LMFDB - Embedded newform 160.6.o.a.47.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,6,Mod(47,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 1]))

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

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

chi := DirichletCharacter("160.47");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	160.o (of order $4$, degree $2$, 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:	$25.6614111701$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.8
Character	$\chi$	$=$	160.47
Dual form			160.6.o.a.143.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.6033 + 10.6033i) q^{3} +(-15.3629 + 53.7493i) q^{5} +(-159.941 + 159.941i) q^{7} +18.1393i q^{9} +O(q^{10})$	\(q+(-10.6033 + 10.6033i) q^{3} +(-15.3629 + 53.7493i) q^{5} +(-159.941 + 159.941i) q^{7} +18.1393i q^{9} -516.314 q^{11} +(147.686 + 147.686i) q^{13} +(-407.023 - 732.818i) q^{15} +(890.046 + 890.046i) q^{17} +1009.77i q^{19} -3391.81i q^{21} +(1847.88 + 1847.88i) q^{23} +(-2652.97 - 1651.48i) q^{25} +(-2768.94 - 2768.94i) q^{27} +1847.15 q^{29} +4973.59i q^{31} +(5474.64 - 5474.64i) q^{33} +(-6139.55 - 11053.9i) q^{35} +(2819.25 - 2819.25i) q^{37} -3131.92 q^{39} -12472.0 q^{41} +(11883.2 - 11883.2i) q^{43} +(-974.975 - 278.672i) q^{45} +(11919.6 - 11919.6i) q^{47} -34355.2i q^{49} -18874.9 q^{51} +(10766.7 + 10766.7i) q^{53} +(7932.06 - 27751.5i) q^{55} +(-10706.9 - 10706.9i) q^{57} +8271.39i q^{59} +28492.9i q^{61} +(-2901.22 - 2901.22i) q^{63} +(-10206.9 + 5669.13i) q^{65} +(-9257.64 - 9257.64i) q^{67} -39187.3 q^{69} +18565.5i q^{71} +(-58309.9 + 58309.9i) q^{73} +(45641.4 - 10619.0i) q^{75} +(82579.7 - 82579.7i) q^{77} +10581.9 q^{79} +54312.1 q^{81} +(-12642.5 + 12642.5i) q^{83} +(-61513.0 + 34165.7i) q^{85} +(-19585.9 + 19585.9i) q^{87} -65996.0i q^{89} -47242.0 q^{91} +(-52736.5 - 52736.5i) q^{93} +(-54274.3 - 15512.9i) q^{95} +(14591.8 + 14591.8i) q^{97} -9365.58i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{3}+O(q^{10}) $ 56 * q + 4 * q^3	$ 56 q + 4 q^{3} + 8 q^{11} - 408 q^{17} - 3120 q^{25} - 968 q^{27} - 976 q^{33} + 4780 q^{35} - 8 q^{41} - 1308 q^{43} - 20872 q^{51} + 968 q^{57} + 17680 q^{65} - 89252 q^{67} - 25184 q^{73} + 127740 q^{75} - 67792 q^{81} + 126444 q^{83} - 329432 q^{91} + 212576 q^{97}+O(q^{100}) $ 56 * q + 4 * q^3 + 8 * q^11 - 408 * q^17 - 3120 * q^25 - 968 * q^27 - 976 * q^33 + 4780 * q^35 - 8 * q^41 - 1308 * q^43 - 20872 * q^51 + 968 * q^57 + 17680 * q^65 - 89252 * q^67 - 25184 * q^73 + 127740 * q^75 - 67792 * q^81 + 126444 * q^83 - 329432 * q^91 + 212576 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−10.6033	+	10.6033i	−0.680203	+	0.680203i	−0.960046	−	0.279843i	$-0.909718\pi$
$3$	−10.6033	+	10.6033i	−0.680203	+	0.680203i	0.279843	+	0.960046i	$0.409718\pi$
$4$		0			0
$5$	−15.3629	+	53.7493i	−0.274819	+	0.961496i
$5$	−15.3629	+	53.7493i	−0.274819	+	0.961496i
$6$		0			0
$7$	−159.941	+	159.941i	−1.23371	+	1.23371i	−0.271187	+	0.962527i	$0.587416\pi$
$7$	−159.941	+	159.941i	−1.23371	+	1.23371i	−0.962527	+	0.271187i	$0.912584\pi$
$8$		0			0
$9$			18.1393i			0.0746474i
$10$		0			0
$11$	−516.314			−1.28657			−0.643283	−	0.765628i	$-0.722428\pi$
$11$	−516.314			−1.28657			−0.643283	+	0.765628i	$0.722428\pi$
$12$		0			0
$13$	147.686	+	147.686i	0.242371	+	0.242371i	0.817830	−	0.575459i	$-0.195177\pi$
$13$	147.686	+	147.686i	0.242371	+	0.242371i	−0.575459	+	0.817830i	$0.695177\pi$
$14$		0			0
$15$	−407.023	−	732.818i	−0.467080	−	0.840945i
$16$		0			0
$17$	890.046	+	890.046i	0.746948	+	0.746948i	0.973905	−	0.226957i	$-0.0728777\pi$
$17$	890.046	+	890.046i	0.746948	+	0.746948i	−0.226957	+	0.973905i	$0.572878\pi$
$18$		0			0
$19$			1009.77i			0.641709i	0.947128	+	0.320854i	$0.103970\pi$
$19$			1009.77i			0.641709i	−0.947128	+	0.320854i	$0.896030\pi$
$20$		0			0
$21$		−	3391.81i		−	1.67835i
$22$		0			0
$23$	1847.88	+	1847.88i	0.728374	+	0.728374i	0.970296	−	0.241922i	$-0.0777778\pi$
$23$	1847.88	+	1847.88i	0.728374	+	0.728374i	−0.241922	+	0.970296i	$0.577778\pi$
$24$		0			0
$25$	−2652.97	−	1651.48i	−0.848949	−	0.528475i
$26$		0			0
$27$	−2768.94	−	2768.94i	−0.730979	−	0.730979i
$28$		0			0
$29$	1847.15			0.407856			0.203928	−	0.978986i	$-0.434629\pi$
$29$	1847.15			0.407856			0.203928	+	0.978986i	$0.434629\pi$
$30$		0			0
$31$			4973.59i			0.929535i	0.885433	+	0.464767i	$0.153862\pi$
$31$			4973.59i			0.929535i	−0.885433	+	0.464767i	$0.846138\pi$
$32$		0			0
$33$	5474.64	−	5474.64i	0.875126	−	0.875126i
$34$		0			0
$35$	−6139.55	−	11053.9i	−0.847162	−	1.52526i
$36$		0			0
$37$	2819.25	−	2819.25i	0.338555	−	0.338555i	−0.517269	−	0.855823i	$-0.673051\pi$
$37$	2819.25	−	2819.25i	0.338555	−	0.338555i	0.855823	+	0.517269i	$0.173051\pi$
$38$		0			0
$39$	−3131.92			−0.329723
$40$		0			0
$41$	−12472.0			−1.15872			−0.579359	−	0.815072i	$-0.696697\pi$
$41$	−12472.0			−1.15872			−0.579359	+	0.815072i	$0.696697\pi$
$42$		0			0
$43$	11883.2	−	11883.2i	0.980078	−	0.980078i	−0.0197274	−	0.999805i	$-0.506280\pi$
$43$	11883.2	−	11883.2i	0.980078	−	0.980078i	0.999805	+	0.0197274i	$0.00627982\pi$
$44$		0			0
$45$	−974.975	−	278.672i	−0.0717732	−	0.0205145i
$46$		0			0
$47$	11919.6	−	11919.6i	0.787080	−	0.787080i	−0.193935	−	0.981014i	$-0.562125\pi$
$47$	11919.6	−	11919.6i	0.787080	−	0.787080i	0.981014	+	0.193935i	$0.0621251\pi$
$48$		0			0
$49$		−	34355.2i		−	2.04410i
$50$		0			0
$51$	−18874.9			−1.01615
$52$		0			0
$53$	10766.7	+	10766.7i	0.526494	+	0.526494i	0.919525	−	0.393031i	$-0.128573\pi$
$53$	10766.7	+	10766.7i	0.526494	+	0.526494i	−0.393031	+	0.919525i	$0.628573\pi$
$54$		0			0
$55$	7932.06	−	27751.5i	0.353573	−	1.23703i
$56$		0			0
$57$	−10706.9	−	10706.9i	−0.436492	−	0.436492i
$58$		0			0
$59$			8271.39i			0.309349i	0.987965	+	0.154674i	$0.0494329\pi$
$59$			8271.39i			0.309349i	−0.987965	+	0.154674i	$0.950567\pi$
$60$		0			0
$61$			28492.9i			0.980420i	0.871604	+	0.490210i	$0.163080\pi$
$61$			28492.9i			0.980420i	−0.871604	+	0.490210i	$0.836920\pi$
$62$		0			0
$63$	−2901.22	−	2901.22i	−0.0920935	−	0.0920935i
$64$		0			0
$65$	−10206.9	+	5669.13i	−0.299647	+	0.166430i
$66$		0			0
$67$	−9257.64	−	9257.64i	−0.251949	−	0.251949i	0.569820	−	0.821769i	$-0.307013\pi$
$67$	−9257.64	−	9257.64i	−0.251949	−	0.251949i	−0.821769	+	0.569820i	$0.807013\pi$
$68$		0			0
$69$	−39187.3			−0.990884
$70$		0			0
$71$			18565.5i			0.437079i	0.975828	+	0.218539i	$0.0701292\pi$
$71$			18565.5i			0.437079i	−0.975828	+	0.218539i	$0.929871\pi$
