LMFDB - Embedded newform 322.4.e.d.93.9

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 = [22,22,0,-44,23] 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			93.9
Character	$\chi$	$=$	322.93
Dual form			322.4.e.d.277.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.73205i) q^{2} +(3.65246 + 6.32625i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.77669 - 6.54142i) q^{5} +14.6098 q^{6} +(-18.3937 + 2.16118i) q^{7} -8.00000 q^{8} +(-13.1810 + 22.8301i) q^{9} +(-7.55338 - 13.0828i) q^{10} +(-28.1561 - 48.7678i) q^{11} +(14.6098 - 25.3050i) q^{12} -65.8379 q^{13} +(-14.6505 + 34.0201i) q^{14} +55.1768 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-54.4173 - 94.2535i) q^{17} +(26.3619 + 45.6602i) q^{18} +(46.1829 - 79.9912i) q^{19} -30.2135 q^{20} +(-80.8546 - 108.470i) q^{21} -112.624 q^{22} +(-11.5000 + 19.9186i) q^{23} +(-29.2197 - 50.6100i) q^{24} +(33.9733 + 58.8434i) q^{25} +(-65.8379 + 114.035i) q^{26} +4.66115 q^{27} +(44.2740 + 59.3954i) q^{28} +58.1564 q^{29} +(55.1768 - 95.5691i) q^{30} +(117.440 + 203.413i) q^{31} +(16.0000 + 27.7128i) q^{32} +(205.678 - 356.245i) q^{33} -217.669 q^{34} +(-55.3302 + 128.483i) q^{35} +105.448 q^{36} +(61.4557 - 106.444i) q^{37} +(-92.3659 - 159.982i) q^{38} +(-240.470 - 416.507i) q^{39} +(-30.2135 + 52.3313i) q^{40} -359.331 q^{41} +(-268.730 + 31.5745i) q^{42} -33.0320 q^{43} +(-112.624 + 195.071i) q^{44} +(99.5607 + 172.444i) q^{45} +(23.0000 + 39.8372i) q^{46} +(-73.9247 + 128.041i) q^{47} -116.879 q^{48} +(333.659 - 79.5043i) q^{49} +135.893 q^{50} +(397.514 - 688.515i) q^{51} +(131.676 + 228.069i) q^{52} +(-320.360 - 554.881i) q^{53} +(4.66115 - 8.07334i) q^{54} -425.347 q^{55} +(147.150 - 17.2894i) q^{56} +674.726 q^{57} +(58.1564 - 100.730i) q^{58} +(-201.015 - 348.168i) q^{59} +(-110.354 - 191.138i) q^{60} +(-120.197 + 208.188i) q^{61} +469.762 q^{62} +(193.107 - 448.417i) q^{63} +64.0000 q^{64} +(-248.649 + 430.673i) q^{65} +(-411.356 - 712.490i) q^{66} +(-56.4426 - 97.7615i) q^{67} +(-217.669 + 377.014i) q^{68} -168.013 q^{69} +(167.209 + 224.318i) q^{70} +171.363 q^{71} +(105.448 - 182.641i) q^{72} +(180.860 + 313.258i) q^{73} +(-122.911 - 212.889i) q^{74} +(-248.172 + 429.847i) q^{75} -369.464 q^{76} +(623.292 + 836.171i) q^{77} -961.881 q^{78} +(421.158 - 729.467i) q^{79} +(60.4270 + 104.663i) q^{80} +(372.911 + 645.900i) q^{81} +(-359.331 + 622.379i) q^{82} -1374.29 q^{83} +(-214.041 + 497.028i) q^{84} -822.069 q^{85} +(-33.0320 + 57.2131i) q^{86} +(212.414 + 367.912i) q^{87} +(225.249 + 390.142i) q^{88} +(-620.557 + 1074.84i) q^{89} +398.243 q^{90} +(1211.00 - 142.287i) q^{91} +92.0000 q^{92} +(-857.894 + 1485.92i) q^{93} +(147.849 + 256.083i) q^{94} +(-348.837 - 604.204i) q^{95} +(-116.879 + 202.440i) q^{96} +997.907 q^{97} +(195.953 - 657.418i) q^{98} +1484.50 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} - 44 q^{4} + 23 q^{5} + 43 q^{7} - 176 q^{8} - 171 q^{9} - 46 q^{10} + 48 q^{11} - 154 q^{13} - 20 q^{14} + 208 q^{15} - 176 q^{16} + 97 q^{17} + 342 q^{18} + 138 q^{19} - 184 q^{20} - 125 q^{21}+ \cdots - 5090 q^{99}+O(q^{100}) $ 22 * q + 22 * q^2 - 44 * q^4 + 23 * q^5 + 43 * q^7 - 176 * q^8 - 171 * q^9 - 46 * q^10 + 48 * q^11 - 154 * q^13 - 20 * q^14 + 208 * q^15 - 176 * q^16 + 97 * q^17 + 342 * q^18 + 138 * q^19 - 184 * q^20 - 125 * q^21 + 192 * q^22 - 253 * q^23 - 30 * q^25 - 154 * q^26 - 630 * q^27 - 212 * q^28 + 274 * q^29 + 208 * q^30 + 234 * q^31 + 352 * q^32 + 28 * q^33 + 388 * q^34 - 235 * q^35 + 1368 * q^36 - 87 * q^37 - 276 * q^38 - 129 * q^39 - 184 * q^40 - 1224 * q^41 - 536 * q^42 + 374 * q^43 + 192 * q^44 + 597 * q^45 + 506 * q^46 + 793 * q^47 - 1123 * q^49 - 120 * q^50 + 1257 * q^51 + 308 * q^52 - 575 * q^53 - 630 * q^54 + 1098 * q^55 - 344 * q^56 + 78 * q^57 + 274 * q^58 + 1241 * q^59 - 416 * q^60 + 187 * q^61 + 936 * q^62 - 1141 * q^63 + 1408 * q^64 + 937 * q^65 - 56 * q^66 - 2275 * q^67 + 388 * q^68 + 956 * q^70 + 230 * q^71 + 1368 * q^72 + 2385 * q^73 + 174 * q^74 + 196 * q^75 - 1104 * q^76 - 1645 * q^77 - 516 * q^78 + 1225 * q^79 + 368 * q^80 - 3635 * q^81 - 1224 * q^82 + 1194 * q^83 - 572 * q^84 - 4986 * q^85 + 374 * q^86 + 1428 * q^87 - 384 * q^88 + 602 * q^89 + 2388 * q^90 + 2324 * q^91 + 2024 * q^92 + 1360 * q^93 - 1586 * q^94 - 4835 * q^95 + 2078 * q^97 + 854 * q^98 - 5090 * 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
$3$	3.65246	+	6.32625i	0.702917	+	1.21749i	0.967438	+	0.253108i	$0.0814527\pi$
$3$	3.65246	+	6.32625i	0.702917	+	1.21749i	−0.264521	+	0.964380i	$0.585214\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	3.77669	−	6.54142i	0.337797	−	0.585082i	−0.646221	−	0.763150i	$-0.723652\pi$
$5$	3.77669	−	6.54142i	0.337797	−	0.585082i	0.984018	+	0.178068i	$0.0569848\pi$
$6$	14.6098			0.994074
$7$	−18.3937	+	2.16118i	−0.993168	+	0.116693i
$7$	−18.3937	+	2.16118i	−0.993168	+	0.116693i
$8$	−8.00000			−0.353553
$9$	−13.1810	+	22.8301i	−0.488184	+	0.845559i
$10$	−7.55338	−	13.0828i	−0.238859	−	0.413715i
$11$	−28.1561	−	48.7678i	−0.771762	−	1.33673i	−0.936596	−	0.350410i	$-0.886042\pi$
$11$	−28.1561	−	48.7678i	−0.771762	−	1.33673i	0.164834	−	0.986321i	$-0.447291\pi$
$12$	14.6098	−	25.3050i	0.351458	−	0.608744i
$13$	−65.8379			−1.40463			−0.702313	−	0.711868i	$-0.747849\pi$
$13$	−65.8379			−1.40463			−0.702313	+	0.711868i	$0.747849\pi$
$14$	−14.6505	+	34.0201i	−0.279679	+	0.649446i
$15$	55.1768			0.949773
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−54.4173	−	94.2535i	−0.776361	−	1.34470i	−0.934026	−	0.357204i	$-0.883730\pi$
$17$	−54.4173	−	94.2535i	−0.776361	−	1.34470i	0.157666	−	0.987493i	$-0.449603\pi$
$18$	26.3619	+	45.6602i	0.345198	+	0.597900i
$19$	46.1829	−	79.9912i	0.557637	−	0.965855i	−0.440057	−	0.897970i	$-0.645042\pi$
$19$	46.1829	−	79.9912i	0.557637	−	0.965855i	0.997693	−	0.0678848i	$-0.0216250\pi$
$20$	−30.2135			−0.337797
$21$	−80.8546	−	108.470i	−0.840186	−	1.12714i
$22$	−112.624			−1.09144
$23$	−11.5000	+	19.9186i	−0.104257	+	0.180579i
$23$	−11.5000	+	19.9186i	−0.104257	+	0.180579i
$24$	−29.2197	−	50.6100i	−0.248519	−	0.430447i
$25$	33.9733	+	58.8434i	0.271786	+	0.470747i
$26$	−65.8379	+	114.035i	−0.496610	+	0.860154i
$27$	4.66115			0.0332236
$28$	44.2740	+	59.3954i	0.298821	+	0.400881i
$29$	58.1564			0.372392			0.186196	−	0.982513i	$-0.440384\pi$
$29$	58.1564			0.372392			0.186196	+	0.982513i	$0.440384\pi$
$30$	55.1768	−	95.5691i	0.335796	−	0.581615i
$31$	117.440	+	203.413i	0.680417	+	1.17852i	0.974854	+	0.222846i	$0.0715347\pi$
$31$	117.440	+	203.413i	0.680417	+	1.17852i	−0.294437	+	0.955671i	$0.595132\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	205.678	−	356.245i	1.08497	−	1.87922i
$34$	−217.669			−1.09794
$35$	−55.3302	+	128.483i	−0.267215	+	0.620503i
$36$	105.448			0.488184
$37$	61.4557	−	106.444i	0.273061	−	0.472955i	−0.696583	−	0.717476i	$-0.745297\pi$
$37$	61.4557	−	106.444i	0.273061	−	0.472955i	0.969644	+	0.244521i	$0.0786307\pi$
$38$	−92.3659	−	159.982i	−0.394309	−	0.682962i
$39$	−240.470	−	416.507i	−0.987335	−	1.71011i
$40$	−30.2135	+	52.3313i	−0.119429	+	0.206858i
$41$	−359.331			−1.36873			−0.684366	−	0.729139i	$-0.739921\pi$
$41$	−359.331			−1.36873			−0.684366	+	0.729139i	$0.739921\pi$
$42$	−268.730	+	31.5745i	−0.987283	+	0.116001i
$43$	−33.0320			−0.117147			−0.0585736	−	0.998283i	$-0.518655\pi$
$43$	−33.0320			−0.117147			−0.0585736	+	0.998283i	$0.518655\pi$
$44$	−112.624	+	195.071i	−0.385881	+	0.668366i
$45$	99.5607	+	172.444i	0.329814	+	0.571255i
$46$	23.0000	+	39.8372i	0.0737210	+	0.127688i
$47$	−73.9247	+	128.041i	−0.229426	+	0.397378i	−0.957638	−	0.287974i	$-0.907018\pi$
$47$	−73.9247	+	128.041i	−0.229426	+	0.397378i	0.728212	+	0.685352i	$0.240352\pi$
$48$	−116.879			−0.351458
$49$	333.659	−	79.5043i	0.972766	−	0.231791i
$50$	135.893			0.384363
$51$	397.514	−	688.515i	1.09143	−	1.89042i
$52$	131.676	+	228.069i	0.351157	+	0.608221i
$53$	−320.360	−	554.881i	−0.830281	−	1.43809i	−0.897815	−	0.440372i	$-0.854847\pi$
$53$	−320.360	−	554.881i	−0.830281	−	1.43809i	0.0675344	−	0.997717i	$-0.478487\pi$
$54$	4.66115	−	8.07334i	0.0117463	−	0.0203452i
$55$	−425.347			−1.04280
$56$	147.150	−	17.2894i	0.351138	−	0.0412571i
$57$	674.726			1.56789
$58$	58.1564	−	100.730i	0.131660	−	0.228043i
$59$	−201.015	−	348.168i	−0.443557	−	0.768264i	0.554393	−	0.832255i	$-0.312950\pi$
$59$	−201.015	−	348.168i	−0.443557	−	0.768264i	−0.997950	+	0.0639909i	$0.979617\pi$
$60$	−110.354	−	191.138i	−0.237443	−	0.411264i
$61$	−120.197	+	208.188i	−0.252290	+	0.436979i	−0.964156	−	0.265336i	$-0.914517\pi$
$61$	−120.197	+	208.188i	−0.252290	+	0.436979i	0.711866	+	0.702315i	$0.247850\pi$
$62$	469.762			0.962255
$63$	193.107	−	448.417i	0.386178	−	0.896750i
