LMFDB - Embedded newform 27.5.f.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,5,Mod(2,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("27.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, 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:	$2.79098900326$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			2.4
Character	$\chi$	$=$	27.2
Dual form			27.5.f.a.14.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.58910 - 0.632855i) q^{2} +(8.76651 + 2.03673i) q^{3} +(-2.55397 - 0.929568i) q^{4} +(12.8585 + 15.3241i) q^{5} +(-30.1749 - 12.8580i) q^{6} +(75.5885 - 27.5120i) q^{7} +(59.0773 + 34.1083i) q^{8} +(72.7034 + 35.7101i) q^{9} +(-36.4523 - 63.1373i) q^{10} +(-73.4332 + 87.5142i) q^{11} +(-20.4961 - 13.3508i) q^{12} +(-36.1566 - 205.054i) q^{13} +(-288.705 + 50.9066i) q^{14} +(81.5128 + 160.528i) q^{15} +(-157.137 - 131.853i) q^{16} +(-163.954 + 94.6591i) q^{17} +(-238.340 - 174.178i) q^{18} +(-227.463 + 393.977i) q^{19} +(-18.5953 - 51.0902i) q^{20} +(718.682 - 87.2304i) q^{21} +(318.943 - 267.625i) q^{22} +(216.433 - 594.644i) q^{23} +(448.433 + 419.336i) q^{24} +(39.0415 - 221.415i) q^{25} +758.841i q^{26} +(564.624 + 461.130i) q^{27} -218.625 q^{28} +(-598.503 - 105.532i) q^{29} +(-190.966 - 627.738i) q^{30} +(-320.106 - 116.509i) q^{31} +(-221.047 - 263.433i) q^{32} +(-821.996 + 617.631i) q^{33} +(648.354 - 235.981i) q^{34} +(1393.55 + 804.566i) q^{35} +(-152.487 - 158.785i) q^{36} +(551.400 + 955.053i) q^{37} +(1065.72 - 1270.07i) q^{38} +(100.673 - 1871.25i) q^{39} +(236.964 + 1343.89i) q^{40} +(-894.918 + 157.798i) q^{41} +(-2634.62 - 141.743i) q^{42} +(-987.620 - 828.712i) q^{43} +(268.896 - 155.247i) q^{44} +(387.629 + 1573.29i) q^{45} +(-1153.12 + 1997.26i) q^{46} +(-161.256 - 443.048i) q^{47} +(-1108.99 - 1475.94i) q^{48} +(3117.44 - 2615.84i) q^{49} +(-280.247 + 769.973i) q^{50} +(-1630.10 + 495.899i) q^{51} +(-98.2691 + 557.312i) q^{52} +293.218i q^{53} +(-1734.66 - 2012.37i) q^{54} -2285.32 q^{55} +(5403.95 + 952.863i) q^{56} +(-2796.48 + 2990.53i) q^{57} +(2081.30 + 757.531i) q^{58} +(-3379.85 - 4027.95i) q^{59} +(-58.9589 - 485.756i) q^{60} +(-2379.12 + 865.931i) q^{61} +(1075.16 + 620.743i) q^{62} +(6478.00 + 699.057i) q^{63} +(2267.66 + 3927.70i) q^{64} +(2677.36 - 3190.75i) q^{65} +(3341.09 - 1696.53i) q^{66} +(933.925 + 5296.55i) q^{67} +(506.726 - 89.3495i) q^{68} +(3108.49 - 4772.14i) q^{69} +(-4492.41 - 3769.58i) q^{70} +(-4919.78 + 2840.43i) q^{71} +(3077.12 + 4589.45i) q^{72} +(1385.76 - 2400.21i) q^{73} +(-1374.62 - 3776.73i) q^{74} +(793.221 - 1861.52i) q^{75} +(947.162 - 794.763i) q^{76} +(-3143.01 + 8635.36i) q^{77} +(-1545.56 + 6652.39i) q^{78} +(1459.18 - 8275.44i) q^{79} -4103.41i q^{80} +(4010.58 + 5192.49i) q^{81} +3311.81 q^{82} +(-6331.63 - 1116.44i) q^{83} +(-1916.58 - 445.280i) q^{84} +(-3558.77 - 1295.29i) q^{85} +(3020.21 + 3599.35i) q^{86} +(-5031.84 - 2144.14i) q^{87} +(-7323.20 + 2665.43i) q^{88} +(6738.82 + 3890.66i) q^{89} +(-395.572 - 5892.02i) q^{90} +(-8374.46 - 14505.0i) q^{91} +(-1105.52 + 1317.51i) q^{92} +(-2568.92 - 1673.35i) q^{93} +(298.379 + 1692.19i) q^{94} +(-8962.18 + 1580.27i) q^{95} +(-1401.27 - 2759.60i) q^{96} +(8458.98 + 7097.93i) q^{97} +(-12844.2 + 7415.62i) q^{98} +(-8463.98 + 3740.28i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 3 q^{5} + 90 q^{6} - 6 q^{7} - 9 q^{8} - 108 q^{9} - 3 q^{10} - 492 q^{11} - 339 q^{12} - 6 q^{13} + 1137 q^{14} + 1017 q^{15} - 54 q^{16} - 9 q^{17} + 603 q^{18} - 3 q^{19}+ \cdots - 162405 q^{99}+O(q^{100}) $ 66 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 3 * q^5 + 90 * q^6 - 6 * q^7 - 9 * q^8 - 108 * q^9 - 3 * q^10 - 492 * q^11 - 339 * q^12 - 6 * q^13 + 1137 * q^14 + 1017 * q^15 - 54 * q^16 - 9 * q^17 + 603 * q^18 - 3 * q^19 - 2487 * q^20 - 2784 * q^21 + 1002 * q^22 - 2724 * q^23 - 3312 * q^24 + 435 * q^25 + 1368 * q^27 - 12 * q^28 + 5016 * q^29 + 10773 * q^30 - 1671 * q^31 + 10224 * q^32 + 2925 * q^33 - 342 * q^34 - 2682 * q^35 - 7704 * q^36 - 3 * q^37 - 6564 * q^38 - 1983 * q^39 - 1113 * q^40 + 5754 * q^41 + 8694 * q^42 - 1266 * q^43 - 4545 * q^44 - 7029 * q^45 - 3 * q^46 - 9159 * q^47 - 28383 * q^48 + 5898 * q^49 - 34977 * q^50 - 14814 * q^51 + 2871 * q^52 + 13878 * q^54 - 12 * q^55 + 39243 * q^56 + 15792 * q^57 - 12291 * q^58 + 24762 * q^59 + 50670 * q^60 - 8358 * q^61 + 38304 * q^62 + 21609 * q^63 + 6141 * q^64 + 23727 * q^65 + 11349 * q^66 + 15996 * q^67 - 43533 * q^68 - 26847 * q^69 - 7251 * q^70 - 19773 * q^71 - 77580 * q^72 + 6108 * q^73 - 74847 * q^74 - 49155 * q^75 - 28614 * q^76 - 33909 * q^77 - 9108 * q^78 - 5658 * q^79 - 12600 * q^81 - 12 * q^82 + 18813 * q^83 + 82356 * q^84 + 24219 * q^85 + 96474 * q^86 + 84555 * q^87 + 36042 * q^88 + 110232 * q^89 + 153540 * q^90 - 6042 * q^91 + 73545 * q^92 + 1293 * q^93 + 2631 * q^94 - 65163 * q^95 - 152226 * q^96 - 3696 * q^97 - 259938 * q^98 - 162405 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−3.58910	−	0.632855i	−0.897274	−	0.158214i	−0.294054	−	0.955789i	$-0.595005\pi$
$2$	−3.58910	−	0.632855i	−0.897274	−	0.158214i	−0.603220	+	0.797575i	$0.706116\pi$
$3$	8.76651	+	2.03673i	0.974057	+	0.226304i
$3$	8.76651	+	2.03673i	0.974057	+	0.226304i
$4$	−2.55397	−	0.929568i	−0.159623	−	0.0580980i
$5$	12.8585	+	15.3241i	0.514339	+	0.612965i	0.959232	−	0.282618i	$-0.0912030\pi$
$5$	12.8585	+	15.3241i	0.514339	+	0.612965i	−0.444894	+	0.895583i	$0.646759\pi$
$6$	−30.1749	−	12.8580i	−0.838192	−	0.357166i
$7$	75.5885	−	27.5120i	1.54262	−	0.561469i	0.575950	−	0.817485i	$-0.304632\pi$
$7$	75.5885	−	27.5120i	1.54262	−	0.561469i	0.966672	+	0.256017i	$0.0824102\pi$
$8$	59.0773	+	34.1083i	0.923083	+	0.532943i
$9$	72.7034	+	35.7101i	0.897573	+	0.440865i
$10$	−36.4523	−	63.1373i	−0.364523	−	0.631373i
$11$	−73.4332	+	87.5142i	−0.606886	+	0.723258i	−0.978756	−	0.205026i	$-0.934272\pi$
$11$	−73.4332	+	87.5142i	−0.606886	+	0.723258i	0.371871	+	0.928285i	$0.378716\pi$
$12$	−20.4961	−	13.3508i	−0.142334	−	0.0927140i
$13$	−36.1566	−	205.054i	−0.213944	−	1.21334i	−0.882729	−	0.469882i	$-0.844296\pi$
$13$	−36.1566	−	205.054i	−0.213944	−	1.21334i	0.668785	−	0.743456i	$-0.266815\pi$
$14$	−288.705	+	50.9066i	−1.47299	+	0.259727i
$15$	81.5128	+	160.528i	0.362279	+	0.713460i
$16$	−157.137	−	131.853i	−0.613814	−	0.515051i
$17$	−163.954	+	94.6591i	−0.567316	+	0.327540i	−0.756077	−	0.654483i	$-0.772886\pi$
$17$	−163.954	+	94.6591i	−0.567316	+	0.327540i	0.188760	+	0.982023i	$0.439553\pi$
$18$	−238.340	−	174.178i	−0.735619	−	0.537585i
$19$	−227.463	+	393.977i	−0.630091	+	1.09135i	0.357441	+	0.933936i	$0.383649\pi$
$19$	−227.463	+	393.977i	−0.630091	+	1.09135i	−0.987533	+	0.157414i	$0.949684\pi$
$20$	−18.5953	−	51.0902i	−0.0464882	−	0.127725i
$21$	718.682	−	87.2304i	1.62966	−	0.197801i
$22$	318.943	−	267.625i	0.658972	−	0.552943i
$23$	216.433	−	594.644i	0.409135	−	1.12409i	−0.548511	−	0.836143i	$-0.684805\pi$
$23$	216.433	−	594.644i	0.409135	−	1.12409i	0.957646	−	0.287947i	$-0.0929727\pi$
$24$	448.433	+	419.336i	0.778529	+	0.728013i
$25$	39.0415	−	221.415i	0.0624664	−	0.354264i
$26$			758.841i			1.12255i
$27$	564.624	+	461.130i	0.774518	+	0.632552i
$28$	−218.625			−0.278858
$29$	−598.503	−	105.532i	−0.711657	−	0.125484i	−0.193911	−	0.981019i	$-0.562117\pi$
$29$	−598.503	−	105.532i	−0.711657	−	0.125484i	−0.517745	+	0.855535i	$0.673229\pi$
$30$	−190.966	−	627.738i	−0.212185	−	0.697486i
$31$	−320.106	−	116.509i	−0.333097	−	0.121237i	0.170057	−	0.985434i	$-0.445605\pi$
$31$	−320.106	−	116.509i	−0.333097	−	0.121237i	−0.503154	+	0.864197i	$0.667827\pi$
$32$	−221.047	−	263.433i	−0.215866	−	0.257259i
$33$	−821.996	+	617.631i	−0.754817	+	0.567154i
$34$	648.354	−	235.981i	0.560860	−	0.204136i
$35$	1393.55	+	804.566i	1.13759	+	0.656788i
$36$	−152.487	−	158.785i	−0.117660	−	0.122519i
$37$	551.400	+	955.053i	0.402776	+	0.697628i	0.994060	−	0.108835i	$-0.0347121\pi$
$37$	551.400	+	955.053i	0.402776	+	0.697628i	−0.591284	+	0.806463i	$0.701379\pi$
$38$	1065.72	−	1270.07i	0.738031	−	0.879551i
$39$	100.673	−	1871.25i	0.0661890	−	1.23028i
$40$	236.964	+	1343.89i	0.148102	+	0.839931i
$41$	−894.918	+	157.798i	−0.532372	+	0.0938716i	−0.433371	−	0.901216i	$-0.642676\pi$
$41$	−894.918	+	157.798i	−0.532372	+	0.0938716i	−0.0990014	+	0.995087i	$0.531565\pi$
$42$	−2634.62	−	141.743i	−1.49355	−	0.0803531i
$43$	−987.620	−	828.712i	−0.534137	−	0.448194i	0.335390	−	0.942079i	$-0.391132\pi$
$43$	−987.620	−	828.712i	−0.534137	−	0.448194i	−0.869527	+	0.493885i	$0.835576\pi$
$44$	268.896	−	155.247i	0.138893	−	0.0801898i
$45$	387.629	+	1573.29i	0.191422	+	0.776935i
$46$	−1153.12	+	1997.26i	−0.544953	+	0.943886i
$47$	−161.256	−	443.048i	−0.0729997	−	0.200565i	0.897826	−	0.440349i	$-0.145145\pi$
$47$	−161.256	−	443.048i	−0.0729997	−	0.200565i	−0.970826	+	0.239785i	$0.922923\pi$
$48$	−1108.99	−	1475.94i	−0.481332	−	0.640598i
$49$	3117.44	−	2615.84i	1.29839	−	1.08948i
$50$	−280.247	+	769.973i	−0.112099	+	0.307989i
$51$	−1630.10	+	495.899i	−0.626722	+	0.190657i
$52$	−98.2691	+	557.312i	−0.0363421	+	0.206106i
$53$			293.218i			0.104385i	0.998637	+	0.0521927i	$0.0166210\pi$
$53$			293.218i			0.104385i	−0.998637	+	0.0521927i	$0.983379\pi$
$54$	−1734.66	−	2012.37i	−0.594877	−	0.690112i
$55$	−2285.32			−0.755477
$56$	5403.95	+	952.863i	1.72320	+	0.303847i
$57$	−2796.48	+	2990.53i	−0.860721	+	0.920445i
$58$	2081.30	+	757.531i	0.618698	+	0.225188i
$59$	−3379.85	−	4027.95i	−0.970943	−	1.15713i	−0.987557	−	0.157263i	$-0.949733\pi$
$59$	−3379.85	−	4027.95i	−0.970943	−	1.15713i	0.0166134	−	0.999862i	$-0.494712\pi$
