LMFDB - Embedded newform 1380.2.r.c.737.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(737,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))

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

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

chi := DirichletCharacter("1380.737");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.r (of order $4$, degree $2$, 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:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.13
Character	$\chi$	$=$	1380.737
Dual form			1380.2.r.c.1013.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.966965 + 1.43700i) q^{3} +(-1.81165 - 1.31070i) q^{5} +(-2.64771 - 2.64771i) q^{7} +(-1.12996 - 2.77906i) q^{9} +O(q^{10})$	\(q+(-0.966965 + 1.43700i) q^{3} +(-1.81165 - 1.31070i) q^{5} +(-2.64771 - 2.64771i) q^{7} +(-1.12996 - 2.77906i) q^{9} -2.76062i q^{11} +(0.104331 - 0.104331i) q^{13} +(3.63528 - 1.33594i) q^{15} +(-2.67342 + 2.67342i) q^{17} +2.65891i q^{19} +(6.36501 - 1.24453i) q^{21} +(0.707107 + 0.707107i) q^{23} +(1.56412 + 4.74906i) q^{25} +(5.08615 + 1.06351i) q^{27} -4.22901 q^{29} +0.729179 q^{31} +(3.96702 + 2.66942i) q^{33} +(1.32635 + 8.26708i) q^{35} +(7.92128 + 7.92128i) q^{37} +(0.0490395 + 0.250808i) q^{39} -6.15656i q^{41} +(-1.91148 + 1.91148i) q^{43} +(-1.59544 + 6.51572i) q^{45} +(-2.01115 + 2.01115i) q^{47} +7.02075i q^{49} +(-1.25661 - 6.42682i) q^{51} +(8.22968 + 8.22968i) q^{53} +(-3.61835 + 5.00127i) q^{55} +(-3.82086 - 2.57107i) q^{57} -4.37898 q^{59} +7.62990 q^{61} +(-4.36636 + 10.3500i) q^{63} +(-0.325757 + 0.0522639i) q^{65} +(-0.641130 - 0.641130i) q^{67} +(-1.69986 + 0.332367i) q^{69} -9.31083i q^{71} +(-7.61503 + 7.61503i) q^{73} +(-8.33686 - 2.34452i) q^{75} +(-7.30933 + 7.30933i) q^{77} +11.8828i q^{79} +(-6.44639 + 6.28045i) q^{81} +(-11.2483 - 11.2483i) q^{83} +(8.34735 - 1.33923i) q^{85} +(4.08931 - 6.07710i) q^{87} +5.92131 q^{89} -0.552476 q^{91} +(-0.705091 + 1.04783i) q^{93} +(3.48504 - 4.81700i) q^{95} +(-1.27607 - 1.27607i) q^{97} +(-7.67194 + 3.11938i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 8 q^{3}+O(q^{10}) $ 80 * q + 8 * q^3	$ 80 q + 8 q^{3} + 32 q^{13} + 24 q^{21} - 32 q^{25} - 28 q^{27} - 32 q^{31} - 44 q^{33} + 24 q^{37} - 32 q^{43} + 88 q^{45} + 16 q^{51} + 8 q^{55} + 16 q^{57} - 32 q^{61} - 12 q^{63} - 16 q^{67} - 32 q^{73} + 4 q^{75} - 64 q^{81} - 32 q^{85} + 64 q^{91} + 8 q^{93} - 96 q^{97}+O(q^{100}) $ 80 * q + 8 * q^3 + 32 * q^13 + 24 * q^21 - 32 * q^25 - 28 * q^27 - 32 * q^31 - 44 * q^33 + 24 * q^37 - 32 * q^43 + 88 * q^45 + 16 * q^51 + 8 * q^55 + 16 * q^57 - 32 * q^61 - 12 * q^63 - 16 * q^67 - 32 * q^73 + 4 * q^75 - 64 * q^81 - 32 * q^85 + 64 * q^91 + 8 * q^93 - 96 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$1$

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
$3$	−0.966965	+	1.43700i	−0.558278	+	0.829654i
$3$	−0.966965	+	1.43700i	−0.558278	+	0.829654i
$4$		0			0
$5$	−1.81165	−	1.31070i	−0.810193	−	0.586164i
$5$	−1.81165	−	1.31070i	−0.810193	−	0.586164i
$6$		0			0
$7$	−2.64771	−	2.64771i	−1.00074	−	1.00074i	−1.00000		0.000741135i	$-0.999764\pi$
$7$	−2.64771	−	2.64771i	−1.00074	−	1.00074i	−0.000741135	−	1.00000i	$-0.500236\pi$
$8$		0			0
$9$	−1.12996	−	2.77906i	−0.376652	−	0.926355i
$10$		0			0
$11$		−	2.76062i		−	0.832359i	−0.909283	−	0.416179i	$-0.863369\pi$
$11$		−	2.76062i		−	0.832359i	0.909283	−	0.416179i	$-0.136631\pi$
$12$		0			0
$13$	0.104331	−	0.104331i	0.0289362	−	0.0289362i	−0.692491	−	0.721427i	$-0.743487\pi$
$13$	0.104331	−	0.104331i	0.0289362	−	0.0289362i	0.721427	+	0.692491i	$0.243487\pi$
$14$		0			0
$15$	3.63528	−	1.33594i	0.938626	−	0.344938i
$16$		0			0
$17$	−2.67342	+	2.67342i	−0.648400	+	0.648400i	−0.952606	−	0.304206i	$-0.901609\pi$
$17$	−2.67342	+	2.67342i	−0.648400	+	0.648400i	0.304206	+	0.952606i	$0.401609\pi$
$18$		0			0
$19$			2.65891i			0.609995i	0.952353	+	0.304998i	$0.0986557\pi$
$19$			2.65891i			0.609995i	−0.952353	+	0.304998i	$0.901344\pi$
$20$		0			0
$21$	6.36501	−	1.24453i	1.38896	−	0.271578i
$22$		0			0
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$		0			0
$25$	1.56412	+	4.74906i	0.312824	+	0.949811i
$26$		0			0
$27$	5.08615	+	1.06351i	0.978831	+	0.204672i
$28$		0			0
$29$	−4.22901			−0.785308			−0.392654	−	0.919686i	$-0.628443\pi$
$29$	−4.22901			−0.785308			−0.392654	+	0.919686i	$0.628443\pi$
$30$		0			0
$31$	0.729179			0.130964			0.0654822	−	0.997854i	$-0.479141\pi$
$31$	0.729179			0.130964			0.0654822	+	0.997854i	$0.479141\pi$
$32$		0			0
$33$	3.96702	+	2.66942i	0.690570	+	0.464687i
$34$		0			0
$35$	1.32635	+	8.26708i	0.224195	+	1.39739i
$36$		0			0
$37$	7.92128	+	7.92128i	1.30225	+	1.30225i	0.926872	+	0.375378i	$0.122487\pi$
$37$	7.92128	+	7.92128i	1.30225	+	1.30225i	0.375378	+	0.926872i	$0.377513\pi$
$38$		0			0
$39$	0.0490395	+	0.250808i	0.00785260	+	0.0401614i
$40$		0			0
$41$		−	6.15656i		−	0.961494i	−0.876859	−	0.480747i	$-0.840366\pi$
$41$		−	6.15656i		−	0.961494i	0.876859	−	0.480747i	$-0.159634\pi$
$42$		0			0
$43$	−1.91148	+	1.91148i	−0.291498	+	0.291498i	−0.837672	−	0.546174i	$-0.816084\pi$
$43$	−1.91148	+	1.91148i	−0.291498	+	0.291498i	0.546174	+	0.837672i	$0.316084\pi$
$44$		0			0
$45$	−1.59544	+	6.51572i	−0.237835	+	0.971306i
$46$		0			0
$47$	−2.01115	+	2.01115i	−0.293357	+	0.293357i	−0.838405	−	0.545048i	$-0.816511\pi$
$47$	−2.01115	+	2.01115i	−0.293357	+	0.293357i	0.545048	+	0.838405i	$0.316511\pi$
$48$		0			0
$49$			7.02075i			1.00296i
$50$		0			0
$51$	−1.25661	−	6.42682i	−0.175961	−	0.899935i
$52$		0			0
$53$	8.22968	+	8.22968i	1.13043	+	1.13043i	0.990105	+	0.140328i	$0.0448158\pi$
$53$	8.22968	+	8.22968i	1.13043	+	1.13043i	0.140328	+	0.990105i	$0.455184\pi$
$54$		0			0
$55$	−3.61835	+	5.00127i	−0.487898	+	0.674371i
$56$		0			0
$57$	−3.82086	−	2.57107i	−0.506085	−	0.340547i
$58$		0			0
$59$	−4.37898			−0.570094			−0.285047	−	0.958514i	$-0.592009\pi$
$59$	−4.37898			−0.570094			−0.285047	+	0.958514i	$0.592009\pi$
$60$		0			0
$61$	7.62990			0.976908			0.488454	−	0.872590i	$-0.337561\pi$
$61$	7.62990			0.976908			0.488454	+	0.872590i	$0.337561\pi$
$62$		0			0
$63$	−4.36636	+	10.3500i	−0.550110	+	1.30397i
$64$		0			0
$65$	−0.325757	+	0.0522639i	−0.0404052	+	0.00648253i
$66$		0			0
$67$	−0.641130	−	0.641130i	−0.0783264	−	0.0783264i	0.666858	−	0.745185i	$-0.267639\pi$
$67$	−0.641130	−	0.641130i	−0.0783264	−	0.0783264i	−0.745185	+	0.666858i	$0.767639\pi$
$68$		0			0
$69$	−1.69986	+	0.332367i	−0.204639	+	0.0400123i
$70$		0			0
