LMFDB - Embedded newform 780.2.r.a.577.7

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			577.7
Character	$\chi$	$=$	780.577
Dual form			780.2.r.a.73.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(1.82608 + 1.29052i) q^{5} -0.513301i q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(1.82608 + 1.29052i) q^{5} -0.513301i q^{7} -1.00000i q^{9} +(2.70969 + 2.70969i) q^{11} +(-3.45368 + 1.03542i) q^{13} +(-2.20377 + 0.378695i) q^{15} +(2.65283 - 2.65283i) q^{17} +(4.94524 + 4.94524i) q^{19} +(0.362959 + 0.362959i) q^{21} +(-1.20796 - 1.20796i) q^{23} +(1.66911 + 4.71318i) q^{25} +(0.707107 + 0.707107i) q^{27} -3.33595i q^{29} +(-4.89558 + 4.89558i) q^{31} -3.83208 q^{33} +(0.662426 - 0.937327i) q^{35} -8.27115i q^{37} +(1.70997 - 3.17427i) q^{39} +(-8.18166 + 8.18166i) q^{41} +(7.27336 + 7.27336i) q^{43} +(1.29052 - 1.82608i) q^{45} +5.36883i q^{47} +6.73652 q^{49} +3.75167i q^{51} +(-0.721780 + 0.721780i) q^{53} +(1.45119 + 8.44502i) q^{55} -6.99363 q^{57} +(-8.69717 + 8.69717i) q^{59} +4.33239 q^{61} -0.513301 q^{63} +(-7.64292 - 2.56628i) q^{65} +11.8988 q^{67} +1.70832 q^{69} +(1.66838 - 1.66838i) q^{71} -5.73930 q^{73} +(-4.51296 - 2.15248i) q^{75} +(1.39089 - 1.39089i) q^{77} +5.21919i q^{79} -1.00000 q^{81} -4.62310i q^{83} +(8.26780 - 1.42074i) q^{85} +(2.35887 + 2.35887i) q^{87} +(7.61981 - 7.61981i) q^{89} +(0.531483 + 1.77278i) q^{91} -6.92340i q^{93} +(2.64845 + 15.4123i) q^{95} +1.65723 q^{97} +(2.70969 - 2.70969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.82608	+	1.29052i	0.816646	+	0.577138i
$5$	1.82608	+	1.29052i	0.816646	+	0.577138i
$6$		0			0
$7$		−	0.513301i		−	0.194010i	−0.995284	−	0.0970048i	$-0.969074\pi$
$7$		−	0.513301i		−	0.194010i	0.995284	−	0.0970048i	$-0.0309262\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	2.70969	+	2.70969i	0.817003	+	0.817003i	0.985673	−	0.168669i	$-0.0539470\pi$
$11$	2.70969	+	2.70969i	0.817003	+	0.817003i	−0.168669	+	0.985673i	$0.553947\pi$
$12$		0			0
$13$	−3.45368	+	1.03542i	−0.957878	+	0.287175i
$13$	−3.45368	+	1.03542i	−0.957878	+	0.287175i
$14$		0			0
$15$	−2.20377	+	0.378695i	−0.569010	+	0.0977787i
$16$		0			0
$17$	2.65283	−	2.65283i	0.643406	−	0.643406i	−0.307985	−	0.951391i	$-0.599655\pi$
$17$	2.65283	−	2.65283i	0.643406	−	0.643406i	0.951391	+	0.307985i	$0.0996547\pi$
$18$		0			0
$19$	4.94524	+	4.94524i	1.13452	+	1.13452i	0.989417	+	0.145099i	$0.0463501\pi$
$19$	4.94524	+	4.94524i	1.13452	+	1.13452i	0.145099	+	0.989417i	$0.453650\pi$
$20$		0			0
$21$	0.362959	+	0.362959i	0.0792041	+	0.0792041i
$22$		0			0
$23$	−1.20796	−	1.20796i	−0.251877	−	0.251877i	0.569863	−	0.821740i	$-0.306996\pi$
$23$	−1.20796	−	1.20796i	−0.251877	−	0.251877i	−0.821740	+	0.569863i	$0.806996\pi$
$24$		0			0
$25$	1.66911	+	4.71318i	0.333823	+	0.942636i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$		−	3.33595i		−	0.619469i	−0.950823	−	0.309735i	$-0.899760\pi$
$29$		−	3.33595i		−	0.619469i	0.950823	−	0.309735i	$-0.100240\pi$
$30$		0			0
$31$	−4.89558	+	4.89558i	−0.879272	+	0.879272i	−0.993459	−	0.114187i	$-0.963574\pi$
$31$	−4.89558	+	4.89558i	−0.879272	+	0.879272i	0.114187	+	0.993459i	$0.463574\pi$
$32$		0			0
$33$	−3.83208			−0.667080
$34$		0			0
$35$	0.662426	−	0.937327i	0.111970	−	0.158437i
$36$		0			0
$37$		−	8.27115i		−	1.35977i	−0.733320	−	0.679884i	$-0.762030\pi$
$37$		−	8.27115i		−	1.35977i	0.733320	−	0.679884i	$-0.237970\pi$
$38$		0			0
$39$	1.70997	−	3.17427i	0.273814	−	0.508291i
$40$		0			0
$41$	−8.18166	+	8.18166i	−1.27776	+	1.27776i	−0.335842	+	0.941918i	$0.609021\pi$
$41$	−8.18166	+	8.18166i	−1.27776	+	1.27776i	−0.941918	+	0.335842i	$0.890979\pi$
$42$		0			0
$43$	7.27336	+	7.27336i	1.10918	+	1.10918i	0.993259	+	0.115919i	$0.0369812\pi$
$43$	7.27336	+	7.27336i	1.10918	+	1.10918i	0.115919	+	0.993259i	$0.463019\pi$
$44$		0			0
$45$	1.29052	−	1.82608i	0.192379	−	0.272215i
$46$		0			0
$47$			5.36883i			0.783125i	0.920151	+	0.391563i	$0.128065\pi$
$47$			5.36883i			0.783125i	−0.920151	+	0.391563i	$0.871935\pi$
$48$		0			0
$49$	6.73652			0.962360
$50$		0			0
$51$			3.75167i			0.525339i
$52$		0			0
$53$	−0.721780	+	0.721780i	−0.0991441	+	0.0991441i	−0.754939	−	0.655795i	$-0.772334\pi$
$53$	−0.721780	+	0.721780i	−0.0991441	+	0.0991441i	0.655795	+	0.754939i	$0.272334\pi$
$54$		0			0
$55$	1.45119	+	8.44502i	0.195679	+	1.13873i
$56$		0			0
$57$	−6.99363			−0.926329
$58$		0			0
$59$	−8.69717	+	8.69717i	−1.13227	+	1.13227i	−0.142476	+	0.989798i	$0.545507\pi$
$59$	−8.69717	+	8.69717i	−1.13227	+	1.13227i	−0.989798	+	0.142476i	$0.954493\pi$
$60$		0			0
$61$	4.33239			0.554706			0.277353	−	0.960768i	$-0.410543\pi$
$61$	4.33239			0.554706			0.277353	+	0.960768i	$0.410543\pi$
$62$		0			0
$63$	−0.513301			−0.0646698
$64$		0			0
$65$	−7.64292	−	2.56628i	−0.947987	−	0.318308i
$66$		0			0
$67$	11.8988			1.45367			0.726834	−	0.686813i	$-0.240991\pi$
$67$	11.8988			1.45367			0.726834	+	0.686813i	$0.240991\pi$
$68$		0			0
$69$	1.70832			0.205657
$70$		0			0
$71$	1.66838	−	1.66838i	0.198000	−	0.198000i	−0.601142	−	0.799142i	$-0.705287\pi$
$71$	1.66838	−	1.66838i	0.198000	−	0.198000i	0.799142	+	0.601142i	$0.205287\pi$
$72$		0			0
$73$	−5.73930			−0.671735			−0.335867	−	0.941909i	$-0.609029\pi$
$73$	−5.73930			−0.671735			−0.335867	+	0.941909i	$0.609029\pi$
$74$		0			0
$75$	−4.51296	−	2.15248i	−0.521112	−	0.248547i
$76$		0			0
$77$	1.39089	−	1.39089i	0.158506	−	0.158506i
$78$		0			0
$79$			5.21919i			0.587205i	0.955928	+	0.293603i	$0.0948542\pi$
$79$			5.21919i			0.587205i	−0.955928	+	0.293603i	$0.905146\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$		−	4.62310i		−	0.507451i	−0.967276	−	0.253725i	$-0.918344\pi$
$83$		−	4.62310i		−	0.507451i	0.967276	−	0.253725i	$-0.0816560\pi$
$84$		0			0
$85$	8.26780	−	1.42074i	0.896769	−	0.154101i
$86$		0			0
$87$	2.35887	+	2.35887i	0.252897	+	0.252897i
$88$		0			0
$89$	7.61981	−	7.61981i	0.807698	−	0.807698i	−0.176587	−	0.984285i	$-0.556506\pi$
$89$	7.61981	−	7.61981i	0.807698	−	0.807698i	0.984285	+	0.176587i	$0.0565057\pi$
$90$		0			0
$91$	0.531483	+	1.77278i	0.0557146	+	0.185838i
$92$		0			0
$93$		−	6.92340i		−	0.717923i
$94$		0			0
$95$	2.64845	+	15.4123i	0.271726	+	1.58127i
