LMFDB - Embedded newform 1380.2.t.a.1057.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(1057,1380)]

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, 0, 1, 2]))

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

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

chi := DirichletCharacter("1380.1057");

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.t (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:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1057.6
Character	$\chi$	$=$	1380.1057
Dual form			1380.2.t.a.1333.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(1.68477 + 1.47022i) q^{5} +(2.29608 - 2.29608i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(1.68477 + 1.47022i) q^{5} +(2.29608 - 2.29608i) q^{7} -1.00000i q^{9} +5.35971i q^{11} +(-2.00694 + 2.00694i) q^{13} +(-2.23092 + 0.151706i) q^{15} +(-3.44837 + 3.44837i) q^{17} +0.00250982 q^{19} +3.24714i q^{21} +(-4.38302 - 1.94658i) q^{23} +(0.676885 + 4.95397i) q^{25} +(0.707107 + 0.707107i) q^{27} +1.32182i q^{29} +7.62711 q^{31} +(-3.78989 - 3.78989i) q^{33} +(7.24410 - 0.492610i) q^{35} +(6.26209 - 6.26209i) q^{37} -2.83824i q^{39} -7.53073 q^{41} +(0.265803 + 0.265803i) q^{43} +(1.47022 - 1.68477i) q^{45} +(8.13733 + 8.13733i) q^{47} -3.54394i q^{49} -4.87673i q^{51} +(-2.78761 - 2.78761i) q^{53} +(-7.87997 + 9.02987i) q^{55} +(-0.00177471 + 0.00177471i) q^{57} +10.7480i q^{59} +2.04336i q^{61} +(-2.29608 - 2.29608i) q^{63} +(-6.33187 + 0.430577i) q^{65} +(-2.91533 + 2.91533i) q^{67} +(4.47570 - 1.72282i) q^{69} +7.55392 q^{71} +(-0.944453 + 0.944453i) q^{73} +(-3.98162 - 3.02436i) q^{75} +(12.3063 + 12.3063i) q^{77} -6.43218 q^{79} -1.00000 q^{81} +(2.53189 + 2.53189i) q^{83} +(-10.8796 + 0.739827i) q^{85} +(-0.934669 - 0.934669i) q^{87} -8.05956 q^{89} +9.21617i q^{91} +(-5.39318 + 5.39318i) q^{93} +(0.00422847 + 0.00369000i) q^{95} +(-9.47299 + 9.47299i) q^{97} +5.35971 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 8 q^{13} - 16 q^{23} - 8 q^{25} + 8 q^{31} + 8 q^{35} - 24 q^{41} + 8 q^{47} - 32 q^{55} - 24 q^{71} + 8 q^{73} + 32 q^{75} + 40 q^{77} - 48 q^{81} + 24 q^{85} - 40 q^{87}+O(q^{100}) $ 48 * q - 8 * q^13 - 16 * q^23 - 8 * q^25 + 8 * q^31 + 8 * q^35 - 24 * q^41 + 8 * q^47 - 32 * q^55 - 24 * q^71 + 8 * q^73 + 32 * q^75 + 40 * q^77 - 48 * q^81 + 24 * q^85 - 40 * q^87

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
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	1.68477	+	1.47022i	0.753451	+	0.657504i
$5$	1.68477	+	1.47022i	0.753451	+	0.657504i
$6$		0			0
$7$	2.29608	−	2.29608i	0.867835	−	0.867835i	−0.124397	−	0.992233i	$-0.539700\pi$
$7$	2.29608	−	2.29608i	0.867835	−	0.867835i	0.992233	+	0.124397i	$0.0396997\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$			5.35971i			1.61601i	0.589173	+	0.808007i	$0.299454\pi$
$11$			5.35971i			1.61601i	−0.589173	+	0.808007i	$0.700546\pi$
$12$		0			0
$13$	−2.00694	+	2.00694i	−0.556624	+	0.556624i	−0.928345	−	0.371720i	$-0.878768\pi$
$13$	−2.00694	+	2.00694i	−0.556624	+	0.556624i	0.371720	+	0.928345i	$0.378768\pi$
$14$		0			0
$15$	−2.23092	+	0.151706i	−0.576020	+	0.0391702i
$16$		0			0
$17$	−3.44837	+	3.44837i	−0.836352	+	0.836352i	−0.988377	−	0.152025i	$-0.951421\pi$
$17$	−3.44837	+	3.44837i	−0.836352	+	0.836352i	0.152025	+	0.988377i	$0.451421\pi$
$18$		0			0
$19$	0.00250982			0.000575793			0.000287897	−	1.00000i	$-0.499908\pi$
$19$	0.00250982			0.000575793			0.000287897		1.00000i	$0.499908\pi$
$20$		0			0
$21$			3.24714i			0.708585i
$22$		0			0
$23$	−4.38302	−	1.94658i	−0.913922	−	0.405890i
$23$	−4.38302	−	1.94658i	−0.913922	−	0.405890i
$24$		0			0
$25$	0.676885	+	4.95397i	0.135377	+	0.990794i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$			1.32182i			0.245456i	0.992440	+	0.122728i	$0.0391643\pi$
$29$			1.32182i			0.245456i	−0.992440	+	0.122728i	$0.960836\pi$
$30$		0			0
$31$	7.62711			1.36987			0.684935	−	0.728604i	$-0.259831\pi$
$31$	7.62711			1.36987			0.684935	+	0.728604i	$0.259831\pi$
$32$		0			0
$33$	−3.78989	−	3.78989i	−0.659735	−	0.659735i
$34$		0			0
$35$	7.24410	−	0.492610i	1.22448	−	0.0832663i
$36$		0			0
$37$	6.26209	−	6.26209i	1.02948	−	1.02948i	0.0299295	−	0.999552i	$-0.490472\pi$
$37$	6.26209	−	6.26209i	1.02948	−	1.02948i	0.999552	−	0.0299295i	$-0.00952828\pi$
$38$		0			0
$39$		−	2.83824i		−	0.454482i
$40$		0			0
$41$	−7.53073			−1.17610			−0.588051	−	0.808824i	$-0.700105\pi$
$41$	−7.53073			−1.17610			−0.588051	+	0.808824i	$0.700105\pi$
$42$		0			0
$43$	0.265803	+	0.265803i	0.0405345	+	0.0405345i	0.727084	−	0.686549i	$-0.240875\pi$
$43$	0.265803	+	0.265803i	0.0405345	+	0.0405345i	−0.686549	+	0.727084i	$0.740875\pi$
$44$		0			0
$45$	1.47022	−	1.68477i	0.219168	−	0.251150i
$46$		0			0
$47$	8.13733	+	8.13733i	1.18695	+	1.18695i	0.977906	+	0.209045i	$0.0670355\pi$
$47$	8.13733	+	8.13733i	1.18695	+	1.18695i	0.209045	+	0.977906i	$0.432964\pi$
$48$		0			0
$49$		−	3.54394i		−	0.506277i
$50$		0			0
$51$		−	4.87673i		−	0.682878i
$52$		0			0
$53$	−2.78761	−	2.78761i	−0.382908	−	0.382908i	0.489241	−	0.872149i	$-0.337274\pi$
$53$	−2.78761	−	2.78761i	−0.382908	−	0.382908i	−0.872149	+	0.489241i	$0.837274\pi$
$54$		0			0
$55$	−7.87997	+	9.02987i	−1.06254	+	1.21759i
$56$		0			0
$57$	−0.00177471	+	0.00177471i	−0.000235067	+	0.000235067i
$58$		0			0
$59$			10.7480i			1.39927i	0.714498	+	0.699637i	$0.246655\pi$
$59$			10.7480i			1.39927i	−0.714498	+	0.699637i	$0.753345\pi$
$60$		0			0
$61$			2.04336i			0.261626i	0.991407	+	0.130813i	$0.0417587\pi$
$61$			2.04336i			0.261626i	−0.991407	+	0.130813i	$0.958241\pi$
$62$		0			0
$63$	−2.29608	−	2.29608i	−0.289278	−	0.289278i
$64$		0			0
$65$	−6.33187	+	0.430577i	−0.785372	+	0.0534065i
$66$		0			0
$67$	−2.91533	+	2.91533i	−0.356164	+	0.356164i	−0.862397	−	0.506233i	$-0.831038\pi$
$67$	−2.91533	+	2.91533i	−0.356164	+	0.356164i	0.506233	+	0.862397i	$0.331038\pi$
$68$		0			0
$69$	4.47570	−	1.72282i	0.538811	−	0.207403i
$70$		0			0
$71$	7.55392			0.896485			0.448243	−	0.893912i	$-0.352050\pi$
$71$	7.55392			0.896485			0.448243	+	0.893912i	$0.352050\pi$
$72$		0			0
$73$	−0.944453	+	0.944453i	−0.110540	+	0.110540i	−0.760213	−	0.649674i	$-0.774906\pi$
$73$	−0.944453	+	0.944453i	−0.110540	+	0.110540i	0.649674	+	0.760213i	$0.274906\pi$
