LMFDB - Embedded newform 88.6.i.b.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [88,6,Mod(9,88)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(88, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("88.9");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 88 = 2^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	88.i (of order $5$, degree $4$, 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:	$14.1137761435$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.2
Character	$\chi$	$=$	88.81
Dual form			88.6.i.b.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-7.55065 + 23.2385i) q^{3} +(46.4402 - 33.7408i) q^{5} +(-48.4576 - 149.137i) q^{7} +(-286.424 - 208.100i) q^{9} +(398.299 - 49.0805i) q^{11} +(-895.696 - 650.761i) q^{13} +(433.432 + 1333.97i) q^{15} +(1403.35 - 1019.60i) q^{17} +(-224.617 + 691.302i) q^{19} +3831.61 q^{21} +4796.66 q^{23} +(52.5738 - 161.806i) q^{25} +(2195.02 - 1594.78i) q^{27} +(-1444.65 - 4446.18i) q^{29} +(1618.08 + 1175.60i) q^{31} +(-1866.86 + 9626.46i) q^{33} +(-7282.38 - 5290.96i) q^{35} +(-3187.00 - 9808.56i) q^{37} +(21885.8 - 15901.0i) q^{39} +(-811.722 + 2498.22i) q^{41} -9573.28 q^{43} -20323.0 q^{45} +(1013.95 - 3120.61i) q^{47} +(-6296.59 + 4574.74i) q^{49} +(13097.6 + 40310.4i) q^{51} +(21002.8 + 15259.5i) q^{53} +(16841.1 - 15718.2i) q^{55} +(-14368.8 - 10439.5i) q^{57} +(-1366.86 - 4206.76i) q^{59} +(12513.9 - 9091.90i) q^{61} +(-17155.9 + 52800.5i) q^{63} -63553.5 q^{65} -18768.3 q^{67} +(-36217.9 + 111467. i) q^{69} +(24889.5 - 18083.3i) q^{71} +(-19431.9 - 59805.2i) q^{73} +(3363.15 + 2443.47i) q^{75} +(-26620.3 - 57022.8i) q^{77} +(-53022.4 - 38523.0i) q^{79} +(-6098.88 - 18770.4i) q^{81} +(-6802.87 + 4942.58i) q^{83} +(30770.0 - 94700.4i) q^{85} +114230. q^{87} +774.583 q^{89} +(-53649.4 + 165116. i) q^{91} +(-39536.8 + 28725.2i) q^{93} +(12893.8 + 39683.0i) q^{95} +(108537. + 78856.8i) q^{97} +(-124296. - 68828.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 21 q^{3} + 37 q^{5} - 181 q^{7} - 1123 q^{9} + 563 q^{11} - 753 q^{13} - 1731 q^{15} + 3153 q^{17} - 2022 q^{19} - 2282 q^{21} + 4516 q^{23} - 2551 q^{25} + 11538 q^{27} + 7829 q^{29} - 7643 q^{31}+ \cdots + 689815 q^{99}+O(q^{100}) $ 32 * q - 21 * q^3 + 37 * q^5 - 181 * q^7 - 1123 * q^9 + 563 * q^11 - 753 * q^13 - 1731 * q^15 + 3153 * q^17 - 2022 * q^19 - 2282 * q^21 + 4516 * q^23 - 2551 * q^25 + 11538 * q^27 + 7829 * q^29 - 7643 * q^31 - 20846 * q^33 - 47237 * q^35 - 30139 * q^37 + 15155 * q^39 + 17377 * q^41 + 37862 * q^43 + 46556 * q^45 - 7053 * q^47 - 43539 * q^49 - 55812 * q^51 - 17637 * q^53 + 81511 * q^55 + 137684 * q^57 + 58662 * q^59 + 32619 * q^61 - 29128 * q^63 - 103034 * q^65 + 20982 * q^67 - 183982 * q^69 + 43641 * q^71 + 94725 * q^73 - 14162 * q^75 + 143529 * q^77 + 111121 * q^79 - 97990 * q^81 - 117894 * q^83 + 123843 * q^85 - 154438 * q^87 + 13394 * q^89 - 378075 * q^91 - 83153 * q^93 + 362641 * q^95 - 332002 * q^97 + 689815 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/88\mathbb{Z}\right)^\times$.

$n$	$23$	$45$	$57$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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
$3$	−7.55065	+	23.2385i	−0.484374	+	1.49075i	0.348511	+	0.937305i	$0.386687\pi$
$3$	−7.55065	+	23.2385i	−0.484374	+	1.49075i	−0.832885	+	0.553446i	$0.813313\pi$
$4$		0			0
$5$	46.4402	−	33.7408i	0.830748	−	0.603573i	−0.0890232	−	0.996030i	$-0.528375\pi$
$5$	46.4402	−	33.7408i	0.830748	−	0.603573i	0.919771	+	0.392456i	$0.128375\pi$
$6$		0			0
$7$	−48.4576	−	149.137i	−0.373781	−	1.15038i	−0.944298	−	0.329092i	$-0.893257\pi$
$7$	−48.4576	−	149.137i	−0.373781	−	1.15038i	0.570517	−	0.821286i	$-0.306743\pi$
$8$		0			0
$9$	−286.424	−	208.100i	−1.17870	−	0.856377i
$10$		0			0
$11$	398.299	−	49.0805i	0.992493	−	0.122300i
$11$	398.299	−	49.0805i	0.992493	−	0.122300i
$12$		0			0
$13$	−895.696	−	650.761i	−1.46995	−	1.06798i	−0.980629	−	0.195875i	$-0.937245\pi$
$13$	−895.696	−	650.761i	−1.46995	−	1.06798i	−0.489319	−	0.872105i	$-0.662755\pi$
$14$		0			0
$15$	433.432	+	1333.97i	0.497385	+	1.53079i
$16$		0			0
$17$	1403.35	−	1019.60i	1.17773	−	0.855669i	0.185813	−	0.982585i	$-0.440508\pi$
$17$	1403.35	−	1019.60i	1.17773	−	0.855669i	0.991913	+	0.126916i	$0.0405080\pi$
$18$		0			0
$19$	−224.617	+	691.302i	−0.142745	+	0.439323i	−0.996714	−	0.0810005i	$-0.974188\pi$
$19$	−224.617	+	691.302i	−0.142745	+	0.439323i	0.853970	+	0.520323i	$0.174188\pi$
$20$		0			0
$21$	3831.61			1.89598
$22$		0			0
$23$	4796.66			1.89069			0.945343	−	0.326078i	$-0.105727\pi$
$23$	4796.66			1.89069			0.945343	+	0.326078i	$0.105727\pi$
$24$		0			0
$25$	52.5738	−	161.806i	0.0168236	−	0.0517778i
$26$		0			0
$27$	2195.02	−	1594.78i	0.579468	−	0.421008i
$28$		0			0
$29$	−1444.65	−	4446.18i	−0.318983	−	0.981729i	−0.974084	−	0.226187i	$-0.927374\pi$
$29$	−1444.65	−	4446.18i	−0.318983	−	0.981729i	0.655101	−	0.755542i	$-0.272626\pi$
$30$		0			0
$31$	1618.08	+	1175.60i	0.302410	+	0.219714i	0.728633	−	0.684905i	$-0.240156\pi$
$31$	1618.08	+	1175.60i	0.302410	+	0.219714i	−0.426223	+	0.904618i	$0.640156\pi$
$32$		0			0
$33$	−1866.86	+	9626.46i	−0.298419	+	1.53880i
$34$		0			0
$35$	−7282.38	−	5290.96i	−1.00485	−	0.730070i
$36$		0			0
$37$	−3187.00	−	9808.56i	−0.382716	−	1.17788i	−0.938123	−	0.346301i	$-0.887437\pi$
$37$	−3187.00	−	9808.56i	−0.382716	−	1.17788i	0.555407	−	0.831579i	$-0.312563\pi$
$38$		0			0
$39$	21885.8	−	15901.0i	2.30410	−	1.67402i
$40$		0			0
$41$	−811.722	+	2498.22i	−0.0754132	+	0.232098i	−0.981656	−	0.190659i	$-0.938938\pi$
$41$	−811.722	+	2498.22i	−0.0754132	+	0.232098i	0.906243	+	0.422757i	$0.138938\pi$
$42$		0			0
$43$	−9573.28			−0.789569			−0.394784	−	0.918774i	$-0.629181\pi$
$43$	−9573.28			−0.789569			−0.394784	+	0.918774i	$0.629181\pi$
$44$		0			0
$45$	−20323.0			−1.49609
$46$		0			0
$47$	1013.95	−	3120.61i	0.0669531	−	0.206060i	−0.911983	−	0.410229i	$-0.865449\pi$
$47$	1013.95	−	3120.61i	0.0669531	−	0.206060i	0.978936	+	0.204168i	$0.0654489\pi$
$48$		0			0
$49$	−6296.59	+	4574.74i	−0.374641	+	0.272193i
$50$		0			0
$51$	13097.6	+	40310.4i	0.705128	+	2.17016i
$52$		0			0
$53$	21002.8	+	15259.5i	1.02704	+	0.746190i	0.967715	−	0.252049i	$-0.0811043\pi$
$53$	21002.8	+	15259.5i	1.02704	+	0.746190i	0.0593278	+	0.998239i	$0.481104\pi$
$54$		0			0
$55$	16841.1	−	15718.2i	0.750694	−	0.700643i
$56$		0			0
$57$	−14368.8	−	10439.5i	−0.585779	−	0.425593i
$58$		0			0
$59$	−1366.86	−	4206.76i	−0.0511204	−	0.157332i	0.922237	−	0.386624i	$-0.126359\pi$
$59$	−1366.86	−	4206.76i	−0.0511204	−	0.157332i	−0.973358	+	0.229292i	$0.926359\pi$
$60$		0			0
$61$	12513.9	−	9091.90i	0.430595	−	0.312846i	−0.351292	−	0.936266i	$-0.614257\pi$
$61$	12513.9	−	9091.90i	0.430595	−	0.312846i	0.781887	+	0.623420i	$0.214257\pi$
$62$		0			0
$63$	−17155.9	+	52800.5i	−0.544581	+	1.67605i
$64$		0			0
$65$	−63553.5			−1.86576
$66$		0			0
$67$	−18768.3			−0.510786			−0.255393	−	0.966837i	$-0.582205\pi$
