LMFDB - Embedded newform 207.4.o.a.11.5

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			11.5
Character	$\chi$	$=$	207.11
Dual form			207.4.o.a.113.5

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.14636 + 0.245151i) q^{2} +(1.36351 + 5.01406i) q^{3} +(18.4611 - 1.76282i) q^{4} +(8.59308 + 8.19348i) q^{5} +(-8.24632 - 25.4699i) q^{6} +(3.74898 + 19.4516i) q^{7} +(-53.7774 + 7.73203i) q^{8} +(-23.2817 + 13.6735i) q^{9} +(-46.2317 - 40.0600i) q^{10} +(-39.1715 + 20.1943i) q^{11} +(34.0109 + 90.1617i) q^{12} +(47.8434 + 9.22107i) q^{13} +(-24.0622 - 99.1856i) q^{14} +(-29.3659 + 54.2582i) q^{15} +(129.183 - 24.8979i) q^{16} +(10.0188 + 21.9382i) q^{17} +(116.464 - 76.0761i) q^{18} +(63.6606 + 29.0728i) q^{19} +(173.082 + 136.113i) q^{20} +(-92.4196 + 45.3200i) q^{21} +(196.640 - 113.530i) q^{22} +(49.7049 + 98.4704i) q^{23} +(-112.095 - 259.101i) q^{24} +(0.760083 + 15.9561i) q^{25} +(-248.480 - 35.7260i) q^{26} +(-100.304 - 98.0919i) q^{27} +(103.500 + 352.489i) q^{28} +(12.9526 - 135.645i) q^{29} +(137.826 - 286.431i) q^{30} +(83.6639 - 65.7940i) q^{31} +(-236.325 + 57.3318i) q^{32} +(-154.666 - 168.873i) q^{33} +(-56.9387 - 110.446i) q^{34} +(-127.161 + 197.866i) q^{35} +(-405.702 + 293.469i) q^{36} +(-50.4717 + 171.891i) q^{37} +(-334.748 - 134.013i) q^{38} +(19.0001 + 252.463i) q^{39} +(-525.466 - 374.183i) q^{40} +(-323.103 + 338.861i) q^{41} +(464.514 - 255.890i) q^{42} +(151.804 - 193.035i) q^{43} +(-687.551 + 441.862i) q^{44} +(-312.095 - 73.2608i) q^{45} +(-279.939 - 494.579i) q^{46} +(102.293 + 59.0588i) q^{47} +(300.982 + 613.781i) q^{48} +(-45.8780 + 18.3668i) q^{49} +(-7.82332 - 81.9295i) q^{50} +(-96.3386 + 80.1480i) q^{51} +(899.499 + 85.8918i) q^{52} +(-405.710 - 468.214i) q^{53} +(540.250 + 480.226i) q^{54} +(-502.065 - 147.420i) q^{55} +(-352.010 - 1017.07i) q^{56} +(-58.9711 + 358.840i) q^{57} +(-33.4049 + 701.255i) q^{58} +(124.904 - 648.062i) q^{59} +(-446.480 + 1053.43i) q^{60} +(46.7270 - 116.718i) q^{61} +(-414.435 + 359.110i) q^{62} +(-353.253 - 401.603i) q^{63} +(192.309 - 56.4671i) q^{64} +(335.570 + 471.242i) q^{65} +(837.367 + 831.165i) q^{66} +(-207.973 + 403.411i) q^{67} +(223.632 + 387.342i) q^{68} +(-425.964 + 383.489i) q^{69} +(605.908 - 1049.46i) q^{70} +(430.448 + 669.790i) q^{71} +(1146.30 - 915.338i) q^{72} +(343.731 - 752.665i) q^{73} +(217.606 - 896.985i) q^{74} +(-78.9685 + 25.5674i) q^{75} +(1226.50 + 424.495i) q^{76} +(-539.664 - 686.238i) q^{77} +(-159.673 - 1294.61i) q^{78} +(-1214.54 + 420.357i) q^{79} +(1314.08 + 844.506i) q^{80} +(355.073 - 636.682i) q^{81} +(1579.73 - 1823.11i) q^{82} +(529.889 - 505.248i) q^{83} +(-1626.28 + 999.579i) q^{84} +(-93.6575 + 270.606i) q^{85} +(-733.916 + 1030.64i) q^{86} +(697.796 - 120.009i) q^{87} +(1950.40 - 1388.87i) q^{88} +(54.6882 - 380.365i) q^{89} +(1624.11 + 300.516i) q^{90} +965.199i q^{91} +(1091.20 + 1730.25i) q^{92} +(443.972 + 329.785i) q^{93} +(-540.914 - 278.860i) q^{94} +(308.833 + 771.427i) q^{95} +(-609.697 - 1106.78i) q^{96} +(-1241.48 - 301.180i) q^{97} +(231.602 - 105.769i) q^{98} +(635.851 - 1005.77i) 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

)

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

$2$	−5.14636	+	0.245151i	−1.81951	+	0.0866741i	−0.929402	−	0.369070i	$-0.879676\pi$
$2$	−5.14636	+	0.245151i	−1.81951	+	0.0866741i	−0.890111	+	0.455744i	$0.849373\pi$
$3$	1.36351	+	5.01406i	0.262408	+	0.964957i
$3$	1.36351	+	5.01406i	0.262408	+	0.964957i
$4$	18.4611	−	1.76282i	2.30764	−	0.220353i
$5$	8.59308	+	8.19348i	0.768588	+	0.732848i	0.969053	−	0.246853i	$-0.0793966\pi$
$5$	8.59308	+	8.19348i	0.768588	+	0.732848i	−0.200464	+	0.979701i	$0.564245\pi$
$6$	−8.24632	−	25.4699i	−0.561091	−	1.73301i
$7$	3.74898	+	19.4516i	0.202426	+	1.05029i	0.930917	+	0.365230i	$0.119010\pi$
$7$	3.74898	+	19.4516i	0.202426	+	1.05029i	−0.728491	+	0.685055i	$0.759778\pi$
$8$	−53.7774	+	7.73203i	−2.37665	+	0.341711i
$9$	−23.2817	+	13.6735i	−0.862284	+	0.506425i
$10$	−46.2317	−	40.0600i	−1.46197	−	1.26681i
$11$	−39.1715	+	20.1943i	−1.07369	+	0.553528i	−0.902050	−	0.431631i	$-0.857938\pi$
$11$	−39.1715	+	20.1943i	−1.07369	+	0.553528i	−0.171644	+	0.985159i	$0.554908\pi$
$12$	34.0109	+	90.1617i	0.818175	+	2.16895i
$13$	47.8434	+	9.22107i	1.02072	+	0.196728i	0.672041	−	0.740514i	$-0.265418\pi$
$13$	47.8434	+	9.22107i	1.02072	+	0.196728i	0.348681	+	0.937242i	$0.386630\pi$
$14$	−24.0622	−	99.1856i	−0.459349	−	1.89346i
$15$	−29.3659	+	54.2582i	−0.505483	+	0.933960i
$16$	129.183	−	24.8979i	2.01848	−	0.389030i
$17$	10.0188	+	21.9382i	0.142937	+	0.312988i	0.967538	−	0.252727i	$-0.0813276\pi$
$17$	10.0188	+	21.9382i	0.142937	+	0.312988i	−0.824601	+	0.565715i	$0.808600\pi$
$18$	116.464	−	76.0761i	1.52504	−	0.996184i
$19$	63.6606	+	29.0728i	0.768671	+	0.351040i	0.760849	−	0.648929i	$-0.224783\pi$
$19$	63.6606	+	29.0728i	0.768671	+	0.351040i	0.00782212	+	0.999969i	$0.497510\pi$
$20$	173.082	+	136.113i	1.93511	+	1.52179i
$21$	−92.4196	+	45.3200i	−0.960362	+	0.470935i
$22$	196.640	−	113.530i	1.90562	−	1.10021i
$23$	49.7049	+	98.4704i	0.450617	+	0.892717i
$23$	49.7049	+	98.4704i	0.450617	+	0.892717i
$24$	−112.095	−	259.101i	−0.953387	−	2.20370i
$25$	0.760083	+	15.9561i	0.00608066	+	0.127649i
$26$	−248.480	−	35.7260i	−1.87427	−	0.269479i
$27$	−100.304	−	98.0919i	−0.714948	−	0.699177i
$28$	103.500	+	352.489i	0.698560	+	2.37908i
$29$	12.9526	−	135.645i	0.0829390	−	0.868577i	−0.854275	−	0.519822i	$-0.825998\pi$
$29$	12.9526	−	135.645i	0.0829390	−	0.868577i	0.937214	−	0.348755i	$-0.113396\pi$
$30$	137.826	−	286.431i	0.838782	−	1.74316i
$31$	83.6639	−	65.7940i	0.484725	−	0.381192i	−0.345680	−	0.938353i	$-0.612352\pi$
$31$	83.6639	−	65.7940i	0.484725	−	0.381192i	0.830405	+	0.557161i	$0.188109\pi$
$32$	−236.325	+	57.3318i	−1.30552	+	0.316716i
$33$	−154.666	−	168.873i	−0.815877	−	0.890819i
$34$	−56.9387	−	110.446i	−0.287203	−	0.557096i
$35$	−127.161	+	197.866i	−0.614117	+	0.955584i
$36$	−405.702	+	293.469i	−1.87825	+	1.35865i
$37$	−50.4717	+	171.891i	−0.224257	+	0.763748i	0.768098	+	0.640332i	$0.221203\pi$
$37$	−50.4717	+	171.891i	−0.224257	+	0.763748i	−0.992355	+	0.123416i	$0.960615\pi$
$38$	−334.748	−	134.013i	−1.42903	−	0.572098i
$39$	19.0001	+	252.463i	0.0780114	+	1.03658i
$40$	−525.466	−	374.183i	−2.07709	−	1.47909i
$41$	−323.103	+	338.861i	−1.23074	+	1.29076i	−0.287838	+	0.957679i	$0.592937\pi$
$41$	−323.103	+	338.861i	−1.23074	+	1.29076i	−0.942898	+	0.333080i	$0.891912\pi$
$42$	464.514	−	255.890i	1.70657	−	0.940111i
$43$	151.804	−	193.035i	0.538370	−	0.684593i	−0.438425	−	0.898768i	$-0.644464\pi$
$43$	151.804	−	193.035i	0.538370	−	0.684593i	0.976795	+	0.214174i	$0.0687060\pi$
$44$	−687.551	+	441.862i	−2.35573	+	1.51394i
$45$	−312.095	−	73.2608i	−1.03387	−	0.242691i
$46$	−279.939	−	494.579i	−0.897279	−	1.58525i
$47$	102.293	+	59.0588i	0.317467	+	0.183290i	0.650263	−	0.759709i	$-0.274659\pi$
$47$	102.293	+	59.0588i	0.317467	+	0.183290i	−0.332796	+	0.942999i	$0.607992\pi$
$48$	300.982	+	613.781i	0.905062	+	1.84566i
$49$	−45.8780	+	18.3668i	−0.133755	+	0.0535475i
$50$	−7.82332	−	81.9295i	−0.0221277	−	0.231732i
$51$	−96.3386	+	80.1480i	−0.264512	+	0.220058i
$52$	899.499	+	85.8918i	2.39881	+	0.229059i
$53$	−405.710	−	468.214i	−1.05148	−	1.21348i	−0.976326	−	0.216304i	$-0.930600\pi$
$53$	−405.710	−	468.214i	−1.05148	−	1.21348i	−0.0751562	−	0.997172i	$-0.523946\pi$
$54$	540.250	+	480.226i	1.36146	+	1.21019i
$55$	−502.065	−	147.420i	−1.23088	−	0.361419i
$56$	−352.010	−	1017.07i	−0.839989	−	2.42699i
$57$	−58.9711	+	358.840i	−0.137033	+	0.833850i
$58$	−33.4049	+	701.255i	−0.0756255	+	1.58757i
$59$	124.904	−	648.062i	0.275611	−	1.43001i	−0.535213	−	0.844717i	$-0.679769\pi$
$59$	124.904	−	648.062i	0.275611	−	1.43001i	0.810824	−	0.585290i	$-0.199019\pi$
$60$	−446.480	+	1053.43i	−0.960672	+	2.26663i
$61$	46.7270	−	116.718i	0.0980783	−	0.244988i	−0.871212	−	0.490907i	$-0.836666\pi$
$61$	46.7270	−	116.718i	0.0980783	−	0.244988i	0.969290	+	0.245919i	$0.0790898\pi$
$62$	−414.435	+	359.110i	−0.848924	+	0.735597i
$63$	−353.253	−	401.603i	−0.706439	−	0.803131i
$64$	192.309	−	56.4671i	0.375604	−	0.110287i
$65$	335.570	+	471.242i	0.640343	+	0.899236i
$66$	837.367	+	831.165i	1.56171	+	1.55014i
$67$	−207.973	+	403.411i	−0.379223	+	0.735589i	−0.998781	−	0.0493614i	$-0.984281\pi$
$67$	−207.973	+	403.411i	−0.379223	+	0.735589i	0.619558	+	0.784951i	$0.287312\pi$
$68$	223.632	+	387.342i	0.398814	+	0.690767i
$69$	−425.964	+	383.489i	−0.743188	+	0.669082i
$70$	605.908	−	1049.46i	1.03457	−	1.79193i
$71$	430.448	+	669.790i	0.719504	+	1.11957i	0.987724	+	0.156212i	$0.0499284\pi$
$71$	430.448	+	669.790i	0.719504	+	1.11957i	−0.268220	+	0.963358i	$0.586435\pi$
$72$	1146.30	−	915.338i	1.87630	−	1.49825i
$73$	343.731	−	752.665i	0.551105	−	1.20675i	−0.405160	−	0.914246i	$-0.632784\pi$
