LMFDB - Embedded newform 80.6.j.a.43.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(43,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3]))

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

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

chi := DirichletCharacter("80.43");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.j (of order $4$, 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:	$12.8307055850$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$58$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.19
Character	$\chi$	$=$	80.43
Dual form			80.6.j.a.67.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.87799 - 4.87003i) q^{2} +18.3965i q^{3} +(-15.4344 + 28.0318i) q^{4} +(18.3385 + 52.8081i) q^{5} +(89.5915 - 52.9449i) q^{6} +(-170.706 + 170.706i) q^{7} +(180.935 - 5.50899i) q^{8} -95.4313 q^{9} +O(q^{10})$	\(q+(-2.87799 - 4.87003i) q^{2} +18.3965i q^{3} +(-15.4344 + 28.0318i) q^{4} +(18.3385 + 52.8081i) q^{5} +(89.5915 - 52.9449i) q^{6} +(-170.706 + 170.706i) q^{7} +(180.935 - 5.50899i) q^{8} -95.4313 q^{9} +(204.399 - 241.290i) q^{10} +(311.488 - 311.488i) q^{11} +(-515.686 - 283.939i) q^{12} -1028.71 q^{13} +(1322.63 + 340.054i) q^{14} +(-971.485 + 337.364i) q^{15} +(-547.559 - 865.307i) q^{16} +(1125.08 - 1125.08i) q^{17} +(274.650 + 464.753i) q^{18} +(21.2834 - 21.2834i) q^{19} +(-1763.35 - 301.001i) q^{20} +(-3140.39 - 3140.39i) q^{21} +(-2413.41 - 620.498i) q^{22} +(119.783 + 119.783i) q^{23} +(101.346 + 3328.58i) q^{24} +(-2452.40 + 1936.85i) q^{25} +(2960.62 + 5009.86i) q^{26} +2714.75i q^{27} +(-2150.44 - 7419.93i) q^{28} +(-431.061 - 431.061i) q^{29} +(4438.89 + 3760.23i) q^{30} +5976.18i q^{31} +(-2638.20 + 5156.97i) q^{32} +(5730.29 + 5730.29i) q^{33} +(-8717.15 - 2241.21i) q^{34} +(-12145.2 - 5884.17i) q^{35} +(1472.92 - 2675.11i) q^{36} -417.076 q^{37} +(-164.904 - 42.3975i) q^{38} -18924.7i q^{39} +(3609.01 + 9453.84i) q^{40} -13534.2i q^{41} +(-6255.80 + 24331.8i) q^{42} -6853.57 q^{43} +(3923.92 + 13539.2i) q^{44} +(-1750.07 - 5039.55i) q^{45} +(238.614 - 928.083i) q^{46} +(775.756 + 775.756i) q^{47} +(15918.6 - 10073.2i) q^{48} -41474.1i q^{49} +(16490.5 + 6369.04i) q^{50} +(20697.6 + 20697.6i) q^{51} +(15877.6 - 28836.6i) q^{52} -9297.05i q^{53} +(13220.9 - 7813.01i) q^{54} +(22161.3 + 10736.9i) q^{55} +(-29946.4 + 31827.2i) q^{56} +(391.540 + 391.540i) q^{57} +(-858.692 + 3339.87i) q^{58} +(9095.76 + 9095.76i) q^{59} +(5537.37 - 32439.4i) q^{60} +(-22436.6 + 22436.6i) q^{61} +(29104.2 - 17199.4i) q^{62} +(16290.7 - 16290.7i) q^{63} +(32707.3 - 1993.54i) q^{64} +(-18865.1 - 54324.4i) q^{65} +(11415.0 - 44398.3i) q^{66} -20126.3 q^{67} +(14173.1 + 48903.0i) q^{68} +(-2203.59 + 2203.59i) q^{69} +(6297.49 + 76081.8i) q^{70} +8502.91 q^{71} +(-17266.9 + 525.730i) q^{72} +(-29220.0 + 29220.0i) q^{73} +(1200.34 + 2031.17i) q^{74} +(-35631.2 - 45115.5i) q^{75} +(268.114 + 925.107i) q^{76} +106346. i q^{77} +(-92164.0 + 54465.1i) q^{78} +47566.9 q^{79} +(35653.8 - 44784.0i) q^{80} -73131.7 q^{81} +(-65912.1 + 38951.3i) q^{82} +76241.4i q^{83} +(136501. - 39560.6i) q^{84} +(80045.8 + 38781.2i) q^{85} +(19724.5 + 33377.1i) q^{86} +(7930.01 - 7930.01i) q^{87} +(54643.2 - 58075.2i) q^{88} -79120.5 q^{89} +(-19506.1 + 23026.6i) q^{90} +(175607. - 175607. i) q^{91} +(-5206.52 + 1508.95i) q^{92} -109941. q^{93} +(1545.34 - 6010.57i) q^{94} +(1514.24 + 733.630i) q^{95} +(-94870.2 - 48533.7i) q^{96} +(-64802.3 + 64802.3i) q^{97} +(-201980. + 119362. i) q^{98} +(-29725.7 + 29725.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 2 q^{2} - 20 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 248 q^{8} - 8748 q^{9}+O(q^{10}) $ 116 * q - 2 * q^2 - 20 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^7 - 248 * q^8 - 8748 * q^9	\( 116 q - 2 q^{2} - 20 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 248 q^{8} - 8748 q^{9} - 66 q^{10} - 4 q^{11} - 308 q^{12} - 4 q^{13} + 972 q^{15} - 1224 q^{16} - 4 q^{17} + 4214 q^{18} - 2360 q^{19} - 836 q^{20} - 4 q^{21} - 2440 q^{22} - 4 q^{23} + 972 q^{24} - 884 q^{26} - 12416 q^{28} + 15336 q^{30} - 17612 q^{32} - 4 q^{33} - 12520 q^{34} - 8640 q^{35} + 2380 q^{36} - 4 q^{37} + 15108 q^{38} + 11864 q^{40} - 41092 q^{42} - 1316 q^{43} + 8200 q^{44} - 5766 q^{45} - 35924 q^{46} + 65256 q^{47} + 5180 q^{48} - 44378 q^{50} + 10436 q^{51} + 63080 q^{52} + 33820 q^{54} - 4 q^{55} - 64684 q^{56} + 972 q^{57} - 66940 q^{58} - 14480 q^{59} + 136260 q^{60} + 48076 q^{61} + 109524 q^{62} + 972 q^{63} + 71920 q^{64} - 4 q^{65} + 72436 q^{66} - 89260 q^{67} + 36360 q^{68} - 21348 q^{69} + 59552 q^{70} - 143848 q^{71} + 179728 q^{72} - 10072 q^{73} - 82508 q^{74} - 32272 q^{75} - 128004 q^{76} + 111388 q^{78} + 313732 q^{80} + 551116 q^{81} - 282876 q^{82} - 80928 q^{84} - 6252 q^{85} - 85324 q^{86} - 282188 q^{87} + 80224 q^{88} + 115550 q^{90} - 164724 q^{91} + 474536 q^{92} + 968 q^{93} - 106060 q^{94} + 204760 q^{95} - 62264 q^{96} - 4 q^{97} + 50214 q^{98} - 168788 q^{99}+O(q^{100}) \) 116 * q - 2 * q^2 - 20 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^7 - 248 * q^8 - 8748 * q^9 - 66 * q^10 - 4 * q^11 - 308 * q^12 - 4 * q^13 + 972 * q^15 - 1224 * q^16 - 4 * q^17 + 4214 * q^18 - 2360 * q^19 - 836 * q^20 - 4 * q^21 - 2440 * q^22 - 4 * q^23 + 972 * q^24 - 884 * q^26 - 12416 * q^28 + 15336 * q^30 - 17612 * q^32 - 4 * q^33 - 12520 * q^34 - 8640 * q^35 + 2380 * q^36 - 4 * q^37 + 15108 * q^38 + 11864 * q^40 - 41092 * q^42 - 1316 * q^43 + 8200 * q^44 - 5766 * q^45 - 35924 * q^46 + 65256 * q^47 + 5180 * q^48 - 44378 * q^50 + 10436 * q^51 + 63080 * q^52 + 33820 * q^54 - 4 * q^55 - 64684 * q^56 + 972 * q^57 - 66940 * q^58 - 14480 * q^59 + 136260 * q^60 + 48076 * q^61 + 109524 * q^62 + 972 * q^63 + 71920 * q^64 - 4 * q^65 + 72436 * q^66 - 89260 * q^67 + 36360 * q^68 - 21348 * q^69 + 59552 * q^70 - 143848 * q^71 + 179728 * q^72 - 10072 * q^73 - 82508 * q^74 - 32272 * q^75 - 128004 * q^76 + 111388 * q^78 + 313732 * q^80 + 551116 * q^81 - 282876 * q^82 - 80928 * q^84 - 6252 * q^85 - 85324 * q^86 - 282188 * q^87 + 80224 * q^88 + 115550 * q^90 - 164724 * q^91 + 474536 * q^92 + 968 * q^93 - 106060 * q^94 + 204760 * q^95 - 62264 * q^96 - 4 * q^97 + 50214 * q^98 - 168788 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−2.87799	−	4.87003i	−0.508761	−	0.860908i
$2$	−2.87799	−	4.87003i	−0.508761	−	0.860908i
$3$			18.3965i			1.18014i	0.807354	+	0.590068i	$0.200899\pi$
$3$			18.3965i			1.18014i	−0.807354	+	0.590068i	$0.799101\pi$
$4$	−15.4344	+	28.0318i	−0.482325	+	0.875992i
$5$	18.3385	+	52.8081i	0.328049	+	0.944661i
$5$	18.3385	+	52.8081i	0.328049	+	0.944661i
$6$	89.5915	−	52.9449i	1.01599	−	0.600407i
$7$	−170.706	+	170.706i	−1.31675	+	1.31675i	−0.400418	+	0.916332i	$0.631135\pi$
$7$	−170.706	+	170.706i	−1.31675	+	1.31675i	−0.916332	+	0.400418i	$0.868865\pi$
$8$	180.935	−	5.50899i	0.999537	−	0.0304332i
$9$	−95.4313			−0.392721
$10$	204.399	−	241.290i	0.646367	−	0.763026i
$11$	311.488	−	311.488i	0.776174	−	0.776174i	−0.203004	−	0.979178i	$-0.565070\pi$
$11$	311.488	−	311.488i	0.776174	−	0.776174i	0.979178	+	0.203004i	$0.0650703\pi$
$12$	−515.686	−	283.939i	−1.03379	−	0.569209i
$13$	−1028.71			−1.68825			−0.844123	−	0.536149i	$-0.819878\pi$
$13$	−1028.71			−1.68825			−0.844123	+	0.536149i	$0.819878\pi$
$14$	1322.63	+	340.054i	1.80351	+	0.463690i
$15$	−971.485	+	337.364i	−1.11483	+	0.387143i
$16$	−547.559	−	865.307i	−0.534725	−	0.845026i
$17$	1125.08	−	1125.08i	0.944195	−	0.944195i	−0.0543277	−	0.998523i	$-0.517302\pi$
$17$	1125.08	−	1125.08i	0.944195	−	0.944195i	0.998523	+	0.0543277i	$0.0173016\pi$
$18$	274.650	+	464.753i	0.199801	+	0.338097i
$19$	21.2834	−	21.2834i	0.0135256	−	0.0135256i	−0.700312	−	0.713837i	$-0.746956\pi$
$19$	21.2834	−	21.2834i	0.0135256	−	0.0135256i	0.713837	+	0.700312i	$0.246956\pi$
$20$	−1763.35	−	301.001i	−0.985742	−	0.168265i
$21$	−3140.39	−	3140.39i	−1.55395	−	1.55395i
$22$	−2413.41	−	620.498i	−1.06310	−	0.273328i
$23$	119.783	+	119.783i	0.0472146	+	0.0472146i	0.730320	−	0.683105i	$-0.239371\pi$
$23$	119.783	+	119.783i	0.0472146	+	0.0472146i	−0.683105	+	0.730320i	$0.739371\pi$
$24$	101.346	+	3328.58i	0.0359153	+	1.17959i
$25$	−2452.40	+	1936.85i	−0.784767	+	0.619790i
$26$	2960.62	+	5009.86i	0.858913	+	1.45342i
$27$			2714.75i			0.716672i
$28$	−2150.44	−	7419.93i	−0.518362	−	1.78857i
$29$	−431.061	−	431.061i	−0.0951795	−	0.0951795i	0.657914	−	0.753093i	$-0.271439\pi$
$29$	−431.061	−	431.061i	−0.0951795	−	0.0951795i	−0.753093	+	0.657914i	$0.771439\pi$
$30$	4438.89	+	3760.23i	0.900475	+	0.762801i
$31$			5976.18i			1.11691i	0.829534	+	0.558456i	$0.188606\pi$
$31$			5976.18i			1.11691i	−0.829534	+	0.558456i	$0.811394\pi$
$32$	−2638.20	+	5156.97i	−0.455442	+	0.890265i
$33$	5730.29	+	5730.29i	0.915991	+	0.915991i
$34$	−8717.15	−	2241.21i	−1.29323	−	0.332496i
$35$	−12145.2	−	5884.17i	−1.67584	−	0.811924i
$36$	1472.92	−	2675.11i	0.189419	−	0.344021i
$37$	−417.076			−0.0500854			−0.0250427	−	0.999686i	$-0.507972\pi$
$37$	−417.076			−0.0500854			−0.0250427	+	0.999686i	$0.507972\pi$
$38$	−164.904	−	42.3975i	−0.0185256	−	0.00476300i
$39$		−	18924.7i		−	1.99236i
$40$	3609.01	+	9453.84i	0.356646	+	0.934239i
$41$		−	13534.2i		−	1.25740i	−0.777647	−	0.628701i	$-0.783587\pi$
$41$		−	13534.2i		−	1.25740i	0.777647	−	0.628701i	$-0.216413\pi$
$42$	−6255.80	+	24331.8i	−0.547217	+	2.12839i
$43$	−6853.57			−0.565257			−0.282629	−	0.959229i	$-0.591206\pi$
$43$	−6853.57			−0.565257			−0.282629	+	0.959229i	$0.591206\pi$
$44$	3923.92	+	13539.2i	0.305555	+	1.05429i
$45$	−1750.07	−	5039.55i	−0.128832	−	0.370988i
$46$	238.614	−	928.083i	0.0166265	−	0.0646684i
