LMFDB - Embedded newform 780.2.r.a.577.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [780,2,Mod(73,780)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(780, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("780.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	780.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:	$6.22833135766$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			577.10
Character	$\chi$	$=$	780.577
Dual form			780.2.r.a.73.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(-1.56908 + 1.59311i) q^{5} +2.82733i q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(-1.56908 + 1.59311i) q^{5} +2.82733i q^{7} -1.00000i q^{9} +(-0.572495 - 0.572495i) q^{11} +(-3.60553 + 0.0122487i) q^{13} +(0.0169926 + 2.23600i) q^{15} +(-4.83347 + 4.83347i) q^{17} +(-5.69816 - 5.69816i) q^{19} +(1.99922 + 1.99922i) q^{21} +(4.33569 + 4.33569i) q^{23} +(-0.0759911 - 4.99942i) q^{25} +(-0.707107 - 0.707107i) q^{27} +0.360658i q^{29} +(-3.47450 + 3.47450i) q^{31} -0.809631 q^{33} +(-4.50424 - 4.43630i) q^{35} -3.02731i q^{37} +(-2.54083 + 2.55816i) q^{39} +(-6.80464 + 6.80464i) q^{41} +(-0.183456 - 0.183456i) q^{43} +(1.59311 + 1.56908i) q^{45} +3.78276i q^{47} -0.993789 q^{49} +6.83555i q^{51} +(0.953692 - 0.953692i) q^{53} +(1.81034 - 0.0137577i) q^{55} -8.05841 q^{57} +(-5.73374 + 5.73374i) q^{59} +11.1860 q^{61} +2.82733 q^{63} +(5.63784 - 5.76322i) q^{65} +7.59652 q^{67} +6.13160 q^{69} +(1.43279 - 1.43279i) q^{71} +10.9578 q^{73} +(-3.58886 - 3.48139i) q^{75} +(1.61863 - 1.61863i) q^{77} +12.7130i q^{79} -1.00000 q^{81} +9.99087i q^{83} +(-0.116154 - 15.2843i) q^{85} +(0.255024 + 0.255024i) q^{87} +(-9.06108 + 9.06108i) q^{89} +(-0.0346312 - 10.1940i) q^{91} +4.91369i q^{93} +(18.0186 - 0.136934i) q^{95} -11.3420 q^{97} +(-0.572495 + 0.572495i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q+O(q^{10}) $ 28 * q	$ 28 q + 8 q^{11} - 4 q^{13} - 4 q^{15} - 4 q^{17} - 16 q^{19} + 8 q^{21} - 8 q^{23} + 12 q^{25} - 8 q^{33} + 8 q^{39} + 12 q^{41} + 16 q^{43} + 4 q^{45} - 36 q^{49} + 36 q^{53} + 40 q^{55} + 16 q^{59} + 8 q^{61} - 40 q^{65} + 48 q^{67} - 8 q^{69} + 8 q^{71} + 48 q^{73} - 48 q^{77} - 28 q^{81} - 4 q^{85} - 24 q^{87} - 36 q^{89} - 24 q^{91} + 72 q^{95} - 72 q^{97} + 8 q^{99}+O(q^{100}) $ 28 * q + 8 * q^11 - 4 * q^13 - 4 * q^15 - 4 * q^17 - 16 * q^19 + 8 * q^21 - 8 * q^23 + 12 * q^25 - 8 * q^33 + 8 * q^39 + 12 * q^41 + 16 * q^43 + 4 * q^45 - 36 * q^49 + 36 * q^53 + 40 * q^55 + 16 * q^59 + 8 * q^61 - 40 * q^65 + 48 * q^67 - 8 * q^69 + 8 * q^71 + 48 * q^73 - 48 * q^77 - 28 * q^81 - 4 * q^85 - 24 * q^87 - 36 * q^89 - 24 * q^91 + 72 * q^95 - 72 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/780\mathbb{Z}\right)^\times$.

$n$	$157$	$301$	$391$	$521$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	−1.56908	+	1.59311i	−0.701713	+	0.712460i
$5$	−1.56908	+	1.59311i	−0.701713	+	0.712460i
$6$		0			0
$7$			2.82733i			1.06863i	0.845285	+	0.534315i	$0.179430\pi$
$7$			2.82733i			1.06863i	−0.845285	+	0.534315i	$0.820570\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−0.572495	−	0.572495i	−0.172614	−	0.172614i	0.615513	−	0.788127i	$-0.288949\pi$
$11$	−0.572495	−	0.572495i	−0.172614	−	0.172614i	−0.788127	+	0.615513i	$0.788949\pi$
$12$		0			0
$13$	−3.60553	+	0.0122487i	−0.999994	+	0.00339719i
$13$	−3.60553	+	0.0122487i	−0.999994	+	0.00339719i
$14$		0			0
$15$	0.0169926	+	2.23600i	0.00438748	+	0.577334i
$16$		0			0
$17$	−4.83347	+	4.83347i	−1.17229	+	1.17229i	−0.190625	+	0.981663i	$0.561051\pi$
$17$	−4.83347	+	4.83347i	−1.17229	+	1.17229i	−0.981663	+	0.190625i	$0.938949\pi$
$18$		0			0
$19$	−5.69816	−	5.69816i	−1.30725	−	1.30725i	−0.923394	−	0.383853i	$-0.874597\pi$
$19$	−5.69816	−	5.69816i	−1.30725	−	1.30725i	−0.383853	−	0.923394i	$-0.625403\pi$
$20$		0			0
$21$	1.99922	+	1.99922i	0.436266	+	0.436266i
$22$		0			0
$23$	4.33569	+	4.33569i	0.904054	+	0.904054i	0.995784	−	0.0917295i	$-0.0292395\pi$
$23$	4.33569	+	4.33569i	0.904054	+	0.904054i	−0.0917295	+	0.995784i	$0.529240\pi$
$24$		0			0
$25$	−0.0759911	−	4.99942i	−0.0151982	−	0.999885i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$			0.360658i			0.0669726i	0.999439	+	0.0334863i	$0.0106610\pi$
$29$			0.360658i			0.0669726i	−0.999439	+	0.0334863i	$0.989339\pi$
$30$		0			0
$31$	−3.47450	+	3.47450i	−0.624039	+	0.624039i	−0.946562	−	0.322523i	$-0.895469\pi$
$31$	−3.47450	+	3.47450i	−0.624039	+	0.624039i	0.322523	+	0.946562i	$0.395469\pi$
$32$		0			0
$33$	−0.809631			−0.140939
$34$		0			0
$35$	−4.50424	−	4.43630i	−0.761356	−	0.749871i
$36$		0			0
$37$		−	3.02731i		−	0.497686i	−0.968544	−	0.248843i	$-0.919950\pi$
$37$		−	3.02731i		−	0.497686i	0.968544	−	0.248843i	$-0.0800503\pi$
$38$		0			0
$39$	−2.54083	+	2.55816i	−0.406859	+	0.409633i
$40$		0			0
$41$	−6.80464	+	6.80464i	−1.06271	+	1.06271i	−0.0648087	+	0.997898i	$0.520644\pi$
$41$	−6.80464	+	6.80464i	−1.06271	+	1.06271i	−0.997898	+	0.0648087i	$0.979356\pi$
$42$		0			0
$43$	−0.183456	−	0.183456i	−0.0279767	−	0.0279767i	0.692980	−	0.720957i	$-0.256297\pi$
$43$	−0.183456	−	0.183456i	−0.0279767	−	0.0279767i	−0.720957	+	0.692980i	$0.756297\pi$
$44$		0			0
$45$	1.59311	+	1.56908i	0.237487	+	0.233904i
$46$		0			0
$47$			3.78276i			0.551772i	0.961190	+	0.275886i	$0.0889712\pi$
$47$			3.78276i			0.551772i	−0.961190	+	0.275886i	$0.911029\pi$
$48$		0			0
$49$	−0.993789			−0.141970
$50$		0			0
$51$			6.83555i			0.957169i
$52$		0			0
$53$	0.953692	−	0.953692i	0.131000	−	0.131000i	−0.638567	−	0.769566i	$-0.720472\pi$
$53$	0.953692	−	0.953692i	0.131000	−	0.131000i	0.769566	+	0.638567i	$0.220472\pi$
$54$		0			0
$55$	1.81034	−	0.0137577i	0.244106	−	0.00185509i
$56$		0			0
$57$	−8.05841			−1.06736
$58$		0			0
$59$	−5.73374	+	5.73374i	−0.746469	+	0.746469i	−0.973814	−	0.227345i	$-0.926996\pi$
$59$	−5.73374	+	5.73374i	−0.746469	+	0.746469i	0.227345	+	0.973814i	$0.426996\pi$
$60$		0			0
$61$	11.1860			1.43222			0.716108	−	0.697989i	$-0.245922\pi$
$61$	11.1860			1.43222			0.716108	+	0.697989i	$0.245922\pi$
$62$		0			0
$63$	2.82733			0.356210
$64$		0			0
$65$	5.63784	−	5.76322i	0.699288	−	0.714840i
$66$		0			0
$67$	7.59652			0.928062			0.464031	−	0.885819i	$-0.346403\pi$
$67$	7.59652			0.928062			0.464031	+	0.885819i	$0.346403\pi$
$68$		0			0
$69$	6.13160			0.738157
$70$		0			0
$71$	1.43279	−	1.43279i	0.170041	−	0.170041i	−0.616957	−	0.786997i	$-0.711635\pi$
$71$	1.43279	−	1.43279i	0.170041	−	0.170041i	0.786997	+	0.616957i	$0.211635\pi$