$60$	−58.9589	−	485.756i	−0.0163775	−	0.134932i
$61$	−2379.12	+	865.931i	−0.639378	+	0.232714i	−0.641308	−	0.767284i	$-0.721608\pi$
$61$	−2379.12	+	865.931i	−0.639378	+	0.232714i	0.00193010	+	0.999998i	$0.499386\pi$
$62$	1075.16	+	620.743i	0.279698	+	0.161484i
$63$	6478.00	+	699.057i	1.63215	+	0.176129i
$64$	2267.66	+	3927.70i	0.553628	+	0.958912i
$65$	2677.36	−	3190.75i	0.633694	−	0.755207i
$66$	3341.09	−	1696.53i	0.767010	−	0.389470i
$67$	933.925	+	5296.55i	0.208047	+	1.17990i	0.892572	+	0.450905i	$0.148899\pi$
$67$	933.925	+	5296.55i	0.208047	+	1.17990i	−0.684524	+	0.728990i	$0.739990\pi$
$68$	506.726	−	89.3495i	0.109586	−	0.0193230i
$69$	3108.49	−	4772.14i	0.652907	−	1.00234i
$70$	−4492.41	−	3769.58i	−0.916818	−	0.769302i
$71$	−4919.78	+	2840.43i	−0.975952	+	0.563466i	−0.901046	−	0.433724i	$-0.857199\pi$
$71$	−4919.78	+	2840.43i	−0.975952	+	0.563466i	−0.0749067	+	0.997191i	$0.523866\pi$
$72$	3077.12	+	4589.45i	0.593579	+	0.885310i
$73$	1385.76	−	2400.21i	0.260041	−	0.450404i	−0.706211	−	0.708001i	$-0.749597\pi$
$73$	1385.76	−	2400.21i	0.260041	−	0.450404i	0.966253	+	0.257597i	$0.0829305\pi$
$74$	−1374.62	−	3776.73i	−0.251026	−	0.689689i
$75$	793.221	−	1861.52i	0.141017	−	0.330937i
$76$	947.162	−	794.763i	0.163982	−	0.137598i
$77$	−3143.01	+	8635.36i	−0.530109	+	1.45646i
$78$	−1545.56	+	6652.39i	−0.254036	+	1.09342i
$79$	1459.18	−	8275.44i	0.233806	−	1.32598i	−0.611308	−	0.791393i	$-0.709356\pi$
$79$	1459.18	−	8275.44i	0.233806	−	1.32598i	0.845114	−	0.534587i	$-0.179533\pi$
$80$		−	4103.41i		−	0.641158i
$81$	4010.58	+	5192.49i	0.611276	+	0.791418i
$82$	3311.81			0.492536
$83$	−6331.63	−	1116.44i	−0.919093	−	0.162061i	−0.305963	−	0.952043i	$-0.598978\pi$
$83$	−6331.63	−	1116.44i	−0.919093	−	0.162061i	−0.613129	+	0.789983i	$0.710090\pi$
$84$	−1916.58	−	445.280i	−0.271624	−	0.0631066i
$85$	−3558.77	−	1295.29i	−0.492563	−	0.179278i
$86$	3020.21	+	3599.35i	0.408357	+	0.486661i
$87$	−5031.84	−	2144.14i	−0.664797	−	0.283279i
$88$	−7323.20	+	2665.43i	−0.945661	+	0.344193i
$89$	6738.82	+	3890.66i	0.850753	+	0.491183i	0.860905	−	0.508766i	$-0.169898\pi$
$89$	6738.82	+	3890.66i	0.850753	+	0.491183i	−0.0101517	+	0.999948i	$0.503231\pi$
$90$	−395.572	−	5892.02i	−0.0488361	−	0.727409i
$91$	−8374.46	−	14505.0i	−1.01129	−	1.75160i
$92$	−1105.52	+	1317.51i	−0.130615	+	0.155661i
$93$	−2568.92	−	1673.35i	−0.297019	−	0.193473i
$94$	298.379	+	1692.19i	0.0337686	+	0.191511i
$95$	−8962.18	+	1580.27i	−0.993040	+	0.175100i
$96$	−1401.27	−	2759.60i	−0.152047	−	0.299436i
$97$	8458.98	+	7097.93i	0.899031	+	0.754377i	0.970001	−	0.243102i	$-0.0781649\pi$
$97$	8458.98	+	7097.93i	0.899031	+	0.754377i	−0.0709696	+	0.997478i	$0.522609\pi$
$98$	−12844.2	+	7415.62i	−1.33738	+	0.772139i
$99$	−8463.98	+	3740.28i	−0.863584	+	0.381622i
$100$	−305.531	+	529.196i	−0.0305531	+	0.0529196i
$101$	3965.48	+	10895.1i	0.388734	+	1.06804i	0.967572	+	0.252596i	$0.0812842\pi$
$101$	3965.48	+	10895.1i	0.388734	+	1.06804i	−0.578838	+	0.815443i	$0.696494\pi$
$102$	6164.43	−	748.211i	0.592506	−	0.0719157i
$103$	10494.0	−	8805.50i	0.989159	−	0.830003i	0.00371311	−	0.999993i	$-0.498818\pi$
$103$	10494.0	−	8805.50i	0.989159	−	0.830003i	0.985446	+	0.169990i	$0.0543736\pi$
$104$	4858.02	−	13347.3i	0.449151	−	1.23403i
$105$	10577.9	+	9891.52i	0.959445	+	0.897190i
$106$	185.565	−	1052.39i	0.0165152	−	0.0936623i
$107$		−	9783.48i		−	0.854527i	−0.904127	−	0.427264i	$-0.859478\pi$
$107$		−	9783.48i		−	0.854527i	0.904127	−	0.427264i	$-0.140522\pi$
$108$	−1013.38	−	1702.57i	−0.0868809	−	0.145968i
$109$	5416.41			0.455888			0.227944	−	0.973674i	$-0.426800\pi$
$109$	5416.41			0.455888			0.227944	+	0.973674i	$0.426800\pi$
$110$	8202.23	+	1446.27i	0.677870	+	0.119527i
$111$	2888.67	+	9495.54i	0.234451	+	0.770679i
$112$	−15505.2	−	5643.45i	−1.23607	−	0.449892i
$113$	6637.56	+	7910.34i	0.519818	+	0.619495i	0.960538	−	0.278150i	$-0.0897211\pi$
$113$	6637.56	+	7910.34i	0.519818	+	0.619495i	−0.440719	+	0.897645i	$0.645277\pi$
$114$	11929.4	−	8963.52i	0.917930	−	0.689714i
$115$	11895.4	−	4329.57i	0.899462	−	0.327377i
$116$	1430.46	+	825.876i	0.106306	+	0.0613760i
$117$	4693.79	−	16199.3i	0.342888	−	1.18338i
$118$	9581.52	+	16595.7i	0.688130	+	1.19188i
$119$	−9788.81	+	11665.8i	−0.691251	+	0.823801i
$120$	−659.796	+	12263.9i	−0.0458192	+	0.851657i
$121$	276.071	+	1565.67i	0.0188560	+	0.106938i
$122$	9086.92	−	1602.27i	0.610516	−	0.107650i
$123$	−8166.70	−	439.369i	−0.539804	−	0.0290415i
$124$	709.238	+	595.121i	0.0461263	+	0.0387045i
$125$	14722.6	−	8500.11i	0.942247	−	0.544007i
$126$	−22807.8	−	6608.61i	−1.43662	−	0.416264i
$127$	−4578.46	+	7930.12i	−0.283865	+	0.491668i	−0.972333	−	0.233598i	$-0.924950\pi$
$127$	−4578.46	+	7930.12i	−0.283865	+	0.491668i	0.688468	+	0.725266i	$0.258283\pi$
$128$	−3771.32	−	10361.6i	−0.230183	−	0.632424i
$129$	−6970.12	−	9276.43i	−0.418852	−	0.557444i
$130$	−11628.6	+	9757.54i	−0.688082	+	0.577369i
$131$	7733.68	−	21248.1i	0.450654	−	1.23816i	−0.481611	−	0.876385i	$-0.659948\pi$
$131$	7733.68	−	21248.1i	0.450654	−	1.23816i	0.932265	−	0.361777i	$-0.117830\pi$
$132$	2673.48	−	813.308i	0.153437	−	0.0466775i
$133$	−6354.49	+	36038.1i	−0.359234	+	2.03732i
$134$		−	19600.9i		−	1.09161i
$135$	193.776	+	14581.8i	0.0106325	+	0.800098i
$136$	−12914.7			−0.698240
$137$	−23306.1	−	4109.50i	−1.24173	−	0.218951i	−0.486076	−	0.873917i	$-0.661572\pi$
$137$	−23306.1	−	4109.50i	−1.24173	−	0.218951i	−0.755659	+	0.654965i	$0.772683\pi$
$138$	−14176.7	+	15160.4i	−0.744420	+	0.796074i
$139$	−11956.2	−	4351.70i	−0.618819	−	0.225232i	0.0135387	−	0.999908i	$-0.495690\pi$
$139$	−11956.2	−	4351.70i	−0.618819	−	0.225232i	−0.632357	+	0.774677i	$0.717913\pi$
$140$	−2811.18	−	3350.23i	−0.143428	−	0.170930i
$141$	−511.285	−	4212.42i	−0.0257172	−	0.211882i
$142$	19455.1	−	7081.09i	0.964845	−	0.351175i
$143$	20600.3	+	11893.6i	1.00740	+	0.581621i
$144$	−6715.88	−	15197.5i	−0.323875	−	0.732906i
$145$	−6078.65	−	10528.5i	−0.289115	−	0.500762i
$146$	−6492.61	+	7737.59i	−0.304588	+	0.362994i
$147$	32656.8	−	16582.4i	1.51126	−	0.767384i
$148$	−520.471	−	2951.74i	−0.0237615	−	0.134758i
$149$	28007.9	−	4938.55i	1.26156	−	0.222447i	0.497428	−	0.867505i	$-0.334278\pi$
$149$	28007.9	−	4938.55i	1.26156	−	0.222447i	0.764134	+	0.645058i	$0.223167\pi$
$150$	−4025.02	+	6179.19i	−0.178890	+	0.274631i
$151$	23369.1	+	19609.0i	1.02492	+	0.860008i	0.990237	−	0.139391i	$-0.0445143\pi$
$151$	23369.1	+	19609.0i	1.02492	+	0.860008i	0.0346800	+	0.999398i	$0.488959\pi$
$152$	−26875.8	+	15516.8i	−1.16325	+	0.671605i
$153$	−15300.3	+	1027.22i	−0.653609	+	0.0438814i
$154$	16745.5	−	29004.1i	0.706085	−	1.22297i
$155$	−2330.67	−	6403.48i	−0.0970104	−	0.266534i
$156$	−1996.57	+	4685.53i	−0.0820419	+	0.192535i
$157$	−33200.8	+	27858.8i	−1.34695	+	1.13022i	−0.367162	+	0.930157i	$0.619671\pi$
$157$	−33200.8	+	27858.8i	−1.34695	+	1.13022i	−0.979783	+	0.200064i	$0.935885\pi$
$158$	−10474.3	+	28777.9i	−0.419576	+	1.15278i
$159$	−597.207	+	2570.50i	−0.0236228	+	0.101677i
$160$	1194.56	−	6774.70i	0.0466626	−	0.264637i
$161$		−	50902.7i		−	1.96376i
$162$	−11108.3	−	21174.5i	−0.423269	−	0.806831i
$163$	2612.38			0.0983243			0.0491622	−	0.998791i	$-0.484345\pi$
$163$	2612.38			0.0983243			0.0491622	+	0.998791i	$0.484345\pi$
$164$	2432.27	+	428.876i	0.0904326	+	0.0159457i
$165$	−20034.3	−	4654.58i	−0.735877	−	0.170967i
$166$	22018.3	+	8014.00i	0.799038	+	0.290826i
$167$	10495.0	+	12507.5i	0.376314	+	0.448474i	0.920647	−	0.390395i	$-0.127662\pi$
$167$	10495.0	+	12507.5i	0.376314	+	0.448474i	−0.544333	+	0.838869i	$0.683217\pi$
$168$	45433.1	+	19359.7i	1.60973	+	0.685930i
$169$	−13901.4	+	5059.68i	−0.486725	+	0.177153i
$170$	11953.0	+	6901.09i	0.413600	+	0.238792i
$171$	−30606.3	+	20520.8i	−1.04669	+	0.701781i
$172$	1752.01	+	3034.56i	0.0592214	+	0.102574i
$173$	−1963.78	+	2340.34i	−0.0656146	+	0.0781964i	−0.797853	−	0.602852i	$-0.794031\pi$
$173$	−1963.78	+	2340.34i	−0.0656146	+	0.0781964i	0.732239	+	0.681048i	$0.238476\pi$
$174$	16702.9	+	10880.0i	0.551686	+	0.359359i
$175$	−3140.48	−	17810.5i	−0.102546	−	0.581569i
$176$	23078.1	−	4069.29i	0.745030	−	0.131369i
$177$	−21425.7	−	42195.0i	−0.683892	−	1.34683i
$178$	−21724.0	−	18228.6i	−0.685647	−	0.575326i
$179$	−29485.4	+	17023.4i	−0.920241	+	0.531302i	−0.883712	−	0.468031i	$-0.844964\pi$
$179$	−29485.4	+	17023.4i	−0.920241	+	0.531302i	−0.0365292	+	0.999333i	$0.511630\pi$
$180$	472.492	−	4378.47i	0.0145831	−	0.135138i
$181$	11868.0	−	20555.9i	0.362259	−	0.627451i	−0.626073	−	0.779764i	$-0.715339\pi$
$181$	11868.0	−	20555.9i	0.362259	−	0.627451i	0.988332	+	0.152313i	$0.0486722\pi$
$182$	20877.2	+	57359.7i	0.630274	+	1.73166i
$183$	−22620.3	+	2745.55i	−0.675454	+	0.0819836i
$184$	33068.6	−	27747.8i	0.976742	−	0.819583i
$185$	−7545.19	+	20730.2i	−0.220459	+	0.605705i
$186$	8161.10	+	7631.56i	0.235897	+	0.220591i
$187$	3755.67	−	21299.5i	0.107400	−	0.609096i
$188$			1281.43i			0.0362559i
$189$	55365.6	+	19322.2i	1.54995	+	0.540921i
$190$	33166.2			0.918732
$191$	8026.32	+	1415.26i	0.220014	+	0.0387944i	0.282568	−	0.959247i	$-0.408814\pi$
$191$	8026.32	+	1415.26i	0.220014	+	0.0387944i	−0.0625545	+	0.998042i	$0.519925\pi$
$192$	11879.8	+	39050.9i	0.322260	+	1.05932i
$193$	13058.7	+	4752.99i	0.350580	+	0.127601i	0.511307	−	0.859398i	$-0.329162\pi$
$193$	13058.7	+	4752.99i	0.350580	+	0.127601i	−0.160727	+	0.986999i	$0.551384\pi$
$194$	−25868.2	−	30828.5i	−0.687325	−	0.819122i
$195$	29969.8	−	22518.7i	0.788160	−	0.592208i
