LMFDB - Embedded newform 240.3.bg.a.97.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,3,Mod(97,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("240.97");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	240.bg (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:	$6.53952634465$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.2
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	240.97
Dual form			240.3.bg.a.193.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 1.22474i) q^{3} +(-4.67423 + 1.77526i) q^{5} +(-3.44949 - 3.44949i) q^{7} -3.00000i q^{9} +O(q^{10})$	\(q+(1.22474 - 1.22474i) q^{3} +(-4.67423 + 1.77526i) q^{5} +(-3.44949 - 3.44949i) q^{7} -3.00000i q^{9} -11.3485 q^{11} +(-5.55051 + 5.55051i) q^{13} +(-3.55051 + 7.89898i) q^{15} +(-17.3485 - 17.3485i) q^{17} -8.69694i q^{19} -8.44949 q^{21} +(-11.5505 + 11.5505i) q^{23} +(18.6969 - 16.5959i) q^{25} +(-3.67423 - 3.67423i) q^{27} +35.1464i q^{29} -10.6969 q^{31} +(-13.8990 + 13.8990i) q^{33} +(22.2474 + 10.0000i) q^{35} +(-6.04541 - 6.04541i) q^{37} +13.5959i q^{39} +0.696938 q^{41} +(26.4949 - 26.4949i) q^{43} +(5.32577 + 14.0227i) q^{45} +(-44.2474 - 44.2474i) q^{47} -25.2020i q^{49} -42.4949 q^{51} +(-0.696938 + 0.696938i) q^{53} +(53.0454 - 20.1464i) q^{55} +(-10.6515 - 10.6515i) q^{57} +39.9342i q^{59} +5.90918 q^{61} +(-10.3485 + 10.3485i) q^{63} +(16.0908 - 35.7980i) q^{65} +(45.1010 + 45.1010i) q^{67} +28.2929i q^{69} +68.0000 q^{71} +(77.7878 - 77.7878i) q^{73} +(2.57321 - 43.2247i) q^{75} +(39.1464 + 39.1464i) q^{77} +24.4949i q^{79} -9.00000 q^{81} +(-13.1464 + 13.1464i) q^{83} +(111.889 + 50.2929i) q^{85} +(43.0454 + 43.0454i) q^{87} +82.1816i q^{89} +38.2929 q^{91} +(-13.1010 + 13.1010i) q^{93} +(15.4393 + 40.6515i) q^{95} +(-24.5959 - 24.5959i) q^{97} +34.0454i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{5} - 4 q^{7}+O(q^{10}) $ 4 * q - 4 * q^5 - 4 * q^7	$ 4 q - 4 q^{5} - 4 q^{7} - 16 q^{11} - 32 q^{13} - 24 q^{15} - 40 q^{17} - 24 q^{21} - 56 q^{23} + 16 q^{25} + 16 q^{31} - 36 q^{33} + 40 q^{35} + 64 q^{37} - 56 q^{41} + 8 q^{43} + 36 q^{45} - 128 q^{47} - 72 q^{51} + 56 q^{53} + 124 q^{55} - 72 q^{57} + 200 q^{61} - 12 q^{63} - 112 q^{65} + 200 q^{67} + 272 q^{71} + 76 q^{73} - 24 q^{75} + 88 q^{77} - 36 q^{81} + 16 q^{83} + 232 q^{85} + 84 q^{87} + 16 q^{91} - 72 q^{93} - 144 q^{95} - 20 q^{97}+O(q^{100}) $ 4 * q - 4 * q^5 - 4 * q^7 - 16 * q^11 - 32 * q^13 - 24 * q^15 - 40 * q^17 - 24 * q^21 - 56 * q^23 + 16 * q^25 + 16 * q^31 - 36 * q^33 + 40 * q^35 + 64 * q^37 - 56 * q^41 + 8 * q^43 + 36 * q^45 - 128 * q^47 - 72 * q^51 + 56 * q^53 + 124 * q^55 - 72 * q^57 + 200 * q^61 - 12 * q^63 - 112 * q^65 + 200 * q^67 + 272 * q^71 + 76 * q^73 - 24 * q^75 + 88 * q^77 - 36 * q^81 + 16 * q^83 + 232 * q^85 + 84 * q^87 + 16 * q^91 - 72 * q^93 - 144 * q^95 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$4$		0			0
$5$	−4.67423	+	1.77526i	−0.934847	+	0.355051i
$5$	−4.67423	+	1.77526i	−0.934847	+	0.355051i
$6$		0			0
$7$	−3.44949	−	3.44949i	−0.492784	−	0.492784i	0.416398	−	0.909182i	$-0.363292\pi$
$7$	−3.44949	−	3.44949i	−0.492784	−	0.492784i	−0.909182	+	0.416398i	$0.863292\pi$
$8$		0			0
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	−11.3485			−1.03168			−0.515840	−	0.856685i	$-0.672520\pi$
$11$	−11.3485			−1.03168			−0.515840	+	0.856685i	$0.672520\pi$
$12$		0			0
$13$	−5.55051	+	5.55051i	−0.426962	+	0.426962i	−0.887592	−	0.460630i	$-0.847624\pi$
$13$	−5.55051	+	5.55051i	−0.426962	+	0.426962i	0.460630	+	0.887592i	$0.347624\pi$
$14$		0			0
$15$	−3.55051	+	7.89898i	−0.236701	+	0.526599i
$16$		0			0
$17$	−17.3485	−	17.3485i	−1.02050	−	1.02050i	−0.999785	−	0.0207127i	$-0.993406\pi$
$17$	−17.3485	−	17.3485i	−1.02050	−	1.02050i	−0.0207127	−	0.999785i	$-0.506594\pi$
$18$		0			0
$19$		−	8.69694i		−	0.457734i	−0.973458	−	0.228867i	$-0.926498\pi$
$19$		−	8.69694i		−	0.457734i	0.973458	−	0.228867i	$-0.0735020\pi$
$20$		0			0
$21$	−8.44949			−0.402357
$22$		0			0
$23$	−11.5505	+	11.5505i	−0.502196	+	0.502196i	−0.912120	−	0.409924i	$-0.865555\pi$
$23$	−11.5505	+	11.5505i	−0.502196	+	0.502196i	0.409924	+	0.912120i	$0.365555\pi$
$24$		0			0
$25$	18.6969	−	16.5959i	0.747878	−	0.663837i
$26$		0			0
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$		0			0
$29$			35.1464i			1.21195i	0.795485	+	0.605973i	$0.207216\pi$
$29$			35.1464i			1.21195i	−0.795485	+	0.605973i	$0.792784\pi$
$30$		0			0
$31$	−10.6969			−0.345063			−0.172531	−	0.985004i	$-0.555195\pi$
$31$	−10.6969			−0.345063			−0.172531	+	0.985004i	$0.555195\pi$
$32$		0			0
$33$	−13.8990	+	13.8990i	−0.421181	+	0.421181i
$34$		0			0
$35$	22.2474	+	10.0000i	0.635641	+	0.285714i
$36$		0			0
$37$	−6.04541	−	6.04541i	−0.163389	−	0.163389i	0.620677	−	0.784066i	$-0.286858\pi$
$37$	−6.04541	−	6.04541i	−0.163389	−	0.163389i	−0.784066	+	0.620677i	$0.786858\pi$
$38$		0			0
$39$			13.5959i			0.348613i
$40$		0			0
$41$	0.696938			0.0169985			0.00849925	−	0.999964i	$-0.497295\pi$
$41$	0.696938			0.0169985			0.00849925	+	0.999964i	$0.497295\pi$
$42$		0			0
$43$	26.4949	−	26.4949i	0.616160	−	0.616160i	−0.328384	−	0.944544i	$-0.606504\pi$
$43$	26.4949	−	26.4949i	0.616160	−	0.616160i	0.944544	+	0.328384i	$0.106504\pi$
$44$		0			0
$45$	5.32577	+	14.0227i	0.118350	+	0.311616i
$46$		0			0
$47$	−44.2474	−	44.2474i	−0.941435	−	0.941435i	0.0569424	−	0.998377i	$-0.481865\pi$
$47$	−44.2474	−	44.2474i	−0.941435	−	0.941435i	−0.998377	+	0.0569424i	$0.981865\pi$
$48$		0			0
$49$		−	25.2020i		−	0.514327i
$50$		0			0
$51$	−42.4949			−0.833233
$52$		0			0
$53$	−0.696938	+	0.696938i	−0.0131498	+	0.0131498i	−0.713651	−	0.700501i	$-0.752960\pi$
$53$	−0.696938	+	0.696938i	−0.0131498	+	0.0131498i	0.700501	+	0.713651i	$0.252960\pi$
$54$		0			0
$55$	53.0454	−	20.1464i	0.964462	−	0.366299i
$56$		0			0
$57$	−10.6515	−	10.6515i	−0.186869	−	0.186869i
$58$		0			0
$59$			39.9342i			0.676851i	0.940993	+	0.338425i	$0.109894\pi$
$59$			39.9342i			0.676851i	−0.940993	+	0.338425i	$0.890106\pi$
$60$		0			0
$61$	5.90918			0.0968719			0.0484359	−	0.998826i	$-0.484576\pi$
$61$	5.90918			0.0968719			0.0484359	+	0.998826i	$0.484576\pi$
$62$		0			0
$63$	−10.3485	+	10.3485i	−0.164261	+	0.164261i
$64$		0			0
$65$	16.0908	−	35.7980i	0.247551	−	0.550738i
$66$		0			0
$67$	45.1010	+	45.1010i	0.673150	+	0.673150i	0.958441	−	0.285291i	$-0.0920903\pi$
$67$	45.1010	+	45.1010i	0.673150	+	0.673150i	−0.285291	+	0.958441i	$0.592090\pi$
$68$		0			0
$69$			28.2929i			0.410041i
$70$		0			0
$71$	68.0000			0.957746			0.478873	−	0.877884i	$-0.341045\pi$
