8.94348i) q^{91} +(-9.32666 + 10.5282i) q^{92} +(323.922 - 86.7948i) q^{93} +(36.3173 - 154.012i) q^{94} +(28.2917 - 71.9950i) q^{95} +(71.4918 + 163.188i) q^{96} +(-92.1829 - 92.1829i) q^{97} +(-94.3025 - 26.6653i) q^{98} -187.384 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8}+O(q^{10}) $ 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8	$ 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8} - 6 q^{10} - 6 q^{12} - 28 q^{16} - 12 q^{17} - 36 q^{18} - 32 q^{21} - 24 q^{22} - 4 q^{25} - 12 q^{26} + 114 q^{28} + 28 q^{30} + 58 q^{32} - 156 q^{33} - 144 q^{36} - 4 q^{37} + 192 q^{38} + 54 q^{40} - 218 q^{42} - 12 q^{45} + 68 q^{46} - 332 q^{50} - 264 q^{52} - 4 q^{53} - 300 q^{56} - 24 q^{57} - 146 q^{58} - 434 q^{60} - 24 q^{61} + 92 q^{65} - 660 q^{66} - 72 q^{68} + 488 q^{70} - 80 q^{72} - 12 q^{73} - 156 q^{77} + 688 q^{78} + 588 q^{80} + 288 q^{81} + 798 q^{82} + 272 q^{85} - 72 q^{86} + 588 q^{88} + 524 q^{92} + 164 q^{93} + 1080 q^{96} - 766 q^{98}+O(q^{100}) $ 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8 - 6 * q^10 - 6 * q^12 - 28 * q^16 - 12 * q^17 - 36 * q^18 - 32 * q^21 - 24 * q^22 - 4 * q^25 - 12 * q^26 + 114 * q^28 + 28 * q^30 + 58 * q^32 - 156 * q^33 - 144 * q^36 - 4 * q^37 + 192 * q^38 + 54 * q^40 - 218 * q^42 - 12 * q^45 + 68 * q^46 - 332 * q^50 - 264 * q^52 - 4 * q^53 - 300 * q^56 - 24 * q^57 - 146 * q^58 - 434 * q^60 - 24 * q^61 + 92 * q^65 - 660 * q^66 - 72 * q^68 + 488 * q^70 - 80 * q^72 - 12 * q^73 - 156 * q^77 + 688 * q^78 + 588 * q^80 + 288 * q^81 + 798 * q^82 + 272 * q^85 - 72 * q^86 + 588 * q^88 + 524 * q^92 + 164 * q^93 + 1080 * q^96 - 766 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.76148	+	0.947205i	0.880739	+	0.473602i
$2$	1.76148	+	0.947205i	0.880739	+	0.473602i
$3$	1.44098	−	5.37782i	0.480327	−	1.79261i	−0.119912	−	0.992785i	$-0.538261\pi$
$3$	1.44098	−	5.37782i	0.480327	−	1.79261i	0.600239	−	0.799821i	$-0.295072\pi$
$4$	2.20561	+	3.33696i	0.551401	+	0.834240i
$5$	−0.743084	−	4.94447i	−0.148617	−	0.988895i
$5$	−0.743084	−	4.94447i	−0.148617	−	0.988895i
$6$	7.63215	−	8.10800i	1.27203	−	1.35133i
$7$	0.760820	+	6.95853i	0.108689	+	0.994076i
$7$	0.760820	+	6.95853i	0.108689	+	0.994076i
$8$	0.724341	+	7.96714i	0.0905426	+	0.995893i
$9$	−19.0503	−	10.9987i	−2.11669	−	1.22207i
$10$	3.37450	−	9.41343i	0.337450	−	0.941343i
$11$	7.37723	−	4.25924i	0.670657	−	0.387204i	−0.125669	−	0.992072i	$-0.540108\pi$
$11$	7.37723	−	4.25924i	0.670657	−	0.387204i	0.796326	+	0.604868i	$0.206774\pi$
$12$	21.1238	−	7.05285i	1.76032	−	0.587737i
$13$	−1.44303	+	1.44303i	−0.111002	+	0.111002i	−0.760426	−	0.649424i	$-0.775010\pi$
$13$	−1.44303	+	1.44303i	−0.111002	+	0.111002i	0.649424	+	0.760426i	$0.275010\pi$
$14$	−5.25099	+	12.9779i	−0.375071	+	0.926996i
$15$	−27.6612	−	3.12873i	−1.84408	−	0.208582i
$16$	−6.27060	+	14.7200i	−0.391913	+	0.920002i
$17$	1.06723	−	3.98297i	0.0627784	−	0.234292i	−0.927407	−	0.374055i	$-0.877967\pi$
$17$	1.06723	−	3.98297i	0.0627784	−	0.234292i	0.990185	+	0.139763i	$0.0446339\pi$
$18$	−23.1386	−	37.4184i	−1.28548	−	2.07880i
$19$	13.3982	+	7.73543i	0.705166	+	0.407128i	0.809269	−	0.587439i	$-0.199864\pi$
$19$	13.3982	+	7.73543i	0.705166	+	0.407128i	−0.104102	+	0.994567i	$0.533197\pi$
$20$	14.8606	−	13.3852i	0.743028	−	0.669260i
$21$	38.5180	+	5.93557i	1.83419	+	0.282646i
$22$	17.0292	−	0.514817i	0.774054	−	0.0234008i
$23$	0.910087	+	3.39649i	0.0395690	+	0.147674i	0.982884	−	0.184225i	$-0.0589775\pi$
$23$	0.910087	+	3.39649i	0.0395690	+	0.147674i	−0.943315	+	0.331899i	$0.892311\pi$
$24$	43.8896	+	7.58513i	1.82873	+	0.316047i
$25$	−23.8957	+	7.34832i	−0.955826	+	0.293933i
$26$	−3.90871	+	1.17502i	−0.150335	+	0.0451931i
$27$	−51.1684	+	51.1684i	−1.89512	+	1.89512i
$28$	−21.5423	+	17.8866i	−0.769367	+	0.638807i
$29$			18.6820i			0.644207i	0.946705	+	0.322103i	$0.104390\pi$
$29$			18.6820i			0.644207i	−0.946705	+	0.322103i	$0.895610\pi$
$30$	−45.7611	−	31.7120i	−1.52537	−	1.05707i
$31$	30.1165	+	52.1634i	0.971501	+	1.68269i	0.691028	+	0.722828i	$0.257158\pi$
$31$	30.1165	+	52.1634i	0.971501	+	1.68269i	0.280473	+	0.959862i	$0.409509\pi$
$32$	−24.9884	+	19.9895i	−0.780888	+	0.624671i
$33$	−12.2750	−	45.8109i	−0.371969	−	1.38821i
$34$	5.65259	−	6.00502i	0.166253	−	0.176618i
$35$	33.8409	−	8.93263i	0.966884	−	0.255218i
$36$	−5.31523	−	87.8287i	−0.147645	−	2.43969i
$37$	1.66479	+	6.21307i	0.0449943	+	0.167921i	0.984767	−	0.173879i	$-0.0556302\pi$
$37$	1.66479	+	6.21307i	0.0449943	+	0.167921i	−0.939773	+	0.341800i	$0.888963\pi$
$38$	16.2735	+	26.3166i	0.428251	+	0.692542i
$39$	5.68097	+	9.83973i	0.145666	+	0.252301i
$40$	38.8551	−	9.50174i	0.971377	−	0.237543i
$41$		−	40.6046i		−	0.990357i	−0.868791	−	0.495179i	$-0.835103\pi$
$41$		−	40.6046i		−	0.990357i	0.868791	−	0.495179i	$-0.164897\pi$
$42$	62.2264	+	46.9398i	1.48158	+	1.11762i
$43$	−3.57455	+	3.57455i	−0.0831291	+	0.0831291i	−0.747449	−	0.664320i	$-0.768721\pi$
$43$	−3.57455	+	3.57455i	−0.0831291	+	0.0831291i	0.664320	+	0.747449i	$0.268721\pi$
$44$	30.4842	+	15.2233i	0.692822	+	0.345984i
$45$	−40.2267	+	102.366i	−0.893926	+	2.27481i
$46$	−1.61408	+	6.84488i	−0.0350886	+	0.148802i
$47$	−20.4773	−	76.4223i	−0.435687	−	1.62601i	−0.739417	−	0.673248i	$-0.764899\pi$
$47$	−20.4773	−	76.4223i	−0.435687	−	1.62601i	0.303730	−	0.952758i	$-0.401768\pi$
$48$	70.1258	+	54.9335i	1.46095	+	1.14445i
$49$	−47.8423	+	10.5884i	−0.976374	+	0.216089i
$50$	−49.0520	−	9.69017i	−0.981040	−	0.193803i
$51$	−19.8818	−	11.4788i	−0.389839	−	0.225074i
$52$	−7.99809	−	1.63258i	−0.153809	−	0.0313957i
$53$	−5.69408	+	21.2506i	−0.107436	+	0.400955i	−0.998610	−	0.0527057i	$-0.983215\pi$
$53$	−5.69408	+	21.2506i	−0.107436	+	0.400955i	0.891175	+	0.453661i	$0.149882\pi$
$54$	−138.599	+	41.6650i	−2.56665	+	0.771574i
$55$	−26.5416	−	33.3115i	−0.482575	−	0.605664i
$56$	−54.8885	+	11.1019i	−0.980152	+	0.198248i
$57$	60.9062	−	60.9062i	1.06853	−	1.06853i
$58$	−17.6957	+	32.9079i	−0.305098	+	0.567378i
$59$	−21.5785	+	12.4584i	−0.365738	+	0.211159i	−0.671595	−	0.740919i	$-0.734390\pi$
$59$	−21.5785	+	12.4584i	−0.365738	+	0.211159i	0.305857	+	0.952078i	$0.401057\pi$
$60$	−50.5694	−	99.2052i	−0.842823	−	1.65342i
$61$	−41.6775	−	24.0625i	−0.683238	−	0.394468i	0.117836	−	0.993033i	$-0.462404\pi$
$61$	−41.6775	−	24.0625i	−0.683238	−	0.394468i	−0.801074	+	0.598565i	$0.795738\pi$
$62$	3.64020	+	120.411i	0.0587130	+	1.94212i
$63$	62.0408	−	140.930i	0.984774	−	2.23698i
$64$	−62.9507	+	11.5418i	−0.983604	+	0.180341i
$65$	8.20732	+	6.06273i	0.126266	+	0.0932728i
$66$	21.7702	−	92.3217i	0.329851	−	1.39881i
$67$	15.8822	−	59.2733i	0.237048	−	0.884677i	−0.740166	−	0.672424i	$-0.765253\pi$
$67$	15.8822	−	59.2733i	0.237048	−	0.884677i	0.977215	−	0.212253i	$-0.0680801\pi$
$68$	15.6449	−	5.22354i	0.230072	−	0.0768168i
$69$	19.5771			0.283727
$70$	68.0711	+	16.3197i	0.972444	+	0.233138i
$71$			73.0217i			1.02847i	0.857648	+	0.514237i	$0.171925\pi$
$71$			73.0217i			1.02847i	−0.857648	+	0.514237i	$0.828075\pi$
$72$	73.8291	−	159.743i	1.02540	−	2.21865i
$73$	−103.355	−	27.6940i	−1.41583	−	0.379369i	−0.531825	−	0.846854i	$-0.678494\pi$
$73$	−103.355	−	27.6940i	−1.41583	−	0.379369i	−0.884001	+	0.467485i	$0.845160\pi$
$74$	−2.95257	+	12.5211i	−0.0398996	+	0.169204i
$75$	5.08473	+	139.095i	0.0677964	+	1.85460i
$76$	3.73824	+	61.7705i	0.0491873	+	0.812769i
$77$	35.2508	+	48.0941i	0.457803	+	0.624599i
$78$	0.686662	+	22.7135i	0.00880336	+	0.291199i
$79$	27.9522	−	48.4147i	0.353826	−	0.612844i	−0.633091	−	0.774078i	$-0.718214\pi$
$79$	27.9522	−	48.4147i	0.353826	−	0.612844i	0.986916	+	0.161234i	$0.0515473\pi$
$80$	77.4424	+	20.0666i	0.968030	+	0.250833i
$81$	102.453	+	177.454i	1.26486	+	2.19080i
$82$	38.4609	−	71.5242i	0.469036	−	0.872246i
$83$	3.69632	+	3.69632i	0.0445340	+	0.0445340i	0.729023	−	0.684489i	$-0.239975\pi$
$83$	3.69632	+	3.69632i	0.0445340	+	0.0445340i	−0.684489	+	0.729023i	$0.739975\pi$
$84$	65.1488	+	141.625i	0.775581	+	1.68601i
$85$	−20.4867	−	2.31722i	−0.241020	−	0.0272615i
$86$	−9.68233	+	2.91066i	−0.112585	+	0.0338449i
$87$	100.468	+	26.9204i	1.15481	+	0.309430i
$88$	39.2776	+	55.6903i	0.446337	+	0.632844i
$89$	1.02734	−	1.77940i	0.0115431	−	0.0199933i	−0.860196	−	0.509963i	$-0.829659\pi$
$89$	1.02734	−	1.77940i	0.0115431	−	0.0199933i	0.871739	+	0.489970i	$0.162992\pi$
$90$	−167.820	+	142.213i	−1.86467	+	1.58015i
$91$	−11.1393	−	8.94348i	−0.122409	−	0.0982800i
$92$	−9.32666	+	10.5282i	−0.101377	+	0.114437i
$93$	323.922	−	86.7948i	3.48304	−	0.933277i
$94$	36.3173	−	154.012i	0.386354	−	1.63843i
$95$	28.2917	−	71.9950i	0.297807	−	0.757842i
$96$	71.4918	+	163.188i	0.744707	+	1.69987i
$97$	−92.1829	−	92.1829i	−0.950339	−	0.950339i	0.0484852	−	0.998824i	$-0.484561\pi$
$97$	−92.1829	−	92.1829i	−0.950339	−	0.950339i	−0.998824	+	0.0484852i	$0.984561\pi$
$98$	−94.3025	−	26.6653i	−0.962270	−	0.272095i
$99$	−187.384			−1.89277
$100$	−77.2254	−	63.5313i	−0.772254	−	0.635313i
$101$	91.1064	−	52.6003i	0.902044	−	0.520795i	0.0241812	−	0.999708i	$-0.492302\pi$
$101$	91.1064	−	52.6003i	0.902044	−	0.520795i	0.877863	+	0.478912i	$0.158969\pi$
$102$	−24.1486	−	39.0517i	−0.236751	−	0.382860i