$64$	64.0000			0.125000
$65$	−248.649	+	430.673i	−0.474479	+	0.821822i
$66$	−411.356	−	712.490i	−0.767189	−	1.32881i
$67$	−56.4426	−	97.7615i	−0.102919	−	0.178261i	0.809967	−	0.586475i	$-0.199485\pi$
$67$	−56.4426	−	97.7615i	−0.102919	−	0.178261i	−0.912886	+	0.408215i	$0.866152\pi$
$68$	−217.669	+	377.014i	−0.388180	+	0.672348i
$69$	−168.013			−0.293137
$70$	167.209	+	224.318i	0.285504	+	0.383016i
$71$	171.363			0.286437			0.143219	−	0.989691i	$-0.454255\pi$
$71$	171.363			0.286437			0.143219	+	0.989691i	$0.454255\pi$
$72$	105.448	−	182.641i	0.172599	−	0.298950i
$73$	180.860	+	313.258i	0.289973	+	0.502248i	0.973803	−	0.227394i	$-0.0730204\pi$
$73$	180.860	+	313.258i	0.289973	+	0.502248i	−0.683830	+	0.729641i	$0.739687\pi$
$74$	−122.911	−	212.889i	−0.193083	−	0.334430i
$75$	−248.172	+	429.847i	−0.382086	+	0.661792i
$76$	−369.464			−0.557637
$77$	623.292	+	836.171i	0.922476	+	1.23754i
$78$	−961.881			−1.39630
$79$	421.158	−	729.467i	0.599797	−	1.03888i	−0.393053	−	0.919516i	$-0.628581\pi$
$79$	421.158	−	729.467i	0.599797	−	1.03888i	0.992851	−	0.119364i	$-0.0380855\pi$
$80$	60.4270	+	104.663i	0.0844493	+	0.146271i
$81$	372.911	+	645.900i	0.511537	+	0.886008i
$82$	−359.331	+	622.379i	−0.483920	+	0.838174i
$83$	−1374.29			−1.81744			−0.908721	−	0.417404i	$-0.862940\pi$
$83$	−1374.29			−1.81744			−0.908721	+	0.417404i	$0.862940\pi$
$84$	−214.041	+	497.028i	−0.278021	+	0.645597i
$85$	−822.069			−1.04901
$86$	−33.0320	+	57.2131i	−0.0414178	+	0.0717377i
$87$	212.414	+	367.912i	0.261760	+	0.453382i
$88$	225.249	+	390.142i	0.272859	+	0.472606i
$89$	−620.557	+	1074.84i	−0.739088	+	1.28014i	0.213818	+	0.976874i	$0.431410\pi$
$89$	−620.557	+	1074.84i	−0.739088	+	1.28014i	−0.952906	+	0.303265i	$0.901923\pi$
$90$	398.243			0.466428
$91$	1211.00	−	142.287i	1.39503	−	0.163910i
$92$	92.0000			0.104257
$93$	−857.894	+	1485.92i	−0.956553	+	1.65680i
$94$	147.849	+	256.083i	0.162229	+	0.280988i
$95$	−348.837	−	604.204i	−0.376736	−	0.652526i
$96$	−116.879	+	202.440i	−0.124259	+	0.215223i
$97$	997.907			1.04456			0.522279	−	0.852775i	$-0.325082\pi$
$97$	997.907			1.04456			0.522279	+	0.852775i	$0.325082\pi$
$98$	195.953	−	657.418i	0.201982	−	0.677645i
$99$	1484.50			1.50705
$100$	135.893	−	235.374i	0.135893	−	0.235374i
$101$	−473.324	−	819.822i	−0.466312	−	0.807676i	0.532948	−	0.846148i	$-0.321084\pi$
$101$	−473.324	−	819.822i	−0.466312	−	0.807676i	−0.999260	+	0.0384720i	$0.987751\pi$
$102$	−795.028	−	1377.03i	−0.771760	−	1.33673i
$103$	−211.106	+	365.647i	−0.201951	+	0.349789i	−0.949157	−	0.314803i	$-0.898061\pi$
$103$	−211.106	+	365.647i	−0.201951	+	0.349789i	0.747206	+	0.664592i	$0.231395\pi$
$104$	526.703			0.496610
$105$	−1014.91	+	119.247i	−0.943284	+	0.110832i
$106$	−1281.44			−1.17419
$107$	−294.423	+	509.956i	−0.266009	+	0.460741i	−0.967827	−	0.251615i	$-0.919038\pi$
$107$	−294.423	+	509.956i	−0.266009	+	0.460741i	0.701818	+	0.712356i	$0.252372\pi$
$108$	−9.32230	−	16.1467i	−0.00830591	−	0.0143863i
$109$	−53.4270	−	92.5383i	−0.0469484	−	0.0813171i	0.841596	−	0.540107i	$-0.181616\pi$
$109$	−53.4270	−	92.5383i	−0.0469484	−	0.0813171i	−0.888545	+	0.458790i	$0.848283\pi$
$110$	−425.347	+	736.723i	−0.368684	+	0.638580i
$111$	897.858			0.767756
$112$	117.204	−	272.160i	0.0988813	−	0.229614i
$113$	21.1869			0.0176380			0.00881901	−	0.999961i	$-0.497193\pi$
$113$	21.1869			0.0176380			0.00881901	+	0.999961i	$0.497193\pi$
$114$	674.726	−	1168.66i	0.554332	−	0.960131i
$115$	86.8638	+	150.453i	0.0704356	+	0.121998i
$116$	−116.313	−	201.460i	−0.0930980	−	0.161250i
$117$	867.806	−	1503.08i	0.685716	−	1.18769i
$118$	−804.059			−0.627285
$119$	1204.64	+	1616.07i	0.927973	+	1.24491i
$120$	−441.415			−0.335796
$121$	−920.032	+	1593.54i	−0.691233	+	1.19725i
$122$	240.394	+	416.375i	0.178396	+	0.308991i
$123$	−1312.44	−	2273.22i	−0.962105	−	1.66641i
$124$	469.762	−	813.651i	0.340209	−	0.589258i
$125$	1457.40			1.04283
$126$	−583.574	−	782.888i	−0.412610	−	0.553534i
$127$	2173.95			1.51895			0.759475	−	0.650536i	$-0.225456\pi$
$127$	2173.95			1.51895			0.759475	+	0.650536i	$0.225456\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	−120.648	−	208.969i	−0.0823447	−	0.142625i
$130$	497.298	+	861.346i	0.335507	+	0.581116i
$131$	1227.89	−	2126.76i	0.818939	−	1.41844i	−0.0875259	−	0.996162i	$-0.527896\pi$
$131$	1227.89	−	2126.76i	0.818939	−	1.41844i	0.906465	−	0.422281i	$-0.138771\pi$
$132$	−1645.43			−1.08497
$133$	−676.601	+	1571.15i	−0.441119	+	1.02433i
$134$	−225.770			−0.145549
$135$	17.6037	−	30.4905i	0.0112229	−	0.0194386i
$136$	435.338	+	754.028i	0.274485	+	0.475422i
$137$	−510.645	−	884.464i	−0.318448	−	0.551568i	0.661716	−	0.749754i	$-0.269828\pi$
$137$	−510.645	−	884.464i	−0.318448	−	0.551568i	−0.980164	+	0.198186i	$0.936495\pi$
$138$	−168.013	+	291.007i	−0.103639	+	0.179509i
$139$	418.904			0.255619			0.127809	−	0.991799i	$-0.459205\pi$
$139$	418.904			0.255619			0.127809	+	0.991799i	$0.459205\pi$
$140$	555.739	−	65.2968i	0.335489	−	0.0394185i
$141$	−1080.03			−0.645069
$142$	171.363	−	296.809i	0.101271	−	0.175406i
$143$	1853.74	+	3210.77i	1.08404	+	1.87761i
$144$	−210.895	−	365.281i	−0.122046	−	0.211390i
$145$	219.638	−	380.425i	0.125793	−	0.217880i
$146$	723.438			0.410083
$147$	1721.64	+	1820.42i	0.965976	+	1.02140i
$148$	−491.645			−0.273061
$149$	−492.160	+	852.446i	−0.270599	+	0.468692i	−0.969015	−	0.247000i	$-0.920555\pi$
$149$	−492.160	+	852.446i	−0.270599	+	0.468692i	0.698416	+	0.715692i	$0.253889\pi$
$150$	496.344	+	859.693i	0.270176	+	0.467958i
$151$	−1002.50	−	1736.38i	−0.540278	−	0.935789i	−0.998888	−	0.0471515i	$-0.984986\pi$
$151$	−1002.50	−	1736.38i	−0.540278	−	0.935789i	0.458609	−	0.888638i	$-0.348348\pi$
$152$	−369.464	+	639.930i	−0.197154	+	0.341481i
$153$	2869.09			1.51603
$154$	2071.58	−	243.401i	1.08398	−	0.127363i
$155$	1774.14			0.919372
$156$	−961.881	+	1666.03i	−0.493668	+	0.855057i
$157$	192.934	+	334.171i	0.0980752	+	0.169871i	0.910888	−	0.412654i	$-0.135398\pi$
$157$	192.934	+	334.171i	0.0980752	+	0.169871i	−0.812813	+	0.582525i	$0.802065\pi$
$158$	−842.316	−	1458.93i	−0.424121	−	0.734599i
$159$	2340.21	−	4053.36i	1.16724	−	2.02171i
$160$	241.708			0.119429
$161$	168.480	−	391.231i	0.0824727	−	0.191511i
$162$	1491.64			0.723423
$163$	1198.69	−	2076.19i	0.576003	−	0.997666i	−0.419929	−	0.907557i	$-0.637945\pi$
$163$	1198.69	−	2076.19i	0.576003	−	0.997666i	0.995932	−	0.0901093i	$-0.0287216\pi$
$164$	718.661	+	1244.76i	0.342183	+	0.592678i
$165$	−1553.56	−	2690.85i	−0.732999	−	1.26959i
$166$	−1374.29	+	2380.34i	−0.642563	+	1.11295i
$167$	3438.93			1.59349			0.796743	−	0.604318i	$-0.206554\pi$
$167$	3438.93			1.59349			0.796743	+	0.604318i	$0.206554\pi$
$168$	646.836	+	867.758i	0.297051	+	0.398506i
$169$	2137.63			0.972975
$170$	−822.069	+	1423.86i	−0.370881	+	0.642385i
$171$	1217.47	+	2108.72i	0.544458	+	0.943029i
$172$	66.0640	+	114.426i	0.0292868	+	0.0507262i
$173$	−1004.49	+	1739.84i	−0.441447	+	0.764609i	−0.997797	−	0.0663393i	$-0.978868\pi$
$173$	−1004.49	+	1739.84i	−0.441447	+	0.764609i	0.556350	+	0.830948i	$0.312201\pi$
$174$	849.656			0.370185
$175$	−752.066	−	1008.93i	−0.324862	−	0.435816i
$176$	900.995			0.385881
$177$	1468.40	−	2543.34i	0.623568	−	1.08005i
$178$	1241.11	+	2149.67i	0.522614	+	0.905195i
$179$	−2006.12	−	3474.70i	−0.837677	−	1.45090i	−0.891832	−	0.452367i	$-0.850580\pi$
$179$	−2006.12	−	3474.70i	−0.837677	−	1.45090i	0.0541550	−	0.998533i	$-0.482754\pi$
$180$	398.243	−	689.777i	0.164907	−	0.285627i
$181$	2231.44			0.916361			0.458181	−	0.888859i	$-0.348501\pi$
$181$	2231.44			0.916361			0.458181	+	0.888859i	$0.348501\pi$
$182$	964.555	−	2239.81i	0.392844	−	0.912229i
$183$	−1756.06			−0.709355
$184$	92.0000	−	159.349i	0.0368605	−	0.0638442i
$185$	−464.198	−	804.014i	−0.184478	−	0.319526i
$186$	1715.79	+	2971.83i	0.676385	+	1.17153i
$187$	−3064.36	+	5307.62i	−1.19833	+	2.07557i
$188$	591.397			0.229426
$189$	−85.7359	+	10.0736i	−0.0329967	+	0.00387695i
$190$	−1395.35			−0.532785
$191$	−65.3333	+	113.161i	−0.0247505	+	0.0428692i	−0.878135	−	0.478412i	$-0.841212\pi$
$191$	−65.3333	+	113.161i	−0.0247505	+	0.0428692i	0.853385	+	0.521281i	$0.174546\pi$
$192$	233.758	+	404.880i	0.0878646	+	0.152186i
$193$	1721.66	+	2982.00i	0.642113	+	1.11217i	0.984960	+	0.172781i	$0.0552754\pi$
$193$	1721.66	+	2982.00i	0.642113	+	1.11217i	−0.342847	+	0.939391i	$0.611391\pi$
$194$	997.907	−	1728.43i	0.369307	−	0.639658i
$195$	−3632.73			−1.33408
$196$	−942.728	−	996.819i	−0.343560	−	0.363272i
$197$	−2976.33			−1.07642			−0.538211	−	0.842810i	$-0.680900\pi$
$197$	−2976.33			−1.07642			−0.538211	+	0.842810i	$0.680900\pi$
$198$	1484.50	−	2571.22i	0.532821	−	0.922874i
