LMFDB - Embedded newform 61.6.g.a.3.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,6,Mod(3,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("61.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	61.g (of order $10$, degree $4$, 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:	$9.78341300859$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$26$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			3.12
Character	$\chi$	$=$	61.3
Dual form			61.6.g.a.41.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.28313 - 0.741832i) q^{2} +(-0.718823 + 2.21231i) q^{3} +(-21.2262 - 15.4217i) q^{4} +(-84.4577 - 61.3621i) q^{5} +(3.28233 - 4.51774i) q^{6} +(78.0713 - 25.3669i) q^{7} +(82.1753 + 113.105i) q^{8} +(192.214 + 139.651i) q^{9} +O(q^{10})$	\(q+(-2.28313 - 0.741832i) q^{2} +(-0.718823 + 2.21231i) q^{3} +(-21.2262 - 15.4217i) q^{4} +(-84.4577 - 61.3621i) q^{5} +(3.28233 - 4.51774i) q^{6} +(78.0713 - 25.3669i) q^{7} +(82.1753 + 113.105i) q^{8} +(192.214 + 139.651i) q^{9} +(147.307 + 202.751i) q^{10} +281.836i q^{11} +(49.3755 - 35.8734i) q^{12} -627.079 q^{13} -197.065 q^{14} +(196.462 - 142.738i) q^{15} +(155.734 + 479.300i) q^{16} +(165.107 - 227.250i) q^{17} +(-335.250 - 461.432i) q^{18} +(-509.277 + 1567.39i) q^{19} +(846.406 + 2604.97i) q^{20} +190.952i q^{21} +(209.075 - 643.467i) q^{22} +(1537.23 - 2115.82i) q^{23} +(-309.292 + 100.495i) q^{24} +(2402.12 + 7392.96i) q^{25} +(1431.70 + 465.187i) q^{26} +(-904.422 + 657.101i) q^{27} +(-2048.36 - 665.552i) q^{28} +1277.42i q^{29} +(-554.436 + 180.147i) q^{30} +(5915.81 - 1922.16i) q^{31} -5683.59i q^{32} +(-623.509 - 202.590i) q^{33} +(-545.542 + 396.359i) q^{34} +(-8150.29 - 2648.19i) q^{35} +(-1926.30 - 5928.53i) q^{36} +(-9701.46 + 3152.20i) q^{37} +(2325.49 - 3200.76i) q^{38} +(450.759 - 1387.29i) q^{39} -14595.0i q^{40} +(2703.05 + 8319.13i) q^{41} +(141.655 - 435.968i) q^{42} +(9303.90 + 12805.7i) q^{43} +(4346.40 - 5982.31i) q^{44} +(-7664.61 - 23589.3i) q^{45} +(-5079.27 + 3690.31i) q^{46} -5842.74 q^{47} -1172.31 q^{48} +(-8145.50 + 5918.05i) q^{49} -18661.0i q^{50} +(384.066 + 528.621i) q^{51} +(13310.5 + 9670.64i) q^{52} +(4526.16 + 6229.73i) q^{53} +(2552.37 - 829.315i) q^{54} +(17294.1 - 23803.2i) q^{55} +(9284.65 + 6745.69i) q^{56} +(-3101.48 - 2253.36i) q^{57} +(947.628 - 2916.50i) q^{58} +(-36599.2 - 11891.8i) q^{59} -6371.41 q^{60} +(-26711.3 + 11450.0i) q^{61} -14932.5 q^{62} +(18548.9 + 6026.90i) q^{63} +(767.219 - 2361.26i) q^{64} +(52961.6 + 38478.9i) q^{65} +(1273.26 + 925.078i) q^{66} +(8020.59 - 11039.4i) q^{67} +(-7009.19 + 2277.42i) q^{68} +(3575.84 + 4921.73i) q^{69} +(16643.6 + 12092.3i) q^{70} +(1510.23 + 2078.66i) q^{71} +33216.1i q^{72} +(-56278.5 + 40888.7i) q^{73} +24488.1 q^{74} -18082.2 q^{75} +(34982.0 - 25415.9i) q^{76} +(7149.31 + 22003.3i) q^{77} +(-2058.28 + 2832.98i) q^{78} +(335.956 + 462.403i) q^{79} +(16257.9 - 50036.8i) q^{80} +(17037.2 + 52435.2i) q^{81} -20998.8i q^{82} +(-6463.39 + 19892.3i) q^{83} +(2944.82 - 4053.19i) q^{84} +(-27889.1 + 9061.73i) q^{85} +(-11742.3 - 36139.0i) q^{86} +(-2826.04 - 918.236i) q^{87} +(-31877.0 + 23160.0i) q^{88} +(358.811 + 116.585i) q^{89} +59543.1i q^{90} +(-48956.9 + 15907.0i) q^{91} +(-65259.1 + 21204.0i) q^{92} +14469.3i q^{93} +(13339.7 + 4334.34i) q^{94} +(139191. - 101128. i) q^{95} +(12573.9 + 4085.50i) q^{96} +(22653.9 + 69721.4i) q^{97} +(22987.4 - 7469.06i) q^{98} +(-39358.8 + 54172.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9}+O(q^{10}) $ 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9} - 595 q^{10} + 1982 q^{12} + 2372 q^{13} - 4474 q^{14} - 1149 q^{15} - 8631 q^{16} + 950 q^{17} + 4340 q^{18} - 5597 q^{19} - 6627 q^{20} - 8639 q^{22} + 9065 q^{23} + 17220 q^{24} - 7694 q^{25} + 14810 q^{26} + 4500 q^{27} + 19835 q^{28} - 44585 q^{30} + 10905 q^{31} - 19205 q^{33} - 15376 q^{34} - 43790 q^{35} - 25135 q^{36} - 5 q^{37} + 17555 q^{38} + 29401 q^{39} - 21014 q^{41} + 62197 q^{42} - 31625 q^{43} + 146190 q^{44} + 153742 q^{45} + 13387 q^{46} + 27326 q^{47} - 82968 q^{48} + 14694 q^{49} + 34090 q^{51} + 90072 q^{52} - 40270 q^{53} - 13760 q^{54} + 25140 q^{55} - 97860 q^{56} + 114893 q^{57} - 18003 q^{58} - 117435 q^{59} - 536650 q^{60} - 121867 q^{61} - 157388 q^{62} - 160825 q^{63} + 132509 q^{64} - 155852 q^{65} + 308443 q^{66} + 101665 q^{67} + 303780 q^{68} + 281945 q^{69} + 264985 q^{70} + 160970 q^{71} + 127669 q^{73} - 133952 q^{74} - 139592 q^{75} - 641111 q^{76} + 128917 q^{77} + 1670 q^{78} + 187940 q^{79} + 785373 q^{80} - 453473 q^{81} - 301209 q^{83} + 100475 q^{84} - 340045 q^{85} - 462669 q^{86} + 189245 q^{87} - 881635 q^{88} - 201970 q^{89} + 93865 q^{91} - 622085 q^{92} - 285265 q^{94} - 113308 q^{95} + 1215465 q^{96} - 342131 q^{97} - 616150 q^{98} + 714235 q^{99}+O(q^{100}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9 - 595 * q^10 + 1982 * q^12 + 2372 * q^13 - 4474 * q^14 - 1149 * q^15 - 8631 * q^16 + 950 * q^17 + 4340 * q^18 - 5597 * q^19 - 6627 * q^20 - 8639 * q^22 + 9065 * q^23 + 17220 * q^24 - 7694 * q^25 + 14810 * q^26 + 4500 * q^27 + 19835 * q^28 - 44585 * q^30 + 10905 * q^31 - 19205 * q^33 - 15376 * q^34 - 43790 * q^35 - 25135 * q^36 - 5 * q^37 + 17555 * q^38 + 29401 * q^39 - 21014 * q^41 + 62197 * q^42 - 31625 * q^43 + 146190 * q^44 + 153742 * q^45 + 13387 * q^46 + 27326 * q^47 - 82968 * q^48 + 14694 * q^49 + 34090 * q^51 + 90072 * q^52 - 40270 * q^53 - 13760 * q^54 + 25140 * q^55 - 97860 * q^56 + 114893 * q^57 - 18003 * q^58 - 117435 * q^59 - 536650 * q^60 - 121867 * q^61 - 157388 * q^62 - 160825 * q^63 + 132509 * q^64 - 155852 * q^65 + 308443 * q^66 + 101665 * q^67 + 303780 * q^68 + 281945 * q^69 + 264985 * q^70 + 160970 * q^71 + 127669 * q^73 - 133952 * q^74 - 139592 * q^75 - 641111 * q^76 + 128917 * q^77 + 1670 * q^78 + 187940 * q^79 + 785373 * q^80 - 453473 * q^81 - 301209 * q^83 + 100475 * q^84 - 340045 * q^85 - 462669 * q^86 + 189245 * q^87 - 881635 * q^88 - 201970 * q^89 + 93865 * q^91 - 622085 * q^92 - 285265 * q^94 - 113308 * q^95 + 1215465 * q^96 - 342131 * q^97 - 616150 * q^98 + 714235 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−2.28313	−	0.741832i	−0.403603	−	0.131139i	0.100179	−	0.994969i	$-0.468059\pi$
$2$	−2.28313	−	0.741832i	−0.403603	−	0.131139i	−0.503782	+	0.863831i	$0.668059\pi$
$3$	−0.718823	+	2.21231i	−0.0461125	+	0.141920i	−0.971462	−	0.237196i	$-0.923772\pi$
$3$	−0.718823	+	2.21231i	−0.0461125	+	0.141920i	0.925349	+	0.379116i	$0.123772\pi$
$4$	−21.2262	−	15.4217i	−0.663319	−	0.481929i
$5$	−84.4577	−	61.3621i	−1.51083	−	1.09768i	−0.965809	−	0.259253i	$-0.916524\pi$
$5$	−84.4577	−	61.3621i	−1.51083	−	1.09768i	−0.545016	−	0.838426i	$-0.683476\pi$
$6$	3.28233	−	4.51774i	0.0372223	−	0.0512322i
$7$	78.0713	−	25.3669i	0.602208	−	0.195669i	0.00798299	−	0.999968i	$-0.497459\pi$
$7$	78.0713	−	25.3669i	0.602208	−	0.195669i	0.594225	+	0.804299i	$0.297459\pi$
$8$	82.1753	+	113.105i	0.453959	+	0.624821i
$9$	192.214	+	139.651i	0.791002	+	0.574697i
$10$	147.307	+	202.751i	0.465826	+	0.641155i
$11$			281.836i			0.702287i	0.936322	+	0.351144i	$0.114207\pi$
$11$			281.836i			0.702287i	−0.936322	+	0.351144i	$0.885793\pi$
$12$	49.3755	−	35.8734i	0.0989826	−	0.0719150i
$13$	−627.079			−1.02911			−0.514557	−	0.857456i	$-0.672044\pi$
$13$	−627.079			−1.02911			−0.514557	+	0.857456i	$0.672044\pi$
$14$	−197.065			−0.268713
$15$	196.462	−	142.738i	0.225450	−	0.163799i
$16$	155.734	+	479.300i	0.152084	+	0.468067i
$17$	165.107	−	227.250i	0.138562	−	0.190714i	−0.734097	−	0.679045i	$-0.762394\pi$
$17$	165.107	−	227.250i	0.138562	−	0.190714i	0.872658	+	0.488331i	$0.162394\pi$
$18$	−335.250	−	461.432i	−0.243886	−	0.335681i
$19$	−509.277	+	1567.39i	−0.323646	+	0.996080i	0.648402	+	0.761298i	$0.275438\pi$
$19$	−509.277	+	1567.39i	−0.323646	+	0.996080i	−0.972048	+	0.234782i	$0.924562\pi$
$20$	846.406	+	2604.97i	0.473155	+	1.45622i
$21$			190.952i			0.0944880i
$22$	209.075	−	643.467i	0.0920971	−	0.283446i
$23$	1537.23	−	2115.82i	0.605925	−	0.833985i	−0.390309	−	0.920684i	$-0.627632\pi$
$23$	1537.23	−	2115.82i	0.605925	−	0.833985i	0.996235	+	0.0866990i	$0.0276318\pi$
$24$	−309.292	+	100.495i	−0.109608	+	0.0356137i
$25$	2402.12	+	7392.96i	0.768678	+	2.36575i
$26$	1431.70	+	465.187i	0.415354	+	0.134957i
$27$	−904.422	+	657.101i	−0.238760	+	0.173469i
$28$	−2048.36	−	665.552i	−0.493754	−	0.160431i
$29$			1277.42i			0.282057i	0.990006	+	0.141029i	$0.0450410\pi$
$29$			1277.42i			0.282057i	−0.990006	+	0.141029i	$0.954959\pi$
$30$	−554.436	+	180.147i	−0.112473	+	0.0365447i
$31$	5915.81	−	1922.16i	1.10563	−	0.359241i	0.301363	−	0.953509i	$-0.402558\pi$
$31$	5915.81	−	1922.16i	1.10563	−	0.359241i	0.804267	+	0.594268i	$0.202558\pi$
$32$		−	5683.59i		−	0.981178i
$33$	−623.509	−	202.590i	−0.0996685	−	0.0323842i
$34$	−545.542	+	396.359i	−0.0809340	+	0.0588020i
$35$	−8150.29	−	2648.19i	−1.12461	−	0.365409i
$36$	−1926.30	−	5928.53i	−0.247723	−	0.762414i
$37$	−9701.46	+	3152.20i	−1.16502	+	0.378538i	−0.826782	−	0.562523i	$-0.809831\pi$
$37$	−9701.46	+	3152.20i	−1.16502	+	0.378538i	−0.338237	+	0.941061i	$0.609831\pi$
$38$	2325.49	−	3200.76i	0.261249	−	0.359579i
$39$	450.759	−	1387.29i	0.0474551	−	0.146052i
$40$		−	14595.0i		−	1.44230i
$41$	2703.05	+	8319.13i	0.251128	+	0.772891i	0.994568	+	0.104089i	$0.0331927\pi$
$41$	2703.05	+	8319.13i	0.251128	+	0.772891i	−0.743440	+	0.668802i	$0.766807\pi$
$42$	141.655	−	435.968i	0.0123910	−	0.0381357i
$43$	9303.90	+	12805.7i	0.767351	+	1.05617i	0.996567	+	0.0827925i	$0.0263839\pi$
$43$	9303.90	+	12805.7i	0.767351	+	1.05617i	−0.229216	+	0.973376i	$0.573616\pi$
$44$	4346.40	−	5982.31i	0.338453	−	0.465840i
$45$	−7664.61	−	23589.3i	−0.564234	−	1.73653i
$46$	−5079.27	+	3690.31i	−0.353921	+	0.257139i
