LMFDB - Embedded newform 140.3.x.a.103.9

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			103.9
Character	$\chi$	$=$	140.103
Dual form			140.3.x.a.87.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65553 + 1.12215i) q^{2} +(-1.14118 + 4.25894i) q^{3} +(1.48154 - 3.71551i) q^{4} +(-0.260280 + 4.99322i) q^{5} +(-2.88993 - 8.33136i) q^{6} +(-2.82094 + 6.40643i) q^{7} +(1.71664 + 7.81365i) q^{8} +(-9.04202 - 5.22041i) q^{9} +O(q^{10})$	\(q+(-1.65553 + 1.12215i) q^{2} +(-1.14118 + 4.25894i) q^{3} +(1.48154 - 3.71551i) q^{4} +(-0.260280 + 4.99322i) q^{5} +(-2.88993 - 8.33136i) q^{6} +(-2.82094 + 6.40643i) q^{7} +(1.71664 + 7.81365i) q^{8} +(-9.04202 - 5.22041i) q^{9} +(-5.17226 - 8.55849i) q^{10} +(9.03625 - 5.21708i) q^{11} +(14.1334 + 10.5499i) q^{12} +(-9.09457 + 9.09457i) q^{13} +(-2.51885 - 13.7715i) q^{14} +(-20.9688 - 6.80667i) q^{15} +(-11.6101 - 11.0094i) q^{16} +(5.20491 - 19.4250i) q^{17} +(20.8274 - 1.50400i) q^{18} +(9.19700 + 5.30989i) q^{19} +(18.1668 + 8.36475i) q^{20} +(-24.0654 - 19.3251i) q^{21} +(-9.10540 + 18.7771i) q^{22} +(-10.6904 - 39.8972i) q^{23} +(-35.2368 - 1.60572i) q^{24} +(-24.8645 - 2.59927i) q^{25} +(4.85081 - 25.2618i) q^{26} +(4.49215 - 4.49215i) q^{27} +(19.6238 + 19.9726i) q^{28} +21.0153i q^{29} +(42.3525 - 12.2616i) q^{30} +(13.2570 + 22.9618i) q^{31} +(31.5750 + 5.19807i) q^{32} +(11.9072 + 44.4384i) q^{33} +(13.1810 + 37.9993i) q^{34} +(-31.2545 - 15.7530i) q^{35} +(-32.7927 + 25.8615i) q^{36} +(11.4730 + 42.8179i) q^{37} +(-21.1844 + 1.52977i) q^{38} +(-28.3547 - 49.1117i) q^{39} +(-39.4621 + 6.53782i) q^{40} +50.4479i q^{41} +(61.5266 + 4.98817i) q^{42} +(8.33652 - 8.33652i) q^{43} +(-5.99653 - 41.3036i) q^{44} +(28.4201 - 43.7900i) q^{45} +(62.4691 + 54.0547i) q^{46} +(11.9305 + 44.5253i) q^{47} +(60.1374 - 36.8828i) q^{48} +(-33.0846 - 36.1443i) q^{49} +(44.0807 - 23.5986i) q^{50} +(76.7901 + 44.3348i) q^{51} +(20.3170 + 47.2650i) q^{52} +(11.7051 - 43.6841i) q^{53} +(-2.39600 + 12.4778i) q^{54} +(23.6981 + 46.4779i) q^{55} +(-54.9001 - 11.0443i) q^{56} +(-33.1099 + 33.1099i) q^{57} +(-23.5824 - 34.7915i) q^{58} +(-1.46292 + 0.844616i) q^{59} +(-56.3564 + 67.8254i) q^{60} +(-12.3117 - 7.10816i) q^{61} +(-47.7139 - 23.1375i) q^{62} +(58.9512 - 43.2006i) q^{63} +(-58.1063 + 26.8264i) q^{64} +(-43.0440 - 47.7783i) q^{65} +(-69.5795 - 60.2073i) q^{66} +(-4.66529 + 17.4111i) q^{67} +(-64.4625 - 48.1179i) q^{68} +182.120 q^{69} +(69.4200 - 8.99272i) q^{70} +98.8542i q^{71} +(25.2686 - 79.6128i) q^{72} +(-41.0846 - 11.0086i) q^{73} +(-67.0421 - 58.0117i) q^{74} +(39.4450 - 102.930i) q^{75} +(33.3547 - 26.3047i) q^{76} +(7.93213 + 72.6072i) q^{77} +(102.053 + 49.4875i) q^{78} +(-55.6625 + 96.4102i) q^{79} +(57.9942 - 55.1061i) q^{80} +(-32.9783 - 57.1201i) q^{81} +(-56.6103 - 83.5179i) q^{82} +(-18.8283 - 18.8283i) q^{83} +(-107.456 + 60.7842i) q^{84} +(95.6386 + 31.0452i) q^{85} +(-4.44649 + 23.1562i) q^{86} +(-89.5029 - 23.9822i) q^{87} +(56.2764 + 61.6503i) q^{88} +(8.53722 - 14.7869i) q^{89} +(2.08883 + 104.387i) q^{90} +(-32.6084 - 83.9189i) q^{91} +(-164.077 - 19.3891i) q^{92} +(-112.921 + 30.2572i) q^{93} +(-69.7156 - 60.3250i) q^{94} +(-28.9072 + 44.5406i) q^{95} +(-58.1710 + 128.544i) q^{96} +(-8.41224 - 8.41224i) q^{97} +(95.3319 + 22.7119i) q^{98} -108.941 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 $

$2$	−1.65553	+	1.12215i	−0.827764	+	0.561077i
$2$	−1.65553	+	1.12215i	−0.827764	+	0.561077i
$3$	−1.14118	+	4.25894i	−0.380393	+	1.41965i	0.464910	+	0.885358i	$0.346087\pi$
$3$	−1.14118	+	4.25894i	−0.380393	+	1.41965i	−0.845303	+	0.534288i	$0.820580\pi$
$4$	1.48154	−	3.71551i	0.370386	−	0.928878i
$5$	−0.260280	+	4.99322i	−0.0520560	+	0.998644i
$5$	−0.260280	+	4.99322i	−0.0520560	+	0.998644i
$6$	−2.88993	−	8.33136i	−0.481655	−	1.38856i
$7$	−2.82094	+	6.40643i	−0.402991	+	0.915204i
$7$	−2.82094	+	6.40643i	−0.402991	+	0.915204i
$8$	1.71664	+	7.81365i	0.214580	+	0.976706i
$9$	−9.04202	−	5.22041i	−1.00467	−	0.580046i
$10$	−5.17226	−	8.55849i	−0.517226	−	0.855849i
$11$	9.03625	−	5.21708i	0.821478	−	0.474280i	−0.0294482	−	0.999566i	$-0.509375\pi$
$11$	9.03625	−	5.21708i	0.821478	−	0.474280i	0.850926	+	0.525286i	$0.176042\pi$
$12$	14.1334	+	10.5499i	1.17779	+	0.879155i
$13$	−9.09457	+	9.09457i	−0.699582	+	0.699582i	−0.964320	−	0.264738i	$-0.914714\pi$
$13$	−9.09457	+	9.09457i	−0.699582	+	0.699582i	0.264738	+	0.964320i	$0.414714\pi$
$14$	−2.51885	−	13.7715i	−0.179918	−	0.983682i
$15$	−20.9688	−	6.80667i	−1.39792	−	0.453778i
$16$	−11.6101	−	11.0094i	−0.725629	−	0.688087i
$17$	5.20491	−	19.4250i	0.306171	−	1.14265i	−0.625761	−	0.780015i	$-0.715211\pi$
$17$	5.20491	−	19.4250i	0.306171	−	1.14265i	0.931932	−	0.362632i	$-0.118122\pi$
$18$	20.8274	−	1.50400i	1.15708	−	0.0835554i
$19$	9.19700	+	5.30989i	0.484053	+	0.279468i	0.722104	−	0.691785i	$-0.243175\pi$
$19$	9.19700	+	5.30989i	0.484053	+	0.279468i	−0.238051	+	0.971253i	$0.576509\pi$
$20$	18.1668	+	8.36475i	0.908338	+	0.418237i
$21$	−24.0654	−	19.3251i	−1.14597	−	0.920242i
$22$	−9.10540	+	18.7771i	−0.413882	+	0.853504i
$23$	−10.6904	−	39.8972i	−0.464802	−	1.73466i	−0.657547	−	0.753414i	$-0.728406\pi$
$23$	−10.6904	−	39.8972i	−0.464802	−	1.73466i	0.192745	−	0.981249i	$-0.438261\pi$
$24$	−35.2368	−	1.60572i	−1.46820	−	0.0669049i
$25$	−24.8645	−	2.59927i	−0.994580	−	0.103971i
$26$	4.85081	−	25.2618i	0.186569	−	0.971608i
$27$	4.49215	−	4.49215i	0.166376	−	0.166376i
$28$	19.6238	+	19.9726i	0.700850	+	0.713308i
$29$			21.0153i			0.724666i	0.932049	+	0.362333i	$0.118020\pi$
$29$			21.0153i			0.724666i	−0.932049	+	0.362333i	$0.881980\pi$
$30$	42.3525	−	12.2616i	1.41175	−	0.408719i
$31$	13.2570	+	22.9618i	0.427645	+	0.740703i	0.996663	−	0.0816222i	$-0.0260101\pi$
$31$	13.2570	+	22.9618i	0.427645	+	0.740703i	−0.569019	+	0.822325i	$0.692677\pi$
$32$	31.5750	+	5.19807i	0.986718	+	0.162440i
$33$	11.9072	+	44.4384i	0.360826	+	1.34662i
$34$	13.1810	+	37.9993i	0.387675	+	1.11763i
$35$	−31.2545	−	15.7530i	−0.892985	−	0.450087i
$36$	−32.7927	+	25.8615i	−0.910907	+	0.718374i
$37$	11.4730	+	42.8179i	0.310081	+	1.15724i	0.928482	+	0.371377i	$0.121114\pi$
$37$	11.4730	+	42.8179i	0.310081	+	1.15724i	−0.618401	+	0.785863i	$0.712219\pi$
$38$	−21.1844	+	1.52977i	−0.557484	+	0.0402572i
$39$	−28.3547	−	49.1117i	−0.727042	−	1.25927i
$40$	−39.4621	+	6.53782i	−0.986552	+	0.163445i
$41$			50.4479i			1.23044i	0.788357	+	0.615218i	$0.210932\pi$
$41$			50.4479i			1.23044i	−0.788357	+	0.615218i	$0.789068\pi$
$42$	61.5266	+	4.98817i	1.46492	+	0.118766i
$43$	8.33652	−	8.33652i	0.193873	−	0.193873i	−0.603495	−	0.797367i	$-0.706225\pi$
$43$	8.33652	−	8.33652i	0.193873	−	0.193873i	0.797367	+	0.603495i	$0.206225\pi$
$44$	−5.99653	−	41.3036i	−0.136285	−	0.938719i
$45$	28.4201	−	43.7900i	0.631559	−	0.973112i
$46$	62.4691	+	54.0547i	1.35802	+	1.17510i
$47$	11.9305	+	44.5253i	0.253841	+	0.947347i	0.968732	+	0.248111i	$0.0798098\pi$
$47$	11.9305	+	44.5253i	0.253841	+	0.947347i	−0.714891	+	0.699236i	$0.753524\pi$
$48$	60.1374	−	36.8828i	1.25286	−	0.768392i
$49$	−33.0846	−	36.1443i	−0.675196	−	0.737638i
$50$	44.0807	−	23.5986i	0.881613	−	0.471973i
$51$	76.7901	+	44.3348i	1.50569	+	0.869310i
$52$	20.3170	+	47.2650i	0.390711	+	0.908942i
$53$	11.7051	−	43.6841i	0.220851	−	0.824228i	−0.763173	−	0.646194i	$-0.776360\pi$
$53$	11.7051	−	43.6841i	0.220851	−	0.824228i	0.984024	−	0.178034i	$-0.0569737\pi$
$54$	−2.39600	+	12.4778i	−0.0443703	+	0.231070i
$55$	23.6981	+	46.4779i	0.430874	+	0.845053i
$56$	−54.9001	−	11.0443i	−0.980359	−	0.197220i
$57$	−33.1099	+	33.1099i	−0.580875	+	0.580875i
$58$	−23.5824	−	34.7915i	−0.406593	−	0.599853i
$59$	−1.46292	+	0.844616i	−0.0247952	+	0.0143155i	−0.512346	−	0.858779i	$-0.671224\pi$
$59$	−1.46292	+	0.844616i	−0.0247952	+	0.0143155i	0.487551	+	0.873094i	$0.337890\pi$
$60$	−56.3564	+	67.8254i	−0.939274	+	1.13042i
$61$	−12.3117	−	7.10816i	−0.201831	−	0.116527i	0.395678	−	0.918389i	$-0.370510\pi$
$61$	−12.3117	−	7.10816i	−0.201831	−	0.116527i	−0.597509	+	0.801862i	$0.703843\pi$
$62$	−47.7139	−	23.1375i	−0.769580	−	0.373185i
$63$	58.9512	−	43.2006i	0.935733	−	0.685723i
$64$	−58.1063	+	26.8264i	−0.907911	+	0.419163i
$65$	−43.0440	−	47.7783i	−0.662216	−	0.735051i
$66$	−69.5795	−	60.2073i	−1.05424	−	0.912232i
$67$	−4.66529	+	17.4111i	−0.0696312	+	0.259867i	−0.991962	−	0.126533i	$-0.959615\pi$
$67$	−4.66529	+	17.4111i	−0.0696312	+	0.259867i	0.922331	+	0.386400i	$0.126282\pi$
$68$	−64.4625	−	48.1179i	−0.947978	−	0.707616i
$69$	182.120			2.63941
$70$	69.4200	−	8.99272i	0.991714	−	0.128467i
$71$			98.8542i			1.39231i	0.717890	+	0.696156i	$0.245108\pi$
$71$			98.8542i			1.39231i	−0.717890	+	0.696156i	$0.754892\pi$
$72$	25.2686	−	79.6128i	0.350953	−	1.10573i
$73$	−41.0846	−	11.0086i	−0.562802	−	0.150802i	−0.0338089	−	0.999428i	$-0.510764\pi$
$73$	−41.0846	−	11.0086i	−0.562802	−	0.150802i	−0.528994	+	0.848626i	$0.677430\pi$
$74$	−67.0421	−	58.0117i	−0.905974	−	0.783941i
$75$	39.4450	−	102.930i	0.525933	−	1.37240i
$76$	33.3547	−	26.3047i	0.438878	−	0.346115i
$77$	7.93213	+	72.6072i	0.103015	+	0.942950i
$78$	102.053	+	49.4875i	1.30837	+	0.634455i
$79$	−55.6625	+	96.4102i	−0.704588	+	1.22038i	0.262252	+	0.965000i	$0.415535\pi$
