LMFDB - Embedded newform 322.4.e.b.93.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [322,4,Mod(93,322)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(322, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("322.93"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	322.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22,-22,6,-44,27] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$18.9986150218$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.10
Character	$\chi$	$=$	322.93
Dual form			322.4.e.b.277.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.73205i) q^{2} +(3.73605 + 6.47103i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(2.65469 - 4.59806i) q^{5} -14.9442 q^{6} +(9.31488 - 16.0073i) q^{7} +8.00000 q^{8} +(-14.4162 + 24.9695i) q^{9} +(5.30939 + 9.19613i) q^{10} +(-7.53617 - 13.0530i) q^{11} +(14.9442 - 25.8841i) q^{12} +19.5834 q^{13} +(18.4105 + 32.1411i) q^{14} +39.6723 q^{15} +(-8.00000 + 13.8564i) q^{16} +(57.4595 + 99.5228i) q^{17} +(-28.8323 - 49.9390i) q^{18} +(-25.9174 + 44.8903i) q^{19} -21.2376 q^{20} +(138.384 + 0.472845i) q^{21} +30.1447 q^{22} +(11.5000 - 19.9186i) q^{23} +(29.8884 + 51.7682i) q^{24} +(48.4052 + 83.8403i) q^{25} +(-19.5834 + 33.9194i) q^{26} -13.6912 q^{27} +(-74.0806 - 0.253126i) q^{28} +227.585 q^{29} +(-39.6723 + 68.7144i) q^{30} +(89.0122 + 154.174i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(56.3110 - 97.5336i) q^{33} -229.838 q^{34} +(-48.8744 - 85.3248i) q^{35} +115.329 q^{36} +(-10.3699 + 17.9612i) q^{37} +(-51.8349 - 89.7806i) q^{38} +(73.1644 + 126.725i) q^{39} +(21.2376 - 36.7845i) q^{40} -107.492 q^{41} +(-139.203 + 239.216i) q^{42} +138.795 q^{43} +(-30.1447 + 52.2121i) q^{44} +(76.5410 + 132.573i) q^{45} +(23.0000 + 39.8372i) q^{46} +(-10.7254 + 18.5769i) q^{47} -119.554 q^{48} +(-169.466 - 298.212i) q^{49} -193.621 q^{50} +(-429.343 + 743.644i) q^{51} +(-39.1667 - 67.8387i) q^{52} +(-214.602 - 371.701i) q^{53} +(13.6912 - 23.7139i) q^{54} -80.0249 q^{55} +(74.5190 - 128.058i) q^{56} -387.316 q^{57} +(-227.585 + 394.189i) q^{58} +(-64.2821 - 111.340i) q^{59} +(-79.3446 - 137.429i) q^{60} +(-112.966 + 195.662i) q^{61} -356.049 q^{62} +(265.409 + 463.351i) q^{63} +64.0000 q^{64} +(51.9878 - 90.0455i) q^{65} +(112.622 + 195.067i) q^{66} +(-239.358 - 414.580i) q^{67} +(229.838 - 398.091i) q^{68} +171.858 q^{69} +(196.661 + 0.671971i) q^{70} +652.010 q^{71} +(-115.329 + 199.756i) q^{72} +(258.209 + 447.231i) q^{73} +(-20.7398 - 35.9223i) q^{74} +(-361.689 + 626.463i) q^{75} +207.340 q^{76} +(-279.142 - 0.953799i) q^{77} -292.658 q^{78} +(174.698 - 302.586i) q^{79} +(42.4751 + 73.5690i) q^{80} +(338.085 + 585.581i) q^{81} +(107.492 - 186.181i) q^{82} +373.014 q^{83} +(-275.131 - 480.324i) q^{84} +610.150 q^{85} +(-138.795 + 240.399i) q^{86} +(850.269 + 1472.71i) q^{87} +(-60.2894 - 104.424i) q^{88} +(-448.347 + 776.560i) q^{89} -306.164 q^{90} +(182.417 - 313.476i) q^{91} -92.0000 q^{92} +(-665.108 + 1152.00i) q^{93} +(-21.4507 - 37.1537i) q^{94} +(137.606 + 238.340i) q^{95} +(119.554 - 207.073i) q^{96} -1294.92 q^{97} +(685.984 + 4.68793i) q^{98} +434.570 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{2} + 6 q^{3} - 44 q^{4} + 27 q^{5} - 24 q^{6} + q^{7} + 176 q^{8} - 59 q^{9} + 54 q^{10} - 56 q^{11} + 24 q^{12} - 206 q^{13} - 64 q^{14} + 124 q^{15} - 176 q^{16} + 157 q^{17} - 118 q^{18}+ \cdots + 202 q^{99}+O(q^{100}) $ 22 * q - 22 * q^2 + 6 * q^3 - 44 * q^4 + 27 * q^5 - 24 * q^6 + q^7 + 176 * q^8 - 59 * q^9 + 54 * q^10 - 56 * q^11 + 24 * q^12 - 206 * q^13 - 64 * q^14 + 124 * q^15 - 176 * q^16 + 157 * q^17 - 118 * q^18 + 266 * q^19 - 216 * q^20 - 137 * q^21 + 224 * q^22 + 253 * q^23 + 48 * q^24 - 142 * q^25 + 206 * q^26 - 1062 * q^27 + 124 * q^28 - 390 * q^29 - 124 * q^30 + 316 * q^31 - 352 * q^32 + 682 * q^33 - 628 * q^34 + 539 * q^35 + 472 * q^36 - 347 * q^37 + 532 * q^38 + 99 * q^39 + 216 * q^40 - 1080 * q^41 + 116 * q^42 + 386 * q^43 - 224 * q^44 + 609 * q^45 + 506 * q^46 + 731 * q^47 - 192 * q^48 + 505 * q^49 + 568 * q^50 + 303 * q^51 + 412 * q^52 - 413 * q^53 + 1062 * q^54 - 3618 * q^55 + 8 * q^56 + 686 * q^57 + 390 * q^58 + 1061 * q^59 - 248 * q^60 + 1157 * q^61 - 1264 * q^62 - 557 * q^63 + 1408 * q^64 + 37 * q^65 + 1364 * q^66 + 841 * q^67 + 628 * q^68 + 276 * q^69 - 632 * q^70 + 1738 * q^71 - 472 * q^72 + 409 * q^73 - 694 * q^74 + 2024 * q^75 - 2128 * q^76 + 565 * q^77 - 396 * q^78 - 247 * q^79 + 432 * q^80 - 1019 * q^81 + 1080 * q^82 - 5726 * q^83 + 316 * q^84 + 1570 * q^85 - 386 * q^86 + 670 * q^87 - 448 * q^88 + 1610 * q^89 - 2436 * q^90 - 1766 * q^91 - 2024 * q^92 + 1290 * q^93 + 1462 * q^94 + 209 * q^95 + 192 * q^96 - 3566 * q^97 - 166 * q^98 + 202 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$3$	3.73605	+	6.47103i	0.719003	+	1.24535i	0.961395	+	0.275172i	$0.0887348\pi$
$3$	3.73605	+	6.47103i	0.719003	+	1.24535i	−0.242392	+	0.970178i	$0.577932\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	2.65469	−	4.59806i	0.237443	−	0.411263i	−0.722537	−	0.691332i	$-0.757024\pi$
$5$	2.65469	−	4.59806i	0.237443	−	0.411263i	0.959980	+	0.280069i	$0.0903574\pi$
$6$	−14.9442			−1.01682
$7$	9.31488	−	16.0073i	0.502956	−	0.864312i
$7$	9.31488	−	16.0073i	0.502956	−	0.864312i
$8$	8.00000			0.353553
$9$	−14.4162	+	24.9695i	−0.533932	+	0.924797i
$10$	5.30939	+	9.19613i	0.167898	+	0.290807i
$11$	−7.53617	−	13.0530i	−0.206567	−	0.357785i	0.744064	−	0.668109i	$-0.232896\pi$
$11$	−7.53617	−	13.0530i	−0.206567	−	0.357785i	−0.950631	+	0.310324i	$0.899563\pi$
$12$	14.9442	−	25.8841i	0.359502	−	0.622675i
$13$	19.5834			0.417804			0.208902	−	0.977937i	$-0.433011\pi$
$13$	19.5834			0.417804			0.208902	+	0.977937i	$0.433011\pi$
$14$	18.4105	+	32.1411i	0.351459	+	0.613577i
$15$	39.6723			0.682889
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	57.4595	+	99.5228i	0.819763	+	1.41987i	0.905856	+	0.423585i	$0.139228\pi$
$17$	57.4595	+	99.5228i	0.819763	+	1.41987i	−0.0860930	+	0.996287i	$0.527438\pi$
$18$	−28.8323	−	49.9390i	−0.377547	−	0.653930i
$19$	−25.9174	+	44.8903i	−0.312940	+	0.542029i	−0.978998	−	0.203872i	$-0.934647\pi$
$19$	−25.9174	+	44.8903i	−0.312940	+	0.542029i	0.666057	+	0.745901i	$0.267981\pi$
$20$	−21.2376			−0.237443
$21$	138.384	+	0.472845i	1.43800	+	0.00491349i
$22$	30.1447			0.292130
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$24$	29.8884	+	51.7682i	0.254206	+	0.440298i
$25$	48.4052	+	83.8403i	0.387242	+	0.670722i
$26$	−19.5834	+	33.9194i	−0.147716	+	0.255851i
$27$	−13.6912			−0.0975881
$28$	−74.0806	−	0.253126i	−0.499997	−	0.00170844i
$29$	227.585			1.45729			0.728646	−	0.684890i	$-0.240150\pi$
$29$	227.585			1.45729			0.728646	+	0.684890i	$0.240150\pi$
$30$	−39.6723	+	68.7144i	−0.241438	+	0.418183i
$31$	89.0122	+	154.174i	0.515712	+	0.893239i	0.999834	+	0.0182383i	$0.00580574\pi$
$31$	89.0122	+	154.174i	0.515712	+	0.893239i	−0.484122	+	0.875000i	$0.660861\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	56.3110	−	97.5336i	0.297045	−	0.514497i
$34$	−229.838			−1.15932
$35$	−48.8744	−	85.3248i	−0.236036	−	0.412072i
$36$	115.329			0.533932
$37$	−10.3699	+	17.9612i	−0.0460756	+	0.0798054i	−0.888143	−	0.459566i	$-0.848005\pi$
$37$	−10.3699	+	17.9612i	−0.0460756	+	0.0798054i	0.842068	+	0.539372i	$0.181338\pi$
$38$	−51.8349	−	89.7806i	−0.221282	−	0.383272i
$39$	73.1644	+	126.725i	0.300402	+	0.520312i
$40$	21.2376	−	36.7845i	0.0839488	−	0.145404i
$41$	−107.492			−0.409449			−0.204724	−	0.978820i	$-0.565630\pi$
$41$	−107.492			−0.409449			−0.204724	+	0.978820i	$0.565630\pi$
$42$	−139.203	+	239.216i	−0.511418	+	0.878853i
$43$	138.795			0.492232			0.246116	−	0.969240i	$-0.420846\pi$
$43$	138.795			0.492232			0.246116	+	0.969240i	$0.420846\pi$
$44$	−30.1447	+	52.2121i	−0.103284	+	0.178893i
$45$	76.5410	+	132.573i	0.253557	+	0.439173i
$46$	23.0000	+	39.8372i	0.0737210	+	0.127688i
$47$	−10.7254	+	18.5769i	−0.0332863	+	0.0576535i	−0.882189	−	0.470896i	$-0.843931\pi$
$47$	−10.7254	+	18.5769i	−0.0332863	+	0.0576535i	0.848902	+	0.528550i	$0.177264\pi$
$48$	−119.554			−0.359502
$49$	−169.466	−	298.212i	−0.494070	−	0.869422i
$50$	−193.621			−0.547642
$51$	−429.343	+	743.644i	−1.17883	+	2.04179i
$52$	−39.1667	−	67.8387i	−0.104451	−	0.180914i
$53$	−214.602	−	371.701i	−0.556185	−	0.963341i	−0.997810	−	0.0661410i	$-0.978931\pi$
$53$	−214.602	−	371.701i	−0.556185	−	0.963341i	0.441625	−	0.897200i	$-0.354402\pi$
$54$	13.6912	−	23.7139i	0.0345026	−	0.0597603i
$55$	−80.0249			−0.196192
$56$	74.5190	−	128.058i	0.177822	−	0.305580i
$57$	−387.316			−0.900021
$58$	−227.585	+	394.189i	−0.515231	+	0.892406i
$59$	−64.2821	−	111.340i	−0.141844	−	0.245682i	0.786347	−	0.617785i	$-0.211970\pi$
$59$	−64.2821	−	111.340i	−0.141844	−	0.245682i	−0.928191	+	0.372104i	$0.878637\pi$