$103$	58.4192	−	15.6534i	0.567177	−	0.151975i	0.0361754	−	0.999345i	$-0.488483\pi$
$103$	58.4192	−	15.6534i	0.567177	−	0.151975i	0.531002	+	0.847371i	$0.321816\pi$
$104$	−12.5421	−	10.4516i	−0.120597	−	0.100496i
$105$	0.726118	−	194.862i	0.00691541	−	1.85583i
$106$	−30.1587	+	32.0390i	−0.284516	+	0.302255i
$107$	−29.8361	+	7.99456i	−0.278842	+	0.0747155i	−0.395530	−	0.918453i	$-0.629439\pi$
$107$	−29.8361	+	7.99456i	−0.278842	+	0.0747155i	0.116688	+	0.993169i	$0.462772\pi$
$108$	−283.604	−	57.8895i	−2.62596	−	0.536014i
$109$	33.6346	−	19.4190i	0.308575	−	0.178156i	−0.337714	−	0.941249i	$-0.609654\pi$
$109$	33.6346	−	19.4190i	0.308575	−	0.178156i	0.646288	+	0.763093i	$0.276320\pi$
$110$	−15.1996	−	83.8179i	−0.138178	−	0.761981i
$111$	35.8117			0.322628
$112$	−107.201	−	32.4349i	−0.957149	−	0.289597i
$113$	108.868	+	108.868i	0.963435	+	0.963435i	0.999355	−	0.0359201i	$-0.0114362\pi$
$113$	108.868	+	108.868i	0.963435	+	0.963435i	−0.0359201	+	0.999355i	$0.511436\pi$
$114$	164.976	−	49.5943i	1.44716	−	0.435038i
$115$	16.1176	−	7.02378i	0.140153	−	0.0610764i
$116$	−62.3411	+	41.2051i	−0.537423	+	0.355217i
$117$	43.3615	−	11.6187i	0.370611	−	0.0993049i
$118$	−49.8108	+	1.50585i	−0.422125	+	0.0127615i
$119$	28.5276	+	4.39605i	0.239727	+	0.0369416i
$120$	4.89084	−	222.647i	0.0407570	−	1.85539i
$121$	−24.2177	+	41.9463i	−0.200146	+	0.346663i
$122$	−50.6219	−	81.8628i	−0.414933	−	0.671006i
$123$	−218.364	−	58.5105i	−1.77532	−	0.475695i
$124$	−107.642	+	215.550i	−0.868080	+	1.73830i
$125$	54.0901	+	112.691i	0.432721	+	0.901528i
$126$	242.773	−	189.479i	1.92677	−	1.50380i
$127$	−102.336	−	102.336i	−0.805798	−	0.805798i	0.178197	−	0.983995i	$-0.442974\pi$
$127$	−102.336	−	102.336i	−0.805798	−	0.805798i	−0.983995	+	0.178197i	$0.942974\pi$
$128$	−121.819	−	39.2965i	−0.951708	−	0.307004i
$129$	14.0724	+	24.3741i	0.109089	+	0.188947i
$130$	8.71435	+	18.4534i	0.0670335	+	0.141949i
$131$	77.7868	−	134.731i	0.593792	−	1.02848i	−0.399924	−	0.916548i	$-0.630964\pi$
$131$	77.7868	−	134.731i	0.593792	−	1.02848i	0.993716	−	0.111930i	$-0.0357032\pi$
$132$	125.795	−	142.002i	0.952994	−	1.07577i
$133$	−43.6337	+	99.1168i	−0.328073	+	0.745239i
$134$	84.1202	−	89.3649i	0.627763	−	0.666902i
$135$	291.023	+	214.978i	2.15573	+	1.59243i
$136$	32.5059	+	5.61777i	0.239014	+	0.0413071i
$137$	−99.7646	−	26.7318i	−0.728209	−	0.195123i	−0.124377	−	0.992235i	$-0.539693\pi$
$137$	−99.7646	−	26.7318i	−0.728209	−	0.195123i	−0.603831	+	0.797112i	$0.706360\pi$
$138$	34.4847	+	18.5436i	0.249889	+	0.134374i
$139$			119.545i			0.860035i	0.902821	+	0.430017i	$0.141493\pi$
$139$			119.545i			0.860035i	−0.902821	+	0.430017i	$0.858507\pi$
$140$	104.448	+	93.2240i	0.746054	+	0.665885i
$141$	−440.493			−3.12406
$142$	−69.1665	+	128.626i	−0.487088	+	0.905818i
$143$	−4.49934	+	16.7918i	−0.0314639	+	0.117425i
$144$	281.357	−	211.452i	1.95387	−	1.46842i
$145$	92.3726	−	13.8823i	0.637053	−	0.0957400i
$146$	−155.826	−	146.681i	−1.06730	−	1.00466i
$147$	−11.9976	+	272.545i	−0.0816160	+	1.85405i
$148$	−17.0609	+	19.2589i	−0.115276	+	0.130128i
$149$	−44.0559	−	25.4357i	−0.295677	−	0.170709i	0.344822	−	0.938668i	$-0.387939\pi$
$149$	−44.0559	−	25.4357i	−0.295677	−	0.170709i	−0.640499	+	0.767959i	$0.721273\pi$
$150$	−122.795	+	249.829i	−0.818634	+	1.66553i
$151$	−91.6694	+	52.9253i	−0.607082	+	0.350499i	−0.771822	−	0.635838i	$-0.780655\pi$
$151$	−91.6694	+	52.9253i	−0.607082	+	0.350499i	0.164741	+	0.986337i	$0.447321\pi$
$152$	−51.9245	+	112.348i	−0.341608	+	0.739133i
$153$	−64.1384	+	64.1384i	−0.419205	+	0.419205i
$154$	16.5385	+	118.107i	0.107393	+	0.766925i
$155$	235.541	−	187.672i	1.51962	−	1.21079i
$156$	−20.3048	+	40.6597i	−0.130159	+	0.260639i
$157$	50.7835	−	189.527i	0.323462	−	1.20718i	−0.592387	−	0.805653i	$-0.701815\pi$
$157$	50.7835	−	189.527i	0.323462	−	1.20718i	0.915849	−	0.401522i	$-0.131519\pi$
$158$	95.0958	−	58.8049i	0.601872	−	0.372183i
$159$	106.077	+	61.2435i	0.667150	+	0.385179i
$160$	117.406	+	108.701i	0.733787	+	0.679380i
$161$	−22.9422	+	8.91699i	−0.142498	+	0.0553850i
$162$	12.3836	+	409.626i	0.0764420	+	2.52856i
$163$	−22.1058	−	82.5000i	−0.135618	−	0.506135i	−0.999995	−	0.00328919i	$-0.998953\pi$
$163$	−22.1058	−	82.5000i	−0.135618	−	0.506135i	0.864376	−	0.502846i	$-0.167714\pi$
$164$	135.496	−	89.5578i	0.826196	−	0.546084i
$165$	−217.389	+	94.7347i	−1.31751	+	0.574150i
$166$	3.00981	+	10.0122i	0.0181314	+	0.0603142i
$167$	−41.3374	+	41.3374i	−0.247529	+	0.247529i	−0.819956	−	0.572427i	$-0.806002\pi$
$167$	−41.3374	+	41.3374i	−0.247529	+	0.247529i	0.572427	+	0.819956i	$0.306002\pi$
$168$	−19.3893	+	311.178i	−0.115413	+	1.85225i
$169$			164.835i			0.975357i
$170$	−33.8920	−	23.4869i	−0.199365	−	0.138158i
$171$	−170.159	−	294.724i	−0.995081	−	1.72353i
$172$	−19.8122	−	4.04408i	−0.115187	−	0.0235121i
$173$	9.62523	+	35.9219i	0.0556372	+	0.207641i	0.988149	−	0.153499i	$-0.0490543\pi$
$173$	9.62523	+	35.9219i	0.0556372	+	0.207641i	−0.932512	+	0.361140i	$0.882388\pi$
$174$	151.474	+	142.584i	0.870538	+	0.819447i
$175$	−69.3138	−	160.688i	−0.396079	−	0.918216i
$176$	16.4366	+	135.301i	0.0933895	+	0.768756i
$177$	35.9046	+	133.998i	0.202851	+	0.757049i
$178$	3.49509	−	2.16128i	0.0196353	−	0.0121420i
$179$	−21.5448	−	37.3167i	−0.120362	−	0.208473i	0.799548	−	0.600602i	$-0.205072\pi$
$179$	−21.5448	−	37.3167i	−0.120362	−	0.208473i	−0.919911	+	0.392128i	$0.871739\pi$
$180$	−430.317	+	91.5451i	−2.39065	+	0.508584i
$181$			226.048i			1.24888i	0.781071	+	0.624442i	$0.214674\pi$
$181$			226.048i			1.24888i	−0.781071	+	0.624442i	$0.785326\pi$
$182$	−11.1502	−	26.3049i	−0.0612650	−	0.144532i
$183$	−189.460	+	189.460i	−1.03530	+	1.03530i
$184$	−26.4011	+	9.71101i	−0.143484	+	0.0527772i
$185$	29.4833	−	12.8483i	0.159369	−	0.0694505i
$186$	652.795	+	153.934i	3.50965	+	0.827602i
$187$	−9.09121	−	33.9288i	−0.0486161	−	0.181438i
$188$	209.853	−	236.889i	1.11624	−	1.26005i
$189$	−394.987	−	317.127i	−2.08988	−	1.67792i
$190$	118.029	−	100.019i	0.621206	−	0.526418i
$191$	52.0942	+	30.0766i	0.272744	+	0.157469i	0.630134	−	0.776486i	$-0.283000\pi$
$191$	52.0942	+	30.0766i	0.272744	+	0.157469i	−0.357390	+	0.933955i	$0.616333\pi$
$192$	−28.6408	+	355.169i	−0.149171	+	1.84984i
$193$	67.9702	−	253.668i	0.352177	−	1.31434i	−0.531823	−	0.846856i	$-0.678493\pi$
$193$	67.9702	−	253.668i	0.352177	−	1.31434i	0.884000	−	0.467487i	$-0.154840\pi$
$194$	−75.0620	−	249.694i	−0.386917	−	1.28708i
$195$	44.4308	−	35.4012i	0.227850	−	0.181544i
$196$	−140.854	−	136.294i	−0.718644	−	0.695378i
$197$	160.515	−	160.515i	0.814795	−	0.814795i	−0.170553	−	0.985348i	$-0.554556\pi$
$197$	160.515	−	160.515i	0.814795	−	0.814795i	0.985348	+	0.170553i	$0.0545555\pi$
$198$	−330.073	−	177.491i	−1.66703	−	0.896420i
$199$	−186.679	+	107.779i	−0.938083	+	0.541602i	−0.889359	−	0.457210i	$-0.848849\pi$
$199$	−186.679	+	107.779i	−0.938083	+	0.541602i	−0.0487241	+	0.998812i	$0.515516\pi$
$200$	−75.8537	−	185.057i	−0.379269	−	0.925287i
$201$	−295.875	−	170.824i	−1.47202	−	0.849868i
$202$	210.305	−	6.35783i	1.04112	−	0.0314744i
$203$	−129.999	+	14.2136i	−0.640390	+	0.0700179i
$204$	−5.54724	−	91.6624i	−0.0271924	−	0.449325i
$205$	−200.769	+	30.1727i	−0.979359	+	0.147184i
$206$	117.731	+	27.7619i	0.571510	+	0.134766i
$207$	20.0195	−	74.7138i	0.0967125	−	0.360936i
$208$	−12.1928	−	30.2901i	−0.0586191	−	0.145626i
$209$	131.788			0.630566
$210$	185.853	−	342.557i	0.885016	−	1.63123i
$211$			262.317i			1.24321i	0.783332	+	0.621604i	$0.213519\pi$
$211$			262.317i			1.24321i	−0.783332	+	0.621604i	$0.786481\pi$
$212$	−83.4713	+	27.8695i	−0.393733	+	0.131460i
$213$	392.697	+	105.223i	1.84365	+	0.494004i
$214$	−60.1281	−	14.1787i	−0.280973	−	0.0662555i
$215$	20.3305	+	15.0181i	0.0945603	+	0.0698516i
$216$	−444.729	−	370.602i	−2.05893	−	1.71575i
$217$	−340.067	+	249.254i	−1.56713	+	1.14864i
$218$	77.6404	−	2.34718i	0.356149	−	0.0107669i
$219$	−297.866	+	515.919i	−1.36012	+	2.35580i
$220$	52.6189	−	162.040i	0.239177	−	0.736547i
$221$	4.20749	+	7.28759i	0.0190384	+	0.0329755i
$222$	63.0815	+	33.9210i	0.284151	+	0.152797i
$223$	129.017	+	129.017i	0.578550	+	0.578550i	0.934504	−	0.355954i	$-0.115844\pi$
$223$	129.017	+	129.017i	0.578550	+	0.578550i	−0.355954	+	0.934504i	$0.615844\pi$
$224$	−158.109	−	158.674i	−0.705844	−	0.708367i
$225$	536.040	+	122.833i	2.38240	+	0.545924i
$226$	88.6483	+	294.889i	0.392249	+	1.30482i
$227$	−104.559	−	28.0164i	−0.460611	−	0.123420i	0.0210491	−	0.999778i	$-0.493299\pi$
$227$	−104.559	−	28.0164i	−0.460611	−	0.123420i	−0.481660	+	0.876358i	$0.659966\pi$
$228$	337.577	+	68.9065i	1.48060	+	0.302222i
$229$	110.800	−	191.911i	0.483843	−	0.838040i	−0.515985	−	0.856598i	$-0.672574\pi$
$229$	110.800	−	191.911i	0.483843	−	0.838040i	0.999828	+	0.0185575i	$0.00590737\pi$
$230$	35.0437	+	2.89443i	0.152364	+	0.0125845i
$231$	309.437	−	120.270i	1.33956	−	0.520648i
$232$	−148.842	+	13.5321i	−0.641561	+	0.0583281i
$233$	−192.854	+	51.6751i	−0.827699	+	0.221781i	−0.647710	−	0.761887i	$-0.724273\pi$
$233$	−192.854	+	51.6751i	−0.827699	+	0.221781i	−0.179990	+	0.983669i	$0.557606\pi$
$234$	87.3855	+	20.6062i	0.373443	+	0.0880606i
