LMFDB - Embedded newform 40.6.k.a.3.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,6,Mod(3,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("40.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	40.k (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:	$6.41535279252$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.18
Character	$\chi$	$=$	40.3
Dual form			40.6.k.a.27.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.14651 - 5.23378i) q^{2} +(-17.0411 - 17.0411i) q^{3} +(-22.7850 - 22.4688i) q^{4} +(28.8684 - 47.8708i) q^{5} +(-125.768 + 52.6104i) q^{6} +(87.4493 + 87.4493i) q^{7} +(-166.505 + 71.0220i) q^{8} +337.797i q^{9} +O(q^{10})$	\(q+(2.14651 - 5.23378i) q^{2} +(-17.0411 - 17.0411i) q^{3} +(-22.7850 - 22.4688i) q^{4} +(28.8684 - 47.8708i) q^{5} +(-125.768 + 52.6104i) q^{6} +(87.4493 + 87.4493i) q^{7} +(-166.505 + 71.0220i) q^{8} +337.797i q^{9} +(-188.579 - 253.846i) q^{10} -393.659 q^{11} +(5.38823 + 771.173i) q^{12} +(196.367 - 196.367i) q^{13} +(645.402 - 269.980i) q^{14} +(-1307.72 + 323.822i) q^{15} +(14.3088 + 1023.90i) q^{16} +(998.609 - 998.609i) q^{17} +(1767.96 + 725.087i) q^{18} -1736.77i q^{19} +(-1733.36 + 442.098i) q^{20} -2980.46i q^{21} +(-844.994 + 2060.33i) q^{22} +(-3380.45 + 3380.45i) q^{23} +(4047.72 + 1627.13i) q^{24} +(-1458.23 - 2763.91i) q^{25} +(-606.238 - 1449.25i) q^{26} +(1615.45 - 1615.45i) q^{27} +(-27.6506 - 3957.41i) q^{28} +261.856 q^{29} +(-1112.22 + 7539.41i) q^{30} -9288.24i q^{31} +(5389.58 + 2122.93i) q^{32} +(6708.38 + 6708.38i) q^{33} +(-3082.97 - 7370.03i) q^{34} +(6710.79 - 1661.75i) q^{35} +(7589.89 - 7696.70i) q^{36} +(2183.00 + 2183.00i) q^{37} +(-9089.87 - 3728.00i) q^{38} -6692.61 q^{39} +(-1406.84 + 10021.0i) q^{40} -2983.44 q^{41} +(-15599.1 - 6397.60i) q^{42} +(-1797.48 - 1797.48i) q^{43} +(8969.50 + 8845.03i) q^{44} +(16170.6 + 9751.66i) q^{45} +(10436.4 + 24948.7i) q^{46} +(1531.91 + 1531.91i) q^{47} +(17204.5 - 17692.2i) q^{48} -1512.23i q^{49} +(-17595.8 + 1699.31i) q^{50} -34034.8 q^{51} +(-8886.34 + 62.0893i) q^{52} +(3705.62 - 3705.62i) q^{53} +(-4987.33 - 11922.5i) q^{54} +(-11364.3 + 18844.8i) q^{55} +(-20771.6 - 8349.91i) q^{56} +(-29596.4 + 29596.4i) q^{57} +(562.078 - 1370.50i) q^{58} +12961.1i q^{59} +(37072.2 + 22004.6i) q^{60} -20333.4i q^{61} +(-48612.6 - 19937.3i) q^{62} +(-29540.2 + 29540.2i) q^{63} +(22679.7 - 23651.0i) q^{64} +(-3731.45 - 15069.0i) q^{65} +(49509.8 - 20710.6i) q^{66} +(42794.2 - 42794.2i) q^{67} +(-45190.8 + 315.750i) q^{68} +115213. q^{69} +(5707.56 - 38689.8i) q^{70} +4333.39i q^{71} +(-23991.0 - 56244.9i) q^{72} +(62225.0 + 62225.0i) q^{73} +(16111.2 - 6739.52i) q^{74} +(-22250.1 + 71949.9i) q^{75} +(-39023.1 + 39572.2i) q^{76} +(-34425.2 - 34425.2i) q^{77} +(-14365.8 + 35027.7i) q^{78} +44768.8 q^{79} +(49428.0 + 28873.4i) q^{80} +27026.7 q^{81} +(-6403.99 + 15614.7i) q^{82} +(-28353.0 - 28353.0i) q^{83} +(-66967.3 + 67909.7i) q^{84} +(-18976.0 - 76632.5i) q^{85} +(-13265.9 + 5549.31i) q^{86} +(-4462.31 - 4462.31i) q^{87} +(65546.1 - 27958.5i) q^{88} -113502. i q^{89} +(85748.6 - 63701.5i) q^{90} +34344.3 q^{91} +(152978. - 1068.87i) q^{92} +(-158282. + 158282. i) q^{93} +(11306.0 - 4729.42i) q^{94} +(-83140.5 - 50137.7i) q^{95} +(-55667.4 - 128021. i) q^{96} +(-5975.44 + 5975.44i) q^{97} +(-7914.69 - 3246.02i) q^{98} -132977. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

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

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 $

$2$	2.14651	−	5.23378i	0.379454	−	0.925211i
$2$	2.14651	−	5.23378i	0.379454	−	0.925211i
$3$	−17.0411	−	17.0411i	−1.09319	−	1.09319i	−0.995186	−	0.0979999i	$-0.968756\pi$
$3$	−17.0411	−	17.0411i	−1.09319	−	1.09319i	−0.0979999	−	0.995186i	$-0.531244\pi$
$4$	−22.7850	−	22.4688i	−0.712030	−	0.702149i
$5$	28.8684	−	47.8708i	0.516413	−	0.856339i
$5$	28.8684	−	47.8708i	0.516413	−	0.856339i
$6$	−125.768	+	52.6104i	−1.42624	+	0.596614i
$7$	87.4493	+	87.4493i	0.674546	+	0.674546i	0.958761	−	0.284215i	$-0.0917329\pi$
$7$	87.4493	+	87.4493i	0.674546	+	0.674546i	−0.284215	+	0.958761i	$0.591733\pi$
$8$	−166.505	+	71.0220i	−0.919818	+	0.392345i
$9$			337.797i			1.39011i
$10$	−188.579	−	253.846i	−0.596340	−	0.802732i
$11$	−393.659			−0.980931			−0.490465	−	0.871461i	$-0.663173\pi$
$11$	−393.659			−0.980931			−0.490465	+	0.871461i	$0.663173\pi$
$12$	5.38823	+	771.173i	0.0108017	+	1.54596i
$13$	196.367	−	196.367i	0.322263	−	0.322263i	−0.527372	−	0.849635i	$-0.676823\pi$
$13$	196.367	−	196.367i	0.322263	−	0.322263i	0.849635	+	0.527372i	$0.176823\pi$
$14$	645.402	−	269.980i	0.880056	−	0.368138i
$15$	−1307.72	+	323.822i	−1.50067	+	0.371603i
$16$	14.3088	+	1023.90i	0.0139734	+	0.999902i
$17$	998.609	−	998.609i	0.838056	−	0.838056i	−0.150547	−	0.988603i	$-0.548103\pi$
$17$	998.609	−	998.609i	0.838056	−	0.838056i	0.988603	+	0.150547i	$0.0481034\pi$
$18$	1767.96	+	725.087i	1.28615	+	0.527483i
$19$		−	1736.77i		−	1.10372i	−0.833938	−	0.551859i	$-0.813919\pi$
$19$		−	1736.77i		−	1.10372i	0.833938	−	0.551859i	$-0.186081\pi$
$20$	−1733.36	+	442.098i	−0.968980	+	0.247140i
$21$		−	2980.46i		−	1.47481i
$22$	−844.994	+	2060.33i	−0.372218	+	0.907568i
$23$	−3380.45	+	3380.45i	−1.33246	+	1.33246i	−0.429303	+	0.903160i	$0.641241\pi$
$23$	−3380.45	+	3380.45i	−1.33246	+	1.33246i	−0.903160	+	0.429303i	$0.858759\pi$
$24$	4047.72	+	1627.13i	1.43444	+	0.576627i
$25$	−1458.23	−	2763.91i	−0.466635	−	0.884450i
$26$	−606.238	−	1449.25i	−0.175877	−	0.420445i
$27$	1615.45	−	1615.45i	0.426466	−	0.426466i
$28$	−27.6506	−	3957.41i	−0.00666515	−	0.953928i
$29$	261.856			0.0578186			0.0289093	−	0.999582i	$-0.490797\pi$
$29$	261.856			0.0578186			0.0289093	+	0.999582i	$0.490797\pi$
$30$	−1112.22	+	7539.41i	−0.225626	+	1.52945i
$31$		−	9288.24i		−	1.73592i	−0.496636	−	0.867959i	$-0.665432\pi$
$31$		−	9288.24i		−	1.73592i	0.496636	−	0.867959i	$-0.334568\pi$
$32$	5389.58	+	2122.93i	0.930423	+	0.366488i
$33$	6708.38	+	6708.38i	1.07234	+	1.07234i
$34$	−3082.97	−	7370.03i	−0.457375	−	1.09338i
$35$	6710.79	−	1661.75i	0.925984	−	0.229296i
$36$	7589.89	−	7696.70i	0.976066	−	0.989802i
$37$	2183.00	+	2183.00i	0.262150	+	0.262150i	0.825927	−	0.563777i	$-0.190652\pi$
$37$	2183.00	+	2183.00i	0.262150	+	0.262150i	−0.563777	+	0.825927i	$0.690652\pi$
$38$	−9089.87	−	3728.00i	−1.02117	−	0.418810i
$39$	−6692.61			−0.704586
$40$	−1406.84	+	10021.0i	−0.139026	+	0.990289i
$41$	−2983.44			−0.277177			−0.138588	−	0.990350i	$-0.544257\pi$
$41$	−2983.44			−0.277177			−0.138588	+	0.990350i	$0.544257\pi$
$42$	−15599.1	−	6397.60i	−1.36451	−	0.559621i
$43$	−1797.48	−	1797.48i	−0.148249	−	0.148249i	0.629086	−	0.777336i	$-0.283429\pi$
$43$	−1797.48	−	1797.48i	−0.148249	−	0.148249i	−0.777336	+	0.629086i	$0.783429\pi$
$44$	8969.50	+	8845.03i	0.698452	+	0.688760i
$45$	16170.6	+	9751.66i	1.19041	+	0.717873i
$46$	10436.4	+	24948.7i	0.727202	+	1.73842i
$47$	1531.91	+	1531.91i	0.101155	+	0.101155i	0.755873	−	0.654718i	$-0.227213\pi$
$47$	1531.91	+	1531.91i	0.101155	+	0.101155i	−0.654718	+	0.755873i	$0.727213\pi$
$48$	17204.5	−	17692.2i	1.07780	−	1.10836i
$49$		−	1512.23i		−	0.0899762i
$50$	−17595.8	+	1699.31i	−0.995369	+	0.0961275i
$51$	−34034.8			−1.83230
$52$	−8886.34	+	62.0893i	−0.455737	+	0.00318426i
$53$	3705.62	−	3705.62i	0.181206	−	0.181206i	−0.610675	−	0.791881i	$-0.709102\pi$
$53$	3705.62	−	3705.62i	0.181206	−	0.181206i	0.791881	+	0.610675i	$0.209102\pi$
$54$	−4987.33	−	11922.5i	−0.232747	−	0.556395i
$55$	−11364.3	+	18844.8i	−0.506566	+	0.840010i
$56$	−20771.6	−	8349.91i	−0.885114	−	0.355805i
$57$	−29596.4	+	29596.4i	−1.20657	+	1.20657i
$58$	562.078	−	1370.50i	0.0219395	−	0.0534944i
$59$			12961.1i			0.484743i	0.970183	+	0.242372i	$0.0779253\pi$
$59$			12961.1i			0.484743i	−0.970183	+	0.242372i	$0.922075\pi$
$60$	37072.2	+	22004.6i	1.32945	+	0.789105i
$61$		−	20333.4i		−	0.699656i	−0.936814	−	0.349828i	$-0.886240\pi$
$61$		−	20333.4i		−	0.699656i	0.936814	−	0.349828i	$-0.113760\pi$
$62$	−48612.6	−	19937.3i	−1.60609	−	0.658700i
$63$	−29540.2	+	29540.2i	−0.937694	+	0.937694i
$64$	22679.7	−	23651.0i	0.692131	−	0.721772i
$65$	−3731.45	−	15069.0i	−0.109545	−	0.442387i
$66$	49509.8	−	20710.6i	1.39904	−	0.585237i
$67$	42794.2	−	42794.2i	1.16466	−	1.16466i	0.181212	−	0.983444i	$-0.441998\pi$
$67$	42794.2	−	42794.2i	1.16466	−	1.16466i	0.983444	−	0.181212i	$-0.0580021\pi$
$68$	−45190.8	+	315.750i	−1.18516	+	0.00828079i
$69$	115213.			2.91326
$70$	5707.56	−	38689.8i	0.139221	−	0.943738i
$71$			4333.39i			0.102019i	0.998698	+	0.0510096i	$0.0162439\pi$
$71$			4333.39i			0.102019i	−0.998698	+	0.0510096i	$0.983756\pi$
$72$	−23991.0	−	56244.9i	−0.545404	−	1.27865i
$73$	62225.0	+	62225.0i	1.36665	+	1.36665i	0.865167	+	0.501483i	$0.167212\pi$
$73$	62225.0	+	62225.0i	1.36665	+	1.36665i	0.501483	+	0.865167i	$0.332788\pi$
$74$	16111.2	−	6739.52i	0.342018	−	0.143070i
$75$	−22250.1	+	71949.9i	−0.456750	+	1.47699i
$76$	−39023.1	+	39572.2i	−0.774974	+	0.785880i
$77$	−34425.2	−	34425.2i	−0.661683	−	0.661683i
