LMFDB - Embedded newform 21.6.g.c.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,6,Mod(5,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("21.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	21.g (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:	$3.36806021607$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 171 x^{14} + 21495 x^{12} - 1128902 x^{10} + 42970860 x^{8} - 655075344 x^{6} + \cdots + 90230547456 $ x^16 - 171x^14 + 21495x^12 - 1128902x^10 + 42970860x^8 - 655075344x^6 + 7244325760x^4 - 29387167488*x^2 + 90230547456
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.4
Root			$-1.84692 + 1.06632i$ of defining polynomial
Character	$\chi$	$=$	21.17
Dual form			21.6.g.c.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.84692 + 1.06632i) q^{2} +(-6.34074 - 14.2406i) q^{3} +(-13.7259 + 23.7740i) q^{4} +(47.5262 + 82.3179i) q^{5} +(26.8959 + 19.5400i) q^{6} +(-95.0499 + 88.1619i) q^{7} -126.790i q^{8} +(-162.590 + 180.592i) q^{9} +O(q^{10})$	\(q+(-1.84692 + 1.06632i) q^{2} +(-6.34074 - 14.2406i) q^{3} +(-13.7259 + 23.7740i) q^{4} +(47.5262 + 82.3179i) q^{5} +(26.8959 + 19.5400i) q^{6} +(-95.0499 + 88.1619i) q^{7} -126.790i q^{8} +(-162.590 + 180.592i) q^{9} +(-175.555 - 101.356i) q^{10} +(113.171 + 65.3395i) q^{11} +(425.589 + 44.7208i) q^{12} -14.6710i q^{13} +(81.5410 - 264.182i) q^{14} +(870.905 - 1198.76i) q^{15} +(-304.031 - 526.597i) q^{16} +(-320.246 + 554.683i) q^{17} +(107.722 - 506.913i) q^{18} +(-469.972 + 271.339i) q^{19} -2609.37 q^{20} +(1858.17 + 794.558i) q^{21} -278.692 q^{22} +(3545.78 - 2047.16i) q^{23} +(-1805.56 + 803.939i) q^{24} +(-2954.99 + 5118.19i) q^{25} +(15.6440 + 27.0962i) q^{26} +(3602.68 + 1170.29i) q^{27} +(-791.312 - 3469.82i) q^{28} +3594.70i q^{29} +(-330.233 + 3142.68i) q^{30} +(-2512.28 - 1450.47i) q^{31} +(4636.74 + 2677.02i) q^{32} +(212.884 - 2025.93i) q^{33} -1365.94i q^{34} +(-11774.7 - 3634.30i) q^{35} +(-2061.69 - 6344.20i) q^{36} +(2171.02 + 3760.32i) q^{37} +(578.668 - 1002.28i) q^{38} +(-208.924 + 93.0249i) q^{39} +(10437.0 - 6025.83i) q^{40} +10945.3 q^{41} +(-4279.14 + 513.915i) q^{42} +20541.6 q^{43} +(-3106.76 + 1793.69i) q^{44} +(-22593.2 - 4801.21i) q^{45} +(-4365.85 + 7561.88i) q^{46} +(-4408.02 - 7634.91i) q^{47} +(-5571.28 + 7668.60i) q^{48} +(1261.97 - 16759.6i) q^{49} -12603.9i q^{50} +(9929.62 + 1043.40i) q^{51} +(348.788 + 201.373i) q^{52} +(6042.65 + 3488.72i) q^{53} +(-7901.79 + 1680.17i) q^{54} +12421.4i q^{55} +(11178.0 + 12051.3i) q^{56} +(6844.00 + 4972.20i) q^{57} +(-3833.11 - 6639.14i) q^{58} +(-20010.1 + 34658.4i) q^{59} +(16545.3 + 37159.0i) q^{60} +(-28760.9 + 16605.1i) q^{61} +6186.66 q^{62} +(-467.159 - 31499.5i) q^{63} +8039.72 q^{64} +(1207.68 - 697.257i) q^{65} +(1767.11 + 3968.74i) q^{66} +(-3218.09 + 5573.90i) q^{67} +(-8791.35 - 15227.1i) q^{68} +(-51635.6 - 37513.6i) q^{69} +(25622.2 - 5843.29i) q^{70} -32493.9i q^{71} +(22897.2 + 20614.7i) q^{72} +(-11031.2 - 6368.89i) q^{73} +(-8019.42 - 4630.02i) q^{74} +(91623.0 + 9627.73i) q^{75} -14897.5i q^{76} +(-16517.4 + 3766.88i) q^{77} +(286.672 - 394.590i) q^{78} +(-4298.94 - 7445.99i) q^{79} +(28898.9 - 50054.4i) q^{80} +(-6177.95 - 58724.9i) q^{81} +(-20215.0 + 11671.2i) q^{82} +31669.6 q^{83} +(-44394.8 + 33270.0i) q^{84} -60880.4 q^{85} +(-37938.7 + 21903.9i) q^{86} +(51190.8 - 22793.1i) q^{87} +(8284.36 - 14348.9i) q^{88} +(15972.9 + 27665.9i) q^{89} +(46847.6 - 15224.2i) q^{90} +(1293.42 + 1394.48i) q^{91} +112396. i q^{92} +(-4725.81 + 44973.5i) q^{93} +(16282.5 + 9400.72i) q^{94} +(-44672.0 - 25791.4i) q^{95} +(8722.08 - 83004.3i) q^{96} +143107. i q^{97} +(15540.3 + 32299.3i) q^{98} +(-30200.3 + 9814.28i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 18 q^{3} + 86 q^{4} - 616 q^{7} - 606 q^{9}+O(q^{10}) $ 16 * q + 18 * q^3 + 86 * q^4 - 616 * q^7 - 606 * q^9	$ 16 q + 18 q^{3} + 86 q^{4} - 616 q^{7} - 606 q^{9} - 546 q^{10} + 4128 q^{12} + 1188 q^{15} - 2858 q^{16} - 438 q^{18} + 3258 q^{19} + 882 q^{21} - 21900 q^{22} + 10374 q^{24} - 6578 q^{25} + 34006 q^{28} + 450 q^{30} - 9792 q^{31} + 17556 q^{33} - 15132 q^{36} - 10466 q^{37} - 17418 q^{39} - 60774 q^{40} - 56994 q^{42} + 111052 q^{43} - 31374 q^{45} + 81696 q^{46} - 51548 q^{49} + 31596 q^{51} + 126960 q^{52} + 7434 q^{54} - 31368 q^{57} - 41706 q^{58} + 60066 q^{60} - 128580 q^{61} - 123606 q^{63} - 158884 q^{64} - 160314 q^{66} - 102202 q^{67} + 234318 q^{70} + 330864 q^{72} + 345150 q^{73} + 428202 q^{75} - 277512 q^{78} - 251308 q^{79} + 179262 q^{81} - 534576 q^{82} + 106176 q^{84} + 205152 q^{85} - 551922 q^{87} - 359514 q^{88} + 65814 q^{91} + 17676 q^{93} + 276612 q^{94} + 1043910 q^{96} + 215472 q^{99}+O(q^{100}) $ 16 * q + 18 * q^3 + 86 * q^4 - 616 * q^7 - 606 * q^9 - 546 * q^10 + 4128 * q^12 + 1188 * q^15 - 2858 * q^16 - 438 * q^18 + 3258 * q^19 + 882 * q^21 - 21900 * q^22 + 10374 * q^24 - 6578 * q^25 + 34006 * q^28 + 450 * q^30 - 9792 * q^31 + 17556 * q^33 - 15132 * q^36 - 10466 * q^37 - 17418 * q^39 - 60774 * q^40 - 56994 * q^42 + 111052 * q^43 - 31374 * q^45 + 81696 * q^46 - 51548 * q^49 + 31596 * q^51 + 126960 * q^52 + 7434 * q^54 - 31368 * q^57 - 41706 * q^58 + 60066 * q^60 - 128580 * q^61 - 123606 * q^63 - 158884 * q^64 - 160314 * q^66 - 102202 * q^67 + 234318 * q^70 + 330864 * q^72 + 345150 * q^73 + 428202 * q^75 - 277512 * q^78 - 251308 * q^79 + 179262 * q^81 - 534576 * q^82 + 106176 * q^84 + 205152 * q^85 - 551922 * q^87 - 359514 * q^88 + 65814 * q^91 + 17676 * q^93 + 276612 * q^94 + 1043910 * q^96 + 215472 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.84692	+	1.06632i	−0.326493	+	0.188501i	−0.654283	−	0.756250i	$-0.727029\pi$
$2$	−1.84692	+	1.06632i	−0.326493	+	0.188501i	0.327790	+	0.944751i	$0.393696\pi$
$3$	−6.34074	−	14.2406i	−0.406759	−	0.913536i
$3$	−6.34074	−	14.2406i	−0.406759	−	0.913536i
$4$	−13.7259	+	23.7740i	−0.428935	+	0.742937i
$5$	47.5262	+	82.3179i	0.850175	+	1.47255i	0.881050	+	0.473024i	$0.156837\pi$
$5$	47.5262	+	82.3179i	0.850175	+	1.47255i	−0.0308744	+	0.999523i	$0.509829\pi$
$6$	26.8959	+	19.5400i	0.305006	+	0.221589i
$7$	−95.0499	+	88.1619i	−0.733173	+	0.680042i
$7$	−95.0499	+	88.1619i	−0.733173	+	0.680042i
$8$		−	126.790i		−	0.700420i
$9$	−162.590	+	180.592i	−0.669095	+	0.743177i
$10$	−175.555	−	101.356i	−0.555152	−	0.320517i
$11$	113.171	+	65.3395i	0.282004	+	0.162815i	0.634330	−	0.773062i	$-0.281276\pi$
$11$	113.171	+	65.3395i	0.282004	+	0.162815i	−0.352327	+	0.935877i	$0.614609\pi$
$12$	425.589	+	44.7208i	0.853173	+	0.0896513i
$13$		−	14.6710i		−	0.0240769i	−0.999928	−	0.0120385i	$-0.996168\pi$
$13$		−	14.6710i		−	0.0240769i	0.999928	−	0.0120385i	$-0.00383205\pi$
$14$	81.5410	−	264.182i	0.111187	−	0.360233i
$15$	870.905	−	1198.76i	0.999408	−	1.37564i
$16$	−304.031	−	526.597i	−0.296905	−	0.514255i
$17$	−320.246	+	554.683i	−0.268758	+	0.465503i	−0.968541	−	0.248852i	$-0.919947\pi$
$17$	−320.246	+	554.683i	−0.268758	+	0.465503i	0.699783	+	0.714355i	$0.253280\pi$
$18$	107.722	−	506.913i	0.0783653	−	0.368767i
$19$	−469.972	+	271.339i	−0.298668	+	0.172436i	−0.641844	−	0.766835i	$-0.721830\pi$
$19$	−469.972	+	271.339i	−0.298668	+	0.172436i	0.343177	+	0.939271i	$0.388497\pi$
$20$	−2609.37			−1.45868
$21$	1858.17	+	794.558i	0.919467	+	0.393167i
$22$	−278.692			−0.122763
$23$	3545.78	−	2047.16i	1.39763	−	0.806922i	0.403485	−	0.914986i	$-0.367799\pi$
$23$	3545.78	−	2047.16i	1.39763	−	0.806922i	0.994144	+	0.108065i	$0.0344653\pi$
$24$	−1805.56	+	803.939i	−0.639858	+	0.284902i
$25$	−2954.99	+	5118.19i	−0.945596	+	1.63782i
$26$	15.6440	+	27.0962i	0.00453852	+	0.00786094i
$27$	3602.68	+	1170.29i	0.951079	+	0.308948i
$28$	−791.312	−	3469.82i	−0.190745	−	0.836395i
$29$			3594.70i			0.793721i	0.917879	+	0.396861i	$0.129900\pi$
$29$			3594.70i			0.793721i	−0.917879	+	0.396861i	$0.870100\pi$
$30$	−330.233	+	3142.68i	−0.0669910	+	0.637525i
$31$	−2512.28	−	1450.47i	−0.469531	−	0.271084i	0.246512	−	0.969140i	$-0.420715\pi$
$31$	−2512.28	−	1450.47i	−0.469531	−	0.271084i	−0.716043	+	0.698056i	$0.754049\pi$
$32$	4636.74	+	2677.02i	0.800456	+	0.462144i
$33$	212.884	−	2025.93i	0.0340298	−	0.323847i
$34$		−	1365.94i		−	0.202644i
$35$	−11774.7	−	3634.30i	−1.62472	−	0.501477i
$36$	−2061.69	−	6344.20i	−0.265136	−	0.815870i
$37$	2171.02	+	3760.32i	0.260712	+	0.451566i	0.966431	−	0.256926i	$-0.0827095\pi$
$37$	2171.02	+	3760.32i	0.260712	+	0.451566i	−0.705720	+	0.708491i	$0.749376\pi$
$38$	578.668	−	1002.28i	0.0650086	−	0.112598i
$39$	−208.924	+	93.0249i	−0.0219951	+	0.00979349i
$40$	10437.0	−	6025.83i	1.03140	−	0.595480i
$41$	10945.3			1.01687			0.508436	−	0.861100i	$-0.330224\pi$
$41$	10945.3			1.01687			0.508436	+	0.861100i	$0.330224\pi$
$42$	−4279.14	+	513.915i	−0.374312	+	0.0449540i
$43$	20541.6			1.69419			0.847096	−	0.531440i	$-0.178349\pi$
$43$	20541.6			1.69419			0.847096	+	0.531440i	$0.178349\pi$
$44$	−3106.76	+	1793.69i	−0.241922	+	0.139674i
$45$	−22593.2	−	4801.21i	−1.66321	−	0.353443i
$46$	−4365.85	+	7561.88i	−0.304211	+	0.526908i
$47$	−4408.02	−	7634.91i	−0.291071	−	0.504149i	0.682992	−	0.730425i	$-0.260678\pi$
$47$	−4408.02	−	7634.91i	−0.291071	−	0.504149i	−0.974063	+	0.226276i	$0.927345\pi$
$48$	−5571.28	+	7668.60i	−0.349022	+	0.480411i
$49$	1261.97	−	16759.6i	0.0750861	−	0.997177i
$50$		−	12603.9i		−	0.712982i
$51$	9929.62	+	1043.40i	0.534573	+	0.0561729i
$52$	348.788	+	201.373i	0.0178876	+	0.0103274i
$53$	6042.65	+	3488.72i	0.295486	+	0.170599i	0.640413	−	0.768030i	$-0.278763\pi$
$53$	6042.65	+	3488.72i	0.295486	+	0.170599i	−0.344927	+	0.938629i	$0.612096\pi$
$54$	−7901.79	+	1680.17i	−0.368757	+	0.0784096i
