LMFDB - Embedded newform 253.3.g.a.24.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [253,3,Mod(24,253)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("253.24"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(253, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 253 = 11 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	253.g (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.89375068832$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			24.2
Character	$\chi$	$=$	253.24
Dual form			253.3.g.a.116.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.56389 - 1.15798i) q^{2} +(-4.16114 + 3.02325i) q^{3} +(8.12432 + 5.90266i) q^{4} +(-0.312727 - 0.962476i) q^{5} +(18.3307 - 5.95601i) q^{6} +(-2.38519 + 3.28293i) q^{7} +(-13.3086 - 18.3177i) q^{8} +(5.39393 - 16.6008i) q^{9} +3.79229i q^{10} +(-10.3311 - 3.77738i) q^{11} -51.6516 q^{12} +(2.16358 + 0.702988i) q^{13} +(12.3021 - 8.93801i) q^{14} +(4.21111 + 3.05955i) q^{15} +(13.8060 + 42.4904i) q^{16} +(-20.8812 + 6.78471i) q^{17} +(-38.4468 + 52.9174i) q^{18} +(-9.37083 - 12.8978i) q^{19} +(3.14047 - 9.66538i) q^{20} -20.8718i q^{21} +(32.4447 + 25.4253i) q^{22} -4.79583 q^{23} +(110.758 + 35.9874i) q^{24} +(19.3969 - 14.0926i) q^{25} +(-6.89669 - 5.01074i) q^{26} +(13.4387 + 41.3602i) q^{27} +(-38.7561 + 12.5926i) q^{28} +(21.2593 - 29.2609i) q^{29} +(-11.4650 - 15.7803i) q^{30} +(-4.62767 + 14.2425i) q^{31} -76.8505i q^{32} +(54.4091 - 15.5152i) q^{33} +82.2747 q^{34} +(3.90566 + 1.26903i) q^{35} +(141.811 - 103.032i) q^{36} +(18.9388 + 13.7598i) q^{37} +(18.4612 + 56.8176i) q^{38} +(-11.1283 + 3.61579i) q^{39} +(-13.4684 + 18.5376i) q^{40} +(-26.6808 - 36.7230i) q^{41} +(-24.1691 + 74.3847i) q^{42} +68.1713i q^{43} +(-61.6364 - 91.6695i) q^{44} -17.6647 q^{45} +(17.0918 + 5.55346i) q^{46} +(56.7643 - 41.2417i) q^{47} +(-185.908 - 135.070i) q^{48} +(10.0533 + 30.9409i) q^{49} +(-85.4472 + 27.7635i) q^{50} +(66.3778 - 91.3611i) q^{51} +(13.4281 + 18.4821i) q^{52} +(-15.3036 + 47.0997i) q^{53} -162.965i q^{54} +(-0.404824 + 11.1247i) q^{55} +91.8793 q^{56} +(77.9867 + 25.3394i) q^{57} +(-109.649 + 79.6648i) q^{58} +(82.6193 + 60.0265i) q^{59} +(16.1529 + 49.7135i) q^{60} +(56.1067 - 18.2302i) q^{61} +(32.9850 - 45.3999i) q^{62} +(41.6339 + 57.3041i) q^{63} +(-33.7672 + 103.925i) q^{64} -2.30223i q^{65} +(-211.874 - 7.71001i) q^{66} -119.105 q^{67} +(-209.693 - 68.1334i) q^{68} +(19.9561 - 14.4990i) q^{69} +(-12.4498 - 9.04533i) q^{70} +(39.3122 + 120.991i) q^{71} +(-375.875 + 122.129i) q^{72} +(29.4054 - 40.4731i) q^{73} +(-51.5620 - 70.9691i) q^{74} +(-38.1076 + 117.283i) q^{75} -160.099i q^{76} +(37.0425 - 24.9065i) q^{77} +43.8468 q^{78} +(-50.9445 - 16.5529i) q^{79} +(36.5785 - 26.5758i) q^{80} +(-53.8689 - 39.1381i) q^{81} +(52.5630 + 161.772i) q^{82} +(19.2968 - 6.26992i) q^{83} +(123.199 - 169.569i) q^{84} +(13.0602 + 17.9759i) q^{85} +(78.9409 - 242.955i) q^{86} +186.031i q^{87} +(68.2993 + 239.513i) q^{88} +44.1854 q^{89} +(62.9551 + 20.4554i) q^{90} +(-7.46841 + 5.42611i) q^{91} +(-38.9628 - 28.3082i) q^{92} +(-23.8022 - 73.2556i) q^{93} +(-250.059 + 81.2490i) q^{94} +(-9.48334 + 13.0527i) q^{95} +(232.338 + 319.786i) q^{96} +(45.1224 - 138.872i) q^{97} -121.911i q^{98} +(-118.433 + 151.130i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 8 q^{3} + 88 q^{4} - 40 q^{6} - 120 q^{9} - 8 q^{14} - 12 q^{15} - 272 q^{16} - 80 q^{17} + 80 q^{18} - 60 q^{19} + 40 q^{20} + 136 q^{22} - 60 q^{24} - 268 q^{25} + 40 q^{26} + 148 q^{27} - 240 q^{28}+ \cdots - 414 q^{99}+O(q^{100}) $ 176 * q - 8 * q^3 + 88 * q^4 - 40 * q^6 - 120 * q^9 - 8 * q^14 - 12 * q^15 - 272 * q^16 - 80 * q^17 + 80 * q^18 - 60 * q^19 + 40 * q^20 + 136 * q^22 - 60 * q^24 - 268 * q^25 + 40 * q^26 + 148 * q^27 - 240 * q^28 + 160 * q^29 + 240 * q^30 + 108 * q^31 - 160 * q^33 - 420 * q^34 + 150 * q^35 + 32 * q^36 + 96 * q^37 + 70 * q^38 - 320 * q^39 + 270 * q^40 - 362 * q^42 + 174 * q^44 + 180 * q^45 - 138 * q^47 - 182 * q^48 + 464 * q^49 + 410 * q^50 + 500 * q^51 - 70 * q^52 - 130 * q^53 + 88 * q^55 + 472 * q^56 - 100 * q^57 + 468 * q^58 - 126 * q^59 - 376 * q^60 - 570 * q^62 - 160 * q^63 + 1096 * q^64 - 562 * q^66 - 472 * q^67 - 480 * q^68 + 380 * q^70 - 264 * q^71 + 1050 * q^72 - 840 * q^73 + 530 * q^74 - 64 * q^75 + 326 * q^77 - 576 * q^78 + 90 * q^79 + 274 * q^80 - 276 * q^81 - 132 * q^82 + 180 * q^83 - 1120 * q^84 + 360 * q^85 - 704 * q^86 + 272 * q^88 + 340 * q^89 + 1600 * q^90 + 514 * q^91 - 838 * q^93 - 690 * q^94 - 520 * q^95 - 1240 * q^96 + 832 * q^97 - 414 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/253\mathbb{Z}\right)^\times$.

$n$	$24$	$166$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−3.56389	−	1.15798i	−1.78194	−	0.578989i	−0.782877	−	0.622177i	$-0.786249\pi$
$2$	−3.56389	−	1.15798i	−1.78194	−	0.578989i	−0.999067	+	0.0431880i	$0.986249\pi$
$3$	−4.16114	+	3.02325i	−1.38705	+	1.00775i	−0.390866	+	0.920448i	$0.627824\pi$
$3$	−4.16114	+	3.02325i	−1.38705	+	1.00775i	−0.996182	+	0.0873015i	$0.972176\pi$
$4$	8.12432	+	5.90266i	2.03108	+	1.47567i
$5$	−0.312727	−	0.962476i	−0.0625455	−	0.192495i	0.914901	−	0.403678i	$-0.132268\pi$
$5$	−0.312727	−	0.962476i	−0.0625455	−	0.192495i	−0.977447	+	0.211183i	$0.932268\pi$
$6$	18.3307	−	5.95601i	3.05512	−	0.992668i
$7$	−2.38519	+	3.28293i	−0.340742	+	0.468991i	−0.944658	−	0.328057i	$-0.893606\pi$
$7$	−2.38519	+	3.28293i	−0.340742	+	0.468991i	0.603916	+	0.797048i	$0.293606\pi$
$8$	−13.3086	−	18.3177i	−1.66357	−	2.28971i
$9$	5.39393	−	16.6008i	0.599326	−	1.84454i
$10$			3.79229i			0.379229i
$11$	−10.3311	−	3.77738i	−0.939190	−	0.343398i
$11$	−10.3311	−	3.77738i	−0.939190	−	0.343398i
$12$	−51.6516			−4.30430
$13$	2.16358	+	0.702988i	0.166429	+	0.0540760i	0.391046	−	0.920371i	$-0.372113\pi$
$13$	2.16358	+	0.702988i	0.166429	+	0.0540760i	−0.224617	+	0.974447i	$0.572113\pi$
$14$	12.3021	−	8.93801i	0.878723	−	0.638429i
$15$	4.21111	+	3.05955i	0.280740	+	0.203970i
$16$	13.8060	+	42.4904i	0.862874	+	2.65565i
$17$	−20.8812	+	6.78471i	−1.22831	+	0.399101i	−0.850100	−	0.526621i	$-0.823459\pi$
$17$	−20.8812	+	6.78471i	−1.22831	+	0.399101i	−0.378205	+	0.925722i	$0.623459\pi$
$18$	−38.4468	+	52.9174i	−2.13593	+	2.93986i
$19$	−9.37083	−	12.8978i	−0.493201	−	0.678833i	0.487773	−	0.872970i	$-0.337809\pi$
$19$	−9.37083	−	12.8978i	−0.493201	−	0.678833i	−0.980974	+	0.194137i	$0.937809\pi$
$20$	3.14047	−	9.66538i	0.157024	−	0.483269i
$21$		−	20.8718i		−	0.993895i
$22$	32.4447	+	25.4253i	1.47476	+	1.15570i
$23$	−4.79583			−0.208514
$23$	−4.79583			−0.208514
$24$	110.758	+	35.9874i	4.61491	+	1.49948i
$25$	19.3969	−	14.0926i	0.775875	−	0.563706i
$26$	−6.89669	−	5.01074i	−0.265257	−	0.192721i
$27$	13.4387	+	41.3602i	0.497731	+	1.53186i
$28$	−38.7561	+	12.5926i	−1.38415	+	0.449736i
$29$	21.2593	−	29.2609i	0.733079	−	1.00900i	−0.265908	−	0.963998i	$-0.585672\pi$
$29$	21.2593	−	29.2609i	0.733079	−	1.00900i	0.998987	−	0.0449984i	$-0.0143283\pi$
$30$	−11.4650	−	15.7803i	−0.382167	−	0.526008i
$31$	−4.62767	+	14.2425i	−0.149280	+	0.459435i	−0.997536	−	0.0701497i	$-0.977652\pi$
$31$	−4.62767	+	14.2425i	−0.149280	+	0.459435i	0.848257	+	0.529585i	$0.177652\pi$
$32$		−	76.8505i		−	2.40158i
$33$	54.4091	−	15.5152i	1.64876	−	0.470158i
$34$	82.2747			2.41985
$35$	3.90566	+	1.26903i	0.111590	+	0.0362579i
$36$	141.811	−	103.032i	3.93920	−	2.86199i
$37$	18.9388	+	13.7598i	0.511858	+	0.371887i	0.813528	−	0.581526i	$-0.197544\pi$
$37$	18.9388	+	13.7598i	0.511858	+	0.371887i	−0.301670	+	0.953412i	$0.597544\pi$
$38$	18.4612	+	56.8176i	0.485820	+	1.49520i
$39$	−11.1283	+	3.61579i	−0.285340	+	0.0927125i
$40$	−13.4684	+	18.5376i	−0.336710	+	0.463441i
$41$	−26.6808	−	36.7230i	−0.650751	−	0.895683i	0.348380	−	0.937353i	$-0.386732\pi$
$41$	−26.6808	−	36.7230i	−0.650751	−	0.895683i	−0.999131	+	0.0416709i	$0.986732\pi$
$42$	−24.1691	+	74.3847i	−0.575454	+	1.77106i
$43$			68.1713i			1.58538i	0.609625	+	0.792690i	$0.291320\pi$
$43$			68.1713i			1.58538i	−0.609625	+	0.792690i	$0.708680\pi$
$44$	−61.6364	−	91.6695i	−1.40083	−	2.08340i
$45$	−17.6647			−0.392549
$46$	17.0918	+	5.55346i	0.371561	+	0.120727i
$47$	56.7643	−	41.2417i	1.20775	−	0.877483i	0.212727	−	0.977112i	$-0.431766\pi$
$47$	56.7643	−	41.2417i	1.20775	−	0.877483i	0.995025	+	0.0996288i	$0.0317655\pi$
$48$	−185.908	−	135.070i	−3.87308	−	2.81396i
$49$	10.0533	+	30.9409i	0.205170	+	0.631447i
$50$	−85.4472	+	27.7635i	−1.70894	+	0.555270i
$51$	66.3778	−	91.3611i	1.30152	−	1.79139i
$52$	13.4281	+	18.4821i	0.258232	+	0.355426i
$53$	−15.3036	+	47.0997i	−0.288747	+	0.888673i	0.696503	+	0.717554i	$0.254738\pi$
$53$	−15.3036	+	47.0997i	−0.288747	+	0.888673i	−0.985250	+	0.171119i	$0.945262\pi$
$54$		−	162.965i		−	3.01786i
$55$	−0.404824	+	11.1247i	−0.00736043	+	0.202268i
$56$	91.8793			1.64070
$57$	77.9867	+	25.3394i	1.36819	+	0.444551i
$58$	−109.649	+	79.6648i	−1.89050	+	1.37353i
$59$	82.6193	+	60.0265i	1.40033	+	1.01740i	0.994641	+	0.103385i	$0.0329675\pi$
$59$	82.6193	+	60.0265i	1.40033	+	1.01740i	0.405686	+	0.914012i	$0.367033\pi$