$71$		−	9.31083i		−	1.10499i	−0.833515	−	0.552496i	$-0.813675\pi$
$71$		−	9.31083i		−	1.10499i	0.833515	−	0.552496i	$-0.186325\pi$
$72$		0			0
$73$	−7.61503	+	7.61503i	−0.891272	+	0.891272i	−0.994643	−	0.103371i	$-0.967037\pi$
$73$	−7.61503	+	7.61503i	−0.891272	+	0.891272i	0.103371	+	0.994643i	$0.467037\pi$
$74$		0			0
$75$	−8.33686	−	2.34452i	−0.962657	−	0.270722i
$76$		0			0
$77$	−7.30933	+	7.30933i	−0.832975	+	0.832975i
$78$		0			0
$79$			11.8828i			1.33692i	0.743748	+	0.668460i	$0.233046\pi$
$79$			11.8828i			1.33692i	−0.743748	+	0.668460i	$0.766954\pi$
$80$		0			0
$81$	−6.44639	+	6.28045i	−0.716266	+	0.697827i
$82$		0			0
$83$	−11.2483	−	11.2483i	−1.23466	−	1.23466i	−0.962154	−	0.272506i	$-0.912148\pi$
$83$	−11.2483	−	11.2483i	−1.23466	−	1.23466i	−0.272506	−	0.962154i	$-0.587852\pi$
$84$		0			0
$85$	8.34735	−	1.33923i	0.905398	−	0.145260i
$86$		0			0
$87$	4.08931	−	6.07710i	0.438420	−	0.651534i
$88$		0			0
$89$	5.92131			0.627658			0.313829	−	0.949480i	$-0.398388\pi$
$89$	5.92131			0.627658			0.313829	+	0.949480i	$0.398388\pi$
$90$		0			0
$91$	−0.552476			−0.0579152
$92$		0			0
$93$	−0.705091	+	1.04783i	−0.0731145	+	0.108655i
$94$		0			0
$95$	3.48504	−	4.81700i	0.357557	−	0.494214i
$96$		0			0
$97$	−1.27607	−	1.27607i	−0.129566	−	0.129566i	0.639350	−	0.768916i	$-0.279203\pi$
$97$	−1.27607	−	1.27607i	−0.129566	−	0.129566i	−0.768916	+	0.639350i	$0.779203\pi$
$98$		0			0
$99$	−7.67194	+	3.11938i	−0.771059	+	0.313510i
$100$		0			0
$101$		−	10.0451i		−	0.999524i	−0.866163	−	0.499762i	$-0.833421\pi$
$101$		−	10.0451i		−	0.999524i	0.866163	−	0.499762i	$-0.166579\pi$
$102$		0			0
$103$	−0.894069	+	0.894069i	−0.0880952	+	0.0880952i	−0.749781	−	0.661686i	$-0.769841\pi$
$103$	−0.894069	+	0.894069i	−0.0880952	+	0.0880952i	0.661686	+	0.749781i	$0.269841\pi$
$104$		0			0
$105$	−13.1624	−	6.08800i	−1.28451	−	0.594128i
$106$		0			0
$107$	−2.85219	+	2.85219i	−0.275731	+	0.275731i	−0.831402	−	0.555671i	$-0.812461\pi$
$107$	−2.85219	+	2.85219i	−0.275731	+	0.275731i	0.555671	+	0.831402i	$0.312461\pi$
$108$		0			0
$109$			17.2383i			1.65113i	0.564310	+	0.825563i	$0.309142\pi$
$109$			17.2383i			1.65113i	−0.564310	+	0.825563i	$0.690858\pi$
$110$		0			0
$111$	−19.0425	+	3.72330i	−1.80743	+	0.353400i
$112$		0			0
$113$	10.4914	+	10.4914i	0.986947	+	0.986947i	0.999916	−	0.0129685i	$-0.00412811\pi$
$113$	10.4914	+	10.4914i	0.986947	+	0.986947i	−0.0129685	+	0.999916i	$0.504128\pi$
$114$		0			0
$115$	−0.354221	−	2.20783i	−0.0330312	−	0.205882i
$116$		0			0
$117$	−0.407831	−	0.172053i	−0.0377040	−	0.0159063i
$118$		0			0
$119$	14.1569			1.29776
$120$		0			0
$121$	3.37897			0.307179
$122$		0			0
$123$	8.84700	+	5.95318i	0.797707	+	0.536780i
$124$		0			0
$125$	3.39097	−	10.6537i	0.303297	−	0.952896i
$126$		0			0
$127$	2.77884	+	2.77884i	0.246582	+	0.246582i	0.819566	−	0.572984i	$-0.194214\pi$
$127$	2.77884	+	2.77884i	0.246582	+	0.246582i	−0.572984	+	0.819566i	$0.694214\pi$
$128$		0			0
$129$	−0.898469	−	4.59514i	−0.0791058	−	0.404580i
$130$		0			0
$131$		−	7.92031i		−	0.692000i	−0.938234	−	0.346000i	$-0.887540\pi$
$131$		−	7.92031i		−	0.692000i	0.938234	−	0.346000i	$-0.112460\pi$
$132$		0			0
$133$	7.04002	−	7.04002i	0.610447	−	0.610447i
$134$		0			0
$135$	−7.82037	−	8.59313i	−0.673070	−	0.739579i
$136$		0			0
$137$	−10.0837	+	10.0837i	−0.861513	+	0.861513i	−0.991514	−	0.130001i	$-0.958502\pi$
$137$	−10.0837	+	10.0837i	−0.861513	+	0.861513i	0.130001	+	0.991514i	$0.458502\pi$
$138$		0			0
$139$		−	12.4291i		−	1.05423i	−0.849795	−	0.527113i	$-0.823275\pi$
$139$		−	12.4291i		−	1.05423i	0.849795	−	0.527113i	$-0.176725\pi$
$140$		0			0
$141$	−0.945319	−	4.83475i	−0.0796102	−	0.407159i
$142$		0			0
$143$	−0.288018	−	0.288018i	−0.0240853	−	0.0240853i
$144$		0			0
$145$	7.66147	+	5.54298i	0.636251	+	0.460319i
$146$		0			0
$147$	−10.0888	−	6.78882i	−0.832114	−	0.559933i
$148$		0			0
$149$	−11.9231			−0.976782			−0.488391	−	0.872625i	$-0.662416\pi$
$149$	−11.9231			−0.976782			−0.488391	+	0.872625i	$0.662416\pi$
$150$		0			0
$151$	9.86347			0.802678			0.401339	−	0.915930i	$-0.368545\pi$
$151$	9.86347			0.802678			0.401339	+	0.915930i	$0.368545\pi$
$152$		0			0
$153$	10.4505	+	4.40876i	0.844870	+	0.356427i
$154$		0			0
$155$	−1.32101	−	0.955737i	−0.106106	−	0.0767666i
$156$		0			0
$157$	10.1279	+	10.1279i	0.808293	+	0.808293i	0.984375	−	0.176082i	$-0.0563425\pi$
$157$	10.1279	+	10.1279i	0.808293	+	0.808293i	−0.176082	+	0.984375i	$0.556343\pi$
$158$		0			0
$159$	−19.7839	+	3.86826i	−1.56896	+	0.306773i
$160$		0			0
$161$		−	3.74443i		−	0.295102i
$162$		0			0
$163$	−4.62574	+	4.62574i	−0.362316	+	0.362316i	−0.864665	−	0.502349i	$-0.832469\pi$
$163$	−4.62574	+	4.62574i	−0.362316	+	0.362316i	0.502349	+	0.864665i	$0.332469\pi$
$164$		0			0
$165$	−3.68802	−	10.0356i	−0.287112	−	0.781273i
$166$		0			0
$167$	−13.6343	+	13.6343i	−1.05505	+	1.05505i	−0.0566563	+	0.998394i	$0.518044\pi$
$167$	−13.6343	+	13.6343i	−1.05505	+	1.05505i	−0.998394	+	0.0566563i	$0.981956\pi$
$168$		0			0
$169$			12.9782i			0.998325i
$170$		0			0
$171$	7.38928	−	3.00445i	0.565072	−	0.229756i
$172$		0			0
$173$	8.81716	+	8.81716i	0.670356	+	0.670356i	0.957798	−	0.287442i	$-0.0928048\pi$
$173$	8.81716	+	8.81716i	0.670356	+	0.670356i	−0.287442	+	0.957798i	$0.592805\pi$
$174$		0			0
$175$	8.43279	−	16.7155i	0.637459	−	1.26357i
$176$		0			0
$177$	4.23432	−	6.29260i	0.318271	−	0.472981i
$178$		0			0
$179$	7.89477			0.590083			0.295042	−	0.955484i	$-0.404666\pi$
$179$	7.89477			0.590083			0.295042	+	0.955484i	$0.404666\pi$
$180$		0			0
$181$	20.6973			1.53842			0.769210	−	0.638996i	$-0.220650\pi$
$181$	20.6973			1.53842			0.769210	+	0.638996i	$0.220650\pi$
$182$		0			0
$183$	−7.37784	+	10.9642i	−0.545386	+	0.810496i
$184$		0			0
$185$	−3.96811	−	24.7330i	−0.291741	−	1.81841i
$186$		0			0
$187$	7.38031	+	7.38031i	0.539701	+	0.539701i
$188$		0			0
$189$	−10.6508	−	16.2825i	−0.774732	−	1.18438i
$190$		0			0
$191$			16.0971i			1.16474i	0.812922	+	0.582372i	$0.197875\pi$
$191$			16.0971i			1.16474i	−0.812922	+	0.582372i	$0.802125\pi$
$192$		0			0
$193$	3.16109	−	3.16109i	0.227541	−	0.227541i	−0.584124	−	0.811664i	$-0.698562\pi$
$193$	3.16109	−	3.16109i	0.227541	−	0.227541i	0.811664	+	0.584124i	$0.198562\pi$
$194$		0			0
$195$	0.239892	−	0.518651i	0.0171791	−	0.0371414i
$196$		0			0
$197$	−2.50872	+	2.50872i	−0.178739	+	0.178739i	−0.790806	−	0.612067i	$-0.790338\pi$
$197$	−2.50872	+	2.50872i	−0.178739	+	0.178739i	0.612067	+	0.790806i	$0.290338\pi$
$198$		0			0