$67$	−18768.3			−0.510786			−0.255393	+	0.966837i	$0.582205\pi$
$68$		0			0
$69$	−36217.9	+	111467.i	−0.915799	+	2.81854i
$70$		0			0
$71$	24889.5	−	18083.3i	0.585964	−	0.425728i	−0.254905	−	0.966966i	$-0.582044\pi$
$71$	24889.5	−	18083.3i	0.585964	−	0.425728i	0.840869	+	0.541238i	$0.182044\pi$
$72$		0			0
$73$	−19431.9	−	59805.2i	−0.426784	−	1.31351i	−0.901276	−	0.433245i	$-0.857368\pi$
$73$	−19431.9	−	59805.2i	−0.426784	−	1.31351i	0.474492	−	0.880260i	$-0.342632\pi$
$74$		0			0
$75$	3363.15	+	2443.47i	0.0690388	+	0.0501596i
$76$		0			0
$77$	−26620.3	−	57022.8i	−0.511666	−	1.09603i
$78$		0			0
$79$	−53022.4	−	38523.0i	−0.955854	−	0.694469i	−0.00366994	−	0.999993i	$-0.501168\pi$
$79$	−53022.4	−	38523.0i	−0.955854	−	0.694469i	−0.952184	+	0.305525i	$0.901168\pi$
$80$		0			0
$81$	−6098.88	−	18770.4i	−0.103285	−	0.317879i
$82$		0			0
$83$	−6802.87	+	4942.58i	−0.108392	+	0.0787514i	−0.640661	−	0.767824i	$-0.721340\pi$
$83$	−6802.87	+	4942.58i	−0.108392	+	0.0787514i	0.532269	+	0.846575i	$0.321340\pi$
$84$		0			0
$85$	30770.0	−	94700.4i	0.461935	−	1.42169i
$86$		0			0
$87$	114230.			1.61802
$88$		0			0
$89$	774.583			0.0103656			0.00518278	−	0.999987i	$-0.498350\pi$
$89$	774.583			0.0103656			0.00518278	+	0.999987i	$0.498350\pi$
$90$		0			0
$91$	−53649.4	+	165116.i	−0.679143	+	2.09019i
$92$		0			0
$93$	−39536.8	+	28725.2i	−0.474017	+	0.344394i
$94$		0			0
$95$	12893.8	+	39683.0i	0.146579	+	0.451123i
$96$		0			0
$97$	108537.	+	78856.8i	1.17125	+	0.850962i	0.991158	−	0.132688i	$-0.0423610\pi$
$97$	108537.	+	78856.8i	1.17125	+	0.850962i	0.180090	+	0.983650i	$0.442361\pi$
$98$		0			0
$99$	−124296.	−	68828.0i	−1.27459	−	0.705793i
$100$		0			0
$101$	−20551.9	−	14931.8i	−0.200470	−	0.145650i	0.483021	−	0.875608i	$-0.339539\pi$
$101$	−20551.9	−	14931.8i	−0.200470	−	0.145650i	−0.683491	+	0.729959i	$0.739539\pi$
$102$		0			0
$103$	−11027.1	−	33937.8i	−0.102416	−	0.315203i	0.886700	−	0.462346i	$-0.152992\pi$
$103$	−11027.1	−	33937.8i	−0.102416	−	0.315203i	−0.989115	+	0.147143i	$0.952992\pi$
$104$		0			0
$105$	177941.	−	129281.i	1.57508	−	1.14436i
$106$		0			0
$107$	27769.9	−	85466.9i	0.234485	−	0.721669i	−0.762705	−	0.646747i	$-0.776129\pi$
$107$	27769.9	−	85466.9i	0.234485	−	0.721669i	0.997189	−	0.0749225i	$-0.0238710\pi$
$108$		0			0
$109$	−12869.0			−0.103747			−0.0518737	−	0.998654i	$-0.516519\pi$
$109$	−12869.0			−0.103747			−0.0518737	+	0.998654i	$0.516519\pi$
$110$		0			0
$111$	252000.			1.94130
$112$		0			0
$113$	−27896.9	+	85857.7i	−0.205522	+	0.632533i	0.794169	+	0.607697i	$0.207906\pi$
$113$	−27896.9	+	85857.7i	−0.205522	+	0.632533i	−0.999692	+	0.0248363i	$0.992094\pi$
$114$		0			0
$115$	222758.	−	161843.i	1.57068	−	1.14117i
$116$		0			0
$117$	121126.	+	372788.i	0.818037	+	2.51766i
$118$		0			0
$119$	−220063.	−	159885.i	−1.42455	−	1.03500i
$120$		0			0
$121$	156233.	−	39097.4i	0.970085	−	0.242764i
$122$		0			0
$123$	−51925.9	−	37726.4i	−0.309472	−	0.224845i
$124$		0			0
$125$	52415.1	+	161317.i	0.300042	+	0.923434i
$126$		0			0
$127$	−24728.8	+	17966.5i	−0.136048	+	0.0988450i	−0.653728	−	0.756730i	$-0.726796\pi$
$127$	−24728.8	+	17966.5i	−0.136048	+	0.0988450i	0.517680	+	0.855575i	$0.326796\pi$
$128$		0			0
$129$	72284.5	−	222469.i	0.382447	−	1.17705i
$130$		0			0
$131$	−323898.			−1.64904			−0.824518	−	0.565836i	$-0.808553\pi$
$131$	−323898.			−1.64904			−0.824518	+	0.565836i	$0.808553\pi$
$132$		0			0
$133$	113983.			0.558742
$134$		0			0
$135$	48128.3	−	148124.i	0.227282	−	0.699503i
$136$		0			0
$137$	149351.	−	108510.i	0.679838	−	0.493931i	−0.193466	−	0.981107i	$-0.561973\pi$
$137$	149351.	−	108510.i	0.679838	−	0.493931i	0.873304	+	0.487176i	$0.161973\pi$
$138$		0			0
$139$	84689.0	+	260646.i	0.371783	+	1.14423i	0.945623	+	0.325264i	$0.105453\pi$
$139$	84689.0	+	260646.i	0.371783	+	1.14423i	−0.573840	+	0.818967i	$0.694547\pi$
$140$		0			0
$141$	64862.3	+	47125.2i	0.274754	+	0.199621i
$142$		0			0
$143$	−388694.	−	215236.i	−1.58953	−	0.880188i
$144$		0			0
$145$	−217107.	−	157738.i	−0.857540	−	0.623039i
$146$		0			0
$147$	−58766.8	−	180866.i	−0.224305	−	0.690339i
$148$		0			0
$149$	174705.	−	126931.i	0.644673	−	0.468382i	−0.216780	−	0.976221i	$-0.569555\pi$
$149$	174705.	−	126931.i	0.644673	−	0.468382i	0.861452	+	0.507838i	$0.169555\pi$
$150$		0			0
$151$	−124138.	+	382056.i	−0.443058	+	1.36359i	0.441541	+	0.897241i	$0.354432\pi$
$151$	−124138.	+	382056.i	−0.443058	+	1.36359i	−0.884599	+	0.466352i	$0.845568\pi$
$152$		0			0
$153$	−614132.			−2.12096
$154$		0			0
$155$	114810.			0.383839
$156$		0			0
$157$	100910.	−	310570.i	0.326728	−	1.00557i	−0.643926	−	0.765088i	$-0.722696\pi$
$157$	100910.	−	310570.i	0.326728	−	1.00557i	0.970654	−	0.240479i	$-0.0773045\pi$
$158$		0			0
$159$	−513192.	+	372856.i	−1.60986	+	1.16963i
$160$		0			0
$161$	−232435.	−	715360.i	−0.706701	−	2.17500i
$162$		0			0
$163$	61752.1	+	44865.5i	0.182047	+	0.132265i	0.675076	−	0.737748i	$-0.264111\pi$
$163$	61752.1	+	44865.5i	0.182047	+	0.132265i	−0.493030	+	0.870012i	$0.664111\pi$
$164$		0			0
$165$	238107.	+	510044.i	0.680867	+	1.45847i
$166$		0			0
$167$	499684.	+	363042.i	1.38645	+	1.00731i	0.996244	+	0.0865869i	$0.0275960\pi$
$167$	499684.	+	363042.i	1.38645	+	1.00731i	0.390205	+	0.920728i	$0.372404\pi$
$168$		0			0
$169$	264045.	+	812647.i	0.711150	+	2.18869i
$170$		0			0
$171$	208195.	−	151263.i	0.544479	−	0.395587i
$172$		0			0
$173$	−93586.5	+	288030.i	−0.237738	+	0.731681i	0.759009	+	0.651080i	$0.225684\pi$
$173$	−93586.5	+	288030.i	−0.237738	+	0.731681i	−0.996746	+	0.0806008i	$0.974316\pi$
$174$		0			0
$175$	−26678.8			−0.0658524
$176$		0			0
$177$	108080.			0.259305
$178$		0			0
$179$	−261660.	+	805307.i	−0.610387	+	1.87858i	−0.156043	+	0.987750i	$0.549874\pi$
$179$	−261660.	+	805307.i	−0.610387	+	1.87858i	−0.454344	+	0.890826i	$0.650126\pi$
$180$		0			0
$181$	−414948.	+	301477.i	−0.941449	+	0.684003i	−0.948769	−	0.315971i	$-0.897670\pi$
$181$	−414948.	+	301477.i	−0.941449	+	0.684003i	0.00732012	+	0.999973i	$0.497670\pi$
$182$		0			0
$183$	116794.	+	359455.i	0.257806	+	0.793444i
$184$		0			0
$185$	−478953.	−	347980.i	−1.02888	−	0.747523i
$186$		0			0
$187$	508912.	−	474981.i	1.06424	−	0.993281i
$188$		0			0
$189$	−344206.	−	250080.i	−0.700913	−	0.509243i
$190$		0			0
$191$	102624.	+	315843.i	0.203546	+	0.626452i	0.999770	+	0.0214489i	$0.00682793\pi$
$191$	102624.	+	315843.i	0.203546	+	0.626452i	−0.796224	+	0.605003i	$0.793172\pi$
$192$		0			0
$193$	88719.3	−	64458.3i	0.171445	−	0.124562i	−0.498754	−	0.866744i	$-0.666209\pi$
$193$	88719.3	−	64458.3i	0.171445	−	0.124562i	0.670199	+	0.742182i	$0.266209\pi$
$194$		0			0
$195$	479870.	−	1.47689e6i	0.903726	−	2.78138i
$196$		0			0
$197$	199830.			0.366855			0.183428	−	0.983033i	$-0.441281\pi$
$197$	199830.			0.366855			0.183428	+	0.983033i	$0.441281\pi$
$198$		0			0
$199$	−814887.			−1.45870			−0.729348	−	0.684143i	$-0.760176\pi$
$199$	−814887.			−1.45870			−0.729348	+	0.684143i	$0.760176\pi$