$79$	−55.6625	+	96.4102i	−0.704588	+	1.22038i	−0.966840	+	0.255383i	$0.917798\pi$
$80$	57.9942	−	55.1061i	0.724927	−	0.688826i
$81$	−32.9783	−	57.1201i	−0.407139	−	0.705186i
$82$	−56.6103	−	83.5179i	−0.690369	−	1.01851i
$83$	−18.8283	−	18.8283i	−0.226847	−	0.226847i	0.584527	−	0.811374i	$-0.301280\pi$
$83$	−18.8283	−	18.8283i	−0.226847	−	0.226847i	−0.811374	+	0.584527i	$0.801280\pi$
$84$	−107.456	+	60.7842i	−1.27924	+	0.723622i
$85$	95.6386	+	31.0452i	1.12516	+	0.365238i
$86$	−4.44649	+	23.1562i	−0.0517033	+	0.269258i
$87$	−89.5029	−	23.9822i	−1.02877	−	0.275658i
$88$	56.2764	+	61.6503i	0.639505	+	0.700571i
$89$	8.53722	−	14.7869i	0.0959238	−	0.166145i	−0.814070	−	0.580767i	$-0.802753\pi$
$89$	8.53722	−	14.7869i	0.0959238	−	0.166145i	0.909994	+	0.414622i	$0.136086\pi$
$90$	2.08883	+	104.387i	0.0232092	+	1.15986i
$91$	−32.6084	−	83.9189i	−0.358335	−	0.922186i
$92$	−164.077	−	19.3891i	−1.78345	−	0.210751i
$93$	−112.921	+	30.2572i	−1.21421	+	0.325346i
$94$	−69.7156	−	60.3250i	−0.741655	−	0.641756i
$95$	−28.9072	+	44.5406i	−0.304287	+	0.468848i
$96$	−58.1710	+	128.544i	−0.605948	+	1.33900i
$97$	−8.41224	−	8.41224i	−0.0867241	−	0.0867241i	0.662414	−	0.749138i	$-0.269532\pi$
$97$	−8.41224	−	8.41224i	−0.0867241	−	0.0867241i	−0.749138	+	0.662414i	$0.769532\pi$
$98$	95.3319	+	22.7119i	0.972774	+	0.231754i
$99$	−108.941			−1.10042
$100$	−46.4955	+	88.5334i	−0.464955	+	0.885334i
$101$	134.989	−	77.9357i	1.33652	−	0.771641i	0.350232	−	0.936663i	$-0.386103\pi$
$101$	134.989	−	77.9357i	1.33652	−	0.771641i	0.986290	+	0.165022i	$0.0527696\pi$
$102$	−176.879	+	12.7728i	−1.73410	+	0.125224i
$103$	36.3243	−	9.73306i	0.352663	−	0.0944957i	−0.0781385	−	0.996943i	$-0.524898\pi$
$103$	36.3243	−	9.73306i	0.352663	−	0.0944957i	0.430801	+	0.902447i	$0.358231\pi$
$104$	−86.6739	−	55.4497i	−0.833402	−	0.533170i
$105$	102.758	−	115.134i	0.978649	−	1.09651i
$106$	29.6421	+	85.4552i	0.279643	+	0.806181i
$107$	60.3678	−	16.1755i	0.564185	−	0.151173i	0.0345569	−	0.999403i	$-0.488998\pi$
$107$	60.3678	−	16.1755i	0.564185	−	0.151173i	0.529629	+	0.848230i	$0.322331\pi$
$108$	−10.0353	−	23.3460i	−0.0929197	−	0.216166i
$109$	30.5601	−	17.6439i	0.280368	−	0.161870i	−0.353222	−	0.935539i	$-0.614914\pi$
$109$	30.5601	−	17.6439i	0.280368	−	0.161870i	0.633590	+	0.773669i	$0.281581\pi$
$110$	−91.3882	−	50.3526i	−0.830802	−	0.457751i
$111$	−195.451			−1.76082
$112$	103.282	−	43.3222i	0.922161	−	0.386805i
$113$	5.12789	+	5.12789i	0.0453796	+	0.0453796i	0.729432	−	0.684053i	$-0.239784\pi$
$113$	5.12789	+	5.12789i	0.0453796	+	0.0453796i	−0.684053	+	0.729432i	$0.739784\pi$
$114$	17.6600	−	91.9688i	0.154912	−	0.806743i
$115$	201.998	−	42.9953i	1.75651	−	0.373872i
$116$	78.0827	+	31.1351i	0.673127	+	0.268406i
$117$	129.711	−	34.7559i	1.10864	−	0.297059i
$118$	1.47411	−	3.03990i	0.0124925	−	0.0257619i
$119$	109.762	+	88.1417i	0.922371	+	0.740686i
$120$	17.1891	−	175.527i	0.143243	−	1.46273i
$121$	−6.06409	+	10.5033i	−0.0501164	+	0.0868042i
$122$	28.3588	−	2.04786i	0.232449	−	0.0167857i
$123$	−214.854	−	57.5701i	−1.74678	−	0.468049i
$124$	104.956	−	15.2376i	0.846416	−	0.122884i
$125$	19.4505	−	123.477i	0.155604	−	0.987820i
$126$	−49.1177	+	137.672i	−0.389823	+	1.09264i
$127$	−10.0898	−	10.0898i	−0.0794472	−	0.0794472i	0.666267	−	0.745714i	$-0.267891\pi$
$127$	−10.0898	−	10.0898i	−0.0794472	−	0.0794472i	−0.745714	+	0.666267i	$0.767891\pi$
$128$	66.0932	−	109.616i	0.516353	−	0.856376i
$129$	25.9913	+	45.0182i	0.201483	+	0.348978i
$130$	124.875	+	30.7963i	0.960578	+	0.236895i
$131$	42.7990	−	74.1301i	0.326710	−	0.565879i	−0.655147	−	0.755502i	$-0.727393\pi$
$131$	42.7990	−	74.1301i	0.326710	−	0.565879i	0.981857	+	0.189623i	$0.0607265\pi$
$132$	182.753	+	21.5960i	1.38449	+	0.163606i
$133$	−59.9616	+	43.9410i	−0.450839	+	0.330384i
$134$	−11.8144	−	34.0597i	−0.0881673	−	0.254177i
$135$	21.2611	+	23.5995i	0.157490	+	0.174811i
$136$	160.715	+	7.32368i	1.18173	+	0.0538506i
$137$	42.3472	+	11.3469i	0.309104	+	0.0828241i	0.410036	−	0.912069i	$-0.365516\pi$
$137$	42.3472	+	11.3469i	0.309104	+	0.0828241i	−0.100933	+	0.994893i	$0.532183\pi$
$138$	−301.504	+	204.366i	−2.18481	+	1.48091i
$139$			84.7216i			0.609508i	0.952431	+	0.304754i	$0.0985742\pi$
$139$			84.7216i			0.609508i	−0.952431	+	0.304754i	$0.901426\pi$
$140$	−104.835	+	92.7875i	−0.748825	+	0.662768i
$141$	−203.245			−1.44146
$142$	−110.930	−	163.656i	−0.781194	−	1.15251i
$143$	−34.7337	+	129.628i	−0.242893	+	0.906489i
$144$	47.5049	+	160.156i	0.329895	+	1.11220i
$145$	−104.934	−	5.46987i	−0.723684	−	0.0377232i
$146$	80.3700	−	27.8782i	0.550479	−	0.190947i
$147$	191.692	−	99.6581i	1.30402	−	0.677946i
$148$	176.088	+	20.8084i	1.18978	+	0.140597i
$149$	−46.6007	−	26.9049i	−0.312756	−	0.180570i	0.335403	−	0.942075i	$-0.391128\pi$
$149$	−46.6007	−	26.9049i	−0.312756	−	0.180570i	−0.648159	+	0.761505i	$0.724461\pi$
$150$	50.2012	+	214.667i	0.334674	+	1.43111i
$151$	129.613	−	74.8324i	0.858367	−	0.495579i	−0.00509797	−	0.999987i	$-0.501623\pi$
$151$	129.613	−	74.8324i	0.858367	−	0.495579i	0.863465	+	0.504408i	$0.168289\pi$
$152$	−25.7017	+	80.9773i	−0.169090	+	0.532745i
$153$	−148.469	+	148.469i	−0.970389	+	0.970389i
$154$	−94.6082	−	111.302i	−0.614339	−	0.722741i
$155$	−118.104	+	60.2186i	−0.761960	+	0.388507i
$156$	−224.484	+	32.5909i	−1.43900	+	0.208916i
$157$	−77.8329	+	290.476i	−0.495751	+	1.85017i	0.0300337	+	0.999549i	$0.490439\pi$
$157$	−77.8329	+	290.476i	−0.495751	+	1.85017i	−0.525784	+	0.850618i	$0.676228\pi$
$158$	−16.0363	−	222.072i	−0.101496	−	1.40552i
$159$	172.690	+	99.7027i	1.08610	+	0.627061i
$160$	−34.1735	+	156.308i	−0.213584	+	0.976925i
$161$	285.756	+	44.0602i	1.77488	+	0.273666i
$162$	118.694	+	57.5571i	0.732679	+	0.355291i
$163$	74.3697	+	277.552i	0.456256	+	1.70277i	0.684369	+	0.729136i	$0.260078\pi$
$163$	74.3697	+	277.552i	0.456256	+	1.70277i	−0.228113	+	0.973635i	$0.573256\pi$
$164$	187.440	+	74.7407i	1.14293	+	0.455736i
$165$	−224.990	+	47.8891i	−1.36358	+	0.290237i
$166$	52.2990	+	10.0425i	0.315054	+	0.0604971i
$167$	−44.1362	+	44.1362i	−0.264289	+	0.264289i	−0.826794	−	0.562505i	$-0.809838\pi$
$167$	−44.1362	+	44.1362i	−0.264289	+	0.264289i	0.562505	+	0.826794i	$0.309838\pi$
$168$	109.688	−	221.213i	0.652904	−	1.31674i
$169$			3.57774i			0.0211701i
$170$	−193.170	+	55.9249i	−1.13629	+	0.328970i
$171$	−55.4396	−	96.0243i	−0.324208	−	0.561546i
$172$	−18.6235	−	43.3254i	−0.108276	−	0.251892i
$173$	55.4217	+	206.837i	0.320357	+	1.19559i	0.918898	+	0.394496i	$0.129081\pi$
$173$	55.4217	+	206.837i	0.320357	+	1.19559i	−0.598541	+	0.801092i	$0.704253\pi$
$174$	175.086	−	60.7328i	1.00624	−	0.349039i
$175$	86.7933	−	151.960i	0.495962	−	0.868344i
$176$	−162.348	−	38.9129i	−0.922434	−	0.221096i
$177$	−1.92772	−	7.19433i	−0.0108910	−	0.0406459i
$178$	2.45957	+	34.0602i	0.0138178	+	0.191349i
$179$	−107.724	−	186.583i	−0.601809	−	1.04236i	−0.992547	−	0.121862i	$-0.961113\pi$
$179$	−107.724	−	186.583i	−0.601809	−	1.04236i	0.390738	−	0.920502i	$-0.372220\pi$
$180$	−120.597	−	170.472i	−0.669982	−	0.947068i
$181$		−	250.393i		−	1.38339i	−0.722192	−	0.691693i	$-0.756865\pi$
$181$		−	250.393i		−	1.38339i	0.722192	−	0.691693i	$-0.243135\pi$
$182$	148.154	+	102.338i	0.814033	+	0.562299i
$183$	44.3231	−	44.3231i	0.242203	−	0.242203i
$184$	293.392	−	152.020i	1.59452	−	0.826198i
$185$	−216.785	+	46.1426i	−1.17181	+	0.249420i
$186$	152.991	−	176.807i	0.822533	−	0.950573i
$187$	−54.3089	−	202.684i	−0.290422	−	1.08387i
$188$	183.110	+	21.6382i	0.973989	+	0.115097i
$189$	16.1065	+	41.4507i	0.0852198	+	0.219316i
$190$	−2.12463	−	106.177i	−0.0111823	−	0.558824i
$191$	−17.5729	−	10.1457i	−0.0920046	−	0.0531189i	0.453292	−	0.891362i	$-0.350250\pi$
$191$	−17.5729	−	10.1457i	−0.0920046	−	0.0531189i	−0.545296	+	0.838243i	$0.683583\pi$
$192$	−47.9424	−	278.085i	−0.249700	−	1.44836i
$193$	−17.3957	+	64.9217i	−0.0901333	+	0.336382i	−0.996237	−	0.0866742i	$-0.972376\pi$
$193$	−17.3957	+	64.9217i	−0.0901333	+	0.336382i	0.906103	+	0.423056i	$0.139043\pi$
$194$	23.3665	+	4.48687i	0.120446	+	0.0231282i
$195$	252.606	−	128.798i	1.29541	−	0.660504i
$196$	−183.311	+	69.3769i	−0.935259	+	0.353964i
$197$	190.767	−	190.767i	0.968359	−	0.968359i	−0.0311554	−	0.999515i	$-0.509919\pi$
$197$	190.767	−	190.767i	0.968359	−	0.968359i	0.999515	+	0.0311554i	$0.00991868\pi$
$198$	180.355	−	122.249i	0.910886	−	0.617419i
$199$	10.1503	−	5.86031i	0.0510068	−	0.0294488i	−0.474280	−	0.880374i	$-0.657291\pi$
$199$	10.1503	−	5.86031i	0.0510068	−	0.0294488i	0.525287	+	0.850925i	$0.323958\pi$
$200$	−22.3736	−	198.745i	−0.111868	−	0.993723i
$201$	−68.8289	−	39.7384i	−0.342432	−	0.197703i
$202$	−136.022	+	280.503i	−0.673374	+	1.38863i
$203$	−134.633	−	59.2830i	−0.663217	−	0.292034i
$204$	278.494	−	219.631i	1.36517	−	1.07662i
$205$	−251.897	−	13.1306i	−1.22877	−	0.0640516i
$206$	−49.2139	+	56.8748i	−0.238902	+	0.276091i
$207$	−111.617	+	416.560i	−0.539212	+	2.01237i
$208$	205.714	−	5.46287i	0.989010	−	0.0262638i
$209$	110.809			0.530184
$210$	−40.9212	+	305.917i	−0.194863	+	1.45675i
$211$			41.4945i			0.196656i	0.995154	+	0.0983282i	$0.0313495\pi$
$211$			41.4945i			0.196656i	−0.995154	+	0.0983282i	$0.968651\pi$
