LMFDB - Embedded newform 207.4.o.a.11.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,4,Mod(5,207)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("207.5"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([55, 3])) N = Newforms(chi, 4, names="a")

Level:	$N$	$=$	$207 = 3^{2} \cdot 23$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	207.o (of order $66$ , degree $20$ , minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$12.2133953712$
Analytic rank:	$0$
Dimension:	$1400$
Relative dimension:	$70$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	207.11
Dual form			207.4.o.a.113.12

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.01239 + 0.191134i) q^{2} +(-4.21361 + 3.04064i) q^{3} +(8.09899 - 0.773360i) q^{4} +(-10.4658 - 9.97910i) q^{5} +(16.3255 - 13.0056i) q^{6} +(3.79903 + 19.7112i) q^{7} +(-0.540075 + 0.0776511i) q^{8} +(8.50897 - 25.6242i) q^{9} +(43.9002 + 38.0397i) q^{10} +(-16.4757 + 8.49379i) q^{11} +(-31.7745 + 27.8848i) q^{12} +(47.9243 + 9.23665i) q^{13} +(-19.0107 - 78.3630i) q^{14} +(74.4416 + 10.2253i) q^{15} +(-61.7583 + 11.9029i) q^{16} +(49.9455 + 109.365i) q^{17} +(-29.2437 + 104.441i) q^{18} +(71.0219 + 32.4346i) q^{19} +(-92.4797 - 72.7268i) q^{20} +(-75.9424 - 71.5038i) q^{21} +(64.4834 - 37.2295i) q^{22} +(-10.6494 - 109.789i) q^{23} +(2.03956 - 1.96937i) q^{24} +(4.00235 + 84.0197i) q^{25} +(-194.056 - 27.9011i) q^{26} +(42.0605 + 133.843i) q^{27} +(46.0121 + 156.703i) q^{28} +(23.7447 - 248.665i) q^{29} +(-300.643 - 26.7996i) q^{30} +(-225.558 + 177.380i) q^{31} +(249.766 - 60.5925i) q^{32} +(43.5954 - 85.8861i) q^{33} +(-221.304 - 429.270i) q^{34} +(156.940 - 244.204i) q^{35} +(49.0974 - 214.110i) q^{36} +(57.2240 - 194.887i) q^{37} +(-291.167 - 116.566i) q^{38} +(-230.019 + 106.801i) q^{39} +(6.42720 + 4.57679i) q^{40} +(-185.085 + 194.112i) q^{41} +(318.377 + 272.386i) q^{42} +(-258.948 + 329.280i) q^{43} +(-126.867 + 81.5328i) q^{44} +(-344.759 + 183.265i) q^{45} +(63.7141 + 438.481i) q^{46} +(-333.916 - 192.787i) q^{47} +(224.033 - 237.939i) q^{48} +(-55.6692 + 22.2866i) q^{49} +(-32.1180 - 336.355i) q^{50} +(-542.992 - 308.956i) q^{51} +(395.282 + 37.7448i) q^{52} +(-285.184 - 329.120i) q^{53} +(-194.345 - 528.991i) q^{54} +(257.191 + 75.5181i) q^{55} +(-3.58236 - 10.3505i) q^{56} +(-397.881 + 79.2856i) q^{57} +(-47.7446 + 1002.28i) q^{58} +(-136.244 + 706.902i) q^{59} +(610.810 + 25.2445i) q^{60} +(100.709 - 251.558i) q^{61} +(871.123 - 754.832i) q^{62} +(537.409 + 70.3753i) q^{63} +(-507.799 + 149.103i) q^{64} +(-409.391 - 574.910i) q^{65} +(-158.506 + 352.941i) q^{66} +(41.9510 - 81.3736i) q^{67} +(489.087 + 847.123i) q^{68} +(378.701 + 430.226i) q^{69} +(-583.031 + 1009.84i) q^{70} +(329.121 + 512.123i) q^{71} +(-2.60574 + 14.4997i) q^{72} +(185.582 - 406.369i) q^{73} +(-192.356 + 792.901i) q^{74} +(-272.338 - 341.856i) q^{75} +(600.289 + 207.762i) q^{76} +(-230.014 - 292.487i) q^{77} +(902.515 - 472.492i) q^{78} +(377.569 - 130.678i) q^{79} +(765.129 + 491.719i) q^{80} +(-584.195 - 436.070i) q^{81} +(705.534 - 814.229i) q^{82} +(-151.467 + 144.423i) q^{83} +(-670.355 - 520.378i) q^{84} +(568.649 - 1643.00i) q^{85} +(976.066 - 1370.69i) q^{86} +(656.052 + 1119.98i) q^{87} +(8.23855 - 5.86664i) q^{88} +(-136.751 + 951.123i) q^{89} +(1348.28 - 801.226i) q^{90} +979.736i q^{91} +(-171.156 - 880.943i) q^{92} +(411.060 - 1433.25i) q^{93} +(1376.65 + 709.713i) q^{94} +(-419.631 - 1048.19i) q^{95} +(-868.174 + 1014.76i) q^{96} +(75.3288 + 18.2746i) q^{97} +(219.107 - 100.063i) q^{98} +(77.4554 + 494.448i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$1400 q - 27 q^{2} - 22 q^{3} - 281 q^{4} - 33 q^{5} + 29 q^{6} - 11 q^{7} - 22 q^{9} - 44 q^{10} - 33 q^{11} + 86 q^{12} - 9 q^{13} - 33 q^{14} + 726 q^{15} + 999 q^{16} + 51 q^{18} - 44 q^{19} - 33 q^{20}+ \cdots - 9262 q^{99}+O(q^{100})$ 1400 * q - 27 * q^2 - 22 * q^3 - 281 * q^4 - 33 * q^5 + 29 * q^6 - 11 * q^7 - 22 * q^9 - 44 * q^10 - 33 * q^11 + 86 * q^12 - 9 * q^13 - 33 * q^14 + 726 * q^15 + 999 * q^16 + 51 * q^18 - 44 * q^19 - 33 * q^20 + 638 * q^21 + 252 * q^23 - 2564 * q^24 + 1397 * q^25 - 178 * q^27 - 44 * q^28 - 135 * q^29 - 1518 * q^30 - 45 * q^31 - 339 * q^32 + 1914 * q^33 - 11 * q^34 - 2137 * q^36 - 44 * q^37 - 33 * q^38 + 374 * q^39 + 979 * q^40 + 441 * q^41 - 22 * q^42 - 11 * q^43 + 516 * q^46 - 1992 * q^47 - 20 * q^48 - 4633 * q^49 - 6231 * q^50 - 22 * q^51 + 178 * q^52 + 2640 * q^54 + 256 * q^55 + 17391 * q^56 + 2090 * q^57 + 320 * q^58 - 2061 * q^59 + 418 * q^60 - 11 * q^61 - 2112 * q^63 + 8546 * q^64 - 12969 * q^65 - 5775 * q^66 - 11 * q^67 - 519 * q^69 - 1582 * q^70 - 4156 * q^72 - 36 * q^73 - 10065 * q^74 - 7876 * q^75 - 11 * q^76 + 1317 * q^77 - 10053 * q^78 - 11 * q^79 + 12442 * q^81 + 698 * q^82 + 14025 * q^83 + 16720 * q^84 + 241 * q^85 - 33 * q^86 + 11672 * q^87 - 1419 * q^88 - 37136 * q^90 + 3141 * q^92 + 1138 * q^93 + 396 * q^94 + 5883 * q^95 + 9218 * q^96 + 6325 * q^97 - 9262 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$ .

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−4.01239	+	0.191134i	−1.41860	+	0.0675760i	−0.742800	−	0.669513i	$-0.766503\pi$
$2$	−4.01239	+	0.191134i	−1.41860	+	0.0675760i	−0.675795	+	0.737089i	$0.736200\pi$
$3$	−4.21361	+	3.04064i	−0.810909	+	0.585172i
$3$	−4.21361	+	3.04064i	−0.810909	+	0.585172i
$4$	8.09899	−	0.773360i	1.01237	−	0.0966700i
$5$	−10.4658	−	9.97910i	−0.936088	−	0.892558i	0.0583059	−	0.998299i	$-0.481430\pi$
$5$	−10.4658	−	9.97910i	−0.936088	−	0.892558i	−0.994394	+	0.105741i	$0.966279\pi$
$6$	16.3255	−	13.0056i	1.11081	−	0.884920i
$7$	3.79903	+	19.7112i	0.205128	+	1.06431i	0.927790	+	0.373104i	$0.121706\pi$
$7$	3.79903	+	19.7112i	0.205128	+	1.06431i	−0.722662	+	0.691202i	$0.757081\pi$
$8$	−0.540075	+	0.0776511i	−0.0238682	+	0.00343173i
$9$	8.50897	−	25.6242i	0.315147	−	0.949043i
$10$	43.9002	+	38.0397i	1.38825	+	1.20292i
$11$	−16.4757	+	8.49379i	−0.451600	+	0.232816i	−0.668994	−	0.743268i	$-0.733275\pi$
$11$	−16.4757	+	8.49379i	−0.451600	+	0.232816i	0.217394	+	0.976084i	$0.430244\pi$
$12$	−31.7745	+	27.8848i	−0.764375	+	0.670804i
$13$	47.9243	+	9.23665i	1.02245	+	0.197060i	0.672802	−	0.739822i	$-0.265090\pi$
$13$	47.9243	+	9.23665i	1.02245	+	0.197060i	0.349644	+	0.936883i	$0.386303\pi$
$14$	−19.0107	−	78.3630i	−0.362915	−	1.49596i
$15$	74.4416	+	10.2253i	1.28138	+	0.176011i
$16$	−61.7583	+	11.9029i	−0.964973	+	0.185983i
$17$	49.9455	+	109.365i	0.712562	+	1.56029i	0.824043	+	0.566527i	$0.191713\pi$
$17$	49.9455	+	109.365i	0.712562	+	1.56029i	−0.111481	+	0.993767i	$0.535559\pi$
$18$	−29.2437	+	104.441i	−0.382934	+	1.36760i
$19$	71.0219	+	32.4346i	0.857555	+	0.391632i	0.795146	−	0.606418i	$-0.207394\pi$
$19$	71.0219	+	32.4346i	0.857555	+	0.391632i	0.0624092	+	0.998051i	$0.480122\pi$
$20$	−92.4797	−	72.7268i	−1.03395	−	0.813111i
$21$	−75.9424	−	71.5038i	−0.789142	−	0.743020i
$22$	64.4834	−	37.2295i	0.624905	−	0.360789i
$23$	−10.6494	−	109.789i	−0.0965461	−	0.995329i
$23$	−10.6494	−	109.789i	−0.0965461	−	0.995329i
$24$	2.03956	−	1.96937i	0.0173468	−	0.0167498i
$25$	4.00235	+	84.0197i	0.0320188	+	0.672158i
$26$	−194.056	−	27.9011i	−1.46375	−	0.210456i
$27$	42.0605	+	133.843i	0.299798	+	0.954003i
$28$	46.0121	+	156.703i	0.310553	+	1.05765i
$29$	23.7447	−	248.665i	0.152044	−	1.59228i	−0.521581	−	0.853202i	$-0.674657\pi$
$29$	23.7447	−	248.665i	0.152044	−	1.59228i	0.673625	−	0.739074i	$-0.264737\pi$
$30$	−300.643	−	26.7996i	−1.82966	−	0.163097i
$31$	−225.558	+	177.380i	−1.30682	+	1.02769i	−0.309778	+	0.950809i	$0.600255\pi$
$31$	−225.558	+	177.380i	−1.30682	+	1.02769i	−0.997040	+	0.0768837i	$0.975503\pi$
$32$	249.766	−	60.5925i	1.37977	−	0.334729i
$33$	43.5954	−	85.8861i	0.229969	−	0.453056i
$34$	−221.304	−	429.270i	−1.11628	−	2.16527i
$35$	156.940	−	244.204i	0.757936	−	1.17937i
$36$	49.0974	−	214.110i	0.227303	−	0.991252i
$37$	57.2240	−	194.887i	0.254259	−	0.865926i	−0.729124	−	0.684381i	$-0.760072\pi$
$37$	57.2240	−	194.887i	0.254259	−	0.865926i	0.983383	−	0.181544i	$-0.0581095\pi$
$38$	−291.167	−	116.566i	−1.24299	−	0.497617i
$39$	−230.019	+	106.801i	−0.944425	+	0.438509i
$40$	6.42720	+	4.57679i	0.0254057	+	0.0180913i
$41$	−185.085	+	194.112i	−0.705012	+	0.739395i	−0.974691	−	0.223555i	$-0.928234\pi$
$41$	−185.085	+	194.112i	−0.705012	+	0.739395i	0.269680	+	0.962950i	$0.413082\pi$
$42$	318.377	+	272.386i	1.16968	+	1.00072i
$43$	−258.948	+	329.280i	−0.918355	+	1.16778i	0.0670834	+	0.997747i	$0.478631\pi$
$43$	−258.948	+	329.280i	−0.918355	+	1.16778i	−0.985438	+	0.170035i	$0.945612\pi$
$44$	−126.867	+	81.5328i	−0.434682	+	0.279353i
$45$	−344.759	+	183.265i	−1.14208	+	0.607100i
$46$	63.7141	+	438.481i	0.204220	+	1.40544i
$47$	−333.916	−	192.787i	−1.03631	−	0.598315i	−0.117526	−	0.993070i	$-0.537496\pi$
$47$	−333.916	−	192.787i	−1.03631	−	0.598315i	−0.918787	+	0.394754i	$0.870830\pi$
$48$	224.033	−	237.939i	0.673673	−	0.715491i
$49$	−55.6692	+	22.2866i	−0.162301	+	0.0649754i
$50$	−32.1180	−	336.355i	−0.0908435	−	0.951356i
$51$	−542.992	−	308.956i	−1.49086	−	0.848285i
$52$	395.282	+	37.7448i	1.05415	+	0.100659i
$53$	−285.184	−	329.120i	−0.739114	−	0.852983i	0.254352	−	0.967112i	$-0.418138\pi$