$199$	451.479	+	781.985i	0.160827	+	0.278560i	0.935165	−	0.354211i	$-0.115251\pi$
$199$	451.479	+	781.985i	0.160827	+	0.278560i	−0.774339	+	0.632771i	$0.781917\pi$
$200$	−271.786	−	470.747i	−0.0960909	−	0.166434i
$201$	412.309	−	714.140i	0.144687	−	0.250605i
$202$	−1893.30			−0.659465
$203$	−1069.71	+	125.686i	−0.369848	+	0.0434554i
$204$	−3180.11			−1.09143
$205$	−1357.08	+	2350.53i	−0.462354	+	0.800820i
$206$	422.213	+	731.294i	0.142801	+	0.247338i
$207$	−303.162	−	525.092i	−0.101793	−	0.176311i
$208$	526.703	−	912.276i	0.175578	−	0.304111i
$209$	−5201.33			−1.72145
$210$	−808.366	+	1877.12i	−0.265631	+	0.616826i
$211$	−2439.95			−0.796081			−0.398041	−	0.917368i	$-0.630310\pi$
$211$	−2439.95			−0.796081			−0.398041	+	0.917368i	$0.630310\pi$
$212$	−1281.44	+	2219.52i	−0.415141	+	0.719044i
$213$	625.897	+	1084.08i	0.201341	+	0.348734i
$214$	588.846	+	1019.91i	0.188097	+	0.325793i
$215$	−124.752	+	216.076i	−0.0395720	+	0.0685407i
$216$	−37.2892			−0.0117463
$217$	−2599.78	−	3487.71i	−0.813293	−	1.09107i
$218$	−213.708			−0.0663951
$219$	−1321.17	+	2288.33i	−0.407653	+	0.706076i
$220$	850.694	+	1473.45i	0.260699	+	0.451544i
$221$	3582.72	+	6205.45i	1.09050	+	1.88880i
$222$	897.858	−	1555.14i	0.271443	−	0.470152i
$223$	−5414.35			−1.62588			−0.812941	−	0.582346i	$-0.802135\pi$
$223$	−5414.35			−1.62588			−0.812941	+	0.582346i	$0.802135\pi$
$224$	−354.192	−	475.163i	−0.105649	−	0.141733i
$225$	−1791.20			−0.530726
$226$	21.1869	−	36.6968i	0.00623598	−	0.0108010i
$227$	−2239.77	−	3879.39i	−0.654884	−	1.13429i	−0.981923	−	0.189282i	$-0.939384\pi$
$227$	−2239.77	−	3879.39i	−0.654884	−	1.13429i	0.327039	−	0.945011i	$-0.393949\pi$
$228$	−1349.45	−	2337.32i	−0.391972	−	0.678915i
$229$	1813.95	−	3141.85i	0.523445	−	0.906634i	−0.476182	−	0.879347i	$-0.657980\pi$
$229$	1813.95	−	3141.85i	0.523445	−	0.906634i	0.999628	−	0.0272874i	$-0.00868694\pi$
$230$	347.455			0.0996110
$231$	−3013.28	+	6997.18i	−0.858265	+	1.99299i
$232$	−465.251			−0.131660
$233$	1841.37	−	3189.34i	0.517734	−	0.896741i	−0.482054	−	0.876142i	$-0.660109\pi$
$233$	1841.37	−	3189.34i	0.517734	−	0.896741i	0.999788	−	0.0205997i	$-0.00655757\pi$
$234$	−1735.61	−	3006.17i	−0.484874	−	0.839827i
$235$	558.381	+	967.144i	0.154999	+	0.268466i
$236$	−804.059	+	1392.67i	−0.221779	+	0.384132i
$237$	6153.06			1.68643
$238$	4003.75	−	470.422i	1.09044	−	0.128122i
$239$	1289.59			0.349025			0.174512	−	0.984655i	$-0.444165\pi$
$239$	1289.59			0.349025			0.174512	+	0.984655i	$0.444165\pi$
$240$	−441.415	+	764.553i	−0.118722	+	0.205632i
$241$	332.076	+	575.173i	0.0887590	+	0.153735i	0.906987	−	0.421159i	$-0.138377\pi$
$241$	332.076	+	575.173i	0.0887590	+	0.153735i	−0.818228	+	0.574894i	$0.805043\pi$
$242$	1840.06	+	3187.08i	0.488776	+	0.846584i
$243$	−2661.16	+	4609.26i	−0.702524	+	1.21681i
$244$	961.578			0.252290
$245$	740.054	−	2482.86i	0.192981	−	0.647446i
$246$	−5249.77			−1.36062
$247$	−3040.59	+	5266.45i	−0.783271	+	1.35667i
$248$	−939.524	−	1627.30i	−0.240564	−	0.416669i
$249$	−5019.53	−	8694.09i	−1.27751	−	2.21271i
$250$	1457.40	−	2524.29i	0.368696	−	0.638600i
$251$	4771.08			1.19979			0.599896	−	0.800078i	$-0.295209\pi$
$251$	4771.08			1.19979			0.599896	+	0.800078i	$0.295209\pi$
$252$	−1939.58	+	227.891i	−0.484848	+	0.0569674i
$253$	1295.18			0.321847
$254$	2173.95	−	3765.39i	0.537030	−	0.930164i
$255$	−3002.57	−	5200.61i	−0.737367	−	1.27716i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	1067.14	−	1848.35i	0.259014	−	0.448626i	−0.706964	−	0.707250i	$-0.749936\pi$
$257$	1067.14	−	1848.35i	0.259014	−	0.448626i	0.965978	+	0.258624i	$0.0832690\pi$
$258$	−482.592			−0.116453
$259$	−900.354	+	2090.72i	−0.216005	+	0.501588i
$260$	1989.19			0.474479
$261$	−766.557	+	1327.72i	−0.181796	+	0.314879i
$262$	−2455.77	−	4253.53i	−0.579077	−	1.00299i
$263$	−3405.12	−	5897.84i	−0.798360	−	1.38280i	−0.920683	−	0.390310i	$-0.872368\pi$
$263$	−3405.12	−	5897.84i	−0.798360	−	1.38280i	0.122323	−	0.992490i	$-0.460966\pi$
$264$	−1645.43	+	2849.96i	−0.383594	+	0.664405i
$265$	−4839.61			−1.12187
$266$	2044.70	+	2743.05i	0.471311	+	0.632284i
$267$	−9066.24			−2.07807
$268$	−225.770	+	391.046i	−0.0514594	+	0.0891303i
$269$	3346.56	+	5796.42i	0.758526	+	1.31381i	0.943602	+	0.331082i	$0.107414\pi$
$269$	3346.56	+	5796.42i	0.758526	+	1.31381i	−0.185076	+	0.982724i	$0.559253\pi$
$270$	−35.2074	−	60.9810i	−0.00793576	−	0.0137451i
$271$	4320.68	−	7483.64i	0.968497	−	1.67749i	0.268588	−	0.963255i	$-0.413443\pi$
$271$	4320.68	−	7483.64i	0.968497	−	1.67749i	0.699909	−	0.714232i	$-0.253224\pi$
$272$	1741.35			0.388180
$273$	5323.29	+	7141.42i	1.18015	+	1.58322i
$274$	−2042.58			−0.450353
$275$	1913.11	−	3313.60i	0.419508	−	0.726610i
$276$	336.027	+	582.015i	0.0732841	+	0.126932i
$277$	3746.79	+	6489.63i	0.812718	+	1.40767i	0.910955	+	0.412506i	$0.135346\pi$
$277$	3746.79	+	6489.63i	0.812718	+	1.40767i	−0.0982373	+	0.995163i	$0.531320\pi$
$278$	418.904	−	725.563i	0.0903748	−	0.156534i
$279$	−6191.91			−1.32867
$280$	442.642	−	1027.87i	0.0944747	−	0.219381i
$281$	1976.73			0.419651			0.209825	−	0.977739i	$-0.432710\pi$
$281$	1976.73			0.419651			0.209825	+	0.977739i	$0.432710\pi$
$282$	−1080.03	+	1870.66i	−0.228066	+	0.395023i
$283$	−3077.31	−	5330.05i	−0.646384	−	1.11957i	−0.983980	−	0.178279i	$-0.942947\pi$
$283$	−3077.31	−	5330.05i	−0.646384	−	1.11957i	0.337595	−	0.941291i	$-0.390386\pi$
$284$	−342.726	−	593.619i	−0.0716093	−	0.124031i
$285$	2548.23	−	4413.66i	0.529628	−	0.917343i
$286$	7414.95			1.53306
$287$	6609.43	−	776.577i	1.35938	−	0.159721i
$288$	−843.581			−0.172599
$289$	−3465.98	+	6003.26i	−0.705472	+	1.22191i
$290$	−439.277	−	760.850i	−0.0889491	−	0.154064i
$291$	3644.82	+	6313.01i	0.734237	+	1.27174i
$292$	723.438	−	1253.03i	0.144986	−	0.251124i
$293$	−1905.58			−0.379950			−0.189975	−	0.981789i	$-0.560841\pi$
$293$	−1905.58			−0.379950			−0.189975	+	0.981789i	$0.560841\pi$
$294$	4874.70	−	1161.55i	0.967001	−	0.230417i
$295$	−3036.68			−0.599330
$296$	−491.645	+	851.555i	−0.0965416	+	0.167215i
$297$	−131.240	−	227.314i	−0.0256407	−	0.0444111i
$298$	984.319	+	1704.89i	0.191343	+	0.331415i
$299$	757.136	−	1311.40i	0.146442	−	0.253646i
$300$	1985.38			0.382086
$301$	607.582	−	71.3880i	0.116347	−	0.0136702i
$302$	−4009.99			−0.764069
$303$	3457.60	−	5988.73i	0.655557	−	1.13546i
$304$	738.927	+	1279.86i	0.139409	+	0.241464i
$305$	907.895	+	1572.52i	0.170446	+	0.295220i
$306$	2869.09	−	4969.41i	0.535996	−	0.928373i
$307$	643.667			0.119661			0.0598307	−	0.998209i	$-0.480944\pi$
$307$	643.667			0.119661			0.0598307	+	0.998209i	$0.480944\pi$
$308$	1650.00	−	3831.49i	0.305251	−	0.708829i
$309$	−3084.23			−0.567818
$310$	1774.14	−	3072.91i	0.325047	−	0.562998i
$311$	2565.52	+	4443.62i	0.467773	+	0.810207i	0.999322	−	0.0368206i	$-0.0117230\pi$
$311$	2565.52	+	4443.62i	0.467773	+	0.810207i	−0.531549	+	0.847028i	$0.678390\pi$
$312$	1923.76	+	3332.06i	0.349076	+	0.604617i
$313$	−2422.97	+	4196.70i	−0.437553	+	0.757864i	−0.997500	−	0.0706642i	$-0.977488\pi$
$313$	−2422.97	+	4196.70i	−0.437553	+	0.757864i	0.559947	+	0.828528i	$0.310821\pi$
$314$	771.736			0.138699
$315$	−2203.98	−	2956.72i	−0.394222	−	0.528865i
$316$	−3369.27			−0.599797
$317$	−1074.53	+	1861.15i	−0.190384	+	0.329756i	−0.945378	−	0.325977i	$-0.894307\pi$
$317$	−1074.53	+	1861.15i	−0.190384	+	0.329756i	0.754993	+	0.655733i	$0.227640\pi$
$318$	−4680.42	−	8106.72i	−0.825361	−	1.42957i
$319$	−1637.46	−	2836.16i	−0.287398	−	0.497788i
$320$	241.708	−	418.651i	0.0422247	−	0.0731353i
$321$	−4301.48			−0.747929
$322$	−509.151	−	683.047i	−0.0881176	−	0.118213i
$323$	−10052.6			−1.73171
$324$	1491.64	−	2583.60i	0.255769	−	0.443004i
$325$	−2236.73	−	3874.12i	−0.381758	−	0.661224i
$326$	−2397.38	−	4152.38i	−0.407296	−	0.705457i
$327$	390.280	−	675.985i	0.0660017	−	0.114318i
$328$	2874.64			0.483920
$329$	1083.03	−	2514.92i	0.181488	−	0.421435i
$330$	−6214.26			−1.03662
$331$	−366.672	+	635.094i	−0.0608886	+	0.105462i	−0.894863	−	0.446341i	$-0.852727\pi$
$331$	−366.672	+	635.094i	−0.0608886	+	0.105462i	0.833974	+	0.551803i	$0.186060\pi$
$332$	2748.58	+	4760.67i	0.454361	+	0.786976i
$333$	1620.09	+	2806.08i	0.266608	+	0.461778i
$334$	3438.93	−	5956.40i	0.563383	−	0.975807i
$335$	−852.665			−0.139063
$336$	2149.84	−	252.596i	0.349057	−	0.0410126i
$337$	−1922.41			−0.310743			−0.155372	−	0.987856i	$-0.549657\pi$
$337$	−1922.41			−0.310743			−0.155372	+	0.987856i	$0.549657\pi$
$338$	2137.63	−	3702.48i	0.343999	−	0.595823i
$339$	77.3844	+	134.034i	0.0123981	+	0.0214741i
$340$	1644.14	+	2847.73i	0.262253	+	0.454235i
$341$	6613.33	−	11454.6i	1.05024	−	1.81907i
$342$	4869.88			0.769980
$343$	−5965.40	+	2183.48i	−0.939071	+	0.343722i