$200$		0			0
$201$	141713.	−	436148.i	0.247411	−	0.761454i
$202$		0			0
$203$	−593086.	+	430902.i	−1.01013	+	0.733902i
$204$		0			0
$205$	46595.5	+	143406.i	0.0774389	+	0.238332i
$206$		0			0
$207$	−1.37388e6	−	998183.i	−2.22855	−	1.61914i
$208$		0			0
$209$	−55535.5	+	286369.i	−0.0879438	+	0.453482i
$210$		0			0
$211$	296144.	+	215161.i	0.457928	+	0.332704i	0.792718	−	0.609589i	$-0.208665\pi$
$211$	296144.	+	215161.i	0.457928	+	0.332704i	−0.334790	+	0.942293i	$0.608665\pi$
$212$		0			0
$213$	232297.	+	714936.i	0.350828	+	1.07974i
$214$		0			0
$215$	−444585.	+	323010.i	−0.655932	+	0.476563i
$216$		0			0
$217$	96917.9	−	298283.i	0.139719	−	0.430010i
$218$		0			0
$219$	1.53651e6			2.16483
$220$		0			0
$221$	−1.92049e6			−2.64503
$222$		0			0
$223$	335147.	−	1.03148e6i	0.451309	−	1.38898i	−0.424106	−	0.905612i	$-0.639412\pi$
$223$	335147.	−	1.03148e6i	0.451309	−	1.38898i	0.875415	−	0.483372i	$-0.160588\pi$
$224$		0			0
$225$	−48730.1	+	35404.5i	−0.0641713	+	0.0466232i
$226$		0			0
$227$	151458.	+	466139.i	0.195086	+	0.600414i	0.999976	+	0.00698886i	$0.00222464\pi$
$227$	151458.	+	466139.i	0.195086	+	0.600414i	−0.804889	+	0.593425i	$0.797775\pi$
$228$		0			0
$229$	171663.	+	124720.i	0.216315	+	0.157162i	0.690666	−	0.723173i	$-0.257317\pi$
$229$	171663.	+	124720.i	0.216315	+	0.157162i	−0.474351	+	0.880336i	$0.657317\pi$
$230$		0			0
$231$	1.52613e6	−	188057.i	1.88174	−	0.231878i
$232$		0			0
$233$	439005.	+	318956.i	0.529761	+	0.384894i	0.820268	−	0.571979i	$-0.193824\pi$
$233$	439005.	+	318956.i	0.529761	+	0.384894i	−0.290508	+	0.956873i	$0.593824\pi$
$234$		0			0
$235$	−58203.9	−	179133.i	−0.0687515	−	0.211595i
$236$		0			0
$237$	1.29557e6	−	941287.i	1.49827	−	1.08856i
$238$		0			0
$239$	104295.	−	320988.i	0.118105	−	0.363491i	−0.874477	−	0.485068i	$-0.838795\pi$
$239$	104295.	−	320988.i	0.118105	−	0.363491i	0.992582	+	0.121577i	$0.0387950\pi$
$240$		0			0
$241$	−540867.			−0.599857			−0.299929	−	0.953962i	$-0.596963\pi$
$241$	−540867.			−0.599857			−0.299929	+	0.953962i	$0.596963\pi$
$242$		0			0
$243$	1.14155e6			1.24017
$244$		0			0
$245$	−138060.	+	424904.i	−0.146944	+	0.452247i
$246$		0			0
$247$	651061.	−	473023.i	0.679015	−	0.493333i
$248$		0			0
$249$	−63492.0	−	195408.i	−0.0648964	−	0.199731i
$250$		0			0
$251$	−294371.	−	213873.i	−0.294924	−	0.214275i	0.430477	−	0.902602i	$-0.358345\pi$
$251$	−294371.	−	213873.i	−0.294924	−	0.214275i	−0.725401	+	0.688327i	$0.758345\pi$
$252$		0			0
$253$	1.91050e6	−	235422.i	1.87649	−	0.231231i
$254$		0			0
$255$	1.96836e6	+	1.43010e6i	1.89563	+	1.37726i
$256$		0			0
$257$	−603096.	−	1.85614e6i	−0.569579	−	1.75298i	−0.653938	−	0.756549i	$-0.726884\pi$
$257$	−603096.	−	1.85614e6i	−0.569579	−	1.75298i	0.0843585	−	0.996435i	$-0.473116\pi$
$258$		0			0
$259$	−1.30839e6	+	950598.i	−1.21196	+	0.880537i
$260$		0			0
$261$	−511464.	+	1.57412e6i	−0.464744	+	1.43033i
$262$		0			0
$263$	878155.			0.782856			0.391428	−	0.920209i	$-0.371981\pi$
$263$	878155.			0.782856			0.391428	+	0.920209i	$0.371981\pi$
$264$		0			0
$265$	1.49024e6			1.30359
$266$		0			0
$267$	−5848.60	+	18000.2i	−0.00502081	+	0.0154525i
$268$		0			0
$269$	−1.52482e6	+	1.10784e6i	−1.28480	+	0.933465i	−0.999687	−	0.0250282i	$-0.992032\pi$
$269$	−1.52482e6	+	1.10784e6i	−1.28480	+	0.933465i	−0.285117	+	0.958493i	$0.592032\pi$
$270$		0			0
$271$	491772.	+	1.51352e6i	0.406762	+	1.25188i	0.919415	+	0.393289i	$0.128663\pi$
$271$	491772.	+	1.51352e6i	0.406762	+	1.25188i	−0.512653	+	0.858596i	$0.671337\pi$
$272$		0			0
$273$	−3.43195e6	−	2.49346e6i	−2.78699	−	2.02486i
$274$		0			0
$275$	12998.6	−	67027.3i	0.0103649	−	0.0534466i
$276$		0			0
$277$	1.45252e6	+	1.05532e6i	1.13743	+	0.826390i	0.986759	−	0.162194i	$-0.0518571\pi$
$277$	1.45252e6	+	1.05532e6i	1.13743	+	0.826390i	0.150669	+	0.988584i	$0.451857\pi$
$278$		0			0
$279$	−218815.	−	673443.i	−0.168293	−	0.517953i
$280$		0			0
$281$	1.18403e6	−	860246.i	0.894532	−	0.649916i	−0.0425236	−	0.999095i	$-0.513540\pi$
$281$	1.18403e6	−	860246.i	0.894532	−	0.649916i	0.937056	+	0.349180i	$0.113540\pi$
$282$		0			0
$283$	53111.4	−	163460.i	0.0394204	−	0.121324i	−0.929410	−	0.369050i	$-0.879683\pi$
$283$	53111.4	−	163460.i	0.0394204	−	0.121324i	0.968830	+	0.247726i	$0.0796833\pi$
$284$		0			0
$285$	−1.01953e6			−0.743511
$286$		0			0
$287$	411912.			0.295189
$288$		0			0
$289$	491064.	−	1.51134e6i	0.345855	−	1.06443i
$290$		0			0
$291$	−2.65204e6	+	1.92682e6i	−1.83589	+	1.33385i
$292$		0			0
$293$	−34149.7	−	105102.i	−0.0232390	−	0.0715224i	0.938764	−	0.344560i	$-0.111972\pi$
$293$	−34149.7	−	105102.i	−0.0232390	−	0.0715224i	−0.962003	+	0.273037i	$0.911972\pi$
$294$		0			0
$295$	−205417.	−	149244.i	−0.137430	−	0.0998486i
$296$		0			0
$297$	796003.	−	742931.i	0.523629	−	0.488717i
$298$		0			0
$299$	−4.29635e6	−	3.12148e6i	−2.77921	−	2.01921i
$300$		0			0
$301$	463898.	+	1.42773e6i	0.295125	+	0.908302i
$302$		0			0
$303$	502174.	−	364851.i	0.314230	−	0.228301i
$304$		0			0
$305$	274381.	−	844459.i	0.168890	−	0.519791i
$306$		0			0
$307$	−79497.8			−0.0481404			−0.0240702	−	0.999710i	$-0.507663\pi$
$307$	−79497.8			−0.0481404			−0.0240702	+	0.999710i	$0.507663\pi$
$308$		0			0
$309$	871925.			0.519497
$310$		0			0
$311$	113313.	−	348743.i	0.0664324	−	0.204458i	−0.912330	−	0.409456i	$-0.865719\pi$
$311$	113313.	−	348743.i	0.0664324	−	0.204458i	0.978762	+	0.204998i	$0.0657187\pi$
$312$		0			0
$313$	−2.04217e6	+	1.48372e6i	−1.17823	+	0.856036i	−0.991971	−	0.126464i	$-0.959637\pi$
$313$	−2.04217e6	+	1.48372e6i	−1.17823	+	0.856036i	−0.186262	+	0.982500i	$0.559637\pi$
$314$		0			0
$315$	984806.	+	3.03092e6i	0.559209	+	1.72107i
$316$		0			0
$317$	−1.95095e6	−	1.41745e6i	−1.09043	−	0.792245i	−0.110959	−	0.993825i	$-0.535392\pi$
$317$	−1.95095e6	−	1.41745e6i	−1.09043	−	0.792245i	−0.979472	+	0.201580i	$0.935392\pi$
$318$		0			0
$319$	−793623.	−	1.70000e6i	−0.436654	−	0.935348i
$320$		0			0
$321$	1.77644e6	+	1.29066e6i	0.962251	+	0.699116i
$322$		0			0
$323$	389630.	+	1.19916e6i	0.207800	+	0.639544i
$324$		0			0
$325$	−152387.	+	110716.i	−0.0800275	+	0.0581434i
$326$		0			0
$327$	97168.9	−	299055.i	0.0502525	−	0.154661i
$328$		0			0
$329$	−514532.			−0.262073
$330$		0			0
$331$	−779307.			−0.390966			−0.195483	−	0.980707i	$-0.562627\pi$
$331$	−779307.			−0.390966			−0.195483	+	0.980707i	$0.562627\pi$
$332$		0			0
$333$	−1.12832e6	+	3.47262e6i	−0.557601	+	1.71612i
$334$		0			0
$335$	−871606.	+	633259.i	−0.424334	+	0.308297i
$336$		0			0
$337$	88729.1	+	273080.i	0.0425590	+	0.130983i	0.970078	−	0.242792i	$-0.0780632\pi$
$337$	88729.1	+	273080.i	0.0425590	+	0.130983i	−0.927519	+	0.373775i	$0.878063\pi$
$338$		0			0
$339$	−1.78457e6	−	1.29656e6i	−0.843399	−	0.612765i
$340$		0			0
$341$	702179.	+	388826.i	0.327011	+	0.181079i
$342$		0			0
$343$	−1.14482e6	−	831757.i	−0.525412	−	0.381734i
$344$		0			0
$345$	2.07902e6	+	6.39858e6i	0.940398	+	2.89425i
$346$		0			0
