LMFDB - Embedded newform 644.2.bc.a.493.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(5,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 3]))

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

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

chi := DirichletCharacter("644.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.bc (of order $66$, degree $20$, 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:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			493.9
Character	$\chi$	$=$	644.493
Dual form			644.2.bc.a.145.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.206600 + 0.400748i) q^{3} +(-3.92969 + 0.375240i) q^{5} +(-0.614617 + 2.57337i) q^{7} +(1.62226 - 2.27814i) q^{9} +O(q^{10})$	\(q+(0.206600 + 0.400748i) q^{3} +(-3.92969 + 0.375240i) q^{5} +(-0.614617 + 2.57337i) q^{7} +(1.62226 - 2.27814i) q^{9} +(0.784113 - 0.271384i) q^{11} +(-0.984024 - 3.35128i) q^{13} +(-0.962249 - 1.49729i) q^{15} +(-4.14039 - 1.65756i) q^{17} +(5.45682 - 2.18458i) q^{19} +(-1.15825 + 0.285352i) q^{21} +(-3.94103 - 2.73282i) q^{23} +(10.3920 - 2.00289i) q^{25} +(2.58695 + 0.371948i) q^{27} +(-1.38222 - 9.61357i) q^{29} +(-5.34673 + 0.254696i) q^{31} +(0.270754 + 0.258163i) q^{33} +(1.44962 - 10.3432i) q^{35} +(-2.15028 - 1.53121i) q^{37} +(1.13972 - 1.08672i) q^{39} +(-3.07836 - 1.40584i) q^{41} +(2.66242 - 4.14280i) q^{43} +(-5.52011 + 9.56111i) q^{45} +(-2.49473 + 1.44033i) q^{47} +(-6.24449 - 3.16328i) q^{49} +(-0.191140 - 2.00170i) q^{51} +(9.87470 + 10.3563i) q^{53} +(-2.97948 + 1.36068i) q^{55} +(2.00284 + 1.73547i) q^{57} +(0.928157 + 0.225169i) q^{59} +(-4.28630 - 2.20974i) q^{61} +(4.86543 + 5.57485i) q^{63} +(5.12444 + 12.8002i) q^{65} +(2.44546 + 12.6883i) q^{67} +(0.280954 - 2.14396i) q^{69} +(-8.80089 - 10.1568i) q^{71} +(-4.12935 + 5.25090i) q^{73} +(2.94964 + 3.75077i) q^{75} +(0.216443 + 2.18461i) q^{77} +(3.89653 - 4.08656i) q^{79} +(-2.35874 - 6.81514i) q^{81} +(-4.78253 - 10.4723i) q^{83} +(16.8924 + 4.96006i) q^{85} +(3.56705 - 2.54008i) q^{87} +(-0.388686 + 8.15953i) q^{89} +(9.22888 - 0.472507i) q^{91} +(-1.20670 - 2.09007i) q^{93} +(-20.6239 + 10.6323i) q^{95} +(0.200937 - 0.439990i) q^{97} +(0.653780 - 2.22657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 20 q^{9}+O(q^{10}) $ 320 * q - 20 * q^9	$ 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) $ 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{22}\right)$	$1$

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
$3$	0.206600	+	0.400748i	0.119280	+	0.231372i	0.940915	−	0.338643i	$-0.109968\pi$
$3$	0.206600	+	0.400748i	0.119280	+	0.231372i	−0.821635	+	0.570015i	$0.806938\pi$
$4$		0			0
$5$	−3.92969	+	0.375240i	−1.75741	+	0.167812i	−0.923375	−	0.383900i	$-0.874581\pi$
$5$	−3.92969	+	0.375240i	−1.75741	+	0.167812i	−0.834035	+	0.551712i	$0.813975\pi$
$6$		0			0
$7$	−0.614617	+	2.57337i	−0.232303	+	0.972643i
$7$	−0.614617	+	2.57337i	−0.232303	+	0.972643i
$8$		0			0
$9$	1.62226	−	2.27814i	0.540752	−	0.759380i
$10$		0			0
$11$	0.784113	−	0.271384i	0.236419	−	0.0818254i	−0.206290	−	0.978491i	$-0.566139\pi$
$11$	0.784113	−	0.271384i	0.236419	−	0.0818254i	0.442708	+	0.896666i	$0.354018\pi$
$12$		0			0
$13$	−0.984024	−	3.35128i	−0.272919	−	0.929477i	−0.975891	−	0.218259i	$-0.929962\pi$
$13$	−0.984024	−	3.35128i	−0.272919	−	0.929477i	0.702972	−	0.711218i	$-0.251856\pi$
$14$		0			0
$15$	−0.962249	−	1.49729i	−0.248452	−	0.386598i
$16$		0			0
$17$	−4.14039	−	1.65756i	−1.00419	−	0.402018i	−0.189481	−	0.981884i	$-0.560681\pi$
$17$	−4.14039	−	1.65756i	−1.00419	−	0.402018i	−0.814712	+	0.579866i	$0.803105\pi$
$18$		0			0
$19$	5.45682	−	2.18458i	1.25188	−	0.501178i	0.351462	−	0.936202i	$-0.385685\pi$
$19$	5.45682	−	2.18458i	1.25188	−	0.501178i	0.900419	+	0.435024i	$0.143260\pi$
$20$		0			0
$21$	−1.15825	+	0.285352i	−0.252751	+	0.0622688i
$22$		0			0
$23$	−3.94103	−	2.73282i	−0.821761	−	0.569832i
$23$	−3.94103	−	2.73282i	−0.821761	−	0.569832i
$24$		0			0
$25$	10.3920	−	2.00289i	2.07840	−	0.400578i
$26$		0			0
$27$	2.58695	+	0.371948i	0.497859	+	0.0715814i
$28$		0			0
$29$	−1.38222	−	9.61357i	−0.256672	−	1.78519i	−0.556141	−	0.831088i	$-0.687718\pi$
$29$	−1.38222	−	9.61357i	−0.256672	−	1.78519i	0.299468	−	0.954106i	$-0.403191\pi$
$30$		0			0
$31$	−5.34673	+	0.254696i	−0.960300	+	0.0457447i	−0.521874	−	0.853022i	$-0.674767\pi$
$31$	−5.34673	+	0.254696i	−0.960300	+	0.0457447i	−0.438426	+	0.898767i	$0.644464\pi$
$32$		0			0
$33$	0.270754	+	0.258163i	0.0471322	+	0.0449405i
$34$		0			0
$35$	1.44962	−	10.3432i	0.245031	−	1.74832i
$36$		0			0
$37$	−2.15028	−	1.53121i	−0.353504	−	0.251729i	0.389485	−	0.921033i	$-0.372653\pi$
$37$	−2.15028	−	1.53121i	−0.353504	−	0.251729i	−0.742989	+	0.669304i	$0.766592\pi$
$38$		0			0
$39$	1.13972	−	1.08672i	0.182501	−	0.174014i
$40$		0			0
$41$	−3.07836	−	1.40584i	−0.480759	−	0.219555i	0.160268	−	0.987074i	$-0.448764\pi$
$41$	−3.07836	−	1.40584i	−0.480759	−	0.219555i	−0.641027	+	0.767518i	$0.721491\pi$
$42$		0			0
$43$	2.66242	−	4.14280i	0.406015	−	0.631772i	−0.576687	−	0.816965i	$-0.695655\pi$
$43$	2.66242	−	4.14280i	0.406015	−	0.631772i	0.982702	+	0.185193i	$0.0592912\pi$
$44$		0			0
$45$	−5.52011	+	9.56111i	−0.822889	+	1.42529i
$46$		0			0
$47$	−2.49473	+	1.44033i	−0.363893	+	0.210094i	−0.670787	−	0.741650i	$-0.734044\pi$
$47$	−2.49473	+	1.44033i	−0.363893	+	0.210094i	0.306894	+	0.951744i	$0.400710\pi$
$48$		0			0
$49$	−6.24449	−	3.16328i	−0.892070	−	0.451897i
$50$		0			0
$51$	−0.191140	−	2.00170i	−0.0267649	−	0.280295i
$52$		0			0
$53$	9.87470	+	10.3563i	1.35639	+	1.42254i	0.811922	+	0.583766i	$0.198421\pi$
$53$	9.87470	+	10.3563i	1.35639	+	1.42254i	0.544472	+	0.838779i	$0.316730\pi$
$54$		0			0
$55$	−2.97948	+	1.36068i	−0.401753	+	0.183475i
$56$		0			0
$57$	2.00284	+	1.73547i	0.265283	+	0.229869i
$58$		0			0
$59$	0.928157	+	0.225169i	0.120836	+	0.0293145i	0.295721	−	0.955274i	$-0.404440\pi$
$59$	0.928157	+	0.225169i	0.120836	+	0.0293145i	−0.174885	+	0.984589i	$0.555955\pi$
$60$		0			0
$61$	−4.28630	−	2.20974i	−0.548804	−	0.282928i	0.161441	−	0.986882i	$-0.448386\pi$
$61$	−4.28630	−	2.20974i	−0.548804	−	0.282928i	−0.710245	+	0.703954i	$0.751416\pi$
$62$		0			0
$63$	4.86543	+	5.57485i	0.612987	+	0.702365i
$64$		0			0
$65$	5.12444	+	12.8002i	0.635608	+	1.58767i
$66$		0			0
$67$	2.44546	+	12.6883i	0.298760	+	1.55012i	0.752264	+	0.658862i	$0.228962\pi$
$67$	2.44546	+	12.6883i	0.298760	+	1.55012i	−0.453503	+	0.891255i	$0.649826\pi$
$68$		0			0
$69$	0.280954	−	2.14396i	0.0338229	−	0.258102i
$70$		0			0
$71$	−8.80089	−	10.1568i	−1.04447	−	1.20539i	−0.978217	−	0.207584i	$-0.933440\pi$
$71$	−8.80089	−	10.1568i	−1.04447	−	1.20539i	−0.0662567	−	0.997803i	$-0.521106\pi$
