LMFDB - Embedded newform 200.6.f.d.149.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,6,Mod(149,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("200.149");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	200.f (of order $2$, degree $1$, not 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:	$32.0767639626$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.22
Character	$\chi$	$=$	200.149
Dual form			200.6.f.d.149.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.438664 + 5.63982i) q^{2} +17.0419 q^{3} +(-31.6151 + 4.94797i) q^{4} +(7.47566 + 96.1131i) q^{6} +191.207i q^{7} +(-41.7741 - 176.133i) q^{8} +47.4256 q^{9} +O(q^{10})$	\(q+(0.438664 + 5.63982i) q^{2} +17.0419 q^{3} +(-31.6151 + 4.94797i) q^{4} +(7.47566 + 96.1131i) q^{6} +191.207i q^{7} +(-41.7741 - 176.133i) q^{8} +47.4256 q^{9} -669.441i q^{11} +(-538.782 + 84.3227i) q^{12} -1154.46 q^{13} +(-1078.37 + 83.8754i) q^{14} +(975.035 - 312.862i) q^{16} +1039.28i q^{17} +(20.8039 + 267.472i) q^{18} -1517.49i q^{19} +3258.52i q^{21} +(3775.53 - 293.660i) q^{22} +1961.72i q^{23} +(-711.909 - 3001.64i) q^{24} +(-506.420 - 6510.95i) q^{26} -3332.95 q^{27} +(-946.085 - 6045.03i) q^{28} -2027.77i q^{29} -5588.69 q^{31} +(2192.20 + 5361.78i) q^{32} -11408.5i q^{33} +(-5861.37 + 455.896i) q^{34} +(-1499.37 + 234.661i) q^{36} -1100.43 q^{37} +(8558.37 - 665.668i) q^{38} -19674.2 q^{39} +2252.91 q^{41} +(-18377.5 + 1429.39i) q^{42} -3008.27 q^{43} +(3312.37 + 21164.5i) q^{44} +(-11063.8 + 860.537i) q^{46} -16226.7i q^{47} +(16616.4 - 5331.75i) q^{48} -19753.0 q^{49} +17711.3i q^{51} +(36498.4 - 5712.24i) q^{52} -2099.27 q^{53} +(-1462.05 - 18797.3i) q^{54} +(33677.8 - 7987.48i) q^{56} -25860.9i q^{57} +(11436.3 - 889.510i) q^{58} -32947.1i q^{59} +23054.3i q^{61} +(-2451.56 - 31519.2i) q^{62} +9068.10i q^{63} +(-29277.9 + 14715.6i) q^{64} +(64342.1 - 5004.51i) q^{66} -54954.6 q^{67} +(-5142.35 - 32857.1i) q^{68} +33431.4i q^{69} +41508.4 q^{71} +(-1981.16 - 8353.23i) q^{72} +64631.1i q^{73} +(-482.720 - 6206.25i) q^{74} +(7508.50 + 47975.7i) q^{76} +128002. q^{77} +(-8630.35 - 110959. i) q^{78} -16550.9 q^{79} -68324.2 q^{81} +(988.272 + 12706.0i) q^{82} +48327.8 q^{83} +(-16123.1 - 103019. i) q^{84} +(-1319.62 - 16966.1i) q^{86} -34557.0i q^{87} +(-117911. + 27965.3i) q^{88} -77748.4 q^{89} -220740. i q^{91} +(-9706.55 - 62020.2i) q^{92} -95241.8 q^{93} +(91515.4 - 7118.05i) q^{94} +(37359.1 + 91374.8i) q^{96} -132778. i q^{97} +(-8664.91 - 111403. i) q^{98} -31748.7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9}+O(q^{10}) $ 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9	$ 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9} + 848 q^{14} - 110 q^{16} - 18918 q^{24} + 18344 q^{26} + 14320 q^{31} + 19182 q^{34} + 29656 q^{36} - 44904 q^{39} - 11608 q^{41} + 23186 q^{44} - 75224 q^{46} - 125304 q^{49} - 177894 q^{54} - 73816 q^{56} - 230354 q^{64} + 262878 q^{66} - 15448 q^{71} - 4224 q^{74} + 111902 q^{76} + 15560 q^{79} + 193968 q^{81} + 195112 q^{84} - 131972 q^{86} + 6320 q^{89} + 117080 q^{94} + 115582 q^{96}+O(q^{100}) $ 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9 + 848 * q^14 - 110 * q^16 - 18918 * q^24 + 18344 * q^26 + 14320 * q^31 + 19182 * q^34 + 29656 * q^36 - 44904 * q^39 - 11608 * q^41 + 23186 * q^44 - 75224 * q^46 - 125304 * q^49 - 177894 * q^54 - 73816 * q^56 - 230354 * q^64 + 262878 * q^66 - 15448 * q^71 - 4224 * q^74 + 111902 * q^76 + 15560 * q^79 + 193968 * q^81 + 195112 * q^84 - 131972 * q^86 + 6320 * q^89 + 117080 * q^94 + 115582 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	0.438664	+	5.63982i	0.0775455	+	0.996989i
$2$	0.438664	+	5.63982i	0.0775455	+	0.996989i
$3$	17.0419			1.09324			0.546619	−	0.837382i	$-0.315915\pi$
$3$	17.0419			1.09324			0.546619	+	0.837382i	$0.315915\pi$
$4$	−31.6151	+	4.94797i	−0.987973	+	0.154624i
$5$		0			0
$5$		0			0
$6$	7.47566	+	96.1131i	0.0847757	+	1.08995i
$7$			191.207i			1.47488i	0.675411	+	0.737442i	$0.263966\pi$
$7$			191.207i			1.47488i	−0.675411	+	0.737442i	$0.736034\pi$
$8$	−41.7741	−	176.133i	−0.230771	−	0.973008i
$9$	47.4256			0.195167
$10$		0			0
$11$		−	669.441i		−	1.66813i	−0.551664	−	0.834066i	$-0.686007\pi$
$11$		−	669.441i		−	1.66813i	0.551664	−	0.834066i	$-0.313993\pi$
$12$	−538.782	+	84.3227i	−1.08009	+	0.169041i
$13$	−1154.46			−1.89461			−0.947307	−	0.320328i	$-0.896207\pi$
$13$	−1154.46			−1.89461			−0.947307	+	0.320328i	$0.896207\pi$
$14$	−1078.37	+	83.8754i	−1.47044	+	0.114371i
$15$		0			0
$16$	975.035	−	312.862i	0.952183	−	0.305529i
$17$			1039.28i			0.872192i	0.899900	+	0.436096i	$0.143639\pi$
$17$			1039.28i			0.872192i	−0.899900	+	0.436096i	$0.856361\pi$
$18$	20.8039	+	267.472i	0.0151344	+	0.194580i
$19$		−	1517.49i		−	0.964366i	−0.876070	−	0.482183i	$-0.839844\pi$
$19$		−	1517.49i		−	0.964366i	0.876070	−	0.482183i	$-0.160156\pi$
$20$		0			0
$21$			3258.52i			1.61240i
$22$	3775.53	−	293.660i	1.66311	−	0.129356i
$23$			1961.72i			0.773247i	0.922238	+	0.386623i	$0.126359\pi$
$23$			1961.72i			0.773247i	−0.922238	+	0.386623i	$0.873641\pi$
$24$	−711.909	−	3001.64i	−0.252288	−	1.06373i
$25$		0			0
$26$	−506.420	−	6510.95i	−0.146919	−	1.88891i
$27$	−3332.95			−0.879873
$28$	−946.085	−	6045.03i	−0.228053	−	1.45715i
$29$		−	2027.77i		−	0.447738i	−0.974619	−	0.223869i	$-0.928131\pi$
$29$		−	2027.77i		−	0.447738i	0.974619	−	0.223869i	$-0.0718688\pi$
$30$		0			0
$31$	−5588.69			−1.04449			−0.522247	−	0.852794i	$-0.674906\pi$
$31$	−5588.69			−1.04449			−0.522247	+	0.852794i	$0.674906\pi$
$32$	2192.20	+	5361.78i	0.378446	+	0.925623i
$33$		−	11408.5i		−	1.82366i
$34$	−5861.37	+	455.896i	−0.869565	+	0.0676346i
$35$		0			0
$36$	−1499.37	+	234.661i	−0.192820	+	0.0301776i
$37$	−1100.43			−0.132148			−0.0660738	−	0.997815i	$-0.521047\pi$
$37$	−1100.43			−0.132148			−0.0660738	+	0.997815i	$0.521047\pi$
$38$	8558.37	−	665.668i	0.961462	−	0.0747823i
$39$	−19674.2			−2.07126
$40$		0			0
$41$	2252.91			0.209308			0.104654	−	0.994509i	$-0.466627\pi$
$41$	2252.91			0.209308			0.104654	+	0.994509i	$0.466627\pi$
$42$	−18377.5	+	1429.39i	−1.60754	+	0.125034i
$43$	−3008.27			−0.248111			−0.124055	−	0.992275i	$-0.539590\pi$
$43$	−3008.27			−0.248111			−0.124055	+	0.992275i	$0.539590\pi$
$44$	3312.37	+	21164.5i	0.257933	+	1.64807i
$45$		0			0
$46$	−11063.8	+	860.537i	−0.770918	+	0.0599618i
$47$		−	16226.7i		−	1.07148i	−0.844383	−	0.535741i	$-0.820033\pi$
$47$		−	16226.7i		−	1.07148i	0.844383	−	0.535741i	$-0.179967\pi$
$48$	16616.4	−	5331.75i	1.04096	−	0.334016i
$49$	−19753.0			−1.17528
$50$		0			0
$51$			17711.3i			0.953512i
$52$	36498.4	−	5712.24i	1.87183	−	0.292953i
$53$	−2099.27			−0.102655			−0.0513273	−	0.998682i	$-0.516345\pi$
$53$	−2099.27			−0.102655			−0.0513273	+	0.998682i	$0.516345\pi$
$54$	−1462.05	−	18797.3i	−0.0682302	−	0.877224i
$55$		0			0
$56$	33677.8	−	7987.48i	1.43507	−	0.340361i
$57$		−	25860.9i		−	1.05428i
$58$	11436.3	−	889.510i	0.446390	−	0.0347201i
$59$		−	32947.1i		−	1.23222i	−0.787662	−	0.616108i	$-0.788709\pi$
$59$		−	32947.1i		−	1.23222i	0.787662	−	0.616108i	$-0.211291\pi$
$60$		0			0
$61$			23054.3i			0.793283i	0.917974	+	0.396641i	$0.129824\pi$
$61$			23054.3i			0.793283i	−0.917974	+	0.396641i	$0.870176\pi$
$62$	−2451.56	−	31519.2i	−0.0809958	−	1.04135i
$63$			9068.10i			0.287849i
$64$	−29277.9	+	14715.6i	−0.893489	+	0.449085i
$65$		0			0
$66$	64342.1	−	5004.51i	1.81817	−	0.141417i
$67$	−54954.6			−1.49560			−0.747802	−	0.663921i	$-0.768891\pi$
