LMFDB - Embedded newform 656.2.u.h.305.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [656,2,Mod(305,656)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(656, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("656.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.u (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.23818637260$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 7 x^{18} - 6 x^{17} + 60 x^{16} - 92 x^{15} + 603 x^{14} - 690 x^{13} + 2935 x^{12} + \cdots + 4096 $ x^20 - 2x^19 + 7x^18 - 6x^17 + 60x^16 - 92x^15 + 603x^14 - 690x^13 + 2935x^12 - 3168x^11 + 7811x^10 - 7928x^9 + 15482x^8 - 24314x^7 + 44829x^6 - 45930x^5 + 53273x^4 - 47528x^3 + 33216x^2 - 12800*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 328)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			305.4
Root			$-0.330131 - 1.01604i$ of defining polynomial
Character	$\chi$	$=$	656.305
Dual form			656.2.u.h.385.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.06833 q^{3} +(-1.23890 + 0.900114i) q^{5} +(-0.620323 + 1.90916i) q^{7} -1.85868 q^{9} +O(q^{10})$	\(q+1.06833 q^{3} +(-1.23890 + 0.900114i) q^{5} +(-0.620323 + 1.90916i) q^{7} -1.85868 q^{9} +(3.22289 + 2.34156i) q^{11} +(0.978921 + 3.01281i) q^{13} +(-1.32355 + 0.961615i) q^{15} +(-6.52985 - 4.74421i) q^{17} +(-0.345714 + 1.06400i) q^{19} +(-0.662707 + 2.03960i) q^{21} +(1.86662 + 5.74487i) q^{23} +(-0.820416 + 2.52498i) q^{25} -5.19065 q^{27} +(-0.753010 + 0.547094i) q^{29} +(7.24812 + 5.26607i) q^{31} +(3.44309 + 2.50155i) q^{33} +(-0.949940 - 2.92362i) q^{35} +(-6.42806 + 4.67026i) q^{37} +(1.04581 + 3.21866i) q^{39} +(6.25170 + 1.38427i) q^{41} +(-2.73847 - 8.42814i) q^{43} +(2.30272 - 1.67302i) q^{45} +(-0.0721934 - 0.222188i) q^{47} +(2.40304 + 1.74591i) q^{49} +(-6.97601 - 5.06837i) q^{51} +(6.78861 - 4.93221i) q^{53} -6.10051 q^{55} +(-0.369336 + 1.13670i) q^{57} +(0.0170575 + 0.0524974i) q^{59} +(1.83643 - 5.65196i) q^{61} +(1.15298 - 3.54851i) q^{63} +(-3.92466 - 2.85143i) q^{65} +(0.687445 - 0.499458i) q^{67} +(1.99416 + 6.13740i) q^{69} +(1.04040 + 0.755892i) q^{71} +6.77575 q^{73} +(-0.876472 + 2.69750i) q^{75} +(-6.46964 + 4.70047i) q^{77} -3.41670 q^{79} +0.0307261 q^{81} +8.64029 q^{83} +12.3602 q^{85} +(-0.804461 + 0.584475i) q^{87} +(-0.779174 + 2.39805i) q^{89} -6.35917 q^{91} +(7.74336 + 5.62588i) q^{93} +(-0.529415 - 1.62937i) q^{95} +(-4.77046 + 3.46594i) q^{97} +(-5.99031 - 4.35222i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9	$ 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9} - 9 q^{11} + 7 q^{13} - q^{15} - 8 q^{17} - q^{19} - 6 q^{21} + 11 q^{23} + 15 q^{25} - 2 q^{27} + 21 q^{29} + 5 q^{31} + 19 q^{33} - 4 q^{37} - 4 q^{39} + 9 q^{41} + 17 q^{43} + 11 q^{45} - 15 q^{47} - 25 q^{49} + 22 q^{51} + 10 q^{53} + 28 q^{55} - 20 q^{57} + 24 q^{59} + 15 q^{61} + 65 q^{63} - 29 q^{65} + 26 q^{67} - 47 q^{69} - 16 q^{71} + 14 q^{73} - 11 q^{75} + 12 q^{77} + 26 q^{79} - 60 q^{81} - 20 q^{83} - 94 q^{85} - 57 q^{87} + 5 q^{89} + 46 q^{91} + 43 q^{93} - 71 q^{95} - 22 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9 - 9 * q^11 + 7 * q^13 - q^15 - 8 * q^17 - q^19 - 6 * q^21 + 11 * q^23 + 15 * q^25 - 2 * q^27 + 21 * q^29 + 5 * q^31 + 19 * q^33 - 4 * q^37 - 4 * q^39 + 9 * q^41 + 17 * q^43 + 11 * q^45 - 15 * q^47 - 25 * q^49 + 22 * q^51 + 10 * q^53 + 28 * q^55 - 20 * q^57 + 24 * q^59 + 15 * q^61 + 65 * q^63 - 29 * q^65 + 26 * q^67 - 47 * q^69 - 16 * q^71 + 14 * q^73 - 11 * q^75 + 12 * q^77 + 26 * q^79 - 60 * q^81 - 20 * q^83 - 94 * q^85 - 57 * q^87 + 5 * q^89 + 46 * q^91 + 43 * q^93 - 71 * q^95 - 22 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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
$3$	1.06833			0.616798			0.308399	−	0.951257i	$-0.400207\pi$
$3$	1.06833			0.616798			0.308399	+	0.951257i	$0.400207\pi$
$4$		0			0
$5$	−1.23890	+	0.900114i	−0.554053	+	0.402543i	−0.829278	−	0.558837i	$-0.811248\pi$
$5$	−1.23890	+	0.900114i	−0.554053	+	0.402543i	0.275225	+	0.961380i	$0.411248\pi$
$6$		0			0
$7$	−0.620323	+	1.90916i	−0.234460	+	0.721593i	0.762733	+	0.646714i	$0.223857\pi$
$7$	−0.620323	+	1.90916i	−0.234460	+	0.721593i	−0.997193	+	0.0748795i	$0.976143\pi$
$8$		0			0
$9$	−1.85868			−0.619560
$10$		0			0
$11$	3.22289	+	2.34156i	0.971737	+	0.706008i	0.955847	−	0.293866i	$-0.0949418\pi$
$11$	3.22289	+	2.34156i	0.971737	+	0.706008i	0.0158901	+	0.999874i	$0.494942\pi$
$12$		0			0
$13$	0.978921	+	3.01281i	0.271504	+	0.835603i	0.990123	+	0.140200i	$0.0447744\pi$
$13$	0.978921	+	3.01281i	0.271504	+	0.835603i	−0.718619	+	0.695404i	$0.755226\pi$
$14$		0			0
$15$	−1.32355	+	0.961615i	−0.341739	+	0.248288i
$16$		0			0
$17$	−6.52985	−	4.74421i	−1.58372	−	1.15064i	−0.912269	−	0.409592i	$-0.865671\pi$
$17$	−6.52985	−	4.74421i	−1.58372	−	1.15064i	−0.671452	−	0.741048i	$-0.734329\pi$
$18$		0			0
$19$	−0.345714	+	1.06400i	−0.0793123	+	0.244098i	−0.982849	−	0.184413i	$-0.940962\pi$
$19$	−0.345714	+	1.06400i	−0.0793123	+	0.244098i	0.903537	+	0.428511i	$0.140962\pi$
$20$		0			0
$21$	−0.662707	+	2.03960i	−0.144614	+	0.445078i
$22$		0			0
$23$	1.86662	+	5.74487i	0.389218	+	1.19789i	0.933374	+	0.358905i	$0.116850\pi$
$23$	1.86662	+	5.74487i	0.389218	+	1.19789i	−0.544157	+	0.838984i	$0.683150\pi$
$24$		0			0
$25$	−0.820416	+	2.52498i	−0.164083	+	0.504996i
$26$		0			0
$27$	−5.19065			−0.998942
$28$		0			0
$29$	−0.753010	+	0.547094i	−0.139831	+	0.101593i	−0.655501	−	0.755194i	$-0.727543\pi$
$29$	−0.753010	+	0.547094i	−0.139831	+	0.101593i	0.515671	+	0.856787i	$0.327543\pi$
$30$		0			0
$31$	7.24812	+	5.26607i	1.30180	+	0.945814i	0.999972	−	0.00754756i	$-0.00240248\pi$
$31$	7.24812	+	5.26607i	1.30180	+	0.945814i	0.301830	+	0.953362i	$0.402402\pi$
$32$		0			0
$33$	3.44309	+	2.50155i	0.599366	+	0.435465i
$34$		0			0
$35$	−0.949940	−	2.92362i	−0.160569	−	0.494181i
$36$		0			0
$37$	−6.42806	+	4.67026i	−1.05677	+	0.767785i	−0.973487	−	0.228741i	$-0.926539\pi$
$37$	−6.42806	+	4.67026i	−1.05677	+	0.767785i	−0.0832785	+	0.996526i	$0.526539\pi$
$38$		0			0
$39$	1.04581	+	3.21866i	0.167463	+	0.515399i
$40$		0			0
$41$	6.25170	+	1.38427i	0.976352	+	0.216187i
$41$	6.25170	+	1.38427i	0.976352	+	0.216187i
$42$		0			0
$43$	−2.73847	−	8.42814i	−0.417612	−	1.28528i	−0.909893	−	0.414842i	$-0.863837\pi$
$43$	−2.73847	−	8.42814i	−0.417612	−	1.28528i	0.492281	−	0.870436i	$-0.336163\pi$
$44$		0			0
$45$	2.30272	−	1.67302i	0.343269	−	0.249399i
$46$		0			0
$47$	−0.0721934	−	0.222188i	−0.0105305	−	0.0324095i	0.945653	−	0.325177i	$-0.105424\pi$
$47$	−0.0721934	−	0.222188i	−0.0105305	−	0.0324095i	−0.956184	+	0.292767i	$0.905424\pi$
$48$		0			0
$49$	2.40304	+	1.74591i	0.343291	+	0.249416i
$50$		0			0
$51$	−6.97601	−	5.06837i	−0.976836	−	0.709713i
$52$		0			0
$53$	6.78861	−	4.93221i	0.932487	−	0.677492i	−0.0141134	−	0.999900i	$-0.504493\pi$
