LMFDB - Embedded newform 38.6.e.a.35.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,6,Mod(5,38)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.09458515289$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			35.2
Character	$\chi$	$=$	38.35
Dual form			38.6.e.a.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.06418 - 2.57115i) q^{2} +(0.577036 - 0.210024i) q^{3} +(2.77837 + 15.7569i) q^{4} +(2.13367 - 12.1006i) q^{5} +(-2.30814 - 0.840095i) q^{6} +(-76.5898 - 132.657i) q^{7} +(32.0000 - 55.4256i) q^{8} +(-185.860 + 155.955i) q^{9} +(-37.6505 + 31.5925i) q^{10} +(-240.378 + 416.347i) q^{11} +(4.91255 + 8.50879i) q^{12} +(-644.196 - 234.468i) q^{13} +(-106.397 + 603.410i) q^{14} +(-1.31022 - 7.43062i) q^{15} +(-240.561 + 87.5572i) q^{16} +(-999.534 - 838.709i) q^{17} +970.492 q^{18} +(-158.111 + 1565.60i) q^{19} +196.597 q^{20} +(-72.0563 - 60.4624i) q^{21} +(1807.05 - 657.713i) q^{22} +(-754.517 - 4279.08i) q^{23} +(6.82444 - 38.7033i) q^{24} +(2794.67 + 1017.18i) q^{25} +(1371.08 + 2374.78i) q^{26} +(-149.103 + 258.254i) q^{27} +(1877.48 - 1575.39i) q^{28} +(3611.82 - 3030.68i) q^{29} +(-15.0905 + 26.1375i) q^{30} +(225.148 + 389.967i) q^{31} +(962.245 + 350.229i) q^{32} +(-51.2639 + 290.732i) q^{33} +(906.304 + 5139.91i) q^{34} +(-1768.66 + 643.738i) q^{35} +(-2973.76 - 2495.28i) q^{36} -5230.15 q^{37} +(4509.87 - 4390.75i) q^{38} -420.968 q^{39} +(-602.408 - 505.480i) q^{40} +(253.464 - 92.2535i) q^{41} +(65.3353 + 370.535i) q^{42} +(-1631.13 + 9250.60i) q^{43} +(-7228.20 - 2630.85i) q^{44} +(1490.59 + 2581.78i) q^{45} +(-8690.18 + 15051.8i) q^{46} +(-2066.91 + 1734.35i) q^{47} +(-120.423 + 101.047i) q^{48} +(-3328.50 + 5765.12i) q^{49} +(-5948.04 - 10302.3i) q^{50} +(-752.916 - 274.039i) q^{51} +(1904.68 - 10802.0i) q^{52} +(-4771.68 - 27061.6i) q^{53} +(1120.89 - 407.970i) q^{54} +(4525.17 + 3797.07i) q^{55} -9803.49 q^{56} +(237.577 + 936.614i) q^{57} -18859.6 q^{58} +(21314.0 + 17884.6i) q^{59} +(113.443 - 41.2900i) q^{60} +(-2378.75 - 13490.5i) q^{61} +(312.772 - 1773.82i) q^{62} +(34923.6 + 12711.1i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(-4211.72 + 7294.91i) q^{65} +(904.598 - 759.048i) q^{66} +(-52419.6 + 43985.2i) q^{67} +(10438.4 - 18079.8i) q^{68} +(-1334.09 - 2310.71i) q^{69} +(7074.62 + 2574.95i) q^{70} +(2294.65 - 13013.6i) q^{71} +(2696.39 + 15292.0i) q^{72} +(76895.4 - 27987.6i) q^{73} +(16026.1 + 13447.5i) q^{74} +1826.25 q^{75} +(-25108.3 + 1858.47i) q^{76} +73642.0 q^{77} +(1289.92 + 1082.37i) q^{78} +(-32158.1 + 11704.6i) q^{79} +(546.219 + 3097.76i) q^{80} +(10206.0 - 57881.3i) q^{81} +(-1013.86 - 369.014i) q^{82} +(-21306.5 - 36904.0i) q^{83} +(752.502 - 1303.37i) q^{84} +(-12281.6 + 10305.5i) q^{85} +(28782.8 - 24151.6i) q^{86} +(1447.64 - 2507.38i) q^{87} +(15384.2 + 26646.2i) q^{88} +(-53651.3 - 19527.5i) q^{89} +(2070.71 - 11743.6i) q^{90} +(18234.9 + 103415. i) q^{91} +(65328.8 - 23777.7i) q^{92} +(211.821 + 177.739i) q^{93} +10792.7 q^{94} +(18607.4 + 5253.71i) q^{95} +628.806 q^{96} +(-50106.3 - 42044.2i) q^{97} +(25022.1 - 9107.30i) q^{98} +(-20254.7 - 114870. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 18 q^{3} - 72 q^{6} + 438 q^{7} + 768 q^{8} + 378 q^{9} + 600 q^{11} - 1662 q^{13} - 1776 q^{14} - 1206 q^{15} + 4194 q^{17} - 4368 q^{18} + 9570 q^{19} - 1344 q^{20} + 2430 q^{21} - 5160 q^{22}+ \cdots + 656436 q^{99}+O(q^{100}) $ 24 * q + 18 * q^3 - 72 * q^6 + 438 * q^7 + 768 * q^8 + 378 * q^9 + 600 * q^11 - 1662 * q^13 - 1776 * q^14 - 1206 * q^15 + 4194 * q^17 - 4368 * q^18 + 9570 * q^19 - 1344 * q^20 + 2430 * q^21 - 5160 * q^22 - 1170 * q^23 - 1152 * q^24 + 5940 * q^25 - 1776 * q^26 - 5130 * q^27 + 768 * q^28 - 7554 * q^29 + 294 * q^31 - 45912 * q^33 + 1584 * q^34 + 22116 * q^35 + 6048 * q^36 + 28608 * q^37 - 9528 * q^38 - 38868 * q^39 + 37278 * q^41 - 9720 * q^42 + 13212 * q^43 + 20640 * q^44 - 34344 * q^45 - 29856 * q^46 - 3054 * q^47 - 9216 * q^48 + 1422 * q^49 + 16584 * q^50 + 2352 * q^51 - 1824 * q^52 + 73806 * q^53 + 136944 * q^54 - 41598 * q^55 + 56064 * q^56 + 178248 * q^57 - 52848 * q^58 + 123528 * q^59 + 46944 * q^60 - 149172 * q^61 + 58344 * q^62 - 170124 * q^63 - 49152 * q^64 - 202674 * q^65 - 84840 * q^66 - 313212 * q^67 + 35520 * q^68 - 19938 * q^69 - 88464 * q^70 + 75810 * q^71 + 48384 * q^72 + 172872 * q^73 + 4872 * q^74 + 174960 * q^75 + 31008 * q^76 - 115056 * q^77 + 101304 * q^78 + 158058 * q^79 - 47250 * q^81 - 149112 * q^82 - 148440 * q^83 - 176736 * q^84 - 226752 * q^85 - 57528 * q^86 + 182874 * q^87 - 38400 * q^88 - 322464 * q^89 + 48816 * q^90 - 27264 * q^91 + 88992 * q^92 + 779424 * q^93 + 143712 * q^94 + 634752 * q^95 - 108552 * q^97 - 173544 * q^98 + 656436 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−3.06418	−	2.57115i	−0.541675	−	0.454519i
$2$	−3.06418	−	2.57115i	−0.541675	−	0.454519i
$3$	0.577036	−	0.210024i	0.0370169	−	0.0134730i	−0.323445	−	0.946247i	$-0.604841\pi$
$3$	0.577036	−	0.210024i	0.0370169	−	0.0134730i	0.360462	+	0.932774i	$0.382619\pi$
$4$	2.77837	+	15.7569i	0.0868241	+	0.492404i
$5$	2.13367	−	12.1006i	0.0381682	−	0.216463i	−0.959758	−	0.280828i	$-0.909391\pi$
$5$	2.13367	−	12.1006i	0.0381682	−	0.216463i	0.997926	+	0.0643650i	$0.0205022\pi$
$6$	−2.30814	−	0.840095i	−0.0261749	−	0.00952688i
$7$	−76.5898	−	132.657i	−0.590780	−	1.02326i	−0.994128	−	0.108214i	$-0.965487\pi$
$7$	−76.5898	−	132.657i	−0.590780	−	1.02326i	0.403348	−	0.915047i	$-0.367847\pi$
$8$	32.0000	−	55.4256i	0.176777	−	0.306186i
$9$	−185.860	+	155.955i	−0.764856	+	0.641790i
$10$	−37.6505	+	31.5925i	−0.119061	+	0.0999043i
$11$	−240.378	+	416.347i	−0.598981	+	1.03747i	0.393991	+	0.919114i	$0.371094\pi$
$11$	−240.378	+	416.347i	−0.598981	+	1.03747i	−0.992972	+	0.118351i	$0.962239\pi$
$12$	4.91255	+	8.50879i	0.00984813	+	0.0170575i
$13$	−644.196	−	234.468i	−1.05721	−	0.384792i	−0.245829	−	0.969313i	$-0.579060\pi$
$13$	−644.196	−	234.468i	−1.05721	−	0.384792i	−0.811378	+	0.584522i	$0.801282\pi$
$14$	−106.397	+	603.410i	−0.145081	+	0.822796i
$15$	−1.31022	−	7.43062i	−0.00150354	−	0.00852701i
$16$	−240.561	+	87.5572i	−0.234923	+	0.0855050i
$17$	−999.534	−	838.709i	−0.838833	−	0.703864i	0.118468	−	0.992958i	$-0.462202\pi$
$17$	−999.534	−	838.709i	−0.838833	−	0.703864i	−0.957301	+	0.289093i	$0.906646\pi$
$18$	970.492			0.706010
$19$	−158.111	+	1565.60i	−0.100480	+	0.994939i
$19$	−158.111	+	1565.60i	−0.100480	+	0.994939i
$20$	196.597			0.109901
$21$	−72.0563	−	60.4624i	−0.0356553	−	0.0299183i
$22$	1807.05	−	657.713i	0.796001	−	0.289721i
$23$	−754.517	−	4279.08i	−0.297406	−	1.68667i	−0.657261	−	0.753663i	$-0.728285\pi$
$23$	−754.517	−	4279.08i	−0.297406	−	1.68667i	0.359855	−	0.933008i	$-0.382826\pi$
$24$	6.82444	−	38.7033i	0.00241846	−	0.0137158i
$25$	2794.67	+	1017.18i	0.894293	+	0.325496i
$26$	1371.08	+	2374.78i	0.397767	+	0.688953i
$27$	−149.103	+	258.254i	−0.0393620	+	0.0681769i
$28$	1877.48	−	1575.39i	0.452564	−	0.379746i
$29$	3611.82	−	3030.68i	0.797501	−	0.669183i	−0.150089	−	0.988673i	$-0.547956\pi$
$29$	3611.82	−	3030.68i	0.797501	−	0.669183i	0.947590	+	0.319490i	$0.103512\pi$
$30$	−15.0905	+	26.1375i	−0.00306126	+	0.00530226i
$31$	225.148	+	389.967i	0.0420788	+	0.0728826i	0.886298	−	0.463116i	$-0.153269\pi$
$31$	225.148	+	389.967i	0.0420788	+	0.0728826i	−0.844219	+	0.535998i	$0.819935\pi$
$32$	962.245	+	350.229i	0.166116	+	0.0604612i
$33$	−51.2639	+	290.732i	−0.00819458	+	0.0464738i
$34$	906.304	+	5139.91i	0.134455	+	0.762532i
$35$	−1768.66	+	643.738i	−0.244047	+	0.0888258i
$36$	−2973.76	−	2495.28i	−0.382428	−	0.320895i
$37$	−5230.15			−0.628073			−0.314037	−	0.949411i	$-0.601681\pi$
$37$	−5230.15			−0.628073			−0.314037	+	0.949411i	$0.601681\pi$
$38$	4509.87	−	4390.75i	0.506647	−	0.493264i
$39$	−420.968			−0.0443188
$40$	−602.408	−	505.480i	−0.0595306	−	0.0499521i
$41$	253.464	−	92.2535i	0.0235482	−	0.00857084i	−0.330219	−	0.943904i	$-0.607123\pi$
$41$	253.464	−	92.2535i	0.0235482	−	0.00857084i	0.353767	+	0.935333i	$0.384900\pi$
$42$	65.3353	+	370.535i	0.00571511	+	0.0324120i
$43$	−1631.13	+	9250.60i	−0.134529	+	0.762955i	0.840657	+	0.541568i	$0.182169\pi$
$43$	−1631.13	+	9250.60i	−0.134529	+	0.762955i	−0.975186	+	0.221386i	$0.928942\pi$
$44$	−7228.20	−	2630.85i	−0.562858	−	0.204863i
$45$	1490.59	+	2581.78i	0.109730	+	0.190059i
$46$	−8690.18	+	15051.8i	−0.605528	+	1.04880i
$47$	−2066.91	+	1734.35i	−0.136483	+	0.114523i	−0.708473	−	0.705737i	$-0.750616\pi$
$47$	−2066.91	+	1734.35i	−0.136483	+	0.114523i	0.571991	+	0.820260i	$0.306171\pi$
$48$	−120.423	+	101.047i	−0.00754411	+	0.00633026i
$49$	−3328.50	+	5765.12i	−0.198042	+	0.343019i
$50$	−5948.04	−	10302.3i	−0.336472	−	0.582787i
$51$	−752.916	−	274.039i	−0.0405342	−	0.0147532i
$52$	1904.68	−	10802.0i	0.0976820	−	0.553982i
$53$	−4771.68	−	27061.6i	−0.233336	−	1.32332i	−0.846089	−	0.533041i	$-0.821049\pi$
$53$	−4771.68	−	27061.6i	−0.233336	−	1.32332i	0.612753	−	0.790274i	$-0.290062\pi$
$54$	1120.89	−	407.970i	0.0523091	−	0.0190390i
$55$	4525.17	+	3797.07i	0.201710	+	0.169255i
$56$	−9803.49			−0.417745
$57$	237.577	+	936.614i	0.00968540	+	0.0381833i
$58$	−18859.6			−0.736143
$59$	21314.0	+	17884.6i	0.797140	+	0.668880i	0.947502	−	0.319751i	$-0.103599\pi$
$59$	21314.0	+	17884.6i	0.797140	+	0.668880i	−0.150362	+	0.988631i	$0.548044\pi$
$60$	113.443	−	41.2900i	0.00406819	−	0.00148070i
$61$	−2378.75	−	13490.5i	−0.0818509	−	0.464199i	−0.997992	−	0.0633431i	$-0.979824\pi$
$61$	−2378.75	−	13490.5i	−0.0818509	−	0.464199i	0.916141	−	0.400856i	$-0.131287\pi$
$62$	312.772	−	1773.82i	0.0103335	−	0.0586043i
$63$	34923.6	+	12711.1i	1.10858	+	0.403490i
$64$	−2048.00	−	3547.24i	−0.0625000	−	0.108253i
$65$	−4211.72	+	7294.91i	−0.123645	+	0.214159i
