LMFDB - Embedded newform 200.6.f.d.149.10

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			149.10
Character	$\chi$	$=$	200.149
Dual form			200.6.f.d.149.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.83252 + 2.94053i) q^{2} -0.457817 q^{3} +(14.7065 - 28.4204i) q^{4} +(2.21241 - 1.34622i) q^{6} -195.837i q^{7} +(12.5013 + 180.587i) q^{8} -242.790 q^{9} -358.513i q^{11} +(-6.73290 + 13.0113i) q^{12} -951.826 q^{13} +(575.865 + 946.387i) q^{14} +(-591.435 - 835.931i) q^{16} +2101.46i q^{17} +(1173.29 - 713.933i) q^{18} -2882.77i q^{19} +89.6574i q^{21} +(1054.22 + 1732.52i) q^{22} +1537.16i q^{23} +(-5.72328 - 82.6758i) q^{24} +(4599.72 - 2798.88i) q^{26} +222.403 q^{27} +(-5565.76 - 2880.09i) q^{28} +3875.11i q^{29} +5182.92 q^{31} +(5316.20 + 2300.52i) q^{32} +164.133i q^{33} +(-6179.41 - 10155.4i) q^{34} +(-3570.61 + 6900.19i) q^{36} +9494.97 q^{37} +(8476.87 + 13931.0i) q^{38} +435.762 q^{39} +3802.93 q^{41} +(-263.641 - 433.272i) q^{42} +4330.63 q^{43} +(-10189.1 - 5272.49i) q^{44} +(-4520.08 - 7428.38i) q^{46} +12506.7i q^{47} +(270.769 + 382.703i) q^{48} -21545.1 q^{49} -962.084i q^{51} +(-13998.1 + 27051.3i) q^{52} -25075.5 q^{53} +(-1074.77 + 653.983i) q^{54} +(35365.6 - 2448.21i) q^{56} +1319.78i q^{57} +(-11394.9 - 18726.5i) q^{58} +18453.8i q^{59} +17488.7i q^{61} +(-25046.6 + 15240.5i) q^{62} +47547.3i q^{63} +(-32455.4 + 4515.13i) q^{64} +(-482.639 - 793.177i) q^{66} +7490.73 q^{67} +(59724.3 + 30905.2i) q^{68} -703.739i q^{69} +1056.69 q^{71} +(-3035.19 - 43844.8i) q^{72} +55286.5i q^{73} +(-45884.7 + 27920.3i) q^{74} +(-81929.3 - 42395.6i) q^{76} -70210.1 q^{77} +(-2105.83 + 1281.37i) q^{78} -89387.0 q^{79} +58896.2 q^{81} +(-18377.8 + 11182.6i) q^{82} -103847. q^{83} +(2548.10 + 1318.55i) q^{84} +(-20927.8 + 12734.3i) q^{86} -1774.09i q^{87} +(64742.8 - 4481.86i) q^{88} +38137.1 q^{89} +186403. i q^{91} +(43686.8 + 22606.4i) q^{92} -2372.83 q^{93} +(-36776.3 - 60438.8i) q^{94} +(-2433.85 - 1053.22i) q^{96} -22739.9i q^{97} +(104117. - 63354.2i) q^{98} +87043.5i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

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 $

$2$	−4.83252	+	2.94053i	−0.854277	+	0.519817i
$2$	−4.83252	+	2.94053i	−0.854277	+	0.519817i
$3$	−0.457817			−0.0293689			−0.0146845	−	0.999892i	$-0.504674\pi$
$3$	−0.457817			−0.0293689			−0.0146845	+	0.999892i	$0.504674\pi$
$4$	14.7065	−	28.4204i	0.459580	−	0.888137i
$5$		0			0
$5$		0			0
$6$	2.21241	−	1.34622i	0.0250892	−	0.0152665i
$7$		−	195.837i		−	1.51060i	−0.655379	−	0.755300i	$-0.727491\pi$
$7$		−	195.837i		−	1.51060i	0.655379	−	0.755300i	$-0.272509\pi$
$8$	12.5013	+	180.587i	0.0690604	+	0.997612i
$9$	−242.790			−0.999137
$10$		0			0
$11$		−	358.513i		−	0.893353i	−0.894696	−	0.446676i	$-0.852608\pi$
$11$		−	358.513i		−	0.893353i	0.894696	−	0.446676i	$-0.147392\pi$
$12$	−6.73290	+	13.0113i	−0.0134974	+	0.0260836i
$13$	−951.826			−1.56207			−0.781033	−	0.624490i	$-0.785307\pi$
$13$	−951.826			−1.56207			−0.781033	+	0.624490i	$0.785307\pi$
$14$	575.865	+	946.387i	0.785237	+	1.29047i
$15$		0			0
$16$	−591.435	−	835.931i	−0.577573	−	0.816339i
$17$			2101.46i			1.76360i	0.471628	+	0.881798i	$0.343667\pi$
$17$			2101.46i			1.76360i	−0.471628	+	0.881798i	$0.656333\pi$
$18$	1173.29	−	713.933i	0.853541	−	0.519369i
$19$		−	2882.77i		−	1.83200i	−0.401178	−	0.916000i	$-0.631399\pi$
$19$		−	2882.77i		−	1.83200i	0.401178	−	0.916000i	$-0.368601\pi$
$20$		0			0
$21$			89.6574i			0.0443648i
$22$	1054.22	+	1732.52i	0.464380	+	0.763171i
$23$			1537.16i			0.605899i	0.953007	+	0.302950i	$0.0979714\pi$
$23$			1537.16i			0.605899i	−0.953007	+	0.302950i	$0.902029\pi$
$24$	−5.72328	−	82.6758i	−0.00202823	−	0.0292988i
$25$		0			0
$26$	4599.72	−	2798.88i	1.33444	−	0.811989i
$27$	222.403			0.0587126
$28$	−5565.76	−	2880.09i	−1.34162	−	0.694241i
$29$			3875.11i			0.855636i	0.903865	+	0.427818i	$0.140718\pi$
$29$			3875.11i			0.855636i	−0.903865	+	0.427818i	$0.859282\pi$
$30$		0			0
$31$	5182.92			0.968658			0.484329	−	0.874886i	$-0.339064\pi$
$31$	5182.92			0.968658			0.484329	+	0.874886i	$0.339064\pi$
$32$	5316.20	+	2300.52i	0.917755	+	0.397147i
$33$			164.133i			0.0262368i
$34$	−6179.41	−	10155.4i	−0.916748	−	1.50660i
$35$		0			0
$36$	−3570.61	+	6900.19i	−0.459183	+	0.887371i
$37$	9494.97			1.14022			0.570111	−	0.821568i	$-0.306900\pi$
$37$	9494.97			1.14022			0.570111	+	0.821568i	$0.306900\pi$
$38$	8476.87	+	13931.0i	0.952306	+	1.56504i
$39$	435.762			0.0458762
$40$		0			0
$41$	3802.93			0.353312			0.176656	−	0.984273i	$-0.443472\pi$
$41$	3802.93			0.353312			0.176656	+	0.984273i	$0.443472\pi$
$42$	−263.641	−	433.272i	−0.0230616	−	0.0378998i
$43$	4330.63			0.357174			0.178587	−	0.983924i	$-0.442847\pi$
$43$	4330.63			0.357174			0.178587	+	0.983924i	$0.442847\pi$
$44$	−10189.1	−	5272.49i	−0.793419	−	0.410567i
$45$		0			0
$46$	−4520.08	−	7428.38i	−0.314957	−	0.517606i
$47$			12506.7i			0.825842i	0.910767	+	0.412921i	$0.135492\pi$
$47$			12506.7i			0.825842i	−0.910767	+	0.412921i	$0.864508\pi$
$48$	270.769	+	382.703i	0.0169627	+	0.0239750i
$49$	−21545.1			−1.28191
$50$		0			0
$51$		−	962.084i		−	0.0517949i
$52$	−13998.1	+	27051.3i	−0.717894	+	1.38733i
$53$	−25075.5			−1.22620			−0.613099	−	0.790006i	$-0.710077\pi$
$53$	−25075.5			−1.22620			−0.613099	+	0.790006i	$0.710077\pi$
$54$	−1074.77	+	653.983i	−0.0501568	+	0.0305198i
$55$		0			0
$56$	35365.6	−	2448.21i	1.50699	−	0.104323i
$57$			1319.78i			0.0538039i
$58$	−11394.9	−	18726.5i	−0.444774	−	0.730950i
$59$			18453.8i			0.690171i	0.938571	+	0.345085i	$0.112150\pi$
$59$			18453.8i			0.690171i	−0.938571	+	0.345085i	$0.887850\pi$
$60$		0			0
$61$			17488.7i			0.601774i	0.953660	+	0.300887i	$0.0972827\pi$
$61$			17488.7i			0.601774i	−0.953660	+	0.300887i	$0.902717\pi$
$62$	−25046.6	+	15240.5i	−0.827502	+	0.503525i
$63$			47547.3i			1.50930i
$64$	−32455.4	+	4515.13i	−0.990461	+	0.137791i
$65$		0			0
$66$	−482.639	−	793.177i	−0.0136384	−	0.0224135i
$67$	7490.73			0.203862			0.101931	−	0.994791i	$-0.467498\pi$
$67$	7490.73			0.203862			0.101931	+	0.994791i	$0.467498\pi$
$68$	59724.3	+	30905.2i	1.56631	+	0.810513i
$69$		−	703.739i		−	0.0177946i
$70$		0			0
$71$	1056.69			0.0248773			0.0124387	−	0.999923i	$-0.496041\pi$
$71$	1056.69			0.0248773			0.0124387	+	0.999923i	$0.496041\pi$
$72$	−3035.19	−	43844.8i	−0.0690008	−	0.996752i
$73$			55286.5i			1.21426i	0.794602	+	0.607130i	$0.207679\pi$
$73$			55286.5i			1.21426i	−0.794602	+	0.607130i	$0.792321\pi$
$74$	−45884.7	+	27920.3i	−0.974066	+	0.592707i
$75$		0			0
$76$	−81929.3	−	42395.6i	−1.62707	−	0.841950i
$77$	−70210.1			−1.34950
$78$	−2105.83	+	1281.37i	−0.0391910	+	0.0238473i
$79$	−89387.0			−1.61141			−0.805706	−	0.592316i	$-0.798214\pi$
$79$	−89387.0			−1.61141			−0.805706	+	0.592316i	$0.798214\pi$
$80$		0			0
$81$	58896.2			0.997413
$82$	−18377.8	+	11182.6i	−0.301827	+	0.183658i
$83$	−103847.			−1.65462			−0.827310	−	0.561746i	$-0.810130\pi$
$83$	−103847.			−1.65462			−0.827310	+	0.561746i	$0.810130\pi$
$84$	2548.10	+	1318.55i	0.0394020	+	0.0203891i
$85$		0			0
$86$	−20927.8	+	12734.3i	−0.305125	+	0.185665i
$87$		−	1774.09i		−	0.0251291i
$88$	64742.8	−	4481.86i	0.891220	−	0.0616953i