$72$		0			0
$73$	10.9578			1.28251			0.641255	−	0.767327i	$-0.278414\pi$
$73$	10.9578			1.28251			0.641255	+	0.767327i	$0.278414\pi$
$74$		0			0
$75$	−3.58886	−	3.48139i	−0.414406	−	0.401996i
$76$		0			0
$77$	1.61863	−	1.61863i	0.184460	−	0.184460i
$78$		0			0
$79$			12.7130i			1.43032i	0.698959	+	0.715162i	$0.253647\pi$
$79$			12.7130i			1.43032i	−0.698959	+	0.715162i	$0.746353\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$			9.99087i			1.09664i	0.836268	+	0.548320i	$0.184733\pi$
$83$			9.99087i			1.09664i	−0.836268	+	0.548320i	$0.815267\pi$
$84$		0			0
$85$	−0.116154	−	15.2843i	−0.0125987	−	1.65782i
$86$		0			0
$87$	0.255024	+	0.255024i	0.0273414	+	0.0273414i
$88$		0			0
$89$	−9.06108	+	9.06108i	−0.960472	+	0.960472i	−0.999248	−	0.0387757i	$-0.987654\pi$
$89$	−9.06108	+	9.06108i	−0.960472	+	0.960472i	0.0387757	+	0.999248i	$0.487654\pi$
$90$		0			0
$91$	−0.0346312	−	10.1940i	−0.00363034	−	1.06862i
$92$		0			0
$93$			4.91369i			0.509526i
$94$		0			0
$95$	18.0186	−	0.136934i	1.84867	−	0.0140491i
$96$		0			0
$97$	−11.3420			−1.15161			−0.575804	−	0.817588i	$-0.695311\pi$
$97$	−11.3420			−1.15161			−0.575804	+	0.817588i	$0.695311\pi$
$98$		0			0
$99$	−0.572495	+	0.572495i	−0.0575380	+	0.0575380i
$100$		0			0
$101$		−	13.6700i		−	1.36022i	−0.733112	−	0.680108i	$-0.761933\pi$
$101$		−	13.6700i		−	1.36022i	0.733112	−	0.680108i	$-0.238067\pi$
$102$		0			0
$103$	−7.60186	−	7.60186i	−0.749034	−	0.749034i	0.225264	−	0.974298i	$-0.427676\pi$
$103$	−7.60186	−	7.60186i	−0.749034	−	0.749034i	−0.974298	+	0.225264i	$0.927676\pi$
$104$		0			0
$105$	−6.32192	+	0.0480437i	−0.616956	+	0.00468859i
$106$		0			0
$107$	7.74469	+	7.74469i	0.748708	+	0.748708i	0.974236	−	0.225529i	$-0.0724110\pi$
$107$	7.74469	+	7.74469i	0.748708	+	0.748708i	−0.225529	+	0.974236i	$0.572411\pi$
$108$		0			0
$109$	−2.95797	−	2.95797i	−0.283322	−	0.283322i	0.551111	−	0.834432i	$-0.314204\pi$
$109$	−2.95797	−	2.95797i	−0.283322	−	0.283322i	−0.834432	+	0.551111i	$0.814204\pi$
$110$		0			0
$111$	−2.14063	−	2.14063i	−0.203180	−	0.203180i
$112$		0			0
$113$	10.1966	−	10.1966i	0.959215	−	0.959215i	−0.0399848	−	0.999200i	$-0.512731\pi$
$113$	10.1966	−	10.1966i	0.959215	−	0.959215i	0.999200	+	0.0399848i	$0.0127309\pi$
$114$		0			0
$115$	−13.7103	+	0.104192i	−1.27849	+	0.00971594i
$116$		0			0
$117$	0.0122487	+	3.60553i	0.00113240	+	0.333331i
$118$		0			0
$119$	−13.6658	−	13.6658i	−1.25274	−	1.25274i
$120$		0			0
$121$		−	10.3445i		−	0.940409i
$122$		0			0
$123$			9.62322i			0.867696i
$124$		0			0
$125$	8.08386	+	7.72342i	0.723042	+	0.690804i
$126$		0			0
$127$	−0.659534	+	0.659534i	−0.0585242	+	0.0585242i	−0.735763	−	0.677239i	$-0.763176\pi$
$127$	−0.659534	+	0.659534i	−0.0585242	+	0.0585242i	0.677239	+	0.735763i	$0.263176\pi$
$128$		0			0
$129$	−0.259446			−0.0228429
$130$		0			0
$131$	−2.52359			−0.220487			−0.110244	−	0.993905i	$-0.535163\pi$
$131$	−2.52359			−0.220487			−0.110244	+	0.993905i	$0.535163\pi$
$132$		0			0
$133$	16.1106	−	16.1106i	1.39696	−	1.39696i
$134$		0			0
$135$	2.23600	−	0.0169926i	0.192445	−	0.00146249i
$136$		0			0
$137$		−	10.4196i		−	0.890206i	−0.895479	−	0.445103i	$-0.853167\pi$
$137$		−	10.4196i		−	0.890206i	0.895479	−	0.445103i	$-0.146833\pi$
$138$		0			0
$139$			8.27964i			0.702270i	0.936325	+	0.351135i	$0.114204\pi$
$139$			8.27964i			0.702270i	−0.936325	+	0.351135i	$0.885796\pi$
$140$		0			0
$141$	2.67481	+	2.67481i	0.225260	+	0.225260i
$142$		0			0
$143$	2.07116	+	2.05714i	0.173199	+	0.172026i
$144$		0			0
$145$	−0.574568	−	0.565901i	−0.0477153	−	0.0469955i
$146$		0			0
$147$	−0.702715	+	0.702715i	−0.0579590	+	0.0579590i
$148$		0			0
$149$	3.46007	+	3.46007i	0.283460	+	0.283460i	0.834487	−	0.551027i	$-0.185764\pi$
$149$	3.46007	+	3.46007i	0.283460	+	0.283460i	−0.551027	+	0.834487i	$0.685764\pi$
$150$		0			0
$151$	−6.26368	−	6.26368i	−0.509731	−	0.509731i	0.404713	−	0.914444i	$-0.367371\pi$
$151$	−6.26368	−	6.26368i	−0.509731	−	0.509731i	−0.914444	+	0.404713i	$0.867371\pi$
$152$		0			0
$153$	4.83347	+	4.83347i	0.390763	+	0.390763i
$154$		0			0
$155$	−0.0834964	−	10.9870i	−0.00670659	−	0.882499i
$156$		0			0
$157$	5.84946	+	5.84946i	0.466838	+	0.466838i	0.900889	−	0.434051i	$-0.142916\pi$
$157$	5.84946	+	5.84946i	0.466838	+	0.466838i	−0.434051	+	0.900889i	$0.642916\pi$
$158$		0			0
$159$		−	1.34872i		−	0.106961i
$160$		0			0
$161$	−12.2584	+	12.2584i	−0.966100	+	0.966100i
$162$		0			0
$163$	−20.7430			−1.62472			−0.812359	−	0.583157i	$-0.801817\pi$
$163$	−20.7430			−1.62472			−0.812359	+	0.583157i	$0.801817\pi$
$164$		0			0
$165$	1.27037	−	1.28983i	0.0988984	−	0.100413i
$166$		0			0
$167$		−	6.34267i		−	0.490811i	−0.969421	−	0.245405i	$-0.921079\pi$
$167$		−	6.34267i		−	0.490811i	0.969421	−	0.245405i	$-0.0789210\pi$
$168$		0			0
$169$	12.9997	−	0.0883264i	0.999977	−	0.00679434i
$170$		0			0
$171$	−5.69816	+	5.69816i	−0.435749	+	0.435749i
$172$		0			0
$173$	15.3552	+	15.3552i	1.16743	+	1.16743i	0.982809	+	0.184624i	$0.0591067\pi$
$173$	15.3552	+	15.3552i	1.16743	+	1.16743i	0.184624	+	0.982809i	$0.440893\pi$
$174$		0			0
$175$	14.1350	−	0.214852i	1.06851	−	0.0162413i
$176$		0			0
$177$			8.10873i			0.609490i
$178$		0			0
$179$	−8.19440			−0.612478			−0.306239	−	0.951955i	$-0.599071\pi$
$179$	−8.19440			−0.612478			−0.306239	+	0.951955i	$0.599071\pi$
$180$		0			0
$181$		−	20.2271i		−	1.50347i	−0.659467	−	0.751734i	$-0.729218\pi$
$181$		−	20.2271i		−	1.50347i	0.659467	−	0.751734i	$-0.270782\pi$
$182$		0			0
$183$	7.90968	−	7.90968i	0.584700	−	0.584700i
$184$		0			0
$185$	4.82283	+	4.75008i	0.354581	+	0.349233i
$186$		0			0
$187$	5.53427			0.404706
$188$		0			0
$189$	1.99922	−	1.99922i	0.145422	−	0.145422i
$190$		0			0
$191$	−13.6670			−0.988908			−0.494454	−	0.869204i	$-0.664632\pi$
$191$	−13.6670			−0.988908			−0.494454	+	0.869204i	$0.664632\pi$
$192$		0			0
$193$	25.1114			1.80756			0.903778	−	0.428001i	$-0.140782\pi$
$193$	25.1114			1.80756			0.903778	+	0.428001i	$0.140782\pi$
$194$		0			0
$195$	−0.0886556	−	8.06177i	−0.00634876	−	0.577315i
$196$		0			0
$197$	16.0428			1.14300			0.571501	−	0.820602i	$-0.306361\pi$
$197$	16.0428			1.14300			0.571501	+	0.820602i	$0.306361\pi$
$198$		0			0
$199$	−8.66921			−0.614544			−0.307272	−	0.951622i	$-0.599416\pi$
$199$	−8.66921			−0.614544			−0.307272	+	0.951622i	$0.599416\pi$
$200$		0			0
$201$	5.37155	−	5.37155i	0.378880	−	0.378880i
$202$		0			0
$203$	−1.01970			−0.0715689
$204$		0			0