$67$	−54954.6			−1.49560			−0.747802	+	0.663921i	$0.768891\pi$
$68$	−5142.35	−	32857.1i	−0.134862	−	0.861702i
$69$			33431.4i			0.845342i
$70$		0			0
$71$	41508.4			0.977215			0.488607	−	0.872504i	$-0.337505\pi$
$71$	41508.4			0.977215			0.488607	+	0.872504i	$0.337505\pi$
$72$	−1981.16	−	8353.23i	−0.0450390	−	0.189899i
$73$			64631.1i			1.41950i	0.704455	+	0.709748i	$0.251191\pi$
$73$			64631.1i			1.41950i	−0.704455	+	0.709748i	$0.748809\pi$
$74$	−482.720	−	6206.25i	−0.0102475	−	0.131750i
$75$		0			0
$76$	7508.50	+	47975.7i	0.149114	+	0.952768i
$77$	128002.			2.46030
$78$	−8630.35	−	110959.i	−0.160617	−	2.06502i
$79$	−16550.9			−0.298370			−0.149185	−	0.988809i	$-0.547665\pi$
$79$	−16550.9			−0.298370			−0.149185	+	0.988809i	$0.547665\pi$
$80$		0			0
$81$	−68324.2			−1.15708
$82$	988.272	+	12706.0i	0.0162309	+	0.208677i
$83$	48327.8			0.770020			0.385010	−	0.922912i	$-0.374198\pi$
$83$	48327.8			0.770020			0.385010	+	0.922912i	$0.374198\pi$
$84$	−16123.1	−	103019.i	−0.249316	−	1.59301i
$85$		0			0
$86$	−1319.62	−	16966.1i	−0.0192399	−	0.247364i
$87$		−	34557.0i		−	0.489484i
$88$	−117911.	+	27965.3i	−1.62311	+	0.384957i
$89$	−77748.4			−1.04044			−0.520219	−	0.854033i	$-0.674150\pi$
$89$	−77748.4			−1.04044			−0.520219	+	0.854033i	$0.674150\pi$
$90$		0			0
$91$		−	220740.i		−	2.79433i
$92$	−9706.55	−	62020.2i	−0.119563	−	0.763947i
$93$	−95241.8			−1.14188
$94$	91515.4	−	7118.05i	1.06825	−	0.0830886i
$95$		0			0
$96$	37359.1	+	91374.8i	0.413732	+	1.01193i
$97$		−	132778.i		−	1.43284i	−0.697669	−	0.716420i	$-0.745779\pi$
$97$		−	132778.i		−	1.43284i	0.697669	−	0.716420i	$-0.254221\pi$
$98$	−8664.91	−	111403.i	−0.0911379	−	1.17174i
$99$		−	31748.7i		−	0.325565i
$100$		0			0
$101$			10797.9i			0.105326i	0.998612	+	0.0526629i	$0.0167709\pi$
$101$			10797.9i			0.105326i	−0.998612	+	0.0526629i	$0.983229\pi$
$102$	−99888.8	+	7769.33i	−0.950641	+	0.0739406i
$103$			103331.i			0.959708i	0.877348	+	0.479854i	$0.159310\pi$
$103$			103331.i			0.959708i	−0.877348	+	0.479854i	$0.840690\pi$
$104$	48226.5	+	203339.i	0.437223	+	1.84347i
$105$		0			0
$106$	−920.874	−	11839.5i	−0.00796041	−	0.102346i
$107$	73988.1			0.624745			0.312372	−	0.949960i	$-0.398876\pi$
$107$	73988.1			0.624745			0.312372	+	0.949960i	$0.398876\pi$
$108$	105372.	−	16491.4i	0.869291	−	0.136050i
$109$			11369.6i			0.0916595i	0.998949	+	0.0458297i	$0.0145932\pi$
$109$			11369.6i			0.0916595i	−0.998949	+	0.0458297i	$0.985407\pi$
$110$		0			0
$111$	−18753.5			−0.144469
$112$	59821.2	+	186433.i	0.450620	+	1.40436i
$113$			73037.6i			0.538084i	0.963128	+	0.269042i	$0.0867071\pi$
$113$			73037.6i			0.538084i	−0.963128	+	0.269042i	$0.913293\pi$
$114$	145851.	−	11344.2i	1.05111	−	0.0817548i
$115$		0			0
$116$	10033.4	+	64108.3i	0.0692311	+	0.442353i
$117$	−54751.0			−0.369766
$118$	185815.	−	14452.7i	1.22850	−	0.0955528i
$119$	−198718.			−1.28638
$120$		0			0
$121$	−287100.			−1.78267
$122$	−130022.	+	10113.1i	−0.790894	+	0.0615155i
$123$	38393.9			0.228823
$124$	176687.	−	27652.7i	1.03193	−	0.161504i
$125$		0			0
$126$	−51142.4	+	3977.85i	−0.286982	+	0.0223214i
$127$			186263.i			1.02475i	0.858763	+	0.512373i	$0.171234\pi$
$127$			186263.i			1.02475i	−0.858763	+	0.512373i	$0.828766\pi$
$128$	−95836.5	−	158667.i	−0.517019	−	0.855974i
$129$	−51266.6			−0.271244
$130$		0			0
$131$			310611.i			1.58139i	0.612210	+	0.790695i	$0.290281\pi$
$131$			310611.i			1.58139i	−0.612210	+	0.790695i	$0.709719\pi$
$132$	56449.1	+	360682.i	0.281982	+	1.80173i
$133$	290154.			1.42233
$134$	−24106.6	−	309934.i	−0.115978	−	1.49110i
$135$		0			0
$136$	183052.	−	43415.1i	0.848649	−	0.201277i
$137$			178684.i			0.813363i	0.913570	+	0.406681i	$0.133314\pi$
$137$			178684.i			0.813363i	−0.913570	+	0.406681i	$0.866686\pi$
$138$	−188547.	+	14665.2i	−0.842797	+	0.0655525i
$139$			70585.2i			0.309868i	0.987925	+	0.154934i	$0.0495165\pi$
$139$			70585.2i			0.309868i	−0.987925	+	0.154934i	$0.950484\pi$
$140$		0			0
$141$		−	276533.i		−	1.17138i
$142$	18208.2	+	234100.i	0.0757787	+	0.974272i
$143$			772843.i			3.16047i
$144$	46241.7	−	14837.7i	0.185835	−	0.0596292i
$145$		0			0
$146$	−364508.	+	28351.3i	−1.41522	+	0.110076i
$147$	−336628.			−1.28486
$148$	34790.4	−	5444.91i	0.130558	−	0.0204332i
$149$			96518.2i			0.356159i	0.984016	+	0.178079i	$0.0569884\pi$
$149$			96518.2i			0.356159i	−0.984016	+	0.178079i	$0.943012\pi$
$150$		0			0
$151$	−212176.			−0.757277			−0.378639	−	0.925545i	$-0.623608\pi$
$151$	−212176.			−0.757277			−0.378639	+	0.925545i	$0.623608\pi$
$152$	−267281.	+	63391.8i	−0.938336	+	0.222548i
$153$			49288.7i			0.170223i
$154$	56149.6	+	721906.i	0.190785	+	2.45289i
$155$		0			0
$156$	622002.	−	97347.2i	2.04635	−	0.320267i
$157$	4153.63			0.0134487			0.00672433	−	0.999977i	$-0.497860\pi$
$157$	4153.63			0.0134487			0.00672433	+	0.999977i	$0.497860\pi$
$158$	−7260.30	−	93344.3i	−0.0231372	−	0.297471i
$159$	−35775.5			−0.112226
$160$		0			0
$161$	−375094.			−1.14045
$162$	−29971.4	−	385336.i	−0.0897262	−	1.15359i
$163$	−605063.			−1.78374			−0.891870	−	0.452292i	$-0.850607\pi$
$163$	−605063.			−1.78374			−0.891870	+	0.452292i	$0.850607\pi$
$164$	−71226.2	+	11147.3i	−0.206790	+	0.0323640i
$165$		0			0
$166$	21199.7	+	272560.i	0.0597117	+	0.767702i
$167$			151058.i			0.419135i	0.977794	+	0.209567i	$0.0672056\pi$
$167$			151058.i			0.419135i	−0.977794	+	0.209567i	$0.932794\pi$
$168$	573934.	−	136122.i	1.56888	−	0.372095i
$169$	961486.			2.58956
$170$		0			0
$171$		−	71967.9i		−	0.188213i
$172$	95107.0	−	14884.8i	0.245127	−	0.0383639i
$173$	−709157.			−1.80147			−0.900735	−	0.434368i	$-0.856972\pi$
$173$	−709157.			−1.80147			−0.900735	+	0.434368i	$0.856972\pi$
$174$	194896.	−	15158.9i	0.488010	−	0.0379573i
$175$		0			0
$176$	−209442.	−	652728.i	−0.509663	−	1.58837i
$177$		−	561480.i		−	1.34710i
$178$	−34105.4	−	438487.i	−0.0806813	−	1.03731i
$179$		−	210175.i		−	0.490285i	−0.969487	−	0.245142i	$-0.921165\pi$
$179$		−	210175.i		−	0.490285i	0.969487	−	0.245142i	$-0.0788347\pi$
$180$		0			0
$181$			581317.i			1.31891i	0.751742	+	0.659457i	$0.229214\pi$
$181$			581317.i			1.31891i	−0.751742	+	0.659457i	$0.770786\pi$
$182$	1.24494e6	−	96830.9i	2.78592	−	0.216688i
$183$			392889.i			0.867246i
$184$	345525.	−	81949.2i	0.752375	−	0.178443i
$185$		0			0
$186$	−41779.1	−	537146.i	−0.0885476	−	1.13844i
$187$	695739.			1.45493
$188$	80289.0	+	513008.i	0.165677	+	1.05859i
$189$		−	637283.i		−	1.29771i
$190$		0			0
$191$	830661.			1.64756			0.823779	−	0.566912i	$-0.191862\pi$
$191$	830661.			1.64756			0.823779	+	0.566912i	$0.191862\pi$
$192$	−498950.	+	250782.i	−0.976795	+	0.490956i
$193$		−	475580.i		−	0.919031i	−0.888170	−	0.459516i	$-0.848023\pi$
$193$		−	475580.i		−	0.919031i	0.888170	−	0.459516i	$-0.151977\pi$
$194$	748846.	−	58245.0i	1.42853	−	0.111110i
$195$		0			0
$196$	624493.	−	97737.1i	1.16115	−	0.181727i
$197$	−835761.			−1.53432			−0.767161	−	0.641455i	$-0.778331\pi$
$197$	−835761.			−1.53432			−0.767161	+	0.641455i	$0.778331\pi$
$198$	179057.	−	13927.0i	0.324584	−	0.0252461i
$199$	−117271.			−0.209922			−0.104961	−	0.994476i	$-0.533472\pi$
$199$	−117271.			−0.209922			−0.104961	+	0.994476i	$0.533472\pi$
$200$		0			0
$201$	−936529.			−1.63505
$202$	−60898.1	+	4736.64i	−0.105009	+	0.00816755i
$203$	387723.			0.660362
$204$	−87635.2	−	559947.i	−0.147436	−	0.942045i
$205$		0			0
$206$	−582770.	+	45327.7i	−0.956818	+	0.0744211i
$207$			93036.0i			0.150912i
$208$	−1.12564e6	+	361186.i	−1.80402	+	0.578859i