$72$		0			0
$73$	−4.12935	+	5.25090i	−0.483304	+	0.614571i	−0.965154	−	0.261683i	$-0.915723\pi$
$73$	−4.12935	+	5.25090i	−0.483304	+	0.614571i	0.481850	+	0.876254i	$0.339965\pi$
$74$		0			0
$75$	2.94964	+	3.75077i	0.340595	+	0.433101i
$76$		0			0
$77$	0.216443	+	2.18461i	0.0246660	+	0.248960i
$78$		0			0
$79$	3.89653	−	4.08656i	0.438394	−	0.459774i	−0.467056	−	0.884228i	$-0.654685\pi$
$79$	3.89653	−	4.08656i	0.438394	−	0.459774i	0.905450	+	0.424454i	$0.139534\pi$
$80$		0			0
$81$	−2.35874	−	6.81514i	−0.262083	−	0.757238i
$82$		0			0
$83$	−4.78253	−	10.4723i	−0.524951	−	1.14948i	−0.967531	−	0.252753i	$-0.918664\pi$
$83$	−4.78253	−	10.4723i	−0.524951	−	1.14948i	0.442580	−	0.896729i	$-0.354063\pi$
$84$		0			0
$85$	16.8924	+	4.96006i	1.83224	+	0.537995i
$86$		0			0
$87$	3.56705	−	2.54008i	0.382427	−	0.272325i
$88$		0			0
$89$	−0.388686	+	8.15953i	−0.0412007	+	0.864909i	0.879799	+	0.475346i	$0.157677\pi$
$89$	−0.388686	+	8.15953i	−0.0412007	+	0.864909i	−0.921000	+	0.389563i	$0.872626\pi$
$90$		0			0
$91$	9.22888	−	0.472507i	0.967450	−	0.0495322i
$92$		0			0
$93$	−1.20670	−	2.09007i	−0.125129	−	0.216730i
$94$		0			0
$95$	−20.6239	+	10.6323i	−2.11596	+	1.09086i
$96$		0			0
$97$	0.200937	−	0.439990i	0.0204020	−	0.0446742i	−0.899157	−	0.437627i	$-0.855819\pi$
$97$	0.200937	−	0.439990i	0.0204020	−	0.0446742i	0.919559	+	0.392953i	$0.128546\pi$
$98$		0			0
$99$	0.653780	−	2.22657i	0.0657074	−	0.223779i
$100$		0			0
$101$	−0.354750	+	3.71511i	−0.0352989	+	0.369667i	0.960513	+	0.278237i	$0.0897500\pi$
$101$	−0.354750	+	3.71511i	−0.0352989	+	0.369667i	−0.995811	+	0.0914305i	$0.970856\pi$
$102$		0			0
$103$	−1.88854	−	0.363986i	−0.186083	−	0.0358646i	0.0953581	−	0.995443i	$-0.469600\pi$
$103$	−1.88854	−	0.363986i	−0.186083	−	0.0358646i	−0.281441	+	0.959578i	$0.590813\pi$
$104$		0			0
$105$	4.44449	−	1.55597i	0.433738	−	0.151847i
$106$		0			0
$107$	4.16902	−	8.08678i	0.403035	−	0.781778i	−0.596752	−	0.802426i	$-0.703542\pi$
$107$	4.16902	−	8.08678i	0.403035	−	0.781778i	0.999787	+	0.0206474i	$0.00657274\pi$
$108$		0			0
$109$	4.91094	−	12.2669i	0.470383	−	1.17496i	−0.483651	−	0.875261i	$-0.660690\pi$
$109$	4.91094	−	12.2669i	0.470383	−	1.17496i	0.954034	−	0.299698i	$-0.0968860\pi$
$110$		0			0
$111$	0.169380	−	1.17807i	0.0160769	−	0.111817i
$112$		0			0
$113$	−13.2085	+	11.4452i	−1.24255	+	1.07667i	−0.248398	+	0.968658i	$0.579904\pi$
$113$	−13.2085	+	11.4452i	−1.24255	+	1.07667i	−0.994149	+	0.108015i	$0.965551\pi$
$114$		0			0
$115$	16.5125	+	9.26028i	1.53980	+	0.863526i
$116$		0			0
$117$	−9.23101	−	3.19488i	−0.853408	−	0.295367i
$118$		0			0
$119$	6.81028	−	9.63600i	0.624298	−	0.883331i
$120$		0			0
$121$	−8.10540	+	6.37416i	−0.736855	+	0.579469i
$122$		0			0
$123$	−0.0726014	−	1.52409i	−0.00654625	−	0.137423i
$124$		0			0
$125$	−21.1474	+	6.20944i	−1.89148	+	0.555390i
$126$		0			0
$127$	11.3142	−	13.0573i	1.00397	−	1.15865i	0.0166608	−	0.999861i	$-0.494696\pi$
$127$	11.3142	−	13.0573i	1.00397	−	1.15865i	0.987313	−	0.158786i	$-0.0507581\pi$
$128$		0			0
$129$	2.21027	+	0.211055i	0.194604	+	0.0185824i
$130$		0			0
$131$	14.6905	−	3.56387i	1.28351	−	0.311377i	0.464716	−	0.885460i	$-0.346156\pi$
$131$	14.6905	−	3.56387i	1.28351	−	0.311377i	0.818797	+	0.574083i	$0.194641\pi$
$132$		0			0
$133$	2.26789	+	15.3851i	0.196651	+	1.33406i
$134$		0			0
$135$	−10.3055	−	0.490911i	−0.886955	−	0.0422509i
$136$		0			0
$137$	−11.4130	−	6.58932i	−0.975082	−	0.562964i	−0.0743000	−	0.997236i	$-0.523672\pi$
$137$	−11.4130	−	6.58932i	−0.975082	−	0.562964i	−0.900782	+	0.434272i	$0.857006\pi$
$138$		0			0
$139$		−	4.38994i		−	0.372350i	−0.982517	−	0.186175i	$-0.940391\pi$
$139$		−	4.38994i		−	0.372350i	0.982517	−	0.186175i	$-0.0596092\pi$
$140$		0			0
$141$	−1.09262	−	0.702184i	−0.0920151	−	0.0591345i
$142$		0			0
$143$	−1.68107	−	2.36073i	−0.140578	−	0.197414i
$144$		0			0
$145$	9.03909	+	37.2596i	0.750656	+	3.09424i
$146$		0			0
$147$	−0.0224345	−	3.15600i	−0.00185037	−	0.260302i
$148$		0			0
$149$	−3.89487	+	20.2085i	−0.319080	+	1.65555i	0.368642	+	0.929572i	$0.379823\pi$
$149$	−3.89487	+	20.2085i	−0.319080	+	1.65555i	−0.687722	+	0.725974i	$0.741389\pi$
$150$		0			0
$151$	−2.29305	+	9.45206i	−0.186605	+	0.769198i	0.799167	+	0.601110i	$0.205274\pi$
$151$	−2.29305	+	9.45206i	−0.186605	+	0.769198i	−0.985772	+	0.168088i	$0.946241\pi$
$152$		0			0
$153$	−10.4929	+	6.74340i	−0.848303	+	0.545171i
$154$		0			0
$155$	20.9154	−	3.00718i	1.67996	−	0.241542i
$156$		0			0
$157$	−11.2946	−	8.88217i	−0.901407	−	0.708874i	0.0557498	−	0.998445i	$-0.482245\pi$
$157$	−11.2946	−	8.88217i	−0.901407	−	0.708874i	−0.957157	+	0.289571i	$0.906488\pi$
$158$		0			0
$159$	−2.11015	+	6.09687i	−0.167345	+	0.483513i
$160$		0			0
$161$	9.45478	−	8.46210i	0.745141	−	0.666907i
$162$		0			0
$163$	−3.75734	+	10.8561i	−0.294298	+	0.850318i	0.696810	+	0.717256i	$0.254602\pi$
$163$	−3.75734	+	10.8561i	−0.294298	+	0.850318i	−0.991108	+	0.133062i	$0.957519\pi$
$164$		0			0
$165$	−1.16085	−	0.912903i	−0.0903721	−	0.0710694i
$166$		0			0
$167$	−2.24401	+	0.322639i	−0.173646	+	0.0249666i	−0.228589	−	0.973523i	$-0.573411\pi$
$167$	−2.24401	+	0.322639i	−0.173646	+	0.0249666i	0.0549431	+	0.998489i	$0.482502\pi$
$168$		0			0
$169$	0.673540	−	0.432858i	0.0518108	−	0.0332968i
$170$		0			0
$171$	3.87558	−	15.9754i	0.296373	−	1.22167i
$172$		0			0
$173$	1.64792	−	8.55022i	0.125289	−	0.650061i	−0.863929	−	0.503613i	$-0.832004\pi$
$173$	1.64792	−	8.55022i	0.125289	−	0.650061i	0.989218	−	0.146448i	$-0.0467841\pi$
$174$		0			0
$175$	−1.23291	+	27.9735i	−0.0931991	+	2.11460i
$176$		0			0
$177$	0.101521	+	0.418477i	0.00763081	+	0.0314546i
$178$		0			0
$179$	−7.90970	−	11.1076i	−0.591199	−	0.830223i	0.405269	−	0.914197i	$-0.367178\pi$
$179$	−7.90970	−	11.1076i	−0.591199	−	0.830223i	−0.996468	+	0.0839749i	$0.973238\pi$
$180$		0			0
$181$	15.5494	+	9.99302i	1.15578	+	0.742776i	0.970782	−	0.239963i	$-0.0771353\pi$
$181$	15.5494	+	9.99302i	1.15578	+	0.742776i	0.184999	+	0.982739i	$0.440772\pi$
$182$		0			0
$183$		−	2.17425i		−	0.160725i
$184$		0			0
$185$	9.02449	+	5.21029i	0.663494	+	0.383068i
$186$		0			0
$187$	−3.69637	−	0.176080i	−0.270305	−	0.0128762i
$188$		0			0
$189$	−2.54715	+	6.42859i	−0.185278	+	0.467611i
$190$		0			0
$191$	5.05817	−	1.22710i	0.365997	−	0.0887898i	−0.0485430	−	0.998821i	$-0.515458\pi$
$191$	5.05817	−	1.22710i	0.365997	−	0.0887898i	0.414540	+	0.910031i	$0.363943\pi$
$192$		0			0
$193$	4.33744	+	0.414175i	0.312216	+	0.0298130i	0.249988	−	0.968249i	$-0.419573\pi$
$193$	4.33744	+	0.414175i	0.312216	+	0.0298130i	0.0622279	+	0.998062i	$0.480179\pi$
$194$		0			0
$195$	−4.07095	+	4.69813i	−0.291527	+	0.336440i
$196$		0			0