$89$	38137.1			0.510355			0.255178	−	0.966894i	$-0.417866\pi$
$89$	38137.1			0.510355			0.255178	+	0.966894i	$0.417866\pi$
$90$		0			0
$91$			186403.i			2.35966i
$92$	43686.8	+	22606.4i	0.538121	+	0.278459i
$93$	−2372.83			−0.0284485
$94$	−36776.3	−	60438.8i	−0.429287	−	0.705498i
$95$		0			0
$96$	−2433.85	−	1053.22i	−0.0269535	−	0.0116638i
$97$		−	22739.9i		−	0.245391i	−0.992444	−	0.122696i	$-0.960846\pi$
$97$		−	22739.9i		−	0.245391i	0.992444	−	0.122696i	$-0.0391539\pi$
$98$	104117.	−	63354.2i	1.09511	−	0.666362i
$99$			87043.5i			0.892582i
$100$		0			0
$101$		−	52711.9i		−	0.514168i	−0.966389	−	0.257084i	$-0.917238\pi$
$101$		−	52711.9i		−	0.514168i	0.966389	−	0.257084i	$-0.0827618\pi$
$102$	2829.04	+	4649.29i	0.0269239	+	0.0442473i
$103$		−	38301.0i		−	0.355727i	−0.984055	−	0.177863i	$-0.943081\pi$
$103$		−	38301.0i		−	0.355727i	0.984055	−	0.177863i	$-0.0569185\pi$
$104$	−11899.0	−	171888.i	−0.107877	−	1.55834i
$105$		0			0
$106$	121178.	−	73735.4i	1.04751	−	0.637399i
$107$	151431.			1.27866			0.639329	−	0.768933i	$-0.279212\pi$
$107$	151431.			1.27866			0.639329	+	0.768933i	$0.279212\pi$
$108$	3270.78	−	6320.77i	0.0269831	−	0.0521448i
$109$			146420.i			1.18041i	0.807253	+	0.590206i	$0.200953\pi$
$109$			146420.i			1.18041i	−0.807253	+	0.590206i	$0.799047\pi$
$110$		0			0
$111$	−4346.96			−0.0334871
$112$	−163706.	+	115825.i	−1.23316	+	0.872482i
$113$			59368.9i			0.437384i	0.975794	+	0.218692i	$0.0701789\pi$
$113$			59368.9i			0.437384i	−0.975794	+	0.218692i	$0.929821\pi$
$114$	−3880.85	−	6377.86i	−0.0279682	−	0.0459635i
$115$		0			0
$116$	110132.	+	56989.5i	0.759921	+	0.393233i
$117$	231094.			1.56072
$118$	−54264.1	−	89178.6i	−0.358763	−	0.589597i
$119$	411544.			2.66409
$120$		0			0
$121$	32519.6			0.201921
$122$	−51426.1	−	84514.6i	−0.312812	−	0.514082i
$123$	−1741.05			−0.0103764
$124$	76222.9	−	147300.i	0.445175	−	0.860300i
$125$		0			0
$126$	−139814.	−	229774.i	−0.784559	−	1.28936i
$127$		−	13242.9i		−	0.0728577i	−0.999336	−	0.0364288i	$-0.988402\pi$
$127$		−	13242.9i		−	0.0728577i	0.999336	−	0.0364288i	$-0.0115982\pi$
$128$	143565.	−	117256.i	0.774503	−	0.632571i
$129$	−1982.63			−0.0104898
$130$		0			0
$131$		−	29434.9i		−	0.149860i	−0.997189	−	0.0749298i	$-0.976127\pi$
$131$		−	29434.9i		−	0.149860i	0.997189	−	0.0749298i	$-0.0238733\pi$
$132$	4664.72	+	2413.83i	0.0233019	+	0.0120579i
$133$	−564553.			−2.76742
$134$	−36199.1	+	22026.7i	−0.174155	+	0.105971i
$135$		0			0
$136$	−379497.	+	26270.9i	−1.75938	+	0.121795i
$137$		−	226821.i		−	1.03248i	−0.856443	−	0.516241i	$-0.827331\pi$
$137$		−	226821.i		−	1.03248i	0.856443	−	0.516241i	$-0.172669\pi$
$138$	2069.37	+	3400.84i	0.00924996	+	0.0152016i
$139$		−	206068.i		−	0.904637i	−0.891856	−	0.452319i	$-0.850597\pi$
$139$		−	206068.i		−	0.904637i	0.891856	−	0.452319i	$-0.149403\pi$
$140$		0			0
$141$		−	5725.76i		−	0.0242541i
$142$	−5106.50	+	3107.24i	−0.0212521	+	0.0129317i
$143$			341242.i			1.39548i
$144$	143595.	+	202956.i	0.577075	+	0.815635i
$145$		0			0
$146$	−162572.	−	267173.i	−0.631194	−	1.03732i
$147$	9863.72			0.0376485
$148$	139638.	−	269851.i	0.524023	−	1.01267i
$149$			276062.i			1.01869i	0.860563	+	0.509344i	$0.170112\pi$
$149$			276062.i			1.01869i	−0.860563	+	0.509344i	$0.829888\pi$
$150$		0			0
$151$	−88898.4			−0.317287			−0.158643	−	0.987336i	$-0.550712\pi$
$151$	−88898.4			−0.317287			−0.158643	+	0.987336i	$0.550712\pi$
$152$	520591.	−	36038.2i	1.82763	−	0.126519i
$153$		−	510215.i		−	1.76207i
$154$	339292.	−	206455.i	1.15285	−	0.701493i
$155$		0			0
$156$	6408.55	−	12384.5i	0.0210838	−	0.0407444i
$157$	−273937.			−0.886954			−0.443477	−	0.896286i	$-0.646255\pi$
$157$	−273937.			−0.886954			−0.443477	+	0.896286i	$0.646255\pi$
$158$	431965.	−	262845.i	1.37659	−	0.837640i
$159$	11480.0			0.0360122
$160$		0			0
$161$	301034.			0.915272
$162$	−284617.	+	173186.i	−0.852067	+	0.518473i
$163$	22520.3			0.0663902			0.0331951	−	0.999449i	$-0.489432\pi$
$163$	22520.3			0.0663902			0.0331951	+	0.999449i	$0.489432\pi$
$164$	55928.0	−	108081.i	0.162375	−	0.313790i
$165$		0			0
$166$	501842.	−	305365.i	1.41350	−	0.860100i
$167$			4216.06i			0.0116981i	0.999983	+	0.00584906i	$0.00186182\pi$
$167$			4216.06i			0.0116981i	−0.999983	+	0.00584906i	$0.998138\pi$
$168$	−16191.0	+	1120.83i	−0.0442588	+	0.00306385i
$169$	534680.			1.44005
$170$		0			0
$171$			699908.i			1.83042i
$172$	63688.6	−	123078.i	0.164150	−	0.317219i
$173$	−240365.			−0.610599			−0.305299	−	0.952256i	$-0.598757\pi$
$173$	−240365.			−0.610599			−0.305299	+	0.952256i	$0.598757\pi$
$174$	5216.76	+	8573.32i	0.0130626	+	0.0214672i
$175$		0			0
$176$	−299692.	+	212037.i	−0.729279	+	0.515976i
$177$		−	8448.47i		−	0.0202696i
$178$	−184298.	+	112143.i	−0.435985	+	0.265292i
$179$			245501.i			0.572691i	0.958126	+	0.286346i	$0.0924406\pi$
$179$			245501.i			0.572691i	−0.958126	+	0.286346i	$0.907559\pi$
$180$		0			0
$181$			16588.7i			0.0376370i	0.999823	+	0.0188185i	$0.00599048\pi$
$181$			16588.7i			0.0376370i	−0.999823	+	0.0188185i	$0.994010\pi$
$182$	−548123.	−	900796.i	−1.22659	−	2.01580i
$183$		−	8006.62i		−	0.0176735i
$184$	−277592.	+	19216.5i	−0.604453	+	0.0418436i
$185$		0			0
$186$	11466.7	−	6977.37i	0.0243029	−	0.0147880i
$187$	753401.			1.57551
$188$	355444.	+	183930.i	0.733461	+	0.379540i
$189$		−	43554.7i		−	0.0886912i
$190$		0			0
$191$	−555884.			−1.10256			−0.551278	−	0.834322i	$-0.685860\pi$
$191$	−555884.			−1.10256			−0.551278	+	0.834322i	$0.685860\pi$
$192$	14858.6	−	2067.10i	0.0290888	−	0.00404678i
$193$			397154.i			0.767477i	0.923442	+	0.383738i	$0.125364\pi$
$193$			397154.i			0.767477i	−0.923442	+	0.383738i	$0.874636\pi$
$194$	66867.3	+	109891.i	0.127559	+	0.209632i
$195$		0			0
$196$	−316855.	+	612321.i	−0.589142	+	1.13852i
$197$	−722243.			−1.32592			−0.662961	−	0.748654i	$-0.730700\pi$
$197$	−722243.			−1.32592			−0.662961	+	0.748654i	$0.730700\pi$
$198$	−255954.	−	420640.i	−0.463980	−	0.762513i
$199$	129890.			0.232511			0.116256	−	0.993219i	$-0.462911\pi$
$199$	129890.			0.232511			0.116256	+	0.993219i	$0.462911\pi$
$200$		0			0
$201$	−3429.38			−0.00598722
$202$	155001.	+	254732.i	0.267274	+	0.439242i
$203$	758890.			1.29252
$204$	−27342.8	−	14148.9i	−0.0460010	−	0.0238039i
$205$		0			0
$206$	112625.	+	185090.i	0.184913	+	0.303889i
$207$		−	373209.i		−	0.605377i
$208$	562943.	+	795661.i	0.902207	+	1.27518i
$209$	−1.03351e6			−1.63662
$210$		0			0
$211$			608872.i			0.941499i	0.882267	+	0.470749i	$0.156016\pi$
$211$			608872.i			0.941499i	−0.882267	+	0.470749i	$0.843984\pi$
$212$	−368775.	+	712656.i	−0.563536	+	1.08903i
$213$	−483.772			−0.000730620
$214$	−731792.	+	445287.i	−1.09233	+	0.664669i
$215$		0			0
$216$	2780.32	+	40163.1i	0.00405471	+	0.0585724i
$217$		−	1.01501e6i		−	1.46325i
$218$	−430552.	−	707577.i	−0.613598	−	1.00840i
$219$		−	25311.1i		−	0.0356615i
$220$		0			0
$221$		−	2.00023e6i		−	2.75485i
$222$	21006.8	−	12782.4i	0.0286073	−	0.0174072i
$223$		−	22540.8i		−	0.0303534i	−0.999885	−	0.0151767i	$-0.995169\pi$
$223$		−	22540.8i		−	0.0303534i	0.999885	−	0.0151767i	$-0.00483108\pi$
$224$	450528.	−	1.04111e6i	0.599931	−	1.38636i
$225$		0			0
$226$	−174576.	−	286901.i	−0.227360	−	0.373647i