$74$		0			0
$75$	−3.98162	−	3.02436i	−0.459757	−	0.349223i
$76$		0			0
$77$	12.3063	+	12.3063i	1.40243	+	1.40243i
$78$		0			0
$79$	−6.43218			−0.723677			−0.361838	−	0.932241i	$-0.617851\pi$
$79$	−6.43218			−0.723677			−0.361838	+	0.932241i	$0.617851\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	2.53189	+	2.53189i	0.277911	+	0.277911i	0.832274	−	0.554364i	$-0.187038\pi$
$83$	2.53189	+	2.53189i	0.277911	+	0.277911i	−0.554364	+	0.832274i	$0.687038\pi$
$84$		0			0
$85$	−10.8796	+	0.739827i	−1.18005	+	0.0802455i
$86$		0			0
$87$	−0.934669	−	0.934669i	−0.100207	−	0.100207i
$88$		0			0
$89$	−8.05956			−0.854312			−0.427156	−	0.904178i	$-0.640484\pi$
$89$	−8.05956			−0.854312			−0.427156	+	0.904178i	$0.640484\pi$
$90$		0			0
$91$			9.21617i			0.966117i
$92$		0			0
$93$	−5.39318	+	5.39318i	−0.559247	+	0.559247i
$94$		0			0
$95$	0.00422847	+	0.00369000i	0.000433832	+	0.000378586i
$96$		0			0
$97$	−9.47299	+	9.47299i	−0.961837	+	0.961837i	−0.999298	−	0.0374612i	$-0.988073\pi$
$97$	−9.47299	+	9.47299i	−0.961837	+	0.961837i	0.0374612	+	0.999298i	$0.488073\pi$
$98$		0			0
$99$	5.35971			0.538671
$100$		0			0
$101$	−6.81553			−0.678171			−0.339086	−	0.940756i	$-0.610118\pi$
$101$	−6.81553			−0.678171			−0.339086	+	0.940756i	$0.610118\pi$
$102$		0			0
$103$	−7.60293	−	7.60293i	−0.749139	−	0.749139i	0.225179	−	0.974317i	$-0.427703\pi$
$103$	−7.60293	−	7.60293i	−0.749139	−	0.749139i	−0.974317	+	0.225179i	$0.927703\pi$
$104$		0			0
$105$	−4.77403	+	5.47068i	−0.465897	+	0.533884i
$106$		0			0
$107$	7.09059	−	7.09059i	0.685473	−	0.685473i	−0.275755	−	0.961228i	$-0.588928\pi$
$107$	7.09059	−	7.09059i	0.685473	−	0.685473i	0.961228	+	0.275755i	$0.0889277\pi$
$108$		0			0
$109$	3.17758			0.304357			0.152178	−	0.988353i	$-0.451371\pi$
$109$	3.17758			0.304357			0.152178	+	0.988353i	$0.451371\pi$
$110$		0			0
$111$			8.85593i			0.840568i
$112$		0			0
$113$	−4.93769	−	4.93769i	−0.464499	−	0.464499i	0.435628	−	0.900127i	$-0.356526\pi$
$113$	−4.93769	−	4.93769i	−0.464499	−	0.464499i	−0.900127	+	0.435628i	$0.856526\pi$
$114$		0			0
$115$	−4.52246	−	9.72355i	−0.421721	−	0.906725i
$116$		0			0
$117$	2.00694	+	2.00694i	0.185541	+	0.185541i
$118$		0			0
$119$			15.8354i			1.45163i
$120$		0			0
$121$	−17.7265			−1.61150
$122$		0			0
$123$	5.32503	−	5.32503i	0.480142	−	0.480142i
$124$		0			0
$125$	−6.14305	+	9.34146i	−0.549451	+	0.835526i
$126$		0			0
$127$	2.89475	+	2.89475i	0.256868	+	0.256868i	0.823779	−	0.566911i	$-0.191862\pi$
$127$	2.89475	+	2.89475i	0.256868	+	0.256868i	−0.566911	+	0.823779i	$0.691862\pi$
$128$		0			0
$129$	−0.375902			−0.0330963
$130$		0			0
$131$	19.8735			1.73635			0.868176	−	0.496256i	$-0.165292\pi$
$131$	19.8735			1.73635			0.868176	+	0.496256i	$0.165292\pi$
$132$		0			0
$133$	0.00576275	−	0.00576275i	0.000499694	−	0.000499694i
$134$		0			0
$135$	0.151706	+	2.23092i	0.0130567	+	0.192007i
$136$		0			0
$137$	−1.04908	+	1.04908i	−0.0896291	+	0.0896291i	−0.750500	−	0.660871i	$-0.770187\pi$
$137$	−1.04908	+	1.04908i	−0.0896291	+	0.0896291i	0.660871	+	0.750500i	$0.270187\pi$
$138$		0			0
$139$			10.0772i			0.854740i	0.904077	+	0.427370i	$0.140560\pi$
$139$			10.0772i			0.854740i	−0.904077	+	0.427370i	$0.859440\pi$
$140$		0			0
$141$	−11.5079			−0.969141
$142$		0			0
$143$	−10.7566	−	10.7566i	−0.899513	−	0.899513i
$144$		0			0
$145$	−1.94337	+	2.22696i	−0.161388	+	0.184939i
$146$		0			0
$147$	2.50594	+	2.50594i	0.206687	+	0.206687i
$148$		0			0
$149$	16.0437			1.31435			0.657176	−	0.753737i	$-0.271751\pi$
$149$	16.0437			1.31435			0.657176	+	0.753737i	$0.271751\pi$
$150$		0			0
$151$	11.8099			0.961074			0.480537	−	0.876974i	$-0.340442\pi$
$151$	11.8099			0.961074			0.480537	+	0.876974i	$0.340442\pi$
$152$		0			0
$153$	3.44837	+	3.44837i	0.278784	+	0.278784i
$154$		0			0
$155$	12.8499	+	11.2136i	1.03213	+	0.900695i
$156$		0			0
$157$	16.6476	−	16.6476i	1.32862	−	1.32862i	0.422052	−	0.906571i	$-0.361310\pi$
$157$	16.6476	−	16.6476i	1.32862	−	1.32862i	0.906571	−	0.422052i	$-0.138690\pi$
$158$		0			0
$159$	3.94227			0.312643
$160$		0			0
$161$	−14.5332	+	5.59425i	−1.14538	+	0.440888i
$162$		0			0
$163$	17.4608	−	17.4608i	1.36764	−	1.36764i	0.503842	−	0.863796i	$-0.331919\pi$
$163$	17.4608	−	17.4608i	1.36764	−	1.36764i	0.863796	−	0.503842i	$-0.168081\pi$
$164$		0			0
$165$	−0.813099	−	11.9571i	−0.0632997	−	0.930856i
$166$		0			0
$167$	−7.50817	−	7.50817i	−0.581000	−	0.581000i	0.354178	−	0.935178i	$-0.384761\pi$
$167$	−7.50817	−	7.50817i	−0.581000	−	0.581000i	−0.935178	+	0.354178i	$0.884761\pi$
$168$		0			0
$169$			4.94440i			0.380339i
$170$		0			0
$171$		−	0.00250982i		−	0.000191931i
$172$		0			0
$173$	16.0750	−	16.0750i	1.22216	−	1.22216i	0.255297	−	0.966863i	$-0.417827\pi$
$173$	16.0750	−	16.0750i	1.22216	−	1.22216i	0.966863	−	0.255297i	$-0.0821734\pi$
$174$		0			0
$175$	12.9289	+	9.82052i	0.977331	+	0.742361i
$176$		0			0
$177$	−7.60000	−	7.60000i	−0.571251	−	0.571251i
$178$		0			0
$179$			17.0883i			1.27724i	0.769521	+	0.638621i	$0.220495\pi$
$179$			17.0883i			1.27724i	−0.769521	+	0.638621i	$0.779505\pi$
$180$		0			0
$181$		−	7.97758i		−	0.592969i	−0.955038	−	0.296484i	$-0.904186\pi$
$181$		−	7.97758i		−	0.592969i	0.955038	−	0.296484i	$-0.0958143\pi$
$182$		0			0
$183$	−1.44488	−	1.44488i	−0.106808	−	0.106808i
$184$		0			0
$185$	19.7568	−	1.34350i	1.45255	−	0.0987758i
$186$		0			0
$187$	−18.4823	−	18.4823i	−1.35156	−	1.35156i
$188$		0			0
$189$	3.24714			0.236195
$190$		0			0
$191$			6.88551i			0.498218i	0.968475	+	0.249109i	$0.0801377\pi$
$191$			6.88551i			0.498218i	−0.968475	+	0.249109i	$0.919862\pi$
$192$		0			0
$193$	−11.1417	+	11.1417i	−0.802001	+	0.802001i	−0.983408	−	0.181407i	$-0.941935\pi$
$193$	−11.1417	+	11.1417i	−0.802001	+	0.802001i	0.181407	+	0.983408i	$0.441935\pi$
$194$		0			0
$195$	4.17285	−	4.78177i	0.298824	−	0.342430i
$196$		0			0
$197$	8.99038	+	8.99038i	0.640538	+	0.640538i	0.950688	−	0.310150i	$-0.100379\pi$
$197$	8.99038	+	8.99038i	0.640538	+	0.640538i	−0.310150	+	0.950688i	$0.600379\pi$
$198$		0			0
$199$	10.4973			0.744136			0.372068	−	0.928205i	$-0.378649\pi$
$199$	10.4973			0.744136			0.372068	+	0.928205i	$0.378649\pi$
$200$		0			0
$201$		−	4.12290i		−	0.290807i
$202$		0			0
$203$	3.03501	+	3.03501i	0.213016	+	0.213016i
$204$		0			0