$205$	−0.163524	−	21.5175i	−0.0114210	−	1.50285i
$206$		0			0
$207$	4.33569	−	4.33569i	0.301351	−	0.301351i
$208$		0			0
$209$			6.52434i			0.451298i
$210$		0			0
$211$	8.64368			0.595055			0.297528	−	0.954713i	$-0.403838\pi$
$211$	8.64368			0.595055			0.297528	+	0.954713i	$0.403838\pi$
$212$		0			0
$213$		−	2.02627i		−	0.138838i
$214$		0			0
$215$	0.580121	−	0.00440866i	0.0395639	−	0.000300668i
$216$		0			0
$217$	−9.82356	−	9.82356i	−0.666867	−	0.666867i
$218$		0			0
$219$	7.74832	−	7.74832i	0.523583	−	0.523583i
$220$		0			0
$221$	17.3680	−	17.4864i	1.16830	−	1.17626i
$222$		0			0
$223$			12.0245i			0.805221i	0.915371	+	0.402611i	$0.131897\pi$
$223$			12.0245i			0.805221i	−0.915371	+	0.402611i	$0.868103\pi$
$224$		0			0
$225$	−4.99942	+	0.0759911i	−0.333295	+	0.00506607i
$226$		0			0
$227$	−8.43494			−0.559847			−0.279923	−	0.960022i	$-0.590309\pi$
$227$	−8.43494			−0.559847			−0.279923	+	0.960022i	$0.590309\pi$
$228$		0			0
$229$	−6.49004	+	6.49004i	−0.428874	+	0.428874i	−0.888245	−	0.459371i	$-0.848075\pi$
$229$	−6.49004	+	6.49004i	−0.428874	+	0.428874i	0.459371	+	0.888245i	$0.348075\pi$
$230$		0			0
$231$		−	2.28909i		−	0.150611i
$232$		0			0
$233$	−2.60410	−	2.60410i	−0.170600	−	0.170600i	0.616643	−	0.787243i	$-0.288492\pi$
$233$	−2.60410	−	2.60410i	−0.170600	−	0.170600i	−0.787243	+	0.616643i	$0.788492\pi$
$234$		0			0
$235$	−6.02634	−	5.93544i	−0.393115	−	0.387185i
$236$		0			0
$237$	8.98945	+	8.98945i	0.583927	+	0.583927i
$238$		0			0
$239$	14.7260	+	14.7260i	0.952547	+	0.952547i	0.998924	−	0.0463773i	$-0.0147677\pi$
$239$	14.7260	+	14.7260i	0.952547	+	0.952547i	−0.0463773	+	0.998924i	$0.514768\pi$
$240$		0			0
$241$	−8.42906	−	8.42906i	−0.542964	−	0.542964i	0.381433	−	0.924397i	$-0.375431\pi$
$241$	−8.42906	−	8.42906i	−0.542964	−	0.542964i	−0.924397	+	0.381433i	$0.875431\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	1.55933	−	1.58321i	0.0996221	−	0.101148i
$246$		0			0
$247$	20.6147	+	20.4751i	1.31168	+	1.30280i
$248$		0			0
$249$	7.06461	+	7.06461i	0.447702	+	0.447702i
$250$		0			0
$251$		−	13.1855i		−	0.832261i	−0.909305	−	0.416131i	$-0.863386\pi$
$251$		−	13.1855i		−	0.832261i	0.909305	−	0.416131i	$-0.136614\pi$
$252$		0			0
$253$		−	4.96433i		−	0.312105i
$254$		0			0
$255$	−10.8898	−	10.7255i	−0.681944	−	0.671658i
$256$		0			0
$257$	−2.11360	+	2.11360i	−0.131842	+	0.131842i	−0.769948	−	0.638106i	$-0.779718\pi$
$257$	−2.11360	+	2.11360i	−0.131842	+	0.131842i	0.638106	+	0.769948i	$0.279718\pi$
$258$		0			0
$259$	8.55919			0.531842
$260$		0			0
$261$	0.360658			0.0223242
$262$		0			0
$263$	−17.1911	+	17.1911i	−1.06005	+	1.06005i	−0.0619718	+	0.998078i	$0.519739\pi$
$263$	−17.1911	+	17.1911i	−1.06005	+	1.06005i	−0.998078	+	0.0619718i	$0.980261\pi$
$264$		0			0
$265$	0.0229184	+	3.01575i	0.00140786	+	0.185256i
$266$		0			0
$267$			12.8143i			0.784222i
$268$		0			0
$269$			12.6645i			0.772166i	0.922464	+	0.386083i	$0.126172\pi$
$269$			12.6645i			0.772166i	−0.922464	+	0.386083i	$0.873828\pi$
$270$		0			0
$271$	18.6922	+	18.6922i	1.13547	+	1.13547i	0.989252	+	0.146221i	$0.0467110\pi$
$271$	18.6922	+	18.6922i	1.13547	+	1.13547i	0.146221	+	0.989252i	$0.453289\pi$
$272$		0			0
$273$	−7.23275	−	7.18377i	−0.437746	−	0.434782i
$274$		0			0
$275$	−2.81864	+	2.90565i	−0.169970	+	0.175217i
$276$		0			0
$277$	−13.2604	+	13.2604i	−0.796742	+	0.796742i	−0.982580	−	0.185839i	$-0.940500\pi$
$277$	−13.2604	+	13.2604i	−0.796742	+	0.796742i	0.185839	+	0.982580i	$0.440500\pi$
$278$		0			0
$279$	3.47450	+	3.47450i	0.208013	+	0.208013i
$280$		0			0
$281$	−0.980712	−	0.980712i	−0.0585044	−	0.0585044i	0.677249	−	0.735754i	$-0.263172\pi$
$281$	−0.980712	−	0.980712i	−0.0585044	−	0.0585044i	−0.735754	+	0.677249i	$0.763172\pi$
$282$		0			0
$283$	8.83480	+	8.83480i	0.525174	+	0.525174i	0.919130	−	0.393955i	$-0.128894\pi$
$283$	8.83480	+	8.83480i	0.525174	+	0.525174i	−0.393955	+	0.919130i	$0.628894\pi$
$284$		0			0
$285$	12.6443	−	12.8379i	0.748982	−	0.760453i
$286$		0			0
$287$	−19.2390	−	19.2390i	−1.13564	−	1.13564i
$288$		0			0
$289$		−	29.7248i		−	1.74852i
$290$		0			0
$291$	−8.02002	+	8.02002i	−0.470142	+	0.470142i
$292$		0			0
$293$	17.4402			1.01887			0.509434	−	0.860510i	$-0.329855\pi$
$293$	17.4402			1.01887			0.509434	+	0.860510i	$0.329855\pi$
$294$		0			0
$295$	−0.137789	−	18.1312i	−0.00802236	−	1.05564i
$296$		0			0
$297$			0.809631i			0.0469795i
$298$		0			0
$299$	−15.6856	−	15.5794i	−0.907120	−	0.900978i
$300$		0			0
$301$	0.518690	−	0.518690i	0.0298968	−	0.0298968i
$302$		0			0
$303$	−9.66615	−	9.66615i	−0.555306	−	0.555306i
$304$		0			0
$305$	−17.5517	+	17.8205i	−1.00500	+	1.02040i
$306$		0			0
$307$			6.37294i			0.363723i	0.983324	+	0.181861i	$0.0582122\pi$
$307$			6.37294i			0.363723i	−0.983324	+	0.181861i	$0.941788\pi$
$308$		0			0
$309$	−10.7507			−0.611584
$310$		0			0
$311$		−	31.9435i		−	1.81135i	−0.423973	−	0.905675i	$-0.639365\pi$
$311$		−	31.9435i		−	1.81135i	0.423973	−	0.905675i	$-0.360635\pi$
$312$		0			0
$313$	−7.37468	+	7.37468i	−0.416842	+	0.416842i	−0.884114	−	0.467272i	$-0.845237\pi$
$313$	−7.37468	+	7.37468i	−0.416842	+	0.416842i	0.467272	+	0.884114i	$0.345237\pi$
$314$		0			0
$315$	−4.43630	+	4.50424i	−0.249957	+	0.253785i
$316$		0			0
$317$	−19.6383			−1.10300			−0.551498	−	0.834176i	$-0.685944\pi$
$317$	−19.6383			−1.10300			−0.551498	+	0.834176i	$0.685944\pi$
$318$		0			0
$319$	0.206475	−	0.206475i	0.0115604	−	0.0115604i
$320$		0			0
$321$	10.9526			0.611317
$322$		0			0
$323$	55.0837			3.06494
$324$		0			0
$325$	0.335225	+	18.0246i	0.0185949	+	0.999827i
$326$		0			0
$327$	−4.18319			−0.231331
$328$		0			0
$329$	−10.6951			−0.589640
$330$		0			0
$331$	−12.1075	+	12.1075i	−0.665490	+	0.665490i	−0.956669	−	0.291178i	$-0.905953\pi$
$331$	−12.1075	+	12.1075i	−0.665490	+	0.665490i	0.291178	+	0.956669i	$0.405953\pi$
$332$		0			0
$333$	−3.02731			−0.165895
$334$		0			0
$335$	−11.9195	+	12.1021i	−0.651233	+	0.661207i
$336$		0			0
$337$	−16.3580	+	16.3580i	−0.891076	+	0.891076i	−0.994624	−	0.103548i	$-0.966980\pi$
$337$	−16.3580	+	16.3580i	−0.891076	+	0.891076i	0.103548	+	0.994624i	$0.466980\pi$
$338$		0			0
$339$		−	14.4202i		−	0.783196i
$340$		0			0
$341$	3.97827			0.215435
$342$		0			0
$343$			16.9815i			0.916917i
$344$		0			0
$345$	−9.62095	+	9.76830i	−0.517975	+	0.525908i
$346$		0			0
$347$	18.2799	+	18.2799i	0.981314	+	0.981314i	0.999829	−	0.0185143i	$-0.00589362\pi$
$347$	18.2799	+	18.2799i	0.981314	+	0.981314i	−0.0185143	+	0.999829i	$0.505894\pi$