$347$	1.21041e6	−	879413.i	0.539645	−	0.392075i	−0.284308	−	0.958733i	$-0.591764\pi$
$347$	1.21041e6	−	879413.i	0.539645	−	0.392075i	0.823953	+	0.566658i	$0.191764\pi$
$348$		0			0
$349$	−122209.	+	376121.i	−0.0537081	+	0.165297i	−0.974313	−	0.225200i	$-0.927697\pi$
$349$	−122209.	+	376121.i	−0.0537081	+	0.165297i	0.920604	+	0.390496i	$0.127697\pi$
$350$		0			0
$351$	−3.00389e6			−1.30142
$352$		0			0
$353$	−414432.			−0.177017			−0.0885087	−	0.996075i	$-0.528210\pi$
$353$	−414432.			−0.177017			−0.0885087	+	0.996075i	$0.528210\pi$
$354$		0			0
$355$	545730.	−	1.67958e6i	0.229830	−	0.707345i
$356$		0			0
$357$	5.37710e6	−	3.90669e6i	2.23294	−	1.62233i
$358$		0			0
$359$	562938.	+	1.73254e6i	0.230528	+	0.709493i	0.997683	+	0.0680314i	$0.0216718\pi$
$359$	562938.	+	1.73254e6i	0.230528	+	0.709493i	−0.767155	+	0.641462i	$0.778328\pi$
$360$		0			0
$361$	1.57576e6	+	1.14486e6i	0.636389	+	0.462363i
$362$		0			0
$363$	−271097.	+	3.92584e6i	−0.107984	+	1.56374i
$364$		0			0
$365$	−2.92029e6	−	2.12172e6i	−1.14735	−	0.833596i
$366$		0			0
$367$	−305378.	−	939856.i	−0.118351	−	0.364247i	0.874280	−	0.485422i	$-0.161334\pi$
$367$	−305378.	−	939856.i	−0.118351	−	0.364247i	−0.992631	+	0.121174i	$0.961334\pi$
$368$		0			0
$369$	752376.	−	546633.i	0.287653	−	0.208992i
$370$		0			0
$371$	1.25800e6	−	3.87174e6i	0.474512	−	1.46040i
$372$		0			0
$373$	1.33761e6			0.497802			0.248901	−	0.968529i	$-0.419931\pi$
$373$	1.33761e6			0.497802			0.248901	+	0.968529i	$0.419931\pi$
$374$		0			0
$375$	−4.14454e6			−1.52194
$376$		0			0
$377$	−1.59943e6	+	4.92254e6i	−0.579578	+	1.78376i
$378$		0			0
$379$	−989419.	+	718855.i	−0.353820	+	0.257065i	−0.750470	−	0.660905i	$-0.770173\pi$
$379$	−989419.	+	718855.i	−0.353820	+	0.257065i	0.396650	+	0.917970i	$0.370173\pi$
$380$		0			0
$381$	−230797.	−	710319.i	−0.0814548	−	0.250692i
$382$		0			0
$383$	1.84702e6	+	1.34194e6i	0.643389	+	0.467450i	0.861013	−	0.508583i	$-0.169831\pi$
$383$	1.84702e6	+	1.34194e6i	0.643389	+	0.467450i	−0.217624	+	0.976033i	$0.569831\pi$
$384$		0			0
$385$	−3.16025e6	−	1.74996e6i	−1.08660	−	0.601695i
$386$		0			0
$387$	2.74202e6	+	1.99220e6i	0.930665	+	0.676168i
$388$		0			0
$389$	−410756.	−	1.26418e6i	−0.137629	−	0.423579i	0.858361	−	0.513047i	$-0.171483\pi$
$389$	−410756.	−	1.26418e6i	−0.137629	−	0.423579i	−0.995990	+	0.0894681i	$0.971483\pi$
$390$		0			0
$391$	6.73141e6	−	4.89065e6i	2.22671	−	1.61780i
$392$		0			0
$393$	2.44564e6	−	7.52690e6i	0.798750	−	2.45830i
$394$		0			0
$395$	−3.76217e6			−1.21324
$396$		0			0
$397$	2.18246e6			0.694975			0.347488	−	0.937685i	$-0.387035\pi$
$397$	2.18246e6			0.694975			0.347488	+	0.937685i	$0.387035\pi$
$398$		0			0
$399$	−860646.	+	2.64880e6i	−0.270640	+	0.832945i
$400$		0			0
$401$	1.81331e6	−	1.31745e6i	0.563134	−	0.409141i	−0.269471	−	0.963009i	$-0.586849\pi$
$401$	1.81331e6	−	1.31745e6i	0.563134	−	0.409141i	0.832605	+	0.553868i	$0.186849\pi$
$402$		0			0
$403$	−684270.	−	2.10597e6i	−0.209877	−	0.645935i
$404$		0			0
$405$	−916561.	−	665921.i	−0.277667	−	0.201737i
$406$		0			0
$407$	−1.75079e6	−	3.75032e6i	−0.523898	−	1.12223i
$408$		0			0
$409$	3.55804e6	+	2.58507e6i	1.05173	+	0.764125i	0.972540	−	0.232735i	$-0.0747675\pi$
$409$	3.55804e6	+	2.58507e6i	1.05173	+	0.764125i	0.0791871	+	0.996860i	$0.474768\pi$
$410$		0			0
$411$	1.39391e6	+	4.29000e6i	0.407032	+	1.25272i
$412$		0			0
$413$	−561150.	+	407699.i	−0.161884	+	0.117616i
$414$		0			0
$415$	−149160.	+	459069.i	−0.0425141	+	0.130845i
$416$		0			0
$417$	−6.69647e6			−1.88585
$418$		0			0
$419$	5.12999e6			1.42752			0.713759	−	0.700391i	$-0.246991\pi$
$419$	5.12999e6			1.42752			0.713759	+	0.700391i	$0.246991\pi$
$420$		0			0
$421$	−383685.	+	1.18086e6i	−0.105504	+	0.324708i	−0.989848	−	0.142127i	$-0.954606\pi$
$421$	−383685.	+	1.18086e6i	−0.105504	+	0.324708i	0.884344	+	0.466835i	$0.154606\pi$
$422$		0			0
$423$	−939817.	+	682817.i	−0.255383	+	0.185547i
$424$		0			0
$425$	−91196.6	−	280674.i	−0.0244910	−	0.0753755i
$426$		0			0
$427$	−1.96233e6	−	1.42572e6i	−0.520839	−	0.378411i
$428$		0			0
$429$	7.93666e6	−	7.40750e6i	2.08207	−	1.94325i
$430$		0			0
$431$	−218627.	−	158842.i	−0.0566905	−	0.0411881i	0.559079	−	0.829114i	$-0.311155\pi$
$431$	−218627.	−	158842.i	−0.0566905	−	0.0411881i	−0.615770	+	0.787926i	$0.711155\pi$
$432$		0			0
$433$	−801876.	−	2.46792e6i	−0.205536	−	0.632574i	−0.999691	−	0.0248592i	$-0.992086\pi$
$433$	−801876.	−	2.46792e6i	−0.205536	−	0.632574i	0.794155	−	0.607715i	$-0.207914\pi$
$434$		0			0
$435$	5.30489e6	−	3.85423e6i	1.34417	−	0.976594i
$436$		0			0
$437$	−1.07741e6	+	3.31594e6i	−0.269885	+	0.830621i
$438$		0			0
$439$	−6.26302e6			−1.55104			−0.775519	−	0.631325i	$-0.782512\pi$
$439$	−6.26302e6			−1.55104			−0.775519	+	0.631325i	$0.782512\pi$
$440$		0			0
$441$	2.75550e6			0.674689
$442$		0			0
$443$	30337.8	−	93370.0i	0.00734470	−	0.0226047i	−0.947317	−	0.320298i	$-0.896217\pi$
$443$	30337.8	−	93370.0i	0.00734470	−	0.0226047i	0.954662	+	0.297693i	$0.0962171\pi$
$444$		0			0
$445$	35971.8	−	26135.0i	0.00861117	−	0.00625638i
$446$		0			0
$447$	1.63054e6	+	5.01829e6i	0.385978	+	1.18792i
$448$		0			0
$449$	6.70282e6	+	4.86989e6i	1.56907	+	1.14000i	0.928041	+	0.372478i	$0.121492\pi$
$449$	6.70282e6	+	4.86989e6i	1.56907	+	1.14000i	0.641028	+	0.767518i	$0.278508\pi$
$450$		0			0
$451$	−200694.	+	1.03488e6i	−0.0464615	+	0.239579i
$452$		0			0
$453$	−7.94109e6	−	5.76954e6i	−1.81817	−	1.32098i
$454$		0			0
$455$	3.07965e6	+	9.47818e6i	0.697385	+	2.14633i
$456$		0			0
$457$	−1.25899e6	+	914708.i	−0.281988	+	0.204876i	−0.719784	−	0.694198i	$-0.755759\pi$
$457$	−1.25899e6	+	914708.i	−0.281988	+	0.204876i	0.437796	+	0.899074i	$0.355759\pi$
$458$		0			0
$459$	1.45436e6	−	4.47607e6i	0.322212	−	0.991666i
$460$		0			0
$461$	−601195.			−0.131754			−0.0658769	−	0.997828i	$-0.520984\pi$
$461$	−601195.			−0.131754			−0.0658769	+	0.997828i	$0.520984\pi$
$462$		0			0
$463$	−1.17902e6			−0.255605			−0.127802	−	0.991800i	$-0.540792\pi$
$463$	−1.17902e6			−0.255605			−0.127802	+	0.991800i	$0.540792\pi$
$464$		0			0
$465$	−866888.	+	2.66801e6i	−0.185922	+	0.572209i
$466$		0			0
$467$	2.59158e6	−	1.88290e6i	0.549887	−	0.399516i	−0.277857	−	0.960622i	$-0.589624\pi$
$467$	2.59158e6	−	1.88290e6i	0.549887	−	0.399516i	0.827744	+	0.561106i	$0.189624\pi$
$468$		0			0
$469$	909469.	+	2.79906e6i	0.190922	+	0.587597i
$470$		0			0
$471$	6.45525e6	+	4.69001e6i	1.34079	+	0.974141i
$472$		0			0
$473$	−3.81303e6	+	469861.i	−0.783641	+	0.0965643i
$474$		0			0
$475$	100047.	+	72688.7i	0.0203457	+	0.0147820i
$476$		0			0
$477$	−2.84024e6	−	8.74136e6i	−0.571557	−	1.75907i
$478$		0			0
$479$	5.18757e6	−	3.76899e6i	1.03306	−	0.750561i	0.0641398	−	0.997941i	$-0.479570\pi$
$479$	5.18757e6	−	3.76899e6i	1.03306	−	0.750561i	0.968918	+	0.247380i	$0.0795697\pi$
$480$		0			0
$481$	−3.52845e6	+	1.08595e7i	−0.695379	+	2.14016i
$482$		0			0
$483$	1.83789e7			3.58470
$484$		0			0
$485$	7.70118e6			1.48663
