LMFDB - Embedded newform 36.5.f.a.7.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,5,Mod(7,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("36.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	36.f (of order $6$, degree $2$, 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:	$3.72131867102$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.22
Character	$\chi$	$=$	36.7
Dual form			36.5.f.a.31.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.99035 + 0.277636i) q^{2} +(-3.18543 - 8.41742i) q^{3} +(15.8458 + 2.21573i) q^{4} +(-23.3466 - 40.4374i) q^{5} +(-10.3740 - 34.4729i) q^{6} +(52.4363 + 30.2741i) q^{7} +(62.6153 + 13.2409i) q^{8} +(-60.7060 + 53.6263i) q^{9} +O(q^{10})$	\(q+(3.99035 + 0.277636i) q^{2} +(-3.18543 - 8.41742i) q^{3} +(15.8458 + 2.21573i) q^{4} +(-23.3466 - 40.4374i) q^{5} +(-10.3740 - 34.4729i) q^{6} +(52.4363 + 30.2741i) q^{7} +(62.6153 + 13.2409i) q^{8} +(-60.7060 + 53.6263i) q^{9} +(-81.9341 - 167.841i) q^{10} +(63.7631 + 36.8136i) q^{11} +(-31.8252 - 140.439i) q^{12} +(15.5924 + 27.0068i) q^{13} +(200.834 + 135.363i) q^{14} +(-266.010 + 325.329i) q^{15} +(246.181 + 70.2201i) q^{16} +53.8013 q^{17} +(-257.127 + 197.134i) q^{18} +54.9619i q^{19} +(-280.347 - 692.494i) q^{20} +(87.7977 - 537.815i) q^{21} +(244.217 + 164.602i) q^{22} +(-243.863 + 140.795i) q^{23} +(-88.0027 - 569.238i) q^{24} +(-777.624 + 1346.88i) q^{25} +(54.7210 + 112.096i) q^{26} +(644.770 + 340.165i) q^{27} +(763.818 + 595.904i) q^{28} +(223.597 - 387.282i) q^{29} +(-1151.80 + 1224.32i) q^{30} +(-240.584 + 138.901i) q^{31} +(962.854 + 348.552i) q^{32} +(106.763 - 653.989i) q^{33} +(214.686 + 14.9372i) q^{34} -2827.19i q^{35} +(-1080.76 + 715.246i) q^{36} +1016.51 q^{37} +(-15.2594 + 219.317i) q^{38} +(177.659 - 217.276i) q^{39} +(-926.424 - 2841.13i) q^{40} +(-946.158 - 1638.79i) q^{41} +(499.660 - 2121.70i) q^{42} +(-666.266 - 384.669i) q^{43} +(928.811 + 724.625i) q^{44} +(3585.79 + 1202.81i) q^{45} +(-1012.19 + 494.115i) q^{46} +(2374.81 + 1371.10i) q^{47} +(-193.121 - 2295.89i) q^{48} +(632.546 + 1095.60i) q^{49} +(-3476.94 + 5158.64i) q^{50} +(-171.381 - 452.869i) q^{51} +(187.235 + 462.494i) q^{52} -4647.69 q^{53} +(2478.42 + 1536.39i) q^{54} -3437.89i q^{55} +(2882.46 + 2589.93i) q^{56} +(462.637 - 175.078i) q^{57} +(999.756 - 1483.31i) q^{58} +(-262.792 + 151.723i) q^{59} +(-4935.99 + 4565.70i) q^{60} +(-478.174 + 828.222i) q^{61} +(-998.577 + 487.469i) q^{62} +(-4806.69 + 974.145i) q^{63} +(3745.36 + 1658.17i) q^{64} +(728.057 - 1261.03i) q^{65} +(607.592 - 2580.00i) q^{66} +(-6010.96 + 3470.43i) q^{67} +(852.527 + 119.209i) q^{68} +(1961.94 + 1604.21i) q^{69} +(784.928 - 11281.5i) q^{70} +5971.60i q^{71} +(-4511.19 + 2554.03i) q^{72} -4339.17 q^{73} +(4056.25 + 282.220i) q^{74} +(13814.4 + 2255.18i) q^{75} +(-121.781 + 870.917i) q^{76} +(2229.00 + 3860.75i) q^{77} +(769.246 - 817.683i) q^{78} +(3294.15 + 1901.88i) q^{79} +(-2907.96 - 11594.3i) q^{80} +(809.440 - 6510.88i) q^{81} +(-3320.52 - 6802.05i) q^{82} +(-2730.64 - 1576.53i) q^{83} +(2582.88 - 8327.59i) q^{84} +(-1256.08 - 2175.59i) q^{85} +(-2551.84 - 1719.94i) q^{86} +(-3972.17 - 648.452i) q^{87} +(3505.10 + 3149.38i) q^{88} -7132.44 q^{89} +(13974.6 + 5795.16i) q^{90} +1888.18i q^{91} +(-4176.18 + 1690.67i) q^{92} +(1935.55 + 1582.63i) q^{93} +(9095.67 + 6130.50i) q^{94} +(2222.52 - 1283.17i) q^{95} +(-133.201 - 9215.04i) q^{96} +(980.405 - 1698.11i) q^{97} +(2219.91 + 4547.46i) q^{98} +(-5844.98 + 1184.57i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9}+O(q^{10}) $ 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9	$ 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9} + 28 q^{10} - 228 q^{12} - 2 q^{13} + 252 q^{14} - q^{16} - 56 q^{17} + 72 q^{18} - 140 q^{20} + 138 q^{21} - 33 q^{22} - 951 q^{24} - 1752 q^{25} + 1096 q^{26} - 516 q^{28} + 526 q^{29} - 1980 q^{30} - 121 q^{32} + 2994 q^{33} + 385 q^{34} - 1005 q^{36} - 8 q^{37} + 1395 q^{38} - 2276 q^{40} - 2762 q^{41} + 3330 q^{42} + 6714 q^{44} + 4110 q^{45} + 3576 q^{46} + 2163 q^{48} + 3428 q^{49} + 6375 q^{50} + 1438 q^{52} - 10088 q^{53} - 4983 q^{54} - 7506 q^{56} + 1752 q^{57} - 4064 q^{58} - 16392 q^{60} - 2 q^{61} - 18324 q^{62} + 9026 q^{64} - 2014 q^{65} - 17358 q^{66} - 11405 q^{68} + 3354 q^{69} + 3666 q^{70} + 4083 q^{72} - 3416 q^{73} + 14620 q^{74} + 1581 q^{76} - 3942 q^{77} + 34566 q^{78} + 45520 q^{80} - 1164 q^{81} - 8486 q^{82} + 51078 q^{84} - 1252 q^{85} + 22113 q^{86} + 1995 q^{88} + 13048 q^{89} - 4692 q^{90} - 30294 q^{92} + 12090 q^{93} + 7524 q^{94} - 76164 q^{96} + 5638 q^{97} - 92938 q^{98}+O(q^{100}) $ 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9 + 28 * q^10 - 228 * q^12 - 2 * q^13 + 252 * q^14 - q^16 - 56 * q^17 + 72 * q^18 - 140 * q^20 + 138 * q^21 - 33 * q^22 - 951 * q^24 - 1752 * q^25 + 1096 * q^26 - 516 * q^28 + 526 * q^29 - 1980 * q^30 - 121 * q^32 + 2994 * q^33 + 385 * q^34 - 1005 * q^36 - 8 * q^37 + 1395 * q^38 - 2276 * q^40 - 2762 * q^41 + 3330 * q^42 + 6714 * q^44 + 4110 * q^45 + 3576 * q^46 + 2163 * q^48 + 3428 * q^49 + 6375 * q^50 + 1438 * q^52 - 10088 * q^53 - 4983 * q^54 - 7506 * q^56 + 1752 * q^57 - 4064 * q^58 - 16392 * q^60 - 2 * q^61 - 18324 * q^62 + 9026 * q^64 - 2014 * q^65 - 17358 * q^66 - 11405 * q^68 + 3354 * q^69 + 3666 * q^70 + 4083 * q^72 - 3416 * q^73 + 14620 * q^74 + 1581 * q^76 - 3942 * q^77 + 34566 * q^78 + 45520 * q^80 - 1164 * q^81 - 8486 * q^82 + 51078 * q^84 - 1252 * q^85 + 22113 * q^86 + 1995 * q^88 + 13048 * q^89 - 4692 * q^90 - 30294 * q^92 + 12090 * q^93 + 7524 * q^94 - 76164 * q^96 + 5638 * q^97 - 92938 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	3.99035	+	0.277636i	0.997588	+	0.0694089i
$2$	3.99035	+	0.277636i	0.997588	+	0.0694089i
$3$	−3.18543	−	8.41742i	−0.353937	−	0.935269i
$3$	−3.18543	−	8.41742i	−0.353937	−	0.935269i
$4$	15.8458	+	2.21573i	0.990365	+	0.138483i
$5$	−23.3466	−	40.4374i	−0.933862	−	1.61750i	−0.776650	−	0.629932i	$-0.783083\pi$
$5$	−23.3466	−	40.4374i	−0.933862	−	1.61750i	−0.157212	−	0.987565i	$-0.550251\pi$
$6$	−10.3740	−	34.4729i	−0.288168	−	0.957580i
$7$	52.4363	+	30.2741i	1.07013	+	0.617839i	0.928217	−	0.372040i	$-0.121341\pi$
$7$	52.4363	+	30.2741i	1.07013	+	0.617839i	0.141913	+	0.989879i	$0.454675\pi$
$8$	62.6153	+	13.2409i	0.978364	+	0.206889i
$9$	−60.7060	+	53.6263i	−0.749457	+	0.662053i
$10$	−81.9341	−	167.841i	−0.819341	−	1.67841i
$11$	63.7631	+	36.8136i	0.526968	+	0.304245i	0.739781	−	0.672848i	$-0.234929\pi$
$11$	63.7631	+	36.8136i	0.526968	+	0.304245i	−0.212813	+	0.977093i	$0.568263\pi$
$12$	−31.8252	−	140.439i	−0.221008	−	0.975272i
$13$	15.5924	+	27.0068i	0.0922626	+	0.159803i	0.908463	−	0.417966i	$-0.137257\pi$
$13$	15.5924	+	27.0068i	0.0922626	+	0.159803i	−0.816200	+	0.577769i	$0.803923\pi$
$14$	200.834	+	135.363i	1.02466	+	0.690626i
$15$	−266.010	+	325.329i	−1.18227	+	1.44590i
$16$	246.181	+	70.2201i	0.961645	+	0.274297i
$17$	53.8013			0.186164			0.0930819	−	0.995658i	$-0.470328\pi$
$17$	53.8013			0.186164			0.0930819	+	0.995658i	$0.470328\pi$
$18$	−257.127	+	197.134i	−0.793602	+	0.608437i
$19$			54.9619i			0.152249i	0.997098	+	0.0761245i	$0.0242546\pi$
$19$			54.9619i			0.152249i	−0.997098	+	0.0761245i	$0.975745\pi$
$20$	−280.347	−	692.494i	−0.700869	−	1.73124i
$21$	87.7977	−	537.815i	0.199088	−	1.21954i
$22$	244.217	+	164.602i	0.504580	+	0.340088i
$23$	−243.863	+	140.795i	−0.460990	+	0.266152i	−0.712460	−	0.701712i	$-0.752419\pi$
$23$	−243.863	+	140.795i	−0.460990	+	0.266152i	0.251471	+	0.967865i	$0.419086\pi$
$24$	−88.0027	−	569.238i	−0.152782	−	0.988260i
$25$	−777.624	+	1346.88i	−1.24420	+	2.15501i
$26$	54.7210	+	112.096i	0.0809483	+	0.165822i
$27$	644.770	+	340.165i	0.884459	+	0.466619i
$28$	763.818	+	595.904i	0.974258	+	0.760081i
$29$	223.597	−	387.282i	0.265871	−	0.460502i	−0.701921	−	0.712255i	$-0.747674\pi$
$29$	223.597	−	387.282i	0.265871	−	0.460502i	0.967791	+	0.251753i	$0.0810072\pi$
$30$	−1151.80	+	1224.32i	−1.27977	+	1.36036i
$31$	−240.584	+	138.901i	−0.250347	+	0.144538i	−0.619923	−	0.784663i	$-0.712836\pi$
$31$	−240.584	+	138.901i	−0.250347	+	0.144538i	0.369576	+	0.929200i	$0.379503\pi$
$32$	962.854	+	348.552i	0.940287	+	0.340383i
$33$	106.763	−	653.989i	0.0980375	−	0.600540i
$34$	214.686	+	14.9372i	0.185715	+	0.0129214i
$35$		−	2827.19i		−	2.30791i
$36$	−1080.76	+	715.246i	−0.833919	+	0.551887i
$37$	1016.51			0.742522			0.371261	−	0.928528i	$-0.378925\pi$
$37$	1016.51			0.742522			0.371261	+	0.928528i	$0.378925\pi$
$38$	−15.2594	+	219.317i	−0.0105674	+	0.151882i
$39$	177.659	−	217.276i	0.116804	−	0.142851i
$40$	−926.424	−	2841.13i	−0.579015	−	1.77571i
$41$	−946.158	−	1638.79i	−0.562854	−	0.974892i	−0.997246	−	0.0741680i	$-0.976370\pi$
$41$	−946.158	−	1638.79i	−0.562854	−	0.974892i	0.434392	−	0.900724i	$-0.356963\pi$
$42$	499.660	−	2121.70i	0.283254	−	1.20278i
$43$	−666.266	−	384.669i	−0.360339	−	0.208042i	0.308891	−	0.951098i	$-0.400042\pi$
$43$	−666.266	−	384.669i	−0.360339	−	0.208042i	−0.669229	+	0.743056i	$0.733376\pi$
$44$	928.811	+	724.625i	0.479758	+	0.374290i
$45$	3585.79	+	1202.81i	1.77076	+	0.593978i
$46$	−1012.19	+	494.115i	−0.478351	+	0.233514i
$47$	2374.81	+	1371.10i	1.07506	+	0.620687i	0.929560	−	0.368671i	$-0.120187\pi$
$47$	2374.81	+	1371.10i	1.07506	+	0.620687i	0.145502	+	0.989358i	$0.453520\pi$
$48$	−193.121	−	2295.89i	−0.0838200	−	0.996481i
$49$	632.546	+	1095.60i	0.263451	+	0.456311i
$50$	−3476.94	+	5158.64i	−1.39077	+	2.06346i
$51$	−171.381	−	452.869i	−0.0658903	−	0.174113i
$52$	187.235	+	462.494i	0.0692435	+	0.171041i