$47$	775.756	+	775.756i	0.0512249	+	0.0512249i	0.732255	−	0.681030i	$-0.238468\pi$
$47$	775.756	+	775.756i	0.0512249	+	0.0512249i	−0.681030	+	0.732255i	$0.738468\pi$
$48$	15918.6	−	10073.2i	0.997246	−	0.631049i
$49$		−	41474.1i		−	2.46767i
$50$	16490.5	+	6369.04i	0.932841	+	0.360287i
$51$	20697.6	+	20697.6i	1.11428	+	1.11428i
$52$	15877.6	−	28836.6i	0.814283	−	1.47889i
$53$		−	9297.05i		−	0.454628i	−0.973822	−	0.227314i	$-0.927006\pi$
$53$		−	9297.05i		−	0.454628i	0.973822	−	0.227314i	$-0.0729943\pi$
$54$	13220.9	−	7813.01i	0.616988	−	0.364614i
$55$	22161.3	+	10736.9i	0.987845	+	0.478598i
$56$	−29946.4	+	31827.2i	−1.27607	+	1.35621i
$57$	391.540	+	391.540i	0.0159621	+	0.0159621i
$58$	−858.692	+	3339.87i	−0.0335172	+	0.130364i
$59$	9095.76	+	9095.76i	0.340180	+	0.340180i	0.856435	−	0.516255i	$-0.172674\pi$
$59$	9095.76	+	9095.76i	0.340180	+	0.340180i	−0.516255	+	0.856435i	$0.672674\pi$
$60$	5537.37	−	32439.4i	0.198575	−	1.16331i
$61$	−22436.6	+	22436.6i	−0.772027	+	0.772027i	−0.978461	−	0.206434i	$-0.933814\pi$
$61$	−22436.6	+	22436.6i	−0.772027	+	0.772027i	0.206434	+	0.978461i	$0.433814\pi$
$62$	29104.2	−	17199.4i	0.961559	−	0.568241i
$63$	16290.7	−	16290.7i	0.517116	−	0.517116i
$64$	32707.3	−	1993.54i	0.998148	−	0.0608381i
$65$	−18865.1	−	54324.4i	−0.553828	−	1.59482i
$66$	11415.0	−	44398.3i	0.322564	−	1.25460i
$67$	−20126.3			−0.547744			−0.273872	−	0.961766i	$-0.588305\pi$
$67$	−20126.3			−0.547744			−0.273872	+	0.961766i	$0.588305\pi$
$68$	14173.1	+	48903.0i	0.371699	+	1.28252i
$69$	−2203.59	+	2203.59i	−0.0557197	+	0.0557197i
$70$	6297.49	+	76081.8i	0.153611	+	1.85582i
$71$	8502.91			0.200180			0.100090	−	0.994978i	$-0.468087\pi$
$71$	8502.91			0.200180			0.100090	+	0.994978i	$0.468087\pi$
$72$	−17266.9	+	525.730i	−0.392539	+	0.0119518i
$73$	−29220.0	+	29220.0i	−0.641760	+	0.641760i	−0.950988	−	0.309228i	$-0.899929\pi$
$73$	−29220.0	+	29220.0i	−0.641760	+	0.641760i	0.309228	+	0.950988i	$0.399929\pi$
$74$	1200.34	+	2031.17i	0.0254815	+	0.0431189i
$75$	−35631.2	−	45115.5i	−0.731437	−	0.926132i
$76$	268.114	+	925.107i	0.00532459	+	0.0183721i
$77$			106346.i			2.04406i
$78$	−92164.0	+	54465.1i	−1.71524	+	1.01363i
$79$	47566.9			0.857507			0.428753	−	0.903422i	$-0.358953\pi$
$79$	47566.9			0.857507			0.428753	+	0.903422i	$0.358953\pi$
$80$	35653.8	−	44784.0i	0.622847	−	0.782344i
$81$	−73131.7			−1.23849
$82$	−65912.1	+	38951.3i	−1.08251	+	0.639717i
$83$			76241.4i			1.21477i	0.794406	+	0.607387i	$0.207782\pi$
$83$			76241.4i			1.21477i	−0.794406	+	0.607387i	$0.792218\pi$
$84$	136501.	−	39560.6i	2.11075	−	0.611738i
$85$	80045.8	+	38781.2i	1.20169	+	0.582202i
$86$	19724.5	+	33377.1i	0.287581	+	0.486634i
$87$	7930.01	−	7930.01i	0.112325	−	0.112325i
$88$	54643.2	−	58075.2i	0.752193	−	0.799436i
$89$	−79120.5			−1.05880			−0.529400	−	0.848372i	$-0.677583\pi$
$89$	−79120.5			−1.05880			−0.529400	+	0.848372i	$0.677583\pi$
$90$	−19506.1	+	23026.6i	−0.253842	+	0.299657i
$91$	175607.	−	175607.i	2.22300	−	2.22300i
$92$	−5206.52	+	1508.95i	−0.0641325	+	0.0185869i
$93$	−109941.			−1.31811
$94$	1545.34	−	6010.57i	0.0180387	−	0.0701611i
$95$	1514.24	+	733.630i	0.0172142	+	0.00834004i
$96$	−94870.2	−	48533.7i	−1.05063	−	0.537484i
$97$	−64802.3	+	64802.3i	−0.699297	+	0.699297i	−0.964259	−	0.264962i	$-0.914641\pi$
$97$	−64802.3	+	64802.3i	−0.699297	+	0.699297i	0.264962	+	0.964259i	$0.414641\pi$
$98$	−201980.	+	119362.i	−2.12443	+	1.25545i
$99$	−29725.7	+	29725.7i	−0.304820	+	0.304820i
$100$	−16441.9	−	98639.1i	−0.164419	−	0.986391i
$101$	−100556.	−	100556.i	−0.980859	−	0.980859i	0.0189613	−	0.999820i	$-0.493964\pi$
$101$	−100556.	−	100556.i	−0.980859	−	0.980859i	−0.999820	+	0.0189613i	$0.993964\pi$
$102$	41230.5	−	160365.i	0.392390	−	1.52619i
$103$	12133.0	+	12133.0i	0.112687	+	0.112687i	0.761202	−	0.648515i	$-0.224610\pi$
$103$	12133.0	+	12133.0i	0.112687	+	0.112687i	−0.648515	+	0.761202i	$0.724610\pi$
$104$	−186131.	+	5667.17i	−1.68746	+	0.0513787i
$105$	108248.	−	223428.i	0.958180	−	1.97772i
$106$	−45276.9	+	26756.8i	−0.391392	+	0.231297i
$107$			114611.i			0.967759i	0.875135	+	0.483879i	$0.160773\pi$
$107$			114611.i			0.967759i	−0.875135	+	0.483879i	$0.839227\pi$
$108$	−76099.2	−	41900.5i	−0.627799	−	0.345669i
$109$	65758.4	+	65758.4i	0.530133	+	0.530133i	0.920612	−	0.390479i	$-0.127690\pi$
$109$	65758.4	+	65758.4i	0.530133	+	0.530133i	−0.390479	+	0.920612i	$0.627690\pi$
$110$	−11491.1	−	138827.i	−0.0905479	−	1.09394i
$111$		−	7672.74i		−	0.0591076i
$112$	241185.	+	54241.5i	1.81679	+	0.408589i
$113$	137250.	+	137250.i	1.01115	+	1.01115i	0.999937	+	0.0112129i	$0.00356925\pi$
$113$	137250.	+	137250.i	1.01115	+	1.01115i	0.0112129	+	0.999937i	$0.496431\pi$
$114$	779.965	−	3033.66i	0.00562099	−	0.0218627i
$115$	−4128.89	+	8522.18i	−0.0291131	+	0.0600906i
$116$	18736.6	−	5430.23i	0.129284	−	0.0374691i
$117$	98171.4			0.663010
$118$	18119.2	−	70474.1i	0.119794	−	0.465934i
$119$			384116.i			2.48654i
$120$	−173918.	+	66393.1i	−1.10253	+	0.420891i
$121$		−	32998.3i		−	0.204893i
$122$	173839.	+	44694.7i	1.05742	+	0.271867i
$123$	248983.			1.48390
$124$	−167523.	−	92238.7i	−0.978407	−	0.538715i
$125$	−147255.	−	93987.7i	−0.842934	−	0.538017i
$126$	−126221.	−	32451.8i	−0.708278	−	0.182101i
$127$	−39879.0	−	39879.0i	−0.219399	−	0.219399i	0.588846	−	0.808245i	$-0.299582\pi$
$127$	−39879.0	−	39879.0i	−0.219399	−	0.219399i	−0.808245	+	0.588846i	$0.799582\pi$
$128$	−103840.	−	153548.i	−0.560194	−	0.828361i
$129$		−	126082.i		−	0.667080i
$130$	−210268.	+	248218.i	−1.09123	+	1.28818i
$131$	82010.3	+	82010.3i	0.417532	+	0.417532i	0.884352	−	0.466820i	$-0.154600\pi$
$131$	82010.3	+	82010.3i	0.417532	+	0.417532i	−0.466820	+	0.884352i	$0.654600\pi$
$132$	−249073.	+	72186.5i	−1.24421	+	0.360596i
$133$			7266.40i			0.0356197i
$134$	57923.3	+	98015.9i	0.278671	+	0.471558i
$135$	−143361.	+	49784.4i	−0.677011	+	0.235104i
$136$	197369.	−	209765.i	0.915023	−	0.972493i
$137$	−139807.	−	139807.i	−0.636397	−	0.636397i	0.313268	−	0.949665i	$-0.398576\pi$
$137$	−139807.	−	139807.i	−0.636397	−	0.636397i	−0.949665	+	0.313268i	$0.898576\pi$
$138$	17073.5	+	4389.66i	0.0763175	+	0.0196215i
$139$	90200.7	+	90200.7i	0.395980	+	0.395980i	0.876812	−	0.480833i	$-0.159666\pi$
$139$	90200.7	+	90200.7i	0.395980	+	0.395980i	−0.480833	+	0.876812i	$0.659666\pi$
$140$	352397.	−	249631.i	1.51954	−	1.07641i
$141$	−14271.2	+	14271.2i	−0.0604523	+	0.0604523i
$142$	−24471.2	−	41409.4i	−0.101844	−	0.172337i
$143$	−320431.	+	320431.i	−1.31037	+	1.31037i
$144$	52254.2	+	82577.3i	0.209998	+	0.331860i
$145$	14858.5	−	30668.5i	0.0586888	−	0.121136i
$146$	226397.	+	58207.5i	0.878998	+	0.225994i
$147$	762978.			2.91218
$148$	6437.32	−	11691.4i	0.0241574	−	0.0438744i
$149$	138036.	−	138036.i	0.509362	−	0.509362i	−0.404969	−	0.914330i	$-0.632718\pi$
$149$	138036.	−	138036.i	0.509362	−	0.509362i	0.914330	+	0.404969i	$0.132718\pi$
$150$	−117168.	+	303367.i	−0.425188	+	1.10088i
$151$	−500326.			−1.78571			−0.892854	−	0.450346i	$-0.851301\pi$
$151$	−500326.			−1.78571			−0.892854	+	0.450346i	$0.851301\pi$
$152$	3733.67	−	3968.17i	0.0131077	−	0.0139310i
$153$	−107368.	+	107368.i	−0.370806	+	0.370806i
$154$	517907.	−	306061.i	1.75974	−	1.03994i
$155$	−315591.	+	109594.i	−1.05510	+	0.366402i
$156$	530493.	+	292092.i	1.74529	+	0.960965i
$157$			198235.i			0.641846i	0.947105	+	0.320923i	$0.103993\pi$
$157$			198235.i			0.641846i	−0.947105	+	0.320923i	$0.896007\pi$
$158$	−136897.	−	231652.i	−0.436266	−	0.738234i
$159$	171033.			0.536522
$160$	−320711.	−	44747.5i	−0.990406	−	0.138188i
$161$	−40895.5			−0.124340
$162$	210472.	+	356153.i	0.630096	+	1.06623i
$163$			51553.9i			0.151982i	0.997108	+	0.0759911i	$0.0242121\pi$
$163$			51553.9i			0.151982i	−0.997108	+	0.0759911i	$0.975788\pi$
$164$	379388.	+	208893.i	1.10147	+	0.606476i
$165$	−197521.	+	407691.i	−0.564811	+	1.16579i
$166$	371298.	−	219422.i	1.04581	−	0.618029i
$167$	263932.	−	263932.i	0.732319	−	0.732319i	−0.238760	−	0.971079i	$-0.576741\pi$
$167$	263932.	−	263932.i	0.732319	−	0.732319i	0.971079	+	0.238760i	$0.0767409\pi$
$168$	−585509.	−	550908.i	−1.60052	−	1.50593i
$169$	686957.			1.85017
$170$	−41505.3	−	501437.i	−0.110149	−	1.33074i
$171$	−2031.10	+	2031.10i	−0.00531179	+	0.00531179i
$172$	105781.	−	192118.i	0.272638	−	0.495161i
$173$	−23035.1			−0.0585160			−0.0292580	−	0.999572i	$-0.509314\pi$
$173$	−23035.1			−0.0585160			−0.0292580	+	0.999572i	$0.509314\pi$
$174$	−61441.8	−	15796.9i	−0.153848	−	0.0395549i
$175$	88008.0	−	749270.i	0.217234	−	1.84945i
$176$	−440090.	−	98974.6i	−1.07093	−	0.240847i
$177$	−167330.	+	167330.i	−0.401459	+	0.401459i
$178$	227708.	+	385319.i	0.538676	+	0.911530i
$179$	−407751.	+	407751.i	−0.951179	+	0.951179i	−0.998862	−	0.0476836i	$-0.984816\pi$
$179$	−407751.	+	407751.i	−0.951179	+	0.951179i	0.0476836	+	0.998862i	$0.484816\pi$
$180$	168279.	+	28724.9i	0.387122	+	0.0660811i
$181$	192992.	+	192992.i	0.437868	+	0.437868i	0.891294	−	0.453426i	$-0.149798\pi$
$181$	192992.	+	192992.i	0.437868	+	0.437868i	−0.453426	+	0.891294i	$0.649798\pi$
$182$	−1.36061e6	−	349818.i	−3.04477	−	0.782823i
$183$	−412755.	−	412755.i	−0.911096	−	0.911096i
$184$	22332.9	+	21013.2i	0.0486297	+	0.0457559i
$185$	−7648.56	−	22025.0i	−0.0164305	−	0.0473137i
$186$	316408.	+	535415.i	0.670602	+	1.13477i
$187$		−	700899.i		−	1.46572i
$188$	−33719.2	+	9772.48i	−0.0695796	+	0.0201656i
$189$	−463424.	−	463424.i	−0.943678	−	0.943678i
$190$	−785.163	−	9485.78i	−0.00157789	−	0.0190629i
$191$		−	709993.i		−	1.40822i	−0.710090	−	0.704111i	$-0.751346\pi$
$191$		−	709993.i		−	1.40822i	0.710090	−	0.704111i	$-0.248654\pi$
$192$	36674.2	+	601700.i	0.0717973	+	1.17795i