$196$	−10393.4	+	3782.90i	−0.270550	+	0.0984721i
$197$	7299.39	+	4214.30i	0.188085	+	0.108591i	0.591086	−	0.806609i	$-0.298699\pi$
$197$	7299.39	+	4214.30i	0.188085	+	0.108591i	−0.403001	+	0.915200i	$0.632033\pi$
$198$	32745.1	−	8067.76i	0.835249	−	0.205789i
$199$	−10447.1	−	18094.8i	−0.263808	−	0.456929i	0.703443	−	0.710752i	$-0.251645\pi$
$199$	−10447.1	−	18094.8i	−0.263808	−	0.456929i	−0.967251	+	0.253823i	$0.918312\pi$
$200$	9858.57	−	11749.0i	0.246464	−	0.293725i
$201$	−2600.40	+	48334.4i	−0.0643646	+	1.19637i
$202$	−7337.49	−	41613.0i	−0.179823	−	1.01983i
$203$	−48143.4	+	8488.97i	−1.16827	+	0.205998i
$204$	4624.20	+	248.783i	0.111116	+	0.00597805i
$205$	−13925.4	−	11684.8i	−0.331360	−	0.278044i
$206$	−43236.5	+	24962.6i	−1.01886	+	0.588242i
$207$	36970.2	−	35503.8i	0.862801	−	0.828580i
$208$	−21355.5	+	36988.9i	−0.493610	+	0.854957i
$209$	−17775.3	−	48837.2i	−0.406934	−	1.11804i
$210$	−31705.1	−	42195.9i	−0.718937	−	0.956823i
$211$	−59352.0	+	49802.2i	−1.33312	+	1.11862i	−0.349786	+	0.936830i	$0.613746\pi$
$211$	−59352.0	+	49802.2i	−1.33312	+	1.11862i	−0.983337	+	0.181793i	$0.941810\pi$
$212$	272.566	−	748.870i	0.00606458	−	0.0166623i
$213$	−48914.5	+	14880.4i	−1.07815	+	0.327987i
$214$	−6191.52	+	35113.9i	−0.135198	+	0.766745i
$215$		−	25790.4i		−	0.557931i
$216$	17628.1	+	46500.7i	0.377831	+	0.996672i
$217$	−27401.7			−0.581914
$218$	−19440.0	−	3427.80i	−0.409057	−	0.0721277i
$219$	17036.9	−	18219.0i	0.355223	−	0.379871i
$220$	5836.63	+	2124.36i	0.120591	+	0.0438917i
$221$	25338.3	+	30197.0i	0.518791	+	0.618271i
$222$	−4358.41	−	35908.5i	−0.0884347	−	0.728604i
$223$	11279.7	−	4105.47i	0.226823	−	0.0825568i	−0.226109	−	0.974102i	$-0.572600\pi$
$223$	11279.7	−	4105.47i	0.226823	−	0.0825568i	0.452932	+	0.891545i	$0.350378\pi$
$224$	−23956.1	−	13831.1i	−0.477442	−	0.275651i
$225$	10745.2	−	14703.5i	0.212251	−	0.290439i
$226$	−18816.8	−	32591.6i	−0.368407	−	0.638100i
$227$	16872.7	−	20108.1i	0.327441	−	0.390229i	−0.577059	−	0.816702i	$-0.695800\pi$
$227$	16872.7	−	20108.1i	0.327441	−	0.390229i	0.904500	+	0.426474i	$0.140244\pi$
$228$	9922.03	−	5038.18i	0.190867	−	0.0969180i
$229$	10216.5	+	57940.6i	0.194819	+	1.10487i	0.912676	+	0.408683i	$0.134012\pi$
$229$	10216.5	+	57940.6i	0.194819	+	1.10487i	−0.717858	+	0.696190i	$0.754877\pi$
$230$	−45433.7	+	8011.19i	−0.858860	+	0.151440i
$231$	−45141.2	+	69300.5i	−0.845958	+	1.29871i
$232$	−31758.5	−	26648.5i	−0.590043	−	0.495105i
$233$	38277.1	−	22099.3i	0.705062	−	0.407068i	−0.104168	−	0.994560i	$-0.533218\pi$
$233$	38277.1	−	22099.3i	0.705062	−	0.407068i	0.809230	+	0.587492i	$0.199885\pi$
$234$	−27098.3	+	55170.4i	−0.494892	+	1.00757i
$235$	4715.81	−	8168.03i	0.0853927	−	0.147905i
$236$	4887.78	+	13429.1i	0.0877582	+	0.241114i
$237$	29646.8	−	69574.8i	0.527814	−	1.23867i
$238$	42515.8	−	35675.0i	0.750578	−	0.629810i
$239$	−9592.71	+	26355.7i	−0.167937	+	0.461402i	−0.994901	−	0.100852i	$-0.967843\pi$
$239$	−9592.71	+	26355.7i	−0.167937	+	0.461402i	0.826965	+	0.562254i	$0.190066\pi$
$240$	8357.55	−	35972.6i	0.145096	−	0.624524i
$241$	12199.4	−	69186.4i	0.210042	−	1.19121i	−0.679264	−	0.733894i	$-0.737701\pi$
$241$	12199.4	−	69186.4i	0.210042	−	1.19121i	0.889306	−	0.457312i	$-0.151188\pi$
$242$		−	5794.07i		−	0.0989357i
$243$	24583.1	+	53688.5i	0.416317	+	0.909220i
$244$	6881.15			0.115580
$245$	80171.0	+	14136.3i	1.33563	+	0.235507i
$246$	29033.0	+	6745.27i	0.479758	+	0.111463i
$247$	89011.0	+	32397.3i	1.45898	+	0.531026i
$248$	−14937.1	−	17801.3i	−0.242864	−	0.289434i
$249$	−53232.4	−	22683.1i	−0.858573	−	0.365850i
$250$	−58220.2	+	21190.4i	−0.931524	+	0.339047i
$251$	98020.2	+	56592.0i	1.55585	+	0.898272i	0.997646	+	0.0685690i	$0.0218433\pi$
$251$	98020.2	+	56592.0i	1.55585	+	0.898272i	0.558206	+	0.829703i	$0.311490\pi$
$252$	−15894.8	−	7807.11i	−0.250296	−	0.122939i
$253$	36146.5	+	62607.5i	0.564709	+	0.978105i
$254$	21451.1	−	25564.5i	0.332493	−	0.396250i
$255$	−28559.9	−	18603.4i	−0.439213	−	0.286096i
$256$	−5622.56	−	31887.1i	−0.0857934	−	0.486559i
$257$	−14639.9	+	2581.41i	−0.221652	+	0.0390832i	−0.283371	−	0.959010i	$-0.591453\pi$
$257$	−14639.9	+	2581.41i	−0.221652	+	0.0390832i	0.0617192	+	0.998094i	$0.480342\pi$
$258$	19145.8	+	37705.1i	0.287630	+	0.566448i
$259$	67954.9	+	57020.9i	1.01303	+	0.850031i
$260$	−9803.91	+	5660.29i	−0.145028	+	0.0837321i
$261$	−39744.7	−	29045.2i	−0.583442	−	0.426376i
$262$	−41203.9	+	71367.2i	−0.600255	+	1.03967i
$263$	−31408.8	−	86295.1i	−0.454088	−	1.24760i	−0.929822	−	0.368008i	$-0.880040\pi$
$263$	−31408.8	−	86295.1i	−0.454088	−	1.24760i	0.475734	−	0.879589i	$-0.342182\pi$
$264$	−69627.7	+	8451.09i	−0.999020	+	0.121257i
$265$	−4493.31	+	3770.34i	−0.0639845	+	0.0536894i
$266$	45613.8	−	125323.i	0.644663	−	1.77120i
$267$	51151.7	+	47832.7i	0.717526	+	0.670968i
$268$	2538.29	−	14395.4i	0.0353404	−	0.200426i
$269$			96636.1i			1.33547i	0.744398	+	0.667736i	$0.232736\pi$
$269$			96636.1i			1.33547i	−0.744398	+	0.667736i	$0.767264\pi$
$270$	8532.67	−	52458.1i	0.117046	−	0.719590i
$271$	12128.1			0.165140			0.0825701	−	0.996585i	$-0.473687\pi$
$271$	12128.1			0.165140			0.0825701	+	0.996585i	$0.473687\pi$
$272$	38244.3	+	6743.51i	0.516927	+	0.0911482i
$273$	−43872.0	−	144215.i	−0.588657	−	1.93502i
$274$	81047.2	+	29498.8i	1.07954	+	0.392919i
$275$	16510.0	+	19675.9i	0.218315	+	0.260177i
$276$	−12375.0	+	9298.33i	−0.162453	+	0.122064i
$277$	−34773.7	+	12656.6i	−0.453201	+	0.164952i	−0.558527	−	0.829486i	$-0.688633\pi$
$277$	−34773.7	+	12656.6i	−0.453201	+	0.164952i	0.105327	+	0.994438i	$0.466411\pi$
$278$	40158.0	+	23185.2i	0.519615	+	0.300000i
$279$	−19112.3	−	19901.6i	−0.245530	−	0.255670i
$280$	54884.8	+	95063.2i	0.700061	+	1.21254i
$281$	15897.6	−	18946.0i	0.201335	−	0.239941i	−0.655924	−	0.754827i	$-0.727721\pi$
$281$	15897.6	−	18946.0i	0.201335	−	0.239941i	0.857259	+	0.514885i	$0.172165\pi$
$282$	−830.800	+	15442.4i	−0.0104472	+	0.194185i
$283$	−13223.6	−	74994.8i	−0.165111	−	0.936393i	−0.948950	−	0.315428i	$-0.897852\pi$
$283$	−13223.6	−	74994.8i	−0.165111	−	0.936393i	0.783838	−	0.620965i	$-0.213259\pi$
$284$	15205.3	−	2681.11i	0.188521	−	0.0332413i
$285$	−81785.7	−	4400.08i	−1.00690	−	0.0541714i
$286$	−66409.4	−	55724.1i	−0.811891	−	0.681257i
$287$	−63304.1	+	36548.7i	−0.768543	+	0.443719i
$288$	−6663.63	−	27046.1i	−0.0803390	−	0.326077i
$289$	−23839.8	+	41291.8i	−0.285435	+	0.494388i
$290$	15153.8	+	41634.8i	0.180188	+	0.495063i
$291$	59699.2	+	79452.8i	0.704989	+	0.938260i
$292$	−5770.34	+	4841.89i	−0.0676762	+	0.0567870i
$293$	11979.5	−	32913.3i	0.139541	−	0.383386i	−0.850162	−	0.526521i	$-0.823496\pi$
$293$	11979.5	−	32913.3i	0.139541	−	0.383386i	0.989703	+	0.143135i	$0.0457183\pi$
$294$	−127703.	+	38848.9i	−1.47743	+	0.449452i
$295$	18265.1	−	103587.i	0.209884	−	1.19031i
$296$			75229.3i			0.858626i
$297$	−81817.6	+	15550.4i	−0.927542	+	0.176290i
$298$	−103649.			−1.16716
$299$	−129760.	−	22880.1i	−1.45143	−	0.255927i
$300$	−3756.27	+	4016.91i	−0.0417364	+	0.0446324i
$301$	−97452.2	−	35469.7i	−1.07562	−	0.391493i
$302$	−71464.5	−	85168.0i	−0.783567	−	0.933819i
$303$	12573.1	+	103588.i	0.136948	+	1.12830i
$304$	87689.9	−	31916.5i	0.948861	−	0.345357i
$305$	−43861.5	−	25323.5i	−0.471503	−	0.272222i
$306$	55564.5	+	5996.10i	0.593409	+	0.0640363i
$307$	−9364.32	−	16219.5i	−0.0993572	−	0.172092i	0.812062	−	0.583572i	$-0.198345\pi$
$307$	−9364.32	−	16219.5i	−0.0993572	−	0.172092i	−0.911419	+	0.411480i	$0.865012\pi$
$308$	16054.3	−	19132.8i	0.169235	−	0.201686i
$309$	109930.	−	55820.1i	1.15133	−	0.584620i
$310$	4312.55	+	24457.7i	0.0448756	+	0.254502i
$311$	−47860.6	+	8439.12i	−0.494832	+	0.0872522i	−0.415495	−	0.909596i	$-0.636391\pi$
$311$	−47860.6	+	8439.12i	−0.494832	+	0.0872522i	−0.0793371	+	0.996848i	$0.525280\pi$
$312$	69772.8	−	107115.i	0.716765	−	1.10037i
$313$	34100.2	+	28613.5i	0.348071	+	0.292066i	0.800015	−	0.599980i	$-0.204825\pi$
$313$	34100.2	+	28613.5i	0.348071	+	0.292066i	−0.451944	+	0.892046i	$0.649269\pi$
$314$	136792.	−	78976.7i	1.38740	−	0.801013i
$315$	72584.7	+	108258.i	0.731516	+	1.09104i
$316$	−11419.3	+	19778.8i	−0.114358	+	0.198073i
$317$	21930.6	+	60253.9i	0.218239	+	0.599607i	0.999704	−	0.0243426i	$-0.00774925\pi$
$317$	21930.6	+	60253.9i	0.218239	+	0.599607i	−0.781465	+	0.623950i	$0.785527\pi$
$318$	3770.19	−	8847.84i	0.0372828	−	0.0874949i
$319$	53185.6	−	44628.0i	0.522652	−	0.438557i
$320$	−31030.0	+	85254.2i	−0.303027	+	0.832560i
$321$	19926.3	−	85767.0i	0.193383	−	0.832358i
$322$	−32214.0	+	182695.i	−0.310694	+	1.76203i
$323$		−	86125.8i		−	0.825521i
$324$	−5416.12	−	16989.6i	−0.0515939	−	0.161842i
$325$	−46813.7			−0.443207
$326$	−9376.08	−	1653.26i	−0.0882239	−	0.0155563i
$327$	47483.0	+	11031.8i	0.444061	+	0.103169i
$328$	−58251.6	−	21201.8i	−0.541452	−	0.197072i
$329$	−24378.2	−	29052.8i	−0.225222	−	0.268409i
$330$	68959.2	+	29384.5i	0.633234	+	0.269830i
$331$	38407.2	−	13979.1i	0.350555	−	0.127592i	−0.160740	−	0.986997i	$-0.551388\pi$
$331$	38407.2	−	13979.1i	0.350555	−	0.127592i	0.511295	+	0.859405i	$0.329166\pi$
$332$	15133.0	+	8737.03i	0.137293	+	0.0792661i
$333$	5983.67	+	89126.2i	0.0539609	+	0.803742i
$334$	−29752.3	−	51532.4i	−0.266703	−	0.461942i
$335$	−69156.2	+	82417.1i	−0.616228	+	0.734392i
$336$	−124433.	−	81053.4i	−1.10219	−	0.717948i
$337$	6145.73	+	34854.2i	0.0541145	+	0.306899i	0.999837	−	0.0180778i	$-0.00575467\pi$
$337$	6145.73	+	34854.2i	0.0541145	+	0.306899i	−0.945722	+	0.324977i	$0.894644\pi$
$338$	53095.4	−	9362.15i	0.464754	−	0.0819487i