$227$	−150889.			−0.194354			−0.0971770	−	0.995267i	$-0.530981\pi$
$227$	−150889.			−0.194354			−0.0971770	+	0.995267i	$0.530981\pi$
$228$	37508.6	+	19409.4i	0.0477852	+	0.0247272i
$229$			724516.i			0.912976i	0.889730	+	0.456488i	$0.150893\pi$
$229$			724516.i			0.912976i	−0.889730	+	0.456488i	$0.849107\pi$
$230$		0			0
$231$	32143.3			0.0396334
$232$	−699795.	+	48443.7i	−0.853593	+	0.0590905i
$233$		−	336561.i		−	0.406138i	−0.979164	−	0.203069i	$-0.934908\pi$
$233$		−	336561.i		−	0.406138i	0.979164	−	0.203069i	$-0.0650916\pi$
$234$	−1.11677e6	+	679540.i	−1.33329	+	0.811289i
$235$		0			0
$236$	524465.	+	271392.i	0.612966	+	0.317188i
$237$	40922.8			0.0473255
$238$	−1.98879e6	+	1.21016e6i	−2.27587	+	1.38484i
$239$	−330500.			−0.374262			−0.187131	−	0.982335i	$-0.559919\pi$
$239$	−330500.			−0.374262			−0.187131	+	0.982335i	$0.559919\pi$
$240$		0			0
$241$	900033.			0.998196			0.499098	−	0.866546i	$-0.333665\pi$
$241$	900033.			0.998196			0.499098	+	0.866546i	$0.333665\pi$
$242$	−157152.	+	95624.9i	−0.172497	+	0.104962i
$243$	−81007.6			−0.0880055
$244$	497036.	+	257199.i	0.534457	+	0.276563i
$245$		0			0
$246$	8413.64	−	5119.60i	0.00886433	−	0.00539384i
$247$			2.74389e6i			2.86171i
$248$	64793.0	+	935969.i	0.0668958	+	0.966345i
$249$	47542.8			0.0485944
$250$		0			0
$251$			963725.i			0.965537i	0.875748	+	0.482768i	$0.160369\pi$
$251$			963725.i			0.965537i	−0.875748	+	0.482768i	$0.839631\pi$
$252$	1.35131e6	+	699257.i	1.34046	+	0.693643i
$253$	551093.			0.541282
$254$	38941.3	+	63996.8i	0.0378727	+	0.0622406i
$255$		0			0
$256$	−348986.	+	988798.i	−0.332819	+	0.942991i
$257$			1.50847e6i			1.42463i	0.701857	+	0.712317i	$0.252354\pi$
$257$			1.50847e6i			1.42463i	−0.701857	+	0.712317i	$0.747646\pi$
$258$	9581.11	−	5829.99i	0.00896121	−	0.00545279i
$259$		−	1.85947e6i		−	1.72242i
$260$		0			0
$261$		−	940839.i		−	0.854898i
$262$	86554.3	+	142245.i	0.0778997	+	0.128022i
$263$			721202.i			0.642936i	0.946920	+	0.321468i	$0.104176\pi$
$263$			721202.i			0.642936i	−0.946920	+	0.321468i	$0.895824\pi$
$264$	−29640.3	+	2051.87i	−0.0261742	+	0.00181192i
$265$		0			0
$266$	2.72821e6	−	1.66008e6i	2.36415	−	1.43855i
$267$	−17459.8			−0.0149886
$268$	110163.	−	212889.i	0.0936910	−	0.181058i
$269$		−	1.43076e6i		−	1.20556i	−0.797909	−	0.602778i	$-0.794061\pi$
$269$		−	1.43076e6i		−	1.20556i	0.797909	−	0.602778i	$-0.205939\pi$
$270$		0			0
$271$	−1.94059e6			−1.60514			−0.802568	−	0.596561i	$-0.796533\pi$
$271$	−1.94059e6			−1.60514			−0.802568	+	0.596561i	$0.796533\pi$
$272$	1.75668e6	−	1.24288e6i	1.43969	−	1.01861i
$273$		−	85338.3i		−	0.0693007i
$274$	666975.	+	1.09612e6i	0.536702	+	0.882026i
$275$		0			0
$276$	−20000.5	−	10349.6i	−0.0158041	−	0.00817805i
$277$	−1.71081e6			−1.33968			−0.669842	−	0.742504i	$-0.733638\pi$
$277$	−1.71081e6			−1.33968			−0.669842	+	0.742504i	$0.733638\pi$
$278$	605951.	+	995830.i	0.470246	+	0.772811i
$279$	−1.25836e6			−0.967822
$280$		0			0
$281$	1.44573e6			1.09225			0.546126	−	0.837703i	$-0.316102\pi$
$281$	1.44573e6			1.09225			0.546126	+	0.837703i	$0.316102\pi$
$282$	16836.8	+	27669.9i	0.0126077	+	0.0207197i
$283$	1.07186e6			0.795555			0.397777	−	0.917482i	$-0.369782\pi$
$283$	1.07186e6			0.795555			0.397777	+	0.917482i	$0.369782\pi$
$284$	15540.3	−	30031.6i	0.0114331	−	0.0220944i
$285$		0			0
$286$	−1.00343e6	−	1.64906e6i	−0.725393	−	1.19212i
$287$		−	744755.i		−	0.533714i
$288$	−1.29072e6	−	558545.i	−0.916963	−	0.396805i
$289$	−2.99628e6			−2.11027
$290$		0			0
$291$			10410.7i			0.00720688i
$292$	1.57126e6	+	813073.i	1.07843	+	0.558049i
$293$	−176850.			−0.120347			−0.0601735	−	0.998188i	$-0.519165\pi$
$293$	−176850.			−0.120347			−0.0601735	+	0.998188i	$0.519165\pi$
$294$	−47666.7	+	29004.6i	−0.0321622	+	0.0195703i
$295$		0			0
$296$	118699.	+	1.71467e6i	0.0787442	+	1.13750i
$297$		−	79734.3i		−	0.0524510i
$298$	−811769.	−	1.33408e6i	−0.529532	−	0.870242i
$299$		−	1.46311e6i		−	0.946455i
$300$		0			0
$301$		−	848097.i		−	0.539547i
$302$	429604.	−	261409.i	0.271051	−	0.164931i
$303$			24132.4i			0.0151006i
$304$	−2.40979e6	+	1.70497e6i	−1.49553	+	1.05811i
$305$		0			0
$306$	1.50030e6	+	2.46562e6i	0.915957	+	1.50530i
$307$	2.76503e6			1.67438			0.837189	−	0.546914i	$-0.184198\pi$
$307$	2.76503e6			1.67438			0.837189	+	0.546914i	$0.184198\pi$
$308$	−1.03255e6	+	1.99540e6i	−0.620202	+	1.19854i
$309$			17534.8i			0.0104473i
$310$		0			0
$311$	748055.			0.438564			0.219282	−	0.975662i	$-0.429629\pi$
$311$	748055.			0.438564			0.219282	+	0.975662i	$0.429629\pi$
$312$	5447.57	+	78693.0i	0.00316823	+	0.0457667i
$313$		−	2.84259e6i		−	1.64003i	−0.572340	−	0.820017i	$-0.693964\pi$
$313$		−	2.84259e6i		−	1.64003i	0.572340	−	0.820017i	$-0.306036\pi$
$314$	1.32381e6	−	805520.i	0.757705	−	0.461054i
$315$		0			0
$316$	−1.31457e6	+	2.54041e6i	−0.740572	+	1.43115i
$317$	−97492.6			−0.0544908			−0.0272454	−	0.999629i	$-0.508674\pi$
$317$	−97492.6			−0.0544908			−0.0272454	+	0.999629i	$0.508674\pi$
$318$	−55477.4	+	33757.3i	−0.0307644	+	0.0187197i
$319$	1.38928e6			0.764384
$320$		0			0
$321$	−69327.5			−0.0375528
$322$	−1.45475e6	+	885199.i	−0.781896	+	0.475774i
$323$	6.05802e6			3.23091
$324$	866161.	−	1.67385e6i	0.458391	−	0.885839i
$325$		0			0
$326$	−108830.	+	66221.5i	−0.0567157	+	0.0345108i
$327$		−	67033.4i		−	0.0346674i
$328$	47541.4	+	686761.i	0.0243999	+	0.352469i
$329$	2.44927e6			1.24752
$330$		0			0
$331$		−	2.71471e6i		−	1.36193i	−0.732317	−	0.680964i	$-0.761561\pi$
$331$		−	2.71471e6i		−	1.36193i	0.732317	−	0.680964i	$-0.238439\pi$
$332$	−1.52723e6	+	2.95137e6i	−0.760429	+	1.46953i
$333$	−2.30529e6			−1.13924
$334$	−12397.5	−	20374.2i	−0.00608089	−	0.00999344i
$335$		0			0
$336$	74947.4	−	53026.5i	0.0362167	−	0.0256239i
$337$		−	495886.i		−	0.237852i	−0.992903	−	0.118926i	$-0.962055\pi$
$337$		−	495886.i		−	0.237852i	0.992903	−	0.118926i	$-0.0379452\pi$
$338$	−2.58385e6	+	1.57224e6i	−1.23020	+	0.748563i
$339$		−	27180.0i		−	0.0128455i
$340$		0			0
$341$		−	1.85814e6i		−	0.865353i
$342$	−2.05810e6	−	3.38232e6i	−0.951484	−	1.56369i
$343$			927903.i			0.425860i
$344$	54138.3	+	782055.i	0.0246665	+	0.356321i
$345$		0			0
$346$	1.16157e6	−	706801.i	0.521621	−	0.317400i
$347$	−3.14504e6			−1.40217			−0.701087	−	0.713076i	$-0.747302\pi$
$347$	−3.14504e6			−1.40217			−0.701087	+	0.713076i	$0.747302\pi$
$348$	−50420.3	−	26090.7i	−0.0223181	−	0.0115488i
$349$			2.62573e6i			1.15395i	0.816762	+	0.576975i	$0.195767\pi$
$349$			2.62573e6i			1.15395i	−0.816762	+	0.576975i	$0.804233\pi$
$350$		0			0
$351$	−211689.			−0.0917129
$352$	824767.	−	1.90593e6i	0.354793	−	0.819879i
$353$		−	536996.i		−	0.229369i	−0.993402	−	0.114684i	$-0.963414\pi$
$353$		−	536996.i		−	0.229369i	0.993402	−	0.114684i	$-0.0365857\pi$
$354$	24843.0	+	40827.4i	0.0105365	+	0.0173159i
$355$		0			0
$356$	560865.	−	1.08387e6i	0.234549	−	0.453265i
$357$	−188412.			−0.0782415
$358$	−721903.	−	1.18639e6i	−0.297695	−	0.489237i
$359$	369981.			0.151511			0.0757553	−	0.997126i	$-0.475863\pi$
$359$	369981.			0.151511			0.0757553	+	0.997126i	$0.475863\pi$
$360$		0			0
$361$	−5.83425e6			−2.35623
$362$	−48779.5	−	80165.2i	−0.0195644	−	0.0321525i
$363$	−14888.0			−0.00593021