$193$	−24430.7	−	24430.7i	−0.0472110	−	0.0472110i	0.683107	−	0.730318i	$-0.260628\pi$
$193$	−24430.7	−	24430.7i	−0.0472110	−	0.0472110i	−0.730318	+	0.683107i	$0.760628\pi$
$194$	502090.	+	129089.i	0.957805	+	0.246255i
$195$	999379.	−	347051.i	1.88210	−	0.653592i
$196$	1.16259e6	+	640127.i	2.16166	+	1.19022i
$197$	659639.			1.21099			0.605495	−	0.795849i	$-0.292975\pi$
$197$	659639.			1.21099			0.605495	+	0.795849i	$0.292975\pi$
$198$	230315.	+	59214.9i	0.417503	+	0.107342i
$199$			750798.i			1.34397i	0.740563	+	0.671987i	$0.234559\pi$
$199$			750798.i			1.34397i	−0.740563	+	0.671987i	$0.765441\pi$
$200$	−433056.	+	363954.i	−0.765542	+	0.643386i
$201$		−	370254.i		−	0.646413i
$202$	−200313.	+	779113.i	−0.345407	+	1.34345i
$203$	147169.			0.250655
$204$	−899644.	+	260735.i	−1.51354	+	0.438655i
$205$	714718.	−	248198.i	1.18782	−	0.412490i
$206$	24169.4	−	94006.4i	0.0396824	−	0.154344i
$207$	−11431.1	−	11431.1i	−0.0185422	−	0.0185422i
$208$	563281.	+	890152.i	0.902748	+	1.42661i
$209$		−	13259.0i		−	0.0209965i
$210$	−1.39964e6	+	115852.i	−2.19012	+	0.181282i
$211$	38825.6	+	38825.6i	0.0600360	+	0.0600360i	0.736487	−	0.676451i	$-0.236483\pi$
$211$	38825.6	+	38825.6i	0.0600360	+	0.0600360i	−0.676451	+	0.736487i	$0.736483\pi$
$212$	260613.	+	143494.i	0.398250	+	0.219278i
$213$			156424.i			0.236240i
$214$	558159.	−	329849.i	0.833151	−	0.492358i
$215$	−125684.	−	361924.i	−0.185432	−	0.533976i
$216$	14955.5	+	491194.i	0.0218106	+	0.716340i
$217$	−1.02017e6	−	1.02017e6i	−1.47070	−	1.47070i
$218$	130994.	−	509497.i	0.186685	−	0.726107i
$219$	−537545.	−	537545.i	−0.757364	−	0.757364i
$220$	−643020.	+	455503.i	−0.895710	+	0.634505i
$221$	−1.15739e6	+	1.15739e6i	−1.59403	+	1.59403i
$222$	−37366.5	+	22082.0i	−0.0508862	+	0.0300716i
$223$	−680726.	+	680726.i	−0.916664	+	0.916664i	−0.996785	−	0.0801212i	$-0.974469\pi$
$223$	−680726.	+	680726.i	−0.916664	+	0.916664i	0.0801212	+	0.996785i	$0.474469\pi$
$224$	−429968.	−	1.33068e6i	−0.572554	−	1.77196i
$225$	234035.	−	184836.i	0.308195	−	0.243405i
$226$	273408.	−	1.06341e6i	0.356074	−	1.38494i
$227$	−438975.			−0.565425			−0.282713	−	0.959205i	$-0.591234\pi$
$227$	−438975.			−0.565425			−0.282713	+	0.959205i	$0.591234\pi$
$228$	−17018.7	+	4932.37i	−0.0216815	+	0.00628374i
$229$	−785341.	+	785341.i	−0.989623	+	0.989623i	−0.999947	−	0.0103240i	$-0.996714\pi$
$229$	−785341.	+	785341.i	−0.989623	+	0.989623i	0.0103240	+	0.999947i	$0.496714\pi$
$230$	53386.2	−	4418.91i	0.0665440	−	0.00550802i
$231$	−1.95639e6			−2.41227
$232$	−80368.9	−	75619.5i	−0.0980320	−	0.0922388i
$233$	160758.	−	160758.i	0.193992	−	0.193992i	−0.603427	−	0.797418i	$-0.706198\pi$
$233$	160758.	−	160758.i	0.193992	−	0.193992i	0.797418	+	0.603427i	$0.206198\pi$
$234$	−282536.	−	478098.i	−0.337314	−	0.570791i
$235$	−26740.0	+	55192.5i	−0.0315858	+	0.0651944i
$236$	−395358.	+	114583.i	−0.462073	+	0.133918i
$237$			875065.i			1.01197i
$238$	1.87066e6	−	1.10548e6i	2.14068	−	1.26505i
$239$	240900.			0.272798			0.136399	−	0.990654i	$-0.456447\pi$
$239$	240900.			0.272798			0.136399	+	0.990654i	$0.456447\pi$
$240$	823869.	+	655905.i	0.923272	+	0.735044i
$241$	−15888.3			−0.0176212			−0.00881059	−	0.999961i	$-0.502805\pi$
$241$	−15888.3			−0.0176212			−0.00881059	+	0.999961i	$0.502805\pi$
$242$	−160703.	+	94968.6i	−0.176394	+	0.104242i
$243$		−	685683.i		−	0.744917i
$244$	−282642.	−	975232.i	−0.303922	−	1.04866i
$245$	2.19017e6	−	760572.i	2.33111	−	0.809516i
$246$	−716568.	−	1.21255e6i	−0.754953	−	1.27751i
$247$	−21894.5	+	21894.5i	−0.0228345	+	0.0228345i
$248$	32922.7	+	1.08130e6i	0.0339912	+	1.11640i
$249$	−1.40257e6			−1.43360
$250$	−33926.7	+	987629.i	−0.0343314	+	0.999411i
$251$	−298379.	+	298379.i	−0.298940	+	0.298940i	−0.840599	−	0.541659i	$-0.817797\pi$
$251$	−298379.	+	298379.i	−0.298940	+	0.298940i	0.541659	+	0.840599i	$0.317797\pi$
$252$	205220.	+	708094.i	0.203572	+	0.702408i
$253$	74622.1			0.0732936
$254$	−79440.8	+	308983.i	−0.0772608	+	0.300504i
$255$	−713438.	+	1.47256e6i	−0.687077	+	1.41815i
$256$	−448935.	+	947612.i	−0.428138	+	0.903713i
$257$	860953.	−	860953.i	0.813105	−	0.813105i	−0.171993	−	0.985098i	$-0.555021\pi$
$257$	860953.	−	860953.i	0.813105	−	0.813105i	0.985098	+	0.171993i	$0.0550207\pi$
$258$	−614022.	+	362862.i	−0.574295	+	0.339384i
$259$	71197.4	−	71197.4i	0.0659500	−	0.0659500i
$260$	1.81398e6	+	309644.i	1.66417	+	0.284072i
$261$	41136.7	+	41136.7i	0.0373790	+	0.0373790i
$262$	163368.	−	635417.i	0.147033	−	0.571881i
$263$	−1.29519e6	−	1.29519e6i	−1.15463	−	1.15463i	−0.985612	−	0.169021i	$-0.945939\pi$
$263$	−1.29519e6	−	1.29519e6i	−1.15463	−	1.15463i	−0.169021	−	0.985612i	$-0.554061\pi$
$264$	1.06838e6	+	1.00524e6i	0.943444	+	0.887691i
$265$	490960.	−	170494.i	0.429469	−	0.149140i
$266$	35387.6	−	20912.6i	0.0306653	−	0.0181219i
$267$		−	1.45554e6i		−	1.24953i
$268$	310638.	−	564177.i	0.264191	−	0.479820i
$269$	1.12498e6	+	1.12498e6i	0.947906	+	0.947906i	0.998709	−	0.0508023i	$-0.0161778\pi$
$269$	1.12498e6	+	1.12498e6i	0.947906	+	0.947906i	−0.0508023	+	0.998709i	$0.516178\pi$
$270$	655042.	+	554893.i	0.546839	+	0.463233i
$271$		−	113900.i		−	0.0942110i	−0.998890	−	0.0471055i	$-0.985000\pi$
$271$		−	113900.i		−	0.0942110i	0.998890	−	0.0471055i	$-0.0149997\pi$
$272$	−1.58959e6	−	357492.i	−1.30275	−	0.292985i
$273$	3.23056e6	+	3.23056e6i	2.62344	+	2.62344i
$274$	−278502.	+	1.08323e6i	−0.224105	+	0.871653i
$275$	−160588.	+	1.36720e6i	−0.128051	+	1.09018i
$276$	−27759.5	−	95781.8i	−0.0219350	−	0.0756851i
$277$	−1.49013e6			−1.16687			−0.583437	−	0.812158i	$-0.698292\pi$
$277$	−1.49013e6			−1.16687			−0.583437	+	0.812158i	$0.698292\pi$
$278$	179684.	−	698876.i	0.139443	−	0.542361i
$279$		−	570314.i		−	0.438635i
$280$	−2.22991e6	−	997748.i	−1.69977	−	0.760546i
$281$		−	2.04016e6i		−	1.54134i	−0.637233	−	0.770672i	$-0.719921\pi$
$281$		−	2.04016e6i		−	1.54134i	0.637233	−	0.770672i	$-0.280079\pi$
$282$	110574.	+	28428.9i	0.0827996	+	0.0212881i
$283$	1.32684e6			0.984812			0.492406	−	0.870366i	$-0.336117\pi$
$283$	1.32684e6			0.984812			0.492406	+	0.870366i	$0.336117\pi$
$284$	−131237.	+	238351.i	−0.0965520	+	0.175357i
$285$	−13496.2	+	27856.7i	−0.00984238	+	0.0203151i
$286$	2.48271e6	+	638314.i	1.79478	+	0.461444i
$287$	2.31037e6	+	2.31037e6i	1.65568	+	1.65568i
$288$	251767.	−	492136.i	0.178862	−	0.349626i
$289$		−	1.11176e6i		−	0.783010i
$290$	−192119.	+	15902.2i	−0.134145	+	0.0111036i
$291$	−1.19214e6	−	1.19214e6i	−0.825265	−	0.825265i
$292$	−368094.	−	1.27008e6i	−0.252640	−	0.871713i
$293$			1.78304e6i			1.21336i	0.794944	+	0.606682i	$0.207500\pi$
$293$			1.78304e6i			1.21336i	−0.794944	+	0.606682i	$0.792500\pi$
$294$	−2.19584e6	−	3.71572e6i	−1.48160	−	2.50712i
$295$	−313527.	+	647133.i	−0.209759	+	0.432951i
$296$	−75463.9	+	2297.67i	−0.0500622	+	0.00152426i
$297$	845611.	+	845611.i	0.556262	+	0.556262i
$298$	−1.06950e6	−	274974.i	−0.697657	−	0.179370i
$299$	−123223.	−	123223.i	−0.0797099	−	0.0797099i
$300$	1.81461e6	−	302473.i	1.16408	−	0.194037i
$301$	1.16995e6	−	1.16995e6i	0.744303	−	0.744303i
$302$	1.43993e6	+	2.43660e6i	0.908498	+	1.53733i
$303$	1.84989e6	−	1.84989e6i	1.15755	−	1.15755i
$304$	−30070.5	−	6762.75i	−0.0186620	−	0.00419700i
$305$	−1.59629e6	−	773381.i	−0.982566	−	0.476040i
$306$	831889.	+	213882.i	0.507881	+	0.130578i
$307$	1.39116e6			0.842424			0.421212	−	0.906962i	$-0.361605\pi$
$307$	1.39116e6			0.842424			0.421212	+	0.906962i	$0.361605\pi$
$308$	−2.98106e6	−	1.64138e6i	−1.79058	−	0.985900i
$309$	−223204.	+	223204.i	−0.132986	+	0.132986i
$310$	1.44199e6	+	1.22153e6i	0.852234	+	0.721936i
$311$	1.55852e6			0.913717			0.456859	−	0.889539i	$-0.348975\pi$
$311$	1.55852e6			0.913717			0.456859	+	0.889539i	$0.348975\pi$
$312$	−104256.	−	3.42415e6i	−0.0606338	−	1.99144i
$313$	367527.	−	367527.i	0.212045	−	0.212045i	−0.593091	−	0.805136i	$-0.702092\pi$
$313$	367527.	−	367527.i	0.212045	−	0.212045i	0.805136	+	0.593091i	$0.202092\pi$
$314$	965410.	−	570517.i	0.552571	−	0.326546i
$315$	1.15903e6	+	561534.i	0.658139	+	0.318860i
$316$	−734167.	+	1.33338e6i	−0.413597	+	0.751169i
$317$			463116.i			0.258846i	0.991589	+	0.129423i	$0.0413125\pi$
$317$			463116.i			0.258846i	−0.991589	+	0.129423i	$0.958688\pi$
$318$	−492231.	−	832937.i	−0.272962	−	0.461896i
$319$	−268540.			−0.147752
$320$	705079.	+	1.69065e6i	0.384913	+	0.922953i
$321$	−2.10844e6			−1.14209
$322$	117697.	+	199162.i	0.0632592	+	0.107045i
$323$		−	47891.1i		−	0.0255416i
$324$	1.12874e6	−	2.05001e6i	0.597355	−	1.08491i
$325$	2.52281e6	−	1.99246e6i	1.32488	−	1.04636i
$326$	251069.	−	148372.i	0.130843	−	0.0773226i
$327$	−1.20973e6	+	1.20973e6i	−0.625630	+	0.625630i
$328$	−74560.0	−	2.44882e6i	−0.0382667	−	1.25682i
$329$	−264853.			−0.134901
$330$	2.55393e6	−	211395.i	1.29099	−	0.106859i
$331$	−2.76050e6	+	2.76050e6i	−1.38490	+	1.38490i	−0.549217	+	0.835680i	$0.685074\pi$
$331$	−2.76050e6	+	2.76050e6i	−1.38490	+	1.38490i	−0.835680	+	0.549217i	$0.814926\pi$
$332$	−2.13718e6	−	1.17674e6i	−1.06413	−	0.585916i
$333$	39802.1			0.0196696
$334$	−2.04495e6	−	525764.i	−1.00303	−	0.257884i
$335$	−369087.	−	1.06283e6i	−0.179687	−	0.517433i
$336$	−997853.	+	4.43695e6i	−0.482190	+	2.14406i
$337$	1.90102e6	−	1.90102e6i	0.911827	−	0.911827i	−0.0845888	−	0.996416i	$-0.526958\pi$
$337$	1.90102e6	−	1.90102e6i	0.911827	−	0.911827i	0.996416	+	0.0845888i	$0.0269577\pi$
$338$	−1.97705e6	−	3.34550e6i	−0.941296	−	1.59283i
$339$	−2.52492e6	+	2.52492e6i	−1.19329	+	1.19329i
$340$	−2.32256e6	+	1.64526e6i	−1.08961	+	0.771858i
$341$	1.86151e6	+	1.86151e6i	0.866919	+	0.866919i
$342$	15737.0	+	4046.04i	0.00727539	+	0.00187053i
$343$	4.21081e6	+	4.21081e6i	1.93255	+	1.93255i