$53$	−4647.69			−1.65457			−0.827286	−	0.561780i	$-0.810117\pi$
$53$	−4647.69			−1.65457			−0.827286	+	0.561780i	$0.810117\pi$
$54$	2478.42	+	1536.39i	0.849938	+	0.526883i
$55$		−	3437.89i		−	1.13649i
$56$	2882.46	+	2589.93i	0.919152	+	0.825870i
$57$	462.637	−	175.078i	0.142394	−	0.0538866i
$58$	999.756	−	1483.31i	0.297193	−	0.440937i
$59$	−262.792	+	151.723i	−0.0754934	+	0.0435861i	−0.537272	−	0.843409i	$-0.680545\pi$
$59$	−262.792	+	151.723i	−0.0754934	+	0.0435861i	0.461778	+	0.886995i	$0.347212\pi$
$60$	−4935.99	+	4565.70i	−1.37111	+	1.26825i
$61$	−478.174	+	828.222i	−0.128507	+	0.222580i	−0.923098	−	0.384564i	$-0.874352\pi$
$61$	−478.174	+	828.222i	−0.128507	+	0.222580i	0.794591	+	0.607145i	$0.207685\pi$
$62$	−998.577	+	487.469i	−0.259776	+	0.126813i
$63$	−4806.69	+	974.145i	−1.21106	+	0.245438i
$64$	3745.36	+	1658.17i	0.914394	+	0.404826i
$65$	728.057	−	1261.03i	0.172321	−	0.298469i
$66$	607.592	−	2580.00i	0.139484	−	0.592287i
$67$	−6010.96	+	3470.43i	−1.33904	+	0.773096i	−0.986665	−	0.162762i	$-0.947960\pi$
$67$	−6010.96	+	3470.43i	−1.33904	+	0.773096i	−0.352376	+	0.935858i	$0.614626\pi$
$68$	852.527	+	119.209i	0.184370	+	0.0257805i
$69$	1961.94	+	1604.21i	0.412086	+	0.336948i
$70$	784.928	−	11281.5i	0.160189	−	2.30234i
$71$			5971.60i			1.18461i	0.805715	+	0.592303i	$0.201781\pi$
$71$			5971.60i			1.18461i	−0.805715	+	0.592303i	$0.798219\pi$
$72$	−4511.19	+	2554.03i	−0.870214	+	0.492675i
$73$	−4339.17			−0.814257			−0.407128	−	0.913371i	$-0.633470\pi$
$73$	−4339.17			−0.814257			−0.407128	+	0.913371i	$0.633470\pi$
$74$	4056.25	+	282.220i	0.740732	+	0.0515377i
$75$	13814.4	+	2255.18i	2.45589	+	0.400920i
$76$	−121.781	+	870.917i	−0.0210839	+	0.150782i
$77$	2229.00	+	3860.75i	0.375949	+	0.651163i
$78$	769.246	−	817.683i	0.126438	−	0.134399i
$79$	3294.15	+	1901.88i	0.527824	+	0.304740i	0.740130	−	0.672464i	$-0.234764\pi$
$79$	3294.15	+	1901.88i	0.527824	+	0.304740i	−0.212306	+	0.977203i	$0.568097\pi$
$80$	−2907.96	−	11594.3i	−0.454369	−	1.81161i
$81$	809.440	−	6510.88i	0.123371	−	0.992361i
$82$	−3320.52	−	6802.05i	−0.493831	−	1.01161i
$83$	−2730.64	−	1576.53i	−0.396376	−	0.228848i	0.288543	−	0.957467i	$-0.406829\pi$
$83$	−2730.64	−	1576.53i	−0.396376	−	0.228848i	−0.684919	+	0.728619i	$0.740163\pi$
$84$	2582.88	−	8327.59i	0.366054	−	1.18021i
$85$	−1256.08	−	2175.59i	−0.173851	−	0.301119i
$86$	−2551.84	−	1719.94i	−0.345030	−	0.232551i
$87$	−3972.17	−	648.452i	−0.524795	−	0.0856721i
$88$	3505.10	+	3149.38i	0.452622	+	0.406686i
$89$	−7132.44			−0.900447			−0.450224	−	0.892916i	$-0.648656\pi$
$89$	−7132.44			−0.900447			−0.450224	+	0.892916i	$0.648656\pi$
$90$	13974.6	+	5795.16i	1.72526	+	0.715452i
$91$			1888.18i			0.228014i
$92$	−4176.18	+	1690.67i	−0.493405	+	0.199749i
$93$	1935.55	+	1582.63i	0.223789	+	0.182985i
$94$	9095.67	+	6130.50i	1.02939	+	0.693809i
$95$	2222.52	−	1283.17i	0.246262	−	0.142180i
$96$	−133.201	−	9215.04i	−0.0144532	−	0.999896i
$97$	980.405	−	1698.11i	0.104199	−	0.180477i	−0.809212	−	0.587517i	$-0.800106\pi$
$97$	980.405	−	1698.11i	0.104199	−	0.180477i	0.913411	+	0.407040i	$0.133439\pi$
$98$	2219.91	+	4547.46i	0.231144	+	0.473496i
$99$	−5844.98	+	1184.57i	−0.596366	+	0.120862i
$100$	−15306.4	+	19619.5i	−1.53064	+	1.96195i
$101$	3849.96	−	6668.32i	0.377410	−	0.653693i	−0.613275	−	0.789870i	$-0.710148\pi$
$101$	3849.96	−	6668.32i	0.377410	−	0.653693i	0.990685	+	0.136177i	$0.0434815\pi$
$102$	−558.137	−	1854.69i	−0.0536464	−	0.178267i
$103$	3195.22	−	1844.76i	0.301180	−	0.173886i	−0.341793	−	0.939775i	$-0.611034\pi$
$103$	3195.22	−	1844.76i	0.301180	−	0.173886i	0.642973	+	0.765889i	$0.277701\pi$
$104$	618.727	+	1897.50i	0.0572048	+	0.175434i
$105$	−23797.6	+	9005.82i	−2.15852	+	0.816854i
$106$	−18545.9	−	1290.37i	−1.65058	−	0.114842i
$107$		−	13741.5i		−	1.20024i	−0.799911	−	0.600118i	$-0.795120\pi$
$107$		−	13741.5i		−	1.20024i	0.799911	−	0.600118i	$-0.204880\pi$
$108$	9463.21	+	6818.84i	0.811318	+	0.584605i
$109$	18709.9			1.57478			0.787388	−	0.616458i	$-0.211433\pi$
$109$	18709.9			1.57478			0.787388	+	0.616458i	$0.211433\pi$
$110$	954.480	−	13718.4i	0.0788826	−	1.13375i
$111$	−3238.04	−	8556.42i	−0.262806	−	0.694458i
$112$	10783.0	+	11135.0i	0.859613	+	0.887676i
$113$	5000.50	+	8661.12i	0.391613	+	0.678293i	0.992662	−	0.120919i	$-0.0385840\pi$
$113$	5000.50	+	8661.12i	0.391613	+	0.678293i	−0.601050	+	0.799212i	$0.705251\pi$
$114$	1894.69	−	570.176i	0.145791	−	0.0438732i
$115$	11386.7	+	6574.14i	0.861002	+	0.497099i
$116$	4401.20	−	5641.38i	0.327081	−	0.419246i
$117$	−2394.83	−	803.313i	−0.174945	−	0.0586831i
$118$	−1090.76	+	532.469i	−0.0783366	+	0.0382411i
$119$	2821.15	+	1628.79i	0.199219	+	0.115019i
$120$	−20963.9	+	16848.3i	−1.45583	+	1.17002i
$121$	−4610.01	−	7984.77i	−0.314870	−	0.545371i
$122$	−2138.03	+	3172.14i	−0.143646	+	0.213124i
$123$	−10780.5	+	13184.5i	−0.712572	+	0.871471i
$124$	−4120.01	+	1667.93i	−0.267951	+	0.108477i
$125$	43436.1			2.77991
$126$	−19450.9	+	2552.67i	−1.22517	+	0.160788i
$127$		−	18883.8i		−	1.17080i	−0.810745	−	0.585400i	$-0.800937\pi$
$127$		−	18883.8i		−	1.17080i	0.810745	−	0.585400i	$-0.199063\pi$
$128$	14484.9	+	7656.52i	0.884090	+	0.467317i
$129$	−1115.57	+	6833.58i	−0.0670377	+	0.410647i
$130$	3255.31	−	4829.82i	0.192622	−	0.285788i
$131$	−25700.9	+	14838.4i	−1.49763	+	0.864660i	−0.999996	−	0.00272458i	$-0.999133\pi$
$131$	−25700.9	+	14838.4i	−1.49763	+	0.864660i	−0.497639	+	0.867384i	$0.665799\pi$
$132$	3140.81	−	10126.4i	0.180258	−	0.581178i
$133$	−1663.92	+	2882.00i	−0.0940654	+	0.162926i
$134$	−24949.4	+	12179.4i	−1.38947	+	0.678290i
$135$	−1297.77	−	34014.5i	−0.0712080	−	1.86637i
$136$	3368.79	+	712.379i	0.182136	+	0.0385153i
$137$	−8332.79	+	14432.8i	−0.443965	+	0.768971i	−0.997980	−	0.0635366i	$-0.979762\pi$
$137$	−8332.79	+	14432.8i	−0.443965	+	0.768971i	0.554014	+	0.832507i	$0.313095\pi$
$138$	7383.44	+	6946.07i	0.387704	+	0.364738i
$139$	3545.95	−	2047.25i	0.183528	−	0.105960i	−0.405421	−	0.914130i	$-0.632875\pi$
$139$	3545.95	−	2047.25i	0.183528	−	0.105960i	0.588949	+	0.808170i	$0.299542\pi$
$140$	6264.28	−	44799.1i	0.319606	−	2.28567i
$141$	3976.30	−	24357.3i	0.200005	−	1.22516i
$142$	−1657.93	+	23828.8i	−0.0822222	+	1.18175i
$143$			2296.05i			0.112282i
$144$	−18710.3	+	8939.00i	−0.902311	+	0.431086i
$145$	−20880.9			−0.993147
$146$	−17314.8	−	1204.71i	−0.812293	−	0.0565167i
$147$	7207.21	−	8814.38i	0.333528	−	0.407903i
$148$	16107.5	+	2252.32i	0.735368	+	0.102827i
$149$	2934.59	+	5082.86i	0.132183	+	0.228947i	0.924518	−	0.381139i	$-0.124468\pi$
$149$	2934.59	+	5082.86i	0.132183	+	0.228947i	−0.792335	+	0.610086i	$0.791135\pi$
$150$	54498.0	+	12834.3i	2.42214	+	0.570414i
$151$	28725.6	+	16584.7i	1.25984	+	0.727369i	0.973043	−	0.230622i	$-0.0740760\pi$
$151$	28725.6	+	16584.7i	1.25984	+	0.727369i	0.286797	+	0.957991i	$0.407409\pi$
$152$	−727.745	+	3441.46i	−0.0314987	+	0.148955i
$153$	−3266.07	+	2885.17i	−0.139522	+	0.123250i
$154$	7822.63	+	16024.6i	0.329846	+	0.675687i
$155$	11233.6	+	6485.72i	0.467579	+	0.269957i
$156$	3296.58	−	3049.28i	0.135461	−	0.125299i
$157$	−11089.2	−	19207.1i	−0.449886	−	0.779226i	0.548492	−	0.836156i	$-0.315202\pi$
$157$	−11089.2	−	19207.1i	−0.449886	−	0.779226i	−0.998378	+	0.0569302i	$0.981869\pi$
$158$	12616.8	+	8503.74i	0.505400	+	0.340640i
$159$	14804.9	+	39121.6i	0.585615	+	1.54747i
$160$	−8384.79	−	47072.8i	−0.327531	−	1.83878i
$161$	−17049.7			−0.657758
$162$	5037.60	−	25756.0i	0.191953	−	0.981404i
$163$		−	31303.8i		−	1.17821i	−0.808057	−	0.589104i	$-0.799481\pi$
$163$		−	31303.8i		−	1.17821i	0.808057	−	0.589104i	$-0.200519\pi$
$164$	−11361.5	−	28064.5i	−0.422425	−	1.04344i
$165$	−28938.2	+	10951.2i	−1.06293	+	0.402247i
$166$	−10458.5	−	7049.04i	−0.379536	−	0.255808i
$167$	22551.7	−	13020.2i	0.808622	−	0.466858i	−0.0378548	−	0.999283i	$-0.512052\pi$
$167$	22551.7	−	13020.2i	0.808622	−	0.466858i	0.846477	+	0.532425i	$0.178719\pi$
$168$	12618.6	−	32512.9i	0.447089	−	1.15196i
$169$	13794.3	−	23892.4i	0.482975	−	0.836538i
$170$	−4408.17	−	9030.10i	−0.152532	−	0.312460i
$171$	−2947.40	−	3336.52i	−0.100797	−	0.114104i
$172$	−9705.23	−	7571.67i	−0.328057	−	0.255938i
$173$	−7830.38	+	13562.6i	−0.261632	+	0.453160i	−0.966676	−	0.256004i	$-0.917594\pi$
$173$	−7830.38	+	13562.6i	−0.261632	+	0.453160i	0.705044	+	0.709164i	$0.250927\pi$
$174$	−15670.3	−	3690.37i	−0.517583	−	0.121891i
$175$	−81551.5	+	47083.8i	−2.66290	+	1.53743i
$176$	13112.2	+	13540.3i	0.423302	+	0.437122i
$177$	2114.23	+	1728.73i	0.0674846	+	0.0551799i
$178$	−28461.0	−	1980.22i	−0.898276	−	0.0624991i
$179$			36836.7i			1.14967i	0.818268	+	0.574837i	$0.194935\pi$
$179$			36836.7i			1.14967i	−0.818268	+	0.574837i	$0.805065\pi$
$180$	54154.7	+	27004.6i	1.67144	+	0.833475i
$181$	56961.0			1.73868			0.869342	−	0.494211i	$-0.164543\pi$
$181$	56961.0			1.73868			0.869342	+	0.494211i	$0.164543\pi$
$182$	−524.227	+	7534.52i	−0.0158262	+	0.227464i
$183$	8494.68	+	1386.75i	0.253656	+	0.0414090i
$184$	−17133.8	+	5586.93i	−0.506080	+	0.165020i
$185$	−23732.1	−	41105.2i	−0.693414	−	1.20103i
$186$	7284.14	+	6852.65i	0.210549	+	0.198076i
$187$	3430.54	+	1980.62i	0.0981024	+	0.0566394i
$188$	34592.9	+	26988.1i	0.978749	+	0.763584i
$189$	23511.2	+	37356.9i	0.658190	+	1.04580i
$190$	9224.88	−	4503.26i	0.255537	−	0.124744i
$191$	−33837.1	−	19535.9i	−0.927527	−	0.535508i	−0.0414986	−	0.999139i	$-0.513213\pi$
$191$	−33837.1	−	19535.9i	−0.927527	−	0.535508i	−0.886029	+	0.463630i	$0.846547\pi$
$192$	2026.90	−	36808.2i	0.0549833	−	0.998487i
$193$	−2025.97	−	3509.08i	−0.0543898	−	0.0942059i	0.837549	−	0.546363i	$-0.183988\pi$