$212$	−144.967	−	108.210i	−0.683807	−	0.510426i
$213$	−421.014	−	112.810i	−1.97659	−	0.529626i
$214$	−81.7892	+	94.5210i	−0.382193	+	0.441687i
$215$	39.4563	+	43.7959i	0.183518	+	0.203702i
$216$	42.8115	+	27.3887i	0.198201	+	0.126800i
$217$	−184.500	+	20.1561i	−0.850231	+	0.0928854i
$218$	−30.7939	+	63.5030i	−0.141256	+	0.291298i
$219$	93.7697	−	162.414i	0.428172	−	0.741616i
$220$	207.799	−	19.1915i	0.944541	−	0.0872341i
$221$	129.326	+	223.998i	0.585183	+	1.01357i
$222$	323.575	−	219.326i	1.45754	−	0.987956i
$223$	−114.799	−	114.799i	−0.514792	−	0.514792i	0.401199	−	0.915991i	$-0.368594\pi$
$223$	−114.799	−	114.799i	−0.514792	−	0.514792i	−0.915991	+	0.401199i	$0.868594\pi$
$224$	−122.372	+	187.619i	−0.546305	+	0.837587i
$225$	211.256	+	153.306i	0.938916	+	0.681359i
$226$	−14.2437	−	2.73509i	−0.0630250	−	0.0121022i
$227$	−64.2531	−	17.2166i	−0.283053	−	0.0758439i	0.114499	−	0.993423i	$-0.463474\pi$
$227$	−64.2531	−	17.2166i	−0.283053	−	0.0758439i	−0.397553	+	0.917579i	$0.630140\pi$
$228$	73.9665	+	172.074i	0.324414	+	0.754711i
$229$	−182.830	+	316.672i	−0.798386	+	1.38285i	0.122280	+	0.992496i	$0.460979\pi$
$229$	−182.830	+	316.672i	−0.798386	+	1.38285i	−0.920667	+	0.390350i	$0.872354\pi$
$230$	−286.166	+	297.853i	−1.24420	+	1.29501i
$231$	−318.281	−	49.0753i	−1.37784	−	0.212447i
$232$	−164.206	+	36.0757i	−0.707786	+	0.155499i
$233$	447.600	−	119.934i	1.92103	−	0.514739i	0.933161	−	0.359459i	$-0.117039\pi$
$233$	447.600	−	119.934i	1.92103	−	0.514739i	0.987871	−	0.155280i	$-0.0496279\pi$
$234$	−175.738	+	203.095i	−0.751018	+	0.867925i
$235$	−225.430	+	47.9827i	−0.959277	+	0.204182i
$236$	0.970805	+	6.68682i	0.00411358	+	0.0283340i
$237$	−347.084	−	347.084i	−1.46449	−	1.46449i
$238$	−280.623	−	22.7510i	−1.17909	−	0.0955926i
$239$	1.58923			0.00664950			0.00332475	−	0.999994i	$-0.498942\pi$
$239$	1.58923			0.00664950			0.00332475	+	0.999994i	$0.498942\pi$
$240$	168.512	+	309.879i	0.702131	+	1.29116i
$241$	11.1690	−	6.44843i	0.0463445	−	0.0267570i	−0.476649	−	0.879094i	$-0.658149\pi$
$241$	11.1690	−	6.44843i	0.0463445	−	0.0267570i	0.522993	+	0.852337i	$0.324815\pi$
$242$	−1.74706	−	24.1934i	−0.00721925	−	0.0999726i
$243$	336.132	−	90.0664i	1.38326	−	0.370644i
$244$	−44.6508	+	35.2132i	−0.182995	+	0.144316i
$245$	189.088	−	155.791i	0.771786	−	0.635882i
$246$	420.300	−	145.791i	1.70854	−	0.592645i
$247$	−131.934	+	35.3516i	−0.534145	+	0.143124i
$248$	−156.658	+	143.003i	−0.631685	+	0.576623i
$249$	101.675	−	58.7020i	0.408333	−	0.235751i
$250$	106.360	+	226.247i	0.425439	+	0.904987i
$251$	225.097			0.896802			0.448401	−	0.893832i	$-0.351994\pi$
$251$	225.097			0.896802			0.448401	+	0.893832i	$0.351994\pi$
$252$	−73.1735	−	283.037i	−0.290371	−	1.12316i
$253$	−304.749	−	304.749i	−1.20454	−	1.20454i
$254$	28.0262	+	5.38163i	0.110339	+	0.0211875i
$255$	−241.360	+	371.891i	−0.946511	+	1.45839i
$256$	13.5869	+	255.639i	0.0530738	+	0.998591i
$257$	194.465	−	52.1067i	0.756672	−	0.202750i	0.140197	−	0.990124i	$-0.455227\pi$
$257$	194.465	−	52.1067i	0.756672	−	0.202750i	0.616476	+	0.787374i	$0.288560\pi$
$258$	−93.5466	−	45.3627i	−0.362584	−	0.175824i
$259$	−306.674	−	47.2856i	−1.18407	−	0.182570i
$260$	−241.292	+	89.1450i	−0.928048	+	0.342865i
$261$	109.709	−	190.021i	0.420340	−	0.728050i
$262$	12.3304	+	170.752i	0.0470625	+	0.651723i
$263$	−185.700	−	49.7580i	−0.706082	−	0.189194i	−0.112129	−	0.993694i	$-0.535767\pi$
$263$	−185.700	−	49.7580i	−0.706082	−	0.189194i	−0.593953	+	0.804500i	$0.702434\pi$
$264$	−326.786	+	169.324i	−1.23783	+	0.641378i
$265$	215.078	+	69.8163i	0.811614	+	0.263458i
$266$	49.9595	−	140.032i	0.187818	−	0.526435i
$267$	53.2340	+	53.2340i	0.199378	+	0.199378i
$268$	57.7793	+	43.1293i	0.215595	+	0.160930i
$269$	86.6940	+	150.158i	0.322282	+	0.558210i	0.980959	−	0.194217i	$-0.0622166\pi$
$269$	86.6940	+	150.158i	0.322282	+	0.558210i	−0.658676	+	0.752427i	$0.728883\pi$
$270$	−61.6806	−	15.2115i	−0.228447	−	0.0563387i
$271$	108.262	−	187.515i	0.399489	−	0.691935i	−0.594174	−	0.804337i	$-0.702521\pi$
$271$	108.262	−	187.515i	0.399489	−	0.691935i	0.993663	+	0.112401i	$0.0358542\pi$
$272$	−274.287	+	168.222i	−1.00841	+	0.618465i
$273$	394.617	−	43.1109i	1.44548	−	0.157915i
$274$	−82.8399	+	28.7350i	−0.302335	+	0.104872i
$275$	−238.243	+	106.233i	−0.866337	+	0.386300i
$276$	269.818	−	676.667i	0.977601	−	2.45169i
$277$	433.209	+	116.078i	1.56393	+	0.419054i	0.933905	−	0.357521i	$-0.116378\pi$
$277$	433.209	+	116.078i	1.56393	+	0.419054i	0.630025	+	0.776575i	$0.283045\pi$
$278$	−95.0706	−	140.259i	−0.341981	−	0.504529i
$279$		−	276.828i		−	0.992215i
$280$	69.4361	−	271.254i	0.247986	−	0.968764i
$281$	−420.800			−1.49751			−0.748755	−	0.662847i	$-0.769348\pi$
$281$	−420.800			−1.49751			−0.748755	+	0.662847i	$0.769348\pi$
$282$	336.478	−	228.072i	1.19319	−	0.808768i
$283$	105.600	−	394.106i	0.373146	−	1.39260i	−0.482888	−	0.875682i	$-0.660412\pi$
$283$	105.600	−	394.106i	0.373146	−	1.39260i	0.856034	−	0.516919i	$-0.172921\pi$
$284$	367.294	+	146.457i	1.29329	+	0.515693i
$285$	−156.707	−	173.943i	−0.549850	−	0.610326i
$286$	−87.9598	−	253.579i	−0.307552	−	0.886640i
$287$	−323.191	−	142.310i	−1.12610	−	0.495855i
$288$	−258.366	−	211.836i	−0.897103	−	0.735540i
$289$	−99.9582	−	57.7109i	−0.345876	−	0.199692i
$290$	179.859	−	108.697i	0.620205	−	0.374816i
$291$	45.4271	−	26.2273i	0.156107	−	0.0901283i
$292$	−101.771	+	136.341i	−0.348531	+	0.466920i
$293$	−347.332	+	347.332i	−1.18543	+	1.18543i	−0.207117	+	0.978316i	$0.566408\pi$
$293$	−347.332	+	347.332i	−1.18543	+	1.18543i	−0.978316	+	0.207117i	$0.933592\pi$
$294$	−205.519	+	380.094i	−0.699045	+	1.29284i
$295$	−3.83659	−	7.52451i	−0.0130054	−	0.0255068i
$296$	−314.869	+	163.149i	−1.06375	+	0.551179i
$297$	17.1563	−	64.0281i	0.0577653	−	0.215583i
$298$	107.340	−	7.75128i	0.360202	−	0.0260110i
$299$	460.073	+	265.623i	1.53871	+	0.888372i
$300$	−323.999	−	299.054i	−1.08000	−	0.996846i
$301$	29.8905	+	76.9242i	0.0993040	+	0.255562i
$302$	−130.605	+	269.333i	−0.432468	+	0.891832i
$303$	177.877	+	663.847i	0.587053	+	2.19091i
$304$	−48.3191	−	162.901i	−0.158944	−	0.535860i
$305$	38.6971	−	59.6249i	0.126876	−	0.195492i
$306$	79.1898	−	412.401i	0.258790	−	1.34772i
$307$	143.127	−	143.127i	0.466213	−	0.466213i	−0.434472	−	0.900685i	$-0.643065\pi$
$307$	143.127	−	143.127i	0.466213	−	0.466213i	0.900685	+	0.434472i	$0.143065\pi$
$308$	281.525	+	78.0987i	0.914041	+	0.253567i
$309$			165.810i			0.536602i
$310$	127.950	−	232.224i	0.412740	−	0.749110i
$311$	214.613	+	371.720i	0.690073	+	1.19524i	0.971814	+	0.235751i	$0.0757548\pi$
$311$	214.613	+	371.720i	0.690073	+	1.19524i	−0.281741	+	0.959491i	$0.590912\pi$
$312$	335.067	−	305.860i	1.07393	−	0.980322i
$313$	−105.355	−	393.189i	−0.336597	−	1.25620i	−0.902128	−	0.431469i	$-0.857995\pi$
$313$	−105.355	−	393.189i	−0.336597	−	1.25620i	0.565531	−	0.824727i	$-0.308671\pi$
$314$	−197.104	−	568.232i	−0.627721	−	1.80966i
$315$	200.366	+	305.601i	0.636083	+	0.970161i
$316$	275.747	+	349.651i	0.872617	+	1.10649i
$317$	83.1447	+	310.300i	0.262286	+	0.978865i	0.963891	+	0.266298i	$0.0858006\pi$
$317$	83.1447	+	310.300i	0.262286	+	0.978865i	−0.701605	+	0.712566i	$0.747533\pi$
$318$	−397.775	+	28.7243i	−1.25086	+	0.0903279i
$319$	109.639	+	189.900i	0.343695	+	0.595297i
$320$	−118.826	−	297.120i	−0.371332	−	0.928500i
$321$			275.562i			0.858448i
$322$	−522.519	+	247.719i	−1.62273	+	0.769313i
$323$	151.014	−	151.014i	0.467536	−	0.467536i
$324$	−261.089	+	37.9054i	−0.805830	+	0.116992i
$325$	249.771	−	202.493i	0.768527	−	0.623054i
$326$	−434.577	−	376.040i	−1.33306	−	1.15350i
$327$	40.2696	+	150.288i	0.123149	+	0.459597i
$328$	−394.182	+	86.6008i	−1.20178	+	0.264027i
$329$	−318.903	−	49.1712i	−0.969312	−	0.149457i
$330$	318.739	−	331.755i	0.965875	−	1.00532i
$331$	283.486	+	163.671i	0.856455	+	0.494474i	0.862823	−	0.505505i	$-0.168694\pi$
$331$	283.486	+	163.671i	0.856455	+	0.494474i	−0.00636888	+	0.999980i	$0.502027\pi$
$332$	−97.8516	+	42.0618i	−0.294734	+	0.126692i
$333$	119.788	−	447.054i	0.359723	−	1.34250i
$334$	23.5411	−	122.596i	0.0704824	−	0.367055i
$335$	−85.7232	−	27.8266i	−0.255890	−	0.0830644i
$336$	66.6431	+	489.310i	0.198342	+	1.45628i
$337$	264.190	−	264.190i	0.783948	−	0.783948i	−0.196547	−	0.980494i	$-0.562973\pi$
$337$	264.190	−	264.190i	0.783948	−	0.783948i	0.980494	+	0.196547i	$0.0629727\pi$
$338$	−4.01477	−	5.92305i	−0.0118780	−	0.0175238i
$339$	−27.6912	+	15.9875i	−0.0816850	+	0.0471609i
$340$	257.042	−	309.351i	0.756005	−	0.909857i
$341$	239.587	+	138.326i	0.702601	+	0.405647i
$342$	199.536	+	96.7591i	0.583438	+	0.282921i
$343$	324.885	−	109.993i	0.947188	−	0.320680i
$344$	79.4495	+	50.8279i	0.230958	+	0.147756i
$345$	−47.4020	+	909.363i	−0.137397	+	2.63583i
$346$	−323.855	−	280.232i	−0.935996	−	0.809919i
$347$	113.514	−	423.642i	0.327131	−	1.22087i	−0.585021	−	0.811018i	$-0.698914\pi$
$347$	113.514	−	423.642i	0.327131	−	1.22087i	0.912152	−	0.409851i	$-0.134419\pi$
$348$	−221.709	+	297.019i	−0.637094	+	0.853501i
$349$	330.032			0.945649			0.472825	−	0.881156i	$-0.343234\pi$
$349$	330.032			0.945649			0.472825	+	0.881156i	$0.343234\pi$
$350$	26.8340	+	348.970i	0.0766686	+	0.997057i