$53$	6.78861	−	4.93221i	0.932487	−	0.677492i	0.946601	+	0.322409i	$0.104493\pi$
$54$		0			0
$55$	−6.10051			−0.822592
$56$		0			0
$57$	−0.369336	+	1.13670i	−0.0489197	+	0.150559i
$58$		0			0
$59$	0.0170575	+	0.0524974i	0.00222069	+	0.00683458i	0.952161	−	0.305598i	$-0.0988563\pi$
$59$	0.0170575	+	0.0524974i	0.00222069	+	0.00683458i	−0.949940	+	0.312432i	$0.898856\pi$
$60$		0			0
$61$	1.83643	−	5.65196i	0.235131	−	0.723659i	−0.761973	−	0.647609i	$-0.775769\pi$
$61$	1.83643	−	5.65196i	0.235131	−	0.723659i	0.997104	−	0.0760504i	$-0.0242310\pi$
$62$		0			0
$63$	1.15298	−	3.54851i	0.145262	−	0.447070i
$64$		0			0
$65$	−3.92466	−	2.85143i	−0.486794	−	0.353676i
$66$		0			0
$67$	0.687445	−	0.499458i	0.0839848	−	0.0610185i	−0.545001	−	0.838436i	$-0.683471\pi$
$67$	0.687445	−	0.499458i	0.0839848	−	0.0610185i	0.628985	+	0.777417i	$0.283471\pi$
$68$		0			0
$69$	1.99416	+	6.13740i	0.240069	+	0.738856i
$70$		0			0
$71$	1.04040	+	0.755892i	0.123472	+	0.0897078i	0.647807	−	0.761804i	$-0.275686\pi$
$71$	1.04040	+	0.755892i	0.123472	+	0.0897078i	−0.524335	+	0.851512i	$0.675686\pi$
$72$		0			0
$73$	6.77575			0.793041			0.396521	−	0.918026i	$-0.370218\pi$
$73$	6.77575			0.793041			0.396521	+	0.918026i	$0.370218\pi$
$74$		0			0
$75$	−0.876472	+	2.69750i	−0.101206	+	0.311481i
$76$		0			0
$77$	−6.46964	+	4.70047i	−0.737284	+	0.535668i
$78$		0			0
$79$	−3.41670			−0.384409			−0.192205	−	0.981355i	$-0.561564\pi$
$79$	−3.41670			−0.384409			−0.192205	+	0.981355i	$0.561564\pi$
$80$		0			0
$81$	0.0307261			0.00341401
$82$		0			0
$83$	8.64029			0.948395			0.474198	−	0.880418i	$-0.342738\pi$
$83$	8.64029			0.948395			0.474198	+	0.880418i	$0.342738\pi$
$84$		0			0
$85$	12.3602			1.34065
$86$		0			0
$87$	−0.804461	+	0.584475i	−0.0862472	+	0.0626623i
$88$		0			0
$89$	−0.779174	+	2.39805i	−0.0825923	+	0.254193i	−0.983822	−	0.179149i	$-0.942666\pi$
$89$	−0.779174	+	2.39805i	−0.0825923	+	0.254193i	0.901230	+	0.433342i	$0.142666\pi$
$90$		0			0
$91$	−6.35917			−0.666623
$92$		0			0
$93$	7.74336	+	5.62588i	0.802949	+	0.583377i
$94$		0			0
$95$	−0.529415	−	1.62937i	−0.0543168	−	0.167170i
$96$		0			0
$97$	−4.77046	+	3.46594i	−0.484367	+	0.351913i	−0.803014	−	0.595960i	$-0.796772\pi$
$97$	−4.77046	+	3.46594i	−0.484367	+	0.351913i	0.318647	+	0.947873i	$0.396772\pi$
$98$		0			0
$99$	−5.99031	−	4.35222i	−0.602049	−	0.437414i
$100$		0			0
$101$	0.988454	−	3.04215i	0.0983548	−	0.302705i	−0.889759	−	0.456431i	$-0.849127\pi$
$101$	0.988454	−	3.04215i	0.0983548	−	0.302705i	0.988113	+	0.153726i	$0.0491274\pi$
$102$		0			0
$103$	−3.98010	+	12.2495i	−0.392171	+	1.20698i	0.538973	+	0.842323i	$0.318813\pi$
$103$	−3.98010	+	12.2495i	−0.392171	+	1.20698i	−0.931143	+	0.364654i	$0.881187\pi$
$104$		0			0
$105$	−1.01485	−	3.12338i	−0.0990388	−	0.304810i
$106$		0			0
$107$	5.98366	−	18.4158i	0.578463	−	1.78032i	−0.0456111	−	0.998959i	$-0.514524\pi$
$107$	5.98366	−	18.4158i	0.578463	−	1.78032i	0.624074	−	0.781365i	$-0.285476\pi$
$108$		0			0
$109$	−10.0147			−0.959237			−0.479618	−	0.877477i	$-0.659225\pi$
$109$	−10.0147			−0.959237			−0.479618	+	0.877477i	$0.659225\pi$
$110$		0			0
$111$	−6.86726	+	4.98936i	−0.651811	+	0.473569i
$112$		0			0
$113$	−12.5610	−	9.12613i	−1.18164	−	0.858514i	−0.189288	−	0.981922i	$-0.560618\pi$
$113$	−12.5610	−	9.12613i	−1.18164	−	0.858514i	−0.992356	+	0.123407i	$0.960618\pi$
$114$		0			0
$115$	−7.48360	−	5.43715i	−0.697849	−	0.507017i
$116$		0			0
$117$	−1.81950	−	5.59985i	−0.168213	−	0.517706i
$118$		0			0
$119$	13.1081	−	9.52356i	1.20161	−	0.873023i
$120$		0			0
$121$	1.50489	+	4.63157i	0.136808	+	0.421052i
$122$		0			0
$123$	6.67886	+	1.47885i	0.602212	+	0.133344i
$124$		0			0
$125$	−3.62245	−	11.1487i	−0.324001	−	0.997174i
$126$		0			0
$127$	10.9720	−	7.97162i	0.973607	−	0.707367i	0.0173359	−	0.999850i	$-0.494482\pi$
$127$	10.9720	−	7.97162i	0.973607	−	0.707367i	0.956271	+	0.292483i	$0.0944815\pi$
$128$		0			0
$129$	−2.92558	−	9.00400i	−0.257583	−	0.792758i
$130$		0			0
$131$	0.159569	+	0.115934i	0.0139416	+	0.0101292i	0.594734	−	0.803922i	$-0.297257\pi$
$131$	0.159569	+	0.115934i	0.0139416	+	0.0101292i	−0.580793	+	0.814052i	$0.697257\pi$
$132$		0			0
$133$	−1.81689	−	1.32005i	−0.157544	−	0.114462i
$134$		0			0
$135$	6.43070	−	4.67218i	0.553467	−	0.402117i
$136$		0			0
$137$	7.61019			0.650182			0.325091	−	0.945683i	$-0.394605\pi$
$137$	7.61019			0.650182			0.325091	+	0.945683i	$0.394605\pi$
$138$		0			0
$139$	−5.17613	+	15.9305i	−0.439034	+	1.35121i	0.449862	+	0.893098i	$0.351473\pi$
$139$	−5.17613	+	15.9305i	−0.439034	+	1.35121i	−0.888896	+	0.458109i	$0.848527\pi$
$140$		0			0
$141$	−0.0771261	−	0.237370i	−0.00649519	−	0.0199901i
$142$		0			0
$143$	−3.89974	+	12.0022i	−0.326112	+	1.00367i
$144$		0			0
$145$	0.440458	−	1.35559i	0.0365780	−	0.112576i
$146$		0			0
$147$	2.56723	+	1.86520i	0.211742	+	0.153839i
$148$		0			0
$149$	17.1662	−	12.4720i	1.40631	−	1.02175i	0.412466	−	0.910973i	$-0.364668\pi$
$149$	17.1662	−	12.4720i	1.40631	−	1.02175i	0.993846	−	0.110772i	$-0.0353323\pi$
$150$		0			0
$151$	3.51593	+	10.8209i	0.286123	+	0.880595i	0.986060	+	0.166391i	$0.0532113\pi$
$151$	3.51593	+	10.8209i	0.286123	+	0.880595i	−0.699937	+	0.714204i	$0.746789\pi$
$152$		0			0
$153$	12.1369	+	8.81797i	0.981210	+	0.712890i
$154$		0			0
$155$	−13.7198			−1.10200
$156$		0			0
$157$	−1.86421	+	5.73745i	−0.148780	+	0.457899i	−0.997478	−	0.0709801i	$-0.977387\pi$
$157$	−1.86421	+	5.73745i	−0.148780	+	0.457899i	0.848697	+	0.528879i	$0.177387\pi$
$158$		0			0
$159$	7.25245	−	5.26921i	0.575157	−	0.417876i
$160$		0			0
$161$	−12.1258			−0.955644
$162$		0			0
$163$	7.17632			0.562093			0.281046	−	0.959694i	$-0.409318\pi$
$163$	7.17632			0.562093			0.281046	+	0.959694i	$0.409318\pi$
$164$		0			0
$165$	−6.51733			−0.507374
$166$		0			0
$167$	20.6624			1.59891			0.799454	−	0.600727i	$-0.205122\pi$
$167$	20.6624			1.59891			0.799454	+	0.600727i	$0.205122\pi$
$168$		0			0
$169$	2.39848	−	1.74260i	0.184499	−	0.134046i
$170$		0			0
$171$	0.642572	−	1.97763i	0.0491387	−	0.151233i
$172$		0			0
$173$	−25.8846			−1.96797			−0.983984	−	0.178258i	$-0.942954\pi$
$173$	−25.8846			−1.96797			−0.983984	+	0.178258i	$0.942954\pi$
$174$		0			0
$175$	−4.31166	−	3.13260i	−0.325931	−	0.236803i
$176$		0			0
$177$	0.0182229	+	0.0560844i	0.00136972	+	0.00421556i
$178$		0			0
$179$	15.5191	−	11.2753i	1.15995	−	0.842756i	0.170182	−	0.985413i	$-0.445564\pi$
$179$	15.5191	−	11.2753i	1.15995	−	0.842756i	0.989772	+	0.142657i	$0.0455645\pi$
$180$		0			0
$181$	−2.74927	−	1.99746i	−0.204352	−	0.148470i	0.480903	−	0.876774i	$-0.340309\pi$
$181$	−2.74927	−	1.99746i	−0.204352	−	0.148470i	−0.685255	+	0.728304i	$0.740309\pi$
$182$		0			0
$183$	1.96191	−	6.03814i	0.145029	−	0.446352i
$184$		0			0
$185$	3.75996	−	11.5720i	0.276438	−	0.850788i
$186$		0			0
$187$	−9.93608	−	30.5801i	−0.726598	−	2.23624i
$188$		0			0
$189$	3.21988	−	9.90977i	0.234212	−	0.720830i