$55$			12421.4i			0.553685i
$56$	11178.0	+	12051.3i	0.476315	+	0.513529i
$57$	6844.00	+	4972.20i	0.279012	+	0.202704i
$58$	−3833.11	−	6639.14i	−0.149617	−	0.259144i
$59$	−20010.1	+	34658.4i	−0.748373	+	1.29622i	0.200229	+	0.979749i	$0.435831\pi$
$59$	−20010.1	+	34658.4i	−0.748373	+	1.29622i	−0.948602	+	0.316471i	$0.897502\pi$
$60$	16545.3	+	37159.0i	0.593330	+	1.33256i
$61$	−28760.9	+	16605.1i	−0.989641	+	0.571370i	−0.905167	−	0.425056i	$-0.860254\pi$
$61$	−28760.9	+	16605.1i	−0.989641	+	0.571370i	−0.0844740	+	0.996426i	$0.526921\pi$
$62$	6186.66			0.204398
$63$	−467.159	−	31499.5i	−0.0148290	−	0.999890i
$64$	8039.72			0.245353
$65$	1207.68	−	697.257i	0.0354544	−	0.0204696i
$66$	1767.11	+	3968.74i	0.0499349	+	0.112148i
$67$	−3218.09	+	5573.90i	−0.0875813	+	0.151695i	−0.906488	−	0.422231i	$-0.861247\pi$
$67$	−3218.09	+	5573.90i	−0.0875813	+	0.151695i	0.818907	+	0.573926i	$0.194580\pi$
$68$	−8791.35	−	15227.1i	−0.230560	−	0.399341i
$69$	−51635.6	−	37513.6i	−1.30565	−	0.948562i
$70$	25622.2	−	5843.29i	0.624988	−	0.142532i
$71$		−	32493.9i		−	0.764990i	−0.923958	−	0.382495i	$-0.875065\pi$
$71$		−	32493.9i		−	0.764990i	0.923958	−	0.382495i	$-0.124935\pi$
$72$	22897.2	+	20614.7i	0.520536	+	0.468647i
$73$	−11031.2	−	6368.89i	−0.242280	−	0.139880i	0.373944	−	0.927451i	$-0.378005\pi$
$73$	−11031.2	−	6368.89i	−0.242280	−	0.139880i	−0.616224	+	0.787571i	$0.711338\pi$
$74$	−8019.42	−	4630.02i	−0.170241	−	0.0982886i
$75$	91623.0	+	9627.73i	1.88084	+	0.197638i
$76$		−	14897.5i		−	0.295855i
$77$	−16517.4	+	3766.88i	−0.317478	+	0.0724028i
$78$	286.672	−	394.590i	0.00533517	−	0.00734360i
$79$	−4298.94	−	7445.99i	−0.0774986	−	0.134232i	0.824671	−	0.565612i	$-0.191360\pi$
$79$	−4298.94	−	7445.99i	−0.0774986	−	0.134232i	−0.902170	+	0.431380i	$0.858027\pi$
$80$	28898.9	−	50054.4i	0.504843	−	0.874414i
$81$	−6177.95	−	58724.9i	−0.104624	−	0.994512i
$82$	−20215.0	+	11671.2i	−0.332002	+	0.191681i
$83$	31669.6			0.504601			0.252300	−	0.967649i	$-0.418813\pi$
$83$	31669.6			0.504601			0.252300	+	0.967649i	$0.418813\pi$
$84$	−44394.8	+	33270.0i	−0.686490	+	0.514463i
$85$	−60880.4			−0.913966
$86$	−37938.7	+	21903.9i	−0.553142	+	0.319356i
$87$	51190.8	−	22793.1i	0.725093	−	0.322853i
$88$	8284.36	−	14348.9i	0.114039	−	0.197521i
$89$	15972.9	+	27665.9i	0.213752	+	0.370229i	0.952886	−	0.303330i	$-0.0980983\pi$
$89$	15972.9	+	27665.9i	0.213752	+	0.370229i	−0.739134	+	0.673558i	$0.764765\pi$
$90$	46847.6	−	15224.2i	0.609651	−	0.198120i
$91$	1293.42	+	1394.48i	0.0163733	+	0.0176525i
$92$			112396.i			1.38447i
$93$	−4725.81	+	44973.5i	−0.0566590	+	0.539199i
$94$	16282.5	+	9400.72i	0.190065	+	0.109734i
$95$	−44672.0	−	25791.4i	−0.507840	−	0.293201i
$96$	8722.08	−	83004.3i	0.0965922	−	0.919226i
$97$			143107.i			1.54430i	0.635441	+	0.772149i	$0.280818\pi$
$97$			143107.i			1.54430i	−0.635441	+	0.772149i	$0.719182\pi$
$98$	15540.3	+	32299.3i	0.163454	+	0.339725i
$99$	−30200.3	+	9814.28i	−0.309687	+	0.100640i
$100$	−81119.8	−	140504.i	−0.811198	−	1.40504i
$101$	26793.8	−	46408.3i	0.261355	−	0.452681i	−0.705247	−	0.708962i	$-0.749164\pi$
$101$	26793.8	−	46408.3i	0.261355	−	0.452681i	0.966602	+	0.256281i	$0.0824972\pi$
$102$	−19451.8	+	8661.08i	−0.185123	+	0.0824274i
$103$	−133209.	+	76908.2i	−1.23720	+	0.714298i	−0.968521	−	0.248932i	$-0.919920\pi$
$103$	−133209.	+	76908.2i	−1.23720	+	0.714298i	−0.268679	+	0.963230i	$0.586587\pi$
$104$	−1860.13			−0.0168639
$105$	22905.4	+	190723.i	0.202751	+	1.68822i
$106$	−14880.4			−0.128632
$107$	132860.	−	76706.5i	1.12185	−	0.647698i	0.179975	−	0.983671i	$-0.442398\pi$
$107$	132860.	−	76706.5i	1.12185	−	0.647698i	0.941872	+	0.335973i	$0.109065\pi$
$108$	−77272.7	+	69586.7i	−0.637480	+	0.574073i
$109$	63869.7	−	110626.i	0.514907	−	0.891845i	−0.484943	−	0.874546i	$-0.661160\pi$
$109$	63869.7	−	110626.i	0.514907	−	0.891845i	0.999850	−	0.0172995i	$-0.00550688\pi$
$110$	−13245.2	−	22941.3i	−0.104370	−	0.180774i
$111$	39783.4	−	54759.9i	0.306475	−	0.421847i
$112$	75323.9	+	23249.1i	0.567398	+	0.175130i
$113$			90418.2i			0.666131i	0.942904	+	0.333066i	$0.108083\pi$
$113$			90418.2i			0.666131i	−0.942904	+	0.333066i	$0.891917\pi$
$114$	−17942.3	−	1885.38i	−0.129305	−	0.0135874i
$115$	337035.	+	194587.i	2.37646	+	1.37205i
$116$	−85460.4	−	49340.6i	−0.589685	−	0.340455i
$117$	2649.46	+	2385.36i	0.0178934	+	0.0161097i
$118$		−	85348.6i		−	0.564276i
$119$	−18462.5	−	80956.0i	−0.119515	−	0.524061i
$120$	−151990.	−	110422.i	−0.963523	−	0.700005i
$121$	−71987.0	−	124685.i	−0.446983	−	0.774197i
$122$	35412.8	−	61336.7i	0.215407	−	0.373096i
$123$	−69401.0	−	155867.i	−0.413622	−	0.928949i
$124$	68966.8	−	39818.0i	0.402797	−	0.232555i
$125$	−264719.			−1.51534
$126$	34451.4	+	57679.0i	0.193322	+	0.323662i
$127$	132321.			0.727982			0.363991	−	0.931402i	$-0.381414\pi$
$127$	132321.			0.727982			0.363991	+	0.931402i	$0.381414\pi$
$128$	−163224.	+	94237.6i	−0.880562	+	0.508393i
$129$	−130249.	−	292525.i	−0.689127	−	1.54770i
$130$	−1487.00	+	2575.56i	−0.00771707	+	0.0133664i
$131$	73888.8	+	127979.i	0.376184	+	0.651570i	0.990504	−	0.137487i	$-0.0439026\pi$
$131$	73888.8	+	127979.i	0.376184	+	0.651570i	−0.614319	+	0.789058i	$0.710569\pi$
$132$	45242.4	+	32868.8i	0.226001	+	0.164191i
$133$	20749.1	−	67224.3i	0.101712	−	0.329532i
$134$		−	13726.1i		−	0.0660366i
$135$	74885.8	+	352185.i	0.353643	+	1.66317i
$136$	70327.9	+	40603.9i	0.326047	+	0.188244i
$137$	196313.	+	113341.i	0.893608	+	0.515925i	0.875121	−	0.483904i	$-0.160782\pi$
$137$	196313.	+	113341.i	0.893608	+	0.515925i	0.0184870	+	0.999829i	$0.494115\pi$
$138$	135368.	+	14224.5i	0.605090	+	0.0635828i
$139$		−	230678.i		−	1.01267i	−0.862335	−	0.506337i	$-0.830999\pi$
$139$		−	230678.i		−	1.01267i	0.862335	−	0.506337i	$-0.169001\pi$
$140$	248020.	−	230047.i	1.06946	−	0.991963i
$141$	−80775.7	+	111184.i	−0.342163	+	0.470971i
$142$	34648.9	+	60013.7i	0.144201	+	0.249764i
$143$	958.594	−	1660.33i	0.00392008	−	0.00678977i
$144$	144532.	+	30713.9i	0.580840	+	0.123432i
$145$	−295908.	+	170843.i	−1.16879	+	0.674802i
$146$	27165.1			0.105470
$147$	−246668.	+	88296.7i	−0.941499	+	0.337017i
$148$	−119197.			−0.447313
$149$	−8104.11	+	4678.91i	−0.0299047	+	0.0172655i	−0.514878	−	0.857264i	$-0.672163\pi$
$149$	−8104.11	+	4678.91i	−0.0299047	+	0.0172655i	0.484973	+	0.874529i	$0.338829\pi$
$150$	−179487.	+	79917.8i	−0.651335	+	0.290012i
$151$	−69228.6	+	119907.i	−0.247083	+	0.427961i	−0.962715	−	0.270517i	$-0.912805\pi$
$151$	−69228.6	+	119907.i	−0.247083	+	0.427961i	0.715632	+	0.698477i	$0.246139\pi$
$152$	34402.9	+	59587.5i	0.120777	+	0.209193i
$153$	−48102.4	−	148020.i	−0.166126	−	0.511200i
$154$	26489.6	−	24570.0i	0.0900065	−	0.0834839i
$155$		−	275741.i		−	0.921876i
$156$	656.098	−	6243.80i	0.00215853	−	0.0205418i
$157$	−13393.0	−	7732.45i	−0.0433640	−	0.0250362i	0.478161	−	0.878272i	$-0.341303\pi$
$157$	−13393.0	−	7732.45i	−0.0433640	−	0.0250362i	−0.521525	+	0.853236i	$0.674637\pi$
$158$	15879.6	+	9168.11i	0.0506055	+	0.0292171i
$159$	11366.7	−	108172.i	0.0356568	−	0.339330i
$160$			508915.i			1.57161i
$161$	−156545.	+	507184.i	−0.475964	+	1.54206i
$162$	74029.8	+	101873.i	0.221625	+	0.304979i
$163$	−144822.	−	250840.i	−0.426940	−	0.739482i	0.569659	−	0.821881i	$-0.307075\pi$
$163$	−144822.	−	250840.i	−0.426940	−	0.739482i	−0.996599	+	0.0823992i	$0.973742\pi$
$164$	−150234.	+	260212.i	−0.436172	+	0.755472i
$165$	176888.	−	78760.6i	0.505811	−	0.225216i
$166$	−58491.4	+	33770.0i	−0.164749	+	0.0951176i
$167$	347837.			0.965128			0.482564	−	0.875861i	$-0.339706\pi$
$167$	347837.			0.965128			0.482564	+	0.875861i	$0.339706\pi$
$168$	100742.	−	235596.i	0.275382	−	0.644013i
$169$	371078.			0.999420
$170$	112441.	−	64918.1i	0.298403	−	0.172283i
$171$	27411.2	−	128990.i	0.0716866	−	0.337339i
$172$	−281952.	+	488355.i	−0.726698	+	1.25868i
$173$	−254069.	−	440060.i	−0.645411	−	1.11788i	−0.984206	−	0.177024i	$-0.943353\pi$
$173$	−254069.	−	440060.i	−0.645411	−	1.11788i	0.338796	−	0.940860i	$-0.389980\pi$
$174$	−70240.7	+	96682.9i	−0.175880	+	0.242090i
$175$	−170358.	−	747001.i	−0.420501	−	1.84385i
$176$		−	79460.9i		−	0.193362i
$177$	620436.	+	65195.3i	1.48855	+	0.156417i
$178$	−59001.6	−	34064.6i	−0.139577	−	0.0805847i
$179$	−346765.	−	200205.i	−0.808914	−	0.467026i	0.0376649	−	0.999290i	$-0.488008\pi$
$179$	−346765.	−	200205.i	−0.808914	−	0.467026i	−0.846578	+	0.532264i	$0.821341\pi$
$180$	424257.	−	471231.i	0.975995	−	1.08406i
$181$			10694.7i			0.0242646i	0.999926	+	0.0121323i	$0.00386192\pi$
$181$			10694.7i			0.0242646i	−0.999926	+	0.0121323i	$0.996138\pi$
$182$	−3875.81	−	1196.29i	−0.00867329	−	0.00267705i
$183$	418832.	+	304284.i	0.924511	+	0.671663i
$184$	−259558.	−	449567.i	−0.565184	−	0.978927i
$185$	−206361.	+	357428.i	−0.443301	+	0.767820i
$186$	−39228.0	−	88101.8i	−0.0831407	−	0.186725i
$187$	−72485.4	+	41849.4i	−0.151582	+	0.0875156i
$188$	242016.			0.499402
$189$	−445610.	+	206383.i	−0.907403	+	0.420261i
$190$	110008.			0.221075
$191$	−170825.	+	98626.1i	−0.338820	+	0.195618i	−0.659750	−	0.751485i	$-0.729338\pi$
$191$	−170825.	+	98626.1i	−0.338820	+	0.195618i	0.320930	+	0.947103i	$0.396005\pi$
$192$	−50977.8	−	114491.i	−0.0997994	−	0.224139i
$193$	62755.4	−	108695.i	0.121271	−	0.210048i	−0.798998	−	0.601334i	$-0.794636\pi$
$193$	62755.4	−	108695.i	0.121271	−	0.210048i	0.920269	+	0.391286i	$0.127970\pi$
$194$	−152598.	−	264307.i	−0.291101	−	0.504202i
$195$	−17587.0	−	12777.0i	−0.0331211	−	0.0240627i
$196$	381120.	+	260042.i	0.708633	+	0.483508i
$197$		−	631690.i		−	1.15968i	−0.814730	−	0.579841i	$-0.803115\pi$
$197$		−	631690.i		−	1.15968i	0.814730	−	0.579841i	$-0.196885\pi$