$66$	904.598	−	759.048i	0.0255620	−	0.0214491i
$67$	−52419.6	+	43985.2i	−1.42661	+	1.19707i	−0.478932	+	0.877852i	$0.658976\pi$
$67$	−52419.6	+	43985.2i	−1.42661	+	1.19707i	−0.947681	+	0.319219i	$0.896579\pi$
$68$	10438.4	−	18079.8i	0.273755	−	0.474157i
$69$	−1334.09	−	2310.71i	−0.0337336	−	0.0584283i
$70$	7074.62	+	2574.95i	0.172567	+	0.0628093i
$71$	2294.65	−	13013.6i	0.0540219	−	0.306373i	−0.945810	−	0.324721i	$-0.894730\pi$
$71$	2294.65	−	13013.6i	0.0540219	−	0.306373i	0.999832	+	0.0183479i	$0.00584065\pi$
$72$	2696.39	+	15292.0i	0.0612986	+	0.347642i
$73$	76895.4	−	27987.6i	1.68886	−	0.614694i	0.694377	−	0.719611i	$-0.255680\pi$
$73$	76895.4	−	27987.6i	1.68886	−	0.614694i	0.994481	+	0.104917i	$0.0334578\pi$
$74$	16026.1	+	13447.5i	0.340212	+	0.285471i
$75$	1826.25			0.0374894
$76$	−25108.3	+	1858.47i	−0.498636	+	0.0369080i
$77$	73642.0			1.41546
$78$	1289.92	+	1082.37i	0.0240064	+	0.0201438i
$79$	−32158.1	+	11704.6i	−0.579725	+	0.211003i	−0.615204	−	0.788368i	$-0.710927\pi$
$79$	−32158.1	+	11704.6i	−0.579725	+	0.211003i	0.0354790	+	0.999370i	$0.488704\pi$
$80$	546.219	+	3097.76i	0.00954205	+	0.0541157i
$81$	10206.0	−	57881.3i	0.172840	−	0.980226i
$82$	−1013.86	−	369.014i	−0.0166511	−	0.00606050i
$83$	−21306.5	−	36904.0i	−0.339482	−	0.588001i	0.644853	−	0.764307i	$-0.276919\pi$
$83$	−21306.5	−	36904.0i	−0.339482	−	0.588001i	−0.984335	+	0.176306i	$0.943585\pi$
$84$	752.502	−	1303.37i	0.0116362	−	0.0201544i
$85$	−12281.6	+	10305.5i	−0.184377	+	0.154711i
$86$	28782.8	−	24151.6i	0.419649	−	0.352127i
$87$	1447.64	−	2507.38i	0.0205051	−	0.0355158i
$88$	15384.2	+	26646.2i	0.211772	+	0.366799i
$89$	−53651.3	−	19527.5i	−0.717968	−	0.261319i	−0.0429051	−	0.999079i	$-0.513661\pi$
$89$	−53651.3	−	19527.5i	−0.717968	−	0.261319i	−0.675063	+	0.737760i	$0.735884\pi$
$90$	2070.71	−	11743.6i	0.0269471	−	0.152825i
$91$	18234.9	+	103415.i	0.230834	+	1.30913i
$92$	65328.8	−	23777.7i	0.804702	−	0.292887i
$93$	211.821	+	177.739i	0.00253957	+	0.00213096i
$94$	10792.7			0.125982
$95$	18607.4	+	5253.71i	0.211532	+	0.0597252i
$96$	628.806			0.00696368
$97$	−50106.3	−	42044.2i	−0.540709	−	0.453708i	0.331072	−	0.943606i	$-0.392590\pi$
$97$	−50106.3	−	42044.2i	−0.540709	−	0.453708i	−0.871780	+	0.489897i	$0.837034\pi$
$98$	25022.1	−	9107.30i	0.263183	−	0.0957909i
$99$	−20254.7	−	114870.i	−0.207701	−	1.17793i
$100$	−8262.94	+	46861.4i	−0.0826294	+	0.468614i
$101$	−132973.	−	48398.1i	−1.29706	−	0.472090i	−0.401019	−	0.916070i	$-0.631344\pi$
$101$	−132973.	−	48398.1i	−1.29706	−	0.472090i	−0.896037	+	0.443980i	$0.853566\pi$
$102$	1602.47	+	2775.56i	0.0152507	+	0.0264150i
$103$	−98460.3	+	170538.i	−0.914467	+	1.58390i	−0.106788	+	0.994282i	$0.534057\pi$
$103$	−98460.3	+	170538.i	−0.914467	+	1.58390i	−0.807679	+	0.589622i	$0.799277\pi$
$104$	−33609.8	+	28202.0i	−0.304707	+	0.255680i
$105$	−885.377	+	742.920i	−0.00783710	+	0.00657610i
$106$	−54958.1	+	95190.2i	−0.475080	+	0.822863i
$107$	−22780.8	−	39457.5i	−0.192358	−	0.333173i	0.753674	−	0.657249i	$-0.228280\pi$
$107$	−22780.8	−	39457.5i	−0.192358	−	0.333173i	−0.946031	+	0.324076i	$0.894947\pi$
$108$	−4483.55	−	1631.88i	−0.0369881	−	0.0134626i
$109$	−4381.75	+	24850.1i	−0.0353249	+	0.200338i	−0.997363	−	0.0725788i	$-0.976877\pi$
$109$	−4381.75	+	24850.1i	−0.0353249	+	0.200338i	0.962038	+	0.272916i	$0.0879882\pi$
$110$	−4103.09	−	23269.8i	−0.0323318	−	0.183363i
$111$	−3017.99	+	1098.46i	−0.0232493	+	0.00846205i
$112$	30039.7	+	25206.3i	0.226282	+	0.189873i
$113$	−103039.			−0.759108			−0.379554	−	0.925170i	$-0.623923\pi$
$113$	−103039.			−0.759108			−0.379554	+	0.925170i	$0.623923\pi$
$114$	1680.20	−	3480.80i	0.0121087	−	0.0250851i
$115$	−53389.4			−0.376453
$116$	57789.1	+	48490.8i	0.398750	+	0.334591i
$117$	156297.	−	56887.4i	1.05557	−	0.384195i
$118$	−19326.0	−	109603.i	−0.127772	−	0.724631i
$119$	−34706.8	+	196832.i	−0.224671	+	1.27417i
$120$	−453.774	−	165.160i	−0.00287664	−	0.00104701i
$121$	−35037.6	−	60686.9i	−0.217556	−	0.376818i
$122$	−27397.3	+	47453.5i	−0.166651	+	0.288648i
$123$	126.883	−	106.467i	0.000756205	−	0.000634531i
$124$	−5519.14	+	4631.11i	−0.0322342	+	0.0270477i
$125$	37470.3	−	64900.4i	0.214492	−	0.371512i
$126$	−74329.8	−	128743.i	−0.417096	−	0.722432i
$127$	−85328.3	−	31056.9i	−0.469444	−	0.170864i	0.0964566	−	0.995337i	$-0.469249\pi$
$127$	−85328.3	−	31056.9i	−0.469444	−	0.170864i	−0.565900	+	0.824474i	$0.691471\pi$
$128$	−2845.05	+	16135.1i	−0.0153485	+	0.0870455i
$129$	1001.63	+	5680.50i	0.00529946	+	0.0300547i
$130$	31661.7	−	11523.9i	0.164315	−	0.0598057i
$131$	186743.	+	156696.i	0.950750	+	0.797774i	0.979424	−	0.201815i	$-0.0646840\pi$
$131$	186743.	+	156696.i	0.950750	+	0.797774i	−0.0286739	+	0.999589i	$0.509128\pi$
$132$	−4723.47			−0.0235954
$133$	219798.	−	98934.3i	1.07744	−	0.484973i
$134$	273715.			1.31685
$135$	2806.90	+	2355.27i	0.0132554	+	0.0111226i
$136$	−78471.1	+	28561.1i	−0.363800	+	0.132412i
$137$	−12566.4	−	71267.4i	−0.0572016	−	0.324407i	0.942757	−	0.333480i	$-0.108223\pi$
$137$	−12566.4	−	71267.4i	−0.0572016	−	0.324407i	−0.999959	+	0.00907335i	$0.997112\pi$
$138$	−1853.30	+	10510.6i	−0.00828415	+	0.0469818i
$139$	181189.	+	65947.3i	0.795416	+	0.289508i	0.707586	−	0.706628i	$-0.249784\pi$
$139$	181189.	+	65947.3i	0.795416	+	0.289508i	0.0878304	+	0.996135i	$0.472007\pi$
$140$	−15057.3	−	26080.0i	−0.0649273	−	0.112457i
$141$	−828.430	+	1434.88i	−0.00350920	+	0.00607811i
$142$	−40491.1	+	33976.0i	−0.168515	+	0.141401i
$143$	252471.	−	211848.i	1.03245	−	0.866332i
$144$	31055.7	−	53790.1i	0.124806	−	0.216170i
$145$	−28966.7	−	50171.8i	−0.114414	−	0.198171i
$146$	−307582.	−	111951.i	−1.19420	−	0.434654i
$147$	−709.848	+	4025.75i	−0.00270939	+	0.0153657i
$148$	−14531.3	−	82411.1i	−0.0545319	−	0.309266i
$149$	376875.	−	137171.i	1.39070	−	0.506172i	0.465293	−	0.885157i	$-0.345949\pi$
$149$	376875.	−	137171.i	1.39070	−	0.506172i	0.925403	+	0.378985i	$0.123727\pi$
$150$	−5595.97	−	4695.57i	−0.0203071	−	0.0170396i
$151$	−86535.9			−0.308855			−0.154427	−	0.988004i	$-0.549353\pi$
$151$	−86535.9			−0.308855			−0.154427	+	0.988004i	$0.549353\pi$
$152$	81714.7	+	58862.6i	0.286874	+	0.206648i
$153$	316574.			1.09332
$154$	−225652.	−	189345.i	−0.766722	−	0.643356i
$155$	5199.24	−	1892.37i	0.0173824	−	0.00632669i
$156$	−1169.61	−	6633.17i	−0.00384794	−	0.0218227i
$157$	−77073.9	+	437108.i	−0.249550	+	1.41527i	0.560133	+	0.828403i	$0.310750\pi$
$157$	−77073.9	+	437108.i	−0.249550	+	1.41527i	−0.809683	+	0.586867i	$0.800361\pi$
$158$	128632.	+	46818.3i	0.409928	+	0.149201i
$159$	−8437.01	−	14613.3i	−0.0264664	−	0.0458412i
$160$	6291.10	−	10896.5i	0.0194279	−	0.0336502i
$161$	−509863.	+	427826.i	−1.55020	+	1.30078i
$162$	−180095.	+	151117.i	−0.539155	+	0.452405i
$163$	22388.0	−	38777.1i	0.0660003	−	0.114316i	−0.831137	−	0.556068i	$-0.812310\pi$
$163$	22388.0	−	38777.1i	0.0660003	−	0.114316i	0.897137	+	0.441752i	$0.145643\pi$
$164$	2157.85	+	3737.51i	0.00626486	+	0.0108511i
$165$	3408.66	+	1240.65i	0.00974707	+	0.00354764i
$166$	−29598.7	+	167863.i	−0.0833686	+	0.472807i
$167$	28936.2	+	164105.i	0.0802879	+	0.455335i	0.998274	+	0.0587235i	$0.0187030\pi$
$167$	28936.2	+	164105.i	0.0802879	+	0.455335i	−0.917986	+	0.396612i	$0.870186\pi$
$168$	−5656.97	+	2058.97i	−0.0154636	+	0.00562829i
$169$	75586.7	+	63424.8i	0.203577	+	0.170821i
$170$	64129.9			0.170192
$171$	−214776.	−	315640.i	−0.561690	−	0.825472i
$172$	−150293.			−0.387362
$173$	−177499.	−	148939.i	−0.450901	−	0.378351i	0.388869	−	0.921293i	$-0.372866\pi$
$173$	−177499.	−	148939.i	−0.450901	−	0.378351i	−0.839770	+	0.542942i	$0.817310\pi$
$174$	−10882.7	+	3960.96i	−0.0272497	+	0.00991808i
$175$	−79107.1	−	448639.i	−0.195263	−	1.10739i
$176$	21371.5	−	121204.i	0.0520060	−	0.294940i
$177$	16055.1	+	5843.58i	0.0385195	+	0.0140199i
$178$	114189.	+	197781.i	0.270131	+	0.467880i
$179$	−250114.	+	433210.i	−0.583452	+	1.01057i	0.411615	+	0.911358i	$0.364965\pi$
$179$	−250114.	+	433210.i	−0.583452	+	1.01057i	−0.995066	+	0.0992102i	$0.968368\pi$
$180$	−36539.5	+	30660.3i	−0.0840584	+	0.0705334i
$181$	−578842.	+	485706.i	−1.31330	+	1.10199i	−0.325619	+	0.945501i	$0.605573\pi$
$181$	−578842.	+	485706.i	−1.31330	+	1.10199i	−0.987680	+	0.156488i	$0.949983\pi$
$182$	210021.	−	363768.i	0.469986	−	0.814040i
$183$	−4205.96	−	7284.93i	−0.00928404	−	0.0160804i
$184$	−261315.	−	95110.9i	−0.569010	−	0.207103i
$185$	−11159.4	+	63288.2i	−0.0239724	+	0.135954i
$186$	−192.063	−	1089.25i	−0.000407064	−	0.00230857i
$187$	589460.	−	214546.i	1.23268	−	0.448659i
$188$	−33070.6	−	27749.6i	−0.0682414	−	0.0572613i
$189$	45679.0			0.0930170
$190$	−43508.2	−	63940.7i	−0.0874354	−	0.128497i
$191$	−725976.			−1.43992			−0.719961	−	0.694015i	$-0.755840\pi$
$191$	−725976.			−1.43992			−0.719961	+	0.694015i	$0.755840\pi$
$192$	−1926.77	−	1616.76i	−0.00377205	−	0.00316513i
$193$	669990.	−	243856.i	1.29472	−	0.471239i	0.399445	−	0.916757i	$-0.369203\pi$
$193$	669990.	−	243856.i	1.29472	−	0.471239i	0.895273	+	0.445519i	$0.146981\pi$
$194$	45432.7	+	257662.i	0.0866692	+	0.491525i
$195$	−898.207	+	5093.98i	−0.00169157	+	0.00959336i
$196$	−100088.	−	36429.2i	−0.186099	−	0.0677344i
$197$	−250212.	−	433380.i	−0.459349	−	0.795615i	0.539578	−	0.841936i	$-0.318584\pi$
$197$	−250212.	−	433380.i	−0.459349	−	0.795615i	−0.998927	+	0.0463205i	$0.985250\pi$
$198$	−233285.	+	404061.i	−0.422886	+	0.732460i
$199$	276501.	−	232012.i	0.494953	−	0.415315i	−0.360844	−	0.932626i	$-0.617511\pi$
$199$	276501.	−	232012.i	0.494953	−	0.415315i	0.855797	+	0.517311i	$0.173067\pi$
$200$	145807.	−	122347.i	0.257753	−	0.216280i
$201$	−21010.0	+	36390.4i	−0.0366806	+	0.0635326i
$202$	283013.	+	490193.i	0.488009	+	0.845257i
$203$	−678670.	−	247016.i	−1.15590	−	0.420712i
