LMFDB - Embedded newform 160.6.o.a.47.18

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			47.18
Character	$\chi$	$=$	160.47
Dual form			160.6.o.a.143.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.85746 - 5.85746i) q^{3} +(-13.4330 + 54.2637i) q^{5} +(-100.487 + 100.487i) q^{7} +174.380i q^{9} +O(q^{10})$	\(q+(5.85746 - 5.85746i) q^{3} +(-13.4330 + 54.2637i) q^{5} +(-100.487 + 100.487i) q^{7} +174.380i q^{9} +546.323 q^{11} +(-619.525 - 619.525i) q^{13} +(239.164 + 396.531i) q^{15} +(-1509.84 - 1509.84i) q^{17} -1145.03i q^{19} +1177.20i q^{21} +(-2136.97 - 2136.97i) q^{23} +(-2764.11 - 1457.85i) q^{25} +(2444.79 + 2444.79i) q^{27} +1309.79 q^{29} +4695.04i q^{31} +(3200.07 - 3200.07i) q^{33} +(-4102.97 - 6802.67i) q^{35} +(-7598.37 + 7598.37i) q^{37} -7257.68 q^{39} -8811.44 q^{41} +(745.885 - 745.885i) q^{43} +(-9462.53 - 2342.46i) q^{45} +(-26.5684 + 26.5684i) q^{47} -3388.42i q^{49} -17687.6 q^{51} +(189.847 + 189.847i) q^{53} +(-7338.77 + 29645.5i) q^{55} +(-6706.96 - 6706.96i) q^{57} -39197.3i q^{59} -1750.39i q^{61} +(-17523.0 - 17523.0i) q^{63} +(41939.8 - 25295.7i) q^{65} +(-20889.0 - 20889.0i) q^{67} -25034.4 q^{69} -15059.6i q^{71} +(-2616.06 + 2616.06i) q^{73} +(-24730.0 + 7651.34i) q^{75} +(-54898.6 + 54898.6i) q^{77} -17424.9 q^{79} -13734.0 q^{81} +(-31132.3 + 31132.3i) q^{83} +(102211. - 61647.7i) q^{85} +(7672.05 - 7672.05i) q^{87} +33401.4i q^{89} +124509. q^{91} +(27501.0 + 27501.0i) q^{93} +(62133.6 + 15381.2i) q^{95} +(3265.58 + 3265.58i) q^{97} +95268.1i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	5.85746	−	5.85746i	0.375756	−	0.375756i	−0.493812	−	0.869568i	$-0.664397\pi$
$3$	5.85746	−	5.85746i	0.375756	−	0.375756i	0.869568	+	0.493812i	$0.164397\pi$
$4$		0			0
$5$	−13.4330	+	54.2637i	−0.240297	+	0.970699i
$5$	−13.4330	+	54.2637i	−0.240297	+	0.970699i
$6$		0			0
$7$	−100.487	+	100.487i	−0.775115	+	0.775115i	−0.978996	−	0.203880i	$-0.934645\pi$
$7$	−100.487	+	100.487i	−0.775115	+	0.775115i	0.203880	+	0.978996i	$0.434645\pi$
$8$		0			0
$9$			174.380i			0.717615i
$10$		0			0
$11$	546.323			1.36134			0.680672	−	0.732588i	$-0.261688\pi$
$11$	546.323			1.36134			0.680672	+	0.732588i	$0.261688\pi$
$12$		0			0
$13$	−619.525	−	619.525i	−1.01672	−	1.01672i	−0.999858	−	0.0168600i	$-0.994633\pi$
$13$	−619.525	−	619.525i	−1.01672	−	1.01672i	−0.0168600	−	0.999858i	$-0.505367\pi$
$14$		0			0
$15$	239.164	+	396.531i	0.274453	+	0.455039i
$16$		0			0
$17$	−1509.84	−	1509.84i	−1.26709	−	1.26709i	−0.947585	−	0.319505i	$-0.896483\pi$
$17$	−1509.84	−	1509.84i	−1.26709	−	1.26709i	−0.319505	−	0.947585i	$-0.603517\pi$
$18$		0			0
$19$		−	1145.03i		−	0.727667i	−0.931464	−	0.363833i	$-0.881468\pi$
$19$		−	1145.03i		−	0.727667i	0.931464	−	0.363833i	$-0.118532\pi$
$20$		0			0
$21$			1177.20i			0.582509i
$22$		0			0
$23$	−2136.97	−	2136.97i	−0.842321	−	0.842321i	0.146839	−	0.989160i	$-0.453090\pi$
$23$	−2136.97	−	2136.97i	−0.842321	−	0.842321i	−0.989160	+	0.146839i	$0.953090\pi$
$24$		0			0
$25$	−2764.11	−	1457.85i	−0.884514	−	0.466513i
$26$		0			0
$27$	2444.79	+	2444.79i	0.645404	+	0.645404i
$28$		0			0
$29$	1309.79			0.289206			0.144603	−	0.989490i	$-0.453810\pi$
$29$	1309.79			0.289206			0.144603	+	0.989490i	$0.453810\pi$
$30$		0			0
$31$			4695.04i			0.877476i	0.898615	+	0.438738i	$0.144574\pi$
$31$			4695.04i			0.877476i	−0.898615	+	0.438738i	$0.855426\pi$
$32$		0			0
$33$	3200.07	−	3200.07i	0.511533	−	0.511533i
$34$		0			0
$35$	−4102.97	−	6802.67i	−0.566146	−	0.938662i
$36$		0			0
$37$	−7598.37	+	7598.37i	−0.912464	+	0.912464i	−0.996466	−	0.0840014i	$-0.973230\pi$
$37$	−7598.37	+	7598.37i	−0.912464	+	0.912464i	0.0840014	+	0.996466i	$0.473230\pi$
$38$		0			0
$39$	−7257.68			−0.764076
$40$		0			0
$41$	−8811.44			−0.818629			−0.409314	−	0.912393i	$-0.634232\pi$
$41$	−8811.44			−0.818629			−0.409314	+	0.912393i	$0.634232\pi$
$42$		0			0
$43$	745.885	−	745.885i	0.0615178	−	0.0615178i	−0.675679	−	0.737196i	$-0.736149\pi$
$43$	745.885	−	745.885i	0.0615178	−	0.0615178i	0.737196	+	0.675679i	$0.236149\pi$
$44$		0			0
$45$	−9462.53	−	2342.46i	−0.696588	−	0.172441i
$46$		0			0
$47$	−26.5684	+	26.5684i	−0.00175437	+	0.00175437i	−0.707983	−	0.706229i	$-0.750395\pi$
$47$	−26.5684	+	26.5684i	−0.00175437	+	0.00175437i	0.706229	+	0.707983i	$0.250395\pi$
$48$		0			0
$49$		−	3388.42i		−	0.201608i
$50$		0			0
$51$	−17687.6			−0.952233
$52$		0			0
$53$	189.847	+	189.847i	0.00928357	+	0.00928357i	0.711733	−	0.702450i	$-0.247910\pi$
$53$	189.847	+	189.847i	0.00928357	+	0.00928357i	−0.702450	+	0.711733i	$0.747910\pi$
$54$		0			0
$55$	−7338.77	+	29645.5i	−0.327127	+	1.32146i
$56$		0			0
$57$	−6706.96	−	6706.96i	−0.273425	−	0.273425i
$58$		0			0
$59$		−	39197.3i		−	1.46597i	−0.680242	−	0.732987i	$-0.738125\pi$
$59$		−	39197.3i		−	1.46597i	0.680242	−	0.732987i	$-0.261875\pi$
$60$		0			0
$61$		−	1750.39i		−	0.0602296i	−0.999546	−	0.0301148i	$-0.990413\pi$
$61$		−	1750.39i		−	0.0602296i	0.999546	−	0.0301148i	$-0.00958729\pi$
$62$		0			0
$63$	−17523.0	−	17523.0i	−0.556234	−	0.556234i
$64$		0			0
$65$	41939.8	−	25295.7i	1.23124	−	0.742613i
$66$		0			0
$67$	−20889.0	−	20889.0i	−0.568501	−	0.568501i	0.363207	−	0.931708i	$-0.381682\pi$
$67$	−20889.0	−	20889.0i	−0.568501	−	0.568501i	−0.931708	+	0.363207i	$0.881682\pi$
$68$		0			0
$69$	−25034.4			−0.633015
$70$		0			0
$71$		−	15059.6i		−	0.354541i	−0.984162	−	0.177271i	$-0.943273\pi$
$71$		−	15059.6i		−	0.354541i	0.984162	−	0.177271i	$-0.0567268\pi$
$72$		0			0
$73$	−2616.06	+	2616.06i	−0.0574566	+	0.0574566i	−0.735251	−	0.677795i	$-0.762936\pi$
$73$	−2616.06	+	2616.06i	−0.0574566	+	0.0574566i	0.677795	+	0.735251i	$0.262936\pi$
$74$		0			0
$75$	−24730.0	+	7651.34i	−0.507657	+	0.157067i
$76$		0			0
$77$	−54898.6	+	54898.6i	−1.05520	+	1.05520i
$78$		0			0
$79$	−17424.9			−0.314125			−0.157062	−	0.987589i	$-0.550202\pi$
$79$	−17424.9			−0.314125			−0.157062	+	0.987589i	$0.550202\pi$
$80$		0			0
$81$	−13734.0			−0.232586
$82$		0			0
$83$	−31132.3	+	31132.3i	−0.496039	+	0.496039i	−0.910203	−	0.414163i	$-0.864074\pi$
$83$	−31132.3	+	31132.3i	−0.496039	+	0.496039i	0.414163	+	0.910203i	$0.364074\pi$
$84$		0			0
$85$	102211.	−	61647.7i	1.53444	−	0.925485i
$86$		0			0
$87$	7672.05	−	7672.05i	0.108671	−	0.108671i
$88$		0			0