$198$	45312.5	−	50329.5i	0.0821400	−	0.0912345i
$199$	−538997.	−	311190.i	−0.964837	−	0.557049i	−0.0671784	−	0.997741i	$-0.521400\pi$
$199$	−538997.	−	311190.i	−0.964837	−	0.557049i	−0.897658	+	0.440692i	$0.854733\pi$
$200$	648933.	+	374662.i	1.14716	+	0.662314i
$201$	99780.8	+	10485.0i	0.174203	+	0.0183053i
$202$			114283.i			0.197063i
$203$	−316916.	−	341676.i	−0.539764	−	0.581935i
$204$	−161099.	+	221745.i	−0.271030	+	0.373060i
$205$	520187.	+	900991.i	0.864520	+	1.49739i
$206$	164018.	−	284087.i	0.269291	−	0.466426i
$207$	−206808.	+	973186.i	−0.335461	+	1.57859i
$208$	−7725.70	+	4460.43i	−0.0123817	+	0.00714856i
$209$	−70916.5			−0.112300
$210$	−245676.	−	327825.i	−0.384427	−	0.512973i
$211$	−271742.			−0.420195			−0.210098	−	0.977680i	$-0.567378\pi$
$211$	−271742.			−0.420195			−0.210098	+	0.977680i	$0.567378\pi$
$212$	−165882.	+	95771.9i	−0.253489	+	0.146352i
$213$	−462733.	+	206035.i	−0.698845	+	0.311166i
$214$	−163588.	+	283342.i	−0.244183	+	0.422938i
$215$	976264.	+	1.69094e6i	1.44036	+	2.49478i
$216$	148381.	−	456782.i	0.216394	−	0.666154i
$217$	366668.	−	83620.8i	0.528596	−	0.120549i
$218$			272423.i			0.388241i
$219$	−20750.7	+	197475.i	−0.0292362	+	0.278229i
$220$	−295305.	−	170495.i	−0.411353	−	0.237495i
$221$	8137.74	+	4698.33i	0.0112079	+	0.00647087i
$222$	−15085.2	+	143559.i	−0.0205432	+	0.195501i
$223$			256397.i			0.345264i	0.984986	+	0.172632i	$0.0552271\pi$
$223$			256397.i			0.345264i	−0.984986	+	0.172632i	$0.944773\pi$
$224$	−676733.	+	154333.i	−0.901150	+	0.205512i
$225$	−443852.	−	1.36581e6i	−0.584497	−	1.79860i
$226$	−96414.9	−	166996.i	−0.125566	−	0.217487i
$227$	58947.5	−	102100.i	0.0759278	−	0.131511i	−0.825562	−	0.564312i	$-0.809141\pi$
$227$	58947.5	−	102100.i	0.0759278	−	0.131511i	0.901489	+	0.432801i	$0.142475\pi$
$228$	−212149.	+	94461.0i	−0.270274	+	0.120342i
$229$	323704.	−	186890.i	0.407905	−	0.235504i	−0.281984	−	0.959419i	$-0.590993\pi$
$229$	323704.	−	186890.i	0.407905	−	0.235504i	0.689889	+	0.723915i	$0.257659\pi$
$230$	−829970.			−1.03453
$231$	158375.	+	211333.i	0.195280	+	0.260577i
$232$	455771.			0.555938
$233$	1.09535e6	−	632398.i	1.32179	−	0.763134i	0.337773	−	0.941227i	$-0.390326\pi$
$233$	1.09535e6	−	632398.i	1.32179	−	0.763134i	0.984014	+	0.178093i	$0.0569929\pi$
$234$	−7436.91	−	1580.39i	−0.00887877	−	0.00188679i
$235$	418993.	−	725717.i	0.494922	−	0.857231i
$236$	−549313.	−	951438.i	−0.642007	−	1.11199i
$237$	−78776.9	+	108433.i	−0.0911021	+	0.125398i
$238$	120424.	+	129833.i	0.137807	+	0.148573i
$239$			520817.i			0.589780i	0.955531	+	0.294890i	$0.0952830\pi$
$239$			520817.i			0.589780i	−0.955531	+	0.294890i	$0.904717\pi$
$240$	−896045.	−	94156.4i	−1.00416	−	0.105517i
$241$	826439.	+	477145.i	0.916575	+	0.529185i	0.882541	−	0.470236i	$-0.155831\pi$
$241$	826439.	+	477145.i	0.916575	+	0.529185i	0.0340341	+	0.999421i	$0.489165\pi$
$242$	265909.	+	153523.i	0.291873	+	0.168513i
$243$	−797106.	+	460337.i	−0.865965	+	0.500104i
$244$		−	911681.i		−	0.980321i
$245$	1.43959e6	−	692636.i	1.53223	−	0.737208i
$246$	294383.	+	213871.i	0.310152	+	0.225327i
$247$	3980.80	+	6894.95i	0.00415172	+	0.00719099i
$248$	−183904.	+	318531.i	−0.189873	+	0.328869i
$249$	−200809.	−	450995.i	−0.205251	−	0.460971i
$250$	488915.	−	282275.i	0.494748	−	0.285643i
$251$	−789792.			−0.791277			−0.395638	−	0.918406i	$-0.629477\pi$
$251$	−789792.			−0.791277			−0.395638	+	0.918406i	$0.629477\pi$
$252$	755281.	+	421253.i	0.749216	+	0.417871i
$253$	535040.			0.525515
$254$	−244387.	+	141097.i	−0.237681	+	0.137225i
$255$	386027.	+	866974.i	0.371764	+	0.834941i
$256$	72339.6	−	125296.i	0.0689884	−	0.119491i
$257$	−553845.	−	959287.i	−0.523064	−	0.905974i	−0.999640	−	0.0268405i	$-0.991455\pi$
$257$	−553845.	−	959287.i	−0.523064	−	0.905974i	0.476575	−	0.879134i	$-0.341878\pi$
$258$	552485.	+	401383.i	0.516739	+	0.375414i
$259$	−537873.	−	166017.i	−0.498230	−	0.153781i
$260$			38281.9i			0.0351205i
$261$	−649175.	−	584463.i	−0.589875	−	0.531075i
$262$	−272934.	−	157578.i	−0.245643	−	0.141822i
$263$	−912781.	−	526995.i	−0.813724	−	0.469804i	0.0345231	−	0.999404i	$-0.489009\pi$
$263$	−912781.	−	526995.i	−0.813724	−	0.469804i	−0.848248	+	0.529600i	$0.822342\pi$
$264$	−256867.	−	26991.5i	−0.226829	−	0.0238351i
$265$			663224.i			0.580157i
$266$	33360.7	+	146283.i	0.0289089	+	0.126762i
$267$	292700.	−	402887.i	0.251272	−	0.345864i
$268$	−88342.5	−	153014.i	−0.0751334	−	0.130135i
$269$	229948.	−	398282.i	0.193753	−	0.335591i	−0.752738	−	0.658320i	$-0.771267\pi$
$269$	229948.	−	398282.i	0.193753	−	0.335591i	0.946491	+	0.322730i	$0.104601\pi$
$270$	−513850.	−	570606.i	−0.428970	−	0.476351i
$271$	−767031.	+	442845.i	−0.634438	+	0.366293i	−0.782469	−	0.622690i	$-0.786040\pi$
$271$	−767031.	+	442845.i	−0.634438	+	0.366293i	0.148031	+	0.988983i	$0.452707\pi$
$272$	389459.			0.319183
$273$	11656.9	−	27261.1i	0.00946625	−	0.0221379i
$274$	−483433.			−0.389009
$275$	−668840.	+	386155.i	−0.533323	+	0.307914i
$276$	1.60059e6	−	712676.i	1.26476	−	0.563144i
$277$	385228.	−	667234.i	0.301660	−	0.522491i	−0.674852	−	0.737953i	$-0.735792\pi$
$277$	385228.	−	667234.i	0.301660	−	0.522491i	0.976512	+	0.215462i	$0.0691258\pi$
$278$	245977.	+	426045.i	0.190890	+	0.330631i
$279$	670415.	−	217867.i	0.515624	−	0.167564i
$280$	−460792.	+	1.49290e6i	−0.351244	+	1.13799i
$281$			2.25084e6i			1.70051i	0.526374	+	0.850253i	$0.323551\pi$
$281$			2.25084e6i			1.70051i	−0.526374	+	0.850253i	$0.676449\pi$
$282$	30628.8	−	291481.i	0.0229354	−	0.218266i
$283$	4389.23	+	2534.12i	0.00325779	+	0.00188088i	0.501628	−	0.865083i	$-0.332735\pi$
$283$	4389.23	+	2534.12i	0.00325779	+	0.00188088i	−0.498370	+	0.866964i	$0.666068\pi$
$284$	772509.	+	446008.i	0.568339	+	0.328131i
$285$	−84031.7	+	799693.i	−0.0612817	+	0.583192i
$286$			4088.68i			0.00295575i
$287$	−1.04035e6	+	964955.i	−0.745544	+	0.691516i
$288$	−1.23734e6	+	402101.i	−0.879036	+	0.285663i
$289$	504813.	+	874362.i	0.355538	+	0.615810i
$290$	364346.	−	631067.i	0.254401	−	0.440636i
$291$	2.03793e6	−	907403.i	1.41077	−	0.628157i
$292$	302828.	−	174838.i	0.207844	−	0.119999i
$293$	2.51767e6			1.71329			0.856643	−	0.515909i	$-0.172546\pi$
$293$	2.51767e6			1.71329			0.856643	+	0.515909i	$0.172546\pi$
$294$	361424.	−	426105.i	0.243865	−	0.287507i
$295$	−3.80401e6			−2.54499
$296$	476769.	−	275263.i	0.316285	−	0.182607i
$297$	331254.	+	367841.i	0.217906	+	0.241974i
$298$	9978.45	−	17283.2i	0.00650912	−	0.0112741i
$299$	−30033.8	−	52020.0i	−0.0194282	−	0.0336506i
$300$	−1.48650e6	+	2.04609e6i	−0.953589	+	1.31257i
$301$	−1.95247e6	+	1.81098e6i	−1.24214	+	1.15212i
$302$		−	295280.i		−	0.186301i
$303$	−830775.	−	87297.8i	−0.519848	−	0.0546256i
$304$	285772.	+	164991.i	0.177352	+	0.102394i
$305$	−2.73379e6	−	1.57836e6i	−1.68274	−	0.971529i
$306$	246678.	+	222088.i	0.150601	+	0.135588i
$307$		−	2.31011e6i		−	1.39890i	−0.714681	−	0.699451i	$-0.753428\pi$
$307$		−	2.31011e6i		−	1.39890i	0.714681	−	0.699451i	$-0.246572\pi$
$308$	137162.	−	444388.i	0.0823869	−	0.266923i
$309$	1.93986e6	+	1.40932e6i	1.15578	+	0.839680i
$310$	294029.	+	509273.i	0.173774	+	0.300986i
$311$	1.17643e6	−	2.03763e6i	0.689707	−	1.19461i	−0.282226	−	0.959348i	$-0.591073\pi$
$311$	1.17643e6	−	2.03763e6i	0.689707	−	1.19461i	0.971933	−	0.235260i	$-0.0755940\pi$
$312$	11794.6	+	26489.3i	0.00685955	+	0.0154058i
$313$	1.72440e6	−	995586.i	0.994898	−	0.574404i	0.0881630	−	0.996106i	$-0.471900\pi$
$313$	1.72440e6	−	995586.i	0.994898	−	0.574404i	0.906735	+	0.421702i	$0.138567\pi$
$314$	32981.1			0.0188774
$315$	2.57077e6	−	1.53551e6i	1.45978	−	0.871918i
$316$	236028.			0.132967
$317$	−1.81332e6	+	1.04692e6i	−1.01350	+	0.585147i	−0.912216	−	0.409710i	$-0.865630\pi$
$317$	−1.81332e6	+	1.04692e6i	−1.01350	+	0.585147i	−0.101289	+	0.994857i	$0.532297\pi$
$318$	94352.7	+	211906.i	0.0523223	+	0.117510i
$319$	−234876.	+	406817.i	−0.129230	+	0.223832i
$320$	382098.	+	661813.i	0.208593	+	0.361294i
$321$	−1.93478e6	−	1.40563e6i	−1.04802	−	0.761390i
$322$	−251695.	−	1.10366e6i	−0.135281	−	0.593191i
$323$		−	347581.i		−	0.185374i
$324$	1.48092e6	+	659179.i	0.783737	+	0.348852i
$325$	75088.9	+	43352.6i	0.0394337	+	0.0227670i
$326$	534952.	+	308854.i	0.278786	+	0.160957i
$327$	−1.98036e6	−	208096.i	−1.02418	−	0.107620i
$328$		−	1.38774e6i		−	0.712237i
$329$	1.09209e6	+	337078.i	0.556248	+	0.171688i
$330$	−242714.	+	334084.i	−0.122690	+	0.168877i
$331$	−137622.	−	238368.i	−0.0690426	−	0.119585i	0.829438	−	0.558599i	$-0.188661\pi$
$331$	−137622.	−	238368.i	−0.0690426	−	0.119585i	−0.898480	+	0.439014i	$0.855328\pi$
$332$	−434695.	+	752914.i	−0.216441	+	0.374887i
$333$	−1.03207e6	−	219322.i	−0.510034	−	0.108385i
$334$	−642428.	+	370906.i	−0.315107	+	0.181927i
$335$	−611775.			−0.297838
$336$	−146528.	−	1.22007e6i	−0.0708065	−	0.589574i
$337$	455651.			0.218553			0.109277	−	0.994011i	$-0.465147\pi$
$337$	455651.			0.218553			0.109277	+	0.994011i	$0.465147\pi$
$338$	−685352.	+	395688.i	−0.326304	+	0.188391i
$339$	1.28761e6	−	573319.i	0.608535	−	0.270955i
$340$	835639.	−	1.44737e6i	0.392032	−	0.679019i
$341$	−189546.	−	328303.i	−0.0882730	−	0.152893i
$342$	86918.5	+	267464.i	0.0401834	+	0.123652i
$343$	1.35760e6	+	1.70425e6i	0.623071	+	0.782165i
$344$		−	2.60446e6i		−	1.18665i
$345$	633990.	−	6.03341e6i	0.286771	−	2.72907i
$346$	938491.	+	541838.i	0.421444	+	0.243321i
$347$	1.48263e6	+	855997.i	0.661012	+	0.381636i	0.792663	−	0.609661i	$-0.208694\pi$
$347$	1.48263e6	+	855997.i	0.661012	+	0.381636i	−0.131650	+	0.991296i	$0.542028\pi$
$348$	−160758.	+	1.52986e6i	−0.0711581	+	0.677181i