$73$	343.731	−	752.665i	0.551105	−	1.20675i	0.956264	−	0.292505i	$-0.0944887\pi$
$74$	217.606	−	896.985i	0.341841	−	1.40909i
$75$	−78.9685	+	25.5674i	−0.121580	+	0.0393636i
$76$	1226.50	+	424.495i	1.85117	+	0.640696i
$77$	−539.664	−	686.238i	−0.798706	−	1.01564i
$78$	−159.673	−	1294.61i	−0.231787	−	1.87930i
$79$	−1214.54	+	420.357i	−1.72970	+	0.598656i	−0.996670	−	0.0815383i	$-0.974017\pi$
$79$	−1214.54	+	420.357i	−1.72970	+	0.598656i	−0.733032	+	0.680194i	$0.761895\pi$
$80$	1314.08	+	844.506i	1.83648	+	1.18023i
$81$	355.073	−	636.682i	0.487068	−	0.873364i
$82$	1579.73	−	1823.11i	2.12747	−	2.45523i
$83$	529.889	−	505.248i	0.700757	−	0.668171i	−0.253439	−	0.967351i	$-0.581562\pi$
$83$	529.889	−	505.248i	0.700757	−	0.668171i	0.954196	+	0.299181i	$0.0967133\pi$
$84$	−1626.28	+	999.579i	−2.11240	+	1.29837i
$85$	−93.6575	+	270.606i	−0.119513	+	0.345309i
$86$	−733.916	+	1030.64i	−0.920235	+	1.29229i
$87$	697.796	−	120.009i	0.859903	−	0.147889i
$88$	1950.40	−	1388.87i	2.36265	−	1.68243i
$89$	54.6882	−	380.365i	0.0651341	−	0.453018i	−0.930989	−	0.365047i	$-0.881053\pi$
$89$	54.6882	−	380.365i	0.0651341	−	0.453018i	0.996123	−	0.0879703i	$-0.0280381\pi$
$90$	1624.11	+	300.516i	1.90218	+	0.351969i
$91$			965.199i			1.11187i
$92$	1091.20	+	1730.25i	1.23658	+	1.96078i
$93$	443.972	+	329.785i	0.495030	+	0.367711i
$94$	−540.914	−	278.860i	−0.593521	−	0.305981i
$95$	308.833	+	771.427i	0.333533	+	0.833124i
$96$	−609.697	−	1106.78i	−0.648197	−	1.17666i
$97$	−1241.48	−	301.180i	−1.29952	−	0.315259i	−0.474444	−	0.880286i	$-0.657351\pi$
$97$	−1241.48	−	301.180i	−1.29952	−	0.315259i	−0.825073	+	0.565026i	$0.808866\pi$
$98$	231.602	−	105.769i	0.238728	−	0.109023i
$99$	635.851	−	1005.77i	0.645510	−	1.02104i
$100$	42.1598	+	293.228i	0.0421598	+	0.293228i
$101$	1031.62	+	1081.93i	1.01634	+	1.06590i	0.997815	+	0.0660765i	$0.0210482\pi$
$101$	1031.62	+	1081.93i	1.01634	+	1.06590i	0.0185238	+	0.999828i	$0.494103\pi$
$102$	476.145	−	436.088i	0.462209	−	0.423325i
$103$	−131.396	−	6.25917i	−0.125698	−	0.00598772i	−0.0153612	−	0.999882i	$-0.504890\pi$
$103$	−131.396	−	6.25917i	−0.125698	−	0.00598772i	−0.110336	+	0.993894i	$0.535193\pi$
$104$	−2644.19	−	125.959i	−2.49312	−	0.118762i
$105$	−1165.50	−	367.800i	−1.08325	−	0.341843i
$106$	2202.71	+	2310.14i	2.01836	+	2.11680i
$107$	−90.9259	−	632.404i	−0.0821508	−	0.571372i	−0.988773	−	0.149427i	$-0.952257\pi$
$107$	−90.9259	−	632.404i	−0.0821508	−	0.571372i	0.906622	−	0.421944i	$-0.138652\pi$
$108$	−2024.65	−	1634.07i	−1.80391	−	1.45591i
$109$	−1834.84	+	837.943i	−1.61235	+	0.736334i	−0.998586	−	0.0531589i	$-0.983071\pi$
$109$	−1834.84	+	837.943i	−1.61235	+	0.736334i	−0.613760	+	0.789493i	$0.710344\pi$
$110$	2619.95	+	635.592i	2.27093	+	0.550921i
$111$	−930.691	−	18.6932i	−0.795831	−	0.0159845i
$112$	968.606	+	2419.46i	0.817185	+	2.04123i
$113$	309.597	+	159.608i	0.257738	+	0.132873i	0.582254	−	0.813007i	$-0.302171\pi$
$113$	309.597	+	159.608i	0.257738	+	0.132873i	−0.324516	+	0.945880i	$0.605201\pi$
$114$	215.516	−	1861.17i	0.177061	−	1.52908i
$115$	−379.697	+	1253.42i	−0.307887	+	1.01637i
$116$		−	2527.00i		−	2.02264i
$117$	−1239.96	+	439.504i	−0.979780	+	0.347283i
$118$	−483.926	+	3365.78i	−0.377534	+	2.62580i
$119$	−389.171	+	277.128i	−0.299792	+	0.213481i
$120$	1159.70	−	3144.92i	0.882211	−	2.39242i
$121$	354.539	−	497.880i	0.266370	−	0.374065i
$122$	−211.860	+	612.130i	−0.157221	+	0.454259i
$123$	−2139.62	−	1158.02i	−1.56848	−	0.848903i
$124$	1428.55	−	1362.12i	1.03457	−	0.986465i
$125$	847.711	−	978.311i	0.606573	−	0.700023i
$126$	1916.42	+	1980.19i	1.35499	+	1.40008i
$127$	316.302	+	203.275i	0.221002	+	0.142029i	0.646457	−	0.762950i	$-0.276250\pi$
$127$	316.302	+	203.275i	0.221002	+	0.142029i	−0.425456	+	0.904979i	$0.639886\pi$
$128$	862.590	−	298.545i	0.595648	−	0.206156i
$129$	1174.88	+	497.951i	0.801876	+	0.339861i
$130$	−1842.49	−	2342.91i	−1.24305	−	1.58067i
$131$	−939.302	−	325.096i	−0.626467	−	0.216822i	−0.00465544	−	0.999989i	$-0.501482\pi$
$131$	−939.302	−	325.096i	−0.626467	−	0.216822i	−0.621812	+	0.783167i	$0.713603\pi$
$132$	−3153.01	−	2844.94i	−2.07905	−	1.87591i
$133$	−326.849	+	1347.29i	−0.213094	+	0.878384i
$134$	971.406	−	2127.08i	0.626244	−	1.37128i
$135$	−58.2100	−	1664.75i	−0.0371105	−	1.06133i
$136$	−708.413	−	1102.31i	−0.446661	−	0.695019i
$137$	664.327	−	1150.65i	0.414287	−	0.717566i	−0.581067	−	0.813856i	$-0.697364\pi$
$137$	664.327	−	1150.65i	0.414287	−	0.717566i	0.995353	+	0.0962904i	$0.0306978\pi$
$138$	2098.15	−	2078.00i	1.29425	−	1.28182i
$139$	1216.96	+	2107.84i	0.742598	+	1.28622i	0.951308	+	0.308240i	$0.0997401\pi$
$139$	1216.96	+	2107.84i	0.742598	+	1.28622i	−0.208710	+	0.977978i	$0.566927\pi$
$140$	−1998.73	+	3876.99i	−1.20660	+	2.34047i
$141$	−156.647	+	593.430i	−0.0935607	+	0.354438i
$142$	−2379.44	−	3341.46i	−1.40618	−	1.97471i
$143$	−2060.31	+	604.962i	−1.20484	+	0.353772i
$144$	−2667.15	+	2346.04i	−1.54349	+	1.35766i
$145$	1222.71	−	1059.49i	0.700280	−	0.606796i
$146$	−1584.44	+	3957.75i	−0.898148	+	2.24346i
$147$	−154.647	−	204.992i	−0.0867694	−	0.115017i
$148$	−628.752	+	3262.27i	−0.349210	+	1.81187i
$149$	−67.7230	+	1421.68i	−0.0372355	+	0.781669i	0.900613	+	0.434623i	$0.143118\pi$
$149$	−67.7230	+	1421.68i	−0.0372355	+	0.781669i	−0.937848	+	0.347046i	$0.887185\pi$
$150$	400.132	−	150.938i	0.217805	−	0.0821604i
$151$	1159.37	+	3349.79i	0.624824	+	1.80531i	0.592128	+	0.805844i	$0.298288\pi$
$151$	1159.37	+	3349.79i	0.624824	+	1.80531i	0.0326950	+	0.999465i	$0.489591\pi$
$152$	−3648.30	−	1071.24i	−1.94682	−	0.571636i
$153$	−533.226	−	373.765i	−0.281757	−	0.197498i
$154$	2945.53	+	3399.33i	1.54129	+	1.77874i
$155$	1258.01	+	120.126i	0.651910	+	0.0622498i
$156$	795.811	+	4627.26i	0.408435	+	2.37485i
$157$	−197.507	−	2068.39i	−0.100400	−	1.05144i	−0.895531	−	0.444998i	$-0.853204\pi$
$157$	−197.507	−	2068.39i	−0.100400	−	1.05144i	0.795131	−	0.606437i	$-0.207402\pi$
$158$	6147.41	−	2461.05i	3.09533	−	1.23918i
$159$	1794.47	−	2672.67i	0.895034	−	1.33306i
$160$	−2500.50	−	1443.67i	−1.23551	−	0.713324i
$161$	−1729.06	+	1336.00i	−0.846391	+	0.653986i
$162$	−1671.25	+	3363.64i	−0.810528	+	1.63131i
$163$	1366.32	−	878.080i	0.656555	−	0.421942i	−0.169501	−	0.985530i	$-0.554216\pi$
$163$	1366.32	−	878.080i	0.656555	−	0.421942i	0.826056	+	0.563588i	$0.190579\pi$
$164$	−5367.49	+	6825.32i	−2.55568	+	3.24981i
$165$	54.5999	−	2718.40i	0.0257612	−	1.28259i
$166$	−2603.14	+	2730.09i	−1.21712	+	1.27648i
$167$	1790.01	+	1274.66i	0.829433	+	0.590637i	0.913969	−	0.405784i	$-0.133001\pi$
$167$	1790.01	+	1274.66i	0.829433	+	0.590637i	−0.0845360	+	0.996420i	$0.526941\pi$
$168$	4619.67	−	3151.79i	2.12152	−	1.44741i
$169$	164.343	+	65.7929i	0.0748032	+	0.0299467i
$170$	415.656	−	1415.59i	0.187526	−	0.638653i
$171$	−1879.65	+	193.597i	−0.840588	+	0.0865775i
$172$	2462.19	−	3831.24i	1.09151	−	1.69843i
$173$	−498.684	−	967.312i	−0.219157	−	0.425106i	0.753468	−	0.657485i	$-0.228380\pi$
$173$	−498.684	−	967.312i	−0.219157	−	0.425106i	−0.972625	+	0.232378i	$0.925349\pi$
$174$	−3561.69	+	788.675i	−1.55179	+	0.343617i
$175$	−307.521	+	74.6039i	−0.132837	+	0.0322259i
$176$	−4557.48	+	3584.04i	−1.95189	+	1.53498i
$177$	3419.73	−	257.365i	1.45222	−	0.109292i
$178$	−188.198	+	1970.90i	−0.0792474	+	0.829917i
$179$	−602.225	−	2050.99i	−0.251466	−	0.856415i	−0.984375	−	0.176088i	$-0.943656\pi$
$179$	−602.225	−	2050.99i	−0.251466	−	0.856415i	0.732908	−	0.680327i	$-0.238162\pi$
$180$	−5890.77	−	802.310i	−2.43929	−	0.332226i
$181$	424.342	+	61.0111i	0.174260	+	0.0250548i	0.228892	−	0.973452i	$-0.426490\pi$
$181$	424.342	+	61.0111i	0.174260	+	0.0250548i	−0.0546324	+	0.998507i	$0.517399\pi$
$182$	−236.620	−	4967.26i	−0.0963705	−	2.02307i
$183$	648.946	+	75.1453i	0.262139	+	0.0303546i
$184$	−3434.38	−	4911.16i	−1.37601	−	1.96769i
$185$	−1842.09	+	1063.53i	−0.732072	+	0.422662i
$186$	−2365.69	−	1588.35i	−0.932583	−	0.626149i
$187$	−835.478	−	657.027i	−0.326718	−	0.256934i
$188$	1992.55	+	909.968i	0.772988	+	0.353012i
$189$	1532.00	−	2318.82i	0.589612	−	0.892431i
$190$	−1778.48	−	3894.33i	−0.679077	−	1.48697i
$191$	2848.03	−	548.914i	1.07893	−	0.207948i	0.381336	−	0.924436i	$-0.375464\pi$
$191$	2848.03	−	548.914i	1.07893	−	0.207948i	0.697599	+	0.716489i	$0.254252\pi$
$192$	545.346	+	887.258i	0.204984	+	0.333502i
$193$	−20.2863	−	83.6212i	−0.00756601	−	0.0311875i	0.967903	−	0.251322i	$-0.0808654\pi$
$193$	−20.2863	−	83.6212i	−0.00756601	−	0.0311875i	−0.975469	+	0.220135i	$0.929350\pi$
$194$	6462.93	+	1245.63i	2.39181	+	0.460984i
$195$	−1905.28	+	2325.11i	−0.699693	+	0.853870i
$196$	−814.583	+	419.947i	−0.296860	+	0.153042i
$197$	2048.01	+	1774.61i	0.740685	+	0.641807i	0.941187	−	0.337886i	$-0.109712\pi$
$197$	2048.01	+	1774.61i	0.740685	+	0.641807i	−0.200502	+	0.979693i	$0.564257\pi$
$198$	−3025.75	+	5331.92i	−1.08602	+	1.91375i