$60$	16.1529	+	49.7135i	0.269215	+	0.828558i
$61$	56.1067	−	18.2302i	0.919782	−	0.298855i	0.189405	−	0.981899i	$-0.439344\pi$
$61$	56.1067	−	18.2302i	0.919782	−	0.298855i	0.730377	+	0.683044i	$0.239344\pi$
$62$	32.9850	−	45.3999i	0.532016	−	0.732257i
$63$	41.6339	+	57.3041i	0.660855	+	0.909589i
$64$	−33.7672	+	103.925i	−0.527612	+	1.62382i
$65$		−	2.30223i		−	0.0354190i
$66$	−211.874	−	7.71001i	−3.21021	−	0.116818i
$67$	−119.105			−1.77769			−0.888845	−	0.458208i	$-0.848492\pi$
$67$	−119.105			−1.77769			−0.888845	+	0.458208i	$0.848492\pi$
$68$	−209.693	−	68.1334i	−3.08372	−	1.00196i
$69$	19.9561	−	14.4990i	0.289219	−	0.210130i
$70$	−12.4498	−	9.04533i	−0.177855	−	0.129219i
$71$	39.3122	+	120.991i	0.553693	+	1.70409i	0.699369	+	0.714761i	$0.253464\pi$
$71$	39.3122	+	120.991i	0.553693	+	1.70409i	−0.145676	+	0.989332i	$0.546536\pi$
$72$	−375.875	+	122.129i	−5.22048	+	1.69624i
$73$	29.4054	−	40.4731i	0.402814	−	0.554426i	−0.558634	−	0.829415i	$-0.688674\pi$
$73$	29.4054	−	40.4731i	0.402814	−	0.554426i	0.961447	+	0.274989i	$0.0886742\pi$
$74$	−51.5620	−	70.9691i	−0.696784	−	0.959041i
$75$	−38.1076	+	117.283i	−0.508101	+	1.56377i
$76$		−	160.099i		−	2.10656i
$77$	37.0425	−	24.9065i	0.481072	−	0.323461i
$78$	43.8468			0.562139
$79$	−50.9445	−	16.5529i	−0.644867	−	0.209530i	−0.0317176	−	0.999497i	$-0.510098\pi$
$79$	−50.9445	−	16.5529i	−0.644867	−	0.209530i	−0.613150	+	0.789967i	$0.710098\pi$
$80$	36.5785	−	26.5758i	0.457231	−	0.332198i
$81$	−53.8689	−	39.1381i	−0.665048	−	0.483186i
$82$	52.5630	+	161.772i	0.641013	+	1.97283i
$83$	19.2968	−	6.26992i	0.232492	−	0.0755413i	−0.190454	−	0.981696i	$-0.560996\pi$
$83$	19.2968	−	6.26992i	0.232492	−	0.0755413i	0.422946	+	0.906155i	$0.360996\pi$
$84$	123.199	−	169.569i	1.46666	−	2.01868i
$85$	13.0602	+	17.9759i	0.153650	+	0.211481i
$86$	78.9409	−	242.955i	0.917917	−	2.82506i
$87$			186.031i			2.13829i
$88$	68.2993	+	239.513i	0.776128	+	2.72174i
$89$	44.1854			0.496466			0.248233	−	0.968700i	$-0.420150\pi$
$89$	44.1854			0.496466			0.248233	+	0.968700i	$0.420150\pi$
$90$	62.9551	+	20.4554i	0.699501	+	0.227282i
$91$	−7.46841	+	5.42611i	−0.0820704	+	0.0596276i
$92$	−38.9628	−	28.3082i	−0.423509	−	0.307697i
$93$	−23.8022	−	73.2556i	−0.255938	−	0.787695i
$94$	−250.059	+	81.2490i	−2.66020	+	0.864351i
$95$	−9.48334	+	13.0527i	−0.0998247	+	0.137397i
$96$	232.338	+	319.786i	2.42019	+	3.33110i
$97$	45.1224	−	138.872i	0.465179	−	1.43167i	−0.393578	−	0.919291i	$-0.628763\pi$
$97$	45.1224	−	138.872i	0.465179	−	1.43167i	0.858757	−	0.512383i	$-0.171237\pi$
$98$		−	121.911i		−	1.24399i
$99$	−118.433	+	151.130i	−1.19629	+	1.52656i
$100$	240.770			2.40770
$101$	30.8613	+	10.0274i	0.305557	+	0.0992815i	0.457782	−	0.889064i	$-0.348644\pi$
$101$	30.8613	+	10.0274i	0.305557	+	0.0992815i	−0.152225	+	0.988346i	$0.548644\pi$
$102$	−342.357	+	248.737i	−3.35644	+	2.43860i
$103$	16.5525	+	12.0261i	0.160704	+	0.116758i	0.665231	−	0.746638i	$-0.268333\pi$
$103$	16.5525	+	12.0261i	0.160704	+	0.116758i	−0.504527	+	0.863396i	$0.668333\pi$
$104$	−15.9170	−	48.9875i	−0.153048	−	0.471034i
$105$	−20.0886	+	6.52718i	−0.191320	+	0.0621636i
$106$	109.081	−	150.137i	1.02906	−	1.41638i
$107$	−49.4813	−	68.1052i	−0.462442	−	0.636497i	0.512571	−	0.858645i	$-0.328693\pi$
$107$	−49.4813	−	68.1052i	−0.462442	−	0.636497i	−0.975013	+	0.222148i	$0.928693\pi$
$108$	−134.954	+	415.347i	−1.24958	+	3.84581i
$109$			13.6961i			0.125652i	0.998024	+	0.0628261i	$0.0200113\pi$
$109$			13.6961i			0.125652i	−0.998024	+	0.0628261i	$0.979989\pi$
$110$	14.3249	−	39.1785i	0.130226	−	0.356168i
$111$	−120.406			−1.08474
$112$	−172.423	−	56.0237i	−1.53949	−	0.500212i
$113$	46.2604	−	33.6102i	0.409384	−	0.297435i	−0.363968	−	0.931411i	$-0.618578\pi$
$113$	46.2604	−	33.6102i	0.409384	−	0.297435i	0.773353	+	0.633976i	$0.218578\pi$
$114$	−248.593	−	180.614i	−2.18064	−	1.58433i
$115$	1.49979	+	4.61587i	0.0130416	+	0.0401380i
$116$	345.434	−	112.238i	2.97788	−	0.967573i
$117$	23.3404	−	32.1253i	0.199490	−	0.274575i
$118$	−224.937	−	309.599i	−1.90624	−	2.62372i
$119$	27.5319	−	84.7344i	0.231360	−	0.712054i
$120$		−	117.856i		−	0.982134i
$121$	92.4628	+	78.0489i	0.764155	+	0.645032i
$122$	−221.068			−1.81203
$123$	222.045	+	72.1469i	1.80525	+	0.586560i
$124$	−121.665	+	88.3950i	−0.981171	+	0.712863i
$125$	−40.0980	−	29.1329i	−0.320784	−	0.233063i
$126$	−82.0216	−	252.436i	−0.650965	−	2.00346i
$127$	141.765	−	46.0622i	1.11626	−	0.362694i	0.307920	−	0.951412i	$-0.400367\pi$
$127$	141.765	−	46.0622i	1.11626	−	0.362694i	0.808338	+	0.588718i	$0.200367\pi$
$128$	59.9986	−	82.5809i	0.468739	−	0.645164i
$129$	−206.099	−	283.671i	−1.59767	−	2.19900i
$130$	−2.66593	+	8.20490i	−0.0205072	+	0.0631146i
$131$		−	58.5724i		−	0.447117i	−0.974690	−	0.223559i	$-0.928233\pi$
$131$		−	58.5724i		−	0.447117i	0.974690	−	0.223559i	$-0.0717674\pi$
$132$	533.618	+	195.108i	4.04256	+	1.47809i
$133$	64.6940			0.486421
$134$	424.478	+	137.921i	3.16774	+	1.02926i
$135$	35.6055	−	25.8689i	0.263744	−	0.191622i
$136$	402.179	+	292.200i	2.95720	+	2.14853i
$137$	−73.5289	−	226.299i	−0.536707	−	1.65181i	−0.739931	−	0.672683i	$-0.765142\pi$
$137$	−73.5289	−	226.299i	−0.536707	−	1.65181i	0.203224	−	0.979132i	$-0.434858\pi$
$138$	−87.9109	+	28.5640i	−0.637036	+	0.206985i
$139$	84.5112	−	116.320i	0.607994	−	0.836832i	−0.388416	−	0.921484i	$-0.626978\pi$
$139$	84.5112	−	116.320i	0.607994	−	0.836832i	0.996411	+	0.0846517i	$0.0269778\pi$
$140$	24.2402	+	33.3638i	0.173144	+	0.238313i
$141$	−111.521	+	343.225i	−0.790926	+	2.43422i
$142$		−	476.720i		−	3.35718i
$143$	−19.6966	−	15.4353i	−0.137739	−	0.107939i
$144$	779.845			5.41559
$145$	−34.8113	−	11.3109i	−0.240078	−	0.0780060i
$146$	−151.664	+	110.191i	−1.03880	+	0.754731i
$147$	−135.375	−	98.3559i	−0.920920	−	0.669088i
$148$	72.6449	+	223.578i	0.490844	+	1.51066i
$149$	−109.627	+	35.6200i	−0.735752	+	0.239060i	−0.652839	−	0.757496i	$-0.726422\pi$
$149$	−109.627	+	35.6200i	−0.735752	+	0.239060i	−0.0829129	+	0.996557i	$0.526422\pi$
$150$	271.622	−	373.856i	1.81081	−	2.49237i
$151$	72.2340	+	99.4216i	0.478371	+	0.658421i	0.978191	−	0.207708i	$-0.0666004\pi$
$151$	72.2340	+	99.4216i	0.478371	+	0.658421i	−0.499820	+	0.866129i	$0.666600\pi$
$152$	−111.546	+	343.304i	−0.733857	+	2.25858i
$153$			383.241i			2.50484i
$154$	−160.857	+	45.8696i	−1.04452	+	0.297855i
$155$	15.1553			0.0977758
$156$	−111.752	−	36.3105i	−0.716360	−	0.232760i
$157$	15.5954	−	11.3307i	0.0993338	−	0.0721702i	−0.537010	−	0.843576i	$-0.680446\pi$
$157$	15.5954	−	11.3307i	0.0993338	−	0.0721702i	0.636343	+	0.771406i	$0.280446\pi$
$158$	162.393	+	117.985i	1.02780	+	0.746742i
$159$	−78.7134	−	242.255i	−0.495053	−	1.52362i
$160$	−73.9667	+	24.0332i	−0.462292	+	0.150208i
$161$	11.4390	−	15.7444i	0.0710496	−	0.0977913i
$162$	146.662	+	201.863i	0.905320	+	1.24607i
$163$	16.4242	−	50.5485i	0.100762	−	0.310114i	−0.887950	−	0.459939i	$-0.847871\pi$
$163$	16.4242	−	50.5485i	0.100762	−	0.310114i	0.988712	+	0.149825i	$0.0478712\pi$
$164$		−	455.837i		−	2.77949i
$165$	−31.9482	−	47.5154i	−0.193626	−	0.287972i
$166$	−76.0322			−0.458025
$167$	78.9262	+	25.6447i	0.472612	+	0.153561i	0.535632	−	0.844451i	$-0.320073\pi$
$167$	78.9262	+	25.6447i	0.472612	+	0.153561i	−0.0630202	+	0.998012i	$0.520073\pi$
$168$	−382.323	+	277.774i	−2.27573	+	1.65342i
$169$	−132.537	−	96.2938i	−0.784243	−	0.569786i
$170$	−25.7296	−	79.1875i	−0.151350	−	0.465809i
$171$	−264.660	+	85.9934i	−1.54772	+	0.502885i
$172$	−402.392	+	553.845i	−2.33949	+	3.22003i
$173$	183.532	+	252.611i	1.06088	+	1.46018i	0.878979	+	0.476861i	$0.158226\pi$
$173$	183.532	+	252.611i	1.06088	+	1.46018i	0.181902	+	0.983317i	$0.441774\pi$
$174$	215.420	−	662.993i	1.23804	−	3.81031i
$175$			97.2923i			0.555956i
$176$	17.8717	−	491.123i	0.101544	−	2.79047i
$177$	−525.266			−2.96760
$178$	−157.472	−	51.1657i	−0.884674	−	0.287448i
$179$	−189.505	+	137.683i	−1.05869	+	0.769181i	−0.973845	−	0.227213i	$-0.927039\pi$
$179$	−189.505	+	137.683i	−1.05869	+	0.769181i	−0.0848420	+	0.996394i	$0.527039\pi$
$180$	−143.514	−	104.269i	−0.797299	−	0.579272i
$181$	56.6810	+	174.446i	0.313155	+	0.963791i	0.976507	+	0.215484i	$0.0691330\pi$
$181$	56.6810	+	174.446i	0.313155	+	0.963791i	−0.663352	+	0.748307i	$0.730867\pi$
$182$	32.8999	−	10.6898i	0.180769	−	0.0587353i
$183$	−178.354	+	245.483i	−0.974611	+	1.34144i
$184$	63.8257	+	87.8486i	0.346879	+	0.477438i
$185$	7.32082	−	22.5312i	0.0395720	−	0.121790i
$186$			288.637i			1.55181i
$187$	241.354	+	8.78276i	1.29066	+	0.0469666i
$188$	704.607			3.74791
$189$	−167.837	−	54.5334i	−0.888025	−	0.288537i
$190$	48.9123	−	35.5369i	0.257433	−	0.187036i
$191$	125.379	+	91.0932i	0.656435	+	0.476928i	0.865457	−	0.500983i	$-0.167028\pi$
$191$	125.379	+	91.0932i	0.656435	+	0.476928i	−0.209022	+	0.977911i	$0.567028\pi$
$192$	−173.680	−	534.532i	−0.904583	−	2.78402i
$193$	171.431	−	55.7012i	0.888243	−	0.288607i	0.170867	−	0.985294i	$-0.445343\pi$
$193$	171.431	−	55.7012i	0.888243	−	0.288607i	0.717376	+	0.696687i	$0.245343\pi$
$194$	−321.622	+	442.675i	−1.65785	+	2.28183i