$204$	2226.13	−	12625.0i	0.00374520	−	0.0212401i
$205$	−575.517	−	3263.92i	−0.000956475	−	0.00542444i
$206$	740179.	−	269403.i	1.21526	−	0.442318i
$207$	807578.	+	677638.i	1.30996	+	1.09919i
$208$	175498.			0.281264
$209$	−613826.	−	442165.i	−0.972029	−	0.700194i
$210$	4623.11			0.00723413
$211$	−476424.	−	399767.i	−0.736695	−	0.618160i	0.195253	−	0.980753i	$-0.437447\pi$
$211$	−476424.	−	399767.i	−0.736695	−	0.618160i	−0.931948	+	0.362593i	$0.881892\pi$
$212$	413150.	−	150374.i	0.631346	−	0.229791i
$213$	−1409.07	−	7991.23i	−0.00212806	−	0.0120688i
$214$	−31646.7	+	179478.i	−0.0472383	+	0.267902i
$215$	108458.	+	39475.4i	0.160016	+	0.0582412i
$216$	9542.59	+	16528.2i	0.0139166	+	0.0241042i
$217$	34488.0	−	59735.0i	0.0497186	−	0.0861152i
$218$	77319.9	−	64879.1i	0.110192	−	0.0924620i
$219$	38493.3	−	32299.7i	0.0542344	−	0.0455081i
$220$	−47257.5	+	81852.5i	−0.0658286	+	0.114018i
$221$	447246.	+	774653.i	0.615979	+	1.06691i
$222$	12071.9	+	4393.83i	0.0164397	+	0.00598357i
$223$	58954.3	−	334347.i	0.0793877	−	0.450230i	−0.919039	−	0.394166i	$-0.871034\pi$
$223$	58954.3	−	334347.i	0.0793877	−	0.450230i	0.998427	−	0.0560646i	$-0.0178553\pi$
$224$	−27237.7	−	154473.i	−0.0362703	−	0.205699i
$225$	−678050.	+	246790.i	−0.892906	+	0.324991i
$226$	315728.	+	264928.i	0.411190	+	0.345029i
$227$	752959.			0.969854			0.484927	−	0.874555i	$-0.338846\pi$
$227$	752959.			0.969854			0.484927	+	0.874555i	$0.338846\pi$
$228$	−14098.1	+	6345.75i	−0.0179607	+	0.00808436i
$229$	813952.			1.02568			0.512838	−	0.858485i	$-0.328594\pi$
$229$	813952.			1.02568			0.512838	+	0.858485i	$0.328594\pi$
$230$	163595.	+	137272.i	0.203915	+	0.171105i
$231$	42494.1	−	15466.6i	0.0523960	−	0.0190706i
$232$	−52398.9	−	297169.i	−0.0639149	−	0.362480i
$233$	−215443.	+	1.22184e6i	−0.259982	+	1.47443i	0.522973	+	0.852349i	$0.324823\pi$
$233$	−215443.	+	1.22184e6i	−0.259982	+	1.47443i	−0.782954	+	0.622079i	$0.786288\pi$
$234$	−625187.	−	227550.i	−0.746398	−	0.271667i
$235$	16576.6	+	28711.5i	0.0195806	+	0.0339146i
$236$	−222587.	+	385533.i	−0.260148	+	0.450590i
$237$	−16098.1	+	13507.9i	−0.0186168	+	0.0156213i
$238$	612433.	−	513892.i	0.700836	−	0.588071i
$239$	719866.	−	1.24684e6i	0.815186	−	1.41194i	−0.0940084	−	0.995571i	$-0.529968\pi$
$239$	719866.	−	1.24684e6i	0.815186	−	1.41194i	0.909194	−	0.416372i	$-0.136699\pi$
$240$	965.792	+	1672.80i	0.00108232	+	0.00187463i
$241$	−1.48011e6	−	538715.i	−1.64154	−	0.597471i	−0.654231	−	0.756295i	$-0.727007\pi$
$241$	−1.48011e6	−	538715.i	−1.64154	−	0.597471i	−0.987307	+	0.158824i	$0.949230\pi$
$242$	−48673.7	+	276042.i	−0.0534264	+	0.302996i
$243$	−18850.5	−	106906.i	−0.0204789	−	0.116141i
$244$	205960.	−	74963.4i	0.221467	−	0.0806074i
$245$	62659.7	+	52577.8i	0.0666919	+	0.0559612i
$246$	−662.534			−0.000698024
$247$	468938.	−	971481.i	0.489072	−	1.01319i
$248$	28818.9			0.0297542
$249$	−20045.3	−	16820.0i	−0.0204887	−	0.0171921i
$250$	−281684.	+	102525.i	−0.285044	+	0.103748i
$251$	−242561.	−	1.37563e6i	−0.243017	−	1.37822i	−0.825053	−	0.565055i	$-0.808855\pi$
$251$	−242561.	−	1.37563e6i	−0.243017	−	1.37822i	0.582036	−	0.813163i	$-0.302256\pi$
$252$	−103258.	+	585604.i	−0.102429	+	0.580902i
$253$	1.96295e6	+	714455.i	1.92800	+	0.701736i
$254$	181609.	+	314556.i	0.176625	+	0.305924i
$255$	−4922.52	+	8526.05i	−0.00474064	+	0.00821103i
$256$	50203.5	−	42125.7i	0.0478778	−	0.0401742i
$257$	−1.10363e6	+	926055.i	−1.04229	+	0.874589i	−0.992262	−	0.124158i	$-0.960377\pi$
$257$	−1.10363e6	+	926055.i	−1.04229	+	0.874589i	−0.0500323	+	0.998748i	$0.515932\pi$
$258$	11536.3	−	19981.4i	0.0107899	−	0.0186886i
$259$	400576.	+	693819.i	0.371053	+	0.642683i
$260$	−126647.	−	46095.7i	−0.116188	−	0.0422890i
$261$	−198643.	+	1.12656e6i	−0.180498	+	1.02366i
$262$	−169325.	−	960289.i	−0.152394	−	0.864269i
$263$	−1.18023e6	+	429567.i	−1.05214	+	0.382949i	−0.809472	−	0.587159i	$-0.800246\pi$
$263$	−1.18023e6	+	429567.i	−1.05214	+	0.382949i	−0.242673	+	0.970108i	$0.578024\pi$
$264$	14473.6	+	12144.8i	0.0127810	+	0.0107246i
$265$	−337643.			−0.295354
$266$	−927875.	−	261982.i	−0.804054	−	0.227021i
$267$	−35059.9			−0.0300977
$268$	−838713.	−	703764.i	−0.713307	−	0.598535i
$269$	930095.	−	338527.i	0.783694	−	0.285241i	0.0809820	−	0.996716i	$-0.474194\pi$
$269$	930095.	−	338527.i	0.783694	−	0.285241i	0.702712	+	0.711474i	$0.251972\pi$
$270$	−2545.09	−	14433.9i	−0.00212468	−	0.0120497i
$271$	−63366.0	+	359366.i	−0.0524123	+	0.297245i	−0.999735	−	0.0230369i	$-0.992666\pi$
$271$	−63366.0	+	359366.i	−0.0524123	+	0.297245i	0.947322	+	0.320282i	$0.103778\pi$
$272$	313884.	+	114245.i	0.257245	+	0.0936296i
$273$	32241.9	+	55844.6i	0.0261827	+	0.0453497i
$274$	−144734.	+	250686.i	−0.116464	+	0.201722i
$275$	−1.09527e6	+	919044.i	−0.873355	+	0.732832i
$276$	32703.1	−	27441.2i	0.0258414	−	0.0216835i
$277$	506546.	−	877364.i	0.396661	−	0.687037i	−0.596651	−	0.802501i	$-0.703502\pi$
$277$	506546.	−	877364.i	0.396661	−	0.687037i	0.993312	+	0.115464i	$0.0368355\pi$
$278$	−385634.	−	667938.i	−0.299270	−	0.518351i
$279$	−102663.	−	37366.4i	−0.0789595	−	0.0287389i
$280$	−20917.4	+	118628.i	−0.0159446	+	0.0904261i
$281$	−200730.	−	1.13840e6i	−0.151652	−	0.860060i	−0.961783	−	0.273812i	$-0.911715\pi$
$281$	−200730.	−	1.13840e6i	−0.151652	−	0.860060i	0.810132	−	0.586248i	$-0.199396\pi$
$282$	6227.75	−	2266.72i	0.00466346	−	0.00169736i
$283$	−113524.	−	95258.0i	−0.0842601	−	0.0707026i	0.599685	−	0.800236i	$-0.295293\pi$
$283$	−113524.	−	95258.0i	−0.0842601	−	0.0707026i	−0.683945	+	0.729534i	$0.739737\pi$
$284$	211429.			0.155550
$285$	11840.5	−	876.412i	0.00863493	−	0.000639140i
$286$	−1.31831e6			−0.953020
$287$	−31650.9	−	26558.3i	−0.0226820	−	0.0190325i
$288$	−233463.	+	84973.5i	−0.165858	+	0.0603674i
$289$	49080.8	+	278351.i	0.0345674	+	0.196042i
$290$	−40240.1	+	228213.i	−0.0280973	+	0.159347i
$291$	−37743.4	−	13737.5i	−0.0261282	−	0.00950988i
$292$	654643.	+	1.13387e6i	0.449311	+	0.778230i
$293$	−513832.	+	889982.i	−0.349665	+	0.605637i	−0.986190	−	0.165619i	$-0.947038\pi$
$293$	−513832.	+	889982.i	−0.349665	+	0.605637i	0.636525	+	0.771256i	$0.280371\pi$
$294$	12525.9	−	10510.5i	0.00845163	−	0.00709176i
$295$	261891.	−	219753.i	0.175213	−	0.147021i
$296$	−167365.	+	289885.i	−0.111029	+	0.192307i
$297$	−71682.1	−	124157.i	−0.0471541	−	0.0816733i
$298$	−1.50750e6	−	548686.i	−0.983371	−	0.357918i
$299$	−517251.	+	2.93348e6i	−0.334598	+	1.89760i
$300$	5074.01	+	28776.1i	0.00325498	+	0.0184599i
$301$	1.35209e6	−	492120.i	0.860179	−	0.313080i
$302$	265161.	+	222497.i	0.167299	+	0.140380i
$303$	−86894.7			−0.0543734
$304$	−99043.9	−	390466.i	−0.0614673	−	0.242326i
$305$	−168319.			−0.103606
$306$	−970040.	−	813960.i	−0.592224	−	0.496935i
$307$	2.45360e6	−	893038.i	1.48579	−	0.540784i	0.533454	−	0.845829i	$-0.320894\pi$
$307$	2.45360e6	−	893038.i	1.48579	−	0.540784i	0.952338	+	0.305045i	$0.0986715\pi$
$308$	204605.	+	1.16037e6i	0.122896	+	0.696980i
$309$	−20998.0	+	119086.i	−0.0125107	+	0.0709518i
$310$	−20797.0	−	7569.47i	−0.0122912	−	0.00447364i
$311$	−794521.	−	1.37615e6i	−0.465805	−	0.806798i	0.533432	−	0.845843i	$-0.320902\pi$
$311$	−794521.	−	1.37615e6i	−0.465805	−	0.806798i	−0.999237	+	0.0390444i	$0.987569\pi$
$312$	−13471.0	+	23332.4i	−0.00783453	+	0.0135698i
$313$	−1.56675e6	+	1.31466e6i	−0.903940	+	0.758496i	−0.970957	−	0.239256i	$-0.923096\pi$
$313$	−1.56675e6	+	1.31466e6i	−0.903940	+	0.758496i	0.0670164	+	0.997752i	$0.478652\pi$
$314$	1.36004e6	−	1.14121e6i	0.778443	−	0.653191i
$315$	228328.	−	395476.i	0.129653	−	0.224566i
$316$	−273775.	−	474193.i	−0.154233	−	0.267139i
$317$	1.81175e6	+	659423.i	1.01263	+	0.368566i	0.794441	−	0.607341i	$-0.207764\pi$
$317$	1.81175e6	+	659423.i	1.01263	+	0.368566i	0.218186	+	0.975907i	$0.429986\pi$
$318$	−11720.6	+	66470.6i	−0.00649951	+	0.0368606i
$319$	393611.	+	2.23228e6i	0.216566	+	1.22821i
$320$	−47293.6	+	17213.5i	−0.0258183	+	0.00939709i
$321$	−21432.3	−	17983.9i	−0.0116093	−	0.00974138i
$322$	2.66232e6			1.43093
$323$	1.47112e6	−	1.43226e6i	0.784588	−	0.763863i
$324$	940388.			0.497674
$325$	−1.56182e6	−	1.31052e6i	−0.820205	−	0.688233i
$326$	−168302.	+	61257.1i	−0.0877095	+	0.0319236i
$327$	2690.69	+	15259.7i	0.00139154	+	0.00789180i
$328$	2997.65	−	17000.5i	0.00153850	−	0.00872525i
$329$	388379.	+	141358.i	0.197818	+	0.0719998i
$330$	−7254.84	−	12565.8i	−0.00366727	−	0.00635190i
$331$	1.33523e6	−	2.31269e6i	0.669865	−	1.16024i	−0.308077	−	0.951362i	$-0.599685\pi$
$331$	1.33523e6	−	2.31269e6i	0.669865	−	1.16024i	0.977942	−	0.208879i	$-0.0669814\pi$
$332$	522296.	−	438258.i	0.260059	−	0.218215i
$333$	972076.	−	815669.i	0.480385	−	0.403091i
$334$	333274.	−	577247.i	0.163469	−	0.283136i
$335$	420403.	+	728159.i	0.204670	+	0.354499i
$336$	22627.9	+	8235.87i	0.0109344	+	0.00397980i
$337$	545463.	−	3.09348e6i	0.261632	−	1.48379i	−0.516825	−	0.856091i	$-0.672886\pi$
$337$	545463.	−	3.09348e6i	0.261632	−	1.48379i	0.778457	−	0.627697i	$-0.216002\pi$
$338$	−68536.5	−	388690.i	−0.0326310	−	0.185059i
$339$	−59456.9	+	21640.6i	−0.0280998	+	0.0102275i
$340$	−196505.	−	164888.i	−0.0921886	−	0.0773554i
$341$	−216482.			−0.100818
$342$	−153446.	+	1.51940e6i	−0.0709397	+	0.702436i
$343$	−1.55477e6			−0.713563
$344$	460524.	+	386426.i	0.209824	+	0.176064i
$345$	−30807.6	+	11213.1i	−0.0139351	+	0.00507196i
$346$	160943.	+	912754.i	0.0722740	+	0.409886i
$347$	−268590.	+	1.52325e6i	−0.119747	+	0.679121i	0.864542	+	0.502560i	$0.167608\pi$
$347$	−268590.	+	1.52325e6i	−0.119747	+	0.679121i	−0.984290	+	0.176561i	$0.943503\pi$
$348$	43530.6	+	15843.9i	0.0192685	+	0.00701314i
$349$	−403020.	−	698051.i	−0.177118	−	0.306778i	0.763774	−	0.645484i	$-0.223344\pi$
