LMFDB - Embedded newform 1360.2.bt.b.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1360,2,Mod(81,1360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1360, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1360.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1360 = 2^{4} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1360.bt (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:	$10.8596546749$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.23045668864.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 26x^{6} + 237x^{4} + 892x^{2} + 1156 $ x^8 + 26x^6 + 237x^4 + 892*x^2 + 1156
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.2
Root			$3.26843i$ of defining polynomial
Character	$\chi$	$=$	1360.81
Dual form			1360.2.bt.b.1041.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.60402 - 1.60402i) q^{3} +(0.707107 + 0.707107i) q^{5} +(-2.26843 + 2.26843i) q^{7} +2.14578i q^{9} +O(q^{10})$	\(q+(-1.60402 - 1.60402i) q^{3} +(0.707107 + 0.707107i) q^{5} +(-2.26843 + 2.26843i) q^{7} +2.14578i q^{9} +(1.82843 - 1.82843i) q^{11} -5.68265 q^{13} -2.26843i q^{15} +(0.604023 - 4.07862i) q^{17} +4.35383i q^{19} +7.27723 q^{21} +(3.41421 - 3.41421i) q^{23} +1.00000i q^{25} +(-1.37019 + 1.37019i) q^{27} +(6.01824 + 6.01824i) q^{29} +(1.16402 + 1.16402i) q^{31} -5.86568 q^{33} -3.20805 q^{35} +(3.09686 + 3.09686i) q^{37} +(9.11510 + 9.11510i) q^{39} +(5.53686 - 5.53686i) q^{41} +7.20805i q^{43} +(-1.51730 + 1.51730i) q^{45} +4.89069 q^{47} -3.29156i q^{49} +(-7.51107 + 5.57334i) q^{51} +1.14578i q^{53} +2.58579 q^{55} +(6.98364 - 6.98364i) q^{57} -8.01068i q^{59} +(-4.51863 + 4.51863i) q^{61} +(-4.86756 - 4.86756i) q^{63} +(-4.01824 - 4.01824i) q^{65} +14.0729 q^{67} -10.9530 q^{69} +(4.37207 + 4.37207i) q^{71} +(3.62981 + 3.62981i) q^{73} +(1.60402 - 1.60402i) q^{75} +8.29532i q^{77} +(1.29344 - 1.29344i) q^{79} +10.8330 q^{81} -12.1572i q^{83} +(3.31113 - 2.45691i) q^{85} -19.3068i q^{87} +16.2925 q^{89} +(12.8907 - 12.8907i) q^{91} -3.73423i q^{93} +(-3.07862 + 3.07862i) q^{95} +(-12.5312 - 12.5312i) q^{97} +(3.92341 + 3.92341i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^7	$ 8 q + 4 q^{7} - 8 q^{11} - 12 q^{13} - 8 q^{17} + 16 q^{21} + 16 q^{23} - 12 q^{27} + 24 q^{29} - 4 q^{31} + 16 q^{33} - 20 q^{37} + 4 q^{39} - 8 q^{45} - 20 q^{47} - 4 q^{51} + 32 q^{55} + 40 q^{57} - 16 q^{61} + 64 q^{63} - 8 q^{65} + 16 q^{67} + 8 q^{69} - 4 q^{71} + 28 q^{73} - 8 q^{79} - 8 q^{81} + 8 q^{85} - 44 q^{89} + 44 q^{91} - 4 q^{95} + 20 q^{97} + 4 q^{99}+O(q^{100}) $ 8 * q + 4 * q^7 - 8 * q^11 - 12 * q^13 - 8 * q^17 + 16 * q^21 + 16 * q^23 - 12 * q^27 + 24 * q^29 - 4 * q^31 + 16 * q^33 - 20 * q^37 + 4 * q^39 - 8 * q^45 - 20 * q^47 - 4 * q^51 + 32 * q^55 + 40 * q^57 - 16 * q^61 + 64 * q^63 - 8 * q^65 + 16 * q^67 + 8 * q^69 - 4 * q^71 + 28 * q^73 - 8 * q^79 - 8 * q^81 + 8 * q^85 - 44 * q^89 + 44 * q^91 - 4 * q^95 + 20 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1360\mathbb{Z}\right)^\times$.

$n$	$241$	$341$	$511$	$817$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.60402	−	1.60402i	−0.926083	−	0.926083i	0.0713668	−	0.997450i	$-0.477264\pi$
$3$	−1.60402	−	1.60402i	−0.926083	−	0.926083i	−0.997450	+	0.0713668i	$0.977264\pi$
$4$		0			0
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$		0			0
$7$	−2.26843	+	2.26843i	−0.857387	+	0.857387i	−0.991030	−	0.133643i	$-0.957332\pi$
$7$	−2.26843	+	2.26843i	−0.857387	+	0.857387i	0.133643	+	0.991030i	$0.457332\pi$
$8$		0			0
$9$			2.14578i			0.715261i
$10$		0			0
$11$	1.82843	−	1.82843i	0.551292	−	0.551292i	−0.375522	−	0.926813i	$-0.622537\pi$
$11$	1.82843	−	1.82843i	0.551292	−	0.551292i	0.926813	+	0.375522i	$0.122537\pi$
$12$		0			0
$13$	−5.68265			−1.57608			−0.788041	−	0.615623i	$-0.788905\pi$
$13$	−5.68265			−1.57608			−0.788041	+	0.615623i	$0.788905\pi$
$14$		0			0
$15$		−	2.26843i		−	0.585707i
$16$		0			0
$17$	0.604023	−	4.07862i	0.146497	−	0.989211i
$17$	0.604023	−	4.07862i	0.146497	−	0.989211i
$18$		0			0
$19$			4.35383i			0.998837i	0.866361	+	0.499418i	$0.166453\pi$
$19$			4.35383i			0.998837i	−0.866361	+	0.499418i	$0.833547\pi$
$20$		0			0
$21$	7.27723			1.58802
$22$		0			0
$23$	3.41421	−	3.41421i	0.711913	−	0.711913i	−0.255022	−	0.966935i	$-0.582083\pi$
$23$	3.41421	−	3.41421i	0.711913	−	0.711913i	0.966935	+	0.255022i	$0.0820828\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	−1.37019	+	1.37019i	−0.263692	+	0.263692i
$28$		0			0
$29$	6.01824	+	6.01824i	1.11756	+	1.11756i	0.992099	+	0.125460i	$0.0400406\pi$
$29$	6.01824	+	6.01824i	1.11756	+	1.11756i	0.125460	+	0.992099i	$0.459959\pi$
$30$		0			0
$31$	1.16402	+	1.16402i	0.209064	+	0.209064i	0.803870	−	0.594806i	$-0.202771\pi$
$31$	1.16402	+	1.16402i	0.209064	+	0.209064i	−0.594806	+	0.803870i	$0.702771\pi$
$32$		0			0
$33$	−5.86568			−1.02108
$34$		0			0
$35$	−3.20805			−0.542259
$36$		0			0
$37$	3.09686	+	3.09686i	0.509120	+	0.509120i	0.914256	−	0.405136i	$-0.132776\pi$
$37$	3.09686	+	3.09686i	0.509120	+	0.509120i	−0.405136	+	0.914256i	$0.632776\pi$
$38$		0			0
$39$	9.11510	+	9.11510i	1.45958	+	1.45958i
$40$		0			0
$41$	5.53686	−	5.53686i	0.864713	−	0.864713i	−0.127168	−	0.991881i	$-0.540589\pi$
$41$	5.53686	−	5.53686i	0.864713	−	0.864713i	0.991881	+	0.127168i	$0.0405889\pi$
$42$		0			0
$43$			7.20805i			1.09922i	0.835422	+	0.549608i	$0.185223\pi$
$43$			7.20805i			1.09922i	−0.835422	+	0.549608i	$0.814777\pi$
$44$		0			0
$45$	−1.51730	+	1.51730i	−0.226185	+	0.226185i
$46$		0			0
$47$	4.89069			0.713381			0.356690	−	0.934223i	$-0.383905\pi$
$47$	4.89069			0.713381			0.356690	+	0.934223i	$0.383905\pi$
$48$		0			0
$49$		−	3.29156i		−	0.470223i
$50$		0			0
$51$	−7.51107	+	5.57334i	−1.05176	+	0.780423i
$52$		0			0
$53$			1.14578i			0.157385i	0.996899	+	0.0786926i	$0.0250746\pi$
$53$			1.14578i			0.157385i	−0.996899	+	0.0786926i	$0.974925\pi$
$54$		0			0
$55$	2.58579			0.348667
$56$		0			0
$57$	6.98364	−	6.98364i	0.925006	−	0.925006i
$58$		0			0
$59$		−	8.01068i		−	1.04290i	−0.853281	−	0.521451i	$-0.825391\pi$
$59$		−	8.01068i		−	1.04290i	0.853281	−	0.521451i	$-0.174609\pi$
$60$		0			0
$61$	−4.51863	+	4.51863i	−0.578551	+	0.578551i	−0.934504	−	0.355953i	$-0.884156\pi$
$61$	−4.51863	+	4.51863i	−0.578551	+	0.578551i	0.355953	+	0.934504i	$0.384156\pi$
$62$		0			0
$63$	−4.86756	−	4.86756i	−0.613255	−	0.613255i
$64$		0			0