$209$	−1.01587e6			−1.60869
$210$		0			0
$211$			613202.i			0.948194i	0.880473	+	0.474097i	$0.157225\pi$
$211$			613202.i			0.948194i	−0.880473	+	0.474097i	$0.842775\pi$
$212$	66368.8	−	10387.1i	0.101420	−	0.0158729i
$213$	707381.			1.06833
$214$	32455.9	+	417280.i	0.0484462	+	0.622864i
$215$		0			0
$216$	139231.	+	587044.i	0.203050	+	0.856123i
$217$		−	1.06859e6i		−	1.54051i
$218$	−64122.3	+	4987.42i	−0.0913835	+	0.00710779i
$219$			1.10144e6i			1.55185i
$220$		0			0
$221$		−	1.19981e6i		−	1.65247i
$222$	−8226.46	−	105766.i	−0.0112029	−	0.144034i
$223$		−	916335.i		−	1.23393i	−0.786989	−	0.616967i	$-0.788361\pi$
$223$		−	916335.i		−	1.23393i	0.786989	−	0.616967i	$-0.211639\pi$
$224$	−1.02521e6	+	419162.i	−1.36519	+	0.558165i
$225$		0			0
$226$	−411919.	+	32038.9i	−0.536464	+	0.0417260i
$227$	964145.			1.24187			0.620937	−	0.783860i	$-0.286752\pi$
$227$	964145.			1.24187			0.620937	+	0.783860i	$0.286752\pi$
$228$	127959.	+	817596.i	0.163017	+	1.04160i
$229$		−	44135.5i		−	0.0556159i	−0.999613	−	0.0278079i	$-0.991147\pi$
$229$		−	44135.5i		−	0.0556159i	0.999613	−	0.0278079i	$-0.00885269\pi$
$230$		0			0
$231$	2.18139e6			2.68969
$232$	−357158.	+	84708.3i	−0.435653	+	0.103325i
$233$			132906.i			0.160382i	0.996780	+	0.0801908i	$0.0255530\pi$
$233$			132906.i			0.160382i	−0.996780	+	0.0801908i	$0.974447\pi$
$234$	−24017.3	−	308786.i	−0.0286737	−	0.368653i
$235$		0			0
$236$	163021.	+	1.04163e6i	0.190530	+	1.21740i
$237$	−282059.			−0.326189
$238$	−87170.4	−	1.12073e6i	−0.0997531	−	1.28251i
$239$	−536631.			−0.607688			−0.303844	−	0.952722i	$-0.598270\pi$
$239$	−536631.			−0.607688			−0.303844	+	0.952722i	$0.598270\pi$
$240$		0			0
$241$	−51107.9			−0.0566821			−0.0283410	−	0.999598i	$-0.509022\pi$
$241$	−51107.9			−0.0566821			−0.0283410	+	0.999598i	$0.509022\pi$
$242$	−125940.	−	1.61919e6i	−0.138238	−	1.77730i
$243$	−354465.			−0.385086
$244$	−114072.	−	728866.i	−0.122661	−	0.783742i
$245$		0			0
$246$	16842.0	+	216535.i	0.0177442	+	0.228134i
$247$			1.75188e6i			1.82710i
$248$	233462.	+	984354.i	0.241039	+	1.01630i
$249$	823597.			0.841815
$250$		0			0
$251$			564796.i			0.565858i	0.959141	+	0.282929i	$0.0913061\pi$
$251$			564796.i			0.565858i	−0.959141	+	0.282929i	$0.908694\pi$
$252$	−44868.7	−	286689.i	−0.0445084	−	0.284387i
$253$	1.31326e6			1.28988
$254$	−1.05049e6	+	81706.7i	−1.02166	+	0.0794645i
$255$		0			0
$256$	852811.	−	610102.i	0.813304	−	0.581839i
$257$		−	658592.i		−	0.621990i	−0.950412	−	0.310995i	$-0.899338\pi$
$257$		−	658592.i		−	0.621990i	0.950412	−	0.310995i	$-0.100662\pi$
$258$	−22488.8	−	289134.i	−0.0210338	−	0.270427i
$259$		−	210410.i		−	0.194902i
$260$		0			0
$261$		−	96168.4i		−	0.0873838i
$262$	−1.75179e6	+	136254.i	−1.57663	+	0.122630i
$263$			161952.i			0.144377i	0.997391	+	0.0721885i	$0.0229983\pi$
$263$			161952.i			0.144377i	−0.997391	+	0.0721885i	$0.977002\pi$
$264$	−2.00942e6	+	476581.i	−1.77444	+	0.420850i
$265$		0			0
$266$	127280.	+	1.63642e6i	0.110295	+	1.41805i
$267$	−1.32498e6			−1.13745
$268$	1.73740e6	−	271914.i	1.47762	−	0.231257i
$269$			355854.i			0.299841i	0.988698	+	0.149920i	$0.0479017\pi$
$269$			355854.i			0.299841i	−0.988698	+	0.149920i	$0.952098\pi$
$270$		0			0
$271$	848597.			0.701905			0.350952	−	0.936393i	$-0.385858\pi$
$271$	848597.			0.701905			0.350952	+	0.936393i	$0.385858\pi$
$272$	325152.	+	1.01334e6i	0.266480	+	0.830486i
$273$		−	3.76183e6i		−	3.05487i
$274$	−1.00775e6	+	78382.2i	−0.810914	+	0.0630727i
$275$		0			0
$276$	−165418.	−	1.05694e6i	−0.130710	−	0.835175i
$277$	1.80087e6			1.41020			0.705102	−	0.709105i	$-0.250901\pi$
$277$	1.80087e6			1.41020			0.705102	+	0.709105i	$0.250901\pi$
$278$	−398088.	+	30963.2i	−0.308935	+	0.0240289i
$279$	−265047.			−0.203851
$280$		0			0
$281$	−1.45513e6			−1.09935			−0.549674	−	0.835379i	$-0.685248\pi$
$281$	−1.45513e6			−1.09935			−0.549674	+	0.835379i	$0.685248\pi$
$282$	1.55960e6	−	121305.i	1.16786	−	0.0908355i
$283$	995296.			0.738731			0.369365	−	0.929284i	$-0.379575\pi$
$283$	995296.			0.738731			0.369365	+	0.929284i	$0.379575\pi$
$284$	−1.31229e6	+	205382.i	−0.965462	+	0.151101i
$285$		0			0
$286$	−4.35870e6	+	339018.i	−3.15095	+	0.245080i
$287$			430772.i			0.308704i
$288$	103966.	+	254286.i	0.0738604	+	0.180651i
$289$	339746.			0.239282
$290$		0			0
$291$		−	2.26279e6i		−	1.56643i
$292$	−319793.	−	2.04332e6i	−0.219488	−	1.40243i
$293$	−852050.			−0.579824			−0.289912	−	0.957053i	$-0.593626\pi$
$293$	−852050.			−0.579824			−0.289912	+	0.957053i	$0.593626\pi$
$294$	−147666.	−	1.89852e6i	−0.0996353	−	1.28099i
$295$		0			0
$296$	45969.6	+	193823.i	0.0304959	+	0.128581i
$297$			2.23122e6i			1.46774i
$298$	−544345.	+	42339.0i	−0.355086	+	0.0276185i
$299$		−	2.26473e6i		−	1.46500i
$300$		0			0
$301$		−	575202.i		−	0.365935i
$302$	−93074.1	−	1.19664e6i	−0.0587235	−	0.754997i
$303$			184016.i			0.115146i
$304$	−474765.	−	1.47961e6i	−0.294642	−	0.918253i
$305$		0			0
$306$	−277979.	+	21621.2i	−0.169711	+	0.0132001i
$307$	−730190.			−0.442171			−0.221085	−	0.975254i	$-0.570960\pi$
$307$	−730190.			−0.442171			−0.221085	+	0.975254i	$0.570960\pi$
$308$	−4.04679e6	+	633348.i	−2.43071	+	0.380422i
$309$			1.76096e6i			1.04919i
$310$		0			0
$311$	958205.			0.561769			0.280884	−	0.959742i	$-0.409372\pi$
$311$	958205.			0.561769			0.280884	+	0.959742i	$0.409372\pi$
$312$	821871.	+	3.46528e6i	0.477988	+	2.01535i
$313$		−	2.75640e6i		−	1.59031i	−0.606408	−	0.795154i	$-0.707390\pi$
$313$		−	2.75640e6i		−	1.59031i	0.606408	−	0.795154i	$-0.292610\pi$
$314$	1822.05	+	23425.8i	0.00104288	+	0.0134082i
$315$		0			0
$316$	523260.	−	81893.5i	0.294781	−	0.0461351i
$317$	1.84693e6			1.03229			0.516146	−	0.856501i	$-0.327366\pi$
$317$	1.84693e6			1.03229			0.516146	+	0.856501i	$0.327366\pi$
$318$	−15693.4	−	201767.i	−0.00870262	−	0.111888i
$319$	−1.35747e6			−0.746887
$320$		0			0
$321$	1.26090e6			0.682994
$322$	−164540.	−	2.11547e6i	−0.0884368	−	1.13702i
$323$	1.57710e6			0.841112
$324$	2.16008e6	−	338066.i	1.14316	−	0.178912i
$325$		0			0
$326$	−265419.	−	3.41245e6i	−0.138321	−	1.77837i
$327$			193759.i			0.100206i
$328$	−94113.4	−	396813.i	−0.0483022	−	0.203658i
$329$	3.10264e6			1.58031
$330$		0			0
$331$			775769.i			0.389191i	0.980884	+	0.194595i	$0.0623394\pi$
$331$			775769.i			0.389191i	−0.980884	+	0.194595i	$0.937661\pi$
$332$	−1.52789e6	+	239125.i	−0.760760	+	0.119064i
$333$	−52188.8			−0.0257909
$334$	−851942.	+	66263.9i	−0.417873	+	0.0325020i
$335$		0			0
$336$	1.01947e6	+	3.17717e6i	0.492634	+	1.53530i
$337$		−	3.63273e6i		−	1.74244i	−0.490891	−	0.871221i	$-0.663329\pi$
$337$		−	3.63273e6i		−	1.74244i	0.490891	−	0.871221i	$-0.336671\pi$
$338$	421769.	+	5.42261e6i	0.200809	+	2.58176i
$339$			1.24470e6i			0.588254i
$340$		0			0
$341$			3.74130e6i			1.74235i
$342$	405886.	−	31569.7i	0.187646	−	0.0145951i
$343$		−	563289.i		−	0.258521i
$344$	125668.	+	529857.i	0.0572569	+	0.241414i
$345$		0			0
$346$	−311082.	−	3.99952e6i	−0.139696	−	1.79605i
$347$	−1.34356e6			−0.599009			−0.299504	−	0.954095i	$-0.596821\pi$
$347$	−1.34356e6			−0.599009			−0.299504	+	0.954095i	$0.596821\pi$
$348$	170987.	+	1.09253e6i	0.0756860	+	0.483597i
$349$		−	399038.i		−	0.175368i	−0.996148	−	0.0876841i	$-0.972053\pi$
$349$		−	399038.i		−	0.175368i	0.996148	−	0.0876841i	$-0.0279466\pi$
$350$		0			0
$351$	3.84776e6			1.66702
$352$	3.58940e6	−	1.46755e6i	1.54406	−	0.631299i
$353$		−	1.48409e6i		−	0.633903i	−0.948442	−	0.316951i	$-0.897341\pi$