$486$		0			0
$487$	1.68901e6	−	5.19823e6i	0.322708	−	0.993192i	−0.649757	−	0.760142i	$-0.725129\pi$
$487$	1.68901e6	−	5.19823e6i	0.322708	−	0.993192i	0.972465	−	0.233050i	$-0.0748706\pi$
$488$		0			0
$489$	−1.50888e6	+	1.09626e6i	−0.285352	+	0.207320i
$490$		0			0
$491$	1.38828e6	+	4.27269e6i	0.259881	+	0.799831i	0.992829	+	0.119546i	$0.0381439\pi$
$491$	1.38828e6	+	4.27269e6i	0.259881	+	0.799831i	−0.732948	+	0.680285i	$0.761856\pi$
$492$		0			0
$493$	−6.56065e6	−	4.76659e6i	−1.21571	−	0.883265i
$494$		0			0
$495$	−8.09465e6	+	997465.i	−1.48486	+	0.182972i
$496$		0			0
$497$	−3.90298e6	−	2.83568e6i	−0.708770	−	0.514951i
$498$		0			0
$499$	−2.13673e6	−	6.57618e6i	−0.384148	−	1.18229i	−0.937096	−	0.349071i	$-0.886497\pi$
$499$	−2.13673e6	−	6.57618e6i	−0.384148	−	1.18229i	0.552948	−	0.833215i	$-0.313503\pi$
$500$		0			0
$501$	−1.22095e7	+	8.87070e6i	−2.17322	+	1.57893i
$502$		0			0
$503$	−403980.	+	1.24332e6i	−0.0711934	+	0.219111i	−0.980322	−	0.197404i	$-0.936749\pi$
$503$	−403980.	+	1.24332e6i	−0.0711934	+	0.219111i	0.909129	+	0.416515i	$0.136749\pi$
$504$		0			0
$505$	−1.45825e6			−0.254450
$506$		0			0
$507$	−2.08784e7			−3.60726
$508$		0			0
$509$	−1.69502e6	+	5.21674e6i	−0.289988	+	0.892492i	0.694871	+	0.719135i	$0.255462\pi$
$509$	−1.69502e6	+	5.21674e6i	−0.289988	+	0.892492i	−0.984859	+	0.173358i	$0.944538\pi$
$510$		0			0
$511$	−7.97755e6	+	5.79603e6i	−1.35150	+	0.981925i
$512$		0			0
$513$	609432.	+	1.87564e6i	0.102243	+	0.314670i
$514$		0			0
$515$	−1.65719e6	−	1.20402e6i	−0.275330	−	0.200039i
$516$		0			0
$517$	250693.	−	1.29270e6i	0.0412493	−	0.212702i
$518$		0			0
$519$	−5.98674e6	−	4.34962e6i	−0.975600	−	0.708815i
$520$		0			0
$521$	−1.46235e6	−	4.50065e6i	−0.236024	−	0.726408i	−0.996984	−	0.0776089i	$-0.975271\pi$
$521$	−1.46235e6	−	4.50065e6i	−0.236024	−	0.726408i	0.760960	−	0.648799i	$-0.224729\pi$
$522$		0			0
$523$	−1.20010e6	+	871927.i	−0.191851	+	0.139388i	−0.679564	−	0.733616i	$-0.737831\pi$
$523$	−1.20010e6	+	871927.i	−0.191851	+	0.139388i	0.487713	+	0.873004i	$0.337831\pi$
$524$		0			0
$525$	201442.	−	619975.i	0.0318972	−	0.0981694i
$526$		0			0
$527$	3.46938e6			0.544158
$528$		0			0
$529$	1.65716e7			2.57469
$530$		0			0
$531$	−483923.	+	1.48936e6i	−0.0744801	+	0.229226i
$532$		0			0
$533$	2.35280e6	−	1.70941e6i	0.358730	−	0.260632i
$534$		0			0
$535$	−1.59408e6	−	4.90607e6i	−0.240783	−	0.741054i
$536$		0			0
$537$	−1.67384e7	−	1.21612e7i	−2.50483	−	1.81987i
$538$		0			0
$539$	−2.28340e6	+	2.13115e6i	−0.338539	+	0.315968i
$540$		0			0
$541$	2.89312e6	+	2.10198e6i	0.424985	+	0.308770i	0.779640	−	0.626227i	$-0.215402\pi$
$541$	2.89312e6	+	2.10198e6i	0.424985	+	0.308770i	−0.354655	+	0.934997i	$0.615402\pi$
$542$		0			0
$543$	−3.87275e6	−	1.19191e7i	−0.563664	−	1.73478i
$544$		0			0
$545$	−597637.	+	434208.i	−0.0861878	+	0.0626191i
$546$		0			0
$547$	−2.13110e6	+	6.55885e6i	−0.304534	+	0.937259i	0.675317	+	0.737528i	$0.264007\pi$
$547$	−2.13110e6	+	6.55885e6i	−0.304534	+	0.937259i	−0.979851	+	0.199731i	$0.935993\pi$
$548$		0			0
$549$	−5.47631e6			−0.775457
$550$		0			0
$551$	3.39814e6			0.476829
$552$		0			0
$553$	−3.17588e6	+	9.77434e6i	−0.441622	+	1.35917i
$554$		0			0
$555$	1.17029e7	−	8.50268e6i	1.61273	−	1.17172i
$556$		0			0
$557$	−1.15000e6	−	3.53935e6i	−0.157058	−	0.483376i	0.841305	−	0.540560i	$-0.181788\pi$
$557$	−1.15000e6	−	3.53935e6i	−0.157058	−	0.483376i	−0.998364	+	0.0571843i	$0.981788\pi$
$558$		0			0
$559$	8.57475e6	+	6.22992e6i	1.16062	+	0.843243i
$560$		0			0
$561$	7.19523e6	+	1.54128e7i	0.965246	+	2.06763i
$562$		0			0
$563$	4.36375e6	+	3.17045e6i	0.580215	+	0.421551i	0.838802	−	0.544437i	$-0.183257\pi$
$563$	4.36375e6	+	3.17045e6i	0.580215	+	0.421551i	−0.258586	+	0.965988i	$0.583257\pi$
$564$		0			0
$565$	1.60137e6	+	4.92851e6i	0.211043	+	0.649523i
$566$		0			0
$567$	−2.50383e6	+	1.81914e6i	−0.327075	+	0.237634i
$568$		0			0
$569$	897590.	−	2.76250e6i	0.116224	−	0.357702i	−0.875976	−	0.482355i	$-0.839782\pi$
$569$	897590.	−	2.76250e6i	0.116224	−	0.357702i	0.992200	+	0.124653i	$0.0397817\pi$
$570$		0			0
$571$	636912.			0.0817503			0.0408752	−	0.999164i	$-0.486985\pi$
$571$	636912.			0.0817503			0.0408752	+	0.999164i	$0.486985\pi$
$572$		0			0
$573$	−8.11458e6			−1.03248
$574$		0			0
$575$	252179.	−	776126.i	0.0318082	−	0.0978955i
$576$		0			0
$577$	−1.04365e7	+	7.58253e6i	−1.30501	+	0.948145i	−0.999991	−	0.00420152i	$-0.998663\pi$
$577$	−1.04365e7	+	7.58253e6i	−1.30501	+	0.948145i	−0.305018	+	0.952346i	$0.598663\pi$
$578$		0			0
$579$	828027.	+	2.54841e6i	0.102647	+	0.315916i
$580$		0			0
$581$	1.06677e6	+	775056.i	0.131109	+	0.0952560i
$582$		0			0
$583$	9.11435e6	+	5.04700e6i	1.11059	+	0.614981i
$584$		0			0
$585$	1.82033e7	+	1.32254e7i	2.19917	+	1.59779i
$586$		0			0
$587$	3.87594e6	+	1.19289e7i	0.464282	+	1.42891i	0.859883	+	0.510492i	$0.170537\pi$
$587$	3.87594e6	+	1.19289e7i	0.464282	+	1.42891i	−0.395600	+	0.918423i	$0.629463\pi$
$588$		0			0
$589$	−1.17615e6	+	854520.i	−0.139692	+	0.101493i
$590$		0			0
$591$	−1.50885e6	+	4.64375e6i	−0.177695	+	0.546890i
$592$		0			0
$593$	1.61155e7			1.88195			0.940973	−	0.338483i	$-0.109914\pi$
$593$	1.61155e7			1.88195			0.940973	+	0.338483i	$0.109914\pi$
$594$		0			0
$595$	−1.56144e7			−1.80814
$596$		0			0
$597$	6.15292e6	−	1.89368e7i	0.706555	−	2.17455i
$598$		0			0
$599$	3.51007e6	−	2.55022e6i	0.399714	−	0.290409i	−0.369711	−	0.929147i	$-0.620543\pi$
$599$	3.51007e6	−	2.55022e6i	0.399714	−	0.290409i	0.769424	+	0.638738i	$0.220543\pi$
$600$		0			0
$601$	−4.99748e6	−	1.53807e7i	−0.564371	−	1.73696i	−0.669812	−	0.742531i	$-0.733625\pi$
$601$	−4.99748e6	−	1.53807e7i	−0.564371	−	1.73696i	0.105440	−	0.994426i	$-0.466375\pi$
$602$		0			0
$603$	5.37571e6	+	3.90568e6i	0.602064	+	0.437425i
$604$		0			0
$605$	5.93632e6	−	7.08712e6i	0.659370	−	0.787193i
$606$		0			0
$607$	−922914.	−	670536.i	−0.101669	−	0.0738670i	0.535789	−	0.844352i	$-0.320014\pi$
$607$	−922914.	−	670536.i	−0.101669	−	0.0738670i	−0.637458	+	0.770485i	$0.720014\pi$
$608$		0			0
$609$	−5.53533e6	−	1.70360e7i	−0.604784	−	1.86133i
$610$		0			0
$611$	−2.93896e6	+	2.13528e6i	−0.318486	+	0.231394i
$612$		0			0
$613$	2.52586e6	−	7.77381e6i	0.271493	−	0.835570i	−0.718633	−	0.695390i	$-0.755232\pi$
$613$	2.52586e6	−	7.77381e6i	0.271493	−	0.835570i	0.990126	−	0.140180i	$-0.0447682\pi$
$614$		0			0
$615$	−3.68437e6			−0.392803
$616$		0			0
$617$	7.66601e6			0.810693			0.405346	−	0.914163i	$-0.367151\pi$
$617$	7.66601e6			0.810693			0.405346	+	0.914163i	$0.367151\pi$
$618$		0			0
$619$	4.47942e6	−	1.37862e7i	0.469889	−	1.44617i	−0.382839	−	0.923815i	$-0.625054\pi$
$619$	4.47942e6	−	1.37862e7i	0.469889	−	1.44617i	0.852728	−	0.522355i	$-0.174946\pi$
$620$		0			0
$621$	1.05288e7	−	7.64960e6i	1.09559	−	0.795994i
$622$		0			0
$623$	−37534.4	−	115519.i	−0.00387445	−	0.0119243i
$624$		0			0
$625$	8.30726e6	+	6.03558e6i	0.850664	+	0.618043i
$626$		0			0
$627$	−6.23546e6	−	3.45283e6i	−0.633431	−	0.350757i