$65$	−4.01824	−	4.01824i	−0.498401	−	0.498401i
$66$		0			0
$67$	14.0729			1.71928			0.859642	−	0.510897i	$-0.170687\pi$
$67$	14.0729			1.71928			0.859642	+	0.510897i	$0.170687\pi$
$68$		0			0
$69$	−10.9530			−1.31858
$70$		0			0
$71$	4.37207	+	4.37207i	0.518869	+	0.518869i	0.917229	−	0.398360i	$-0.130421\pi$
$71$	4.37207	+	4.37207i	0.518869	+	0.518869i	−0.398360	+	0.917229i	$0.630421\pi$
$72$		0			0
$73$	3.62981	+	3.62981i	0.424838	+	0.424838i	0.886865	−	0.462028i	$-0.152878\pi$
$73$	3.62981	+	3.62981i	0.424838	+	0.424838i	−0.462028	+	0.886865i	$0.652878\pi$
$74$		0			0
$75$	1.60402	−	1.60402i	0.185217	−	0.185217i
$76$		0			0
$77$			8.29532i			0.945340i
$78$		0			0
$79$	1.29344	−	1.29344i	0.145524	−	0.145524i	−0.630591	−	0.776115i	$-0.717188\pi$
$79$	1.29344	−	1.29344i	0.145524	−	0.145524i	0.776115	+	0.630591i	$0.217188\pi$
$80$		0			0
$81$	10.8330			1.20366
$82$		0			0
$83$		−	12.1572i		−	1.33443i	−0.744865	−	0.667215i	$-0.767486\pi$
$83$		−	12.1572i		−	1.33443i	0.744865	−	0.667215i	$-0.232514\pi$
$84$		0			0
$85$	3.31113	−	2.45691i	0.359142	−	0.266490i
$86$		0			0
$87$		−	19.3068i		−	2.06990i
$88$		0			0
$89$	16.2925			1.72700			0.863498	−	0.504351i	$-0.168268\pi$
$89$	16.2925			1.72700			0.863498	+	0.504351i	$0.168268\pi$
$90$		0			0
$91$	12.8907	−	12.8907i	1.35131	−	1.35131i
$92$		0			0
$93$		−	3.73423i		−	0.387221i
$94$		0			0
$95$	−3.07862	+	3.07862i	−0.315860	+	0.315860i
$96$		0			0
$97$	−12.5312	−	12.5312i	−1.27235	−	1.27235i	−0.944852	−	0.327497i	$-0.893795\pi$
$97$	−12.5312	−	12.5312i	−1.27235	−	1.27235i	−0.327497	−	0.944852i	$-0.606205\pi$
$98$		0			0
$99$	3.92341	+	3.92341i	0.394317	+	0.394317i
$100$		0			0
$101$	7.65685			0.761885			0.380943	−	0.924599i	$-0.375599\pi$
$101$	7.65685			0.761885			0.380943	+	0.924599i	$0.375599\pi$
$102$		0			0
$103$	7.58767			0.747635			0.373817	−	0.927502i	$-0.378049\pi$
$103$	7.58767			0.747635			0.373817	+	0.927502i	$0.378049\pi$
$104$		0			0
$105$	5.14578	+	5.14578i	0.502177	+	0.502177i
$106$		0			0
$107$	3.85422	+	3.85422i	0.372601	+	0.372601i	0.868424	−	0.495823i	$-0.165133\pi$
$107$	3.85422	+	3.85422i	0.372601	+	0.372601i	−0.495823	+	0.868424i	$0.665133\pi$
$108$		0			0
$109$	−6.01824	+	6.01824i	−0.576443	+	0.576443i	−0.933921	−	0.357479i	$-0.883636\pi$
$109$	−6.01824	+	6.01824i	−0.576443	+	0.576443i	0.357479	+	0.933921i	$0.383636\pi$
$110$		0			0
$111$		−	9.93487i		−	0.942976i
$112$		0			0
$113$	−5.57823	+	5.57823i	−0.524756	+	0.524756i	−0.919004	−	0.394248i	$-0.871005\pi$
$113$	−5.57823	+	5.57823i	−0.524756	+	0.524756i	0.394248	+	0.919004i	$0.371005\pi$
$114$		0			0
$115$	4.82843			0.450253
$116$		0			0
$117$		−	12.1937i		−	1.12731i
$118$		0			0
$119$	7.88189	+	10.6223i	0.722532	+	0.973741i
$120$		0			0
$121$			4.31371i			0.392155i
$122$		0			0
$123$	−17.7625			−1.60159
$124$		0			0
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$			6.76992i			0.600733i	0.953824	+	0.300367i	$0.0971091\pi$
$127$			6.76992i			0.600733i	−0.953824	+	0.300367i	$0.902891\pi$
$128$		0			0
$129$	11.5619	−	11.5619i	1.01797	−	1.01797i
$130$		0			0
$131$	−7.32804	−	7.32804i	−0.640254	−	0.640254i	0.310364	−	0.950618i	$-0.399549\pi$
$131$	−7.32804	−	7.32804i	−0.640254	−	0.640254i	−0.950618	+	0.310364i	$0.899549\pi$
$132$		0			0
$133$	−9.87636	−	9.87636i	−0.856389	−	0.856389i
$134$		0			0
$135$	−1.93774			−0.166774
$136$		0			0
$137$	−1.74115			−0.148756			−0.0743782	−	0.997230i	$-0.523697\pi$
$137$	−1.74115			−0.148756			−0.0743782	+	0.997230i	$0.523697\pi$
$138$		0			0
$139$	−0.587666	−	0.587666i	−0.0498452	−	0.0498452i	0.681745	−	0.731590i	$-0.261221\pi$
$139$	−0.587666	−	0.587666i	−0.0498452	−	0.0498452i	−0.731590	+	0.681745i	$0.761221\pi$
$140$		0			0
$141$	−7.84478	−	7.84478i	−0.660650	−	0.660650i
$142$		0			0
$143$	−10.3903	+	10.3903i	−0.868881	+	0.868881i
$144$		0			0
$145$			8.51107i			0.706806i
$146$		0			0
$147$	−5.27975	+	5.27975i	−0.435466	+	0.435466i
$148$		0			0
$149$	−2.44881			−0.200614			−0.100307	−	0.994957i	$-0.531983\pi$
$149$	−2.44881			−0.200614			−0.100307	+	0.994957i	$0.531983\pi$
$150$		0			0
$151$		−	4.53686i		−	0.369205i	−0.982813	−	0.184602i	$-0.940900\pi$
$151$		−	4.53686i		−	0.369205i	0.982813	−	0.184602i	$-0.0590997\pi$
$152$		0			0
$153$	8.75183	+	1.29610i	0.707544	+	0.104784i
$154$		0			0
$155$			1.64617i			0.132224i
$156$		0			0
$157$	23.5074			1.87610			0.938048	−	0.346504i	$-0.112631\pi$
$157$	23.5074			1.87610			0.938048	+	0.346504i	$0.112631\pi$
$158$		0			0
$159$	1.83786	−	1.83786i	0.145752	−	0.145752i
$160$		0			0
$161$			15.4898i			1.22077i
$162$		0			0
$163$	−16.0479	+	16.0479i	−1.25697	+	1.25697i	−0.304440	+	0.952532i	$0.598469\pi$
$163$	−16.0479	+	16.0479i	−1.25697	+	1.25697i	−0.952532	+	0.304440i	$0.901531\pi$
$164$		0			0
$165$	−4.14766	−	4.14766i	−0.322895	−	0.322895i
$166$		0			0
$167$	14.4364	+	14.4364i	1.11712	+	1.11712i	0.992162	+	0.124957i	$0.0398792\pi$
$167$	14.4364	+	14.4364i	1.11712	+	1.11712i	0.124957	+	0.992162i	$0.460121\pi$
$168$		0			0
$169$	19.2925			1.48404
$170$		0			0
$171$	−9.34237			−0.714429
$172$		0			0
$173$	−6.65873	−	6.65873i	−0.506254	−	0.506254i	0.407120	−	0.913375i	$-0.366533\pi$
$173$	−6.65873	−	6.65873i	−0.506254	−	0.506254i	−0.913375	+	0.407120i	$0.866533\pi$
$174$		0			0
$175$	−2.26843	−	2.26843i	−0.171477	−	0.171477i
$176$		0			0
$177$	−12.8493	+	12.8493i	−0.965814	+	0.965814i
$178$		0			0
$179$		−	6.65763i		−	0.497615i	−0.968553	−	0.248807i	$-0.919961\pi$
$179$		−	6.65763i		−	0.497615i	0.968553	−	0.248807i	$-0.0800386\pi$
$180$		0			0
$181$	0.0853971	−	0.0853971i	0.00634752	−	0.00634752i	−0.703926	−	0.710273i	$-0.748571\pi$
$181$	0.0853971	−	0.0853971i	0.00634752	−	0.00634752i	0.710273	+	0.703926i	$0.248571\pi$
$182$		0			0
$183$	14.4960			1.07157
$184$		0			0
$185$			4.37962i			0.321996i
$186$		0			0
$187$	−6.35305	−	8.56188i	−0.464581	−	0.626106i
$188$		0			0
$189$		−	6.21635i		−	0.452173i
$190$		0			0
$191$	9.52253			0.689026			0.344513	−	0.938781i	$-0.388044\pi$
$191$	9.52253			0.689026			0.344513	+	0.938781i	$0.388044\pi$
$192$		0			0
$193$	11.6318	−	11.6318i	0.837278	−	0.837278i	−0.151222	−	0.988500i	$-0.548321\pi$
$193$	11.6318	−	11.6318i	0.837278	−	0.837278i	0.988500	+	0.151222i	$0.0483207\pi$
$194$		0			0
$195$			12.8907i			0.923122i
$196$		0			0
$197$	−16.3414	+	16.3414i	−1.16428	+	1.16428i	−0.180745	+	0.983530i	$0.557851\pi$
$197$	−16.3414	+	16.3414i	−1.16428	+	1.16428i	−0.983530	+	0.180745i	$0.942149\pi$