$96$		0			0
$97$	1.65723			0.168266			0.0841331	−	0.996455i	$-0.473188\pi$
$97$	1.65723			0.168266			0.0841331	+	0.996455i	$0.473188\pi$
$98$		0			0
$99$	2.70969	−	2.70969i	0.272334	−	0.272334i
$100$		0			0
$101$		−	14.8825i		−	1.48087i	−0.672130	−	0.740433i	$-0.734621\pi$
$101$		−	14.8825i		−	1.48087i	0.672130	−	0.740433i	$-0.265379\pi$
$102$		0			0
$103$	−13.9279	−	13.9279i	−1.37235	−	1.37235i	−0.856942	−	0.515413i	$-0.827639\pi$
$103$	−13.9279	−	13.9279i	−1.37235	−	1.37235i	−0.515413	−	0.856942i	$-0.672361\pi$
$104$		0			0
$105$	0.194385	+	1.13120i	0.0189700	+	0.110393i
$106$		0			0
$107$	−6.28458	−	6.28458i	−0.607553	−	0.607553i	0.334753	−	0.942306i	$-0.391347\pi$
$107$	−6.28458	−	6.28458i	−0.607553	−	0.607553i	−0.942306	+	0.334753i	$0.891347\pi$
$108$		0			0
$109$	11.3399	+	11.3399i	1.08616	+	1.08616i	0.995920	+	0.0902430i	$0.0287644\pi$
$109$	11.3399	+	11.3399i	1.08616	+	1.08616i	0.0902430	+	0.995920i	$0.471236\pi$
$110$		0			0
$111$	5.84858	+	5.84858i	0.555123	+	0.555123i
$112$		0			0
$113$	0.231611	−	0.231611i	0.0217881	−	0.0217881i	−0.696129	−	0.717917i	$-0.745096\pi$
$113$	0.231611	−	0.231611i	0.0217881	−	0.0217881i	0.717917	+	0.696129i	$0.245096\pi$
$114$		0			0
$115$	−0.646931	−	3.76473i	−0.0603267	−	0.351063i
$116$		0			0
$117$	1.03542	+	3.45368i	0.0957249	+	0.319293i
$118$		0			0
$119$	−1.36170	−	1.36170i	−0.124827	−	0.124827i
$120$		0			0
$121$			3.68487i			0.334989i
$122$		0			0
$123$		−	11.5706i		−	1.04329i
$124$		0			0
$125$	−3.03453	+	10.7607i	−0.271416	+	0.962462i
$126$		0			0
$127$	−0.195726	+	0.195726i	−0.0173679	+	0.0173679i	−0.715737	−	0.698370i	$-0.753909\pi$
$127$	−0.195726	+	0.195726i	−0.0173679	+	0.0173679i	0.698370	+	0.715737i	$0.253909\pi$
$128$		0			0
$129$	−10.2861			−0.905640
$130$		0			0
$131$	7.85996			0.686728			0.343364	−	0.939202i	$-0.388434\pi$
$131$	7.85996			0.686728			0.343364	+	0.939202i	$0.388434\pi$
$132$		0			0
$133$	2.53840	−	2.53840i	0.220107	−	0.220107i
$134$		0			0
$135$	0.378695	+	2.20377i	0.0325929	+	0.189670i
$136$		0			0
$137$		−	17.5613i		−	1.50037i	−0.661231	−	0.750183i	$-0.729966\pi$
$137$		−	17.5613i		−	1.50037i	0.661231	−	0.750183i	$-0.270034\pi$
$138$		0			0
$139$		−	18.2230i		−	1.54566i	−0.634615	−	0.772829i	$-0.718841\pi$
$139$		−	18.2230i		−	1.54566i	0.634615	−	0.772829i	$-0.281159\pi$
$140$		0			0
$141$	−3.79634	−	3.79634i	−0.319709	−	0.319709i
$142$		0			0
$143$	−12.1641	−	6.55273i	−1.01721	−	0.547967i
$144$		0			0
$145$	4.30511	−	6.09169i	0.357520	−	0.505887i
$146$		0			0
$147$	−4.76344	+	4.76344i	−0.392882	+	0.392882i
$148$		0			0
$149$	−13.6949	−	13.6949i	−1.12193	−	1.12193i	−0.991451	−	0.130483i	$-0.958347\pi$
$149$	−13.6949	−	13.6949i	−1.12193	−	1.12193i	−0.130483	−	0.991451i	$-0.541653\pi$
$150$		0			0
$151$	3.80693	+	3.80693i	0.309803	+	0.309803i	0.844833	−	0.535030i	$-0.179700\pi$
$151$	3.80693	+	3.80693i	0.309803	+	0.309803i	−0.535030	+	0.844833i	$0.679700\pi$
$152$		0			0
$153$	−2.65283	−	2.65283i	−0.214469	−	0.214469i
$154$		0			0
$155$	−15.2576	+	2.62186i	−1.22552	+	0.210593i
$156$		0			0
$157$	6.59689	+	6.59689i	0.526490	+	0.526490i	0.919524	−	0.393034i	$-0.128575\pi$
$157$	6.59689	+	6.59689i	0.526490	+	0.526490i	−0.393034	+	0.919524i	$0.628575\pi$
$158$		0			0
$159$		−	1.02075i		−	0.0809508i
$160$		0			0
$161$	−0.620048	+	0.620048i	−0.0488666	+	0.0488666i
$162$		0			0
$163$	−17.1211			−1.34103			−0.670514	−	0.741897i	$-0.733926\pi$
$163$	−17.1211			−1.34103			−0.670514	+	0.741897i	$0.733926\pi$
$164$		0			0
$165$	−6.99768	−	4.94538i	−0.544769	−	0.384998i
$166$		0			0
$167$		−	15.3626i		−	1.18879i	−0.804173	−	0.594396i	$-0.797391\pi$
$167$		−	15.3626i		−	1.18879i	0.804173	−	0.594396i	$-0.202609\pi$
$168$		0			0
$169$	10.8558	−	7.15204i	0.835062	−	0.550157i
$170$		0			0
$171$	4.94524	−	4.94524i	0.378172	−	0.378172i
$172$		0			0
$173$	−12.8800	−	12.8800i	−0.979248	−	0.979248i	0.0205407	−	0.999789i	$-0.493461\pi$
$173$	−12.8800	−	12.8800i	−0.979248	−	0.979248i	−0.999789	+	0.0205407i	$0.993461\pi$
$174$		0			0
$175$	2.41928	−	0.856757i	0.182880	−	0.0647647i
$176$		0			0
$177$		−	12.2997i		−	0.924498i
$178$		0			0
$179$	−5.15538			−0.385331			−0.192666	−	0.981264i	$-0.561713\pi$
$179$	−5.15538			−0.385331			−0.192666	+	0.981264i	$0.561713\pi$
$180$		0			0
$181$			2.91907i			0.216973i	0.994098	+	0.108486i	$0.0346004\pi$
$181$			2.91907i			0.216973i	−0.994098	+	0.108486i	$0.965400\pi$
$182$		0			0
$183$	−3.06346	+	3.06346i	−0.226458	+	0.226458i
$184$		0			0
$185$	10.6741	−	15.1037i	0.784774	−	1.11045i
$186$		0			0
$187$	14.3767			1.05133
$188$		0			0
$189$	0.362959	−	0.362959i	0.0264014	−	0.0264014i
$190$		0			0
$191$	18.1293			1.31179			0.655893	−	0.754853i	$-0.272292\pi$
$191$	18.1293			1.31179			0.655893	+	0.754853i	$0.272292\pi$
$192$		0			0
$193$	5.42506			0.390504			0.195252	−	0.980753i	$-0.437447\pi$
$193$	5.42506			0.390504			0.195252	+	0.980753i	$0.437447\pi$
$194$		0			0
$195$	7.21900	−	3.58972i	0.516963	−	0.257065i
$196$		0			0
$197$	5.82077			0.414713			0.207356	−	0.978265i	$-0.433514\pi$
$197$	5.82077			0.414713			0.207356	+	0.978265i	$0.433514\pi$
$198$		0			0
$199$	12.5300			0.888225			0.444112	−	0.895971i	$-0.353519\pi$
$199$	12.5300			0.888225			0.444112	+	0.895971i	$0.353519\pi$
$200$		0			0
$201$	−8.41371	+	8.41371i	−0.593457	+	0.593457i
$202$		0			0
$203$	−1.71234			−0.120183
$204$		0			0
$205$	−25.4989	+	4.38174i	−1.78092	+	0.306034i
$206$		0			0
$207$	−1.20796	+	1.20796i	−0.0839592	+	0.0839592i
$208$		0			0
$209$			26.8002i			1.85381i
$210$		0			0
$211$	−0.637170			−0.0438646			−0.0219323	−	0.999759i	$-0.506982\pi$
$211$	−0.637170			−0.0438646			−0.0219323	+	0.999759i	$0.506982\pi$
$212$		0			0
$213$			2.35944i			0.161666i
$214$		0			0
$215$	3.89529	+	22.6681i	0.265657	+	1.54595i
$216$		0			0
$217$	2.51291	+	2.51291i	0.170587	+	0.170587i
$218$		0			0
$219$	4.05830	−	4.05830i	0.274234	−	0.274234i
$220$		0			0
$221$	−6.41522	+	11.9088i	−0.431535	+	0.801074i
$222$		0			0
$223$			2.23495i			0.149664i	0.997196	+	0.0748318i	$0.0238420\pi$
$223$			2.23495i			0.149664i	−0.997196	+	0.0748318i	$0.976158\pi$
$224$		0			0
$225$	4.71318	−	1.66911i	0.314212	−	0.111274i
