LMFDB - Embedded newform 200.5.e.e.99.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,5,Mod(99,200)]

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([1, 1, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("200.99");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	200.e (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:	$20.6739926168$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.26
Character	$\chi$	$=$	200.99
Dual form			200.5.e.e.99.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.97910 + 2.66926i) q^{2} +4.51805i q^{3} +(1.75006 + 15.9040i) q^{4} +(-12.0599 + 13.4597i) q^{6} +50.0881 q^{7} +(-37.2384 + 52.0510i) q^{8} +60.5872 q^{9} +158.856 q^{11} +(-71.8551 + 7.90685i) q^{12} +97.3070 q^{13} +(149.217 + 133.698i) q^{14} +(-249.875 + 55.6658i) q^{16} +285.416i q^{17} +(180.495 + 161.723i) q^{18} -414.217 q^{19} +226.301i q^{21} +(473.249 + 424.030i) q^{22} -546.228 q^{23} +(-235.169 - 168.245i) q^{24} +(289.887 + 259.738i) q^{26} +639.698i q^{27} +(87.6570 + 796.601i) q^{28} -1162.39i q^{29} +369.759i q^{31} +(-892.988 - 501.147i) q^{32} +717.721i q^{33} +(-761.850 + 850.282i) q^{34} +(106.031 + 963.579i) q^{36} +1423.26 q^{37} +(-1233.99 - 1105.65i) q^{38} +439.638i q^{39} -2901.21 q^{41} +(-604.056 + 674.172i) q^{42} -905.493i q^{43} +(278.008 + 2526.45i) q^{44} +(-1627.27 - 1458.03i) q^{46} +3025.75 q^{47} +(-251.501 - 1128.95i) q^{48} +107.819 q^{49} -1289.52 q^{51} +(170.293 + 1547.57i) q^{52} +1605.79 q^{53} +(-1707.52 + 1905.72i) q^{54} +(-1865.20 + 2607.13i) q^{56} -1871.45i q^{57} +(3102.73 - 3462.88i) q^{58} +1809.93 q^{59} +1119.29i q^{61} +(-986.984 + 1101.55i) q^{62} +3034.70 q^{63} +(-1322.60 - 3876.59i) q^{64} +(-1915.79 + 2138.16i) q^{66} +3916.26i q^{67} +(-4539.25 + 499.494i) q^{68} -2467.89i q^{69} +4224.11i q^{71} +(-2256.17 + 3153.62i) q^{72} -4667.66i q^{73} +(4240.03 + 3799.06i) q^{74} +(-724.902 - 6587.70i) q^{76} +7956.81 q^{77} +(-1173.51 + 1309.73i) q^{78} -6812.31i q^{79} +2017.38 q^{81} +(-8642.99 - 7744.10i) q^{82} +3166.94i q^{83} +(-3599.09 + 396.039i) q^{84} +(2417.00 - 2697.55i) q^{86} +5251.74 q^{87} +(-5915.55 + 8268.62i) q^{88} -10721.2 q^{89} +4873.93 q^{91} +(-955.931 - 8687.22i) q^{92} -1670.59 q^{93} +(9014.02 + 8076.54i) q^{94} +(2264.21 - 4034.56i) q^{96} +10051.4i q^{97} +(321.203 + 287.797i) q^{98} +9624.66 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{4} + 168 q^{6} - 864 q^{9} + 384 q^{11} - 1944 q^{14} - 1648 q^{16} + 1408 q^{19} + 2512 q^{24} + 216 q^{26} - 1848 q^{34} - 4800 q^{36} - 4416 q^{41} - 7632 q^{44} - 1304 q^{46} + 4960 q^{49}+ \cdots - 5248 q^{99}+O(q^{100}) $ 32 * q - 16 * q^4 + 168 * q^6 - 864 * q^9 + 384 * q^11 - 1944 * q^14 - 1648 * q^16 + 1408 * q^19 + 2512 * q^24 + 216 * q^26 - 1848 * q^34 - 4800 * q^36 - 4416 * q^41 - 7632 * q^44 - 1304 * q^46 + 4960 * q^49 - 35584 * q^51 - 12976 * q^54 - 25104 * q^56 - 28032 * q^59 + 7424 * q^64 - 26624 * q^66 + 23016 * q^74 + 18624 * q^76 + 20768 * q^81 + 25040 * q^84 + 51528 * q^86 - 13632 * q^89 + 49152 * q^91 + 56776 * q^94 + 13568 * q^96 - 5248 * q^99

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 $

$2$	2.97910	+	2.66926i	0.744775	+	0.667316i
$2$	2.97910	+	2.66926i	0.744775	+	0.667316i
$3$			4.51805i			0.502006i	0.967986	+	0.251003i	$0.0807603\pi$
$3$			4.51805i			0.502006i	−0.967986	+	0.251003i	$0.919240\pi$
$4$	1.75006	+	15.9040i	0.109379	+	0.994000i
$5$		0			0
$5$		0			0
$6$	−12.0599	+	13.4597i	−0.334996	+	0.373881i
$7$	50.0881			1.02221			0.511103	−	0.859519i	$-0.329237\pi$
$7$	50.0881			1.02221			0.511103	+	0.859519i	$0.329237\pi$
$8$	−37.2384	+	52.0510i	−0.581850	+	0.813296i
$9$	60.5872			0.747990
$10$		0			0
$11$	158.856			1.31286			0.656431	−	0.754386i	$-0.272065\pi$
$11$	158.856			1.31286			0.656431	+	0.754386i	$0.272065\pi$
$12$	−71.8551	+	7.90685i	−0.498994	+	0.0549087i
$13$	97.3070			0.575781			0.287891	−	0.957663i	$-0.407046\pi$
$13$	97.3070			0.575781			0.287891	+	0.957663i	$0.407046\pi$
$14$	149.217	+	133.698i	0.761313	+	0.682135i
$15$		0			0
$16$	−249.875	+	55.6658i	−0.976073	+	0.217445i
$17$			285.416i			0.987598i	0.869576	+	0.493799i	$0.164392\pi$
$17$			285.416i			0.987598i	−0.869576	+	0.493799i	$0.835608\pi$
$18$	180.495	+	161.723i	0.557084	+	0.499146i
$19$	−414.217			−1.14741			−0.573707	−	0.819061i	$-0.694495\pi$
$19$	−414.217			−1.14741			−0.573707	+	0.819061i	$0.694495\pi$
$20$		0			0
$21$			226.301i			0.513153i
$22$	473.249	+	424.030i	0.977787	+	0.876094i
$23$	−546.228			−1.03257			−0.516284	−	0.856418i	$-0.672685\pi$
$23$	−546.228			−1.03257			−0.516284	+	0.856418i	$0.672685\pi$
$24$	−235.169	−	168.245i	−0.408279	−	0.292092i
$25$		0			0
$26$	289.887	+	259.738i	0.428827	+	0.384228i
$27$			639.698i			0.877501i
$28$	87.6570	+	796.601i	0.111807	+	1.01607i
$29$		−	1162.39i		−	1.38215i	−0.722781	−	0.691077i	$-0.757137\pi$
$29$		−	1162.39i		−	1.38215i	0.722781	−	0.691077i	$-0.242863\pi$
$30$		0			0
$31$			369.759i			0.384765i	0.981320	+	0.192382i	$0.0616214\pi$
$31$			369.759i			0.384765i	−0.981320	+	0.192382i	$0.938379\pi$
$32$	−892.988	−	501.147i	−0.872058	−	0.489402i
$33$			717.721i			0.659064i
$34$	−761.850	+	850.282i	−0.659040	+	0.735538i
$35$		0			0
$36$	106.031	+	963.579i	0.0818141	+	0.743502i
$37$	1423.26			1.03964			0.519818	−	0.854277i	$-0.326000\pi$
$37$	1423.26			1.03964			0.519818	+	0.854277i	$0.326000\pi$
$38$	−1233.99	−	1105.65i	−0.854565	−	0.765688i
$39$			439.638i			0.289045i
$40$		0			0
$41$	−2901.21			−1.72588			−0.862942	−	0.505303i	$-0.831381\pi$
$41$	−2901.21			−1.72588			−0.862942	+	0.505303i	$0.831381\pi$
$42$	−604.056	+	674.172i	−0.342435	+	0.382184i
$43$		−	905.493i		−	0.489720i	−0.969558	−	0.244860i	$-0.921258\pi$
$43$		−	905.493i		−	0.489720i	0.969558	−	0.244860i	$-0.0787421\pi$
$44$	278.008	+	2526.45i	0.143599	+	1.30499i
$45$		0			0
$46$	−1627.27	−	1458.03i	−0.769030	−	0.689049i
$47$	3025.75			1.36974			0.684870	−	0.728665i	$-0.259859\pi$
$47$	3025.75			1.36974			0.684870	+	0.728665i	$0.259859\pi$
$48$	−251.501	−	1128.95i	−0.109158	−	0.489994i
$49$	107.819			0.0449058
$50$		0			0
$51$	−1289.52			−0.495780
$52$	170.293	+	1547.57i	0.0629781	+	0.572327i
$53$	1605.79			0.571661			0.285830	−	0.958280i	$-0.407731\pi$
$53$	1605.79			0.571661			0.285830	+	0.958280i	$0.407731\pi$
$54$	−1707.52	+	1905.72i	−0.585571	+	0.653541i
$55$		0			0
$56$	−1865.20	+	2607.13i	−0.594771	+	0.831357i
$57$		−	1871.45i		−	0.576008i
$58$	3102.73	−	3462.88i	0.922333	−	1.02939i
$59$	1809.93			0.519946			0.259973	−	0.965616i	$-0.416286\pi$
$59$	1809.93			0.519946			0.259973	+	0.965616i	$0.416286\pi$
$60$		0			0
$61$			1119.29i			0.300804i	0.988625	+	0.150402i	$0.0480567\pi$
$61$			1119.29i			0.300804i	−0.988625	+	0.150402i	$0.951943\pi$
$62$	−986.984	+	1101.55i	−0.256760	+	0.286563i
$63$	3034.70			0.764600
$64$	−1322.60	−	3876.59i	−0.322901	−	0.946433i
$65$		0			0
$66$	−1915.79	+	2138.16i	−0.439804	+	0.490854i
$67$			3916.26i			0.872412i	0.899847	+	0.436206i	$0.143678\pi$
$67$			3916.26i			0.872412i	−0.899847	+	0.436206i	$0.856322\pi$
$68$	−4539.25	+	499.494i	−0.981672	+	0.108022i
$69$		−	2467.89i		−	0.518355i
$70$		0			0
$71$			4224.11i			0.837951i	0.907998	+	0.418975i	$0.137611\pi$