$197$	−2.80730	+	0.824297i	−0.200012	+	0.0587287i	−0.380204	−	0.924903i	$-0.624146\pi$
$197$	−2.80730	+	0.824297i	−0.200012	+	0.0587287i	0.180192	+	0.983631i	$0.442328\pi$
$198$		0			0
$199$	0.0892693	+	1.87399i	0.00632813	+	0.132844i	0.999821	+	0.0189453i	$0.00603085\pi$
$199$	0.0892693	+	1.87399i	0.00632813	+	0.132844i	−0.993492	+	0.113899i	$0.963666\pi$
$200$		0			0
$201$	−4.57955	+	3.60140i	−0.323017	+	0.254023i
$202$		0			0
$203$	25.5888	+	2.35169i	1.79598	+	0.165056i
$204$		0			0
$205$	12.6245	+	4.36939i	0.881735	+	0.305171i
$206$		0			0
$207$	−12.6191	+	4.54489i	−0.877088	+	0.315891i
$208$		0			0
$209$	3.68590	−	3.19385i	0.254959	−	0.220923i
$210$		0			0
$211$	−1.30517	+	9.07764i	−0.0898514	+	0.624931i	0.894282	+	0.447503i	$0.147687\pi$
$211$	−1.30517	+	9.07764i	−0.0898514	+	0.624931i	−0.984134	+	0.177428i	$0.943222\pi$
$212$		0			0
$213$	2.25204	−	5.62532i	0.154307	−	0.385441i
$214$		0			0
$215$	−8.90793	+	17.2790i	−0.607516	+	1.17842i
$216$		0			0
$217$	2.63076	−	13.9157i	0.178588	−	0.944656i
$218$		0			0
$219$	−2.95741	−	0.569993i	−0.199843	−	0.0385166i
$220$		0			0
$221$	−1.48071	+	15.5067i	−0.0996032	+	1.04309i
$222$		0			0
$223$	−2.46382	+	8.39099i	−0.164989	+	0.561902i	0.834944	+	0.550335i	$0.185500\pi$
$223$	−2.46382	+	8.39099i	−0.164989	+	0.561902i	−0.999933	+	0.0115669i	$0.996318\pi$
$224$		0			0
$225$	12.2956	−	26.9236i	0.819707	−	1.79491i
$226$		0			0
$227$	−6.26790	+	3.23133i	−0.416015	+	0.214471i	−0.653510	−	0.756918i	$-0.726704\pi$
$227$	−6.26790	+	3.23133i	−0.416015	+	0.214471i	0.237494	+	0.971389i	$0.423674\pi$
$228$		0			0
$229$	3.68237	+	6.37805i	0.243338	+	0.421473i	0.961663	−	0.274234i	$-0.0884243\pi$
$229$	3.68237	+	6.37805i	0.243338	+	0.421473i	−0.718325	+	0.695707i	$0.755091\pi$
$230$		0			0
$231$	−0.830760	+	0.538079i	−0.0546600	+	0.0354030i
$232$		0			0
$233$	0.212285	−	4.45640i	0.0139072	−	0.291949i	−0.981190	−	0.193045i	$-0.938164\pi$
$233$	0.212285	−	4.45640i	0.0139072	−	0.291949i	0.995097	−	0.0989032i	$-0.0315334\pi$
$234$		0			0
$235$	9.26303	−	6.59617i	0.604253	−	0.430287i
$236$		0			0
$237$	2.44270	+	0.717241i	0.158670	+	0.0465898i
$238$		0			0
$239$	1.79448	+	3.92937i	0.116075	+	0.254170i	0.958748	−	0.284256i	$-0.0917466\pi$
$239$	1.79448	+	3.92937i	0.116075	+	0.254170i	−0.842673	+	0.538426i	$0.819019\pi$
$240$		0			0
$241$	−6.36580	−	18.3928i	−0.410057	−	1.18478i	−0.941302	−	0.337565i	$-0.890397\pi$
$241$	−6.36580	−	18.3928i	−0.410057	−	1.18478i	0.531245	−	0.847218i	$-0.321724\pi$
$242$		0			0
$243$	7.65451	−	8.02782i	0.491037	−	0.514985i
$244$		0			0
$245$	25.7259	+	10.0875i	1.64357	+	0.644467i
$246$		0			0
$247$	−12.6908	−	16.1376i	−0.807495	−	1.02681i
$248$		0			0
$249$	3.20867	−	4.08015i	0.203341	−	0.258569i
$250$		0			0
$251$	−20.3636	−	23.5008i	−1.28534	−	1.48336i	−0.787818	−	0.615908i	$-0.788789\pi$
$251$	−20.3636	−	23.5008i	−1.28534	−	1.48336i	−0.497521	−	0.867452i	$-0.665756\pi$
$252$		0			0
$253$	−3.83185	−	1.07330i	−0.240907	−	0.0674780i
$254$		0			0
$255$	1.50224	+	7.79435i	0.0940737	+	0.488101i
$256$		0			0
$257$	0.978101	+	2.44318i	0.0610123	+	0.152401i	0.955742	−	0.294208i	$-0.0950557\pi$
$257$	0.978101	+	2.44318i	0.0610123	+	0.152401i	−0.894729	+	0.446609i	$0.852632\pi$
$258$		0			0
$259$	5.26196	−	4.59236i	0.326963	−	0.285356i
$260$		0			0
$261$	−24.1434	−	12.4468i	−1.49444	−	0.770436i
$262$		0			0
$263$	6.27459	+	1.52220i	0.386908	+	0.0938628i	0.424494	−	0.905431i	$-0.360452\pi$
$263$	6.27459	+	1.52220i	0.386908	+	0.0938628i	−0.0375866	+	0.999293i	$0.511967\pi$
$264$		0			0
$265$	−42.6906	−	36.9916i	−2.62246	−	2.27237i
$266$		0			0
$267$	−3.35021	+	1.52999i	−0.205030	+	0.0936340i
$268$		0			0
$269$	−4.25631	−	4.46389i	−0.259512	−	0.272168i	0.581069	−	0.813854i	$-0.302635\pi$
$269$	−4.25631	−	4.46389i	−0.259512	−	0.272168i	−0.840581	+	0.541686i	$0.817786\pi$
$270$		0			0
$271$	−2.10371	−	22.0310i	−0.127791	−	1.33829i	−0.800924	−	0.598766i	$-0.795658\pi$
$271$	−2.10371	−	22.0310i	−0.127791	−	1.33829i	0.673133	−	0.739522i	$-0.264948\pi$
$272$		0			0
$273$	2.09604	+	3.60083i	0.126858	+	0.217932i
$274$		0			0
$275$	7.60494	−	4.39071i	0.458595	−	0.264770i
$276$		0			0
$277$	6.85909	−	11.8803i	0.412123	−	0.713817i	−0.582999	−	0.812473i	$-0.698121\pi$
$277$	6.85909	−	11.8803i	0.412123	−	0.713817i	0.995122	+	0.0986556i	$0.0314542\pi$
$278$		0			0
$279$	−8.09352	+	12.5938i	−0.484547	+	0.753969i
$280$		0			0
$281$	6.67542	+	3.04856i	0.398222	+	0.181862i	0.604452	−	0.796642i	$-0.293392\pi$
$281$	6.67542	+	3.04856i	0.398222	+	0.181862i	−0.206230	+	0.978504i	$0.566119\pi$
$282$		0			0
$283$	−22.0865	+	21.0594i	−1.31290	+	1.25185i	−0.365892	+	0.930657i	$0.619236\pi$
$283$	−22.0865	+	21.0594i	−1.31290	+	1.25185i	−0.947013	+	0.321195i	$0.895915\pi$
$284$		0			0
$285$	−8.52177	−	6.06832i	−0.504786	−	0.359457i
$286$		0			0
$287$	5.50976	−	7.05771i	0.325231	−	0.416604i
$288$		0			0
$289$	2.09185	+	1.99458i	0.123050	+	0.117328i
$290$		0			0
$291$	0.217838	−	0.0103769i	0.0127699	−	0.000608306i
$292$		0			0
$293$	−1.41389	−	9.83380i	−0.0826002	−	0.574497i	−0.988525	−	0.151058i	$-0.951732\pi$
$293$	−1.41389	−	9.83380i	−0.0826002	−	0.574497i	0.905925	−	0.423439i	$-0.139177\pi$
$294$		0			0
$295$	−3.73186	−	0.536561i	−0.217277	−	0.0312398i
$296$		0			0
$297$	2.12940	−	0.410409i	0.123560	−	0.0238143i
$298$		0			0
$299$	−5.28036	+	15.8966i	−0.305371	+	0.919326i
$300$		0			0
$301$	9.02461	+	9.39763i	0.520170	+	0.541670i
$302$		0			0
$303$	−1.56211	+	0.625376i	−0.0897410	+	0.0359269i
$304$		0			0
$305$	17.6730	+	7.07520i	1.01195	+	0.405125i
$306$		0			0
$307$	11.8093	+	18.3756i	0.673993	+	1.04875i	0.994824	+	0.101617i	$0.0324016\pi$
$307$	11.8093	+	18.3756i	0.673993	+	1.04875i	−0.320831	+	0.947137i	$0.603962\pi$
$308$		0			0
$309$	−0.244305	−	0.832027i	−0.0138980	−	0.0473324i
$310$		0			0
$311$	13.0958	−	4.53250i	0.742594	−	0.257014i	0.0705326	−	0.997509i	$-0.477530\pi$
$311$	13.0958	−	4.53250i	0.742594	−	0.257014i	0.672062	+	0.740495i	$0.265409\pi$
$312$		0			0
$313$	2.47153	−	3.47078i	0.139699	−	0.196180i	−0.738799	−	0.673926i	$-0.764607\pi$
$313$	2.47153	−	3.47078i	0.139699	−	0.196180i	0.878498	+	0.477746i	$0.158546\pi$
$314$		0			0
$315$	−21.2115	−	20.0817i	−1.19513	−	1.13148i
$316$		0			0
$317$	−3.55261	+	0.339233i	−0.199535	+	0.0190533i	−0.194345	−	0.980933i	$-0.562258\pi$
$317$	−3.55261	+	0.339233i	−0.199535	+	0.0190533i	−0.00518988	+	0.999987i	$0.501652\pi$
$318$		0			0
$319$	−3.69279	−	7.16300i	−0.206756	−	0.401051i
$320$		0			0
$321$	4.10207			0.228955
$322$		0			0
$323$	−26.2145			−1.45861
$324$		0			0
$325$	−16.9382	−	32.8556i	−0.939563	−	1.82250i
$326$		0			0
$327$	5.93054	−	0.566298i	0.327960	−	0.0313164i
$328$		0			0