$226$		0			0
$227$	5.74222			0.381124			0.190562	−	0.981675i	$-0.438969\pi$
$227$	5.74222			0.381124			0.190562	+	0.981675i	$0.438969\pi$
$228$		0			0
$229$	6.11330	−	6.11330i	0.403978	−	0.403978i	−0.475654	−	0.879632i	$-0.657789\pi$
$229$	6.11330	−	6.11330i	0.403978	−	0.403978i	0.879632	+	0.475654i	$0.157789\pi$
$230$		0			0
$231$			1.96701i			0.129420i
$232$		0			0
$233$	4.83355	+	4.83355i	0.316656	+	0.316656i	0.847481	−	0.530825i	$-0.178118\pi$
$233$	4.83355	+	4.83355i	0.316656	+	0.316656i	−0.530825	+	0.847481i	$0.678118\pi$
$234$		0			0
$235$	−6.92859	+	9.80390i	−0.451972	+	0.639536i
$236$		0			0
$237$	−3.69053	−	3.69053i	−0.239726	−	0.239726i
$238$		0			0
$239$	3.05539	+	3.05539i	0.197637	+	0.197637i	0.798986	−	0.601349i	$-0.205370\pi$
$239$	3.05539	+	3.05539i	0.197637	+	0.197637i	−0.601349	+	0.798986i	$0.705370\pi$
$240$		0			0
$241$	−7.82927	−	7.82927i	−0.504327	−	0.504327i	0.408452	−	0.912780i	$-0.366069\pi$
$241$	−7.82927	−	7.82927i	−0.504327	−	0.504327i	−0.912780	+	0.408452i	$0.866069\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	12.3014	+	8.69362i	0.785908	+	0.555415i
$246$		0			0
$247$	−22.1997	−	11.9589i	−1.41253	−	0.760924i
$248$		0			0
$249$	3.26902	+	3.26902i	0.207166	+	0.207166i
$250$		0			0
$251$		−	16.2689i		−	1.02688i	−0.858125	−	0.513441i	$-0.828370\pi$
$251$		−	16.2689i		−	1.02688i	0.858125	−	0.513441i	$-0.171630\pi$
$252$		0			0
$253$		−	6.54641i		−	0.411569i
$254$		0			0
$255$	−4.84161	+	6.85083i	−0.303193	+	0.429016i
$256$		0			0
$257$	−1.10373	+	1.10373i	−0.0688486	+	0.0688486i	−0.740693	−	0.671844i	$-0.765503\pi$
$257$	−1.10373	+	1.10373i	−0.0688486	+	0.0688486i	0.671844	+	0.740693i	$0.265503\pi$
$258$		0			0
$259$	−4.24559			−0.263808
$260$		0			0
$261$	−3.33595			−0.206490
$262$		0			0
$263$	14.4502	−	14.4502i	0.891040	−	0.891040i	−0.103581	−	0.994621i	$-0.533030\pi$
$263$	14.4502	−	14.4502i	0.891040	−	0.891040i	0.994621	+	0.103581i	$0.0330300\pi$
$264$		0			0
$265$	−2.24950	+	0.386554i	−0.138186	+	0.0237458i
$266$		0			0
$267$			10.7760i			0.659483i
$268$		0			0
$269$		−	21.3208i		−	1.29995i	−0.759954	−	0.649977i	$-0.774778\pi$
$269$		−	21.3208i		−	1.29995i	0.759954	−	0.649977i	$-0.225222\pi$
$270$		0			0
$271$	10.3062	+	10.3062i	0.626058	+	0.626058i	0.947074	−	0.321016i	$-0.104024\pi$
$271$	10.3062	+	10.3062i	0.626058	+	0.626058i	−0.321016	+	0.947074i	$0.604024\pi$
$272$		0			0
$273$	−1.62936	−	0.877727i	−0.0986132	−	0.0531225i
$274$		0			0
$275$	−8.24849	+	17.2941i	−0.497403	+	1.04287i
$276$		0			0
$277$	1.32982	−	1.32982i	0.0799013	−	0.0799013i	−0.666027	−	0.745928i	$-0.732006\pi$
$277$	1.32982	−	1.32982i	0.0799013	−	0.0799013i	0.745928	+	0.666027i	$0.232006\pi$
$278$		0			0
$279$	4.89558	+	4.89558i	0.293091	+	0.293091i
$280$		0			0
$281$	−18.5931	−	18.5931i	−1.10917	−	1.10917i	−0.993260	−	0.115909i	$-0.963022\pi$
$281$	−18.5931	−	18.5931i	−1.10917	−	1.10917i	−0.115909	−	0.993260i	$-0.536978\pi$
$282$		0			0
$283$	−1.19879	−	1.19879i	−0.0712609	−	0.0712609i	0.670578	−	0.741839i	$-0.266046\pi$
$283$	−1.19879	−	1.19879i	−0.0712609	−	0.0712609i	−0.741839	+	0.670578i	$0.766046\pi$
$284$		0			0
$285$	−12.7709	−	9.02542i	−0.756483	−	0.534620i
$286$		0			0
$287$	4.19965	+	4.19965i	0.247898	+	0.247898i
$288$		0			0
$289$			2.92498i			0.172058i
$290$		0			0
$291$	−1.17184	+	1.17184i	−0.0686944	+	0.0686944i
$292$		0			0
$293$	−14.5785			−0.851687			−0.425843	−	0.904797i	$-0.640023\pi$
$293$	−14.5785			−0.851687			−0.425843	+	0.904797i	$0.640023\pi$
$294$		0			0
$295$	−27.1056	+	4.65782i	−1.57815	+	0.271189i
$296$		0			0
$297$			3.83208i			0.222360i
$298$		0			0
$299$	5.42266	+	2.92116i	0.313601	+	0.168935i
$300$		0			0
$301$	3.73342	−	3.73342i	0.215191	−	0.215191i
$302$		0			0
$303$	10.5235	+	10.5235i	0.604561	+	0.604561i
$304$		0			0
$305$	7.91128	+	5.59104i	0.452998	+	0.320142i
$306$		0			0
$307$			18.5582i			1.05917i	0.848256	+	0.529587i	$0.177653\pi$
$307$			18.5582i			1.05917i	−0.848256	+	0.529587i	$0.822347\pi$
$308$		0			0
$309$	19.6970			1.12052
$310$		0			0
$311$			4.89382i			0.277503i	0.990327	+	0.138751i	$0.0443089\pi$
$311$			4.89382i			0.277503i	−0.990327	+	0.138751i	$0.955691\pi$
$312$		0			0
$313$	−12.7640	+	12.7640i	−0.721462	+	0.721462i	−0.968903	−	0.247441i	$-0.920410\pi$
$313$	−12.7640	+	12.7640i	−0.721462	+	0.721462i	0.247441	+	0.968903i	$0.420410\pi$
$314$		0			0
$315$	−0.937327	−	0.662426i	−0.0528124	−	0.0373234i
$316$		0			0
$317$	32.6779			1.83538			0.917688	−	0.397301i	$-0.130053\pi$
$317$	32.6779			1.83538			0.917688	+	0.397301i	$0.130053\pi$
$318$		0			0
$319$	9.03939	−	9.03939i	0.506109	−	0.506109i
$320$		0			0
$321$	8.88774			0.496065
$322$		0			0
$323$	26.2378			1.45991
$324$		0			0
$325$	−10.6447	−	14.5496i	−0.590462	−	0.807065i
$326$		0			0
$327$	−16.0370			−0.886848
$328$		0			0
$329$	2.75583			0.151934
$330$		0			0
$331$	14.5289	−	14.5289i	0.798578	−	0.798578i	−0.184293	−	0.982871i	$-0.559000\pi$
$331$	14.5289	−	14.5289i	0.798578	−	0.798578i	0.982871	+	0.184293i	$0.0589996\pi$
$332$		0			0
$333$	−8.27115			−0.453256
$334$		0			0
$335$	21.7281	+	15.3556i	1.18713	+	0.838968i
$336$		0			0
$337$	−19.8941	+	19.8941i	−1.08370	+	1.08370i	−0.0875425	+	0.996161i	$0.527901\pi$
$337$	−19.8941	+	19.8941i	−1.08370	+	1.08370i	−0.996161	+	0.0875425i	$0.972099\pi$
$338$		0			0
$339$			0.327547i			0.0177899i
$340$		0			0
$341$	−26.5310			−1.43674
$342$		0			0
$343$		−	7.05097i		−	0.380717i
$344$		0			0
$345$	3.11952	+	2.20462i	0.167949	+	0.118693i
$346$		0			0
$347$	−10.2419	−	10.2419i	−0.549814	−	0.549814i	0.376573	−	0.926387i	$-0.377103\pi$
$347$	−10.2419	−	10.2419i	−0.549814	−	0.549814i	−0.926387	+	0.376573i	$0.877103\pi$
$348$		0			0
$349$	7.93275	−	7.93275i	0.424630	−	0.424630i	−0.462164	−	0.886794i	$-0.652927\pi$
$349$	7.93275	−	7.93275i	0.424630	−	0.424630i	0.886794	+	0.462164i	$0.152927\pi$
$350$		0			0
$351$	−3.17427	−	1.70997i	−0.169430	−	0.0912712i
$352$		0			0
$353$			16.5324i			0.879933i	0.898014	+	0.439966i	$0.145010\pi$
$353$			16.5324i			0.879933i	−0.898014	+	0.439966i	$0.854990\pi$
$354$		0			0
$355$	5.19966	−	0.893510i	0.275969	−	0.0474226i
$356$		0			0
$357$	1.92574			0.101921