$364$	5.29764e6	+	2.74134e6i	2.09570	+	1.08445i
$365$		0			0
$366$	23543.7	+	38692.2i	0.00918697	+	0.0150980i
$367$			1.41712e6i			0.549214i	0.961557	+	0.274607i	$0.0885478\pi$
$367$			1.41712e6i			0.549214i	−0.961557	+	0.274607i	$0.911452\pi$
$368$	1.28496e6	−	909132.i	0.494619	−	0.349951i
$369$	−923315.			−0.353008
$370$		0			0
$371$			4.91072e6i			1.85230i
$372$	−34896.1	+	67436.6i	−0.0130743	+	0.0252661i
$373$	2.16053e6			0.804060			0.402030	−	0.915626i	$-0.368305\pi$
$373$	2.16053e6			0.804060			0.402030	+	0.915626i	$0.368305\pi$
$374$	−3.64083e6	+	2.21540e6i	−1.34592	+	0.818979i
$375$		0			0
$376$	−2.25854e6	+	156349.i	−0.823871	+	0.0570330i
$377$		−	3.68843e6i		−	1.33656i
$378$	128074.	+	210479.i	0.0461033	+	0.0757669i
$379$			1.60069e6i			0.572412i	0.958168	+	0.286206i	$0.0923942\pi$
$379$			1.60069e6i			0.572412i	−0.958168	+	0.286206i	$0.907606\pi$
$380$		0			0
$381$			6062.84i			0.00213975i
$382$	2.68632e6	−	1.63459e6i	0.941888	−	0.573128i
$383$		−	3.07943e6i		−	1.07269i	−0.844000	−	0.536344i	$-0.819805\pi$
$383$		−	3.07943e6i		−	1.07269i	0.844000	−	0.536344i	$-0.180195\pi$
$384$	−65726.3	+	53681.6i	−0.0227463	+	0.0185779i
$385$		0			0
$386$	−1.16784e6	−	1.91925e6i	−0.398948	−	0.655638i
$387$	−1.05143e6			−0.356866
$388$	−646276.	−	334425.i	−0.217941	−	0.112777i
$389$		−	2.71294e6i		−	0.909006i	−0.890745	−	0.454503i	$-0.849817\pi$
$389$		−	2.71294e6i		−	0.909006i	0.890745	−	0.454503i	$-0.150183\pi$
$390$		0			0
$391$	−3.23029e6			−1.06856
$392$	−269341.	−	3.89078e6i	−0.0885295	−	1.27885i
$393$			13475.8i			0.00440122i
$394$	3.49026e6	−	2.12378e6i	1.13270	−	0.689237i
$395$		0			0
$396$	2.47381e6	+	1.28011e6i	0.792735	+	0.410213i
$397$	−4.05795e6			−1.29220			−0.646101	−	0.763252i	$-0.723601\pi$
$397$	−4.05795e6			−1.29220			−0.646101	+	0.763252i	$0.723601\pi$
$398$	−627698.	+	381947.i	−0.198629	+	0.120863i
$399$	258462.			0.0812762
$400$		0			0
$401$	5.22811e6			1.62362			0.811809	−	0.583923i	$-0.198483\pi$
$401$	5.22811e6			1.62362			0.811809	+	0.583923i	$0.198483\pi$
$402$	16572.5	−	10084.2i	0.00511475	−	0.00311226i
$403$	−4.93324e6			−1.51311
$404$	−1.49809e6	−	775210.i	−0.456652	−	0.236301i
$405$		0			0
$406$	−3.66735e6	+	2.23154e6i	−1.10417	+	0.671876i
$407$		−	3.40407e6i		−	1.01862i
$408$	173740.	−	12027.3i	0.0516713	−	0.00357698i
$409$	1.89554e6			0.560306			0.280153	−	0.959955i	$-0.409615\pi$
$409$	1.89554e6			0.560306			0.280153	+	0.959955i	$0.409615\pi$
$410$		0			0
$411$			103843.i			0.0303229i
$412$	−1.08853e6	−	563275.i	−0.315934	−	0.163485i
$413$	3.61394e6			1.04257
$414$	1.09743e6	+	1.80354e6i	0.314685	+	0.517160i
$415$		0			0
$416$	−5.06010e6	−	2.18970e6i	−1.43359	−	0.620370i
$417$			94341.5i			0.0265682i
$418$	4.99445e6	−	3.03907e6i	1.39813	−	0.850745i
$419$		−	663430.i		−	0.184612i	−0.995731	−	0.0923060i	$-0.970576\pi$
$419$		−	663430.i		−	0.184612i	0.995731	−	0.0923060i	$-0.0294238\pi$
$420$		0			0
$421$		−	1.14330e6i		−	0.314381i	−0.987568	−	0.157190i	$-0.949756\pi$
$421$		−	1.14330e6i		−	0.314381i	0.987568	−	0.157190i	$-0.0502436\pi$
$422$	−1.79041e6	−	2.94239e6i	−0.489407	−	0.804301i
$423$		−	3.03650e6i		−	0.825130i
$424$	−313476.	−	4.52832e6i	−0.0846817	−	1.22327i
$425$		0			0
$426$	2337.84	−	1422.55i	0.000624153	−	0.000379789i
$427$	3.42494e6			0.909040
$428$	2.22702e6	−	4.30372e6i	0.587645	−	1.13562i
$429$		−	156226.i		−	0.0409837i
$430$		0			0
$431$	559165.			0.144993			0.0724964	−	0.997369i	$-0.476903\pi$
$431$	559165.			0.144993			0.0724964	+	0.997369i	$0.476903\pi$
$432$	−131537.	−	185914.i	−0.0339108	−	0.0479294i
$433$			4.04780e6i			1.03753i	0.854918	+	0.518764i	$0.173608\pi$
$433$			4.04780e6i			1.03753i	−0.854918	+	0.518764i	$0.826392\pi$
$434$	2.98466e6	+	4.90505e6i	0.760625	+	1.25003i
$435$		0			0
$436$	4.16130e6	+	2.15333e6i	1.04837	+	0.542493i
$437$	4.43129e6			1.11001
$438$	74428.0	+	122316.i	0.0185375	+	0.0304649i
$439$	4.17879e6			1.03488			0.517439	−	0.855720i	$-0.326886\pi$
$439$	4.17879e6			1.03488			0.517439	+	0.855720i	$0.326886\pi$
$440$		0			0
$441$	5.23095e6			1.28081
$442$	5.88173e6	+	9.66614e6i	1.43202	+	2.35341i
$443$	−6.19142e6			−1.49893			−0.749464	−	0.662045i	$-0.769689\pi$
$443$	−6.19142e6			−1.49893			−0.749464	+	0.662045i	$0.769689\pi$
$444$	−63928.7	+	123542.i	−0.0153900	+	0.0297411i
$445$		0			0
$446$	66281.9	+	108929.i	0.0157782	+	0.0259302i
$447$		−	126386.i		−	0.0299178i
$448$	884230.	+	6.35598e6i	0.208147	+	1.49619i
$449$	3.11618e6			0.729469			0.364735	−	0.931111i	$-0.381160\pi$
$449$	3.11618e6			0.729469			0.364735	+	0.931111i	$0.381160\pi$
$450$		0			0
$451$		−	1.36340e6i		−	0.315633i
$452$	1.68728e6	+	873111.i	0.388456	+	0.201013i
$453$	40699.2			0.00931837
$454$	729175.	−	443694.i	0.166032	−	0.101029i
$455$		0			0
$456$	−238335.	+	16498.9i	−0.0536755	+	0.00371572i
$457$			4.44694e6i			0.996026i	0.867170	+	0.498013i	$0.165937\pi$
$457$			4.44694e6i			0.996026i	−0.867170	+	0.498013i	$0.834063\pi$
$458$	−2.13046e6	−	3.50124e6i	−0.474581	−	0.779934i
$459$			467371.i			0.103545i
$460$		0			0
$461$			7.51985e6i			1.64800i	0.566590	+	0.824000i	$0.308262\pi$
$461$			7.51985e6i			1.64800i	−0.566590	+	0.824000i	$0.691738\pi$
$462$	−155333.	+	94518.5i	−0.0338579	+	0.0206021i
$463$			4.34253e6i			0.941434i	0.882284	+	0.470717i	$0.156005\pi$
$463$			4.34253e6i			0.941434i	−0.882284	+	0.470717i	$0.843995\pi$
$464$	3.23932e6	−	2.29187e6i	0.698489	−	0.494192i
$465$		0			0
$466$	989668.	+	1.62644e6i	0.211118	+	0.346955i
$467$	890290.			0.188903			0.0944515	−	0.995529i	$-0.469890\pi$
$467$	890290.			0.188903			0.0944515	+	0.995529i	$0.469890\pi$
$468$	3.39860e6	−	6.56779e6i	0.717274	−	1.38613i
$469$		−	1.46696e6i		−	0.307955i
$470$		0			0
$471$	125413.			0.0260489
$472$	−3.33253e6	+	230696.i	−0.688523	+	0.0476634i
$473$		−	1.55258e6i		−	0.319082i
$474$	−197761.	+	120335.i	−0.0404291	+	0.0246006i
$475$		0			0
$476$	6.05239e6	−	1.16962e7i	1.22436	−	2.36607i
$477$	6.08810e6			1.22514
$478$	1.59715e6	−	971844.i	0.319724	−	0.194548i
$479$	−3.93305e6			−0.783233			−0.391617	−	0.920128i	$-0.628084\pi$
$479$	−3.93305e6			−0.783233			−0.391617	+	0.920128i	$0.628084\pi$
$480$		0			0
$481$	−9.03757e6			−1.78110
$482$	−4.34943e6	+	2.64657e6i	−0.852736	+	0.518879i
$483$	−137818.			−0.0268806
$484$	478251.	−	924219.i	0.0927988	−	0.179333i
$485$		0			0
$486$	391471.	−	238205.i	0.0751811	−	0.0457468i
$487$		−	3.91119e6i		−	0.747286i	−0.927573	−	0.373643i	$-0.878109\pi$
$487$		−	3.91119e6i		−	0.747286i	0.927573	−	0.373643i	$-0.121891\pi$
$488$	−3.15824e6	+	218631.i	−0.600337	+	0.0415587i
$489$	−10310.1			−0.00194981
$490$		0			0
$491$		−	4.43336e6i		−	0.829907i	−0.909843	−	0.414954i	$-0.863798\pi$
$491$		−	4.43336e6i		−	0.829907i	0.909843	−	0.414954i	$-0.136202\pi$
$492$	−25604.8	+	49481.1i	−0.00476879	+	0.00921567i
$493$	−8.14339e6			−1.50900
$494$	−8.06851e6	−	1.32599e7i	−1.48756	−	2.44469i
$495$		0			0
$496$	−3.06536e6	−	4.33256e6i	−0.559470	−	0.790753i
$497$		−	206940.i		−	0.0375797i
$498$	−229752.	+	139801.i	−0.0415131	+	0.0252602i
$499$			4.84134e6i			0.870391i	0.900336	+	0.435196i	$0.143321\pi$
$499$			4.84134e6i			0.870391i	−0.900336	+	0.435196i	$0.856679\pi$
$500$		0			0