$329$	−2.17321	−	7.30511i	−0.119813	−	0.402744i
$330$		0			0
$331$	11.1788	−	15.6984i	0.614440	−	0.862861i	−0.383723	−	0.923448i	$-0.625358\pi$
$331$	11.1788	−	15.6984i	0.614440	−	0.862861i	0.998163	+	0.0605877i	$0.0192975\pi$
$332$		0			0
$333$	−6.97661	+	2.41463i	−0.382316	+	0.132321i
$334$		0			0
$335$	−14.3710	−	48.9432i	−0.785173	−	2.67405i
$336$		0			0
$337$	−1.33748	−	2.08116i	−0.0728571	−	0.113368i	0.802913	−	0.596096i	$-0.203282\pi$
$337$	−1.33748	−	2.08116i	−0.0728571	−	0.113368i	−0.875770	+	0.482728i	$0.839646\pi$
$338$		0			0
$339$	−7.31550	−	2.92868i	−0.397323	−	0.159064i
$340$		0			0
$341$	−4.12331	+	1.65073i	−0.223290	+	0.0893918i
$342$		0			0
$343$	11.9783	−	14.1252i	0.646765	−	0.762689i
$344$		0			0
$345$	−0.299564	+	8.53051i	−0.0161280	+	0.459267i
$346$		0			0
$347$	3.68159	−	0.709569i	0.197638	−	0.0380916i	−0.0894713	−	0.995989i	$-0.528518\pi$
$347$	3.68159	−	0.709569i	0.197638	−	0.0380916i	0.287110	+	0.957898i	$0.407306\pi$
$348$		0			0
$349$	28.0036	+	4.02631i	1.49900	+	0.215523i	0.842455	−	0.538767i	$-0.181109\pi$
$349$	28.0036	+	4.02631i	1.49900	+	0.215523i	0.656542	+	0.754290i	$0.272019\pi$
$350$		0			0
$351$	−1.29912	−	9.03560i	−0.0693421	−	0.482285i
$352$		0			0
$353$	27.7243	−	1.32067i	1.47561	−	0.0702922i	0.705732	−	0.708478i	$-0.250618\pi$
$353$	27.7243	−	1.32067i	1.47561	−	0.0702922i	0.769882	+	0.638186i	$0.220315\pi$
$354$		0			0
$355$	38.3960	+	36.6105i	2.03785	+	1.94308i
$356$		0			0
$357$	5.26861	+	0.738408i	0.278844	+	0.0390807i
$358$		0			0
$359$	−3.76795	−	2.68314i	−0.198865	−	0.141611i	0.476287	−	0.879290i	$-0.341982\pi$
$359$	−3.76795	−	2.68314i	−0.198865	−	0.141611i	−0.675152	+	0.737679i	$0.735922\pi$
$360$		0			0
$361$	11.2536	−	10.7303i	0.592293	−	0.564750i
$362$		0			0
$363$	−4.22900	−	1.93132i	−0.221965	−	0.101368i
$364$		0			0
$365$	14.2567	−	22.1839i	0.746230	−	1.16116i
$366$		0			0
$367$	−4.52660	+	7.84030i	−0.236287	+	0.409260i	−0.959646	−	0.281211i	$-0.909264\pi$
$367$	−4.52660	+	7.84030i	−0.236287	+	0.409260i	0.723359	+	0.690472i	$0.242597\pi$
$368$		0			0
$369$	−8.19658	+	4.73230i	−0.426697	+	0.246354i
$370$		0			0
$371$	−32.7197	+	19.0461i	−1.69872	+	0.988825i
$372$		0			0
$373$	0.0719428	+	0.753419i	0.00372506	+	0.0390106i	0.997143	−	0.0755325i	$-0.0240657\pi$
$373$	0.0719428	+	0.753419i	0.00372506	+	0.0390106i	−0.993418	+	0.114543i	$0.963460\pi$
$374$		0			0
$375$	−6.85747	−	7.19191i	−0.354118	−	0.371389i
$376$		0			0
$377$	−30.8576	+	14.0922i	−1.58925	+	0.725785i
$378$		0			0
$379$	−13.5418	−	11.7340i	−0.695595	−	0.602736i	0.233597	−	0.972333i	$-0.424950\pi$
$379$	−13.5418	−	11.7340i	−0.695595	−	0.602736i	−0.929192	+	0.369597i	$0.879496\pi$
$380$		0			0
$381$	7.57019	+	1.83651i	0.387833	+	0.0940872i
$382$		0			0
$383$	25.1535	+	12.9675i	1.28528	+	0.662610i	0.959199	−	0.282731i	$-0.0912403\pi$
$383$	25.1535	+	12.9675i	1.28528	+	0.662610i	0.326085	+	0.945341i	$0.394271\pi$
$384$		0			0
$385$	−1.67031	−	8.50362i	−0.0851267	−	0.433385i
$386$		0			0
$387$	−5.11876	−	12.7860i	−0.260201	−	0.649951i
$388$		0			0
$389$	4.16157	+	21.5923i	0.211000	+	1.09477i	0.920701	+	0.390269i	$0.127618\pi$
$389$	4.16157	+	21.5923i	0.211000	+	1.09477i	−0.709701	+	0.704503i	$0.751170\pi$
$390$		0			0
$391$	11.7876	+	17.8474i	0.596124	+	0.902584i
$392$		0			0
$393$	4.46326	+	5.15088i	0.225142	+	0.259827i
$394$		0			0
$395$	−13.7787	+	17.5210i	−0.693281	+	0.881579i
$396$		0			0
$397$	9.59043	+	12.1952i	0.481330	+	0.612061i	0.964699	−	0.263356i	$-0.0848294\pi$
$397$	9.59043	+	12.1952i	0.481330	+	0.612061i	−0.483369	+	0.875417i	$0.660587\pi$
$398$		0			0
$399$	−5.69700	+	4.08741i	−0.285207	+	0.204627i
$400$		0			0
$401$	24.2670	−	25.4505i	1.21184	−	1.27094i	0.259550	−	0.965730i	$-0.416426\pi$
$401$	24.2670	−	25.4505i	1.21184	−	1.27094i	0.952286	−	0.305207i	$-0.0987258\pi$
$402$		0			0
$403$	6.11486	+	17.6677i	0.304603	+	0.880092i
$404$		0			0
$405$	11.8264	+	25.8963i	0.587660	+	1.28680i
$406$		0			0
$407$	−2.10161	−	0.617087i	−0.104173	−	0.0305879i
$408$		0			0
$409$	−8.16597	+	5.81496i	−0.403781	+	0.287531i	−0.763849	−	0.645395i	$-0.776693\pi$
$409$	−8.16597	+	5.81496i	−0.403781	+	0.287531i	0.360068	+	0.932926i	$0.382753\pi$
$410$		0			0
$411$	0.282724	−	5.93510i	0.0139457	−	0.292757i
$412$		0			0
$413$	−1.14990	+	2.25010i	−0.0565831	+	0.110720i
$414$		0			0
$415$	22.7234	+	39.3582i	1.11545	+	1.93202i
$416$		0			0
$417$	1.75926	−	0.906961i	0.0861513	−	0.0444141i
$418$		0			0
$419$	9.87208	−	21.6168i	0.482283	−	1.05605i	−0.499547	−	0.866287i	$-0.666500\pi$
$419$	9.87208	−	21.6168i	0.482283	−	1.05605i	0.981830	−	0.189765i	$-0.0607726\pi$
$420$		0			0
$421$	7.42000	−	25.2702i	0.361629	−	1.23159i	−0.554999	−	0.831851i	$-0.687281\pi$
$421$	7.42000	−	25.2702i	0.361629	−	1.23159i	0.916627	−	0.399743i	$-0.130901\pi$
$422$		0			0
$423$	−0.765810	+	8.01992i	−0.0372349	+	0.389942i
$424$		0			0
$425$	−46.3468	−	8.93262i	−2.24815	−	0.433296i
$426$		0			0
$427$	8.32091	−	9.67209i	0.402677	−	0.468065i
$428$		0			0
$429$	0.598749	−	1.16141i	0.0289079	−	0.0560734i
$430$		0			0
$431$	−4.89543	+	12.2282i	−0.235804	+	0.589011i	−0.998319	−	0.0579601i	$-0.981540\pi$
$431$	−4.89543	+	12.2282i	−0.235804	+	0.589011i	0.762514	+	0.646971i	$0.223965\pi$
$432$		0			0
$433$	1.88602	−	13.1175i	0.0906362	−	0.630389i	−0.892978	−	0.450101i	$-0.851388\pi$
$433$	1.88602	−	13.1175i	0.0906362	−	0.630389i	0.983614	−	0.180288i	$-0.0577029\pi$
$434$		0			0
$435$	−13.0642	+	11.3202i	−0.626382	+	0.542763i
$436$		0			0
$437$	−27.4756	−	6.30299i	−1.31433	−	0.301513i
$438$		0			0
$439$	−6.01040	−	2.08022i	−0.286861	−	0.0992834i	0.179848	−	0.983694i	$-0.442439\pi$
$439$	−6.01040	−	2.08022i	−0.286861	−	0.0992834i	−0.466709	+	0.884411i	$0.654560\pi$
$440$		0			0
$441$	−17.3365	+	9.09418i	−0.825550	+	0.433056i
$442$		0			0
$443$	−7.41401	+	5.83044i	−0.352250	+	0.277013i	−0.778567	−	0.627561i	$-0.784053\pi$
$443$	−7.41401	+	5.83044i	−0.352250	+	0.277013i	0.426317	+	0.904574i	$0.359811\pi$
$444$		0			0
$445$	−1.53436	−	32.2103i	−0.0727358	−	1.52691i
$446$		0			0
$447$	−8.90319	+	2.61421i	−0.421106	+	0.123648i
$448$		0			0
$449$	−4.58682	+	5.29347i	−0.216466	+	0.249815i	−0.853589	−	0.520947i	$-0.825579\pi$
$449$	−4.58682	+	5.29347i	−0.216466	+	0.249815i	0.637123	+	0.770762i	$0.280124\pi$
$450$		0			0
$451$	−2.79530	−	0.266919i	−0.131626	−	0.0125687i
$452$		0			0
$453$	−4.26163	+	1.03386i	−0.200229	+	0.0485750i
$454$		0			0
$455$	−36.0893	+	5.31985i	−1.69189	+	0.249398i
$456$		0			0
$457$	−10.2021	−	0.485987i	−0.477235	−	0.0227335i	−0.192413	−	0.981314i	$-0.561631\pi$
$457$	−10.2021	−	0.485987i	−0.477235	−	0.0227335i	−0.284822	+	0.958580i	$0.591934\pi$
$458$		0			0
$459$	−10.0945	−	5.82805i	−0.471170	−	0.272030i