$190$		0			0
$191$	−17.6926			−1.28019			−0.640097	−	0.768294i	$-0.721106\pi$
$191$	−17.6926			−1.28019			−0.640097	+	0.768294i	$0.721106\pi$
$192$		0			0
$193$	11.7305	−	8.52270i	0.844379	−	0.613477i	−0.0792113	−	0.996858i	$-0.525240\pi$
$193$	11.7305	−	8.52270i	0.844379	−	0.613477i	0.923591	+	0.383380i	$0.125240\pi$
$194$		0			0
$195$	−4.19282	−	3.04626i	−0.300254	−	0.218147i
$196$		0			0
$197$	1.30122	+	0.945389i	0.0927078	+	0.0673562i	0.633174	−	0.774010i	$-0.281752\pi$
$197$	1.30122	+	0.945389i	0.0927078	+	0.0673562i	−0.540466	+	0.841366i	$0.681752\pi$
$198$		0			0
$199$	3.22267	+	9.91836i	0.228449	+	0.703094i	0.997923	+	0.0644158i	$0.0205184\pi$
$199$	3.22267	+	9.91836i	0.228449	+	0.703094i	−0.769474	+	0.638678i	$0.779482\pi$
$200$		0			0
$201$	0.734416	−	0.533584i	0.0518017	−	0.0376361i
$202$		0			0
$203$	−0.577379	−	1.77699i	−0.0405241	−	0.124720i
$204$		0			0
$205$	−8.99124	+	3.91227i	−0.627975	+	0.273245i
$206$		0			0
$207$	−3.46945	−	10.6779i	−0.241144	−	0.742163i
$208$		0			0
$209$	−3.60562	+	2.61964i	−0.249406	+	0.181204i
$210$		0			0
$211$	5.64490	+	17.3732i	0.388611	+	1.19602i	0.933827	+	0.357725i	$0.116448\pi$
$211$	5.64490	+	17.3732i	0.388611	+	1.19602i	−0.545216	+	0.838295i	$0.683552\pi$
$212$		0			0
$213$	1.11148	+	0.807539i	0.0761575	+	0.0553317i
$214$		0			0
$215$	10.9790	+	7.97669i	0.748759	+	0.544006i
$216$		0			0
$217$	−14.5499	+	10.5711i	−0.987714	+	0.717616i
$218$		0			0
$219$	7.23871			0.489147
$220$		0			0
$221$	7.90120	−	24.3174i	0.531492	−	1.63577i
$222$		0			0
$223$	0.192749	+	0.593221i	0.0129074	+	0.0397250i	0.957303	−	0.289087i	$-0.0933517\pi$
$223$	0.192749	+	0.593221i	0.0129074	+	0.0397250i	−0.944395	+	0.328812i	$0.893352\pi$
$224$		0			0
$225$	1.52489	−	4.69313i	0.101659	−	0.312875i
$226$		0			0
$227$	0.301268	−	0.927208i	0.0199959	−	0.0615409i	−0.940561	−	0.339626i	$-0.889700\pi$
$227$	0.301268	−	0.927208i	0.0199959	−	0.0615409i	0.960557	+	0.278085i	$0.0896996\pi$
$228$		0			0
$229$	0.724997	+	0.526741i	0.0479092	+	0.0348080i	0.611482	−	0.791258i	$-0.290574\pi$
$229$	0.724997	+	0.526741i	0.0479092	+	0.0348080i	−0.563573	+	0.826066i	$0.690574\pi$
$230$		0			0
$231$	−6.91169	+	5.02163i	−0.454756	+	0.330399i
$232$		0			0
$233$	1.14425	+	3.52165i	0.0749626	+	0.230711i	0.981516	−	0.191380i	$-0.0612963\pi$
$233$	1.14425	+	3.52165i	0.0749626	+	0.230711i	−0.906553	+	0.422091i	$0.861296\pi$
$234$		0			0
$235$	0.289435	+	0.210287i	0.0188807	+	0.0137176i
$236$		0			0
$237$	−3.65015			−0.237103
$238$		0			0
$239$	−1.95546	+	6.01828i	−0.126488	+	0.389290i	−0.994169	−	0.107831i	$-0.965609\pi$
$239$	−1.95546	+	6.01828i	−0.126488	+	0.389290i	0.867681	+	0.497121i	$0.165609\pi$
$240$		0			0
$241$	15.4945	−	11.2574i	0.998088	−	0.725154i	0.0364109	−	0.999337i	$-0.488407\pi$
$241$	15.4945	−	11.2574i	0.998088	−	0.725154i	0.961677	+	0.274183i	$0.0884075\pi$
$242$		0			0
$243$	15.6048			1.00105
$244$		0			0
$245$	−4.54864			−0.290602
$246$		0			0
$247$	−3.54405			−0.225503
$248$		0			0
$249$	9.23065			0.584969
$250$		0			0
$251$	−9.17319	+	6.66471i	−0.579006	+	0.420673i	−0.838366	−	0.545108i	$-0.816489\pi$
$251$	−9.17319	+	6.66471i	−0.579006	+	0.420673i	0.259359	+	0.965781i	$0.416489\pi$
$252$		0			0
$253$	−7.43607	+	22.8859i	−0.467502	+	1.43882i
$254$		0			0
$255$	13.2047			0.826909
$256$		0			0
$257$	−5.42154	−	3.93898i	−0.338186	−	0.245707i	0.405710	−	0.914002i	$-0.367024\pi$
$257$	−5.42154	−	3.93898i	−0.338186	−	0.245707i	−0.743896	+	0.668295i	$0.767024\pi$
$258$		0			0
$259$	−4.92878	−	15.1692i	−0.306260	−	0.942570i
$260$		0			0
$261$	1.39960	−	1.01687i	0.0866334	−	0.0629428i
$262$		0			0
$263$	−6.84272	−	4.97153i	−0.421940	−	0.306558i	0.356478	−	0.934304i	$-0.383978\pi$
$263$	−6.84272	−	4.97153i	−0.421940	−	0.306558i	−0.778418	+	0.627746i	$0.783978\pi$
$264$		0			0
$265$	−3.97086	+	12.2210i	−0.243928	+	0.750732i
$266$		0			0
$267$	−0.832412	+	2.56190i	−0.0509428	+	0.156786i
$268$		0			0
$269$	−3.68989	−	11.3563i	−0.224977	−	0.692407i	−0.998294	−	0.0583880i	$-0.981404\pi$
$269$	−3.68989	−	11.3563i	−0.224977	−	0.692407i	0.773317	−	0.634019i	$-0.218596\pi$
$270$		0			0
$271$	−7.58639	+	23.3485i	−0.460840	+	1.41832i	0.403299	+	0.915068i	$0.367863\pi$
$271$	−7.58639	+	23.3485i	−0.460840	+	1.41832i	−0.864139	+	0.503252i	$0.832137\pi$
$272$		0			0
$273$	−6.79367			−0.411172
$274$		0			0
$275$	−8.55651	+	6.21667i	−0.515977	+	0.374879i
$276$		0			0
$277$	7.40220	+	5.37801i	0.444755	+	0.323133i	0.787521	−	0.616287i	$-0.211364\pi$
$277$	7.40220	+	5.37801i	0.444755	+	0.323133i	−0.342767	+	0.939421i	$0.611364\pi$
$278$		0			0
$279$	−13.4719	−	9.78794i	−0.806544	−	0.585988i
$280$		0			0
$281$	8.25660	+	25.4112i	0.492547	+	1.51591i	0.820744	+	0.571296i	$0.193559\pi$
$281$	8.25660	+	25.4112i	0.492547	+	1.51591i	−0.328197	+	0.944609i	$0.606441\pi$
$282$		0			0
$283$	9.29390	−	6.75241i	0.552465	−	0.401389i	−0.276229	−	0.961092i	$-0.589085\pi$
$283$	9.29390	−	6.75241i	0.552465	−	0.401389i	0.828693	+	0.559703i	$0.189085\pi$
$284$		0			0
$285$	−0.565587	−	1.74070i	−0.0335025	−	0.103110i
$286$		0			0
$287$	−6.52087	+	11.0768i	−0.384915	+	0.653842i
$288$		0			0
$289$	14.8781	+	45.7900i	0.875181	+	2.69353i
$290$		0			0
$291$	−5.09641	+	3.70276i	−0.298757	+	0.217060i
$292$		0			0
$293$	6.94083	+	21.3617i	0.405488	+	1.24796i	0.920487	+	0.390773i	$0.127792\pi$
$293$	6.94083	+	21.3617i	0.405488	+	1.24796i	−0.514999	+	0.857191i	$0.672208\pi$
$294$		0			0
$295$	−0.0683861	−	0.0496854i	−0.00398160	−	0.00289280i
$296$		0			0
$297$	−16.7289	−	12.1542i	−0.970709	−	0.705261i
$298$		0			0
$299$	−15.4809	+	11.2476i	−0.895285	+	0.650463i
$300$		0			0
$301$	17.7894			1.02536
$302$		0			0
$303$	1.05599	−	3.25001i	0.0606651	−	0.186708i
$304$		0			0
$305$	2.81225	+	8.65521i	0.161029	+	0.495596i
$306$		0			0
$307$	−2.61991	+	8.06326i	−0.149526	+	0.460195i	−0.997565	−	0.0697392i	$-0.977783\pi$
$307$	−2.61991	+	8.06326i	−0.149526	+	0.460195i	0.848039	+	0.529934i	$0.177783\pi$
$308$		0			0
$309$	−4.25204	+	13.0864i	−0.241890	+	0.744461i
$310$		0			0
$311$	3.81440	+	2.77132i	0.216295	+	0.157147i	0.690657	−	0.723182i	$-0.257321\pi$
$311$	3.81440	+	2.77132i	0.216295	+	0.157147i	−0.474362	+	0.880330i	$0.657321\pi$
$312$		0			0
$313$	11.3778	−	8.26643i	0.643109	−	0.467246i	−0.217808	−	0.975992i	$-0.569891\pi$
$313$	11.3778	−	8.26643i	0.643109	−	0.467246i	0.860917	+	0.508746i	$0.169891\pi$
$314$		0			0
$315$	1.76563	+	5.43406i	0.0994822	+	0.306175i
$316$		0			0
$317$	10.6591	+	7.74427i	0.598673	+	0.434962i	0.845408	−	0.534122i	$-0.179358\pi$
$317$	10.6591	+	7.74427i	0.598673	+	0.434962i	−0.246734	+	0.969083i	$0.579358\pi$
$318$		0			0
$319$	−3.70792			−0.207604
$320$		0			0
$321$	6.39250	−	19.6741i	0.356795	−	1.09810i
$322$		0			0
$323$	7.30530	−	5.30761i	0.406478	−	0.295323i
$324$		0			0
$325$	−8.41041			−0.466526
$326$		0			0
$327$	−10.6990			−0.591656
$328$		0			0