$205$	−12.6875	−	11.0719i	−0.886136	−	0.773292i
$206$		0			0
$207$	−1.94658	+	4.38302i	−0.135297	+	0.304641i
$208$		0			0
$209$			0.0134519i			0.000930490i
$210$		0			0
$211$	−8.90726			−0.613201			−0.306601	−	0.951838i	$-0.599192\pi$
$211$	−8.90726			−0.613201			−0.306601	+	0.951838i	$0.599192\pi$
$212$		0			0
$213$	−5.34143	+	5.34143i	−0.365989	+	0.365989i
$214$		0			0
$215$	0.0570264	+	0.838605i	0.00388917	+	0.0571924i
$216$		0			0
$217$	17.5124	−	17.5124i	1.18882	−	1.18882i
$218$		0			0
$219$		−	1.33566i		−	0.0902554i
$220$		0			0
$221$		−	13.8413i		−	0.931067i
$222$		0			0
$223$	7.05589	−	7.05589i	0.472497	−	0.472497i	−0.430225	−	0.902722i	$-0.641566\pi$
$223$	7.05589	−	7.05589i	0.472497	−	0.472497i	0.902722	+	0.430225i	$0.141566\pi$
$224$		0			0
$225$	4.95397	−	0.676885i	0.330265	−	0.0451257i
$226$		0			0
$227$	7.93717	−	7.93717i	0.526808	−	0.526808i	−0.392811	−	0.919619i	$-0.628497\pi$
$227$	7.93717	−	7.93717i	0.526808	−	0.526808i	0.919619	+	0.392811i	$0.128497\pi$
$228$		0			0
$229$	−19.9540			−1.31860			−0.659298	−	0.751882i	$-0.729146\pi$
$229$	−19.9540			−1.31860			−0.659298	+	0.751882i	$0.729146\pi$
$230$		0			0
$231$	−17.4037			−1.14508
$232$		0			0
$233$	8.44690	−	8.44690i	0.553375	−	0.553375i	−0.374038	−	0.927413i	$-0.622027\pi$
$233$	8.44690	−	8.44690i	0.553375	−	0.553375i	0.927413	+	0.374038i	$0.122027\pi$
$234$		0			0
$235$	1.74582	+	25.6732i	0.113885	+	1.67473i
$236$		0			0
$237$	4.54824	−	4.54824i	0.295440	−	0.295440i
$238$		0			0
$239$		−	16.5868i		−	1.07291i	−0.843928	−	0.536457i	$-0.819762\pi$
$239$		−	16.5868i		−	1.07291i	0.843928	−	0.536457i	$-0.180238\pi$
$240$		0			0
$241$		−	6.17292i		−	0.397632i	−0.980037	−	0.198816i	$-0.936290\pi$
$241$		−	6.17292i		−	0.397632i	0.980037	−	0.198816i	$-0.0637097\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	5.21038	−	5.97071i	0.332879	−	0.381455i
$246$		0			0
$247$	−0.00503706	+	0.00503706i	−0.000320501	+	0.000320501i
$248$		0			0
$249$	−3.58063			−0.226913
$250$		0			0
$251$			21.2737i			1.34278i	0.741103	+	0.671391i	$0.234303\pi$
$251$			21.2737i			1.34278i	−0.741103	+	0.671391i	$0.765697\pi$
$252$		0			0
$253$	10.4331	−	23.4917i	0.655924	−	1.47691i
$254$		0			0
$255$	7.16988	−	8.21615i	0.448995	−	0.514515i
$256$		0			0
$257$	−5.88088	−	5.88088i	−0.366839	−	0.366839i	0.499484	−	0.866323i	$-0.333523\pi$
$257$	−5.88088	−	5.88088i	−0.366839	−	0.366839i	−0.866323	+	0.499484i	$0.833523\pi$
$258$		0			0
$259$		−	28.7565i		−	1.78684i
$260$		0			0
$261$	1.32182			0.0818187
$262$		0			0
$263$	−5.54517	−	5.54517i	−0.341930	−	0.341930i	0.515163	−	0.857093i	$-0.327732\pi$
$263$	−5.54517	−	5.54517i	−0.341930	−	0.341930i	−0.857093	+	0.515163i	$0.827732\pi$
$264$		0			0
$265$	−0.598065	−	8.79488i	−0.0367389	−	0.540265i
$266$		0			0
$267$	5.69897	−	5.69897i	0.348771	−	0.348771i
$268$		0			0
$269$		−	1.96291i		−	0.119681i	−0.998208	−	0.0598404i	$-0.980941\pi$
$269$		−	1.96291i		−	0.119681i	0.998208	−	0.0598404i	$-0.0190592\pi$
$270$		0			0
$271$	−10.0313			−0.609355			−0.304678	−	0.952456i	$-0.598549\pi$
$271$	−10.0313			−0.609355			−0.304678	+	0.952456i	$0.598549\pi$
$272$		0			0
$273$	−6.51681	−	6.51681i	−0.394415	−	0.394415i
$274$		0			0
$275$	−26.5519	+	3.62791i	−1.60114	+	0.218771i
$276$		0			0
$277$	−15.6821	−	15.6821i	−0.942248	−	0.942248i	0.0561730	−	0.998421i	$-0.482110\pi$
$277$	−15.6821	−	15.6821i	−0.942248	−	0.942248i	−0.998421	+	0.0561730i	$0.982110\pi$
$278$		0			0
$279$		−	7.62711i		−	0.456623i
$280$		0			0
$281$			15.5018i			0.924762i	0.886681	+	0.462381i	$0.153005\pi$
$281$			15.5018i			0.924762i	−0.886681	+	0.462381i	$0.846995\pi$
$282$		0			0
$283$	−2.72459	−	2.72459i	−0.161960	−	0.161960i	0.621474	−	0.783435i	$-0.286534\pi$
$283$	−2.72459	−	2.72459i	−0.161960	−	0.161960i	−0.783435	+	0.621474i	$0.786534\pi$
$284$		0			0
$285$	−0.00559921		0.000380755i	−0.000331668		2.25540e-5i
$286$		0			0
$287$	−17.2911	+	17.2911i	−1.02066	+	1.02066i
$288$		0			0
$289$		−	6.78246i		−	0.398968i
$290$		0			0
$291$		−	13.3968i		−	0.785336i
$292$		0			0
$293$	−9.12495	−	9.12495i	−0.533085	−	0.533085i	0.388404	−	0.921489i	$-0.373026\pi$
$293$	−9.12495	−	9.12495i	−0.533085	−	0.533085i	−0.921489	+	0.388404i	$0.873026\pi$
$294$		0			0
$295$	−15.8020	+	18.1079i	−0.920028	+	1.05428i
$296$		0			0
$297$	−3.78989	+	3.78989i	−0.219912	+	0.219912i
$298$		0			0
$299$	12.7031	−	4.88978i	0.734639	−	0.282783i
$300$		0			0
$301$	1.22061			0.0703546
$302$		0			0
$303$	4.81931	−	4.81931i	0.276862	−	0.276862i
$304$		0			0
$305$	−3.00420	+	3.44259i	−0.172020	+	0.197122i
$306$		0			0
$307$	3.36045	+	3.36045i	0.191791	+	0.191791i	0.796470	−	0.604679i	$-0.206698\pi$
$307$	3.36045	+	3.36045i	0.191791	+	0.191791i	−0.604679	+	0.796470i	$0.706698\pi$
$308$		0			0
$309$	10.7522			0.611669
$310$		0			0
$311$	31.5893			1.79127			0.895633	−	0.444794i	$-0.146723\pi$
$311$	31.5893			1.79127			0.895633	+	0.444794i	$0.146723\pi$
$312$		0			0
$313$	−8.25763	−	8.25763i	−0.466749	−	0.466749i	0.434111	−	0.900859i	$-0.357063\pi$
$313$	−8.25763	−	8.25763i	−0.466749	−	0.466749i	−0.900859	+	0.434111i	$0.857063\pi$
$314$		0			0
$315$	−0.492610	−	7.24410i	−0.0277554	−	0.408159i
$316$		0			0
$317$	−4.33631	−	4.33631i	−0.243552	−	0.243552i	0.574766	−	0.818318i	$-0.305093\pi$
$317$	−4.33631	−	4.33631i	−0.243552	−	0.243552i	−0.818318	+	0.574766i	$0.805093\pi$
$318$		0			0
$319$	−7.08459			−0.396661
$320$		0			0
$321$			10.0276i			0.559687i
$322$		0			0
$323$	−0.00865480	+	0.00865480i	−0.000481566	+	0.000481566i
$324$		0			0
$325$	−11.3008	−	8.58384i	−0.626854	−	0.476146i
$326$		0			0
$327$	−2.24689	+	2.24689i	−0.124253	+	0.124253i
$328$		0			0
$329$	37.3679			2.06016
$330$		0			0
$331$	8.17004			0.449066			0.224533	−	0.974466i	$-0.427914\pi$
$331$	8.17004			0.449066			0.224533	+	0.974466i	$0.427914\pi$
$332$		0			0
$333$	−6.26209	−	6.26209i	−0.343161	−	0.343161i
$334$		0			0
$335$	−9.19784	+	0.625468i	−0.502532	+	0.0341729i
$336$		0			0
$337$	18.8595	−	18.8595i	1.02734	−	1.02734i	0.0277293	−	0.999615i	$-0.491172\pi$
$337$	18.8595	−	18.8595i	1.02734	−	1.02734i	0.999615	−	0.0277293i	$-0.00882765\pi$
$338$		0			0
$339$	6.98295			0.379262
$340$		0			0
$341$			40.8791i			2.21373i
$342$		0			0
$343$	7.93539	+	7.93539i	0.428471	+	0.428471i
$344$		0			0