$89$			33401.4i			0.446982i	0.974706	+	0.223491i	$0.0717454\pi$
$89$			33401.4i			0.446982i	−0.974706	+	0.223491i	$0.928255\pi$
$90$		0			0
$91$	124509.			1.57615
$92$		0			0
$93$	27501.0	+	27501.0i	0.329717	+	0.329717i
$94$		0			0
$95$	62133.6	+	15381.2i	0.706346	+	0.174856i
$96$		0			0
$97$	3265.58	+	3265.58i	0.0352396	+	0.0352396i	0.724507	−	0.689267i	$-0.242067\pi$
$97$	3265.58	+	3265.58i	0.0352396	+	0.0352396i	−0.689267	+	0.724507i	$0.742067\pi$
$98$		0			0
$99$			95268.1i			0.976921i
$100$		0			0
$101$		−	17293.5i		−	0.168686i	−0.996437	−	0.0843431i	$-0.973121\pi$
$101$		−	17293.5i		−	0.168686i	0.996437	−	0.0843431i	$-0.0268792\pi$
$102$		0			0
$103$	−41987.6	−	41987.6i	−0.389967	−	0.389967i	0.484709	−	0.874676i	$-0.338926\pi$
$103$	−41987.6	−	41987.6i	−0.389967	−	0.389967i	−0.874676	+	0.484709i	$0.838926\pi$
$104$		0			0
$105$	−63879.3	−	15813.4i	−0.565441	−	0.139975i
$106$		0			0
$107$	107361.	+	107361.i	0.906538	+	0.906538i	0.995991	−	0.0894528i	$-0.0285118\pi$
$107$	107361.	+	107361.i	0.906538	+	0.906538i	−0.0894528	+	0.995991i	$0.528512\pi$
$108$		0			0
$109$	−51260.4			−0.413253			−0.206626	−	0.978420i	$-0.566248\pi$
$109$	−51260.4			−0.413253			−0.206626	+	0.978420i	$0.566248\pi$
$110$		0			0
$111$			89014.2i			0.685728i
$112$		0			0
$113$	−150086.	+	150086.i	−1.10571	+	1.10571i	−0.112006	+	0.993707i	$0.535728\pi$
$113$	−150086.	+	150086.i	−1.10571	+	1.10571i	−0.993707	+	0.112006i	$0.964272\pi$
$114$		0			0
$115$	144666.	−	87253.8i	1.02005	−	0.615233i
$116$		0			0
$117$	108033.	−	108033.i	0.729612	−	0.729612i
$118$		0			0
$119$	303439.			1.96428
$120$		0			0
$121$	137418.			0.853259
$122$		0			0
$123$	−51612.6	+	51612.6i	−0.307605	+	0.307605i
$124$		0			0
$125$	116239.	−	130407.i	0.665390	−	0.746496i
$126$		0			0
$127$	196504.	−	196504.i	1.08109	−	1.08109i	0.0846831	−	0.996408i	$-0.473012\pi$
$127$	196504.	−	196504.i	1.08109	−	1.08109i	0.996408	−	0.0846831i	$-0.0269878\pi$
$128$		0			0
$129$		−	8737.98i		−	0.0462314i
$130$		0			0
$131$	−146773.			−0.747254			−0.373627	−	0.927579i	$-0.621886\pi$
$131$	−146773.			−0.747254			−0.373627	+	0.927579i	$0.621886\pi$
$132$		0			0
$133$	115061.	+	115061.i	0.564026	+	0.564026i
$134$		0			0
$135$	−165504.	+	99822.4i	−0.781582	+	0.471405i
$136$		0			0
$137$	127282.	+	127282.i	0.579381	+	0.579381i	0.934733	−	0.355351i	$-0.115639\pi$
$137$	127282.	+	127282.i	0.579381	+	0.579381i	−0.355351	+	0.934733i	$0.615639\pi$
$138$		0			0
$139$			127272.i			0.558722i	0.960186	+	0.279361i	$0.0901226\pi$
$139$			127272.i			0.558722i	−0.960186	+	0.279361i	$0.909877\pi$
$140$		0			0
$141$			311.247i			0.00131843i
$142$		0			0
$143$	−338461.	−	338461.i	−1.38410	−	1.38410i
$144$		0			0
$145$	−17594.5	+	71074.2i	−0.0694954	+	0.280732i
$146$		0			0
$147$	−19847.5	−	19847.5i	−0.0757553	−	0.0757553i
$148$		0			0
$149$	−206774.			−0.763011			−0.381506	−	0.924367i	$-0.624594\pi$
$149$	−206774.			−0.763011			−0.381506	+	0.924367i	$0.624594\pi$
$150$		0			0
$151$			251221.i			0.896632i	0.893875	+	0.448316i	$0.147976\pi$
$151$			251221.i			0.896632i	−0.893875	+	0.448316i	$0.852024\pi$
$152$		0			0
$153$	263286.	−	263286.i	0.909282	−	0.909282i
$154$		0			0
$155$	−254771.	−	63068.6i	−0.851765	−	0.210855i
$156$		0			0
$157$	−74099.0	+	74099.0i	−0.239918	+	0.239918i	−0.816816	−	0.576898i	$-0.804263\pi$
$157$	−74099.0	+	74099.0i	−0.239918	+	0.239918i	0.576898	+	0.816816i	$0.304263\pi$
$158$		0			0
$159$	2224.05			0.00697672
$160$		0			0
$161$	429476.			1.30579
$162$		0			0
$163$	80376.6	−	80376.6i	0.236952	−	0.236952i	−0.578635	−	0.815587i	$-0.696414\pi$
$163$	80376.6	−	80376.6i	0.236952	−	0.236952i	0.815587	+	0.578635i	$0.196414\pi$
$164$		0			0
$165$	130661.	+	216634.i	0.373625	+	0.619465i
$166$		0			0
$167$	−67918.4	+	67918.4i	−0.188450	+	0.188450i	−0.795026	−	0.606576i	$-0.792543\pi$
$167$	−67918.4	+	67918.4i	−0.188450	+	0.188450i	0.606576	+	0.795026i	$0.292543\pi$
$168$		0			0
$169$			396329.i			1.06743i
$170$		0			0
$171$	199671.			0.522185
$172$		0			0
$173$	−68660.9	−	68660.9i	−0.174419	−	0.174419i	0.614499	−	0.788918i	$-0.289358\pi$
$173$	−68660.9	−	68660.9i	−0.174419	−	0.174419i	−0.788918	+	0.614499i	$0.789358\pi$
$174$		0			0
$175$	424254.	−	131262.i	1.04720	−	0.324000i
$176$		0			0
$177$	−229597.	−	229597.i	−0.550849	−	0.550849i
$178$		0			0
$179$			346919.i			0.809274i	0.914477	+	0.404637i	$0.132602\pi$
$179$			346919.i			0.809274i	−0.914477	+	0.404637i	$0.867398\pi$
$180$		0			0
$181$		−	79034.8i		−	0.179317i	−0.995973	−	0.0896586i	$-0.971422\pi$
$181$		−	79034.8i		−	0.179317i	0.995973	−	0.0896586i	$-0.0285776\pi$
$182$		0			0
$183$	−10252.8	−	10252.8i	−0.0226316	−	0.0226316i
$184$		0			0
$185$	−310247.	−	514385.i	−0.666466	−	1.10499i
$186$		0			0
$187$	−824858.	−	824858.i	−1.72495	−	1.72495i
$188$		0			0
$189$	−491341.			−1.00053
$190$		0			0
$191$			724824.i			1.43764i	0.695198	+	0.718819i	$0.255317\pi$
$191$			724824.i			1.43764i	−0.695198	+	0.718819i	$0.744683\pi$
$192$		0			0
$193$	−508619.	+	508619.i	−0.982877	+	0.982877i	−0.999856	−	0.0169786i	$-0.994595\pi$
$193$	−508619.	+	508619.i	−0.982877	+	0.982877i	0.0169786	+	0.999856i	$0.494595\pi$
$194$		0			0
$195$	97492.6	−	393829.i	0.183605	−	0.741688i
$196$		0			0
$197$	190061.	−	190061.i	0.348922	−	0.348922i	−0.510786	−	0.859708i	$-0.670646\pi$
$197$	190061.	−	190061.i	0.348922	−	0.348922i	0.859708	+	0.510786i	$0.170646\pi$
$198$		0			0
$199$	−945435.			−1.69238			−0.846192	−	0.532878i	$-0.821111\pi$
$199$	−945435.			−1.69238			−0.846192	+	0.532878i	$0.821111\pi$
$200$		0			0
$201$	−244713.			−0.427236
$202$		0			0
$203$	−131617.	+	131617.i	−0.224168	+	0.224168i
$204$		0			0
$205$	118364.	−	478141.i	0.196714	−	0.794642i
$206$		0			0
$207$	372645.	−	372645.i	0.604462	−	0.604462i
$208$		0			0
$209$		−	625556.i		−	0.990605i
$210$		0			0
$211$	1.01059e6			1.56267			0.781337	−	0.624109i	$-0.214538\pi$
$211$	1.01059e6			1.56267			0.781337	+	0.624109i	$0.214538\pi$
$212$		0			0
$213$	−88210.8	−	88210.8i	−0.133221	−	0.133221i
$214$		0			0
$215$	30455.0	+	50494.0i	0.0449327	+	0.0744978i
$216$		0			0
$217$	−471792.	−	471792.i	−0.680145	−	0.680145i
$218$		0			0
$219$			30646.9i			0.0431794i
$220$		0			0
$221$			1.87076e6i			2.57655i
$222$		0			0
$223$	−320886.	−	320886.i	−0.432104	−	0.432104i	0.457239	−	0.889344i	$-0.348838\pi$