$71$			4224.11i			0.837951i	−0.907998	+	0.418975i	$0.862389\pi$
$72$	−2256.17	+	3153.62i	−0.435218	+	0.608338i
$73$		−	4667.66i		−	0.875897i	−0.899000	−	0.437949i	$-0.855705\pi$
$73$		−	4667.66i		−	0.875897i	0.899000	−	0.437949i	$-0.144295\pi$
$74$	4240.03	+	3799.06i	0.774294	+	0.693765i
$75$		0			0
$76$	−724.902	−	6587.70i	−0.125503	−	1.14053i
$77$	7956.81			1.34202
$78$	−1173.51	+	1309.73i	−0.192885	+	0.215274i
$79$		−	6812.31i		−	1.09154i	−0.837935	−	0.545771i	$-0.816237\pi$
$79$		−	6812.31i		−	1.09154i	0.837935	−	0.545771i	$-0.183763\pi$
$80$		0			0
$81$	2017.38			0.307480
$82$	−8642.99	−	7744.10i	−1.28539	−	1.15171i
$83$			3166.94i			0.459709i	0.973225	+	0.229855i	$0.0738251\pi$
$83$			3166.94i			0.459709i	−0.973225	+	0.229855i	$0.926175\pi$
$84$	−3599.09	+	396.039i	−0.510075	+	0.0561280i
$85$		0			0
$86$	2417.00	−	2697.55i	0.326798	−	0.364731i
$87$	5251.74			0.693849
$88$	−5915.55	+	8268.62i	−0.763889	+	1.06775i
$89$	−10721.2			−1.35351			−0.676756	−	0.736207i	$-0.736615\pi$
$89$	−10721.2			−1.35351			−0.676756	+	0.736207i	$0.736615\pi$
$90$		0			0
$91$	4873.93			0.588567
$92$	−955.931	−	8687.22i	−0.112941	−	1.02637i
$93$	−1670.59			−0.193154
$94$	9014.02	+	8076.54i	1.02015	+	0.914049i
$95$		0			0
$96$	2264.21	−	4034.56i	0.245682	−	0.437778i
$97$			10051.4i			1.06828i	0.845396	+	0.534140i	$0.179364\pi$
$97$			10051.4i			1.06828i	−0.845396	+	0.534140i	$0.820636\pi$
$98$	321.203	+	287.797i	0.0334447	+	0.0299663i
$99$	9624.66			0.982008
$100$		0			0
$101$		−	15016.7i		−	1.47208i	−0.676935	−	0.736042i	$-0.736692\pi$
$101$		−	15016.7i		−	1.47208i	0.676935	−	0.736042i	$-0.263308\pi$
$102$	−3841.62	−	3442.08i	−0.369244	−	0.330842i
$103$	13177.3			1.24209			0.621045	−	0.783775i	$-0.286708\pi$
$103$	13177.3			1.24209			0.621045	+	0.783775i	$0.286708\pi$
$104$	−3623.56	+	5064.92i	−0.335018	+	0.468281i
$105$		0			0
$106$	4783.82	+	4286.29i	0.425758	+	0.381478i
$107$		−	13284.8i		−	1.16035i	−0.814493	−	0.580173i	$-0.802985\pi$
$107$		−	13284.8i		−	1.16035i	0.814493	−	0.580173i	$-0.197015\pi$
$108$	−10173.8	+	1119.51i	−0.872236	+	0.0959798i
$109$		−	19211.6i		−	1.61700i	−0.588493	−	0.808502i	$-0.700279\pi$
$109$		−	19211.6i		−	1.61700i	0.588493	−	0.808502i	$-0.299721\pi$
$110$		0			0
$111$			6430.36i			0.521903i
$112$	−12515.7	+	2788.20i	−0.997748	+	0.222273i
$113$			20975.3i			1.64268i	0.570442	+	0.821338i	$0.306772\pi$
$113$			20975.3i			1.64268i	−0.570442	+	0.821338i	$0.693228\pi$
$114$	4995.40	−	5575.24i	0.384380	−	0.428996i
$115$		0			0
$116$	18486.7	−	2034.25i	1.37386	−	0.151178i
$117$	5895.56			0.430679
$118$	5391.96	+	4831.18i	0.387242	+	0.346968i
$119$			14295.9i			1.00953i
$120$		0			0
$121$	10594.3			0.723607
$122$	−2987.68	+	3334.47i	−0.200731	+	0.224031i
$123$		−	13107.8i		−	0.866403i
$124$	−5880.65	+	647.099i	−0.382456	+	0.0420850i
$125$		0			0
$126$	9040.67	+	8100.41i	0.569455	+	0.510230i
$127$	−10769.3			−0.667696			−0.333848	−	0.942627i	$-0.608347\pi$
$127$	−10769.3			−0.667696			−0.333848	+	0.942627i	$0.608347\pi$
$128$	6407.47	−	15079.1i	0.391081	−	0.920356i
$129$	4091.06			0.245842
$130$		0			0
$131$	15667.6			0.912975			0.456487	−	0.889730i	$-0.349107\pi$
$131$	15667.6			0.912975			0.456487	+	0.889730i	$0.349107\pi$
$132$	−11414.6	+	1256.05i	−0.655110	+	0.0720875i
$133$	−20747.3			−1.17289
$134$	−10453.5	+	11666.9i	−0.582175	+	0.649751i
$135$		0			0
$136$	−14856.2	−	10628.4i	−0.803210	−	0.574634i
$137$		−	25231.8i		−	1.34433i	−0.740399	−	0.672167i	$-0.765364\pi$
$137$		−	25231.8i		−	1.34433i	0.740399	−	0.672167i	$-0.234636\pi$
$138$	6587.44	−	7352.08i	0.345906	−	0.386058i
$139$	21388.1			1.10699			0.553494	−	0.832853i	$-0.313294\pi$
$139$	21388.1			1.10699			0.553494	+	0.832853i	$0.313294\pi$
$140$		0			0
$141$			13670.5i			0.687617i
$142$	−11275.3	+	12584.0i	−0.559178	+	0.624084i
$143$	15457.8			0.755922
$144$	−15139.2	+	3372.64i	−0.730093	+	0.162646i
$145$		0			0
$146$	12459.2	−	13905.4i	0.584500	−	0.652346i
$147$			487.131i			0.0225429i
$148$	2490.79	+	22635.5i	0.113714	+	1.03340i
$149$		−	40319.2i		−	1.81610i	−0.418863	−	0.908049i	$-0.637571\pi$
$149$		−	40319.2i		−	1.81610i	0.418863	−	0.908049i	$-0.362429\pi$
$150$		0			0
$151$		−	28388.2i		−	1.24504i	−0.782603	−	0.622521i	$-0.786109\pi$
$151$		−	28388.2i		−	1.24504i	0.782603	−	0.622521i	$-0.213891\pi$
$152$	15424.8	−	21560.4i	0.667623	−	0.933188i
$153$			17292.5i			0.738714i
$154$	23704.1	+	21238.8i	0.999500	+	0.895549i
$155$		0			0
$156$	−6992.01	+	769.392i	−0.287311	+	0.0316154i
$157$	4835.50			0.196174			0.0980872	−	0.995178i	$-0.468728\pi$
$157$	4835.50			0.196174			0.0980872	+	0.995178i	$0.468728\pi$
$158$	18183.9	−	20294.5i	0.728403	−	0.812952i
$159$			7255.06i			0.286977i
$160$		0			0
$161$	−27359.5			−1.05550
$162$	6009.96	+	5384.91i	0.229003	+	0.205186i
$163$		−	26938.1i		−	1.01389i	−0.861977	−	0.506947i	$-0.830774\pi$
$163$		−	26938.1i		−	1.01389i	0.861977	−	0.506947i	$-0.169226\pi$
$164$	−5077.28	−	46140.9i	−0.188775	−	1.71553i
$165$		0			0
$166$	−8453.39	+	9434.62i	−0.306771	+	0.342380i
$167$	24228.8			0.868760			0.434380	−	0.900730i	$-0.356968\pi$
$167$	24228.8			0.868760			0.434380	+	0.900730i	$0.356968\pi$
$168$	−11779.2	−	8427.07i	−0.417346	−	0.298578i
$169$	−19092.3			−0.668476
$170$		0			0
$171$	−25096.2			−0.858255
$172$	14401.0	−	1584.66i	0.486782	−	0.0535649i
$173$	−15853.9			−0.529716			−0.264858	−	0.964287i	$-0.585325\pi$
$173$	−15853.9			−0.529716			−0.264858	+	0.964287i	$0.585325\pi$
$174$	15645.5	+	14018.3i	0.516761	+	0.463017i
$175$		0			0
$176$	−39694.2	+	8842.87i	−1.28145	+	0.285475i
$177$			8177.36i			0.261016i
$178$	−31939.4	−	28617.6i	−1.00806	−	0.903220i
$179$	−5340.06			−0.166663			−0.0833316	−	0.996522i	$-0.526556\pi$
$179$	−5340.06			−0.166663			−0.0833316	+	0.996522i	$0.526556\pi$
$180$		0			0
$181$		−	16455.4i		−	0.502286i	−0.967950	−	0.251143i	$-0.919193\pi$
$181$		−	16455.4i		−	0.502286i	0.967950	−	0.251143i	$-0.0808065\pi$
$182$	14519.9	+	13009.8i	0.438350	+	0.392760i
$183$	−5057.01			−0.151005
$184$	20340.7	−	28431.7i	0.600799	−	0.839783i
$185$		0			0
$186$	−4976.85	−	4459.25i	−0.143856	−	0.128895i
$187$			45340.1i			1.29658i
$188$	5295.24	+	48121.6i	0.149820	+	1.36152i
$189$			32041.3i			0.896987i
$190$		0			0
$191$			36286.3i			0.994663i	0.867561	+	0.497331i	$0.165687\pi$
$191$			36286.3i			0.994663i	−0.867561	+	0.497331i	$0.834313\pi$
$192$	17514.6	−	5975.59i	0.475115	−	0.162098i
$193$		−	1934.56i		−	0.0519358i	−0.999663	−	0.0259679i	$-0.991733\pi$
$193$		−	1934.56i		−	0.0519358i	0.999663	−	0.0259679i	$-0.00826676\pi$
$194$	−26830.0	+	29944.2i	−0.712880	+	0.795628i
$195$		0			0
$196$	188.689	+	1714.75i	0.00491173	+	0.0446363i
$197$	−72587.7			−1.87038			−0.935192	−	0.354142i	$-0.884773\pi$
$197$	−72587.7			−1.87038			−0.935192	+	0.354142i	$0.884773\pi$
$198$	28672.8	+	25690.8i	0.731375	+	0.655310i
$199$			77717.2i			1.96251i	0.192723	+	0.981253i	$0.438268\pi$
$199$			77717.2i			1.96251i	−0.192723	+	0.981253i	$0.561732\pi$
$200$		0			0
$201$	−17693.9			−0.437956
$202$	40083.6	−	44736.3i	0.982346	−	1.09637i
$203$		−	58222.0i		−	1.41285i
$204$	−2256.74	−	20508.6i	−0.0542277	−	0.492805i
$205$		0			0
$206$	39256.6	+	35173.8i	0.925078	+	0.828867i
