LMFDB - Embedded newform 36.5.f.a.31.18

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			31.18
Character	$\chi$	$=$	36.31
Dual form			36.5.f.a.7.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.42968 + 2.05847i) q^{2} +(2.72970 + 8.57606i) q^{3} +(7.52540 + 14.1198i) q^{4} +(16.6139 - 28.7760i) q^{5} +(-8.29157 + 35.0321i) q^{6} +(-39.9759 + 23.0801i) q^{7} +(-3.25547 + 63.9171i) q^{8} +(-66.0975 + 46.8201i) q^{9} +O(q^{10})$	\(q+(3.42968 + 2.05847i) q^{2} +(2.72970 + 8.57606i) q^{3} +(7.52540 + 14.1198i) q^{4} +(16.6139 - 28.7760i) q^{5} +(-8.29157 + 35.0321i) q^{6} +(-39.9759 + 23.0801i) q^{7} +(-3.25547 + 63.9171i) q^{8} +(-66.0975 + 46.8201i) q^{9} +(116.215 - 64.4935i) q^{10} +(63.6109 - 36.7258i) q^{11} +(-100.550 + 103.081i) q^{12} +(151.520 - 262.440i) q^{13} +(-184.614 - 3.13190i) q^{14} +(292.136 + 63.9314i) q^{15} +(-142.737 + 212.514i) q^{16} -182.019 q^{17} +(-323.071 + 24.5183i) q^{18} -314.215i q^{19} +(531.337 + 18.0330i) q^{20} +(-307.059 - 279.834i) q^{21} +(293.764 + 4.98356i) q^{22} +(290.919 + 167.962i) q^{23} +(-557.044 + 146.556i) q^{24} +(-239.540 - 414.896i) q^{25} +(1059.89 - 588.185i) q^{26} +(-581.958 - 439.051i) q^{27} +(-626.721 - 390.765i) q^{28} +(357.370 + 618.983i) q^{29} +(870.331 + 820.617i) q^{30} +(-985.186 - 568.798i) q^{31} +(-926.995 + 435.035i) q^{32} +(488.601 + 445.280i) q^{33} +(-624.267 - 374.681i) q^{34} +1533.80i q^{35} +(-1158.50 - 580.942i) q^{36} +1008.45 q^{37} +(646.803 - 1077.66i) q^{38} +(2664.30 + 583.059i) q^{39} +(1785.20 + 1155.59i) q^{40} +(-557.553 + 965.709i) q^{41} +(-477.082 - 1591.81i) q^{42} +(-2182.06 + 1259.82i) q^{43} +(997.257 + 621.796i) q^{44} +(249.164 + 2679.89i) q^{45} +(652.014 + 1174.90i) q^{46} +(-980.476 + 566.078i) q^{47} +(-2212.16 - 644.019i) q^{48} +(-135.117 + 234.029i) q^{49} +(32.5048 - 1916.05i) q^{50} +(-496.857 - 1561.00i) q^{51} +(4845.84 + 164.462i) q^{52} -1057.77 q^{53} +(-1092.16 - 2703.75i) q^{54} -2440.63i q^{55} +(-1345.07 - 2630.28i) q^{56} +(2694.73 - 857.713i) q^{57} +(-48.4939 + 2858.55i) q^{58} +(-878.476 - 507.188i) q^{59} +(1295.74 + 4606.00i) q^{60} +(-430.304 - 745.308i) q^{61} +(-2208.02 - 3978.77i) q^{62} +(1561.69 - 3397.22i) q^{63} +(-4074.80 - 416.161i) q^{64} +(-5034.65 - 8720.27i) q^{65} +(759.148 + 2532.94i) q^{66} +(-559.041 - 322.762i) q^{67} +(-1369.76 - 2570.07i) q^{68} +(-646.331 + 2953.42i) q^{69} +(-3157.28 + 5260.44i) q^{70} +9567.89i q^{71} +(-2777.43 - 4377.18i) q^{72} +1899.10 q^{73} +(3458.66 + 2075.86i) q^{74} +(2904.30 - 3186.85i) q^{75} +(4436.65 - 2364.59i) q^{76} +(-1695.27 + 2936.29i) q^{77} +(7937.48 + 7484.09i) q^{78} +(6768.11 - 3907.57i) q^{79} +(3743.90 + 7638.08i) q^{80} +(2176.75 - 6189.38i) q^{81} +(-3900.11 + 2164.37i) q^{82} +(7052.56 - 4071.80i) q^{83} +(1640.46 - 6441.47i) q^{84} +(-3024.04 + 5237.78i) q^{85} +(-10077.1 - 170.953i) q^{86} +(-4332.92 + 4754.46i) q^{87} +(2140.32 + 4185.39i) q^{88} +7653.39 q^{89} +(-4661.92 + 9704.05i) q^{90} +13988.4i q^{91} +(-182.309 + 5371.70i) q^{92} +(2188.78 - 10001.7i) q^{93} +(-4527.97 - 76.8149i) q^{94} +(-9041.87 - 5220.33i) q^{95} +(-6261.31 - 6762.45i) q^{96} +(-6366.75 - 11027.5i) q^{97} +(-945.149 + 524.510i) q^{98} +(-2485.01 + 5405.75i) 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 $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

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

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 $

$2$	3.42968	+	2.05847i	0.857420	+	0.514618i
$2$	3.42968	+	2.05847i	0.857420	+	0.514618i
$3$	2.72970	+	8.57606i	0.303300	+	0.952895i
$3$	2.72970	+	8.57606i	0.303300	+	0.952895i
$4$	7.52540	+	14.1198i	0.470337	+	0.882487i
$5$	16.6139	−	28.7760i	0.664554	−	1.15104i	−0.314852	−	0.949141i	$-0.601955\pi$
$5$	16.6139	−	28.7760i	0.664554	−	1.15104i	0.979406	−	0.201901i	$-0.0647118\pi$
$6$	−8.29157	+	35.0321i	−0.230321	+	0.973115i
$7$	−39.9759	+	23.0801i	−0.815835	+	0.471023i	−0.848978	−	0.528428i	$-0.822782\pi$
$7$	−39.9759	+	23.0801i	−0.815835	+	0.471023i	0.0331429	+	0.999451i	$0.489448\pi$
$8$	−3.25547	+	63.9171i	−0.0508667	+	0.998705i
$9$	−66.0975	+	46.8201i	−0.816018	+	0.578026i
$10$	116.215	−	64.4935i	1.16215	−	0.644935i
$11$	63.6109	−	36.7258i	0.525710	−	0.303519i	−0.213558	−	0.976930i	$-0.568505\pi$
$11$	63.6109	−	36.7258i	0.525710	−	0.303519i	0.739268	+	0.673412i	$0.235172\pi$
$12$	−100.550	+	103.081i	−0.698264	+	0.715840i
$13$	151.520	−	262.440i	0.896566	−	1.55290i	0.0647110	−	0.997904i	$-0.479387\pi$
$13$	151.520	−	262.440i	0.896566	−	1.55290i	0.831855	−	0.554993i	$-0.187279\pi$
$14$	−184.614	−	3.13190i	−0.941910	−	0.0159791i
$15$	292.136	+	63.9314i	1.29838	+	0.284140i
$16$	−142.737	+	212.514i	−0.557566	+	0.830133i
$17$	−182.019			−0.629823			−0.314912	−	0.949121i	$-0.601975\pi$
$17$	−182.019			−0.629823			−0.314912	+	0.949121i	$0.601975\pi$
$18$	−323.071	+	24.5183i	−0.997133	+	0.0756736i
$19$		−	314.215i		−	0.870402i	−0.900333	−	0.435201i	$-0.856677\pi$
$19$		−	314.215i		−	0.870402i	0.900333	−	0.435201i	$-0.143323\pi$
$20$	531.337	+	18.0330i	1.32834	+	0.0450824i
$21$	−307.059	−	279.834i	−0.696278	−	0.634544i
$22$	293.764	+	4.98356i	0.606950	+	0.0102966i
$23$	290.919	+	167.962i	0.549941	+	0.317509i	0.749098	−	0.662459i	$-0.230487\pi$
$23$	290.919	+	167.962i	0.549941	+	0.317509i	−0.199157	+	0.979968i	$0.563820\pi$
$24$	−557.044	+	146.556i	−0.967089	+	0.254437i
$25$	−239.540	−	414.896i	−0.383265	−	0.663834i
$26$	1059.89	−	588.185i	1.56788	−	0.870096i
$27$	−581.958	−	439.051i	−0.798297	−	0.602265i
$28$	−626.721	−	390.765i	−0.799389	−	0.498424i
$29$	357.370	+	618.983i	0.424935	+	0.736008i	0.996414	−	0.0846079i	$-0.0269638\pi$
$29$	357.370	+	618.983i	0.424935	+	0.736008i	−0.571480	+	0.820616i	$0.693630\pi$
$30$	870.331	+	820.617i	0.967034	+	0.911797i
$31$	−985.186	−	568.798i	−1.02517	−	0.591881i	−0.109571	−	0.993979i	$-0.534948\pi$
$31$	−985.186	−	568.798i	−1.02517	−	0.591881i	−0.915597	+	0.402098i	$0.868281\pi$
$32$	−926.995	+	435.035i	−0.905269	+	0.424839i
$33$	488.601	+	445.280i	0.448669	+	0.408889i
$34$	−624.267	−	374.681i	−0.540023	−	0.324118i
$35$			1533.80i			1.25208i
$36$	−1158.50	−	580.942i	−0.893904	−	0.448258i
$37$	1008.45			0.736632			0.368316	−	0.929701i	$-0.379934\pi$
$37$	1008.45			0.736632			0.368316	+	0.929701i	$0.379934\pi$
$38$	646.803	−	1077.66i	0.447924	−	0.746300i
$39$	2664.30	+	583.059i	1.75168	+	0.383339i
$40$	1785.20	+	1155.59i	1.11575	+	0.722244i
$41$	−557.553	+	965.709i	−0.331679	+	0.574485i	−0.982841	−	0.184454i	$-0.940948\pi$
$41$	−557.553	+	965.709i	−0.331679	+	0.574485i	0.651162	+	0.758939i	$0.274282\pi$
$42$	−477.082	−	1591.81i	−0.270455	−	0.902388i
$43$	−2182.06	+	1259.82i	−1.18013	+	0.681349i	−0.956045	−	0.293220i	$-0.905273\pi$
$43$	−2182.06	+	1259.82i	−1.18013	+	0.681349i	−0.224087	+	0.974569i	$0.571940\pi$
$44$	997.257	+	621.796i	0.515112	+	0.321176i
$45$	249.164	+	2679.89i	0.123044	+	1.32340i
$46$	652.014	+	1174.90i	0.308135	+	0.555248i
$47$	−980.476	+	566.078i	−0.443855	+	0.256260i	−0.705232	−	0.708977i	$-0.749157\pi$
$47$	−980.476	+	566.078i	−0.443855	+	0.256260i	0.261376	+	0.965237i	$0.415824\pi$
$48$	−2212.16	−	644.019i	−0.960139	−	0.279522i
$49$	−135.117	+	234.029i	−0.0562752	+	0.0974714i
$50$	32.5048	−	1916.05i	0.0130019	−	0.766419i
$51$	−496.857	−	1561.00i	−0.191025	−	0.600156i
$52$	4845.84	+	164.462i	1.79210	+	0.0608218i
$53$	−1057.77			−0.376566			−0.188283	−	0.982115i	$-0.560292\pi$
$53$	−1057.77			−0.376566			−0.188283	+	0.982115i	$0.560292\pi$
$54$	−1092.16	−	2703.75i	−0.374539	−	0.927211i
$55$		−	2440.63i		−	0.806818i
$56$	−1345.07	−	2630.28i	−0.428914	−	0.838739i
$57$	2694.73	−	857.713i	0.829402	−	0.263993i
$58$	−48.4939	+	2858.55i	−0.0144156	+	0.849747i
$59$	−878.476	−	507.188i	−0.252363	−	0.145702i	0.368483	−	0.929635i	$-0.379877\pi$
$59$	−878.476	−	507.188i	−0.252363	−	0.145702i	−0.620846	+	0.783933i	$0.713211\pi$
$60$	1295.74	+	4606.00i	0.359928	+	1.27945i
$61$	−430.304	−	745.308i	−0.115642	−	0.200298i	0.802394	−	0.596794i	$-0.203559\pi$
$61$	−430.304	−	745.308i	−0.115642	−	0.200298i	−0.918036	+	0.396497i	$0.870226\pi$
$62$	−2208.02	−	3978.77i	−0.574407	−	1.03506i
$63$	1561.69	−	3397.22i	0.393473	−	0.855937i
$64$	−4074.80	−	416.161i	−0.994825	−	0.101602i
$65$	−5034.65	−	8720.27i	−1.19163	−	2.06397i
$66$	759.148	+	2532.94i	0.174276	+	0.581483i
$67$	−559.041	−	322.762i	−0.124536	−	0.0719008i	0.436438	−	0.899734i	$-0.356240\pi$
$67$	−559.041	−	322.762i	−0.124536	−	0.0719008i	−0.560974	+	0.827834i	$0.689573\pi$
$68$	−1369.76	−	2570.07i	−0.296229	−	0.555811i
$69$	−646.331	+	2953.42i	−0.135755	+	0.620337i
$70$	−3157.28	+	5260.44i	−0.644343	+	1.07356i
$71$			9567.89i			1.89801i	0.315254	+	0.949007i	$0.397910\pi$
$71$			9567.89i			1.89801i	−0.315254	+	0.949007i	$0.602090\pi$
$72$	−2777.43	−	4377.18i	−0.535770	−	0.844364i
$73$	1899.10			0.356372			0.178186	−	0.983997i	$-0.442977\pi$
$73$	1899.10			0.356372			0.178186	+	0.983997i	$0.442977\pi$
$74$	3458.66	+	2075.86i	0.631603	+	0.379084i
$75$	2904.30	−	3186.85i	0.516320	−	0.566552i