$460$		0			0
$461$		−	15.0965i		−	0.703113i	−0.936167	−	0.351556i	$-0.885653\pi$
$461$		−	15.0965i		−	0.703113i	0.936167	−	0.351556i	$-0.114347\pi$
$462$		0			0
$463$	17.4625	+	11.2225i	0.811551	+	0.521552i	0.879366	−	0.476146i	$-0.157967\pi$
$463$	17.4625	+	11.2225i	0.811551	+	0.521552i	−0.0678155	+	0.997698i	$0.521603\pi$
$464$		0			0
$465$	5.52623	+	7.76051i	0.256273	+	0.359885i
$466$		0			0
$467$	−7.17960	−	29.5947i	−0.332232	−	1.36948i	−0.855717	−	0.517445i	$-0.826883\pi$
$467$	−7.17960	−	29.5947i	−0.332232	−	1.36948i	0.523485	−	0.852035i	$-0.324632\pi$
$468$		0			0
$469$	−34.1546	−	1.50534i	−1.57711	−	0.0695100i
$470$		0			0
$471$	1.22605	−	6.36133i	0.0564933	−	0.293115i
$472$		0			0
$473$	0.963345	−	3.97096i	0.0442946	−	0.182585i
$474$		0			0
$475$	52.3318	−	33.6316i	2.40115	−	1.54312i
$476$		0			0
$477$	39.6123	−	5.69539i	1.81372	−	0.260774i
$478$		0			0
$479$	5.08869	+	4.00179i	0.232508	+	0.182846i	0.727615	−	0.685986i	$-0.240629\pi$
$479$	5.08869	+	4.00179i	0.232508	+	0.182846i	−0.495107	+	0.868832i	$0.664871\pi$
$480$		0			0
$481$	−3.01557	+	8.71293i	−0.137498	+	0.397275i
$482$		0			0
$483$	5.34452	+	2.04071i	0.243184	+	0.0928556i
$484$		0			0
$485$	−0.624517	+	1.80442i	−0.0283579	+	0.0819346i
$486$		0			0
$487$	17.7092	+	13.9267i	0.802482	+	0.631079i	0.932801	−	0.360393i	$-0.117357\pi$
$487$	17.7092	+	13.9267i	0.802482	+	0.631079i	−0.130318	+	0.991472i	$0.541600\pi$
$488$		0			0
$489$	−5.12683	+	0.737127i	−0.231843	+	0.0333341i
$490$		0			0
$491$	11.4500	−	7.35849i	0.516733	−	0.332084i	−0.256146	−	0.966638i	$-0.582453\pi$
$491$	11.4500	−	7.35849i	0.516733	−	0.332084i	0.772878	+	0.634554i	$0.218816\pi$
$492$		0			0
$493$	−10.2121	+	42.0951i	−0.459932	+	1.89587i
$494$		0			0
$495$	−1.73365	+	8.99505i	−0.0779220	+	0.404298i
$496$		0			0
$497$	31.5463	−	16.4054i	1.41505	−	0.735885i
$498$		0			0
$499$	−4.57251	−	18.8481i	−0.204694	−	0.843758i	−0.977810	−	0.209494i	$-0.932818\pi$
$499$	−4.57251	−	18.8481i	−0.204694	−	0.843758i	0.773116	−	0.634264i	$-0.218697\pi$
$500$		0			0
$501$	−0.592908	−	0.832623i	−0.0264892	−	0.0371988i
$502$		0			0
$503$	26.3387	+	16.9269i	1.17438	+	0.754731i	0.974346	−	0.225057i	$-0.0722567\pi$
$503$	26.3387	+	16.9269i	1.17438	+	0.754731i	0.200039	+	0.979788i	$0.435893\pi$
$504$		0			0
$505$		−	14.7323i		−	0.655580i
$506$		0			0
$507$	0.312620	+	0.180491i	0.0138839	+	0.00801590i
$508$		0			0
$509$	−10.8710	−	0.517851i	−0.481850	−	0.0229534i	−0.194748	−	0.980853i	$-0.562389\pi$
$509$	−10.8710	−	0.517851i	−0.481850	−	0.0229534i	−0.287102	+	0.957900i	$0.592692\pi$
$510$		0			0
$511$	−10.9745	−	13.8536i	−0.485485	−	0.612849i
$512$		0			0
$513$	14.9291	−	3.62176i	0.659136	−	0.159905i
$514$		0			0
$515$	7.55795	+	0.721697i	0.333043	+	0.0318018i
$516$		0			0
$517$	−1.56526	+	1.80641i	−0.0688402	+	0.0794459i
$518$		0			0
$519$	3.76694	−	1.10607i	0.165350	−	0.0485512i
$520$		0			0
$521$	0.879149	+	18.4556i	0.0385162	+	0.808555i	0.932656	+	0.360767i	$0.117485\pi$
$521$	0.879149	+	18.4556i	0.0385162	+	0.808555i	−0.894140	+	0.447788i	$0.852212\pi$
$522$		0			0
$523$	16.2723	−	12.7967i	0.711539	−	0.559561i	−0.195450	−	0.980714i	$-0.562617\pi$
$523$	16.2723	−	12.7967i	0.711539	−	0.559561i	0.906990	+	0.421153i	$0.138374\pi$
$524$		0			0
$525$	−11.4650	+	5.28523i	−0.500375	+	0.230666i
$526$		0			0
$527$	22.5597	+	7.80799i	0.982717	+	0.340122i
$528$		0			0
$529$	8.06343	+	21.5402i	0.350584	+	0.936531i
$530$		0			0
$531$	2.01867	−	1.74919i	0.0876030	−	0.0759084i
$532$		0			0
$533$	−1.68218	+	11.6998i	−0.0728633	+	0.506775i
$534$		0			0
$535$	−13.3485	+	33.3429i	−0.577105	+	1.44154i
$536$		0			0
$537$	2.81721	−	5.46462i	0.121572	−	0.235816i
$538$		0			0
$539$	−5.75485	−	0.785711i	−0.247879	−	0.0338429i
$540$		0			0
$541$	−13.1229	−	2.52924i	−0.564199	−	0.108740i	−0.100827	−	0.994904i	$-0.532149\pi$
$541$	−13.1229	−	2.52924i	−0.564199	−	0.108740i	−0.463373	+	0.886164i	$0.653361\pi$
$542$		0			0
$543$	−0.792168	+	8.29596i	−0.0339952	+	0.356014i
$544$		0			0
$545$	−14.6954	+	50.0480i	−0.629482	+	2.14382i
$546$		0			0
$547$	13.5452	−	29.6598i	0.579149	−	1.26816i	−0.362632	−	0.931932i	$-0.618122\pi$
$547$	13.5452	−	29.6598i	0.579149	−	1.26816i	0.941781	−	0.336227i	$-0.109151\pi$
$548$		0			0
$549$	−11.9876	+	6.18002i	−0.511617	+	0.263757i
$550$		0			0
$551$	−28.5442	−	49.4399i	−1.21602	−	2.10621i
$552$		0			0
$553$	8.12137	+	12.5389i	0.345356	+	0.533208i
$554$		0			0
$555$	−0.223555	+	4.69299i	−0.00948937	+	0.199206i
$556$		0			0
$557$	−8.87585	+	6.32046i	−0.376082	+	0.267807i	−0.752431	−	0.658671i	$-0.771119\pi$
$557$	−8.87585	+	6.32046i	−0.376082	+	0.267807i	0.376349	+	0.926478i	$0.377179\pi$
$558$		0			0
$559$	−16.5036	−	4.84588i	−0.698026	−	0.204959i
$560$		0			0
$561$	−0.693105	−	1.51769i	−0.0292629	−	0.0640769i
$562$		0			0
$563$	11.7641	+	33.9901i	0.495797	+	1.43251i	0.864344	+	0.502901i	$0.167734\pi$
$563$	11.7641	+	33.9901i	0.495797	+	1.43251i	−0.368547	+	0.929609i	$0.620145\pi$
$564$		0			0
$565$	47.6104	−	49.9324i	2.00299	−	2.10067i
$566$		0			0
$567$	18.9876	−	1.88122i	0.797405	−	0.0790039i
$568$		0			0
$569$	−9.42841	−	11.9892i	−0.395260	−	0.502614i	0.547168	−	0.837023i	$-0.315706\pi$
$569$	−9.42841	−	11.9892i	−0.395260	−	0.502614i	−0.942428	+	0.334409i	$0.891463\pi$
$570$		0			0
$571$	−21.9977	+	27.9724i	−0.920577	+	1.17061i	0.0643999	+	0.997924i	$0.479487\pi$
$571$	−21.9977	+	27.9724i	−0.920577	+	1.17061i	−0.984977	+	0.172685i	$0.944756\pi$
$572$		0			0
$573$	1.53677	+	1.77353i	0.0641997	+	0.0740904i
$574$		0			0
$575$	−46.4287	−	20.5060i	−1.93621	−	0.855157i
$576$		0			0
$577$	−5.56380	−	28.8677i	−0.231624	−	1.20178i	−0.892417	−	0.451211i	$-0.850992\pi$
$577$	−5.56380	−	28.8677i	−0.231624	−	1.20178i	0.660793	−	0.750568i	$-0.270220\pi$
$578$		0			0
$579$	0.730134	+	1.82379i	0.0303433	+	0.0757940i
$580$		0			0
$581$	29.8885	−	5.87078i	1.23998	−	0.243561i
$582$		0			0
$583$	10.5534	+	5.44066i	0.437077	+	0.225329i
$584$		0			0
$585$	37.4738	+	9.09106i	1.54935	+	0.375869i
$586$		0			0
$587$	22.1541	+	19.1966i	0.914397	+	0.792330i	0.978635	−	0.205605i	$-0.0659162\pi$
$587$	22.1541	+	19.1966i	0.914397	+	0.792330i	−0.0642380	+	0.997935i	$0.520462\pi$
$588$		0			0
$589$	−28.6197	+	13.0702i	−1.17926	+	0.538548i
$590$		0			0
$591$	−0.910322	−	0.954718i	−0.0374457	−	0.0392719i
$592$		0			0
$593$	−0.0482041	−	0.504817i	−0.00197951	−	0.0207303i	0.994428	−	0.105416i	$-0.0336174\pi$
$593$	−0.0482041	−	0.504817i	−0.00197951	−	0.0207303i	−0.996408	+	0.0846857i	$0.973011\pi$
$594$		0			0
$595$	−23.1465	+	40.4220i	−0.948913	+	1.65714i
$596$		0			0
$597$	−0.732555	+	0.422941i	−0.0299815	+	0.0173098i
$598$		0			0
$599$	0.920217	−	1.59386i	0.0375990	−	0.0651235i	−0.846614	−	0.532208i	$-0.821362\pi$