$199$	−1911.11	+	274.776i	−0.680780	+	0.0978813i	−0.474025	−	0.880511i	$-0.657199\pi$
$199$	−1911.11	+	274.776i	−0.680780	+	0.0978813i	−0.206755	+	0.978393i	$0.566290\pi$
$200$	−164.248	−	852.201i	−0.0580705	−	0.301299i
$201$	−2306.30	−	492.733i	−0.809323	−	0.172909i
$202$	−5574.33	−	5315.11i	−1.94163	−	1.85134i
$203$	2687.07	−	256.584i	0.929042	−	0.0887128i
$204$	−1637.23	+	1649.45i	−0.561908	+	0.566101i
$205$	−5552.90	+	264.517i	−1.89186	+	0.0901204i
$206$	677.747			0.229227
$207$	−2503.65	−	1612.92i	−0.840654	−	0.541572i
$208$	6410.13			2.13684
$209$	−3080.79	+	146.756i	−1.01963	+	0.0485709i
$210$	6088.24	+	1607.11i	2.00061	+	0.528099i
$211$	5320.55	−	508.051i	1.73593	−	0.165761i	0.821421	−	0.570322i	$-0.193182\pi$
$211$	5320.55	−	508.051i	1.73593	−	0.165761i	0.914511	+	0.404561i	$0.132576\pi$
$212$	−8315.25	−	7928.57i	−2.69384	−	2.56857i
$213$	−2771.45	+	3071.56i	−0.891533	+	0.988074i
$214$	622.972	+	3232.28i	0.198998	+	1.03250i
$215$	2886.09	−	414.957i	0.915488	−	0.131627i
$216$	6152.56	+	4499.57i	1.93810	+	1.41739i
$217$	1593.45	+	1380.73i	0.498481	+	0.431936i
$218$	9237.32	−	4762.17i	2.86986	−	1.47952i
$219$	4242.59	+	697.220i	1.30908	+	0.215131i
$220$	−9528.57	−	1836.48i	−2.92007	−	0.562798i
$221$	277.042	+	1141.98i	0.0843251	+	0.347593i
$222$	4794.25	−	131.958i	1.44941	−	0.0398938i
$223$	3031.84	−	584.338i	0.910434	−	0.175472i	0.287531	−	0.957771i	$-0.407165\pi$
$223$	3031.84	−	584.338i	0.910434	−	0.175472i	0.622902	+	0.782299i	$0.285953\pi$
$224$	−2001.17	−	4381.95i	−0.596914	−	1.30706i
$225$	−235.871	−	361.092i	−0.0698878	−	0.106990i
$226$	−1632.42	−	745.503i	−0.480475	−	0.219425i
$227$	897.715	+	705.971i	0.262482	+	0.206418i	0.740723	−	0.671810i	$-0.234483\pi$
$227$	897.715	+	705.971i	0.262482	+	0.206418i	−0.478241	+	0.878229i	$0.658725\pi$
$228$	−456.101	+	6728.54i	−0.132483	+	1.95442i
$229$	2536.98	−	1464.73i	0.732089	−	0.422672i	−0.0870972	−	0.996200i	$-0.527759\pi$
$229$	2536.98	−	1464.73i	0.732089	−	0.422672i	0.819186	+	0.573528i	$0.194426\pi$
$230$	1646.78	−	6543.63i	0.472111	−	1.87598i
$231$	2705.00	−	3641.60i	0.770460	−	1.03723i
$232$	352.258	+	7394.81i	0.0996849	+	2.09264i
$233$	4024.94	+	578.699i	1.13168	+	0.162712i	0.682610	−	0.730783i	$-0.260845\pi$
$233$	4024.94	+	578.699i	1.13168	+	0.162712i	0.449074	+	0.893494i	$0.351754\pi$
$234$	6273.53	−	2565.82i	1.75262	−	0.716808i
$235$	395.113	+	1345.63i	0.109678	+	0.373529i
$236$	1163.44	−	12184.1i	0.320906	−	3.36068i
$237$	−3763.73	−	5516.62i	−1.03156	−	1.51200i
$238$	1934.88	−	1521.60i	0.526972	−	0.414416i
$239$	2644.13	−	641.459i	0.715626	−	0.173609i	0.138616	−	0.990346i	$-0.455735\pi$
$239$	2644.13	−	641.459i	0.715626	−	0.173609i	0.577010	+	0.816737i	$0.304219\pi$
$240$	−2442.65	+	7740.36i	−0.656968	+	2.08183i
$241$	525.374	+	1019.08i	0.140425	+	0.272386i	0.948552	−	0.316623i	$-0.102549\pi$
$241$	525.374	+	1019.08i	0.140425	+	0.272386i	−0.808127	+	0.589008i	$0.799519\pi$
$242$	−1702.53	+	2649.18i	−0.452242	+	0.703703i
$243$	3676.51	+	912.233i	0.970569	+	0.240822i
$244$	656.879	−	2237.12i	0.172346	−	0.586956i
$245$	−544.721	−	218.074i	−0.142045	−	0.0568662i
$246$	11295.2	+	5435.05i	2.92745	+	1.40864i
$247$	2777.66	+	1977.96i	0.715540	+	0.509534i
$248$	−3990.51	+	4185.12i	−1.02176	+	1.07160i
$249$	3255.85	+	1967.98i	0.828640	+	0.500867i
$250$	−4122.79	+	5242.56i	−1.04299	+	1.32627i
$251$	−2547.27	+	1637.03i	−0.640567	+	0.411667i	−0.820208	−	0.572065i	$-0.806143\pi$
$251$	−2547.27	+	1637.03i	−0.640567	+	0.411667i	0.179642	+	0.983732i	$0.442506\pi$
$252$	−7229.40	−	6791.33i	−1.80718	−	1.69767i
$253$	−3935.56	−	2853.47i	−0.977969	−	0.709077i
$254$	−1677.64	−	968.583i	−0.414426	−	0.239269i
$255$	−1484.54	−	100.631i	−0.364570	−	0.0247128i
$256$	−5854.58	+	2343.82i	−1.42934	+	0.572221i
$257$	73.2032	+	766.618i	0.0177677	+	0.186071i	0.999999	−	0.00160434i	$-0.000510677\pi$
$257$	73.2032	+	766.618i	0.0177677	+	0.186071i	−0.982231	+	0.187676i	$0.939905\pi$
$258$	−6168.40	−	2274.61i	−1.48848	−	0.548880i
$259$	−3532.76	−	337.338i	−0.847549	−	0.0809311i
$260$	7025.72	+	8108.11i	1.67583	+	1.93401i
$261$	1553.19	+	3335.16i	0.368352	+	0.790962i
$262$	4913.68	+	1442.79i	1.15866	+	0.340213i
$263$	2400.32	+	6935.27i	0.562776	+	1.62604i	0.763082	+	0.646302i	$0.223685\pi$
$263$	2400.32	+	6935.27i	0.562776	+	1.62604i	−0.200305	+	0.979734i	$0.564193\pi$
$264$	9623.28	+	7885.68i	2.24346	+	1.83837i
$265$	350.008	−	7347.58i	0.0811353	−	1.70324i
$266$	1351.79	−	7013.77i	0.311593	−	1.61670i
$267$	1981.74	−	244.421i	0.454234	−	0.0560238i
$268$	−3128.27	+	7814.04i	−0.713020	+	1.78104i
$269$	−5131.60	+	4446.56i	−1.16312	+	1.00785i	−0.163346	+	0.986569i	$0.552229\pi$
$269$	−5131.60	+	4446.56i	−1.16312	+	1.00785i	−0.999774	+	0.0212796i	$0.993226\pi$
$270$	707.686	+	8553.15i	0.159513	+	1.92788i
$271$	−5632.41	+	1653.83i	−1.26253	+	0.370711i	−0.843434	−	0.537232i	$-0.819470\pi$
$271$	−5632.41	+	1653.83i	−1.26253	+	0.370711i	−0.419093	+	0.907944i	$0.637652\pi$
$272$	1840.47	+	2584.58i	0.410276	+	0.576152i
$273$	−4839.57	+	1316.06i	−1.07291	+	0.291764i
$274$	−3136.78	+	6084.51i	−0.691605	+	1.34153i
$275$	−351.996	−	609.675i	−0.0771860	−	0.133690i
$276$	−7187.75	+	7830.54i	−1.56758	+	1.70777i
$277$	−1160.86	+	2010.67i	−0.251802	+	0.436134i	−0.964022	−	0.265822i	$-0.914357\pi$
$277$	−1160.86	+	2010.67i	−0.251802	+	0.436134i	0.712220	+	0.701956i	$0.247690\pi$
$278$	−6779.65	−	10549.3i	−1.46265	−	2.27593i
$279$	−1048.20	+	2675.77i	−0.224926	+	0.574173i
$280$	5308.47	−	11623.9i	1.13301	−	2.48094i
$281$	1767.11	−	7284.14i	0.375150	−	1.54639i	−0.401142	−	0.916016i	$-0.631387\pi$
$281$	1767.11	−	7284.14i	0.375150	−	1.54639i	0.776292	−	0.630373i	$-0.217098\pi$
$282$	660.682	−	3092.41i	0.139514	−	0.653014i
$283$	−670.520	−	232.069i	−0.140842	−	0.0487459i	0.255738	−	0.966746i	$-0.417682\pi$
$283$	−670.520	−	232.069i	−0.140842	−	0.0487459i	−0.396580	+	0.918000i	$0.629803\pi$
$284$	9127.28	+	11606.3i	1.90706	+	2.42502i
$285$	−3446.89	+	2600.36i	−0.716407	+	0.540463i
$286$	10454.8	−	3618.44i	2.16156	−	0.748122i
$287$	−7802.67	−	5014.47i	−1.60480	−	1.03134i
$288$	4718.11	−	4566.16i	0.965338	−	0.934248i
$289$	2836.42	−	3273.41i	0.577330	−	0.666275i
$290$	−6032.78	+	5752.24i	−1.22158	+	1.16477i
$291$	−182.637	−	6635.52i	−0.0367917	−	1.33670i
$292$	5018.84	−	14501.0i	1.00584	−	2.90619i
$293$	−5537.36	+	7776.13i	−1.10408	+	1.55047i	−0.301946	+	0.953325i	$0.597636\pi$
$293$	−5537.36	+	7776.13i	−1.10408	+	1.55047i	−0.802136	+	0.597141i	$0.796303\pi$
$294$	846.125	+	1017.05i	0.167847	+	0.201754i
$295$	6383.19	−	4545.45i	1.25981	−	0.897106i
$296$	1385.17	−	9634.10i	0.271999	−	1.89179i
$297$	5909.97	+	1816.82i	1.15465	+	0.354959i
$298$		−	7333.08i		−	1.42548i
$299$	1470.05	+	5169.50i	0.284332	+	0.999865i
$300$	−1412.78	+	611.211i	−0.271889	+	0.117628i
$301$	4323.94	+	2229.14i	0.827999	+	0.426863i
$302$	−6787.75	−	16955.0i	−1.29335	−	3.23063i
$303$	−4018.26	+	6647.84i	−0.761857	+	1.26042i
$304$	8947.70	+	2170.69i	1.68811	+	0.409531i
$305$	1357.86	−	620.113i	0.254921	−	0.116418i
$306$	2835.80	+	1792.81i	0.529778	+	0.334928i
$307$	−58.8563	−	409.355i	−0.0109417	−	0.0761013i	0.983619	−	0.180260i	$-0.0576940\pi$
$307$	−58.8563	−	409.355i	−0.0109417	−	0.0761013i	−0.994561	+	0.104159i	$0.966785\pi$
$308$	−11172.5	−	11717.4i	−2.06693	−	2.16773i
$309$	−147.776	−	667.364i	−0.0272062	−	0.122864i
$310$	−6503.63	−	309.806i	−1.19155	−	0.0567607i
$311$	−2834.25	−	135.012i	−0.516770	−	0.0246168i	−0.212423	−	0.977178i	$-0.568135\pi$
$311$	−2834.25	−	135.012i	−0.516770	−	0.0246168i	−0.304348	+	0.952561i	$0.598438\pi$
$312$	−2973.83	−	13429.9i	−0.539614	−	2.43692i
$313$	3251.64	+	3410.22i	0.587199	+	0.615837i	0.948563	−	0.316588i	$-0.102537\pi$
$313$	3251.64	+	3410.22i	0.587199	+	0.615837i	−0.361364	+	0.932425i	$0.617689\pi$
$314$	1523.51	+	10596.3i	0.273811	+	1.90440i
$315$	255.001	−	6345.38i	0.0456117	−	1.13499i
$316$	−21680.8	+	9901.28i	−3.85962	+	1.76263i
$317$	2580.90	+	626.119i	0.457280	+	0.110935i	0.457781	−	0.889065i	$-0.348644\pi$
$317$	2580.90	+	626.119i	0.457280	+	0.110935i	−0.000501074		1.00000i	$0.500159\pi$
$318$	−8579.76	+	14194.4i	−1.51298	+	2.50310i
$319$	2231.89	+	5575.00i	0.391730	+	0.978495i
$320$	2115.19	+	1090.46i	0.369509	+	0.190495i
$321$	3046.93	−	1318.20i	0.529792	−	0.229204i
$322$	8570.84	−	7299.43i	1.48334	−	1.26330i
$323$			1687.87i			0.290761i
$324$	5432.68	−	12379.8i	0.931530	−	2.12274i
$325$	−110.767	+	770.403i	−0.0189054	+	0.131490i
$326$	−6816.31	+	4853.87i	−1.15804	+	0.824635i
$327$	−6703.32	−	8057.46i	−1.13362	−	1.36262i
$328$	14755.6	−	20721.3i	2.48396	−	3.48824i
$329$	−765.291	+	2211.16i	−0.128243	+	0.370533i
$330$	385.427	+	14003.2i	0.0642942	+	2.33592i
$331$	135.012	−	128.734i	0.0224197	−	0.0213772i	−0.678786	−	0.734336i	$-0.737494\pi$
$331$	135.012	−	128.734i	0.0224197	−	0.0213772i	0.701206	+	0.712959i	$0.252645\pi$