$329$	0.468976			0.0258555
$330$		0			0
$331$	−26.2715			−1.44401			−0.722007	−	0.691886i	$-0.756780\pi$
$331$	−26.2715			−1.44401			−0.722007	+	0.691886i	$0.756780\pi$
$332$		0			0
$333$	11.9477	−	8.68051i	0.654730	−	0.475689i
$334$		0			0
$335$	−0.402107	+	1.23756i	−0.0219694	+	0.0676150i
$336$		0			0
$337$	−22.7454			−1.23902			−0.619509	−	0.784989i	$-0.712668\pi$
$337$	−22.7454			−1.23902			−0.619509	+	0.784989i	$0.712668\pi$
$338$		0			0
$339$	−13.4193	−	9.74969i	−0.728836	−	0.529530i
$340$		0			0
$341$	11.0290	+	33.9439i	0.597256	+	1.83816i
$342$		0			0
$343$	−16.1921	+	11.7642i	−0.874289	+	0.635208i
$344$		0			0
$345$	−7.99492	−	5.80865i	−0.430432	−	0.312727i
$346$		0			0
$347$	5.78311	−	17.7986i	0.310454	−	0.955479i	−0.667132	−	0.744940i	$-0.732478\pi$
$347$	5.78311	−	17.7986i	0.310454	−	0.955479i	0.977585	−	0.210539i	$-0.0675218\pi$
$348$		0			0
$349$	−4.76278	+	14.6583i	−0.254946	+	0.784643i	0.738894	+	0.673821i	$0.235348\pi$
$349$	−4.76278	+	14.6583i	−0.254946	+	0.784643i	−0.993840	+	0.110822i	$0.964652\pi$
$350$		0			0
$351$	−5.08124	−	15.6385i	−0.271217	−	0.834719i
$352$		0			0
$353$	−5.26702	+	16.2102i	−0.280335	+	0.862783i	0.707423	+	0.706790i	$0.249858\pi$
$353$	−5.26702	+	16.2102i	−0.280335	+	0.862783i	−0.987758	+	0.155992i	$0.950142\pi$
$354$		0			0
$355$	−1.96934			−0.104521
$356$		0			0
$357$	14.0037	−	10.1743i	0.741153	−	0.538479i
$358$		0			0
$359$	14.7180	+	10.6932i	0.776784	+	0.564367i	0.904012	−	0.427507i	$-0.140608\pi$
$359$	14.7180	+	10.6932i	0.776784	+	0.564367i	−0.127228	+	0.991874i	$0.540608\pi$
$360$		0			0
$361$	14.3587	+	10.4322i	0.755724	+	0.549065i
$362$		0			0
$363$	1.60771	+	4.94802i	0.0843829	+	0.259704i
$364$		0			0
$365$	−8.39448	+	6.09894i	−0.439387	+	0.319233i
$366$		0			0
$367$	10.1337	+	31.1885i	0.528977	+	1.62802i	0.756314	+	0.654208i	$0.226998\pi$
$367$	10.1337	+	31.1885i	0.528977	+	1.62802i	−0.227337	+	0.973816i	$0.573002\pi$
$368$		0			0
$369$	−11.6199	−	2.57292i	−0.604908	−	0.133941i
$370$		0			0
$371$	5.20524	+	16.0201i	0.270243	+	0.831721i
$372$		0			0
$373$	−3.58052	+	2.60140i	−0.185392	+	0.134696i	−0.676610	−	0.736341i	$-0.736552\pi$
$373$	−3.58052	+	2.60140i	−0.185392	+	0.134696i	0.491218	+	0.871037i	$0.336552\pi$
$374$		0			0
$375$	−3.86995	−	11.9105i	−0.199844	−	0.615055i
$376$		0			0
$377$	−2.38543	−	1.73312i	−0.122856	−	0.0892600i
$378$		0			0
$379$	11.8506	+	8.60996i	0.608724	+	0.442264i	0.848965	−	0.528449i	$-0.177226\pi$
$379$	11.8506	+	8.60996i	0.608724	+	0.442264i	−0.240241	+	0.970713i	$0.577226\pi$
$380$		0			0
$381$	11.7217	−	8.51629i	0.600519	−	0.436303i
$382$		0			0
$383$	3.40234			0.173851			0.0869257	−	0.996215i	$-0.472296\pi$
$383$	3.40234			0.173851			0.0869257	+	0.996215i	$0.472296\pi$
$384$		0			0
$385$	3.78428	−	11.6468i	0.192865	−	0.593577i
$386$		0			0
$387$	5.08993	+	15.6652i	0.258736	+	0.796307i
$388$		0			0
$389$	2.94829	−	9.07392i	0.149484	−	0.460066i	−0.848076	−	0.529875i	$-0.822239\pi$
$389$	2.94829	−	9.07392i	0.149484	−	0.460066i	0.997560	+	0.0698089i	$0.0222389\pi$
$390$		0			0
$391$	15.0661	−	46.3688i	0.761927	−	2.34497i
$392$		0			0
$393$	0.170472	+	0.123855i	0.00859916	+	0.00624765i
$394$		0			0
$395$	4.23295	−	3.07542i	0.212983	−	0.154741i
$396$		0			0
$397$	−7.84989	−	24.1595i	−0.393975	−	1.21253i	−0.929757	−	0.368174i	$-0.879983\pi$
$397$	−7.84989	−	24.1595i	−0.393975	−	1.21253i	0.535782	−	0.844356i	$-0.320017\pi$
$398$		0			0
$399$	−1.94103	−	1.41024i	−0.0971729	−	0.0706002i
$400$		0			0
$401$	−5.18678			−0.259016			−0.129508	−	0.991578i	$-0.541340\pi$
$401$	−5.18678			−0.259016			−0.129508	+	0.991578i	$0.541340\pi$
$402$		0			0
$403$	−8.77033	+	26.9923i	−0.436881	+	1.34458i
$404$		0			0
$405$	−0.0380665	+	0.0276569i	−0.00189154	+	0.00137428i
$406$		0			0
$407$	−31.6526			−1.56896
$408$		0			0
$409$	−27.0908			−1.33955			−0.669776	−	0.742563i	$-0.733610\pi$
$409$	−27.0908			−1.33955			−0.669776	+	0.742563i	$0.733610\pi$
$410$		0			0
$411$	8.13016			0.401031
$412$		0			0
$413$	−0.110807			−0.00545245
$414$		0			0
$415$	−10.7045	+	7.77724i	−0.525461	+	0.381770i
$416$		0			0
$417$	−5.52980	+	17.0190i	−0.270795	+	0.833423i
$418$		0			0
$419$	2.85038			0.139250			0.0696252	−	0.997573i	$-0.477820\pi$
$419$	2.85038			0.139250			0.0696252	+	0.997573i	$0.477820\pi$
$420$		0			0
$421$	4.19502	+	3.04786i	0.204453	+	0.148544i	0.685300	−	0.728261i	$-0.259671\pi$
$421$	4.19502	+	3.04786i	0.204453	+	0.148544i	−0.480848	+	0.876804i	$0.659671\pi$
$422$		0			0
$423$	0.134184	+	0.412977i	0.00652427	+	0.0200796i
$424$		0			0
$425$	17.3362	−	12.5955i	0.840931	−	0.610972i
$426$		0			0
$427$	9.65130	+	7.01208i	0.467059	+	0.339338i
$428$		0			0
$429$	−4.16619	+	12.8222i	−0.201146	+	0.619062i
$430$		0			0
$431$	9.34689	−	28.7668i	0.450224	−	1.38565i	−0.426428	−	0.904521i	$-0.640228\pi$
$431$	9.34689	−	28.7668i	0.450224	−	1.38565i	0.876652	−	0.481125i	$-0.159772\pi$
$432$		0			0
$433$	−11.2445	−	34.6070i	−0.540376	−	1.66311i	−0.731737	−	0.681587i	$-0.761290\pi$
$433$	−11.2445	−	34.6070i	−0.540376	−	1.66311i	0.191361	−	0.981520i	$-0.438710\pi$
$434$		0			0
$435$	0.470553	−	1.44821i	0.0225613	−	0.0694365i
$436$		0			0
$437$	−6.75785			−0.323272
$438$		0			0
$439$	6.23696	−	4.53141i	0.297674	−	0.216273i	−0.428916	−	0.903344i	$-0.641104\pi$
$439$	6.23696	−	4.53141i	0.297674	−	0.216273i	0.726589	+	0.687072i	$0.241104\pi$
$440$		0			0
$441$	−4.46648	−	3.24509i	−0.212690	−	0.154528i
$442$		0			0
$443$	10.1539	+	7.37723i	0.482426	+	0.350503i	0.802264	−	0.596969i	$-0.203629\pi$
$443$	10.1539	+	7.37723i	0.482426	+	0.350503i	−0.319838	+	0.947472i	$0.603629\pi$
$444$		0			0
$445$	−1.19320	−	3.67229i	−0.0565631	−	0.174083i
$446$		0			0
$447$	18.3391	−	13.3242i	0.867411	−	0.630211i
$448$		0			0
$449$	4.41718	+	13.5947i	0.208460	+	0.641572i	0.999554	+	0.0298778i	$0.00951183\pi$
$449$	4.41718	+	13.5947i	0.208460	+	0.641572i	−0.791094	+	0.611695i	$0.790488\pi$
$450$		0			0
$451$	16.9072	+	19.1001i	0.796127	+	0.899389i
$452$		0			0
$453$	3.75616	+	11.5603i	0.176480	+	0.543150i
$454$		0			0
$455$	7.87838	−	5.72398i	0.369344	−	0.268344i
$456$		0			0
$457$	10.9485	+	33.6959i	0.512147	+	1.57623i	0.788413	+	0.615146i	$0.210903\pi$
$457$	10.9485	+	33.6959i	0.512147	+	1.57623i	−0.276265	+	0.961081i	$0.589097\pi$
$458$		0			0
$459$	33.8942	+	24.6256i	1.58204	+	1.14942i
$460$		0			0
$461$	−15.8694	−	11.5298i	−0.739112	−	0.536996i	0.153321	−	0.988176i	$-0.451003\pi$
$461$	−15.8694	−	11.5298i	−0.739112	−	0.536996i	−0.892433	+	0.451180i	$0.851003\pi$
$462$		0			0
$463$	−5.46532	+	3.97079i	−0.253995	+	0.184538i	−0.707496	−	0.706718i	$-0.750175\pi$
$463$	−5.46532	+	3.97079i	−0.253995	+	0.184538i	0.453500	+	0.891256i	$0.350175\pi$
$464$		0			0
$465$	−14.6572			−0.679711
$466$		0			0
$467$	−9.49148	+	29.2118i	−0.439213	+	1.35176i	0.449493	+	0.893284i	$0.351604\pi$