$72$		0			0
$73$	−58309.9	+	58309.9i	−1.28066	+	1.28066i	−0.340375	+	0.940290i	$0.610554\pi$
$73$	−58309.9	+	58309.9i	−1.28066	+	1.28066i	−0.940290	+	0.340375i	$0.889446\pi$
$74$		0			0
$75$	45641.4	−	10619.0i	0.936928	−	0.217987i
$76$		0			0
$77$	82579.7	−	82579.7i	1.58725	−	1.58725i
$78$		0			0
$79$	10581.9			0.190764			0.0953822	−	0.995441i	$-0.469593\pi$
$79$	10581.9			0.190764			0.0953822	+	0.995441i	$0.469593\pi$
$80$		0			0
$81$	54312.1			0.919780
$82$		0			0
$83$	−12642.5	+	12642.5i	−0.201436	+	0.201436i	−0.800615	−	0.599179i	$-0.795494\pi$
$83$	−12642.5	+	12642.5i	−0.201436	+	0.201436i	0.599179	+	0.800615i	$0.295494\pi$
$84$		0			0
$85$	−61513.0	+	34165.7i	−0.923463	+	0.512912i
$86$		0			0
$87$	−19585.9	+	19585.9i	−0.277425	+	0.277425i
$88$		0			0
$89$		−	65996.0i		−	0.883166i	−0.897220	−	0.441583i	$-0.854417\pi$
$89$		−	65996.0i		−	0.883166i	0.897220	−	0.441583i	$-0.145583\pi$
$90$		0			0
$91$	−47242.0			−0.598032
$92$		0			0
$93$	−52736.5	−	52736.5i	−0.632272	−	0.632272i
$94$		0			0
$95$	−54274.3	−	15512.9i	−0.617001	−	0.176354i
$96$		0			0
$97$	14591.8	+	14591.8i	0.157464	+	0.157464i	0.781442	−	0.623978i	$-0.214485\pi$
$97$	14591.8	+	14591.8i	0.157464	+	0.157464i	−0.623978	+	0.781442i	$0.714485\pi$
$98$		0			0
$99$		−	9365.58i		−	0.0960388i
$100$		0			0
$101$			105351.i			1.02763i	0.857901	+	0.513814i	$0.171768\pi$
$101$			105351.i			1.02763i	−0.857901	+	0.513814i	$0.828232\pi$
$102$		0			0
$103$	95388.9	+	95388.9i	0.885941	+	0.885941i	0.994130	−	0.108189i	$-0.0345052\pi$
$103$	95388.9	+	95388.9i	0.885941	+	0.885941i	−0.108189	+	0.994130i	$0.534505\pi$
$104$		0			0
$105$	182307.	+	52107.9i	1.61373	+	0.461243i
$106$		0			0
$107$	98246.9	+	98246.9i	0.829582	+	0.829582i	0.987459	−	0.157876i	$-0.0504648\pi$
$107$	98246.9	+	98246.9i	0.829582	+	0.829582i	−0.157876	+	0.987459i	$0.550465\pi$
$108$		0			0
$109$	90675.6			0.731012			0.365506	−	0.930809i	$-0.380896\pi$
$109$	90675.6			0.731012			0.365506	+	0.930809i	$0.380896\pi$
$110$		0			0
$111$			59786.7i			0.460572i
$112$		0			0
$113$	−45073.6	+	45073.6i	−0.332067	+	0.332067i	−0.853371	−	0.521304i	$-0.825446\pi$
$113$	−45073.6	+	45073.6i	−0.332067	+	0.332067i	0.521304	+	0.853371i	$0.325446\pi$
$114$		0			0
$115$	−127711.	+	70933.5i	−0.900500	+	0.500157i
$116$		0			0
$117$	−2678.92	+	2678.92i	−0.0180923	+	0.0180923i
$118$		0			0
$119$	−284709.			−1.84304
$120$		0			0
$121$	105529.			0.655252
$122$		0			0
$123$	132245.	−	132245.i	0.788164	−	0.788164i
$124$		0			0
$125$	129523.	−	117223.i	0.741434	−	0.671026i
$126$		0			0
$127$	77703.2	−	77703.2i	0.427494	−	0.427494i	−0.460280	−	0.887774i	$-0.652251\pi$
$127$	77703.2	−	77703.2i	0.427494	−	0.427494i	0.887774	+	0.460280i	$0.152251\pi$
$128$		0			0
$129$			252002.i			1.33330i
$130$		0			0
$131$	−11817.8			−0.0601671			−0.0300836	−	0.999547i	$-0.509577\pi$
$131$	−11817.8			−0.0601671			−0.0300836	+	0.999547i	$0.509577\pi$
$132$		0			0
$133$	−161503.	−	161503.i	−0.791685	−	0.791685i
$134$		0			0
$135$	191368.	−	106290.i	0.903720	−	0.501946i
$136$		0			0
$137$	24545.6	+	24545.6i	0.111731	+	0.111731i	0.760762	−	0.649031i	$-0.224826\pi$
$137$	24545.6	+	24545.6i	0.111731	+	0.111731i	−0.649031	+	0.760762i	$0.724826\pi$
$138$		0			0
$139$			318666.i			1.39894i	0.714662	+	0.699470i	$0.246581\pi$
$139$			318666.i			1.39894i	−0.714662	+	0.699470i	$0.753419\pi$
$140$		0			0
$141$			252776.i			1.07075i
$142$		0			0
$143$	−76252.2	−	76252.2i	−0.311826	−	0.311826i
$144$		0			0
$145$	−28377.5	+	99282.9i	−0.112087	+	0.392152i
$146$		0			0
$147$	364279.	+	364279.i	1.39040	+	1.39040i
$148$		0			0
$149$	−355298.			−1.31108			−0.655538	−	0.755162i	$-0.727558\pi$
$149$	−355298.			−1.31108			−0.655538	+	0.755162i	$0.727558\pi$
$150$		0			0
$151$			246649.i			0.880313i	0.897921	+	0.440157i	$0.145077\pi$
$151$			246649.i			0.880313i	−0.897921	+	0.440157i	$0.854923\pi$
$152$		0			0
$153$	−16144.8	+	16144.8i	−0.0557577	+	0.0557577i
$154$		0			0
$155$	−267327.	−	76408.5i	−0.893744	−	0.255454i
$156$		0			0
$157$	−124781.	+	124781.i	−0.404017	+	0.404017i	−0.879646	−	0.475629i	$-0.842220\pi$
$157$	−124781.	+	124781.i	−0.404017	+	0.404017i	0.475629	+	0.879646i	$0.342220\pi$
$158$		0			0
$159$	−228326.			−0.716246
$160$		0			0
$161$	−591103.			−1.79721
$162$		0			0
$163$	225521.	−	225521.i	0.664841	−	0.664841i	−0.291676	−	0.956517i	$-0.594213\pi$
$163$	225521.	−	225521.i	0.664841	−	0.664841i	0.956517	+	0.291676i	$0.0942129\pi$
$164$		0			0
$165$	210152.	+	378364.i	0.600929	+	1.08193i
$166$		0			0
$167$	−45151.0	+	45151.0i	−0.125278	+	0.125278i	−0.766966	−	0.641688i	$-0.778235\pi$
$167$	−45151.0	+	45151.0i	−0.125278	+	0.125278i	0.641688	+	0.766966i	$0.278235\pi$
$168$		0			0
$169$		−	327671.i		−	0.882513i
$170$		0			0
$171$	−18316.5			−0.0479019
$172$		0			0
$173$	−188840.	−	188840.i	−0.479710	−	0.479710i	0.425329	−	0.905039i	$-0.360158\pi$
$173$	−188840.	−	188840.i	−0.479710	−	0.479710i	−0.905039	+	0.425329i	$0.860158\pi$
$174$		0			0
$175$	688457.	−	160178.i	1.69935	−	0.395373i
$176$		0			0
$177$	−87704.2	−	87704.2i	−0.210420	−	0.210420i
$178$		0			0
$179$		−	286829.i		−	0.669098i	−0.942378	−	0.334549i	$-0.891416\pi$
$179$		−	286829.i		−	0.669098i	0.942378	−	0.334549i	$-0.108584\pi$
$180$		0			0
$181$			120295.i			0.272930i	0.990645	+	0.136465i	$0.0435741\pi$
$181$			120295.i			0.272930i	−0.990645	+	0.136465i	$0.956426\pi$
$182$		0			0
$183$	−302119.	−	302119.i	−0.666885	−	0.666885i
$184$		0			0
$185$	108221.	+	194844.i	0.232478	+	0.418560i
$186$		0			0
$187$	−459543.	−	459543.i	−0.960998	−	0.960998i
$188$		0			0
$189$	885734.			1.80364
$190$		0			0
$191$		−	492807.i		−	0.977448i	−0.872439	−	0.488724i	$-0.837463\pi$
$191$		−	492807.i		−	0.977448i	0.872439	−	0.488724i	$-0.162537\pi$
$192$		0			0
$193$	662231.	−	662231.i	1.27972	−	1.27972i	0.338902	−	0.940822i	$-0.389945\pi$
$193$	662231.	−	662231.i	1.27972	−	1.27972i	0.940822	−	0.338902i	$-0.110055\pi$
$194$		0			0
$195$	48115.2	−	168338.i	0.0906141	−	0.317027i
$196$		0			0
$197$	350433.	−	350433.i	0.643339	−	0.643339i	−0.308036	−	0.951375i	$-0.599672\pi$
$197$	350433.	−	350433.i	0.643339	−	0.643339i	0.951375	+	0.308036i	$0.0996717\pi$
$198$		0			0
$199$	95737.5			0.171376			0.0856879	−	0.996322i	$-0.472691\pi$
$199$	95737.5			0.171376			0.0856879	+	0.996322i	$0.472691\pi$
$200$		0			0
$201$	196323.			0.342754
$202$		0			0
$203$	−295435.	+	295435.i	−0.503177	+	0.503177i
$204$		0			0
$205$	191606.	−	670363.i	0.318438	−	1.11410i
$206$		0			0