$345$	10.0734	+	3.67773i	0.542336	+	0.198002i
$346$		0			0
$347$	−10.0059	−	10.0059i	−0.537147	−	0.537147i	0.385543	−	0.922690i	$-0.374014\pi$
$347$	−10.0059	−	10.0059i	−0.537147	−	0.537147i	−0.922690	+	0.385543i	$0.874014\pi$
$348$		0			0
$349$		−	8.15361i		−	0.436453i	−0.975898	−	0.218226i	$-0.929973\pi$
$349$		−	8.15361i		−	0.436453i	0.975898	−	0.218226i	$-0.0700271\pi$
$350$		0			0
$351$	−2.83824			−0.151494
$352$		0			0
$353$	−14.1024	+	14.1024i	−0.750592	+	0.750592i	−0.974590	−	0.223997i	$-0.928089\pi$
$353$	−14.1024	+	14.1024i	−0.750592	+	0.750592i	0.223997	+	0.974590i	$0.428089\pi$
$354$		0			0
$355$	12.7266	+	11.1059i	0.675458	+	0.589443i
$356$		0			0
$357$	−11.1973	−	11.1973i	−0.592626	−	0.592626i
$358$		0			0
$359$	18.3502			0.968487			0.484244	−	0.874933i	$-0.339095\pi$
$359$	18.3502			0.968487			0.484244	+	0.874933i	$0.339095\pi$
$360$		0			0
$361$	−19.0000			−1.00000
$362$		0			0
$363$	12.5345	−	12.5345i	0.657893	−	0.657893i
$364$		0			0
$365$	−2.97974	+	0.202627i	−0.155967	+	0.0106060i
$366$		0			0
$367$	23.6140	−	23.6140i	1.23264	−	1.23264i	0.269695	−	0.962946i	$-0.413077\pi$
$367$	23.6140	−	23.6140i	1.23264	−	1.23264i	0.962946	−	0.269695i	$-0.0869227\pi$
$368$		0			0
$369$			7.53073i			0.392034i
$370$		0			0
$371$	−12.8011			−0.664601
$372$		0			0
$373$	−7.62175	−	7.62175i	−0.394639	−	0.394639i	0.481698	−	0.876337i	$-0.340020\pi$
$373$	−7.62175	−	7.62175i	−0.394639	−	0.394639i	−0.876337	+	0.481698i	$0.840020\pi$
$374$		0			0
$375$	−2.26162	−	10.9492i	−0.116790	−	0.565414i
$376$		0			0
$377$	−2.65281	−	2.65281i	−0.136627	−	0.136627i
$378$		0			0
$379$	25.1086			1.28974			0.644870	−	0.764292i	$-0.276911\pi$
$379$	25.1086			1.28974			0.644870	+	0.764292i	$0.276911\pi$
$380$		0			0
$381$	−4.09380			−0.209732
$382$		0			0
$383$	−16.0351	−	16.0351i	−0.819357	−	0.819357i	0.166657	−	0.986015i	$-0.446703\pi$
$383$	−16.0351	−	16.0351i	−0.819357	−	0.819357i	−0.986015	+	0.166657i	$0.946703\pi$
$384$		0			0
$385$	2.64025	+	38.8263i	0.134559	+	1.97877i
$386$		0			0
$387$	0.265803	−	0.265803i	0.0135115	−	0.0135115i
$388$		0			0
$389$	15.9369			0.808032			0.404016	−	0.914752i	$-0.367614\pi$
$389$	15.9369			0.808032			0.404016	+	0.914752i	$0.367614\pi$
$390$		0			0
$391$	21.8268	−	8.40173i	1.10383	−	0.424894i
$392$		0			0
$393$	−14.0527	+	14.0527i	−0.708863	+	0.708863i
$394$		0			0
$395$	−10.8367	−	9.45674i	−0.545255	−	0.475820i
$396$		0			0
$397$	19.0995	+	19.0995i	0.958577	+	0.958577i	0.999176	−	0.0405981i	$-0.0129263\pi$
$397$	19.0995	+	19.0995i	0.958577	+	0.958577i	−0.0405981	+	0.999176i	$0.512926\pi$
$398$		0			0
$399$			0.00814976i			0.000407998i
$400$		0			0
$401$		−	22.0030i		−	1.09878i	−0.835567	−	0.549389i	$-0.814861\pi$
$401$		−	22.0030i		−	1.09878i	0.835567	−	0.549389i	$-0.185139\pi$
$402$		0			0
$403$	−15.3071	+	15.3071i	−0.762503	+	0.762503i
$404$		0			0
$405$	−1.68477	−	1.47022i	−0.0837168	−	0.0730560i
$406$		0			0
$407$	33.5630	+	33.5630i	1.66366	+	1.66366i
$408$		0			0
$409$			30.6719i			1.51663i	0.651889	+	0.758314i	$0.273977\pi$
$409$			30.6719i			1.51663i	−0.651889	+	0.758314i	$0.726023\pi$
$410$		0			0
$411$		−	1.48363i		−	0.0731819i
$412$		0			0
$413$	24.6783	+	24.6783i	1.21434	+	1.21434i
$414$		0			0
$415$	0.543202	+	7.98808i	0.0266647	+	0.392119i
$416$		0			0
$417$	−7.12569	−	7.12569i	−0.348946	−	0.348946i
$418$		0			0
$419$	−18.2883			−0.893444			−0.446722	−	0.894673i	$-0.647409\pi$
$419$	−18.2883			−0.893444			−0.446722	+	0.894673i	$0.647409\pi$
$420$		0			0
$421$			9.61292i			0.468505i	0.972176	+	0.234252i	$0.0752642\pi$
$421$			9.61292i			0.468505i	−0.972176	+	0.234252i	$0.924736\pi$
$422$		0			0
$423$	8.13733	−	8.13733i	0.395650	−	0.395650i
$424$		0			0
$425$	−19.4173	−	14.7490i	−0.941875	−	0.715430i
$426$		0			0
$427$	4.69172	+	4.69172i	0.227048	+	0.227048i
$428$		0			0
$429$	15.2121			0.734449
$430$		0			0
$431$		−	30.1350i		−	1.45155i	−0.687930	−	0.725777i	$-0.741480\pi$
$431$		−	30.1350i		−	1.45155i	0.687930	−	0.725777i	$-0.258520\pi$
$432$		0			0
$433$	6.89397	+	6.89397i	0.331303	+	0.331303i	0.853081	−	0.521778i	$-0.174731\pi$
$433$	6.89397	+	6.89397i	0.331303	+	0.331303i	−0.521778	+	0.853081i	$0.674731\pi$
$434$		0			0
$435$	−0.200528	−	2.94887i	−0.00961458	−	0.141388i
$436$		0			0
$437$	−0.0110006	−	0.00488557i	−0.000526230	−	0.000233709i
$438$		0			0
$439$		−	34.6386i		−	1.65321i	−0.562781	−	0.826606i	$-0.690269\pi$
$439$		−	34.6386i		−	1.65321i	0.562781	−	0.826606i	$-0.309731\pi$
$440$		0			0
$441$	−3.54394			−0.168759
$442$		0			0
$443$	−0.400276	+	0.400276i	−0.0190177	+	0.0190177i	−0.716552	−	0.697534i	$-0.754281\pi$
$443$	−0.400276	+	0.400276i	−0.0190177	+	0.0190177i	0.697534	+	0.716552i	$0.254281\pi$
$444$		0			0
$445$	−13.5785	−	11.8494i	−0.643682	−	0.561713i
$446$		0			0
$447$	−11.3446	+	11.3446i	−0.536582	+	0.536582i
$448$		0			0
$449$		−	39.8963i		−	1.88282i	−0.337258	−	0.941412i	$-0.609499\pi$
$449$		−	39.8963i		−	1.88282i	0.337258	−	0.941412i	$-0.390501\pi$
$450$		0			0
$451$		−	40.3626i		−	1.90060i
$452$		0			0
$453$	−8.35084	+	8.35084i	−0.392357	+	0.392357i
$454$		0			0
$455$	−13.5498	+	15.5271i	−0.635226	+	0.727922i
$456$		0			0
$457$	17.8152	−	17.8152i	0.833359	−	0.833359i	−0.154616	−	0.987975i	$-0.549414\pi$
$457$	17.8152	−	17.8152i	0.833359	−	0.833359i	0.987975	+	0.154616i	$0.0494140\pi$
$458$		0			0
$459$	−4.87673			−0.227626
$460$		0			0
$461$	31.1416			1.45041			0.725205	−	0.688533i	$-0.241745\pi$
$461$	31.1416			1.45041			0.725205	+	0.688533i	$0.241745\pi$
$462$		0			0
$463$	−20.7190	+	20.7190i	−0.962895	+	0.962895i	−0.999336	−	0.0364405i	$-0.988398\pi$
$463$	−20.7190	+	20.7190i	−0.962895	+	0.962895i	0.0364405	+	0.999336i	$0.488398\pi$
$464$		0			0
$465$	−17.0154	+	1.15708i	−0.789072	+	0.0536581i
$466$		0			0
$467$	14.3240	−	14.3240i	0.662838	−	0.662838i	−0.293210	−	0.956048i	$-0.594724\pi$
$467$	14.3240	−	14.3240i	0.662838	−	0.662838i	0.956048	+	0.293210i	$0.0947235\pi$
$468$		0			0
$469$			13.3876i			0.618184i
$470$		0			0
$471$			23.5433i			1.08482i
$472$		0			0
$473$	−1.42463	+	1.42463i	−0.0655043	+	0.0655043i
$474$		0			0
$475$	0.00169886	+	0.0124336i	7.79492e−5	+	0.000570493i
$476$		0			0
$477$	−2.78761	+	2.78761i	−0.127636	+	0.127636i
$478$		0			0
$479$	−37.6682			−1.72110			−0.860552	−	0.509363i	$-0.829881\pi$