$235$	−362.652	+	158.038i	−1.54320	+	0.672501i
$236$	−89.1669	−	44.5285i	−0.377826	−	0.188680i
$237$	−220.087	−	220.087i	−0.928635	−	0.928635i
$238$	46.0867	+	34.7650i	0.193642	+	0.146071i
$239$	306.660			1.28309			0.641547	−	0.767083i	$-0.278293\pi$
$239$	306.660			1.28309			0.641547	+	0.767083i	$0.278293\pi$
$240$	219.508	−	387.556i	0.914615	−	1.61481i
$241$	232.453	−	134.207i	0.964535	−	0.556875i	0.0669693	−	0.997755i	$-0.478667\pi$
$241$	232.453	−	134.207i	0.964535	−	0.556875i	0.897566	+	0.440880i	$0.145334\pi$
$242$	−82.3906	+	50.9483i	−0.340457	+	0.210530i
$243$	472.876	−	126.707i	1.94599	−	0.521426i
$244$	−11.6285	−	192.149i	−0.0476578	−	0.787495i
$245$	87.9048	+	228.687i	0.358795	+	0.933416i
$246$	−329.222	−	309.901i	−1.33830	−	1.25976i
$247$	−30.4964	+	8.17149i	−0.123467	+	0.0330829i
$248$	−393.778	+	277.727i	−1.58782	+	1.11987i
$249$	25.2045	−	14.5518i	0.101223	−	0.0584410i
$250$	−11.4630	+	249.737i	−0.0458521	+	0.998948i
$251$	242.727			0.967039			0.483519	−	0.875334i	$-0.339358\pi$
$251$	242.727			0.967039			0.483519	+	0.875334i	$0.339358\pi$
$252$	607.115	−	103.808i	2.40918	−	0.411936i
$253$	21.1804	+	21.1804i	0.0837170	+	0.0837170i
$254$	−83.3297	−	277.197i	−0.328070	−	1.09133i
$255$	−41.9826	+	106.835i	−0.164638	+	0.418960i
$256$	−177.359	−	184.607i	−0.692809	−	0.721121i
$257$	307.368	−	82.3591i	1.19599	−	0.320464i	0.394737	−	0.918794i	$-0.370836\pi$
$257$	307.368	−	82.3591i	1.19599	−	0.320464i	0.801249	+	0.598331i	$0.204169\pi$
$258$	1.70094	+	56.2640i	0.00659280	+	0.218077i
$259$	−41.9673	+	16.3115i	−0.162036	+	0.0629788i
$260$	−2.12899	+	40.7595i	−0.00818840	+	0.156767i
$261$	205.477	−	355.897i	0.787268	−	1.36359i
$262$	264.637	−	163.645i	1.01007	−	0.624599i
$263$	358.528	+	96.0672i	1.36322	+	0.365275i	0.864999	−	0.501773i	$-0.167319\pi$
$263$	358.528	+	96.0672i	1.36322	+	0.365275i	0.498224	+	0.867048i	$0.333986\pi$
$264$	356.090	−	130.979i	1.34883	−	0.496133i
$265$	109.304	+	12.3633i	0.412469	+	0.0466538i
$266$	−170.744	+	133.262i	−0.641893	+	0.500985i
$267$	−8.08892	−	8.08892i	−0.0302956	−	0.0302956i
$268$	232.823	−	77.7352i	0.868741	−	0.290057i
$269$	−113.205	−	196.078i	−0.420838	−	0.728913i	0.575184	−	0.818024i	$-0.304931\pi$
$269$	−113.205	−	196.078i	−0.420838	−	0.728913i	−0.996022	+	0.0891116i	$0.971597\pi$
$270$	309.002	+	654.338i	1.14445	+	2.42347i
$271$	−16.6801	+	28.8907i	−0.0615501	+	0.106608i	−0.895158	−	0.445748i	$-0.852938\pi$
$271$	−16.6801	+	28.8907i	−0.0615501	+	0.106608i	0.833608	+	0.552356i	$0.186271\pi$
$272$	51.9372	+	40.6853i	0.190946	+	0.149578i
$273$	−64.1479	+	47.0175i	−0.234974	+	0.172225i
$274$	−150.413	−	141.585i	−0.548951	−	0.516734i
$275$	−144.985	+	155.988i	−0.527219	+	0.567228i
$276$	43.1794	+	65.3281i	0.156447	+	0.236696i
$277$	−31.7226	−	8.50005i	−0.114522	−	0.0306861i	0.201103	−	0.979570i	$-0.435547\pi$
$277$	−31.7226	−	8.50005i	−0.114522	−	0.0306861i	−0.315625	+	0.948884i	$0.602214\pi$
$278$	−113.233	+	210.575i	−0.407314	+	0.757466i
$279$		−	1324.97i		−	4.74899i
$280$	95.6799	+	263.145i	0.341714	+	0.939804i
$281$	162.575			0.578557			0.289279	−	0.957245i	$-0.406585\pi$
$281$	162.575			0.578557			0.289279	+	0.957245i	$0.406585\pi$
$282$	−775.918	−	417.237i	−2.75148	−	1.47956i
$283$	−2.21740	+	8.27544i	−0.00783532	+	0.0292418i	−0.969733	−	0.244168i	$-0.921485\pi$
$283$	−2.21740	+	8.27544i	−0.00783532	+	0.0292418i	0.961898	+	0.273410i	$0.0881517\pi$
$284$	−243.671	+	161.057i	−0.857995	+	0.567103i
$285$	−346.408	−	255.891i	−1.21547	−	0.897863i
$286$	−23.8307	+	25.3165i	−0.0833243	+	0.0885193i
$287$	282.549	−	30.8928i	0.984490	−	0.107640i
$288$	695.893	−	105.965i	2.41630	−	0.367934i
$289$	235.556	+	135.998i	0.815074	+	0.470583i
$290$	175.862	+	63.0425i	0.606420	+	0.217388i
$291$	−628.576	+	362.909i	−2.16006	+	1.24711i
$292$	−135.547	−	405.975i	−0.464203	−	1.39032i
$293$	−310.655	+	310.655i	−1.06026	+	1.06026i	−0.0621920	+	0.998064i	$0.519809\pi$
$293$	−310.655	+	310.655i	−1.06026	+	1.06026i	−0.998064	+	0.0621920i	$0.980191\pi$
$294$	−279.289	+	468.717i	−0.949963	+	1.59428i
$295$	77.6348	+	97.4369i	0.263169	+	0.330295i
$296$	−48.2946	+	17.7640i	−0.163157	+	0.0600135i
$297$	−159.542	+	595.419i	−0.537179	+	2.00478i
$298$	−53.5107	−	86.5343i	−0.179566	−	0.290384i
$299$	−6.21452	−	3.58796i	−0.0207844	−	0.0119999i
$300$	−452.940	+	323.757i	−1.50980	+	1.07919i
$301$	−27.5932	−	22.1540i	−0.0916718	−	0.0736015i
$302$	−211.605	+	6.39711i	−0.700678	+	0.0211825i
$303$	−151.592	−	565.750i	−0.500304	−	1.86716i
$304$	−197.880	+	148.716i	−0.650923	+	0.489196i
$305$	−88.0067	+	223.954i	−0.288546	+	0.734275i
$306$	−173.730	+	52.2261i	−0.567747	+	0.170674i
$307$	−299.256	+	299.256i	−0.974774	+	0.974774i	−0.999690	−	0.0249155i	$-0.992068\pi$
$307$	−299.256	+	299.256i	−0.974774	+	0.974774i	0.0249155	+	0.999690i	$0.492068\pi$
$308$	−82.7388	+	223.707i	−0.268633	+	0.726322i
$309$		−	336.724i		−	1.08972i
$310$	592.665	−	107.475i	1.91182	−	0.346692i
$311$	−30.0004	−	51.9622i	−0.0964642	−	0.167081i	0.813755	−	0.581209i	$-0.197420\pi$
$311$	−30.0004	−	51.9622i	−0.0964642	−	0.167081i	−0.910219	+	0.414128i	$0.864087\pi$
$312$	−74.2795	+	52.3884i	−0.238075	+	0.167912i
$313$	−75.2300	−	280.762i	−0.240351	−	0.897003i	−0.975663	−	0.219274i	$-0.929631\pi$
$313$	−75.2300	−	280.762i	−0.240351	−	0.897003i	0.735312	−	0.677729i	$-0.237036\pi$
$314$	268.974	−	285.744i	0.856607	−	0.910014i
$315$	−742.925	−	202.036i	−2.35849	−	0.641385i
$316$	223.209	−	13.5082i	0.706359	−	0.0427476i
$317$	96.5515	+	360.335i	0.304579	+	1.13670i	0.933307	+	0.359079i	$0.116909\pi$
$317$	96.5515	+	360.335i	0.304579	+	1.13670i	−0.628728	+	0.777625i	$0.716424\pi$
$318$	128.842	+	208.355i	0.405163	+	0.655206i
$319$	79.5712	+	137.821i	0.249439	+	0.432042i
$320$	103.846	+	302.681i	0.324519	+	0.945879i
$321$			171.973i			0.535742i
$322$	−48.8584	−	6.02387i	−0.151734	−	0.0187077i
$323$	45.1089	−	45.1089i	0.139656	−	0.139656i
$324$	−366.187	+	733.278i	−1.13021	+	2.26320i
$325$	23.8783	−	45.0860i	0.0734717	−	0.138726i
$326$	39.2055	−	166.261i	0.120262	−	0.510002i
$327$	−55.9647	−	208.863i	−0.171146	−	0.638726i
$328$	323.503	−	29.4116i	0.986289	−	0.0896695i
$329$	516.207	−	200.635i	1.56902	−	0.609834i
$330$	−472.659	−	39.0392i	−1.43230	−	0.118301i
$331$	517.048	+	298.518i	1.56208	+	0.901866i	0.997047	+	0.0767959i	$0.0244690\pi$
$331$	517.048	+	298.518i	1.56208	+	0.901866i	0.565031	+	0.825070i	$0.308864\pi$
$332$	−4.18185	+	20.4871i	−0.0125959	+	0.0617082i
$333$	36.6209	−	136.671i	0.109973	−	0.410424i
$334$	−111.970	+	33.6599i	−0.335239	+	0.100778i
$335$	−304.877	−	34.4843i	−0.910082	−	0.102938i
$336$	−328.903	+	529.767i	−0.978878	+	1.57669i
$337$	−218.359	+	218.359i	−0.647948	+	0.647948i	−0.952497	−	0.304549i	$-0.901494\pi$
$337$	−218.359	+	218.359i	−0.647948	+	0.647948i	0.304549	+	0.952497i	$0.401494\pi$
$338$	−156.133	+	290.354i	−0.461931	+	0.859035i
$339$	742.350	−	428.596i	2.18982	−	1.26429i
$340$	−37.4531	−	73.4742i	−0.110156	−	0.216101i
$341$	444.353	+	256.547i	1.30309	+	0.752338i
$342$	−20.5672	−	680.325i	−0.0601380	−	1.98925i
$343$	−110.079	−	324.856i	−0.320930	−	0.947103i
$344$	−31.0682	−	25.8898i	−0.0903144	−	0.0752609i
$345$	−14.5475	−	96.7986i	−0.0421665	−	0.280576i
$346$	−17.0707	+	72.3926i	−0.0493374	+	0.209227i
$347$	119.890	−	447.435i	0.345504	−	1.28944i	−0.546518	−	0.837447i	$-0.684047\pi$
$347$	119.890	−	447.435i	0.345504	−	1.28944i	0.892022	−	0.451991i	$-0.149286\pi$
$348$	131.761	+	394.635i	0.378624	+	1.13401i
$349$	292.354			0.837690			0.418845	−	0.908058i	$-0.362435\pi$
$349$	292.354			0.837690			0.418845	+	0.908058i	$0.362435\pi$
$350$	30.1096	−	348.702i	0.0860275	−	0.996293i
$351$		−	147.675i		−	0.420726i
$352$	−99.2052	+	253.899i	−0.281833	+	0.721303i
$353$	−220.998	−	59.2163i	−0.626057	−	0.167752i	−0.0681775	−	0.997673i	$-0.521718\pi$
$353$	−220.998	−	59.2163i	−0.626057	−	0.167752i	−0.557880	+	0.829922i	$0.688385\pi$
$354$	−63.6782	+	270.043i	−0.179882	+	0.762833i
$355$	361.054	−	54.2613i	1.01705	−	0.152849i
$356$	8.20370	−	0.496473i	0.0230441	−	0.00139459i
$357$	64.7489	−	147.081i	0.181369	−	0.411993i
$358$	−2.60414	−	86.1399i	−0.00727412	−	0.240614i
$359$	−220.510	+	381.935i	−0.614235	+	1.06389i	0.376284	+	0.926504i	$0.377202\pi$
$359$	−220.510	+	381.935i	−0.614235	+	1.06389i	−0.990518	+	0.137381i	$0.956132\pi$
$360$	−844.705	−	246.344i	−2.34640	−	0.684288i
$361$	−60.8261	−	105.354i	−0.168493	−	0.291839i
$362$	−214.114	+	398.178i	−0.591474	+	1.09994i
$363$	190.682	+	190.682i	0.525295	+	0.525295i
$364$	5.27524	−	56.8970i	0.0144924	−	0.156311i
$365$	−60.1304	+	531.617i	−0.164741	+	1.45648i
$366$	−513.188	+	154.272i	−1.40215	+	0.421509i
$367$	274.392	+	73.5230i	0.747661	+	0.200335i	0.612481	−	0.790486i	$-0.290172\pi$
$367$	274.392	+	73.5230i	0.747661	+	0.200335i	0.135181	+	0.990821i	$0.456838\pi$
$368$	−55.7033	−	7.90154i	−0.151368	−	0.0214716i
$369$	−446.597	+	773.529i	−1.21029	+	2.09628i
$370$	64.1042	+	5.29467i	0.173255	+	0.0143099i
$371$	−152.205	−	23.4546i	−0.410256	−	0.0632199i
$372$	1004.08	+	889.481i	2.69913	+	2.39108i
$373$	260.223	−	69.7264i	0.697648	−	0.186934i	0.107471	−	0.994208i	$-0.465725\pi$
$373$	260.223	−	69.7264i	0.697648	−	0.186934i	0.590177	+	0.807274i	$0.299058\pi$