$193$	−2025.97	−	3509.08i	−0.0543898	−	0.0942059i	−0.891938	+	0.452157i	$0.850655\pi$
$194$	4383.62	−	6503.87i	0.116474	−	0.172810i
$195$	−12933.8	−	2111.43i	−0.340140	−	0.0555274i
$196$	7595.67	+	18762.3i	0.197721	+	0.488398i
$197$	−44869.6			−1.15617			−0.578083	−	0.815978i	$-0.696199\pi$
$197$	−44869.6			−1.15617			−0.578083	+	0.815978i	$0.696199\pi$
$198$	−23652.4	+	3104.08i	−0.603317	+	0.0791775i
$199$			56256.7i			1.42059i	0.703905	+	0.710294i	$0.251438\pi$
$199$			56256.7i			1.42059i	−0.703905	+	0.710294i	$0.748562\pi$
$200$	−66525.1	+	74039.1i	−1.66313	+	1.85098i
$201$	48359.6	+	39542.0i	1.19699	+	0.978737i
$202$	17214.1	−	25540.1i	0.421872	−	0.625921i
$203$	23449.3	−	13538.4i	0.569032	−	0.328531i
$204$	−1712.24	−	7555.82i	−0.0411437	−	0.181560i
$205$	−44179.1	+	76520.4i	−1.05126	+	1.82083i
$206$	13262.2	−	6474.13i	0.312523	−	0.152562i
$207$	7253.68	−	21624.6i	0.169285	−	0.504669i
$208$	1942.13	+	7743.46i	0.0448902	+	0.178982i
$209$	−2023.35	+	3504.54i	−0.0463210	+	0.0802303i
$210$	−97461.3	+	29329.3i	−2.21001	+	0.665064i
$211$	63309.8	−	36552.0i	1.42202	−	0.821005i	0.425551	−	0.904935i	$-0.360080\pi$
$211$	63309.8	−	36552.0i	1.42202	−	0.821005i	0.996472	+	0.0839298i	$0.0267471\pi$
$212$	−73646.6	−	10298.0i	−1.63863	−	0.229130i
$213$	50265.5	−	19022.1i	1.10793	−	0.419276i
$214$	3815.13	−	54833.4i	0.0833071	−	1.19734i
$215$			35922.8i			0.777129i
$216$	35868.4	+	29836.9i	0.768784	+	0.639508i
$217$	−16820.4			−0.357205
$218$	74659.2	+	5194.54i	1.57098	+	0.109303i
$219$	13822.2	+	36524.7i	0.288196	+	0.761549i
$220$	7617.42	−	54476.2i	0.157385	−	1.12554i
$221$	838.891	+	1453.00i	0.0171760	+	0.0297496i
$222$	−10545.3	−	35042.1i	−0.213971	−	0.711024i
$223$	−65737.1	−	37953.3i	−1.32191	−	0.763203i	−0.337873	−	0.941192i	$-0.609708\pi$
$223$	−65737.1	−	37953.3i	−1.32191	−	0.763203i	−0.984032	+	0.177989i	$0.943041\pi$
$224$	39936.4	+	47426.3i	0.795927	+	0.945200i
$225$	−25022.0	−	123465.i	−0.494261	−	2.43881i
$226$	17549.1	+	35949.3i	0.343589	+	0.703839i
$227$	−35712.5	−	20618.6i	−0.693057	−	0.400136i	0.111700	−	0.993742i	$-0.464371\pi$
$227$	−35712.5	−	20618.6i	−0.693057	−	0.400136i	−0.804756	+	0.593606i	$0.797704\pi$
$228$	7718.80	−	1749.17i	0.148484	−	0.0336483i
$229$	−13792.1	−	23888.7i	−0.263003	−	0.455534i	0.704036	−	0.710165i	$-0.251379\pi$
$229$	−13792.1	−	23888.7i	−0.263003	−	0.455534i	−0.967038	+	0.254630i	$0.918046\pi$
$230$	43611.9	+	29394.5i	0.824422	+	0.555662i
$231$	25397.2	−	31060.6i	0.475950	−	0.582084i
$232$	19128.6	−	21289.2i	0.355391	−	0.395533i
$233$	49430.2			0.910502			0.455251	−	0.890363i	$-0.349550\pi$
$233$	49430.2			0.910502			0.455251	+	0.890363i	$0.349550\pi$
$234$	−9333.17	−	3870.39i	−0.170450	−	0.0706843i
$235$		−	128042.i		−	2.31855i
$236$	−4500.34	+	1821.91i	−0.0808019	+	0.0327116i
$237$	5515.62	−	33786.6i	0.0981968	−	0.601517i
$238$	10805.2	+	7282.69i	0.190756	+	0.128570i
$239$	97042.8	−	56027.7i	1.69890	−	0.980859i	0.752091	−	0.659060i	$-0.229045\pi$
$239$	97042.8	−	56027.7i	1.69890	−	0.980859i	0.946808	−	0.321800i	$-0.104288\pi$
$240$	−88331.2	+	61410.5i	−1.53353	+	1.06615i
$241$	−20548.3	+	35590.7i	−0.353787	+	0.612776i	−0.986910	−	0.161275i	$-0.948439\pi$
$241$	−20548.3	+	35590.7i	−0.353787	+	0.612776i	0.633123	+	0.774051i	$0.281773\pi$
$242$	−16178.7	−	33142.0i	−0.276257	−	0.565910i
$243$	−57383.2	+	13926.6i	−0.971790	+	0.235848i
$244$	−9412.18	+	12064.4i	−0.158092	+	0.202640i
$245$	29535.6	−	51157.1i	0.492054	−	0.852263i
$246$	−46678.5	+	49617.7i	−0.771341	+	0.819910i
$247$	−1484.34	+	856.986i	−0.0243299	+	0.0140469i
$248$	−16903.4	+	5511.79i	−0.274834	+	0.0896167i
$249$	−4572.08	+	28006.9i	−0.0737421	+	0.451716i
$250$	173326.	+	12059.4i	2.77321	+	0.192951i
$251$		−	50848.1i		−	0.807099i	−0.914958	−	0.403550i	$-0.867776\pi$
$251$		−	50848.1i		−	0.807099i	0.914958	−	0.403550i	$-0.132224\pi$
$252$	−78324.5	+	4785.82i	−1.23338	+	0.0753625i
$253$	−20732.7			−0.323902
$254$	5242.83	−	75353.2i	0.0812640	−	1.16798i
$255$	−14311.7	+	17503.1i	−0.220095	+	0.269175i
$256$	55674.3	+	34573.7i	0.849522	+	0.527553i
$257$	−6405.02	−	11093.8i	−0.0969738	−	0.167964i	0.813457	−	0.581625i	$-0.197583\pi$
$257$	−6405.02	−	11093.8i	−0.0969738	−	0.167964i	−0.910431	+	0.413662i	$0.864250\pi$
$258$	−6348.78	+	26958.7i	−0.0953786	+	0.405004i
$259$	53302.2	+	30774.1i	0.794595	+	0.458760i
$260$	14330.8	−	18368.9i	0.211994	−	0.271730i
$261$	7194.80	+	35501.0i	0.105618	+	0.521147i
$262$	−106675.	+	52075.1i	−1.55404	+	0.758625i
$263$	27445.5	+	15845.6i	0.396789	+	0.229086i	0.685097	−	0.728452i	$-0.259760\pi$
$263$	27445.5	+	15845.6i	0.396789	+	0.229086i	−0.288309	+	0.957537i	$0.593093\pi$
$264$	15344.4	−	39536.1i	0.220162	−	0.567264i
$265$	108508.	+	187941.i	1.54514	+	2.67627i
$266$	−7439.79	+	11038.2i	−0.105147	+	0.156004i
$267$	22719.9	+	60036.8i	0.318702	+	0.842161i
$268$	−102938.	+	41673.2i	−1.43320	+	0.580213i
$269$	−54892.9			−0.758598			−0.379299	−	0.925274i	$-0.623835\pi$
$269$	−54892.9			−0.758598			−0.379299	+	0.925274i	$0.623835\pi$
$270$	4265.10	−	136090.i	0.0585062	−	1.86681i
$271$			106332.i			1.44785i	0.689877	+	0.723927i	$0.257665\pi$
$271$			106332.i			1.44785i	−0.689877	+	0.723927i	$0.742335\pi$
$272$	13244.9	+	3777.94i	0.179024	+	0.0510643i
$273$	15893.6	−	6014.68i	0.213254	−	0.0807026i
$274$	−37257.8	+	55278.5i	−0.496268	+	0.736301i
$275$	−99167.4	+	57254.3i	−1.31130	+	0.757082i
$276$	27534.1	+	29767.2i	0.361453	+	0.390768i
$277$	25166.6	−	43589.8i	0.327993	−	0.568100i	−0.654121	−	0.756390i	$-0.726961\pi$
$277$	25166.6	−	43589.8i	0.327993	−	0.568100i	0.982113	+	0.188290i	$0.0602945\pi$
$278$	14718.0	−	7184.78i	0.190440	−	0.0929660i
$279$	7156.12	−	21333.7i	0.0919326	−	0.274068i
$280$	37434.5	−	177025.i	0.477481	−	2.25797i
$281$	3048.20	−	5279.64i	0.0386039	−	0.0668640i	−0.846078	−	0.533059i	$-0.821042\pi$
$281$	3048.20	−	5279.64i	0.0386039	−	0.0668640i	0.884682	+	0.466195i	$0.154376\pi$
$282$	22629.3	−	96090.4i	0.284560	−	1.20832i
$283$	−44494.8	+	25689.1i	−0.555567	+	0.320757i	−0.751364	−	0.659888i	$-0.770604\pi$
$283$	−44494.8	+	25689.1i	−0.555567	+	0.320757i	0.195797	+	0.980644i	$0.437271\pi$
$284$	−13231.4	+	94625.0i	−0.164048	+	1.17319i
$285$	−17880.7	−	14620.4i	−0.220138	−	0.179999i
$286$	−637.465	+	9162.05i	−0.00779335	+	0.112011i
$287$		−	114576.i		−	1.39101i
$288$	−77142.6	+	30475.1i	−0.930056	+	0.367418i
$289$	−80626.4			−0.965343
$290$	−83322.2	−	5797.29i	−0.990752	−	0.0689332i
$291$	−17416.7	−	2843.26i	−0.205675	−	0.0335761i
$292$	−68757.8	−	9614.43i	−0.806411	−	0.112761i
$293$	−45640.7	−	79051.9i	−0.531639	−	0.920825i	−0.999318	−	0.0369270i	$-0.988243\pi$
$293$	−45640.7	−	79051.9i	−0.531639	−	0.920825i	0.467679	−	0.883898i	$-0.345090\pi$
$294$	31206.5	−	33171.5i	0.361036	−	0.383770i
$295$	12270.6	+	7084.43i	0.141001	+	0.0814068i
$296$	63649.3	+	13459.6i	0.726457	+	0.153620i
$297$	28589.8	+	45426.3i	0.324115	+	0.514985i
$298$	10298.9	+	21097.1i	0.115973	+	0.237570i
$299$	−7604.82	−	4390.65i	−0.0850642	−	0.0491118i
$300$	213903.	+	66344.0i	2.37670	+	0.737156i
$301$	−23291.0	−	40341.3i	−0.257073	−	0.445263i
$302$	110021.	+	74154.3i	1.20632	+	0.813059i
$303$	−68393.9	−	11165.2i	−0.744958	−	0.121614i
$304$	−3859.43	+	13530.6i	−0.0417615	+	0.146409i
$305$	44654.9			0.480031
$306$	−13833.8	+	10606.1i	−0.147740	+	0.113269i
$307$			108180.i			1.14781i	0.818923	+	0.573904i	$0.194572\pi$
$307$			108180.i			1.14781i	−0.818923	+	0.573904i	$0.805428\pi$
$308$	26766.0	+	66115.6i	0.282152	+	0.696952i
$309$	−25706.3	−	21019.1i	−0.269229	−	0.220139i
$310$	43025.4	+	28999.2i	0.447714	+	0.301760i
$311$	−86673.2	+	50040.8i	−0.896116	+	0.517373i	−0.875938	−	0.482424i	$-0.839757\pi$
$311$	−86673.2	+	50040.8i	−0.896116	+	0.517373i	−0.0201778	+	0.999796i	$0.506423\pi$
$312$	14001.1	−	11252.4i	0.143831	−	0.115595i
$313$	75895.3	−	131455.i	0.774687	−	1.34180i	−0.160283	−	0.987071i	$-0.551241\pi$
$313$	75895.3	−	131455.i	0.774687	−	1.34180i	0.934970	−	0.354726i	$-0.115426\pi$
$314$	−38917.4	−	79722.0i	−0.394716	−	0.808572i
$315$	151612.	+	171627.i	1.52796	+	1.72968i
$316$	47984.5	+	37435.8i	0.480537	+	0.374898i
$317$	−56202.0	+	97344.7i	−0.559285	+	0.968710i	0.438271	+	0.898843i	$0.355591\pi$
$317$	−56202.0	+	97344.7i	−0.559285	+	0.968710i	−0.997556	+	0.0698672i	$0.977742\pi$
$318$	48215.3	+	160219.i	0.476794	+	1.58439i
$319$	28514.5	−	16462.9i	0.280211	−	0.161780i
$320$	−20389.2	−	190165.i	−0.199113	−	1.85708i
$321$	−115668.	+	43772.7i	−1.12254	+	0.424808i
$322$	−68034.5	−	4733.62i	−0.656172	−	0.0456543i
$323$			2957.02i			0.0283433i
$324$	27252.6	−	101377.i	0.259608	−	0.965714i
$325$	−48500.0			−0.459172
$326$	8691.05	−	124913.i	0.0817781	−	1.17537i
$327$	−59599.2	−	157489.i	−0.557372	−	1.47284i
$328$	−37544.9	−	115142.i	−0.348982	−	1.07025i
$329$	83017.6	+	143791.i	0.766970	+	1.32843i
$330$	−118514.	+	35664.8i	−1.08828	+	0.327500i
$331$	−99528.9	−	57463.0i	−0.908433	−	0.524484i	−0.0285065	−	0.999594i	$-0.509075\pi$
$331$	−99528.9	−	57463.0i	−0.908433	−	0.524484i	−0.879927	+	0.475109i	$0.842408\pi$
$332$	−39776.0	−	31031.8i	−0.360865	−	0.281534i
$333$	−61708.5	+	54511.8i	−0.556488	+	0.491589i
$334$	93604.0	−	45694.1i	0.839076	−	0.409607i
$335$	280670.	+	162045.i	2.50096	+	1.44393i
$336$	59379.6	−	126235.i	0.525967	−	1.11815i
$337$	−61646.2	−	106774.i	−0.542808	−	0.940171i	−0.998741	−	0.0501573i	$-0.984028\pi$
$337$	−61646.2	−	106774.i	−0.542808	−	0.940171i	0.455933	−	0.890014i	$-0.349306\pi$
$338$	61677.3	−	91509.1i	0.539874	−	0.800997i
$339$	56975.6	−	69680.8i	0.495780	−	0.606336i
$340$	−15083.1	−	37257.1i	−0.130476	−	0.322294i