$479$	−37.6682			−1.72110			−0.860552	+	0.509363i	$0.829881\pi$
$480$		0			0
$481$			25.1353i			1.14607i
$482$		0			0
$483$	6.32082	−	14.2323i	0.287607	−	0.647591i
$484$		0			0
$485$	−29.8872	+	2.03238i	−1.35711	+	0.0922855i
$486$		0			0
$487$	−8.90248	−	8.90248i	−0.403410	−	0.403410i	0.476023	−	0.879433i	$-0.342078\pi$
$487$	−8.90248	−	8.90248i	−0.403410	−	0.403410i	−0.879433	+	0.476023i	$0.842078\pi$
$488$		0			0
$489$			24.6933i			1.11667i
$490$		0			0
$491$	−14.8878			−0.671878			−0.335939	−	0.941884i	$-0.609054\pi$
$491$	−14.8878			−0.671878			−0.335939	+	0.941884i	$0.609054\pi$
$492$		0			0
$493$	−4.55813	−	4.55813i	−0.205288	−	0.205288i
$494$		0			0
$495$	9.02987	+	7.87997i	0.405862	+	0.354179i
$496$		0			0
$497$	17.3444	−	17.3444i	0.778001	−	0.778001i
$498$		0			0
$499$		−	11.5637i		−	0.517663i	−0.965922	−	0.258832i	$-0.916662\pi$
$499$		−	11.5637i		−	0.517663i	0.965922	−	0.258832i	$-0.0833375\pi$
$500$		0			0
$501$	10.6182			0.474384
$502$		0			0
$503$	−2.49630	−	2.49630i	−0.111305	−	0.111305i	0.649261	−	0.760566i	$-0.275078\pi$
$503$	−2.49630	−	2.49630i	−0.111305	−	0.111305i	−0.760566	+	0.649261i	$0.775078\pi$
$504$		0			0
$505$	−11.4826	−	10.0204i	−0.510969	−	0.445900i
$506$		0			0
$507$	−3.49622	−	3.49622i	−0.155273	−	0.155273i
$508$		0			0
$509$		−	1.80920i		−	0.0801913i	−0.999196	−	0.0400957i	$-0.987234\pi$
$509$		−	1.80920i		−	0.0801913i	0.999196	−	0.0400957i	$-0.0127663\pi$
$510$		0			0
$511$			4.33707i			0.191861i
$512$		0			0
$513$	0.00177471	+	0.00177471i	7.83555e−5	+	7.83555e-5i
$514$		0			0
$515$	−1.63116	−	23.9872i	−0.0718777	−	1.05700i
$516$		0			0
$517$	−43.6137	+	43.6137i	−1.91813	+	1.91813i
$518$		0			0
$519$			22.7335i			0.997889i
$520$		0			0
$521$			23.1952i			1.01620i	0.861298	+	0.508100i	$0.169652\pi$
$521$			23.1952i			1.01620i	−0.861298	+	0.508100i	$0.830348\pi$
$522$		0			0
$523$	17.6106	+	17.6106i	0.770058	+	0.770058i	0.978116	−	0.208059i	$-0.0667145\pi$
$523$	17.6106	+	17.6106i	0.770058	+	0.770058i	−0.208059	+	0.978116i	$0.566714\pi$
$524$		0			0
$525$	−16.0863	+	2.19794i	−0.702062	+	0.0959261i
$526$		0			0
$527$	−26.3011	+	26.3011i	−1.14569	+	1.14569i
$528$		0			0
$529$	15.4217	+	17.0638i	0.670507	+	0.741903i
$530$		0			0
$531$	10.7480			0.466425
$532$		0			0
$533$	15.1137	−	15.1137i	0.654647	−	0.654647i
$534$		0			0
$535$	22.3708	−	1.52125i	0.967172	−	0.0657692i
$536$		0			0
$537$	−12.0833	−	12.0833i	−0.521432	−	0.521432i
$538$		0			0
$539$	18.9945			0.818150
$540$		0			0
$541$	−33.0570			−1.42123			−0.710615	−	0.703581i	$-0.751583\pi$
$541$	−33.0570			−1.42123			−0.710615	+	0.703581i	$0.751583\pi$
$542$		0			0
$543$	5.64100	+	5.64100i	0.242079	+	0.242079i
$544$		0			0
$545$	5.35348	+	4.67175i	0.229318	+	0.200116i
$546$		0			0
$547$	29.8409	+	29.8409i	1.27590	+	1.27590i	0.942940	+	0.332963i	$0.108048\pi$
$547$	29.8409	+	29.8409i	1.27590	+	1.27590i	0.332963	+	0.942940i	$0.391952\pi$
$548$		0			0
$549$	2.04336			0.0872086
$550$		0			0
$551$			0.00331754i			0.000141332i
$552$		0			0
$553$	−14.7688	+	14.7688i	−0.628032	+	0.628032i
$554$		0			0
$555$	−13.0202	+	14.9202i	−0.552677	+	0.633327i
$556$		0			0
$557$	−19.0581	+	19.0581i	−0.807518	+	0.807518i	−0.984258	−	0.176740i	$-0.943445\pi$
$557$	−19.0581	+	19.0581i	−0.807518	+	0.807518i	0.176740	+	0.984258i	$0.443445\pi$
$558$		0			0
$559$	−1.06690			−0.0451250
$560$		0			0
$561$	26.1378			1.10354
$562$		0			0
$563$	−29.0966	−	29.0966i	−1.22628	−	1.22628i	−0.965362	−	0.260914i	$-0.915976\pi$
$563$	−29.0966	−	29.0966i	−1.22628	−	1.22628i	−0.260914	−	0.965362i	$-0.584024\pi$
$564$		0			0
$565$	−1.05935	−	15.5784i	−0.0445674	−	0.655387i
$566$		0			0
$567$	−2.29608	+	2.29608i	−0.0964262	+	0.0964262i
$568$		0			0
$569$	12.7185			0.533188			0.266594	−	0.963809i	$-0.414102\pi$
$569$	12.7185			0.533188			0.266594	+	0.963809i	$0.414102\pi$
$570$		0			0
$571$		−	42.6397i		−	1.78441i	−0.451626	−	0.892207i	$-0.649156\pi$
$571$		−	42.6397i		−	1.78441i	0.451626	−	0.892207i	$-0.350844\pi$
$572$		0			0
$573$	−4.86879	−	4.86879i	−0.203397	−	0.203397i
$574$		0			0
$575$	6.67650	−	23.0309i	0.278429	−	0.960457i
$576$		0			0
$577$	28.1720	+	28.1720i	1.17282	+	1.17282i	0.981535	+	0.191282i	$0.0612646\pi$
$577$	28.1720	+	28.1720i	1.17282	+	1.17282i	0.191282	+	0.981535i	$0.438735\pi$
$578$		0			0
$579$		−	15.7568i		−	0.654831i
$580$		0			0
$581$	11.6268			0.482361
$582$		0			0
$583$	14.9408	−	14.9408i	0.618784	−	0.618784i
$584$		0			0
$585$	0.430577	+	6.33187i	0.0178022	+	0.261791i
$586$		0			0
$587$	−20.7490	−	20.7490i	−0.856403	−	0.856403i	0.134509	−	0.990912i	$-0.457054\pi$
$587$	−20.7490	−	20.7490i	−0.856403	−	0.856403i	−0.990912	+	0.134509i	$0.957054\pi$
$588$		0			0
$589$	0.0191427			0.000788762
$590$		0			0
$591$	−12.7143			−0.522997
$592$		0			0
$593$	17.8636	−	17.8636i	0.733570	−	0.733570i	−0.237755	−	0.971325i	$-0.576412\pi$
$593$	17.8636	−	17.8636i	0.733570	−	0.733570i	0.971325	+	0.237755i	$0.0764115\pi$
$594$		0			0
$595$	−23.2816	+	26.6790i	−0.954453	+	1.09373i
$596$		0			0
$597$	−7.42273	+	7.42273i	−0.303792	+	0.303792i
$598$		0			0
$599$			16.2783i			0.665114i	0.943083	+	0.332557i	$0.107911\pi$
$599$			16.2783i			0.665114i	−0.943083	+	0.332557i	$0.892089\pi$
$600$		0			0
$601$	39.3242			1.60407			0.802035	−	0.597278i	$-0.203751\pi$
$601$	39.3242			1.60407			0.802035	+	0.597278i	$0.203751\pi$
$602$		0			0
$603$	2.91533	+	2.91533i	0.118721	+	0.118721i
$604$		0			0
$605$	−29.8651	−	26.0619i	−1.21419	−	1.05957i
$606$		0			0
$607$	11.1086	+	11.1086i	0.450885	+	0.450885i	0.895648	−	0.444763i	$-0.146712\pi$
$607$	11.1086	+	11.1086i	0.450885	+	0.450885i	−0.444763	+	0.895648i	$0.646712\pi$
$608$		0			0
$609$	−4.29215			−0.173927
$610$		0			0
$611$	−32.6622			−1.32137
$612$		0			0
$613$	4.92796	+	4.92796i	0.199039	+	0.199039i	0.799588	−	0.600549i	$-0.205051\pi$
$613$	4.92796	+	4.92796i	0.199039	+	0.199039i	−0.600549	+	0.799588i	$0.705051\pi$
$614$		0			0
$615$	16.8004	−	1.14245i	0.677459	−	0.0460682i
$616$		0			0
$617$	13.7567	−	13.7567i	0.553823	−	0.553823i	−0.373719	−	0.927542i	$-0.621918\pi$
$617$	13.7567	−	13.7567i	0.553823	−	0.553823i	0.927542	+	0.373719i	$0.121918\pi$
$618$		0			0
$619$	16.8009			0.675284			0.337642	−	0.941275i	$-0.390371\pi$