$351$			81.7083i			0.232787i
$352$	312.438	−	117.758i	0.887609	−	0.334540i
$353$	597.404	+	160.074i	1.69236	+	0.453468i	0.970998	−	0.239087i	$-0.0768481\pi$
$353$	597.404	+	160.074i	1.69236	+	0.453468i	0.721366	+	0.692554i	$0.243515\pi$
$354$	11.2645	+	9.74722i	0.0318207	+	0.0275345i
$355$	−493.601	−	25.7297i	−1.39042	−	0.0724782i
$356$	−42.2926	−	53.6276i	−0.118800	−	0.150639i
$357$	−500.648	+	366.884i	−1.40237	+	1.02769i
$358$	387.715	+	188.011i	1.08300	+	0.525170i
$359$	206.502	−	357.673i	0.575215	−	0.996302i	−0.420803	−	0.907152i	$-0.638252\pi$
$359$	206.502	−	357.673i	0.575215	−	0.996302i	0.996018	−	0.0891501i	$-0.0284151\pi$
$360$	390.947	+	146.893i	1.08596	+	0.408037i
$361$	−124.110	−	214.965i	−0.343795	−	0.595471i
$362$	280.979	+	414.532i	0.776185	+	1.14512i
$363$	−37.8127	−	37.8127i	−0.104167	−	0.104167i
$364$	−360.112	−	3.17241i	−0.989320	−	0.00871542i
$365$	65.6618	−	202.279i	0.179895	−	0.554189i
$366$	−23.6408	+	123.115i	−0.0645923	+	0.336381i
$367$	−79.6230	−	21.3349i	−0.216956	−	0.0581333i	0.148704	−	0.988882i	$-0.452490\pi$
$367$	−79.6230	−	21.3349i	−0.216956	−	0.0581333i	−0.365660	+	0.930749i	$0.619157\pi$
$368$	−315.128	+	580.904i	−0.856325	+	1.57854i
$369$	263.359	−	456.151i	0.713710	−	1.23618i
$370$	307.115	−	319.657i	0.830040	−	0.863937i
$371$	246.839	+	198.218i	0.665336	+	0.534281i
$372$	−54.8769	+	464.388i	−0.147519	+	1.24835i
$373$	491.243	−	131.628i	1.31700	−	0.352890i	0.469149	−	0.883119i	$-0.344561\pi$
$373$	491.243	−	131.628i	1.31700	−	0.352890i	0.847855	+	0.530229i	$0.177894\pi$
$374$	317.352	+	274.605i	0.848535	+	0.734239i
$375$	503.686	+	223.748i	1.34316	+	0.596662i
$376$	−327.425	+	169.655i	−0.870811	+	0.451210i
$377$	−191.125	−	191.125i	−0.506964	−	0.506964i
$378$	−73.1789	−	50.5488i	−0.193595	−	0.133727i
$379$	206.147			0.543924			0.271962	−	0.962308i	$-0.412327\pi$
$379$	206.147			0.543924			0.271962	+	0.962308i	$0.412327\pi$
$380$	122.664	+	173.394i	0.322799	+	0.456300i
$381$	54.4860	−	31.4575i	0.143008	−	0.0825657i
$382$	40.4774	−	2.92297i	0.105962	−	0.00765175i
$383$	−687.083	+	184.103i	−1.79395	+	0.480688i	−0.993007	−	0.118053i	$-0.962335\pi$
$383$	−687.083	+	184.103i	−1.79395	+	0.480688i	−0.800943	+	0.598741i	$0.795668\pi$
$384$	391.424	+	406.578i	1.01933	+	1.05880i
$385$	−364.608	+	20.7087i	−0.947034	+	0.0537889i
$386$	−44.0530	−	127.000i	−0.114127	−	0.329017i
$387$	−118.899	+	31.8589i	−0.307233	+	0.0823228i
$388$	−43.7189	+	18.7927i	−0.112678	+	0.0484347i
$389$	87.2918	−	50.3979i	0.224400	−	0.129558i	−0.383586	−	0.923505i	$-0.625311\pi$
$389$	87.2918	−	50.3979i	0.224400	−	0.129558i	0.607986	+	0.793948i	$0.291978\pi$
$390$	−273.664	+	496.691i	−0.701703	+	1.27357i
$391$	−830.647			−2.12442
$392$	225.625	−	320.558i	0.575573	−	0.817750i
$393$	266.874	+	266.874i	0.679069	+	0.679069i
$394$	−101.750	+	529.889i	−0.258249	+	1.34490i
$395$	−466.910	−	303.029i	−1.18205	−	0.767161i
$396$	−161.401	+	404.773i	−0.407579	+	1.02215i
$397$	−37.4926	+	10.0461i	−0.0944397	+	0.0253050i	−0.305729	−	0.952118i	$-0.598900\pi$
$397$	−37.4926	+	10.0461i	−0.0944397	+	0.0253050i	0.211290	+	0.977423i	$0.432234\pi$
$398$	−10.2280	+	21.0921i	−0.0256985	+	0.0529954i
$399$	−118.715	−	305.517i	−0.297532	−	0.765707i
$400$	260.062	+	303.921i	0.650155	+	0.759802i
$401$	−112.745	+	195.279i	−0.281159	+	0.486981i	−0.971670	−	0.236340i	$-0.924052\pi$
$401$	−112.745	+	195.279i	−0.281159	+	0.486981i	0.690512	+	0.723321i	$0.257385\pi$
$402$	158.541	−	11.4486i	0.394380	−	0.0284791i
$403$	−329.394	−	88.2608i	−0.817355	−	0.219010i
$404$	−89.5796	−	617.017i	−0.221732	−	1.52727i
$405$	293.797	−	149.801i	0.725424	−	0.369878i
$406$	289.413	−	52.9344i	0.712841	−	0.130380i
$407$	327.057	+	327.057i	0.803581	+	0.803581i
$408$	−214.596	+	676.118i	−0.525970	+	1.65715i
$409$	−4.92961	−	8.53833i	−0.0120528	−	0.0208761i	0.859936	−	0.510402i	$-0.170503\pi$
$409$	−4.92961	−	8.53833i	−0.0120528	−	0.0208761i	−0.871989	+	0.489526i	$0.837170\pi$
$410$	431.758	−	260.930i	1.05307	−	0.636414i
$411$	−96.6514	+	167.405i	−0.235162	+	0.407312i
$412$	17.6527	−	149.383i	0.0428463	−	0.362581i
$413$	−1.28417	−	11.7547i	−0.00310936	−	0.0284617i
$414$	−282.660	−	814.878i	−0.682752	−	1.96831i
$415$	98.9144	−	89.1132i	0.238348	−	0.214731i
$416$	−334.435	+	239.887i	−0.803930	+	0.576651i
$417$	−360.824	−	96.6825i	−0.865285	−	0.231852i
$418$	−183.447	+	124.344i	−0.438868	+	0.297474i
$419$			495.477i			1.18252i	0.806480	+	0.591261i	$0.201370\pi$
$419$			495.477i			1.18252i	−0.806480	+	0.591261i	$0.798630\pi$
$420$	−275.540	−	552.375i	−0.656048	−	1.31518i
$421$	−89.1126			−0.211669			−0.105834	−	0.994384i	$-0.533751\pi$
$421$	−89.1126			−0.211669			−0.105834	+	0.994384i	$0.533751\pi$
$422$	−46.5632	−	68.6953i	−0.110339	−	0.162785i
$423$	124.565	−	464.881i	0.294479	−	1.09901i
$424$	361.426	+	16.4699i	0.852419	+	0.0388442i
$425$	−179.908	+	469.464i	−0.423314	+	1.10462i
$426$	823.590	−	285.681i	1.93331	−	0.670613i
$427$	80.2685	−	58.8223i	0.187982	−	0.137757i
$428$	29.3373	−	248.262i	0.0685450	−	0.580052i
$429$	−512.440	−	295.857i	−1.19450	−	0.689644i
$430$	−114.467	−	28.2294i	−0.266202	−	0.0656497i
$431$	500.391	−	288.901i	1.16100	−	0.670304i	0.209457	−	0.977818i	$-0.432830\pi$
$431$	500.391	−	288.901i	1.16100	−	0.670304i	0.951544	+	0.307514i	$0.0994970\pi$
$432$	−101.610	+	2.69832i	−0.235208	+	0.00624610i
$433$	7.04665	−	7.04665i	0.0162740	−	0.0162740i	−0.698923	−	0.715197i	$-0.746337\pi$
$433$	7.04665	−	7.04665i	0.0162740	−	0.0162740i	0.715197	+	0.698923i	$0.246337\pi$
$434$	282.827	−	240.406i	0.651675	−	0.553932i
$435$	143.044	−	440.666i	0.328838	−	1.01302i
$436$	−20.2799	−	139.686i	−0.0465136	−	0.320382i
$437$	113.530	−	423.700i	0.259794	−	0.969565i
$438$	27.0150	+	374.105i	0.0616780	+	0.854120i
$439$	−247.072	−	142.647i	−0.562807	−	0.324937i	0.191465	−	0.981500i	$-0.438676\pi$
$439$	−247.072	−	142.647i	−0.562807	−	0.324937i	−0.754271	+	0.656563i	$0.772010\pi$
$440$	−322.481	+	264.954i	−0.732912	+	0.602169i
$441$	110.464	+	499.533i	0.250484	+	1.13273i
$442$	−465.463	−	225.712i	−1.05308	−	0.510662i
$443$	−38.1870	−	142.516i	−0.0862009	−	0.321706i	0.909338	−	0.416058i	$-0.136589\pi$
$443$	−38.1870	−	142.516i	−0.0862009	−	0.321706i	−0.995539	+	0.0943520i	$0.969922\pi$
$444$	−289.570	+	726.202i	−0.652184	+	1.63559i
$445$	71.6122	+	46.4770i	0.160926	+	0.104443i
$446$	318.874	+	61.2306i	0.714964	+	0.137288i
$447$	167.766	−	167.766i	0.375315	−	0.375315i
$448$	−7.94715	−	447.930i	−0.0177392	−	0.999843i
$449$		−	447.480i		−	0.996614i	−0.867001	−	0.498307i	$-0.833955\pi$
$449$		−	447.480i		−	0.996614i	0.867001	−	0.498307i	$-0.166045\pi$
$450$	−521.773	−	16.7400i	−1.15950	−	0.0371999i
$451$	263.191	+	455.860i	0.583572	+	1.01078i
$452$	26.6500	−	11.4556i	0.0589601	−	0.0253441i
$453$	170.794	+	637.413i	0.377029	+	1.40709i
$454$	125.692	−	43.5994i	0.276856	−	0.0960338i
$455$	427.513	−	140.979i	0.939589	−	0.309843i
$456$	−315.547	−	201.872i	−0.691989	−	0.442701i
$457$	−128.538	−	479.711i	−0.281265	−	1.04970i	−0.951525	−	0.307570i	$-0.900484\pi$
$457$	−128.538	−	479.711i	−0.281265	−	1.04970i	0.670260	−	0.742126i	$-0.266183\pi$
$458$	−52.6733	−	729.423i	−0.115007	−	1.59263i
$459$	−63.8788	−	110.641i	−0.139169	−	0.241049i
$460$	139.520	−	814.226i	0.303304	−	1.77006i
$461$			520.254i			1.12853i	0.825593	+	0.564266i	$0.190841\pi$
$461$			520.254i			1.12853i	−0.825593	+	0.564266i	$0.809159\pi$
$462$	581.993	−	275.915i	1.25973	−	0.597218i
$463$	−11.1352	+	11.1352i	−0.0240500	+	0.0240500i	−0.719030	−	0.694980i	$-0.755413\pi$
$463$	−11.1352	+	11.1352i	−0.0240500	+	0.0240500i	0.694980	+	0.719030i	$0.255413\pi$
$464$	231.366	−	243.989i	0.498633	−	0.525839i
$465$	−121.690	−	571.717i	−0.261698	−	1.22950i
$466$	−606.430	+	700.831i	−1.30135	+	1.50393i
$467$	47.1252	+	175.874i	0.100911	+	0.376603i	0.997849	−	0.0655518i	$-0.0208808\pi$
$467$	47.1252	+	175.874i	0.100911	+	0.376603i	−0.896939	+	0.442155i	$0.854214\pi$
$468$	63.0361	−	533.434i	0.134693	−	1.13982i
$469$	−98.3825	−	79.0035i	−0.209771	−	0.168451i
$470$	319.362	−	332.404i	0.679493	−	0.707242i
$471$	−1148.30	−	662.970i	−2.43800	−	1.40758i
$472$	−9.11084	−	9.98083i	−0.0193026	−	0.0211458i
$473$	31.8386	−	118.823i	0.0673121	−	0.251212i
$474$	964.089	+	185.126i	2.03394	+	0.390561i
$475$	−214.877	−	155.933i	−0.452373	−	0.328281i
$476$	490.109	−	277.237i	1.02964	−	0.582430i
$477$	−333.887	+	333.887i	−0.699973	+	0.699973i
$478$	−2.63101	+	1.78336i	−0.00550422	+	0.00373088i
$479$	9.15652	−	5.28652i	0.0191159	−	0.0110366i	−0.490412	−	0.871491i	$-0.663154\pi$
$479$	9.15652	−	5.28652i	0.0191159	−	0.0110366i	0.509527	+	0.860454i	$0.329820\pi$
$480$	−626.708	−	323.918i	−1.30564	−	0.674829i
$481$	−493.752	−	285.068i	−1.02651	−	0.592656i
$482$	−11.2545	+	23.2089i	−0.0233495	+	0.0481513i
$483$	−513.748	+	1166.74i	−1.06366	+	2.41560i
$484$	30.0410	+	38.0923i	0.0620681	+	0.0787031i
$485$	44.1937	−	39.8146i	0.0911210	−	0.0820920i
$486$	−455.408	+	526.299i	−0.937054	+	1.08292i
$487$	33.2326	−	124.026i	0.0682395	−	0.254673i	−0.923376	−	0.383897i	$-0.874582\pi$
$487$	33.2326	−	124.026i	0.0682395	−	0.254673i	0.991615	+	0.129224i	$0.0412485\pi$
$488$	34.4060	−	108.401i	0.0705040	−	0.222134i