$348$		0			0
$349$	12.9654	−	12.9654i	0.694024	−	0.694024i	−0.269091	−	0.963115i	$-0.586723\pi$
$349$	12.9654	−	12.9654i	0.694024	−	0.694024i	0.963115	+	0.269091i	$0.0867233\pi$
$350$		0			0
$351$	2.55816	+	2.54083i	0.136544	+	0.135620i
$352$		0			0
$353$		−	21.8438i		−	1.16263i	−0.813680	−	0.581313i	$-0.802539\pi$
$353$		−	21.8438i		−	1.16263i	0.813680	−	0.581313i	$-0.197461\pi$
$354$		0			0
$355$	0.0344316	+	4.53074i	0.00182744	+	0.240467i
$356$		0			0
$357$	−19.3264			−1.02286
$358$		0			0
$359$	−13.9440	+	13.9440i	−0.735936	+	0.735936i	−0.971789	−	0.235853i	$-0.924212\pi$
$359$	−13.9440	+	13.9440i	−0.735936	+	0.735936i	0.235853	+	0.971789i	$0.424212\pi$
$360$		0			0
$361$			45.9380i			2.41779i
$362$		0			0
$363$	−7.31466	−	7.31466i	−0.383920	−	0.383920i
$364$		0			0
$365$	−17.1936	+	17.4569i	−0.899954	+	0.913738i
$366$		0			0
$367$	12.4448	+	12.4448i	0.649612	+	0.649612i	0.952899	−	0.303287i	$-0.0980842\pi$
$367$	12.4448	+	12.4448i	0.649612	+	0.649612i	−0.303287	+	0.952899i	$0.598084\pi$
$368$		0			0
$369$	6.80464	+	6.80464i	0.354235	+	0.354235i
$370$		0			0
$371$	2.69640	+	2.69640i	0.139990	+	0.139990i
$372$		0			0
$373$	−21.0113	+	21.0113i	−1.08793	+	1.08793i	−0.0921833	+	0.995742i	$0.529385\pi$
$373$	−21.0113	+	21.0113i	−1.08793	+	1.08793i	−0.995742	+	0.0921833i	$0.970615\pi$
$374$		0			0
$375$	11.1774	−	0.254870i	0.577200	−	0.0131614i
$376$		0			0
$377$	−0.00441761	−	1.30036i	−0.000227518	−	0.0669722i
$378$		0			0
$379$	−9.47180	−	9.47180i	−0.486534	−	0.486534i	0.420677	−	0.907211i	$-0.361793\pi$
$379$	−9.47180	−	9.47180i	−0.486534	−	0.486534i	−0.907211	+	0.420677i	$0.861793\pi$
$380$		0			0
$381$			0.932722i			0.0477848i
$382$		0			0
$383$			13.6682i			0.698410i	0.937046	+	0.349205i	$0.113548\pi$
$383$			13.6682i			0.698410i	−0.937046	+	0.349205i	$0.886452\pi$
$384$		0			0
$385$	0.0388977	+	5.11842i	0.00198241	+	0.260859i
$386$		0			0
$387$	−0.183456	+	0.183456i	−0.00932558	+	0.00932558i
$388$		0			0
$389$	−37.6914			−1.91103			−0.955516	−	0.294939i	$-0.904701\pi$
$389$	−37.6914			−1.91103			−0.955516	+	0.294939i	$0.904701\pi$
$390$		0			0
$391$	−41.9128			−2.11962
$392$		0			0
$393$	−1.78445	+	1.78445i	−0.0900135	+	0.0900135i
$394$		0			0
$395$	−20.2532	−	19.9477i	−1.01905	−	1.00368i
$396$		0			0
$397$		−	21.6109i		−	1.08462i	−0.840178	−	0.542310i	$-0.817550\pi$
$397$		−	21.6109i		−	1.08462i	0.840178	−	0.542310i	$-0.182450\pi$
$398$		0			0
$399$		−	22.7838i		−	1.14062i
$400$		0			0
$401$	3.33534	+	3.33534i	0.166559	+	0.166559i	0.785465	−	0.618906i	$-0.212424\pi$
$401$	3.33534	+	3.33534i	0.166559	+	0.166559i	−0.618906	+	0.785465i	$0.712424\pi$
$402$		0			0
$403$	12.4849	−	12.5700i	0.621915	−	0.626155i
$404$		0			0
$405$	1.56908	−	1.59311i	0.0779681	−	0.0791622i
$406$		0			0
$407$	−1.73312	+	1.73312i	−0.0859075	+	0.0859075i
$408$		0			0
$409$	−5.15659	−	5.15659i	−0.254977	−	0.254977i	0.568030	−	0.823008i	$-0.307706\pi$
$409$	−5.15659	−	5.15659i	−0.254977	−	0.254977i	−0.823008	+	0.568030i	$0.807706\pi$
$410$		0			0
$411$	−7.36776	−	7.36776i	−0.363425	−	0.363425i
$412$		0			0
$413$	−16.2112	−	16.2112i	−0.797699	−	0.797699i
$414$		0			0
$415$	−15.9165	−	15.6765i	−0.781313	−	0.769527i
$416$		0			0
$417$	5.85459	+	5.85459i	0.286701	+	0.286701i
$418$		0			0
$419$		−	0.204499i		−	0.00999045i	−0.999988	−	0.00499523i	$-0.998410\pi$
$419$		−	0.204499i		−	0.00999045i	0.999988	−	0.00499523i	$-0.00159004\pi$
$420$		0			0
$421$	−13.8470	+	13.8470i	−0.674860	+	0.674860i	−0.958832	−	0.283973i	$-0.908347\pi$
$421$	−13.8470	+	13.8470i	−0.674860	+	0.674860i	0.283973	+	0.958832i	$0.408347\pi$
$422$		0			0
$423$	3.78276			0.183924
$424$		0			0
$425$	24.5318	+	23.7972i	1.18997	+	1.15434i
$426$		0			0
$427$			31.6264i			1.53051i
$428$		0			0
$429$	2.91915	−	0.00991696i	0.140938	−	0.000478795i
$430$		0			0
$431$	1.26394	−	1.26394i	0.0608818	−	0.0608818i	−0.676010	−	0.736892i	$-0.736293\pi$
$431$	1.26394	−	1.26394i	0.0608818	−	0.0608818i	0.736892	+	0.676010i	$0.236293\pi$
$432$		0			0
$433$	−1.58537	−	1.58537i	−0.0761879	−	0.0761879i	0.667986	−	0.744174i	$-0.267157\pi$
$433$	−1.58537	−	1.58537i	−0.0761879	−	0.0761879i	−0.744174	+	0.667986i	$0.767157\pi$
$434$		0			0
$435$	−0.806433	+	0.00612853i	−0.0386655	+	0.000293841i
$436$		0			0
$437$		−	49.4109i		−	2.36365i
$438$		0			0
$439$	23.5293			1.12299			0.561495	−	0.827480i	$-0.310226\pi$
$439$	23.5293			1.12299			0.561495	+	0.827480i	$0.310226\pi$
$440$		0			0
$441$			0.993789i			0.0473233i
$442$		0			0
$443$	−2.31257	+	2.31257i	−0.109874	+	0.109874i	−0.759906	−	0.650033i	$-0.774755\pi$
$443$	−2.31257	+	2.31257i	−0.109874	+	0.109874i	0.650033	+	0.759906i	$0.274755\pi$
$444$		0			0
$445$	−0.217749	−	28.6528i	−0.0103223	−	1.35827i
$446$		0			0
$447$	4.89327			0.231444
$448$		0			0
$449$	6.36910	−	6.36910i	0.300576	−	0.300576i	−0.540663	−	0.841239i	$-0.681827\pi$
$449$	6.36910	−	6.36910i	0.300576	−	0.300576i	0.841239	+	0.540663i	$0.181827\pi$
$450$		0			0
$451$	7.79125			0.366876
$452$		0			0
$453$	−8.85818			−0.416194
$454$		0			0
$455$	16.2945	+	15.9400i	0.763899	+	0.747281i
$456$		0			0
$457$	−34.1105			−1.59562			−0.797811	−	0.602908i	$-0.794009\pi$
$457$	−34.1105			−1.59562			−0.797811	+	0.602908i	$0.794009\pi$
$458$		0			0
$459$	6.83555			0.319056
$460$		0			0
$461$	8.92219	−	8.92219i	0.415548	−	0.415548i	−0.468118	−	0.883666i	$-0.655068\pi$
$461$	8.92219	−	8.92219i	0.415548	−	0.415548i	0.883666	+	0.468118i	$0.155068\pi$
$462$		0			0
$463$	29.0432			1.34975			0.674877	−	0.737930i	$-0.264197\pi$
$463$	29.0432			1.34975			0.674877	+	0.737930i	$0.264197\pi$
$464$		0			0
$465$	−7.82804	−	7.70996i	−0.363017	−	0.357541i
$466$		0			0
$467$	7.88453	−	7.88453i	0.364853	−	0.364853i	−0.500743	−	0.865596i	$-0.666940\pi$
$467$	7.88453	−	7.88453i	0.364853	−	0.364853i	0.865596	+	0.500743i	$0.166940\pi$
$468$		0			0
$469$			21.4779i			0.991755i
$470$		0			0
$471$	8.27239			0.381172
$472$		0			0
$473$			0.210055i			0.00965834i
$474$		0			0
$475$	−28.0545	+	28.9205i	−1.28723	+	1.32696i
$476$		0			0
$477$	−0.953692	−	0.953692i	−0.0436666	−	0.0436666i
$478$		0			0
$479$	−29.4336	+	29.4336i	−1.34485	+	1.34485i	−0.453701	+	0.891154i	$0.649896\pi$
$479$	−29.4336	+	29.4336i	−1.34485	+	1.34485i	−0.891154	+	0.453701i	$0.850104\pi$
$480$		0			0
$481$	0.0370807	+	10.9150i	0.00169073	+	0.497683i
$482$		0			0
$483$			17.3360i			0.788817i
$484$		0			0
$485$	17.7965	−	18.0691i	0.808098	−	0.820474i