$207$	−33519.3	+	33519.3i	−0.0543712	+	0.0543712i
$208$		0			0
$209$		−	521358.i		−	0.825601i
$210$		0			0
$211$	−30783.5			−0.0476006			−0.0238003	−	0.999717i	$-0.507577\pi$
$211$	−30783.5			−0.0476006			−0.0238003	+	0.999717i	$0.507577\pi$
$212$		0			0
$213$	−196855.	−	196855.i	−0.297302	−	0.297302i
$214$		0			0
$215$	456152.	+	821270.i	0.672997	+	1.21169i
$216$		0			0
$217$	−795480.	−	795480.i	−1.14678	−	1.14678i
$218$		0			0
$219$		−	1.23656e6i		−	1.74222i
$220$		0			0
$221$			262894.i			0.362077i
$222$		0			0
$223$	−357053.	−	357053.i	−0.480807	−	0.480807i	0.424582	−	0.905389i	$-0.360421\pi$
$223$	−357053.	−	357053.i	−0.480807	−	0.480807i	−0.905389	+	0.424582i	$0.860421\pi$
$224$		0			0
$225$	29956.8	−	48123.0i	0.0394493	−	0.0633718i
$226$		0			0
$227$	−817733.	−	817733.i	−1.05329	−	1.05329i	−0.998498	−	0.0547891i	$-0.982551\pi$
$227$	−817733.	−	817733.i	−1.05329	−	1.05329i	−0.0547891	−	0.998498i	$-0.517449\pi$
$228$		0			0
$229$	−1.37993e6			−1.73888			−0.869440	−	0.494039i	$-0.835520\pi$
$229$	−1.37993e6			−1.73888			−0.869440	+	0.494039i	$0.835520\pi$
$230$		0			0
$231$			1.75124e6i			2.15931i
$232$		0			0
$233$	−935667.	+	935667.i	−1.12910	+	1.12910i	−0.138774	+	0.990324i	$0.544316\pi$
$233$	−935667.	+	935667.i	−1.12910	+	1.12910i	−0.990324	+	0.138774i	$0.955684\pi$
$234$		0			0
$235$	457552.	+	823792.i	0.540469	+	0.973078i
$236$		0			0
$237$	−112204.	+	112204.i	−0.129759	+	0.129759i
$238$		0			0
$239$	141812.			0.160590			0.0802951	−	0.996771i	$-0.474414\pi$
$239$	141812.			0.160590			0.0802951	+	0.996771i	$0.474414\pi$
$240$		0			0
$241$	353109.			0.391621			0.195811	−	0.980642i	$-0.437266\pi$
$241$	353109.			0.391621			0.195811	+	0.980642i	$0.437266\pi$
$242$		0			0
$243$	96964.6	−	96964.6i	0.105341	−	0.105341i
$244$		0			0
$245$	1.84656e6	+	527794.i	1.96539	+	0.561758i
$246$		0			0
$247$	−149129.	+	149129.i	−0.155532	+	0.155532i
$248$		0			0
$249$		−	268105.i		−	0.274035i
$250$		0			0
$251$	−1.19095e6			−1.19319			−0.596596	−	0.802542i	$-0.703481\pi$
$251$	−1.19095e6			−1.19319			−0.596596	+	0.802542i	$0.703481\pi$
$252$		0			0
$253$	−954086.	−	954086.i	−0.937101	−	0.937101i
$254$		0			0
$255$	289972.	−	1.01451e6i	0.279258	−	0.977026i
$256$		0			0
$257$	1.13900e6	+	1.13900e6i	1.07570	+	1.07570i	0.996890	+	0.0788094i	$0.0251118\pi$
$257$	1.13900e6	+	1.13900e6i	1.07570	+	1.07570i	0.0788094	+	0.996890i	$0.474888\pi$
$258$		0			0
$259$			901825.i			0.835359i
$260$		0			0
$261$			33506.0i			0.0304454i
$262$		0			0
$263$	−999582.	−	999582.i	−0.891105	−	0.891105i	0.103522	−	0.994627i	$-0.466989\pi$
$263$	−999582.	−	999582.i	−0.891105	−	0.891105i	−0.994627	+	0.103522i	$0.966989\pi$
$264$		0			0
$265$	−744111.	+	413296.i	−0.650913	+	0.361531i
$266$		0			0
$267$	699776.	+	699776.i	0.600732	+	0.600732i
$268$		0			0
$269$	−1.07177e6			−0.903072			−0.451536	−	0.892253i	$-0.649124\pi$
$269$	−1.07177e6			−0.903072			−0.451536	+	0.892253i	$0.649124\pi$
$270$		0			0
$271$			523663.i			0.433141i	0.976267	+	0.216570i	$0.0694870\pi$
$271$			523663.i			0.433141i	−0.976267	+	0.216570i	$0.930513\pi$
$272$		0			0
$273$	500922.	−	500922.i	0.406783	−	0.406783i
$274$		0			0
$275$	1.36976e6	+	852684.i	1.09223	+	0.679918i
$276$		0			0
$277$	970729.	−	970729.i	0.760149	−	0.760149i	−0.216200	−	0.976349i	$-0.569366\pi$
$277$	970729.	−	970729.i	0.760149	−	0.760149i	0.976349	+	0.216200i	$0.0693663\pi$
$278$		0			0
$279$	−90217.5			−0.0693873
$280$		0			0
$281$	−571060.			−0.431435			−0.215718	−	0.976456i	$-0.569209\pi$
$281$	−571060.			−0.431435			−0.215718	+	0.976456i	$0.569209\pi$
$282$		0			0
$283$	546336.	−	546336.i	0.405503	−	0.405503i	−0.474664	−	0.880167i	$-0.657430\pi$
$283$	546336.	−	546336.i	0.405503	−	0.405503i	0.880167	+	0.474664i	$0.157430\pi$
$284$		0			0
$285$	739977.	−	410999.i	0.539642	−	0.299729i
$286$		0			0
$287$	1.99479e6	−	1.99479e6i	1.42953	−	1.42953i
$288$		0			0
$289$			164507.i			0.115862i
$290$		0			0
$291$	−309444.			−0.214215
$292$		0			0
$293$	1.04865e6	+	1.04865e6i	0.713608	+	0.713608i	0.967288	−	0.253680i	$-0.0816410\pi$
$293$	1.04865e6	+	1.04865e6i	0.713608	+	0.713608i	−0.253680	+	0.967288i	$0.581641\pi$
$294$		0			0
$295$	−444581.	−	127072.i	−0.297438	−	0.0850150i
$296$		0			0
$297$	1.42964e6	+	1.42964e6i	0.940452	+	0.940452i
$298$		0			0
$299$			545811.i			0.353073i
$300$		0			0
$301$			3.80120e6i			2.41827i
$302$		0			0
$303$	−1.11707e6	−	1.11707e6i	−0.698996	−	0.698996i
$304$		0			0
$305$	−1.53147e6	−	437733.i	−0.942670	−	0.269438i
$306$		0			0
$307$	397765.	+	397765.i	0.240869	+	0.240869i	0.817210	−	0.576341i	$-0.195520\pi$
$307$	397765.	+	397765.i	0.240869	+	0.240869i	−0.576341	+	0.817210i	$0.695520\pi$
$308$		0			0
$309$	−2.02288e6			−1.20524
$310$		0			0
$311$			2.28317e6i			1.33856i	0.743011	+	0.669279i	$0.233397\pi$
$311$			2.28317e6i			1.33856i	−0.743011	+	0.669279i	$0.766603\pi$
$312$		0			0
$313$	2.40862e6	−	2.40862e6i	1.38965	−	1.38965i	0.563621	−	0.826034i	$-0.309408\pi$
$313$	2.40862e6	−	2.40862e6i	1.38965	−	1.38965i	0.826034	−	0.563621i	$-0.190592\pi$
$314$		0			0
$315$	200509.	−	111367.i	0.113857	−	0.0632385i
$316$		0			0
$317$	−2.25260e6	+	2.25260e6i	−1.25903	+	1.25903i	−0.307473	+	0.951557i	$0.599484\pi$
$317$	−2.25260e6	+	2.25260e6i	−1.25903	+	1.25903i	−0.951557	+	0.307473i	$0.900516\pi$
$318$		0			0
$319$	−953708.			−0.524734
$320$		0			0
$321$	−2.08349e6			−1.12857
$322$		0			0
$323$	−898741.	+	898741.i	−0.479323	+	0.479323i
$324$		0			0
$325$	−147904.	−	635706.i	−0.0776735	−	0.333847i
$326$		0			0
$327$	−961462.	+	961462.i	−0.497236	+	0.497236i
$328$		0			0
$329$			3.81288e6i			1.94206i
$330$		0			0
$331$	3.68065e6			1.84652			0.923262	−	0.384171i	$-0.125513\pi$
$331$	3.68065e6			1.84652			0.923262	+	0.384171i	$0.125513\pi$
$332$		0			0
$333$	51139.2	+	51139.2i	0.0252722	+	0.0252722i
$334$		0			0
$335$	639815.	−	355367.i	0.311489	−	0.173008i
$336$		0			0
$337$	884212.	+	884212.i	0.424113	+	0.424113i	0.886617	−	0.462504i	$-0.153049\pi$
$337$	884212.	+	884212.i	0.424113	+	0.424113i	−0.462504	+	0.886617i	$0.653049\pi$
$338$		0			0
$339$		−	955860.i		−	0.451747i
$340$		0			0
$341$		−	2.56793e6i		−	1.19591i
$342$		0			0
$343$	2.80667e6	+	2.80667e6i	1.28812	+	1.28812i
$344$		0			0
$345$	602029.	−	2.10629e6i	0.272314	−	0.952731i
$346$		0			0
$347$	1.23778e6	+	1.23778e6i	0.551849	+	0.551849i	0.926974	−	0.375125i	$-0.122400\pi$
$347$	1.23778e6	+	1.23778e6i	0.551849	+	0.551849i	−0.375125	+	0.926974i	$0.622400\pi$
$348$		0			0