$78$	−14365.8	+	35027.7i	−0.267358	+	0.651891i
$79$	44768.8			0.807064			0.403532	−	0.914966i	$-0.367782\pi$
$79$	44768.8			0.807064			0.403532	+	0.914966i	$0.367782\pi$
$80$	49428.0	+	28873.4i	0.863472	+	0.504397i
$81$	27026.7			0.457700
$82$	−6403.99	+	15614.7i	−0.105176	+	0.256447i
$83$	−28353.0	−	28353.0i	−0.451756	−	0.451756i	0.444181	−	0.895937i	$-0.353495\pi$
$83$	−28353.0	−	28353.0i	−0.451756	−	0.451756i	−0.895937	+	0.444181i	$0.853495\pi$
$84$	−66967.3	+	67909.7i	−1.03554	+	1.05011i
$85$	−18976.0	−	76632.5i	−0.284877	−	1.15044i
$86$	−13265.9	+	5549.31i	−0.193416	+	0.0809082i
$87$	−4462.31	−	4462.31i	−0.0632065	−	0.0632065i
$88$	65546.1	−	27958.5i	0.902278	−	0.384863i
$89$		−	113502.i		−	1.51889i	−0.650569	−	0.759447i	$-0.725470\pi$
$89$		−	113502.i		−	1.51889i	0.650569	−	0.759447i	$-0.274530\pi$
$90$	85748.6	−	63701.5i	1.11589	−	0.828979i
$91$	34344.3			0.434762
$92$	152978.	−	1068.87i	1.88434	−	0.0131660i
$93$	−158282.	+	158282.i	−1.89768	+	1.89768i
$94$	11306.0	−	4729.42i	0.131974	−	0.0552062i
$95$	−83140.5	−	50137.7i	−0.945157	−	0.569974i
$96$	−55667.4	−	128021.i	−0.616486	−	1.41777i
$97$	−5975.44	+	5975.44i	−0.0644823	+	0.0644823i	−0.738613	−	0.674130i	$-0.764519\pi$
$97$	−5975.44	+	5975.44i	−0.0644823	+	0.0644823i	0.674130	+	0.738613i	$0.264519\pi$
$98$	−7914.69	−	3246.02i	−0.0832470	−	0.0341418i
$99$		−	132977.i		−	1.36360i
$100$	−28875.8	+	95740.2i	−0.288758	+	0.957402i
$101$			56250.4i			0.548684i	0.961632	+	0.274342i	$0.0884600\pi$
$101$			56250.4i			0.548684i	−0.961632	+	0.274342i	$0.911540\pi$
$102$	−73056.1	+	178131.i	−0.695274	+	1.69527i
$103$	108093.	−	108093.i	1.00393	−	1.00393i	0.00393564	−	0.999992i	$-0.498747\pi$
$103$	108093.	−	108093.i	1.00393	−	1.00393i	0.999992	−	0.00393564i	$-0.00125276\pi$
$104$	−18749.7	+	46642.4i	−0.169985	+	0.422861i
$105$	−142677.	−	86041.2i	−1.26294	−	0.761611i
$106$	−11440.3	−	27348.6i	−0.0988943	−	0.236412i
$107$	27439.8	−	27439.8i	0.231698	−	0.231698i	−0.581703	−	0.813401i	$-0.697614\pi$
$107$	27439.8	−	27439.8i	0.231698	−	0.231698i	0.813401	+	0.581703i	$0.197614\pi$
$108$	−73105.1	+	510.790i	−0.603099	+	0.00421388i
$109$	−191730.			−1.54570			−0.772848	−	0.634591i	$-0.781169\pi$
$109$	−191730.			−1.54570			−0.772848	+	0.634591i	$0.781169\pi$
$110$	74235.9	+	99928.8i	0.584968	+	0.787425i
$111$		−	74401.5i		−	0.573158i
$112$	−88288.1	+	90790.7i	−0.665054	+	0.683906i
$113$	−20796.1	−	20796.1i	−0.153210	−	0.153210i	0.626340	−	0.779550i	$-0.284552\pi$
$113$	−20796.1	−	20796.1i	−0.153210	−	0.153210i	−0.779550	+	0.626340i	$0.784552\pi$
$114$	91372.1	+	218430.i	0.658494	+	1.57417i
$115$	64236.9	+	259413.i	0.452939	+	1.82914i
$116$	−5966.38	−	5883.58i	−0.0411686	−	0.0405973i
$117$	66332.2	+	66332.2i	0.447981	+	0.447981i
$118$	67835.6	+	27821.2i	0.448490	+	0.183938i
$119$	174655.			1.13061
$120$	194743.	−	146795.i	1.23455	−	0.930589i
$121$	−6083.62			−0.0377745
$122$	−106420.	−	43645.8i	−0.647329	−	0.265487i
$123$	50841.0	+	50841.0i	0.303006	+	0.303006i
$124$	−208695.	+	211632.i	−1.21887	+	1.23603i
$125$	−174407.	−	9982.70i	−0.998366	−	0.0571443i
$126$	91198.4	+	218015.i	0.511754	+	1.22338i
$127$	151142.	+	151142.i	0.831526	+	0.831526i	0.987725	−	0.156200i	$-0.0499244\pi$
$127$	151142.	+	151142.i	0.831526	+	0.831526i	−0.156200	+	0.987725i	$0.549924\pi$
$128$	−75101.9	−	169468.i	−0.405160	−	0.914246i
$129$			61262.1i			0.324129i
$130$	−86877.7	−	12816.3i	−0.450869	−	0.0665126i
$131$	−36439.6			−0.185522			−0.0927611	−	0.995688i	$-0.529569\pi$
$131$	−36439.6			−0.185522			−0.0927611	+	0.995688i	$0.529569\pi$
$132$	−2121.12	−	303579.i	−0.0105957	−	1.51648i
$133$	151879.	−	151879.i	0.744508	−	0.744508i
$134$	−132117.	−	315834.i	−0.635620	−	1.51949i
$135$	−30697.5	−	123968.i	−0.144967	−	0.585432i
$136$	−95350.0	+	237196.i	−0.442052	+	1.09967i
$137$	184328.	−	184328.i	0.839053	−	0.839053i	−0.149682	−	0.988734i	$-0.547825\pi$
$137$	184328.	−	184328.i	0.839053	−	0.839053i	0.988734	+	0.149682i	$0.0478249\pi$
$138$	247307.	−	603001.i	1.10545	−	2.69538i
$139$			35996.1i			0.158022i	0.996874	+	0.0790111i	$0.0251763\pi$
$139$			35996.1i			0.158022i	−0.996874	+	0.0790111i	$0.974824\pi$
$140$	−190243.	−	112920.i	−0.820328	−	0.486914i
$141$		−	52210.8i		−	0.221163i
$142$	22680.0	+	9301.68i	0.0943893	+	0.0387116i
$143$	−77301.6	+	77301.6i	−0.316117	+	0.316117i
$144$	−345871.	+	4833.47i	−1.38998	+	0.0194246i
$145$	7559.36	−	12535.3i	0.0298583	−	0.0495124i
$146$	459239.	−	192105.i	1.78302	−	0.745859i
$147$	−25770.1	+	25770.1i	−0.0983608	+	0.0983608i
$148$	−690.244	−	98789.0i	−0.00259029	−	0.370727i
$149$	−121917.			−0.449882			−0.224941	−	0.974372i	$-0.572219\pi$
$149$	−121917.			−0.449882			−0.224941	+	0.974372i	$0.572219\pi$
$150$	328810.	+	270894.i	1.19321	+	0.983038i
$151$			166304.i			0.593554i	0.954947	+	0.296777i	$0.0959119\pi$
$151$			166304.i			0.593554i	−0.954947	+	0.296777i	$0.904088\pi$
$152$	123349.	+	289180.i	0.433038	+	1.01522i
$153$	337327.	+	337327.i	1.16499	+	1.16499i
$154$	−254068.	+	106280.i	−0.863274	+	0.361118i
$155$	−444636.	−	268136.i	−1.48653	−	0.896451i
$156$	152491.	+	150375.i	0.501687	+	0.494725i
$157$	104830.	+	104830.i	0.339420	+	0.339420i	0.856149	−	0.516729i	$-0.172850\pi$
$157$	104830.	+	104830.i	0.339420	+	0.339420i	−0.516729	+	0.856149i	$0.672850\pi$
$158$	96096.8	−	234310.i	0.306243	−	0.746704i
$159$	−126296.			−0.396183
$160$	257215.	−	196718.i	0.794321	−	0.607498i
$161$	−591237.			−1.79762
$162$	58013.2	−	141452.i	0.173676	−	0.423469i
$163$	93.6666	+	93.6666i	0.000276131	+	0.000276131i	0.707245	−	0.706969i	$-0.249938\pi$
$163$	93.6666	+	93.6666i	0.000276131	+	0.000276131i	−0.706969	+	0.707245i	$0.749938\pi$
$164$	67977.5	+	67034.1i	0.197358	+	0.194620i
$165$	514796.	−	127476.i	1.47206	−	0.364516i
$166$	−209254.	+	87533.4i	−0.589390	+	0.246549i
$167$	268881.	+	268881.i	0.746051	+	0.746051i	0.973735	−	0.227684i	$-0.0731154\pi$
$167$	268881.	+	268881.i	0.746051	+	0.746051i	−0.227684	+	0.973735i	$0.573115\pi$
$168$	211678.	+	496262.i	0.578633	+	1.35656i
$169$			294173.i			0.792294i
$170$	−441810.	−	65176.3i	−1.17250	−	0.172969i
$171$	586676.			1.53429
$172$	568.346	+	81342.7i	0.00146484	+	0.209651i
$173$	−388127.	+	388127.i	−0.985958	+	0.985958i	−0.999903	−	0.0139450i	$-0.995561\pi$
$173$	−388127.	+	388127.i	−0.985958	+	0.985958i	0.0139450	+	0.999903i	$0.495561\pi$
$174$	−32933.2	+	13776.4i	−0.0824633	+	0.0344954i
$175$	114180.	−	369223.i	0.281836	−	0.911368i
$176$	−5632.78	−	403067.i	−0.0137070	−	0.980835i
$177$	220871.	−	220871.i	0.529915	−	0.529915i
$178$	−594043.	−	243633.i	−1.40530	−	0.576350i
$179$			48400.7i			0.112907i	0.998405	+	0.0564533i	$0.0179792\pi$
$179$			48400.7i			0.112907i	−0.998405	+	0.0564533i	$0.982021\pi$
$180$	−149340.	−	585526.i	−0.343553	−	1.34699i
$181$		−	556521.i		−	1.26266i	−0.775516	−	0.631328i	$-0.782510\pi$
$181$		−	556521.i		−	1.26266i	0.775516	−	0.631328i	$-0.217490\pi$
$182$	73720.5	−	179751.i	0.164972	−	0.402246i
$183$	−346503.	+	346503.i	−0.764854	+	0.764854i
$184$	322775.	−	802949.i	0.702839	−	1.74841i
$185$	167522.	−	41482.4i	0.359867	−	0.0891117i
$186$	488658.	+	1.16817e6i	1.03567	+	2.47584i
$187$	−393111.	+	393111.i	−0.822075	+	0.822075i
$188$	−484.375	−	69324.7i	−0.000999510	−	0.143052i
$189$	282540.			0.575341
$190$	−440872.	+	327518.i	−0.885990	+	0.658190i
$191$			31969.4i			0.0634091i	0.999497	+	0.0317046i	$0.0100936\pi$
$191$			31969.4i			0.0634091i	−0.999497	+	0.0317046i	$0.989906\pi$
$192$	−789527.	+	16551.6i	−1.54566	+	0.0324030i
$193$	60863.3	+	60863.3i	0.117615	+	0.117615i	0.763465	−	0.645850i	$-0.223497\pi$
$193$	60863.3	+	60863.3i	0.117615	+	0.117615i	−0.645850	+	0.763465i	$0.723497\pi$
$194$	18447.8	+	44100.5i	0.0351917	+	0.0841277i
$195$	−193205.	+	320381.i	−0.363858	+	0.603365i
$196$	−33978.0	+	34456.1i	−0.0631767	+	0.0640658i
$197$	657829.	+	657829.i	1.20767	+	1.20767i	0.971781	+	0.235887i	$0.0757994\pi$
$197$	657829.	+	657829.i	1.20767	+	1.20767i	0.235887	+	0.971781i	$0.424201\pi$
$198$	−695972.	−	285437.i	−1.26162	−	0.517425i
$199$	176528.			0.315995			0.157997	−	0.987440i	$-0.449496\pi$
$199$	176528.			0.315995			0.157997	+	0.987440i	$0.449496\pi$
$200$	439101.	+	356637.i	0.776228	+	0.630452i
$201$	−1.45852e6			−2.54637
$202$	294402.	+	120742.i	0.507648	+	0.208200i
$203$	22899.1	+	22899.1i	0.0390013	+	0.0390013i
$204$	775481.	+	764719.i	1.30465	+	1.28655i
$205$	−86127.0	+	142820.i	−0.143138	+	0.237358i
$206$	−333711.	−	797755.i	−0.547901	−	1.30979i
$207$	−1.14191e6	−	1.14191e6i	−1.85227	−	1.85227i
$208$	203870.	+	198250.i	0.326734	+	0.317728i
$209$			683694.i			1.08267i
$210$	−756579.	+	562053.i	−1.18388	+	0.879487i
$211$	581283.			0.898838			0.449419	−	0.893321i	$-0.351631\pi$
$211$	581283.			0.898838			0.449419	+	0.893321i	$0.351631\pi$
$212$	−167693.	+	1171.68i	−0.256257	+	0.00179048i
$213$	73845.7	−	73845.7i	0.111526	−	0.111526i
$214$	−84714.1	−	202514.i	−0.126451	−	0.302288i
$215$	−137937.	+	34156.5i	−0.203510	+	0.0503939i
$216$	−154248.	+	383713.i	−0.224949	+	0.559593i
$217$	812250.	−	812250.i	1.17096	−	1.17096i