$47$	−5842.74			−0.385809			−0.192904	−	0.981218i	$-0.561791\pi$
$47$	−5842.74			−0.385809			−0.192904	+	0.981218i	$0.561791\pi$
$48$	−1172.31			−0.0734409
$49$	−8145.50	+	5918.05i	−0.484649	+	0.352118i
$50$		−	18661.0i		−	1.05563i
$51$	384.066	+	528.621i	0.0206766	+	0.0284590i
$52$	13310.5	+	9670.64i	0.682631	+	0.495960i
$53$	4526.16	+	6229.73i	0.221330	+	0.304635i	0.905214	−	0.424956i	$-0.139710\pi$
$53$	4526.16	+	6229.73i	0.221330	+	0.304635i	−0.683884	+	0.729591i	$0.739710\pi$
$54$	2552.37	−	829.315i	0.119113	−	0.0387021i
$55$	17294.1	−	23803.2i	0.770886	−	1.06103i
$56$	9284.65	+	6745.69i	0.395636	+	0.287446i
$57$	−3101.48	−	2253.36i	−0.126439	−	0.0918635i
$58$	947.628	−	2916.50i	0.0369886	−	0.113839i
$59$	−36599.2	−	11891.8i	−1.36881	−	0.444752i	−0.469832	−	0.882756i	$-0.655686\pi$
$59$	−36599.2	−	11891.8i	−1.36881	−	0.444752i	−0.898973	+	0.438004i	$0.855686\pi$
$60$	−6371.41			−0.228485
$61$	−26711.3	+	11450.0i	−0.919117	+	0.393984i
$61$	−26711.3	+	11450.0i	−0.919117	+	0.393984i
$62$	−14932.5			−0.493346
$63$	18548.9	+	6026.90i	0.588798	+	0.191312i
$64$	767.219	−	2361.26i	0.0234137	−	0.0720598i
$65$	52961.6	+	38478.9i	1.55481	+	1.12964i
$66$	1273.26	+	925.078i	0.0359797	+	0.0261408i
$67$	8020.59	−	11039.4i	0.218283	−	0.300440i	−0.685807	−	0.727784i	$-0.740550\pi$
$67$	8020.59	−	11039.4i	0.218283	−	0.300440i	0.904089	+	0.427343i	$0.140550\pi$
$68$	−7009.19	+	2277.42i	−0.183821	+	0.0597271i
$69$	3575.84	+	4921.73i	0.0904182	+	0.124450i
$70$	16643.6	+	12092.3i	0.405978	+	0.294961i
$71$	1510.23	+	2078.66i	0.0355548	+	0.0489369i	0.826424	−	0.563048i	$-0.190371\pi$
$71$	1510.23	+	2078.66i	0.0355548	+	0.0489369i	−0.790870	+	0.611985i	$0.790371\pi$
$72$			33216.1i			0.755123i
$73$	−56278.5	+	40888.7i	−1.23605	+	0.898041i	−0.997328	−	0.0730480i	$-0.976727\pi$
$73$	−56278.5	+	40888.7i	−1.23605	+	0.898041i	−0.238719	+	0.971089i	$0.576727\pi$
$74$	24488.1			0.519847
$75$	−18082.2			−0.371192
$76$	34982.0	−	25415.9i	0.694720	−	0.504744i
$77$	7149.31	+	22003.3i	0.137416	+	0.422923i
$78$	−2058.28	+	2832.98i	−0.0383060	+	0.0527237i
$79$	335.956	+	462.403i	0.00605639	+	0.00833591i	0.812034	−	0.583609i	$-0.198360\pi$
$79$	335.956	+	462.403i	0.00605639	+	0.00833591i	−0.805978	+	0.591945i	$0.798360\pi$
$80$	16257.9	−	50036.8i	0.284014	−	0.874106i
$81$	17037.2	+	52435.2i	0.288527	+	0.887995i
$82$		−	20998.8i		−	0.344874i
$83$	−6463.39	+	19892.3i	−0.102983	+	0.316949i	−0.989252	−	0.146222i	$-0.953288\pi$
$83$	−6463.39	+	19892.3i	−0.102983	+	0.316949i	0.886269	+	0.463171i	$0.153288\pi$
$84$	2944.82	−	4053.19i	0.0455365	−	0.0626757i
$85$	−27889.1	+	9061.73i	−0.418685	+	0.136039i
$86$	−11742.3	−	36139.0i	−0.171201	−	0.526902i
$87$	−2826.04	−	918.236i	−0.0400295	−	0.0130064i
$88$	−31877.0	+	23160.0i	−0.438804	+	0.318810i
$89$	358.811	+	116.585i	0.00480165	+	0.00156015i	0.311417	−	0.950273i	$-0.399196\pi$
$89$	358.811	+	116.585i	0.00480165	+	0.00156015i	−0.306615	+	0.951834i	$0.599196\pi$
$90$			59543.1i			0.774863i
$91$	−48956.9	+	15907.0i	−0.619741	+	0.201366i
$92$	−65259.1	+	21204.0i	−0.803843	+	0.261185i
$93$			14469.3i			0.173476i
$94$	13339.7	+	4334.34i	0.155714	+	0.0505945i
$95$	139191.	−	101128.i	1.58235	−	1.14964i
$96$	12573.9	+	4085.50i	0.139249	+	0.0452446i
$97$	22653.9	+	69721.4i	0.244463	+	0.752379i	0.995724	+	0.0923746i	$0.0294457\pi$
$97$	22653.9	+	69721.4i	0.244463	+	0.752379i	−0.751262	+	0.660005i	$0.770554\pi$
$98$	22987.4	−	7469.06i	0.241782	−	0.0785598i
$99$	−39358.8	+	54172.7i	−0.403602	+	0.555511i
$100$	63024.4	−	193969.i	0.630244	−	1.93969i
$101$			19937.6i			0.194478i	0.995261	+	0.0972389i	$0.0310011\pi$
$101$			19937.6i			0.194478i	−0.995261	+	0.0972389i	$0.968999\pi$
$102$	−484.722	−	1491.82i	−0.00461309	−	0.0141976i
$103$	−53951.4	+	166045.i	−0.501083	+	1.54217i	0.306174	+	0.951975i	$0.400951\pi$
$103$	−53951.4	+	166045.i	−0.501083	+	1.54217i	−0.807257	+	0.590200i	$0.799049\pi$
$104$	−51530.4	−	70925.5i	−0.467175	−	0.643012i
$105$	11717.2	−	16127.4i	0.103717	−	0.142755i
$106$	−5712.39	−	17580.9i	−0.0493802	−	0.151977i
$107$	94562.8	−	68703.9i	0.798474	−	0.580125i	−0.111992	−	0.993709i	$-0.535723\pi$
$107$	94562.8	−	68703.9i	0.798474	−	0.580125i	0.910466	+	0.413584i	$0.135723\pi$
$108$	29331.1			0.241974
$109$	172369.			1.38961			0.694806	−	0.719197i	$-0.255490\pi$
$109$	172369.			1.38961			0.694806	+	0.719197i	$0.255490\pi$
$110$	−57142.5	+	41516.5i	−0.450275	+	0.327144i
$111$		−	23728.5i		−	0.182795i
$112$	24316.7	+	33469.1i	0.183172	+	0.252115i
$113$	−165367.	−	120146.i	−1.21829	−	0.885142i	−0.222336	−	0.974970i	$-0.571368\pi$
$113$	−165367.	−	120146.i	−1.21829	−	0.885142i	−0.995957	+	0.0898280i	$0.971368\pi$
$114$	5409.46	+	7445.48i	0.0389845	+	0.0536575i
$115$	−259662.	+	84369.2i	−1.83090	+	0.594894i
$116$	19700.0	−	27114.7i	0.135932	−	0.187094i
$117$	−120533.	−	87572.3i	−0.814032	−	0.591429i
$118$	74738.9	+	54301.0i	0.494130	+	0.359007i
$119$	7125.49	−	21930.0i	0.0461261	−	0.141962i
$120$	32288.7	+	10491.2i	0.204690	+	0.0665079i
$121$	81619.4			0.506792
$122$	69479.3	−	6326.35i	0.422625	−	0.0384816i
$123$	−20347.5			−0.121269
$124$	−155213.	−	50431.8i	−0.906514	−	0.294544i
$125$	149958.	−	461522.i	0.858408	−	2.64191i
$126$	−37878.5	−	27520.3i	−0.212553	−	0.154428i
$127$	13132.0	+	9540.93i	0.0722471	+	0.0524906i	0.623323	−	0.781965i	$-0.285782\pi$
$127$	13132.0	+	9540.93i	0.0722471	+	0.0524906i	−0.551075	+	0.834455i	$0.685782\pi$
$128$	−110407.	+	151962.i	−0.595622	+	0.819803i
$129$	−35018.1	+	11378.1i	−0.185276	+	0.0601997i
$130$	−92373.2	−	127141.i	−0.479388	−	0.659821i
$131$	−98302.7	−	71421.1i	−0.500480	−	0.363620i	0.308720	−	0.951153i	$-0.400099\pi$
$131$	−98302.7	−	71421.1i	−0.500480	−	0.363620i	−0.809200	+	0.587533i	$0.800099\pi$
$132$	10110.4	+	13915.8i	0.0505050	+	0.0695142i
$133$			135287.i			0.663175i
$134$	−26501.4	+	19254.4i	−0.127499	+	0.0926334i
$135$	116707.			0.551138
$136$	39270.8			0.182063
$137$	323058.	−	234715.i	1.47055	−	1.06842i	0.490092	−	0.871670i	$-0.336963\pi$
$137$	323058.	−	234715.i	1.47055	−	1.06842i	0.980455	−	0.196745i	$-0.0630370\pi$
$138$	−4513.00	−	13889.6i	−0.0201729	−	0.0620857i
$139$	−229987.	+	316550.i	−1.00964	+	1.38965i	−0.0904179	+	0.995904i	$0.528820\pi$
$139$	−229987.	+	316550.i	−1.00964	+	1.38965i	−0.919220	+	0.393744i	$0.871180\pi$
$140$	132160.	+	181903.i	0.569876	+	0.784366i
$141$	4199.90	−	12926.0i	0.0177906	−	0.0547539i
$142$	−1906.03	−	5866.17i	−0.00793250	−	0.0244137i
$143$		−	176733.i		−	0.722734i
$144$	−37000.7	+	113876.i	−0.148698	+	0.457644i
$145$	78384.9	−	107888.i	0.309608	−	0.426139i
$146$	158823.	−	51604.8i	0.616641	−	0.200359i
$147$	−7237.39	−	22274.4i	−0.0276241	−	0.0850183i
$148$	254538.	+	82704.3i	0.955207	+	0.310366i
$149$	−109509.	+	79563.0i	−0.404096	+	0.293593i	−0.771207	−	0.636584i	$-0.780347\pi$
$149$	−109509.	+	79563.0i	−0.404096	+	0.293593i	0.367111	+	0.930177i	$0.380347\pi$
$150$	41284.0	+	13414.0i	0.149814	+	0.0486776i
$151$			61173.8i			0.218335i	0.994023	+	0.109167i	$0.0348185\pi$
$151$			61173.8i			0.218335i	−0.994023	+	0.109167i	$0.965182\pi$
$152$	−219129.	+	71199.5i	−0.769293	+	0.249958i
$153$	63471.6	−	20623.2i	0.219205	−	0.0712241i
$154$		−	55539.9i		−	0.188714i
$155$	−617584.	−	200665.i	−2.06475	−	0.670876i
$156$	−30962.3	+	22495.5i	−0.101864	+	0.0740088i
$157$	356763.	+	115919.i	1.15513	+	0.375324i	0.823073	−	0.567936i	$-0.192258\pi$
$157$	356763.	+	115919.i	1.15513	+	0.375324i	0.332056	+	0.943260i	$0.392258\pi$
$158$	−424.003	−	1304.95i	−0.00135122	−	0.00415863i
$159$	−17035.6	+	5535.20i	−0.0534398	+	0.0173636i
$160$	−348757.	+	480023.i	−1.07702	+	1.48239i
$161$	66341.9	−	204179.i	0.201708	−	0.620793i
$162$		−	132355.i		−	0.396235i
$163$	164867.	+	507407.i	0.486030	+	1.49585i	0.830483	+	0.557044i	$0.188065\pi$
$163$	164867.	+	507407.i	0.486030	+	1.49585i	−0.344453	+	0.938804i	$0.611935\pi$
$164$	70920.0	−	218269.i	0.205901	−	0.633699i
$165$	40228.8	+	55370.1i	0.115034	+	0.158331i
$166$	29513.4	−	40621.8i	0.0831285	−	0.114417i
$167$	−36532.7	−	112436.i	−0.101366	−	0.311971i	0.887495	−	0.460818i	$-0.152444\pi$
$167$	−36532.7	−	112436.i	−0.101366	−	0.311971i	−0.988860	+	0.148847i	$0.952444\pi$
$168$	−21597.6	+	15691.6i	−0.0590380	+	0.0428936i
$169$	21934.6			0.0590763
$170$	70396.7			0.186823
$171$	−316779.	+	230153.i	−0.828448	+	0.601903i
$172$		−	415299.i		−	1.07038i
$173$	−43508.4	−	59884.2i	−0.110524	−	0.152124i	0.750171	−	0.661243i	$-0.229971\pi$
$173$	−43508.4	−	59884.2i	−0.110524	−	0.152124i	−0.860696	+	0.509120i	$0.829971\pi$
$174$	5771.03	+	4192.90i	0.0144504	+	0.0104988i
$175$	375073.	+	516244.i	0.925807	+	1.27426i
$176$	−135084.	+	43891.5i	−0.328717	+	0.106807i
$177$	52616.7	−	72420.7i	0.126238	−	0.173752i
$178$	−732.724	−	532.355i	−0.00173337	−	0.00125936i
$179$	581647.	+	422592.i	1.35684	+	0.985799i	0.998639	+	0.0521524i	$0.0166082\pi$
$179$	581647.	+	422592.i	1.35684	+	0.985799i	0.358196	+	0.933646i	$0.383392\pi$
$180$	−201097.	+	618912.i	−0.462619	+	1.42380i
$181$	−756490.	−	245799.i	−1.71635	−	0.557677i	−0.724984	−	0.688766i	$-0.758153\pi$
$181$	−756490.	−	245799.i	−1.71635	−	0.557677i	−0.991371	+	0.131089i	$0.958153\pi$
$182$	123575.			0.276536
$183$	−6130.12	−	67324.2i	−0.0135314	−	0.148608i
$184$	365631.			0.796156
$185$	1.01279e6	+	329075.i	2.17565	+	0.706913i
$186$	10733.8	−	33035.2i	0.0227494	−	0.0700156i
$187$	64047.4	+	46533.1i	0.133936	+	0.0973102i
$188$	124019.	+	90105.2i	0.255914	+	0.185932i
$189$	−53940.8	+	74243.1i	−0.109841	+	0.151183i
$190$	−392811.	+	127632.i	−0.789404	+	0.256493i
$191$	546324.	+	751951.i	1.08360	+	1.49144i	0.855501	+	0.517802i	$0.173249\pi$
$191$	546324.	+	751951.i	1.08360	+	1.49144i	0.228094	+	0.973639i	$0.426751\pi$
$192$	4672.34	+	3394.65i	0.00914705	+	0.00664572i
$193$	−312099.	−	429567.i	−0.603113	−	0.830113i	0.392876	−	0.919591i	$-0.371480\pi$