$71$	68.0000			0.957746			0.478873	+	0.877884i	$0.341045\pi$
$72$		0			0
$73$	77.7878	−	77.7878i	1.06559	−	1.06559i	0.0678931	−	0.997693i	$-0.478372\pi$
$73$	77.7878	−	77.7878i	1.06559	−	1.06559i	0.997693	−	0.0678931i	$-0.0216277\pi$
$74$		0			0
$75$	2.57321	−	43.2247i	0.0343095	−	0.576330i
$76$		0			0
$77$	39.1464	+	39.1464i	0.508395	+	0.508395i
$78$		0			0
$79$			24.4949i			0.310062i	0.987910	+	0.155031i	$0.0495477\pi$
$79$			24.4949i			0.310062i	−0.987910	+	0.155031i	$0.950452\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$		0			0
$83$	−13.1464	+	13.1464i	−0.158391	+	0.158391i	−0.781853	−	0.623463i	$-0.785725\pi$
$83$	−13.1464	+	13.1464i	−0.158391	+	0.158391i	0.623463	+	0.781853i	$0.285725\pi$
$84$		0			0
$85$	111.889	+	50.2929i	1.31634	+	0.591681i
$86$		0			0
$87$	43.0454	+	43.0454i	0.494775	+	0.494775i
$88$		0			0
$89$			82.1816i			0.923389i	0.887039	+	0.461695i	$0.152758\pi$
$89$			82.1816i			0.923389i	−0.887039	+	0.461695i	$0.847242\pi$
$90$		0			0
$91$	38.2929			0.420801
$92$		0			0
$93$	−13.1010	+	13.1010i	−0.140871	+	0.140871i
$94$		0			0
$95$	15.4393	+	40.6515i	0.162519	+	0.427911i
$96$		0			0
$97$	−24.5959	−	24.5959i	−0.253566	−	0.253566i	0.568865	−	0.822431i	$-0.307383\pi$
$97$	−24.5959	−	24.5959i	−0.253566	−	0.253566i	−0.822431	+	0.568865i	$0.807383\pi$
$98$		0			0
$99$			34.0454i			0.343893i
$100$		0			0
$101$	−105.621			−1.04575			−0.522876	−	0.852409i	$-0.675141\pi$
$101$	−105.621			−1.04575			−0.522876	+	0.852409i	$0.675141\pi$
$102$		0			0
$103$	89.2474	−	89.2474i	0.866480	−	0.866480i	−0.125601	−	0.992081i	$-0.540086\pi$
$103$	89.2474	−	89.2474i	0.866480	−	0.866480i	0.992081	+	0.125601i	$0.0400858\pi$
$104$		0			0
$105$	39.4949	−	15.0000i	0.376142	−	0.142857i
$106$		0			0
$107$	−68.7423	−	68.7423i	−0.642452	−	0.642452i	0.308706	−	0.951158i	$-0.400104\pi$
$107$	−68.7423	−	68.7423i	−0.642452	−	0.642452i	−0.951158	+	0.308706i	$0.900104\pi$
$108$		0			0
$109$			68.6969i			0.630247i	0.949051	+	0.315124i	$0.102046\pi$
$109$			68.6969i			0.630247i	−0.949051	+	0.315124i	$0.897954\pi$
$110$		0			0
$111$	−14.8082			−0.133407
$112$		0			0
$113$	97.6413	−	97.6413i	0.864083	−	0.864083i	−0.127727	−	0.991809i	$-0.540768\pi$
$113$	97.6413	−	97.6413i	0.864083	−	0.864083i	0.991809	+	0.127727i	$0.0407681\pi$
$114$		0			0
$115$	33.4847	−	74.4949i	0.291171	−	0.647782i
$116$		0			0
$117$	16.6515	+	16.6515i	0.142321	+	0.142321i
$118$		0			0
$119$			119.687i			1.00577i
$120$		0			0
$121$	7.78775			0.0643616
$122$		0			0
$123$	0.853572	−	0.853572i	0.00693961	−	0.00693961i
$124$		0			0
$125$	−57.9319	+	110.765i	−0.463455	+	0.886120i
$126$		0			0
$127$	−164.621	−	164.621i	−1.29623	−	1.29623i	−0.930865	−	0.365362i	$-0.880945\pi$
$127$	−164.621	−	164.621i	−1.29623	−	1.29623i	−0.365362	−	0.930865i	$-0.619055\pi$
$128$		0			0
$129$		−	64.8990i		−	0.503093i
$130$		0			0
$131$	−106.136			−0.810200			−0.405100	−	0.914272i	$-0.632763\pi$
$131$	−106.136			−0.810200			−0.405100	+	0.914272i	$0.632763\pi$
$132$		0			0
$133$	−30.0000	+	30.0000i	−0.225564	+	0.225564i
$134$		0			0
$135$	23.6969	+	10.6515i	0.175533	+	0.0789002i
$136$		0			0
$137$	−166.631	−	166.631i	−1.21629	−	1.21629i	−0.968923	−	0.247363i	$-0.920436\pi$
$137$	−166.631	−	166.631i	−1.21629	−	1.21629i	−0.247363	−	0.968923i	$-0.579564\pi$
$138$		0			0
$139$			191.171i			1.37533i	0.726026	+	0.687667i	$0.241365\pi$
$139$			191.171i			1.37533i	−0.726026	+	0.687667i	$0.758635\pi$
$140$		0			0
$141$	−108.384			−0.768679
$142$		0			0
$143$	62.9898	−	62.9898i	0.440488	−	0.440488i
$144$		0			0
$145$	−62.3939	−	164.283i	−0.430303	−	1.13298i
$146$		0			0
$147$	−30.8661	−	30.8661i	−0.209973	−	0.209973i
$148$		0			0
$149$			84.8536i			0.569487i	0.958604	+	0.284744i	$0.0919084\pi$
$149$			84.8536i			0.569487i	−0.958604	+	0.284744i	$0.908092\pi$
$150$		0			0
$151$	−148.969			−0.986552			−0.493276	−	0.869873i	$-0.664201\pi$
$151$	−148.969			−0.986552			−0.493276	+	0.869873i	$0.664201\pi$
$152$		0			0
$153$	−52.0454	+	52.0454i	−0.340166	+	0.340166i
$154$		0			0
$155$	50.0000	−	18.9898i	0.322581	−	0.122515i
$156$		0			0
$157$	16.8536	+	16.8536i	0.107348	+	0.107348i	0.758741	−	0.651393i	$-0.225815\pi$
$157$	16.8536	+	16.8536i	0.107348	+	0.107348i	−0.651393	+	0.758741i	$0.725815\pi$
$158$		0			0
$159$			1.70714i			0.0107368i
$160$		0			0
$161$	79.6867			0.494949
$162$		0			0
$163$	−130.606	+	130.606i	−0.801265	+	0.801265i	−0.983293	−	0.182029i	$-0.941734\pi$
$163$	−130.606	+	130.606i	−0.801265	+	0.801265i	0.182029	+	0.983293i	$0.441734\pi$
$164$		0			0
$165$	40.2929	−	89.6413i	0.244199	−	0.543281i
$166$		0			0
$167$	45.0352	+	45.0352i	0.269672	+	0.269672i	0.828968	−	0.559296i	$-0.188929\pi$
$167$	45.0352	+	45.0352i	0.269672	+	0.269672i	−0.559296	+	0.828968i	$0.688929\pi$
$168$		0			0
$169$			107.384i			0.635406i
$170$		0			0
$171$	−26.0908			−0.152578
$172$		0			0
$173$	146.631	−	146.631i	0.847579	−	0.847579i	−0.142252	−	0.989831i	$-0.545434\pi$
$173$	146.631	−	146.631i	0.847579	−	0.847579i	0.989831	+	0.142252i	$0.0454343\pi$
$174$		0			0
$175$	−121.742	−	7.24745i	−0.695671	−	0.0414140i
$176$		0			0
$177$	48.9092	+	48.9092i	0.276323	+	0.276323i
$178$		0			0
$179$		−	183.712i		−	1.02632i	−0.858292	−	0.513161i	$-0.828474\pi$
$179$		−	183.712i		−	1.02632i	0.858292	−	0.513161i	$-0.171526\pi$
$180$		0			0
$181$	−286.272			−1.58162			−0.790808	−	0.612064i	$-0.790339\pi$
$181$	−286.272			−1.58162			−0.790808	+	0.612064i	$0.790339\pi$
$182$		0			0
$183$	7.23724	−	7.23724i	0.0395478	−	0.0395478i
$184$		0			0
$185$	38.9898	+	17.5255i	0.210756	+	0.0947325i
$186$		0			0
$187$	196.879	+	196.879i	1.05283	+	1.05283i
$188$		0			0
$189$			25.3485i			0.134119i
$190$		0			0
$191$	−48.0908			−0.251784			−0.125892	−	0.992044i	$-0.540179\pi$
$191$	−48.0908			−0.251784			−0.125892	+	0.992044i	$0.540179\pi$
$192$		0			0
$193$	−255.565	+	255.565i	−1.32417	+	1.32417i	−0.413809	+	0.910364i	$0.635802\pi$
$193$	−255.565	+	255.565i	−1.32417	+	1.32417i	−0.910364	+	0.413809i	$0.864198\pi$
$194$		0			0
$195$	−24.1362	−	63.5505i	−0.123776	−	0.325900i
$196$		0			0
$197$	−96.6969	−	96.6969i	−0.490847	−	0.490847i	0.417726	−	0.908573i	$-0.362827\pi$
$197$	−96.6969	−	96.6969i	−0.490847	−	0.490847i	−0.908573	+	0.417726i	$0.862827\pi$
$198$		0			0
$199$		−	192.606i		−	0.967870i	−0.875104	−	0.483935i	$-0.839207\pi$
$199$		−	192.606i		−	0.967870i	0.875104	−	0.483935i	$-0.160793\pi$
$200$		0			0
$201$	110.474			0.549624
$202$		0			0
$203$	121.237	−	121.237i	0.597228	−	0.597228i
$204$		0			0
$205$	−3.25765	+	1.23724i	−0.0158910	+	0.00603533i