$353$		−	1.48409e6i		−	0.633903i	0.948442	−	0.316951i	$-0.102659\pi$
$354$	3.16664e6	−	246301.i	1.34305	−	0.104462i
$355$		0			0
$356$	2.45803e6	−	384697.i	1.02793	−	0.160877i
$357$	−3.38653e6			−1.40632
$358$	1.18535e6	−	92196.2i	0.488809	−	0.0380194i
$359$	1.85819e6			0.760945			0.380472	−	0.924792i	$-0.375761\pi$
$359$	1.85819e6			0.760945			0.380472	+	0.924792i	$0.375761\pi$
$360$		0			0
$361$	173322.			0.0699981
$362$	−3.27852e6	+	255003.i	−1.31494	+	0.102276i
$363$	−4.89273e6			−1.94888
$364$	1.09222e6	+	6.97874e6i	0.432071	+	2.76073i
$365$		0			0
$366$	−2.21582e6	+	172346.i	−0.864634	+	0.0672511i
$367$			873341.i			0.338469i	0.985576	+	0.169234i	$0.0541295\pi$
$367$			873341.i			0.338469i	−0.985576	+	0.169234i	$0.945871\pi$
$368$	613748.	+	1.91275e6i	0.236249	+	0.736272i
$369$	106846.			0.0408500
$370$		0			0
$371$		−	401394.i		−	0.151404i
$372$	3.01108e6	−	471253.i	1.12815	−	0.176562i
$373$	−4.82966e6			−1.79740			−0.898700	−	0.438564i	$-0.855487\pi$
$373$	−4.82966e6			−1.79740			−0.898700	+	0.438564i	$0.855487\pi$
$374$	305196.	+	3.92384e6i	0.112823	+	1.45055i
$375$		0			0
$376$	−2.85805e6	+	677854.i	−1.04256	+	0.247267i
$377$			2.34098e6i			0.848291i
$378$	3.59416e6	−	279553.i	1.29380	−	0.100632i
$379$		−	797234.i		−	0.285094i	−0.989788	−	0.142547i	$-0.954471\pi$
$379$		−	797234.i		−	0.285094i	0.989788	−	0.142547i	$-0.0455292\pi$
$380$		0			0
$381$			3.17427e6i			1.12029i
$382$	364381.	+	4.68478e6i	0.127761	+	1.64260i
$383$			2.59047e6i			0.902364i	0.892432	+	0.451182i	$0.148997\pi$
$383$			2.59047e6i			0.902364i	−0.892432	+	0.451182i	$0.851003\pi$
$384$	−1.63323e6	−	2.70398e6i	−0.565224	−	0.935783i
$385$		0			0
$386$	2.68219e6	−	208620.i	0.916264	−	0.0712668i
$387$	−142669.			−0.0484231
$388$	656983.	+	4.19780e6i	0.221552	+	1.41561i
$389$		−	3.63240e6i		−	1.21708i	−0.793523	−	0.608541i	$-0.791755\pi$
$389$		−	3.63240e6i		−	1.21708i	0.793523	−	0.608541i	$-0.208245\pi$
$390$		0			0
$391$	−2.03879e6			−0.674419
$392$	825162.	+	3.47916e6i	0.271222	+	1.14356i
$393$			5.29340e6i			1.72883i
$394$	−366618.	−	4.71354e6i	−0.118980	−	1.52970i
$395$		0			0
$396$	157091.	+	1.00374e6i	0.0503402	+	0.321649i
$397$	2.08693e6			0.664555			0.332278	−	0.943182i	$-0.392183\pi$
$397$	2.08693e6			0.664555			0.332278	+	0.943182i	$0.392183\pi$
$398$	−51442.5	−	661387.i	−0.0162785	−	0.209290i
$399$	4.94477e6			1.55494
$400$		0			0
$401$	−3.80075e6			−1.18034			−0.590171	−	0.807278i	$-0.700940\pi$
$401$	−3.80075e6			−1.18034			−0.590171	+	0.807278i	$0.700940\pi$
$402$	−410822.	−	5.28186e6i	−0.126791	−	1.63013i
$403$	6.45192e6			1.97891
$404$	−53427.6	−	341376.i	−0.0162859	−	0.104059i
$405$		0			0
$406$	170080.	+	2.18669e6i	0.0512081	+	0.658373i
$407$			736675.i			0.220440i
$408$	3.11956e6	−	739875.i	0.927775	−	0.220043i
$409$	4.09840e6			1.21145			0.605725	−	0.795674i	$-0.292883\pi$
$409$	4.09840e6			1.21145			0.605725	+	0.795674i	$0.292883\pi$
$410$		0			0
$411$			3.04511e6i			0.889198i
$412$	−511281.	−	3.26684e6i	−0.148394	−	0.948166i
$413$	6.29969e6			1.81737
$414$	−524706.	+	40811.5i	−0.150458	+	0.0117026i
$415$		0			0
$416$	−2.53080e6	−	6.18996e6i	−0.717010	−	1.75370i
$417$			1.20290e6i			0.338759i
$418$	−445625.	−	5.72932e6i	−0.124747	−	1.60385i
$419$			925304.i			0.257483i	0.991678	+	0.128742i	$0.0410938\pi$
$419$			925304.i			0.257483i	−0.991678	+	0.128742i	$0.958906\pi$
$420$		0			0
$421$		−	3.60597e6i		−	0.991555i	−0.868450	−	0.495778i	$-0.834883\pi$
$421$		−	3.60597e6i		−	0.991555i	0.868450	−	0.495778i	$-0.165117\pi$
$422$	−3.45835e6	+	268990.i	−0.945339	+	0.0735283i
$423$		−	769560.i		−	0.209118i
$424$	87695.1	+	369751.i	0.0236898	+	0.0998838i
$425$		0			0
$426$	310302.	+	3.98950e6i	0.0828440	+	1.06511i
$427$	−4.40814e6			−1.17000
$428$	−2.33915e6	+	366091.i	−0.617231	+	0.0966006i
$429$			1.31707e7i			3.45514i
$430$		0			0
$431$	−3.89211e6			−1.00923			−0.504617	−	0.863343i	$-0.668366\pi$
$431$	−3.89211e6			−1.00923			−0.504617	+	0.863343i	$0.668366\pi$
$432$	−3.24975e6	+	1.04275e6i	−0.837800	+	0.268827i
$433$			4.27607e6i			1.09604i	0.836467	+	0.548018i	$0.184617\pi$
$433$			4.27607e6i			1.09604i	−0.836467	+	0.548018i	$0.815383\pi$
$434$	6.02668e6	−	468754.i	1.53587	−	0.119459i
$435$		0			0
$436$	−56256.3	−	359450.i	−0.0141728	−	0.0905571i
$437$	2.97690e6			0.745693
$438$	−6.21190e6	+	483160.i	−1.54717	+	0.120339i
$439$	2.46292e6			0.609943			0.304972	−	0.952361i	$-0.401353\pi$
$439$	2.46292e6			0.609943			0.304972	+	0.952361i	$0.401353\pi$
$440$		0			0
$441$	−936797.			−0.229377
$442$	6.76672e6	−	526314.i	1.64749	−	0.128141i
$443$	−3.24738e6			−0.786184			−0.393092	−	0.919499i	$-0.628595\pi$
$443$	−3.24738e6			−0.786184			−0.393092	+	0.919499i	$0.628595\pi$
$444$	592893.	−	92791.5i	0.142731	−	0.0223383i
$445$		0			0
$446$	5.16797e6	−	401963.i	1.23022	−	0.0956862i
$447$			1.64485e6i			0.389366i
$448$	−2.81372e6	−	5.59812e6i	−0.662348	−	1.31779i
$449$	−6.47353e6			−1.51539			−0.757696	−	0.652608i	$-0.773675\pi$
$449$	−6.47353e6			−1.51539			−0.757696	+	0.652608i	$0.773675\pi$
$450$		0			0
$451$		−	1.50819e6i		−	0.349153i
$452$	−361388.	−	2.30909e6i	−0.0832008	−	0.531613i
$453$	−3.61589e6			−0.827883
$454$	422936.	+	5.43761e6i	0.0963019	+	1.23814i
$455$		0			0
$456$	−4.55496e6	+	1.08031e6i	−1.02582	+	0.243298i
$457$		−	3.12151e6i		−	0.699156i	−0.936907	−	0.349578i	$-0.886325\pi$
$457$		−	3.12151e6i		−	0.699156i	0.936907	−	0.349578i	$-0.113675\pi$
$458$	248916.	−	19360.6i	0.0554484	−	0.00431276i
$459$		−	3.46389e6i		−	0.767418i
$460$		0			0
$461$		−	6.58945e6i		−	1.44410i	−0.691842	−	0.722049i	$-0.743200\pi$
$461$		−	6.58945e6i		−	1.44410i	0.691842	−	0.722049i	$-0.256800\pi$
$462$	956895.	+	1.23026e7i	0.208574	+	2.68159i
$463$		−	2.51619e6i		−	0.545494i	−0.962086	−	0.272747i	$-0.912068\pi$
$463$		−	2.51619e6i		−	0.545494i	0.962086	−	0.272747i	$-0.0879322\pi$
$464$	−634412.	−	1.97715e6i	−0.136797	−	0.426329i
$465$		0			0
$466$	−749566.	+	58301.0i	−0.159899	+	0.0124369i
$467$	280503.			0.0595176			0.0297588	−	0.999557i	$-0.490526\pi$
$467$	280503.			0.0595176			0.0297588	+	0.999557i	$0.490526\pi$
$468$	1.73096e6	−	270906.i	0.365319	−	0.0571748i
$469$		−	1.05077e7i		−	2.20584i
$470$		0			0
$471$	70785.7			0.0147026
$472$	−5.80307e6	+	1.37633e6i	−1.19896	+	0.284360i
$473$			2.01386e6i			0.413882i
$474$	−123729.	−	1.59076e6i	−0.0252945	−	0.325207i
$475$		0			0
$476$	6.28250e6	−	983251.i	1.27091	−	0.198906i
$477$	−99559.3			−0.0200348
$478$	−235401.	−	3.02650e6i	−0.0471235	−	0.605859i
$479$	−7.04779e6			−1.40350			−0.701752	−	0.712421i	$-0.747599\pi$
$479$	−7.04779e6			−1.40350			−0.701752	+	0.712421i	$0.747599\pi$
$480$		0			0
$481$	1.27041e6			0.250369
$482$	−22419.2	−	288240.i	−0.00439544	−	0.0565114i
$483$	−6.39231e6			−1.24678
$484$	9.07671e6	−	1.42056e6i	1.76123	−	0.275643i
$485$		0			0
$486$	−155491.	−	1.99912e6i	−0.0298617	−	0.383927i
$487$		−	4.98658e6i		−	0.952752i	−0.879242	−	0.476376i	$-0.841950\pi$
$487$		−	4.98658e6i		−	0.952752i	0.879242	−	0.476376i	$-0.158050\pi$
$488$	4.06063e6	−	963074.i	0.771870	−	0.183067i
$489$	−1.03114e7			−1.95005
$490$		0			0
$491$		−	5.28330e6i		−	0.989012i	−0.869174	−	0.494506i	$-0.835349\pi$
$491$		−	5.28330e6i		−	0.989012i	0.869174	−	0.494506i	$-0.164651\pi$
$492$	−1.21383e6	+	189972.i	−0.226071	+	0.0353815i
$493$	2.10743e6			0.390513
$494$	−9.88030e6	+	768487.i	−1.82160	+	0.141684i
$495$		0			0
$496$	−5.44917e6	+	1.74849e6i	−0.994549	+	0.319123i
$497$			7.93668e6i			1.44128i