$486$		0			0
$487$	−0.791622			−0.0358718			−0.0179359	−	0.999839i	$-0.505709\pi$
$487$	−0.791622			−0.0358718			−0.0179359	+	0.999839i	$0.505709\pi$
$488$		0			0
$489$	−14.6675	+	14.6675i	−0.663289	+	0.663289i
$490$		0			0
$491$			2.13632i			0.0964109i	0.998837	+	0.0482055i	$0.0153502\pi$
$491$			2.13632i			0.0964109i	−0.998837	+	0.0482055i	$0.984650\pi$
$492$		0			0
$493$	−1.74323	−	1.74323i	−0.0785111	−	0.0785111i
$494$		0			0
$495$	−0.0137577	−	1.81034i	−0.000618365	−	0.0813686i
$496$		0			0
$497$	4.05096	+	4.05096i	0.181710	+	0.181710i
$498$		0			0
$499$	3.96691	+	3.96691i	0.177583	+	0.177583i	0.790301	−	0.612718i	$-0.209924\pi$
$499$	3.96691	+	3.96691i	0.177583	+	0.177583i	−0.612718	+	0.790301i	$0.709924\pi$
$500$		0			0
$501$	−4.48495	−	4.48495i	−0.200373	−	0.200373i
$502$		0			0
$503$	20.2862	−	20.2862i	0.904519	−	0.904519i	−0.0913043	−	0.995823i	$-0.529104\pi$
$503$	20.2862	−	20.2862i	0.904519	−	0.904519i	0.995823	+	0.0913043i	$0.0291036\pi$
$504$		0			0
$505$	21.7778	+	21.4493i	0.969099	+	0.954481i
$506$		0			0
$507$	9.12972	−	9.25463i	0.405465	−	0.411013i
$508$		0			0
$509$	18.0027	+	18.0027i	0.797957	+	0.797957i	0.982773	−	0.184816i	$-0.0591690\pi$
$509$	18.0027	+	18.0027i	0.797957	+	0.797957i	−0.184816	+	0.982773i	$0.559169\pi$
$510$		0			0
$511$			30.9812i			1.37053i
$512$		0			0
$513$			8.05841i			0.355788i
$514$		0			0
$515$	24.0385	−	0.182682i	1.05926	−	0.00804993i
$516$		0			0
$517$	2.16561	−	2.16561i	0.0952434	−	0.0952434i
$518$		0			0
$519$	21.7155			0.953205
$520$		0			0
$521$	−15.6669			−0.686381			−0.343190	−	0.939266i	$-0.611508\pi$
$521$	−15.6669			−0.686381			−0.343190	+	0.939266i	$0.611508\pi$
$522$		0			0
$523$	−20.9435	+	20.9435i	−0.915795	+	0.915795i	−0.996720	−	0.0809249i	$-0.974213\pi$
$523$	−20.9435	+	20.9435i	−0.915795	+	0.915795i	0.0809249	+	0.996720i	$0.474213\pi$
$524$		0			0
$525$	9.84304	−	10.1469i	0.429585	−	0.442846i
$526$		0			0
$527$		−	33.5878i		−	1.46311i
$528$		0			0
$529$			14.5965i			0.634629i
$530$		0			0
$531$	5.73374	+	5.73374i	0.248823	+	0.248823i
$532$		0			0
$533$	24.4510	−	24.6177i	1.05909	−	1.06631i
$534$		0			0
$535$	−24.4902	+	0.186114i	−1.05880	+	0.00804642i
$536$		0			0
$537$	−5.79432	+	5.79432i	−0.250043	+	0.250043i
$538$		0			0
$539$	0.568940	+	0.568940i	0.0245060	+	0.0245060i
$540$		0			0
$541$	−2.10688	−	2.10688i	−0.0905820	−	0.0905820i	0.660364	−	0.750946i	$-0.270402\pi$
$541$	−2.10688	−	2.10688i	−0.0905820	−	0.0905820i	−0.750946	+	0.660364i	$0.770402\pi$
$542$		0			0
$543$	−14.3027	−	14.3027i	−0.613788	−	0.613788i
$544$		0			0
$545$	9.35364	−	0.0710834i	0.400666	−	0.00304488i
$546$		0			0
$547$	−9.62853	−	9.62853i	−0.411686	−	0.411686i	0.470640	−	0.882326i	$-0.344023\pi$
$547$	−9.62853	−	9.62853i	−0.411686	−	0.411686i	−0.882326	+	0.470640i	$0.844023\pi$
$548$		0			0
$549$		−	11.1860i		−	0.477406i
$550$		0			0
$551$	2.05509	−	2.05509i	0.0875497	−	0.0875497i
$552$		0			0
$553$	−35.9438			−1.52849
$554$		0			0
$555$	6.76907	−	0.0514419i	0.287331	−	0.00218359i
$556$		0			0
$557$			5.80125i			0.245807i	0.992419	+	0.122903i	$0.0392206\pi$
$557$			5.80125i			0.245807i	−0.992419	+	0.122903i	$0.960779\pi$
$558$		0			0
$559$	0.663702	+	0.659208i	0.0280716	+	0.0278815i
$560$		0			0
$561$	3.91332	−	3.91332i	0.165221	−	0.165221i
$562$		0			0
$563$	13.2709	+	13.2709i	0.559303	+	0.559303i	0.929109	−	0.369806i	$-0.120576\pi$
$563$	13.2709	+	13.2709i	0.559303	+	0.559303i	−0.369806	+	0.929109i	$0.620576\pi$
$564$		0			0
$565$	0.245037	+	32.2436i	0.0103088	+	1.35650i
$566$		0			0
$567$		−	2.82733i		−	0.118737i
$568$		0			0
$569$	−18.4542			−0.773642			−0.386821	−	0.922155i	$-0.626427\pi$
$569$	−18.4542			−0.773642			−0.386821	+	0.922155i	$0.626427\pi$
$570$		0			0
$571$		−	8.91337i		−	0.373013i	−0.982454	−	0.186507i	$-0.940283\pi$
$571$		−	8.91337i		−	0.373013i	0.982454	−	0.186507i	$-0.0597166\pi$
$572$		0			0
$573$	−9.66401	+	9.66401i	−0.403720	+	0.403720i
$574$		0			0
$575$	21.3465	−	22.0054i	0.890210	−	0.917690i
$576$		0			0
$577$	−9.37399			−0.390245			−0.195122	−	0.980779i	$-0.562510\pi$
$577$	−9.37399			−0.390245			−0.195122	+	0.980779i	$0.562510\pi$
$578$		0			0
$579$	17.7564	−	17.7564i	0.737932	−	0.737932i
$580$		0			0
$581$	−28.2475			−1.17190
$582$		0			0
$583$	−1.09197			−0.0452247
$584$		0			0
$585$	−5.76322	−	5.63784i	−0.238280	−	0.233096i
$586$		0			0
$587$	−22.3246			−0.921434			−0.460717	−	0.887547i	$-0.652408\pi$
$587$	−22.3246			−0.921434			−0.460717	+	0.887547i	$0.652408\pi$
$588$		0			0
$589$	39.5965			1.63155
$590$		0			0
$591$	11.3440	−	11.3440i	0.466628	−	0.466628i
$592$		0			0
$593$	−37.5209			−1.54080			−0.770399	−	0.637563i	$-0.779943\pi$
$593$	−37.5209			−1.54080			−0.770399	+	0.637563i	$0.779943\pi$
$594$		0			0
$595$	43.2138	−	0.328405i	1.77159	−	0.0134633i
$596$		0			0
$597$	−6.13006	+	6.13006i	−0.250887	+	0.250887i
$598$		0			0
$599$		−	5.53645i		−	0.226213i	−0.993583	−	0.113107i	$-0.963920\pi$
$599$		−	5.53645i		−	0.226213i	0.993583	−	0.113107i	$-0.0360801\pi$
$600$		0			0
$601$	40.3784			1.64707			0.823535	−	0.567266i	$-0.191999\pi$
$601$	40.3784			1.64707			0.823535	+	0.567266i	$0.191999\pi$
$602$		0			0
$603$		−	7.59652i		−	0.309354i
$604$		0			0
$605$	16.4799	+	16.2313i	0.670004	+	0.659897i
$606$		0			0
$607$	−1.59621	−	1.59621i	−0.0647882	−	0.0647882i	0.673970	−	0.738758i	$-0.264588\pi$
$607$	−1.59621	−	1.59621i	−0.0647882	−	0.0647882i	−0.738758	+	0.673970i	$0.764588\pi$
$608$		0			0
$609$	−0.721037	+	0.721037i	−0.0292179	+	0.0292179i
$610$		0			0
$611$	−0.0463340	−	13.6388i	−0.00187447	−	0.551769i
$612$		0			0
$613$		−	12.9131i		−	0.521555i	−0.965399	−	0.260777i	$-0.916021\pi$
$613$		−	12.9131i		−	0.521555i	0.965399	−	0.260777i	$-0.0839788\pi$
$614$		0			0
$615$	−15.3308	−	15.0996i	−0.618199	−	0.608873i
$616$		0			0
$617$	36.4649			1.46802			0.734011	−	0.679138i	$-0.237646\pi$
$617$	36.4649			1.46802			0.734011	+	0.679138i	$0.237646\pi$
$618$		0			0
$619$	−0.901794	+	0.901794i	−0.0362461	+	0.0362461i	−0.724998	−	0.688751i	$-0.758159\pi$
$619$	−0.901794	+	0.901794i	−0.0362461	+	0.0362461i	0.688751	+	0.724998i	$0.258159\pi$
$620$		0			0
$621$		−	6.13160i		−	0.246052i
$622$		0			0
$623$	−25.6186	−	25.6186i	−1.02639	−	1.02639i
$624$		0			0
$625$	−24.9885	+	0.759823i	−0.999538	+	0.0303929i
$626$		0			0
$627$	4.61340	+	4.61340i	0.184242	+	0.184242i
$628$		0			0
$629$	14.6324	+	14.6324i	0.583431	+	0.583431i
$630$		0			0