$467$	−9.49148	+	29.2118i	−0.439213	+	1.35176i	−0.888707	+	0.458476i	$0.848396\pi$
$468$		0			0
$469$	0.527106	+	1.62227i	0.0243395	+	0.0749093i
$470$		0			0
$471$	−1.99159	+	6.12947i	−0.0917674	+	0.282431i
$472$		0			0
$473$	10.9093	−	33.5752i	0.501608	−	1.54379i
$474$		0			0
$475$	−2.40295	−	1.74584i	−0.110255	−	0.0801048i
$476$		0			0
$477$	−12.6178	+	9.16740i	−0.577731	+	0.419746i
$478$		0			0
$479$	1.57053	+	4.83358i	0.0717592	+	0.220852i	0.980504	−	0.196501i	$-0.0629579\pi$
$479$	1.57053	+	4.83358i	0.0717592	+	0.220852i	−0.908744	+	0.417353i	$0.862958\pi$
$480$		0			0
$481$	−20.3632	−	14.7947i	−0.928480	−	0.674580i
$482$		0			0
$483$	−12.9543			−0.589440
$484$		0			0
$485$	2.79038	−	8.58792i	0.126705	−	0.389957i
$486$		0			0
$487$	31.2683	−	22.7177i	1.41690	−	1.02944i	0.424629	−	0.905368i	$-0.360405\pi$
$487$	31.2683	−	22.7177i	1.41690	−	1.02944i	0.992273	−	0.124072i	$-0.0395953\pi$
$488$		0			0
$489$	7.66665			0.346698
$490$		0			0
$491$	5.97169			0.269498			0.134749	−	0.990880i	$-0.456977\pi$
$491$	5.97169			0.269498			0.134749	+	0.990880i	$0.456977\pi$
$492$		0			0
$493$	7.51257			0.338349
$494$		0			0
$495$	11.3389			0.509645
$496$		0			0
$497$	−2.08850	+	1.51738i	−0.0936819	+	0.0680639i
$498$		0			0
$499$	3.13232	−	9.64028i	0.140222	−	0.431558i	−0.856144	−	0.516738i	$-0.827146\pi$
$499$	3.13232	−	9.64028i	0.140222	−	0.431558i	0.996366	+	0.0851793i	$0.0271463\pi$
$500$		0			0
$501$	22.0742			0.986204
$502$		0			0
$503$	−34.9778	−	25.4128i	−1.55958	−	1.13310i	−0.936351	−	0.351066i	$-0.885819\pi$
$503$	−34.9778	−	25.4128i	−1.55958	−	1.13310i	−0.623232	−	0.782037i	$-0.714181\pi$
$504$		0			0
$505$	1.51368	+	4.65864i	0.0673580	+	0.207307i
$506$		0			0
$507$	2.56236	−	1.86166i	0.113798	−	0.0826794i
$508$		0			0
$509$	−35.5690	−	25.8424i	−1.57657	−	1.14544i	−0.920500	−	0.390743i	$-0.872218\pi$
$509$	−35.5690	−	25.8424i	−1.57657	−	1.14544i	−0.656069	−	0.754701i	$-0.727782\pi$
$510$		0			0
$511$	−4.20315	+	12.9360i	−0.185936	+	0.572253i
$512$		0			0
$513$	1.79448	−	5.52285i	0.0792284	−	0.243840i
$514$		0			0
$515$	−6.09498	−	18.7584i	−0.268577	−	0.826595i
$516$		0			0
$517$	0.287597	−	0.885133i	0.0126485	−	0.0389281i
$518$		0			0
$519$	−27.6532			−1.21384
$520$		0			0
$521$	24.8853	−	18.0803i	1.09025	−	0.792111i	0.110806	−	0.993842i	$-0.464657\pi$
$521$	24.8853	−	18.0803i	1.09025	−	0.792111i	0.979441	+	0.201731i	$0.0646568\pi$
$522$		0			0
$523$	20.1998	+	14.6760i	0.883277	+	0.641738i	0.934116	−	0.356968i	$-0.116190\pi$
$523$	20.1998	+	14.6760i	0.883277	+	0.641738i	−0.0508393	+	0.998707i	$0.516190\pi$
$524$		0			0
$525$	−4.60626	−	3.34664i	−0.201034	−	0.146060i
$526$		0			0
$527$	−22.3458	−	68.7733i	−0.973398	−	2.99581i
$528$		0			0
$529$	−10.9119	+	7.92794i	−0.474429	+	0.344693i
$530$		0			0
$531$	−0.0317043	−	0.0975759i	−0.00137585	−	0.00423443i
$532$		0			0
$533$	1.94938	+	20.1903i	0.0844368	+	0.874539i
$534$		0			0
$535$	9.16317	+	28.2013i	0.396158	+	1.21925i
$536$		0			0
$537$	16.5795	−	12.0457i	0.715458	−	0.519811i
$538$		0			0
$539$	3.65656	+	11.2537i	0.157499	+	0.484733i
$540$		0			0
$541$	−5.86103	−	4.25829i	−0.251985	−	0.183078i	0.454621	−	0.890685i	$-0.349775\pi$
$541$	−5.86103	−	4.25829i	−0.251985	−	0.183078i	−0.706606	+	0.707607i	$0.749775\pi$
$542$		0			0
$543$	−2.93712	−	2.13394i	−0.126044	−	0.0915763i
$544$		0			0
$545$	12.4072	−	9.01439i	0.531468	−	0.386134i
$546$		0			0
$547$	−38.5141			−1.64674			−0.823371	−	0.567503i	$-0.807909\pi$
$547$	−38.5141			−1.64674			−0.823371	+	0.567503i	$0.807909\pi$
$548$		0			0
$549$	−3.41334	+	10.5052i	−0.145678	+	0.448350i
$550$		0			0
$551$	−0.321781	−	0.990340i	−0.0137083	−	0.0421899i
$552$		0			0
$553$	2.11946	−	6.52302i	0.0901285	−	0.277387i
$554$		0			0
$555$	4.01686	−	12.3626i	0.170506	−	0.524764i
$556$		0			0
$557$	−30.2307	−	21.9639i	−1.28092	−	0.930640i	−0.281335	−	0.959610i	$-0.590777\pi$
$557$	−30.2307	−	21.9639i	−1.28092	−	0.930640i	−0.999580	+	0.0289699i	$0.990777\pi$
$558$		0			0
$559$	22.7116	−	16.5010i	0.960600	−	0.697917i
$560$		0			0
$561$	−10.6150	−	32.6695i	−0.448165	−	1.37931i
$562$		0			0
$563$	10.9061	+	7.92377i	0.459639	+	0.333947i	0.793390	−	0.608714i	$-0.208314\pi$
$563$	10.9061	+	7.92377i	0.459639	+	0.333947i	−0.333751	+	0.942661i	$0.608314\pi$
$564$		0			0
$565$	23.7764			1.00028
$566$		0			0
$567$	−0.0190601	+	0.0586608i	−0.000800447	+	0.00246352i
$568$		0			0
$569$	10.2483	−	7.44581i	0.429630	−	0.312145i	−0.351871	−	0.936049i	$-0.614454\pi$
$569$	10.2483	−	7.44581i	0.429630	−	0.312145i	0.781501	+	0.623904i	$0.214454\pi$
$570$		0			0
$571$	13.3038			0.556748			0.278374	−	0.960473i	$-0.410205\pi$
$571$	13.3038			0.556748			0.278374	+	0.960473i	$0.410205\pi$
$572$		0			0
$573$	−18.9015			−0.789621
$574$		0			0
$575$	−16.0371			−0.668793
$576$		0			0
$577$	−36.4393			−1.51699			−0.758495	−	0.651679i	$-0.774065\pi$
$577$	−36.4393			−1.51699			−0.758495	+	0.651679i	$0.774065\pi$
$578$		0			0
$579$	12.5320	−	9.10502i	0.520812	−	0.378392i
$580$		0			0
$581$	−5.35977	+	16.4957i	−0.222361	+	0.684356i
$582$		0			0
$583$	33.4280			1.38445
$584$		0			0
$585$	7.29468	+	5.29990i	0.301598	+	0.219124i
$586$		0			0
$587$	−7.28217	−	22.4122i	−0.300567	−	0.925051i	−0.981294	−	0.192514i	$-0.938336\pi$
$587$	−7.28217	−	22.4122i	−0.300567	−	0.925051i	0.680727	−	0.732537i	$-0.261664\pi$
$588$		0			0
$589$	−8.10887	+	5.89144i	−0.334120	+	0.242753i
$590$		0			0
$591$	1.39012	+	1.00998i	0.0571820	+	0.0415452i
$592$		0			0
$593$	−7.64183	+	23.5191i	−0.313812	+	0.965815i	0.662428	+	0.749125i	$0.269526\pi$
$593$	−7.64183	+	23.5191i	−0.313812	+	0.965815i	−0.976241	+	0.216690i	$0.930474\pi$
$594$		0			0
$595$	−7.66729	+	23.5975i	−0.314328	+	0.967402i
$596$		0			0
$597$	3.44286	+	10.5960i	0.140907	+	0.433667i
$598$		0			0
$599$	6.64281	−	20.4445i	0.271418	−	0.835339i	−0.718727	−	0.695292i	$-0.755275\pi$
$599$	6.64281	−	20.4445i	0.271418	−	0.835339i	0.990145	−	0.140046i	$-0.0447251\pi$
$600$		0			0
$601$	22.2210			0.906415			0.453208	−	0.891405i	$-0.350280\pi$
$601$	22.2210			0.906415			0.453208	+	0.891405i	$0.350280\pi$
$602$		0			0
$603$	−1.27774	+	0.928332i	−0.0520336	+	0.0378046i
$604$		0			0
$605$	−6.03334	−	4.38348i	−0.245290	−	0.178214i
$606$		0			0
$607$	15.5603	+	11.3052i	0.631574	+	0.458865i	0.856945	−	0.515408i	$-0.172360\pi$
$607$	15.5603	+	11.3052i	0.631574	+	0.458865i	−0.225371	+	0.974273i	$0.572360\pi$
$608$		0			0
$609$	−0.616829	−	1.89840i	−0.0249952	−	0.0769272i
$610$		0			0
$611$	0.598740	−	0.435010i	0.0242224	−	0.0175986i
$612$		0			0
$613$	−3.94117	−	12.1297i	−0.159182	−	0.489913i	0.839378	−	0.543548i	$-0.182919\pi$
$613$	−3.94117	−	12.1297i	−0.159182	−	0.489913i	−0.998561	+	0.0536347i	$0.982919\pi$
$614$		0			0
$615$	−9.60558	+	4.17958i	−0.387334	+	0.168537i
$616$		0			0
$617$	1.70468	+	5.24646i	0.0686277	+	0.211214i	0.979489	−	0.201499i	$-0.0645812\pi$
$617$	1.70468	+	5.24646i	0.0686277	+	0.211214i	−0.910861	+	0.412713i	$0.864581\pi$