$341$	−20453.8			−0.175900
$342$	−10834.8	−	14132.2i	−0.0926340	−	0.120825i
$343$		−	68777.2i		−	0.584597i
$344$	−36625.1	−	32908.2i	−0.309501	−	0.278091i
$345$	19065.6	−	116789.i	0.160181	−	0.981210i
$346$	−35011.5	+	51945.7i	−0.292454	+	0.433907i
$347$	−82843.4	+	47829.7i	−0.688017	+	0.397227i	−0.802869	−	0.596156i	$-0.796694\pi$
$347$	−82843.4	+	47829.7i	−0.688017	+	0.397227i	0.114852	+	0.993383i	$0.463361\pi$
$348$	−61505.6	−	19076.5i	−0.507874	−	0.157522i
$349$	−21543.6	+	37314.5i	−0.176875	+	0.306357i	−0.940809	−	0.338938i	$-0.889932\pi$
$349$	−21543.6	+	37314.5i	−0.176875	+	0.306357i	0.763934	+	0.645295i	$0.223266\pi$
$350$	−338491.	+	165239.i	−2.76319	+	1.34889i
$351$	866.734	+	22717.2i	0.00703512	+	0.184391i
$352$	48563.1	+	57670.9i	0.391941	+	0.465448i
$353$	56436.9	−	97751.7i	0.452912	−	0.784467i	−0.545653	−	0.838011i	$-0.683718\pi$
$353$	56436.9	−	97751.7i	0.452912	−	0.784467i	0.998565	+	0.0535440i	$0.0170517\pi$
$354$	7956.55	+	7485.23i	0.0634919	+	0.0597308i
$355$	241476.	−	139416.i	1.91610	−	1.10626i
$356$	−113020.	−	15803.6i	−0.891771	−	0.124697i
$357$	4723.63	−	28935.2i	0.0370629	−	0.227033i
$358$	−10227.2	+	146992.i	−0.0797977	+	1.14690i
$359$			223134.i			1.73132i	0.500632	+	0.865660i	$0.333101\pi$
$359$			223134.i			1.73132i	−0.500632	+	0.865660i	$0.666899\pi$
$360$	208599.	+	122793.i	1.60956	+	0.947478i
$361$	127300.			0.976820
$362$	227295.	+	15814.4i	1.73449	+	0.120680i
$363$	−52526.3	+	64239.4i	−0.398624	+	0.487515i
$364$	−4183.70	+	29919.8i	−0.0315760	+	0.225817i
$365$	101305.	+	175465.i	0.760404	+	1.31706i
$366$	33511.8	+	7892.04i	0.250170	+	0.0589151i
$367$	−92257.6	−	53265.0i	−0.684968	−	0.395466i	0.116756	−	0.993161i	$-0.462750\pi$
$367$	−92257.6	−	53265.0i	−0.684968	−	0.395466i	−0.801724	+	0.597694i	$0.796084\pi$
$368$	−69921.2	+	17536.9i	−0.516313	+	0.129496i
$369$	145320.	+	48745.7i	1.06727	+	0.358000i
$370$	−83287.1	−	170613.i	−0.608379	−	1.24626i
$371$	−243708.	−	140705.i	−1.77061	−	1.02226i
$372$	27163.7	+	29366.8i	0.196293	+	0.212212i
$373$	−71440.5	−	123739.i	−0.513484	−	0.889380i	−0.999878	−	0.0156403i	$-0.995021\pi$
$373$	−71440.5	−	123739.i	−0.513484	−	0.889380i	0.486394	−	0.873740i	$-0.338312\pi$
$374$	13139.2	+	8855.83i	0.0939345	+	0.0633120i
$375$	−138363.	−	365620.i	−0.983914	−	2.59997i
$376$	130545.	+	117296.i	0.923389	+	0.829677i
$377$	13945.7			0.0981197
$378$	83446.3	+	155595.i	0.584015	+	1.08896i
$379$			95242.7i			0.663061i	0.943445	+	0.331530i	$0.107565\pi$
$379$			95242.7i			0.663061i	−0.943445	+	0.331530i	$0.892435\pi$
$380$	38060.8	−	15408.4i	0.263579	−	0.106707i
$381$	−158953.	+	60153.2i	−1.09501	+	0.414390i
$382$	−129598.	−	87349.4i	−0.888121	−	0.598595i
$383$	46899.6	−	27077.5i	0.319721	−	0.184591i	−0.331547	−	0.943439i	$-0.607571\pi$
$383$	46899.6	−	27077.5i	0.319721	−	0.184591i	0.651268	+	0.758848i	$0.274237\pi$
$384$	18307.3	−	146315.i	0.124155	−	0.992263i
$385$	104079.	−	180270.i	0.702169	−	1.21619i
$386$	−7110.07	−	14564.9i	−0.0477199	−	0.0977538i
$387$	61074.8	−	12377.7i	0.407793	−	0.0826451i
$388$	19297.9	−	24735.7i	0.128188	−	0.164309i
$389$	−6513.23	+	11281.2i	−0.0430425	+	0.0745518i	−0.886744	−	0.462261i	$-0.847038\pi$
$389$	−6513.23	+	11281.2i	−0.0430425	+	0.0745518i	0.843702	+	0.536813i	$0.180372\pi$
$390$	−51024.3	−	12016.2i	−0.335465	−	0.0790022i
$391$	−13120.2	+	7574.94i	−0.0858196	+	0.0495480i
$392$	25100.3	+	76977.0i	0.163346	+	0.500943i
$393$	206770.	+	169069.i	1.33876	+	1.09466i
$394$	−179046.	−	12457.4i	−1.15338	−	0.0802481i
$395$		−	177609.i		−	1.13834i
$396$	−95243.3	+	5819.60i	−0.607357	+	0.0371110i
$397$	54407.2			0.345204			0.172602	−	0.984992i	$-0.444783\pi$
$397$	54407.2			0.345204			0.172602	+	0.984992i	$0.444783\pi$
$398$	−15618.9	+	224484.i	−0.0986014	+	1.41716i
$399$	29559.3	+	4825.53i	0.185673	+	0.0303109i
$400$	−286015.	+	276972.i	−1.78759	+	1.73108i
$401$	−25211.2	−	43667.1i	−0.156785	−	0.271560i	0.776922	−	0.629596i	$-0.216780\pi$
$401$	−25211.2	−	43667.1i	−0.156785	−	0.271560i	−0.933708	+	0.358036i	$0.883446\pi$
$402$	181994.	+	171213.i	1.12617	+	1.05946i
$403$	−7502.54	−	4331.59i	−0.0461953	−	0.0266709i
$404$	75781.0	−	97134.7i	0.464299	−	0.595130i
$405$	−282181.	+	119275.i	−1.72035	+	0.727175i
$406$	97329.6	−	47512.8i	0.590463	−	0.288243i
$407$	64816.0	+	37421.6i	0.391285	+	0.225909i
$408$	−4734.66	−	30625.8i	−0.0284426	−	0.183978i
$409$	−20416.9	−	35363.2i	−0.122052	−	0.211400i	0.798525	−	0.601962i	$-0.205614\pi$
$409$	−20416.9	−	35363.2i	−0.122052	−	0.211400i	−0.920577	+	0.390562i	$0.872281\pi$
$410$	−197535.	+	293078.i	−1.17510	+	1.74347i
$411$	148031.	+	24165.8i	0.876331	+	0.143060i
$412$	54718.4	−	22152.0i	0.322358	−	0.130503i
$413$	−18373.2			−0.107717
$414$	34948.5	−	84275.8i	0.203905	−	0.491702i
$415$			147226.i			0.854850i
$416$	5599.92	+	31438.3i	0.0323590	+	0.181666i
$417$	−28528.0	−	23326.3i	−0.164059	−	0.134145i
$418$	−9046.86	+	13422.6i	−0.0517780	+	0.0768217i
$419$	28866.9	−	16666.3i	0.164427	−	0.0949318i	−0.415529	−	0.909580i	$-0.636403\pi$
$419$	28866.9	−	16666.3i	0.164427	−	0.0949318i	0.579955	+	0.814648i	$0.303070\pi$
$420$	−397048.	+	89975.7i	−2.25084	+	0.510066i
$421$	−4180.31	+	7240.51i	−0.0235855	+	0.0408512i	−0.877577	−	0.479435i	$-0.840842\pi$
$421$	−4180.31	+	7240.51i	−0.0235855	+	0.0408512i	0.853992	+	0.520287i	$0.174175\pi$
$422$	262777.	−	128278.i	1.47558	−	0.720324i
$423$	−217692.	+	44118.5i	−1.21664	+	0.246570i
$424$	−291017.	−	61539.7i	−1.61877	−	0.342313i
$425$	−41837.2	+	72464.1i	−0.231625	+	0.401186i
$426$	205858.	−	61949.6i	1.13436	−	0.341365i
$427$	−50147.4	+	28952.6i	−0.275038	+	0.158793i
$428$	30447.4	−	217746.i	0.166212	−	1.18867i
$429$	19326.8	−	7313.91i	0.105014	−	0.0397407i
$430$	−9973.45	+	143345.i	−0.0539397	+	0.775255i
$431$		−	88445.3i		−	0.476124i	−0.971250	−	0.238062i	$-0.923488\pi$
$431$		−	88445.3i		−	0.476124i	0.971250	−	0.238062i	$-0.0765122\pi$
$432$	134844.	+	129018.i	0.722543	+	0.691326i
$433$	119092.			0.635195			0.317598	−	0.948226i	$-0.397124\pi$
$433$	119092.			0.635195			0.317598	+	0.948226i	$0.397124\pi$
$434$	−67119.5	−	4669.95i	−0.356344	−	0.0247932i
$435$	66514.8	+	175763.i	0.351512	+	0.928860i
$436$	296474.	+	41456.1i	1.55960	+	0.218080i
$437$	−7738.34	−	13403.2i	−0.0405214	−	0.0701852i
$438$	45014.7	+	149584.i	0.234642	+	0.779716i
$439$	103483.	+	59746.2i	0.536960	+	0.310014i	0.743846	−	0.668351i	$-0.233000\pi$
$439$	103483.	+	59746.2i	0.536960	+	0.310014i	−0.206886	+	0.978365i	$0.566333\pi$
$440$	45520.7	−	215264.i	0.235128	−	1.11190i
$441$	−97152.5	−	32588.5i	−0.499547	−	0.167567i
$442$	2944.07	+	6030.90i	0.0150696	+	0.0308700i
$443$	−176414.	−	101853.i	−0.898930	−	0.518998i	−0.0220772	−	0.999756i	$-0.507028\pi$
$443$	−176414.	−	101853.i	−0.898930	−	0.518998i	−0.876853	+	0.480759i	$0.840361\pi$
$444$	−32350.7	−	142758.i	−0.164103	−	0.724161i
$445$	166518.	+	288418.i	0.840894	+	1.45647i
$446$	−251777.	−	169698.i	−1.26574	−	0.853114i
$447$	33436.6	−	40892.8i	0.167343	−	0.204659i
$448$	146193.	+	200336.i	0.728402	+	0.998165i
$449$	77156.2			0.382717			0.191359	−	0.981520i	$-0.438711\pi$
$449$	77156.2			0.382717			0.191359	+	0.981520i	$0.438711\pi$
$450$	−65568.1	−	499616.i	−0.323793	−	2.46724i
$451$		−	139326.i		−	0.684982i
$452$	60046.4	+	148322.i	0.293907	+	0.725989i
$453$	48097.2	−	294625.i	0.234382	−	1.43573i
$454$	−136781.	−	92190.7i	−0.663612	−	0.447276i
$455$	76353.2	−	44082.6i	0.368812	−	0.212934i
$456$	31286.4	−	4836.80i	0.150462	−	0.0232610i
$457$	−140420.	+	243215.i	−0.672353	+	1.16455i	0.304882	+	0.952390i	$0.401383\pi$
$457$	−140420.	+	243215.i	−0.672353	+	1.16455i	−0.977235	+	0.212159i	$0.931951\pi$
$458$	−48403.1	−	99153.4i	−0.230750	−	0.472690i
$459$	34689.5	+	18301.3i	0.164654	+	0.0868675i
$460$	165866.	+	129403.i	0.783866	+	0.611544i
$461$	200811.	−	347814.i	0.944898	−	1.63661i	0.188942	−	0.981988i	$-0.439494\pi$
$461$	200811.	−	347814.i	0.944898	−	1.63661i	0.755956	−	0.654623i	$-0.227173\pi$
$462$	109967.	−	116892.i	0.515204	−	0.547645i
$463$	51806.1	−	29910.3i	0.241668	−	0.139527i	−0.374275	−	0.927318i	$-0.622108\pi$
$463$	51806.1	−	29910.3i	0.241668	−	0.139527i	0.615943	+	0.787791i	$0.288775\pi$
$464$	82240.4	−	79640.5i	0.381988	−	0.369912i
$465$	18809.2	−	115218.i	0.0869888	−	0.532861i
$466$	197244.	+	13723.6i	0.908306	+	0.0631969i
$467$			208473.i			0.955909i	0.878385	+	0.477955i	$0.158622\pi$
$467$			208473.i			0.955909i	−0.878385	+	0.477955i	$0.841378\pi$
$468$	−36168.1	−	18035.4i	−0.165133	−	0.0823446i
$469$	−420257.			−1.91060
$470$	35548.9	−	510931.i	0.160928	−	2.31295i
$471$	−126350.	+	154526.i	−0.569554	+	0.696562i
$472$	−18463.8	+	6020.59i	−0.0828775	+	0.0270243i
$473$	−28322.1	−	49055.4i	−0.126591	−	0.219263i
$474$	31389.6	−	133289.i	0.139711	−	0.593250i
$475$	−74027.3	−	42739.7i	−0.328099	−	0.189428i
$476$	41094.5	+	32060.4i	0.181372	+	0.141500i
$477$	282143.	−	249239.i	1.24003	−	1.09541i
$478$	402790.	−	196628.i	1.76288	−	0.860575i
$479$	138667.	+	80059.3i	0.604368	+	0.348932i	0.770758	−	0.637128i	$-0.219878\pi$
$479$	138667.	+	80059.3i	0.604368	+	0.348932i	−0.166390	+	0.986060i	$0.553211\pi$
$480$	−369523.	+	220526.i	−1.60383	+	0.957143i
$481$	15849.9	+	27452.8i	0.0685070	+	0.118658i
$482$	−91876.1	+	136314.i	−0.395466	+	0.586743i
$483$	54310.8	+	143515.i	0.232805	+	0.615181i
$484$	−55357.4	−	136740.i	−0.236312	−	0.583720i
$485$	−91556.4			−0.389229
$486$	−232846.	+	39640.3i	−0.985816	+	0.167828i
$487$			371960.i			1.56834i	0.620549	+	0.784168i	$0.286910\pi$
$487$			371960.i			1.56834i	−0.620549	+	0.784168i	$0.713090\pi$