$349$			1.94736e6i			0.855822i	0.903821	+	0.427911i	$0.140750\pi$
$349$			1.94736e6i			0.855822i	−0.903821	+	0.427911i	$0.859250\pi$
$350$	1.11118e6	+	1.19800e6i	0.484858	+	0.522740i
$351$	17169.4	−	52854.9i	0.00743852	−	0.0228990i
$352$	349830.	+	605924.i	0.150488	+	0.260652i
$353$	−1.79675e6	+	3.11207e6i	−0.767452	+	1.32927i	0.171488	+	0.985186i	$0.445143\pi$
$353$	−1.79675e6	+	3.11207e6i	−0.767452	+	1.32927i	−0.938940	+	0.344080i	$0.888191\pi$
$354$	−1.21542e6	+	541173.i	−0.515486	+	0.229524i
$355$	2.67483e6	−	1.54431e6i	1.12648	−	0.650375i
$356$	−876973.			−0.366742
$357$	−1.03580e6	+	776238.i	−0.430135	+	0.322348i
$358$	853930.			0.352139
$359$	2.23739e6	−	1.29176e6i	0.916232	−	0.528987i	0.0338008	−	0.999429i	$-0.489239\pi$
$359$	2.23739e6	−	1.29176e6i	0.916232	−	0.528987i	0.882431	+	0.470442i	$0.155905\pi$
$360$	−608743.	+	2.86459e6i	−0.247558	+	1.16495i
$361$	−1.09080e6	+	1.88932e6i	−0.440532	+	0.763023i
$362$	−11404.0	−	19752.3i	−0.00457389	−	0.00792221i
$363$	−1.31914e6	+	1.81574e6i	−0.525442	+	0.723246i
$364$	−50905.6	+	11609.3i	−0.0201378	+	0.00459254i
$365$		−	1.21076e6i		−	0.475691i
$366$	−1.09802e6	−	115379.i	−0.428455	−	0.0450221i
$367$	−3.26113e6	−	1.88281e6i	−1.26387	−	0.729696i	−0.290050	−	0.957012i	$-0.593672\pi$
$367$	−3.26113e6	−	1.88281e6i	−1.26387	−	0.729696i	−0.973821	+	0.227315i	$0.927005\pi$
$368$	−2.15605e6	−	1.24480e6i	−0.829927	−	0.479159i
$369$	−1.77959e6	+	1.97663e6i	−0.680384	+	0.755716i
$370$		−	880189.i		−	0.334250i
$371$	−881925.	+	201128.i	−0.332657	+	0.0758644i
$372$	−1.00433e6	−	729654.i	−0.376288	−	0.273376i
$373$	968610.	+	1.67768e6i	0.360476	+	0.624363i	0.988039	−	0.154203i	$-0.0492809\pi$
$373$	968610.	+	1.67768e6i	0.360476	+	0.624363i	−0.627563	+	0.778566i	$0.715948\pi$
$374$	89249.9	−	154585.i	0.0329935	−	0.0571465i
$375$	1.67851e6	+	3.76976e6i	0.616377	+	1.38432i
$376$	−968026.	+	558890.i	−0.353116	+	0.203872i
$377$	52737.8			0.0191104
$378$	602937.	−	856336.i	0.217041	−	0.308258i
$379$	2.04113e6			0.729917			0.364959	−	0.931024i	$-0.381083\pi$
$379$	2.04113e6			0.729917			0.364959	+	0.931024i	$0.381083\pi$
$380$	1.22633e6	−	708021.i	0.435660	−	0.251529i
$381$	−839015.	−	1.88434e6i	−0.296113	−	0.665038i
$382$	210334.	−	364309.i	0.0737482	−	0.127736i
$383$	235350.	+	407639.i	0.0819819	+	0.141997i	0.904101	−	0.427319i	$-0.140542\pi$
$383$	235350.	+	407639.i	0.0819819	+	0.141997i	−0.822119	+	0.569315i	$0.807208\pi$
$384$	2.37696e6	+	1.72688e6i	0.822611	+	0.597632i
$385$	−1.09509e6	−	1.18065e6i	−0.376529	−	0.405947i
$386$			267670.i			0.0914388i
$387$	−3.33986e6	+	3.70964e6i	−1.13358	+	1.25908i
$388$	−3.40222e6	−	1.96427e6i	−1.14732	−	0.662403i
$389$	3.97621e6	+	2.29567e6i	1.33228	+	0.769193i	0.985649	−	0.168808i	$-0.0539919\pi$
$389$	3.97621e6	+	2.29567e6i	1.33228	+	0.769193i	0.346632	+	0.938001i	$0.387325\pi$
$390$	46106.2	+	4844.84i	0.0153496	+	0.00161294i
$391$			2.62238e6i			0.867467i
$392$	−2.12494e6	−	160005.i	−0.698442	−	0.0525918i
$393$	1.35399e6	−	1.86371e6i	0.442216	−	0.608690i
$394$	673585.	+	1.16668e6i	0.218601	+	0.378628i
$395$	408625.	−	707760.i	0.131775	−	0.228241i
$396$	181202.	−	852692.i	0.0580665	−	0.273246i
$397$	3.94532e6	−	2.27783e6i	1.25634	−	0.725346i	0.283976	−	0.958831i	$-0.408346\pi$
$397$	3.94532e6	−	2.27783e6i	1.25634	−	0.725346i	0.972360	+	0.233485i	$0.0750129\pi$
$398$	1.32731e6			0.420016
$399$	−1.08888e6	+	130772.i	−0.342411	+	0.0411228i
$400$	3.59363e6			1.12301
$401$	−2.09361e6	+	1.20875e6i	−0.650183	+	0.375383i	−0.788526	−	0.615001i	$-0.789156\pi$
$401$	−2.09361e6	+	1.20875e6i	−0.650183	+	0.375383i	0.138344	+	0.990384i	$0.455822\pi$
$402$	−195468.	+	87033.5i	−0.0603268	+	0.0268609i
$403$	−21279.8	+	36857.7i	−0.00652687	+	0.0113049i
$404$	735540.	+	1.27399e6i	0.224209	+	0.388341i
$405$	4.54050e6	−	3.29953e6i	1.37552	−	0.999573i
$406$	949655.	+	293116.i	0.285924	+	0.0882518i
$407$			567414.i			0.169791i
$408$	132293.	−	1.25897e6i	0.0393446	−	0.374426i
$409$	56278.8	+	32492.6i	0.0166355	+	0.00960452i	0.508295	−	0.861183i	$-0.330276\pi$
$409$	56278.8	+	32492.6i	0.0166355	+	0.00960452i	−0.491659	+	0.870788i	$0.663609\pi$
$410$	−1.92149e6	−	1.10937e6i	−0.564519	−	0.325925i
$411$	369280.	−	3.51428e6i	0.107833	−	1.02620i
$412$		−	4.22254e6i		−	1.22555i
$413$	−1.15360e6	−	5.05840e6i	−0.332797	−	1.45928i
$414$	−655771.	−	2.01792e6i	−0.188040	−	0.578634i
$415$	1.50514e6	+	2.60698e6i	0.428999	+	0.743048i
$416$	39274.5	−	68025.5i	0.0111270	−	0.0192725i
$417$	−3.28500e6	+	1.46267e6i	−0.925115	+	0.411914i
$418$	130977.	−	75619.7i	0.0366653	−	0.0211687i
$419$	−4.52870e6			−1.26020			−0.630098	−	0.776515i	$-0.716985\pi$
$419$	−4.52870e6			−1.26020			−0.630098	+	0.776515i	$0.716985\pi$
$420$	−4.84863e6	−	2.07329e6i	−1.34121	−	0.573505i
$421$	−3.77935e6			−1.03923			−0.519615	−	0.854401i	$-0.673925\pi$
$421$	−3.77935e6			−1.03923			−0.519615	+	0.854401i	$0.673925\pi$
$422$	501887.	−	289764.i	0.137191	−	0.0792071i
$423$	2.09550e6	+	445308.i	0.569426	+	0.121007i
$424$	442334.	−	766144.i	0.119491	−	0.206964i
$425$	−1.89265e6	−	3.27816e6i	−0.508273	−	0.880355i
$426$	634932.	−	873953.i	0.169513	−	0.233326i
$427$	1.26978e6	−	4.11393e6i	0.337023	−	1.09191i
$428$			4.21147e6i			1.11128i
$429$	−29722.4	−	3123.22i	−0.00779723	−	0.000819332i
$430$	−3.60617e6	−	2.08202e6i	−0.940535	−	0.543018i
$431$	5.73218e6	+	3.30947e6i	1.48637	+	0.858155i	0.999879	−	0.0155318i	$-0.00494413\pi$
$431$	5.73218e6	+	3.30947e6i	1.48637	+	0.858155i	0.486489	+	0.873687i	$0.338277\pi$
$432$	−479053.	−	2.25297e6i	−0.123502	−	0.580825i
$433$			5.25855e6i			1.34786i	0.738794	+	0.673932i	$0.235396\pi$
$433$			5.25855e6i			1.34786i	−0.738794	+	0.673932i	$0.764604\pi$
$434$	−588041.	+	545427.i	−0.149859	+	0.138999i
$435$	4.30918e6	+	3.13065e6i	1.09187	+	0.793251i
$436$	1.75334e6	+	3.03688e6i	0.441723	+	0.765087i
$437$	−1.11094e6	+	1.92421e6i	−0.278284	+	0.482003i
$438$	−172247.	−	386848.i	−0.0429009	−	0.0963507i
$439$	−360657.	+	208225.i	−0.0893168	+	0.0515671i	−0.543993	−	0.839090i	$-0.683088\pi$
$439$	−360657.	+	208225.i	−0.0893168	+	0.0515671i	0.454676	+	0.890657i	$0.349755\pi$
$440$	1.57490e6			0.387812
$441$	2.82146e6	+	2.95284e6i	0.690839	+	0.723008i
$442$	−20039.7			−0.00487905
$443$	6.06848e6	−	3.50364e6i	1.46916	−	0.848222i	0.469762	−	0.882793i	$-0.344340\pi$
$443$	6.06848e6	−	3.50364e6i	1.46916	−	0.848222i	0.999402	+	0.0345711i	$0.0110065\pi$
$444$	755798.	+	1.69744e6i	0.181948	+	0.408636i
$445$	−1.51827e6	+	2.62972e6i	−0.363453	+	0.629519i
$446$	−273402.	−	473546.i	−0.0650825	−	0.112726i
$447$	118017.	+	85739.8i	0.0279367	+	0.0202961i
$448$	−764175.	+	708797.i	−0.179886	+	0.166850i
$449$		−	1.63032e6i		−	0.381643i	−0.981625	−	0.190822i	$-0.938885\pi$
$449$		−	1.63032e6i		−	0.381643i	0.981625	−	0.190822i	$-0.0611152\pi$
$450$	2.27616e6	+	2.04926e6i	0.529872	+	0.477053i
$451$	1.23869e6	+	715158.i	0.286762	+	0.165562i
$452$	−2.14960e6	−	1.24107e6i	−0.494894	−	0.285727i
$453$	2.14652e6	+	225556.i	0.491461	+	0.0516426i
$454$			251428.i			0.0572498i
$455$	−53318.8	+	172746.i	−0.0120740	+	0.0391182i
$456$	630423.	−	867747.i	0.141978	−	0.195425i
$457$	−4.19448e6	−	7.26504e6i	−0.939479	−	1.62723i	−0.766445	−	0.642310i	$-0.777976\pi$
$457$	−4.19448e6	−	7.26504e6i	−0.939479	−	1.62723i	−0.173034	−	0.984916i	$-0.555357\pi$
$458$	−398570.	+	690344.i	−0.0887853	+	0.153781i
$459$	−1.80289e6	+	1.62356e6i	−0.399427	+	0.359697i
$460$	−9.25223e6	+	5.34178e6i	−2.03869	+	1.17704i
$461$	−186426.			−0.0408560			−0.0204280	−	0.999791i	$-0.506503\pi$
$461$	−186426.			−0.0408560			−0.0204280	+	0.999791i	$0.506503\pi$
$462$	−517855.	−	221436.i	−0.112876	−	0.0482663i
$463$	−5.23908e6			−1.13580			−0.567901	−	0.823097i	$-0.692244\pi$
$463$	−5.23908e6			−1.13580			−0.567901	+	0.823097i	$0.692244\pi$
$464$	1.89296e6	−	1.09290e6i	0.408175	−	0.235660i
$465$	−3.92672e6	+	1.74840e6i	−0.842166	+	0.374981i
$466$	−1.34868e6	+	2.33598e6i	−0.287703	+	0.498316i
$467$	−282111.	−	488631.i	−0.0598589	−	0.103679i	0.834543	−	0.550943i	$-0.185732\pi$
$467$	−282111.	−	488631.i	−0.0598589	−	0.103679i	−0.894402	+	0.447264i	$0.852398\pi$
$468$	−93075.7	+	30247.1i	−0.0196436	+	0.00638365i
$469$	−185526.	−	813511.i	−0.0389469	−	0.170778i
$470$			1.78712e6i			0.373173i
$471$	−25193.3	+	239754.i	−0.00523279	+	0.0497982i
$472$	4.39433e6	+	2.53707e6i	0.907898	+	0.524175i
$473$	2.32472e6	+	1.34218e6i	0.477768	+	0.275840i
$474$	29870.9	−	284268.i	0.00610664	−	0.0581142i
$475$		−	3.20721e6i		−	0.652219i
$476$	2.17806e6	+	672269.i	0.440609	+	0.135996i
$477$	−1.61251e6	+	524022.i	−0.324494	+	0.105452i
$478$	−555358.	−	961908.i	−0.111174	−	0.192559i
$479$	−1.34863e6	+	2.33590e6i	−0.268568	+	0.465174i	−0.968492	−	0.249043i	$-0.919884\pi$
$479$	−1.34863e6	+	2.33590e6i	−0.268568	+	0.465174i	0.699924	+	0.714217i	$0.253217\pi$
$480$	7.24726e6	−	3.22690e6i	1.43572	−	0.639267i
$481$	55167.6	−	31851.0i	0.0108723	−	0.00627713i
$482$	−2.03516e6			−0.399007
$483$	8.21523e6	−	986630.i	1.60233	−	0.192436i
$484$	3.95235e6			0.766906
$485$	−1.17803e7	+	6.80133e6i	−2.27405	+	1.31292i
$486$	981326.	−	1.70018e6i	0.188461	−	0.326516i
$487$	1.42182e6	−	2.46267e6i	0.271658	−	0.470526i	−0.697628	−	0.716460i	$-0.745761\pi$
$487$	1.42182e6	−	2.46267e6i	0.271658	−	0.470526i	0.969287	+	0.245934i	$0.0790946\pi$
$488$	2.10535e6	+	3.64658e6i	0.400198	+	0.693164i
$489$	−2.65383e6	+	3.65287e6i	−0.501881	+	0.690815i
$490$	−1.92023e6	+	2.81431e6i	−0.361297	+	0.529519i
$491$		−	7.38962e6i		−	1.38331i	−0.722229	−	0.691654i	$-0.756882\pi$
$491$		−	7.38962e6i		−	1.38331i	0.722229	−	0.691654i	$-0.243118\pi$
$492$	4.65818e6	+	489481.i	0.867568	+	0.0911639i