$619$	16.8009			0.675284			0.337642	+	0.941275i	$0.390371\pi$
$620$		0			0
$621$	−1.72282	−	4.47570i	−0.0691344	−	0.179604i
$622$		0			0
$623$	−18.5054	+	18.5054i	−0.741402	+	0.741402i
$624$		0			0
$625$	−24.0837	+	6.70654i	−0.963346	+	0.268262i
$626$		0			0
$627$	−0.00951196	−	0.00951196i	−0.000379871	−	0.000379871i
$628$		0			0
$629$			43.1880i			1.72202i
$630$		0			0
$631$		−	21.8184i		−	0.868575i	−0.900774	−	0.434288i	$-0.857000\pi$
$631$		−	21.8184i		−	0.868575i	0.900774	−	0.434288i	$-0.143000\pi$
$632$		0			0
$633$	6.29838	−	6.29838i	0.250338	−	0.250338i
$634$		0			0
$635$	0.621053	+	9.13293i	0.0246457	+	0.362429i
$636$		0			0
$637$	7.11246	+	7.11246i	0.281806	+	0.281806i
$638$		0			0
$639$		−	7.55392i		−	0.298828i
$640$		0			0
$641$		−	15.4018i		−	0.608333i	−0.952619	−	0.304167i	$-0.901622\pi$
$641$		−	15.4018i		−	0.608333i	0.952619	−	0.304167i	$-0.0983780\pi$
$642$		0			0
$643$	−20.6574	−	20.6574i	−0.814650	−	0.814650i	0.170677	−	0.985327i	$-0.445404\pi$
$643$	−20.6574	−	20.6574i	−0.814650	−	0.814650i	−0.985327	+	0.170677i	$0.945404\pi$
$644$		0			0
$645$	−0.633307	−	0.552659i	−0.0249364	−	0.0217609i
$646$		0			0
$647$	31.8099	+	31.8099i	1.25058	+	1.25058i	0.955462	+	0.295114i	$0.0953578\pi$
$647$	31.8099	+	31.8099i	1.25058	+	1.25058i	0.295114	+	0.955462i	$0.404642\pi$
$648$		0			0
$649$	−57.6063			−2.26125
$650$		0			0
$651$			24.7663i			0.970669i
$652$		0			0
$653$	−5.52842	+	5.52842i	−0.216344	+	0.216344i	−0.806956	−	0.590612i	$-0.798886\pi$
$653$	−5.52842	+	5.52842i	−0.216344	+	0.216344i	0.590612	+	0.806956i	$0.298886\pi$
$654$		0			0
$655$	33.4822	+	29.2184i	1.30826	+	1.14166i
$656$		0			0
$657$	0.944453	+	0.944453i	0.0368466	+	0.0368466i
$658$		0			0
$659$	29.6656			1.15561			0.577803	−	0.816176i	$-0.303910\pi$
$659$	29.6656			1.15561			0.577803	+	0.816176i	$0.303910\pi$
$660$		0			0
$661$			18.4917i			0.719245i	0.933098	+	0.359623i	$0.117095\pi$
$661$			18.4917i			0.719245i	−0.933098	+	0.359623i	$0.882905\pi$
$662$		0			0
$663$	9.78729	+	9.78729i	0.380107	+	0.380107i
$664$		0			0
$665$	0.0181814	−	0.00123637i	0.000705046	−	4.79442e-5i
$666$		0			0
$667$	2.57303	−	5.79357i	0.0996282	−	0.224328i
$668$		0			0
$669$			9.97853i			0.385792i
$670$		0			0
$671$	−10.9518			−0.422791
$672$		0			0
$673$	16.4881	−	16.4881i	0.635571	−	0.635571i	−0.313888	−	0.949460i	$-0.601632\pi$
$673$	16.4881	−	16.4881i	0.635571	−	0.635571i	0.949460	+	0.313888i	$0.101632\pi$
$674$		0			0
$675$	−3.02436	+	3.98162i	−0.116408	+	0.153252i
$676$		0			0
$677$	−10.9328	+	10.9328i	−0.420180	+	0.420180i	−0.885266	−	0.465085i	$-0.846024\pi$
$677$	−10.9328	+	10.9328i	−0.420180	+	0.420180i	0.465085	+	0.885266i	$0.346024\pi$
$678$		0			0
$679$			43.5014i			1.66943i
$680$		0			0
$681$			11.2249i			0.430137i
$682$		0			0
$683$	14.3457	−	14.3457i	0.548924	−	0.548924i	−0.377205	−	0.926130i	$-0.623115\pi$
$683$	14.3457	−	14.3457i	0.548924	−	0.548924i	0.926130	+	0.377205i	$0.123115\pi$
$684$		0			0
$685$	−3.30984	+	0.225074i	−0.126463	+	0.00859965i
$686$		0			0
$687$	14.1096	−	14.1096i	0.538315	−	0.538315i
$688$		0			0
$689$	11.1891			0.426271
$690$		0			0
$691$	17.3580			0.660329			0.330165	−	0.943923i	$-0.392896\pi$
$691$	17.3580			0.660329			0.330165	+	0.943923i	$0.392896\pi$
$692$		0			0
$693$	12.3063	−	12.3063i	0.467478	−	0.467478i
$694$		0			0
$695$	−14.8158	+	16.9778i	−0.561995	+	0.644005i
$696$		0			0
$697$	25.9687	−	25.9687i	0.983635	−	0.983635i
$698$		0			0
$699$			11.9457i			0.451829i
$700$		0			0
$701$		−	28.4053i		−	1.07285i	−0.843947	−	0.536426i	$-0.819774\pi$
$701$		−	28.4053i		−	1.07285i	0.843947	−	0.536426i	$-0.180226\pi$
$702$		0			0
$703$	0.0157168	−	0.0157168i	0.000592769	−	0.000592769i
$704$		0			0
$705$	−19.3882	−	16.9192i	−0.730201	−	0.637214i
$706$		0			0
$707$	−15.6490	+	15.6490i	−0.588541	+	0.588541i
$708$		0			0
$709$	−45.8428			−1.72166			−0.860831	−	0.508892i	$-0.830055\pi$
$709$	−45.8428			−1.72166			−0.860831	+	0.508892i	$0.830055\pi$
$710$		0			0
$711$			6.43218i			0.241226i
$712$		0			0
$713$	−33.4297	−	14.8468i	−1.25195	−	0.556016i
$714$		0			0
$715$	−2.30777	−	33.9370i	−0.0863056	−	1.26917i
$716$		0			0
$717$	11.7287	+	11.7287i	0.438015	+	0.438015i
$718$		0			0
$719$			48.1698i			1.79643i	0.439558	+	0.898214i	$0.355135\pi$
$719$			48.1698i			1.79643i	−0.439558	+	0.898214i	$0.644865\pi$
$720$		0			0
$721$	−34.9138			−1.30026
$722$		0			0
$723$	4.36491	+	4.36491i	0.162333	+	0.162333i
$724$		0			0
$725$	−6.54827	+	0.894722i	−0.243197	+	0.0332291i
$726$		0			0
$727$	7.87374	−	7.87374i	0.292021	−	0.292021i	−0.545857	−	0.837878i	$-0.683796\pi$
$727$	7.87374	−	7.87374i	0.292021	−	0.292021i	0.837878	+	0.545857i	$0.183796\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−1.83317			−0.0678022
$732$		0			0
$733$	28.0552	+	28.0552i	1.03624	+	1.03624i	0.999318	+	0.0369226i	$0.0117555\pi$
$733$	28.0552	+	28.0552i	1.03624	+	1.03624i	0.0369226	+	0.999318i	$0.488245\pi$
$734$		0			0
$735$	0.537635	+	7.90622i	0.0198310	+	0.291625i
$736$		0			0
$737$	−15.6253	−	15.6253i	−0.575567	−	0.575567i
$738$		0			0
$739$		−	27.9573i		−	1.02843i	−0.857662	−	0.514214i	$-0.828084\pi$
$739$		−	27.9573i		−	1.02843i	0.857662	−	0.514214i	$-0.171916\pi$
$740$		0			0
$741$		−	0.00712348i		−	0.000261688i
$742$		0			0
$743$	14.1326	+	14.1326i	0.518476	+	0.518476i	0.917110	−	0.398634i	$-0.130516\pi$
$743$	14.1326	+	14.1326i	0.518476	+	0.518476i	−0.398634	+	0.917110i	$0.630516\pi$
$744$		0			0
$745$	27.0299	+	23.5878i	0.990299	+	0.864191i
$746$		0			0
$747$	2.53189	−	2.53189i	0.0926369	−	0.0926369i
$748$		0			0
$749$		−	32.5611i		−	1.18976i
$750$		0			0
$751$		−	32.2782i		−	1.17785i	−0.808188	−	0.588925i	$-0.799551\pi$
$751$		−	32.2782i		−	1.17785i	0.808188	−	0.588925i	$-0.200449\pi$
$752$		0			0
$753$	−15.0428	−	15.0428i	−0.548188	−	0.548188i
$754$		0			0
$755$	19.8969	+	17.3632i	0.724122	+	0.631910i
$756$		0			0
$757$	1.19305	−	1.19305i	0.0433621	−	0.0433621i	−0.685093	−	0.728455i	$-0.740239\pi$
$757$	1.19305	−	1.19305i	0.0433621	−	0.0433621i	0.728455	+	0.685093i	$0.240239\pi$
$758$		0			0
$759$	9.23382	+	23.9885i	0.335167	+	0.870726i
$760$		0			0
$761$	−7.69802			−0.279053			−0.139527	−	0.990218i	$-0.544558\pi$
$761$	−7.69802			−0.279053			−0.139527	+	0.990218i	$0.544558\pi$
$762$		0			0
$763$	7.29596	−	7.29596i	0.264132	−	0.264132i