$374$	16.1236	−	68.3761i	0.0431113	−	0.182824i
$375$	683.974	−	128.501i	1.82393	−	0.342669i
$376$	594.035	−	218.501i	1.57988	−	0.581120i
$377$	−26.9587	−	26.9587i	−0.0715084	−	0.0715084i
$378$	−395.376	−	932.745i	−1.04597	−	2.46758i
$379$	142.516			0.376033			0.188016	−	0.982166i	$-0.439794\pi$
$379$	142.516			0.376033			0.188016	+	0.982166i	$0.439794\pi$
$380$	302.645	−	64.3843i	0.796433	−	0.169432i
$381$	−697.811	+	402.881i	−1.83153	+	1.05743i
$382$	63.2740	+	102.323i	0.165639	+	0.267861i
$383$	−526.600	+	141.102i	−1.37493	+	0.368413i	−0.869279	−	0.494323i	$-0.835416\pi$
$383$	−526.600	+	141.102i	−1.37493	+	0.368413i	−0.505656	+	0.862735i	$0.668749\pi$
$384$	−386.868	+	598.493i	−1.00747	+	1.55858i
$385$	211.606	−	210.035i	0.549626	−	0.545545i
$386$	360.004	−	382.449i	0.932652	−	0.990800i
$387$	107.411	−	28.7808i	0.277549	−	0.0743690i
$388$	104.291	−	510.930i	0.268792	−	1.31683i
$389$	−523.912	+	302.481i	−1.34682	+	0.777586i	−0.987798	−	0.155743i	$-0.950223\pi$
$389$	−523.912	+	302.481i	−1.34682	+	0.777586i	−0.359021	+	0.933329i	$0.616889\pi$
$390$	111.796	−	20.2732i	0.286657	−	0.0519826i
$391$	14.4994			0.0370828
$392$	−119.013	−	373.497i	−0.303605	−	0.952798i
$393$	−612.467	−	612.467i	−1.55844	−	1.55844i
$394$	434.783	−	130.703i	1.10351	−	0.331733i
$395$	−260.156	−	102.233i	−0.658623	−	0.258817i
$396$	−413.295	−	625.293i	−1.04368	−	1.57902i
$397$	131.335	−	35.1911i	0.330818	−	0.0886425i	−0.0895867	−	0.995979i	$-0.528555\pi$
$397$	131.335	−	35.1911i	0.330818	−	0.0886425i	0.420405	+	0.907336i	$0.361888\pi$
$398$	−430.919	+	13.0273i	−1.08271	+	0.0327319i
$399$	470.157	+	377.479i	1.17834	+	0.946064i
$400$	41.6726	−	397.823i	0.104182	−	0.994558i
$401$	306.126	−	530.226i	0.763407	−	1.32226i	−0.177678	−	0.984089i	$-0.556859\pi$
$401$	306.126	−	530.226i	0.763407	−	1.32226i	0.941085	−	0.338171i	$-0.109808\pi$
$402$	−359.372	−	581.156i	−0.893961	−	1.44566i
$403$	−118.732	−	31.8142i	−0.294621	−	0.0789435i
$404$	376.470	+	188.003i	0.931857	+	0.465354i
$405$	801.288	−	638.442i	1.97849	−	1.57640i
$406$	−242.454	−	98.0989i	−0.597177	−	0.241623i
$407$	38.7445	+	38.7445i	0.0951954	+	0.0951954i
$408$	77.0517	−	166.716i	0.188852	−	0.408617i
$409$	166.789	+	288.887i	0.407797	+	0.706324i	0.994643	−	0.103374i	$-0.0329639\pi$
$409$	166.789	+	288.887i	0.407797	+	0.706324i	−0.586846	+	0.809699i	$0.699631\pi$
$410$	−382.229	−	137.021i	−0.932266	−	0.334196i
$411$	−287.518	+	497.996i	−0.699557	+	1.21167i
$412$	181.085	+	160.417i	0.439525	+	0.389363i
$413$	−103.109	−	140.676i	−0.249660	−	0.340621i
$414$	106.033	−	112.644i	0.256119	−	0.272087i
$415$	15.5297	−	21.0230i	0.0374209	−	0.0506579i
$416$	7.21364	−	64.9044i	0.0173405	−	0.156020i
$417$	642.890	+	172.262i	1.54170	+	0.413098i
$418$	232.142	+	124.831i	0.555364	+	0.298638i
$419$			254.061i			0.606350i	0.952935	+	0.303175i	$0.0980467\pi$
$419$			254.061i			0.606350i	−0.952935	+	0.303175i	$0.901953\pi$
$420$	651.848	−	427.366i	1.55202	−	1.01754i
$421$	−52.5835			−0.124901			−0.0624507	−	0.998048i	$-0.519892\pi$
$421$	−52.5835			−0.124901			−0.0624507	+	0.998048i	$0.519892\pi$
$422$	−248.468	+	462.065i	−0.588786	+	1.09494i
$423$	−450.446	+	1681.09i	−1.06488	+	3.97420i
$424$	−173.431	−	29.9729i	−0.409035	−	0.0706908i
$425$	3.76590	+	103.018i	0.00886094	+	0.242395i
$426$	592.060	+	557.313i	1.38981	+	1.30825i
$427$	135.731	−	308.322i	0.317871	−	0.722065i
$428$	−92.4842	−	81.9291i	−0.216085	−	0.191423i
$429$	83.8196	+	48.3933i	0.195384	+	0.112805i
$430$	21.5865	+	45.7111i	0.0502011	+	0.106305i
$431$	341.648	−	197.250i	0.792686	−	0.457657i	−0.0482214	−	0.998837i	$-0.515355\pi$
$431$	341.648	−	197.250i	0.792686	−	0.457657i	0.840907	+	0.541179i	$0.182022\pi$
$432$	−432.344	−	1074.06i	−1.00080	−	2.48624i
$433$	−310.022	+	310.022i	−0.715986	+	0.715986i	−0.967781	−	0.251795i	$-0.918979\pi$
$433$	−310.022	+	310.022i	−0.715986	+	0.715986i	0.251795	+	0.967781i	$0.418979\pi$
$434$	−835.115	+	116.942i	−1.92423	+	0.269451i
$435$	58.4508	−	516.767i	0.134370	−	1.18797i
$436$	138.985	+	69.4068i	0.318773	+	0.159190i
$437$	−14.0798	+	52.5467i	−0.0322193	+	0.120244i
$438$	−1013.37	+	626.640i	−2.31362	+	1.43069i
$439$	−552.104	−	318.757i	−1.25764	−	0.726099i	−0.285025	−	0.958520i	$-0.592002\pi$
$439$	−552.104	−	318.757i	−1.25764	−	0.726099i	−0.972615	+	0.232421i	$0.925335\pi$
$440$	246.172	−	235.590i	0.559483	−	0.535431i
$441$	1027.87	+	324.490i	2.33076	+	0.735806i
$442$	0.508562	+	16.8223i	0.00115059	+	0.0380594i
$443$	−63.1078	−	235.522i	−0.142456	−	0.531652i	−0.999855	−	0.0170007i	$-0.994588\pi$
$443$	−63.1078	−	235.522i	−0.142456	−	0.531652i	0.857400	−	0.514651i	$-0.172078\pi$
$444$	78.9865	+	119.502i	0.177898	+	0.269149i
$445$	−9.56161	−	3.75740i	−0.0214868	−	0.00844360i
$446$	105.055	+	349.465i	0.235549	+	0.783554i
$447$	−200.272	+	200.272i	−0.448036	+	0.448036i
$448$	−128.208	−	429.263i	−0.286179	−	0.958176i
$449$			144.570i			0.321982i	0.986956	+	0.160991i	$0.0514691\pi$
$449$			144.570i			0.321982i	−0.986956	+	0.160991i	$0.948531\pi$
$450$	827.874	+	724.107i	1.83972	+	1.60913i
$451$	−172.945	−	299.550i	−0.383470	−	0.664190i
$452$	−123.168	+	603.409i	−0.272496	+	1.33497i
$453$	152.529	+	569.245i	0.336708	+	1.25661i
$454$	−157.641	−	148.389i	−0.347226	−	0.326848i
$455$	−35.9434	+	61.7235i	−0.0789965	+	0.135656i
$456$	529.365	+	441.132i	1.16089	+	0.967394i
$457$	−182.841	−	682.373i	−0.400090	−	1.49316i	−0.812934	−	0.582355i	$-0.802131\pi$
$457$	−182.841	−	682.373i	−0.400090	−	1.49316i	0.412844	−	0.910802i	$-0.364535\pi$
$458$	376.951	−	233.097i	0.823037	−	0.508945i
$459$	149.193	+	258.410i	0.325040	+	0.562986i
$460$	58.9871	+	38.2921i	0.128233	+	0.0832436i
$461$		−	724.271i		−	1.57109i	−0.618807	−	0.785543i	$-0.712384\pi$
$461$		−	724.271i		−	1.57109i	0.618807	−	0.785543i	$-0.287616\pi$
$462$	658.987	+	81.2482i	1.42638	+	0.175862i
$463$	−100.647	+	100.647i	−0.217381	+	0.217381i	−0.807394	−	0.590013i	$-0.799123\pi$
$463$	−100.647	+	100.647i	−0.217381	+	0.217381i	0.590013	+	0.807394i	$0.299123\pi$
$464$	−275.000	−	117.147i	−0.592672	−	0.252473i
$465$	−669.856	−	1537.13i	−1.44055	−	3.30566i
$466$	−388.655	−	91.6477i	−0.834023	−	0.196669i
$467$	18.4242	+	68.7601i	0.0394523	+	0.147238i	0.982842	−	0.184447i	$-0.0590495\pi$
$467$	18.4242	+	68.7601i	0.0394523	+	0.147238i	−0.943390	+	0.331685i	$0.892383\pi$
$468$	134.409	+	119.069i	0.287200	+	0.254422i
$469$	424.539	+	65.4208i	0.905200	+	0.139490i
$470$	−788.497	−	65.1257i	−1.67765	−	0.138565i
$471$	−946.061	−	546.209i	−2.00862	−	1.15968i
$472$	−114.888	−	162.895i	−0.243406	−	0.345117i
$473$	−11.1454	+	41.5952i	−0.0235632	+	0.0879390i
$474$	−179.210	−	596.144i	−0.378081	−	1.25769i
$475$	−377.000	−	86.3892i	−0.793685	−	0.181872i
$476$	48.2511	+	104.891i	0.101368	+	0.220360i
$477$	342.202	−	342.202i	0.717405	−	0.717405i
$478$	540.174	+	290.469i	1.13007	+	0.607677i
$479$	−169.173	+	97.6724i	−0.353181	+	0.203909i	−0.666085	−	0.745876i	$-0.732031\pi$
$479$	−169.173	+	97.6724i	−0.353181	+	0.203909i	0.312905	+	0.949785i	$0.398698\pi$
$480$	753.752	−	474.752i	1.57032	−	0.989066i
$481$	−11.3680	−	6.56331i	−0.0236341	−	0.0136451i
$482$	536.582	−	16.2217i	1.11324	−	0.0336549i
$483$	14.8947	+	136.228i	0.0308378	+	0.282046i
$484$	−193.388	+	11.7035i	−0.399561	+	0.0241807i
$485$	−387.296	+	524.295i	−0.798549	+	1.08102i
$486$	952.977	+	224.719i	1.96086	+	0.462385i
$487$	−92.0270	+	343.450i	−0.188967	+	0.705235i	0.804779	+	0.593574i	$0.202284\pi$
$487$	−92.0270	+	343.450i	−0.188967	+	0.705235i	−0.993746	+	0.111661i	$0.964383\pi$
$488$	161.521	−	349.480i	0.330985	−	0.716148i
$489$	−475.524			−0.972442
$490$	−61.7711	+	486.091i	−0.126063	+	0.992022i
$491$		−	141.733i		−	0.288663i	−0.989529	−	0.144331i	$-0.953897\pi$
$491$		−	141.733i		−	0.288663i	0.989529	−	0.144331i	$-0.0461031\pi$
$492$	−286.378	−	857.724i	−0.582070	−	1.74334i
$493$	74.4098	+	19.9380i	0.150933	+	0.0404423i
$494$	−61.4588	−	14.4925i	−0.124411	−	0.0293369i
$495$	139.242	+	926.516i	0.281297	+	1.87175i
$496$	−956.696	+	116.221i	−1.92882	+	0.234316i
$497$	−508.124	+	55.5564i	−1.02238	+	0.111783i
$498$	58.1807	−	1.75889i	0.116829	−	0.00353190i
$499$	97.5019	−	168.878i	0.195395	−	0.338433i	−0.751635	−	0.659579i	$-0.770735\pi$
$499$	97.5019	−	168.878i	0.195395	−	0.338433i	0.947030	+	0.321146i	$0.104068\pi$
$500$	−256.744	+	429.048i	−0.513488	+	0.858097i
$501$	162.739	+	281.872i	0.324828	+	0.562618i
$502$	427.558	+	229.912i	0.851708	+	0.457992i
$503$	−159.054	−	159.054i	−0.316212	−	0.316212i	0.531098	−	0.847310i	$-0.321779\pi$
$503$	−159.054	−	159.054i	−0.316212	−	0.316212i	−0.847310	+	0.531098i	$0.821779\pi$
$504$	1167.75	+	392.206i	2.31696	+	0.778187i
$505$	−327.781	−	411.387i	−0.649071	−	0.814628i
$506$	17.2466	+	57.3710i	0.0340842	+	0.113381i
$507$	886.454	+	237.525i	1.74843	+	0.468490i
$508$	115.779	−	567.206i	0.227911	−	1.11655i
$509$	25.6969	−	44.5083i	0.0504850	−	0.0874427i	−0.839679	−	0.543084i	$-0.817257\pi$
$509$	25.6969	−	44.5083i	0.0504850	−	0.0874427i	0.890164	+	0.455641i	$0.150590\pi$
$510$	−175.146	+	148.421i	−0.343423	+	0.291021i
$511$	114.075	−	740.271i	0.223238	−	1.44867i