$339$	42077.0	+	82865.0i	0.366139	+	0.721060i
$340$	7884.93	+	6616.24i	0.0682087	+	0.0572339i
$341$	33702.6	−	19458.2i	0.289838	−	0.167338i
$342$	122836.	−	54281.8i	1.05020	−	0.464090i
$343$	67107.8	−	116234.i	0.570407	−	0.987973i
$344$	−30080.0	−	82644.1i	−0.254191	−	0.698385i
$345$	113099.	−	13727.5i	0.950214	−	0.115333i
$346$	8529.29	−	7156.93i	0.0712460	−	0.0597825i
$347$	−47338.2	+	130061.i	−0.393145	+	1.08016i	0.572412	+	0.819966i	$0.306008\pi$
$347$	−47338.2	+	130061.i	−0.393145	+	1.08016i	−0.965557	+	0.260191i	$0.916214\pi$
$348$	10858.0	+	10153.5i	0.0896588	+	0.0838413i
$349$	29.9066	−	169.609i	0.000245537	−	0.00139251i	−0.984685	−	0.174344i	$-0.944219\pi$
$349$	29.9066	−	169.609i	0.000245537	−	0.00139251i	0.984930	+	0.172952i	$0.0553305\pi$
$350$			65911.3i			0.538051i
$351$	74141.8	−	132451.i	0.601796	−	1.07508i
$352$	39286.3			0.317071
$353$	83193.1	+	14669.2i	0.667633	+	0.117722i	0.497185	−	0.867645i	$-0.334367\pi$
$353$	83193.1	+	14669.2i	0.667633	+	0.117722i	0.170449	+	0.985367i	$0.445478\pi$
$354$	50195.5	+	165001.i	0.400552	+	1.31668i
$355$	−106788.	−	38867.6i	−0.847355	−	0.308412i
$356$	−13594.1	−	16200.8i	−0.107263	−	0.127831i
$357$	−109574.	+	82331.6i	−0.859747	+	0.645996i
$358$	116600.	−	42438.7i	0.909768	−	0.331128i
$359$	−190874.	−	110201.i	−1.48101	−	0.855060i	−0.481239	−	0.876589i	$-0.659813\pi$
$359$	−190874.	−	110201.i	−1.48101	−	0.855060i	−0.999768	+	0.0215290i	$0.993147\pi$
$360$	−30762.3	+	106167.i	−0.237363	+	0.819193i
$361$	−38318.3	−	66369.2i	−0.294030	−	0.509275i
$362$	−55604.2	+	66266.5i	−0.424317	+	0.505681i
$363$	−768.684	+	14287.8i	−0.00583357	+	0.108431i
$364$	7904.73	+	44829.9i	0.0596601	+	0.338349i
$365$	54599.8	−	9627.42i	0.409831	−	0.0722643i
$366$	82924.0	+	4461.32i	0.619039	+	0.0333043i
$367$	−115293.	−	96742.6i	−0.855996	−	0.718266i	0.105105	−	0.994461i	$-0.466482\pi$
$367$	−115293.	−	96742.6i	−0.855996	−	0.718266i	−0.961102	+	0.276195i	$0.910926\pi$
$368$	−112415.	+	64902.9i	−0.830098	+	0.479257i
$369$	−70698.6	−	20485.1i	−0.519228	−	0.150448i
$370$	40199.7	−	69627.9i	0.293643	−	0.508604i
$371$	8067.01	+	22163.9i	0.0586091	+	0.161027i
$372$	5005.44	+	6661.66i	0.0361706	+	0.0481390i
$373$	95850.7	−	80428.3i	0.688934	−	0.578084i	−0.229668	−	0.973269i	$-0.573764\pi$
$373$	95850.7	−	80428.3i	0.688934	−	0.578084i	0.918602	+	0.395185i	$0.129319\pi$
$374$	−26958.9	+	74069.1i	−0.192734	+	0.529534i
$375$	146378.	−	44530.2i	1.04091	−	0.316659i
$376$	5585.03	−	31674.3i	0.0395048	−	0.224043i
$377$			126541.i			0.890327i
$378$	−186484.	−	104388.i	−1.30515	−	0.730577i
$379$	168468.			1.17284			0.586419	−	0.810008i	$-0.300537\pi$
$379$	168468.			1.17284			0.586419	+	0.810008i	$0.300537\pi$
$380$	24358.1	+	4294.99i	0.168685	+	0.0297437i
$381$	−56288.6	+	60194.4i	−0.387767	+	0.414673i
$382$	−27911.6	−	10159.0i	−0.191275	−	0.0696184i
$383$	100371.	+	119618.i	0.684245	+	0.815452i	0.990647	−	0.136451i	$-0.0435695\pi$
$383$	100371.	+	119618.i	0.684245	+	0.815452i	−0.306402	+	0.951902i	$0.599125\pi$
$384$	−11957.5	−	98516.5i	−0.0810919	−	0.668108i
$385$	−172744.	+	62873.6i	−1.16542	+	0.424176i
$386$	−43861.1	−	25323.2i	−0.294378	−	0.169959i
$387$	−42210.0	−	95518.2i	−0.281834	−	0.637770i
$388$	−15006.0	−	25991.1i	−0.0996783	−	0.172648i
$389$	3006.53	−	3583.04i	0.0198686	−	0.0236784i	−0.756019	−	0.654550i	$-0.772858\pi$
$389$	3006.53	−	3583.04i	0.0198686	−	0.0236784i	0.775887	+	0.630872i	$0.217303\pi$
$390$	−121816.	+	61855.2i	−0.800891	+	0.406675i
$391$	20803.4	+	117982.i	0.136076	+	0.771723i
$392$	273392.	−	48206.4i	1.77915	−	0.313713i
$393$	111074.	−	170520.i	0.719163	−	1.10406i
$394$	−23531.2	−	19745.0i	−0.151583	−	0.127193i
$395$	145577.	−	84048.8i	0.933035	−	0.538688i
$396$	25093.6	−	1684.71i	0.160019	−	0.0107432i
$397$	16900.1	−	29271.7i	0.107228	−	0.185724i	−0.807418	−	0.589979i	$-0.799136\pi$
$397$	16900.1	−	29271.7i	0.107228	−	0.185724i	0.914646	+	0.404255i	$0.132469\pi$
$398$	26044.1	+	71555.6i	0.164416	+	0.451728i
$399$	−129107.	+	302986.i	−0.810966	+	1.90317i
$400$	−35329.1	+	29644.7i	−0.220807	+	0.185279i
$401$	56821.5	−	156116.i	0.353366	−	0.970864i	−0.627915	−	0.778282i	$-0.716092\pi$
$401$	56821.5	−	156116.i	0.353366	−	0.970864i	0.981281	−	0.192582i	$-0.0616862\pi$
$402$	39921.7	−	171831.i	0.247034	−	1.06329i
$403$	−12316.7	+	69851.7i	−0.0758378	+	0.430097i
$404$		−	31511.8i		−	0.193068i
$405$	−28000.5	+	128226.i	−0.170709	+	0.781747i
$406$	178163.			1.08085
$407$	−124072.	−	21877.2i	−0.749004	−	0.132070i
$408$	−113216.	−	26303.7i	−0.680126	−	0.158014i
$409$	−118234.	−	43033.6i	−0.706798	−	0.257254i	−0.0364877	−	0.999334i	$-0.511617\pi$
$409$	−118234.	−	43033.6i	−0.706798	−	0.257254i	−0.670311	+	0.742080i	$0.733839\pi$
$410$	42584.8	+	50750.6i	0.253330	+	0.301907i
$411$	−195943.	−	83494.3i	−1.15997	−	0.494280i
$412$	−34986.6	+	12734.1i	−0.206114	+	0.0750194i
$413$	−366295.	−	211480.i	−2.14749	−	1.23985i
$414$	−155158.	+	104030.i	−0.905262	+	0.606956i
$415$	−64306.6	−	111382.i	−0.373387	−	0.646726i
$416$	−46025.8	+	54851.4i	−0.265959	+	0.316957i
$417$	−95950.9	−	62500.8i	−0.551794	−	0.359429i
$418$	32890.4	+	186531.i	0.188242	+	1.06757i
$419$	−284781.	+	50214.6i	−1.62212	+	0.286023i	−0.909555	−	0.415583i	$-0.863578\pi$
$419$	−284781.	+	50214.6i	−1.62212	+	0.286023i	−0.712565	+	0.701607i	$0.752466\pi$
$420$	−17820.7	−	35095.5i	−0.101024	−	0.198954i
$421$	162213.	+	136113.i	0.915210	+	0.767952i	0.973103	−	0.230371i	$-0.0739938\pi$
$421$	162213.	+	136113.i	0.915210	+	0.767952i	−0.0578932	+	0.998323i	$0.518438\pi$
$422$	244538.	−	141184.i	1.37316	−	0.792793i
$423$	4097.39	−	37969.6i	0.0228995	−	0.212205i
$424$	−10001.2	+	17322.6i	−0.0556314	+	0.0963564i
$425$	14557.9	+	39997.6i	0.0805976	+	0.221440i
$426$	184976.	−	22451.5i	1.01929	−	0.123716i
$427$	−156011.	+	130909.i	−0.855656	+	0.717981i
$428$	−9094.41	+	24986.7i	−0.0496463	+	0.136402i
$429$	156368.	+	146222.i	0.849639	+	0.794509i
$430$	−16321.6	+	92564.2i	−0.0882724	+	0.500617i
$431$		−	1455.79i		−	0.00783688i	−0.999992	−	0.00391844i	$-0.998753\pi$
$431$		−	1455.79i		−	0.00783688i	0.999992	−	0.00391844i	$-0.00124728\pi$
$432$	−27921.5	−	146908.i	−0.149614	−	0.787186i
$433$	−85562.0			−0.456357			−0.228179	−	0.973619i	$-0.573277\pi$
$433$	−85562.0			−0.456357			−0.228179	+	0.973619i	$0.573277\pi$
$434$	98347.5	+	17341.3i	0.522136	+	0.0920667i
$435$	−31844.7	−	104679.i	−0.168290	−	0.553199i
$436$	−13833.3	−	5034.92i	−0.0727702	−	0.0264862i
$437$	185046.	+	220529.i	0.968983	+	1.15479i
$438$	−72676.9	+	54607.9i	−0.378833	+	0.284648i
$439$	65703.4	−	23914.1i	0.340925	−	0.124087i	−0.165883	−	0.986145i	$-0.553047\pi$
$439$	65703.4	−	23914.1i	0.340925	−	0.124087i	0.506808	+	0.862059i	$0.330825\pi$
$440$	−135010.	−	77948.3i	−0.697368	−	0.402626i
$441$	320060.	−	78856.7i	1.64572	−	0.405472i
$442$	−71831.2	−	124415.i	−0.367679	−	0.636839i
$443$	201497.	−	240135.i	1.02674	−	1.22363i	0.0523843	−	0.998627i	$-0.483318\pi$
$443$	201497.	−	240135.i	1.02674	−	1.22363i	0.974359	−	0.224998i	$-0.0722376\pi$
$444$	1449.19	−	26936.5i	0.00735120	−	0.136639i
$445$	27029.9	+	153294.i	0.136498	+	0.774116i
$446$	−43082.0	+	7596.52i	−0.216584	+	0.0381896i
$447$	255590.	+	13750.8i	1.27917	+	0.0688196i
$448$	279468.	+	234501.i	1.39244	+	1.16839i
$449$	249646.	−	144133.i	1.23832	−	0.714943i	0.269567	−	0.962982i	$-0.413120\pi$
$449$	249646.	−	144133.i	1.23832	−	0.714943i	0.968750	+	0.248039i	$0.0797862\pi$
$450$	−47870.8	+	45972.1i	−0.236399	+	0.227022i
$451$	51907.0	−	89905.6i	0.255196	−	0.442012i
$452$	−9598.92	−	26372.8i	−0.0469835	−	0.129086i
$453$	164927.	+	219500.i	0.803705	+	1.06964i
$454$	−73283.3	+	61492.0i	−0.355544	+	0.298337i
$455$	114594.	−	314843.i	0.553525	−	1.52080i
$456$	−267211.	+	81289.0i	−1.28506	+	0.390933i
$457$	−9696.26	+	54990.2i	−0.0464271	+	0.263301i	−0.999182	−	0.0404389i	$-0.987124\pi$
$457$	−9696.26	+	54990.2i	−0.0464271	+	0.263301i	0.952755	+	0.303740i	$0.0982355\pi$
$458$		−	214420.i		−	1.02220i
$459$	−136223.	−	22157.6i	−0.646583	−	0.105171i
$460$	−34405.1			−0.162595
$461$	−125241.	−	22083.3i	−0.589309	−	0.103911i	−0.128961	−	0.991650i	$-0.541164\pi$
$461$	−125241.	−	22083.3i	−0.589309	−	0.103911i	−0.460348	+	0.887739i	$0.652275\pi$
$462$	205873.	−	220158.i	0.964530	−	1.03146i
$463$	100428.	+	36552.9i	0.468483	+	0.170514i	0.565465	−	0.824772i	$-0.308697\pi$
$463$	100428.	+	36552.9i	0.468483	+	0.170514i	−0.0969821	+	0.995286i	$0.530919\pi$
$464$	80131.9	+	95497.5i	0.372194	+	0.443564i
$465$	−7389.72	−	60883.1i	−0.0341760	−	0.281573i
$466$	−151366.	+	55092.7i	−0.697038	+	0.253701i
$467$	319824.	+	184650.i	1.46648	+	0.846674i	0.999297	−	0.0374855i	$-0.0119348\pi$
$467$	319824.	+	184650.i	1.46648	+	0.846674i	0.467185	+	0.884159i	$0.345268\pi$
$468$	−27046.2	+	37009.3i	−0.123485	+	0.168974i
$469$	216312.	+	374664.i	0.983412	+	1.70332i
$470$	−22094.7	+	26331.4i	−0.100021	+	0.119201i
$471$	−347797.	+	176603.i	−1.56777	+	0.796081i
$472$	−62286.1	−	353242.i	−0.279581	−	1.58558i
$473$	145048.	−	25575.9i	0.648321	−	0.114316i
$474$	−150436.	+	230948.i	−0.669568	+	1.02792i
$475$	78352.1	+	65745.2i	0.347267	+	0.291392i
$476$	35844.5	−	20694.8i	0.158201	−	0.0913373i
$477$	−10470.8	+	21318.0i	−0.0460198	+	0.0936935i
$478$	51108.5	−	88522.5i	0.223685	−	0.387434i
$479$	68595.4	+	188464.i	0.298968	+	0.821406i	0.994673	+	0.103079i	$0.0328696\pi$
$479$	68595.4	+	188464.i	0.298968	+	0.821406i	−0.695706	+	0.718327i	$0.744908\pi$
$480$	24270.4	−	56957.4i	0.105340	−	0.247211i
$481$	175901.	−	147598.i	0.760288	−	0.637957i