$53$	−285.184	−	329.120i	−0.739114	−	0.852983i	−0.993466	+	0.114128i	$0.963592\pi$
$54$	−194.345	−	528.991i	−0.489759	−	1.33308i
$55$	257.191	+	75.5181i	0.630539	+	0.185143i
$56$	−3.58236	−	10.3505i	−0.00854844	−	0.0246991i
$57$	−397.881	+	79.2856i	−0.924571	+	0.184239i
$58$	−47.7446	+	1002.28i	−0.108089	+	2.26907i
$59$	−136.244	+	706.902i	−0.300635	+	1.55984i	0.446261	+	0.894903i	$0.352755\pi$
$59$	−136.244	+	706.902i	−0.300635	+	1.55984i	−0.746896	+	0.664940i	$0.768457\pi$
$60$	610.810	+	25.2445i	1.31425	+	0.0543176i
$61$	100.709	−	251.558i	0.211384	−	0.528012i	−0.784346	−	0.620323i	$-0.787001\pi$
$61$	100.709	−	251.558i	0.211384	−	0.528012i	0.995730	+	0.0923116i	$0.0294256\pi$
$62$	871.123	−	754.832i	1.78440	−	1.54619i
$63$	537.409	+	70.3753i	1.07472	+	0.140737i
$64$	−507.799	+	149.103i	−0.991794	+	0.291217i
$65$	−409.391	−	574.910i	−0.781212	−	1.09706i
$66$	−158.506	+	352.941i	−0.295617	+	0.658244i
$67$	41.9510	−	81.3736i	0.0764945	−	0.148379i	−0.847487	−	0.530817i	$-0.821885\pi$
$67$	41.9510	−	81.3736i	0.0764945	−	0.148379i	0.923981	+	0.382438i	$0.124916\pi$
$68$	489.087	+	847.123i	0.872213	+	1.51072i
$69$	378.701	+	430.226i	0.660729	+	0.750625i
$70$	−583.031	+	1009.84i	−0.995508	+	1.72427i
$71$	329.121	+	512.123i	0.550134	+	0.856025i	0.999299	−	0.0374236i	$-0.0119151\pi$
$71$	329.121	+	512.123i	0.550134	+	0.856025i	−0.449166	+	0.893448i	$0.648279\pi$
$72$	−2.60574	+	14.4997i	−0.00426513	+	0.0237334i
$73$	185.582	−	406.369i	0.297545	−	0.651532i	−0.700525	−	0.713627i	$-0.747051\pi$
$73$	185.582	−	406.369i	0.297545	−	0.651532i	0.998070	+	0.0620952i	$0.0197782\pi$
$74$	−192.356	+	792.901i	−0.302174	+	1.24558i
$75$	−272.338	−	341.856i	−0.419292	−	0.526322i
$76$	600.289	+	207.762i	0.906025	+	0.313578i
$77$	−230.014	−	292.487i	−0.340423	−	0.432883i
$78$	902.515	−	472.492i	1.31012	−	0.685887i
$79$	377.569	−	130.678i	0.537719	−	0.186107i	−0.0446918	−	0.999001i	$-0.514231\pi$
$79$	377.569	−	130.678i	0.537719	−	0.186107i	0.582411	+	0.812894i	$0.302109\pi$
$80$	765.129	+	491.719i	1.06930	+	0.687198i
$81$	−584.195	−	436.070i	−0.801365	−	0.598176i
$82$	705.534	−	814.229i	0.950161	−	1.09654i
$83$	−151.467	+	144.423i	−0.200309	+	0.190994i	−0.783594	−	0.621274i	$-0.786616\pi$
$83$	−151.467	+	144.423i	−0.200309	+	0.190994i	0.583285	+	0.812268i	$0.301767\pi$
$84$	−670.355	−	520.378i	−0.870735	−	0.675928i
$85$	568.649	−	1643.00i	0.725632	−	2.09657i
$86$	976.066	−	1370.69i	1.22386	−	1.71867i
$87$	656.052	+	1119.98i	0.808462	+	1.38016i
$88$	8.23855	−	5.86664i	0.00997991	−	0.00710666i
$89$	−136.751	+	951.123i	−0.162872	+	1.13280i	0.730315	+	0.683110i	$0.239373\pi$
$89$	−136.751	+	951.123i	−0.162872	+	1.13280i	−0.893187	+	0.449686i	$0.851536\pi$
$90$	1348.28	−	801.226i	1.57913	−	0.938407i
$91$			979.736i			1.12862i
$92$	−171.156	−	880.943i	−0.193959	−	0.998312i
$93$	411.060	−	1433.25i	0.458333	−	1.59808i
$94$	1376.65	+	709.713i	1.51054	+	0.778737i
$95$	−419.631	−	1048.19i	−0.453192	−	1.13202i
$96$	−868.174	+	1014.76i	−0.922996	+	1.07884i
$97$	75.3288	+	18.2746i	0.0788503	+	0.0191289i	0.274990	−	0.961447i	$-0.411325\pi$
$97$	75.3288	+	18.2746i	0.0788503	+	0.0191289i	−0.196140	+	0.980576i	$0.562841\pi$
$98$	219.107	−	100.063i	0.225848	−	0.103141i
$99$	77.4554	+	494.448i	0.0786319	+	0.501959i
$100$	97.3925	+	677.380i	0.0973925	+	0.677380i
$101$	−856.681	−	898.461i	−0.843990	−	0.885151i	0.150646	−	0.988588i	$-0.451865\pi$
$101$	−856.681	−	898.461i	−0.843990	−	0.885151i	−0.994636	+	0.103437i	$0.967016\pi$
$102$	2237.75	+	1135.87i	2.17226	+	1.10263i
$103$	−1140.06	−	54.3077i	−1.09062	−	0.0519524i	−0.505442	−	0.862861i	$-0.668671\pi$
$103$	−1140.06	−	54.3077i	−1.09062	−	0.0519524i	−0.585173	+	0.810908i	$0.698974\pi$
$104$	−26.6000	−	1.26711i	−0.0250802	−	0.00119472i
$105$	81.2523	+	1506.18i	0.0755182	+	1.39989i
$106$	1207.18	+	1266.05i	1.10615	+	1.16009i
$107$	157.039	+	1092.23i	0.141883	+	0.986820i	0.929017	+	0.370037i	$0.120655\pi$
$107$	157.039	+	1092.23i	0.141883	+	0.986820i	−0.787134	+	0.616783i	$0.788436\pi$
$108$	444.156	+	1051.46i	0.395731	+	0.936826i
$109$	−765.041	+	349.382i	−0.672272	+	0.307016i	−0.722147	−	0.691739i	$-0.756845\pi$
$109$	−765.041	+	349.382i	−0.672272	+	0.307016i	0.0498756	+	0.998755i	$0.484118\pi$
$110$	−1046.39	−	253.850i	−0.906991	−	0.220034i
$111$	351.463	+	995.176i	0.300535	+	0.850972i
$112$	−469.243	−	1172.11i	−0.395886	−	0.988876i
$113$	−345.716	−	178.229i	−0.287807	−	0.148375i	0.308278	−	0.951296i	$-0.400247\pi$
$113$	−345.716	−	178.229i	−0.287807	−	0.148375i	−0.596085	+	0.802922i	$0.703278\pi$
$114$	1581.30	−	394.173i	1.29914	−	0.323840i
$115$	−984.139	+	1255.30i	−0.798013	+	1.01789i
$116$		−	2032.30i		−	1.62668i
$117$	644.467	−	1149.42i	0.509240	−	0.908242i
$118$	411.552	−	2862.41i	0.321072	−	2.23310i
$119$	−1965.98	+	1399.97i	−1.51446	+	1.07844i
$120$	−40.9981	+	0.258037i	−0.0311883	+	0.000196295i
$121$	−572.753	+	804.319i	−0.430318	+	0.604297i
$122$	−356.002	+	1028.60i	−0.264187	+	0.763320i
$123$	189.652	−	1380.69i	0.139027	−	1.01214i
$124$	−1689.61	+	1611.04i	−1.22364	+	1.16674i
$125$	−387.173	+	446.822i	−0.277039	+	0.319720i
$126$	−2169.75	−	179.656i	−1.53410	−	0.127024i
$127$	−741.032	−	476.232i	−0.517763	−	0.332746i	0.255523	−	0.966803i	$-0.417752\pi$
$127$	−741.032	−	476.232i	−0.517763	−	0.332746i	−0.773287	+	0.634057i	$0.781389\pi$
$128$	65.9898	−	22.8393i	0.0455682	−	0.0157713i
$129$	89.8846	−	2174.82i	0.0613481	−	1.48436i
$130$	1752.52	+	2228.52i	1.18236	+	1.50349i
$131$	−789.141	−	273.124i	−0.526317	−	0.182160i	0.0509718	−	0.998700i	$-0.483768\pi$
$131$	−789.141	−	273.124i	−0.526317	−	0.182160i	−0.577289	+	0.816540i	$0.695889\pi$
$132$	286.658	−	729.306i	0.189018	−	0.480893i
$133$	−369.512	+	1523.15i	−0.240908	+	0.993035i
$134$	−152.771	+	334.521i	−0.0984879	+	0.215658i
$135$	895.436	−	1820.50i	0.570866	−	1.16062i
$136$	−35.4667	−	55.1872i	−0.0223621	−	0.0347961i
$137$	−12.8028	+	22.1751i	−0.00798406	+	0.0138288i	−0.869990	−	0.493070i	$-0.835875\pi$
$137$	−12.8028	+	22.1751i	−0.00798406	+	0.0138288i	0.862006	+	0.506898i	$0.169208\pi$
$138$	−1601.73	−	1653.85i	−0.988031	−	1.02018i
$139$	−264.712	−	458.495i	−0.161529	−	0.279777i	0.773888	−	0.633323i	$-0.218309\pi$
$139$	−264.712	−	458.495i	−0.161529	−	0.279777i	−0.935417	+	0.353545i	$0.884976\pi$
$140$	1082.20	−	2099.18i	0.653305	−	1.26724i
$141$	1993.19	−	202.993i	1.19047	−	0.121242i
$142$	−1418.45	−	1991.93i	−0.838264	−	1.17718i
$143$	−868.038	+	254.879i	−0.507615	+	0.149049i
$144$	−220.497	+	1683.79i	−0.127602	+	0.974413i
$145$	−2729.96	+	2365.53i	−1.56352	+	1.35480i
$146$	−666.959	+	1665.98i	−0.378068	+	0.944367i
$147$	166.802	−	263.177i	0.0935894	−	0.147663i
$148$	312.739	−	1622.64i	0.173696	−	0.901220i
$149$	16.6141	−	348.773i	0.00913478	−	0.191763i	−0.989687	−	0.143244i	$-0.954247\pi$
$149$	16.6141	−	348.773i	0.00913478	−	0.191763i	0.998822	−	0.0485191i	$-0.0154502\pi$
$150$	1158.07	+	1319.61i	0.630373	+	0.718304i
$151$	−549.806	−	1588.56i	−0.296308	−	0.856126i	−0.990644	−	0.136475i	$-0.956423\pi$
$151$	−549.806	−	1588.56i	−0.296308	−	0.856126i	0.694335	−	0.719652i	$-0.255698\pi$
$152$	−40.8758	−	12.0022i	−0.0218123	−	0.00640466i
$153$	3227.38	−	349.224i	1.70535	−	0.184530i
$154$	978.813	+	1129.61i	0.512175	+	0.591082i
$155$	4130.73	+	394.437i	2.14057	+	0.204400i
$156$	−1780.33	+	1042.87i	−0.913721	+	0.535233i
$157$	−54.6702	−	572.533i	−0.0277908	−	0.291039i	−0.998674	−	0.0514844i	$-0.983605\pi$
$157$	−54.6702	−	572.533i	−0.0277908	−	0.291039i	0.970883	−	0.239554i	$-0.0770013\pi$
$158$	−1489.98	+	596.497i	−0.750230	+	0.300347i
$159$	2202.39	+	519.639i	1.09850	+	0.259183i
$160$	−3218.65	−	1858.29i	−1.59035	−	0.918191i
$161$	2123.61	−	627.004i	1.03953	−	0.306924i
$162$	2427.37	+	1638.03i	1.17723	+	0.794417i
$163$	2866.17	−	1841.97i	1.37727	−	0.885120i	0.378100	−	0.925765i	$-0.376578\pi$
$163$	2866.17	−	1841.97i	1.37727	−	0.885120i	0.999174	+	0.0406448i	$0.0129412\pi$
$164$	−1348.89	+	1715.25i	−0.642258	+	0.816698i
$165$	−1313.33	+	463.823i	−0.619650	+	0.218840i
$166$	580.139	−	608.433i	0.271250	−	0.284479i
$167$	−2335.25	−	1662.93i	−1.08208	−	0.770546i	−0.107415	−	0.994214i	$-0.534257\pi$
$167$	−2335.25	−	1662.93i	−1.08208	−	0.770546i	−0.974665	+	0.223668i	$0.928197\pi$
$168$	46.5670	+	32.7204i	0.0213852	+	0.0150264i
$169$	171.795	+	68.7764i	0.0781954	+	0.0313047i
$170$	−1967.61	+	6701.07i	−0.887699	+	3.02323i
$171$	1435.43	−	1543.89i	0.641932	−	0.690435i
$172$	−1842.57	+	2867.09i	−0.816829	+	1.27101i
$173$	2033.79	+	3944.99i	0.893791	+	1.73371i	0.643334	+	0.765585i	$0.277551\pi$
$173$	2033.79	+	3944.99i	0.893791	+	1.73371i	0.250457	+	0.968128i	$0.419419\pi$
$174$	−2846.40	−	4368.39i	−1.24015	−	1.90326i
$175$	−1640.93	+	398.084i	−0.708813	+	0.171956i
$176$	916.408	−	720.671i	0.392482	−	0.308651i
$177$	−1575.36	−	3392.88i	−0.668989	−	1.44081i
$178$	366.906	−	3842.42i	0.154499	−	1.61799i
$179$	−813.197	−	2769.50i	−0.339560	−	1.15643i	−0.935477	−	0.353388i	$-0.885029\pi$
$179$	−813.197	−	2769.50i	−0.339560	−	1.15643i	0.595917	−	0.803046i	$-0.296789\pi$
$180$	−2650.47	+	1750.88i	−1.09752	+	0.725018i