$488$	−40907.4	+	45527.9i	−0.171776	+	0.191178i
$489$	−263497.	+	99716.2i	−1.10194	+	0.417011i
$490$	132060.	−	195935.i	0.550022	−	0.816055i
$491$	57863.4	−	33407.4i	0.240016	−	0.138574i	−0.375168	−	0.926957i	$-0.622415\pi$
$491$	57863.4	−	33407.4i	0.240016	−	0.138574i	0.615184	+	0.788383i	$0.289082\pi$
$492$	−200039.	+	185033.i	−0.826390	+	0.764395i
$493$	12029.8	−	20836.3i	0.0494955	−	0.0857288i
$494$	−6160.99	+	3007.57i	−0.0252462	+	0.0123243i
$495$	184361.	+	208700.i	0.752418	+	0.851752i
$496$	−68980.8	+	17301.0i	−0.280391	+	0.0703246i
$497$	−180785.	+	313129.i	−0.731896	+	1.26768i
$498$	−26019.9	+	110488.i	−0.104917	+	0.445508i
$499$	288151.	−	166364.i	1.15723	−	0.668127i	0.206591	−	0.978427i	$-0.433763\pi$
$499$	288151.	−	166364.i	1.15723	−	0.668127i	0.950638	+	0.310301i	$0.100430\pi$
$500$	688282.	+	96242.7i	2.75313	+	0.384971i
$501$	−181434.	−	148352.i	−0.722840	−	0.591041i
$502$	14117.2	−	202902.i	0.0560199	−	0.805153i
$503$			12673.0i			0.0500892i	0.999686	+	0.0250446i	$0.00797278\pi$
$503$			12673.0i			0.0500892i	−0.999686	+	0.0250446i	$0.992027\pi$
$504$	−313871.	−	2648.55i	−1.23563	−	0.0104267i
$505$	−359533.			−1.40980
$506$	−82730.6	−	5756.12i	−0.323121	−	0.0224817i
$507$	−245053.	−	40004.6i	−0.953331	−	0.155630i
$508$	41841.5	−	299230.i	0.162136	−	1.15952i
$509$	19452.7	+	33693.0i	0.0750834	+	0.130048i	0.901123	−	0.433564i	$-0.142744\pi$
$509$	19452.7	+	33693.0i	0.0750834	+	0.130048i	−0.826039	+	0.563613i	$0.809411\pi$
$510$	−61968.2	+	65870.2i	−0.238248	+	0.253249i
$511$	−227530.	−	131365.i	−0.871360	−	0.503080i
$512$	212561.	+	153419.i	0.810856	+	0.585245i
$513$	−18696.1	+	35437.8i	−0.0710422	+	0.134658i
$514$	−22478.3	−	46046.5i	−0.0850817	−	0.174289i
$515$	−149195.	−	86137.5i	−0.562521	−	0.324772i
$516$	−32818.6	+	105812.i	−0.123259	+	0.397407i
$517$	100950.	+	174851.i	0.377682	+	0.654164i
$518$	204151.	+	137598.i	0.760837	+	0.512805i
$519$	139105.	+	22708.8i	0.516428	+	0.0843062i
$520$	62284.7	−	69319.7i	0.230343	−	0.256360i
$521$	28001.3			0.103158			0.0515790	−	0.998669i	$-0.483575\pi$
$521$	28001.3			0.103158			0.0515790	+	0.998669i	$0.483575\pi$
$522$	18853.4	+	143659.i	0.0691909	+	0.527221i
$523$		−	306435.i		−	1.12030i	−0.828391	−	0.560151i	$-0.810743\pi$
$523$		−	306435.i		−	1.12030i	0.828391	−	0.560151i	$-0.189257\pi$
$524$	−440130.	+	178181.i	−1.60295	+	0.648932i
$525$	656101.	+	536471.i	2.38041	+	1.94638i
$526$	105118.	+	70849.6i	0.379931	+	0.256074i
$527$	−12943.7	+	7473.06i	−0.0466056	+	0.0269077i
$528$	72206.1	−	153503.i	0.259004	−	0.550615i
$529$	−100274.	+	173680.i	−0.358326	+	0.620638i
$530$	380805.	+	780076.i	1.35566	+	2.77706i
$531$	7816.72	−	23303.1i	0.0277227	−	0.0826465i
$532$	−32752.0	+	41980.9i	−0.115722	+	0.148330i
$533$	29505.7	−	51105.4i	0.103861	−	0.179892i
$534$	73992.2	+	245876.i	0.259480	+	0.862250i
$535$	−555671.	+	320817.i	−1.94138	+	1.12086i
$536$	−422330.	+	137711.i	−1.47002	+	0.479336i
$537$	310070.	−	117341.i	1.07526	−	0.406913i
$538$	−219042.	−	15240.2i	−0.756768	−	0.0526534i
$539$			93145.3i			0.320615i
$540$	54802.8	−	541864.i	0.187938	−	1.85824i
$541$	387269.			1.32318			0.661590	−	0.749866i	$-0.269882\pi$
$541$	387269.			1.32318			0.661590	+	0.749866i	$0.269882\pi$
$542$	−29521.5	+	424302.i	−0.100494	+	1.44436i
$543$	−181446.	−	479465.i	−0.615385	−	1.62614i
$544$	51802.8	+	18752.6i	0.175047	+	0.0633669i
$545$	−436812.	−	756581.i	−1.47062	−	2.54720i
$546$	65091.1	−	19588.1i	0.218341	−	0.0657062i
$547$	220183.	+	127123.i	0.735883	+	0.424862i	0.820570	−	0.571545i	$-0.193656\pi$
$547$	220183.	+	127123.i	0.735883	+	0.424862i	−0.0846877	+	0.996408i	$0.526989\pi$
$548$	−164019.	+	210237.i	−0.546177	+	0.700080i
$549$	−15386.4	−	75920.7i	−0.0510497	−	0.251893i
$550$	−411609.	+	200933.i	−1.36069	+	0.664240i
$551$	21285.8	+	12289.3i	0.0701109	+	0.0404786i
$552$	101606.	+	126426.i	0.333459	+	0.414914i
$553$	115156.	+	199455.i	0.376560	+	0.652221i
$554$	112526.	−	166951.i	0.366633	−	0.543965i
$555$	−270403.	+	330701.i	−0.877859	+	1.07362i
$556$	60724.6	−	24583.6i	0.196433	−	0.0795235i
$557$	−154243.			−0.497159			−0.248580	−	0.968611i	$-0.579964\pi$
$557$	−154243.			−0.497159			−0.248580	+	0.968611i	$0.579964\pi$
$558$	34478.5	−	83142.3i	0.110734	−	0.267026i
$559$		−	23991.6i		−	0.0767779i
$560$	198525.	−	696000.i	0.633053	−	2.21939i
$561$	5743.98	−	35185.5i	0.0182510	−	0.111799i
$562$	13629.2	−	20221.4i	0.0431518	−	0.0640232i
$563$	188653.	−	108919.i	0.595177	−	0.343626i	−0.171965	−	0.985103i	$-0.555012\pi$
$563$	188653.	−	108919.i	0.595177	−	0.343626i	0.767142	+	0.641477i	$0.221678\pi$
$564$	116977.	−	377152.i	0.367742	−	1.18565i
$565$	233489.	−	404415.i	0.731425	−	1.26686i
$566$	−184682.	+	90155.2i	−0.576490	+	0.281422i
$567$	239555.	−	316901.i	0.745143	−	0.985730i
$568$	−79069.4	+	373914.i	−0.245082	+	1.15898i
$569$	−112165.	+	194275.i	−0.346443	+	0.600057i	−0.985615	−	0.169007i	$-0.945944\pi$
$569$	−112165.	+	194275.i	−0.346443	+	0.600057i	0.639172	+	0.769064i	$0.279277\pi$
$570$	−67291.1	−	63304.9i	−0.207113	−	0.194844i
$571$	227168.	−	131156.i	0.696748	−	0.402268i	−0.109387	−	0.993999i	$-0.534889\pi$
$571$	227168.	−	131156.i	0.696748	−	0.402268i	0.806135	+	0.591732i	$0.201555\pi$
$572$	−5087.42	+	36382.8i	−0.0155491	+	0.111200i
$573$	−56655.8	+	347052.i	−0.172558	+	1.05702i
$574$	31810.5	−	457201.i	0.0965488	−	1.38766i
$575$		−	437941.i		−	1.32458i
$576$	−316287.	+	100189.i	−0.953315	+	0.301978i
$577$	450994.			1.35462			0.677312	−	0.735696i	$-0.263145\pi$
$577$	450994.			1.35462			0.677312	+	0.735696i	$0.263145\pi$
$578$	−321728.	−	22384.8i	−0.963015	−	0.0670034i
$579$	−23083.8	+	28231.3i	−0.0688573	+	0.0842121i
$580$	−330876.	−	46266.4i	−0.983578	−	0.137534i
$581$	−95456.3	−	165335.i	−0.282782	−	0.489794i
$582$	−68709.6	−	16181.1i	−0.202848	−	0.0477708i
$583$	−296351.	−	171099.i	−0.871907	−	0.503396i
$584$	−271699.	−	57454.6i	−0.796640	−	0.168461i
$585$	23427.0	+	115595.i	0.0684550	+	0.337775i
$586$	−160175.	−	328117.i	−0.466443	−	0.955505i
$587$	307738.	+	177673.i	0.893111	+	0.515638i	0.874959	−	0.484197i	$-0.160888\pi$
$587$	307738.	+	177673.i	0.893111	+	0.515638i	0.0181523	+	0.999835i	$0.494222\pi$
$588$	133735.	−	123702.i	0.386802	−	0.357785i
$589$	−7634.26	−	13222.9i	−0.0220058	−	0.0381151i
$590$	46997.1	+	31676.1i	0.135010	+	0.0909972i
$591$	142929.	+	377686.i	0.409210	+	1.08133i
$592$	250246.	+	71379.7i	0.714043	+	0.203672i
$593$	89819.5			0.255424			0.127712	−	0.991811i	$-0.459237\pi$
$593$	89819.5			0.255424			0.127712	+	0.991811i	$0.459237\pi$
$594$	101472.	+	189205.i	0.287589	+	0.536240i
$595$		−	152106.i		−	0.429649i
$596$	35238.8	+	87044.4i	0.0992038	+	0.245046i
$597$	473536.	−	179202.i	1.32863	−	0.502799i
$598$	−29126.9	−	19631.6i	−0.0814502	−	0.0548976i
$599$	357687.	−	206511.i	0.996896	−	0.575558i	0.0895677	−	0.995981i	$-0.471451\pi$
$599$	357687.	−	206511.i	0.996896	−	0.575558i	0.907328	+	0.420422i	$0.138118\pi$
$600$	835130.	+	324123.i	2.31980	+	0.900342i
$601$	−129317.	+	223984.i	−0.358020	+	0.620110i	−0.987630	−	0.156802i	$-0.949882\pi$
$601$	−129317.	+	223984.i	−0.358020	+	0.620110i	0.629610	+	0.776912i	$0.283215\pi$
$602$	−81739.3	−	167442.i	−0.225548	−	0.462032i
$603$	178795.	−	533021.i	0.491723	−	1.46592i
$604$	418434.	+	326447.i	1.14697	+	0.894828i
$605$	−215256.	+	372834.i	−0.588090	+	1.01860i
$606$	−269816.	−	63541.7i	−0.734721	−	0.173027i
$607$	−267430.	+	154401.i	−0.725825	+	0.419055i	−0.816893	−	0.576789i	$-0.804305\pi$
$607$	−267430.	+	154401.i	−0.725825	+	0.419055i	0.0910678	+	0.995845i	$0.470972\pi$
$608$	−19157.1	+	52920.3i	−0.0518229	+	0.143158i
$609$	−188655.	−	154256.i	−0.508667	−	0.415919i
$610$	178189.	+	12397.8i	0.478873	+	0.0333184i
$611$			85514.7i			0.229065i
$612$	−58146.3	+	38481.2i	−0.155246	+	0.102741i
$613$	−464349.			−1.23573			−0.617865	−	0.786284i	$-0.712002\pi$
$613$	−464349.			−1.23573			−0.617865	+	0.786284i	$0.712002\pi$
$614$	−30034.6	+	431675.i	−0.0796681	+	1.14504i
$615$	784834.	+	128123.i	2.07505	+	0.338749i
$616$	88449.9	+	271256.i	0.233097	+	0.714855i
$617$	253688.	+	439401.i	0.666392	+	1.15423i	0.978906	+	0.204312i	$0.0654958\pi$
$617$	253688.	+	439401.i	0.666392	+	1.15423i	−0.312513	+	0.949913i	$0.601171\pi$
$618$	−96741.4	−	91010.7i	−0.253300	−	0.238295i
$619$	−244884.	−	141384.i	−0.639115	−	0.368993i	0.145159	−	0.989408i	$-0.453631\pi$
$619$	−244884.	−	141384.i	−0.639115	−	0.368993i	−0.784273	+	0.620415i	$0.786964\pi$
$620$	163635.	+	127662.i	0.425690	+	0.332108i
$621$	−205129.	+	7826.35i	−0.531918	+	0.0202944i
$622$	−359750.	+	175617.i	−0.929865	+	0.453927i
$623$	−373999.	−	215929.i	−0.963595	−	0.556332i
$624$	58993.4	−	41014.0i	0.151508	−	0.105333i
$625$	−528069.	−	914643.i	−1.35186	−	2.34149i
$626$	339346.	−	503479.i	0.865951	−	1.28479i
$627$	35944.4	+	5867.89i	0.0914317	+	0.0149261i
$628$	−133161.	−	328924.i	−0.337642	−	0.834019i
$629$	54689.8			0.138231
$630$	557334.	+	726946.i	1.40422	+	1.83156i
$631$		−	403620.i		−	1.01371i	−0.862031	−	0.506855i	$-0.830808\pi$
$631$		−	403620.i		−	1.01371i	0.862031	−	0.506855i	$-0.169192\pi$
$632$	181082.	+	162704.i	0.453357	+	0.407347i
$633$	−509343.	−	416472.i	−1.27117	−	1.03939i
$634$	−251292.	+	372836.i	−0.625173	+	0.927554i
$635$	−763614.	+	440873.i	−1.89377	+	1.09337i
$636$	147914.	+	652718.i	0.365674	+	1.61366i
$637$	−19725.8	+	34166.1i	−0.0486134	+	0.0842008i
$638$	118354.	−	57776.0i	0.290764	−	0.141940i
$639$	−320235.	−	362512.i	−0.784272	−	0.887811i
$640$	−28563.4	−	764487.i	−0.0697350	−	1.86642i
$641$	181028.	−	313549.i	0.440584	−	0.763114i	−0.557149	−	0.830413i	$-0.688105\pi$