$198$		0			0
$199$	6.99322	+	6.99322i	0.495737	+	0.495737i	0.910108	−	0.414371i	$-0.135999\pi$
$199$	6.99322	+	6.99322i	0.495737	+	0.495737i	−0.414371	+	0.910108i	$0.635999\pi$
$200$		0			0
$201$	−22.5733	−	22.5733i	−1.59220	−	1.59220i
$202$		0			0
$203$	−27.3039			−1.91636
$204$		0			0
$205$	7.83031			0.546892
$206$		0			0
$207$	7.32616	+	7.32616i	0.509203	+	0.509203i
$208$		0			0
$209$	7.96066	+	7.96066i	0.550650	+	0.550650i
$210$		0			0
$211$	−11.8907	+	11.8907i	−0.818589	+	0.818589i	−0.985904	−	0.167315i	$-0.946490\pi$
$211$	−11.8907	+	11.8907i	−0.818589	+	0.818589i	0.167315	+	0.985904i	$0.446490\pi$
$212$		0			0
$213$		−	14.0258i		−	0.961031i
$214$		0			0
$215$	−5.09686	+	5.09686i	−0.347603	+	0.347603i
$216$		0			0
$217$	−5.28099			−0.358497
$218$		0			0
$219$		−	11.6446i		−	0.786870i
$220$		0			0
$221$	−3.43245	+	23.1774i	−0.230892	+	1.55908i
$222$		0			0
$223$		−	9.25144i		−	0.619522i	−0.950814	−	0.309761i	$-0.899751\pi$
$223$		−	9.25144i		−	0.619522i	0.950814	−	0.309761i	$-0.100249\pi$
$224$		0			0
$225$	−2.14578			−0.143052
$226$		0			0
$227$	−14.5205	+	14.5205i	−0.963760	+	0.963760i	−0.999366	−	0.0356061i	$-0.988664\pi$
$227$	−14.5205	+	14.5205i	−0.963760	+	0.963760i	0.0356061	+	0.999366i	$0.488664\pi$
$228$		0			0
$229$			15.1618i			1.00192i	0.865471	+	0.500959i	$0.167019\pi$
$229$			15.1618i			1.00192i	−0.865471	+	0.500959i	$0.832981\pi$
$230$		0			0
$231$	13.3059	−	13.3059i	0.875463	−	0.875463i
$232$		0			0
$233$	−6.28745	−	6.28745i	−0.411904	−	0.411904i	0.470497	−	0.882402i	$-0.344075\pi$
$233$	−6.28745	−	6.28745i	−0.411904	−	0.411904i	−0.882402	+	0.470497i	$0.844075\pi$
$234$		0			0
$235$	3.45824	+	3.45824i	0.225591	+	0.225591i
$236$		0			0
$237$	−4.14943			−0.269534
$238$		0			0
$239$	0.0827385			0.00535191			0.00267595	−	0.999996i	$-0.499148\pi$
$239$	0.0827385			0.00535191			0.00267595	+	0.999996i	$0.499148\pi$
$240$		0			0
$241$	−0.829206	−	0.829206i	−0.0534138	−	0.0534138i	0.679895	−	0.733309i	$-0.262025\pi$
$241$	−0.829206	−	0.829206i	−0.0534138	−	0.0534138i	−0.733309	+	0.679895i	$0.762025\pi$
$242$		0			0
$243$	−13.2658	−	13.2658i	−0.851000	−	0.851000i
$244$		0			0
$245$	2.32749	−	2.32749i	0.148698	−	0.148698i
$246$		0			0
$247$		−	24.7413i		−	1.57425i
$248$		0			0
$249$	−19.5005	+	19.5005i	−1.23579	+	1.23579i
$250$		0			0
$251$	18.1245			1.14401			0.572005	−	0.820250i	$-0.306166\pi$
$251$	18.1245			1.14401			0.572005	+	0.820250i	$0.306166\pi$
$252$		0			0
$253$		−	12.4853i		−	0.784943i
$254$		0			0
$255$	−9.25207	−	1.37019i	−0.579387	−	0.0858044i
$256$		0			0
$257$			25.3539i			1.58154i	0.612116	+	0.790768i	$0.290318\pi$
$257$			25.3539i			1.58154i	−0.612116	+	0.790768i	$0.709682\pi$
$258$		0			0
$259$	−14.0500			−0.873026
$260$		0			0
$261$	−12.9138	+	12.9138i	−0.799346	+	0.799346i
$262$		0			0
$263$		−	2.11385i		−	0.130345i	−0.997874	−	0.0651727i	$-0.979240\pi$
$263$		−	2.11385i		−	0.130345i	0.997874	−	0.0651727i	$-0.0207598\pi$
$264$		0			0
$265$	−0.810190	+	0.810190i	−0.0497696	+	0.0497696i
$266$		0			0
$267$	−26.1335	−	26.1335i	−1.59934	−	1.59934i
$268$		0			0
$269$	15.1898	+	15.1898i	0.926139	+	0.926139i	0.997454	−	0.0713148i	$-0.0227195\pi$
$269$	15.1898	+	15.1898i	0.926139	+	0.926139i	−0.0713148	+	0.997454i	$0.522719\pi$
$270$		0			0
$271$	−22.5922			−1.37238			−0.686189	−	0.727423i	$-0.740718\pi$
$271$	−22.5922			−1.37238			−0.686189	+	0.727423i	$0.740718\pi$
$272$		0			0
$273$	−41.3539			−2.50285
$274$		0			0
$275$	1.82843	+	1.82843i	0.110258	+	0.110258i
$276$		0			0
$277$	18.0756	+	18.0756i	1.08606	+	1.08606i	0.995930	+	0.0901277i	$0.0287275\pi$
$277$	18.0756	+	18.0756i	1.08606	+	1.08606i	0.0901277	+	0.995930i	$0.471272\pi$
$278$		0			0
$279$	−2.49773	+	2.49773i	−0.149535	+	0.149535i
$280$		0			0
$281$		−	15.8248i		−	0.944027i	−0.881591	−	0.472014i	$-0.843527\pi$
$281$		−	15.8248i		−	0.944027i	0.881591	−	0.472014i	$-0.156473\pi$
$282$		0			0
$283$	12.4325	−	12.4325i	0.739032	−	0.739032i	−0.233358	−	0.972391i	$-0.574972\pi$
$283$	12.4325	−	12.4325i	0.739032	−	0.739032i	0.972391	+	0.233358i	$0.0749715\pi$
$284$		0			0
$285$	9.87636			0.585025
$286$		0			0
$287$			25.1200i			1.48279i
$288$		0			0
$289$	−16.2703	−	4.92717i	−0.957077	−	0.289833i
$290$		0			0
$291$			40.2006i			2.35660i
$292$		0			0
$293$	−29.6524			−1.73231			−0.866157	−	0.499773i	$-0.833417\pi$
$293$	−29.6524			−1.73231			−0.866157	+	0.499773i	$0.833417\pi$
$294$		0			0
$295$	5.66441	−	5.66441i	0.329795	−	0.329795i
$296$		0			0
$297$			5.01057i			0.290743i
$298$		0			0
$299$	−19.4018	+	19.4018i	−1.12203	+	1.12203i
$300$		0			0
$301$	−16.3510	−	16.3510i	−0.942454	−	0.942454i
$302$		0			0
$303$	−12.2818	−	12.2818i	−0.705569	−	0.705569i
$304$		0			0
$305$	−6.39030			−0.365908
$306$		0			0
$307$	−32.0116			−1.82700			−0.913499	−	0.406842i	$-0.866630\pi$
$307$	−32.0116			−1.82700			−0.913499	+	0.406842i	$0.866630\pi$
$308$		0			0
$309$	−12.1708	−	12.1708i	−0.692372	−	0.692372i
$310$		0			0
$311$	−8.72792	−	8.72792i	−0.494915	−	0.494915i	0.414936	−	0.909851i	$-0.363804\pi$
$311$	−8.72792	−	8.72792i	−0.494915	−	0.494915i	−0.909851	+	0.414936i	$0.863804\pi$
$312$		0			0
$313$	1.39030	−	1.39030i	0.0785845	−	0.0785845i	−0.666722	−	0.745307i	$-0.732303\pi$
$313$	1.39030	−	1.39030i	0.0785845	−	0.0785845i	0.745307	+	0.666722i	$0.232303\pi$
$314$		0			0
$315$		−	6.88377i		−	0.387856i
$316$		0			0
$317$	8.08540	−	8.08540i	0.454121	−	0.454121i	−0.442599	−	0.896720i	$-0.645943\pi$
$317$	8.08540	−	8.08540i	0.454121	−	0.454121i	0.896720	+	0.442599i	$0.145943\pi$
$318$		0			0
$319$	22.0078			1.23220
$320$		0			0
$321$		−	12.3645i		−	0.690120i
$322$		0			0
$323$	17.7576	+	2.62981i	0.988060	+	0.146327i
$324$		0			0
$325$		−	5.68265i		−	0.315216i
$326$		0			0
$327$	19.3068			1.06767
$328$		0			0
$329$	−11.0942	+	11.0942i	−0.611643	+	0.611643i
$330$		0			0
$331$			18.4784i			1.01566i	0.861457	+	0.507831i	$0.169553\pi$
$331$			18.4784i			1.01566i	−0.861457	+	0.507831i	$0.830447\pi$
$332$		0			0
$333$	−6.64518	+	6.64518i	−0.364154	+	0.364154i
$334$		0			0
$335$	9.95108	+	9.95108i	0.543685	+	0.543685i
$336$		0			0
$337$	−1.83708	−	1.83708i	−0.100072	−	0.100072i	0.655298	−	0.755370i	$-0.272543\pi$
$337$	−1.83708	−	1.83708i	−0.100072	−	0.100072i	−0.755370	+	0.655298i	$0.772543\pi$
$338$		0			0
$339$	17.8952			0.971936
$340$		0			0
$341$	4.25665			0.230510