$599$	0.920217	−	1.59386i	0.0375990	−	0.0651235i	0.884213	+	0.467085i	$0.154696\pi$
$600$		0			0
$601$	−21.0011	+	32.6783i	−0.856653	+	1.33298i	0.0849964	+	0.996381i	$0.472912\pi$
$601$	−21.0011	+	32.6783i	−0.856653	+	1.33298i	−0.941649	+	0.336596i	$0.890724\pi$
$602$		0			0
$603$	32.8728	+	15.0125i	1.33868	+	0.611356i
$604$		0			0
$605$	29.4599	−	28.0899i	1.19771	−	1.14202i
$606$		0			0
$607$	10.6032	+	7.55052i	0.430371	+	0.306466i	0.774637	−	0.632406i	$-0.217933\pi$
$607$	10.6032	+	7.55052i	0.430371	+	0.306466i	−0.344266	+	0.938872i	$0.611872\pi$
$608$		0			0
$609$	4.34421	+	10.7405i	0.176036	+	0.435228i
$610$		0			0
$611$	7.28182	+	6.94320i	0.294591	+	0.280892i
$612$		0			0
$613$	5.47229	−	0.260677i	0.221024	−	0.0105287i	0.0632221	−	0.997999i	$-0.479862\pi$
$613$	5.47229	−	0.260677i	0.221024	−	0.0105287i	0.157802	+	0.987471i	$0.449559\pi$
$614$		0			0
$615$	0.857200	+	5.96196i	0.0345656	+	0.240409i
$616$		0			0
$617$	−38.4283	−	5.52516i	−1.54707	−	0.222435i	−0.684740	−	0.728787i	$-0.740084\pi$
$617$	−38.4283	−	5.52516i	−1.54707	−	0.222435i	−0.862327	+	0.506353i	$0.830993\pi$
$618$		0			0
$619$	42.7823	−	8.24562i	1.71957	−	0.331419i	0.768371	−	0.640005i	$-0.221068\pi$
$619$	42.7823	−	8.24562i	1.71957	−	0.331419i	0.951196	+	0.308586i	$0.0998557\pi$
$620$		0			0
$621$	−9.17879	−	8.53552i	−0.368332	−	0.342519i
$622$		0			0
$623$	−20.7586	−	6.01522i	−0.831677	−	0.240995i
$624$		0			0
$625$	31.6470	−	12.6696i	1.26588	−	0.506782i
$626$		0			0
$627$	2.04143	+	0.817267i	0.0815271	+	0.0326385i
$628$		0			0
$629$	6.36493	+	9.90402i	0.253786	+	0.394899i
$630$		0			0
$631$	11.9330	+	40.6401i	0.475046	+	1.61786i	0.753528	+	0.657416i	$0.228350\pi$
$631$	11.9330	+	40.6401i	0.475046	+	1.61786i	−0.278482	+	0.960441i	$0.589831\pi$
$632$		0			0
$633$	−3.90749	+	1.35240i	−0.155309	+	0.0537529i
$634$		0			0
$635$	−39.5617	+	55.5566i	−1.56996	+	2.20470i
$636$		0			0
$637$	−4.45629	+	24.0398i	−0.176565	+	0.952490i
$638$		0			0
$639$	−37.4158	+	3.57278i	−1.48015	+	0.141337i
$640$		0			0
$641$	0.614149	+	1.19128i	0.0242574	+	0.0470528i	0.900653	−	0.434540i	$-0.143089\pi$
$641$	0.614149	+	1.19128i	0.0242574	+	0.0470528i	−0.876395	+	0.481592i	$0.840059\pi$
$642$		0			0
$643$	−40.3560			−1.59148			−0.795742	−	0.605636i	$-0.792919\pi$
$643$	−40.3560			−1.59148			−0.795742	+	0.605636i	$0.792919\pi$
$644$		0			0
$645$	−8.76488			−0.345117
$646$		0			0
$647$	5.58285	+	10.8292i	0.219485	+	0.425741i	0.972711	−	0.232021i	$-0.0745338\pi$
$647$	5.58285	+	10.8292i	0.219485	+	0.425741i	−0.753226	+	0.657762i	$0.771503\pi$
$648$		0			0
$649$	0.788887	−	0.0753296i	0.0309665	−	0.00295694i
$650$		0			0
$651$	6.12018	−	1.82070i	0.239869	−	0.0713588i
$652$		0			0
$653$	−18.2711	+	25.6582i	−0.715004	+	1.00408i	0.283972	+	0.958833i	$0.408348\pi$
$653$	−18.2711	+	25.6582i	−0.715004	+	1.00408i	−0.998976	+	0.0452497i	$0.985592\pi$
$654$		0			0
$655$	−56.3917	+	19.5174i	−2.20341	+	0.762606i
$656$		0			0
$657$	5.26341	+	17.9255i	0.205345	+	0.699342i
$658$		0			0
$659$	20.3930	+	31.7321i	0.794398	+	1.23611i	0.967915	+	0.251276i	$0.0808502\pi$
$659$	20.3930	+	31.7321i	0.794398	+	1.23611i	−0.173518	+	0.984831i	$0.555513\pi$
$660$		0			0
$661$	0.525609	+	0.210422i	0.0204438	+	0.00818447i	0.381862	−	0.924219i	$-0.375283\pi$
$661$	0.525609	+	0.210422i	0.0204438	+	0.00818447i	−0.361418	+	0.932404i	$0.617707\pi$
$662$		0			0
$663$	−6.52018	+	2.61029i	−0.253223	+	0.101375i
$664$		0			0
$665$	−14.6852	−	59.6077i	−0.569467	−	2.31149i
$666$		0			0
$667$	−20.8247	+	41.6647i	−0.806337	+	1.61326i
$668$		0			0
$669$	−3.87169	+	0.746208i	−0.149688	+	0.0288501i
$670$		0			0
$671$	−3.96063	−	0.569452i	−0.152898	−	0.0219835i
$672$		0			0
$673$	5.74311	+	39.9442i	0.221381	+	1.53974i	0.732824	+	0.680419i	$0.238202\pi$
$673$	5.74311	+	39.9442i	0.221381	+	1.53974i	−0.511443	+	0.859317i	$0.670889\pi$
$674$		0			0
$675$	27.6286	−	1.31611i	1.06342	−	0.0506571i
$676$		0			0
$677$	3.54970	+	3.38463i	0.136426	+	0.130082i	0.755220	−	0.655471i	$-0.227530\pi$
$677$	3.54970	+	3.38463i	0.136426	+	0.130082i	−0.618794	+	0.785553i	$0.712378\pi$
$678$		0			0
$679$	1.00876	+	0.787511i	0.0387126	+	0.0302219i
$680$		0			0
$681$	−2.58989	−	1.84425i	−0.0992449	−	0.0706720i
$682$		0			0
$683$	0.864291	−	0.824100i	0.0330712	−	0.0315333i	−0.673363	−	0.739312i	$-0.735151\pi$
$683$	0.864291	−	0.824100i	0.0330712	−	0.0315333i	0.706434	+	0.707778i	$0.250303\pi$
$684$		0			0
$685$	47.3222	+	21.6113i	1.80809	+	0.825727i
$686$		0			0
$687$	−1.79521	+	2.79340i	−0.0684916	+	0.106575i
$688$		0			0
$689$	24.9898	−	43.2837i	0.952037	−	1.64898i
$690$		0			0
$691$	17.9901	−	10.3866i	0.684376	−	0.395125i	−0.117126	−	0.993117i	$-0.537368\pi$
$691$	17.9901	−	10.3866i	0.684376	−	0.395125i	0.801502	+	0.597992i	$0.204035\pi$
$692$		0			0
$693$	5.32797	+	3.05091i	0.202393	+	0.115894i
$694$		0			0
$695$	1.64728	+	17.2511i	0.0624849	+	0.654372i
$696$		0			0
$697$	10.4153	+	10.9233i	0.394509	+	0.413750i
$698$		0			0
$699$	1.82975	−	0.835619i	0.0692075	−	0.0316060i
$700$		0			0
$701$	−29.4913	−	25.5543i	−1.11387	−	0.965174i	−0.114270	−	0.993450i	$-0.536453\pi$
$701$	−29.4913	−	25.5543i	−1.11387	−	0.965174i	−0.999600	+	0.0282754i	$0.990998\pi$
$702$		0			0
$703$	−15.0787	−	3.65806i	−0.568706	−	0.137966i
$704$		0			0
$705$	4.55714	+	2.34937i	0.171632	+	0.0884823i
$706$		0			0
$707$	−9.34233	−	3.19627i	−0.351354	−	0.120208i
$708$		0			0
$709$	14.6584	+	36.6148i	0.550506	+	1.37510i	0.899067	+	0.437812i	$0.144246\pi$
$709$	14.6584	+	36.6148i	0.550506	+	1.37510i	−0.348561	+	0.937286i	$0.613329\pi$
$710$		0			0
$711$	−2.98859	−	15.5063i	−0.112081	−	0.581531i
$712$		0			0
$713$	21.7676	+	13.6079i	0.815205	+	0.509618i
$714$		0			0
$715$	7.49191	+	8.64613i	0.280182	+	0.323347i
$716$		0			0
$717$	−1.20394	+	1.53094i	−0.0449621	+	0.0571740i
$718$		0			0
$719$	15.2417	+	19.3814i	0.568420	+	0.722805i	0.982256	−	0.187546i	$-0.0600535\pi$
$719$	15.2417	+	19.3814i	0.568420	+	0.722805i	−0.413835	+	0.910352i	$0.635811\pi$
$720$		0			0
$721$	2.09740	−	4.63620i	0.0781113	−	0.172661i
$722$		0			0
$723$	6.05569	−	6.35102i	0.225213	−	0.236197i
$724$		0			0
$725$	−33.6190	−	97.1357i	−1.24858	−	3.60753i
$726$		0			0
$727$	−10.8882	−	23.8419i	−0.403821	−	0.884246i	−0.996868	−	0.0790777i	$-0.974802\pi$
$727$	−10.8882	−	23.8419i	−0.403821	−	0.884246i	0.593047	−	0.805168i	$-0.297925\pi$
$728$		0			0
$729$	−15.9604	−	4.68640i	−0.591127	−	0.173570i
$730$		0			0
$731$	−17.8904	+	12.7397i	−0.661701	+	0.471195i
$732$		0			0
$733$	1.59691	−	33.5232i	0.0589831	−	1.23821i	−0.754375	−	0.656444i	$-0.772060\pi$
$733$	1.59691	−	33.5232i	0.0589831	−	1.23821i	0.813358	−	0.581764i	$-0.197637\pi$