$358$		0			0
$359$	−1.04003	+	1.04003i	−0.0548906	+	0.0548906i	−0.734019	−	0.679129i	$-0.762358\pi$
$359$	−1.04003	+	1.04003i	−0.0548906	+	0.0548906i	0.679129	+	0.734019i	$0.262358\pi$
$360$		0			0
$361$			29.9108i			1.57425i
$362$		0			0
$363$	−2.60560	−	2.60560i	−0.136758	−	0.136758i
$364$		0			0
$365$	−10.4804	−	7.40669i	−0.548570	−	0.387684i
$366$		0			0
$367$	−16.1317	−	16.1317i	−0.842067	−	0.842067i	0.147061	−	0.989127i	$-0.453019\pi$
$367$	−16.1317	−	16.1317i	−0.842067	−	0.842067i	−0.989127	+	0.147061i	$0.953019\pi$
$368$		0			0
$369$	8.18166	+	8.18166i	0.425920	+	0.425920i
$370$		0			0
$371$	0.370490	+	0.370490i	0.0192349	+	0.0192349i
$372$		0			0
$373$	8.18820	−	8.18820i	0.423969	−	0.423969i	−0.462599	−	0.886568i	$-0.653083\pi$
$373$	8.18820	−	8.18820i	0.423969	−	0.423969i	0.886568	+	0.462599i	$0.153083\pi$
$374$		0			0
$375$	−5.46319	−	9.75467i	−0.282118	−	0.503729i
$376$		0			0
$377$	3.45411	+	11.5213i	0.177896	+	0.593376i
$378$		0			0
$379$	13.7307	+	13.7307i	0.705297	+	0.705297i	0.965543	−	0.260245i	$-0.0838035\pi$
$379$	13.7307	+	13.7307i	0.705297	+	0.705297i	−0.260245	+	0.965543i	$0.583803\pi$
$380$		0			0
$381$		−	0.276798i		−	0.0141808i
$382$		0			0
$383$			38.0569i			1.94461i	0.233705	+	0.972307i	$0.424915\pi$
$383$			38.0569i			1.94461i	−0.233705	+	0.972307i	$0.575085\pi$
$384$		0			0
$385$	4.33484	−	0.744898i	0.220924	−	0.0379635i
$386$		0			0
$387$	7.27336	−	7.27336i	0.369726	−	0.369726i
$388$		0			0
$389$	−36.7993			−1.86580			−0.932899	−	0.360137i	$-0.882730\pi$
$389$	−36.7993			−1.86580			−0.932899	+	0.360137i	$0.882730\pi$
$390$		0			0
$391$	−6.40904			−0.324119
$392$		0			0
$393$	−5.55783	+	5.55783i	−0.280356	+	0.280356i
$394$		0			0
$395$	−6.73548	+	9.53065i	−0.338899	+	0.479539i
$396$		0			0
$397$			1.17039i			0.0587400i	0.999569	+	0.0293700i	$0.00935011\pi$
$397$			1.17039i			0.0587400i	−0.999569	+	0.0293700i	$0.990650\pi$
$398$		0			0
$399$			3.58984i			0.179717i
$400$		0			0
$401$	0.645804	+	0.645804i	0.0322499	+	0.0322499i	0.723048	−	0.690798i	$-0.242741\pi$
$401$	0.645804	+	0.645804i	0.0322499	+	0.0322499i	−0.690798	+	0.723048i	$0.742741\pi$
$402$		0			0
$403$	11.8388	−	21.9768i	0.589731	−	1.09474i
$404$		0			0
$405$	−1.82608	−	1.29052i	−0.0907385	−	0.0641265i
$406$		0			0
$407$	22.4123	−	22.4123i	1.11093	−	1.11093i
$408$		0			0
$409$	11.6877	+	11.6877i	0.577921	+	0.577921i	0.934330	−	0.356409i	$-0.115999\pi$
$409$	11.6877	+	11.6877i	0.577921	+	0.577921i	−0.356409	+	0.934330i	$0.615999\pi$
$410$		0			0
$411$	12.4177	+	12.4177i	0.612522	+	0.612522i
$412$		0			0
$413$	4.46426	+	4.46426i	0.219672	+	0.219672i
$414$		0			0
$415$	5.96620	−	8.44213i	0.292869	−	0.414408i
$416$		0			0
$417$	12.8856	+	12.8856i	0.631012	+	0.631012i
$418$		0			0
$419$			1.92637i			0.0941093i	0.998892	+	0.0470547i	$0.0149835\pi$
$419$			1.92637i			0.0941093i	−0.998892	+	0.0470547i	$0.985017\pi$
$420$		0			0
$421$	6.14615	−	6.14615i	0.299545	−	0.299545i	−0.541290	−	0.840836i	$-0.682064\pi$
$421$	6.14615	−	6.14615i	0.299545	−	0.299545i	0.840836	+	0.541290i	$0.182064\pi$
$422$		0			0
$423$	5.36883			0.261042
$424$		0			0
$425$	16.9311	+	8.07539i	0.821281	+	0.391714i
$426$		0			0
$427$		−	2.22382i		−	0.107618i
$428$		0			0
$429$	13.2348	−	3.96783i	0.638982	−	0.191569i
$430$		0			0
$431$	14.0451	−	14.0451i	0.676530	−	0.676530i	−0.282683	−	0.959213i	$-0.591225\pi$
$431$	14.0451	−	14.0451i	0.676530	−	0.676530i	0.959213	+	0.282683i	$0.0912245\pi$
$432$		0			0
$433$	13.1703	+	13.1703i	0.632923	+	0.632923i	0.948800	−	0.315877i	$-0.102299\pi$
$433$	13.1703	+	13.1703i	0.632923	+	0.632923i	−0.315877	+	0.948800i	$0.602299\pi$
$434$		0			0
$435$	1.26331	+	7.35165i	0.0605709	+	0.352484i
$436$		0			0
$437$		−	11.9473i		−	0.571518i
$438$		0			0
$439$	−31.6805			−1.51203			−0.756013	−	0.654556i	$-0.772856\pi$
$439$	−31.6805			−1.51203			−0.756013	+	0.654556i	$0.772856\pi$
$440$		0			0
$441$		−	6.73652i		−	0.320787i
$442$		0			0
$443$	2.06870	−	2.06870i	0.0982867	−	0.0982867i	−0.656254	−	0.754540i	$-0.727860\pi$
$443$	2.06870	−	2.06870i	0.0982867	−	0.0982867i	0.754540	+	0.656254i	$0.227860\pi$
$444$		0			0
$445$	23.7479	−	4.08083i	1.12576	−	0.193450i
$446$		0			0
$447$	19.3676			0.916055
$448$		0			0
$449$	−23.3162	+	23.3162i	−1.10036	+	1.10036i	−0.105994	+	0.994367i	$0.533803\pi$
$449$	−23.3162	+	23.3162i	−1.10036	+	1.10036i	−0.994367	+	0.105994i	$0.966197\pi$
$450$		0			0
$451$	−44.3396			−2.08787
$452$		0			0
$453$	−5.38381			−0.252953
$454$		0			0
$455$	−1.31728	+	3.92312i	−0.0617548	+	0.183919i
$456$		0			0
$457$	25.8855			1.21087			0.605437	−	0.795893i	$-0.292998\pi$
$457$	25.8855			1.21087			0.605437	+	0.795893i	$0.292998\pi$
$458$		0			0
$459$	3.75167			0.175113
$460$		0			0
$461$	−6.42519	+	6.42519i	−0.299251	+	0.299251i	−0.840720	−	0.541469i	$-0.817868\pi$
$461$	−6.42519	+	6.42519i	−0.299251	+	0.299251i	0.541469	+	0.840720i	$0.317868\pi$
$462$		0			0
$463$	−24.6157			−1.14399			−0.571993	−	0.820258i	$-0.693830\pi$
$463$	−24.6157			−1.14399			−0.571993	+	0.820258i	$0.693830\pi$
$464$		0			0
$465$	8.93479	−	12.6427i	0.414341	−	0.586289i
$466$		0			0
$467$	−6.69564	+	6.69564i	−0.309837	+	0.309837i	−0.844846	−	0.535009i	$-0.820308\pi$
$467$	−6.69564	+	6.69564i	−0.309837	+	0.309837i	0.535009	+	0.844846i	$0.320308\pi$
$468$		0			0
$469$		−	6.10766i		−	0.282025i
$470$		0			0
$471$	−9.32942			−0.429877
$472$		0			0
$473$			39.4172i			1.81240i
$474$		0			0
$475$	−15.0536	+	31.5620i	−0.690709	+	1.44816i
$476$		0			0
$477$	0.721780	+	0.721780i	0.0330480	+	0.0330480i
$478$		0			0
$479$	2.92409	−	2.92409i	0.133605	−	0.133605i	−0.637142	−	0.770747i	$-0.719883\pi$
$479$	2.92409	−	2.92409i	0.133605	−	0.133605i	0.770747	+	0.637142i	$0.219883\pi$
$480$		0			0
$481$	8.56413	+	28.5659i	0.390491	+	1.30249i
$482$		0			0
$483$		−	0.876880i		−	0.0398994i
$484$		0			0
$485$	3.02623	+	2.13869i	0.137414	+	0.0971128i
$486$		0			0
$487$	−33.1274			−1.50115			−0.750573	−	0.660788i	$-0.770222\pi$
$487$	−33.1274			−1.50115			−0.750573	+	0.660788i	$0.770222\pi$
$488$		0			0
$489$	12.1064	−	12.1064i	0.547473	−	0.547473i
$490$		0			0
$491$			2.33036i			0.105168i	0.998617	+	0.0525839i	$0.0167457\pi$