$207$	−33094.5			−0.772351
$208$	−24314.6	+	5416.68i	−0.562004	+	0.125201i
$209$	−65800.9			−1.50640
$210$		0			0
$211$	35806.9			0.804271			0.402135	−	0.915580i	$-0.368268\pi$
$211$	35806.9			0.804271			0.402135	+	0.915580i	$0.368268\pi$
$212$	2810.23	+	25538.6i	0.0625274	+	0.568231i
$213$	−19084.7			−0.420656
$214$	35460.6	−	39576.7i	0.774317	−	0.864196i
$215$		0			0
$216$	−33296.9	−	23821.3i	−0.713668	−	0.510574i
$217$			18520.5i			0.393309i
$218$	51280.9	−	57233.3i	1.07905	−	1.20430i
$219$	21088.7			0.439705
$220$		0			0
$221$			27773.0i			0.568640i
$222$	−17164.3	+	19156.7i	−0.348274	+	0.388700i
$223$	66087.5			1.32895			0.664477	−	0.747309i	$-0.268655\pi$
$223$	66087.5			1.32895			0.664477	+	0.747309i	$0.268655\pi$
$224$	−44728.1	−	25101.5i	−0.891424	−	0.500270i
$225$		0			0
$226$	−55988.7	+	62487.6i	−1.09618	+	1.22342i
$227$		−	6504.85i		−	0.126237i	−0.998006	−	0.0631184i	$-0.979895\pi$
$227$		−	6504.85i		−	0.126237i	0.998006	−	0.0631184i	$-0.0201046\pi$
$228$	29763.6	−	3275.15i	0.572552	−	0.0630030i
$229$		−	5180.89i		−	0.0987946i	−0.998779	−	0.0493973i	$-0.984270\pi$
$229$		−	5180.89i		−	0.0987946i	0.998779	−	0.0493973i	$-0.0157301\pi$
$230$		0			0
$231$			35949.3i			0.673700i
$232$	60503.6	+	43285.6i	1.12410	+	0.804206i
$233$			45055.0i			0.829910i	0.909842	+	0.414955i	$0.136203\pi$
$233$			45055.0i			0.829910i	−0.909842	+	0.414955i	$0.863797\pi$
$234$	17563.5	+	15736.8i	0.320759	+	0.287399i
$235$		0			0
$236$	3167.48	+	28785.1i	0.0568709	+	0.516826i
$237$	30778.4			0.547960
$238$	−38159.6	+	42589.0i	−0.673675	+	0.751871i
$239$			71745.9i			1.25603i	0.778200	+	0.628017i	$0.216133\pi$
$239$			71745.9i			1.25603i	−0.778200	+	0.628017i	$0.783867\pi$
$240$		0			0
$241$	−13213.7			−0.227504			−0.113752	−	0.993509i	$-0.536287\pi$
$241$	−13213.7			−0.227504			−0.113752	+	0.993509i	$0.536287\pi$
$242$	31561.6	+	28279.1i	0.538924	+	0.482875i
$243$			60930.2i			1.03186i
$244$	−17801.2	+	1958.82i	−0.298999	+	0.0329015i
$245$		0			0
$246$	34988.2	−	39049.5i	0.578165	−	0.645275i
$247$	−40306.2			−0.660660
$248$	−19246.3	−	13769.2i	−0.312928	−	0.223875i
$249$	−14308.4			−0.230777
$250$		0			0
$251$	−9203.91			−0.146091			−0.0730457	−	0.997329i	$-0.523272\pi$
$251$	−9203.91			−0.146091			−0.0730457	+	0.997329i	$0.523272\pi$
$252$	5310.90	+	48263.9i	0.0836309	+	0.760013i
$253$	−86771.8			−1.35562
$254$	−32082.7	−	28746.0i	−0.497283	−	0.445564i
$255$		0			0
$256$	59338.6	−	27818.9i	0.905436	−	0.424483i
$257$		−	32215.5i		−	0.487751i	−0.969807	−	0.243876i	$-0.921581\pi$
$257$		−	32215.5i		−	0.487751i	0.969807	−	0.243876i	$-0.0784189\pi$
$258$	12187.7	+	10920.1i	0.183097	+	0.164055i
$259$	71288.4			1.06272
$260$		0			0
$261$		−	70426.0i		−	1.03384i
$262$	46675.2	+	41820.9i	0.679960	+	0.609243i
$263$	−90235.1			−1.30456			−0.652280	−	0.757978i	$-0.726187\pi$
$263$	−90235.1			−1.30456			−0.652280	+	0.757978i	$0.726187\pi$
$264$	−37358.1	−	26726.8i	−0.536014	−	0.383476i
$265$		0			0
$266$	−61808.3	−	55380.1i	−0.873542	−	0.782691i
$267$		−	48438.8i		−	0.679471i
$268$	−62284.2	+	6853.68i	−0.867178	+	0.0954232i
$269$			10715.9i			0.148090i	0.997255	+	0.0740448i	$0.0235908\pi$
$269$			10715.9i			0.148090i	−0.997255	+	0.0740448i	$0.976409\pi$
$270$		0			0
$271$			40139.7i			0.546557i	0.961935	+	0.273278i	$0.0881080\pi$
$271$			40139.7i			0.546557i	−0.961935	+	0.273278i	$0.911892\pi$
$272$	−15887.9	−	71318.1i	−0.214748	−	0.963967i
$273$			22020.6i			0.295464i
$274$	67350.4	−	75168.1i	0.897096	−	1.00123i
$275$		0			0
$276$	39249.3	−	4318.94i	0.515245	−	0.0566969i
$277$	9941.96			0.129572			0.0647862	−	0.997899i	$-0.479363\pi$
$277$	9941.96			0.129572			0.0647862	+	0.997899i	$0.479363\pi$
$278$	63717.3	+	57090.5i	0.824456	+	0.738711i
$279$			22402.7i			0.287800i
$280$		0			0
$281$	3041.90			0.0385241			0.0192621	−	0.999814i	$-0.493868\pi$
$281$	3041.90			0.0385241			0.0192621	+	0.999814i	$0.493868\pi$
$282$	−36490.2	+	40725.8i	−0.458858	+	0.512120i
$283$			63175.8i			0.788821i	0.918934	+	0.394410i	$0.129051\pi$
$283$			63175.8i			0.788821i	−0.918934	+	0.394410i	$0.870949\pi$
$284$	−67180.2	+	7392.43i	−0.832923	+	0.0916538i
$285$		0			0
$286$	46050.4	+	41261.1i	0.562991	+	0.504439i
$287$	−145316.			−1.76421
$288$	−54103.6	−	30363.1i	−0.652291	−	0.366068i
$289$	2058.84			0.0246506
$290$		0			0
$291$	−45412.9			−0.536282
$292$	74234.4	−	8168.67i	0.870642	−	0.0958044i
$293$	50125.3			0.583877			0.291939	−	0.956437i	$-0.405700\pi$
$293$	50125.3			0.583877			0.291939	+	0.956437i	$0.405700\pi$
$294$	−1300.28	+	1451.21i	−0.0150433	+	0.0167894i
$295$		0			0
$296$	−52999.9	+	74082.1i	−0.604912	+	0.845531i
$297$			101620.i			1.15204i
$298$	107623.	−	120115.i	1.21191	−	1.35258i
$299$	−53151.9			−0.594533
$300$		0			0
$301$		−	45354.4i		−	0.500595i
$302$	75775.6	−	84571.3i	0.830837	−	0.927276i
$303$	67846.4			0.738995
$304$	103502.	−	23057.7i	1.11996	−	0.249499i
$305$		0			0
$306$	−46158.4	+	51516.2i	−0.492955	+	0.550175i
$307$		−	49587.2i		−	0.526129i	−0.964778	−	0.263065i	$-0.915267\pi$
$307$		−	49587.2i		−	0.526129i	0.964778	−	0.263065i	$-0.0847332\pi$
$308$	13924.9	+	126545.i	0.146788	+	1.33396i
$309$			59535.9i			0.623537i
$310$		0			0
$311$		−	122692.i		−	1.26852i	−0.773120	−	0.634260i	$-0.781305\pi$
$311$		−	122692.i		−	1.26852i	0.773120	−	0.634260i	$-0.218695\pi$
$312$	−22883.6	−	16371.4i	−0.235080	−	0.168181i
$313$		−	178246.i		−	1.81942i	−0.415248	−	0.909708i	$-0.636305\pi$
$313$		−	178246.i		−	1.81942i	0.415248	−	0.909708i	$-0.363695\pi$
$314$	14405.4	+	12907.2i	0.146106	+	0.130910i
$315$		0			0
$316$	108343.	−	11921.9i	1.08499	−	0.119391i
$317$	−9020.39			−0.0897650			−0.0448825	−	0.998992i	$-0.514291\pi$
$317$	−9020.39			−0.0897650			−0.0448825	+	0.998992i	$0.514291\pi$
$318$	−19365.7	+	21613.5i	−0.191504	+	0.213733i
$319$		−	184653.i		−	1.81458i
$320$		0			0
$321$	60021.4			0.582500
$322$	−81506.8	−	73029.8i	−0.786108	−	0.704350i
$323$		−	118224.i		−	1.13318i
$324$	3530.52	+	32084.3i	0.0336317	+	0.305635i
$325$		0			0
$326$	71905.0	−	80251.4i	0.676587	−	0.755122i
$327$	86799.1			0.811745
$328$	108036.	−	151011.i	1.00421	−	1.40365i
$329$	151554.			1.40016
$330$		0			0
$331$	70357.4			0.642175			0.321088	−	0.947049i	$-0.395952\pi$
$331$	70357.4			0.642175			0.321088	+	0.947049i	$0.395952\pi$
$332$	−50367.0	+	5542.32i	−0.456951	+	0.0502823i
$333$	86231.4			0.777637
$334$	72180.1	+	64673.2i	0.647030	+	0.579737i
$335$		0			0
$336$	−12597.2	−	56546.8i	−0.111582	−	0.500875i
$337$		−	148629.i		−	1.30871i	−0.756186	−	0.654356i	$-0.772940\pi$
$337$		−	148629.i		−	1.30871i	0.756186	−	0.654356i	$-0.227060\pi$
$338$	−56878.0	−	50962.5i	−0.497864	−	0.446085i
$339$	−94767.6			−0.824633
$340$		0			0
$341$			58738.5i			0.505143i
$342$	−74764.1	−	66988.5i	−0.639206	−	0.572727i
$343$	−114861.			−0.976303
$344$	47131.8	+	33719.1i	0.398288	+	0.284944i
$345$		0			0
$346$	−47230.2	−	42318.2i	−0.394519	−	0.353488i
$347$			94414.8i			0.784117i	0.919940	+	0.392059i	$0.128237\pi$
$347$			94414.8i			0.784117i	−0.919940	+	0.392059i	$0.871763\pi$
$348$	9190.85	+	83523.7i	0.0758922	+	0.689686i
$349$		−	72082.1i		−	0.591802i	−0.955219	−	0.295901i	$-0.904380\pi$