$349$	101130.			0.0444442			0.0222221	−	0.999753i	$-0.492926\pi$
$349$	101130.			0.0444442			0.0222221	+	0.999753i	$0.492926\pi$
$350$		0			0
$351$		−	817867.i		−	0.354336i
$352$		0			0
$353$	−901480.	+	901480.i	−0.385052	+	0.385052i	−0.872918	−	0.487866i	$-0.837775\pi$
$353$	−901480.	+	901480.i	−0.385052	+	0.385052i	0.487866	+	0.872918i	$0.337775\pi$
$354$		0			0
$355$	−997879.	−	285218.i	−0.420249	−	0.120118i
$356$		0			0
$357$	3.01886e6	−	3.01886e6i	1.25364	−	1.25364i
$358$		0			0
$359$	−3.32311e6			−1.36084			−0.680422	−	0.732820i	$-0.738204\pi$
$359$	−3.32311e6			−1.36084			−0.680422	+	0.732820i	$0.738204\pi$
$360$		0			0
$361$	1.45647e6			0.588210
$362$		0			0
$363$	−1.11896e6	+	1.11896e6i	−0.445705	+	0.445705i
$364$		0			0
$365$	−2.23831e6	−	4.02992e6i	−0.879403	−	1.58331i
$366$		0			0
$367$	2.11644e6	−	2.11644e6i	0.820239	−	0.820239i	−0.165903	−	0.986142i	$-0.553054\pi$
$367$	2.11644e6	−	2.11644e6i	0.820239	−	0.820239i	0.986142	+	0.165903i	$0.0530540\pi$
$368$		0			0
$369$		−	226234.i		−	0.0864953i
$370$		0			0
$371$	−3.44408e6			−1.29909
$372$		0			0
$373$	1.46519e6	+	1.46519e6i	0.545283	+	0.545283i	0.925073	−	0.379790i	$-0.124004\pi$
$373$	1.46519e6	+	1.46519e6i	0.545283	+	0.545283i	−0.379790	+	0.925073i	$0.624004\pi$
$374$		0			0
$375$	−130419.	+	2.61633e6i	−0.0478919	+	0.960760i
$376$		0			0
$377$	272798.	+	272798.i	0.0988524	+	0.0988524i
$378$		0			0
$379$		−	518674.i		−	0.185480i	−0.995690	−	0.0927399i	$-0.970437\pi$
$379$		−	518674.i		−	0.185480i	0.995690	−	0.0927399i	$-0.0295625\pi$
$380$		0			0
$381$			1.64782e6i			0.581565i
$382$		0			0
$383$	−3.41844e6	−	3.41844e6i	−1.19078	−	1.19078i	−0.976849	−	0.213930i	$-0.931373\pi$
$383$	−3.41844e6	−	3.41844e6i	−1.19078	−	1.19078i	−0.213930	−	0.976849i	$-0.568627\pi$
$384$		0			0
$385$	3.16994e6	+	5.70726e6i	1.08993	+	1.96235i
$386$		0			0
$387$	215552.	+	215552.i	0.0731603	+	0.0731603i
$388$		0			0
$389$	682389.			0.228643			0.114322	−	0.993444i	$-0.463531\pi$
$389$	682389.			0.228643			0.114322	+	0.993444i	$0.463531\pi$
$390$		0			0
$391$			3.28940e6i			1.08811i
$392$		0			0
$393$	125308.	−	125308.i	0.0409259	−	0.0409259i
$394$		0			0
$395$	−162569.	+	568771.i	−0.0524257	+	0.183419i
$396$		0			0
$397$	1.10424e6	−	1.10424e6i	0.351631	−	0.351631i	−0.509085	−	0.860716i	$-0.670016\pi$
$397$	1.10424e6	−	1.10424e6i	0.351631	−	0.351631i	0.860716	+	0.509085i	$0.170016\pi$
$398$		0			0
$399$	3.42494e6			1.07701
$400$		0			0
$401$	−2.52254e6			−0.783390			−0.391695	−	0.920095i	$-0.628111\pi$
$401$	−2.52254e6			−0.783390			−0.391695	+	0.920095i	$0.628111\pi$
$402$		0			0
$403$	−734528.	+	734528.i	−0.225292	+	0.225292i
$404$		0			0
$405$	−834389.	+	2.91924e6i	−0.252773	+	0.884365i
$406$		0			0
$407$	−1.45562e6	+	1.45562e6i	−0.435573	+	0.435573i
$408$		0			0
$409$		−	3.08388e6i		−	0.911569i	−0.890090	−	0.455784i	$-0.849359\pi$
$409$		−	3.08388e6i		−	0.911569i	0.890090	−	0.455784i	$-0.150641\pi$
$410$		0			0
$411$	−520529.			−0.151999
$412$		0			0
$413$	−1.32293e6	−	1.32293e6i	−0.381648	−	0.381648i
$414$		0			0
$415$	−485300.	−	873750.i	−0.138322	−	0.249039i
$416$		0			0
$417$	−3.37892e6	−	3.37892e6i	−0.951564	−	0.951564i
$418$		0			0
$419$		−	2.04163e6i		−	0.568123i	−0.958806	−	0.284061i	$-0.908318\pi$
$419$		−	2.04163e6i		−	0.568123i	0.958806	−	0.284061i	$-0.0916820\pi$
$420$		0			0
$421$			2.04322e6i			0.561836i	0.959732	+	0.280918i	$0.0906389\pi$
$421$			2.04322e6i			0.561836i	−0.959732	+	0.280918i	$0.909361\pi$
$422$		0			0
$423$	216214.	+	216214.i	0.0587534	+	0.0587534i
$424$		0			0
$425$	−891364.	−	3.83116e6i	−0.239377	−	1.02886i
$426$		0			0
$427$	−4.55718e6	−	4.55718e6i	−1.20956	−	1.20956i
$428$		0			0
$429$	1.61705e6			0.424210
$430$		0			0
$431$		−	1.73952e6i		−	0.451061i	−0.974236	−	0.225531i	$-0.927588\pi$
$431$		−	1.73952e6i		−	0.451061i	0.974236	−	0.225531i	$-0.0724116\pi$
$432$		0			0
$433$	395725.	−	395725.i	0.101432	−	0.101432i	−0.654570	−	0.756002i	$-0.727150\pi$
$433$	395725.	−	395725.i	0.101432	−	0.101432i	0.756002	+	0.654570i	$0.227150\pi$
$434$		0			0
$435$	−751832.	−	1.35362e6i	−0.190501	−	0.342985i
$436$		0			0
$437$	−1.86593e6	+	1.86593e6i	−0.467404	+	0.467404i
$438$		0			0
$439$	−484857.			−0.120075			−0.0600375	−	0.998196i	$-0.519122\pi$
$439$	−484857.			−0.120075			−0.0600375	+	0.998196i	$0.519122\pi$
$440$		0			0
$441$	623179.			0.152587
$442$		0			0
$443$	−1.14644e6	+	1.14644e6i	−0.277550	+	0.277550i	−0.832130	−	0.554580i	$-0.812879\pi$
$443$	−1.14644e6	+	1.14644e6i	−0.277550	+	0.277550i	0.554580	+	0.832130i	$0.312879\pi$
$444$		0			0
$445$	3.54723e6	+	1.01389e6i	0.849161	+	0.242711i
$446$		0			0
$447$	3.76734e6	−	3.76734e6i	0.891798	−	0.891798i
$448$		0			0
$449$		−	6.29177e6i		−	1.47284i	−0.676522	−	0.736422i	$-0.736514\pi$
$449$		−	6.29177e6i		−	1.47284i	0.676522	−	0.736422i	$-0.263486\pi$
$450$		0			0
$451$	6.43949e6			1.49077
$452$		0			0
$453$	−2.61530e6	−	2.61530e6i	−0.598792	−	0.598792i
$454$		0			0
$455$	725772.	−	2.53922e6i	0.164351	−	0.575006i
$456$		0			0
$457$	−3.45893e6	−	3.45893e6i	−0.774732	−	0.774732i	0.204198	−	0.978930i	$-0.434541\pi$
$457$	−3.45893e6	−	3.45893e6i	−0.774732	−	0.774732i	−0.978930	+	0.204198i	$0.934541\pi$
$458$		0			0
$459$		−	4.92897e6i		−	1.09201i
$460$		0			0
$461$		−	3.70309e6i		−	0.811544i	−0.913974	−	0.405772i	$-0.867003\pi$
$461$		−	3.70309e6i		−	0.811544i	0.913974	−	0.405772i	$-0.132997\pi$
$462$		0			0
$463$	2.86396e6	+	2.86396e6i	0.620889	+	0.620889i	0.945759	−	0.324870i	$-0.105320\pi$
$463$	2.86396e6	+	2.86396e6i	0.620889	+	0.620889i	−0.324870	+	0.945759i	$0.605320\pi$
$464$		0			0
$465$	3.64473e6	−	2.02437e6i	0.781688	−	0.434167i
$466$		0			0
$467$	599549.	+	599549.i	0.127213	+	0.127213i	0.767847	−	0.640633i	$-0.221328\pi$
$467$	599549.	+	599549.i	0.127213	+	0.127213i	−0.640633	+	0.767847i	$0.721328\pi$
$468$		0			0
$469$	2.96135e6			0.621667
$470$		0			0
$471$		−	2.64618e6i		−	0.549627i
$472$		0			0
$473$	−6.13544e6	+	6.13544e6i	−1.26094	+	1.26094i
$474$		0			0
$475$	1.66762e6	−	2.67888e6i	0.339127	−	0.544778i
$476$		0			0
$477$	−195301.	+	195301.i	−0.0393014	+	0.0393014i
$478$		0			0
$479$	−70233.6			−0.0139864			−0.00699321	−	0.999976i	$-0.502226\pi$
$479$	−70233.6			−0.0139864			−0.00699321	+	0.999976i	$0.502226\pi$
$480$		0			0
$481$	832725.			0.164111
$482$		0			0
$483$	6.26766e6	−	6.26766e6i	1.22247	−	1.22247i
$484$		0			0
$485$	−1.00847e6	+	560128.i	−0.194675	+	0.108127i
$486$		0			0
$487$	−4.67856e6	+	4.67856e6i	−0.893902	+	0.893902i	−0.994888	−	0.100986i	$-0.967800\pi$