$764$		0			0
$765$	0.739827	+	10.8796i	0.0267485	+	0.393352i
$766$		0			0
$767$	−21.5706	−	21.5706i	−0.778870	−	0.778870i
$768$		0			0
$769$	−18.8925			−0.681280			−0.340640	−	0.940194i	$-0.610644\pi$
$769$	−18.8925			−0.681280			−0.340640	+	0.940194i	$0.610644\pi$
$770$		0			0
$771$	8.31682			0.299523
$772$		0			0
$773$	12.1025	+	12.1025i	0.435297	+	0.435297i	0.890426	−	0.455129i	$-0.150407\pi$
$773$	12.1025	+	12.1025i	0.435297	+	0.435297i	−0.455129	+	0.890426i	$0.650407\pi$
$774$		0			0
$775$	5.16268	+	37.7845i	0.185449	+	1.35726i
$776$		0			0
$777$	20.3339	+	20.3339i	0.729475	+	0.729475i
$778$		0			0
$779$	−0.0189008			−0.000677192
$780$		0			0
$781$			40.4868i			1.44873i
$782$		0			0
$783$	−0.934669	+	0.934669i	−0.0334024	+	0.0334024i
$784$		0			0
$785$	52.5231	−	3.57165i	1.87463	−	0.127478i
$786$		0			0
$787$	−34.2130	+	34.2130i	−1.21956	+	1.21956i	−0.251775	+	0.967786i	$0.581014\pi$
$787$	−34.2130	+	34.2130i	−1.21956	+	1.21956i	−0.967786	+	0.251775i	$0.918986\pi$
$788$		0			0
$789$	7.84206			0.279185
$790$		0			0
$791$	−22.6746			−0.806218
$792$		0			0
$793$	−4.10090	−	4.10090i	−0.145627	−	0.145627i
$794$		0			0
$795$	6.64182	+	5.79602i	0.235561	+	0.205564i
$796$		0			0
$797$	32.7305	−	32.7305i	1.15937	−	1.15937i	0.174763	−	0.984611i	$-0.444084\pi$
$797$	32.7305	−	32.7305i	1.15937	−	1.15937i	0.984611	−	0.174763i	$-0.0559159\pi$
$798$		0			0
$799$	−56.1210			−1.98542
$800$		0			0
$801$			8.05956i			0.284771i
$802$		0			0
$803$	−5.06199	−	5.06199i	−0.178634	−	0.178634i
$804$		0			0
$805$	−32.7099	−	11.9421i	−1.15287	−	0.420904i
$806$		0			0
$807$	1.38799	+	1.38799i	0.0488595	+	0.0488595i
$808$		0			0
$809$			7.67827i			0.269954i	0.990849	+	0.134977i	$0.0430960\pi$
$809$			7.67827i			0.269954i	−0.990849	+	0.134977i	$0.956904\pi$
$810$		0			0
$811$	26.3589			0.925585			0.462792	−	0.886467i	$-0.346848\pi$
$811$	26.3589			0.925585			0.462792	+	0.886467i	$0.346848\pi$
$812$		0			0
$813$	7.09317	−	7.09317i	0.248768	−	0.248768i
$814$		0			0
$815$	55.0888	−	3.74612i	1.92968	−	0.131221i
$816$		0			0
$817$	0.000667118	0	0.000667118i	2.33395e−5	0	2.33395e-5i
$818$		0			0
$819$	9.21617			0.322039
$820$		0			0
$821$	7.85009			0.273970			0.136985	−	0.990573i	$-0.456259\pi$
$821$	7.85009			0.273970			0.136985	+	0.990573i	$0.456259\pi$
$822$		0			0
$823$	−35.0506	+	35.0506i	−1.22179	+	1.22179i	−0.254792	+	0.966996i	$0.582007\pi$
$823$	−35.0506	+	35.0506i	−1.22179	+	1.22179i	−0.966996	+	0.254792i	$0.917993\pi$
$824$		0			0
$825$	16.2097	−	21.3403i	0.564349	−	0.742974i
$826$		0			0
$827$	−21.5188	+	21.5188i	−0.748282	+	0.748282i	−0.974157	−	0.225874i	$-0.927476\pi$
$827$	−21.5188	+	21.5188i	−0.748282	+	0.748282i	0.225874	+	0.974157i	$0.427476\pi$
$828$		0			0
$829$		−	30.7941i		−	1.06952i	−0.845003	−	0.534762i	$-0.820401\pi$
$829$		−	30.7941i		−	1.06952i	0.845003	−	0.534762i	$-0.179599\pi$
$830$		0			0
$831$	22.1779			0.769342
$832$		0			0
$833$	12.2208	+	12.2208i	0.423425	+	0.423425i
$834$		0			0
$835$	−1.61083	−	23.6882i	−0.0557452	−	0.819764i
$836$		0			0
$837$	5.39318	+	5.39318i	0.186416	+	0.186416i
$838$		0			0
$839$	35.3062			1.21891			0.609453	−	0.792823i	$-0.291389\pi$
$839$	35.3062			1.21891			0.609453	+	0.792823i	$0.291389\pi$
$840$		0			0
$841$	27.2528			0.939751
$842$		0			0
$843$	−10.9614	−	10.9614i	−0.377532	−	0.377532i
$844$		0			0
$845$	−7.26938	+	8.33017i	−0.250074	+	0.286567i
$846$		0			0
$847$	−40.7014	+	40.7014i	−1.39852	+	1.39852i
$848$		0			0
$849$	3.85316			0.132240
$850$		0			0
$851$	−39.6365	+	15.2572i	−1.35872	+	0.523010i
$852$		0			0
$853$	−19.4531	+	19.4531i	−0.666063	+	0.666063i	−0.956802	−	0.290739i	$-0.906099\pi$
$853$	−19.4531	+	19.4531i	−0.666063	+	0.666063i	0.290739	+	0.956802i	$0.406099\pi$
$854$		0			0
$855$	0.00369000	−	0.00422847i	0.000126195	−	0.000144611i
$856$		0			0
$857$	−40.1385	−	40.1385i	−1.37111	−	1.37111i	−0.858808	−	0.512297i	$-0.828795\pi$
$857$	−40.1385	−	40.1385i	−1.37111	−	1.37111i	−0.512297	−	0.858808i	$-0.671205\pi$
$858$		0			0
$859$			11.3298i			0.386567i	0.981143	+	0.193284i	$0.0619137\pi$
$859$			11.3298i			0.386567i	−0.981143	+	0.193284i	$0.938086\pi$
$860$		0			0
$861$		−	24.4534i		−	0.833368i
$862$		0			0
$863$	−36.6078	+	36.6078i	−1.24615	+	1.24615i	−0.288737	+	0.957408i	$0.593235\pi$
$863$	−36.6078	+	36.6078i	−1.24615	+	1.24615i	−0.957408	+	0.288737i	$0.906765\pi$
$864$		0			0
$865$	50.7165	−	3.44880i	1.72441	−	0.117263i
$866$		0			0
$867$	4.79592	+	4.79592i	0.162878	+	0.162878i
$868$		0			0
$869$		−	34.4746i		−	1.16947i
$870$		0			0
$871$		−	11.7018i		−	0.396500i
$872$		0			0
$873$	9.47299	+	9.47299i	0.320612	+	0.320612i
$874$		0			0
$875$	7.34380	+	35.5536i	0.248266	+	1.20193i
$876$		0			0
$877$	34.9225	+	34.9225i	1.17925	+	1.17925i	0.979935	+	0.199315i	$0.0638717\pi$
$877$	34.9225	+	34.9225i	1.17925	+	1.17925i	0.199315	+	0.979935i	$0.436128\pi$
$878$		0			0
$879$	12.9046			0.435262
$880$		0			0
$881$			33.9183i			1.14274i	0.820694	+	0.571368i	$0.193587\pi$
$881$			33.9183i			1.14274i	−0.820694	+	0.571368i	$0.806413\pi$
$882$		0			0
$883$	−1.98943	+	1.98943i	−0.0669496	+	0.0669496i	−0.739789	−	0.672839i	$-0.765075\pi$
$883$	−1.98943	+	1.98943i	−0.0669496	+	0.0669496i	0.672839	+	0.739789i	$0.265075\pi$
$884$		0			0
$885$	−1.63054	−	23.9779i	−0.0548099	−	0.806010i
$886$		0			0
$887$	−22.5496	−	22.5496i	−0.757142	−	0.757142i	0.218659	−	0.975801i	$-0.429832\pi$
$887$	−22.5496	−	22.5496i	−0.757142	−	0.757142i	−0.975801	+	0.218659i	$0.929832\pi$
$888$		0			0
$889$	13.2932			0.445838
$890$		0			0
$891$		−	5.35971i		−	0.179557i
$892$		0			0
$893$	0.0204233	+	0.0204233i	0.000683439	+	0.000683439i
$894$		0			0
$895$	−25.1237	+	28.7899i	−0.839792	+	0.962340i
$896$		0			0
$897$	−5.52486	+	12.4400i	−0.184470	+	0.415361i
$898$		0			0
$899$			10.0817i			0.336243i
$900$		0			0
$901$	19.2254			0.640491
$902$		0			0
$903$	−0.863099	+	0.863099i	−0.0287221	+	0.0287221i
$904$		0			0
$905$	11.7288	−	13.4404i	0.389879	−	0.446773i
$906$		0			0
$907$	14.2244	−	14.2244i	0.472314	−	0.472314i	−0.430349	−	0.902663i	$-0.641609\pi$
$907$	14.2244	−	14.2244i	0.472314	−	0.472314i	0.902663	+	0.430349i	$0.141609\pi$
$908$		0			0
$909$			6.81553i			0.226057i
$910$		0			0
$911$		−	24.7252i		−	0.819184i	−0.912269	−	0.409592i	$-0.865671\pi$