$181$	−2788.01	−	400.856i	−1.14492	−	0.164615i	−0.456364	−	0.889793i	$-0.650848\pi$
$181$	−2788.01	−	400.856i	−1.14492	−	0.164615i	−0.688561	+	0.725178i	$0.741757\pi$
$182$	−187.261	−	3931.08i	−0.0762675	−	1.60105i
$183$	340.552	+	1366.19i	0.137565	+	0.551866i
$184$	14.2767	+	58.4673i	0.00572008	+	0.0234254i
$185$	−2543.69	+	1468.60i	−1.01090	+	0.583642i
$186$	−1375.39	+	5829.34i	−0.542197	+	2.29800i
$187$	−1751.81	−	1377.64i	−0.685054	−	0.538733i
$188$	−2853.48	−	1303.14i	−1.10698	−	0.505539i
$189$	−2478.42	+	1337.54i	−0.953853	+	0.514769i
$190$	1884.07	+	4125.54i	0.719394	+	1.57525i
$191$	−4685.57	+	903.070i	−1.77506	+	0.342114i	−0.968495	−	0.249035i	$-0.919887\pi$
$191$	−4685.57	+	903.070i	−1.77506	+	0.342114i	−0.806563	+	0.591149i	$0.798675\pi$
$192$	1686.29	−	2172.30i	0.633843	−	0.816521i
$193$	−700.125	−	2885.96i	−0.261120	−	1.07635i	−0.939748	−	0.341868i	$-0.888940\pi$
$193$	−700.125	−	2885.96i	−0.261120	−	1.07635i	0.678628	−	0.734482i	$-0.262575\pi$
$194$	−305.742	−	58.9269i	−0.113149	−	0.0218077i
$195$	3473.11	+	1177.63i	1.27546	+	0.432471i
$196$	−433.629	+	223.551i	−0.158028	+	0.0814690i
$197$	−230.589	−	199.806i	−0.0833948	−	0.0722620i	0.612166	−	0.790729i	$-0.290298\pi$
$197$	−230.589	−	199.806i	−0.0833948	−	0.0722620i	−0.695561	+	0.718467i	$0.744844\pi$
$198$	−405.287	−	1969.12i	−0.145467	−	0.706763i
$199$	−608.895	+	87.5458i	−0.216901	+	0.0311857i	−0.249909	−	0.968269i	$-0.580401\pi$
$199$	−608.895	+	87.5458i	−0.216901	+	0.0311857i	0.0330073	+	0.999455i	$0.489492\pi$
$200$	−8.68580	−	45.0662i	−0.00307089	−	0.0159333i
$201$	70.6631	+	470.435i	0.0247970	+	0.165084i
$202$	3609.07	+	3441.24i	1.25709	+	1.19864i
$203$	4991.70	−	476.650i	1.72586	−	0.164799i
$204$	−4636.62	−	2082.31i	−1.59132	−	0.714660i
$205$	3874.13	−	184.547i	1.31991	−	0.0628748i
$206$	4584.75			1.55065
$207$	−2903.86	−	661.307i	−0.975036	−	0.222048i
$208$	−3069.66			−1.02328
$209$	−1445.63	+	68.8636i	−0.478450	+	0.0227914i
$210$	−613.898	−	6027.86i	−0.201729	−	1.98077i
$211$	−9.13284	+	0.872080i	−0.00297977	+	0.000284533i	−0.0965458	−	0.995329i	$-0.530779\pi$
$211$	−9.13284	+	0.872080i	−0.00297977	+	0.000284533i	0.0935661	+	0.995613i	$0.470173\pi$
$212$	−2564.23	−	2444.99i	−0.830718	−	0.792088i
$213$	−2943.97	−	1157.14i	−0.947030	−	0.372235i
$214$	−838.863	−	4352.44i	−0.267960	−	1.39031i
$215$	5996.01	−	862.096i	1.90197	−	0.273463i
$216$	−33.1089	−	69.0192i	−0.0104295	−	0.0217415i
$217$	−4353.28	−	3772.14i	−1.36184	−	1.18004i
$218$	3002.87	−	1548.09i	0.932935	−	0.480961i
$219$	453.651	+	2276.57i	0.139977	+	0.702448i
$220$	2141.39	+	412.719i	0.656239	+	0.126480i
$221$	1383.43	+	5702.58i	0.421084	+	1.73573i
$222$	−1600.42	−	3925.86i	−0.483843	−	1.18688i
$223$	−478.735	+	92.2686i	−0.143760	+	0.0277075i	−0.260623	−	0.965441i	$-0.583928\pi$
$223$	−478.735	+	92.2686i	−0.143760	+	0.0277075i	0.116864	+	0.993148i	$0.462716\pi$
$224$	2143.22	+	4692.99i	0.639284	+	1.39984i
$225$	2186.99	+	612.365i	0.647997	+	0.181441i
$226$	1421.21	+	649.046i	0.418308	+	0.191035i
$227$	2110.99	+	1660.10i	0.617230	+	0.485395i	0.877138	−	0.480238i	$-0.159450\pi$
$227$	2110.99	+	1660.10i	0.617230	+	0.485395i	−0.259908	+	0.965633i	$0.583692\pi$
$228$	−3161.12	+	949.838i	−0.918202	+	0.275897i
$229$	−456.863	+	263.770i	−0.131836	+	0.0761154i	−0.564467	−	0.825455i	$-0.690918\pi$
$229$	−456.863	+	263.770i	−0.131836	+	0.0761154i	0.432632	+	0.901571i	$0.357585\pi$
$230$	3708.82	−	5224.85i	1.06327	−	1.49790i
$231$	1858.54	+	533.034i	0.529363	+	0.151823i
$232$	6.48523	+	136.142i	0.00183524	+	0.0385265i
$233$	−1371.11	−	197.135i	−0.385511	−	0.0554281i	−0.0531653	−	0.998586i	$-0.516931\pi$
$233$	−1371.11	−	197.135i	−0.385511	−	0.0554281i	−0.332346	+	0.943158i	$0.607840\pi$
$234$	−2366.16	+	4735.12i	−0.661030	+	1.32284i
$235$	1570.86	+	5349.85i	0.436049	+	1.48504i
$236$	−556.751	+	5830.56i	−0.153565	+	1.60821i
$237$	−1193.58	+	1698.68i	−0.327137	+	0.465574i
$238$	7620.70	−	5992.99i	2.07553	−	1.63222i
$239$	−937.571	+	227.452i	−0.253751	+	0.0615593i	−0.360616	−	0.932714i	$-0.617434\pi$
$239$	−937.571	+	227.452i	−0.253751	+	0.0615593i	0.106866	+	0.994273i	$0.465919\pi$
$240$	−4719.10	+	254.576i	−1.26923	+	0.0684700i
$241$	−654.257	−	1269.08i	−0.174873	−	0.339206i	0.785067	−	0.619410i	$-0.212628\pi$
$241$	−654.257	−	1269.08i	−0.174873	−	0.339206i	−0.959941	+	0.280204i	$0.909598\pi$
$242$	2144.38	−	3336.72i	0.569611	−	0.886332i
$243$	3787.50	+	61.1012i	0.999870	+	0.0161302i
$244$	621.094	−	2115.25i	0.162957	−	0.554980i
$245$	805.021	+	322.282i	0.209922	+	0.0840401i
$246$	−497.061	+	5576.12i	−0.128827	+	1.44520i
$247$	3104.09	+	2210.41i	0.799628	+	0.569413i
$248$	108.044	−	113.314i	0.0276646	−	0.0290138i
$249$	199.081	−	1069.10i	0.0506678	−	0.272094i
$250$	1468.09	−	1866.83i	0.371400	−	0.472274i
$251$	2209.48	−	1419.95i	0.555623	−	0.357077i	−0.232498	−	0.972597i	$-0.574690\pi$
$251$	2209.48	−	1419.95i	0.555623	−	0.357077i	0.788122	+	0.615519i	$0.211054\pi$
$252$	4406.90	+	154.359i	1.10162	+	0.0385860i
$253$	1107.98	+	1718.39i	0.275329	+	0.427013i
$254$	3064.34	+	1769.20i	0.756982	+	0.437044i
$255$	2599.73	+	8652.04i	0.638436	+	2.12475i
$256$	3670.20	−	1469.33i	0.896044	−	0.358722i
$257$	400.254	+	4191.65i	0.0971484	+	1.01738i	0.904259	+	0.426984i	$0.140424\pi$
$257$	400.254	+	4191.65i	0.0971484	+	1.01738i	−0.807111	+	0.590400i	$0.798970\pi$
$258$	55.0301	+	8743.43i	0.0132792	+	2.10985i
$259$	4058.86	+	387.574i	0.973765	+	0.0929833i
$260$	−3760.27	−	4339.58i	−0.896931	−	1.03511i
$261$	−6169.80	−	2724.32i	−1.46322	−	0.646097i
$262$	3218.55	+	945.050i	0.758941	+	0.222845i
$263$	−1303.35	−	3765.77i	−0.305581	−	0.882917i	−0.988339	−	0.152273i	$-0.951341\pi$
$263$	−1303.35	−	3765.77i	−0.305581	−	0.882917i	0.682758	−	0.730645i	$-0.260780\pi$
$264$	−16.8756	+	49.7702i	−0.00393418	+	0.0116028i
$265$	−299.648	+	6290.38i	−0.0694612	+	1.45817i
$266$	1191.50	−	6182.09i	0.274645	−	1.42499i
$267$	−2315.81	−	4423.47i	−0.530807	−	1.01390i
$268$	276.830	−	691.488i	0.0630973	−	0.157609i
$269$	−2494.82	+	2161.77i	−0.565471	+	0.489983i	−0.890042	−	0.455878i	$-0.849325\pi$
$269$	−2494.82	+	2161.77i	−0.565471	+	0.489983i	0.324572	+	0.945861i	$0.394780\pi$
$270$	−3244.88	+	7475.69i	−0.731397	+	1.68502i
$271$	2815.02	−	826.564i	0.630997	−	0.185277i	0.0494320	−	0.998777i	$-0.484259\pi$
$271$	2815.02	−	826.564i	0.630997	−	0.185277i	0.581565	+	0.813500i	$0.302441\pi$
$272$	−4386.32	−	6159.72i	−0.977792	−	1.37312i
$273$	−2979.03	−	4128.22i	−0.660436	−	0.915206i
$274$	47.1314	−	91.4222i	0.0103917	−	0.0201570i
$275$	−779.588	−	1350.29i	−0.170949	−	0.296092i
$276$	3399.82	+	3191.52i	0.741467	+	0.696040i
$277$	1472.29	−	2550.08i	0.319355	−	0.553140i	−0.660998	−	0.750387i	$-0.729867\pi$
$277$	1472.29	−	2550.08i	0.319355	−	0.553140i	0.980354	+	0.197248i	$0.0632003\pi$
$278$	1149.76	+	1789.07i	0.248051	+	0.385975i
$279$	2625.96	+	7289.05i	0.563485	+	1.56410i
$280$	−65.7969	+	144.075i	−0.0140433	+	0.0307505i
$281$	−479.601	+	1976.94i	−0.101817	+	0.419696i	−0.999793	−	0.0203490i	$-0.993522\pi$
$281$	−479.601	+	1976.94i	−0.101817	+	0.419696i	0.897976	+	0.440045i	$0.145037\pi$
$282$	−7958.65	+	1195.45i	−1.68061	+	0.252441i
$283$	1678.74	+	581.017i	0.352617	+	0.122042i	0.497634	−	0.867387i	$-0.334202\pi$
$283$	1678.74	+	581.017i	0.352617	+	0.122042i	−0.145017	+	0.989429i	$0.546324\pi$
$284$	3061.60	+	3893.15i	0.639693	+	0.813436i
$285$	4955.33	+	3140.70i	1.02992	+	0.652769i
$286$	3434.19	−	1188.59i	0.710029	−	0.245743i
$287$	−4529.33	−	2910.82i	−0.931560	−	0.598677i
$288$	572.617	−	6915.61i	0.117159	−	1.41495i
$289$	−6248.89	+	7211.61i	−1.27191	+	1.46786i
$290$	10501.6	−	10013.2i	2.12646	−	2.02757i
$291$	−372.972	+	152.046i	−0.0751341	+	0.0306292i
$292$	1188.76	−	3434.70i	0.238243	−	0.688358i
$293$	1997.45	−	2805.02i	0.398266	−	0.559287i	−0.565938	−	0.824448i	$-0.691486\pi$
$293$	1997.45	−	2805.02i	0.398266	−	0.559287i	0.964204	+	0.265161i	$0.0854251\pi$
$294$	−618.975	+	1087.85i	−0.122787	+	0.215798i
$295$	8480.14	−	6038.68i	1.67367	−	1.19182i
$296$	−15.7721	+	109.697i	−0.00309707	+	0.0215406i
$297$	−1829.81	−	1847.90i	−0.357496	−	0.361030i
$298$			1402.59i			0.272651i
$299$	503.714	−	5359.91i	0.0974265	−	1.03670i
$300$	−2470.05	−	2558.08i	−0.475360	−	0.492302i
$301$	−7474.25	−	3853.24i	−1.43126	−	0.737865i
$302$	2509.66	+	6268.84i	0.478195	+	1.19447i
$303$	6341.62	+	1180.90i	1.20236	+	0.223898i
$304$	−4772.26	−	1157.74i	−0.900355	−	0.218424i
$305$	−3564.32	+	1627.77i	−0.669155	+	0.305593i
$306$	−12882.8	+	2018.09i	−2.40673	+	0.377014i
$307$	−438.950	−	3052.96i	−0.0816033	−	0.567563i	−0.989071	−	0.147441i	$-0.952896\pi$
$307$	−438.950	−	3052.96i	−0.0816033	−	0.567563i	0.907468	−	0.420122i	$-0.138013\pi$
$308$	−2089.08	−	2190.97i	−0.386482	−	0.405331i
$309$	4968.89	−	3237.68i	0.914791	−	0.596069i
$310$	−16649.5	−	793.114i	−3.05042	−	0.145309i
$311$	−4110.13	−	195.790i	−0.749403	−	0.0356985i	−0.330594	−	0.943773i	$-0.607249\pi$
$311$	−4110.13	−	195.790i	−0.749403	−	0.0356985i	−0.418809	+	0.908074i	$0.637552\pi$
$312$	115.935	−	75.5419i	0.0210369	−	0.0137074i
$313$	1188.67	+	1246.64i	0.214656	+	0.225125i	0.822255	−	0.569119i	$-0.192716\pi$
$313$	1188.67	+	1246.64i	0.214656	+	0.225125i	−0.607599	+	0.794244i	$0.707867\pi$