$342$		0			0
$343$	−8.41233	−	8.41233i	−0.454223	−	0.454223i
$344$		0			0
$345$	−7.74491	−	7.74491i	−0.416972	−	0.416972i
$346$		0			0
$347$	9.15522	−	9.15522i	0.491478	−	0.491478i	−0.417294	−	0.908772i	$-0.637021\pi$
$347$	9.15522	−	9.15522i	0.491478	−	0.491478i	0.908772	+	0.417294i	$0.137021\pi$
$348$		0			0
$349$		−	20.3698i		−	1.09037i	−0.838315	−	0.545186i	$-0.816459\pi$
$349$		−	20.3698i		−	1.09037i	0.838315	−	0.545186i	$-0.183541\pi$
$350$		0			0
$351$	7.78628	−	7.78628i	0.415601	−	0.415601i
$352$		0			0
$353$	33.1680			1.76536			0.882678	−	0.469978i	$-0.155738\pi$
$353$	33.1680			1.76536			0.882678	+	0.469978i	$0.155738\pi$
$354$		0			0
$355$			6.18303i			0.328161i
$356$		0			0
$357$	4.39562	−	29.6811i	0.232641	−	1.57089i
$358$		0			0
$359$		−	17.2272i		−	0.909217i	−0.890691	−	0.454609i	$-0.849779\pi$
$359$		−	17.2272i		−	0.909217i	0.890691	−	0.454609i	$-0.150221\pi$
$360$		0			0
$361$	0.0441757			0.00232503
$362$		0			0
$363$	6.91929	−	6.91929i	0.363169	−	0.363169i
$364$		0			0
$365$			5.13333i			0.268691i
$366$		0			0
$367$	−16.4879	+	16.4879i	−0.860663	+	0.860663i	−0.991415	−	0.130752i	$-0.958261\pi$
$367$	−16.4879	+	16.4879i	−0.860663	+	0.860663i	0.130752	+	0.991415i	$0.458261\pi$
$368$		0			0
$369$	11.8809	+	11.8809i	0.618495	+	0.618495i
$370$		0			0
$371$	−2.59913	−	2.59913i	−0.134940	−	0.134940i
$372$		0			0
$373$	10.6098			0.549355			0.274678	−	0.961536i	$-0.411429\pi$
$373$	10.6098			0.549355			0.274678	+	0.961536i	$0.411429\pi$
$374$		0			0
$375$	2.26843			0.117141
$376$		0			0
$377$	−34.1995	−	34.1995i	−1.76136	−	1.76136i
$378$		0			0
$379$	19.6872	+	19.6872i	1.01126	+	1.01126i	0.999936	+	0.0113269i	$0.00360553\pi$
$379$	19.6872	+	19.6872i	1.01126	+	1.01126i	0.0113269	+	0.999936i	$0.496394\pi$
$380$		0			0
$381$	10.8591	−	10.8591i	0.556329	−	0.556329i
$382$		0			0
$383$			0.426776i			0.0218073i	0.999941	+	0.0109036i	$0.00347080\pi$
$383$			0.426776i			0.0218073i	−0.999941	+	0.0109036i	$0.996529\pi$
$384$		0			0
$385$	−5.86568	+	5.86568i	−0.298943	+	0.298943i
$386$		0			0
$387$	−15.4669			−0.786227
$388$		0			0
$389$			0.807061i			0.0409196i	0.999791	+	0.0204598i	$0.00651302\pi$
$389$			0.807061i			0.0409196i	−0.999791	+	0.0204598i	$0.993487\pi$
$390$		0			0
$391$	−11.8630	−	15.9876i	−0.599939	−	0.808525i
$392$		0			0
$393$			23.5087i			1.18586i
$394$		0			0
$395$	1.82921			0.0920373
$396$		0			0
$397$	18.9138	−	18.9138i	0.949258	−	0.949258i	−0.0495157	−	0.998773i	$-0.515768\pi$
$397$	18.9138	−	18.9138i	0.949258	−	0.949258i	0.998773	+	0.0495157i	$0.0157678\pi$
$398$		0			0
$399$			31.6838i			1.58618i
$400$		0			0
$401$	−10.9226	+	10.9226i	−0.545450	+	0.545450i	−0.925121	−	0.379671i	$-0.876037\pi$
$401$	−10.9226	+	10.9226i	−0.545450	+	0.545450i	0.379671	+	0.925121i	$0.376037\pi$
$402$		0			0
$403$	−6.61471	−	6.61471i	−0.329502	−	0.329502i
$404$		0			0
$405$	7.66006	+	7.66006i	0.380632	+	0.380632i
$406$		0			0
$407$	11.3248			0.561348
$408$		0			0
$409$	9.19581			0.454703			0.227352	−	0.973813i	$-0.426993\pi$
$409$	9.19581			0.454703			0.227352	+	0.973813i	$0.426993\pi$
$410$		0			0
$411$	2.79285	+	2.79285i	0.137761	+	0.137761i
$412$		0			0
$413$	18.1717	+	18.1717i	0.894170	+	0.894170i
$414$		0			0
$415$	8.59647	−	8.59647i	0.421984	−	0.421984i
$416$		0			0
$417$			1.88526i			0.0923216i
$418$		0			0
$419$	−6.93774	+	6.93774i	−0.338931	+	0.338931i	−0.855965	−	0.517034i	$-0.827036\pi$
$419$	−6.93774	+	6.93774i	−0.338931	+	0.338931i	0.517034	+	0.855965i	$0.327036\pi$
$420$		0			0
$421$	−17.0410			−0.830528			−0.415264	−	0.909701i	$-0.636311\pi$
$421$	−17.0410			−0.830528			−0.415264	+	0.909701i	$0.636311\pi$
$422$		0			0
$423$			10.4944i			0.510253i
$424$		0			0
$425$	4.07862	+	0.604023i	0.197842	+	0.0292994i
$426$		0			0
$427$		−	20.5004i		−	0.992083i
$428$		0			0
$429$	33.3326			1.60931
$430$		0			0
$431$	−13.8152	+	13.8152i	−0.665455	+	0.665455i	−0.956660	−	0.291206i	$-0.905944\pi$
$431$	−13.8152	+	13.8152i	−0.665455	+	0.665455i	0.291206	+	0.956660i	$0.405944\pi$
$432$		0			0
$433$		−	16.7404i		−	0.804491i	−0.915532	−	0.402245i	$-0.868230\pi$
$433$		−	16.7404i		−	0.804491i	0.915532	−	0.402245i	$-0.131770\pi$
$434$		0			0
$435$	13.6520	−	13.6520i	0.654561	−	0.654561i
$436$		0			0
$437$	14.8649	+	14.8649i	0.711085	+	0.711085i
$438$		0			0
$439$	−7.98755	−	7.98755i	−0.381225	−	0.381225i	0.490318	−	0.871543i	$-0.336880\pi$
$439$	−7.98755	−	7.98755i	−0.381225	−	0.381225i	−0.871543	+	0.490318i	$0.836880\pi$
$440$		0			0
$441$	7.06298			0.336332
$442$		0			0
$443$	19.7084			0.936376			0.468188	−	0.883629i	$-0.344907\pi$
$443$	19.7084			0.936376			0.468188	+	0.883629i	$0.344907\pi$
$444$		0			0
$445$	11.5205	+	11.5205i	0.546124	+	0.546124i
$446$		0			0
$447$	3.92794	+	3.92794i	0.185785	+	0.185785i
$448$		0			0
$449$	−6.43042	+	6.43042i	−0.303470	+	0.303470i	−0.842370	−	0.538900i	$-0.818840\pi$
$449$	−6.43042	+	6.43042i	−0.303470	+	0.303470i	0.538900	+	0.842370i	$0.318840\pi$
$450$		0			0
$451$		−	20.2475i		−	0.953418i
$452$		0			0
$453$	−7.27723	+	7.27723i	−0.341914	+	0.341914i
$454$		0			0
$455$	18.2302			0.854645
$456$		0			0
$457$			7.73959i			0.362043i	0.983479	+	0.181021i	$0.0579403\pi$
$457$			7.73959i			0.362043i	−0.983479	+	0.181021i	$0.942060\pi$
$458$		0			0
$459$	4.76085	+	6.41609i	0.222217	+	0.299478i
$460$		0			0
$461$		−	25.0045i		−	1.16458i	−0.812982	−	0.582289i	$-0.802157\pi$
$461$		−	25.0045i		−	1.16458i	0.812982	−	0.582289i	$-0.197843\pi$
$462$		0			0
$463$	29.7745			1.38374			0.691868	−	0.722024i	$-0.256788\pi$
$463$	29.7745			1.38374			0.691868	+	0.722024i	$0.256788\pi$
$464$		0			0
$465$	2.64050	−	2.64050i	0.122450	−	0.122450i
$466$		0			0
$467$		−	12.3104i		−	0.569659i	−0.958578	−	0.284829i	$-0.908063\pi$
$467$		−	12.3104i		−	0.569659i	0.958578	−	0.284829i	$-0.0919370\pi$
$468$		0			0
$469$	−31.9235	+	31.9235i	−1.47409	+	1.47409i
$470$		0			0
$471$	−37.7065	−	37.7065i	−1.73742	−	1.73742i
$472$		0			0
$473$	13.1794	+	13.1794i	0.605989	+	0.605989i
$474$		0			0
$475$	−4.35383			−0.199767
$476$		0			0
$477$	−2.45860			−0.112571
$478$		0			0
$479$	4.61361	+	4.61361i	0.210801	+	0.210801i	0.804608	−	0.593807i	$-0.202376\pi$
$479$	4.61361	+	4.61361i	0.210801	+	0.210801i	−0.593807	+	0.804608i	$0.702376\pi$
$480$		0			0
$481$	−17.5983	−	17.5983i	−0.802416	−	0.802416i
$482$		0			0
$483$	24.8460	−	24.8460i	1.13053	−	1.13053i
$484$		0			0
$485$		−	17.7218i		−	0.804704i