$493$	−1.99392e6	−	1.15119e6i	−0.369479	−	0.213319i
$494$	−14704.5	−	8489.63i	−0.00271102	−	0.00156521i
$495$	−2.24320e6	−	2.01959e6i	−0.411486	−	0.370468i
$496$			1.76395e6i			0.321945i
$497$	2.86472e6	+	3.08854e6i	0.520225	+	0.560870i
$498$	851784.	+	618826.i	0.153906	+	0.111814i
$499$	−1.06838e6	−	1.85048e6i	−0.192076	−	0.332685i	0.753862	−	0.657033i	$-0.228189\pi$
$499$	−1.06838e6	−	1.85048e6i	−0.192076	−	0.332685i	−0.945938	+	0.324347i	$0.894855\pi$
$500$	3.63351e6	−	6.29342e6i	0.649982	−	1.12580i
$501$	−2.20554e6	−	4.95341e6i	−0.392574	−	0.881679i
$502$	1.45868e6	−	842172.i	0.258346	−	0.149156i
$503$	2.60933e6			0.459842			0.229921	−	0.973209i	$-0.426153\pi$
$503$	2.60933e6			0.459842			0.229921	+	0.973209i	$0.426153\pi$
$504$	−3.99381e6	+	59230.8i	−0.700343	+	0.0103866i
$505$	5.09364e6			0.888791
$506$	−988178.	+	570525.i	−0.171577	+	0.0990600i
$507$	−2.35291e6	−	5.28437e6i	−0.406523	−	0.913006i
$508$	−1.81623e6	+	3.14581e6i	−0.312257	+	0.540845i
$509$	2.89433e6	+	5.01313e6i	0.495169	+	0.857658i	0.999984	−	0.00556926i	$-0.00177276\pi$
$509$	2.89433e6	+	5.01313e6i	0.495169	+	0.857658i	−0.504815	+	0.863227i	$0.668439\pi$
$510$	−1.63743e6	−	1.18961e6i	−0.278765	−	0.202524i
$511$	1.61001e6	−	367172.i	0.272757	−	0.0622039i
$512$		−	5.72266e6i		−	0.964768i
$513$	−2.01071e6	+	427540.i	−0.337330	+	0.0717272i
$514$	2.04582e6	+	1.18115e6i	0.341554	+	0.197196i
$515$	−1.26618e7	−	7.31031e6i	−2.10367	−	1.21456i
$516$	8.74226e6	+	918636.i	1.44544	+	0.151887i
$517$		−	1.15207e6i		−	0.189563i
$518$	1.17044e6	−	266925.i	0.191656	−	0.0437083i
$519$	−4.65574e6	+	6.40840e6i	−0.758701	+	1.04431i
$520$	−88404.8	−	153122.i	−0.0143373	−	0.0248329i
$521$	153113.	−	265199.i	0.0247125	−	0.0428033i	−0.853405	−	0.521249i	$-0.825466\pi$
$521$	153113.	−	265199.i	0.0247125	−	0.0428033i	0.878117	+	0.478446i	$0.158800\pi$
$522$	1.82220e6	+	387229.i	0.292698	+	0.0622002i
$523$	6.22250e6	−	3.59256e6i	0.994743	−	0.574315i	0.0880542	−	0.996116i	$-0.471935\pi$
$523$	6.22250e6	−	3.59256e6i	0.994743	−	0.574315i	0.906689	+	0.421801i	$0.138602\pi$
$524$	−4.05677e6			−0.645434
$525$	−9.55755e6	+	7.16254e6i	−1.51338	+	1.13414i
$526$	2.24778e6			0.354234
$527$	1.60910e6	−	929014.i	0.252381	−	0.145712i
$528$	−1.13157e6	+	503841.i	−0.176643	+	0.0786518i
$529$	5.16352e6	−	8.94348e6i	0.802245	−	1.38953i
$530$	−707210.	−	1.22492e6i	−0.109360	−	0.189417i
$531$	−3.00560e6	−	9.24877e6i	−0.462589	−	1.42347i
$532$	1.31339e6	+	1.41600e6i	0.201194	+	0.216913i
$533$		−	160578.i		−	0.0244831i
$534$	−110987.	+	1.05621e6i	−0.0168429	+	0.160287i
$535$	1.26286e7	+	7.29114e6i	1.90753	+	1.10131i
$536$	706712.	+	408020.i	0.106250	+	0.0613437i
$537$	−652292.	+	6.20758e6i	−0.0976128	+	0.928938i
$538$			980795.i			0.146091i
$539$	1.23788e6	−	1.81424e6i	0.183530	−	0.268982i
$540$	−9.40071e6	−	3.05373e6i	−1.38732	−	0.450657i
$541$	−3.88242e6	−	6.72454e6i	−0.570307	−	0.987801i	−0.996534	−	0.0831849i	$-0.973491\pi$
$541$	−3.88242e6	−	6.72454e6i	−0.570307	−	0.987801i	0.426227	−	0.904616i	$-0.359843\pi$
$542$	944431.	−	1.63580e6i	0.138093	−	0.239184i
$543$	152299.	−	67812.4i	0.0221666	−	0.00986983i
$544$	−2.96980e6	+	1.71461e6i	−0.430258	+	0.248410i
$545$	1.21420e7			1.75104
$546$	7539.64	+	62779.2i	0.00108235	+	0.00901227i
$547$	−7.87821e6			−1.12580			−0.562898	−	0.826527i	$-0.690313\pi$
$547$	−7.87821e6			−1.12580			−0.562898	+	0.826527i	$0.690313\pi$
$548$	−5.38914e6	+	3.11142e6i	−0.766599	+	0.442596i
$549$	1.67748e6	−	7.89381e6i	0.237535	−	1.11778i
$550$	823530.	−	1.42640e6i	0.116084	−	0.201064i
$551$	−975381.	−	1.68941e6i	−0.136866	−	0.237059i
$552$	−4.75633e6	+	6.54685e6i	−0.664391	+	0.914503i
$553$	1.06507e6	+	328738.i	0.148103	+	0.0457127i
$554$			1.64311e6i			0.227453i
$555$	6.39848e6	+	672351.i	0.881747	+	0.0926539i
$556$	5.48415e6	+	3.16627e6i	0.752354	+	0.434372i
$557$	3.98169e6	+	2.29883e6i	0.543788	+	0.313956i	0.746613	−	0.665259i	$-0.231679\pi$
$557$	3.98169e6	+	2.29883e6i	0.543788	+	0.313956i	−0.202825	+	0.979215i	$0.565012\pi$
$558$	−1.00589e6	+	1.11726e6i	−0.136762	+	0.151904i
$559$		−	301365.i		−	0.0407909i
$560$	1.66605e6	+	7.30545e6i	0.224501	+	0.984411i
$561$	1.05557e6	+	766879.i	0.141606	+	0.102877i
$562$	−2.40012e6	−	4.15712e6i	−0.320547	−	0.555203i
$563$	−1.36209e6	+	2.35921e6i	−0.181107	+	0.313687i	−0.942258	−	0.334888i	$-0.891301\pi$
$563$	−1.36209e6	+	2.35921e6i	−0.181107	+	0.313687i	0.761151	+	0.648575i	$0.224635\pi$
$564$	−1.53456e6	−	3.44646e6i	−0.203136	−	0.456221i
$565$	−7.44304e6	+	4.29724e6i	−0.980910	+	0.566329i
$566$	−10808.8			−0.00141819
$567$	5.76451e6	+	5.03714e6i	0.753017	+	0.658001i
$568$	−4.11988e6			−0.535814
$569$	7.51548e6	−	4.33907e6i	0.973142	−	0.561844i	0.0729494	−	0.997336i	$-0.476759\pi$
$569$	7.51548e6	−	4.33907e6i	0.973142	−	0.561844i	0.900193	+	0.435492i	$0.143425\pi$
$570$	−697530.	−	1.56658e6i	−0.0899240	−	0.201960i
$571$	−5.36922e6	+	9.29976e6i	−0.689161	+	1.19366i	0.282948	+	0.959135i	$0.408688\pi$
$571$	−5.36922e6	+	9.29976e6i	−0.689161	+	1.19366i	−0.972110	+	0.234527i	$0.924646\pi$
$572$	26315.2	+	45579.2i	0.00336292	+	0.00582474i
$573$	2.48765e6	+	1.80730e6i	0.316522	+	0.229955i
$574$	892487.	−	2.89154e6i	0.113063	−	0.366311i
$575$			2.41973e7i			3.05209i
$576$	−1.30718e6	+	1.45191e6i	−0.164164	+	0.182341i
$577$	6.12168e6	+	3.53435e6i	0.765475	+	0.441947i	0.831258	−	0.555887i	$-0.187621\pi$
$577$	6.12168e6	+	3.53435e6i	0.765475	+	0.441947i	−0.0657833	+	0.997834i	$0.520955\pi$
$578$	−1.86470e6	−	1.07659e6i	−0.232161	−	0.134038i
$579$	−1.94581e6	−	204465.i	−0.241214	−	0.0253468i
$580$		−	9.37989e6i		−	1.15779i
$581$	−3.01020e6	+	2.79206e6i	−0.369960	+	0.343150i
$582$	−2.79631e6	+	3.84899e6i	−0.342199	+	0.471020i
$583$	455903.	+	789647.i	0.0555521	+	0.0962191i
$584$	−807508.	+	1.39865e6i	−0.0979749	+	0.169697i
$585$	−70438.4	+	331465.i	−0.00850981	+	0.0400450i
$586$	−4.64994e6	+	2.68465e6i	−0.559376	+	0.322956i
$587$	−3.96818e6			−0.475331			−0.237666	−	0.971347i	$-0.576382\pi$
$587$	−3.96818e6			−0.475331			−0.237666	+	0.971347i	$0.576382\pi$
$588$	1.28658e6	−	7.07624e6i	0.153460	−	0.844033i
$589$	1.57427e6			0.186978
$590$	7.02571e6	−	4.05630e6i	0.830922	−	0.479733i
$591$	−8.99566e6	+	4.00538e6i	−1.05941	+	0.471710i
$592$	1.32012e6	−	2.28651e6i	0.154813	−	0.268144i
$593$	−8.37107e6	−	1.44991e7i	−0.977562	−	1.69319i	−0.671208	−	0.741269i	$-0.734224\pi$
$593$	−8.37107e6	−	1.44991e7i	−0.977562	−	1.69319i	−0.306354	−	0.951918i	$-0.599109\pi$
$594$	−1.00404e6	−	326151.i	−0.116757	−	0.0379274i
$595$	5.78668e6	−	5.36733e6i	0.670096	−	0.621535i
$596$		−	256889.i		−	0.0296231i
$597$	−1.01390e6	+	9.64882e6i	−0.116428	+	1.10800i
$598$	110940.	+	64051.3i	0.0126863	+	0.00732445i
$599$	−9.42358e6	−	5.44071e6i	−1.07312	−	0.619567i	−0.144089	−	0.989565i	$-0.546025\pi$
$599$	−9.42358e6	−	5.44071e6i	−1.07312	−	0.619567i	−0.929033	+	0.369998i	$0.879358\pi$
$600$	1.22070e6	−	1.16168e7i	0.138430	−	1.31738i
$601$			1.72048e7i			1.94296i	0.237128	+	0.971478i	$0.423794\pi$
$601$			1.72048e7i			1.94296i	−0.237128	+	0.971478i	$0.576206\pi$
$602$	1.67498e6	−	5.42671e6i	0.188373	−	0.610303i
$603$	−483372.	−	1.48742e6i	−0.0541362	−	0.166587i
$604$	−1.90045e6	−	3.29168e6i	−0.211965	−	0.367135i
$605$	6.84254e6	−	1.18516e7i	0.760027	−	1.31641i
$606$	1.62746e6	−	724641.i	0.180024	−	0.0801569i
$607$	−4.81974e6	+	2.78268e6i	−0.530947	+	0.306543i	−0.741402	−	0.671061i	$-0.765839\pi$
$607$	−4.81974e6	+	2.78268e6i	−0.530947	+	0.306543i	0.210455	+	0.977604i	$0.432506\pi$
$608$	−2.90552e6			−0.318760
$609$	−2.85620e6	+	6.67955e6i	−0.312065	+	0.729801i
$610$	6.73214e6			0.732535
$611$	−112012.	+	64669.9i	−0.0121384	+	0.00700808i
$612$	4.17927e6	+	888121.i	0.451047	+	0.0958503i
$613$	5.90377e6	−	1.02256e7i	0.634568	−	1.09910i	−0.352038	−	0.935986i	$-0.614511\pi$
$613$	5.90377e6	−	1.02256e7i	0.634568	−	1.09910i	0.986606	−	0.163119i	$-0.0521554\pi$
$614$	2.46332e6	+	4.26660e6i	0.263694	+	0.456731i
$615$	9.53229e6	−	1.31207e7i	1.01627	−	1.39885i
$616$	477601.	+	2.09423e6i	0.0507123	+	0.222368i
$617$		−	5.91582e6i		−	0.625608i	−0.949818	−	0.312804i	$-0.898732\pi$
$617$		−	5.91582e6i		−	0.625608i	0.949818	−	0.312804i	$-0.101268\pi$
$618$	−5.08556e6	−	534391.i	−0.535634	−	0.0562843i
$619$	2.44978e6	+	1.41438e6i	0.256981	+	0.148368i	0.622956	−	0.782256i	$-0.285931\pi$
$619$	2.44978e6	+	1.41438e6i	0.256981	+	0.148368i	−0.365976	+	0.930624i	$0.619265\pi$
$620$	6.55547e6	+	3.78480e6i	0.684896	+	0.395425i
$621$	1.51701e7	−	3.22565e6i	1.57855	−	0.335651i
$622$			5.01780e6i			0.520041i
$623$	−3.95731e6	−	1.22144e6i	−0.408488	−	0.126082i
$624$	112506.	+	81736.2i	0.0115668	+	0.00840336i
$625$	−3.34676e6	−	5.79676e6i	−0.342708	−	0.593588i
$626$	−2.12323e6	+	3.67754e6i	−0.216551	+	0.375078i
$627$	449663.	+	1.00989e6i	0.0456792	+	0.102590i
$628$	367663.	−	212270.i	0.0372006	−	0.0214778i
$629$	−2.78105e6			−0.280273
$630$	−3.11067e6	+	5.57723e6i	−0.312250	+	0.559844i
$631$	−9.60301e6			−0.960139			−0.480069	−	0.877231i	$-0.659389\pi$
$631$	−9.60301e6			−0.960139			−0.480069	+	0.877231i	$0.659389\pi$
$632$	−944073.	+	545061.i	−0.0940184	+	0.0542816i
$633$	1.72305e6	+	3.86978e6i	0.170918	+	0.383863i
$634$	2.23270e6	−	3.86716e6i	0.220601	−	0.382093i
$635$	6.28874e6	+	1.08924e7i	0.618912	+	1.07199i
$636$	2.41566e6	+	1.75499e6i	0.236806	+	0.172041i
$637$	−245879.	−	18514.4i	−0.0240089	−	0.00180784i
$638$		−	1.00181e6i		−	0.0974395i
$639$	5.86813e6	+	5.28318e6i	0.568523	+	0.511851i
$640$	−1.55149e7	−	8.95752e6i	−1.49726	−	0.864446i
$641$	7.79558e6	+	4.50078e6i	0.749383	+	0.432656i	0.825471	−	0.564445i	$-0.190910\pi$
$641$	7.79558e6	+	4.50078e6i	0.749383	+	0.432656i	−0.0760882	+	0.997101i	$0.524243\pi$
