LMFDB - Embedded newform 48.7.l.a.19.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,7,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	48.l (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:	$11.0425960138$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.17
Character	$\chi$	$=$	48.19
Dual form			48.7.l.a.43.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.87132 + 6.34588i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(-16.5404 + 61.8257i) q^{4} +(-95.7535 + 95.7535i) q^{5} +(-123.644 - 16.2536i) q^{6} +338.697 q^{7} +(-472.912 + 196.210i) q^{8} -243.000i q^{9} +O(q^{10})$	\(q+(4.87132 + 6.34588i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(-16.5404 + 61.8257i) q^{4} +(-95.7535 + 95.7535i) q^{5} +(-123.644 - 16.2536i) q^{6} +338.697 q^{7} +(-472.912 + 196.210i) q^{8} -243.000i q^{9} +(-1074.09 - 141.194i) q^{10} +(-1594.02 - 1594.02i) q^{11} +(-499.166 - 863.806i) q^{12} +(602.697 + 602.697i) q^{13} +(1649.90 + 2149.33i) q^{14} -2110.92i q^{15} +(-3548.83 - 2045.24i) q^{16} -1410.09 q^{17} +(1542.05 - 1183.73i) q^{18} +(-6642.31 + 6642.31i) q^{19} +(-4336.23 - 7503.83i) q^{20} +(-3733.36 + 3733.36i) q^{21} +(2350.48 - 17880.5i) q^{22} +14966.5 q^{23} +(3050.01 - 7375.53i) q^{24} -2712.47i q^{25} +(-888.711 + 6760.58i) q^{26} +(2678.52 + 2678.52i) q^{27} +(-5602.18 + 20940.2i) q^{28} +(-25687.3 - 25687.3i) q^{29} +(13395.7 - 10283.0i) q^{30} +52243.3i q^{31} +(-4308.64 - 32483.5i) q^{32} +35140.9 q^{33} +(-6868.99 - 8948.24i) q^{34} +(-32431.4 + 32431.4i) q^{35} +(15023.6 + 4019.32i) q^{36} +(-11201.3 + 11201.3i) q^{37} +(-74508.2 - 9794.46i) q^{38} -13286.7 q^{39} +(26495.2 - 64070.7i) q^{40} +78047.4i q^{41} +(-41877.9 - 5505.05i) q^{42} +(62949.8 + 62949.8i) q^{43} +(124917. - 72185.8i) q^{44} +(23268.1 + 23268.1i) q^{45} +(72906.8 + 94975.8i) q^{46} +59196.3i q^{47} +(61661.8 - 16573.6i) q^{48} -2933.21 q^{49} +(17213.0 - 13213.3i) q^{50} +(15543.0 - 15543.0i) q^{51} +(-47231.0 + 27293.3i) q^{52} +(-45616.2 + 45616.2i) q^{53} +(-3949.62 + 30045.5i) q^{54} +305266. q^{55} +(-160174. + 66455.6i) q^{56} -146432. i q^{57} +(37877.3 - 288139. i) q^{58} +(40115.2 + 40115.2i) q^{59} +(130509. + 34915.5i) q^{60} +(-68015.9 - 68015.9i) q^{61} +(-331530. + 254494. i) q^{62} -82303.4i q^{63} +(185148. - 185580. i) q^{64} -115421. q^{65} +(171183. + 223000. i) q^{66} +(75821.1 - 75821.1i) q^{67} +(23323.4 - 87179.5i) q^{68} +(-164972. + 164972. i) q^{69} +(-363790. - 47822.0i) q^{70} -520740. q^{71} +(47678.9 + 114918. i) q^{72} -349935. i q^{73} +(-125647. - 16516.9i) q^{74} +(29898.7 + 29898.7i) q^{75} +(-300799. - 520532. i) q^{76} +(-539891. - 539891. i) q^{77} +(-64723.9 - 84315.8i) q^{78} +584164. i q^{79} +(535652. - 143974. i) q^{80} -59049.0 q^{81} +(-495280. + 380194. i) q^{82} +(-75532.5 + 75532.5i) q^{83} +(-169066. - 292569. i) q^{84} +(135021. - 135021. i) q^{85} +(-92822.9 + 706121. i) q^{86} +566286. q^{87} +(1.06659e6 + 441070. i) q^{88} -881047. i q^{89} +(-34310.1 + 261003. i) q^{90} +(204132. + 204132. i) q^{91} +(-247552. + 925316. i) q^{92} +(-575863. - 575863. i) q^{93} +(-375653. + 288365. i) q^{94} -1.27205e6i q^{95} +(405549. + 310563. i) q^{96} +463594. q^{97} +(-14288.6 - 18613.8i) q^{98} +(-387347. + 387347. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 180 q^{4} - 1932 q^{8}+O(q^{10}) $ 48 * q - 180 * q^4 - 1932 * q^8	\( 48 q - 180 q^{4} - 1932 q^{8} + 744 q^{10} - 2720 q^{11} - 1944 q^{12} - 15388 q^{14} + 3744 q^{16} + 4860 q^{18} - 3936 q^{19} - 14000 q^{20} - 41184 q^{22} + 26240 q^{23} + 18468 q^{24} - 5300 q^{26} - 96120 q^{28} + 66400 q^{29} - 33048 q^{30} - 52960 q^{32} + 122208 q^{34} + 162336 q^{35} + 32076 q^{36} - 7200 q^{37} + 16968 q^{38} - 309072 q^{40} - 231660 q^{42} + 340704 q^{43} - 193192 q^{44} - 450264 q^{46} + 299376 q^{48} + 806736 q^{49} + 537764 q^{50} + 80352 q^{51} + 1126224 q^{52} + 443680 q^{53} + 78732 q^{54} + 232704 q^{55} - 420448 q^{56} - 1295664 q^{58} - 886144 q^{59} - 627912 q^{60} - 326496 q^{61} - 719652 q^{62} - 192024 q^{64} - 372832 q^{65} + 775656 q^{66} - 962112 q^{67} + 3197632 q^{68} + 541728 q^{69} + 642816 q^{70} + 534016 q^{71} + 82620 q^{72} - 4894836 q^{74} - 1073088 q^{75} - 3162552 q^{76} - 932960 q^{77} - 337284 q^{78} + 4668072 q^{80} - 2834352 q^{81} + 5077560 q^{82} - 2497760 q^{83} + 1312200 q^{84} - 372000 q^{85} + 4142928 q^{86} - 2794272 q^{88} - 507384 q^{90} + 775008 q^{91} - 9470992 q^{92} - 5050728 q^{94} + 1879200 q^{96} + 12708584 q^{98} - 660960 q^{99}+O(q^{100}) \) 48 * q - 180 * q^4 - 1932 * q^8 + 744 * q^10 - 2720 * q^11 - 1944 * q^12 - 15388 * q^14 + 3744 * q^16 + 4860 * q^18 - 3936 * q^19 - 14000 * q^20 - 41184 * q^22 + 26240 * q^23 + 18468 * q^24 - 5300 * q^26 - 96120 * q^28 + 66400 * q^29 - 33048 * q^30 - 52960 * q^32 + 122208 * q^34 + 162336 * q^35 + 32076 * q^36 - 7200 * q^37 + 16968 * q^38 - 309072 * q^40 - 231660 * q^42 + 340704 * q^43 - 193192 * q^44 - 450264 * q^46 + 299376 * q^48 + 806736 * q^49 + 537764 * q^50 + 80352 * q^51 + 1126224 * q^52 + 443680 * q^53 + 78732 * q^54 + 232704 * q^55 - 420448 * q^56 - 1295664 * q^58 - 886144 * q^59 - 627912 * q^60 - 326496 * q^61 - 719652 * q^62 - 192024 * q^64 - 372832 * q^65 + 775656 * q^66 - 962112 * q^67 + 3197632 * q^68 + 541728 * q^69 + 642816 * q^70 + 534016 * q^71 + 82620 * q^72 - 4894836 * q^74 - 1073088 * q^75 - 3162552 * q^76 - 932960 * q^77 - 337284 * q^78 + 4668072 * q^80 - 2834352 * q^81 + 5077560 * q^82 - 2497760 * q^83 + 1312200 * q^84 - 372000 * q^85 + 4142928 * q^86 - 2794272 * q^88 - 507384 * q^90 + 775008 * q^91 - 9470992 * q^92 - 5050728 * q^94 + 1879200 * q^96 + 12708584 * q^98 - 660960 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	4.87132	+	6.34588i	0.608916	+	0.793235i
$2$	4.87132	+	6.34588i	0.608916	+	0.793235i
$3$	−11.0227	+	11.0227i	−0.408248	+	0.408248i
$3$	−11.0227	+	11.0227i	−0.408248	+	0.408248i
$4$	−16.5404	+	61.8257i	−0.258444	+	0.966026i
$5$	−95.7535	+	95.7535i	−0.766028	+	0.766028i	−0.977405	−	0.211377i	$-0.932205\pi$
$5$	−95.7535	+	95.7535i	−0.766028	+	0.766028i	0.211377	+	0.977405i	$0.432205\pi$
$6$	−123.644	−	16.2536i	−0.572426	−	0.0752481i
$7$	338.697			0.987455			0.493728	−	0.869617i	$-0.335634\pi$
$7$	338.697			0.987455			0.493728	+	0.869617i	$0.335634\pi$
$8$	−472.912	+	196.210i	−0.923656	+	0.383222i
$9$		−	243.000i		−	0.333333i
$10$	−1074.09	−	141.194i	−1.07409	−	0.141194i
$11$	−1594.02	−	1594.02i	−1.19761	−	1.19761i	−0.974879	−	0.222733i	$-0.928502\pi$
$11$	−1594.02	−	1594.02i	−1.19761	−	1.19761i	−0.222733	−	0.974879i	$-0.571498\pi$
$12$	−499.166	−	863.806i	−0.288869	−	0.499888i
$13$	602.697	+	602.697i	0.274327	+	0.274327i	0.830839	−	0.556512i	$-0.187861\pi$
$13$	602.697	+	602.697i	0.274327	+	0.274327i	−0.556512	+	0.830839i	$0.687861\pi$
$14$	1649.90	+	2149.33i	0.601277	+	0.783284i
$15$		−	2110.92i		−	0.625459i
$16$	−3548.83	−	2045.24i	−0.866414	−	0.499327i
$17$	−1410.09			−0.287011			−0.143506	−	0.989650i	$-0.545838\pi$
$17$	−1410.09			−0.287011			−0.143506	+	0.989650i	$0.545838\pi$
$18$	1542.05	−	1183.73i	0.264412	−	0.202972i
$19$	−6642.31	+	6642.31i	−0.968408	+	0.968408i	−0.999516	−	0.0311079i	$-0.990096\pi$
$19$	−6642.31	+	6642.31i	−0.968408	+	0.968408i	0.0311079	+	0.999516i	$0.490096\pi$
$20$	−4336.23	−	7503.83i	−0.542028	−	0.937978i
$21$	−3733.36	+	3733.36i	−0.403127	+	0.403127i
$22$	2350.48	−	17880.5i	0.220743	−	1.67923i
$23$	14966.5			1.23009			0.615046	−	0.788491i	$-0.289137\pi$
$23$	14966.5			1.23009			0.615046	+	0.788491i	$0.289137\pi$
$24$	3050.01	−	7375.53i	0.220631	−	0.533531i
$25$		−	2712.47i		−	0.173598i
$26$	−888.711	+	6760.58i	−0.0505639	+	0.384648i
$27$	2678.52	+	2678.52i	0.136083	+	0.136083i
$28$	−5602.18	+	20940.2i	−0.255202	+	0.953908i
$29$	−25687.3	−	25687.3i	−1.05323	−	1.05323i	−0.998501	−	0.0547301i	$-0.982570\pi$
$29$	−25687.3	−	25687.3i	−1.05323	−	1.05323i	−0.0547301	−	0.998501i	$-0.517430\pi$
$30$	13395.7	−	10283.0i	0.496136	−	0.380852i
$31$			52243.3i			1.75366i	0.480799	+	0.876831i	$0.340347\pi$
$31$			52243.3i			1.75366i	−0.480799	+	0.876831i	$0.659653\pi$
$32$	−4308.64	−	32483.5i	−0.131489	−	0.991318i
$33$	35140.9			0.977847
$34$	−6868.99	−	8948.24i	−0.174766	−	0.227667i
$35$	−32431.4	+	32431.4i	−0.756418	+	0.756418i
$36$	15023.6	+	4019.32i	0.322009	+	0.0861479i
$37$	−11201.3	+	11201.3i	−0.221138	+	0.221138i	−0.808977	−	0.587840i	$-0.799979\pi$
$37$	−11201.3	+	11201.3i	−0.221138	+	0.221138i	0.587840	+	0.808977i	$0.299979\pi$
$38$	−74508.2	−	9794.46i	−1.35785	−	0.178496i
$39$	−13286.7			−0.223987
$40$	26495.2	−	64070.7i	0.413988	−	1.00111i
$41$			78047.4i			1.13242i	0.824261	+	0.566209i	$0.191591\pi$
$41$			78047.4i			1.13242i	−0.824261	+	0.566209i	$0.808409\pi$
$42$	−41877.9	−	5505.05i	−0.565245	−	0.0743041i
$43$	62949.8	+	62949.8i	0.791751	+	0.791751i	0.981779	−	0.190027i	$-0.0608577\pi$
$43$	62949.8	+	62949.8i	0.791751	+	0.791751i	−0.190027	+	0.981779i	$0.560858\pi$
$44$	124917.	−	72185.8i	1.46644	−	0.847410i
$45$	23268.1	+	23268.1i	0.255343	+	0.255343i
$46$	72906.8	+	94975.8i	0.749022	+	0.975752i
$47$			59196.3i			0.570166i	0.958503	+	0.285083i	$0.0920211\pi$
$47$			59196.3i			0.570166i	−0.958503	+	0.285083i	$0.907979\pi$
$48$	61661.8	−	16573.6i	0.557561	−	0.149863i
$49$	−2933.21			−0.0249319
$50$	17213.0	−	13213.3i	0.137704	−	0.105706i
$51$	15543.0	−	15543.0i	0.117172	−	0.117172i
$52$	−47231.0	+	27293.3i	−0.335906	+	0.194109i
$53$	−45616.2	+	45616.2i	−0.306402	+	0.306402i	−0.843512	−	0.537110i	$-0.819516\pi$
$53$	−45616.2	+	45616.2i	−0.306402	+	0.306402i	0.537110	+	0.843512i	$0.319516\pi$