$486$		0			0
$487$	9.85234	−	9.85234i	0.446452	−	0.446452i	−0.447721	−	0.894173i	$-0.647764\pi$
$487$	9.85234	−	9.85234i	0.446452	−	0.446452i	0.894173	+	0.447721i	$0.147764\pi$
$488$		0			0
$489$	51.4825			2.32812
$490$		0			0
$491$		−	0.302247i		−	0.0136402i	−0.999977	−	0.00682010i	$-0.997829\pi$
$491$		−	0.302247i		−	0.0136402i	0.999977	−	0.00682010i	$-0.00217092\pi$
$492$		0			0
$493$	28.1813	−	20.9110i	1.26922	−	0.941782i
$494$		0			0
$495$			5.54853i			0.249388i
$496$		0			0
$497$	−19.8355			−0.889742
$498$		0			0
$499$	−11.6941	+	11.6941i	−0.523500	+	0.523500i	−0.918627	−	0.395127i	$-0.870701\pi$
$499$	−11.6941	+	11.6941i	−0.523500	+	0.523500i	0.395127	+	0.918627i	$0.370701\pi$
$500$		0			0
$501$		−	46.3125i		−	2.06909i
$502$		0			0
$503$	0.399884	−	0.399884i	0.0178300	−	0.0178300i	−0.698136	−	0.715966i	$-0.745987\pi$
$503$	0.399884	−	0.399884i	0.0178300	−	0.0178300i	0.715966	+	0.698136i	$0.245987\pi$
$504$		0			0
$505$	5.41421	+	5.41421i	0.240929	+	0.240929i
$506$		0			0
$507$	−30.9456	−	30.9456i	−1.37434	−	1.37434i
$508$		0			0
$509$	9.94842			0.440956			0.220478	−	0.975392i	$-0.429238\pi$
$509$	9.94842			0.440956			0.220478	+	0.975392i	$0.429238\pi$
$510$		0			0
$511$	−16.4680			−0.728500
$512$		0			0
$513$	−5.96555	−	5.96555i	−0.263386	−	0.263386i
$514$		0			0
$515$	5.36529	+	5.36529i	0.236423	+	0.236423i
$516$		0			0
$517$	8.94227	−	8.94227i	0.393281	−	0.393281i
$518$		0			0
$519$			21.3615i			0.937667i
$520$		0			0
$521$	−8.68265	+	8.68265i	−0.380394	+	0.380394i	−0.871244	−	0.490850i	$-0.836686\pi$
$521$	−8.68265	+	8.68265i	−0.380394	+	0.380394i	0.490850	+	0.871244i	$0.336686\pi$
$522$		0			0
$523$	−13.1024			−0.572927			−0.286464	−	0.958091i	$-0.592480\pi$
$523$	−13.1024			−0.572927			−0.286464	+	0.958091i	$0.592480\pi$
$524$		0			0
$525$			7.27723i			0.317605i
$526$		0			0
$527$	5.45069	−	4.04450i	0.237436	−	0.176181i
$528$		0			0
$529$		−	0.313708i		−	0.0136395i
$530$		0			0
$531$	17.1892			0.745947
$532$		0			0
$533$	−31.4640	+	31.4640i	−1.36286	+	1.36286i
$534$		0			0
$535$			5.45069i			0.235654i
$536$		0			0
$537$	−10.6790	+	10.6790i	−0.460833	+	0.460833i
$538$		0			0
$539$	−6.01838	−	6.01838i	−0.259230	−	0.259230i
$540$		0			0
$541$	7.74601	+	7.74601i	0.333027	+	0.333027i	0.853735	−	0.520708i	$-0.174332\pi$
$541$	7.74601	+	7.74601i	0.333027	+	0.333027i	−0.520708	+	0.853735i	$0.674332\pi$
$542$		0			0
$543$	−0.273958			−0.0117567
$544$		0			0
$545$	−8.51107			−0.364574
$546$		0			0
$547$	−10.2981	−	10.2981i	−0.440316	−	0.440316i	0.451802	−	0.892118i	$-0.350781\pi$
$547$	−10.2981	−	10.2981i	−0.440316	−	0.440316i	−0.892118	+	0.451802i	$0.850781\pi$
$548$		0			0
$549$	−9.69599	−	9.69599i	−0.413815	−	0.413815i
$550$		0			0
$551$	−26.2024	+	26.2024i	−1.11626	+	1.11626i
$552$		0			0
$553$			5.86818i			0.249540i
$554$		0			0
$555$	7.02501	−	7.02501i	0.298195	−	0.298195i
$556$		0			0
$557$	−5.85876			−0.248243			−0.124122	−	0.992267i	$-0.539611\pi$
$557$	−5.85876			−0.248243			−0.124122	+	0.992267i	$0.539611\pi$
$558$		0			0
$559$		−	40.9608i		−	1.73246i
$560$		0			0
$561$	−3.54301	+	23.9239i	−0.149586	+	1.01007i
$562$		0			0
$563$		−	15.8330i		−	0.667280i	−0.942701	−	0.333640i	$-0.891723\pi$
$563$		−	15.8330i		−	0.667280i	0.942701	−	0.333640i	$-0.108277\pi$
$564$		0			0
$565$	−7.88881			−0.331885
$566$		0			0
$567$	−24.5738	+	24.5738i	−1.03200	+	1.03200i
$568$		0			0
$569$		−	15.0288i		−	0.630039i	−0.949085	−	0.315019i	$-0.897989\pi$
$569$		−	15.0288i		−	0.630039i	0.949085	−	0.315019i	$-0.102011\pi$
$570$		0			0
$571$	−4.81410	+	4.81410i	−0.201464	+	0.201464i	−0.800627	−	0.599163i	$-0.795500\pi$
$571$	−4.81410	+	4.81410i	−0.201464	+	0.201464i	0.599163	+	0.800627i	$0.295500\pi$
$572$		0			0
$573$	−15.2744	−	15.2744i	−0.638096	−	0.638096i
$574$		0			0
$575$	3.41421	+	3.41421i	0.142383	+	0.142383i
$576$		0			0
$577$	−22.6806			−0.944204			−0.472102	−	0.881544i	$-0.656505\pi$
$577$	−22.6806			−0.944204			−0.472102	+	0.881544i	$0.656505\pi$
$578$		0			0
$579$	−37.3155			−1.55078
$580$		0			0
$581$	27.5779	+	27.5779i	1.14412	+	1.14412i
$582$		0			0
$583$	2.09498	+	2.09498i	0.0867652	+	0.0867652i
$584$		0			0
$585$	8.62226	−	8.62226i	0.356487	−	0.356487i
$586$		0			0
$587$			40.9919i			1.69192i	0.533248	+	0.845959i	$0.320971\pi$
$587$			40.9919i			1.69192i	−0.533248	+	0.845959i	$0.679029\pi$
$588$		0			0
$589$	−5.06794	+	5.06794i	−0.208821	+	0.208821i
$590$		0			0
$591$	52.4239			2.15643
$592$		0			0
$593$		−	12.4390i		−	0.510809i	−0.966834	−	0.255405i	$-0.917791\pi$
$593$		−	12.4390i		−	0.510809i	0.966834	−	0.255405i	$-0.0822087\pi$
$594$		0			0
$595$	−1.93774	+	13.0844i	−0.0794394	+	0.536408i
$596$		0			0
$597$		−	22.4346i		−	0.918187i
$598$		0			0
$599$	15.4382			0.630789			0.315395	−	0.948961i	$-0.397863\pi$
$599$	15.4382			0.630789			0.315395	+	0.948961i	$0.397863\pi$
$600$		0			0
$601$	1.63560	−	1.63560i	0.0667176	−	0.0667176i	−0.672961	−	0.739678i	$-0.734978\pi$
$601$	1.63560	−	1.63560i	0.0667176	−	0.0667176i	0.739678	+	0.672961i	$0.234978\pi$
$602$		0			0
$603$			30.1975i			1.22974i
$604$		0			0
$605$	−3.05025	+	3.05025i	−0.124010	+	0.124010i
$606$		0			0
$607$	18.4798	+	18.4798i	0.750070	+	0.750070i	0.974492	−	0.224422i	$-0.0720494\pi$
$607$	18.4798	+	18.4798i	0.750070	+	0.750070i	−0.224422	+	0.974492i	$0.572049\pi$
$608$		0			0
$609$	43.7961	+	43.7961i	1.77471	+	1.77471i
$610$		0			0
$611$	−27.7921			−1.12435
$612$		0			0
$613$	41.1938			1.66380			0.831902	−	0.554923i	$-0.187252\pi$
$613$	41.1938			1.66380			0.831902	+	0.554923i	$0.187252\pi$
$614$		0			0
$615$	−12.5600	−	12.5600i	−0.506468	−	0.506468i
$616$		0			0
$617$	26.9435	+	26.9435i	1.08471	+	1.08471i	0.996064	+	0.0886418i	$0.0282526\pi$
$617$	26.9435	+	26.9435i	1.08471	+	1.08471i	0.0886418	+	0.996064i	$0.471747\pi$
$618$		0			0
$619$	24.1574	−	24.1574i	0.970966	−	0.970966i	−0.0286241	−	0.999590i	$-0.509113\pi$
$619$	24.1574	−	24.1574i	0.970966	−	0.970966i	0.999590	+	0.0286241i	$0.00911257\pi$
$620$		0			0
$621$			9.35621i			0.375452i
$622$		0			0
$623$	−36.9583	+	36.9583i	−1.48070	+	1.48070i
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$		−	25.5382i		−	1.01990i
$628$		0			0
$629$	14.5015	−	10.7603i	0.578212	−	0.429043i
$630$		0			0
$631$			31.9751i			1.27291i	0.771314	+	0.636454i	$0.219600\pi$
$631$			31.9751i			1.27291i	−0.771314	+	0.636454i	$0.780400\pi$
$632$		0			0