$489$	−1266.94			−2.59089
$490$	−138.218	+	470.102i	−0.282078	+	0.959391i
$491$		−	175.310i		−	0.357046i	−0.983936	−	0.178523i	$-0.942868\pi$
$491$		−	175.310i		−	0.357046i	0.983936	−	0.178523i	$-0.0571319\pi$
$492$	−532.218	+	713.001i	−1.08174	+	1.44919i
$493$	408.223	+	109.383i	0.828038	+	0.221872i
$494$	178.750	−	206.576i	0.361843	−	0.418169i
$495$	28.3552	−	543.968i	0.0572833	−	1.09893i
$496$	98.8806	−	412.539i	0.199356	−	0.831732i
$497$	−633.302	−	278.862i	−1.27425	−	0.561090i
$498$	−102.453	+	211.278i	−0.205729	+	0.424252i
$499$	−339.167	+	587.454i	−0.679693	+	1.17726i	0.295380	+	0.955380i	$0.404554\pi$
$499$	−339.167	+	587.454i	−0.679693	+	1.17726i	−0.975073	+	0.221883i	$0.928780\pi$
$500$	−429.965	−	255.206i	−0.859930	−	0.510411i
$501$	−137.606	−	238.341i	−0.274663	−	0.475730i
$502$	−372.655	+	252.594i	−0.742340	+	0.503175i
$503$	546.779	+	546.779i	1.08704	+	1.08704i	0.995832	+	0.0912034i	$0.0290714\pi$
$503$	546.779	+	546.779i	1.08704	+	1.08704i	0.0912034	+	0.995832i	$0.470929\pi$
$504$	438.752	+	386.464i	0.870540	+	0.766794i
$505$	354.016	+	694.313i	0.701021	+	1.37488i
$506$	846.495	+	162.545i	1.67291	+	0.321235i
$507$	−15.2374	−	4.08284i	−0.0300540	−	0.00805294i
$508$	−52.4372	+	22.5403i	−0.103223	+	0.0443706i
$509$	95.2297	−	164.943i	0.187092	−	0.324052i	−0.757188	−	0.653197i	$-0.773427\pi$
$509$	95.2297	−	164.943i	0.187092	−	0.324052i	0.944279	+	0.329145i	$0.106761\pi$
$510$	−17.7395	−	886.518i	−0.0347834	−	1.73827i
$511$	186.423	−	232.151i	0.364820	−	0.454307i
$512$	−309.360	−	407.971i	−0.604219	−	0.796819i
$513$	65.1671	−	17.4615i	0.127031	−	0.0340380i
$514$	−263.470	+	304.483i	−0.512588	+	0.592380i
$515$	39.1448	+	183.908i	0.0760094	+	0.357104i
$516$	205.773	−	29.8744i	0.398784	−	0.0578962i
$517$	340.100	+	340.100i	0.657833	+	0.657833i
$518$	560.769	−	265.853i	1.08257	−	0.513229i
$519$	−944.150			−1.81917
$520$	299.432	−	418.349i	0.575831	−	0.804518i
$521$	−439.847	+	253.946i	−0.844236	+	0.487420i	−0.858702	−	0.512476i	$-0.828728\pi$
$521$	−439.847	+	253.946i	−0.844236	+	0.487420i	0.0144662	+	0.999895i	$0.495395\pi$
$522$	31.6070	+	437.695i	0.0605498	+	0.838496i
$523$	143.171	−	38.3627i	0.273750	−	0.0733512i	−0.119332	−	0.992854i	$-0.538075\pi$
$523$	143.171	−	38.3627i	0.273750	−	0.0733512i	0.393083	+	0.919503i	$0.371409\pi$
$524$	−212.023	−	268.847i	−0.404623	−	0.513067i
$525$	548.142	+	543.061i	1.04408	+	1.03440i
$526$	363.267	−	126.008i	0.690622	−	0.239558i
$527$	515.034	−	138.003i	0.977294	−	0.261865i
$528$	350.996	−	647.024i	0.664765	−	1.22543i
$529$	−1019.38	+	588.538i	−1.92699	+	1.11255i
$530$	−434.412	+	125.767i	−0.819645	+	0.237297i
$531$	17.6370			0.0332147
$532$	74.4277	+	287.889i	0.139902	+	0.541144i
$533$	−458.802	−	458.802i	−0.860791	−	0.860791i
$534$	−147.867	−	28.3936i	−0.276904	−	0.0531716i
$535$	65.0554	+	305.640i	0.121599	+	0.571290i
$536$	−144.053	−	6.56439i	−0.268755	−	0.0122470i
$537$	917.578	−	245.864i	1.70871	−	0.457848i
$538$	−312.025	−	151.307i	−0.579972	−	0.281241i
$539$	−487.529	−	154.004i	−0.904506	−	0.285721i
$540$	119.184	−	44.0321i	0.220710	−	0.0815409i
$541$	139.097	−	240.923i	0.257110	−	0.445328i	−0.708356	−	0.705855i	$-0.750563\pi$
$541$	139.097	−	240.923i	0.257110	−	0.445328i	0.965467	+	0.260527i	$0.0838963\pi$
$542$	31.1901	+	431.922i	0.0575462	+	0.796903i
$543$	1066.41	+	285.743i	1.96392	+	0.526230i
$544$	265.318	−	586.289i	0.487716	−	1.07774i
$545$	80.1455	+	157.185i	0.147056	+	0.288414i
$546$	−604.923	+	514.192i	−1.10792	+	0.941744i
$547$	214.119	+	214.119i	0.391442	+	0.391442i	0.875201	−	0.483759i	$-0.160729\pi$
$547$	214.119	+	214.119i	0.391442	+	0.391442i	−0.483759	+	0.875201i	$0.660729\pi$
$548$	104.899	−	140.531i	0.191421	−	0.256443i
$549$	74.2151	+	128.544i	0.135182	+	0.234143i
$550$	275.208	−	443.216i	0.500378	−	0.805847i
$551$	−111.589	+	193.278i	−0.202521	+	0.350777i
$552$	312.633	+	1423.02i	0.566365	+	2.57793i
$553$	−460.625	−	628.565i	−0.832956	−	1.13665i
$554$	−847.446	+	293.956i	−1.52969	+	0.530607i
$555$	50.8720	−	975.931i	0.0916613	−	1.75843i
$556$	314.784	+	125.519i	0.566158	+	0.225753i
$557$	−741.427	−	198.665i	−1.33111	−	0.356669i	−0.477979	−	0.878371i	$-0.658631\pi$
$557$	−741.427	−	198.665i	−1.33111	−	0.356669i	−0.853128	+	0.521702i	$0.825297\pi$
$558$	310.643	+	458.296i	0.556708	+	0.821319i
$559$			151.634i			0.271260i
$560$	189.435	+	526.986i	0.338277	+	0.941047i
$561$	925.193			1.64919
$562$	696.647	−	472.203i	1.23958	−	0.840218i
$563$	220.048	−	821.229i	0.390848	−	1.45867i	−0.437890	−	0.899029i	$-0.644274\pi$
$563$	220.048	−	821.229i	0.390848	−	1.45867i	0.828738	−	0.559637i	$-0.189059\pi$
$564$	−301.117	+	755.161i	−0.533895	+	1.33894i
$565$	−26.9394	+	24.2700i	−0.0476803	+	0.0429558i
$566$	267.423	+	770.953i	0.472479	+	1.36211i
$567$	458.965	−	50.1407i	0.809462	−	0.0884315i
$568$	−772.412	+	169.697i	−1.35988	+	0.298762i
$569$	−164.316	−	94.8677i	−0.288780	−	0.166727i	0.348612	−	0.937267i	$-0.386653\pi$
$569$	−164.316	−	94.8677i	−0.288780	−	0.166727i	−0.637391	+	0.770540i	$0.719987\pi$
$570$	454.624	+	112.118i	0.797586	+	0.196698i
$571$	−532.631	+	307.514i	−0.932803	+	0.538554i	−0.887697	−	0.460428i	$-0.847696\pi$
$571$	−532.631	+	307.514i	−0.932803	+	0.538554i	−0.0451061	+	0.998982i	$0.514363\pi$
$572$	430.175	+	321.103i	0.752053	+	0.561369i
$573$	63.2637	−	63.2637i	0.110408	−	0.110408i
$574$	694.745	−	127.071i	1.21036	−	0.221377i
$575$	162.109	+	1019.81i	0.281928	+	1.77359i
$576$	665.444	+	60.7738i	1.15528	+	0.105510i
$577$	−120.196	+	448.579i	−0.208313	+	0.777434i	0.780101	+	0.625653i	$0.215167\pi$
$577$	−120.196	+	448.579i	−0.208313	+	0.777434i	−0.988414	+	0.151781i	$0.951499\pi$
$578$	230.244	−	16.6265i	0.398346	−	0.0287655i
$579$	−256.646	−	148.175i	−0.443257	−	0.255915i
$580$	−175.788	+	381.780i	−0.303083	+	0.658242i
$581$	173.735	−	67.5086i	0.299028	−	0.116194i
$582$	−45.7747	+	94.3962i	−0.0786506	+	0.162193i
$583$	−122.133	−	455.807i	−0.209491	−	0.781830i
$584$	15.4898	−	339.918i	0.0265237	−	0.582052i
$585$	139.783	+	656.720i	0.238945	+	1.12260i
$586$	185.258	−	964.777i	0.316140	−	1.64638i
$587$	49.7897	−	49.7897i	0.0848207	−	0.0848207i	−0.663423	−	0.748244i	$-0.730897\pi$
$587$	49.7897	−	49.7897i	0.0848207	−	0.0848207i	0.748244	+	0.663423i	$0.230897\pi$
$588$	−86.2814	−	859.880i	−0.146737	−	1.46238i
$589$			281.573i			0.478052i
$590$	14.7952	+	8.15179i	0.0250767	+	0.0138166i
$591$	594.765	+	1030.16i	1.00637	+	1.74308i
$592$	338.196	−	623.429i	0.571277	−	1.05309i
$593$	25.4246	+	94.8858i	0.0428745	+	0.160010i	0.984044	−	0.177925i	$-0.0569384\pi$
$593$	25.4246	+	94.8858i	0.0428745	+	0.160010i	−0.941170	+	0.337935i	$0.890272\pi$
$594$	43.4467	+	125.252i	0.0731426	+	0.210863i
$595$	−468.680	+	525.125i	−0.787697	+	0.882563i
$596$	−169.006	+	133.285i	−0.283568	+	0.223632i
$597$	13.3753	+	49.9173i	0.0224042	+	0.0836137i
$598$	−1059.73	+	76.5258i	−1.77213	+	0.127970i
$599$	−90.0450	−	155.962i	−0.150325	−	0.260371i	0.781022	−	0.624504i	$-0.214699\pi$
$599$	−90.0450	−	155.962i	−0.150325	−	0.260371i	−0.931347	+	0.364133i	$0.881365\pi$
$600$	871.973	+	131.515i	1.45329	+	0.219192i
$601$		−	429.695i		−	0.714967i	−0.933919	−	0.357483i	$-0.883635\pi$
$601$		−	429.695i		−	0.714967i	0.933919	−	0.357483i	$-0.116365\pi$
$602$	−135.805	−	93.8083i	−0.225590	−	0.155828i
$603$	133.077	−	133.077i	0.220691	−	0.220691i
$604$	−86.0126	−	592.448i	−0.142405	−	0.980874i
$605$	−50.8670	−	33.0131i	−0.0840777	−	0.0545672i
$606$	−1039.42	−	899.411i	−1.71521	−	1.48418i
$607$	113.674	+	424.239i	0.187273	+	0.698911i	0.994133	+	0.108168i	$0.0344985\pi$
$607$	113.674	+	424.239i	0.187273	+	0.698911i	−0.806860	+	0.590743i	$0.798835\pi$
$608$	262.794	+	215.466i	0.432227	+	0.354386i
$609$	406.123	−	505.742i	0.666868	−	0.830446i
$610$	2.84417	+	142.135i	0.00466257	+	0.233008i
$611$	−513.441	−	296.436i	−0.840330	−	0.485165i
$612$	331.676	+	771.604i	0.541954	+	1.26079i
$613$	−60.1847	+	224.612i	−0.0981806	+	0.366415i	−0.997482	−	0.0709134i	$-0.977409\pi$
$613$	−60.1847	+	224.612i	−0.0981806	+	0.366415i	0.899302	+	0.437328i	$0.144075\pi$
$614$	−76.3405	+	397.562i	−0.124333	+	0.647496i
$615$	343.382	−	1057.83i	0.558345	−	1.72005i
$616$	−553.711	+	186.619i	−0.898881	+	0.302953i
$617$	−173.070	+	173.070i	−0.280502	+	0.280502i	−0.833309	−	0.552807i	$-0.813557\pi$
$617$	−173.070	+	173.070i	−0.280502	+	0.280502i	0.552807	+	0.833309i	$0.313557\pi$
$618$	−186.064	−	274.503i	−0.301075	−	0.444179i
$619$	363.620	−	209.936i	0.587432	−	0.339154i	−0.176649	−	0.984274i	$-0.556526\pi$
$619$	363.620	−	209.936i	0.587432	−	0.339154i	0.764081	+	0.645120i	$0.223193\pi$
$620$	48.7670	+	528.032i	0.0786565	+	0.851665i
$621$	−227.248	−	131.201i	−0.365938	−	0.211274i
$622$	−772.424	−	374.564i	−1.24184	−	0.602194i
$623$	70.6482	+	96.4060i	0.113400	+	0.154745i
$624$	−211.490	+	882.357i	−0.338927	+	1.41403i
$625$	611.488	+	129.259i	0.978380	+	0.206815i
$626$	615.637	+	532.712i	0.983445	+	0.850977i
$627$	−126.452	+	471.927i	−0.201678	+	0.752674i
$628$	963.955	+	719.542i	1.53496	+	1.14577i
$629$	891.453			1.41725
$630$	−674.643	−	281.089i	−1.07086	−	0.446172i
$631$		−	1063.68i		−	1.68571i	−0.538139	−	0.842856i	$-0.680872\pi$
$631$		−	1063.68i		−	1.68571i	0.538139	−	0.842856i	$-0.319128\pi$