$349$	−403020.	−	698051.i	−0.177118	−	0.306778i	−0.940892	+	0.338706i	$0.890011\pi$
$350$	−911119.	+	1.57810e6i	−0.397562	+	0.688598i
$351$	156604.	−	131406.i	0.0678476	−	0.0569309i
$352$	−377119.	+	316440.i	−0.162227	+	0.136124i
$353$	494359.	−	856255.i	0.211157	−	0.365735i	−0.740920	−	0.671593i	$-0.765610\pi$
$353$	494359.	−	856255.i	0.211157	−	0.365735i	0.952077	+	0.305859i	$0.0989435\pi$
$354$	−34171.0	−	59185.9i	−0.0144927	−	0.0251021i
$355$	−152577.	−	55533.3i	−0.0642565	−	0.0233874i
$356$	158630.	−	899634.i	0.0663376	−	0.376219i
$357$	21312.4	+	120869.i	0.00885037	+	0.0501929i
$358$	1.88024e6	−	684352.i	0.775364	−	0.282210i
$359$	1.64490e6	+	1.38023e6i	0.673602	+	0.565219i	0.914129	−	0.405423i	$-0.132876\pi$
$359$	1.64490e6	+	1.38023e6i	0.673602	+	0.565219i	−0.240527	+	0.970642i	$0.577320\pi$
$360$	190796.			0.0775911
$361$	−2.42610e6	−	495078.i	−0.979808	−	0.199943i
$362$	3.02250e6			1.21226
$363$	−32963.7	−	27659.8i	−0.0131301	−	0.0110175i
$364$	−1.57884e6	+	574652.i	−0.624577	+	0.227327i
$365$	−174599.	−	990199.i	−0.0685976	−	0.389037i
$366$	−5842.85	+	33136.5i	−0.00227993	+	0.0129301i
$367$	−1.40860e6	−	512688.i	−0.545911	−	0.198695i	0.0543176	−	0.998524i	$-0.482702\pi$
$367$	−1.40860e6	−	512688.i	−0.545911	−	0.198695i	−0.600229	+	0.799828i	$0.704924\pi$
$368$	556171.	+	963317.i	0.214086	+	0.370808i
$369$	−32721.5	+	56675.3i	−0.0125103	+	0.0216684i
$370$	196918.	−	165234.i	0.0747792	−	0.0627472i
$371$	−3.22446e6	+	2.70564e6i	−1.21625	+	1.02055i
$372$	−2212.10	+	3831.47i	−0.000828795	+	0.00143551i
$373$	1.18696e6	+	2.05588e6i	0.441738	+	0.765112i	0.997819	−	0.0660159i	$-0.0210288\pi$
$373$	1.18696e6	+	2.05588e6i	0.441738	+	0.765112i	−0.556081	+	0.831128i	$0.687695\pi$
$374$	−2.35784e6	−	858183.i	−0.871636	−	0.317250i
$375$	7991.05	−	45319.5i	0.00293444	−	0.0166421i
$376$	29986.0	+	170059.i	0.0109383	+	0.0620341i
$377$	−3.03732e6	+	1.10549e6i	−1.10062	+	0.400593i
$378$	−139969.	−	117448.i	−0.0503850	−	0.0422781i
$379$	−2.68115e6			−0.958789			−0.479394	−	0.877600i	$-0.659144\pi$
$379$	−2.68115e6			−0.958789			−0.479394	+	0.877600i	$0.659144\pi$
$380$	−31084.2	+	307792.i	−0.0110428	+	0.109345i
$381$	−55760.2			−0.0196794
$382$	2.22452e6	+	1.86659e6i	0.779970	+	0.654472i
$383$	−3.08110e6	+	1.12143e6i	−1.07327	+	0.390638i	−0.817398	−	0.576073i	$-0.804584\pi$
$383$	−3.08110e6	+	1.12143e6i	−1.07327	+	0.390638i	−0.255871	+	0.966711i	$0.582362\pi$
$384$	1747.06	+	9908.05i	0.000604615	+	0.00342894i
$385$	157128.	−	891115.i	0.0540257	−	0.306395i
$386$	−2.67996e6	−	975425.i	−0.915503	−	0.333216i
$387$	−1.13952e6	−	1.97370e6i	−0.386761	−	0.669890i
$388$	523273.	−	906336.i	0.176461	−	0.305640i
$389$	2.95632e6	−	2.48065e6i	0.990554	−	0.831173i	0.00490586	−	0.999988i	$-0.498438\pi$
$389$	2.95632e6	−	2.48065e6i	0.990554	−	0.831173i	0.985648	+	0.168815i	$0.0539940\pi$
$390$	15849.7	−	13299.4i	0.00527665	−	0.00442764i
$391$	−2.83473e6	+	4.90990e6i	−0.937714	+	1.62417i
$392$	213024.	+	368968.i	0.0700185	+	0.121276i
$393$	140667.	+	51198.7i	0.0459422	+	0.0167216i
$394$	−347591.	+	1.97129e6i	−0.112805	+	0.639748i
$395$	73018.2	+	414107.i	0.0235471	+	0.133542i
$396$	1.75373e6	−	638305.i	0.561984	−	0.204546i
$397$	434217.	+	364351.i	0.138271	+	0.116023i	0.709300	−	0.704907i	$-0.249011\pi$
$397$	434217.	+	364351.i	0.138271	+	0.116023i	−0.571029	+	0.820930i	$0.693456\pi$
$398$	−1.44379e6			−0.456872
$399$	106053.	−	103251.i	0.0333495	−	0.0324686i
$400$	−761350.			−0.237922
$401$	92996.8	+	78033.5i	0.0288806	+	0.0242337i	0.657114	−	0.753791i	$-0.271777\pi$
$401$	92996.8	+	78033.5i	0.0288806	+	0.0242337i	−0.628233	+	0.778025i	$0.716222\pi$
$402$	157944.	−	57486.8i	0.0487458	−	0.0177420i
$403$	−53604.4	−	304005.i	−0.0164414	−	0.0932435i
$404$	393158.	−	2.22971e6i	0.119843	−	0.679664i
$405$	−678624.	−	246999.i	−0.205585	−	0.0748269i
$406$	1.44445e6	+	2.50186e6i	0.434899	+	0.753267i
$407$	1.25721e6	−	2.17756e6i	0.376204	−	0.651604i
$408$	−39282.1	+	32961.6i	−0.0116827	+	0.00980297i
$409$	−205345.	+	172305.i	−0.0606982	+	0.0509319i	−0.672632	−	0.739977i	$-0.734836\pi$
$409$	−205345.	+	172305.i	−0.0606982	+	0.0509319i	0.611934	+	0.790909i	$0.290392\pi$
$410$	−6628.54	+	11481.0i	−0.00194741	+	0.00337302i
$411$	−22219.1	−	38484.6i	−0.00648817	−	0.0112378i
$412$	−2.96072e6	−	1.07761e6i	−0.859318	−	0.312766i
$413$	740085.	−	4.19723e6i	0.213504	−	1.21084i
$414$	−732252.	−	4.15281e6i	−0.209971	−	1.19081i
$415$	−492022.	+	179082.i	−0.140238	+	0.0510423i
$416$	−537757.	−	451232.i	−0.152354	−	0.127840i
$417$	118403.			0.0333444
$418$	743999.	+	2.93311e6i	0.208272	+	0.821084i
$419$	3.55021e6			0.987914			0.493957	−	0.869486i	$-0.335550\pi$
$419$	3.55021e6			0.987914			0.493957	+	0.869486i	$0.335550\pi$
$420$	−14166.0	−	11886.7i	−0.00391855	−	0.00328805i
$421$	1.16921e6	−	425556.i	0.321504	−	0.117018i	−0.176227	−	0.984350i	$-0.556389\pi$
$421$	1.16921e6	−	425556.i	0.321504	−	0.117018i	0.497730	+	0.867332i	$0.334167\pi$
$422$	431986.	+	2.44992e6i	0.118083	+	0.669684i
$423$	113677.	−	644691.i	0.0308901	−	0.175187i
$424$	−1.65260e6	−	601497.i	−0.446429	−	0.162487i
$425$	−1.94025e6	−	3.36061e6i	−0.521058	−	0.902498i
$426$	−16229.0	+	28109.5i	−0.00433280	+	0.00750462i
$427$	−1.60743e6	+	1.34880e6i	−0.426641	+	0.357995i
$428$	558435.	−	468583.i	0.147354	−	0.123645i
$429$	101192.	−	175269.i	0.0265461	−	0.0459792i
$430$	−230837.	−	399821.i	−0.0602052	−	0.104278i
$431$	5.37437e6	+	1.95611e6i	1.39359	+	0.507225i	0.926269	−	0.376864i	$-0.122997\pi$
$431$	5.37437e6	+	1.95611e6i	1.39359	+	0.507225i	0.467320	+	0.884088i	$0.345220\pi$
$432$	13256.4	−	75180.9i	0.00341757	−	0.0193820i
$433$	1.24548e6	+	7.06349e6i	0.319241	+	1.81051i	0.547388	+	0.836879i	$0.315622\pi$
$433$	1.24548e6	+	7.06349e6i	0.319241	+	1.81051i	−0.228147	+	0.973627i	$0.573267\pi$
$434$	−259265.	+	94364.8i	−0.0660724	+	0.0240484i
$435$	−27252.1	−	22867.2i	−0.00690520	−	0.00579415i
$436$	−403736.			−0.101714
$437$	6.81862e6	−	504700.i	1.70802	−	0.126424i
$438$	−200998.			−0.0500618
$439$	3.80848e6	+	3.19569e6i	0.943170	+	0.791414i	0.978134	−	0.207975i	$-0.0666871\pi$
$439$	3.80848e6	+	3.19569e6i	0.943170	+	0.791414i	−0.0349638	+	0.999389i	$0.511132\pi$
$440$	355261.	−	129304.i	0.0874813	−	0.0318406i
$441$	−280466.	−	1.59060e6i	−0.0686726	−	0.389462i
$442$	621307.	−	3.52361e6i	0.151269	−	0.857891i
$443$	3.33080e6	+	1.21231e6i	0.806380	+	0.293498i	0.712128	−	0.702050i	$-0.247732\pi$
$443$	3.33080e6	+	1.21231e6i	0.806380	+	0.293498i	0.0942524	+	0.995548i	$0.469954\pi$
$444$	−25693.4	−	44502.3i	−0.00618535	−	0.0107133i
$445$	−350769.	+	607549.i	−0.0839694	+	0.145439i
$446$	−1.04030e6	+	872917.i	−0.247641	+	0.207795i
$447$	188661.	−	158306.i	0.0446595	−	0.0374738i
$448$	−313712.	+	543365.i	−0.0738475	+	0.127908i
$449$	−3.58070e6	−	6.20196e6i	−0.838210	−	1.45182i	−0.891390	−	0.453237i	$-0.850269\pi$
$449$	−3.58070e6	−	6.20196e6i	−0.838210	−	1.45182i	0.0531807	−	0.998585i	$-0.483064\pi$
$450$	2.71220e6	+	987160.i	0.631380	+	0.229803i
$451$	−22517.8	+	127705.i	−0.00521296	+	0.0295642i
$452$	−286279.	−	1.62357e6i	−0.0659089	−	0.373788i
$453$	−49934.3	+	18174.6i	−0.0114328	+	0.00416121i
$454$	−2.30720e6	−	1.93597e6i	−0.525346	−	0.440818i
$455$	1.29030e6			0.292187
$456$	59514.9	+	16803.8i	0.0134034	+	0.00378438i
$457$	−4.92309e6			−1.10267			−0.551337	−	0.834283i	$-0.685882\pi$
$457$	−4.92309e6			−1.10267			−0.551337	+	0.834283i	$0.685882\pi$
$458$	−2.49409e6	−	2.09279e6i	−0.555583	−	0.466190i
$459$	365633.	−	133080.i	0.0810054	−	0.0294836i
$460$	−148336.	−	841253.i	−0.0326852	−	0.185367i
$461$	463401.	−	2.62808e6i	0.101556	−	0.575952i	−0.890984	−	0.454034i	$-0.849984\pi$
$461$	463401.	−	2.62808e6i	0.101556	−	0.575952i	0.992540	−	0.121918i	$-0.0389045\pi$
$462$	−169976.	−	61866.3i	−0.0370496	−	0.0134849i
$463$	571854.	+	990480.i	0.123975	+	0.214730i	0.921332	−	0.388778i	$-0.127103\pi$
$463$	571854.	+	990480.i	0.123975	+	0.214730i	−0.797357	+	0.603508i	$0.793769\pi$
$464$	−603507.	+	1.04530e6i	−0.130133	+	0.225397i
$465$	2602.70	−	2183.93i	0.000558203	−	0.000468388i
$466$	3.80168e6	−	3.18999e6i	0.810982	−	0.680495i
$467$	−628262.	+	1.08818e6i	−0.133306	+	0.230892i	−0.924949	−	0.380091i	$-0.875893\pi$
$467$	−628262.	+	1.08818e6i	−0.133306	+	0.230892i	0.791643	+	0.610984i	$0.209226\pi$
$468$	1.33062e6	+	2.30470e6i	0.280828	+	0.486408i
$469$	9.84977e6	+	3.58502e6i	2.06773	+	0.752592i
$470$	23028.0	−	130598.i	0.00480851	−	0.0272704i
$471$	47328.7	+	268414.i	0.00983042	+	0.0557511i
$472$	1.67331e6	−	609035.i	0.345718	−	0.125831i
$473$	−3.45937e6	−	2.90276e6i	−0.710958	−	0.596565i
$474$	84058.4			0.0171844
$475$	−2.03436e6	+	4.21450e6i	−0.413707	+	0.857062i
$476$	−3.19790e6			−0.646915
$477$	5.10725e6	+	4.28549e6i	1.02776	+	0.862392i
$478$	−5.41162e6	+	1.96967e6i	−1.08332	+	0.394297i
$479$	−144125.	−	817376.i	−0.0287013	−	0.162773i	0.967088	−	0.254441i	$-0.0818914\pi$
$479$	−144125.	−	817376.i	−0.0287013	−	0.162773i	−0.995790	+	0.0916676i	$0.970780\pi$
$480$	1341.66	−	7608.95i	0.000265791	−	0.00150738i
$481$	3.36925e6	+	1.22631e6i	0.664003	+	0.241677i
$482$	3.15020e6	+	5.45630e6i	0.617618	+	1.06975i
$483$	−204356.	+	353954.i	−0.0398583	+	0.0690366i
$484$	858892.	−	720696.i	0.166658	−	0.139842i
$485$	−615672.	+	516610.i	−0.118849	+	0.0997260i
$486$	−217111.	+	376047.i	−0.0416957	+	0.0722190i
$487$	−3.18206e6	−	5.51148e6i	−0.607975	−	1.05304i	−0.991574	−	0.129543i	$-0.958649\pi$
$487$	−3.18206e6	−	5.51148e6i	−0.607975	−	1.05304i	0.383599	−	0.923500i	$-0.374684\pi$
$488$	−823841.	−	299854.i	−0.156601	−	0.0569980i
$489$	4774.54	−	27077.8i	0.000902942	−	0.00512084i
$490$	−56815.2	−	322215.i	−0.0106899	−	0.0606256i
$491$	828450.	−	301531.i	0.155082	−	0.0564454i	−0.263313	−	0.964711i	$-0.584815\pi$