$223$	−320886.	−	320886.i	−0.432104	−	0.432104i	−0.889344	+	0.457239i	$0.848838\pi$
$224$		0			0
$225$	254221.	−	482006.i	0.334776	−	0.634741i
$226$		0			0
$227$	307496.	+	307496.i	0.396073	+	0.396073i	0.876845	−	0.480772i	$-0.159644\pi$
$227$	307496.	+	307496.i	0.396073	+	0.396073i	−0.480772	+	0.876845i	$0.659644\pi$
$228$		0			0
$229$	−821991.			−1.03581			−0.517903	−	0.855439i	$-0.673287\pi$
$229$	−821991.			−1.03581			−0.517903	+	0.855439i	$0.673287\pi$
$230$		0			0
$231$			643132.i			0.792995i
$232$		0			0
$233$	−444211.	+	444211.i	−0.536043	+	0.536043i	−0.922364	−	0.386321i	$-0.873746\pi$
$233$	−444211.	+	444211.i	−0.536043	+	0.536043i	0.386321	+	0.922364i	$0.373746\pi$
$234$		0			0
$235$	−1084.81	−	1798.60i	−0.00128140	−	0.00212454i
$236$		0			0
$237$	−102066.	+	102066.i	−0.118034	+	0.118034i
$238$		0			0
$239$	−668811.			−0.757371			−0.378685	−	0.925526i	$-0.623624\pi$
$239$	−668811.			−0.757371			−0.378685	+	0.925526i	$0.623624\pi$
$240$		0			0
$241$	923504.			1.02423			0.512114	−	0.858918i	$-0.328863\pi$
$241$	923504.			1.02423			0.512114	+	0.858918i	$0.328863\pi$
$242$		0			0
$243$	−674529.	+	674529.i	−0.732800	+	0.732800i
$244$		0			0
$245$	183868.	+	45516.7i	0.195700	+	0.0484457i
$246$		0			0
$247$	−709374.	+	709374.i	−0.739832	+	0.739832i
$248$		0			0
$249$			364712.i			0.372780i
$250$		0			0
$251$	428698.			0.429504			0.214752	−	0.976669i	$-0.431106\pi$
$251$	428698.			0.429504			0.214752	+	0.976669i	$0.431106\pi$
$252$		0			0
$253$	−1.16747e6	−	1.16747e6i	−1.14669	−	1.14669i
$254$		0			0
$255$	237598.	−	959795.i	0.228819	−	0.924332i
$256$		0			0
$257$	−935603.	−	935603.i	−0.883606	−	0.883606i	0.110293	−	0.993899i	$-0.464821\pi$
$257$	−935603.	−	935603.i	−0.883606	−	0.883606i	−0.993899	+	0.110293i	$0.964821\pi$
$258$		0			0
$259$		−	1.52708e6i		−	1.41453i
$260$		0			0
$261$			228402.i			0.207538i
$262$		0			0
$263$	1.11658e6	+	1.11658e6i	0.995411	+	0.995411i	0.999990	−	0.00457866i	$-0.00145744\pi$
$263$	1.11658e6	+	1.11658e6i	0.995411	+	0.995411i	−0.00457866	+	0.999990i	$0.501457\pi$
$264$		0			0
$265$	−12852.1	+	7751.61i	−0.0112424	+	0.00678074i
$266$		0			0
$267$	195648.	+	195648.i	0.167956	+	0.167956i
$268$		0			0
$269$	2.11682e6			1.78362			0.891810	−	0.452410i	$-0.149436\pi$
$269$	2.11682e6			1.78362			0.891810	+	0.452410i	$0.149436\pi$
$270$		0			0
$271$		−	2.01962e6i		−	1.67050i	−0.549868	−	0.835252i	$-0.685322\pi$
$271$		−	2.01962e6i		−	1.67050i	0.549868	−	0.835252i	$-0.314678\pi$
$272$		0			0
$273$	729305.	−	729305.i	0.592247	−	0.592247i
$274$		0			0
$275$	−1.51010e6	−	796459.i	−1.20413	−	0.635084i
$276$		0			0
$277$	418515.	−	418515.i	0.327727	−	0.327727i	−0.523995	−	0.851721i	$-0.675559\pi$
$277$	418515.	−	418515.i	0.327727	−	0.327727i	0.851721	+	0.523995i	$0.175559\pi$
$278$		0			0
$279$	−818723.			−0.629690
$280$		0			0
$281$	293805.			0.221969			0.110985	−	0.993822i	$-0.464600\pi$
$281$	293805.			0.221969			0.110985	+	0.993822i	$0.464600\pi$
$282$		0			0
$283$	133050.	−	133050.i	0.0987527	−	0.0987527i	−0.656004	−	0.754757i	$-0.727755\pi$
$283$	133050.	−	133050.i	0.0987527	−	0.0987527i	0.754757	+	0.656004i	$0.227755\pi$
$284$		0			0
$285$	454040.	−	273850.i	0.331117	−	0.199710i
$286$		0			0
$287$	885438.	−	885438.i	0.634532	−	0.634532i
$288$		0			0
$289$			3.13935e6i			2.21103i
$290$		0			0
$291$	38256.0			0.0264830
$292$		0			0
$293$	−686968.	−	686968.i	−0.467484	−	0.467484i	0.433614	−	0.901099i	$-0.357238\pi$
$293$	−686968.	−	686968.i	−0.467484	−	0.467484i	−0.901099	+	0.433614i	$0.857238\pi$
$294$		0			0
$295$	2.12699e6	+	526539.i	1.42302	+	0.352270i
$296$		0			0
$297$	1.33564e6	+	1.33564e6i	0.878617	+	0.878617i
$298$		0			0
$299$			2.64781e6i			1.71281i
$300$		0			0
$301$			149904.i			0.0953667i
$302$		0			0
$303$	−101296.	−	101296.i	−0.0633849	−	0.0633849i
$304$		0			0
$305$	94982.7	+	23513.0i	0.0584649	+	0.0144730i
$306$		0			0
$307$	397372.	+	397372.i	0.240631	+	0.240631i	0.817111	−	0.576480i	$-0.195574\pi$
$307$	397372.	+	397372.i	0.240631	+	0.240631i	−0.576480	+	0.817111i	$0.695574\pi$
$308$		0			0
$309$	−491881.			−0.293065
$310$		0			0
$311$			2.55376e6i			1.49720i	0.663023	+	0.748599i	$0.269273\pi$
$311$			2.55376e6i			1.49720i	−0.663023	+	0.748599i	$0.730727\pi$
$312$		0			0
$313$	93894.6	−	93894.6i	0.0541726	−	0.0541726i	−0.679501	−	0.733674i	$-0.737804\pi$
$313$	93894.6	−	93894.6i	0.0541726	−	0.0541726i	0.733674	+	0.679501i	$0.237804\pi$
$314$		0			0
$315$	1.18625e6	−	715478.i	0.673598	−	0.406275i
$316$		0			0
$317$	1.55567e6	−	1.55567e6i	0.869497	−	0.869497i	−0.122920	−	0.992417i	$-0.539226\pi$
$317$	1.55567e6	−	1.55567e6i	0.869497	−	0.869497i	0.992417	+	0.122920i	$0.0392258\pi$
$318$		0			0
$319$	715569.			0.393709
$320$		0			0
$321$	1.25772e6			0.681274
$322$		0			0
$323$	−1.72881e6	+	1.72881e6i	−0.922019	+	0.922019i
$324$		0			0
$325$	809258.	+	2.61561e6i	0.424990	+	1.37361i
$326$		0			0
$327$	−300256.	+	300256.i	−0.155282	+	0.155282i
$328$		0			0
$329$		−	5339.58i		−	0.00271968i
$330$		0			0
$331$	976781.			0.490035			0.245018	−	0.969519i	$-0.421206\pi$
$331$	976781.			0.490035			0.245018	+	0.969519i	$0.421206\pi$
$332$		0			0
$333$	−1.32501e6	−	1.32501e6i	−0.654798	−	0.654798i
$334$		0			0
$335$	1.41412e6	−	852915.i	0.688453	−	0.415235i
$336$		0			0
$337$	1.02826e6	+	1.02826e6i	0.493207	+	0.493207i	0.909315	−	0.416108i	$-0.136606\pi$
$337$	1.02826e6	+	1.02826e6i	0.493207	+	0.493207i	−0.416108	+	0.909315i	$0.636606\pi$
$338$		0			0
$339$			1.75824e6i			0.830957i
$340$		0			0
$341$			2.56501e6i			1.19455i
$342$		0			0
$343$	−1.34840e6	−	1.34840e6i	−0.618846	−	0.618846i
$344$		0			0
$345$	336287.	−	1.35846e6i	0.152112	−	0.614467i
$346$		0			0
$347$	−404120.	−	404120.i	−0.180172	−	0.180172i	0.611259	−	0.791431i	$-0.290663\pi$
$347$	−404120.	−	404120.i	−0.180172	−	0.180172i	−0.791431	+	0.611259i	$0.790663\pi$
$348$		0			0
$349$	2.80363e6			1.23213			0.616065	−	0.787695i	$-0.288726\pi$
$349$	2.80363e6			1.23213			0.616065	+	0.787695i	$0.288726\pi$
$350$		0			0
$351$		−	3.02921e6i		−	1.31239i
$352$		0			0
$353$	−2.76762e6	+	2.76762e6i	−1.18214	+	1.18214i	−0.202956	+	0.979188i	$0.565055\pi$
$353$	−2.76762e6	+	2.76762e6i	−1.18214	+	1.18214i	−0.979188	+	0.202956i	$0.934945\pi$
$354$		0			0
$355$	817189.	+	202296.i	0.344153	+	0.0851953i