$501$		−	1930.18i		−	0.000343561i
$502$	−2.83386e6	−	4.65722e6i	−0.501903	−	0.824836i
$503$			1.68379e6i			0.296735i	0.988932	+	0.148367i	$0.0474018\pi$
$503$			1.68379e6i			0.296735i	−0.988932	+	0.148367i	$0.952598\pi$
$504$	−8.58644e6	+	594402.i	−1.50569	+	0.104233i
$505$		0			0
$506$	−2.66317e6	+	1.62051e6i	−0.462405	+	0.281368i
$507$	−244786.			−0.0422927
$508$	−376369.	−	194758.i	−0.0647075	−	0.0334839i
$509$			9.81220e6i			1.67869i	0.543595	+	0.839347i	$0.317063\pi$
$509$			9.81220e6i			1.67869i	−0.543595	+	0.839347i	$0.682937\pi$
$510$		0			0
$511$	1.08271e7			1.83426
$512$	−1.22111e6	−	5.80459e6i	−0.205864	−	0.978581i
$513$		−	641136.i		−	0.107561i
$514$	−4.43570e6	−	7.28971e6i	−0.740550	−	1.21703i
$515$		0			0
$516$	−29157.7	+	56347.1i	−0.00482091	+	0.00931639i
$517$	4.48380e6			0.737768
$518$	5.46782e6	+	8.98592e6i	0.895344	+	1.47142i
$519$	110043.			0.0179326
$520$		0			0
$521$	−2.02601e6			−0.327000			−0.163500	−	0.986543i	$-0.552278\pi$
$521$	−2.02601e6			−0.327000			−0.163500	+	0.986543i	$0.552278\pi$
$522$	2.76657e6	+	4.54663e6i	0.444391	+	0.730320i
$523$	402702.			0.0643768			0.0321884	−	0.999482i	$-0.489752\pi$
$523$	402702.			0.0643768			0.0321884	+	0.999482i	$0.489752\pi$
$524$	−836551.	−	432886.i	−0.133096	−	0.0688724i
$525$		0			0
$526$	−2.12072e6	−	3.48523e6i	−0.334209	−	0.549245i
$527$			1.08917e7i			1.70832i
$528$	137204.	−	97074.0i	0.0214181	−	0.0151537i
$529$	4.07347e6			0.632886
$530$		0			0
$531$		−	4.48041e6i		−	0.689575i
$532$	−8.30262e6	+	1.60448e7i	−1.27185	+	2.45785i
$533$	−3.61973e6			−0.551897
$534$	84374.9	−	51341.1i	0.0128044	−	0.00779134i
$535$		0			0
$536$	93643.5	+	1.35273e6i	0.0140788	+	0.203376i
$537$		−	112394.i		−	0.0168193i
$538$	4.20721e6	+	6.91420e6i	0.626669	+	1.02988i
$539$			7.72421e6i			1.14520i
$540$		0			0
$541$			8.47881e6i			1.24549i	0.782423	+	0.622747i	$0.213984\pi$
$541$			8.47881e6i			1.24549i	−0.782423	+	0.622747i	$0.786016\pi$
$542$	9.37797e6	−	5.70638e6i	1.37123	−	0.834377i
$543$		−	7594.57i		−	0.00110536i
$544$	−4.83446e6	+	1.11718e7i	−0.700407	+	1.61855i
$545$		0			0
$546$	250940.	+	412399.i	0.0360237	+	0.0592020i
$547$	−7.10206e6			−1.01488			−0.507441	−	0.861686i	$-0.669409\pi$
$547$	−7.10206e6			−1.01488			−0.507441	+	0.861686i	$0.669409\pi$
$548$	−6.44634e6	−	3.33576e6i	−0.916985	−	0.474508i
$549$		−	4.24609e6i		−	0.601255i
$550$		0			0
$551$	1.11710e7			1.56752
$552$	127086.	−	8797.63i	0.0177521	−	0.00122890i
$553$			1.75053e7i			2.43420i
$554$	8.26753e6	−	5.03069e6i	1.14446	−	0.696391i
$555$		0			0
$556$	−5.85654e6	−	3.03055e6i	−0.803441	−	0.415753i
$557$	−2.42337e6			−0.330965			−0.165482	−	0.986213i	$-0.552918\pi$
$557$	−2.42337e6			−0.330965			−0.165482	+	0.986213i	$0.552918\pi$
$558$	6.08107e6	−	3.70026e6i	0.826788	−	0.503091i
$559$	−4.12200e6			−0.557929
$560$		0			0
$561$	−344919.			−0.0462712
$562$	−6.98655e6	+	4.25123e6i	−0.933086	+	0.567772i
$563$	−1.03666e7			−1.37837			−0.689184	−	0.724586i	$-0.742031\pi$
$563$	−1.03666e7			−1.37837			−0.689184	+	0.724586i	$0.742031\pi$
$564$	−162728.	−	84206.2i	−0.0215410	−	0.0111467i
$565$		0			0
$566$	−5.17976e6	+	3.15182e6i	−0.679624	+	0.413543i
$567$		−	1.15341e7i		−	1.50669i
$568$	13210.0	+	190825.i	0.00171804	+	0.0248179i
$569$	−1.33323e7			−1.72633			−0.863165	−	0.504921i	$-0.831521\pi$
$569$	−1.33323e7			−1.72633			−0.863165	+	0.504921i	$0.831521\pi$
$570$		0			0
$571$			4.77970e6i			0.613494i	0.951791	+	0.306747i	$0.0992405\pi$
$571$			4.77970e6i			0.613494i	−0.951791	+	0.306747i	$0.900760\pi$
$572$	9.69822e6	+	5.01849e6i	1.23937	+	0.641332i
$573$	254493.			0.0323809
$574$	2.18997e6	+	3.59904e6i	0.277434	+	0.455940i
$575$		0			0
$576$	7.87987e6	−	1.09623e6i	0.989607	−	0.137672i
$577$			5.73641e6i			0.717300i	0.933472	+	0.358650i	$0.116763\pi$
$577$			5.73641e6i			0.717300i	−0.933472	+	0.358650i	$0.883237\pi$
$578$	1.44796e7	−	8.81066e6i	1.80276	−	1.09695i
$579$		−	181823.i		−	0.0225400i
$580$		0			0
$581$			2.03371e7i			2.49947i
$582$	−30613.0	−	50309.9i	−0.00374626	−	0.00615667i
$583$			8.98990e6i			1.09543i
$584$	−9.98403e6	+	691151.i	−1.21136	+	0.0838572i
$585$		0			0
$586$	854630.	−	520032.i	0.102810	−	0.0625585i
$587$	−5.32016e6			−0.637279			−0.318639	−	0.947876i	$-0.603226\pi$
$587$	−5.32016e6			−0.637279			−0.318639	+	0.947876i	$0.603226\pi$
$588$	145061.	−	280331.i	0.0173025	−	0.0334370i
$589$		−	1.49412e7i		−	1.77458i
$590$		0			0
$591$	330655.			0.0389409
$592$	−5.61566e6	−	7.93714e6i	−0.658562	−	0.930808i
$593$		−	828623.i		−	0.0967654i	−0.998829	−	0.0483827i	$-0.984593\pi$
$593$		−	828623.i		−	0.0967654i	0.998829	−	0.0483827i	$-0.0154067\pi$
$594$	234461.	+	385318.i	0.0272650	+	0.0448077i
$595$		0			0
$596$	7.84578e6	+	4.05992e6i	0.904734	+	0.468168i
$597$	−59465.9			−0.00682861
$598$	4.30233e6	+	7.07053e6i	0.491984	+	0.808535i
$599$	−5.87196e6			−0.668676			−0.334338	−	0.942453i	$-0.608513\pi$
$599$	−5.87196e6			−0.668676			−0.334338	+	0.942453i	$0.608513\pi$
$600$		0			0
$601$	3.38777e6			0.382584			0.191292	−	0.981533i	$-0.438732\pi$
$601$	3.38777e6			0.382584			0.191292	+	0.981533i	$0.438732\pi$
$602$	2.49386e6	+	4.09845e6i	0.280466	+	0.460923i
$603$	−1.81868e6			−0.203686
$604$	−1.30739e6	+	2.52653e6i	−0.145818	+	0.281794i
$605$		0			0
$606$	−70962.0	−	116620.i	−0.00784955	−	0.0129001i
$607$		−	4.02635e6i		−	0.443547i	−0.975098	−	0.221774i	$-0.928815\pi$
$607$		−	4.02635e6i		−	0.443547i	0.975098	−	0.221774i	$-0.0711846\pi$
$608$	6.63187e6	−	1.53254e7i	0.727574	−	1.68133i
$609$	−347432.			−0.0379601
$610$		0			0
$611$		−	1.19042e7i		−	1.29002i
$612$	−1.45005e7	−	7.50350e6i	−1.56496	−	0.809814i
$613$	5.30633e6			0.570352			0.285176	−	0.958475i	$-0.407948\pi$
$613$	5.30633e6			0.570352			0.285176	+	0.958475i	$0.407948\pi$
$614$	−1.33621e7	+	8.13065e6i	−1.43038	+	0.870370i
$615$		0			0
$616$	−877714.	−	1.26790e7i	−0.0931969	−	1.34628i
$617$			9.56854e6i			1.01189i	0.862566	+	0.505944i	$0.168856\pi$
$617$			9.56854e6i			1.01189i	−0.862566	+	0.505944i	$0.831144\pi$
$618$	−51561.7	−	84737.4i	−0.00543070	−	0.00892491i
$619$		−	6.58401e6i		−	0.690659i	−0.938481	−	0.345330i	$-0.887767\pi$
$619$		−	6.58401e6i		−	0.690659i	0.938481	−	0.345330i	$-0.112233\pi$
$620$		0			0
$621$			341870.i			0.0355739i
$622$	−3.61499e6	+	2.19968e6i	−0.374655	+	0.227973i
$623$		−	7.46866e6i		−	0.770943i
$624$	−257725.	−	364267.i	−0.0264969	−	0.0374506i
$625$		0			0
$626$	8.35871e6	+	1.37369e7i	0.852518	+	1.40104i
$627$	473157.			0.0480659
$628$	−4.02866e6	+	7.78538e6i	−0.407626	+	0.787736i
$629$			1.99533e7i			2.01089i
$630$		0			0
$631$	−1.34839e7			−1.34816			−0.674079	−	0.738659i	$-0.735459\pi$
$631$	−1.34839e7			−1.34816			−0.674079	+	0.738659i	$0.735459\pi$
$632$	−1.11745e6	−	1.61421e7i	−0.111285	−	1.60756i
$633$		−	278752.i		−	0.0276508i
$634$	471135.	−	286680.i	0.0465503	−	0.0283253i
$635$		0			0
$636$	168831.	−	326266.i	0.0165505	−	0.0319837i
$637$	2.05072e7			2.00244
$638$	−6.71371e6	+	4.08521e6i	−0.652996	+	0.397340i
$639$	−256555.			−0.0248559
$640$		0			0
$641$	−7.72929e6			−0.743010			−0.371505	−	0.928431i	$-0.621158\pi$
$641$	−7.72929e6			−0.743010			−0.371505	+	0.928431i	$0.621158\pi$
$642$	335027.	−	203860.i	0.0320805	−	0.0195206i