$314$	328.789	+	2286.78i	0.0590912	+	0.410988i
$315$	−4922.12	−	6099.39i	−0.880413	−	1.09099i
$316$	2956.87	−	1350.36i	0.526382	−	0.240391i
$317$	7196.84	+	1745.94i	1.27513	+	0.309342i	0.815493	−	0.578767i	$-0.196466\pi$
$317$	7196.84	+	1745.94i	1.27513	+	0.309342i	0.459633	+	0.888109i	$0.347981\pi$
$318$	−8936.18	−	1664.05i	−1.57584	−	0.293444i
$319$	1720.90	+	4298.61i	0.302044	+	0.754470i
$320$	6802.42	+	3506.89i	1.18833	+	0.612629i
$321$	−3982.78	−	4124.72i	−0.692514	−	0.717195i
$322$	−8400.93	+	2921.68i	−1.45393	+	0.505649i
$323$			9387.30i			1.61710i
$324$	−5068.63	−	3079.94i	−0.869106	−	0.528110i
$325$	−584.251	+	4063.55i	−0.0997181	+	0.693555i
$326$	−11148.1	+	7938.55i	−1.89398	+	1.34870i
$327$	2161.23	−	3798.38i	0.365494	−	0.642357i
$328$	84.8870	−	119.207i	0.0142899	−	0.0200674i
$329$	2531.50	−	7314.30i	0.424214	−	1.22568i
$330$	5180.93	−	2112.06i	0.864245	−	0.352318i
$331$	−2851.27	+	2718.68i	−0.473475	+	0.451457i	−0.888854	−	0.458191i	$-0.848497\pi$
$331$	−2851.27	+	2718.68i	−0.473475	+	0.451457i	0.415379	+	0.909648i	$0.363649\pi$
$332$	−1115.04	+	1286.82i	−0.184324	+	0.212721i
$333$	−4506.90	−	3124.61i	−0.741672	−	0.514196i
$334$	9687.80	+	6225.97i	1.58710	+	1.01997i
$335$	−1251.09	+	433.005i	−0.204042	+	0.0706197i
$336$	5541.18	+	3512.02i	0.899691	+	0.570227i
$337$	3546.52	+	4509.77i	0.573268	+	0.728970i	0.983075	−	0.183202i	$-0.0586464\pi$
$337$	3546.52	+	4509.77i	0.573268	+	0.728970i	−0.409807	+	0.912172i	$0.634404\pi$
$338$	−702.456	−	243.122i	−0.113043	−	0.0391246i
$339$	1998.64	−	300.212i	0.320210	−	0.0480982i
$340$	3334.85	−	13746.5i	0.531935	−	2.19266i
$341$	2209.58	−	4838.30i	0.350895	−	0.768354i
$342$	−5464.43	+	6469.06i	−0.863984	+	1.02283i
$343$	3071.73	+	4779.71i	0.483551	+	0.752419i
$344$	114.283	−	197.943i	0.0179119	−	0.0310244i
$345$	329.863	−	8281.75i	0.0514761	−	1.29239i
$346$	−8914.37	−	15440.1i	−1.38509	−	2.39904i
$347$	446.064	−	865.244i	0.0690086	−	0.133858i	−0.851808	−	0.523855i	$-0.824494\pi$
$347$	446.064	−	865.244i	0.0690086	−	0.133858i	0.920816	+	0.389997i	$0.127524\pi$
$348$	6179.51	+	8563.32i	0.951886	+	1.31909i
$349$	−675.827	−	949.066i	−0.103657	−	0.145565i	0.759490	−	0.650520i	$-0.225449\pi$
$349$	−675.827	−	949.066i	−0.103657	−	0.145565i	−0.863146	+	0.504954i	$0.831509\pi$
$350$	6507.95	−	1910.91i	0.993899	−	0.291835i
$351$	779.458	+	6802.82i	0.118531	+	1.03449i
$352$	−3600.39	+	3119.76i	−0.545175	+	0.472397i
$353$	−822.602	+	2054.76i	−0.124030	+	0.309813i	−0.977368	−	0.211546i	$-0.932150\pi$
$353$	−822.602	+	2054.76i	−0.124030	+	0.309813i	0.853338	+	0.521358i	$0.174575\pi$
$354$	6969.44	+	13312.4i	1.04639	+	1.99872i
$355$	1666.01	−	8644.10i	0.249078	−	1.29234i
$356$	−371.984	+	7808.90i	−0.0553795	+	1.16256i
$357$	4027.06	−	11876.8i	0.597016	−	1.76074i
$358$	3792.21	+	10956.9i	0.559845	+	1.61757i
$359$	−7535.73	−	2212.69i	−1.10786	−	0.325296i	−0.323887	−	0.946096i	$-0.604990\pi$
$359$	−7535.73	−	2212.69i	−1.10786	−	0.325296i	−0.783969	+	0.620799i	$0.786808\pi$
$360$	171.965	−	125.748i	0.0251760	−	0.0184097i
$361$	−499.583	−	576.550i	−0.0728361	−	0.0840574i
$362$	11263.2	+	1075.51i	1.63531	+	0.156153i
$363$	−32.2915	−	5130.62i	−0.00466905	−	0.741840i
$364$	757.688	+	7934.87i	0.109103	+	1.14258i
$365$	−5997.46	+	2401.02i	−0.860058	+	0.344315i
$366$	−1627.55	−	5416.59i	−0.232441	−	0.773578i
$367$	−524.588	−	302.871i	−0.0746138	−	0.0430783i	0.462229	−	0.886761i	$-0.347050\pi$
$367$	−524.588	−	302.871i	−0.0746138	−	0.0430783i	−0.536843	+	0.843682i	$0.680383\pi$
$368$	1964.50	+	6653.61i	0.278279	+	0.942510i
$369$	3399.07	+	6394.35i	0.479535	+	0.902104i
$370$	9925.59	−	6378.79i	1.39461	−	0.896264i
$371$	5403.94	−	6871.66i	0.756222	−	0.961614i
$372$	2220.76	−	11925.8i	0.309518	−	1.66216i
$373$	−6678.21	+	7003.90i	−0.927036	+	0.972248i	−0.999685	−	0.0251098i	$-0.992006\pi$
$373$	−6678.21	+	7003.90i	−0.927036	+	0.972248i	0.0726483	+	0.997358i	$0.476855\pi$
$374$	7292.27	+	5192.80i	1.00822	+	0.717950i
$375$	272.770	−	3059.99i	0.0375621	−	0.421379i
$376$	195.310	+	78.1903i	0.0267882	+	0.0107244i
$377$	3434.78	−	11697.8i	0.469231	−	1.59805i
$378$	9688.73	−	5840.43i	1.31835	−	0.794707i
$379$	298.489	−	464.459i	0.0404548	−	0.0629489i	−0.820437	−	0.571737i	$-0.806270\pi$
$379$	298.489	−	464.459i	0.0404548	−	0.0629489i	0.860892	+	0.508788i	$0.169906\pi$
$380$	−4209.22	−	8164.74i	−0.568232	−	1.10222i
$381$	4570.47	−	246.558i	0.614573	−	0.0331537i
$382$	18627.7	−	4519.04i	2.49497	−	0.605273i
$383$	−3268.96	+	2570.74i	−0.436126	+	0.342973i	−0.811959	−	0.583714i	$-0.801599\pi$
$383$	−3268.96	+	2570.74i	−0.436126	+	0.342973i	0.375833	+	0.926687i	$0.377356\pi$
$384$	−208.609	+	296.887i	−0.0277228	+	0.0394544i
$385$	−511.478	+	5356.44i	−0.0677074	+	0.709064i
$386$	3360.78	+	11445.8i	0.443159	+	1.50926i
$387$	6234.13	+	9437.16i	0.818859	+	1.23958i
$388$	624.220	+	89.7493i	0.0816752	+	0.0117431i
$389$	644.460	+	13528.9i	0.0839985	+	1.76335i	0.511455	+	0.859310i	$0.329107\pi$
$389$	644.460	+	13528.9i	0.0839985	+	1.76335i	−0.427456	+	0.904036i	$0.640590\pi$
$390$	−14160.6	−	4061.29i	−1.83859	−	0.527311i
$391$	11475.2	−	6648.13i	1.48421	−	0.859874i
$392$	28.3350	−	16.3592i	0.00365085	−	0.00210782i
$393$	4155.60	−	1248.66i	0.533390	−	0.160271i
$394$	963.403	+	757.628i	0.123187	+	0.0968751i
$395$	−5255.60	−	2400.15i	−0.669464	−	0.305734i
$396$	1009.70	+	3944.63i	0.128129	+	0.500569i
$397$	545.913	+	1195.38i	0.0690141	+	0.151120i	0.940995	−	0.338419i	$-0.109892\pi$
$397$	545.913	+	1195.38i	0.0690141	+	0.151120i	−0.871981	+	0.489539i	$0.837165\pi$
$398$	2426.39	−	467.649i	0.305588	−	0.0588973i
$399$	−3074.37	−	7541.50i	−0.385742	−	0.946234i
$400$	−1247.26	−	5141.28i	−0.155908	−	0.642660i
$401$	−12776.5	−	2462.47i	−1.59109	−	0.306658i	−0.684612	−	0.728908i	$-0.740028\pi$
$401$	−12776.5	−	2462.47i	−1.59109	−	0.306658i	−0.906479	+	0.422250i	$0.861240\pi$
$402$	−373.444	−	1874.06i	−0.0463326	−	0.232512i
$403$	−12448.1	+	6417.43i	−1.53867	+	0.793239i
$404$	−7633.09	−	6614.11i	−0.940001	−	0.814515i
$405$	1762.46	+	10393.6i	0.216241	+	1.27521i
$406$	−19937.6	+	2866.59i	−2.43716	+	0.350410i
$407$	712.527	+	3696.94i	0.0867781	+	0.450247i
$408$	317.247	+	124.696i	0.0384953	+	0.0151308i
$409$	−957.687	−	913.152i	−0.115781	−	0.110397i	0.629977	−	0.776614i	$-0.283064\pi$
$409$	−957.687	−	913.152i	−0.115781	−	0.110397i	−0.745758	+	0.666216i	$0.767913\pi$
$410$	−15509.2	+	1480.95i	−1.86816	+	0.178388i
$411$	−13.4806	−	132.366i	−0.00161788	−	0.0158859i
$412$	−9275.33	+	441.838i	−1.10913	+	0.0528345i
$413$	−14451.5			−1.72182
$414$	11777.8	+	2098.40i	1.39819	+	0.249108i
$415$	3026.43			0.357980
$416$	12529.5	−	596.854i	1.47671	−	0.0703441i
$417$	2509.51	+	1127.02i	0.294704	+	0.132351i
$418$	5787.26	−	552.616i	0.677187	−	0.0646635i
$419$	3170.56	+	3023.12i	0.369670	+	0.352480i	0.852030	−	0.523493i	$-0.175372\pi$
$419$	3170.56	+	3023.12i	0.369670	+	0.352480i	−0.482359	+	0.875973i	$0.660220\pi$
$420$	1822.88	+	12135.7i	0.211780	+	1.40991i
$421$	−1895.27	−	9833.60i	−0.219406	−	1.13839i	−0.909830	−	0.414981i	$-0.863788\pi$
$421$	−1895.27	−	9833.60i	−0.219406	−	1.13839i	0.690424	−	0.723405i	$-0.257424\pi$
$422$	36.4779	−	5.24472i	0.00420785	−	0.000604998i
$423$	−7781.28	+	6915.91i	−0.894418	+	0.794948i
$424$	179.578	+	155.605i	0.0205685	+	0.0178227i
$425$	−8988.95	+	4634.12i	−1.02595	+	0.528913i
$426$	12033.5	+	4080.22i	1.36861	+	0.464055i
$427$	5341.11	+	1029.41i	0.605327	+	0.116667i
$428$	2116.54	+	8724.50i	0.239035	+	0.985315i
$429$	2882.58	−	3713.35i	0.324410	−	0.417908i
$430$	−23893.6	+	4605.11i	−2.67965	+	0.516461i
$431$	3335.65	+	7304.06i	0.372791	+	0.816297i	0.999319	+	0.0368989i	$0.0117480\pi$
$431$	3335.65	+	7304.06i	0.372791	+	0.816297i	−0.626528	+	0.779399i	$0.715525\pi$
$432$	−4190.71	−	7765.27i	−0.466726	−	0.864830i
$433$	−5351.42	−	2443.91i	−0.593933	−	0.271240i	0.0956871	−	0.995411i	$-0.469495\pi$
$433$	−5351.42	−	2443.91i	−0.593933	−	0.271240i	−0.689620	+	0.724171i	$0.742222\pi$
$434$	18188.1	+	14303.3i	2.01165	+	1.58198i
$435$	4310.27	−	18268.2i	0.475084	−	2.01355i
$436$	−5925.86	+	3421.30i	−0.650911	+	0.375804i
$437$	2804.62	−	8142.82i	0.307009	−	0.891359i
$438$	−2255.36	−	9047.78i	−0.246039	−	0.987031i
$439$	348.820	+	7322.63i	0.0379232	+	0.796105i	0.935089	+	0.354412i	$0.115319\pi$
$439$	348.820	+	7322.63i	0.0379232	+	0.796105i	−0.897166	+	0.441693i	$0.854378\pi$
$440$	−144.767	−	20.8143i	−0.0156852	−	0.00225519i
$441$	97.3873	+	1616.11i	0.0105158	+	0.174507i
$442$	−6640.83	−	22616.6i	−0.714642	−	2.43385i
$443$	144.509	−	1513.36i	0.0154984	−	0.162307i	−0.984409	−	0.175893i	$-0.943719\pi$
$443$	144.509	−	1513.36i	0.0154984	−	0.162307i	0.999908	+	0.0135861i	$0.00432473\pi$
$444$	3616.12	+	7788.11i	0.386517	+	0.832449i
$445$	10922.6	−	8589.60i	1.16355	−	0.915025i
$446$	1903.24	−	461.721i	0.202065	−	0.0490204i
$447$	990.491	+	1520.11i	0.104807	+	0.160848i
$448$	−4868.14	−	9442.88i	−0.513389	−	0.995835i
$449$	4876.98	−	7588.73i	0.512604	−	0.797627i	−0.484411	−	0.874841i	$-0.660966\pi$
$449$	4876.98	−	7588.73i	0.512604	−	0.797627i	0.997015	+	0.0772136i	$0.0246024\pi$
$450$	−8892.11	−	2039.04i	−0.931507	−	0.213603i