$487$	−4.67856e6	+	4.67856e6i	−0.893902	+	0.893902i	0.100986	+	0.994888i	$0.467800\pi$
$488$		0			0
$489$			4.78254e6i			0.904454i
$490$		0			0
$491$	−7.83994e6			−1.46760			−0.733802	−	0.679363i	$-0.762256\pi$
$491$	−7.83994e6			−1.46760			−0.733802	+	0.679363i	$0.762256\pi$
$492$		0			0
$493$	1.64405e6	+	1.64405e6i	0.304647	+	0.304647i
$494$		0			0
$495$	503393.	+	143882.i	0.0923409	+	0.0263933i
$496$		0			0
$497$	−2.96937e6	−	2.96937e6i	−0.539230	−	0.539230i
$498$		0			0
$499$			1.64729e6i			0.296154i	0.988976	+	0.148077i	$0.0473084\pi$
$499$			1.64729e6i			0.296154i	−0.988976	+	0.148077i	$0.952692\pi$
$500$		0			0
$501$		−	957501.i		−	0.170430i
$502$		0			0
$503$	7.27235e6	+	7.27235e6i	1.28161	+	1.28161i	0.939753	+	0.341854i	$0.111055\pi$
$503$	7.27235e6	+	7.27235e6i	1.28161	+	1.28161i	0.341854	+	0.939753i	$0.388945\pi$
$504$		0			0
$505$	−5.66255e6	−	1.61850e6i	−0.988061	−	0.282412i
$506$		0			0
$507$	3.47440e6	+	3.47440e6i	0.600288	+	0.600288i
$508$		0			0
$509$	6.59314e6			1.12797			0.563985	−	0.825785i	$-0.309268\pi$
$509$	6.59314e6			1.12797			0.563985	+	0.825785i	$0.309268\pi$
$510$		0			0
$511$		−	1.86523e7i		−	3.15995i
$512$		0			0
$513$	2.79599e6	−	2.79599e6i	0.469075	−	0.469075i
$514$		0			0
$515$	−6.59253e6	+	3.66164e6i	−1.09530	+	0.608355i
$516$		0			0
$517$	−6.15428e6	+	6.15428e6i	−1.01263	+	1.01263i
$518$		0			0
$519$	4.00466e6			0.652601
$520$		0			0
$521$	4.60672e6			0.743529			0.371765	−	0.928327i	$-0.378753\pi$
$521$	4.60672e6			0.743529			0.371765	+	0.928327i	$0.378753\pi$
$522$		0			0
$523$	3.89376e6	−	3.89376e6i	0.622465	−	0.622465i	−0.323696	−	0.946161i	$-0.604926\pi$
$523$	3.89376e6	−	3.89376e6i	0.622465	−	0.622465i	0.946161	+	0.323696i	$0.104926\pi$
$524$		0			0
$525$	−5.60152e6	+	8.99835e6i	−0.886967	+	1.42483i
$526$		0			0
$527$	−4.42672e6	+	4.42672e6i	−0.694314	+	0.694314i
$528$		0			0
$529$			392982.i			0.0610568i
$530$		0			0
$531$	−150037.			−0.0230921
$532$		0			0
$533$	−1.84194e6	−	1.84194e6i	−0.280840	−	0.280840i
$534$		0			0
$535$	−6.79005e6	+	3.77135e6i	−1.02563	+	0.569655i
$536$		0			0
$537$	3.04133e6	+	3.04133e6i	0.455123	+	0.455123i
$538$		0			0
$539$			1.77381e7i			2.62987i
$540$		0			0
$541$		−	1.10906e7i		−	1.62915i	−0.580060	−	0.814574i	$-0.696971\pi$
$541$		−	1.10906e7i		−	1.62915i	0.580060	−	0.814574i	$-0.303029\pi$
$542$		0			0
$543$	−1.27553e6	−	1.27553e6i	−0.185648	−	0.185648i
$544$		0			0
$545$	−1.39304e6	+	4.87375e6i	−0.200896	+	0.702865i
$546$		0			0
$547$	1.76847e6	+	1.76847e6i	0.252714	+	0.252714i	0.822083	−	0.569368i	$-0.192812\pi$
$547$	1.76847e6	+	1.76847e6i	0.252714	+	0.252714i	−0.569368	+	0.822083i	$0.692812\pi$
$548$		0			0
$549$	−516842.			−0.0731858
$550$		0			0
$551$			1.86519e6i			0.261725i
$552$		0			0
$553$	−1.69248e6	+	1.69248e6i	−0.235349	+	0.235349i
$554$		0			0
$555$	−3.21349e6	−	918495.i	−0.442838	−	0.126574i
$556$		0			0
$557$	3.02444e6	−	3.02444e6i	0.413054	−	0.413054i	−0.469747	−	0.882801i	$-0.655655\pi$
$557$	3.02444e6	−	3.02444e6i	0.413054	−	0.413054i	0.882801	+	0.469747i	$0.155655\pi$
$558$		0			0
$559$	3.50995e6			0.475085
$560$		0			0
$561$	9.74536e6			1.30735
$562$		0			0
$563$	−1.06508e6	+	1.06508e6i	−0.141616	+	0.141616i	−0.774360	−	0.632745i	$-0.781928\pi$
$563$	−1.06508e6	+	1.06508e6i	−0.141616	+	0.141616i	0.632745	+	0.774360i	$0.281928\pi$
$564$		0			0
$565$	−1.73021e6	−	3.11513e6i	−0.228023	−	0.410540i
$566$		0			0
$567$	−8.68673e6	+	8.68673e6i	−1.13475	+	1.13475i
$568$		0			0
$569$			6.43884e6i			0.833733i	0.908968	+	0.416866i	$0.136872\pi$
$569$			6.43884e6i			0.833733i	−0.908968	+	0.416866i	$0.863128\pi$
$570$		0			0
$571$	−1.08005e6			−0.138629			−0.0693144	−	0.997595i	$-0.522081\pi$
$571$	−1.08005e6			−0.138629			−0.0693144	+	0.997595i	$0.522081\pi$
$572$		0			0
$573$	5.22539e6	+	5.22539e6i	0.664863	+	0.664863i
$574$		0			0
$575$	−1.85062e6	−	7.95411e6i	−0.233425	−	1.00328i
$576$		0			0
$577$	1.01103e7	+	1.01103e7i	1.26422	+	1.26422i	0.949028	+	0.315191i	$0.102069\pi$
$577$	1.01103e7	+	1.01103e7i	1.26422	+	1.26422i	0.315191	+	0.949028i	$0.397931\pi$
$578$		0			0
$579$			1.40437e7i			1.74094i
$580$		0			0
$581$		−	4.04410e6i		−	0.497029i
$582$		0			0
$583$	−5.55901e6	−	5.55901e6i	−0.677370	−	0.677370i
$584$		0			0
$585$	−102834.	−	185146.i	−0.0124236	−	0.0223678i
$586$		0			0
$587$	−4.48142e6	−	4.48142e6i	−0.536810	−	0.536810i	0.385781	−	0.922590i	$-0.373932\pi$
$587$	−4.48142e6	−	4.48142e6i	−0.536810	−	0.536810i	−0.922590	+	0.385781i	$0.873932\pi$
$588$		0			0
$589$	−5.02218e6			−0.596491
$590$		0			0
$591$			7.43151e6i			0.875202i
$592$		0			0
$593$	−5.03742e6	+	5.03742e6i	−0.588263	+	0.588263i	−0.937161	−	0.348898i	$-0.886556\pi$
$593$	−5.03742e6	+	5.03742e6i	−0.588263	+	0.588263i	0.348898	+	0.937161i	$0.386556\pi$
$594$		0			0
$595$	4.37395e6	−	1.53029e7i	0.506502	−	1.77207i
$596$		0			0
$597$	−1.01513e6	+	1.01513e6i	−0.116570	+	0.116570i
$598$		0			0
$599$	4.33756e6			0.493945			0.246973	−	0.969022i	$-0.420564\pi$
$599$	4.33756e6			0.493945			0.246973	+	0.969022i	$0.420564\pi$
$600$		0			0
$601$	8.62330e6			0.973839			0.486920	−	0.873447i	$-0.338120\pi$
$601$	8.62330e6			0.973839			0.486920	+	0.873447i	$0.338120\pi$
$602$		0			0
$603$	167927.	−	167927.i	0.0188074	−	0.0188074i
$604$		0			0
$605$	−1.62123e6	+	5.67211e6i	−0.180076	+	0.630023i
$606$		0			0
$607$	−1.08203e7	+	1.08203e7i	−1.19197	+	1.19197i	−0.215458	+	0.976513i	$0.569125\pi$
$607$	−1.08203e7	+	1.08203e7i	−1.19197	+	1.19197i	−0.976513	+	0.215458i	$0.930875\pi$
$608$		0			0
$609$		−	6.26517e6i		−	0.684526i
$610$		0			0
$611$	3.52072e6			0.381530
$612$		0			0
$613$	1.97923e6	+	1.97923e6i	0.212738	+	0.212738i	0.805429	−	0.592692i	$-0.201935\pi$
$613$	1.97923e6	+	1.97923e6i	0.212738	+	0.212738i	−0.592692	+	0.805429i	$0.701935\pi$
$614$		0			0
$615$	5.07641e6	+	9.13973e6i	0.541214	+	0.974419i
$616$		0			0
$617$	−3.94210e6	−	3.94210e6i	−0.416884	−	0.416884i	0.467244	−	0.884128i	$-0.345247\pi$
$617$	−3.94210e6	−	3.94210e6i	−0.416884	−	0.416884i	−0.884128	+	0.467244i	$0.845247\pi$
$618$		0			0
$619$		−	3.91209e6i		−	0.410377i	−0.978723	−	0.205188i	$-0.934219\pi$
$619$		−	3.91209e6i		−	0.410377i	0.978723	−	0.205188i	$-0.0657807\pi$
$620$		0			0
$621$		−	1.02334e7i		−	1.06485i
$622$		0			0
$623$	1.05555e7	+	1.05555e7i	1.08957	+	1.08957i
$624$		0			0
$625$	4.31082e6	+	8.76266e6i	0.441428	+	0.897297i
$626$		0			0
$627$	5.52812e6	+	5.52812e6i	0.561576	+	0.561576i
$628$		0			0
$629$	5.01852e6			0.505765
$630$		0			0