$76$	4436.65	−	2364.59i	0.768119	−	0.409383i
$77$	−1695.27	+	2936.29i	−0.285928	+	0.495242i
$78$	7937.48	+	7484.09i	1.30465	+	1.23013i
$79$	6768.11	−	3907.57i	1.08446	−	0.626113i	0.152363	−	0.988325i	$-0.451312\pi$
$79$	6768.11	−	3907.57i	1.08446	−	0.626113i	0.932096	+	0.362212i	$0.117978\pi$
$80$	3743.90	+	7638.08i	0.584985	+	1.19345i
$81$	2176.75	−	6189.38i	0.331772	−	0.943360i
$82$	−3900.11	+	2164.37i	−0.580028	+	0.321887i
$83$	7052.56	−	4071.80i	1.02374	−	0.591058i	0.108556	−	0.994090i	$-0.465377\pi$
$83$	7052.56	−	4071.80i	1.02374	−	0.591058i	0.915186	+	0.403032i	$0.132044\pi$
$84$	1640.46	−	6441.47i	0.232491	−	0.912906i
$85$	−3024.04	+	5237.78i	−0.418552	+	0.724953i
$86$	−10077.1	−	170.953i	−1.36250	−	0.0231142i
$87$	−4332.92	+	4754.46i	−0.572456	+	0.628149i
$88$	2140.32	+	4185.39i	0.276385	+	0.540468i
$89$	7653.39			0.966215			0.483107	−	0.875561i	$-0.339508\pi$
$89$	7653.39			0.966215			0.483107	+	0.875561i	$0.339508\pi$
$90$	−4661.92	+	9704.05i	−0.575545	+	1.19803i
$91$			13988.4i			1.68921i
$92$	−182.309	+	5371.70i	−0.0215394	+	0.634652i
$93$	2188.78	−	10001.7i	0.253067	−	1.15640i
$94$	−4527.97	−	76.8149i	−0.512446	−	0.00869340i
$95$	−9041.87	−	5220.33i	−1.00187	−	0.578430i
$96$	−6261.31	−	6762.45i	−0.679395	−	0.733773i
$97$	−6366.75	−	11027.5i	−0.676666	−	1.17202i	−0.975979	−	0.217865i	$-0.930091\pi$
$97$	−6366.75	−	11027.5i	−0.676666	−	1.17202i	0.299313	−	0.954155i	$-0.403243\pi$
$98$	−945.149	+	524.510i	−0.0984120	+	0.0546137i
$99$	−2485.01	+	5405.75i	−0.253547	+	0.551551i
$100$	4055.61	−	6504.52i	0.405561	−	0.650452i
$101$	6873.20	+	11904.7i	0.673777	+	1.16702i	0.976825	+	0.214040i	$0.0686624\pi$
$101$	6873.20	+	11904.7i	0.673777	+	1.16702i	−0.303048	+	0.952975i	$0.598004\pi$
$102$	1509.22	−	6376.51i	0.145062	−	0.612890i
$103$	−11251.5	−	6496.03i	−1.06056	−	0.612313i	−0.134971	−	0.990850i	$-0.543094\pi$
$103$	−11251.5	−	6496.03i	−1.06056	−	0.612313i	−0.925587	+	0.378536i	$0.876428\pi$
$104$	16281.1	+	10539.1i	1.50528	+	0.974396i
$105$	−13153.9	+	4186.81i	−1.19310	+	0.379756i
$106$	−3627.82	−	2177.40i	−0.322875	−	0.193787i
$107$		−	14891.8i		−	1.30071i	−0.759631	−	0.650354i	$-0.774621\pi$
$107$		−	14891.8i		−	1.30071i	0.759631	−	0.650354i	$-0.225379\pi$
$108$	1819.84	−	11521.2i	0.156022	−	0.987754i
$109$	7539.02			0.634544			0.317272	−	0.948335i	$-0.397233\pi$
$109$	7539.02			0.634544			0.317272	+	0.948335i	$0.397233\pi$
$110$	5023.96	−	8370.56i	0.415203	−	0.691782i
$111$	2752.76	+	8648.52i	0.223421	+	0.701933i
$112$	801.189	−	11789.8i	0.0638703	−	0.939878i
$113$	496.140	−	859.339i	0.0388550	−	0.0672988i	−0.845944	−	0.533272i	$-0.820962\pi$
$113$	496.140	−	859.339i	0.0388550	−	0.0672988i	0.884799	+	0.465973i	$0.154296\pi$
$114$	11007.6	+	2605.34i	0.847001	+	0.200472i
$115$	9666.57	−	5581.00i	0.730932	−	0.422004i
$116$	−6050.56	+	9704.08i	−0.449655	+	0.721171i
$117$	2272.39	+	24440.8i	0.166001	+	1.78543i
$118$	−1968.86	−	3547.81i	−0.141400	−	0.254798i
$119$	7276.38	−	4201.02i	0.513832	−	0.296661i
$120$	−5037.35	+	18464.4i	−0.349816	+	1.28225i
$121$	−4622.94	+	8007.16i	−0.315753	+	0.546900i
$122$	58.3908	−	3441.94i	0.00392306	−	0.231251i
$123$	−9803.93	−	2145.51i	−0.648022	−	0.141814i
$124$	617.383	−	18191.1i	0.0401524	−	1.18308i
$125$	4848.57			0.310308
$126$	12349.2	−	8436.65i	0.777852	−	0.531409i
$127$			7123.52i			0.441659i	0.975312	+	0.220829i	$0.0708764\pi$
$127$			7123.52i			0.441659i	−0.975312	+	0.220829i	$0.929124\pi$
$128$	−13118.6	−	9815.16i	−0.800697	−	0.599070i
$129$	−16760.6	−	15274.6i	−1.00719	−	0.917889i
$130$	683.185	−	40271.4i	0.0404252	−	2.38292i
$131$	6027.16	+	3479.78i	0.351212	+	0.202773i	0.665219	−	0.746648i	$-0.268338\pi$
$131$	6027.16	+	3479.78i	0.351212	+	0.202773i	−0.314007	+	0.949421i	$0.601671\pi$
$132$	−2610.35	+	10249.8i	−0.149813	+	0.588260i
$133$	7252.12	+	12561.0i	0.409979	+	0.710105i
$134$	−1252.93	−	2257.74i	−0.0697780	−	0.125737i
$135$	−22302.7	+	9452.13i	−1.22374	+	0.518635i
$136$	592.557	−	11634.1i	0.0320371	−	0.629008i
$137$	4244.42	+	7351.56i	0.226140	+	0.391686i	0.956661	−	0.291204i	$-0.0940559\pi$
$137$	4244.42	+	7351.56i	0.226140	+	0.391686i	−0.730521	+	0.682891i	$0.760723\pi$
$138$	−8296.25	+	8798.84i	−0.435636	+	0.462027i
$139$	18483.9	+	10671.7i	0.956673	+	0.552335i	0.895147	−	0.445770i	$-0.147070\pi$
$139$	18483.9	+	10671.7i	0.956673	+	0.552335i	0.0615252	+	0.998106i	$0.480404\pi$
$140$	−21656.9	+	11542.4i	−1.10494	+	0.588900i
$141$	−7531.12	−	6863.39i	−0.378810	−	0.345224i
$142$	−19695.2	+	32814.8i	−0.976752	+	1.62740i
$143$		−	22258.7i		−	1.08850i
$144$	−515.388	−	20729.6i	−0.0248548	−	0.999691i
$145$	23749.2			1.12957
$146$	6513.32	+	3909.25i	0.305560	+	0.183395i
$147$	−2375.87	−	519.939i	−0.109948	−	0.0240612i
$148$	7588.98	+	14239.1i	0.346466	+	0.650068i
$149$	6366.78	−	11027.6i	0.286779	−	0.496716i	−0.686260	−	0.727356i	$-0.740749\pi$
$149$	6366.78	−	11027.6i	0.286779	−	0.496716i	0.973039	+	0.230640i	$0.0740821\pi$
$150$	16520.9	−	4951.47i	0.734260	−	0.220065i
$151$	3061.84	−	1767.75i	0.134285	−	0.0775296i	−0.431352	−	0.902184i	$-0.641963\pi$
$151$	3061.84	−	1767.75i	0.134285	−	0.0775296i	0.565638	+	0.824654i	$0.308630\pi$
$152$	20083.7	+	1022.92i	0.869276	+	0.0442745i
$153$	12031.0	−	8522.15i	0.513947	−	0.364054i
$154$	−11858.5	+	6580.88i	−0.500021	+	0.277487i
$155$	−32735.5	+	18899.8i	−1.36256	+	0.786674i
$156$	11817.2	+	42007.1i	0.485587	+	1.72613i
$157$	−14870.6	+	25756.6i	−0.603292	+	1.04493i	0.389027	+	0.921227i	$0.372811\pi$
$157$	−14870.6	+	25756.6i	−0.603292	+	1.04493i	−0.992319	+	0.123706i	$0.960522\pi$
$158$	31256.1	+	530.244i	1.25205	+	0.0212404i
$159$	−2887.40	−	9071.53i	−0.114212	−	0.358828i
$160$	−2882.37	+	33902.9i	−0.112593	+	1.32433i
$161$	−15506.3			−0.598216
$162$	20206.2	−	16746.8i	0.769937	−	0.638120i
$163$		−	5903.96i		−	0.222213i	−0.993809	−	0.111106i	$-0.964561\pi$
$163$		−	5903.96i		−	0.222213i	0.993809	−	0.111106i	$-0.0354394\pi$
$164$	−17831.4	−	605.177i	−0.662976	−	0.0225006i
$165$	20930.9	−	6662.18i	0.768813	−	0.244708i
$166$	32569.7	+	552.529i	1.18195	+	0.0200511i
$167$	17810.7	+	10283.0i	0.638628	+	0.368712i	0.784086	−	0.620652i	$-0.213132\pi$
$167$	17810.7	+	10283.0i	0.638628	+	0.368712i	−0.145458	+	0.989364i	$0.546465\pi$
$168$	18885.8	−	18715.3i	0.669140	−	0.663100i
$169$	−31635.9	−	54795.0i	−1.10766	−	1.91852i
$170$	−21153.3	+	11739.0i	−0.731948	+	0.406195i
$171$	14711.6	+	20768.8i	0.503115	+	0.710264i
$172$	−34209.2	−	21329.7i	−1.15634	−	0.720987i
$173$	−3054.99	−	5291.39i	−0.102074	−	0.176798i	0.810465	−	0.585787i	$-0.199215\pi$
$173$	−3054.99	−	5291.39i	−0.102074	−	0.176798i	−0.912539	+	0.408989i	$0.865881\pi$
$174$	−24647.4	+	7387.09i	−0.814092	+	0.243992i
$175$	19151.7	+	11057.2i	0.625361	+	0.361053i
$176$	−1274.87	+	18760.3i	−0.0411569	+	0.605641i
$177$	1951.70	−	8918.33i	0.0622969	−	0.284667i
$178$	26248.7	+	15754.3i	0.828451	+	0.497231i
$179$		−	11534.8i		−	0.360001i	−0.983667	−	0.180001i	$-0.942390\pi$
$179$		−	11534.8i		−	0.360001i	0.983667	−	0.180001i	$-0.0576099\pi$
$180$	−35964.4	+	23685.3i	−1.11001	+	0.731029i
$181$	−25544.2			−0.779713			−0.389857	−	0.920876i	$-0.627475\pi$
$181$	−25544.2			−0.779713			−0.389857	+	0.920876i	$0.627475\pi$
$182$	−28794.6	+	47975.6i	−0.869298	+	1.44836i
$183$	5217.20	−	5724.78i	0.155789	−	0.170945i
$184$	−11682.7	+	18047.9i	−0.345072	+	0.533079i
$185$	16754.2	−	29019.2i	0.489532	−	0.847894i
$186$	28094.9	−	29797.0i	0.812086	−	0.861283i
$187$	−11578.4	+	6684.78i	−0.331104	+	0.191163i
$188$	−15371.4	−	9584.15i	−0.434908	−	0.271168i
$189$	33397.7	+	4119.80i	0.934959	+	0.115333i
$190$	−20264.8	−	36516.5i	−0.561353	−	1.01154i
$191$	33833.7	−	19533.9i	0.927433	−	0.535454i	0.0414344	−	0.999141i	$-0.486807\pi$
$191$	33833.7	−	19533.9i	0.927433	−	0.535454i	0.885999	+	0.463687i	$0.153474\pi$
$192$	−7553.97	−	36081.7i	−0.204915	−	0.978780i
$193$	−13915.2	+	24101.8i	−0.373572	+	0.647045i	−0.990112	−	0.140278i	$-0.955200\pi$
$193$	−13915.2	+	24101.8i	−0.373572	+	0.647045i	0.616541	+	0.787323i	$0.288534\pi$
$194$	863.947	−	50926.7i	0.0229553	−	1.35314i
$195$	61042.4	−	66981.2i	1.60532	−	1.76150i
$196$	−4321.25	−	146.658i	−0.112486	−	0.00381763i
$197$	−21103.0			−0.543765			−0.271883	−	0.962330i	$-0.587646\pi$
$197$	−21103.0			−0.543765			−0.271883	+	0.962330i	$0.587646\pi$
$198$	−19650.4	+	13424.7i	−0.501234	+	0.342431i
$199$		−	5447.97i		−	0.137572i	−0.997631	−	0.0687858i	$-0.978087\pi$
$199$		−	5447.97i		−	0.137572i	0.997631	−	0.0687858i	$-0.0219125\pi$
$200$	27298.8	−	13960.1i	0.682470	−	0.349001i
$201$	1242.02	−	5675.41i	0.0307422	−	0.140477i
$202$	−932.670	+	54977.7i	−0.0228573	+	1.34736i
$203$	−28572.4	−	16496.3i	−0.693353	−	0.400308i
$204$	18302.0	−	18762.7i	0.439783	−	0.450853i
$205$	18526.2	+	32088.3i	0.440837	+	0.763553i
$206$	−25217.0	−	45440.1i	−0.594236	−	1.07079i
$207$	−27093.0	+	2518.99i	−0.632291	+	0.0587875i
$208$	34144.7	+	69659.8i	0.789217	+	1.61011i
$209$	−11539.8	−	19987.5i	−0.264183	−	0.457579i
$210$	−53732.2	−	12717.6i	−1.21842	−	0.288381i