$451$	1400.66	−	4770.20i	0.146240	−	0.498049i
$452$	−2937.78	−	1176.11i	−0.305712	−	0.122389i
$453$	7146.91	+	5021.80i	0.741260	+	0.520849i
$454$	−8787.42	−	6257.49i	−0.908401	−	0.646869i
$455$	9776.88	−	10253.7i	1.00736	−	1.05649i
$456$	208.729	−	73.7161i	0.0214356	−	0.00757033i
$457$	−2147.65	+	2730.96i	−0.219831	+	0.279538i	−0.883443	−	0.468539i	$-0.844780\pi$
$457$	−2147.65	+	2730.96i	−0.219831	+	0.279538i	0.663611	+	0.748077i	$0.269023\pi$
$458$	1782.70	−	1145.67i	0.181878	−	0.116886i
$459$	−12537.0	+	11284.8i	−1.27490	+	1.14756i
$460$	−6999.74	+	10927.7i	−0.709488	+	1.10763i
$461$	2194.04	+	1266.73i	0.221663	+	0.127977i	0.606720	−	0.794915i	$-0.292485\pi$
$461$	2194.04	+	1266.73i	0.221663	+	0.127977i	−0.385057	+	0.922893i	$0.625818\pi$
$462$	−7559.07	−	1783.51i	−0.761212	−	0.179603i
$463$	−17765.1	+	7112.09i	−1.78319	+	0.713881i	−0.788024	+	0.615644i	$0.788896\pi$
$463$	−17765.1	+	7112.09i	−1.78319	+	0.713881i	−0.995163	+	0.0982367i	$0.968680\pi$
$464$	1493.42	+	15639.8i	0.149419	+	1.56478i
$465$	−18604.6	+	10898.1i	−1.85542	+	1.08685i
$466$	5539.09	+	528.919i	0.550630	+	0.0525788i
$467$	−3157.19	−	3643.59i	−0.312843	−	0.361040i	0.577452	−	0.816425i	$-0.304047\pi$
$467$	−3157.19	−	3643.59i	−0.312843	−	0.361040i	−0.890295	+	0.455385i	$0.849502\pi$
$468$	4330.62	−	9807.59i	0.427741	−	0.968709i
$469$	1763.35	+	517.765i	0.173611	+	0.0509769i
$470$	−7325.43	−	21165.4i	−0.718930	−	2.07721i
$471$	1971.23	+	2246.20i	0.192844	+	0.219744i
$472$	18.6904	−	392.360i	0.00182266	−	0.0382623i
$473$	1469.51	−	7624.55i	0.142850	−	0.741178i
$474$	4464.45	−	7043.90i	0.432614	−	0.682568i
$475$	−2440.89	+	6097.06i	−0.235781	+	0.588952i
$476$	−14839.8	+	12858.7i	−1.42895	+	1.23819i
$477$	−10860.0	+	4507.13i	−1.04245	+	0.432636i
$478$	3718.43	−	1091.83i	0.355810	−	0.104475i
$479$	−855.378	−	1201.21i	−0.0815933	−	0.114582i	0.771762	−	0.635911i	$-0.219376\pi$
$479$	−855.378	−	1201.21i	−0.0815933	−	0.114582i	−0.853355	+	0.521330i	$0.825436\pi$
$480$	19212.5	−	1956.67i	1.82693	−	0.186061i
$481$	4542.52	−	8811.26i	0.430605	−	0.835258i
$482$	2867.70	+	4967.00i	0.270996	+	0.469379i
$483$	−7041.58	+	9099.10i	−0.663360	+	0.857191i
$484$	−4016.69	+	6957.12i	−0.377225	+	0.653373i
$485$	−606.011	−	942.971i	−0.0567372	−	0.0882848i
$486$	−15208.6	+	478.758i	−1.41950	+	0.0446850i
$487$	3344.05	−	7322.45i	0.311157	−	0.681338i	−0.687852	−	0.725851i	$-0.741446\pi$
$487$	3344.05	−	7322.45i	0.311157	−	0.681338i	0.999009	+	0.0445127i	$0.0141735\pi$
$488$	−34.8565	+	143.680i	−0.00323336	+	0.0133281i
$489$	−6476.12	+	16476.4i	−0.598896	+	1.52369i
$490$	−3291.66	−	1139.25i	−0.303474	−	0.105033i
$491$	7742.09	+	9844.87i	0.711600	+	0.904873i	0.998591	−	0.0530603i	$-0.0168976\pi$
$491$	7742.09	+	9844.87i	0.711600	+	0.904873i	−0.286991	+	0.957933i	$0.592655\pi$
$492$	468.218	−	11328.9i	0.0429042	−	1.03810i
$493$	28381.3	−	9822.87i	2.59276	−	0.897362i
$494$	−12877.3	−	8275.74i	−1.17283	−	0.753731i
$495$	4123.52	−	5947.72i	0.374421	−	0.540061i
$496$	11818.7	−	13639.5i	1.06991	−	1.23474i
$497$	−8844.22	+	8432.94i	−0.798224	+	0.761105i
$498$	−594.452	+	4327.69i	−0.0534901	+	0.389415i
$499$	−4606.28	+	13309.0i	−0.413237	+	1.19397i	0.525936	+	0.850524i	$0.323715\pi$
$499$	−4606.28	+	13309.0i	−0.413237	+	1.19397i	−0.939173	+	0.343445i	$0.888406\pi$
$500$	−2790.16	+	3918.23i	−0.249559	+	0.350457i
$501$	14896.2	−	93.7550i	1.32837	−	0.00836061i
$502$	−8593.92	+	6119.70i	−0.764075	+	0.544095i
$503$	2323.72	−	16161.9i	0.205984	−	1.43265i	−0.580109	−	0.814539i	$-0.696990\pi$
$503$	2323.72	−	16161.9i	0.205984	−	1.43265i	0.786093	−	0.618108i	$-0.212101\pi$
$504$	−295.706	+	3.72242i	−0.0261345	+	0.000328988i
$505$			17952.0i			1.58189i
$506$	−4774.10	−	6683.08i	−0.419436	−	0.587153i
$507$	−933.002	+	232.571i	−0.0817280	+	0.0203725i
$508$	−6369.91	−	3283.92i	−0.556337	−	0.286812i
$509$	−3085.73	−	7707.79i	−0.268709	−	0.671202i	0.731232	−	0.682129i	$-0.238946\pi$
$509$	−3085.73	−	7707.79i	−0.268709	−	0.671202i	−0.999940	+	0.0109275i	$0.996522\pi$
$510$	−12084.8	−	34218.5i	−1.04926	−	2.97102i
$511$	8715.05	+	2114.25i	0.754464	+	0.183031i
$512$	−14953.6	+	6829.08i	−1.29075	+	0.589464i
$513$	−1353.93	+	10870.0i	−0.116525	+	0.935520i
$514$	−2407.14	−	16742.0i	−0.206565	−	1.43669i
$515$	11389.7	+	11945.1i	0.974541	+	1.02207i
$516$	−953.947	−	17683.4i	−0.0813860	−	1.50866i
$517$	7138.98	+	340.072i	0.607296	+	0.0289291i
$518$	−16359.8	−	779.314i	−1.38766	−	0.0661025i
$519$	−20564.9	−	10438.6i	−1.73930	−	0.882862i
$520$	265.745	+	278.705i	0.0224109	+	0.0235039i
$521$	−241.749	−	1681.40i	−0.0203287	−	0.141389i	0.977129	−	0.212646i	$-0.0682081\pi$
$521$	−241.749	−	1681.40i	−0.0203287	−	0.141389i	−0.997458	+	0.0712569i	$0.977299\pi$
$522$	25276.4	+	9751.80i	2.11938	+	0.817672i
$523$	2736.05	−	1249.51i	0.228755	−	0.104469i	−0.297740	−	0.954647i	$-0.596233\pi$
$523$	2736.05	−	1249.51i	0.228755	−	0.104469i	0.526496	+	0.850178i	$0.323506\pi$
$524$	−6602.47	−	1601.74i	−0.550439	−	0.133535i
$525$	5703.79	−	6666.84i	0.474159	−	0.554219i
$526$	5949.30	+	14860.6i	0.493159	+	1.23185i
$527$	−30664.9	−	15808.8i	−2.53469	−	1.30672i
$528$	−1670.08	+	5823.09i	−0.137653	+	0.479958i
$529$	−11940.2	+	2338.38i	−0.981358	+	0.192190i
$530$		−	25296.8i		−	2.07325i
$531$	16954.5	+	9506.14i	1.38561	+	0.776896i
$532$	−1814.73	+	12621.7i	−0.147892	+	1.02861i
$533$	−10663.0	+	7593.10i	−0.866542	+	0.617062i
$534$	10137.4	+	17306.1i	0.821516	+	1.40245i
$535$	9255.93	−	12998.1i	0.747979	−	1.05039i
$536$	−16.3380	+	47.2054i	−0.00131659	+	0.00380404i
$537$	11847.5	+	9196.92i	0.952065	+	0.739062i
$538$	9596.99	−	9150.71i	0.769063	−	0.733300i
$539$	727.889	−	840.028i	0.0581677	−	0.0671291i
$540$	5844.23	−	15436.7i	0.465733	−	1.23016i
$541$	−20730.1	−	13322.4i	−1.64742	−	1.05873i	−0.933544	−	0.358462i	$-0.883301\pi$
$541$	−20730.1	−	13322.4i	−1.64742	−	1.05873i	−0.713877	−	0.700272i	$-0.753062\pi$
$542$	−11137.0	+	3854.54i	−0.882609	+	0.305474i
$543$	12966.5	−	6788.31i	1.02476	−	0.536490i
$544$	19101.4	+	24289.4i	1.50545	+	1.91433i
$545$	11493.3	+	3977.86i	0.903335	+	0.312647i
$546$	12742.1	+	15994.7i	0.998737	+	1.25368i
$547$	−2545.59	+	10493.1i	−0.198979	+	0.820205i	0.781552	+	0.623841i	$0.214429\pi$
$547$	−2545.59	+	10493.1i	−0.198979	+	0.820205i	−0.980531	+	0.196364i	$0.937087\pi$
$548$	−86.5404	+	189.497i	−0.00674602	+	0.0147717i
$549$	−5589.04	−	4721.08i	−0.434489	−	0.367014i
$550$	3386.10	+	5268.87i	0.262516	+	0.408483i
$551$	9751.76	−	16890.5i	0.753972	−	1.30592i
$552$	−237.935	−	202.948i	−0.0183463	−	0.0156486i
$553$	4010.21	+	6945.90i	0.308376	+	0.534122i
$554$	−5420.01	+	10513.3i	−0.415657	+	0.806262i
$555$	6252.63	−	13922.6i	0.478215	−	1.06483i
$556$	−2498.48	−	3508.63i	−0.190574	−	0.267624i
$557$	20806.3	−	6109.29i	1.58275	−	0.464737i	0.632070	−	0.774911i	$-0.282205\pi$
$557$	20806.3	−	6109.29i	1.58275	−	0.464737i	0.950680	+	0.310174i	$0.100387\pi$
$558$	−11929.6	−	28744.6i	−0.905052	−	2.18075i
$559$	−15451.3	+	13388.7i	−1.16909	+	1.01302i
$560$	−6785.63	+	16949.7i	−0.512045	+	1.27903i
$561$	11570.4	+	478.198i	0.870768	+	0.0359885i
$562$	1546.49	−	8023.94i	0.116076	−	0.602259i
$563$	33.6855	−	707.145i	0.00252162	−	0.0529354i	−0.997256	−	0.0740329i	$-0.976413\pi$
$563$	33.6855	−	707.145i	0.00252162	−	0.0529354i	0.999777	+	0.0210975i	$0.00671605\pi$
$564$	15985.8	−	3185.49i	1.19348	−	0.237825i
$565$	1839.62	+	5315.24i	0.136980	+	0.395776i
$566$	−6846.82	−	2010.41i	−0.508468	−	0.149300i
$567$	6376.11	−	13171.8i	0.472260	−	0.975600i
$568$	−217.517	−	251.028i	−0.0160683	−	0.0185438i
$569$	−8549.97	−	816.423i	−0.629936	−	0.0601516i	−0.224795	−	0.974406i	$-0.572171\pi$
$569$	−8549.97	−	816.423i	−0.629936	−	0.0601516i	−0.405140	+	0.914254i	$0.632777\pi$
$570$	−20483.0	−	11654.6i	−1.50516	−	0.856417i
$571$	354.181	+	3709.15i	0.0259580	+	0.271844i	0.999128	+	0.0417564i	$0.0132953\pi$
$571$	354.181	+	3709.15i	0.0259580	+	0.271844i	−0.973170	+	0.230088i	$0.926099\pi$
$572$	−6833.12	+	2735.57i	−0.499488	+	0.199965i
$573$	16997.2	−	18052.3i	1.23921	−	1.31614i
$574$	18729.8	+	10813.7i	1.36196	+	0.786329i
$575$	9181.81	−	1334.18i	0.665927	−	0.0967635i
$576$	−500.202	+	14280.6i	−0.0361836	+	1.03303i
$577$	−13988.5	+	8989.86i	−1.00927	+	0.648619i	−0.937204	−	0.348781i	$-0.886596\pi$
$577$	−13988.5	+	8989.86i	−1.00927	+	0.648619i	−0.0720660	+	0.997400i	$0.522959\pi$
$578$	23694.6	−	30130.2i	1.70513	−	2.16825i
$579$	11725.2	+	10031.5i	0.841595	+	0.720022i
$580$	−20280.5	+	21269.6i	−1.45190	+	1.52271i
$581$	−3422.18	−	2436.92i	−0.244365	−	0.174011i
$582$	1467.45	−	681.357i	0.104515	−	0.0485277i
$583$	7494.08	+	3000.18i	0.532372	+	0.213130i
$584$	−68.6735	+	233.880i	−0.00486597	+	0.0165720i
$585$	−18215.1	+	5598.42i	−1.28735	+	0.395669i
$586$	−7478.41	+	11636.6i	−0.527184	+	0.820315i
$587$	−2686.92	−	5211.89i	−0.188928	−	0.366470i	0.775279	−	0.631619i	$-0.217609\pi$
$587$	−2686.92	−	5211.89i	−0.188928	−	0.366470i	−0.964207	+	0.265149i	$0.914579\pi$
$588$	1147.40	−	2260.47i	0.0804728	−	0.158538i
$589$	−21772.8	+	5282.02i	−1.52315	+	0.369511i
$590$	−32871.5	+	25850.4i	−2.29372	+	1.80380i
$591$	1579.15	+	140.767i	0.109911	+	0.00979760i