$631$	16.5075	+	16.5075i	0.657152	+	0.657152i	0.954705	−	0.297554i	$-0.0961707\pi$
$631$	16.5075	+	16.5075i	0.657152	+	0.657152i	−0.297554	+	0.954705i	$0.596171\pi$
$632$		0			0
$633$	6.11200	−	6.11200i	0.242930	−	0.242930i
$634$		0			0
$635$	−0.0158494	−	2.08557i	−0.000628964	−	0.0827633i
$636$		0			0
$637$	3.58314	−	0.0121727i	0.141969	−	0.000482299i
$638$		0			0
$639$	−1.43279	−	1.43279i	−0.0566802	−	0.0566802i
$640$		0			0
$641$			39.9005i			1.57598i	0.615691	+	0.787988i	$0.288877\pi$
$641$			39.9005i			1.57598i	−0.615691	+	0.787988i	$0.711123\pi$
$642$		0			0
$643$		−	9.69615i		−	0.382379i	−0.981553	−	0.191189i	$-0.938766\pi$
$643$		−	9.69615i		−	0.382379i	0.981553	−	0.191189i	$-0.0612345\pi$
$644$		0			0
$645$	0.407090	−	0.413325i	0.0160292	−	0.0162747i
$646$		0			0
$647$	25.9454	−	25.9454i	1.02002	−	1.02002i	0.0202246	−	0.999795i	$-0.493562\pi$
$647$	25.9454	−	25.9454i	1.02002	−	1.02002i	0.999795	−	0.0202246i	$-0.00643812\pi$
$648$		0			0
$649$	6.56508			0.257702
$650$		0			0
$651$	−13.8926			−0.544494
$652$		0			0
$653$	−14.9663	+	14.9663i	−0.585676	+	0.585676i	−0.936457	−	0.350781i	$-0.885916\pi$
$653$	−14.9663	+	14.9663i	−0.585676	+	0.585676i	0.350781	+	0.936457i	$0.385916\pi$
$654$		0			0
$655$	3.95971	−	4.02035i	0.154719	−	0.157088i
$656$		0			0
$657$		−	10.9578i		−	0.427504i
$658$		0			0
$659$		−	36.3358i		−	1.41544i	−0.706491	−	0.707722i	$-0.749723\pi$
$659$		−	36.3358i		−	1.41544i	0.706491	−	0.707722i	$-0.250277\pi$
$660$		0			0
$661$	−2.82355	−	2.82355i	−0.109823	−	0.109823i	0.650060	−	0.759883i	$-0.274744\pi$
$661$	−2.82355	−	2.82355i	−0.109823	−	0.109823i	−0.759883	+	0.650060i	$0.774744\pi$
$662$		0			0
$663$	−0.0837269	−	24.6458i	−0.00325168	−	0.957163i
$664$		0			0
$665$	0.387156	+	50.9446i	0.0150133	+	1.97555i
$666$		0			0
$667$	−1.56370	+	1.56370i	−0.0605468	+	0.0605468i
$668$		0			0
$669$	8.50262	+	8.50262i	0.328730	+	0.328730i
$670$		0			0
$671$	−6.40392	−	6.40392i	−0.247220	−	0.247220i
$672$		0			0
$673$	9.57777	+	9.57777i	0.369196	+	0.369196i	0.867184	−	0.497988i	$-0.165928\pi$
$673$	9.57777	+	9.57777i	0.369196	+	0.369196i	−0.497988	+	0.867184i	$0.665928\pi$
$674$		0			0
$675$	−3.48139	+	3.58886i	−0.133999	+	0.138135i
$676$		0			0
$677$	3.73583	+	3.73583i	0.143580	+	0.143580i	0.775243	−	0.631663i	$-0.217627\pi$
$677$	3.73583	+	3.73583i	0.143580	+	0.143580i	−0.631663	+	0.775243i	$0.717627\pi$
$678$		0			0
$679$		−	32.0676i		−	1.23064i
$680$		0			0
$681$	−5.96440	+	5.96440i	−0.228556	+	0.228556i
$682$		0			0
$683$	−48.7002			−1.86346			−0.931730	−	0.363152i	$-0.881700\pi$
$683$	−48.7002			−1.86346			−0.931730	+	0.363152i	$0.881700\pi$
$684$		0			0
$685$	16.5995	+	16.3491i	0.634236	+	0.624669i
$686$		0			0
$687$			9.17830i			0.350174i
$688$		0			0
$689$	−3.42688	+	3.45025i	−0.130554	+	0.131444i
$690$		0			0
$691$	35.2384	−	35.2384i	1.34053	−	1.34053i	0.445001	−	0.895530i	$-0.353203\pi$
$691$	35.2384	−	35.2384i	1.34053	−	1.34053i	0.895530	−	0.445001i	$-0.146797\pi$
$692$		0			0
$693$	−1.61863	−	1.61863i	−0.0614868	−	0.0614868i
$694$		0			0
$695$	−13.1904	−	12.9914i	−0.500339	−	0.492792i
$696$		0			0
$697$		−	65.7800i		−	2.49159i
$698$		0			0
$699$	−3.68276			−0.139295
$700$		0			0
$701$		−	26.2701i		−	0.992206i	−0.868264	−	0.496103i	$-0.834764\pi$
$701$		−	26.2701i		−	0.992206i	0.868264	−	0.496103i	$-0.165236\pi$
$702$		0			0
$703$	−17.2501	+	17.2501i	−0.650599	+	0.650599i
$704$		0			0
$705$	−8.45826	+	0.0642790i	−0.318556	+	0.00242089i
$706$		0			0
$707$	38.6496			1.45357
$708$		0			0
$709$	1.98224	−	1.98224i	0.0744446	−	0.0744446i	−0.668904	−	0.743349i	$-0.733236\pi$
$709$	1.98224	−	1.98224i	0.0744446	−	0.0744446i	0.743349	+	0.668904i	$0.233236\pi$
$710$		0			0
$711$	12.7130			0.476775
$712$		0			0
$713$	−30.1287			−1.12833
$714$		0			0
$715$	−6.52706	+	0.0717783i	−0.244098	+	0.00268436i
$716$		0			0
$717$	20.8257			0.777751
$718$		0			0
$719$	−46.9237			−1.74996			−0.874980	−	0.484159i	$-0.839126\pi$
$719$	−46.9237			−1.74996			−0.874980	+	0.484159i	$0.839126\pi$
$720$		0			0
$721$	21.4930	−	21.4930i	0.800440	−	0.800440i
$722$		0			0
$723$	−11.9205			−0.443328
$724$		0			0
$725$	1.80308	−	0.0274068i	0.0669648	−	0.00101786i
$726$		0			0
$727$	12.3303	−	12.3303i	0.457306	−	0.457306i	−0.440464	−	0.897770i	$-0.645186\pi$
$727$	12.3303	−	12.3303i	0.457306	−	0.457306i	0.897770	+	0.440464i	$0.145186\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	1.77345			0.0655935
$732$		0			0
$733$		−	36.5671i		−	1.35064i	−0.737527	−	0.675318i	$-0.764006\pi$
$733$		−	36.5671i		−	1.35064i	0.737527	−	0.675318i	$-0.235994\pi$
$734$		0			0
$735$	−0.0168871	−	2.22212i	−0.000622890	−	0.0819640i
$736$		0			0
$737$	−4.34897	−	4.34897i	−0.160196	−	0.160196i
$738$		0			0
$739$	22.2656	−	22.2656i	0.819052	−	0.819052i	−0.166919	−	0.985971i	$-0.553382\pi$
$739$	22.2656	−	22.2656i	0.819052	−	0.819052i	0.985971	+	0.166919i	$0.0533819\pi$
$740$		0			0
$741$	29.0549	−	0.0987054i	1.06736	−	0.00362603i
$742$		0			0
$743$			31.5470i			1.15735i	0.815560	+	0.578673i	$0.196429\pi$
$743$			31.5470i			1.15735i	−0.815560	+	0.578673i	$0.803571\pi$
$744$		0			0
$745$	−10.9414	+	0.0831495i	−0.400861	+	0.00304636i
$746$		0			0
$747$	9.99087			0.365547
$748$		0			0
$749$	−21.8968	+	21.8968i	−0.800091	+	0.800091i
$750$		0			0
$751$			43.9344i			1.60319i	0.597868	+	0.801595i	$0.296015\pi$
$751$			43.9344i			1.60319i	−0.597868	+	0.801595i	$0.703985\pi$
$752$		0			0
$753$	−9.32355	−	9.32355i	−0.339769	−	0.339769i
$754$		0			0
$755$	19.8069	−	0.150524i	0.720848	−	0.00547812i
$756$		0			0
$757$	7.08910	+	7.08910i	0.257658	+	0.257658i	0.824101	−	0.566443i	$-0.191681\pi$
$757$	7.08910	+	7.08910i	0.257658	+	0.257658i	−0.566443	+	0.824101i	$0.691681\pi$
$758$		0			0
$759$	−3.51031	−	3.51031i	−0.127416	−	0.127416i
$760$		0			0
$761$	−11.1147	−	11.1147i	−0.402906	−	0.402906i	0.476350	−	0.879256i	$-0.341960\pi$
$761$	−11.1147	−	11.1147i	−0.402906	−	0.402906i	−0.879256	+	0.476350i	$0.841960\pi$
$762$		0			0
$763$	8.36314	−	8.36314i	0.302766	−	0.302766i
$764$		0			0
$765$	−15.2843	+	0.116154i	−0.552606	+	0.00419956i
$766$		0			0
$767$	20.6029	−	20.7434i	0.743929	−	0.749001i
$768$		0			0
$769$	16.8418	+	16.8418i	0.607331	+	0.607331i	0.942248	−	0.334916i	$-0.108708\pi$
$769$	16.8418	+	16.8418i	0.607331	+	0.607331i	−0.334916	+	0.942248i	$0.608708\pi$
$770$		0			0
$771$			2.98908i			0.107649i
$772$		0			0
$773$			1.43314i			0.0515465i	0.999668	+	0.0257732i	$0.00820479\pi$
$773$			1.43314i			0.0515465i	−0.999668	+	0.0257732i	$0.991795\pi$