$206$		0			0
$207$	34.6515	+	34.6515i	0.167399	+	0.167399i
$208$		0			0
$209$			98.6969i			0.472234i
$210$		0			0
$211$	−147.212			−0.697688			−0.348844	−	0.937181i	$-0.613426\pi$
$211$	−147.212			−0.697688			−0.348844	+	0.937181i	$0.613426\pi$
$212$		0			0
$213$	83.2827	−	83.2827i	0.390998	−	0.390998i
$214$		0			0
$215$	−76.8082	+	170.879i	−0.357247	+	0.794784i
$216$		0			0
$217$	36.8990	+	36.8990i	0.170041	+	0.170041i
$218$		0			0
$219$		−	190.540i		−	0.870047i
$220$		0			0
$221$	192.586			0.871429
$222$		0			0
$223$	−167.429	+	167.429i	−0.750803	+	0.750803i	−0.974629	−	0.223826i	$-0.928145\pi$
$223$	−167.429	+	167.429i	−0.750803	+	0.750803i	0.223826	+	0.974629i	$0.428145\pi$
$224$		0			0
$225$	−49.7878	−	56.0908i	−0.221279	−	0.249293i
$226$		0			0
$227$	−253.171	−	253.171i	−1.11529	−	1.11529i	−0.992423	−	0.122870i	$-0.960790\pi$
$227$	−253.171	−	253.171i	−1.11529	−	1.11529i	−0.122870	−	0.992423i	$-0.539210\pi$
$228$		0			0
$229$		−	224.202i		−	0.979048i	−0.871990	−	0.489524i	$-0.837171\pi$
$229$		−	224.202i		−	0.979048i	0.871990	−	0.489524i	$-0.162829\pi$
$230$		0			0
$231$	95.8888			0.415103
$232$		0			0
$233$	−205.712	+	205.712i	−0.882883	+	0.882883i	−0.993827	−	0.110944i	$-0.964613\pi$
$233$	−205.712	+	205.712i	−0.882883	+	0.882883i	0.110944	+	0.993827i	$0.464613\pi$
$234$		0			0
$235$	285.373	+	128.272i	1.21436	+	0.545840i
$236$		0			0
$237$	30.0000	+	30.0000i	0.126582	+	0.126582i
$238$		0			0
$239$			345.798i			1.44685i	0.690401	+	0.723427i	$0.257434\pi$
$239$			345.798i			1.44685i	−0.690401	+	0.723427i	$0.742566\pi$
$240$		0			0
$241$	101.576			0.421475			0.210738	−	0.977543i	$-0.432413\pi$
$241$	101.576			0.421475			0.210738	+	0.977543i	$0.432413\pi$
$242$		0			0
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	44.7401	+	117.800i	0.182612	+	0.480817i
$246$		0			0
$247$	48.2724	+	48.2724i	0.195435	+	0.195435i
$248$		0			0
$249$			32.2020i			0.129325i
$250$		0			0
$251$	331.258			1.31975			0.659876	−	0.751375i	$-0.270609\pi$
$251$	331.258			1.31975			0.659876	+	0.751375i	$0.270609\pi$
$252$		0			0
$253$	131.081	−	131.081i	0.518105	−	0.518105i
$254$		0			0
$255$	198.631	−	75.4393i	0.778946	−	0.295840i
$256$		0			0
$257$	33.2372	+	33.2372i	0.129328	+	0.129328i	0.768808	−	0.639480i	$-0.220850\pi$
$257$	33.2372	+	33.2372i	0.129328	+	0.129328i	−0.639480	+	0.768808i	$0.720850\pi$
$258$		0			0
$259$			41.7071i			0.161031i
$260$		0			0
$261$	105.439			0.403982
$262$		0			0
$263$	278.157	−	278.157i	1.05763	−	1.05763i	0.0593952	−	0.998235i	$-0.481083\pi$
$263$	278.157	−	278.157i	1.05763	−	1.05763i	0.998235	−	0.0593952i	$-0.0189172\pi$
$264$		0			0
$265$	2.02041	−	4.49490i	0.00762419	−	0.0169619i
$266$		0			0
$267$	100.652	+	100.652i	0.376972	+	0.376972i
$268$		0			0
$269$		−	488.499i		−	1.81598i	−0.418988	−	0.907992i	$-0.637615\pi$
$269$		−	488.499i		−	1.81598i	0.418988	−	0.907992i	$-0.362385\pi$
$270$		0			0
$271$	−131.576			−0.485518			−0.242759	−	0.970087i	$-0.578053\pi$
$271$	−131.576			−0.485518			−0.242759	+	0.970087i	$0.578053\pi$
$272$		0			0
$273$	46.8990	−	46.8990i	0.171791	−	0.171791i
$274$		0			0
$275$	−212.182	+	188.338i	−0.771570	+	0.684866i
$276$		0			0
$277$	101.510	+	101.510i	0.366461	+	0.366461i	0.866185	−	0.499724i	$-0.166565\pi$
$277$	101.510	+	101.510i	0.366461	+	0.366461i	−0.499724	+	0.866185i	$0.666565\pi$
$278$		0			0
$279$			32.0908i			0.115021i
$280$		0			0
$281$	343.303			1.22172			0.610860	−	0.791739i	$-0.290824\pi$
$281$	343.303			1.22172			0.610860	+	0.791739i	$0.290824\pi$
$282$		0			0
$283$	−1.19184	+	1.19184i	−0.00421143	+	0.00421143i	−0.709209	−	0.704998i	$-0.750948\pi$
$283$	−1.19184	+	1.19184i	−0.00421143	+	0.00421143i	0.704998	+	0.709209i	$0.250948\pi$
$284$		0			0
$285$	68.6969	+	30.8786i	0.241042	+	0.108346i
$286$		0			0
$287$	−2.40408	−	2.40408i	−0.00837659	−	0.00837659i
$288$		0			0
$289$			312.939i			1.08283i
$290$		0			0
$291$	−60.2474			−0.207036
$292$		0			0
$293$	96.5653	−	96.5653i	0.329574	−	0.329574i	−0.522850	−	0.852425i	$-0.675131\pi$
$293$	96.5653	−	96.5653i	0.329574	−	0.329574i	0.852425	+	0.522850i	$0.175131\pi$
$294$		0			0
$295$	−70.8934	−	186.662i	−0.240316	−	0.632752i
$296$		0			0
$297$	41.6969	+	41.6969i	0.140394	+	0.140394i
$298$		0			0
$299$		−	128.222i		−	0.428838i
$300$		0			0
$301$	−182.788			−0.607268
$302$		0			0
$303$	−129.359	+	129.359i	−0.426926	+	0.426926i
$304$		0			0
$305$	−27.6209	+	10.4903i	−0.0905604	+	0.0343945i
$306$		0			0
$307$	124.969	+	124.969i	0.407066	+	0.407066i	0.880714	−	0.473648i	$-0.157063\pi$
$307$	124.969	+	124.969i	0.407066	+	0.407066i	−0.473648	+	0.880714i	$0.657063\pi$
$308$		0			0
$309$		−	218.611i		−	0.707478i
$310$		0			0
$311$	586.302			1.88522			0.942608	−	0.333902i	$-0.108365\pi$
$311$	586.302			1.88522			0.942608	+	0.333902i	$0.108365\pi$
$312$		0			0
$313$	−102.373	+	102.373i	−0.327072	+	0.327072i	−0.851472	−	0.524400i	$-0.824290\pi$
$313$	−102.373	+	102.373i	−0.327072	+	0.327072i	0.524400	+	0.851472i	$0.324290\pi$
$314$		0			0
$315$	30.0000	−	66.7423i	0.0952381	−	0.211880i
$316$		0			0
$317$	−108.783	−	108.783i	−0.343165	−	0.343165i	0.514391	−	0.857556i	$-0.328018\pi$
$317$	−108.783	−	108.783i	−0.343165	−	0.343165i	−0.857556	+	0.514391i	$0.828018\pi$
$318$		0			0
$319$		−	398.858i		−	1.25034i
$320$		0			0
$321$	−168.384			−0.524560
$322$		0			0
$323$	−150.879	+	150.879i	−0.467116	+	0.467116i
$324$		0			0
$325$	−11.6617	+	195.893i	−0.0358823	+	0.602749i
$326$		0			0
$327$	84.1362	+	84.1362i	0.257297	+	0.257297i
$328$		0			0
$329$			305.262i			0.927849i
$330$		0			0
$331$	245.423			0.741461			0.370730	−	0.928741i	$-0.379107\pi$
$331$	245.423			0.741461			0.370730	+	0.928741i	$0.379107\pi$
$332$		0			0
$333$	−18.1362	+	18.1362i	−0.0544631	+	0.0544631i
$334$		0			0
$335$	−290.879	−	130.747i	−0.868294	−	0.390289i
$336$		0			0
$337$	213.808	+	213.808i	0.634446	+	0.634446i	0.949180	−	0.314734i	$-0.101915\pi$
$337$	213.808	+	213.808i	0.634446	+	0.634446i	−0.314734	+	0.949180i	$0.601915\pi$
$338$		0			0
$339$		−	239.171i		−	0.705520i
$340$		0			0
$341$	121.394			0.355994
$342$		0			0
$343$	−255.959	+	255.959i	−0.746237	+	0.746237i
$344$		0			0
$345$	−50.2270	−	132.247i	−0.145586	−	0.383326i
$346$		0			0
$347$	160.050	+	160.050i	0.461239	+	0.461239i	0.899062	−	0.437822i	$-0.144250\pi$
$347$	160.050	+	160.050i	0.461239	+	0.461239i	−0.437822	+	0.899062i	$0.644250\pi$
$348$		0			0
$349$		−	298.009i		−	0.853894i	−0.904277	−	0.426947i	$-0.859589\pi$
$349$		−	298.009i		−	0.853894i	0.904277	−	0.426947i	$-0.140411\pi$