$332$	8891.68	−	10261.5i	1.46986	−	1.69631i
$333$	−1175.28	−	4692.03i	−0.193408	−	0.772137i
$334$	−9524.53	−	6121.04i	−1.56036	−	1.00278i
$335$	−5092.47	+	1762.52i	−0.830541	+	0.287453i
$336$	−10810.6	+	8155.62i	−1.75526	+	1.32418i
$337$	−172.855	−	219.803i	−0.0279407	−	0.0355295i	0.771882	−	0.635766i	$-0.219316\pi$
$337$	−172.855	−	219.803i	−0.0279407	−	0.0355295i	−0.799823	+	0.600236i	$0.795073\pi$
$338$	−861.896	−	298.305i	−0.138701	−	0.0480049i
$339$	−378.147	+	1769.97i	−0.0605845	+	0.283573i
$340$	−1251.99	+	5160.79i	−0.199703	+	0.823185i
$341$	−1948.57	+	4266.78i	−0.309446	+	0.677593i
$342$	9625.90	−	1457.12i	1.52196	−	0.230386i
$343$	3144.22	+	4892.50i	0.494962	+	0.770175i
$344$	−6671.09	+	11554.7i	−1.04558	+	1.81100i
$345$	−6802.45	−	194.774i	−1.06154	−	0.0303950i
$346$	2803.54	+	4855.88i	0.435605	+	0.754491i
$347$	−2059.17	+	3994.22i	−0.318564	+	0.617929i	−0.992691	−	0.120688i	$-0.961490\pi$
$347$	−2059.17	+	3994.22i	−0.318564	+	0.617929i	0.674126	+	0.738616i	$0.264520\pi$
$348$	12670.5	−	3445.59i	1.95176	−	0.530756i
$349$	575.822	+	808.629i	0.0883182	+	0.124026i	0.856371	−	0.516361i	$-0.172714\pi$
$349$	575.822	+	808.629i	0.0883182	+	0.124026i	−0.768053	+	0.640386i	$0.778774\pi$
$350$	1564.33	−	459.328i	0.238905	−	0.0701488i
$351$	−3894.40	−	5617.97i	−0.592216	−	0.854316i
$352$	8099.41	−	7018.18i	1.22642	−	1.06270i
$353$	−3400.28	+	8493.48i	−0.512687	+	1.28063i	0.415865	+	0.909426i	$0.363479\pi$
$353$	−3400.28	+	8493.48i	−0.512687	+	1.28063i	−0.928552	+	0.371203i	$0.878945\pi$
$354$	−17536.1	+	2162.84i	−2.63286	+	0.324728i
$355$	−1789.04	+	9282.43i	−0.267472	+	1.38778i
$356$	339.090	−	7118.37i	0.0504823	−	1.05975i
$357$	−1920.17	−	1573.46i	−0.284668	−	0.233267i
$358$	3602.07	+	10407.5i	0.531775	+	1.53646i
$359$	590.344	+	173.341i	0.0867888	+	0.0254835i	0.324839	−	0.945769i	$-0.394690\pi$
$359$	590.344	+	173.341i	0.0867888	+	0.0254835i	−0.238050	+	0.971253i	$0.576508\pi$
$360$	17350.1	+	1526.66i	2.54008	+	0.223505i
$361$	−1284.24	−	1482.10i	−0.187235	−	0.216081i
$362$	−2198.77	−	209.957i	−0.319240	−	0.0304837i
$363$	2979.82	+	1098.81i	0.430854	+	0.158878i
$364$	1701.48	+	17818.7i	0.245004	+	2.56580i
$365$	9120.66	−	3651.36i	1.30794	−	0.523619i
$366$	−3358.13	−	227.635i	−0.479597	−	0.0325100i
$367$	−5011.77	−	2893.55i	−0.712840	−	0.411559i	0.0992715	−	0.995060i	$-0.468349\pi$
$367$	−5011.77	−	2893.55i	−0.712840	−	0.411559i	−0.812112	+	0.583502i	$0.801682\pi$
$368$	8872.72	+	11483.1i	1.25685	+	1.62663i
$369$	2888.98	−	12307.2i	0.407572	−	1.73628i
$370$	9219.34	−	5924.91i	1.29538	−	0.832491i
$371$	7586.50	−	9647.02i	1.06165	−	1.35000i
$372$	8777.58	+	5305.56i	1.22338	+	0.739464i
$373$	−5149.93	+	5401.09i	−0.714888	+	0.749753i	−0.976523	−	0.215414i	$-0.930890\pi$
$373$	−5149.93	+	5401.09i	−0.714888	+	0.749753i	0.261634	+	0.965167i	$0.415739\pi$
$374$	4460.74	+	3176.48i	0.616737	+	0.439176i
$375$	6061.18	+	2916.54i	0.834661	+	0.401625i
$376$	−5957.69	−	2385.10i	−0.817139	−	0.327133i
$377$	1870.49	−	6370.31i	0.255531	−	0.870259i
$378$	−7315.76	+	12309.1i	−0.995455	+	1.67489i
$379$	98.4017	−	153.116i	0.0133366	−	0.0207521i	−0.834521	−	0.550976i	$-0.814256\pi$
$379$	98.4017	−	153.116i	0.0133366	−	0.0207521i	0.847858	+	0.530224i	$0.177892\pi$
$380$	7061.30	+	13697.0i	0.953255	+	1.84906i
$381$	−587.952	+	1863.12i	−0.0790595	+	0.250527i
$382$	−14522.4	+	3523.11i	−1.94511	+	0.471879i
$383$	9763.24	−	7677.89i	1.30255	−	1.02434i	0.305152	−	0.952304i	$-0.401293\pi$
$383$	9763.24	−	7677.89i	1.30255	−	1.02434i	0.997402	−	0.0720357i	$-0.0229496\pi$
$384$	2673.08	+	3918.01i	0.355234	+	0.520677i
$385$	985.309	−	10318.6i	0.130431	−	1.36594i
$386$	124.900	+	425.372i	0.0164696	+	0.0560903i
$387$	−894.802	+	6569.86i	−0.117533	+	0.862958i
$388$	−23450.0	−	3371.61i	−3.06829	−	0.441153i
$389$	−497.212	−	10437.8i	−0.0648063	−	1.36045i	−0.763859	−	0.645383i	$-0.776698\pi$
$389$	−497.212	−	10437.8i	−0.0648063	−	1.36045i	0.699053	−	0.715070i	$-0.253605\pi$
$390$	9235.27	−	12432.9i	1.19909	−	1.61427i
$391$	−1662.28	+	2076.99i	−0.215000	+	0.268640i
$392$	2325.19	−	1342.45i	0.299591	−	0.172969i
$393$	349.301	−	5152.99i	0.0448344	−	0.661410i
$394$	−10974.9	−	8630.73i	−1.40331	−	1.10358i
$395$	−13880.8	−	6339.16i	−1.76815	−	0.807488i
$396$	9965.55	−	19688.5i	1.26461	−	2.49844i
$397$	5026.01	+	11005.4i	0.635386	+	1.39130i	0.903782	+	0.427993i	$0.140779\pi$
$397$	5026.01	+	11005.4i	0.635386	+	1.39130i	−0.268396	+	0.963309i	$0.586494\pi$
$398$	9767.91	−	1882.61i	1.23020	−	0.237102i
$399$	−7201.07	+	198.204i	−0.903520	+	0.0248687i
$400$	495.463	+	2042.33i	0.0619329	+	0.255291i
$401$	−9256.82	−	1784.11i	−1.15278	−	0.222180i	−0.423173	−	0.906049i	$-0.639084\pi$
$401$	−9256.82	−	1784.11i	−1.15278	−	0.222180i	−0.729604	+	0.683869i	$0.760296\pi$
$402$	11989.8	+	1970.39i	1.48756	+	0.244463i
$403$	4609.46	−	2376.34i	0.569761	−	0.293732i
$404$	20952.2	+	18155.1i	2.58022	+	2.23577i
$405$	8267.81	−	2561.78i	1.01440	−	0.314311i
$406$	−13765.7	+	1979.21i	−1.68272	+	0.241938i
$407$	−1494.16	−	7752.46i	−0.181973	−	0.944165i
$408$	4561.14	−	5055.05i	0.553456	−	0.613387i
$409$	−4807.22	−	4583.67i	−0.581178	−	0.554152i	0.341422	−	0.939910i	$-0.389091\pi$
$409$	−4807.22	−	4583.67i	−0.581178	−	0.554152i	−0.922600	+	0.385758i	$0.873940\pi$
$410$	28512.4	−	2722.60i	3.43445	−	0.327950i
$411$	6675.24	+	1762.06i	0.801132	+	0.211474i
$412$	−2436.76	+	116.077i	−0.291384	+	0.0138804i
$413$	13074.1			1.55771
$414$	13280.1	+	7686.88i	1.57652	+	0.912535i
$415$	8693.12			1.02826
$416$	−11835.3	+	563.783i	−1.39488	+	0.0664464i
$417$	−8909.49	+	8975.97i	−1.04628	+	1.05409i
$418$	15818.8	−	1510.52i	1.85102	−	0.176751i
$419$	10260.9	+	9783.78i	1.19637	+	1.14074i	0.986629	+	0.162981i	$0.0521108\pi$
$419$	10260.9	+	9783.78i	1.19637	+	1.14074i	0.209742	+	0.977757i	$0.432738\pi$
$420$	−22164.8	−	4735.43i	−2.57507	−	0.550155i
$421$	−1362.42	−	7068.92i	−0.157721	−	0.818333i	−0.971478	−	0.237129i	$-0.923794\pi$
$421$	−1362.42	−	7068.92i	−0.157721	−	0.818333i	0.813757	−	0.581205i	$-0.197418\pi$
$422$	−27256.9	+	3918.95i	−3.14418	+	0.452065i
$423$	−3189.09	+	23.7100i	−0.366569	+	0.00272535i
$424$	25438.3	+	22042.4i	2.91366	+	2.52470i
$425$	−342.433	+	176.536i	−0.0390833	+	0.0201489i
$426$	13509.9	−	16486.8i	1.53652	−	1.87509i
$427$	2445.53	+	471.338i	0.277161	+	0.0534183i
$428$	−2793.41	−	11514.6i	−0.315478	−	1.30042i
$429$	−5842.58	−	9505.66i	−0.657534	−	1.06978i
$430$	−14751.1	+	2843.05i	−1.65433	+	0.318846i
$431$	1531.02	+	3352.48i	0.171106	+	0.374671i	0.975686	−	0.219175i	$-0.0703364\pi$
$431$	1531.02	+	3352.48i	0.171106	+	0.374671i	−0.804579	+	0.593845i	$0.797609\pi$
$432$	−15399.9	−	10174.4i	−1.71511	−	1.13314i
$433$	4293.16	+	1960.62i	0.476481	+	0.217601i	0.639154	−	0.769078i	$-0.279284\pi$
$433$	4293.16	+	1960.62i	0.476481	+	0.217601i	−0.162674	+	0.986680i	$0.552012\pi$
$434$	−8538.95	−	6715.11i	−0.944431	−	0.742708i
$435$	6979.51	+	4686.13i	0.769291	+	0.516512i
$436$	−32396.1	+	18703.9i	−3.55846	+	2.05448i
$437$	301.433	+	7713.75i	0.0329965	+	0.844391i
$438$	−22004.8	−	2548.07i	−2.40053	−	0.277971i
$439$	−166.876	−	3503.16i	−0.0181425	−	0.380859i	−0.989618	−	0.143720i	$-0.954094\pi$
$439$	−166.876	−	3503.16i	−0.0181425	−	0.380859i	0.971476	−	0.237139i	$-0.0762095\pi$
$440$	28139.6	+	4045.87i	3.04887	+	0.438362i
$441$	816.979	−	1054.92i	0.0882172	−	0.113910i
$442$	−1705.72	−	5809.13i	−0.183558	−	0.625141i
$443$	1061.22	−	11113.6i	0.113815	−	1.19192i	−0.740460	−	0.672101i	$-0.765392\pi$
$443$	1061.22	−	11113.6i	0.113815	−	1.19192i	0.854275	−	0.519822i	$-0.174002\pi$
$444$	−17214.6	+	1295.55i	−1.84002	+	0.138477i
$445$	3586.45	−	2820.42i	0.382054	−	0.300451i
$446$	−15459.7	+	3750.47i	−1.64134	+	0.398184i
$447$	−7220.74	+	1598.91i	−0.764048	+	0.169185i
$448$	1819.34	+	3529.02i	0.191865	+	0.372167i
$449$	−590.872	+	919.415i	−0.0621047	+	0.0966367i	−0.870917	−	0.491430i	$-0.836474\pi$
$449$	−590.872	+	919.415i	−0.0621047	+	0.0966367i	0.808812	+	0.588067i	$0.200111\pi$
$450$	1302.40	+	1800.48i	0.136435	+	0.188612i
$451$	5813.37	−	19798.5i	0.606964	−	2.06713i
$452$	5996.87	+	2400.78i	0.624046	+	0.249831i
$453$	−15215.2	+	10380.6i	−1.57809	+	1.07666i
$454$	−4793.03	−	3413.10i	−0.495481	−	0.352830i
$455$	−7908.34	+	8294.03i	−0.814833	+	0.854572i
$456$	396.754	−	19753.4i	0.0407450	−	2.02859i
$457$	−3369.93	+	4285.22i	−0.344943	+	0.438631i	−0.927309	−	0.374296i	$-0.877884\pi$
$457$	−3369.93	+	4285.22i	−0.344943	+	0.438631i	0.582366	+	0.812926i	$0.302127\pi$
$458$	−12697.1	+	8159.95i	−1.29541	+	0.832509i
$459$	1147.02	−	3183.26i	0.116642	−	0.323708i
$460$	−4800.08	+	23808.9i	−0.486533	+	2.41325i
$461$	−3019.61	−	1743.38i	−0.305070	−	0.176133i	0.339648	−	0.940553i	$-0.389692\pi$
$461$	−3019.61	−	1743.38i	−0.305070	−	0.176133i	−0.644718	+	0.764420i	$0.723025\pi$
$462$	−13028.2	+	19404.1i	−1.31196	+	1.95403i