$349$		−	72082.1i		−	0.591802i	0.955219	−	0.295901i	$-0.0956198\pi$
$350$		0			0
$351$			62247.1i			0.505249i
$352$	−141857.	−	79610.4i	−1.14489	−	0.642517i
$353$			31879.4i			0.255836i	0.991785	+	0.127918i	$0.0408294\pi$
$353$			31879.4i			0.255836i	−0.991785	+	0.127918i	$0.959171\pi$
$354$	−21827.5	+	24361.2i	−0.174180	+	0.194398i
$355$		0			0
$356$	−18762.7	−	170509.i	−0.148045	−	1.34539i
$357$	−64589.8			−0.506789
$358$	−15908.6	−	14254.0i	−0.124127	−	0.111217i
$359$			34649.8i			0.268851i	0.990924	+	0.134426i	$0.0429189\pi$
$359$			34649.8i			0.268851i	−0.990924	+	0.134426i	$0.957081\pi$
$360$		0			0
$361$	41254.3			0.316559
$362$	43923.8	−	49022.3i	0.335184	−	0.374090i
$363$			47865.7i			0.363255i
$364$	8529.65	+	77514.9i	0.0643766	+	0.585036i
$365$		0			0
$366$	−15065.3	−	13498.5i	−0.112465	−	0.100768i
$367$	90234.4			0.669946			0.334973	−	0.942228i	$-0.391273\pi$
$367$	90234.4			0.669946			0.334973	+	0.942228i	$0.391273\pi$
$368$	136489.	−	30406.2i	1.00786	−	0.224526i
$369$	−175776.			−1.29094
$370$		0			0
$371$	80431.2			0.584355
$372$	−2923.63	−	26569.1i	−0.0211269	−	0.191995i
$373$	18934.5			0.136093			0.0680466	−	0.997682i	$-0.478323\pi$
$373$	18934.5			0.136093			0.0680466	+	0.997682i	$0.478323\pi$
$374$	−121025.	+	135073.i	−0.865229	+	0.965660i
$375$		0			0
$376$	−112674.	+	157493.i	−0.796983	+	1.11400i
$377$		−	113109.i		−	0.795818i
$378$	−85526.6	+	95454.1i	−0.598574	+	0.668053i
$379$	146129.			1.01732			0.508661	−	0.860967i	$-0.330141\pi$
$379$	146129.			1.01732			0.508661	+	0.860967i	$0.330141\pi$
$380$		0			0
$381$		−	48656.1i		−	0.335187i
$382$	−96857.7	+	108100.i	−0.663755	+	0.740800i
$383$	−63738.0			−0.434511			−0.217255	−	0.976115i	$-0.569710\pi$
$383$	−63738.0			−0.434511			−0.217255	+	0.976115i	$0.569710\pi$
$384$	68128.2	+	28949.3i	0.462024	+	0.196325i
$385$		0			0
$386$	5163.84	−	5763.23i	0.0346576	−	0.0386804i
$387$		−	54861.3i		−	0.366306i
$388$	−159858.	+	17590.6i	−1.06187	+	0.116847i
$389$		−	73071.2i		−	0.482889i	−0.970415	−	0.241444i	$-0.922379\pi$
$389$		−	73071.2i		−	0.482889i	0.970415	−	0.241444i	$-0.0776212\pi$
$390$		0			0
$391$		−	155902.i		−	1.01976i
$392$	−4015.00	+	5612.07i	−0.0261284	+	0.0365217i
$393$			70786.8i			0.458318i
$394$	−216246.	−	193756.i	−1.39301	−	1.24814i
$395$		0			0
$396$	16843.7	+	153071.i	0.107411	+	0.976116i
$397$	−17918.3			−0.113689			−0.0568443	−	0.998383i	$-0.518104\pi$
$397$	−17918.3			−0.113689			−0.0568443	+	0.998383i	$0.518104\pi$
$398$	−207448.	+	231527.i	−1.30961	+	1.46162i
$399$		−	93737.5i		−	0.588799i
$400$		0			0
$401$	−66769.8			−0.415232			−0.207616	−	0.978210i	$-0.566570\pi$
$401$	−66769.8			−0.415232			−0.207616	+	0.978210i	$0.566570\pi$
$402$	−52711.7	−	47229.6i	−0.326178	−	0.292255i
$403$			35980.1i			0.221540i
$404$	238826.	−	26280.1i	1.46325	−	0.161015i
$405$		0			0
$406$	155410.	−	173449.i	0.942815	−	1.05225i
$407$	226094.			1.36490
$408$	48019.8	−	67120.9i	0.288469	−	0.403216i
$409$	291009.			1.73964			0.869822	−	0.493366i	$-0.164234\pi$
$409$	291009.			1.73964			0.869822	+	0.493366i	$0.164234\pi$
$410$		0			0
$411$	113999.			0.674863
$412$	23061.1	+	209572.i	0.135858	+	1.23464i
$413$	90656.0			0.531492
$414$	−98591.6	−	88337.8i	−0.575227	−	0.515402i
$415$		0			0
$416$	−86894.0	−	48765.2i	−0.502115	−	0.281788i
$417$			96632.6i			0.555714i
$418$	−196027.	−	175640.i	−1.12193	−	1.00524i
$419$	−199703.			−1.13751			−0.568757	−	0.822506i	$-0.692576\pi$
$419$	−199703.			−1.13751			−0.568757	+	0.822506i	$0.692576\pi$
$420$		0			0
$421$			116540.i			0.657525i	0.944413	+	0.328763i	$0.106632\pi$
$421$			116540.i			0.657525i	−0.944413	+	0.328763i	$0.893368\pi$
$422$	106672.	+	95578.2i	0.599001	+	0.536703i
$423$	183322.			1.02455
$424$	−59797.2	+	83583.1i	−0.332621	+	0.464929i
$425$		0			0
$426$	−56855.3	−	50942.2i	−0.313294	−	0.280710i
$427$			56063.1i			0.307483i
$428$	211281.	−	23249.1i	1.15338	−	0.126917i
$429$			69839.3i			0.379477i
$430$		0			0
$431$			57475.2i			0.309404i	0.987961	+	0.154702i	$0.0494417\pi$
$431$			57475.2i			0.309404i	−0.987961	+	0.154702i	$0.950558\pi$
$432$	−35609.3	−	159844.i	−0.190808	−	0.856505i
$433$			78282.3i			0.417530i	0.977966	+	0.208765i	$0.0669444\pi$
$433$			78282.3i			0.417530i	−0.977966	+	0.208765i	$0.933056\pi$
$434$	−49436.2	+	55174.5i	−0.262461	+	0.292927i
$435$		0			0
$436$	305542.	−	33621.4i	1.60730	−	0.176866i
$437$	226257.			1.18478
$438$	62825.4	+	56291.3i	0.327481	+	0.293423i
$439$		−	248919.i		−	1.29160i	−0.763506	−	0.645801i	$-0.776524\pi$
$439$		−	248919.i		−	1.29160i	0.763506	−	0.645801i	$-0.223476\pi$
$440$		0			0
$441$	6532.44			0.0335891
$442$	−74133.4	+	82738.4i	−0.379463	+	0.423509i
$443$			305178.i			1.55505i	0.628849	+	0.777527i	$0.283526\pi$
$443$			305178.i			1.55505i	−0.628849	+	0.777527i	$0.716474\pi$
$444$	−102269.	+	11253.5i	−0.518771	+	0.0570850i
$445$		0			0
$446$	196881.	+	176405.i	0.989771	+	0.886832i
$447$	182164.			0.911692
$448$	−66246.7	−	194171.i	−0.330072	−	0.967449i
$449$	106754.			0.529529			0.264765	−	0.964313i	$-0.414706\pi$
$449$	106754.			0.529529			0.264765	+	0.964313i	$0.414706\pi$
$450$		0			0
$451$	−460876.			−2.26585
$452$	−333592.	+	36708.0i	−1.63282	+	0.179673i
$453$	128259.			0.625018
$454$	17363.2	−	19378.6i	0.0842398	−	0.0940179i
$455$		0			0
$456$	97410.8	+	69689.8i	0.468465	+	0.335150i
$457$			212418.i			1.01709i	0.861036	+	0.508543i	$0.169816\pi$
$457$			212418.i			1.01709i	−0.861036	+	0.508543i	$0.830184\pi$
$458$	13829.2	−	15434.4i	0.0659272	−	0.0735797i
$459$	−182580.			−0.866618
$460$		0			0
$461$			377548.i			1.77652i	0.459340	+	0.888261i	$0.348086\pi$
$461$			377548.i			1.77652i	−0.459340	+	0.888261i	$0.651914\pi$
$462$	−95958.2	+	107096.i	−0.449571	+	0.501754i
$463$	−64579.0			−0.301252			−0.150626	−	0.988591i	$-0.548129\pi$
$463$	−64579.0			−0.301252			−0.150626	+	0.988591i	$0.548129\pi$
$464$	64705.5	+	290452.i	0.300542	+	1.34908i
$465$		0			0
$466$	−120264.	+	134223.i	−0.553812	+	0.618096i
$467$			100635.i			0.461439i	0.973020	+	0.230720i	$0.0741080\pi$
$467$			100635.i			0.461439i	−0.973020	+	0.230720i	$0.925892\pi$
$468$	10317.6	+	93763.1i	0.0471070	+	0.428095i
$469$			196158.i			0.891785i
$470$		0			0
$471$			21847.0i			0.0984806i
$472$	−67398.9	+	94208.6i	−0.302530	+	0.422870i
$473$		−	143843.i		−	0.642936i
$474$	91691.8	+	82155.6i	0.408107	+	0.365662i
$475$		0			0
$476$	−227363.	+	25018.7i	−1.00347	+	0.110421i
$477$	97290.6			0.427597
$478$	−191509.	+	213738.i	−0.838171	+	0.935462i
$479$		−	188868.i		−	0.823168i	−0.911372	−	0.411584i	$-0.864976\pi$
$479$		−	188868.i		−	0.823168i	0.911372	−	0.411584i	$-0.135024\pi$
$480$		0			0
$481$	138493.			0.598603
$482$	−39364.8	−	35270.7i	−0.169439	−	0.151817i
$483$		−	123612.i		−	0.529866i
$484$	18540.7	+	168492.i	0.0791471	+	0.719266i
$485$		0			0
$486$	−162639.	+	181517.i	−0.688575	+	0.768501i
$487$	−105446.			−0.444604			−0.222302	−	0.974978i	$-0.571357\pi$
$487$	−105446.			−0.444604			−0.222302	+	0.974978i	$0.571357\pi$
$488$	−58260.1	−	41680.6i	−0.244642	−	0.175022i
$489$	121708.			0.508980
$490$		0			0
$491$	−248385.			−1.03030			−0.515149	−	0.857101i	$-0.672263\pi$
$491$	−248385.			−1.03030			−0.515149	+	0.857101i	$0.672263\pi$
$492$	208467.	−	22939.4i	0.861205	−	0.0947659i