$356$		0			0
$357$	1.77738e6	−	1.77738e6i	0.738090	−	0.738090i
$358$		0			0
$359$	−1.57792e6			−0.646175			−0.323088	−	0.946369i	$-0.604721\pi$
$359$	−1.57792e6			−0.646175			−0.323088	+	0.946369i	$0.604721\pi$
$360$		0			0
$361$	1.16501e6			0.470501
$362$		0			0
$363$	804921.	−	804921.i	0.320617	−	0.320617i
$364$		0			0
$365$	−106816.	−	177099.i	−0.0419665	−	0.0695798i
$366$		0			0
$367$	1.27870e6	−	1.27870e6i	0.495567	−	0.495567i	−0.414488	−	0.910055i	$-0.636039\pi$
$367$	1.27870e6	−	1.27870e6i	0.495567	−	0.495567i	0.910055	+	0.414488i	$0.136039\pi$
$368$		0			0
$369$		−	1.53654e6i		−	0.587460i
$370$		0			0
$371$	−38154.5			−0.0143917
$372$		0			0
$373$	−954700.	−	954700.i	−0.355300	−	0.355300i	0.506777	−	0.862077i	$-0.330837\pi$
$373$	−954700.	−	954700.i	−0.355300	−	0.355300i	−0.862077	+	0.506777i	$0.830837\pi$
$374$		0			0
$375$	−82992.2	−	1.44472e6i	−0.0304761	−	0.530525i
$376$		0			0
$377$	−811448.	−	811448.i	−0.294041	−	0.294041i
$378$		0			0
$379$		−	732358.i		−	0.261894i	−0.991389	−	0.130947i	$-0.958198\pi$
$379$		−	732358.i		−	0.261894i	0.991389	−	0.130947i	$-0.0418017\pi$
$380$		0			0
$381$		−	2.30203e6i		−	0.812453i
$382$		0			0
$383$	1.21103e6	+	1.21103e6i	0.421851	+	0.421851i	0.885841	−	0.463989i	$-0.153582\pi$
$383$	1.21103e6	+	1.21103e6i	0.421851	+	0.421851i	−0.463989	+	0.885841i	$0.653582\pi$
$384$		0			0
$385$	−2.24155e6	−	3.71646e6i	−0.770720	−	1.27784i
$386$		0			0
$387$	130068.	+	130068.i	0.0441461	+	0.0441461i
$388$		0			0
$389$	−3.87126e6			−1.29711			−0.648557	−	0.761166i	$-0.724627\pi$
$389$	−3.87126e6			−1.29711			−0.648557	+	0.761166i	$0.724627\pi$
$390$		0			0
$391$			6.45293e6i			2.13459i
$392$		0			0
$393$	−859717.	+	859717.i	−0.280785	+	0.280785i
$394$		0			0
$395$	234069.	−	945540.i	0.0754834	−	0.304921i
$396$		0			0
$397$	−3.28430e6	+	3.28430e6i	−1.04584	+	1.04584i	−0.0469472	+	0.998897i	$0.514949\pi$
$397$	−3.28430e6	+	3.28430e6i	−1.04584	+	1.04584i	−0.998897	+	0.0469472i	$0.985051\pi$
$398$		0			0
$399$	1.34793e6			0.423872
$400$		0			0
$401$	−4.96788e6			−1.54280			−0.771401	−	0.636349i	$-0.780444\pi$
$401$	−4.96788e6			−1.54280			−0.771401	+	0.636349i	$0.780444\pi$
$402$		0			0
$403$	2.90870e6	−	2.90870e6i	0.892145	−	0.892145i
$404$		0			0
$405$	184489.	−	745256.i	0.0558897	−	0.225771i
$406$		0			0
$407$	−4.15116e6	+	4.15116e6i	−1.24218	+	1.24218i
$408$		0			0
$409$		−	4.77068e6i		−	1.41017i	−0.709122	−	0.705085i	$-0.750909\pi$
$409$		−	4.77068e6i		−	1.41017i	0.709122	−	0.705085i	$-0.249091\pi$
$410$		0			0
$411$	1.49109e6			0.435412
$412$		0			0
$413$	3.93884e6	+	3.93884e6i	1.13630	+	1.13630i
$414$		0			0
$415$	−1.27115e6	−	2.10756e6i	−0.362308	−	0.600702i
$416$		0			0
$417$	745490.	+	745490.i	0.209943	+	0.209943i
$418$		0			0
$419$		−	144488.i		−	0.0402065i	−0.999798	−	0.0201032i	$-0.993601\pi$
$419$		−	144488.i		−	0.0402065i	0.999798	−	0.0201032i	$-0.00639949\pi$
$420$		0			0
$421$		−	4.80073e6i		−	1.32008i	−0.751229	−	0.660042i	$-0.770538\pi$
$421$		−	4.80073e6i		−	1.32008i	0.751229	−	0.660042i	$-0.229462\pi$
$422$		0			0
$423$	−4633.01	−	4633.01i	−0.00125896	−	0.00125896i
$424$		0			0
$425$	1.97223e6	+	6.37446e6i	0.529646	+	1.71187i
$426$		0			0
$427$	175892.	+	175892.i	0.0466849	+	0.0466849i
$428$		0			0
$429$	−3.96504e6			−1.04017
$430$		0			0
$431$		−	5.19074e6i		−	1.34597i	−0.739655	−	0.672986i	$-0.765011\pi$
$431$		−	5.19074e6i		−	1.34597i	0.739655	−	0.672986i	$-0.234989\pi$
$432$		0			0
$433$	3.29626e6	−	3.29626e6i	0.844894	−	0.844894i	−0.144597	−	0.989491i	$-0.546188\pi$
$433$	3.29626e6	−	3.29626e6i	0.844894	−	0.844894i	0.989491	+	0.144597i	$0.0461885\pi$
$434$		0			0
$435$	313255.	+	519373.i	0.0793734	+	0.131600i
$436$		0			0
$437$	−2.44689e6	+	2.44689e6i	−0.612929	+	0.612929i
$438$		0			0
$439$	−906765.			−0.224561			−0.112280	−	0.993677i	$-0.535815\pi$
$439$	−906765.			−0.224561			−0.112280	+	0.993677i	$0.535815\pi$
$440$		0			0
$441$	590874.			0.144677
$442$		0			0
$443$	−4.04046e6	+	4.04046e6i	−0.978186	+	0.978186i	−0.999767	−	0.0215808i	$-0.993130\pi$
$443$	−4.04046e6	+	4.04046e6i	−0.978186	+	0.978186i	0.0215808	+	0.999767i	$0.493130\pi$
$444$		0			0
$445$	−1.81249e6	−	448682.i	−0.433885	−	0.107409i
$446$		0			0
$447$	−1.21117e6	+	1.21117e6i	−0.286706	+	0.286706i
$448$		0			0
$449$			567297.i			0.132799i	0.997793	+	0.0663995i	$0.0211512\pi$
$449$			567297.i			0.132799i	−0.997793	+	0.0663995i	$0.978849\pi$
$450$		0			0
$451$	−4.81389e6			−1.11444
$452$		0			0
$453$	1.47152e6	+	1.47152e6i	0.336915	+	0.336915i
$454$		0			0
$455$	−1.67253e6	+	6.75632e6i	−0.378744	+	1.52997i
$456$		0			0
$457$	−3.73989e6	−	3.73989e6i	−0.837662	−	0.837662i	0.150889	−	0.988551i	$-0.451787\pi$
$457$	−3.73989e6	−	3.73989e6i	−0.837662	−	0.837662i	−0.988551	+	0.150889i	$0.951787\pi$
$458$		0			0
$459$		−	7.38245e6i		−	1.63557i
$460$		0			0
$461$			3.97764e6i			0.871711i	0.900017	+	0.435856i	$0.143554\pi$
$461$			3.97764e6i			0.871711i	−0.900017	+	0.435856i	$0.856446\pi$
$462$		0			0
$463$	−4.06996e6	−	4.06996e6i	−0.882343	−	0.882343i	0.111429	−	0.993772i	$-0.464457\pi$
$463$	−4.06996e6	−	4.06996e6i	−0.882343	−	0.882343i	−0.993772	+	0.111429i	$0.964457\pi$
$464$		0			0
$465$	−1.86173e6	+	1.12289e6i	−0.399286	+	0.240826i
$466$		0			0
$467$	−5.80864e6	−	5.80864e6i	−1.23249	−	1.23249i	−0.963006	−	0.269481i	$-0.913148\pi$
$467$	−5.80864e6	−	5.80864e6i	−1.23249	−	1.23249i	−0.269481	−	0.963006i	$-0.586852\pi$
$468$		0			0
$469$	4.19817e6			0.881308
$470$		0			0
$471$			868064.i			0.180302i
$472$		0			0
$473$	407494.	−	407494.i	0.0837469	−	0.0837469i
$474$		0			0
$475$	−1.66928e6	+	3.16498e6i	−0.339466	+	0.643632i
$476$		0			0
$477$	−33105.7	+	33105.7i	−0.00666203	+	0.00666203i
$478$		0			0
$479$	5.53752e6			1.10275			0.551374	−	0.834258i	$-0.314104\pi$
$479$	5.53752e6			1.10275			0.551374	+	0.834258i	$0.314104\pi$
$480$		0			0
$481$	9.41475e6			1.85544
$482$		0			0
$483$	2.51564e6	−	2.51564e6i	0.490659	−	0.490659i
$484$		0			0
$485$	−221069.	+	133336.i	−0.0426750	+	0.0257391i
$486$		0			0
$487$	1.55138e6	−	1.55138e6i	0.296412	−	0.296412i	−0.543195	−	0.839607i	$-0.682786\pi$
$487$	1.55138e6	−	1.55138e6i	0.296412	−	0.296412i	0.839607	+	0.543195i	$0.182786\pi$
$488$		0			0
$489$		−	941605.i		−	0.178072i
$490$		0			0
$491$	−8.21995e6			−1.53874			−0.769370	−	0.638803i	$-0.779430\pi$