$211$	−59935.1	−	34603.5i	−1.34622	−	0.777241i	−0.358509	−	0.933526i	$-0.616715\pi$
$211$	−59935.1	−	34603.5i	−1.34622	−	0.777241i	−0.987712	+	0.156286i	$0.950048\pi$
$212$	−7960.17	−	14935.5i	−0.177113	−	0.332314i
$213$	−82054.8	+	26117.5i	−1.80861	+	0.575668i
$214$	30654.4	−	51074.1i	0.669367	−	1.11525i
$215$			83721.5i			1.81117i
$216$	29957.4	−	35767.8i	0.642092	−	0.766628i
$217$	52511.7			1.11516
$218$	25856.4	+	15518.9i	0.544071	+	0.326548i
$219$	5183.98	+	16286.8i	0.108088	+	0.339585i
$220$	34461.1	−	18366.7i	0.712007	−	0.379477i
$221$	−27579.4	+	47769.0i	−0.564678	+	0.978051i
$222$	−8361.63	+	35328.1i	−0.169662	+	0.716828i
$223$	21934.5	−	12663.9i	0.441080	−	0.254658i	−0.262976	−	0.964802i	$-0.584704\pi$
$223$	21934.5	−	12663.9i	0.441080	−	0.254658i	0.704056	+	0.710145i	$0.251371\pi$
$224$	27016.8	−	38786.1i	0.538441	−	0.773001i
$225$	35258.5	+	16208.3i	0.696464	+	0.320163i
$226$	3470.52	−	1925.97i	0.0679482	−	0.0377079i
$227$	−84184.1	+	48603.7i	−1.63372	+	0.943230i	−0.650792	+	0.759256i	$0.725563\pi$
$227$	−84184.1	+	48603.7i	−1.63372	+	0.943230i	−0.982931	+	0.183975i	$0.941104\pi$
$228$	32389.6	+	31594.4i	0.623069	+	0.607771i
$229$	42946.4	−	74385.3i	0.818947	−	1.41846i	−0.0875119	−	0.996163i	$-0.527892\pi$
$229$	42946.4	−	74385.3i	0.818947	−	1.41846i	0.906459	−	0.422294i	$-0.138775\pi$
$230$	44641.6	+	757.323i	0.843886	+	0.0143161i
$231$	−29809.4	−	6523.53i	−0.558636	−	0.122253i
$232$	−40727.0	+	20827.0i	−0.756671	+	0.386946i
$233$	−12774.0			−0.235297			−0.117649	−	0.993055i	$-0.537536\pi$
$233$	−12774.0			−0.235297			−0.117649	+	0.993055i	$0.537536\pi$
$234$	−42517.0	+	88501.6i	−0.776482	+	1.61629i
$235$			37619.0i			0.681194i
$236$	550.511	−	16220.7i	0.00988421	−	0.291236i
$237$	51986.4	+	47377.2i	0.925536	+	0.843476i
$238$	33603.3	+	570.064i	0.593237	+	0.0100640i
$239$	91748.4	+	52971.0i	1.60621	+	0.927347i	0.990207	+	0.139605i	$0.0445832\pi$
$239$	91748.4	+	52971.0i	1.60621	+	0.927347i	0.616005	+	0.787742i	$0.288750\pi$
$240$	−55284.8	+	52957.6i	−0.959806	+	0.919402i
$241$	5089.73	+	8815.67i	0.0876316	+	0.151782i	0.906510	−	0.422185i	$-0.138737\pi$
$241$	5089.73	+	8815.67i	0.0876316	+	0.151782i	−0.818878	+	0.573968i	$0.805404\pi$
$242$	−32337.7	+	17945.8i	−0.552177	+	0.306431i
$243$	59022.4	+	1772.80i	0.999549	+	0.0300225i
$244$	7285.38	−	11684.5i	0.122369	−	0.196260i
$245$	4489.62	+	7776.25i	0.0747958	+	0.129550i
$246$	−29207.9	−	27539.5i	−0.482647	−	0.455078i
$247$	−82462.6	−	47609.8i	−1.35165	−	0.780373i
$248$	39563.2	−	61118.6i	0.643262	−	0.993734i
$249$	54171.3	+	49368.4i	0.873717	+	0.796251i
$250$	16629.0	+	9980.63i	0.266064	+	0.159690i
$251$		−	21848.1i		−	0.346790i	−0.984852	−	0.173395i	$-0.944526\pi$
$251$		−	21848.1i		−	0.346790i	0.984852	−	0.173395i	$-0.0554738\pi$
$252$	59720.3	−	3514.60i	0.940418	−	0.0553445i
$253$	24674.2			0.385479
$254$	−14663.5	+	24431.4i	−0.227285	+	0.378687i
$255$	−53174.2	−	11636.7i	−0.817751	−	0.178958i
$256$	−24788.4	−	60667.1i	−0.378241	−	0.925707i
$257$	−27780.7	+	48117.6i	−0.420608	+	0.728514i	−0.995999	−	0.0893643i	$-0.971516\pi$
$257$	−27780.7	+	48117.6i	−0.420608	+	0.728514i	0.575391	+	0.817878i	$0.304850\pi$
$258$	−26041.3	−	86888.2i	−0.391222	−	1.30533i
$259$	−40313.7	+	23275.1i	−0.600971	+	0.346971i
$260$	85240.6	−	136712.i	1.26096	−	2.02236i
$261$	−52602.1	−	24181.1i	−0.772186	−	0.354973i
$262$	13508.2	+	24341.3i	0.196786	+	0.354601i
$263$	21792.0	−	12581.6i	0.315055	−	0.181897i	−0.334131	−	0.942527i	$-0.608443\pi$
$263$	21792.0	−	12581.6i	0.315055	−	0.181897i	0.649186	+	0.760629i	$0.275110\pi$
$264$	−30051.7	+	29780.4i	−0.431182	+	0.427290i
$265$	−17573.7	+	30438.5i	−0.250248	+	0.433443i
$266$	−984.089	+	58008.6i	−0.0139082	+	0.819841i
$267$	20891.4	+	65635.9i	0.293053	+	0.920701i
$268$	350.332	−	10322.5i	0.00487765	−	0.143719i
$269$	54154.0			0.748386			0.374193	−	0.927351i	$-0.377920\pi$
$269$	54154.0			0.748386			0.374193	+	0.927351i	$0.377920\pi$
$270$	−95948.1	−	13491.7i	−1.31616	−	0.185072i
$271$		−	94942.5i		−	1.29277i	−0.763011	−	0.646386i	$-0.776280\pi$
$271$		−	94942.5i		−	1.29277i	0.763011	−	0.646386i	$-0.223720\pi$
$272$	25980.8	−	38681.6i	0.351168	−	0.522837i
$273$	−119965.	+	38184.0i	−1.60964	+	0.512338i
$274$	−575.954	+	33950.5i	−0.00767162	+	0.452215i
$275$	−30474.7	−	17594.6i	−0.402972	−	0.232656i
$276$	−46565.6	+	13099.6i	−0.611290	+	0.171965i
$277$	−54019.7	−	93564.9i	−0.704033	−	1.21942i	−0.967039	−	0.254627i	$-0.918047\pi$
$277$	−54019.7	−	93564.9i	−0.704033	−	1.21942i	0.263006	−	0.964794i	$-0.415286\pi$
$278$	41426.4	+	74648.9i	0.536029	+	0.965904i
$279$	91749.5	−	8530.45i	1.17868	−	0.109588i
$280$	−98036.0	−	4993.24i	−1.25046	−	0.0636893i
$281$	34463.0	+	59691.7i	0.436456	+	0.755964i	0.997413	−	0.0718805i	$-0.0229000\pi$
$281$	34463.0	+	59691.7i	0.436456	+	0.755964i	−0.560957	+	0.827845i	$0.689567\pi$
$282$	−11701.2	−	39041.8i	−0.147141	−	0.490944i
$283$	39154.2	+	22605.7i	0.488884	+	0.282257i	0.724111	−	0.689683i	$-0.242250\pi$
$283$	39154.2	+	22605.7i	0.488884	+	0.282257i	−0.235228	+	0.971940i	$0.575584\pi$
$284$	−135097.	+	72002.2i	−1.67497	+	0.892707i
$285$	20088.2	−	91793.5i	0.247316	−	1.13011i
$286$	45818.9	−	76340.2i	0.560160	−	0.933299i
$287$		−	51473.5i		−	0.624914i
$288$	40903.6	−	72156.8i	0.493148	−	0.869946i
$289$	−50390.1			−0.603323
$290$	81452.0	+	48887.0i	0.968514	+	0.581296i
$291$	77193.4	−	84703.5i	0.911579	−	1.00027i
$292$	14291.5	+	26814.9i	0.167615	+	0.314493i
$293$	35853.6	−	62100.3i	0.417636	−	0.723366i	−0.578065	−	0.815990i	$-0.696192\pi$
$293$	35853.6	−	62100.3i	0.417636	−	0.723366i	0.995701	+	0.0926242i	$0.0295255\pi$
$294$	−7078.20	−	6673.89i	−0.0818895	−	0.0772119i
$295$	−29189.7	+	16852.7i	−0.335418	+	0.193654i
$296$	−3282.98	+	64457.2i	−0.0374701	+	0.735679i
$297$	−53143.3	−	6555.55i	−0.602471	−	0.0743184i
$298$	44536.0	−	24715.3i	0.501509	−	0.278313i
$299$	88159.9	−	50899.1i	0.986117	−	0.569335i
$300$	66853.7	+	17025.7i	0.742819	+	0.189175i
$301$	58153.4	−	100725.i	0.641862	−	1.11174i
$302$	14140.0	+	239.878i	0.155037	+	0.00263013i
$303$	−83333.8	+	91441.2i	−0.907687	+	0.995994i
$304$	66775.2	+	44850.1i	0.722550	+	0.485306i
$305$	−28596.0			−0.307401
$306$	58805.0	−	4462.79i	0.628017	−	0.0476610i
$307$			95866.9i			1.01717i	0.861013	+	0.508583i	$0.169830\pi$
$307$			95866.9i			1.01717i	−0.861013	+	0.508583i	$0.830170\pi$
$308$	−54217.4	−	1840.08i	−0.571528	−	0.0193970i
$309$	24997.2	−	114225.i	0.261803	−	1.19632i
$310$	−151177.	−	2564.65i	−1.57312	−	0.0266873i
$311$	−20844.0	−	12034.3i	−0.215506	−	0.124423i	0.388362	−	0.921507i	$-0.373041\pi$
$311$	−20844.0	−	12034.3i	−0.215506	−	0.124423i	−0.603868	+	0.797085i	$0.706374\pi$
$312$	−45941.0	+	168396.i	−0.471945	+	1.72991i
$313$	49654.5	+	86004.2i	0.506839	+	0.877871i	0.999969	+	0.00791525i	$0.00251953\pi$
$313$	49654.5	+	86004.2i	0.506839	+	0.877871i	−0.493130	+	0.869956i	$0.664147\pi$
$314$	−104020.	+	57726.1i	−1.05502	+	0.585481i
$315$	−71812.6	−	101380.i	−0.723735	−	1.02172i
$316$	106107.	+	66158.2i	1.06260	+	0.662536i
$317$	−29720.5	−	51477.4i	−0.295759	−	0.512269i	0.679402	−	0.733766i	$-0.262239\pi$
$317$	−29720.5	−	51477.4i	−0.295759	−	0.512269i	−0.975161	+	0.221497i	$0.928906\pi$
$318$	8770.60	−	37056.1i	0.0867311	−	0.366442i
$319$	45465.2	+	26249.4i	0.446785	+	0.257951i
$320$	−79673.7	+	110343.i	−0.778063	+	1.07757i
$321$	127713.	−	40650.2i	1.23944	−	0.394505i
$322$	−53181.8	−	31919.4i	−0.512922	−	0.307852i
$323$			57193.1i			0.548200i
$324$	103774.	−	15842.3i	0.988547	−	0.150913i
$325$	−145180.			−1.37449
$326$	12153.1	−	20248.7i	0.114354	−	0.190529i
$327$	20579.3	+	64655.1i	0.192457	+	0.604654i
$328$	−59910.3	−	38781.0i	−0.556870	−	0.360472i
$329$	26130.3	−	45259.0i	0.241408	−	0.418132i
$330$	85500.3	+	20236.6i	0.785127	+	0.185827i
$331$	79852.0	−	46102.6i	0.728836	−	0.420794i	−0.0891599	−	0.996017i	$-0.528418\pi$
$331$	79852.0	−	46102.6i	0.728836	−	0.420794i	0.817996	+	0.575223i	$0.195085\pi$
$332$	110566.	+	68938.8i	1.00310	+	0.625442i
$333$	−66656.0	+	47215.7i	−0.601105	+	0.425793i
$334$	39917.7	+	71930.3i	0.357827	+	0.644791i
$335$	−18575.7	+	10724.7i	−0.165522	+	0.0955639i
$336$	103297.	−	25311.6i	0.914977	−	0.224203i
$337$	−22954.2	+	39757.8i	−0.202117	+	0.350076i	−0.949210	−	0.314643i	$-0.898115\pi$
$337$	−22954.2	+	39757.8i	−0.202117	+	0.350076i	0.747094	+	0.664719i	$0.231449\pi$
$338$	4292.89	−	253051.i	0.0375765	−	2.21500i
$339$	8724.05	+	1909.18i	0.0759135	+	0.0166130i
$340$	−96713.5	−	3282.34i	−0.836622	−	0.0283940i
$341$	−83558.1			−0.718588
$342$	7704.01	+	101514.i	0.0658665	+	0.867907i
$343$		−	123305.i		−	1.04807i
$344$	−73420.1	−	143573.i	−0.620438	−	1.21326i
$345$	74249.8	+	67666.6i	0.623817	+	0.568508i
$346$	414.552	−	24436.4i	0.00346279	−	0.204120i
$347$	−131615.	−	75987.9i	−1.09306	−	0.631081i	−0.158674	−	0.987331i	$-0.550722\pi$
$347$	−131615.	−	75987.9i	−1.09306	−	0.631081i	−0.934391	+	0.356250i	$0.884055\pi$
$348$	−99739.0	−	25400.7i	−0.823581	−	0.209743i
$349$	93645.6	+	162199.i	0.768841	+	1.33167i	0.938192	+	0.346116i	$0.112500\pi$