$482$	−87569.9	+	240596.i	−0.376930	+	1.03561i
$483$	103675.	−	446239.i	0.444407	−	1.91282i
$484$	750.326	−	4255.31i	0.00320302	−	0.0181652i
$485$			220895.i			0.939080i
$486$	−54254.0	−	208251.i	−0.229699	−	0.881686i
$487$	−355215.			−1.49773			−0.748865	−	0.662722i	$-0.769401\pi$
$487$	−355215.			−1.49773			−0.748865	+	0.662722i	$0.769401\pi$
$488$	−170088.	−	29991.1i	−0.714223	−	0.125937i
$489$	22901.5	+	5320.72i	0.0957735	+	0.0222512i
$490$	−278795.	−	101473.i	−1.16116	−	0.422629i
$491$	−218986.	−	260977.i	−0.908349	−	1.08253i	−0.996261	−	0.0863997i	$-0.972464\pi$
$491$	−218986.	−	260977.i	−0.908349	−	1.08253i	0.0879117	−	0.996128i	$-0.471981\pi$
$492$	20449.1	+	8713.64i	0.0844779	+	0.0359972i
$493$	108117.	−	39351.3i	0.444836	−	0.161907i
$494$	−298966.	−	172608.i	−1.22509	−	0.707307i
$495$	−166150.	−	81608.9i	−0.678096	−	0.333063i
$496$	34938.3	+	60514.8i	0.142016	+	0.245979i
$497$	−293733.	+	350057.i	−1.18916	+	1.41718i
$498$	176701.	+	115100.i	0.712493	+	0.464106i
$499$	−24501.9	−	138957.i	−0.0984006	−	0.558058i	−0.993652	−	0.112496i	$-0.964115\pi$
$499$	−24501.9	−	138957.i	−0.0984006	−	0.558058i	0.895252	−	0.445561i	$-0.146996\pi$
$500$	−45502.5	+	8023.32i	−0.182010	+	0.0320933i
$501$	66530.4	+	131023.i	0.265060	+	0.522001i
$502$	−315990.	−	265147.i	−1.25391	−	1.05215i
$503$	−368754.	+	212900.i	−1.45747	+	0.841473i	−0.998887	−	0.0471760i	$-0.984978\pi$
$503$	−368754.	+	212900.i	−1.45747	+	0.841473i	−0.458588	+	0.888649i	$0.651644\pi$
$504$	358859.	+	262252.i	1.41274	+	1.03242i
$505$	−115967.	+	200861.i	−0.454729	+	0.787614i
$506$	−90111.7	−	247580.i	−0.351949	−	0.966973i
$507$	−132172.	+	16042.4i	−0.514188	+	0.0624099i
$508$	19064.8	−	15997.3i	0.0738763	−	0.0619896i
$509$	119089.	−	327195.i	0.459661	−	1.26291i	−0.466078	−	0.884743i	$-0.654333\pi$
$509$	119089.	−	327195.i	0.459661	−	1.26291i	0.925739	−	0.378164i	$-0.123444\pi$
$510$	90730.8	+	84843.7i	0.348831	+	0.326196i
$511$	38713.1	−	219553.i	0.148257	−	0.840809i
$512$			294430.i			1.12316i
$513$	−310106.	+	117559.i	−1.17835	+	0.446705i
$514$	54177.6			0.205066
$515$	269873.	+	47585.9i	1.01753	+	0.179417i
$516$	9178.38	+	30170.9i	0.0344720	+	0.113315i
$517$	50614.6	+	18422.2i	0.189363	+	0.0689224i
$518$	−207811.	−	247659.i	−0.774477	−	0.922986i
$519$	−21982.1	+	16516.9i	−0.0816085	+	0.0613190i
$520$	267002.	−	97180.9i	0.987435	−	0.359397i
$521$	190108.	+	109759.i	0.700365	+	0.404356i	0.807483	−	0.589891i	$-0.200829\pi$
$521$	190108.	+	109759.i	0.700365	+	0.404356i	−0.107119	+	0.994246i	$0.534162\pi$
$522$	124266.	+	129399.i	0.456049	+	0.474885i
$523$	−58738.0	−	101737.i	−0.214741	−	0.371943i	0.738451	−	0.674307i	$-0.235557\pi$
$523$	−58738.0	−	101737.i	−0.214741	−	0.371943i	−0.953193	+	0.302364i	$0.902224\pi$
$524$	−39503.1	+	47078.0i	−0.143870	+	0.171457i
$525$	8744.27	−	162533.i	0.0317252	−	0.589688i
$526$	58117.1	+	329599.i	0.210055	+	1.19128i
$527$	63511.5	−	11198.8i	0.228681	−	0.0403227i
$528$	210602.	+	11330.4i	0.755431	+	0.0406423i
$529$	−92387.4	−	77522.2i	−0.330143	−	0.277022i
$530$	18513.0	−	10688.5i	0.0659061	−	0.0380509i
$531$	−101888.	−	413541.i	−0.361357	−	1.46666i
$532$	49729.0	−	86133.2i	0.175706	−	0.304332i
$533$	64714.3	+	177801.i	0.227796	+	0.625864i
$534$	−153317.	−	204048.i	−0.537661	−	0.715565i
$535$	149923.	−	125801.i	0.523795	−	0.439516i
$536$	−125483.	+	344761.i	−0.436771	+	1.20002i
$537$	−293157.	+	89182.1i	−1.01660	+	0.309264i
$538$	61156.6	−	346836.i	0.211290	−	1.19828i
$539$			464910.i			1.60026i
$540$	13059.9	−	37421.6i	0.0447869	−	0.128332i
$541$	421114.			1.43882			0.719408	−	0.694588i	$-0.244413\pi$
$541$	421114.			1.43882			0.719408	+	0.694588i	$0.244413\pi$
$542$	−43528.8	−	7675.30i	−0.148176	−	0.0261274i
$543$	145908.	−	156032.i	0.494855	−	0.529192i
$544$	61177.9	+	22266.9i	0.206727	+	0.0752424i
$545$	69646.7	+	83001.7i	0.234481	+	0.279444i
$546$	66194.0	+	545365.i	0.222041	+	1.82937i
$547$	−301567.	+	109761.i	−1.00788	+	0.366839i	−0.792619	−	0.609718i	$-0.791283\pi$
$547$	−301567.	+	109761.i	−1.00788	+	0.366839i	−0.215262	+	0.976556i	$0.569061\pi$
$548$	55703.0	+	32160.2i	0.185489	+	0.107092i
$549$	−203893.	−	22002.6i	−0.676484	−	0.0730011i
$550$	−46804.2	−	81067.2i	−0.154725	−	0.267991i
$551$	177715.	−	211792.i	0.585356	−	0.697600i
$552$	346411.	−	175900.i	1.13688	−	0.577281i
$553$	−117376.	−	665673.i	−0.383822	−	2.17676i
$554$	132816.	−	23419.0i	0.432743	−	0.0763043i
$555$	−108367.	+	166364.i	−0.351812	+	0.540100i
$556$	26490.5	+	22228.2i	0.0856922	+	0.0719043i
$557$	246377.	−	142246.i	0.794127	−	0.458489i	−0.0472867	−	0.998881i	$-0.515057\pi$
$557$	246377.	−	142246.i	0.794127	−	0.458489i	0.841413	+	0.540392i	$0.181724\pi$
$558$	56000.9	+	83524.2i	0.179857	+	0.268252i
$559$	−134222.	+	232479.i	−0.429536	+	0.743978i
$560$	−112893.	−	310170.i	−0.359990	−	0.989064i
$561$	76305.4	−	179073.i	0.242454	−	0.568989i
$562$	−69048.1	+	57938.2i	−0.218614	+	0.183439i
$563$	−58933.8	+	161919.i	−0.185929	+	0.510836i	−0.997279	−	0.0737253i	$-0.976511\pi$
$563$	−58933.8	+	161919.i	−0.185929	+	0.510836i	0.811349	+	0.584561i	$0.198733\pi$
$564$	−2609.93	+	11233.7i	−0.00820484	+	0.0353153i
$565$	−35870.1	+	203430.i	−0.112366	+	0.637261i
$566$			277532.i			0.866324i
$567$	446009.	+	282154.i	1.38732	+	0.877646i
$568$	−387530.			−1.20118
$569$	−148034.	−	26102.4i	−0.457232	−	0.0806224i	−0.0597116	−	0.998216i	$-0.519018\pi$
$569$	−148034.	−	26102.4i	−0.457232	−	0.0806224i	−0.397520	+	0.917593i	$0.630129\pi$
$570$	290752.	+	67550.8i	0.894897	+	0.207912i
$571$	362690.	+	132008.i	1.11241	+	0.404883i	0.831876	−	0.554962i	$-0.187267\pi$
$571$	362690.	+	132008.i	1.11241	+	0.404883i	0.280531	+	0.959845i	$0.409489\pi$
$572$	−41556.5	−	49525.1i	−0.127013	−	0.151368i
$573$	67480.4	+	28754.3i	0.205527	+	0.0875778i
$574$	250335.	−	91114.4i	0.759796	−	0.276543i
$575$	−123213.	−	71137.3i	−0.372668	−	0.215160i
$576$	24608.1	+	366536.i	0.0741709	+	1.10477i
$577$	12415.1	+	21503.6i	0.0372906	+	0.0645892i	0.884068	−	0.467358i	$-0.154794\pi$
$577$	12415.1	+	21503.6i	0.0372906	+	0.0645892i	−0.846778	+	0.531947i	$0.821461\pi$
$578$	111695.	−	133113.i	0.334332	−	0.398442i
$579$	104799.	+	68264.3i	0.312608	+	0.203628i
$580$	5737.68	+	32540.0i	0.0170561	+	0.0967302i
$581$	−509314.	+	89805.7i	−1.50880	+	0.266043i
$582$	−163984.	−	322945.i	−0.484123	−	0.953415i
$583$	−25660.8	−	21532.0i	−0.0754975	−	0.0633499i
$584$	163734.	−	94531.8i	0.480079	−	0.277174i
$585$	308595.	−	136370.i	0.901732	−	0.398480i
$586$	−63824.8	+	110548.i	−0.185864	+	0.321925i
$587$	−66760.6	−	183423.i	−0.193751	−	0.532327i	0.804334	−	0.594177i	$-0.202522\pi$
$587$	−66760.6	−	183423.i	−0.193751	−	0.532327i	−0.998085	+	0.0618503i	$0.980300\pi$
$588$	−98819.0	+	11994.2i	−0.285815	+	0.0346910i
$589$	118714.	−	99613.1i	0.342194	−	0.287135i
$590$	−131111.	+	360223.i	−0.376646	+	1.03483i
$591$	55406.8	+	51811.6i	0.158631	+	0.148338i
$592$	39281.7	−	222778.i	0.112085	−	0.635665i
$593$		−	421811.i		−	1.19952i	−0.800179	−	0.599761i	$-0.795262\pi$
$593$		−	421811.i		−	1.19952i	0.800179	−	0.599761i	$-0.204738\pi$
$594$	303492.	−	4033.09i	0.860151	−	0.0114305i
$595$	−304638.			−0.860498
$596$	−76122.1	−	13422.4i	−0.214298	−	0.0377865i
$597$	−54729.9	−	179906.i	−0.153559	−	0.504775i
$598$	451240.	+	164238.i	1.26184	+	0.459273i
$599$	−308462.	−	367610.i	−0.859701	−	1.02455i	−0.999410	−	0.0343593i	$-0.989061\pi$
$599$	−308462.	−	367610.i	−0.859701	−	1.02455i	0.139708	−	0.990193i	$-0.455384\pi$
$600$	110355.	−	82918.3i	0.306541	−	0.230329i
$601$	−489106.	+	178020.i	−1.35411	+	0.492856i	−0.914228	−	0.405199i	$-0.867202\pi$
$601$	−489106.	+	178020.i	−1.35411	+	0.492856i	−0.439882	+	0.898055i	$0.644980\pi$
$602$	327318.	+	188977.i	0.903186	+	0.521455i
$603$	−121241.	+	418428.i	−0.333437	+	1.15076i
$604$	−41456.1	−	71804.1i	−0.113636	−	0.196823i
$605$	−20442.7	+	24362.7i	−0.0558507	+	0.0665603i
$606$	20430.3	−	379745.i	0.0556327	−	1.03406i
$607$	51395.7	+	291480.i	0.139492	+	0.791099i	0.971626	+	0.236524i	$0.0760081\pi$
$607$	51395.7	+	291480.i	0.139492	+	0.791099i	−0.832134	+	0.554575i	$0.812881\pi$
$608$	154067.	−	27166.1i	0.416775	−	0.0734886i
$609$	−439339.	−	23636.5i	−1.18458	−	0.0637306i
$610$	141397.	+	118646.i	0.379998	+	0.318856i
$611$	−85018.3	+	49085.4i	−0.227735	+	0.131483i
$612$	40031.4	+	11599.2i	0.106880	+	0.0309689i
$613$	−226603.	+	392488.i	−0.603038	+	1.04449i	0.389321	+	0.921102i	$0.372710\pi$
$613$	−226603.	+	392488.i	−0.603038	+	1.04449i	−0.992358	+	0.123390i	$0.960624\pi$
$614$	23344.9	+	64139.5i	0.0619234	+	0.170133i
$615$	−98278.3	−	130797.i	−0.259841	−	0.345818i
$616$	−480218.	+	402951.i	−1.26554	+	1.06192i
$617$	183856.	−	505140.i	0.482956	−	1.32691i	−0.423991	−	0.905666i	$-0.639371\pi$
$617$	183856.	−	505140.i	0.482956	−	1.32691i	0.906947	−	0.421244i	$-0.138406\pi$
$618$	−429876.	+	130774.i	−1.12555	+	0.342408i
$619$	−12278.3	+	69633.5i	−0.0320447	+	0.181734i	−0.996629	−	0.0820403i	$-0.973856\pi$
$619$	−12278.3	+	69633.5i	−0.0320447	+	0.181734i	0.964584	+	0.263775i	$0.0849675\pi$
$620$			18520.8i			0.0481810i
$621$	396411.	−	235946.i	1.02793	−	0.611829i
$622$	177117.			0.457804
$623$	616416.	+	108691.i	1.58817	+	0.280038i
$624$	−262550.	+	280768.i	−0.674284	+	0.721071i
$625$	187522.	+	68252.4i	0.480056	+	0.174726i
$626$	−104281.	−	124277.i	−0.266106	−	0.317133i
$627$	−56359.0	−	464336.i	−0.143360	−	1.18113i
$628$	110691.	−	40288.1i	0.280667	−	0.102154i
$629$	−180809.	−	104390.i	−0.457003	−	0.263851i
$630$	−192002.	−	434486.i	−0.483753	−	1.09470i