$54$	−3949.62	+	30045.5i	−0.0250827	+	0.190809i
$55$	305266.			1.83481
$56$	−160174.	+	66455.6i	−0.912069	+	0.378415i
$57$		−	146432.i		−	0.790702i
$58$	37877.3	−	288139.i	0.194131	−	1.47679i
$59$	40115.2	+	40115.2i	0.195323	+	0.195323i	0.797992	−	0.602669i	$-0.205896\pi$
$59$	40115.2	+	40115.2i	0.195323	+	0.195323i	−0.602669	+	0.797992i	$0.705896\pi$
$60$	130509.	+	34915.5i	0.604210	+	0.161646i
$61$	−68015.9	−	68015.9i	−0.299654	−	0.299654i	0.541224	−	0.840878i	$-0.317961\pi$
$61$	−68015.9	−	68015.9i	−0.299654	−	0.299654i	−0.840878	+	0.541224i	$0.817961\pi$
$62$	−331530.	+	254494.i	−1.39107	+	1.06783i
$63$		−	82303.4i		−	0.329152i
$64$	185148.	−	185580.i	0.706282	−	0.707931i
$65$	−115421.			−0.420285
$66$	171183.	+	223000.i	0.595426	+	0.775662i
$67$	75821.1	−	75821.1i	0.252096	−	0.252096i	−0.569734	−	0.821829i	$-0.692954\pi$
$67$	75821.1	−	75821.1i	0.252096	−	0.252096i	0.821829	+	0.569734i	$0.192954\pi$
$68$	23323.4	−	87179.5i	0.0741762	−	0.277260i
$69$	−164972.	+	164972.i	−0.502183	+	0.502183i
$70$	−363790.	−	47822.0i	−1.06061	−	0.139423i
$71$	−520740.			−1.45494			−0.727472	−	0.686137i	$-0.759305\pi$
$71$	−520740.			−1.45494			−0.727472	+	0.686137i	$0.759305\pi$
$72$	47678.9	+	114918.i	0.127741	+	0.307885i
$73$		−	349935.i		−	0.899537i	−0.893145	−	0.449768i	$-0.851506\pi$
$73$		−	349935.i		−	0.899537i	0.893145	−	0.449768i	$-0.148494\pi$
$74$	−125647.	−	16516.9i	−0.310068	−	0.0407600i
$75$	29898.7	+	29898.7i	0.0708710	+	0.0708710i
$76$	−300799.	−	520532.i	−0.685229	−	1.18579i
$77$	−539891.	−	539891.i	−1.18259	−	1.18259i
$78$	−64723.9	−	84315.8i	−0.136389	−	0.177675i
$79$			584164.i			1.18482i	0.805635	+	0.592412i	$0.201824\pi$
$79$			584164.i			1.18482i	−0.805635	+	0.592412i	$0.798176\pi$
$80$	535652.	−	143974.i	1.04620	−	0.281199i
$81$	−59049.0			−0.111111
$82$	−495280.	+	380194.i	−0.898274	+	0.689547i
$83$	−75532.5	+	75532.5i	−0.132099	+	0.132099i	−0.770065	−	0.637966i	$-0.779776\pi$
$83$	−75532.5	+	75532.5i	−0.132099	+	0.132099i	0.637966	+	0.770065i	$0.279776\pi$
$84$	−169066.	−	292569.i	−0.285246	−	0.493617i
$85$	135021.	−	135021.i	0.219859	−	0.219859i
$86$	−92822.9	+	706121.i	−0.145935	+	1.11015i
$87$	566286.			0.859960
$88$	1.06659e6	+	441070.i	1.56513	+	0.647231i
$89$		−	881047.i		−	1.24977i	−0.780718	−	0.624884i	$-0.785146\pi$
$89$		−	881047.i		−	1.24977i	0.780718	−	0.624884i	$-0.214854\pi$
$90$	−34310.1	+	261003.i	−0.0470646	+	0.358029i
$91$	204132.	+	204132.i	0.270886	+	0.270886i
$92$	−247552.	+	925316.i	−0.317910	+	1.18830i
$93$	−575863.	−	575863.i	−0.715929	−	0.715929i
$94$	−375653.	+	288365.i	−0.452276	+	0.347183i
$95$		−	1.27205e6i		−	1.48366i
$96$	405549.	+	310563.i	0.458384	+	0.351023i
$97$	463594.			0.507952			0.253976	−	0.967211i	$-0.418262\pi$
$97$	463594.			0.507952			0.253976	+	0.967211i	$0.418262\pi$
$98$	−14288.6	−	18613.8i	−0.0151814	−	0.0197768i
$99$	−387347.	+	387347.i	−0.399204	+	0.399204i
$100$	167700.	+	44865.3i	0.167700	+	0.0448653i
$101$	457625.	−	457625.i	0.444166	−	0.444166i	−0.449243	−	0.893409i	$-0.648306\pi$
$101$	457625.	−	457625.i	0.444166	−	0.444166i	0.893409	+	0.449243i	$0.148306\pi$
$102$	174349.	+	22919.0i	0.164293	+	0.0215970i
$103$	1.49249e6			1.36584			0.682921	−	0.730492i	$-0.260709\pi$
$103$	1.49249e6			1.36584			0.682921	+	0.730492i	$0.260709\pi$
$104$	−403278.	−	166768.i	−0.358512	−	0.148256i
$105$		−	714964.i		−	0.617613i
$106$	−511687.	−	67263.7i	−0.429622	−	0.0564759i
$107$	1.61763e6	+	1.61763e6i	1.32047	+	1.32047i	0.913396	+	0.407072i	$0.133450\pi$
$107$	1.61763e6	+	1.61763e6i	1.32047	+	1.32047i	0.407072	+	0.913396i	$0.366550\pi$
$108$	−209905.	+	121297.i	−0.166629	+	0.0962898i
$109$	−212604.	−	212604.i	−0.164170	−	0.164170i	0.620241	−	0.784411i	$-0.287035\pi$
$109$	−212604.	−	212604.i	−0.164170	−	0.164170i	−0.784411	+	0.620241i	$0.787035\pi$
$110$	1.48705e6	+	1.93718e6i	1.11724	+	1.45544i
$111$		−	246937.i		−	0.180558i
$112$	−1.20198e6	−	692718.i	−0.855545	−	0.493063i
$113$	1.23333e6			0.854760			0.427380	−	0.904072i	$-0.359437\pi$
$113$	1.23333e6			0.854760			0.427380	+	0.904072i	$0.359437\pi$
$114$	929243.	−	713320.i	0.627212	−	0.481471i
$115$	−1.43310e6	+	1.43310e6i	−0.942285	+	0.942285i
$116$	2.01301e6	−	1.16325e6i	1.28965	−	0.745248i
$117$	146455.	−	146455.i	0.0914425	−	0.0914425i
$118$	−59152.1	+	449980.i	−0.0360018	+	0.273872i
$119$	−477592.			−0.283411
$120$	414184.	+	998282.i	0.239690	+	0.577709i
$121$			3.31025e6i			1.86855i
$122$	100293.	−	762948.i	0.0552321	−	0.420161i
$123$	−860294.	−	860294.i	−0.462308	−	0.462308i
$124$	−3.22998e6	−	864125.i	−1.69408	−	0.453223i
$125$	−1.23642e6	−	1.23642e6i	−0.633047	−	0.633047i
$126$	522288.	−	400927.i	0.261095	−	0.200426i
$127$		−	2.86669e6i		−	1.39949i	−0.714394	−	0.699744i	$-0.753297\pi$
$127$		−	2.86669e6i		−	1.39949i	0.714394	−	0.699744i	$-0.246703\pi$
$128$	2.07958e6	+	270905.i	0.991621	+	0.129178i
$129$	−1.38775e6			−0.646462
$130$	−562252.	−	732446.i	−0.255918	−	0.333385i
$131$	−1.18710e6	+	1.18710e6i	−0.528046	+	0.528046i	−0.919989	−	0.391943i	$-0.871803\pi$
$131$	−1.18710e6	+	1.18710e6i	−0.528046	+	0.528046i	0.391943	+	0.919989i	$0.371803\pi$
$132$	−581244.	+	2.17261e6i	−0.252718	+	0.944626i
$133$	−2.24973e6	+	2.24973e6i	−0.956260	+	0.956260i
$134$	850501.	+	111802.i	0.353476	+	0.0464662i
$135$	−512955.			−0.208486
$136$	666847.	−	276672.i	0.265100	−	0.109989i
$137$			4.54167e6i			1.76626i	0.469132	+	0.883128i	$0.344567\pi$
$137$			4.54167e6i			1.76626i	−0.469132	+	0.883128i	$0.655433\pi$
$138$	−1.85052e6	−	243260.i	−0.704136	−	0.0925621i
$139$	3.47603e6	+	3.47603e6i	1.29431	+	1.29431i	0.932093	+	0.362218i	$0.117980\pi$
$139$	3.47603e6	+	3.47603e6i	1.29431	+	1.29431i	0.362218	+	0.932093i	$0.382020\pi$
$140$	−1.46867e6	−	2.54152e6i	−0.535229	−	0.926212i
$141$	−652504.	−	652504.i	−0.232769	−	0.232769i
$142$	−2.53670e6	−	3.30456e6i	−0.885938	−	1.15411i
$143$		−	1.92143e6i		−	0.657076i
$144$	−496994.	+	862366.i	−0.166442	+	0.288805i
$145$	4.91929e6			1.61361
$146$	2.22065e6	−	1.70465e6i	0.713544	−	0.547742i
$147$	32331.9	−	32331.9i	0.0101784	−	0.0101784i
$148$	−507253.	−	877801.i	−0.156473	−	0.270776i
$149$	1.14413e6	−	1.14413e6i	0.345873	−	0.345873i	−0.512697	−	0.858570i	$-0.671354\pi$
$149$	1.14413e6	−	1.14413e6i	0.345873	−	0.345873i	0.858570	+	0.512697i	$0.171354\pi$
$150$	−44087.3	+	335380.i	−0.0130629	+	0.0993719i
$151$	−2.06680e6			−0.600300			−0.300150	−	0.953892i	$-0.597037\pi$
$151$	−2.06680e6			−0.600300			−0.300150	+	0.953892i	$0.597037\pi$
$152$	1.83794e6	−	4.44451e6i	0.523361	−	1.26559i
$153$			342651.i			0.0956704i
$154$	796099.	−	6.05607e6i	0.217974	−	1.65817i
$155$	−5.00248e6	−	5.00248e6i	−1.34335	−	1.34335i
$156$	219767.	−	821460.i	0.0578881	−	0.216378i
$157$	−994443.	−	994443.i	−0.256969	−	0.256969i	0.566851	−	0.823820i	$-0.308161\pi$
$157$	−994443.	−	994443.i	−0.256969	−	0.256969i	−0.823820	+	0.566851i	$0.808161\pi$
$158$	−3.70704e6	+	2.84565e6i	−0.939843	+	0.721457i
$159$		−	1.00563e6i		−	0.250176i
$160$	3.52298e6	+	2.69784e6i	0.860102	+	0.658653i
$161$	5.06912e6			1.21466
$162$	−287647.	−	374718.i	−0.0676573	−	0.0881372i
$163$	−477011.	+	477011.i	−0.110145	+	0.110145i	−0.760032	−	0.649886i	$-0.774817\pi$
$163$	−477011.	+	477011.i	−0.110145	+	0.110145i	0.649886	+	0.760032i	$0.274817\pi$
$164$	−4.82534e6	−	1.29094e6i	−1.09395	−	0.292666i
$165$	−3.36486e6	+	3.36486e6i	−0.749058	+	0.749058i
$166$	−847264.	−	111377.i	−0.185223	−	0.0243484i
$167$	566969.			0.121733			0.0608667	−	0.998146i	$-0.480614\pi$
$167$	566969.			0.121733			0.0608667	+	0.998146i	$0.480614\pi$
$168$	1.03303e6	−	2.49807e6i	0.217864	−	0.526838i
$169$		−	4.10032e6i		−	0.849489i
$170$	1.51455e6	+	199095.i	0.308275	+	0.0405242i
$171$	1.61408e6	+	1.61408e6i	0.322803	+	0.322803i
$172$	−4.93313e6	+	2.85070e6i	−0.969476	+	0.560230i
$173$	6.06937e6	+	6.06937e6i	1.17221	+	1.17221i	0.981682	+	0.190528i	$0.0610202\pi$
$173$	6.06937e6	+	6.06937e6i	1.17221	+	1.17221i	0.190528	+	0.981682i	$0.438980\pi$
$174$	2.75856e6	+	3.59358e6i	0.523643	+	0.682150i
$175$		−	918705.i		−	0.171420i
$176$	2.39675e6	+	8.91708e6i	0.439628	+	1.63563i
$177$	−884356.			−0.159480
$178$	5.59102e6	−	4.29187e6i	0.991359	−	0.761003i
$179$	−6.12901e6	+	6.12901e6i	−1.06864	+	1.06864i	−0.0711761	+	0.997464i	$0.522675\pi$
$179$	−6.12901e6	+	6.12901e6i	−1.06864	+	1.06864i	−0.997464	+	0.0711761i	$0.977325\pi$
$180$	−1.82343e6	+	1.05370e6i	−0.312659	+	0.180676i
$181$	−3.73717e6	+	3.73717e6i	−0.630242	+	0.630242i	−0.948129	−	0.317886i	$-0.897027\pi$
$181$	−3.73717e6	+	3.73717e6i	−0.630242	+	0.630242i	0.317886	+	0.948129i	$0.397027\pi$
$182$	−301004.	+	2.28979e6i	−0.0499296	+	0.379823i
$183$	1.49944e6			0.244667
$184$	−7.07785e6	+	2.93658e6i	−1.13618	+	0.471398i
$185$		−	2.14512e6i		−	0.338795i
$186$	849142.	−	6.45957e6i	0.131960	−	1.00384i
$187$	2.24771e6	+	2.24771e6i	0.343728	+	0.343728i
$188$	−3.65985e6	−	979131.i	−0.550795	−	0.147356i
$189$	907206.	+	907206.i	0.134376	+	0.134376i
$190$	8.07227e6	−	6.19656e6i	1.17689	−	0.903421i
$191$		−	7.48444e6i		−	1.07414i	−0.843539	−	0.537068i	$-0.819532\pi$
$191$		−	7.48444e6i		−	1.07414i	0.843539	−	0.537068i	$-0.180468\pi$
$192$	4764.10	+	4.08642e6i	0.000673096	+	0.577350i
$193$	1.84618e6			0.256804			0.128402	−	0.991722i	$-0.459015\pi$
$193$	1.84618e6			0.256804			0.128402	+	0.991722i	$0.459015\pi$
$194$	2.25832e6	+	2.94191e6i	0.309300	+	0.402925i
$195$	1.27225e6	−	1.27225e6i	0.171581	−	0.171581i
$196$	48516.5	−	181348.i	0.00644349	−	0.0240849i
$197$	−5.01650e6	+	5.01650e6i	−0.656149	+	0.656149i	−0.954467	−	0.298318i	$-0.903575\pi$
$197$	−5.01650e6	+	5.01650e6i	−0.656149	+	0.656149i	0.298318	+	0.954467i	$0.403575\pi$