$491$			2.33036i			0.105168i	−0.998617	+	0.0525839i	$0.983254\pi$
$492$		0			0
$493$	−8.84970	−	8.84970i	−0.398570	−	0.398570i
$494$		0			0
$495$	8.44502	−	1.45119i	0.379576	−	0.0652263i
$496$		0			0
$497$	−0.856380	−	0.856380i	−0.0384139	−	0.0384139i
$498$		0			0
$499$	9.55223	+	9.55223i	0.427617	+	0.427617i	0.887816	−	0.460199i	$-0.152222\pi$
$499$	9.55223	+	9.55223i	0.427617	+	0.427617i	−0.460199	+	0.887816i	$0.652222\pi$
$500$		0			0
$501$	10.8630	+	10.8630i	0.485322	+	0.485322i
$502$		0			0
$503$	−8.58760	+	8.58760i	−0.382902	+	0.382902i	−0.872147	−	0.489244i	$-0.837273\pi$
$503$	−8.58760	+	8.58760i	−0.382902	+	0.382902i	0.489244	+	0.872147i	$0.337273\pi$
$504$		0			0
$505$	19.2062	−	27.1766i	0.854664	−	1.20934i
$506$		0			0
$507$	−2.61896	+	12.7335i	−0.116312	+	0.565513i
$508$		0			0
$509$	18.8561	+	18.8561i	0.835784	+	0.835784i	0.988301	−	0.152517i	$-0.0487379\pi$
$509$	18.8561	+	18.8561i	0.835784	+	0.835784i	−0.152517	+	0.988301i	$0.548738\pi$
$510$		0			0
$511$			2.94599i			0.130323i
$512$		0			0
$513$			6.99363i			0.308776i
$514$		0			0
$515$	−7.45916	−	43.4076i	−0.328690	−	1.91277i
$516$		0			0
$517$	−14.5479	+	14.5479i	−0.639816	+	0.639816i
$518$		0			0
$519$	18.2151			0.799553
$520$		0			0
$521$	−10.7556			−0.471211			−0.235606	−	0.971849i	$-0.575707\pi$
$521$	−10.7556			−0.471211			−0.235606	+	0.971849i	$0.575707\pi$
$522$		0			0
$523$	−9.99839	+	9.99839i	−0.437199	+	0.437199i	−0.891068	−	0.453869i	$-0.850043\pi$
$523$	−9.99839	+	9.99839i	−0.437199	+	0.437199i	0.453869	+	0.891068i	$0.350043\pi$
$524$		0			0
$525$	−1.10487	+	2.31651i	−0.0482205	+	0.101101i
$526$		0			0
$527$			25.9743i			1.13146i
$528$		0			0
$529$		−	20.0817i		−	0.873115i
$530$		0			0
$531$	8.69717	+	8.69717i	0.377425	+	0.377425i
$532$		0			0
$533$	19.7853	−	36.7283i	0.856999	−	1.59088i
$534$		0			0
$535$	−3.36574	−	19.5865i	−0.145514	−	0.846798i
$536$		0			0
$537$	3.64540	−	3.64540i	0.157311	−	0.157311i
$538$		0			0
$539$	18.2539	+	18.2539i	0.786251	+	0.786251i
$540$		0			0
$541$	24.8499	+	24.8499i	1.06838	+	1.06838i	0.997484	+	0.0708951i	$0.0225856\pi$
$541$	24.8499	+	24.8499i	1.06838	+	1.06838i	0.0708951	+	0.997484i	$0.477414\pi$
$542$		0			0
$543$	−2.06409	−	2.06409i	−0.0885787	−	0.0885787i
$544$		0			0
$545$	6.07314	+	35.3418i	0.260145	+	1.51388i
$546$		0			0
$547$	−22.4433	−	22.4433i	−0.959604	−	0.959604i	0.0396108	−	0.999215i	$-0.487388\pi$
$547$	−22.4433	−	22.4433i	−0.959604	−	0.959604i	−0.999215	+	0.0396108i	$0.987388\pi$
$548$		0			0
$549$		−	4.33239i		−	0.184902i
$550$		0			0
$551$	16.4971	−	16.4971i	0.702798	−	0.702798i
$552$		0			0
$553$	2.67902			0.113923
$554$		0			0
$555$	3.13224	+	18.2277i	0.132956	+	0.773722i
$556$		0			0
$557$		−	37.9238i		−	1.60688i	−0.595384	−	0.803441i	$-0.703000\pi$
$557$		−	37.9238i		−	1.60688i	0.595384	−	0.803441i	$-0.297000\pi$
$558$		0			0
$559$	−32.6509	−	17.5889i	−1.38098	−	0.743929i
$560$		0			0
$561$	−10.1659	+	10.1659i	−0.429203	+	0.429203i
$562$		0			0
$563$	18.5422	+	18.5422i	0.781461	+	0.781461i	0.980077	−	0.198616i	$-0.0636446\pi$
$563$	18.5422	+	18.5422i	0.781461	+	0.781461i	−0.198616	+	0.980077i	$0.563645\pi$
$564$		0			0
$565$	0.721837	−	0.124041i	0.0303679	−	0.00521842i
$566$		0			0
$567$			0.513301i			0.0215566i
$568$		0			0
$569$	−13.4006			−0.561784			−0.280892	−	0.959739i	$-0.590630\pi$
$569$	−13.4006			−0.561784			−0.280892	+	0.959739i	$0.590630\pi$
$570$		0			0
$571$		−	30.2734i		−	1.26690i	−0.773782	−	0.633452i	$-0.781637\pi$
$571$		−	30.2734i		−	1.26690i	0.773782	−	0.633452i	$-0.218363\pi$
$572$		0			0
$573$	−12.8193	+	12.8193i	−0.535535	+	0.535535i
$574$		0			0
$575$	3.67712	−	7.70957i	0.153346	−	0.321511i
$576$		0			0
$577$	18.0535			0.751579			0.375789	−	0.926705i	$-0.377372\pi$
$577$	18.0535			0.751579			0.375789	+	0.926705i	$0.377372\pi$
$578$		0			0
$579$	−3.83610	+	3.83610i	−0.159423	+	0.159423i
$580$		0			0
$581$	−2.37304			−0.0984503
$582$		0			0
$583$	−3.91160			−0.162002
$584$		0			0
$585$	−2.56628	+	7.64292i	−0.106103	+	0.315996i
$586$		0			0
$587$	−32.3047			−1.33336			−0.666678	−	0.745346i	$-0.732284\pi$
$587$	−32.3047			−1.33336			−0.666678	+	0.745346i	$0.732284\pi$
$588$		0			0
$589$	−48.4197			−1.99510
$590$		0			0
$591$	−4.11591	+	4.11591i	−0.169306	+	0.169306i
$592$		0			0
$593$	15.6675			0.643386			0.321693	−	0.946844i	$-0.395748\pi$
$593$	15.6675			0.643386			0.321693	+	0.946844i	$0.395748\pi$
$594$		0			0
$595$	−0.729267	−	4.24387i	−0.0298970	−	0.173982i
$596$		0			0
$597$	−8.86001	+	8.86001i	−0.362616	+	0.362616i
$598$		0			0
$599$			19.1035i			0.780550i	0.920698	+	0.390275i	$0.127620\pi$
$599$			19.1035i			0.780550i	−0.920698	+	0.390275i	$0.872380\pi$
$600$		0			0
$601$	14.9677			0.610547			0.305273	−	0.952265i	$-0.401252\pi$
$601$	14.9677			0.610547			0.305273	+	0.952265i	$0.401252\pi$
$602$		0			0
$603$		−	11.8988i		−	0.484556i
$604$		0			0
$605$	−4.75541	+	6.72886i	−0.193335	+	0.273567i
$606$		0			0
$607$	0.947407	+	0.947407i	0.0384541	+	0.0384541i	0.726072	−	0.687618i	$-0.241344\pi$
$607$	0.947407	+	0.947407i	0.0384541	+	0.0384541i	−0.687618	+	0.726072i	$0.741344\pi$
$608$		0			0
$609$	1.21081	−	1.21081i	0.0490645	−	0.0490645i
$610$		0			0
$611$	−5.55901	−	18.5422i	−0.224894	−	0.750138i
$612$		0			0
$613$		−	28.4712i		−	1.14994i	−0.818174	−	0.574971i	$-0.805013\pi$
$613$		−	28.4712i		−	1.14994i	0.818174	−	0.574971i	$-0.194987\pi$
$614$		0			0
$615$	14.9321	−	21.1288i	0.602121	−	0.851996i
$616$		0			0
$617$	−6.82929			−0.274937			−0.137468	−	0.990506i	$-0.543897\pi$
$617$	−6.82929			−0.274937			−0.137468	+	0.990506i	$0.543897\pi$
$618$		0			0
$619$	9.43936	−	9.43936i	0.379400	−	0.379400i	−0.491486	−	0.870886i	$-0.663546\pi$
$619$	9.43936	−	9.43936i	0.379400	−	0.379400i	0.870886	+	0.491486i	$0.163546\pi$
$620$		0			0
$621$		−	1.70832i		−	0.0685524i
$622$		0			0
$623$	−3.91125	−	3.91125i	−0.156701	−	0.156701i
$624$		0			0
$625$	−19.4281	+	15.7337i	−0.777125	+	0.629346i
$626$		0			0
$627$	−18.9506	−	18.9506i	−0.756813	−	0.756813i
$628$		0			0
$629$	−21.9419	−	21.9419i	−0.874883	−	0.874883i
$630$		0			0
$631$	−14.2465	−	14.2465i	−0.567143	−	0.567143i	0.364184	−	0.931327i	$-0.381348\pi$