$349$	93645.6	+	162199.i	0.768841	+	1.33167i	−0.169350	+	0.985556i	$0.554167\pi$
$350$	42923.2	+	77346.0i	0.350393	+	0.631396i
$351$	−203402.	+	86204.1i	−1.65098	+	0.699703i
$352$	−42990.0	+	61717.6i	−0.346962	+	0.498108i
$353$	−22707.8	−	39331.1i	−0.182232	−	0.315636i	0.760408	−	0.649446i	$-0.224999\pi$
$353$	−22707.8	−	39331.1i	−0.182232	−	0.315636i	−0.942640	+	0.333810i	$0.891666\pi$
$354$	25051.8	−	26569.5i	0.199909	−	0.212020i
$355$	275326.	+	158960.i	2.18469	+	1.26133i
$356$	57594.8	+	108064.i	0.454447	+	0.852671i
$357$	55890.5	+	50935.1i	0.438532	+	0.399651i
$358$	23744.0	−	39560.6i	0.185263	−	0.308672i
$359$			71504.2i			0.554808i	0.960753	+	0.277404i	$0.0894740\pi$
$359$			71504.2i			0.554808i	−0.960753	+	0.277404i	$0.910526\pi$
$360$	−172102.	+	7201.54i	−1.32795	+	0.0555674i
$361$	31589.8			0.242400
$362$	−87608.4	−	52582.0i	−0.668542	−	0.401254i
$363$	−81289.1	−	17789.4i	−0.616906	−	0.135005i
$364$	−197513.	+	105268.i	−1.49071	+	0.794499i
$365$	31551.4	−	54648.7i	0.236828	−	0.410199i
$366$	29677.6	−	8894.69i	0.221548	−	0.0664001i
$367$	57406.0	−	33143.4i	0.426211	−	0.246073i	−0.271520	−	0.962433i	$-0.587526\pi$
$367$	57406.0	−	33143.4i	0.426211	−	0.246073i	0.697731	+	0.716360i	$0.254193\pi$
$368$	−77219.2	+	37850.0i	−0.570203	+	0.279492i
$369$	−8361.81	−	89935.6i	−0.0614112	−	0.660509i
$370$	117197.	−	65038.4i	0.856076	−	0.475080i
$371$	42285.5	−	24413.5i	0.307216	−	0.177371i
$372$	157693.	−	44361.4i	1.13953	−	0.320567i
$373$	−71784.3	+	124334.i	−0.515955	+	0.893660i	0.483873	+	0.875138i	$0.339229\pi$
$373$	−71784.3	+	124334.i	−0.515955	+	0.893660i	−0.999828	+	0.0185223i	$0.994104\pi$
$374$	−53470.6	−	907.103i	−0.382271	−	0.00648505i
$375$	13235.1	+	41581.6i	0.0941165	+	0.295691i
$376$	−32990.2	−	64512.1i	−0.233351	−	0.456316i
$377$	216594.			1.52393
$378$	106063.	+	82877.7i	0.742300	+	0.580035i
$379$			183178.i			1.27525i	0.770348	+	0.637624i	$0.220083\pi$
$379$			183178.i			1.27525i	−0.770348	+	0.637624i	$0.779917\pi$
$380$	5666.23	−	166954.i	0.0392398	−	1.15619i
$381$	−61091.7	+	19445.1i	−0.420855	+	0.133955i
$382$	156249.	+	2650.69i	1.07075	+	0.0181648i
$383$	−15175.9	−	8761.79i	−0.103456	−	0.0597303i	0.447379	−	0.894344i	$-0.352357\pi$
$383$	−15175.9	−	8761.79i	−0.103456	−	0.0597303i	−0.550835	+	0.834614i	$0.685691\pi$
$384$	48365.5	−	139298.i	0.328000	−	0.944678i
$385$	56329.9	+	97566.3i	0.380030	+	0.658231i
$386$	−97337.4	+	54017.4i	−0.653288	+	0.362543i
$387$	85244.2	−	185435.i	0.569171	−	1.23814i
$388$	107794.	−	172884.i	0.716031	−	1.14839i
$389$	−38430.8	−	66564.0i	−0.253968	−	0.439886i	0.710646	−	0.703549i	$-0.248403\pi$
$389$	−38430.8	−	66564.0i	−0.253968	−	0.439886i	−0.964615	+	0.263663i	$0.915069\pi$
$390$	347235.	−	104070.i	2.28294	−	0.684220i
$391$	−52952.8	−	30572.3i	−0.346366	−	0.199974i
$392$	−14518.6	−	9398.15i	−0.0944827	−	0.0611604i
$393$	−13390.5	+	61188.0i	−0.0866983	+	0.396169i
$394$	−72376.5	−	43439.9i	−0.466235	−	0.279831i
$395$		−	259679.i		−	1.66434i
$396$	−95028.7	+	5592.53i	−0.605989	+	0.0356630i
$397$	−73295.7			−0.465047			−0.232524	−	0.972591i	$-0.574698\pi$
$397$	−73295.7			−0.465047			−0.232524	+	0.972591i	$0.574698\pi$
$398$	11214.5	−	18684.8i	0.0707968	−	0.117957i
$399$	−87928.1	+	96482.5i	−0.552309	+	0.606042i
$400$	122362.	+	8315.25i	0.764765	+	0.0519703i
$401$	−142274.	+	246426.i	−0.884784	+	1.53249i	−0.0388226	+	0.999246i	$0.512361\pi$
$401$	−142274.	+	246426.i	−0.884784	+	1.53249i	−0.845961	+	0.533244i	$0.820973\pi$
$402$	15942.4	−	16908.2i	0.0986509	−	0.104627i
$403$	−298550.	+	172368.i	−1.83826	+	1.06132i
$404$	−116369.	+	186636.i	−0.712973	+	1.14349i
$405$	−141942.	−	165468.i	−0.865366	−	1.00880i
$406$	−64037.0	−	115392.i	−0.388489	−	0.700044i
$407$	64148.4	−	37036.1i	0.387255	−	0.223582i
$408$	101392.	−	26675.9i	0.609095	−	0.160250i
$409$	56577.0	−	97994.2i	0.338215	−	0.585806i	−0.645882	−	0.763437i	$-0.723510\pi$
$409$	56577.0	−	97994.2i	0.338215	−	0.585806i	0.984097	+	0.177632i	$0.0568435\pi$
$410$	−2513.94	+	148188.i	−0.0149550	+	0.881548i
$411$	−51461.4	+	56468.0i	−0.304648	+	0.334286i
$412$	7050.91	−	207753.i	0.0415385	−	1.22392i
$413$	46823.9			0.274516
$414$	−98105.6	−	47130.9i	−0.572392	−	0.274982i
$415$		−	270593.i		−	1.57116i
$416$	−26287.4	+	309197.i	−0.151901	+	1.78669i
$417$	−41065.4	+	187649.i	−0.236159	+	1.07913i
$418$	1565.91	−	92305.1i	0.00896220	−	0.528291i
$419$	−237314.	−	137013.i	−1.35175	−	0.780431i	−0.363252	−	0.931691i	$-0.618334\pi$
$419$	−237314.	−	137013.i	−1.35175	−	0.780431i	−0.988494	+	0.151260i	$0.951667\pi$
$420$	−158106.	−	154223.i	−0.896290	−	0.874283i
$421$	−6241.89	−	10811.3i	−0.0352170	−	0.0609976i	0.847880	−	0.530189i	$-0.177879\pi$
$421$	−6241.89	−	10811.3i	−0.0352170	−	0.0609976i	−0.883097	+	0.469191i	$0.844546\pi$
$422$	−134328.	−	242054.i	−0.754294	−	1.35921i
$423$	38303.1	−	83322.3i	0.214069	−	0.465673i
$424$	3443.55	−	67609.9i	0.0191547	−	0.376078i
$425$	43600.9	+	75518.9i	0.241389	+	0.418098i
$426$	−335184.	−	79332.8i	−1.84699	−	0.437153i
$427$	34403.6	+	19862.9i	0.188690	+	0.108940i
$428$	210269.	−	112067.i	1.14786	−	0.611772i
$429$	190892.	−	60759.5i	1.03722	−	0.330141i
$430$	−172338.	+	287138.i	−0.932062	+	1.55294i
$431$			119855.i			0.645211i	0.946533	+	0.322606i	$0.104559\pi$
$431$			119855.i			0.645211i	−0.946533	+	0.322606i	$0.895441\pi$
$432$	176371.	−	61005.6i	0.945062	−	0.326890i
$433$	−282465.			−1.50657			−0.753284	−	0.657696i	$-0.771531\pi$
$433$	−282465.			−1.50657			−0.753284	+	0.657696i	$0.771531\pi$
$434$	180098.	+	108094.i	0.956158	+	0.573880i
$435$	64828.1	+	203674.i	0.342598	+	1.07636i
$436$	56734.1	+	106449.i	0.298450	+	0.559977i
$437$	52776.3	−	91411.2i	0.276360	−	0.478670i
$438$	−15746.5	+	66529.7i	−0.0820800	+	0.346790i
$439$	148459.	−	85712.8i	0.770331	−	0.444751i	−0.0626618	−	0.998035i	$-0.519959\pi$
$439$	148459.	−	85712.8i	0.770331	−	0.444751i	0.832993	+	0.553284i	$0.186626\pi$
$440$	155998.	+	7945.39i	0.805774	+	0.0410402i
$441$	−2026.39	−	21794.9i	−0.0104195	−	0.112067i
$442$	−192920.	+	107061.i	−0.987488	+	0.548007i
$443$	71888.2	−	41504.7i	0.366311	−	0.211490i	−0.305535	−	0.952181i	$-0.598835\pi$
$443$	71888.2	−	41504.7i	0.366311	−	0.211490i	0.671846	+	0.740691i	$0.265502\pi$
$444$	−101400.	+	103952.i	−0.514364	+	0.527311i
$445$	127152.	−	220234.i	0.642102	−	1.11215i
$446$	101296.	+	1718.45i	0.509242	+	0.00863905i
$447$	111953.	+	24499.9i	0.560298	+	0.122616i
$448$	172499.	−	77410.5i	0.859470	−	0.385695i
$449$	252767.			1.25380			0.626898	−	0.779101i	$-0.284324\pi$
$449$	252767.			1.25380			0.626898	+	0.779101i	$0.284324\pi$
$450$	87561.1	+	128168.i	0.432400	+	0.632927i
$451$			81906.2i			0.402683i
$452$	15867.3	+	538.519i	0.0776653	+	0.00263587i
$453$	23518.2	+	21433.1i	0.114606	+	0.104445i
$454$	−388774.	−	6595.37i	−1.88619	−	0.0319983i
$455$	402530.	+	232401.i	1.94435	+	1.12257i
$456$	46050.0	+	175032.i	0.221462	+	0.841757i
$457$	9489.80	+	16436.8i	0.0454386	+	0.0787019i	0.887850	−	0.460133i	$-0.152198\pi$
$457$	9489.80	+	16436.8i	0.0454386	+	0.0787019i	−0.842412	+	0.538835i	$0.818865\pi$
$458$	300412.	−	166714.i	1.43214	−	0.794769i
$459$	105927.	+	79915.6i	0.502786	+	0.379320i
$460$	151547.	+	94490.7i	0.716197	+	0.446554i
$461$	97075.9	+	168140.i	0.456783	+	0.791171i	0.998789	−	0.0492038i	$-0.0156684\pi$
$461$	97075.9	+	168140.i	0.456783	+	0.791171i	−0.542006	+	0.840375i	$0.682335\pi$
$462$	−88808.1	−	83735.4i	−0.416072	−	0.392306i
$463$	86227.9	+	49783.7i	0.402240	+	0.232234i	0.687450	−	0.726232i	$-0.258730\pi$
$463$	86227.9	+	49783.7i	0.402240	+	0.232234i	−0.285210	+	0.958465i	$0.592063\pi$
$464$	−182552.	−	12405.5i	−0.847914	−	0.0576208i
$465$	−251444.	−	229150.i	−1.16288	−	1.05978i
$466$	−43810.9	−	26295.0i	−0.201748	−	0.121088i
$467$			126990.i			0.582287i	0.956679	+	0.291144i	$0.0940358\pi$
$467$			126990.i			0.582287i	−0.956679	+	0.291144i	$0.905964\pi$
$468$	−327998.	+	216012.i	−1.49754	+	0.986249i
$469$	29797.6			0.135468
$470$	−77437.5	+	129021.i	−0.350555	+	0.584069i
$471$	−261482.	−	57223.0i	−1.17869	−	0.257946i
$472$	35277.9	−	54498.5i	0.158350	−	0.244625i
$473$	−92535.3	+	160276.i	−0.413605	+	0.716384i
$474$	80772.2	+	269501.i	0.359505	+	1.19951i
$475$	−130367.	+	75267.2i	−0.577802	+	0.333594i
$476$	114075.	+	71126.6i	0.503474	+	0.313919i
$477$	69916.2	−	49525.1i	0.307285	−	0.217665i
$478$	205628.	+	370535.i	0.899969	+	1.62171i
$479$	−48437.8	+	27965.6i	−0.211112	+	0.121886i	−0.601828	−	0.798626i	$-0.705561\pi$
$479$	−48437.8	+	27965.6i	−0.211112	+	0.121886i	0.390716	+	0.920511i	$0.372227\pi$
$480$	−298621.	+	67825.3i	−1.29610	+	0.294381i
$481$	152800.	−	264657.i	0.660439	−	1.14391i
$482$	−690.660	+	40712.0i	−0.00297283	+	0.175238i
$483$	−42327.7	−	132983.i	−0.181439	−	0.570037i
$484$	−147849.	−	5017.82i	−0.631142	−	0.0214202i
$485$	−423105.			−1.79872
$486$	198779.	+	127576.i	0.841583	+	0.540128i
$487$		−	274913.i		−	1.15914i	−0.814921	−	0.579572i	$-0.803220\pi$
$487$		−	274913.i		−	1.15914i	0.814921	−	0.579572i	$-0.196780\pi$
$488$	49038.8	−	25077.5i	0.205921	−	0.105304i