$631$		−	5.32710e6i		−	0.532620i	−0.963887	−	0.266310i	$-0.914195\pi$
$631$		−	5.32710e6i		−	0.532620i	0.963887	−	0.266310i	$-0.0858045\pi$
$632$		0			0
$633$	326408.	−	326408.i	0.0323781	−	0.0323781i
$634$		0			0
$635$	2.98275e6	+	5.37023e6i	0.293550	+	0.528517i
$636$		0			0
$637$	5.07377e6	−	5.07377e6i	0.495430	−	0.495430i
$638$		0			0
$639$	−336765.			−0.0326268
$640$		0			0
$641$	−1.83912e7			−1.76793			−0.883966	−	0.467550i	$-0.845137\pi$
$641$	−1.83912e7			−1.76793			−0.883966	+	0.467550i	$0.845137\pi$
$642$		0			0
$643$	−4.78115e6	+	4.78115e6i	−0.456042	+	0.456042i	−0.897354	−	0.441312i	$-0.854513\pi$
$643$	−4.78115e6	+	4.78115e6i	−0.456042	+	0.456042i	0.441312	+	0.897354i	$0.354513\pi$
$644$		0			0
$645$	−1.35449e7	−	3.87147e6i	−1.28197	−	0.366418i
$646$		0			0
$647$	1.12140e7	−	1.12140e7i	1.05318	−	1.05318i	0.0546725	−	0.998504i	$-0.482589\pi$
$647$	1.12140e7	−	1.12140e7i	1.05318	−	1.05318i	0.998504	−	0.0546725i	$-0.0174115\pi$
$648$		0			0
$649$		−	4.27064e6i		−	0.397998i
$650$		0			0
$651$	1.68695e7			1.56009
$652$		0			0
$653$	272189.	+	272189.i	0.0249797	+	0.0249797i	0.719486	−	0.694507i	$-0.244377\pi$
$653$	272189.	+	272189.i	0.0249797	+	0.0249797i	−0.694507	+	0.719486i	$0.744377\pi$
$654$		0			0
$655$	181556.	−	635199.i	0.0165351	−	0.0578504i
$656$		0			0
$657$	−1.05770e6	−	1.05770e6i	−0.0955983	−	0.0955983i
$658$		0			0
$659$		−	9.27375e6i		−	0.831844i	−0.909400	−	0.415922i	$-0.863459\pi$
$659$		−	9.27375e6i		−	0.831844i	0.909400	−	0.415922i	$-0.136541\pi$
$660$		0			0
$661$			1.18368e7i			1.05374i	0.849947	+	0.526868i	$0.176634\pi$
$661$			1.18368e7i			1.05374i	−0.849947	+	0.526868i	$0.823366\pi$
$662$		0			0
$663$	−2.78755e6	−	2.78755e6i	−0.246286	−	0.246286i
$664$		0			0
$665$	1.11618e7	−	6.19953e6i	0.978772	−	0.543632i
$666$		0			0
$667$	3.41331e6	+	3.41331e6i	0.297072	+	0.297072i
$668$		0			0
$669$	7.57190e6			0.654093
$670$		0			0
$671$		−	1.47113e7i		−	1.26138i
$672$		0			0
$673$	3.32488e6	−	3.32488e6i	0.282969	−	0.282969i	−0.551323	−	0.834292i	$-0.685877\pi$
$673$	3.32488e6	−	3.32488e6i	0.282969	−	0.282969i	0.834292	+	0.551323i	$0.185877\pi$
$674$		0			0
$675$	2.77304e6	+	1.19188e7i	0.234259	+	1.00687i
$676$		0			0
$677$	−1.32971e7	+	1.32971e7i	−1.11503	+	1.11503i	−0.122567	+	0.992460i	$0.539113\pi$
$677$	−1.32971e7	+	1.32971e7i	−1.11503	+	1.11503i	−0.992460	+	0.122567i	$0.960887\pi$
$678$		0			0
$679$	−4.66766e6			−0.388530
$680$		0			0
$681$	1.73414e7			1.43290
$682$		0			0
$683$	−1.02763e7	+	1.02763e7i	−0.842921	+	0.842921i	−0.989238	−	0.146316i	$-0.953258\pi$
$683$	−1.02763e7	+	1.02763e7i	−0.842921	+	0.842921i	0.146316	+	0.989238i	$0.453258\pi$
$684$		0			0
$685$	−1.69640e6	+	942217.i	−0.138134	+	0.0767228i
$686$		0			0
$687$	1.46319e7	−	1.46319e7i	1.18279	−	1.18279i
$688$		0			0
$689$			3.18018e6i			0.255214i
$690$		0			0
$691$	−6.84499e6			−0.545353			−0.272676	−	0.962106i	$-0.587909\pi$
$691$	−6.84499e6			−0.545353			−0.272676	+	0.962106i	$0.587909\pi$
$692$		0			0
$693$	1.49794e6	+	1.49794e6i	0.118484	+	0.118484i
$694$		0			0
$695$	−1.71281e7	−	4.89563e6i	−1.34508	−	0.384456i
$696$		0			0
$697$	−1.11007e7	−	1.11007e7i	−0.865502	−	0.865502i
$698$		0			0
$699$		−	1.98424e7i		−	1.53603i
$700$		0			0
$701$		−	1.42933e6i		−	0.109859i	−0.998490	−	0.0549297i	$-0.982507\pi$
$701$		−	1.42933e6i		−	0.109859i	0.998490	−	0.0549297i	$-0.0174935\pi$
$702$		0			0
$703$	2.84679e6	+	2.84679e6i	0.217254	+	0.217254i
$704$		0			0
$705$	−1.35865e7	−	3.88335e6i	−1.02952	−	0.294262i
$706$		0			0
$707$	−1.68500e7	−	1.68500e7i	−1.26780	−	1.26780i
$708$		0			0
$709$	1.95653e7			1.46174			0.730870	−	0.682517i	$-0.239115\pi$
$709$	1.95653e7			1.46174			0.730870	+	0.682517i	$0.239115\pi$
$710$		0			0
$711$			191949.i			0.0142401i
$712$		0			0
$713$	−9.19060e6	+	9.19060e6i	−0.677049	+	0.677049i
$714$		0			0
$715$	5.26995e6	−	2.92705e6i	0.385515	−	0.214124i
$716$		0			0
$717$	−1.50368e6	+	1.50368e6i	−0.109234	+	0.109234i
$718$		0			0
$719$	−4.68265e6			−0.337807			−0.168904	−	0.985633i	$-0.554023\pi$
$719$	−4.68265e6			−0.337807			−0.168904	+	0.985633i	$0.554023\pi$
$720$		0			0
$721$	−3.05132e7			−2.18600
$722$		0			0
$723$	−3.74413e6	+	3.74413e6i	−0.266382	+	0.266382i
$724$		0			0
$725$	−4.90042e6	−	3.05054e6i	−0.346249	−	0.215542i
$726$		0			0
$727$	3.84912e6	−	3.84912e6i	0.270101	−	0.270101i	−0.559040	−	0.829141i	$-0.688830\pi$
$727$	3.84912e6	−	3.84912e6i	0.270101	−	0.270101i	0.829141	+	0.559040i	$0.188830\pi$
$728$		0			0
$729$			1.52541e7i			1.06309i
$730$		0			0
$731$	2.11531e7			1.46413
$732$		0			0
$733$	1.41189e7	+	1.41189e7i	0.970598	+	0.970598i	0.999580	−	0.0289819i	$-0.00922652\pi$
$733$	1.41189e7	+	1.41189e7i	0.970598	+	0.970598i	−0.0289819	+	0.999580i	$0.509227\pi$
$734$		0			0
$735$	−2.51761e7	+	1.39833e7i	−1.71898	+	0.954757i
$736$		0			0
$737$	4.77985e6	+	4.77985e6i	0.324150	+	0.324150i
$738$		0			0
$739$			2.46897e6i			0.166305i	0.996537	+	0.0831525i	$0.0264989\pi$
$739$			2.46897e6i			0.166305i	−0.996537	+	0.0831525i	$0.973501\pi$
$740$		0			0
$741$		−	3.16251e6i		−	0.211586i
$742$		0			0
$743$	6.03463e6	+	6.03463e6i	0.401032	+	0.401032i	0.878597	−	0.477565i	$-0.158480\pi$
$743$	6.03463e6	+	6.03463e6i	0.401032	+	0.401032i	−0.477565	+	0.878597i	$0.658480\pi$
$744$		0			0
$745$	5.45840e6	−	1.90970e7i	0.360309	−	1.26059i
$746$		0			0
$747$	−229326.	−	229326.i	−0.0150367	−	0.0150367i
$748$		0			0
$749$	−3.14274e7			−2.04693
$750$		0			0
$751$			1.45047e7i			0.938444i	0.883080	+	0.469222i	$0.155466\pi$
$751$			1.45047e7i			0.938444i	−0.883080	+	0.469222i	$0.844534\pi$
$752$		0			0
$753$	1.26281e7	−	1.26281e7i	0.811613	−	0.811613i
$754$		0			0
$755$	−1.32572e7	−	3.78924e6i	−0.846417	−	0.241927i
$756$		0			0
$757$	3.36048e6	−	3.36048e6i	0.213138	−	0.213138i	−0.592461	−	0.805599i	$-0.701843\pi$
$757$	3.36048e6	−	3.36048e6i	0.213138	−	0.213138i	0.805599	+	0.592461i	$0.201843\pi$
$758$		0			0
$759$	2.02330e7			1.27484
$760$		0			0
$761$	9.65654e6			0.604449			0.302225	−	0.953237i	$-0.402271\pi$
$761$	9.65654e6			0.604449			0.302225	+	0.953237i	$0.402271\pi$
$762$		0			0
$763$	−1.45027e7	+	1.45027e7i	−0.901859	+	0.901859i
$764$		0			0
$765$	−619742.	−	1.11580e6i	−0.0382875	−	0.0689341i
$766$		0			0
$767$	−1.22157e6	+	1.22157e6i	−0.0749771	+	0.0749771i
$768$		0			0
$769$			398573.i			0.0243048i	0.999926	+	0.0121524i	$0.00386832\pi$
$769$			398573.i			0.0243048i	−0.999926	+	0.0121524i	$0.996132\pi$
$770$		0			0
$771$	−2.41544e7			−1.46339
$772$		0			0