$218$	−411552.	+	1.00347e6i	−0.586520	+	1.43010i
$219$		−	2.12076e6i		−	2.98801i
$220$	682354.	−	174036.i	0.950502	−	0.242428i
$221$		−	392187.i		−	0.540148i
$222$	−389401.	−	159704.i	−0.530292	−	0.217487i
$223$	93599.2	−	93599.2i	0.126040	−	0.126040i	−0.641273	−	0.767313i	$-0.721593\pi$
$223$	93599.2	−	93599.2i	0.126040	−	0.126040i	0.767313	+	0.641273i	$0.221593\pi$
$224$	285667.	+	656964.i	0.380400	+	0.874826i
$225$	933640.	−	492587.i	1.22949	−	0.648675i
$226$	−153481.	+	64203.2i	−0.199887	+	0.0836152i
$227$	−43525.3	+	43525.3i	−0.0560631	+	0.0560631i	−0.734582	−	0.678519i	$-0.762622\pi$
$227$	−43525.3	+	43525.3i	−0.0560631	+	0.0560631i	0.678519	+	0.734582i	$0.262622\pi$
$228$	1.33935e6	−	9358.10i	1.70630	−	0.0119220i
$229$	−449216.			−0.566065			−0.283033	−	0.959110i	$-0.591340\pi$
$229$	−449216.			−0.566065			−0.283033	+	0.959110i	$0.591340\pi$
$230$	1.49560e6	+	220632.i	1.86421	+	0.275011i
$231$			1.17329e6i			1.44669i
$232$	−43600.3	+	18597.5i	−0.0531826	+	0.0226848i
$233$	−31445.0	−	31445.0i	−0.0379456	−	0.0379456i	0.687879	−	0.725825i	$-0.258542\pi$
$233$	−31445.0	−	31445.0i	−0.0379456	−	0.0379456i	−0.725825	+	0.687879i	$0.758542\pi$
$234$	489551.	−	204785.i	0.584465	−	0.244489i
$235$	117558.	−	29110.0i	0.138861	−	0.0343853i
$236$	291220.	−	295318.i	0.340362	−	0.345152i
$237$	−762909.	−	762909.i	−0.882271	−	0.882271i
$238$	374900.	−	914108.i	0.429016	−	1.04606i
$239$	−1.10786e6			−1.25455			−0.627275	−	0.778798i	$-0.715830\pi$
$239$	−1.10786e6			−1.25455			−0.627275	+	0.778798i	$0.715830\pi$
$240$	−350274.	−	1.33434e6i	−0.392536	−	1.49534i
$241$	1.21171e6			1.34387			0.671935	−	0.740610i	$-0.265463\pi$
$241$	1.21171e6			1.34387			0.671935	+	0.740610i	$0.265463\pi$
$242$	−13058.6	+	31840.3i	−0.0143337	+	0.0349494i
$243$	−853119.	−	853119.i	−0.926817	−	0.926817i
$244$	−456866.	+	463295.i	−0.491263	+	0.498176i
$245$	−72391.7	−	43655.7i	−0.0770502	−	0.0464649i
$246$	375222.	−	156960.i	0.395321	−	0.165368i
$247$	−341044.	−	341044.i	−0.355687	−	0.355687i
$248$	659669.	+	1.54654e6i	0.681078	+	1.59673i
$249$			966332.i			0.987707i
$250$	−426615.	+	891382.i	−0.431704	+	0.902015i
$251$	1.47622e6			1.47899			0.739496	−	0.673161i	$-0.235064\pi$
$251$	1.47622e6			1.47899			0.739496	+	0.673161i	$0.235064\pi$
$252$	1.33680e6	−	9340.31i	1.32607	−	0.00926531i
$253$	1.33075e6	−	1.33075e6i	1.30705	−	1.30705i
$254$	1.11547e6	−	466616.i	1.08486	−	0.453811i
$255$	−982528.	+	1.62927e6i	−0.946226	+	1.56907i
$256$	−1.04817e6	+	29301.5i	−0.999609	+	0.0279441i
$257$	−581010.	+	581010.i	−0.548720	+	0.548720i	−0.926071	−	0.377350i	$-0.876835\pi$
$257$	−581010.	+	581010.i	−0.548720	+	0.548720i	0.377350	+	0.926071i	$0.376835\pi$
$258$	320632.	+	131500.i	0.299887	+	0.122992i
$259$			381804.i			0.353664i
$260$	−253562.	+	427189.i	−0.232622	+	0.391910i
$261$			88454.3i			0.0803744i
$262$	−78218.2	+	190717.i	−0.0703970	+	0.171647i
$263$	981805.	−	981805.i	0.875257	−	0.875257i	−0.117782	−	0.993039i	$-0.537578\pi$
$263$	981805.	−	981805.i	0.875257	−	0.875257i	0.993039	+	0.117782i	$0.0375784\pi$
$264$	−1.59342e6	−	640535.i	−1.40709	−	0.565631i
$265$	−70415.9	−	284367.i	−0.0615965	−	0.248750i
$266$	−468892.	−	1.12091e6i	−0.406321	−	0.971333i
$267$	−1.93419e6	+	1.93419e6i	−1.66043	+	1.66043i
$268$	−1.93660e6	+	13531.1i	−1.64703	+	0.0115079i
$269$	1.47782e6			1.24520			0.622601	−	0.782539i	$-0.286076\pi$
$269$	1.47782e6			1.24520			0.622601	+	0.782539i	$0.286076\pi$
$270$	−714716.	−	105436.i	−0.596656	−	0.0880194i
$271$			406018.i			0.335832i	0.985801	+	0.167916i	$0.0537038\pi$
$271$			406018.i			0.335832i	−0.985801	+	0.167916i	$0.946296\pi$
$272$	1.03676e6	+	1.00819e6i	0.849685	+	0.826264i
$273$	−585264.	−	585264.i	−0.475276	−	0.475276i
$274$	−569069.	−	1.36039e6i	−0.457919	−	1.09468i
$275$	574046.	+	1.08804e6i	0.457736	+	0.867585i
$276$	−2.62513e6	−	2.58870e6i	−2.07433	−	2.04554i
$277$	−269838.	−	269838.i	−0.211302	−	0.211302i	0.593519	−	0.804820i	$-0.297738\pi$
$277$	−269838.	−	269838.i	−0.211302	−	0.211302i	−0.804820	+	0.593519i	$0.797738\pi$
$278$	188396.	+	77266.0i	0.146204	+	0.0599621i
$279$	3.13754e6			2.41312
$280$	−999359.	+	753304.i	−0.761774	+	0.574216i
$281$	−1.13283e6			−0.855854			−0.427927	−	0.903813i	$-0.640756\pi$
$281$	−1.13283e6			−0.855854			−0.427927	+	0.903813i	$0.640756\pi$
$282$	−273260.	−	112071.i	−0.204623	−	0.0839212i
$283$	−593049.	−	593049.i	−0.440174	−	0.440174i	0.451896	−	0.892070i	$-0.350748\pi$
$283$	−593049.	−	593049.i	−0.440174	−	0.440174i	−0.892070	+	0.451896i	$0.850748\pi$
$284$	97366.0	−	98736.1i	0.0716327	−	0.0726407i
$285$	562405.	+	2.27121e6i	0.410144	+	1.65632i
$286$	238651.	+	570509.i	0.172523	+	0.412427i
$287$	−260899.	−	260899.i	−0.186968	−	0.186968i
$288$	−717119.	+	1.82059e6i	−0.509460	+	1.29339i
$289$		−	574582.i		−	0.404676i
$290$	−49380.6	−	66471.2i	−0.0344795	−	0.0464129i
$291$	203656.			0.140982
$292$	−19674.9	−	2.81591e6i	−0.0135038	−	1.93269i
$293$	−1.56665e6	+	1.56665e6i	−1.06611	+	1.06611i	−0.0684596	+	0.997654i	$0.521808\pi$
$293$	−1.56665e6	+	1.56665e6i	−1.06611	+	1.06611i	−0.997654	+	0.0684596i	$0.978192\pi$
$294$	79559.1	+	190191.i	0.0536811	+	0.128328i
$295$	620459.	+	374166.i	0.415105	+	0.250328i
$296$	−518522.	−	208439.i	−0.343984	−	0.138277i
$297$	−635936.	+	635936.i	−0.418333	+	0.418333i
$298$	−261696.	+	638087.i	−0.170709	+	0.416235i
$299$			1.32762e6i			0.858807i
$300$	2.12359e6	−	1.13944e6i	1.36229	−	0.730952i
$301$		−	314377.i		−	0.200002i
$302$	870399.	+	356974.i	0.549163	+	0.225226i
$303$	958568.	−	958568.i	0.599814	−	0.599814i
$304$	1.77828e6	−	24851.1i	1.10361	−	0.0154227i
$305$	−973375.	−	586991.i	−0.599143	−	0.361312i
$306$	2.48958e6	−	1.04142e6i	1.51992	−	0.635803i
$307$	996619.	−	996619.i	0.603509	−	0.603509i	−0.337733	−	0.941242i	$-0.609660\pi$
$307$	996619.	−	996619.i	0.603509	−	0.603509i	0.941242	+	0.337733i	$0.109660\pi$
$308$	10884.9	+	1.55787e6i	0.00653805	+	0.935738i
$309$	−3.68403e6			−2.19496
$310$	−2.35778e6	+	1.75157e6i	−1.39348	+	1.03520i
$311$		−	1.68351e6i		−	0.986994i	−0.869747	−	0.493497i	$-0.835718\pi$
$311$		−	1.68351e6i		−	0.986994i	0.869747	−	0.493497i	$-0.164282\pi$
$312$	1.11435e6	−	475323.i	0.648091	−	0.276441i
$313$	1.25981e6	+	1.25981e6i	0.726850	+	0.726850i	0.969991	−	0.243141i	$-0.0781778\pi$
$313$	1.25981e6	+	1.25981e6i	0.726850	+	0.726850i	−0.243141	+	0.969991i	$0.578178\pi$
$314$	773679.	−	323639.i	0.442830	−	0.185241i
$315$	561335.	+	2.26689e6i	0.318747	+	1.28722i
$316$	−1.02006e6	−	1.00590e6i	−0.574654	−	0.566679i
$317$	423231.	+	423231.i	0.236554	+	0.236554i	0.815421	−	0.578868i	$-0.196505\pi$
$317$	423231.	+	423231.i	0.236554	+	0.236554i	−0.578868	+	0.815421i	$0.696505\pi$
$318$	−271095.	+	661004.i	−0.150333	+	0.366553i
$319$	−103082.			−0.0567161
$320$	−477466.	−	1.76847e6i	−0.260656	−	0.965432i
$321$	−935208.			−0.506577
$322$	−1.26910e6	+	3.09440e6i	−0.682111	+	1.66317i
$323$	−1.73435e6	−	1.73435e6i	−0.924977	−	0.924977i
$324$	−615802.	−	607257.i	−0.325896	−	0.321373i
$325$	−829089.	−	256391.i	−0.435404	−	0.134646i
$326$	691.287	−	289.174i	0.000360259	−	0.000150701i
$327$	3.26729e6	+	3.26729e6i	1.68973	+	1.68973i
$328$	496757.	−	211890.i	0.254952	−	0.108749i
$329$			267929.i			0.136468i
$330$	437836.	−	2.96796e6i	0.221323	−	1.50028i
$331$	608898.			0.305474			0.152737	−	0.988267i	$-0.451191\pi$
$331$	608898.			0.305474			0.152737	+	0.988267i	$0.451191\pi$
$332$	8964.94	+	1.28308e6i	0.00446378	+	0.638864i
$333$	−737413.	+	737413.i	−0.364418	+	0.364418i
$334$	1.98442e6	−	830107.i	0.973346	−	0.407163i
$335$	−813194.	−	3.28399e6i	−0.395897	−	1.59879i
$336$	3.05170e6	−	42646.8i	1.47466	−	0.0206081i
$337$	−828055.	+	828055.i	−0.397177	+	0.397177i	−0.877236	−	0.480059i	$-0.840615\pi$
$337$	−828055.	+	828055.i	−0.397177	+	0.397177i	0.480059	+	0.877236i	$0.340615\pi$
$338$	1.53964e6	+	631446.i	0.733039	+	0.300639i
$339$			708776.i			0.334973i
$340$	−1.28947e6	+	2.17243e6i	−0.604942	+	1.01918i
$341$			3.65640e6i			1.70282i
$342$	1.25931e6	−	3.07053e6i	0.582192	−	1.41954i
$343$	1.60200e6	−	1.60200e6i	0.735239	−	0.735239i
$344$	426950.	+	171629.i	0.194527	+	0.0781976i
$345$	3.32602e6	−	5.51535e6i	1.50445	−	2.49474i
$346$	1.19825e6	+	2.86449e6i	0.538094	+	1.28634i
$347$	1.47278e6	−	1.47278e6i	0.656622	−	0.656622i	−0.297957	−	0.954579i	$-0.596305\pi$
$347$	1.47278e6	−	1.47278e6i	0.656622	−	0.656622i	0.954579	+	0.297957i	$0.0963053\pi$
$348$	1410.94	+	201936.i	0.000624540	+	0.0893853i
$349$	−352439.			−0.154889			−0.0774445	−	0.996997i	$-0.524676\pi$
$349$	−352439.			−0.154889			−0.0774445	+	0.996997i	$0.524676\pi$
$350$	−1.68734e6	−	1.39014e6i	−0.736264	−	0.606579i
$351$		−	634442.i		−	0.274868i
$352$	−2.12166e6	−	835709.i	−0.912680	−	0.359500i
$353$	1.01727e6	+	1.01727e6i	0.434511	+	0.434511i	0.890160	−	0.455649i	$-0.150593\pi$
$353$	1.01727e6	+	1.01727e6i	0.434511	+	0.434511i	−0.455649	+	0.890160i	$0.650593\pi$
$354$	−681889.	−	1.63010e6i	−0.289205	−	0.691361i
$355$	207443.	+	125098.i	0.0873631	+	0.0526841i
$356$	−2.55024e6	+	2.58613e6i	−1.06649	+	1.08150i