$734$		0			0
$735$	1.27242	+	12.3937i	0.0469338	+	0.457147i
$736$		0			0
$737$	5.36090	+	9.28536i	0.197471	+	0.342031i
$738$		0			0
$739$	25.6790	−	13.2385i	0.944619	−	0.486985i	0.0841305	−	0.996455i	$-0.473189\pi$
$739$	25.6790	−	13.2385i	0.944619	−	0.486985i	0.860489	+	0.509470i	$0.170158\pi$
$740$		0			0
$741$	3.84521	−	8.41983i	0.141257	−	0.309310i
$742$		0			0
$743$	−8.29004	+	28.2333i	−0.304132	+	1.03578i	0.655657	+	0.755059i	$0.272392\pi$
$743$	−8.29004	+	28.2333i	−0.304132	+	1.03578i	−0.959790	+	0.280721i	$0.909427\pi$
$744$		0			0
$745$	7.72259	−	80.8746i	0.282934	−	2.96302i
$746$		0			0
$747$	−31.6158	−	6.09344i	−1.15676	−	0.222947i
$748$		0			0
$749$	18.2479	+	15.6987i	0.666765	+	0.573619i
$750$		0			0
$751$	−2.42494	+	4.70373i	−0.0884873	+	0.171641i	−0.928926	−	0.370265i	$-0.879267\pi$
$751$	−2.42494	+	4.70373i	−0.0884873	+	0.171641i	0.840439	+	0.541906i	$0.182297\pi$
$752$		0			0
$753$	5.21079	−	13.0159i	0.189892	−	0.474327i
$754$		0			0
$755$	5.46416	−	38.0041i	0.198861	−	1.38311i
$756$		0			0
$757$	−15.2825	+	13.2423i	−0.555451	+	0.481301i	−0.886766	−	0.462220i	$-0.847053\pi$
$757$	−15.2825	+	13.2423i	−0.555451	+	0.481301i	0.331315	+	0.943520i	$0.392508\pi$
$758$		0			0
$759$	−0.361536	−	1.75735i	−0.0131229	−	0.0637878i
$760$		0			0
$761$	34.9321	+	12.0901i	1.26629	+	0.438267i	0.875949	−	0.482404i	$-0.160236\pi$
$761$	34.9321	+	12.0901i	1.26629	+	0.438267i	0.390340	+	0.920671i	$0.372357\pi$
$762$		0			0
$763$	28.5490	+	20.1771i	1.03354	+	0.730462i
$764$		0			0
$765$	38.7036	−	30.4368i	1.39933	−	1.10045i
$766$		0			0
$767$	−0.158727	−	3.33208i	−0.00573129	−	0.120315i
$768$		0			0
$769$	−37.0973	+	10.8928i	−1.33776	+	0.392803i	−0.870871	−	0.491511i	$-0.836445\pi$
$769$	−37.0973	+	10.8928i	−1.33776	+	0.392803i	−0.466893	+	0.884314i	$0.654627\pi$
$770$		0			0
$771$	−0.777022	+	0.896732i	−0.0279838	+	0.0322950i
$772$		0			0
$773$	7.71694	+	0.736879i	0.277559	+	0.0265037i	0.232907	−	0.972499i	$-0.425176\pi$
$773$	7.71694	+	0.736879i	0.277559	+	0.0265037i	0.0446518	+	0.999003i	$0.485782\pi$
$774$		0			0
$775$	−55.0530	+	13.3557i	−1.97756	+	0.479751i
$776$		0			0
$777$	2.92750	+	1.15994i	0.105023	+	0.0416126i
$778$		0			0
$779$	−19.8692	−	0.946488i	−0.711889	−	0.0339115i
$780$		0			0
$781$	−9.65728	−	5.57563i	−0.345564	−	0.199512i
$782$		0			0
$783$		−	25.3840i		−	0.907149i
$784$		0			0
$785$	47.7172	+	30.6660i	1.70310	+	1.09452i
$786$		0			0
$787$	−24.7390	−	34.7411i	−0.881852	−	1.23839i	−0.970202	−	0.242298i	$-0.922099\pi$
$787$	−24.7390	−	34.7411i	−0.881852	−	1.23839i	0.0883500	−	0.996089i	$-0.471841\pi$
$788$		0			0
$789$	0.686311	+	2.82901i	0.0244333	+	0.100716i
$790$		0			0
$791$	−21.3346	−	41.0247i	−0.758571	−	1.45867i
$792$		0			0
$793$	−3.18763	+	16.5390i	−0.113196	+	0.587317i
$794$		0			0
$795$	6.00443	−	24.7506i	0.212955	−	0.877813i
$796$		0			0
$797$	19.2056	−	12.3427i	0.680298	−	0.437201i	−0.154327	−	0.988020i	$-0.549321\pi$
$797$	19.2056	−	12.3427i	0.680298	−	0.437201i	0.834625	+	0.550819i	$0.185684\pi$
$798$		0			0
$799$	12.7166	−	1.82837i	0.449880	−	0.0646830i
$800$		0			0
$801$	17.9580	+	14.1223i	0.634515	+	0.498988i
$802$		0			0
$803$	−1.81287	+	5.23793i	−0.0639747	+	0.184843i
$804$		0			0
$805$	−33.9790	+	36.8012i	−1.19760	+	1.29707i
$806$		0			0
$807$	0.909541	−	2.62795i	0.0320173	−	0.0925081i
$808$		0			0
$809$	22.6080	+	17.7791i	0.794856	+	0.625081i	0.930756	−	0.365641i	$-0.119150\pi$
$809$	22.6080	+	17.7791i	0.794856	+	0.625081i	−0.135900	+	0.990723i	$0.543393\pi$
$810$		0			0
$811$	11.3835	−	1.63671i	0.399730	−	0.0574725i	0.0604815	−	0.998169i	$-0.480736\pi$
$811$	11.3835	−	1.63671i	0.399730	−	0.0574725i	0.339248	+	0.940697i	$0.389827\pi$
$812$		0			0
$813$	8.39424	−	5.39465i	0.294399	−	0.189199i
$814$		0			0
$815$	10.6915	−	44.0711i	0.374508	−	1.54374i
$816$		0			0
$817$	5.47805	−	28.4228i	0.191653	−	0.994388i
$818$		0			0
$819$	13.8952	−	21.7912i	0.485536	−	0.761446i
$820$		0			0
$821$	−5.25197	−	21.6489i	−0.183295	−	0.755552i	−0.987026	−	0.160559i	$-0.948670\pi$
$821$	−5.25197	−	21.6489i	−0.183295	−	0.755552i	0.803731	−	0.594992i	$-0.202845\pi$
$822$		0			0
$823$	−31.2298	−	43.8561i	−1.08860	−	1.52873i	−0.825873	−	0.563856i	$-0.809317\pi$
$823$	−31.2298	−	43.8561i	−1.08860	−	1.52873i	−0.262728	−	0.964870i	$-0.584622\pi$
$824$		0			0
$825$	3.33075	+	2.14054i	0.115962	+	0.0745240i
$826$		0			0
$827$			25.7798i			0.896451i	0.893921	+	0.448225i	$0.147944\pi$
$827$			25.7798i			0.896451i	−0.893921	+	0.448225i	$0.852056\pi$
$828$		0			0
$829$	−4.18640	−	2.41702i	−0.145400	−	0.0839466i	0.425535	−	0.904942i	$-0.360086\pi$
$829$	−4.18640	−	2.41702i	−0.145400	−	0.0839466i	−0.570935	+	0.820995i	$0.693419\pi$
$830$		0			0
$831$	6.17808	+	0.294298i	0.214315	+	0.0102091i
$832$		0			0
$833$	20.6113	+	23.4478i	0.714140	+	0.812420i
$834$		0			0
$835$	8.69718	−	2.10991i	0.300978	−	0.0730165i
$836$		0			0
$837$	−13.9265	−	1.32982i	−0.481369	−	0.0459652i
$838$		0			0
$839$	2.42981	−	2.80415i	0.0838865	−	0.0968102i	−0.712255	−	0.701921i	$-0.752326\pi$
$839$	2.42981	−	2.80415i	0.0838865	−	0.0968102i	0.796141	+	0.605111i	$0.206871\pi$
$840$		0			0
$841$	−62.6848	+	18.4059i	−2.16155	+	0.634687i
$842$		0			0
$843$	0.157436	+	3.30499i	0.00542239	+	0.113830i
$844$		0			0
$845$	−2.48438	+	1.95374i	−0.0854652	+	0.0672106i
$846$		0			0
$847$	−11.4214	−	24.7759i	−0.392443	−	0.851309i
$848$		0			0
$849$	−13.0026	−	4.50023i	−0.446247	−	0.154448i
$850$		0			0
$851$	4.28981	+	11.9109i	0.147053	+	0.408299i
$852$		0			0
$853$	7.12279	−	6.17193i	0.243880	−	0.211323i	−0.524341	−	0.851509i	$-0.675688\pi$
$853$	7.12279	−	6.17193i	0.243880	−	0.211323i	0.768220	+	0.640186i	$0.221143\pi$
$854$		0			0
$855$	−9.23523	+	64.2324i	−0.315838	+	2.19670i
$856$		0			0
$857$	5.01707	−	12.5320i	0.171380	−	0.428086i	−0.817666	−	0.575692i	$-0.804733\pi$
$857$	5.01707	−	12.5320i	0.171380	−	0.428086i	0.989046	+	0.147606i	$0.0471568\pi$
$858$		0			0
$859$	23.5043	−	45.5919i	0.801955	−	1.55558i	−0.0292249	−	0.999573i	$-0.509304\pi$
$859$	23.5043	−	45.5919i	0.801955	−	1.55558i	0.831180	−	0.556003i	$-0.187666\pi$
$860$		0			0
$861$	3.96668	+	0.749902i	0.135184	+	0.0255566i
$862$		0			0
$863$	16.4856	+	3.17734i	0.561177	+	0.108158i	0.461949	−	0.886907i	$-0.347150\pi$
$863$	16.4856	+	3.17734i	0.561177	+	0.108158i	0.0992284	+	0.995065i	$0.468363\pi$
$864$		0			0
$865$	−3.26743	+	34.2180i	−0.111096	+	1.16345i
$866$		0			0
$867$	−0.367146	+	1.25038i	−0.0124689	+	0.0424652i
$868$		0			0
$869$	1.94629	−	4.26178i	0.0660233	−	0.144571i
$870$		0			0
$871$	40.1155	−	20.6810i	1.35926	−	0.700747i
$872$		0			0
$873$	−0.676388	−	1.17154i	−0.0228923	−	0.0396506i
$874$		0			0
$875$	−2.98164	−	58.2366i	−0.100798	−	1.96876i