$628$		0			0
$629$	−1.44732e7	−	1.05154e7i	−1.45861	−	1.05974i
$630$		0			0
$631$	924286.	+	2.84466e6i	0.0924129	+	0.284418i	0.986571	−	0.163334i	$-0.0522248\pi$
$631$	924286.	+	2.84466e6i	0.0924129	+	0.284418i	−0.894158	+	0.447752i	$0.852225\pi$
$632$		0			0
$633$	−7.23611e6	+	5.25734e6i	−0.717788	+	0.521503i
$634$		0			0
$635$	−542206.	+	1.66874e6i	−0.0533617	+	0.164230i
$636$		0			0
$637$	8.61689e6			0.841399
$638$		0			0
$639$	−1.08921e7			−1.05526
$640$		0			0
$641$	−1.48890e6	+	4.58237e6i	−0.143127	+	0.440499i	−0.996765	−	0.0803667i	$-0.974391\pi$
$641$	−1.48890e6	+	4.58237e6i	−0.143127	+	0.440499i	0.853638	+	0.520866i	$0.174391\pi$
$642$		0			0
$643$	−1.40425e7	+	1.02025e7i	−1.33942	+	0.973145i	−0.339954	+	0.940442i	$0.610412\pi$
$643$	−1.40425e7	+	1.02025e7i	−1.33942	+	0.973145i	−0.999465	+	0.0327030i	$0.989588\pi$
$644$		0			0
$645$	−4.14936e6	−	1.27704e7i	−0.392719	−	1.20867i
$646$		0			0
$647$	6.17453e6	+	4.48606e6i	0.579887	+	0.421313i	0.838683	−	0.544619i	$-0.183326\pi$
$647$	6.17453e6	+	4.48606e6i	0.579887	+	0.421313i	−0.258796	+	0.965932i	$0.583326\pi$
$648$		0			0
$649$	−750889.	−	1.60846e6i	−0.0699784	−	0.149899i
$650$		0			0
$651$	6.19985e6	+	4.50445e6i	0.573362	+	0.416572i
$652$		0			0
$653$	3.60037e6	+	1.10808e7i	0.330418	+	1.01692i	0.968935	+	0.247315i	$0.0795484\pi$
$653$	3.60037e6	+	1.10808e7i	0.330418	+	1.01692i	−0.638517	+	0.769608i	$0.720452\pi$
$654$		0			0
$655$	−1.50419e7	+	1.09286e7i	−1.36993	+	0.995314i
$656$		0			0
$657$	−6.87967e6	+	2.11734e7i	−0.621805	+	1.91372i
$658$		0			0
$659$	8.86205e6			0.794915			0.397458	−	0.917621i	$-0.369893\pi$
$659$	8.86205e6			0.794915			0.397458	+	0.917621i	$0.369893\pi$
$660$		0			0
$661$	−1.73414e6			−0.154376			−0.0771882	−	0.997017i	$-0.524594\pi$
$661$	−1.73414e6			−0.154376			−0.0771882	+	0.997017i	$0.524594\pi$
$662$		0			0
$663$	1.45009e7	−	4.46293e7i	1.28119	−	3.94309i
$664$		0			0
$665$	5.29340e6	−	3.84588e6i	0.464174	−	0.337242i
$666$		0			0
$667$	−6.92949e6	−	2.13268e7i	−0.603097	−	1.85614i
$668$		0			0
$669$	2.14394e7	+	1.55766e7i	1.85203	+	1.34558i
$670$		0			0
$671$	4.53805e6	−	4.23548e6i	0.389102	−	0.363159i
$672$		0			0
$673$	1.71629e7	+	1.24695e7i	1.46067	+	1.06124i	0.983188	+	0.182597i	$0.0584504\pi$
$673$	1.71629e7	+	1.24695e7i	1.46067	+	1.06124i	0.477482	+	0.878642i	$0.341550\pi$
$674$		0			0
$675$	−142643.	−	439010.i	−0.0120501	−	0.0370865i
$676$		0			0
$677$	5.75993e6	−	4.18483e6i	0.482998	−	0.350919i	−0.319487	−	0.947591i	$-0.603511\pi$
$677$	5.75993e6	−	4.18483e6i	0.482998	−	0.350919i	0.802485	+	0.596672i	$0.203511\pi$
$678$		0			0
$679$	6.50103e6	−	2.00081e7i	0.541138	−	1.66545i
$680$		0			0
$681$	−1.19760e7			−0.989562
$682$		0			0
$683$	−6.49102e6			−0.532428			−0.266214	−	0.963914i	$-0.585773\pi$
$683$	−6.49102e6			−0.532428			−0.266214	+	0.963914i	$0.585773\pi$
$684$		0			0
$685$	3.27467e6	−	1.00784e7i	0.266650	−	0.820664i
$686$		0			0
$687$	−4.19448e6	+	3.04746e6i	−0.339067	+	0.246347i
$688$		0			0
$689$	−8.88189e6	−	2.73357e7i	−0.712783	−	2.19372i
$690$		0			0
$691$	−2.71270e6	−	1.97089e6i	−0.216126	−	0.157025i	0.474455	−	0.880280i	$-0.342645\pi$
$691$	−2.71270e6	−	1.97089e6i	−0.216126	−	0.157025i	−0.690581	+	0.723255i	$0.742645\pi$
$692$		0			0
$693$	−4.24171e6	+	2.18724e7i	−0.335512	+	1.73007i
$694$		0			0
$695$	1.27274e7	+	9.24697e6i	0.999486	+	0.726169i
$696$		0			0
$697$	1.40804e6	+	4.33352e6i	0.109783	+	0.337877i
$698$		0			0
$699$	−1.07268e7	+	7.79349e6i	−0.830383	+	0.603308i
$700$		0			0
$701$	−6.88781e6	+	2.11985e7i	−0.529403	+	1.62933i	0.226039	+	0.974118i	$0.427422\pi$
$701$	−6.88781e6	+	2.11985e7i	−0.529403	+	1.62933i	−0.755442	+	0.655216i	$0.772578\pi$
$702$		0			0
$703$	7.49653e6			0.572100
$704$		0			0
$705$	4.60226e6			0.348737
$706$		0			0
$707$	−1.23100e6	+	3.78862e6i	−0.0926207	+	0.285057i
$708$		0			0
$709$	1.78239e7	−	1.29499e7i	1.33164	−	0.967496i	0.331937	−	0.943302i	$-0.392298\pi$
$709$	1.78239e7	−	1.29499e7i	1.33164	−	0.967496i	0.999707	−	0.0241946i	$-0.00770214\pi$
$710$		0			0
$711$	7.17029e6	+	2.20679e7i	0.531940	+	1.63714i
$712$		0			0
$713$	7.76138e6	+	5.63897e6i	0.571762	+	0.415409i
$714$		0			0
$715$	−2.53133e7	+	3.11923e6i	−1.85175	+	0.228183i
$716$		0			0
$717$	6.67177e6	+	4.84733e6i	0.484667	+	0.352131i
$718$		0			0
$719$	−3.99208e6	−	1.22864e7i	−0.287990	−	0.886342i	−0.985487	−	0.169754i	$-0.945703\pi$
$719$	−3.99208e6	−	1.22864e7i	−0.287990	−	0.886342i	0.697497	−	0.716588i	$-0.254297\pi$
$720$		0			0
$721$	−4.52704e6	+	3.28909e6i	−0.324322	+	0.235634i
$722$		0			0
$723$	4.08389e6	−	1.25689e7i	0.290555	−	0.894237i
$724$		0			0
$725$	−795367.			−0.0561982
$726$		0			0
$727$	4.83500e6			0.339282			0.169641	−	0.985506i	$-0.445739\pi$
$727$	4.83500e6			0.339282			0.169641	+	0.985506i	$0.445739\pi$
$728$		0			0
$729$	−7.13744e6	+	2.19668e7i	−0.497420	+	1.53090i
$730$		0			0
$731$	−1.34347e7	+	9.76088e6i	−0.929896	+	0.675609i
$732$		0			0
$733$	2.01485e6	+	6.20107e6i	0.138511	+	0.426292i	0.996120	−	0.0880106i	$-0.0280509\pi$
$733$	2.01485e6	+	6.20107e6i	0.138511	+	0.426292i	−0.857609	+	0.514302i	$0.828051\pi$
$734$		0			0
$735$	−8.83169e6	−	6.41660e6i	−0.603011	−	0.438113i
$736$		0			0
$737$	−7.47541e6	+	921159.i	−0.506952	+	0.0624692i
$738$		0			0
$739$	−2.17281e7	−	1.57864e7i	−1.46356	−	1.06334i	−0.982417	−	0.186697i	$-0.940222\pi$
$739$	−2.17281e7	−	1.57864e7i	−1.46356	−	1.06334i	−0.481144	−	0.876642i	$-0.659778\pi$
$740$		0			0
$741$	6.07642e6	+	1.87013e7i	0.406539	+	1.25120i
$742$		0			0
$743$	5.57432e6	−	4.04998e6i	0.370442	−	0.269142i	−0.386952	−	0.922100i	$-0.626472\pi$
$743$	5.57432e6	−	4.04998e6i	0.370442	−	0.269142i	0.757394	+	0.652958i	$0.226472\pi$
$744$		0			0
$745$	3.83059e6	−	1.17894e7i	0.252857	−	0.778215i
$746$		0			0
$747$	2.97706e6			0.195203
$748$		0			0
$749$	−1.40919e7			−0.917838
$750$		0			0
$751$	−2.03794e6	+	6.27213e6i	−0.131853	+	0.405803i	−0.995087	−	0.0990011i	$-0.968435\pi$
$751$	−2.03794e6	+	6.27213e6i	−0.131853	+	0.405803i	0.863234	+	0.504804i	$0.168435\pi$
$752$		0			0
$753$	7.19277e6	−	5.22585e6i	0.462284	−	0.335869i
$754$		0			0
$755$	7.12590e6	+	2.19313e7i	0.454959	+	1.40022i
$756$		0			0
$757$	−2.29214e7	−	1.66534e7i	−1.45379	−	1.05624i	−0.984927	−	0.172970i	$-0.944664\pi$
$757$	−2.29214e7	−	1.66534e7i	−1.45379	−	1.05624i	−0.468863	−	0.883271i	$-0.655336\pi$
$758$		0			0
$759$	−8.95469e6	+	4.61749e7i	−0.564217	+	2.90938i
$760$		0			0
$761$	2.45479e6	+	1.78351e6i	0.153657	+	0.111638i	0.661957	−	0.749541i	$-0.269726\pi$
$761$	2.45479e6	+	1.78351e6i	0.153657	+	0.111638i	−0.508300	+	0.861180i	$0.669726\pi$
$762$		0			0
$763$	623598.	+	1.91924e6i	0.0387787	+	0.119349i
$764$		0			0
$765$	−2.85204e7	+	2.07213e7i	−1.76198	+	1.28016i
$766$		0			0
$767$	−1.51331e6	+	4.65748e6i	−0.0928835	+	0.285866i
$768$		0			0
$769$	−1.31846e7			−0.803993			−0.401996	−	0.915641i	$-0.631684\pi$
$769$	−1.31846e7			−0.803993			−0.401996	+	0.915641i	$0.631684\pi$