$198$	−4.34496e6	−	571165.i	−0.559744	−	0.0735811i
$199$	3.90212e6			0.495155			0.247578	−	0.968868i	$-0.420365\pi$
$199$	3.90212e6			0.495155			0.247578	+	0.968868i	$0.420365\pi$
$200$	532212.	+	1.28276e6i	0.0665265	+	0.160345i
$201$			1.67151e6i			0.205835i
$202$	5.13327e6	+	674793.i	0.622787	+	0.0818684i
$203$	−8.70020e6	−	8.70020e6i	−1.04002	−	1.04002i
$204$	703867.	+	1.21804e6i	0.0829087	+	0.143473i
$205$	−7.47331e6	−	7.47331e6i	−0.867464	−	0.867464i
$206$	7.27041e6	+	9.47118e6i	0.831682	+	1.08343i
$207$		−	3.63687e6i		−	0.410031i
$208$	−906209.	−	3.37153e6i	−0.100702	−	0.374660i
$209$	2.11760e7			2.31956
$210$	4.53708e6	−	3.48282e6i	0.489912	−	0.376074i
$211$	9.10818e6	−	9.10818e6i	0.969581	−	0.969581i	−0.0299699	−	0.999551i	$-0.509541\pi$
$211$	9.10818e6	−	9.10818e6i	0.969581	−	0.969581i	0.999551	+	0.0299699i	$0.00954116\pi$
$212$	−2.06574e6	−	3.57477e6i	−0.216805	−	0.375180i
$213$	5.73997e6	−	5.73997e6i	0.593978	−	0.593978i
$214$	−2.38529e6	+	1.81453e7i	−0.243388	+	1.85150i
$215$	−1.20553e7			−1.21301
$216$	−1.79225e6	−	741152.i	−0.177844	−	0.0735438i
$217$			1.76947e7i			1.73166i
$218$	313497.	−	2.38483e6i	0.0302596	−	0.230190i
$219$	3.85723e6	+	3.85723e6i	0.367234	+	0.367234i
$220$	−5.04923e6	+	1.88733e7i	−0.474195	+	1.77247i
$221$	−849855.	−	849855.i	−0.0787350	−	0.0787350i
$222$	1.56703e6	−	1.20291e6i	0.143225	−	0.109945i
$223$		−	3.47876e6i		−	0.313697i	−0.987623	−	0.156848i	$-0.949867\pi$
$223$		−	3.47876e6i		−	0.313697i	0.987623	−	0.156848i	$-0.0501334\pi$
$224$	−1.45933e6	−	1.10021e7i	−0.129840	−	0.978882i
$225$	−659129.			−0.0578660
$226$	6.00795e6	+	7.82657e6i	0.520477	+	0.678025i
$227$	−8.39488e6	+	8.39488e6i	−0.717690	+	0.717690i	−0.968132	−	0.250441i	$-0.919424\pi$
$227$	−8.39488e6	+	8.39488e6i	−0.717690	+	0.717690i	0.250441	+	0.968132i	$0.419424\pi$
$228$	9.05329e6	+	2.42205e6i	0.763839	+	0.204352i
$229$	9.40100e6	−	9.40100e6i	0.782830	−	0.782830i	−0.197477	−	0.980308i	$-0.563275\pi$
$229$	9.40100e6	−	9.40100e6i	0.782830	−	0.782830i	0.980308	+	0.197477i	$0.0632748\pi$
$230$	−1.60754e7	−	2.11318e6i	−1.32123	−	0.173681i
$231$	1.19021e7			0.965580
$232$	1.71879e7	+	7.10773e6i	1.37644	+	0.569202i
$233$		−	1.24039e7i		−	0.980599i	−0.871554	−	0.490299i	$-0.836887\pi$
$233$		−	1.24039e7i		−	0.980599i	0.871554	−	0.490299i	$-0.163113\pi$
$234$	1.64282e6	+	215957.i	0.128216	+	0.0168546i
$235$	−5.66826e6	−	5.66826e6i	−0.436763	−	0.436763i
$236$	−3.14367e6	+	1.81663e6i	−0.239167	+	0.138207i
$237$	−6.43907e6	−	6.43907e6i	−0.483702	−	0.483702i
$238$	−2.32651e6	−	3.03074e6i	−0.172573	−	0.224811i
$239$		−	3.38975e6i		−	0.248299i	−0.992264	−	0.124149i	$-0.960380\pi$
$239$		−	3.38975e6i		−	0.248299i	0.992264	−	0.124149i	$-0.0396202\pi$
$240$	−4.31735e6	+	7.49132e6i	−0.312309	+	0.541907i
$241$	−7.75493e6			−0.554022			−0.277011	−	0.960867i	$-0.589344\pi$
$241$	−7.75493e6			−0.554022			−0.277011	+	0.960867i	$0.589344\pi$
$242$	−2.10065e7	+	1.61253e7i	−1.48220	+	1.13779i
$243$	650880.	−	650880.i	0.0453609	−	0.0453609i
$244$	5.33014e6	−	3.08012e6i	0.366918	−	0.212030i
$245$	280865.	−	280865.i	0.0190985	−	0.0190985i
$246$	1.26855e6	−	9.65009e6i	0.0852124	−	0.648225i
$247$	−8.00660e6			−0.531322
$248$	−1.02506e7	−	2.47065e7i	−0.672042	−	1.61978i
$249$		−	1.66515e6i		−	0.107858i
$250$	1.82317e6	−	1.38692e7i	0.116683	−	0.887628i
$251$	6.71306e6	+	6.71306e6i	0.424521	+	0.424521i	0.886757	−	0.462236i	$-0.152953\pi$
$251$	6.71306e6	+	6.71306e6i	0.424521	+	0.424521i	−0.462236	+	0.886757i	$0.652953\pi$
$252$	5.08847e6	+	1.36133e6i	0.317969	+	0.0850672i
$253$	−2.38570e7	−	2.38570e7i	−1.47317	−	1.47317i
$254$	1.81917e7	−	1.39646e7i	1.11012	−	0.852170i
$255$			2.97659e6i			0.179514i
$256$	8.41118e6	+	1.45164e7i	0.501346	+	0.865247i
$257$	−1.78180e7			−1.04969			−0.524844	−	0.851198i	$-0.675876\pi$
$257$	−1.78180e7			−1.04969			−0.524844	+	0.851198i	$0.675876\pi$
$258$	−6.76020e6	−	8.80652e6i	−0.393641	−	0.512797i
$259$	−3.79384e6	+	3.79384e6i	−0.218364	+	0.218364i
$260$	1.90910e6	−	7.13597e6i	0.108620	−	0.406006i
$261$	−6.24200e6	+	6.24200e6i	−0.351077	+	0.351077i
$262$	−1.33159e7	−	1.75044e6i	−0.740401	−	0.0973292i
$263$	1.27225e7			0.699365			0.349683	−	0.936868i	$-0.386289\pi$
$263$	1.27225e7			0.699365			0.349683	+	0.936868i	$0.386289\pi$
$264$	−1.66185e7	+	6.89498e6i	−0.903194	+	0.374732i
$265$		−	8.73583e6i		−	0.469425i
$266$	−2.52357e7	−	3.31736e6i	−1.34082	−	0.176257i
$267$	9.71152e6	+	9.71152e6i	0.510215	+	0.510215i
$268$	3.43358e6	+	5.94180e6i	0.178379	+	0.308684i
$269$	1.77250e7	+	1.77250e7i	0.910604	+	0.910604i	0.996320	−	0.0857153i	$-0.0273176\pi$
$269$	1.77250e7	+	1.77250e7i	0.910604	+	0.910604i	−0.0857153	+	0.996320i	$0.527318\pi$
$270$	−2.49877e6	−	3.25515e6i	−0.126951	−	0.165379i
$271$		−	4.03947e6i		−	0.202963i	−0.994837	−	0.101481i	$-0.967642\pi$
$271$		−	4.03947e6i		−	0.202963i	0.994837	−	0.101481i	$-0.0323582\pi$
$272$	5.00416e6	+	2.88397e6i	0.248670	+	0.143312i
$273$	−4.50017e6			−0.221178
$274$	−2.88209e7	+	2.21239e7i	−1.40106	+	1.07550i
$275$	−4.32373e6	+	4.32373e6i	−0.207903	+	0.207903i
$276$	−7.47079e6	−	1.29282e7i	−0.355336	−	0.614908i
$277$	2.71660e6	−	2.71660e6i	0.127816	−	0.127816i	−0.640305	−	0.768121i	$-0.721192\pi$
$277$	2.71660e6	−	2.71660e6i	0.127816	−	0.127816i	0.768121	+	0.640305i	$0.221192\pi$
$278$	−5.12560e6	+	3.89913e7i	−0.238567	+	1.81482i
$279$	1.26951e7			0.584554
$280$	8.97386e6	−	2.17006e7i	0.408795	−	0.988547i
$281$		−	3.00632e6i		−	0.135493i	−0.997703	−	0.0677464i	$-0.978419\pi$
$281$		−	3.00632e6i		−	0.135493i	0.997703	−	0.0677464i	$-0.0215809\pi$
$282$	962153.	−	7.31927e6i	0.0429039	−	0.326378i
$283$	−7.04093e6	−	7.04093e6i	−0.310650	−	0.310650i	0.534512	−	0.845161i	$-0.320496\pi$
$283$	−7.04093e6	−	7.04093e6i	−0.310650	−	0.310650i	−0.845161	+	0.534512i	$0.820496\pi$
$284$	8.61325e6	−	3.21951e7i	0.376021	−	1.40551i
$285$	1.40214e7	+	1.40214e7i	0.605700	+	0.605700i
$286$	1.21931e7	−	9.35989e6i	0.521216	−	0.400104i
$287$			2.64344e7i			1.11821i
$288$	−7.89349e6	+	1.04700e6i	−0.330439	+	0.0438298i
$289$	−2.21492e7			−0.917625
$290$	2.39635e7	+	3.12172e7i	0.982552	+	1.27997i
$291$	−5.11006e6	+	5.11006e6i	−0.207370	+	0.207370i
$292$	2.16350e7	+	5.78807e6i	0.868976	+	0.232480i
$293$	−1.09177e6	+	1.09177e6i	−0.0434037	+	0.0434037i	−0.728476	−	0.685072i	$-0.759771\pi$
$293$	−1.09177e6	+	1.09177e6i	−0.0434037	+	0.0434037i	0.685072	+	0.728476i	$0.259771\pi$
$294$	362674.	+	47675.2i	0.0142717	+	0.00187608i
$295$	−7.68234e6			−0.299245
$296$	3.09942e6	−	7.49502e6i	0.119510	−	0.289000i
$297$		−	8.53923e6i		−	0.325949i
$298$	1.28339e7	+	1.68708e6i	0.484966	+	0.0637511i
$299$	9.02029e6	+	9.02029e6i	0.337448	+	0.337448i
$300$	−2.34304e6	+	1.35397e6i	−0.0867794	+	0.0501471i
$301$	2.13209e7	+	2.13209e7i	0.781819	+	0.781819i
$302$	−1.00681e7	−	1.31157e7i	−0.365532	−	0.476179i
$303$			1.00885e7i			0.362660i
$304$	3.71576e7	−	9.98730e6i	1.32259	−	0.355490i
$305$	1.30255e7			0.459087
$306$	−2.17442e6	+	1.66916e6i	−0.0758891	+	0.0582552i
$307$	3.35575e7	−	3.35575e7i	1.15978	−	1.15978i	0.175252	−	0.984524i	$-0.443926\pi$
$307$	3.35575e7	−	3.35575e7i	1.15978	−	1.15978i	0.984524	−	0.175252i	$-0.0560740\pi$
$308$	4.23091e7	−	2.44491e7i	1.44804	−	0.836780i
$309$	−1.64513e7	+	1.64513e7i	−0.557603	+	0.557603i
$310$	7.37644e6	−	5.61139e7i	0.247606	−	1.88358i
$311$	−7.25043e6			−0.241036			−0.120518	−	0.992711i	$-0.538456\pi$
$311$	−7.25043e6			−0.241036			−0.120518	+	0.992711i	$0.538456\pi$
$312$	6.28344e6	−	2.60698e6i	0.206887	−	0.0858369i
$313$			5.86126e6i			0.191143i	0.995423	+	0.0955714i	$0.0304678\pi$
$313$			5.86126e6i			0.191143i	−0.995423	+	0.0955714i	$0.969532\pi$
$314$	1.46636e6	−	1.11549e7i	0.0473644	−	0.360310i
$315$	7.88084e6	+	7.88084e6i	0.252139	+	0.252139i
$316$	−3.61163e7	−	9.66230e6i	−1.14457	−	0.306210i
$317$	1.42197e7	+	1.42197e7i	0.446388	+	0.446388i	0.894152	−	0.447764i	$-0.147779\pi$
$317$	1.42197e7	+	1.42197e7i	0.446388	+	0.446388i	−0.447764	+	0.894152i	$0.647779\pi$
$318$	6.38160e6	−	4.89874e6i	0.198449	−	0.152336i
$319$			8.18921e7i			2.52273i
$320$	41385.4	+	3.54984e7i	0.00126298	+	1.08333i
$321$	−3.56613e7			−1.07816
$322$	2.46933e7	+	3.21680e7i	0.739626	+	0.963512i
$323$	9.36623e6	−	9.36623e6i	0.277944	−	0.277944i
$324$	976694.	−	3.65074e6i	0.0287160	−	0.107336i
$325$	1.63480e6	−	1.63480e6i	0.0476226	−	0.0476226i
$326$	−5.35074e6	−	703380.i	−0.154440	−	0.0203019i
$327$	4.68695e6			0.134044
$328$	−1.53137e7	−	3.69096e7i	−0.433968	−	1.04597i
$329$			2.00496e7i			0.563013i
$330$	−3.77443e7	−	4.96168e6i	−1.05029	−	0.138066i
$331$	4.55754e7	+	4.55754e7i	1.25674	+	1.25674i	0.952638	+	0.304106i	$0.0983577\pi$
$331$	4.55754e7	+	4.55754e7i	1.25674	+	1.25674i	0.304106	+	0.952638i	$0.401642\pi$
$332$	−3.42051e6	−	5.91919e6i	−0.0934710	−	0.161751i
$333$	2.72191e6	+	2.72191e6i	0.0737125	+	0.0737125i
$334$	2.76189e6	+	3.59792e6i	0.0741254	+	0.0965632i
$335$			1.45203e7i			0.386225i
$336$	2.08847e7	−	5.61343e6i	0.550567	−	0.147983i
$337$	−5.70761e7			−1.49130			−0.745650	−	0.666338i	$-0.767861\pi$
$337$	−5.70761e7			−1.49130			−0.745650	+	0.666338i	$0.767861\pi$
$338$	2.60201e7	−	1.99740e7i	0.673844	−	0.517267i
$339$	−1.35946e7	+	1.35946e7i	−0.348954	+	0.348954i
$340$	6.11445e6	+	1.05810e7i	0.155568	+	0.269210i
$341$	8.32771e7	−	8.32771e7i	2.10021	−	2.10021i
$342$	−2.38005e6	+	1.81055e7i	−0.0594988	+	0.452618i
$343$	−4.08409e7			−1.01207
$344$	−4.21211e7	−	1.74184e7i	−1.03472	−	0.427890i
$345$		−	3.15932e7i		−	0.769373i
$346$	−8.94963e6	+	6.80814e7i	−0.216061	+	1.64362i