$199$		−	5.66274i		−	0.401421i	−0.979651	−	0.200710i	$-0.935675\pi$
$199$		−	5.66274i		−	0.401421i	0.979651	−	0.200710i	$-0.0643250\pi$
$200$		0			0
$201$	1.54126	−	0.301355i	0.108712	−	0.0212560i
$202$		0			0
$203$	11.1972	+	11.1972i	0.785890	+	0.785890i
$204$		0			0
$205$	−8.06942	+	11.1535i	−0.563593	+	0.778995i
$206$		0			0
$207$	1.16609	−	2.76410i	0.0810492	−	0.192118i
$208$		0			0
$209$	7.34024			0.507735
$210$		0			0
$211$	−12.5957			−0.867121			−0.433561	−	0.901124i	$-0.642743\pi$
$211$	−12.5957			−0.867121			−0.433561	+	0.901124i	$0.642743\pi$
$212$		0			0
$213$	13.3797	+	9.00325i	0.916762	+	0.616893i
$214$		0			0
$215$	5.96831	−	0.957544i	0.407035	−	0.0653040i
$216$		0			0
$217$	−1.93066	−	1.93066i	−0.131061	−	0.131061i
$218$		0			0
$219$	−3.57936	−	18.3063i	−0.241870	−	1.23702i
$220$		0			0
$221$			0.557841i			0.0375244i
$222$		0			0
$223$	3.86808	−	3.86808i	0.259025	−	0.259025i	−0.565632	−	0.824658i	$-0.691368\pi$
$223$	3.86808	−	3.86808i	0.259025	−	0.259025i	0.824658	+	0.565632i	$0.191368\pi$
$224$		0			0
$225$	11.4305	−	9.71302i	0.762036	−	0.647535i
$226$		0			0
$227$	15.2290	−	15.2290i	1.01079	−	1.01079i	0.0108447	−	0.999941i	$-0.496548\pi$
$227$	15.2290	−	15.2290i	1.01079	−	1.01079i	0.999941	−	0.0108447i	$-0.00345204\pi$
$228$		0			0
$229$		−	13.2562i		−	0.875991i	−0.898977	−	0.437996i	$-0.855689\pi$
$229$		−	13.2562i		−	0.875991i	0.898977	−	0.437996i	$-0.144311\pi$
$230$		0			0
$231$	−3.43566	−	17.5714i	−0.226050	−	1.15611i
$232$		0			0
$233$	−5.57053	−	5.57053i	−0.364938	−	0.364938i	0.500689	−	0.865627i	$-0.333080\pi$
$233$	−5.57053	−	5.57053i	−0.364938	−	0.364938i	−0.865627	+	0.500689i	$0.833080\pi$
$234$		0			0
$235$	6.27952	−	1.00747i	0.409631	−	0.0657204i
$236$		0			0
$237$	−17.0756	−	11.4903i	−1.10918	−	0.746373i
$238$		0			0
$239$	−4.32756			−0.279927			−0.139963	−	0.990157i	$-0.544698\pi$
$239$	−4.32756			−0.279927			−0.139963	+	0.990157i	$0.544698\pi$
$240$		0			0
$241$	−1.98173			−0.127654			−0.0638271	−	0.997961i	$-0.520331\pi$
$241$	−1.98173			−0.127654			−0.0638271	+	0.997961i	$0.520331\pi$
$242$		0			0
$243$	−2.79159	−	15.3365i	−0.179080	−	0.983834i
$244$		0			0
$245$	9.20211	−	12.7191i	0.587901	−	0.812594i
$246$		0			0
$247$	0.277406	+	0.277406i	0.0176509	+	0.0176509i
$248$		0			0
$249$	27.0405	−	5.28713i	1.71362	−	0.335058i
$250$		0			0
$251$			25.0181i			1.57913i	0.613669	+	0.789563i	$0.289693\pi$
$251$			25.0181i			1.57913i	−0.613669	+	0.789563i	$0.710307\pi$
$252$		0			0
$253$	1.95205	−	1.95205i	0.122725	−	0.122725i
$254$		0			0
$255$	−6.14712	+	13.2902i	−0.384947	+	0.832263i
$256$		0			0
$257$	−16.8686	+	16.8686i	−1.05223	+	1.05223i	−0.0536748	+	0.998558i	$0.517093\pi$
$257$	−16.8686	+	16.8686i	−1.05223	+	1.05223i	−0.998558	+	0.0536748i	$0.982907\pi$
$258$		0			0
$259$		−	41.9465i		−	2.60643i
$260$		0			0
$261$	4.77860	+	11.7527i	0.295788	+	0.727474i
$262$		0			0
$263$	13.0698	+	13.0698i	0.805916	+	0.805916i	0.984013	−	0.178097i	$-0.0569940\pi$
$263$	13.0698	+	13.0698i	0.805916	+	0.805916i	−0.178097	+	0.984013i	$0.556994\pi$
$264$		0			0
$265$	−4.12260	−	25.6959i	−0.253250	−	1.57849i
$266$		0			0
$267$	−5.72570	+	8.50894i	−0.350407	+	0.520739i
$268$		0			0
$269$	28.5324			1.73965			0.869825	−	0.493360i	$-0.164231\pi$
$269$	28.5324			1.73965			0.869825	+	0.493360i	$0.164231\pi$
$270$		0			0
$271$	−25.0410			−1.52114			−0.760568	−	0.649259i	$-0.775079\pi$
$271$	−25.0410			−1.52114			−0.760568	+	0.649259i	$0.775079\pi$
$272$		0			0
$273$	0.534225	−	0.793910i	0.0323328	−	0.0480496i
$274$		0			0
$275$	13.1103	−	4.31794i	0.790583	−	0.260382i
$276$		0			0
$277$	1.45901	+	1.45901i	0.0876633	+	0.0876633i	0.749579	−	0.661915i	$-0.230256\pi$
$277$	1.45901	+	1.45901i	0.0876633	+	0.0876633i	−0.661915	+	0.749579i	$0.730256\pi$
$278$		0			0
$279$	−0.823941	−	2.02644i	−0.0493281	−	0.121320i
$280$		0			0
$281$		−	2.89762i		−	0.172858i	−0.996258	−	0.0864289i	$-0.972454\pi$
$281$		−	2.89762i		−	0.172858i	0.996258	−	0.0864289i	$-0.0275455\pi$
$282$		0			0
$283$	7.13148	−	7.13148i	0.423923	−	0.423923i	−0.462629	−	0.886552i	$-0.653094\pi$
$283$	7.13148	−	7.13148i	0.423923	−	0.423923i	0.886552	+	0.462629i	$0.153094\pi$
$284$		0			0
$285$	3.55214	+	9.66588i	0.210410	+	0.572557i
$286$		0			0
$287$	−16.3008	+	16.3008i	−0.962206	+	0.962206i
$288$		0			0
$289$			2.70563i			0.159155i
$290$		0			0
$291$	3.06764	−	0.599803i	0.179828	−	0.0351611i
$292$		0			0
$293$	9.01296	+	9.01296i	0.526543	+	0.526543i	0.919540	−	0.392997i	$-0.128562\pi$
$293$	9.01296	+	9.01296i	0.526543	+	0.526543i	−0.392997	+	0.919540i	$0.628562\pi$
$294$		0			0
$295$	7.93315	+	5.73953i	0.461886	+	0.334168i
$296$		0			0
$297$	2.93594	−	14.0409i	0.170360	−	0.814738i
$298$		0			0
$299$	0.147546			0.00853281
$300$		0			0
$301$	10.1221			0.583428
$302$		0			0
$303$	14.4348	+	9.71326i	0.829260	+	0.558012i
$304$		0			0
$305$	−13.8227	−	10.0005i	−0.791484	−	0.572628i
$306$		0			0
$307$	−20.1861	−	20.1861i	−1.15208	−	1.15208i	−0.986135	−	0.165947i	$-0.946932\pi$
$307$	−20.1861	−	20.1861i	−1.15208	−	1.15208i	−0.165947	−	0.986135i	$-0.553068\pi$
$308$		0			0
$309$	−0.420247	−	2.14931i	−0.0239070	−	0.122270i
$310$		0			0
$311$			8.73575i			0.495359i	0.968842	+	0.247679i	$0.0796680\pi$
$311$			8.73575i			0.495359i	−0.968842	+	0.247679i	$0.920332\pi$
$312$		0			0
$313$	−17.4206	+	17.4206i	−0.984670	+	0.984670i	−0.999884	−	0.0152145i	$-0.995157\pi$
$313$	−17.4206	+	17.4206i	−0.984670	+	0.984670i	0.0152145	+	0.999884i	$0.495157\pi$
$314$		0			0
$315$	21.4760	−	13.0275i	1.21004	−	0.734014i
$316$		0			0
$317$	15.2127	−	15.2127i	0.854430	−	0.854430i	−0.136245	−	0.990675i	$-0.543503\pi$
$317$	15.2127	−	15.2127i	0.854430	−	0.854430i	0.990675	+	0.136245i	$0.0435034\pi$
$318$		0			0
$319$			11.6747i			0.653658i
$320$		0			0
$321$	−1.34064	−	6.85657i	−0.0748271	−	0.382697i
$322$		0			0
$323$	−7.10838	−	7.10838i	−0.395521	−	0.395521i
$324$		0			0
$325$	0.658659	+	0.332287i	0.0365358	+	0.0184320i
$326$		0			0
$327$	−24.7714	−	16.6688i	−1.36986	−	0.921786i
$328$		0			0
$329$	10.6499			0.587148
$330$		0			0
$331$	15.1399			0.832164			0.416082	−	0.909327i	$-0.363403\pi$
$331$	15.1399			0.832164			0.416082	+	0.909327i	$0.363403\pi$
$332$		0			0
$333$	13.0630	−	30.9644i	0.715850	−	1.69684i
$334$		0			0
$335$	0.321170	+	2.00183i	0.0175474	+	0.109372i
$336$		0			0
$337$	−21.5577	−	21.5577i	−1.17432	−	1.17432i	−0.981169	−	0.193152i	$-0.938129\pi$
$337$	−21.5577	−	21.5577i	−1.17432	−	1.17432i	−0.193152	−	0.981169i	$-0.561871\pi$