$195$	6.96022	+	9.57992i	0.0356934	+	0.0491278i
$196$	−100.957	+	310.715i	−0.515089	+	1.58528i
$197$		−	41.5484i		−	0.210906i	−0.994424	−	0.105453i	$-0.966371\pi$
$197$		−	41.5484i		−	0.210906i	0.994424	−	0.105453i	$-0.0336292\pi$
$198$	597.086	−	401.467i	3.01559	−	2.02761i
$199$	308.661			1.55106			0.775531	−	0.631310i	$-0.217482\pi$
$199$	308.661			1.55106			0.775531	+	0.631310i	$0.217482\pi$
$200$	−516.290	−	167.753i	−2.58145	−	0.838763i
$201$	495.614	−	360.085i	2.46574	−	1.79147i
$202$	−98.3745	−	71.4733i	−0.487003	−	0.353828i
$203$	45.3542	+	139.586i	0.223420	+	0.687615i
$204$	1078.55	−	350.441i	5.28700	−	1.71785i
$205$	−27.0012	+	37.1639i	−0.131713	+	0.181287i
$206$	−45.0653	−	62.0271i	−0.218764	−	0.301102i
$207$	−25.8684	+	79.6148i	−0.124968	+	0.384612i
$208$			101.637i			0.488638i
$209$	48.0908	+	168.646i	0.230100	+	0.806918i
$210$	79.1518			0.376913
$211$	−180.505	−	58.6497i	−0.855475	−	0.277961i	−0.151737	−	0.988421i	$-0.548487\pi$
$211$	−180.505	−	58.6497i	−0.855475	−	0.277961i	−0.703737	+	0.710460i	$0.748487\pi$
$212$	−402.345	+	292.321i	−1.89785	+	1.37887i
$213$	−529.368	−	384.609i	−2.48530	−	1.80567i
$214$	97.4816	+	300.017i	0.455521	+	1.40195i
$215$	65.6133	−	21.3190i	0.305178	−	0.0991583i
$216$	578.772	−	796.612i	2.67950	−	3.68802i
$217$	−35.7193	−	49.1634i	−0.164605	−	0.226559i
$218$	15.8598	−	48.8113i	0.0727512	−	0.223905i
$219$			257.314i			1.17495i
$220$	−68.9543	+	87.9912i	−0.313429	+	0.399960i
$221$	−49.9476			−0.226007
$222$	429.114	+	139.428i	1.93295	+	0.628052i
$223$	238.043	−	172.948i	1.06746	−	0.775553i	0.0920031	−	0.995759i	$-0.470673\pi$
$223$	238.043	−	172.948i	1.06746	−	0.775553i	0.975453	+	0.220206i	$0.0706730\pi$
$224$	252.295	+	183.303i	1.12632	+	0.818317i
$225$	−129.324	−	398.019i	−0.574774	−	1.76897i
$226$	−203.787	+	66.2144i	−0.901712	+	0.292984i
$227$	−3.06476	+	4.21828i	−0.0135011	+	0.0185827i	−0.815714	−	0.578455i	$-0.803656\pi$
$227$	−3.06476	+	4.21828i	−0.0135011	+	0.0185827i	0.802213	+	0.597038i	$0.203656\pi$
$228$	484.019	+	666.194i	2.12289	+	2.92191i
$229$	77.1717	−	237.510i	0.336994	−	1.03716i	−0.628737	−	0.777618i	$-0.716428\pi$
$229$	77.1717	−	237.510i	0.336994	−	1.03716i	0.965731	−	0.259544i	$-0.0835722\pi$
$230$		−	18.1872i		−	0.0790747i
$231$	−78.8407	+	215.628i	−0.341302	+	0.933456i
$232$	−818.924			−3.52984
$233$	−107.493	−	34.9267i	−0.461345	−	0.149900i	0.0691174	−	0.997609i	$-0.477982\pi$
$233$	−107.493	−	34.9267i	−0.461345	−	0.149900i	−0.530462	+	0.847708i	$0.677982\pi$
$234$	−120.383	+	87.4632i	−0.514456	+	0.373774i
$235$	−57.4459	−	41.7369i	−0.244451	−	0.177604i
$236$	316.910	+	975.348i	1.34284	+	4.13283i
$237$	262.031	−	85.1390i	1.10562	−	0.359236i
$238$	−196.241	+	270.103i	−0.824542	+	1.13488i
$239$	−107.977	−	148.618i	−0.451789	−	0.621834i	0.520992	−	0.853562i	$-0.325562\pi$
$239$	−107.977	−	148.618i	−0.451789	−	0.621834i	−0.972781	+	0.231728i	$0.925562\pi$
$240$	−71.8631	+	221.172i	−0.299429	+	0.921549i
$241$			102.563i			0.425574i	0.977099	+	0.212787i	$0.0682541\pi$
$241$			102.563i			0.425574i	−0.977099	+	0.212787i	$0.931746\pi$
$242$	−239.148	−	385.227i	−0.988215	−	1.59185i
$243$	−48.9174			−0.201306
$244$	563.435	+	183.071i	2.30916	+	0.750292i
$245$	26.6359	−	19.3521i	0.108718	−	0.0789883i
$246$	−707.800	−	514.247i	−2.87724	−	2.09043i
$247$	−11.2075	−	34.4930i	−0.0453743	−	0.139648i
$248$	322.477	−	104.779i	1.30031	−	0.422497i
$249$	−61.3414	+	84.4292i	−0.246351	+	0.339073i
$250$	109.170	+	150.259i	0.436679	+	0.601036i
$251$	−1.98002	+	6.09389i	−0.00788854	+	0.0242784i	−0.954923	−	0.296853i	$-0.904063\pi$
$251$	−1.98002	+	6.09389i	−0.00788854	+	0.0242784i	0.947035	+	0.321131i	$0.104063\pi$
$252$			711.307i			2.82265i
$253$	49.5462	+	18.1157i	0.195835	+	0.0716035i
$254$	−558.573			−2.19910
$255$	−108.691	−	35.3159i	−0.426239	−	0.138494i
$256$	44.1595	−	32.0837i	0.172498	−	0.125327i
$257$	6.89156	+	5.00701i	0.0268154	+	0.0194825i	0.601112	−	0.799165i	$-0.294724\pi$
$257$	6.89156	+	5.00701i	0.0268154	+	0.0194825i	−0.574297	+	0.818647i	$0.694724\pi$
$258$	406.029	+	1249.63i	1.57376	+	4.84352i
$259$	−90.3451	+	29.3549i	−0.348823	+	0.113339i
$260$	13.5893	−	18.7041i	0.0522665	−	0.0719387i
$261$	−371.084	−	510.753i	−1.42178	−	1.95691i
$262$	−67.8255	+	208.745i	−0.258876	+	0.796738i
$263$		−	143.234i		−	0.544618i	−0.962210	−	0.272309i	$-0.912213\pi$
$263$		−	143.234i		−	0.544618i	0.962210	−	0.272309i	$-0.0877872\pi$
$264$	−1008.31	−	790.164i	−3.81936	−	2.99304i
$265$	50.1182			0.189125
$266$	−230.562	−	74.9141i	−0.866775	−	0.281632i
$267$	−183.862	+	133.584i	−0.688622	+	0.500313i
$268$	−967.649	−	703.038i	−3.61063	−	2.62328i
$269$	57.3253	+	176.429i	0.213105	+	0.655871i	0.999283	+	0.0378697i	$0.0120572\pi$
$269$	57.3253	+	176.429i	0.213105	+	0.655871i	−0.786177	+	0.618001i	$0.787943\pi$
$270$	−156.850	+	50.9635i	−0.580924	+	0.188754i
$271$	313.900	−	432.047i	1.15830	−	1.59427i	0.441003	−	0.897506i	$-0.354623\pi$
$271$	313.900	−	432.047i	1.15830	−	1.59427i	0.717301	−	0.696763i	$-0.245377\pi$
$272$	−576.570	−	793.581i	−2.11974	−	2.91758i
$273$	14.6726	−	45.1577i	0.0537459	−	0.165413i
$274$			891.648i			3.25419i
$275$	−253.624	+	72.3230i	−0.922269	+	0.262993i
$276$	247.713			0.897509
$277$	−172.813	−	56.1505i	−0.623875	−	0.202709i	−0.0200151	−	0.999800i	$-0.506371\pi$
$277$	−172.813	−	56.1505i	−0.623875	−	0.202709i	−0.603860	+	0.797090i	$0.706371\pi$
$278$	−435.884	+	316.688i	−1.56793	+	1.13917i
$279$	211.476	+	153.646i	0.757978	+	0.550703i
$280$	−28.7332	−	88.4316i	−0.102619	−	0.315827i
$281$	252.291	−	81.9743i	0.897832	−	0.291723i	0.176490	−	0.984302i	$-0.443526\pi$
$281$	252.291	−	81.9743i	0.897832	−	0.291723i	0.721342	+	0.692579i	$0.243526\pi$
$282$	794.894	−	1094.08i	2.81877	−	3.87971i
$283$	−225.605	−	310.519i	−0.797191	−	1.09724i	−0.993175	−	0.116632i	$-0.962790\pi$
$283$	−225.605	−	310.519i	−0.797191	−	1.09724i	0.195984	−	0.980607i	$-0.437210\pi$
$284$	−394.782	+	1215.01i	−1.39008	+	4.27821i
$285$		−	82.9846i		−	0.291174i
$286$	52.3229	+	77.8179i	0.182947	+	0.272090i
$287$	184.198			0.641805
$288$	−1275.78	−	414.526i	−4.42980	−	1.43933i
$289$	156.186	−	113.476i	0.540435	−	0.392649i
$290$	110.966	+	80.6213i	0.382641	+	0.278005i
$291$	232.085	+	714.284i	0.797543	+	2.45458i
$292$	477.798	−	155.246i	1.63629	−	0.531664i
$293$	−235.584	+	324.253i	−0.804041	+	1.10667i	0.188175	+	0.982136i	$0.439743\pi$
$293$	−235.584	+	324.253i	−0.804041	+	1.10667i	−0.992216	+	0.124532i	$0.960257\pi$
$294$	368.568	+	507.291i	1.25363	+	1.72548i
$295$	31.9367	−	98.2910i	0.108260	−	0.333190i
$296$		−	530.038i		−	1.79067i
$297$	17.3963	−	478.059i	0.0585736	−	1.60963i
$298$	431.946			1.44948
$299$	−10.3761	−	3.37141i	−0.0347028	−	0.0112756i
$300$	−1001.88	+	727.908i	−3.33960	+	2.42636i
$301$	−223.802	−	162.602i	−0.743528	−	0.540205i
$302$	−142.306	−	437.973i	−0.471212	−	1.45024i
$303$	−158.734	+	51.5756i	−0.523873	+	0.170217i
$304$	418.661	−	576.238i	1.37717	−	1.89552i
$305$	−35.0922	−	48.3003i	−0.115056	−	0.158362i
$306$	443.785	−	1365.83i	1.45028	−	4.46349i
$307$		−	214.923i		−	0.700074i	−0.936736	−	0.350037i	$-0.886169\pi$
$307$		−	214.923i		−	0.700074i	0.936736	−	0.350037i	$-0.113831\pi$
$308$	447.960	+	16.3011i	1.45442	+	0.0529255i
$309$	−105.235			−0.340567
$310$	−54.0116	−	17.5494i	−0.174231	−	0.0566111i
$311$	109.989	−	79.9117i	0.353662	−	0.256951i	−0.396741	−	0.917930i	$-0.629859\pi$
$311$	109.989	−	79.9117i	0.353662	−	0.256951i	0.750404	+	0.660980i	$0.229859\pi$
$312$	214.334	+	155.723i	0.686969	+	0.499112i
$313$	14.6250	+	45.0110i	0.0467251	+	0.143805i	0.971697	−	0.236230i	$-0.0759119\pi$
$313$	14.6250	+	45.0110i	0.0467251	+	0.143805i	−0.924972	+	0.380035i	$0.875912\pi$
$314$	−68.7010	+	22.3223i	−0.218793	+	0.0710902i
$315$	42.1338	−	57.9921i	0.133758	−	0.184102i
$316$	−316.183	−	435.189i	−1.00058	−	1.37718i
$317$	60.7603	−	187.001i	0.191673	−	0.589908i	−0.808326	−	0.588735i	$-0.799626\pi$
$317$	60.7603	−	187.001i	0.191673	−	0.589908i	0.999999	−	0.00117386i	$-0.000373653\pi$
$318$			954.518i			3.00163i
$319$	−330.161	+	221.993i	−1.03499	+	0.695902i
$320$	110.585			0.345578
$321$	411.798	+	133.801i	1.28286	+	0.416826i
$322$	−58.9989	+	42.8652i	−0.183226	+	0.133122i
$323$	283.182	+	205.744i	0.876724	+	0.636978i
$324$	−206.629	−	635.940i	−0.637745	−	1.96278i
$325$	51.8735	−	16.8547i	0.159611	−	0.0518607i
$326$	−117.068	+	161.130i	−0.359105	+	0.494265i
$327$	−41.4067	−	56.9914i	−0.126626	−	0.174286i
$328$	−317.597	+	977.462i	−0.968282	+	2.98007i
$329$			284.723i			0.865419i
$330$	58.8382	+	206.335i	0.178297	+	0.625257i
$331$	−201.413			−0.608499			−0.304250	−	0.952592i	$-0.598406\pi$
$331$	−201.413			−0.608499			−0.304250	+	0.952592i	$0.598406\pi$
$332$	193.783	+	62.9639i	0.583683	+	0.189650i
$333$	330.579	−	240.179i	0.992728	−	0.721259i
$334$	−251.588	−	182.790i	−0.753258	−	0.547274i
$335$	37.2475	+	114.636i	0.111186	+	0.342197i
$336$	886.851	−	288.155i	2.63944	−	0.857606i
$337$	257.017	−	353.754i	0.762662	−	1.04971i	−0.234326	−	0.972158i	$-0.575288\pi$
$337$	257.017	−	353.754i	0.762662	−	1.04971i	0.996988	−	0.0775558i	$-0.0247116\pi$