$347$	−1.33582e7	−	1.33582e7i	−0.319713	−	0.319713i	0.528944	−	0.848657i	$-0.322588\pi$
$347$	−1.33582e7	−	1.33582e7i	−0.319713	−	0.319713i	−0.848657	+	0.528944i	$0.822588\pi$
$348$	−9.36659e6	+	3.50110e7i	−0.222251	+	0.830744i
$349$	−5.81390e7	−	5.81390e7i	−1.36770	−	1.36770i	−0.863708	−	0.503993i	$-0.831864\pi$
$349$	−5.81390e7	−	5.81390e7i	−1.36770	−	1.36770i	−0.503993	−	0.863708i	$-0.668136\pi$
$350$	5.82999e6	−	4.47531e6i	0.135976	−	0.104380i
$351$			3.22867e6i			0.0746625i
$352$	−4.49113e7	+	5.86475e7i	−1.02974	+	1.34469i
$353$	−3.25741e7			−0.740539			−0.370269	−	0.928924i	$-0.620735\pi$
$353$	−3.25741e7			−0.740539			−0.370269	+	0.928924i	$0.620735\pi$
$354$	−4.30799e6	−	5.61202e6i	−0.0971101	−	0.126505i
$355$	4.98627e7	−	4.98627e7i	1.11453	−	1.11453i
$356$	5.44713e7	+	1.45729e7i	1.20731	+	0.322994i
$357$	5.26436e6	−	5.26436e6i	0.115702	−	0.115702i
$358$	−6.87504e7	−	9.03757e6i	−1.49839	−	0.196971i
$359$	−1.13980e7			−0.246346			−0.123173	−	0.992385i	$-0.539307\pi$
$359$	−1.13980e7			−0.246346			−0.123173	+	0.992385i	$0.539307\pi$
$360$	−1.55692e7	−	6.43834e6i	−0.333702	−	0.137996i
$361$		−	4.11947e7i		−	0.875628i
$362$	−4.19207e7	−	5.51067e6i	−0.883695	−	0.116166i
$363$	−3.64880e7	−	3.64880e7i	−0.762833	−	0.762833i
$364$	−1.59970e7	+	9.24417e6i	−0.331692	+	0.191674i
$365$	3.35075e7	+	3.35075e7i	0.689071	+	0.689071i
$366$	7.30425e6	+	9.51525e6i	0.148981	+	0.194078i
$367$			6.66527e6i			0.134840i	0.997725	+	0.0674201i	$0.0214768\pi$
$367$			6.66527e6i			0.134840i	−0.997725	+	0.0674201i	$0.978523\pi$
$368$	−5.31137e7	−	3.06102e7i	−1.06577	−	0.614218i
$369$	1.89655e7			0.377473
$370$	1.36127e7	−	1.04496e7i	0.268744	−	0.206298i
$371$	−1.54501e7	+	1.54501e7i	−0.302559	+	0.302559i
$372$	4.51281e7	−	2.60781e7i	0.876634	−	0.506579i
$373$	−3.13045e7	+	3.13045e7i	−0.603226	+	0.603226i	−0.941167	−	0.337941i	$-0.890269\pi$
$373$	−3.13045e7	+	3.13045e7i	−0.603226	+	0.603226i	0.337941	+	0.941167i	$0.390269\pi$
$374$	−3.31437e6	+	2.52130e7i	−0.0633558	+	0.481959i
$375$	2.72574e7			0.516881
$376$	−1.16149e7	−	2.79947e7i	−0.218500	−	0.526637i
$377$		−	3.09633e7i		−	0.577860i
$378$	−1.33773e6	+	1.01763e7i	−0.0247680	+	0.188415i
$379$	−3.59578e7	−	3.59578e7i	−0.660503	−	0.660503i	0.294995	−	0.955499i	$-0.404682\pi$
$379$	−3.59578e7	−	3.59578e7i	−0.660503	−	0.660503i	−0.955499	+	0.294995i	$0.904682\pi$
$380$	7.86453e7	+	2.10402e7i	1.43325	+	0.383441i
$381$	3.15986e7	+	3.15986e7i	0.571338	+	0.571338i
$382$	4.74953e7	−	3.64591e7i	0.852042	−	0.654058i
$383$		−	4.29186e6i		−	0.0763923i	−0.999270	−	0.0381962i	$-0.987839\pi$
$383$		−	4.29186e6i		−	0.0763923i	0.999270	−	0.0381962i	$-0.0121612\pi$
$384$	−2.59087e7	+	1.99365e7i	−0.457564	+	0.352091i
$385$	1.03393e8			1.81179
$386$	8.99333e6	+	1.17156e7i	0.156372	+	0.203706i
$387$	1.52968e7	−	1.52968e7i	0.263917	−	0.263917i
$388$	−7.66803e6	+	2.86620e7i	−0.131277	+	0.490695i
$389$	−2.81391e7	+	2.81391e7i	−0.478037	+	0.478037i	−0.904503	−	0.426467i	$-0.859758\pi$
$389$	−2.81391e7	+	2.81391e7i	−0.478037	+	0.478037i	0.426467	+	0.904503i	$0.359758\pi$
$390$	1.42711e7	+	1.87600e6i	0.240582	+	0.0316256i
$391$	−2.11041e7			−0.353050
$392$	1.38715e6	−	575524.i	0.0230285	−	0.00955445i
$393$		−	2.61700e7i		−	0.431148i
$394$	−5.62712e7	−	7.39712e6i	−0.920020	−	0.120941i
$395$	−5.59358e7	−	5.59358e7i	−0.907608	−	0.907608i
$396$	−1.75411e7	−	3.03549e7i	−0.282470	−	0.488814i
$397$	−102931.	−	102931.i	−0.00164504	−	0.00164504i	0.706284	−	0.707929i	$-0.250370\pi$
$397$	−102931.	−	102931.i	−0.00164504	−	0.00164504i	−0.707929	+	0.706284i	$0.750370\pi$
$398$	1.90085e7	+	2.47624e7i	0.301508	+	0.392774i
$399$		−	4.95963e7i		−	0.780783i
$400$	−5.54765e6	+	9.62608e6i	−0.0866821	+	0.150408i
$401$	−9.77419e7			−1.51582			−0.757910	−	0.652359i	$-0.773779\pi$
$401$	−9.77419e7			−1.51582			−0.757910	+	0.652359i	$0.773779\pi$
$402$	−1.06072e7	+	8.14245e6i	−0.163276	+	0.125336i
$403$	−3.14869e7	+	3.14869e7i	−0.481077	+	0.481077i
$404$	2.07237e7	+	3.58622e7i	0.314284	+	0.543868i
$405$	5.65415e6	−	5.65415e6i	0.0851142	−	0.0851142i
$406$	1.28289e7	−	9.75919e7i	0.191696	−	1.45826i
$407$	3.57102e7			0.529674
$408$	−4.30077e6	+	1.04001e7i	−0.0633237	+	0.153129i
$409$			1.16185e8i			1.69817i	0.528255	+	0.849086i	$0.322847\pi$
$409$			1.16185e8i			1.69817i	−0.528255	+	0.849086i	$0.677153\pi$
$410$	1.10198e7	−	8.38297e7i	0.159891	−	1.21632i
$411$	−5.00615e7	−	5.00615e7i	−0.721071	−	0.721071i
$412$	−2.46864e7	+	9.22743e7i	−0.352993	+	1.31944i
$413$	1.35869e7	+	1.35869e7i	0.192873	+	0.192873i
$414$	2.30791e7	−	1.77164e7i	0.325251	−	0.249674i
$415$		−	1.44650e7i		−	0.202383i
$416$	1.69809e7	−	2.21745e7i	0.235874	−	0.308017i
$417$	−7.66304e7			−1.05680
$418$	1.03155e8	+	1.34380e8i	1.41241	+	1.83995i
$419$	1.00557e8	−	1.00557e8i	1.36701	−	1.36701i	0.502341	−	0.864669i	$-0.332472\pi$
$419$	1.00557e8	−	1.00557e8i	1.36701	−	1.36701i	0.864669	−	0.502341i	$-0.167528\pi$
$420$	4.42032e7	+	1.18258e7i	0.596631	+	0.159618i
$421$	6.79990e7	−	6.79990e7i	0.911289	−	0.911289i	−0.0850844	−	0.996374i	$-0.527116\pi$
$421$	6.79990e7	−	6.79990e7i	0.911289	−	0.911289i	0.996374	+	0.0850844i	$0.0271160\pi$
$422$	1.02168e8	+	1.34305e7i	1.35950	+	0.178713i
$423$	1.43847e7			0.190055
$424$	1.26221e7	−	3.05228e7i	0.165590	−	0.400430i
$425$			3.82481e6i			0.0498245i
$426$	6.43864e7	+	8.46390e6i	0.832847	+	0.109482i
$427$	−2.30368e7	−	2.30368e7i	−0.295895	−	0.295895i
$428$	−1.26767e8	+	7.32549e7i	−1.61687	+	0.934340i
$429$	2.11793e7	+	2.11793e7i	0.268250	+	0.268250i
$430$	−5.87254e7	−	7.65016e7i	−0.738619	−	0.962200i
$431$		−	8.48038e7i		−	1.05921i	−0.848243	−	0.529607i	$-0.822340\pi$
$431$		−	8.48038e7i		−	1.05921i	0.848243	−	0.529607i	$-0.177660\pi$
$432$	−4.02739e6	−	1.49838e7i	−0.0499542	−	0.185854i
$433$	1.35872e8			1.67366			0.836830	−	0.547463i	$-0.184406\pi$
$433$	1.35872e8			1.67366			0.836830	+	0.547463i	$0.184406\pi$
$434$	−1.12288e8	+	8.61965e7i	−1.37362	+	1.05444i
$435$	−5.42239e7	+	5.42239e7i	−0.658753	+	0.658753i
$436$	1.66610e7	−	9.62785e6i	0.201021	−	0.116164i
$437$	−9.94124e7	+	9.94124e7i	−1.19123	+	1.19123i
$438$	−5.68770e6	+	4.32674e7i	−0.0676885	+	0.514918i
$439$	−2.21120e7			−0.261357			−0.130679	−	0.991425i	$-0.541716\pi$
$439$	−2.21120e7			−0.261357			−0.130679	+	0.991425i	$0.541716\pi$
$440$	−1.44364e8	+	5.98962e7i	−1.69473	+	0.703139i
$441$			712770.i			0.00831063i
$442$	1.25316e6	−	9.53300e6i	0.0145124	−	0.110398i
$443$	−1.39108e7	−	1.39108e7i	−0.160008	−	0.160008i	0.622562	−	0.782570i	$-0.286092\pi$
$443$	−1.39108e7	−	1.39108e7i	−0.160008	−	0.160008i	−0.782570	+	0.622562i	$0.786092\pi$
$444$	1.52670e7	+	4.08443e6i	0.174424	+	0.0466641i
$445$	8.43634e7	+	8.43634e7i	0.957357	+	0.957357i
$446$	2.20758e7	−	1.69462e7i	0.248835	−	0.191015i
$447$			2.52228e7i			0.282404i
$448$	6.27090e7	−	6.28553e7i	0.697422	−	0.699050i
$449$	3.72059e7			0.411029			0.205515	−	0.978654i	$-0.434113\pi$
$449$	3.72059e7			0.411029			0.205515	+	0.978654i	$0.434113\pi$
$450$	−3.21083e6	−	4.18276e6i	−0.0352355	−	0.0459013i
$451$	1.24409e8	−	1.24409e8i	1.35620	−	1.35620i
$452$	−2.03998e7	+	7.62515e7i	−0.220907	+	0.825721i
$453$	2.27818e7	−	2.27818e7i	0.245071	−	0.245071i
$454$	−9.41671e7	−	1.23787e7i	−1.00631	−	0.132284i
$455$	−3.90927e7			−0.415013
$456$	2.87315e7	+	6.92497e7i	0.303014	+	0.730337i
$457$			1.71918e8i			1.80124i	0.434603	+	0.900622i	$0.356889\pi$
$457$			1.71918e8i			1.80124i	−0.434603	+	0.900622i	$0.643111\pi$
$458$	1.05453e8	+	1.38623e7i	1.09765	+	0.144291i
$459$	−3.77694e6	−	3.77694e6i	−0.0390573	−	0.0390573i
$460$	−6.48983e7	−	1.12306e8i	−0.666745	−	1.15380i
$461$	−5.67322e7	−	5.67322e7i	−0.579064	−	0.579064i	0.355581	−	0.934645i	$-0.384283\pi$
$461$	−5.67322e7	−	5.67322e7i	−0.579064	−	0.579064i	−0.934645	+	0.355581i	$0.884283\pi$
$462$	5.79791e7	+	7.55294e7i	0.587957	+	0.765932i
$463$			1.56654e8i			1.57833i	0.614180	+	0.789166i	$0.289487\pi$
$463$			1.56654e8i			1.57833i	−0.614180	+	0.789166i	$0.710513\pi$
$464$	3.86231e7	+	1.43696e8i	0.386628	+	1.43844i
$465$	1.10282e8			1.09684
$466$	7.87138e7	−	6.04235e7i	0.777845	−	0.597102i
$467$	−1.11254e8	+	1.11254e8i	−1.09236	+	1.09236i	−0.0970811	+	0.995276i	$0.530951\pi$
$467$	−1.11254e8	+	1.11254e8i	−1.09236	+	1.09236i	−0.995276	+	0.0970811i	$0.969049\pi$
$468$	6.63228e6	+	1.14771e7i	0.0647031	+	0.111969i
$469$	2.56804e7	−	2.56804e7i	0.248933	−	0.248933i
$470$	8.35816e6	−	6.35820e7i	0.0805039	−	0.612407i
$471$	2.19229e7			0.209814
$472$	−2.68420e7	−	1.11000e7i	−0.255263	−	0.105559i
$473$		−	2.00687e8i		−	1.89642i
$474$	9.49476e6	−	7.22283e7i	0.0891557	−	0.678223i
$475$	1.80170e7	+	1.80170e7i	0.168114	+	0.168114i
$476$	7.89956e6	−	2.95275e7i	0.0732457	−	0.273782i
$477$	1.10847e7	+	1.10847e7i	0.102134	+	0.102134i
$478$	2.15110e7	−	1.65126e7i	0.196959	−	0.151193i
$479$			4.71347e7i			0.428878i	0.976737	+	0.214439i	$0.0687924\pi$
$479$			4.71347e7i			0.428878i	−0.976737	+	0.214439i	$0.931208\pi$
$480$	−6.85702e7	+	9.09522e6i	−0.620029	+	0.0822412i
$481$	−1.35020e7			−0.121328
$482$	−3.77768e7	−	4.92119e7i	−0.337352	−	0.439469i
$483$	−5.58754e7	+	5.58754e7i	−0.495883	+	0.495883i
$484$	−2.04659e8	−	5.47529e7i	−1.80507	−	0.482916i
$485$	−4.43907e7	+	4.43907e7i	−0.389105	+	0.389105i
$486$	7.30105e6	+	959758.i	0.0636028	+	0.00836090i
$487$	−1.00829e8			−0.872972			−0.436486	−	0.899711i	$-0.643777\pi$
$487$	−1.00829e8			−0.872972			−0.436486	+	0.899711i	$0.643777\pi$
$488$	4.55109e7	+	1.88202e7i	0.391612	+	0.161944i
$489$		−	1.05159e7i		−	0.0899333i
$490$	3.15052e6	+	414152.i	0.0267790	+	0.00352023i
$491$	9.12387e7	+	9.12387e7i	0.770788	+	0.770788i	0.978244	−	0.207457i	$-0.0665185\pi$