$498$	361282.	+	4.64494e6i	0.0652790	+	0.839280i
$499$			3.04090e6i			0.546703i	0.961914	+	0.273352i	$0.0881322\pi$
$499$			3.04090e6i			0.546703i	−0.961914	+	0.273352i	$0.911868\pi$
$500$		0			0
$501$			2.57432e6i			0.458214i
$502$	−3.18535e6	+	247756.i	−0.564154	+	0.0438798i
$503$		−	494450.i		−	0.0871370i	−0.999050	−	0.0435685i	$-0.986127\pi$
$503$		−	494450.i		−	0.0871370i	0.999050	−	0.0435685i	$-0.0138727\pi$
$504$	1.59719e6	−	378811.i	0.280079	−	0.0664273i
$505$		0			0
$506$	576079.	+	7.40654e6i	0.100024	+	1.28599i
$507$	1.63855e7			2.83100
$508$	−921622.	−	5.88872e6i	−0.158451	−	1.01242i
$509$		−	9.82310e6i		−	1.68056i	−0.542153	−	0.840280i	$-0.682391\pi$
$509$		−	9.82310e6i		−	1.68056i	0.542153	−	0.840280i	$-0.317609\pi$
$510$		0			0
$511$	−1.23579e7			−2.09359
$512$	3.81496e6	+	4.54207e6i	0.643155	+	0.765736i
$513$			5.05773e6i			0.848520i
$514$	3.71434e6	−	288900.i	0.620117	−	0.0482326i
$515$		0			0
$516$	1.62080e6	−	253666.i	0.267982	−	0.0419409i
$517$	−1.08628e7			−1.78737
$518$	1.18668e6	−	92299.3i	0.194316	−	0.0151138i
$519$	−1.20854e7			−1.96943
$520$		0			0
$521$	8.78805e6			1.41840			0.709199	−	0.705008i	$-0.249057\pi$
$521$	8.78805e6			1.41840			0.709199	+	0.705008i	$0.249057\pi$
$522$	542372.	−	42185.6i	0.0871207	−	0.00677623i
$523$	9.71136e6			1.55248			0.776240	−	0.630438i	$-0.217125\pi$
$523$	9.71136e6			1.55248			0.776240	+	0.630438i	$0.217125\pi$
$524$	−1.53690e6	−	9.82002e6i	−0.244521	−	1.56237i
$525$		0			0
$526$	−913383.	+	71042.7i	−0.143942	+	0.0111958i
$527$		−	5.80823e6i		−	0.910998i
$528$	−3.56929e6	−	1.11237e7i	−0.557182	−	1.73646i
$529$	2.58799e6			0.402089
$530$		0			0
$531$		−	1.56253e6i		−	0.240488i
$532$	−9.17327e6	+	1.43567e6i	−1.40522	+	0.219926i
$533$	−2.60090e6			−0.396557
$534$	−581220.	−	7.47264e6i	−0.0882038	−	1.13402i
$535$		0			0
$536$	2.29568e6	+	9.67933e6i	0.345143	+	1.45524i
$537$		−	3.58178e6i		−	0.535998i
$538$	−2.00695e6	+	156100.i	−0.298938	+	0.0232513i
$539$			1.32234e7i			1.96053i
$540$		0			0
$541$		−	6.92139e6i		−	1.01672i	−0.861146	−	0.508358i	$-0.830252\pi$
$541$		−	6.92139e6i		−	1.01672i	0.861146	−	0.508358i	$-0.169748\pi$
$542$	372249.	+	4.78593e6i	0.0544296	+	0.699791i
$543$			9.90674e6i			1.44189i
$544$	−5.57241e6	+	2.27831e6i	−0.807321	+	0.330078i
$545$		0			0
$546$	2.12161e7	−	1.65018e6i	3.04567	−	0.236892i
$547$	1.15358e7			1.64846			0.824230	−	0.566255i	$-0.191608\pi$
$547$	1.15358e7			1.64846			0.824230	+	0.566255i	$0.191608\pi$
$548$	−884123.	−	5.64912e6i	−0.125765	−	0.803581i
$549$			1.09337e6i			0.154823i
$550$		0			0
$551$	−3.07712e6			−0.431783
$552$	5.88839e6	−	1.39657e6i	0.822525	−	0.195081i
$553$		−	3.16465e6i		−	0.440061i
$554$	789975.	+	1.01566e7i	0.109355	+	1.40596i
$555$		0			0
$556$	−349253.	−	2.23156e6i	−0.0479130	−	0.306141i
$557$	−5.11026e6			−0.697919			−0.348959	−	0.937138i	$-0.613465\pi$
$557$	−5.11026e6			−0.697919			−0.348959	+	0.937138i	$0.613465\pi$
$558$	−116267.	−	1.49482e6i	−0.0158077	−	0.203237i
$559$	3.47293e6			0.470074
$560$		0			0
$561$	1.18567e7			1.59058
$562$	−638312.	−	8.20666e6i	−0.0852496	−	1.09604i
$563$	−2.81303e6			−0.374027			−0.187013	−	0.982357i	$-0.559881\pi$
$563$	−2.81303e6			−0.374027			−0.187013	+	0.982357i	$0.559881\pi$
$564$	1.36828e6	+	8.74262e6i	0.181124	+	1.15729i
$565$		0			0
$566$	436600.	+	5.61329e6i	0.0572853	+	0.736506i
$567$		−	1.30640e7i		−	1.70655i
$568$	−1.73398e6	−	7.31101e6i	−0.225513	−	0.950838i
$569$	−7.58369e6			−0.981974			−0.490987	−	0.871167i	$-0.663364\pi$
$569$	−7.58369e6			−0.981974			−0.490987	+	0.871167i	$0.663364\pi$
$570$		0			0
$571$			7.03989e6i			0.903598i	0.892120	+	0.451799i	$0.149218\pi$
$571$			7.03989e6i			0.903598i	−0.892120	+	0.451799i	$0.850782\pi$
$572$	−3.82400e6	−	2.44335e7i	−0.488684	−	3.12246i
$573$	1.41560e7			1.80117
$574$	−2.42948e6	+	188964.i	−0.307775	+	0.0239386i
$575$		0			0
$576$	−1.38852e6	+	697897.i	−0.174380	+	0.0876467i
$577$		−	2.33220e6i		−	0.291626i	−0.989312	−	0.145813i	$-0.953420\pi$
$577$		−	2.33220e6i		−	0.291626i	0.989312	−	0.145813i	$-0.0465797\pi$
$578$	149034.	+	1.91611e6i	0.0185552	+	0.238561i
$579$		−	8.10478e6i		−	1.00472i
$580$		0			0
$581$			9.24060e6i			1.13569i
$582$	1.27617e7	−	992605.i	1.56172	−	0.121470i
$583$			1.40534e6i			0.171242i
$584$	1.13837e7	−	2.69991e6i	1.38118	−	0.327579i
$585$		0			0
$586$	−373764.	−	4.80541e6i	−0.0449628	−	0.578078i
$587$	−1.03503e7			−1.23982			−0.619911	−	0.784672i	$-0.712831\pi$
$587$	−1.03503e7			−1.23982			−0.619911	+	0.784672i	$0.712831\pi$
$588$	1.06425e7	−	1.66562e6i	1.26941	−	0.198671i
$589$			8.48078e6i			1.00727i
$590$		0			0
$591$	−1.42429e7			−1.67738
$592$	−1.07296e6	+	344283.i	−0.125829	+	0.0403749i
$593$			1.02855e7i			1.20113i	0.799577	+	0.600564i	$0.205057\pi$
$593$			1.02855e7i			1.20113i	−0.799577	+	0.600564i	$0.794943\pi$
$594$	−1.25837e7	+	978754.i	−1.46333	+	0.113817i
$595$		0			0
$596$	−477569.	−	3.05144e6i	−0.0550707	−	0.351875i
$597$	−1.99852e6			−0.229494
$598$	1.27727e7	−	993456.i	1.46059	−	0.113605i
$599$	3.50730e6			0.399398			0.199699	−	0.979857i	$-0.436004\pi$
$599$	3.50730e6			0.399398			0.199699	+	0.979857i	$0.436004\pi$
$600$		0			0
$601$	−4.45868e6			−0.503524			−0.251762	−	0.967789i	$-0.581010\pi$
$601$	−4.45868e6			−0.503524			−0.251762	+	0.967789i	$0.581010\pi$
$602$	3.24403e6	−	252320.i	0.364833	−	0.0283766i
$603$	−2.60626e6			−0.291893
$604$	6.70799e6	−	1.04984e6i	0.748170	−	0.117093i
$605$		0			0
$606$	−1.03782e6	+	80721.2i	−0.114799	+	0.00892907i
$607$		−	1.47085e7i		−	1.62030i	−0.586220	−	0.810152i	$-0.699385\pi$
$607$		−	1.47085e7i		−	1.62030i	0.586220	−	0.810152i	$-0.300615\pi$
$608$	8.13645e6	−	3.32664e6i	0.892640	−	0.364961i
$609$	6.60754e6			0.721932
$610$		0			0
$611$			1.87330e7i			2.03004i
$612$	−243879.	−	1.55827e6i	−0.0263206	−	0.168176i
$613$	−9.99920e6			−1.07477			−0.537383	−	0.843338i	$-0.680587\pi$
$613$	−9.99920e6			−1.07477			−0.537383	+	0.843338i	$0.680587\pi$
$614$	−320308.	−	4.11814e6i	−0.0342884	−	0.440839i
$615$		0			0
$616$	−5.34715e6	−	2.25453e7i	−0.567767	−	2.39389i
$617$			4.04354e6i			0.427611i	0.976876	+	0.213806i	$0.0685859\pi$
$617$			4.04354e6i			0.427611i	−0.976876	+	0.213806i	$0.931414\pi$
$618$	−9.93150e6	+	772470.i	−1.04603	+	0.0813599i
$619$		−	4.03646e6i		−	0.423423i	−0.977332	−	0.211711i	$-0.932096\pi$
$619$		−	4.03646e6i		−	0.423423i	0.977332	−	0.211711i	$-0.0679037\pi$
$620$		0			0
$621$		−	6.53833e6i		−	0.680359i
$622$	420330.	+	5.40410e6i	0.0435627	+	0.560077i
$623$		−	1.48660e7i		−	1.53453i
$624$	−1.91830e7	+	6.15529e6i	−1.97222	+	0.632830i
$625$		0			0
$626$	1.55456e7	−	1.20913e6i	1.58552	−	0.123321i
$627$	−1.73123e7			−1.75868
$628$	−131318.	+	20552.1i	−0.0132869	+	0.00207949i
$629$		−	1.14366e6i		−	0.115258i
$630$		0			0
$631$	−8.89808e6			−0.889658			−0.444829	−	0.895616i	$-0.646736\pi$
$631$	−8.89808e6			−0.889658			−0.444829	+	0.895616i	$0.646736\pi$
$632$	691400.	+	2.91517e6i	0.0688552	+	0.290316i
$633$			1.04501e7i			1.03660i
$634$	810182.	+	1.04164e7i	0.0800497	+	1.02918i
$635$		0			0
$636$	1.13105e6	−	177016.i	0.110876	−	0.0173528i
$637$	2.28040e7			2.22671
$638$	−595475.	−	7.65591e6i	−0.0579177	−	0.744638i
$639$	1.96856e6			0.190720
$640$		0			0
$641$	7.85756e6			0.755340			0.377670	−	0.925940i	$-0.376725\pi$
$641$	7.85756e6			0.755340			0.377670	+	0.925940i	$0.376725\pi$
$642$	553110.	+	7.11123e6i	0.0529632	+	0.680938i
$643$	−1.71100e7			−1.63201			−0.816004	−	0.578046i	$-0.803816\pi$