$643$	−9.41828e6			−0.898347			−0.449174	−	0.893444i	$-0.648282\pi$
$643$	−9.41828e6			−0.898347			−0.449174	+	0.893444i	$0.648282\pi$
$644$	4.42717e6	−	8.55549e6i	0.420641	−	0.812887i
$645$		0			0
$646$	−2.92755e7	+	1.78138e7i	−2.76009	+	1.67948i
$647$		−	3.44122e6i		−	0.323185i	−0.986858	−	0.161593i	$-0.948337\pi$
$647$		−	3.44122e6i		−	0.323185i	0.986858	−	0.161593i	$-0.0516631\pi$
$648$	736277.	+	1.06359e7i	0.0688817	+	0.995032i
$649$	6.61593e6			0.616566
$650$		0			0
$651$			464687.i			0.0429743i
$652$	331195.	−	640034.i	0.0305116	−	0.0589636i
$653$	1.39531e7			1.28053			0.640263	−	0.768155i	$-0.278825\pi$
$653$	1.39531e7			1.28053			0.640263	+	0.768155i	$0.278825\pi$
$654$	197114.	+	323940.i	0.0180207	+	0.0296156i
$655$		0			0
$656$	−2.24919e6	−	3.17899e6i	−0.204064	−	0.288423i
$657$		−	1.34230e7i		−	1.21321i
$658$	−1.18362e7	+	7.20215e6i	−1.06573	+	0.648482i
$659$			1.16197e7i			1.04227i	0.853474	+	0.521135i	$0.174491\pi$
$659$			1.16197e7i			1.04227i	−0.853474	+	0.521135i	$0.825509\pi$
$660$		0			0
$661$			2.02640e6i			0.180394i	0.995924	+	0.0901970i	$0.0287497\pi$
$661$			2.02640e6i			0.180394i	−0.995924	+	0.0901970i	$0.971250\pi$
$662$	7.98270e6	+	1.31189e7i	0.707954	+	1.16346i
$663$			915737.i			0.0809071i
$664$	−1.29822e6	−	1.87534e7i	−0.114269	−	1.65067i
$665$		0			0
$666$	1.11404e7	−	6.77877e6i	0.973226	−	0.592196i
$667$	−5.95668e6			−0.518429
$668$	119822.	+	62003.8i	0.0103895	+	0.00537622i
$669$			10319.6i			0.000891447i
$670$		0			0
$671$	6.26993e6			0.537596
$672$	−206259.	+	476637.i	−0.0176193	+	0.0407160i
$673$		−	5.84126e6i		−	0.497129i	−0.968615	−	0.248564i	$-0.920041\pi$
$673$		−	5.84126e6i		−	0.497129i	0.968615	−	0.248564i	$-0.0799587\pi$
$674$	1.45817e6	+	2.39638e6i	0.123640	+	0.203192i
$675$		0			0
$676$	7.86330e6	−	1.51958e7i	0.661818	−	1.27896i
$677$	−1.28265e7			−1.07557			−0.537784	−	0.843083i	$-0.680738\pi$
$677$	−1.28265e7			−1.07557			−0.537784	+	0.843083i	$0.680738\pi$
$678$	79923.8	+	131348.i	0.00667731	+	0.0109736i
$679$	−4.45331e6			−0.370688
$680$		0			0
$681$	69079.6			0.00570797
$682$	5.46393e6	+	8.97952e6i	0.449825	+	0.739251i
$683$	−7.24686e6			−0.594426			−0.297213	−	0.954811i	$-0.596057\pi$
$683$	−7.24686e6			−0.594426			−0.297213	+	0.954811i	$0.596057\pi$
$684$	1.98916e7	+	1.02932e7i	1.62566	+	0.841224i
$685$		0			0
$686$	−2.72853e6	−	4.48411e6i	−0.221370	−	0.363803i
$687$		−	331695.i		−	0.0268131i
$688$	−2.56128e6	−	3.62010e6i	−0.206294	−	0.291575i
$689$	2.38676e7			1.91540
$690$		0			0
$691$		−	2.08754e7i		−	1.66318i	−0.555388	−	0.831592i	$-0.687430\pi$
$691$		−	2.08754e7i		−	1.66318i	0.555388	−	0.831592i	$-0.312570\pi$
$692$	−3.53494e6	+	6.83126e6i	−0.280619	+	0.542295i
$693$	1.70463e7			1.34834
$694$	1.51985e7	−	9.24808e6i	1.19785	−	0.728874i
$695$		0			0
$696$	320378.	−	22178.3i	0.0250691	−	0.00173543i
$697$			7.99171e6i			0.623100i
$698$	−7.72105e6	−	1.26889e7i	−0.599843	−	0.985793i
$699$			154083.i			0.0119279i
$700$		0			0
$701$		−	1.73225e7i		−	1.33142i	−0.746209	−	0.665712i	$-0.768128\pi$
$701$		−	1.73225e7i		−	1.33142i	0.746209	−	0.665712i	$-0.231872\pi$
$702$	1.02299e6	−	622478.i	0.0783482	−	0.0476740i
$703$		−	2.73718e7i		−	2.08889i
$704$	1.61873e6	+	1.16357e7i	0.123096	+	0.884831i
$705$		0			0
$706$	1.57905e6	+	2.59505e6i	0.119230	+	0.195945i
$707$	−1.03229e7			−0.776703
$708$	−240109.	−	124248.i	−0.0180022	−	0.00931549i
$709$		−	1.99424e7i		−	1.48991i	−0.667113	−	0.744956i	$-0.732470\pi$
$709$		−	1.99424e7i		−	1.48991i	0.667113	−	0.744956i	$-0.267530\pi$
$710$		0			0
$711$	2.17023e7			1.61002
$712$	476762.	+	6.88707e6i	0.0352453	+	0.509137i
$713$			7.96700e6i			0.586909i
$714$	910503.	−	554030.i	0.0668399	−	0.0406713i
$715$		0			0
$716$	6.97723e6	+	3.61047e6i	0.508628	+	0.263197i
$717$	151308.			0.0109917
$718$	−1.78794e6	+	1.08794e6i	−0.129432	+	0.0787579i
$719$	2.44269e7			1.76217			0.881083	−	0.472962i	$-0.156815\pi$
$719$	2.44269e7			1.76217			0.881083	+	0.472962i	$0.156815\pi$
$720$		0			0
$721$	−7.50075e6			−0.537361
$722$	2.81941e7	−	1.71558e7i	2.01287	−	1.22481i
$723$	−412050.			−0.0293160
$724$	471457.	+	243962.i	0.0334268	+	0.0172972i
$725$		0			0
$726$	71946.6	−	43778.6i	0.00506604	−	0.00308263i
$727$			1.52812e7i			1.07231i	0.844119	+	0.536155i	$0.180124\pi$
$727$			1.52812e7i			1.07231i	−0.844119	+	0.536155i	$0.819876\pi$
$728$	−3.36620e7	+	2.33027e6i	−2.35402	+	0.162959i
$729$	−1.42747e7			−0.994829
$730$		0			0
$731$			9.10064e6i			0.629910i
$732$	−227551.	−	117750.i	−0.0156964	−	0.00812236i
$733$	7.69123e6			0.528732			0.264366	−	0.964422i	$-0.414837\pi$
$733$	7.69123e6			0.528732			0.264366	+	0.964422i	$0.414837\pi$
$734$	−4.16709e6	−	6.84827e6i	−0.285491	−	0.469181i
$735$		0			0
$736$	−3.53628e6	+	8.17188e6i	−0.240631	+	0.556067i
$737$		−	2.68552e6i		−	0.182121i
$738$	4.46194e6	−	2.71504e6i	0.301566	−	0.183500i
$739$			7.32363e6i			0.493305i	0.969104	+	0.246652i	$0.0793306\pi$
$739$			7.32363e6i			0.493305i	−0.969104	+	0.246652i	$0.920669\pi$
$740$		0			0
$741$		−	1.25620e6i		−	0.0840453i
$742$	−1.44401e7	−	2.37312e7i	−0.962856	−	1.58237i
$743$		−	1.61613e7i		−	1.07400i	−0.843582	−	0.537001i	$-0.819557\pi$
$743$		−	1.61613e7i		−	1.07400i	0.843582	−	0.537001i	$-0.180443\pi$
$744$	−29663.3	−	428502.i	−0.00196466	−	0.0283805i
$745$		0			0
$746$	−1.04408e7	+	6.35311e6i	−0.686891	+	0.417965i
$747$	2.52130e7			1.65319
$748$	1.10799e7	−	2.14119e7i	0.724074	−	1.39927i
$749$		−	2.96557e7i		−	1.93154i
$750$		0			0
$751$	−3.01764e7			−1.95240			−0.976199	−	0.216879i	$-0.930412\pi$
$751$	−3.01764e7			−1.95240			−0.976199	+	0.216879i	$0.930412\pi$
$752$	1.04547e7	−	7.39688e6i	0.674167	−	0.476984i
$753$		−	441209.i		−	0.0283568i
$754$	1.08459e7	+	1.78244e7i	0.694767	+	1.14179i
$755$		0			0
$756$	−1.23784e6	−	640540.i	−0.0787699	−	0.0407607i
$757$	1.40193e7			0.889171			0.444586	−	0.895736i	$-0.353351\pi$
$757$	1.40193e7			0.889171			0.444586	+	0.895736i	$0.353351\pi$
$758$	−4.70687e6	−	7.73536e6i	−0.297550	−	0.488999i
$759$	−252299.			−0.0158969
$760$		0			0
$761$	−1.39222e7			−0.871456			−0.435728	−	0.900078i	$-0.643509\pi$
$761$	−1.39222e7			−0.871456			−0.435728	+	0.900078i	$0.643509\pi$
$762$	−17828.0	−	29298.8i	−0.00111228	−	0.00182794i
$763$	2.86744e7			1.78313
$764$	−8.17513e6	+	1.57984e7i	−0.506712	+	0.979220i
$765$		0			0
$766$	9.05516e6	+	1.48814e7i	0.557602	+	0.916373i
$767$		−	1.75648e7i		−	1.07809i
$768$	159771.	−	452688.i	0.00977454	−	0.0276946i
$769$	1.41369e7			0.862063			0.431031	−	0.902337i	$-0.358150\pi$
$769$	1.41369e7			0.862063			0.431031	+	0.902337i	$0.358150\pi$
$770$		0			0
$771$		−	690602.i		−	0.0418400i
$772$	1.12872e7	+	5.84076e6i	0.681624	+	0.352717i
$773$	−1.39310e7			−0.838558			−0.419279	−	0.907858i	$-0.637717\pi$
$773$	−1.39310e7			−0.838558			−0.419279	+	0.907858i	$0.637717\pi$
$774$	5.08108e6	−	3.09178e6i	0.304862	−	0.185505i
$775$		0			0
$776$	4.10653e6	−	284277.i	0.244805	−	0.0169468i
$777$			851295.i			0.0505857i
$778$	7.97749e6	+	1.31104e7i	0.472517	+	0.776543i
$779$		−	1.09630e7i		−	0.647268i
$780$		0			0
$781$		−	378838.i		−	0.0222242i
$782$	1.56104e7	−	9.49877e6i	0.912848	−	0.555457i
$783$			861835.i			0.0502366i
$784$	1.27425e7	+	1.80103e7i	0.740399	+	1.04648i