$491$	828450.	−	301531.i	0.155082	−	0.0564454i	0.418395	+	0.908265i	$0.362593\pi$
$492$	2030.12	+	1703.47i	0.000378102	+	0.000317266i
$493$	−6.15200e6			−1.13998
$494$	−3.93473e6	+	1.77108e6i	−0.725434	+	0.326528i
$495$	−1.43322e6			−0.262906
$496$	−88306.2	−	74097.7i	−0.0161171	−	0.0135239i
$497$	−1.90209e6	+	692306.i	−0.345415	+	0.125721i
$498$	18175.6	+	103079.i	0.00328410	+	0.0186251i
$499$	−144231.	+	817974.i	−0.0259303	+	0.147058i	−0.995024	−	0.0996345i	$-0.968233\pi$
$499$	−144231.	+	817974.i	−0.0259303	+	0.147058i	0.969094	+	0.246692i	$0.0793437\pi$
$500$	1.12674e6	+	410099.i	0.201557	+	0.0733607i
$501$	51163.2	+	88617.3i	0.00910676	+	0.0157734i
$502$	−2.79371e6	+	4.83884e6i	−0.494790	+	0.857002i
$503$	5.17365e6	−	4.34120e6i	0.911752	−	0.765051i	−0.0606995	−	0.998156i	$-0.519333\pi$
$503$	5.17365e6	−	4.34120e6i	0.911752	−	0.765051i	0.972451	+	0.233105i	$0.0748887\pi$
$504$	1.82208e6	−	1.52890e6i	0.319514	−	0.268104i
$505$	−869367.	+	1.50579e6i	−0.151696	+	0.262745i
$506$	−4.17785e6	−	7.23625e6i	−0.725399	−	1.25643i
$507$	56937.0	+	20723.4i	0.00983727	+	0.00358047i
$508$	252288.	−	1.43080e6i	0.0433748	−	0.245991i
$509$	1.11742e6	+	6.33719e6i	0.191171	+	1.08418i	0.917767	+	0.397118i	$0.129990\pi$
$509$	1.11742e6	+	6.33719e6i	0.191171	+	1.08418i	−0.726597	+	0.687064i	$0.758899\pi$
$510$	37005.2	−	13468.8i	0.00629996	−	0.00229300i
$511$	−9.60217e6	−	8.05718e6i	−1.62674	−	1.36499i
$512$	−262144.			−0.0441942
$513$	−380747.	−	274268.i	−0.0638768	−	0.0460132i
$514$	5.76274e6			0.962103
$515$	1.85354e6	+	1.55530e6i	0.307952	+	0.258403i
$516$	−86724.4	+	31565.1i	−0.0143389	+	0.00521894i
$517$	−225249.	−	1.27745e6i	−0.0370627	−	0.210193i
$518$	556475.	−	3.15593e6i	0.0911216	−	0.516776i
$519$	−133704.	−	48664.3i	−0.0217885	−	0.00793035i
$520$	269550.	+	466874.i	0.0437150	+	0.0757166i
$521$	4.12090e6	−	7.13762e6i	0.665117	−	1.15202i	−0.314136	−	0.949378i	$-0.601715\pi$
$521$	4.12090e6	−	7.13762e6i	0.665117	−	1.15202i	0.979254	−	0.202639i	$-0.0649518\pi$
$522$	3.50524e6	−	2.94125e6i	0.563043	−	0.472449i
$523$	−4.67246e6	+	3.92066e6i	−0.746950	+	0.626766i	−0.934694	−	0.355452i	$-0.884327\pi$
$523$	−4.67246e6	+	3.92066e6i	−0.746950	+	0.626766i	0.187744	+	0.982218i	$0.439882\pi$
$524$	−1.95021e6	+	3.37786e6i	−0.310279	+	0.537419i
$525$	−139872.	−	242266.i	−0.0221480	−	0.0383614i
$526$	4.72090e6	+	1.71827e6i	0.743979	+	0.270786i
$527$	102026.	−	578619.i	0.0160024	−	0.0907541i
$528$	−13123.6	−	74427.4i	−0.00204865	−	0.0116184i
$529$	−1.16930e7	+	4.25591e6i	−1.81672	+	0.661231i
$530$	1.03460e6	+	868132.i	0.159986	+	0.134244i
$531$	−6.75060e6			−1.03898
$532$	2.16958e6	+	3.18846e6i	0.332351	+	0.488430i
$533$	−184911.			−0.0281933
$534$	107430.	+	90144.4i	0.0163032	+	0.0136800i
$535$	−526067.	+	191473.i	−0.0794615	+	0.0289216i
$536$	760483.	+	4.31291e6i	0.114335	+	0.648424i
$537$	−53340.2	+	302507.i	−0.00798213	+	0.0452689i
$538$	−3.72038e6	−	1.35411e6i	−0.554156	−	0.201696i
$539$	−1.60019e6	−	2.77162e6i	−0.237247	−	0.410924i
$540$	−29313.2	+	50771.9i	−0.00432592	+	0.00749271i
$541$	−4.07950e6	+	3.42311e6i	−0.599258	+	0.502837i	−0.891207	−	0.453597i	$-0.850141\pi$
$541$	−4.07950e6	+	3.42311e6i	−0.599258	+	0.502837i	0.291949	+	0.956434i	$0.405696\pi$
$542$	1.11815e6	−	938239.i	0.163494	−	0.137188i
$543$	−232003.	+	401840.i	−0.0337671	+	0.0584863i
$544$	−668057.	−	1.15711e6i	−0.0967869	−	0.167640i
$545$	291353.	+	106044.i	0.0420173	+	0.0152931i
$546$	44790.0	−	254016.i	0.00642982	−	0.0364653i
$547$	−1.80162e6	−	1.02175e7i	−0.257452	−	1.46008i	−0.789700	−	0.613493i	$-0.789764\pi$
$547$	−1.80162e6	−	1.02175e7i	−0.257452	−	1.46008i	0.532248	−	0.846588i	$-0.321347\pi$
$548$	1.08804e6	−	396015.i	0.154773	−	0.0563326i
$549$	2.54603e6	+	2.13637e6i	0.360523	+	0.302514i
$550$	5.71911e6			0.806162
$551$	4.17376e6	+	6.13385e6i	0.585663	+	0.860704i
$552$	−170764.			−0.0238533
$553$	4.01568e6	+	3.36956e6i	0.558401	+	0.468554i
$554$	−3.80798e6	+	1.38599e6i	−0.527133	+	0.191861i
$555$	6852.65	+	38863.3i	0.000944334	+	0.00535559i
$556$	−535717.	+	3.03820e6i	−0.0734935	+	0.416802i
$557$	−7.88396e6	−	2.86953e6i	−1.07673	−	0.391897i	−0.258040	−	0.966134i	$-0.583077\pi$
$557$	−7.88396e6	−	2.86953e6i	−1.07673	−	0.391897i	−0.818689	+	0.574237i	$0.805299\pi$
$558$	218504.	+	378460.i	0.0297080	+	0.0514558i
$559$	3.21974e6	−	5.57675e6i	0.435804	−	0.754835i
$560$	369106.	−	309717.i	0.0497372	−	0.0417345i
$561$	295080.	−	247601.i	0.0395851	−	0.0332159i
$562$	−2.31192e6	+	4.00436e6i	−0.308768	+	0.534802i
$563$	3.90482e6	+	6.76335e6i	0.519195	+	0.899272i	0.999751	+	0.0223081i	$0.00710147\pi$
$563$	3.90482e6	+	6.76335e6i	0.519195	+	0.899272i	−0.480556	+	0.876964i	$0.659565\pi$
$564$	−24911.0	−	9066.87i	−0.00329757	−	0.00120022i
$565$	−219850.	+	1.24683e6i	−0.0289738	+	0.164319i
$566$	102935.	+	583775.i	0.0135059	+	0.0765957i
$567$	−8.46007e6	+	3.07921e6i	−1.10514	+	0.402237i
$568$	−647857.	−	543617.i	−0.0842575	−	0.0707004i
$569$	187804.			0.0243178			0.0121589	−	0.999926i	$-0.496130\pi$
$569$	187804.			0.0243178			0.0121589	+	0.999926i	$0.496130\pi$
$570$	−38534.9	−	27758.3i	−0.00496783	−	0.00357854i
$571$	9.61777e6			1.23448			0.617240	−	0.786775i	$-0.288251\pi$
$571$	9.61777e6			1.23448			0.617240	+	0.786775i	$0.288251\pi$
$572$	4.03953e6	+	3.38957e6i	0.516227	+	0.433166i
$573$	−418914.	+	152472.i	−0.0533014	+	0.0194001i
$574$	28698.7	+	162758.i	0.00363566	+	0.0206188i
$575$	2.24395e6	−	1.27261e7i	0.283037	−	1.60518i
$576$	933851.	+	339894.i	0.117279	+	0.0426862i
$577$	−3.14754e6	−	5.45171e6i	−0.393579	−	0.681699i	0.599339	−	0.800495i	$-0.295430\pi$
$577$	−3.14754e6	−	5.45171e6i	−0.393579	−	0.681699i	−0.992919	+	0.118796i	$0.962097\pi$
$578$	565290.	−	979111.i	0.0703804	−	0.121902i
$579$	335392.	−	281428.i	0.0415774	−	0.0348875i
$580$	710073.	−	595822.i	0.0876461	−	0.0735438i
$581$	−3.26372e6	+	5.65294e6i	−0.401119	+	0.694758i
$582$	80331.5	+	139138.i	0.00983056	+	0.0170270i
$583$	1.24140e7	+	4.51833e6i	1.51266	+	0.550562i
$584$	909420.	−	5.15758e6i	0.110340	−	0.625769i
$585$	−354888.	−	2.01267e6i	−0.0428747	−	0.243155i
$586$	3.86275e6	−	1.40593e6i	0.464678	−	0.169129i
$587$	−1.58144e6	−	1.32699e6i	−0.189434	−	0.158954i	0.543138	−	0.839643i	$-0.317236\pi$
$587$	−1.58144e6	−	1.32699e6i	−0.189434	−	0.158954i	−0.732572	+	0.680689i	$0.761680\pi$
$588$	−65405.6			−0.00780138
$589$	−646131.	+	290833.i	−0.0767418	+	0.0345426i
$590$	−1.36750e6			−0.161732
$591$	−235401.	−	197525.i	−0.0277230	−	0.0232624i
$592$	1.25817e6	−	457937.i	0.147549	−	0.0537034i
$593$	1.22828e6	+	6.96593e6i	0.143437	+	0.813472i	0.968609	+	0.248590i	$0.0799671\pi$
$593$	1.22828e6	+	6.96593e6i	0.143437	+	0.813472i	−0.825172	+	0.564882i	$0.808922\pi$
$594$	−99579.7	+	564745.i	−0.0115799	+	0.0656729i
$595$	2.30774e6	+	839949.i	0.267236	+	0.0972659i
$596$	3.20850e6	+	5.55729e6i	0.369987	+	0.640836i
$597$	110823.	−	191951.i	0.0127261	−	0.0220422i
$598$	9.12736e6	−	7.65876e6i	1.04374	−	0.875801i
$599$	−3.52238e6	+	2.95562e6i	−0.401115	+	0.336575i	−0.820924	−	0.571037i	$-0.806541\pi$
$599$	−3.52238e6	+	2.95562e6i	−0.401115	+	0.336575i	0.419810	+	0.907612i	$0.362097\pi$
$600$	58440.1	−	101221.i	0.00662724	−	0.0114787i
$601$	5.69256e6	+	9.85980e6i	0.642867	+	1.11348i	0.984790	+	0.173750i	$0.0555886\pi$
$601$	5.69256e6	+	9.85980e6i	0.642867	+	1.11348i	−0.341923	+	0.939728i	$0.611078\pi$
$602$	−5.40835e6	−	1.96848e6i	−0.608238	−	0.221381i
$603$	2.88298e6	−	1.63502e7i	0.322885	−	1.83117i
$604$	−240429.	−	1.36354e6i	−0.0268160	−	0.152081i
$605$	−809109.	+	294491.i	−0.0898708	+	0.0327103i
$606$	266261.	+	223419.i	0.0294527	+	0.0247138i
$607$	−2.44402e6			−0.269236			−0.134618	−	0.990898i	$-0.542981\pi$
$607$	−2.44402e6			−0.269236			−0.134618	+	0.990898i	$0.542981\pi$
$608$	−700459.	+	1.45111e6i	−0.0768465	+	0.159200i
$609$	−443496.			−0.0484559
$610$	515761.	+	432775.i	0.0561208	+	0.0470909i
$611$	1.73815e6	−	632634.i	0.188358	−	0.0685567i
$612$	879561.	+	4.98824e6i	0.0949265	+	0.538355i
$613$	2.93447e6	−	1.66422e7i	0.315412	−	1.78879i	−0.254489	−	0.967076i	$-0.581907\pi$
$613$	2.93447e6	−	1.66422e7i	0.315412	−	1.78879i	0.569901	−	0.821713i	$-0.306982\pi$
$614$	−9.81440e6	−	3.57215e6i	−1.05061	−	0.382392i
$615$	−1017.59	−	1762.53i	−0.000108489	−	0.000187909i
$616$	2.35654e6	−	4.08165e6i	0.250221	−	0.433395i
$617$	3.99864e6	−	3.35526e6i	0.422863	−	0.354824i	−0.406388	−	0.913701i	$-0.633212\pi$
$617$	3.99864e6	−	3.35526e6i	0.422863	−	0.354824i	0.829251	+	0.558876i	$0.188767\pi$
$618$	370529.	−	310911.i	0.0390257	−	0.0327465i
$619$	6.42039e6	−	1.11204e7i	0.673496	−	1.16653i	−0.303411	−	0.952860i	$-0.598125\pi$
$619$	6.42039e6	−	1.11204e7i	0.673496	−	1.16653i	0.976906	−	0.213669i	$-0.0685413\pi$
$620$	44263.3	+	76666.3i	0.00462450	+	0.00800987i
$621$	1.21759e6	+	443166.i	0.126699	+	0.0461145i
$622$	−1.10374e6	+	6.25960e6i	−0.114390	+	0.648740i
$623$	1.51868e6	+	8.61285e6i	0.156764	+	0.889051i
$624$	101269.	−	36858.8i	0.0104115	−	0.00378948i
$625$	6.41409e6	+	5.38206e6i	0.656803	+	0.551123i
$626$	8.18100e6			0.834393
$627$	−447064.	−	126227.i	−0.0454152	−	0.0128228i
$628$	−7.10161e6			−0.718551
$629$	5.22772e6	+	4.38658e6i	0.526848	+	0.442078i
$630$	−1.71647e6	+	624742.i	−0.172299	+	0.0627119i
$631$	−175269.	−	994001.i	−0.0175240	−	0.0993834i	0.974791	−	0.223119i	$-0.0716237\pi$
$631$	−175269.	−	994001.i	−0.0175240	−	0.0993834i	−0.992315	+	0.123735i	$0.960513\pi$
$632$	−380325.	+	2.15693e6i	−0.0378758	+	0.214804i
$633$	−358874.	−	130620.i	−0.0355986	−	0.0129568i
$634$	−3.85604e6	−	6.67887e6i	−0.380995	−	0.659902i
$635$	−557871.	+	966261.i	−0.0549034	+	0.0950955i
$636$	206820.	−	173543.i	0.0202745	−	0.0170123i
$637$	3.49594e6	−	2.93345e6i	0.341363	−	0.286437i
$638$	4.53343e6	−	7.85213e6i	0.440936	−	0.763723i