$493$	331765.			1.36501
$494$	−120076.	−	107588.i	−0.492043	−	0.440869i
$495$		0			0
$496$	−20582.9	−	92393.4i	−0.0836650	−	0.375558i
$497$			211578.i			0.856558i
$498$	−42626.1	−	38192.8i	−0.171877	−	0.154001i
$499$	−194138.			−0.779668			−0.389834	−	0.920885i	$-0.627468\pi$
$499$	−194138.			−0.779668			−0.389834	+	0.920885i	$0.627468\pi$
$500$		0			0
$501$			109467.i			0.436122i
$502$	−27419.4	−	24567.7i	−0.108805	−	0.0974892i
$503$	−323180.			−1.27735			−0.638673	−	0.769478i	$-0.720516\pi$
$503$	−323180.			−1.27735			−0.638673	+	0.769478i	$0.720516\pi$
$504$	−113007.	+	157959.i	−0.444883	+	0.621847i
$505$		0			0
$506$	−258502.	−	231617.i	−1.00963	−	0.904626i
$507$		−	86260.2i		−	0.335579i
$508$	−18846.8	−	171275.i	−0.0730317	−	0.663690i
$509$			148319.i			0.572481i	0.958158	+	0.286240i	$0.0924056\pi$
$509$			148319.i			0.572481i	−0.958158	+	0.286240i	$0.907594\pi$
$510$		0			0
$511$		−	233794.i		−	0.895348i
$512$	251032.	+	75515.1i	0.957610	+	0.288067i
$513$		−	264974.i		−	1.00686i
$514$	85991.7	−	95973.1i	0.325484	−	0.363265i
$515$		0			0
$516$	7159.59	+	65064.3i	0.0268899	+	0.244367i
$517$	480660.			1.79828
$518$	212375.	+	190288.i	0.791488	+	0.709171i
$519$		−	71628.6i		−	0.265920i
$520$		0			0
$521$	88345.8			0.325470			0.162735	−	0.986670i	$-0.447969\pi$
$521$	88345.8			0.325470			0.162735	+	0.986670i	$0.447969\pi$
$522$	187986.	−	209806.i	0.689896	−	0.769976i
$523$		−	116531.i		−	0.426028i	−0.977049	−	0.213014i	$-0.931672\pi$
$523$		−	116531.i		−	0.426028i	0.977049	−	0.213014i	$-0.0683279\pi$
$524$	27419.1	+	249177.i	0.0998598	+	0.907497i
$525$		0			0
$526$	−268819.	−	240861.i	−0.971603	−	0.870554i
$527$	−105535.			−0.379993
$528$	−39952.5	−	179340.i	−0.143310	−	0.643295i
$529$	18524.3			0.0661959
$530$		0			0
$531$	109659.			0.388914
$532$	−36309.0	−	329965.i	−0.128289	−	1.16586i
$533$	−282308.			−0.993732
$534$	129296.	−	144304.i	0.453422	−	0.506053i
$535$		0			0
$536$	−203845.	−	145835.i	−0.709530	−	0.507613i
$537$		−	24126.7i		−	0.0836659i
$538$	−28603.6	+	31923.8i	−0.0988226	+	0.110293i
$539$	17127.7			0.0589551
$540$		0			0
$541$		−	468624.i		−	1.60114i	−0.599237	−	0.800572i	$-0.704529\pi$
$541$		−	468624.i		−	1.60114i	0.599237	−	0.800572i	$-0.295471\pi$
$542$	−107143.	+	119580.i	−0.364726	+	0.407062i
$543$	74346.4			0.252151
$544$	143035.	−	254873.i	0.483332	−	0.861243i
$545$		0			0
$546$	−58778.9	+	65601.7i	−0.197168	+	0.220054i
$547$		−	362111.i		−	1.21023i	−0.796139	−	0.605114i	$-0.793128\pi$
$547$		−	362111.i		−	1.21023i	0.796139	−	0.605114i	$-0.206872\pi$
$548$	401287.	−	44157.1i	1.33627	−	0.147041i
$549$			67814.7i			0.224998i
$550$		0			0
$551$			481482.i			1.58590i
$552$	128456.	+	91900.2i	0.421576	+	0.301605i
$553$		−	341216.i		−	1.11578i
$554$	29618.1	+	26537.7i	0.0965022	+	0.0864657i
$555$		0			0
$556$	37430.4	+	340157.i	0.121081	+	1.10035i
$557$	−498265.			−1.60602			−0.803008	−	0.595968i	$-0.796769\pi$
$557$	−498265.			−1.60602			−0.803008	+	0.595968i	$0.796769\pi$
$558$	−59798.6	+	66739.7i	−0.192054	+	0.214346i
$559$		−	88110.9i		−	0.281972i
$560$		0			0
$561$	−204849.			−0.650890
$562$	9062.13	+	8119.65i	0.0286918	+	0.0257078i
$563$			245981.i			0.776041i	0.921651	+	0.388021i	$0.126841\pi$
$563$			245981.i			0.776041i	−0.921651	+	0.388021i	$0.873159\pi$
$564$	−217416.	+	23924.2i	−0.683491	+	0.0752106i
$565$		0			0
$566$	−168633.	+	188207.i	−0.526393	+	0.587494i
$567$	101047.			0.314308
$568$	−219869.	−	157299.i	−0.681502	−	0.487561i
$569$	−385802.			−1.19163			−0.595813	−	0.803123i	$-0.703170\pi$
$569$	−385802.			−1.19163			−0.595813	+	0.803123i	$0.703170\pi$
$570$		0			0
$571$	−14171.0			−0.0434640			−0.0217320	−	0.999764i	$-0.506918\pi$
$571$	−14171.0			−0.0434640			−0.0217320	+	0.999764i	$0.506918\pi$
$572$	27052.1	+	245842.i	0.0826816	+	0.751386i
$573$	−163943.			−0.499326
$574$	−432911.	−	387887.i	−1.31394	−	1.17729i
$575$		0			0
$576$	−80132.9	−	234872.i	−0.241527	−	0.707922i
$577$		−	109691.i		−	0.329474i	−0.986338	−	0.164737i	$-0.947323\pi$
$577$		−	109691.i		−	0.329474i	0.986338	−	0.164737i	$-0.0526775\pi$
$578$	6133.50	+	5495.60i	0.0183591	+	0.0164497i
$579$	8740.42			0.0260720
$580$		0			0
$581$			158626.i			0.469918i
$582$	−135290.	−	121219.i	−0.399410	−	0.357870i
$583$	255091.			0.750512
$584$	242956.	+	173816.i	0.712364	+	0.509641i
$585$		0			0
$586$	149328.	+	133798.i	0.434857	+	0.389631i
$587$			377043.i			1.09425i	0.837052	+	0.547123i	$0.184277\pi$
$587$			377043.i			1.09425i	−0.837052	+	0.547123i	$0.815723\pi$
$588$	−7747.32	+	852.506i	−0.0224077	+	0.00246571i
$589$		−	153160.i		−	0.441485i
$590$		0			0
$591$		−	327955.i		−	0.938943i
$592$	−355637.	+	79227.0i	−1.01476	+	0.226063i
$593$			27615.5i			0.0785314i	0.999229	+	0.0392657i	$0.0125019\pi$
$593$			27615.5i			0.0785314i	−0.999229	+	0.0392657i	$0.987498\pi$
$594$	−271251.	+	302736.i	−0.768773	+	0.858009i
$595$		0			0
$596$	641237.	−	70560.9i	1.80520	−	0.198642i
$597$	−351130.			−0.985189
$598$	−158345.	−	141876.i	−0.442793	−	0.396742i
$599$		−	170000.i		−	0.473802i	−0.971534	−	0.236901i	$-0.923868\pi$
$599$		−	170000.i		−	0.473802i	0.971534	−	0.236901i	$-0.0761316\pi$
$600$		0			0
$601$	297213.			0.822846			0.411423	−	0.911445i	$-0.365032\pi$
$601$	297213.			0.822846			0.411423	+	0.911445i	$0.365032\pi$
$602$	121063.	−	135115.i	0.334055	−	0.372831i
$603$			237275.i			0.652556i
$604$	451486.	−	49681.0i	1.23757	−	0.136181i
$605$		0			0
$606$	202121.	+	181100.i	0.550385	+	0.493143i
$607$	−23984.9			−0.0650969			−0.0325485	−	0.999470i	$-0.510362\pi$
$607$	−23984.9			−0.0650969			−0.0325485	+	0.999470i	$0.510362\pi$
$608$	369890.	+	207584.i	1.00061	+	0.561547i
$609$	263050.			0.709257
$610$		0			0
$611$	294427.			0.788671
$612$	−275021.	+	30262.9i	−0.734281	+	0.0807994i
$613$	291516.			0.775785			0.387893	−	0.921705i	$-0.373203\pi$
$613$	291516.			0.775785			0.387893	+	0.921705i	$0.373203\pi$
$614$	132361.	−	147725.i	0.351094	−	0.391848i
$615$		0			0
$616$	−296299.	+	414160.i	−0.780852	+	1.09146i
$617$		−	111058.i		−	0.291729i	−0.989305	−	0.145864i	$-0.953404\pi$
$617$		−	111058.i		−	0.291729i	0.989305	−	0.145864i	$-0.0465963\pi$
$618$	−158917.	+	177363.i	−0.416096	+	0.464394i
$619$	300205.			0.783496			0.391748	−	0.920073i	$-0.371871\pi$
$619$	300205.			0.783496			0.391748	+	0.920073i	$0.371871\pi$
$620$		0			0
$621$		−	349421.i		−	0.906079i
$622$	327499.	−	365513.i	0.846503	−	0.944761i
$623$	−537003.			−1.38357
$624$	−24472.8	−	109854.i	−0.0628514	−	0.282129i
$625$		0			0
$626$	475787.	−	531014.i	1.21413	−	1.35506i
$627$		−	297292.i		−	0.756220i
$628$	8462.40	+	76903.8i	0.0214573	+	0.194997i
$629$			406221.i			1.02674i
$630$		0			0
$631$		−	150496.i		−	0.377979i	−0.981979	−	0.188989i	$-0.939479\pi$
$631$		−	150496.i		−	0.377979i	0.981979	−	0.188989i	$-0.0605212\pi$
$632$	354587.	+	253679.i	0.887746	+	0.635113i
$633$			161778.i			0.403749i
$634$	−26872.6	−	24077.8i	−0.0668547	−	0.0599016i
$635$		0			0
$636$	−115385.	+	12696.8i	−0.285255	+	0.0313891i
$637$	10491.5			0.0258559
$638$	492888.	−	550100.i	1.21090	−	1.35145i
$639$			255927.i			0.626779i
$640$		0			0
$641$	−341612.			−0.831414			−0.415707	−	0.909499i	$-0.636466\pi$