$631$	205642.	+	356183.i	0.516481	+	0.894571i	0.999817	+	0.0191360i	$0.00609154\pi$
$631$	205642.	+	356183.i	0.516481	+	0.894571i	−0.483336	+	0.875435i	$0.660575\pi$
$632$	368466.	−	439121.i	0.922493	−	1.09938i
$633$	−621743.	+	315708.i	−1.55169	+	0.787912i
$634$	−40579.2	−	230136.i	−0.100954	−	0.572540i
$635$	−180394.	+	31808.4i	−0.447378	+	0.0788849i
$636$	3914.71	−	6009.83i	0.00967798	−	0.0148576i
$637$	−649105.	−	544664.i	−1.59969	−	1.34230i
$638$	−219131.	+	126515.i	−0.538348	+	0.310815i
$639$	−459117.	+	30823.7i	−1.12440	+	0.0754890i
$640$	110289.	−	191027.i	0.269261	−	0.466374i
$641$	112303.	+	308550.i	0.273323	+	0.750948i	0.998080	+	0.0619434i	$0.0197298\pi$
$641$	112303.	+	308550.i	0.273323	+	0.750948i	−0.724757	+	0.689005i	$0.758048\pi$
$642$	−125796.	+	295216.i	−0.305208	+	0.716258i
$643$	−217884.	+	182826.i	−0.526990	+	0.442197i	−0.867061	−	0.498203i	$-0.833994\pi$
$643$	−217884.	+	182826.i	−0.526990	+	0.442197i	0.340070	+	0.940400i	$0.389549\pi$
$644$	−47317.5	+	130004.i	−0.114091	+	0.313462i
$645$	52528.1	−	226092.i	0.126262	−	0.543457i
$646$	−54505.1	+	309114.i	−0.130609	+	0.740719i
$647$		−	338284.i		−	0.808114i	−0.914734	−	0.404057i	$-0.867600\pi$
$647$		−	338284.i		−	0.808114i	0.914734	−	0.404057i	$-0.132400\pi$
$648$	59827.3	+	443553.i	0.142478	+	1.05632i
$649$	600697.			1.42615
$650$	168019.	+	29626.3i	0.397678	+	0.0701214i
$651$	−240218.	−	55810.0i	−0.566817	−	0.131689i
$652$	−6671.93	−	2428.38i	−0.0156948	−	0.00571245i
$653$	410668.	+	489416.i	0.963086	+	1.14776i	0.988973	+	0.148096i	$0.0473145\pi$
$653$	410668.	+	489416.i	0.963086	+	1.14776i	−0.0258872	+	0.999665i	$0.508241\pi$
$654$	−163440.	−	69643.9i	−0.382122	−	0.162828i
$655$	425052.	−	154706.i	0.990739	−	0.360600i
$656$	161430.	+	93201.9i	0.375126	+	0.216579i
$657$	186461.	−	125018.i	0.431974	−	0.289628i
$658$	69109.6	+	119701.i	0.159620	+	0.276469i
$659$	306063.	−	364752.i	0.704759	−	0.839899i	−0.288297	−	0.957541i	$-0.593089\pi$
$659$	306063.	−	364752.i	0.704759	−	0.839899i	0.993056	+	0.117642i	$0.0375336\pi$
$660$	46840.1	+	30510.9i	0.107530	+	0.0700433i
$661$	−56228.4	−	318887.i	−0.128692	−	0.729851i	−0.979046	−	0.203639i	$-0.934723\pi$
$661$	−56228.4	−	318887.i	−0.128692	−	0.729851i	0.850354	−	0.526212i	$-0.176388\pi$
$662$	−146694.	+	25866.1i	−0.334731	+	0.0590221i
$663$	160625.	+	316330.i	0.365415	+	0.719636i
$664$	−335976.	−	281917.i	−0.762030	−	0.639419i
$665$	−633961.	+	366018.i	−1.43357	+	0.827673i
$666$	34928.0	−	323669.i	0.0787453	−	0.729715i
$667$	−192290.	+	333056.i	−0.432220	+	0.748626i
$668$	−15177.4	−	41699.6i	−0.0340130	−	0.0934499i
$669$	107245.	−	13016.9i	0.239621	−	0.0290842i
$670$	300366.	−	252037.i	0.669116	−	0.561455i
$671$	98925.4	−	271795.i	0.219717	−	0.603666i
$672$	−181842.	−	170043.i	−0.402675	−	0.376547i
$673$	−68023.9	+	385783.i	−0.150187	+	0.851751i	0.812869	+	0.582447i	$0.197905\pi$
$673$	−68023.9	+	385783.i	−0.150187	+	0.851751i	−0.963055	+	0.269304i	$0.913206\pi$
$674$		−	128984.i		−	0.283934i
$675$	124145.	−	107013.i	0.272472	−	0.234871i
$676$	40206.9			0.0879848
$677$	301876.	+	53228.9i	0.658645	+	0.116137i	0.492974	−	0.870044i	$-0.335910\pi$
$677$	301876.	+	53228.9i	0.658645	+	0.116137i	0.165671	+	0.986181i	$0.447021\pi$
$678$	−98577.0	−	324039.i	−0.214445	−	0.704917i
$679$	834680.	+	303799.i	1.81042	+	0.658940i
$680$	−166063.	−	197906.i	−0.359132	−	0.427997i
$681$	188870.	−	141913.i	0.407256	−	0.306004i
$682$	−133276.	+	48508.6i	−0.286539	+	0.104292i
$683$	399708.	+	230772.i	0.856844	+	0.494699i	0.862954	−	0.505282i	$-0.168612\pi$
$683$	399708.	+	230772.i	0.856844	+	0.494699i	−0.00611018	+	0.999981i	$0.501945\pi$
$684$	97243.0	−	23958.8i	0.207848	−	0.0512098i
$685$	−236707.	−	409988.i	−0.504463	−	0.873755i
$686$	−314416.	+	374706.i	−0.668122	+	0.796237i
$687$	−28446.5	+	528745.i	−0.0602721	+	1.12030i
$688$	45922.9	+	260442.i	0.0970180	+	0.550216i
$689$	60125.6	−	10601.8i	0.126655	−	0.0223326i
$690$	−414612.	−	22306.1i	−0.870850	−	0.0468518i
$691$	52014.2	+	43645.1i	0.108935	+	0.0914071i	0.695628	−	0.718402i	$-0.255126\pi$
$691$	52014.2	+	43645.1i	0.108935	+	0.0914071i	−0.586693	+	0.809809i	$0.699571\pi$
$692$	7190.94	−	4151.69i	0.0150167	−	0.00866987i
$693$	−536877.	+	515583.i	−1.11791	+	1.07357i
$694$	252211.	−	436842.i	0.523655	−	0.906997i
$695$	−87052.4	−	239174.i	−0.180223	−	0.495160i
$696$	−224135.	−	298298.i	−0.462691	−	0.615789i
$697$	131789.	−	110584.i	0.271277	−	0.227628i
$698$	−214.676	+	589.816i	−0.000440628	+	0.00121061i
$699$	380567.	−	115774.i	0.778891	−	0.236949i
$700$	−8535.44	+	48406.9i	−0.0174193	+	0.0987895i
$701$		−	124351.i		−	0.253054i	−0.991963	−	0.126527i	$-0.959617\pi$
$701$		−	124351.i		−	0.253054i	0.991963	−	0.126527i	$-0.0403830\pi$
$702$	−349925.	+	428460.i	−0.710069	+	0.869432i
$703$	−501692.			−1.01514
$704$	−510251.	−	89971.1i	−1.02953	−	0.181534i
$705$	57977.3	−	62000.3i	0.116649	−	0.124743i
$706$	−289305.	−	105298.i	−0.580425	−	0.211257i
$707$	599489.	+	714443.i	1.19934	+	1.42932i
$708$	15497.4	+	127681.i	0.0309166	+	0.254718i
$709$	−243010.	+	88448.3i	−0.483427	+	0.175953i	−0.572225	−	0.820097i	$-0.693920\pi$
$709$	−243010.	+	88448.3i	−0.483427	+	0.175953i	0.0887980	+	0.996050i	$0.471697\pi$
$710$	358675.	+	207081.i	0.711515	+	0.410793i
$711$	401604.	−	549545.i	0.794436	−	1.08709i
$712$	265408.	+	459699.i	0.523544	+	0.906805i
$713$	−138563.	+	165133.i	−0.272563	+	0.324828i
$714$	445375.	−	226152.i	0.873634	−	0.443612i
$715$	82629.3	+	468614.i	0.161630	+	0.916649i
$716$	91129.3	−	16068.6i	0.177759	−	0.0313437i
$717$	−137774.	+	211510.i	−0.267997	+	0.411427i
$718$	615323.	+	516317.i	1.19359	+	1.00154i
$719$	360037.	−	207867.i	0.696449	−	0.402095i	−0.109575	−	0.993979i	$-0.534949\pi$
$719$	360037.	−	207867.i	0.696449	−	0.402095i	0.806023	+	0.591884i	$0.201616\pi$
$720$	146533.	−	298332.i	0.282664	−	0.575486i
$721$	550968.	−	954304.i	1.05988	−	1.83576i
$722$	95525.9	+	262455.i	0.183251	+	0.503479i
$723$	247861.	−	581677.i	0.474167	−	1.11277i
$724$	−49418.5	+	41467.1i	−0.0942785	+	0.0791091i
$725$	−46732.9	+	128398.i	−0.0889092	+	0.244276i
$726$	11801.0	−	50793.8i	0.0223895	−	0.0963690i
$727$	50277.5	−	285138.i	0.0951271	−	0.539493i	−0.899581	−	0.436754i	$-0.856128\pi$
$727$	50277.5	−	285138.i	0.0951271	−	0.539493i	0.994708	−	0.102739i	$-0.0327607\pi$
$728$		−	1.14256e6i		−	2.15583i
$729$	106159.	+	520730.i	0.199756	+	0.979846i
$730$	−202057.			−0.379164
$731$	240370.	+	42383.7i	0.449826	+	0.0793165i
$732$	60323.7	+	14015.1i	0.112581	+	0.0261561i
$733$	−617196.	−	224641.i	−1.14872	−	0.418101i	−0.303666	−	0.952778i	$-0.598211\pi$
$733$	−617196.	−	224641.i	−1.14872	−	0.418101i	−0.845056	+	0.534678i	$0.820433\pi$
$734$	352575.	+	420182.i	0.654424	+	0.779912i
$735$	674028.	+	287213.i	1.24768	+	0.531654i
$736$	−204491.	+	74428.5i	−0.377501	+	0.137399i
$737$	−532105.	−	307211.i	−0.979630	−	0.565590i
$738$	240780.	+	118265.i	0.442087	+	0.217142i
$739$	−255257.	−	442119.i	−0.467401	−	0.809562i	0.531906	−	0.846804i	$-0.321476\pi$
$739$	−255257.	−	442119.i	−0.467401	−	0.809562i	−0.999306	+	0.0372420i	$0.988143\pi$
$740$	38540.4	−	45930.6i	0.0703805	−	0.0838762i
$741$	714331.	+	465303.i	1.30096	+	0.847422i
$742$	−14926.7	−	84653.7i	−0.0271117	−	0.153758i
$743$	−576592.	+	101669.i	−1.04446	+	0.184166i	−0.669451	−	0.742856i	$-0.733471\pi$
$743$	−576592.	+	101669.i	−1.04446	+	0.184166i	−0.375007	+	0.927022i	$0.622360\pi$
$744$	−94689.6	−	186478.i	−0.171063	−	0.336886i
$745$	435818.	+	365695.i	0.785222	+	0.658880i
$746$	−394917.	+	228005.i	−0.709624	+	0.409701i
$747$	−420463.	−	307272.i	−0.753506	−	0.550657i
$748$	−29391.2	+	50907.0i	−0.0525308	+	0.0909859i
$749$	−269163.	−	739519.i	−0.479790	−	1.31821i
$750$	−553547.	+	67187.1i	−0.984084	+	0.119444i
$751$	−748006.	+	627652.i	−1.32625	+	1.11286i	−0.341311	+	0.939950i	$0.610871\pi$
$751$	−748006.	+	627652.i	−1.32625	+	1.11286i	−0.984938	+	0.172905i	$0.944685\pi$
$752$	−33078.0	+	90881.1i	−0.0584930	+	0.160708i
$753$	744033.	+	695755.i	1.31221	+	1.22706i
$754$	80082.2	−	454169.i	0.140862	−	0.798868i
$755$			610254.i			1.07057i
$756$	−123441.	−	100815.i	−0.215981	−	0.176392i
$757$	644723.			1.12507			0.562537	−	0.826772i	$-0.309825\pi$
$757$	644723.			1.12507			0.562537	+	0.826772i	$0.309825\pi$
$758$	−604647.	−	106616.i	−1.05236	−	0.185559i
$759$	189364.	+	622470.i	0.328710	+	1.08053i
$760$	−583363.	−	212327.i	−1.00998	−	0.367601i
$761$	−619111.	−	737828.i	−1.06905	−	1.27405i	−0.959997	−	0.280012i	$-0.909662\pi$
$761$	−619111.	−	737828.i	−1.06905	−	1.27405i	−0.109056	−	0.994036i	$-0.534783\pi$
$762$	240120.	−	180421.i	0.413540	−	0.310726i
$763$	409418.	−	149016.i	0.703263	−	0.255967i
$764$	−19183.4	−	11075.5i	−0.0328654	−	0.0189748i
$765$	−212480.	−	221256.i	−0.363074	−	0.378070i
$766$	−284542.	−	492840.i	−0.484940	−	0.839941i
$767$	−703745.	+	838690.i	−1.19626	+	1.42564i
$768$	15655.3	−	290990.i	0.0265423	−	0.493351i
$769$	−79070.3	−	448430.i	−0.133709	−	0.758302i	−0.975750	−	0.218888i	$-0.929757\pi$
$769$	−79070.3	−	448430.i	−0.133709	−	0.758302i	0.842041	−	0.539414i	$-0.181354\pi$
$770$	659784.	−	116338.i	1.11281	−	0.196218i
$771$	−133598.	−	7187.60i	−0.224746	−	0.0120914i
$772$	−28933.4	−	24278.0i	−0.0485472	−	0.0407360i
$773$	−841371.	+	485766.i	−1.40808	+	0.812957i	−0.995203	−	0.0978280i	$-0.968810\pi$
$773$	−841371.	+	485766.i	−1.40808	+	0.812957i	−0.412880	+	0.910785i	$0.635477\pi$
$774$	91046.7	+	369537.i	0.151979	+	0.616845i
$775$	−38294.3	+	66327.7i	−0.0637574	+	0.110431i
$776$	257636.	+	707849.i	0.427841	+	1.17548i