$491$	−8.21995e6			−1.53874			−0.769370	+	0.638803i	$0.779430\pi$
$492$		0			0
$493$	−1.97757e6	−	1.97757e6i	−0.366450	−	0.366450i
$494$		0			0
$495$	−5.16960e6	−	1.27974e6i	−0.948296	−	0.234751i
$496$		0			0
$497$	1.51330e6	+	1.51330e6i	0.274810	+	0.274810i
$498$		0			0
$499$			3.17479e6i			0.570774i	0.958412	+	0.285387i	$0.0921221\pi$
$499$			3.17479e6i			0.570774i	−0.958412	+	0.285387i	$0.907878\pi$
$500$		0			0
$501$			795658.i			0.141622i
$502$		0			0
$503$	3.83730e6	+	3.83730e6i	0.676247	+	0.676247i	0.959149	−	0.282902i	$-0.0912971\pi$
$503$	3.83730e6	+	3.83730e6i	0.676247	+	0.676247i	−0.282902	+	0.959149i	$0.591297\pi$
$504$		0			0
$505$	938410.	+	232304.i	0.163744	+	0.0405348i
$506$		0			0
$507$	2.32148e6	+	2.32148e6i	0.401093	+	0.401093i
$508$		0			0
$509$	−4.82930e6			−0.826208			−0.413104	−	0.910684i	$-0.635555\pi$
$509$	−4.82930e6			−0.826208			−0.413104	+	0.910684i	$0.635555\pi$
$510$		0			0
$511$		−	525762.i		−	0.0890711i
$512$		0			0
$513$	2.79935e6	−	2.79935e6i	0.469639	−	0.469639i
$514$		0			0
$515$	2.84242e6	−	1.71438e6i	0.472249	−	0.284833i
$516$		0			0
$517$	−14514.9	+	14514.9i	−0.00238830	+	0.00238830i
$518$		0			0
$519$	−804356.			−0.131078
$520$		0			0
$521$	−1.06985e7			−1.72674			−0.863372	−	0.504569i	$-0.831652\pi$
$521$	−1.06985e7			−1.72674			−0.863372	+	0.504569i	$0.831652\pi$
$522$		0			0
$523$	367714.	−	367714.i	0.0587836	−	0.0587836i	−0.677104	−	0.735887i	$-0.736765\pi$
$523$	367714.	−	367714.i	0.0587836	−	0.0587836i	0.735887	+	0.677104i	$0.236765\pi$
$524$		0			0
$525$	1.71618e6	−	3.25391e6i	0.271748	−	0.515237i
$526$		0			0
$527$	7.08874e6	−	7.08874e6i	1.11184	−	1.11184i
$528$		0			0
$529$			2.69690e6i			0.419011i
$530$		0			0
$531$	6.83525e6			1.05201
$532$		0			0
$533$	5.45890e6	+	5.45890e6i	0.832315	+	0.832315i
$534$		0			0
$535$	−7.26798e6	+	4.38362e6i	−1.09781	+	0.662137i
$536$		0			0
$537$	2.03206e6	+	2.03206e6i	0.304090	+	0.304090i
$538$		0			0
$539$		−	1.85117e6i		−	0.274457i
$540$		0			0
$541$		−	4.61678e6i		−	0.678182i	−0.940754	−	0.339091i	$-0.889881\pi$
$541$		−	4.61678e6i		−	0.678182i	0.940754	−	0.339091i	$-0.110119\pi$
$542$		0			0
$543$	−462943.	−	462943.i	−0.0673795	−	0.0673795i
$544$		0			0
$545$	688582.	−	2.78158e6i	0.0993035	−	0.401144i
$546$		0			0
$547$	8.25355e6	+	8.25355e6i	1.17943	+	1.17943i	0.979889	+	0.199542i	$0.0639453\pi$
$547$	8.25355e6	+	8.25355e6i	1.17943	+	1.17943i	0.199542	+	0.979889i	$0.436055\pi$
$548$		0			0
$549$	305234.			0.0432217
$550$		0			0
$551$		−	1.49975e6i		−	0.210446i
$552$		0			0
$553$	1.75098e6	−	1.75098e6i	0.243483	−	0.243483i
$554$		0			0
$555$	−4.83024e6	−	1.19573e6i	−0.665636	−	0.164779i
$556$		0			0
$557$	1.93310e6	−	1.93310e6i	0.264008	−	0.264008i	−0.562672	−	0.826680i	$-0.690227\pi$
$557$	1.93310e6	−	1.93310e6i	0.264008	−	0.264008i	0.826680	+	0.562672i	$0.190227\pi$
$558$		0			0
$559$	−924189.			−0.125092
$560$		0			0
$561$	−9.66314e6			−1.29632
$562$		0			0
$563$	6.10842e6	−	6.10842e6i	0.812190	−	0.812190i	−0.172772	−	0.984962i	$-0.555272\pi$
$563$	6.10842e6	−	6.10842e6i	0.812190	−	0.812190i	0.984962	+	0.172772i	$0.0552723\pi$
$564$		0			0
$565$	−6.12810e6	−	1.01603e7i	−0.807616	−	1.33902i
$566$		0			0
$567$	1.38009e6	−	1.38009e6i	0.180281	−	0.180281i
$568$		0			0
$569$			6.95880e6i			0.901060i	0.892761	+	0.450530i	$0.148765\pi$
$569$			6.95880e6i			0.901060i	−0.892761	+	0.450530i	$0.851235\pi$
$570$		0			0
$571$	3.46936e6			0.445306			0.222653	−	0.974898i	$-0.428528\pi$
$571$	3.46936e6			0.445306			0.222653	+	0.974898i	$0.428528\pi$
$572$		0			0
$573$	4.24563e6	+	4.24563e6i	0.540201	+	0.540201i
$574$		0			0
$575$	2.79142e6	+	9.02218e6i	0.352092	+	1.13800i
$576$		0			0
$577$	−2.25638e6	−	2.25638e6i	−0.282145	−	0.282145i	0.551819	−	0.833964i	$-0.313934\pi$
$577$	−2.25638e6	−	2.25638e6i	−0.282145	−	0.282145i	−0.833964	+	0.551819i	$0.813934\pi$
$578$		0			0
$579$			5.95843e6i			0.738644i
$580$		0			0
$581$		−	6.25681e6i		−	0.768975i
$582$		0			0
$583$	103718.	+	103718.i	0.0126381	+	0.0126381i
$584$		0			0
$585$	4.41107e6	+	7.31349e6i	0.532910	+	0.883557i
$586$		0			0
$587$	4.93652e6	+	4.93652e6i	0.591324	+	0.591324i	0.937989	−	0.346665i	$-0.112686\pi$
$587$	4.93652e6	+	4.93652e6i	0.591324	+	0.591324i	−0.346665	+	0.937989i	$0.612686\pi$
$588$		0			0
$589$	5.37596e6			0.638510
$590$		0			0
$591$		−	2.22655e6i		−	0.262219i
$592$		0			0
$593$	−227180.	+	227180.i	−0.0265298	+	0.0265298i	−0.720247	−	0.693717i	$-0.755972\pi$
$593$	−227180.	+	227180.i	−0.0265298	+	0.0265298i	0.693717	+	0.720247i	$0.255972\pi$
$594$		0			0
$595$	−4.07610e6	+	1.64657e7i	−0.472011	+	1.90673i
$596$		0			0
$597$	−5.53785e6	+	5.53785e6i	−0.635924	+	0.635924i
$598$		0			0
$599$	1.51009e7			1.71963			0.859815	−	0.510605i	$-0.170579\pi$
$599$	1.51009e7			1.71963			0.859815	+	0.510605i	$0.170579\pi$
$600$		0			0
$601$	−4.90619e6			−0.554061			−0.277031	−	0.960861i	$-0.589350\pi$
$601$	−4.90619e6			−0.554061			−0.277031	+	0.960861i	$0.589350\pi$
$602$		0			0
$603$	3.64264e6	−	3.64264e6i	0.407965	−	0.407965i
$604$		0			0
$605$	−1.84594e6	+	7.45682e6i	−0.205036	+	0.828258i
$606$		0			0
$607$	5.77545e6	−	5.77545e6i	0.636230	−	0.636230i	−0.313393	−	0.949623i	$-0.601466\pi$
$607$	5.77545e6	−	5.77545e6i	0.636230	−	0.636230i	0.949623	+	0.313393i	$0.101466\pi$
$608$		0			0
$609$			1.54189e6i			0.168465i
$610$		0			0
$611$	32919.6			0.00356740
$612$		0			0
$613$	5.92087e6	+	5.92087e6i	0.636406	+	0.636406i	0.949667	−	0.313261i	$-0.101421\pi$
$613$	5.92087e6	+	5.92087e6i	0.636406	+	0.636406i	−0.313261	+	0.949667i	$0.601421\pi$
$614$		0			0
$615$	−2.10738e6	−	3.49401e6i	−0.224675	−	0.372508i
$616$		0			0
$617$	6.30723e6	+	6.30723e6i	0.667000	+	0.667000i	0.957020	−	0.290021i	$-0.0936622\pi$
$617$	6.30723e6	+	6.30723e6i	0.667000	+	0.667000i	−0.290021	+	0.957020i	$0.593662\pi$
$618$		0			0
$619$		−	5.28850e6i		−	0.554761i	−0.960760	−	0.277380i	$-0.910534\pi$
$619$		−	5.28850e6i		−	0.554761i	0.960760	−	0.277380i	$-0.0894662\pi$
$620$		0			0
$621$		−	1.04489e7i		−	1.08728i
$622$		0			0
$623$	−3.35642e6	−	3.35642e6i	−0.346463	−	0.346463i
$624$		0			0
$625$	5.51496e6	+	8.05932e6i	0.564732	+	0.825275i
$626$		0			0
$627$	−3.66417e6	−	3.66417e6i	−0.372226	−	0.372226i
$628$		0			0
$629$	2.29446e7			2.31235
$630$		0			0