$489$	50632.7	−	16116.1i	0.211745	−	0.0673971i
$490$	−609.226	+	35911.8i	−0.00253739	+	0.149570i
$491$	28037.6	+	16187.5i	0.116299	+	0.0671455i	0.557021	−	0.830498i	$-0.311944\pi$
$491$	28037.6	+	16187.5i	0.116299	+	0.0671455i	−0.440722	+	0.897644i	$0.645277\pi$
$492$	−43484.4	−	154575.i	−0.179640	−	0.638571i
$493$	−65048.1	−	112667.i	−0.267634	−	0.463555i
$494$	−184817.	−	333033.i	−0.757334	−	1.36469i
$495$	114270.	+	161319.i	0.466362	+	0.658379i
$496$	261500.	−	128178.i	1.06294	−	0.521013i
$497$	−220828.	−	382485.i	−0.894008	−	1.54847i
$498$	84167.0	+	280828.i	0.339377	+	1.13235i
$499$	−251446.	−	145172.i	−1.00982	−	0.583019i	−0.0986806	−	0.995119i	$-0.531462\pi$
$499$	−251446.	−	145172.i	−1.00982	−	0.583019i	−0.911139	+	0.412100i	$0.864796\pi$
$500$	36487.4	+	68460.7i	0.145950	+	0.273843i
$501$	−39569.8	+	180815.i	−0.157648	+	0.720376i
$502$	44973.7	−	74932.1i	0.178464	−	0.297345i
$503$		−	9486.90i		−	0.0374963i	−0.999824	−	0.0187481i	$-0.994032\pi$
$503$		−	9486.90i		−	0.0374963i	0.999824	−	0.0187481i	$-0.00596807\pi$
$504$	212056.	+	110879.i	0.834815	+	0.436502i
$505$	456761.			1.79104
$506$	84624.4	+	50791.0i	0.330518	+	0.198375i
$507$	383568.	−	420885.i	1.49220	−	1.63737i
$508$	−100583.	+	53607.3i	−0.389758	+	0.207729i
$509$	146376.	−	253530.i	0.564980	−	0.978575i	−0.432071	−	0.901839i	$-0.642217\pi$
$509$	146376.	−	253530.i	0.564980	−	0.978575i	0.997052	−	0.0767350i	$-0.0244496\pi$
$510$	−158417.	−	149368.i	−0.609061	−	0.574271i
$511$	−75918.5	+	43831.5i	−0.290741	+	0.167859i
$512$	39865.2	−	259095.i	0.152074	−	0.988369i
$513$	−137956.	+	182860.i	−0.524213	+	0.694839i
$514$	−194328.	+	107842.i	−0.735544	+	0.408190i
$515$	−373860.	+	215848.i	−1.40960	+	0.813831i
$516$	89543.5	−	351604.i	0.336306	−	1.32055i
$517$	−41579.3	+	72017.4i	−0.155559	+	0.269437i
$518$	−186174.	−	3158.36i	−0.693841	−	0.0117707i
$519$	37040.1	−	40643.7i	0.137511	−	0.150889i
$520$	573765.	−	293412.i	2.12191	−	1.08510i
$521$	−344253.			−1.26824			−0.634120	−	0.773234i	$-0.718638\pi$
$521$	−344253.			−1.26824			−0.634120	+	0.773234i	$0.718638\pi$
$522$	−130632.	−	191213.i	−0.479413	−	0.701742i
$523$		−	79326.1i		−	0.290010i	−0.989431	−	0.145005i	$-0.953680\pi$
$523$		−	79326.1i		−	0.290010i	0.989431	−	0.145005i	$-0.0463198\pi$
$524$	−3777.01	+	111289.i	−0.0137558	+	0.405312i
$525$	−42549.1	+	194429.i	−0.154373	+	0.705411i
$526$	100639.	+	1707.29i	0.363742	+	0.00617071i
$527$	179323.	+	103532.i	0.645675	+	0.372780i
$528$	−164370.	+	40276.6i	−0.589595	+	0.144473i
$529$	−83497.9	−	144623.i	−0.298376	−	0.516803i
$530$	−122929.	+	68219.5i	−0.437625	+	0.242860i
$531$	81811.7	−	7606.48i	0.290152	−	0.0269771i
$532$	−122784.	+	196925.i	−0.433830	+	0.695790i
$533$	168960.	+	292648.i	0.594744	+	1.03013i
$534$	−63458.5	+	268114.i	−0.222540	+	0.940237i
$535$	−428527.	−	247410.i	−1.49717	−	0.864391i
$536$	22450.0	−	34681.6i	0.0781424	−	0.120717i
$537$	98923.0	−	31486.5i	0.343043	−	0.109188i
$538$	185731.	+	111474.i	0.641681	+	0.385133i
$539$			19849.0i			0.0683223i
$540$	−301299.	−	243779.i	−1.03326	−	0.836003i
$541$	167330.			0.571715			0.285857	−	0.958272i	$-0.407722\pi$
$541$	167330.			0.571715			0.285857	+	0.958272i	$0.407722\pi$
$542$	195436.	−	325622.i	0.665283	−	1.10845i
$543$	−69728.0	−	219068.i	−0.236487	−	0.742985i
$544$	168731.	−	79184.7i	0.570159	−	0.267574i
$545$	125252.	−	216943.i	0.421689	−	0.730387i
$546$	−490042.	−	115985.i	−1.64380	−	0.389061i
$547$	246877.	−	142535.i	0.825100	−	0.476372i	−0.0270722	−	0.999633i	$-0.508618\pi$
$547$	246877.	−	142535.i	0.825100	−	0.476372i	0.852172	+	0.523262i	$0.175285\pi$
$548$	−71861.5	+	115254.i	−0.239296	+	0.383790i
$549$	63337.4	+	29116.1i	0.210143	+	0.0966026i
$550$	−68300.6	−	123075.i	−0.225787	−	0.406860i
$551$	194494.	−	112291.i	0.640623	−	0.369864i
$552$	−186670.	−	50926.5i	−0.612628	−	0.167134i
$553$	−180374.	+	312417.i	−0.589827	+	1.02161i
$554$	7330.30	−	432096.i	0.0238837	−	1.40786i
$555$	294604.	+	64471.6i	0.956429	+	0.209306i
$556$	−11583.2	+	341297.i	−0.0374696	+	1.10403i
$557$	51271.9			0.165260			0.0826302	−	0.996580i	$-0.473668\pi$
$557$	51271.9			0.165260			0.0826302	+	0.996580i	$0.473668\pi$
$558$	332231.	+	159607.i	1.06702	+	0.512606i
$559$			763547.i			2.44350i
$560$	−325954.	−	218930.i	−1.03939	−	0.698117i
$561$	−88934.6	−	81049.4i	−0.282582	−	0.257528i
$562$	−4676.52	+	275665.i	−0.0148064	+	0.872787i
$563$	2488.80	+	1436.91i	0.00785187	+	0.00453328i	0.503921	−	0.863750i	$-0.331890\pi$
$563$	2488.80	+	1436.91i	0.00785187	+	0.00453328i	−0.496069	+	0.868283i	$0.665224\pi$
$564$	40235.0	−	157988.i	0.126487	−	0.496666i
$565$	−16485.6	−	28553.9i	−0.0516425	−	0.0894474i
$566$	87753.2	+	158128.i	0.273924	+	0.493601i
$567$	55833.9	+	297666.i	0.173673	+	0.925898i
$568$	−611552.	−	31148.0i	−1.89556	−	0.0965458i
$569$	56876.7	+	98513.3i	0.175675	+	0.304278i	0.940395	−	0.340085i	$-0.110456\pi$
$569$	56876.7	+	98513.3i	0.175675	+	0.304278i	−0.764720	+	0.644363i	$0.777123\pi$
$570$	257850.	−	273471.i	0.793630	−	0.841709i
$571$	27258.4	+	15737.7i	0.0836043	+	0.0482689i	0.541219	−	0.840881i	$-0.317963\pi$
$571$	27258.4	+	15737.7i	0.0836043	+	0.0482689i	−0.457615	+	0.889150i	$0.651296\pi$
$572$	314288.	−	167505.i	0.960585	−	0.511961i
$573$	259880.	+	236838.i	0.791522	+	0.721344i
$574$	105957.	−	176538.i	0.321592	−	0.535813i
$575$		−	160935.i		−	0.486760i
$576$	288819.	−	163276.i	0.870524	−	0.492126i
$577$	−654654.			−1.96635			−0.983174	−	0.182671i	$-0.941526\pi$
$577$	−654654.			−1.96635			−0.983174	+	0.182671i	$0.941526\pi$
$578$	−172822.	−	103727.i	−0.517301	−	0.310480i
$579$	−244682.	−	53546.6i	−0.729870	−	0.159726i
$580$	178722.	+	335333.i	0.531278	+	0.996829i
$581$	−187955.	+	325548.i	−0.556803	+	0.964412i
$582$	439108.	−	131605.i	1.29636	−	0.388532i
$583$	−67285.9	+	38847.5i	−0.197964	+	0.114295i
$584$	−6182.48	+	121385.i	−0.0181275	+	0.355910i
$585$	741062.	+	340665.i	2.16542	+	0.995441i
$586$	250798.	−	139180.i	0.730346	−	0.405306i
$587$	−557280.	+	321746.i	−1.61732	+	0.933763i	−0.629716	+	0.776825i	$0.716829\pi$
$587$	−557280.	+	321746.i	−1.61732	+	0.933763i	−0.987609	+	0.156937i	$0.949838\pi$
$588$	−10538.0	−	37459.6i	−0.0304791	−	0.108345i
$589$	−178725.	+	309561.i	−0.515175	+	0.892309i
$590$	−134802.	−	2286.86i	−0.387251	−	0.00656954i
$591$	−57604.8	−	180980.i	−0.164924	−	0.518151i
$592$	−143943.	+	214310.i	−0.410721	+	0.611503i
$593$	−183090.			−0.520661			−0.260330	−	0.965520i	$-0.583831\pi$
$593$	−183090.			−0.520661			−0.260330	+	0.965520i	$0.583831\pi$
$594$	−168770.	−	131877.i	−0.478325	−	0.373764i
$595$		−	279180.i		−	0.788589i
$596$	203620.	+	6910.62i	0.573228	+	0.0194547i
$597$	46722.1	−	14871.3i	0.131091	−	0.0417255i
$598$	407134.	+	6906.84i	1.13851	+	0.0193142i
$599$	−24104.3	−	13916.6i	−0.0671800	−	0.0387864i	0.466034	−	0.884767i	$-0.345683\pi$
$599$	−24104.3	−	13916.6i	−0.0671800	−	0.0387864i	−0.533214	+	0.845981i	$0.679016\pi$
$600$	194240.	+	196009.i	0.539555	+	0.544470i
$601$	135764.	+	235150.i	0.375868	+	0.651022i	0.990457	−	0.137826i	$-0.0440113\pi$
$601$	135764.	+	235150.i	0.375868	+	0.651022i	−0.614589	+	0.788848i	$0.710678\pi$
$602$	406786.	−	225746.i	1.12247	−	0.622912i
$603$	52063.0	−	4840.58i	0.143184	−	0.0133126i
$604$	48001.8	+	29929.5i	0.131578	+	0.0820399i
$605$	153610.	+	266060.i	0.419670	+	0.726889i
$606$	−474037.	+	142074.i	−1.29082	+	0.386873i
$607$	−86991.8	−	50224.8i	−0.236103	−	0.136314i	0.377281	−	0.926099i	$-0.376859\pi$
$607$	−86991.8	−	50224.8i	−0.236103	−	0.136314i	−0.613384	+	0.789785i	$0.710192\pi$
$608$	136695.	+	291276.i	0.369781	+	0.787948i
$609$	63479.0	−	290068.i	0.171157	−	0.782106i
$610$	−98075.2	−	58864.1i	−0.263572	−	0.158194i
$611$			343088.i			0.919015i
$612$	210869.	+	105743.i	0.563002	+	0.282323i
$613$	458408.			1.21992			0.609960	−	0.792432i	$-0.291185\pi$
$613$	458408.			1.21992			0.609960	+	0.792432i	$0.291185\pi$
$614$	−197339.	+	328793.i	−0.523451	+	0.872138i
$615$	−224620.	+	246473.i	−0.593880	+	0.651657i
$616$	−182161.	−	117916.i	−0.480057	−	0.310750i
$617$	237317.	−	411046.i	0.623389	−	1.07974i	−0.365461	−	0.930827i	$-0.619089\pi$
$617$	237317.	−	411046.i	0.623389	−	1.07974i	0.988850	−	0.148915i	$-0.0475781\pi$
$618$	320862.	−	340300.i	0.840120	−	0.891016i
$619$	5714.30	−	3299.15i	0.0149136	−	0.00861036i	−0.492525	−	0.870298i	$-0.663926\pi$
$619$	5714.30	−	3299.15i	0.0149136	−	0.00861036i	0.507438	+	0.861688i	$0.330593\pi$
$620$	−513209.	−	319989.i	−1.33509	−	0.832438i
$621$	−95558.8	−	225475.i	−0.247792	−	0.584676i
$622$	−46715.9	−	84180.4i	−0.120749	−	0.217586i
$623$	−305951.	+	176641.i	−0.788272	+	0.455109i
$624$	−504202.	+	482977.i	−1.29490	+	1.24039i
$625$	230266.	−	398833.i	0.589481	−	1.02101i
$626$	−6737.96	+	397179.i	−0.0171941	+	1.01353i
$627$	139914.	−	153526.i	0.355898	−	0.390523i
$628$	−475584.	−	16140.8i	−1.20589	−	0.0409265i
$629$	−183557.			−0.463948
$630$	−37606.1	−	495526.i	−0.0947495	−	1.24849i
$631$		−	102946.i		−	0.258553i	−0.991609	−	0.129277i	$-0.958734\pi$
$631$		−	102946.i		−	0.258553i	0.991609	−	0.129277i	$-0.0412655\pi$