$633$	38.1459			1.51616
$634$		0			0
$635$	−4.78706	+	4.78706i	−0.189969	+	0.189969i
$636$		0			0
$637$			18.7048i			0.741111i
$638$		0			0
$639$	−9.38150	+	9.38150i	−0.371126	+	0.371126i
$640$		0			0
$641$	−32.0152	−	32.0152i	−1.26453	−	1.26453i	−0.948876	−	0.315649i	$-0.897778\pi$
$641$	−32.0152	−	32.0152i	−1.26453	−	1.26453i	−0.315649	−	0.948876i	$-0.602222\pi$
$642$		0			0
$643$	24.9629	+	24.9629i	0.984439	+	0.984439i	0.999881	−	0.0154416i	$-0.00491542\pi$
$643$	24.9629	+	24.9629i	0.984439	+	0.984439i	−0.0154416	+	0.999881i	$0.504915\pi$
$644$		0			0
$645$	16.3510			0.643818
$646$		0			0
$647$	24.6950			0.970861			0.485430	−	0.874275i	$-0.338663\pi$
$647$	24.6950			0.970861			0.485430	+	0.874275i	$0.338663\pi$
$648$		0			0
$649$	−14.6469	−	14.6469i	−0.574943	−	0.574943i
$650$		0			0
$651$	8.47084	+	8.47084i	0.331998	+	0.331998i
$652$		0			0
$653$	11.2541	−	11.2541i	0.440407	−	0.440407i	−0.451742	−	0.892149i	$-0.649197\pi$
$653$	11.2541	−	11.2541i	0.440407	−	0.440407i	0.892149	+	0.451742i	$0.149197\pi$
$654$		0			0
$655$		−	10.3634i		−	0.404932i
$656$		0			0
$657$	−7.78879	+	7.78879i	−0.303870	+	0.303870i
$658$		0			0
$659$	−2.52086			−0.0981989			−0.0490994	−	0.998794i	$-0.515635\pi$
$659$	−2.52086			−0.0981989			−0.0490994	+	0.998794i	$0.515635\pi$
$660$		0			0
$661$			12.1208i			0.471443i	0.971821	+	0.235722i	$0.0757454\pi$
$661$			12.1208i			0.471443i	−0.971821	+	0.235722i	$0.924255\pi$
$662$		0			0
$663$	42.6828	−	31.6713i	1.65766	−	1.23001i
$664$		0			0
$665$		−	13.9673i		−	0.541628i
$666$		0			0
$667$	41.0951			1.59121
$668$		0			0
$669$	−14.8395	+	14.8395i	−0.573729	+	0.573729i
$670$		0			0
$671$			16.5240i			0.637900i
$672$		0			0
$673$	−16.4469	+	16.4469i	−0.633981	+	0.633981i	−0.949064	−	0.315083i	$-0.897968\pi$
$673$	−16.4469	+	16.4469i	−0.633981	+	0.633981i	0.315083	+	0.949064i	$0.397968\pi$
$674$		0			0
$675$	−1.37019	−	1.37019i	−0.0527385	−	0.0527385i
$676$		0			0
$677$	−1.45511	−	1.45511i	−0.0559245	−	0.0559245i	0.678591	−	0.734516i	$-0.262591\pi$
$677$	−1.45511	−	1.45511i	−0.0559245	−	0.0559245i	−0.734516	+	0.678591i	$0.762591\pi$
$678$		0			0
$679$	56.8523			2.18179
$680$		0			0
$681$	46.5825			1.78504
$682$		0			0
$683$	9.73834	+	9.73834i	0.372627	+	0.372627i	0.868433	−	0.495806i	$-0.165127\pi$
$683$	9.73834	+	9.73834i	0.372627	+	0.372627i	−0.495806	+	0.868433i	$0.665127\pi$
$684$		0			0
$685$	−1.23118	−	1.23118i	−0.0470409	−	0.0470409i
$686$		0			0
$687$	24.3199	−	24.3199i	0.927860	−	0.927860i
$688$		0			0
$689$		−	6.51107i		−	0.248052i
$690$		0			0
$691$	−14.3615	+	14.3615i	−0.546338	+	0.546338i	−0.925380	−	0.379041i	$-0.876254\pi$
$691$	−14.3615	+	14.3615i	−0.546338	+	0.546338i	0.379041	+	0.925380i	$0.376254\pi$
$692$		0			0
$693$	−17.8000			−0.676164
$694$		0			0
$695$		−	0.831086i		−	0.0315249i
$696$		0			0
$697$	−19.2384	−	25.9272i	−0.728705	−	0.982061i
$698$		0			0
$699$			20.1704i			0.762916i
$700$		0			0
$701$	−41.7527			−1.57698			−0.788489	−	0.615048i	$-0.789136\pi$
$701$	−41.7527			−1.57698			−0.788489	+	0.615048i	$0.789136\pi$
$702$		0			0
$703$	−13.4832	+	13.4832i	−0.508528	+	0.508528i
$704$		0			0
$705$		−	11.0942i		−	0.417832i
$706$		0			0
$707$	−17.3691	+	17.3691i	−0.653230	+	0.653230i
$708$		0			0
$709$	−36.3578	−	36.3578i	−1.36545	−	1.36545i	−0.866811	−	0.498637i	$-0.833834\pi$
$709$	−36.3578	−	36.3578i	−1.36545	−	1.36545i	−0.498637	−	0.866811i	$-0.666166\pi$
$710$		0			0
$711$	2.77545	+	2.77545i	0.104087	+	0.104087i
$712$		0			0
$713$	7.94842			0.297671
$714$		0			0
$715$	−14.6941			−0.549528
$716$		0			0
$717$	−0.132714	−	0.132714i	−0.00495631	−	0.00495631i
$718$		0			0
$719$	−31.1026	−	31.1026i	−1.15993	−	1.15993i	−0.984490	−	0.175443i	$-0.943864\pi$
$719$	−31.1026	−	31.1026i	−1.15993	−	1.15993i	−0.175443	−	0.984490i	$-0.556136\pi$
$720$		0			0
$721$	−17.2121	+	17.2121i	−0.641012	+	0.641012i
$722$		0			0
$723$			2.66013i			0.0989313i
$724$		0			0
$725$	−6.01824	+	6.01824i	−0.223512	+	0.223512i
$726$		0			0
$727$	−34.1619			−1.26699			−0.633497	−	0.773745i	$-0.718381\pi$
$727$	−34.1619			−1.26699			−0.633497	+	0.773745i	$0.718381\pi$
$728$		0			0
$729$			10.0583i			0.372530i
$730$		0			0
$731$	29.3989	+	4.35383i	1.08736	+	0.161032i
$732$		0			0
$733$			9.63393i			0.355837i	0.984045	+	0.177919i	$0.0569364\pi$
$733$			9.63393i			0.355837i	−0.984045	+	0.177919i	$0.943064\pi$
$734$		0			0
$735$	−7.46669			−0.275413
$736$		0			0
$737$	25.7314	−	25.7314i	0.947827	−	0.947827i
$738$		0			0
$739$		−	34.3768i		−	1.26457i	−0.774736	−	0.632285i	$-0.782117\pi$
$739$		−	34.3768i		−	1.26457i	0.774736	−	0.632285i	$-0.217883\pi$
$740$		0			0
$741$	−39.6856	+	39.6856i	−1.45789	+	1.45789i
$742$		0			0
$743$	−10.4068	−	10.4068i	−0.381789	−	0.381789i	0.489958	−	0.871746i	$-0.337012\pi$
$743$	−10.4068	−	10.4068i	−0.381789	−	0.381789i	−0.871746	+	0.489958i	$0.837012\pi$
$744$		0			0
$745$	−1.73157	−	1.73157i	−0.0634398	−	0.0634398i
$746$		0			0
$747$	26.0868			0.954466
$748$		0			0
$749$	−17.4861			−0.638927
$750$		0			0
$751$	2.95895	+	2.95895i	0.107974	+	0.107974i	0.759030	−	0.651056i	$-0.225674\pi$
$751$	2.95895	+	2.95895i	0.107974	+	0.107974i	−0.651056	+	0.759030i	$0.725674\pi$
$752$		0			0
$753$	−29.0722	−	29.0722i	−1.05945	−	1.05945i
$754$		0			0
$755$	3.20805	−	3.20805i	0.116753	−	0.116753i
$756$		0			0
$757$			23.3964i			0.850357i	0.905110	+	0.425178i	$0.139789\pi$
$757$			23.3964i			0.850357i	−0.905110	+	0.425178i	$0.860211\pi$
$758$		0			0
$759$	−20.0267	+	20.0267i	−0.726923	+	0.726923i
$760$		0			0
$761$	26.2704			0.952302			0.476151	−	0.879363i	$-0.342032\pi$
$761$	26.2704			0.952302			0.476151	+	0.879363i	$0.342032\pi$
$762$		0			0
$763$		−	27.3039i		−	0.988468i
$764$		0			0
$765$	5.27200	+	7.10496i	0.190609	+	0.256880i
$766$		0			0
$767$			45.5219i			1.64370i
$768$		0			0
$769$	27.1033			0.977369			0.488685	−	0.872461i	$-0.337477\pi$
$769$	27.1033			0.977369			0.488685	+	0.872461i	$0.337477\pi$
$770$		0			0
$771$	40.6683	−	40.6683i	1.46463	−	1.46463i
$772$		0			0
$773$		−	31.6782i		−	1.13939i	−0.821857	−	0.569693i	$-0.807062\pi$
$773$		−	31.6782i		−	1.13939i	0.821857	−	0.569693i	$-0.192938\pi$
$774$		0			0
$775$	−1.16402	+	1.16402i	−0.0418128	+	0.0418128i
$776$		0			0
$777$	22.5366	+	22.5366i	0.808495	+	0.808495i
$778$		0			0
$779$	24.1066	+	24.1066i	0.863707	+	0.863707i
$780$		0			0
$781$	15.9880			0.572096
$782$		0			0
$783$	−16.4922			−0.589383