$344$	−1.24005e6	+	37756.3i	−0.564995	+	0.0172026i
$345$	−156778.	−	75957.1i	−0.0709150	−	0.0343574i
$346$	66294.6	+	112182.i	0.0297706	+	0.0503769i
$347$			1.45616e6i			0.649210i	0.945850	+	0.324605i	$0.105231\pi$
$347$			1.45616e6i			0.649210i	−0.945850	+	0.324605i	$0.894769\pi$
$348$	99897.2	+	344687.i	0.0442186	+	0.152573i
$349$	1.63074e6	+	1.63074e6i	0.716671	+	0.716671i	0.967922	−	0.251251i	$-0.0808419\pi$
$349$	1.63074e6	+	1.63074e6i	0.716671	+	0.716671i	−0.251251	+	0.967922i	$0.580842\pi$
$350$	−3.90225e6	+	1.72779e6i	−1.70273	+	0.753911i
$351$		−	2.79270e6i		−	1.20992i
$352$	784564.	+	2.42810e6i	0.337498	+	1.04450i
$353$	−886943.	−	886943.i	−0.378843	−	0.378843i	0.491842	−	0.870685i	$-0.336324\pi$
$353$	−886943.	−	886943.i	−0.378843	−	0.378843i	−0.870685	+	0.491842i	$0.836324\pi$
$354$	1.29648e6	+	333329.i	0.549866	+	0.141373i
$355$	155931.	+	449023.i	0.0656690	+	0.189103i
$356$	1.22118e6	−	2.21789e6i	0.510686	−	0.927501i
$357$	−7.06640e6			−2.93446
$358$	3.15926e6	+	812258.i	1.30280	+	0.334955i
$359$		−	2.30927e6i		−	0.945667i	−0.881152	−	0.472834i	$-0.843231\pi$
$359$		−	2.30927e6i		−	0.945667i	0.881152	−	0.472834i	$-0.156769\pi$
$360$	−344412.	−	902192.i	−0.140063	−	0.366896i
$361$			2.47519e6i			0.999634i
$362$	384449.	−	1.49531e6i	0.154194	−	0.599734i
$363$	607053.			0.241802
$364$	2.21219e6	+	7.63298e6i	0.875122	+	3.01954i
$365$	−2.07890e6	−	1.00720e6i	−0.816774	−	0.395716i
$366$	−822226.	+	3.19803e6i	−0.320840	+	1.24790i
$367$	−1.51398e6	−	1.51398e6i	−0.586753	−	0.586753i	0.349997	−	0.936751i	$-0.386182\pi$
$367$	−1.51398e6	−	1.51398e6i	−0.586753	−	0.586753i	−0.936751	+	0.349997i	$0.886182\pi$
$368$	38060.9	−	169238.i	0.0146507	−	0.0651445i
$369$			1.29159e6i			0.493808i
$370$	−85250.1	+	100636.i	−0.0323736	+	0.0382165i
$371$	1.58706e6	+	1.58706e6i	0.598631	+	0.598631i
$372$	1.69687e6	−	3.08183e6i	0.635757	−	1.15465i
$373$		−	1.04809e6i		−	0.390057i	−0.980798	−	0.195028i	$-0.937520\pi$
$373$		−	1.04809e6i		−	0.390057i	0.980798	−	0.195028i	$-0.0624799\pi$
$374$	−3.41340e6	+	2.01718e6i	−1.26185	+	0.745701i
$375$	1.72905e6	−	2.70897e6i	0.634933	−	0.994777i
$376$	144636.	+	136088.i	0.0527601	+	0.0496422i
$377$	443438.	+	443438.i	0.160686	+	0.160686i
$378$	−923161.	+	3.59061e6i	−0.332314	+	1.29253i
$379$	−624699.	−	624699.i	−0.223395	−	0.223395i	0.586532	−	0.809926i	$-0.300493\pi$
$379$	−624699.	−	624699.i	−0.223395	−	0.223395i	−0.809926	+	0.586532i	$0.800493\pi$
$380$	−43936.3	+	31123.7i	−0.0156086	+	0.0110569i
$381$	733634.	−	733634.i	0.258921	−	0.258921i
$382$	−3.45769e6	+	2.04335e6i	−1.21235	+	0.716448i
$383$	−1.72780e6	+	1.72780e6i	−0.601861	+	0.601861i	−0.940806	−	0.338945i	$-0.889930\pi$
$383$	−1.72780e6	+	1.72780e6i	−0.601861	+	0.601861i	0.338945	+	0.940806i	$0.389930\pi$
$384$	2.82475e6	−	1.91029e6i	0.977579	−	0.661106i
$385$	−5.61592e6	+	1.95022e6i	−1.93094	+	0.670551i
$386$	−48667.1	+	189290.i	−0.0166252	+	0.0646634i
$387$	654045.			0.221988
$388$	−816338.	−	2.81671e6i	−0.275290	−	0.949867i
$389$	−408372.	+	408372.i	−0.136830	+	0.136830i	−0.772204	−	0.635374i	$-0.780846\pi$
$389$	−408372.	+	408372.i	−0.136830	+	0.136830i	0.635374	+	0.772204i	$0.280846\pi$
$390$	−4.56635e6	−	3.86820e6i	−1.52022	−	1.28780i
$391$	269532.			0.0891597
$392$	−228480.	−	7.50413e6i	−0.0750989	−	2.46652i
$393$	−1.50870e6	+	1.50870e6i	−0.492745	+	0.492745i
$394$	−1.89843e6	−	3.21246e6i	−0.616104	−	1.04255i
$395$	872307.	+	2.51192e6i	0.281304	+	0.810053i
$396$	−374465.	−	1.29206e6i	−0.119998	−	0.414043i
$397$		−	1.02992e6i		−	0.327965i	−0.986463	−	0.163983i	$-0.947566\pi$
$397$		−	1.02992e6i		−	0.327965i	0.986463	−	0.163983i	$-0.0524341\pi$
$398$	3.65641e6	−	2.16079e6i	1.15704	−	0.683761i
$399$	−133676.			−0.0420361
$400$	3.01880e6	+	1.06154e6i	0.943374	+	0.331731i
$401$	2.91342e6			0.904777			0.452389	−	0.891821i	$-0.350572\pi$
$401$	2.91342e6			0.904777			0.452389	+	0.891821i	$0.350572\pi$
$402$	−1.80315e6	+	1.06559e6i	−0.556502	+	0.328870i
$403$		−	6.14777e6i		−	1.88562i
$404$	4.37080e6	−	1.26675e6i	1.33232	−	0.386132i
$405$	−1.34113e6	−	3.86195e6i	−0.406286	−	1.16995i
$406$	−423551.	−	716719.i	−0.127524	−	0.215791i
$407$	−129914.	+	129914.i	−0.0388750	+	0.0388750i
$408$	3.85895e6	+	3.63090e6i	1.14767	+	1.07985i
$409$	4.66275e6			1.37827			0.689134	−	0.724633i	$-0.257991\pi$
$409$	4.66275e6			1.37827			0.689134	+	0.724633i	$0.257991\pi$
$410$	−3.26568e6	−	2.76639e6i	−0.959431	−	0.812743i
$411$	2.57196e6	−	2.57196e6i	0.751035	−	0.751035i
$412$	−527374.	+	152843.i	−0.153065	+	0.0443612i
$413$	−3.10540e6			−0.895865
$414$	−22771.2	+	88568.2i	−0.00652958	+	0.0253967i
$415$	−4.02616e6	+	1.39815e6i	−1.14755	+	0.398506i
$416$	2.71395e6	−	5.30504e6i	0.768899	−	1.50299i
$417$	−1.65938e6	+	1.65938e6i	−0.467310	+	0.467310i
$418$	−64571.9	+	38159.3i	−0.0180760	+	0.0106822i
$419$	−1.15596e6	+	1.15596e6i	−0.321669	+	0.321669i	−0.849407	−	0.527738i	$-0.823040\pi$
$419$	−1.15596e6	+	1.15596e6i	−0.321669	+	0.321669i	0.527738	+	0.849407i	$0.323040\pi$
$420$	4.59235e6	+	6.48287e6i	1.27031	+	1.79326i
$421$	741858.	+	741858.i	0.203993	+	0.203993i	0.801708	−	0.597715i	$-0.203925\pi$
$421$	741858.	+	741858.i	0.203993	+	0.203993i	−0.597715	+	0.801708i	$0.703925\pi$
$422$	77342.3	−	300821.i	0.0211415	−	0.0822294i
$423$	−74031.4	−	74031.4i	−0.0201171	−	0.0201171i
$424$	−51217.4	−	1.68217e6i	−0.0138358	−	0.454417i
$425$	−580039.	+	4.93826e6i	−0.155770	+	1.32618i
$426$	761789.	−	450185.i	0.203381	−	0.120190i
$427$		−	7.66012e6i		−	2.03313i
$428$	−3.21275e6	−	1.76895e6i	−0.847749	−	0.466774i
$429$	−5.89482e6	−	5.89482e6i	−1.54642	−	1.54642i
$430$	−1.40087e6	+	1.65370e6i	−0.365364	+	0.431306i
$431$		−	995475.i		−	0.258129i	−0.991636	−	0.129065i	$-0.958803\pi$
$431$		−	995475.i		−	0.258129i	0.991636	−	0.129065i	$-0.0411975\pi$
$432$	2.34909e6	−	1.48648e6i	0.605606	−	0.383222i
$433$	−2.52571e6	−	2.52571e6i	−0.647388	−	0.647388i	0.304973	−	0.952361i	$-0.401352\pi$
$433$	−2.52571e6	−	2.52571e6i	−0.647388	−	0.647388i	−0.952361	+	0.304973i	$0.901352\pi$
$434$	−2.03222e6	+	7.90429e6i	−0.517901	+	2.01437i
$435$	564194.	+	273344.i	0.142957	+	0.0692607i
$436$	−2.85827e6	+	828382.i	−0.720089	+	0.208696i
$437$	5098.79			0.00127721
$438$	−1.07081e6	+	4.16491e6i	−0.266704	+	1.03734i
$439$			467613.i			0.115804i	0.998322	+	0.0579022i	$0.0184412\pi$
$439$			467613.i			0.115804i	−0.998322	+	0.0579022i	$0.981559\pi$
$440$	4.06892e6	+	1.82059e6i	1.00195	+	0.448313i
$441$			3.95792e6i			0.969105i
$442$	8.96745e6	+	2.30557e6i	2.18330	+	0.561335i
$443$	1.01199e6			0.245000			0.122500	−	0.992469i	$-0.460909\pi$
$443$	1.01199e6			0.245000			0.122500	+	0.992469i	$0.460909\pi$
$444$	215080.	+	118424.i	0.0517778	+	0.0285091i
$445$	−1.45095e6	−	4.17821e6i	−0.347339	−	1.00021i
$446$	5.27428e6	+	1.35604e6i	1.25553	+	0.322801i
$447$	2.53938e6	+	2.53938e6i	0.601116	+	0.601116i
$448$	−5.24302e6	+	5.92364e6i	−1.23420	+	1.39442i
$449$			2.49543e6i			0.584158i	0.956394	+	0.292079i	$0.0943470\pi$
$449$			2.49543e6i			0.584158i	−0.956394	+	0.292079i	$0.905653\pi$
$450$	−1.57371e6	−	607806.i	−0.366347	−	0.141493i
$451$	−4.21575e6	−	4.21575e6i	−0.975963	−	0.975963i
$452$	−5.96572e6	+	1.72898e6i	−1.37346	+	0.398057i
$453$		−	9.20424e6i		−	2.10738i
$454$	1.26336e6	+	2.13782e6i	0.287666	+	0.486779i
$455$	1.24939e7	+	6.05312e6i	2.82923	+	1.37073i
$456$	73000.4	+	68686.4i	0.0164404	+	0.0154689i
$457$	1.69287e6	+	1.69287e6i	0.379170	+	0.379170i	0.870803	−	0.491633i	$-0.163600\pi$
$457$	1.69287e6	+	1.69287e6i	0.379170	+	0.379170i	−0.491633	+	0.870803i	$0.663600\pi$
$458$	6.08484e6	+	1.56444e6i	1.35546	+	0.348493i
$459$	3.05431e6	+	3.05431e6i	0.676678	+	0.676678i
$460$	−175165.	−	247275.i	−0.0385969	−	0.0544860i
$461$	2.24258e6	−	2.24258e6i	0.491468	−	0.491468i	−0.417300	−	0.908769i	$-0.637024\pi$
$461$	2.24258e6	−	2.24258e6i	0.491468	−	0.491468i	0.908769	+	0.417300i	$0.137024\pi$
$462$	5.63046e6	+	9.52767e6i	1.22727	+	2.07674i
$463$	−3.60161e6	+	3.60161e6i	−0.780809	+	0.780809i	−0.979967	−	0.199159i	$-0.936179\pi$
$463$	−3.60161e6	+	3.60161e6i	−0.780809	+	0.780809i	0.199159	+	0.979967i	$0.436179\pi$
$464$	−136969.	+	609031.i	−0.0295343	+	0.131324i
$465$	−2.01615e6	−	5.80577e6i	−0.432405	−	1.24517i
$466$	−1.24556e6	−	320238.i	−0.265704	−	0.0683136i
$467$	7.70558e6			1.63498			0.817491	−	0.575942i	$-0.195364\pi$
$467$	7.70558e6			1.63498			0.817491	+	0.575942i	$0.195364\pi$
$468$	−1.51522e6	+	2.75192e6i	−0.319786	+	0.580792i
$469$	3.43569e6	−	3.43569e6i	0.721243	−	0.721243i
$470$	345746.	−	28618.3i	0.0721960	−	0.00597585i
$471$	−3.64683e6			−0.757466
$472$	1.69585e6	+	1.59564e6i	0.350375	+	0.329670i
$473$	−2.13480e6	+	2.13480e6i	−0.438738	+	0.438738i
$474$	4.26159e6	−	2.51843e6i	0.871217	−	0.514853i
$475$	−10972.7	+	93417.9i	−0.00223141	+	0.0189975i
$476$	−1.07675e7	−	5.92861e6i	−2.17819	−	1.19932i
$477$			887230.i			0.178542i
$478$	−693305.	−	1.17319e6i	−0.138789	−	0.234854i
$479$	5.59264e6			1.11373			0.556863	−	0.830604i	$-0.312005\pi$
$479$	5.59264e6			1.11373			0.556863	+	0.830604i	$0.312005\pi$
$480$	823198.	−	5.89995e6i	0.163080	−	1.16881i
$481$	429052.			0.0845565
$482$	45726.3	+	77376.5i	0.00896496	+	0.0151702i
$483$		−	752333.i		−	0.146738i
$484$	925000.	+	509309.i	0.179485	+	0.0988252i
$485$	−4.61047e6	−	2.23371e6i	−0.890002	−	0.431194i
$486$	−3.33930e6	+	1.97339e6i	−0.641305	+	0.378984i
$487$	3.92342e6	−	3.92342e6i	0.749621	−	0.749621i	−0.224787	−	0.974408i	$-0.572168\pi$
$487$	3.92342e6	−	3.92342e6i	0.749621	−	0.749621i	0.974408	+	0.224787i	$0.0721685\pi$
$488$	−3.93597e6	+	4.18318e6i	−0.748174	+	0.795164i
$489$	−948412.			−0.179360
$490$	−1.00073e7	−	8.47727e6i	−1.88289	−	1.59502i