$632$	227727.	+	445319.i	0.570139	+	1.11490i
$633$	133157.	−	608464.i	0.332320	−	1.51854i
$634$	4032.97	−	237730.i	0.0100334	−	0.591432i
$635$	204987.	+	118349.i	0.508368	+	0.293506i
$636$	106359.	−	109036.i	0.262942	−	0.269561i
$637$	40945.7	+	70919.9i	0.100909	+	0.174779i
$638$	101898.	+	183616.i	0.250336	+	0.451096i
$639$	−447970.	−	632413.i	−1.09710	−	1.54881i
$640$	−500392.	+	214434.i	−1.22166	+	0.523521i
$641$	−202403.	−	350572.i	−0.492607	−	0.853221i	0.507356	−	0.861736i	$-0.330623\pi$
$641$	−202403.	−	350572.i	−0.492607	−	0.853221i	−0.999964	+	0.00851530i	$0.997289\pi$
$642$	521692.	+	123476.i	1.26574	+	0.299581i
$643$	426111.	+	246015.i	1.03063	+	0.595032i	0.917164	−	0.398510i	$-0.130473\pi$
$643$	426111.	+	246015.i	1.03063	+	0.595032i	0.113462	+	0.993542i	$0.463806\pi$
$644$	−116691.	−	218946.i	−0.281363	−	0.527917i
$645$	−718001.	+	228535.i	−1.72586	+	0.549329i
$646$	−117730.	+	196154.i	−0.282113	+	0.470037i
$647$		−	306912.i		−	0.733171i	−0.930384	−	0.366586i	$-0.880527\pi$
$647$		−	306912.i		−	0.733171i	0.930384	−	0.366586i	$-0.119473\pi$
$648$	388521.	+	159281.i	0.925262	+	0.379328i
$649$	−74507.5			−0.176893
$650$	−497922.	−	298849.i	−1.17851	−	0.707335i
$651$	143341.	+	450343.i	0.338227	+	1.06263i
$652$	83362.7	−	44429.7i	0.196100	−	0.104515i
$653$	−97661.8	+	169155.i	−0.229033	+	0.396697i	−0.957522	−	0.288361i	$-0.906890\pi$
$653$	−97661.8	+	169155.i	−0.229033	+	0.396697i	0.728489	+	0.685058i	$0.240223\pi$
$654$	−62510.3	+	264108.i	−0.146149	+	0.617484i
$655$	200269.	−	115625.i	0.466799	−	0.269507i
$656$	−125644.	−	256330.i	−0.291966	−	0.595651i
$657$	−125526.	+	88916.3i	−0.290806	+	0.205992i
$658$	182783.	−	101435.i	0.422166	−	0.234281i
$659$	678872.	−	391947.i	1.56321	−	0.902519i	0.566279	−	0.824213i	$-0.308382\pi$
$659$	678872.	−	391947.i	1.56321	−	0.902519i	0.996929	−	0.0783055i	$-0.0249510\pi$
$660$	251582.	+	245405.i	0.577553	+	0.563372i
$661$	−371075.	+	642721.i	−0.849295	+	1.47102i	0.0325431	+	0.999470i	$0.489639\pi$
$661$	−371075.	+	642721.i	−0.849295	+	1.47102i	−0.881838	+	0.471552i	$0.843694\pi$
$662$	368768.	+	6255.97i	0.841467	+	0.0142751i
$663$	−484953.	−	106128.i	−1.10325	−	0.241436i
$664$	237298.	+	464035.i	0.538218	+	1.05248i
$665$	481943.			1.08981
$666$	−325801.	+	24725.4i	−0.734520	+	0.0557436i
$667$			240099.i			0.539682i
$668$	−11161.4	+	328867.i	−0.0250129	+	0.737000i
$669$	168481.	+	153543.i	0.376442	+	0.343065i
$670$	−85784.9	−	1455.30i	−0.191100	−	0.00324193i
$671$	−54744.0	−	31606.5i	−0.121588	−	0.0701990i
$672$	406380.	+	125823.i	0.899898	+	0.278627i
$673$	−211601.	−	366503.i	−0.467183	−	0.809185i	0.532114	−	0.846673i	$-0.321398\pi$
$673$	−211601.	−	366503.i	−0.467183	−	0.809185i	−0.999297	+	0.0374878i	$0.988064\pi$
$674$	−160566.	+	89106.0i	−0.353454	+	0.196149i
$675$	−42758.0	+	346623.i	−0.0938447	+	0.760763i
$676$	535621.	−	859046.i	1.17210	−	1.87985i
$677$	−154122.	−	266947.i	−0.336269	−	0.582435i	0.647459	−	0.762100i	$-0.275832\pi$
$677$	−154122.	−	266947.i	−0.336269	−	0.582435i	−0.983728	+	0.179665i	$0.942498\pi$
$678$	25990.7	+	24506.1i	0.0565404	+	0.0533107i
$679$	509034.	+	293891.i	1.10410	+	0.637450i
$680$	−324940.	−	210339.i	−0.702724	−	0.454886i
$681$	−646626.	−	589294.i	−1.39431	−	1.27069i
$682$	−286577.	−	172002.i	−0.616131	−	0.369798i
$683$		−	760287.i		−	1.62981i	−0.579597	−	0.814903i	$-0.696790\pi$
$683$		−	760287.i		−	1.62981i	0.579597	−	0.814903i	$-0.303210\pi$
$684$	−182541.	+	364018.i	−0.390165	+	0.778056i
$685$	282065.			0.601130
$686$	253819.	−	422896.i	0.539357	−	0.898639i
$687$	755164.	+	165261.i	1.60003	+	0.350152i
$688$	43732.4	−	643541.i	0.0923904	−	1.35956i
$689$	−160273.	+	277602.i	−0.337616	+	0.584768i
$690$	115363.	+	384916.i	0.242309	+	0.808477i
$691$	313235.	−	180846.i	0.656016	−	0.378751i	−0.134742	−	0.990881i	$-0.543020\pi$
$691$	313235.	−	180846.i	0.656016	−	0.378751i	0.790757	+	0.612130i	$0.209687\pi$
$692$	51723.4	−	82955.6i	0.108013	−	0.173234i
$693$	−25424.5	−	273454.i	−0.0529403	−	0.569401i
$694$	−294978.	−	531539.i	−0.612450	−	1.10361i
$695$	614177.	−	354595.i	1.27152	−	0.734113i
$696$	−289786.	−	292426.i	−0.598217	−	0.603667i
$697$	101485.	−	175777.i	0.208899	−	0.361824i
$698$	−12707.4	+	749057.i	−0.0260823	+	1.53746i
$699$	−34869.3	−	109551.i	−0.0713656	−	0.224214i
$700$	−12001.7	+	353628.i	−0.0244933	+	0.721690i
$701$	878492.			1.78773			0.893864	−	0.448337i	$-0.147984\pi$
$701$	878492.			1.78773			0.893864	+	0.448337i	$0.147984\pi$
$702$	−875054.	−	123046.i	−1.77566	−	0.249684i
$703$		−	316870.i		−	0.641167i
$704$	−274486.	+	123178.i	−0.553827	+	0.248535i
$705$	−322622.	+	102688.i	−0.649107	+	0.206606i
$706$	3081.37	−	181636.i	0.00618208	−	0.364412i
$707$	−549525.	−	317268.i	−1.09938	−	0.634728i
$708$	140612.	−	39556.4i	0.280515	−	0.0789133i
$709$	−431190.	−	746844.i	−0.857781	−	1.48572i	−0.874041	−	0.485853i	$-0.838509\pi$
$709$	−431190.	−	746844.i	−0.857781	−	1.48572i	0.0162593	−	0.999868i	$-0.494824\pi$
$710$	617066.	+	1.11193e6i	1.22409	+	2.20577i
$711$	−264402.	+	575164.i	−0.523029	+	1.13776i
$712$	−24915.4	+	489183.i	−0.0491482	+	0.964964i
$713$	−191073.	−	330948.i	−0.375855	−	0.651000i
$714$	86838.0	+	289740.i	0.170339	+	0.568345i
$715$	−640517.	−	369803.i	−1.25291	−	0.723366i
$716$	162869.	−	86803.9i	0.317696	−	0.169322i
$717$	−203836.	+	931435.i	−0.396500	+	1.81182i
$718$	−147189.	+	245236.i	−0.285514	+	0.475703i
$719$			424008.i			0.820193i	0.912042	+	0.410097i	$0.134505\pi$
$719$			424008.i			0.820193i	−0.912042	+	0.410097i	$0.865495\pi$
$720$	−605078.	−	329568.i	−1.16720	−	0.635740i
$721$	599717.			1.15365
$722$	108343.	+	65026.6i	0.207838	+	0.124743i
$723$	−61710.3	+	67714.0i	−0.118054	+	0.129539i
$724$	−192230.	−	360679.i	−0.366728	−	0.688087i
$725$	171209.	−	296543.i	0.325725	−	0.564172i
$726$	−242177.	−	228343.i	−0.459472	−	0.433226i
$727$	−78836.8	+	45516.5i	−0.149163	+	0.0861191i	−0.572724	−	0.819748i	$-0.694113\pi$
$727$	−78836.8	+	45516.5i	−0.149163	+	0.0861191i	0.423561	+	0.905868i	$0.360780\pi$
$728$	−894096.	−	45538.7i	−1.68702	−	0.0859247i
$729$	145910.	+	511018.i	0.274555	+	0.961571i
$730$	220704.	−	122480.i	0.414157	−	0.229836i
$731$	397177.	−	229310.i	0.743275	−	0.429130i
$732$	120094.	+	30584.6i	0.224130	+	0.0570795i
$733$	6638.99	−	11499.1i	0.0123565	−	0.0214020i	−0.859781	−	0.510663i	$-0.829400\pi$
$733$	6638.99	−	11499.1i	0.0123565	−	0.0214020i	0.872138	+	0.489261i	$0.162733\pi$
$734$	265109.	+	4497.44i	0.492076	+	0.00834783i
$735$	−54434.2	+	59730.0i	−0.100762	+	0.110565i
$736$	−342750.	−	29140.1i	−0.632735	−	0.0537942i
$737$	−47414.8			−0.0872929
$738$	156452.	−	325663.i	0.287255	−	0.597937i
$739$			622195.i			1.13930i	0.821888	+	0.569650i	$0.192921\pi$
$739$			622195.i			1.13930i	−0.821888	+	0.569650i	$0.807079\pi$
$740$	535827.	+	18185.3i	0.978501	+	0.0332092i
$741$	183206.	−	837164.i	0.333660	−	1.52466i
$742$	195280.	+	3312.84i	0.354691	+	0.00601717i
$743$	−606588.	−	350214.i	−1.09879	−	0.634389i	−0.162890	−	0.986644i	$-0.552082\pi$
$743$	−606588.	−	350214.i	−1.09879	−	0.634389i	−0.935904	+	0.352255i	$0.885415\pi$
$744$	632152.	+	172461.i	1.14203	+	0.311562i
$745$	−211554.	−	366422.i	−0.381161	−	0.660189i
$746$	−502135.	+	278660.i	−0.902283	+	0.500722i
$747$	−275514.	+	599337.i	−0.493745	+	1.07406i
$748$	−181520.	−	113179.i	−0.324430	−	0.202284i
$749$	343705.	+	595314.i	0.612663	+	1.06116i
$750$	−40202.2	+	169856.i	−0.0714706	+	0.301965i
$751$	73727.4	+	42566.6i	0.130722	+	0.0754725i	0.563935	−	0.825819i	$-0.309287\pi$
$751$	73727.4	+	42566.6i	0.130722	+	0.0754725i	−0.433213	+	0.901292i	$0.642620\pi$
$752$	19650.5	−	289165.i	0.0347486	−	0.511340i
$753$	187371.	−	59638.8i	0.330455	−	0.105181i
$754$	742849.	+	445853.i	1.30665	+	0.784240i
$755$		−	117477.i		−	0.206091i
$756$	193160.	+	502571.i	0.337966	+	0.879334i
$757$	319528.			0.557592			0.278796	−	0.960350i	$-0.410065\pi$
$757$	319528.			0.557592			0.278796	+	0.960350i	$0.410065\pi$
$758$	−377066.	+	628241.i	−0.656265	+	1.09342i
$759$	67353.0	+	211607.i	0.116916	+	0.367321i
$760$	363104.	−	560936.i	0.628643	−	0.971150i
$761$	−376888.	+	652790.i	−0.650794	+	1.12721i	0.332137	+	0.943231i	$0.392230\pi$
$761$	−376888.	+	652790.i	−0.650794	+	1.12721i	−0.982931	+	0.183977i	$0.941103\pi$
$762$	−249552.	−	59065.1i	−0.429785	−	0.101723i
$763$	−301379.	+	174001.i	−0.517684	+	0.298885i
$764$	530426.	+	330724.i	0.908737	+	0.566604i
$765$	−45352.5	−	487790.i	−0.0774958	−	0.833509i
$766$	−34012.4	−	61289.2i	−0.0579669	−	0.104454i
$767$	−266213.	+	153698.i	−0.452520	+	0.261263i
$768$	452620.	−	378190.i	0.767381	−	0.641191i
$769$	−425156.	+	736392.i	−0.718945	+	1.24525i	0.242473	+	0.970158i	$0.422041\pi$
$769$	−425156.	+	736392.i	−0.718945	+	1.24525i	−0.961418	+	0.275091i	$0.911292\pi$
$770$	−7643.78	+	450575.i	−0.0128922	+	0.759950i
$771$	−488492.	−	106902.i	−0.821768	−	0.179837i
$772$	−445029.	−	15103.8i	−0.746713	−	0.0253426i
$773$	13034.7			0.0218143			0.0109071	−	0.999941i	$-0.496528\pi$
$773$	13034.7			0.0218143			0.0109071	+	0.999941i	$0.496528\pi$