$491$	9.12387e7	+	9.12387e7i	0.770788	+	0.770788i	−0.207457	+	0.978244i	$0.566519\pi$
$492$	6.74178e7	−	3.89586e7i	0.566082	−	0.327121i
$493$	3.62212e7	+	3.62212e7i	0.302289	+	0.302289i
$494$	−3.90028e7	−	5.08090e7i	−0.323530	−	0.421463i
$495$		−	7.41798e7i		−	0.611603i
$496$	1.06850e8	−	1.85403e8i	0.875650	−	1.51940i
$497$	−1.76373e8			−1.43669
$498$	1.05668e7	−	8.11146e6i	0.0855571	−	0.0656767i
$499$	7.61214e7	−	7.61214e7i	0.612640	−	0.612640i	−0.330994	−	0.943633i	$-0.607384\pi$
$499$	7.61214e7	−	7.61214e7i	0.612640	−	0.612640i	0.943633	+	0.330994i	$0.107384\pi$
$500$	9.68934e7	−	5.59917e7i	0.775147	−	0.447933i
$501$	−6.24953e6	+	6.24953e6i	−0.0496975	+	0.0496975i
$502$	−9.89879e6	+	7.53018e7i	−0.0782476	+	0.595243i
$503$	1.11499e8			0.876127			0.438063	−	0.898944i	$-0.355665\pi$
$503$	1.11499e8			0.876127			0.438063	+	0.898944i	$0.355665\pi$
$504$	1.61487e7	+	3.89223e7i	0.126138	+	0.304023i
$505$			8.76383e7i			0.680487i
$506$	3.51785e7	−	2.67609e8i	0.271535	−	2.06561i
$507$	4.51966e7	+	4.51966e7i	0.346802	+	0.346802i
$508$	1.77235e8	+	4.74161e7i	1.35194	+	0.361689i
$509$	7.40728e7	+	7.40728e7i	0.561701	+	0.561701i	0.929790	−	0.368089i	$-0.119988\pi$
$509$	7.40728e7	+	7.40728e7i	0.561701	+	0.561701i	−0.368089	+	0.929790i	$0.619988\pi$
$510$	−1.88891e7	+	1.44999e7i	−0.142397	+	0.109309i
$511$		−	1.18522e8i		−	0.888253i
$512$	−5.11460e7	+	1.24091e8i	−0.381067	+	0.924547i
$513$	−3.55831e7			−0.263567
$514$	−8.67974e7	−	1.13071e8i	−0.639171	−	0.832649i
$515$	−1.42911e8	+	1.42911e8i	−1.04627	+	1.04627i
$516$	2.29540e7	−	8.57988e7i	0.167074	−	0.624500i
$517$	9.43603e7	−	9.43603e7i	0.682838	−	0.682838i
$518$	−4.25563e7	−	5.59423e6i	−0.306179	−	0.0402486i
$519$	−1.33802e8			−0.957106
$520$	5.45839e7	−	2.26467e7i	0.388199	−	0.161062i
$521$			8.30371e7i			0.587163i	0.955934	+	0.293582i	$0.0948472\pi$
$521$			8.30371e7i			0.587163i	−0.955934	+	0.293582i	$0.905153\pi$
$522$	−7.00178e7	−	9.20418e6i	−0.492263	−	0.0647103i
$523$	8.42929e7	+	8.42929e7i	0.589231	+	0.589231i	0.937423	−	0.348192i	$-0.113204\pi$
$523$	8.42929e7	+	8.42929e7i	0.589231	+	0.589231i	−0.348192	+	0.937423i	$0.613204\pi$
$524$	−5.37580e7	−	9.30281e7i	−0.373636	−	0.646577i
$525$	1.01266e7	+	1.01266e7i	0.0699820	+	0.0699820i
$526$	6.19752e7	+	8.07352e7i	0.425854	+	0.554761i
$527$		−	7.36676e7i		−	0.503320i
$528$	−1.24709e8	−	7.18716e7i	−0.847220	−	0.488265i
$529$	7.59612e7			0.513127
$530$	5.54365e7	−	4.25551e7i	0.372365	−	0.285840i
$531$	9.74799e6	−	9.74799e6i	0.0651076	−	0.0651076i
$532$	−1.01880e8	−	1.76303e8i	−0.676633	−	1.17091i
$533$	−4.70390e7	+	4.70390e7i	−0.310653	+	0.310653i
$534$	−1.43202e7	+	1.08936e8i	−0.0940426	+	0.715399i
$535$	−3.09788e8			−2.02303
$536$	−2.09799e7	+	5.07335e7i	−0.136241	+	0.329459i
$537$		−	1.35117e8i		−	0.872541i
$538$	−2.61365e7	+	1.98825e8i	−0.167842	+	1.27680i
$539$	4.67561e6	+	4.67561e6i	0.0298587	+	0.0298587i
$540$	8.48447e6	−	3.17138e7i	0.0538820	−	0.201403i
$541$	−2.21061e8	−	2.21061e8i	−1.39611	−	1.39611i	−0.810826	−	0.585287i	$-0.800982\pi$
$541$	−2.21061e8	−	2.21061e8i	−1.39611	−	1.39611i	−0.585287	−	0.810826i	$-0.699018\pi$
$542$	2.56340e7	−	1.96776e7i	0.160997	−	0.123587i
$543$		−	8.23875e7i		−	0.514591i
$544$	6.07556e6	+	4.58045e7i	0.0377389	+	0.284519i
$545$	4.07152e7			0.251517
$546$	−2.19218e7	−	2.85575e7i	−0.134678	−	0.175446i
$547$	−1.41321e8	+	1.41321e8i	−0.863464	+	0.863464i	−0.991739	−	0.128275i	$-0.959056\pi$
$547$	−1.41321e8	+	1.41321e8i	−0.863464	+	0.863464i	0.128275	+	0.991739i	$0.459056\pi$
$548$	−2.80792e8	−	7.51210e7i	−1.70625	−	0.456478i
$549$	−1.65279e7	+	1.65279e7i	−0.0998848	+	0.0998848i
$550$	−4.85002e7	−	6.37558e6i	−0.291511	−	0.0383206i
$551$	3.41246e8			2.03992
$552$	4.56481e7	−	1.10386e8i	0.271397	−	0.656292i
$553$			1.97855e8i			1.16996i
$554$	3.04726e7	+	4.00577e6i	0.179217	+	0.0235590i
$555$	2.36451e7	+	2.36451e7i	0.138313	+	0.138313i
$556$	−2.72403e8	+	1.57413e8i	−1.58485	+	0.915832i
$557$	−4.48748e7	−	4.48748e7i	−0.259679	−	0.259679i	0.565244	−	0.824924i	$-0.308782\pi$
$557$	−4.48748e7	−	4.48748e7i	−0.259679	−	0.259679i	−0.824924	+	0.565244i	$0.808782\pi$
$558$	6.18421e7	+	8.05618e7i	0.355944	+	0.463689i
$559$			7.58793e7i			0.434398i
$560$	1.81424e8	−	4.87635e7i	1.03307	−	0.277671i
$561$	−4.95517e7			−0.280653
$562$	1.90777e7	−	1.46448e7i	0.107478	−	0.0825037i
$563$	6.88093e7	−	6.88093e7i	0.385586	−	0.385586i	−0.487523	−	0.873110i	$-0.662100\pi$
$563$	6.88093e7	−	6.88093e7i	0.385586	−	0.385586i	0.873110	+	0.487523i	$0.162100\pi$
$564$	5.11341e7	−	2.95488e7i	0.285019	−	0.164703i
$565$	−1.18096e8	+	1.18096e8i	−0.654770	+	0.654770i
$566$	1.03822e7	−	7.89795e7i	0.0572588	−	0.435577i
$567$	−1.99997e7			−0.109717
$568$	2.46264e8	−	1.02174e8i	1.34387	−	0.557566i
$569$		−	2.18716e7i		−	0.118726i	−0.998236	−	0.0593628i	$-0.981093\pi$
$569$		−	2.18716e7i		−	0.118726i	0.998236	−	0.0593628i	$-0.0189069\pi$
$570$	−2.06754e7	+	1.57281e8i	−0.111642	+	0.849282i
$571$	6.28910e7	+	6.28910e7i	0.337816	+	0.337816i	0.855545	−	0.517729i	$-0.173222\pi$
$571$	6.28910e7	+	6.28910e7i	0.337816	+	0.337816i	−0.517729	+	0.855545i	$0.673222\pi$
$572$	1.18793e8	+	3.17811e7i	0.634753	+	0.169817i
$573$	8.24987e7	+	8.24987e7i	0.438514	+	0.438514i
$574$	−1.67750e8	+	1.28771e8i	−0.887006	+	0.680897i
$575$		−	4.05962e7i		−	0.213541i
$576$	−4.50959e7	−	4.49909e7i	−0.235977	−	0.235427i
$577$	1.05532e8			0.549359			0.274680	−	0.961536i	$-0.411428\pi$
$577$	1.05532e8			0.549359			0.274680	+	0.961536i	$0.411428\pi$
$578$	−1.07896e8	−	1.40556e8i	−0.558756	−	0.727892i
$579$	−2.03499e7	+	2.03499e7i	−0.104840	+	0.104840i
$580$	−8.13670e7	+	3.04138e8i	−0.417027	+	1.55879i
$581$	−2.55827e7	+	2.55827e7i	−0.130442	+	0.130442i
$582$	−5.73206e7	−	7.53507e6i	−0.290765	−	0.0382224i
$583$	1.45427e8			0.733902
$584$	6.86606e7	+	1.65489e8i	0.344722	+	0.830863i
$585$			2.80472e7i			0.140095i
$586$	−1.22466e7	−	1.60987e6i	−0.0608586	−	0.00800015i
$587$	2.86519e6	+	2.86519e6i	0.0141657	+	0.0141657i	0.714154	−	0.699988i	$-0.246812\pi$
$587$	2.86519e6	+	2.86519e6i	0.0141657	+	0.0141657i	−0.699988	+	0.714154i	$0.746812\pi$
$588$	1.46416e6	+	2.53373e6i	0.00720206	+	0.0124631i
$589$	−3.47016e8	−	3.47016e8i	−1.69826	−	1.69826i
$590$	−3.74232e7	−	4.87512e7i	−0.182215	−	0.237372i
$591$		−	1.10591e8i		−	0.535743i
$592$	6.26608e7	−	1.68421e7i	0.302017	−	0.0811767i
$593$	7.90158e7			0.378922			0.189461	−	0.981888i	$-0.439326\pi$
$593$	7.90158e7			0.378922			0.189461	+	0.981888i	$0.439326\pi$
$594$	5.41890e7	−	4.15974e7i	0.258554	−	0.198475i
$595$	4.57311e7	−	4.57311e7i	0.217101	−	0.217101i
$596$	5.18122e7	+	8.96610e7i	0.244734	+	0.423511i
$597$	−4.30119e7	+	4.30119e7i	−0.202146	+	0.202146i
$598$	−1.33009e7	+	1.01182e8i	−0.0621982	+	0.473153i
$599$	3.85910e8			1.79558			0.897792	−	0.440419i	$-0.145170\pi$
$599$	3.85910e8			1.79558			0.897792	+	0.440419i	$0.145170\pi$
$600$	−2.00059e7	−	8.27305e6i	−0.0926198	−	0.0383011i
$601$		−	2.00376e8i		−	0.923044i	−0.887129	−	0.461522i	$-0.847303\pi$
$601$		−	2.00376e8i		−	0.923044i	0.887129	−	0.461522i	$-0.152697\pi$
$602$	−3.14389e7	+	2.39161e8i	−0.144104	+	1.09623i
$603$	−1.84245e7	−	1.84245e7i	−0.0840320	−	0.0840320i
$604$	3.41857e7	−	1.27782e8i	0.155144	−	0.579906i
$605$	−3.16968e8	−	3.16968e8i	−1.43136	−	1.43136i
$606$	−6.40205e7	+	4.91445e7i	−0.287675	+	0.220829i
$607$		−	1.61943e7i		−	0.0724094i	−0.999344	−	0.0362047i	$-0.988473\pi$
$607$		−	1.61943e7i		−	0.0724094i	0.999344	−	0.0362047i	$-0.0115268\pi$
$608$	2.44385e8	+	1.87146e8i	1.08734	+	0.832665i
$609$	1.91799e8			0.849172
$610$	6.34515e7	+	8.26583e7i	0.279545	+	0.364164i
$611$	−3.56775e7	+	3.56775e7i	−0.156412	+	0.156412i
$612$	−2.11846e7	−	5.66758e6i	−0.0924201	−	0.0247254i
$613$	1.23680e8	−	1.23680e8i	0.536932	−	0.536932i	−0.385695	−	0.922626i	$-0.626038\pi$
$613$	1.23680e8	−	1.23680e8i	0.536932	−	0.536932i	0.922626	+	0.385695i	$0.126038\pi$
$614$	3.76421e8	+	4.94823e7i	1.62618	+	0.213769i
$615$	1.64752e8			0.708282
$616$	3.61253e8	+	1.49389e8i	1.54550	+	0.639112i
$617$		−	9.47161e7i		−	0.403244i	−0.979463	−	0.201622i	$-0.935379\pi$
$617$		−	9.47161e7i		−	0.403244i	0.979463	−	0.201622i	$-0.0646213\pi$
$618$	−1.84538e8	−	2.42584e7i	−0.781843	−	0.102777i
$619$	9.92581e7	+	9.92581e7i	0.418499	+	0.418499i	0.884686	−	0.466187i	$-0.154373\pi$
$619$	9.92581e7	+	9.92581e7i	0.418499	+	0.418499i	−0.466187	+	0.884686i	$0.654373\pi$
$620$	3.92025e8	−	2.26539e8i	1.64490	−	0.950534i
$621$	4.00881e7	+	4.00881e7i	0.167394	+	0.167394i
$622$	−3.53192e7	−	4.60103e7i	−0.146771	−	0.191198i
$623$		−	2.98408e8i		−	1.23409i
$624$	4.71523e7	+	2.71745e7i	0.194066	+	0.111843i
$625$	2.79165e8			1.14346
$626$	−3.71948e7	+	2.85521e7i	−0.151621	+	0.116390i
$627$	−2.33417e8	+	2.33417e8i	−0.946955	+	0.946955i
$628$	7.79306e7	−	4.50337e7i	0.314651	−	0.181827i
$629$	1.57948e7	−	1.57948e7i	0.0634690	−	0.0634690i
$630$	−1.16207e7	+	8.84010e7i	−0.0464742	+	0.353538i
$631$	−1.48727e8			−0.591975			−0.295987	−	0.955192i	$-0.595649\pi$
$631$	−1.48727e8			−0.591975			−0.295987	+	0.955192i	$0.595649\pi$
$632$	−1.14619e8	−	2.76258e8i	−0.454050	−	1.09437i
$633$			2.00793e8i			0.791659i
$634$	−2.09678e7	+	1.59505e8i	−0.0822781	+	0.625904i
$635$	2.74495e8	+	2.74495e8i	1.07205	+	1.07205i
$636$	6.21737e7	+	1.66335e7i	0.241677	+	0.0646565i
$637$	−1.76784e6	−	1.76784e6i	−0.00683950	−	0.00683950i
$638$	−5.19678e8	+	3.98923e8i	−2.00111	+	1.53613i
$639$			1.26540e8i			0.484981i
$640$	−2.25067e8	+	1.73187e8i	−0.858563	+	0.660656i
$641$	1.07227e8			0.407127			0.203564	−	0.979062i	$-0.434748\pi$
$641$	1.07227e8			0.407127			0.203564	+	0.979062i	$0.434748\pi$