$350$		0			0
$351$	40.7878			0.116204
$352$		0			0
$353$	−22.5199	+	22.5199i	−0.0637957	+	0.0637957i	−0.738285	−	0.674489i	$-0.764364\pi$
$353$	−22.5199	+	22.5199i	−0.0637957	+	0.0637957i	0.674489	+	0.738285i	$0.264364\pi$
$354$		0			0
$355$	−317.848	+	120.717i	−0.895346	+	0.340049i
$356$		0			0
$357$	146.586	+	146.586i	0.410604	+	0.410604i
$358$		0			0
$359$		−	48.2724i		−	0.134464i	−0.997737	−	0.0672318i	$-0.978583\pi$
$359$		−	48.2724i		−	0.134464i	0.997737	−	0.0672318i	$-0.0214167\pi$
$360$		0			0
$361$	285.363			0.790480
$362$		0			0
$363$	9.53801	−	9.53801i	0.0262755	−	0.0262755i
$364$		0			0
$365$	−225.505	+	501.691i	−0.617822	+	1.37450i
$366$		0			0
$367$	−146.510	−	146.510i	−0.399209	−	0.399209i	0.478745	−	0.877954i	$-0.341092\pi$
$367$	−146.510	−	146.510i	−0.399209	−	0.399209i	−0.877954	+	0.478745i	$0.841092\pi$
$368$		0			0
$369$		−	2.09082i		−	0.00566617i
$370$		0			0
$371$	4.80816			0.0129600
$372$		0			0
$373$	86.2066	−	86.2066i	0.231117	−	0.231117i	−0.582042	−	0.813159i	$-0.697746\pi$
$373$	86.2066	−	86.2066i	0.231117	−	0.231117i	0.813159	+	0.582042i	$0.197746\pi$
$374$		0			0
$375$	64.7071	+	206.611i	0.172552	+	0.550962i
$376$		0			0
$377$	−195.081	−	195.081i	−0.517455	−	0.517455i
$378$		0			0
$379$			210.000i			0.554090i	0.960857	+	0.277045i	$0.0893551\pi$
$379$			210.000i			0.554090i	−0.960857	+	0.277045i	$0.910645\pi$
$380$		0			0
$381$	−403.237			−1.05837
$382$		0			0
$383$	10.6311	−	10.6311i	0.0277575	−	0.0277575i	−0.693092	−	0.720849i	$-0.743752\pi$
$383$	10.6311	−	10.6311i	0.0277575	−	0.0277575i	0.720849	+	0.693092i	$0.243752\pi$
$384$		0			0
$385$	−252.474	−	113.485i	−0.655778	−	0.294765i
$386$		0			0
$387$	−79.4847	−	79.4847i	−0.205387	−	0.205387i
$388$		0			0
$389$		−	535.337i		−	1.37619i	−0.725621	−	0.688094i	$-0.758448\pi$
$389$		−	535.337i		−	1.37619i	0.725621	−	0.688094i	$-0.241552\pi$
$390$		0			0
$391$	400.767			1.02498
$392$		0			0
$393$	−129.990	+	129.990i	−0.330763	+	0.330763i
$394$		0			0
$395$	−43.4847	−	114.495i	−0.110088	−	0.289860i
$396$		0			0
$397$	118.742	+	118.742i	0.299099	+	0.299099i	0.840661	−	0.541562i	$-0.182167\pi$
$397$	118.742	+	118.742i	0.299099	+	0.299099i	−0.541562	+	0.840661i	$0.682167\pi$
$398$		0			0
$399$			73.4847i			0.184172i
$400$		0			0
$401$	420.302			1.04813			0.524067	−	0.851677i	$-0.324414\pi$
$401$	420.302			1.04813			0.524067	+	0.851677i	$0.324414\pi$
$402$		0			0
$403$	59.3735	−	59.3735i	0.147329	−	0.147329i
$404$		0			0
$405$	42.0681	−	15.9773i	0.103872	−	0.0394501i
$406$		0			0
$407$	68.6061	+	68.6061i	0.168565	+	0.168565i
$408$		0			0
$409$		−	515.110i		−	1.25944i	−0.776823	−	0.629719i	$-0.783170\pi$
$409$		−	515.110i		−	1.25944i	0.776823	−	0.629719i	$-0.216830\pi$
$410$		0			0
$411$	−408.161			−0.993093
$412$		0			0
$413$	137.753	−	137.753i	0.333541	−	0.333541i
$414$		0			0
$415$	38.1112	−	84.7878i	0.0918343	−	0.204308i
$416$		0			0
$417$	234.136	+	234.136i	0.561478	+	0.561478i
$418$		0			0
$419$			88.6015i			0.211460i	0.994395	+	0.105730i	$0.0337178\pi$
$419$			88.6015i			0.211460i	−0.994395	+	0.105730i	$0.966282\pi$
$420$		0			0
$421$	−257.151			−0.610810			−0.305405	−	0.952223i	$-0.598792\pi$
$421$	−257.151			−0.610810			−0.305405	+	0.952223i	$0.598792\pi$
$422$		0			0
$423$	−132.742	+	132.742i	−0.313812	+	0.313812i
$424$		0			0
$425$	−612.277	−	36.4495i	−1.44065	−	0.0857635i
$426$		0			0
$427$	−20.3837	−	20.3837i	−0.0477369	−	0.0477369i
$428$		0			0
$429$		−	154.293i		−	0.359657i
$430$		0			0
$431$	−804.636			−1.86690			−0.933452	−	0.358702i	$-0.883219\pi$
$431$	−804.636			−1.86690			−0.933452	+	0.358702i	$0.883219\pi$
$432$		0			0
$433$	−344.848	+	344.848i	−0.796416	+	0.796416i	−0.982528	−	0.186113i	$-0.940411\pi$
$433$	−344.848	+	344.848i	−0.796416	+	0.796416i	0.186113	+	0.982528i	$0.440411\pi$
$434$		0			0
$435$	−277.621	−	124.788i	−0.638209	−	0.286868i
$436$		0			0
$437$	100.454	+	100.454i	0.229872	+	0.229872i
$438$		0			0
$439$		−	432.929i		−	0.986170i	−0.869981	−	0.493085i	$-0.835869\pi$
$439$		−	432.929i		−	0.986170i	0.869981	−	0.493085i	$-0.164131\pi$
$440$		0			0
$441$	−75.6061			−0.171442
$442$		0			0
$443$	−245.131	+	245.131i	−0.553342	+	0.553342i	−0.927404	−	0.374062i	$-0.877965\pi$
$443$	−245.131	+	245.131i	−0.553342	+	0.553342i	0.374062	+	0.927404i	$0.377965\pi$
$444$		0			0
$445$	−145.893	−	384.136i	−0.327850	−	0.863227i
$446$		0			0
$447$	103.924	+	103.924i	0.232492	+	0.232492i
$448$		0			0
$449$			386.091i			0.859890i	0.902855	+	0.429945i	$0.141467\pi$
$449$			386.091i			0.859890i	−0.902855	+	0.429945i	$0.858533\pi$
$450$		0			0
$451$	−7.90918			−0.0175370
$452$		0			0
$453$	−182.449	+	182.449i	−0.402758	+	0.402758i
$454$		0			0
$455$	−178.990	+	67.9796i	−0.393384	+	0.149406i
$456$		0			0
$457$	−223.747	−	223.747i	−0.489599	−	0.489599i	0.418580	−	0.908180i	$-0.362528\pi$
$457$	−223.747	−	223.747i	−0.489599	−	0.489599i	−0.908180	+	0.418580i	$0.862528\pi$
$458$		0			0
$459$			127.485i			0.277744i
$460$		0			0
$461$	−722.620			−1.56751			−0.783753	−	0.621073i	$-0.786697\pi$
$461$	−722.620			−1.56751			−0.783753	+	0.621073i	$0.786697\pi$
$462$		0			0
$463$	129.702	−	129.702i	0.280133	−	0.280133i	−0.553029	−	0.833162i	$-0.686528\pi$
$463$	129.702	−	129.702i	0.280133	−	0.280133i	0.833162	+	0.553029i	$0.186528\pi$
$464$		0			0
$465$	37.9796	−	84.4949i	0.0816765	−	0.181709i
$466$		0			0
$467$	−415.258	−	415.258i	−0.889203	−	0.889203i	0.105244	−	0.994446i	$-0.466438\pi$
$467$	−415.258	−	415.258i	−0.889203	−	0.889203i	−0.994446	+	0.105244i	$0.966438\pi$
$468$		0			0
$469$		−	311.151i		−	0.663435i
$470$		0			0
$471$	41.2827			0.0876489
$472$		0			0
$473$	−300.677	+	300.677i	−0.635680	+	0.635680i
$474$		0			0
$475$	−144.334	−	162.606i	−0.303860	−	0.342329i
$476$		0			0
$477$	2.09082	+	2.09082i	0.00438326	+	0.00438326i
$478$		0			0
$479$		−	304.949i		−	0.636637i	−0.947984	−	0.318318i	$-0.896882\pi$
$479$		−	304.949i		−	0.636637i	0.947984	−	0.318318i	$-0.103118\pi$
$480$		0			0
$481$	67.1102			0.139522
$482$		0			0
$483$	97.5959	−	97.5959i	0.202062	−	0.202062i
$484$		0			0
$485$	158.631	+	71.3031i	0.327074	+	0.147017i
$486$		0			0
$487$	429.318	+	429.318i	0.881556	+	0.881556i	0.993693	−	0.112137i	$-0.0357694\pi$
$487$	429.318	+	429.318i	0.881556	+	0.881556i	−0.112137	+	0.993693i	$0.535769\pi$
$488$		0			0
$489$			319.918i			0.654230i
$490$		0			0
$491$	414.318			0.843825			0.421912	−	0.906637i	$-0.361359\pi$
$491$	414.318			0.843825			0.421912	+	0.906637i	$0.361359\pi$
$492$		0			0
$493$	609.737	−	609.737i	1.23679	−	1.23679i
$494$		0			0