$618$		0			0
$619$	3.04729	−	2.21398i	0.122481	−	0.0889875i	−0.524858	−	0.851190i	$-0.675882\pi$
$619$	3.04729	−	2.21398i	0.122481	−	0.0889875i	0.647339	+	0.762202i	$0.275882\pi$
$620$		0			0
$621$	−9.68899	−	29.8196i	−0.388806	−	1.19662i
$622$		0			0
$623$	−4.09492	−	2.97513i	−0.164059	−	0.119196i
$624$		0			0
$625$	3.78360	+	2.74895i	0.151344	+	0.109958i
$626$		0			0
$627$	−3.85198	+	2.79863i	−0.153833	+	0.111766i
$628$		0			0
$629$	64.1309			2.55707
$630$		0			0
$631$	−13.7815	+	42.4152i	−0.548635	+	1.68852i	0.163553	+	0.986535i	$0.447704\pi$
$631$	−13.7815	+	42.4152i	−0.548635	+	1.68852i	−0.712188	+	0.701989i	$0.752296\pi$
$632$		0			0
$633$	6.03059	+	18.5602i	0.239694	+	0.737704i
$634$		0			0
$635$	−6.41784	+	19.7521i	−0.254684	+	0.783837i
$636$		0			0
$637$	−2.90771	+	8.94901i	−0.115208	+	0.354573i
$638$		0			0
$639$	−1.93376	−	1.40496i	−0.0764984	−	0.0555794i
$640$		0			0
$641$	33.4210	−	24.2818i	1.32005	−	0.959073i	0.320120	−	0.947377i	$-0.396277\pi$
$641$	33.4210	−	24.2818i	1.32005	−	0.959073i	0.999932	−	0.0116963i	$-0.00372313\pi$
$642$		0			0
$643$	−10.7600	−	33.1159i	−0.424333	−	1.30596i	−0.903632	−	0.428310i	$-0.859109\pi$
$643$	−10.7600	−	33.1159i	−0.424333	−	1.30596i	0.479299	−	0.877652i	$-0.340891\pi$
$644$		0			0
$645$	11.7291	+	8.52170i	0.461834	+	0.335542i
$646$		0			0
$647$	−46.5990			−1.83200			−0.915998	−	0.401184i	$-0.868599\pi$
$647$	−46.5990			−1.83200			−0.915998	+	0.401184i	$0.868599\pi$
$648$		0			0
$649$	−0.0679519	+	0.209134i	−0.00266734	+	0.00820924i
$650$		0			0
$651$	−15.5441	+	11.2934i	−0.609220	+	0.442624i
$652$		0			0
$653$	9.06470			0.354729			0.177365	−	0.984145i	$-0.443243\pi$
$653$	9.06470			0.354729			0.177365	+	0.984145i	$0.443243\pi$
$654$		0			0
$655$	−0.302043			−0.0118018
$656$		0			0
$657$	−12.5939			−0.491336
$658$		0			0
$659$	40.0914			1.56174			0.780869	−	0.624695i	$-0.214777\pi$
$659$	40.0914			1.56174			0.780869	+	0.624695i	$0.214777\pi$
$660$		0			0
$661$	−1.79310	+	1.30276i	−0.0697433	+	0.0506715i	−0.622111	−	0.782929i	$-0.713725\pi$
$661$	−1.79310	+	1.30276i	−0.0697433	+	0.0506715i	0.552367	+	0.833601i	$0.313725\pi$
$662$		0			0
$663$	8.44106	−	25.9789i	0.327824	−	1.00894i
$664$		0			0
$665$	3.43913			0.133364
$666$		0			0
$667$	−4.54857	−	3.30473i	−0.176121	−	0.127960i
$668$		0			0
$669$	0.205919	+	0.633754i	0.00796129	+	0.0245023i
$670$		0			0
$671$	19.1530	−	13.9155i	0.739395	−	0.537202i
$672$		0			0
$673$	2.55597	+	1.85702i	0.0985252	+	0.0715828i	0.635957	−	0.771724i	$-0.280605\pi$
$673$	2.55597	+	1.85702i	0.0985252	+	0.0715828i	−0.537432	+	0.843307i	$0.680605\pi$
$674$		0			0
$675$	4.25849	−	13.1063i	0.163910	−	0.504462i
$676$		0			0
$677$	0.879258	−	2.70608i	0.0337926	−	0.104003i	−0.932737	−	0.360556i	$-0.882587\pi$
$677$	0.879258	−	2.70608i	0.0337926	−	0.104003i	0.966530	+	0.256553i	$0.0825869\pi$
$678$		0			0
$679$	−3.65780	−	11.2576i	−0.140374	−	0.432026i
$680$		0			0
$681$	0.321853	−	0.990560i	0.0123334	−	0.0379583i
$682$		0			0
$683$	9.02010			0.345145			0.172572	−	0.984997i	$-0.444792\pi$
$683$	9.02010			0.345145			0.172572	+	0.984997i	$0.444792\pi$
$684$		0			0
$685$	−9.42827	+	6.85004i	−0.360236	+	0.261726i
$686$		0			0
$687$	0.774533	+	0.562731i	0.0295503	+	0.0214695i
$688$		0			0
$689$	21.5053	+	15.6245i	0.819288	+	0.595248i
$690$		0			0
$691$	−11.2550	−	34.6394i	−0.428161	−	1.31775i	−0.899934	−	0.436025i	$-0.856386\pi$
$691$	−11.2550	−	34.6394i	−0.428161	−	1.31775i	0.471773	−	0.881720i	$-0.343614\pi$
$692$		0			0
$693$	12.0250	−	8.73667i	0.456792	−	0.331878i
$694$		0			0
$695$	−7.92655	−	24.3954i	−0.300671	−	0.925371i
$696$		0			0
$697$	−34.2554	−	38.6985i	−1.29752	−	1.46581i
$698$		0			0
$699$	1.22244	+	3.76227i	0.0462368	+	0.142302i
$700$		0			0
$701$	19.7027	−	14.3148i	0.744160	−	0.540664i	−0.149851	−	0.988709i	$-0.547879\pi$
$701$	19.7027	−	14.3148i	0.744160	−	0.540664i	0.894011	+	0.448044i	$0.147879\pi$
$702$		0			0
$703$	−2.74688	−	8.45402i	−0.103600	−	0.318849i
$704$		0			0
$705$	0.309211	+	0.224655i	0.0116456	+	0.00846100i
$706$		0			0
$707$	5.19478	+	3.77423i	0.195370	+	0.141944i
$708$		0			0
$709$	−2.67897	+	1.94639i	−0.100611	+	0.0730980i	−0.636953	−	0.770902i	$-0.719806\pi$
$709$	−2.67897	+	1.94639i	−0.100611	+	0.0730980i	0.536342	+	0.844000i	$0.319806\pi$
$710$		0			0
$711$	6.35055			0.238164
$712$		0			0
$713$	−16.7234	+	51.4693i	−0.626296	+	1.92754i
$714$		0			0
$715$	−5.97192	−	18.3797i	−0.223337	−	0.687361i
$716$		0			0
$717$	−2.08907	+	6.42948i	−0.0780176	+	0.240113i
$718$		0			0
$719$	−1.32927	+	4.09107i	−0.0495734	+	0.152571i	−0.972779	−	0.231736i	$-0.925560\pi$
$719$	−1.32927	+	4.09107i	−0.0495734	+	0.152571i	0.923205	+	0.384307i	$0.125560\pi$
$720$		0			0
$721$	−20.9172	−	15.1973i	−0.778998	−	0.565975i
$722$		0			0
$723$	16.5532	−	12.0266i	0.615619	−	0.447274i
$724$		0			0
$725$	−0.763620	−	2.35018i	−0.0283601	−	0.0872835i
$726$		0			0
$727$	−23.3289	−	16.9494i	−0.865220	−	0.628619i	0.0640799	−	0.997945i	$-0.479589\pi$
$727$	−23.3289	−	16.9494i	−0.865220	−	0.628619i	−0.929300	+	0.369326i	$0.879589\pi$
$728$		0			0
$729$	16.5788			0.614031
$730$		0			0
$731$	−22.1031	+	68.0263i	−0.817512	+	2.51604i
$732$		0			0
$733$	38.4217	−	27.9150i	1.41914	−	1.03106i	0.427225	−	0.904145i	$-0.359491\pi$
$733$	38.4217	−	27.9150i	1.41914	−	1.03106i	0.991913	−	0.126919i	$-0.0405089\pi$
$734$		0			0
$735$	−4.85944			−0.179243
$736$		0			0
$737$	3.38507			0.124691
$738$		0			0
$739$	43.3553			1.59485			0.797426	−	0.603417i	$-0.206194\pi$
$739$	43.3553			1.59485			0.797426	+	0.603417i	$0.206194\pi$
$740$		0			0
$741$	−3.78621			−0.139090
$742$		0			0
$743$	−6.91998	+	5.02766i	−0.253870	+	0.184447i	−0.707440	−	0.706773i	$-0.750150\pi$
$743$	−6.91998	+	5.02766i	−0.253870	+	0.184447i	0.453570	+	0.891220i	$0.350150\pi$
$744$		0			0
$745$	−10.0410	+	30.9031i	−0.367875	+	1.13220i
$746$		0			0
$747$	−16.0595			−0.587587
$748$		0			0
$749$	31.4469	+	22.8475i	1.14904	+	0.834830i
$750$		0			0
$751$	−6.84297	−	21.0605i	−0.249704	−	0.768509i	−0.994827	−	0.101582i	$-0.967609\pi$
$751$	−6.84297	−	21.0605i	−0.249704	−	0.768509i	0.745123	−	0.666927i	$-0.232391\pi$
$752$		0			0
$753$	−9.79996	+	7.12009i	−0.357130	+	0.259470i
$754$		0			0
$755$	−14.0960	−	10.2413i	−0.513005	−	0.372720i
$756$		0			0
$757$	13.1646	−	40.5164i	0.478475	−	1.47259i	−0.362738	−	0.931891i	$-0.618158\pi$
$757$	13.1646	−	40.5164i	0.478475	−	1.47259i	0.841213	−	0.540703i	$-0.181842\pi$
$758$		0			0
$759$	−7.94415	+	24.4496i	−0.288354	+	0.887464i
$760$		0			0
$761$	6.29620	+	19.3777i	0.228237	+	0.702442i	0.997947	+	0.0640475i	$0.0204009\pi$
$761$	6.29620	+	19.3777i	0.228237	+	0.702442i	−0.769710	+	0.638394i	$0.779599\pi$
$762$		0			0
$763$	6.21236	−	19.1197i	0.224903	−	0.692179i
$764$		0			0
$765$	−22.9736			−0.830611
$766$		0			0
$767$	−0.141467	+	0.102782i	−0.00510807	+	0.00371123i