$643$	−1.71100e7			−1.63201			−0.816004	+	0.578046i	$0.803816\pi$
$644$	1.18587e7	−	1.85596e6i	1.12673	−	0.176341i
$645$		0			0
$646$	691818.	+	8.89458e6i	0.0652245	+	0.838579i
$647$			1.62409e7i			1.52528i	0.646823	+	0.762640i	$0.276097\pi$
$647$			1.62409e7i			1.52528i	−0.646823	+	0.762640i	$0.723903\pi$
$648$	2.85418e6	+	1.20342e7i	0.267020	+	1.12585i
$649$	−2.20561e7			−2.05550
$650$		0			0
$651$		−	1.82109e7i		−	1.68414i
$652$	1.91292e7	−	2.99383e6i	1.76229	−	0.275809i
$653$	−1.51705e7			−1.39225			−0.696123	−	0.717922i	$-0.745093\pi$
$653$	−1.51705e7			−1.39225			−0.696123	+	0.717922i	$0.745093\pi$
$654$	−1.09276e6	+	84994.9i	−0.0999038	+	0.00777049i
$655$		0			0
$656$	2.19667e6	−	704850.i	0.199299	−	0.0639495i
$657$			3.06517e6i			0.277039i
$658$	1.36102e6	+	1.74984e7i	0.122546	+	1.57555i
$659$		−	1.00533e7i		−	0.901768i	−0.892583	−	0.450884i	$-0.851109\pi$
$659$		−	1.00533e7i		−	0.901768i	0.892583	−	0.450884i	$-0.148891\pi$
$660$		0			0
$661$			1.90699e7i			1.69764i	0.528681	+	0.848821i	$0.322687\pi$
$661$			1.90699e7i			1.69764i	−0.528681	+	0.848821i	$0.677313\pi$
$662$	−4.37520e6	+	340302.i	−0.388019	+	0.0301800i
$663$		−	2.04470e7i		−	1.80654i
$664$	−2.01885e6	−	8.51214e6i	−0.177699	−	0.749236i
$665$		0			0
$666$	−22893.3	−	294335.i	−0.00199997	−	0.0257132i
$667$	3.97793e6			0.346212
$668$	−747433.	−	4.77573e6i	−0.0648083	−	0.414094i
$669$		−	1.56161e7i		−	1.34898i
$670$		0			0
$671$	1.54335e7			1.32330
$672$	−1.74715e7	+	7.14332e6i	−1.49247	+	0.610206i
$673$			6.72068e6i			0.571973i	0.958234	+	0.285986i	$0.0923212\pi$
$673$			6.72068e6i			0.571973i	−0.958234	+	0.285986i	$0.907679\pi$
$674$	2.04879e7	−	1.59355e6i	1.73720	−	0.135119i
$675$		0			0
$676$	−3.03975e7	+	4.75740e6i	−2.55842	+	0.400408i
$677$	−5.66127e6			−0.474725			−0.237363	−	0.971421i	$-0.576283\pi$
$677$	−5.66127e6			−0.474725			−0.237363	+	0.971421i	$0.576283\pi$
$678$	−7.01987e6	+	546004.i	−0.586482	+	0.0456164i
$679$	2.53881e7			2.11327
$680$		0			0
$681$	1.64308e7			1.35766
$682$	−2.11002e7	+	1.64117e6i	−1.73711	+	0.135112i
$683$	2.22779e7			1.82735			0.913676	−	0.406444i	$-0.133231\pi$
$683$	2.22779e7			1.82735			0.913676	+	0.406444i	$0.133231\pi$
$684$	356095.	+	2.27528e6i	0.0291022	+	0.185949i
$685$		0			0
$686$	3.17685e6	−	247095.i	0.257743	−	0.0200472i
$687$		−	752151.i		−	0.0608014i
$688$	−2.93317e6	+	941173.i	−0.236247	+	0.0758051i
$689$	2.42352e6			0.194491
$690$		0			0
$691$		−	3.60209e6i		−	0.286985i	−0.989651	−	0.143493i	$-0.954167\pi$
$691$		−	3.60209e6i		−	0.286985i	0.989651	−	0.143493i	$-0.0458333\pi$
$692$	2.24201e7	−	3.50889e6i	1.77981	−	0.278551i
$693$	6.07055e6			0.480170
$694$	−589371.	−	7.57744e6i	−0.0464505	−	0.597205i
$695$		0			0
$696$	−6.08664e6	+	1.44359e6i	−0.476272	+	0.112959i
$697$			2.34142e6i			0.182556i
$698$	2.25050e6	−	175044.i	0.174840	−	0.0135990i
$699$			2.26497e6i			0.175335i
$700$		0			0
$701$		−	1.55464e7i		−	1.19491i	−0.801903	−	0.597454i	$-0.796179\pi$
$701$		−	1.55464e7i		−	1.19491i	0.801903	−	0.597454i	$-0.203821\pi$
$702$	1.68787e6	+	2.17007e7i	0.129270	+	1.66200i
$703$			1.66990e6i			0.127439i
$704$	9.85123e6	+	1.95998e7i	0.749133	+	1.49046i
$705$		0			0
$706$	8.36999e6	−	651016.i	0.631994	−	0.0491564i
$707$	−2.06463e6			−0.155343
$708$	2.77818e6	+	1.77513e7i	0.208295	+	1.33090i
$709$			1.54030e7i			1.15078i	0.817880	+	0.575388i	$0.195149\pi$
$709$			1.54030e7i			1.15078i	−0.817880	+	0.575388i	$0.804851\pi$
$710$		0			0
$711$	−784938.			−0.0582320
$712$	3.24787e6	+	1.36941e7i	0.240103	+	1.01235i
$713$		−	1.09635e7i		−	0.807651i
$714$	−1.48555e6	−	1.90994e7i	−0.109054	−	1.40208i
$715$		0			0
$716$	1.03994e6	+	6.64471e6i	0.0758099	+	0.484388i
$717$	−9.14520e6			−0.664347
$718$	815119.	+	1.04798e7i	0.0590079	+	0.758653i
$719$	−1.24382e7			−0.897297			−0.448648	−	0.893708i	$-0.648094\pi$
$719$	−1.24382e7			−0.897297			−0.448648	+	0.893708i	$0.648094\pi$
$720$		0			0
$721$	−1.97576e7			−1.41546
$722$	76030.2	+	977506.i	0.00542804	+	0.0697873i
$723$	−870975.			−0.0619670
$724$	−2.87634e6	−	1.83784e7i	−0.203936	−	1.30305i
$725$		0			0
$726$	−2.14626e6	−	2.75941e7i	−0.151127	−	1.94301i
$727$		−	8.88087e6i		−	0.623189i	−0.950215	−	0.311594i	$-0.899137\pi$
$727$		−	8.88087e6i		−	0.623189i	0.950215	−	0.311594i	$-0.100863\pi$
$728$	−3.88797e7	+	9.22123e6i	−2.71891	+	0.644853i
$729$	1.05620e7			0.736086
$730$		0			0
$731$		−	3.12645e6i		−	0.216400i
$732$	−1.94400e6	−	1.24212e7i	−0.134097	−	0.856816i
$733$	1.37572e6			0.0945738			0.0472869	−	0.998881i	$-0.484942\pi$
$733$	1.37572e6			0.0945738			0.0472869	+	0.998881i	$0.484942\pi$
$734$	−4.92549e6	+	383103.i	−0.337450	+	0.0262467i
$735$		0			0
$736$	−1.05183e7	+	4.30048e6i	−0.715735	+	0.292633i
$737$			3.67888e7i			2.49487i
$738$	46869.4	+	602591.i	0.00316773	+	0.0407270i
$739$			1.36773e7i			0.921275i	0.887588	+	0.460637i	$0.152379\pi$
$739$			1.36773e7i			0.921275i	−0.887588	+	0.460637i	$0.847621\pi$
$740$		0			0
$741$			2.98554e7i			1.99745i
$742$	2.26379e6	−	176077.i	0.150948	−	0.0117407i
$743$		−	1.16450e7i		−	0.773870i	−0.922107	−	0.386935i	$-0.873534\pi$
$743$		−	1.16450e7i		−	0.773870i	0.922107	−	0.386935i	$-0.126466\pi$
$744$	3.97864e6	+	1.67752e7i	0.263513	+	1.11106i
$745$		0			0
$746$	−2.11860e6	−	2.72384e7i	−0.139380	−	1.79199i
$747$	2.29198e6			0.150283
$748$	−2.19959e7	+	3.44250e6i	−1.43743	+	0.224967i
$749$			1.41470e7i			0.921426i
$750$		0			0
$751$	−1.73741e7			−1.12409			−0.562046	−	0.827106i	$-0.689986\pi$
$751$	−1.73741e7			−1.12409			−0.562046	+	0.827106i	$0.689986\pi$
$752$	−5.07670e6	−	1.58216e7i	−0.327368	−	1.02025i
$753$			9.62519e6i			0.618617i
$754$	−1.32027e7	+	1.02690e6i	−0.845736	+	0.0657812i
$755$		0			0
$756$	3.15326e6	+	2.01478e7i	0.200657	+	1.28210i
$757$	−8.26445e6			−0.524173			−0.262086	−	0.965044i	$-0.584411\pi$
$757$	−8.26445e6			−0.524173			−0.262086	+	0.965044i	$0.584411\pi$
$758$	4.49626e6	−	349718.i	0.284235	−	0.0221078i
$759$	2.23804e7			1.41014
$760$		0			0
$761$	2.02244e7			1.26594			0.632970	−	0.774176i	$-0.281835\pi$
$761$	2.02244e7			1.26594			0.632970	+	0.774176i	$0.281835\pi$
$762$	−1.79023e7	+	1.39244e6i	−1.11692	+	0.0868736i
$763$	−2.17394e6			−0.135187
$764$	−2.62615e7	+	4.11009e6i	−1.62774	+	0.254752i
$765$		0			0
$766$	−1.46098e7	+	1.13635e6i	−0.899647	+	0.0699743i
$767$			3.80361e7i			2.33457i
$768$	1.45335e7	−	1.03973e7i	0.889134	−	0.636088i
$769$	2.51942e7			1.53633			0.768167	−	0.640250i	$-0.221169\pi$
$769$	2.51942e7			1.53633			0.768167	+	0.640250i	$0.221169\pi$
$770$		0			0
$771$		−	1.12236e7i		−	0.679983i
$772$	2.35316e6	+	1.50355e7i	0.142104	+	0.907978i
$773$	−7.04402e6			−0.424006			−0.212003	−	0.977269i	$-0.567999\pi$
$773$	−7.04402e6			−0.424006			−0.212003	+	0.977269i	$0.567999\pi$
$774$	−62583.8	−	804629.i	−0.00375500	−	0.0482773i
$775$		0			0
$776$	−2.33867e7	+	5.54669e6i	−1.39416	+	0.330659i
$777$		−	3.58578e6i		−	0.213075i
$778$	2.04861e7	−	1.59340e6i	1.21342	−	0.0943792i
$779$		−	3.41877e6i		−	0.201849i
$780$		0			0
$781$		−	2.77874e7i		−	1.63012i
$782$	−894342.	−	1.14984e7i	−0.0522982	−	0.672388i
$783$			6.75847e6i			0.393953i
$784$	−1.92598e7	+	6.17995e6i	−1.11908	+	0.359083i
$785$		0			0
$786$	−2.98538e7	+	2.32202e6i	−1.72363	+	0.134063i
$787$	−1.57971e7			−0.909160			−0.454580	−	0.890706i	$-0.650211\pi$
$787$	−1.57971e7			−0.909160			−0.454580	+	0.890706i	$0.650211\pi$
$788$	2.64227e7	−	4.13532e6i	1.51587	−	0.237243i
$789$			2.75997e6i			0.157838i
$790$		0			0
$791$	−1.39653e7			−0.793612