$357$	−2.97632e6	−	2.97632e6i	−1.23597	−	1.23597i
$358$	253319.	+	103893.i	0.104462	+	0.0428428i
$359$	−1.99389e6			−0.816518			−0.408259	−	0.912866i	$-0.633864\pi$
$359$	−1.99389e6			−0.816518			−0.408259	+	0.912866i	$0.633864\pi$
$360$	−3.38507e6	−	475228.i	−1.37661	−	0.193262i
$361$	−540266.			−0.218192
$362$	−2.91271e6	−	1.19458e6i	−1.16822	−	0.479120i
$363$	103672.	+	103672.i	0.0412946	+	0.0412946i
$364$	−782534.	−	771674.i	−0.309563	−	0.305268i
$365$	4.77509e6	−	1.18243e6i	1.87607	−	0.464560i
$366$	1.06975e6	+	2.55729e6i	0.417425	+	0.997878i
$367$	−2.86292e6	−	2.86292e6i	−1.10954	−	1.10954i	−0.993210	−	0.116333i	$-0.962886\pi$
$367$	−2.86292e6	−	2.86292e6i	−1.10954	−	1.10954i	−0.116333	−	0.993210i	$-0.537114\pi$
$368$	−3.50962e6	−	3.41288e6i	−1.35095	−	1.31371i
$369$		−	1.00780e6i		−	0.385307i
$370$	142478.	−	965816.i	0.0541058	−	0.366767i
$371$	648109.			0.244463
$372$	7.16284e6	−	50047.1i	2.68366	−	0.0187509i
$373$	1.23841e6	−	1.23841e6i	0.460886	−	0.460886i	−0.438060	−	0.898946i	$-0.644334\pi$
$373$	1.23841e6	−	1.23841e6i	0.460886	−	0.460886i	0.898946	+	0.438060i	$0.144334\pi$
$374$	1.21364e6	+	2.90128e6i	0.448653	+	1.07253i
$375$	2.80197e6	+	3.14221e6i	1.02893	+	1.15387i
$376$	−363870.	−	146271.i	−0.132732	−	0.0533567i
$377$	51419.9	−	51419.9i	0.0186328	−	0.0186328i
$378$	606476.	−	1.47875e6i	0.218315	−	0.532312i
$379$			2.18671e6i			0.781977i	0.920396	+	0.390989i	$0.127867\pi$
$379$			2.18671e6i			0.781977i	−0.920396	+	0.390989i	$0.872133\pi$
$380$	767822.	+	3.01045e6i	0.272773	+	1.06948i
$381$		−	5.15125e6i		−	1.81803i
$382$	167321.	+	68622.8i	0.0586668	+	0.0240608i
$383$	−1.81151e6	+	1.81151e6i	−0.631021	+	0.631021i	−0.948324	−	0.317303i	$-0.897223\pi$
$383$	−1.81151e6	+	1.81151e6i	−0.631021	+	0.631021i	0.317303	+	0.948324i	$0.397223\pi$
$384$	−1.60810e6	+	4.16774e6i	−0.556526	+	1.44236i
$385$	−2.64176e6	+	654163.i	−0.908327	+	0.224923i
$386$	449189.	−	187901.i	0.153448	−	0.0641891i
$387$	607184.	−	607184.i	0.206083	−	0.206083i
$388$	270411.	−	1889.38i	0.0911895	−	0.000637146i
$389$	−1.90713e6			−0.639007			−0.319504	−	0.947585i	$-0.603516\pi$
$389$	−1.90713e6			−0.639007			−0.319504	+	0.947585i	$0.603516\pi$
$390$	1.26209e6	+	1.69889e6i	0.420173	+	0.565594i
$391$			6.75150e6i			2.23336i
$392$	107402.	+	251794.i	0.0353017	+	0.0827618i
$393$	620971.	+	620971.i	0.202810	+	0.202810i
$394$	4.85497e6	−	2.03089e6i	1.57560	−	0.659093i
$395$	1.29240e6	−	2.14312e6i	0.416778	−	0.691120i
$396$	−2.98783e6	+	3.02987e6i	−0.957454	+	0.970927i
$397$	592558.	+	592558.i	0.188693	+	0.188693i	0.795131	−	0.606438i	$-0.207402\pi$
$397$	592558.	+	592558.i	0.188693	+	0.188693i	−0.606438	+	0.795131i	$0.707402\pi$
$398$	378919.	−	923907.i	0.119905	−	0.292362i
$399$	−5.17637e6			−1.62777
$400$	2.80910e6	−	1.53263e6i	0.877843	−	0.478948i
$401$	4.18432e6			1.29946			0.649732	−	0.760164i	$-0.274881\pi$
$401$	4.18432e6			1.29946			0.649732	+	0.760164i	$0.274881\pi$
$402$	−3.13073e6	+	7.63357e6i	−0.966230	+	2.35593i
$403$	−1.82390e6	−	1.82390e6i	−0.559421	−	0.559421i
$404$	1.26388e6	−	1.28166e6i	0.385258	−	0.390680i
$405$	780217.	−	1.29379e6i	0.236362	−	0.391946i
$406$	169002.	−	70695.8i	0.0508836	−	0.0212852i
$407$	−859359.	−	859359.i	−0.257151	−	0.257151i
$408$	5.66695e6	−	2.41722e6i	1.68539	−	0.718895i
$409$			4.57447e6i			1.35217i	0.736822	+	0.676087i	$0.236326\pi$
$409$			4.57447e6i			1.35217i	−0.736822	+	0.676087i	$0.763674\pi$
$410$	562614.	+	757334.i	0.165292	+	0.222499i
$411$	−6.28229e6			−1.83448
$412$	−4.89159e6	+	34177.8i	−1.41973	+	0.00991976i
$413$	−1.13344e6	+	1.13344e6i	−0.326982	+	0.326982i
$414$	−8.42762e6	+	3.52538e6i	−2.41660	+	1.01089i
$415$	−2.17579e6	+	538777.i	−0.620149	+	0.153564i
$416$	1.47521e6	−	641464.i	0.417946	−	0.181735i
$417$	613412.	−	613412.i	0.172748	−	0.172748i
$418$	3.57831e6	+	1.46756e6i	1.00170	+	0.410823i
$419$		−	2.74512e6i		−	0.763883i	−0.924186	−	0.381942i	$-0.875256\pi$
$419$		−	2.74512e6i		−	0.763883i	0.924186	−	0.381942i	$-0.124744\pi$
$420$	1.31766e6	+	5.16623e6i	0.364484	+	1.42906i
$421$			1.53930e6i			0.423272i	0.977349	+	0.211636i	$0.0678791\pi$
$421$			1.53930e6i			0.423272i	−0.977349	+	0.211636i	$0.932121\pi$
$422$	1.24773e6	−	3.04231e6i	0.341067	−	0.831615i
$423$	−517475.	+	517475.i	−0.140617	+	0.140617i
$424$	−353824.	+	880185.i	−0.0955811	+	0.237771i
$425$	−4.21627e6	−	1.30386e6i	−1.13228	−	0.350153i
$426$	−227982.	−	545003.i	−0.0608661	−	0.145504i
$427$	1.77814e6	−	1.77814e6i	0.471950	−	0.471950i
$428$	−1.24175e6	+	8676.20i	−0.327662	+	0.00228939i
$429$	2.63461e6			0.691150
$430$	−117316.	+	795251.i	−0.0305976	+	0.207412i
$431$		−	6.63408e6i		−	1.72023i	−0.510097	−	0.860117i	$-0.670391\pi$
$431$		−	6.63408e6i		−	1.72023i	0.510097	−	0.860117i	$-0.329609\pi$
$432$	1.67717e6	+	1.63094e6i	0.432383	+	0.420465i
$433$	−2.39961e6	−	2.39961e6i	−0.615066	−	0.615066i	0.329196	−	0.944262i	$-0.393222\pi$
$433$	−2.39961e6	−	2.39961e6i	−0.615066	−	0.615066i	−0.944262	+	0.329196i	$0.893222\pi$
$434$	−2.50763e6	−	5.99465e6i	−0.639058	−	1.52770i
$435$	−342434.	+	84794.9i	−0.0867669	+	0.0214855i
$436$	4.36857e6	+	4.30794e6i	1.10058	+	1.08531i
$437$	5.87106e6	+	5.87106e6i	1.47066	+	1.47066i
$438$	−1.10996e7	−	4.55224e6i	−2.76454	−	1.13381i
$439$	524709.			0.129944			0.0649721	−	0.997887i	$-0.479304\pi$
$439$	524709.			0.129944			0.0649721	+	0.997887i	$0.479304\pi$
$440$	553817.	−	3.94486e6i	0.136375	−	0.971405i
$441$	510828.			0.125077
$442$	−2.05262e6	−	841836.i	−0.499751	−	0.204961i
$443$	1.58528e6	+	1.58528e6i	0.383793	+	0.383793i	0.872467	−	0.488674i	$-0.162519\pi$
$443$	1.58528e6	+	1.58528e6i	0.383793	+	0.383793i	−0.488674	+	0.872467i	$0.662519\pi$
$444$	−1.67171e6	+	1.69524e6i	−0.402442	+	0.408106i
$445$	−5.43342e6	−	3.27661e6i	−1.30069	−	0.784377i
$446$	−288966.	−	690790.i	−0.0687875	−	0.164441i
$447$	2.07760e6	+	2.07760e6i	0.491804	+	0.491804i
$448$	4.05159e6	−	84937.2i	0.953742	−	0.0199941i
$449$		−	1.50759e6i		−	0.352912i	−0.984309	−	0.176456i	$-0.943537\pi$
$449$		−	1.50759e6i		−	0.352912i	0.984309	−	0.176456i	$-0.0564634\pi$
$450$	−574023.	−	5.94382e6i	−0.133628	−	1.38368i
$451$	1.17446e6			0.271891
$452$	6575.53	+	941101.i	0.00151386	+	0.216666i
$453$	2.83400e6	−	2.83400e6i	0.648866	−	0.648866i
$454$	134374.	+	321229.i	0.0305968	+	0.0731435i
$455$	991465.	−	1.64409e6i	0.224517	−	0.372304i
$456$	2.82595e6	−	7.02995e6i	0.636433	−	1.58322i
$457$	494801.	−	494801.i	0.110826	−	0.110826i	−0.649519	−	0.760345i	$-0.725030\pi$
$457$	494801.	−	494801.i	0.110826	−	0.110826i	0.760345	+	0.649519i	$0.225030\pi$
$458$	−964248.	+	2.35110e6i	−0.214795	+	0.523730i
$459$		−	3.22641e6i		−	0.714804i
$460$	4.36506e6	−	7.35405e6i	0.961825	−	1.62044i
$461$			6.05609e6i			1.32721i	0.748083	+	0.663606i	$0.230975\pi$
$461$			6.05609e6i			1.32721i	−0.748083	+	0.663606i	$0.769025\pi$
$462$	6.14072e6	+	2.51847e6i	1.33849	+	0.548950i
$463$	−516873.	+	516873.i	−0.112055	+	0.112055i	−0.760911	−	0.648856i	$-0.775248\pi$
$463$	−516873.	+	516873.i	−0.112055	+	0.112055i	0.648856	+	0.760911i	$0.275248\pi$
$464$	3746.84	+	268114.i	0.000807924	+	0.0578130i
$465$	3.00774e6	+	1.21464e7i	0.645071	+	2.60505i
$466$	−232073.	+	97079.0i	−0.0495062	+	0.0207091i
$467$	−4.71207e6	+	4.71207e6i	−0.999816	+	0.999816i	−1.00000		0.000184243i	$-0.999941\pi$
$467$	−4.71207e6	+	4.71207e6i	−0.999816	+	0.999816i	0.000184243		1.00000i	$0.499941\pi$
$468$	−20973.6	−	3.00178e6i	−0.00442648	−	0.633526i
$469$	7.48465e6			1.57123
$470$	99983.3	−	677756.i	0.0208777	−	0.141524i
$471$		−	3.57285e6i		−	0.742099i
$472$	−920524.	−	2.15809e6i	−0.190187	−	0.445876i
$473$	707594.	+	707594.i	0.145422	+	0.145422i
$474$	−5.63050e6	+	2.35531e6i	−1.15107	+	0.481506i
$475$	−4.80027e6	+	2.53261e6i	−0.976183	+	0.515033i
$476$	−3.97951e6	−	3.92429e6i	−0.805031	−	0.793860i
$477$	1.25175e6	+	1.25175e6i	0.251896	+	0.251896i
$478$	−2.37803e6	+	5.79827e6i	−0.476044	+	1.16072i
$479$	−163309.			−0.0325216			−0.0162608	−	0.999868i	$-0.505176\pi$
$479$	−163309.			−0.0325216			−0.0162608	+	0.999868i	$0.505176\pi$
$480$	−7.73552e6	−	1.03092e6i	−1.53245	−	0.204232i
$481$	857339.			0.168962
$482$	2.60096e6	−	6.34184e6i	0.509936	−	1.24336i
$483$	1.00753e7	+	1.00753e7i	1.96513	+	1.96513i
$484$	138615.	+	136691.i	0.0268966	+	0.0265233i
$485$	113548.	+	458550.i	0.0219192	+	0.0885182i
$486$	−6.29627e6	+	2.63381e6i	−1.20918	+	0.505817i
$487$	5.12902e6	+	5.12902e6i	0.979969	+	0.979969i	0.999803	−	0.0198345i	$-0.00631393\pi$
$487$	5.12902e6	+	5.12902e6i	0.979969	+	0.979969i	−0.0198345	+	0.999803i	$0.506314\pi$
$488$	1.44412e6	+	3.38560e6i	0.274506	+	0.643556i
$489$		−	3192.36i		−	0.000603726i
$490$	−383874.	+	285175.i	−0.0722268	+	0.0536564i
$491$	5.08438e6			0.951775			0.475888	−	0.879506i	$-0.342127\pi$
$491$	5.08438e6			0.951775			0.475888	+	0.879506i	$0.342127\pi$
$492$	−16075.4	−	2.30074e6i	−0.00299399	−	0.428505i
$493$	261492.	−	261492.i	0.0484552	−	0.0484552i
$494$	−2.51700e6	+	1.05289e6i	−0.464052	+	0.194119i
$495$	−6.36572e6	−	3.83883e6i	−1.16771	−	0.704184i