$495$	−60.4393	−	159.136i	−0.122100	−	0.321487i
$496$		0			0
$497$	−234.565	−	234.565i	−0.471962	−	0.471962i
$498$		0			0
$499$		−	367.585i		−	0.736643i	−0.929699	−	0.368321i	$-0.879933\pi$
$499$		−	367.585i		−	0.736643i	0.929699	−	0.368321i	$-0.120067\pi$
$500$		0			0
$501$	110.313			0.220186
$502$		0			0
$503$	9.59133	−	9.59133i	0.0190683	−	0.0190683i	−0.697508	−	0.716577i	$-0.745708\pi$
$503$	9.59133	−	9.59133i	0.0190683	−	0.0190683i	0.716577	+	0.697508i	$0.245708\pi$
$504$		0			0
$505$	493.697	−	187.504i	0.977618	−	0.371295i
$506$		0			0
$507$	131.518	+	131.518i	0.259404	+	0.259404i
$508$		0			0
$509$			777.489i			1.52748i	0.645522	+	0.763742i	$0.276640\pi$
$509$			777.489i			1.52748i	−0.645522	+	0.763742i	$0.723360\pi$
$510$		0			0
$511$	−536.656			−1.05021
$512$		0			0
$513$	−31.9546	+	31.9546i	−0.0622897	+	0.0622897i
$514$		0			0
$515$	−258.727	+	575.601i	−0.502382	+	1.11767i
$516$		0			0
$517$	502.141	+	502.141i	0.971259	+	0.971259i
$518$		0			0
$519$		−	359.171i		−	0.692045i
$520$		0			0
$521$	321.605			0.617284			0.308642	−	0.951178i	$-0.400125\pi$
$521$	321.605			0.617284			0.308642	+	0.951178i	$0.400125\pi$
$522$		0			0
$523$	582.454	−	582.454i	1.11368	−	1.11368i	0.121030	−	0.992649i	$-0.461380\pi$
$523$	582.454	−	582.454i	1.11368	−	1.11368i	0.992649	−	0.121030i	$-0.0386198\pi$
$524$		0			0
$525$	−157.980	+	140.227i	−0.300914	+	0.267099i
$526$		0			0
$527$	185.576	+	185.576i	0.352136	+	0.352136i
$528$		0			0
$529$			262.171i			0.495598i
$530$		0			0
$531$	119.803			0.225617
$532$		0			0
$533$	−3.86836	+	3.86836i	−0.00725772	+	0.00725772i
$534$		0			0
$535$	443.353	+	199.283i	0.828697	+	0.372491i
$536$		0			0
$537$	−225.000	−	225.000i	−0.418994	−	0.418994i
$538$		0			0
$539$			286.005i			0.530621i
$540$		0			0
$541$	460.697			0.851566			0.425783	−	0.904825i	$-0.359999\pi$
$541$	460.697			0.851566			0.425783	+	0.904825i	$0.359999\pi$
$542$		0			0
$543$	−350.611	+	350.611i	−0.645692	+	0.645692i
$544$		0			0
$545$	−121.955	−	321.106i	−0.223770	−	0.589185i
$546$		0			0
$547$	661.778	+	661.778i	1.20983	+	1.20983i	0.971081	+	0.238750i	$0.0767376\pi$
$547$	661.778	+	661.778i	1.20983	+	1.20983i	0.238750	+	0.971081i	$0.423262\pi$
$548$		0			0
$549$		−	17.7276i		−	0.0322906i
$550$		0			0
$551$	305.666			0.554748
$552$		0			0
$553$	84.4949	−	84.4949i	0.152794	−	0.152794i
$554$		0			0
$555$	69.2168	−	26.2883i	0.124715	−	0.0473663i
$556$		0			0
$557$	125.909	+	125.909i	0.226049	+	0.226049i	0.811040	−	0.584991i	$-0.198902\pi$
$557$	125.909	+	125.909i	0.226049	+	0.226049i	−0.584991	+	0.811040i	$0.698902\pi$
$558$		0			0
$559$			294.120i			0.526155i
$560$		0			0
$561$	482.252			0.859629
$562$		0			0
$563$	200.009	−	200.009i	0.355256	−	0.355256i	−0.506805	−	0.862061i	$-0.669174\pi$
$563$	200.009	−	200.009i	0.355256	−	0.355256i	0.862061	+	0.506805i	$0.169174\pi$
$564$		0			0
$565$	−283.060	+	629.737i	−0.500992	+	1.11458i
$566$		0			0
$567$	31.0454	+	31.0454i	0.0547538	+	0.0547538i
$568$		0			0
$569$		−	599.839i		−	1.05420i	−0.849804	−	0.527099i	$-0.823280\pi$
$569$		−	599.839i		−	1.05420i	0.849804	−	0.527099i	$-0.176720\pi$
$570$		0			0
$571$	247.970			0.434274			0.217137	−	0.976141i	$-0.430328\pi$
$571$	247.970			0.434274			0.217137	+	0.976141i	$0.430328\pi$
$572$		0			0
$573$	−58.8990	+	58.8990i	−0.102791	+	0.102791i
$574$		0			0
$575$	−24.2679	+	407.650i	−0.0422050	+	0.708957i
$576$		0			0
$577$	−292.121	−	292.121i	−0.506276	−	0.506276i	0.407105	−	0.913381i	$-0.366538\pi$
$577$	−292.121	−	292.121i	−0.506276	−	0.506276i	−0.913381	+	0.407105i	$0.866538\pi$
$578$		0			0
$579$			626.005i			1.08118i
$580$		0			0
$581$	90.6969			0.156105
$582$		0			0
$583$	7.90918	−	7.90918i	0.0135664	−	0.0135664i
$584$		0			0
$585$	−107.394	−	48.2724i	−0.183579	−	0.0825170i
$586$		0			0
$587$	−611.217	−	611.217i	−1.04126	−	1.04126i	−0.999112	−	0.0421437i	$-0.986581\pi$
$587$	−611.217	−	611.217i	−1.04126	−	1.04126i	−0.0421437	−	0.999112i	$-0.513419\pi$
$588$		0			0
$589$			93.0306i			0.157947i
$590$		0			0
$591$	−236.858			−0.400775
$592$		0			0
$593$	524.742	−	524.742i	0.884894	−	0.884894i	−0.109133	−	0.994027i	$-0.534807\pi$
$593$	524.742	−	524.742i	0.884894	−	0.884894i	0.994027	+	0.109133i	$0.0348074\pi$
$594$		0			0
$595$	−212.474	−	559.444i	−0.357100	−	0.940242i
$596$		0			0
$597$	−235.893	−	235.893i	−0.395131	−	0.395131i
$598$		0			0
$599$			368.858i			0.615790i	0.951420	+	0.307895i	$0.0996245\pi$
$599$			368.858i			0.615790i	−0.951420	+	0.307895i	$0.900375\pi$
$600$		0			0
$601$	932.484			1.55155			0.775777	−	0.631007i	$-0.217358\pi$
$601$	932.484			1.55155			0.775777	+	0.631007i	$0.217358\pi$
$602$		0			0
$603$	135.303	−	135.303i	0.224383	−	0.224383i
$604$		0			0
$605$	−36.4018	+	13.8252i	−0.0601682	+	0.0228517i
$606$		0			0
$607$	−513.611	−	513.611i	−0.846146	−	0.846146i	0.143504	−	0.989650i	$-0.454163\pi$
$607$	−513.611	−	513.611i	−0.846146	−	0.846146i	−0.989650	+	0.143504i	$0.954163\pi$
$608$		0			0
$609$		−	296.969i		−	0.487634i
$610$		0			0
$611$	491.192			0.803915
$612$		0			0
$613$	−615.287	+	615.287i	−1.00373	+	1.00373i	−0.00373821	+	0.999993i	$0.501190\pi$
$613$	−615.287	+	615.287i	−1.00373	+	1.00373i	−0.999993	+	0.00373821i	$0.998810\pi$
$614$		0			0
$615$	−2.47449	+	5.50510i	−0.00402356	+	0.00895139i
$616$		0			0
$617$	546.752	+	546.752i	0.886145	+	0.886145i	0.994150	−	0.108005i	$-0.0344463\pi$
$617$	546.752	+	546.752i	0.886145	+	0.886145i	−0.108005	+	0.994150i	$0.534446\pi$
$618$		0			0
$619$		−	152.869i		−	0.246962i	−0.992347	−	0.123481i	$-0.960594\pi$
$619$		−	152.869i		−	0.246962i	0.992347	−	0.123481i	$-0.0394058\pi$
$620$		0			0
$621$	84.8786			0.136680
$622$		0			0
$623$	283.485	−	283.485i	0.455032	−	0.455032i
$624$		0			0
$625$	74.1510	−	620.586i	0.118642	−	0.992937i
$626$		0			0
$627$	120.879	+	120.879i	0.192789	+	0.192789i
$628$		0			0
$629$			209.757i			0.333477i
$630$		0			0
$631$	41.4847			0.0657444			0.0328722	−	0.999460i	$-0.489535\pi$
$631$	41.4847			0.0657444			0.0328722	+	0.999460i	$0.489535\pi$
$632$		0			0
$633$	−180.297	+	180.297i	−0.284830	+	0.284830i
$634$		0			0
$635$	1061.72	+	477.233i	1.67200	+	0.751547i
$636$		0			0
$637$	139.884	+	139.884i	0.219598	+	0.219598i
$638$		0			0
$639$		−	204.000i		−	0.319249i
$640$		0			0
$641$	47.2122			0.0736541			0.0368270	−	0.999322i	$-0.488275\pi$
$641$	47.2122			0.0736541			0.0368270	+	0.999322i	$0.488275\pi$
$642$		0			0
$643$	−460.372	+	460.372i	−0.715976	+	0.715976i	−0.967779	−	0.251803i	$-0.918977\pi$
$643$	−460.372	+	460.372i	−0.715976	+	0.715976i	0.251803	+	0.967779i	$0.418977\pi$