$512$	−137.553	−	493.177i	−0.268659	−	0.963235i
$513$	−1081.37	+	289.753i	−2.10794	+	0.564820i
$514$	619.434	+	146.067i	1.20512	+	0.284177i
$515$	−120.808	−	277.221i	−0.234579	−	0.538292i
$516$	−50.2973	+	100.719i	−0.0974755	+	0.195192i
$517$	−476.567	−	476.567i	−0.921793	−	0.921793i
$518$	−89.3747	−	11.0192i	−0.172538	−	0.0212727i
$519$	207.051			0.398942
$520$	−42.3577	+	69.7803i	−0.0814572	+	0.134193i
$521$	−285.569	+	164.873i	−0.548116	+	0.316455i	−0.748362	−	0.663291i	$-0.769159\pi$
$521$	−285.569	+	164.873i	−0.548116	+	0.316455i	0.200246	+	0.979746i	$0.435826\pi$
$522$	699.050	−	432.275i	1.33918	−	0.828113i
$523$	497.936	−	133.422i	0.952077	−	0.255108i	0.250834	−	0.968030i	$-0.419295\pi$
$523$	497.936	−	133.422i	0.952077	−	0.255108i	0.701243	+	0.712922i	$0.252629\pi$
$524$	621.158	−	37.5913i	1.18542	−	0.0717392i
$525$	−964.030	+	141.209i	−1.83625	+	0.268969i
$526$	540.543	+	508.820i	1.02765	+	0.967338i
$527$	239.906	−	64.2827i	0.455230	−	0.121979i
$528$	751.309	+	106.574i	1.42293	+	0.201844i
$529$	447.420	−	258.318i	0.845784	−	0.488313i
$530$	180.826	+	125.311i	0.341182	+	0.236436i
$531$	548.102			1.03221
$532$	−426.987	+	73.0088i	−0.802608	+	0.137235i
$533$	58.5937	+	58.5937i	0.109932	+	0.109932i
$534$	−6.58659	−	21.9103i	−0.0123344	−	0.0410306i
$535$	61.6996	+	141.583i	0.115326	+	0.264642i
$536$	483.743	+	83.6020i	0.902506	+	0.155974i
$537$	−231.728	+	62.0914i	−0.431524	+	0.115626i
$538$	−13.6832	−	452.615i	−0.0254335	−	0.841292i
$539$	−307.845	+	281.885i	−0.571141	+	0.522978i
$540$	−75.4917	+	1445.29i	−0.139799	+	2.67646i
$541$	−201.757	+	349.454i	−0.372934	+	0.645941i	−0.990016	−	0.140958i	$-0.954982\pi$
$541$	−201.757	+	349.454i	−0.372934	+	0.645941i	0.617081	+	0.786899i	$0.288315\pi$
$542$	−56.7470	+	35.0909i	−0.104699	+	0.0647434i
$543$	1215.64	+	325.731i	2.23876	+	0.599873i
$544$	52.9489	+	120.861i	0.0973326	+	0.222172i
$545$	−121.010	−	151.876i	−0.222037	−	0.278671i
$546$	−157.530	+	22.0590i	−0.288517	+	0.0404012i
$547$	250.250	+	250.250i	0.457496	+	0.457496i	0.897833	−	0.440337i	$-0.145141\pi$
$547$	250.250	+	250.250i	0.457496	+	0.457496i	−0.440337	+	0.897833i	$0.645141\pi$
$548$	−130.838	−	391.870i	−0.238756	−	0.715092i
$549$	529.312	+	916.795i	0.964138	+	1.66994i
$550$	−403.141	+	137.438i	−0.732983	+	0.249887i
$551$	−144.513	+	250.304i	−0.262275	+	0.454273i
$552$	14.1805	+	155.974i	0.0256893	+	0.282561i
$553$	358.162	+	157.672i	0.647670	+	0.285120i
$554$	−47.8274	−	45.0205i	−0.0863311	−	0.0812644i
$555$	−26.6111	−	177.070i	−0.0479480	−	0.319045i
$556$	−398.916	+	263.669i	−0.717475	+	0.474224i
$557$	565.179	+	151.439i	1.01468	+	0.271884i	0.727585	−	0.686018i	$-0.240643\pi$
$557$	565.179	+	151.439i	1.01468	+	0.271884i	0.287098	+	0.957901i	$0.407309\pi$
$558$	1255.02	−	2333.90i	2.24913	−	4.18262i
$559$		−	10.3164i		−	0.0184550i
$560$	−80.7144	+	554.153i	−0.144133	+	0.989558i
$561$	−195.563			−0.348598
$562$	286.372	+	153.991i	0.509558	+	0.274006i
$563$	128.347	−	478.997i	0.227969	−	0.850794i	−0.753224	−	0.657765i	$-0.771502\pi$
$563$	128.347	−	478.997i	0.227969	−	0.850794i	0.981193	−	0.193029i	$-0.0618312\pi$
$564$	−971.553	−	1469.91i	−1.72261	−	2.60622i
$565$	457.397	−	619.194i	0.809553	−	1.09592i
$566$	−11.7444	+	12.4767i	−0.0207499	+	0.0220436i
$567$	−1156.87	+	847.936i	−2.04034	+	1.49548i
$568$	−581.774	+	52.8926i	−1.02425	+	0.0931208i
$569$	−745.688	−	430.523i	−1.31052	−	0.756631i	−0.328341	−	0.944559i	$-0.606490\pi$
$569$	−745.688	−	430.523i	−1.31052	−	0.756631i	−0.982183	+	0.187928i	$0.939823\pi$
$570$	−367.809	−	778.865i	−0.645278	−	1.36643i
$571$	228.321	−	131.821i	0.399862	−	0.230860i	−0.286562	−	0.958062i	$-0.592513\pi$
$571$	228.321	−	131.821i	0.399862	−	0.230860i	0.686424	+	0.727201i	$0.259179\pi$
$572$	−65.9572	+	22.0219i	−0.115310	+	0.0384998i
$573$	236.813	−	236.813i	0.413286	−	0.413286i
$574$	526.965	+	213.214i	0.918057	+	0.371454i
$575$	−46.7056	−	74.4738i	−0.0812272	−	0.129520i
$576$	1326.17	+	472.498i	2.30238	+	0.820310i
$577$	135.075	−	504.106i	0.234099	−	0.873668i	−0.744455	−	0.667673i	$-0.767290\pi$
$577$	135.075	−	504.106i	0.234099	−	0.873668i	0.978553	−	0.205995i	$-0.0660429\pi$
$578$	286.109	+	462.678i	0.494998	+	0.800482i
$579$	−1266.24	−	731.062i	−2.18694	−	1.26263i
$580$	250.062	+	277.625i	0.431142	+	0.478664i
$581$	−22.9087	+	28.5332i	−0.0394298	+	0.0491105i
$582$	−1450.97	+	43.8650i	−2.49308	+	0.0753694i
$583$	48.5050	+	181.023i	0.0831989	+	0.310503i
$584$	145.777	−	843.506i	0.249619	−	1.44436i
$585$	−89.6695	−	205.766i	−0.153281	−	0.351737i
$586$	−841.466	+	252.958i	−1.43595	+	0.431669i
$587$	564.779	−	564.779i	0.962145	−	0.962145i	−0.0371639	−	0.999309i	$-0.511832\pi$
$587$	564.779	−	564.779i	0.962145	−	0.962145i	0.999309	+	0.0371639i	$0.0118324\pi$
$588$	−935.933	+	561.091i	−1.59172	+	0.954236i
$589$			931.858i			1.58210i
$590$	44.4592	+	245.169i	0.0753546	+	0.415541i
$591$	−631.920	−	1094.52i	−1.06924	−	1.85197i
$592$	−101.896	−	14.4540i	−0.172122	−	0.0244155i
$593$	−237.294	−	885.592i	−0.400158	−	1.49341i	−0.812814	−	0.582523i	$-0.802066\pi$
$593$	−237.294	−	885.592i	−0.400158	−	1.49341i	0.412656	−	0.910887i	$-0.364601\pi$
$594$	−845.014	+	897.699i	−1.42258	+	1.51128i
$595$	0.537784	−	144.320i	0.000903839	−	0.242555i
$596$	−12.2921	−	203.114i	−0.0206243	−	0.340795i
$597$	310.615	+	1159.23i	0.520293	+	1.94176i
$598$	−7.54821	−	12.2065i	−0.0126224	−	0.0204123i
$599$	126.701	+	219.453i	0.211521	+	0.366365i	0.952191	−	0.305504i	$-0.0988250\pi$
$599$	126.701	+	219.453i	0.211521	+	0.366365i	−0.740670	+	0.671869i	$0.765492\pi$
$600$	−1104.51	+	141.263i	−1.84085	+	0.235438i
$601$		−	267.924i		−	0.445797i	−0.974842	−	0.222899i	$-0.928448\pi$
$601$		−	267.924i		−	0.445797i	0.974842	−	0.222899i	$-0.0715519\pi$
$602$	−27.6204	−	65.1603i	−0.0458811	−	0.108240i
$603$	−954.488	+	954.488i	−1.58290	+	1.58290i
$604$	−378.796	−	189.165i	−0.627146	−	0.313186i
$605$	225.398	+	88.5741i	0.372559	+	0.146403i
$606$	268.855	−	1140.14i	0.443655	−	1.88143i
$607$	−39.3324	−	146.790i	−0.0647980	−	0.241829i	0.925929	−	0.377698i	$-0.123284\pi$
$607$	−39.3324	−	146.790i	−0.0647980	−	0.241829i	−0.990727	+	0.135868i	$0.956618\pi$
$608$	−489.426	+	74.5259i	−0.804977	+	0.122576i
$609$	−110.888	+	719.594i	−0.182082	+	1.18160i
$610$	−367.152	+	311.130i	−0.601889	+	0.510048i
$611$	139.829	+	80.7303i	0.228853	+	0.132128i
$612$	−355.491	−	72.5632i	−0.580868	−	0.118567i
$613$	−148.079	+	552.639i	−0.241565	+	0.901531i	0.733515	+	0.679674i	$0.237879\pi$
$613$	−148.079	+	552.639i	−0.241565	+	0.901531i	−0.975079	+	0.221858i	$0.928788\pi$
$614$	−810.588	+	243.676i	−1.32018	+	0.396866i
$615$	−127.041	+	1123.17i	−0.206570	+	1.82630i
$616$	−357.639	+	315.685i	−0.580583	+	0.512475i
$617$	−28.0558	+	28.0558i	−0.0454714	+	0.0454714i	−0.729477	−	0.684005i	$-0.760236\pi$
$617$	−28.0558	+	28.0558i	−0.0454714	+	0.0454714i	0.684005	+	0.729477i	$0.260236\pi$
$618$	318.947	−	593.132i	0.516095	−	0.959760i
$619$	−751.053	+	433.620i	−1.21333	+	0.700518i	−0.963484	−	0.267767i	$-0.913714\pi$
$619$	−751.053	+	433.620i	−1.21333	+	0.700518i	−0.249848	+	0.968285i	$0.580381\pi$
$620$	1145.77	+	372.061i	1.84801	+	0.600099i
$621$	−220.361	−	127.225i	−0.354848	−	0.204872i
$622$	−3.62616	−	119.947i	−0.00582984	−	0.192840i
$623$	13.1636	+	5.79496i	0.0211294	+	0.00930170i
$624$	−180.464	+	21.9230i	−0.289206	+	0.0351331i
$625$	517.004	−	351.186i	0.827207	−	0.561897i
$626$	133.423	−	565.814i	0.213136	−	0.903856i
$627$	189.905	−	708.734i	0.302878	−	1.13036i
$628$	744.451	−	248.558i	1.18543	−	0.395794i
$629$	26.5232			0.0421672
$630$	−1117.28	−	1059.58i	−1.77345	−	1.68188i
$631$			289.957i			0.459519i	0.973247	+	0.229760i	$0.0737940\pi$
$631$			289.957i			0.459519i	−0.973247	+	0.229760i	$0.926206\pi$
$632$	405.973	+	187.631i	0.642363	+	0.296884i
$633$	1410.69	+	377.994i	2.22858	+	0.597146i
$634$	−171.238	+	726.176i	−0.270091	+	1.14539i
$635$	−429.955	+	582.044i	−0.677095	+	0.916605i
$636$	29.5966	+	489.053i	0.0465355	+	0.768951i
$637$	53.7585	−	84.3172i	0.0843933	−	0.132366i
$638$	9.61781	+	318.139i	0.0150749	+	0.498651i
$639$	803.142	−	1391.08i	1.25687	−	2.17697i
$640$	−103.779	+	631.530i	−0.162154	+	0.986765i
$641$	−633.637	−	1097.49i	−0.988513	−	1.71215i	−0.625144	−	0.780509i	$-0.714960\pi$
$641$	−633.637	−	1097.49i	−0.988513	−	1.71215i	−0.363369	−	0.931645i	$-0.618373\pi$
$642$	−162.894	+	302.927i	−0.253729	+	0.471849i
$643$	536.286	+	536.286i	0.834037	+	0.834037i	0.988066	−	0.154029i	$-0.0492250\pi$
$643$	536.286	+	536.286i	0.834037	+	0.834037i	−0.154029	+	0.988066i	$0.549225\pi$
$644$	−80.3570	−	56.8898i	−0.124778	−	0.0883382i
$645$	110.060	−	87.6928i	0.170636	−	0.135958i
$646$	122.186	−	36.7310i	0.189142	−	0.0568591i
$647$	−49.5832	−	13.2858i	−0.0766356	−	0.0205344i	0.220298	−	0.975433i	$-0.429297\pi$
$647$	−49.5832	−	13.2858i	−0.0766356	−	0.0205344i	−0.296933	+	0.954898i	$0.595964\pi$
$648$	−1339.59	+	944.798i	−2.06727	+	1.45802i
$649$	−106.127	+	183.817i	−0.163523	+	0.283230i
$650$	84.7667	−	56.8003i	0.130410	−	0.0873851i
$651$	850.411	+	2187.99i	1.30631	+	3.36097i
$652$	226.543	−	255.729i	0.347458	−	0.392222i
$653$	90.5677	−	24.2675i	0.138695	−	0.0371632i	−0.188804	−	0.982015i	$-0.560461\pi$