$338$	360.841	+	496.655i	1.06758	+	1.46939i
$339$	−90.8844	+	279.714i	−0.268096	+	0.825114i
$340$			223.132i			0.656270i
$341$	101.608	−	129.660i	0.297971	−	0.380235i
$342$	1042.80			3.04912
$343$	−314.663	−	102.240i	−0.917384	−	0.298076i
$344$	1248.74	−	907.264i	3.63006	−	2.63740i
$345$	−20.1958	−	14.6731i	−0.0585384	−	0.0425307i
$346$	−361.572	−	1112.80i	−1.04500	−	3.21619i
$347$	172.365	−	56.0049i	0.496730	−	0.161397i	−0.0499287	−	0.998753i	$-0.515899\pi$
$347$	172.365	−	56.0049i	0.496730	−	0.161397i	0.546659	+	0.837355i	$0.315899\pi$
$348$	−1098.08	+	1511.37i	−3.15540	+	4.34303i
$349$	−99.7130	−	137.243i	−0.285711	−	0.393247i	0.641904	−	0.766785i	$-0.278145\pi$
$349$	−99.7130	−	137.243i	−0.285711	−	0.393247i	−0.927615	+	0.373538i	$0.878145\pi$
$350$	112.662	−	346.739i	0.321892	−	0.990682i
$351$			98.9331i			0.281861i
$352$	−290.293	+	793.949i	−0.824697	+	2.25554i
$353$	580.453			1.64434			0.822171	−	0.569240i	$-0.192763\pi$
$353$	580.453			1.64434			0.822171	+	0.569240i	$0.192763\pi$
$354$	1871.99	+	608.246i	5.28810	+	1.71821i
$355$	104.157	−	75.6742i	0.293399	−	0.213167i
$356$	358.976	+	260.812i	1.00836	+	0.732617i
$357$	141.609	+	435.828i	0.396664	+	1.22081i
$358$	834.809	−	271.246i	2.33187	−	0.757670i
$359$	−53.8229	+	74.0809i	−0.149924	+	0.206353i	−0.877373	−	0.479809i	$-0.840706\pi$
$359$	−53.8229	+	74.0809i	−0.149924	+	0.206353i	0.727449	+	0.686162i	$0.240706\pi$
$360$	235.093	+	323.577i	0.653035	+	0.898825i
$361$	33.0134	−	101.605i	0.0914498	−	0.281453i
$362$		−	687.342i		−	1.89874i
$363$	−620.712	−	45.2348i	−1.70995	−	0.124614i
$364$	−92.7042			−0.254682
$365$	−48.1502	−	15.6450i	−0.131918	−	0.0428629i
$366$	919.896	−	668.344i	2.51338	−	1.82608i
$367$	502.053	+	364.763i	1.36799	+	0.993905i	0.997891	+	0.0649132i	$0.0206771\pi$
$367$	502.053	+	364.763i	1.36799	+	0.993905i	0.370101	+	0.928991i	$0.379323\pi$
$368$	−66.2111	−	203.777i	−0.179922	−	0.553742i
$369$	−753.546	+	244.842i	−2.04213	+	0.663529i
$370$	−52.1811	+	71.8212i	−0.141030	+	0.194111i
$371$	−118.123	−	162.582i	−0.318391	−	0.438228i
$372$	239.027	−	735.648i	0.642545	−	1.97755i
$373$			432.074i			1.15838i	0.815194	+	0.579188i	$0.196630\pi$
$373$			432.074i			1.15838i	−0.815194	+	0.579188i	$0.803370\pi$
$374$	−849.988	−	310.783i	−2.27269	−	0.830971i
$375$	254.930			0.679813
$376$	−1510.91	−	490.923i	−4.01837	−	1.30565i
$377$	66.5661	−	48.3631i	0.176568	−	0.128284i
$378$	535.002	+	388.702i	1.41535	+	1.02831i
$379$	−77.9880	−	240.022i	−0.205773	−	0.633305i	−0.999681	−	0.0252662i	$-0.991957\pi$
$379$	−77.9880	−	240.022i	−0.205773	−	0.633305i	0.793908	−	0.608038i	$-0.208043\pi$
$380$	−154.091	+	50.0673i	−0.405503	+	0.131756i
$381$	−450.646	+	620.261i	−1.18280	+	1.62798i
$382$	−341.353	−	469.832i	−0.893594	−	1.22993i
$383$	35.3440	−	108.777i	0.0922819	−	0.284014i	−0.894254	−	0.447560i	$-0.852293\pi$
$383$	35.3440	−	108.777i	0.0922819	−	0.284014i	0.986536	+	0.163546i	$0.0522931\pi$
$384$			525.022i			1.36724i
$385$	−35.5561	−	27.8636i	−0.0923536	−	0.0723730i
$386$	−675.461			−1.74990
$387$	1131.70	+	367.712i	2.92429	+	0.950160i
$388$	1186.31	−	861.901i	3.05749	−	2.22139i
$389$	−365.589	−	265.616i	−0.939819	−	0.682818i	0.00855837	−	0.999963i	$-0.497276\pi$
$389$	−365.589	−	265.616i	−0.939819	−	0.682818i	−0.948377	+	0.317145i	$0.897276\pi$
$390$	−13.7121	−	42.2015i	−0.0351593	−	0.108209i
$391$	100.143	−	32.5383i	0.256119	−	0.0832182i
$392$	432.971	−	595.933i	1.10452	−	1.52024i
$393$	177.079	+	243.728i	0.450582	+	0.620173i
$394$	−48.1121	+	148.074i	−0.122112	+	0.375822i
$395$			54.2094i			0.137239i
$396$	−1854.25	+	528.756i	−4.68246	+	1.33524i
$397$	232.782			0.586352			0.293176	−	0.956059i	$-0.405288\pi$
$397$	232.782			0.586352			0.293176	+	0.956059i	$0.405288\pi$
$398$	−1100.03	−	357.423i	−2.76390	−	0.898047i
$399$	−269.201	+	195.586i	−0.674689	+	0.490190i
$400$	866.595	+	629.618i	2.16649	+	1.57405i
$401$	−159.080	−	489.599i	−0.396709	−	1.22095i	−0.927622	−	0.373520i	$-0.878151\pi$
$401$	−159.080	−	489.599i	−0.396709	−	1.22095i	0.530913	−	0.847426i	$-0.321849\pi$
$402$	−2183.28	+	709.391i	−5.43105	+	1.76466i
$403$	−20.0246	+	27.5615i	−0.0496888	+	0.0683908i
$404$	191.538	+	263.630i	0.474104	+	0.652548i
$405$	−20.8232	+	64.0871i	−0.0514152	+	0.158240i
$406$		−	549.987i		−	1.35465i
$407$	−143.682	−	213.693i	−0.353027	−	0.525043i
$408$	−2556.92			−6.26696
$409$	−106.215	−	34.5113i	−0.259694	−	0.0843796i	0.176276	−	0.984341i	$-0.443595\pi$
$409$	−106.215	−	34.5113i	−0.259694	−	0.0843796i	−0.435970	+	0.899961i	$0.643595\pi$
$410$	139.264	−	101.181i	0.339669	−	0.246784i
$411$	990.121	+	719.365i	2.40905	+	1.75028i
$412$	63.4918	+	195.408i	0.154106	+	0.474290i
$413$	−394.126	+	128.059i	−0.954300	+	0.310071i
$414$	184.384	−	253.783i	0.445372	−	0.613002i
$415$	−12.0693	−	16.6120i	−0.0290827	−	0.0400288i
$416$	54.0250	−	166.272i	0.129868	−	0.399692i
$417$			739.521i			1.77343i
$418$	23.8979	−	656.723i	0.0571719	−	1.57111i
$419$	−49.3683			−0.117824			−0.0589120	−	0.998263i	$-0.518763\pi$
$419$	−49.3683			−0.117824			−0.0589120	+	0.998263i	$0.518763\pi$
$420$	−201.734	−	65.5473i	−0.480319	−	0.156065i
$421$	−258.640	+	187.913i	−0.614347	+	0.446349i	−0.850942	−	0.525259i	$-0.823968\pi$
$421$	−258.640	+	187.913i	−0.614347	+	0.446349i	0.236595	+	0.971608i	$0.423968\pi$
$422$	575.385	+	418.042i	1.36347	+	0.990620i
$423$	−378.463	−	1164.79i	−0.894712	−	2.75364i
$424$	1066.43	−	346.503i	2.51516	−	0.817224i
$425$	−309.415	+	425.873i	−0.728035	+	1.00205i
$426$	1441.24	+	1983.70i	3.38320	+	4.65657i
$427$	−73.9768	+	227.677i	−0.173248	+	0.533202i
$428$		−	845.380i		−	1.97519i
$429$	128.625	+	4.68061i	0.299826	+	0.0109105i
$430$	−258.525			−0.601222
$431$	710.839	+	230.966i	1.64928	+	0.535883i	0.978584	−	0.205850i	$-0.0659958\pi$
$431$	710.839	+	230.966i	1.64928	+	0.535883i	0.670695	+	0.741733i	$0.265996\pi$
$432$	−1571.88	+	1142.03i	−3.63860	+	2.64360i
$433$	431.773	+	313.702i	0.997167	+	0.724485i	0.961479	−	0.274878i	$-0.0886376\pi$
$433$	431.773	+	313.702i	0.997167	+	0.724485i	0.0356884	+	0.999363i	$0.488638\pi$
$434$	70.3695	+	216.575i	0.162142	+	0.499021i
$435$	179.050	−	58.1770i	0.411610	−	0.133740i
$436$	−80.8434	+	111.271i	−0.185421	+	0.255209i
$437$	44.9409	+	61.8558i	0.102840	+	0.141547i
$438$	297.964	−	917.039i	0.680283	−	2.09370i
$439$			120.570i			0.274646i	0.990526	+	0.137323i	$0.0438499\pi$
$439$			120.570i			0.274646i	−0.990526	+	0.137323i	$0.956150\pi$
$440$	209.167	−	140.639i	0.475379	−	0.319634i
$441$	567.872			1.28769
$442$	178.008	+	57.8382i	0.402732	+	0.130856i
$443$	−22.9703	+	16.6889i	−0.0518517	+	0.0376725i	−0.613409	−	0.789765i	$-0.710202\pi$
$443$	−22.9703	+	16.6889i	−0.0518517	+	0.0376725i	0.561558	+	0.827438i	$0.310202\pi$
$444$	−978.218	−	710.717i	−2.20319	−	1.60071i
$445$	−13.8180	−	42.5274i	−0.0310517	−	0.0955672i
$446$	−1048.63	+	340.720i	−2.35118	+	0.763946i
$447$	348.486	−	479.650i	0.779611	−	1.07304i
$448$	−260.637	−	358.736i	−0.581778	−	0.800749i
$449$	−170.156	+	523.686i	−0.378967	+	1.16634i	0.561797	+	0.827275i	$0.310110\pi$
$449$	−170.156	+	523.686i	−0.378967	+	1.16634i	−0.940763	+	0.339064i	$0.889890\pi$
$450$			1568.25i			3.48500i
$451$	136.925	+	480.172i	0.303603	+	1.06468i
$452$	574.224			1.27041
$453$	−601.152	−	195.326i	−1.32705	−	0.431184i
$454$	15.8071	−	11.4846i	0.0348175	−	0.0252964i
$455$	7.55808	+	5.49127i	0.0166112	+	0.0120687i
$456$	−573.733	−	1765.77i	−1.25819	−	3.87230i
$457$	155.470	−	50.5153i	0.340197	−	0.110537i	−0.133936	−	0.990990i	$-0.542762\pi$
$457$	155.470	−	50.5153i	0.340197	−	0.110537i	0.474133	+	0.880453i	$0.342762\pi$
$458$	−550.063	+	757.096i	−1.20101	+	1.65305i
$459$	−561.233	−	772.471i	−1.22273	−	1.68294i
$460$	−15.0612	+	46.3535i	−0.0327417	+	0.100769i
$461$			392.758i			0.851971i	0.904730	+	0.425985i	$0.140072\pi$
$461$			392.758i			0.851971i	−0.904730	+	0.425985i	$0.859928\pi$
$462$	530.672	−	677.179i	1.14864	−	1.46576i
$463$	−275.562			−0.595167			−0.297583	−	0.954696i	$-0.596181\pi$
$463$	−275.562			−0.595167			−0.297583	+	0.954696i	$0.596181\pi$
$464$	1536.81	+	499.341i	3.31210	+	1.07617i
$465$	−63.0632	+	45.8181i	−0.135620	+	0.0985335i
$466$	342.650	+	248.950i	0.735300	+	0.534227i
$467$	170.947	+	526.121i	0.366054	+	1.12660i	0.949318	+	0.314316i	$0.101775\pi$
$467$	170.947	+	526.121i	0.366054	+	1.12660i	−0.583264	+	0.812282i	$0.698225\pi$
$468$	379.249	−	123.225i	0.810361	−	0.263302i
$469$	284.089	−	391.015i	0.605733	−	0.833720i
$470$	156.400	+	215.267i	0.332767	+	0.458014i
$471$	−30.6391	+	94.2976i	−0.0650512	+	0.200207i
$472$		−	2312.26i		−	4.89886i
$473$	257.509	−	704.284i	0.544417	−	1.48897i
$474$	−1032.44			−2.17814
$475$	−363.529	−	118.118i	−0.765325	−	0.248669i
$476$	723.836	−	525.898i	1.52066	−	1.10483i
$477$	699.347	+	508.105i	1.46614	+	1.06521i
$478$	212.723	+	654.694i	0.445027	+	1.36965i
$479$	−344.661	+	111.987i	−0.719543	+	0.233794i	−0.645825	−	0.763485i	$-0.723486\pi$
$479$	−344.661	+	111.987i	−0.719543	+	0.233794i	−0.0737180	+	0.997279i	$0.523486\pi$
$480$	235.128	−	323.625i	0.489849	−	0.674220i