$60$	−79.3446	−	137.429i	−0.170722	−	0.295700i
$61$	−112.966	+	195.662i	−0.237111	+	0.410688i	−0.959884	−	0.280397i	$-0.909534\pi$
$61$	−112.966	+	195.662i	−0.237111	+	0.410688i	0.722773	+	0.691085i	$0.242867\pi$
$62$	−356.049			−0.729326
$63$	265.409	+	463.351i	0.530769	+	0.926616i
$64$	64.0000			0.125000
$65$	51.9878	−	90.0455i	0.0992046	−	0.171827i
$66$	112.622	+	195.067i	0.210043	+	0.363805i
$67$	−239.358	−	414.580i	−0.436451	−	0.755955i	0.560962	−	0.827842i	$-0.310431\pi$
$67$	−239.358	−	414.580i	−0.436451	−	0.755955i	−0.997413	+	0.0718863i	$0.977098\pi$
$68$	229.838	−	398.091i	0.409882	−	0.709936i
$69$	171.858			0.299845
$70$	196.661	+	0.671971i	0.335793	+	0.00114737i
$71$	652.010			1.08985			0.544925	−	0.838485i	$-0.316558\pi$
$71$	652.010			1.08985			0.544925	+	0.838485i	$0.316558\pi$
$72$	−115.329	+	199.756i	−0.188773	+	0.326965i
$73$	258.209	+	447.231i	0.413987	+	0.717047i	0.995322	−	0.0966178i	$-0.0308025\pi$
$73$	258.209	+	447.231i	0.413987	+	0.717047i	−0.581334	+	0.813665i	$0.697469\pi$
$74$	−20.7398	−	35.9223i	−0.0325804	−	0.0564309i
$75$	−361.689	+	626.463i	−0.556856	+	0.964503i
$76$	207.340			0.312940
$77$	−279.142	−	0.953799i	−0.413132	−	0.00141163i
$78$	−292.658			−0.424833
$79$	174.698	−	302.586i	0.248799	−	0.430932i	−0.714394	−	0.699744i	$-0.753298\pi$
$79$	174.698	−	302.586i	0.248799	−	0.430932i	0.963193	+	0.268812i	$0.0866309\pi$
$80$	42.4751	+	73.5690i	0.0593608	+	0.102816i
$81$	338.085	+	585.581i	0.463766	+	0.803265i
$82$	107.492	−	186.181i	0.144762	−	0.250735i
$83$	373.014			0.493297			0.246649	−	0.969105i	$-0.420671\pi$
$83$	373.014			0.493297			0.246649	+	0.969105i	$0.420671\pi$
$84$	−275.131	−	480.324i	−0.357372	−	0.623900i
$85$	610.150			0.778588
$86$	−138.795	+	240.399i	−0.174030	+	0.301430i
$87$	850.269	+	1472.71i	1.04780	+	1.81484i
$88$	−60.2894	−	104.424i	−0.0730326	−	0.126496i
$89$	−448.347	+	776.560i	−0.533985	+	0.924890i	0.465226	+	0.885192i	$0.345973\pi$
$89$	−448.347	+	776.560i	−0.533985	+	0.924890i	−0.999212	+	0.0396981i	$0.987360\pi$
$90$	−306.164			−0.358583
$91$	182.417	−	313.476i	0.210137	−	0.361113i
$92$	−92.0000			−0.104257
$93$	−665.108	+	1152.00i	−0.741597	+	1.28448i
$94$	−21.4507	−	37.1537i	−0.0235369	−	0.0407672i
$95$	137.606	+	238.340i	0.148611	+	0.257402i
$96$	119.554	−	207.073i	0.127103	−	0.220149i
$97$	−1294.92			−1.35546			−0.677729	−	0.735312i	$-0.737036\pi$
$97$	−1294.92			−1.35546			−0.677729	+	0.735312i	$0.737036\pi$
$98$	685.984	+	4.68793i	0.707090	+	0.00483216i
$99$	434.570			0.441171
$100$	193.621	−	335.361i	0.193621	−	0.335361i
$101$	−154.615	−	267.801i	−0.152325	−	0.263834i	0.779757	−	0.626082i	$-0.215343\pi$
$101$	−154.615	−	267.801i	−0.152325	−	0.263834i	−0.932082	+	0.362248i	$0.882009\pi$
$102$	−858.687	−	1487.29i	−0.833555	−	1.44376i
$103$	−308.814	+	534.882i	−0.295421	+	0.511684i	−0.975083	−	0.221842i	$-0.928793\pi$
$103$	−308.814	+	534.882i	−0.295421	+	0.511684i	0.679662	+	0.733526i	$0.262127\pi$
$104$	156.667			0.147716
$105$	369.543	−	635.045i	0.343463	−	0.590229i
$106$	858.407			0.786564
$107$	612.602	−	1061.06i	0.553481	−	0.958657i	−0.444539	−	0.895759i	$-0.646633\pi$
$107$	612.602	−	1061.06i	0.553481	−	0.958657i	0.998020	−	0.0628975i	$-0.0200341\pi$
$108$	27.3825	+	47.4278i	0.0243970	+	0.0422569i
$109$	−78.6223	−	136.178i	−0.0690886	−	0.119665i	0.829412	−	0.558638i	$-0.188676\pi$
$109$	−78.6223	−	136.178i	−0.0690886	−	0.119665i	−0.898500	+	0.438973i	$0.855342\pi$
$110$	80.0249	−	138.607i	0.0693643	−	0.120143i
$111$	−154.970			−0.132514
$112$	147.284	+	257.129i	0.124259	+	0.216932i
$113$	−1226.97			−1.02145			−0.510723	−	0.859745i	$-0.670622\pi$
$113$	−1226.97			−1.02145			−0.510723	+	0.859745i	$0.670622\pi$
$114$	387.316	−	670.850i	0.318205	−	0.551148i
$115$	−61.0580	−	105.755i	−0.0495103	−	0.0857543i
$116$	−455.170	−	788.378i	−0.364323	−	0.631026i
$117$	−282.317	+	488.987i	−0.223079	+	0.386383i
$118$	257.128			0.200598
$119$	2128.32	+	7.27224i	1.63952	+	0.00560206i
$120$	317.378			0.241438
$121$	551.912	−	955.940i	0.414660	−	0.718212i
$122$	−225.931	−	391.324i	−0.167663	−	0.290400i
$123$	−401.595	−	695.583i	−0.294395	−	0.509907i
$124$	356.049	−	616.695i	0.257856	−	0.446619i
$125$	1177.68			0.842677
$126$	−1067.96	−	3.64910i	−0.755089	−	0.00258006i
$127$	1229.19			0.858840			0.429420	−	0.903105i	$-0.358718\pi$
$127$	1229.19			0.858840			0.429420	+	0.903105i	$0.358718\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	518.544	+	898.145i	0.353917	+	0.613002i
$130$	103.976	+	180.091i	0.0701482	+	0.121500i
$131$	1210.47	−	2096.59i	0.807321	−	1.39832i	−0.107393	−	0.994217i	$-0.534250\pi$
$131$	1210.47	−	2096.59i	0.807321	−	1.39832i	0.914713	−	0.404104i	$-0.132417\pi$
$132$	−450.488			−0.297045
$133$	477.154	+	833.016i	0.311087	+	0.543095i
$134$	957.432			0.617235
$135$	−36.3460	+	62.9532i	−0.0231716	+	0.0401344i
$136$	459.676	+	796.182i	0.289830	+	0.502001i
$137$	−1601.35	−	2773.63i	−0.998635	−	1.72969i	−0.544556	−	0.838724i	$-0.683302\pi$
$137$	−1601.35	−	2773.63i	−0.998635	−	1.72969i	−0.454078	−	0.890962i	$-0.650031\pi$
$138$	−171.858	+	297.667i	−0.106011	+	0.183617i
$139$	−1710.35			−1.04367			−0.521833	−	0.853048i	$-0.674752\pi$
$139$	−1710.35			−1.04367			−0.521833	+	0.853048i	$0.674752\pi$
$140$	−197.825	+	339.955i	−0.119423	+	0.205225i
$141$	−160.282			−0.0957317
$142$	−652.010	+	1129.32i	−0.385320	+	0.667395i
$143$	−147.584	−	255.622i	−0.0863046	−	0.149484i
$144$	−230.659	−	399.512i	−0.133483	−	0.231199i
$145$	604.169	−	1046.45i	0.346024	−	0.599331i
$146$	−1032.84			−0.585466
$147$	1296.60	−	2210.75i	0.727497	−	1.24041i
$148$	82.9591			0.0460756
$149$	1323.72	−	2292.75i	0.727807	−	1.26060i	−0.230001	−	0.973191i	$-0.573873\pi$
$149$	1323.72	−	2292.75i	0.727807	−	1.26060i	0.957808	−	0.287409i	$-0.0927939\pi$
$150$	−723.377	−	1252.93i	−0.393757	−	0.682007i
$151$	505.407	+	875.391i	0.272381	+	0.471777i	0.969471	−	0.245206i	$-0.0788557\pi$
$151$	505.407	+	875.391i	0.272381	+	0.471777i	−0.697090	+	0.716983i	$0.745522\pi$
$152$	−207.340	+	359.123i	−0.110641	+	0.191636i
$153$	−3313.38			−1.75079
$154$	280.794	−	482.534i	0.146929	−	0.252492i
$155$	945.200			0.489809
$156$	292.658	−	506.898i	0.150201	−	0.260156i
$157$	−38.3946	−	66.5013i	−0.0195173	−	0.0338050i	0.856102	−	0.516807i	$-0.172880\pi$
$157$	−38.3946	−	66.5013i	−0.0195173	−	0.0338050i	−0.875619	+	0.483002i	$0.839546\pi$
$158$	349.397	+	605.173i	0.175927	+	0.304715i
$159$	1603.53	−	2777.39i	0.799798	−	1.38529i
$160$	−169.900			−0.0839488
$161$	−211.721	−	369.623i	−0.103640	−	0.180934i
$162$	−1352.34			−0.655864
$163$	−1074.61	+	1861.27i	−0.516379	+	0.894394i	0.483440	+	0.875377i	$0.339387\pi$
$163$	−1074.61	+	1861.27i	−0.516379	+	0.894394i	−0.999819	+	0.0190171i	$0.993946\pi$
$164$	214.984	+	372.362i	0.102362	+	0.177296i
$165$	−298.977	−	517.843i	−0.141063	−	0.244328i
$166$	−373.014	+	646.080i	−0.174407	+	0.302082i
$167$	−2071.34			−0.959791			−0.479896	−	0.877326i	$-0.659325\pi$
$167$	−2071.34			−0.959791			−0.479896	+	0.877326i	$0.659325\pi$
$168$	1107.08	+	3.78276i	0.508409	+	0.00173718i
$169$	−1813.49			−0.825440
$170$	−610.150	+	1056.81i	−0.275273	+	0.476786i
$171$	−747.260	−	1294.29i	−0.334178	−	0.578813i
$172$	−277.589	−	480.799i	−0.123058	−	0.213143i
$173$	−1560.93	+	2703.60i	−0.685983	+	1.18816i	0.287144	+	0.957887i	$0.407294\pi$
$173$	−1560.93	+	2703.60i	−0.685983	+	1.18816i	−0.973127	+	0.230270i	$0.926039\pi$
$174$	−3401.08			−1.48181
$175$	1792.94	+	6.12630i	0.774479	+	0.00264631i
$176$	241.157			0.103284
$177$	480.322	−	831.943i	0.203973	−	0.353292i
$178$	−896.694	−	1553.12i	−0.377585	−	0.653996i
$179$	1534.64	+	2658.08i	0.640808	+	1.10991i	0.985253	+	0.171106i	$0.0547340\pi$
$179$	1534.64	+	2658.08i	0.640808	+	1.10991i	−0.344444	+	0.938807i	$0.611933\pi$
$180$	306.164	−	530.291i	0.126778	−	0.219587i
$181$	1108.70			0.455300			0.227650	−	0.973743i	$-0.426896\pi$
$181$	1108.70			0.455300			0.227650	+	0.973743i	$0.426896\pi$
$182$	360.540	+	629.431i	0.146841	+	0.256355i
$183$	−1688.18			−0.681934
$184$	92.0000	−	159.349i	0.0368605	−	0.0638442i
$185$	55.0578	+	95.3628i	0.0218807	+	0.0378985i
$186$	−1330.22	−	2304.00i	−0.524388	−	0.908267i
$187$	866.049	−	1500.04i	0.338673	−	0.586598i
$188$	85.8028			0.0332863
$189$	−127.532	+	219.159i	−0.0490825	+	0.0843466i
$190$	−550.423			−0.210168
$191$	1590.31	−	2754.50i	0.602465	−	1.04350i	−0.389982	−	0.920822i	$-0.627519\pi$
$191$	1590.31	−	2754.50i	0.602465	−	1.04350i	0.992447	−	0.122677i	$-0.0391479\pi$
$192$	239.107	+	414.146i	0.0898754	+	0.155669i
$193$	406.163	+	703.494i	0.151483	+	0.262376i	0.931773	−	0.363042i	$-0.118262\pi$
$193$	406.163	+	703.494i	0.151483	+	0.262376i	−0.780290	+	0.625418i	$0.784928\pi$
$194$	1294.92	−	2242.87i	0.479227	−	0.830045i
$195$	776.917			0.285314
$196$	−694.104	+	1183.47i	−0.252953	+	0.431294i