$642$	5.07223e6	+	532989.i	0.485692	+	0.0510365i
$643$		−	6.92082e6i		−	0.660131i	−0.943958	−	0.330065i	$-0.892929\pi$
$643$		−	6.92082e6i		−	0.660131i	0.943958	−	0.330065i	$-0.107071\pi$
$644$	−9.90907e6	−	1.06833e7i	−0.941496	−	1.01505i
$645$	1.78898e7	−	2.46244e7i	1.69319	−	2.33059i
$646$	370632.	+	641954.i	0.0349432	+	0.0605233i
$647$	834251.	−	1.44497e6i	0.0783495	−	0.135705i	−0.824188	−	0.566316i	$-0.808368\pi$
$647$	834251.	−	1.44497e6i	0.0783495	−	0.135705i	0.902538	+	0.430610i	$0.141702\pi$
$648$	−7.44571e6	+	783299.i	−0.696576	+	0.0732808i
$649$	−4.52913e6	+	2.61489e6i	−0.422088	+	0.243693i
$650$	−184911.			−0.0171664
$651$	−3.51576e6	−	4.69136e6i	−0.325137	−	0.433857i
$652$	7.95128e6			0.732518
$653$	−1.57452e7	+	9.09048e6i	−1.44499	+	0.834265i	−0.998177	−	0.0603628i	$-0.980774\pi$
$653$	−1.57452e7	+	9.09048e6i	−1.44499	+	0.834265i	−0.446813	+	0.894628i	$0.647441\pi$
$654$	3.87946e6	−	1.72736e6i	0.354672	−	0.157921i
$655$	−7.02332e6	+	1.21647e7i	−0.639645	+	1.10790i
$656$	−3.32770e6	−	5.76374e6i	−0.301915	−	0.522932i
$657$	2.94374e6	−	956635.i	0.266064	−	0.0864635i
$658$	−2.37644e6	+	541960.i	−0.213974	+	0.0487981i
$659$		−	5.58660e6i		−	0.501111i	−0.968102	−	0.250556i	$-0.919387\pi$
$659$		−	5.58660e6i		−	0.501111i	0.968102	−	0.250556i	$-0.0806133\pi$
$660$	−555493.	+	5.28639e6i	−0.0496385	+	0.472388i
$661$	−1.13323e7	−	6.54273e6i	−1.00882	−	0.582445i	−0.0979774	−	0.995189i	$-0.531237\pi$
$661$	−1.13323e7	−	6.54273e6i	−1.00882	−	0.582445i	−0.910847	+	0.412743i	$0.864571\pi$
$662$	508353.	+	293498.i	0.0450838	+	0.0260292i
$663$	15307.8	−	145677.i	0.00135247	−	0.0128709i
$664$		−	4.01538e6i		−	0.353432i
$665$	6.51989e6	−	1.48690e6i	0.571724	−	0.130385i
$666$	2.14002e6	−	695449.i	0.186953	−	0.0607547i
$667$	7.35892e6	+	1.27460e7i	0.640471	+	1.10933i
$668$	−4.77438e6	+	8.26948e6i	−0.413977	+	0.717029i
$669$	3.65125e6	−	1.62575e6i	0.315411	−	0.140439i
$670$	1.12990e6	−	652349.i	0.0972419	−	0.0561427i
$671$	−4.33988e6			−0.372110
$672$	6.48878e6	+	8.65850e6i	0.554293	+	0.739639i
$673$	9.79316e6			0.833461			0.416730	−	0.909030i	$-0.363176\pi$
$673$	9.79316e6			0.833461			0.416730	+	0.909030i	$0.363176\pi$
$674$	−841551.	+	485870.i	−0.0713561	+	0.0411974i
$675$	−1.66357e7	+	1.49810e7i	−1.40534	+	1.26556i
$676$	−5.09338e6	+	8.82200e6i	−0.428686	+	0.742506i
$677$	4.00458e6	+	6.93614e6i	0.335804	+	0.581629i	0.983639	−	0.180151i	$-0.0576587\pi$
$677$	4.00458e6	+	6.93614e6i	0.335804	+	0.581629i	−0.647835	+	0.761781i	$0.724325\pi$
$678$	−1.76678e6	+	2.43188e6i	−0.147607	+	0.203174i
$679$	−1.26166e7	−	1.36023e7i	−1.05019	−	1.13224i
$680$			7.71900e6i			0.640160i
$681$	−1.82774e6	−	192059.i	−0.151024	−	0.0158696i
$682$	700152.	+	404233.i	0.0576410	+	0.0332790i
$683$	1.74062e7	+	1.00495e7i	1.42775	+	0.824314i	0.996943	−	0.0781292i	$-0.0248947\pi$
$683$	1.74062e7	+	1.00495e7i	1.42775	+	0.824314i	0.430810	+	0.902443i	$0.358228\pi$
$684$	2.69037e6	+	2.42218e6i	0.219873	+	0.197955i
$685$			2.15467e7i			1.75451i
$686$	−4.32467e6	−	1.69998e6i	−0.350867	−	0.137922i
$687$	−4.71395e6	−	3.42471e6i	−0.381060	−	0.276842i
$688$	−6.24528e6	−	1.08171e7i	−0.503015	−	0.871247i
$689$	51183.0	−	88651.5i	0.00410750	−	0.00711440i
$690$	5.26262e6	+	1.18193e7i	0.420804	+	0.945080i
$691$	−6.74144e6	+	3.89217e6i	−0.537103	+	0.310097i	−0.743904	−	0.668286i	$-0.767028\pi$
$691$	−6.74144e6	+	3.89217e6i	−0.537103	+	0.310097i	0.206801	+	0.978383i	$0.433695\pi$
$692$	1.39493e7			1.10736
$693$	2.00529e6	−	3.59536e6i	0.158615	−	0.284387i
$694$	−3.65107e6			−0.287754
$695$	1.89890e7	−	1.09633e7i	1.49121	−	0.860951i
$696$	−2.88992e6	−	6.49045e6i	−0.226133	−	0.507869i
$697$	−3.50518e6	+	6.07115e6i	−0.273293	+	0.473357i
$698$	−2.07652e6	−	3.59663e6i	−0.161323	−	0.279420i
$699$	−1.59510e7	−	1.15885e7i	−1.23480	−	0.897088i
$700$	2.00975e7	+	6.20319e6i	1.55023	+	0.478487i
$701$		−	1.12400e7i		−	0.863912i	−0.901895	−	0.431956i	$-0.857824\pi$
$701$		−	1.12400e7i		−	0.863912i	0.901895	−	0.431956i	$-0.142176\pi$
$702$	24649.8	+	115927.i	0.00188786	+	0.00887854i
$703$	−2.04064e6	−	1.17816e6i	−0.155732	−	0.0899120i
$704$	909866.	+	525311.i	0.0691904	+	0.0399471i
$705$	−1.29914e7	−	1.36513e6i	−0.984425	−	0.103443i
$706$		−	7.66366e6i		−	0.578661i
$707$	1.54469e6	+	6.77330e6i	0.116223	+	0.509626i
$708$	−1.00660e7	+	1.38554e7i	−0.754699	+	1.03881i
$709$	5.78480e6	+	1.00196e7i	0.432188	+	0.748572i	0.997061	−	0.0766058i	$-0.0244083\pi$
$709$	5.78480e6	+	1.00196e7i	0.432188	+	0.748572i	−0.564873	+	0.825178i	$0.691075\pi$
$710$	−3.29346e6	+	5.70445e6i	−0.245192	+	0.424686i
$711$	2.04365e6	+	434289.i	0.151612	+	0.0322184i
$712$	3.50775e6	−	2.02520e6i	0.259316	−	0.149716i
$713$	−1.18773e7			−0.874974
$714$	1.08532e6	−	2.53815e6i	0.0796731	−	0.186325i
$715$	182234.			0.0133310
$716$	9.51932e6	−	5.49598e6i	0.693943	−	0.400648i
$717$	7.41675e6	−	3.30236e6i	0.538785	−	0.239898i
$718$	−2.75486e6	+	4.77155e6i	−0.199429	+	0.345421i
$719$	−230645.	−	399490.i	−0.0166388	−	0.0288193i	0.857586	−	0.514340i	$-0.171963\pi$
$719$	−230645.	−	399490.i	−0.0166388	−	0.0288193i	−0.874225	+	0.485521i	$0.838630\pi$
$720$	4.34075e6	+	1.33573e7i	0.312056	+	0.960254i
$721$	5.88112e6	−	1.90541e7i	0.421330	−	1.36505i
$722$		−	4.65257e6i		−	0.332162i
$723$	1.55460e6	−	1.47944e7i	0.110604	−	1.05257i
$724$	−254256.	−	146795.i	−0.0180271	−	0.0104079i
$725$	−1.83984e7	−	1.06223e7i	−1.29997	−	0.750540i
$726$	500196.	−	4.76015e6i	0.0352208	−	0.335181i
$727$		−	2.83046e6i		−	0.198619i	−0.995057	−	0.0993096i	$-0.968337\pi$
$727$		−	2.83046e6i		−	0.198619i	0.995057	−	0.0993096i	$-0.0316634\pi$
$728$	176805.	−	163992.i	0.0123642	−	0.0114682i
$729$	1.16097e7	+	8.43240e6i	0.809102	+	0.587669i
$730$	1.29106e6	+	2.23617e6i	0.0896681	+	0.155310i
$731$	−6.57836e6	+	1.13941e7i	−0.455328	+	0.788651i
$732$	−1.29829e7	+	5.78073e6i	−0.895559	+	0.398754i
$733$	1.77803e7	−	1.02655e7i	1.22230	−	0.705698i	0.256896	−	0.966439i	$-0.417300\pi$
$733$	1.77803e7	−	1.02655e7i	1.22230	−	0.705698i	0.965409	+	0.260741i	$0.0839670\pi$
$734$	8.03073e6			0.550193
$735$	−1.89916e7	−	1.61088e7i	−1.29671	−	1.09988i
$736$	2.19211e7			1.49165
$737$	−728391.	+	420537.i	−0.0493965	+	0.0285191i
$738$	1.17905e6	−	5.54829e6i	0.0796875	−	0.374989i
$739$	7.57397e6	−	1.31185e7i	0.510167	−	0.883635i	−0.489764	−	0.871855i	$-0.662917\pi$
$739$	7.57397e6	−	1.31185e7i	0.510167	−	0.883635i	0.999931	−	0.0117799i	$-0.00374974\pi$
$740$	−5.66499e6	−	9.81206e6i	−0.380295	−	0.658689i
$741$	72947.1	−	100408.i	0.00488048	−	0.00671774i
$742$	1.41438e6	−	1.31188e6i	0.0943097	−	0.0874753i
$743$		−	3.14063e6i		−	0.208711i	−0.994540	−	0.104355i	$-0.966722\pi$
$743$		−	3.14063e6i		−	0.208711i	0.994540	−	0.104355i	$-0.0332779\pi$
$744$	5.70217e6	+	599183.i	0.377666	+	0.0396851i
$745$	−770316.	−	444742.i	−0.0508485	−	0.0293574i
$746$	−3.57789e6	−	2.06570e6i	−0.235386	−	0.135900i
$747$	−5.14917e6	+	5.71929e6i	−0.337626	+	0.375008i
$748$		−	2.29769e6i		−	0.150154i
$749$	−5.86570e6	+	1.90041e7i	−0.382046	+	1.23778i
$750$	−7.11986e6	−	5.17262e6i	−0.462188	−	0.335782i
$751$	716880.	+	1.24167e6i	0.0463817	+	0.0803354i	0.888284	−	0.459294i	$-0.151898\pi$
$751$	716880.	+	1.24167e6i	0.0463817	+	0.0803354i	−0.841903	+	0.539630i	$0.818564\pi$
$752$	−2.68035e6	+	4.64250e6i	−0.172841	+	0.299369i
$753$	5.00786e6	+	1.12471e7i	0.321859	+	0.722860i
$754$	−97402.7	+	56235.5i	−0.00623940	+	0.00360232i
$755$	−1.31607e7			−0.840256
$756$	1.20987e6	−	1.34267e7i	0.0769897	−	0.854408i
$757$	−6.81110e6			−0.431994			−0.215997	−	0.976394i	$-0.569300\pi$
$757$	−6.81110e6			−0.431994			−0.215997	+	0.976394i	$0.569300\pi$
$758$	−3.76982e6	+	2.17650e6i	−0.238313	+	0.137590i
$759$	−3.39255e6	−	7.61930e6i	−0.213758	−	0.480077i
$760$	−3.27008e6	+	5.66394e6i	−0.205364	+	0.355701i
$761$	−55135.1	−	95496.9i	−0.00345117	−	0.00597761i	0.864295	−	0.502986i	$-0.167765\pi$
$761$	−55135.1	−	95496.9i	−0.00345117	−	0.00597761i	−0.867746	+	0.497008i	$0.834432\pi$
$762$	3.55890e6	+	2.58557e6i	0.222039	+	0.161313i
$763$	3.68215e6	+	1.61458e7i	0.228976	+	1.00404i
$764$		−	5.41493e6i		−	0.335629i
$765$	9.89855e6	−	1.09945e7i	0.611530	−	0.679239i
$766$	−869348.	−	501918.i	−0.0535330	−	0.0309073i
$767$	508473.	+	293567.i	0.0312090	+	0.0180185i
$768$	−2.24298e6	−	235692.i	−0.137221	−	0.0144192i
$769$		−	1.61688e7i		−	0.985968i	−0.870038	−	0.492984i	$-0.835906\pi$
$769$		−	1.61688e7i		−	0.985968i	0.870038	−	0.492984i	$-0.164094\pi$
$770$	3.28150e6	+	1.01285e6i	0.199455	+	0.0615628i
$771$	−1.01491e7	+	1.39697e7i	−0.614879	+	0.846351i
$772$	1.72275e6	+	2.98389e6i	0.104035	+	0.180194i
$773$	8.38057e6	−	1.45156e7i	0.504458	−	0.873747i	−0.495529	−	0.868592i	$-0.665026\pi$
$773$	8.38057e6	−	1.45156e7i	0.504458	−	0.873747i	0.999987	−	0.00515528i	$-0.00164098\pi$
$774$	2.21278e6	−	1.04128e7i	0.132766	−	0.624762i
$775$	1.48475e7	−	8.57223e6i	0.887974	−	0.512672i
$776$	1.81445e7			1.08166
$777$	1.04633e6	+	8.71231e6i	0.0621749	+	0.517703i
$778$	−9.79168e6			−0.579974
$779$	−5.14397e6	+	2.96987e6i	−0.303707	+	0.175345i
$780$	545158.	−	242736.i	0.0320838	−	0.0142856i
$781$	2.12313e6	−	3.67737e6i	0.124552	−	0.215730i
$782$	−2.79629e6	−	4.84332e6i	−0.163518	−	0.283222i
$783$	−4.20686e6	+	1.29506e7i	−0.245219	+	0.754891i
$784$	−9.20921e6	+	4.43087e6i	−0.535097	+	0.257454i
$785$		−	1.46998e6i		−	0.0851406i
$786$	−513411.	+	4.88591e6i	−0.0296421	+	0.282091i
$787$	1.78819e7	+	1.03241e7i	1.02915	+	0.594178i	0.916740	−	0.399485i	$-0.130811\pi$
$787$	1.78819e7	+	1.03241e7i	1.02915	+	0.594178i	0.112406	+	0.993662i	$0.464144\pi$
$788$	1.50178e7	+	8.67053e6i	0.861570	+	0.497428i