$631$	−14.2465	−	14.2465i	−0.567143	−	0.567143i	−0.931327	+	0.364184i	$0.881348\pi$
$632$		0			0
$633$	0.450547	−	0.450547i	0.0179077	−	0.0179077i
$634$		0			0
$635$	−0.609999	+	0.104822i	−0.0242071	+	0.00415974i
$636$		0			0
$637$	−23.2658	+	6.97515i	−0.921824	+	0.276365i
$638$		0			0
$639$	−1.66838	−	1.66838i	−0.0660000	−	0.0660000i
$640$		0			0
$641$		−	29.0026i		−	1.14553i	−0.819719	−	0.572766i	$-0.805870\pi$
$641$		−	29.0026i		−	1.14553i	0.819719	−	0.572766i	$-0.194130\pi$
$642$		0			0
$643$		−	0.145448i		−	0.00573591i	−0.999996	−	0.00286796i	$-0.999087\pi$
$643$		−	0.145448i		−	0.00573591i	0.999996	−	0.00286796i	$-0.000912900\pi$
$644$		0			0
$645$	−18.7832	−	13.2744i	−0.739587	−	0.522679i
$646$		0			0
$647$	14.3504	−	14.3504i	0.564173	−	0.564173i	−0.366317	−	0.930490i	$-0.619381\pi$
$647$	14.3504	−	14.3504i	0.564173	−	0.564173i	0.930490	+	0.366317i	$0.119381\pi$
$648$		0			0
$649$	−47.1333			−1.85014
$650$		0			0
$651$	−3.55379			−0.139284
$652$		0			0
$653$	−1.30050	+	1.30050i	−0.0508923	+	0.0508923i	−0.732095	−	0.681203i	$-0.761457\pi$
$653$	−1.30050	+	1.30050i	−0.0508923	+	0.0508923i	0.681203	+	0.732095i	$0.261457\pi$
$654$		0			0
$655$	14.3529	+	10.1434i	0.560814	+	0.396337i
$656$		0			0
$657$			5.73930i			0.223912i
$658$		0			0
$659$		−	17.6095i		−	0.685967i	−0.939341	−	0.342983i	$-0.888563\pi$
$659$		−	17.6095i		−	0.685967i	0.939341	−	0.342983i	$-0.111437\pi$
$660$		0			0
$661$	−26.7100	−	26.7100i	−1.03890	−	1.03890i	−0.999212	−	0.0396855i	$-0.987364\pi$
$661$	−26.7100	−	26.7100i	−1.03890	−	1.03890i	−0.0396855	−	0.999212i	$-0.512636\pi$
$662$		0			0
$663$	−3.88456	−	12.9571i	−0.150864	−	0.503211i
$664$		0			0
$665$	7.91116	−	1.35945i	0.306782	−	0.0527174i
$666$		0			0
$667$	−4.02969	+	4.02969i	−0.156030	+	0.156030i
$668$		0			0
$669$	−1.58035	−	1.58035i	−0.0610999	−	0.0610999i
$670$		0			0
$671$	11.7394	+	11.7394i	0.453196	+	0.453196i
$672$		0			0
$673$	20.1262	+	20.1262i	0.775810	+	0.775810i	0.979115	−	0.203306i	$-0.0651685\pi$
$673$	20.1262	+	20.1262i	0.775810	+	0.775810i	−0.203306	+	0.979115i	$0.565168\pi$
$674$		0			0
$675$	−2.15248	+	4.51296i	−0.0828490	+	0.173704i
$676$		0			0
$677$	35.5701	+	35.5701i	1.36707	+	1.36707i	0.864586	+	0.502484i	$0.167581\pi$
$677$	35.5701	+	35.5701i	1.36707	+	1.36707i	0.502484	+	0.864586i	$0.332419\pi$
$678$		0			0
$679$		−	0.850657i		−	0.0326452i
$680$		0			0
$681$	−4.06036	+	4.06036i	−0.155593	+	0.155593i
$682$		0			0
$683$	15.9648			0.610877			0.305439	−	0.952212i	$-0.401197\pi$
$683$	15.9648			0.610877			0.305439	+	0.952212i	$0.401197\pi$
$684$		0			0
$685$	22.6633	−	32.0683i	0.865918	−	1.22527i
$686$		0			0
$687$			8.64551i			0.329847i
$688$		0			0
$689$	1.74545	−	3.24014i	0.0664963	−	0.123440i
$690$		0			0
$691$	−17.6948	+	17.6948i	−0.673141	+	0.673141i	−0.958439	−	0.285298i	$-0.907908\pi$
$691$	−17.6948	+	17.6948i	−0.673141	+	0.673141i	0.285298	+	0.958439i	$0.407908\pi$
$692$		0			0
$693$	−1.39089	−	1.39089i	−0.0528355	−	0.0528355i
$694$		0			0
$695$	23.5172	−	33.2767i	0.892058	−	1.26226i
$696$		0			0
$697$			43.4091i			1.64424i
$698$		0			0
$699$	−6.83567			−0.258549
$700$		0			0
$701$		−	24.0814i		−	0.909544i	−0.890608	−	0.454772i	$-0.849721\pi$
$701$		−	24.0814i		−	0.909544i	0.890608	−	0.454772i	$-0.150279\pi$
$702$		0			0
$703$	40.9028	−	40.9028i	1.54268	−	1.54268i
$704$		0			0
$705$	−2.03315	−	11.8317i	−0.0765730	−	0.445606i
$706$		0			0
$707$	−7.63921			−0.287302
$708$		0			0
$709$	10.2449	−	10.2449i	0.384755	−	0.384755i	−0.488057	−	0.872812i	$-0.662294\pi$
$709$	10.2449	−	10.2449i	0.384755	−	0.384755i	0.872812	+	0.488057i	$0.162294\pi$
$710$		0			0
$711$	5.21919			0.195735
$712$		0			0
$713$	11.8273			0.442938
$714$		0			0
$715$	−13.7561	−	27.6638i	−0.514450	−	1.03457i
$716$		0			0
$717$	−4.32098			−0.161370
$718$		0			0
$719$	−44.5570			−1.66169			−0.830847	−	0.556500i	$-0.812144\pi$
$719$	−44.5570			−1.66169			−0.830847	+	0.556500i	$0.812144\pi$
$720$		0			0
$721$	−7.14919	+	7.14919i	−0.266250	+	0.266250i
$722$		0			0
$723$	11.0723			0.411782
$724$		0			0
$725$	15.7229	−	5.56807i	0.583934	−	0.206793i
$726$		0			0
$727$	8.30425	−	8.30425i	0.307988	−	0.307988i	−0.536141	−	0.844128i	$-0.680118\pi$
$727$	8.30425	−	8.30425i	0.307988	−	0.307988i	0.844128	+	0.536141i	$0.180118\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	38.5900			1.42730
$732$		0			0
$733$			25.4459i			0.939866i	0.882702	+	0.469933i	$0.155722\pi$
$733$			25.4459i			0.939866i	−0.882702	+	0.469933i	$0.844278\pi$
$734$		0			0
$735$	−14.8457	+	2.55109i	−0.547593	+	0.0940983i
$736$		0			0
$737$	32.2421	+	32.2421i	1.18765	+	1.18765i
$738$		0			0
$739$	13.5831	−	13.5831i	0.499662	−	0.499662i	−0.411671	−	0.911333i	$-0.635055\pi$
$739$	13.5831	−	13.5831i	0.499662	−	0.499662i	0.911333	+	0.411671i	$0.135055\pi$
$740$		0			0
$741$	24.1537	−	7.24136i	0.887310	−	0.266018i
$742$		0			0
$743$			5.34597i			0.196125i	0.995180	+	0.0980624i	$0.0312645\pi$
$743$			5.34597i			0.196125i	−0.995180	+	0.0980624i	$0.968736\pi$
$744$		0			0
$745$	−7.33441	−	42.6816i	−0.268712	−	1.56373i
$746$		0			0
$747$	−4.62310			−0.169150
$748$		0			0
$749$	−3.22588	+	3.22588i	−0.117871	+	0.117871i
$750$		0			0
$751$			4.70684i			0.171755i	0.996306	+	0.0858774i	$0.0273694\pi$
$751$			4.70684i			0.171755i	−0.996306	+	0.0858774i	$0.972631\pi$
$752$		0			0
$753$	11.5038	+	11.5038i	0.419223	+	0.419223i
$754$		0			0
$755$	2.03882	+	11.8647i	0.0742004	+	0.431799i
$756$		0			0
$757$	11.7122	+	11.7122i	0.425688	+	0.425688i	0.887157	−	0.461469i	$-0.152677\pi$
$757$	11.7122	+	11.7122i	0.425688	+	0.425688i	−0.461469	+	0.887157i	$0.652677\pi$
$758$		0			0
$759$	4.62901	+	4.62901i	0.168023	+	0.168023i
$760$		0			0
$761$	4.10087	+	4.10087i	0.148656	+	0.148656i	0.777518	−	0.628861i	$-0.216479\pi$
$761$	4.10087	+	4.10087i	0.148656	+	0.148656i	−0.628861	+	0.777518i	$0.716479\pi$
$762$		0			0
$763$	5.82077	−	5.82077i	0.210726	−	0.210726i
$764$		0			0
$765$	−1.42074	−	8.26780i	−0.0513669	−	0.298923i
$766$		0			0
$767$	21.0320	−	39.0425i	0.759421	−	1.40974i
$768$		0			0
$769$	19.3396	+	19.3396i	0.697405	+	0.697405i	0.963850	−	0.266445i	$-0.0858491\pi$
