LMFDB - Embedded newform 1360.2.bt.b.1041.2

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			1041.2
Root			$-3.26843i$ of defining polynomial
Character	$\chi$	$=$	1360.1041
Dual form			1360.2.bt.b.81.2

$q$-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 $\left(\mathbb{Z}/1360\mathbb{Z}\right)^\times$.

$n$	$241$	$341$	$511$	$817$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

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	−0.997450	−	0.0713668i	$-0.977264\pi$
$3$	−1.60402	+	1.60402i	−0.926083	+	0.926083i	0.0713668	+	0.997450i	$0.477264\pi$
$4$		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	0.133643	−	0.991030i	$-0.457332\pi$
$7$	−2.26843	−	2.26843i	−0.857387	−	0.857387i	−0.991030	+	0.133643i	$0.957332\pi$
$8$		0			0
$9$		−	2.14578i		−	0.715261i
$10$		0			0
$11$	1.82843	+	1.82843i	0.551292	+	0.551292i	0.926813	−	0.375522i	$-0.122537\pi$
$11$	1.82843	+	1.82843i	0.551292	+	0.551292i	−0.375522	+	0.926813i	$0.622537\pi$
$12$		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	$-0.833547\pi$
$19$		−	4.35383i		−	0.998837i	0.866361	−	0.499418i	$-0.166453\pi$
$20$		0			0
$21$	7.27723			1.58802
$22$		0			0
$23$	3.41421	+	3.41421i	0.711913	+	0.711913i	0.966935	−	0.255022i	$-0.0820828\pi$
$23$	3.41421	+	3.41421i	0.711913	+	0.711913i	−0.255022	+	0.966935i	$0.582083\pi$
$24$		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	0.125460	−	0.992099i	$-0.459959\pi$
$29$	6.01824	−	6.01824i	1.11756	−	1.11756i	0.992099	−	0.125460i	$-0.0400406\pi$
$30$		0			0
$31$	1.16402	−	1.16402i	0.209064	−	0.209064i	−0.594806	−	0.803870i	$-0.702771\pi$
$31$	1.16402	−	1.16402i	0.209064	−	0.209064i	0.803870	+	0.594806i	$0.202771\pi$
$32$		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	−0.405136	−	0.914256i	$-0.632776\pi$
$37$	3.09686	−	3.09686i	0.509120	−	0.509120i	0.914256	+	0.405136i	$0.132776\pi$
$38$		0			0
$39$	9.11510	−	9.11510i	1.45958	−	1.45958i
$40$		0			0
$41$	5.53686	+	5.53686i	0.864713	+	0.864713i	0.991881	−	0.127168i	$-0.0405889\pi$
$41$	5.53686	+	5.53686i	0.864713	+	0.864713i	−0.127168	+	0.991881i	$0.540589\pi$
$42$		0			0
$43$		−	7.20805i		−	1.09922i	−0.835422	−	0.549608i	$-0.814777\pi$
$43$		−	7.20805i		−	1.09922i	0.835422	−	0.549608i	$-0.185223\pi$
$44$		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	$-0.974925\pi$
$53$		−	1.14578i		−	0.157385i	0.996899	−	0.0786926i	$-0.0250746\pi$
$54$		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	$0.174609\pi$
$59$			8.01068i			1.04290i	−0.853281	+	0.521451i	$0.825391\pi$
$60$		0			0
$61$	−4.51863	−	4.51863i	−0.578551	−	0.578551i	0.355953	−	0.934504i	$-0.384156\pi$
$61$	−4.51863	−	4.51863i	−0.578551	−	0.578551i	−0.934504	+	0.355953i	$0.884156\pi$
$62$		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	−0.398360	−	0.917229i	$-0.630421\pi$
$71$	4.37207	−	4.37207i	0.518869	−	0.518869i	0.917229	+	0.398360i	$0.130421\pi$
$72$		0			0
$73$	3.62981	−	3.62981i	0.424838	−	0.424838i	−0.462028	−	0.886865i	$-0.652878\pi$
$73$	3.62981	−	3.62981i	0.424838	−	0.424838i	0.886865	+	0.462028i	$0.152878\pi$