$463$	13875.3	−	5554.84i	1.39275	−	0.557571i	0.450585	−	0.892734i	$-0.351215\pi$
$463$	13875.3	−	5554.84i	1.39275	−	0.557571i	0.942160	+	0.335162i	$0.108791\pi$
$464$	−1704.04	−	17845.5i	−0.170492	−	1.78547i
$465$	1113.00	+	6471.55i	0.110998	+	0.645400i
$466$	−20855.6	−	1991.47i	−2.07322	−	0.197968i
$467$	−705.169	−	813.809i	−0.0698744	−	0.0806393i	0.719736	−	0.694248i	$-0.244263\pi$
$467$	−705.169	−	813.809i	−0.0698744	−	0.0806393i	−0.789610	+	0.613608i	$0.789717\pi$
$468$	−22116.3	+	10299.6i	−2.18446	+	1.01730i
$469$	−8626.65	−	2533.01i	−0.849343	−	0.249390i
$470$	−2363.28	−	6828.24i	−0.231936	−	0.670134i
$471$	10101.7	−	3810.58i	0.988244	−	0.372787i
$472$	−1706.17	+	35816.8i	−0.166383	+	3.49280i
$473$	−2048.19	+	10627.0i	−0.199104	+	1.03305i
$474$	20721.9	+	27467.8i	2.00800	+	2.66169i
$475$	−415.502	+	1037.87i	−0.0401358	+	0.100254i
$476$	−6696.01	+	5802.13i	−0.644772	+	0.558698i
$477$	15847.7	+	5353.35i	1.52121	+	0.513864i
$478$	−13450.4	+	3949.39i	−1.28704	+	0.377910i
$479$	−8691.97	−	12206.2i	−0.829116	−	1.16433i	−0.984310	−	0.176446i	$-0.943540\pi$
$479$	−8691.97	−	12206.2i	−0.829116	−	1.16433i	0.155195	−	0.987884i	$-0.450399\pi$
$480$	3829.17	−	14506.1i	0.364119	−	1.37940i
$481$	−3999.76	+	7758.45i	−0.379154	+	0.735457i
$482$	−2953.59	−	5115.77i	−0.279113	−	0.483438i
$483$	−9056.39	−	6847.96i	−0.853168	−	0.645120i
$484$	5667.51	−	9816.42i	0.532261	−	0.921902i
$485$	−8200.42	−	12760.1i	−0.767756	−	1.19465i
$486$	−19144.3	−	3793.38i	−1.78684	−	0.354056i
$487$	6611.22	−	14476.6i	0.615160	−	1.34701i	−0.303828	−	0.952727i	$-0.598265\pi$
$487$	6611.22	−	14476.6i	0.615160	−	1.34701i	0.918988	−	0.394286i	$-0.129008\pi$
$488$	−1610.39	+	6638.11i	−0.149383	+	0.615764i
$489$	6265.74	+	5653.54i	0.579441	+	0.522826i
$490$	2856.79	+	988.746i	0.263381	+	0.0911571i
$491$	6800.16	+	8647.11i	0.625025	+	0.794783i	0.990715	−	0.135953i	$-0.0434096\pi$
$491$	6800.16	+	8647.11i	0.625025	+	0.794783i	−0.365691	+	0.930736i	$0.619167\pi$
$492$	−41541.2	−	17606.6i	−3.80655	−	1.61334i
$493$	3105.58	−	1074.85i	0.283709	−	0.0981925i
$494$	−14779.7	−	9498.36i	−1.34610	−	0.865084i
$495$	13704.7	−	3432.80i	1.24440	−	0.311702i
$496$	9169.79	−	10582.5i	0.830112	−	0.958000i
$497$	−11414.7	+	10883.9i	−1.03022	+	0.982314i
$498$	−17238.2	−	9329.78i	−1.55113	−	0.839513i
$499$	−1989.61	+	5748.59i	−0.178491	+	0.515716i	−0.998386	−	0.0567983i	$-0.981911\pi$
$499$	−1989.61	+	5748.59i	−0.178491	+	0.515716i	0.819895	+	0.572515i	$0.194032\pi$
$500$	13925.1	−	19555.1i	1.24550	−	1.74906i
$501$	−3950.53	+	10713.3i	−0.352289	+	0.955355i
$502$	12707.8	−	9049.22i	1.12984	−	0.804554i
$503$	−1484.81	+	10327.1i	−0.131619	+	0.915428i	0.811826	+	0.583899i	$0.198474\pi$
$503$	−1484.81	+	10327.1i	−0.131619	+	0.915428i	−0.943445	+	0.331529i	$0.892435\pi$
$504$	22102.2	+	18865.8i	1.95340	+	1.66736i
$505$			17749.7i			1.56406i
$506$	20953.3	+	13720.2i	1.84089	+	1.20541i
$507$	−105.807	+	913.734i	−0.00926832	+	0.0800401i
$508$	6197.63	+	3195.10i	0.541290	+	0.279054i
$509$	3237.74	+	8087.48i	0.281946	+	0.704266i	0.999966	+	0.00824406i	$0.00262419\pi$
$509$	3237.74	+	8087.48i	0.281946	+	0.704266i	−0.718020	+	0.696022i	$0.754952\pi$
$510$	7664.63	+	153.947i	0.665481	+	0.0133664i
$511$	15929.1	+	3864.37i	1.37899	+	0.334539i
$512$	22912.7	−	10463.9i	1.97775	−	0.903208i
$513$	−3533.64	−	9160.72i	−0.304121	−	0.788413i
$514$	−564.667	−	3927.35i	−0.0484560	−	0.337019i
$515$	−1077.81	−	1130.38i	−0.0922216	−	0.0967193i
$516$	22567.3	+	7121.64i	1.92533	+	0.607582i
$517$	−5199.61	−	247.688i	−0.442318	−	0.0210702i
$518$	18263.6	+	870.001i	1.54914	+	0.0737947i
$519$	4170.20	−	3819.37i	0.352700	−	0.323029i
$520$	−21689.7	−	22747.5i	−1.82915	−	1.91836i
$521$	868.309	+	6039.22i	0.0730159	+	0.507837i	0.993206	+	0.116366i	$0.0371246\pi$
$521$	868.309	+	6039.22i	0.0730159	+	0.507837i	−0.920190	+	0.391471i	$0.871966\pi$
$522$	−8810.87	−	16783.2i	−0.738776	−	1.40724i
$523$	7852.63	−	3586.18i	0.656542	−	0.299833i	−0.0591494	−	0.998249i	$-0.518839\pi$
$523$	7852.63	−	3586.18i	0.656542	−	0.299833i	0.715692	+	0.698416i	$0.246112\pi$
$524$	−17913.7	−	4345.81i	−1.49344	−	0.362304i
$525$	−793.378	−	1440.21i	−0.0659540	−	0.119725i
$526$	−14053.1	−	35103.0i	−1.16491	−	2.90981i
$527$	2281.61	+	1176.25i	0.188593	+	0.0972266i
$528$	−24184.8	−	17964.6i	−1.99339	−	1.48070i
$529$	−7225.84	+	9788.93i	−0.593888	+	0.804547i
$530$			37899.1i			3.10610i
$531$	5953.28	+	16795.8i	0.486536	+	1.37265i
$532$	−3658.97	+	25448.7i	−0.298189	+	2.07395i
$533$	−18583.0	+	13232.9i	−1.51017	+	1.07539i
$534$	−10138.8	+	1743.71i	−0.821629	+	0.141306i
$535$	4400.25	−	6179.29i	0.355588	−	0.499354i
$536$	8065.05	−	23302.4i	0.649920	−	1.87782i
$537$	9462.66	−	5816.15i	0.760417	−	0.467384i
$538$	25319.0	−	24141.6i	2.02896	−	1.93461i
$539$	1426.20	−	1645.93i	0.113972	−	0.131531i
$540$	−4009.29	−	30630.6i	−0.319504	−	2.44099i
$541$	−2611.72	−	1678.45i	−0.207554	−	0.133387i	0.432735	−	0.901521i	$-0.357549\pi$
$541$	−2611.72	−	1678.45i	−0.207554	−	0.133387i	−0.640288	+	0.768135i	$0.721185\pi$
$542$	28581.0	−	9891.98i	2.26505	−	0.783942i
$543$	272.681	+	2210.86i	0.0215504	+	0.174728i
$544$	−3625.45	−	4610.14i	−0.285735	−	0.363342i
$545$	−22632.6	−	7833.22i	−1.77885	−	0.615666i
$546$	24583.5	−	7959.34i	1.92688	−	0.623862i
$547$	−1797.79	+	7410.59i	−0.140526	+	0.579258i	0.857386	+	0.514674i	$0.172087\pi$
$547$	−1797.79	+	7410.59i	−0.140526	+	0.579258i	−0.997912	+	0.0645836i	$0.979428\pi$
$548$	10235.8	−	22413.4i	0.797907	−	1.74717i
$549$	508.062	+	3356.32i	0.0394965	+	0.260918i
$550$	1960.96	+	3051.31i	0.152028	+	0.236561i
$551$	4768.17	−	8258.70i	0.368658	−	0.638535i
$552$	19942.1	−	23916.6i	1.53767	−	1.84413i
$553$	−12729.9	−	22048.8i	−0.978896	−	1.69550i
$554$	5481.28	−	10632.2i	0.420356	−	0.815376i
$555$	−7844.34	−	7786.23i	−0.599952	−	0.595508i
$556$	26182.2	+	36767.7i	1.99707	+	2.80450i
$557$	9951.10	−	2921.91i	0.756986	−	0.222271i	0.119607	−	0.992821i	$-0.461837\pi$
$557$	9951.10	−	2921.91i	0.756986	−	0.222271i	0.637380	+	0.770550i	$0.280018\pi$
$558$	4738.46	−	14027.4i	0.359489	−	1.06421i
$559$	9042.82	−	7835.65i	0.684205	−	0.592867i
$560$	−11500.5	+	28726.9i	−0.867831	+	2.16774i
$561$	2155.19	−	5085.01i	0.162197	−	0.382690i
$562$	−7308.48	+	37920.0i	−0.548558	+	2.84619i
$563$	−495.684	+	10405.7i	−0.0371058	+	0.778947i	0.901255	+	0.433289i	$0.142647\pi$
$563$	−495.684	+	10405.7i	−0.0371058	+	0.778947i	−0.938361	+	0.345658i	$0.887656\pi$
$564$	−1845.77	+	11231.5i	−0.137803	+	0.838533i
$565$	1352.64	+	3908.20i	0.100719	+	0.291008i
$566$	3507.63	+	1029.93i	0.260489	+	0.0764864i
$567$	13715.6	+	4519.81i	1.01588	+	0.334769i
$568$	−28327.2	−	32691.4i	−2.09258	−	2.41496i
$569$	−3673.96	−	350.821i	−0.270686	−	0.0258474i	−0.0411698	−	0.999152i	$-0.513108\pi$
$569$	−3673.96	−	350.821i	−0.270686	−	0.0258474i	−0.229517	+	0.973305i	$0.573715\pi$
$570$	17101.4	−	14227.4i	1.25667	−	1.04547i
$571$	1149.17	+	12034.7i	0.0842231	+	0.882024i	0.934565	+	0.355793i	$0.115789\pi$
$571$	1149.17	+	12034.7i	0.0842231	+	0.882024i	−0.850342	+	0.526231i	$0.823605\pi$
$572$	−36969.2	+	14800.2i	−2.70238	+	1.08187i
$573$	6635.62	+	13531.8i	0.483781	+	0.986559i
$574$	41384.7	+	23893.4i	3.00934	+	1.73744i
$575$	−1533.42	+	867.942i	−0.111214	+	0.0629490i
$576$	−3705.18	+	3944.18i	−0.268025	+	0.285314i
$577$	−768.689	+	494.007i	−0.0554609	+	0.0356426i	−0.568077	−	0.822975i	$-0.692313\pi$
$577$	−768.689	+	494.007i	−0.0554609	+	0.0356426i	0.512617	+	0.858618i	$0.328676\pi$
$578$	−13794.8	+	17541.5i	−0.992711	+	1.26233i
$579$	391.622	−	215.735i	0.0281092	−	0.0154847i
$580$	20704.9	−	21714.7i	1.48229	−	1.55458i
$581$	11814.4	+	8413.00i	0.843621	+	0.600740i
$582$	2566.62	+	34104.0i	0.182801	+	2.42896i
$583$	25347.5	+	10147.6i	1.80066	+	0.720877i
$584$	−12665.3	+	43134.1i	−0.897423	+	3.05634i
$585$	−14256.1	−	6382.90i	−1.00755	−	0.451112i
$586$	26590.9	−	41376.3i	1.87451	−	2.91679i
$587$	−3027.98	−	5873.47i	−0.212910	−	0.412988i	0.758061	−	0.652183i	$-0.226147\pi$
$587$	−3027.98	−	5873.47i	−0.212910	−	0.412988i	−0.970972	+	0.239195i	$0.923116\pi$
$588$	−3216.33	−	3511.77i	−0.225577	−	0.246297i
$589$	7238.91	−	1756.14i	0.506408	−	0.122853i
$590$	−31735.9	+	24957.4i	−2.21448	+	1.74149i
$591$	−6105.54	+	12688.6i	−0.424955	+	0.883145i
$592$	−2240.35	+	23462.0i	−0.155537	+	1.62885i
$593$	434.298	+	1479.08i	0.0300750	+	0.102426i	0.973163	−	0.230118i	$-0.0739112\pi$
$593$	434.298	+	1479.08i	0.0300750	+	0.102426i	−0.943088	+	0.332544i	$0.892093\pi$
$594$	−30860.2	−	7901.20i	−2.13167	−	0.545774i
$595$	−5614.82	−	807.289i	−0.386866	−	0.0556229i
$596$	1255.93	+	26365.2i	0.0863170	+	1.81202i
$597$	−3983.57	−	9207.78i	−0.273093	−	0.631238i
$598$	−8832.72	−	26243.7i	−0.604008	−	1.79462i
$599$	21672.7	−	12512.8i	1.47834	−	0.853518i	0.478637	−	0.878013i	$-0.341131\pi$
$599$	21672.7	−	12512.8i	1.47834	−	0.853518i	0.999700	+	0.0244951i	$0.00779781\pi$