$639$	1.60305e6	+	2.77656e6i	0.155308	+	0.269002i
$640$	189174.	+	68853.8i	0.0182563	+	0.00664474i
$641$	−1.29707e6	+	7.35604e6i	−0.124686	+	0.707130i	0.856808	+	0.515636i	$0.172444\pi$
$641$	−1.29707e6	+	7.35604e6i	−0.124686	+	0.707130i	−0.981494	+	0.191494i	$0.938667\pi$
$642$	19433.3	+	110212.i	0.00186084	+	0.0105533i
$643$	−739571.	+	269182.i	−0.0705428	+	0.0256755i	−0.377051	−	0.926193i	$-0.623062\pi$
$643$	−739571.	+	269182.i	−0.0705428	+	0.0256755i	0.306508	+	0.951868i	$0.400839\pi$
$644$	−8.15781e6	−	6.84521e6i	−0.775102	−	0.650388i
$645$	70874.8			0.00670799
$646$	−8.19033e6	+	606231.i	−0.772183	+	0.0571554i
$647$	−1.35735e7			−1.27477			−0.637383	−	0.770547i	$-0.719983\pi$
$647$	−1.35735e7			−1.27477			−0.637383	+	0.770547i	$0.719983\pi$
$648$	−2.88152e6	−	2.41788e6i	−0.269577	−	0.226202i
$649$	−1.25696e7	+	4.57496e6i	−1.17141	+	0.426359i
$650$	1.41614e6	+	8.03134e6i	0.131469	+	0.745598i
$651$	7355.05	−	41712.6i	0.000680194	−	0.00385757i
$652$	673210.	+	245028.i	0.0620200	+	0.0225734i
$653$	4.32892e6	+	7.49790e6i	0.397280	+	0.688109i	0.993389	−	0.114795i	$-0.0366210\pi$
$653$	4.32892e6	+	7.49790e6i	0.397280	+	0.688109i	−0.596110	+	0.802903i	$0.703288\pi$
$654$	30990.2	−	53676.6i	0.00283322	−	0.00490728i
$655$	2.29457e6	−	1.92537e6i	0.208977	−	0.175352i
$656$	−52896.3	+	44385.3i	−0.00479916	+	0.00402698i
$657$	−9.92696e6	+	1.71940e7i	−0.897228	+	1.55404i
$658$	−826608.	−	1.43173e6i	−0.0744277	−	0.128913i
$659$	7.47424e6	+	2.72040e6i	0.670430	+	0.244017i	0.654733	−	0.755860i	$-0.272781\pi$
$659$	7.47424e6	+	2.72040e6i	0.670430	+	0.244017i	0.0156972	+	0.999877i	$0.495003\pi$
$660$	−10078.3	+	57157.0i	−0.000900593	+	0.00510752i
$661$	2.23111e6	+	1.26532e7i	0.198617	+	1.12641i	0.907172	+	0.420759i	$0.138236\pi$
$661$	2.23111e6	+	1.26532e7i	0.198617	+	1.12641i	−0.708555	+	0.705656i	$0.750653\pi$
$662$	−1.00377e7	+	3.65341e6i	−0.890201	+	0.324007i
$663$	420772.	+	353070.i	0.0371761	+	0.0311944i
$664$	−2.72723e6			−0.240050
$665$	−728191.	−	2.87079e6i	−0.0638545	−	0.251737i
$666$	−5.07582e6			−0.443426
$667$	−1.56937e7	−	1.31686e7i	−1.36587	−	1.14610i
$668$	−2.50540e6	+	911891.i	−0.217238	+	0.0790682i
$669$	−36202.0	−	205312.i	−0.00312728	−	0.0177357i
$670$	584018.	−	3.31213e6i	0.0502619	−	0.285050i
$671$	6.18854e6	+	2.25244e6i	0.530618	+	0.193129i
$672$	−48160.2	−	83415.8i	−0.00411400	−	0.00712566i
$673$	1.16010e7	−	2.00934e7i	0.987316	−	1.71008i	0.356160	−	0.934425i	$-0.384086\pi$
$673$	1.16010e7	−	2.00934e7i	0.987316	−	1.71008i	0.631155	−	0.775656i	$-0.282581\pi$
$674$	−9.62519e6	+	8.07649e6i	−0.816130	+	0.684815i
$675$	−679382.	+	570070.i	−0.0573925	+	0.0481580i
$676$	−789372.	+	1.36723e6i	−0.0664377	+	0.115074i
$677$	−6.33898e6	−	1.09794e7i	−0.531554	−	0.920679i	−0.999322	−	0.0368271i	$-0.988275\pi$
$677$	−6.33898e6	−	1.09794e7i	−0.531554	−	0.920679i	0.467768	−	0.883851i	$-0.345058\pi$
$678$	237828.	+	86562.2i	0.0198696	+	0.00723193i
$679$	−1.73984e6	+	9.86714e6i	−0.144822	+	0.821328i
$680$	178177.	+	1.01049e6i	0.0147767	+	0.0838030i
$681$	434484.	−	158139.i	0.0359010	−	0.0130669i
$682$	663340.	+	556608.i	0.0546104	+	0.0458235i
$683$	−1.59744e6			−0.131031			−0.0655153	−	0.997852i	$-0.520869\pi$
$683$	−1.59744e6			−0.131031			−0.0655153	+	0.997852i	$0.520869\pi$
$684$	4.37679e6	−	4.26118e6i	0.357697	−	0.348249i
$685$	−889193.			−0.0724052
$686$	4.76411e6	+	3.99756e6i	0.386519	+	0.324328i
$687$	469680.	−	170949.i	0.0379673	−	0.0138190i
$688$	−417569.	−	2.36815e6i	−0.0336324	−	0.190739i
$689$	−3.27118e6	+	1.85518e7i	−0.262516	+	1.48880i
$690$	123230.	+	44852.2i	0.00985361	+	0.00358642i
$691$	−2.35943e6	−	4.08666e6i	−0.187980	−	0.325592i	0.756596	−	0.653882i	$-0.226861\pi$
$691$	−2.35943e6	−	4.08666e6i	−0.187980	−	0.325592i	−0.944577	+	0.328291i	$0.893527\pi$
$692$	1.85367e6	−	3.21065e6i	0.147152	−	0.254875i
$693$	−1.36871e7	+	1.14848e7i	−1.08263	+	0.908431i
$694$	4.73951e6	−	3.97692e6i	0.373538	−	0.313435i
$695$	1.18460e6	−	2.05179e6i	0.0930272	−	0.161128i
$696$	−92648.7	−	160472.i	−0.00724963	−	0.0125567i
$697$	−330720.	−	120372.i	−0.0257857	−	0.00938523i
$698$	−559870.	+	3.17518e6i	−0.0434959	+	0.246677i
$699$	132297.	+	750292.i	0.0102413	+	0.0580815i
$700$	6.84937e6	−	2.49297e6i	0.528331	−	0.192297i
$701$	−7.98995e6	−	6.70436e6i	−0.614114	−	0.515303i	0.281833	−	0.959463i	$-0.409058\pi$
$701$	−7.98995e6	−	6.70436e6i	−0.614114	−	0.515303i	−0.895947	+	0.444161i	$0.853502\pi$
$702$	−817728.			−0.0626276
$703$	826947.	−	8.18832e6i	0.0631087	−	0.624894i
$704$	1.96918e6			0.149745
$705$	15595.4	+	13086.1i	0.00118174	+	0.000991601i
$706$	−3.71636e6	+	1.35265e6i	−0.280612	+	0.102134i
$707$	3.76398e6	+	2.13466e7i	0.283204	+	1.60613i
$708$	−47469.8	+	269215.i	−0.00355905	+	0.0201844i
$709$	−5.42513e6	−	1.97458e6i	−0.405316	−	0.147523i	0.131313	−	0.991341i	$-0.458081\pi$
$709$	−5.42513e6	−	1.97458e6i	−0.405316	−	0.147523i	−0.536630	+	0.843818i	$0.680303\pi$
$710$	324737.	+	562461.i	0.0241761	+	0.0418742i
$711$	4.15151e6	−	7.19063e6i	0.307987	−	0.533449i
$712$	−2.79916e6	+	2.34878e6i	−0.206932	+	0.173637i
$713$	1.49882e6	−	1.25766e6i	0.110415	−	0.0926488i
$714$	245466.	−	425160.i	0.0180196	−	0.0312109i
$715$	−2.02481e6	−	3.50707e6i	−0.148122	−	0.256554i
$716$	−7.52096e6	−	2.73741e6i	−0.548265	−	0.199552i
$717$	153521.	−	870662.i	0.0111525	−	0.0632487i
$718$	−1.49147e6	−	8.45857e6i	−0.107970	−	0.612330i
$719$	−8.45336e6	+	3.07677e6i	−0.609828	+	0.221959i	−0.628428	−	0.777868i	$-0.716301\pi$
$719$	−8.45336e6	+	3.07677e6i	−0.609828	+	0.221959i	0.0186002	+	0.999827i	$0.494079\pi$
$720$	−584632.	−	490564.i	−0.0420292	−	0.0352667i
$721$	3.01642e7			2.16100
$722$	6.16108e6	+	7.75488e6i	0.439860	+	0.553646i
$723$	−967218.			−0.0688143
$724$	−9.26147e6	−	7.77130e6i	−0.656650	−	0.550994i
$725$	1.31766e7	−	4.79588e6i	0.931016	−	0.338862i
$726$	29889.0	+	169509.i	0.00210460	+	0.0119358i
$727$	−1.32834e6	+	7.53340e6i	−0.0932124	+	0.528634i	0.902068	+	0.431594i	$0.142049\pi$
$727$	−1.32834e6	+	7.53340e6i	−0.0932124	+	0.528634i	−0.995280	+	0.0970399i	$0.969063\pi$
$728$	6.31538e6	+	2.29861e6i	0.441642	+	0.160745i
$729$	7.10774e6	+	1.23110e7i	0.495351	+	0.857973i
$730$	−2.01095e6	+	3.48307e6i	−0.139667	+	0.241910i
$731$	9.38893e6	−	7.87825e6i	0.649864	−	0.545301i
$732$	103102.	−	86513.1i	0.00711199	−	0.00596766i
$733$	4.97455e6	−	8.61618e6i	0.341975	−	0.592318i	−0.642825	−	0.766013i	$-0.722238\pi$
$733$	4.97455e6	−	8.61618e6i	0.341975	−	0.592318i	0.984799	+	0.173696i	$0.0555709\pi$
$734$	2.99800e6	+	5.19269e6i	0.205396	+	0.355756i
$735$	47199.5	+	17179.2i	0.00322269	+	0.00117296i
$736$	772625.	−	4.38177e6i	0.0525744	−	0.298164i
$737$	−5.71260e6	−	3.23978e7i	−0.387405	−	2.19708i
$738$	245985.	−	89531.3i	0.0166252	−	0.00605109i
$739$	−1.67771e6	−	1.40776e6i	−0.113007	−	0.0948241i	0.584533	−	0.811370i	$-0.301278\pi$
$739$	−1.67771e6	−	1.40776e6i	−0.113007	−	0.0948241i	−0.697540	+	0.716546i	$0.745722\pi$
$740$	−1.02823e6			−0.0690258
$741$	66559.9	−	659068.i	0.00445315	−	0.0440945i
$742$	1.68369e7			1.12267
$743$	3.22994e6	+	2.71024e6i	0.214646	+	0.180109i	0.743771	−	0.668435i	$-0.233035\pi$
$743$	3.22994e6	+	2.71024e6i	0.214646	+	0.180109i	−0.529125	+	0.848544i	$0.677480\pi$
$744$	16629.5	−	6052.66i	0.00110141	−	0.000400879i
$745$	−855734.	−	4.85311e6i	−0.0564870	−	0.320353i
$746$	1.64891e6	−	9.35143e6i	0.108480	−	0.615221i
$747$	9.71539e6	+	3.53611e6i	0.637028	+	0.231859i
$748$	5.01832e6	+	8.69199e6i	0.327948	+	0.568022i
$749$	−3.48955e6	+	6.04408e6i	−0.227282	+	0.393664i
$750$	−141009.	+	118321.i	−0.00915365	+	0.00768083i
$751$	9.89038e6	−	8.29902e6i	0.639902	−	0.536941i	−0.264086	−	0.964499i	$-0.585070\pi$
$751$	9.89038e6	−	8.29902e6i	0.639902	−	0.536941i	0.903988	+	0.427558i	$0.140626\pi$
$752$	345365.	−	598190.i	0.0222707	−	0.0385740i
$753$	−428882.	−	742845.i	−0.0275645	−	0.0477431i
$754$	1.21493e7	+	4.42198e6i	0.778255	+	0.283262i
$755$	−184639.	+	1.04714e6i	−0.0117884	+	0.0668555i
$756$	126913.	+	719761.i	0.00807612	+	0.0458020i
$757$	−1.04315e7	+	3.79674e6i	−0.661615	+	0.240808i	−0.650934	−	0.759135i	$-0.725622\pi$
$757$	−1.04315e7	+	3.79674e6i	−0.661615	+	0.240808i	−0.0106817	+	0.999943i	$0.503400\pi$
$758$	8.21552e6	+	6.89364e6i	0.519352	+	0.435788i
$759$	1.28274e6			0.0808231
$760$	886626.	−	863207.i	0.0556810	−	0.0542102i
$761$	−4.78027e6			−0.299220			−0.149610	−	0.988745i	$-0.547802\pi$
$761$	−4.78027e6			−0.299220			−0.149610	+	0.988745i	$0.547802\pi$
$762$	170859.	+	143368.i	0.0106598	+	0.00894466i
$763$	3.63215e6	−	1.32200e6i	0.225867	−	0.0822088i
$764$	−2.01703e6	−	1.14391e7i	−0.125020	−	0.709023i
$765$	675464.	−	3.83075e6i	0.0417300	−	0.236663i
$766$	1.23244e7	+	4.48571e6i	0.758916	+	0.276223i
$767$	−9.53703e6	−	1.65186e7i	−0.585362	−	1.01388i
$768$	20121.8	−	34852.0i	0.00123102	−	0.00213218i
$769$	6.00903e6	−	5.04217e6i	0.366428	−	0.307469i	−0.440919	−	0.897547i	$-0.645347\pi$
$769$	6.00903e6	−	5.04217e6i	0.366428	−	0.307469i	0.807347	+	0.590078i	$0.200903\pi$
$770$	−2.77266e6	+	2.32654e6i	−0.168527	+	0.141411i
$771$	−442340.	+	766156.i	−0.0267991	+	0.0464174i
$772$	5.70391e6	+	9.87946e6i	0.344452	+	0.596609i
$773$	−2.94584e7	−	1.07220e7i	−1.77321	−	0.645396i	−0.999936	−	0.0113271i	$-0.996394\pi$
$773$	−2.94584e7	−	1.07220e7i	−1.77321	−	0.645396i	−0.773276	−	0.634069i	$-0.781383\pi$
$774$	−1.58300e6	+	8.97763e6i	−0.0949791	+	0.538653i
$775$	232548.	+	1.31884e6i	0.0139078	+	0.0788749i
$776$	−3.93373e6	+	1.43176e6i	−0.234504	+	0.0853525i
$777$	376865.	+	316228.i	0.0223941	+	0.0187909i
$778$	−1.54368e7			−0.914343
$779$	104356.	+	411410.i	0.00616134	+	0.0242902i
$780$	−82761.1			−0.00487068
$781$	4.86658e6	+	4.08355e6i	0.285494	+	0.239558i