$911$		−	24.7252i		−	0.819184i	0.912269	−	0.409592i	$-0.134329\pi$
$912$		0			0
$913$	−13.5702	+	13.5702i	−0.449108	+	0.449108i
$914$		0			0
$915$	−0.309990	−	4.55857i	−0.0102479	−	0.150702i
$916$		0			0
$917$	45.6310	−	45.6310i	1.50687	−	1.50687i
$918$		0			0
$919$	−55.1324			−1.81865			−0.909325	−	0.416087i	$-0.863401\pi$
$919$	−55.1324			−1.81865			−0.909325	+	0.416087i	$0.863401\pi$
$920$		0			0
$921$	−4.75239			−0.156597
$922$		0			0
$923$	−15.1602	+	15.1602i	−0.499005	+	0.499005i
$924$		0			0
$925$	35.2609	+	26.7835i	1.15937	+	0.880636i
$926$		0			0
$927$	−7.60293	+	7.60293i	−0.249713	+	0.249713i
$928$		0			0
$929$			20.0979i			0.659392i	0.944087	+	0.329696i	$0.106946\pi$
$929$			20.0979i			0.659392i	−0.944087	+	0.329696i	$0.893054\pi$
$930$		0			0
$931$		−	0.00889466i		−	0.000291511i
$932$		0			0
$933$	−22.3370	+	22.3370i	−0.731281	+	0.731281i
$934$		0			0
$935$	−3.96526	−	58.3113i	−0.129678	−	1.90698i
$936$		0			0
$937$	7.12645	−	7.12645i	0.232811	−	0.232811i	−0.581054	−	0.813865i	$-0.697360\pi$
$937$	7.12645	−	7.12645i	0.232811	−	0.232811i	0.813865	+	0.581054i	$0.197360\pi$
$938$		0			0
$939$	11.6780			0.381099
$940$		0			0
$941$			42.1911i			1.37539i	0.726000	+	0.687695i	$0.241377\pi$
$941$			42.1911i			1.37539i	−0.726000	+	0.687695i	$0.758623\pi$
$942$		0			0
$943$	33.0073	+	14.6592i	1.07487	+	0.477368i
$944$		0			0
$945$	5.47068	+	4.77403i	0.177961	+	0.155299i
$946$		0			0
$947$	−8.90825	−	8.90825i	−0.289479	−	0.289479i	0.547395	−	0.836874i	$-0.315620\pi$
$947$	−8.90825	−	8.90825i	−0.289479	−	0.289479i	−0.836874	+	0.547395i	$0.815620\pi$
$948$		0			0
$949$		−	3.79092i		−	0.123058i
$950$		0			0
$951$	6.13247			0.198859
$952$		0			0
$953$	−13.0737	−	13.0737i	−0.423499	−	0.423499i	0.462907	−	0.886407i	$-0.346806\pi$
$953$	−13.0737	−	13.0737i	−0.423499	−	0.423499i	−0.886407	+	0.462907i	$0.846806\pi$
$954$		0			0
$955$	−10.1232	+	11.6005i	−0.327580	+	0.375383i
$956$		0			0
$957$	5.00956	−	5.00956i	0.161936	−	0.161936i
$958$		0			0
$959$			4.81754i			0.155567i
$960$		0			0
$961$	27.1728			0.876543
$962$		0			0
$963$	−7.09059	−	7.09059i	−0.228491	−	0.228491i
$964$		0			0
$965$	−35.1521	+	2.39040i	−1.13159	+	0.0769496i
$966$		0			0
$967$	−4.67247	−	4.67247i	−0.150257	−	0.150257i	0.627976	−	0.778233i	$-0.283884\pi$
$967$	−4.67247	−	4.67247i	−0.150257	−	0.150257i	−0.778233	+	0.627976i	$0.783884\pi$
$968$		0			0
$969$		−	0.0122397i		−	0.000393197i
$970$		0			0
$971$			9.40004i			0.301662i	0.988560	+	0.150831i	$0.0481949\pi$
$971$			9.40004i			0.301662i	−0.988560	+	0.150831i	$0.951805\pi$
$972$		0			0
$973$	23.1381	+	23.1381i	0.741774	+	0.741774i
$974$		0			0
$975$	14.0606	−	1.92116i	0.450298	−	0.0615264i
$976$		0			0
$977$	−11.4884	+	11.4884i	−0.367545	+	0.367545i	−0.866581	−	0.499036i	$-0.833688\pi$
$977$	−11.4884	+	11.4884i	−0.367545	+	0.367545i	0.499036	+	0.866581i	$0.333688\pi$
$978$		0			0
$979$		−	43.1969i		−	1.38058i
$980$		0			0
$981$		−	3.17758i		−	0.101452i
$982$		0			0
$983$	11.8053	+	11.8053i	0.376529	+	0.376529i	0.869848	−	0.493319i	$-0.164216\pi$
$983$	11.8053	+	11.8053i	0.376529	+	0.376529i	−0.493319	+	0.869848i	$0.664216\pi$
$984$		0			0
$985$	1.92883	+	28.3646i	0.0614578	+	0.903770i
$986$		0			0
$987$	−26.4231	+	26.4231i	−0.841055	+	0.841055i
$988$		0			0
$989$	−0.647611	−	1.68242i	−0.0205928	−	0.0534979i
$990$		0			0
$991$	1.09464			0.0347724			0.0173862	−	0.999849i	$-0.494466\pi$
$991$	1.09464			0.0347724			0.0173862	+	0.999849i	$0.494466\pi$
$992$		0			0
$993$	−5.77709	+	5.77709i	−0.183331	+	0.183331i
$994$		0			0
$995$	17.6856	+	15.4334i	0.560670	+	0.489272i
$996$		0			0
$997$	−13.1175	−	13.1175i	−0.415434	−	0.415434i	0.468192	−	0.883627i	$-0.344905\pi$
$997$	−13.1175	−	13.1175i	−0.415434	−	0.415434i	−0.883627	+	0.468192i	$0.844905\pi$
$998$		0			0
$999$	8.85593			0.280189

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.t.a.1057.6	yes	48
5.3	odd	4	inner	1380.2.t.a.1333.5	yes	48
23.22	odd	2	inner	1380.2.t.a.1057.5	✓	48
115.68	even	4	inner	1380.2.t.a.1333.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.t.a.1057.5	✓	48	23.22	odd	2	inner
1380.2.t.a.1057.6	yes	48	1.1	even	1	trivial
1380.2.t.a.1333.5	yes	48	5.3	odd	4	inner
1380.2.t.a.1333.6	yes	48	115.68	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.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(1.68477 + 1.47022i) q^{5} +(2.29608 - 2.29608i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(1.68477 + 1.47022i) q^{5} +(2.29608 - 2.29608i) q^{7} -1.00000i q^{9} +5.35971i q^{11} +(-2.00694 + 2.00694i) q^{13} +(-2.23092 + 0.151706i) q^{15} +(-3.44837 + 3.44837i) q^{17} +0.00250982 q^{19} +3.24714i q^{21} +(-4.38302 - 1.94658i) q^{23} +(0.676885 + 4.95397i) q^{25} +(0.707107 + 0.707107i) q^{27} +1.32182i q^{29} +7.62711 q^{31} +(-3.78989 - 3.78989i) q^{33} +(7.24410 - 0.492610i) q^{35} +(6.26209 - 6.26209i) q^{37} -2.83824i q^{39} -7.53073 q^{41} +(0.265803 + 0.265803i) q^{43} +(1.47022 - 1.68477i) q^{45} +(8.13733 + 8.13733i) q^{47} -3.54394i q^{49} -4.87673i q^{51} +(-2.78761 - 2.78761i) q^{53} +(-7.87997 + 9.02987i) q^{55} +(-0.00177471 + 0.00177471i) q^{57} +10.7480i q^{59} +2.04336i q^{61} +(-2.29608 - 2.29608i) q^{63} +(-6.33187 + 0.430577i) q^{65} +(-2.91533 + 2.91533i) q^{67} +(4.47570 - 1.72282i) q^{69} +7.55392 q^{71} +(-0.944453 + 0.944453i) q^{73} +(-3.98162 - 3.02436i) q^{75} +(12.3063 + 12.3063i) q^{77} -6.43218 q^{79} -1.00000 q^{81} +(2.53189 + 2.53189i) q^{83} +(-10.8796 + 0.739827i) q^{85} +(-0.934669 - 0.934669i) q^{87} -8.05956 q^{89} +9.21617i q^{91} +(-5.39318 + 5.39318i) q^{93} +(0.00422847 + 0.00369000i) q^{95} +(-9.47299 + 9.47299i) q^{97} +5.35971 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 8 q^{13} - 16 q^{23} - 8 q^{25} + 8 q^{31} + 8 q^{35} - 24 q^{41} + 8 q^{47} - 32 q^{55} - 24 q^{71} + 8 q^{73} + 32 q^{75} + 40 q^{77} - 48 q^{81} + 24 q^{85} - 40 q^{87}+O(q^{100}) \) 48 * q - 8 * q^13 - 16 * q^23 - 8 * q^25 + 8 * q^31 + 8 * q^35 - 24 * q^41 + 8 * q^47 - 32 * q^55 - 24 * q^71 + 8 * q^73 + 32 * q^75 + 40 * q^77 - 48 * q^81 + 24 * q^85 - 40 * q^87

Introduction

L-functions

Modular forms

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Database

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