$193$	−312099.	−	429567.i	−0.603113	−	0.830113i	−0.995989	+	0.0894780i	$0.971480\pi$
$194$		−	175988.i		−	0.335721i
$195$	−123197.	+	89508.0i	−0.232014	+	0.168568i
$196$	264165.			0.491173
$197$	−235472.			−0.432288			−0.216144	−	0.976362i	$-0.569348\pi$
$197$	−235472.			−0.432288			−0.216144	+	0.976362i	$0.569348\pi$
$198$	130048.	−	94485.5i	0.235744	−	0.171278i
$199$	−187769.	−	577893.i	−0.336117	−	1.03446i	−0.966169	−	0.257910i	$-0.916966\pi$
$199$	−187769.	−	577893.i	−0.336117	−	1.03446i	0.630052	−	0.776553i	$-0.283034\pi$
$200$	−638783.	+	879209.i	−1.12922	+	1.55424i
$201$	18657.2	+	25679.4i	0.0325728	+	0.0448327i
$202$	14790.4	−	45520.1i	0.0255036	−	0.0784919i
$203$	32404.1	+	99729.5i	0.0551899	+	0.169857i
$204$		−	17143.6i		−	0.0288420i
$205$	282186.	−	868479.i	0.468976	−	1.44336i
$206$	246356.	−	339079.i	0.404478	−	0.556716i
$207$	590953.	−	192012.i	0.958577	−	0.311460i
$208$	−97657.5	−	300559.i	−0.156512	−	0.481694i
$209$	−441748.	−	143533.i	−0.699534	−	0.227293i
$210$	−38715.7	+	28128.6i	−0.0605814	+	0.0440150i
$211$	−1.08646e6	−	353014.i	−1.68000	−	0.545865i	−0.695088	−	0.718924i	$-0.744635\pi$
$211$	−1.08646e6	−	353014.i	−1.68000	−	0.545865i	−0.984911	+	0.173059i	$0.944635\pi$
$212$		−	202035.i		−	0.308735i
$213$	−5684.22	+	1846.92i	−0.00858464	+	0.00278932i
$214$	−266865.	+	86709.8i	−0.398344	+	0.129430i
$215$		−	1.65245e6i		−	2.43799i
$216$	−148642.	−	48296.8i	−0.216774	−	0.0704343i
$217$	413096.	−	300132.i	0.595527	−	0.432676i
$218$	−393541.	−	127869.i	−0.560852	−	0.182232i
$219$	−50004.2	−	153897.i	−0.0704525	−	0.216830i
$220$	−734174.	+	238548.i	−1.02269	+	0.332291i
$221$	−103535.	+	142504.i	−0.142596	+	0.196266i
$222$	−17602.6	+	54175.2i	−0.0239714	+	0.0737765i
$223$		−	1.32027e6i		−	1.77787i	−0.458035	−	0.888934i	$-0.651447\pi$
$223$		−	1.32027e6i		−	1.77787i	0.458035	−	0.888934i	$-0.348553\pi$
$224$	−144175.	−	443725.i	−0.191986	−	0.590873i
$225$	−570717.	+	1.75649e6i	−0.751561	+	2.31307i
$226$	288425.	+	396983.i	0.375631	+	0.517012i
$227$	50741.4	−	69839.6i	0.0653579	−	0.0899575i	−0.775087	−	0.631855i	$-0.782294\pi$
$227$	50741.4	−	69839.6i	0.0653579	−	0.0899575i	0.840445	+	0.541897i	$0.182294\pi$
$228$	31082.0	+	95660.4i	0.0395978	+	0.121870i
$229$	503657.	−	365928.i	0.634667	−	0.461112i	−0.223347	−	0.974739i	$-0.571698\pi$
$229$	503657.	−	365928.i	0.634667	−	0.461112i	0.858014	+	0.513627i	$0.171698\pi$
$230$	655428.			0.816969
$231$	−53817.2			−0.0663577
$232$	−144482.	+	104972.i	−0.176235	+	0.128042i
$233$		−	1.13856e6i		−	1.37394i	−0.726686	−	0.686969i	$-0.758941\pi$
$233$		−	1.13856e6i		−	1.37394i	0.726686	−	0.686969i	$-0.241059\pi$
$234$	210228.	+	289354.i	0.250987	+	0.345454i
$235$	493465.	+	358523.i	0.582890	+	0.423494i
$236$	593470.	+	816841.i	0.693615	+	0.954680i
$237$	−1264.47	+	410.852i	−0.00146231	+	0.000475132i
$238$	−32536.8	+	44783.0i	−0.0372333	+	0.0512473i
$239$	−1.26479e6	−	918927.i	−1.43227	−	1.04061i	−0.989588	−	0.143928i	$-0.954027\pi$
$239$	−1.26479e6	−	918927.i	−1.43227	−	1.04061i	−0.442683	−	0.896678i	$-0.645973\pi$
$240$	99010.3	+	71935.2i	0.110956	+	0.0806145i
$241$	−269620.	+	829804.i	−0.299026	+	0.920308i	0.682813	+	0.730593i	$0.260756\pi$
$241$	−269620.	+	829804.i	−0.299026	+	0.920308i	−0.981839	+	0.189715i	$0.939244\pi$
$242$	−186347.	−	60547.9i	−0.204543	−	0.0664601i
$243$	−399906.			−0.434452
$244$	743558.	+	168896.i	0.799540	+	0.181612i
$245$	1.05109e6			1.11873
$246$	46455.9	+	15094.4i	0.0489444	+	0.0159030i
$247$	319357.	−	982879.i	0.333069	−	1.02508i
$248$	703539.	+	511151.i	0.726372	+	0.527740i
$249$	−39361.8	−	28598.0i	−0.0402325	−	0.0292306i
$250$	−684745.	+	942470.i	−0.692913	+	0.953713i
$251$	206884.	−	67220.8i	0.207273	−	0.0673472i	−0.203540	−	0.979067i	$-0.565245\pi$
$251$	206884.	−	67220.8i	0.207273	−	0.0673472i	0.410813	+	0.911719i	$0.365245\pi$
$252$	−300777.	−	413984.i	−0.298362	−	0.410660i
$253$	596313.	+	433247.i	0.585697	+	0.425534i
$254$	−22904.1	−	31524.8i	−0.0222756	−	0.0306598i
$255$		−	68213.2i		−	0.0656928i
$256$	300527.	−	218346.i	0.286605	−	0.208231i
$257$	574677.			0.542739			0.271369	−	0.962475i	$-0.412524\pi$
$257$	574677.			0.542739			0.271369	+	0.962475i	$0.412524\pi$
$258$	88391.3			0.0826724
$259$	−677445.	+	492192.i	−0.627515	+	0.455917i
$260$	−530763.	−	1.63352e6i	−0.486931	−	1.49862i
$261$	−178393.	+	245537.i	−0.162097	+	0.223108i
$262$	171455.	+	235987.i	0.154311	+	0.212391i
$263$	−476562.	+	1.46671e6i	−0.424844	+	1.30754i	0.478299	+	0.878197i	$0.341253\pi$
$263$	−476562.	+	1.46671e6i	−0.424844	+	1.30754i	−0.903143	+	0.429339i	$0.858747\pi$
$264$	−28323.1	−	87169.6i	−0.0250110	−	0.0769760i
$265$		−	803884.i		−	0.703200i
$266$	100361.	−	308878.i	0.0869679	−	0.267660i
$267$	−515.843	+	709.997i	−0.000442832	+	0.000609507i
$268$	−340493.	+	110633.i	−0.289582	+	0.0940908i
$269$	−118257.	−	363957.i	−0.0996427	−	0.306669i	0.888793	−	0.458309i	$-0.151545\pi$
$269$	−118257.	−	363957.i	−0.0996427	−	0.306669i	−0.988436	+	0.151640i	$0.951545\pi$
$270$	−266456.	−	86576.7i	−0.222441	−	0.0722756i
$271$	−1.16577e6	+	846979.i	−0.964247	+	0.700567i	−0.954133	−	0.299382i	$-0.903219\pi$
$271$	−1.16577e6	+	846979.i	−0.964247	+	0.700567i	−0.0101140	+	0.999949i	$0.503219\pi$
$272$	134634.	+	43745.2i	0.110340	+	0.0358516i
$273$		−	119742.i		−	0.0972389i
$274$	−911701.	+	296230.i	−0.733628	+	0.238370i
$275$	−2.08360e6	+	677003.i	−1.66143	+	0.539833i
$276$		−	159615.i		−	0.126125i
$277$	1.13389e6	+	368424.i	0.887918	+	0.288502i	0.717241	−	0.696825i	$-0.245405\pi$
$277$	1.13389e6	+	368424.i	0.887918	+	0.288502i	0.170677	+	0.985327i	$0.445405\pi$
$278$	759915.	−	552111.i	0.589730	−	0.428464i
$279$	1.40553e6	+	456685.i	1.08101	+	0.351242i
$280$	−370230.	−	1.13945e6i	−0.282213	−	0.868562i
$281$	462030.	−	150123.i	0.349063	−	0.113418i	−0.129237	−	0.991614i	$-0.541253\pi$
$281$	462030.	−	150123.i	0.349063	−	0.113418i	0.478301	+	0.878196i	$0.341253\pi$
$282$	−19177.8	+	26396.0i	−0.0143607	+	0.0197658i
$283$	−270184.	+	831541.i	−0.200537	+	0.617189i	0.799330	+	0.600892i	$0.205188\pi$
$283$	−270184.	+	831541.i	−0.200537	+	0.617189i	−0.999867	+	0.0162969i	$0.994812\pi$
$284$		−	67412.3i		−	0.0495957i
$285$	123673.	+	380627.i	0.0901910	+	0.277579i
$286$	−131107.	+	403505.i	−0.0947784	+	0.291698i
$287$	422061.	+	580917.i	0.302462	+	0.416303i
$288$	793721.	−	1.09246e6i	0.563880	−	0.776114i
$289$	414378.	+	1.27532e6i	0.291845	+	0.898205i
$290$	−258997.	+	188172.i	−0.180842	+	0.131390i
$291$	−170529.			−0.118050
$292$	1.82515e6			1.25269
$293$	−813238.	+	590852.i	−0.553412	+	0.402077i	−0.829042	−	0.559187i	$-0.811114\pi$
$293$	−813238.	+	590852.i	−0.553412	+	0.402077i	0.275630	+	0.961264i	$0.411114\pi$
$294$			56224.2i			0.0379363i
$295$	2.36138e6	+	3.25016e6i	1.57983	+	2.17445i
$296$	−1.15375e6	−	838248.i	−0.765389	−	0.556087i
$297$	−185195.	−	254899.i	−0.121825	−	0.167678i
$298$	309045.	−	100415.i	0.201596	−	0.0655025i
$299$	−963964.	+	1.32678e6i	−0.623567	+	0.858266i
$300$	383817.	+	278859.i	0.246218	+	0.178888i
$301$	1.05121e6	+	763749.i	0.668764	+	0.485886i
$302$	45380.7	−	139667.i	0.0286321	−	0.0881207i
$303$	−44108.2	−	14331.6i	−0.0276002	−	0.00896786i
$304$	−830564.			−0.515453
$305$	2.95857e6	+	672027.i	1.82109	+	0.413654i
$306$	−160213.			−0.0978122
$307$	−191968.	−	62374.2i	−0.116247	−	0.0377711i	0.250316	−	0.968164i	$-0.419466\pi$
$307$	−191968.	−	62374.2i	−0.116247	−	0.0377711i	−0.366563	+	0.930393i	$0.619466\pi$
$308$	187577.	−	577302.i	0.112668	−	0.346758i
$309$	−328562.	−	238714.i	−0.195759	−	0.142227i
$310$	1.26116e6	+	916287.i	0.745360	+	0.541536i
$311$	−245655.	+	338115.i	−0.144021	+	0.198227i	−0.874933	−	0.484244i	$-0.839095\pi$
$311$	−245655.	+	338115.i	−0.144021	+	0.198227i	0.730912	+	0.682471i	$0.239095\pi$
$312$	193950.	−	63018.3i	0.112799	−	0.0366505i
$313$	−339278.	−	466976.i	−0.195747	−	0.269422i	0.699849	−	0.714291i	$-0.253251\pi$
$313$	−339278.	−	466976.i	−0.195747	−	0.269422i	−0.895596	+	0.444868i	$0.853251\pi$
$314$	−728542.	−	529316.i	−0.416994	−	0.302964i
$315$	−1.19677e6	−	1.64722e6i	−0.679572	−	0.935351i
$316$		−	14996.1i		−	0.00844812i
$317$	−1.38918e6	+	1.00930e6i	−0.776443	+	0.564119i	−0.903910	−	0.427724i	$-0.859316\pi$
$317$	−1.38918e6	+	1.00930e6i	−0.776443	+	0.564119i	0.127466	+	0.991843i	$0.459316\pi$
$318$	43000.6			0.0238455
$319$	−360022.			−0.198085
$320$	−209689.	+	152348.i	−0.114473	+	0.0831691i
$321$	84020.4	+	258588.i	0.0455116	+	0.140070i
$322$	−302934.	+	416952.i	−0.162820	+	0.224103i
$323$	272106.	+	374521.i	0.145121	+	0.199742i
$324$	447006.	−	1.37574e6i	0.236565	−	0.728073i
$325$	−1.50632e6	−	4.63597e6i	−0.791057	−	2.43462i
$326$		−	1.28078e6i		−	0.667467i
$327$	−123903.	+	381334.i	−0.0640785	+	0.197213i
$328$	−718808.	+	989354.i	−0.368917	+	0.507770i
$329$	−456151.	+	148212.i	−0.232337	+	0.0754909i
$330$	−50771.9	−	156260.i	−0.0256649	−	0.0789883i
$331$	−194309.	−	63134.9i	−0.0974817	−	0.0316737i	0.259870	−	0.965644i	$-0.416320\pi$
$331$	−194309.	−	63134.9i	−0.0974817	−	0.0316737i	−0.357352	+	0.933970i	$0.616320\pi$
$332$	443966.	−	322560.i	0.221057	−	0.160607i
$333$	−2.30496e6	−	748927.i	−1.13908	−	0.370108i
$334$			283807.i			0.139206i
$335$	−1.35480e6	+	440201.i	−0.659574	+	0.214309i
$336$	−91523.5	+	29737.8i	−0.0442267	+	0.0143701i
$337$		−	3.62412e6i		−	1.73831i	−0.494536	−	0.869157i	$-0.664662\pi$
$337$		−	3.62412e6i		−	1.73831i	0.494536	−	0.869157i	$-0.335338\pi$
$338$	−50079.5	−	16271.8i	−0.0238434	−	0.00774718i
$339$	384669.	−	279479.i	0.181798	−	0.132084i
$340$	731728.	+	237753.i	0.343283	+	0.111539i
$341$	541735.	+	1.66729e6i	0.252290	+	0.776470i
$342$	893980.	−	290472.i	0.413297	−	0.134288i
$343$	−1.29676e6	+	1.78483e6i	−0.595146	+	0.819148i
$344$	−683835.	+	2.10463e6i	−0.311570	+	0.958913i
$345$		−	635099.i		−	0.287272i