$74$		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	0.776115	−	0.630591i	$-0.217188\pi$
$79$	1.29344	+	1.29344i	0.145524	+	0.145524i	−0.630591	+	0.776115i	$0.717188\pi$
$80$		0			0
$81$	10.8330			1.20366
$82$		0			0
$83$			12.1572i			1.33443i	0.744865	+	0.667215i	$0.232514\pi$
$83$			12.1572i			1.33443i	−0.744865	+	0.667215i	$0.767486\pi$
$84$		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	−0.327497	+	0.944852i	$0.606205\pi$
$97$	−12.5312	+	12.5312i	−1.27235	+	1.27235i	−0.944852	+	0.327497i	$0.893795\pi$
$98$		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	−0.495823	−	0.868424i	$-0.665133\pi$
$107$	3.85422	−	3.85422i	0.372601	−	0.372601i	0.868424	+	0.495823i	$0.165133\pi$
$108$		0			0
$109$	−6.01824	−	6.01824i	−0.576443	−	0.576443i	0.357479	−	0.933921i	$-0.383636\pi$
$109$	−6.01824	−	6.01824i	−0.576443	−	0.576443i	−0.933921	+	0.357479i	$0.883636\pi$
$110$		0			0
$111$			9.93487i			0.942976i
$112$		0			0
$113$	−5.57823	−	5.57823i	−0.524756	−	0.524756i	0.394248	−	0.919004i	$-0.371005\pi$
$113$	−5.57823	−	5.57823i	−0.524756	−	0.524756i	−0.919004	+	0.394248i	$0.871005\pi$
$114$		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	$-0.902891\pi$
$127$		−	6.76992i		−	0.600733i	0.953824	−	0.300367i	$-0.0971091\pi$
$128$		0			0
$129$	11.5619	+	11.5619i	1.01797	+	1.01797i
$130$		0			0
$131$	−7.32804	+	7.32804i	−0.640254	+	0.640254i	−0.950618	−	0.310364i	$-0.899549\pi$
$131$	−7.32804	+	7.32804i	−0.640254	+	0.640254i	0.310364	+	0.950618i	$0.399549\pi$
$132$		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	−0.731590	−	0.681745i	$-0.761221\pi$
$139$	−0.587666	+	0.587666i	−0.0498452	+	0.0498452i	0.681745	+	0.731590i	$0.261221\pi$
$140$		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	$0.0590997\pi$
$151$			4.53686i			0.369205i	−0.982813	+	0.184602i	$0.940900\pi$
$152$		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	−0.952532	−	0.304440i	$-0.901531\pi$
$163$	−16.0479	−	16.0479i	−1.25697	−	1.25697i	−0.304440	−	0.952532i	$-0.598469\pi$
$164$		0			0
$165$	−4.14766	+	4.14766i	−0.322895	+	0.322895i
$166$		0			0
$167$	14.4364	−	14.4364i	1.11712	−	1.11712i	0.124957	−	0.992162i	$-0.460121\pi$
$167$	14.4364	−	14.4364i	1.11712	−	1.11712i	0.992162	−	0.124957i	$-0.0398792\pi$
$168$		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	−0.913375	−	0.407120i	$-0.866533\pi$
$173$	−6.65873	+	6.65873i	−0.506254	+	0.506254i	0.407120	+	0.913375i	$0.366533\pi$
$174$		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	$0.0800386\pi$
$179$			6.65763i			0.497615i	−0.968553	+	0.248807i	$0.919961\pi$
$180$		0			0
$181$	0.0853971	+	0.0853971i	0.00634752	+	0.00634752i	0.710273	−	0.703926i	$-0.248571\pi$
$181$	0.0853971	+	0.0853971i	0.00634752	+	0.00634752i	−0.703926	+	0.710273i	$0.748571\pi$
$182$		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	0.988500	−	0.151222i	$-0.0483207\pi$
$193$	11.6318	+	11.6318i	0.837278	+	0.837278i	−0.151222	+	0.988500i	$0.548321\pi$
$194$		0			0
$195$		−	12.8907i		−	0.923122i
$196$		0			0
$197$	−16.3414	−	16.3414i	−1.16428	−	1.16428i	−0.983530	−	0.180745i	$-0.942149\pi$