$641$	181028.	−	313549.i	0.440584	−	0.763114i	0.997733	+	0.0672990i	$0.0214381\pi$
$642$	−473709.	+	142555.i	−1.14932	+	0.345869i
$643$	−346651.	+	200139.i	−0.838437	+	0.484072i	−0.856733	−	0.515761i	$-0.827509\pi$
$643$	−346651.	+	200139.i	−0.838437	+	0.484072i	0.0182957	+	0.999833i	$0.494176\pi$
$644$	−270167.	−	37777.6i	−0.651420	−	0.0910883i
$645$	302377.	−	114430.i	0.726825	−	0.275055i
$646$	−820.975	+	11799.6i	−0.00196727	+	0.0282749i
$647$			98990.1i			0.236474i	0.992985	+	0.118237i	$0.0377242\pi$
$647$			98990.1i			0.236474i	−0.992985	+	0.118237i	$0.962276\pi$
$648$	136893.	−	396963.i	0.326011	−	0.945366i
$649$	−22341.9			−0.0530434
$650$	−193532.	−	13465.3i	−0.458064	−	0.0318706i
$651$	53580.4	+	141585.i	0.126428	+	0.334083i
$652$	69360.7	−	496035.i	0.163162	−	1.16686i
$653$	269165.	+	466208.i	0.631237	+	1.09333i	0.987299	+	0.158872i	$0.0507859\pi$
$653$	269165.	+	466208.i	0.631237	+	1.09333i	−0.356062	+	0.934462i	$0.615881\pi$
$654$	−194097.	−	644985.i	−0.453799	−	1.50797i
$655$	1.20006e6	+	692852.i	2.79717	+	1.61495i
$656$	−117850.	−	469879.i	−0.273856	−	1.09189i
$657$	263414.	−	232694.i	0.610250	−	0.539081i
$658$	291348.	+	596824.i	0.672915	+	1.37846i
$659$	126219.	+	72872.6i	0.290639	+	0.167801i	0.638230	−	0.769846i	$-0.279667\pi$
$659$	126219.	+	72872.6i	0.290639	+	0.167801i	−0.347591	+	0.937646i	$0.613000\pi$
$660$	−482814.	+	109411.i	−1.10839	+	0.251174i
$661$	126176.	+	218543.i	0.288784	+	0.500189i	0.973520	−	0.228603i	$-0.0734157\pi$
$661$	126176.	+	218543.i	0.288784	+	0.500189i	−0.684736	+	0.728792i	$0.740082\pi$
$662$	−381201.	−	256930.i	−0.869838	−	0.586273i
$663$	9558.30	−	11689.7i	0.0217447	−	0.0265936i
$664$	−150105.	−	134871.i	−0.340454	−	0.305903i
$665$	155388.			0.351377
$666$	−261373.	+	200389.i	−0.589267	+	0.451778i
$667$			125925.i			0.283049i
$668$	386199.	−	156348.i	0.865483	−	0.350380i
$669$	−110068.	+	674234.i	−0.245928	+	1.50646i
$670$	1.07498e6	+	724541.i	2.39471	+	1.61404i
$671$	−60979.7	+	35206.7i	−0.135438	+	0.0781951i
$672$	271993.	−	487235.i	0.602308	−	1.07895i
$673$	−327332.	+	566956.i	−0.722701	+	1.25175i	0.237213	+	0.971458i	$0.423766\pi$
$673$	−327332.	+	566956.i	−0.722701	+	1.25175i	−0.959913	+	0.280297i	$0.909567\pi$
$674$	−216346.	−	443182.i	−0.476243	−	0.975580i
$675$	−959551.	+	603910.i	−2.10601	+	1.32545i
$676$	271520.	−	348030.i	0.594168	−	0.761594i
$677$	106756.	−	184907.i	0.232924	−	0.403437i	−0.725743	−	0.687966i	$-0.758504\pi$
$677$	106756.	−	184907.i	0.232924	−	0.403437i	0.958667	+	0.284529i	$0.0918372\pi$
$678$	246698.	−	262232.i	0.536670	−	0.570462i
$679$	102818.	−	59361.8i	0.223012	−	0.128756i
$680$	−49842.9	−	152857.i	−0.107792	−	0.330572i
$681$	−59795.8	+	366287.i	−0.128937	+	0.789818i
$682$	−81617.9	−	5678.71i	−0.175476	−	0.0122090i
$683$			885039.i			1.89724i	0.316425	+	0.948618i	$0.397517\pi$
$683$			885039.i			1.89724i	−0.316425	+	0.948618i	$0.602483\pi$
$684$	−39311.2	−	59400.6i	−0.0840242	−	0.126963i
$685$	778168.			1.65841
$686$	19095.0	−	274445.i	0.0405762	−	0.583187i
$687$	−157147.	+	192190.i	−0.332961	+	0.407209i
$688$	−137011.	−	141484.i	−0.289453	−	0.298902i
$689$	−72468.6	−	125519.i	−0.152655	−	0.264406i
$690$	108503.	−	460734.i	0.227900	−	0.967726i
$691$	382656.	+	220927.i	0.801406	+	0.462692i	0.843963	−	0.536402i	$-0.180217\pi$
$691$	382656.	+	220927.i	0.801406	+	0.462692i	−0.0425567	+	0.999094i	$0.513550\pi$
$692$	−154130.	+	197561.i	−0.321866	+	0.412562i
$693$	−342351.	−	114837.i	−0.712862	−	0.239120i
$694$	−343854.	+	167857.i	−0.713929	+	0.348514i
$695$	−165571.	−	95592.6i	−0.342780	−	0.197904i
$696$	−240133.	−	93198.2i	−0.495716	−	0.192393i
$697$	−50904.6	−	88169.3i	−0.104783	−	0.181490i
$698$	−96326.3	+	142917.i	−0.197712	+	0.293341i
$699$	−157457.	−	416075.i	−0.322260	−	0.851564i
$700$	−1.39658e6	+	565386.i	−2.85015	+	1.15385i
$701$	340679.			0.693281			0.346640	−	0.937998i	$-0.387322\pi$
$701$	340679.			0.693281			0.346640	+	0.937998i	$0.387322\pi$
$702$	−2848.52	+	90890.1i	−0.00578022	+	0.184435i
$703$			55869.5i			0.113048i
$704$	177772.	+	243610.i	0.358690	+	0.491530i
$705$	−1.07778e6	+	407868.i	−2.16846	+	0.820619i
$706$	252343.	−	374395.i	0.506269	−	0.751139i
$707$	403755.	−	233108.i	0.807755	−	0.466357i
$708$	29671.3	+	32077.7i	0.0591929	+	0.0639937i
$709$	292720.	−	507006.i	0.582318	−	1.00860i	−0.412886	−	0.910783i	$-0.635479\pi$
$709$	292720.	−	507006.i	0.582318	−	1.00860i	0.995204	−	0.0978214i	$-0.0311874\pi$
$710$	1.00228e6	−	489278.i	1.98826	−	0.970597i
$711$	−301966.	+	61197.7i	−0.597335	+	0.121059i
$712$	−446600.	−	94440.0i	−0.880966	−	0.186293i
$713$	39113.0	−	67745.8i	0.0769383	−	0.133261i
$714$	26882.4	−	114150.i	0.0527317	−	0.223913i
$715$	92846.3	−	53604.8i	0.181615	−	0.104856i
$716$	−81620.2	+	583709.i	−0.159210	+	1.13860i
$717$	−780732.	−	638378.i	−1.51867	−	1.24176i
$718$	−61950.0	+	890385.i	−0.120169	+	1.72715i
$719$			306988.i			0.593832i	0.954904	+	0.296916i	$0.0959581\pi$
$719$			306988.i			0.593832i	−0.954904	+	0.296916i	$0.904042\pi$
$720$	798292.	+	547902.i	1.53991	+	1.05691i
$721$	223394.			0.429735
$722$	507973.	+	35343.1i	0.974464	+	0.0678000i
$723$	365037.	+	59591.8i	0.698329	+	0.114001i
$724$	902595.	+	126210.i	1.72193	+	0.240778i
$725$	347749.	+	602319.i	0.661592	+	1.14591i
$726$	−227434.	+	241755.i	−0.431501	+	0.458671i
$727$	−488481.	−	282025.i	−0.924227	−	0.533603i	−0.0392459	−	0.999230i	$-0.512496\pi$
$727$	−488481.	−	282025.i	−0.924227	−	0.533603i	−0.884981	+	0.465627i	$0.845829\pi$
$728$	−25001.2	+	118229.i	−0.0471736	+	0.223081i
$729$	300016.	+	438657.i	0.564534	+	0.825410i
$730$	355526.	+	728293.i	0.667154	+	1.36666i
$731$	−35846.0	−	20695.7i	−0.0670821	−	0.0387298i
$732$	131533.	+	40796.1i	0.245477	+	0.0761371i
$733$	−290960.	−	503957.i	−0.541533	−	0.937963i	−0.998816	−	0.0486418i	$-0.984511\pi$
$733$	−290960.	−	503957.i	−0.541533	−	0.937963i	0.457283	−	0.889321i	$-0.348823\pi$
$734$	−353352.	−	238160.i	−0.655867	−	0.442055i
$735$	−524694.	−	85655.7i	−0.971252	−	0.158556i
$736$	−283879.	+	50565.6i	−0.524056	+	0.0933469i
$737$	−511037.			−0.940843
$738$	566344.	+	234858.i	1.03984	+	0.431215i
$739$		−	193774.i		−	0.354818i	−0.984137	−	0.177409i	$-0.943228\pi$
$739$		−	193774.i		−	0.354818i	0.984137	−	0.177409i	$-0.0567715\pi$
$740$	−284977.	−	703930.i	−0.520411	−	1.28548i
$741$	11941.9	+	9764.48i	0.0217489	+	0.0177833i
$742$	−933417.	−	629124.i	−1.69538	−	1.14269i
$743$	76480.8	−	44156.2i	0.138540	−	0.0799861i	−0.429128	−	0.903244i	$-0.641179\pi$
$743$	76480.8	−	44156.2i	0.138540	−	0.0799861i	0.567668	+	0.823258i	$0.307846\pi$
$744$	100240.	+	124726.i	0.181090	+	0.225325i
$745$	137025.	−	237334.i	0.246881	−	0.427610i
$746$	−250719.	−	513595.i	−0.450514	−	0.922875i
$747$	250310.	−	50728.8i	0.448576	−	0.0909104i
$748$	49971.3	+	38985.8i	0.0893135	+	0.0696792i
$749$	416012.	−	720554.i	0.741553	−	1.28441i
$750$	−450608.	−	1.49737e6i	−0.801081	−	2.66199i
$751$	474180.	−	273768.i	0.840743	−	0.485403i	−0.0167738	−	0.999859i	$-0.505340\pi$
$751$	474180.	−	273768.i	0.840743	−	0.485403i	0.857517	+	0.514456i	$0.172006\pi$
$752$	488355.	+	504298.i	0.863575	+	0.891767i
$753$	−428010.	+	161973.i	−0.754855	+	0.285662i
$754$	55648.1	+	3871.81i	0.0978831	+	0.00681038i
$755$		−	1.54879e6i		−	2.71705i
$756$	289782.	+	644045.i	0.507023	+	1.12687i
$757$	−45164.0			−0.0788135			−0.0394068	−	0.999223i	$-0.512547\pi$
$757$	−45164.0			−0.0788135			−0.0394068	+	0.999223i	$0.512547\pi$
$758$	−26442.8	+	380052.i	−0.0460223	+	0.661462i
$759$	66042.5	+	174516.i	0.114641	+	0.302936i
$760$	156154.	−	50918.0i	0.270350	−	0.0881545i
$761$	100185.	+	173525.i	0.172995	+	0.299636i	0.939465	−	0.342644i	$-0.111322\pi$
$761$	100185.	+	173525.i	0.172995	+	0.299636i	−0.766471	+	0.642279i	$0.777989\pi$
$762$	−650980.	+	195902.i	−1.12113	+	0.337387i
$763$	981079.	+	566426.i	1.68521	+	0.972959i
$764$	−492891.	−	384536.i	−0.844432	−	0.658795i
$765$	192920.	+	64712.5i	0.329651	+	0.110577i
$766$	194663.	−	95027.7i	0.331762	−	0.161954i
$767$	−8195.11	−	4731.45i	−0.0139304	−	0.00804273i
$768$	113675.	−	578766.i	0.192727	−	0.981252i
$769$	−212834.	−	368639.i	−0.359905	−	0.623374i	0.628039	−	0.778181i	$-0.283858\pi$
$769$	−212834.	−	368639.i	−0.359905	−	0.623374i	−0.987945	+	0.154807i	$0.950524\pi$
$770$	465362.	−	690446.i	0.784891	−	1.16452i
$771$	−72978.6	+	89252.4i	−0.122768	+	0.150145i
$772$	−24328.0	−	60093.2i	−0.0408198	−	0.100830i
$773$	199528.			0.333922			0.166961	−	0.985964i	$-0.446605\pi$
$773$	199528.			0.333922			0.166961	+	0.985964i	$0.446605\pi$
$774$	247146.	−	32434.8i	0.412546	−	0.0541413i
$775$		−	432051.i		−	0.719335i
$776$	83872.9	−	93346.4i	0.139283	−	0.155015i
$777$	89247.5	−	546696.i	0.147827	−	0.905532i
$778$	−29122.2	+	43207.9i	−0.0481132	+	0.0713844i
$779$	90071.2	−	52002.6i	0.148426	−	0.0856940i
$780$	−200269.	−	62115.2i	−0.329173	−	0.102096i
$781$	−219836.	+	380768.i	−0.360411	+	0.624249i
$782$	−54457.2	+	26584.1i	−0.0890517	+	0.0434718i
$783$	275909.	−	173648.i	0.450031	−	0.283234i
$784$	78787.6	+	314134.i	0.128182	+	0.511073i
$785$	−517791.	+	896841.i	−0.840263	+	1.45538i
$786$	778145.	+	732050.i	1.25955	+	1.18494i
$787$	−899924.	+	519571.i	−1.45297	+	0.838872i	−0.998649	−	0.0519669i	$-0.983451\pi$
$787$	−899924.	+	519571.i	−1.45297	+	0.838872i	−0.454320	+	0.890839i	$0.650118\pi$
$788$	−710997.	−	99418.9i	−1.14503	−	0.160109i
$789$	45953.8	−	281495.i	0.0738188	−	0.452186i
$790$	49310.7	−	708724.i	0.0790109	−	1.13559i
$791$			605543.i			0.967815i
$792$	−381670.	−	3220.66i	−0.608468	−	0.00513446i
$793$	−29823.5			−0.0474255