$632$	−848.868	−	269.426i	−1.34315	−	0.426307i
$633$	−176.722	−	47.3526i	−0.279182	−	0.0748067i
$634$	−485.853	−	420.409i	−0.766329	−	0.663106i
$635$	53.0067	−	47.7544i	0.0834751	−	0.0752037i
$636$	626.295	−	493.918i	0.984740	−	0.776601i
$637$	629.607	+	27.8265i	0.988393	+	0.0436837i
$638$	−394.607	−	191.353i	−0.618506	−	0.299926i
$639$	516.060	−	893.842i	0.807605	−	1.39881i
$640$	530.135	+	358.549i	0.828335	+	0.560233i
$641$	73.8167	+	127.854i	0.115159	+	0.199461i	0.917843	−	0.396943i	$-0.129929\pi$
$641$	73.8167	+	127.854i	0.115159	+	0.199461i	−0.802685	+	0.596404i	$0.796596\pi$
$642$	−309.223	−	456.200i	−0.481655	−	0.710593i
$643$	451.801	+	451.801i	0.702645	+	0.702645i	0.964978	−	0.262332i	$-0.0844916\pi$
$643$	451.801	+	451.801i	0.702645	+	0.702645i	−0.262332	+	0.964978i	$0.584492\pi$
$644$	587.066	−	996.452i	0.911593	−	1.54729i
$645$	−231.551	+	118.063i	−0.358993	+	0.183043i
$646$	−80.5471	+	419.469i	−0.124686	+	0.649333i
$647$	−868.573	−	232.733i	−1.34246	−	0.359712i	−0.485115	−	0.874450i	$-0.661222\pi$
$647$	−868.573	−	232.733i	−1.34246	−	0.359712i	−0.857347	+	0.514739i	$0.827889\pi$
$648$	389.704	−	355.735i	0.601396	−	0.548974i
$649$	−8.81286	+	15.2643i	−0.0135791	+	0.0235198i
$650$	−186.275	+	615.514i	−0.286577	+	0.946944i
$651$	124.704	−	808.776i	0.191557	−	1.24236i
$652$	1141.43	+	134.883i	1.75066	+	0.206876i
$653$	307.835	−	82.4841i	0.471416	−	0.126316i	−0.0152866	−	0.999883i	$-0.504866\pi$
$653$	307.835	−	82.4841i	0.471416	−	0.126316i	0.486703	+	0.873568i	$0.338199\pi$
$654$	−235.314	−	203.618i	−0.359807	−	0.311342i
$655$	359.008	+	233.000i	0.548104	+	0.355725i
$656$	555.400	−	585.703i	0.846647	−	0.892840i
$657$	314.018	+	314.018i	0.477958	+	0.477958i
$658$	583.131	−	276.454i	0.886218	−	0.420143i
$659$	392.214			0.595165			0.297583	−	0.954696i	$-0.403820\pi$
$659$	392.214			0.595165			0.297583	+	0.954696i	$0.403820\pi$
$660$	−155.400	+	906.904i	−0.235455	+	1.37410i
$661$	−441.667	+	254.996i	−0.668180	+	0.385774i	−0.795387	−	0.606103i	$-0.792732\pi$
$661$	−441.667	+	254.996i	−0.668180	+	0.385774i	0.127207	+	0.991876i	$0.459399\pi$
$662$	−652.984	+	47.1535i	−0.986380	+	0.0712288i
$663$	−1101.58	+	295.167i	−1.66151	+	0.445199i
$664$	114.796	−	179.439i	0.172886	−	0.270240i
$665$	−203.800	−	310.838i	−0.306467	−	0.467426i
$666$	303.351	+	874.530i	0.455482	+	1.31311i
$667$	838.454	−	224.663i	1.25705	−	0.336826i
$668$	98.5990	+	229.378i	0.147603	+	0.343381i
$669$	619.925	−	357.914i	0.926645	−	0.534999i
$670$	173.143	−	50.1269i	0.258422	−	0.0748163i
$671$	−148.336			−0.221066
$672$	−659.411	−	735.283i	−0.981266	−	1.09417i
$673$	−122.927	−	122.927i	−0.182656	−	0.182656i	0.609856	−	0.792512i	$-0.291227\pi$
$673$	−122.927	−	122.927i	−0.182656	−	0.182656i	−0.792512	+	0.609856i	$0.791227\pi$
$674$	−140.912	+	733.837i	−0.209069	+	1.08878i
$675$	−123.371	+	100.019i	−0.182773	+	0.148176i
$676$	13.2931	+	5.30058i	0.0196644	+	0.00784109i
$677$	−1194.36	+	320.029i	−1.76420	+	0.472716i	−0.987562	−	0.157231i	$-0.949743\pi$
$677$	−1194.36	+	320.029i	−1.76420	+	0.472716i	−0.776638	+	0.629947i	$0.783077\pi$
$678$	27.9031	−	57.5416i	0.0411550	−	0.0848696i
$679$	77.6228	−	30.1620i	0.114319	−	0.0444212i
$680$	−78.3997	+	800.580i	−0.115294	+	1.17732i
$681$	146.649	−	254.003i	0.215343	−	0.372985i
$682$	−551.865	+	39.8515i	−0.809187	+	0.0584333i
$683$	−423.110	−	113.372i	−0.619488	−	0.165991i	−0.0645930	−	0.997912i	$-0.520575\pi$
$683$	−423.110	−	113.372i	−0.619488	−	0.165991i	−0.554895	+	0.831920i	$0.687242\pi$
$684$	−438.916	+	63.7225i	−0.641690	+	0.0931616i
$685$	−67.6797	+	208.496i	−0.0988025	+	0.304373i
$686$	−414.427	+	546.668i	−0.604122	+	0.796892i
$687$	−1140.04	−	1140.04i	−1.65945	−	1.65945i
$688$	−188.568	+	5.00753i	−0.274081	+	0.00727839i
$689$	290.835	+	503.741i	0.422112	+	0.731119i
$690$	−941.969	−	1558.67i	−1.36517	−	2.25894i
$691$	−117.334	+	203.229i	−0.169804	+	0.294108i	−0.938351	−	0.345685i	$-0.887647\pi$
$691$	−117.334	+	203.229i	−0.169804	+	0.294108i	0.768547	+	0.639793i	$0.220980\pi$
$692$	850.614	+	100.517i	1.22921	+	0.145256i
$693$	307.317	−	697.925i	0.443459	−	1.00711i
$694$	287.465	+	828.731i	0.414214	+	1.19414i
$695$	−423.034	−	22.0513i	−0.608681	−	0.0317285i
$696$	33.7447	−	740.514i	0.0484838	−	1.06396i
$697$	979.950	+	262.577i	1.40595	+	0.376724i
$698$	−546.377	+	370.346i	−0.782774	+	0.530582i
$699$			2043.17i			2.92299i
$700$	−436.022	−	547.617i	−0.622889	−	0.782310i
$701$	406.782			0.580288			0.290144	−	0.956983i	$-0.406297\pi$
$701$	406.782			0.580288			0.290144	+	0.956983i	$0.406297\pi$
$702$	−91.6893	−	135.270i	−0.130612	−	0.192693i
$703$	−121.841	+	454.716i	−0.173316	+	0.646822i
$704$	−385.108	+	545.556i	−0.547028	+	0.774937i
$705$	52.9007	−	1014.85i	0.0750364	−	1.43950i
$706$	−1168.65	+	405.372i	−1.65531	+	0.574182i
$707$	118.495	+	1084.65i	0.167602	+	1.53415i
$708$	−29.5866	−	3.49627i	−0.0417890	−	0.00493823i
$709$	−650.134	−	375.355i	−0.916974	−	0.529415i	−0.0343054	−	0.999411i	$-0.510922\pi$
$709$	−650.134	−	375.355i	−0.916974	−	0.529415i	−0.882668	+	0.469996i	$0.844255\pi$
$710$	846.042	−	511.299i	1.19161	−	0.720140i
$711$	1006.60	−	581.162i	1.41576	−	0.817387i
$712$	130.195	+	41.3231i	0.182858	+	0.0580381i
$713$	774.389	−	774.389i	1.08610	−	1.08610i
$714$	417.136	−	1169.19i	0.584224	−	1.63752i
$715$	−638.220	−	207.173i	−0.892616	−	0.289752i
$716$	−852.850	+	123.818i	−1.19113	+	0.172930i
$717$	−1.81360	+	6.76843i	−0.00252942	+	0.00943993i
$718$	59.4931	+	823.864i	0.0828595	+	1.14744i
$719$	−271.531	−	156.769i	−0.377651	−	0.218037i	0.299145	−	0.954208i	$-0.403299\pi$
$719$	−271.531	−	156.769i	−0.377651	−	0.218037i	−0.676796	+	0.736171i	$0.736632\pi$
$720$	−812.061	+	195.517i	−1.12786	+	0.271551i
$721$	−40.1145	+	260.165i	−0.0556372	+	0.360839i
$722$	446.692	+	216.610i	0.618686	+	0.300014i
$723$	14.7176	+	54.9269i	0.0203563	+	0.0759709i
$724$	−930.337	−	370.968i	−1.28500	−	0.512386i
$725$	54.6245	−	522.536i	0.0753441	−	0.720739i
$726$	105.032	+	20.1683i	0.144672	+	0.0277801i
$727$	−139.707	+	139.707i	−0.192170	+	0.192170i	−0.796633	−	0.604463i	$-0.793388\pi$
$727$	−139.707	+	139.707i	−0.192170	+	0.192170i	0.604463	+	0.796633i	$0.293388\pi$
$728$	599.736	−	398.849i	0.823813	−	0.547870i
$729$			940.739i			1.29045i
$730$	118.283	+	408.561i	0.162032	+	0.559673i
$731$	−118.546	−	205.328i	−0.162170	−	0.280886i
$732$	−99.0163	−	230.349i	−0.135268	−	0.314685i
$733$	124.060	+	462.998i	0.169250	+	0.631648i	0.997460	+	0.0712304i	$0.0226926\pi$
$733$	124.060	+	462.998i	0.169250	+	0.631648i	−0.828210	+	0.560417i	$0.810641\pi$
$734$	155.759	−	54.0287i	0.212206	−	0.0736085i
$735$	447.721	+	983.098i	0.609145	+	1.33755i
$736$	−130.162	−	1315.32i	−0.176850	−	1.78713i
$737$	48.6784	+	181.670i	0.0660494	+	0.246500i
$738$	75.8735	+	1050.70i	0.102810	+	1.42371i
$739$	191.338	+	331.406i	0.258914	+	0.448453i	0.965951	−	0.258724i	$-0.0833020\pi$
$739$	191.338	+	331.406i	0.258914	+	0.448453i	−0.707037	+	0.707176i	$0.749969\pi$
$740$	−149.733	+	873.830i	−0.202342	+	1.18085i
$741$		−	602.240i		−	0.812740i
$742$	−631.081	−	51.1639i	−0.850513	−	0.0689540i
$743$	465.522	−	465.522i	0.626544	−	0.626544i	−0.320653	−	0.947197i	$-0.603902\pi$
$743$	465.522	−	465.522i	0.626544	−	0.626544i	0.947197	+	0.320653i	$0.103902\pi$
$744$	−430.264	−	830.387i	−0.578312	−	1.11611i
$745$	146.471	−	225.685i	0.196606	−	0.302932i
$746$	−665.559	+	769.163i	−0.892170	+	1.03105i
$747$	71.9543	+	268.537i	0.0963244	+	0.359488i
$748$	−833.535	−	98.4992i	−1.11435	−	0.131683i
$749$	−66.6668	+	432.372i	−0.0890077	+	0.577266i
$750$	−1084.95	+	194.792i	−1.44659	+	0.259723i
$751$	678.325	+	391.631i	0.903229	+	0.521479i	0.878246	−	0.478209i	$-0.158714\pi$
$751$	678.325	+	391.631i	0.903229	+	0.521479i	0.0249823	+	0.999688i	$0.492047\pi$
$752$	351.682	−	648.289i	0.467663	−	0.862087i
$753$	−256.876	+	958.675i	−0.341137	+	1.27314i
$754$	530.885	+	101.941i	0.704092	+	0.135201i
$755$	339.919	+	666.666i	0.450223	+	0.883001i
$756$	177.873	+	1.56698i	0.235282	+	0.00207272i
$757$	980.806	−	980.806i	1.29565	−	1.29565i	0.364411	−	0.931238i	$-0.381270\pi$
$757$	980.806	−	980.806i	1.29565	−	1.29565i	0.931238	−	0.364411i	$-0.118730\pi$
$758$	−341.282	+	231.329i	−0.450241	+	0.305183i
$759$	1645.68	−	950.133i	2.16822	−	1.25182i
$760$	−397.648	−	149.411i	−0.523221	−	0.196594i
$761$	−578.986	−	334.278i	−0.760822	−	0.439261i	0.0687686	−	0.997633i	$-0.478093\pi$
$761$	−578.986	−	334.278i	−0.760822	−	0.439261i	−0.829591	+	0.558372i	$0.811426\pi$
$762$	−54.9029	+	113.220i	−0.0720511	+	0.148583i
$763$	26.8260	+	245.553i	0.0351586	+	0.321826i
$764$	−63.7315	+	50.2609i	−0.0834182	+	0.0657866i
$765$	−702.697	−	779.985i	−0.918559	−	1.01959i
$766$	930.893	−	1075.80i	1.21526	−	1.40444i
$767$	5.62319	−	20.9860i	0.00733140	−	0.0273612i
$768$	−1104.26	−	233.864i	−1.43783	−	0.304511i
$769$	424.259			0.551703			0.275851	−	0.961200i	$-0.411040\pi$
$769$	424.259			0.551703			0.275851	+	0.961200i	$0.411040\pi$
$770$	580.381	−	443.430i	0.753741	−	0.575883i
$771$			887.676i			1.15133i
$772$	215.445	+	160.818i	0.279074	+	0.208314i
$773$	−943.747	−	252.876i	−1.22089	−	0.327136i	−0.409863	−	0.912147i	$-0.634424\pi$