$197$	−3772.40			−1.36433			−0.682164	−	0.731199i	$-0.738961\pi$
$197$	−3772.40			−1.36433			−0.682164	+	0.731199i	$0.738961\pi$
$198$	−434.570	+	752.698i	−0.155978	+	0.270161i
$199$	762.138	+	1320.06i	0.271490	+	0.470235i	0.969244	−	0.246103i	$-0.0791503\pi$
$199$	762.138	+	1320.06i	0.271490	+	0.470235i	−0.697754	+	0.716338i	$0.745817\pi$
$200$	387.242	+	670.722i	0.136911	+	0.237136i
$201$	1788.51	−	3097.78i	0.627620	−	1.08707i
$202$	618.460			0.215419
$203$	2119.93	−	3643.02i	0.732954	−	1.25956i
$204$	3434.75			1.17883
$205$	−285.358	+	494.254i	−0.0972207	+	0.168391i
$206$	−617.628	−	1069.76i	−0.208894	−	0.361815i
$207$	331.572	+	574.299i	0.111332	+	0.192833i
$208$	−156.667	+	271.355i	−0.0522254	+	0.0904571i
$209$	781.273			0.258573
$210$	730.388	+	1275.11i	0.240008	+	0.419005i
$211$	910.563			0.297089			0.148544	−	0.988906i	$-0.452541\pi$
$211$	910.563			0.297089			0.148544	+	0.988906i	$0.452541\pi$
$212$	−858.407	+	1486.80i	−0.278092	+	0.481670i
$213$	2435.94	+	4219.18i	0.783606	+	1.35725i
$214$	1225.20	+	2122.11i	0.391370	+	0.677873i
$215$	368.457	−	638.187i	0.116877	−	0.202437i
$216$	−109.530			−0.0345026
$217$	3297.04	+	11.2656i	1.03142	+	0.00352424i
$218$	314.489			0.0977060
$219$	−1929.36	+	3341.76i	−0.595316	+	1.03112i
$220$	160.050	+	277.214i	0.0490480	+	0.0849536i
$221$	1125.25	+	1948.99i	0.342500	+	0.593228i
$222$	154.970	−	268.415i	0.0468508	−	0.0811480i
$223$	1289.30			0.387166			0.193583	−	0.981084i	$-0.437989\pi$
$223$	1289.30			0.387166			0.193583	+	0.981084i	$0.437989\pi$
$224$	−592.645	−	2.02501i	−0.176776	−	0.000604024i
$225$	−2791.27			−0.827042
$226$	1226.97	−	2125.17i	0.361136	−	0.625506i
$227$	−706.968	−	1224.50i	−0.206710	−	0.358032i	0.743966	−	0.668217i	$-0.232942\pi$
$227$	−706.968	−	1224.50i	−0.206710	−	0.358032i	−0.950676	+	0.310185i	$0.899609\pi$
$228$	774.631	+	1341.70i	0.225005	+	0.389721i
$229$	399.583	−	692.098i	0.115306	−	0.199717i	−0.802596	−	0.596523i	$-0.796548\pi$
$229$	399.583	−	692.098i	0.115306	−	0.199717i	0.917902	+	0.396807i	$0.129882\pi$
$230$	244.232			0.0700181
$231$	−1036.72	−	1809.90i	−0.295286	−	0.515509i
$232$	1820.68			0.515231
$233$	−777.205	+	1346.16i	−0.218525	+	0.378497i	−0.954357	−	0.298667i	$-0.903458\pi$
$233$	−777.205	+	1346.16i	−0.218525	+	0.378497i	0.735832	+	0.677164i	$0.236791\pi$
$234$	−564.634	−	977.974i	−0.157740	−	0.273214i
$235$	56.9451	+	98.6318i	0.0158072	+	0.0273788i
$236$	−257.128	+	445.359i	−0.0709222	+	0.122841i
$237$	2610.73			0.715548
$238$	−2140.91	+	3679.08i	−0.583087	+	1.00201i
$239$	−6967.81			−1.88582			−0.942908	−	0.333052i	$-0.891922\pi$
$239$	−6967.81			−1.88582			−0.942908	+	0.333052i	$0.891922\pi$
$240$	−317.378	+	549.715i	−0.0853612	+	0.147850i
$241$	2529.12	+	4380.57i	0.675996	+	1.17086i	0.976177	+	0.216977i	$0.0696197\pi$
$241$	2529.12	+	4380.57i	0.675996	+	1.17086i	−0.300181	+	0.953882i	$0.597047\pi$
$242$	1103.82	+	1911.88i	0.293209	+	0.507853i
$243$	−2711.04	+	4695.66i	−0.715692	+	1.23961i
$244$	903.725			0.237111
$245$	−1821.08	−	12.4450i	−0.474875	−	0.00324523i
$246$	1606.38			0.416337
$247$	−507.551	+	879.103i	−0.130748	+	0.226462i
$248$	712.097	+	1233.39i	0.182332	+	0.315808i
$249$	1393.60	+	2413.79i	0.354682	+	0.614328i
$250$	−1177.68	+	2039.80i	−0.297931	+	0.516032i
$251$	−3363.38			−0.845796			−0.422898	−	0.906177i	$-0.638987\pi$
$251$	−3363.38			−0.845796			−0.422898	+	0.906177i	$0.638987\pi$
$252$	1074.28	−	1846.11i	0.268544	−	0.461484i
$253$	−346.664			−0.0861445
$254$	−1229.19	+	2129.01i	−0.303646	+	0.525930i
$255$	2279.55	+	3948.30i	0.559808	+	0.969615i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	3510.14	−	6079.75i	0.851972	−	1.47566i	−0.0274543	−	0.999623i	$-0.508740\pi$
$257$	3510.14	−	6079.75i	0.851972	−	1.47566i	0.879426	−	0.476035i	$-0.157927\pi$
$258$	−2074.18			−0.500514
$259$	190.915	+	333.300i	0.0458027	+	0.0799623i
$260$	−415.903			−0.0992046
$261$	−3280.90	+	5682.69i	−0.778095	+	1.34770i
$262$	2420.93	+	4193.18i	0.570862	+	0.988762i
$263$	559.283	+	968.707i	0.131129	+	0.227122i	0.924112	−	0.382122i	$-0.124807\pi$
$263$	559.283	+	968.707i	0.131129	+	0.227122i	−0.792983	+	0.609244i	$0.791473\pi$
$264$	450.488	−	780.269i	0.105021	−	0.181902i
$265$	−2278.81			−0.528249
$266$	−1919.98	−	6.56037i	−0.442562	−	0.00151219i
$267$	−6700.19			−1.53575
$268$	−957.432	+	1658.32i	−0.218226	+	0.377978i
$269$	1392.93	+	2412.63i	0.315720	+	0.546843i	0.979590	−	0.201005i	$-0.0644207\pi$
$269$	1392.93	+	2412.63i	0.315720	+	0.546843i	−0.663871	+	0.747848i	$0.731087\pi$
$270$	−72.6921	−	125.906i	−0.0163848	−	0.0283793i
$271$	1344.77	−	2329.21i	0.301435	−	0.522100i	−0.675026	−	0.737794i	$-0.735868\pi$
$271$	1344.77	−	2329.21i	0.301435	−	0.522100i	0.976461	+	0.215693i	$0.0692011\pi$
$272$	−1838.70			−0.409882
$273$	2710.03	+	9.25990i	0.600801	+	0.00205287i
$274$	6405.42			1.41228
$275$	729.580	−	1263.67i	0.159983	−	0.277099i
$276$	−343.717	−	595.335i	−0.0749613	−	0.129837i
$277$	415.418	+	719.525i	0.0901085	+	0.156072i	0.907557	−	0.419930i	$-0.137945\pi$
$277$	415.418	+	719.525i	0.0901085	+	0.156072i	−0.817448	+	0.576002i	$0.804612\pi$
$278$	1710.35	−	2962.41i	0.368992	−	0.639113i
$279$	−5132.85			−1.10142
$280$	−390.995	−	682.599i	−0.0834515	−	0.145690i
$281$	−8850.37			−1.87889			−0.939447	−	0.342695i	$-0.888660\pi$
$281$	−8850.37			−1.87889			−0.939447	+	0.342695i	$0.888660\pi$
$282$	160.282	−	277.616i	0.0338463	−	0.0586235i
$283$	278.788	+	482.874i	0.0585590	+	0.101427i	0.893819	−	0.448428i	$-0.148016\pi$
$283$	278.788	+	482.874i	0.0585590	+	0.101427i	−0.835260	+	0.549856i	$0.814683\pi$
$284$	−1304.02	−	2258.63i	−0.272463	−	0.471919i
$285$	−1028.20	+	1780.90i	−0.213704	+	0.370146i
$286$	590.334			0.122053
$287$	−1001.27	+	1720.65i	−0.205935	+	0.353891i
$288$	922.634			0.188773
$289$	−4146.69	+	7182.28i	−0.844024	+	1.46189i
$290$	1208.34	+	2092.90i	0.244676	+	0.423791i
$291$	−4837.90	−	8379.48i	−0.974579	−	1.68802i
$292$	1032.84	−	1788.92i	0.206994	−	0.358523i
$293$	−263.506			−0.0525400			−0.0262700	−	0.999655i	$-0.508363\pi$
$293$	−263.506			−0.0525400			−0.0262700	+	0.999655i	$0.508363\pi$
$294$	2532.54	+	4456.54i	0.502383	+	0.884049i
$295$	−682.597			−0.134720
$296$	−82.9591	+	143.689i	−0.0162902	+	0.0282155i
$297$	103.179	+	178.712i	0.0201585	+	0.0349156i
$298$	2647.44	+	4585.50i	0.514638	+	0.891378i
$299$	225.209	−	390.073i	0.0435590	−	0.0754465i
$300$	2893.51			0.556856
$301$	1292.86	−	2221.73i	0.247571	−	0.425442i
$302$	−2021.63			−0.385204
$303$	1155.30	−	2001.04i	0.219044	−	0.379395i
$304$	−414.679	−	718.245i	−0.0782351	−	0.135507i
$305$	599.778	+	1038.85i	0.112601	+	0.195030i
$306$	3313.38	−	5738.94i	0.618998	−	1.07214i
$307$	6200.77			1.15276			0.576379	−	0.817182i	$-0.304465\pi$
$307$	6200.77			1.15276			0.576379	+	0.817182i	$0.304465\pi$
$308$	554.980	+	968.884i	0.102672	+	0.179244i
$309$	−4614.98			−0.849635
$310$	−945.200	+	1637.14i	−0.173173	+	0.299945i
$311$	−4212.12	−	7295.61i	−0.767999	−	1.33021i	−0.938647	−	0.344880i	$-0.887919\pi$
$311$	−4212.12	−	7295.61i	−0.767999	−	1.33021i	0.170648	−	0.985332i	$-0.445414\pi$
$312$	585.315	+	1013.80i	0.106208	+	0.183958i
$313$	1210.55	−	2096.74i	0.218609	−	0.378642i	−0.735774	−	0.677227i	$-0.763181\pi$
$313$	1210.55	−	2096.74i	0.218609	−	0.378642i	0.954383	+	0.298585i	$0.0965148\pi$
$314$	153.578			0.0276017
$315$	2835.10	+	9.68724i	0.507111	+	0.00173274i
$316$	−1397.59			−0.248799
$317$	516.132	−	893.966i	0.0914474	−	0.158392i	−0.816673	−	0.577101i	$-0.804184\pi$
$317$	516.132	−	893.966i	0.0914474	−	0.158392i	0.908120	+	0.418709i	$0.137517\pi$
$318$	3207.05	+	5554.77i	0.565542	+	0.979548i
$319$	−1715.12	−	2970.67i	−0.301029	−	0.521398i
$320$	169.900	−	294.276i	0.0296804	−	0.0514079i
$321$	9154.85			1.59182
$322$	851.927	+	2.91095i	0.147441	+	0.000503791i
$323$	−5956.81			−1.02615
$324$	1352.34	−	2342.32i	0.231883	−	0.401633i
$325$	947.936	+	1641.87i	0.161791	+	0.280230i
$326$	−2149.22	−	3722.55i	−0.365135	−	0.632432i
$327$	587.474	−	1017.53i	0.0993498	−	0.172079i
$328$	−859.934			−0.144762
$329$	197.460	+	344.725i	0.0330891	+	0.0577669i
$330$	1195.91			0.199493
$331$	−907.676	+	1572.14i	−0.150726	+	0.261066i	−0.931495	−	0.363755i	$-0.881495\pi$
$331$	−907.676	+	1572.14i	−0.150726	+	0.261066i	0.780768	+	0.624821i	$0.214828\pi$
$332$	−746.029	−	1292.16i	−0.123324	−	0.213604i
$333$	−298.988	−	517.862i	−0.0492025	−	0.0852212i
$334$	2071.34	−	3587.67i	0.339337	−	0.587750i
$335$	−2541.69			−0.414529
$336$	−1113.63	+	1913.73i	−0.180814	+	0.310722i
$337$	−8160.36			−1.31906			−0.659530	−	0.751678i	$-0.729245\pi$
$337$	−8160.36			−1.31906			−0.659530	+	0.751678i	$0.729245\pi$
$338$	1813.49	−	3141.06i	0.291837	−	0.505477i
$339$	−4584.02	−	7939.75i	−0.734424	−	1.27206i
$340$	−1220.30	−	2113.62i	−0.194647	−	0.337139i