$794$	217104.	+	15105.4i	0.344371	+	0.0239602i
$795$	1.23633e6	−	1.51203e6i	1.95615	−	2.39235i
$796$	−124650.	+	891434.i	−0.196727	+	1.40690i
$797$	−12577.0	−	21783.9i	−0.0197997	−	0.0342941i	0.855956	−	0.517049i	$-0.172970\pi$
$797$	−12577.0	−	21783.9i	−0.0197997	−	0.0342941i	−0.875755	+	0.482755i	$0.839636\pi$
$798$	116612.	+	27462.3i	0.183121	+	0.0431252i
$799$	127768.	+	73766.9i	0.200138	+	0.115549i
$800$	−1.21820e6	+	1.02581e6i	−1.90343	+	1.60283i
$801$	432982.	−	382487.i	0.674847	−	0.596144i
$802$	−88478.1	−	181247.i	−0.137558	−	0.281787i
$803$	−276679.	−	159741.i	−0.429087	−	0.247734i
$804$	678684.	+	733727.i	1.04992	+	1.13507i
$805$	398053.	+	689448.i	0.614255	+	1.06392i
$806$	−28735.2	−	19367.6i	−0.0442327	−	0.0298129i
$807$	174858.	+	462057.i	0.268496	+	0.709493i
$808$	329361.	−	366562.i	0.504486	−	0.561468i
$809$	975055.			1.48981			0.744907	−	0.667168i	$-0.232494\pi$
$809$	975055.			1.48981			0.744907	+	0.667168i	$0.232494\pi$
$810$	−1.15912e6	+	397606.i	−1.76668	+	0.606014i
$811$		−	240015.i		−	0.364919i	−0.983213	−	0.182460i	$-0.941594\pi$
$811$		−	240015.i		−	0.364919i	0.983213	−	0.182460i	$-0.0584059\pi$
$812$	401571.	−	162571.i	0.609046	−	0.246564i
$813$	895040.	−	338713.i	1.35413	−	0.512449i
$814$	248249.	+	167320.i	0.374662	+	0.252523i
$815$	−1.26584e6	+	730836.i	−1.90575	+	1.10028i
$816$	−10390.2	−	123522.i	−0.0156042	−	0.185509i
$817$	21142.1	−	36619.3i	0.0316741	−	0.0548612i
$818$	−71652.7	−	146780.i	−0.107084	−	0.219361i
$819$	−101256.	−	114624.i	−0.150957	−	0.170887i
$820$	−869603.	+	1.11464e6i	−1.29328	+	1.65770i
$821$	406806.	−	704608.i	0.603533	−	1.04535i	−0.388749	−	0.921344i	$-0.627093\pi$
$821$	406806.	−	704608.i	0.603533	−	1.04535i	0.992282	−	0.124005i	$-0.0395740\pi$
$822$	583985.	+	137529.i	0.864287	+	0.203540i
$823$	−24117.0	+	13924.0i	−0.0356061	+	0.0205572i	−0.517697	−	0.855564i	$-0.673211\pi$
$823$	−24117.0	+	13924.0i	−0.0356061	+	0.0205572i	0.482091	+	0.876121i	$0.339877\pi$
$824$	224496.	−	73202.6i	0.330639	−	0.107813i
$825$	797825.	+	652354.i	1.17219	+	0.958463i
$826$	−73315.4	−	5101.04i	−0.107457	−	0.00747651i
$827$		−	1.05969e6i		−	1.54941i	−0.632323	−	0.774705i	$-0.717898\pi$
$827$		−	1.05969e6i		−	1.54941i	0.632323	−	0.774705i	$-0.282102\pi$
$828$	162855.	−	326587.i	0.237542	−	0.476364i
$829$	−904280.			−1.31581			−0.657906	−	0.753100i	$-0.728558\pi$
$829$	−904280.			−1.31581			−0.657906	+	0.753100i	$0.728558\pi$
$830$	−40875.3	+	587486.i	−0.0593342	+	0.852788i
$831$	−447080.	−	72985.3i	−0.647416	−	0.105690i
$832$	13617.2	+	127005.i	0.0196717	+	0.183474i
$833$	34031.8	+	58944.9i	0.0490451	+	0.0849486i
$834$	−107360.	−	101001.i	−0.154352	−	0.145209i
$835$	−1.05301e6	−	607954.i	−1.51028	−	0.871963i
$836$	−39826.7	+	51049.2i	−0.0569852	+	0.0730426i
$837$	−202370.	+	7721.09i	−0.288866	+	0.0110212i
$838$	119816.	−	58490.0i	0.170619	−	0.0832902i
$839$	308829.	+	178303.i	0.438727	+	0.253299i	0.703058	−	0.711133i	$-0.251818\pi$
$839$	308829.	+	178303.i	0.438727	+	0.253299i	−0.264330	+	0.964432i	$0.585151\pi$
$840$	−1.60934e6	+	248800.i	−2.28081	+	0.352608i
$841$	253649.	+	439333.i	0.358625	+	0.621157i
$842$	−18691.1	+	27731.6i	−0.0263640	+	0.0391156i
$843$	−54150.9	−	8840.06i	−0.0761992	−	0.0124394i
$844$	1.08419e6	−	438919.i	1.52202	−	0.616168i
$845$	−1.28819e6			−1.80413
$846$	−880918.	+	115609.i	−1.23082	+	0.161529i
$847$		−	558256.i		−	0.778156i
$848$	−1.14417e6	−	326362.i	−1.59111	−	0.453845i
$849$	357971.	+	292701.i	0.496630	+	0.406077i
$850$	−187064.	+	277542.i	−0.258912	+	0.384141i
$851$	−247890.	+	143120.i	−0.342295	+	0.197624i
$852$	838646.	−	190047.i	1.15531	−	0.261807i
$853$	93966.4	−	162755.i	0.129144	−	0.223684i	−0.794201	−	0.607655i	$-0.792110\pi$
$853$	93966.4	−	162755.i	0.129144	−	0.223684i	0.923345	+	0.383971i	$0.125444\pi$
$854$	−208144.	+	101608.i	−0.285396	+	0.139320i
$855$	−66108.5	+	197082.i	−0.0904325	+	0.269596i
$856$	181950.	−	860429.i	0.248316	−	1.17427i
$857$	−424830.	+	735827.i	−0.578434	+	1.00188i	0.417226	+	0.908803i	$0.363002\pi$
$857$	−424830.	+	735827.i	−0.578434	+	1.00188i	−0.995659	+	0.0930735i	$0.970331\pi$
$858$	79151.4	−	23819.3i	0.107519	−	0.0323560i
$859$	−1.04585e6	+	603819.i	−1.41736	+	0.818315i	−0.996067	−	0.0886072i	$-0.971758\pi$
$859$	−1.04585e6	+	603819.i	−1.41736	+	0.818315i	−0.421297	+	0.906923i	$0.638425\pi$
$860$	−79595.2	+	569227.i	−0.107619	+	0.769641i
$861$	−964438.	+	364976.i	−1.30097	+	0.492332i
$862$	24555.6	−	352928.i	0.0330473	−	0.474976i
$863$			77194.2i			0.103648i	0.998656	+	0.0518242i	$0.0165036\pi$
$863$			77194.2i			0.103648i	−0.998656	+	0.0518242i	$0.983496\pi$
$864$	502254.	+	552265.i	0.672816	+	0.739810i
$865$	731250.			0.977313
$866$	475220.	+	33064.2i	0.633664	+	0.0440882i
$867$	256830.	+	678667.i	0.341671	+	0.902856i
$868$	−266534.	−	37269.5i	−0.353763	−	0.0494668i
$869$	140030.	+	242539.i	0.185431	+	0.321176i
$870$	216619.	+	719825.i	0.286193	+	0.951018i
$871$	−187450.	−	108224.i	−0.247087	−	0.142656i
$872$	1.17153e6	+	247736.i	1.54070	+	0.325804i
$873$	31547.0	+	155661.i	0.0413932	+	0.204245i
$874$	−27157.5	−	55631.9i	−0.0355522	−	0.0728285i
$875$	2.27763e6	+	1.31499e6i	2.97487	+	1.71754i
$876$	138095.	+	609390.i	0.179957	+	0.794122i
$877$	−71455.2	−	123764.i	−0.0929040	−	0.160914i	0.815828	−	0.578295i	$-0.196282\pi$
$877$	−71455.2	−	123764.i	−0.0929040	−	0.160914i	−0.908732	+	0.417380i	$0.862948\pi$
$878$	396348.	+	267139.i	0.514147	+	0.346536i
$879$	−520028.	+	635991.i	−0.673053	+	0.823140i
$880$	241409.	−	846343.i	0.311737	−	1.09290i
$881$	−305226.			−0.393250			−0.196625	−	0.980479i	$-0.562998\pi$
$881$	−305226.			−0.393250			−0.196625	+	0.980479i	$0.562998\pi$
$882$	−378625.	−	157013.i	−0.486712	−	0.201836i
$883$			902045.i			1.15693i	0.815707	+	0.578465i	$0.196348\pi$
$883$			902045.i			1.15693i	−0.815707	+	0.578465i	$0.803652\pi$
$884$	10073.5	+	24882.8i	0.0128906	+	0.0318416i
$885$	20545.5	−	125854.i	0.0262319	−	0.160687i
$886$	−675677.	−	455407.i	−0.860739	−	0.580140i
$887$	797270.	−	460304.i	1.01335	−	0.585056i	0.101177	−	0.994868i	$-0.467739\pi$
$887$	797270.	−	460304.i	1.01335	−	0.585056i	0.912170	+	0.409813i	$0.134406\pi$
$888$	−89455.9	−	578638.i	−0.113444	−	0.733805i
$889$	571692.	−	990199.i	0.723367	−	1.25291i
$890$	584391.	+	1.19712e6i	0.737774	+	1.51132i
$891$	291302.	−	385355.i	0.366934	−	0.485407i
$892$	−957564.	−	747057.i	−1.20348	−	0.938911i
$893$	−75358.1	+	130524.i	−0.0944990	+	0.163677i
$894$	144777.	−	153893.i	0.181144	−	0.192551i
$895$	1.48958e6	−	860011.i	1.85960	−	1.07364i
$896$	527742.	+	839998.i	0.657364	+	1.04631i
$897$	−12733.3	+	77999.1i	−0.0158254	+	0.0969404i
$898$	307881.	+	21421.3i	0.381794	+	0.0265640i
$899$			124232.i			0.153714i
$900$	−122929.	−	2.01185e6i	−0.151764	−	2.48376i
$901$	−250052.			−0.308022
$902$	38681.9	−	555960.i	0.0475439	−	0.683330i
$903$	−265377.	+	324555.i	−0.325453	+	0.398027i
$904$	198427.	+	608530.i	0.242808	+	0.744638i
$905$	−1.32984e6	−	2.30336e6i	−1.62369	−	2.81232i
$906$	273723.	−	1.16231e6i	0.333469	−	1.41600i
$907$	−426945.	−	246497.i	−0.518988	−	0.299638i	0.217533	−	0.976053i	$-0.430199\pi$
$907$	−426945.	−	246497.i	−0.518988	−	0.299638i	−0.736520	+	0.676415i	$0.763532\pi$
$908$	−520209.	−	405849.i	−0.630967	−	0.492258i
$909$	123882.	+	611266.i	0.149927	+	0.739780i
$910$	316915.	−	154707.i	0.382702	−	0.186821i
$911$	−208640.	−	120458.i	−0.251397	−	0.145144i	0.369007	−	0.929427i	$-0.379698\pi$
$911$	−208640.	−	120458.i	−0.251397	−	0.145144i	−0.620404	+	0.784283i	$0.713031\pi$
$912$	126187.	−	10614.3i	0.151713	−	0.0127615i
$913$	−116076.	−	201049.i	−0.139252	−	0.241191i
$914$	−627851.	+	931528.i	−0.751561	+	1.11507i
$915$	−142245.	−	375879.i	−0.169901	−	0.448958i
$916$	−165617.	−	409095.i	−0.197385	−	0.487566i
$917$	−1.79688e6			−2.13688
$918$	133342.	+	82659.9i	0.158228	+	0.0980865i
$919$		−	155183.i		−	0.183744i	−0.995771	−	0.0918719i	$-0.970715\pi$
$919$		−	155183.i		−	0.183744i	0.995771	−	0.0918719i	$-0.0292850\pi$
$920$	625937.	+	562413.i	0.739529	+	0.664476i
$921$	910595.	−	344600.i	1.07351	−	0.406252i
$922$	897871.	−	1.33215e6i	1.05621	−	1.56708i
$923$	−161274.	+	93111.4i	−0.189304	+	0.109295i
$924$	471262.	−	435908.i	0.551973	−	0.510565i
$925$	−790464.	+	1.36912e6i	−0.923844	+	1.60015i
$926$	215029.	−	104969.i	0.250769	−	0.122417i
$927$	−95041.2	+	283336.i	−0.110599	+	0.329717i
$928$	350279.	−	294961.i	0.406742	−	0.342506i
$929$	352354.	−	610296.i	0.408271	−	0.707145i	−0.586425	−	0.810003i	$-0.699465\pi$
$929$	352354.	−	610296.i	0.408271	−	0.707145i	0.994696	+	0.102858i	$0.0327986\pi$
$930$	107044.	−	454537.i	0.123764	−	0.525538i
$931$	−60216.4	+	34765.9i	−0.0694729	+	0.0401102i
$932$	783263.	+	109524.i	0.901729	+	0.126089i
$933$	697306.	+	570163.i	0.801051	+	0.654992i
$934$	−57879.6	+	831882.i	−0.0663486	+	0.953604i
$935$		−	184963.i		−	0.211574i
$936$	−139316.	−	82009.4i	−0.159019	−	0.0936077i
$937$	−237273.			−0.270252			−0.135126	−	0.990828i	$-0.543144\pi$
$937$	−237273.			−0.270252			−0.135126	+	0.990828i	$0.543144\pi$
$938$	−1.67697e6	−	116678.i	−1.90599	−	0.132612i
$939$	−1.34827e6	−	220103.i	−1.52913	−	0.249629i
$940$	283706.	−	2.02893e6i	0.321079	−	2.29621i
$941$	−57476.2	−	99551.7i	−0.0649096	−	0.112427i	0.831744	−	0.555159i	$-0.187343\pi$
$941$	−57476.2	−	99551.7i	−0.0649096	−	0.112427i	−0.896654	+	0.442732i	$0.854009\pi$
$942$	−547085.	+	581534.i	−0.616528	+	0.655349i
$943$	461467.	+	266428.i	0.518940	+	0.299610i
$944$	−75348.5	+	18898.1i	−0.0845534	+	0.0212067i
$945$	961710.	−	1.82289e6i	1.07691	−	2.04125i
$946$	−99395.8	−	203612.i	−0.111067	−	0.227520i