$785$		0			0
$786$	−39626.0	−	65122.1i	−0.00228783	−	0.00375986i
$787$	−9.60345e6			−0.552701			−0.276351	−	0.961057i	$-0.589125\pi$
$787$	−9.60345e6			−0.552701			−0.276351	+	0.961057i	$0.589125\pi$
$788$	−1.06217e7	+	2.05264e7i	−0.609366	+	1.17760i
$789$		−	330178.i		−	0.0188823i
$790$		0			0
$791$	1.16266e7			0.660712
$792$	−1.57189e7	+	1.08815e6i	−0.890451	+	0.0616420i
$793$		−	1.66462e7i		−	0.940010i
$794$	1.96101e7	−	1.19325e7i	1.10390	−	0.671709i
$795$		0			0
$796$	1.91024e6	−	3.69153e6i	0.106857	−	0.206502i
$797$	−1.97451e7			−1.10107			−0.550534	−	0.834813i	$-0.685576\pi$
$797$	−1.97451e7			−1.10107			−0.550534	+	0.834813i	$0.685576\pi$
$798$	−1.24902e6	+	760014.i	−0.0694325	+	0.0422488i
$799$	−2.62823e7			−1.45645
$800$		0			0
$801$	−9.25932e6			−0.509915
$802$	−2.52650e7	+	1.53734e7i	−1.38702	+	0.843985i
$803$	1.98209e7			1.08476
$804$	−50434.3	+	97464.2i	−0.00275160	+	0.00531747i
$805$		0			0
$806$	2.38400e7	−	1.45063e7i	1.29261	−	0.786539i
$807$			655027.i			0.0354059i
$808$	9.51909e6	−	658965.i	0.512941	−	0.0355087i
$809$	−1.73178e7			−0.930296			−0.465148	−	0.885233i	$-0.653999\pi$
$809$	−1.73178e7			−0.930296			−0.465148	+	0.885233i	$0.653999\pi$
$810$		0			0
$811$		−	3.16102e7i		−	1.68762i	−0.536642	−	0.843810i	$-0.680307\pi$
$811$		−	3.16102e7i		−	1.68762i	0.536642	−	0.843810i	$-0.319693\pi$
$812$	1.11606e7	−	2.15679e7i	0.594018	−	1.14794i
$813$	888436.			0.0471411
$814$	1.00098e7	+	1.64502e7i	0.529497	+	0.870184i
$815$		0			0
$816$	−804236.	+	569010.i	−0.0422822	+	0.0299154i
$817$		−	1.24842e7i		−	0.654342i
$818$	−9.16026e6	+	5.57390e6i	−0.478657	+	0.291257i
$819$		−	4.52568e7i		−	2.35762i
$820$		0			0
$821$			1.86667e7i			0.966519i	0.875477	+	0.483260i	$0.160547\pi$
$821$			1.86667e7i			0.966519i	−0.875477	+	0.483260i	$0.839453\pi$
$822$	−305352.	−	501821.i	−0.0157624	−	0.0259042i
$823$			3.88081e7i			1.99720i	0.0528555	+	0.998602i	$0.483168\pi$
$823$			3.88081e7i			1.99720i	−0.0528555	+	0.998602i	$0.516832\pi$
$824$	6.91666e6	−	478810.i	0.354878	−	0.0245666i
$825$		0			0
$826$	−1.74645e7	+	1.06269e7i	−0.890646	+	0.541947i
$827$	−2.98829e7			−1.51935			−0.759677	−	0.650301i	$-0.774643\pi$
$827$	−2.98829e7			−1.51935			−0.759677	+	0.650301i	$0.774643\pi$
$828$	−1.06067e7	−	5.48861e6i	−0.537657	−	0.278219i
$829$			2.10001e7i			1.06129i	0.847594	+	0.530645i	$0.178050\pi$
$829$			2.10001e7i			1.06129i	−0.847594	+	0.530645i	$0.821950\pi$
$830$		0			0
$831$	783237.			0.0393451
$832$	3.08919e7	−	4.29762e6i	1.54717	−	0.215239i
$833$		−	4.52763e7i		−	2.26078i
$834$	−277414.	−	455908.i	−0.0138106	−	0.0226966i
$835$		0			0
$836$	−1.51993e7	+	2.93727e7i	−0.752158	+	1.45354i
$837$	1.15270e6			0.0568724
$838$	1.95084e6	+	3.20604e6i	0.0959645	+	0.157710i
$839$	7.61546e6			0.373501			0.186750	−	0.982407i	$-0.440204\pi$
$839$	7.61546e6			0.373501			0.186750	+	0.982407i	$0.440204\pi$
$840$		0			0
$841$	5.49468e6			0.267888
$842$	3.36192e6	+	5.52503e6i	0.163421	+	0.268568i
$843$	−661881.			−0.0320783
$844$	1.73044e7	+	8.95440e6i	0.836179	+	0.432694i
$845$		0			0
$846$	8.92892e6	+	1.46740e7i	0.428917	+	0.704890i
$847$		−	6.36854e6i		−	0.305022i
$848$	1.48306e7	+	2.09614e7i	0.708219	+	1.00099i
$849$	−490713.			−0.0233646
$850$		0			0
$851$			1.45953e7i			0.690860i
$852$	−7114.62	+	13749.0i	−0.000335778	+	0.000648891i
$853$	−9.56553e6			−0.450128			−0.225064	−	0.974344i	$-0.572259\pi$
$853$	−9.56553e6			−0.450128			−0.225064	+	0.974344i	$0.572259\pi$
$854$	−1.65511e7	+	1.00711e7i	−0.776572	+	0.472535i
$855$		0			0
$856$	1.89307e6	+	2.73464e7i	0.0883046	+	1.27561i
$857$			2.34556e7i			1.09092i	0.838136	+	0.545462i	$0.183646\pi$
$857$			2.34556e7i			1.09092i	−0.838136	+	0.545462i	$0.816354\pi$
$858$	459388.	+	754967.i	0.0213040	+	0.0350114i
$859$			9.13964e6i			0.422616i	0.977420	+	0.211308i	$0.0677723\pi$
$859$			9.13964e6i			0.422616i	−0.977420	+	0.211308i	$0.932228\pi$
$860$		0			0
$861$			340961.i			0.0156746i
$862$	−2.70218e6	+	1.64424e6i	−0.123864	+	0.0753698i
$863$		−	1.04151e7i		−	0.476034i	−0.971261	−	0.238017i	$-0.923503\pi$
$863$		−	1.04151e7i		−	0.476034i	0.971261	−	0.238017i	$-0.0764974\pi$
$864$	1.18234e6	+	511643.i	0.0538837	+	0.0233175i
$865$		0			0
$866$	−1.19027e7	−	1.95611e7i	−0.539325	−	0.886336i
$867$	1.37175e6			0.0619764
$868$	−2.88469e7	−	1.49273e7i	−1.29957	−	0.672482i
$869$			3.20464e7i			1.43956i
$870$		0			0
$871$	−7.12987e6			−0.318446
$872$	−2.64415e7	+	1.83043e6i	−1.17759	+	0.0815196i
$873$			5.52102e6i			0.245179i
$874$	−2.14143e7	+	1.30303e7i	−0.948255	+	0.577002i
$875$		0			0
$876$	−719350.	−	372238.i	−0.0316723	−	0.0163893i
$877$	−2.02537e7			−0.889210			−0.444605	−	0.895727i	$-0.646656\pi$
$877$	−2.02537e7			−0.889210			−0.444605	+	0.895727i	$0.646656\pi$
$878$	−2.01941e7	+	1.22879e7i	−0.884072	+	0.537947i
$879$	80964.7			0.00353447
$880$		0			0
$881$	2.74936e7			1.19341			0.596707	−	0.802459i	$-0.296475\pi$
$881$	2.74936e7			1.19341			0.596707	+	0.802459i	$0.296475\pi$
$882$	−2.52787e7	+	1.53818e7i	−1.09417	+	0.665787i
$883$	3.50971e7			1.51485			0.757425	−	0.652922i	$-0.226457\pi$
$883$	3.50971e7			1.51485			0.757425	+	0.652922i	$0.226457\pi$
$884$	−5.68472e7	−	2.94164e7i	−2.44669	−	1.26607i
$885$		0			0
$886$	2.99202e7	−	1.82061e7i	1.28050	−	0.779169i
$887$			1.77301e7i			0.756660i	0.925671	+	0.378330i	$0.123502\pi$
$887$			1.77301e7i			0.756660i	−0.925671	+	0.378330i	$0.876498\pi$
$888$	−54342.4	−	785005.i	−0.00231263	−	0.0334072i
$889$	−2.59346e6			−0.110059
$890$		0			0
$891$		−	2.11151e7i		−	0.891042i
$892$	−640618.	−	331497.i	−0.0269580	−	0.0139498i
$893$	3.60538e7			1.51294
$894$	371641.	+	610762.i	0.0155518	+	0.0255581i
$895$		0			0
$896$	−2.29630e7	−	2.81153e7i	−0.955562	−	1.16996i
$897$			669837.i			0.0277964i
$898$	−1.50590e7	+	9.16323e6i	−0.623169	+	0.379191i
$899$			2.00844e7i			0.828818i
$900$		0			0
$901$		−	5.26953e7i		−	2.16252i
$902$	4.00912e6	+	6.58866e6i	0.164071	+	0.269638i
$903$			388273.i			0.0158459i
$904$	−1.07213e7	+	742186.i	−0.436339	+	0.0302059i
$905$		0			0
$906$	−196680.	+	119677.i	−0.00796047	+	0.00484385i
$907$	1.04686e7			0.422542			0.211271	−	0.977428i	$-0.432240\pi$
$907$	1.04686e7			0.422542			0.211271	+	0.977428i	$0.432240\pi$
$908$	−2.21906e6	+	4.28833e6i	−0.0893211	+	0.172613i
$909$			1.27979e7i			0.513725i
$910$		0			0
$911$	−4.87147e7			−1.94475			−0.972376	−	0.233420i	$-0.925008\pi$
$911$	−4.87147e7			−1.94475			−0.972376	+	0.233420i	$0.925008\pi$
$912$	1.10324e6	−	780563.i	0.0439222	−	0.0310757i
$913$			3.72304e7i			1.47816i
$914$	−1.30764e7	−	2.14899e7i	−0.517752	−	0.850882i
$915$		0			0
$916$	2.05910e7	+	1.06551e7i	0.810847	+	0.419585i
$917$	−5.76445e6			−0.226378
$918$	−1.37432e6	−	2.25858e6i	−0.0538246	−	0.0884563i
$919$	2.63015e7			1.02729			0.513643	−	0.858004i	$-0.328296\pi$
$919$	2.63015e7			1.02729			0.513643	+	0.858004i	$0.328296\pi$
$920$		0			0
$921$	−1.26587e6			−0.0491747
$922$	−2.21124e7	−	3.63399e7i	−0.856659	−	1.40785i
$923$	−1.00579e6			−0.0388600
$924$	472718.	−	913526.i	0.0182147	−	0.0351998i
$925$		0			0
$926$	−1.27693e7	−	2.09854e7i	−0.489374	−	0.804246i
$927$			9.29911e6i			0.355420i
$928$	−8.91478e6	+	2.06009e7i	−0.339813	+	0.785264i