$653$	90.5677	−	24.2675i	0.138695	−	0.0371632i	0.327499	+	0.944852i	$0.393794\pi$
$654$	99.2557	−	420.918i	0.151767	−	0.643605i
$655$	−723.974	−	284.498i	−1.10530	−	0.434349i
$656$	597.702	+	254.616i	0.911131	+	0.388134i
$657$	1664.35	+	1664.35i	2.53325	+	2.53325i
$658$	1099.33	+	135.539i	1.67072	+	0.205987i
$659$	422.173			0.640627			0.320313	−	0.947312i	$-0.396212\pi$
$659$	422.173			0.640627			0.320313	+	0.947312i	$0.396212\pi$
$660$	−795.601	−	516.472i	−1.20546	−	0.782533i
$661$	−614.106	+	354.554i	−0.929056	+	0.536391i	−0.886513	−	0.462704i	$-0.846879\pi$
$661$	−614.106	+	354.554i	−0.929056	+	0.536391i	−0.0425429	+	0.999095i	$0.513546\pi$
$662$	628.010	+	1015.58i	0.948656	+	1.53411i
$663$	45.2542	−	12.1258i	0.0682567	−	0.0182893i
$664$	−26.7717	+	32.1265i	−0.0403189	+	0.0483833i
$665$	522.504	+	142.093i	0.785720	+	0.213674i
$666$	193.962	−	206.056i	0.291235	−	0.309393i
$667$	−63.4532	+	17.0022i	−0.0951323	+	0.0254906i
$668$	−229.115	−	46.7673i	−0.342987	−	0.0700109i
$669$	879.739	−	507.917i	1.31501	−	0.759219i
$670$	−504.371	−	349.525i	−0.752792	−	0.521678i
$671$	−409.953			−0.610958
$672$	−1081.15	+	621.634i	−1.60886	+	0.925051i
$673$	−150.039	−	150.039i	−0.222941	−	0.222941i	0.586795	−	0.809736i	$-0.300390\pi$
$673$	−150.039	−	150.039i	−0.222941	−	0.222941i	−0.809736	+	0.586795i	$0.800390\pi$
$674$	−591.464	+	177.803i	−0.877543	+	0.263803i
$675$	846.700	−	1598.70i	1.25437	−	2.36845i
$676$	−550.049	+	363.562i	−0.813682	+	0.537813i
$677$	−920.162	+	246.557i	−1.35918	+	0.364190i	−0.863513	−	0.504326i	$-0.831741\pi$
$677$	−920.162	+	246.557i	−1.35918	+	0.364190i	−0.495662	+	0.868516i	$0.665074\pi$
$678$	1713.60	−	51.8046i	2.52743	−	0.0764080i
$679$	571.323	−	711.592i	0.841418	−	1.04800i
$680$	3.62230	−	164.899i	0.00532690	−	0.242499i
$681$	−301.334	+	521.926i	−0.442488	+	0.766412i
$682$	539.715	+	872.796i	0.791371	+	1.27976i
$683$	−337.146	−	90.3381i	−0.493626	−	0.132267i	0.00341436	−	0.999994i	$-0.498913\pi$
$683$	−337.146	−	90.3381i	−0.493626	−	0.132267i	−0.497040	+	0.867728i	$0.665580\pi$
$684$	608.178	−	1217.86i	0.889150	−	1.78049i
$685$	−58.0414	+	513.147i	−0.0847320	+	0.749120i
$686$	113.804	−	676.494i	0.165895	−	0.986143i
$687$	−872.402	−	872.402i	−1.26987	−	1.26987i
$688$	−30.2029	−	75.0321i	−0.0438996	−	0.109058i
$689$	−22.4485	−	38.8820i	−0.0325813	−	0.0564325i
$690$	66.0631	−	184.288i	0.0957436	−	0.267084i
$691$	645.897	−	1118.73i	0.934727	−	1.61900i	0.159608	−	0.987181i	$-0.448977\pi$
$691$	645.897	−	1118.73i	0.934727	−	1.61900i	0.775120	−	0.631814i	$-0.217690\pi$
$692$	−98.6404	+	111.349i	−0.142544	+	0.160908i
$693$	−142.565	−	1303.92i	−0.205722	−	1.88156i
$694$	634.996	−	674.587i	0.914980	−	0.972027i
$695$	591.086	−	88.8319i	0.850484	−	0.127816i
$696$	−141.705	+	819.945i	−0.203600	+	1.17808i
$697$	−161.727	−	43.3346i	−0.232033	−	0.0621730i
$698$	514.974	+	276.919i	0.737786	+	0.396732i
$699$			1111.60i			1.59027i
$700$	383.330	−	585.712i	0.547614	−	0.836731i
$701$	898.756			1.28211			0.641053	−	0.767497i	$-0.278498\pi$
$701$	898.756			1.28211			0.641053	+	0.767497i	$0.278498\pi$
$702$	139.878	−	260.126i	0.199257	−	0.370550i
$703$	−25.7557	+	96.1217i	−0.0366369	+	0.136731i
$704$	−415.242	+	353.269i	−0.589832	+	0.501803i
$705$	327.323	+	2178.00i	0.464288	+	3.08937i
$706$	−333.194	−	313.639i	−0.471946	−	0.444248i
$707$	435.337	+	593.948i	0.615752	+	0.840096i
$708$	−367.954	+	415.358i	−0.519709	+	0.586664i
$709$	−923.202	−	533.011i	−1.30212	−	0.751778i	−0.321351	−	0.946960i	$-0.604137\pi$
$709$	−923.202	−	533.011i	−1.30212	−	0.751778i	−0.980767	+	0.195182i	$0.937470\pi$
$710$	687.385	+	246.412i	0.968148	+	0.347059i
$711$	−1064.99	+	614.874i	−1.49788	+	0.864802i
$712$	14.9209	+	6.89605i	0.0209563	+	0.00968547i
$713$	−149.764	+	149.764i	−0.210047	+	0.210047i
$714$	253.370	−	197.750i	0.354860	−	0.276961i
$715$	86.3699	+	9.76918i	0.120797	+	0.0136632i
$716$	77.0051	−	154.200i	0.107549	−	0.215363i
$717$	441.891	−	1649.16i	0.616305	−	2.30008i
$718$	−750.194	+	463.901i	−1.04484	+	0.646102i
$719$	359.285	+	207.433i	0.499700	+	0.288502i	0.728590	−	0.684950i	$-0.240176\pi$
$719$	359.285	+	207.433i	0.499700	+	0.288502i	−0.228889	+	0.973452i	$0.573509\pi$
$720$	−1254.59	−	1234.04i	−1.74249	−	1.71394i
$721$	153.371	+	394.603i	0.212720	+	0.547299i
$722$	−7.35209	−	243.193i	−0.0101830	−	0.336833i
$723$	−386.779	−	1443.48i	−0.534964	−	1.99651i
$724$	−754.313	+	498.573i	−1.04187	+	0.688636i
$725$	−137.281	−	446.418i	−0.189354	−	0.615750i
$726$	155.267	+	516.497i	0.213867	+	0.711428i
$727$	−398.915	+	398.915i	−0.548714	+	0.548714i	−0.926069	−	0.377355i	$-0.876834\pi$
$727$	−398.915	+	398.915i	−0.548714	+	0.548714i	0.377355	+	0.926069i	$0.376834\pi$
$728$	63.1854	−	95.2261i	0.0867931	−	0.130805i
$729$		−	881.458i		−	1.20913i
$730$	−609.468	+	879.475i	−0.834888	+	1.20476i
$731$	10.4224	+	18.0522i	0.0142578	+	0.0246952i
$732$	−1050.10	−	214.347i	−1.43456	−	0.292824i
$733$	331.160	+	1235.91i	0.451787	+	1.68609i	0.697366	+	0.716715i	$0.254355\pi$
$733$	331.160	+	1235.91i	0.451787	+	1.68609i	−0.245579	+	0.969377i	$0.578978\pi$
$734$	413.693	+	389.414i	0.563615	+	0.530537i
$735$	1356.51	−	143.202i	1.84559	−	0.194833i
$736$	−90.6357	−	66.6808i	−0.123146	−	0.0905989i
$737$	−135.293	−	504.919i	−0.183572	−	0.685101i
$738$	−1519.36	+	939.535i	−2.05875	+	1.27308i
$739$	−282.489	−	489.285i	−0.382258	−	0.662091i	0.609126	−	0.793073i	$-0.291520\pi$
$739$	−282.489	−	489.285i	−0.382258	−	0.662091i	−0.991385	+	0.130982i	$0.958187\pi$
$740$	107.903	+	70.0463i	0.145815	+	0.0946571i
$741$			175.779i			0.237219i
$742$	−245.890	−	185.484i	−0.331388	−	0.249979i
$743$	517.421	−	517.421i	0.696395	−	0.696395i	−0.267236	−	0.963631i	$-0.586110\pi$
$743$	517.421	−	517.421i	0.696395	−	0.696395i	0.963631	+	0.267236i	$0.0861105\pi$
$744$	926.136	+	2517.87i	1.24481	+	3.38423i
$745$	−93.0288	+	236.734i	−0.124871	+	0.317764i
$746$	524.421	+	123.663i	0.702978	+	0.165767i
$747$	−29.7612	−	111.070i	−0.0398410	−	0.148689i
$748$	93.1676	−	105.171i	0.124556	−	0.140602i
$749$	−78.3303	−	201.533i	−0.104580	−	0.269070i
$750$	1326.52	+	421.513i	1.76870	+	0.562017i
$751$	615.837	+	355.554i	0.820023	+	0.473441i	0.850424	−	0.526097i	$-0.176345\pi$
$751$	615.837	+	355.554i	0.820023	+	0.473441i	−0.0304012	+	0.999538i	$0.509679\pi$
$752$	1253.34	+	177.788i	1.66668	+	0.236420i
$753$	349.765	−	1305.34i	0.464495	−	1.73352i
$754$	−21.9517	−	73.0225i	−0.0291137	−	0.0968468i
$755$	329.806	+	413.929i	0.436829	+	0.548250i
$756$	187.055	−	2017.51i	0.247427	−	2.66867i
$757$	−100.589	+	100.589i	−0.132879	+	0.132879i	−0.770418	−	0.637539i	$-0.779952\pi$
$757$	−100.589	+	100.589i	−0.132879	+	0.132879i	0.637539	+	0.770418i	$0.279952\pi$
$758$	251.039	+	134.992i	0.331186	+	0.178090i
$759$	144.425	−	83.3838i	0.190283	−	0.109860i
$760$	594.087	+	173.255i	0.781693	+	0.227967i
$761$	−26.1122	−	15.0759i	−0.0343130	−	0.0198106i	0.482745	−	0.875761i	$-0.339640\pi$
$761$	−26.1122	−	15.0759i	−0.0343130	−	0.0198106i	−0.517058	+	0.855950i	$0.672973\pi$
$762$	−1610.79	+	48.6965i	−2.11390	+	0.0639062i
$763$	160.717	+	219.273i	0.210639	+	0.287383i
$764$	14.5349	+	240.173i	0.0190247	+	0.314363i
$765$	364.791	+	269.470i	0.476851	+	0.352249i
$766$	−1061.25	−	250.250i	−1.38544	−	0.326697i
$767$	13.1607	−	49.1163i	0.0171586	−	0.0640369i
$768$	−1248.35	+	687.789i	−1.62546	+	0.895558i
$769$	−220.204			−0.286352			−0.143176	−	0.989697i	$-0.545731\pi$
$769$	−220.204			−0.286352			−0.143176	+	0.989697i	$0.545731\pi$
$770$	571.685	−	169.537i	0.742448	−	0.220178i
$771$		−	1771.65i		−	2.29786i
$772$	996.396	−	332.678i	1.29067	−	0.430930i
$773$	−645.235	−	172.890i	−0.834716	−	0.223661i	−0.183946	−	0.982936i	$-0.558887\pi$
$773$	−645.235	−	172.890i	−0.834716	−	0.223661i	−0.650770	+	0.759275i	$0.725554\pi$
$774$	216.464	+	51.0439i	0.279669	+	0.0659482i
$775$	−1102.97	−	1025.17i	−1.42318	−	1.32280i
$776$	667.662	−	801.206i	0.860389	−	1.03248i
$777$	27.2462	+	249.197i	0.0350660	+	0.320717i
$778$	−1209.37	+	36.5611i	−1.55446	+	0.0469936i
$779$	314.094	−	544.028i	0.403202	−	0.698367i
$780$	216.129	+	70.1829i	0.277089	+	0.0899781i
$781$	311.017	+	538.698i	0.398230	+	0.689754i
$782$	25.5403	+	13.7339i	0.0326603	+	0.0175625i
$783$	−955.927	−	955.927i	−1.22085	−	1.22085i
$784$	144.139	−	770.636i	0.183851	−	0.982954i
$785$	−974.846	−	110.263i	−1.24184	−	0.140463i
$786$	−498.715	−	1658.98i	−0.634498	−	2.11066i
$787$	1055.78	+	282.895i	1.34152	+	0.359460i	0.856998	−	0.515319i	$-0.172327\pi$
$787$	1055.78	+	282.895i	1.34152	+	0.359460i	0.484523	+	0.874779i	$0.338993\pi$
$788$	889.663	+	181.599i	1.12901	+	0.230455i
$789$	1033.26	−	1789.67i	1.30959	−	2.26827i
$790$	−361.423	−	426.502i	−0.457498	−	0.539876i
$791$	−674.733	+	840.391i	−0.853013	+	1.06244i
$792$	−135.730	−	1492.92i	−0.171376	−	1.88499i
$793$	94.8649	−	25.4190i	0.119628	−	0.0320542i
$794$	264.677	+	62.4128i	0.333346	+	0.0786055i
$795$	223.993	−	570.003i	0.281752	−	0.716985i
$796$	−771.393	−	385.221i	−0.969087	−	0.483946i
$797$	216.337	+	216.337i	0.271439	+	0.271439i	0.829679	−	0.558240i	$-0.188523\pi$
$797$	216.337	+	216.337i	0.271439	+	0.271439i	−0.558240	+	0.829679i	$0.688523\pi$