$642$	−1.73718e8	−	2.26302e8i	−0.656507	−	0.855232i
$643$	−1.39954e8	+	1.39954e8i	−0.526444	+	0.526444i	−0.919510	−	0.393067i	$-0.871414\pi$
$643$	−1.39954e8	+	1.39954e8i	−0.526444	+	0.526444i	0.393067	+	0.919510i	$0.371414\pi$
$644$	−8.38453e7	+	3.13402e8i	−0.313921	+	1.17339i
$645$	1.32882e8	−	1.32882e8i	0.495208	−	0.495208i
$646$	1.05063e8	+	1.38110e7i	0.389719	+	0.0512305i
$647$	1.74204e8			0.643198			0.321599	−	0.946876i	$-0.395780\pi$
$647$	1.74204e8			0.643198			0.321599	+	0.946876i	$0.395780\pi$
$648$	2.79250e7	−	1.15860e7i	0.102628	−	0.0425802i
$649$		−	1.27889e8i		−	0.467842i
$650$	1.83378e7	+	2.41060e6i	0.0667741	+	0.00877778i
$651$	−1.95043e8	−	1.95043e8i	−0.706948	−	0.706948i
$652$	−2.16016e7	−	3.73815e7i	−0.0779369	−	0.134870i
$653$	2.12946e8	+	2.12946e8i	0.764769	+	0.764769i	0.977180	−	0.212411i	$-0.0681316\pi$
$653$	2.12946e8	+	2.12946e8i	0.764769	+	0.764769i	−0.212411	+	0.977180i	$0.568132\pi$
$654$	2.28316e7	+	2.97428e7i	0.0816214	+	0.106328i
$655$		−	2.27337e8i		−	0.808997i
$656$	1.59626e8	−	2.76977e8i	0.565447	−	0.981143i
$657$	−8.50342e7			−0.299846
$658$	−1.27233e8	+	9.76683e7i	−0.446602	+	0.342828i
$659$	−1.00416e8	+	1.00416e8i	−0.350870	+	0.350870i	−0.860433	−	0.509563i	$-0.829807\pi$
$659$	−1.00416e8	+	1.00416e8i	−0.350870	+	0.350870i	0.509563	+	0.860433i	$0.329807\pi$
$660$	−1.52379e8	−	2.63691e8i	−0.530020	−	0.917199i
$661$	−1.71149e8	+	1.71149e8i	−0.592611	+	0.592611i	−0.938336	−	0.345725i	$-0.887633\pi$
$661$	−1.71149e8	+	1.71149e8i	−0.592611	+	0.592611i	0.345725	+	0.938336i	$0.387633\pi$
$662$	−6.72035e7	+	5.11229e8i	−0.231642	+	1.76214i
$663$	1.87354e7			0.0642869
$664$	2.09000e7	−	5.05405e7i	0.0713909	−	0.172637i
$665$		−	4.30839e8i		−	1.46504i
$666$	−4.01361e6	+	3.05322e7i	−0.0135867	+	0.103356i
$667$	−3.84449e8	−	3.84449e8i	−1.29557	−	1.29557i
$668$	−9.37789e6	+	3.50532e7i	−0.0314612	+	0.117598i
$669$	3.83454e7	+	3.83454e7i	0.128066	+	0.128066i
$670$	−9.21439e7	+	7.07330e7i	−0.306367	+	0.235178i
$671$			2.16838e8i			0.717740i
$672$	1.37358e8	+	1.05187e8i	0.452634	+	0.346620i
$673$	−4.72365e8			−1.54965			−0.774823	−	0.632178i	$-0.782161\pi$
$673$	−4.72365e8			−1.54965			−0.774823	+	0.632178i	$0.782161\pi$
$674$	−2.78036e8	−	3.62198e8i	−0.908075	−	1.18295i
$675$	7.26539e6	−	7.26539e6i	0.0236237	−	0.0236237i
$676$	2.53505e8	+	6.78209e7i	0.820629	+	0.219545i
$677$	−1.35510e8	+	1.35510e8i	−0.436721	+	0.436721i	−0.890907	−	0.454186i	$-0.849930\pi$
$677$	−1.35510e8	+	1.35510e8i	−0.436721	+	0.436721i	0.454186	+	0.890907i	$0.349930\pi$
$678$	−1.52494e8	−	2.00460e7i	−0.489286	−	0.0643191i
$679$	1.57018e8			0.501580
$680$	−3.73605e7	+	9.03452e7i	−0.118819	+	0.287328i
$681$		−	1.85069e8i		−	0.585992i
$682$	9.34136e8	+	1.22797e8i	2.94481	+	0.387109i
$683$	1.86498e8	+	1.86498e8i	0.585344	+	0.585344i	0.936367	−	0.351023i	$-0.114166\pi$
$683$	1.86498e8	+	1.86498e8i	0.585344	+	0.585344i	−0.351023	+	0.936367i	$0.614166\pi$
$684$	−1.26489e8	+	7.30942e7i	−0.395262	+	0.228410i
$685$	−4.34881e8	−	4.34881e8i	−1.35300	−	1.35300i
$686$	−1.98949e8	−	2.59171e8i	−0.616268	−	0.802813i
$687$			2.07249e8i			0.639178i
$688$	−9.46505e7	−	3.52146e8i	−0.290642	−	1.08133i
$689$	−5.49856e7			−0.168109
$690$	2.00487e8	−	1.53901e8i	0.610293	−	0.468483i
$691$	2.83368e8	−	2.83368e8i	0.858849	−	0.858849i	−0.132354	−	0.991203i	$-0.542254\pi$
$691$	2.83368e8	−	2.83368e8i	0.858849	−	0.858849i	0.991203	+	0.132354i	$0.0422535\pi$
$692$	−4.75633e8	+	2.74853e8i	−1.43534	+	0.829436i
$693$	−1.31194e8	+	1.31194e8i	−0.394196	+	0.394196i
$694$	1.96975e7	−	1.49842e8i	0.0589293	−	0.448286i
$695$	−6.65684e8			−1.98296
$696$	−2.67803e8	+	1.11111e8i	−0.794307	+	0.329555i
$697$		−	1.10054e8i		−	0.325017i
$698$	8.57291e7	−	6.52157e8i	0.252094	−	1.91772i
$699$	1.36725e8	+	1.36725e8i	0.400328	+	0.400328i
$700$	5.67996e7	+	1.51957e7i	0.165596	+	0.0443024i
$701$	−2.30227e8	−	2.30227e8i	−0.668347	−	0.668347i	0.288986	−	0.957333i	$-0.406682\pi$
$701$	−2.30227e8	−	2.30227e8i	−0.668347	−	0.668347i	−0.957333	+	0.288986i	$0.906682\pi$
$702$	−2.04888e7	+	1.57279e7i	−0.0592249	+	0.0454631i
$703$		−	1.48805e8i		−	0.428303i
$704$	−5.90948e8	+	688949.i	−1.69368	+	0.00197455i
$705$	1.24959e8			0.356615
$706$	−1.58679e8	−	2.06711e8i	−0.450926	−	0.587421i
$707$	1.54996e8	−	1.54996e8i	0.438594	−	0.438594i
$708$	1.46276e7	−	5.46759e7i	0.0412167	−	0.154062i
$709$	4.24526e7	−	4.24526e7i	0.119115	−	0.119115i	−0.645037	−	0.764152i	$-0.723158\pi$
$709$	4.24526e7	−	4.24526e7i	0.119115	−	0.119115i	0.764152	+	0.645037i	$0.223158\pi$
$710$	5.59320e8	+	7.35254e7i	1.56274	+	0.205429i
$711$	1.41952e8			0.394941
$712$	1.72870e8	+	4.16658e8i	0.478938	+	1.15436i
$713$			7.81902e8i			2.15717i
$714$	5.90514e7	+	7.76259e6i	0.162232	+	0.0213261i
$715$	1.83983e8	+	1.83983e8i	0.503339	+	0.503339i
$716$	−2.77554e8	−	4.80307e8i	−0.756151	−	1.30852i
$717$	3.73642e7	+	3.73642e7i	0.101367	+	0.101367i
$718$	−5.55233e7	−	7.23302e7i	−0.150004	−	0.195410i
$719$			2.52511e8i			0.679351i	0.940543	+	0.339676i	$0.110317\pi$
$719$			2.52511e8i			0.679351i	−0.940543	+	0.339676i	$0.889683\pi$
$720$	−3.49856e7	−	1.30163e8i	−0.0937330	−	0.348732i
$721$	5.05503e8			1.34871
$722$	2.61417e8	−	2.00673e8i	0.694579	−	0.533184i
$723$	8.54803e7	−	8.54803e7i	0.226178	−	0.226178i
$724$	−1.69239e8	−	2.92868e8i	−0.445949	−	0.771713i
$725$	−6.96758e7	+	6.96758e7i	−0.182839	+	0.182839i
$726$	5.38035e7	−	4.09293e8i	0.140605	−	1.06961i
$727$	−5.00217e8			−1.30183			−0.650916	−	0.759150i	$-0.725615\pi$
$727$	−5.00217e8			−1.30183			−0.650916	+	0.759150i	$0.725615\pi$
$728$	−1.36589e8	−	5.64838e7i	−0.354015	−	0.146396i
$729$			1.43489e7i			0.0370370i
$730$	−4.94087e7	+	3.75861e8i	−0.127009	+	0.966181i
$731$	−8.87646e7	−	8.87646e7i	−0.227241	−	0.227241i
$732$	−2.48013e7	+	9.27037e7i	−0.0632326	+	0.236355i
$733$	3.76387e8	+	3.76387e8i	0.955703	+	0.955703i	0.999060	−	0.0433569i	$-0.0138053\pi$
$733$	3.76387e8	+	3.76387e8i	0.955703	+	0.955703i	−0.0433569	+	0.999060i	$0.513805\pi$
$734$	−4.22970e7	+	3.24687e7i	−0.106960	+	0.0821063i
$735$			6.19179e6i			0.0155939i
$736$	−6.44854e7	−	4.86165e8i	−0.161744	−	1.21941i
$737$	−2.41721e8			−0.603826
$738$	9.23872e7	+	1.20353e8i	0.229849	+	0.299425i
$739$	−1.52550e8	+	1.52550e8i	−0.377989	+	0.377989i	−0.870376	−	0.492387i	$-0.836124\pi$
$739$	−1.52550e8	+	1.52550e8i	−0.377989	+	0.377989i	0.492387	+	0.870376i	$0.336124\pi$
$740$	1.32624e8	+	3.54812e7i	0.327285	+	0.0875595i
$741$	8.82544e7	−	8.82544e7i	0.216911	−	0.216911i
$742$	−1.73307e8	−	2.27820e7i	−0.424233	−	0.0557674i
$743$	−5.90150e8			−1.43878			−0.719392	−	0.694604i	$-0.755580\pi$
$743$	−5.90150e8			−1.43878			−0.719392	+	0.694604i	$0.755580\pi$
$744$	3.85322e8	+	1.59343e8i	0.935632	+	0.386913i
$745$			2.19109e8i			0.529897i
$746$	−3.51149e8	−	4.61602e7i	−0.845813	−	0.111186i
$747$	1.83544e7	+	1.83544e7i	0.0440330	+	0.0440330i
$748$	−1.76144e8	+	1.01788e8i	−0.420885	+	0.243216i
$749$	5.47887e8	+	5.47887e8i	1.30390	+	1.30390i
$750$	1.32780e8	+	1.72972e8i	0.314737	+	0.410008i
$751$			9.72140e7i			0.229514i	0.993394	+	0.114757i	$0.0366089\pi$
$751$			9.72140e7i			0.229514i	−0.993394	+	0.114757i	$0.963391\pi$
$752$	1.21071e8	−	2.10078e8i	0.284699	−	0.494000i
$753$	−1.47992e8			−0.346620
$754$	1.96489e8	−	1.50832e8i	0.458379	−	0.351868i
$755$	1.97904e8	−	1.97904e8i	0.459847	−	0.459847i
$756$	−7.10942e7	+	4.10831e7i	−0.164539	+	0.0950819i
$757$	−9.05372e7	+	9.05372e7i	−0.208708	+	0.208708i	−0.803718	−	0.595010i	$-0.797148\pi$
$757$	−9.05372e7	+	9.05372e7i	−0.208708	+	0.208708i	0.595010	+	0.803718i	$0.297148\pi$
$758$	5.30217e7	−	4.03346e8i	0.121744	−	0.926125i
$759$	5.25937e8			1.20284
$760$	2.49588e8	+	6.01567e8i	0.568569	+	1.37039i
$761$			1.81374e8i			0.411549i	0.978599	+	0.205774i	$0.0659713\pi$
$761$			1.81374e8i			0.411549i	−0.978599	+	0.205774i	$0.934029\pi$
$762$	−4.65940e7	+	3.54448e8i	−0.105309	+	0.801103i
$763$	−7.20085e7	−	7.20085e7i	−0.162110	−	0.162110i
$764$	4.62730e8	+	1.23796e8i	1.03764	+	0.277603i
$765$	−3.28100e7	−	3.28100e7i	−0.0732862	−	0.0732862i
$766$	2.72357e7	−	2.09071e7i	0.0605971	−	0.0465165i
$767$			4.83546e7i			0.107165i
$768$	−2.52724e8	−	6.72964e7i	−0.557909	−	0.148562i
$769$	3.12737e8			0.687701			0.343851	−	0.939024i	$-0.388269\pi$
$769$	3.12737e8			0.687701			0.343851	+	0.939024i	$0.388269\pi$
$770$	5.03660e8	+	6.56119e8i	1.10323	+	1.43718i
$771$	1.96403e8	−	1.96403e8i	0.428533	−	0.428533i
$772$	−3.05365e7	+	1.14141e8i	−0.0663693	+	0.248079i
$773$	5.33319e8	−	5.33319e8i	1.15464	−	1.15464i	0.169035	−	0.985610i	$-0.445935\pi$
$773$	5.33319e8	−	5.33319e8i	1.15464	−	1.15464i	0.985610	−	0.169035i	$-0.0540650\pi$
$774$	1.71587e8	+	2.25560e7i	0.370052	+	0.0486451i
$775$	1.41708e8			0.304432
$776$	−2.19239e8	+	9.09616e7i	−0.469173	+	0.194658i
$777$		−	8.36368e7i		−	0.178293i
$778$	−3.15642e8	−	4.14927e7i	−0.670280	−	0.0881115i
$779$	−5.18415e8	−	5.18415e8i	−1.09664	−	1.09664i
$780$	5.76142e7	+	9.97011e7i	0.121407	+	0.210095i
$781$	8.30072e8	+	8.30072e8i	1.74246	+	1.74246i
$782$	−1.02805e8	−	1.33924e8i	−0.214978	−	0.280052i
$783$		−	1.37608e8i		−	0.286653i
$784$	1.04095e7	+	5.99913e6i	0.0216013	+	0.0124492i
$785$	1.90443e8			0.393691
$786$	1.66072e8	−	1.27483e8i	0.342002	−	0.262533i
$787$	−2.52168e7	+	2.52168e7i	−0.0517328	+	0.0517328i	−0.732500	−	0.680767i	$-0.761647\pi$
$787$	−2.52168e7	+	2.52168e7i	−0.0517328	+	0.0517328i	0.680767	+	0.732500i	$0.261647\pi$
$788$	−2.27174e8	−	3.93124e8i	−0.464280	−	0.803435i
$789$	−1.40236e8	+	1.40236e8i	−0.285515	+	0.285515i
$790$	8.24804e7	−	6.27443e8i	0.167290	−	1.27260i
$791$	4.17726e8			0.844037