$929$	−4.91045e7			−1.86673			−0.933366	−	0.358925i	$-0.883143\pi$
$929$	−4.91045e7			−1.86673			−0.933366	+	0.358925i	$0.883143\pi$
$930$		0			0
$931$			6.21096e7i			2.34847i
$932$	−9.56519e6	−	4.94965e6i	−0.360706	−	0.186653i
$933$	−342472.			−0.0128802
$934$	−4.30234e6	+	2.61792e6i	−0.161376	+	0.0981951i
$935$		0			0
$936$	2.88897e6	+	4.17327e7i	0.107784	+	1.55699i
$937$		−	3.24439e7i		−	1.20721i	−0.797282	−	0.603607i	$-0.793729\pi$
$937$		−	3.24439e7i		−	1.20721i	0.797282	−	0.603607i	$-0.206271\pi$
$938$	4.31365e6	+	7.08912e6i	0.160080	+	0.263079i
$939$			1.30138e6i			0.0481660i
$940$		0			0
$941$		−	5.58017e6i		−	0.205435i	−0.994711	−	0.102717i	$-0.967246\pi$
$941$		−	5.58017e6i		−	0.205435i	0.994711	−	0.102717i	$-0.0327537\pi$
$942$	−606060.	+	368780.i	−0.0222530	+	0.0135407i
$943$			5.84573e6i			0.214072i
$944$	1.54261e7	−	1.09142e7i	0.563413	−	0.398624i
$945$		0			0
$946$	4.56542e6	+	7.50290e6i	0.165864	+	0.272585i
$947$	2.29821e7			0.832748			0.416374	−	0.909193i	$-0.363301\pi$
$947$	2.29821e7			0.832748			0.416374	+	0.909193i	$0.363301\pi$
$948$	601834.	−	1.16304e6i	0.0217498	−	0.0420315i
$949$		−	5.26231e7i		−	1.89675i
$950$		0			0
$951$	44633.7			0.00160034
$952$	5.14482e6	+	7.43195e7i	0.183983	+	2.65773i
$953$			2.98158e7i			1.06344i	0.846920	+	0.531721i	$0.178455\pi$
$953$			2.98158e7i			1.06344i	−0.846920	+	0.531721i	$0.821545\pi$
$954$	−2.94209e7	+	1.79023e7i	−1.04661	+	0.636850i
$955$		0			0
$956$	−4.86051e6	+	9.39292e6i	−0.172003	+	0.332396i
$957$	−636034.			−0.0224492
$958$	1.90066e7	−	1.15653e7i	0.669099	−	0.407138i
$959$	−4.44200e7			−1.55967
$960$		0			0
$961$	−1.76649e6			−0.0617026
$962$	4.36742e7	−	2.65752e7i	1.52156	−	0.925848i
$963$	−3.67659e7			−1.27756
$964$	1.32364e7	−	2.55793e7i	0.458750	−	0.886534i
$965$		0			0
$966$	666009.	−	405259.i	0.0229635	−	0.0139730i
$967$		−	4.13822e6i		−	0.142314i	−0.997465	−	0.0711570i	$-0.977331\pi$
$967$		−	4.13822e6i		−	0.142314i	0.997465	−	0.0711570i	$-0.0226691\pi$
$968$	406536.	+	5.87262e6i	0.0139447	+	0.201439i
$969$	−2.77346e6			−0.0948884
$970$		0			0
$971$			5.43256e7i			1.84908i	0.381081	+	0.924542i	$0.375552\pi$
$971$			5.43256e7i			1.84908i	−0.381081	+	0.924542i	$0.624448\pi$
$972$	−1.19134e6	+	2.30227e6i	−0.0404456	+	0.0781609i
$973$	−4.03558e7			−1.36655
$974$	1.15010e7	+	1.89009e7i	0.388452	+	0.638389i
$975$		0			0
$976$	1.46194e7	−	1.03434e7i	0.491251	−	0.347568i
$977$			2.00334e7i			0.671456i	0.941959	+	0.335728i	$0.108982\pi$
$977$			2.00334e7i			0.671456i	−0.941959	+	0.335728i	$0.891018\pi$
$978$	49824.0	−	30317.3i	0.00166568	−	0.00101355i
$979$		−	1.36726e7i		−	0.455927i
$980$		0			0
$981$		−	3.55493e7i		−	1.17939i
$982$	1.30364e7	+	2.14243e7i	0.431400	+	0.708971i
$983$		−	2.92947e6i		−	0.0966953i	−0.998831	−	0.0483476i	$-0.984604\pi$
$983$		−	2.92947e6i		−	0.0966953i	0.998831	−	0.0483476i	$-0.0153955\pi$
$984$	−21765.3	−	314410.i	−0.000716599	−	0.0103516i
$985$		0			0
$986$	3.93531e7	−	2.39459e7i	1.28910	−	0.784402i
$987$	−1.12132e6			−0.0366383
$988$	7.79825e7	+	4.03532e7i	2.54158	+	1.31518i
$989$			6.65688e6i			0.216411i
$990$		0			0
$991$	5.27467e7			1.70613			0.853064	−	0.521807i	$-0.174742\pi$
$991$	5.27467e7			1.70613			0.853064	+	0.521807i	$0.174742\pi$
$992$	2.75535e7	+	1.19234e7i	0.888990	+	0.384700i
$993$			1.24284e6i			0.0399984i
$994$	608513.	+	1.00004e6i	0.0195346	+	0.0321035i
$995$		0			0
$996$	699191.	−	1.35118e6i	0.0223330	−	0.0431585i
$997$	1.04084e7			0.331625			0.165812	−	0.986157i	$-0.446975\pi$
$997$	1.04084e7			0.331625			0.165812	+	0.986157i	$0.446975\pi$
$998$	−1.42361e7	−	2.33959e7i	−0.452444	−	0.743555i
$999$	2.11171e6			0.0669454

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.f.d.149.10		40
4.3	odd	2		800.6.f.d.49.21		40
5.2	odd	4		200.6.d.d.101.5	yes	20
5.3	odd	4		200.6.d.c.101.16	yes	20
5.4	even	2	inner	200.6.f.d.149.31		40
8.3	odd	2		800.6.f.d.49.19		40
8.5	even	2	inner	200.6.f.d.149.32		40
20.3	even	4		800.6.d.d.401.11		20
20.7	even	4		800.6.d.b.401.10		20
20.19	odd	2		800.6.f.d.49.20		40
40.3	even	4		800.6.d.d.401.10		20
40.13	odd	4		200.6.d.c.101.15	✓	20
40.19	odd	2		800.6.f.d.49.22		40
40.27	even	4		800.6.d.b.401.11		20
40.29	even	2	inner	200.6.f.d.149.9		40
40.37	odd	4		200.6.d.d.101.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.6.d.c.101.15	✓	20	40.13	odd	4
200.6.d.c.101.16	yes	20	5.3	odd	4
200.6.d.d.101.5	yes	20	5.2	odd	4
200.6.d.d.101.6	yes	20	40.37	odd	4
200.6.f.d.149.9		40	40.29	even	2	inner
200.6.f.d.149.10		40	1.1	even	1	trivial
200.6.f.d.149.31		40	5.4	even	2	inner
200.6.f.d.149.32		40	8.5	even	2	inner
800.6.d.b.401.10		20	20.7	even	4
800.6.d.b.401.11		20	40.27	even	4
800.6.d.d.401.10		20	40.3	even	4
800.6.d.d.401.11		20	20.3	even	4
800.6.f.d.49.19		40	8.3	odd	2
800.6.f.d.49.20		40	20.19	odd	2
800.6.f.d.49.21		40	4.3	odd	2
800.6.f.d.49.22		40	40.19	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)

\(f(q)\)	\(=\)	\(q+(-4.83252 + 2.94053i) q^{2} -0.457817 q^{3} +(14.7065 - 28.4204i) q^{4} +(2.21241 - 1.34622i) q^{6} -195.837i q^{7} +(12.5013 + 180.587i) q^{8} -242.790 q^{9} -358.513i q^{11} +(-6.73290 + 13.0113i) q^{12} -951.826 q^{13} +(575.865 + 946.387i) q^{14} +(-591.435 - 835.931i) q^{16} +2101.46i q^{17} +(1173.29 - 713.933i) q^{18} -2882.77i q^{19} +89.6574i q^{21} +(1054.22 + 1732.52i) q^{22} +1537.16i q^{23} +(-5.72328 - 82.6758i) q^{24} +(4599.72 - 2798.88i) q^{26} +222.403 q^{27} +(-5565.76 - 2880.09i) q^{28} +3875.11i q^{29} +5182.92 q^{31} +(5316.20 + 2300.52i) q^{32} +164.133i q^{33} +(-6179.41 - 10155.4i) q^{34} +(-3570.61 + 6900.19i) q^{36} +9494.97 q^{37} +(8476.87 + 13931.0i) q^{38} +435.762 q^{39} +3802.93 q^{41} +(-263.641 - 433.272i) q^{42} +4330.63 q^{43} +(-10189.1 - 5272.49i) q^{44} +(-4520.08 - 7428.38i) q^{46} +12506.7i q^{47} +(270.769 + 382.703i) q^{48} -21545.1 q^{49} -962.084i q^{51} +(-13998.1 + 27051.3i) q^{52} -25075.5 q^{53} +(-1074.77 + 653.983i) q^{54} +(35365.6 - 2448.21i) q^{56} +1319.78i q^{57} +(-11394.9 - 18726.5i) q^{58} +18453.8i q^{59} +17488.7i q^{61} +(-25046.6 + 15240.5i) q^{62} +47547.3i q^{63} +(-32455.4 + 4515.13i) q^{64} +(-482.639 - 793.177i) q^{66} +7490.73 q^{67} +(59724.3 + 30905.2i) q^{68} -703.739i q^{69} +1056.69 q^{71} +(-3035.19 - 43844.8i) q^{72} +55286.5i q^{73} +(-45884.7 + 27920.3i) q^{74} +(-81929.3 - 42395.6i) q^{76} -70210.1 q^{77} +(-2105.83 + 1281.37i) q^{78} -89387.0 q^{79} +58896.2 q^{81} +(-18377.8 + 11182.6i) q^{82} -103847. q^{83} +(2548.10 + 1318.55i) q^{84} +(-20927.8 + 12734.3i) q^{86} -1774.09i q^{87} +(64742.8 - 4481.86i) q^{88} +38137.1 q^{89} +186403. i q^{91} +(43686.8 + 22606.4i) q^{92} -2372.83 q^{93} +(-36776.3 - 60438.8i) q^{94} +(-2433.85 - 1053.22i) q^{96} -22739.9i q^{97} +(104117. - 63354.2i) q^{98} +87043.5i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9} + 848 q^{14} - 110 q^{16} - 18918 q^{24} + 18344 q^{26} + 14320 q^{31} + 19182 q^{34} + 29656 q^{36} - 44904 q^{39} - 11608 q^{41} + 23186 q^{44} - 75224 q^{46} - 125304 q^{49}+ \cdots + 115582 q^{96}+O(q^{100}) \) 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

Introduction

L-functions

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