$798$	470.620	+	1110.26i	0.589750	+	1.39130i
$799$	−326.241			−0.408312
$800$	450.226	−	661.284i	0.562782	−	0.826605i
$801$	−39.1421	+	22.5987i	−0.0488665	+	0.0282131i
$802$	1041.47	−	644.017i	1.29859	−	0.803014i
$803$	−880.431	+	235.911i	−1.09643	+	0.293787i
$804$	−82.5525	−	1364.09i	−0.102677	−	1.69663i
$805$	61.1378	+	106.811i	0.0759476	+	0.132684i
$806$	−179.010	−	168.504i	−0.222097	−	0.209062i
$807$	−1217.60	+	326.254i	−1.50879	+	0.404280i
$808$	485.066	+	687.757i	0.600330	+	0.851185i
$809$	559.636	−	323.106i	0.691762	−	0.399389i	−0.112510	−	0.993651i	$-0.535889\pi$
$809$	559.636	−	323.106i	0.691762	−	0.399389i	0.804272	+	0.594262i	$0.202556\pi$
$810$	2016.19	−	365.617i	2.48912	−	0.451379i
$811$	495.089			0.610467			0.305234	−	0.952278i	$-0.401265\pi$
$811$	495.089			0.610467			0.305234	+	0.952278i	$0.401265\pi$
$812$	−334.157	−	402.453i	−0.411524	−	0.495631i
$813$	131.333	+	131.333i	0.161542	+	0.161542i
$814$	31.5486	+	104.947i	0.0387575	+	0.128927i
$815$	−391.493	+	170.606i	−0.480359	+	0.209333i
$816$	293.639	−	220.682i	0.359851	−	0.270444i
$817$	−75.5431	+	20.2417i	−0.0924641	+	0.0247757i
$818$	20.1599	+	666.851i	0.0246453	+	0.815221i
$819$	113.839	+	292.893i	0.138998	+	0.357622i
$820$	−543.501	−	603.408i	−0.662807	−	0.735863i
$821$	384.705	−	666.328i	0.468581	−	0.811606i	−0.530774	−	0.847513i	$-0.678099\pi$
$821$	384.705	−	666.328i	0.468581	−	0.811606i	0.999355	+	0.0359075i	$0.0114322\pi$
$822$	−978.160	+	604.870i	−1.18998	+	0.735851i
$823$	99.7629	+	26.7314i	0.121219	+	0.0324804i	0.318918	−	0.947782i	$-0.396680\pi$
$823$	99.7629	+	26.7314i	0.121219	+	0.0324804i	−0.197700	+	0.980263i	$0.563347\pi$
$824$	167.028	+	454.096i	0.202704	+	0.551087i
$825$	629.952	+	1004.48i	0.763578	+	1.21755i
$826$	−48.3755	−	345.464i	−0.0585660	−	0.418237i
$827$	507.961	+	507.961i	0.614221	+	0.614221i	0.944043	−	0.329822i	$-0.106989\pi$
$827$	507.961	+	507.961i	0.614221	+	0.614221i	−0.329822	+	0.944043i	$0.606989\pi$
$828$	293.472	−	97.9849i	0.354435	−	0.118339i
$829$	−89.6597	−	155.295i	−0.108154	−	0.187328i	0.806868	−	0.590731i	$-0.201161\pi$
$829$	−89.6597	−	155.295i	−0.108154	−	0.187328i	−0.915022	+	0.403403i	$0.867827\pi$
$830$	47.2683	−	22.3218i	0.0569498	−	0.0268938i
$831$	−91.4234	+	158.350i	−0.110016	+	0.190554i
$832$	74.1844	−	107.495i	0.0891640	−	0.129201i
$833$	−8.88574	+	201.855i	−0.0106672	+	0.242322i
$834$	969.269	+	912.384i	1.16219	+	1.09399i
$835$	235.109	+	173.675i	0.281568	+	0.207994i
$836$	290.673	+	439.773i	0.347695	+	0.526044i
$837$	−4210.13	−	1128.10i	−5.03002	−	1.34779i
$838$	−240.648	+	447.522i	−0.287169	+	0.534036i
$839$			408.701i			0.487129i	0.969885	+	0.243564i	$0.0783168\pi$
$839$			408.701i			0.487129i	−0.969885	+	0.243564i	$0.921683\pi$
$840$	1553.02	−	135.361i	1.84883	−	0.161145i
$841$	491.983			0.584998
$842$	−92.6247	−	49.8073i	−0.110006	−	0.0591536i
$843$	234.267	−	874.297i	0.277897	−	1.03713i
$844$	−875.341	+	578.568i	−1.03713	+	0.685507i
$845$	815.024	−	122.487i	0.964526	−	0.144954i
$846$	−2385.78	+	2534.53i	−2.82008	+	2.99590i
$847$	−310.310	−	136.606i	−0.366363	−	0.161282i
$848$	−277.104	−	217.071i	−0.326774	−	0.255980i
$849$	41.3085	+	23.8495i	0.0486555	+	0.0280913i
$850$	−90.9455	+	185.031i	−0.106995	+	0.217683i
$851$	−19.5876	+	11.3089i	−0.0230171	+	0.0132889i
$852$	515.011	+	1542.50i	0.604473	+	1.81044i
$853$	−710.510	+	710.510i	−0.832955	+	0.832955i	−0.987920	−	0.154965i	$-0.950473\pi$
$853$	−710.510	+	710.510i	−0.832955	+	0.832955i	0.154965	+	0.987920i	$0.450473\pi$
$854$	531.131	−	414.537i	0.621933	−	0.485406i
$855$	−1330.81	+	1060.35i	−1.55651	+	1.24018i
$856$	−85.3053	−	231.918i	−0.0996557	−	0.270932i
$857$	−252.283	+	941.532i	−0.294379	+	1.09864i	0.647330	+	0.762210i	$0.275885\pi$
$857$	−252.283	+	941.532i	−0.294379	+	1.09864i	−0.941709	+	0.336428i	$0.890781\pi$
$858$	101.808	+	164.638i	0.118657	+	0.191886i
$859$	794.722	+	458.833i	0.925171	+	0.534148i	0.885281	−	0.465056i	$-0.153966\pi$
$859$	794.722	+	458.833i	0.925171	+	0.534148i	0.0398899	+	0.999204i	$0.487299\pi$
$860$	−5.27374	+	100.966i	−0.00613226	+	0.117402i
$861$	241.012	−	1564.01i	0.279921	−	1.81650i
$862$	788.641	−	23.8418i	0.914897	−	0.0276587i
$863$	−70.8702	−	264.491i	−0.0821208	−	0.306479i	0.912633	−	0.408781i	$-0.134046\pi$
$863$	−70.8702	−	264.491i	−0.0821208	−	0.306479i	−0.994753	+	0.102302i	$0.967379\pi$
$864$	255.788	−	2301.45i	0.296051	−	2.66371i
$865$	170.462	−	74.2847i	0.197066	−	0.0858783i
$866$	−839.751	+	252.442i	−0.969689	+	0.291504i
$867$	1070.81	−	1070.81i	1.23507	−	1.23507i
$868$	−1581.80	−	585.035i	−1.82236	−	0.674004i
$869$		−	476.221i		−	0.548011i
$870$	592.444	−	854.909i	0.680970	−	0.982654i
$871$	62.6146	+	108.452i	0.0718882	+	0.124514i
$872$	179.077	+	253.906i	0.205363	+	0.291176i
$873$	742.218	+	2770.00i	0.850192	+	3.17296i
$874$	−74.5738	+	79.2233i	−0.0853247	+	0.0906445i
$875$	−743.011	+	462.125i	−0.849156	+	0.528143i
$876$	−2378.58	+	143.947i	−2.71527	+	0.164323i
$877$	322.012	+	1201.77i	0.367175	+	1.37031i	0.864449	+	0.502721i	$0.167668\pi$
$877$	322.012	+	1201.77i	0.367175	+	1.37031i	−0.497274	+	0.867593i	$0.665666\pi$
$878$	−670.590	−	1084.44i	−0.763770	−	1.23512i
$879$	1223.00	+	2118.29i	1.39135	+	2.40989i
$880$	656.779	−	181.810i	0.746340	−	0.206603i
$881$		−	1591.42i		−	1.80638i	−0.429241	−	0.903190i	$-0.641219\pi$
$881$		−	1591.42i		−	1.80638i	0.429241	−	0.903190i	$-0.358781\pi$
$882$	1503.20	+	1545.18i	1.70431	+	1.75191i
$883$	687.709	−	687.709i	0.778832	−	0.778832i	−0.200800	−	0.979632i	$-0.564354\pi$
$883$	687.709	−	687.709i	0.778832	−	0.778832i	0.979632	+	0.200800i	$0.0643542\pi$
$884$	−15.0383	+	30.1138i	−0.0170117	+	0.0340654i
$885$	635.868	−	277.101i	0.718495	−	0.313108i
$886$	111.924	−	474.642i	0.126325	−	0.535713i
$887$	−132.351	−	493.941i	−0.149212	−	0.556867i	−0.999532	−	0.0306005i	$-0.990258\pi$
$887$	−132.351	−	493.941i	−0.149212	−	0.556867i	0.850320	−	0.526267i	$-0.176409\pi$
$888$	25.9399	+	285.317i	0.0292116	+	0.321303i
$889$	634.251	−	789.970i	0.713444	−	0.888606i
$890$	−13.2835	−	15.6754i	−0.0149253	−	0.0176128i
$891$	1511.64	+	872.748i	1.69657	+	0.979515i
$892$	−145.964	+	715.083i	−0.163636	+	0.801663i
$893$	316.801	−	1182.32i	0.354761	−	1.32399i
$894$	−542.474	+	163.076i	−0.606794	+	0.182412i
$895$	−168.502	+	134.257i	−0.188270	+	0.150008i
$896$	180.764	−	877.576i	0.201745	−	0.979438i
$897$	−28.2504	+	28.2504i	−0.0314943	+	0.0314943i
$898$	−136.937	+	254.657i	−0.152492	+	0.283582i
$899$	−974.516	+	562.637i	−1.08400	+	0.625848i
$900$	772.404	+	2059.67i	0.858227	+	2.28852i
$901$	78.5635	+	45.3587i	0.0871959	+	0.0503426i
$902$	−20.9040	−	691.464i	−0.0231751	−	0.766590i
$903$	−158.902	+	116.468i	−0.175971	+	0.128979i
$904$	−788.510	+	946.225i	−0.872245	+	1.04671i
$905$	1117.69	−	167.973i	1.23501	−	0.185605i
$906$	−270.516	+	1147.19i	−0.298583	+	1.26621i
$907$	−438.187	+	1635.34i	−0.483117	+	1.80302i	0.105275	+	0.994443i	$0.466428\pi$
$907$	−438.187	+	1635.34i	−0.483117	+	1.80302i	−0.588392	+	0.808576i	$0.700239\pi$
$908$	−137.126	−	410.701i	−0.151019	−	0.452314i
$909$	−2314.13			−2.54580
$910$	−121.778	+	74.6788i	−0.133822	+	0.0820646i
$911$			1091.13i			1.19773i	0.800851	+	0.598863i	$0.204381\pi$
$911$			1091.13i			1.19773i	−0.800851	+	0.598863i	$0.795619\pi$
$912$	514.623	+	1278.46i	0.564280	+	1.40182i
$913$	43.0121	+	11.5251i	0.0471108	+	0.0126233i
$914$	324.276	−	1375.17i	0.354788	−	1.50457i
$915$	1077.57	+	795.997i	1.17767	+	0.869942i
$916$	884.781	−	53.5454i	0.965918	−	0.0584556i
$917$	996.709	+	438.776i	1.08692	+	0.478491i
$918$	18.0331	+	596.501i	0.0196439	+	0.649783i
$919$	−545.099	+	944.139i	−0.593144	+	1.02735i	0.400662	+	0.916226i	$0.368780\pi$
$919$	−545.099	+	944.139i	−0.593144	+	1.02735i	−0.993806	+	0.111129i	$0.964553\pi$
$920$	67.6341	+	123.324i	0.0735153	+	0.134047i
$921$	1178.12	+	2040.56i	1.27917	+	2.21560i
$922$	686.033	−	1275.79i	0.744071	−	1.38372i
$923$	−105.373	−	105.373i	−0.114163	−	0.114163i
$924$	1083.83	+	767.312i	1.17298	+	0.830425i
$925$	−85.4369	−	136.232i	−0.0923642	−	0.147278i
$926$	−272.622	+	81.9544i	−0.294408	+	0.0885037i
$927$	−1285.07	−	344.333i	−1.38626	−	0.371448i
$928$	−373.443	−	466.834i	−0.402417	−	0.503053i
$929$	−324.980	+	562.881i	−0.349817	+	0.605900i	−0.986217	−	0.165459i	$-0.947089\pi$
$929$	−324.980	+	562.881i	−0.349817	+	0.605900i	0.636400	+	0.771359i	$0.280423\pi$
$930$	276.041	−	3342.11i	0.296818	−	3.59367i
$931$	−722.905	−	228.216i	−0.776482	−	0.245130i
$932$	−597.797	−	529.571i	−0.641413	−	0.568209i
$933$	−322.673	+	86.4600i	−0.345845	+	0.0926688i
$934$	−32.6761	+	138.571i	−0.0349851	+	0.148363i
$935$	−161.005	+	70.1632i	−0.172198	+	0.0750409i
$936$	123.976	+	337.051i	0.132453	+	0.360097i
$937$	−816.492	−	816.492i	−0.871390	−	0.871390i	0.121234	−	0.992624i	$-0.461315\pi$
$937$	−816.492	−	816.492i	−0.871390	−	0.871390i	−0.992624	+	0.121234i	$0.961315\pi$
$938$	685.849	+	517.362i	0.731182	+	0.551559i
$939$	−1618.29			−1.72342
$940$	−1327.23	−	861.586i	−1.41195	−	0.916580i
$941$	−853.868	+	492.981i	−0.907405	+	0.523891i	−0.879595	−	0.475723i	$-0.842187\pi$
$941$	−853.868	+	492.981i	−0.907405	+	0.523891i	−0.0278098	+	0.999613i	$0.508853\pi$