$774$	674073.	−	460510.i	1.12519	−	0.768701i
$775$			545000.i			0.907388i
$776$	725575.	−	371045.i	1.20492	−	0.616173i
$777$	−309653.	−	282199.i	−0.512901	−	0.467426i
$778$	5214.93	−	307402.i	0.00861567	−	0.507864i
$779$	303441.	+	175192.i	0.500033	+	0.288694i
$780$	1.40513e6	+	357846.i	2.30955	+	0.588176i
$781$	351388.	+	608622.i	0.576083	+	0.997805i
$782$	−118679.	−	213855.i	−0.194071	−	0.349708i
$783$	63790.6	−	517126.i	0.104048	−	0.843476i
$784$	−30448.3	−	62118.7i	−0.0495372	−	0.101063i
$785$	494114.	+	855831.i	0.801841	+	1.38883i
$786$	−171879.	+	182291.i	−0.278213	+	0.295067i
$787$	473891.	+	273601.i	0.765120	+	0.441742i	0.831131	−	0.556077i	$-0.187694\pi$
$787$	473891.	+	273601.i	0.765120	+	0.441742i	−0.0660112	+	0.997819i	$0.521027\pi$
$788$	−158808.	−	297970.i	−0.255753	−	0.479866i
$789$	167387.	+	152546.i	0.268885	+	0.245045i
$790$	534542.	−	890616.i	0.856500	−	1.42704i
$791$			45803.8i			0.0732064i
$792$	−337430.	−	176433.i	−0.537940	−	0.281274i
$793$	−260798.			−0.414723
$794$	−251381.	−	150877.i	−0.398741	−	0.239322i
$795$	−309014.	−	67624.9i	−0.488926	−	0.106997i
$796$	76924.2	−	40998.2i	0.121405	−	0.0647050i
$797$	104227.	−	180527.i	0.164083	−	0.284201i	−0.772246	−	0.635324i	$-0.780867\pi$
$797$	104227.	−	180527.i	0.164083	−	0.284201i	0.936329	+	0.351123i	$0.114200\pi$
$798$	−500172.	+	149907.i	−0.785441	+	0.235405i
$799$	178465.	−	103037.i	0.279550	−	0.161398i
$800$	402547.	+	280398.i	0.628980	+	0.438122i
$801$	−505869.	+	358332.i	−0.788449	+	0.558497i
$802$	−995215.	+	552295.i	−1.54728	+	0.858662i
$803$	120804.	−	69746.0i	0.187348	−	0.108165i
$804$	89482.3	−	25172.7i	0.138428	−	0.0389420i
$805$	−257620.	+	446211.i	−0.397547	+	0.688571i
$806$	−1.37875e6	−	23389.8i	−2.12234	−	0.0360044i
$807$	147824.	+	464427.i	0.226985	+	0.713133i
$808$	−783292.	+	400560.i	−1.19978	+	0.613542i
$809$	844500.			1.29034			0.645168	−	0.764041i	$-0.276787\pi$
$809$	844500.			1.29034			0.645168	+	0.764041i	$0.276787\pi$
$810$	−146204.	−	859684.i	−0.222837	−	1.31029i
$811$		−	769174.i		−	1.16945i	−0.811230	−	0.584727i	$-0.801202\pi$
$811$		−	769174.i		−	1.16945i	0.811230	−	0.584727i	$-0.198798\pi$
$812$	17905.4	−	527577.i	0.0271563	−	0.800155i
$813$	814232.	−	259164.i	1.23188	−	0.392098i
$814$	296246.	+	5025.67i	0.447099	+	0.00758482i
$815$	−169893.	−	98087.6i	−0.255776	−	0.147672i
$816$	402655.	+	117224.i	0.604718	+	0.176050i
$817$	395853.	+	685638.i	0.593048	+	1.02719i
$818$	395759.	−	219627.i	0.591458	−	0.328230i
$819$	−654937.	−	924595.i	−0.976408	−	1.37843i
$820$	−313663.	+	503063.i	−0.466483	+	0.748161i
$821$	−322867.	−	559222.i	−0.479002	−	0.829656i	0.520708	−	0.853735i	$-0.325668\pi$
$821$	−322867.	−	559222.i	−0.479002	−	0.829656i	−0.999710	+	0.0240788i	$0.992335\pi$
$822$	−292734.	+	87735.3i	−0.433240	+	0.129847i
$823$	202697.	+	117027.i	0.299260	+	0.172778i	0.642110	−	0.766612i	$-0.278059\pi$
$823$	202697.	+	117027.i	0.299260	+	0.172778i	−0.342851	+	0.939390i	$0.611392\pi$
$824$	451837.	−	698013.i	0.665468	−	1.02804i
$825$	67705.4	−	309381.i	0.0994753	−	0.454554i
$826$	160591.	+	96385.5i	0.235375	+	0.141271i
$827$			1.14409e6i			1.67282i	0.548108	+	0.836408i	$0.315348\pi$
$827$			1.14409e6i			1.67282i	−0.548108	+	0.836408i	$0.684652\pi$
$828$	−239453.	−	363591.i	−0.349269	−	0.530338i
$829$	−563769.			−0.820336			−0.410168	−	0.912010i	$-0.634530\pi$
$829$	−563769.			−0.820336			−0.410168	+	0.912010i	$0.634530\pi$
$830$	557008.	−	928047.i	0.808547	−	1.34714i
$831$	654961.	−	718681.i	0.948447	−	1.04072i
$832$	−726630.	+	1.00633e6i	−1.04970	+	1.45377i
$833$	24593.8	−	42597.7i	0.0354434	−	0.0613898i
$834$	−527111.	+	559044.i	−0.757827	+	0.803738i
$835$	591809.	−	341681.i	0.848806	−	0.490059i
$836$	195378.	−	313353.i	0.279552	−	0.448355i
$837$	323606.	+	763563.i	0.461919	+	1.08992i
$838$	−531873.	−	958415.i	−0.757390	−	1.36479i
$839$	−231599.	+	133714.i	−0.329013	+	0.189956i	−0.655403	−	0.755279i	$-0.727501\pi$
$839$	−231599.	+	133714.i	−0.329013	+	0.189956i	0.326390	+	0.945235i	$0.394168\pi$
$840$	−224787.	−	854393.i	−0.318575	−	1.21087i
$841$	98213.9	−	170111.i	0.138861	−	0.240515i
$842$	847.004	−	49927.9i	0.00119471	−	0.0704238i
$843$	−417846.	+	458497.i	−0.587978	+	0.645181i
$844$	37559.3	−	1.10668e6i	0.0527269	−	1.55359i
$845$	−2.10238e6			−2.94440
$846$	302884.	−	206923.i	0.423190	−	0.289113i
$847$		−	426792.i		−	0.594907i
$848$	150983.	−	224792.i	0.209960	−	0.312600i
$849$	−86988.4	+	397495.i	−0.120683	+	0.551463i
$850$	−5916.50	+	348757.i	−0.00818892	+	0.482708i
$851$	293377.	+	169381.i	0.405105	+	0.233887i
$852$	−986268.	−	962052.i	−1.35868	−	1.32532i
$853$	−183417.	−	317688.i	−0.252082	−	0.436619i	0.712017	−	0.702162i	$-0.247782\pi$
$853$	−183417.	−	317688.i	−0.252082	−	0.436619i	−0.964099	+	0.265544i	$0.914449\pi$
$854$	77106.0	+	138942.i	0.105724	+	0.190510i
$855$	842061.	−	78291.0i	1.15189	−	0.107098i
$856$	951842.	+	48479.9i	1.29902	+	0.0661628i
$857$	−576064.	−	997772.i	−0.784348	−	1.35853i	−0.929388	−	0.369105i	$-0.879664\pi$
$857$	−576064.	−	997772.i	−0.784348	−	1.35853i	0.145039	−	0.989426i	$-0.453669\pi$
$858$	779769.	+	184559.i	1.05923	+	0.250704i
$859$	−1.26237e6	−	728827.i	−1.71080	−	0.987730i	−0.933486	−	0.358615i	$-0.883249\pi$
$859$	−1.26237e6	−	728827.i	−1.71080	−	0.987730i	−0.777313	−	0.629115i	$-0.783418\pi$
$860$	−1.18213e6	+	630038.i	−1.59834	+	0.851863i
$861$	441440.	−	140507.i	0.595477	−	0.189536i
$862$	−246718.	+	411064.i	−0.332037	+	0.553217i
$863$			237901.i			0.319430i	0.987163	+	0.159715i	$0.0510575\pi$
$863$			237901.i			0.319430i	−0.987163	+	0.159715i	$0.948943\pi$
$864$	730475.	+	153826.i	0.978539	+	0.206064i
$865$	−203020.			−0.271336
$866$	−968764.	−	581445.i	−1.29176	−	0.775306i
$867$	−137550.	−	432148.i	−0.182988	−	0.574903i
$868$	395171.	+	741453.i	0.524500	+	0.984112i
$869$	287017.	−	497128.i	0.380074	−	0.658307i
$870$	−196918.	+	831984.i	−0.260164	+	1.09920i
$871$	−169411.	+	97809.7i	−0.223309	+	0.128928i
$872$	−24543.1	+	481873.i	−0.0322772	+	0.633723i
$873$	937137.	+	430800.i	1.22963	+	0.565259i
$874$	369173.	−	204873.i	0.483289	−	0.268201i
$875$	−193826.	+	111905.i	−0.253160	+	0.146162i
$876$	−190955.	+	195762.i	−0.248841	+	0.255105i
$877$	331033.	−	573367.i	0.430400	−	0.745475i	−0.566507	−	0.824057i	$-0.691706\pi$
$877$	331033.	−	573367.i	0.430400	−	0.745475i	0.996908	+	0.0785815i	$0.0250391\pi$
$878$	685604.	+	11630.9i	0.889373	+	0.0150878i
$879$	630445.	+	137967.i	0.815961	+	0.178566i
$880$	518667.	+	348367.i	0.669766	+	0.449854i
$881$	245234.			0.315957			0.157979	−	0.987443i	$-0.449502\pi$
$881$	245234.			0.315957			0.157979	+	0.987443i	$0.449502\pi$
$882$	37914.3	−	78920.8i	0.0487378	−	0.101451i
$883$			924835.i			1.18616i	0.805144	+	0.593079i	$0.202088\pi$
$883$			924835.i			1.18616i	−0.805144	+	0.593079i	$0.797912\pi$
$884$	−882034.	−	29935.2i	−1.12871	−	0.0383070i
$885$	−224209.	−	204330.i	−0.286264	−	0.260883i
$886$	331990.	+	5632.05i	0.422919	+	0.00717462i
$887$	−1.09941e6	−	634747.i	−1.39738	−	0.806776i	−0.403260	−	0.915085i	$-0.632123\pi$
$887$	−1.09941e6	−	634747.i	−1.39738	−	0.806776i	−0.994117	+	0.108309i	$0.965456\pi$
$888$	−561750.	+	147794.i	−0.712389	+	0.187426i
$889$	−164412.	−	284769.i	−0.208031	−	0.360321i
$890$	889437.	−	493593.i	1.12288	−	0.623145i
$891$	−88844.6	−	473655.i	−0.111912	−	0.596632i
$892$	343877.	+	214409.i	0.432188	+	0.269472i
$893$	177870.	+	308081.i	0.223049	+	0.386333i
$894$	333529.	+	314478.i	0.417310	+	0.393473i
$895$	−331926.	−	191637.i	−0.414376	−	0.239240i
$896$	750964.	+	89591.1i	0.935412	+	0.111596i
$897$	677164.	+	617125.i	0.841606	+	0.766987i
$898$	866908.	+	520313.i	1.07503	+	0.645226i
$899$		−	813085.i		−	1.00604i
$900$	36476.8	+	619816.i	0.0450330	+	0.765205i
$901$	192535.			0.237170
$902$	−168601.	+	280912.i	−0.207228	+	0.345269i
$903$	1.02256e6	+	223779.i	1.25405	+	0.274437i
$904$	53311.3	+	34509.4i	0.0652353	+	0.0422280i
$905$	−424388.	+	735061.i	−0.518162	+	0.897483i
$906$	36540.7	+	121920.i	0.0445165	+	0.148532i
$907$	−41146.3	+	23755.8i	−0.0500169	+	0.0288772i	−0.524800	−	0.851226i	$-0.675860\pi$
$907$	−41146.3	+	23755.8i	−0.0500169	+	0.0288772i	0.474783	+	0.880103i	$0.342527\pi$
$908$	−1.31979e6	−	822900.i	−1.60079	−	0.998102i
$909$	−1.01168e6	−	465068.i	−1.22438	−	0.562845i
$910$	902158.	+	1.62565e6i	1.08943	+	1.96311i
$911$	−421729.	+	243485.i	−0.508155	+	0.293383i	−0.732075	−	0.681224i	$-0.761448\pi$
$911$	−421729.	+	243485.i	−0.508155	+	0.293383i	0.223920	+	0.974608i	$0.428115\pi$
$912$	−202361.	+	695095.i	−0.243297	+	0.835708i
$913$	299080.	−	518021.i	0.358794	−	0.621450i
$914$	−1287.73	+	75907.4i	−0.00154147	+	0.0908640i
$915$	−78058.5	−	245241.i	−0.0932349	−	0.292921i
$916$	1.37349e6	+	46614.8i	1.63695	+	0.0555562i
$917$	−321255.			−0.382042
$918$	198793.	+	492133.i	0.235894	+	0.583979i
$919$			1.08957e6i			1.29010i	0.764141	+	0.645049i	$0.223163\pi$
$919$			1.08957e6i			1.29010i	−0.764141	+	0.645049i	$0.776837\pi$
$920$	325252.	+	636029.i	0.384277	+	0.751452i
$921$	−822159.	+	261688.i	−0.969252	+	0.308506i