$341$	1341.62	−	2323.76i	0.213058	−	0.369028i
$342$	2989.04			0.472599
$343$	−6352.12	−	65.1156i	−0.999947	−	0.0102505i
$344$	1110.36			0.174030
$345$	456.231	−	790.216i	0.0711961	−	0.123315i
$346$	−3121.85	−	5407.21i	−0.485063	−	0.840154i
$347$	2846.90	+	4930.97i	0.440431	+	0.762848i	0.997721	−	0.0674692i	$-0.0214924\pi$
$347$	2846.90	+	4930.97i	0.440431	+	0.762848i	−0.557291	+	0.830317i	$0.688159\pi$
$348$	3401.08	−	5890.84i	0.523899	−	0.907420i
$349$	4560.60			0.699494			0.349747	−	0.936844i	$-0.386267\pi$
$349$	4560.60			0.699494			0.349747	+	0.936844i	$0.386267\pi$
$350$	−1803.55	+	3099.34i	−0.275440	+	0.473334i
$351$	−268.120			−0.0407727
$352$	−241.157	+	417.697i	−0.0365163	+	0.0632481i
$353$	−4290.24	−	7430.92i	−0.646874	−	1.12042i	−0.983865	−	0.178911i	$-0.942742\pi$
$353$	−4290.24	−	7430.92i	−0.646874	−	1.12042i	0.336991	−	0.941508i	$-0.390591\pi$
$354$	960.645	+	1663.89i	0.144231	+	0.249815i
$355$	1730.89	−	2997.99i	0.258777	−	0.448216i
$356$	3586.78			0.533985
$357$	7904.44	+	13799.6i	1.17184	+	2.04580i
$358$	−6138.58			−0.906240
$359$	−994.576	+	1722.66i	−0.146217	+	0.253254i	−0.929826	−	0.367999i	$-0.880043\pi$
$359$	−994.576	+	1722.66i	−0.146217	+	0.253254i	0.783610	+	0.621254i	$0.213376\pi$
$360$	612.328	+	1060.58i	0.0896458	+	0.155271i
$361$	2086.07	+	3613.18i	0.304137	+	0.526780i
$362$	−1108.70	+	1920.33i	−0.160973	+	0.278813i
$363$	8247.89			1.19257
$364$	−1450.75	−	4.95705i	−0.208901	−	0.000713791i
$365$	2741.86			0.393194
$366$	1688.18	−	2924.02i	0.241100	−	0.417598i
$367$	57.4441	+	99.4961i	0.00817046	+	0.0141516i	0.870082	−	0.492907i	$-0.164066\pi$
$367$	57.4441	+	99.4961i	0.00817046	+	0.0141516i	−0.861911	+	0.507059i	$0.830733\pi$
$368$	184.000	+	318.697i	0.0260643	+	0.0451447i
$369$	1549.62	−	2684.02i	0.218618	−	0.378657i
$370$	−220.231			−0.0309440
$371$	−7948.91	−	27.1606i	−1.11236	−	0.00380083i
$372$	5320.87			0.741597
$373$	−6284.35	+	10884.8i	−0.872363	+	1.51098i	−0.0128183	+	0.999918i	$0.504080\pi$
$373$	−6284.35	+	10884.8i	−0.872363	+	1.51098i	−0.859545	+	0.511060i	$0.829253\pi$
$374$	1732.10	+	3000.08i	0.239478	+	0.414788i
$375$	4399.86	+	7620.79i	0.605888	+	1.04943i
$376$	−85.8028	+	148.615i	−0.0117685	+	0.0203836i
$377$	4456.88			0.608862
$378$	−252.063	−	440.052i	−0.0342982	−	0.0598778i
$379$	−12075.5			−1.63662			−0.818308	−	0.574781i	$-0.805087\pi$
$379$	−12075.5			−1.63662			−0.818308	+	0.574781i	$0.805087\pi$
$380$	550.423	−	953.360i	0.0743055	−	0.128701i
$381$	4592.31	+	7954.11i	0.617509	+	1.06956i
$382$	3180.62	+	5508.99i	0.426007	+	0.737865i
$383$	6114.01	−	10589.8i	0.815695	−	1.41283i	−0.0931328	−	0.995654i	$-0.529688\pi$
$383$	6114.01	−	10589.8i	0.815695	−	1.41283i	0.908828	−	0.417171i	$-0.136979\pi$
$384$	−956.429			−0.127103
$385$	−745.422	+	1280.98i	−0.0986759	+	0.169571i
$386$	−1624.65			−0.214229
$387$	−2000.89	+	3465.64i	−0.262818	+	0.455215i
$388$	2589.84	+	4485.74i	0.338865	+	0.586931i
$389$	−1568.78	−	2717.21i	−0.204474	−	0.354159i	0.745491	−	0.666516i	$-0.232215\pi$
$389$	−1568.78	−	2717.21i	−0.204474	−	0.354159i	−0.949965	+	0.312356i	$0.898882\pi$
$390$	−776.917	+	1345.66i	−0.100874	+	0.174718i
$391$	2643.14			0.341865
$392$	−1355.73	−	2385.69i	−0.174680	−	0.307387i
$393$	18089.5			2.32187
$394$	3772.40	−	6533.99i	0.482363	−	0.835477i
$395$	−927.541	−	1606.55i	−0.118151	−	0.204644i
$396$	−869.141	−	1505.40i	−0.110293	−	0.191033i
$397$	−7744.89	+	13414.5i	−0.979106	+	1.69586i	−0.313445	+	0.949606i	$0.601483\pi$
$397$	−7744.89	+	13414.5i	−0.979106	+	1.69586i	−0.665661	+	0.746254i	$0.731850\pi$
$398$	−3048.55			−0.383945
$399$	−3607.80	+	6199.87i	−0.452671	+	0.777899i
$400$	−1548.97			−0.193621
$401$	3026.26	−	5241.64i	0.376869	−	0.652755i	−0.613736	−	0.789511i	$-0.710334\pi$
$401$	3026.26	−	5241.64i	0.376869	−	0.652755i	0.990605	+	0.136756i	$0.0436675\pi$
$402$	3577.01	+	6195.57i	0.443794	+	0.768674i
$403$	1743.16	+	3019.24i	0.215466	+	0.373198i
$404$	−618.460	+	1071.20i	−0.0761623	+	0.131917i
$405$	3590.05			0.440472
$406$	4189.96	+	7314.84i	0.512178	+	0.894161i
$407$	312.597			0.0380709
$408$	−3434.75	+	5949.16i	−0.416778	+	0.721880i
$409$	−5960.88	−	10324.6i	−0.720652	−	1.24821i	−0.960739	−	0.277454i	$-0.910509\pi$
$409$	−5960.88	−	10324.6i	−0.720652	−	1.24821i	0.240087	−	0.970751i	$-0.422824\pi$
$410$	−570.716	−	988.508i	−0.0687454	−	0.119071i
$411$	11965.5	−	20724.8i	1.43604	−	2.48730i
$412$	2470.51			0.295421
$413$	−2381.03	−	8.13572i	−0.283687	−	0.000969329i
$414$	−1326.29			−0.157448
$415$	990.239	−	1715.14i	0.117130	−	0.202875i
$416$	−313.334	−	542.710i	−0.0369290	−	0.0639629i
$417$	−6389.94	−	11067.7i	−0.750400	−	1.29973i
$418$	−781.273	+	1353.20i	−0.0914194	+	0.158343i
$419$	−7468.53			−0.870792			−0.435396	−	0.900239i	$-0.643392\pi$
$419$	−7468.53			−0.870792			−0.435396	+	0.900239i	$0.643392\pi$
$420$	−2938.95	−	10.0421i	−0.341443	−	0.00116667i
$421$	6039.59			0.699172			0.349586	−	0.936904i	$-0.386322\pi$
$421$	6039.59			0.699172			0.349586	+	0.936904i	$0.386322\pi$
$422$	−910.563	+	1577.14i	−0.105037	+	0.181929i
$423$	−309.237	−	535.614i	−0.0355452	−	0.0615660i
$424$	−1716.81	−	2973.61i	−0.196641	−	0.340592i
$425$	−5562.68	+	9634.84i	−0.634893	+	1.09967i
$426$	−9743.78			−1.10819
$427$	2079.76	+	3630.84i	0.235706	+	0.411496i
$428$	−4900.81			−0.553481
$429$	1102.76	−	1910.03i	0.124107	−	0.214959i
$430$	736.915	+	1276.37i	0.0826446	+	0.143145i
$431$	−6776.07	−	11736.5i	−0.757289	−	1.31166i	−0.944228	−	0.329292i	$-0.893190\pi$
$431$	−6776.07	−	11736.5i	−0.757289	−	1.31166i	0.186939	−	0.982372i	$-0.440143\pi$
$432$	109.530	−	189.711i	0.0121985	−	0.0211284i
$433$	2807.93			0.311641			0.155821	−	0.987785i	$-0.450198\pi$
$433$	2807.93			0.311641			0.155821	+	0.987785i	$0.450198\pi$
$434$	−3316.55	+	5699.37i	−0.366819	+	0.630365i
$435$	9028.82			0.995169
$436$	−314.489	+	544.711i	−0.0345443	+	0.0598324i
$437$	596.101	+	1032.48i	0.0652526	+	0.113021i
$438$	−3858.73	−	6683.51i	−0.420952	−	0.729111i
$439$	7949.37	−	13768.7i	0.864243	−	1.49691i	−0.00355438	−	0.999994i	$-0.501131\pi$
$439$	7949.37	−	13768.7i	0.864243	−	1.49691i	0.867797	−	0.496919i	$-0.165535\pi$
$440$	−640.199			−0.0693643
$441$	9889.25	+	67.5819i	1.06784	+	0.00729747i
$442$	−4501.00			−0.484368
$443$	4597.32	−	7962.79i	0.493059	−	0.854004i	−0.506909	−	0.862000i	$-0.669212\pi$
$443$	4597.32	−	7962.79i	0.493059	−	0.854004i	0.999968	+	0.00799607i	$0.00254525\pi$
$444$	309.939	+	536.831i	0.0331285	+	0.0573803i
$445$	2380.45	+	4123.06i	0.253582	+	0.439217i
$446$	−1289.30	+	2233.14i	−0.136884	+	0.237090i
$447$	19781.9			2.09318
$448$	596.152	−	1024.47i	0.0628695	−	0.108039i
$449$	−11231.7			−1.18053			−0.590265	−	0.807209i	$-0.700977\pi$
$449$	−11231.7			−1.18053			−0.590265	+	0.807209i	$0.700977\pi$
$450$	2791.27	−	4834.62i	0.292404	−	0.506458i
$451$	810.076	+	1403.09i	0.0845787	+	0.146495i
$452$	2453.94	+	4250.34i	0.255362	+	0.442299i
$453$	−3776.46	+	6541.01i	−0.391685	+	0.678419i
$454$	2827.87			0.292332
$455$	−957.124	−	1670.95i	−0.0986169	−	0.172165i
$456$	−3098.52			−0.318205
$457$	4875.98	−	8445.45i	0.499100	−	0.864467i	−0.500899	−	0.865506i	$-0.666997\pi$
$457$	4875.98	−	8445.45i	0.499100	−	0.864467i	0.999999	+	0.00103874i	$0.000330643\pi$
$458$	799.165	+	1384.20i	0.0815339	+	0.141221i
$459$	−786.692	−	1362.59i	−0.0799992	−	0.138563i
$460$	−244.232	+	423.022i	−0.0247551	+	0.0428772i
$461$	−6728.85			−0.679813			−0.339906	−	0.940459i	$-0.610395\pi$
$461$	−6728.85			−0.679813			−0.339906	+	0.940459i	$0.610395\pi$
$462$	4171.56	+	14.2538i	0.420083	+	0.00143538i
$463$	−7665.18			−0.769398			−0.384699	−	0.923042i	$-0.625695\pi$
$463$	−7665.18			−0.769398			−0.384699	+	0.923042i	$0.625695\pi$
$464$	−1820.68	+	3153.51i	−0.182162	+	0.315513i
$465$	3531.32	+	6116.42i	0.352174	+	0.609983i
$466$	−1554.41	−	2692.32i	−0.154521	−	0.267638i
$467$	8377.96	−	14511.1i	0.830163	−	1.43788i	−0.0677464	−	0.997703i	$-0.521581\pi$
$467$	8377.96	−	14511.1i	0.830163	−	1.43788i	0.897909	−	0.440181i	$-0.145086\pi$
$468$	2258.53			0.223079
$469$	−8865.89	−	30.2938i	−0.872897	−	0.00298260i
$470$	−227.780			−0.0223547
$471$	286.888	−	496.905i	0.0280660	−	0.0486118i
$472$	−514.257	−	890.719i	−0.0501496	−	0.0868616i
$473$	−1045.98	−	1811.69i	−0.101679	−	0.176113i
$474$	−2610.73	+	4521.91i	−0.252985	+	0.438182i
$475$	−5018.16			−0.484734
$476$	−4231.44	−	7387.25i	−0.407454	−	0.711332i
$477$	12374.9			1.18786
$478$	6967.81	−	12068.6i	0.666737	−	1.15482i
$479$	−2759.29	−	4779.22i	−0.263205	−	0.455884i	0.703887	−	0.710312i	$-0.251446\pi$
$479$	−2759.29	−	4779.22i	−0.263205	−	0.455884i	−0.967092	+	0.254428i	$0.918113\pi$
$480$	−634.757	−	1099.43i	−0.0603595	−	0.104546i
$481$	−203.077	+	351.740i	−0.0192506	+	0.0333430i
$482$	−10116.5			−0.956003
$483$	1600.84	−	2750.98i	0.150809	−	0.259160i