$768$		0			0
$769$	0.278924	+	0.202650i	0.0100583	+	0.00730775i	0.592803	−	0.805347i	$-0.298021\pi$
$769$	0.278924	+	0.202650i	0.0100583	+	0.00730775i	−0.582745	+	0.812655i	$0.698021\pi$
$770$		0			0
$771$	−5.79197	−	4.20812i	−0.208593	−	0.151552i
$772$		0			0
$773$	−0.0109236	−	0.0336193i	−0.000392893	−	0.00120920i	0.950860	−	0.309622i	$-0.100202\pi$
$773$	−0.0109236	−	0.0336193i	−0.000392893	−	0.00120920i	−0.951253	+	0.308412i	$0.900202\pi$
$774$		0			0
$775$	−19.2432	+	13.9810i	−0.691236	+	0.502212i
$776$		0			0
$777$	−5.26555	−	16.2057i	−0.188900	−	0.581376i
$778$		0			0
$779$	−3.63417	+	6.17324i	−0.130208	+	0.221179i
$780$		0			0
$781$	1.58311	+	4.87231i	0.0566481	+	0.174345i
$782$		0			0
$783$	3.90862	−	2.83978i	0.139683	−	0.101485i
$784$		0			0
$785$	−2.85479	−	8.78613i	−0.101892	−	0.313591i
$786$		0			0
$787$	−23.9618	−	17.4093i	−0.854146	−	0.620573i	0.0721402	−	0.997394i	$-0.477017\pi$
$787$	−23.9618	−	17.4093i	−0.854146	−	0.620573i	−0.926286	+	0.376821i	$0.877017\pi$
$788$		0			0
$789$	−7.31026	−	5.31121i	−0.260252	−	0.189084i
$790$		0			0
$791$	25.2151	−	18.3199i	0.896546	−	0.651379i
$792$		0			0
$793$	18.8260			0.668531
$794$		0			0
$795$	−4.24217	+	13.0561i	−0.150454	+	0.463051i
$796$		0			0
$797$	12.5113	+	38.5058i	0.443172	+	1.36394i	0.884476	+	0.466586i	$0.154516\pi$
$797$	12.5113	+	38.5058i	0.443172	+	1.36394i	−0.441303	+	0.897358i	$0.645484\pi$
$798$		0			0
$799$	−0.582697	+	1.79336i	−0.0206143	+	0.0634444i
$800$		0			0
$801$	1.44824	−	4.45721i	0.0511709	−	0.157488i
$802$		0			0
$803$	21.8375	+	15.8658i	0.770627	+	0.559894i
$804$		0			0
$805$	15.0226	−	10.9146i	0.529478	−	0.384688i
$806$		0			0
$807$	−3.94201	−	12.1323i	−0.138765	−	0.427076i
$808$		0			0
$809$	20.0467	+	14.5648i	0.704805	+	0.512071i	0.881494	−	0.472196i	$-0.156538\pi$
$809$	20.0467	+	14.5648i	0.704805	+	0.512071i	−0.176688	+	0.984267i	$0.556538\pi$
$810$		0			0
$811$	−10.6132			−0.372679			−0.186340	−	0.982485i	$-0.559662\pi$
$811$	−10.6132			−0.372679			−0.186340	+	0.982485i	$0.559662\pi$
$812$		0			0
$813$	−8.10474	+	24.9438i	−0.284246	+	0.874818i
$814$		0			0
$815$	−8.89075	+	6.45951i	−0.311429	+	0.226267i
$816$		0			0
$817$	9.91425			0.346856
$818$		0			0
$819$	11.8197			0.413013
$820$		0			0
$821$	−21.5633			−0.752563			−0.376282	−	0.926505i	$-0.622798\pi$
$821$	−21.5633			−0.752563			−0.376282	+	0.926505i	$0.622798\pi$
$822$		0			0
$823$	−1.56533			−0.0545639			−0.0272820	−	0.999628i	$-0.508685\pi$
$823$	−1.56533			−0.0545639			−0.0272820	+	0.999628i	$0.508685\pi$
$824$		0			0
$825$	−9.14114	+	6.64143i	−0.318254	+	0.231225i
$826$		0			0
$827$	−8.64697	+	26.6127i	−0.300685	+	0.925413i	0.680568	+	0.732685i	$0.261733\pi$
$827$	−8.64697	+	26.6127i	−0.300685	+	0.925413i	−0.981252	+	0.192727i	$0.938267\pi$
$828$		0			0
$829$	−24.4897			−0.850563			−0.425282	−	0.905061i	$-0.639825\pi$
$829$	−24.4897			−0.850563			−0.425282	+	0.905061i	$0.639825\pi$
$830$		0			0
$831$	7.90796	+	5.74547i	0.274324	+	0.199308i
$832$		0			0
$833$	−7.40851	−	22.8011i	−0.256690	−	0.790010i
$834$		0			0
$835$	−25.5987	+	18.5985i	−0.885880	+	0.643629i
$836$		0			0
$837$	−37.6225	−	27.3344i	−1.30042	−	0.944813i
$838$		0			0
$839$	−5.47141	+	16.8393i	−0.188894	+	0.581356i	−0.999994	−	0.00355195i	$-0.998869\pi$
$839$	−5.47141	+	16.8393i	−0.188894	+	0.581356i	0.811100	+	0.584908i	$0.198869\pi$
$840$		0			0
$841$	−8.69378	+	26.7567i	−0.299786	+	0.922645i
$842$		0			0
$843$	8.82074	+	27.1475i	0.303802	+	0.935008i
$844$		0			0
$845$	−1.40294	+	4.31781i	−0.0482627	+	0.148537i
$846$		0			0
$847$	−9.77590			−0.335904
$848$		0			0
$849$	9.92891	−	7.21378i	0.340759	−	0.247576i
$850$		0			0
$851$	−38.8288	−	28.2107i	−1.33103	−	0.967052i
$852$		0			0
$853$	18.0591	+	13.1207i	0.618333	+	0.449245i	0.852339	−	0.522990i	$-0.175184\pi$
$853$	18.0591	+	13.1207i	0.618333	+	0.449245i	−0.234006	+	0.972235i	$0.575184\pi$
$854$		0			0
$855$	0.984012	+	3.02848i	0.0336525	+	0.103572i
$856$		0			0
$857$	−24.0541	+	17.4763i	−0.821672	+	0.596980i	−0.917191	−	0.398448i	$-0.869549\pi$
$857$	−24.0541	+	17.4763i	−0.821672	+	0.596980i	0.0955187	+	0.995428i	$0.469549\pi$
$858$		0			0
$859$	−6.92582	−	21.3155i	−0.236306	−	0.727274i	−0.996946	−	0.0781002i	$-0.975115\pi$
$859$	−6.92582	−	21.3155i	−0.236306	−	0.727274i	0.760640	−	0.649174i	$-0.224885\pi$
$860$		0			0
$861$	−6.96641	+	11.8336i	−0.237415	+	0.403289i
$862$		0			0
$863$	−10.2083	−	31.4179i	−0.347494	−	1.06948i	−0.960235	−	0.279193i	$-0.909933\pi$
$863$	−10.2083	−	31.4179i	−0.347494	−	1.06948i	0.612741	−	0.790284i	$-0.290067\pi$
$864$		0			0
$865$	32.0684	−	23.2991i	1.09036	−	0.792192i
$866$		0			0
$867$	15.8946	+	48.9187i	0.539810	+	1.66136i
$868$		0			0
$869$	−11.0116	−	8.00043i	−0.373544	−	0.271396i
$870$		0			0
$871$	2.17773	+	1.58221i	0.0737895	+	0.0536112i
$872$		0			0
$873$	8.86676	−	6.44208i	0.300094	−	0.218031i
$874$		0			0
$875$	23.5318			0.795519
$876$		0			0
$877$	10.2370	−	31.5063i	0.345679	−	1.06389i	−0.615540	−	0.788106i	$-0.711062\pi$
$877$	10.2370	−	31.5063i	0.345679	−	1.06389i	0.961219	−	0.275786i	$-0.0889381\pi$
$878$		0			0
$879$	7.41507	+	22.8213i	0.250104	+	0.769742i
$880$		0			0
$881$	−0.185802	+	0.571838i	−0.00625981	+	0.0192657i	−0.954138	−	0.299368i	$-0.903224\pi$
$881$	−0.185802	+	0.571838i	−0.00625981	+	0.0192657i	0.947878	+	0.318634i	$0.103224\pi$
$882$		0			0
$883$	9.51888	−	29.2961i	0.320336	−	0.985893i	−0.653166	−	0.757215i	$-0.726560\pi$
$883$	9.51888	−	29.2961i	0.320336	−	0.985893i	0.973502	−	0.228678i	$-0.0734403\pi$
$884$		0			0
$885$	−0.0730587	−	0.0530803i	−0.00245584	−	0.00178427i
$886$		0			0
$887$	−6.81187	+	4.94912i	−0.228720	+	0.166175i	−0.696243	−	0.717806i	$-0.745147\pi$
$887$	−6.81187	+	4.94912i	−0.228720	+	0.166175i	0.467523	+	0.883981i	$0.345147\pi$
$888$		0			0
$889$	8.41289	+	25.8922i	0.282159	+	0.868397i
$890$		0			0
$891$	0.0990266	+	0.0719470i	0.00331751	+	0.00241032i
$892$		0			0
$893$	0.261366			0.00874629
$894$		0			0
$895$	−9.07759	+	27.9380i	−0.303431	+	0.933863i
$896$		0			0
$897$	−16.5387	+	12.0161i	−0.552211	+	0.401204i
$898$		0			0
$899$	−8.33895			−0.278119
$900$		0			0
$901$	−67.7280			−2.25635
$902$		0			0
$903$	19.0048			0.632442
$904$		0			0
$905$	5.20402			0.172988
$906$		0			0
$907$	24.8465	−	18.0520i	0.825014	−	0.599407i	−0.0931306	−	0.995654i	$-0.529687\pi$
$907$	24.8465	−	18.0520i	0.825014	−	0.599407i	0.918144	+	0.396246i	$0.129687\pi$
$908$		0			0
$909$	−1.83722	+	5.65438i	−0.0609367	+	0.187544i
$910$		0			0
$911$	28.6722			0.949951			0.474975	−	0.879999i	$-0.342457\pi$
$911$	28.6722			0.949951			0.474975	+	0.879999i	$0.342457\pi$
$912$		0			0
$913$	27.8467	+	20.2318i	0.921590	+	0.669575i
$914$		0			0
$915$	3.00440	+	9.24659i	0.0993224	+	0.305683i
$916$		0			0
$917$	−0.320320	+	0.232726i	−0.0105779	+	0.00768528i
$918$		0			0
$919$	−0.997235	−	0.724534i	−0.0328958	−	0.0239002i	0.571216	−	0.820800i	$-0.306472\pi$