$792$	−5.59200e6	+	1.32627e6i	−0.316777	+	0.0751310i
$793$		−	2.66153e7i		−	1.50296i
$794$	915460.	+	1.17699e7i	0.0515333	+	0.662554i
$795$		0			0
$796$	3.70754e6	−	580253.i	0.207397	−	0.0324590i
$797$	3.47240e7			1.93635			0.968176	−	0.250271i	$-0.0805198\pi$
$797$	3.47240e7			1.93635			0.968176	+	0.250271i	$0.0805198\pi$
$798$	2.16909e6	+	2.78876e7i	0.120579	+	1.55026i
$799$	1.68641e7			0.934537
$800$		0			0
$801$	−3.68727e6			−0.203059
$802$	−1.66725e6	−	2.14355e7i	−0.0915303	−	1.17679i
$803$	4.32667e7			2.36791
$804$	2.96085e7	−	4.63392e6i	1.61539	−	0.252818i
$805$		0			0
$806$	2.83022e6	+	3.63877e7i	0.153456	+	1.97295i
$807$			6.06441e6i			0.327797i
$808$	1.90187e6	−	451071.i	0.102483	−	0.0243062i
$809$	1.85338e7			0.995618			0.497809	−	0.867287i	$-0.334138\pi$
$809$	1.85338e7			0.995618			0.497809	+	0.867287i	$0.334138\pi$
$810$		0			0
$811$		−	2.10118e7i		−	1.12179i	−0.827888	−	0.560894i	$-0.810458\pi$
$811$		−	2.10118e7i		−	1.12179i	0.827888	−	0.560894i	$-0.189542\pi$
$812$	−1.22579e7	+	1.91844e6i	−0.652420	+	0.102108i
$813$	1.44617e7			0.767348
$814$	−4.15472e6	+	323153.i	−0.219776	+	0.0170941i
$815$		0			0
$816$	5.54120e6	+	1.72692e7i	0.291326	+	0.907918i
$817$			4.56502e6i			0.239270i
$818$	1.79782e6	+	2.31142e7i	0.0939426	+	1.20780i
$819$		−	1.04688e7i		−	0.545363i
$820$		0			0
$821$			7.40030e6i			0.383170i	0.981476	+	0.191585i	$0.0613627\pi$
$821$			7.40030e6i			0.383170i	−0.981476	+	0.191585i	$0.938637\pi$
$822$	−1.71739e7	+	1.33578e6i	−0.886521	+	0.0689534i
$823$			6.13247e6i			0.315599i	0.987471	+	0.157800i	$0.0504400\pi$
$823$			6.13247e6i			0.315599i	−0.987471	+	0.157800i	$0.949560\pi$
$824$	1.82001e7	−	4.31657e6i	0.933804	−	0.221473i
$825$		0			0
$826$	2.76345e6	+	3.55291e7i	0.140929	+	1.81190i
$827$	−2.64222e6			−0.134340			−0.0671699	−	0.997742i	$-0.521397\pi$
$827$	−2.64222e6			−0.134340			−0.0671699	+	0.997742i	$0.521397\pi$
$828$	−460339.	−	2.94135e6i	−0.0233347	−	0.149097i
$829$			6.86453e6i			0.346916i	0.984841	+	0.173458i	$0.0554941\pi$
$829$			6.86453e6i			0.346916i	−0.984841	+	0.173458i	$0.944506\pi$
$830$		0			0
$831$	3.06902e7			1.54169
$832$	3.38001e7	−	1.69886e7i	1.69282	−	0.850842i
$833$		−	2.05289e7i		−	1.02507i
$834$	−6.78416e6	+	527670.i	−0.337739	+	0.0262693i
$835$		0			0
$836$	3.21169e7	−	5.02650e6i	1.58934	−	0.248742i
$837$	1.86268e7			0.919022
$838$	−5.21855e6	+	405897.i	−0.256708	+	0.0199667i
$839$	−1.30476e7			−0.639918			−0.319959	−	0.947431i	$-0.603669\pi$
$839$	−1.30476e7			−0.639918			−0.319959	+	0.947431i	$0.603669\pi$
$840$		0			0
$841$	1.63993e7			0.799531
$842$	2.03370e7	−	1.58181e6i	0.988569	−	0.0768907i
$843$	−2.47981e7			−1.20185
$844$	−3.03411e6	−	1.93865e7i	−0.146614	−	0.936791i
$845$		0			0
$846$	4.34018e6	−	337578.i	0.208488	−	0.0162162i
$847$		−	5.48954e7i		−	2.62922i
$848$	−2.04686e6	+	656781.i	−0.0977460	+	0.0313640i
$849$	1.69617e7			0.807608
$850$		0			0
$851$		−	2.15875e6i		−	0.102183i
$852$	−2.23640e7	+	3.50010e6i	−1.05548	+	0.165189i
$853$	1.81475e7			0.853974			0.426987	−	0.904258i	$-0.359575\pi$
$853$	1.81475e7			0.853974			0.426987	+	0.904258i	$0.359575\pi$
$854$	−1.93369e6	−	2.48611e7i	−0.0907283	−	1.16648i
$855$		0			0
$856$	−3.09079e6	−	1.30318e7i	−0.144173	−	0.607882i
$857$		−	3.06550e6i		−	0.142577i	−0.997456	−	0.0712885i	$-0.977289\pi$
$857$		−	3.06550e6i		−	0.142577i	0.997456	−	0.0712885i	$-0.0227111\pi$
$858$	−7.42804e7	+	5.77751e6i	−3.44473	+	0.267931i
$859$			4.43575e6i			0.205109i	0.994727	+	0.102554i	$0.0327016\pi$
$859$			4.43575e6i			0.205109i	−0.994727	+	0.102554i	$0.967298\pi$
$860$		0			0
$861$			7.34116e6i			0.337487i
$862$	−1.70733e6	−	2.19508e7i	−0.0782616	−	1.00620i
$863$			6.42645e6i			0.293727i	0.989157	+	0.146864i	$0.0469178\pi$
$863$			6.42645e6i			0.293727i	−0.989157	+	0.146864i	$0.953082\pi$
$864$	−7.30649e6	−	1.78706e7i	−0.332985	−	0.814431i
$865$		0			0
$866$	−2.41162e7	+	1.87576e6i	−1.09274	+	0.0849927i
$867$	5.78991e6			0.261592
$868$	5.28737e6	+	3.37838e7i	0.238199	+	1.52198i
$869$			1.10799e7i			0.497720i
$870$		0			0
$871$	6.34429e7			2.83359
$872$	2.00256e6	−	474953.i	0.0891854	−	0.0211524i
$873$		−	6.29709e6i		−	0.279643i
$874$	1.30586e6	+	1.67892e7i	0.0578252	+	0.743448i
$875$		0			0
$876$	−5.44987e6	−	3.48220e7i	−0.239953	−	1.53318i
$877$	1.32005e7			0.579551			0.289775	−	0.957095i	$-0.406419\pi$
$877$	1.32005e7			0.579551			0.289775	+	0.957095i	$0.406419\pi$
$878$	1.08039e6	+	1.38904e7i	0.0472984	+	0.608106i
$879$	−1.45205e7			−0.633885
$880$		0			0
$881$	6.44281e6			0.279663			0.139832	−	0.990175i	$-0.455344\pi$
$881$	6.44281e6			0.279663			0.139832	+	0.990175i	$0.455344\pi$
$882$	−410939.	−	5.28337e6i	−0.0177871	−	0.228686i
$883$	−1.74148e6			−0.0751653			−0.0375826	−	0.999294i	$-0.511966\pi$
$883$	−1.74148e6			−0.0751653			−0.0375826	+	0.999294i	$0.511966\pi$
$884$	5.93663e6	+	3.79322e7i	0.255511	+	1.63259i
$885$		0			0
$886$	−1.42451e6	−	1.83147e7i	−0.0609651	−	0.783816i
$887$			2.58814e7i			1.10453i	0.833667	+	0.552267i	$0.186237\pi$
$887$			2.58814e7i			1.10453i	−0.833667	+	0.552267i	$0.813763\pi$
$888$	783408.	+	3.30311e6i	0.0333392	+	0.140569i
$889$	−3.56147e7			−1.51138
$890$		0			0
$891$			4.57390e7i			1.93016i
$892$	4.53400e6	+	2.89701e7i	0.190796	+	1.21909i
$893$	−2.46238e7			−1.03330
$894$	−9.27667e6	+	721537.i	−0.388193	+	0.0301936i
$895$		0			0
$896$	3.03381e7	−	1.83246e7i	1.26246	−	0.762543i
$897$		−	3.85953e7i		−	1.60160i
$898$	−2.83970e6	−	3.65095e7i	−0.117512	−	1.51083i
$899$			1.13326e7i			0.467660i
$900$		0			0
$901$		−	2.18174e6i		−	0.0895345i
$902$	8.50593e6	−	661589.i	0.348101	−	0.0270752i
$903$		−	9.80251e6i		−	0.400054i
$904$	1.28643e7	−	3.05108e6i	0.523560	−	0.124174i
$905$		0			0
$906$	−1.58616e6	−	2.03929e7i	−0.0641987	−	0.825390i
$907$	−2.01080e7			−0.811615			−0.405808	−	0.913958i	$-0.633010\pi$
$907$	−2.01080e7			−0.811615			−0.405808	+	0.913958i	$0.633010\pi$
$908$	−3.04816e7	+	4.77056e6i	−1.22694	+	0.192024i
$909$			512096.i			0.0205562i
$910$		0			0
$911$	−4.10389e7			−1.63833			−0.819163	−	0.573561i	$-0.805562\pi$
$911$	−4.10389e7			−1.63833			−0.819163	+	0.573561i	$0.805562\pi$
$912$	−8.09088e6	−	2.52153e7i	−0.322113	−	1.00387i
$913$		−	3.23526e7i		−	1.28450i
$914$	1.76047e7	−	1.36929e6i	0.697050	−	0.0542164i
$915$		0			0
$916$	218381.	+	1.39535e6i	0.00859956	+	0.0549470i
$917$	−5.93909e7			−2.33237
$918$	1.95357e7	−	1.51948e6i	0.765107	−	0.0595098i
$919$	−1.17509e7			−0.458969			−0.229484	−	0.973312i	$-0.573704\pi$
$919$	−1.17509e7			−0.458969			−0.229484	+	0.973312i	$0.573704\pi$
$920$		0			0
$921$	−1.24438e7			−0.483398
$922$	3.71633e7	−	2.89055e6i	1.43975	−	0.111983i
$923$	−4.79198e7			−1.85144
$924$	−6.89649e7	+	1.07934e7i	−2.65734	+	0.415891i
$925$		0			0
$926$	1.41908e7	−	1.10376e6i	0.543852	−	0.0423006i
$927$			4.90056e6i			0.187304i
$928$	1.08725e7	−	4.44527e6i	0.414437	−	0.169445i
$929$	−1.21230e7			−0.460860			−0.230430	−	0.973089i	$-0.574013\pi$
$929$	−1.21230e7			−0.460860			−0.230430	+	0.973089i	$0.574013\pi$
$930$		0			0
$931$			2.99749e7i			1.13340i
$932$	−657615.	−	4.20184e6i	−0.0247989	−	0.158453i
$933$	1.63296e7			0.614146
$934$	123047.	+	1.58199e6i	0.00461532	+	0.0593384i
$935$		0			0
$936$	2.28717e6	+	9.64347e6i	0.0853315	+	0.359786i
$937$		−	2.32455e7i		−	0.864947i	−0.901647	−	0.432473i	$-0.857641\pi$
$937$		−	2.32455e7i		−	0.864947i	0.901647	−	0.432473i	$-0.142359\pi$
$938$	5.92614e7	−	4.60934e6i	2.19920	−	0.171053i
$939$		−	4.69742e7i		−	1.73858i
$940$		0			0