$344$	264.256			0.0414178
$345$	−634.534	+	1099.04i	−0.0990207	+	0.171509i
$346$	2008.99	+	3479.67i	0.312150	+	0.540660i
$347$	−5654.75	−	9794.32i	−0.874821	−	1.51523i	−0.856953	−	0.515394i	$-0.827645\pi$
$347$	−5654.75	−	9794.32i	−0.874821	−	1.51523i	−0.0178681	−	0.999840i	$-0.505688\pi$
$348$	849.656	−	1471.65i	0.130880	−	0.226691i
$349$	5202.37			0.797927			0.398963	−	0.916967i	$-0.369370\pi$
$349$	5202.37			0.797927			0.398963	+	0.916967i	$0.369370\pi$
$350$	−2499.58	+	293.689i	−0.381738	+	0.0448524i
$351$	−306.880			−0.0466668
$352$	900.995	−	1560.57i	0.136430	−	0.236303i
$353$	−3151.34	−	5458.28i	−0.475153	−	0.822989i	0.524442	−	0.851446i	$-0.324274\pi$
$353$	−3151.34	−	5458.28i	−0.475153	−	0.822989i	−0.999595	+	0.0284571i	$0.990941\pi$
$354$	−2936.79	−	5086.68i	−0.440929	−	0.763712i
$355$	647.184	−	1120.96i	0.0967577	−	0.167589i
$356$	4964.45			0.739088
$357$	−5823.77	+	13523.5i	−0.863379	+	2.00487i
$358$	−8024.47			−1.18465
$359$	6398.94	−	11083.3i	0.940733	−	1.62940i	0.176655	−	0.984273i	$-0.443472\pi$
$359$	6398.94	−	11083.3i	0.940733	−	1.62940i	0.764078	−	0.645124i	$-0.223194\pi$
$360$	−796.486	−	1379.55i	−0.116607	−	0.201969i
$361$	−836.229	−	1448.39i	−0.121917	−	0.211166i
$362$	2231.44	−	3864.96i	0.323983	−	0.561154i
$363$	−13441.5			−1.94352
$364$	−2914.91	−	3910.47i	−0.419732	−	0.563088i
$365$	2732.20			0.391808
$366$	−1756.06	+	3041.59i	−0.250795	+	0.434389i
$367$	3897.37	+	6750.44i	0.554335	+	0.960136i	0.997955	+	0.0639213i	$0.0203607\pi$
$367$	3897.37	+	6750.44i	0.554335	+	0.960136i	−0.443620	+	0.896215i	$0.646306\pi$
$368$	−184.000	−	318.697i	−0.0260643	−	0.0451447i
$369$	4736.32	−	8203.55i	0.668193	−	1.15734i
$370$	−1856.79			−0.260892
$371$	7091.82	+	9513.97i	0.992423	+	1.33138i
$372$	6863.15			0.956553
$373$	−4676.01	+	8099.08i	−0.649101	+	1.12428i	0.334237	+	0.942489i	$0.391521\pi$
$373$	−4676.01	+	8099.08i	−0.649101	+	1.12428i	−0.983338	+	0.181786i	$0.941812\pi$
$374$	6128.71	+	10615.2i	0.847348	+	1.46765i
$375$	5323.09	+	9219.86i	0.733022	+	1.26963i
$376$	591.397	−	1024.33i	0.0811143	−	0.140494i
$377$	−3828.89			−0.523072
$378$	−68.2880	+	158.572i	−0.00929194	+	0.0215770i
$379$	−671.508			−0.0910107			−0.0455054	−	0.998964i	$-0.514490\pi$
$379$	−671.508			−0.0910107			−0.0455054	+	0.998964i	$0.514490\pi$
$380$	−1395.35	+	2416.81i	−0.188368	+	0.326263i
$381$	7940.26	+	13752.9i	1.06770	+	1.84930i
$382$	130.667	+	226.321i	0.0175013	+	0.0303131i
$383$	−2961.57	+	5129.58i	−0.395115	+	0.684359i	−0.993116	−	0.117136i	$-0.962629\pi$
$383$	−2961.57	+	5129.58i	−0.395115	+	0.684359i	0.598001	+	0.801495i	$0.295962\pi$
$384$	935.030			0.124259
$385$	7823.72	−	919.251i	1.03567	−	0.121687i
$386$	6886.64			0.908085
$387$	435.393	−	754.123i	0.0571894	−	0.0990549i
$388$	−1995.81	−	3456.85i	−0.261139	−	0.452307i
$389$	1726.23	+	2989.91i	0.224995	+	0.389703i	0.956318	−	0.292328i	$-0.0944300\pi$
$389$	1726.23	+	2989.91i	0.224995	+	0.389703i	−0.731323	+	0.682032i	$0.761097\pi$
$390$	−3632.73	+	6292.07i	−0.471667	+	0.816952i
$391$	2503.20			0.323765
$392$	−2669.27	+	636.034i	−0.343925	+	0.0819504i
$393$	17939.2			2.30258
$394$	−2976.33	+	5155.16i	−0.380573	+	0.659171i
$395$	−3181.17	−	5509.94i	−0.405220	−	0.701861i
$396$	−2968.99	−	5142.45i	−0.376762	−	0.652570i
$397$	1231.35	−	2132.77i	0.155667	−	0.269624i	−0.777635	−	0.628717i	$-0.783581\pi$
$397$	1231.35	−	2132.77i	0.155667	−	0.269624i	0.933302	+	0.359093i	$0.116914\pi$
$398$	1805.92			0.227443
$399$	−12410.7	+	1458.20i	−1.55718	+	0.182961i
$400$	−1087.14			−0.135893
$401$	6314.01	−	10936.2i	0.786301	−	1.36191i	−0.141917	−	0.989879i	$-0.545327\pi$
$401$	6314.01	−	10936.2i	0.786301	−	1.36191i	0.928219	−	0.372035i	$-0.121340\pi$
$402$	−824.618	−	1428.28i	−0.102309	−	0.177204i
$403$	−7732.03	−	13392.3i	−0.955732	−	1.65538i
$404$	−1893.30	+	3279.29i	−0.233156	+	0.403838i
$405$	5633.47			0.691183
$406$	−852.017	+	1978.48i	−0.104150	+	0.241848i
$407$	−6921.41			−0.842952
$408$	−3180.11	+	5508.12i	−0.385880	+	0.668364i
$409$	−4928.87	−	8537.06i	−0.595885	−	1.03210i	−0.993421	−	0.114517i	$-0.963468\pi$
$409$	−4928.87	−	8537.06i	−0.595885	−	1.03210i	0.397536	−	0.917587i	$-0.369865\pi$
$410$	2714.16	+	4701.06i	0.326934	+	0.566266i
$411$	3730.23	−	6460.94i	0.447685	−	0.775413i
$412$	1688.85			0.201951
$413$	4449.86	+	5969.68i	0.530178	+	0.711255i
$414$	−1212.65			−0.143958
$415$	−5190.26	+	8989.79i	−0.613927	+	1.06335i
$416$	−1053.41	−	1824.55i	−0.124153	−	0.215039i
$417$	1530.03	+	2650.09i	0.179679	+	0.311212i
$418$	−5201.33	+	9008.96i	−0.608625	+	1.05417i
$419$	−15594.0			−1.81818			−0.909090	−	0.416599i	$-0.863222\pi$
$419$	−15594.0			−1.81818			−0.909090	+	0.416599i	$0.863222\pi$
$420$	2442.90	+	3277.25i	0.283813	+	0.380746i
$421$	−2429.98			−0.281306			−0.140653	−	0.990059i	$-0.544920\pi$
$421$	−2429.98			−0.281306			−0.140653	+	0.990059i	$0.544920\pi$
$422$	−2439.95	+	4226.12i	−0.281457	+	0.487498i
$423$	−1948.80	−	3375.41i	−0.224004	−	0.387986i
$424$	2562.88	+	4439.04i	0.293549	+	0.508441i
$425$	3697.47	−	6404.20i	0.422008	−	0.730939i
$426$	2503.59			0.284740
$427$	1760.94	−	4089.12i	0.199574	−	0.463434i
$428$	2355.39			0.266009
$429$	−13541.4	+	23454.4i	−1.52398	+	2.63960i
$430$	249.503	+	432.152i	0.0279816	+	0.0484656i
$431$	2270.14	+	3932.00i	0.253710	+	0.439438i	0.964544	−	0.263921i	$-0.0850158\pi$
$431$	2270.14	+	3932.00i	0.253710	+	0.439438i	−0.710834	+	0.703359i	$0.751683\pi$
$432$	−37.2892	+	64.5868i	−0.00415296	+	0.00719313i
$433$	−15322.6			−1.70060			−0.850299	−	0.526300i	$-0.823579\pi$
$433$	−15322.6			−1.70060			−0.850299	+	0.526300i	$0.823579\pi$
$434$	−8640.67	+	1015.24i	−0.955681	+	0.112288i
$435$	3208.88			0.353688
$436$	−213.708	+	370.153i	−0.0234742	+	0.0406585i
$437$	1062.21	+	1839.80i	0.116275	+	0.201395i
$438$	2642.33	+	4576.65i	0.288254	+	0.499271i
$439$	2570.90	−	4452.92i	0.279504	−	0.484115i	−0.691758	−	0.722130i	$-0.743163\pi$
$439$	2570.90	−	4452.92i	0.279504	−	0.484115i	0.971262	+	0.238015i	$0.0764967\pi$
$440$	3402.78			0.368684
$441$	−2582.85	+	8665.40i	−0.278895	+	0.935687i
$442$	14330.9			1.54220
$443$	3769.16	−	6528.38i	0.404240	−	0.700165i	−0.589993	−	0.807409i	$-0.700869\pi$
$443$	3769.16	−	6528.38i	0.404240	−	0.700165i	0.994233	+	0.107244i	$0.0342027\pi$
$444$	−1795.72	−	3110.27i	−0.191939	−	0.332448i
$445$	4687.30	+	8118.64i	0.499324	+	0.864855i
$446$	−5414.35	+	9377.93i	−0.574836	+	0.995646i
$447$	−7190.38			−0.760835
$448$	−1177.20	+	138.315i	−0.124146	+	0.0145866i
$449$	−7253.14			−0.762354			−0.381177	−	0.924502i	$-0.624481\pi$
$449$	−7253.14			−0.762354			−0.381177	+	0.924502i	$0.624481\pi$
$450$	−1791.20	+	3102.45i	−0.187640	+	0.325002i
$451$	10117.3	+	17523.8i	1.05634	+	1.82963i
$452$	−42.3738	−	73.3936i	−0.00440950	−	0.00763749i
$453$	7323.16	−	12684.1i	0.759541	−	1.31556i
$454$	−8959.08			−0.926146
$455$	3642.82	−	8459.06i	0.375337	−	0.871575i
$456$	−5397.81			−0.554332
$457$	7056.72	−	12222.6i	0.722319	−	1.25109i	−0.237750	−	0.971326i	$-0.576410\pi$
$457$	7056.72	−	12222.6i	0.722319	−	1.25109i	0.960068	−	0.279766i	$-0.0902569\pi$
$458$	−3627.89	−	6283.70i	−0.370132	−	0.641087i
$459$	−253.647	−	439.330i	−0.0257935	−	0.0446757i
$460$	347.455	−	601.810i	0.0352178	−	0.0609990i
$461$	1996.06			0.201662			0.100831	−	0.994904i	$-0.467850\pi$
$461$	1996.06			0.201662			0.100831	+	0.994904i	$0.467850\pi$
$462$	9106.19	+	12216.3i	0.917010	+	1.23021i
$463$	8301.53			0.833271			0.416636	−	0.909074i	$-0.363209\pi$
$463$	8301.53			0.833271			0.416636	+	0.909074i	$0.363209\pi$
$464$	−465.251	+	805.838i	−0.0465490	+	0.0806252i
$465$	6479.99	+	11223.7i	0.646242	+	1.11932i
$466$	−3682.73	−	6378.68i	−0.366093	−	0.634092i
$467$	2258.92	−	3912.57i	0.223834	−	0.387692i	−0.732135	−	0.681159i	$-0.761476\pi$
$467$	2258.92	−	3912.57i	0.223834	−	0.387692i	0.955969	+	0.293468i	$0.0948094\pi$
$468$	−6942.45			−0.685716
$469$	1249.47	+	1676.22i	0.123017	+	0.165033i
$470$	2233.52			0.219202
$471$	−1409.37	+	2441.10i	−0.137877	+	0.238811i
$472$	1608.12	+	2785.34i	0.156821	+	0.271622i
$473$	930.052	+	1610.90i	0.0904098	+	0.156594i
$474$	6153.06	−	10657.4i	0.596243	−	1.03272i
$475$	6275.94			0.606231
$476$	3188.95	−	7405.12i	0.307070	−	0.713053i
$477$	16890.6			1.62132
$478$	1289.59	−	2233.64i	0.123399	−	0.213733i
$479$	8257.82	+	14303.0i	0.787702	+	1.36434i	0.927371	+	0.374142i	$0.122063\pi$
$479$	8257.82	+	14303.0i	0.787702	+	1.36434i	−0.139669	+	0.990198i	$0.544604\pi$
$480$	882.829	+	1529.11i	0.0839489	+	0.145404i
$481$	−4046.11	+	7008.07i	−0.383548	+	0.664325i
$482$	1328.31			0.125524
$483$	3090.39	−	363.107i	0.291134	−	0.0342069i
$484$	7360.25			0.691233
$485$	3768.78	−	6527.72i	0.352849	−	0.611152i
$486$	5322.32	+	9218.52i	0.496760	+	0.860413i