$491$	−4.03568e6	+	4.03568e6i	−0.755462	+	0.755462i	−0.975493	−	0.220031i	$-0.929384\pi$
$491$	−4.03568e6	+	4.03568e6i	−0.755462	+	0.755462i	0.220031	+	0.975493i	$0.429384\pi$
$492$	−3.84290e6	+	6.97942e6i	−0.715724	+	1.29989i
$493$	−969957.			−0.179736
$494$	169639.	+	43614.8i	0.0312758	+	0.00804112i
$495$	−2.11488e6	−	1.02463e6i	−0.387948	−	0.187956i
$496$	5.17123e6	−	3.27231e6i	0.943820	−	0.597242i
$497$	−1.45150e6	+	1.45150e6i	−0.263588	+	0.263588i
$498$	4.03659e6	+	6.83058e6i	0.729359	+	1.23420i
$499$	−3.09266e6	+	3.09266e6i	−0.556007	+	0.556007i	−0.928168	−	0.372161i	$-0.878617\pi$
$499$	−3.09266e6	+	3.09266e6i	−0.556007	+	0.556007i	0.372161	+	0.928168i	$0.378617\pi$
$500$	4.90743e6	−	2.67716e6i	0.877867	−	0.478905i
$501$	4.85542e6	+	4.85542e6i	0.864236	+	0.864236i
$502$	2.31184e6	+	594384.i	0.409449	+	0.105271i
$503$	−2.16426e6	−	2.16426e6i	−0.381407	−	0.381407i	0.490202	−	0.871609i	$-0.336923\pi$
$503$	−2.16426e6	−	2.16426e6i	−0.381407	−	0.381407i	−0.871609	+	0.490202i	$0.836923\pi$
$504$	2.85782e6	−	3.03731e6i	0.501139	−	0.532614i
$505$	3.46614e6	−	7.15425e6i	0.604809	−	1.24835i
$506$	−214761.	−	363412.i	−0.0372889	−	0.0630990i
$507$			1.26376e7i			2.18346i
$508$	1.73339e6	−	502370.i	0.298014	−	0.0863703i
$509$	1.98672e6	+	1.98672e6i	0.339892	+	0.339892i	0.856327	−	0.516434i	$-0.172741\pi$
$509$	1.98672e6	+	1.98672e6i	0.339892	+	0.339892i	−0.516434	+	0.856327i	$0.672741\pi$
$510$	9.22469e6	−	763552.i	1.57046	−	0.129991i
$511$		−	9.97604e6i		−	1.69008i
$512$	5.90693e6	−	540887.i	0.995834	−	0.0911868i
$513$	57779.0	+	57779.0i	0.00969341	+	0.00969341i
$514$	−6.67068e6	−	1.71506e6i	−1.11368	−	0.286333i
$515$	−418219.	+	863220.i	−0.0694841	+	0.143418i
$516$	3.53429e6	+	1.94600e6i	0.584357	+	0.321749i
$517$	483277.			0.0795188
$518$	−551639.	−	141828.i	−0.0903296	−	0.0232241i
$519$		−	423765.i		−	0.0690568i
$520$	−3.71263e6	−	9.72528e6i	−0.602107	−	1.57723i
$521$			1.48056e6i			0.238963i	0.992836	+	0.119482i	$0.0381232\pi$
$521$			1.48056e6i			0.238963i	−0.992836	+	0.119482i	$0.961877\pi$
$522$	81946.1	−	318728.i	0.0131629	−	0.0511969i
$523$	−3.48830e6			−0.557648			−0.278824	−	0.960342i	$-0.589945\pi$
$523$	−3.48830e6			−0.557648			−0.278824	+	0.960342i	$0.589945\pi$
$524$	−3.56467e6	+	1.03311e6i	−0.567141	+	0.164369i
$525$	1.37839e7	+	1.61904e6i	2.18261	+	0.256365i
$526$	−2.58008e6	+	1.00352e7i	−0.406601	+	1.58147i
$527$	6.72369e6	+	6.72369e6i	1.05458	+	1.05458i
$528$	1.82079e6	−	8.09612e6i	0.284233	−	1.26384i
$529$		−	6.40765e6i		−	0.995542i
$530$	−2.24329e6	−	1.90031e6i	−0.346893	−	0.293856i
$531$	−868020.	−	868020.i	−0.133596	−	0.133596i
$532$	−203690.	−	112153.i	−0.0312026	−	0.0171803i
$533$			1.39228e7i			2.12280i
$534$	−7.08853e6	+	4.18903e6i	−1.07573	+	0.635711i
$535$	−6.05240e6	+	2.10180e6i	−0.914204	+	0.317473i
$536$	−3.64157e6	+	110876.i	−0.547491	+	0.0166696i
$537$	−7.50119e6	−	7.50119e6i	−1.12252	−	1.12252i
$538$	2.24102e6	−	8.71639e6i	0.333803	−	1.29832i
$539$	−1.29187e7	−	1.29187e7i	−1.91534	−	1.91534i
$540$	817142.	−	4.78705e6i	0.120591	−	0.706453i
$541$	−2.35238e6	+	2.35238e6i	−0.345553	+	0.345553i	−0.858450	−	0.512897i	$-0.828572\pi$
$541$	−2.35238e6	+	2.35238e6i	−0.345553	+	0.345553i	0.512897	+	0.858450i	$0.328572\pi$
$542$	−554698.	+	327803.i	−0.0811070	+	0.0479309i
$543$	−3.55038e6	+	3.55038e6i	−0.516743	+	0.516743i
$544$	2.83382e6	+	8.77021e6i	0.410558	+	1.27061i
$545$	−2.26667e6	+	4.67849e6i	−0.326886	+	0.674706i
$546$	6.43543e6	−	2.50304e7i	0.923838	−	3.59325i
$547$	−9.41403e6			−1.34526			−0.672631	−	0.739978i	$-0.734836\pi$
$547$	−9.41403e6			−1.34526			−0.672631	+	0.739978i	$0.734836\pi$
$548$	6.07688e6	−	1.76120e6i	0.864429	−	0.250529i
$549$	2.14115e6	−	2.14115e6i	0.303191	−	0.303191i
$550$	7.12046e6	−	3.15270e6i	1.00369	−	0.444402i
$551$	−18348.9			−0.00257472
$552$	−386569.	+	410848.i	−0.0539982	+	0.0573896i
$553$	−8.11996e6	+	8.11996e6i	−1.12912	+	1.12912i
$554$	4.28857e6	+	7.25697e6i	0.593660	+	1.00457i
$555$	405183.	−	140707.i	0.0558366	−	0.0193902i
$556$	−3.92068e6	+	1.13629e6i	−0.537866	+	0.155884i
$557$		−	1.26333e7i		−	1.72536i	−0.505753	−	0.862679i	$-0.668785\pi$
$557$		−	1.26333e7i		−	1.72536i	0.505753	−	0.862679i	$-0.331215\pi$
$558$	−2.77745e6	+	1.64136e6i	−0.377625	+	0.223160i
$559$	7.05036e6			0.954293
$560$	1.55857e6	+	1.37312e7i	0.210018	+	1.85029i
$561$	1.28941e7			1.72975
$562$	−9.93566e6	+	5.87156e6i	−1.32695	+	0.784175i
$563$		−	2.05569e6i		−	0.273330i	−0.990617	−	0.136665i	$-0.956362\pi$
$563$		−	2.05569e6i		−	0.273330i	0.990617	−	0.136665i	$-0.0436384\pi$
$564$	−179779.	−	620314.i	−0.0237981	−	0.0821134i
$565$	−4.73095e6	+	9.76486e6i	−0.623487	+	1.28690i
$566$	−3.81863e6	−	6.46177e6i	−0.501034	−	0.847833i
$567$	1.24840e7	−	1.24840e7i	1.63078	−	1.63078i
$568$	1.53848e6	−	46842.5i	0.200088	−	0.00609213i
$569$	1.52099e7			1.96945			0.984726	−	0.174110i	$-0.0557049\pi$
$569$	1.52099e7			1.96945			0.984726	+	0.174110i	$0.0557049\pi$
$570$	174505.	−	14444.2i	0.0224968	−	0.00186212i
$571$	−4.28365e6	+	4.28365e6i	−0.549824	+	0.549824i	−0.926390	−	0.376566i	$-0.877105\pi$
$571$	−4.28365e6	+	4.28365e6i	−0.549824	+	0.549824i	0.376566	+	0.926390i	$0.377105\pi$
$572$	−4.03659e6	−	1.39279e7i	−0.515851	−	1.77990i
$573$	1.30614e7			1.66189
$574$	4.60237e6	−	1.79008e7i	0.583045	−	2.26774i
$575$	−525758.	−	61754.7i	−0.0663157	−	0.00778933i
$576$	−3.12130e6	+	190246.i	−0.391994	+	0.0238924i
$577$	−6.12506e6	+	6.12506e6i	−0.765897	+	0.765897i	−0.977381	−	0.211484i	$-0.932170\pi$
$577$	−6.12506e6	+	6.12506e6i	−0.765897	+	0.765897i	0.211484	+	0.977381i	$0.432170\pi$
$578$	−5.41432e6	+	3.19964e6i	−0.674100	+	0.398365i
$579$	449440.	−	449440.i	0.0557154	−	0.0557154i
$580$	630361.	+	889860.i	0.0778071	+	0.109838i
$581$	−1.30149e7	−	1.30149e7i	−1.59955	−	1.59955i
$582$	−2.37479e6	+	9.23669e6i	−0.290615	+	1.13034i
$583$	−2.89592e6	−	2.89592e6i	−0.352870	−	0.352870i
$584$	−5.12595e6	+	5.44790e6i	−0.621932	+	0.660993i
$585$	1.80032e6	+	5.18425e6i	0.217500	+	0.626320i
$586$	8.68345e6	−	5.13156e6i	1.04460	−	0.617312i
$587$			9.39079e6i			1.12488i	0.826837	+	0.562441i	$0.190138\pi$
$587$			9.39079e6i			1.12488i	−0.826837	+	0.562441i	$0.809862\pi$
$588$	−1.17761e7	+	2.13876e7i	−1.40462	+	2.55105i
$589$	127193.	+	127193.i	0.0151069	+	0.0151069i
$590$	4.05388e6	−	335551.i	0.479448	−	0.0396852i
$591$			1.21350e7i			1.42913i
$592$	228374.	+	360899.i	0.0267819	+	0.0423235i
$593$	2.87335e6	+	2.87335e6i	0.335546	+	0.335546i	0.854688	−	0.519142i	$-0.173748\pi$
$593$	2.87335e6	+	2.87335e6i	0.335546	+	0.335546i	−0.519142	+	0.854688i	$0.673748\pi$
$594$	1.68450e6	−	6.55181e6i	0.195886	−	0.761895i
$595$	−2.02845e7	+	7.04412e6i	−2.34894	+	0.815708i
$596$	1.73889e6	+	5.99989e6i	0.200519	+	0.691875i
$597$	−1.38121e7			−1.58607
$598$	−245465.	+	954731.i	−0.0280696	+	0.109176i
$599$			6.34849e6i			0.722942i	0.932383	+	0.361471i	$0.117725\pi$
$599$			6.34849e6i			0.722942i	−0.932383	+	0.361471i	$0.882275\pi$
$600$	−6.69548e6	−	7.96671e6i	−0.759283	−	0.903443i
$601$			9.36597e6i			1.05771i	0.848712	+	0.528855i	$0.177379\pi$
$601$			9.36597e6i			1.05771i	−0.848712	+	0.528855i	$0.822621\pi$
$602$	−9.06476e6	−	2.33059e6i	−1.01945	−	0.262104i
$603$	1.92068e6			0.215111
$604$	7.72223e6	−	1.40250e7i	0.861292	−	1.56427i
$605$	1.74258e6	−	605139.i	0.193555	−	0.0672151i
$606$	−1.43330e7	−	3.68506e6i	−1.58546	−	0.407627i
$607$	−9.58241e6	−	9.58241e6i	−1.05561	−	1.05561i	−0.998360	−	0.0572486i	$-0.981767\pi$
$607$	−9.58241e6	−	9.58241e6i	−1.05561	−	1.05561i	−0.0572486	−	0.998360i	$-0.518233\pi$
$608$	53607.8	+	165908.i	0.00588124	+	0.0182015i
$609$			2.70740e6i			0.295808i
$610$	827706.	+	9.99975e6i	0.0900640	+	1.08809i
$611$	−798031.	−	798031.i	−0.0864802	−	0.0864802i
$612$	−1.35255e6	−	4.66687e6i	−0.145974	−	0.503672i
$613$		−	893370.i		−	0.0960241i	−0.998847	−	0.0480120i	$-0.984711\pi$
$613$		−	893370.i		−	0.0960241i	0.998847	−	0.0480120i	$-0.0152886\pi$
$614$	−4.00373e6	−	6.77498e6i	−0.428592	−	0.725249i
$615$	4.56597e6	+	1.31483e7i	0.486794	+	1.40179i
$616$	585857.	+	1.92417e7i	0.0622071	+	2.04311i
$617$	−1.62609e6	−	1.62609e6i	−0.171961	−	0.171961i	0.615879	−	0.787841i	$-0.288801\pi$
$617$	−1.62609e6	−	1.62609e6i	−0.171961	−	0.171961i	−0.787841	+	0.615879i	$0.788801\pi$
$618$	1.72939e6	+	444633.i	0.182147	+	0.0468307i
$619$	1.16516e7	+	1.16516e7i	1.22224	+	1.22224i	0.966832	+	0.255412i	$0.0822111\pi$
$619$	1.16516e7	+	1.16516e7i	1.22224	+	1.22224i	0.255412	+	0.966832i	$0.417789\pi$
$620$	1.79884e6	−	1.05381e7i	0.187937	−	1.10099i
$621$	−325182.	+	325182.i	−0.0338374	+	0.0338374i
$622$	−4.48540e6	−	7.59005e6i	−0.464864	−	0.786626i
$623$	1.35063e7	−	1.35063e7i	1.39418	−	1.39418i
$624$	−1.63757e7	+	1.03624e7i	−1.68360	+	1.06537i
$625$	2.26289e6	−	9.49983e6i	0.231720	−	0.972783i
$626$	−2.84760e6	−	732130.i	−0.290431	−	0.0746710i
$627$	243920.			0.0247787
$628$	−5.55687e6	−	3.05964e6i	−0.562253	−	0.309579i
$629$	−469245.	+	469245.i	−0.0472904	+	0.0472904i
$630$	−600978.	−	7.26059e6i	−0.0603264	−	0.728820i
$631$	9.65100e6			0.964937			0.482468	−	0.875913i	$-0.339740\pi$
$631$	9.65100e6			0.964937			0.482468	+	0.875913i	$0.339740\pi$
$632$	8.60655e6	−	262046.i	0.857109	−	0.0260966i
$633$	−714255.	+	714255.i	−0.0708507	+	0.0708507i
$634$	2.25539e6	−	1.33284e6i	0.222842	−	0.131691i
$635$	1.37461e6	−	2.83726e6i	0.135284	−	0.279232i
$636$	−2.63980e6	+	4.79436e6i	−0.258778	+	0.469989i
$637$			4.26649e7i			4.16603i
$638$	772855.	+	1.30780e6i	0.0751703	+	0.127201i
$639$	−811443.			−0.0786151
$640$	6.20433e6	−	8.29943e6i	0.598749	−	0.800937i
$641$	1.61139e7			1.54902			0.774508	−	0.632565i	$-0.217998\pi$
$641$	1.61139e7			1.54902			0.774508	+	0.632565i	$0.217998\pi$