$792$	1.07180e8	−	2.59183e8i	0.215744	−	0.521711i
$793$		−	8.19859e7i		−	0.164407i
$794$	151778.	−	1.15460e6i	0.000303213	−	0.00230659i
$795$	9.62925e7	+	9.62925e7i	0.191642	+	0.191642i
$796$	−6.45426e7	+	2.41251e8i	−0.127970	+	0.478333i
$797$	−2.19556e7	−	2.19556e7i	−0.0433682	−	0.0433682i	0.685090	−	0.728458i	$-0.259763\pi$
$797$	−2.19556e7	−	2.19556e7i	−0.0433682	−	0.0433682i	−0.728458	+	0.685090i	$0.759763\pi$
$798$	3.14732e8	−	2.41599e8i	0.619344	−	0.475431i
$799$		−	8.34719e7i		−	0.163644i
$800$	−8.81104e7	+	1.16870e7i	−0.172091	+	0.0228263i
$801$	−2.14094e8			−0.416589
$802$	−4.76132e8	−	6.20258e8i	−0.923006	−	1.20240i
$803$	−5.57805e8	+	5.57805e8i	−1.07730	+	1.07730i
$804$	−1.03342e8	−	2.76474e7i	−0.198842	−	0.0531969i
$805$	−4.85386e8	+	4.85386e8i	−0.930464	+	0.930464i
$806$	−3.53195e8	−	4.64292e7i	−0.674543	−	0.0886719i
$807$	−3.90755e8			−0.743505
$808$	−1.26626e8	+	3.06206e8i	−0.240043	+	0.580471i
$809$			4.91857e7i			0.0928951i	0.998921	+	0.0464476i	$0.0147900\pi$
$809$			4.91857e7i			0.0928951i	−0.998921	+	0.0464476i	$0.985210\pi$
$810$	6.34237e7	+	8.33736e6i	0.119343	+	0.0156882i
$811$	−1.05349e8	−	1.05349e8i	−0.197501	−	0.197501i	0.601427	−	0.798928i	$-0.294599\pi$
$811$	−1.05349e8	−	1.05349e8i	−0.197501	−	0.197501i	−0.798928	+	0.601427i	$0.794599\pi$
$812$	6.81801e8	−	3.93991e8i	1.27347	−	0.735899i
$813$	4.45259e7	+	4.45259e7i	0.0828592	+	0.0828592i
$814$	1.73956e8	+	2.26613e8i	0.322527	+	0.420156i
$815$		−	9.13510e7i		−	0.168749i
$816$	−8.69484e7	+	2.33702e7i	−0.160026	+	0.0430123i
$817$	−8.36264e8			−1.53348
$818$	−7.37299e8	+	5.65977e8i	−1.34705	+	1.03404i
$819$	4.96040e7	−	4.96040e7i	0.0902953	−	0.0902953i
$820$	5.85654e8	−	3.38431e8i	1.06218	−	0.613803i
$821$	−1.42572e8	+	1.42572e8i	−0.257635	+	0.257635i	−0.824091	−	0.566457i	$-0.808314\pi$
$821$	−1.42572e8	+	1.42572e8i	−0.257635	+	0.257635i	0.566457	+	0.824091i	$0.308314\pi$
$822$	7.38184e7	−	5.61550e8i	0.132907	−	1.01105i
$823$	8.79812e8			1.57830			0.789152	−	0.614199i	$-0.210521\pi$
$823$	8.79812e8			1.57830			0.789152	+	0.614199i	$0.210521\pi$
$824$	−7.05817e8	+	2.92841e8i	−1.26157	+	0.523420i
$825$		−	9.53184e7i		−	0.169752i
$826$	−2.00347e7	+	1.52407e8i	−0.0355502	+	0.270436i
$827$	−2.06154e8	−	2.06154e8i	−0.364481	−	0.364481i	0.500979	−	0.865460i	$-0.332973\pi$
$827$	−2.06154e8	−	2.06154e8i	−0.364481	−	0.364481i	−0.865460	+	0.500979i	$0.832973\pi$
$828$	2.24852e8	+	6.01552e7i	0.396100	+	0.105970i
$829$	−2.98660e7	−	2.98660e7i	−0.0524219	−	0.0524219i	0.680410	−	0.732832i	$-0.261802\pi$
$829$	−2.98660e7	−	2.98660e7i	−0.0524219	−	0.0524219i	−0.732832	+	0.680410i	$0.761802\pi$
$830$	9.17932e7	−	7.04638e7i	0.160537	−	0.123234i
$831$			5.98884e7i			0.104361i
$832$	2.23436e8	−	260490.i	0.387957	−	0.000452295i
$833$	4.13608e6			0.00715573
$834$	−3.73292e8	−	4.86288e8i	−0.643503	−	0.838292i
$835$	−5.42893e7	+	5.42893e7i	−0.0932512	+	0.0932512i
$836$	−3.50259e8	+	1.30922e9i	−0.599474	+	2.24075i
$837$	−1.39935e8	+	1.39935e8i	−0.238643	+	0.238643i
$838$	1.12797e9	+	1.48277e8i	1.91675	+	0.251967i
$839$	−7.67224e8			−1.29908			−0.649541	−	0.760327i	$-0.725039\pi$
$839$	−7.67224e8			−1.29908			−0.649541	+	0.760327i	$0.725039\pi$
$840$	1.40283e8	+	3.38115e8i	0.236683	+	0.570462i
$841$			7.24847e8i			1.21859i
$842$	7.62759e8	+	1.00268e8i	1.27776	+	0.167968i
$843$	3.31378e7	+	3.31378e7i	0.0553147	+	0.0553147i
$844$	4.12466e8	+	7.13772e8i	0.686059	+	1.18722i
$845$	3.92620e8	+	3.92620e8i	0.650732	+	0.650732i
$846$	7.00726e7	+	9.12836e7i	0.115728	+	0.150759i
$847$			1.12117e9i			1.84511i
$848$	2.55181e8	−	6.85881e7i	0.418466	−	0.112476i
$849$	1.55220e8			0.253644
$850$	−2.42718e7	+	1.86319e7i	−0.0395226	+	0.0303389i
$851$	−1.67644e8	+	1.67644e8i	−0.272020	+	0.272020i
$852$	2.59936e8	+	4.49819e8i	0.420289	+	0.727309i
$853$	8.60861e8	−	8.60861e8i	1.38703	−	1.38703i	0.555542	−	0.831489i	$-0.312511\pi$
$853$	8.60861e8	−	8.60861e8i	1.38703	−	1.38703i	0.831489	−	0.555542i	$-0.187489\pi$
$854$	3.39690e7	−	2.58408e8i	0.0545393	−	0.414890i
$855$	−3.09108e8			−0.494552
$856$	−1.08239e9	−	4.47602e8i	−1.72569	−	0.713626i
$857$			5.10264e8i			0.810685i	0.914165	+	0.405343i	$0.132848\pi$
$857$			5.10264e8i			0.810685i	−0.914165	+	0.405343i	$0.867152\pi$
$858$	−3.12301e7	+	2.37573e8i	−0.0494437	+	0.376127i
$859$	−2.06652e8	−	2.06652e8i	−0.326032	−	0.326032i	0.525043	−	0.851076i	$-0.324049\pi$
$859$	−2.06652e8	−	2.06652e8i	−0.326032	−	0.326032i	−0.851076	+	0.525043i	$0.824049\pi$
$860$	1.99400e8	−	7.45329e8i	0.313494	−	1.17180i
$861$	−2.91379e8	−	2.91379e8i	−0.456509	−	0.456509i
$862$	5.38155e8	−	4.13107e8i	0.840205	−	0.644971i
$863$		−	1.09999e9i		−	1.71142i	−0.517456	−	0.855710i	$-0.673121\pi$
$863$		−	1.09999e9i		−	1.71142i	0.517456	−	0.855710i	$-0.326879\pi$
$864$	7.54668e7	−	9.85484e7i	0.117008	−	0.152795i
$865$	−1.16233e9			−1.79589
$866$	6.61878e8	+	8.62229e8i	1.01912	+	1.32761i
$867$	2.44144e8	−	2.44144e8i	0.374619	−	0.374619i
$868$	−1.09399e9	−	2.92677e8i	−1.67283	−	0.447537i
$869$	9.31171e8	−	9.31171e8i	1.41896	−	1.41896i
$870$	−6.08240e8	−	7.99561e7i	−0.923671	−	0.121421i
$871$	9.13943e7			0.138314
$872$	1.42258e8	+	5.88281e7i	0.214550	+	0.0887229i
$873$		−	1.12653e8i		−	0.169317i
$874$	−1.11513e9	−	1.46589e8i	−1.67029	−	0.219567i
$875$	−4.18772e8	−	4.18772e8i	−0.625106	−	0.625106i
$876$	−3.02276e8	+	1.74676e8i	−0.449668	+	0.259849i
$877$	9.87963e7	+	9.87963e7i	0.146468	+	0.146468i	0.776538	−	0.630070i	$-0.216974\pi$
$877$	9.87963e7	+	9.87963e7i	0.146468	+	0.146468i	−0.630070	+	0.776538i	$0.716974\pi$
$878$	−1.07715e8	−	1.40320e8i	−0.159144	−	0.207318i
$879$		−	2.40685e7i		−	0.0354390i
$880$	−1.08334e9	−	6.24344e8i	−1.58970	−	0.916170i
$881$	7.70267e8			1.12645			0.563227	−	0.826302i	$-0.309560\pi$
$881$	7.70267e8			1.12645			0.563227	+	0.826302i	$0.309560\pi$
$882$	−4.52316e6	+	3.47214e6i	−0.00659228	+	0.00506047i
$883$	8.65914e8	−	8.65914e8i	1.25775	−	1.25775i	0.305578	−	0.952167i	$-0.401150\pi$
$883$	8.65914e8	−	8.65914e8i	1.25775	−	1.25775i	0.952167	−	0.305578i	$-0.0988497\pi$
$884$	6.65998e7	−	3.84859e7i	0.0964087	−	0.0557115i
$885$	8.46802e7	−	8.46802e7i	0.122166	−	0.122166i
$886$	2.05123e7	−	1.56040e8i	0.0294925	−	0.224355i
$887$	−4.32770e8			−0.620136			−0.310068	−	0.950714i	$-0.600352\pi$
$887$	−4.32770e8			−0.620136			−0.310068	+	0.950714i	$0.600352\pi$
$888$	4.84514e7	+	1.16779e8i	0.0691938	+	0.166774i
$889$		−	9.70939e8i		−	1.38193i
$890$	−1.24398e8	+	9.46321e8i	−0.176459	+	1.34236i
$891$	9.41254e7	+	9.41254e7i	0.133068	+	0.133068i
$892$	2.15077e8	+	5.75401e7i	0.303039	+	0.0810729i
$893$	−3.93200e8	−	3.93200e8i	−0.552153	−	0.552153i
$894$	−1.60061e8	+	1.22868e8i	−0.224013	+	0.171960i
$895$		−	1.17375e9i		−	1.63722i
$896$	7.04348e8	+	9.17548e7i	0.979182	+	0.127557i
$897$	−1.98856e8			−0.275525
$898$	1.81242e8	+	2.36104e8i	0.250282	+	0.326043i
$899$	1.34199e9	−	1.34199e9i	1.84701	−	1.84701i
$900$	1.09023e7	−	4.07511e7i	0.0149551	−	0.0559000i
$901$	6.43228e7	−	6.43228e7i	0.0879409	−	0.0879409i
$902$	1.39553e9	+	1.83449e8i	1.90160	+	0.249974i
$903$	−4.70028e8			−0.638353
$904$	−5.83257e8	+	2.41991e8i	−0.789504	+	0.327563i
$905$		−	7.15695e8i		−	0.965567i
$906$	2.55548e8	+	3.35930e7i	0.343627	+	0.0451714i
$907$	1.78126e8	+	1.78126e8i	0.238729	+	0.238729i	0.816324	−	0.577595i	$-0.196009\pi$
$907$	1.78126e8	+	1.78126e8i	0.238729	+	0.238729i	−0.577595	+	0.816324i	$0.696009\pi$
$908$	−3.80165e8	−	6.57874e8i	−0.507825	−	0.878790i
$909$	−1.11203e8	−	1.11203e8i	−0.148055	−	0.148055i
$910$	−1.90433e8	−	2.48077e8i	−0.252708	−	0.329203i
$911$			1.02858e9i			1.36045i	0.733002	+	0.680226i	$0.238118\pi$
$911$			1.02858e9i			1.36045i	−0.733002	+	0.680226i	$0.761882\pi$
$912$	−2.99490e8	+	5.19664e8i	−0.394819	+	0.685075i
$913$	2.40801e8			0.316407
$914$	−1.09097e9	+	8.37468e8i	−1.42881	+	1.09681i
$915$	−1.43576e8	+	1.43576e8i	−0.187422	+	0.187422i
$916$	4.25727e8	+	7.36720e8i	0.553917	+	0.958552i
$917$	−4.02066e8	+	4.02066e8i	−0.521422	+	0.521422i
$918$	5.56931e6	−	4.23667e7i	0.00719902	−	0.0547642i
$919$	6.52230e7			0.0840339			0.0420169	−	0.999117i	$-0.486622\pi$
$919$	6.52230e7			0.0840339			0.0420169	+	0.999117i	$0.486622\pi$
$920$	3.96542e8	−	9.58917e8i	0.509243	−	1.23145i
$921$			7.39788e8i			0.946953i
$922$	8.36548e7	−	6.36377e8i	0.106733	−	0.811935i
$923$	−3.13849e8	−	3.13849e8i	−0.399131	−	0.399131i
$924$	−1.96866e8	+	7.35856e8i	−0.249548	+	0.932776i
$925$	3.03831e7	+	3.03831e7i	0.0383890	+	0.0383890i
$926$	−9.94107e8	+	7.63112e8i	−1.25199	+	0.961071i
$927$		−	3.62676e8i		−	0.455281i
$928$	−7.23735e8	+	9.45089e8i	−0.905598	+	1.18258i
$929$	−7.88148e8			−0.983016			−0.491508	−	0.870873i	$-0.663554\pi$
$929$	−7.88148e8			−0.983016			−0.491508	+	0.870873i	$0.663554\pi$
$930$	5.37218e8	+	6.99835e8i	0.667885	+	0.870055i
$931$	1.94833e7	−	1.94833e7i	0.0241442	−	0.0241442i
$932$	7.66881e8	+	2.05166e8i	0.947284	+	0.253430i
$933$	7.99193e7	−	7.99193e7i	0.0984027	−	0.0984027i
$934$	−1.24796e9	−	1.64050e8i	−1.53165	−	0.201343i
$935$	−4.30452e8			−0.526611
$936$	−4.05246e7	+	9.79965e7i	−0.0494186	+	0.119504i
$937$		−	5.31183e8i		−	0.645692i	−0.946451	−	0.322846i	$-0.895360\pi$
$937$		−	5.31183e8i		−	0.645692i	0.946451	−	0.322846i	$-0.104640\pi$
$938$	2.88062e8	+	3.78672e7i	0.349042	+	0.0458833i
$939$	−6.46069e7	−	6.46069e7i	−0.0780337	−	0.0780337i
$940$	4.44199e8	−	2.56689e8i	0.534803	−	0.309046i
$941$	1.68586e8	+	1.68586e8i	0.202327	+	0.202327i	0.800996	−	0.598670i	$-0.204304\pi$
$941$	1.68586e8	+	1.68586e8i	0.202327	+	0.202327i	−0.598670	+	0.800996i	$0.704304\pi$
$942$	1.06794e8	+	1.39120e8i	0.127759	+	0.166432i
$943$			1.16810e9i			1.39298i