$197$	−16.3414	−	16.3414i	−1.16428	−	1.16428i	−0.180745	−	0.983530i	$-0.557851\pi$
$198$		0			0
$199$	6.99322	−	6.99322i	0.495737	−	0.495737i	−0.414371	−	0.910108i	$-0.635999\pi$
$199$	6.99322	−	6.99322i	0.495737	−	0.495737i	0.910108	+	0.414371i	$0.135999\pi$
$200$		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	0.167315	−	0.985904i	$-0.446490\pi$
$211$	−11.8907	−	11.8907i	−0.818589	−	0.818589i	−0.985904	+	0.167315i	$0.946490\pi$
$212$		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	$0.100249\pi$
$223$			9.25144i			0.619522i	−0.950814	+	0.309761i	$0.899751\pi$
$224$		0			0
$225$	−2.14578			−0.143052
$226$		0			0
$227$	−14.5205	−	14.5205i	−0.963760	−	0.963760i	0.0356061	−	0.999366i	$-0.488664\pi$
$227$	−14.5205	−	14.5205i	−0.963760	−	0.963760i	−0.999366	+	0.0356061i	$0.988664\pi$
$228$		0			0
$229$		−	15.1618i		−	1.00192i	−0.865471	−	0.500959i	$-0.832981\pi$
$229$		−	15.1618i		−	1.00192i	0.865471	−	0.500959i	$-0.167019\pi$
$230$		0			0
$231$	13.3059	+	13.3059i	0.875463	+	0.875463i
$232$		0			0
$233$	−6.28745	+	6.28745i	−0.411904	+	0.411904i	−0.882402	−	0.470497i	$-0.844075\pi$
$233$	−6.28745	+	6.28745i	−0.411904	+	0.411904i	0.470497	+	0.882402i	$0.344075\pi$
$234$		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	−0.733309	−	0.679895i	$-0.762025\pi$
$241$	−0.829206	+	0.829206i	−0.0534138	+	0.0534138i	0.679895	+	0.733309i	$0.262025\pi$
$242$		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	$-0.709682\pi$
$257$		−	25.3539i		−	1.58154i	0.612116	−	0.790768i	$-0.290318\pi$
$258$		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	$0.0207598\pi$
$263$			2.11385i			0.130345i	−0.997874	+	0.0651727i	$0.979240\pi$
$264$		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	−0.0713148	−	0.997454i	$-0.522719\pi$
$269$	15.1898	−	15.1898i	0.926139	−	0.926139i	0.997454	+	0.0713148i	$0.0227195\pi$
$270$		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	0.0901277	−	0.995930i	$-0.471272\pi$
$277$	18.0756	−	18.0756i	1.08606	−	1.08606i	0.995930	−	0.0901277i	$-0.0287275\pi$
$278$		0			0
$279$	−2.49773	−	2.49773i	−0.149535	−	0.149535i
$280$		0			0
$281$			15.8248i			0.944027i	0.881591	+	0.472014i	$0.156473\pi$
$281$			15.8248i			0.944027i	−0.881591	+	0.472014i	$0.843527\pi$
$282$		0			0
$283$	12.4325	+	12.4325i	0.739032	+	0.739032i	0.972391	−	0.233358i	$-0.0749715\pi$
$283$	12.4325	+	12.4325i	0.739032	+	0.739032i	−0.233358	+	0.972391i	$0.574972\pi$
$284$		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	−0.909851	−	0.414936i	$-0.863804\pi$
$311$	−8.72792	+	8.72792i	−0.494915	+	0.494915i	0.414936	+	0.909851i	$0.363804\pi$
$312$		0			0
$313$	1.39030	+	1.39030i	0.0785845	+	0.0785845i	0.745307	−	0.666722i	$-0.232303\pi$
$313$	1.39030	+	1.39030i	0.0785845	+	0.0785845i	−0.666722	+	0.745307i	$0.732303\pi$
$314$		0			0
$315$			6.88377i			0.387856i
$316$		0			0
$317$	8.08540	+	8.08540i	0.454121	+	0.454121i	0.896720	−	0.442599i	$-0.145943\pi$
$317$	8.08540	+	8.08540i	0.454121	+	0.454121i	−0.442599	+	0.896720i	$0.645943\pi$