$487$	−4526.54	−	7840.20i	−0.421185	−	0.729514i	0.574871	−	0.818244i	$-0.305052\pi$
$487$	−4526.54	−	7840.20i	−0.421185	−	0.729514i	−0.996056	+	0.0887304i	$0.971719\pi$
$488$	961.578	−	1665.50i	0.0891979	−	0.154495i
$489$	17512.6			1.61953
$490$	−3560.39	−	3764.67i	−0.328249	−	0.347083i
$491$	−7398.88			−0.680055			−0.340027	−	0.940416i	$-0.610436\pi$
$491$	−7398.88			−0.680055			−0.340027	+	0.940416i	$0.610436\pi$
$492$	−5249.77	+	9092.86i	−0.481052	+	0.833207i
$493$	−3164.71	−	5481.44i	−0.289110	−	0.500754i
$494$	6081.17	+	10532.9i	0.553856	+	0.959307i
$495$	5606.48	−	9710.71i	0.509076	−	0.881746i
$496$	−3758.09			−0.340209
$497$	−3152.00	+	370.346i	−0.284480	+	0.0334251i
$498$	−20078.1			−1.80667
$499$	358.911	−	621.652i	0.0321985	−	0.0557694i	−0.849477	−	0.527625i	$-0.823082\pi$
$499$	358.911	−	621.652i	0.0321985	−	0.0557694i	0.881676	+	0.471856i	$0.156416\pi$
$500$	−2914.80	−	5048.57i	−0.260707	−	0.451558i
$501$	12560.6	+	21755.5i	1.12009	+	1.94005i
$502$	4771.08	−	8263.75i	0.424190	−	0.734719i
$503$	−1927.68			−0.170877			−0.0854385	−	0.996343i	$-0.527229\pi$
$503$	−1927.68			−0.170877			−0.0854385	+	0.996343i	$0.527229\pi$
$504$	−1544.86	+	3587.34i	−0.136535	+	0.317049i
$505$	−7150.39			−0.630076
$506$	1295.18	−	2243.32i	0.113790	−	0.197090i
$507$	7807.60	+	13523.2i	0.683920	+	1.18459i
$508$	−4347.90	−	7530.78i	−0.379738	−	0.657725i
$509$	3902.44	−	6759.22i	0.339828	−	0.588600i	−0.644572	−	0.764544i	$-0.722964\pi$
$509$	3902.44	−	6759.22i	0.339828	−	0.588600i	0.984400	+	0.175944i	$0.0562978\pi$
$510$	−12010.3			−1.04279
$511$	−4003.69	−	5371.11i	−0.346600	−	0.464979i
$512$	−512.000			−0.0441942
$513$	215.266	−	372.851i	0.0185267	−	0.0320892i
$514$	−2134.29	−	3696.70i	−0.183151	−	0.317226i
$515$	1594.57	+	2761.87i	0.136437	+	0.236316i
$516$	−482.592	+	835.874i	−0.0411724	+	0.0713126i
$517$	8325.72			0.708249
$518$	2720.89	+	3650.18i	0.230789	+	0.309614i
$519$	−14675.5			−1.24120
$520$	1989.19	−	3445.38i	0.167754	−	0.290558i
$521$	10703.4	+	18538.9i	0.900049	+	1.55893i	0.827429	+	0.561570i	$0.189803\pi$
$521$	10703.4	+	18538.9i	0.900049	+	1.55893i	0.0726198	+	0.997360i	$0.476864\pi$
$522$	1533.11	+	2655.43i	0.128549	+	0.222653i
$523$	−5663.92	+	9810.20i	−0.473549	+	0.820211i	−0.999542	−	0.0302784i	$-0.990361\pi$
$523$	−5663.92	+	9810.20i	−0.473549	+	0.820211i	0.525993	+	0.850489i	$0.323694\pi$
$524$	−9823.10			−0.818939
$525$	3635.83	−	8442.83i	0.302249	−	0.701857i
$526$	−13620.5			−1.12905
$527$	12781.6	−	22138.4i	1.05650	−	1.82991i
$528$	3290.85	+	5699.92i	0.271242	+	0.469805i
$529$	−264.500	−	458.127i	−0.0217391	−	0.0376533i
$530$	−4839.61	+	8382.44i	−0.396640	+	0.687000i
$531$	10598.3			0.866150
$532$	6795.81	−	798.477i	0.553827	−	0.0650721i
$533$	23657.6			1.92256
$534$	−9066.24	+	15703.2i	−0.734709	+	1.27255i
$535$	2223.89	+	3851.89i	0.179714	+	0.311274i
$536$	451.541	+	782.092i	0.0363873	+	0.0630247i
$537$	14654.5	−	25382.4i	1.17763	−	2.03972i
$538$	13386.3			1.07272
$539$	−13271.8	−	14033.3i	−1.06059	−	1.12144i
$540$	−140.830			−0.0112229
$541$	4254.43	−	7368.89i	0.338100	−	0.585607i	−0.645975	−	0.763358i	$-0.723549\pi$
$541$	4254.43	−	7368.89i	0.338100	−	0.585607i	0.984075	+	0.177752i	$0.0568824\pi$
$542$	−8641.37	−	14967.3i	−0.684831	−	1.18616i
$543$	8150.24	+	14116.6i	0.644125	+	1.11566i
$544$	1741.35	−	3016.11i	0.137242	−	0.237711i
$545$	−807.109			−0.0634362
$546$	17692.6	−	2078.80i	1.38676	−	0.162938i
$547$	7097.86			0.554813			0.277406	−	0.960753i	$-0.410525\pi$
$547$	7097.86			0.554813			0.277406	+	0.960753i	$0.410525\pi$
$548$	−2042.58	+	3537.85i	−0.159224	+	0.275784i
$549$	−3168.63	−	5488.23i	−0.246327	−	0.426652i
$550$	−3826.22	−	6627.20i	−0.296637	−	0.513791i
$551$	2685.83	−	4652.00i	0.207659	−	0.359677i
$552$	1344.11			0.103639
$553$	−6170.16	+	14327.8i	−0.474470	+	1.10177i
$554$	14987.2			1.14936
$555$	3390.93	−	5873.26i	0.259346	−	0.449200i
$556$	−837.808	−	1451.13i	−0.0639046	−	0.110686i
$557$	−134.978	−	233.790i	−0.0102679	−	0.0177845i	0.860846	−	0.508866i	$-0.169935\pi$
$557$	−134.978	−	233.790i	−0.0102679	−	0.0177845i	−0.871114	+	0.491081i	$0.836602\pi$
$558$	−6191.91	+	10724.7i	−0.469757	+	0.813643i
$559$	2174.76			0.164548
$560$	−1337.67	−	1794.54i	−0.100941	−	0.135417i
$561$	−44769.8			−3.36931
$562$	1976.73	−	3423.80i	0.148369	−	0.256983i
$563$	11374.8	+	19701.7i	0.851491	+	1.47482i	0.879863	+	0.475228i	$0.157634\pi$
$563$	11374.8	+	19701.7i	0.851491	+	1.47482i	−0.0283723	+	0.999597i	$0.509032\pi$
$564$	2160.06	+	3741.33i	0.161267	+	0.279323i
$565$	80.0163	−	138.592i	0.00595807	−	0.0103197i
$566$	−12309.2			−0.914126
$567$	−8255.12	−	11074.6i	−0.611433	−	0.820262i
$568$	−1370.90			−0.101271
$569$	46.8598	−	81.1636i	0.00345249	−	0.00597988i	−0.864294	−	0.502987i	$-0.832234\pi$
$569$	46.8598	−	81.1636i	0.00345249	−	0.00597988i	0.867746	+	0.497007i	$0.165568\pi$
$570$	−5096.46	−	8827.32i	−0.374504	−	0.648660i
$571$	−1755.96	−	3041.41i	−0.128695	−	0.222906i	0.794476	−	0.607295i	$-0.207745\pi$
$571$	−1755.96	−	3041.41i	−0.128695	−	0.222906i	−0.923171	+	0.384389i	$0.874412\pi$
$572$	7414.95	−	12843.1i	0.542019	−	0.938804i
$573$	−954.510			−0.0695903
$574$	5264.36	−	12224.4i	0.382805	−	0.888917i
$575$	−1562.77			−0.113343
$576$	−843.581	+	1461.13i	−0.0610230	+	0.105695i
$577$	1821.94	+	3155.69i	0.131453	+	0.227683i	0.924237	−	0.381820i	$-0.124703\pi$
$577$	1821.94	+	3155.69i	0.131453	+	0.227683i	−0.792784	+	0.609503i	$0.791369\pi$
$578$	6931.97	+	12006.5i	0.498844	+	0.864023i
$579$	−12576.6	+	21783.3i	−0.902704	+	1.56353i
$580$	−1757.11			−0.125793
$581$	25278.3	−	2970.08i	1.80503	−	0.212082i
$582$	14579.3			1.03837
$583$	−18040.2	+	31246.5i	−1.28156	+	2.21972i
$584$	−1446.88	−	2506.06i	−0.102521	−	0.177571i
$585$	−6554.87	−	11353.4i	−0.463266	−	0.802400i
$586$	−1905.58	+	3300.56i	−0.134332	+	0.232671i
$587$	12611.0			0.886730			0.443365	−	0.896341i	$-0.353784\pi$
$587$	12611.0			0.886730			0.443365	+	0.896341i	$0.353784\pi$
$588$	2862.85	−	9604.78i	0.200785	−	0.673630i
$589$	21695.0			1.51770
$590$	−3036.68	+	5259.68i	−0.211895	+	0.367013i
$591$	−10870.9	−	18829.0i	−0.756635	−	1.31053i
$592$	983.291	+	1703.11i	0.0682652	+	0.118239i
$593$	258.426	−	447.607i	0.0178959	−	0.0309967i	−0.856939	−	0.515418i	$-0.827637\pi$
$593$	258.426	−	447.607i	0.0178959	−	0.0309967i	0.874835	+	0.484422i	$0.160970\pi$
$594$	−524.959			−0.0362615
$595$	15120.9	−	1776.64i	1.04184	−	0.122412i
$596$	3937.28			0.270599
$597$	−3298.02	+	5712.34i	−0.226096	+	0.391609i
$598$	−1514.27	−	2622.79i	−0.103550	−	0.179355i
$599$	3119.99	+	5403.98i	0.212820	+	0.368615i	0.952596	−	0.304238i	$-0.0984018\pi$
$599$	3119.99	+	5403.98i	0.212820	+	0.368615i	−0.739776	+	0.672853i	$0.765068\pi$
$600$	1985.38	−	3438.77i	0.135088	−	0.233979i
$601$	−22085.1			−1.49895			−0.749477	−	0.662031i	$-0.769695\pi$
$601$	−22085.1			−1.49895			−0.749477	+	0.662031i	$0.769695\pi$
$602$	483.934	−	1123.75i	0.0327636	−	0.0760808i
$603$	2975.87			0.200973
$604$	−4009.99	+	6945.50i	−0.270139	+	0.467895i
$605$	6949.34	+	12036.6i	0.466993	+	0.808856i
$606$	−6915.20	−	11977.5i	−0.463549	−	0.802890i
$607$	−11694.2	+	20254.9i	−0.781963	+	1.35440i	0.148833	+	0.988862i	$0.452448\pi$
$607$	−11694.2	+	20254.9i	−0.781963	+	1.35440i	−0.930797	+	0.365538i	$0.880885\pi$
$608$	2955.71			0.197154
$609$	−4702.21	−	6308.20i	−0.312879	−	0.419739i
$610$	3631.58			0.241046
$611$	4867.04	−	8429.97i	0.322258	−	0.558167i
$612$	−5738.18	−	9938.81i	−0.379007	−	0.656459i
$613$	−11597.6	−	20087.7i	−0.764149	−	1.32355i	−0.940695	−	0.339253i	$-0.889826\pi$
$613$	−11597.6	−	20087.7i	−0.764149	−	1.32355i	0.176546	−	0.984292i	$-0.443508\pi$
$614$	643.667	−	1114.86i	0.0423067	−	0.0732773i
$615$	−19826.7			−1.29999
$616$	−4986.33	−	6689.37i	−0.326145	−	0.437536i
$617$	−4370.58			−0.285175			−0.142588	−	0.989782i	$-0.545542\pi$
$617$	−4370.58			−0.285175			−0.142588	+	0.989782i	$0.545542\pi$
$618$	−3084.23	+	5342.05i	−0.200754	+	0.347716i
$619$	−2877.30	−	4983.64i	−0.186831	−	0.323601i	0.757361	−	0.652997i	$-0.226488\pi$
$619$	−2877.30	−	4983.64i	−0.186831	−	0.323601i	−0.944192	+	0.329395i	$0.893155\pi$
$620$	−3548.29	−	6145.81i	−0.229843	−	0.398100i
$621$	−53.6032	+	92.8435i	−0.00346380	+	0.00599948i
$622$	10262.1			0.661531
$623$	9091.44	−	21111.4i	0.584656	−	1.35764i
$624$	7695.05			0.493668
$625$	1257.48	−	2178.02i	0.0804787	−	0.139393i
$626$	4845.93	+	8393.40i	0.309397	+	0.535891i
$627$	−18997.6	−	32904.9i	−1.21004	−	2.09584i
$628$	771.736	−	1336.69i	0.0490376	−	0.0849356i
$629$	−13377.0			−0.847975
$630$	−7325.17	+	860.674i	−0.463241	+	0.0544287i
$631$	−10487.6			−0.661658			−0.330829	−	0.943691i	$-0.607328\pi$