$642$	6.06807e6	+	1.02682e7i	0.581049	+	0.983232i
$643$		−	2.02823e7i		−	1.93460i	−0.253639	−	0.967299i	$-0.581628\pi$
$643$		−	2.02823e7i		−	1.93460i	0.253639	−	0.967299i	$-0.418372\pi$
$644$	631197.	−	1.14637e6i	0.0599722	−	0.108921i
$645$	6.65814e6	−	2.31215e6i	0.630164	−	0.218835i
$646$	−233231.	+	137830.i	−0.0219890	+	0.0129946i
$647$	−1.80603e6	+	1.80603e6i	−0.169615	+	0.169615i	−0.786810	−	0.617195i	$-0.788269\pi$
$647$	−1.80603e6	+	1.80603e6i	−0.169615	+	0.169615i	0.617195	+	0.786810i	$0.288269\pi$
$648$	−1.32321e7	+	402882.i	−1.23792	+	0.0376912i
$649$	5.66644e6			0.528078
$650$	−1.69639e7	−	6.55191e6i	−1.57487	−	0.608254i
$651$	1.87675e7	−	1.87675e7i	1.73562	−	1.73562i
$652$	−1.44515e6	−	795704.i	−0.133135	−	0.0733048i
$653$	−45138.8			−0.00414254			−0.00207127	−	0.999998i	$-0.500659\pi$
$653$	−45138.8			−0.00414254			−0.00207127	+	0.999998i	$0.500659\pi$
$654$	9.37297e6	+	2.40983e6i	0.856905	+	0.220314i
$655$	−2.82686e6	+	5.83476e6i	−0.257455	+	0.531397i
$656$	−1.17113e7	+	7.41079e6i	−1.06254	+	0.672364i
$657$	2.78850e6	−	2.78850e6i	0.252033	−	0.252033i
$658$	762242.	+	1.28984e6i	0.0686322	+	0.116137i
$659$	321979.	−	321979.i	0.0288811	−	0.0288811i	−0.692519	−	0.721400i	$-0.743499\pi$
$659$	321979.	−	321979.i	0.0288811	−	0.0288811i	0.721400	+	0.692519i	$0.243499\pi$
$660$	−8.37967e6	−	1.18293e7i	−0.748802	−	1.05706i
$661$	1.33439e7	+	1.33439e7i	1.18789	+	1.18789i	0.977649	+	0.210245i	$0.0674261\pi$
$661$	1.33439e7	+	1.33439e7i	1.18789	+	1.18789i	0.210245	+	0.977649i	$0.432574\pi$
$662$	2.13884e7	+	5.49904e6i	1.89685	+	0.487687i
$663$	−2.12919e7	−	2.12919e7i	−1.88118	−	1.88118i
$664$	420013.	+	1.37948e7i	0.0369694	+	1.21421i
$665$	−383725.	+	133255.i	−0.0336485	+	0.0116850i
$666$	−114550.	−	193838.i	−0.0100071	−	0.0169337i
$667$		−	103268.i		−	0.00898773i
$668$	3.32484e6	+	1.14721e7i	0.288290	+	0.994721i
$669$	−1.25230e7	−	1.25230e7i	−1.08179	−	1.08179i
$670$	−4.11381e6	+	4.85629e6i	−0.354044	+	0.417944i
$671$			1.39774e7i			1.19845i
$672$	2.44799e7	−	7.90991e6i	2.09116	−	0.675691i
$673$	5.84526e6	+	5.84526e6i	0.497469	+	0.497469i	0.910649	−	0.413180i	$-0.135582\pi$
$673$	5.84526e6	+	5.84526e6i	0.497469	+	0.497469i	−0.413180	+	0.910649i	$0.635582\pi$
$674$	−1.47292e7	−	3.78692e6i	−1.24890	−	0.321097i
$675$	−5.25805e6	−	6.65764e6i	−0.444186	−	0.562420i
$676$	−1.06028e7	+	1.92566e7i	−0.892386	+	1.62074i
$677$	1.39034e7			1.16587			0.582933	−	0.812520i	$-0.301905\pi$
$677$	1.39034e7			1.16587			0.582933	+	0.812520i	$0.301905\pi$
$678$	1.95631e7	+	5.02975e6i	1.63442	+	0.420215i
$679$		−	2.21243e7i		−	1.84160i
$680$	1.46968e7	+	6.57592e6i	1.21885	+	0.545361i
$681$		−	8.07561e6i		−	0.667279i
$682$	3.70820e6	−	1.44230e7i	0.305283	−	1.18739i
$683$	−9.17647e6			−0.752704			−0.376352	−	0.926477i	$-0.622822\pi$
$683$	−9.17647e6			−0.752704			−0.376352	+	0.926477i	$0.622822\pi$
$684$	−25586.5	−	88284.1i	−0.00209108	−	0.00721510i
$685$	4.81910e6	−	9.94681e6i	0.392410	−	0.809949i
$686$	8.38813e6	−	3.26255e7i	0.680542	−	2.64695i
$687$	−1.44475e7	−	1.44475e7i	−1.16789	−	1.16789i
$688$	3.75273e6	+	5.93044e6i	0.302257	+	0.477657i
$689$			9.56400e6i			0.767523i
$690$	81292.5	+	982119.i	0.00650022	+	0.0785310i
$691$	1.25413e7	+	1.25413e7i	0.999186	+	0.999186i	1.00000		0.000813850i	$-0.000259057\pi$
$691$	1.25413e7	+	1.25413e7i	0.999186	+	0.999186i	−0.000813850		1.00000i	$0.500259\pi$
$692$	355533.	−	645714.i	0.0282237	−	0.0512596i
$693$		−	1.01487e7i		−	0.802745i
$694$	7.09154e6	−	4.19081e6i	0.558910	−	0.330293i
$695$	−3.10918e6	+	6.41748e6i	−0.244166	+	0.503967i
$696$	1.39113e6	−	1.47851e6i	0.108854	−	0.115691i
$697$	−1.52271e7	−	1.52271e7i	−1.18723	−	1.18723i
$698$	3.24850e6	−	1.26350e7i	0.252374	−	0.981602i
$699$	2.95739e6	+	2.95739e6i	0.228937	+	0.228937i
$700$	1.96450e7	+	1.40316e7i	1.51533	+	1.08233i
$701$	−5.10972e6	+	5.10972e6i	−0.392737	+	0.392737i	−0.875662	−	0.482925i	$-0.839575\pi$
$701$	−5.10972e6	+	5.10972e6i	−0.392737	+	0.392737i	0.482925	+	0.875662i	$0.339575\pi$
$702$	−1.36005e7	+	8.03734e6i	−1.04163	+	0.615559i
$703$	−8876.79	+	8876.79i	−0.000677435	+	0.000677435i
$704$	9.56696e6	−	1.08089e7i	0.727516	−	0.821958i
$705$	−1.01535e6	−	491923.i	−0.0769382	−	0.0372756i
$706$	−1.76683e6	+	6.87205e6i	−0.133408	+	0.518889i
$707$	3.43312e7			2.58309
$708$	−2.10792e6	−	7.27320e6i	−0.158041	−	0.545309i
$709$	−5.21116e6	+	5.21116e6i	−0.389331	+	0.389331i	−0.874449	−	0.485118i	$-0.838777\pi$
$709$	−5.21116e6	+	5.21116e6i	−0.389331	+	0.389331i	0.485118	+	0.874449i	$0.338777\pi$
$710$	1.73799e6	−	2.05167e6i	0.129390	−	0.152743i
$711$	−4.53937e6			−0.336761
$712$	−1.43157e7	+	435874.i	−1.05831	+	0.0322227i
$713$	−715846.	+	715846.i	−0.0527346	+	0.0527346i
$714$	2.03370e7	+	3.44136e7i	1.49294	+	2.52630i
$715$	−2.27976e7	−	1.10452e7i	−1.66773	−	0.807991i
$716$	−5.13658e6	−	1.77234e7i	−0.374448	−	1.29200i
$717$			4.43171e6i			0.321939i
$718$	−1.12462e7	+	6.64604e6i	−0.814132	+	0.481118i
$719$	−1.70710e6			−0.123150			−0.0615752	−	0.998102i	$-0.519612\pi$
$719$	−1.70710e6			−0.123150			−0.0615752	+	0.998102i	$0.519612\pi$
$720$	−3.40249e6	+	4.27379e6i	−0.244605	+	0.307243i
$721$	−4.14234e6			−0.296762
$722$	1.20543e7	−	7.12357e6i	0.860593	−	0.508575i
$723$		−	292289.i		−	0.0207954i
$724$	−8.38862e6	+	2.43119e6i	−0.594763	+	0.172374i
$725$	1.89203e6	+	222235.i	0.133685	+	0.0157024i
$726$	−1.74709e6	−	2.95637e6i	−0.123019	−	0.208169i
$727$	−1.54826e7	+	1.54826e7i	−1.08644	+	1.08644i	−0.0905524	+	0.995892i	$0.528863\pi$
$727$	−1.54826e7	+	1.54826e7i	−1.08644	+	1.08644i	−0.995892	+	0.0905524i	$0.971137\pi$
$728$	3.08062e7	−	3.27410e7i	2.15432	−	2.28962i
$729$	−5.15683e6			−0.359388
$730$	1.07795e6	+	1.30230e7i	0.0748672	+	0.904492i
$731$	−7.71083e6	+	7.71083e6i	−0.533713	+	0.533713i
$732$	1.79409e7	−	5.19962e6i	1.23756	−	0.358669i
$733$	1.62353e7			1.11609			0.558046	−	0.829810i	$-0.311551\pi$
$733$	1.62353e7			1.11609			0.558046	+	0.829810i	$0.311551\pi$
$734$	−3.01592e6	+	1.17304e7i	−0.206624	+	0.803658i
$735$	1.39919e7	+	4.02914e7i	0.955339	+	2.75102i
$736$	−933732.	+	301706.i	−0.0635371	+	0.0205300i
$737$	−6.26911e6	+	6.26911e6i	−0.425145	+	0.425145i
$738$	6.29008e6	−	3.71717e6i	0.425124	−	0.251230i
$739$	−1.07667e7	+	1.07667e7i	−0.725223	+	0.725223i	−0.969664	−	0.244441i	$-0.921396\pi$
$739$	−1.07667e7	+	1.07667e7i	−0.725223	+	0.725223i	0.244441	+	0.969664i	$0.421396\pi$
$740$	735451.	+	125540.i	0.0493713	+	0.00842761i
$741$	−402782.	−	402782.i	−0.0269479	−	0.0269479i
$742$	3.16150e6	−	1.22966e7i	0.210806	−	0.819926i
$743$	1.30481e7	+	1.30481e7i	0.867112	+	0.867112i	0.992152	−	0.125040i	$-0.0399060\pi$
$743$	1.30481e7	+	1.30481e7i	0.867112	+	0.867112i	−0.125040	+	0.992152i	$0.539906\pi$
$744$	−1.98922e7	+	605663.i	−1.31750	+	0.0401142i
$745$	9.82079e6	+	4.75804e6i	0.648269	+	0.314078i
$746$	−5.10425e6	+	3.01640e6i	−0.335803	+	0.198446i
$747$		−	7.27581e6i		−	0.477067i
$748$	1.96474e7	+	1.08179e7i	1.28396	+	0.706954i
$749$	−1.95648e7	−	1.95648e7i	−1.27430	−	1.27430i
$750$	−1.81689e7	−	624133.i	−1.17944	−	0.0405158i
$751$		−	2.28000e7i		−	1.47514i	−0.675269	−	0.737572i	$-0.735972\pi$
$751$		−	2.28000e7i		−	1.47514i	0.675269	−	0.737572i	$-0.264028\pi$
$752$	246495.	−	1.09604e6i	0.0158951	−	0.0706776i
$753$	−5.48913e6	−	5.48913e6i	−0.352790	−	0.352790i
$754$	883348.	−	3.43576e6i	0.0565853	−	0.220087i
$755$	−9.17523e6	−	2.64213e7i	−0.585800	−	1.68689i
$756$	2.01432e7	−	5.83791e6i	1.28181	−	0.371495i
$757$	6.14317e6			0.389630			0.194815	−	0.980840i	$-0.437589\pi$
$757$	6.14317e6			0.389630			0.194815	+	0.980840i	$0.437589\pi$
$758$	−1.24443e6	+	4.84018e6i	−0.0786678	+	0.305977i
$759$			1.37279e6i			0.0864964i
$760$	278022.	+	124398.i	0.0174600	+	0.00781229i
$761$		−	9.47101e6i		−	0.592836i	−0.955058	−	0.296418i	$-0.904208\pi$
$761$		−	9.47101e6i		−	0.592836i	0.955058	−	0.296418i	$-0.0957921\pi$
$762$	−5.68421e6	−	1.46143e6i	−0.354636	−	0.0911783i
$763$	−2.24507e7			−1.39611
$764$	1.99024e7	+	1.09583e7i	1.23359	+	0.679220i
$765$	−7.63887e6	−	3.70093e6i	−0.471928	−	0.228643i
$766$	1.33870e7	+	3.44186e6i	0.824351	+	0.211944i
$767$	−9.35693e6	−	9.35693e6i	−0.574308	−	0.574308i
$768$	−1.74328e7	−	8.25883e6i	−1.06650	−	0.505261i
$769$		−	6.29596e6i		−	0.383925i	−0.981402	−	0.191963i	$-0.938515\pi$
$769$		−	6.29596e6i		−	0.383925i	0.981402	−	0.191963i	$-0.0614852\pi$
$770$	2.56602e7	+	2.17370e7i	1.55967	+	1.32121i
$771$	1.58385e7	+	1.58385e7i	0.959575	+	0.959575i
$772$	1.06191e6	−	307763.i	0.0641275	−	0.0185854i
$773$			2.73549e7i			1.64659i	0.567610	+	0.823297i	$0.307868\pi$
$773$			2.73549e7i			1.64659i	−0.567610	+	0.823297i	$0.692132\pi$
$774$	−1.88233e6	−	3.18522e6i	−0.112939	−	0.191112i
$775$	−1.15749e7	−	1.46560e7i	−0.692252	−	0.876517i
$776$	−1.13680e7	+	1.20820e7i	−0.677691	+	0.720254i
$777$	1.30978e6	+	1.30978e6i	0.0778300	+	0.0778300i
$778$	3.16407e6	+	813496.i	0.187412	+	0.0481844i
$779$	−288054.	−	288054.i	−0.0170071	−	0.0170071i
$780$	−5.69636e6	+	3.33709e7i	−0.335244	+	1.96395i
$781$	2.64855e6	−	2.64855e6i	0.155375	−	0.155375i
$782$	−775710.	−	1.31263e6i	−0.0453610	−	0.0767583i
$783$	1.17022e6	−	1.17022e6i	0.0682125	−	0.0682125i
$784$	−3.58878e7	+	2.27095e7i	−2.08524	+	1.31952i
$785$	−1.04684e7	+	3.63533e6i	−0.606327	+	0.210557i
$786$	1.16894e7	+	3.00540e6i	0.674897	+	0.173519i
$787$	2.94075e7			1.69247			0.846236	−	0.532809i	$-0.178863\pi$
$787$	2.94075e7			1.69247			0.846236	+	0.532809i	$0.178863\pi$
$788$	−1.01811e7	+	1.84908e7i	−0.584091	+	1.06082i
$789$	2.38270e7	−	2.38270e7i	1.36262	−	1.36262i
$790$	9.72265e6	−	1.14774e7i	0.554264	−	0.654300i
$791$	−4.68587e7			−2.66287
$792$	−5.21467e6	+	5.54219e6i	−0.295402	+	0.313956i