$318$		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	$-0.830447\pi$
$331$		−	18.4784i		−	1.01566i	0.861457	−	0.507831i	$-0.169553\pi$
$332$		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	−0.755370	−	0.655298i	$-0.772543\pi$
$337$	−1.83708	+	1.83708i	−0.100072	+	0.100072i	0.655298	+	0.755370i	$0.272543\pi$
$338$		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	0.908772	−	0.417294i	$-0.137021\pi$
$347$	9.15522	+	9.15522i	0.491478	+	0.491478i	−0.417294	+	0.908772i	$0.637021\pi$
$348$		0			0
$349$			20.3698i			1.09037i	0.838315	+	0.545186i	$0.183541\pi$
$349$			20.3698i			1.09037i	−0.838315	+	0.545186i	$0.816459\pi$
$350$		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	$0.150221\pi$
$359$			17.2272i			0.909217i	−0.890691	+	0.454609i	$0.849779\pi$
$360$		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	0.130752	−	0.991415i	$-0.458261\pi$
$367$	−16.4879	−	16.4879i	−0.860663	−	0.860663i	−0.991415	+	0.130752i	$0.958261\pi$
$368$		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	0.0113269	−	0.999936i	$-0.496394\pi$
$379$	19.6872	−	19.6872i	1.01126	−	1.01126i	0.999936	−	0.0113269i	$-0.00360553\pi$
$380$		0			0
$381$	10.8591	+	10.8591i	0.556329	+	0.556329i
$382$		0			0
$383$		−	0.426776i		−	0.0218073i	−0.999941	−	0.0109036i	$-0.996529\pi$
$383$		−	0.426776i		−	0.0218073i	0.999941	−	0.0109036i	$-0.00347080\pi$
$384$		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	$-0.993487\pi$
$389$		−	0.807061i		−	0.0409196i	0.999791	−	0.0204598i	$-0.00651302\pi$
$390$		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	0.998773	−	0.0495157i	$-0.0157678\pi$
$397$	18.9138	+	18.9138i	0.949258	+	0.949258i	−0.0495157	+	0.998773i	$0.515768\pi$
$398$		0			0
$399$		−	31.6838i		−	1.58618i
$400$		0			0
$401$	−10.9226	−	10.9226i	−0.545450	−	0.545450i	0.379671	−	0.925121i	$-0.376037\pi$
$401$	−10.9226	−	10.9226i	−0.545450	−	0.545450i	−0.925121	+	0.379671i	$0.876037\pi$
$402$		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	0.517034	−	0.855965i	$-0.327036\pi$
$419$	−6.93774	−	6.93774i	−0.338931	−	0.338931i	−0.855965	+	0.517034i	$0.827036\pi$
$420$		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	0.291206	−	0.956660i	$-0.405944\pi$
$431$	−13.8152	−	13.8152i	−0.665455	−	0.665455i	−0.956660	+	0.291206i	$0.905944\pi$
$432$		0			0
$433$			16.7404i			0.804491i	0.915532	+	0.402245i	$0.131770\pi$
$433$			16.7404i			0.804491i	−0.915532	+	0.402245i	$0.868230\pi$
$434$		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	−0.871543	−	0.490318i	$-0.836880\pi$
$439$	−7.98755	+	7.98755i	−0.381225	+	0.381225i	0.490318	+	0.871543i	$0.336880\pi$
$440$		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	0.538900	−	0.842370i	$-0.318840\pi$
$449$	−6.43042	−	6.43042i	−0.303470	−	0.303470i	−0.842370	+	0.538900i	$0.818840\pi$
$450$		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	$-0.942060\pi$
$457$		−	7.73959i		−	0.362043i	0.983479	−	0.181021i	$-0.0579403\pi$
$458$		0			0
$459$	4.76085	−	6.41609i	0.222217	−	0.299478i
$460$		0			0
$461$			25.0045i			1.16458i	0.812982	+	0.582289i	$0.197843\pi$