$338$		0			0
$339$	−25.2210	+	4.93136i	−1.36982	+	0.267835i
$340$		0			0
$341$		−	2.01299i		−	0.109009i
$342$		0			0
$343$	0.0549447	−	0.0549447i	0.00296674	−	0.00296674i
$344$		0			0
$345$	3.51518	+	1.62588i	0.189251	+	0.0875345i
$346$		0			0
$347$	−11.3651	+	11.3651i	−0.610108	+	0.610108i	−0.942974	−	0.332866i	$-0.891984\pi$
$347$	−11.3651	+	11.3651i	−0.610108	+	0.610108i	0.332866	+	0.942974i	$0.391984\pi$
$348$		0			0
$349$		−	13.1795i		−	0.705481i	−0.935721	−	0.352741i	$-0.885250\pi$
$349$		−	13.1795i		−	0.705481i	0.935721	−	0.352741i	$-0.114750\pi$
$350$		0			0
$351$	0.641599	−	0.419686i	0.0342460	−	0.0224012i
$352$		0			0
$353$	−18.3118	−	18.3118i	−0.974640	−	0.974640i	0.0250462	−	0.999686i	$-0.492027\pi$
$353$	−18.3118	−	18.3118i	−0.974640	−	0.974640i	−0.999686	+	0.0250462i	$0.992027\pi$
$354$		0			0
$355$	−12.2037	+	16.8679i	−0.647707	+	0.895257i
$356$		0			0
$357$	−13.6892	+	20.3435i	−0.724511	+	1.07669i
$358$		0			0
$359$	−36.0344			−1.90183			−0.950913	−	0.309460i	$-0.899852\pi$
$359$	−36.0344			−1.90183			−0.950913	+	0.309460i	$0.899852\pi$
$360$		0			0
$361$	11.9302			0.627906
$362$		0			0
$363$	−3.26735	+	4.85559i	−0.171491	+	0.254852i
$364$		0			0
$365$	23.7768	−	3.81470i	1.24453	−	0.199671i
$366$		0			0
$367$	10.6276	+	10.6276i	0.554757	+	0.554757i	0.927810	−	0.373053i	$-0.121689\pi$
$367$	10.6276	+	10.6276i	0.554757	+	0.554757i	−0.373053	+	0.927810i	$0.621689\pi$
$368$		0			0
$369$	−17.1095	+	6.95665i	−0.890684	+	0.362149i
$370$		0			0
$371$		−	43.5796i		−	2.26254i
$372$		0			0
$373$	18.8103	−	18.8103i	0.973959	−	0.973959i	−0.0257103	−	0.999669i	$-0.508185\pi$
$373$	18.8103	−	18.8103i	0.973959	−	0.973959i	0.999669	+	0.0257103i	$0.00818474\pi$
$374$		0			0
$375$	12.0305	+	15.1746i	0.621250	+	0.783612i
$376$		0			0
$377$	−0.441216	+	0.441216i	−0.0227238	+	0.0227238i
$378$		0			0
$379$			10.5004i			0.539367i	0.962949	+	0.269684i	$0.0869191\pi$
$379$			10.5004i			0.539367i	−0.962949	+	0.269684i	$0.913081\pi$
$380$		0			0
$381$	−6.68024	+	1.30616i	−0.342239	+	0.0669166i
$382$		0			0
$383$	−10.6653	−	10.6653i	−0.544972	−	0.544972i	0.380010	−	0.924982i	$-0.375921\pi$
$383$	−10.6653	−	10.6653i	−0.544972	−	0.544972i	−0.924982	+	0.380010i	$0.875921\pi$
$384$		0			0
$385$	22.8223	−	3.66156i	1.16313	−	0.186610i
$386$		0			0
$387$	7.47202	+	3.15224i	0.379824	+	0.160237i
$388$		0			0
$389$	−19.6628			−0.996944			−0.498472	−	0.866906i	$-0.666105\pi$
$389$	−19.6628			−0.996944			−0.498472	+	0.866906i	$0.666105\pi$
$390$		0			0
$391$	−3.78079			−0.191203
$392$		0			0
$393$	11.3815	+	7.65866i	0.574121	+	0.386328i
$394$		0			0
$395$	15.5748	−	21.5274i	0.783654	−	1.08316i
$396$		0			0
$397$	6.32139	+	6.32139i	0.317261	+	0.317261i	0.847714	−	0.530453i	$-0.177978\pi$
$397$	6.32139	+	6.32139i	0.317261	+	0.317261i	−0.530453	+	0.847714i	$0.677978\pi$
$398$		0			0
$399$	3.30908	+	16.9240i	0.165661	+	0.847259i
$400$		0			0
$401$			20.3381i			1.01564i	0.861464	+	0.507818i	$0.169548\pi$
$401$			20.3381i			1.01564i	−0.861464	+	0.507818i	$0.830452\pi$
$402$		0			0
$403$	0.0760759	−	0.0760759i	0.00378961	−	0.00378961i
$404$		0			0
$405$	19.9104	−	2.92864i	0.989355	−	0.145525i
$406$		0			0
$407$	21.8676	−	21.8676i	1.08394	−	1.08394i
$408$		0			0
$409$		−	15.8873i		−	0.785578i	−0.919629	−	0.392789i	$-0.871510\pi$
$409$		−	15.8873i		−	0.785578i	0.919629	−	0.392789i	$-0.128490\pi$
$410$		0			0
$411$	−4.73975	−	24.2410i	−0.233794	−	1.19572i
$412$		0			0
$413$	11.5943	+	11.5943i	0.570516	+	0.570516i
$414$		0			0
$415$	5.63476	+	35.1211i	0.276599	+	1.72403i
$416$		0			0
$417$	17.8607	+	12.0185i	0.874643	+	0.588550i
$418$		0			0
$419$	−13.2765			−0.648600			−0.324300	−	0.945954i	$-0.605129\pi$
$419$	−13.2765			−0.648600			−0.324300	+	0.945954i	$0.605129\pi$
$420$		0			0
$421$	−21.4835			−1.04704			−0.523520	−	0.852013i	$-0.675382\pi$
$421$	−21.4835			−1.04704			−0.523520	+	0.852013i	$0.675382\pi$
$422$		0			0
$423$	7.86164	+	3.31661i	0.382246	+	0.161259i
$424$		0			0
$425$	−16.8778	−	8.51468i	−0.818693	−	0.413022i
$426$		0			0
$427$	−20.2018	−	20.2018i	−0.977632	−	0.977632i
$428$		0			0
$429$	0.692386	−	0.135379i	0.0334287	−	0.00653618i
$430$		0			0
$431$			6.35177i			0.305954i	0.988230	+	0.152977i	$0.0488860\pi$
$431$			6.35177i			0.305954i	−0.988230	+	0.152977i	$0.951114\pi$
$432$		0			0
$433$	−26.7697	+	26.7697i	−1.28647	+	1.28647i	−0.349553	+	0.936916i	$0.613667\pi$
$433$	−26.7697	+	26.7697i	−1.28647	+	1.28647i	−0.936916	+	0.349553i	$0.886333\pi$
$434$		0			0
$435$	−15.3736	+	5.64970i	−0.737110	+	0.270882i
$436$		0			0
$437$	−1.88013	+	1.88013i	−0.0899389	+	0.0899389i
$438$		0			0
$439$		−	13.5448i		−	0.646460i	−0.946320	−	0.323230i	$-0.895231\pi$
$439$		−	13.5448i		−	0.646460i	0.946320	−	0.323230i	$-0.104769\pi$
$440$		0			0
$441$	19.5111	−	7.93315i	0.929101	−	0.377769i
$442$		0			0
$443$	−18.9879	−	18.9879i	−0.902140	−	0.902140i	0.0934807	−	0.995621i	$-0.470201\pi$
$443$	−18.9879	−	18.9879i	−0.902140	−	0.902140i	−0.995621	+	0.0934807i	$0.970201\pi$
$444$		0			0
$445$	−10.7273	−	7.76107i	−0.508524	−	0.367910i
$446$		0			0
$447$	11.5293	−	17.1336i	0.545316	−	0.810392i
$448$		0			0
$449$	−19.1796			−0.905143			−0.452571	−	0.891728i	$-0.649493\pi$
$449$	−19.1796			−0.905143			−0.452571	+	0.891728i	$0.649493\pi$
$450$		0			0
$451$	−16.9959			−0.800308
$452$		0			0
$453$	−9.53763	+	14.1738i	−0.448117	+	0.665945i
$454$		0			0
$455$	1.00089	+	0.724131i	0.0469225	+	0.0339478i
$456$		0			0
$457$	9.07806	+	9.07806i	0.424654	+	0.424654i	0.886802	−	0.462149i	$-0.152921\pi$
$457$	9.07806	+	9.07806i	0.424654	+	0.424654i	−0.462149	+	0.886802i	$0.652921\pi$
$458$		0			0
$459$	−16.4406	+	10.7542i	−0.767383	+	0.501965i
$460$		0			0
$461$			21.8240i			1.01644i	0.861226	+	0.508221i	$0.169697\pi$
$461$			21.8240i			1.01644i	−0.861226	+	0.508221i	$0.830303\pi$
$462$		0			0
$463$	−9.17031	+	9.17031i	−0.426181	+	0.426181i	−0.887325	−	0.461145i	$-0.847439\pi$
$463$	−9.17031	+	9.17031i	−0.426181	+	0.426181i	0.461145	+	0.887325i	$0.347439\pi$
$464$		0			0
$465$	2.65077	−	0.974138i	0.122927	−	0.0451746i
$466$		0			0
$467$	−20.2067	+	20.2067i	−0.935053	+	0.935053i	−0.998016	−	0.0629631i	$-0.979945\pi$
$467$	−20.2067	+	20.2067i	−0.935053	+	0.935053i	0.0629631	+	0.998016i	$0.479945\pi$
$468$		0			0
$469$			3.39505i			0.156769i
$470$		0			0
$471$	−24.3471	+	4.76049i	−1.12186	+	0.219352i
$472$		0			0
$473$	5.27688	+	5.27688i	0.242631	+	0.242631i
$474$		0			0
$475$	−12.6273	+	4.15885i	−0.579380	+	0.190821i
$476$		0			0