$789$	−1.71702e6	+	1.63401e7i	−0.0981933	+	0.934463i
$790$			1.74290e6i			0.0993586i
$791$	−7.97144e6	−	8.59425e6i	−0.452997	−	0.488390i
$792$	1.24435e6	+	3.82908e6i	0.0704902	+	0.216911i
$793$	243613.	+	421950.i	0.0137568	+	0.0238275i
$794$	−4.85780e6	+	8.41396e6i	−0.273457	+	0.473641i
$795$	9.44471e6	−	4.20533e6i	0.529994	−	0.235984i
$796$	1.47965e7	−	8.54274e6i	0.827704	−	0.477875i
$797$	2.91426e7			1.62511			0.812556	−	0.582884i	$-0.198076\pi$
$797$	2.91426e7			1.62511			0.812556	+	0.582884i	$0.198076\pi$
$798$	1.87163e6	−	1.40262e6i	0.104043	−	0.0779710i
$799$	5.64660e6			0.312911
$800$	−2.74030e7	+	1.58211e7i	−1.51382	+	0.874002i
$801$	−7.59329e6	−	1.61362e6i	−0.418166	−	0.0888629i
$802$	2.57783e6	−	4.46493e6i	0.141520	−	0.245120i
$803$	−832280.	−	1.44155e6i	−0.0455492	−	0.0788935i
$804$	−1.61885e6	+	2.22827e6i	−0.0883216	+	0.121570i
$805$	−4.91903e7	+	1.12181e7i	−2.67541	+	0.610142i
$806$		−	90764.4i		−	0.00492128i
$807$	−7.12982e6	−	749201.i	−0.385385	−	0.0404962i
$808$	−5.88408e6	−	3.39718e6i	−0.317066	−	0.183058i
$809$	−1.89125e7	−	1.09191e7i	−1.01596	−	0.586567i	−0.103031	−	0.994678i	$-0.532854\pi$
$809$	−1.89125e7	−	1.09191e7i	−1.01596	−	0.586567i	−0.912932	+	0.408111i	$0.866187\pi$
$810$	−4.86759e6	+	1.09356e7i	−0.260676	+	0.585639i
$811$			2.56638e6i			0.137015i	0.997651	+	0.0685077i	$0.0218238\pi$
$811$			2.56638e6i			0.137015i	−0.997651	+	0.0685077i	$0.978176\pi$
$812$	1.24730e7	−	2.84453e6i	0.663865	−	0.151398i
$813$	1.11699e7	+	8.11502e6i	0.592685	+	0.430589i
$814$	−605046.	−	1.04797e6i	−0.0320057	−	0.0554355i
$815$	1.37657e7	−	2.38429e7i	0.725948	−	1.25738i
$816$	−2.46946e6	−	5.54614e6i	−0.129830	−	0.291585i
$817$	−9.65397e6	+	5.57372e6i	−0.506000	+	0.292139i
$818$	−138590.			−0.00724184
$819$	−462129.	+	6853.68i	−0.0240743	+	0.000357037i
$820$	−2.85602e7			−1.48329
$821$	−835911.	+	482613.i	−0.0432815	+	0.0249886i	−0.521485	−	0.853261i	$-0.674622\pi$
$821$	−835911.	+	482613.i	−0.0432815	+	0.0249886i	0.478203	+	0.878249i	$0.341288\pi$
$822$	3.06532e6	+	6.88438e6i	0.158233	+	0.355373i
$823$	−1.03904e7	+	1.79967e7i	−0.534726	+	0.926173i	0.464450	+	0.885599i	$0.346252\pi$
$823$	−1.03904e7	+	1.79967e7i	−0.534726	+	0.926173i	−0.999177	+	0.0405740i	$0.987081\pi$
$824$	9.75115e6	+	1.68895e7i	0.500308	+	0.866559i
$825$	9.74002e6	+	7.07618e6i	0.498224	+	0.361963i
$826$	7.52449e6	+	8.11238e6i	0.383731	+	0.413712i
$827$			5.06026e6i			0.257282i	0.991691	+	0.128641i	$0.0410615\pi$
$827$			5.06026e6i			0.257282i	−0.991691	+	0.128641i	$0.958939\pi$
$828$	−2.02979e7	−	1.82745e7i	−1.02890	−	0.926340i
$829$	−1.44566e7	−	8.34655e6i	−0.730603	−	0.421814i	0.0880399	−	0.996117i	$-0.471940\pi$
$829$	−1.44566e7	−	8.34655e6i	−0.730603	−	0.421814i	−0.818643	+	0.574303i	$0.805273\pi$
$830$	−5.55975e6	−	3.20992e6i	−0.280130	−	0.161733i
$831$	−1.19445e7	−	1.25512e6i	−0.600017	−	0.0630498i
$832$		−	117951.i		−	0.00590734i
$833$	8.89209e6	+	6.06718e6i	0.444009	+	0.302952i
$834$	4.50747e6	−	6.20431e6i	0.224397	−	0.308872i
$835$	1.65314e7	+	2.86332e7i	0.820528	+	1.42120i
$836$	973394.	−	1.68597e6i	0.0481696	−	0.0834322i
$837$	−7.35349e6	−	8.16569e6i	−0.362810	−	0.402883i
$838$	8.36415e6	−	4.82905e6i	0.411445	−	0.237548i
$839$	−1.76055e7			−0.863461			−0.431731	−	0.902003i	$-0.642097\pi$
$839$	−1.76055e7			−0.863461			−0.431731	+	0.902003i	$0.642097\pi$
$840$	2.41816e7	−	2.90416e6i	1.18246	−	0.142011i
$841$	7.58926e6			0.370007
$842$	6.98016e6	−	4.03000e6i	0.339301	−	0.195896i
$843$	3.20533e7	−	1.42720e7i	1.55347	−	0.691696i
$844$	3.72991e6	−	6.46040e6i	0.180236	−	0.312179i
$845$	1.76359e7	+	3.05463e7i	0.849682	+	1.47169i
$846$	−4.34507e6	+	1.41203e6i	−0.208723	+	0.0678294i
$847$	1.78348e7	+	5.50480e6i	0.854202	+	0.263653i
$848$		−	4.24272e6i		−	0.202607i
$849$	8256.51	−	78573.6i	0.000393122	−	0.00374117i
$850$	6.99115e6	+	4.03634e6i	0.331895	+	0.191620i
$851$	1.53959e7	+	8.88885e6i	0.728756	+	0.420747i
$852$	1.45315e6	−	1.38290e7i	0.0685823	−	0.652668i
$853$		−	5.38585e6i		−	0.253444i	−0.991938	−	0.126722i	$-0.959554\pi$
$853$		−	5.38585e6i		−	0.253444i	0.991938	−	0.126722i	$-0.0404456\pi$
$854$	2.04158e6	+	8.95210e6i	0.0957902	+	0.420030i
$855$	1.19209e7	−	3.87398e6i	0.557693	−	0.181235i
$856$	−9.72558e6	−	1.68452e7i	−0.453661	−	0.785763i
$857$	−1.12451e7	+	1.94771e7i	−0.523011	+	0.905882i	0.476630	+	0.879104i	$0.341858\pi$
$857$	−1.12451e7	+	1.94771e7i	−0.523011	+	0.905882i	−0.999641	+	0.0267782i	$0.991475\pi$
$858$	58225.3	−	25925.2i	0.00270018	−	0.00120228i
$859$	−2.71033e7	+	1.56481e7i	−1.25325	+	0.723566i	−0.971754	−	0.235995i	$-0.924165\pi$
$859$	−2.71033e7	+	1.56481e7i	−1.25325	+	0.723566i	−0.281500	+	0.959561i	$0.590832\pi$
$860$	−5.36005e7			−2.47128
$861$	2.03381e7	+	8.69664e6i	0.934981	+	0.399801i
$862$	−1.41158e7			−0.647051
$863$	1.55675e7	−	8.98793e6i	0.711530	−	0.410802i	−0.100097	−	0.994978i	$-0.531915\pi$
$863$	1.55675e7	−	8.98793e6i	0.711530	−	0.410802i	0.811627	+	0.584176i	$0.198582\pi$
$864$	1.35718e7	+	1.50708e7i	0.618518	+	0.686835i
$865$	2.41499e7	−	4.18288e7i	1.09742	−	1.90080i
$866$	−5.60730e6	−	9.71213e6i	−0.254073	−	0.440068i
$867$	9.25056e6	−	1.27330e7i	0.417946	−	0.575283i
$868$	−3.04486e6	+	9.86494e6i	−0.137173	+	0.444422i
$869$		−	1.12356e6i		−	0.0504717i
$870$	−1.12970e7	−	1.18709e6i	−0.506017	−	0.0531722i
$871$	81774.5	+	47212.6i	0.00365235	+	0.00210869i
$872$	−1.40262e7	−	8.09801e6i	−0.624666	−	0.360651i
$873$	−2.58440e7	−	2.32678e7i	−1.14769	−	1.03328i
$874$		−	4.73850e6i		−	0.209827i
$875$	2.51615e7	−	2.33381e7i	1.11101	−	1.03049i
$876$	−4.40995e6	−	3.20385e6i	−0.194166	−	0.141063i
$877$	−1.05975e7	−	1.83554e7i	−0.465270	−	0.805871i	0.533944	−	0.845520i	$-0.320709\pi$
$877$	−1.05975e7	−	1.83554e7i	−0.465270	−	0.805871i	−0.999214	+	0.0396489i	$0.987376\pi$
$878$	444070.	−	769153.i	0.0194409	−	0.0336726i
$879$	−1.59639e7	−	3.58532e7i	−0.696894	−	1.56515i
$880$	6.54105e6	−	3.77648e6i	0.284735	−	0.164392i
$881$	−6.16325e6			−0.267529			−0.133764	−	0.991013i	$-0.542707\pi$
$881$	−6.16325e6			−0.267529			−0.133764	+	0.991013i	$0.542707\pi$
$882$	−8.35969e6	−	2.44508e6i	−0.361842	−	0.105833i
$883$	−1.51180e7			−0.652519			−0.326260	−	0.945280i	$-0.605788\pi$
$883$	−1.51180e7			−0.652519			−0.326260	+	0.945280i	$0.605788\pi$
$884$	−223396.	+	128978.i	−0.00961489	+	0.00555116i
$885$	2.41202e7	+	5.41714e7i	1.03520	+	2.32494i
$886$	−7.47200e6	+	1.29419e7i	−0.319781	+	0.553877i
$887$	−1.21390e7	−	2.10253e7i	−0.518051	−	0.897290i	−0.999780	−	0.0209699i	$-0.993325\pi$
$887$	−1.21390e7	−	2.10253e7i	−0.518051	−	0.897290i	0.481730	−	0.876320i	$-0.340009\pi$
$888$	−6.94298e6	−	5.04412e6i	−0.295470	−	0.214661i
$889$	−1.25771e7	+	1.16657e7i	−0.533737	+	0.495058i
$890$		−	6.47584e6i		−	0.274045i
$891$	3.13789e6	−	7.04964e6i	0.132417	−	0.297490i
$892$	−6.09558e6	−	3.51929e6i	−0.256509	−	0.148096i
$893$	4.14329e6	+	2.39213e6i	0.173867	+	0.100382i
$894$	−309394.	−	32511.1i	−0.0129470	−	0.00136047i
$895$		−	3.80599e7i		−	1.58822i
$896$	7.20630e6	−	2.33474e7i	0.299876	−	0.971559i
$897$	−550361.	+	757545.i	−0.0228384	+	0.0314360i
$898$	1.73845e6	+	3.01108e6i	0.0719400	+	0.124604i
$899$	5.21400e6	−	9.03092e6i	0.215165	−	0.372677i
$900$	3.85631e7	+	8.19491e6i	1.58696	+	0.337239i
$901$	−3.87027e6	+	2.23450e6i	−0.158829	+	0.0916998i
$902$	−3.05035e6			−0.124834
$903$	3.81696e7	+	1.63215e7i	1.55775	+	0.666100i
$904$	1.14641e7			0.466572
$905$	−880366.	+	508280.i	−0.0357307	+	0.0206292i
$906$	−4.20496e6	+	1.87229e6i	−0.170193	+	0.0757797i
$907$	1.03386e7	−	1.79070e7i	0.417295	−	0.722777i	−0.578371	−	0.815774i	$-0.696311\pi$
$907$	1.03386e7	−	1.79070e7i	0.417295	−	0.722777i	0.995666	+	0.0929971i	$0.0296447\pi$
$908$	1.61822e6	+	2.80283e6i	0.0651361	+	0.112819i
$909$	4.02455e6	+	1.23843e7i	0.161550	+	0.497120i
$910$	−85726.9	−	375903.i	−0.00343173	−	0.0150478i
$911$			4.74564e7i			1.89452i	0.320466	+	0.947260i	$0.396161\pi$
$911$			4.74564e7i			1.89452i	−0.320466	+	0.947260i	$0.603839\pi$
$912$	537561.	−	5.11573e6i	0.0214013	−	0.203667i
$913$	3.58410e6	+	2.06928e6i	0.142299	+	0.0821565i
$914$	1.54937e7	+	8.94532e6i	0.613467	+	0.354185i
$915$	−5.14249e6	+	4.89388e7i	−0.203058	+	1.93242i
$916$			1.02610e7i			0.404063i
$917$	−1.83060e7	−	5.65024e6i	−0.718903	−	0.221893i
$918$	1.59855e6	−	4.92105e6i	0.0626067	−	0.192731i
$919$	2.49210e7	+	4.31645e7i	0.973368	+	1.68592i	0.685220	+	0.728337i	$0.259706\pi$
$919$	2.49210e7	+	4.31645e7i	0.973368	+	1.68592i	0.288148	+	0.957586i	$0.406960\pi$
$920$	2.46716e7	−	4.27325e7i	0.961011	−	1.66452i
$921$	−3.28974e7	+	1.46478e7i	−1.27795	+	0.569015i
$922$	344315.	−	198791.i	0.0133392	−	0.00770138i
$923$	−476717.			−0.0184186
$924$	−7.19806e6	+	864471.i	−0.277355	+	0.0333097i
$925$	−2.56614e7			−0.986111
$926$	9.67617e6	−	5.58654e6i	0.370831	−	0.214099i
$927$	7.76943e6	−	3.65610e7i	0.296955	−	1.39739i
$928$	−9.62310e6	+	1.66677e7i	−0.366813	+	0.635339i
$929$	−49366.4	−	85505.1i	−0.00187669	−	0.00325052i	0.865086	−	0.501624i	$-0.167264\pi$
$929$	−49366.4	−	85505.1i	−0.00187669	−	0.00325052i	−0.866962	+	0.498374i	$0.833931\pi$
$930$	5.38799e6	−	7.41631e6i	0.204277	−	0.281178i
$931$	3.95442e6	+	8.21894e6i	0.149523	+	0.310772i
$932$			3.47210e7i			1.30934i
$933$	−3.64766e7	−	3.83296e6i	−1.37186	−	0.144155i
$934$	1.04208e6	+	601643.i	0.0390870	+	0.0225669i
$935$	−6.88991e6	−	3.97789e6i	−0.257742	−	0.148807i
$936$	302438.	−	335924.i	0.0112836	−	0.0125329i
$937$			2.17619e7i			0.809743i	0.914373	+	0.404872i	$0.132684\pi$
$937$			2.17619e7i			0.809743i	−0.914373	+	0.404872i	$0.867316\pi$
$938$	1.21012e6	+	1.30466e6i	0.0449076	+	0.0484162i
$939$	−2.51118e7	−	1.82438e7i	−0.929422	−	0.675231i