$773$	1.84740e6	+	1.84740e6i	0.111202	+	0.111202i	0.760518	−	0.649317i	$-0.224945\pi$
$773$	1.84740e6	+	1.84740e6i	0.111202	+	0.111202i	−0.649317	+	0.760518i	$0.724945\pi$
$774$		0			0
$775$	8.21380e6	−	1.31948e7i	0.491236	−	0.789127i
$776$		0			0
$777$	−9.56234e6	−	9.56234e6i	−0.568214	−	0.568214i
$778$		0			0
$779$		−	1.25939e7i		−	0.743560i
$780$		0			0
$781$		−	9.58560e6i		−	0.562331i
$782$		0			0
$783$	−5.11465e6	−	5.11465e6i	−0.298134	−	0.298134i
$784$		0			0
$785$	−4.78989e6	−	8.62387e6i	−0.277429	−	0.499492i
$786$		0			0
$787$	8.91667e6	+	8.91667e6i	0.513175	+	0.513175i	0.915498	−	0.402323i	$-0.131797\pi$
$787$	8.91667e6	+	8.91667e6i	0.513175	+	0.513175i	−0.402323	+	0.915498i	$0.631797\pi$
$788$		0			0
$789$	2.11978e7			1.21227
$790$		0			0
$791$		−	1.44182e7i		−	0.819352i
$792$		0			0
$793$	−4.20800e6	+	4.20800e6i	−0.237625	+	0.237625i
$794$		0			0
$795$	3.50774e6	−	1.22723e7i	0.196838	−	0.688668i
$796$		0			0
$797$	1.17690e7	−	1.17690e7i	0.656289	−	0.656289i	−0.298211	−	0.954500i	$-0.596390\pi$
$797$	1.17690e7	−	1.17690e7i	0.656289	−	0.656289i	0.954500	+	0.298211i	$0.0963900\pi$
$798$		0			0
$799$	2.12181e7			1.17581
$800$		0			0
$801$	1.19712e6			0.0659260
$802$		0			0
$803$	3.01062e7	−	3.01062e7i	1.64766	−	1.64766i
$804$		0			0
$805$	9.08104e6	−	3.17714e7i	0.493908	−	1.72801i
$806$		0			0
$807$	1.13644e7	−	1.13644e7i	0.614272	−	0.614272i
$808$		0			0
$809$		−	1.40431e7i		−	0.754380i	−0.926136	−	0.377190i	$-0.876890\pi$
$809$		−	1.40431e7i		−	0.754380i	0.926136	−	0.377190i	$-0.123110\pi$
$810$		0			0
$811$	−1.59685e7			−0.852536			−0.426268	−	0.904597i	$-0.640172\pi$
$811$	−1.59685e7			−0.852536			−0.426268	+	0.904597i	$0.640172\pi$
$812$		0			0
$813$	−5.55257e6	−	5.55257e6i	−0.294624	−	0.294624i
$814$		0			0
$815$	8.65694e6	+	1.55862e7i	0.456531	+	0.821953i
$816$		0			0
$817$	1.19992e7	+	1.19992e7i	0.628925	+	0.628925i
$818$		0			0
$819$		−	856937.i		−	0.0446415i
$820$		0			0
$821$		−	1.36995e7i		−	0.709327i	−0.934994	−	0.354664i	$-0.884595\pi$
$821$		−	1.36995e7i		−	0.709327i	0.934994	−	0.354664i	$-0.115405\pi$
$822$		0			0
$823$	1.16517e7	+	1.16517e7i	0.599641	+	0.599641i	0.940217	−	0.340576i	$-0.110622\pi$
$823$	1.16517e7	+	1.16517e7i	0.599641	+	0.599641i	−0.340576	+	0.940217i	$0.610622\pi$
$824$		0			0
$825$	−2.35653e7	+	5.48275e6i	−1.20542	+	0.280455i
$826$		0			0
$827$	−1.01220e7	−	1.01220e7i	−0.514638	−	0.514638i	0.401306	−	0.915944i	$-0.368556\pi$
$827$	−1.01220e7	−	1.01220e7i	−0.514638	−	0.514638i	−0.915944	+	0.401306i	$0.868556\pi$
$828$		0			0
$829$	−3.25318e7			−1.64407			−0.822037	−	0.569434i	$-0.807162\pi$
$829$	−3.25318e7			−1.64407			−0.822037	+	0.569434i	$0.807162\pi$
$830$		0			0
$831$			2.05859e7i			1.03411i
$832$		0			0
$833$	3.05777e7	−	3.05777e7i	1.52683	−	1.52683i
$834$		0			0
$835$	−1.73319e6	−	3.12048e6i	−0.0860258	−	0.154884i
$836$		0			0
$837$	1.37716e7	−	1.37716e7i	0.679470	−	0.679470i
$838$		0			0
$839$	−3.86903e7			−1.89757			−0.948784	−	0.315925i	$-0.897685\pi$
$839$	−3.86903e7			−1.89757			−0.948784	+	0.315925i	$0.897685\pi$
$840$		0			0
$841$	−1.70992e7			−0.833654
$842$		0			0
$843$	6.05513e6	−	6.05513e6i	0.293464	−	0.293464i
$844$		0			0
$845$	1.76121e7	+	5.03396e6i	0.848532	+	0.242531i
$846$		0			0
$847$	−1.68784e7	+	1.68784e7i	−0.808394	+	0.808394i
$848$		0			0
$849$			1.15860e7i			0.551649i
$850$		0			0
$851$	1.04193e7			0.493189
$852$		0			0
$853$	6.17213e6	+	6.17213e6i	0.290444	+	0.290444i	0.837256	−	0.546812i	$-0.184159\pi$
$853$	6.17213e6	+	6.17213e6i	0.290444	+	0.290444i	−0.546812	+	0.837256i	$0.684159\pi$
$854$		0			0
$855$	281394.	−	984499.i	0.0131644	−	0.0460575i
$856$		0			0
$857$	1.57290e7	+	1.57290e7i	0.731559	+	0.731559i	0.970929	−	0.239369i	$-0.0769407\pi$
$857$	1.57290e7	+	1.57290e7i	0.731559	+	0.731559i	−0.239369	+	0.970929i	$0.576941\pi$
$858$		0			0
$859$		−	2.09256e7i		−	0.967597i	−0.875179	−	0.483799i	$-0.839257\pi$
$859$		−	2.09256e7i		−	0.967597i	0.875179	−	0.483799i	$-0.160743\pi$
$860$		0			0
$861$			4.23028e7i			1.94474i
$862$		0			0
$863$	−2.82335e6	−	2.82335e6i	−0.129044	−	0.129044i	0.639635	−	0.768679i	$-0.279086\pi$
$863$	−2.82335e6	−	2.82335e6i	−0.129044	−	0.129044i	−0.768679	+	0.639635i	$0.779086\pi$
$864$		0			0
$865$	1.30511e7	−	7.24889e6i	0.593073	−	0.329406i
$866$		0			0
$867$	−1.74432e6	−	1.74432e6i	−0.0788094	−	0.0788094i
$868$		0			0
$869$	−5.46360e6			−0.245431
$870$		0			0
$871$		−	2.73444e6i		−	0.122130i
$872$		0			0
$873$	−264686.	+	264686.i	−0.0117543	+	0.0117543i
$874$		0			0
$875$	−1.96724e6	+	3.94649e7i	−0.0868636	+	1.74257i
$876$		0			0
$877$	−2.56987e7	+	2.56987e7i	−1.12827	+	1.12827i	−0.137807	+	0.990459i	$0.544005\pi$
$877$	−2.56987e7	+	2.56987e7i	−1.12827	+	1.12827i	−0.990459	+	0.137807i	$0.955995\pi$
$878$		0			0
$879$	−2.22383e7			−0.970797
$880$		0			0
$881$	1.37523e7			0.596945			0.298473	−	0.954418i	$-0.403523\pi$
$881$	1.37523e7			0.596945			0.298473	+	0.954418i	$0.403523\pi$
$882$		0			0
$883$	−2.38462e7	+	2.38462e7i	−1.02924	+	1.02924i	−0.0296818	+	0.999559i	$0.509449\pi$
$883$	−2.38462e7	+	2.38462e7i	−1.02924	+	1.02924i	−0.999559	+	0.0296818i	$0.990551\pi$
$884$		0			0
$885$	6.06142e6	−	3.36665e6i	0.260146	−	0.144491i
$886$		0			0
$887$	1.46935e6	−	1.46935e6i	0.0627070	−	0.0627070i	−0.675058	−	0.737765i	$-0.735881\pi$
$887$	1.46935e6	−	1.46935e6i	0.0627070	−	0.0627070i	0.737765	+	0.675058i	$0.235881\pi$
$888$		0			0
$889$			2.48558e7i			1.05481i
$890$		0			0
$891$	−2.80421e7			−1.18336
$892$		0			0
$893$	1.20361e7	+	1.20361e7i	0.505076	+	0.505076i
$894$		0			0
$895$	1.54168e7	+	4.40651e6i	0.643335	+	0.183881i
$896$		0			0
$897$	−5.78741e6	−	5.78741e6i	−0.240161	−	0.240161i
$898$		0			0
$899$			9.18696e6i			0.379116i
$900$		0			0
$901$			1.91658e7i			0.786527i
$902$		0			0
$903$	−4.03054e7	−	4.03054e7i	−1.64492	−	1.64492i
$904$		0			0
$905$	−6.46577e6	−	1.84808e6i	−0.262421	−	0.0750064i
$906$		0			0
$907$	1.23019e7	+	1.23019e7i	0.496541	+	0.496541i	0.910359	−	0.413819i	$-0.135805\pi$
$907$	1.23019e7	+	1.23019e7i	0.496541	+	0.496541i	−0.413819	+	0.910359i	$0.635805\pi$
$908$		0			0
$909$	−1.91100e6			−0.0767098
$910$		0			0
$911$			3.71961e7i			1.48491i	0.669894	+	0.742457i	$0.266340\pi$
$911$			3.71961e7i			1.48491i	−0.669894	+	0.742457i	$0.733660\pi$
$912$		0			0
$913$	6.52750e6	−	6.52750e6i	0.259161	−	0.259161i
$914$		0			0
$915$	2.08801e7	−	1.15973e7i	0.824480	−	0.457934i
$916$		0			0
$917$	1.89015e6	−	1.89015e6i	0.0742290	−	0.0742290i
$918$		0			0