$644$		0			0
$645$	115.212	+	303.353i	0.178624	+	0.470315i
$646$		0			0
$647$	281.287	+	281.287i	0.434756	+	0.434756i	0.890243	−	0.455487i	$-0.150535\pi$
$647$	281.287	+	281.287i	0.434756	+	0.434756i	−0.455487	+	0.890243i	$0.650535\pi$
$648$		0			0
$649$		−	453.192i		−	0.698293i
$650$		0			0
$651$	90.3837			0.138838
$652$		0			0
$653$	89.8230	−	89.8230i	0.137554	−	0.137554i	−0.634977	−	0.772531i	$-0.718990\pi$
$653$	89.8230	−	89.8230i	0.137554	−	0.137554i	0.772531	+	0.634977i	$0.218990\pi$
$654$		0			0
$655$	496.106	−	188.419i	0.757413	−	0.287662i
$656$		0			0
$657$	−233.363	−	233.363i	−0.355195	−	0.355195i
$658$		0			0
$659$		−	1081.24i		−	1.64072i	−0.571844	−	0.820362i	$-0.693772\pi$
$659$		−	1081.24i		−	1.64072i	0.571844	−	0.820362i	$-0.306228\pi$
$660$		0			0
$661$	−632.393			−0.956721			−0.478361	−	0.878163i	$-0.658769\pi$
$661$	−632.393			−0.956721			−0.478361	+	0.878163i	$0.658769\pi$
$662$		0			0
$663$	235.868	−	235.868i	0.355759	−	0.355759i
$664$		0			0
$665$	86.9694	−	193.485i	0.130781	−	0.290954i
$666$		0			0
$667$	−405.959	−	405.959i	−0.608634	−	0.608634i
$668$		0			0
$669$			410.116i			0.613028i
$670$		0			0
$671$	−67.0602			−0.0999407
$672$		0			0
$673$	233.293	−	233.293i	0.346646	−	0.346646i	−0.512213	−	0.858859i	$-0.671174\pi$
$673$	233.293	−	233.293i	0.346646	−	0.346646i	0.858859	+	0.512213i	$0.171174\pi$
$674$		0			0
$675$	−129.674	−	7.71964i	−0.192110	−	0.0114365i
$676$		0			0
$677$	−48.3883	−	48.3883i	−0.0714745	−	0.0714745i	0.670466	−	0.741940i	$-0.266094\pi$
$677$	−48.3883	−	48.3883i	−0.0714745	−	0.0714745i	−0.741940	+	0.670466i	$0.766094\pi$
$678$		0			0
$679$			169.687i			0.249907i
$680$		0			0
$681$	−620.141			−0.910633
$682$		0			0
$683$	−213.410	+	213.410i	−0.312459	+	0.312459i	−0.845862	−	0.533402i	$-0.820913\pi$
$683$	−213.410	+	213.410i	−0.312459	+	0.312459i	0.533402	+	0.845862i	$0.320913\pi$
$684$		0			0
$685$	1074.69	+	483.060i	1.56888	+	0.705197i
$686$		0			0
$687$	−274.590	−	274.590i	−0.399695	−	0.399695i
$688$		0			0
$689$		−	7.73673i		−	0.0112289i
$690$		0			0
$691$	−151.121			−0.218700			−0.109350	−	0.994003i	$-0.534877\pi$
$691$	−151.121			−0.218700			−0.109350	+	0.994003i	$0.534877\pi$
$692$		0			0
$693$	117.439	−	117.439i	0.169465	−	0.169465i
$694$		0			0
$695$	−339.378	−	893.580i	−0.488314	−	1.28573i
$696$		0			0
$697$	−12.0908	−	12.0908i	−0.0173469	−	0.0173469i
$698$		0			0
$699$			503.889i			0.720871i
$700$		0			0
$701$	−745.680			−1.06374			−0.531869	−	0.846827i	$-0.678510\pi$
$701$	−745.680			−1.06374			−0.531869	+	0.846827i	$0.678510\pi$
$702$		0			0
$703$	−52.5765	+	52.5765i	−0.0747888	+	0.0747888i
$704$		0			0
$705$	506.611	−	192.409i	0.718597	−	0.272920i
$706$		0			0
$707$	364.338	+	364.338i	0.515330	+	0.515330i
$708$		0			0
$709$			719.049i			1.01417i	0.861895	+	0.507087i	$0.169278\pi$
$709$			719.049i			1.01417i	−0.861895	+	0.507087i	$0.830722\pi$
$710$		0			0
$711$	73.4847			0.103354
$712$		0			0
$713$	123.555	−	123.555i	0.173289	−	0.173289i
$714$		0			0
$715$	−182.606	+	406.252i	−0.255393	+	0.568185i
$716$		0			0
$717$	423.514	+	423.514i	0.590675	+	0.590675i
$718$		0			0
$719$			605.271i			0.841824i	0.907101	+	0.420912i	$0.138290\pi$
$719$			605.271i			0.841824i	−0.907101	+	0.420912i	$0.861710\pi$
$720$		0			0
$721$	−615.716			−0.853975
$722$		0			0
$723$	124.404	−	124.404i	0.172067	−	0.172067i
$724$		0			0
$725$	583.287	+	657.131i	0.804534	+	0.906387i
$726$		0			0
$727$	246.126	+	246.126i	0.338550	+	0.338550i	0.855821	−	0.517271i	$-0.173052\pi$
$727$	246.126	+	246.126i	0.338550	+	0.338550i	−0.517271	+	0.855821i	$0.673052\pi$
$728$		0			0
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	−919.292			−1.25758
$732$		0			0
$733$	−270.763	+	270.763i	−0.369390	+	0.369390i	−0.867255	−	0.497865i	$-0.834118\pi$
$733$	−270.763	+	270.763i	−0.369390	+	0.369390i	0.497865	+	0.867255i	$0.334118\pi$
$734$		0			0
$735$	199.070	+	89.4801i	0.270844	+	0.121742i
$736$		0			0
$737$	−511.828	−	511.828i	−0.694474	−	0.694474i
$738$		0			0
$739$			515.666i			0.697789i	0.937162	+	0.348895i	$0.113443\pi$
$739$			515.666i			0.697789i	−0.937162	+	0.348895i	$0.886557\pi$
$740$		0			0
$741$	118.243			0.159572
$742$		0			0
$743$	−420.702	+	420.702i	−0.566220	+	0.566220i	−0.931067	−	0.364847i	$-0.881121\pi$
$743$	−420.702	+	420.702i	−0.566220	+	0.566220i	0.364847	+	0.931067i	$0.381121\pi$
$744$		0			0
$745$	−150.637	−	396.626i	−0.202197	−	0.532383i
$746$		0			0
$747$	39.4393	+	39.4393i	0.0527969	+	0.0527969i
$748$		0			0
$749$			474.252i			0.633180i
$750$		0			0
$751$	859.787			1.14486			0.572428	−	0.819955i	$-0.306002\pi$
$751$	859.787			1.14486			0.572428	+	0.819955i	$0.306002\pi$
$752$		0			0
$753$	405.706	−	405.706i	0.538786	−	0.538786i
$754$		0			0
$755$	696.318	−	264.459i	0.922275	−	0.350276i
$756$		0			0
$757$	−956.075	−	956.075i	−1.26298	−	1.26298i	−0.949642	−	0.313337i	$-0.898553\pi$
$757$	−956.075	−	956.075i	−1.26298	−	1.26298i	−0.313337	−	0.949642i	$-0.601447\pi$
$758$		0			0
$759$		−	321.081i		−	0.423031i
$760$		0			0
$761$	−322.758			−0.424124			−0.212062	−	0.977256i	$-0.568018\pi$
$761$	−322.758			−0.424124			−0.212062	+	0.977256i	$0.568018\pi$
$762$		0			0
$763$	236.969	−	236.969i	0.310576	−	0.310576i
$764$		0			0
$765$	150.879	−	335.666i	0.197227	−	0.438780i
$766$		0			0
$767$	−221.655	−	221.655i	−0.288990	−	0.288990i
$768$		0			0
$769$			692.402i			0.900393i	0.892930	+	0.450196i	$0.148646\pi$
$769$			692.402i			0.900393i	−0.892930	+	0.450196i	$0.851354\pi$
$770$		0			0
$771$	81.4143			0.105596
$772$		0			0
$773$	375.226	−	375.226i	0.485415	−	0.485415i	−0.421441	−	0.906856i	$-0.638475\pi$
$773$	375.226	−	375.226i	0.485415	−	0.485415i	0.906856	+	0.421441i	$0.138475\pi$
$774$		0			0
$775$	−200.000	+	177.526i	−0.258065	+	0.229065i
$776$		0			0
$777$	51.0806	+	51.0806i	0.0657408	+	0.0657408i
$778$		0			0
$779$		−	6.06123i		−	0.00778078i
$780$		0			0
$781$	−771.696			−0.988087
$782$		0			0
$783$	129.136	−	129.136i	0.164925	−	0.164925i
$784$		0			0
$785$	−108.697	−	48.8582i	−0.138467	−	0.0622397i
$786$		0			0
$787$	−910.990	−	910.990i	−1.15755	−	1.15755i	−0.985001	−	0.172546i	$-0.944801\pi$
$787$	−910.990	−	910.990i	−1.15755	−	1.15755i	−0.172546	−	0.985001i	$-0.555199\pi$
$788$		0			0
$789$		−	681.342i		−	0.863551i
$790$		0			0
$791$	−673.626			−0.851613
$792$		0			0
$793$	−32.7990	+	32.7990i	−0.0413606	+	0.0413606i
$794$		0			0
$795$	−3.03062	−	7.97959i	−0.00381209	−	0.0100372i
$796$		0			0
$797$	−7.21683	−	7.21683i	−0.00905500	−	0.00905500i	0.702565	−	0.711620i	$-0.252038\pi$