$346$	54911.1	+	168999.i	0.0246587	+	0.0758916i
$347$	721521.	−	2.22061e6i	0.321681	−	0.990032i	−0.651236	−	0.758876i	$-0.725749\pi$
$347$	721521.	−	2.22061e6i	0.321681	−	0.990032i	0.972917	−	0.231157i	$-0.0742510\pi$
$348$	45825.3	+	63073.1i	0.0202842	+	0.0279187i
$349$	−618260.	+	850962.i	−0.271711	+	0.373978i	−0.922966	−	0.384880i	$-0.874243\pi$
$349$	−618260.	+	850962.i	−0.271711	+	0.373978i	0.651255	+	0.758859i	$0.274243\pi$
$350$	−473372.	−	1.45689e6i	−0.206554	−	0.635707i
$351$	567144.	−	412054.i	0.245711	−	0.178520i
$352$	1.60184e6			0.689069
$353$	1.05353e6			0.449997			0.224998	−	0.974359i	$-0.427762\pi$
$353$	1.05353e6			0.449997			0.224998	+	0.974359i	$0.427762\pi$
$354$	−173855.	+	126313.i	−0.0737358	+	0.0535722i
$355$		−	268230.i		−	0.112963i
$356$	−5818.25	−	8008.14i	−0.00243314	−	0.00334893i
$357$	43394.0	+	31527.6i	0.0180202	+	0.0130924i
$358$	−1.01448e6	−	1.39631e6i	−0.418347	−	0.575805i
$359$	−2.82398e6	+	917566.i	−1.15645	+	0.375752i	−0.823568	−	0.567218i	$-0.808020\pi$
$359$	−2.82398e6	+	917566.i	−1.15645	+	0.375752i	−0.332878	+	0.942970i	$0.608020\pi$
$360$	2.03821e6	−	2.80536e6i	0.828883	−	1.14086i
$361$	−194154.	−	141061.i	−0.0784114	−	0.0569692i
$362$	1.54482e6	+	1.12238e6i	0.619593	+	0.450161i
$363$	−58669.9	+	180567.i	−0.0233695	+	0.0719238i
$364$	1.28448e6	+	417354.i	0.508130	+	0.165101i
$365$	7.26217e6			2.85321
$366$	−35947.5	+	158257.i	−0.0140270	+	0.0617534i
$367$	−556111.			−0.215524			−0.107762	−	0.994177i	$-0.534368\pi$
$367$	−556111.			−0.215524			−0.107762	+	0.994177i	$0.534368\pi$
$368$	1.25351e6	+	407290.i	0.482512	+	0.156778i
$369$	−642215.	+	1.97653e6i	−0.245536	+	0.755681i
$370$	−2.06821e6	−	1.50264e6i	−0.785397	−	0.570625i
$371$	511393.	+	371549.i	0.192894	+	0.140146i
$372$	223142.	−	307128.i	0.0836033	−	0.115070i
$373$	333721.	−	108433.i	0.124197	−	0.0403541i	−0.246259	−	0.969204i	$-0.579201\pi$
$373$	333721.	−	108433.i	0.124197	−	0.0403541i	0.370456	+	0.928850i	$0.379201\pi$
$374$	−111708.	−	153753.i	−0.0412959	−	0.0568389i
$375$	913238.	+	663506.i	0.335356	+	0.243650i
$376$	−480129.	−	660841.i	−0.175141	−	0.241061i
$377$		−	801040.i		−	0.290269i
$378$	178230.	−	129491.i	0.0641579	−	0.0466135i
$379$	−2.79654e6			−1.00005			−0.500027	−	0.866010i	$-0.666677\pi$
$379$	−2.79654e6			−1.00005			−0.500027	+	0.866010i	$0.666677\pi$
$380$	−4.51407e6			−1.60365
$381$	−30547.0	+	22193.7i	−0.0107809	+	0.00783281i
$382$	−689505.	−	2.12208e6i	−0.241757	−	0.744052i
$383$	306172.	−	421410.i	0.106652	−	0.146794i	−0.752355	−	0.658758i	$-0.771082\pi$
$383$	306172.	−	421410.i	0.106652	−	0.146794i	0.859007	+	0.511964i	$0.171082\pi$
$384$	−256824.	−	353487.i	−0.0888806	−	0.122334i
$385$	746356.	−	2.29705e6i	0.256622	−	0.789802i
$386$	393894.	+	1.21228e6i	0.134558	+	0.414128i
$387$			3.76074e6i			1.27643i
$388$	594370.	−	1.82928e6i	0.200437	−	0.616881i
$389$	−1.88974e6	+	2.60100e6i	−0.633180	+	0.871498i	−0.998229	−	0.0594908i	$-0.981052\pi$
$389$	−1.88974e6	+	2.60100e6i	−0.633180	+	0.871498i	0.365049	+	0.930988i	$0.381052\pi$
$390$	347675.	−	112966.i	0.115747	−	0.0376086i
$391$	−227012.	−	698672.i	−0.0750944	−	0.231117i
$392$	−1.33872e6	−	434976.i	−0.440021	−	0.142972i
$393$	228668.	−	166137.i	0.0746833	−	0.0542606i
$394$	537611.	+	174680.i	0.174473	+	0.0566896i
$395$		−	59668.5i		−	0.0192421i
$396$	1.67087e6	−	542900.i	0.535434	−	0.173973i
$397$	5.14469e6	−	1.67161e6i	1.63826	−	0.532303i	0.662112	−	0.749405i	$-0.269660\pi$
$397$	5.14469e6	−	1.67161e6i	1.63826	−	0.532303i	0.976149	+	0.217101i	$0.0696601\pi$
$398$			1.45870e6i			0.461591i
$399$	−299297.	−	97247.6i	−0.0941176	−	0.0305807i
$400$	−3.16935e6	+	2.30267e6i	−0.990423	+	0.719585i
$401$	−5.73941e6	−	1.86485e6i	−1.78240	−	0.579138i	−0.783308	−	0.621634i	$-0.786469\pi$
$401$	−5.73941e6	−	1.86485e6i	−1.78240	−	0.579138i	−0.999097	+	0.0424957i	$0.986469\pi$
$402$	−23546.9	−	72469.8i	−0.00726721	−	0.0223662i
$403$	−3.70968e6	+	1.20535e6i	−1.13782	+	0.369700i
$404$	307473.	−	423200.i	0.0937245	−	0.129001i
$405$	1.77861e6	−	5.47400e6i	0.538819	−	1.65832i
$406$		−	251733.i		−	0.0757924i
$407$	−888403.	−	2.73422e6i	−0.265842	−	0.818178i
$408$	−28228.8	+	86879.2i	−0.00839540	+	0.0258384i
$409$	1.87168e6	+	2.57614e6i	0.553252	+	0.761486i	0.990449	−	0.137880i	$-0.0440288\pi$
$409$	1.87168e6	+	2.57614e6i	0.553252	+	0.761486i	−0.437197	+	0.899366i	$0.644029\pi$
$410$	−1.28853e6	+	1.77351e6i	−0.378561	+	0.521044i
$411$	287042.	+	883423.i	0.0838186	+	0.257967i
$412$	3.70589e6	−	2.69249e6i	1.07560	−	0.781467i
$413$	−3.15901e6			−0.911330
$414$	−1.49166e6			−0.427729
$415$	1.76651e6	−	1.28345e6i	0.503497	−	0.365812i
$416$			3.56406e6i			1.00974i
$417$	−534986.	−	736345.i	−0.150661	−	0.207368i
$418$	902089.	+	655406.i	0.252528	+	0.183472i
$419$	2.12747e6	+	2.92821e6i	0.592008	+	0.814829i	0.994947	−	0.100398i	$-0.0320115\pi$
$419$	2.12747e6	+	2.92821e6i	0.592008	+	0.814829i	−0.402939	+	0.915227i	$0.632011\pi$
$420$	−497425.	+	161623.i	−0.137595	+	0.0447075i
$421$	1.04873e6	−	1.44345e6i	0.288376	−	0.396915i	−0.640110	−	0.768283i	$-0.721111\pi$
$421$	1.04873e6	−	1.44345e6i	0.288376	−	0.396915i	0.928486	+	0.371368i	$0.121111\pi$
$422$	2.21866e6	+	1.61195e6i	0.606470	+	0.440626i
$423$	−1.12305e6	−	815946.i	−0.305176	−	0.221723i
$424$	−332672.	+	1.02386e6i	−0.0898674	+	0.276583i
$425$	2.07666e6	+	674747.i	0.557690	+	0.181204i
$426$	14347.9			0.00383058
$427$	−1.79494e6	+	1.57150e6i	−0.476409	+	0.417103i
$428$	−3.06674e6			−0.809222
$429$	390989.	+	127040.i	0.102570	+	0.0333271i
$430$	−1.22584e6	+	3.77275e6i	−0.319715	+	0.983981i
$431$	1.40046e6	+	1.01749e6i	0.363143	+	0.263839i	0.754362	−	0.656459i	$-0.227946\pi$
$431$	1.40046e6	+	1.01749e6i	0.363143	+	0.263839i	−0.391219	+	0.920298i	$0.627946\pi$
$432$	−455798.	−	331157.i	−0.117507	−	0.0853737i
$433$	1.83462e6	−	2.52514e6i	0.470247	−	0.647240i	−0.506347	−	0.862330i	$-0.669004\pi$
$433$	1.83462e6	−	2.52514e6i	0.470247	−	0.647240i	0.976594	+	0.215090i	$0.0690045\pi$
$434$	−1.16580e6	+	378790.i	−0.297097	+	0.0965327i
$435$	182336.	+	250964.i	0.0462008	+	0.0635899i
$436$	−3.65874e6	−	2.65823e6i	−0.921756	−	0.669695i
$437$	2.53344e6	+	3.48698e6i	0.634610	+	0.873466i
$438$			388461.i			0.0967525i
$439$	4.91975e6	−	3.57441e6i	1.21838	−	0.885203i	0.222413	−	0.974952i	$-0.428607\pi$
$439$	4.91975e6	−	3.57441e6i	1.21838	−	0.885203i	0.995964	+	0.0897492i	$0.0286066\pi$
$440$	4.11340e6			1.01291
$441$	−2.39214e6			−0.585720
$442$	342098.	−	248549.i	0.0832903	−	0.0605139i
$443$	1.62609e6	+	5.00459e6i	0.393673	+	1.21160i	0.929990	+	0.367584i	$0.119815\pi$
$443$	1.62609e6	+	5.00459e6i	0.393673	+	1.21160i	−0.536318	+	0.844016i	$0.680185\pi$
$444$	−365935.	+	503666.i	−0.0880940	+	0.121251i
$445$	−23150.5	−	31863.9i	−0.00554191	−	0.00762779i
$446$	−979417.	+	3.01433e6i	−0.233147	+	0.717554i
$447$	−97300.4	−	299460.i	−0.0230328	−	0.0708875i
$448$		−	203808.i		−	0.0479763i
$449$	−2.11487e6	+	6.50890e6i	−0.495071	+	1.52367i	0.321775	+	0.946816i	$0.395721\pi$
$449$	−2.11487e6	+	6.50890e6i	−0.495071	+	1.52367i	−0.816846	+	0.576856i	$0.804279\pi$
$450$	2.60604e6	−	3.58690e6i	0.606665	−	0.835003i
$451$	−2.34463e6	+	761817.i	−0.542792	+	0.176364i
$452$	1.65725e6	+	5.10048e6i	0.381541	+	1.17426i
$453$	−135335.	−	43973.1i	−0.0309860	−	0.0100680i
$454$	−167658.	+	121811.i	−0.0381756	+	0.0277362i
$455$	5.11087e6	+	1.66062e6i	1.15736	+	0.376048i
$456$		−	535962.i		−	0.120704i
$457$	1.86470e6	−	605878.i	0.417656	−	0.135705i	−0.0926476	−	0.995699i	$-0.529533\pi$
$457$	1.86470e6	−	605878.i	0.417656	−	0.135705i	0.510304	+	0.859994i	$0.329533\pi$
$458$	−1.42137e6	+	461831.i	−0.316623	+	0.102877i
$459$			314022.i			0.0695711i
$460$	6.81275e6	+	2.21360e6i	1.50116	+	0.487758i
$461$	−164945.	+	119840.i	−0.0361482	+	0.0262632i	−0.605713	−	0.795683i	$-0.707112\pi$
$461$	−164945.	+	119840.i	−0.0361482	+	0.0262632i	0.569564	+	0.821947i	$0.307112\pi$
$462$	122872.	+	39923.4i	0.0267822	+	0.00870207i
$463$	1.10587e6	+	3.40352e6i	0.239747	+	0.737864i	0.996456	+	0.0841129i	$0.0268056\pi$
$463$	1.10587e6	+	3.40352e6i	0.239747	+	0.737864i	−0.756710	+	0.653751i	$0.773194\pi$
$464$	−612266.	+	198937.i	−0.132022	+	0.0428964i
$465$	887867.	−	1.22204e6i	0.190421	−	0.262092i
$466$	−844623.	+	2.59948e6i	−0.180177	+	0.554526i
$467$		−	6.26864e6i		−	1.33009i	−0.746803	−	0.665045i	$-0.768412\pi$
$467$		−	6.26864e6i		−	1.33009i	0.746803	−	0.665045i	$-0.231588\pi$
$468$	1.20794e6	+	3.71766e6i	0.254936	+	0.784611i
$469$	346143.	−	1.06532e6i	0.0726646	−	0.223639i
$470$	−860678.	−	1.18462e6i	−0.179720	−	0.247363i
$471$	−512899.	+	705945.i	−0.106532	+	0.146628i
$472$	−1.66253e6	−	5.11675e6i	−0.343491	−	1.05716i
$473$	−3.60912e6	+	2.62218e6i	−0.741734	+	0.538901i
$474$	3191.73			0.000652500
$475$	−1.28110e7			−2.60525
$476$	−489446.	+	355603.i	−0.0990118	+	0.0719363i
$477$			1.82952e6i			0.368165i
$478$	2.20599e6	+	3.03629e6i	0.441606	+	0.607818i
$479$	−6.59125e6	−	4.78882e6i	−1.31259	−	0.953652i	−0.999993	−	0.00376585i	$-0.998801\pi$
$479$	−6.59125e6	−	4.78882e6i	−1.31259	−	0.953652i	−0.312596	−	0.949886i	$-0.601199\pi$
$480$	−811265.	−	1.11661e6i	−0.160716	−	0.221207i
$481$	6.08358e6	−	1.97668e6i	1.19894	−	0.389558i
$482$	1.23115e6	−	1.69453e6i	0.241376	−	0.332225i
$483$	404020.	+	293538.i	0.0788016	+	0.0572527i
$484$	−1.73247e6	−	1.25871e6i	−0.336165	−	0.244238i
$485$	2.36496e6	−	7.27860e6i	0.456530	−	1.40506i
$486$	913036.	+	296663.i	0.175346	+	0.0569735i
$487$	1.42461e6			0.272191			0.136096	−	0.990696i	$-0.456545\pi$
$487$	1.42461e6			0.272191			0.136096	+	0.990696i	$0.456545\pi$
$488$	−3.49005e6	−	2.08027e6i	−0.663411	−	0.395431i
$489$	−1.24105e6			−0.234702
$490$	−2.39978e6	−	779736.i	−0.451524	−	0.146709i
$491$	1.94337e6	−	5.98109e6i	0.363792	−	1.11964i	−0.586943	−	0.809628i	$-0.699669\pi$