$944$	−6.03168e7	−	2.24407e8i	−0.0717005	−	0.266760i
$945$	−1.73736e8			−0.205871
$946$	1.27353e9	−	9.77610e8i	1.50431	−	1.15476i
$947$	−1.02795e8	+	1.02795e8i	−0.121039	+	0.121039i	−0.765031	−	0.643993i	$-0.777277\pi$
$947$	−1.02795e8	+	1.02795e8i	−0.121039	+	0.121039i	0.643993	+	0.765031i	$0.277277\pi$
$948$	5.04605e8	−	2.91595e8i	0.592279	−	0.342259i
$949$	2.10905e8	−	2.10905e8i	0.246768	−	0.246768i
$950$	−2.65671e7	+	2.02101e8i	−0.0309866	+	0.235721i
$951$	−3.13479e8			−0.364475
$952$	2.25859e8	−	9.37082e7i	0.261774	−	0.108609i
$953$		−	9.78404e8i		−	1.13042i	−0.824947	−	0.565210i	$-0.808795\pi$
$953$		−	9.78404e8i		−	1.13042i	0.824947	−	0.565210i	$-0.191205\pi$
$954$	−1.63451e7	+	1.24340e8i	−0.0188253	+	0.143207i
$955$	7.16661e8	+	7.16661e8i	0.822818	+	0.822818i
$956$	2.09574e8	+	5.60678e7i	0.239863	+	0.0641712i
$957$	−9.02673e8	−	9.02673e8i	−1.02990	−	1.02990i
$958$	−2.99111e8	+	2.29608e8i	−0.340201	+	0.261151i
$959$			1.53825e9i			1.74410i
$960$	−3.91745e8	−	3.90833e8i	−0.442782	−	0.441751i
$961$	−1.84186e9			−2.07533
$962$	−6.57725e7	−	8.56819e7i	−0.0738786	−	0.0962418i
$963$	3.93084e8	−	3.93084e8i	0.440156	−	0.440156i
$964$	1.28270e8	−	4.79454e8i	0.143183	−	0.535199i
$965$	−1.76778e8	+	1.76778e8i	−0.196719	+	0.196719i
$966$	−6.26766e8	−	8.23914e7i	−0.695303	−	0.0914010i
$967$	7.24279e8			0.800989			0.400495	−	0.916299i	$-0.368838\pi$
$967$	7.24279e8			0.800989			0.400495	+	0.916299i	$0.368838\pi$
$968$	−6.49504e8	−	1.56546e9i	−0.716070	−	1.72590i
$969$			2.06482e8i			0.226940i
$970$	−4.97940e8	−	6.54566e7i	−0.545584	−	0.0717197i
$971$	2.79870e6	+	2.79870e6i	0.00305702	+	0.00305702i	0.708634	−	0.705577i	$-0.249312\pi$
$971$	2.79870e6	+	2.79870e6i	0.00305702	+	0.00305702i	−0.705577	+	0.708634i	$0.749312\pi$
$972$	2.94753e7	+	5.10069e7i	0.0320966	+	0.0555431i
$973$	1.17732e9	+	1.17732e9i	1.27807	+	1.27807i
$974$	−4.91172e8	−	6.39851e8i	−0.531566	−	0.692472i
$975$			3.60397e7i			0.0388837i
$976$	1.02268e8	+	3.80486e8i	0.109999	+	0.409250i
$977$	8.62168e8			0.924503			0.462252	−	0.886749i	$-0.347042\pi$
$977$	8.62168e8			0.924503			0.462252	+	0.886749i	$0.347042\pi$
$978$	6.67327e7	−	5.12264e7i	0.0713382	−	0.0547618i
$979$	−1.40441e9	+	1.40441e9i	−1.49674	+	1.49674i
$980$	1.27191e7	+	2.20103e7i	0.0135138	+	0.0233856i
$981$	−5.16629e7	+	5.16629e7i	−0.0547232	+	0.0547232i
$982$	−1.34537e8	+	1.02344e9i	−0.142071	+	1.08076i
$983$	6.29606e8			0.662839			0.331419	−	0.943484i	$-0.392472\pi$
$983$	6.29606e8			0.662839			0.331419	+	0.943484i	$0.392472\pi$
$984$	5.75641e8	+	2.38045e8i	0.604180	+	0.249847i
$985$		−	9.60696e8i		−	1.00526i
$986$	−5.34102e7	+	4.06301e8i	−0.0557178	+	0.423855i
$987$	−2.21001e8	−	2.21001e8i	−0.229849	−	0.229849i
$988$	1.32432e8	−	4.95014e8i	0.137317	−	0.513271i
$989$	9.42140e8	+	9.42140e8i	0.973927	+	0.973927i
$990$	4.70736e8	−	3.61354e8i	0.485145	−	0.372415i
$991$			1.51486e9i			1.55651i	0.627947	+	0.778256i	$0.283895\pi$
$991$			1.51486e9i			1.55651i	−0.627947	+	0.778256i	$0.716105\pi$
$992$	1.69705e9	−	2.25098e8i	1.73844	−	0.230588i
$993$	−1.00473e9			−1.02613
$994$	−8.59172e8	−	1.11924e9i	−0.874824	−	1.13963i
$995$	−3.73642e8	+	3.73642e8i	−0.379303	+	0.379303i
$996$	1.02949e8	+	2.75422e7i	0.104194	+	0.0278753i
$997$	8.68297e7	−	8.68297e7i	0.0876159	−	0.0876159i	−0.661940	−	0.749556i	$-0.730267\pi$
$997$	8.68297e7	−	8.68297e7i	0.0876159	−	0.0876159i	0.749556	+	0.661940i	$0.230267\pi$
$998$	8.53869e8	+	1.12245e8i	0.859013	+	0.112921i
$999$	−6.00057e7			−0.0601860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.l.a.19.17	✓	48
4.3	odd	2		192.7.l.a.175.16		48
8.3	odd	2		384.7.l.a.223.9		48
8.5	even	2		384.7.l.b.223.16		48
16.3	odd	4		384.7.l.b.31.16		48
16.5	even	4		192.7.l.a.79.16		48
16.11	odd	4	inner	48.7.l.a.43.17	yes	48
16.13	even	4		384.7.l.a.31.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.17	✓	48	1.1	even	1	trivial
48.7.l.a.43.17	yes	48	16.11	odd	4	inner
192.7.l.a.79.16		48	16.5	even	4
192.7.l.a.175.16		48	4.3	odd	2
384.7.l.a.31.9		48	16.13	even	4
384.7.l.a.223.9		48	8.3	odd	2
384.7.l.b.31.16		48	16.3	odd	4
384.7.l.b.223.16		48	8.5	even	2

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.87132 + 6.34588i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(-16.5404 + 61.8257i) q^{4} +(-95.7535 + 95.7535i) q^{5} +(-123.644 - 16.2536i) q^{6} +338.697 q^{7} +(-472.912 + 196.210i) q^{8} -243.000i q^{9} +O(q^{10})\)	\(q+(4.87132 + 6.34588i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(-16.5404 + 61.8257i) q^{4} +(-95.7535 + 95.7535i) q^{5} +(-123.644 - 16.2536i) q^{6} +338.697 q^{7} +(-472.912 + 196.210i) q^{8} -243.000i q^{9} +(-1074.09 - 141.194i) q^{10} +(-1594.02 - 1594.02i) q^{11} +(-499.166 - 863.806i) q^{12} +(602.697 + 602.697i) q^{13} +(1649.90 + 2149.33i) q^{14} -2110.92i q^{15} +(-3548.83 - 2045.24i) q^{16} -1410.09 q^{17} +(1542.05 - 1183.73i) q^{18} +(-6642.31 + 6642.31i) q^{19} +(-4336.23 - 7503.83i) q^{20} +(-3733.36 + 3733.36i) q^{21} +(2350.48 - 17880.5i) q^{22} +14966.5 q^{23} +(3050.01 - 7375.53i) q^{24} -2712.47i q^{25} +(-888.711 + 6760.58i) q^{26} +(2678.52 + 2678.52i) q^{27} +(-5602.18 + 20940.2i) q^{28} +(-25687.3 - 25687.3i) q^{29} +(13395.7 - 10283.0i) q^{30} +52243.3i q^{31} +(-4308.64 - 32483.5i) q^{32} +35140.9 q^{33} +(-6868.99 - 8948.24i) q^{34} +(-32431.4 + 32431.4i) q^{35} +(15023.6 + 4019.32i) q^{36} +(-11201.3 + 11201.3i) q^{37} +(-74508.2 - 9794.46i) q^{38} -13286.7 q^{39} +(26495.2 - 64070.7i) q^{40} +78047.4i q^{41} +(-41877.9 - 5505.05i) q^{42} +(62949.8 + 62949.8i) q^{43} +(124917. - 72185.8i) q^{44} +(23268.1 + 23268.1i) q^{45} +(72906.8 + 94975.8i) q^{46} +59196.3i q^{47} +(61661.8 - 16573.6i) q^{48} -2933.21 q^{49} +(17213.0 - 13213.3i) q^{50} +(15543.0 - 15543.0i) q^{51} +(-47231.0 + 27293.3i) q^{52} +(-45616.2 + 45616.2i) q^{53} +(-3949.62 + 30045.5i) q^{54} +305266. q^{55} +(-160174. + 66455.6i) q^{56} -146432. i q^{57} +(37877.3 - 288139. i) q^{58} +(40115.2 + 40115.2i) q^{59} +(130509. + 34915.5i) q^{60} +(-68015.9 - 68015.9i) q^{61} +(-331530. + 254494. i) q^{62} -82303.4i q^{63} +(185148. - 185580. i) q^{64} -115421. q^{65} +(171183. + 223000. i) q^{66} +(75821.1 - 75821.1i) q^{67} +(23323.4 - 87179.5i) q^{68} +(-164972. + 164972. i) q^{69} +(-363790. - 47822.0i) q^{70} -520740. q^{71} +(47678.9 + 114918. i) q^{72} -349935. i q^{73} +(-125647. - 16516.9i) q^{74} +(29898.7 + 29898.7i) q^{75} +(-300799. - 520532. i) q^{76} +(-539891. - 539891. i) q^{77} +(-64723.9 - 84315.8i) q^{78} +584164. i q^{79} +(535652. - 143974. i) q^{80} -59049.0 q^{81} +(-495280. + 380194. i) q^{82} +(-75532.5 + 75532.5i) q^{83} +(-169066. - 292569. i) q^{84} +(135021. - 135021. i) q^{85} +(-92822.9 + 706121. i) q^{86} +566286. q^{87} +(1.06659e6 + 441070. i) q^{88} -881047. i q^{89} +(-34310.1 + 261003. i) q^{90} +(204132. + 204132. i) q^{91} +(-247552. + 925316. i) q^{92} +(-575863. - 575863. i) q^{93} +(-375653. + 288365. i) q^{94} -1.27205e6i q^{95} +(405549. + 310563. i) q^{96} +463594. q^{97} +(-14288.6 - 18613.8i) q^{98} +(-387347. + 387347. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 180 q^{4} - 1932 q^{8}+O(q^{10}) \) 48 * q - 180 * q^4 - 1932 * q^8	\( 48 q - 180 q^{4} - 1932 q^{8} + 744 q^{10} - 2720 q^{11} - 1944 q^{12} - 15388 q^{14} + 3744 q^{16} + 4860 q^{18} - 3936 q^{19} - 14000 q^{20} - 41184 q^{22} + 26240 q^{23} + 18468 q^{24} - 5300 q^{26} - 96120 q^{28} + 66400 q^{29} - 33048 q^{30} - 52960 q^{32} + 122208 q^{34} + 162336 q^{35} + 32076 q^{36} - 7200 q^{37} + 16968 q^{38} - 309072 q^{40} - 231660 q^{42} + 340704 q^{43} - 193192 q^{44} - 450264 q^{46} + 299376 q^{48} + 806736 q^{49} + 537764 q^{50} + 80352 q^{51} + 1126224 q^{52} + 443680 q^{53} + 78732 q^{54} + 232704 q^{55} - 420448 q^{56} - 1295664 q^{58} - 886144 q^{59} - 627912 q^{60} - 326496 q^{61} - 719652 q^{62} - 192024 q^{64} - 372832 q^{65} + 775656 q^{66} - 962112 q^{67} + 3197632 q^{68} + 541728 q^{69} + 642816 q^{70} + 534016 q^{71} + 82620 q^{72} - 4894836 q^{74} - 1073088 q^{75} - 3162552 q^{76} - 932960 q^{77} - 337284 q^{78} + 4668072 q^{80} - 2834352 q^{81} + 5077560 q^{82} - 2497760 q^{83} + 1312200 q^{84} - 372000 q^{85} + 4142928 q^{86} - 2794272 q^{88} - 507384 q^{90} + 775008 q^{91} - 9470992 q^{92} - 5050728 q^{94} + 1879200 q^{96} + 12708584 q^{98} - 660960 q^{99}+O(q^{100}) \) 48 * q - 180 * q^4 - 1932 * q^8 + 744 * q^10 - 2720 * q^11 - 1944 * q^12 - 15388 * q^14 + 3744 * q^16 + 4860 * q^18 - 3936 * q^19 - 14000 * q^20 - 41184 * q^22 + 26240 * q^23 + 18468 * q^24 - 5300 * q^26 - 96120 * q^28 + 66400 * q^29 - 33048 * q^30 - 52960 * q^32 + 122208 * q^34 + 162336 * q^35 + 32076 * q^36 - 7200 * q^37 + 16968 * q^38 - 309072 * q^40 - 231660 * q^42 + 340704 * q^43 - 193192 * q^44 - 450264 * q^46 + 299376 * q^48 + 806736 * q^49 + 537764 * q^50 + 80352 * q^51 + 1126224 * q^52 + 443680 * q^53 + 78732 * q^54 + 232704 * q^55 - 420448 * q^56 - 1295664 * q^58 - 886144 * q^59 - 627912 * q^60 - 326496 * q^61 - 719652 * q^62 - 192024 * q^64 - 372832 * q^65 + 775656 * q^66 - 962112 * q^67 + 3197632 * q^68 + 541728 * q^69 + 642816 * q^70 + 534016 * q^71 + 82620 * q^72 - 4894836 * q^74 - 1073088 * q^75 - 3162552 * q^76 - 932960 * q^77 - 337284 * q^78 + 4668072 * q^80 - 2834352 * q^81 + 5077560 * q^82 - 2497760 * q^83 + 1312200 * q^84 - 372000 * q^85 + 4142928 * q^86 - 2794272 * q^88 - 507384 * q^90 + 775008 * q^91 - 9470992 * q^92 - 5050728 * q^94 + 1879200 * q^96 + 12708584 * q^98 - 660960 * q^99

Introduction

L-functions

Modular forms

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