$773$	−943.747	−	252.876i	−1.22089	−	0.327136i	−0.811025	+	0.585011i	$0.801090\pi$
$774$	161.090	−	186.166i	0.208127	−	0.240525i
$775$	−269.945	−	605.392i	−0.348316	−	0.781151i
$776$	51.2895	−	80.1711i	0.0660948	−	0.103313i
$777$	551.356	−	1252.14i	0.709596	−	1.61151i
$778$	−87.9597	+	181.390i	−0.113059	+	0.233149i
$779$	−267.873	+	463.969i	−0.343867	+	0.595596i
$780$	−104.305	−	1129.38i	−0.133725	−	1.44792i
$781$	515.730	+	893.271i	0.660346	+	1.14375i
$782$	1375.16	−	932.113i	1.75851	−	1.19196i
$783$	94.4040	+	94.4040i	0.120567	+	0.120567i
$784$	−13.8122	+	783.878i	−0.0176177	+	0.999845i
$785$	−1430.15	−	464.242i	−1.82185	−	0.591391i
$786$	−741.291	−	142.344i	−0.943118	−	0.181099i
$787$	−428.410	−	114.792i	−0.544358	−	0.145860i	−0.0238475	−	0.999716i	$-0.507592\pi$
$787$	−428.410	−	114.792i	−0.544358	−	0.145860i	−0.520510	+	0.853855i	$0.674258\pi$
$788$	−426.167	−	991.425i	−0.540821	−	1.25815i
$789$	423.833	−	734.100i	0.537177	−	0.930418i
$790$	1113.03	−	22.2721i	1.40889	−	0.0281925i
$791$	−47.3170	+	18.3860i	−0.0598192	+	0.0232440i
$792$	−187.013	−	851.230i	−0.236127	−	1.07478i
$793$	176.615	−	47.3239i	0.222718	−	0.0596771i
$794$	50.7967	−	58.7040i	0.0639757	−	0.0739345i
$795$	−542.785	+	836.329i	−0.682749	+	1.05199i
$796$	−6.73586	−	46.3960i	−0.00846213	−	0.0582865i
$797$	162.182	+	162.182i	0.203490	+	0.203490i	0.801494	−	0.598003i	$-0.204039\pi$
$797$	162.182	+	162.182i	0.203490	+	0.203490i	−0.598003	+	0.801494i	$0.704039\pi$
$798$	539.373	+	372.576i	0.675906	+	0.466887i
$799$	927.002			1.16020
$800$	−771.585	−	211.319i	−0.964482	−	0.264149i
$801$	−154.387	+	89.1357i	−0.192743	+	0.111280i
$802$	−32.4816	−	449.807i	−0.0405008	−	0.560857i
$803$	−428.683	+	114.865i	−0.533852	+	0.143045i
$804$	−249.621	+	196.860i	−0.310474	+	0.244851i
$805$	−294.379	+	1415.37i	−0.365688	+	1.75823i
$806$	644.363	−	223.512i	0.799458	−	0.277311i
$807$	−738.448	+	197.867i	−0.915054	+	0.245188i
$808$	840.689	+	920.967i	1.04046	+	1.13981i
$809$	814.311	−	470.143i	1.00656	−	0.581140i	0.0963807	−	0.995345i	$-0.469273\pi$
$809$	814.311	−	470.143i	1.00656	−	0.581140i	0.910184	+	0.414204i	$0.135940\pi$
$810$	−318.289	+	577.684i	−0.392950	+	0.713190i
$811$	405.924			0.500523			0.250262	−	0.968178i	$-0.419483\pi$
$811$	405.924			0.500523			0.250262	+	0.968178i	$0.419483\pi$
$812$	−419.731	+	412.401i	−0.516911	+	0.507883i
$813$	675.067	+	675.067i	0.830340	+	0.830340i
$814$	−908.461	−	174.444i	−1.11605	−	0.214305i
$815$	−1405.23	+	299.103i	−1.72421	+	0.366998i
$816$	−403.439	−	1360.14i	−0.494410	−	1.66684i
$817$	120.937	−	32.4050i	0.148026	−	0.0396634i
$818$	17.7424	+	8.60367i	0.0216900	+	0.0105179i
$819$	−143.245	+	929.026i	−0.174902	+	1.13434i
$820$	−421.984	+	916.475i	−0.514614	+	1.11765i
$821$	−592.610	+	1026.43i	−0.721815	+	1.25022i	0.238456	+	0.971153i	$0.423359\pi$
$821$	−592.610	+	1026.43i	−0.721815	+	1.25022i	−0.960272	+	0.279067i	$0.909975\pi$
$822$	−27.8452	−	385.602i	−0.0338749	−	0.469102i
$823$	−673.982	−	180.593i	−0.818933	−	0.219432i	−0.175053	−	0.984559i	$-0.556010\pi$
$823$	−673.982	−	180.593i	−0.818933	−	0.219432i	−0.643880	+	0.765127i	$0.722676\pi$
$824$	138.406	+	267.117i	0.167969	+	0.324171i
$825$	−180.560	−	1135.89i	−0.218861	−	1.37684i
$826$	15.3165	+	18.0192i	0.0185430	+	0.0218150i
$827$	−761.539	−	761.539i	−0.920845	−	0.920845i	0.0762444	−	0.997089i	$-0.475707\pi$
$827$	−761.539	−	761.539i	−0.920845	−	0.920845i	−0.997089	+	0.0762444i	$0.975707\pi$
$828$	1382.37	+	1031.87i	1.66953	+	1.24622i
$829$	−134.720	−	233.341i	−0.162508	−	0.281473i	0.773259	−	0.634090i	$-0.218625\pi$
$829$	−134.720	−	233.341i	−0.162508	−	0.281473i	−0.935768	+	0.352617i	$0.885292\pi$
$830$	−63.7569	+	258.526i	−0.0768155	+	0.311478i
$831$	−988.737	+	1712.54i	−1.18982	+	2.06082i
$832$	284.477	−	772.426i	0.341919	−	0.928397i
$833$	−874.305	+	454.540i	−1.04959	+	0.545667i
$834$	705.846	−	244.839i	0.846339	−	0.293572i
$835$	−208.894	−	231.870i	−0.250173	−	0.277688i
$836$	164.168	−	411.710i	0.196373	−	0.492477i
$837$	162.700	+	43.5954i	0.194385	+	0.0520853i
$838$	−556.001	−	820.276i	−0.663486	−	0.978850i
$839$		−	1247.70i		−	1.48713i	−0.668665	−	0.743563i	$-0.733134\pi$
$839$		−	1247.70i		−	1.48713i	0.668665	−	0.743563i	$-0.266866\pi$
$840$	1076.01	+	605.273i	1.28097	+	0.720563i
$841$	399.356			0.474859
$842$	147.528	−	99.9980i	0.175212	−	0.118762i
$843$	480.208	−	1792.16i	0.569642	−	2.12593i
$844$	154.173	+	61.4759i	0.182670	+	0.0728387i
$845$	−17.8644	−	0.931214i	−0.0211414	−	0.00110203i
$846$	315.448	+	909.404i	0.372870	+	1.07495i
$847$	−50.1823	−	68.4783i	−0.0592471	−	0.0808481i
$848$	−616.832	+	378.309i	−0.727396	+	0.446119i
$849$	1557.96	+	899.491i	1.83506	+	1.05947i
$850$	−228.967	−	979.096i	−0.269373	−	1.15188i
$851$	1585.66	−	915.483i	1.86329	−	1.07577i
$852$	−1042.90	+	1397.15i	−1.22406	+	1.63984i
$853$	−377.761	+	377.761i	−0.442862	+	0.442862i	−0.892973	−	0.450111i	$-0.851385\pi$
$853$	−377.761	+	377.761i	−0.442862	+	0.442862i	0.450111	+	0.892973i	$0.351385\pi$
$854$	−66.8791	+	187.455i	−0.0783127	+	0.219503i
$855$	493.900	−	251.829i	0.577661	−	0.294537i
$856$	230.020	+	443.926i	0.268714	+	0.518605i
$857$	−59.3309	+	221.426i	−0.0692310	+	0.258374i	−0.991863	−	0.127307i	$-0.959367\pi$
$857$	−59.3309	+	221.426i	−0.0692310	+	0.258374i	0.922632	+	0.385681i	$0.126033\pi$
$858$	1180.36	−	85.2362i	1.37571	−	0.0993429i
$859$	87.3501	+	50.4316i	0.101688	+	0.0587097i	0.549982	−	0.835177i	$-0.314635\pi$
$859$	87.3501	+	50.4316i	0.101688	+	0.0587097i	−0.448293	+	0.893886i	$0.647968\pi$
$860$	221.180	−	81.7147i	0.257187	−	0.0950171i
$861$	974.910	−	1214.05i	1.13230	−	1.41004i
$862$	−504.220	+	1039.80i	−0.584942	+	1.20626i
$863$	−142.044	−	530.115i	−0.164593	−	0.614270i	−0.998092	−	0.0617484i	$-0.980332\pi$
$863$	−142.044	−	530.115i	−0.164593	−	0.614270i	0.833499	−	0.552522i	$-0.186334\pi$
$864$	165.190	−	118.489i	0.191192	−	0.137140i
$865$	−1047.21	+	222.897i	−1.21064	+	0.257685i
$866$	−3.75850	+	19.5733i	−0.00434007	+	0.0226020i
$867$	359.857	−	359.857i	0.415060	−	0.415060i
$868$	−198.455	+	715.375i	−0.228634	+	0.824164i
$869$			1161.58i			1.33669i
$870$	257.681	+	890.052i	0.296185	+	1.02305i
$871$	−115.918	−	200.775i	−0.133086	−	0.230511i
$872$	190.324	+	208.498i	0.218261	+	0.239103i
$873$	32.1483	+	119.979i	0.0368251	+	0.137433i
$874$	287.504	+	828.845i	0.328952	+	0.948335i
$875$	736.181	+	472.930i	0.841349	+	0.540492i
$876$	−464.527	−	589.026i	−0.530282	−	0.672404i
$877$	−325.167	−	1213.54i	−0.370771	−	1.38374i	−0.859426	−	0.511260i	$-0.829179\pi$
$877$	−325.167	−	1213.54i	−0.370771	−	1.38374i	0.488654	−	0.872477i	$-0.337488\pi$
$878$	569.107	−	41.0965i	0.648185	−	0.0468070i
$879$	−1082.90	−	1875.63i	−1.23196	−	2.13383i
$880$	236.557	−	800.513i	0.268815	−	0.909673i
$881$		−	723.385i		−	0.821095i	−0.911839	−	0.410548i	$-0.865338\pi$
$881$		−	723.385i		−	0.821095i	0.911839	−	0.410548i	$-0.134662\pi$
$882$	−743.428	−	703.033i	−0.842889	−	0.797090i
$883$	−766.931	+	766.931i	−0.868551	+	0.868551i	−0.992312	−	0.123761i	$-0.960504\pi$
$883$	−766.931	+	766.931i	−0.868551	+	0.868551i	0.123761	+	0.992312i	$0.460504\pi$
$884$	1023.87	−	148.647i	1.15822	−	0.168153i
$885$	36.4246	−	7.75297i	0.0411578	−	0.00876042i
$886$	223.144	+	193.087i	0.251856	+	0.217932i
$887$	−261.013	−	974.112i	−0.294264	−	1.09821i	−0.941800	−	0.336174i	$-0.890867\pi$
$887$	−261.013	−	974.112i	−0.294264	−	1.09821i	0.647535	−	0.762035i	$-0.275800\pi$
$888$	−335.519	−	1527.19i	−0.377837	−	1.71981i
$889$	93.1022	−	36.1768i	0.104727	−	0.0406938i
$890$	−170.710	+	3.41597i	−0.191809	+	0.00383817i
$891$	−596.000	−	344.101i	−0.668912	−	0.386196i
$892$	−596.614	+	256.456i	−0.668850	+	0.287507i
$893$	−126.700	+	472.849i	−0.141881	+	0.529506i
$894$	−89.4821	+	466.001i	−0.100092	+	0.521253i
$895$	959.690	−	489.325i	1.07228	−	0.546732i
$896$	515.802	+	732.642i	0.575672	+	0.817681i
$897$	−1656.30	+	1656.30i	−1.84649	+	1.84649i
$898$	502.141	+	740.815i	0.559177	+	0.824961i
$899$	−482.549	+	278.600i	−0.536762	+	0.309900i
$900$	882.594	−	557.796i	0.980660	−	0.619773i
$901$	−787.639	−	454.744i	−0.874184	−	0.504710i
$902$	−947.264	−	459.348i	−1.05018	−	0.509255i
$903$	−361.725	+	39.5175i	−0.400582	+	0.0437625i
$904$	−31.2648	+	48.8703i	−0.0345850	+	0.0540601i
$905$	1250.27	+	65.1722i	1.38151	+	0.0720135i
$906$	−998.029	−	863.597i	−1.10158	−	0.953197i
$907$	−408.664	+	1525.15i	−0.450566	+	1.68154i	0.250239	+	0.968184i	$0.419491\pi$
$907$	−408.664	+	1525.15i	−0.450566	+	1.68154i	−0.700805	+	0.713353i	$0.747176\pi$
$908$	−159.162	+	213.226i	−0.175289	+	0.234831i
$909$	−1627.43			−1.79035
$910$	−549.560	+	713.129i	−0.603912	+	0.783659i
$911$			621.921i			0.682680i	0.939940	+	0.341340i	$0.110881\pi$
$911$			621.921i			0.682680i	−0.939940	+	0.341340i	$0.889119\pi$
$912$	748.928	−	19.8882i	0.821192	−	0.0218073i
$913$	−268.366	−	71.9084i	−0.293939	−	0.0787606i
$914$	751.108	+	649.936i	0.821782	+	0.711089i
$915$	209.778	+	232.851i	0.229266	+	0.254482i
$916$	905.726	+	1148.47i	0.988784	+	1.25379i
$917$	354.176	+	483.306i	0.386233	+	0.527051i
$918$	229.910	+	111.488i	0.250446	+	0.121447i
$919$	416.971	−	722.215i	0.453722	−	0.785870i	−0.544891	−	0.838507i	$-0.683429\pi$