$770$		0			0
$771$	4.76877e7			2.88915
$772$		0			0
$773$	7.94707e6	−	2.44586e7i	0.478364	−	1.47225i	−0.363004	−	0.931788i	$-0.618249\pi$
$773$	7.94707e6	−	2.44586e7i	0.478364	−	1.47225i	0.841367	−	0.540464i	$-0.181751\pi$
$774$		0			0
$775$	275288.	−	200008.i	0.0164639	−	0.0119617i
$776$		0			0
$777$	−1.22113e7	−	3.75826e7i	−0.725621	−	2.23323i
$778$		0			0
$779$	−1.54470e6	−	1.12229e6i	−0.0912011	−	0.0662615i
$780$		0			0
$781$	9.02594e6	−	8.42415e6i	0.529499	−	0.494195i
$782$		0			0
$783$	−1.02617e7	−	7.45556e6i	−0.598157	−	0.434586i
$784$		0			0
$785$	−5.79259e6	−	1.78277e7i	−0.335505	−	1.03258i
$786$		0			0
$787$	−5.09188e6	+	3.69947e6i	−0.293050	+	0.212913i	−0.724589	−	0.689181i	$-0.757971\pi$
$787$	−5.09188e6	+	3.69947e6i	−0.293050	+	0.212913i	0.431540	+	0.902094i	$0.357971\pi$
$788$		0			0
$789$	−6.63064e6	+	2.04070e7i	−0.379195	+	1.16704i
$790$		0			0
$791$	1.41564e7			0.804473
$792$		0			0
$793$	−1.71253e7			−0.967065
$794$		0			0
$795$	−1.12523e7	+	3.46310e7i	−0.631427	+	1.94333i
$796$		0			0
$797$	1.71285e7	−	1.24446e7i	0.955157	−	0.693962i	0.00313577	−	0.999995i	$-0.499002\pi$
$797$	1.71285e7	−	1.24446e7i	0.955157	−	0.693962i	0.952021	+	0.306033i	$0.0990019\pi$
$798$		0			0
$799$	−1.75883e6	−	5.41313e6i	−0.0974670	−	0.299973i
$800$		0			0
$801$	−221860.	−	161190.i	−0.0122179	−	0.00887683i
$802$		0			0
$803$	−1.06750e7	−	2.28666e7i	−0.584222	−	1.25145i
$804$		0			0
$805$	−3.49311e7	−	2.53789e7i	−1.89986	−	1.38033i
$806$		0			0
$807$	−1.42313e7	−	4.37994e7i	−0.769237	−	2.36747i
$808$		0			0
$809$	8.37543e6	−	6.08510e6i	0.449920	−	0.326886i	−0.339644	−	0.940554i	$-0.610307\pi$
$809$	8.37543e6	−	6.08510e6i	0.449920	−	0.326886i	0.789564	+	0.613668i	$0.210307\pi$
$810$		0			0
$811$	−8.80616e6	+	2.71026e7i	−0.470148	+	1.44697i	0.382244	+	0.924062i	$0.375152\pi$
$811$	−8.80616e6	+	2.71026e7i	−0.470148	+	1.44697i	−0.852391	+	0.522904i	$0.824848\pi$
$812$		0			0
$813$	−3.88851e7			−2.06327
$814$		0			0
$815$	4.38158e6			0.231066
$816$		0			0
$817$	2.15033e6	−	6.61803e6i	0.112707	−	0.346875i
$818$		0			0
$819$	4.97270e7	−	3.61288e7i	2.59049	−	1.88210i
$820$		0			0
$821$	−653756.	−	2.01205e6i	−0.0338499	−	0.104179i	0.932704	−	0.360643i	$-0.117443\pi$
$821$	−653756.	−	2.01205e6i	−0.0338499	−	0.104179i	−0.966554	+	0.256463i	$0.917443\pi$
$822$		0			0
$823$	2.59528e7	+	1.88558e7i	1.33563	+	0.970390i	0.999593	+	0.0285409i	$0.00908608\pi$
$823$	2.59528e7	+	1.88558e7i	1.33563	+	0.970390i	0.336035	+	0.941849i	$0.390914\pi$
$824$		0			0
$825$	1.45947e6	+	808168.i	0.0746551	+	0.0413396i
$826$		0			0
$827$	−4.96864e6	−	3.60993e6i	−0.252623	−	0.183542i	0.454265	−	0.890866i	$-0.349902\pi$
$827$	−4.96864e6	−	3.60993e6i	−0.252623	−	0.183542i	−0.706889	+	0.707325i	$0.749902\pi$
$828$		0			0
$829$	1.10609e7	+	3.40421e7i	0.558992	+	1.72040i	0.685161	+	0.728391i	$0.259732\pi$
$829$	1.10609e7	+	3.40421e7i	0.558992	+	1.72040i	−0.126170	+	0.992009i	$0.540268\pi$
$830$		0			0
$831$	−3.54916e7	+	2.57861e7i	−1.78288	+	1.29534i
$832$		0			0
$833$	−4.17195e6	+	1.28400e7i	−0.208318	+	0.641137i
$834$		0			0
$835$	3.54547e7			1.75978
$836$		0			0
$837$	5.42655e6			0.267738
$838$		0			0
$839$	−5.65447e6	+	1.74027e7i	−0.277324	+	0.853514i	0.711272	+	0.702917i	$0.248120\pi$
$839$	−5.65447e6	+	1.74027e7i	−0.277324	+	0.853514i	−0.988595	+	0.150597i	$0.951880\pi$
$840$		0			0
$841$	−1.08759e6	+	790184.i	−0.0530246	+	0.0385246i
$842$		0			0
$843$	1.10507e7	+	3.40104e7i	0.535574	+	1.64833i
$844$		0			0
$845$	3.96816e7	+	2.88304e7i	1.91182	+	1.38902i
$846$		0			0
$847$	−1.34016e7	−	2.14056e7i	−0.641870	−	1.02522i
$848$		0			0
$849$	3.39754e6	+	2.46846e6i	0.161769	+	0.117532i
$850$		0			0
$851$	−1.52869e7	−	4.70483e7i	−0.723596	−	2.22700i
$852$		0			0
$853$	−2.13878e7	+	1.55392e7i	−1.00645	+	0.731232i	−0.963462	−	0.267844i	$-0.913689\pi$
$853$	−2.13878e7	+	1.55392e7i	−1.00645	+	0.731232i	−0.0429918	+	0.999075i	$0.513689\pi$
$854$		0			0
$855$	4.56491e6	−	1.40494e7i	0.213559	−	0.657266i
$856$		0			0
$857$	7.98183e6			0.371236			0.185618	−	0.982622i	$-0.440571\pi$
$857$	7.98183e6			0.371236			0.185618	+	0.982622i	$0.440571\pi$
$858$		0			0
$859$	3.32876e7			1.53922			0.769609	−	0.638516i	$-0.220451\pi$
$859$	3.32876e7			1.53922			0.769609	+	0.638516i	$0.220451\pi$
$860$		0			0
$861$	−3.11020e6	+	9.57221e6i	−0.142982	+	0.440052i
$862$		0			0
$863$	−3.16130e7	+	2.29682e7i	−1.44491	+	1.04979i	−0.457917	+	0.888995i	$0.651404\pi$
$863$	−3.16130e7	+	2.29682e7i	−1.44491	+	1.04979i	−0.986989	+	0.160790i	$0.948596\pi$
$864$		0			0
$865$	5.37217e6	+	1.65338e7i	0.244123	+	0.751334i
$866$		0			0
$867$	3.14134e7	+	2.28232e7i	1.41928	+	1.03117i
$868$		0			0
$869$	−2.30095e7	−	1.27413e7i	−1.03361	−	0.572354i
$870$		0			0
$871$	1.68107e7	+	1.22137e7i	0.750829	+	0.545509i
$872$		0			0
$873$	−1.46776e7	−	4.51730e7i	−0.651808	−	2.00606i
$874$		0			0
$875$	2.15185e7	−	1.56341e7i	0.950148	−	0.690323i
$876$		0			0
$877$	2.49335e6	−	7.67376e6i	0.109467	−	0.336906i	−0.881286	−	0.472584i	$-0.843321\pi$
$877$	2.49335e6	−	7.67376e6i	0.109467	−	0.336906i	0.990753	+	0.135678i	$0.0433212\pi$
$878$		0			0
$879$	2.70026e6			0.117878
$880$		0			0
$881$	−8.26109e6			−0.358589			−0.179295	−	0.983795i	$-0.557382\pi$
$881$	−8.26109e6			−0.358589			−0.179295	+	0.983795i	$0.557382\pi$
$882$		0			0
$883$	1.07419e7	−	3.30603e7i	0.463640	−	1.42694i	−0.397045	−	0.917799i	$-0.629964\pi$
$883$	1.07419e7	−	3.30603e7i	0.463640	−	1.42694i	0.860685	−	0.509138i	$-0.170036\pi$
$884$		0			0
$885$	5.01924e6	−	3.64669e6i	0.215417	−	0.156509i
$886$		0			0
$887$	−6.20105e6	−	1.90849e7i	−0.264640	−	0.814479i	−0.991776	−	0.127985i	$-0.959149\pi$
$887$	−6.20105e6	−	1.90849e7i	−0.264640	−	0.814479i	0.727136	−	0.686494i	$-0.240851\pi$
$888$		0			0
$889$	3.87777e6	+	2.81737e6i	0.164561	+	0.119561i
$890$		0			0
$891$	−3.35044e6	−	7.17690e6i	−0.141386	−	0.302860i
$892$		0			0
$893$	1.92953e6	+	1.40189e6i	0.0809698	+	0.0588280i
$894$		0			0
$895$	1.50201e7	+	4.62272e7i	0.626782	+	1.92904i
$896$		0			0
$897$	1.04979e8	−	7.62715e7i	4.35632	−	3.16505i
$898$		0			0
$899$	2.88938e6	−	8.89260e6i	0.119236	−	0.366969i
$900$		0			0
$901$	4.50329e7			1.84807
$902$		0			0
$903$	−3.66811e7			−1.49700
$904$		0			0
$905$	−9.09818e6	+	2.80013e7i	−0.369261	+	1.13647i
$906$		0			0
$907$	7.40035e6	−	5.37667e6i	0.298699	−	0.217018i	−0.428333	−	0.903621i	$-0.640899\pi$
$907$	7.40035e6	−	5.37667e6i	0.298699	−	0.217018i	0.727032	+	0.686603i	$0.240899\pi$
$908$		0			0
$909$	2.77926e6	+	8.55369e6i	0.111563	+	0.343355i
$910$		0			0
$911$	8.32498e6	+	6.04845e6i	0.332344	+	0.241462i	0.741424	−	0.671036i	$-0.234151\pi$
$911$	8.32498e6	+	6.04845e6i	0.332344	+	0.241462i	−0.409081	+	0.912498i	$0.634151\pi$
$912$		0			0
$913$	−2.46699e6	+	2.30251e6i	−0.0979470	+	0.0914166i
$914$		0			0
$915$	1.75522e7	+	1.27524e7i	0.693073	+	0.503547i
$916$		0			0
$917$	1.56953e7	+	4.83052e7i	0.616377	+	1.89701i
$918$		0			0