$784$		0			0
$785$	16.6223	+	16.6223i	0.593274	+	0.593274i
$786$		0			0
$787$	12.3579	+	12.3579i	0.440513	+	0.440513i	0.892184	−	0.451671i	$-0.149172\pi$
$787$	12.3579	+	12.3579i	0.440513	+	0.440513i	−0.451671	+	0.892184i	$0.649172\pi$
$788$		0			0
$789$	−3.39066	+	3.39066i	−0.120711	+	0.120711i
$790$		0			0
$791$		−	25.3077i		−	0.899837i
$792$		0			0
$793$	25.6777	−	25.6777i	0.911844	−	0.911844i
$794$		0			0
$795$	2.59913			0.0921816
$796$		0			0
$797$		−	14.1900i		−	0.502634i	−0.967905	−	0.251317i	$-0.919136\pi$
$797$		−	14.1900i		−	0.502634i	0.967905	−	0.251317i	$-0.0808637\pi$
$798$		0			0
$799$	2.95409	−	19.9473i	0.104508	−	0.705684i
$800$		0			0
$801$			34.9601i			1.23525i
$802$		0			0
$803$	13.2737			0.468419
$804$		0			0
$805$	−10.9530	+	10.9530i	−0.386041	+	0.386041i
$806$		0			0
$807$		−	48.7296i		−	1.71536i
$808$		0			0
$809$	17.2453	−	17.2453i	0.606312	−	0.606312i	−0.335668	−	0.941980i	$-0.608962\pi$
$809$	17.2453	−	17.2453i	0.606312	−	0.606312i	0.941980	+	0.335668i	$0.108962\pi$
$810$		0			0
$811$	9.10566	+	9.10566i	0.319743	+	0.319743i	0.848668	−	0.528925i	$-0.177405\pi$
$811$	9.10566	+	9.10566i	0.319743	+	0.319743i	−0.528925	+	0.848668i	$0.677405\pi$
$812$		0			0
$813$	36.2384	+	36.2384i	1.27094	+	1.27094i
$814$		0			0
$815$	−22.6952			−0.794978
$816$		0			0
$817$	−31.3826			−1.09794
$818$		0			0
$819$	27.6606	+	27.6606i	0.966540	+	0.966540i
$820$		0			0
$821$	13.4527	+	13.4527i	0.469503	+	0.469503i	0.901754	−	0.432251i	$-0.142280\pi$
$821$	13.4527	+	13.4527i	0.469503	+	0.469503i	−0.432251	+	0.901754i	$0.642280\pi$
$822$		0			0
$823$	11.4872	−	11.4872i	0.400417	−	0.400417i	−0.477963	−	0.878380i	$-0.658625\pi$
$823$	11.4872	−	11.4872i	0.400417	−	0.400417i	0.878380	+	0.477963i	$0.158625\pi$
$824$		0			0
$825$		−	5.86568i		−	0.204217i
$826$		0			0
$827$	12.4889	−	12.4889i	0.434283	−	0.434283i	−0.455800	−	0.890082i	$-0.650647\pi$
$827$	12.4889	−	12.4889i	0.434283	−	0.434283i	0.890082	+	0.455800i	$0.150647\pi$
$828$		0			0
$829$	−1.81004			−0.0628654			−0.0314327	−	0.999506i	$-0.510007\pi$
$829$	−1.81004			−0.0628654			−0.0314327	+	0.999506i	$0.510007\pi$
$830$		0			0
$831$		−	57.9874i		−	2.01156i
$832$		0			0
$833$	−13.4250	−	1.98818i	−0.465150	−	0.0688864i
$834$		0			0
$835$			20.4161i			0.706528i
$836$		0			0
$837$	−3.18984			−0.110257
$838$		0			0
$839$	−19.0797	+	19.0797i	−0.658705	+	0.658705i	−0.955074	−	0.296368i	$-0.904224\pi$
$839$	−19.0797	+	19.0797i	−0.658705	+	0.658705i	0.296368	+	0.955074i	$0.404224\pi$
$840$		0			0
$841$			43.4384i			1.49787i
$842$		0			0
$843$	−25.3833	+	25.3833i	−0.874248	+	0.874248i
$844$		0			0
$845$	13.6418	+	13.6418i	0.469293	+	0.469293i
$846$		0			0
$847$	−9.78535	−	9.78535i	−0.336229	−	0.336229i
$848$		0			0
$849$	−39.8839			−1.36881
$850$		0			0
$851$	21.1467			0.724899
$852$		0			0
$853$	−12.8918	−	12.8918i	−0.441407	−	0.441407i	0.451078	−	0.892485i	$-0.351040\pi$
$853$	−12.8918	−	12.8918i	−0.441407	−	0.441407i	−0.892485	+	0.451078i	$0.851040\pi$
$854$		0			0
$855$	−6.60605	−	6.60605i	−0.225922	−	0.225922i
$856$		0			0
$857$	−7.32470	+	7.32470i	−0.250207	+	0.250207i	−0.821055	−	0.570848i	$-0.806614\pi$
$857$	−7.32470	+	7.32470i	−0.250207	+	0.250207i	0.570848	+	0.821055i	$0.306614\pi$
$858$		0			0
$859$		−	54.5456i		−	1.86107i	−0.366202	−	0.930535i	$-0.619342\pi$
$859$		−	54.5456i		−	1.86107i	0.366202	−	0.930535i	$-0.380658\pi$
$860$		0			0
$861$	40.2931	−	40.2931i	1.37318	−	1.37318i
$862$		0			0
$863$	−1.42063			−0.0483589			−0.0241794	−	0.999708i	$-0.507697\pi$
$863$	−1.42063			−0.0483589			−0.0241794	+	0.999708i	$0.507697\pi$
$864$		0			0
$865$		−	9.41687i		−	0.320183i
$866$		0			0
$867$	18.1947	+	34.0012i	0.617923	+	1.15474i
$868$		0			0
$869$		−	4.72994i		−	0.160452i
$870$		0			0
$871$	−79.9716			−2.70973
$872$		0			0
$873$	26.8892	−	26.8892i	0.910062	−	0.910062i
$874$		0			0
$875$		−	3.20805i		−	0.108452i
$876$		0			0
$877$	20.4621	−	20.4621i	0.690958	−	0.690958i	−0.271485	−	0.962443i	$-0.587515\pi$
$877$	20.4621	−	20.4621i	0.690958	−	0.690958i	0.962443	+	0.271485i	$0.0875147\pi$
$878$		0			0
$879$	47.5632	+	47.5632i	1.60427	+	1.60427i
$880$		0			0
$881$	13.0607	+	13.0607i	0.440026	+	0.440026i	0.892021	−	0.451994i	$-0.149287\pi$
$881$	13.0607	+	13.0607i	0.440026	+	0.440026i	−0.451994	+	0.892021i	$0.649287\pi$
$882$		0			0
$883$	−13.7927			−0.464162			−0.232081	−	0.972696i	$-0.574554\pi$
$883$	−13.7927			−0.464162			−0.232081	+	0.972696i	$0.574554\pi$
$884$		0			0
$885$	−18.1717			−0.610835
$886$		0			0
$887$	14.8015	+	14.8015i	0.496987	+	0.496987i	0.910499	−	0.413512i	$-0.135698\pi$
$887$	14.8015	+	14.8015i	0.496987	+	0.496987i	−0.413512	+	0.910499i	$0.635698\pi$
$888$		0			0
$889$	−15.3571	−	15.3571i	−0.515061	−	0.515061i
$890$		0			0
$891$	19.8073	−	19.8073i	0.663569	−	0.663569i
$892$		0			0
$893$			21.2932i			0.712551i
$894$		0			0
$895$	4.70766	−	4.70766i	0.157360	−	0.157360i
$896$		0			0
$897$	62.2418			2.07819
$898$		0			0
$899$			14.0107i			0.467282i
$900$		0			0
$901$	4.67321	+	0.692079i	0.155687	+	0.0230565i
$902$		0			0
$903$			52.4546i			1.74558i
$904$		0			0
$905$	0.120770			0.00401452
$906$		0			0
$907$	20.0606	−	20.0606i	0.666103	−	0.666103i	−0.290709	−	0.956812i	$-0.593891\pi$
$907$	20.0606	−	20.0606i	0.666103	−	0.666103i	0.956812	+	0.290709i	$0.0938911\pi$
$908$		0			0
$909$			16.4299i			0.544947i
$910$		0			0
$911$	19.9375	−	19.9375i	0.660560	−	0.660560i	−0.294952	−	0.955512i	$-0.595304\pi$
$911$	19.9375	−	19.9375i	0.660560	−	0.660560i	0.955512	+	0.294952i	$0.0953038\pi$
$912$		0			0
$913$	−22.2286	−	22.2286i	−0.735660	−	0.735660i
$914$		0			0
$915$	10.2502	+	10.2502i	0.338861	+	0.338861i
$916$		0			0
$917$	33.2463			1.09789
$918$		0			0
$919$	−5.49805			−0.181364			−0.0906820	−	0.995880i	$-0.528905\pi$
$919$	−5.49805			−0.181364			−0.0906820	+	0.995880i	$0.528905\pi$
$920$		0			0
$921$	51.3473	+	51.3473i	1.69195	+	1.69195i
$922$		0			0
$923$	−24.8449	−	24.8449i	−0.817780	−	0.817780i
$924$		0			0
$925$	−3.09686	+	3.09686i	−0.101824	+	0.101824i
$926$		0			0
$927$			16.2815i			0.534754i
$928$		0			0
$929$	7.24530	−	7.24530i	0.237711	−	0.237711i	−0.578191	−	0.815901i	$-0.696241\pi$
$929$	7.24530	−	7.24530i	0.237711	−	0.237711i	0.815901	+	0.578191i	$0.196241\pi$
$930$		0			0
$931$	14.3309			0.469676
$932$		0			0
$933$			27.9996i			0.916665i
$934$		0			0
$935$	1.56188	−	10.5464i	0.0510788	−	0.344906i