$631$		−	1.31906e7i		−	1.31884i	−0.751777	−	0.659418i	$-0.770803\pi$
$631$		−	1.31906e7i		−	1.31884i	0.751777	−	0.659418i	$-0.229197\pi$
$632$		0			0
$633$	5.91948e6	−	5.91948e6i	0.587184	−	0.587184i
$634$		0			0
$635$	8.02340e6	+	1.33027e7i	0.789631	+	1.30920i
$636$		0			0
$637$	−2.09921e6	+	2.09921e6i	−0.204978	+	0.204978i
$638$		0			0
$639$	2.62609e6			0.254424
$640$		0			0
$641$	3.49015e6			0.335505			0.167752	−	0.985829i	$-0.446349\pi$
$641$	3.49015e6			0.335505			0.167752	+	0.985829i	$0.446349\pi$
$642$		0			0
$643$	−4.40501e6	+	4.40501e6i	−0.420165	+	0.420165i	−0.885260	−	0.465096i	$-0.846020\pi$
$643$	−4.40501e6	+	4.40501e6i	−0.420165	+	0.420165i	0.465096	+	0.885260i	$0.346020\pi$
$644$		0			0
$645$	474155.	+	117377.i	0.0448767	+	0.0111093i
$646$		0			0
$647$	−1.25788e7	+	1.25788e7i	−1.18135	+	1.18135i	−0.201960	+	0.979394i	$0.564731\pi$
$647$	−1.25788e7	+	1.25788e7i	−1.18135	+	1.18135i	−0.979394	+	0.201960i	$0.935269\pi$
$648$		0			0
$649$		−	2.14144e7i		−	1.99570i
$650$		0			0
$651$	−5.52701e6			−0.511137
$652$		0			0
$653$	1.35390e6	+	1.35390e6i	0.124252	+	0.124252i	0.766498	−	0.642246i	$-0.221997\pi$
$653$	1.35390e6	+	1.35390e6i	0.124252	+	0.124252i	−0.642246	+	0.766498i	$0.721997\pi$
$654$		0			0
$655$	1.97161e6	−	7.96446e6i	0.179563	−	0.725359i
$656$		0			0
$657$	−456189.	−	456189.i	−0.0412317	−	0.0412317i
$658$		0			0
$659$		−	9.42856e6i		−	0.845730i	−0.906193	−	0.422865i	$-0.861024\pi$
$659$		−	9.42856e6i		−	0.845730i	0.906193	−	0.422865i	$-0.138976\pi$
$660$		0			0
$661$		−	4.10961e6i		−	0.365845i	−0.983127	−	0.182923i	$-0.941444\pi$
$661$		−	4.10961e6i		−	0.365845i	0.983127	−	0.182923i	$-0.0585558\pi$
$662$		0			0
$663$	1.09579e7	+	1.09579e7i	0.968152	+	0.968152i
$664$		0			0
$665$	−7.78926e6	+	4.69802e6i	−0.683033	+	0.411966i
$666$		0			0
$667$	−2.79898e6	−	2.79898e6i	−0.243604	−	0.243604i
$668$		0			0
$669$	−3.75915e6			−0.324732
$670$		0			0
$671$		−	956279.i		−	0.0819933i
$672$		0			0
$673$	−1.18829e7	+	1.18829e7i	−1.01131	+	1.01131i	−0.0113747	+	0.999935i	$0.503621\pi$
$673$	−1.18829e7	+	1.18829e7i	−1.01131	+	1.01131i	−0.999935	+	0.0113747i	$0.996379\pi$
$674$		0			0
$675$	−3.19352e6	−	1.03218e7i	−0.269780	−	0.871959i
$676$		0			0
$677$	2.69398e6	−	2.69398e6i	0.225904	−	0.225904i	−0.585075	−	0.810979i	$-0.698935\pi$
$677$	2.69398e6	−	2.69398e6i	0.225904	−	0.225904i	0.810979	+	0.585075i	$0.198935\pi$
$678$		0			0
$679$	−656299.			−0.0546295
$680$		0			0
$681$	3.60229e6			0.297654
$682$		0			0
$683$	−5.78117e6	+	5.78117e6i	−0.474203	+	0.474203i	−0.903272	−	0.429069i	$-0.858842\pi$
$683$	−5.78117e6	+	5.78117e6i	−0.474203	+	0.474203i	0.429069	+	0.903272i	$0.358842\pi$
$684$		0			0
$685$	−8.61656e6	+	5.19700e6i	−0.701629	+	0.423181i
$686$		0			0
$687$	−4.81478e6	+	4.81478e6i	−0.389210	+	0.389210i
$688$		0			0
$689$		−	235230.i		−	0.0188775i
$690$		0			0
$691$	−2.16912e7			−1.72818			−0.864091	−	0.503336i	$-0.832106\pi$
$691$	−2.16912e7			−1.72818			−0.864091	+	0.503336i	$0.832106\pi$
$692$		0			0
$693$	−9.57324e6	−	9.57324e6i	−0.757226	−	0.757226i
$694$		0			0
$695$	−6.90626e6	−	1.70965e6i	−0.542351	−	0.134259i
$696$		0			0
$697$	1.33038e7	+	1.33038e7i	1.03728	+	1.03728i
$698$		0			0
$699$			5.20390e6i			0.402843i
$700$		0			0
$701$		−	324553.i		−	0.0249454i	−0.999922	−	0.0124727i	$-0.996030\pi$
$701$		−	324553.i		−	0.0249454i	0.999922	−	0.0124727i	$-0.00397029\pi$
$702$		0			0
$703$	8.70035e6	+	8.70035e6i	0.663970	+	0.663970i
$704$		0			0
$705$	−16889.4	−	4180.98i	−0.00127980	−	0.000316815i
$706$		0			0
$707$	1.73778e6	+	1.73778e6i	0.130751	+	0.130751i
$708$		0			0
$709$	−1.29646e7			−0.968596			−0.484298	−	0.874903i	$-0.660925\pi$
$709$	−1.29646e7			−0.968596			−0.484298	+	0.874903i	$0.660925\pi$
$710$		0			0
$711$		−	3.03856e6i		−	0.225421i
$712$		0			0
$713$	1.00331e7	−	1.00331e7i	0.739117	−	0.739117i
$714$		0			0
$715$	2.29127e7	−	1.38196e7i	1.67614	−	1.01095i
$716$		0			0
$717$	−3.91753e6	+	3.91753e6i	−0.284587	+	0.284587i
$718$		0			0
$719$	−1.03596e7			−0.747346			−0.373673	−	0.927561i	$-0.621902\pi$
$719$	−1.03596e7			−0.747346			−0.373673	+	0.927561i	$0.621902\pi$
$720$		0			0
$721$	8.43844e6			0.604539
$722$		0			0
$723$	5.40939e6	−	5.40939e6i	0.384860	−	0.384860i
$724$		0			0
$725$	−3.62040e6	−	1.90948e6i	−0.255807	−	0.134918i
$726$		0			0
$727$	−724947.	+	724947.i	−0.0508710	+	0.0508710i	−0.732085	−	0.681214i	$-0.761452\pi$
$727$	−724947.	+	724947.i	−0.0508710	+	0.0508710i	0.681214	+	0.732085i	$0.261452\pi$
$728$		0			0
$729$			4.56470e6i			0.318122i
$730$		0			0
$731$	−2.25233e6			−0.155897
$732$		0			0
$733$	8.37353e6	+	8.37353e6i	0.575637	+	0.575637i	0.933698	−	0.358061i	$-0.116562\pi$
$733$	8.37353e6	+	8.37353e6i	0.575637	+	0.575637i	−0.358061	+	0.933698i	$0.616562\pi$
$734$		0			0
$735$	1.34361e6	−	810388.i	0.0917394	−	0.0553318i
$736$		0			0
$737$	−1.14122e7	−	1.14122e7i	−0.773926	−	0.773926i
$738$		0			0
$739$		−	1.89309e7i		−	1.27515i	−0.770390	−	0.637573i	$-0.779939\pi$
$739$		−	1.89309e7i		−	1.27515i	0.770390	−	0.637573i	$-0.220061\pi$
$740$		0			0
$741$			8.31026e6i			0.555993i
$742$		0			0
$743$	−8.69837e6	−	8.69837e6i	−0.578051	−	0.578051i	0.356315	−	0.934366i	$-0.384033\pi$
$743$	−8.69837e6	−	8.69837e6i	−0.578051	−	0.578051i	−0.934366	+	0.356315i	$0.884033\pi$
$744$		0			0
$745$	2.77760e6	−	1.12203e7i	0.183349	−	0.740655i
$746$		0			0
$747$	−5.42886e6	−	5.42886e6i	−0.355965	−	0.355965i
$748$		0			0
$749$	−2.15768e7			−1.40534
$750$		0			0
$751$			1.96100e7i			1.26875i	0.773025	+	0.634376i	$0.218743\pi$
$751$			1.96100e7i			1.26875i	−0.773025	+	0.634376i	$0.781257\pi$
$752$		0			0
$753$	2.51108e6	−	2.51108e6i	0.161389	−	0.161389i
$754$		0			0
$755$	−1.36322e7	−	3.37466e6i	−0.870360	−	0.215458i
$756$		0			0
$757$	−3.43229e6	+	3.43229e6i	−0.217693	+	0.217693i	−0.807525	−	0.589833i	$-0.799194\pi$
$757$	−3.43229e6	+	3.43229e6i	−0.217693	+	0.217693i	0.589833	+	0.807525i	$0.299194\pi$
$758$		0			0
$759$	−1.36769e7			−0.861751
$760$		0			0
$761$	−1.87574e7			−1.17412			−0.587059	−	0.809544i	$-0.699714\pi$
$761$	−1.87574e7			−1.17412			−0.587059	+	0.809544i	$0.699714\pi$
$762$		0			0
$763$	5.15102e6	−	5.15102e6i	0.320319	−	0.320319i
$764$		0			0
$765$	1.07501e7	+	1.78236e7i	0.664142	+	1.10114i
$766$		0			0
$767$	−2.42837e7	+	2.42837e7i	−1.49048	+	1.49048i