$461$			25.0045i			1.16458i	−0.812982	+	0.582289i	$0.802157\pi$
$462$		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	$0.0919370\pi$
$467$			12.3104i			0.569659i	−0.958578	+	0.284829i	$0.908063\pi$
$468$		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	−0.593807	−	0.804608i	$-0.702376\pi$
$479$	4.61361	−	4.61361i	0.210801	−	0.210801i	0.804608	+	0.593807i	$0.202376\pi$
$480$		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	0.894173	−	0.447721i	$-0.147764\pi$
$487$	9.85234	+	9.85234i	0.446452	+	0.446452i	−0.447721	+	0.894173i	$0.647764\pi$
$488$		0			0
$489$	51.4825			2.32812
$490$		0			0
$491$			0.302247i			0.0136402i	0.999977	+	0.00682010i	$0.00217092\pi$
$491$			0.302247i			0.0136402i	−0.999977	+	0.00682010i	$0.997829\pi$
$492$		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	0.395127	−	0.918627i	$-0.370701\pi$
$499$	−11.6941	−	11.6941i	−0.523500	−	0.523500i	−0.918627	+	0.395127i	$0.870701\pi$
$500$		0			0
$501$			46.3125i			2.06909i
$502$		0			0
$503$	0.399884	+	0.399884i	0.0178300	+	0.0178300i	0.715966	−	0.698136i	$-0.245987\pi$
$503$	0.399884	+	0.399884i	0.0178300	+	0.0178300i	−0.698136	+	0.715966i	$0.745987\pi$
$504$		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	0.490850	−	0.871244i	$-0.336686\pi$
$521$	−8.68265	−	8.68265i	−0.380394	−	0.380394i	−0.871244	+	0.490850i	$0.836686\pi$
$522$		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	−0.520708	−	0.853735i	$-0.674332\pi$
$541$	7.74601	−	7.74601i	0.333027	−	0.333027i	0.853735	+	0.520708i	$0.174332\pi$
$542$		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	−0.892118	−	0.451802i	$-0.850781\pi$
$547$	−10.2981	+	10.2981i	−0.440316	+	0.440316i	0.451802	+	0.892118i	$0.350781\pi$
$548$		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	$0.108277\pi$
$563$			15.8330i			0.667280i	−0.942701	+	0.333640i	$0.891723\pi$
$564$		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	$0.102011\pi$
$569$			15.0288i			0.630039i	−0.949085	+	0.315019i	$0.897989\pi$
$570$		0			0
$571$	−4.81410	−	4.81410i	−0.201464	−	0.201464i	0.599163	−	0.800627i	$-0.295500\pi$
$571$	−4.81410	−	4.81410i	−0.201464	−	0.201464i	−0.800627	+	0.599163i	$0.795500\pi$
$572$		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	$-0.679029\pi$
$587$		−	40.9919i		−	1.69192i	0.533248	−	0.845959i	$-0.320971\pi$
$588$		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	$0.0822087\pi$
$593$			12.4390i			0.510809i	−0.966834	+	0.255405i	$0.917791\pi$
$594$		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	0.739678	−	0.672961i	$-0.234978\pi$
$601$	1.63560	+	1.63560i	0.0667176	+	0.0667176i	−0.672961	+	0.739678i	$0.734978\pi$
$602$		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	−0.224422	−	0.974492i	$-0.572049\pi$
$607$	18.4798	−	18.4798i	0.750070	−	0.750070i	0.974492	+	0.224422i	$0.0720494\pi$
$608$		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	0.0886418	−	0.996064i	$-0.471747\pi$
$617$	26.9435	−	26.9435i	1.08471	−	1.08471i	0.996064	−	0.0886418i	$-0.0282526\pi$
$618$		0			0