$491$	1.94337e6	−	5.98109e6i	0.363792	−	1.11964i	0.950734	−	0.310007i	$-0.100331\pi$
$492$	431900.	+	313794.i	0.0804397	+	0.0584429i
$493$	290293.	+	210910.i	0.0537922	+	0.0390823i
$494$	−1.45826e6	+	2.00713e6i	−0.268855	+	0.370048i
$495$	6.64830e6	−	2.16017e6i	1.21955	−	0.396254i
$496$	1.84259e6	+	2.53610e6i	0.336297	+	0.462874i
$497$	170635.	+	123973.i	0.0309868	+	0.0225132i
$498$	68653.0	+	94492.8i	0.0124047	+	0.0170736i
$499$		−	3.89418e6i		−	0.700107i	−0.936730	−	0.350053i	$-0.886163\pi$
$499$		−	3.89418e6i		−	0.700107i	0.936730	−	0.350053i	$-0.113837\pi$
$500$	−1.03005e7	+	7.48376e6i	−1.84261	+	1.33874i
$501$	275004.			0.0489491
$502$	−522209.			−0.0924880
$503$	−5.17946e6	+	3.76310e6i	−0.912777	+	0.663171i	−0.941716	−	0.336410i	$-0.890787\pi$
$503$	−5.17946e6	+	3.76310e6i	−0.912777	+	0.663171i	0.0289386	+	0.999581i	$0.490787\pi$
$504$	842590.	+	2.59323e6i	0.147754	+	0.454741i
$505$	1.22342e6	−	1.68389e6i	0.213474	−	0.293822i
$506$	−1.04006e6	−	1.43152e6i	−0.180585	−	0.248554i
$507$	−15767.1	+	48526.1i	−0.00272416	+	0.00838409i
$508$	−131604.	−	405035.i	−0.0226261	−	0.0696359i
$509$			1.91689e6i			0.327946i	0.986465	+	0.163973i	$0.0524310\pi$
$509$			1.91689e6i			0.327946i	−0.986465	+	0.163973i	$0.947569\pi$
$510$	−50602.8	+	155739.i	−0.00861487	+	0.0265138i
$511$	−3.35651e6	+	4.61984e6i	−0.568638	+	0.782664i
$512$	4.86842e6	−	1.58185e6i	0.820754	−	0.266679i
$513$	−569335.	−	1.75223e6i	−0.0955156	−	0.293967i
$514$	−1.31206e6	−	426314.i	−0.219051	−	0.0711740i
$515$	1.47455e7	−	1.07132e7i	2.44986	−	1.77993i
$516$	918771.	+	298527.i	0.151909	+	0.0493581i
$517$		−	1.64670e6i		−	0.270949i
$518$	1.91182e6	−	621187.i	0.313056	−	0.101718i
$519$	163757.	−	53207.9i	0.0266859	−	0.00867077i
$520$			9.15222e6i			1.48429i
$521$	6.31930e6	+	2.05327e6i	1.01994	+	0.331399i	0.770806	−	0.637070i	$-0.219854\pi$
$521$	6.31930e6	+	2.05327e6i	1.01994	+	0.331399i	0.249135	+	0.968469i	$0.419854\pi$
$522$	589440.	−	428253.i	0.0946811	−	0.0687899i
$523$	4.51836e6	+	1.46811e6i	0.722316	+	0.234695i	0.647027	−	0.762467i	$-0.276012\pi$
$523$	4.51836e6	+	1.46811e6i	0.722316	+	0.234695i	0.0752887	+	0.997162i	$0.476012\pi$
$524$	985155.	+	3.03200e6i	0.156739	+	0.482392i
$525$	−1.41170e6	+	458690.i	−0.223535	+	0.0726308i
$526$	2.17610e6	−	2.99514e6i	0.342937	−	0.472012i
$527$	539930.	−	1.66173e6i	0.0846858	−	0.260636i
$528$		−	330398.i		−	0.0515766i
$529$	−124660.	−	383663.i	−0.0193681	−	0.0596089i
$530$	−596347.	+	1.83537e6i	−0.0922167	+	0.283814i
$531$	−5.37416e6	−	7.39689e6i	−0.827131	−	1.13845i
$532$	2.08636e6	−	2.87163e6i	0.319603	−	0.439896i
$533$	−1.69502e6	−	5.21675e6i	−0.258439	−	0.795393i
$534$	1704.43	−	1238.34i	0.000258659	−	0.000187926i
$535$	−1.22024e7			−1.84315
$536$	1.90770e6			0.286812
$537$	−1.35301e6	+	983016.i	−0.202471	+	0.147104i
$538$			918686.i			0.136840i
$539$	−1.66792e6	−	2.29570e6i	−0.247288	−	0.340363i
$540$	−2.47724e6	−	1.79982e6i	−0.365580	−	0.265610i
$541$	−6.05994e6	−	8.34079e6i	−0.890174	−	1.22522i	−0.973498	−	0.228697i	$-0.926553\pi$
$541$	−6.05994e6	−	8.34079e6i	−0.890174	−	1.22522i	0.0833234	−	0.996523i	$-0.473447\pi$
$542$	3.28991e6	−	1.06896e6i	0.481045	−	0.156301i
$543$	1.08757e6	−	1.49691e6i	0.158291	−	0.217869i
$544$	−1.29160e6	−	938401.i	−0.187124	−	0.135954i
$545$	−1.45579e7	−	1.05769e7i	−2.09946	−	1.52535i
$546$	−88828.6	+	273386.i	−0.0127518	+	0.0392460i
$547$	6.60035e6	+	2.14459e6i	0.943190	+	0.306461i	0.739945	−	0.672667i	$-0.234851\pi$
$547$	6.60035e6	+	2.14459e6i	0.943190	+	0.306461i	0.203244	+	0.979128i	$0.434851\pi$
$548$	−1.04770e7			−1.49034
$549$	−6.73328e6	−	1.52944e6i	−0.953445	−	0.216571i
$550$	5.25935e6			0.741353
$551$	−2.00221e6	−	650559.i	−0.280952	−	0.0912867i
$552$	−262824.	+	808889.i	−0.0367128	+	0.112990i
$553$	37958.2	+	27578.3i	0.00527829	+	0.00383490i
$554$	−2.31551e6	−	1.68232e6i	−0.320533	−	0.232881i
$555$	−1.45603e6	+	2.00406e6i	−0.200650	+	0.276171i
$556$	9.76349e6	−	3.17235e6i	1.33942	−	0.435205i
$557$	−2.59567e6	−	3.57263e6i	−0.354496	−	0.487921i	0.594109	−	0.804384i	$-0.297505\pi$
$557$	−2.59567e6	−	3.57263e6i	−0.354496	−	0.487921i	−0.948605	+	0.316463i	$0.897505\pi$
$558$	−2.87022e6	−	2.08534e6i	−0.390238	−	0.283525i
$559$	−5.83428e6	−	8.03020e6i	−0.789692	−	1.08692i
$560$		−	4.31885e6i		−	0.581967i
$561$	−148984.	+	108244.i	−0.0199864	+	0.0145209i
$562$	−1.16624e6			−0.155757
$563$	1.06911e7			1.42152			0.710759	−	0.703436i	$-0.248352\pi$
$563$	1.06911e7			1.42152			0.710759	+	0.703436i	$0.248352\pi$
$564$	−288489.	+	209599.i	−0.0381883	+	0.0277455i
$565$	6.59408e6	+	2.02945e7i	0.869027	+	2.67459i
$566$	1.23373e6	−	1.69808e6i	0.161875	−	0.222801i
$567$	2.66024e6	+	3.66150e6i	0.347507	+	0.478302i
$568$	−111002.	+	341628.i	−0.0144364	+	0.0444307i
$569$	1.24872e6	+	3.84318e6i	0.161691	+	0.497634i	0.998777	−	0.0494372i	$-0.0157428\pi$
$569$	1.24872e6	+	3.84318e6i	0.161691	+	0.497634i	−0.837086	+	0.547071i	$0.815743\pi$
$570$		−	960764.i		−	0.123860i
$571$	992855.	−	3.05569e6i	0.127437	−	0.392211i	−0.866900	−	0.498482i	$-0.833891\pi$
$571$	992855.	−	3.05569e6i	0.127437	−	0.392211i	0.994337	+	0.106271i	$0.0338911\pi$
$572$	−2.72554e6	+	3.75138e6i	−0.348307	+	0.479403i
$573$	−2.05626e6	+	668119.i	−0.261632	+	0.0850095i
$574$	−532675.	−	1.63941e6i	−0.0674812	−	0.207686i
$575$	1.93347e7	+	6.28224e6i	2.43876	+	0.792400i
$576$	477222.	−	346722.i	0.0599328	−	0.0435437i
$577$	8.76681e6	+	2.84851e6i	1.09623	+	0.356187i	0.800651	−	0.599131i	$-0.204487\pi$
$577$	8.76681e6	+	2.84851e6i	1.09623	+	0.356187i	0.295580	+	0.955318i	$0.404487\pi$
$578$		−	3.21912e6i		−	0.400791i
$579$	1.17468e6	−	381676.i	0.145621	−	0.0473150i
$580$	−3.32763e6	+	1.08121e6i	−0.410738	+	0.133457i
$581$			1.71697e6i			0.211020i
$582$	389340.	+	126504.i	0.0476455	+	0.0154810i
$583$	−1.75576e6	+	1.27564e6i	−0.213941	+	0.155437i
$584$	−9.24940e6	−	3.00531e6i	−1.12223	−	0.364634i
$585$	4.80632e6	+	1.47923e7i	0.580661	+	1.78709i
$586$	2.29504e6	−	745703.i	0.276087	−	0.0897060i
$587$	2.02247e6	−	2.78369e6i	0.242262	−	0.333446i	−0.670520	−	0.741891i	$-0.733929\pi$
$587$	2.02247e6	−	2.78369e6i	0.242262	−	0.333446i	0.912783	+	0.408446i	$0.133929\pi$
$588$	−189888.	+	584414.i	−0.0226492	+	0.0697071i
$589$			1.02513e7i			1.21756i
$590$	−2.98025e6	−	9.17227e6i	−0.352471	−	1.08479i
$591$	169262.	−	520936.i	0.0199339	−	0.0613502i
$592$	−3.02170e6	−	4.15901e6i	−0.354362	−	0.487737i
$593$	−8.44598e6	+	1.16249e7i	−0.986310	+	1.35754i	−0.0529498	+	0.998597i	$0.516862\pi$
$593$	−8.44598e6	+	1.16249e7i	−0.986310	+	1.35754i	−0.933360	+	0.358942i	$0.883138\pi$
$594$	233731.	+	719349.i	0.0271800	+	0.0836515i
$595$	−1.94747e6	+	1.41492e6i	−0.225517	+	0.163848i
$596$	3.55146e6			0.409535
$597$	1.41345e6			0.162310
$598$	3.18510e6	−	2.31411e6i	0.364225	−	0.264625i
$599$			1.05363e7i			1.19983i	0.800062	+	0.599917i	$0.204800\pi$
$599$			1.05363e7i			1.19983i	−0.800062	+	0.599917i	$0.795200\pi$
$600$	−1.48591e6	−	2.04518e6i	−0.168506	−	0.231928i
$601$	2.24204e6	+	1.62893e6i	0.253196	+	0.183957i	0.707142	−	0.707072i	$-0.249984\pi$
$601$	2.24204e6	+	1.62893e6i	0.253196	+	0.183957i	−0.453946	+	0.891029i	$0.649984\pi$
$602$	−1.83347e6	−	2.52356e6i	−0.206197	−	0.283806i
$603$	3.08333e6	−	1.00183e6i	0.345324	−	0.112203i
$604$	943406.	−	1.29849e6i	0.105222	−	0.144826i
$605$	−6.89339e6	−	5.00834e6i	−0.765675	−	0.556295i
$606$	90072.9	+	65441.8i	0.00996352	+	0.00723892i
$607$	−945301.	+	2.90934e6i	−0.104135	+	0.320496i	−0.989527	−	0.144351i	$-0.953891\pi$
$607$	−945301.	+	2.90934e6i	−0.104135	+	0.320496i	0.885391	+	0.464847i	$0.153891\pi$
$608$	8.90842e6	+	2.89452e6i	0.977332	+	0.317554i
$609$	−243925.			−0.0266510
$610$	−6.25626e6	−	3.72909e6i	−0.680754	−	0.405768i
$611$	3.66386e6			0.397041
$612$	−1.66531e6	−	541091.i	−0.179728	−	0.0583972i
$613$	−2.23745e6	+	6.88616e6i	−0.240493	+	0.740160i	0.755852	+	0.654742i	$0.227223\pi$
$613$	−2.23745e6	+	6.88616e6i	−0.240493	+	0.740160i	−0.996345	+	0.0854185i	$0.972777\pi$
$614$	392016.	+	284816.i	0.0419646	+	0.0304891i
$615$	1.71850e6	+	1.24857e6i	0.183216	+	0.133114i
$616$	−1.90118e6	+	2.61675e6i	−0.201870	+	0.277850i
$617$	3.05457e6	−	992489.i	0.323025	−	0.104957i	−0.143016	−	0.989720i	$-0.545680\pi$
$617$	3.05457e6	−	992489.i	0.323025	−	0.104957i	0.466041	+	0.884763i	$0.345680\pi$
$618$	573063.	+	788753.i	0.0603575	+	0.0830749i
$619$	−1.79183e6	−	1.30184e6i	−0.187963	−	0.136563i	0.489824	−	0.871821i	$-0.337061\pi$
$619$	−1.79183e6	−	1.30184e6i	−0.187963	−	0.136563i	−0.677787	+	0.735258i	$0.737061\pi$
$620$	1.00143e7	+	1.37836e7i	1.04627	+	1.44007i
$621$			2.92371e6i			0.304232i
$622$	811686.	−	589725.i	0.0841225	−	0.0611186i
$623$	30970.2			0.00319687
$624$	735128.			0.0755791
$625$	−2.13325e7	+	1.54990e7i	−2.18445	+	1.58709i
$626$	428196.	+	1.31785e6i	0.0436724	+	0.134410i
$627$	635078.	−	874109.i	0.0645146	−	0.0887967i
$628$	−5.78504e6	−	7.96243e6i	−0.585339	−	0.805650i
$629$	−885443.	+	2.72511e6i	−0.0892347	+	0.274636i
$630$	1.51042e6	+	4.64861e6i	0.151617	+	0.466629i
$631$		−	1.01975e7i		−	1.01958i	−0.860300	−	0.509788i	$-0.829724\pi$
$631$		−	1.01975e7i		−	1.01958i	0.860300	−	0.509788i	$-0.170276\pi$
$632$	−24692.7	+	75996.2i	−0.00245910	+	0.00756832i
$633$	1.56195e6	−	2.14984e6i	0.154938	−	0.213254i
$634$	3.92040e6	−	1.27381e6i	0.387353	−	0.125859i
$635$	−523644.	−	1.61161e6i	−0.0515349	−	0.158608i
$636$	446964.	+	145227.i	0.0438157	+	0.0142366i
$637$	5.10787e6	−	3.71108e6i	0.498759	−	0.362370i
$638$	821975.	+	267076.i	0.0799479	+	0.0259766i
$639$			610452.i			0.0591424i
$640$	1.86494e7	−	6.05956e6i	1.79976	−	0.584778i
$641$	1.30050e7	−	4.22557e6i	1.25016	−	0.406200i	0.392179	−	0.919889i	$-0.371721\pi$
$641$	1.30050e7	−	4.22557e6i	1.25016	−	0.406200i	0.857977	+	0.513688i	$0.171721\pi$
$642$		−	652718.i		−	0.0625012i