$592$	−1214.33	+	12717.0i	−0.0843051	+	0.882883i
$593$	5595.34	+	19056.0i	0.387476	+	1.31962i	0.890356	+	0.455266i	$0.150456\pi$
$593$	5595.34	+	19056.0i	0.387476	+	1.31962i	−0.502880	+	0.864356i	$0.667726\pi$
$594$	7695.10	+	7064.75i	0.531539	+	0.487997i
$595$	34545.9	+	4966.95i	2.38024	+	0.342227i
$596$	−135.170	−	2837.56i	−0.00928988	−	0.195019i
$597$	2299.45	−	2220.32i	0.157638	−	0.152214i
$598$	−996.638	+	21602.4i	−0.0681531	+	1.47723i
$599$	2894.85	−	1671.35i	0.197463	−	0.114006i	−0.398008	−	0.917382i	$-0.630299\pi$
$599$	2894.85	−	1671.35i	0.197463	−	0.114006i	0.595472	+	0.803376i	$0.296965\pi$
$600$	173.629	+	163.481i	0.0118139	+	0.0111235i
$601$	−5684.47	−	4470.32i	−0.385814	−	0.303408i	0.406348	−	0.913718i	$-0.366802\pi$
$601$	−5684.47	−	4470.32i	−0.385814	−	0.303408i	−0.792162	+	0.610311i	$0.791045\pi$
$602$	30726.1	+	14032.1i	2.08024	+	0.950013i
$603$	−1728.17	−	1767.37i	−0.116711	−	0.119358i
$604$	−5681.40	−	12440.5i	−0.382736	−	0.838076i
$605$	14020.7	−	2702.27i	0.942185	−	0.181591i
$606$	−25670.8	−	3526.14i	−1.72080	−	0.236369i
$607$	4334.29	+	17866.2i	0.289825	+	1.19467i	0.911467	+	0.411372i	$0.134950\pi$
$607$	4334.29	+	17866.2i	0.289825	+	1.19467i	−0.621643	+	0.783301i	$0.713534\pi$
$608$	19704.1	+	3797.66i	1.31432	+	0.253315i
$609$	−19583.8	+	17186.4i	−1.30308	+	1.14356i
$610$	13990.3	−	7212.52i	0.928610	−	0.478732i
$611$	−14222.0	−	12323.4i	−0.941670	−	0.815961i
$612$	25868.4	−	5324.29i	1.70861	−	0.351669i
$613$	22104.7	−	3178.17i	1.45644	−	0.209405i	0.631832	−	0.775106i	$-0.282303\pi$
$613$	22104.7	−	3178.17i	1.45644	−	0.209405i	0.824610	+	0.565701i	$0.191394\pi$
$614$	2344.77	+	12165.8i	0.154116	+	0.799628i
$615$	−15762.9	+	12557.4i	−1.03353	+	0.823358i
$616$	146.937	+	140.104i	0.00961082	+	0.00916390i
$617$	28470.2	−	2718.57i	1.85764	−	0.177384i	0.894626	−	0.446817i	$-0.147442\pi$
$617$	28470.2	−	2718.57i	1.85764	−	0.177384i	0.963019	+	0.269433i	$0.0868363\pi$
$618$	−19318.3	+	13940.6i	−1.25744	+	0.907399i
$619$	−13887.2	+	661.528i	−0.901733	+	0.0429548i	−0.493326	−	0.869845i	$-0.664219\pi$
$619$	−13887.2	+	661.528i	−0.901733	+	0.0429548i	−0.408408	+	0.912800i	$0.633916\pi$
$620$	33759.8			2.18682
$621$	14246.5	−	6043.12i	0.920602	−	0.390503i
$622$	16528.9			1.06551
$623$	−19267.3	+	917.815i	−1.23905	+	0.0590233i
$624$	12934.4	−	9333.76i	0.829790	−	0.598797i
$625$	18977.7	−	1812.15i	1.21457	−	0.115978i
$626$	−5007.67	−	4774.80i	−0.319723	−	0.304855i
$627$	5881.91	−	4685.80i	0.374643	−	0.298457i
$628$	−885.548	−	4594.66i	−0.0562694	−	0.291954i
$629$	24172.0	−	3475.41i	1.53227	−	0.220308i
$630$	20915.3	+	23532.4i	1.32267	+	1.48818i
$631$	14585.1	+	12638.1i	0.920165	+	0.797328i	0.979611	−	0.200904i	$-0.0643878\pi$
$631$	14585.1	+	12638.1i	0.920165	+	0.797328i	−0.0594456	+	0.998232i	$0.518933\pi$
$632$	−193.768	+	99.8946i	−0.0121957	+	0.00628733i
$633$	35.8305	−	31.4443i	0.00224982	−	0.00197441i
$634$	−29210.3	−	5629.82i	−1.82979	−	0.352664i
$635$	3003.11	+	12379.0i	0.187677	+	0.773614i
$636$	18239.0	+	2505.31i	1.13714	+	0.156198i
$637$	−2873.76	+	553.871i	−0.178748	+	0.0344508i
$638$	−7726.55	−	16918.8i	−0.479462	−	1.04988i
$639$	15923.2	−	4075.82i	0.985777	−	0.252327i
$640$	−918.551	−	419.488i	−0.0567327	−	0.0259089i
$641$	−20376.6	−	16024.3i	−1.25558	−	0.987399i	−0.999786	−	0.0206678i	$-0.993421\pi$
$641$	−20376.6	−	16024.3i	−1.25558	−	0.987399i	−0.255794	−	0.966731i	$-0.582337\pi$
$642$	16768.8	+	15788.8i	1.03086	+	0.970612i
$643$	3315.01	−	1913.92i	0.203314	−	0.117384i	−0.394886	−	0.918730i	$-0.629216\pi$
$643$	3315.01	−	1913.92i	0.203314	−	0.117384i	0.598201	+	0.801346i	$0.295883\pi$
$644$	16714.2	−	6720.42i	1.02272	−	0.411214i
$645$	−22643.5	+	21864.3i	−1.38231	+	1.33474i
$646$	−1794.23	−	37665.5i	−0.109277	−	2.29401i
$647$	−5525.54	−	794.452i	−0.335752	−	0.0482738i	−0.0276227	−	0.999618i	$-0.508794\pi$
$647$	−5525.54	−	794.452i	−0.335752	−	0.0482738i	−0.308129	+	0.951345i	$0.599703\pi$
$648$	349.371	+	190.148i	0.0211799	+	0.0115273i
$649$	−3759.56	−	12803.9i	−0.227390	−	0.774418i
$650$	1567.56	−	16416.2i	0.0945920	−	0.990612i
$651$	29812.8	+	2657.54i	1.79486	+	0.159996i
$652$	21788.6	−	17134.7i	1.30875	−	1.02921i
$653$	−23429.6	+	5683.95i	−1.40409	+	0.340628i	−0.865064	−	0.501661i	$-0.832722\pi$
$653$	−23429.6	+	5683.95i	−1.40409	+	0.340628i	−0.539025	+	0.842290i	$0.681207\pi$
$654$	−7945.72	+	15653.7i	−0.475080	+	0.935943i
$655$	5533.44	+	10733.4i	0.330091	+	0.640286i
$656$	9120.05	−	14191.1i	0.542802	−	0.844617i
$657$	−8833.74	−	8213.17i	−0.524562	−	0.487711i
$658$	−8759.37	+	29831.7i	−0.518960	+	1.76742i
$659$	27890.3	+	11165.6i	1.64864	+	0.660015i	0.995281	−	0.0970361i	$-0.0309362\pi$
$659$	27890.3	+	11165.6i	1.64864	+	0.660015i	0.653356	+	0.757051i	$0.273360\pi$
$660$	−10277.9	+	4772.17i	−0.606163	+	0.281449i
$661$	15648.1	+	11142.9i	0.920786	+	0.655689i	0.938916	−	0.344147i	$-0.111832\pi$
$661$	15648.1	+	11142.9i	0.920786	+	0.655689i	−0.0181300	+	0.999836i	$0.505771\pi$
$662$	10920.8	−	11453.4i	0.641161	−	0.672431i
$663$	−23168.8	−	19821.9i	−1.35716	−	1.16112i
$664$	70.5887	−	89.7609i	0.00412556	−	0.00524608i
$665$	19066.9	−	12253.5i	1.11185	−	0.714544i
$666$	18680.7	+	11675.7i	1.08688	+	0.679317i
$667$	−27553.5	+	41.2472i	−1.59952	+	0.00239445i
$668$	−20199.2	−	11662.0i	−1.16996	−	0.675476i
$669$	1736.65	−	1844.45i	0.100363	−	0.106593i
$670$	4937.09	−	1976.51i	0.284681	−	0.113969i
$671$	477.441	+	4999.99i	0.0274685	+	0.287664i
$672$	−23300.4	−	13257.7i	−1.33755	−	0.761049i
$673$	15818.9	+	1510.52i	0.906051	+	0.0865174i	0.537668	−	0.843157i	$-0.319305\pi$
$673$	15818.9	+	1510.52i	0.906051	+	0.0865174i	0.368383	+	0.929674i	$0.379912\pi$
$674$	−15092.0	−	17417.1i	−0.862497	−	0.995374i
$675$	−11077.1	+	4069.60i	−0.631641	+	0.232058i
$676$	1444.56	+	424.160i	0.0821892	+	0.0241329i
$677$	−5444.53	−	15730.9i	−0.309085	−	0.893041i	−0.987396	−	0.158267i	$-0.949409\pi$
$677$	−5444.53	−	15730.9i	−0.309085	−	0.893041i	0.678312	−	0.734774i	$-0.262712\pi$
$678$	−7961.95	+	1586.58i	−0.450998	+	0.0898703i
$679$	−74.0379	+	1554.25i	−0.00418456	+	0.0878447i
$680$	−179.532	+	931.502i	−0.0101246	+	0.0525316i
$681$	−13942.6	−	576.244i	−0.784557	−	0.0324254i
$682$	−7940.93	+	19835.5i	−0.445856	+	1.11370i
$683$	−406.136	+	351.919i	−0.0227531	+	0.0197157i	−0.666163	−	0.745806i	$-0.732065\pi$
$683$	−406.136	+	351.919i	−0.0227531	+	0.0197157i	0.643410	+	0.765522i	$0.277519\pi$
$684$	10431.6	−	13614.1i	0.583131	−	0.761034i
$685$	355.279	−	104.319i	0.0198168	−	0.00581873i
$686$	−13238.6	−	18590.9i	−0.736808	−	1.03470i
$687$	1123.01	−	2500.58i	0.0623662	−	0.138869i
$688$	12072.8	−	23418.0i	0.669000	−	1.29768i
$689$	−10627.3	−	18407.0i	−0.587615	−	1.01778i
$690$	259.381	+	33292.7i	0.0143108	+	1.83686i
$691$	1614.69	−	2796.73i	0.0888939	−	0.153969i	−0.818150	−	0.575005i	$-0.805000\pi$
$691$	1614.69	−	2796.73i	0.0888939	−	0.153969i	0.907044	+	0.421036i	$0.138333\pi$
$692$	19522.5	+	30377.6i	1.07245	+	1.66876i
$693$	−9451.92	+	3405.16i	−0.518108	+	0.186654i
$694$	−1624.41	+	3556.96i	−0.0888497	+	0.194554i
$695$	−1804.95	+	7440.10i	−0.0985116	+	0.406070i
$696$	−441.285	−	553.929i	−0.0240329	−	0.0301676i
$697$	−30473.3	−	10546.9i	−1.65604	−	0.573160i
$698$	2893.08	+	3678.85i	0.156884	+	0.199494i
$699$	6376.72	−	3338.39i	0.345049	−	0.180643i
$700$	−12982.0	+	4493.11i	−0.700961	+	0.242605i
$701$	−16556.3	−	10640.1i	−0.892042	−	0.573281i	0.0123782	−	0.999923i	$-0.496060\pi$
$701$	−16556.3	−	10640.1i	−0.892042	−	0.573281i	−0.904420	+	0.426643i	$0.859696\pi$
$702$	−4427.74	−	27146.6i	−0.238055	−	1.45952i
$703$	10385.2	−	11985.2i	0.557165	−	0.643003i
$704$	7099.87	−	6769.71i	0.380094	−	0.362419i
$705$	−22886.0	−	17765.7i	−1.22260	−	0.949073i
$706$	2907.87	−	8401.73i	0.155013	−	0.447880i
$707$	14455.2	−	20299.5i	0.768945	−	1.07983i
$708$	−15382.7	−	26260.6i	−0.816551	−	1.39397i
$709$	11417.6	−	8130.41i	0.604789	−	0.430669i	−0.236212	−	0.971702i	$-0.575906\pi$
$709$	11417.6	−	8130.41i	0.604789	−	0.430669i	0.841001	+	0.541033i	$0.181967\pi$
$710$	−5032.52	+	35001.9i	−0.266010	+	1.85014i
$711$	−135.787	−	10786.8i	−0.00716234	−	0.568970i
$712$		−	524.297i		−	0.0275967i
$713$	21876.5	+	22874.7i	1.14906	+	1.20149i
$714$	−13888.1	+	48423.9i	−0.727940	+	2.53812i
$715$	11628.2	+	5994.73i	0.608208	+	0.313553i
$716$	−8727.89	−	21801.2i	−0.455554	−	1.13792i
$717$	3258.96	−	3809.22i	0.169746	−	0.198407i
$718$	30659.2	+	7437.85i	1.59358	+	0.386599i
$719$	−27924.1	+	12752.5i	−1.44839	+	0.661458i	−0.975567	−	0.219700i	$-0.929492\pi$
$719$	−27924.1	+	12752.5i	−1.44839	+	0.661458i	−0.472823	+	0.881158i	$0.656765\pi$
$720$	19110.3	−	15421.8i	0.989167	−	0.798244i
$721$	−3260.64	−	22678.3i	−0.168423	−	1.17140i
$722$	2114.72	+	2217.86i	0.109005	+	0.114321i
$723$	6615.61	+	3358.05i	0.340300	+	0.172735i
$724$	−22890.1	−	1090.39i	−1.17501	−	0.0559724i
$725$	20987.8	+	999.774i	1.07513	+	0.0512147i
$726$	1110.20	+	20579.9i	0.0567541	+	1.05205i
$727$	10181.1	+	10677.6i	0.519390	+	0.544720i	0.930225	−	0.366989i	$-0.119611\pi$
$727$	10181.1	+	10677.6i	0.519390	+	0.544720i	−0.410835	+	0.911710i	$0.634763\pi$
$728$	−76.0776	−	529.131i	−0.00387311	−	0.0269381i
$729$	−16144.8	+	11259.0i	−0.820243	+	0.572016i