$941$		−	3.23629e7i		−	1.19144i	−0.803191	−	0.595721i	$-0.796866\pi$
$941$		−	3.23629e7i		−	1.19144i	0.803191	−	0.595721i	$-0.203134\pi$
$942$	31051.1	+	399219.i	0.00114012	+	0.0146583i
$943$			4.41959e6i			0.161846i
$944$	−1.03079e7	−	3.21245e7i	−0.376477	−	1.17329i
$945$		0			0
$946$	−1.13578e7	+	883408.i	−0.412636	+	0.0320947i
$947$	4.26595e7			1.54576			0.772878	−	0.634554i	$-0.218816\pi$
$947$	4.26595e7			1.54576			0.772878	+	0.634554i	$0.218816\pi$
$948$	8.91734e6	−	1.39562e6i	0.322266	−	0.0504366i
$949$		−	7.46140e7i		−	2.68940i
$950$		0			0
$951$	3.14752e7			1.12854
$952$	8.30126e6	+	3.50008e7i	0.296860	+	1.25166i
$953$		−	5.97182e6i		−	0.212997i	−0.994313	−	0.106499i	$-0.966036\pi$
$953$		−	5.97182e6i		−	0.212997i	0.994313	−	0.106499i	$-0.0339640\pi$
$954$	−43673.0	−	561496.i	−0.00155361	−	0.0199745i
$955$		0			0
$956$	1.69657e7	−	2.65523e6i	0.600380	−	0.0939633i
$957$	−2.31339e7			−0.816524
$958$	−3.09161e6	−	3.97482e7i	−0.108836	−	1.39928i
$959$	−3.41656e7			−1.19962
$960$		0			0
$961$	2.60429e6			0.0909665
$962$	557281.	+	7.16487e6i	0.0194150	+	0.249615i
$963$	3.50893e6			0.121930
$964$	1.61579e6	−	252881.i	0.0560004	−	0.00876442i
$965$		0			0
$966$	−2.80408e6	−	3.60515e7i	−0.0966823	−	1.24303i
$967$			3.72285e7i			1.28029i	0.768252	+	0.640147i	$0.221127\pi$
$967$			3.72285e7i			1.28029i	−0.768252	+	0.640147i	$0.778873\pi$
$968$	1.19933e7	+	5.05679e7i	0.411388	+	1.73455i
$969$	2.68768e7			0.919535
$970$		0			0
$971$			2.50967e7i			0.854218i	0.904200	+	0.427109i	$0.140468\pi$
$971$			2.50967e7i			0.854218i	−0.904200	+	0.427109i	$0.859532\pi$
$972$	1.12065e7	−	1.75388e6i	0.380455	−	0.0595436i
$973$	−1.34964e7			−0.457019
$974$	2.81234e7	−	2.18743e6i	0.949883	−	0.0738817i
$975$		0			0
$976$	7.21282e6	+	2.24788e7i	0.242371	+	0.755350i
$977$		−	2.17043e7i		−	0.727459i	−0.931505	−	0.363730i	$-0.881503\pi$
$977$		−	2.17043e7i		−	0.727459i	0.931505	−	0.363730i	$-0.118497\pi$
$978$	−4.52324e6	−	5.81545e7i	−0.151218	−	1.94418i
$979$			5.20479e7i			1.73559i
$980$		0			0
$981$			539209.i			0.0178889i
$982$	2.97969e7	−	2.31759e6i	0.986034	−	0.0766935i
$983$		−	4.20831e7i		−	1.38907i	−0.719459	−	0.694535i	$-0.755610\pi$
$983$		−	4.20831e7i		−	1.38907i	0.719459	−	0.694535i	$-0.244390\pi$
$984$	−1.60387e6	−	6.76244e6i	−0.0528058	−	0.222646i
$985$		0			0
$986$	924454.	+	1.18855e7i	0.0302826	+	0.389338i
$987$	5.28749e7			1.72765
$988$	−8.66826e6	−	5.53860e7i	−0.282514	−	1.80513i
$989$		−	5.90140e6i		−	0.191851i
$990$		0			0
$991$	4.02111e7			1.30065			0.650327	−	0.759654i	$-0.274632\pi$
$991$	4.02111e7			1.30065			0.650327	+	0.759654i	$0.274632\pi$
$992$	−1.22515e7	−	2.99653e7i	−0.395285	−	0.966807i
$993$			1.32206e7i			0.425478i
$994$	−4.47614e7	+	3.48153e6i	−1.43694	+	0.111765i
$995$		0			0
$996$	−2.60382e7	+	4.07514e6i	−0.831691	+	0.130165i
$997$	−2.43059e7			−0.774417			−0.387208	−	0.921992i	$-0.626561\pi$
$997$	−2.43059e7			−0.774417			−0.387208	+	0.921992i	$0.626561\pi$
$998$	−1.71502e7	+	1.33394e6i	−0.545057	+	0.0423944i
$999$	3.66769e6			0.116273

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.f.d.149.22		40
4.3	odd	2		800.6.f.d.49.12		40
5.2	odd	4		200.6.d.c.101.2	yes	20
5.3	odd	4		200.6.d.d.101.19	yes	20
5.4	even	2	inner	200.6.f.d.149.19		40
8.3	odd	2		800.6.f.d.49.30		40
8.5	even	2	inner	200.6.f.d.149.20		40
20.3	even	4		800.6.d.b.401.6		20
20.7	even	4		800.6.d.d.401.15		20
20.19	odd	2		800.6.f.d.49.29		40
40.3	even	4		800.6.d.b.401.15		20
40.13	odd	4		200.6.d.d.101.20	yes	20
40.19	odd	2		800.6.f.d.49.11		40
40.27	even	4		800.6.d.d.401.6		20
40.29	even	2	inner	200.6.f.d.149.21		40
40.37	odd	4		200.6.d.c.101.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.6.d.c.101.1	✓	20	40.37	odd	4
200.6.d.c.101.2	yes	20	5.2	odd	4
200.6.d.d.101.19	yes	20	5.3	odd	4
200.6.d.d.101.20	yes	20	40.13	odd	4
200.6.f.d.149.19		40	5.4	even	2	inner
200.6.f.d.149.20		40	8.5	even	2	inner
200.6.f.d.149.21		40	40.29	even	2	inner
200.6.f.d.149.22		40	1.1	even	1	trivial
800.6.d.b.401.6		20	20.3	even	4
800.6.d.b.401.15		20	40.3	even	4
800.6.d.d.401.6		20	40.27	even	4
800.6.d.d.401.15		20	20.7	even	4
800.6.f.d.49.11		40	40.19	odd	2
800.6.f.d.49.12		40	4.3	odd	2
800.6.f.d.49.29		40	20.19	odd	2
800.6.f.d.49.30		40	8.3	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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.438664 + 5.63982i) q^{2} +17.0419 q^{3} +(-31.6151 + 4.94797i) q^{4} +(7.47566 + 96.1131i) q^{6} +191.207i q^{7} +(-41.7741 - 176.133i) q^{8} +47.4256 q^{9} +O(q^{10})\)	\(q+(0.438664 + 5.63982i) q^{2} +17.0419 q^{3} +(-31.6151 + 4.94797i) q^{4} +(7.47566 + 96.1131i) q^{6} +191.207i q^{7} +(-41.7741 - 176.133i) q^{8} +47.4256 q^{9} -669.441i q^{11} +(-538.782 + 84.3227i) q^{12} -1154.46 q^{13} +(-1078.37 + 83.8754i) q^{14} +(975.035 - 312.862i) q^{16} +1039.28i q^{17} +(20.8039 + 267.472i) q^{18} -1517.49i q^{19} +3258.52i q^{21} +(3775.53 - 293.660i) q^{22} +1961.72i q^{23} +(-711.909 - 3001.64i) q^{24} +(-506.420 - 6510.95i) q^{26} -3332.95 q^{27} +(-946.085 - 6045.03i) q^{28} -2027.77i q^{29} -5588.69 q^{31} +(2192.20 + 5361.78i) q^{32} -11408.5i q^{33} +(-5861.37 + 455.896i) q^{34} +(-1499.37 + 234.661i) q^{36} -1100.43 q^{37} +(8558.37 - 665.668i) q^{38} -19674.2 q^{39} +2252.91 q^{41} +(-18377.5 + 1429.39i) q^{42} -3008.27 q^{43} +(3312.37 + 21164.5i) q^{44} +(-11063.8 + 860.537i) q^{46} -16226.7i q^{47} +(16616.4 - 5331.75i) q^{48} -19753.0 q^{49} +17711.3i q^{51} +(36498.4 - 5712.24i) q^{52} -2099.27 q^{53} +(-1462.05 - 18797.3i) q^{54} +(33677.8 - 7987.48i) q^{56} -25860.9i q^{57} +(11436.3 - 889.510i) q^{58} -32947.1i q^{59} +23054.3i q^{61} +(-2451.56 - 31519.2i) q^{62} +9068.10i q^{63} +(-29277.9 + 14715.6i) q^{64} +(64342.1 - 5004.51i) q^{66} -54954.6 q^{67} +(-5142.35 - 32857.1i) q^{68} +33431.4i q^{69} +41508.4 q^{71} +(-1981.16 - 8353.23i) q^{72} +64631.1i q^{73} +(-482.720 - 6206.25i) q^{74} +(7508.50 + 47975.7i) q^{76} +128002. q^{77} +(-8630.35 - 110959. i) q^{78} -16550.9 q^{79} -68324.2 q^{81} +(988.272 + 12706.0i) q^{82} +48327.8 q^{83} +(-16123.1 - 103019. i) q^{84} +(-1319.62 - 16966.1i) q^{86} -34557.0i q^{87} +(-117911. + 27965.3i) q^{88} -77748.4 q^{89} -220740. i q^{91} +(-9706.55 - 62020.2i) q^{92} -95241.8 q^{93} +(91515.4 - 7118.05i) q^{94} +(37359.1 + 91374.8i) q^{96} -132778. i q^{97} +(-8664.91 - 111403. i) q^{98} -31748.7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9}+O(q^{10}) \) 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9	\( 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9} + 848 q^{14} - 110 q^{16} - 18918 q^{24} + 18344 q^{26} + 14320 q^{31} + 19182 q^{34} + 29656 q^{36} - 44904 q^{39} - 11608 q^{41} + 23186 q^{44} - 75224 q^{46} - 125304 q^{49} - 177894 q^{54} - 73816 q^{56} - 230354 q^{64} + 262878 q^{66} - 15448 q^{71} - 4224 q^{74} + 111902 q^{76} + 15560 q^{79} + 193968 q^{81} + 195112 q^{84} - 131972 q^{86} + 6320 q^{89} + 117080 q^{94} + 115582 q^{96}+O(q^{100}) \) 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9 + 848 * q^14 - 110 * q^16 - 18918 * q^24 + 18344 * q^26 + 14320 * q^31 + 19182 * q^34 + 29656 * q^36 - 44904 * q^39 - 11608 * q^41 + 23186 * q^44 - 75224 * q^46 - 125304 * q^49 - 177894 * q^54 - 73816 * q^56 - 230354 * q^64 + 262878 * q^66 - 15448 * q^71 - 4224 * q^74 + 111902 * q^76 + 15560 * q^79 + 193968 * q^81 + 195112 * q^84 - 131972 * q^86 + 6320 * q^89 + 117080 * q^94 + 115582 * q^96

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