$797$	−7.21683	−	7.21683i	−0.00905500	−	0.00905500i	−0.711620	+	0.702565i	$0.752038\pi$
$798$		0			0
$799$			1535.25i			1.92147i
$800$		0			0
$801$	246.545			0.307796
$802$		0			0
$803$	−882.772	+	882.772i	−1.09934	+	1.09934i
$804$		0			0
$805$	−372.474	+	141.464i	−0.462701	+	0.175732i
$806$		0			0
$807$	−598.287	−	598.287i	−0.741372	−	0.741372i
$808$		0			0
$809$		−	150.000i		−	0.185414i	−0.995693	−	0.0927070i	$-0.970448\pi$
$809$		−	150.000i		−	0.185414i	0.995693	−	0.0927070i	$-0.0295520\pi$
$810$		0			0
$811$	−1336.85			−1.64839			−0.824197	−	0.566304i	$-0.808373\pi$
$811$	−1336.85			−1.64839			−0.824197	+	0.566304i	$0.808373\pi$
$812$		0			0
$813$	−161.146	+	161.146i	−0.198212	+	0.198212i
$814$		0			0
$815$	378.624	−	842.343i	0.464570	−	1.03355i
$816$		0			0
$817$	−230.424	−	230.424i	−0.282037	−	0.282037i
$818$		0			0
$819$		−	114.879i		−	0.140267i
$820$		0			0
$821$	−33.8934			−0.0412830			−0.0206415	−	0.999787i	$-0.506571\pi$
$821$	−33.8934			−0.0412830			−0.0206415	+	0.999787i	$0.506571\pi$
$822$		0			0
$823$	−481.631	+	481.631i	−0.585214	+	0.585214i	−0.936331	−	0.351117i	$-0.885802\pi$
$823$	−481.631	+	481.631i	−0.585214	+	0.585214i	0.351117	+	0.936331i	$0.385802\pi$
$824$		0			0
$825$	−29.2020	+	490.535i	−0.0353964	+	0.594587i
$826$		0			0
$827$	−350.756	−	350.756i	−0.424131	−	0.424131i	0.462492	−	0.886623i	$-0.346955\pi$
$827$	−350.756	−	350.756i	−0.424131	−	0.424131i	−0.886623	+	0.462492i	$0.846955\pi$
$828$		0			0
$829$		−	697.423i		−	0.841283i	−0.907227	−	0.420641i	$-0.861805\pi$
$829$		−	697.423i		−	0.841283i	0.907227	−	0.420641i	$-0.138195\pi$
$830$		0			0
$831$	248.647			0.299214
$832$		0			0
$833$	−437.217	+	437.217i	−0.524870	+	0.524870i
$834$		0			0
$835$	−290.454	−	130.556i	−0.347849	−	0.156355i
$836$		0			0
$837$	39.3031	+	39.3031i	0.0469571	+	0.0469571i
$838$		0			0
$839$		−	72.3724i		−	0.0862604i	−0.999069	−	0.0431302i	$-0.986267\pi$
$839$		−	72.3724i		−	0.0862604i	0.999069	−	0.0431302i	$-0.0137330\pi$
$840$		0			0
$841$	−394.271			−0.468813
$842$		0			0
$843$	420.459	−	420.459i	0.498765	−	0.498765i
$844$		0			0
$845$	−190.633	−	501.936i	−0.225602	−	0.594008i
$846$		0			0
$847$	−26.8638	−	26.8638i	−0.0317164	−	0.0317164i
$848$		0			0
$849$			2.91939i			0.00343862i
$850$		0			0
$851$	139.655			0.164107
$852$		0			0
$853$	−74.5699	+	74.5699i	−0.0874207	+	0.0874207i	−0.749465	−	0.662044i	$-0.769689\pi$
$853$	−74.5699	+	74.5699i	−0.0874207	+	0.0874207i	0.662044	+	0.749465i	$0.269689\pi$
$854$		0			0
$855$	121.955	−	46.3179i	0.142637	−	0.0541729i
$856$		0			0
$857$	−293.176	−	293.176i	−0.342096	−	0.342096i	0.515059	−	0.857155i	$-0.327770\pi$
$857$	−293.176	−	293.176i	−0.342096	−	0.342096i	−0.857155	+	0.515059i	$0.827770\pi$
$858$		0			0
$859$			786.867i			0.916027i	0.888945	+	0.458014i	$0.151439\pi$
$859$			786.867i			0.916027i	−0.888945	+	0.458014i	$0.848561\pi$
$860$		0			0
$861$	−5.88877			−0.00683946
$862$		0			0
$863$	1072.68	−	1072.68i	1.24297	−	1.24297i	0.284204	−	0.958764i	$-0.408271\pi$
$863$	1072.68	−	1072.68i	1.24297	−	1.24297i	0.958764	−	0.284204i	$-0.0917292\pi$
$864$		0			0
$865$	−425.081	+	945.696i	−0.491423	+	1.09329i
$866$		0			0
$867$	383.270	+	383.270i	0.442065	+	0.442065i
$868$		0			0
$869$		−	277.980i		−	0.319884i
$870$		0			0
$871$	−500.667			−0.574819
$872$		0			0
$873$	−73.7878	+	73.7878i	−0.0845221	+	0.0845221i
$874$		0			0
$875$	581.918	−	182.247i	0.665050	−	0.208283i
$876$		0			0
$877$	239.460	+	239.460i	0.273044	+	0.273044i	0.830324	−	0.557280i	$-0.188155\pi$
$877$	239.460	+	239.460i	0.273044	+	0.273044i	−0.557280	+	0.830324i	$0.688155\pi$
$878$		0			0
$879$		−	236.536i		−	0.269096i
$880$		0			0
$881$	62.8490			0.0713382			0.0356691	−	0.999364i	$-0.488644\pi$
$881$	62.8490			0.0713382			0.0356691	+	0.999364i	$0.488644\pi$
$882$		0			0
$883$	158.061	−	158.061i	0.179005	−	0.179005i	−0.611917	−	0.790922i	$-0.709601\pi$
$883$	158.061	−	158.061i	0.179005	−	0.179005i	0.790922	+	0.611917i	$0.209601\pi$
$884$		0			0
$885$	−315.439	−	141.787i	−0.356429	−	0.160211i
$886$		0			0
$887$	−30.2066	−	30.2066i	−0.0340548	−	0.0340548i	0.689874	−	0.723929i	$-0.257666\pi$
$887$	−30.2066	−	30.2066i	−0.0340548	−	0.0340548i	−0.723929	+	0.689874i	$0.757666\pi$
$888$		0			0
$889$			1135.72i			1.27752i
$890$		0			0
$891$	102.136			0.114631
$892$		0			0
$893$	−384.817	+	384.817i	−0.430926	+	0.430926i
$894$		0			0
$895$	326.135	+	858.712i	0.364397	+	0.959454i
$896$		0			0
$897$	−157.040	−	157.040i	−0.175072	−	0.175072i
$898$		0			0
$899$		−	375.959i		−	0.418197i
$900$		0			0
$901$	24.1816			0.0268387
$902$		0			0
$903$	−223.868	+	223.868i	−0.247916	+	0.247916i
$904$		0			0
$905$	1338.10	−	508.207i	1.47857	−	0.561554i
$906$		0			0
$907$	−571.342	−	571.342i	−0.629925	−	0.629925i	0.318124	−	0.948049i	$-0.396947\pi$
$907$	−571.342	−	571.342i	−0.629925	−	0.629925i	−0.948049	+	0.318124i	$0.896947\pi$
$908$		0			0
$909$			316.863i			0.348584i
$910$		0			0
$911$	−173.362			−0.190299			−0.0951494	−	0.995463i	$-0.530333\pi$
$911$	−173.362			−0.190299			−0.0951494	+	0.995463i	$0.530333\pi$
$912$		0			0
$913$	149.192	−	149.192i	0.163408	−	0.163408i
$914$		0			0
$915$	−20.9806	+	46.6765i	−0.0229296	+	0.0510126i
$916$		0			0
$917$	366.116	+	366.116i	0.399254	+	0.399254i
$918$		0			0
$919$		−	1147.42i		−	1.24856i	−0.781202	−	0.624278i	$-0.785393\pi$
$919$		−	1147.42i		−	1.24856i	0.781202	−	0.624278i	$-0.214607\pi$
$920$		0			0
$921$	306.111			0.332368
$922$		0			0
$923$	−377.435	+	377.435i	−0.408922	+	0.408922i
$924$		0			0
$925$	−213.360	−	12.7015i	−0.230659	−	0.0137314i
$926$		0			0
$927$	−267.742	−	267.742i	−0.288827	−	0.288827i
$928$		0			0
$929$		−	220.293i		−	0.237129i	−0.992946	−	0.118565i	$-0.962171\pi$
$929$		−	220.293i		−	0.237129i	0.992946	−	0.118565i	$-0.0378292\pi$
$930$		0			0
$931$	−219.181			−0.235425
$932$		0			0
$933$	718.070	−	718.070i	0.769636	−	0.769636i
$934$		0			0
$935$	−1269.77	−	570.747i	−1.35804	−	0.610425i
$936$		0			0
$937$	−396.090	−	396.090i	−0.422721	−	0.422721i	0.463418	−	0.886140i	$-0.346623\pi$
$937$	−396.090	−	396.090i	−0.422721	−	0.422721i	−0.886140	+	0.463418i	$0.846623\pi$
$938$		0			0
$939$			250.763i			0.267053i
$940$		0			0
$941$	185.771			0.197419			0.0987093	−	0.995116i	$-0.468529\pi$
$941$	185.771			0.197419			0.0987093	+	0.995116i	$0.468529\pi$
$942$		0			0
$943$	−8.04999	+	8.04999i	−0.00853658	+	0.00853658i
$944$		0			0
$945$	−45.0000	−	118.485i	−0.0476190	−	0.125381i
$946$		0			0
$947$	845.190	+	845.190i	0.892492	+	0.892492i	0.994757	−	0.102265i	$-0.0326091\pi$