$619$	24.1574	+	24.1574i	0.970966	+	0.970966i	0.999590	−	0.0286241i	$-0.00911257\pi$
$619$	24.1574	+	24.1574i	0.970966	+	0.970966i	−0.0286241	+	0.999590i	$0.509113\pi$
$620$		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	$-0.780400\pi$
$631$		−	31.9751i		−	1.27291i	0.771314	−	0.636454i	$-0.219600\pi$
$632$		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	−0.315649	+	0.948876i	$0.602222\pi$
$641$	−32.0152	+	32.0152i	−1.26453	+	1.26453i	−0.948876	+	0.315649i	$0.897778\pi$
$642$		0			0
$643$	24.9629	−	24.9629i	0.984439	−	0.984439i	−0.0154416	−	0.999881i	$-0.504915\pi$
$643$	24.9629	−	24.9629i	0.984439	−	0.984439i	0.999881	+	0.0154416i	$0.00491542\pi$
$644$		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	0.892149	−	0.451742i	$-0.149197\pi$
$653$	11.2541	+	11.2541i	0.440407	+	0.440407i	−0.451742	+	0.892149i	$0.649197\pi$
$654$		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	$-0.924255\pi$
$661$		−	12.1208i		−	0.471443i	0.971821	−	0.235722i	$-0.0757454\pi$
$662$		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	0.315083	−	0.949064i	$-0.397968\pi$
$673$	−16.4469	−	16.4469i	−0.633981	−	0.633981i	−0.949064	+	0.315083i	$0.897968\pi$
$674$		0			0
$675$	−1.37019	+	1.37019i	−0.0527385	+	0.0527385i
$676$		0			0
$677$	−1.45511	+	1.45511i	−0.0559245	+	0.0559245i	−0.734516	−	0.678591i	$-0.762591\pi$
$677$	−1.45511	+	1.45511i	−0.0559245	+	0.0559245i	0.678591	+	0.734516i	$0.262591\pi$
$678$		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	−0.495806	−	0.868433i	$-0.665127\pi$
$683$	9.73834	−	9.73834i	0.372627	−	0.372627i	0.868433	+	0.495806i	$0.165127\pi$
$684$		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	0.379041	−	0.925380i	$-0.376254\pi$
$691$	−14.3615	−	14.3615i	−0.546338	−	0.546338i	−0.925380	+	0.379041i	$0.876254\pi$
$692$		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	−0.498637	+	0.866811i	$0.666166\pi$
$709$	−36.3578	+	36.3578i	−1.36545	+	1.36545i	−0.866811	+	0.498637i	$0.833834\pi$
$710$		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	−0.175443	+	0.984490i	$0.556136\pi$
$719$	−31.1026	+	31.1026i	−1.15993	+	1.15993i	−0.984490	+	0.175443i	$0.943864\pi$
$720$		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	$-0.943064\pi$
$733$		−	9.63393i		−	0.355837i	0.984045	−	0.177919i	$-0.0569364\pi$
$734$		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	$0.217883\pi$
$739$			34.3768i			1.26457i	−0.774736	+	0.632285i	$0.782117\pi$
$740$		0			0
$741$	−39.6856	−	39.6856i	−1.45789	−	1.45789i
$742$		0			0
$743$	−10.4068	+	10.4068i	−0.381789	+	0.381789i	−0.871746	−	0.489958i	$-0.837012\pi$
$743$	−10.4068	+	10.4068i	−0.381789	+	0.381789i	0.489958	+	0.871746i	$0.337012\pi$
$744$		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	−0.651056	−	0.759030i	$-0.725674\pi$
$751$	2.95895	−	2.95895i	0.107974	−	0.107974i	0.759030	+	0.651056i	$0.225674\pi$
$752$		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	$-0.860211\pi$
$757$		−	23.3964i		−	0.850357i	0.905110	−	0.425178i	$-0.139789\pi$
$758$		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	$0.192938\pi$