$484$	−4415.30			−0.414660
$485$	−3437.62	+	5954.14i	−0.321844	+	0.557450i
$486$	−5422.08	−	9391.31i	−0.506071	−	0.876540i
$487$	−1976.96	−	3424.19i	−0.183952	−	0.318614i	0.759271	−	0.650775i	$-0.225556\pi$
$487$	−1976.96	−	3424.19i	−0.183952	−	0.318614i	−0.943223	+	0.332161i	$0.892222\pi$
$488$	−903.725	+	1565.30i	−0.0838313	+	0.145200i
$489$	−16059.2			−1.48511
$490$	1842.63	−	3141.75i	0.169881	−	0.289653i
$491$	12730.6			1.17011			0.585053	−	0.810995i	$-0.301074\pi$
$491$	12730.6			1.17011			0.585053	+	0.810995i	$0.301074\pi$
$492$	−1606.38	+	2782.33i	−0.147197	+	0.254954i
$493$	13076.9	+	22649.9i	1.19464	+	2.06917i
$494$	−1015.10	−	1758.21i	−0.0924525	−	0.160133i
$495$	1153.65	−	1998.18i	0.104753	−	0.181438i
$496$	−2848.39			−0.257856
$497$	6073.40	−	10436.9i	0.548147	−	0.941971i
$498$	−5574.40			−0.501596
$499$	9009.94	−	15605.7i	0.808297	−	1.40001i	−0.105745	−	0.994393i	$-0.533723\pi$
$499$	9009.94	−	15605.7i	0.808297	−	1.40001i	0.914042	−	0.405619i	$-0.132944\pi$
$500$	−2355.35	−	4079.59i	−0.210669	−	0.364890i
$501$	−7738.63	−	13403.7i	−0.690093	−	1.19528i
$502$	3363.38	−	5825.55i	0.299034	−	0.517942i
$503$	−10200.1			−0.904175			−0.452087	−	0.891974i	$-0.649320\pi$
$503$	−10200.1			−0.904175			−0.452087	+	0.891974i	$0.649320\pi$
$504$	2123.27	+	3706.81i	0.187655	+	0.327608i
$505$	−1641.82			−0.144674
$506$	346.664	−	600.439i	0.0304567	−	0.0527525i
$507$	−6775.30	−	11735.2i	−0.593494	−	1.02796i
$508$	−2458.37	−	4258.03i	−0.214710	−	0.371889i
$509$	−6186.28	+	10714.9i	−0.538707	+	0.933068i	0.460267	+	0.887781i	$0.347754\pi$
$509$	−6186.28	+	10714.9i	−0.538707	+	0.933068i	−0.998974	+	0.0452876i	$0.985580\pi$
$510$	−9118.20			−0.791688
$511$	9564.14	+	32.6797i	0.827970	+	0.00282909i
$512$	512.000			0.0441942
$513$	354.842	−	614.604i	0.0305393	−	0.0528956i
$514$	7020.29	+	12159.5i	0.602435	+	1.04345i
$515$	1639.61	+	2839.89i	0.140291	+	0.242992i
$516$	2074.18	−	3592.58i	0.176958	−	0.306501i
$517$	323.312			0.0275034
$518$	−768.208	−	2.62488i	−0.0651604	−	0.000222646i
$519$	−23326.8			−1.97290
$520$	415.903	−	720.364i	0.0350741	−	0.0607501i
$521$	−5830.30	−	10098.4i	−0.490269	−	0.849171i	0.509668	−	0.860371i	$-0.329768\pi$
$521$	−5830.30	−	10098.4i	−0.490269	−	0.849171i	−0.999937	+	0.0112002i	$0.996435\pi$
$522$	−6561.80	−	11365.4i	−0.550196	−	0.952967i
$523$	1992.69	−	3451.44i	0.166605	−	0.288568i	−0.770619	−	0.637296i	$-0.780053\pi$
$523$	1992.69	−	3451.44i	0.166605	−	0.288568i	0.937224	+	0.348728i	$0.113386\pi$
$524$	−9683.74			−0.807321
$525$	6658.88	+	11625.1i	0.553557	+	0.966400i
$526$	−2237.13			−0.185444
$527$	−10229.2	+	17717.5i	−0.845523	+	1.46449i
$528$	900.976	+	1560.54i	0.0742613	+	0.128624i
$529$	−264.500	−	458.127i	−0.0217391	−	0.0376533i
$530$	2278.81	−	3947.01i	0.186764	−	0.323485i
$531$	3706.80			0.302941
$532$	1931.34	−	3318.94i	0.157395	−	0.270478i
$533$	−2105.05			−0.171069
$534$	6700.19	−	11605.1i	0.542969	−	0.940451i
$535$	−3252.54	−	5633.56i	−0.262840	−	0.455253i
$536$	−1914.86	−	3316.64i	−0.154309	−	0.267271i
$537$	−11467.0	+	19861.5i	−0.921487	+	1.59606i
$538$	−5571.73			−0.446495
$539$	−2615.44	+	4459.42i	−0.209008	+	0.356365i
$540$	290.768			0.0231716
$541$	−4283.59	+	7419.40i	−0.340418	+	0.589621i	−0.984510	−	0.175326i	$-0.943902\pi$
$541$	−4283.59	+	7419.40i	−0.340418	+	0.589621i	0.644092	+	0.764948i	$0.277235\pi$
$542$	2689.54	+	4658.41i	0.213147	+	0.369181i
$543$	4142.17	+	7174.45i	0.327362	+	0.567008i
$544$	1838.70	−	3184.73i	0.144915	−	0.251000i
$545$	−834.873			−0.0656184
$546$	−2726.07	+	4684.65i	−0.213672	+	0.367188i
$547$	−14381.3			−1.12413			−0.562067	−	0.827091i	$-0.689994\pi$
$547$	−14381.3			−1.12413			−0.562067	+	0.827091i	$0.689994\pi$
$548$	−6405.42	+	11094.5i	−0.499317	+	0.864843i
$549$	−3257.06	−	5641.39i	−0.253202	−	0.438559i
$550$	1459.16	+	2527.34i	0.113125	+	0.195938i
$551$	−5898.42	+	10216.4i	−0.456046	+	0.789894i
$552$	1374.87			0.106011
$553$	−3216.29	−	5615.00i	−0.247325	−	0.431780i
$554$	−1661.67			−0.127433
$555$	−411.397	+	712.561i	−0.0314646	+	0.0544982i
$556$	3420.69	+	5924.81i	0.260917	+	0.451921i
$557$	879.823	+	1523.90i	0.0669287	+	0.115924i	0.897548	−	0.440917i	$-0.145347\pi$
$557$	879.823	+	1523.90i	0.0669287	+	0.115924i	−0.830619	+	0.556841i	$0.812013\pi$
$558$	5132.85	−	8890.36i	0.389411	−	0.674479i
$559$	2718.07			0.205656
$560$	1573.29	+	5.37577i	0.118721	+	0.000405657i
$561$	12942.4			0.974027
$562$	8850.37	−	15329.3i	0.664289	−	1.15058i
$563$	6298.53	+	10909.4i	0.471495	+	0.816653i	0.999468	−	0.0326082i	$-0.0103814\pi$
$563$	6298.53	+	10909.4i	0.471495	+	0.816653i	−0.527974	+	0.849261i	$0.677048\pi$
$564$	320.564	+	555.233i	0.0239329	+	0.0414530i
$565$	−3257.23	+	5641.68i	−0.242535	+	0.420084i
$566$	−1115.15			−0.0828149
$567$	12522.8	+	42.7890i	0.927526	+	0.00316926i
$568$	5216.08			0.385320
$569$	3214.85	−	5568.29i	0.236860	−	0.410254i	−0.722951	−	0.690899i	$-0.757215\pi$
$569$	3214.85	−	5568.29i	0.236860	−	0.410254i	0.959812	+	0.280645i	$0.0905483\pi$
$570$	−2056.41	−	3561.80i	−0.151111	−	0.261733i
$571$	2545.07	+	4408.19i	0.186529	+	0.323077i	0.944091	−	0.329686i	$-0.106943\pi$
$571$	2545.07	+	4408.19i	0.186529	+	0.323077i	−0.757562	+	0.652763i	$0.773610\pi$
$572$	−590.334	+	1022.49i	−0.0431523	+	0.0747420i
$573$	23765.9			1.73270
$574$	−1978.98	−	3454.91i	−0.143904	−	0.251228i
$575$	2226.64			0.161491
$576$	−922.634	+	1598.05i	−0.0667415	+	0.115600i
$577$	6374.46	+	11040.9i	0.459917	+	0.796600i	0.998956	−	0.0456809i	$-0.0145457\pi$
$577$	6374.46	+	11040.9i	0.459917	+	0.796600i	−0.539039	+	0.842281i	$0.681212\pi$
$578$	−8293.38	−	14364.6i	−0.596815	−	1.03371i
$579$	−3034.89	+	5256.58i	−0.217834	+	0.377299i
$580$	−4833.35			−0.346024
$581$	3474.58	−	5970.95i	0.248107	−	0.426363i
$582$	19351.6			1.37826
$583$	−3234.55	+	5602.40i	−0.229779	+	0.397989i
$584$	2065.67	+	3577.85i	0.146367	+	0.253514i
$585$	1498.93	+	2596.22i	0.105937	+	0.183488i
$586$	263.506	−	456.406i	0.0185757	−	0.0321740i
$587$	7455.98			0.524261			0.262131	−	0.965032i	$-0.415575\pi$
$587$	7455.98			0.524261			0.262131	+	0.965032i	$0.415575\pi$
$588$	−10251.5	−	70.0573i	−0.718987	−	0.00491346i
$589$	−9227.87			−0.645548
$590$	682.597	−	1182.29i	0.0476306	−	0.0824987i
$591$	−14093.9	−	24411.3i	−0.980956	−	1.69907i
$592$	−165.918	−	287.379i	−0.0115189	−	0.0199513i
$593$	−4502.80	+	7799.08i	−0.311817	+	0.540084i	−0.978756	−	0.205029i	$-0.934271\pi$
$593$	−4502.80	+	7799.08i	−0.311817	+	0.540084i	0.666938	+	0.745113i	$0.267604\pi$
$594$	−412.718			−0.0285084
$595$	5683.47	−	9766.84i	0.391596	−	0.672943i
$596$	−10589.8			−0.727807
$597$	−5694.77	+	9863.64i	−0.390405	+	0.676201i
$598$	450.417	+	780.146i	0.0308009	+	0.0533487i
$599$	7098.17	+	12294.4i	0.484179	+	0.838623i	0.999835	−	0.0181728i	$-0.00578489\pi$
$599$	7098.17	+	12294.4i	0.484179	+	0.838623i	−0.515656	+	0.856796i	$0.672452\pi$
$600$	−2893.51	+	5011.70i	−0.196878	+	0.341003i
$601$	4208.80			0.285658			0.142829	−	0.989747i	$-0.454380\pi$
$601$	4208.80			0.285658			0.142829	+	0.989747i	$0.454380\pi$
$602$	2555.29	+	4461.02i	0.172999	+	0.302022i
$603$	13802.5			0.932140
$604$	2021.63	−	3501.57i	0.136190	−	0.235889i
$605$	−2930.32	−	5075.46i	−0.196916	−	0.341069i
$606$	2310.60	+	4002.08i	0.154887	+	0.268273i
$607$	6715.91	−	11632.3i	0.449078	−	0.777825i	−0.549248	−	0.835659i	$-0.685086\pi$
$607$	6715.91	−	11632.3i	0.449078	−	0.777825i	0.998326	+	0.0578336i	$0.0184193\pi$
$608$	1658.72			0.110641
$609$	31494.2	+	107.612i	2.09558	+	0.00716039i
$610$	−2399.11			−0.159241
$611$	−210.038	+	363.797i	−0.0139071	+	0.0240878i
$612$	6626.76	+	11477.9i	0.437698	+	0.758115i
$613$	−13887.1	−	24053.1i	−0.914999	−	1.58482i	−0.806903	−	0.590684i	$-0.798858\pi$
$613$	−13887.1	−	24053.1i	−0.914999	−	1.58482i	−0.108096	−	0.994140i	$-0.534475\pi$
$614$	−6200.77	+	10740.1i	−0.407562	+	0.705917i
$615$	−4264.44			−0.279608
$616$	−2233.14	−	7.63039i	−0.146064	−	0.000499086i
$617$	10560.5			0.689061			0.344530	−	0.938775i	$-0.388038\pi$
$617$	10560.5			0.689061			0.344530	+	0.938775i	$0.388038\pi$
$618$	4614.98	−	7993.38i	0.300391	−	0.520293i
$619$	10219.4	+	17700.6i	0.663577	+	1.14935i	0.979669	+	0.200620i	$0.0642956\pi$
$619$	10219.4	+	17700.6i	0.663577	+	1.14935i	−0.316093	+	0.948728i	$0.602371\pi$
$620$	−1890.40	−	3274.27i	−0.122452	−	0.212093i
$621$	−157.449	+	272.710i	−0.0101743	+	0.0176223i
$622$	16848.5			1.08611
$623$	8254.31	+	14410.4i	0.530822	+	0.926709i
$624$	−2341.26			−0.150201
$625$	−2924.28	+	5065.00i	−0.187154	+	0.324160i
$626$	2421.11	+	4193.48i	0.154580	+	0.267740i
$627$	2918.88	+	5055.64i	0.185915	+	0.322014i
$628$	−153.578	+	266.005i	−0.00975866	+	0.0169025i
$629$	−2383.39			−0.151085
$630$	−2851.88	+	4900.85i	−0.180352	+	0.309928i
$631$	−15693.6			−0.990099			−0.495049	−	0.868865i	$-0.664850\pi$