$940$	1.15021e7	+	1.99223e7i	0.424579	+	0.735392i
$941$	−1.44807e7	+	2.50813e7i	−0.533109	+	0.923372i	0.466143	+	0.884709i	$0.345643\pi$
$941$	−1.44807e7	+	2.50813e7i	−0.533109	+	0.923372i	−0.999252	+	0.0386629i	$0.987690\pi$
$942$	−209125.	−	469671.i	−0.00767853	−	0.0172451i
$943$	3.88095e7	−	2.24067e7i	1.42121	−	0.820536i
$944$	2.43347e7			0.888784
$945$	−3.81672e7	−	2.68731e7i	−1.39031	−	0.978899i
$946$	−5.72476e6			−0.207984
$947$	−2.69772e7	+	1.55753e7i	−0.977513	+	0.564367i	−0.901518	−	0.432741i	$-0.857546\pi$
$947$	−2.69772e7	+	1.55753e7i	−0.977513	+	0.564367i	−0.0759944	+	0.997108i	$0.524213\pi$
$948$	−1.49659e6	−	3.36118e6i	−0.0540857	−	0.121471i
$949$	−93437.8	+	161839.i	−0.00336788	+	0.00583335i
$950$	3.41991e6	+	5.92347e6i	0.122944	+	0.212945i
$951$	2.64065e7	+	1.91845e7i	0.946804	+	0.687859i
$952$	−1.02644e7	+	2.34085e6i	−0.367063	+	0.0837107i
$953$		−	6.07840e6i		−	0.216799i	−0.994107	−	0.108399i	$-0.965427\pi$
$953$		−	6.07840e6i		−	0.216799i	0.994107	−	0.108399i	$-0.0345725\pi$
$954$	2.41940e6	−	2.68728e6i	0.0860672	−	0.0955965i
$955$	−1.62374e7	−	9.37465e6i	−0.576113	−	0.332619i
$956$	−1.23819e7	−	7.14869e6i	−0.438169	−	0.252977i
$957$	7.28261e6	+	765256.i	0.257044	+	0.0270102i
$958$		−	5.75230e6i		−	0.202501i
$959$	−2.86519e7	+	6.53422e6i	−1.00602	+	0.229429i
$960$	7.00184e6	−	9.63769e6i	0.245208	−	0.337516i
$961$	−1.01069e7	−	1.75056e7i	−0.353027	−	0.611461i
$962$	−67926.9	+	117653.i	−0.00236649	+	0.00409887i
$963$	−7.74906e6	+	3.64651e7i	−0.269267	+	1.26710i
$964$	−2.26873e7	+	1.30985e7i	−0.786302	+	0.453972i
$965$	1.19301e7			0.412407
$966$	−1.41208e7	+	1.05823e7i	−0.486875	+	0.364869i
$967$	412575.			0.0141885			0.00709426	−	0.999975i	$-0.497742\pi$
$967$	412575.			0.0141885			0.00709426	+	0.999975i	$0.497742\pi$
$968$	−1.58088e7	+	9.12720e6i	−0.542263	+	0.313075i
$969$	−4.94976e6	+	2.20392e6i	−0.169346	+	0.0754025i
$970$	1.45048e7	−	2.51231e7i	0.494974	−	0.857321i
$971$	1.17301e7	+	2.03171e7i	0.399258	+	0.691535i	0.993635	−	0.112652i	$-0.0359344\pi$
$971$	1.17301e7	+	2.03171e7i	0.399258	+	0.691535i	−0.594376	+	0.804187i	$0.702601\pi$
$972$	−3038.63	−	2.52689e7i	−0.000103160	−	0.857870i
$973$	2.03370e7	+	2.19260e7i	0.688661	+	0.742466i
$974$			6.06448e6i			0.204831i
$975$	141248.	−	1.34420e6i	0.00475852	−	0.0452847i
$976$	1.74884e7	+	1.00969e7i	0.587659	+	0.339285i
$977$	−1.35560e7	−	7.82655e6i	−0.454354	−	0.262322i	0.255313	−	0.966858i	$-0.417821\pi$
$977$	−1.35560e7	−	7.82655e6i	−0.454354	−	0.262322i	−0.709667	+	0.704537i	$0.751155\pi$
$978$	1.00629e6	−	9.57640e6i	0.0336415	−	0.320151i
$979$			4.17465e6i			0.139208i
$980$	−3.29294e6	+	4.37318e7i	−0.109527	+	1.45456i
$981$	9.59352e6	+	2.95210e7i	0.318277	+	0.979396i
$982$	7.87971e6	+	1.36481e7i	0.260754	+	0.451640i
$983$	3.05705e6	−	5.29497e6i	0.100906	−	0.174775i	−0.811152	−	0.584835i	$-0.801159\pi$
$983$	3.05705e6	−	5.29497e6i	0.100906	−	0.174775i	0.912058	+	0.410060i	$0.134492\pi$
$984$	−1.97623e7	+	8.79932e6i	−0.650654	+	0.289709i
$985$	5.19994e7	−	3.00219e7i	1.70768	−	0.985932i
$986$	4.91015e6			0.160843
$987$	−2.12445e6	−	1.76893e7i	−0.0694151	−	0.577988i
$988$	−218561.			−0.00712327
$989$	7.28359e7	−	4.20518e7i	2.36785	−	1.36708i
$990$	6.29655e6	+	1.33806e6i	0.204181	+	0.0433896i
$991$	1.78142e7	−	3.08550e7i	0.576211	−	0.998026i	−0.419698	−	0.907664i	$-0.637864\pi$
$991$	1.78142e7	−	3.08550e7i	0.576211	−	0.998026i	0.995909	−	0.0903627i	$-0.0288026\pi$
$992$	−7.76587e6	−	1.34509e7i	−0.250559	−	0.433982i
$993$	−2.52188e6	+	3.47125e6i	−0.0811617	+	0.111715i
$994$	−8.58429e6	−	2.64958e6i	−0.275574	−	0.0850572i
$995$		−	5.91588e7i		−	1.89436i
$996$	1.34782e7	+	1.41629e6i	0.430512	+	0.0452381i
$997$	−4.99143e7	−	2.88180e7i	−1.59033	−	0.918177i	−0.993250	−	0.115994i	$-0.962995\pi$
$997$	−4.99143e7	−	2.88180e7i	−1.59033	−	0.918177i	−0.597079	−	0.802183i	$-0.703672\pi$
$998$	3.94642e6	+	2.27846e6i	0.125423	+	0.0724129i
$999$	3.42082e6	+	1.60880e7i	0.108447	+	0.510021i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.6.g.c.17.4	yes	16
3.2	odd	2	inner	21.6.g.c.17.5	yes	16
7.3	odd	6		147.6.c.c.146.8		16
7.4	even	3		147.6.c.c.146.7		16
7.5	odd	6	inner	21.6.g.c.5.5	yes	16
21.5	even	6	inner	21.6.g.c.5.4	✓	16
21.11	odd	6		147.6.c.c.146.10		16
21.17	even	6		147.6.c.c.146.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.g.c.5.4	✓	16	21.5	even	6	inner
21.6.g.c.5.5	yes	16	7.5	odd	6	inner
21.6.g.c.17.4	yes	16	1.1	even	1	trivial
21.6.g.c.17.5	yes	16	3.2	odd	2	inner
147.6.c.c.146.7		16	7.4	even	3
147.6.c.c.146.8		16	7.3	odd	6
147.6.c.c.146.9		16	21.17	even	6
147.6.c.c.146.10		16	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	21.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.84692 + 1.06632i) q^{2} +(-6.34074 - 14.2406i) q^{3} +(-13.7259 + 23.7740i) q^{4} +(47.5262 + 82.3179i) q^{5} +(26.8959 + 19.5400i) q^{6} +(-95.0499 + 88.1619i) q^{7} -126.790i q^{8} +(-162.590 + 180.592i) q^{9} +O(q^{10})\)	\(q+(-1.84692 + 1.06632i) q^{2} +(-6.34074 - 14.2406i) q^{3} +(-13.7259 + 23.7740i) q^{4} +(47.5262 + 82.3179i) q^{5} +(26.8959 + 19.5400i) q^{6} +(-95.0499 + 88.1619i) q^{7} -126.790i q^{8} +(-162.590 + 180.592i) q^{9} +(-175.555 - 101.356i) q^{10} +(113.171 + 65.3395i) q^{11} +(425.589 + 44.7208i) q^{12} -14.6710i q^{13} +(81.5410 - 264.182i) q^{14} +(870.905 - 1198.76i) q^{15} +(-304.031 - 526.597i) q^{16} +(-320.246 + 554.683i) q^{17} +(107.722 - 506.913i) q^{18} +(-469.972 + 271.339i) q^{19} -2609.37 q^{20} +(1858.17 + 794.558i) q^{21} -278.692 q^{22} +(3545.78 - 2047.16i) q^{23} +(-1805.56 + 803.939i) q^{24} +(-2954.99 + 5118.19i) q^{25} +(15.6440 + 27.0962i) q^{26} +(3602.68 + 1170.29i) q^{27} +(-791.312 - 3469.82i) q^{28} +3594.70i q^{29} +(-330.233 + 3142.68i) q^{30} +(-2512.28 - 1450.47i) q^{31} +(4636.74 + 2677.02i) q^{32} +(212.884 - 2025.93i) q^{33} -1365.94i q^{34} +(-11774.7 - 3634.30i) q^{35} +(-2061.69 - 6344.20i) q^{36} +(2171.02 + 3760.32i) q^{37} +(578.668 - 1002.28i) q^{38} +(-208.924 + 93.0249i) q^{39} +(10437.0 - 6025.83i) q^{40} +10945.3 q^{41} +(-4279.14 + 513.915i) q^{42} +20541.6 q^{43} +(-3106.76 + 1793.69i) q^{44} +(-22593.2 - 4801.21i) q^{45} +(-4365.85 + 7561.88i) q^{46} +(-4408.02 - 7634.91i) q^{47} +(-5571.28 + 7668.60i) q^{48} +(1261.97 - 16759.6i) q^{49} -12603.9i q^{50} +(9929.62 + 1043.40i) q^{51} +(348.788 + 201.373i) q^{52} +(6042.65 + 3488.72i) q^{53} +(-7901.79 + 1680.17i) q^{54} +12421.4i q^{55} +(11178.0 + 12051.3i) q^{56} +(6844.00 + 4972.20i) q^{57} +(-3833.11 - 6639.14i) q^{58} +(-20010.1 + 34658.4i) q^{59} +(16545.3 + 37159.0i) q^{60} +(-28760.9 + 16605.1i) q^{61} +6186.66 q^{62} +(-467.159 - 31499.5i) q^{63} +8039.72 q^{64} +(1207.68 - 697.257i) q^{65} +(1767.11 + 3968.74i) q^{66} +(-3218.09 + 5573.90i) q^{67} +(-8791.35 - 15227.1i) q^{68} +(-51635.6 - 37513.6i) q^{69} +(25622.2 - 5843.29i) q^{70} -32493.9i q^{71} +(22897.2 + 20614.7i) q^{72} +(-11031.2 - 6368.89i) q^{73} +(-8019.42 - 4630.02i) q^{74} +(91623.0 + 9627.73i) q^{75} -14897.5i q^{76} +(-16517.4 + 3766.88i) q^{77} +(286.672 - 394.590i) q^{78} +(-4298.94 - 7445.99i) q^{79} +(28898.9 - 50054.4i) q^{80} +(-6177.95 - 58724.9i) q^{81} +(-20215.0 + 11671.2i) q^{82} +31669.6 q^{83} +(-44394.8 + 33270.0i) q^{84} -60880.4 q^{85} +(-37938.7 + 21903.9i) q^{86} +(51190.8 - 22793.1i) q^{87} +(8284.36 - 14348.9i) q^{88} +(15972.9 + 27665.9i) q^{89} +(46847.6 - 15224.2i) q^{90} +(1293.42 + 1394.48i) q^{91} +112396. i q^{92} +(-4725.81 + 44973.5i) q^{93} +(16282.5 + 9400.72i) q^{94} +(-44672.0 - 25791.4i) q^{95} +(8722.08 - 83004.3i) q^{96} +143107. i q^{97} +(15540.3 + 32299.3i) q^{98} +(-30200.3 + 9814.28i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 18 q^{3} + 86 q^{4} - 616 q^{7} - 606 q^{9}+O(q^{10}) \) 16 * q + 18 * q^3 + 86 * q^4 - 616 * q^7 - 606 * q^9	\( 16 q + 18 q^{3} + 86 q^{4} - 616 q^{7} - 606 q^{9} - 546 q^{10} + 4128 q^{12} + 1188 q^{15} - 2858 q^{16} - 438 q^{18} + 3258 q^{19} + 882 q^{21} - 21900 q^{22} + 10374 q^{24} - 6578 q^{25} + 34006 q^{28} + 450 q^{30} - 9792 q^{31} + 17556 q^{33} - 15132 q^{36} - 10466 q^{37} - 17418 q^{39} - 60774 q^{40} - 56994 q^{42} + 111052 q^{43} - 31374 q^{45} + 81696 q^{46} - 51548 q^{49} + 31596 q^{51} + 126960 q^{52} + 7434 q^{54} - 31368 q^{57} - 41706 q^{58} + 60066 q^{60} - 128580 q^{61} - 123606 q^{63} - 158884 q^{64} - 160314 q^{66} - 102202 q^{67} + 234318 q^{70} + 330864 q^{72} + 345150 q^{73} + 428202 q^{75} - 277512 q^{78} - 251308 q^{79} + 179262 q^{81} - 534576 q^{82} + 106176 q^{84} + 205152 q^{85} - 551922 q^{87} - 359514 q^{88} + 65814 q^{91} + 17676 q^{93} + 276612 q^{94} + 1043910 q^{96} + 215472 q^{99}+O(q^{100}) \) 16 * q + 18 * q^3 + 86 * q^4 - 616 * q^7 - 606 * q^9 - 546 * q^10 + 4128 * q^12 + 1188 * q^15 - 2858 * q^16 - 438 * q^18 + 3258 * q^19 + 882 * q^21 - 21900 * q^22 + 10374 * q^24 - 6578 * q^25 + 34006 * q^28 + 450 * q^30 - 9792 * q^31 + 17556 * q^33 - 15132 * q^36 - 10466 * q^37 - 17418 * q^39 - 60774 * q^40 - 56994 * q^42 + 111052 * q^43 - 31374 * q^45 + 81696 * q^46 - 51548 * q^49 + 31596 * q^51 + 126960 * q^52 + 7434 * q^54 - 31368 * q^57 - 41706 * q^58 + 60066 * q^60 - 128580 * q^61 - 123606 * q^63 - 158884 * q^64 - 160314 * q^66 - 102202 * q^67 + 234318 * q^70 + 330864 * q^72 + 345150 * q^73 + 428202 * q^75 - 277512 * q^78 - 251308 * q^79 + 179262 * q^81 - 534576 * q^82 + 106176 * q^84 + 205152 * q^85 - 551922 * q^87 - 359514 * q^88 + 65814 * q^91 + 17676 * q^93 + 276612 * q^94 + 1043910 * q^96 + 215472 * q^99

Introduction

L-functions

Modular forms

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