$919$	2.37352e7	−	1.72446e7i	0.927051	−	0.673542i	−0.0182177	−	0.999834i	$-0.505799\pi$
$919$	2.37352e7	−	1.72446e7i	0.927051	−	0.673542i	0.945269	+	0.326292i	$0.105799\pi$
$920$		0			0
$921$	600260.	−	1.84741e6i	0.0233180	−	0.0717653i
$922$		0			0
$923$	−3.40614e7			−1.31601
$924$		0			0
$925$	−1.75463e6			−0.0674267
$926$		0			0
$927$	−3.90402e6	+	1.20153e7i	−0.149215	+	0.459237i
$928$		0			0
$929$	−4.08360e7	+	2.96691e7i	−1.55240	+	1.12789i	−0.610491	+	0.792023i	$0.709028\pi$
$929$	−4.08360e7	+	2.96691e7i	−1.55240	+	1.12789i	−0.941911	+	0.335863i	$0.890972\pi$
$930$		0			0
$931$	−1.74820e6	−	5.38041e6i	−0.0661024	−	0.203442i
$932$		0			0
$933$	7.24866e6	+	5.26646e6i	0.272618	+	0.198068i
$934$		0			0
$935$	7.60773e6	−	3.92293e7i	0.284594	−	1.46751i
$936$		0			0
$937$	−3.50632e7	−	2.54749e7i	−1.30468	−	0.947903i	−0.304687	−	0.952453i	$-0.598552\pi$
$937$	−3.50632e7	−	2.54749e7i	−1.30468	−	0.947903i	−0.999990	+	0.00454983i	$0.998552\pi$
$938$		0			0
$939$	−1.90598e7	−	5.86601e7i	−0.705431	−	2.17109i
$940$		0			0
$941$	−1.38774e7	+	1.00825e7i	−0.510897	+	0.371188i	−0.813164	−	0.582035i	$-0.802257\pi$
$941$	−1.38774e7	+	1.00825e7i	−0.510897	+	0.371188i	0.302267	+	0.953223i	$0.402257\pi$
$942$		0			0
$943$	−3.89355e6	+	1.19831e7i	−0.142583	+	0.438825i
$944$		0			0
$945$	−2.44229e7			−0.889647
$946$		0			0
$947$	4.69793e6			0.170228			0.0851141	−	0.996371i	$-0.472875\pi$
$947$	4.69793e6			0.170228			0.0851141	+	0.996371i	$0.472875\pi$
$948$		0			0
$949$	−2.15138e7	+	6.62128e7i	−0.775447	+	2.38658i
$950$		0			0
$951$	4.76703e7	−	3.46345e7i	1.70922	−	1.24182i
$952$		0			0
$953$	−1.45737e7	−	4.48533e7i	−0.519802	−	1.59979i	−0.774371	−	0.632732i	$-0.781934\pi$
$953$	−1.45737e7	−	4.48533e7i	−0.519802	−	1.59979i	0.254569	−	0.967055i	$-0.418066\pi$
$954$		0			0
$955$	1.54226e7	+	1.12052e7i	0.547205	+	0.397568i
$956$		0			0
$957$	4.54979e7	−	5.60648e6i	1.60587	−	0.197884i
$958$		0			0
$959$	−2.34200e7	−	1.70156e7i	−0.822318	−	0.597449i
$960$		0			0
$961$	−7.61076e6	−	2.34235e7i	−0.265839	−	0.818169i
$962$		0			0
$963$	−2.57396e7	+	1.87009e7i	−0.894408	+	0.649825i
$964$		0			0
$965$	1.94527e6	−	5.98692e6i	0.0672451	−	0.206959i
$966$		0			0
$967$	2.66682e6			0.0917124			0.0458562	−	0.998948i	$-0.485398\pi$
$967$	2.66682e6			0.0917124			0.0458562	+	0.998948i	$0.485398\pi$
$968$		0			0
$969$	−3.08086e7			−1.05405
$970$		0			0
$971$	−5.09144e6	+	1.56698e7i	−0.173298	+	0.533355i	−0.999552	−	0.0299424i	$-0.990468\pi$
$971$	−5.09144e6	+	1.56698e7i	−0.173298	+	0.533355i	0.826254	+	0.563298i	$0.190468\pi$
$972$		0			0
$973$	3.47681e7	−	2.52605e7i	1.17733	−	0.855383i
$974$		0			0
$975$	−1.42224e6	−	4.37722e6i	−0.0479140	−	0.147464i
$976$		0			0
$977$	−1.10142e7	−	8.00226e6i	−0.369161	−	0.268211i	0.387702	−	0.921785i	$-0.373269\pi$
$977$	−1.10142e7	−	8.00226e6i	−0.369161	−	0.268211i	−0.756863	+	0.653574i	$0.773269\pi$
$978$		0			0
$979$	308516.	−	38016.9i	0.0102878	−	0.00126771i
$980$		0			0
$981$	3.68598e6	+	2.67802e6i	0.122287	+	0.0888468i
$982$		0			0
$983$	3.19591e6	+	9.83599e6i	0.105490	+	0.324664i	0.989845	−	0.142150i	$-0.0454016\pi$
$983$	3.19591e6	+	9.83599e6i	0.105490	+	0.324664i	−0.884355	+	0.466814i	$0.845402\pi$
$984$		0			0
$985$	9.28014e6	−	6.74242e6i	0.304764	−	0.221424i
$986$		0			0
$987$	3.88505e6	−	1.19570e7i	0.126942	−	0.390686i
$988$		0			0
$989$	−4.59198e7			−1.49283
$990$		0			0
$991$	−1.65697e7			−0.535959			−0.267979	−	0.963425i	$-0.586356\pi$
$991$	−1.65697e7			−0.535959			−0.267979	+	0.963425i	$0.586356\pi$
$992$		0			0
$993$	5.88427e6	−	1.81099e7i	0.189374	−	0.582832i
$994$		0			0
$995$	−3.78435e7	+	2.74949e7i	−1.21181	+	0.880430i
$996$		0			0
$997$	3.01325e6	+	9.27384e6i	0.0960059	+	0.295476i	0.987515	−	0.157528i	$-0.0503524\pi$
$997$	3.01325e6	+	9.27384e6i	0.0960059	+	0.295476i	−0.891509	+	0.453004i	$0.850352\pi$
$998$		0			0
$999$	−2.26380e7	−	1.64475e7i	−0.717669	−	0.521417i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	88.6.i.b.81.2	yes	32
11.3	even	5	inner	88.6.i.b.25.2	✓	32
11.5	even	5		968.6.a.q.1.2		16
11.6	odd	10		968.6.a.p.1.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.6.i.b.25.2	✓	32	11.3	even	5	inner
88.6.i.b.81.2	yes	32	1.1	even	1	trivial
968.6.a.p.1.2		16	11.6	odd	10
968.6.a.q.1.2		16	11.5	even	5

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:	\( N \)	\(=\)	\( 88 = 2^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	88.i (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.55065 + 23.2385i) q^{3} +(46.4402 - 33.7408i) q^{5} +(-48.4576 - 149.137i) q^{7} +(-286.424 - 208.100i) q^{9} +(398.299 - 49.0805i) q^{11} +(-895.696 - 650.761i) q^{13} +(433.432 + 1333.97i) q^{15} +(1403.35 - 1019.60i) q^{17} +(-224.617 + 691.302i) q^{19} +3831.61 q^{21} +4796.66 q^{23} +(52.5738 - 161.806i) q^{25} +(2195.02 - 1594.78i) q^{27} +(-1444.65 - 4446.18i) q^{29} +(1618.08 + 1175.60i) q^{31} +(-1866.86 + 9626.46i) q^{33} +(-7282.38 - 5290.96i) q^{35} +(-3187.00 - 9808.56i) q^{37} +(21885.8 - 15901.0i) q^{39} +(-811.722 + 2498.22i) q^{41} -9573.28 q^{43} -20323.0 q^{45} +(1013.95 - 3120.61i) q^{47} +(-6296.59 + 4574.74i) q^{49} +(13097.6 + 40310.4i) q^{51} +(21002.8 + 15259.5i) q^{53} +(16841.1 - 15718.2i) q^{55} +(-14368.8 - 10439.5i) q^{57} +(-1366.86 - 4206.76i) q^{59} +(12513.9 - 9091.90i) q^{61} +(-17155.9 + 52800.5i) q^{63} -63553.5 q^{65} -18768.3 q^{67} +(-36217.9 + 111467. i) q^{69} +(24889.5 - 18083.3i) q^{71} +(-19431.9 - 59805.2i) q^{73} +(3363.15 + 2443.47i) q^{75} +(-26620.3 - 57022.8i) q^{77} +(-53022.4 - 38523.0i) q^{79} +(-6098.88 - 18770.4i) q^{81} +(-6802.87 + 4942.58i) q^{83} +(30770.0 - 94700.4i) q^{85} +114230. q^{87} +774.583 q^{89} +(-53649.4 + 165116. i) q^{91} +(-39536.8 + 28725.2i) q^{93} +(12893.8 + 39683.0i) q^{95} +(108537. + 78856.8i) q^{97} +(-124296. - 68828.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 21 q^{3} + 37 q^{5} - 181 q^{7} - 1123 q^{9} + 563 q^{11} - 753 q^{13} - 1731 q^{15} + 3153 q^{17} - 2022 q^{19} - 2282 q^{21} + 4516 q^{23} - 2551 q^{25} + 11538 q^{27} + 7829 q^{29} - 7643 q^{31}+ \cdots + 689815 q^{99}+O(q^{100}) \) 32 * q - 21 * q^3 + 37 * q^5 - 181 * q^7 - 1123 * q^9 + 563 * q^11 - 753 * q^13 - 1731 * q^15 + 3153 * q^17 - 2022 * q^19 - 2282 * q^21 + 4516 * q^23 - 2551 * q^25 + 11538 * q^27 + 7829 * q^29 - 7643 * q^31 - 20846 * q^33 - 47237 * q^35 - 30139 * q^37 + 15155 * q^39 + 17377 * q^41 + 37862 * q^43 + 46556 * q^45 - 7053 * q^47 - 43539 * q^49 - 55812 * q^51 - 17637 * q^53 + 81511 * q^55 + 137684 * q^57 + 58662 * q^59 + 32619 * q^61 - 29128 * q^63 - 103034 * q^65 + 20982 * q^67 - 183982 * q^69 + 43641 * q^71 + 94725 * q^73 - 14162 * q^75 + 143529 * q^77 + 111121 * q^79 - 97990 * q^81 - 117894 * q^83 + 123843 * q^85 - 154438 * q^87 + 13394 * q^89 - 378075 * q^91 - 83153 * q^93 + 362641 * q^95 - 332002 * q^97 + 689815 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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