$936$		0			0
$937$			18.3456i			0.599326i	0.954045	+	0.299663i	$0.0968743\pi$
$937$			18.3456i			0.599326i	−0.954045	+	0.299663i	$0.903126\pi$
$938$		0			0
$939$	−4.46016			−0.145552
$940$		0			0
$941$	−0.741002	+	0.741002i	−0.0241560	+	0.0241560i	−0.719082	−	0.694926i	$-0.755437\pi$
$941$	−0.741002	+	0.741002i	−0.0241560	+	0.0241560i	0.694926	+	0.719082i	$0.255437\pi$
$942$		0			0
$943$		−	37.8081i		−	1.23120i
$944$		0			0
$945$	4.39562	−	4.39562i	0.142990	−	0.142990i
$946$		0			0
$947$	−25.4030	−	25.4030i	−0.825487	−	0.825487i	0.161402	−	0.986889i	$-0.448399\pi$
$947$	−25.4030	−	25.4030i	−0.825487	−	0.825487i	−0.986889	+	0.161402i	$0.948399\pi$
$948$		0			0
$949$	−20.6269	−	20.6269i	−0.669579	−	0.669579i
$950$		0			0
$951$	−25.9383			−0.841108
$952$		0			0
$953$	0.289066			0.00936376			0.00468188	−	0.999989i	$-0.498510\pi$
$953$	0.289066			0.00936376			0.00468188	+	0.999989i	$0.498510\pi$
$954$		0			0
$955$	6.73345	+	6.73345i	0.217889	+	0.217889i
$956$		0			0
$957$	−35.3011	−	35.3011i	−1.14112	−	1.14112i
$958$		0			0
$959$	3.94968	−	3.94968i	0.127542	−	0.127542i
$960$		0			0
$961$		−	28.2901i		−	0.912585i
$962$		0			0
$963$	−8.27031	+	8.27031i	−0.266507	+	0.266507i
$964$		0			0
$965$	16.4499			0.529541
$966$		0			0
$967$			31.1696i			1.00235i	0.865347	+	0.501173i	$0.167098\pi$
$967$			31.1696i			1.00235i	−0.865347	+	0.501173i	$0.832902\pi$
$968$		0			0
$969$	−24.2654	−	32.7019i	−0.779516	−	1.05054i
$970$		0			0
$971$		−	19.6962i		−	0.632081i	−0.948746	−	0.316041i	$-0.897646\pi$
$971$		−	19.6962i		−	0.632081i	0.948746	−	0.316041i	$-0.102354\pi$
$972$		0			0
$973$	2.66616			0.0854732
$974$		0			0
$975$	−9.11510	+	9.11510i	−0.291917	+	0.291917i
$976$		0			0
$977$		−	20.4047i		−	0.652806i	−0.945231	−	0.326403i	$-0.894163\pi$
$977$		−	20.4047i		−	0.652806i	0.945231	−	0.326403i	$-0.105837\pi$
$978$		0			0
$979$	29.7896	−	29.7896i	0.952079	−	0.952079i
$980$		0			0
$981$	−12.9138	−	12.9138i	−0.412307	−	0.412307i
$982$		0			0
$983$	16.9814	+	16.9814i	0.541623	+	0.541623i	0.924004	−	0.382382i	$-0.124896\pi$
$983$	16.9814	+	16.9814i	0.541623	+	0.541623i	−0.382382	+	0.924004i	$0.624896\pi$
$984$		0			0
$985$	−23.1102			−0.736352
$986$		0			0
$987$	35.5907			1.13286
$988$		0			0
$989$	24.6098	+	24.6098i	0.782546	+	0.782546i
$990$		0			0
$991$	−18.5907	−	18.5907i	−0.590552	−	0.590552i	0.347228	−	0.937781i	$-0.387123\pi$
$991$	−18.5907	−	18.5907i	−0.590552	−	0.590552i	−0.937781	+	0.347228i	$0.887123\pi$
$992$		0			0
$993$	29.6397	−	29.6397i	0.940588	−	0.940588i
$994$		0			0
$995$			9.88991i			0.313531i
$996$		0			0
$997$	−23.5532	+	23.5532i	−0.745937	+	0.745937i	−0.973713	−	0.227777i	$-0.926854\pi$
$997$	−23.5532	+	23.5532i	−0.745937	+	0.745937i	0.227777	+	0.973713i	$0.426854\pi$
$998$		0			0
$999$	−8.48654			−0.268502

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1360.2.bt.b.81.2		8
4.3	odd	2		170.2.h.b.81.3	yes	8
12.11	even	2		1530.2.q.g.1441.2		8
17.4	even	4	inner	1360.2.bt.b.1041.2		8
20.3	even	4		850.2.g.l.149.2		8
20.7	even	4		850.2.g.i.149.3		8
20.19	odd	2		850.2.h.n.251.2		8
68.15	odd	8		2890.2.a.be.1.1		4
68.19	odd	8		2890.2.a.bd.1.4		4
68.43	odd	8		2890.2.b.o.2311.6		8
68.55	odd	4		170.2.h.b.21.3	✓	8
68.59	odd	8		2890.2.b.o.2311.3		8
204.191	even	4		1530.2.q.g.361.2		8
340.123	even	4		850.2.g.i.599.3		8
340.259	odd	4		850.2.h.n.701.2		8
340.327	even	4		850.2.g.l.599.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.h.b.21.3	✓	8	68.55	odd	4
170.2.h.b.81.3	yes	8	4.3	odd	2
850.2.g.i.149.3		8	20.7	even	4
850.2.g.i.599.3		8	340.123	even	4
850.2.g.l.149.2		8	20.3	even	4
850.2.g.l.599.2		8	340.327	even	4
850.2.h.n.251.2		8	20.19	odd	2
850.2.h.n.701.2		8	340.259	odd	4
1360.2.bt.b.81.2		8	1.1	even	1	trivial
1360.2.bt.b.1041.2		8	17.4	even	4	inner
1530.2.q.g.361.2		8	204.191	even	4
1530.2.q.g.1441.2		8	12.11	even	2
2890.2.a.bd.1.4		4	68.19	odd	8
2890.2.a.be.1.1		4	68.15	odd	8
2890.2.b.o.2311.3		8	68.59	odd	8
2890.2.b.o.2311.6		8	68.43	odd	8

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:	\( N \)	\(=\)	\( 1360 = 2^{4} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1360.bt (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.60402 - 1.60402i) q^{3} +(0.707107 + 0.707107i) q^{5} +(-2.26843 + 2.26843i) q^{7} +2.14578i q^{9} +O(q^{10})\)	\(q+(-1.60402 - 1.60402i) q^{3} +(0.707107 + 0.707107i) q^{5} +(-2.26843 + 2.26843i) q^{7} +2.14578i q^{9} +(1.82843 - 1.82843i) q^{11} -5.68265 q^{13} -2.26843i q^{15} +(0.604023 - 4.07862i) q^{17} +4.35383i q^{19} +7.27723 q^{21} +(3.41421 - 3.41421i) q^{23} +1.00000i q^{25} +(-1.37019 + 1.37019i) q^{27} +(6.01824 + 6.01824i) q^{29} +(1.16402 + 1.16402i) q^{31} -5.86568 q^{33} -3.20805 q^{35} +(3.09686 + 3.09686i) q^{37} +(9.11510 + 9.11510i) q^{39} +(5.53686 - 5.53686i) q^{41} +7.20805i q^{43} +(-1.51730 + 1.51730i) q^{45} +4.89069 q^{47} -3.29156i q^{49} +(-7.51107 + 5.57334i) q^{51} +1.14578i q^{53} +2.58579 q^{55} +(6.98364 - 6.98364i) q^{57} -8.01068i q^{59} +(-4.51863 + 4.51863i) q^{61} +(-4.86756 - 4.86756i) q^{63} +(-4.01824 - 4.01824i) q^{65} +14.0729 q^{67} -10.9530 q^{69} +(4.37207 + 4.37207i) q^{71} +(3.62981 + 3.62981i) q^{73} +(1.60402 - 1.60402i) q^{75} +8.29532i q^{77} +(1.29344 - 1.29344i) q^{79} +10.8330 q^{81} -12.1572i q^{83} +(3.31113 - 2.45691i) q^{85} -19.3068i q^{87} +16.2925 q^{89} +(12.8907 - 12.8907i) q^{91} -3.73423i q^{93} +(-3.07862 + 3.07862i) q^{95} +(-12.5312 - 12.5312i) q^{97} +(3.92341 + 3.92341i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^7	\( 8 q + 4 q^{7} - 8 q^{11} - 12 q^{13} - 8 q^{17} + 16 q^{21} + 16 q^{23} - 12 q^{27} + 24 q^{29} - 4 q^{31} + 16 q^{33} - 20 q^{37} + 4 q^{39} - 8 q^{45} - 20 q^{47} - 4 q^{51} + 32 q^{55} + 40 q^{57} - 16 q^{61} + 64 q^{63} - 8 q^{65} + 16 q^{67} + 8 q^{69} - 4 q^{71} + 28 q^{73} - 8 q^{79} - 8 q^{81} + 8 q^{85} - 44 q^{89} + 44 q^{91} - 4 q^{95} + 20 q^{97} + 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^7 - 8 * q^11 - 12 * q^13 - 8 * q^17 + 16 * q^21 + 16 * q^23 - 12 * q^27 + 24 * q^29 - 4 * q^31 + 16 * q^33 - 20 * q^37 + 4 * q^39 - 8 * q^45 - 20 * q^47 - 4 * q^51 + 32 * q^55 + 40 * q^57 - 16 * q^61 + 64 * q^63 - 8 * q^65 + 16 * q^67 + 8 * q^69 - 4 * q^71 + 28 * q^73 - 8 * q^79 - 8 * q^81 + 8 * q^85 - 44 * q^89 + 44 * q^91 - 4 * q^95 + 20 * q^97 + 4 * q^99

Introduction

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