$643$	−341051.	−	110814.i	−0.0325306	−	0.0105698i	0.292706	−	0.956202i	$-0.405444\pi$
$643$	−341051.	−	110814.i	−0.0325306	−	0.0105698i	−0.325237	+	0.945632i	$0.605444\pi$
$644$	−4.55698e6	+	3.31084e6i	−0.432975	+	0.314575i
$645$	3.65573e6	+	1.18782e6i	0.345999	+	0.112422i
$646$	−343419.	−	1.05694e6i	−0.0323775	−	0.0996477i
$647$	−1.34188e7	+	4.36002e6i	−1.26024	+	0.409476i	−0.861579	−	0.507624i	$-0.830524\pi$
$647$	−1.34188e7	+	4.36002e6i	−1.26024	+	0.409476i	−0.398658	+	0.917100i	$0.630524\pi$
$648$	−4.53062e6	+	6.23587e6i	−0.423858	+	0.583391i
$649$	3.35154e6	−	1.03150e7i	0.312344	−	0.961295i
$650$			1.17019e7i			1.08636i
$651$	367041.	+	1.12964e6i	0.0339440	+	0.104469i
$652$	4.32561e6	−	1.33128e7i	0.398500	−	1.22646i
$653$	6.23562e6	+	8.58260e6i	0.572265	+	0.787655i	0.992821	−	0.119612i	$-0.0381650\pi$
$653$	6.23562e6	+	8.58260e6i	0.572265	+	0.787655i	−0.420556	+	0.907267i	$0.638165\pi$
$654$	565772.	−	778719.i	0.0517246	−	0.0711928i
$655$	3.91987e6	+	1.20641e7i	0.357000	+	1.09873i
$656$	−3.56640e6	+	2.59114e6i	−0.323572	+	0.235089i
$657$	−1.65276e7			−1.49382
$658$	1.15140e6			0.103672
$659$	−8.54538e6	+	6.20858e6i	−0.766510	+	0.556902i	−0.900900	−	0.434026i	$-0.857093\pi$
$659$	−8.54538e6	+	6.20858e6i	−0.766510	+	0.556902i	0.134390	+	0.990929i	$0.457093\pi$
$660$		−	1.79569e6i		−	0.160462i
$661$	2.12191e6	+	2.92056e6i	0.188897	+	0.259994i	0.892953	−	0.450150i	$-0.148630\pi$
$661$	2.12191e6	+	2.92056e6i	0.188897	+	0.259994i	−0.704056	+	0.710144i	$0.748630\pi$
$662$	396797.	+	288290.i	0.0351903	+	0.0255673i
$663$	−240839.	−	331487.i	−0.0212786	−	0.0292875i
$664$	−2.78104e6	+	903614.i	−0.244786	+	0.0795358i
$665$	8.30152e6	−	1.14261e7i	0.727953	−	1.00194i
$666$	4.70694e6	+	3.41979e6i	0.411200	+	0.298754i
$667$	2.70278e6	+	1.96368e6i	0.235231	+	0.170906i
$668$	−958510.	+	2.94999e6i	−0.0831104	+	0.255788i
$669$	2.92084e6	+	949038.i	0.252315	+	0.0819820i
$670$	3.41974e6			0.294310
$671$	−3.22701e6	−	7.52822e6i	−0.276690	−	0.645484i
$672$	1.08529e6			0.0927095
$673$	−1.46805e7	−	4.76998e6i	−1.24940	−	0.405956i	−0.391696	−	0.920095i	$-0.628112\pi$
$673$	−1.46805e7	−	4.76998e6i	−1.24940	−	0.405956i	−0.857707	+	0.514139i	$0.828112\pi$
$674$	−2.68849e6	+	8.27433e6i	−0.227960	+	0.701590i
$675$	−7.03045e6	−	5.10792e6i	−0.593914	−	0.431504i
$676$	−465588.	−	338270.i	−0.0391864	−	0.0284706i
$677$	1.06189e7	−	1.46157e7i	0.890447	−	1.22560i	−0.0829690	−	0.996552i	$-0.526440\pi$
$677$	1.06189e7	−	1.46157e7i	0.890447	−	1.22560i	0.973416	−	0.229043i	$-0.0735598\pi$
$678$	−1.08558e6	+	352725.i	−0.0906955	+	0.0294687i
$679$	3.53723e6	+	4.86858e6i	0.294435	+	0.405255i
$680$	−3.31672e6	−	2.40974e6i	−0.275066	−	0.199847i
$681$	118033.	+	162458.i	0.00975292	+	0.0134237i
$682$		−	4.20851e6i		−	0.346471i
$683$	8.22732e6	−	5.97750e6i	0.674849	−	0.490306i	−0.196796	−	0.980444i	$-0.563054\pi$
$683$	8.22732e6	−	5.97750e6i	0.674849	−	0.490306i	0.871645	+	0.490138i	$0.163054\pi$
$684$	1.02734e7			0.839600
$685$	−4.16874e7			−3.39452
$686$	4.28471e6	−	3.11302e6i	0.347625	−	0.252564i
$687$	447506.	+	1.37728e6i	0.0361749	+	0.111335i
$688$	−4.68885e6	+	6.45365e6i	−0.377655	+	0.519798i
$689$	−2.83826e6	−	3.90653e6i	−0.227774	−	0.313504i
$690$	−471137.	+	1.45001e6i	−0.0376725	+	0.115944i
$691$	−244796.	−	753406.i	−0.0195034	−	0.0600253i	0.940831	−	0.338876i	$-0.110047\pi$
$691$	−244796.	−	753406.i	−0.0195034	−	0.0600253i	−0.960335	+	0.278850i	$0.910047\pi$
$692$			1.94209e6i			0.154171i
$693$	−1.69860e6	+	5.22775e6i	−0.134356	+	0.413506i
$694$	−3.29465e6	+	4.53469e6i	−0.259663	+	0.357396i
$695$	3.88483e7	−	1.26226e7i	3.05077	−	0.991257i
$696$	−128374.	−	395094.i	−0.0100451	−	0.0309156i
$697$	2.33682e6	+	759278.i	0.182198	+	0.0591996i
$698$	2.04284e6	−	1.48421e6i	0.158707	−	0.115307i
$699$	2.51885e6	+	818426.i	0.194989	+	0.0633558i
$700$		−	1.67422e7i		−	1.29142i
$701$	−1.78570e7	+	5.80209e6i	−1.37250	+	0.445954i	−0.900198	−	0.435481i	$-0.856578\pi$
$701$	−1.78570e7	+	5.80209e6i	−1.37250	+	0.445954i	−0.472306	+	0.881435i	$0.656578\pi$
$702$	−1.60054e6	+	520045.i	−0.122581	+	0.0398289i
$703$		−	1.68114e7i		−	1.28296i
$704$	665487.	+	216230.i	0.0506067	+	0.0164431i
$705$	−1.14788e6	+	833982.i	−0.0869807	+	0.0631952i
$706$	−2.40534e6	−	781542.i	−0.181620	−	0.0590120i
$707$	505756.	+	1.55656e6i	0.0380533	+	0.117116i
$708$	−2.23371e6	+	725775.i	−0.167472	+	0.0544150i
$709$	1.21307e7	−	1.66965e7i	0.906297	−	1.24741i	−0.0621190	−	0.998069i	$-0.519786\pi$
$709$	1.21307e7	−	1.66965e7i	0.906297	−	1.24741i	0.968416	−	0.249342i	$-0.0802142\pi$
$710$	−198981.	+	612402.i	−0.0148138	+	0.0455922i
$711$			135797.i			0.0100743i
$712$	16299.1	+	50163.5i	0.00120494	+	0.00370841i
$713$	5.02702e6	−	1.54716e7i	0.370328	−	1.13975i
$714$	−75685.7	−	104172.i	−0.00555608	−	0.00764729i
$715$	−1.08447e7	+	1.49265e7i	−0.793330	+	1.09193i
$716$	−5.82907e6	−	1.79400e7i	−0.424929	−	1.30780i
$717$	2.94212e6	−	2.13757e6i	0.213728	−	0.155283i
$718$	7.12818e6			0.516021
$719$	−1.53759e7			−1.10922			−0.554611	−	0.832110i	$-0.687133\pi$
$719$	−1.53759e7			−1.10922			−0.554611	+	0.832110i	$0.687133\pi$
$720$	1.01127e7	−	7.34730e6i	0.727002	−	0.528198i
$721$			1.43320e7i			1.02676i
$722$	338635.	+	466091.i	0.0241762	+	0.0332757i
$723$	−1.64198e6	−	1.19297e6i	−0.116821	−	0.0848754i
$724$	1.22668e7	+	1.68838e7i	0.869729	+	1.19708i
$725$	−9.44388e6	+	3.06850e6i	−0.667276	+	0.216811i
$726$	267902.	−	368735.i	0.0188640	−	0.0259641i
$727$	−3.46042e6	−	2.51414e6i	−0.242825	−	0.176422i	0.459716	−	0.888066i	$-0.347951\pi$
$727$	−3.46042e6	−	2.51414e6i	−0.242825	−	0.176422i	−0.702541	+	0.711643i	$0.747951\pi$
$728$	−5.82220e6	−	4.23008e6i	−0.407154	−	0.295815i
$729$	−3.85259e6	+	1.18570e7i	−0.268493	+	0.826338i
$730$	−1.65804e7	−	5.38731e6i	−1.15157	−	0.374166i
$731$	4.44625e6			0.307751
$732$	−908137.	+	1.52357e6i	−0.0626432	+	0.105096i
$733$	−4.12456e6			−0.283542			−0.141771	−	0.989899i	$-0.545280\pi$
$733$	−4.12456e6			−0.283542			−0.141771	+	0.989899i	$0.545280\pi$
$734$	1.26967e6	+	412541.i	0.0869863	+	0.0282636i
$735$	−755551.	+	2.32535e6i	−0.0515876	+	0.158770i
$736$	−1.20254e7	−	8.73698e6i	−0.818288	−	0.594521i
$737$	3.11130e6	+	2.26049e6i	0.210995	+	0.153297i
$738$	2.93251e6	−	4.03626e6i	0.198198	−	0.272796i
$739$	3.43698e6	−	1.11674e6i	0.231508	−	0.0752214i	−0.190966	−	0.981597i	$-0.561162\pi$
$739$	3.43698e6	−	1.11674e6i	0.231508	−	0.0752214i	0.422473	+	0.906375i	$0.361162\pi$
$740$	−1.64228e7	−	2.26040e7i	−1.10247	−	1.51742i
$741$	1.94487e6	+	1.41303e6i	0.130120	+	0.0945381i
$742$	−891947.	−	1.22766e6i	−0.0594743	−	0.0818593i
$743$		−	1.17354e6i		−	0.0779879i	−0.999239	−	0.0389939i	$-0.987585\pi$
$743$		−	1.17354e6i		−	0.0779879i	0.999239	−	0.0389939i	$-0.0124153\pi$
$744$	−1.63654e6	+	1.18902e6i	−0.108392	+	0.0787511i
$745$	1.41310e7			0.932789
$746$	−842366.			−0.0554184
$747$	−4.02033e6	+	2.92094e6i	−0.263609	+	0.191523i
$748$	−641860.	−	1.97544e6i	−0.0419456	−	0.129095i
$749$	5.63984e6	−	7.76257e6i	0.367335	−	0.505593i
$750$	−1.59283e6	−	2.19234e6i	−0.103399	−	0.142316i
$751$	−6.35780e6	+	1.95673e7i	−0.411346	+	1.26599i	0.504133	+	0.863626i	$0.331812\pi$
$751$	−6.35780e6	+	1.95673e7i	−0.411346	+	1.26599i	−0.915479	+	0.402366i	$0.868188\pi$
$752$	−909914.	−	2.80043e6i	−0.0586754	−	0.180584i
$753$			506012.i			0.0325217i
$754$	−594237.	+	1.82887e6i	−0.0380655	+	0.117154i
$755$	3.75375e6	−	5.16660e6i	0.239661	−	0.329866i
$756$	2.28992e6	−	744039.i	0.145719	−	0.0473469i
$757$	−573183.	−	1.76408e6i	−0.0363541	−	0.111886i	0.931233	−	0.364425i	$-0.118734\pi$
$757$	−573183.	−	1.76408e6i	−0.0363541	−	0.111886i	−0.967587	+	0.252539i	$0.918734\pi$
$758$	6.38486e6	+	2.07457e6i	0.403625	+	0.131146i
$759$	−1.38712e6	+	1.00780e6i	−0.0873996	+	0.0634996i
$760$	2.28761e7	+	7.43290e6i	1.43664	+	0.466793i
$761$			7.18105e6i			0.449497i	0.974417	+	0.224748i	$0.0721560\pi$
$761$			7.18105e6i			0.449497i	−0.974417	+	0.224748i	$0.927844\pi$
$762$	86206.8	−	28010.3i	0.00537841	−	0.00174755i
$763$	1.34571e7	−	4.37248e6i	0.836835	−	0.271904i
$764$		−	2.43863e7i		−	1.51152i
$765$	−6.62615e6	−	2.15297e6i	−0.409362	−	0.133010i
$766$	−1.01164e6	+	735003.i	−0.0622954	+	0.0452603i
$767$	2.29506e7	+	7.45710e6i	1.40866	+	0.457701i
$768$	267023.	+	821811.i	0.0163360	+	0.0502770i
$769$	3.66651e6	−	1.19132e6i	0.223582	−	0.0726461i	−0.195084	−	0.980787i	$-0.562498\pi$
$769$	3.66651e6	−	1.19132e6i	0.223582	−	0.0726461i	0.418666	+	0.908140i	$0.362498\pi$
$770$	−3.40805e6	+	4.69078e6i	−0.207147	+	0.285114i
$771$	−413091.	+	1.27136e6i	−0.0250270	+	0.0770253i
$772$			1.39312e7i			0.841287i
$773$	1.95640e6	+	6.02119e6i	0.117763	+	0.362438i	0.992513	−	0.122136i	$-0.0389745\pi$
$773$	1.95640e6	+	6.02119e6i	0.117763	+	0.362438i	−0.874750	+	0.484574i	$0.838975\pi$
$774$	2.78984e6	−	8.58623e6i	0.167389	−	0.515170i
$775$	2.84209e7	+	3.91181e7i	1.69975	+	2.33950i
$776$	−6.02422e6	+	8.29163e6i	−0.359126	+	0.494294i
$777$	−601919.	−	1.85252e6i	−0.0357673	−	0.110080i
$778$	6.24401e6	−	4.53654e6i	0.369841	−	0.268705i
$779$	−1.44160e7			−0.851138
$780$	3.99538e6			0.235137
$781$	−585840.	+	425638.i	−0.0343678	+	0.0249697i
$782$			1.76356e6i			0.103127i
$783$	−839391.	−	1.15532e6i	−0.0489283	−	0.0673440i
$784$	−4.10505e6	−	2.98250e6i	−0.238522	−	0.173296i
$785$	−2.30183e7	−	3.16820e7i	−1.33321	−	1.83501i
$786$	−645323.	+	209678.i	−0.0372581	+	0.0121059i
$787$	−1.20434e7	+	1.65763e7i	−0.693125	+	0.954004i	0.306873	+	0.951751i	$0.400717\pi$
$787$	−1.20434e7	+	1.65763e7i	−0.693125	+	0.954004i	−0.999997	+	0.00225382i	$0.999283\pi$
$788$	4.99817e6	+	3.63138e6i	0.286744	+	0.208332i
$789$	−2.90224e6	−	2.10860e6i	−0.165975	−	0.120588i
$790$	−44264.0	+	136231.i	−0.00252338	+	0.00776617i
$791$	−1.59581e7	−	5.18511e6i	−0.906861	−	0.294657i
$792$	−9.36150e6			−0.530313