$631$	−10487.6			−0.661658			−0.330829	+	0.943691i	$0.607328\pi$
$632$	−3369.27	+	5835.74i	−0.212060	+	0.367299i
$633$	−8911.83	−	15435.7i	−0.559579	−	0.969219i
$634$	2149.07	+	3722.30i	0.134622	+	0.233172i
$635$	8210.33	−	14220.7i	0.513097	−	0.888711i
$636$	−18721.7			−1.16724
$637$	−21967.4	+	5234.39i	−1.36637	+	0.325580i
$638$	−6549.82			−0.406442
$639$	−2258.73	+	3912.23i	−0.139834	+	0.242199i
$640$	−483.416	−	837.301i	−0.0298573	−	0.0517144i
$641$	−11321.7	−	19609.8i	−0.697631	−	1.20833i	−0.969286	−	0.245938i	$-0.920904\pi$
$641$	−11321.7	−	19609.8i	−0.697631	−	1.20833i	0.271654	−	0.962395i	$-0.412429\pi$
$642$	−4301.48	+	7450.38i	−0.264433	+	0.458011i
$643$	−8247.48			−0.505830			−0.252915	−	0.967488i	$-0.581389\pi$
$643$	−8247.48			−0.505830			−0.252915	+	0.967488i	$0.581389\pi$
$644$	−1692.22	+	198.828i	−0.103545	+	0.0121661i
$645$	−1822.60			−0.111263
$646$	−10052.6	+	17411.6i	−0.612251	+	1.06045i
$647$	−1679.09	−	2908.27i	−0.102027	−	0.176717i	0.810492	−	0.585749i	$-0.199200\pi$
$647$	−1679.09	−	2908.27i	−0.102027	−	0.176717i	−0.912520	+	0.409032i	$0.865866\pi$
$648$	−2983.28	−	5167.20i	−0.180856	−	0.313251i
$649$	−11319.6	+	19606.1i	−0.684642	+	1.18583i
$650$	−8946.91			−0.539887
$651$	12568.5	−	29185.6i	0.756682	−	1.75710i
$652$	−9589.50			−0.576003
$653$	5621.76	−	9737.17i	0.336901	−	0.583529i	−0.646947	−	0.762535i	$-0.723955\pi$
$653$	5621.76	−	9737.17i	0.336901	−	0.583529i	0.983848	+	0.179005i	$0.0572879\pi$
$654$	−780.561	−	1351.97i	−0.0466702	−	0.0808352i
$655$	−9274.69	−	16064.2i	−0.553271	−	0.958293i
$656$	2874.64	−	4979.03i	0.171091	−	0.296339i
$657$	−9535.61			−0.566240
$658$	−3272.94	−	4390.79i	−0.193910	−	0.260138i
$659$	28375.7			1.67733			0.838664	−	0.544650i	$-0.183337\pi$
$659$	28375.7			1.67733			0.838664	+	0.544650i	$0.183337\pi$
$660$	−6214.26	+	10763.4i	−0.366499	+	0.634796i
$661$	13260.5	+	22967.8i	0.780292	+	1.35151i	0.931771	+	0.363045i	$0.118263\pi$
$661$	13260.5	+	22967.8i	0.780292	+	1.35151i	−0.151479	+	0.988460i	$0.548404\pi$
$662$	733.344	+	1270.19i	0.0430547	+	0.0745729i
$663$	−26171.5	+	45330.4i	−1.53306	+	2.65533i
$664$	10994.3			0.642563
$665$	7722.21	+	10359.7i	0.450307	+	0.604106i
$666$	6480.36			0.377040
$667$	−668.798	+	1158.39i	−0.0388245	+	0.0672461i
$668$	−6877.86	−	11912.8i	−0.398372	−	0.690000i
$669$	−19775.7	−	34252.5i	−1.14286	−	1.97949i
$670$	−852.665	+	1476.86i	−0.0491661	+	0.0851582i
$671$	13537.1			0.778831
$672$	1712.33	−	3976.22i	0.0982954	−	0.228253i
$673$	−11574.0			−0.662921			−0.331460	−	0.943469i	$-0.607541\pi$
$673$	−11574.0			−0.662921			−0.331460	+	0.943469i	$0.607541\pi$
$674$	−1922.41	+	3329.71i	−0.109864	+	0.190290i
$675$	158.354	+	274.278i	0.00902972	+	0.0156399i
$676$	−4275.25	−	7404.96i	−0.243244	−	0.421311i
$677$	−9982.29	+	17289.8i	−0.566692	+	0.981539i	0.430198	+	0.902735i	$0.358444\pi$
$677$	−9982.29	+	17289.8i	−0.566692	+	0.981539i	−0.996890	+	0.0788049i	$0.974890\pi$
$678$	309.537			0.0175335
$679$	−18355.2	+	2156.65i	−1.03742	+	0.121892i
$680$	6576.55			0.370881
$681$	16361.3	−	28338.7i	0.920658	−	1.59463i
$682$	−13226.7	−	22909.2i	−0.742632	−	1.28628i
$683$	−15477.8	−	26808.4i	−0.867120	−	1.50190i	−0.864927	−	0.501898i	$-0.832635\pi$
$683$	−15477.8	−	26808.4i	−0.867120	−	1.50190i	−0.00219336	−	0.999998i	$-0.500698\pi$
$684$	4869.88	−	8434.89i	0.272229	−	0.471515i
$685$	−7714.19			−0.430283
$686$	−2183.51	+	12515.9i	−0.121526	+	0.696586i
$687$	26501.5			1.47175
$688$	264.256	−	457.705i	0.0146434	−	0.0253631i
$689$	21091.9	+	36532.2i	1.16623	+	2.01998i
$690$	1269.07	+	2198.09i	0.0700182	+	0.121275i
$691$	5178.01	−	8968.58i	0.285066	−	0.493750i	−0.687559	−	0.726129i	$-0.741318\pi$
$691$	5178.01	−	8968.58i	0.285066	−	0.493750i	0.972625	+	0.232379i	$0.0746510\pi$
$692$	8035.96			0.441447
$693$	−27305.4	+	3208.26i	−1.49675	+	0.175861i
$694$	−22619.0			−1.23718
$695$	1582.07	−	2740.23i	0.0863472	−	0.149558i
$696$	−1699.31	−	2943.29i	−0.0925463	−	0.160295i
$697$	19553.8	+	33868.2i	1.06263	+	1.84053i
$698$	5202.37	−	9010.77i	0.282110	−	0.488628i
$699$	26902.1			1.45569
$700$	−1990.90	+	4623.09i	−0.107498	+	0.249623i
$701$	−736.621			−0.0396887			−0.0198444	−	0.999803i	$-0.506317\pi$
$701$	−736.621			−0.0396887			−0.0198444	+	0.999803i	$0.506317\pi$
$702$	−306.880	+	531.532i	−0.0164992	+	0.0285775i
$703$	−5676.41	−	9831.82i	−0.304537	−	0.527474i
$704$	−1801.99	−	3121.14i	−0.0964703	−	0.167091i
$705$	−4078.93	+	7064.91i	−0.217903	+	0.377419i
$706$	−12605.4			−0.671968
$707$	10478.0	+	14056.6i	0.557376	+	0.747743i
$708$	−11747.2			−0.623568
$709$	16138.8	−	27953.2i	0.854873	−	1.48068i	−0.0218904	−	0.999760i	$-0.506969\pi$
$709$	16138.8	−	27953.2i	0.854873	−	1.48068i	0.876763	−	0.480923i	$-0.159698\pi$
$710$	−1294.37	−	2241.91i	−0.0684180	−	0.118503i
$711$	11102.5	+	19230.2i	0.585623	+	1.01433i
$712$	4964.45	−	8598.68i	0.261307	−	0.452597i
$713$	−5402.26			−0.283754
$714$	17599.5	+	23610.5i	0.922474	+	1.23754i
$715$	28004.0			1.46474
$716$	−8024.47	+	13898.8i	−0.418839	+	0.725450i
$717$	4710.19	+	8158.29i	0.245335	+	0.424933i
$718$	−12797.9	−	22166.6i	−0.665199	−	1.15216i
$719$	−17395.4	+	30129.6i	−0.902277	+	1.56279i	−0.0777468	+	0.996973i	$0.524773\pi$
$719$	−17395.4	+	30129.6i	−0.902277	+	1.56279i	−0.824531	+	0.565817i	$0.808561\pi$
$720$	−3185.94			−0.164907
$721$	3092.81	−	7181.85i	0.159753	−	0.370966i
$722$	−3344.92			−0.172417
$723$	−2425.79	+	4201.60i	−0.124780	+	0.216126i
$724$	−4462.87	−	7729.92i	−0.229090	−	0.396796i
$725$	1975.76	+	3422.12i	0.101211	+	0.175302i
$726$	−13441.5	+	23281.4i	−0.687137	+	1.19016i
$727$	21693.3			1.10668			0.553341	−	0.832955i	$-0.313353\pi$
$727$	21693.3			1.10668			0.553341	+	0.832955i	$0.313353\pi$
$728$	−9688.03	+	1138.30i	−0.493218	+	0.0579508i
$729$	−18741.9			−0.952189
$730$	2732.20	−	4732.31i	0.138525	−	0.239932i
$731$	1797.51	+	3113.38i	0.0909485	+	0.157527i
$732$	3512.13	+	6083.18i	0.177339	+	0.307160i
$733$	−9132.29	+	15817.6i	−0.460176	+	0.797048i	−0.998969	−	0.0453898i	$-0.985547\pi$
$733$	−9132.29	+	15817.6i	−0.460176	+	0.797048i	0.538793	+	0.842438i	$0.318880\pi$
$734$	15589.5			0.783948
$735$	18410.2	−	4386.79i	0.923907	−	0.220149i
$736$	−736.000			−0.0368605
$737$	−3178.41	+	5505.16i	−0.158858	+	0.275150i
$738$	−9472.64	−	16407.1i	−0.472484	−	0.818365i
$739$	−5243.74	−	9082.42i	−0.261020	−	0.452100i	0.705493	−	0.708717i	$-0.250726\pi$
$739$	−5243.74	−	9082.42i	−0.261020	−	0.452100i	−0.966513	+	0.256617i	$0.917392\pi$
$740$	−1856.79	+	3216.06i	−0.0922392	+	0.159763i
$741$	−44422.5			−2.20230
$742$	23570.5	−	2769.42i	1.16617	−	0.137020i
$743$	6519.14			0.321889			0.160945	−	0.986963i	$-0.448546\pi$
$743$	6519.14			0.321889			0.160945	+	0.986963i	$0.448546\pi$
$744$	6863.15	−	11887.3i	0.338193	−	0.585767i
$745$	3717.47	+	6438.84i	0.182815	+	0.316646i
$746$	9352.02	+	16198.2i	0.458983	+	0.794983i
$747$	18114.4	−	31375.1i	0.887246	−	1.53675i
$748$	24514.9			1.19833
$749$	4313.44	−	10016.3i	0.210427	−	0.488635i
$750$	21292.4			1.03665
$751$	12205.4	−	21140.4i	0.593053	−	1.02720i	−0.400766	−	0.916180i	$-0.631256\pi$
$751$	12205.4	−	21140.4i	0.593053	−	1.02720i	0.993819	−	0.111017i	$-0.0354107\pi$
$752$	−1182.79	−	2048.66i	−0.0573565	−	0.0993444i
$753$	17426.2	+	30183.0i	0.843353	+	1.46073i
$754$	−3828.89	+	6631.84i	−0.184934	+	0.320315i
$755$	−15144.5			−0.730018
$756$	206.368	+	276.851i	0.00992794	+	0.0133187i
$757$	−36222.9			−1.73916			−0.869580	−	0.493793i	$-0.835610\pi$
$757$	−36222.9			−1.73916			−0.869580	+	0.493793i	$0.835610\pi$
$758$	−671.508	+	1163.09i	−0.0321772	+	0.0557325i
$759$	4730.60	+	8193.64i	0.226232	+	0.391845i
$760$	2790.70	+	4833.63i	0.133196	+	0.230703i
$761$	−5181.73	+	8975.02i	−0.246830	+	0.427522i	−0.962645	−	0.270768i	$-0.912722\pi$
$761$	−5181.73	+	8975.02i	−0.246830	+	0.427522i	0.715815	+	0.698290i	$0.246056\pi$
$762$	31761.1			1.50995
$763$	1182.71	+	1586.66i	0.0561168	+	0.0752830i
$764$	522.667			0.0247505
$765$	10835.7	−	18767.9i	0.512110	−	0.887000i
$766$	5923.13	+	10259.2i	0.279388	+	0.483915i
$767$	13234.4	+	22922.6i	0.623033	+	1.07912i
$768$	935.030	−	1619.52i	0.0439323	−	0.0760930i
$769$	−3915.55			−0.183613			−0.0918065	−	0.995777i	$-0.529264\pi$
$769$	−3915.55			−0.183613			−0.0918065	+	0.995777i	$0.529264\pi$
$770$	6231.53	−	14470.3i	0.291648	−	0.677240i
$771$	15590.8			0.728262
$772$	6886.64	−	11928.0i	0.321057	−	0.556086i
$773$	−14410.1	−	24959.1i	−0.670500	−	1.16134i	−0.977763	−	0.209715i	$-0.932746\pi$
$773$	−14410.1	−	24959.1i	−0.670500	−	1.16134i	0.307263	−	0.951625i	$-0.400587\pi$
$774$	−870.787	−	1508.25i	−0.0404390	−	0.0700424i
$775$	−7979.67	+	13821.2i	−0.369856	+	0.640609i
$776$	−7983.25			−0.369307
$777$	−16515.0	+	1940.43i	−0.762511	+	0.0895915i