$947$	845.190	+	845.190i	0.892492	+	0.892492i	−0.102265	+	0.994757i	$0.532609\pi$
$948$		0			0
$949$			863.523i			0.909930i
$950$		0			0
$951$	−266.463			−0.280193
$952$		0			0
$953$	−630.499	+	630.499i	−0.661594	+	0.661594i	−0.955756	−	0.294161i	$-0.904960\pi$
$953$	−630.499	+	630.499i	−0.661594	+	0.661594i	0.294161	+	0.955756i	$0.404960\pi$
$954$		0			0
$955$	224.788	−	85.3735i	0.235380	−	0.0893963i
$956$		0			0
$957$	−488.499	−	488.499i	−0.510449	−	0.510449i
$958$		0			0
$959$			1149.58i			1.19873i
$960$		0			0
$961$	−846.576			−0.880932
$962$		0			0
$963$	−206.227	+	206.227i	−0.214151	+	0.214151i
$964$		0			0
$965$	740.879	−	1648.27i	0.767750	−	1.70805i
$966$		0			0
$967$	381.690	+	381.690i	0.394716	+	0.394716i	0.876364	−	0.481649i	$-0.159962\pi$
$967$	381.690	+	381.690i	0.394716	+	0.394716i	−0.481649	+	0.876364i	$0.659962\pi$
$968$		0			0
$969$			369.576i			0.381399i
$970$		0			0
$971$	1000.44			1.03032			0.515159	−	0.857095i	$-0.327733\pi$
$971$	1000.44			1.03032			0.515159	+	0.857095i	$0.327733\pi$
$972$		0			0
$973$	659.444	−	659.444i	0.677743	−	0.677743i
$974$		0			0
$975$	225.637	+	254.202i	0.231422	+	0.260720i
$976$		0			0
$977$	593.662	+	593.662i	0.607637	+	0.607637i	0.942328	−	0.334691i	$-0.108632\pi$
$977$	593.662	+	593.662i	0.607637	+	0.607637i	−0.334691	+	0.942328i	$0.608632\pi$
$978$		0			0
$979$		−	932.636i		−	0.952641i
$980$		0			0
$981$	206.091			0.210082
$982$		0			0
$983$	1217.34	−	1217.34i	1.23839	−	1.23839i	0.277731	−	0.960659i	$-0.410418\pi$
$983$	1217.34	−	1217.34i	1.23839	−	1.23839i	0.960659	−	0.277731i	$-0.0895824\pi$
$984$		0			0
$985$	623.646	+	280.322i	0.633143	+	0.284591i
$986$		0			0
$987$	373.868	+	373.868i	0.378793	+	0.378793i
$988$		0			0
$989$			612.059i			0.618867i
$990$		0			0
$991$	544.061			0.549002			0.274501	−	0.961587i	$-0.411487\pi$
$991$	544.061			0.549002			0.274501	+	0.961587i	$0.411487\pi$
$992$		0			0
$993$	300.581	−	300.581i	0.302700	−	0.302700i
$994$		0			0
$995$	341.925	+	900.286i	0.343643	+	0.904810i
$996$		0			0
$997$	−316.733	−	316.733i	−0.317686	−	0.317686i	0.530192	−	0.847878i	$-0.322120\pi$
$997$	−316.733	−	316.733i	−0.317686	−	0.317686i	−0.847878	+	0.530192i	$0.822120\pi$
$998$		0			0
$999$			44.4245i			0.0444690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.3.bg.a.97.2		4
3.2	odd	2		720.3.bh.k.577.2		4
4.3	odd	2		15.3.f.a.7.2	✓	4
5.2	odd	4		1200.3.bg.k.193.1		4
5.3	odd	4	inner	240.3.bg.a.193.2		4
5.4	even	2		1200.3.bg.k.1057.1		4
8.3	odd	2		960.3.bg.i.577.2		4
8.5	even	2		960.3.bg.h.577.1		4
12.11	even	2		45.3.g.b.37.1		4
15.8	even	4		720.3.bh.k.433.2		4
20.3	even	4		15.3.f.a.13.2	yes	4
20.7	even	4		75.3.f.c.43.1		4
20.19	odd	2		75.3.f.c.7.1		4
36.7	odd	6		405.3.l.h.352.2		8
36.11	even	6		405.3.l.f.352.1		8
36.23	even	6		405.3.l.f.217.2		8
36.31	odd	6		405.3.l.h.217.1		8
40.3	even	4		960.3.bg.i.193.2		4
40.13	odd	4		960.3.bg.h.193.1		4
60.23	odd	4		45.3.g.b.28.1		4
60.47	odd	4		225.3.g.a.118.2		4
60.59	even	2		225.3.g.a.82.2		4
180.23	odd	12		405.3.l.f.298.1		8
180.43	even	12		405.3.l.h.28.1		8
180.83	odd	12		405.3.l.f.28.2		8
180.103	even	12		405.3.l.h.298.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.f.a.7.2	✓	4	4.3	odd	2
15.3.f.a.13.2	yes	4	20.3	even	4
45.3.g.b.28.1		4	60.23	odd	4
45.3.g.b.37.1		4	12.11	even	2
75.3.f.c.7.1		4	20.19	odd	2
75.3.f.c.43.1		4	20.7	even	4
225.3.g.a.82.2		4	60.59	even	2
225.3.g.a.118.2		4	60.47	odd	4
240.3.bg.a.97.2		4	1.1	even	1	trivial
240.3.bg.a.193.2		4	5.3	odd	4	inner
405.3.l.f.28.2		8	180.83	odd	12
405.3.l.f.217.2		8	36.23	even	6
405.3.l.f.298.1		8	180.23	odd	12
405.3.l.f.352.1		8	36.11	even	6
405.3.l.h.28.1		8	180.43	even	12
405.3.l.h.217.1		8	36.31	odd	6
405.3.l.h.298.2		8	180.103	even	12
405.3.l.h.352.2		8	36.7	odd	6
720.3.bh.k.433.2		4	15.8	even	4
720.3.bh.k.577.2		4	3.2	odd	2
960.3.bg.h.193.1		4	40.13	odd	4
960.3.bg.h.577.1		4	8.5	even	2
960.3.bg.i.193.2		4	40.3	even	4
960.3.bg.i.577.2		4	8.3	odd	2
1200.3.bg.k.193.1		4	5.2	odd	4
1200.3.bg.k.1057.1		4	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	240.bg (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 1.22474i) q^{3} +(-4.67423 + 1.77526i) q^{5} +(-3.44949 - 3.44949i) q^{7} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.22474 - 1.22474i) q^{3} +(-4.67423 + 1.77526i) q^{5} +(-3.44949 - 3.44949i) q^{7} -3.00000i q^{9} -11.3485 q^{11} +(-5.55051 + 5.55051i) q^{13} +(-3.55051 + 7.89898i) q^{15} +(-17.3485 - 17.3485i) q^{17} -8.69694i q^{19} -8.44949 q^{21} +(-11.5505 + 11.5505i) q^{23} +(18.6969 - 16.5959i) q^{25} +(-3.67423 - 3.67423i) q^{27} +35.1464i q^{29} -10.6969 q^{31} +(-13.8990 + 13.8990i) q^{33} +(22.2474 + 10.0000i) q^{35} +(-6.04541 - 6.04541i) q^{37} +13.5959i q^{39} +0.696938 q^{41} +(26.4949 - 26.4949i) q^{43} +(5.32577 + 14.0227i) q^{45} +(-44.2474 - 44.2474i) q^{47} -25.2020i q^{49} -42.4949 q^{51} +(-0.696938 + 0.696938i) q^{53} +(53.0454 - 20.1464i) q^{55} +(-10.6515 - 10.6515i) q^{57} +39.9342i q^{59} +5.90918 q^{61} +(-10.3485 + 10.3485i) q^{63} +(16.0908 - 35.7980i) q^{65} +(45.1010 + 45.1010i) q^{67} +28.2929i q^{69} +68.0000 q^{71} +(77.7878 - 77.7878i) q^{73} +(2.57321 - 43.2247i) q^{75} +(39.1464 + 39.1464i) q^{77} +24.4949i q^{79} -9.00000 q^{81} +(-13.1464 + 13.1464i) q^{83} +(111.889 + 50.2929i) q^{85} +(43.0454 + 43.0454i) q^{87} +82.1816i q^{89} +38.2929 q^{91} +(-13.1010 + 13.1010i) q^{93} +(15.4393 + 40.6515i) q^{95} +(-24.5959 - 24.5959i) q^{97} +34.0454i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5} - 4 q^{7}+O(q^{10}) \) 4 * q - 4 * q^5 - 4 * q^7	\( 4 q - 4 q^{5} - 4 q^{7} - 16 q^{11} - 32 q^{13} - 24 q^{15} - 40 q^{17} - 24 q^{21} - 56 q^{23} + 16 q^{25} + 16 q^{31} - 36 q^{33} + 40 q^{35} + 64 q^{37} - 56 q^{41} + 8 q^{43} + 36 q^{45} - 128 q^{47} - 72 q^{51} + 56 q^{53} + 124 q^{55} - 72 q^{57} + 200 q^{61} - 12 q^{63} - 112 q^{65} + 200 q^{67} + 272 q^{71} + 76 q^{73} - 24 q^{75} + 88 q^{77} - 36 q^{81} + 16 q^{83} + 232 q^{85} + 84 q^{87} + 16 q^{91} - 72 q^{93} - 144 q^{95} - 20 q^{97}+O(q^{100}) \) 4 * q - 4 * q^5 - 4 * q^7 - 16 * q^11 - 32 * q^13 - 24 * q^15 - 40 * q^17 - 24 * q^21 - 56 * q^23 + 16 * q^25 + 16 * q^31 - 36 * q^33 + 40 * q^35 + 64 * q^37 - 56 * q^41 + 8 * q^43 + 36 * q^45 - 128 * q^47 - 72 * q^51 + 56 * q^53 + 124 * q^55 - 72 * q^57 + 200 * q^61 - 12 * q^63 - 112 * q^65 + 200 * q^67 + 272 * q^71 + 76 * q^73 - 24 * q^75 + 88 * q^77 - 36 * q^81 + 16 * q^83 + 232 * q^85 + 84 * q^87 + 16 * q^91 - 72 * q^93 - 144 * q^95 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more