$481$	31.3024	+	43.0841i	0.0650778	+	0.0895719i
$482$	118.766	−	365.524i	0.246403	−	0.758350i
$483$			100.098i			0.207241i
$484$	290.501	+	1179.87i	0.600208	+	2.43775i
$485$	−147.772			−0.304685
$486$	174.336	+	56.6452i	0.358716	+	0.116554i
$487$	38.5101	−	27.9792i	0.0790762	−	0.0574522i	−0.547545	−	0.836776i	$-0.684437\pi$
$487$	38.5101	−	27.9792i	0.0790762	−	0.0574522i	0.626621	+	0.779324i	$0.284437\pi$
$488$	−1080.64	−	785.128i	−2.21442	−	1.60887i
$489$	84.4772	+	259.994i	0.172755	+	0.531686i
$490$	−117.337	+	38.1250i	−0.239463	+	0.0778062i
$491$	26.8318	−	36.9308i	0.0546472	−	0.0752154i	−0.780819	−	0.624758i	$-0.785198\pi$
$491$	26.8318	−	36.9308i	0.0546472	−	0.0752154i	0.835466	+	0.549542i	$0.185198\pi$
$492$	1378.11	+	1896.80i	2.80103	+	3.85529i
$493$	−245.393	+	755.241i	−0.497754	+	1.53193i
$494$			135.907i			0.275116i
$495$	182.496	+	66.7264i	0.368678	+	0.134801i
$496$	−669.059			−1.34891
$497$	−490.971	−	159.526i	−0.987870	−	0.320978i
$498$	316.381	−	229.864i	0.635303	−	0.461575i
$499$	−508.454	−	369.413i	−1.01895	−	0.740307i	−0.0528790	−	0.998601i	$-0.516840\pi$
$499$	−508.454	−	369.413i	−1.01895	−	0.740307i	−0.966066	+	0.258294i	$0.916840\pi$
$500$	−153.807	−	473.370i	−0.307615	−	0.946740i
$501$	−405.954	+	131.902i	−0.810287	+	0.263278i
$502$	14.1132	−	19.4251i	0.0281139	−	0.0386954i
$503$	−422.159	−	581.053i	−0.839283	−	1.15517i	−0.986123	−	0.166014i	$-0.946910\pi$
$503$	−422.159	−	581.053i	−0.839283	−	1.15517i	0.146840	−	0.989160i	$-0.453090\pi$
$504$	495.591	−	1525.27i	0.983316	−	3.02633i
$505$		−	32.8391i		−	0.0650279i
$506$	−155.599	−	121.936i	−0.307509	−	0.240979i
$507$	842.625			1.66198
$508$	1423.63	+	462.566i	2.80242	+	0.910563i
$509$	388.080	−	281.956i	0.762436	−	0.553942i	−0.137221	−	0.990541i	$-0.543817\pi$
$509$	388.080	−	281.956i	0.762436	−	0.553942i	0.899656	+	0.436598i	$0.143817\pi$
$510$	346.468	+	251.724i	0.679348	+	0.493576i
$511$	62.7329	+	193.072i	0.122765	+	0.377832i
$512$	−582.850	+	189.380i	−1.13838	+	0.369882i
$513$	407.524	−	560.909i	0.794395	−	1.09339i
$514$	−18.7627	−	25.8247i	−0.0365034	−	0.0502426i
$515$	6.39841	−	19.6923i	0.0124241	−	0.0382374i
$516$		−	3521.16i		−	6.82396i
$517$	−742.223	+	211.651i	−1.43563	+	0.409383i
$518$	355.972			0.687205
$519$	−1527.41	−	496.285i	−2.94299	−	0.956234i
$520$	−42.1716	+	30.6395i	−0.0810992	+	0.0589220i
$521$	−44.5907	−	32.3970i	−0.0855867	−	0.0621824i	0.544169	−	0.838976i	$-0.316845\pi$
$521$	−44.5907	−	32.3970i	−0.0855867	−	0.0621824i	−0.629756	+	0.776793i	$0.716845\pi$
$522$	731.061	+	2249.97i	1.40050	+	4.31029i
$523$	180.457	−	58.6339i	0.345041	−	0.112111i	−0.131370	−	0.991333i	$-0.541937\pi$
$523$	180.457	−	58.6339i	0.345041	−	0.112111i	0.476411	+	0.879223i	$0.341937\pi$
$524$	345.733	−	475.860i	0.659795	−	0.908130i
$525$	−294.139	−	404.847i	−0.560264	−	0.771138i
$526$	−165.862	+	510.471i	−0.315327	+	0.970478i
$527$		−	328.797i		−	0.623904i
$528$	1410.42	+	2097.66i	2.67125	+	3.97285i
$529$	23.0000			0.0434783
$530$	−178.615	−	58.0357i	−0.337010	−	0.109501i
$531$	1442.13	−	1047.77i	2.71588	−	1.97320i
$532$	525.594	+	381.867i	0.987959	+	0.717794i
$533$	−31.9101	−	98.2092i	−0.0598689	−	0.184257i
$534$	809.950	−	263.169i	1.51676	−	0.492825i
$535$	−50.0754	+	68.9229i	−0.0935990	+	0.128828i
$536$	1585.12	+	2181.73i	2.95732	+	4.07040i
$537$	372.306	−	1145.84i	0.693308	−	2.13378i
$538$		−	695.155i		−	1.29211i
$539$	13.0139	−	357.628i	0.0241446	−	0.663504i
$540$	441.966			0.818455
$541$	13.2624	+	4.30921i	0.0245145	+	0.00796526i	0.321249	−	0.946995i	$-0.395897\pi$
$541$	13.2624	+	4.30921i	0.0245145	+	0.00796526i	−0.296734	+	0.954960i	$0.595897\pi$
$542$	−1619.01	+	1176.28i	−2.98710	+	2.17025i
$543$	−763.252	−	554.535i	−1.40562	−	1.02124i
$544$	521.408	+	1604.73i	0.958471	+	2.94987i
$545$	13.1822	−	4.28314i	0.0241874	−	0.00785897i
$546$	−104.583	+	143.946i	−0.191544	+	0.263638i
$547$	−250.042	−	344.154i	−0.457116	−	0.629166i	0.516792	−	0.856111i	$-0.327126\pi$
$547$	−250.042	−	344.154i	−0.457116	−	0.629166i	−0.973907	+	0.226945i	$0.927126\pi$
$548$	738.392	−	2272.54i	1.34743	−	4.14697i
$549$		−	1029.75i		−	1.87568i
$550$	987.636	+	35.9396i	1.79570	+	0.0653448i
$551$	−576.620			−1.04650
$552$	−531.176	−	172.590i	−0.962276	−	0.312662i
$553$	175.854	−	127.766i	0.318001	−	0.231041i
$554$	550.867	+	400.228i	0.994344	+	0.722433i
$555$	37.6543	+	115.888i	0.0678456	+	0.208807i
$556$	1373.19	−	446.177i	2.46977	−	0.802476i
$557$	406.441	−	559.419i	0.729697	−	1.00434i	−0.269448	−	0.963015i	$-0.586841\pi$
$557$	406.441	−	559.419i	0.729697	−	1.00434i	0.999146	−	0.0413274i	$-0.0131587\pi$
$558$	−575.757	−	792.462i	−1.03182	−	1.42018i
$559$	−47.9236	+	147.494i	−0.0857310	+	0.263853i
$560$			183.473i			0.327631i
$561$	−1030.86	+	693.126i	−1.83754	+	1.23552i
$562$	−994.061			−1.76879
$563$	706.993	+	229.716i	1.25576	+	0.408021i	0.859982	−	0.510325i	$-0.170475\pi$
$563$	706.993	+	229.716i	1.25576	+	0.408021i	0.395779	+	0.918346i	$0.370475\pi$
$564$	−2931.97	+	2130.20i	−5.19853	+	3.77695i
$565$	−46.8159	−	34.0137i	−0.0828600	−	0.0602013i
$566$	444.457	+	1367.90i	0.785260	+	2.41678i
$567$	256.975	−	83.4964i	0.453219	−	0.147260i
$568$	1693.08	−	2330.32i	2.98077	−	4.10268i
$569$	377.445	+	519.509i	0.663348	+	0.913020i	0.999586	−	0.0287565i	$-0.00915476\pi$
$569$	377.445	+	519.509i	0.663348	+	0.913020i	−0.336238	+	0.941777i	$0.609155\pi$
$570$	−96.0943	+	295.748i	−0.168587	+	0.518856i
$571$			111.787i			0.195774i	0.995198	+	0.0978869i	$0.0312083\pi$
$571$			111.787i			0.195774i	−0.995198	+	0.0978869i	$0.968792\pi$
$572$	−68.9124	−	241.664i	−0.120476	−	0.422489i
$573$	−797.117			−1.39113
$574$	−656.461	−	213.297i	−1.14366	−	0.371598i
$575$	−93.0241	+	67.5860i	−0.161781	+	0.117541i
$576$	1543.10	+	1121.13i	2.67899	+	1.94640i
$577$	−199.729	−	614.703i	−0.346151	−	1.06534i	−0.960965	−	0.276671i	$-0.910769\pi$
$577$	−199.729	−	614.703i	−0.346151	−	1.06534i	0.614814	−	0.788672i	$-0.289231\pi$
$578$	−688.031	+	223.555i	−1.19036	+	0.386773i
$579$	−544.950	+	750.059i	−0.941191	+	1.29544i
$580$	−216.054	−	297.372i	−0.372506	−	0.512711i
$581$	−25.4429	+	78.3053i	−0.0437916	+	0.134777i
$582$		−	2814.38i		−	4.83570i
$583$	336.016	−	428.783i	0.576357	−	0.735477i
$584$	−1132.72			−1.93959
$585$	−38.2190	−	12.4181i	−0.0653316	−	0.0212275i
$586$	1215.07	−	882.802i	2.07350	−	1.50649i
$587$	58.5487	+	42.5381i	0.0997422	+	0.0724670i	0.636539	−	0.771245i	$-0.280366\pi$
$587$	58.5487	+	42.5381i	0.0997422	+	0.0724670i	−0.536796	+	0.843712i	$0.680366\pi$
$588$	−519.270	−	1598.15i	−0.883112	−	2.71794i
$589$	227.062	−	73.7770i	0.385505	−	0.125258i
$590$	−227.638	+	313.316i	−0.385826	+	0.531045i
$591$	125.611	+	172.889i	0.212540	+	0.292536i
$592$	−323.192	+	994.683i	−0.545933	+	1.68021i
$593$			209.050i			0.352529i	0.984343	+	0.176265i	$0.0564015\pi$
$593$			209.050i			0.352529i	−0.984343	+	0.176265i	$0.943599\pi$
$594$	−615.580	+	1683.60i	−1.03633	+	2.83435i
$595$	−90.1648			−0.151537
$596$	−1100.90	−	357.703i	−1.84714	−	0.600173i
$597$	−1284.38	+	933.159i	−2.15140	+	1.56308i
$598$	33.0754	+	24.0307i	0.0553100	+	0.0401851i
$599$	234.064	+	720.376i	0.390759	+	1.20263i	0.932216	+	0.361903i	$0.117873\pi$
$599$	234.064	+	720.376i	0.390759	+	1.20263i	−0.541457	+	0.840728i	$0.682127\pi$
$600$	2655.51	−	862.829i	4.42586	−	1.43805i
$601$	−609.642	+	839.100i	−1.01438	+	1.39617i	−0.0983092	+	0.995156i	$0.531343\pi$
$601$	−609.642	+	839.100i	−1.01438	+	1.39617i	−0.916070	+	0.401018i	$0.868657\pi$
$602$	609.316	+	838.652i	1.01215	+	1.39311i
$603$	−642.446	+	1977.25i	−1.06542	+	3.27901i
$604$			1234.11i			2.04322i
$605$	46.2045	−	113.401i	0.0763712	−	0.187440i
$606$	625.432			1.03207
$607$	−703.019	−	228.425i	−1.15819	−	0.376318i	−0.333965	−	0.942585i	$-0.608387\pi$
$607$	−703.019	−	228.425i	−1.15819	−	0.376318i	−0.824221	+	0.566268i	$0.808387\pi$
$608$	−991.205	+	720.152i	−1.63027	+	1.18446i
$609$	−610.727	−	443.719i	−1.00284	−	0.728603i
$610$	69.1341	+	212.773i	0.113335	+	0.348808i
$611$	151.806	−	49.3249i	0.248455	−	0.0807281i
$612$	−2262.14	+	3113.57i	−3.69631	+	5.08754i
$613$	547.590	+	753.693i	0.893296	+	1.22952i	0.972558	+	0.232662i	$0.0747437\pi$
$613$	547.590	+	753.693i	0.893296	+	1.22952i	−0.0792618	+	0.996854i	$0.525256\pi$
$614$	−248.876	+	765.961i	−0.405335	+	1.24749i
$615$		−	236.276i		−	0.384188i
$616$	−949.214	−	347.063i	−1.54093	−	0.563414i
$617$	379.407			0.614922			0.307461	−	0.951561i	$-0.400521\pi$
$617$	379.407			0.614922			0.307461	+	0.951561i	$0.400521\pi$
$618$	375.047	+	121.860i	0.606871	+	0.197184i
$619$	908.511	−	660.072i	1.46771	−	1.06635i	0.486437	−	0.873716i	$-0.338296\pi$
$619$	908.511	−	660.072i	1.46771	−	1.06635i	0.981270	−	0.192636i	$-0.0617037\pi$
$620$	123.126	+	89.4563i	0.198590	+	0.144284i
$621$	−64.4499	−	198.356i	−0.103784	−	0.319414i
$622$	−484.524	+	157.431i	−0.778978	+	0.253105i
$623$	−105.391	+	145.058i	−0.169167	+	0.232838i
$624$	−307.273	−	422.925i	−0.492424	−	0.677764i
$625$	169.724	−	522.355i	0.271558	−	0.835769i
$626$		−	177.349i		−	0.283306i
$627$	−709.971	−	556.369i	−1.13233	−	0.887351i