$631$	−15693.6			−0.990099			−0.495049	+	0.868865i	$0.664850\pi$
$632$	1397.59	−	2420.69i	0.0879636	−	0.152357i
$633$	3401.91	+	5892.28i	0.213608	+	0.369980i
$634$	1032.26	+	1787.93i	0.0646631	+	0.112000i
$635$	3263.12	−	5651.88i	0.203926	−	0.353210i
$636$	−12828.2			−0.799798
$637$	−3318.71	−	5839.99i	−0.206424	−	0.363248i
$638$	6860.48			0.425719
$639$	−9399.49	+	16280.4i	−0.581906	+	1.00789i
$640$	339.801	+	588.552i	0.0209872	+	0.0363509i
$641$	6949.46	+	12036.8i	0.428217	+	0.741693i	0.996715	−	0.0809913i	$-0.0258086\pi$
$641$	6949.46	+	12036.8i	0.428217	+	0.741693i	−0.568498	+	0.822685i	$0.692475\pi$
$642$	−9154.85	+	15856.7i	−0.562793	+	0.974786i
$643$	18032.4			1.10595			0.552977	−	0.833196i	$-0.313492\pi$
$643$	18032.4			1.10595			0.552977	+	0.833196i	$0.313492\pi$
$644$	−856.969	+	1472.67i	−0.0524368	+	0.0901107i
$645$	5506.30			0.336140
$646$	5956.81	−	10317.5i	0.362798	−	0.628385i
$647$	1011.50	+	1751.97i	0.0614624	+	0.106456i	0.895119	−	0.445827i	$-0.147090\pi$
$647$	1011.50	+	1751.97i	0.0614624	+	0.106456i	−0.833657	+	0.552283i	$0.813757\pi$
$648$	2704.68	+	4684.64i	0.163966	+	0.283997i
$649$	−968.882	+	1678.15i	−0.0586008	+	0.101500i
$650$	−3791.75			−0.228807
$651$	12245.0	+	21377.3i	0.737204	+	1.28701i
$652$	8596.86			0.516379
$653$	76.5213	−	132.539i	0.00458577	−	0.00794279i	−0.863723	−	0.503966i	$-0.831874\pi$
$653$	76.5213	−	132.539i	0.00458577	−	0.00794279i	0.868309	+	0.496023i	$0.165207\pi$
$654$	1174.95	+	2035.07i	0.0702509	+	0.121678i
$655$	−6426.84	−	11131.6i	−0.383385	−	0.664043i
$656$	859.934	−	1489.45i	0.0511811	−	0.0886482i
$657$	−14889.5			−0.884164
$658$	−794.541	−	2.71486i	−0.0470736	−	0.000160846i
$659$	−5171.29			−0.305683			−0.152841	−	0.988251i	$-0.548842\pi$
$659$	−5171.29			−0.305683			−0.152841	+	0.988251i	$0.548842\pi$
$660$	−1195.91	+	2071.37i	−0.0705313	+	0.122164i
$661$	2213.22	+	3833.40i	0.130233	+	0.225570i	0.923766	−	0.382957i	$-0.125094\pi$
$661$	2213.22	+	3833.40i	0.130233	+	0.225570i	−0.793533	+	0.608527i	$0.791761\pi$
$662$	−1815.35	−	3144.28i	−0.106580	−	0.184601i
$663$	−8407.99	+	14563.1i	−0.492517	+	0.853065i
$664$	2984.12			0.174407
$665$	5096.96	+	17.4158i	0.297220	+	0.00101557i
$666$	1195.95			0.0695828
$667$	2617.23	−	4533.17i	0.151933	−	0.263156i
$668$	4142.68	+	7175.33i	0.239948	+	0.415602i
$669$	4816.90	+	8343.12i	0.278374	+	0.482158i
$670$	2541.69	−	4402.33i	0.146558	−	0.253846i
$671$	3405.31			0.195917
$672$	−2201.05	−	3842.59i	−0.126350	−	0.220582i
$673$	19846.7			1.13675			0.568377	−	0.822768i	$-0.307571\pi$
$673$	19846.7			1.13675			0.568377	+	0.822768i	$0.307571\pi$
$674$	8160.36	−	14134.2i	0.466358	−	0.807756i
$675$	−662.727	−	1147.88i	−0.0377902	−	0.0654545i
$676$	3626.98	+	6282.12i	0.206360	+	0.357426i
$677$	11868.9	−	20557.5i	0.673792	−	1.16704i	−0.303028	−	0.952982i	$-0.597998\pi$
$677$	11868.9	−	20557.5i	0.673792	−	1.16704i	0.976820	−	0.214061i	$-0.0686692\pi$
$678$	18336.1			1.03863
$679$	−12062.0	+	20728.2i	−0.681736	+	1.17154i
$680$	4881.20			0.275273
$681$	5282.54	−	9149.62i	0.297250	−	0.514852i
$682$	2683.24	+	4647.51i	0.150655	+	0.260942i
$683$	2366.81	+	4099.44i	0.132597	+	0.229664i	0.924677	−	0.380753i	$-0.124335\pi$
$683$	2366.81	+	4099.44i	0.132597	+	0.229664i	−0.792080	+	0.610417i	$0.791002\pi$
$684$	−2989.04	+	5177.17i	−0.167089	+	0.289406i
$685$	−17004.4			−0.948475
$686$	6464.90	−	10937.1i	0.359812	−	0.608716i
$687$	5971.45			0.331623
$688$	−1110.36	+	1923.20i	−0.0615290	+	0.106571i
$689$	−4202.62	−	7279.15i	−0.232376	−	0.402487i
$690$	912.463	+	1580.43i	0.0503433	+	0.0871971i
$691$	137.772	−	238.628i	0.00758480	−	0.0131373i	−0.862208	−	0.506554i	$-0.830919\pi$
$691$	137.772	−	238.628i	0.00758480	−	0.0131373i	0.869793	+	0.493417i	$0.164252\pi$
$692$	12487.4			0.685983
$693$	4047.97	−	6956.29i	0.221890	−	0.381310i
$694$	−11387.6			−0.622863
$695$	−4540.44	+	7864.28i	−0.247811	+	0.429222i
$696$	6802.15	+	11781.7i	0.370453	+	0.641643i
$697$	−6176.43	−	10697.9i	−0.335651	−	0.581365i
$698$	−4560.60	+	7899.20i	−0.247309	+	0.428351i
$699$	−11614.7			−0.628481
$700$	−3564.66	−	6223.19i	−0.192474	−	0.336021i
$701$	15236.5			0.820933			0.410467	−	0.911876i	$-0.365366\pi$
$701$	15236.5			0.820933			0.410467	+	0.911876i	$0.365366\pi$
$702$	268.120	−	464.398i	0.0144153	−	0.0249681i
$703$	−537.522	−	931.015i	−0.0288379	−	0.0499487i
$704$	−482.315	−	835.394i	−0.0258209	−	0.0447231i
$705$	−425.499	+	736.987i	−0.0227308	+	0.0393709i
$706$	17161.0			0.914819
$707$	−5726.99	−	19.5685i	−0.304647	−	0.00104095i
$708$	−3842.58			−0.203973
$709$	−10131.4	+	17548.0i	−0.536659	+	0.929521i	0.462422	+	0.886660i	$0.346981\pi$
$709$	−10131.4	+	17548.0i	−0.536659	+	0.929521i	−0.999081	+	0.0428611i	$0.986353\pi$
$710$	3461.78	+	5995.97i	0.182983	+	0.316936i
$711$	5036.96	+	8724.26i	0.265683	+	0.460176i
$712$	−3586.78	+	6212.48i	−0.188792	+	0.326998i
$713$	4094.56			0.215067
$714$	−31806.0	−	108.678i	−1.66710	−	0.00569631i
$715$	−1567.16			−0.0819697
$716$	6138.58	−	10632.3i	0.320404	−	0.554956i
$717$	−26032.1	−	45088.9i	−1.35591	−	2.34850i
$718$	−1989.15	−	3445.31i	−0.103391	−	0.179078i
$719$	−2009.28	+	3480.18i	−0.104219	+	0.180513i	−0.913419	−	0.407021i	$-0.866568\pi$
$719$	−2009.28	+	3480.18i	−0.104219	+	0.180513i	0.809200	+	0.587534i	$0.199901\pi$
$720$	−2449.31			−0.126778
$721$	5685.43	+	9925.63i	0.293671	+	0.512690i
$722$	−8344.29			−0.430114
$723$	−18897.9	+	32732.0i	−0.972087	+	1.68370i
$724$	−2217.41	−	3840.66i	−0.113825	−	0.197151i
$725$	11016.3	+	19080.8i	0.564324	+	0.977438i
$726$	−8247.89	+	14285.8i	−0.421636	+	0.730295i
$727$	31658.7			1.61507			0.807536	−	0.589819i	$-0.200801\pi$
$727$	31658.7			1.61507			0.807536	+	0.589819i	$0.200801\pi$
$728$	1459.33	−	2507.81i	0.0742946	−	0.127673i
$729$	−22257.7			−1.13081
$730$	−2741.86	+	4749.05i	−0.139015	+	0.240781i
$731$	7975.08	+	13813.2i	0.403514	+	0.698907i
$732$	3376.36	+	5848.03i	0.170483	+	0.295286i
$733$	−17998.9	+	31175.0i	−0.906963	+	1.57091i	−0.0887026	+	0.996058i	$0.528272\pi$
$733$	−17998.9	+	31175.0i	−0.906963	+	1.57091i	−0.818260	+	0.574848i	$0.805061\pi$
$734$	−229.776			−0.0115548
$735$	−6723.11	−	11830.7i	−0.337395	−	0.593719i
$736$	−736.000			−0.0368605
$737$	−3607.68	+	6248.69i	−0.180313	+	0.312311i
$738$	3099.24	+	5368.04i	0.154586	+	0.267751i
$739$	−4080.24	−	7067.19i	−0.203104	−	0.351787i	0.746423	−	0.665472i	$-0.231770\pi$
$739$	−4080.24	−	7067.19i	−0.203104	−	0.351787i	−0.949527	+	0.313685i	$0.898436\pi$
$740$	220.231	−	381.451i	0.0109403	−	0.0189492i
$741$	−7584.94			−0.376032
$742$	7995.95	−	13740.8i	0.395607	−	0.679837i
$743$	−2264.67			−0.111821			−0.0559104	−	0.998436i	$-0.517806\pi$
$743$	−2264.67			−0.111821			−0.0559104	+	0.998436i	$0.517806\pi$
$744$	−5320.87	+	9216.01i	−0.262194	+	0.454133i
$745$	−7028.14	−	12173.1i	−0.345626	−	0.598641i
$746$	−12568.7	−	21769.6i	−0.616854	−	1.06842i
$747$	−5377.43	+	9313.99i	−0.263387	+	0.456200i
$748$	−6928.39			−0.338673
$749$	−11278.3	−	19689.7i	−0.550202	−	0.960542i
$750$	−17599.5			−0.856855
$751$	10088.6	−	17473.9i	0.490195	−	0.849043i	−0.509741	−	0.860328i	$-0.670259\pi$
$751$	10088.6	−	17473.9i	0.490195	−	0.849043i	0.999936	+	0.0112846i	$0.00359209\pi$
$752$	−171.606	−	297.230i	−0.00832156	−	0.0144134i
$753$	−12565.8	−	21764.6i	−0.608130	−	1.05331i
$754$	−4456.88	+	7719.54i	−0.215265	+	0.372850i
$755$	5366.81			0.258700
$756$	1014.25	+	3.46560i	0.0487938	+	0.000166723i
$757$	2404.49			0.115446			0.0577231	−	0.998333i	$-0.481616\pi$
$757$	2404.49			0.115446			0.0577231	+	0.998333i	$0.481616\pi$
$758$	12075.5	−	20915.4i	0.578631	−	1.00222i
$759$	−1295.15	−	2243.27i	−0.0619382	−	0.107280i
$760$	1100.85	+	1906.72i	0.0525419	+	0.0910053i
$761$	−18198.3	+	31520.4i	−0.866871	+	1.50147i	−0.00169435	+	0.999999i	$0.500539\pi$
$761$	−18198.3	+	31520.4i	−0.866871	+	1.50147i	−0.865177	+	0.501467i	$0.832794\pi$
$762$	−18369.2			−0.873290
$763$	−2912.19	−	9.95066i	−0.138176	−	0.000472134i
$764$	−12722.5			−0.602465
$765$	−8796.01	+	15235.1i	−0.415713	+	0.720036i
$766$	12228.0	+	21179.5i	0.576783	+	0.999018i
$767$	−1258.86	−	2180.41i	−0.0592631	−	0.102647i
$768$	956.429	−	1656.58i	0.0449377	−	0.0778344i
$769$	−29050.2			−1.36226			−0.681129	−	0.732163i	$-0.738511\pi$
$769$	−29050.2			−1.36226			−0.681129	+	0.732163i	$0.738511\pi$
$770$	−1473.30	−	2572.09i	−0.0689534	−	0.120379i
$771$	52456.3			2.45028
$772$	1624.65	−	2813.98i	0.0757415	−	0.131188i
$773$	15384.7	+	26647.1i	0.715847	+	1.23988i	0.962632	+	0.270813i	$0.0872926\pi$
$773$	15384.7	+	26647.1i	0.715847	+	1.23988i	−0.246785	+	0.969070i	$0.579374\pi$
$774$	−4001.77	−	6931.27i	−0.185841	−	0.321886i
$775$	−8617.31	+	14925.6i	−0.399410	+	0.691798i
$776$	−10359.4			−0.479227
$777$	−1443.52	+	2480.64i	−0.0666488	+	0.114534i