$496$	9.51023e6	−	132903.i	1.73575	−	0.0242567i
$497$	−378952.	+	378952.i	−0.0688166	+	0.0688166i
$498$	5.05757e6	+	2.07425e6i	0.913837	+	0.374789i
$499$			547439.i			0.0984202i	0.998788	+	0.0492101i	$0.0156704\pi$
$499$			547439.i			0.0984202i	−0.998788	+	0.0492101i	$0.984330\pi$
$500$	3.74957e6	+	4.14617e6i	0.670743	+	0.741690i
$501$		−	9.16404e6i		−	1.63114i
$502$	3.16872e6	−	7.72620e6i	0.561209	−	1.36838i
$503$	−1.04873e6	+	1.04873e6i	−0.184819	+	0.184819i	−0.793452	−	0.608633i	$-0.791718\pi$
$503$	−1.04873e6	+	1.04873e6i	−0.184819	+	0.184819i	0.608633	+	0.793452i	$0.291718\pi$
$504$	2.82058e6	−	7.01658e6i	0.494609	−	1.23041i
$505$	2.69275e6	+	1.62386e6i	0.469860	+	0.283348i
$506$	−4.10837e6	−	9.82130e6i	−0.713335	−	1.70527i
$507$	5.01303e6	−	5.01303e6i	0.866124	−	0.866124i
$508$	−47789.6	−	6.83974e6i	−0.00821626	−	1.17593i
$509$	559560.			0.0957309			0.0478655	−	0.998854i	$-0.484758\pi$
$509$	559560.			0.0957309			0.0478655	+	0.998854i	$0.484758\pi$
$510$	6.41825e6	+	8.63960e6i	1.09267	+	1.47085i
$511$			1.08831e7i			1.84374i
$512$	−2.09655e6	+	5.54877e6i	−0.353451	+	0.935453i
$513$	−2.80566e6	−	2.80566e6i	−0.470698	−	0.470698i
$514$	1.79374e6	+	4.28803e6i	0.299468	+	0.715896i
$515$	−2.05402e6	−	8.29493e6i	−0.341261	−	1.37814i
$516$	1.37648e6	−	1.39585e6i	0.227587	−	0.230789i
$517$	−603050.	−	603050.i	−0.0992264	−	0.0992264i
$518$	1.99828e6	+	819548.i	0.327214	+	0.134199i
$519$	1.32282e7			2.15567
$520$	1.69154e6	+	2.24405e6i	0.274330	+	0.363936i
$521$	−9.75773e6			−1.57491			−0.787453	−	0.616375i	$-0.788600\pi$
$521$	−9.75773e6			−1.57491			−0.787453	+	0.616375i	$0.788600\pi$
$522$	462951.	+	189868.i	0.0743632	+	0.0304983i
$523$	−6.38456e6	−	6.38456e6i	−1.02065	−	1.02065i	−0.999782	−	0.0208682i	$-0.993357\pi$
$523$	−6.38456e6	−	6.38456e6i	−1.02065	−	1.02065i	−0.0208682	−	0.999782i	$-0.506643\pi$
$524$	830276.	+	818754.i	0.132097	+	0.130264i
$525$	−8.23772e6	+	4.34621e6i	−1.30439	+	0.688196i
$526$	−3.03110e6	−	7.24601e6i	−0.477678	−	1.14192i
$527$	−9.27532e6	−	9.27532e6i	−1.45480	−	1.45480i
$528$	−6.77272e6	+	6.96470e6i	−1.05725	+	1.08722i
$529$		−	1.64186e7i		−	2.55092i
$530$	−1.63946e6	−	241855.i	−0.253520	−	0.0373995i
$531$	−4.37823e6			−0.673848
$532$	−6.87310e6	+	48022.7i	−1.05287	+	0.00735644i
$533$	−585848.	+	585848.i	−0.0893238	+	0.0893238i
$534$	5.97137e6	+	1.42749e7i	0.906194	+	2.16631i
$535$	−521423.	−	2.10571e6i	−0.0787601	−	0.318064i
$536$	−4.08611e6	+	1.01648e7i	−0.614325	+	1.52822i
$537$	824801.	−	824801.i	0.123428	−	0.123428i
$538$	3.17215e6	−	7.73457e6i	0.472497	−	1.15207i
$539$			595303.i			0.0882605i
$540$	−2.08598e6	+	3.51435e6i	−0.307840	+	0.518634i
$541$			3.35735e6i			0.493178i	0.969120	+	0.246589i	$0.0793098\pi$
$541$			3.35735e6i			0.493178i	−0.969120	+	0.246589i	$0.920690\pi$
$542$	2.12501e6	+	871524.i	0.310716	+	0.127433i
$543$	−9.48373e6	+	9.48373e6i	−1.38032	+	1.38032i
$544$	7.50206e6	−	3.26211e6i	1.08688	−	0.472609i
$545$	−5.53494e6	+	9.17829e6i	−0.798219	+	1.32364i
$546$	−4.31942e6	+	1.80687e6i	−0.620075	+	0.259385i
$547$	−8.74841e6	+	8.74841e6i	−1.25015	+	1.25015i	−0.294493	+	0.955654i	$0.595151\pi$
$547$	−8.74841e6	+	8.74841e6i	−1.25015	+	1.25015i	−0.955654	+	0.294493i	$0.904849\pi$
$548$	−8.34152e6	+	58282.6i	−1.18657	+	0.00829063i
$549$	6.86856e6			0.972601
$550$	6.92675e6	−	668949.i	0.976388	−	0.0942945i
$551$		−	454783.i		−	0.0638154i
$552$	−1.91836e7	+	8.18267e6i	−2.67967	+	1.14300i
$553$	3.91500e6	+	3.91500e6i	0.544401	+	0.544401i
$554$	−1.99148e6	+	833061.i	−0.275678	+	0.115319i
$555$	−3.56166e6	−	2.14785e6i	−0.490818	−	0.295986i
$556$	808787.	−	820169.i	0.110955	−	0.112517i
$557$	−6.88911e6	−	6.88911e6i	−0.940861	−	0.940861i	0.0574855	−	0.998346i	$-0.481692\pi$
$557$	−6.88911e6	−	6.88911e6i	−0.940861	−	0.940861i	−0.998346	+	0.0574855i	$0.981692\pi$
$558$	6.73478e6	−	1.64212e7i	0.915667	−	2.23265i
$559$	−705932.			−0.0955505
$560$	1.79749e6	+	6.84740e6i	0.242212	+	0.922690i
$561$	1.33981e7			1.79736
$562$	−2.43164e6	+	5.92900e6i	−0.324757	+	0.791845i
$563$	4.86138e6	+	4.86138e6i	0.646381	+	0.646381i	0.952117	−	0.305735i	$-0.0989022\pi$
$563$	4.86138e6	+	4.86138e6i	0.646381	+	0.646381i	−0.305735	+	0.952117i	$0.598902\pi$
$564$	−1.17311e6	+	1.18962e6i	−0.155290	+	0.157475i
$565$	−1.59588e6	+	395177.i	−0.210319	+	0.0520799i
$566$	−4.37688e6	+	1.83090e6i	−0.574279	+	0.240228i
$567$	2.36347e6	+	2.36347e6i	0.308739	+	0.308739i
$568$	−307766.	−	721531.i	−0.0400267	−	0.0938391i
$569$			3.10047e6i			0.401464i	0.979646	+	0.200732i	$0.0643321\pi$
$569$			3.10047e6i			0.401464i	−0.979646	+	0.200732i	$0.935668\pi$
$570$	1.30942e7	+	1.93167e6i	1.68808	+	0.249027i
$571$	−3.53509e6			−0.453743			−0.226871	−	0.973925i	$-0.572850\pi$
$571$	−3.53509e6			−0.453743			−0.226871	+	0.973925i	$0.572850\pi$
$572$	3.49819e6	−	24442.0i	0.447047	−	0.00312354i
$573$	544794.	−	544794.i	0.0693180	−	0.0693180i
$574$	−1.92552e6	+	805467.i	−0.243931	+	0.102039i
$575$	1.42727e7	+	4.41377e6i	1.80027	+	0.556724i
$576$	7.98925e6	+	7.66116e6i	1.00334	+	0.962140i
$577$	5.07239e6	−	5.07239e6i	0.634268	−	0.634268i	−0.314867	−	0.949136i	$-0.601960\pi$
$577$	5.07239e6	−	5.07239e6i	0.634268	−	0.634268i	0.949136	+	0.314867i	$0.101960\pi$
$578$	−3.00724e6	−	1.23335e6i	−0.374411	−	0.153556i
$579$		−	2.07435e6i		−	0.257150i
$580$	−453892.	+	115766.i	−0.0560251	+	0.0142893i
$581$		−	4.95890e6i		−	0.609460i
$582$	437150.	−	1.06589e6i	0.0534962	−	0.130438i
$583$	−1.45875e6	+	1.45875e6i	−0.177750	+	0.177750i
$584$	−1.47801e7	−	5.94142e6i	−1.79327	−	0.720872i
$585$	5.09028e6	−	1.26047e6i	0.614968	−	0.152281i
$586$	4.83668e6	+	1.15624e7i	0.581839	+	1.39092i
$587$	2.79898e6	−	2.79898e6i	0.335277	−	0.335277i	−0.519309	−	0.854586i	$-0.673811\pi$
$587$	2.79898e6	−	2.79898e6i	0.335277	−	0.335277i	0.854586	+	0.519309i	$0.173811\pi$
$588$	1.16619e6	−	8148.24i	0.139100	−	0.000971898i
$589$	−1.61315e7			−1.91596
$590$	3.29013e6	−	2.44419e6i	0.389119	−	0.289072i
$591$		−	2.24202e7i		−	2.64041i
$592$	−2.20394e6	+	2.26641e6i	−0.258461	+	0.265788i
$593$	−7.12818e6	−	7.12818e6i	−0.832419	−	0.832419i	0.155429	−	0.987847i	$-0.450324\pi$
$593$	−7.12818e6	−	7.12818e6i	−0.832419	−	0.832419i	−0.987847	+	0.155429i	$0.950324\pi$
$594$	1.96331e6	+	4.69340e6i	0.228309	+	0.545785i
$595$	5.04202e6	−	8.36090e6i	0.583864	−	0.968190i
$596$	2.77787e6	+	2.73932e6i	0.320329	+	0.315884i
$597$	−3.00822e6	−	3.00822e6i	−0.345441	−	0.345441i
$598$	6.94847e6	+	2.84975e6i	0.794577	+	0.325877i
$599$	2.14707e6			0.244500			0.122250	−	0.992499i	$-0.460989\pi$
$599$	2.14707e6			0.244500			0.122250	+	0.992499i	$0.460989\pi$
$600$	−1.40527e6	−	1.35602e7i	−0.159361	−	1.53776i
$601$	−8.97465e6			−1.01352			−0.506759	−	0.862088i	$-0.669157\pi$
$601$	−8.97465e6			−1.01352			−0.506759	+	0.862088i	$0.669157\pi$
$602$	−1.64538e6	−	674814.i	−0.185044	−	0.0758915i
$603$	1.44558e7	+	1.44558e7i	1.61900	+	1.61900i
$604$	3.73665e6	−	3.78923e6i	0.416764	−	0.422629i
$605$	−175624.	+	291228.i	−0.0195073	+	0.0323478i
$606$	−2.95936e6	−	7.07452e6i	−0.327353	−	0.782556i
$607$	3.92374e6	+	3.92374e6i	0.432244	+	0.432244i	0.889391	−	0.457147i	$-0.151129\pi$
$607$	3.92374e6	+	3.92374e6i	0.432244	+	0.432244i	−0.457147	+	0.889391i	$0.651129\pi$
$608$	3.68703e6	−	9.36046e6i	0.404499	−	1.02692i
$609$		−	780452.i		−	0.0852714i
$610$	−5.16155e6	+	3.83445e6i	−0.561636	+	0.417233i
$611$	601633.			0.0651972
$612$	−106660.	−	1.52653e7i	−0.0115112	−	1.64751i
$613$	−9.26263e6	+	9.26263e6i	−0.995596	+	0.995596i	−0.999990	−	0.00439430i	$-0.998601\pi$
$613$	−9.26263e6	+	9.26263e6i	−0.995596	+	0.995596i	0.00439430	+	0.999990i	$0.498601\pi$
$614$	−3.07683e6	−	7.35535e6i	−0.329369	−	0.787376i
$615$	3.90150e6	−	966103.i	0.415952	−	0.103000i
$616$	8.17691e6	+	3.28702e6i	0.868236	+	0.349020i
$617$	9.78524e6	−	9.78524e6i	1.03481	−	1.03481i	0.0354333	−	0.999372i	$-0.488719\pi$
$617$	9.78524e6	−	9.78524e6i	1.03481	−	1.03481i	0.999372	−	0.0354333i	$-0.0112811\pi$
$618$	−7.90782e6	+	1.92814e7i	−0.832886	+	2.03080i
$619$			7.11083e6i			0.745922i	0.927847	+	0.372961i	$0.121658\pi$
$619$			7.11083e6i			0.745922i	−0.927847	+	0.372961i	$0.878342\pi$
$620$	4.10631e6	+	1.60999e7i	0.429015	+	1.68207i
$621$			1.09219e7i			1.13650i
$622$	−8.81112e6	−	3.61368e6i	−0.913178	−	0.374518i
$623$	9.92565e6	−	9.92565e6i	1.02456	−	1.02456i
$624$	−95763.2	−	6.85257e6i	−0.00984548	−	0.704517i
$625$	−5.51274e6	+	8.06084e6i	−0.564504	+	0.825430i
$626$	9.29778e6	−	3.88938e6i	0.948295	−	0.396683i
$627$	1.16509e7	−	1.16509e7i	1.18356	−	1.18356i
$628$	−33146.3	−	4.74396e6i	−0.00335379	−	0.480001i
$629$	4.35993e6			0.439393
$630$	1.30693e7	+	1.92800e6i	1.31190	+	0.193533i
$631$		−	9.35449e6i		−	0.935291i	−0.883916	−	0.467645i	$-0.845102\pi$
$631$		−	9.35449e6i		−	0.935291i	0.883916	−	0.467645i	$-0.154898\pi$
$632$	−7.45422e6	+	3.17957e6i	−0.742352	+	0.316647i
$633$	−9.90570e6	−	9.90570e6i	−0.982598	−	0.982598i
$634$	3.12357e6	−	1.30663e6i	0.308623	−	0.129101i
$635$	1.15985e7	−	2.87207e6i	1.14148	−	0.282657i
$636$	2.87764e6	+	2.83771e6i	0.282094	+	0.278179i