$641$	−341612.			−0.831414			−0.415707	+	0.909499i	$0.636466\pi$
$642$	178810.	+	160213.i	0.433831	+	0.388712i
$643$		−	89782.7i		−	0.217156i	−0.994088	−	0.108578i	$-0.965370\pi$
$643$		−	89782.7i		−	0.217156i	0.994088	−	0.108578i	$-0.0346297\pi$
$644$	−47880.8	−	435126.i	−0.115449	−	1.04916i
$645$		0			0
$646$	315571.	−	352201.i	0.756192	−	0.843967i
$647$	−569707.			−1.36095			−0.680477	−	0.732770i	$-0.738227\pi$
$647$	−569707.			−1.36095			−0.680477	+	0.732770i	$0.738227\pi$
$648$	−75123.8	+	105006.i	−0.178907	+	0.250072i
$649$	287519.			0.682617
$650$		0			0
$651$	−83676.7			−0.197443
$652$	428424.	−	47143.3i	1.00781	−	0.110898i
$653$	−258929.			−0.607233			−0.303616	−	0.952794i	$-0.598194\pi$
$653$	−258929.			−0.607233			−0.303616	+	0.952794i	$0.598194\pi$
$654$	258583.	+	231690.i	0.604567	+	0.541691i
$655$		0			0
$656$	724939.	−	161498.i	1.68459	−	0.375284i
$657$		−	282800.i		−	0.655163i
$658$	451495.	+	404539.i	1.04280	+	0.934347i
$659$	43971.3			0.101251			0.0506255	−	0.998718i	$-0.483879\pi$
$659$	43971.3			0.101251			0.0506255	+	0.998718i	$0.483879\pi$
$660$		0			0
$661$			216610.i			0.495765i	0.968790	+	0.247882i	$0.0797347\pi$
$661$			216610.i			0.495765i	−0.968790	+	0.247882i	$0.920265\pi$
$662$	209602.	+	187802.i	0.478276	+	0.428534i
$663$	−125480.			−0.285461
$664$	−164842.	−	117932.i	−0.373880	−	0.267482i
$665$		0			0
$666$	256892.	+	230174.i	0.579164	+	0.518930i
$667$			634931.i			1.42717i
$668$	42401.8	+	385336.i	0.0950237	+	0.863547i
$669$			298587.i			0.667142i
$670$		0			0
$671$			177806.i			0.394914i
$672$	113410.	−	202084.i	0.251138	−	0.447500i
$673$			614134.i			1.35592i	0.735101	+	0.677958i	$0.237135\pi$
$673$			614134.i			1.35592i	−0.735101	+	0.677958i	$0.762865\pi$
$674$	396730.	−	442781.i	0.873325	−	0.974696i
$675$		0			0
$676$	−33412.7	−	303645.i	−0.0731169	−	0.664465i
$677$	−710586.			−1.55038			−0.775192	−	0.631725i	$-0.782347\pi$
$677$	−710586.			−1.55038			−0.775192	+	0.631725i	$0.782347\pi$
$678$	−282322.	−	252960.i	−0.614165	−	0.550291i
$679$			503458.i			1.09200i
$680$		0			0
$681$	29389.3			0.0633716
$682$	−156789.	+	174988.i	−0.337090	+	0.376218i
$683$			187636.i			0.402231i	0.979568	+	0.201116i	$0.0644567\pi$
$683$			187636.i			0.402231i	−0.979568	+	0.201116i	$0.935543\pi$
$684$	−43919.8	−	399130.i	−0.0938747	−	0.853105i
$685$		0			0
$686$	−342183.	−	306595.i	−0.727126	−	0.651503i
$687$	23407.5			0.0495955
$688$	50405.0	+	226260.i	0.106487	+	0.478003i
$689$	156255.			0.329151
$690$		0			0
$691$	628570.			1.31643			0.658215	−	0.752830i	$-0.271312\pi$
$691$	628570.			1.31643			0.658215	+	0.752830i	$0.271312\pi$
$692$	−27745.2	−	252140.i	−0.0579396	−	0.526538i
$693$	482081.			1.00382
$694$	−252018.	+	281271.i	−0.523254	+	0.583991i
$695$		0			0
$696$	−195566.	+	273358.i	−0.403716	+	0.564305i
$697$		−	828051.i		−	1.70448i
$698$	192406.	−	214740.i	0.394919	−	0.440759i
$699$	−203561.			−0.416619
$700$		0			0
$701$		−	149078.i		−	0.303374i	−0.988429	−	0.151687i	$-0.951529\pi$
$701$		−	149078.i		−	0.303374i	0.988429	−	0.151687i	$-0.0484705\pi$
$702$	−166154.	+	185440.i	−0.337161	+	0.376296i
$703$	−589538.			−1.19289
$704$	−210104.	−	615821.i	−0.423925	−	1.24254i
$705$		0			0
$706$	−85094.7	+	94972.0i	−0.170723	+	0.190540i
$707$		−	752160.i		−	1.50477i
$708$	−130053.	+	14310.8i	−0.259450	+	0.0285495i
$709$		−	47510.9i		−	0.0945151i	−0.998883	−	0.0472575i	$-0.984952\pi$
$709$		−	47510.9i		−	0.0945151i	0.998883	−	0.0472575i	$-0.0150481\pi$
$710$		0			0
$711$		−	412739.i		−	0.816462i
$712$	399239.	−	558047.i	0.787541	−	1.10081i
$713$		−	201973.i		−	0.397296i
$714$	−192419.	−	172407.i	−0.377444	−	0.338189i
$715$		0			0
$716$	−9345.40	−	84928.3i	−0.0182294	−	0.165663i
$717$	−324152.			−0.630536
$718$	−92489.5	+	103225.i	−0.179409	+	0.200234i
$719$			843806.i			1.63224i	0.577880	+	0.816122i	$0.303880\pi$
$719$			843806.i			1.63224i	−0.577880	+	0.816122i	$0.696120\pi$
$720$		0			0
$721$	660028.			1.26967
$722$	122901.	+	110119.i	0.235765	+	0.211245i
$723$		−	59700.0i		−	0.114208i
$724$	261707.	−	28797.9i	0.499273	−	0.0549394i
$725$		0			0
$726$	−127766.	+	142597.i	−0.242406	+	0.270543i
$727$	−792065.			−1.49862			−0.749311	−	0.662218i	$-0.769615\pi$
$727$	−792065.			−1.49862			−0.749311	+	0.662218i	$0.769615\pi$
$728$	−181497.	+	253693.i	−0.342458	+	0.478680i
$729$	−111878.			−0.210519
$730$		0			0
$731$	258442.			0.483647
$732$	−8850.05	−	80426.7i	−0.0165167	−	0.150099i
$733$	4047.83			0.00753380			0.00376690	−	0.999993i	$-0.498801\pi$
$733$	4047.83			0.00753380			0.00376690	+	0.999993i	$0.498801\pi$
$734$	268817.	+	240859.i	0.498959	+	0.447066i
$735$		0			0
$736$	487775.	+	273741.i	0.900459	+	0.505340i
$737$			622123.i			1.14536i
$738$	−523655.	−	469193.i	−0.961463	−	0.861468i
$739$	−895023.			−1.63887			−0.819437	−	0.573170i	$-0.805714\pi$
$739$	−895023.			−1.63887			−0.819437	+	0.573170i	$0.805714\pi$
$740$		0			0
$741$		−	182105.i		−	0.331655i
$742$	239613.	+	214692.i	0.435213	+	0.389950i
$743$	616018.			1.11588			0.557938	−	0.829883i	$-0.311593\pi$
$743$	616018.			1.11588			0.557938	+	0.829883i	$0.311593\pi$
$744$	62210.1	−	86955.8i	0.112387	−	0.157091i
$745$		0			0
$746$	56407.8	+	50541.2i	0.101359	+	0.0908172i
$747$			191876.i			0.343858i
$748$	−721089.	+	79347.8i	−1.28880	+	0.141818i
$749$		−	665410.i		−	1.18611i
$750$		0			0
$751$		−	232448.i		−	0.412141i	−0.978537	−	0.206071i	$-0.933932\pi$
$751$		−	232448.i		−	0.412141i	0.978537	−	0.206071i	$-0.0660677\pi$
$752$	−756059.	+	168431.i	−1.33697	+	0.297842i
$753$		−	41583.7i		−	0.0733387i
$754$	301917.	−	336962.i	0.531062	−	0.592705i
$755$		0			0
$756$	−509585.	+	56074.1i	−0.891605	+	0.0981111i
$757$	431771.			0.753462			0.376731	−	0.926323i	$-0.377048\pi$
$757$	431771.			0.753462			0.376731	+	0.926323i	$0.377048\pi$
$758$	435333.	+	390057.i	0.757675	+	0.678875i
$759$		−	392040.i		−	0.680528i
$760$		0			0
$761$	−368807.			−0.636840			−0.318420	−	0.947950i	$-0.603152\pi$
$761$	−368807.			−0.636840			−0.318420	+	0.947950i	$0.603152\pi$
$762$	129876.	−	144951.i	0.223676	−	0.249639i
$763$		−	962274.i		−	1.65291i
$764$	−577097.	+	63503.1i	−0.988695	+	0.108795i
$765$		0			0
$766$	−189882.	−	170133.i	−0.323613	−	0.289956i
$767$	176119.			0.299375
$768$	125687.	+	268095.i	0.213093	+	0.454534i
$769$	−850748.			−1.43863			−0.719313	−	0.694686i	$-0.755544\pi$
$769$	−850748.			−1.43863			−0.719313	+	0.694686i	$0.755544\pi$
$770$		0			0
$771$	145551.			0.244854
$772$	30767.2	−	3385.58i	0.0516242	−	0.00568066i
$773$	−967445.			−1.61908			−0.809538	−	0.587067i	$-0.800282\pi$
$773$	−967445.			−1.61908			−0.809538	+	0.587067i	$0.800282\pi$
$774$	146439.	−	163437.i	0.244442	−	0.272816i
$775$		0			0
$776$	−523187.	−	374300.i	−0.868828	−	0.621578i
$777$			322085.i			0.533492i
$778$	195046.	−	217686.i	0.322240	−	0.359643i
$779$	1.20173e6			1.98030
$780$		0			0
$781$			671026.i			1.10011i
$782$	416144.	−	464448.i	0.680503	−	0.759493i
$783$	743580.			1.21284
$784$	−26941.2	+	6001.82i	−0.0438313	+	0.00976451i
$785$		0			0
$786$	−188949.	+	210881.i	−0.305843	+	0.341344i
$787$			434908.i			0.702178i	0.936342	+	0.351089i	$0.114189\pi$
$787$			434908.i			0.702178i	−0.936342	+	0.351089i	$0.885811\pi$