$782$	2.13102e7	−	7.75629e6i	1.24615	−	0.453563i
$783$	244151.	+	1.38465e6i	0.0142316	+	0.0807115i
$784$	295929.	−	1.67830e6i	0.0171948	−	0.0975168i
$785$	5.12483e6	+	1.86529e6i	0.296828	+	0.108037i
$786$	−299390.	−	518559.i	−0.0172855	−	0.0299393i
$787$	−1.26348e7	+	2.18841e7i	−0.727162	+	1.25948i	0.230915	+	0.972974i	$0.425828\pi$
$787$	−1.26348e7	+	2.18841e7i	−0.727162	+	1.25948i	−0.958078	+	0.286508i	$0.907505\pi$
$788$	6.13355e6	−	5.14666e6i	0.351881	−	0.295264i
$789$	−590813.	+	495751.i	−0.0337876	+	0.0283512i
$790$	840990.	−	1.45664e6i	0.0479428	−	0.0830393i
$791$	7.89170e6	+	1.36688e7i	0.448466	+	0.776766i
$792$	−7.01491e6	−	2.55322e6i	−0.397383	−	0.144636i
$793$	−1.63072e6	+	9.24829e6i	−0.0920868	+	0.522250i
$794$	−393716.	−	2.23288e6i	−0.0221632	−	0.125694i
$795$	−194832.	+	70913.1i	−0.0109331	+	0.00397932i
$796$	4.42401e6	+	3.71219e6i	0.247476	+	0.207657i
$797$	−2.14559e7			−1.19647			−0.598235	−	0.801321i	$-0.704131\pi$
$797$	−2.14559e7			−1.19647			−0.598235	+	0.801321i	$0.704131\pi$
$798$	−590440.	+	43703.1i	−0.0328222	+	0.00242944i
$799$	3.52057e6			0.195095
$800$	2.33291e6	+	1.95754e6i	0.128876	+	0.108140i
$801$	1.30170e7	−	4.73781e6i	0.716854	−	0.260913i
$802$	−84322.6	−	478217.i	−0.00462922	−	0.0262536i
$803$	−6.83139e6	+	3.87428e7i	−0.373870	+	2.12032i
$804$	−631774.	−	229947.i	−0.0344685	−	0.0125455i
$805$	4.08908e6	+	7.08250e6i	0.222401	+	0.385210i
$806$	−617390.	+	1.06935e6i	−0.0334751	+	0.0579806i
$807$	465599.	−	390684.i	0.0251668	−	0.0211175i
$808$	−6.93762e6	+	5.82135e6i	−0.373837	+	0.313686i
$809$	1.66644e7	−	2.88635e7i	0.895194	−	1.55052i	0.0616307	−	0.998099i	$-0.480370\pi$
$809$	1.66644e7	−	2.88635e7i	0.895194	−	1.55052i	0.833564	−	0.552423i	$-0.186297\pi$
$810$	1.44435e6	+	2.50169e6i	0.0773501	+	0.133974i
$811$	−974212.	−	354584.i	−0.0520117	−	0.0189307i	0.315883	−	0.948798i	$-0.397699\pi$
$811$	−974212.	−	354584.i	−0.0520117	−	0.0189307i	−0.367895	+	0.929867i	$0.619921\pi$
$812$	2.00661e6	−	1.13801e7i	0.106800	−	0.605696i
$813$	38911.1	+	220676.i	0.00206465	+	0.0117092i
$814$	−9.45116e6	+	3.43994e6i	−0.499947	+	0.181966i
$815$	−421459.	−	353646.i	−0.0222260	−	0.0186498i
$816$	205117.			0.0107839
$817$	−1.42248e7	−	4.01632e6i	−0.745576	−	0.210510i
$818$	1.07224e6			0.0560282
$819$	−1.95173e7	−	1.63769e7i	−1.01674	−	0.853145i
$820$	49830.3	−	18136.8i	0.00258797	−	0.000941944i
$821$	−2.36464e6	−	1.34105e7i	−0.122435	−	0.694366i	−0.982798	−	0.184684i	$-0.940874\pi$
$821$	−2.36464e6	−	1.34105e7i	−0.122435	−	0.694366i	0.860363	−	0.509682i	$-0.170237\pi$
$822$	−30866.5	+	175052.i	−0.00159334	+	0.00903625i
$823$	−2.41640e7	−	8.79497e6i	−1.24357	−	0.452621i	−0.365344	−	0.930873i	$-0.619049\pi$
$823$	−2.41640e7	−	8.79497e6i	−1.24357	−	0.452621i	−0.878223	+	0.478251i	$0.841271\pi$
$824$	6.30146e6	+	1.09144e7i	0.323313	+	0.559995i
$825$	−438991.	+	760355.i	−0.0224554	+	0.0388939i
$826$	−1.30595e7	+	1.09582e7i	−0.666002	+	0.558842i
$827$	444985.	−	373387.i	0.0226246	−	0.0189843i	−0.631405	−	0.775453i	$-0.717522\pi$
$827$	444985.	−	373387.i	0.0226246	−	0.0189843i	0.654030	+	0.756469i	$0.273077\pi$
$828$	−8.43374e6	+	1.46077e7i	−0.427508	+	0.740466i
$829$	−1.22029e6	−	2.11360e6i	−0.0616702	−	0.106816i	0.833542	−	0.552456i	$-0.186309\pi$
$829$	−1.22029e6	−	2.11360e6i	−0.0616702	−	0.106816i	−0.895212	+	0.445640i	$0.852976\pi$
$830$	1.96809e6	+	716326.i	0.0991630	+	0.0360924i
$831$	108028.	−	612657.i	0.00542667	−	0.0307762i
$832$	487599.	+	2.76531e6i	0.0244205	+	0.138495i
$833$	8.16221e6	−	2.97080e6i	0.407563	−	0.148341i
$834$	−362808.	−	304432.i	−0.0180618	−	0.0151557i
$835$	2.04752e6			0.101628
$836$	5.26172e6	−	1.09005e7i	0.260383	−	0.539425i
$837$	−134281.			−0.00662521
$838$	−1.08785e7	−	9.12813e6i	−0.535129	−	0.449026i
$839$	−1.70730e7	+	6.21406e6i	−0.837346	+	0.304769i	−0.724870	−	0.688886i	$-0.758100\pi$
$839$	−1.70730e7	+	6.21406e6i	−0.837346	+	0.304769i	−0.112476	+	0.993654i	$0.535878\pi$
$840$	12844.7	+	72846.0i	0.000628097	+	0.00356211i
$841$	298519.	−	1.69299e6i	0.0145540	−	0.0825398i
$842$	−4.67683e6	−	1.70223e6i	−0.227337	−	0.0827441i
$843$	−354920.	−	614739.i	−0.0172013	−	0.0297935i
$844$	4.97542e6	−	8.61768e6i	0.240422	−	0.416423i
$845$	928757.	−	779320.i	0.0447466	−	0.0375469i
$846$	−2.00592e6	+	1.68317e6i	−0.0963582	+	0.0808541i
$847$	−5.36705e6	+	9.29600e6i	−0.257055	+	0.445233i
$848$	3.51732e6	+	6.09217e6i	0.167966	+	0.290926i
$849$	−85513.9	−	31124.5i	−0.00407162	−	0.00148195i
$850$	−2.69537e6	+	1.52862e7i	−0.127959	+	0.725692i
$851$	3.94624e6	+	2.23802e7i	0.186793	+	1.05935i
$852$	122002.	−	44405.2i	0.00575797	−	0.00209573i
$853$	9.56943e6	+	8.02971e6i	0.450312	+	0.377857i	0.839552	−	0.543280i	$-0.182818\pi$
$853$	9.56943e6	+	8.02971e6i	0.450312	+	0.377857i	−0.389240	+	0.921137i	$0.627262\pi$
$854$	8.39341e6			0.393817
$855$	−4.27771e6	+	1.92546e6i	−0.200123	+	0.0900780i
$856$	−2.91594e6			−0.136017
$857$	532755.	+	447034.i	0.0247785	+	0.0207916i	0.655093	−	0.755548i	$-0.272630\pi$
$857$	532755.	+	447034.i	0.0247785	+	0.0207916i	−0.630314	+	0.776340i	$0.717074\pi$
$858$	−760711.	+	276876.i	−0.0352778	+	0.0128401i
$859$	−2.62761e6	−	1.49019e7i	−0.121500	−	0.689063i	−0.983325	−	0.181856i	$-0.941789\pi$
$859$	−2.62761e6	−	1.49019e7i	−0.121500	−	0.689063i	0.861825	−	0.507206i	$-0.169322\pi$
$860$	−320675.	+	1.81864e6i	−0.0147849	+	0.0838494i
$861$	−23841.6	−	8677.62i	−0.00109604	−	0.000398927i
$862$	−1.14386e7	−	1.98122e7i	−0.524329	−	0.908164i
$863$	−1.04677e7	+	1.81305e7i	−0.478435	+	0.828673i	−0.999694	−	0.0247248i	$-0.992129\pi$
$863$	−1.04677e7	+	1.81305e7i	−0.478435	+	0.828673i	0.521259	+	0.853398i	$0.325462\pi$
$864$	−233921.	+	196283.i	−0.0106607	+	0.00894539i
$865$	−2.18099e6	+	1.83006e6i	−0.0991089	+	0.0831622i
$866$	1.43449e7	−	2.48461e7i	0.649985	−	1.12581i
$867$	86781.7	+	150310.i	0.00392085	+	0.00679111i
$868$	1.03706e6	+	377459.i	0.0467202	+	0.0170048i
$869$	2.85693e6	−	1.62024e7i	0.128336	−	0.727831i
$870$	24710.2	+	140138.i	0.00110682	+	0.00627710i
$871$	4.40816e7	−	1.60444e7i	1.96885	−	0.716602i
$872$	1.23712e6	+	1.03807e6i	0.0550960	+	0.0462310i
$873$	1.58698e7			0.704750
$874$	−2.21911e7	−	1.59852e7i	−0.982654	−	0.707847i
$875$	−1.14794e7			−0.506871
$876$	615893.	+	516796.i	0.0271172	+	0.0227540i
$877$	4.55928e6	−	1.65944e6i	0.200169	−	0.0728556i	−0.239990	−	0.970775i	$-0.577144\pi$
$877$	4.55928e6	−	1.65944e6i	0.200169	−	0.0728556i	0.440159	+	0.897920i	$0.354922\pi$
$878$	−3.45325e6	−	1.95843e7i	−0.151179	−	0.857379i
$879$	−109582.	+	621469.i	−0.00478372	+	0.0271298i
$880$	−1.42104e6	−	517217.i	−0.0618586	−	0.0225147i
$881$	−6.78779e6	−	1.17568e7i	−0.294638	−	0.510328i	0.680263	−	0.732968i	$-0.261866\pi$
$881$	−6.78779e6	−	1.17568e7i	−0.294638	−	0.510328i	−0.974901	+	0.222641i	$0.928532\pi$
$882$	−3.23028e6	+	5.59500e6i	−0.139820	+	0.242175i
$883$	−8.36166e6	+	7.01627e6i	−0.360903	+	0.302834i	−0.805151	−	0.593070i	$-0.797916\pi$
$883$	−8.36166e6	+	7.01627e6i	−0.360903	+	0.302834i	0.444247	+	0.895904i	$0.353471\pi$
$884$	−1.09635e7	+	9.19949e6i	−0.471867	+	0.395943i
$885$	104967.	−	181809.i	0.00450501	−	0.00780291i
$886$	−7.08914e6	−	1.22787e7i	−0.303395	−	0.525496i
$887$	−2.71112e7	−	9.86767e6i	−1.15702	−	0.421120i	−0.308986	−	0.951067i	$-0.599990\pi$
$887$	−2.71112e7	−	9.86767e6i	−1.15702	−	0.421120i	−0.848031	+	0.529947i	$0.822212\pi$
$888$	−35692.9	+	202424.i	−0.00151897	+	0.00861451i
$889$	2.41534e6	+	1.36981e7i	0.102500	+	0.581306i
$890$	2.63692e6	−	959760.i	0.111589	−	0.0406151i
$891$	2.16454e7	+	1.81626e7i	0.913422	+	0.766452i
$892$	5.43207e6			0.228588
$893$	−2.38849e6	−	3.51018e6i	−0.100229	−	0.147299i
$894$	−985120.			−0.0412235
$895$	4.70845e6	+	3.95086e6i	0.196481	+	0.164867i
$896$	2.35834e6	−	858366.i	0.0981379	−	0.0357193i
$897$	317628.	+	1.80136e6i	0.0131807	+	0.0747512i
$898$	−4.97426e6	+	2.82104e7i	−0.205844	+	1.16740i
$899$	1.99506e6	+	726142.i	0.0823296	+	0.0299655i
$900$	−5.77253e6	−	9.99831e6i	−0.237553	−	0.411453i
$901$	−1.79273e7	+	3.10510e7i	−0.735704	+	1.27428i
$902$	397347.	−	333414.i	0.0162612	−	0.0136448i
$903$	676846.	−	567942.i	0.0276230	−	0.0231784i
$904$	−3.29723e6	+	5.71098e6i	−0.134193	+	0.232428i
$905$	4.64229e6	+	8.04069e6i	0.188413	+	0.326341i
$906$	199737.	+	72698.4i	0.00808423	+	0.00294242i
$907$	−2.32075e6	+	1.31616e7i	−0.0936720	+	0.531241i	0.901474	+	0.432833i	$0.142486\pi$
$907$	−2.32075e6	+	1.31616e7i	−0.0936720	+	0.531241i	−0.995146	+	0.0984076i	$0.968625\pi$
$908$	2.09200e6	+	1.18643e7i	0.0842067	+	0.477560i
$909$	3.22622e7	−	1.17425e7i	1.29504	−	0.471357i
$910$	−3.95370e6	−	3.31755e6i	−0.158271	−	0.132805i
$911$	4.49893e7			1.79603			0.898015	−	0.439965i	$-0.145009\pi$
$911$	4.49893e7			1.79603			0.898015	+	0.439965i	$0.145009\pi$
$912$	−139159.	−	204511.i	−0.00554019	−	0.00814199i
$913$	2.04865e7			0.813374
$914$	1.50852e7	+	1.26580e7i	0.597291	+	0.501187i
$915$	−97126.3	+	35351.1i	−0.00383517	+	0.00139589i
$916$	2.26146e6	+	1.28254e7i	0.0890534	+	0.505047i
$917$	6.48428e6	−	3.67742e7i	0.254647	−	1.44417i
$918$	−1.46253e6	−	532319.i	−0.0572795	−	0.0208480i
$919$	1.91766e7	+	3.32149e7i	0.749003	+	1.29731i	0.948301	+	0.317372i	$0.102800\pi$
$919$	1.91766e7	+	3.32149e7i	0.749003	+	1.29731i	−0.199298	+	0.979939i	$0.563866\pi$
$920$	−1.70846e6	+	2.95914e6i	−0.0665481	+	0.115265i
$921$	1.22826e6	−	1.03063e6i	0.0477134	−	0.0400363i
$922$	−8.17713e6	+	6.86143e6i	−0.316792	+	0.265820i
$923$	−4.52947e6	+	7.84528e6i	−0.175002	+	0.303113i
$924$	361770.	+	626604.i	0.0139397	+	0.0241442i
$925$	−1.46165e7	−	5.31998e6i	−0.561682	−	0.204435i
$926$	794411.	−	4.50533e6i	0.0304451	−	0.172663i
$927$	−8.29647e6	−	4.70516e7i	−0.317098	−	1.79835i
$928$	4.53689e6	−	1.65129e6i	0.172937	−	0.0629439i