$793$	1.67501e7	−	7.18002e6i	0.945877	−	0.405455i
$794$	−1.29860e7			−0.731013
$795$	1.77844e6	+	577850.i	0.0997979	+	0.0324263i
$796$	−4.92650e6	+	1.51622e7i	−0.275585	+	0.848163i
$797$	1.33714e7	+	9.71489e6i	0.745643	+	0.541741i	0.894473	−	0.447121i	$-0.147551\pi$
$797$	1.33714e7	+	9.71489e6i	0.745643	+	0.541741i	−0.148830	+	0.988863i	$0.547551\pi$
$798$	611192.	+	444057.i	0.0339759	+	0.0246849i
$799$	−964678.	+	1.32777e6i	−0.0534583	+	0.0735791i
$800$	4.20185e7	−	1.36527e7i	2.32122	−	0.754210i
$801$	52687.1	+	72517.6i	0.00290150	+	0.00399358i
$802$	1.17204e7	+	8.51536e6i	0.643437	+	0.467484i
$803$	−1.15239e7	−	1.58613e7i	−0.630683	−	0.868060i
$804$		−	832802.i		−	0.0454361i
$805$	−1.81320e7	+	1.31736e7i	−0.986177	+	0.716500i
$806$	9.36382e6			0.507710
$807$	890192.			0.0481171
$808$	−2.25504e6	+	1.63838e6i	−0.121514	+	0.0882849i
$809$	608704.	+	1.87340e6i	0.0326990	+	0.100637i	0.966074	−	0.258266i	$-0.0831510\pi$
$809$	608704.	+	1.87340e6i	0.0326990	+	0.100637i	−0.933375	+	0.358903i	$0.883151\pi$
$810$	−8.12158e6	+	1.11784e7i	−0.434939	+	0.598642i
$811$	−2.58850e6	−	3.56277e6i	−0.138196	−	0.190211i	0.734309	−	0.678815i	$-0.237506\pi$
$811$	−2.58850e6	−	3.56277e6i	−0.138196	−	0.190211i	−0.872506	+	0.488604i	$0.837506\pi$
$812$	850187.	−	2.61661e6i	0.0452506	−	0.139267i
$813$	−1.03580e6	−	3.18787e6i	−0.0549604	−	0.169151i
$814$			6.90162e6i			0.365082i
$815$	1.72113e7	−	5.29710e7i	0.907654	−	2.79347i
$816$	−193556.	+	266407.i	−0.0101761	+	0.0140062i
$817$	−2.48099e7	+	8.06122e6i	−1.30038	+	0.422518i
$818$	−2.36221e6	−	7.27013e6i	−0.123434	−	0.379891i
$819$	−1.16316e7	−	3.77934e6i	−0.605941	−	0.196882i
$820$	−1.93832e7	+	1.40827e7i	−1.00668	+	0.731395i
$821$	−109775.	−	35668.2i	−0.00568391	−	0.00184681i	0.306174	−	0.951976i	$-0.400951\pi$
$821$	−109775.	−	35668.2i	−0.00568391	−	0.00184681i	−0.311858	+	0.950129i	$0.600951\pi$
$822$		−	2.22990e6i		−	0.115108i
$823$	−9.50365e6	+	3.08792e6i	−0.489092	+	0.158916i	−0.543173	−	0.839621i	$-0.682777\pi$
$823$	−9.50365e6	+	3.08792e6i	−0.489092	+	0.158916i	0.0540806	+	0.998537i	$0.482777\pi$
$824$	−2.32140e7	+	7.54267e6i	−1.19105	+	0.386997i
$825$		−	5.09622e6i		−	0.260683i
$826$	7.21241e6	+	2.34345e6i	0.367816	+	0.119511i
$827$	1.66220e6	−	1.20766e6i	0.0845122	−	0.0614017i	−0.544727	−	0.838614i	$-0.683367\pi$
$827$	1.66220e6	−	1.20766e6i	0.0845122	−	0.0614017i	0.629239	+	0.777212i	$0.283367\pi$
$828$	−1.55048e7	−	5.03783e6i	−0.785944	−	0.255369i
$829$	7.80401e6	+	2.40183e7i	0.394395	+	1.21382i	0.929432	+	0.368994i	$0.120298\pi$
$829$	7.80401e6	+	2.40183e7i	0.394395	+	1.21382i	−0.535036	+	0.844829i	$0.679702\pi$
$830$	−4.98528e6	+	1.61981e6i	−0.251185	+	0.0816150i
$831$	−1.63014e6	+	2.24369e6i	−0.0818883	+	0.112710i
$832$	−481106.	+	1.48069e6i	−0.0240953	+	0.0741578i
$833$			2.82818e6i			0.141219i
$834$	675196.	+	2.07804e6i	0.0336136	+	0.103452i
$835$	−3.81385e6	+	1.17378e7i	−0.189299	+	0.582601i
$836$	7.16311e6	+	9.85918e6i	0.354475	+	0.487893i
$837$	−4.08733e6	+	5.62573e6i	−0.201663	+	0.277565i
$838$	−2.68503e6	−	8.26368e6i	−0.132081	−	0.406503i
$839$	2.04315e7	−	1.48444e7i	1.00207	−	0.728043i	0.0395357	−	0.999218i	$-0.487412\pi$
$839$	2.04315e7	−	1.48444e7i	1.00207	−	0.728043i	0.962530	+	0.271175i	$0.0874121\pi$
$840$	2.78695e6			0.136280
$841$	1.88794e7			0.920444
$842$	−3.46518e6	+	2.51760e6i	−0.168440	+	0.122379i
$843$			1.13006e6i			0.0547689i
$844$	1.76174e7	+	2.42483e7i	0.851307	+	1.17172i
$845$	−1.85255e6	−	1.34595e6i	−0.0892539	−	0.0648468i
$846$	1.95878e6	+	2.69603e6i	0.0940934	+	0.129508i
$847$	6.37214e6	−	2.07043e6i	0.305194	−	0.0991637i
$848$	−2.28103e6	+	3.13957e6i	−0.108929	+	0.149927i
$849$	−1.64541e6	−	1.19546e6i	−0.0783440	−	0.0569202i
$850$	−4.24072e6	−	3.08107e6i	−0.201323	−	0.146269i
$851$	−8.24391e6	+	2.53722e7i	−0.390220	+	1.20097i
$852$	149137.	+	48457.6i	0.00703860	+	0.00228698i
$853$	1.78984e7			0.842252			0.421126	−	0.907002i	$-0.361635\pi$
$853$	1.78984e7			0.842252			0.421126	+	0.907002i	$0.361635\pi$
$854$	5.26386e6	−	2.25638e6i	0.246979	−	0.105869i
$855$	4.08771e7			1.91234
$856$	1.55414e7	+	5.04972e6i	0.724948	+	0.235550i
$857$	9.35282e6	−	2.87850e7i	0.435001	−	1.33880i	−0.458084	−	0.888909i	$-0.651464\pi$
$857$	9.35282e6	−	2.87850e7i	0.435001	−	1.33880i	0.893085	−	0.449887i	$-0.148536\pi$
$858$	−798435.	−	580097.i	−0.0370272	−	0.0269019i
$859$	−4.91571e6	−	3.57147e6i	−0.227302	−	0.165145i	0.468305	−	0.883567i	$-0.344865\pi$
$859$	−4.91571e6	−	3.57147e6i	−0.227302	−	0.165145i	−0.695608	+	0.718422i	$0.744865\pi$
$860$	−2.54836e7	+	3.50752e7i	−1.17494	+	1.61716i
$861$	−1.58856e6	+	516153.i	−0.0730289	+	0.0237285i
$862$	−2.44262e6	−	3.36198e6i	−0.111966	−	0.154108i
$863$	2.56067e7	+	1.86044e7i	1.17038	+	0.850331i	0.991054	−	0.133458i	$-0.0426082\pi$
$863$	2.56067e7	+	1.86044e7i	1.17038	+	0.850331i	0.179326	+	0.983790i	$0.442608\pi$
$864$	3.73469e6	+	5.14036e6i	0.170204	+	0.234266i
$865$			7.72745e6i			0.351152i
$866$	−6.06190e6	+	4.40423e6i	−0.274672	+	0.199561i
$867$	−3.11927e6			−0.140931
$868$	−1.33970e7			−0.603543
$869$	−130322.	+	94684.4i	−0.00585421	+	0.00425333i
$870$	−230123.	−	708245.i	−0.0103077	−	0.0317238i
$871$	−5.02954e6	+	6.92257e6i	−0.224638	+	0.309187i
$872$	1.41645e7	+	1.94958e7i	0.630827	+	0.868258i
$873$	−5.38231e6	+	1.65650e7i	−0.239019	+	0.735626i
$874$	−3.19741e6	−	9.84060e6i	−0.141586	−	0.435756i
$875$		−	3.98356e7i		−	1.75894i
$876$	−1.31196e6	+	4.03780e6i	−0.0577645	+	0.177781i
$877$	−103295.	+	142174.i	−0.00453505	+	0.00624196i	−0.811278	−	0.584660i	$-0.801228\pi$
$877$	−103295.	+	142174.i	−0.00453505	+	0.00624196i	0.806743	+	0.590902i	$0.201228\pi$
$878$	−1.38840e7	+	4.51119e6i	−0.607826	+	0.197495i
$879$	−722573.	−	2.22385e6i	−0.0315435	−	0.0970809i
$880$	1.41022e7	+	4.58207e6i	0.613874	+	0.199460i
$881$	−1.35369e7	+	9.83513e6i	−0.587597	+	0.426914i	−0.841455	−	0.540327i	$-0.818300\pi$
$881$	−1.35369e7	+	9.83513e6i	−0.587597	+	0.426914i	0.253858	+	0.967241i	$0.418300\pi$
$882$	5.46155e6	+	1.77457e6i	0.236398	+	0.0768105i
$883$		−	8.05434e6i		−	0.347639i	−0.984778	−	0.173819i	$-0.944389\pi$
$883$		−	8.05434e6i		−	0.347639i	0.984778	−	0.173819i	$-0.0556109\pi$
$884$	4.39531e6	−	1.42812e6i	0.189173	−	0.0614660i
$885$	−8.88778e6	+	2.88781e6i	−0.381448	+	0.123940i
$886$		−	1.26324e7i		−	0.540631i
$887$	2.18090e7	+	7.08618e6i	0.930737	+	0.302415i	0.734864	−	0.678214i	$-0.237246\pi$
$887$	2.18090e7	+	7.08618e6i	0.930737	+	0.302415i	0.195873	+	0.980629i	$0.437246\pi$
$888$	2.68380e6	−	1.94990e6i	0.114214	−	0.0829812i
$889$	1.26725e6	+	411756.i	0.0537785	+	0.0174737i
$890$	29217.7	+	89923.0i	0.00123644	+	0.00380536i
$891$	−1.47781e7	+	4.80171e6i	−0.623628	+	0.202629i
$892$	−2.03608e7	+	2.80242e7i	−0.856807	+	1.17929i
$893$	2.97557e6	−	9.15788e6i	0.124865	−	0.384296i
$894$			755885.i			0.0316309i
$895$	−2.31935e7	−	7.13822e7i	−0.967851	−	2.97874i
$896$	−4.76480e6	+	1.46645e7i	−0.198278	+	0.610237i
$897$	−2.24233e6	−	3.08631e6i	−0.0930506	−	0.128073i
$898$	9.65702e6	−	1.32918e7i	0.399625	−	0.550036i
$899$	2.45540e6	+	7.55695e6i	0.101327	+	0.311851i
$900$	3.92022e7	−	2.84821e7i	1.61326	−	1.17210i
$901$	2.16301e6			0.0887660
$902$	5.91823e6			0.242201
$903$	−2.44528e6	+	1.77660e6i	−0.0997952	+	0.0725055i
$904$		−	2.85768e7i		−	1.16303i
$905$	4.88087e7	+	6.71794e7i	1.98096	+	2.72656i
$906$	276367.	+	200792.i	0.0111858	+	0.00812693i
$907$	−6.69676e6	−	9.21731e6i	−0.270300	−	0.372037i	0.652191	−	0.758055i	$-0.273850\pi$
$907$	−6.69676e6	−	9.21731e6i	−0.270300	−	0.372037i	−0.922491	+	0.386018i	$0.873850\pi$
$908$	−2.15410e6	+	699908.i	−0.0867063	+	0.0281726i
$909$	−2.78432e6	+	3.83228e6i	−0.111766	+	0.153832i
$910$	−1.04369e7	−	7.58282e6i	−0.417798	−	0.303548i
$911$	−1.17500e6	−	853690.i	−0.0469076	−	0.0340804i	0.564084	−	0.825717i	$-0.309229\pi$
$911$	−1.17500e6	−	853690.i	−0.0469076	−	0.0340804i	−0.610992	+	0.791637i	$0.709229\pi$
$912$	597029.	−	1.83747e6i	0.0237688	−	0.0731530i
$913$	−5.60636e6	−	1.82162e6i	−0.222589	−	0.0723236i
$914$	−4.70681e6			−0.186364
$915$	−3.61342e6	+	6.06221e6i	−0.142681	+	0.239375i
$916$	−1.63340e7			−0.643210
$917$	−9.48635e6	−	3.08230e6i	−0.372543	−	0.121046i
$918$	232952.	−	716952.i	0.00912346	−	0.0280791i
$919$	2.65999e7	+	1.93260e7i	1.03894	+	0.754836i	0.970079	−	0.242791i	$-0.0780628\pi$
$919$	2.65999e7	+	1.93260e7i	1.03894	+	0.754836i	0.0688633	+	0.997626i	$0.478063\pi$
$920$	−3.08803e7	−	2.24359e7i	−1.20285	−	0.873924i
$921$	275982.	−	379857.i	0.0107209	−	0.0147561i
$922$	465491.	−	151247.i	0.0180337	−	0.00585949i
$923$	−947034.	−	1.30348e6i	−0.0365899	−	0.0503617i
$924$	1.14234e6	+	829955.i	0.0440163	+	0.0319797i
$925$	−4.66081e7	−	6.41506e7i	−1.79105	−	2.46517i
$926$		−	8.59104e6i		−	0.329244i
$927$	−3.35586e7	+	2.43818e7i	−1.28264	+	0.931893i
$928$	7.26031e6			0.276748
$929$	−1.48254e7			−0.563595			−0.281798	−	0.959474i	$-0.590931\pi$
$929$	−1.48254e7			−0.563595			−0.281798	+	0.959474i	$0.590931\pi$
$930$	−2.93366e6	+	2.13143e6i	−0.111225	+	0.0808098i
$931$	−5.12760e6	−	1.57811e7i	−0.193883	−	0.596711i
$932$	−1.75586e7	+	2.41674e7i	−0.662141	+	0.911359i
$933$	−571433.	−	786510.i	−0.0214912	−	0.0295801i
$934$	−4.65028e6	+	1.43121e7i	−0.174426	+	0.536829i
$935$	−2.55392e6	−	7.86016e6i	−0.0955386	−	0.294037i
$936$		−	2.08291e7i		−	0.777108i
$937$	−69882.7	+	215077.i	−0.00260028	+	0.00800285i	−0.952348	−	0.305013i	$-0.901339\pi$
$937$	−69882.7	+	215077.i	−0.00260028	+	0.00800285i	0.949748	+	0.313016i	$0.101339\pi$
$938$	−1.58057e6	+	2.17547e6i	−0.0586554	+	0.0807322i
$939$	1.27698e6	−	414915.i	0.0472627	−	0.0153566i
$940$	−4.94533e6	−	1.52202e7i	−0.182547	−	0.561823i
$941$	−1.41522e7	−	4.59832e6i	−0.521013	−	0.169288i	0.0366918	−	0.999327i	$-0.488318\pi$
$941$	−1.41522e7	−	4.59832e6i	−0.521013	−	0.169288i	−0.557705	+	0.830039i	$0.688318\pi$