$919$	4.30763e7			1.68248			0.841240	−	0.540663i	$-0.181826\pi$
$919$	4.30763e7			1.68248			0.841240	+	0.540663i	$0.181826\pi$
$920$		0			0
$921$	−8.43526e6			−0.327680
$922$		0			0
$923$	−2.74185e6	+	2.74185e6i	−0.105935	+	0.105935i
$924$		0			0
$925$	−1.21353e7	+	2.82342e6i	−0.466333	+	0.108498i
$926$		0			0
$927$	−1.73029e6	+	1.73029e6i	−0.0661332	+	0.0661332i
$928$		0			0
$929$			4.20699e6i			0.159931i	0.996798	+	0.0799655i	$0.0254810\pi$
$929$			4.20699e6i			0.159931i	−0.996798	+	0.0799655i	$0.974519\pi$
$930$		0			0
$931$	3.46908e7			1.31172
$932$		0			0
$933$	−2.42092e7	−	2.42092e7i	−0.910491	−	0.910491i
$934$		0			0
$935$	3.17600e7	−	1.76402e7i	1.18810	−	0.659895i
$936$		0			0
$937$	9.47934e6	+	9.47934e6i	0.352719	+	0.352719i	0.861120	−	0.508401i	$-0.169763\pi$
$937$	9.47934e6	+	9.47934e6i	0.352719	+	0.352719i	−0.508401	+	0.861120i	$0.669763\pi$
$938$		0			0
$939$			5.10787e7i			1.89049i
$940$		0			0
$941$		−	1.54846e7i		−	0.570068i	−0.958517	−	0.285034i	$-0.907995\pi$
$941$		−	1.54846e7i		−	0.570068i	0.958517	−	0.285034i	$-0.0920049\pi$
$942$		0			0
$943$	−2.30468e7	−	2.30468e7i	−0.843980	−	0.843980i
$944$		0			0
$945$	−1.36074e7	+	4.76076e7i	−0.495674	+	1.73419i
$946$		0			0
$947$	2.49743e7	+	2.49743e7i	0.904938	+	0.904938i	0.995858	−	0.0909198i	$-0.0289807\pi$
$947$	2.49743e7	+	2.49743e7i	0.904938	+	0.904938i	−0.0909198	+	0.995858i	$0.528981\pi$
$948$		0			0
$949$	−1.72231e7			−0.620792
$950$		0			0
$951$		−	4.77701e7i		−	1.71279i
$952$		0			0
$953$	−2.47870e7	+	2.47870e7i	−0.884080	+	0.884080i	−0.993946	−	0.109866i	$-0.964958\pi$
$953$	−2.47870e7	+	2.47870e7i	−0.884080	+	0.884080i	0.109866	+	0.993946i	$0.464958\pi$
$954$		0			0
$955$	2.64880e7	+	7.57093e6i	0.939812	+	0.268621i
$956$		0			0
$957$	1.01125e7	−	1.01125e7i	0.356925	−	0.356925i
$958$		0			0
$959$	−7.85169e6			−0.275687
$960$		0			0
$961$	3.89258e6			0.135965
$962$		0			0
$963$	−1.78213e6	+	1.78213e6i	−0.0619262	+	0.0619262i
$964$		0			0
$965$	2.54207e7	+	4.57682e7i	0.878756	+	1.58214i
$966$		0			0
$967$	7.85405e6	−	7.85405e6i	0.270102	−	0.270102i	−0.559039	−	0.829141i	$-0.688830\pi$
$967$	7.85405e6	−	7.85405e6i	0.270102	−	0.270102i	0.829141	+	0.559039i	$0.188830\pi$
$968$		0			0
$969$		−	1.90593e7i		−	0.652074i
$970$		0			0
$971$	5.25604e7			1.78900			0.894501	−	0.447066i	$-0.147531\pi$
$971$	5.25604e7			1.78900			0.894501	+	0.447066i	$0.147531\pi$
$972$		0			0
$973$	−5.09678e7	−	5.09678e7i	−1.72589	−	1.72589i
$974$		0			0
$975$	8.30887e6	+	5.17231e6i	0.279918	+	0.174250i
$976$		0			0
$977$	1.45106e7	+	1.45106e7i	0.486352	+	0.486352i	0.907153	−	0.420801i	$-0.138251\pi$
$977$	1.45106e7	+	1.45106e7i	0.486352	+	0.486352i	−0.420801	+	0.907153i	$0.638251\pi$
$978$		0			0
$979$			3.40746e7i			1.13625i
$980$		0			0
$981$			1.64479e6i			0.0545681i
$982$		0			0
$983$	2.86088e6	+	2.86088e6i	0.0944312	+	0.0944312i	0.752744	−	0.658313i	$-0.228730\pi$
$983$	2.86088e6	+	2.86088e6i	0.0944312	+	0.0944312i	−0.658313	+	0.752744i	$0.728730\pi$
$984$		0			0
$985$	1.34519e7	+	2.42192e7i	0.441766	+	0.795369i
$986$		0			0
$987$	−4.04291e7	−	4.04291e7i	−1.32100	−	1.32100i
$988$		0			0
$989$	4.39173e7			1.42773
$990$		0			0
$991$			4.15637e7i			1.34440i	0.740368	+	0.672202i	$0.234651\pi$
$991$			4.15637e7i			1.34440i	−0.740368	+	0.672202i	$0.765349\pi$
$992$		0			0
$993$	−3.90271e7	+	3.90271e7i	−1.25601	+	1.25601i
$994$		0			0
$995$	−1.47080e6	+	5.14582e6i	−0.0470973	+	0.164777i
$996$		0			0
$997$	−1.39380e7	+	1.39380e7i	−0.444083	+	0.444083i	−0.893382	−	0.449299i	$-0.851674\pi$
$997$	−1.39380e7	+	1.39380e7i	−0.444083	+	0.444083i	0.449299	+	0.893382i	$0.351674\pi$
$998$		0			0
$999$	−1.56127e7			−0.494952

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.o.a.47.8		56
4.3	odd	2		40.6.k.a.27.11	yes	56
5.3	odd	4	inner	160.6.o.a.143.7		56
8.3	odd	2	inner	160.6.o.a.47.7		56
8.5	even	2		40.6.k.a.27.24	yes	56
20.3	even	4		40.6.k.a.3.24	yes	56
40.3	even	4	inner	160.6.o.a.143.8		56
40.13	odd	4		40.6.k.a.3.11	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.11	✓	56	40.13	odd	4
40.6.k.a.3.24	yes	56	20.3	even	4
40.6.k.a.27.11	yes	56	4.3	odd	2
40.6.k.a.27.24	yes	56	8.5	even	2
160.6.o.a.47.7		56	8.3	odd	2	inner
160.6.o.a.47.8		56	1.1	even	1	trivial
160.6.o.a.143.7		56	5.3	odd	4	inner
160.6.o.a.143.8		56	40.3	even	4	inner

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	160.o (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-10.6033 + 10.6033i) q^{3} +(-15.3629 + 53.7493i) q^{5} +(-159.941 + 159.941i) q^{7} +18.1393i q^{9} +O(q^{10})\)	\(q+(-10.6033 + 10.6033i) q^{3} +(-15.3629 + 53.7493i) q^{5} +(-159.941 + 159.941i) q^{7} +18.1393i q^{9} -516.314 q^{11} +(147.686 + 147.686i) q^{13} +(-407.023 - 732.818i) q^{15} +(890.046 + 890.046i) q^{17} +1009.77i q^{19} -3391.81i q^{21} +(1847.88 + 1847.88i) q^{23} +(-2652.97 - 1651.48i) q^{25} +(-2768.94 - 2768.94i) q^{27} +1847.15 q^{29} +4973.59i q^{31} +(5474.64 - 5474.64i) q^{33} +(-6139.55 - 11053.9i) q^{35} +(2819.25 - 2819.25i) q^{37} -3131.92 q^{39} -12472.0 q^{41} +(11883.2 - 11883.2i) q^{43} +(-974.975 - 278.672i) q^{45} +(11919.6 - 11919.6i) q^{47} -34355.2i q^{49} -18874.9 q^{51} +(10766.7 + 10766.7i) q^{53} +(7932.06 - 27751.5i) q^{55} +(-10706.9 - 10706.9i) q^{57} +8271.39i q^{59} +28492.9i q^{61} +(-2901.22 - 2901.22i) q^{63} +(-10206.9 + 5669.13i) q^{65} +(-9257.64 - 9257.64i) q^{67} -39187.3 q^{69} +18565.5i q^{71} +(-58309.9 + 58309.9i) q^{73} +(45641.4 - 10619.0i) q^{75} +(82579.7 - 82579.7i) q^{77} +10581.9 q^{79} +54312.1 q^{81} +(-12642.5 + 12642.5i) q^{83} +(-61513.0 + 34165.7i) q^{85} +(-19585.9 + 19585.9i) q^{87} -65996.0i q^{89} -47242.0 q^{91} +(-52736.5 - 52736.5i) q^{93} +(-54274.3 - 15512.9i) q^{95} +(14591.8 + 14591.8i) q^{97} -9365.58i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3}+O(q^{10}) \) 56 * q + 4 * q^3	\( 56 q + 4 q^{3} + 8 q^{11} - 408 q^{17} - 3120 q^{25} - 968 q^{27} - 976 q^{33} + 4780 q^{35} - 8 q^{41} - 1308 q^{43} - 20872 q^{51} + 968 q^{57} + 17680 q^{65} - 89252 q^{67} - 25184 q^{73} + 127740 q^{75} - 67792 q^{81} + 126444 q^{83} - 329432 q^{91} + 212576 q^{97}+O(q^{100}) \) 56 * q + 4 * q^3 + 8 * q^11 - 408 * q^17 - 3120 * q^25 - 968 * q^27 - 976 * q^33 + 4780 * q^35 - 8 * q^41 - 1308 * q^43 - 20872 * q^51 + 968 * q^57 + 17680 * q^65 - 89252 * q^67 - 25184 * q^73 + 127740 * q^75 - 67792 * q^81 + 126444 * q^83 - 329432 * q^91 + 212576 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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