$942$	−1149.09	−	1858.25i	−1.21984	−	1.97266i
$943$	137.913	−	36.9538i	0.146250	−	0.0391875i
$944$	−48.0773	−	395.759i	−0.0509293	−	0.419236i
$945$	−1274.52	+	2188.65i	−1.34870	+	2.31603i
$946$	−59.0315	+	62.7120i	−0.0624012	+	0.0662917i
$947$	−1310.90	+	351.254i	−1.38427	+	0.370913i	−0.872669	−	0.488313i	$-0.837613\pi$
$947$	−1310.90	+	351.254i	−1.38427	+	0.370913i	−0.511597	+	0.859226i	$0.670946\pi$
$948$	248.996	−	1219.84i	0.262654	−	1.28676i
$949$	189.108	−	109.182i	0.199271	−	0.115049i
$950$	−582.249	−	509.269i	−0.612894	−	0.536073i
$951$	2076.95			2.18396
$952$	−14.3603	+	230.467i	−0.0150843	+	0.242088i
$953$	859.587	+	859.587i	0.901980	+	0.901980i	0.995607	−	0.0936277i	$-0.0298463\pi$
$953$	859.587	+	859.587i	0.901980	+	0.901980i	−0.0936277	+	0.995607i	$0.529846\pi$
$954$	926.917	−	278.646i	0.971611	−	0.292082i
$955$	110.003	−	279.928i	0.115186	−	0.293118i
$956$	676.370	+	1023.31i	0.707500	+	1.07041i
$957$	855.838	−	229.321i	0.894293	−	0.239625i
$958$	−390.511	+	11.8057i	−0.407632	+	0.0123233i
$959$	110.111	−	714.553i	0.114819	−	0.745102i
$960$	1777.40	−	122.306i	1.85146	−	0.127403i
$961$	−1333.51	+	2309.71i	−1.38763	+	2.40345i
$962$	−13.8077	−	22.3289i	−0.0143531	−	0.0232110i
$963$	656.315	+	175.859i	0.681532	+	0.182616i
$964$	960.542	+	479.679i	0.996413	+	0.497592i
$965$	−1304.76	−	147.580i	−1.35209	−	0.152933i
$966$	−102.799	+	254.071i	−0.106417	+	0.263013i
$967$	281.079	+	281.079i	0.290672	+	0.290672i	0.837346	−	0.546674i	$-0.184106\pi$
$967$	281.079	+	281.079i	0.290672	+	0.290672i	−0.546674	+	0.837346i	$0.684106\pi$
$968$	−351.734	−	162.562i	−0.363361	−	0.167936i
$969$	−177.586	−	307.589i	−0.183268	−	0.317429i
$970$	−1178.83	+	556.686i	−1.21529	+	0.573903i
$971$	−544.948	+	943.878i	−0.561224	+	0.972068i	0.436167	+	0.899866i	$0.356336\pi$
$971$	−544.948	+	943.878i	−0.561224	+	0.972068i	−0.997390	+	0.0722017i	$0.976997\pi$
$972$	1465.79	+	1298.50i	1.50802	+	1.33591i
$973$	−831.856	+	90.9520i	−0.854940	+	0.0934759i
$974$	−487.421	+	517.810i	−0.500432	+	0.531633i
$975$	−208.056	−	193.381i	−0.213391	−	0.198340i
$976$	615.545	−	462.608i	0.630681	−	0.473984i
$977$	34.4579	+	9.23295i	0.0352690	+	0.00945031i	0.276410	−	0.961040i	$-0.410855\pi$
$977$	34.4579	+	9.23295i	0.0352690	+	0.00945031i	−0.241141	+	0.970490i	$0.577522\pi$
$978$	−837.625	−	450.419i	−0.856467	−	0.460551i
$979$		−	17.5027i		−	0.0178782i
$980$	−569.236	+	797.728i	−0.580853	+	0.814008i
$981$	−854.331			−0.870878
$982$	134.251	−	249.660i	0.136711	−	0.254237i
$983$	−167.894	+	626.589i	−0.170798	+	0.637425i	0.826432	+	0.563037i	$0.190367\pi$
$983$	−167.894	+	626.589i	−0.170798	+	0.637425i	−0.997229	+	0.0743882i	$0.976300\pi$
$984$	307.992	−	1782.12i	0.313000	−	1.81110i
$985$	−912.936	−	674.385i	−0.926839	−	0.684654i
$986$	112.186	+	105.602i	0.113779	+	0.107101i
$987$	−335.135	−	3065.18i	−0.339549	−	3.10555i
$988$	−94.5310	−	83.7422i	−0.0956791	−	0.0847593i
$989$	−15.3941	−	8.88778i	−0.0155653	−	0.00898664i
$990$	−632.328	+	1763.93i	−0.638715	+	1.78174i
$991$	−1202.14	+	694.058i	−1.21306	+	0.700361i	−0.963425	−	0.267979i	$-0.913644\pi$
$991$	−1202.14	+	694.058i	−1.21306	+	0.700361i	−0.249636	+	0.968340i	$0.580311\pi$
$992$	−1795.28	−	701.467i	−1.80976	−	0.707124i
$993$	2350.43	−	2350.43i	2.36700	−	2.36700i
$994$	−947.672	−	383.436i	−0.953392	−	0.385751i
$995$	671.628	+	842.938i	0.675003	+	0.847174i
$996$	104.150	+	52.0108i	0.104568	+	0.0522196i
$997$	132.835	−	495.748i	0.133235	−	0.497240i	−0.866764	−	0.498719i	$-0.833804\pi$
$997$	132.835	−	495.748i	0.133235	−	0.497240i	0.999999	+	0.00147879i	$0.000470712\pi$
$998$	331.710	−	205.121i	0.332374	−	0.205532i
$999$	−403.097	−	232.728i	−0.403501	−	0.232961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.3.x.a.103.38	yes	176
4.3	odd	2	inner	140.3.x.a.103.15	yes	176
5.2	odd	4	inner	140.3.x.a.47.17	yes	176
7.3	odd	6	inner	140.3.x.a.3.10	✓	176
20.7	even	4	inner	140.3.x.a.47.10	yes	176
28.3	even	6	inner	140.3.x.a.3.17	yes	176
35.17	even	12	inner	140.3.x.a.87.15	yes	176
140.87	odd	12	inner	140.3.x.a.87.38	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.3.x.a.3.10	✓	176	7.3	odd	6	inner
140.3.x.a.3.17	yes	176	28.3	even	6	inner
140.3.x.a.47.10	yes	176	20.7	even	4	inner
140.3.x.a.47.17	yes	176	5.2	odd	4	inner
140.3.x.a.87.15	yes	176	35.17	even	12	inner
140.3.x.a.87.38	yes	176	140.87	odd	12	inner
140.3.x.a.103.15	yes	176	4.3	odd	2	inner
140.3.x.a.103.38	yes	176	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	140.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.76148 + 0.947205i) q^{2} +(1.44098 - 5.37782i) q^{3} +(2.20561 + 3.33696i) q^{4} +(-0.743084 - 4.94447i) q^{5} +(7.63215 - 8.10800i) q^{6} +(0.760820 + 6.95853i) q^{7} +(0.724341 + 7.96714i) q^{8} +(-19.0503 - 10.9987i) q^{9} +O(q^{10})\)	\(q+(1.76148 + 0.947205i) q^{2} +(1.44098 - 5.37782i) q^{3} +(2.20561 + 3.33696i) q^{4} +(-0.743084 - 4.94447i) q^{5} +(7.63215 - 8.10800i) q^{6} +(0.760820 + 6.95853i) q^{7} +(0.724341 + 7.96714i) q^{8} +(-19.0503 - 10.9987i) q^{9} +(3.37450 - 9.41343i) q^{10} +(7.37723 - 4.25924i) q^{11} +(21.1238 - 7.05285i) q^{12} +(-1.44303 + 1.44303i) q^{13} +(-5.25099 + 12.9779i) q^{14} +(-27.6612 - 3.12873i) q^{15} +(-6.27060 + 14.7200i) q^{16} +(1.06723 - 3.98297i) q^{17} +(-23.1386 - 37.4184i) q^{18} +(13.3982 + 7.73543i) q^{19} +(14.8606 - 13.3852i) q^{20} +(38.5180 + 5.93557i) q^{21} +(17.0292 - 0.514817i) q^{22} +(0.910087 + 3.39649i) q^{23} +(43.8896 + 7.58513i) q^{24} +(-23.8957 + 7.34832i) q^{25} +(-3.90871 + 1.17502i) q^{26} +(-51.1684 + 51.1684i) q^{27} +(-21.5423 + 17.8866i) q^{28} +18.6820i q^{29} +(-45.7611 - 31.7120i) q^{30} +(30.1165 + 52.1634i) q^{31} +(-24.9884 + 19.9895i) q^{32} +(-12.2750 - 45.8109i) q^{33} +(5.65259 - 6.00502i) q^{34} +(33.8409 - 8.93263i) q^{35} +(-5.31523 - 87.8287i) q^{36} +(1.66479 + 6.21307i) q^{37} +(16.2735 + 26.3166i) q^{38} +(5.68097 + 9.83973i) q^{39} +(38.8551 - 9.50174i) q^{40} -40.6046i q^{41} +(62.2264 + 46.9398i) q^{42} +(-3.57455 + 3.57455i) q^{43} +(30.4842 + 15.2233i) q^{44} +(-40.2267 + 102.366i) q^{45} +(-1.61408 + 6.84488i) q^{46} +(-20.4773 - 76.4223i) q^{47} +(70.1258 + 54.9335i) q^{48} +(-47.8423 + 10.5884i) q^{49} +(-49.0520 - 9.69017i) q^{50} +(-19.8818 - 11.4788i) q^{51} +(-7.99809 - 1.63258i) q^{52} +(-5.69408 + 21.2506i) q^{53} +(-138.599 + 41.6650i) q^{54} +(-26.5416 - 33.3115i) q^{55} +(-54.8885 + 11.1019i) q^{56} +(60.9062 - 60.9062i) q^{57} +(-17.6957 + 32.9079i) q^{58} +(-21.5785 + 12.4584i) q^{59} +(-50.5694 - 99.2052i) q^{60} +(-41.6775 - 24.0625i) q^{61} +(3.64020 + 120.411i) q^{62} +(62.0408 - 140.930i) q^{63} +(-62.9507 + 11.5418i) q^{64} +(8.20732 + 6.06273i) q^{65} +(21.7702 - 92.3217i) q^{66} +(15.8822 - 59.2733i) q^{67} +(15.6449 - 5.22354i) q^{68} +19.5771 q^{69} +(68.0711 + 16.3197i) q^{70} +73.0217i q^{71} +(73.8291 - 159.743i) q^{72} +(-103.355 - 27.6940i) q^{73} +(-2.95257 + 12.5211i) q^{74} +(5.08473 + 139.095i) q^{75} +(3.73824 + 61.7705i) q^{76} +(35.2508 + 48.0941i) q^{77} +(0.686662 + 22.7135i) q^{78} +(27.9522 - 48.4147i) q^{79} +(77.4424 + 20.0666i) q^{80} +(102.453 + 177.454i) q^{81} +(38.4609 - 71.5242i) q^{82} +(3.69632 + 3.69632i) q^{83} +(65.1488 + 141.625i) q^{84} +(-20.4867 - 2.31722i) q^{85} +(-9.68233 + 2.91066i) q^{86} +(100.468 + 26.9204i) q^{87} +(39.2776 + 55.6903i) q^{88} +(1.02734 - 1.77940i) q^{89} +(-167.820 + 142.213i) q^{90} +(-11.1393 - 8.94348i) q^{91} +(-9.32666 + 10.5282i) q^{92} +(323.922 - 86.7948i) q^{93} +(36.3173 - 154.012i) q^{94} +(28.2917 - 71.9950i) q^{95} +(71.4918 + 163.188i) q^{96} +(-92.1829 - 92.1829i) q^{97} +(-94.3025 - 26.6653i) q^{98} -187.384 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8}+O(q^{10}) \) 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8	\( 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8} - 6 q^{10} - 6 q^{12} - 28 q^{16} - 12 q^{17} - 36 q^{18} - 32 q^{21} - 24 q^{22} - 4 q^{25} - 12 q^{26} + 114 q^{28} + 28 q^{30} + 58 q^{32} - 156 q^{33} - 144 q^{36} - 4 q^{37} + 192 q^{38} + 54 q^{40} - 218 q^{42} - 12 q^{45} + 68 q^{46} - 332 q^{50} - 264 q^{52} - 4 q^{53} - 300 q^{56} - 24 q^{57} - 146 q^{58} - 434 q^{60} - 24 q^{61} + 92 q^{65} - 660 q^{66} - 72 q^{68} + 488 q^{70} - 80 q^{72} - 12 q^{73} - 156 q^{77} + 688 q^{78} + 588 q^{80} + 288 q^{81} + 798 q^{82} + 272 q^{85} - 72 q^{86} + 588 q^{88} + 524 q^{92} + 164 q^{93} + 1080 q^{96} - 766 q^{98}+O(q^{100}) \) 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8 - 6 * q^10 - 6 * q^12 - 28 * q^16 - 12 * q^17 - 36 * q^18 - 32 * q^21 - 24 * q^22 - 4 * q^25 - 12 * q^26 + 114 * q^28 + 28 * q^30 + 58 * q^32 - 156 * q^33 - 144 * q^36 - 4 * q^37 + 192 * q^38 + 54 * q^40 - 218 * q^42 - 12 * q^45 + 68 * q^46 - 332 * q^50 - 264 * q^52 - 4 * q^53 - 300 * q^56 - 24 * q^57 - 146 * q^58 - 434 * q^60 - 24 * q^61 + 92 * q^65 - 660 * q^66 - 72 * q^68 + 488 * q^70 - 80 * q^72 - 12 * q^73 - 156 * q^77 + 688 * q^78 + 588 * q^80 + 288 * q^81 + 798 * q^82 + 272 * q^85 - 72 * q^86 + 588 * q^88 + 524 * q^92 + 164 * q^93 + 1080 * q^96 - 766 * q^98

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