$477$	13.5716	−	32.1700i	0.621402	−	1.47296i
$478$		0			0
$479$	−2.67551			−0.122247			−0.0611235	−	0.998130i	$-0.519468\pi$
$479$	−2.67551			−0.122247			−0.0611235	+	0.998130i	$0.519468\pi$
$480$		0			0
$481$	1.65287			0.0753642
$482$		0			0
$483$	5.38076	+	3.62073i	0.244833	+	0.164749i
$484$		0			0
$485$	0.639241	+	3.98434i	0.0290264	+	0.180920i
$486$		0			0
$487$	29.9468	+	29.9468i	1.35702	+	1.35702i	0.877571	+	0.479447i	$0.159163\pi$
$487$	29.9468	+	29.9468i	1.35702	+	1.35702i	0.479447	+	0.877571i	$0.340837\pi$
$488$		0			0
$489$	−2.17428	−	11.1201i	−0.0983241	−	0.502870i
$490$		0			0
$491$		−	15.5299i		−	0.700855i	−0.936590	−	0.350427i	$-0.886036\pi$
$491$		−	15.5299i		−	0.700855i	0.936590	−	0.350427i	$-0.113964\pi$
$492$		0			0
$493$	11.3059	−	11.3059i	0.509194	−	0.509194i
$494$		0			0
$495$	17.9874	+	4.40441i	0.808475	+	0.197964i
$496$		0			0
$497$	−24.6524	+	24.6524i	−1.10581	+	1.10581i
$498$		0			0
$499$			5.94512i			0.266140i	0.991107	+	0.133070i	$0.0424835\pi$
$499$			5.94512i			0.266140i	−0.991107	+	0.133070i	$0.957516\pi$
$500$		0			0
$501$	−6.40862	−	32.7763i	−0.286316	−	1.46434i
$502$		0			0
$503$	14.3545	+	14.3545i	0.640037	+	0.640037i	0.950564	−	0.310528i	$-0.100506\pi$
$503$	14.3545	+	14.3545i	0.640037	+	0.640037i	−0.310528	+	0.950564i	$0.600506\pi$
$504$		0			0
$505$	−13.1661	+	18.1982i	−0.585885	+	0.809807i
$506$		0			0
$507$	−18.6498	−	12.5495i	−0.828265	−	0.557343i
$508$		0			0
$509$	−27.6357			−1.22493			−0.612465	−	0.790497i	$-0.709822\pi$
$509$	−27.6357			−1.22493			−0.612465	+	0.790497i	$0.709822\pi$
$510$		0			0
$511$	40.3248			1.78386
$512$		0			0
$513$	−2.82776	+	13.5236i	−0.124849	+	0.597082i
$514$		0			0
$515$	2.79159	−	0.447878i	0.123012	−	0.0197359i
$516$		0			0
$517$	5.55203	+	5.55203i	0.244178	+	0.244178i
$518$		0			0
$519$	−21.1962	+	4.14440i	−0.930409	+	0.181919i
$520$		0			0
$521$		−	11.5107i		−	0.504292i	−0.967689	−	0.252146i	$-0.918864\pi$
$521$		−	11.5107i		−	0.504292i	0.967689	−	0.252146i	$-0.0811363\pi$
$522$		0			0
$523$	−9.80893	+	9.80893i	−0.428914	+	0.428914i	−0.888258	−	0.459344i	$-0.848085\pi$
$523$	−9.80893	+	9.80893i	−0.428914	+	0.428914i	0.459344	+	0.888258i	$0.348085\pi$
$524$		0			0
$525$	15.8660	+	28.2812i	0.692448	+	1.23429i
$526$		0			0
$527$	−1.94940	+	1.94940i	−0.0849174	+	0.0849174i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$		0			0
$531$	4.94805	+	12.1695i	0.214727	+	0.528109i
$532$		0			0
$533$	−0.642319	−	0.642319i	−0.0278219	−	0.0278219i
$534$		0			0
$535$	8.90552	−	1.42879i	0.385019	−	0.0617718i
$536$		0			0
$537$	−7.63397	+	11.3448i	−0.329430	+	0.489565i
$538$		0			0
$539$	19.3816			0.834826
$540$		0			0
$541$	−30.4185			−1.30779			−0.653896	−	0.756585i	$-0.726867\pi$
$541$	−30.4185			−1.30779			−0.653896	+	0.756585i	$0.726867\pi$
$542$		0			0
$543$	−20.0136	+	29.7421i	−0.858865	+	1.27636i
$544$		0			0
$545$	22.5942	−	31.2296i	0.967830	−	1.33773i
$546$		0			0
$547$	10.2100	+	10.2100i	0.436547	+	0.436547i	0.890848	−	0.454301i	$-0.150111\pi$
$547$	10.2100	+	10.2100i	0.436547	+	0.436547i	−0.454301	+	0.890848i	$0.650111\pi$
$548$		0			0
$549$	−8.62146	−	21.2040i	−0.367955	−	0.904963i
$550$		0			0
$551$		−	11.2446i		−	0.479034i
$552$		0			0
$553$	31.4622	−	31.4622i	1.33791	−	1.33791i
$554$		0			0
$555$	39.3784	+	18.2137i	1.67152	+	0.773130i
$556$		0			0
$557$	11.7971	−	11.7971i	0.499859	−	0.499859i	−0.411535	−	0.911394i	$-0.635007\pi$
$557$	11.7971	−	11.7971i	0.499859	−	0.499859i	0.911394	+	0.411535i	$0.135007\pi$
$558$		0			0
$559$			0.398853i			0.0168697i
$560$		0			0
$561$	−17.7420	+	3.46903i	−0.749069	+	0.146462i
$562$		0			0
$563$	27.9980	+	27.9980i	1.17998	+	1.17998i	0.979750	+	0.200226i	$0.0641676\pi$
$563$	27.9980	+	27.9980i	1.17998	+	1.17998i	0.200226	+	0.979750i	$0.435832\pi$
$564$		0			0
$565$	−5.25560	−	32.7578i	−0.221105	−	1.37813i
$566$		0			0
$567$	33.6970	+	0.439379i	1.41514	+	0.0184522i
$568$		0			0
$569$	7.39242			0.309906			0.154953	−	0.987922i	$-0.450477\pi$
$569$	7.39242			0.309906			0.154953	+	0.987922i	$0.450477\pi$
$570$		0			0
$571$	37.7753			1.58085			0.790425	−	0.612559i	$-0.209860\pi$
$571$	37.7753			1.58085			0.790425	+	0.612559i	$0.209860\pi$
$572$		0			0
$573$	−23.1316	−	15.5653i	−0.966335	−	0.650250i
$574$		0			0
$575$	−2.25209	+	4.46409i	−0.0939186	+	0.186165i
$576$		0			0
$577$	−17.5325	−	17.5325i	−0.729887	−	0.729887i	0.240710	−	0.970597i	$-0.422620\pi$
$577$	−17.5325	−	17.5325i	−0.729887	−	0.729887i	−0.970597	+	0.240710i	$0.922620\pi$
$578$		0			0
$579$	1.48584	+	7.59917i	0.0617492	+	0.315811i
$580$		0			0
$581$			59.5644i			2.47115i
$582$		0			0
$583$	22.7190	−	22.7190i	0.940926	−	0.940926i
$584$		0			0
$585$	0.513336	+	0.846244i	0.0212238	+	0.0349879i
$586$		0			0
$587$	−14.4735	+	14.4735i	−0.597387	+	0.597387i	−0.939616	−	0.342229i	$-0.888818\pi$
$587$	−14.4735	+	14.4735i	−0.597387	+	0.597387i	0.342229	+	0.939616i	$0.388818\pi$
$588$		0			0
$589$			1.93882i			0.0798877i
$590$		0			0
$591$	−1.17920	−	6.03089i	−0.0485056	−	0.248078i
$592$		0			0
$593$	23.3324	+	23.3324i	0.958146	+	0.958146i	0.999159	−	0.0410126i	$-0.0130584\pi$
$593$	23.3324	+	23.3324i	0.958146	+	0.958146i	−0.0410126	+	0.999159i	$0.513058\pi$
$594$		0			0
$595$	−25.6473	−	18.5555i	−1.05144	−	0.760701i
$596$		0			0
$597$	8.13737	+	5.47567i	0.333040	+	0.224104i
$598$		0			0
$599$	19.3006			0.788603			0.394301	−	0.918981i	$-0.370987\pi$
$599$	19.3006			0.788603			0.394301	+	0.918981i	$0.370987\pi$
$600$		0			0
$601$	−33.8721			−1.38167			−0.690837	−	0.723011i	$-0.742758\pi$
$601$	−33.8721			−1.38167			−0.690837	+	0.723011i	$0.742758\pi$
$602$		0			0
$603$	−1.05729	+	2.50619i	−0.0430562	+	0.102060i
$604$		0			0
$605$	−6.12150	−	4.42882i	−0.248874	−	0.180057i
$606$		0			0
$607$	17.2287	+	17.2287i	0.699291	+	0.699291i	0.964258	−	0.264967i	$-0.0853610\pi$
$607$	17.2287	+	17.2287i	0.699291	+	0.699291i	−0.264967	+	0.964258i	$0.585361\pi$
$608$		0			0
$609$	−26.9177	+	5.26311i	−1.09076	+	0.213272i
$610$		0			0
$611$			0.419650i			0.0169772i
$612$		0			0
$613$	−11.9810	+	11.9810i	−0.483910	+	0.483910i	−0.906378	−	0.422468i	$-0.861164\pi$
$613$	−11.9810	+	11.9810i	−0.483910	+	0.483910i	0.422468	+	0.906378i	$0.361164\pi$
$614$		0			0
$615$	−8.22479	−	22.3808i	−0.331655	−	0.902483i
$616$		0			0
$617$	23.3622	−	23.3622i	0.940525	−	0.940525i	−0.0578031	−	0.998328i	$-0.518410\pi$
$617$	23.3622	−	23.3622i	0.940525	−	0.940525i	0.998328	+	0.0578031i	$0.0184096\pi$
$618$		0			0
$619$		−	7.99586i		−	0.321381i	−0.987005	−	0.160690i	$-0.948628\pi$