$730$	23605.2	−	10780.2i	1.19681	−	0.546564i
$731$	−48945.1	−	11873.9i	−2.47647	−	0.600785i
$732$	3814.68	+	10801.4i	0.192616	+	0.545396i
$733$	8561.14	+	21384.7i	0.431395	+	1.07757i	0.971724	+	0.236120i	$0.0758757\pi$
$733$	8561.14	+	21384.7i	0.431395	+	1.07757i	−0.540329	+	0.841454i	$0.681700\pi$
$734$	2162.74	+	1114.97i	0.108758	+	0.0560686i
$735$	−4371.99	+	1089.81i	−0.219406	+	0.0546917i
$736$	−9312.24	−	26776.2i	−0.466377	−	1.34101i
$737$			1697.01i			0.0848169i
$738$	−14860.6	−	25007.0i	−0.741227	−	1.24732i
$739$	−3165.37	+	22015.6i	−0.157564	+	1.09588i	0.745540	+	0.666461i	$0.232192\pi$
$739$	−3165.37	+	22015.6i	−0.157564	+	1.09588i	−0.903104	+	0.429422i	$0.858717\pi$
$740$	−19465.6	+	13861.4i	−0.966985	+	0.688587i
$741$	−19800.5	+	124.622i	−0.981631	+	0.00617826i
$742$	−20369.3	+	28604.7i	−1.00779	+	1.41524i
$743$	3226.14	−	9321.32i	0.159294	−	0.460250i	−0.836906	−	0.547347i	$-0.815638\pi$
$743$	3226.14	−	9321.32i	0.159294	−	0.460250i	0.996200	+	0.0870968i	$0.0277589\pi$
$744$	−110.710	+	805.983i	−0.00545541	+	0.0397161i
$745$	−3654.33	+	3484.39i	−0.179710	+	0.171353i
$746$	25456.9	−	29378.9i	1.24939	−	1.44187i
$747$	2411.89	+	5110.09i	0.118135	+	0.250293i
$748$	−15253.3	−	9802.71i	−0.745610	−	0.479175i
$749$	−20932.6	+	7244.83i	−1.02117	+	0.353432i
$750$	−509.594	+	12330.0i	−0.0248103	+	0.600304i
$751$	13534.0	+	17209.9i	0.657606	+	0.836215i	0.994435	−	0.105351i	$-0.0335967\pi$
$751$	13534.0	+	17209.9i	0.657606	+	0.836215i	−0.336829	+	0.941566i	$0.609354\pi$
$752$	22916.8	+	7931.59i	1.11129	+	0.384622i
$753$	−4992.34	+	12701.4i	−0.241608	+	0.614693i
$754$	−11545.8	+	47592.6i	−0.557659	+	2.29870i
$755$	−10098.2	+	22112.1i	−0.486772	+	1.06588i
$756$	−19038.3	+	12749.4i	−0.915894	+	0.613348i
$757$	−1916.42	−	2982.01i	−0.0920125	−	0.143174i	0.792196	−	0.610267i	$-0.208938\pi$
$757$	−1916.42	−	2982.01i	−0.0920125	−	0.143174i	−0.884208	+	0.467093i	$0.845301\pi$
$758$	−1108.88	+	1920.64i	−0.0531352	+	0.0920328i
$759$	−9893.60	−	3871.65i	−0.473142	−	0.185154i
$760$	308.026	+	533.516i	0.0147017	+	0.0254640i
$761$	569.888	−	1105.43i	0.0271464	−	0.0526567i	−0.874872	−	0.484354i	$-0.839055\pi$
$761$	569.888	−	1105.43i	0.0271464	−	0.0526567i	0.902019	+	0.431697i	$0.142085\pi$
$762$	−18291.4	+	1862.86i	−0.869590	+	0.0885621i
$763$	−9793.16	−	13752.6i	−0.464661	−	0.652525i
$764$	−37250.0	+	10937.6i	−1.76395	+	0.517942i
$765$	−37262.0	−	28551.4i	−1.76106	−	1.34938i
$766$	12625.0	−	10939.6i	0.595509	−	0.516012i
$767$	−13058.8	+	32619.3i	−0.614766	+	1.53561i
$768$	−10997.1	+	17350.9i	−0.516696	+	0.815231i
$769$	−4667.84	+	24219.1i	−0.218890	+	1.13571i	0.691632	+	0.722250i	$0.256892\pi$
$769$	−4667.84	+	24219.1i	−0.218890	+	1.13571i	−0.910522	+	0.413461i	$0.864320\pi$
$770$	1028.45	−	21589.9i	0.0481337	−	1.01045i
$771$	−14431.8	−	16444.9i	−0.674123	−	0.768157i
$772$	−7902.19	−	22831.9i	−0.368402	−	1.06443i
$773$	−2961.74	−	869.644i	−0.137809	−	0.0404643i	0.212101	−	0.977248i	$-0.431970\pi$
$773$	−2961.74	−	869.644i	−0.137809	−	0.0404643i	−0.349910	+	0.936783i	$0.613788\pi$
$774$	−26817.5	−	36674.1i	−1.24540	−	1.70313i
$775$	−15806.2	−	18241.4i	−0.732615	−	0.845482i
$776$	−42.1023	−	4.02028i	−0.00194766	−	0.000185979i
$777$	−18280.9	+	10708.5i	−0.844046	+	0.494419i
$778$	−5171.66	−	54160.0i	−0.238320	−	2.49580i
$779$	−19441.1	+	7783.03i	−0.894157	+	0.357966i
$780$	29039.4	+	6851.66i	1.33305	+	0.314524i
$781$	−9772.35	−	5642.07i	−0.447737	−	0.258501i
$782$	−44772.3	+	28868.2i	−2.04739	+	1.32011i
$783$	34280.8	−	7280.93i	1.56462	−	0.332310i
$784$	3172.76	−	2039.01i	0.144532	−	0.0928848i
$785$	−5141.19	+	6537.56i	−0.233754	+	0.297243i
$786$	−16435.2	+	5804.38i	−0.745834	+	0.263404i
$787$	16587.2	−	17396.1i	0.751294	−	0.787935i	−0.231461	−	0.972844i	$-0.574351\pi$
$787$	16587.2	−	17396.1i	0.751294	−	0.787935i	0.982756	+	0.184909i	$0.0591991\pi$
$788$	−2022.06	−	1439.90i	−0.0914123	−	0.0650944i
$789$	16942.1	+	11904.5i	0.764457	+	0.537148i
$790$	21546.3	+	8625.84i	0.970358	+	0.388473i
$791$	2199.72	−	7491.57i	0.0988788	−	0.336750i
$792$	−80.2262	−	261.025i	−0.00359939	−	0.0117110i
$793$	7149.94	−	11125.5i	0.320179	−	0.498208i
$794$	−2418.90	−	4692.00i	−0.108115	−	0.209714i
$795$	−17864.2	−	27416.3i	−0.796954	−	1.22309i
$796$	−4863.73	+	1179.93i	−0.216571	+	0.0525395i
$797$	12403.3	−	9754.09i	0.551253	−	0.433510i	−0.303284	−	0.952900i	$-0.598083\pi$
$797$	12403.3	−	9754.09i	0.551253	−	0.433510i	0.854537	+	0.519390i	$0.173841\pi$
$798$	13777.0	+	29671.8i	0.611155	+	1.31626i
$799$	4406.57	−	46147.7i	0.195110	−	2.04329i
$800$	6090.61	+	20742.7i	0.269170	+	0.916708i
$801$	23208.1	+	11597.2i	1.02374	+	0.511569i
$802$	51735.0	+	7438.36i	2.27784	+	0.327503i
$803$	394.020	+	8271.49i	0.0173159	+	0.363505i
$804$	936.115	+	3755.40i	0.0410625	+	0.164730i
$805$	−28482.2	−	14629.7i	−1.24704	−	0.640532i
$806$	48720.0	−	28128.5i	2.12914	−	1.22926i
$807$	3939.00	−	16694.7i	0.171821	−	0.728229i
$808$	532.439	+	418.715i	0.0231821	+	0.0182306i
$809$	15200.1	+	6941.67i	0.660579	+	0.301676i	0.717352	−	0.696711i	$-0.245354\pi$
$809$	15200.1	+	6941.67i	0.660579	+	0.301676i	−0.0567734	+	0.998387i	$0.518081\pi$
$810$	−9058.26	−	41366.2i	−0.392932	−	1.79439i
$811$	−2655.49	−	5814.72i	−0.114978	−	0.251766i	0.843391	−	0.537301i	$-0.180556\pi$
$811$	−2655.49	−	5814.72i	−0.114978	−	0.251766i	−0.958368	+	0.285535i	$0.907829\pi$
$812$	40059.1	−	7720.77i	1.73128	−	0.333677i
$813$	−9348.09	+	12042.3i	−0.403262	+	0.519485i
$814$	−3565.55	−	14697.4i	−0.153529	−	0.632855i
$815$	−48377.9	−	9324.08i	−2.07927	−	0.400746i
$816$	37211.7	+	12617.4i	1.59641	+	0.541296i
$817$	−29071.1	+	14987.2i	−1.24488	+	0.641781i
$818$	4017.15	+	3480.88i	0.171707	+	0.148785i
$819$	25104.9	+	8336.54i	1.07111	+	0.355681i
$820$	31233.8	−	4490.74i	1.33016	−	0.191248i
$821$	5055.70	+	26231.4i	0.214915	+	1.11508i	0.915746	+	0.401757i	$0.131600\pi$
$821$	5055.70	+	26231.4i	0.214915	+	1.11508i	−0.700832	+	0.713327i	$0.747188\pi$
$822$	79.3890	+	528.527i	0.00336863	+	0.0224264i
$823$	−24051.0	−	22932.5i	−1.01867	−	0.971298i	−0.0190745	−	0.999818i	$-0.506072\pi$
$823$	−24051.0	−	22932.5i	−1.01867	−	0.971298i	−0.999593	+	0.0285204i	$0.990920\pi$
$824$	619.935	−	59.1966i	0.0262093	−	0.00250268i
$825$	7390.61	+	3319.12i	0.311889	+	0.140069i
$826$	57985.0	−	2762.17i	2.44256	−	0.116354i
$827$	46850.7			1.96996			0.984980	−	0.172667i	$-0.0552385\pi$
$827$	46850.7			1.96996			0.984980	+	0.172667i	$0.0552385\pi$
$828$	−24029.8	−	3110.19i	−1.00857	−	0.130539i
$829$	−33994.3			−1.42421			−0.712106	−	0.702071i	$-0.752259\pi$
$829$	−33994.3			−1.42421			−0.712106	+	0.702071i	$0.752259\pi$
$830$	−12143.2	+	578.453i	−0.507828	+	0.0241908i
$831$	1550.24	+	15221.8i	0.0647138	+	0.635424i
$832$	−25713.1	+	2455.30i	−1.07144	+	0.102310i
$833$	−5217.80	−	4975.16i	−0.217030	−	0.206938i
$834$	−10284.6	−	4042.40i	−0.427009	−	0.167838i
$835$	7845.74	+	40707.6i	0.325165	+	1.68712i
$836$	−11654.9	+	1675.72i	−0.482167	+	0.0693252i
$837$	−33228.2	−	22728.6i	−1.37220	−	0.938608i
$838$	−13299.3	−	11523.9i	−0.548232	−	0.475046i
$839$	35908.9	−	18512.3i	1.47761	−	0.761759i	0.484044	−	0.875044i	$-0.339168\pi$
$839$	35908.9	−	18512.3i	1.47761	−	0.761759i	0.993563	+	0.113285i	$0.0361373\pi$
$840$	−160.839	−	807.141i	−0.00660651	−	0.0331536i
$841$	−37322.4	−	7193.30i	−1.53030	−	0.294940i
$842$	9484.11	+	39094.0i	0.388176	+	1.60008i
$843$	−3990.33	−	9788.36i	−0.163030	−	0.399916i
$844$	−73.2924	+	14.1259i	−0.00298913	+	0.000576108i
$845$	−1111.64	−	2434.16i	−0.0452565	−	0.0990979i
$846$	29899.7	−	29236.6i	1.21510	−	1.18815i
$847$	−18030.0	−	8234.03i	−0.731426	−	0.334031i
$848$	21530.0	+	16931.4i	0.871867	+	0.685643i
$849$	−8840.22	+	2656.27i	−0.357356	+	0.107377i
$850$	35181.5	−	20312.0i	1.41966	−	0.819643i
$851$	−22005.8	−	4207.12i	−0.886428	−	0.169469i
$852$	−24738.1	−	7094.94i	−0.994733	−	0.285292i
$853$	1504.49	+	31583.2i	0.0603902	+	1.26775i	0.802167	+	0.597100i	$0.203680\pi$
$853$	1504.49	+	31583.2i	0.0603902	+	1.26775i	−0.741777	+	0.670647i	$0.766017\pi$
$854$	−21627.4	−	3109.55i	−0.866597	−	0.124598i
$855$	−30429.6	+	1833.69i	−1.21716	+	0.0733462i
$856$	−169.626	−	577.692i	−0.00677299	−	0.0230667i
$857$	500.270	−	5239.07i	0.0199404	−	0.208825i	−0.980011	−	0.198944i	$-0.936249\pi$
$857$	500.270	−	5239.07i	0.0199404	−	0.208825i	0.999951	−	0.00988087i	$-0.00314523\pi$
$858$	−10856.3	+	15450.4i	−0.431966	+	0.614764i
$859$	−7483.86	+	5885.37i	−0.297260	+	0.233768i	−0.755638	−	0.654990i	$-0.772673\pi$
$859$	−7483.86	+	5885.37i	−0.297260	+	0.233768i	0.458378	+	0.888757i	$0.348431\pi$
$860$	47894.9	−	11619.2i	1.89907	−	0.460710i
$861$	27935.6	−	1507.01i	1.10574	−	0.0596501i
$862$	−14780.0	−	28669.2i	−0.584001	−	1.13280i
$863$	−22757.2	+	35410.9i	−0.897641	+	1.39676i	0.0201940	+	0.999796i	$0.493572\pi$
$863$	−22757.2	+	35410.9i	−0.897641	+	1.39676i	−0.917835	+	0.396961i	$0.870065\pi$
$864$	18615.1	+	30880.8i	0.732985	+	1.21596i
$865$	18082.3	−	61582.8i	0.710772	−	2.42067i
$866$	21939.1	+	8783.10i	0.860880	+	0.344644i
$867$	4402.45	−	49387.5i	0.172451	−	1.93459i
$868$	−38174.4	−	27183.9i	−1.49277	−	1.06300i
$869$	−5110.75	+	5360.00i	−0.199506	+	0.209235i