$777$	479591.	+	638280.i	0.794381	+	1.05723i
$778$	−13058.3	+	10957.2i	−0.0215738	+	0.0181026i
$779$	141392.	−	388470.i	0.232996	−	0.640152i
$780$	−97474.6	+	29653.0i	−0.160215	+	0.0487394i
$781$	112696.	−	639133.i	0.184760	−	1.04783i
$782$		−	436614.i		−	0.713976i
$783$	−289265.	−	335574.i	−0.471816	−	0.547350i
$784$	−834770.			−1.35811
$785$	−853824.	−	150552.i	−1.38557	−	0.244314i
$786$	−506570.	+	541720.i	−0.819964	+	0.876859i
$787$	−1.06229e6	−	386642.i	−1.71512	−	0.624251i	−0.717717	−	0.696335i	$-0.754813\pi$
$787$	−1.06229e6	−	386642.i	−1.71512	−	0.624251i	−0.997399	+	0.0720836i	$0.977035\pi$
$788$	−14724.9	−	17548.5i	−0.0237138	−	0.0282610i
$789$	−99585.9	−	820478.i	−0.159972	−	1.31799i
$790$	−575680.	+	209530.i	−0.922416	+	0.335732i
$791$	719352.	+	415318.i	1.14971	+	0.663786i
$792$	−627604.	−	67726.4i	−1.00054	−	0.107971i
$793$	263584.	+	456540.i	0.419153	+	0.725994i
$794$	−79180.7	+	94363.9i	−0.125597	+	0.149680i
$795$	−47069.9	+	23901.0i	−0.0744747	+	0.0378166i
$796$	9861.06	+	55924.9i	0.0155632	+	0.0882630i
$797$	169413.	−	29872.1i	0.266704	−	0.0470272i	−0.0386966	−	0.999251i	$-0.512321\pi$
$797$	169413.	−	29872.1i	0.266704	−	0.0470272i	0.305401	+	0.952224i	$0.401209\pi$
$798$	655123.	−	1.00574e6i	1.02877	−	1.57936i
$799$	68377.2	+	57375.3i	0.107107	+	0.0898734i
$800$	−66958.1	+	38658.3i	−0.104622	+	0.0604036i
$801$	350999.	+	523508.i	0.547068	+	0.815940i
$802$	−302737.	+	524355.i	−0.470670	+	0.815224i
$803$	108291.	+	297528.i	0.167943	+	0.461421i
$804$	51571.5	−	121027.i	0.0797806	−	0.187228i
$805$	780039.	−	654531.i	1.20372	−	1.01004i
$806$	88411.9	−	242910.i	0.136095	−	0.373917i
$807$	−196822.	+	847161.i	−0.302222	+	1.30083i
$808$	−137342.	+	778907.i	−0.210369	+	1.19306i
$809$		−	1.07946e6i		−	1.64933i	−0.565621	−	0.824666i	$-0.691363\pi$
$809$		−	1.07946e6i		−	1.64933i	0.565621	−	0.824666i	$-0.308637\pi$
$810$	181645.	−	442496.i	0.276856	−	0.674433i
$811$	−113522.			−0.172599			−0.0862995	−	0.996269i	$-0.527504\pi$
$811$	−113522.			−0.172599			−0.0862995	+	0.996269i	$0.527504\pi$
$812$	130848.	+	23072.0i	0.198451	+	0.0349923i
$813$	106321.	+	24701.6i	0.160856	+	0.0373718i
$814$	431461.	+	157039.i	0.651167	+	0.237005i
$815$	33591.2	+	40032.4i	0.0505720	+	0.0602694i
$816$	321535.	+	137010.i	0.482889	+	0.205766i
$817$	551140.	−	200599.i	0.825692	−	0.300527i
$818$	397119.	+	229277.i	0.593491	+	0.342652i
$819$	−90877.7	−	1.35362e6i	−0.135484	−	2.01803i
$820$	24703.2	+	42787.2i	0.0367388	+	0.0636335i
$821$	−336695.	+	401258.i	−0.499517	+	0.595301i	−0.955611	−	0.294630i	$-0.904804\pi$
$821$	−336695.	+	401258.i	−0.499517	+	0.595301i	0.456094	+	0.889932i	$0.349248\pi$
$822$	650420.	+	423673.i	0.962610	+	0.627028i
$823$	−108163.	−	613424.i	−0.159691	−	0.905652i	−0.954371	−	0.298624i	$-0.903472\pi$
$823$	−108163.	−	613424.i	−0.159691	−	0.905652i	0.794680	−	0.607028i	$-0.207639\pi$
$824$	920298.	−	162273.i	1.35542	−	0.238997i
$825$	104661.	+	206116.i	0.153772	+	0.302833i
$826$	1.18083e6	+	990835.i	1.73072	+	1.45225i
$827$	80950.5	−	46736.8i	0.118361	−	0.0683357i	−0.439651	−	0.898169i	$-0.644898\pi$
$827$	80950.5	−	46736.8i	0.118361	−	0.0683357i	0.558012	+	0.829833i	$0.311564\pi$
$828$	−127424.	+	56309.3i	−0.185862	+	0.0821334i
$829$	−92504.3	+	160222.i	−0.134602	+	0.233138i	−0.925446	−	0.378881i	$-0.876309\pi$
$829$	−92504.3	+	160222.i	−0.134602	+	0.233138i	0.790843	+	0.612019i	$0.209642\pi$
$830$	160314.	+	440459.i	0.232710	+	0.639365i
$831$	−330622.	+	40129.4i	−0.478773	+	0.0581113i
$832$	723401.	−	607006.i	1.04504	−	0.876892i
$833$	−263504.	+	723973.i	−0.379750	+	1.04335i
$834$	304823.	+	285044.i	0.438244	+	0.409808i
$835$	−56716.4	+	321654.i	−0.0813458	+	0.461335i
$836$			141252.i			0.202108i
$837$	−127014.	−	213394.i	−0.181301	−	0.304602i
$838$	1.05389e6			1.50074
$839$	−345551.	−	60930.0i	−0.490895	−	0.0865580i	−0.0772790	−	0.997010i	$-0.524623\pi$
$839$	−345551.	−	60930.0i	−0.490895	−	0.0865580i	−0.413616	+	0.910451i	$0.635734\pi$
$840$	287530.	+	945158.i	0.407497	+	1.33951i
$841$	−317558.	−	115582.i	−0.448984	−	0.163417i
$842$	−496058.	−	591178.i	−0.699694	−	0.833862i
$843$	177954.	−	133711.i	0.250411	−	0.188154i
$844$	197878.	−	72021.5i	0.277787	−	0.101106i
$845$	−256285.	−	147966.i	−0.358930	−	0.207229i
$846$	−38735.2	+	133683.i	−0.0541209	+	0.186783i
$847$	63942.5	+	110752.i	0.0891298	+	0.154377i
$848$	38661.8	−	46075.3i	0.0537638	−	0.0640732i
$849$	36819.5	−	684376.i	0.0510813	−	0.949465i
$850$	−26937.2	−	152768.i	−0.0372833	−	0.211444i
$851$	687257.	−	121182.i	0.948987	−	0.167332i
$852$	138758.	+	7465.21i	0.191153	+	0.0102840i
$853$	−875689.	−	734790.i	−1.20352	−	1.00987i	−0.999523	−	0.0308968i	$-0.990164\pi$
$853$	−875689.	−	734790.i	−1.20352	−	1.00987i	−0.203993	−	0.978972i	$-0.565392\pi$
$854$	642785.	−	371112.i	0.881353	−	0.508849i
$855$	−708013.	−	205149.i	−0.968521	−	0.280632i
$856$	333698.	−	577982.i	0.455414	−	0.788800i
$857$	174673.	+	479909.i	0.237828	+	0.653428i	0.999982	+	0.00603135i	$0.00191985\pi$
$857$	174673.	+	479909.i	0.237828	+	0.653428i	−0.762154	+	0.647396i	$0.775858\pi$
$858$	−468684.	−	623764.i	−0.636657	−	0.847317i
$859$	−632238.	+	530511.i	−0.856830	+	0.718965i	−0.961283	−	0.275564i	$-0.911135\pi$
$859$	−632238.	+	530511.i	−0.856830	+	0.718965i	0.104453	+	0.994530i	$0.466691\pi$
$860$	−23973.9	+	65867.8i	−0.0324147	+	0.0890587i
$861$	−629396.	+	191471.i	−0.849020	+	0.258283i
$862$	−921.302	+	5224.96i	−0.00123990	+	0.00703183i
$863$			314595.i			0.422406i	0.977442	+	0.211203i	$0.0677381\pi$
$863$			314595.i			0.422406i	−0.977442	+	0.211203i	$0.932262\pi$
$864$	−3331.16	−	250672.i	−0.00446240	−	0.335798i
$865$	−61114.9			−0.0816798
$866$	307090.	+	54148.3i	0.409478	+	0.0722020i
$867$	−293092.	+	313429.i	−0.389911	+	0.416967i
$868$	69983.1	+	25471.8i	0.0928868	+	0.0338080i
$869$	617066.	+	735391.i	0.817132	+	0.973820i
$870$	48047.2	+	395856.i	0.0634790	+	0.522997i
$871$	1.05231e6	−	383010.i	1.38710	−	0.504864i
$872$	319987.	+	184745.i	0.420823	+	0.242962i
$873$	361530.	+	818115.i	0.474368	+	1.07346i
$874$	−524584.	−	908607.i	−0.686740	−	1.18947i
$875$	879005.	−	1.04756e6i	1.14809	−	1.36824i
$876$	−60447.4	+	30693.8i	−0.0787715	+	0.0399984i
$877$	189340.	+	1.07380e6i	0.246175	+	1.39613i	0.817749	+	0.575575i	$0.195222\pi$
$877$	189340.	+	1.07380e6i	0.246175	+	1.39613i	−0.571575	+	0.820550i	$0.693667\pi$
$878$	−250950.	+	44249.3i	−0.325536	+	0.0574007i
$879$	172054.	−	264136.i	0.222683	−	0.341861i
$880$	359107.	+	301326.i	0.463723	+	0.389109i
$881$	−705767.	+	407475.i	−0.909304	+	0.524987i	−0.880207	−	0.474589i	$-0.842597\pi$
$881$	−705767.	+	407475.i	−0.909304	+	0.524987i	−0.0290971	+	0.999577i	$0.509263\pi$
$882$	−1.19863e6	+	80472.6i	−1.54081	+	0.103445i
$883$	290090.	−	502451.i	0.372059	−	0.644425i	−0.617823	−	0.786317i	$-0.711985\pi$
$883$	290090.	−	502451.i	0.372059	−	0.644425i	0.989882	+	0.141892i	$0.0453187\pi$
$884$	−36643.0	−	100676.i	−0.0468907	−	0.128831i
$885$	371100.	−	870892.i	0.473810	−	1.11193i
$886$	−875164.	+	734350.i	−1.11486	+	0.935483i
$887$	−149005.	+	409387.i	−0.189388	+	0.520340i	−0.997652	−	0.0684799i	$-0.978185\pi$
$887$	−149005.	+	409387.i	−0.189388	+	0.520340i	0.808264	+	0.588820i	$0.200407\pi$
$888$	−153222.	+	659499.i	−0.194310	+	0.836350i
$889$	−127905.	+	725388.i	−0.161840	+	0.917840i
$890$		−	567294.i		−	0.716190i
$891$	−748927.	−	30318.2i	−0.943374	−	0.0381898i
$892$	−32624.3			−0.0410025
$893$	211231.	+	37245.7i	0.264883	+	0.0467060i
$894$	−908636.	−	211104.i	−1.13688	−	0.264133i
$895$	−640007.	−	232943.i	−0.798985	−	0.290807i
$896$	−570137.	−	679463.i	−0.710172	−	0.846350i
$897$	−1.09094e6	−	464865.i	−1.35586	−	0.577752i
$898$	−987219.	+	359318.i	−1.22422	+	0.445581i
$899$	179289.	+	103513.i	0.221837	+	0.128078i
$900$	−41110.8	+	27563.8i	−0.0507541	+	0.0340294i
$901$	−27755.8	−	48074.4i	−0.0341904	−	0.0592195i
$902$	−243197.	+	289830.i	−0.298913	+	0.356230i
$903$	−782073.	−	509429.i	−0.959118	−	0.624753i
$904$	122321.	+	693718.i	0.149680	+	0.848879i
$905$	467605.	−	82451.5i	0.570929	−	0.100670i
$906$	−453029.	−	892180.i	−0.551912	−	1.08692i
$907$	435560.	+	365478.i	0.529460	+	0.444270i	0.867915	−	0.496713i	$-0.165460\pi$
$907$	435560.	+	365478.i	0.529460	+	0.444270i	−0.338455	+	0.940983i	$0.609904\pi$
$908$	−61784.2	+	35671.1i	−0.0749386	+	0.0432658i
$909$	−100760.	+	933716.i	−0.121944	+	1.13002i
$910$	−610538.	+	1.05748e6i	−0.737275	+	1.27700i
$911$	−335275.	−	921160.i	−0.403984	−	1.10994i	−0.960301	−	0.278967i	$-0.910008\pi$
$911$	−335275.	−	921160.i	−0.403984	−	1.10994i	0.556317	−	0.830970i	$-0.312214\pi$
$912$	833740.	−	101196.i	1.00240	−	0.121667i
$913$	562656.	−	472124.i	0.674996	−	0.566389i
$914$	69601.6	−	191229.i	0.0833157	−	0.228908i
$915$	−332935.	−	311333.i	−0.397665	−	0.371863i
$916$	27767.2	−	157475.i	0.0330933	−	0.187682i
$917$		−	1.81888e6i		−	2.16304i
$918$	474894.	+	165735.i	0.563523	+	0.196666i
$919$	930154.			1.10135			0.550673	−	0.834721i	$-0.314371\pi$
$919$	930154.			1.10135			0.550673	+	0.834721i	$0.314371\pi$
$920$	850422.	+	149952.i	1.00475	+	0.177165i
$921$	−49057.7	−	161261.i	−0.0578346	−	0.190112i
$922$	435525.	+	158518.i	0.512332	+	0.186474i
$923$	760325.	+	906120.i	0.892475	+	1.06361i
$924$	179709.	−	135029.i	0.210487	−	0.158156i
$925$	232991.	−	84801.7i	0.272305	−	0.0991109i
$926$	−337314.	−	194748.i	−0.393380	−	0.227118i
$927$	1.07739e6	−	265449.i	1.25376	−	0.308903i
$928$	104496.	+	180993.i	0.121340	+	0.210168i
$929$	−485187.	+	578223.i	−0.562183	+	0.669983i	−0.970007	−	0.243077i	$-0.921843\pi$