$769$	19.3396	+	19.3396i	0.697405	+	0.697405i	−0.266445	+	0.963850i	$0.585849\pi$
$770$		0			0
$771$		−	1.56091i		−	0.0562147i
$772$		0			0
$773$		−	16.7561i		−	0.602674i	−0.953518	−	0.301337i	$-0.902567\pi$
$773$		−	16.7561i		−	0.602674i	0.953518	−	0.301337i	$-0.0974329\pi$
$774$		0			0
$775$	−31.2450	−	14.9025i	−1.12235	−	0.535313i
$776$		0			0
$777$	3.00208	−	3.00208i	0.107699	−	0.107699i
$778$		0			0
$779$	−80.9206			−2.89928
$780$		0			0
$781$	9.04158			0.323533
$782$		0			0
$783$	2.35887	−	2.35887i	0.0842991	−	0.0842991i
$784$		0			0
$785$	3.53301	+	20.5599i	0.126098	+	0.733813i
$786$		0			0
$787$		−	47.1445i		−	1.68052i	−0.542183	−	0.840260i	$-0.682402\pi$
$787$		−	47.1445i		−	1.68052i	0.542183	−	0.840260i	$-0.317598\pi$
$788$		0			0
$789$			20.4357i			0.727531i
$790$		0			0
$791$	−0.118886	−	0.118886i	−0.00422710	−	0.00422710i
$792$		0			0
$793$	−14.9627	+	4.48585i	−0.531340	+	0.159297i
$794$		0			0
$795$	1.31730	−	1.86397i	0.0467198	−	0.0661082i
$796$		0			0
$797$	−12.9044	+	12.9044i	−0.457097	+	0.457097i	−0.897701	−	0.440604i	$-0.854764\pi$
$797$	−12.9044	+	12.9044i	−0.457097	+	0.457097i	0.440604	+	0.897701i	$0.354764\pi$
$798$		0			0
$799$	14.2426	+	14.2426i	0.503867	+	0.503867i
$800$		0			0
$801$	−7.61981	−	7.61981i	−0.269233	−	0.269233i
$802$		0			0
$803$	−15.5517	−	15.5517i	−0.548809	−	0.548809i
$804$		0			0
$805$	−1.93244	+	0.332070i	−0.0681096	+	0.0117039i
$806$		0			0
$807$	15.0761	+	15.0761i	0.530704	+	0.530704i
$808$		0			0
$809$		−	19.7674i		−	0.694984i	−0.937683	−	0.347492i	$-0.887033\pi$
$809$		−	19.7674i		−	0.694984i	0.937683	−	0.347492i	$-0.112967\pi$
$810$		0			0
$811$	35.1275	−	35.1275i	1.23349	−	1.23349i	0.270883	−	0.962612i	$-0.412684\pi$
$811$	35.1275	−	35.1275i	1.23349	−	1.23349i	0.962612	−	0.270883i	$-0.0873155\pi$
$812$		0			0
$813$	−14.5752			−0.511174
$814$		0			0
$815$	−31.2644	−	22.0951i	−1.09515	−	0.773959i
$816$		0			0
$817$			71.9371i			2.51676i
$818$		0			0
$819$	1.77278	−	0.531483i	0.0619458	−	0.0185715i
$820$		0			0
$821$	10.7308	−	10.7308i	0.374507	−	0.374507i	−0.494609	−	0.869116i	$-0.664689\pi$
$821$	10.7308	−	10.7308i	0.374507	−	0.374507i	0.869116	+	0.494609i	$0.164689\pi$
$822$		0			0
$823$	−14.8390	−	14.8390i	−0.517255	−	0.517255i	0.399485	−	0.916740i	$-0.369189\pi$
$823$	−14.8390	−	14.8390i	−0.517255	−	0.517255i	−0.916740	+	0.399485i	$0.869189\pi$
$824$		0			0
$825$	−6.39618	−	18.0613i	−0.222686	−	0.628814i
$826$		0			0
$827$		−	13.7722i		−	0.478906i	−0.970908	−	0.239453i	$-0.923032\pi$
$827$		−	13.7722i		−	0.478906i	0.970908	−	0.239453i	$-0.0769681\pi$
$828$		0			0
$829$	−47.3432			−1.64430			−0.822149	−	0.569272i	$-0.807225\pi$
$829$	−47.3432			−1.64430			−0.822149	+	0.569272i	$0.807225\pi$
$830$		0			0
$831$			1.88065i			0.0652392i
$832$		0			0
$833$	17.8709	−	17.8709i	0.619188	−	0.619188i
$834$		0			0
$835$	19.8257	−	28.0532i	0.686097	−	0.970822i
$836$		0			0
$837$	−6.92340			−0.239308
$838$		0			0
$839$	−7.16723	+	7.16723i	−0.247440	+	0.247440i	−0.819919	−	0.572479i	$-0.805982\pi$
$839$	−7.16723	+	7.16723i	−0.247440	+	0.247440i	0.572479	+	0.819919i	$0.305982\pi$
$840$		0			0
$841$	17.8715			0.616258
$842$		0			0
$843$	26.2945			0.905632
$844$		0			0
$845$	29.0534	+	0.949469i	0.999466	+	0.0326627i
$846$		0			0
$847$	1.89145			0.0649910
$848$		0			0
$849$	1.69535			0.0581842
$850$		0			0
$851$	−9.99123	+	9.99123i	−0.342495	+	0.342495i
$852$		0			0
$853$	−6.22126			−0.213012			−0.106506	−	0.994312i	$-0.533966\pi$
$853$	−6.22126			−0.213012			−0.106506	+	0.994312i	$0.533966\pi$
$854$		0			0
$855$	15.4123	−	2.64845i	0.527090	−	0.0905752i
$856$		0			0
$857$	−0.965833	+	0.965833i	−0.0329922	+	0.0329922i	−0.723410	−	0.690418i	$-0.757427\pi$
$857$	−0.965833	+	0.965833i	−0.0329922	+	0.0329922i	0.690418	+	0.723410i	$0.257427\pi$
$858$		0			0
$859$			37.0959i			1.26570i	0.774275	+	0.632849i	$0.218115\pi$
$859$			37.0959i			1.26570i	−0.774275	+	0.632849i	$0.781885\pi$
$860$		0			0
$861$	−5.93921			−0.202408
$862$		0			0
$863$		−	0.691413i		−	0.0235360i	−0.999931	−	0.0117680i	$-0.996254\pi$
$863$		−	0.691413i		−	0.0235360i	0.999931	−	0.0117680i	$-0.00374595\pi$
$864$		0			0
$865$	−6.89796	−	40.1418i	−0.234538	−	1.36486i
$866$		0			0
$867$	−2.06827	−	2.06827i	−0.0702423	−	0.0702423i
$868$		0			0
$869$	−14.1424	+	14.1424i	−0.479749	+	0.479749i
$870$		0			0
$871$	−41.0946	+	12.3203i	−1.39244	+	0.417457i
$872$		0			0
$873$		−	1.65723i		−	0.0560887i
$874$		0			0
$875$	5.52345	+	1.55763i	0.186727	+	0.0526574i
$876$		0			0
$877$	10.3608			0.349860			0.174930	−	0.984581i	$-0.444030\pi$
$877$	10.3608			0.349860			0.174930	+	0.984581i	$0.444030\pi$
$878$		0			0
$879$	10.3086	−	10.3086i	0.347700	−	0.347700i
$880$		0			0
$881$		−	35.0496i		−	1.18085i	−0.807092	−	0.590426i	$-0.798960\pi$
$881$		−	35.0496i		−	1.18085i	0.807092	−	0.590426i	$-0.201040\pi$
$882$		0			0
$883$	11.9347	+	11.9347i	0.401636	+	0.401636i	0.878809	−	0.477173i	$-0.158339\pi$
$883$	11.9347	+	11.9347i	0.401636	+	0.401636i	−0.477173	+	0.878809i	$0.658339\pi$
$884$		0			0
$885$	15.8730	−	22.4601i	0.533564	−	0.754988i
$886$		0			0
$887$	−37.3633	−	37.3633i	−1.25454	−	1.25454i	−0.953665	−	0.300871i	$-0.902723\pi$
$887$	−37.3633	−	37.3633i	−1.25454	−	1.25454i	−0.300871	−	0.953665i	$-0.597277\pi$
$888$		0			0
$889$	0.100466	+	0.100466i	0.00336953	+	0.00336953i
$890$		0			0
$891$	−2.70969	−	2.70969i	−0.0907781	−	0.0907781i
$892$		0			0
$893$	−26.5502	+	26.5502i	−0.888468	+	0.888468i
$894$		0			0
$895$	−9.41412	−	6.65312i	−0.314679	−	0.222389i
$896$		0			0
$897$	−5.89998	+	1.76883i	−0.196994	+	0.0590595i
$898$		0			0
$899$	16.3314	+	16.3314i	0.544682	+	0.544682i
$900$		0			0
$901$			3.82952i			0.127580i
$902$		0			0
$903$			5.27986i			0.175703i
$904$		0			0
$905$	−3.76712	+	5.33044i	−0.125223	+	0.177190i
$906$		0			0
$907$	−29.4222	+	29.4222i	−0.976947	+	0.976947i	−0.999740	−	0.0227928i	$-0.992744\pi$
$907$	−29.4222	+	29.4222i	−0.976947	+	0.976947i	0.0227928	+	0.999740i	$0.492744\pi$
$908$		0			0
$909$	−14.8825			−0.493622
$910$		0			0
$911$	−18.0181			−0.596966			−0.298483	−	0.954415i	$-0.596481\pi$
$911$	−18.0181			−0.596966			−0.298483	+	0.954415i	$0.596481\pi$
$912$		0			0
$913$	12.5272	−	12.5272i	0.414589	−	0.414589i