$637$	−296952.	−	296952.i	−0.0289960	−	0.0289960i
$638$	−221267.	+	539509.i	−0.0215211	+	0.0524743i
$639$	−1.46381e6			−0.141818
$640$	−1.02807e7	−	1.29708e6i	−0.992135	−	0.125175i
$641$	1.48514e7			1.42765			0.713825	−	0.700324i	$-0.246961\pi$
$641$	1.48514e7			1.42765			0.713825	+	0.700324i	$0.246961\pi$
$642$	−2.00744e6	+	4.89468e6i	−0.192223	+	0.468691i
$643$	1.34506e6	+	1.34506e6i	0.128297	+	0.128297i	0.768339	−	0.640043i	$-0.221083\pi$
$643$	1.34506e6	+	1.34506e6i	0.128297	+	0.128297i	−0.640043	+	0.768339i	$0.721083\pi$
$644$	1.34713e7	+	1.32844e7i	1.27996	+	1.26219i
$645$	2.93267e6	+	1.76854e6i	0.277564	+	0.167384i
$646$	−1.28000e7	+	5.35441e6i	−1.20678	+	0.504813i
$647$	−3.19115e6	−	3.19115e6i	−0.299699	−	0.299699i	0.541197	−	0.840896i	$-0.317971\pi$
$647$	−3.19115e6	−	3.19115e6i	−0.299699	−	0.299699i	−0.840896	+	0.541197i	$0.817971\pi$
$648$	−4.50008e6	+	1.91949e6i	−0.421000	+	0.179576i
$649$		−	5.10225e6i		−	0.475500i
$650$	−3.12155e6	+	3.78892e6i	−0.289792	+	0.351749i
$651$	−2.76833e7			−2.56015
$652$	−29.6165	−	4238.76i	−2.72844e−6	−	0.000390499i
$653$	−8.97659e6	+	8.97659e6i	−0.823812	+	0.823812i	−0.986652	−	0.162840i	$-0.947934\pi$
$653$	−8.97659e6	+	8.97659e6i	−0.823812	+	0.823812i	0.162840	+	0.986652i	$0.447934\pi$
$654$	2.41136e7	−	1.00870e7i	2.20454	−	0.922185i
$655$	−1.05195e6	+	1.74440e6i	−0.0958061	+	0.158870i
$656$	−42689.4	−	3.05474e6i	−0.00387311	−	0.277150i
$657$	−2.10194e7	+	2.10194e7i	−1.89980	+	1.89980i
$658$	1.40228e6	+	575113.i	0.126261	+	0.0517832i
$659$			9.89164e6i			0.887268i	0.896208	+	0.443634i	$0.146311\pi$
$659$			9.89164e6i			0.887268i	−0.896208	+	0.443634i	$0.853689\pi$
$660$	−1.45938e7	−	8.66230e6i	−1.30409	−	0.774058i
$661$			2.63425e6i			0.234505i	0.993102	+	0.117253i	$0.0374087\pi$
$661$			2.63425e6i			0.234505i	−0.993102	+	0.117253i	$0.962591\pi$
$662$	1.30701e6	−	3.18684e6i	0.115913	−	0.282628i
$663$	−6.68330e6	+	6.68330e6i	−0.590483	+	0.590483i
$664$	6.73460e6	+	2.70723e6i	0.592777	+	0.238289i
$665$	−2.88608e6	−	1.16551e7i	−0.253078	−	1.02203i
$666$	2.27659e6	+	5.44232e6i	0.198884	+	0.475443i
$667$	−885192.	+	885192.i	−0.0770412	+	0.0770412i
$668$	−85017.4	−	1.21678e7i	−0.00737169	−	1.05505i
$669$	−3.19007e6			−0.275571
$670$	−1.89332e7	−	2.79305e6i	−1.62944	−	0.240376i
$671$			8.00441e6i			0.686314i
$672$	6.32730e6	−	1.60635e7i	0.540500	−	1.37220i
$673$	−2.40935e6	−	2.40935e6i	−0.205051	−	0.205051i	0.597109	−	0.802160i	$-0.296316\pi$
$673$	−2.40935e6	−	2.40935e6i	−0.205051	−	0.205051i	−0.802160	+	0.597109i	$0.796316\pi$
$674$	2.55643e6	+	6.11129e6i	0.216762	+	0.518183i
$675$	−6.82066e6	−	2.10925e6i	−0.576191	−	0.178184i
$676$	6.60971e6	−	6.70272e6i	0.556308	−	0.564137i
$677$	5.60330e6	+	5.60330e6i	0.469864	+	0.469864i	0.901871	−	0.432006i	$-0.142194\pi$
$677$	5.60330e6	+	5.60330e6i	0.469864	+	0.469864i	−0.432006	+	0.901871i	$0.642194\pi$
$678$	3.70958e6	+	1.52140e6i	0.309921	+	0.127107i
$679$	−1.04510e6			−0.0869925
$680$	8.60219e6	+	1.14120e7i	0.713406	+	0.946429i
$681$	1.48344e6			0.122575
$682$	1.91368e7	+	7.84851e6i	1.57546	+	0.646139i
$683$	6.50961e6	+	6.50961e6i	0.533953	+	0.533953i	0.921746	−	0.387793i	$-0.126763\pi$
$683$	6.50961e6	+	6.50961e6i	0.533953	+	0.533953i	−0.387793	+	0.921746i	$0.626763\pi$
$684$	−1.33674e7	−	1.31819e7i	−1.09246	−	1.07730i
$685$	−3.50268e6	−	1.41452e7i	−0.285216	−	1.15181i
$686$	−4.94582e6	−	1.18233e7i	−0.401262	−	0.959240i
$687$	7.65513e6	+	7.65513e6i	0.618815	+	0.618815i
$688$	1.81472e6	−	1.86616e6i	0.146163	−	0.150307i
$689$		−	1.45532e6i		−	0.116792i
$690$	−2.17268e7	−	2.92464e7i	−1.73729	−	2.33857i
$691$	−6.73706e6			−0.536754			−0.268377	−	0.963314i	$-0.586487\pi$
$691$	−6.73706e6			−0.536754			−0.268377	+	0.963314i	$0.586487\pi$
$692$	1.75642e7	−	122722.i	1.39432	−	0.00974219i
$693$	1.16287e7	−	1.16287e7i	0.919814	−	0.919814i
$694$	−4.54688e6	−	1.08696e7i	−0.358356	−	0.856671i
$695$	1.72316e6	+	1.03915e6i	0.135321	+	0.0816048i
$696$	1.05992e6	+	426074.i	0.0829373	+	0.0333397i
$697$	−2.97929e6	+	2.97929e6i	−0.232290	+	0.232290i
$698$	−756515.	+	1.84459e6i	−0.0587732	+	0.143305i
$699$			1.07171e6i			0.0829632i
$700$	−1.08976e7	+	5.84725e6i	−0.840592	+	0.451031i
$701$		−	6.49736e6i		−	0.499392i	−0.968324	−	0.249696i	$-0.919669\pi$
$701$		−	6.49736e6i		−	0.499392i	0.968324	−	0.249696i	$-0.0803307\pi$
$702$	−3.32053e6	−	1.36184e6i	−0.254311	−	0.104300i
$703$	3.79137e6	−	3.79137e6i	0.289340	−	0.289340i
$704$	−8.92809e6	+	9.31044e6i	−0.678933	+	0.708008i
$705$	−2.49938e6	−	1.50724e6i	−0.189391	−	0.114212i
$706$	7.50777e6	−	3.14059e6i	0.566890	−	0.237137i
$707$	−4.91906e6	+	4.91906e6i	−0.370112	+	0.370112i
$708$	−9.99525e6	+	69837.3i	−0.749394	+	0.00523606i
$709$	1.79037e7			1.33760			0.668800	−	0.743442i	$-0.266808\pi$
$709$	1.79037e7			1.33760			0.668800	+	0.743442i	$0.266808\pi$
$710$	1.10001e6	−	817187.i	0.0818941	−	0.0608381i
$711$			1.51228e7i			1.12191i
$712$	8.06112e6	+	1.88986e7i	0.595930	+	1.39711i
$713$	3.13985e7	+	3.13985e7i	2.31305	+	2.31305i
$714$	−2.19661e7	+	9.18869e6i	−1.61253	+	0.674541i
$715$	1.46892e6	+	5.93206e6i	0.107457	+	0.433951i
$716$	1.08750e6	−	1.10281e6i	0.0792772	−	0.0803929i
$717$	1.88791e7	+	1.88791e7i	1.37146	+	1.37146i
$718$	−4.27992e6	+	1.04356e7i	−0.309831	+	0.755451i
$719$	−1.35088e7			−0.974532			−0.487266	−	0.873254i	$-0.662006\pi$
$719$	−1.35088e7			−0.974532			−0.487266	+	0.873254i	$0.662006\pi$
$720$	−9.75335e6	+	1.66967e7i	−0.701169	+	1.20032i
$721$	1.89052e7			1.35439
$722$	−1.15969e6	+	2.82763e6i	−0.0827938	+	0.201874i
$723$	−2.06489e7	−	2.06489e7i	−1.46910	−	1.46910i
$724$	−1.25043e7	+	1.26803e7i	−0.886573	+	0.899049i
$725$	−381847.	−	723746.i	−0.0269802	−	0.0511377i
$726$	765126.	−	320062.i	0.0538755	−	0.0225368i
$727$	7.81804e6	+	7.81804e6i	0.548608	+	0.548608i	0.926038	−	0.377430i	$-0.123192\pi$
$727$	7.81804e6	+	7.81804e6i	0.548608	+	0.548608i	−0.377430	+	0.926038i	$0.623192\pi$
$728$	−5.71850e6	+	2.43920e6i	−0.399902	+	0.170577i
$729$			2.25087e7i			1.56867i
$730$	4.06124e6	−	2.75299e7i	0.282067	−	1.91204i
$731$	−3.58996e6			−0.248483
$732$	1.56805e7	−	109561.i	1.08164	−	0.00755748i
$733$	1.82072e7	−	1.82072e7i	1.25165	−	1.25165i	0.296673	−	0.954979i	$-0.404123\pi$
$733$	1.82072e7	−	1.82072e7i	1.25165	−	1.25165i	0.954979	−	0.296673i	$-0.0958773\pi$
$734$	−2.11292e7	+	8.83861e6i	−1.44758	+	0.605541i
$735$	489694.	+	1.97757e6i	0.0334354	+	0.135025i
$736$	−2.53957e7	+	1.10428e7i	−1.72809	+	0.751422i
$737$	−1.68463e7	+	1.68463e7i	−1.14245	+	1.14245i
$738$	−5.27459e6	−	2.16325e6i	−0.356490	−	0.146206i
$739$			9.58116e6i			0.645367i	0.946507	+	0.322684i	$0.104585\pi$
$739$			9.58116e6i			0.645367i	−0.946507	+	0.322684i	$0.895415\pi$
$740$	−4.74904e6	−	2.81884e6i	−0.318806	−	0.189230i
$741$			1.16235e7i			0.777664i
$742$	1.39117e6	−	3.39206e6i	0.0927623	−	0.226180i
$743$	4.83476e6	−	4.83476e6i	0.321294	−	0.321294i	−0.527969	−	0.849263i	$-0.677046\pi$
$743$	4.83476e6	−	4.83476e6i	0.321294	−	0.321294i	0.849263	+	0.527969i	$0.177046\pi$
$744$	1.51132e7	−	3.75962e7i	1.00098	−	2.49007i
$745$	−3.51954e6	+	5.83626e6i	−0.232325	+	0.385251i
$746$	−3.82332e6	−	9.13986e6i	−0.251532	−	0.601302i
$747$	9.57757e6	−	9.57757e6i	0.627992	−	0.627992i
$748$	1.77898e7	−	124298.i	1.16256	−	0.00812288i
$749$	4.79918e6			0.312581
$750$	2.24601e7	−	7.92014e6i	1.45800	−	0.514138i
$751$			4.14370e6i			0.268095i	0.990975	+	0.134047i	$0.0427974\pi$
$751$			4.14370e6i			0.268095i	−0.990975	+	0.134047i	$0.957203\pi$
$752$	−1.54660e6	+	1.59044e6i	−0.0997320	+	0.102559i
$753$	−2.51564e7	−	2.51564e7i	−1.61681	−	1.61681i
$754$	−158747.	−	379494.i	−0.0101690	−	0.0243095i
$755$	7.96111e6	+	4.80093e6i	0.508284	+	0.306519i
$756$	−6.43766e6	−	6.34833e6i	−0.409660	−	0.403975i
$757$	−1.90780e7	−	1.90780e7i	−1.21002	−	1.21002i	−0.971020	−	0.239000i	$-0.923180\pi$
$757$	−1.90780e7	−	1.90780e7i	−1.21002	−	1.21002i	−0.239000	−	0.971020i	$-0.576820\pi$
$758$	1.14448e7	+	4.69381e6i	0.723494	+	0.296724i
$759$	−4.53547e7			−2.85771
$760$	1.74042e7	+	2.44336e6i	1.09300	+	0.153445i
$761$	−3.10449e6			−0.194325			−0.0971626	−	0.995269i	$-0.530977\pi$
$761$	−3.10449e6			−0.194325			−0.0971626	+	0.995269i	$0.530977\pi$
$762$	−2.69605e7	−	1.10572e7i	−1.68206	−	0.689856i
$763$	−1.67667e7	−	1.67667e7i	−1.04264	−	1.04264i
$764$	718314.	−	728423.i	0.0445227	−	0.0451492i
$765$	2.58862e7	−	6.41005e6i	1.59925	−	0.396011i
$766$	5.59262e6	+	1.33695e7i	0.344384	+	0.823271i
$767$	2.54513e6	+	2.54513e6i	0.156215	+	0.156215i
$768$	1.83612e7	+	1.73626e7i	1.12331	+	1.06221i
$769$		−	1.56746e7i		−	0.955830i	−0.878406	−	0.477915i	$-0.841393\pi$
$769$		−	1.56746e7i		−	0.955830i	0.878406	−	0.477915i	$-0.158607\pi$
$770$	−2.24683e6	+	1.52306e7i	−0.136566	+	0.925742i
$771$	1.98021e7			1.19971
$772$	−19244.4	−	2.75429e6i	−0.00116215	−	0.166328i
$773$	1.20737e7	−	1.20737e7i	0.726763	−	0.726763i	−0.243211	−	0.969974i	$-0.578201\pi$
$773$	1.20737e7	−	1.20737e7i	0.726763	−	0.726763i	0.969974	+	0.243211i	$0.0782006\pi$
$774$	−1.87454e6	−	4.48120e6i	−0.112472	−	0.268870i