$600$	4049.04	−	1985.54i	0.275502	−	0.135099i
$601$	−5726.79	−	4503.60i	−0.388686	−	0.305666i	0.404625	−	0.914483i	$-0.367402\pi$
$601$	−5726.79	−	4503.60i	−0.388686	−	0.305666i	−0.793311	+	0.608816i	$0.791645\pi$
$602$	−22799.0	−	10412.0i	−1.54355	−	0.704916i
$603$	−674.071	−	12235.8i	−0.0455229	−	0.826335i
$604$	27308.4	+	59797.1i	1.83967	+	4.02832i
$605$	7125.95	−	1373.41i	0.478861	−	0.0922930i
$606$	19049.7	−	35197.3i	1.27696	−	2.35939i
$607$	−3028.26	−	12482.6i	−0.202493	−	0.834687i	−0.978881	−	0.204432i	$-0.934465\pi$
$607$	−3028.26	−	12482.6i	−0.202493	−	0.834687i	0.776388	−	0.630255i	$-0.217050\pi$
$608$	−16711.4	−	3220.85i	−1.11470	−	0.214840i
$609$	4950.39	+	13123.3i	0.329392	+	0.873207i
$610$	−6836.01	+	3524.21i	−0.453741	+	0.233920i
$611$	4349.45	+	3768.82i	0.287987	+	0.249542i
$612$	−10502.8	−	5960.15i	−0.693713	−	0.393668i
$613$	5997.42	−	862.298i	0.395160	−	0.0568155i	0.0581295	−	0.998309i	$-0.481486\pi$
$613$	5997.42	−	862.298i	0.395160	−	0.0568155i	0.337031	+	0.941494i	$0.390577\pi$
$614$	403.249	+	2092.26i	0.0265046	+	0.137519i
$615$	−8897.75	−	27481.9i	−0.583401	−	1.80192i
$616$	34327.7	+	32731.4i	2.24530	+	2.14089i
$617$	−15878.8	+	1516.25i	−1.03608	+	0.0989332i	−0.599208	−	0.800593i	$-0.704518\pi$
$617$	−15878.8	+	1516.25i	−1.03608	+	0.0989332i	−0.436867	+	0.899526i	$0.643912\pi$
$618$	924.115	+	3398.26i	0.0601511	+	0.221195i
$619$	−10594.0	+	504.654i	−0.687898	+	0.0327686i	−0.388621	−	0.921398i	$-0.627048\pi$
$619$	−10594.0	+	504.654i	−0.687898	+	0.0327686i	−0.299277	+	0.954166i	$0.596745\pi$
$620$	23436.1			1.51809
$621$	4673.52	−	14752.7i	0.302000	−	0.953308i
$622$	14619.2			0.942404
$623$	7603.71	−	362.209i	0.488983	−	0.0232931i
$624$	8740.28	+	32140.8i	0.560723	+	2.06196i
$625$	17288.0	−	1650.80i	1.10643	−	0.105651i
$626$	−17570.1	−	16753.1i	−1.12179	−	1.06963i
$627$	−4936.53	−	15247.2i	−0.314427	−	0.971152i
$628$	−7292.41	−	37836.6i	−0.463374	−	2.40421i
$629$	−4276.64	+	614.888i	−0.271098	+	0.0389780i
$630$	243.251	+	32718.1i	0.0153831	+	2.06908i
$631$	−996.918	−	863.834i	−0.0628949	−	0.0544987i	0.622846	−	0.782344i	$-0.285976\pi$
$631$	−996.918	−	863.834i	−0.0628949	−	0.0544987i	−0.685741	+	0.727846i	$0.740522\pi$
$632$	62064.6	−	31996.5i	3.90633	−	2.01385i
$633$	9802.03	+	25984.8i	0.615475	+	1.63160i
$634$	−13435.7	−	2589.52i	−0.841642	−	0.162213i
$635$	1052.48	+	4338.37i	0.0657737	+	0.271123i
$636$	28416.4	−	52503.9i	1.77167	−	3.27345i
$637$	−2364.32	+	455.686i	−0.147061	+	0.0283437i
$638$	−12852.8	−	28143.8i	−0.797569	−	1.74643i
$639$	−19179.9	−	9708.12i	−1.18739	−	0.601013i
$640$	9858.43	+	4502.19i	0.608888	+	0.278070i
$641$	−14339.2	−	11276.5i	−0.883565	−	0.694843i	0.0695091	−	0.997581i	$-0.477857\pi$
$641$	−14339.2	−	11276.5i	−0.883565	−	0.694843i	−0.953074	+	0.302738i	$0.902099\pi$
$642$	−15357.5	+	7530.88i	−0.944097	+	0.462960i
$643$	20484.7	−	11826.9i	1.25636	−	0.725359i	0.283994	−	0.958826i	$-0.408340\pi$
$643$	20484.7	−	11826.9i	1.25636	−	0.725359i	0.972365	+	0.233467i	$0.0750070\pi$
$644$	−29565.3	+	27712.1i	−1.80906	+	1.69567i
$645$	6015.84	+	13905.3i	0.367246	+	0.848866i
$646$	−413.784	−	8686.40i	−0.0252014	−	0.529043i
$647$	−9277.87	−	1333.96i	−0.563757	−	0.0810560i	−0.145456	−	0.989365i	$-0.546465\pi$
$647$	−9277.87	−	1333.96i	−0.563757	−	0.0810560i	−0.418301	+	0.908309i	$0.637374\pi$
$648$	−14172.0	+	36984.6i	−0.859152	+	2.24212i
$649$	8194.49	+	27907.9i	0.495627	+	1.68795i
$650$	381.183	−	3991.93i	0.0230019	−	0.240887i
$651$	−4750.39	+	9872.30i	−0.285995	+	0.594357i
$652$	23675.9	−	18618.9i	1.42212	−	1.11836i
$653$	6210.89	−	1506.75i	0.372207	−	0.0902964i	−0.0452922	−	0.998974i	$-0.514422\pi$
$653$	6210.89	−	1506.75i	0.372207	−	0.0902964i	0.417499	+	0.908677i	$0.362907\pi$
$654$	36473.0	+	39823.2i	2.18075	+	2.38106i
$655$	−5407.83	−	10489.7i	−0.322598	−	0.625752i
$656$	−33302.4	+	51819.5i	−1.98207	+	3.08416i
$657$	2288.92	+	22223.3i	0.135920	+	1.31965i
$658$	3396.39	−	11567.1i	0.201224	−	0.685305i
$659$	−9997.59	−	4002.43i	−0.590972	−	0.236590i	0.0568480	−	0.998383i	$-0.481895\pi$
$659$	−9997.59	−	4002.43i	−0.590972	−	0.236590i	−0.647820	+	0.761793i	$0.724319\pi$
$660$	−3784.08	−	50280.9i	−0.223174	−	2.96543i
$661$	−8887.41	−	6328.70i	−0.522966	−	0.372402i	0.287876	−	0.957668i	$-0.407051\pi$
$661$	−8887.41	−	6328.70i	−0.522966	−	0.372402i	−0.810842	+	0.585266i	$0.800990\pi$
$662$	−663.261	+	695.608i	−0.0389401	+	0.0408392i
$663$	−5348.22	+	2946.21i	−0.313285	+	0.172581i
$664$	−24589.5	+	31268.0i	−1.43713	+	1.82746i
$665$	−13847.7	+	8899.35i	−0.807502	+	0.518950i
$666$	7198.66	+	23858.8i	0.418833	+	1.38815i
$667$	14000.9	−	5466.80i	0.812767	−	0.317354i
$668$	35292.7	+	20376.2i	2.04418	+	1.18021i
$669$	7063.85	+	14405.1i	0.408228	+	0.832484i
$670$	25775.6	−	10319.0i	1.48626	−	0.595011i
$671$	526.681	+	5515.65i	0.0303015	+	0.317331i
$672$	19242.8	−	16008.8i	1.10462	−	0.918979i
$673$	−18172.0	−	1735.21i	−1.04083	−	0.0993871i	−0.439382	−	0.898300i	$-0.644803\pi$
$673$	−18172.0	−	1735.21i	−1.04083	−	0.0993871i	−0.601447	+	0.798913i	$0.705409\pi$
$674$	943.459	+	1088.81i	0.0539179	+	0.0622246i
$675$	1488.92	−	1675.03i	0.0849018	−	0.0955137i
$676$	3149.93	+	924.904i	0.179218	+	0.0526231i
$677$	−8766.09	−	25328.0i	−0.497649	−	1.43786i	−0.862147	−	0.506658i	$-0.830881\pi$
$677$	−8766.09	−	25328.0i	−0.497649	−	1.43786i	0.364499	−	0.931204i	$-0.381240\pi$
$678$	1512.17	−	9201.58i	0.0856558	−	0.521216i
$679$	1204.13	−	25277.8i	0.0680564	−	1.42868i
$680$	2944.33	−	15276.6i	0.166044	−	0.861518i
$681$	−2315.74	+	5463.80i	−0.130307	+	0.307450i
$682$	8982.05	−	22436.1i	0.504312	−	1.25971i
$683$	5776.18	−	5005.09i	0.323601	−	0.280402i	−0.477876	−	0.878427i	$-0.658593\pi$
$683$	5776.18	−	5005.09i	0.323601	−	0.280402i	0.801477	+	0.598025i	$0.204048\pi$
$684$	−34359.2	+	6887.52i	−1.92070	+	0.385016i
$685$	15136.4	−	4444.46i	0.844282	−	0.247904i
$686$	−17380.7	−	24407.8i	−0.967343	−	1.35844i
$687$	10803.4	+	10723.4i	0.599966	+	0.595522i
$688$	14804.3	−	28716.3i	0.820361	−	1.59128i
$689$	−15093.1	−	26142.1i	−0.834546	−	1.44548i
$690$	35055.6	−	665.253i	1.93412	−	0.0367040i
$691$	9373.39	−	16235.2i	0.516036	−	0.893800i	−0.483791	−	0.875183i	$-0.660741\pi$
$691$	9373.39	−	16235.2i	0.516036	−	0.893800i	0.999827	−	0.0186163i	$-0.00592608\pi$
$692$	−10911.5	−	16978.6i	−0.599410	−	0.932700i
$693$	21947.5	+	8597.70i	1.20306	+	0.471284i
$694$	9618.02	−	21060.5i	0.526073	−	1.15194i
$695$	−6813.09	+	28083.9i	−0.371849	+	1.53278i
$696$	−36597.7	+	11849.2i	−1.99315	+	0.645318i
$697$	−10671.1	−	3693.30i	−0.579909	−	0.200708i
$698$	−3161.62	−	4020.33i	−0.171446	−	0.218011i
$699$	2586.42	+	20970.4i	0.139953	+	1.13472i
$700$	−5545.68	+	1919.38i	−0.299439	+	0.103637i
$701$	−790.724	−	508.168i	−0.0426038	−	0.0273798i	0.519166	−	0.854674i	$-0.326243\pi$
$701$	−790.724	−	508.168i	−0.0426038	−	0.0273798i	−0.561769	+	0.827294i	$0.689879\pi$
$702$	21419.2	+	27957.4i	1.15159	+	1.50311i
$703$	−8210.42	+	9475.33i	−0.440486	+	0.508348i
$704$	−6392.73	+	6095.45i	−0.342237	+	0.326322i
$705$	−6208.34	+	3815.91i	−0.331659	+	0.203851i
$706$	15416.9	−	44544.1i	0.821843	−	2.37456i
$707$	−17177.8	+	24122.8i	−0.913771	+	1.28321i
$708$	62678.4	−	10779.6i	3.32712	−	0.572208i
$709$	−13143.0	+	9359.12i	−0.696188	+	0.495753i	−0.872520	−	0.488578i	$-0.837516\pi$
$709$	−13143.0	+	9359.12i	−0.696188	+	0.495753i	0.176333	+	0.984331i	$0.443577\pi$
$710$	6931.45	−	48209.3i	0.366384	−	2.54826i
$711$	22528.8	−	26393.6i	1.18832	−	1.39218i
$712$			20877.9i			1.09892i
$713$	10637.3	+	4968.13i	0.558722	+	0.260951i
$714$	10267.6	+	7626.87i	0.538175	+	0.399760i
$715$	−22661.2	−	11682.6i	−1.18529	−	0.611057i
$716$	−14733.3	−	36802.0i	−0.769007	−	1.92089i
$717$	6821.62	+	12383.2i	0.355311	+	0.644992i
$718$	−3080.62	−	747.350i	−0.160122	−	0.0388452i
$719$	−12002.3	+	5481.29i	−0.622548	+	0.284308i	−0.701610	−	0.712562i	$-0.747535\pi$
$719$	−12002.3	+	5481.29i	−0.622548	+	0.284308i	0.0790616	+	0.996870i	$0.474808\pi$
$720$	−42141.2	−	1693.53i	−2.18127	−	0.0876583i
$721$	−370.851	−	2579.33i	−0.0191556	−	0.133230i
$722$	6972.52	+	7312.57i	0.359405	+	0.376933i
$723$	−4393.40	+	4023.79i	−0.225992	+	0.206980i
$724$	7941.38	+	378.294i	0.407650	+	0.0194188i
$725$	2174.22	+	103.571i	0.111377	+	0.00530554i
$726$	−15604.6	−	4924.39i	−0.797715	−	0.251737i
$727$	−3746.28	−	3928.99i	−0.191117	−	0.200438i	0.621203	−	0.783650i	$-0.286644\pi$
$727$	−3746.28	−	3928.99i	−0.191117	−	0.200438i	−0.812320	+	0.583212i	$0.801796\pi$
$728$	−7462.94	−	51905.9i	−0.379938	−	2.64253i
$729$	438.970	+	19678.1i	0.0223020	+	0.999751i
$730$	−46043.0	+	21027.1i	−2.33442	+	1.06610i
$731$	5755.73	+	1396.32i	0.291222	+	0.0706497i
$732$	12112.7	+	243.289i	0.611612	+	0.0122844i
$733$	8263.87	+	20642.1i	0.416416	+	1.04016i	0.977224	+	0.212211i	$0.0680663\pi$
$733$	8263.87	+	20642.1i	0.416416	+	1.04016i	−0.560808	+	0.827946i	$0.689509\pi$