$778$	6275.12			0.289170
$779$	2785.91	−	4825.34i	0.128133	−	0.221933i
$780$	−1553.83	−	2691.32i	−0.0713284	−	0.123544i
$781$	−4913.66	−	8510.71i	−0.225128	−	0.389932i
$782$	−2643.14	+	4578.05i	−0.120868	+	0.209349i
$783$	−3115.92			−0.142214
$784$	5487.87	+	37.5034i	0.249994	+	0.00170843i
$785$	−407.703			−0.0185370
$786$	−18089.5	+	31331.9i	−0.820903	+	1.42185i
$787$	−5586.24	−	9675.66i	−0.253022	−	0.438246i	0.711335	−	0.702854i	$-0.248091\pi$
$787$	−5586.24	−	9675.66i	−0.253022	−	0.438246i	−0.964356	+	0.264607i	$0.914758\pi$
$788$	7544.81	+	13068.0i	0.341082	+	0.590771i
$789$	−4179.02	+	7238.28i	−0.188564	+	0.326603i
$790$	3710.16			0.167091
$791$	−11429.1	+	19640.4i	−0.513743	+	0.882849i
$792$	3476.56			0.155978
$793$	−2212.25	+	3831.72i	−0.0990658	+	0.171587i
$794$	−15489.8	−	26829.1i	−0.692332	−	1.19915i
$795$	−8513.74	−	14746.2i	−0.379813	−	0.657855i
$796$	3048.55	−	5280.25i	0.135745	−	0.235117i
$797$	−7065.60			−0.314023			−0.157012	−	0.987597i	$-0.550186\pi$
$797$	−7065.60			−0.314023			−0.157012	+	0.987597i	$0.550186\pi$
$798$	−7130.69	−	12448.8i	−0.316320	−	0.552232i
$799$	−2465.09			−0.109147
$800$	1548.97	−	2682.89i	0.0684553	−	0.118568i
$801$	−12926.9	−	22390.0i	−0.570224	−	0.987656i
$802$	6052.52	+	10483.3i	0.266486	+	0.461568i
$803$	3891.81	−	6740.82i	0.171032	−	0.296237i
$804$	−14308.1			−0.627620
$805$	−2261.61	−	7.72767i	−0.0990200	−	0.000338341i
$806$	−6972.63			−0.304715
$807$	−10408.1	+	18027.4i	−0.454007	+	0.786363i
$808$	−1236.92	−	2142.41i	−0.0538549	−	0.0932794i
$809$	−18934.6	−	32795.7i	−0.822875	−	1.42526i	−0.903532	−	0.428520i	$-0.859035\pi$
$809$	−18934.6	−	32795.7i	−0.822875	−	1.42526i	0.0806569	−	0.996742i	$-0.474298\pi$
$810$	−3590.05	+	6218.15i	−0.155730	+	0.269733i
$811$	33563.4			1.45323			0.726616	−	0.687044i	$-0.241092\pi$
$811$	33563.4			1.45323			0.726616	+	0.687044i	$0.241092\pi$
$812$	−16859.6	−	57.6076i	−0.728642	−	0.00248969i
$813$	20096.5			0.866931
$814$	−312.597	+	541.434i	−0.0134601	+	0.0233136i
$815$	5705.51	+	9882.23i	0.245221	+	0.424735i
$816$	−6869.49	−	11898.3i	−0.294706	−	0.510446i
$817$	−3597.20	+	6230.54i	−0.154039	+	0.266804i
$818$	23843.5			1.01916
$819$	5197.61	+	9073.98i	0.221757	+	0.387143i
$820$	2282.86			0.0972207
$821$	8951.76	−	15504.9i	0.380534	−	0.659105i	−0.610604	−	0.791936i	$-0.709073\pi$
$821$	8951.76	−	15504.9i	0.380534	−	0.659105i	0.991139	+	0.132831i	$0.0424067\pi$
$822$	23931.0	+	41449.7i	1.01544	+	1.75879i
$823$	−3317.99	−	5746.93i	−0.140532	−	0.243409i	0.787165	−	0.616743i	$-0.211548\pi$
$823$	−3317.99	−	5746.93i	−0.140532	−	0.243409i	−0.927697	+	0.373334i	$0.878215\pi$
$824$	−2470.51	+	4279.05i	−0.104447	+	0.180908i
$825$	10903.0			0.460113
$826$	2395.12	−	4115.93i	0.100892	−	0.173379i
$827$	30086.7			1.26508			0.632538	−	0.774529i	$-0.282013\pi$
$827$	30086.7			1.26508			0.632538	+	0.774529i	$0.282013\pi$
$828$	1326.29	−	2297.20i	0.0556662	−	0.0964167i
$829$	−9482.65	−	16424.4i	−0.397281	−	0.688111i	0.596108	−	0.802904i	$-0.296713\pi$
$829$	−9482.65	−	16424.4i	−0.397281	−	0.688111i	−0.993389	+	0.114793i	$0.963380\pi$
$830$	1980.48	+	3430.29i	0.0828234	+	0.143454i
$831$	−3104.05	+	5376.37i	−0.129577	+	0.224433i
$832$	1253.34			0.0522254
$833$	19941.4	−	34000.8i	0.829447	−	1.41424i
$834$	25559.8			1.06123
$835$	−5498.77	+	9524.16i	−0.227896	+	0.394727i
$836$	−1562.55	−	2706.41i	−0.0646433	−	0.111965i
$837$	−1218.69	−	2110.83i	−0.0503273	−	0.0871695i
$838$	7468.53	−	12935.9i	0.307871	−	0.533249i
$839$	−5909.42			−0.243166			−0.121583	−	0.992581i	$-0.538797\pi$
$839$	−5909.42			−0.243166			−0.121583	+	0.992581i	$0.538797\pi$
$840$	2956.34	−	5080.36i	0.121433	−	0.208678i
$841$	27405.9			1.12370
$842$	−6039.59	+	10460.9i	−0.247195	+	0.428154i
$843$	−33065.4	−	57271.0i	−1.35093	−	2.33988i
$844$	−1821.13	−	3154.28i	−0.0742722	−	0.128643i
$845$	−4814.27	+	8338.55i	−0.195995	+	0.339473i
$846$	1236.95			0.0502685
$847$	−10161.0	−	17739.1i	−0.412203	−	0.719625i
$848$	6867.25			0.278092
$849$	−2083.13	+	3608.09i	−0.0842082	+	0.145853i
$850$	−11125.4	−	19269.7i	−0.448937	−	0.777582i
$851$	238.507	+	413.107i	0.00960744	+	0.0166406i
$852$	9743.78	−	16876.7i	0.391803	−	0.678623i
$853$	−4235.96			−0.170031			−0.0850156	−	0.996380i	$-0.527094\pi$
$853$	−4235.96			−0.170031			−0.0850156	+	0.996380i	$0.527094\pi$
$854$	−8368.56	−	28.5945i	−0.335323	−	0.00114576i
$855$	−7934.98			−0.317393
$856$	4900.81	−	8488.46i	0.195685	−	0.338936i
$857$	−11282.5	−	19541.9i	−0.449712	−	0.778924i	0.548655	−	0.836049i	$-0.315140\pi$
$857$	−11282.5	−	19541.9i	−0.449712	−	0.778924i	−0.998367	+	0.0571249i	$0.981807\pi$
$858$	2205.52	+	3820.07i	0.0877566	+	0.151999i
$859$	1670.45	−	2893.31i	0.0663505	−	0.114923i	−0.830942	−	0.556359i	$-0.812198\pi$
$859$	1670.45	−	2893.31i	0.0663505	−	0.114923i	0.897292	+	0.441437i	$0.145531\pi$
$860$	−2947.66			−0.116877
$861$	−14875.2	−	50.8270i	−0.588787	−	0.00201182i
$862$	27104.3			1.07097
$863$	24944.2	−	43204.6i	0.983905	−	1.70417i	0.337202	−	0.941432i	$-0.390520\pi$
$863$	24944.2	−	43204.6i	0.983905	−	1.70417i	0.646703	−	0.762741i	$-0.276147\pi$
$864$	219.060	+	379.423i	0.00862565	+	0.0149401i
$865$	8287.56	+	14354.5i	0.325764	+	0.564239i
$866$	−2807.93	+	4863.48i	−0.110182	+	0.190840i
$867$	−61969.0			−2.42742
$868$	−6555.05	−	11443.8i	−0.256328	−	0.447498i
$869$	−5266.22			−0.205575
$870$	−9028.82	+	15638.4i	−0.351846	+	0.609414i
$871$	−4687.43	−	8118.87i	−0.182351	−	0.315841i
$872$	−628.979	−	1089.42i	−0.0244265	−	0.0423079i
$873$	18667.8	−	32333.6i	0.723722	−	1.25352i
$874$	−2384.40			−0.0922811
$875$	10969.9	−	18851.4i	0.423830	−	0.728336i
$876$	15434.9			0.595316
$877$	−20594.0	+	35669.9i	−0.792942	+	1.37342i	0.131196	+	0.991356i	$0.458118\pi$
$877$	−20594.0	+	35669.9i	−0.792942	+	1.37342i	−0.924138	+	0.382059i	$0.875215\pi$
$878$	15898.7	+	27537.4i	0.611112	+	1.05848i
$879$	−984.473	−	1705.16i	−0.0377764	−	0.0654307i
$880$	640.199	−	1108.86i	0.0245240	−	0.0424768i
$881$	19351.1			0.740018			0.370009	−	0.929028i	$-0.379355\pi$
$881$	19351.1			0.740018			0.370009	+	0.929028i	$0.379355\pi$
$882$	−10006.3	+	17061.1i	−0.382007	+	0.651335i
$883$	−31330.1			−1.19404			−0.597022	−	0.802225i	$-0.703649\pi$
$883$	−31330.1			−1.19404			−0.597022	+	0.802225i	$0.703649\pi$
$884$	4501.00	−	7795.96i	0.171250	−	0.296614i
$885$	−2550.22	−	4417.11i	−0.0968640	−	0.167773i
$886$	9194.64	+	15925.6i	0.348646	+	0.603872i
$887$	9419.34	−	16314.8i	0.356562	−	0.617583i	−0.630822	−	0.775927i	$-0.717282\pi$
$887$	9419.34	−	16314.8i	0.356562	−	0.617583i	0.987384	+	0.158344i	$0.0506156\pi$
$888$	−1239.76			−0.0468508
$889$	11449.7	−	19675.9i	0.431959	−	0.742306i
$890$	−9521.79			−0.358619
$891$	5095.73	−	8826.07i	0.191598	−	0.331857i
$892$	−2578.61	−	4466.28i	−0.0967916	−	0.167648i
$893$	−555.948	−	962.929i	−0.0208332	−	0.0360842i
$894$	−19781.9	+	34263.3i	−0.740052	+	1.28181i
$895$	16296.0			0.608622
$896$	1178.27	+	2057.03i	0.0439324	+	0.0766971i
$897$	3365.56			0.125276
$898$	11231.7	−	19453.9i	0.417381	−	0.722924i
$899$	20257.8	+	35087.6i	0.751543	+	1.30171i
$900$	5582.54	+	9669.24i	0.206761	+	0.358120i
$901$	24661.8	−	42715.5i	0.911880	−	1.57942i
$902$	−3240.31			−0.119612
$903$	19207.0	+	65.6284i	0.707829	+	0.00241858i
$904$	−9815.75			−0.361136
$905$	2943.27	−	5097.89i	0.108108	−	0.187248i
$906$	−7552.91	−	13082.0i	−0.276963	−	0.479714i
$907$	14377.3	+	24902.2i	0.526339	+	0.911646i	0.999529	+	0.0306853i	$0.00976897\pi$
$907$	14377.3	+	24902.2i	0.526339	+	0.911646i	−0.473190	+	0.880960i	$0.656898\pi$
$908$	−2827.87	+	4898.02i	−0.103355	+	0.179016i
$909$	8915.82			0.325324
$910$	3851.29	+	13.1595i	0.140296	+	0.000479375i
$911$	7679.37			0.279285			0.139643	−	0.990202i	$-0.455405\pi$
$911$	7679.37			0.279285			0.139643	+	0.990202i	$0.455405\pi$
$912$	3098.52	−	5366.80i	0.112503	−	0.194860i
$913$	−2811.10	−	4868.97i	−0.101899	−	0.176494i
$914$	9751.96	+	16890.9i	0.352917	+	0.611270i
$915$	−4481.60	+	7762.36i	−0.161920	+	0.280454i
$916$	−3196.66			−0.115306
$917$	−22285.4	−	38905.8i	−0.802538	−	1.40107i
$918$	3146.77			0.113136
$919$	−22968.5	+	39782.6i	−0.824440	+	1.42797i	0.0779068	+	0.996961i	$0.475176\pi$
$919$	−22968.5	+	39782.6i	−0.824440	+	1.42797i	−0.902347	+	0.431011i	$0.858157\pi$
$920$	−488.464	−	846.044i	−0.0175045	−	0.0303187i
$921$	23166.4	+	40125.4i	0.828837	+	1.43559i
$922$	6728.85	−	11654.7i	0.240350	−	0.416299i
$923$	12768.6			0.455344
$924$	−4196.24	+	7211.09i	−0.149401	+	0.256740i
$925$	−2007.83			−0.0713696
$926$	7665.18	−	13276.5i	0.272023	−	0.471158i
$927$	−8903.82	−	15421.9i	−0.315469	−	0.546409i
$928$	−3641.36	−	6307.02i	−0.128808	−	0.223101i
$929$	17842.4	−	30903.9i	0.630129	−	1.09142i	−0.357396	−	0.933953i	$-0.616335\pi$
$929$	17842.4	−	30903.9i	0.630129	−	1.09142i	0.987525	−	0.157463i	$-0.0503315\pi$