$922$	−13172.9	+	776495.i	−0.0154960	+	0.913434i
$923$	2.51099e6	+	1.44972e6i	2.94742	+	1.70169i
$924$	−132217.	−	469994.i	−0.154861	−	0.550489i
$925$	−241564.	−	418402.i	−0.282325	−	0.489001i
$926$	193256.	+	348240.i	0.225377	+	0.406122i
$927$	1.04784e6	−	97423.2i	1.21937	−	0.113371i
$928$	−600560.	−	418326.i	−0.697365	−	0.485757i
$929$	−671427.	−	1.16295e6i	−0.777978	−	1.34750i	−0.933106	−	0.359603i	$-0.882912\pi$
$929$	−671427.	−	1.16295e6i	−0.777978	−	1.34750i	0.155128	−	0.987894i	$-0.450421\pi$
$930$	−390673.	−	1.30350e6i	−0.451698	−	1.50711i
$931$	73535.5	+	42455.7i	0.0848394	+	0.0489820i
$932$	−96129.8	−	180367.i	−0.110669	−	0.207647i
$933$	46308.8	−	211609.i	0.0531986	−	0.243092i
$934$	−261406.	+	435537.i	−0.299655	+	0.499265i
$935$			444240.i			0.508153i
$936$	−1.56958e6	+	65678.6i	−1.79156	+	0.0749673i
$937$	1.37506e6			1.56618			0.783089	−	0.621909i	$-0.213643\pi$
$937$	1.37506e6			1.56618			0.783089	+	0.621909i	$0.213643\pi$
$938$	102196.	+	61337.4i	0.116153	+	0.0697140i
$939$	−602035.	+	660606.i	−0.682795	+	0.749223i
$940$	−531172.	+	283098.i	−0.601145	+	0.320391i
$941$	786864.	−	1.36289e6i	0.888628	−	1.53915i	0.0471309	−	0.998889i	$-0.484992\pi$
$941$	786864.	−	1.36289e6i	0.888628	−	1.53915i	0.841498	−	0.540261i	$-0.181674\pi$
$942$	−779007.	−	734509.i	−0.877888	−	0.827743i
$943$	−324405.	+	187295.i	−0.364808	+	0.210622i
$944$	233175.	−	114294.i	0.261661	−	0.128257i
$945$	673416.	−	892607.i	0.754084	−	0.999532i
$946$	−647290.	+	359214.i	−0.723297	+	0.401394i
$947$	−938964.	+	542111.i	−1.04701	+	0.604489i	−0.921810	−	0.387643i	$-0.873289\pi$
$947$	−938964.	+	542111.i	−1.04701	+	0.604489i	−0.125196	+	0.992132i	$0.539956\pi$
$948$	−277737.	+	1.09057e6i	−0.309042	+	1.21349i
$949$	287752.	−	498400.i	0.319511	−	0.553409i
$950$	−602051.	−	10213.5i	−0.667093	−	0.0113169i
$951$	360345.	−	395403.i	0.398435	−	0.437198i
$952$	244829.	+	478762.i	0.270140	+	0.528257i
$953$	461469.			0.508108			0.254054	−	0.967190i	$-0.418236\pi$
$953$	461469.			0.508108			0.254054	+	0.967190i	$0.418236\pi$
$954$	341736.	−	25934.8i	0.375486	−	0.0284961i
$955$		−	1.29813e6i		−	1.42335i
$956$	−57495.6	+	1.69410e6i	−0.0629099	+	1.85363i
$957$	−101010.	+	461565.i	−0.110291	+	0.503975i
$958$	−223692.	−	3794.83i	−0.243736	−	0.00413487i
$959$	−339350.	−	195924.i	−0.368986	−	0.213034i
$960$	−1.16379e6	−	382083.i	−1.26279	−	0.414587i
$961$	185301.	+	320951.i	0.200646	+	0.347530i
$962$	1.06884e6	−	593155.i	1.15495	−	0.640941i
$963$	697236.	+	984311.i	0.751843	+	1.06140i
$964$	−86173.2	+	138207.i	−0.0927295	+	0.148723i
$965$	462369.	+	800847.i	0.496517	+	0.859993i
$966$	128572.	−	543220.i	0.137782	−	0.582132i
$967$	−998780.	−	576646.i	−1.06811	−	0.616675i	−0.140447	−	0.990088i	$-0.544854\pi$
$967$	−998780.	−	576646.i	−1.06811	−	0.616675i	−0.927665	+	0.373413i	$0.878187\pi$
$968$	−496745.	−	321552.i	−0.530131	−	0.343163i
$969$	−490491.	+	156120.i	−0.522377	+	0.166269i
$970$	−1.45111e6	−	870949.i	−1.54226	−	0.925656i
$971$			438562.i			0.465149i	0.972579	+	0.232575i	$0.0747150\pi$
$971$			438562.i			0.465149i	−0.972579	+	0.232575i	$0.925285\pi$
$972$	419135.	+	846725.i	0.443631	+	0.896210i
$973$	−985213.			−1.04065
$974$	565900.	−	942864.i	0.596516	−	0.993873i
$975$	−396298.	−	1.24507e6i	−0.416882	−	1.30974i
$976$	219809.	+	14937.3i	0.230752	+	0.0156810i
$977$	−388615.	+	673100.i	−0.407127	+	0.705165i	−0.994566	−	0.104103i	$-0.966803\pi$
$977$	−388615.	+	673100.i	−0.407127	+	0.705165i	0.587439	+	0.809268i	$0.300136\pi$
$978$	206828.	+	48953.1i	0.216238	+	0.0511803i
$979$	486839.	−	281076.i	0.507948	−	0.293264i
$980$	−76012.8	+	121912.i	−0.0791470	+	0.126939i
$981$	−498310.	+	352978.i	−0.517800	+	0.366783i
$982$	62838.4	+	113233.i	0.0651632	+	0.117422i
$983$	695782.	−	401710.i	0.720056	−	0.415724i	−0.0947175	−	0.995504i	$-0.530195\pi$
$983$	695782.	−	401710.i	0.720056	−	0.415724i	0.814773	+	0.579780i	$0.196861\pi$
$984$	169051.	−	619655.i	0.174593	−	0.639970i
$985$	−350602.	+	607260.i	−0.361362	+	0.625897i
$986$	8826.81	−	520310.i	0.00907925	−	0.535190i
$987$	459472.	+	100551.i	0.471655	+	0.103218i
$988$	51676.5	−	1.52264e6i	0.0529394	−	1.55985i
$989$	−846405.			−0.865338
$990$	59839.9	+	788495.i	0.0610549	+	0.804505i
$991$		−	206876.i		−	0.210651i	−0.994438	−	0.105325i	$-0.966412\pi$
$991$		−	206876.i		−	0.210651i	0.994438	−	0.105325i	$-0.0335884\pi$
$992$	1.16071e6	+	98681.8i	1.17951	+	0.100280i
$993$	613351.	+	558969.i	0.622028	+	0.566878i
$994$	29965.6	−	1.76637e6i	0.0303285	−	1.78776i
$995$	−156771.	−	90511.8i	−0.158351	−	0.0914238i
$996$	−289410.	+	1.13640e6i	−0.291739	+	1.14555i
$997$	14831.3	+	25688.6i	0.0149207	+	0.0258435i	0.873389	−	0.487023i	$-0.161917\pi$
$997$	14831.3	+	25688.6i	0.0149207	+	0.0258435i	−0.858469	+	0.512866i	$0.828584\pi$
$998$	−563546.	−	1.01549e6i	−0.565807	−	1.01956i
$999$	−586875.	−	442761.i	−0.588051	−	0.443647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.5.f.a.31.18	yes	44
3.2	odd	2		108.5.f.a.91.5		44
4.3	odd	2	inner	36.5.f.a.31.12	yes	44
9.2	odd	6		108.5.f.a.19.11		44
9.4	even	3		324.5.d.f.163.4		22
9.5	odd	6		324.5.d.e.163.19		22
9.7	even	3	inner	36.5.f.a.7.12	✓	44
12.11	even	2		108.5.f.a.91.11		44
36.7	odd	6	inner	36.5.f.a.7.18	yes	44
36.11	even	6		108.5.f.a.19.5		44
36.23	even	6		324.5.d.e.163.20		22
36.31	odd	6		324.5.d.f.163.3		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.12	✓	44	9.7	even	3	inner
36.5.f.a.7.18	yes	44	36.7	odd	6	inner
36.5.f.a.31.12	yes	44	4.3	odd	2	inner
36.5.f.a.31.18	yes	44	1.1	even	1	trivial
108.5.f.a.19.5		44	36.11	even	6
108.5.f.a.19.11		44	9.2	odd	6
108.5.f.a.91.5		44	3.2	odd	2
108.5.f.a.91.11		44	12.11	even	2
324.5.d.e.163.19		22	9.5	odd	6
324.5.d.e.163.20		22	36.23	even	6
324.5.d.f.163.3		22	36.31	odd	6
324.5.d.f.163.4		22	9.4	even	3

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)

\(f(q)\)	\(=\)	\(q+(3.42968 + 2.05847i) q^{2} +(2.72970 + 8.57606i) q^{3} +(7.52540 + 14.1198i) q^{4} +(16.6139 - 28.7760i) q^{5} +(-8.29157 + 35.0321i) q^{6} +(-39.9759 + 23.0801i) q^{7} +(-3.25547 + 63.9171i) q^{8} +(-66.0975 + 46.8201i) q^{9} +O(q^{10})\)	\(q+(3.42968 + 2.05847i) q^{2} +(2.72970 + 8.57606i) q^{3} +(7.52540 + 14.1198i) q^{4} +(16.6139 - 28.7760i) q^{5} +(-8.29157 + 35.0321i) q^{6} +(-39.9759 + 23.0801i) q^{7} +(-3.25547 + 63.9171i) q^{8} +(-66.0975 + 46.8201i) q^{9} +(116.215 - 64.4935i) q^{10} +(63.6109 - 36.7258i) q^{11} +(-100.550 + 103.081i) q^{12} +(151.520 - 262.440i) q^{13} +(-184.614 - 3.13190i) q^{14} +(292.136 + 63.9314i) q^{15} +(-142.737 + 212.514i) q^{16} -182.019 q^{17} +(-323.071 + 24.5183i) q^{18} -314.215i q^{19} +(531.337 + 18.0330i) q^{20} +(-307.059 - 279.834i) q^{21} +(293.764 + 4.98356i) q^{22} +(290.919 + 167.962i) q^{23} +(-557.044 + 146.556i) q^{24} +(-239.540 - 414.896i) q^{25} +(1059.89 - 588.185i) q^{26} +(-581.958 - 439.051i) q^{27} +(-626.721 - 390.765i) q^{28} +(357.370 + 618.983i) q^{29} +(870.331 + 820.617i) q^{30} +(-985.186 - 568.798i) q^{31} +(-926.995 + 435.035i) q^{32} +(488.601 + 445.280i) q^{33} +(-624.267 - 374.681i) q^{34} +1533.80i q^{35} +(-1158.50 - 580.942i) q^{36} +1008.45 q^{37} +(646.803 - 1077.66i) q^{38} +(2664.30 + 583.059i) q^{39} +(1785.20 + 1155.59i) q^{40} +(-557.553 + 965.709i) q^{41} +(-477.082 - 1591.81i) q^{42} +(-2182.06 + 1259.82i) q^{43} +(997.257 + 621.796i) q^{44} +(249.164 + 2679.89i) q^{45} +(652.014 + 1174.90i) q^{46} +(-980.476 + 566.078i) q^{47} +(-2212.16 - 644.019i) q^{48} +(-135.117 + 234.029i) q^{49} +(32.5048 - 1916.05i) q^{50} +(-496.857 - 1561.00i) q^{51} +(4845.84 + 164.462i) q^{52} -1057.77 q^{53} +(-1092.16 - 2703.75i) q^{54} -2440.63i q^{55} +(-1345.07 - 2630.28i) q^{56} +(2694.73 - 857.713i) q^{57} +(-48.4939 + 2858.55i) q^{58} +(-878.476 - 507.188i) q^{59} +(1295.74 + 4606.00i) q^{60} +(-430.304 - 745.308i) q^{61} +(-2208.02 - 3978.77i) q^{62} +(1561.69 - 3397.22i) q^{63} +(-4074.80 - 416.161i) q^{64} +(-5034.65 - 8720.27i) q^{65} +(759.148 + 2532.94i) q^{66} +(-559.041 - 322.762i) q^{67} +(-1369.76 - 2570.07i) q^{68} +(-646.331 + 2953.42i) q^{69} +(-3157.28 + 5260.44i) q^{70} +9567.89i q^{71} +(-2777.43 - 4377.18i) q^{72} +1899.10 q^{73} +(3458.66 + 2075.86i) q^{74} +(2904.30 - 3186.85i) q^{75} +(4436.65 - 2364.59i) q^{76} +(-1695.27 + 2936.29i) q^{77} +(7937.48 + 7484.09i) q^{78} +(6768.11 - 3907.57i) q^{79} +(3743.90 + 7638.08i) q^{80} +(2176.75 - 6189.38i) q^{81} +(-3900.11 + 2164.37i) q^{82} +(7052.56 - 4071.80i) q^{83} +(1640.46 - 6441.47i) q^{84} +(-3024.04 + 5237.78i) q^{85} +(-10077.1 - 170.953i) q^{86} +(-4332.92 + 4754.46i) q^{87} +(2140.32 + 4185.39i) q^{88} +7653.39 q^{89} +(-4661.92 + 9704.05i) q^{90} +13988.4i q^{91} +(-182.309 + 5371.70i) q^{92} +(2188.78 - 10001.7i) q^{93} +(-4527.97 - 76.8149i) q^{94} +(-9041.87 - 5220.33i) q^{95} +(-6261.31 - 6762.45i) q^{96} +(-6366.75 - 11027.5i) q^{97} +(-945.149 + 524.510i) q^{98} +(-2485.01 + 5405.75i) 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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