$773$			31.6782i			1.13939i	−0.821857	+	0.569693i	$0.807062\pi$
$774$		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	−0.451671	−	0.892184i	$-0.649172\pi$
$787$	12.3579	−	12.3579i	0.440513	−	0.440513i	0.892184	+	0.451671i	$0.149172\pi$
$788$		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	$0.0808637\pi$
$797$			14.1900i			0.502634i	−0.967905	+	0.251317i	$0.919136\pi$
$798$		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	0.941980	−	0.335668i	$-0.108962\pi$
$809$	17.2453	+	17.2453i	0.606312	+	0.606312i	−0.335668	+	0.941980i	$0.608962\pi$
$810$		0			0
$811$	9.10566	−	9.10566i	0.319743	−	0.319743i	−0.528925	−	0.848668i	$-0.677405\pi$
$811$	9.10566	−	9.10566i	0.319743	−	0.319743i	0.848668	+	0.528925i	$0.177405\pi$
$812$		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	−0.432251	−	0.901754i	$-0.642280\pi$
$821$	13.4527	−	13.4527i	0.469503	−	0.469503i	0.901754	+	0.432251i	$0.142280\pi$
$822$		0			0
$823$	11.4872	+	11.4872i	0.400417	+	0.400417i	0.878380	−	0.477963i	$-0.158625\pi$
$823$	11.4872	+	11.4872i	0.400417	+	0.400417i	−0.477963	+	0.878380i	$0.658625\pi$
$824$		0			0
$825$			5.86568i			0.204217i
$826$		0			0
$827$	12.4889	+	12.4889i	0.434283	+	0.434283i	0.890082	−	0.455800i	$-0.150647\pi$
$827$	12.4889	+	12.4889i	0.434283	+	0.434283i	−0.455800	+	0.890082i	$0.650647\pi$
$828$		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	0.296368	−	0.955074i	$-0.404224\pi$
$839$	−19.0797	−	19.0797i	−0.658705	−	0.658705i	−0.955074	+	0.296368i	$0.904224\pi$
$840$		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	−0.892485	−	0.451078i	$-0.851040\pi$
$853$	−12.8918	+	12.8918i	−0.441407	+	0.441407i	0.451078	+	0.892485i	$0.351040\pi$
$854$		0			0
$855$	−6.60605	+	6.60605i	−0.225922	+	0.225922i
$856$		0			0
$857$	−7.32470	−	7.32470i	−0.250207	−	0.250207i	0.570848	−	0.821055i	$-0.306614\pi$
$857$	−7.32470	−	7.32470i	−0.250207	−	0.250207i	−0.821055	+	0.570848i	$0.806614\pi$
$858$		0			0
$859$			54.5456i			1.86107i	0.366202	+	0.930535i	$0.380658\pi$
$859$			54.5456i			1.86107i	−0.366202	+	0.930535i	$0.619342\pi$
$860$		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	0.962443	−	0.271485i	$-0.0875147\pi$
$877$	20.4621	+	20.4621i	0.690958	+	0.690958i	−0.271485	+	0.962443i	$0.587515\pi$
$878$		0			0
$879$	47.5632	−	47.5632i	1.60427	−	1.60427i
$880$		0			0
$881$	13.0607	−	13.0607i	0.440026	−	0.440026i	−0.451994	−	0.892021i	$-0.649287\pi$
$881$	13.0607	−	13.0607i	0.440026	−	0.440026i	0.892021	+	0.451994i	$0.149287\pi$
$882$		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	−0.413512	−	0.910499i	$-0.635698\pi$
$887$	14.8015	−	14.8015i	0.496987	−	0.496987i	0.910499	+	0.413512i	$0.135698\pi$
$888$		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	0.956812	−	0.290709i	$-0.0938911\pi$
$907$	20.0606	+	20.0606i	0.666103	+	0.666103i	−0.290709	+	0.956812i	$0.593891\pi$
$908$		0			0
$909$		−	16.4299i		−	0.544947i
$910$		0			0
$911$	19.9375	+	19.9375i	0.660560	+	0.660560i	0.955512	−	0.294952i	$-0.0953038\pi$
$911$	19.9375	+	19.9375i	0.660560	+	0.660560i	−0.294952	+	0.955512i	$0.595304\pi$