$619$		−	7.99586i		−	0.321381i	0.987005	−	0.160690i	$-0.0513720\pi$
$620$		0			0
$621$	2.84444	+	4.34847i	0.114144	+	0.174498i
$622$		0			0
$623$	−15.6779	−	15.6779i	−0.628123	−	0.628123i
$624$		0			0
$625$	−20.1071	+	14.8562i	−0.804282	+	0.594247i
$626$		0			0
$627$	−7.09775	+	10.5479i	−0.283457	+	0.421244i
$628$		0			0
$629$	−42.3538			−1.68876
$630$		0			0
$631$	11.4388			0.455371			0.227686	−	0.973735i	$-0.426884\pi$
$631$	11.4388			0.455371			0.227686	+	0.973735i	$0.426884\pi$
$632$		0			0
$633$	12.1796	−	18.1000i	0.484094	−	0.719411i
$634$		0			0
$635$	−1.39204	−	8.67650i	−0.0552415	−	0.344316i
$636$		0			0
$637$	0.732481	+	0.732481i	0.0290219	+	0.0290219i
$638$		0			0
$639$	−25.8754	+	10.5208i	−1.02362	+	0.416198i
$640$		0			0
$641$			41.1292i			1.62451i	0.583306	+	0.812253i	$0.301759\pi$
$641$			41.1292i			1.62451i	−0.583306	+	0.812253i	$0.698241\pi$
$642$		0			0
$643$	10.2776	−	10.2776i	0.405307	−	0.405307i	−0.474791	−	0.880098i	$-0.657476\pi$
$643$	10.2776	−	10.2776i	0.405307	−	0.405307i	0.880098	+	0.474791i	$0.157476\pi$
$644$		0			0
$645$	−4.39515	+	9.50239i	−0.173059	+	0.374156i
$646$		0			0
$647$	8.99454	−	8.99454i	0.353612	−	0.353612i	−0.507840	−	0.861452i	$-0.669556\pi$
$647$	8.99454	−	8.99454i	0.353612	−	0.353612i	0.861452	+	0.507840i	$0.169556\pi$
$648$		0			0
$649$			12.0887i			0.474523i
$650$		0			0
$651$	4.64124	−	0.907482i	0.181904	−	0.0355670i
$652$		0			0
$653$	−15.3977	−	15.3977i	−0.602560	−	0.602560i	0.338431	−	0.940991i	$-0.390104\pi$
$653$	−15.3977	−	15.3977i	−0.602560	−	0.602560i	−0.940991	+	0.338431i	$0.890104\pi$
$654$		0			0
$655$	−10.3812	+	14.3488i	−0.405626	+	0.560654i
$656$		0			0
$657$	29.7673	+	12.5580i	1.16133	+	0.489934i
$658$		0			0
$659$	41.5614			1.61900			0.809501	−	0.587119i	$-0.199738\pi$
$659$	41.5614			1.61900			0.809501	+	0.587119i	$0.199738\pi$
$660$		0			0
$661$	7.69991			0.299492			0.149746	−	0.988725i	$-0.452154\pi$
$661$	7.69991			0.299492			0.149746	+	0.988725i	$0.452154\pi$
$662$		0			0
$663$	−0.801619	−	0.539412i	−0.0311323	−	0.0209490i
$664$		0			0
$665$	−21.9814	+	3.52665i	−0.852402	+	0.136758i
$666$		0			0
$667$	−2.99036	−	2.99036i	−0.115787	−	0.115787i
$668$		0			0
$669$	1.81814	+	9.29873i	0.0702935	+	0.359510i
$670$		0			0
$671$		−	21.0633i		−	0.813138i
$672$		0			0
$673$	−18.2846	+	18.2846i	−0.704821	+	0.704821i	−0.965441	−	0.260620i	$-0.916073\pi$
$673$	−18.2846	+	18.2846i	−0.704821	+	0.704821i	0.260620	+	0.965441i	$0.416073\pi$
$674$		0			0
$675$	2.90471	+	25.8179i	0.111802	+	0.993730i
$676$		0			0
$677$	35.3177	−	35.3177i	1.35737	−	1.35737i	0.480227	−	0.877144i	$-0.340554\pi$
$677$	35.3177	−	35.3177i	1.35737	−	1.35737i	0.877144	−	0.480227i	$-0.159446\pi$
$678$		0			0
$679$			6.75735i			0.259323i
$680$		0			0
$681$	7.15822	+	36.6101i	0.274304	+	1.40290i
$682$		0			0
$683$	1.07617	+	1.07617i	0.0411785	+	0.0411785i	0.727396	−	0.686218i	$-0.240730\pi$
$683$	1.07617	+	1.07617i	0.0411785	+	0.0411785i	−0.686218	+	0.727396i	$0.740730\pi$
$684$		0			0
$685$	31.4850	−	5.05139i	1.20298	−	0.193004i
$686$		0			0
$687$	19.0491	+	12.8182i	0.726770	+	0.489046i
$688$		0			0
$689$	1.71722			0.0654208
$690$		0			0
$691$	−20.2891			−0.771835			−0.385918	−	0.922533i	$-0.626115\pi$
$691$	−20.2891			−0.771835			−0.385918	+	0.922533i	$0.626115\pi$
$692$		0			0
$693$	28.5723	+	12.0539i	1.08537	+	0.457888i
$694$		0			0
$695$	−16.2909	+	22.5172i	−0.617949	+	0.854126i
$696$		0			0
$697$	16.4591	+	16.4591i	0.623433	+	0.623433i
$698$		0			0
$699$	13.3914	−	2.61836i	0.506508	−	0.0990356i
$700$		0			0
$701$			38.1928i			1.44252i	0.692663	+	0.721262i	$0.256437\pi$
$701$			38.1928i			1.44252i	−0.692663	+	0.721262i	$0.743563\pi$
$702$		0			0
$703$	−21.0619	+	21.0619i	−0.794366	+	0.794366i
$704$		0			0
$705$	−4.62433	+	9.99788i	−0.174162	+	0.376542i
$706$		0			0
$707$	−26.5965	+	26.5965i	−1.00026	+	1.00026i
$708$		0			0
$709$		−	6.43241i		−	0.241574i	−0.992678	−	0.120787i	$-0.961458\pi$
$709$		−	6.43241i		−	0.241574i	0.992678	−	0.120787i	$-0.0385418\pi$
$710$		0			0
$711$	33.0231	−	13.4271i	1.23846	−	0.503554i
$712$		0			0
$713$	0.515608	+	0.515608i	0.0193097	+	0.0193097i
$714$		0			0
$715$	0.144281	+	0.899292i	0.00539579	+	0.0336316i
$716$		0			0
$717$	4.18460	−	6.21872i	0.156277	−	0.232242i
$718$		0			0
$719$	−28.2119			−1.05213			−0.526063	−	0.850446i	$-0.676332\pi$
$719$	−28.2119			−1.05213			−0.526063	+	0.850446i	$0.676332\pi$
$720$		0			0
$721$	4.73447			0.176321
$722$		0			0
$723$	1.91626	−	2.84775i	0.0712664	−	0.105909i
$724$		0			0
$725$	−6.61468	−	20.0838i	−0.245663	−	0.745894i
$726$		0			0
$727$	−16.3850	−	16.3850i	−0.607685	−	0.607685i	0.334656	−	0.942340i	$-0.391380\pi$
$727$	−16.3850	−	16.3850i	−0.607685	−	0.607685i	−0.942340	+	0.334656i	$0.891380\pi$
$728$		0			0
$729$	24.7379	+	10.8183i	0.916219	+	0.400678i
$730$		0			0
$731$		−	10.2204i		−	0.378015i
$732$		0			0
$733$	−27.9652	+	27.9652i	−1.03292	+	1.03292i	−0.0334795	+	0.999439i	$0.510659\pi$
$733$	−27.9652	+	27.9652i	−1.03292	+	1.03292i	−0.999439	+	0.0334795i	$0.989341\pi$
$734$		0			0
$735$	9.37929	+	25.5224i	0.345960	+	0.941408i
$736$		0			0
$737$	−1.76992	+	1.76992i	−0.0651957	+	0.0651957i
$738$		0			0
$739$		−	9.67811i		−	0.356015i	−0.984029	−	0.178007i	$-0.943035\pi$
$739$		−	9.67811i		−	0.356015i	0.984029	−	0.178007i	$-0.0569651\pi$
$740$		0			0
$741$	−0.666875	+	0.130391i	−0.0244983	+	0.00479005i
$742$		0			0
$743$	−6.50920	−	6.50920i	−0.238799	−	0.238799i	0.577553	−	0.816353i	$-0.304007\pi$
$743$	−6.50920	−	6.50920i	−0.238799	−	0.238799i	−0.816353	+	0.577553i	$0.804007\pi$
$744$		0			0
$745$	21.6005	+	15.6277i	0.791382	+	0.572554i
$746$		0			0
$747$	−18.5496	+	43.9698i	−0.678695	+	1.60877i
$748$		0			0
$749$	15.1035			0.551872
$750$		0			0
$751$	30.7825			1.12327			0.561635	−	0.827385i	$-0.310172\pi$
$751$	30.7825			1.12327			0.561635	+	0.827385i	$0.310172\pi$
$752$		0			0
$753$	−35.9510	−	24.1916i	−1.31013	−	0.881591i
$754$		0			0
$755$	−17.8691	−	12.9281i	−0.650324	−	0.470501i
$756$		0			0
$757$	−16.0302	−	16.0302i	−0.582627	−	0.582627i	0.352997	−	0.935624i	$-0.385163\pi$
$757$	−16.0302	−	16.0302i	−0.582627	−	0.582627i	−0.935624	+	0.352997i	$0.885163\pi$
$758$		0			0
$759$	0.917540	+	4.69268i	0.0333046	+	0.170333i
$760$		0			0
$761$			50.0304i			1.81360i	0.421559	+	0.906801i	$0.361483\pi$
$761$			50.0304i			1.81360i	−0.421559	+	0.906801i	$0.638517\pi$
$762$		0			0
$763$	45.6419	−	45.6419i	1.65235	−	1.65235i
$764$		0			0
$765$	−13.1540	−	21.6846i	−0.475583	−	0.784007i