$947$	−890326.	−	514030.i	−0.992772	−	0.573177i	−0.0866700	−	0.996237i	$-0.527623\pi$
$947$	−890326.	−	514030.i	−0.992772	−	0.573177i	−0.906102	+	0.423060i	$0.860956\pi$
$948$	162261.	−	523156.i	0.180551	−	0.582122i
$949$	−67658.0	−	117187.i	−0.0751254	−	0.130121i
$950$	−283529.	−	191099.i	−0.314159	−	0.211744i
$951$	998419.	+	162991.i	1.10396	+	0.180220i
$952$	155080.	+	139342.i	0.171113	+	0.153747i
$953$	837599.			0.922253			0.461127	−	0.887334i	$-0.347445\pi$
$953$	837599.			0.922253			0.461127	+	0.887334i	$0.347445\pi$
$954$	1.19505e6	−	916217.i	1.31307	−	1.00670i
$955$			1.82438e6i			2.00036i
$956$	1.66187e6	−	672785.i	1.81836	−	0.736140i
$957$	−229406.	−	187577.i	−0.250485	−	0.204813i
$958$	531102.	+	357964.i	0.578692	+	0.390039i
$959$	−873882.	+	504536.i	−0.950201	+	0.548599i
$960$	−1.53575e6	+	777383.i	−1.66640	+	0.843514i
$961$	−423174.	+	732958.i	−0.458218	+	0.793656i
$962$	55624.7	+	113947.i	0.0601059	+	0.123126i
$963$	736906.	+	834192.i	0.794620	+	0.899525i
$964$	−404464.	+	518435.i	−0.435237	+	0.557879i
$965$	−94598.6	+	163850.i	−0.101585	+	0.175951i
$966$	176875.	+	587754.i	0.189545	+	0.629856i
$967$	−92494.4	+	53401.7i	−0.0989151	+	0.0571087i	−0.548642	−	0.836058i	$-0.684855\pi$
$967$	−92494.4	+	53401.7i	−0.0989151	+	0.0571087i	0.449726	+	0.893166i	$0.351521\pi$
$968$	−182932.	−	561010.i	−0.195226	−	0.598714i
$969$	24890.5	−	9419.41i	0.0265086	−	0.0100317i
$970$	−365342.	−	25419.3i	−0.388290	−	0.0270159i
$971$			689120.i			0.730897i	0.930832	+	0.365448i	$0.119084\pi$
$971$			689120.i			0.730897i	−0.930832	+	0.365448i	$0.880916\pi$
$972$	−940143.	+	93532.6i	−0.995088	+	0.0989989i
$973$	247915.			0.261865
$974$	−103269.	+	1.48425e6i	−0.108856	+	1.56455i
$975$	154494.	+	408245.i	0.162518	+	0.429449i
$976$	−175875.	+	170315.i	−0.184631	+	0.178794i
$977$	293734.	+	508762.i	0.307726	+	0.532998i	0.977865	−	0.209239i	$-0.0670985\pi$
$977$	293734.	+	508762.i	0.307726	+	0.532998i	−0.670138	+	0.742236i	$0.733765\pi$
$978$	−1.07913e6	+	324747.i	−1.12823	+	0.339521i
$979$	−454787.	−	262571.i	−0.474507	−	0.273957i
$980$	581366.	−	745184.i	0.605337	−	0.775910i
$981$	−1.13580e6	+	1.00334e6i	−1.18023	+	1.04259i
$982$	240170.	−	117243.i	0.249056	−	0.121580i
$983$	−338570.	−	195474.i	−0.350382	−	0.202293i	0.314472	−	0.949267i	$-0.398173\pi$
$983$	−338570.	−	195474.i	−0.350382	−	0.202293i	−0.664853	+	0.746974i	$0.731506\pi$
$984$	−849599.	+	682807.i	−0.877452	+	0.705193i
$985$	1.04755e6	+	1.81441e6i	1.07970	+	1.87009i
$986$	53788.2	−	79804.3i	0.0553265	−	0.0820866i
$987$	945900.	−	1.15683e6i	0.970981	−	1.18750i
$988$	−25419.5	+	10290.8i	−0.0260408	+	0.0105423i
$989$	216637.			0.221483
$990$	677724.	+	883974.i	0.691484	+	0.901922i
$991$		−	462949.i		−	0.471396i	−0.971826	−	0.235698i	$-0.924262\pi$
$991$		−	462949.i		−	0.471396i	0.971826	−	0.235698i	$-0.0757376\pi$
$992$	−280061.	+	49885.5i	−0.284596	+	0.0506934i
$993$	−166648.	+	1.02082e6i	−0.169006	+	1.03526i
$994$	−808332.	+	1.19930e6i	−0.818120	+	1.21382i
$995$	2.27488e6	−	1.31340e6i	2.29780	−	1.32663i
$996$	−134504.	+	433662.i	−0.135587	+	0.437152i
$997$	−386642.	+	669683.i	−0.388972	+	0.673720i	−0.992312	−	0.123765i	$-0.960503\pi$
$997$	−386642.	+	669683.i	−0.388972	+	0.673720i	0.603339	+	0.797485i	$0.293836\pi$
$998$	1.19601e6	−	583851.i	1.20081	−	0.586193i
$999$	655417.	+	345782.i	0.656730	+	0.346475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.5.f.a.7.22	yes	44
3.2	odd	2		108.5.f.a.19.1		44
4.3	odd	2	inner	36.5.f.a.7.7	✓	44
9.2	odd	6		324.5.d.e.163.16		22
9.4	even	3	inner	36.5.f.a.31.7	yes	44
9.5	odd	6		108.5.f.a.91.16		44
9.7	even	3		324.5.d.f.163.7		22
12.11	even	2		108.5.f.a.19.16		44
36.7	odd	6		324.5.d.f.163.8		22
36.11	even	6		324.5.d.e.163.15		22
36.23	even	6		108.5.f.a.91.1		44
36.31	odd	6	inner	36.5.f.a.31.22	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.7	✓	44	4.3	odd	2	inner
36.5.f.a.7.22	yes	44	1.1	even	1	trivial
36.5.f.a.31.7	yes	44	9.4	even	3	inner
36.5.f.a.31.22	yes	44	36.31	odd	6	inner
108.5.f.a.19.1		44	3.2	odd	2
108.5.f.a.19.16		44	12.11	even	2
108.5.f.a.91.1		44	36.23	even	6
108.5.f.a.91.16		44	9.5	odd	6
324.5.d.e.163.15		22	36.11	even	6
324.5.d.e.163.16		22	9.2	odd	6
324.5.d.f.163.7		22	9.7	even	3
324.5.d.f.163.8		22	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	36.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.99035 + 0.277636i) q^{2} +(-3.18543 - 8.41742i) q^{3} +(15.8458 + 2.21573i) q^{4} +(-23.3466 - 40.4374i) q^{5} +(-10.3740 - 34.4729i) q^{6} +(52.4363 + 30.2741i) q^{7} +(62.6153 + 13.2409i) q^{8} +(-60.7060 + 53.6263i) q^{9} +O(q^{10})\)	\(q+(3.99035 + 0.277636i) q^{2} +(-3.18543 - 8.41742i) q^{3} +(15.8458 + 2.21573i) q^{4} +(-23.3466 - 40.4374i) q^{5} +(-10.3740 - 34.4729i) q^{6} +(52.4363 + 30.2741i) q^{7} +(62.6153 + 13.2409i) q^{8} +(-60.7060 + 53.6263i) q^{9} +(-81.9341 - 167.841i) q^{10} +(63.7631 + 36.8136i) q^{11} +(-31.8252 - 140.439i) q^{12} +(15.5924 + 27.0068i) q^{13} +(200.834 + 135.363i) q^{14} +(-266.010 + 325.329i) q^{15} +(246.181 + 70.2201i) q^{16} +53.8013 q^{17} +(-257.127 + 197.134i) q^{18} +54.9619i q^{19} +(-280.347 - 692.494i) q^{20} +(87.7977 - 537.815i) q^{21} +(244.217 + 164.602i) q^{22} +(-243.863 + 140.795i) q^{23} +(-88.0027 - 569.238i) q^{24} +(-777.624 + 1346.88i) q^{25} +(54.7210 + 112.096i) q^{26} +(644.770 + 340.165i) q^{27} +(763.818 + 595.904i) q^{28} +(223.597 - 387.282i) q^{29} +(-1151.80 + 1224.32i) q^{30} +(-240.584 + 138.901i) q^{31} +(962.854 + 348.552i) q^{32} +(106.763 - 653.989i) q^{33} +(214.686 + 14.9372i) q^{34} -2827.19i q^{35} +(-1080.76 + 715.246i) q^{36} +1016.51 q^{37} +(-15.2594 + 219.317i) q^{38} +(177.659 - 217.276i) q^{39} +(-926.424 - 2841.13i) q^{40} +(-946.158 - 1638.79i) q^{41} +(499.660 - 2121.70i) q^{42} +(-666.266 - 384.669i) q^{43} +(928.811 + 724.625i) q^{44} +(3585.79 + 1202.81i) q^{45} +(-1012.19 + 494.115i) q^{46} +(2374.81 + 1371.10i) q^{47} +(-193.121 - 2295.89i) q^{48} +(632.546 + 1095.60i) q^{49} +(-3476.94 + 5158.64i) q^{50} +(-171.381 - 452.869i) q^{51} +(187.235 + 462.494i) q^{52} -4647.69 q^{53} +(2478.42 + 1536.39i) q^{54} -3437.89i q^{55} +(2882.46 + 2589.93i) q^{56} +(462.637 - 175.078i) q^{57} +(999.756 - 1483.31i) q^{58} +(-262.792 + 151.723i) q^{59} +(-4935.99 + 4565.70i) q^{60} +(-478.174 + 828.222i) q^{61} +(-998.577 + 487.469i) q^{62} +(-4806.69 + 974.145i) q^{63} +(3745.36 + 1658.17i) q^{64} +(728.057 - 1261.03i) q^{65} +(607.592 - 2580.00i) q^{66} +(-6010.96 + 3470.43i) q^{67} +(852.527 + 119.209i) q^{68} +(1961.94 + 1604.21i) q^{69} +(784.928 - 11281.5i) q^{70} +5971.60i q^{71} +(-4511.19 + 2554.03i) q^{72} -4339.17 q^{73} +(4056.25 + 282.220i) q^{74} +(13814.4 + 2255.18i) q^{75} +(-121.781 + 870.917i) q^{76} +(2229.00 + 3860.75i) q^{77} +(769.246 - 817.683i) q^{78} +(3294.15 + 1901.88i) q^{79} +(-2907.96 - 11594.3i) q^{80} +(809.440 - 6510.88i) q^{81} +(-3320.52 - 6802.05i) q^{82} +(-2730.64 - 1576.53i) q^{83} +(2582.88 - 8327.59i) q^{84} +(-1256.08 - 2175.59i) q^{85} +(-2551.84 - 1719.94i) q^{86} +(-3972.17 - 648.452i) q^{87} +(3505.10 + 3149.38i) q^{88} -7132.44 q^{89} +(13974.6 + 5795.16i) q^{90} +1888.18i q^{91} +(-4176.18 + 1690.67i) q^{92} +(1935.55 + 1582.63i) q^{93} +(9095.67 + 6130.50i) q^{94} +(2222.52 - 1283.17i) q^{95} +(-133.201 - 9215.04i) q^{96} +(980.405 - 1698.11i) q^{97} +(2219.91 + 4547.46i) q^{98} +(-5844.98 + 1184.57i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9}+O(q^{10}) \) 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9	\( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9} + 28 q^{10} - 228 q^{12} - 2 q^{13} + 252 q^{14} - q^{16} - 56 q^{17} + 72 q^{18} - 140 q^{20} + 138 q^{21} - 33 q^{22} - 951 q^{24} - 1752 q^{25} + 1096 q^{26} - 516 q^{28} + 526 q^{29} - 1980 q^{30} - 121 q^{32} + 2994 q^{33} + 385 q^{34} - 1005 q^{36} - 8 q^{37} + 1395 q^{38} - 2276 q^{40} - 2762 q^{41} + 3330 q^{42} + 6714 q^{44} + 4110 q^{45} + 3576 q^{46} + 2163 q^{48} + 3428 q^{49} + 6375 q^{50} + 1438 q^{52} - 10088 q^{53} - 4983 q^{54} - 7506 q^{56} + 1752 q^{57} - 4064 q^{58} - 16392 q^{60} - 2 q^{61} - 18324 q^{62} + 9026 q^{64} - 2014 q^{65} - 17358 q^{66} - 11405 q^{68} + 3354 q^{69} + 3666 q^{70} + 4083 q^{72} - 3416 q^{73} + 14620 q^{74} + 1581 q^{76} - 3942 q^{77} + 34566 q^{78} + 45520 q^{80} - 1164 q^{81} - 8486 q^{82} + 51078 q^{84} - 1252 q^{85} + 22113 q^{86} + 1995 q^{88} + 13048 q^{89} - 4692 q^{90} - 30294 q^{92} + 12090 q^{93} + 7524 q^{94} - 76164 q^{96} + 5638 q^{97} - 92938 q^{98}+O(q^{100}) \) 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9 + 28 * q^10 - 228 * q^12 - 2 * q^13 + 252 * q^14 - q^16 - 56 * q^17 + 72 * q^18 - 140 * q^20 + 138 * q^21 - 33 * q^22 - 951 * q^24 - 1752 * q^25 + 1096 * q^26 - 516 * q^28 + 526 * q^29 - 1980 * q^30 - 121 * q^32 + 2994 * q^33 + 385 * q^34 - 1005 * q^36 - 8 * q^37 + 1395 * q^38 - 2276 * q^40 - 2762 * q^41 + 3330 * q^42 + 6714 * q^44 + 4110 * q^45 + 3576 * q^46 + 2163 * q^48 + 3428 * q^49 + 6375 * q^50 + 1438 * q^52 - 10088 * q^53 - 4983 * q^54 - 7506 * q^56 + 1752 * q^57 - 4064 * q^58 - 16392 * q^60 - 2 * q^61 - 18324 * q^62 + 9026 * q^64 - 2014 * q^65 - 17358 * q^66 - 11405 * q^68 + 3354 * q^69 + 3666 * q^70 + 4083 * q^72 - 3416 * q^73 + 14620 * q^74 + 1581 * q^76 - 3942 * q^77 + 34566 * q^78 + 45520 * q^80 - 1164 * q^81 - 8486 * q^82 + 51078 * q^84 - 1252 * q^85 + 22113 * q^86 + 1995 * q^88 + 13048 * q^89 - 4692 * q^90 - 30294 * q^92 + 12090 * q^93 + 7524 * q^94 - 76164 * q^96 + 5638 * q^97 - 92938 * q^98

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