$768$		0			0
$769$		−	1.37065e7i		−	0.835815i	−0.908490	−	0.417908i	$-0.862764\pi$
$769$		−	1.37065e7i		−	0.835815i	0.908490	−	0.417908i	$-0.137236\pi$
$770$		0			0
$771$	−1.09605e7			−0.664041
$772$		0			0
$773$	−1.40462e7	−	1.40462e7i	−0.845490	−	0.845490i	0.144076	−	0.989567i	$-0.453979\pi$
$773$	−1.40462e7	−	1.40462e7i	−0.845490	−	0.845490i	−0.989567	+	0.144076i	$0.953979\pi$
$774$		0			0
$775$	6.84468e6	−	1.29776e7i	0.409354	−	0.776140i
$776$		0			0
$777$	−8.94480e6	−	8.94480e6i	−0.531518	−	0.531518i
$778$		0			0
$779$			1.00894e7i			0.595689i
$780$		0			0
$781$		−	8.22740e6i		−	0.482653i
$782$		0			0
$783$	3.20216e6	+	3.20216e6i	0.186655	+	0.186655i
$784$		0			0
$785$	−3.02552e6	−	5.01627e6i	−0.175237	−	0.290540i
$786$		0			0
$787$	7.19838e6	+	7.19838e6i	0.414284	+	0.414284i	0.883228	−	0.468944i	$-0.155365\pi$
$787$	7.19838e6	+	7.19838e6i	0.414284	+	0.414284i	−0.468944	+	0.883228i	$0.655365\pi$
$788$		0			0
$789$	1.30807e7			0.748063
$790$		0			0
$791$		−	3.01634e7i		−	1.71411i
$792$		0			0
$793$	−1.08441e6	+	1.08441e6i	−0.0612365	+	0.0612365i
$794$		0			0
$795$	−29875.7	+	120685.i	−0.00167649	+	0.00677229i
$796$		0			0
$797$	2.25277e7	−	2.25277e7i	1.25624	−	1.25624i	0.303361	−	0.952876i	$-0.401891\pi$
$797$	2.25277e7	−	2.25277e7i	1.25624	−	1.25624i	0.952876	−	0.303361i	$-0.0981087\pi$
$798$		0			0
$799$	80227.9			0.00444589
$800$		0			0
$801$	−5.82456e6			−0.320761
$802$		0			0
$803$	−1.42921e6	+	1.42921e6i	−0.0782183	+	0.0782183i
$804$		0			0
$805$	−5.76916e6	+	2.33050e7i	−0.313778	+	1.26753i
$806$		0			0
$807$	1.23992e7	−	1.23992e7i	0.670206	−	0.670206i
$808$		0			0
$809$		−	7.84195e6i		−	0.421263i	−0.977566	−	0.210631i	$-0.932448\pi$
$809$		−	7.84195e6i		−	0.421263i	0.977566	−	0.210631i	$-0.0675519\pi$
$810$		0			0
$811$	9.65765e6			0.515608			0.257804	−	0.966197i	$-0.417001\pi$
$811$	9.65765e6			0.515608			0.257804	+	0.966197i	$0.417001\pi$
$812$		0			0
$813$	−1.18299e7	−	1.18299e7i	−0.627702	−	0.627702i
$814$		0			0
$815$	3.28184e6	+	5.44124e6i	0.173070	+	0.286948i
$816$		0			0
$817$	−854060.	−	854060.i	−0.0447645	−	0.0447645i
$818$		0			0
$819$			2.17119e7i			1.13107i
$820$		0			0
$821$			3.13878e7i			1.62519i	0.582830	+	0.812594i	$0.301945\pi$
$821$			3.13878e7i			1.62519i	−0.582830	+	0.812594i	$0.698055\pi$
$822$		0			0
$823$	1.52238e6	+	1.52238e6i	0.0783474	+	0.0783474i	0.745195	−	0.666847i	$-0.232357\pi$
$823$	1.52238e6	+	1.52238e6i	0.0783474	+	0.0783474i	−0.666847	+	0.745195i	$0.732357\pi$
$824$		0			0
$825$	−1.35105e7	+	4.18010e6i	−0.691096	+	0.213822i
$826$		0			0
$827$	−1.45364e7	−	1.45364e7i	−0.739082	−	0.739082i	0.233318	−	0.972400i	$-0.425042\pi$
$827$	−1.45364e7	−	1.45364e7i	−0.739082	−	0.739082i	−0.972400	+	0.233318i	$0.925042\pi$
$828$		0			0
$829$	3.42957e7			1.73322			0.866609	−	0.498989i	$-0.166295\pi$
$829$	3.42957e7			1.73322			0.866609	+	0.498989i	$0.166295\pi$
$830$		0			0
$831$		−	4.90287e6i		−	0.246291i
$832$		0			0
$833$	−5.11595e6	+	5.11595e6i	−0.255455	+	0.255455i
$834$		0			0
$835$	−2.77316e6	−	4.59785e6i	−0.137644	−	0.228212i
$836$		0			0
$837$	−1.14784e7	+	1.14784e7i	−0.566327	+	0.566327i
$838$		0			0
$839$	1.82753e7			0.896313			0.448157	−	0.893955i	$-0.352081\pi$
$839$	1.82753e7			0.896313			0.448157	+	0.893955i	$0.352081\pi$
$840$		0			0
$841$	−1.87956e7			−0.916360
$842$		0			0
$843$	1.72095e6	−	1.72095e6i	0.0834063	−	0.0834063i
$844$		0			0
$845$	−2.15063e7	−	5.32390e6i	−1.03615	−	0.256501i
$846$		0			0
$847$	−1.38088e7	+	1.38088e7i	−0.661374	+	0.661374i
$848$		0			0
$849$		−	1.55867e6i		−	0.0742138i
$850$		0			0
$851$	3.24749e7			1.53718
$852$		0			0
$853$	−1.42805e7	−	1.42805e7i	−0.672002	−	0.672002i	0.286175	−	0.958177i	$-0.407616\pi$
$853$	−1.42805e7	−	1.42805e7i	−0.672002	−	0.672002i	−0.958177	+	0.286175i	$0.907616\pi$
$854$		0			0
$855$	−2.68218e6	+	1.08349e7i	−0.125479	+	0.506884i
$856$		0			0
$857$	6.07126e6	+	6.07126e6i	0.282376	+	0.282376i	0.834056	−	0.551680i	$-0.186013\pi$
$857$	6.07126e6	+	6.07126e6i	0.282376	+	0.282376i	−0.551680	+	0.834056i	$0.686013\pi$
$858$		0			0
$859$		−	1.28490e7i		−	0.594135i	−0.954856	−	0.297068i	$-0.903991\pi$
$859$		−	1.28490e7i		−	0.594135i	0.954856	−	0.297068i	$-0.0960087\pi$
$860$		0			0
$861$		−	1.03728e7i		−	0.476858i
$862$		0			0
$863$	4.40683e6	+	4.40683e6i	0.201418	+	0.201418i	0.800608	−	0.599189i	$-0.204510\pi$
$863$	4.40683e6	+	4.40683e6i	0.201418	+	0.201418i	−0.599189	+	0.800608i	$0.704510\pi$
$864$		0			0
$865$	4.64812e6	−	2.80347e6i	0.211221	−	0.127396i
$866$		0			0
$867$	1.83886e7	+	1.83886e7i	0.830809	+	0.830809i
$868$		0			0
$869$	−9.51963e6			−0.427632
$870$		0			0
$871$			2.58826e7i			1.15601i
$872$		0			0
$873$	−569453.	+	569453.i	−0.0252885	+	0.0252885i
$874$		0			0
$875$	1.42377e6	+	2.47848e7i	0.0628665	+	1.09437i
$876$		0			0
$877$	−1.44143e6	+	1.44143e6i	−0.0632839	+	0.0632839i	−0.738040	−	0.674757i	$-0.764249\pi$
$877$	−1.44143e6	+	1.44143e6i	−0.0632839	+	0.0632839i	0.674757	+	0.738040i	$0.264249\pi$
$878$		0			0
$879$	−8.04777e6			−0.351320
$880$		0			0
$881$	3.59518e7			1.56056			0.780280	−	0.625430i	$-0.215077\pi$
$881$	3.59518e7			1.56056			0.780280	+	0.625430i	$0.215077\pi$
$882$		0			0
$883$	1.03739e7	−	1.03739e7i	0.447755	−	0.447755i	−0.446853	−	0.894608i	$-0.647455\pi$
$883$	1.03739e7	−	1.03739e7i	0.447755	−	0.447755i	0.894608	+	0.446853i	$0.147455\pi$
$884$		0			0
$885$	1.55430e7	−	9.37460e6i	0.667076	−	0.402341i
$886$		0			0
$887$	1.39804e7	−	1.39804e7i	0.596637	−	0.596637i	−0.342779	−	0.939416i	$-0.611368\pi$
$887$	1.39804e7	−	1.39804e7i	0.596637	−	0.596637i	0.939416	+	0.342779i	$0.111368\pi$
$888$		0			0
$889$			3.94924e7i			1.67594i
$890$		0			0
$891$	−7.50318e6			−0.316629
$892$		0			0
$893$	30421.6	+	30421.6i	0.00127660	+	0.00127660i
$894$		0			0
$895$	−1.88251e7	−	4.66017e6i	−0.785562	−	0.194466i
$896$		0			0
$897$	1.55094e7	+	1.55094e7i	0.643597	+	0.643597i
$898$		0			0
$899$			6.14952e6i			0.253771i
$900$		0			0
$901$		−	573277.i		−	0.0235262i
$902$		0			0
$903$	878056.	+	878056.i	0.0358346	+	0.0358346i
$904$		0			0
$905$	4.28872e6	+	1.06168e6i	0.174063	+	0.0430894i
$906$		0			0
$907$	−8.08547e6	−	8.08547e6i	−0.326353	−	0.326353i	0.524845	−	0.851198i	$-0.324123\pi$
$907$	−8.08547e6	−	8.08547e6i	−0.326353	−	0.326353i	−0.851198	+	0.524845i	$0.824123\pi$