$793$	2.30808e7	−	2.30808e7i	1.30337	−	1.30337i
$794$	−5.01575e6	+	2.96410e6i	−0.282348	+	0.166856i
$795$	3.13650e6	+	9.03195e6i	0.176006	+	0.506832i
$796$	−2.10462e7	−	1.15881e7i	−1.17731	−	0.648232i
$797$		−	3.00467e7i		−	1.67553i	−0.546034	−	0.837763i	$-0.683863\pi$
$797$		−	3.00467e7i		−	1.67553i	0.546034	−	0.837763i	$-0.316137\pi$
$798$	384719.	+	651008.i	0.0213863	+	0.0361892i
$799$	1.74558e6			0.0967326
$800$	−3.51832e6	−	1.77567e7i	−0.194362	−	0.980930i
$801$	7.55057e6			0.415814
$802$	−8.38477e6	−	1.41884e7i	−0.460315	−	0.778930i
$803$			1.82033e7i			0.996235i
$804$	1.03789e7	+	5.71465e6i	0.566253	+	0.311781i
$805$	−749962.	−	2.15961e6i	−0.0407896	−	0.117459i
$806$	−2.99398e7	+	1.76932e7i	−1.62335	+	0.959331i
$807$	−2.06958e7	+	2.06958e7i	−1.11866	+	1.11866i
$808$	−1.87482e7	−	1.76403e7i	−1.01026	−	0.950554i
$809$	−1.15437e7			−0.620117			−0.310059	−	0.950717i	$-0.600349\pi$
$809$	−1.15437e7			−0.620117			−0.310059	+	0.950717i	$0.600349\pi$
$810$	−1.49481e7	+	1.76460e7i	−0.800520	+	0.945002i
$811$	2.08030e7	−	2.08030e7i	1.11064	−	1.11064i	0.117580	−	0.993063i	$-0.462486\pi$
$811$	2.08030e7	−	2.08030e7i	1.11064	−	1.11064i	0.993063	−	0.117580i	$-0.0375137\pi$
$812$	−2.27147e6	+	4.12541e6i	−0.120897	+	0.219572i
$813$	2.09537e6			0.111182
$814$	1.00658e6	+	258795.i	0.0532459	+	0.0136897i
$815$	−2.72247e6	+	945423.i	−0.143572	+	0.0498577i
$816$	6.57661e6	−	2.92429e7i	0.345762	−	1.53743i
$817$	−145867.	+	145867.i	−0.00764544	+	0.00764544i
$818$	−1.34193e7	−	2.27077e7i	−0.701209	−	1.18656i
$819$	−1.67584e7	+	1.67584e7i	−0.873019	+	0.873019i
$820$	−4.07382e6	+	2.38656e7i	−0.211576	+	1.23947i
$821$	9.21343e6	+	9.21343e6i	0.477050	+	0.477050i	0.904187	−	0.427137i	$-0.140478\pi$
$821$	9.21343e6	+	9.21343e6i	0.477050	+	0.477050i	−0.427137	+	0.904187i	$0.640478\pi$
$822$	−1.99276e7	−	5.12347e6i	−1.02867	−	0.264475i
$823$	1.63830e7	+	1.63830e7i	0.843127	+	0.843127i	0.989264	−	0.146137i	$-0.0466842\pi$
$823$	1.63830e7	+	1.63830e7i	0.843127	+	0.843127i	−0.146137	+	0.989264i	$0.546684\pi$
$824$	2.26213e6	+	2.12844e6i	0.116064	+	0.109205i
$825$	−2.51516e7	−	2.95427e6i	−1.28656	−	0.151117i
$826$	8.93730e6	+	1.51234e7i	0.455781	+	0.771257i
$827$		−	1.76732e7i		−	0.898569i	−0.893389	−	0.449284i	$-0.851679\pi$
$827$		−	1.76732e7i		−	0.898569i	0.893389	−	0.449284i	$-0.148321\pi$
$828$	496865.	−	144001.i	0.0251862	−	0.00729946i
$829$	−1.77908e7	−	1.77908e7i	−0.899101	−	0.899101i	0.0962561	−	0.995357i	$-0.469313\pi$
$829$	−1.77908e7	−	1.77908e7i	−0.899101	−	0.899101i	−0.995357	+	0.0962561i	$0.969313\pi$
$830$	1.83963e7	+	1.55837e7i	0.926904	+	0.785190i
$831$		−	2.74131e7i		−	1.37707i
$832$	−3.36464e7	+	2.05078e6i	−1.68512	+	0.102710i
$833$	−4.66617e7	−	4.66617e7i	−2.32996	−	2.32996i
$834$	1.28569e7	+	3.30555e6i	0.640060	+	0.164562i
$835$	1.87778e7	+	9.09762e6i	0.932029	+	0.451556i
$836$	371674.	+	204645.i	0.0183927	+	0.0101271i
$837$	−1.62238e7			−0.800460
$838$	8.95641e6	+	2.30273e6i	0.440579	+	0.113275i
$839$			1.15585e7i			0.566887i	0.958989	+	0.283443i	$0.0914768\pi$
$839$			1.15585e7i			0.566887i	−0.958989	+	0.283443i	$0.908523\pi$
$840$	1.83551e7	−	4.10225e7i	0.897548	−	2.00597i
$841$		−	2.01395e7i		−	0.981882i
$842$	1.47782e6	−	5.74793e6i	0.0718356	−	0.279403i
$843$	3.75319e7			1.81899
$844$	−1.68760e6	+	489100.i	−0.0815479	+	0.0236342i
$845$	1.25978e7	+	3.62769e7i	0.606949	+	1.74779i
$846$	−147474.	+	573597.i	−0.00708418	+	0.0275538i
$847$	5.63301e6	+	5.63301e6i	0.269794	+	0.269794i
$848$	−8.04480e6	+	5.09068e6i	−0.384172	+	0.243101i
$849$			2.44093e7i			1.16221i
$850$	2.57188e7	−	1.13874e7i	1.22097	−	0.540603i
$851$	−49958.8	−	49958.8i	−0.00236476	−	0.00236476i
$852$	−4.38483e6	−	2.41431e6i	−0.206945	−	0.113945i
$853$			1.25978e7i			0.592817i	0.955061	+	0.296409i	$0.0957890\pi$
$853$			1.25978e7i			0.592817i	−0.955061	+	0.296409i	$0.904211\pi$
$854$	−3.73050e7	+	2.20457e7i	−1.75034	+	1.03438i
$855$	−144506.	−	70011.2i	−0.00676037	−	0.00327531i
$856$	631391.	+	2.07372e7i	0.0294520	+	0.967310i
$857$	−1.18922e7	−	1.18922e7i	−0.553108	−	0.553108i	0.374229	−	0.927337i	$-0.377908\pi$
$857$	−1.18922e7	−	1.18922e7i	−0.553108	−	0.553108i	−0.927337	+	0.374229i	$0.877908\pi$
$858$	−1.17427e7	+	4.56731e7i	−0.544567	+	2.11808i
$859$	3.85912e6	+	3.85912e6i	0.178445	+	0.178445i	0.790678	−	0.612233i	$-0.209728\pi$
$859$	3.85912e6	+	3.85912e6i	0.178445	+	0.178445i	−0.612233	+	0.790678i	$0.709728\pi$
$860$	1.20852e7	+	2.06293e6i	0.557198	+	0.0951128i
$861$	−4.25028e7	+	4.25028e7i	−1.95393	+	1.95393i
$862$	−4.84799e6	+	2.86496e6i	−0.222225	+	0.131326i
$863$	1.00981e7	−	1.00981e7i	0.461544	−	0.461544i	−0.437617	−	0.899161i	$-0.644178\pi$
$863$	1.00981e7	−	1.00981e7i	0.461544	−	0.461544i	0.899161	+	0.437617i	$0.144178\pi$
$864$	−1.39999e7	−	7.16206e6i	−0.638028	−	0.326403i
$865$	−422429.	−	1.21644e6i	−0.0191961	−	0.0552777i
$866$	−5.03134e6	+	1.95693e7i	−0.227976	+	0.886706i
$867$	2.04525e7			0.924059
$868$	4.43428e7	−	1.28514e7i	1.99767	−	0.578965i
$869$	1.48165e7	−	1.48165e7i	0.665575	−	0.665575i
$870$	−292545.	−	3.53432e6i	−0.0131037	−	0.158310i
$871$	2.07042e7			0.924727
$872$	1.22603e7	+	1.15358e7i	0.546022	+	0.513754i
$873$	6.18417e6	−	6.18417e6i	0.274629	−	0.274629i
$874$	−14674.2	−	24831.3i	−0.000649796	−	0.00109956i
$875$	4.11815e7	−	9.09296e6i	1.81837	−	0.401500i
$876$	2.33650e7	−	6.77165e6i	1.02874	−	0.298149i
$877$			2.31299e7i			1.01549i	0.861508	+	0.507744i	$0.169521\pi$
$877$			2.31299e7i			1.01549i	−0.861508	+	0.507744i	$0.830479\pi$
$878$	2.27729e6	−	1.34578e6i	0.0996969	−	0.0589167i
$879$	−3.28016e7			−1.43194
$880$	−2.84394e6	−	2.50554e7i	−0.123798	−	1.09067i
$881$	7.57612e6			0.328857			0.164428	−	0.986389i	$-0.447422\pi$
$881$	7.57612e6			0.328857			0.164428	+	0.986389i	$0.447422\pi$
$882$	1.92752e7	−	1.13908e7i	0.834310	−	0.493042i
$883$			1.72364e7i			0.743953i	0.928242	+	0.371977i	$0.121320\pi$
$883$			1.72364e7i			0.743953i	−0.928242	+	0.371977i	$0.878680\pi$
$884$	−1.45800e7	−	5.03071e7i	−0.627519	−	2.16520i
$885$	−1.19050e7	−	5.76781e6i	−0.510941	−	0.247544i
$886$	−2.91248e6	−	4.92840e6i	−0.124646	−	0.210922i
$887$	1.02883e7	−	1.02883e7i	0.439070	−	0.439070i	−0.452629	−	0.891699i	$-0.649514\pi$
$887$	1.02883e7	−	1.02883e7i	0.439070	−	0.439070i	0.891699	+	0.452629i	$0.149514\pi$
$888$	−42269.1	−	1.38827e6i	−0.00179883	−	0.0590802i
$889$	1.36152e7			0.577788
$890$	−1.61722e7	+	1.90910e7i	−0.684374	+	0.807893i
$891$	−2.27796e7	+	2.27796e7i	−0.961285	+	0.961285i
$892$	−8.57535e6	−	2.95885e7i	−0.360861	−	1.24512i
$893$	33021.4			0.00138569
$894$	5.05855e6	−	1.96751e7i	0.211681	−	0.823330i
$895$	−2.90101e7	−	1.40550e7i	−1.21057	−	0.586508i
$896$	4.39377e7	+	8.48552e6i	1.82838	+	0.353109i
$897$	2.26687e6	−	2.26687e6i	0.0940686	−	0.0940686i
$898$	1.21528e7	−	7.18182e6i	0.502906	−	0.297197i
$899$	2.57610e6	−	2.57610e6i	0.106307	−	0.106307i
$900$	1.56907e6	+	9.41325e6i	0.0645708	+	0.387377i
$901$	−1.04599e7	−	1.04599e7i	−0.429257	−	0.429257i
$902$	−8.39796e6	+	3.26637e7i	−0.343683	+	1.33675i
$903$	2.15229e7	+	2.15229e7i	0.878379	+	0.878379i
$904$	2.55895e7	+	2.40773e7i	1.04145	+	0.979909i
$905$	−6.65236e6	+	1.37307e7i	−0.269994	+	0.557279i
$906$	−4.48249e7	+	2.64897e7i	−1.81426	+	1.07215i
$907$		−	1.10060e7i		−	0.444233i	−0.975020	−	0.222117i	$-0.928703\pi$
$907$		−	1.10060e7i		−	0.444233i	0.975020	−	0.222117i	$-0.0712966\pi$
$908$	6.77532e6	−	1.23052e7i	0.272719	−	0.495308i
$909$	9.59623e6	+	9.59623e6i	0.385204	+	0.385204i
$910$	−6.47831e6	−	7.82664e7i	−0.259333	−	3.13308i
$911$		−	1.00659e6i		−	0.0401844i	−0.999798	−	0.0200922i	$-0.993604\pi$
$911$		−	1.00659e6i		−	0.0401844i	0.999798	−	0.0200922i	$-0.00639598\pi$
$912$	124411.	−	553193.i	0.00495304	−	0.0220237i
$913$	2.37483e7	+	2.37483e7i	0.942876	+	0.942876i
$914$	3.37228e6	−	1.31164e7i	0.133524	−	0.519338i
$915$	1.42275e7	−	2.93661e7i	0.561792	−	1.15956i
$916$	−9.89322e6	−	3.41358e7i	−0.389582	−	1.34422i
$917$	−2.79993e7			−1.09957
$918$	6.08433e6	−	2.36649e7i	0.238290	−	0.926825i
$919$		−	1.74390e7i		−	0.681134i	−0.940220	−	0.340567i	$-0.889381\pi$
$919$		−	1.74390e7i		−	0.681134i	0.940220	−	0.340567i	$-0.110619\pi$
$920$	−700113.	+	1.56471e6i	−0.0272709	+	0.0609487i
$921$			2.55924e7i			0.994175i
$922$	−1.73755e7	−	4.46732e6i	−0.673149	−	0.173069i
$923$	−8.74705e6			−0.337954
$924$	3.01957e7	−	5.48410e7i	1.16350	−	2.11313i
$925$	1.02284e6	−	807812.i	0.0393054	−	0.0310425i
$926$	2.79054e7	+	7.17458e6i	1.06945	+	0.274960i
$927$	−1.15786e6	−	1.15786e6i	−0.0442546	−	0.0442546i
$928$	3.36019e6	−	1.08574e6i	0.128084	−	0.0413862i
$929$			3.65049e7i			1.38775i	0.720095	+	0.693876i	$0.244098\pi$
$929$			3.65049e7i			1.38775i	−0.720095	+	0.693876i	$0.755902\pi$
$930$	−2.24718e7	+	2.65276e7i	−0.851983	+	1.00575i
$931$	−882708.	−	882708.i	−0.0333767	−	0.0333767i
$932$	2.02513e6	+	6.98754e6i	0.0763682	+	0.263502i
$933$			2.86713e7i			1.07831i
$934$	−2.21765e7	−	3.75264e7i	−0.831815	−	1.40757i
$935$	3.70132e7	−	1.28534e7i	1.38461	−	0.480829i
$936$	1.77627e7	−	540825.i	0.662703	−	0.0201775i
$937$	2.51079e7	+	2.51079e7i	0.934247	+	0.934247i	0.997968	−	0.0637204i	$-0.0202966\pi$
$937$	2.51079e7	+	2.51079e7i	0.934247	+	0.934247i	−0.0637204	+	0.997968i	$0.520297\pi$
$938$	−2.66198e7	−	6.84405e6i	−0.987864	−	0.253984i
$939$	6.76120e6	+	6.76120e6i	0.250242	+	0.250242i
$940$	−1.13443e6	−	1.60143e6i	−0.0418751	−	0.0591138i
$941$	−2.56343e7	+	2.56343e7i	−0.943730	+	0.943730i	−0.998499	−	0.0547695i	$-0.982558\pi$
$941$	−2.56343e7	+	2.56343e7i	−0.943730	+	0.943730i	0.0547695	+	0.998499i	$0.482558\pi$
$942$	1.04955e7	+	1.77602e7i	0.385369	+	0.652109i
$943$	1.62118e6	−	1.62118e6i	0.0593678	−	0.0593678i
$944$	2.89016e6	−	1.28511e7i	0.105558	−	0.469364i