$734$	26501.7	+	13662.6i	1.33269	+	0.687051i
$735$	350.701	−	3028.61i	0.0175997	−	0.151989i
$736$	−17392.0	−	20421.3i	−0.871029	−	1.02274i
$737$		−	20002.1i		−	0.999709i
$738$	−11850.6	+	64045.4i	−0.591093	+	3.19450i
$739$	−1631.32	+	11346.1i	−0.0812032	+	0.564780i	0.908083	+	0.418790i	$0.137546\pi$
$739$	−1631.32	+	11346.1i	−0.0812032	+	0.564780i	−0.989286	+	0.145990i	$0.953363\pi$
$740$	−32132.3	+	22881.3i	−1.59623	+	1.13667i
$741$	−6130.26	+	16624.3i	−0.303915	+	0.824171i
$742$	−36677.9	+	51506.9i	−1.81467	+	2.54835i
$743$	6447.68	−	18629.3i	0.318361	−	0.919844i	−0.666348	−	0.745641i	$-0.732144\pi$
$743$	6447.68	−	18629.3i	0.318361	−	0.919844i	0.984710	−	0.174204i	$-0.0557351\pi$
$744$	−26425.6	−	14302.2i	−1.30216	−	0.704763i
$745$	−12230.5	+	11661.7i	−0.601463	+	0.573494i
$746$	25179.3	−	29058.5i	1.23576	−	1.42615i
$747$	−5428.21	+	19008.4i	−0.265874	+	0.931034i
$748$	−16582.1	−	10656.7i	−0.810564	−	0.520918i
$749$	11960.4	−	4139.52i	0.583474	−	0.201942i
$750$	−31908.0	−	13523.7i	−1.55349	−	0.658419i
$751$	3230.61	+	4108.06i	0.156973	+	0.199607i	0.858178	−	0.513352i	$-0.171597\pi$
$751$	3230.61	+	4108.06i	0.156973	+	0.199607i	−0.701205	+	0.712960i	$0.747354\pi$
$752$	14684.9	+	5082.49i	0.712105	+	0.246462i
$753$	−11681.4	−	10540.1i	−0.565331	−	0.510095i
$754$	−8064.53	+	33242.4i	−0.389513	+	1.60559i
$755$	−17483.8	+	38284.3i	−0.842784	+	1.84544i
$756$	24194.8	−	45508.7i	1.16396	−	2.18933i
$757$	706.656	+	1099.58i	0.0339284	+	0.0527937i	0.857804	−	0.513978i	$-0.171829\pi$
$757$	706.656	+	1099.58i	0.0339284	+	0.0527937i	−0.823875	+	0.566771i	$0.808192\pi$
$758$	−468.874	+	812.113i	−0.0224674	+	0.0389146i
$759$	8941.33	−	23623.9i	0.427602	−	1.12977i
$760$	−22572.9	−	39097.5i	−1.07738	−	1.86607i
$761$	14668.3	−	28452.6i	0.698721	−	1.35533i	−0.225790	−	0.974176i	$-0.572496\pi$
$761$	14668.3	−	28452.6i	0.698721	−	1.35533i	0.924512	−	0.381154i	$-0.124473\pi$
$762$	2569.06	−	9732.44i	0.122136	−	0.462689i
$763$	−23178.1	−	32549.0i	−1.09974	−	1.54437i
$764$	51610.3	−	15154.2i	2.44397	−	0.717615i
$765$	−1519.61	−	7580.77i	−0.0718192	−	0.358279i
$766$	−48362.9	+	41906.7i	−2.28123	+	1.97670i
$767$	11951.6	−	29853.8i	0.562645	−	1.40542i
$768$	−19734.8	−	26159.4i	−0.927239	−	1.22910i
$769$	−3772.91	+	19575.7i	−0.176924	+	0.917970i	0.779591	+	0.626289i	$0.215427\pi$
$769$	−3772.91	+	19575.7i	−0.176924	+	0.917970i	−0.956515	+	0.291682i	$0.905785\pi$
$770$	−2541.13	+	53344.9i	−0.118930	+	2.49664i
$771$	−3744.06	+	1412.34i	−0.174888	+	0.0659716i
$772$	−521.917	−	1507.98i	−0.0243319	−	0.0703024i
$773$	19457.6	+	5713.26i	0.905356	+	0.265837i	0.701085	−	0.713078i	$-0.252699\pi$
$773$	19457.6	+	5713.26i	0.905356	+	0.265837i	0.204271	+	0.978914i	$0.434518\pi$
$774$	2994.36	−	34030.2i	0.139057	−	1.58035i
$775$	1113.41	+	1284.94i	0.0516061	+	0.0595567i
$776$	69092.3	+	6597.51i	3.19622	+	0.305202i
$777$	−3125.53	−	18173.5i	−0.144309	−	0.839085i
$778$	5117.67	+	53594.6i	0.235832	+	2.46974i
$779$	−30420.6	+	12178.6i	−1.39914	+	0.560131i
$780$	−31074.9	+	46282.9i	−1.42649	+	2.12461i
$781$	−30387.2	−	17544.1i	−1.39224	−	0.803811i
$782$	8045.49	−	11096.5i	0.367911	−	0.507428i
$783$	−14604.9	+	12335.3i	−0.666586	+	0.562998i
$784$	−5469.35	+	3514.94i	−0.249150	+	0.160119i
$785$	15250.1	−	19392.1i	0.693376	−	0.881699i
$786$	−534.366	+	26604.8i	−0.0242496	+	1.20733i
$787$	14649.2	−	15363.7i	0.663517	−	0.695877i	−0.302851	−	0.953038i	$-0.597939\pi$
$787$	14649.2	−	15363.7i	0.663517	−	0.695877i	0.966369	+	0.257161i	$0.0827870\pi$
$788$	40937.0	+	29151.1i	1.85066	+	1.31785i
$789$	−31501.0	+	21491.7i	−1.42138	+	0.969740i
$790$	72989.8	+	29220.7i	3.28716	+	1.31598i
$791$	−1943.96	+	6620.51i	−0.0873820	+	0.297596i
$792$	−26417.8	+	59004.0i	−1.18525	+	2.64724i
$793$	3311.85	−	5153.34i	0.148307	−	0.230770i
$794$	−28563.7	−	55405.8i	−1.27668	−	2.47642i
$795$	37318.5	−	8263.55i	1.66484	−	0.368651i
$796$	−34796.9	+	8441.64i	−1.54943	+	0.375887i
$797$	−19151.7	+	15061.1i	−0.851176	+	0.669372i	−0.945305	−	0.326188i	$-0.894236\pi$
$797$	−19151.7	+	15061.1i	−0.851176	+	0.669372i	0.0941288	+	0.995560i	$0.469993\pi$
$798$	37010.7	−	2785.38i	1.64181	−	0.123561i
$799$	−270.788	+	2835.82i	−0.0119897	+	0.125562i
$800$	−1094.42	−	3727.24i	−0.0483669	−	0.164723i
$801$	3927.67	+	9603.30i	0.173255	+	0.423615i
$802$	48076.3	+	6912.33i	2.11675	+	0.304343i
$803$	1735.11	+	36424.4i	0.0762523	+	1.60073i
$804$	−43445.5	−	5030.81i	−1.90573	−	0.220675i
$805$	−25804.5	−	2686.66i	−1.12980	−	0.117630i
$806$	−23139.4	+	13359.5i	−1.01123	+	0.583832i
$807$	−29292.3	−	19667.2i	−1.27774	−	0.857893i
$808$	−63843.5	−	50207.1i	−2.77971	−	2.18599i
$809$	−41215.4	−	18822.4i	−1.79117	−	0.818000i	−0.968309	−	0.249757i	$-0.919649\pi$
$809$	−41215.4	−	18822.4i	−1.79117	−	0.818000i	−0.822861	−	0.568243i	$-0.807623\pi$
$810$	−41921.1	+	15210.7i	−1.81847	+	0.659814i
$811$	3979.09	+	8712.98i	0.172287	+	0.377255i	0.976003	−	0.217758i	$-0.0698742\pi$
$811$	3979.09	+	8712.98i	0.172287	+	0.377255i	−0.803716	+	0.595013i	$0.797147\pi$
$812$	49154.1	−	9473.68i	2.12435	−	0.409435i
$813$	−15972.3	−	25986.3i	−0.689018	−	1.12101i
$814$	9590.03	+	39530.6i	0.412937	+	1.70215i
$815$	18935.4	+	3649.51i	0.813840	+	0.156855i
$816$	−10449.8	+	12752.4i	−0.448302	+	0.547086i
$817$	15276.0	−	7875.33i	0.654149	−	0.337237i
$818$	25863.4	+	22410.7i	1.10549	+	0.957913i
$819$	−13197.6	−	22471.4i	−0.563079	−	0.958750i
$820$	−102046.	+	14672.1i	−4.34588	+	0.624843i
$821$	5202.68	+	26994.1i	0.221163	+	1.14750i	0.907446	+	0.420168i	$0.138029\pi$
$821$	5202.68	+	26994.1i	0.221163	+	1.14750i	−0.686283	+	0.727335i	$0.740759\pi$
$822$	−34785.1	−	7431.73i	−1.47600	−	0.315342i
$823$	−10340.2	−	9859.35i	−0.437954	−	0.417588i	0.438757	−	0.898606i	$-0.355419\pi$
$823$	−10340.2	−	9859.35i	−0.437954	−	0.417588i	−0.876711	+	0.481017i	$0.840267\pi$
$824$	7114.55	−	679.357i	0.300785	−	0.0287215i
$825$	2577.00	−	2596.23i	0.108751	−	0.109562i
$826$	−67283.8	+	3205.12i	−2.83427	+	0.135013i
$827$	6652.27			0.279712			0.139856	−	0.990172i	$-0.455336\pi$
$827$	6652.27			0.279712			0.139856	+	0.990172i	$0.455336\pi$
$828$	−49063.4	−	25362.8i	−2.05927	−	1.06451i
$829$	−32865.5			−1.37692			−0.688460	−	0.725274i	$-0.741713\pi$
$829$	−32865.5			−1.37692			−0.688460	+	0.725274i	$0.741713\pi$
$830$	−44737.9	+	2131.13i	−1.87093	+	0.0891236i
$831$	−11664.4	−	3079.05i	−0.486926	−	0.128533i
$832$	9721.43	−	928.284i	0.405084	−	0.0386808i
$833$	−862.578	−	822.466i	−0.0358782	−	0.0342098i
$834$	43650.9	−	48377.7i	1.81236	−	2.00861i
$835$	4937.79	+	25619.7i	0.204646	+	1.06180i
$836$	−56616.1	+	8140.16i	−2.34223	+	0.336762i
$837$	−14845.7	−	1607.31i	−0.613074	−	0.0663762i
$838$	−55205.0	−	47835.4i	−2.27568	−	1.97189i
$839$	6879.59	−	3546.67i	0.283087	−	0.145941i	−0.310836	−	0.950464i	$-0.600609\pi$
$839$	6879.59	−	3546.67i	0.283087	−	0.145941i	0.593922	+	0.804522i	$0.297579\pi$
$840$	65521.3	+	10767.7i	2.69131	+	0.442285i
$841$	5716.35	+	1101.74i	0.234382	+	0.0451735i
$842$	8744.48	+	36045.2i	0.357903	+	1.47530i
$843$	38932.6	−	1071.59i	1.59064	−	0.0437811i
$844$	97327.8	−	18758.4i	3.96938	−	0.765036i
$845$	873.137	+	1911.90i	0.0355465	+	0.0778360i
$846$	16406.4	−	903.829i	0.666741	−	0.0367308i
$847$	11013.7	+	5029.79i	0.446795	+	0.204044i
$848$	−64068.2	−	50383.8i	−2.59447	−	2.04032i
$849$	249.348	−	3678.46i	0.0100796	−	0.148698i
$850$	1719.00	−	992.467i	0.0693662	−	0.0400486i
$851$	−19434.9	+	3573.85i	−0.782865	+	0.143960i
$852$	−45749.5	+	61590.1i	−1.83961	+	2.47657i
$853$	−157.274	−	3301.58i	−0.00631295	−	0.132525i	−0.999824	−	0.0187854i	$-0.994020\pi$
$853$	−157.274	−	3301.58i	−0.00631295	−	0.132525i	0.993511	−	0.113740i	$-0.0362830\pi$
$854$	−12701.1	−	1826.15i	−0.508927	−	0.0731727i
$855$	−17738.2	−	13737.3i	−0.709514	−	0.549481i
$856$	9779.52	+	33306.0i	0.390487	+	1.32988i
$857$	2470.62	−	25873.5i	0.0984771	−	1.03130i	−0.802272	−	0.596959i	$-0.796376\pi$
$857$	2470.62	−	25873.5i	0.0984771	−	1.03130i	0.900749	−	0.434340i	$-0.143018\pi$
$858$	32398.3	+	47487.2i	1.28911	+	1.88950i
$859$	−25737.2	+	20239.9i	−1.02228	+	0.803933i	−0.980762	−	0.195205i	$-0.937463\pi$
$859$	−25737.2	+	20239.9i	−1.02228	+	0.803933i	−0.0415209	+	0.999138i	$0.513220\pi$
$860$	52549.0	−	12748.3i	2.08361	−	0.505479i
$861$	14503.9	−	45960.4i	0.574088	−	1.81919i
$862$	−8701.06	−	16877.7i	−0.343804	−	0.666888i
$863$	−17756.7	+	27630.0i	−0.700401	+	1.08984i	0.290711	+	0.956811i	$0.406108\pi$
$863$	−17756.7	+	27630.0i	−0.700401	+	1.08984i	−0.991112	+	0.133034i	$0.957528\pi$
$864$	29328.2	+	17430.9i	1.15482	+	0.686356i
$865$	3640.42	−	12398.1i	0.143096	−	0.487341i
$866$	−22574.8	−	9037.59i	−0.885823	−	0.354630i
$867$	20280.6	+	9758.68i	0.794423	+	0.382263i
$868$	31850.9	+	22680.9i	1.24549	+	0.886913i
$869$	39086.5	−	40992.8i	1.52580	−	1.60021i
$870$	−37067.9	−	22405.5i	−1.44450	−	0.873123i