$908$		0			0
$909$	3.01565e6			0.121052
$910$		0			0
$911$			345072.i			0.0137757i	0.999976	+	0.00688785i	$0.00219249\pi$
$911$			345072.i			0.0137757i	−0.999976	+	0.00688785i	$0.997808\pi$
$912$		0			0
$913$	−1.70083e7	+	1.70083e7i	−0.675280	+	0.675280i
$914$		0			0
$915$	694084.	−	418631.i	0.0274068	−	0.0165302i
$916$		0			0
$917$	1.47488e7	−	1.47488e7i	0.579208	−	0.579208i
$918$		0			0
$919$	−9.48331e6			−0.370400			−0.185200	−	0.982701i	$-0.559293\pi$
$919$	−9.48331e6			−0.370400			−0.185200	+	0.982701i	$0.559293\pi$
$920$		0			0
$921$	4.65518e6			0.180837
$922$		0			0
$923$	−9.32978e6	+	9.32978e6i	−0.360468	+	0.360468i
$924$		0			0
$925$	3.20800e7	−	9.92541e6i	1.23276	−	0.381412i
$926$		0			0
$927$	7.32181e6	−	7.32181e6i	0.279846	−	0.279846i
$928$		0			0
$929$		−	4.39463e6i		−	0.167064i	−0.996505	−	0.0835320i	$-0.973380\pi$
$929$		−	4.39463e6i		−	0.167064i	0.996505	−	0.0835320i	$-0.0266201\pi$
$930$		0			0
$931$	−3.87984e6			−0.146703
$932$		0			0
$933$	1.49585e7	+	1.49585e7i	0.562581	+	0.562581i
$934$		0			0
$935$	5.58402e7	−	3.36796e7i	2.08890	−	1.25990i
$936$		0			0
$937$	−3.07299e6	−	3.07299e6i	−0.114344	−	0.114344i	0.647620	−	0.761964i	$-0.275765\pi$
$937$	−3.07299e6	−	3.07299e6i	−0.114344	−	0.114344i	−0.761964	+	0.647620i	$0.775765\pi$
$938$		0			0
$939$		−	1.09997e6i		−	0.0407114i
$940$		0			0
$941$			2.12225e7i			0.781309i	0.920537	+	0.390654i	$0.127751\pi$
$941$			2.12225e7i			0.781309i	−0.920537	+	0.390654i	$0.872249\pi$
$942$		0			0
$943$	1.88297e7	+	1.88297e7i	0.689549	+	0.689549i
$944$		0			0
$945$	6.60019e6	−	2.66620e7i	0.240423	−	0.971209i
$946$		0			0
$947$	−5.55954e6	−	5.55954e6i	−0.201448	−	0.201448i	0.599172	−	0.800620i	$-0.295497\pi$
$947$	−5.55954e6	−	5.55954e6i	−0.201448	−	0.201448i	−0.800620	+	0.599172i	$0.795497\pi$
$948$		0			0
$949$	3.24143e6			0.116834
$950$		0			0
$951$		−	1.82245e7i		−	0.653437i
$952$		0			0
$953$	2.16053e7	−	2.16053e7i	0.770599	−	0.770599i	−0.207612	−	0.978211i	$-0.566569\pi$
$953$	2.16053e7	−	2.16053e7i	0.770599	−	0.770599i	0.978211	+	0.207612i	$0.0665691\pi$
$954$		0			0
$955$	−3.93317e7	−	9.73658e6i	−1.39551	−	0.345460i
$956$		0			0
$957$	4.19142e6	−	4.19142e6i	0.147938	−	0.147938i
$958$		0			0
$959$	−2.55804e7			−0.898175
$960$		0			0
$961$	6.58574e6			0.230036
$962$		0			0
$963$	−1.87216e7	+	1.87216e7i	−0.650545	+	0.650545i
$964$		0			0
$965$	−2.07673e7	−	3.44319e7i	−0.717896	−	1.19026i
$966$		0			0
$967$	3.96257e7	−	3.96257e7i	1.36273	−	1.36273i	0.492316	−	0.870417i	$-0.336151\pi$
$967$	3.96257e7	−	3.96257e7i	1.36273	−	1.36273i	0.870417	−	0.492316i	$-0.163849\pi$
$968$		0			0
$969$			2.02528e7i			0.692909i
$970$		0			0
$971$	3.48187e7			1.18513			0.592563	−	0.805524i	$-0.298116\pi$
$971$	3.48187e7			1.18513			0.592563	+	0.805524i	$0.298116\pi$
$972$		0			0
$973$	−1.27892e7	−	1.27892e7i	−0.433074	−	0.433074i
$974$		0			0
$975$	2.00610e7	+	1.05806e7i	0.675836	+	0.356451i
$976$		0			0
$977$	−2.78180e6	−	2.78180e6i	−0.0932373	−	0.0932373i	0.658950	−	0.752187i	$-0.271001\pi$
$977$	−2.78180e6	−	2.78180e6i	−0.0932373	−	0.0932373i	−0.752187	+	0.658950i	$0.771001\pi$
$978$		0			0
$979$			1.82480e7i			0.608497i
$980$		0			0
$981$		−	8.93881e6i		−	0.296556i
$982$		0			0
$983$	−4.07608e7	−	4.07608e7i	−1.34542	−	1.34542i	−0.890563	−	0.454861i	$-0.849689\pi$
$983$	−4.07608e7	−	4.07608e7i	−1.34542	−	1.34542i	−0.454861	−	0.890563i	$-0.650311\pi$
$984$		0			0
$985$	7.76034e6	+	1.28665e7i	0.254853	+	0.422543i
$986$		0			0
$987$	−31276.4	−	31276.4i	−0.00102194	−	0.00102194i
$988$		0			0
$989$	−3.18786e6			−0.103635
$990$		0			0
$991$			4.18330e7i			1.35311i	0.736390	+	0.676557i	$0.236529\pi$
$991$			4.18330e7i			1.35311i	−0.736390	+	0.676557i	$0.763471\pi$
$992$		0			0
$993$	5.72145e6	−	5.72145e6i	0.184134	−	0.184134i
$994$		0			0
$995$	1.27001e7	−	5.13028e7i	0.406675	−	1.64280i
$996$		0			0
$997$	1.02022e7	−	1.02022e7i	0.325056	−	0.325056i	−0.525647	−	0.850703i	$-0.676177\pi$
$997$	1.02022e7	−	1.02022e7i	0.325056	−	0.325056i	0.850703	+	0.525647i	$0.176177\pi$
$998$		0			0
$999$	−3.71528e7			−1.17782

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.o.a.47.18		56
4.3	odd	2		40.6.k.a.27.1	yes	56
5.3	odd	4	inner	160.6.o.a.143.17		56
8.3	odd	2	inner	160.6.o.a.47.17		56
8.5	even	2		40.6.k.a.27.15	yes	56
20.3	even	4		40.6.k.a.3.15	yes	56
40.3	even	4	inner	160.6.o.a.143.18		56
40.13	odd	4		40.6.k.a.3.1	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.1	✓	56	40.13	odd	4
40.6.k.a.3.15	yes	56	20.3	even	4
40.6.k.a.27.1	yes	56	4.3	odd	2
40.6.k.a.27.15	yes	56	8.5	even	2
160.6.o.a.47.17		56	8.3	odd	2	inner
160.6.o.a.47.18		56	1.1	even	1	trivial
160.6.o.a.143.17		56	5.3	odd	4	inner
160.6.o.a.143.18		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)

\(f(q)\)	\(=\)	\(q+(5.85746 - 5.85746i) q^{3} +(-13.4330 + 54.2637i) q^{5} +(-100.487 + 100.487i) q^{7} +174.380i q^{9} +O(q^{10})\)	\(q+(5.85746 - 5.85746i) q^{3} +(-13.4330 + 54.2637i) q^{5} +(-100.487 + 100.487i) q^{7} +174.380i q^{9} +546.323 q^{11} +(-619.525 - 619.525i) q^{13} +(239.164 + 396.531i) q^{15} +(-1509.84 - 1509.84i) q^{17} -1145.03i q^{19} +1177.20i q^{21} +(-2136.97 - 2136.97i) q^{23} +(-2764.11 - 1457.85i) q^{25} +(2444.79 + 2444.79i) q^{27} +1309.79 q^{29} +4695.04i q^{31} +(3200.07 - 3200.07i) q^{33} +(-4102.97 - 6802.67i) q^{35} +(-7598.37 + 7598.37i) q^{37} -7257.68 q^{39} -8811.44 q^{41} +(745.885 - 745.885i) q^{43} +(-9462.53 - 2342.46i) q^{45} +(-26.5684 + 26.5684i) q^{47} -3388.42i q^{49} -17687.6 q^{51} +(189.847 + 189.847i) q^{53} +(-7338.77 + 29645.5i) q^{55} +(-6706.96 - 6706.96i) q^{57} -39197.3i q^{59} -1750.39i q^{61} +(-17523.0 - 17523.0i) q^{63} +(41939.8 - 25295.7i) q^{65} +(-20889.0 - 20889.0i) q^{67} -25034.4 q^{69} -15059.6i q^{71} +(-2616.06 + 2616.06i) q^{73} +(-24730.0 + 7651.34i) q^{75} +(-54898.6 + 54898.6i) q^{77} -17424.9 q^{79} -13734.0 q^{81} +(-31132.3 + 31132.3i) q^{83} +(102211. - 61647.7i) q^{85} +(7672.05 - 7672.05i) q^{87} +33401.4i q^{89} +124509. q^{91} +(27501.0 + 27501.0i) q^{93} +(62133.6 + 15381.2i) q^{95} +(3265.58 + 3265.58i) q^{97} +95268.1i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3}+O(q^{10}) \) 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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