$930$	−14125.3			−0.498049
$931$	17778.9	+	121.499i	0.625866	+	0.00427709i
$932$	6217.64			0.218525
$933$	31473.4	−	54513.5i	1.10439	−	1.91285i
$934$	16755.9	+	29022.1i	0.587014	+	1.01674i
$935$	−4598.19	−	7964.30i	−0.160831	−	0.278567i
$936$	−2258.53	+	3911.90i	−0.0788702	+	0.136607i
$937$	4161.99			0.145108			0.0725540	−	0.997364i	$-0.476885\pi$
$937$	4161.99			0.145108			0.0725540	+	0.997364i	$0.476885\pi$
$938$	8918.36	−	15325.9i	0.310442	−	0.533484i
$939$	18090.8			0.628722
$940$	227.780	−	394.527i	0.00790359	−	0.0136894i
$941$	15330.8	+	26553.8i	0.531106	+	0.919903i	0.999341	+	0.0362989i	$0.0115568\pi$
$941$	15330.8	+	26553.8i	0.531106	+	0.919903i	−0.468235	+	0.883604i	$0.655110\pi$
$942$	573.776	+	993.810i	0.0198457	+	0.0343737i
$943$	−1236.16	+	2141.08i	−0.0426880	+	0.0739377i
$944$	2057.03			0.0709222
$945$	669.150	+	1168.20i	0.0230343	+	0.0402134i
$946$	4183.92			0.143796
$947$	−4582.68	+	7937.43i	−0.157251	+	0.272367i	−0.933877	−	0.357596i	$-0.883597\pi$
$947$	−4582.68	+	7937.43i	−0.157251	+	0.272367i	0.776625	+	0.629963i	$0.216930\pi$
$948$	−5221.45	−	9043.82i	−0.178887	−	0.309842i
$949$	5056.60	+	8758.29i	0.172965	+	0.299585i
$950$	5018.16	−	8691.70i	0.171379	−	0.296838i
$951$	7713.18			0.263004
$952$	17026.5	+	58.1779i	0.579657	+	0.00198063i
$953$	−27150.4			−0.922862			−0.461431	−	0.887176i	$-0.652664\pi$
$953$	−27150.4			−0.922862			−0.461431	+	0.887176i	$0.652664\pi$
$954$	−12374.9	+	21434.0i	−0.419972	+	0.727412i
$955$	−8443.57	−	14624.7i	−0.286102	−	0.495543i
$956$	13935.6	+	24137.2i	0.471454	+	0.816583i
$957$	12815.5	−	22197.2i	0.432882	−	0.749773i
$958$	11037.1			0.372227
$959$	−59314.7	−	202.672i	−1.99726	−	0.00682442i
$960$	2539.03			0.0853612
$961$	−950.839	+	1646.90i	−0.0319170	+	0.0552818i
$962$	−406.154	−	703.480i	−0.0136122	−	0.0235770i
$963$	17662.7	+	30592.7i	0.591042	+	1.02371i
$964$	10116.5	−	17522.3i	0.337998	−	0.585430i
$965$	4312.95			0.143874
$966$	3164.01	+	5523.72i	0.105383	+	0.183978i
$967$	−34024.7			−1.13150			−0.565750	−	0.824577i	$-0.691413\pi$
$967$	−34024.7			−1.13150			−0.565750	+	0.824577i	$0.691413\pi$
$968$	4415.30	−	7647.52i	0.146604	−	0.253926i
$969$	−22255.0	−	38546.7i	−0.737804	−	1.27791i
$970$	−6875.24	−	11908.3i	−0.227578	−	0.394177i
$971$	−9397.19	+	16276.4i	−0.310577	+	0.537935i	−0.978487	−	0.206307i	$-0.933856\pi$
$971$	−9397.19	+	16276.4i	−0.310577	+	0.537935i	0.667911	+	0.744242i	$0.267189\pi$
$972$	21688.3			0.715692
$973$	−15931.7	+	27378.0i	−0.524919	+	0.902053i
$974$	7907.83			0.260147
$975$	−7083.08	+	12268.3i	−0.232656	+	0.402973i
$976$	−1807.45	−	3130.59i	−0.0592777	−	0.102672i
$977$	30213.5	+	52331.3i	0.989371	+	1.71364i	0.620616	+	0.784115i	$0.286883\pi$
$977$	30213.5	+	52331.3i	0.989371	+	1.71364i	0.368756	+	0.929526i	$0.379784\pi$
$978$	16059.2	−	27815.3i	0.525067	−	0.909442i
$979$	13515.3			0.441216
$980$	3599.04	+	6333.29i	0.117314	+	0.206438i
$981$	4533.73			0.147554
$982$	−12730.6	+	22050.0i	−0.413695	+	0.716541i
$983$	−19469.3	−	33721.8i	−0.631713	−	1.09416i	−0.987201	−	0.159478i	$-0.949019\pi$
$983$	−19469.3	−	33721.8i	−0.631713	−	1.09416i	0.355489	−	0.934681i	$-0.384314\pi$
$984$	−3212.76	−	5564.66i	−0.104084	−	0.180279i
$985$	−10014.6	+	17345.8i	−0.323950	+	0.561098i
$986$	−52307.7			−1.68947
$987$	−1493.01	+	2565.68i	−0.0481489	+	0.0827421i
$988$	4060.40			0.130748
$989$	1596.14	−	2764.59i	0.0513188	−	0.0888867i
$990$	2307.30	+	3996.37i	0.0740716	+	0.128296i
$991$	15799.8	+	27366.0i	0.506455	+	0.877205i	0.999972	+	0.00746941i	$0.00237761\pi$
$991$	15799.8	+	27366.0i	0.506455	+	0.877205i	−0.493517	+	0.869736i	$0.664289\pi$
$992$	2848.39	−	4933.56i	0.0911658	−	0.157904i
$993$	−13564.5			−0.433491
$994$	12003.9	+	20956.4i	0.383038	+	0.668707i
$995$	8092.97			0.257854
$996$	5574.40	−	9655.15i	0.177341	−	0.307164i
$997$	−19353.3	−	33520.9i	−0.614770	−	1.06481i	−0.990425	−	0.138053i	$-0.955916\pi$
$997$	−19353.3	−	33520.9i	−0.614770	−	1.06481i	0.375655	−	0.926760i	$-0.377418\pi$
$998$	18019.9	+	31211.4i	0.571552	+	0.989958i
$999$	141.977	−	245.911i	0.00449644	−	0.00778805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.4.e.b.93.10	✓	22
7.2	even	3		2254.4.a.w.1.2		11
7.4	even	3	inner	322.4.e.b.277.10	yes	22
7.5	odd	6		2254.4.a.x.1.10		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.4.e.b.93.10	✓	22	1.1	even	1	trivial
322.4.e.b.277.10	yes	22	7.4	even	3	inner
2254.4.a.w.1.2		11	7.2	even	3
2254.4.a.x.1.10		11	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	322.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(3.73605 + 6.47103i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(2.65469 - 4.59806i) q^{5} -14.9442 q^{6} +(9.31488 - 16.0073i) q^{7} +8.00000 q^{8} +(-14.4162 + 24.9695i) q^{9} +(5.30939 + 9.19613i) q^{10} +(-7.53617 - 13.0530i) q^{11} +(14.9442 - 25.8841i) q^{12} +19.5834 q^{13} +(18.4105 + 32.1411i) q^{14} +39.6723 q^{15} +(-8.00000 + 13.8564i) q^{16} +(57.4595 + 99.5228i) q^{17} +(-28.8323 - 49.9390i) q^{18} +(-25.9174 + 44.8903i) q^{19} -21.2376 q^{20} +(138.384 + 0.472845i) q^{21} +30.1447 q^{22} +(11.5000 - 19.9186i) q^{23} +(29.8884 + 51.7682i) q^{24} +(48.4052 + 83.8403i) q^{25} +(-19.5834 + 33.9194i) q^{26} -13.6912 q^{27} +(-74.0806 - 0.253126i) q^{28} +227.585 q^{29} +(-39.6723 + 68.7144i) q^{30} +(89.0122 + 154.174i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(56.3110 - 97.5336i) q^{33} -229.838 q^{34} +(-48.8744 - 85.3248i) q^{35} +115.329 q^{36} +(-10.3699 + 17.9612i) q^{37} +(-51.8349 - 89.7806i) q^{38} +(73.1644 + 126.725i) q^{39} +(21.2376 - 36.7845i) q^{40} -107.492 q^{41} +(-139.203 + 239.216i) q^{42} +138.795 q^{43} +(-30.1447 + 52.2121i) q^{44} +(76.5410 + 132.573i) q^{45} +(23.0000 + 39.8372i) q^{46} +(-10.7254 + 18.5769i) q^{47} -119.554 q^{48} +(-169.466 - 298.212i) q^{49} -193.621 q^{50} +(-429.343 + 743.644i) q^{51} +(-39.1667 - 67.8387i) q^{52} +(-214.602 - 371.701i) q^{53} +(13.6912 - 23.7139i) q^{54} -80.0249 q^{55} +(74.5190 - 128.058i) q^{56} -387.316 q^{57} +(-227.585 + 394.189i) q^{58} +(-64.2821 - 111.340i) q^{59} +(-79.3446 - 137.429i) q^{60} +(-112.966 + 195.662i) q^{61} -356.049 q^{62} +(265.409 + 463.351i) q^{63} +64.0000 q^{64} +(51.9878 - 90.0455i) q^{65} +(112.622 + 195.067i) q^{66} +(-239.358 - 414.580i) q^{67} +(229.838 - 398.091i) q^{68} +171.858 q^{69} +(196.661 + 0.671971i) q^{70} +652.010 q^{71} +(-115.329 + 199.756i) q^{72} +(258.209 + 447.231i) q^{73} +(-20.7398 - 35.9223i) q^{74} +(-361.689 + 626.463i) q^{75} +207.340 q^{76} +(-279.142 - 0.953799i) q^{77} -292.658 q^{78} +(174.698 - 302.586i) q^{79} +(42.4751 + 73.5690i) q^{80} +(338.085 + 585.581i) q^{81} +(107.492 - 186.181i) q^{82} +373.014 q^{83} +(-275.131 - 480.324i) q^{84} +610.150 q^{85} +(-138.795 + 240.399i) q^{86} +(850.269 + 1472.71i) q^{87} +(-60.2894 - 104.424i) q^{88} +(-448.347 + 776.560i) q^{89} -306.164 q^{90} +(182.417 - 313.476i) q^{91} -92.0000 q^{92} +(-665.108 + 1152.00i) q^{93} +(-21.4507 - 37.1537i) q^{94} +(137.606 + 238.340i) q^{95} +(119.554 - 207.073i) q^{96} -1294.92 q^{97} +(685.984 + 4.68793i) q^{98} +434.570 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{2} + 6 q^{3} - 44 q^{4} + 27 q^{5} - 24 q^{6} + q^{7} + 176 q^{8} - 59 q^{9} + 54 q^{10} - 56 q^{11} + 24 q^{12} - 206 q^{13} - 64 q^{14} + 124 q^{15} - 176 q^{16} + 157 q^{17} - 118 q^{18}+ \cdots + 202 q^{99}+O(q^{100}) \) 22 * q - 22 * q^2 + 6 * q^3 - 44 * q^4 + 27 * q^5 - 24 * q^6 + q^7 + 176 * q^8 - 59 * q^9 + 54 * q^10 - 56 * q^11 + 24 * q^12 - 206 * q^13 - 64 * q^14 + 124 * q^15 - 176 * q^16 + 157 * q^17 - 118 * q^18 + 266 * q^19 - 216 * q^20 - 137 * q^21 + 224 * q^22 + 253 * q^23 + 48 * q^24 - 142 * q^25 + 206 * q^26 - 1062 * q^27 + 124 * q^28 - 390 * q^29 - 124 * q^30 + 316 * q^31 - 352 * q^32 + 682 * q^33 - 628 * q^34 + 539 * q^35 + 472 * q^36 - 347 * q^37 + 532 * q^38 + 99 * q^39 + 216 * q^40 - 1080 * q^41 + 116 * q^42 + 386 * q^43 - 224 * q^44 + 609 * q^45 + 506 * q^46 + 731 * q^47 - 192 * q^48 + 505 * q^49 + 568 * q^50 + 303 * q^51 + 412 * q^52 - 413 * q^53 + 1062 * q^54 - 3618 * q^55 + 8 * q^56 + 686 * q^57 + 390 * q^58 + 1061 * q^59 - 248 * q^60 + 1157 * q^61 - 1264 * q^62 - 557 * q^63 + 1408 * q^64 + 37 * q^65 + 1364 * q^66 + 841 * q^67 + 628 * q^68 + 276 * q^69 - 632 * q^70 + 1738 * q^71 - 472 * q^72 + 409 * q^73 - 694 * q^74 + 2024 * q^75 - 2128 * q^76 + 565 * q^77 - 396 * q^78 - 247 * q^79 + 432 * q^80 - 1019 * q^81 + 1080 * q^82 - 5726 * q^83 + 316 * q^84 + 1570 * q^85 - 386 * q^86 + 670 * q^87 - 448 * q^88 + 1610 * q^89 - 2436 * q^90 - 1766 * q^91 - 2024 * q^92 + 1290 * q^93 + 1462 * q^94 + 209 * q^95 + 192 * q^96 - 3566 * q^97 - 166 * q^98 + 202 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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