$945$	1.59740e7	−	3.29710e7i	0.581883	−	1.20103i
$946$	1.65405e7	+	4.25263e6i	0.600926	+	0.154500i
$947$	−1.45270e7			−0.526382			−0.263191	−	0.964744i	$-0.584775\pi$
$947$	−1.45270e7			−0.526382			−0.263191	+	0.964744i	$0.584775\pi$
$948$	−2.45296e7	−	1.35061e7i	−0.886482	−	0.488101i
$949$	3.00589e7	−	3.00589e7i	1.08345	−	1.08345i
$950$	486527.	−	215418.i	0.0174903	−	0.00774414i
$951$	−8.51971e6			−0.305473
$952$	2.11609e6	+	6.95003e7i	0.0756733	+	2.48539i
$953$	−3.64383e6	+	3.64383e6i	−0.129965	+	0.129965i	−0.769097	−	0.639132i	$-0.779294\pi$
$953$	−3.64383e6	+	3.64383e6i	−0.129965	+	0.129965i	0.639132	+	0.769097i	$0.279294\pi$
$954$	4.32084e6	−	2.55343e6i	0.153708	−	0.0908351i
$955$	3.74934e7	−	1.30202e7i	1.33029	−	0.461966i
$956$	−3.71814e6	+	6.75284e6i	−0.131577	+	0.238969i
$957$		−	4.94020e6i		−	0.174367i
$958$	−1.60955e7	−	2.72363e7i	−0.566620	−	0.958815i
$959$	4.77318e7			1.67595
$960$	−3.11021e7	+	1.29710e7i	−1.08921	+	0.454250i
$961$	−7.08555e6			−0.247494
$962$	−1.23480e6	−	2.08949e6i	−0.0430190	−	0.0727953i
$963$		−	1.09375e7i		−	0.380059i
$964$	245226.	−	445377.i	0.00849913	−	0.0154360i
$965$	842118.	−	1.73816e6i	0.0291108	−	0.0600859i
$966$	−3.66389e6	+	2.16520e6i	−0.126328	+	0.0746545i
$967$	−2.19801e7	+	2.19801e7i	−0.755900	+	0.755900i	−0.975573	−	0.219674i	$-0.929501\pi$
$967$	−2.19801e7	+	2.19801e7i	−0.755900	+	0.755900i	0.219674	+	0.975573i	$0.429501\pi$
$968$	−181787.	−	5.97056e6i	−0.00623556	−	0.204799i
$969$	881029.			0.0301426
$970$	2.39062e6	+	2.88817e7i	0.0815794	+	0.985584i
$971$	716885.	−	716885.i	0.0244006	−	0.0244006i	−0.694801	−	0.719202i	$-0.744508\pi$
$971$	716885.	−	716885.i	0.0244006	−	0.0244006i	0.719202	+	0.694801i	$0.244508\pi$
$972$	1.92209e7	+	1.05831e7i	0.652541	+	0.359292i
$973$	−3.07956e7			−1.04281
$974$	−3.03987e7	−	7.81562e6i	−1.02673	−	0.263977i
$975$	3.66542e7	+	4.64109e7i	1.23485	+	1.56354i
$976$	3.16999e7	+	7.12918e6i	1.06520	+	0.239560i
$977$	2.25670e7	−	2.25670e7i	0.756376	−	0.756376i	−0.219285	−	0.975661i	$-0.570372\pi$
$977$	2.25670e7	−	2.25670e7i	0.756376	−	0.756376i	0.975661	+	0.219285i	$0.0703724\pi$
$978$	2.72952e6	+	4.61880e6i	0.0912512	+	0.154412i
$979$	−2.46451e7	+	2.46451e7i	−0.821814	+	0.821814i
$980$	−1.24837e7	+	7.31332e7i	−0.415221	+	2.43248i
$981$	−6.27541e6	−	6.27541e6i	−0.208195	−	0.208195i
$982$	3.12685e7	+	8.03925e6i	1.03473	+	0.266034i
$983$	−1.33248e7	−	1.33248e7i	−0.439823	−	0.439823i	0.452130	−	0.891952i	$-0.350664\pi$
$983$	−1.33248e7	−	1.33248e7i	−0.439823	−	0.439823i	−0.891952	+	0.452130i	$0.850664\pi$
$984$	4.50498e7	−	1.37164e6i	1.48322	−	0.0451599i
$985$	1.20968e7	+	3.48343e7i	0.397264	+	1.14397i
$986$	2.79152e6	+	4.72372e6i	0.0914427	+	0.154736i
$987$		−	4.87236e6i		−	0.159201i
$988$	−275813.	−	951669.i	−0.00898922	−	0.0310166i
$989$	−820944.	−	820944.i	−0.0266884	−	0.0266884i
$990$	1.09661e6	+	1.32484e7i	0.0355601	+	0.429612i
$991$			1.77566e7i			0.574349i	0.957878	+	0.287174i	$0.0927159\pi$
$991$			1.77566e7i			0.574349i	−0.957878	+	0.287174i	$0.907284\pi$
$992$	−3.08190e7	−	1.57664e7i	−0.994349	−	0.508689i
$993$	−5.07835e7	−	5.07835e7i	−1.63437	−	1.63437i
$994$	1.12462e7	+	2.89145e6i	0.361028	+	0.0928217i
$995$	−3.96483e7	+	1.37685e7i	−1.26960	+	0.440889i
$996$	2.16479e7	−	3.93166e7i	0.691460	−	1.25582i
$997$	6.03762e7			1.92366			0.961828	−	0.273653i	$-0.0882321\pi$
$997$	6.03762e7			1.92366			0.961828	+	0.273653i	$0.0882321\pi$
$998$	2.39620e7	+	6.16072e6i	0.761546	+	0.195796i
$999$		−	1.13226e6i		−	0.0358948i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.j.a.43.19	✓	116
5.2	odd	4		80.6.s.a.27.49	yes	116
16.3	odd	4		80.6.s.a.3.49	yes	116
80.67	even	4	inner	80.6.j.a.67.19	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.j.a.43.19	✓	116	1.1	even	1	trivial
80.6.j.a.67.19	yes	116	80.67	even	4	inner
80.6.s.a.3.49	yes	116	16.3	odd	4
80.6.s.a.27.49	yes	116	5.2	odd	4

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.87799 - 4.87003i) q^{2} +18.3965i q^{3} +(-15.4344 + 28.0318i) q^{4} +(18.3385 + 52.8081i) q^{5} +(89.5915 - 52.9449i) q^{6} +(-170.706 + 170.706i) q^{7} +(180.935 - 5.50899i) q^{8} -95.4313 q^{9} +O(q^{10})\)	\(q+(-2.87799 - 4.87003i) q^{2} +18.3965i q^{3} +(-15.4344 + 28.0318i) q^{4} +(18.3385 + 52.8081i) q^{5} +(89.5915 - 52.9449i) q^{6} +(-170.706 + 170.706i) q^{7} +(180.935 - 5.50899i) q^{8} -95.4313 q^{9} +(204.399 - 241.290i) q^{10} +(311.488 - 311.488i) q^{11} +(-515.686 - 283.939i) q^{12} -1028.71 q^{13} +(1322.63 + 340.054i) q^{14} +(-971.485 + 337.364i) q^{15} +(-547.559 - 865.307i) q^{16} +(1125.08 - 1125.08i) q^{17} +(274.650 + 464.753i) q^{18} +(21.2834 - 21.2834i) q^{19} +(-1763.35 - 301.001i) q^{20} +(-3140.39 - 3140.39i) q^{21} +(-2413.41 - 620.498i) q^{22} +(119.783 + 119.783i) q^{23} +(101.346 + 3328.58i) q^{24} +(-2452.40 + 1936.85i) q^{25} +(2960.62 + 5009.86i) q^{26} +2714.75i q^{27} +(-2150.44 - 7419.93i) q^{28} +(-431.061 - 431.061i) q^{29} +(4438.89 + 3760.23i) q^{30} +5976.18i q^{31} +(-2638.20 + 5156.97i) q^{32} +(5730.29 + 5730.29i) q^{33} +(-8717.15 - 2241.21i) q^{34} +(-12145.2 - 5884.17i) q^{35} +(1472.92 - 2675.11i) q^{36} -417.076 q^{37} +(-164.904 - 42.3975i) q^{38} -18924.7i q^{39} +(3609.01 + 9453.84i) q^{40} -13534.2i q^{41} +(-6255.80 + 24331.8i) q^{42} -6853.57 q^{43} +(3923.92 + 13539.2i) q^{44} +(-1750.07 - 5039.55i) q^{45} +(238.614 - 928.083i) q^{46} +(775.756 + 775.756i) q^{47} +(15918.6 - 10073.2i) q^{48} -41474.1i q^{49} +(16490.5 + 6369.04i) q^{50} +(20697.6 + 20697.6i) q^{51} +(15877.6 - 28836.6i) q^{52} -9297.05i q^{53} +(13220.9 - 7813.01i) q^{54} +(22161.3 + 10736.9i) q^{55} +(-29946.4 + 31827.2i) q^{56} +(391.540 + 391.540i) q^{57} +(-858.692 + 3339.87i) q^{58} +(9095.76 + 9095.76i) q^{59} +(5537.37 - 32439.4i) q^{60} +(-22436.6 + 22436.6i) q^{61} +(29104.2 - 17199.4i) q^{62} +(16290.7 - 16290.7i) q^{63} +(32707.3 - 1993.54i) q^{64} +(-18865.1 - 54324.4i) q^{65} +(11415.0 - 44398.3i) q^{66} -20126.3 q^{67} +(14173.1 + 48903.0i) q^{68} +(-2203.59 + 2203.59i) q^{69} +(6297.49 + 76081.8i) q^{70} +8502.91 q^{71} +(-17266.9 + 525.730i) q^{72} +(-29220.0 + 29220.0i) q^{73} +(1200.34 + 2031.17i) q^{74} +(-35631.2 - 45115.5i) q^{75} +(268.114 + 925.107i) q^{76} +106346. i q^{77} +(-92164.0 + 54465.1i) q^{78} +47566.9 q^{79} +(35653.8 - 44784.0i) q^{80} -73131.7 q^{81} +(-65912.1 + 38951.3i) q^{82} +76241.4i q^{83} +(136501. - 39560.6i) q^{84} +(80045.8 + 38781.2i) q^{85} +(19724.5 + 33377.1i) q^{86} +(7930.01 - 7930.01i) q^{87} +(54643.2 - 58075.2i) q^{88} -79120.5 q^{89} +(-19506.1 + 23026.6i) q^{90} +(175607. - 175607. i) q^{91} +(-5206.52 + 1508.95i) q^{92} -109941. q^{93} +(1545.34 - 6010.57i) q^{94} +(1514.24 + 733.630i) q^{95} +(-94870.2 - 48533.7i) q^{96} +(-64802.3 + 64802.3i) q^{97} +(-201980. + 119362. i) q^{98} +(-29725.7 + 29725.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 2 q^{2} - 20 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 248 q^{8} - 8748 q^{9}+O(q^{10}) \) 116 * q - 2 * q^2 - 20 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^7 - 248 * q^8 - 8748 * q^9	\( 116 q - 2 q^{2} - 20 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 248 q^{8} - 8748 q^{9} - 66 q^{10} - 4 q^{11} - 308 q^{12} - 4 q^{13} + 972 q^{15} - 1224 q^{16} - 4 q^{17} + 4214 q^{18} - 2360 q^{19} - 836 q^{20} - 4 q^{21} - 2440 q^{22} - 4 q^{23} + 972 q^{24} - 884 q^{26} - 12416 q^{28} + 15336 q^{30} - 17612 q^{32} - 4 q^{33} - 12520 q^{34} - 8640 q^{35} + 2380 q^{36} - 4 q^{37} + 15108 q^{38} + 11864 q^{40} - 41092 q^{42} - 1316 q^{43} + 8200 q^{44} - 5766 q^{45} - 35924 q^{46} + 65256 q^{47} + 5180 q^{48} - 44378 q^{50} + 10436 q^{51} + 63080 q^{52} + 33820 q^{54} - 4 q^{55} - 64684 q^{56} + 972 q^{57} - 66940 q^{58} - 14480 q^{59} + 136260 q^{60} + 48076 q^{61} + 109524 q^{62} + 972 q^{63} + 71920 q^{64} - 4 q^{65} + 72436 q^{66} - 89260 q^{67} + 36360 q^{68} - 21348 q^{69} + 59552 q^{70} - 143848 q^{71} + 179728 q^{72} - 10072 q^{73} - 82508 q^{74} - 32272 q^{75} - 128004 q^{76} + 111388 q^{78} + 313732 q^{80} + 551116 q^{81} - 282876 q^{82} - 80928 q^{84} - 6252 q^{85} - 85324 q^{86} - 282188 q^{87} + 80224 q^{88} + 115550 q^{90} - 164724 q^{91} + 474536 q^{92} + 968 q^{93} - 106060 q^{94} + 204760 q^{95} - 62264 q^{96} - 4 q^{97} + 50214 q^{98} - 168788 q^{99}+O(q^{100}) \) 116 * q - 2 * q^2 - 20 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^7 - 248 * q^8 - 8748 * q^9 - 66 * q^10 - 4 * q^11 - 308 * q^12 - 4 * q^13 + 972 * q^15 - 1224 * q^16 - 4 * q^17 + 4214 * q^18 - 2360 * q^19 - 836 * q^20 - 4 * q^21 - 2440 * q^22 - 4 * q^23 + 972 * q^24 - 884 * q^26 - 12416 * q^28 + 15336 * q^30 - 17612 * q^32 - 4 * q^33 - 12520 * q^34 - 8640 * q^35 + 2380 * q^36 - 4 * q^37 + 15108 * q^38 + 11864 * q^40 - 41092 * q^42 - 1316 * q^43 + 8200 * q^44 - 5766 * q^45 - 35924 * q^46 + 65256 * q^47 + 5180 * q^48 - 44378 * q^50 + 10436 * q^51 + 63080 * q^52 + 33820 * q^54 - 4 * q^55 - 64684 * q^56 + 972 * q^57 - 66940 * q^58 - 14480 * q^59 + 136260 * q^60 + 48076 * q^61 + 109524 * q^62 + 972 * q^63 + 71920 * q^64 - 4 * q^65 + 72436 * q^66 - 89260 * q^67 + 36360 * q^68 - 21348 * q^69 + 59552 * q^70 - 143848 * q^71 + 179728 * q^72 - 10072 * q^73 - 82508 * q^74 - 32272 * q^75 - 128004 * q^76 + 111388 * q^78 + 313732 * q^80 + 551116 * q^81 - 282876 * q^82 - 80928 * q^84 - 6252 * q^85 - 85324 * q^86 - 282188 * q^87 + 80224 * q^88 + 115550 * q^90 - 164724 * q^91 + 474536 * q^92 + 968 * q^93 - 106060 * q^94 + 204760 * q^95 - 62264 * q^96 - 4 * q^97 + 50214 * q^98 - 168788 * q^99

Introduction

L-functions

Modular forms

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