$766$		0			0
$767$	−0.456862	+	0.456862i	−0.0164963	+	0.0164963i
$768$		0			0
$769$			50.2656i			1.81263i	0.422608	+	0.906313i	$0.361115\pi$
$769$			50.2656i			1.81263i	−0.422608	+	0.906313i	$0.638885\pi$
$770$		0			0
$771$	−7.92888	−	40.5515i	−0.285552	−	1.46043i
$772$		0			0
$773$	−1.91849	−	1.91849i	−0.0690033	−	0.0690033i	0.671763	−	0.740766i	$-0.265537\pi$
$773$	−1.91849	−	1.91849i	−0.0690033	−	0.0690033i	−0.740766	+	0.671763i	$0.765537\pi$
$774$		0			0
$775$	1.14052	+	3.46291i	0.0409688	+	0.124392i
$776$		0			0
$777$	60.2773	+	40.5608i	2.16244	+	1.45511i
$778$		0			0
$779$	16.3697			0.586507
$780$		0			0
$781$	−25.7037			−0.919750
$782$		0			0
$783$	−21.5094	−	4.49758i	−0.768683	−	0.160730i
$784$		0			0
$785$	−5.07350	−	31.6228i	−0.181081	−	1.12866i
$786$		0			0
$787$	−33.7311	−	33.7311i	−1.20239	−	1.20239i	−0.973439	−	0.228946i	$-0.926472\pi$
$787$	−33.7311	−	33.7311i	−1.20239	−	1.20239i	−0.228946	−	0.973439i	$-0.573528\pi$
$788$		0			0
$789$	−31.4193	+	6.14329i	−1.11856	+	0.218707i
$790$		0			0
$791$		−	55.5564i		−	1.97536i
$792$		0			0
$793$	0.796033	−	0.796033i	0.0282680	−	0.0282680i
$794$		0			0
$795$	40.9115	+	18.9229i	1.45098	+	0.671125i
$796$		0			0
$797$	34.4408	−	34.4408i	1.21995	−	1.21995i	0.252307	−	0.967647i	$-0.418811\pi$
$797$	34.4408	−	34.4408i	1.21995	−	1.21995i	0.967647	−	0.252307i	$-0.0811892\pi$
$798$		0			0
$799$		−	10.7533i		−	0.380425i
$800$		0			0
$801$	−6.69083	−	16.4557i	−0.236409	−	0.581434i
$802$		0			0
$803$	21.0222	+	21.0222i	0.741858	+	0.741858i
$804$		0			0
$805$	−4.90783	+	6.78358i	−0.172978	+	0.239090i
$806$		0			0
$807$	−27.5898	+	41.0011i	−0.971208	+	1.44331i
$808$		0			0
$809$	26.6973			0.938628			0.469314	−	0.883031i	$-0.344501\pi$
$809$	26.6973			0.938628			0.469314	+	0.883031i	$0.344501\pi$
$810$		0			0
$811$	−16.7503			−0.588181			−0.294090	−	0.955778i	$-0.595017\pi$
$811$	−16.7503			−0.588181			−0.294090	+	0.955778i	$0.595017\pi$
$812$		0			0
$813$	24.2138	−	35.9841i	0.849216	−	1.26202i
$814$		0			0
$815$	14.4432	−	2.31724i	0.505922	−	0.0811692i
$816$		0			0
$817$	−5.08245	−	5.08245i	−0.177813	−	0.177813i
$818$		0			0
$819$	0.624274	+	1.53537i	0.0218139	+	0.0536500i
$820$		0			0
$821$			0.692325i			0.0241623i	0.999927	+	0.0120812i	$0.00384565\pi$
$821$			0.692325i			0.0241623i	−0.999927	+	0.0120812i	$0.996154\pi$
$822$		0			0
$823$	−14.3013	+	14.3013i	−0.498511	+	0.498511i	−0.910974	−	0.412463i	$-0.864668\pi$
$823$	−14.3013	+	14.3013i	−0.498511	+	0.498511i	0.412463	+	0.910974i	$0.364668\pi$
$824$		0			0
$825$	−6.47234	+	23.0149i	−0.225338	+	0.801276i
$826$		0			0
$827$	20.9935	−	20.9935i	0.730016	−	0.730016i	−0.240607	−	0.970623i	$-0.577346\pi$
$827$	20.9935	−	20.9935i	0.730016	−	0.730016i	0.970623	+	0.240607i	$0.0773464\pi$
$828$		0			0
$829$			35.2431i			1.22404i	0.790841	+	0.612021i	$0.209643\pi$
$829$			35.2431i			1.22404i	−0.790841	+	0.612021i	$0.790357\pi$
$830$		0			0
$831$	−3.50741	+	0.685789i	−0.121671	+	0.0237898i
$832$		0			0
$833$	−18.7694	−	18.7694i	−0.650322	−	0.650322i
$834$		0			0
$835$	42.5709	−	6.82999i	1.47323	−	0.236362i
$836$		0			0
$837$	3.70872	+	0.775486i	0.128192	+	0.0268047i
$838$		0			0
$839$	52.3070			1.80584			0.902918	−	0.429812i	$-0.141420\pi$
$839$	52.3070			1.80584			0.902918	+	0.429812i	$0.141420\pi$
$840$		0			0
$841$	−11.1155			−0.383292
$842$		0			0
$843$	4.16389	+	2.80190i	0.143412	+	0.0965026i
$844$		0			0
$845$	17.0106	−	23.5120i	0.585182	−	0.808836i
$846$		0			0
$847$	−8.94654	−	8.94654i	−0.307407	−	0.307407i
$848$		0			0
$849$	3.35207	+	17.1439i	0.115043	+	0.588376i
$850$		0			0
$851$			11.2024i			0.384013i
$852$		0			0
$853$	−9.47407	+	9.47407i	−0.324386	+	0.324386i	−0.850447	−	0.526061i	$-0.823668\pi$
$853$	−9.47407	+	9.47407i	−0.324386	+	0.324386i	0.526061	+	0.850447i	$0.323668\pi$
$854$		0			0
$855$	−17.3247	−	4.24214i	−0.592492	−	0.145078i
$856$		0			0
$857$	−24.1798	+	24.1798i	−0.825966	+	0.825966i	−0.986956	−	0.160990i	$-0.948531\pi$
$857$	−24.1798	+	24.1798i	−0.825966	+	0.825966i	0.160990	+	0.986956i	$0.448531\pi$
$858$		0			0
$859$			15.1639i			0.517387i	0.965959	+	0.258694i	$0.0832920\pi$
$859$			15.1639i			0.517387i	−0.965959	+	0.258694i	$0.916708\pi$
$860$		0			0
$861$	−7.66200	−	39.1866i	−0.261120	−	1.33548i
$862$		0			0
$863$	−30.8313	−	30.8313i	−1.04951	−	1.04951i	−0.998709	−	0.0507996i	$-0.983823\pi$
$863$	−30.8313	−	30.8313i	−1.04951	−	1.04951i	−0.0507996	−	0.998709i	$-0.516177\pi$
$864$		0			0
$865$	−4.41690	−	27.5302i	−0.150179	−	0.936056i
$866$		0			0
$867$	−3.88800	−	2.61625i	−0.132043	−	0.0888524i
$868$		0			0
$869$	32.8039			1.11280
$870$		0			0
$871$	−0.133779			−0.00453293
$872$		0			0
$873$	−2.10438	+	4.98820i	−0.0712225	+	0.168825i
$874$		0			0
$875$	−37.1862	+	19.2296i	−1.25712	+	0.650080i
$876$		0			0
$877$	40.9563	+	40.9563i	1.38300	+	1.38300i	0.839249	+	0.543747i	$0.182995\pi$
$877$	40.9563	+	40.9563i	1.38300	+	1.38300i	0.543747	+	0.839249i	$0.317005\pi$
$878$		0			0
$879$	−21.6669	+	4.23644i	−0.730806	+	0.142892i
$880$		0			0
$881$		−	8.05041i		−	0.271225i	−0.990762	−	0.135613i	$-0.956700\pi$
$881$		−	8.05041i		−	0.271225i	0.990762	−	0.135613i	$-0.0433003\pi$
$882$		0			0
$883$	−3.24418	+	3.24418i	−0.109175	+	0.109175i	−0.759584	−	0.650409i	$-0.774598\pi$
$883$	−3.24418	+	3.24418i	−0.109175	+	0.109175i	0.650409	+	0.759584i	$0.274598\pi$
$884$		0			0
$885$	−15.9188	+	5.85004i	−0.535105	+	0.196647i
$886$		0			0
$887$	−13.5436	+	13.5436i	−0.454750	+	0.454750i	−0.896927	−	0.442178i	$-0.854206\pi$
$887$	−13.5436	+	13.5436i	−0.454750	+	0.454750i	0.442178	+	0.896927i	$0.354206\pi$
$888$		0			0
$889$		−	14.7151i		−	0.493529i
$890$		0			0
$891$	17.3379	+	17.7961i	0.580843	+	0.596190i
$892$		0			0
$893$	−5.34747	−	5.34747i	−0.178946	−	0.178946i
$894$		0			0
$895$	−14.3025	−	10.3477i	−0.478081	−	0.345885i
$896$		0			0
$897$	−0.142672	+	0.212024i	−0.00476368	+	0.00707928i
$898$		0			0
$899$	−3.08371			−0.102847
$900$		0			0
$901$	−44.0028			−1.46595
$902$		0			0
$903$	−9.78772	+	14.5455i	−0.325715	+	0.484044i
$904$		0			0
$905$	−37.4962	−	27.1280i	−1.24642	−	0.901766i
$906$		0			0
$907$	−25.1433	−	25.1433i	−0.834869	−	0.834869i	0.153309	−	0.988178i	$-0.451007\pi$
$907$	−25.1433	−	25.1433i	−0.834869	−	0.834869i	−0.988178	+	0.153309i	$0.951007\pi$
$908$		0			0
$909$	−27.9160	+	11.3505i	−0.925914	+	0.376473i
$910$		0			0
$911$			55.5618i			1.84084i	0.390926	+	0.920422i	$0.372155\pi$
$911$			55.5618i			1.84084i	−0.390926	+	0.920422i	$0.627845\pi$
$912$		0			0