$929$	8.33038e6	+	6.99002e6i	0.316684	+	0.265729i	0.787248	−	0.616637i	$-0.211505\pi$
$929$	8.33038e6	+	6.99002e6i	0.316684	+	0.265729i	−0.470564	+	0.882366i	$0.655950\pi$
$930$	−13590.4			−0.000515257
$931$	−8.49960e6	−	6.12262e6i	−0.321384	−	0.231506i
$932$	−1.98510e7			−0.748587
$933$	−747492.	−	627220.i	−0.0281127	−	0.0235893i
$934$	4.72299e6	−	1.71903e6i	0.177153	−	0.0644786i
$935$	−1.33843e6	−	7.59061e6i	−0.0500687	−	0.283954i
$936$	1.84848e6	−	1.04832e7i	0.0689644	−	0.391117i
$937$	4.53545e7	+	1.65077e7i	1.68761	+	0.614239i	0.994321	−	0.106423i	$-0.0339398\pi$
$937$	4.53545e7	+	1.65077e7i	1.68761	+	0.614239i	0.693286	+	0.720662i	$0.256162\pi$
$938$	−2.09638e7	−	3.63104e7i	−0.777971	−	1.34748i
$939$	−627962.	+	1.08766e6i	−0.0232418	+	0.0402560i
$940$	−406349.	+	340967.i	−0.0149996	+	0.0125862i
$941$	−2.87613e7	+	2.41336e7i	−1.05885	+	0.888479i	−0.993996	−	0.109415i	$-0.965102\pi$
$941$	−2.87613e7	+	2.41336e7i	−1.05885	+	0.888479i	−0.0648524	+	0.997895i	$0.520658\pi$
$942$	545110.	−	944158.i	0.0200151	−	0.0346671i
$943$	−586003.	−	1.01499e6i	−0.0214596	−	0.0371690i
$944$	−6.69324e6	−	2.43614e6i	−0.244459	−	0.0889759i
$945$	97463.9	−	552745.i	0.00355029	−	0.0201347i
$946$	3.13670e6	+	1.77891e7i	0.113958	+	0.646289i
$947$	3.77785e7	−	1.37502e7i	1.36889	−	0.498236i	0.450101	−	0.892978i	$-0.351388\pi$
$947$	3.77785e7	−	1.37502e7i	1.36889	−	0.498236i	0.918792	+	0.394742i	$0.129166\pi$
$948$	−257570.	−	216127.i	−0.00930838	−	0.00781066i
$949$	−5.60980e7			−2.02200
$950$	1.70697e7	−	7.68334e6i	0.613646	−	0.276211i
$951$	1.18394e6			0.0424500
$952$	9.79893e6	+	8.22228e6i	0.350418	+	0.294036i
$953$	3.52984e7	−	1.28476e7i	1.25899	−	0.458235i	0.375561	−	0.926798i	$-0.377450\pi$
$953$	3.52984e7	−	1.28476e7i	1.25899	−	0.458235i	0.883430	+	0.468562i	$0.155228\pi$
$954$	−4.63088e6	−	2.62630e7i	−0.164738	−	0.934273i
$955$	−1.54899e6	+	8.78477e6i	−0.0549592	+	0.311689i
$956$	2.16465e7	+	7.87867e6i	0.766024	+	0.278810i
$957$	695959.	+	1.20544e6i	0.0245643	+	0.0425466i
$958$	−1.65997e6	+	2.87515e6i	−0.0584368	+	0.101216i
$959$	−8.49170e6	+	7.12538e6i	−0.298159	+	0.250185i
$960$	−23674.9	+	19865.6i	−0.000829105	+	0.000695701i
$961$	1.42132e7	−	2.46180e7i	0.496459	−	0.859892i
$962$	−7.17096e6	−	1.24205e7i	−0.249827	−	0.432713i
$963$	1.03876e7	+	3.78079e6i	0.360953	+	0.131376i
$964$	4.37621e6	−	2.48187e7i	0.151672	−	0.860174i
$965$	−1.52128e6	−	8.62761e6i	−0.0525885	−	0.298244i
$966$	1.53625e6	−	559150.i	0.0529687	−	0.0192790i
$967$	2.64578e7	+	2.22007e7i	0.909886	+	0.763485i	0.972097	−	0.234578i	$-0.0753708\pi$
$967$	2.64578e7	+	2.22007e7i	0.909886	+	0.763485i	−0.0622113	+	0.998063i	$0.519815\pi$
$968$	−4.48481e6			−0.153835
$969$	548080.	−	1.13544e6i	0.0187514	−	0.0388466i
$970$	3.21481e6			0.109705
$971$	−1.86734e7	−	1.56688e7i	−0.635588	−	0.533321i	0.267072	−	0.963677i	$-0.413944\pi$
$971$	−1.86734e7	−	1.56688e7i	−0.635588	−	0.533321i	−0.902660	+	0.430355i	$0.858388\pi$
$972$	1.63214e6	−	594050.i	0.0554105	−	0.0201678i
$973$	−5.12881e6	−	2.90869e7i	−0.173674	−	0.984954i
$974$	−4.42047e6	+	2.50697e7i	−0.149304	+	0.846743i
$975$	−1.17647e6	−	428199.i	−0.0396340	−	0.0144256i
$976$	1.75343e6	+	3.03702e6i	0.0589201	+	0.102053i
$977$	−1.00584e7	+	1.74217e7i	−0.337128	+	0.583922i	−0.983891	−	0.178768i	$-0.942789\pi$
$977$	−1.00584e7	+	1.74217e7i	−0.337128	+	0.583922i	0.646764	+	0.762691i	$0.276122\pi$
$978$	−84251.1	+	70695.1i	−0.00281662	+	0.00236343i
$979$	2.10268e7	−	1.76436e7i	0.701158	−	0.588342i
$980$	−654372.	+	1.13341e6i	−0.0217650	+	0.0376981i
$981$	−3.06111e6	−	5.30200e6i	−0.101556	−	0.175901i
$982$	−3.31380e6	−	1.20612e6i	−0.109660	−	0.0399129i
$983$	−1.00623e7	+	5.70663e7i	−0.332135	+	1.88363i	0.121735	+	0.992563i	$0.461154\pi$
$983$	−1.00623e7	+	5.70663e7i	−0.332135	+	1.88363i	−0.453870	+	0.891068i	$0.649957\pi$
$984$	−1840.77	−	10439.5i	−6.06053e−5	−	0.000343710i
$985$	−5.77804e6	+	2.10303e6i	−0.189753	+	0.0690646i
$986$	1.88508e7	+	1.58177e7i	0.617501	+	0.518145i
$987$	253797.			0.00829266
$988$	1.66104e7	+	4.68989e6i	0.541363	+	0.152852i
$989$	4.08147e7			1.32686
$990$	4.39164e6	+	3.68503e6i	0.142410	+	0.119496i
$991$	−4.83169e7	+	1.75859e7i	−1.56284	+	0.568828i	−0.971385	−	0.237510i	$-0.923669\pi$
$991$	−4.83169e7	+	1.75859e7i	−1.56284	+	0.568828i	−0.591456	+	0.806337i	$0.701447\pi$
$992$	80069.6	+	454097.i	0.00258338	+	0.0146511i
$993$	284757.	−	1.61494e6i	0.00916434	−	0.0519736i
$994$	7.60838e6	+	2.76922e6i	0.244245	+	0.0888980i
$995$	−2.21753e6	−	3.84087e6i	−0.0710087	−	0.122991i
$996$	209339.	−	362585.i	0.00668653	−	0.0115814i
$997$	−4.71250e7	+	3.95426e7i	−1.50146	+	1.25987i	−0.622844	+	0.782346i	$0.714023\pi$
$997$	−4.71250e7	+	3.95426e7i	−1.50146	+	1.25987i	−0.878616	+	0.477528i	$0.841533\pi$
$998$	2.54508e6	−	2.13558e6i	0.0808865	−	0.0678718i
$999$	779831.	−	1.35071e6i	0.0247222	−	0.0428201i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.e.a.35.2	yes	24
19.5	even	9		722.6.a.o.1.7		12
19.6	even	9	inner	38.6.e.a.25.2	✓	24
19.14	odd	18		722.6.a.p.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.a.25.2	✓	24	19.6	even	9	inner
38.6.e.a.35.2	yes	24	1.1	even	1	trivial
722.6.a.o.1.7		12	19.5	even	9
722.6.a.p.1.6		12	19.14	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.06418 - 2.57115i) q^{2} +(0.577036 - 0.210024i) q^{3} +(2.77837 + 15.7569i) q^{4} +(2.13367 - 12.1006i) q^{5} +(-2.30814 - 0.840095i) q^{6} +(-76.5898 - 132.657i) q^{7} +(32.0000 - 55.4256i) q^{8} +(-185.860 + 155.955i) q^{9} +(-37.6505 + 31.5925i) q^{10} +(-240.378 + 416.347i) q^{11} +(4.91255 + 8.50879i) q^{12} +(-644.196 - 234.468i) q^{13} +(-106.397 + 603.410i) q^{14} +(-1.31022 - 7.43062i) q^{15} +(-240.561 + 87.5572i) q^{16} +(-999.534 - 838.709i) q^{17} +970.492 q^{18} +(-158.111 + 1565.60i) q^{19} +196.597 q^{20} +(-72.0563 - 60.4624i) q^{21} +(1807.05 - 657.713i) q^{22} +(-754.517 - 4279.08i) q^{23} +(6.82444 - 38.7033i) q^{24} +(2794.67 + 1017.18i) q^{25} +(1371.08 + 2374.78i) q^{26} +(-149.103 + 258.254i) q^{27} +(1877.48 - 1575.39i) q^{28} +(3611.82 - 3030.68i) q^{29} +(-15.0905 + 26.1375i) q^{30} +(225.148 + 389.967i) q^{31} +(962.245 + 350.229i) q^{32} +(-51.2639 + 290.732i) q^{33} +(906.304 + 5139.91i) q^{34} +(-1768.66 + 643.738i) q^{35} +(-2973.76 - 2495.28i) q^{36} -5230.15 q^{37} +(4509.87 - 4390.75i) q^{38} -420.968 q^{39} +(-602.408 - 505.480i) q^{40} +(253.464 - 92.2535i) q^{41} +(65.3353 + 370.535i) q^{42} +(-1631.13 + 9250.60i) q^{43} +(-7228.20 - 2630.85i) q^{44} +(1490.59 + 2581.78i) q^{45} +(-8690.18 + 15051.8i) q^{46} +(-2066.91 + 1734.35i) q^{47} +(-120.423 + 101.047i) q^{48} +(-3328.50 + 5765.12i) q^{49} +(-5948.04 - 10302.3i) q^{50} +(-752.916 - 274.039i) q^{51} +(1904.68 - 10802.0i) q^{52} +(-4771.68 - 27061.6i) q^{53} +(1120.89 - 407.970i) q^{54} +(4525.17 + 3797.07i) q^{55} -9803.49 q^{56} +(237.577 + 936.614i) q^{57} -18859.6 q^{58} +(21314.0 + 17884.6i) q^{59} +(113.443 - 41.2900i) q^{60} +(-2378.75 - 13490.5i) q^{61} +(312.772 - 1773.82i) q^{62} +(34923.6 + 12711.1i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(-4211.72 + 7294.91i) q^{65} +(904.598 - 759.048i) q^{66} +(-52419.6 + 43985.2i) q^{67} +(10438.4 - 18079.8i) q^{68} +(-1334.09 - 2310.71i) q^{69} +(7074.62 + 2574.95i) q^{70} +(2294.65 - 13013.6i) q^{71} +(2696.39 + 15292.0i) q^{72} +(76895.4 - 27987.6i) q^{73} +(16026.1 + 13447.5i) q^{74} +1826.25 q^{75} +(-25108.3 + 1858.47i) q^{76} +73642.0 q^{77} +(1289.92 + 1082.37i) q^{78} +(-32158.1 + 11704.6i) q^{79} +(546.219 + 3097.76i) q^{80} +(10206.0 - 57881.3i) q^{81} +(-1013.86 - 369.014i) q^{82} +(-21306.5 - 36904.0i) q^{83} +(752.502 - 1303.37i) q^{84} +(-12281.6 + 10305.5i) q^{85} +(28782.8 - 24151.6i) q^{86} +(1447.64 - 2507.38i) q^{87} +(15384.2 + 26646.2i) q^{88} +(-53651.3 - 19527.5i) q^{89} +(2070.71 - 11743.6i) q^{90} +(18234.9 + 103415. i) q^{91} +(65328.8 - 23777.7i) q^{92} +(211.821 + 177.739i) q^{93} +10792.7 q^{94} +(18607.4 + 5253.71i) q^{95} +628.806 q^{96} +(-50106.3 - 42044.2i) q^{97} +(25022.1 - 9107.30i) q^{98} +(-20254.7 - 114870. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 18 q^{3} - 72 q^{6} + 438 q^{7} + 768 q^{8} + 378 q^{9} + 600 q^{11} - 1662 q^{13} - 1776 q^{14} - 1206 q^{15} + 4194 q^{17} - 4368 q^{18} + 9570 q^{19} - 1344 q^{20} + 2430 q^{21} - 5160 q^{22}+ \cdots + 656436 q^{99}+O(q^{100}) \) 24 * q + 18 * q^3 - 72 * q^6 + 438 * q^7 + 768 * q^8 + 378 * q^9 + 600 * q^11 - 1662 * q^13 - 1776 * q^14 - 1206 * q^15 + 4194 * q^17 - 4368 * q^18 + 9570 * q^19 - 1344 * q^20 + 2430 * q^21 - 5160 * q^22 - 1170 * q^23 - 1152 * q^24 + 5940 * q^25 - 1776 * q^26 - 5130 * q^27 + 768 * q^28 - 7554 * q^29 + 294 * q^31 - 45912 * q^33 + 1584 * q^34 + 22116 * q^35 + 6048 * q^36 + 28608 * q^37 - 9528 * q^38 - 38868 * q^39 + 37278 * q^41 - 9720 * q^42 + 13212 * q^43 + 20640 * q^44 - 34344 * q^45 - 29856 * q^46 - 3054 * q^47 - 9216 * q^48 + 1422 * q^49 + 16584 * q^50 + 2352 * q^51 - 1824 * q^52 + 73806 * q^53 + 136944 * q^54 - 41598 * q^55 + 56064 * q^56 + 178248 * q^57 - 52848 * q^58 + 123528 * q^59 + 46944 * q^60 - 149172 * q^61 + 58344 * q^62 - 170124 * q^63 - 49152 * q^64 - 202674 * q^65 - 84840 * q^66 - 313212 * q^67 + 35520 * q^68 - 19938 * q^69 - 88464 * q^70 + 75810 * q^71 + 48384 * q^72 + 172872 * q^73 + 4872 * q^74 + 174960 * q^75 + 31008 * q^76 - 115056 * q^77 + 101304 * q^78 + 158058 * q^79 - 47250 * q^81 - 149112 * q^82 - 148440 * q^83 - 176736 * q^84 - 226752 * q^85 - 57528 * q^86 + 182874 * q^87 - 38400 * q^88 - 322464 * q^89 + 48816 * q^90 - 27264 * q^91 + 88992 * q^92 + 779424 * q^93 + 143712 * q^94 + 634752 * q^95 - 108552 * q^97 - 173544 * q^98 + 656436 * q^99

Introduction

L-functions

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