$628$	193.583			0.308254
$629$	−488.820	−	158.827i	−0.777138	−	0.252508i
$630$	−217.314	+	157.888i	−0.344942	+	0.250615i
$631$	205.622	+	149.393i	0.325867	+	0.236756i	0.738675	−	0.674062i	$-0.235452\pi$
$631$	205.622	+	149.393i	0.325867	+	0.236756i	−0.412808	+	0.910818i	$0.635452\pi$
$632$	374.789	+	1153.48i	0.593020	+	1.82513i
$633$	928.420	−	301.662i	1.46670	−	0.476559i
$634$	−433.086	+	596.091i	−0.683101	+	0.940207i
$635$	−88.6675	−	122.040i	−0.139634	−	0.192189i
$636$	790.457	−	2432.78i	1.24286	−	3.82512i
$637$			74.0103i			0.116186i
$638$	1433.72	−	408.837i	2.24721	−	0.640811i
$639$	2220.59			3.47510
$640$	−98.2454	−	31.9219i	−0.153508	−	0.0498779i
$641$	86.0342	−	62.5075i	0.134219	−	0.0975156i	−0.518650	−	0.854987i	$-0.673565\pi$
$641$	86.0342	−	62.5075i	0.134219	−	0.0975156i	0.652869	+	0.757471i	$0.273565\pi$
$642$	−1312.66	−	953.705i	−2.04464	−	1.48552i
$643$	−229.337	−	705.828i	−0.356668	−	1.09771i	−0.955036	−	0.296490i	$-0.904184\pi$
$643$	−229.337	−	705.828i	−0.356668	−	1.09771i	0.598368	−	0.801221i	$-0.295816\pi$
$644$	185.868	−	60.3921i	0.288614	−	0.0937765i
$645$	−208.573	+	287.077i	−0.323370	+	0.445080i
$646$	−770.982	−	1061.17i	−1.19347	−	1.64267i
$647$	221.953	−	683.100i	0.343049	−	1.05580i	−0.619571	−	0.784941i	$-0.712693\pi$
$647$	221.953	−	683.100i	0.343049	−	1.05580i	0.962620	−	0.270856i	$-0.0873067\pi$
$648$			1507.63i			2.32658i
$649$	−626.805	−	932.223i	−0.965801	−	1.43640i
$650$	−204.389			−0.314444
$651$	297.266	+	96.5877i	0.456630	+	0.148368i
$652$	431.806	−	313.726i	0.662280	−	0.481174i
$653$	−187.664	−	136.346i	−0.287387	−	0.208799i	0.434746	−	0.900553i	$-0.356838\pi$
$653$	−187.664	−	136.346i	−0.287387	−	0.208799i	−0.722133	+	0.691754i	$0.756838\pi$
$654$	81.5740	+	251.059i	0.124731	+	0.383882i
$655$	−56.3745	+	18.3172i	−0.0860679	+	0.0279652i
$656$	1192.02	−	1640.68i	1.81710	−	2.50103i
$657$	−513.276	−	706.463i	−0.781241	−	1.07529i
$658$	329.703	−	1014.72i	0.501068	−	1.54213i
$659$			1149.60i			1.74446i	0.489096	+	0.872230i	$0.337327\pi$
$659$			1149.60i			1.74446i	−0.489096	+	0.872230i	$0.662673\pi$
$660$	20.9098	−	574.610i	0.0316815	−	0.870621i
$661$	295.345			0.446815			0.223407	−	0.974725i	$-0.428282\pi$
$661$	295.345			0.446815			0.223407	+	0.974725i	$0.428282\pi$
$662$	717.814	+	233.232i	1.08431	+	0.352314i
$663$	207.839	−	151.004i	0.313483	−	0.227759i
$664$	−371.664	−	270.030i	−0.559735	−	0.406672i
$665$	−20.2316	−	62.2664i	−0.0304234	−	0.0936337i
$666$	−1456.27	+	473.170i	−2.18659	+	0.710465i
$667$	−101.956	+	140.330i	−0.152858	+	0.210390i
$668$	489.850	+	674.220i	0.733308	+	1.00931i
$669$	−467.665	+	1439.32i	−0.699051	+	2.15146i
$670$		−	451.681i		−	0.674151i
$671$	−648.506	−	23.5988i	−0.966477	−	0.0351697i
$672$	−1604.01			−2.38691
$673$	−593.451	−	192.824i	−0.881799	−	0.286514i	−0.167095	−	0.985941i	$-0.553439\pi$
$673$	−593.451	−	192.824i	−0.881799	−	0.286514i	−0.714704	+	0.699427i	$0.753439\pi$
$674$	−1325.62	+	963.118i	−1.96679	+	1.42896i
$675$	843.543	+	612.870i	1.24969	+	0.907956i
$676$	−508.383	−	1564.64i	−0.752046	−	2.31456i
$677$	−393.345	+	127.806i	−0.581012	+	0.188782i	−0.584754	−	0.811211i	$-0.698809\pi$
$677$	−393.345	+	127.806i	−0.581012	+	0.188782i	0.00374168	+	0.999993i	$0.498809\pi$
$678$	647.804	−	891.625i	0.955463	−	1.31508i
$679$	348.283	+	479.371i	0.512936	+	0.705996i
$680$	155.463	−	478.467i	0.228623	−	0.703628i
$681$		−	26.8184i		−	0.0393809i
$682$	−512.263	+	344.434i	−0.751119	+	0.505035i
$683$	3.40578			0.00498650			0.00249325	−	0.999997i	$-0.499206\pi$
$683$	3.40578			0.00498650			0.00249325	+	0.999997i	$0.499206\pi$
$684$	−2657.77	−	863.563i	−3.88563	−	1.26252i
$685$	−194.812	+	141.540i	−0.284398	+	0.206627i
$686$	1003.03	+	728.745i	1.46214	+	1.06231i
$687$	396.929	+	1221.62i	0.577772	+	1.77820i
$688$	−2896.63	+	941.172i	−4.21022	+	1.36798i
$689$	−66.2210	+	91.1454i	−0.0961118	+	0.132287i
$690$	54.9843	+	75.6794i	0.0796874	+	0.109680i
$691$	91.1318	−	280.475i	0.131884	−	0.405897i	−0.863208	−	0.504848i	$-0.831549\pi$
$691$	91.1318	−	280.475i	0.131884	−	0.405897i	0.995092	+	0.0989508i	$0.0315486\pi$
$692$			3135.62i			4.53124i
$693$	−213.664	−	749.281i	−0.308317	−	1.08121i
$694$	−679.143			−0.978593
$695$	−138.384	−	44.9636i	−0.199113	−	0.0646959i
$696$	3407.66	−	2475.81i	4.89606	−	3.55720i
$697$	806.282	+	585.798i	1.15679	+	0.840456i
$698$	196.442	+	604.585i	0.281435	+	0.866167i
$699$	552.888	−	179.644i	0.790969	−	0.257002i
$700$	−574.283	+	790.433i	−0.820405	+	1.12919i
$701$	188.836	+	259.910i	0.269380	+	0.370770i	0.922180	−	0.386760i	$-0.126406\pi$
$701$	188.836	+	259.910i	0.269380	+	0.370770i	−0.652800	+	0.757530i	$0.726406\pi$
$702$	114.562	−	352.586i	0.163194	−	0.502260i
$703$		−	373.210i		−	0.530881i
$704$	741.415	−	946.104i	1.05315	−	1.34390i
$705$	365.222			0.518045
$706$	−2068.67	−	672.151i	−2.93013	−	0.952055i
$707$	−106.529	+	77.3981i	−0.150678	+	0.109474i
$708$	−4267.43	−	3100.47i	−6.02744	−	4.37919i
$709$	−153.582	−	472.678i	−0.216618	−	0.666682i	−0.999035	−	0.0439268i	$-0.986013\pi$
$709$	−153.582	−	472.678i	−0.216618	−	0.666682i	0.782417	−	0.622755i	$-0.213987\pi$
$710$	−458.831	+	149.083i	−0.646241	+	0.209976i
$711$	−549.583	+	756.436i	−0.772972	+	1.06390i
$712$	−588.046	−	809.376i	−0.825907	−	1.13676i
$713$	22.1935	−	68.3046i	0.0311269	−	0.0957989i
$714$		−	1717.22i		−	2.40507i
$715$	−8.69641	+	23.7846i	−0.0121628	+	0.0332651i
$716$	−2352.30			−3.28533
$717$	898.620	+	291.979i	1.25331	+	0.407223i
$718$	277.603	−	201.690i	0.386633	−	0.280906i
$719$	336.628	+	244.574i	0.468189	+	0.340159i	0.796735	−	0.604329i	$-0.206559\pi$
$719$	336.628	+	244.574i	0.468189	+	0.340159i	−0.328546	+	0.944488i	$0.606559\pi$
$720$	−243.879	−	750.582i	−0.338721	−	1.04247i
$721$	−78.9618	+	25.6562i	−0.109517	+	0.0355843i
$722$	−235.312	+	323.879i	−0.325917	+	0.448586i
$723$	−310.075	−	426.781i	−0.428872	−	0.590292i
$724$	−569.203	+	1751.83i	−0.786191	+	2.41965i
$725$		−	867.170i		−	1.19610i
$726$	2159.77	+	879.982i	2.97489	+	1.21210i
$727$	−677.429			−0.931815			−0.465907	−	0.884833i	$-0.654272\pi$
$727$	−677.429			−0.931815			−0.465907	+	0.884833i	$0.654272\pi$
$728$	198.788	+	64.5901i	0.273060	+	0.0887226i
$729$	688.373	−	500.132i	0.944270	−	0.686052i
$730$	153.486	+	111.514i	0.210254	+	0.152759i
$731$	−462.523	−	1423.50i	−0.632726	−	1.94733i
$732$	−2898.00	+	941.619i	−3.95902	+	1.28636i
$733$	70.8219	−	97.4779i	0.0966192	−	0.132985i	−0.757970	−	0.652289i	$-0.773809\pi$
$733$	70.8219	−	97.4779i	0.0966192	−	0.132985i	0.854589	+	0.519304i	$0.173809\pi$
$734$	−1366.87	−	1881.34i	−1.86223	−	2.56313i
$735$	−52.3296	+	161.054i	−0.0711968	+	0.219121i
$736$			368.562i			0.500763i
$737$	1230.49	+	449.906i	1.66959	+	0.610456i
$738$	2969.08			4.02314
$739$	718.129	+	233.334i	0.971757	+	0.315743i	0.751525	−	0.659704i	$-0.229319\pi$
$739$	718.129	+	233.334i	0.971757	+	0.315743i	0.220232	+	0.975447i	$0.429319\pi$
$740$	192.470	−	139.838i	0.260095	−	0.188970i
$741$	150.917	+	109.647i	0.203666	+	0.147972i
$742$	232.711	+	716.210i	0.313626	+	0.965242i
$743$	−800.023	+	259.943i	−1.07675	+	0.349856i	−0.793112	−	0.609076i	$-0.791540\pi$
$743$	−800.023	+	259.943i	−1.07675	+	0.349856i	−0.283635	+	0.958932i	$0.591540\pi$
$744$	−1025.10	+	1410.93i	−1.37782	+	1.89641i
$745$	68.5668	+	94.3741i	0.0920359	+	0.126677i
$746$	500.332	−	1539.86i	0.670687	−	2.06416i
$747$		−	354.163i		−	0.474114i
$748$	1908.99	+	1495.98i	2.55213	+	1.99998i
$749$	341.607			0.456085
$750$	−908.541	−	295.203i	−1.21139	−	0.393604i
$751$	−333.753	+	242.486i	−0.444412	+	0.322884i	−0.787385	−	0.616461i	$-0.788566\pi$
$751$	−333.753	+	242.486i	−0.444412	+	0.322884i	0.342974	+	0.939345i	$0.388566\pi$
$752$	2536.06	+	1842.56i	3.37243	+	2.45021i
$753$	−10.1842	−	31.3436i	−0.0135248	−	0.0416250i
$754$	−293.238	+	95.2787i	−0.388909	+	0.126364i
$755$	73.1014	−	100.615i	0.0968230	−	0.133265i
$756$	−1041.67	−	1433.73i	−1.37786	−	1.89647i
$757$	−404.547	+	1245.07i	−0.534409	+	1.64474i	0.210515	+	0.977591i	$0.432486\pi$
$757$	−404.547	+	1245.07i	−0.534409	+	1.64474i	−0.744924	+	0.667150i	$0.767514\pi$
$758$			945.721i			1.24765i
$759$	−260.937	+	74.4084i	−0.343790	+	0.0980347i
$760$	365.305			0.480665
$761$	797.003	+	258.962i	1.04731	+	0.340292i	0.781612	−	0.623765i	$-0.214398\pi$
$761$	797.003	+	258.962i	1.04731	+	0.340292i	0.265698	+	0.964056i	$0.414398\pi$
$762$	2324.30	−	1688.70i	3.05026	−	2.21615i
$763$	−44.9634	−	32.6678i	−0.0589297	−	0.0428149i
$764$	480.927	+	1480.14i	0.629485	+	1.93736i
$765$	368.860	−	119.850i	0.482170	−	0.156667i
$766$	−251.924	+	346.743i	−0.328882	+	0.452667i
$767$	136.555	+	187.952i	0.178038	+	0.245048i
$768$	−86.7568	+	267.010i	−0.112965	+	0.347669i
$769$			364.348i			0.473794i	0.971535	+	0.236897i	$0.0761304\pi$
$769$			364.348i			0.473794i	−0.971535	+	0.236897i	$0.923870\pi$
$770$	94.4527	+	140.476i	0.122666	+	0.182436i
$771$	−43.8142			−0.0568278
$772$	1721.54	+	559.363i	2.22998	+	0.724564i
$773$	805.587	−	585.293i	1.04216	−	0.757171i	0.0714511	−	0.997444i	$-0.477237\pi$