$919$	−0.997235	−	0.724534i	−0.0328958	−	0.0239002i	−0.604112	+	0.796900i	$0.706472\pi$
$920$		0			0
$921$	−2.79892	+	8.61420i	−0.0922276	+	0.283847i
$922$		0			0
$923$	−1.25889	+	3.87447i	−0.0414370	+	0.127530i
$924$		0			0
$925$	−6.51863	−	20.0623i	−0.214331	−	0.659643i
$926$		0			0
$927$	7.39772	−	22.7678i	0.242973	−	0.747794i
$928$		0			0
$929$	−30.5604			−1.00265			−0.501327	−	0.865258i	$-0.667155\pi$
$929$	−30.5604			−1.00265			−0.501327	+	0.865258i	$0.667155\pi$
$930$		0			0
$931$	−2.68841	+	1.95325i	−0.0881091	+	0.0640150i
$932$		0			0
$933$	4.07502	+	2.96068i	0.133410	+	0.0969283i
$934$		0			0
$935$	39.8354	+	28.9421i	1.30276	+	0.946508i
$936$		0			0
$937$	−9.07144	−	27.9190i	−0.296351	−	0.912075i	−0.982764	−	0.184863i	$-0.940816\pi$
$937$	−9.07144	−	27.9190i	−0.296351	−	0.912075i	0.686413	−	0.727212i	$-0.259184\pi$
$938$		0			0
$939$	12.1552	−	8.83124i	0.396669	−	0.288197i
$940$		0			0
$941$	−0.232560	−	0.715746i	−0.00758124	−	0.0233327i	0.947194	−	0.320660i	$-0.103905\pi$
$941$	−0.232560	−	0.715746i	−0.00758124	−	0.0233327i	−0.954776	+	0.297327i	$0.903905\pi$
$942$		0			0
$943$	3.71710	+	38.4991i	0.121045	+	1.25370i
$944$		0			0
$945$	4.93081	+	15.1755i	0.160399	+	0.493658i
$946$		0			0
$947$	33.3188	−	24.2076i	1.08272	−	0.786640i	0.104562	−	0.994518i	$-0.466656\pi$
$947$	33.3188	−	24.2076i	1.08272	−	0.786640i	0.978155	+	0.207878i	$0.0666558\pi$
$948$		0			0
$949$	6.63293	+	20.4140i	0.215314	+	0.662668i
$950$		0			0
$951$	11.3874	+	8.27341i	0.369261	+	0.268284i
$952$		0			0
$953$	−12.2642	−	8.91043i	−0.397275	−	0.288637i	0.371155	−	0.928571i	$-0.378962\pi$
$953$	−12.2642	−	8.91043i	−0.397275	−	0.288637i	−0.768430	+	0.639934i	$0.778962\pi$
$954$		0			0
$955$	21.9194	−	15.9254i	0.709295	−	0.515333i
$956$		0			0
$957$	−3.96127			−0.128050
$958$		0			0
$959$	−4.72077	+	14.5290i	−0.152442	+	0.469167i
$960$		0			0
$961$	15.2243	+	46.8555i	0.491106	+	1.51147i
$962$		0			0
$963$	−11.1217	+	34.2291i	−0.358392	+	1.10302i
$964$		0			0
$965$	−6.86151	+	21.1176i	−0.220880	+	0.679798i
$966$		0			0
$967$	28.2627	+	20.5341i	0.908868	+	0.660331i	0.940728	−	0.339161i	$-0.110143\pi$
$967$	28.2627	+	20.5341i	0.908868	+	0.660331i	−0.0318604	+	0.999492i	$0.510143\pi$
$968$		0			0
$969$	7.80444	−	5.67026i	0.250715	−	0.182155i
$970$		0			0
$971$	−6.21580	−	19.1303i	−0.199474	−	0.613919i	−0.999895	−	0.0144806i	$-0.995391\pi$
$971$	−6.21580	−	19.1303i	−0.199474	−	0.613919i	0.800421	−	0.599439i	$-0.204609\pi$
$972$		0			0
$973$	−27.2030	−	19.7641i	−0.872087	−	0.633608i
$974$		0			0
$975$	−8.98506			−0.287752
$976$		0			0
$977$	−1.70120	+	5.23574i	−0.0544261	+	0.167506i	−0.974575	−	0.224063i	$-0.928068\pi$
$977$	−1.70120	+	5.23574i	−0.0544261	+	0.167506i	0.920149	+	0.391570i	$0.128068\pi$
$978$		0			0
$979$	−8.12638	+	5.90416i	−0.259720	+	0.188698i
$980$		0			0
$981$	18.6142			0.594305
$982$		0			0
$983$	−37.5907			−1.19896			−0.599479	−	0.800391i	$-0.704625\pi$
$983$	−37.5907			−1.19896			−0.599479	+	0.800391i	$0.704625\pi$
$984$		0			0
$985$	−2.46303			−0.0784788
$986$		0			0
$987$	0.501019			0.0159476
$988$		0			0
$989$	43.3069	−	31.4643i	1.37708	−	1.00051i
$990$		0			0
$991$	−11.1187	+	34.2197i	−0.353196	+	1.08702i	0.603853	+	0.797096i	$0.293632\pi$
$991$	−11.1187	+	34.2197i	−0.353196	+	1.08702i	−0.957048	+	0.289929i	$0.906368\pi$
$992$		0			0
$993$	−28.0666			−0.890666
$994$		0			0
$995$	−12.9202	−	9.38709i	−0.409598	−	0.297591i
$996$		0			0
$997$	−5.05400	−	15.5546i	−0.160062	−	0.492619i	0.838577	−	0.544783i	$-0.183388\pi$
$997$	−5.05400	−	15.5546i	−0.160062	−	0.492619i	−0.998639	+	0.0521641i	$0.983388\pi$
$998$		0			0
$999$	33.3658	−	24.2417i	1.05565	−	0.766973i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.u.h.305.4		20
4.3	odd	2		328.2.m.c.305.2	yes	20
41.16	even	5	inner	656.2.u.h.385.4		20
164.139	odd	10		328.2.m.c.57.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
328.2.m.c.57.2	✓	20	164.139	odd	10
328.2.m.c.305.2	yes	20	4.3	odd	2
656.2.u.h.305.4		20	1.1	even	1	trivial
656.2.u.h.385.4		20	41.16	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+1.06833 q^{3} +(-1.23890 + 0.900114i) q^{5} +(-0.620323 + 1.90916i) q^{7} -1.85868 q^{9} +O(q^{10})\)	\(q+1.06833 q^{3} +(-1.23890 + 0.900114i) q^{5} +(-0.620323 + 1.90916i) q^{7} -1.85868 q^{9} +(3.22289 + 2.34156i) q^{11} +(0.978921 + 3.01281i) q^{13} +(-1.32355 + 0.961615i) q^{15} +(-6.52985 - 4.74421i) q^{17} +(-0.345714 + 1.06400i) q^{19} +(-0.662707 + 2.03960i) q^{21} +(1.86662 + 5.74487i) q^{23} +(-0.820416 + 2.52498i) q^{25} -5.19065 q^{27} +(-0.753010 + 0.547094i) q^{29} +(7.24812 + 5.26607i) q^{31} +(3.44309 + 2.50155i) q^{33} +(-0.949940 - 2.92362i) q^{35} +(-6.42806 + 4.67026i) q^{37} +(1.04581 + 3.21866i) q^{39} +(6.25170 + 1.38427i) q^{41} +(-2.73847 - 8.42814i) q^{43} +(2.30272 - 1.67302i) q^{45} +(-0.0721934 - 0.222188i) q^{47} +(2.40304 + 1.74591i) q^{49} +(-6.97601 - 5.06837i) q^{51} +(6.78861 - 4.93221i) q^{53} -6.10051 q^{55} +(-0.369336 + 1.13670i) q^{57} +(0.0170575 + 0.0524974i) q^{59} +(1.83643 - 5.65196i) q^{61} +(1.15298 - 3.54851i) q^{63} +(-3.92466 - 2.85143i) q^{65} +(0.687445 - 0.499458i) q^{67} +(1.99416 + 6.13740i) q^{69} +(1.04040 + 0.755892i) q^{71} +6.77575 q^{73} +(-0.876472 + 2.69750i) q^{75} +(-6.46964 + 4.70047i) q^{77} -3.41670 q^{79} +0.0307261 q^{81} +8.64029 q^{83} +12.3602 q^{85} +(-0.804461 + 0.584475i) q^{87} +(-0.779174 + 2.39805i) q^{89} -6.35917 q^{91} +(7.74336 + 5.62588i) q^{93} +(-0.529415 - 1.62937i) q^{95} +(-4.77046 + 3.46594i) q^{97} +(-5.99031 - 4.35222i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9	\( 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9} - 9 q^{11} + 7 q^{13} - q^{15} - 8 q^{17} - q^{19} - 6 q^{21} + 11 q^{23} + 15 q^{25} - 2 q^{27} + 21 q^{29} + 5 q^{31} + 19 q^{33} - 4 q^{37} - 4 q^{39} + 9 q^{41} + 17 q^{43} + 11 q^{45} - 15 q^{47} - 25 q^{49} + 22 q^{51} + 10 q^{53} + 28 q^{55} - 20 q^{57} + 24 q^{59} + 15 q^{61} + 65 q^{63} - 29 q^{65} + 26 q^{67} - 47 q^{69} - 16 q^{71} + 14 q^{73} - 11 q^{75} + 12 q^{77} + 26 q^{79} - 60 q^{81} - 20 q^{83} - 94 q^{85} - 57 q^{87} + 5 q^{89} + 46 q^{91} + 43 q^{93} - 71 q^{95} - 22 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9 - 9 * q^11 + 7 * q^13 - q^15 - 8 * q^17 - q^19 - 6 * q^21 + 11 * q^23 + 15 * q^25 - 2 * q^27 + 21 * q^29 + 5 * q^31 + 19 * q^33 - 4 * q^37 - 4 * q^39 + 9 * q^41 + 17 * q^43 + 11 * q^45 - 15 * q^47 - 25 * q^49 + 22 * q^51 + 10 * q^53 + 28 * q^55 - 20 * q^57 + 24 * q^59 + 15 * q^61 + 65 * q^63 - 29 * q^65 + 26 * q^67 - 47 * q^69 - 16 * q^71 + 14 * q^73 - 11 * q^75 + 12 * q^77 + 26 * q^79 - 60 * q^81 - 20 * q^83 - 94 * q^85 - 57 * q^87 + 5 * q^89 + 46 * q^91 + 43 * q^93 - 71 * q^95 - 22 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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