$942$	1.69470e6	−	1.23128e6i	0.0622253	−	0.0452093i
$943$	2.17570e7	+	7.06926e6i	0.796744	+	0.258878i
$944$		−	1.93940e7i		−	0.708332i
$945$	9.11143e6	−	2.96048e6i	0.331900	−	0.107841i
$946$	1.01853e7	−	3.30940e6i	0.370037	−	0.120232i
$947$		−	1.83266e7i		−	0.664060i	−0.943269	−	0.332030i	$-0.892266\pi$
$947$		−	1.83266e7i		−	0.664060i	0.943269	−	0.332030i	$-0.107734\pi$
$948$	33176.0	+	10779.5i	0.00119895	+	0.000389564i
$949$	3.52910e7	−	2.56404e7i	1.27203	−	0.924187i
$950$	2.92492e7	+	9.50363e6i	1.05149	+	0.341649i
$951$	−1.23430e6	−	3.79880e6i	−0.0442559	−	0.136206i
$952$	3.06592e6	−	996179.i	0.109640	−	0.0356242i
$953$	−2.48553e7	+	3.42104e7i	−0.886516	+	1.22018i	0.0880571	+	0.996115i	$0.471934\pi$
$953$	−2.48553e7	+	3.42104e7i	−0.886516	+	1.22018i	−0.974573	+	0.224069i	$0.928066\pi$
$954$	1.35720e6	−	4.17703e6i	0.0482806	−	0.148592i
$955$		−	9.70317e7i		−	3.44275i
$956$	1.26753e7	+	3.90107e7i	0.448554	+	1.38051i
$957$	258792.	−	796480.i	0.00913421	−	0.0281122i
$958$	1.14961e7	+	1.58231e7i	0.404705	+	0.557028i
$959$	1.92676e7	−	2.65195e7i	0.676519	−	0.931149i
$960$	−186312.	−	573409.i	−0.00652473	−	0.0200810i
$961$	8.14061e6	−	5.91450e6i	0.284347	−	0.206590i
$962$	−1.53559e7			−0.534982
$963$	2.77708e7			0.964991
$964$	1.85200e7	−	1.34556e7i	0.641873	−	0.466348i
$965$			5.54313e7i			1.91618i
$966$	−704672.	−	969898.i	−0.0242965	−	0.0334413i
$967$	−2.11163e7	−	1.53419e7i	−0.726192	−	0.527610i	0.162164	−	0.986764i	$-0.448153\pi$
$967$	−2.11163e7	−	1.53419e7i	−0.726192	−	0.527610i	−0.888357	+	0.459154i	$0.848153\pi$
$968$	6.70710e6	+	9.23153e6i	0.230063	+	0.316654i
$969$	−1.02415e6	+	332767.i	−0.0350393	+	0.0113850i
$970$	−1.07990e7	+	1.48636e7i	−0.368514	+	0.507216i
$971$	−3.06267e7	−	2.22516e7i	−1.04244	−	0.757379i	−0.0716823	−	0.997428i	$-0.522837\pi$
$971$	−3.06267e7	−	2.22516e7i	−1.04244	−	0.757379i	−0.970761	+	0.240048i	$0.922837\pi$
$972$	8.48848e6	+	6.16724e6i	0.288180	+	0.209375i
$973$	−9.92548e6	+	3.05475e7i	−0.336101	+	1.03441i
$974$	−3.25256e6	−	1.05682e6i	−0.109857	−	0.0356948i
$975$	1.13390e7			0.381999
$976$	−9.64783e6	−	1.10196e7i	−0.324194	−	0.370289i
$977$	−2.53098e7			−0.848306			−0.424153	−	0.905591i	$-0.639428\pi$
$977$	−2.53098e7			−0.848306			−0.424153	+	0.905591i	$0.639428\pi$
$978$	2.83348e6	+	920652.i	0.0947267	+	0.0307786i
$979$	−32857.8	+	101126.i	−0.00109567	+	0.00337214i
$980$	−2.23107e7	−	1.62097e7i	−0.742076	−	0.539150i
$981$	3.31317e7	+	2.40716e7i	1.09919	+	0.798605i
$982$	−8.87393e6	+	1.22139e7i	−0.293655	+	0.404181i
$983$	1.83118e7	−	5.94986e6i	0.604431	−	0.196392i	0.00921556	−	0.999958i	$-0.497067\pi$
$983$	1.83118e7	−	5.94986e6i	0.604431	−	0.196392i	0.595216	+	0.803566i	$0.297067\pi$
$984$	−1.67206e6	−	2.30140e6i	−0.0550509	−	0.0757711i
$985$	1.98874e7	+	1.44490e7i	0.653111	+	0.474513i
$986$	−506316.	−	696884.i	−0.0165855	−	0.0228280i
$987$		−	1.11568e6i		−	0.0364543i
$988$	−2.19364e7	+	1.59378e7i	−0.714947	+	0.519439i
$989$	4.13968e7			1.34579
$990$	−1.67814e7			−0.544177
$991$	1.67151e7	−	1.21442e7i	0.540661	−	0.392813i	−0.283669	−	0.958922i	$-0.591552\pi$
$991$	1.67151e7	−	1.21442e7i	0.540661	−	0.392813i	0.824330	+	0.566109i	$0.191552\pi$
$992$	−1.09248e7	−	3.36230e7i	−0.352479	−	1.08482i
$993$	279348.	−	384489.i	0.00899026	−	0.0123740i
$994$	−297613.	−	409629.i	−0.00955402	−	0.0131500i
$995$	−1.96022e7	+	6.03294e7i	−0.627694	+	1.93184i
$996$	394470.	+	1.21405e6i	0.0125999	+	0.0387784i
$997$		−	3.04805e6i		−	0.0971144i	−0.998820	−	0.0485572i	$-0.984538\pi$
$997$		−	3.04805e6i		−	0.0971144i	0.998820	−	0.0485572i	$-0.0154623\pi$
$998$	−2.88883e6	+	8.89090e6i	−0.0918111	+	0.282566i
$999$	6.70291e6	−	9.22576e6i	0.212495	−	0.292475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.6.g.a.3.12	✓	104
61.41	even	10	inner	61.6.g.a.41.12	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.6.g.a.3.12	✓	104	1.1	even	1	trivial
61.6.g.a.41.12	yes	104	61.41	even	10	inner

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:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	61.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.28313 - 0.741832i) q^{2} +(-0.718823 + 2.21231i) q^{3} +(-21.2262 - 15.4217i) q^{4} +(-84.4577 - 61.3621i) q^{5} +(3.28233 - 4.51774i) q^{6} +(78.0713 - 25.3669i) q^{7} +(82.1753 + 113.105i) q^{8} +(192.214 + 139.651i) q^{9} +O(q^{10})\)	\(q+(-2.28313 - 0.741832i) q^{2} +(-0.718823 + 2.21231i) q^{3} +(-21.2262 - 15.4217i) q^{4} +(-84.4577 - 61.3621i) q^{5} +(3.28233 - 4.51774i) q^{6} +(78.0713 - 25.3669i) q^{7} +(82.1753 + 113.105i) q^{8} +(192.214 + 139.651i) q^{9} +(147.307 + 202.751i) q^{10} +281.836i q^{11} +(49.3755 - 35.8734i) q^{12} -627.079 q^{13} -197.065 q^{14} +(196.462 - 142.738i) q^{15} +(155.734 + 479.300i) q^{16} +(165.107 - 227.250i) q^{17} +(-335.250 - 461.432i) q^{18} +(-509.277 + 1567.39i) q^{19} +(846.406 + 2604.97i) q^{20} +190.952i q^{21} +(209.075 - 643.467i) q^{22} +(1537.23 - 2115.82i) q^{23} +(-309.292 + 100.495i) q^{24} +(2402.12 + 7392.96i) q^{25} +(1431.70 + 465.187i) q^{26} +(-904.422 + 657.101i) q^{27} +(-2048.36 - 665.552i) q^{28} +1277.42i q^{29} +(-554.436 + 180.147i) q^{30} +(5915.81 - 1922.16i) q^{31} -5683.59i q^{32} +(-623.509 - 202.590i) q^{33} +(-545.542 + 396.359i) q^{34} +(-8150.29 - 2648.19i) q^{35} +(-1926.30 - 5928.53i) q^{36} +(-9701.46 + 3152.20i) q^{37} +(2325.49 - 3200.76i) q^{38} +(450.759 - 1387.29i) q^{39} -14595.0i q^{40} +(2703.05 + 8319.13i) q^{41} +(141.655 - 435.968i) q^{42} +(9303.90 + 12805.7i) q^{43} +(4346.40 - 5982.31i) q^{44} +(-7664.61 - 23589.3i) q^{45} +(-5079.27 + 3690.31i) q^{46} -5842.74 q^{47} -1172.31 q^{48} +(-8145.50 + 5918.05i) q^{49} -18661.0i q^{50} +(384.066 + 528.621i) q^{51} +(13310.5 + 9670.64i) q^{52} +(4526.16 + 6229.73i) q^{53} +(2552.37 - 829.315i) q^{54} +(17294.1 - 23803.2i) q^{55} +(9284.65 + 6745.69i) q^{56} +(-3101.48 - 2253.36i) q^{57} +(947.628 - 2916.50i) q^{58} +(-36599.2 - 11891.8i) q^{59} -6371.41 q^{60} +(-26711.3 + 11450.0i) q^{61} -14932.5 q^{62} +(18548.9 + 6026.90i) q^{63} +(767.219 - 2361.26i) q^{64} +(52961.6 + 38478.9i) q^{65} +(1273.26 + 925.078i) q^{66} +(8020.59 - 11039.4i) q^{67} +(-7009.19 + 2277.42i) q^{68} +(3575.84 + 4921.73i) q^{69} +(16643.6 + 12092.3i) q^{70} +(1510.23 + 2078.66i) q^{71} +33216.1i q^{72} +(-56278.5 + 40888.7i) q^{73} +24488.1 q^{74} -18082.2 q^{75} +(34982.0 - 25415.9i) q^{76} +(7149.31 + 22003.3i) q^{77} +(-2058.28 + 2832.98i) q^{78} +(335.956 + 462.403i) q^{79} +(16257.9 - 50036.8i) q^{80} +(17037.2 + 52435.2i) q^{81} -20998.8i q^{82} +(-6463.39 + 19892.3i) q^{83} +(2944.82 - 4053.19i) q^{84} +(-27889.1 + 9061.73i) q^{85} +(-11742.3 - 36139.0i) q^{86} +(-2826.04 - 918.236i) q^{87} +(-31877.0 + 23160.0i) q^{88} +(358.811 + 116.585i) q^{89} +59543.1i q^{90} +(-48956.9 + 15907.0i) q^{91} +(-65259.1 + 21204.0i) q^{92} +14469.3i q^{93} +(13339.7 + 4334.34i) q^{94} +(139191. - 101128. i) q^{95} +(12573.9 + 4085.50i) q^{96} +(22653.9 + 69721.4i) q^{97} +(22987.4 - 7469.06i) q^{98} +(-39358.8 + 54172.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9}+O(q^{10}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9} - 595 q^{10} + 1982 q^{12} + 2372 q^{13} - 4474 q^{14} - 1149 q^{15} - 8631 q^{16} + 950 q^{17} + 4340 q^{18} - 5597 q^{19} - 6627 q^{20} - 8639 q^{22} + 9065 q^{23} + 17220 q^{24} - 7694 q^{25} + 14810 q^{26} + 4500 q^{27} + 19835 q^{28} - 44585 q^{30} + 10905 q^{31} - 19205 q^{33} - 15376 q^{34} - 43790 q^{35} - 25135 q^{36} - 5 q^{37} + 17555 q^{38} + 29401 q^{39} - 21014 q^{41} + 62197 q^{42} - 31625 q^{43} + 146190 q^{44} + 153742 q^{45} + 13387 q^{46} + 27326 q^{47} - 82968 q^{48} + 14694 q^{49} + 34090 q^{51} + 90072 q^{52} - 40270 q^{53} - 13760 q^{54} + 25140 q^{55} - 97860 q^{56} + 114893 q^{57} - 18003 q^{58} - 117435 q^{59} - 536650 q^{60} - 121867 q^{61} - 157388 q^{62} - 160825 q^{63} + 132509 q^{64} - 155852 q^{65} + 308443 q^{66} + 101665 q^{67} + 303780 q^{68} + 281945 q^{69} + 264985 q^{70} + 160970 q^{71} + 127669 q^{73} - 133952 q^{74} - 139592 q^{75} - 641111 q^{76} + 128917 q^{77} + 1670 q^{78} + 187940 q^{79} + 785373 q^{80} - 453473 q^{81} - 301209 q^{83} + 100475 q^{84} - 340045 q^{85} - 462669 q^{86} + 189245 q^{87} - 881635 q^{88} - 201970 q^{89} + 93865 q^{91} - 622085 q^{92} - 285265 q^{94} - 113308 q^{95} + 1215465 q^{96} - 342131 q^{97} - 616150 q^{98} + 714235 q^{99}+O(q^{100}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9 - 595 * q^10 + 1982 * q^12 + 2372 * q^13 - 4474 * q^14 - 1149 * q^15 - 8631 * q^16 + 950 * q^17 + 4340 * q^18 - 5597 * q^19 - 6627 * q^20 - 8639 * q^22 + 9065 * q^23 + 17220 * q^24 - 7694 * q^25 + 14810 * q^26 + 4500 * q^27 + 19835 * q^28 - 44585 * q^30 + 10905 * q^31 - 19205 * q^33 - 15376 * q^34 - 43790 * q^35 - 25135 * q^36 - 5 * q^37 + 17555 * q^38 + 29401 * q^39 - 21014 * q^41 + 62197 * q^42 - 31625 * q^43 + 146190 * q^44 + 153742 * q^45 + 13387 * q^46 + 27326 * q^47 - 82968 * q^48 + 14694 * q^49 + 34090 * q^51 + 90072 * q^52 - 40270 * q^53 - 13760 * q^54 + 25140 * q^55 - 97860 * q^56 + 114893 * q^57 - 18003 * q^58 - 117435 * q^59 - 536650 * q^60 - 121867 * q^61 - 157388 * q^62 - 160825 * q^63 + 132509 * q^64 - 155852 * q^65 + 308443 * q^66 + 101665 * q^67 + 303780 * q^68 + 281945 * q^69 + 264985 * q^70 + 160970 * q^71 + 127669 * q^73 - 133952 * q^74 - 139592 * q^75 - 641111 * q^76 + 128917 * q^77 + 1670 * q^78 + 187940 * q^79 + 785373 * q^80 - 453473 * q^81 - 301209 * q^83 + 100475 * q^84 - 340045 * q^85 - 462669 * q^86 + 189245 * q^87 - 881635 * q^88 - 201970 * q^89 + 93865 * q^91 - 622085 * q^92 - 285265 * q^94 - 113308 * q^95 + 1215465 * q^96 - 342131 * q^97 - 616150 * q^98 + 714235 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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