$913$	−31.0523	+	31.0523i	−1.02768	+	1.02768i
$914$		0			0
$915$	27.7368	−	10.1931i	0.916951	−	0.336972i
$916$		0			0
$917$	−20.9707	+	20.9707i	−0.692513	+	0.692513i
$918$		0			0
$919$		−	16.7528i		−	0.552624i	−0.961068	−	0.276312i	$-0.910888\pi$
$919$		−	16.7528i		−	0.552624i	0.961068	−	0.276312i	$-0.0891123\pi$
$920$		0			0
$921$	48.5268	−	9.48824i	1.59901	−	0.312648i
$922$		0			0
$923$	−0.971407	−	0.971407i	−0.0319742	−	0.0319742i
$924$		0			0
$925$	−25.2288	+	50.0084i	−0.829516	+	1.64427i
$926$		0			0
$927$	3.49493	+	1.47441i	0.114789	+	0.0484261i
$928$		0			0
$929$	−2.57879			−0.0846073			−0.0423037	−	0.999105i	$-0.513470\pi$
$929$	−2.57879			−0.0846073			−0.0423037	+	0.999105i	$0.513470\pi$
$930$		0			0
$931$	−18.6675			−0.611804
$932$		0			0
$933$	−12.5533	−	8.44716i	−0.410977	−	0.276548i
$934$		0			0
$935$	−3.69712	−	23.0439i	−0.120909	−	0.753616i
$936$		0			0
$937$	−11.1866	−	11.1866i	−0.365449	−	0.365449i	0.500365	−	0.865814i	$-0.333199\pi$
$937$	−11.1866	−	11.1866i	−0.365449	−	0.365449i	−0.865814	+	0.500365i	$0.833199\pi$
$938$		0			0
$939$	−8.18834	−	41.8785i	−0.267216	−	1.36665i
$940$		0			0
$941$			37.2225i			1.21342i	0.794924	+	0.606709i	$0.207511\pi$
$941$			37.2225i			1.21342i	−0.794924	+	0.606709i	$0.792489\pi$
$942$		0			0
$943$	4.35335	−	4.35335i	0.141765	−	0.141765i
$944$		0			0
$945$	−2.04604	+	43.4582i	−0.0665577	+	1.41370i
$946$		0			0
$947$	22.6052	−	22.6052i	0.734571	−	0.734571i	−0.236950	−	0.971522i	$-0.576148\pi$
$947$	22.6052	−	22.6052i	0.734571	−	0.734571i	0.971522	+	0.236950i	$0.0761479\pi$
$948$		0			0
$949$			1.58896i			0.0515800i
$950$		0			0
$951$	7.15055	+	36.5708i	0.231873	+	1.18589i
$952$		0			0
$953$	4.69913	+	4.69913i	0.152220	+	0.152220i	0.779109	−	0.626889i	$-0.215672\pi$
$953$	4.69913	+	4.69913i	0.152220	+	0.152220i	−0.626889	+	0.779109i	$0.715672\pi$
$954$		0			0
$955$	21.0985	−	29.1622i	0.682731	−	0.943667i
$956$		0			0
$957$	−16.7766	−	11.2890i	−0.542310	−	0.364922i
$958$		0			0
$959$	53.3977			1.72430
$960$		0			0
$961$	−30.4683			−0.982848
$962$		0			0
$963$	11.1493	+	4.70356i	0.359280	+	0.151570i
$964$		0			0
$965$	−9.87003	+	1.58353i	−0.317728	+	0.0509756i
$966$		0			0
$967$	−27.9042	−	27.9042i	−0.897339	−	0.897339i	0.0978608	−	0.995200i	$-0.468800\pi$
$967$	−27.9042	−	27.9042i	−0.897339	−	0.897339i	−0.995200	+	0.0978608i	$0.968800\pi$
$968$		0			0
$969$	17.0883	−	3.34121i	0.548956	−	0.107335i
$970$		0			0
$971$			5.45098i			0.174930i	0.996168	+	0.0874651i	$0.0278766\pi$
$971$			5.45098i			0.174930i	−0.996168	+	0.0874651i	$0.972123\pi$
$972$		0			0
$973$	−32.9088	+	32.9088i	−1.05501	+	1.05501i
$974$		0			0
$975$	−1.11440	+	0.625185i	−0.0356893	+	0.0200219i
$976$		0			0
$977$	−37.6284	+	37.6284i	−1.20384	+	1.20384i	−0.230850	+	0.972989i	$0.574151\pi$
$977$	−37.6284	+	37.6284i	−1.20384	+	1.20384i	−0.972989	+	0.230850i	$0.925849\pi$
$978$		0			0
$979$		−	16.3465i		−	0.522436i
$980$		0			0
$981$	47.9062	−	19.4785i	1.52953	−	0.621900i
$982$		0			0
$983$	−27.3441	−	27.3441i	−0.872142	−	0.872142i	0.120564	−	0.992706i	$-0.461530\pi$
$983$	−27.3441	−	27.3441i	−0.872142	−	0.872142i	−0.992706	+	0.120564i	$0.961530\pi$
$984$		0			0
$985$	7.83310	−	1.25673i	0.249583	−	0.0400427i
$986$		0			0
$987$	−10.2981	+	15.3039i	−0.327792	+	0.487130i
$988$		0			0
$989$	−2.70324			−0.0859581
$990$		0			0
$991$	3.87023			0.122942			0.0614709	−	0.998109i	$-0.480421\pi$
$991$	3.87023			0.122942			0.0614709	+	0.998109i	$0.480421\pi$
$992$		0			0
$993$	−14.6398	+	21.7561i	−0.464579	+	0.690409i
$994$		0			0
$995$	−7.42216	+	10.2589i	−0.235298	+	0.325228i
$996$		0			0
$997$	−27.2418	−	27.2418i	−0.862758	−	0.862758i	0.128900	−	0.991658i	$-0.458855\pi$
$997$	−27.2418	−	27.2418i	−0.862758	−	0.862758i	−0.991658	+	0.128900i	$0.958855\pi$
$998$		0			0
$999$	31.8645	+	48.7132i	1.00815	+	1.54122i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.r.c.737.13	yes	80
3.2	odd	2	inner	1380.2.r.c.737.7	✓	80
5.3	odd	4	inner	1380.2.r.c.1013.7	yes	80
15.8	even	4	inner	1380.2.r.c.1013.13	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.r.c.737.7	✓	80	3.2	odd	2	inner
1380.2.r.c.737.13	yes	80	1.1	even	1	trivial
1380.2.r.c.1013.7	yes	80	5.3	odd	4	inner
1380.2.r.c.1013.13	yes	80	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.966965 + 1.43700i) q^{3} +(-1.81165 - 1.31070i) q^{5} +(-2.64771 - 2.64771i) q^{7} +(-1.12996 - 2.77906i) q^{9} +O(q^{10})\)	\(q+(-0.966965 + 1.43700i) q^{3} +(-1.81165 - 1.31070i) q^{5} +(-2.64771 - 2.64771i) q^{7} +(-1.12996 - 2.77906i) q^{9} -2.76062i q^{11} +(0.104331 - 0.104331i) q^{13} +(3.63528 - 1.33594i) q^{15} +(-2.67342 + 2.67342i) q^{17} +2.65891i q^{19} +(6.36501 - 1.24453i) q^{21} +(0.707107 + 0.707107i) q^{23} +(1.56412 + 4.74906i) q^{25} +(5.08615 + 1.06351i) q^{27} -4.22901 q^{29} +0.729179 q^{31} +(3.96702 + 2.66942i) q^{33} +(1.32635 + 8.26708i) q^{35} +(7.92128 + 7.92128i) q^{37} +(0.0490395 + 0.250808i) q^{39} -6.15656i q^{41} +(-1.91148 + 1.91148i) q^{43} +(-1.59544 + 6.51572i) q^{45} +(-2.01115 + 2.01115i) q^{47} +7.02075i q^{49} +(-1.25661 - 6.42682i) q^{51} +(8.22968 + 8.22968i) q^{53} +(-3.61835 + 5.00127i) q^{55} +(-3.82086 - 2.57107i) q^{57} -4.37898 q^{59} +7.62990 q^{61} +(-4.36636 + 10.3500i) q^{63} +(-0.325757 + 0.0522639i) q^{65} +(-0.641130 - 0.641130i) q^{67} +(-1.69986 + 0.332367i) q^{69} -9.31083i q^{71} +(-7.61503 + 7.61503i) q^{73} +(-8.33686 - 2.34452i) q^{75} +(-7.30933 + 7.30933i) q^{77} +11.8828i q^{79} +(-6.44639 + 6.28045i) q^{81} +(-11.2483 - 11.2483i) q^{83} +(8.34735 - 1.33923i) q^{85} +(4.08931 - 6.07710i) q^{87} +5.92131 q^{89} -0.552476 q^{91} +(-0.705091 + 1.04783i) q^{93} +(3.48504 - 4.81700i) q^{95} +(-1.27607 - 1.27607i) q^{97} +(-7.67194 + 3.11938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{3}+O(q^{10}) \) 80 * q + 8 * q^3	\( 80 q + 8 q^{3} + 32 q^{13} + 24 q^{21} - 32 q^{25} - 28 q^{27} - 32 q^{31} - 44 q^{33} + 24 q^{37} - 32 q^{43} + 88 q^{45} + 16 q^{51} + 8 q^{55} + 16 q^{57} - 32 q^{61} - 12 q^{63} - 16 q^{67} - 32 q^{73} + 4 q^{75} - 64 q^{81} - 32 q^{85} + 64 q^{91} + 8 q^{93} - 96 q^{97}+O(q^{100}) \) 80 * q + 8 * q^3 + 32 * q^13 + 24 * q^21 - 32 * q^25 - 28 * q^27 - 32 * q^31 - 44 * q^33 + 24 * q^37 - 32 * q^43 + 88 * q^45 + 16 * q^51 + 8 * q^55 + 16 * q^57 - 32 * q^61 - 12 * q^63 - 16 * q^67 - 32 * q^73 + 4 * q^75 - 64 * q^81 - 32 * q^85 + 64 * q^91 + 8 * q^93 - 96 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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