$929$	−485187.	+	578223.i	−0.562183	+	0.669983i	0.407824	+	0.913060i	$0.366288\pi$
$930$	−12007.7	+	223192.i	−0.0138834	+	0.258055i
$931$	321481.	+	1.82321e6i	0.370899	+	2.10347i
$932$	−118301.	+	20859.7i	−0.136194	+	0.0240147i
$933$	−436759.	−	23497.7i	−0.501740	−	0.0269936i
$934$	−1.03102e6	−	865130.i	−1.18188	−	0.991716i
$935$	374688.	−	216326.i	0.428594	−	0.247449i
$936$	829828.	−	796914.i	0.947188	−	0.909620i
$937$	−14627.9	+	25336.2i	−0.0166610	+	0.0288577i	−0.874236	−	0.485502i	$-0.838637\pi$
$937$	−14627.9	+	25336.2i	−0.0166610	+	0.0288577i	0.857575	+	0.514359i	$0.171970\pi$
$938$	−539258.	−	1.48160e6i	−0.612902	−	1.68393i
$939$	240662.	+	320293.i	0.272945	+	0.363259i
$940$	−19636.8	+	16477.2i	−0.0222236	+	0.0186478i
$941$	444219.	−	1.22048e6i	0.501670	−	1.37833i	−0.387974	−	0.921670i	$-0.626825\pi$
$941$	444219.	−	1.22048e6i	0.501670	−	1.37833i	0.889643	−	0.456656i	$-0.150953\pi$
$942$	1.36004e6	−	413742.i	1.53267	−	0.466260i
$943$	−99855.7	+	566310.i	−0.112292	+	0.636840i
$944$			1.07858e6i			1.21035i
$945$	415821.	+	1.09688e6i	0.465632	+	1.22828i
$946$	−536778.			−0.599808
$947$	−1.23922e6	−	218507.i	−1.38181	−	0.243650i	−0.567160	−	0.823607i	$-0.691958\pi$
$947$	−1.23922e6	−	218507.i	−1.38181	−	0.243650i	−0.814647	+	0.579958i	$0.803069\pi$
$948$	−140391.	+	150133.i	−0.156215	+	0.167055i
$949$	−542277.	−	197373.i	−0.602127	−	0.219156i
$950$	−239606.	−	285551.i	−0.265492	−	0.316401i
$951$	69534.0	+	572883.i	0.0768840	+	0.633440i
$952$	−976199.	+	355307.i	−1.07712	+	0.392040i
$953$	556515.	+	321304.i	0.612761	+	0.353778i	0.774045	−	0.633130i	$-0.218230\pi$
$953$	556515.	+	321304.i	0.612761	+	0.353778i	−0.161284	+	0.986908i	$0.551564\pi$
$954$	51072.1	−	69885.8i	0.0561160	−	0.0767878i
$955$	81518.7	+	141194.i	0.0893820	+	0.154814i
$956$	48998.9	−	58394.6i	0.0536131	−	0.0638936i
$957$	557147.	−	282907.i	0.608340	−	0.308901i
$958$	−126925.	−	719828.i	−0.138298	−	0.784328i
$959$	−1.87473e6	+	330566.i	−2.03846	+	0.359436i
$960$	−445665.	+	684182.i	−0.483577	+	0.742385i
$961$	−618565.	−	519037.i	−0.669789	−	0.562020i
$962$	−724734.	+	418425.i	−0.783120	+	0.452135i
$963$	349369.	−	711293.i	0.376731	−	0.767001i
$964$	−95470.5	+	165360.i	−0.102734	+	0.177941i
$965$	95079.9	+	261230.i	0.102102	+	0.280523i
$966$	−654505.	+	1.53598e6i	−0.701388	+	1.64601i
$967$	903515.	−	758139.i	0.966234	−	0.810766i	−0.0157221	−	0.999876i	$-0.505005\pi$
$967$	903515.	−	758139.i	0.966234	−	0.810766i	0.981956	+	0.189110i	$0.0605603\pi$
$968$	−37093.0	+	101912.i	−0.0395860	+	0.108762i
$969$	175415.	−	755022.i	0.186818	−	0.804104i
$970$	139794.	−	792814.i	0.148575	−	0.842612i
$971$			423403.i			0.449072i	0.974466	+	0.224536i	$0.0720866\pi$
$971$			423403.i			0.449072i	−0.974466	+	0.224536i	$0.927913\pi$
$972$	−12877.3	−	159970.i	−0.0136298	−	0.169320i
$973$	−1.02347e6			−1.08106
$974$	1.27490e6	+	224800.i	1.34387	+	0.236961i
$975$	−410393.	−	95347.1i	−0.431709	−	0.100299i
$976$	488023.	+	177626.i	0.512319	+	0.186469i
$977$	619524.	+	738320.i	0.649037	+	0.773492i	0.985768	−	0.168109i	$-0.0537660\pi$
$977$	619524.	+	738320.i	0.649037	+	0.773492i	−0.336732	+	0.941601i	$0.609322\pi$
$978$	−78828.3	−	33589.9i	−0.0824147	−	0.0351181i
$979$	−835341.	+	304039.i	−0.871562	+	0.317223i
$980$	−191613.	−	110628.i	−0.199514	−	0.115190i
$981$	393791.	+	193420.i	0.409193	+	0.200985i
$982$	620800.	+	1.07526e6i	0.643767	+	1.11504i
$983$	994517.	−	1.18522e6i	1.02921	−	1.22657i	0.0555777	−	0.998454i	$-0.482300\pi$
$983$	994517.	−	1.18522e6i	1.02921	−	1.22657i	0.973635	−	0.228113i	$-0.0732556\pi$
$984$	−467481.	−	304509.i	−0.482807	−	0.314492i
$985$	29278.4	+	166046.i	0.0301769	+	0.171142i
$986$	−412946.	+	72813.4i	−0.424755	+	0.0748958i
$987$	−154539.	−	304344.i	−0.158637	−	0.312414i
$988$	−197216.	−	165484.i	−0.202035	−	0.169528i
$989$	−706541.	+	407922.i	−0.722345	+	0.417046i
$990$	544684.	+	398051.i	0.555743	+	0.406133i
$991$	668136.	−	1.15725e6i	0.680327	−	1.17836i	−0.294554	−	0.955635i	$-0.595171\pi$
$991$	668136.	−	1.15725e6i	0.680327	−	1.17836i	0.974881	−	0.222726i	$-0.0714955\pi$
$992$	40066.0	+	110081.i	0.0407149	+	0.111863i
$993$	365169.	−	44322.5i	0.370335	−	0.0449496i
$994$	1.27577e6	−	1.07050e6i	1.29122	−	1.08346i
$995$	142954.	−	392764.i	0.144395	−	0.396721i
$996$	114868.	+	107415.i	0.115793	+	0.108280i
$997$	71152.1	−	403524.i	0.0715809	−	0.405956i	−0.927872	−	0.372898i	$-0.878364\pi$
$997$	71152.1	−	403524.i	0.0715809	−	0.405956i	0.999453	−	0.0330581i	$-0.0105246\pi$
$998$			514236.i			0.516299i
$999$	−129070.	+	793513.i	−0.129329	+	0.795102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.5.f.a.2.4	✓	66
3.2	odd	2		81.5.f.a.8.8		66
27.13	even	9		81.5.f.a.71.8		66
27.14	odd	18	inner	27.5.f.a.14.4	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.2.4	✓	66	1.1	even	1	trivial
27.5.f.a.14.4	yes	66	27.14	odd	18	inner
81.5.f.a.8.8		66	3.2	odd	2
81.5.f.a.71.8		66	27.13	even	9

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.58910 - 0.632855i) q^{2} +(8.76651 + 2.03673i) q^{3} +(-2.55397 - 0.929568i) q^{4} +(12.8585 + 15.3241i) q^{5} +(-30.1749 - 12.8580i) q^{6} +(75.5885 - 27.5120i) q^{7} +(59.0773 + 34.1083i) q^{8} +(72.7034 + 35.7101i) q^{9} +(-36.4523 - 63.1373i) q^{10} +(-73.4332 + 87.5142i) q^{11} +(-20.4961 - 13.3508i) q^{12} +(-36.1566 - 205.054i) q^{13} +(-288.705 + 50.9066i) q^{14} +(81.5128 + 160.528i) q^{15} +(-157.137 - 131.853i) q^{16} +(-163.954 + 94.6591i) q^{17} +(-238.340 - 174.178i) q^{18} +(-227.463 + 393.977i) q^{19} +(-18.5953 - 51.0902i) q^{20} +(718.682 - 87.2304i) q^{21} +(318.943 - 267.625i) q^{22} +(216.433 - 594.644i) q^{23} +(448.433 + 419.336i) q^{24} +(39.0415 - 221.415i) q^{25} +758.841i q^{26} +(564.624 + 461.130i) q^{27} -218.625 q^{28} +(-598.503 - 105.532i) q^{29} +(-190.966 - 627.738i) q^{30} +(-320.106 - 116.509i) q^{31} +(-221.047 - 263.433i) q^{32} +(-821.996 + 617.631i) q^{33} +(648.354 - 235.981i) q^{34} +(1393.55 + 804.566i) q^{35} +(-152.487 - 158.785i) q^{36} +(551.400 + 955.053i) q^{37} +(1065.72 - 1270.07i) q^{38} +(100.673 - 1871.25i) q^{39} +(236.964 + 1343.89i) q^{40} +(-894.918 + 157.798i) q^{41} +(-2634.62 - 141.743i) q^{42} +(-987.620 - 828.712i) q^{43} +(268.896 - 155.247i) q^{44} +(387.629 + 1573.29i) q^{45} +(-1153.12 + 1997.26i) q^{46} +(-161.256 - 443.048i) q^{47} +(-1108.99 - 1475.94i) q^{48} +(3117.44 - 2615.84i) q^{49} +(-280.247 + 769.973i) q^{50} +(-1630.10 + 495.899i) q^{51} +(-98.2691 + 557.312i) q^{52} +293.218i q^{53} +(-1734.66 - 2012.37i) q^{54} -2285.32 q^{55} +(5403.95 + 952.863i) q^{56} +(-2796.48 + 2990.53i) q^{57} +(2081.30 + 757.531i) q^{58} +(-3379.85 - 4027.95i) q^{59} +(-58.9589 - 485.756i) q^{60} +(-2379.12 + 865.931i) q^{61} +(1075.16 + 620.743i) q^{62} +(6478.00 + 699.057i) q^{63} +(2267.66 + 3927.70i) q^{64} +(2677.36 - 3190.75i) q^{65} +(3341.09 - 1696.53i) q^{66} +(933.925 + 5296.55i) q^{67} +(506.726 - 89.3495i) q^{68} +(3108.49 - 4772.14i) q^{69} +(-4492.41 - 3769.58i) q^{70} +(-4919.78 + 2840.43i) q^{71} +(3077.12 + 4589.45i) q^{72} +(1385.76 - 2400.21i) q^{73} +(-1374.62 - 3776.73i) q^{74} +(793.221 - 1861.52i) q^{75} +(947.162 - 794.763i) q^{76} +(-3143.01 + 8635.36i) q^{77} +(-1545.56 + 6652.39i) q^{78} +(1459.18 - 8275.44i) q^{79} -4103.41i q^{80} +(4010.58 + 5192.49i) q^{81} +3311.81 q^{82} +(-6331.63 - 1116.44i) q^{83} +(-1916.58 - 445.280i) q^{84} +(-3558.77 - 1295.29i) q^{85} +(3020.21 + 3599.35i) q^{86} +(-5031.84 - 2144.14i) q^{87} +(-7323.20 + 2665.43i) q^{88} +(6738.82 + 3890.66i) q^{89} +(-395.572 - 5892.02i) q^{90} +(-8374.46 - 14505.0i) q^{91} +(-1105.52 + 1317.51i) q^{92} +(-2568.92 - 1673.35i) q^{93} +(298.379 + 1692.19i) q^{94} +(-8962.18 + 1580.27i) q^{95} +(-1401.27 - 2759.60i) q^{96} +(8458.98 + 7097.93i) q^{97} +(-12844.2 + 7415.62i) q^{98} +(-8463.98 + 3740.28i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 3 q^{5} + 90 q^{6} - 6 q^{7} - 9 q^{8} - 108 q^{9} - 3 q^{10} - 492 q^{11} - 339 q^{12} - 6 q^{13} + 1137 q^{14} + 1017 q^{15} - 54 q^{16} - 9 q^{17} + 603 q^{18} - 3 q^{19}+ \cdots - 162405 q^{99}+O(q^{100}) \) 66 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 3 * q^5 + 90 * q^6 - 6 * q^7 - 9 * q^8 - 108 * q^9 - 3 * q^10 - 492 * q^11 - 339 * q^12 - 6 * q^13 + 1137 * q^14 + 1017 * q^15 - 54 * q^16 - 9 * q^17 + 603 * q^18 - 3 * q^19 - 2487 * q^20 - 2784 * q^21 + 1002 * q^22 - 2724 * q^23 - 3312 * q^24 + 435 * q^25 + 1368 * q^27 - 12 * q^28 + 5016 * q^29 + 10773 * q^30 - 1671 * q^31 + 10224 * q^32 + 2925 * q^33 - 342 * q^34 - 2682 * q^35 - 7704 * q^36 - 3 * q^37 - 6564 * q^38 - 1983 * q^39 - 1113 * q^40 + 5754 * q^41 + 8694 * q^42 - 1266 * q^43 - 4545 * q^44 - 7029 * q^45 - 3 * q^46 - 9159 * q^47 - 28383 * q^48 + 5898 * q^49 - 34977 * q^50 - 14814 * q^51 + 2871 * q^52 + 13878 * q^54 - 12 * q^55 + 39243 * q^56 + 15792 * q^57 - 12291 * q^58 + 24762 * q^59 + 50670 * q^60 - 8358 * q^61 + 38304 * q^62 + 21609 * q^63 + 6141 * q^64 + 23727 * q^65 + 11349 * q^66 + 15996 * q^67 - 43533 * q^68 - 26847 * q^69 - 7251 * q^70 - 19773 * q^71 - 77580 * q^72 + 6108 * q^73 - 74847 * q^74 - 49155 * q^75 - 28614 * q^76 - 33909 * q^77 - 9108 * q^78 - 5658 * q^79 - 12600 * q^81 - 12 * q^82 + 18813 * q^83 + 82356 * q^84 + 24219 * q^85 + 96474 * q^86 + 84555 * q^87 + 36042 * q^88 + 110232 * q^89 + 153540 * q^90 - 6042 * q^91 + 73545 * q^92 + 1293 * q^93 + 2631 * q^94 - 65163 * q^95 - 152226 * q^96 - 3696 * q^97 - 259938 * q^98 - 162405 * q^99

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