$788$	−127033.	−	1.15443e6i	−0.204580	−	1.85916i
$789$		−	407687.i		−	0.654896i
$790$		0			0
$791$			1.05061e6i			1.67915i
$792$	−358407.	+	500973.i	−0.571381	+	0.798664i
$793$			108915.i			0.173197i
$794$	−53380.5	−	47828.8i	−0.0846723	−	0.0758662i
$795$		0			0
$796$	−1.23601e6	+	136010.i	−1.95073	+	0.214656i
$797$	648541.			1.02099			0.510494	−	0.859881i	$-0.329463\pi$
$797$	648541.			1.02099			0.510494	+	0.859881i	$0.329463\pi$
$798$	250210.	−	279253.i	0.392915	−	0.438523i
$799$			863598.i			1.35275i
$800$		0			0
$801$	−649566.			−1.01241
$802$	−198914.	−	178226.i	−0.309255	−	0.277091i
$803$		−	741487.i		−	1.14993i
$804$	−30965.3	−	281403.i	−0.0479030	−	0.435328i
$805$		0			0
$806$	−96040.5	+	107188.i	−0.147837	+	0.164998i
$807$	−48415.0			−0.0743418
$808$	781636.	+	559199.i	1.19724	+	0.856532i
$809$	−338083.			−0.516567			−0.258284	−	0.966069i	$-0.583157\pi$
$809$	−338083.			−0.516567			−0.258284	+	0.966069i	$0.583157\pi$
$810$		0			0
$811$	−941405.			−1.43131			−0.715657	−	0.698452i	$-0.753872\pi$
$811$	−941405.			−1.43131			−0.715657	+	0.698452i	$0.753872\pi$
$812$	925962.	−	101892.i	1.40437	−	0.154535i
$813$	−181353.			−0.274375
$814$	673556.	+	603505.i	1.01654	+	0.910818i
$815$		0			0
$816$	322219.	−	71782.3i	0.483917	−	0.107805i
$817$			375070.i			0.561912i
$818$	866945.	+	776781.i	1.29564	+	1.16089i
$819$	295298.			0.440243
$820$		0			0
$821$		−	702066.i		−	1.04158i	−0.853686	−	0.520789i	$-0.825638\pi$
$821$		−	702066.i		−	1.04158i	0.853686	−	0.520789i	$-0.174362\pi$
$822$	339613.	+	304292.i	0.502621	+	0.450347i
$823$	736652.			1.08758			0.543792	−	0.839220i	$-0.316988\pi$
$823$	736652.			1.08758			0.543792	+	0.839220i	$0.316988\pi$
$824$	−490703.	+	685893.i	−0.722710	+	1.01019i
$825$		0			0
$826$	270073.	+	241985.i	0.395842	+	0.354673i
$827$		−	698186.i		−	1.02085i	−0.859923	−	0.510423i	$-0.829489\pi$
$827$		−	698186.i		−	1.02085i	0.859923	−	0.510423i	$-0.170511\pi$
$828$	−57917.2	−	526334.i	−0.0844786	−	0.767717i
$829$			609784.i			0.887293i	0.896202	+	0.443647i	$0.146315\pi$
$829$			609784.i			0.887293i	−0.896202	+	0.443647i	$0.853685\pi$
$830$		0			0
$831$			44918.3i			0.0650461i
$832$	−128699.	−	377219.i	−0.185921	−	0.544938i
$833$			30773.2i			0.0443488i
$834$	−257938.	+	287878.i	−0.370837	+	0.413882i
$835$		0			0
$836$	−115155.	−	1.04650e6i	−0.164767	−	1.49736i
$837$	−236534.			−0.337631
$838$	−594935.	−	533060.i	−0.847192	−	0.759081i
$839$			245795.i			0.349179i	0.984641	+	0.174590i	$0.0558599\pi$
$839$			245795.i			0.349179i	−0.984641	+	0.174590i	$0.944140\pi$
$840$		0			0
$841$	−643872.			−0.910348
$842$	−311077.	+	347185.i	−0.438777	+	0.489708i
$843$			13743.5i			0.0193393i
$844$	62664.2	+	569474.i	0.0879700	+	0.799445i
$845$		0			0
$846$	546135.	+	489335.i	0.763060	+	0.683700i
$847$	530650.			0.739676
$848$	−401247.	+	89387.9i	−0.557982	+	0.124304i
$849$	−285432.			−0.395992
$850$		0			0
$851$	−777425.			−1.07349
$852$	−33399.4	−	303524.i	−0.0460107	−	0.418132i
$853$	−482861.			−0.663627			−0.331813	−	0.943345i	$-0.607660\pi$
$853$	−482861.			−0.663627			−0.331813	+	0.943345i	$0.607660\pi$
$854$	−149647.	+	167018.i	−0.205189	+	0.229006i
$855$		0			0
$856$	691486.	+	494704.i	0.943705	+	0.675147i
$857$			275704.i			0.375389i	0.982227	+	0.187695i	$0.0601015\pi$
$857$			275704.i			0.375389i	−0.982227	+	0.187695i	$0.939898\pi$
$858$	−186420.	+	208058.i	−0.253231	+	0.282625i
$859$	874456.			1.18509			0.592546	−	0.805537i	$-0.298123\pi$
$859$	874456.			1.18509			0.592546	+	0.805537i	$0.298123\pi$
$860$		0			0
$861$		−	656546.i		−	0.885643i
$862$	−153416.	+	171224.i	−0.206470	+	0.230436i
$863$	−207383.			−0.278453			−0.139227	−	0.990261i	$-0.544462\pi$
$863$	−207383.			−0.278453			−0.139227	+	0.990261i	$0.544462\pi$
$864$	320583.	−	571243.i	0.429451	−	0.765232i
$865$		0			0
$866$	−208956.	+	233211.i	−0.278624	+	0.310966i
$867$			9301.96i			0.0123747i
$868$	−294550.	+	32412.0i	−0.390949	+	0.0430196i
$869$		−	1.08218e6i		−	1.43304i
$870$		0			0
$871$			381080.i			0.502319i
$872$	999984.	+	715410.i	1.31510	+	0.940854i
$873$			608989.i			0.799063i
$874$	674041.	+	603939.i	0.882396	+	0.790625i
$875$		0			0
$876$	36906.4	+	335395.i	0.0480943	+	0.437067i
$877$	287580.			0.373903			0.186952	−	0.982369i	$-0.440139\pi$
$877$	287580.			0.373903			0.186952	+	0.982369i	$0.440139\pi$
$878$	664430.	−	741553.i	0.861906	−	0.961952i
$879$			226468.i			0.293110i
$880$		0			0
$881$	72878.9			0.0938966			0.0469483	−	0.998897i	$-0.485050\pi$
$881$	72878.9			0.0938966			0.0469483	+	0.998897i	$0.485050\pi$
$882$	19460.8	+	17436.8i	0.0250163	+	0.0224145i
$883$			587119.i			0.753017i	0.926413	+	0.376509i	$0.122875\pi$
$883$			587119.i			0.753017i	−0.926413	+	0.376509i	$0.877125\pi$
$884$	−441701.	+	48604.3i	−0.565229	+	0.0621971i
$885$		0			0
$886$	−814601.	+	909155.i	−1.03771	+	1.15817i
$887$	525528.			0.667958			0.333979	−	0.942581i	$-0.391609\pi$
$887$	525528.			0.667958			0.333979	+	0.942581i	$0.391609\pi$
$888$	−334707.	−	239456.i	−0.424462	−	0.303669i
$889$	−539413.			−0.682523
$890$		0			0
$891$	320473.			0.403679
$892$	115657.	+	1.05106e6i	0.145359	+	1.32098i
$893$	−1.25332e6			−1.57166
$894$	542685.	+	486244.i	0.679005	+	0.608387i
$895$		0			0
$896$	320938.	−	755284.i	0.399765	−	0.940794i
$897$		−	240143.i		−	0.298459i
$898$	318030.	+	284954.i	0.394380	+	0.353363i
$899$	429804.			0.531804
$900$		0			0
$901$			458319.i			0.564571i
$902$	−1.37299e6	−	1.23020e6i	−1.68755	−	1.51204i
$903$	204914.			0.251302
$904$	−1.09179e6	−	781088.i	−1.33598	−	0.955791i
$905$		0			0
$906$	382097.	+	342358.i	0.465498	+	0.417085i
$907$			1.45695e6i			1.77105i	0.464596	+	0.885523i	$0.346199\pi$
$907$			1.45695e6i			1.77105i	−0.464596	+	0.885523i	$0.653801\pi$
$908$	103453.	−	11383.9i	0.125479	−	0.0138076i
$909$		−	909822.i		−	1.10111i
$910$		0			0
$911$			546104.i			0.658020i	0.944326	+	0.329010i	$0.106715\pi$
$911$			546104.i			0.658020i	−0.944326	+	0.329010i	$0.893285\pi$
$912$	104176.	+	467628.i	0.125250	+	0.562226i
$913$			503088.i			0.603535i
$914$	−566999.	+	632813.i	−0.678718	+	0.757500i
$915$		0			0
$916$	82396.9	−	9066.85i	0.0982019	−	0.0108060i
$917$	784758.			0.933248
$918$	−543924.	−	487354.i	−0.645435	−	0.578308i
$919$		−	1.30937e6i		−	1.55036i	−0.631740	−	0.775180i	$-0.717659\pi$
$919$		−	1.30937e6i		−	1.55036i	0.631740	−	0.775180i	$-0.282341\pi$
$920$		0			0
$921$	224037.			0.264120
$922$	−1.00778e6	+	1.12475e6i	−1.18550	+	1.32311i
$923$			411036.i			0.482476i
$924$	−571738.	+	62913.3i	−0.669658	+	0.0736883i
$925$		0			0
$926$	−192387.	−	172378.i	−0.224364	−	0.201030i
$927$	798378.			0.929072
$928$	−582529.	+	1.03800e6i	−0.676428	+	1.20532i
$929$	−731556.			−0.847649			−0.423824	−	0.905744i	$-0.639313\pi$
$929$	−731556.			−0.847649			−0.423824	+	0.905744i	$0.639313\pi$
$930$		0			0
$931$	−44660.3			−0.0515255
$932$	−716554.	+	78848.8i	−0.824930	+	0.0907743i
$933$	554331.			0.636804
$934$	−268621.	+	299801.i	−0.307926	+	0.343668i
$935$		0			0
$936$	−219541.	+	306870.i	−0.250590	+	0.350269i
$937$			368844.i			0.420111i	0.977690	+	0.210055i	$0.0673644\pi$
$937$			368844.i			0.420111i	−0.977690	+	0.210055i	$0.932636\pi$
$938$	−523598.	+	584374.i	−0.595103	+	0.664179i
$939$	805327.			0.913358