$912$		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	0.815901	−	0.578191i	$-0.196241\pi$
$929$	7.24530	+	7.24530i	0.237711	+	0.237711i	−0.578191	+	0.815901i	$0.696241\pi$
$930$		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	$-0.903126\pi$
$937$		−	18.3456i		−	0.599326i	0.954045	−	0.299663i	$-0.0968743\pi$
$938$		0			0
$939$	−4.46016			−0.145552
$940$		0			0
$941$	−0.741002	−	0.741002i	−0.0241560	−	0.0241560i	0.694926	−	0.719082i	$-0.255437\pi$
$941$	−0.741002	−	0.741002i	−0.0241560	−	0.0241560i	−0.719082	+	0.694926i	$0.755437\pi$
$942$		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	−0.986889	−	0.161402i	$-0.948399\pi$
$947$	−25.4030	+	25.4030i	−0.825487	+	0.825487i	0.161402	+	0.986889i	$0.448399\pi$
$948$		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	$-0.832902\pi$
$967$		−	31.1696i		−	1.00235i	0.865347	−	0.501173i	$-0.167098\pi$
$968$		0			0
$969$	−24.2654	+	32.7019i	−0.779516	+	1.05054i
$970$		0			0
$971$			19.6962i			0.632081i	0.948746	+	0.316041i	$0.102354\pi$
$971$			19.6962i			0.632081i	−0.948746	+	0.316041i	$0.897646\pi$
$972$		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	$0.105837\pi$
$977$			20.4047i			0.652806i	−0.945231	+	0.326403i	$0.894163\pi$
$978$		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	−0.382382	−	0.924004i	$-0.624896\pi$
$983$	16.9814	−	16.9814i	0.541623	−	0.541623i	0.924004	+	0.382382i	$0.124896\pi$
$984$		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	−0.937781	−	0.347228i	$-0.887123\pi$
$991$	−18.5907	+	18.5907i	−0.590552	+	0.590552i	0.347228	+	0.937781i	$0.387123\pi$
$992$		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	0.227777	−	0.973713i	$-0.426854\pi$
$997$	−23.5532	−	23.5532i	−0.745937	−	0.745937i	−0.973713	+	0.227777i	$0.926854\pi$
$998$		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.1041.2		8
4.3	odd	2		170.2.h.b.21.3	✓	8
12.11	even	2		1530.2.q.g.361.2		8
17.13	even	4	inner	1360.2.bt.b.81.2		8
20.3	even	4		850.2.g.i.599.3		8
20.7	even	4		850.2.g.l.599.2		8
20.19	odd	2		850.2.h.n.701.2		8
68.15	odd	8		2890.2.b.o.2311.6		8
68.19	odd	8		2890.2.b.o.2311.3		8
68.43	odd	8		2890.2.a.bd.1.4		4
68.47	odd	4		170.2.h.b.81.3	yes	8
68.59	odd	8		2890.2.a.be.1.1		4
204.47	even	4		1530.2.q.g.1441.2		8
340.47	even	4		850.2.g.i.149.3		8
340.183	even	4		850.2.g.l.149.2		8
340.319	odd	4		850.2.h.n.251.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.h.b.21.3	✓	8	4.3	odd	2
170.2.h.b.81.3	yes	8	68.47	odd	4
850.2.g.i.149.3		8	340.47	even	4
850.2.g.i.599.3		8	20.3	even	4
850.2.g.l.149.2		8	340.183	even	4
850.2.g.l.599.2		8	20.7	even	4
850.2.h.n.251.2		8	340.319	odd	4
850.2.h.n.701.2		8	20.19	odd	2
1360.2.bt.b.81.2		8	17.13	even	4	inner
1360.2.bt.b.1041.2		8	1.1	even	1	trivial
1530.2.q.g.361.2		8	12.11	even	2
1530.2.q.g.1441.2		8	204.47	even	4
2890.2.a.bd.1.4		4	68.43	odd	8
2890.2.a.be.1.1		4	68.59	odd	8
2890.2.b.o.2311.3		8	68.19	odd	8
2890.2.b.o.2311.6		8	68.15	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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