$775$	−2.56718e7	+	1.35444e7i	−1.53533	+	0.810039i
$776$	570552.	−	1.41933e6i	0.0340127	−	0.0846113i
$777$	6.50636e6	−	6.50636e6i	0.386621	−	0.386621i
$778$	−4.09367e6	+	9.98149e6i	−0.242473	+	0.591216i
$779$			5.18154e6i			0.305925i
$780$	1.16007e7	−	2.95879e6i	0.682730	−	0.174132i
$781$		−	1.70588e6i		−	0.100074i
$782$	3.53359e7	+	1.44922e7i	2.06633	+	0.847456i
$783$	423015.	−	423015.i	0.0246577	−	0.0246577i
$784$	1.54837e6	−	21638.2i	0.0899675	−	0.00125728i
$785$	8.04460e6	−	1.99203e6i	0.465940	−	0.115378i
$786$	4.58295e6	−	1.91710e6i	0.264599	−	0.110685i
$787$	2.05881e7	−	2.05881e7i	1.18489	−	1.18489i	0.206432	−	0.978461i	$-0.433815\pi$
$787$	2.05881e7	−	2.05881e7i	1.18489	−	1.18489i	0.978461	−	0.206432i	$-0.0661854\pi$
$788$	−207999.	−	2.97692e7i	−0.0119329	−	1.70786i
$789$	−3.34620e7			−1.91364
$790$	−8.44246e6	−	1.13644e7i	−0.481284	−	0.647856i
$791$		−	3.63721e6i		−	0.206694i
$792$	9.44429e6	+	2.21413e7i	0.535003	+	1.25427i
$793$	−3.99280e6	−	3.99280e6i	−0.225473	−	0.225473i
$794$	4.37326e6	−	1.82939e6i	0.246181	−	0.102980i
$795$	−3.64595e6	+	6.04588e6i	−0.204594	+	0.339267i
$796$	−4.02217e6	−	3.96636e6i	−0.224998	−	0.221875i
$797$	−1.40968e7	−	1.40968e7i	−0.786097	−	0.786097i	0.194755	−	0.980852i	$-0.437609\pi$
$797$	−1.40968e7	−	1.40968e7i	−0.786097	−	0.786097i	−0.980852	+	0.194755i	$0.937609\pi$
$798$	−1.11112e7	+	2.70920e7i	−0.617664	+	1.50603i
$799$	3.05956e6			0.169548
$800$	−1.99170e6	−	1.79920e7i	−0.110027	−	0.993929i
$801$	3.83406e7			2.11143
$802$	8.98170e6	−	2.18998e7i	0.493086	−	1.20228i
$803$	−2.44954e7	−	2.44954e7i	−1.34059	−	1.34059i
$804$	3.32323e7	+	3.27711e7i	1.81309	+	1.78793i
$805$	−1.70680e7	+	2.83030e7i	−0.928312	+	1.53937i
$806$	−1.34609e7	+	5.63088e6i	−0.729857	+	0.305308i
$807$	−2.51836e7	−	2.51836e7i	−1.36124	−	1.36124i
$808$	−3.99502e6	−	9.36597e6i	−0.215273	−	0.504690i
$809$		−	2.35806e7i		−	1.26673i	−0.773854	−	0.633364i	$-0.781674\pi$
$809$		−	2.35806e7i		−	1.26673i	0.773854	−	0.633364i	$-0.218326\pi$
$810$	−5.09667e6	−	6.86063e6i	−0.272944	−	0.367410i
$811$	2.83159e7			1.51174			0.755872	−	0.654719i	$-0.227213\pi$
$811$	2.83159e7			1.51174			0.755872	+	0.654719i	$0.227213\pi$
$812$	−7240.48	−	1.03627e6i	−0.000385370	−	0.0551548i
$813$	6.91899e6	−	6.91899e6i	0.367127	−	0.367127i
$814$	−6.34232e6	+	2.65307e6i	−0.335496	+	0.140342i
$815$	7187.90	−	1779.89i	0.000379060	−	9.38643e-5i
$816$	−486996.	−	3.48482e7i	−0.0256035	−	1.83212i
$817$	−3.12181e6	+	3.12181e6i	−0.163626	+	0.163626i
$818$	2.39418e7	+	9.81916e6i	1.25105	+	0.513087i
$819$			1.16014e7i			0.604368i
$820$	5.17138e6	−	1.31897e6i	0.268579	−	0.0685016i
$821$			2.38412e7i			1.23444i	0.786791	+	0.617219i	$0.211741\pi$
$821$			2.38412e7i			1.23444i	−0.786791	+	0.617219i	$0.788259\pi$
$822$	−1.34850e7	+	3.28801e7i	−0.696101	+	1.69728i
$823$	2.06706e7	−	2.06706e7i	1.06379	−	1.06379i	0.0659645	−	0.997822i	$-0.478988\pi$
$823$	2.06706e7	−	2.06706e7i	1.06379	−	1.06379i	0.997822	−	0.0659645i	$-0.0210124\pi$
$824$	−1.03210e7	+	2.56749e7i	−0.529545	+	1.31732i
$825$	8.75895e6	−	2.83237e7i	0.448041	−	1.44882i
$826$	3.49923e6	+	8.36512e6i	0.178453	+	0.426601i
$827$	−1.05692e7	+	1.05692e7i	−0.537375	+	0.537375i	−0.922757	−	0.385382i	$-0.874070\pi$
$827$	−1.05692e7	+	1.05692e7i	−0.537375	+	0.537375i	0.385382	+	0.922757i	$0.374070\pi$
$828$	361060.	+	5.16756e7i	0.0183022	+	2.61945i
$829$	2.26115e7			1.14273			0.571364	−	0.820697i	$-0.306414\pi$
$829$	2.26115e7			1.14273			0.571364	+	0.820697i	$0.306414\pi$
$830$	−1.85052e6	+	1.25441e7i	−0.0932391	+	0.632039i
$831$			9.19665e6i			0.461984i
$832$	−190726.	−	9.09783e6i	−0.00955216	−	0.455648i
$833$	−1.51013e6	−	1.51013e6i	−0.0754051	−	0.0754051i
$834$	−1.89377e6	−	4.52716e6i	−0.0942783	−	0.225378i
$835$	2.06337e7	−	5.10939e6i	1.02414	−	0.253602i
$836$	1.53618e7	−	1.55780e7i	0.760196	−	0.770894i
$837$	−1.50047e7	−	1.50047e7i	−0.740309	−	0.740309i
$838$	−1.43674e7	−	5.89245e6i	−0.706753	−	0.289858i
$839$	7.97800e6			0.391281			0.195641	−	0.980676i	$-0.437321\pi$
$839$	7.97800e6			0.391281			0.195641	+	0.980676i	$0.437321\pi$
$840$	2.98673e7	+	4.19305e6i	1.46049	+	0.205037i
$841$	−2.04426e7			−0.996657
$842$	8.05639e6	+	3.30414e6i	0.391616	+	0.160612i
$843$	1.93047e7	+	1.93047e7i	0.935608	+	0.935608i
$844$	−1.32445e7	−	1.30607e7i	−0.640000	−	0.631118i
$845$	1.40823e7	+	8.49230e6i	0.678472	+	0.409151i
$846$	1.59759e6	+	3.81912e6i	0.0767429	+	0.183458i
$847$	−532009.	−	532009.i	−0.0254806	−	0.0254806i
$848$	3.84721e6	+	3.74116e6i	0.183720	+	0.178656i
$849$			2.02124e7i			0.962384i
$850$	−1.58744e7	+	1.92683e7i	−0.753615	+	0.914735i
$851$	−1.47591e7			−0.698611
$852$	−3.34179e6	+	23349.3i	−0.157718	+	0.00110198i
$853$	−1.45181e7	+	1.45181e7i	−0.683183	+	0.683183i	−0.960716	−	0.277533i	$-0.910483\pi$
$853$	−1.45181e7	+	1.45181e7i	−0.683183	+	0.683183i	0.277533	+	0.960716i	$0.410483\pi$
$854$	−5.48959e6	−	1.31232e7i	−0.257570	−	0.615736i
$855$	1.69364e7	−	2.80847e7i	0.792329	−	1.31387i
$856$	−2.62003e6	+	6.51769e6i	−0.122214	+	0.304025i
$857$	−1.92646e7	+	1.92646e7i	−0.896000	+	0.896000i	−0.995080	−	0.0990796i	$-0.968410\pi$
$857$	−1.92646e7	+	1.92646e7i	−0.896000	+	0.896000i	0.0990796	+	0.995080i	$0.468410\pi$
$858$	5.65522e6	−	1.37890e7i	0.262259	−	0.639460i
$859$		−	2.19480e7i		−	1.01488i	−0.861688	−	0.507438i	$-0.830593\pi$
$859$		−	2.19480e7i		−	1.01488i	0.861688	−	0.507438i	$-0.169407\pi$
$860$	3.91035e6	+	2.32103e6i	0.180289	+	0.107012i
$861$			8.89202e6i			0.408783i
$862$	−3.47213e7	−	1.42401e7i	−1.59158	−	0.652749i
$863$	−1.55224e7	+	1.55224e7i	−0.709464	+	0.709464i	−0.966423	−	0.256958i	$-0.917280\pi$
$863$	−1.55224e7	+	1.55224e7i	−0.709464	+	0.709464i	0.256958	+	0.966423i	$0.417280\pi$
$864$	1.21361e7	−	5.27712e6i	0.553088	−	0.240499i
$865$	7.37536e6	+	2.97845e7i	0.335153	+	1.35348i
$866$	−1.77099e7	+	7.40825e6i	−0.802455	+	0.335677i
$867$	−9.79150e6	+	9.79150e6i	−0.442386	+	0.442386i
$868$	−3.67573e7	+	256826.i	−1.65594	+	0.0115701i
$869$	−1.76236e7			−0.791674
$870$	−291242.	+	1.97424e6i	−0.0130454	+	0.0884305i
$871$		−	1.68067e7i		−	0.750650i
$872$	3.19240e7	−	1.36171e7i	1.42176	−	0.606446i
$873$	−2.01849e6	−	2.01849e6i	−0.0896376	−	0.0896376i
$874$	4.33302e7	−	1.81256e7i	1.91872	−	0.802625i
$875$	−1.43788e7	−	1.61248e7i	−0.634897	−	0.711990i
$876$	−4.76509e7	+	4.83215e7i	−2.09803	+	2.12755i
$877$	1.71112e7	+	1.71112e7i	0.751243	+	0.751243i	0.974711	−	0.223468i	$-0.0717378\pi$
$877$	1.71112e7	+	1.71112e7i	0.751243	+	0.751243i	−0.223468	+	0.974711i	$0.571738\pi$
$878$	1.12629e6	−	2.74621e6i	0.0493078	−	0.120226i
$879$	5.33949e7			2.33092
$880$	−1.94578e7	−	1.13663e7i	−0.847006	−	0.494779i
$881$	−4.67184e6			−0.202791			−0.101395	−	0.994846i	$-0.532331\pi$
$881$	−4.67184e6			−0.202791			−0.101395	+	0.994846i	$0.532331\pi$
$882$	1.09650e6	−	2.67356e6i	0.0474610	−	0.115723i
$883$	7.85190e6	+	7.85190e6i	0.338901	+	0.338901i	0.855954	−	0.517053i	$-0.172971\pi$
$883$	7.85190e6	+	7.85190e6i	0.338901	+	0.338901i	−0.517053	+	0.855954i	$0.672971\pi$
$884$	−8.81197e6	+	8.93598e6i	−0.379265	+	0.384602i
$885$	−4.19710e6	−	1.69495e7i	−0.180132	−	0.727442i
$886$	1.16998e7	−	4.89419e6i	0.500721	−	0.209458i
$887$	−1.37642e7	−	1.37642e7i	−0.587410	−	0.587410i	0.349519	−	0.936929i	$-0.386345\pi$
$887$	−1.37642e7	−	1.37642e7i	−0.587410	−	0.587410i	−0.936929	+	0.349519i	$0.886345\pi$
$888$	5.28414e6	+	1.23882e7i	0.224876	+	0.527201i
$889$			2.64345e7i			1.12180i
$890$	−2.88120e7	+	2.14041e7i	−1.21926	+	0.905776i
$891$	−1.06393e7			−0.448972
$892$	−4.23571e6	+	29595.2i	−0.178244	+	0.00124540i
$893$	2.66057e6	−	2.66057e6i	0.111647	−	0.111647i
$894$	1.53333e7	−	6.41410e6i	0.641640	−	0.268406i
$895$	2.31698e6	+	1.39725e6i	0.0966863	+	0.0583065i
$896$	8.25226e6	−	2.13875e7i	0.343402	−	0.889999i
$897$	2.26241e7	−	2.26241e7i	0.938836	−	0.938836i
$898$	−7.89039e6	−	3.23606e6i	−0.326518	−	0.133914i
$899$		−	2.43218e6i		−	0.100368i
$900$	−3.23408e7	−	9.75417e6i	−1.33090	−	0.401406i
$901$		−	7.40094e6i		−	0.303721i
$902$	2.52099e6	−	6.14685e6i	0.103170	−	0.251557i
$903$	−5.35733e6	+	5.35733e6i	−0.218640	+	0.218640i
$904$	4.93963e6	+	1.98567e6i	0.201036	+	0.0808140i
$905$	−2.66411e7	−	1.60659e7i	−1.08126	−	0.652053i
$906$	−8.74933e6	−	2.09158e7i	−0.354123	−	0.846552i
$907$	−2.34357e7	+	2.34357e7i	−0.945932	+	0.945932i	−0.998611	−	0.0526794i	$-0.983224\pi$
$907$	−2.34357e7	+	2.34357e7i	−0.945932	+	0.945932i	0.0526794	+	0.998611i	$0.483224\pi$
$908$	1.96968e6	−	13762.3i	0.0792832	−	0.000553956i
$909$	−1.90012e7			−0.762733
$910$	−6.47662e6	−	8.71817e6i	−0.259266	−	0.348997i
$911$			3.77979e7i			1.50894i	0.656334	+	0.754470i	$0.272106\pi$
$911$			3.77979e7i			1.50894i	−0.656334	+	0.754470i	$0.727894\pi$
$912$	−3.07273e7	−	2.98803e7i	−1.22331	−	1.18959i
$913$	1.11614e7	+	1.11614e7i	0.443141	+	0.443141i
$914$	−1.52758e6	−	3.65178e6i	−0.0604839	−	0.144590i
$915$	6.58440e6	+	2.65903e7i	0.259994	+	1.04996i
$916$	1.02354e7	+	1.00933e7i	0.403055	+	0.397462i
$917$	−3.18662e6	−	3.18662e6i	−0.125143	−	0.125143i
$918$	−1.68863e7	−	6.92552e6i	−0.661345	−	0.271235i