$870$	−13802.8	+	74123.2i	−0.537884	+	2.88852i
$871$	2762.09	−	3512.28i	0.107451	−	0.136635i
$872$	386.050	−	248.099i	0.0149923	−	0.00963497i
$873$	1109.24	−	1774.74i	0.0430036	−	0.0688039i
$874$	−9696.85	+	33208.3i	−0.375287	+	1.28522i
$875$	−10278.3	−	5934.17i	−0.397108	−	0.229270i
$876$	5434.72	+	18087.1i	0.209615	+	0.697609i
$877$	−3677.74	+	1472.35i	−0.141606	+	0.0566905i	−0.441383	−	0.897319i	$-0.645512\pi$
$877$	−3677.74	+	1472.35i	−0.141606	+	0.0566905i	0.299777	+	0.954009i	$0.403088\pi$
$878$	−2799.21	−	29314.6i	−0.107595	−	1.12679i
$879$	112.615	+	17892.8i	0.00432128	+	0.686585i
$880$	−16782.6	−	1602.54i	−0.642887	−	0.0613882i
$881$	5198.97	+	5999.93i	0.198817	+	0.229447i	0.846400	−	0.532548i	$-0.178765\pi$
$881$	5198.97	+	5999.93i	0.198817	+	0.229447i	−0.647583	+	0.761995i	$0.724220\pi$
$882$	−699.650	−	6465.86i	−0.0267102	−	0.246844i
$883$	−41541.8	−	12197.8i	−1.58323	−	0.464879i	−0.632414	−	0.774631i	$-0.717936\pi$
$883$	−41541.8	−	12197.8i	−1.58323	−	0.464879i	−0.950817	+	0.309752i	$0.899754\pi$
$884$	15614.5	+	45115.3i	0.594088	+	1.71651i
$885$	−17370.5	+	51229.7i	−0.659778	+	1.94584i
$886$	−290.571	+	6099.83i	−0.0110180	+	0.231295i
$887$	1242.88	−	6448.68i	0.0470483	−	0.244110i	−0.950789	−	0.309838i	$-0.899725\pi$
$887$	1242.88	−	6448.68i	0.0470483	−	0.244110i	0.997838	+	0.0657286i	$0.0209372\pi$
$888$	−267.093	−	510.178i	−0.0100935	−	0.0192798i
$889$	6571.92	−	16415.9i	0.247936	−	0.619314i
$890$	−42183.8	+	36552.5i	−1.58877	+	1.37668i
$891$	13328.9	+	2222.52i	0.501161	+	0.0835658i
$892$	−3805.92	+	1117.52i	−0.142860	+	0.0419476i
$893$	−17462.4	−	24522.5i	−0.654375	−	0.918942i
$894$	−4264.78	−	5909.97i	−0.159548	−	0.221095i
$895$	−19126.3	+	37099.9i	−0.714327	+	1.38560i
$896$	700.887	+	1213.97i	0.0261328	+	0.0452634i
$897$	14175.1	+	24116.2i	0.527641	+	0.897677i
$898$	−18117.9	+	31381.1i	−0.673277	+	1.16615i
$899$	38752.6	+	60300.2i	1.43768	+	2.23707i
$900$	18186.0	+	3268.21i	0.673556	+	0.121045i
$901$	21750.7	−	47627.3i	0.804240	−	1.76104i
$902$	−4708.24	+	19407.6i	−0.173800	+	0.716412i
$903$	43209.9	−	6490.48i	1.59240	−	0.239191i
$904$	200.552	+	69.4118i	0.00737861	+	0.00255376i
$905$	25178.6	+	32017.1i	0.924822	+	1.17601i
$906$	−29636.0	−	18783.4i	−1.08675	−	0.688783i
$907$	30499.2	−	10555.9i	1.11655	−	0.386441i	0.294381	−	0.955688i	$-0.404887\pi$
$907$	30499.2	−	10555.9i	1.11655	−	0.386441i	0.822166	+	0.569248i	$0.192765\pi$
$908$	18380.7	+	11812.6i	0.671791	+	0.431734i
$909$	−30311.8	+	14306.7i	−1.10603	+	0.522030i
$910$	−37268.9	+	43010.6i	−1.35764	+	1.56680i
$911$	32839.3	−	31312.2i	1.19431	−	1.13877i	0.207270	−	0.978284i	$-0.433542\pi$
$911$	32839.3	−	31312.2i	1.19431	−	1.13877i	0.987038	−	0.160486i	$-0.0513063\pi$
$912$	23628.7	−	9632.49i	0.857921	−	0.349741i
$913$	1268.81	−	3665.99i	0.0459929	−	0.132888i
$914$	8095.24	−	11368.2i	0.292962	−	0.411407i
$915$	10069.2	−	17696.6i	0.363800	−	0.639379i
$916$	−3496.14	+	2489.59i	−0.126109	+	0.0898018i
$917$	2385.64	−	16592.5i	0.0859116	−	0.597528i
$918$	48146.6	−	47675.3i	1.73102	−	1.71407i
$919$		−	16083.2i		−	0.577296i	−0.957435	−	0.288648i	$-0.906794\pi$
$919$		−	16083.2i		−	0.577296i	0.957435	−	0.288648i	$-0.0932058\pi$
$920$	434.034	−	754.375i	0.0155540	−	0.0270337i
$921$	11132.5	+	11529.3i	0.398295	+	0.412490i
$922$	−9045.48	−	4663.27i	−0.323099	−	0.166569i
$923$	11042.6	+	27583.1i	0.393794	+	0.983649i
$924$	15464.5	+	2879.72i	0.550590	+	0.102528i
$925$	16603.4	+	4027.94i	0.590180	+	0.143176i
$926$	69921.3	−	31932.0i	2.48138	−	1.13321i
$927$	−11092.3	+	28751.0i	−0.393009	+	1.01867i
$928$	−9136.65	−	63546.8i	−0.323195	−	2.24787i
$929$	4381.46	+	4595.15i	0.154738	+	0.162284i	0.796540	−	0.604586i	$-0.206661\pi$
$929$	4381.46	+	4595.15i	0.154738	+	0.162284i	−0.641802	+	0.766870i	$0.721813\pi$
$930$	72566.1	−	47283.4i	2.55864	−	1.66719i
$931$	−4676.59	−	222.773i	−0.164628	−	0.00784221i
$932$	−11257.0	−	536.238i	−0.395640	−	0.0188466i
$933$	17913.8	−	11672.5i	0.628587	−	0.409582i
$934$	13364.3	+	14016.1i	0.468195	+	0.491028i
$935$	4586.47	+	31899.6i	0.160421	+	1.11575i
$936$	−258.807	+	670.819i	−0.00903779	+	0.0234257i
$937$	1809.64	−	826.434i	0.0630931	−	0.0288137i	−0.383619	−	0.923492i	$-0.625322\pi$
$937$	1809.64	−	826.434i	0.0630931	−	0.0288137i	0.446712	+	0.894678i	$0.352595\pi$
$938$	−7174.20	−	1740.44i	−0.249729	−	0.0605836i
$939$	−8799.15	−	1638.53i	−0.305803	−	0.0569450i
$940$	16859.7	+	42113.5i	0.585003	+	1.46127i
$941$	−9475.43	−	4884.92i	−0.328257	−	0.169228i	0.286218	−	0.958165i	$-0.407602\pi$
$941$	−9475.43	−	4884.92i	−0.328257	−	0.169228i	−0.614475	+	0.788936i	$0.710632\pi$
$942$	−8338.66	−	8635.85i	−0.288416	−	0.298696i
$943$	23282.4	+	18253.1i	0.804007	+	0.630332i
$944$		−	45278.7i		−	1.56112i
$945$	39286.0	+	10734.0i	1.35235	+	0.369500i
$946$	−4438.95	+	30873.6i	−0.152561	+	1.06109i
$947$	6901.17	−	4914.30i	0.236809	−	0.168631i	−0.455492	−	0.890240i	$-0.650537\pi$
$947$	6901.17	−	4914.30i	0.236809	−	0.168631i	0.692301	+	0.721609i	$0.256597\pi$
$948$	−8353.13	+	14680.7i	−0.286178	+	0.502959i
$949$	12647.4	−	17760.8i	0.432615	−	0.607522i
$950$	8628.47	−	24930.3i	0.294678	−	0.851418i
$951$	−35633.4	+	14526.4i	−1.21503	+	0.495320i
$952$	953.068	−	908.748i	0.0324465	−	0.0309377i
$953$	−27663.0	+	31924.8i	−0.940285	+	1.08515i	0.0559481	+	0.998434i	$0.482182\pi$
$953$	−27663.0	+	31924.8i	−0.940285	+	1.08515i	−0.996233	+	0.0867133i	$0.972364\pi$
$954$	42713.3	−	20160.1i	1.44958	−	0.684180i
$955$	58050.0	+	37306.4i	1.96697	+	1.26409i
$956$	−7417.48	+	2567.22i	−0.250940	+	0.0868511i
$957$	−20321.7	−	12880.0i	−0.686425	−	0.435059i
$958$	3661.70	+	4656.24i	0.123491	+	0.157031i
$959$	−485.736	−	168.115i	−0.0163558	−	0.00566080i
$960$	−39326.0	+	5907.08i	−1.32212	+	0.198594i
$961$	12388.9	−	51067.8i	0.415861	−	1.71420i
$962$	−16542.3	+	36222.5i	−0.554411	+	1.21399i
$963$	29323.7	+	5269.76i	0.981248	+	0.176340i
$964$	−6280.28	−	9772.31i	−0.209828	−	0.326499i
$965$	−21471.9	+	37190.4i	−0.716274	+	1.24062i
$966$	26514.4	−	37855.1i	0.883114	−	1.26083i
$967$	−642.010	−	1111.99i	−0.0213502	−	0.0369797i	0.855153	−	0.518376i	$-0.173463\pi$
$967$	−642.010	−	1111.99i	−0.0213502	−	0.0369797i	−0.876503	+	0.481396i	$0.840130\pi$
$968$	246.873	−	478.868i	0.00819712	−	0.0159002i
$969$	−28543.4	−	39554.4i	−0.946282	−	1.31132i
$970$	2611.79	+	3667.74i	0.0864530	+	0.121406i
$971$	28741.7	−	8439.33i	0.949913	−	0.278920i	0.230162	−	0.973152i	$-0.426074\pi$
$971$	28741.7	−	8439.33i	0.949913	−	0.278920i	0.719751	+	0.694233i	$0.244256\pi$
$972$	30722.2	−	2434.24i	1.01380	−	0.0803276i
$973$	8031.84	−	6959.63i	0.264634	−	0.229307i
$974$	−12018.1	+	30019.7i	−0.395363	+	0.987570i
$975$	−9894.01	−	18898.7i	−0.324987	−	0.620762i
$976$	−3225.32	+	16734.5i	−0.105779	+	0.548831i
$977$	2429.40	−	50999.3i	0.0795530	−	1.67002i	−0.508395	−	0.861124i	$-0.669761\pi$
$977$	2429.40	−	50999.3i	0.0795530	−	1.67002i	0.587948	−	0.808899i	$-0.299936\pi$
$978$	22835.5	−	67347.4i	0.746626	−	2.20198i
$979$	−5825.58	−	16831.9i	−0.190180	−	0.549490i
$980$	6769.10	+	1987.59i	0.220644	+	0.0647869i
$981$	2442.92	+	22576.4i	0.0795071	+	0.734770i
$982$	−32946.0	−	38021.7i	−1.07062	−	1.23556i
$983$	14453.2	+	1380.11i	0.468957	+	0.0447799i	0.326860	−	0.945073i	$-0.394009\pi$
$983$	14453.2	+	1380.11i	0.468957	+	0.0447799i	0.142097	+	0.989853i	$0.454616\pi$
$984$	4.78589	+	760.403i	0.000155049	+	0.0246349i
$985$	419.404	+	4392.20i	0.0135668	+	0.142078i
$986$	−111999.	+	44837.8i	−3.61743	+	1.44820i
$987$	11573.4	+	38517.0i	0.373238	+	1.24216i
$988$	26849.4	+	15501.5i	0.864568	+	0.499159i
$989$	38908.9	+	24923.0i	1.25099	+	0.801320i
$990$	−15408.4	+	24652.7i	−0.494657	+	0.791430i
$991$	−42200.5	+	27120.6i	−1.35272	+	0.869339i	−0.997848	−	0.0655771i	$-0.979111\pi$
$991$	−42200.5	+	27120.6i	−1.35272	+	0.869339i	−0.354870	+	0.934916i	$0.615475\pi$
$992$	−45588.6	+	57970.6i	−1.45911	+	1.85541i
$993$	3747.60	−	20125.2i	0.119765	−	0.643155i
$994$	33874.7	−	35526.7i	1.08092	−	1.13364i
$995$	7246.19	+	5159.99i	0.230874	+	0.164405i
$996$	785.562	−	8812.58i	0.0249914	−	0.280359i
$997$	16368.9	+	6553.11i	0.519967	+	0.208164i	0.616775	−	0.787140i	$-0.288439\pi$
$997$	16368.9	+	6553.11i	0.519967	+	0.208164i	−0.0968076	+	0.995303i	$0.530863\pi$
$998$	15938.4	−	54281.2i	0.505532	−	1.72168i
$999$	28491.1	−	538.016i	0.902322	−	0.0170391i

Display

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a_n

instead) (See

a_n

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a_n

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a_p

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.o.a.11.12	✓	1400
9.5	odd	6	inner	207.4.o.a.149.12	yes	1400
23.21	odd	22	inner	207.4.o.a.182.12	yes	1400
207.113	even	66	inner	207.4.o.a.113.12	yes	1400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.4.o.a.11.12	✓	1400	1.1	even	1	trivial
207.4.o.a.113.12	yes	1400	207.113	even	66	inner
207.4.o.a.149.12	yes	1400	9.5	odd	6	inner
207.4.o.a.182.12	yes	1400	23.21	odd	22	inner

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	207.4.o.a.11.12

Level	$207$
Weight	$4$
Character	207.11
Analytic conductor	$12.213$
Analytic rank	$0$
Dimension	$1400$
Inner twists	$4$