$778$	6904.91			0.318191
$779$	−16594.9	+	28743.3i	−0.763255	+	1.32200i
$780$	7265.45	+	12584.1i	0.333519	+	0.577672i
$781$	−4824.91	−	8356.99i	−0.221061	−	0.382889i
$782$	2503.20	−	4335.66i	0.114468	−	0.198265i
$783$	271.075			0.0123722
$784$	−1567.63	+	5259.34i	−0.0714115	+	0.239584i
$785$	2914.61			0.132518
$786$	17939.2	−	31071.7i	0.814086	−	1.41004i
$787$	−11573.3	−	20045.5i	−0.524196	−	0.907934i	−0.999603	−	0.0281681i	$-0.991033\pi$
$787$	−11573.3	−	20045.5i	−0.524196	−	0.907934i	0.475407	−	0.879766i	$-0.342301\pi$
$788$	5952.67	+	10310.3i	0.269105	+	0.466104i
$789$	24874.1	−	43083.3i	1.12236	−	1.94399i
$790$	−12724.7			−0.573067
$791$	−389.706	+	45.7887i	−0.0175175	+	0.00205823i
$792$	−11876.0			−0.532821
$793$	7913.53	−	13706.6i	0.354373	−	0.613792i
$794$	−2462.71	−	4265.54i	−0.110073	−	0.190653i
$795$	−17676.5	−	30616.6i	−0.788579	−	1.36586i
$796$	1805.92	−	3127.94i	0.0804134	−	0.139280i
$797$	8804.30			0.391298			0.195649	−	0.980674i	$-0.437319\pi$
$797$	8804.30			0.391298			0.195649	+	0.980674i	$0.437319\pi$
$798$	−9885.04	+	22954.2i	−0.438505	+	1.01826i
$799$	16091.1			0.712469
$800$	−1087.14	+	1882.99i	−0.0480454	+	0.0832171i
$801$	−16359.1	−	28334.7i	−0.721622	−	1.24989i
$802$	−12628.0	−	21872.4i	−0.555999	−	0.963019i
$803$	10184.6	−	17640.2i	0.447580	−	0.775231i
$804$	−3298.47			−0.144687
$805$	−1922.90	−	2579.66i	−0.0841907	−	0.112945i
$806$	−30928.1			−1.35161
$807$	−24446.4	+	42342.4i	−1.06636	+	1.84699i
$808$	3786.59	+	6558.57i	0.164866	+	0.285557i
$809$	8154.31	+	14123.7i	0.354376	+	0.613798i	0.987011	−	0.160653i	$-0.0513599\pi$
$809$	8154.31	+	14123.7i	0.354376	+	0.613798i	−0.632635	+	0.774450i	$0.718027\pi$
$810$	5633.47	−	9757.45i	0.244370	−	0.423262i
$811$	8308.25			0.359731			0.179866	−	0.983691i	$-0.442434\pi$
$811$	8308.25			0.359731			0.179866	+	0.983691i	$0.442434\pi$
$812$	2574.82	+	3454.22i	0.111279	+	0.149285i
$813$	63124.5			2.72309
$814$	−6921.41	+	11988.2i	−0.298028	+	0.516200i
$815$	−9054.14	−	15682.2i	−0.389144	−	0.674018i
$816$	6360.23	+	11016.2i	0.272858	+	0.472605i
$817$	−1525.51	+	2642.27i	−0.0653256	+	0.113147i
$818$	−19715.5			−0.842709
$819$	−12713.8	+	29522.8i	−0.542436	+	1.25960i
$820$	10856.6			0.462354
$821$	−14309.4	+	24784.6i	−0.608284	+	1.05358i	0.383240	+	0.923649i	$0.374808\pi$
$821$	−14309.4	+	24784.6i	−0.608284	+	1.05358i	−0.991523	+	0.129929i	$0.958525\pi$
$822$	−7460.45	−	12921.9i	−0.316561	−	0.548300i
$823$	−732.205	−	1268.22i	−0.0310122	−	0.0537147i	0.850103	−	0.526617i	$-0.176540\pi$
$823$	−732.205	−	1268.22i	−0.0310122	−	0.0537147i	−0.881115	+	0.472902i	$0.843206\pi$
$824$	1688.85	−	2925.18i	0.0714004	−	0.123669i
$825$	27950.2			1.17952
$826$	14789.6	−	1737.71i	0.622999	−	0.0731996i
$827$	−38045.8			−1.59974			−0.799869	−	0.600175i	$-0.795098\pi$
$827$	−38045.8			−1.59974			−0.799869	+	0.600175i	$0.795098\pi$
$828$	−1212.65	+	2100.37i	−0.0508967	+	0.0881556i
$829$	−11623.7	−	20132.8i	−0.486980	−	0.843475i	0.512908	−	0.858444i	$-0.328568\pi$
$829$	−11623.7	−	20132.8i	−0.486980	−	0.843475i	−0.999888	+	0.0149692i	$0.995235\pi$
$830$	10380.5	+	17979.6i	0.434112	+	0.751904i
$831$	−27370.0	+	47406.3i	−1.14255	+	1.97895i
$832$	−4213.62			−0.175578
$833$	−25650.4	−	27122.1i	−1.06691	−	1.12812i
$834$	6120.12			0.254104
$835$	12987.8	−	22495.5i	0.538275	−	0.932320i
$836$	10402.7	+	18017.9i	0.430363	+	0.745410i
$837$	547.407	+	948.137i	0.0226059	+	0.0391546i
$838$	−15594.0	+	27009.6i	−0.642824	+	1.11340i
$839$	10511.6			0.432539			0.216270	−	0.976334i	$-0.430611\pi$
$839$	10511.6			0.432539			0.216270	+	0.976334i	$0.430611\pi$
$840$	8119.26	−	953.976i	0.333501	−	0.0391849i
$841$	−21006.8			−0.861324
$842$	−2429.98	+	4208.85i	−0.0994568	+	0.172264i
$843$	7219.93	+	12505.3i	0.294980	+	0.510920i
$844$	4879.90	+	8452.24i	0.199020	+	0.344713i
$845$	8073.15	−	13983.1i	0.328668	−	0.569270i
$846$	−7795.18			−0.316790
$847$	13478.9	−	31299.5i	0.546800	−	1.26973i
$848$	10251.5			0.415141
$849$	22479.5	−	38935.6i	0.908709	−	1.57393i
$850$	−7394.93	−	12808.4i	−0.298405	−	0.516852i
$851$	1413.48	+	2448.22i	0.0569371	+	0.0986180i
$852$	2503.59	−	4336.34i	0.100671	−	0.174367i
$853$	10457.1			0.419748			0.209874	−	0.977728i	$-0.432695\pi$
$853$	10457.1			0.419748			0.209874	+	0.977728i	$0.432695\pi$
$854$	−5321.61	−	7139.16i	−0.213234	−	0.286062i
$855$	18392.0			0.735666
$856$	2355.39	−	4079.65i	0.0940484	−	0.162897i
$857$	8807.68	+	15255.4i	0.351067	+	0.608067i	0.986437	−	0.164142i	$-0.0524855\pi$
$857$	8807.68	+	15255.4i	0.351067	+	0.608067i	−0.635369	+	0.772208i	$0.719152\pi$
$858$	27082.8	+	46908.8i	1.07761	+	1.86648i
$859$	8300.35	−	14376.6i	0.329691	−	0.571041i	−0.652760	−	0.757565i	$-0.726389\pi$
$859$	8300.35	−	14376.6i	0.329691	−	0.571041i	0.982450	+	0.186524i	$0.0597222\pi$
$860$	998.012			0.0395720
$861$	29053.5	+	38976.5i	1.14999	+	1.54276i
$862$	9080.57			0.358800
$863$	5506.96	−	9538.34i	0.217218	−	0.376233i	−0.736738	−	0.676178i	$-0.763635\pi$
$863$	5506.96	−	9538.34i	0.217218	−	0.376233i	0.953956	+	0.299945i	$0.0969684\pi$
$864$	74.5784	+	129.174i	0.00293658	+	0.00508631i
$865$	7587.33	+	13141.6i	0.298239	+	0.516565i
$866$	−15322.6	+	26539.6i	−0.601252	+	1.04140i
$867$	−50637.5			−1.98355
$868$	−6882.23	+	15981.3i	−0.269122	+	0.624933i
$869$	−47432.7			−1.85160
$870$	3208.88	−	5557.95i	0.125048	−	0.216589i
$871$	3716.06	+	6436.41i	0.144563	+	0.250390i
$872$	427.416	+	740.306i	0.0165988	+	0.0287499i
$873$	−13153.4	+	22782.3i	−0.509936	+	0.883235i
$874$	4248.83			0.164438
$875$	−26807.0	+	3149.70i	−1.03570	+	0.121690i
$876$	10569.3			0.407653
$877$	−11038.0	+	19118.4i	−0.425002	+	0.736124i	−0.996421	−	0.0845341i	$-0.973060\pi$
$877$	−11038.0	+	19118.4i	−0.425002	+	0.736124i	0.571419	+	0.820658i	$0.306393\pi$
$878$	−5141.79	−	8905.85i	−0.197639	−	0.342321i
$879$	−6960.06	−	12055.2i	−0.267073	−	0.462584i
$880$	3402.78	−	5893.78i	0.130350	−	0.225772i
$881$	9443.65			0.361140			0.180570	−	0.983562i	$-0.442206\pi$
$881$	9443.65			0.361140			0.180570	+	0.983562i	$0.442206\pi$
$882$	12426.1	+	13139.0i	0.474385	+	0.501603i
$883$	31677.0			1.20727			0.603633	−	0.797262i	$-0.293719\pi$
$883$	31677.0			1.20727			0.603633	+	0.797262i	$0.293719\pi$
$884$	14330.9	−	24821.8i	0.545248	−	0.944398i
$885$	−11091.4	−	19210.8i	−0.421279	−	0.729677i
$886$	−7538.33	−	13056.8i	−0.285841	−	0.495091i
$887$	48.2246	−	83.5275i	0.00182551	−	0.00316187i	−0.865111	−	0.501580i	$-0.832752\pi$
$887$	48.2246	−	83.5275i	0.00182551	−	0.00316187i	0.866937	+	0.498418i	$0.166086\pi$
$888$	−7182.86			−0.271443
$889$	−39987.0	+	4698.29i	−1.50857	+	0.177250i
$890$	18749.2			0.706151
$891$	20999.4	−	36372.0i	0.789570	−	1.36758i
$892$	10828.7	+	18755.9i	0.406471	+	0.704028i
$893$	6828.12	+	11826.6i	0.255873	+	0.443184i
$894$	−7190.38	+	12454.1i	−0.268996	+	0.465914i
$895$	−30305.9			−1.13186
$896$	−937.629	+	2177.28i	−0.0349598	+	0.0811807i
$897$	11061.6			0.411747
$898$	−7253.14	+	12562.8i	−0.269533	+	0.466844i
$899$	6829.91	+	11829.8i	0.253382	+	0.438870i
$900$	3582.40	+	6204.90i	0.132681	+	0.229811i
$901$	−34866.3	+	60390.2i	−1.28920	+	2.23295i
$902$	40469.4			1.49388
$903$	2670.79	+	3582.97i	0.0984255	+	0.132042i
$904$	−169.495			−0.00623598
$905$	8427.44	−	14596.8i	0.309544	−	0.536146i
$906$	−14646.3	−	25368.2i	−0.537077	−	0.930244i
$907$	17360.7	+	30069.6i	0.635559	+	1.10082i	0.986396	+	0.164384i	$0.0525635\pi$
$907$	17360.7	+	30069.6i	0.635559	+	1.10082i	−0.350838	+	0.936436i	$0.614103\pi$
$908$	−8959.08	+	15517.6i	−0.327442	+	0.567146i
$909$	24955.5			0.910584
$910$	−11008.7	−	14768.6i	−0.401027	−	0.537994i
$911$	23562.8			0.856938			0.428469	−	0.903557i	$-0.359053\pi$
$911$	23562.8			0.856938			0.428469	+	0.903557i	$0.359053\pi$
$912$	−5397.81	+	9349.28i	−0.195986	+	0.339458i
$913$	38694.6	+	67021.0i	1.40263	+	2.42943i
$914$	−14113.4	−	24445.2i	−0.510756	−	0.884656i
$915$	−6632.10	+	11487.1i	−0.239618	+	0.415031i
$916$	−14511.6			−0.523445
$917$	−17989.1	+	41772.8i	−0.647822	+	1.50432i
$918$	−1014.59			−0.0364776
$919$	13184.3	−	22835.9i	0.473244	−	0.819682i	−0.526287	−	0.850307i	$-0.676416\pi$
$919$	13184.3	−	22835.9i	0.473244	−	0.819682i	0.999531	+	0.0306249i	$0.00974974\pi$
$920$	−694.911	−	1203.62i	−0.0249027	−	0.0431328i
$921$	2350.97	+	4072.00i	0.0841120	+	0.145686i
$922$	1996.06	−	3457.28i	0.0712981	−	0.123492i
$923$	−11282.2			−0.402337
$924$	30265.5	−	3556.06i	1.07756	−	0.126608i
$925$	8351.39			0.296856
$926$	8301.53	−	14378.7i	0.294606	−	0.510272i
$927$	−5565.17	−	9639.16i	−0.197178	−	0.341523i
$928$	930.502	+	1611.68i	0.0329151	+	0.0570106i
$929$	18018.1	−	31208.3i	0.636336	−	1.10217i	−0.349895	−	0.936789i	$-0.613783\pi$