$919$	−1.46039e7			−0.570402			−0.285201	−	0.958468i	$-0.592060\pi$
$919$	−1.46039e7			−0.570402			−0.285201	+	0.958468i	$0.592060\pi$
$920$	−2.91198e7	−	3.86314e7i	−1.13428	−	1.50477i
$921$	−3.39670e7			−1.31949
$922$	3.16963e7	+	1.29995e7i	1.22795	+	0.503615i
$923$	850935.	+	850935.i	0.0328770	+	0.0328770i
$924$	2.63623e7	−	2.67333e7i	1.01579	−	1.03008i
$925$	2.85029e6	−	9.21694e6i	0.109530	−	0.354187i
$926$	1.59573e6	+	3.81468e6i	0.0611549	+	0.146194i
$927$	3.65134e7	+	3.65134e7i	1.39557	+	1.39557i
$928$	1.41130e6	+	555901.i	0.0537957	+	0.0211898i
$929$		−	2.18158e7i		−	0.829340i	−0.909972	−	0.414670i	$-0.863897\pi$
$929$		−	2.18158e7i		−	0.829340i	0.909972	−	0.414670i	$-0.136103\pi$
$930$	7.00278e7	+	1.03306e7i	2.65499	+	0.391667i
$931$	−2.62639e6			−0.0993083
$932$	9942.59	+	1.42300e6i	0.000374938	+	0.0536618i
$933$	−2.86888e7	+	2.86888e7i	−1.07897	+	1.07897i
$934$	1.45474e7	+	3.47765e7i	0.545657	+	1.30442i
$935$	7.47008e6	+	3.01671e7i	0.279445	+	1.12851i
$936$	−1.57557e7	−	6.33359e6i	−0.587825	−	0.236298i
$937$	3.18781e7	−	3.18781e7i	1.18616	−	1.18616i	0.208042	−	0.978120i	$-0.433291\pi$
$937$	3.18781e7	−	3.18781e7i	1.18616	−	1.18616i	0.978120	−	0.208042i	$-0.0667092\pi$
$938$	1.60659e7	−	3.91730e7i	0.596208	−	1.45372i
$939$		−	4.29371e7i		−	1.58916i
$940$	−3.33261e6	−	1.97810e6i	−0.123017	−	0.0730179i
$941$		−	2.62395e7i		−	0.966011i	−0.875617	−	0.483006i	$-0.839545\pi$
$941$		−	2.62395e7i		−	0.966011i	0.875617	−	0.483006i	$-0.160455\pi$
$942$	−1.86995e7	−	7.66916e6i	−0.686598	−	0.281592i
$943$	1.00854e7	−	1.00854e7i	0.369328	−	0.369328i
$944$	−1.32709e7	+	185458.i	−0.484696	+	0.00677353i
$945$	8.15647e6	−	1.35254e7i	0.297114	−	0.492687i
$946$	5.22226e6	−	2.18453e6i	0.189728	−	0.0793654i
$947$	−3.35524e7	+	3.35524e7i	−1.21576	+	1.21576i	−0.246660	+	0.969102i	$0.579333\pi$
$947$	−3.35524e7	+	3.35524e7i	−1.21576	+	1.21576i	−0.969102	+	0.246660i	$0.920667\pi$
$948$	241224.	+	3.45245e7i	0.00871767	+	1.24769i
$949$	2.44379e7			0.880841
$950$	2.95131e6	+	3.05598e7i	0.106098	+	1.09861i
$951$		−	1.44246e7i		−	0.517194i
$952$	−2.90810e7	+	1.24044e7i	−1.03996	+	0.443591i
$953$	6.20152e6	+	6.20152e6i	0.221190	+	0.221190i	0.809000	−	0.587809i	$-0.200009\pi$
$953$	6.20152e6	+	6.20152e6i	0.221190	+	0.221190i	−0.587809	+	0.809000i	$0.700009\pi$
$954$	9.23828e6	−	3.86449e6i	0.328640	−	0.137474i
$955$	1.53040e6	+	922906.i	0.0542997	+	0.0327453i
$956$	2.52424e7	+	2.48921e7i	0.893278	+	0.880881i
$957$	1.75663e6	+	1.75663e6i	0.0620012	+	0.0620012i
$958$	−350545.	+	854725.i	−0.0123404	+	0.0300893i
$959$	3.22387e7			1.13196
$960$	−2.20000e7	+	3.82731e7i	−0.770451	+	1.34034i
$961$	−5.76422e7			−2.01341
$962$	1.84029e6	−	4.48713e6i	0.0641134	−	0.156326i
$963$	9.26909e6	+	9.26909e6i	0.322086	+	0.322086i
$964$	−2.76088e7	−	2.72257e7i	−0.956876	−	0.943597i
$965$	4.67060e6	−	1.15655e6i	0.161456	−	0.0399804i
$966$	7.43588e7	−	3.11052e7i	2.56383	−	1.07248i
$967$	−2.33541e7	−	2.33541e7i	−0.803151	−	0.803151i	0.180436	−	0.983587i	$-0.442249\pi$
$967$	−2.33541e7	−	2.33541e7i	−0.803151	−	0.803151i	−0.983587	+	0.180436i	$0.942249\pi$
$968$	1.01295e6	−	432071.i	0.0347457	−	0.0148206i
$969$			5.91105e7i			2.02234i
$970$	2.64369e6	+	389999.i	0.0902153	+	0.0133087i
$971$	4.74279e7			1.61430			0.807152	−	0.590343i	$-0.201008\pi$
$971$	4.74279e7			1.61430			0.807152	+	0.590343i	$0.201008\pi$
$972$	269748.	+	3.86068e7i	0.00915782	+	1.31068i
$973$	−3.14783e6	+	3.14783e6i	−0.106593	+	0.106593i
$974$	3.78537e7	−	1.58347e7i	1.27853	−	0.534825i
$975$	9.75939e6	+	1.84978e7i	0.328784	+	0.623171i
$976$	2.08193e7	−	290946.i	0.699588	−	0.00977659i
$977$	2.03702e7	−	2.03702e7i	0.682745	−	0.682745i	−0.277873	−	0.960618i	$-0.589629\pi$
$977$	2.03702e7	−	2.03702e7i	0.682745	−	0.682745i	0.960618	+	0.277873i	$0.0896293\pi$
$978$	−16708.1	−	6852.45i	−0.000558574	−	0.000229086i
$979$			4.46810e7i			1.48993i
$980$	668554.	+	2.62125e6i	0.0222368	+	0.0871851i
$981$		−	6.47660e7i		−	2.14869i
$982$	1.09137e7	−	2.66105e7i	0.361154	−	0.880593i
$983$	−3.29885e7	+	3.29885e7i	−1.08888	+	1.08888i	−0.0932311	+	0.995644i	$0.529720\pi$
$983$	−3.29885e7	+	3.29885e7i	−1.08888	+	1.08888i	−0.995644	+	0.0932311i	$0.970280\pi$
$984$	−1.20761e7	−	4.85444e6i	−0.397593	−	0.159828i
$985$	5.04813e7	−	1.25004e7i	1.65783	−	0.410518i
$986$	−807295.	−	1.92989e6i	−0.0264448	−	0.0632178i
$987$	4.56580e6	−	4.56580e6i	0.149185	−	0.149185i
$988$	107835.	+	1.54335e7i	0.00351452	+	0.503005i
$989$	1.21526e7			0.395074
$990$	−3.37557e7	+	2.50767e7i	−1.09461	+	0.813171i
$991$		−	5.23431e7i		−	1.69307i	−0.532332	−	0.846536i	$-0.678684\pi$
$991$		−	5.23431e7i		−	1.69307i	0.532332	−	0.846536i	$-0.321316\pi$
$992$	1.97182e7	−	5.00597e7i	0.636193	−	1.61514i
$993$	−1.03763e7	−	1.03763e7i	−0.333940	−	0.333940i
$994$	1.16993e6	+	2.79678e6i	0.0375572	+	0.0897826i
$995$	5.09606e6	−	8.45052e6i	0.163184	−	0.270599i
$996$	2.17123e7	−	2.20178e7i	0.693517	−	0.703277i
$997$	4.24529e7	+	4.24529e7i	1.35260	+	1.35260i	0.882742	+	0.469858i	$0.155695\pi$
$997$	4.24529e7	+	4.24529e7i	1.35260	+	1.35260i	0.469858	+	0.882742i	$0.344305\pi$
$998$	2.86517e6	+	1.17508e6i	0.0910594	+	0.0373459i
$999$	7.05307e6			0.223596

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.k.a.3.18	✓	56
4.3	odd	2		160.6.o.a.143.24		56
5.2	odd	4	inner	40.6.k.a.27.25	yes	56
8.3	odd	2	inner	40.6.k.a.3.25	yes	56
8.5	even	2		160.6.o.a.143.23		56
20.7	even	4		160.6.o.a.47.23		56
40.27	even	4	inner	40.6.k.a.27.18	yes	56
40.37	odd	4		160.6.o.a.47.24		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.18	✓	56	1.1	even	1	trivial
40.6.k.a.3.25	yes	56	8.3	odd	2	inner
40.6.k.a.27.18	yes	56	40.27	even	4	inner
40.6.k.a.27.25	yes	56	5.2	odd	4	inner
160.6.o.a.47.23		56	20.7	even	4
160.6.o.a.47.24		56	40.37	odd	4
160.6.o.a.143.23		56	8.5	even	2
160.6.o.a.143.24		56	4.3	odd	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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	40.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.14651 - 5.23378i) q^{2} +(-17.0411 - 17.0411i) q^{3} +(-22.7850 - 22.4688i) q^{4} +(28.8684 - 47.8708i) q^{5} +(-125.768 + 52.6104i) q^{6} +(87.4493 + 87.4493i) q^{7} +(-166.505 + 71.0220i) q^{8} +337.797i q^{9} +O(q^{10})\)	\(q+(2.14651 - 5.23378i) q^{2} +(-17.0411 - 17.0411i) q^{3} +(-22.7850 - 22.4688i) q^{4} +(28.8684 - 47.8708i) q^{5} +(-125.768 + 52.6104i) q^{6} +(87.4493 + 87.4493i) q^{7} +(-166.505 + 71.0220i) q^{8} +337.797i q^{9} +(-188.579 - 253.846i) q^{10} -393.659 q^{11} +(5.38823 + 771.173i) q^{12} +(196.367 - 196.367i) q^{13} +(645.402 - 269.980i) q^{14} +(-1307.72 + 323.822i) q^{15} +(14.3088 + 1023.90i) q^{16} +(998.609 - 998.609i) q^{17} +(1767.96 + 725.087i) q^{18} -1736.77i q^{19} +(-1733.36 + 442.098i) q^{20} -2980.46i q^{21} +(-844.994 + 2060.33i) q^{22} +(-3380.45 + 3380.45i) q^{23} +(4047.72 + 1627.13i) q^{24} +(-1458.23 - 2763.91i) q^{25} +(-606.238 - 1449.25i) q^{26} +(1615.45 - 1615.45i) q^{27} +(-27.6506 - 3957.41i) q^{28} +261.856 q^{29} +(-1112.22 + 7539.41i) q^{30} -9288.24i q^{31} +(5389.58 + 2122.93i) q^{32} +(6708.38 + 6708.38i) q^{33} +(-3082.97 - 7370.03i) q^{34} +(6710.79 - 1661.75i) q^{35} +(7589.89 - 7696.70i) q^{36} +(2183.00 + 2183.00i) q^{37} +(-9089.87 - 3728.00i) q^{38} -6692.61 q^{39} +(-1406.84 + 10021.0i) q^{40} -2983.44 q^{41} +(-15599.1 - 6397.60i) q^{42} +(-1797.48 - 1797.48i) q^{43} +(8969.50 + 8845.03i) q^{44} +(16170.6 + 9751.66i) q^{45} +(10436.4 + 24948.7i) q^{46} +(1531.91 + 1531.91i) q^{47} +(17204.5 - 17692.2i) q^{48} -1512.23i q^{49} +(-17595.8 + 1699.31i) q^{50} -34034.8 q^{51} +(-8886.34 + 62.0893i) q^{52} +(3705.62 - 3705.62i) q^{53} +(-4987.33 - 11922.5i) q^{54} +(-11364.3 + 18844.8i) q^{55} +(-20771.6 - 8349.91i) q^{56} +(-29596.4 + 29596.4i) q^{57} +(562.078 - 1370.50i) q^{58} +12961.1i q^{59} +(37072.2 + 22004.6i) q^{60} -20333.4i q^{61} +(-48612.6 - 19937.3i) q^{62} +(-29540.2 + 29540.2i) q^{63} +(22679.7 - 23651.0i) q^{64} +(-3731.45 - 15069.0i) q^{65} +(49509.8 - 20710.6i) q^{66} +(42794.2 - 42794.2i) q^{67} +(-45190.8 + 315.750i) q^{68} +115213. q^{69} +(5707.56 - 38689.8i) q^{70} +4333.39i q^{71} +(-23991.0 - 56244.9i) q^{72} +(62225.0 + 62225.0i) q^{73} +(16111.2 - 6739.52i) q^{74} +(-22250.1 + 71949.9i) q^{75} +(-39023.1 + 39572.2i) q^{76} +(-34425.2 - 34425.2i) q^{77} +(-14365.8 + 35027.7i) q^{78} +44768.8 q^{79} +(49428.0 + 28873.4i) q^{80} +27026.7 q^{81} +(-6403.99 + 15614.7i) q^{82} +(-28353.0 - 28353.0i) q^{83} +(-66967.3 + 67909.7i) q^{84} +(-18976.0 - 76632.5i) q^{85} +(-13265.9 + 5549.31i) q^{86} +(-4462.31 - 4462.31i) q^{87} +(65546.1 - 27958.5i) q^{88} -113502. i q^{89} +(85748.6 - 63701.5i) q^{90} +34344.3 q^{91} +(152978. - 1068.87i) q^{92} +(-158282. + 158282. i) q^{93} +(11306.0 - 4729.42i) q^{94} +(-83140.5 - 50137.7i) q^{95} +(-55667.4 - 128021. i) q^{96} +(-5975.44 + 5975.44i) q^{97} +(-7914.69 - 3246.02i) q^{98} -132977. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

Introduction

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