$773$	805.587	−	585.293i	1.04216	−	0.757171i	0.970705	+	0.240273i	$0.0772370\pi$
$774$	−3607.45	−	2620.97i	−4.66079	−	3.38626i
$775$	110.952	+	341.476i	0.143164	+	0.440614i
$776$	−3144.34	+	1021.66i	−4.05198	+	1.31657i
$777$	287.192	−	395.286i	0.369616	−	0.508733i
$778$	995.342	+	1369.97i	1.27936	+	1.76089i
$779$	−223.626	+	688.249i	−0.287068	+	0.883504i
$780$			118.914i			0.152454i
$781$	50.8894	−	1398.46i	0.0651593	−	1.79060i
$782$	−394.576			−0.504573
$783$	1495.93	+	486.058i	1.91052	+	0.620764i
$784$	−1175.90	+	854.339i	−1.49987	+	1.08972i
$785$	−15.7827	−	11.4668i	−0.0201053	−	0.0146074i
$786$	−348.857	−	1073.67i	−0.443839	−	1.36600i
$787$	−256.155	+	83.2299i	−0.325483	+	0.105756i	−0.467201	−	0.884151i	$-0.654737\pi$
$787$	−256.155	+	83.2299i	−0.325483	+	0.105756i	0.141718	+	0.989907i	$0.454737\pi$
$788$	245.246	−	337.552i	0.311226	−	0.428366i
$789$	433.033	+	596.019i	0.548838	+	0.755411i
$790$	62.7733	−	193.196i	0.0794598	−	0.244552i
$791$			232.037i			0.293346i
$792$	4344.52	+	158.095i	5.48551	+	0.199615i
$793$	134.207			0.169239
$794$	−829.608	−	269.556i	−1.04485	−	0.339491i
$795$	−208.549	+	151.520i	−0.262326	+	0.190591i
$796$	2507.66	+	1821.92i	3.15033	+	2.28885i
$797$	66.7147	+	205.327i	0.0837073	+	0.257625i	0.984147	−	0.177357i	$-0.0567548\pi$
$797$	66.7147	+	205.327i	0.0837073	+	0.257625i	−0.900439	+	0.434982i	$0.856755\pi$
$798$	1185.89	−	385.318i	1.48607	−	0.482854i
$799$	−905.494	+	1246.30i	−1.13328	+	1.55983i
$800$	−1083.03	−	1490.66i	−1.35378	−	1.86332i
$801$	238.333	−	733.515i	0.297545	−	0.915749i
$802$			1929.09i			2.40535i
$803$	−456.672	+	307.056i	−0.568708	+	0.382385i
$804$	6151.98			7.65172
$805$	−18.7309	−	6.08603i	−0.0232682	−	0.00756029i
$806$	103.281	−	75.0381i	0.128140	−	0.0930993i
$807$	−771.928	−	560.838i	−0.956540	−	0.694967i
$808$	−227.040	−	698.758i	−0.280990	−	0.864800i
$809$	230.355	−	74.8469i	0.284741	−	0.0925178i	−0.163165	−	0.986599i	$-0.552170\pi$
$809$	230.355	−	74.8469i	0.284741	−	0.0925178i	0.447905	+	0.894081i	$0.352170\pi$
$810$	148.423	−	204.286i	0.183238	−	0.252205i
$811$	485.253	+	667.894i	0.598339	+	0.823543i	0.995555	−	0.0941820i	$-0.0300236\pi$
$811$	485.253	+	667.894i	0.598339	+	0.823543i	−0.397216	+	0.917725i	$0.630024\pi$
$812$	−455.456	+	1401.75i	−0.560906	+	1.72629i
$813$			2746.81i			3.37861i
$814$	264.615	+	927.957i	0.325080	+	1.14000i
$815$	−53.7881			−0.0659976
$816$	4798.38	+	1559.09i	5.88037	+	1.91065i
$817$	879.263	−	638.822i	1.07621	−	0.781912i
$818$	338.574	+	245.989i	0.413905	+	0.300720i
$819$	49.7939	+	153.250i	0.0607984	+	0.187118i
$820$	−438.732	+	142.553i	−0.535039	+	0.173845i
$821$	169.554	−	233.371i	0.206521	−	0.284252i	−0.693175	−	0.720770i	$-0.743789\pi$
$821$	169.554	−	233.371i	0.206521	−	0.284252i	0.899695	+	0.436518i	$0.143789\pi$
$822$	−2695.67	−	3710.27i	−3.27941	−	4.51372i
$823$	79.0210	−	243.202i	0.0960158	−	0.295506i	−0.891501	−	0.453018i	$-0.850347\pi$
$823$	79.0210	−	243.202i	0.0960158	−	0.295506i	0.987517	+	0.157512i	$0.0503473\pi$
$824$		−	463.254i		−	0.562202i
$825$	836.715	−	1067.71i	1.01420	−	1.29420i
$826$	1552.91			1.88004
$827$	839.943	+	272.914i	1.01565	+	0.330005i	0.769102	−	0.639126i	$-0.220704\pi$
$827$	839.943	+	272.914i	1.01565	+	0.330005i	0.246548	+	0.969131i	$0.420704\pi$
$828$	−680.102	+	494.123i	−0.821379	+	0.596767i
$829$	281.893	+	204.807i	0.340039	+	0.247053i	0.744679	−	0.667423i	$-0.232603\pi$
$829$	281.893	+	204.807i	0.340039	+	0.247053i	−0.404639	+	0.914477i	$0.632603\pi$
$830$	23.7774	+	73.1792i	0.0286474	+	0.0881677i
$831$	888.858	−	288.808i	1.06962	−	0.347542i
$832$	−146.116	+	201.111i	−0.175620	+	0.241720i
$833$	−419.850	−	577.874i	−0.504022	−	0.693726i
$834$	856.349	−	2635.57i	1.02680	−	3.16016i
$835$		−	83.9844i		−	0.100580i
$836$	−604.754	+	1654.00i	−0.723390	+	1.97846i
$837$	−651.262			−0.778090
$838$	175.943	+	57.1674i	0.209956	+	0.0682188i
$839$	−229.624	+	166.832i	−0.273688	+	0.198846i	−0.716159	−	0.697937i	$-0.754102\pi$
$839$	−229.624	+	166.832i	−0.273688	+	0.198846i	0.442472	+	0.896782i	$0.354102\pi$
$840$	386.914	+	281.109i	0.460612	+	0.334654i
$841$	−144.360	−	444.294i	−0.171653	−	0.528292i
$842$	1139.36	−	370.201i	1.35316	−	0.439669i
$843$	−801.990	+	1103.84i	−0.951352	+	1.30942i
$844$	−1120.29	−	1541.95i	−1.32736	−	1.82695i
$845$	−51.2325	+	157.677i	−0.0606302	+	0.186600i
$846$			4589.43i			5.42486i
$847$	−476.771	+	117.388i	−0.562894	+	0.138592i
$848$	−2212.57			−2.60916
$849$	1877.55	+	610.053i	2.21148	+	0.718555i
$850$	1595.87	−	1159.47i	1.87750	−	1.36408i
$851$	−90.8271	−	65.9897i	−0.106730	−	0.0775437i
$852$	−2030.54	−	6249.36i	−2.38326	−	7.33493i
$853$	−44.4365	+	14.4383i	−0.0520943	+	0.0169265i	−0.334948	−	0.942237i	$-0.608719\pi$
$853$	−44.4365	+	14.4383i	−0.0520943	+	0.0169265i	0.282854	+	0.959163i	$0.408719\pi$
$854$	527.290	−	725.752i	0.617436	−	0.849827i
$855$	165.533	+	227.837i	0.193606	+	0.266476i
$856$	−589.004	+	1812.77i	−0.688089	+	2.11772i
$857$			1176.07i			1.37231i	0.727456	+	0.686155i	$0.240703\pi$
$857$			1176.07i			1.37231i	−0.727456	+	0.686155i	$0.759297\pi$
$858$	−452.986	−	165.626i	−0.527955	−	0.193038i
$859$	−874.921			−1.01853			−0.509267	−	0.860608i	$-0.670084\pi$
$859$	−874.921			−1.01853			−0.509267	+	0.860608i	$0.670084\pi$
$860$	658.902	+	214.090i	0.766165	+	0.248942i
$861$	−766.474	+	556.876i	−0.890214	+	0.646778i
$862$	−2265.90	−	1646.27i	−2.62865	−	1.90983i
$863$	−451.383	−	1389.21i	−0.523039	−	1.60975i	−0.768161	−	0.640257i	$-0.778828\pi$
$863$	−451.383	−	1389.21i	−0.523039	−	1.60975i	0.245122	−	0.969492i	$-0.421172\pi$
$864$	3178.55	−	1032.77i	3.67887	−	1.19534i
$865$	185.736	−	255.644i	0.214724	−	0.295542i
$866$	−1175.53	−	1617.98i	−1.35743	−	1.86834i
$867$	−306.847	+	944.376i	−0.353918	+	1.08925i
$868$		−	610.258i		−	0.703062i
$869$	463.786	+	363.446i	0.533701	+	0.418235i
$870$	−705.483			−0.810900
$871$	−257.693	−	83.7296i	−0.295859	−	0.0961304i
$872$	250.881	−	182.276i	0.287707	−	0.209032i
$873$	−2062.01	−	1498.14i	−2.36198	−	1.71608i
$874$	−88.5367	−	272.488i	−0.101301	−	0.311771i
$875$	191.283	−	62.1516i	0.218609	−	0.0710304i
$876$	−1518.84	+	2090.50i	−1.73383	+	2.38642i
$877$	576.287	+	793.191i	0.657112	+	0.904437i	0.999382	−	0.0351651i	$-0.0111957\pi$
$877$	576.287	+	793.191i	0.657112	+	0.904437i	−0.342270	+	0.939602i	$0.611196\pi$
$878$	139.617	−	429.697i	0.159017	−	0.489404i
$879$		−	2061.49i		−	2.34527i
$880$	−478.283	+	136.386i	−0.543503	+	0.154985i
$881$	−763.750			−0.866913			−0.433456	−	0.901175i	$-0.642706\pi$
$881$	−763.750			−0.866913			−0.433456	+	0.901175i	$0.642706\pi$
$882$	−2023.83	−	657.582i	−2.29459	−	0.745558i
$883$	−763.037	+	554.379i	−0.864142	+	0.627836i	−0.929009	−	0.370058i	$-0.879338\pi$
$883$	−763.037	+	554.379i	−0.864142	+	0.627836i	0.0648670	+	0.997894i	$0.479338\pi$
$884$	−405.790	−	294.824i	−0.459038	−	0.333511i
$885$	164.265	+	505.556i	0.185610	+	0.571249i
$886$	101.189	−	32.8783i	0.114209	−	0.0371087i
$887$	554.429	−	763.106i	0.625061	−	0.860322i	−0.372648	−	0.927973i	$-0.621550\pi$
$887$	554.429	−	763.106i	0.625061	−	0.860322i	0.997709	+	0.0676504i	$0.0215502\pi$
$888$	1602.44	+	2205.56i	1.80455	+	2.48374i
$889$	−186.917	+	575.272i	−0.210255	+	0.647100i
$890$			167.564i			0.188274i
$891$	408.685	+	607.822i	0.458682	+	0.682180i
$892$	2954.79			3.31254
$893$	−1063.86	−	345.668i	−1.19133	−	0.387086i
$894$	−1797.39	+	1305.88i	−2.01050	+	1.46071i
$895$	191.780	+	139.337i	0.214280	+	0.155683i
$896$	128.000	+	393.943i	0.142857	+	0.439668i
$897$	53.3692	−	17.3407i	0.0594975	−	0.0193319i
$898$	1212.83	−	1669.32i	1.35059	−	1.85893i
$899$	318.367	+	438.195i	0.354135	+	0.487425i
$900$	1298.70	−	3996.99i	1.44300	−	4.44110i
$901$		−	1087.33i		−	1.20680i
$902$	68.0425	−	1869.84i	0.0754351	−	2.07299i
$903$	1422.86			1.57570
$904$	−1231.32	−	400.081i	−1.36208	−	0.442567i
$905$	150.175	−	109.108i	0.165939	−	0.120562i
$906$	1916.26	+	1392.24i	2.11507	+	1.53669i
$907$	272.464	+	838.558i	0.300401	+	0.924540i	0.981353	+	0.192212i	$0.0615662\pi$
$907$	272.464	+	838.558i	0.300401	+	0.924540i	−0.680952	+	0.732328i	$0.738434\pi$
$908$	−49.7982	+	16.1804i	−0.0548438	+	0.0178198i
$909$	332.927	−	458.235i	0.366257	−	0.504109i
$910$	−20.5774	−	28.3223i	−0.0226125	−	0.0311234i
$911$	490.443	−	1509.43i	0.538357	−	1.65689i	−0.197924	−	0.980217i	$-0.563420\pi$
$911$	490.443	−	1509.43i	0.538357	−	1.65689i	0.736281	−	0.676676i	$-0.236580\pi$
$912$			3663.52i			4.01702i
$913$	−223.041	−	8.11638i	−0.244295	−	0.00888979i
$914$	−612.573			−0.670212
$915$	292.047	+	94.8920i	0.319178	+	0.103707i
$916$	2028.91	−	1474.09i	2.21497	−	1.60927i
$917$	192.289	+	139.706i	0.209694	+	0.152351i
$918$	1105.67	+	3402.90i	1.20443	+	3.70686i
$919$	95.9911	−	31.1894i	0.104452	−	0.0339384i	−0.256325	−	0.966591i	$-0.582512\pi$
$919$	95.9911	−	31.1894i	0.104452	−	0.0339384i	0.360777	+	0.932652i	$0.382512\pi$
$920$	64.5921	−	88.9034i	0.0702088	−	0.0966341i
$921$	649.765	+	894.324i	0.705499	+	0.971036i
$922$	454.805	−	1399.75i	0.493281	−	1.51816i
$923$			289.408i			0.313552i
$924$	−1913.31	+	1286.46i	−2.07068	+	1.39228i
$925$	561.265			0.606772