$914$		0			0
$915$	−9.54758	+	1.64066i	−0.315633	+	0.0542384i
$916$		0			0
$917$		−	4.03453i		−	0.133232i
$918$		0			0
$919$		−	10.8566i		−	0.358128i	−0.983837	−	0.179064i	$-0.942693\pi$
$919$		−	10.8566i		−	0.358128i	0.983837	−	0.179064i	$-0.0573069\pi$
$920$		0			0
$921$	−13.1227	−	13.1227i	−0.432406	−	0.432406i
$922$		0			0
$923$	−4.03456	+	7.48952i	−0.132799	+	0.246520i
$924$		0			0
$925$	38.9834	−	13.8055i	1.28177	−	0.453921i
$926$		0			0
$927$	−13.9279	+	13.9279i	−0.457452	+	0.457452i
$928$		0			0
$929$	−24.8018	−	24.8018i	−0.813721	−	0.813721i	0.171469	−	0.985190i	$-0.445149\pi$
$929$	−24.8018	−	24.8018i	−0.813721	−	0.813721i	−0.985190	+	0.171469i	$0.945149\pi$
$930$		0			0
$931$	33.3137	+	33.3137i	1.09181	+	1.09181i
$932$		0			0
$933$	−3.46045	−	3.46045i	−0.113290	−	0.113290i
$934$		0			0
$935$	26.2530	+	18.5534i	0.858564	+	0.606763i
$936$		0			0
$937$	−2.53287	−	2.53287i	−0.0827452	−	0.0827452i	0.664523	−	0.747268i	$-0.268635\pi$
$937$	−2.53287	−	2.53287i	−0.0827452	−	0.0827452i	−0.747268	+	0.664523i	$0.768635\pi$
$938$		0			0
$939$		−	18.0510i		−	0.589071i
$940$		0			0
$941$	−29.0014	+	29.0014i	−0.945419	+	0.945419i	−0.998586	−	0.0531665i	$-0.983069\pi$
$941$	−29.0014	+	29.0014i	−0.945419	+	0.945419i	0.0531665	+	0.998586i	$0.483069\pi$
$942$		0			0
$943$	19.7663			0.643678
$944$		0			0
$945$	1.13120	−	0.194385i	0.0367978	−	0.00632333i
$946$		0			0
$947$		−	0.266329i		−	0.00865452i	−0.999991	−	0.00432726i	$-0.998623\pi$
$947$		−	0.266329i		−	0.00865452i	0.999991	−	0.00432726i	$-0.00137741\pi$
$948$		0			0
$949$	19.8217	−	5.94260i	0.643440	−	0.192905i
$950$		0			0
$951$	−23.1068	+	23.1068i	−0.749289	+	0.749289i
$952$		0			0
$953$	25.2555	+	25.2555i	0.818107	+	0.818107i	0.985834	−	0.167727i	$-0.0536426\pi$
$953$	25.2555	+	25.2555i	0.818107	+	0.818107i	−0.167727	+	0.985834i	$0.553643\pi$
$954$		0			0
$955$	33.1054	+	23.3962i	1.07127	+	0.757083i
$956$		0			0
$957$			12.7836i			0.413236i
$958$		0			0
$959$	−9.01424			−0.291085
$960$		0			0
$961$		−	16.9334i		−	0.546239i
$962$		0			0
$963$	−6.28458	+	6.28458i	−0.202518	+	0.202518i
$964$		0			0
$965$	9.90657	+	7.00115i	0.318904	+	0.225375i
$966$		0			0
$967$	−5.50521			−0.177035			−0.0885177	−	0.996075i	$-0.528213\pi$
$967$	−5.50521			−0.177035			−0.0885177	+	0.996075i	$0.528213\pi$
$968$		0			0
$969$	−18.5529	+	18.5529i	−0.596005	+	0.596005i
$970$		0			0
$971$	−21.2984			−0.683498			−0.341749	−	0.939791i	$-0.611019\pi$
$971$	−21.2984			−0.683498			−0.341749	+	0.939791i	$0.611019\pi$
$972$		0			0
$973$	−9.35390			−0.299872
$974$		0			0
$975$	17.8151	+	2.76115i	0.570538	+	0.0884277i
$976$		0			0
$977$	−60.1491			−1.92434			−0.962170	−	0.272450i	$-0.912166\pi$
$977$	−60.1491			−1.92434			−0.962170	+	0.272450i	$0.912166\pi$
$978$		0			0
$979$	41.2947			1.31978
$980$		0			0
$981$	11.3399	−	11.3399i	0.362054	−	0.362054i
$982$		0			0
$983$	25.9392			0.827332			0.413666	−	0.910429i	$-0.364248\pi$
$983$	25.9392			0.827332			0.413666	+	0.910429i	$0.364248\pi$
$984$		0			0
$985$	10.6292	+	7.51182i	0.338674	+	0.239347i
$986$		0			0
$987$	−1.94866	+	1.94866i	−0.0620267	+	0.0620267i
$988$		0			0
$989$		−	17.5719i		−	0.558754i
$990$		0			0
$991$	19.2063			0.610107			0.305054	−	0.952335i	$-0.401326\pi$
$991$	19.2063			0.610107			0.305054	+	0.952335i	$0.401326\pi$
$992$		0			0
$993$			20.5469i			0.652036i
$994$		0			0
$995$	22.8807	+	16.1702i	0.725365	+	0.512629i
$996$		0			0
$997$	−20.0551	−	20.0551i	−0.635152	−	0.635152i	0.314204	−	0.949356i	$-0.398262\pi$
$997$	−20.0551	−	20.0551i	−0.635152	−	0.635152i	−0.949356	+	0.314204i	$0.898262\pi$
$998$		0			0
$999$	5.84858	−	5.84858i	0.185041	−	0.185041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	780.2.r.a.577.7	yes	28
3.2	odd	2		2340.2.u.i.577.3		28
5.2	odd	4		3900.2.bm.b.2293.11		28
5.3	odd	4		780.2.bm.a.733.3	yes	28
5.4	even	2		3900.2.r.b.1357.11		28
13.8	odd	4		780.2.bm.a.697.3	yes	28
15.8	even	4		2340.2.bp.i.1513.9		28
39.8	even	4		2340.2.bp.i.1477.9		28
65.8	even	4	inner	780.2.r.a.73.7	✓	28
65.34	odd	4		3900.2.bm.b.2257.11		28
65.47	even	4		3900.2.r.b.3193.11		28
195.8	odd	4		2340.2.u.i.73.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.r.a.73.7	✓	28	65.8	even	4	inner
780.2.r.a.577.7	yes	28	1.1	even	1	trivial
780.2.bm.a.697.3	yes	28	13.8	odd	4
780.2.bm.a.733.3	yes	28	5.3	odd	4
2340.2.u.i.73.3		28	195.8	odd	4
2340.2.u.i.577.3		28	3.2	odd	2
2340.2.bp.i.1477.9		28	39.8	even	4
2340.2.bp.i.1513.9		28	15.8	even	4
3900.2.r.b.1357.11		28	5.4	even	2
3900.2.r.b.3193.11		28	65.47	even	4
3900.2.bm.b.2257.11		28	65.34	odd	4
3900.2.bm.b.2293.11		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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(1.82608 + 1.29052i) q^{5} -0.513301i q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(1.82608 + 1.29052i) q^{5} -0.513301i q^{7} -1.00000i q^{9} +(2.70969 + 2.70969i) q^{11} +(-3.45368 + 1.03542i) q^{13} +(-2.20377 + 0.378695i) q^{15} +(2.65283 - 2.65283i) q^{17} +(4.94524 + 4.94524i) q^{19} +(0.362959 + 0.362959i) q^{21} +(-1.20796 - 1.20796i) q^{23} +(1.66911 + 4.71318i) q^{25} +(0.707107 + 0.707107i) q^{27} -3.33595i q^{29} +(-4.89558 + 4.89558i) q^{31} -3.83208 q^{33} +(0.662426 - 0.937327i) q^{35} -8.27115i q^{37} +(1.70997 - 3.17427i) q^{39} +(-8.18166 + 8.18166i) q^{41} +(7.27336 + 7.27336i) q^{43} +(1.29052 - 1.82608i) q^{45} +5.36883i q^{47} +6.73652 q^{49} +3.75167i q^{51} +(-0.721780 + 0.721780i) q^{53} +(1.45119 + 8.44502i) q^{55} -6.99363 q^{57} +(-8.69717 + 8.69717i) q^{59} +4.33239 q^{61} -0.513301 q^{63} +(-7.64292 - 2.56628i) q^{65} +11.8988 q^{67} +1.70832 q^{69} +(1.66838 - 1.66838i) q^{71} -5.73930 q^{73} +(-4.51296 - 2.15248i) q^{75} +(1.39089 - 1.39089i) q^{77} +5.21919i q^{79} -1.00000 q^{81} -4.62310i q^{83} +(8.26780 - 1.42074i) q^{85} +(2.35887 + 2.35887i) q^{87} +(7.61981 - 7.61981i) q^{89} +(0.531483 + 1.77278i) q^{91} -6.92340i q^{93} +(2.64845 + 15.4123i) q^{95} +1.65723 q^{97} +(2.70969 - 2.70969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q+O(q^{10}) \) 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

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