$940$		0			0
$941$			1.05710e6i			1.19381i	0.802310	+	0.596907i	$0.203604\pi$
$941$			1.05710e6i			1.19381i	−0.802310	+	0.596907i	$0.796396\pi$
$942$	−58315.5	+	65084.5i	−0.0657177	+	0.0733459i
$943$	1.58472e6			1.78209
$944$	−452256.	+	100751.i	−0.507505	+	0.113059i
$945$		0			0
$946$	383956.	−	428523.i	0.429041	−	0.478842i
$947$		−	1.05246e6i		−	1.17356i	−0.809748	−	0.586778i	$-0.800396\pi$
$947$		−	1.05246e6i		−	1.17356i	0.809748	−	0.586778i	$-0.199604\pi$
$948$	53863.9	+	489499.i	0.0599351	+	0.544672i
$949$		−	454196.i		−	0.504325i
$950$		0			0
$951$		−	40754.6i		−	0.0450625i
$952$	−744117.	−	532358.i	−0.821046	−	0.587394i
$953$		−	65088.8i		−	0.0716672i	−0.999358	−	0.0358336i	$-0.988591\pi$
$953$		−	65088.8i		−	0.0716672i	0.999358	−	0.0358336i	$-0.0114086\pi$
$954$	289838.	+	259694.i	0.318463	+	0.285342i
$955$		0			0
$956$	−1.14105e6	+	125559.i	−1.24850	+	0.137383i
$957$	834273.			0.910928
$958$	504140.	−	562658.i	0.549313	−	0.613074i
$959$		−	1.26381e6i		−	1.37419i
$960$		0			0
$961$	786799.			0.851956
$962$	412585.	+	369675.i	0.445824	+	0.399457i
$963$		−	804889.i		−	0.867927i
$964$	−23124.6	−	210150.i	−0.0248840	−	0.226139i
$965$		0			0
$966$	329953.	−	368252.i	0.353588	−	0.394630i
$967$	481804.			0.515250			0.257625	−	0.966245i	$-0.417060\pi$
$967$	481804.			0.515250			0.257625	+	0.966245i	$0.417060\pi$
$968$	−394516.	+	551445.i	−0.421031	+	0.588507i
$969$	534142.			0.568865
$970$		0			0
$971$	439500.			0.466144			0.233072	−	0.972459i	$-0.425122\pi$
$971$	439500.			0.466144			0.233072	+	0.972459i	$0.425122\pi$
$972$	−969033.	+	106631.i	−1.02567	+	0.112863i
$973$	1.07129e6			1.13157
$974$	−314135.	−	281464.i	−0.331130	−	0.296691i
$975$		0			0
$976$	−62306.2	−	279682.i	−0.0654081	−	0.293606i
$977$		−	1.37613e6i		−	1.44169i	−0.693098	−	0.720844i	$-0.743755\pi$
$977$		−	1.37613e6i		−	1.44169i	0.693098	−	0.720844i	$-0.256245\pi$
$978$	362580.	+	324870.i	0.379076	+	0.339651i
$979$	−1.70313e6			−1.77697
$980$		0			0
$981$		−	1.16398e6i		−	1.20950i
$982$	−739964.	−	663005.i	−0.767339	−	0.687534i
$983$	−767551.			−0.794328			−0.397164	−	0.917748i	$-0.630006\pi$
$983$	−767551.			−0.794328			−0.397164	+	0.917748i	$0.630006\pi$
$984$	682274.	+	488114.i	0.704643	+	0.504117i
$985$		0			0
$986$	988360.	+	885568.i	1.01663	+	0.910894i
$987$			684730.i			0.702887i
$988$	−70538.1	−	641030.i	−0.0722620	−	0.656696i
$989$			494606.i			0.505670i
$990$		0			0
$991$		−	1.85016e6i		−	1.88392i	−0.335722	−	0.941961i	$-0.608980\pi$
$991$		−	1.85016e6i		−	1.88392i	0.335722	−	0.941961i	$-0.391020\pi$
$992$	185304.	−	330190.i	0.188305	−	0.335537i
$993$			317878.i			0.322376i
$994$	−564757.	+	630311.i	−0.571595	+	0.637943i
$995$		0			0
$996$	−25040.5	−	227561.i	−0.0252420	−	0.229392i
$997$	−337598.			−0.339633			−0.169816	−	0.985476i	$-0.554317\pi$
$997$	−337598.			−0.339633			−0.169816	+	0.985476i	$0.554317\pi$
$998$	−578356.	−	518206.i	−0.580677	−	0.520285i
$999$			910457.i			0.912281i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.5.e.e.99.26		32
4.3	odd	2		800.5.e.e.399.11		32
5.2	odd	4		200.5.g.h.51.4		16
5.3	odd	4		40.5.g.a.11.13	✓	16
5.4	even	2	inner	200.5.e.e.99.7		32
8.3	odd	2	inner	200.5.e.e.99.8		32
8.5	even	2		800.5.e.e.399.21		32
15.8	even	4		360.5.g.a.91.4		16
20.3	even	4		160.5.g.a.111.9		16
20.7	even	4		800.5.g.h.751.7		16
20.19	odd	2		800.5.e.e.399.22		32
40.3	even	4		40.5.g.a.11.14	yes	16
40.13	odd	4		160.5.g.a.111.10		16
40.19	odd	2	inner	200.5.e.e.99.25		32
40.27	even	4		200.5.g.h.51.3		16
40.29	even	2		800.5.e.e.399.12		32
40.37	odd	4		800.5.g.h.751.8		16
60.23	odd	4		1440.5.g.a.271.15		16
120.53	even	4		1440.5.g.a.271.2		16
120.83	odd	4		360.5.g.a.91.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.5.g.a.11.13	✓	16	5.3	odd	4
40.5.g.a.11.14	yes	16	40.3	even	4
160.5.g.a.111.9		16	20.3	even	4
160.5.g.a.111.10		16	40.13	odd	4
200.5.e.e.99.7		32	5.4	even	2	inner
200.5.e.e.99.8		32	8.3	odd	2	inner
200.5.e.e.99.25		32	40.19	odd	2	inner
200.5.e.e.99.26		32	1.1	even	1	trivial
200.5.g.h.51.3		16	40.27	even	4
200.5.g.h.51.4		16	5.2	odd	4
360.5.g.a.91.3		16	120.83	odd	4
360.5.g.a.91.4		16	15.8	even	4
800.5.e.e.399.11		32	4.3	odd	2
800.5.e.e.399.12		32	40.29	even	2
800.5.e.e.399.21		32	8.5	even	2
800.5.e.e.399.22		32	20.19	odd	2
800.5.g.h.751.7		16	20.7	even	4
800.5.g.h.751.8		16	40.37	odd	4
1440.5.g.a.271.2		16	120.53	even	4
1440.5.g.a.271.15		16	60.23	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	200.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.97910 + 2.66926i) q^{2} +4.51805i q^{3} +(1.75006 + 15.9040i) q^{4} +(-12.0599 + 13.4597i) q^{6} +50.0881 q^{7} +(-37.2384 + 52.0510i) q^{8} +60.5872 q^{9} +158.856 q^{11} +(-71.8551 + 7.90685i) q^{12} +97.3070 q^{13} +(149.217 + 133.698i) q^{14} +(-249.875 + 55.6658i) q^{16} +285.416i q^{17} +(180.495 + 161.723i) q^{18} -414.217 q^{19} +226.301i q^{21} +(473.249 + 424.030i) q^{22} -546.228 q^{23} +(-235.169 - 168.245i) q^{24} +(289.887 + 259.738i) q^{26} +639.698i q^{27} +(87.6570 + 796.601i) q^{28} -1162.39i q^{29} +369.759i q^{31} +(-892.988 - 501.147i) q^{32} +717.721i q^{33} +(-761.850 + 850.282i) q^{34} +(106.031 + 963.579i) q^{36} +1423.26 q^{37} +(-1233.99 - 1105.65i) q^{38} +439.638i q^{39} -2901.21 q^{41} +(-604.056 + 674.172i) q^{42} -905.493i q^{43} +(278.008 + 2526.45i) q^{44} +(-1627.27 - 1458.03i) q^{46} +3025.75 q^{47} +(-251.501 - 1128.95i) q^{48} +107.819 q^{49} -1289.52 q^{51} +(170.293 + 1547.57i) q^{52} +1605.79 q^{53} +(-1707.52 + 1905.72i) q^{54} +(-1865.20 + 2607.13i) q^{56} -1871.45i q^{57} +(3102.73 - 3462.88i) q^{58} +1809.93 q^{59} +1119.29i q^{61} +(-986.984 + 1101.55i) q^{62} +3034.70 q^{63} +(-1322.60 - 3876.59i) q^{64} +(-1915.79 + 2138.16i) q^{66} +3916.26i q^{67} +(-4539.25 + 499.494i) q^{68} -2467.89i q^{69} +4224.11i q^{71} +(-2256.17 + 3153.62i) q^{72} -4667.66i q^{73} +(4240.03 + 3799.06i) q^{74} +(-724.902 - 6587.70i) q^{76} +7956.81 q^{77} +(-1173.51 + 1309.73i) q^{78} -6812.31i q^{79} +2017.38 q^{81} +(-8642.99 - 7744.10i) q^{82} +3166.94i q^{83} +(-3599.09 + 396.039i) q^{84} +(2417.00 - 2697.55i) q^{86} +5251.74 q^{87} +(-5915.55 + 8268.62i) q^{88} -10721.2 q^{89} +4873.93 q^{91} +(-955.931 - 8687.22i) q^{92} -1670.59 q^{93} +(9014.02 + 8076.54i) q^{94} +(2264.21 - 4034.56i) q^{96} +10051.4i q^{97} +(321.203 + 287.797i) q^{98} +9624.66 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{4} + 168 q^{6} - 864 q^{9} + 384 q^{11} - 1944 q^{14} - 1648 q^{16} + 1408 q^{19} + 2512 q^{24} + 216 q^{26} - 1848 q^{34} - 4800 q^{36} - 4416 q^{41} - 7632 q^{44} - 1304 q^{46} + 4960 q^{49}+ \cdots - 5248 q^{99}+O(q^{100}) \) 32 * q - 16 * q^4 + 168 * q^6 - 864 * q^9 + 384 * q^11 - 1944 * q^14 - 1648 * q^16 + 1408 * q^19 + 2512 * q^24 + 216 * q^26 - 1848 * q^34 - 4800 * q^36 - 4416 * q^41 - 7632 * q^44 - 1304 * q^46 + 4960 * q^49 - 35584 * q^51 - 12976 * q^54 - 25104 * q^56 - 28032 * q^59 + 7424 * q^64 - 26624 * q^66 + 23016 * q^74 + 18624 * q^76 + 20768 * q^81 + 25040 * q^84 + 51528 * q^86 - 13632 * q^89 + 49152 * q^91 + 56776 * q^94 + 13568 * q^96 - 5248 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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