$774$		0			0
$775$	17.6345	+	17.1065i	0.633451	+	0.614482i
$776$		0			0
$777$	6.05226	−	6.05226i	0.217124	−	0.217124i
$778$		0			0
$779$	77.5478			2.77844
$780$		0			0
$781$	−1.64053			−0.0587027
$782$		0			0
$783$	0.255024	−	0.255024i	0.00911381	−	0.00911381i
$784$		0			0
$785$	−18.4971	+	0.140570i	−0.660190	+	0.00501714i
$786$		0			0
$787$			35.4601i			1.26401i	0.774962	+	0.632007i	$0.217769\pi$
$787$			35.4601i			1.26401i	−0.774962	+	0.632007i	$0.782231\pi$
$788$		0			0
$789$			24.3119i			0.865527i
$790$		0			0
$791$	28.8291	+	28.8291i	1.02505	+	1.02505i
$792$		0			0
$793$	−40.3314	+	0.137014i	−1.43221	+	0.00486551i
$794$		0			0
$795$	2.14866	+	2.11625i	0.0762053	+	0.0750558i
$796$		0			0
$797$	8.14292	−	8.14292i	0.288437	−	0.288437i	−0.548025	−	0.836462i	$-0.684620\pi$
$797$	8.14292	−	8.14292i	0.288437	−	0.288437i	0.836462	+	0.548025i	$0.184620\pi$
$798$		0			0
$799$	−18.2838	−	18.2838i	−0.646835	−	0.646835i
$800$		0			0
$801$	9.06108	+	9.06108i	0.320157	+	0.320157i
$802$		0			0
$803$	−6.27328	−	6.27328i	−0.221379	−	0.221379i
$804$		0			0
$805$	−0.294585	−	38.7634i	−0.0103827	−	1.36623i
$806$		0			0
$807$	8.95513	+	8.95513i	0.315235	+	0.315235i
$808$		0			0
$809$		−	30.2129i		−	1.06223i	−0.847300	−	0.531114i	$-0.821774\pi$
$809$		−	30.2129i		−	1.06223i	0.847300	−	0.531114i	$-0.178226\pi$
$810$		0			0
$811$	−28.3029	+	28.3029i	−0.993851	+	0.993851i	−0.999981	−	0.00613062i	$-0.998049\pi$
$811$	−28.3029	+	28.3029i	−0.993851	+	0.993851i	0.00613062	+	0.999981i	$0.498049\pi$
$812$		0			0
$813$	26.4348			0.927110
$814$		0			0
$815$	32.5474	−	33.0459i	1.14009	−	1.15755i
$816$		0			0
$817$			2.09072i			0.0731450i
$818$		0			0
$819$	−10.1940	+	0.0346312i	−0.356208	+	0.00121011i
$820$		0			0
$821$	10.5544	−	10.5544i	0.368350	−	0.368350i	−0.498525	−	0.866875i	$-0.666125\pi$
$821$	10.5544	−	10.5544i	0.368350	−	0.368350i	0.866875	+	0.498525i	$0.166125\pi$
$822$		0			0
$823$	9.06651	+	9.06651i	0.316039	+	0.316039i	0.847243	−	0.531205i	$-0.178261\pi$
$823$	9.06651	+	9.06651i	0.316039	+	0.316039i	−0.531205	+	0.847243i	$0.678261\pi$
$824$		0			0
$825$	0.0615247	+	4.04769i	0.00214202	+	0.140922i
$826$		0			0
$827$		−	15.0241i		−	0.522441i	−0.965279	−	0.261220i	$-0.915875\pi$
$827$		−	15.0241i		−	0.522441i	0.965279	−	0.261220i	$-0.0841249\pi$
$828$		0			0
$829$	37.5940			1.30570			0.652848	−	0.757489i	$-0.273574\pi$
$829$	37.5940			1.30570			0.652848	+	0.757489i	$0.273574\pi$
$830$		0			0
$831$			18.7531i			0.650537i
$832$		0			0
$833$	4.80345	−	4.80345i	0.166430	−	0.166430i
$834$		0			0
$835$	10.1046	+	9.95214i	0.349683	+	0.344408i
$836$		0			0
$837$	4.91369			0.169842
$838$		0			0
$839$	11.8854	−	11.8854i	0.410330	−	0.410330i	−0.471524	−	0.881853i	$-0.656296\pi$
$839$	11.8854	−	11.8854i	0.410330	−	0.410330i	0.881853	+	0.471524i	$0.156296\pi$
$840$		0			0
$841$	28.8699			0.995515
$842$		0			0
$843$	−1.38694			−0.0477686
$844$		0			0
$845$	−20.2568	+	20.8485i	−0.696856	+	0.717211i
$846$		0			0
$847$	29.2473			1.00495
$848$		0			0
$849$	12.4943			0.428803
$850$		0			0
$851$	13.1255	−	13.1255i	0.449935	−	0.449935i
$852$		0			0
$853$	23.8844			0.817785			0.408892	−	0.912583i	$-0.365915\pi$
$853$	23.8844			0.817785			0.408892	+	0.912583i	$0.365915\pi$
$854$		0			0
$855$	−0.136934	−	18.0186i	−0.00468303	−	0.616224i
$856$		0			0
$857$	−30.2778	+	30.2778i	−1.03427	+	1.03427i	−0.0348793	+	0.999392i	$0.511105\pi$
$857$	−30.2778	+	30.2778i	−1.03427	+	1.03427i	−0.999392	+	0.0348793i	$0.988895\pi$
$858$		0			0
$859$		−	14.5490i		−	0.496405i	−0.968708	−	0.248202i	$-0.920160\pi$
$859$		−	14.5490i		−	0.496405i	0.968708	−	0.248202i	$-0.0798398\pi$
$860$		0			0
$861$	−27.2080			−0.927246
$862$		0			0
$863$			38.8915i			1.32388i	0.749555	+	0.661942i	$0.230267\pi$
$863$			38.8915i			1.32388i	−0.749555	+	0.661942i	$0.769733\pi$
$864$		0			0
$865$	−48.5560	+	0.369004i	−1.65095	+	0.0125465i
$866$		0			0
$867$	−21.0186	−	21.0186i	−0.713829	−	0.713829i
$868$		0			0
$869$	7.27813	−	7.27813i	0.246894	−	0.246894i
$870$		0			0
$871$	−27.3895	+	0.0930478i	−0.928057	+	0.00315280i
$872$		0			0
$873$			11.3420i			0.383869i
$874$		0			0
$875$	−21.8366	+	22.8557i	−0.738213	+	0.772665i
$876$		0			0
$877$	−10.9555			−0.369942			−0.184971	−	0.982744i	$-0.559219\pi$
$877$	−10.9555			−0.369942			−0.184971	+	0.982744i	$0.559219\pi$
$878$		0			0
$879$	12.3321	−	12.3321i	0.415951	−	0.415951i
$880$		0			0
$881$		−	40.9443i		−	1.37945i	−0.724072	−	0.689724i	$-0.757732\pi$
$881$		−	40.9443i		−	1.37945i	0.724072	−	0.689724i	$-0.242268\pi$
$882$		0			0
$883$	−22.5695	−	22.5695i	−0.759525	−	0.759525i	0.216711	−	0.976236i	$-0.430467\pi$
$883$	−22.5695	−	22.5695i	−0.759525	−	0.759525i	−0.976236	+	0.216711i	$0.930467\pi$
$884$		0			0
$885$	−12.9181	−	12.7232i	−0.434237	−	0.427687i
$886$		0			0
$887$	6.00975	+	6.00975i	0.201788	+	0.201788i	0.800766	−	0.598978i	$-0.204426\pi$
$887$	6.00975	+	6.00975i	0.201788	+	0.201788i	−0.598978	+	0.800766i	$0.704426\pi$
$888$		0			0
$889$	−1.86472	−	1.86472i	−0.0625407	−	0.0625407i
$890$		0			0
$891$	0.572495	+	0.572495i	0.0191793	+	0.0191793i
$892$		0			0
$893$	21.5547	−	21.5547i	0.721302	−	0.721302i
$894$		0			0
$895$	12.8577	−	13.0546i	0.429784	−	0.436366i
$896$		0			0
$897$	−22.1077	+	0.0751043i	−0.738153	+	0.00250766i
$898$		0			0
$899$	−1.25311	−	1.25311i	−0.0417935	−	0.0417935i
$900$		0			0
$901$			9.21928i			0.307139i
$902$		0			0
$903$		−	0.733538i		−	0.0244106i
$904$		0			0
$905$	32.2239	+	31.7379i	1.07116	+	1.05500i
$906$		0			0
$907$	24.0681	−	24.0681i	0.799169	−	0.799169i	−0.183795	−	0.982965i	$-0.558838\pi$
$907$	24.0681	−	24.0681i	0.799169	−	0.799169i	0.982965	+	0.183795i	$0.0588384\pi$
$908$		0			0
$909$	−13.6700			−0.453405
$910$		0			0
$911$	−8.61551			−0.285445			−0.142722	−	0.989763i	$-0.545586\pi$
$911$	−8.61551			−0.285445			−0.142722	+	0.989763i	$0.545586\pi$
$912$		0			0
$913$	5.71973	−	5.71973i	0.189295	−	0.189295i
$914$		0			0
$915$	0.190079	+	25.0119i	0.00628382	+	0.826867i
$916$		0			0
$917$		−	7.13502i		−	0.235619i
$918$		0			0
$919$			54.7442i			1.80584i	0.429805	+	0.902922i	$0.358582\pi$
$919$			54.7442i			1.80584i	−0.429805	+	0.902922i	$0.641418\pi$
$920$		0			0
$921$	4.50635	+	4.50635i	0.148489	+	0.148489i
$922$		0			0
$923$	−5.14841	+	5.18351i	−0.169462	+	0.170617i
$924$		0			0
$925$	−15.1348	+	0.230048i	−0.497629	+	0.00756395i
$926$		0			0
$927$	−7.60186	+	7.60186i	−0.249678	+	0.249678i
$928$		0			0