$926$	982.073	+	319.095i	1.06055	+	0.344595i
$927$	288.926	−	209.917i	0.311679	−	0.226448i
$928$	−2248.71	−	1633.79i	−2.42318	−	1.76055i
$929$	−6.22059	−	19.1450i	−0.00669600	−	0.0206082i	0.947653	−	0.319303i	$-0.103449\pi$
$929$	−6.22059	−	19.1450i	−0.00669600	−	0.0206082i	−0.954349	+	0.298695i	$0.903449\pi$
$930$	277.806	−	90.2648i	0.298717	−	0.0970589i
$931$	304.863	−	419.608i	0.327458	−	0.450707i
$932$	−667.150	−	918.253i	−0.715826	−	0.985250i
$933$	−216.087	+	665.048i	−0.231605	+	0.712806i
$934$		−	2072.99i		−	2.21948i
$935$	−67.0248	−	235.044i	−0.0716842	−	0.251384i
$936$	−899.088			−0.960564
$937$	977.550	+	317.625i	1.04328	+	0.338981i	0.780026	−	0.625746i	$-0.215206\pi$
$937$	977.550	+	317.625i	1.04328	+	0.338981i	0.263250	+	0.964728i	$0.415206\pi$
$938$	−1465.25	+	1064.56i	−1.56210	+	1.13493i
$939$	−196.936	−	143.082i	−0.209729	−	0.152377i
$940$	−220.350	−	678.167i	−0.234415	−	0.721455i
$941$	692.340	−	224.955i	0.735749	−	0.239059i	0.0829109	−	0.996557i	$-0.473578\pi$
$941$	692.340	−	224.955i	0.735749	−	0.239059i	0.652838	+	0.757498i	$0.273578\pi$
$942$	218.389	−	300.586i	0.231835	−	0.319094i
$943$	127.957	+	176.117i	0.135691	+	0.186763i
$944$	−1409.91	+	4339.26i	−1.49355	+	4.59667i
$945$			178.593i			0.188987i
$946$	−1733.28	+	2211.80i	−1.83222	+	2.33805i
$947$	413.470			0.436610			0.218305	−	0.975881i	$-0.429947\pi$
$947$	413.470			0.436610			0.218305	+	0.975881i	$0.429947\pi$
$948$	2631.37	+	854.983i	2.77570	+	0.901881i
$949$	92.0729	−	66.8949i	0.0970210	−	0.0704899i
$950$	1158.80	+	841.917i	1.21979	+	0.886229i
$951$	312.518	+	961.831i	0.328620	+	1.01139i
$952$	−1918.55	+	623.375i	−2.01528	+	0.654805i
$953$	−715.373	+	984.627i	−0.750654	+	1.03319i	0.247280	+	0.968944i	$0.420463\pi$
$953$	−715.373	+	984.627i	−0.750654	+	1.03319i	−0.997934	+	0.0642429i	$0.979537\pi$
$954$	−1904.02	−	2620.66i	−1.99583	−	2.74702i
$955$	48.4655	−	149.162i	0.0507493	−	0.156190i
$956$		−	1844.78i		−	1.92968i
$957$	702.710	−	1921.90i	0.734284	−	2.00826i
$958$	1358.01			1.41755
$959$	918.304	+	298.375i	0.957564	+	0.311131i
$960$	−460.160	+	334.326i	−0.479333	+	0.348256i
$961$	596.032	+	433.043i	0.620221	+	0.450617i
$962$	−61.6679	−	189.794i	−0.0641039	−	0.197291i
$963$	−1397.50	+	454.076i	−1.45120	+	0.471522i
$964$	−605.397	+	833.258i	−0.628005	+	0.864375i
$965$	−107.222	−	147.579i	−0.111111	−	0.152931i
$966$	115.911	−	356.737i	0.119990	−	0.369292i
$967$			385.117i			0.398259i	0.979973	+	0.199130i	$0.0638115\pi$
$967$			385.117i			0.398259i	−0.979973	+	0.199130i	$0.936189\pi$
$968$	199.127	−	2732.43i	0.205710	−	2.82275i
$969$	−1800.38			−1.85797
$970$	526.644	+	171.117i	0.542932	+	0.176409i
$971$	−221.829	+	161.168i	−0.228455	+	0.165982i	−0.696124	−	0.717921i	$-0.745094\pi$
$971$	−221.829	+	161.168i	−0.228455	+	0.165982i	0.467670	+	0.883903i	$0.345094\pi$
$972$	−397.420	−	288.743i	−0.408869	−	0.297060i
$973$	180.295	+	554.889i	0.185298	+	0.570287i
$974$	−169.645	+	55.1210i	−0.174174	+	0.0565924i
$975$	−164.897	+	226.961i	−0.169125	+	0.232781i
$976$	1549.22	+	2132.31i	1.58731	+	2.18475i
$977$	220.138	−	677.514i	0.225320	−	0.693464i	−0.772939	−	0.634481i	$-0.781214\pi$
$977$	220.138	−	677.514i	0.225320	−	0.693464i	0.998259	−	0.0589835i	$-0.0187859\pi$
$978$		−	1024.41i		−	1.04746i
$979$	−456.484	−	166.905i	−0.466276	−	0.170485i
$980$	330.628			0.337375
$981$	227.366	+	73.8758i	0.231770	+	0.0753066i
$982$	−138.390	+	100.546i	−0.140927	+	0.102390i
$983$	−1105.14	−	802.930i	−1.12425	−	0.816816i	−0.139403	−	0.990236i	$-0.544518\pi$
$983$	−1105.14	−	802.930i	−1.12425	−	0.816816i	−0.984848	+	0.173419i	$0.944518\pi$
$984$	−1633.54	−	5027.53i	−1.66011	−	5.10928i
$985$	−39.9893	+	12.9933i	−0.0405983	+	0.0131912i
$986$	1749.10	−	2407.43i	1.77394	−	2.44162i
$987$	−860.788	−	1184.77i	−0.872126	−	1.20038i
$988$	112.548	−	346.386i	0.113915	−	0.350593i
$989$		−	326.938i		−	0.330575i
$990$	−573.127	−	449.131i	−0.578916	−	0.453668i
$991$	1078.77			1.08857			0.544283	−	0.838902i	$-0.316802\pi$
$991$	1078.77			1.08857			0.544283	+	0.838902i	$0.316802\pi$
$992$	1094.54	+	355.638i	1.10337	+	0.358506i
$993$	838.109	−	608.922i	0.844017	−	0.613215i
$994$	1565.04	+	1137.07i	1.57449	+	1.14393i
$995$	−96.5268	−	297.079i	−0.0970119	−	0.298572i
$996$	−996.714	+	323.852i	−1.00072	+	0.325153i
$997$	993.144	−	1366.94i	0.996132	−	1.37106i	0.0684633	−	0.997654i	$-0.478190\pi$
$997$	993.144	−	1366.94i	0.996132	−	1.37106i	0.927669	−	0.373404i	$-0.121810\pi$
$998$	1384.30	+	1905.33i	1.38707	+	1.90914i
$999$	−314.595	+	968.224i	−0.314910	+	0.969193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	253.3.g.a.24.2	✓	176
11.6	odd	10	inner	253.3.g.a.116.2	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.3.g.a.24.2	✓	176	1.1	even	1	trivial
253.3.g.a.116.2	yes	176	11.6	odd	10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 253 = 11 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	253.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.56389 - 1.15798i) q^{2} +(-4.16114 + 3.02325i) q^{3} +(8.12432 + 5.90266i) q^{4} +(-0.312727 - 0.962476i) q^{5} +(18.3307 - 5.95601i) q^{6} +(-2.38519 + 3.28293i) q^{7} +(-13.3086 - 18.3177i) q^{8} +(5.39393 - 16.6008i) q^{9} +3.79229i q^{10} +(-10.3311 - 3.77738i) q^{11} -51.6516 q^{12} +(2.16358 + 0.702988i) q^{13} +(12.3021 - 8.93801i) q^{14} +(4.21111 + 3.05955i) q^{15} +(13.8060 + 42.4904i) q^{16} +(-20.8812 + 6.78471i) q^{17} +(-38.4468 + 52.9174i) q^{18} +(-9.37083 - 12.8978i) q^{19} +(3.14047 - 9.66538i) q^{20} -20.8718i q^{21} +(32.4447 + 25.4253i) q^{22} -4.79583 q^{23} +(110.758 + 35.9874i) q^{24} +(19.3969 - 14.0926i) q^{25} +(-6.89669 - 5.01074i) q^{26} +(13.4387 + 41.3602i) q^{27} +(-38.7561 + 12.5926i) q^{28} +(21.2593 - 29.2609i) q^{29} +(-11.4650 - 15.7803i) q^{30} +(-4.62767 + 14.2425i) q^{31} -76.8505i q^{32} +(54.4091 - 15.5152i) q^{33} +82.2747 q^{34} +(3.90566 + 1.26903i) q^{35} +(141.811 - 103.032i) q^{36} +(18.9388 + 13.7598i) q^{37} +(18.4612 + 56.8176i) q^{38} +(-11.1283 + 3.61579i) q^{39} +(-13.4684 + 18.5376i) q^{40} +(-26.6808 - 36.7230i) q^{41} +(-24.1691 + 74.3847i) q^{42} +68.1713i q^{43} +(-61.6364 - 91.6695i) q^{44} -17.6647 q^{45} +(17.0918 + 5.55346i) q^{46} +(56.7643 - 41.2417i) q^{47} +(-185.908 - 135.070i) q^{48} +(10.0533 + 30.9409i) q^{49} +(-85.4472 + 27.7635i) q^{50} +(66.3778 - 91.3611i) q^{51} +(13.4281 + 18.4821i) q^{52} +(-15.3036 + 47.0997i) q^{53} -162.965i q^{54} +(-0.404824 + 11.1247i) q^{55} +91.8793 q^{56} +(77.9867 + 25.3394i) q^{57} +(-109.649 + 79.6648i) q^{58} +(82.6193 + 60.0265i) q^{59} +(16.1529 + 49.7135i) q^{60} +(56.1067 - 18.2302i) q^{61} +(32.9850 - 45.3999i) q^{62} +(41.6339 + 57.3041i) q^{63} +(-33.7672 + 103.925i) q^{64} -2.30223i q^{65} +(-211.874 - 7.71001i) q^{66} -119.105 q^{67} +(-209.693 - 68.1334i) q^{68} +(19.9561 - 14.4990i) q^{69} +(-12.4498 - 9.04533i) q^{70} +(39.3122 + 120.991i) q^{71} +(-375.875 + 122.129i) q^{72} +(29.4054 - 40.4731i) q^{73} +(-51.5620 - 70.9691i) q^{74} +(-38.1076 + 117.283i) q^{75} -160.099i q^{76} +(37.0425 - 24.9065i) q^{77} +43.8468 q^{78} +(-50.9445 - 16.5529i) q^{79} +(36.5785 - 26.5758i) q^{80} +(-53.8689 - 39.1381i) q^{81} +(52.5630 + 161.772i) q^{82} +(19.2968 - 6.26992i) q^{83} +(123.199 - 169.569i) q^{84} +(13.0602 + 17.9759i) q^{85} +(78.9409 - 242.955i) q^{86} +186.031i q^{87} +(68.2993 + 239.513i) q^{88} +44.1854 q^{89} +(62.9551 + 20.4554i) q^{90} +(-7.46841 + 5.42611i) q^{91} +(-38.9628 - 28.3082i) q^{92} +(-23.8022 - 73.2556i) q^{93} +(-250.059 + 81.2490i) q^{94} +(-9.48334 + 13.0527i) q^{95} +(232.338 + 319.786i) q^{96} +(45.1224 - 138.872i) q^{97} -121.911i q^{98} +(-118.433 + 151.130i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 8 q^{3} + 88 q^{4} - 40 q^{6} - 120 q^{9} - 8 q^{14} - 12 q^{15} - 272 q^{16} - 80 q^{17} + 80 q^{18} - 60 q^{19} + 40 q^{20} + 136 q^{22} - 60 q^{24} - 268 q^{25} + 40 q^{26} + 148 q^{27} - 240 q^{28}+ \cdots - 414 q^{99}+O(q^{100}) \) 176 * q - 8 * q^3 + 88 * q^4 - 40 * q^6 - 120 * q^9 - 8 * q^14 - 12 * q^15 - 272 * q^16 - 80 * q^17 + 80 * q^18 - 60 * q^19 + 40 * q^20 + 136 * q^22 - 60 * q^24 - 268 * q^25 + 40 * q^26 + 148 * q^27 - 240 * q^28 + 160 * q^29 + 240 * q^30 + 108 * q^31 - 160 * q^33 - 420 * q^34 + 150 * q^35 + 32 * q^36 + 96 * q^37 + 70 * q^38 - 320 * q^39 + 270 * q^40 - 362 * q^42 + 174 * q^44 + 180 * q^45 - 138 * q^47 - 182 * q^48 + 464 * q^49 + 410 * q^50 + 500 * q^51 - 70 * q^52 - 130 * q^53 + 88 * q^55 + 472 * q^56 - 100 * q^57 + 468 * q^58 - 126 * q^59 - 376 * q^60 - 570 * q^62 - 160 * q^63 + 1096 * q^64 - 562 * q^66 - 472 * q^67 - 480 * q^68 + 380 * q^70 - 264 * q^71 + 1050 * q^72 - 840 * q^73 + 530 * q^74 - 64 * q^75 + 326 * q^77 - 576 * q^78 + 90 * q^79 + 274 * q^80 - 276 * q^81 - 132 * q^82 + 180 * q^83 - 1120 * q^84 + 360 * q^85 - 704 * q^86 + 272 * q^88 + 340 * q^89 + 1600 * q^90 + 514 * q^91 - 838 * q^93 - 690 * q^94 - 520 * q^95 - 1240 * q^96 + 832 * q^97 - 414 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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