$871$	−13670.0	+	17382.8i	−0.531792	+	0.676228i
$872$	92193.9	−	59249.4i	3.58037	−	2.30096i
$873$	33021.9	−	9963.36i	1.28021	−	0.386264i
$874$	−3442.32	−	39623.8i	−0.133224	−	1.53352i
$875$	22207.7	+	12821.6i	0.858009	+	0.495372i
$876$	79552.1	+	5392.53i	3.06828	+	0.207987i
$877$	41899.1	−	16773.9i	1.61326	−	0.645853i	0.622643	−	0.782506i	$-0.286059\pi$
$877$	41899.1	−	16773.9i	1.61326	−	0.645853i	0.990619	+	0.136653i	$0.0436346\pi$
$878$	1717.61	+	17987.6i	0.0660211	+	0.691404i
$879$	−46540.3	−	17161.8i	−1.78585	−	0.658537i
$880$	−68528.5	−	6543.68i	−2.62511	−	0.250668i
$881$	6538.07	+	7545.34i	0.250026	+	0.288546i	0.866864	−	0.498545i	$-0.166132\pi$
$881$	6538.07	+	7545.34i	0.250026	+	0.288546i	−0.616838	+	0.787090i	$0.711587\pi$
$882$	−3945.85	+	5629.29i	−0.150639	+	0.214907i
$883$	−12794.8	−	3756.88i	−0.487631	−	0.143181i	0.0286693	−	0.999589i	$-0.490873\pi$
$883$	−12794.8	−	3756.88i	−0.487631	−	0.143181i	−0.516300	+	0.856408i	$0.672691\pi$
$884$	7127.62	+	20593.9i	0.271185	+	0.783538i
$885$	31494.7	+	25807.9i	1.19625	+	0.980254i
$886$	−2736.90	+	57454.6i	−0.103779	+	2.17858i
$887$	2671.13	−	13859.1i	0.101114	−	0.524627i	−0.895686	−	0.444687i	$-0.853315\pi$
$887$	2671.13	−	13859.1i	0.101114	−	0.524627i	0.996800	−	0.0799404i	$-0.0254730\pi$
$888$	50194.7	−	6190.85i	1.89687	−	0.233954i
$889$	−2768.20	+	6914.63i	−0.104435	+	0.260865i
$890$	−17765.7	+	15394.1i	−0.669111	+	0.579788i
$891$	−1051.36	+	32110.2i	−0.0395309	+	1.20733i
$892$	54941.0	−	16132.1i	2.06229	−	0.605543i
$893$	4795.02	+	6733.66i	0.179685	+	0.252333i
$894$	36768.5	−	9998.74i	1.37553	−	0.374058i
$895$	11629.8	−	22558.7i	0.434348	−	0.842517i
$896$	9041.00	+	15659.5i	0.337097	+	0.583869i
$897$	−23915.7	+	14419.6i	−0.890216	+	0.536741i
$898$	2815.45	−	4876.49i	0.104624	−	0.181215i
$899$	−7840.99	−	12200.8i	−0.290892	−	0.452637i
$900$	−4990.99	−	6250.36i	−0.184851	−	0.231495i
$901$	6207.03	−	13591.5i	0.229507	−	0.502551i
$902$	−25064.0	+	103315.i	−0.925212	+	3.81378i
$903$	−5281.33	+	24720.0i	−0.194631	+	0.910995i
$904$	−17883.4	−	6189.51i	−0.657957	−	0.227721i
$905$	3146.51	+	4001.11i	0.115573	+	0.146963i
$906$	75758.2	−	57152.5i	2.77803	−	2.09577i
$907$	19597.8	−	6782.86i	0.717458	−	0.248315i	0.0561426	−	0.998423i	$-0.482120\pi$
$907$	19597.8	−	6782.86i	0.717458	−	0.248315i	0.661315	+	0.750108i	$0.269999\pi$
$908$	17817.3	+	11450.5i	0.651199	+	0.418500i
$909$	−38811.7	−	11083.4i	−1.41617	−	0.404414i
$910$	38665.9	−	44622.8i	1.40853	−	1.62553i
$911$	−2194.62	+	2092.57i	−0.0798146	+	0.0761031i	−0.728936	−	0.684581i	$-0.759985\pi$
$911$	−2194.62	+	2092.57i	−0.0798146	+	0.0761031i	0.649122	+	0.760684i	$0.275137\pi$
$912$	1316.32	+	47824.1i	0.0477935	+	1.73642i
$913$	−10553.4	+	30492.0i	−0.382548	+	1.10530i
$914$	16292.4	−	22879.4i	0.589610	−	0.827991i
$915$	4960.74	+	5962.86i	0.179232	+	0.215438i
$916$	44253.4	−	31512.7i	1.59626	−	1.13669i
$917$	2802.19	−	19489.7i	0.100912	−	0.701860i
$918$	−5122.61	+	16663.4i	−0.184174	+	0.599101i
$919$			23698.7i			0.850651i	0.905040	+	0.425325i	$0.139840\pi$
$919$			23698.7i			0.850651i	−0.905040	+	0.425325i	$0.860160\pi$
$920$	10727.7	−	70341.6i	0.384436	−	2.52075i
$921$	1972.28	−	853.269i	0.0705633	−	0.0305279i
$922$	15967.4	+	8231.77i	0.570346	+	0.294034i
$923$	14417.9	+	36014.3i	0.514163	+	1.28432i
$924$	43517.9	−	71996.5i	1.54939	−	2.56332i
$925$	−2781.07	−	674.681i	−0.0988552	−	0.0239820i
$926$	−70045.6	+	31988.8i	−2.48579	+	1.13522i
$927$	3144.71	−	1650.92i	0.111419	−	0.0584933i
$928$	4715.78	+	32799.0i	0.166814	+	1.16021i
$929$	2403.20	+	2520.40i	0.0848724	+	0.0890116i	0.764801	−	0.644267i	$-0.222838\pi$
$929$	2403.20	+	2520.40i	0.0848724	+	0.0890116i	−0.679928	+	0.733279i	$0.737989\pi$
$930$	−7314.39	−	33032.0i	−0.257901	−	1.16469i
$931$	−3454.60	−	164.563i	−0.121611	−	0.00579305i
$932$	75325.0	+	3588.17i	2.64738	+	0.126110i
$933$	−3187.57	−	14395.2i	−0.111850	−	0.505121i
$934$	3828.56	+	4015.28i	0.134127	+	0.140668i
$935$	−1795.99	−	12491.4i	−0.0628183	−	0.436911i
$936$	63283.6	−	33222.8i	2.20992	−	1.16017i
$937$	18728.6	−	8553.05i	0.652973	−	0.298203i	−0.0612484	−	0.998123i	$-0.519508\pi$
$937$	18728.6	−	8553.05i	0.652973	−	0.298203i	0.714222	+	0.699920i	$0.246781\pi$
$938$	45016.8	+	10921.0i	1.56701	+	0.380152i
$939$	−12665.4	+	20953.8i	−0.440170	+	0.728222i
$940$	9666.34	+	24145.4i	0.335406	+	0.837803i
$941$	1733.11	+	893.479i	0.0600401	+	0.0309528i	0.487985	−	0.872852i	$-0.337732\pi$
$941$	1733.11	+	893.479i	0.0600401	+	0.0309528i	−0.427945	+	0.903805i	$0.640762\pi$
$942$	−51053.0	+	22087.1i	−1.76581	+	0.763945i
$943$	−49427.5	−	14973.0i	−1.70687	−	0.517062i
$944$		−	86828.1i		−	2.99366i
$945$	32163.8	−	7373.41i	1.10718	−	0.253817i
$946$	7935.50	−	55192.6i	0.272733	−	1.89690i
$947$	−7717.40	+	5495.53i	−0.264817	+	0.188575i	−0.704751	−	0.709455i	$-0.748941\pi$
$947$	−7717.40	+	5495.53i	−0.264817	+	0.188575i	0.439934	+	0.898030i	$0.355002\pi$
$948$	−79207.6	−	95208.3i	−2.71365	−	3.26184i
$949$	23385.6	−	32840.5i	0.799926	−	1.12334i
$950$	1883.88	−	5443.13i	0.0643382	−	0.185893i
$951$	379.683	+	13794.5i	0.0129464	+	0.470366i
$952$	18785.9	−	17912.3i	0.639552	−	0.609812i
$953$	7899.49	−	9116.49i	0.268509	−	0.309876i	−0.605442	−	0.795889i	$-0.707004\pi$
$953$	7899.49	−	9116.49i	0.268509	−	0.309876i	0.873952	+	0.486013i	$0.161549\pi$
$954$	−82870.4	−	23665.2i	−2.81240	−	0.803132i
$955$	28970.9	+	18618.5i	0.981651	+	0.630868i
$956$	47682.9	−	16503.2i	1.61315	−	0.558318i
$957$	−24910.2	+	18792.4i	−0.841413	+	0.634768i
$958$	47724.4	+	60686.5i	1.60950	+	2.04665i
$959$	24872.4	+	8608.44i	0.837511	+	0.289865i
$960$	−2583.53	+	12092.6i	−0.0868575	+	0.406548i
$961$	−4352.70	+	17942.1i	−0.146108	+	0.602265i
$962$	18682.2	−	40908.3i	0.626131	−	1.37104i
$963$	10764.1	+	13480.1i	0.360194	+	0.451081i
$964$	11495.5	+	17887.3i	0.384070	+	0.597625i
$965$	510.827	−	884.779i	0.0170405	−	0.0295151i
$966$	48286.2	+	33021.9i	1.60826	+	1.09986i
$967$	15064.4	+	26092.3i	0.500970	+	0.867705i	0.999999	+	0.00112036i	$0.000356621\pi$
$967$	15064.4	+	26092.3i	0.500970	+	0.867705i	−0.499029	+	0.866585i	$0.666310\pi$
$968$	−15216.6	+	29516.0i	−0.505247	+	0.980042i
$969$	−8463.11	+	2301.43i	−0.280572	+	0.0762980i
$970$	45330.5	+	63657.7i	1.50049	+	2.10714i
$971$	−43925.2	+	12897.6i	−1.45173	+	0.426265i	−0.910112	−	0.414362i	$-0.864005\pi$
$971$	−43925.2	+	12897.6i	−1.45173	+	0.426265i	−0.541614	+	0.840627i	$0.682187\pi$
$972$	69480.7	+	10359.8i	2.29279	+	0.341863i
$973$	−36438.3	+	31574.0i	−1.20057	+	1.04030i
$974$	−30474.8	+	76122.3i	−1.00254	+	2.50423i
$975$	−4013.88	+	495.060i	−0.131843	+	0.0162611i
$976$	3130.27	−	16241.4i	0.102661	−	0.532658i
$977$	−1456.53	+	30576.3i	−0.0476955	+	1.00125i	0.840507	+	0.541800i	$0.182257\pi$
$977$	−1456.53	+	30576.3i	−0.0476955	+	1.00125i	−0.888203	+	0.459451i	$0.848046\pi$
$978$	−33631.7	−	27559.1i	−1.09962	−	0.901066i
$979$	5538.98	+	16003.8i	0.180824	+	0.522456i
$980$	−10440.6	−	3065.64i	−0.340319	−	0.0999267i
$981$	31260.5	−	44597.3i	1.01740	−	1.45146i
$982$	−37115.9	−	42834.1i	−1.20613	−	1.39195i
$983$	−40542.6	−	3871.35i	−1.31547	−	0.125612i	−0.586384	−	0.810033i	$-0.699449\pi$
$983$	−40542.6	−	3871.35i	−1.31547	−	0.125612i	−0.729087	+	0.684421i	$0.760055\pi$
$984$	124017.	+	45731.6i	4.01781	+	1.48158i
$985$	3058.47	+	32029.8i	0.0989351	+	1.03609i
$986$	−15718.9	+	6292.91i	−0.507701	+	0.203253i
$987$	−12130.4	−	822.272i	−0.391201	−	0.0265180i
$988$	54765.6	+	31618.9i	1.76349	+	1.01815i
$989$	26553.6	+	5353.44i	0.853747	+	0.172123i
$990$	−69687.5	+	21026.1i	−2.23719	+	0.675004i
$991$	−46194.0	+	29687.1i	−1.48073	+	0.951606i	−0.483646	+	0.875264i	$0.660688\pi$
$991$	−46194.0	+	29687.1i	−1.48073	+	0.951606i	−0.997082	+	0.0763424i	$0.975676\pi$
$992$	−15999.8	+	20345.4i	−0.512090	+	0.651175i
$993$	829.569	+	501.429i	0.0265112	+	0.0160245i
$994$	56076.0	−	58810.9i	1.78936	−	1.87663i
$995$	−18673.7	−	13297.5i	−0.594971	−	0.423677i
$996$	63576.0	+	30591.7i	2.02257	+	0.973229i
$997$	−7048.24	−	2821.69i	−0.223892	−	0.0896327i	0.257005	−	0.966410i	$-0.417264\pi$
$997$	−7048.24	−	2821.69i	−0.223892	−	0.0896327i	−0.480896	+	0.876777i	$0.659689\pi$
$998$	8829.96	−	30072.1i	0.280068	−	0.953823i
$999$	21923.6	−	12290.6i	0.694328	−	0.389245i

Display

a_p

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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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.o.a.11.5	✓	1400
9.5	odd	6	inner	207.4.o.a.149.5	yes	1400
23.21	odd	22	inner	207.4.o.a.182.5	yes	1400
207.113	even	66	inner	207.4.o.a.113.5	yes	1400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.4.o.a.11.5	✓	1400	1.1	even	1	trivial
207.4.o.a.113.5	yes	1400	207.113	even	66	inner
207.4.o.a.149.5	yes	1400	9.5	odd	6	inner
207.4.o.a.182.5	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.11.5

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