$929$	−15.5687	−	15.5687i	−0.510794	−	0.510794i	0.403976	−	0.914770i	$-0.367628\pi$
$929$	−15.5687	−	15.5687i	−0.510794	−	0.510794i	−0.914770	+	0.403976i	$0.867628\pi$
$930$		0			0
$931$	5.66277	+	5.66277i	0.185590	+	0.185590i
$932$		0			0
$933$	−22.5875	−	22.5875i	−0.739480	−	0.739480i
$934$		0			0
$935$	−8.68370	+	8.81670i	−0.283987	+	0.288337i
$936$		0			0
$937$	2.79879	+	2.79879i	0.0914326	+	0.0914326i	0.751344	−	0.659911i	$-0.229406\pi$
$937$	2.79879	+	2.79879i	0.0914326	+	0.0914326i	−0.659911	+	0.751344i	$0.729406\pi$
$938$		0			0
$939$			10.4294i			0.340350i
$940$		0			0
$941$	−7.02060	+	7.02060i	−0.228865	+	0.228865i	−0.812218	−	0.583353i	$-0.801740\pi$
$941$	−7.02060	+	7.02060i	−0.228865	+	0.228865i	0.583353	+	0.812218i	$0.301740\pi$
$942$		0			0
$943$	−59.0057			−1.92149
$944$		0			0
$945$	0.0480437	+	6.32192i	0.00156286	+	0.205652i
$946$		0			0
$947$		−	40.5458i		−	1.31756i	−0.752334	−	0.658781i	$-0.771072\pi$
$947$		−	40.5458i		−	1.31756i	0.752334	−	0.658781i	$-0.228928\pi$
$948$		0			0
$949$	−39.5086	+	0.134219i	−1.28250	+	0.00435693i
$950$		0			0
$951$	−13.8864	+	13.8864i	−0.450297	+	0.450297i
$952$		0			0
$953$	−21.3080	−	21.3080i	−0.690235	−	0.690235i	0.272049	−	0.962283i	$-0.412299\pi$
$953$	−21.3080	−	21.3080i	−0.690235	−	0.690235i	−0.962283	+	0.272049i	$0.912299\pi$
$954$		0			0
$955$	21.4445	−	21.7730i	0.693929	−	0.704557i
$956$		0			0
$957$		−	0.292000i		−	0.00943902i
$958$		0			0
$959$	29.4596			0.951301
$960$		0			0
$961$			6.85569i			0.221151i
$962$		0			0
$963$	7.74469	−	7.74469i	0.249569	−	0.249569i
$964$		0			0
$965$	−39.4017	+	40.0052i	−1.26839	+	1.28781i
$966$		0			0
$967$	−37.4242			−1.20348			−0.601740	−	0.798692i	$-0.705526\pi$
$967$	−37.4242			−1.20348			−0.601740	+	0.798692i	$0.705526\pi$
$968$		0			0
$969$	38.9501	−	38.9501i	1.25126	−	1.25126i
$970$		0			0
$971$	−20.1125			−0.645442			−0.322721	−	0.946494i	$-0.604597\pi$
$971$	−20.1125			−0.645442			−0.322721	+	0.946494i	$0.604597\pi$
$972$		0			0
$973$	−23.4093			−0.750467
$974$		0			0
$975$	12.9824	+	12.5083i	0.415769	+	0.400586i
$976$		0			0
$977$	23.5641			0.753883			0.376941	−	0.926237i	$-0.376976\pi$
$977$	23.5641			0.753883			0.376941	+	0.926237i	$0.376976\pi$
$978$		0			0
$979$	10.3748			0.331582
$980$		0			0
$981$	−2.95797	+	2.95797i	−0.0944406	+	0.0944406i
$982$		0			0
$983$	11.2014			0.357269			0.178635	−	0.983915i	$-0.442832\pi$
$983$	11.2014			0.357269			0.178635	+	0.983915i	$0.442832\pi$
$984$		0			0
$985$	−25.1724	+	25.5579i	−0.802059	+	0.814343i
$986$		0			0
$987$	−7.56258	+	7.56258i	−0.240719	+	0.240719i
$988$		0			0
$989$		−	1.59082i		−	0.0505850i
$990$		0			0
$991$	10.3359			0.328329			0.164165	−	0.986433i	$-0.447507\pi$
$991$	10.3359			0.328329			0.164165	+	0.986433i	$0.447507\pi$
$992$		0			0
$993$			17.1226i			0.543371i
$994$		0			0
$995$	13.6027	−	13.8110i	0.431234	−	0.437838i
$996$		0			0
$997$	19.9360	+	19.9360i	0.631380	+	0.631380i	0.948414	−	0.317034i	$-0.102687\pi$
$997$	19.9360	+	19.9360i	0.631380	+	0.631380i	−0.317034	+	0.948414i	$0.602687\pi$
$998$		0			0
$999$	−2.14063	+	2.14063i	−0.0677265	+	0.0677265i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	780.2.r.a.577.10	yes	28
3.2	odd	2		2340.2.u.i.577.10		28
5.2	odd	4		3900.2.bm.b.2293.6		28
5.3	odd	4		780.2.bm.a.733.8	yes	28
5.4	even	2		3900.2.r.b.1357.6		28
13.8	odd	4		780.2.bm.a.697.8	yes	28
15.8	even	4		2340.2.bp.i.1513.12		28
39.8	even	4		2340.2.bp.i.1477.12		28
65.8	even	4	inner	780.2.r.a.73.10	✓	28
65.34	odd	4		3900.2.bm.b.2257.6		28
65.47	even	4		3900.2.r.b.3193.6		28
195.8	odd	4		2340.2.u.i.73.10		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.r.a.73.10	✓	28	65.8	even	4	inner
780.2.r.a.577.10	yes	28	1.1	even	1	trivial
780.2.bm.a.697.8	yes	28	13.8	odd	4
780.2.bm.a.733.8	yes	28	5.3	odd	4
2340.2.u.i.73.10		28	195.8	odd	4
2340.2.u.i.577.10		28	3.2	odd	2
2340.2.bp.i.1477.12		28	39.8	even	4
2340.2.bp.i.1513.12		28	15.8	even	4
3900.2.r.b.1357.6		28	5.4	even	2
3900.2.r.b.3193.6		28	65.47	even	4
3900.2.bm.b.2257.6		28	65.34	odd	4
3900.2.bm.b.2293.6		28	5.2	odd	4

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:	\( N \)	\(=\)	\( 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	780.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(-1.56908 + 1.59311i) q^{5} +2.82733i q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(-1.56908 + 1.59311i) q^{5} +2.82733i q^{7} -1.00000i q^{9} +(-0.572495 - 0.572495i) q^{11} +(-3.60553 + 0.0122487i) q^{13} +(0.0169926 + 2.23600i) q^{15} +(-4.83347 + 4.83347i) q^{17} +(-5.69816 - 5.69816i) q^{19} +(1.99922 + 1.99922i) q^{21} +(4.33569 + 4.33569i) q^{23} +(-0.0759911 - 4.99942i) q^{25} +(-0.707107 - 0.707107i) q^{27} +0.360658i q^{29} +(-3.47450 + 3.47450i) q^{31} -0.809631 q^{33} +(-4.50424 - 4.43630i) q^{35} -3.02731i q^{37} +(-2.54083 + 2.55816i) q^{39} +(-6.80464 + 6.80464i) q^{41} +(-0.183456 - 0.183456i) q^{43} +(1.59311 + 1.56908i) q^{45} +3.78276i q^{47} -0.993789 q^{49} +6.83555i q^{51} +(0.953692 - 0.953692i) q^{53} +(1.81034 - 0.0137577i) q^{55} -8.05841 q^{57} +(-5.73374 + 5.73374i) q^{59} +11.1860 q^{61} +2.82733 q^{63} +(5.63784 - 5.76322i) q^{65} +7.59652 q^{67} +6.13160 q^{69} +(1.43279 - 1.43279i) q^{71} +10.9578 q^{73} +(-3.58886 - 3.48139i) q^{75} +(1.61863 - 1.61863i) q^{77} +12.7130i q^{79} -1.00000 q^{81} +9.99087i q^{83} +(-0.116154 - 15.2843i) q^{85} +(0.255024 + 0.255024i) q^{87} +(-9.06108 + 9.06108i) q^{89} +(-0.0346312 - 10.1940i) q^{91} +4.91369i q^{93} +(18.0186 - 0.136934i) q^{95} -11.3420 q^{97} +(-0.572495 + 0.572495i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q+O(q^{10}) \) 28 * q	\( 28 q + 8 q^{11} - 4 q^{13} - 4 q^{15} - 4 q^{17} - 16 q^{19} + 8 q^{21} - 8 q^{23} + 12 q^{25} - 8 q^{33} + 8 q^{39} + 12 q^{41} + 16 q^{43} + 4 q^{45} - 36 q^{49} + 36 q^{53} + 40 q^{55} + 16 q^{59} + 8 q^{61} - 40 q^{65} + 48 q^{67} - 8 q^{69} + 8 q^{71} + 48 q^{73} - 48 q^{77} - 28 q^{81} - 4 q^{85} - 24 q^{87} - 36 q^{89} - 24 q^{91} + 72 q^{95} - 72 q^{97} + 8 q^{99}+O(q^{100}) \) 28 * q + 8 * q^11 - 4 * q^13 - 4 * q^15 - 4 * q^17 - 16 * q^19 + 8 * q^21 - 8 * q^23 + 12 * q^25 - 8 * q^33 + 8 * q^39 + 12 * q^41 + 16 * q^43 + 4 * q^45 - 36 * q^49 + 36 * q^53 + 40 * q^55 + 16 * q^59 + 8 * q^61 - 40 * q^65 + 48 * q^67 - 8 * q^69 + 8 * q^71 + 48 * q^73 - 48 * q^77 - 28 * q^81 - 4 * q^85 - 24 * q^87 - 36 * q^89 - 24 * q^91 + 72 * q^95 - 72 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more