$929$	18018.1	−	31208.3i	0.636336	−	1.10217i	0.986230	−	0.165377i	$-0.0528840\pi$
$930$	25920.0			0.913924
$931$	9049.70	−	30361.5i	0.318573	−	1.06881i
$932$	−14730.9			−0.517734
$933$	−18741.0	+	32460.3i	−0.657611	+	1.13902i
$934$	−4517.84	−	7825.13i	−0.158274	−	0.274139i
$935$	23146.2	+	40090.5i	0.809586	+	1.40224i
$936$	−6942.45	+	12024.7i	−0.242437	+	0.419913i
$937$	13236.3			0.461483			0.230742	−	0.973015i	$-0.425885\pi$
$937$	13236.3			0.461483			0.230742	+	0.973015i	$0.425885\pi$
$938$	4152.76	−	487.930i	0.144555	−	0.0169845i
$939$	−35399.2			−1.23025
$940$	2233.52	−	3868.58i	0.0774995	−	0.134233i
$941$	7070.96	+	12247.3i	0.244959	+	0.424282i	0.962120	−	0.272626i	$-0.0878921\pi$
$941$	7070.96	+	12247.3i	0.244959	+	0.424282i	−0.717161	+	0.696908i	$0.754559\pi$
$942$	2818.74	+	4882.19i	0.0974940	+	0.168865i
$943$	4132.30	−	7157.36i	0.142700	−	0.247164i
$944$	6432.47			0.221779
$945$	−257.902	+	598.879i	−0.00887784	+	0.0206154i
$946$	3720.21			0.127859
$947$	−24069.4	+	41689.4i	−0.825923	+	1.43054i	0.0752880	+	0.997162i	$0.476012\pi$
$947$	−24069.4	+	41689.4i	−0.825923	+	1.43054i	−0.901211	+	0.433380i	$0.857321\pi$
$948$	−12306.1	−	21314.8i	−0.421608	−	0.730246i
$949$	−11907.4	−	20624.2i	−0.407303	−	0.705470i
$950$	6275.94	−	10870.2i	0.214335	−	0.371239i
$951$	−15698.8			−0.535298
$952$	−9637.09	−	12928.5i	−0.328088	−	0.440144i
$953$	−35613.3			−1.21052			−0.605262	−	0.796027i	$-0.706932\pi$
$953$	−35613.3			−1.21052			−0.605262	+	0.796027i	$0.706932\pi$
$954$	16890.6	−	29255.4i	0.573223	−	0.992851i
$955$	493.487	+	854.745i	0.0167213	+	0.0289622i
$956$	−2579.19	−	4467.29i	−0.0872562	−	0.151132i
$957$	11961.5	−	20717.9i	0.404034	−	0.699807i
$958$	33031.3			1.11398
$959$	11304.2	+	15165.0i	0.380636	+	0.510639i
$960$	3531.32			0.118722
$961$	−12689.0	+	21978.0i	−0.425935	+	0.737741i
$962$	8092.22	+	14016.1i	0.271210	+	0.469749i
$963$	−7761.56	−	13443.4i	−0.259723	−	0.449853i
$964$	1328.31	−	2300.69i	0.0443795	−	0.0768676i
$965$	26008.7			0.867616
$966$	2461.47	−	5715.82i	0.0819840	−	0.190376i
$967$	−19501.2			−0.648518			−0.324259	−	0.945968i	$-0.605115\pi$
$967$	−19501.2			−0.648518			−0.324259	+	0.945968i	$0.605115\pi$
$968$	7360.25	−	12748.3i	0.244388	−	0.423292i
$969$	−36716.8	−	63595.3i	−1.21725	−	2.10833i
$970$	−7537.57	−	13055.4i	−0.249502	−	0.432150i
$971$	4384.88	−	7594.84i	0.144920	−	0.251009i	−0.784423	−	0.620226i	$-0.787041\pi$
$971$	4384.88	−	7594.84i	0.144920	−	0.251009i	0.929343	+	0.369217i	$0.120374\pi$
$972$	21289.3			0.702524
$973$	−7705.21	+	905.326i	−0.253872	+	0.0298288i
$974$	−18106.2			−0.595646
$975$	16339.1	−	28300.2i	0.536688	−	0.929571i
$976$	−1923.16	−	3331.00i	−0.0630724	−	0.109245i
$977$	2372.31	+	4108.95i	0.0776835	+	0.134552i	0.902250	−	0.431213i	$-0.141914\pi$
$977$	2372.31	+	4108.95i	0.0776835	+	0.134552i	−0.824567	+	0.565765i	$0.808581\pi$
$978$	17512.6	−	30332.8i	0.572590	−	0.991754i
$979$	69889.8			2.28160
$980$	−10081.0	+	2402.10i	−0.328598	+	0.0782983i
$981$	2816.88			0.0916779
$982$	−7398.88	+	12815.2i	−0.240436	+	0.416447i
$983$	27762.1	+	48085.4i	0.900787	+	1.56021i	0.826475	+	0.562974i	$0.190343\pi$
$983$	27762.1	+	48085.4i	0.900787	+	1.56021i	0.0743119	+	0.997235i	$0.476324\pi$
$984$	10499.5	+	18185.7i	0.340155	+	0.589166i
$985$	−11240.7	+	19469.4i	−0.363612	+	0.629795i
$986$	−12658.8			−0.408864
$987$	19865.7	−	2334.13i	0.640662	−	0.0752749i
$988$	24324.7			0.783271
$989$	379.868	−	657.950i	0.0122134	−	0.0211543i
$990$	−11213.0	−	19421.4i	−0.359971	−	0.623488i
$991$	8384.82	+	14522.9i	0.268771	+	0.465526i	0.968545	−	0.248839i	$-0.0800490\pi$
$991$	8384.82	+	14522.9i	0.268771	+	0.465526i	−0.699773	+	0.714365i	$0.746716\pi$
$992$	−3758.09	+	6509.21i	−0.120282	+	0.208334i
$993$	−5357.02			−0.171198
$994$	−2510.55	+	5829.78i	−0.0801103	+	0.186025i
$995$	6820.39			0.217307
$996$	−20078.1	+	34776.4i	−0.638755	+	1.10636i
$997$	−7309.70	−	12660.8i	−0.232197	−	0.402177i	0.726257	−	0.687423i	$-0.241258\pi$
$997$	−7309.70	−	12660.8i	−0.232197	−	0.402177i	−0.958454	+	0.285246i	$0.907925\pi$
$998$	−717.821	−	1243.30i	−0.0227678	−	0.0394349i
$999$	286.454	−	496.153i	0.00907207	−	0.0157133i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.4.e.d.93.9	✓	22
7.2	even	3		2254.4.a.r.1.3		11
7.4	even	3	inner	322.4.e.d.277.9	yes	22
7.5	odd	6		2254.4.a.u.1.9		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.4.e.d.93.9	✓	22	1.1	even	1	trivial
322.4.e.d.277.9	yes	22	7.4	even	3	inner
2254.4.a.r.1.3		11	7.2	even	3
2254.4.a.u.1.9		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} +(3.65246 + 6.32625i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.77669 - 6.54142i) q^{5} +14.6098 q^{6} +(-18.3937 + 2.16118i) q^{7} -8.00000 q^{8} +(-13.1810 + 22.8301i) q^{9} +(-7.55338 - 13.0828i) q^{10} +(-28.1561 - 48.7678i) q^{11} +(14.6098 - 25.3050i) q^{12} -65.8379 q^{13} +(-14.6505 + 34.0201i) q^{14} +55.1768 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-54.4173 - 94.2535i) q^{17} +(26.3619 + 45.6602i) q^{18} +(46.1829 - 79.9912i) q^{19} -30.2135 q^{20} +(-80.8546 - 108.470i) q^{21} -112.624 q^{22} +(-11.5000 + 19.9186i) q^{23} +(-29.2197 - 50.6100i) q^{24} +(33.9733 + 58.8434i) q^{25} +(-65.8379 + 114.035i) q^{26} +4.66115 q^{27} +(44.2740 + 59.3954i) q^{28} +58.1564 q^{29} +(55.1768 - 95.5691i) q^{30} +(117.440 + 203.413i) q^{31} +(16.0000 + 27.7128i) q^{32} +(205.678 - 356.245i) q^{33} -217.669 q^{34} +(-55.3302 + 128.483i) q^{35} +105.448 q^{36} +(61.4557 - 106.444i) q^{37} +(-92.3659 - 159.982i) q^{38} +(-240.470 - 416.507i) q^{39} +(-30.2135 + 52.3313i) q^{40} -359.331 q^{41} +(-268.730 + 31.5745i) q^{42} -33.0320 q^{43} +(-112.624 + 195.071i) q^{44} +(99.5607 + 172.444i) q^{45} +(23.0000 + 39.8372i) q^{46} +(-73.9247 + 128.041i) q^{47} -116.879 q^{48} +(333.659 - 79.5043i) q^{49} +135.893 q^{50} +(397.514 - 688.515i) q^{51} +(131.676 + 228.069i) q^{52} +(-320.360 - 554.881i) q^{53} +(4.66115 - 8.07334i) q^{54} -425.347 q^{55} +(147.150 - 17.2894i) q^{56} +674.726 q^{57} +(58.1564 - 100.730i) q^{58} +(-201.015 - 348.168i) q^{59} +(-110.354 - 191.138i) q^{60} +(-120.197 + 208.188i) q^{61} +469.762 q^{62} +(193.107 - 448.417i) q^{63} +64.0000 q^{64} +(-248.649 + 430.673i) q^{65} +(-411.356 - 712.490i) q^{66} +(-56.4426 - 97.7615i) q^{67} +(-217.669 + 377.014i) q^{68} -168.013 q^{69} +(167.209 + 224.318i) q^{70} +171.363 q^{71} +(105.448 - 182.641i) q^{72} +(180.860 + 313.258i) q^{73} +(-122.911 - 212.889i) q^{74} +(-248.172 + 429.847i) q^{75} -369.464 q^{76} +(623.292 + 836.171i) q^{77} -961.881 q^{78} +(421.158 - 729.467i) q^{79} +(60.4270 + 104.663i) q^{80} +(372.911 + 645.900i) q^{81} +(-359.331 + 622.379i) q^{82} -1374.29 q^{83} +(-214.041 + 497.028i) q^{84} -822.069 q^{85} +(-33.0320 + 57.2131i) q^{86} +(212.414 + 367.912i) q^{87} +(225.249 + 390.142i) q^{88} +(-620.557 + 1074.84i) q^{89} +398.243 q^{90} +(1211.00 - 142.287i) q^{91} +92.0000 q^{92} +(-857.894 + 1485.92i) q^{93} +(147.849 + 256.083i) q^{94} +(-348.837 - 604.204i) q^{95} +(-116.879 + 202.440i) q^{96} +997.907 q^{97} +(195.953 - 657.418i) q^{98} +1484.50 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} - 44 q^{4} + 23 q^{5} + 43 q^{7} - 176 q^{8} - 171 q^{9} - 46 q^{10} + 48 q^{11} - 154 q^{13} - 20 q^{14} + 208 q^{15} - 176 q^{16} + 97 q^{17} + 342 q^{18} + 138 q^{19} - 184 q^{20} - 125 q^{21}+ \cdots - 5090 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 44 * q^4 + 23 * q^5 + 43 * q^7 - 176 * q^8 - 171 * q^9 - 46 * q^10 + 48 * q^11 - 154 * q^13 - 20 * q^14 + 208 * q^15 - 176 * q^16 + 97 * q^17 + 342 * q^18 + 138 * q^19 - 184 * q^20 - 125 * q^21 + 192 * q^22 - 253 * q^23 - 30 * q^25 - 154 * q^26 - 630 * q^27 - 212 * q^28 + 274 * q^29 + 208 * q^30 + 234 * q^31 + 352 * q^32 + 28 * q^33 + 388 * q^34 - 235 * q^35 + 1368 * q^36 - 87 * q^37 - 276 * q^38 - 129 * q^39 - 184 * q^40 - 1224 * q^41 - 536 * q^42 + 374 * q^43 + 192 * q^44 + 597 * q^45 + 506 * q^46 + 793 * q^47 - 1123 * q^49 - 120 * q^50 + 1257 * q^51 + 308 * q^52 - 575 * q^53 - 630 * q^54 + 1098 * q^55 - 344 * q^56 + 78 * q^57 + 274 * q^58 + 1241 * q^59 - 416 * q^60 + 187 * q^61 + 936 * q^62 - 1141 * q^63 + 1408 * q^64 + 937 * q^65 - 56 * q^66 - 2275 * q^67 + 388 * q^68 + 956 * q^70 + 230 * q^71 + 1368 * q^72 + 2385 * q^73 + 174 * q^74 + 196 * q^75 - 1104 * q^76 - 1645 * q^77 - 516 * q^78 + 1225 * q^79 + 368 * q^80 - 3635 * q^81 - 1224 * q^82 + 1194 * q^83 - 572 * q^84 - 4986 * q^85 + 374 * q^86 + 1428 * q^87 - 384 * q^88 + 602 * q^89 + 2388 * q^90 + 2324 * q^91 + 2024 * q^92 + 1360 * q^93 - 1586 * q^94 - 4835 * q^95 + 2078 * q^97 + 854 * q^98 - 5090 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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