$919$	416.971	−	722.215i	0.453722	−	0.785870i	0.998614	+	0.0526365i	$0.0167625\pi$
$920$	682.708	+	1504.54i	0.742074	+	1.63537i
$921$	446.237	+	772.905i	0.484513	+	0.839202i
$922$	−583.804	−	861.294i	−0.633193	−	0.934158i
$923$	−899.036	−	899.036i	−0.974037	−	0.974037i
$924$	−653.887	+	1109.87i	−0.707670	+	1.20116i
$925$	−173.976	−	1094.47i	−0.188082	−	1.18321i
$926$	5.93920	−	30.9299i	0.00641383	−	0.0334016i
$927$	−379.255	−	101.621i	−0.409121	−	0.109624i
$928$	−109.239	+	663.559i	−0.117715	+	0.715042i
$929$	95.7463	−	165.837i	0.103064	−	0.178512i	−0.809882	−	0.586593i	$-0.800469\pi$
$929$	95.7463	−	165.837i	0.103064	−	0.178512i	0.912946	+	0.408081i	$0.133802\pi$
$930$	843.014	+	809.938i	0.906467	+	0.870901i
$931$	−112.357	−	508.095i	−0.120684	−	0.545751i
$932$	217.523	−	1840.75i	0.233393	−	1.97506i
$933$	−1828.04	+	489.823i	−1.95932	+	0.524998i
$934$	−275.374	−	238.282i	−0.294833	−	0.255120i
$935$	1026.18	−	218.422i	1.09752	−	0.233606i
$936$	494.237	+	953.851i	0.528030	+	1.01907i
$937$	842.505	+	842.505i	0.899151	+	0.899151i	0.995361	−	0.0962098i	$-0.0306720\pi$
$937$	842.505	+	842.505i	0.899151	+	0.899151i	−0.0962098	+	0.995361i	$0.530672\pi$
$938$	251.529	+	20.3923i	0.268155	+	0.0217402i
$939$	1794.80			1.91139
$940$	−155.704	+	908.676i	−0.165643	+	0.966677i
$941$	6.77974	−	3.91429i	0.00720483	−	0.00415971i	−0.496393	−	0.868098i	$-0.665343\pi$
$941$	6.77974	−	3.91429i	0.00720483	−	0.00415971i	0.503598	+	0.863938i	$0.332009\pi$
$942$	2644.99	−	191.001i	2.80785	−	0.202761i
$943$	2012.73	−	539.310i	2.13439	−	0.571909i
$944$	26.2833	+	6.29978i	0.0278424	+	0.00667350i
$945$	−211.165	+	69.6348i	−0.223455	+	0.0736876i
$946$	80.6283	+	232.443i	0.0852307	+	0.245711i
$947$	900.871	−	241.388i	0.951290	−	0.254897i	0.250380	−	0.968148i	$-0.419444\pi$
$947$	900.871	−	241.388i	0.951290	−	0.254897i	0.700909	+	0.713250i	$0.252778\pi$
$948$	−1803.82	+	775.375i	−1.90276	+	0.817906i
$949$	473.765	−	273.528i	0.499225	−	0.288228i
$950$	530.716	+	17.0269i	0.558648	+	0.0179230i
$951$	−1416.43			−1.48941
$952$	−500.286	+	1008.95i	−0.525511	+	1.05982i
$953$	−16.6471	−	16.6471i	−0.0174681	−	0.0174681i	0.698319	−	0.715787i	$-0.253932\pi$
$953$	−16.6471	−	16.6471i	−0.0174681	−	0.0174681i	−0.715787	+	0.698319i	$0.753932\pi$
$954$	178.087	−	927.432i	0.186674	−	0.972150i
$955$	55.2336	−	85.1046i	0.0578363	−	0.0891147i
$956$	2.35451	−	5.90480i	0.00246288	−	0.00617657i
$957$	−933.889	+	250.235i	−0.975850	+	0.261478i
$958$	−9.22658	+	19.0270i	−0.00963109	+	0.0198612i
$959$	−192.152	+	239.285i	−0.200367	+	0.249515i
$960$	1401.02	−	167.007i	1.45939	−	0.173966i
$961$	129.005	−	223.442i	0.134240	−	0.232510i
$962$	1137.31	−	82.1278i	1.18223	−	0.0853719i
$963$	−630.290	−	168.886i	−0.654507	−	0.175375i
$964$	−7.41185	−	51.0522i	−0.00768864	−	0.0529587i
$965$	−319.641	−	103.759i	−0.331234	−	0.107522i
$966$	−458.732	−	2508.07i	−0.474878	−	2.59634i
$967$	543.639	+	543.639i	0.562192	+	0.562192i	0.929929	−	0.367738i	$-0.119868\pi$
$967$	543.639	+	543.639i	0.562192	+	0.562192i	−0.367738	+	0.929929i	$0.619868\pi$
$968$	−92.4791	−	29.3523i	−0.0955362	−	0.0303226i
$969$	470.826	+	815.494i	0.485888	+	0.841583i
$970$	−28.4858	+	115.506i	−0.0293668	+	0.119079i
$971$	−281.306	+	487.235i	−0.289707	+	0.501787i	−0.973740	−	0.227664i	$-0.926891\pi$
$971$	−281.306	+	487.235i	−0.289707	+	0.501787i	0.684033	+	0.729451i	$0.260225\pi$
$972$	163.352	−	1382.34i	0.168058	−	1.42216i
$973$	−542.763	−	238.995i	−0.557824	−	0.245626i
$974$	84.1585	+	242.620i	0.0864051	+	0.249097i
$975$	577.370	+	1294.84i	0.592174	+	1.32804i
$976$	64.6830	+	218.070i	0.0662736	+	0.223433i
$977$	−1167.42	−	312.810i	−1.19491	−	0.320174i	−0.394083	−	0.919075i	$-0.628938\pi$
$977$	−1167.42	−	312.810i	−1.19491	−	0.320174i	−0.800823	+	0.598901i	$0.795604\pi$
$978$	2097.46	−	1421.71i	2.14464	−	1.45369i
$979$		−	178.158i		−	0.181979i
$980$	−298.702	−	933.369i	−0.304798	−	0.952417i
$981$	−368.433			−0.375569
$982$	196.724	+	290.230i	0.200330	+	0.295550i
$983$	−77.8177	+	290.420i	−0.0791635	+	0.295442i	−0.994145	−	0.108053i	$-0.965538\pi$
$983$	−77.8177	+	290.420i	−0.0791635	+	0.295442i	0.914982	+	0.403496i	$0.132205\pi$
$984$	81.0051	−	1777.62i	0.0823223	−	1.80653i
$985$	902.888	+	1002.19i	0.916637	+	1.01746i
$986$	−798.568	+	277.002i	−0.809907	+	0.280935i
$987$	573.343	−	1302.08i	0.580895	−	1.31923i
$988$	−64.1166	+	542.577i	−0.0648953	+	0.549167i
$989$	−421.725	−	243.483i	−0.426416	−	0.246191i
$990$	563.473	+	932.373i	0.569164	+	0.941791i
$991$	480.877	−	277.635i	0.485245	−	0.280156i	−0.237355	−	0.971423i	$-0.576280\pi$
$991$	480.877	−	277.635i	0.485245	−	0.280156i	0.722599	+	0.691267i	$0.242947\pi$
$992$	299.232	+	793.929i	0.301645	+	0.800331i
$993$	−1020.57	+	1020.57i	−1.02777	+	1.02777i
$994$	1361.37	−	248.999i	1.36959	−	0.250502i
$995$	26.6199	+	52.2083i	0.0267536	+	0.0524706i
$996$	−67.4723	−	464.744i	−0.0677433	−	0.466610i
$997$	289.226	−	1079.41i	0.290096	−	1.08265i	−0.654938	−	0.755682i	$-0.727305\pi$
$997$	289.226	−	1079.41i	0.290096	−	1.08265i	0.945034	−	0.326971i	$-0.106028\pi$
$998$	−97.7137	−	1353.14i	−0.0979095	−	1.35586i
$999$	243.883	+	140.806i	0.244127	+	0.140947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.3.x.a.103.9	yes	176
4.3	odd	2	inner	140.3.x.a.103.43	yes	176
5.2	odd	4	inner	140.3.x.a.47.14	yes	176
7.3	odd	6	inner	140.3.x.a.3.21	yes	176
20.7	even	4	inner	140.3.x.a.47.21	yes	176
28.3	even	6	inner	140.3.x.a.3.14	✓	176
35.17	even	12	inner	140.3.x.a.87.43	yes	176
140.87	odd	12	inner	140.3.x.a.87.9	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.3.x.a.3.14	✓	176	28.3	even	6	inner
140.3.x.a.3.21	yes	176	7.3	odd	6	inner
140.3.x.a.47.14	yes	176	5.2	odd	4	inner
140.3.x.a.47.21	yes	176	20.7	even	4	inner
140.3.x.a.87.9	yes	176	140.87	odd	12	inner
140.3.x.a.87.43	yes	176	35.17	even	12	inner
140.3.x.a.103.9	yes	176	1.1	even	1	trivial
140.3.x.a.103.43	yes	176	4.3	odd	2	inner

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)

\(f(q)\)	\(=\)	\(q+(-1.65553 + 1.12215i) q^{2} +(-1.14118 + 4.25894i) q^{3} +(1.48154 - 3.71551i) q^{4} +(-0.260280 + 4.99322i) q^{5} +(-2.88993 - 8.33136i) q^{6} +(-2.82094 + 6.40643i) q^{7} +(1.71664 + 7.81365i) q^{8} +(-9.04202 - 5.22041i) q^{9} +O(q^{10})\)	\(q+(-1.65553 + 1.12215i) q^{2} +(-1.14118 + 4.25894i) q^{3} +(1.48154 - 3.71551i) q^{4} +(-0.260280 + 4.99322i) q^{5} +(-2.88993 - 8.33136i) q^{6} +(-2.82094 + 6.40643i) q^{7} +(1.71664 + 7.81365i) q^{8} +(-9.04202 - 5.22041i) q^{9} +(-5.17226 - 8.55849i) q^{10} +(9.03625 - 5.21708i) q^{11} +(14.1334 + 10.5499i) q^{12} +(-9.09457 + 9.09457i) q^{13} +(-2.51885 - 13.7715i) q^{14} +(-20.9688 - 6.80667i) q^{15} +(-11.6101 - 11.0094i) q^{16} +(5.20491 - 19.4250i) q^{17} +(20.8274 - 1.50400i) q^{18} +(9.19700 + 5.30989i) q^{19} +(18.1668 + 8.36475i) q^{20} +(-24.0654 - 19.3251i) q^{21} +(-9.10540 + 18.7771i) q^{22} +(-10.6904 - 39.8972i) q^{23} +(-35.2368 - 1.60572i) q^{24} +(-24.8645 - 2.59927i) q^{25} +(4.85081 - 25.2618i) q^{26} +(4.49215 - 4.49215i) q^{27} +(19.6238 + 19.9726i) q^{28} +21.0153i q^{29} +(42.3525 - 12.2616i) q^{30} +(13.2570 + 22.9618i) q^{31} +(31.5750 + 5.19807i) q^{32} +(11.9072 + 44.4384i) q^{33} +(13.1810 + 37.9993i) q^{34} +(-31.2545 - 15.7530i) q^{35} +(-32.7927 + 25.8615i) q^{36} +(11.4730 + 42.8179i) q^{37} +(-21.1844 + 1.52977i) q^{38} +(-28.3547 - 49.1117i) q^{39} +(-39.4621 + 6.53782i) q^{40} +50.4479i q^{41} +(61.5266 + 4.98817i) q^{42} +(8.33652 - 8.33652i) q^{43} +(-5.99653 - 41.3036i) q^{44} +(28.4201 - 43.7900i) q^{45} +(62.4691 + 54.0547i) q^{46} +(11.9305 + 44.5253i) q^{47} +(60.1374 - 36.8828i) q^{48} +(-33.0846 - 36.1443i) q^{49} +(44.0807 - 23.5986i) q^{50} +(76.7901 + 44.3348i) q^{51} +(20.3170 + 47.2650i) q^{52} +(11.7051 - 43.6841i) q^{53} +(-2.39600 + 12.4778i) q^{54} +(23.6981 + 46.4779i) q^{55} +(-54.9001 - 11.0443i) q^{56} +(-33.1099 + 33.1099i) q^{57} +(-23.5824 - 34.7915i) q^{58} +(-1.46292 + 0.844616i) q^{59} +(-56.3564 + 67.8254i) q^{60} +(-12.3117 - 7.10816i) q^{61} +(-47.7139 - 23.1375i) q^{62} +(58.9512 - 43.2006i) q^{63} +(-58.1063 + 26.8264i) q^{64} +(-43.0440 - 47.7783i) q^{65} +(-69.5795 - 60.2073i) q^{66} +(-4.66529 + 17.4111i) q^{67} +(-64.4625 - 48.1179i) q^{68} +182.120 q^{69} +(69.4200 - 8.99272i) q^{70} +98.8542i q^{71} +(25.2686 - 79.6128i) q^{72} +(-41.0846 - 11.0086i) q^{73} +(-67.0421 - 58.0117i) q^{74} +(39.4450 - 102.930i) q^{75} +(33.3547 - 26.3047i) q^{76} +(7.93213 + 72.6072i) q^{77} +(102.053 + 49.4875i) q^{78} +(-55.6625 + 96.4102i) q^{79} +(57.9942 - 55.1061i) q^{80} +(-32.9783 - 57.1201i) q^{81} +(-56.6103 - 83.5179i) q^{82} +(-18.8283 - 18.8283i) q^{83} +(-107.456 + 60.7842i) q^{84} +(95.6386 + 31.0452i) q^{85} +(-4.44649 + 23.1562i) q^{86} +(-89.5029 - 23.9822i) q^{87} +(56.2764 + 61.6503i) q^{88} +(8.53722 - 14.7869i) q^{89} +(2.08883 + 104.387i) q^{90} +(-32.6084 - 83.9189i) q^{91} +(-164.077 - 19.3891i) q^{92} +(-112.921 + 30.2572i) q^{93} +(-69.7156 - 60.3250i) q^{94} +(-28.9072 + 44.5406i) q^{95} +(-58.1710 + 128.544i) q^{96} +(-8.41224 - 8.41224i) q^{97} +(95.3319 + 22.7119i) q^{98} -108.941 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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