$876$		0			0
$877$	1.94576	−	40.8465i	0.0657036	−	1.37929i	−0.689732	−	0.724065i	$-0.742272\pi$
$877$	1.94576	−	40.8465i	0.0657036	−	1.37929i	0.755436	−	0.655223i	$-0.227425\pi$
$878$		0			0
$879$	3.64876	−	2.59827i	0.123070	−	0.0876376i
$880$		0			0
$881$	24.4539	+	7.18031i	0.823872	+	0.241911i	0.666383	−	0.745610i	$-0.267842\pi$
$881$	24.4539	+	7.18031i	0.823872	+	0.241911i	0.157490	+	0.987521i	$0.449660\pi$
$882$		0			0
$883$	6.11664	+	13.3936i	0.205841	+	0.450730i	0.984193	−	0.177099i	$-0.0566712\pi$
$883$	6.11664	+	13.3936i	0.205841	+	0.450730i	−0.778352	+	0.627828i	$0.783944\pi$
$884$		0			0
$885$	−0.555976	−	1.60639i	−0.0186889	−	0.0539981i
$886$		0			0
$887$	−3.03467	+	3.18267i	−0.101894	+	0.106864i	−0.772706	−	0.634764i	$-0.781097\pi$
$887$	−3.03467	+	3.18267i	−0.101894	+	0.106864i	0.670812	+	0.741628i	$0.265946\pi$
$888$		0			0
$889$	26.6474	+	37.1409i	0.893724	+	1.24567i
$890$		0			0
$891$	−3.69904	−	4.70371i	−0.123923	−	0.157580i
$892$		0			0
$893$	−10.4668	+	13.3096i	−0.350257	+	0.445388i
$894$		0			0
$895$	35.2507	+	40.6814i	1.17830	+	1.35983i
$896$		0			0
$897$	−7.46146	+	1.16815i	−0.249131	+	0.0390034i
$898$		0			0
$899$	9.83890	+	51.0491i	0.328146	+	1.70258i
$900$		0			0
$901$	−23.7189	−	59.2470i	−0.790192	−	1.97380i
$902$		0			0
$903$	−1.90160	+	5.55814i	−0.0632812	+	0.184963i
$904$		0			0
$905$	−64.8542	−	33.4347i	−2.15583	−	1.11141i
$906$		0			0
$907$	−28.5805	−	6.93356i	−0.949001	−	0.230225i	−0.268754	−	0.963209i	$-0.586612\pi$
$907$	−28.5805	−	6.93356i	−0.949001	−	0.230225i	−0.680246	+	0.732984i	$0.738127\pi$
$908$		0			0
$909$	7.88804	+	6.83503i	0.261630	+	0.226704i
$910$		0			0
$911$	−0.275199	+	0.125679i	−0.00911776	+	0.00416394i	−0.419969	−	0.907539i	$-0.637959\pi$
$911$	−0.275199	+	0.125679i	−0.00911776	+	0.00416394i	0.410851	+	0.911703i	$0.365232\pi$
$912$		0			0
$913$	−6.59205	−	6.91354i	−0.218165	−	0.228805i
$914$		0			0
$915$	0.815866	+	8.54414i	0.0269717	+	0.282461i
$916$		0			0
$917$	0.142149	+	39.9945i	0.00469419	+	1.32073i
$918$		0			0
$919$	−1.34456	+	0.776284i	−0.0443531	+	0.0256072i	−0.522013	−	0.852938i	$-0.674819\pi$
$919$	−1.34456	+	0.776284i	−0.0443531	+	0.0256072i	0.477660	+	0.878545i	$0.341485\pi$
$920$		0			0
$921$	−4.92419	+	8.52895i	−0.162258	+	0.281039i
$922$		0			0
$923$	−25.3779	+	39.4887i	−0.835323	+	1.29979i
$924$		0			0
$925$	−25.4125	−	11.6055i	−0.835559	−	0.381587i
$926$		0			0
$927$	−3.89291	+	3.71188i	−0.127860	+	0.121914i
$928$		0			0
$929$	−3.70825	−	2.64063i	−0.121664	−	0.0866362i	0.517605	−	0.855619i	$-0.326824\pi$
$929$	−3.70825	−	2.64063i	−0.121664	−	0.0866362i	−0.639269	+	0.768983i	$0.720763\pi$
$930$		0			0
$931$	−40.9855	−	3.61984i	−1.34325	−	0.118635i
$932$		0			0
$933$	4.52197	+	4.31169i	0.148043	+	0.141159i
$934$		0			0
$935$	14.5916	−	0.695086i	0.477198	−	0.0227317i
$936$		0			0
$937$	−5.58260	−	38.8279i	−0.182376	−	1.26845i	−0.851125	−	0.524963i	$-0.824079\pi$
$937$	−5.58260	−	38.8279i	−0.182376	−	1.26845i	0.668749	−	0.743488i	$-0.266830\pi$
$938$		0			0
$939$	1.90153	+	0.273398i	0.0620540	+	0.00892201i
$940$		0			0
$941$	2.53841	−	0.489238i	0.0827497	−	0.0159487i	−0.147708	−	0.989031i	$-0.547190\pi$
$941$	2.53841	−	0.489238i	0.0827497	−	0.0159487i	0.230458	+	0.973082i	$0.425978\pi$
$942$		0			0
$943$	8.29000	+	13.9530i	0.269960	+	0.454374i
$944$		0			0
$945$	7.59722	−	26.2181i	0.247138	−	0.852876i
$946$		0			0
$947$	32.3990	−	12.9706i	1.05282	−	0.421487i	0.220275	−	0.975438i	$-0.429305\pi$
$947$	32.3990	−	12.9706i	1.05282	−	0.421487i	0.832550	+	0.553950i	$0.186880\pi$
$948$		0			0
$949$	21.6606	+	8.67159i	0.703132	+	0.281492i
$950$		0			0
$951$	−0.869916	−	1.35362i	−0.0282090	−	0.0438940i
$952$		0			0
$953$	8.60524	+	29.3067i	0.278751	+	0.949338i	0.973232	+	0.229827i	$0.0738160\pi$
$953$	8.60524	+	29.3067i	0.278751	+	0.949338i	−0.694481	+	0.719511i	$0.744366\pi$
$954$		0			0
$955$	−19.4166	+	6.72015i	−0.628306	+	0.217459i
$956$		0			0
$957$	2.10763	−	2.95975i	0.0681299	−	0.0956751i
$958$		0			0
$959$	23.9714	−	25.3201i	0.774078	−	0.817628i
$960$		0			0
$961$	−2.33702	+	0.223159i	−0.0753878	+	0.00719867i
$962$		0			0
$963$	−11.6596	−	22.6164i	−0.375725	−	0.728804i
$964$		0			0
$965$	−17.2002			−0.553694
$966$		0			0
$967$	−25.1336			−0.808241			−0.404121	−	0.914706i	$-0.632422\pi$
$967$	−25.1336			−0.808241			−0.404121	+	0.914706i	$0.632422\pi$
$968$		0			0
$969$	−5.41590	−	10.5054i	−0.173984	−	0.337482i
$970$		0			0
$971$	4.51971	−	0.431580i	0.145044	−	0.0138501i	−0.0222812	−	0.999752i	$-0.507093\pi$
$971$	4.51971	−	0.431580i	0.145044	−	0.0138501i	0.167326	+	0.985902i	$0.446487\pi$
$972$		0			0
$973$	11.2970	+	2.69813i	0.362164	+	0.0864982i
$974$		0			0
$975$	9.66735	−	13.5759i	0.309603	−	0.434777i
$976$		0			0
$977$	−30.6308	+	10.6014i	−0.979966	+	0.339170i	−0.769651	−	0.638464i	$-0.779570\pi$
$977$	−30.6308	+	10.6014i	−0.979966	+	0.339170i	−0.210315	+	0.977634i	$0.567449\pi$
$978$		0			0
$979$	1.90959	+	6.50347i	0.0610308	+	0.207852i
$980$		0			0
$981$	−19.9790	−	31.0879i	−0.637880	−	0.992560i
$982$		0			0
$983$	25.6642	+	10.2744i	0.818561	+	0.327702i	0.742876	−	0.669429i	$-0.233461\pi$
$983$	25.6642	+	10.2744i	0.818561	+	0.327702i	0.0756852	+	0.997132i	$0.475886\pi$
$984$		0			0
$985$	10.7225	−	4.29264i	0.341647	−	0.136775i
$986$		0			0
$987$	2.47852	−	2.38014i	0.0788922	−	0.0757607i
$988$		0			0
$989$	−21.8142	+	9.05101i	−0.693651	+	0.287805i
$990$		0			0
$991$	−9.30661	+	1.79370i	−0.295634	+	0.0569788i	−0.334912	−	0.942250i	$-0.608707\pi$
$991$	−9.30661	+	1.79370i	−0.295634	+	0.0569788i	0.0392774	+	0.999228i	$0.487494\pi$
$992$		0			0
$993$	8.60061	+	1.23658i	0.272932	+	0.0392417i
$994$		0			0
$995$	−1.05400	−	7.33071i	−0.0334140	−	0.232399i
$996$		0			0
$997$	−11.6184	+	0.553451i	−0.367957	+	0.0175280i	−0.230747	−	0.973014i	$-0.574117\pi$
$997$	−11.6184	+	0.553451i	−0.367957	+	0.0175280i	−0.137211	+	0.990542i	$0.543814\pi$
$998$		0			0
$999$	−4.99314	−	4.76095i	−0.157976	−	0.150630i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.bc.a.493.9	yes	320
7.5	odd	6	inner	644.2.bc.a.33.9	✓	320
23.7	odd	22	inner	644.2.bc.a.605.9	yes	320
161.145	even	66	inner	644.2.bc.a.145.9	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.bc.a.33.9	✓	320	7.5	odd	6	inner
644.2.bc.a.145.9	yes	320	161.145	even	66	inner
644.2.bc.a.493.9	yes	320	1.1	even	1	trivial
644.2.bc.a.605.9	yes	320	23.7	odd	22	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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.bc (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.206600 + 0.400748i) q^{3} +(-3.92969 + 0.375240i) q^{5} +(-0.614617 + 2.57337i) q^{7} +(1.62226 - 2.27814i) q^{9} +O(q^{10})\)	\(q+(0.206600 + 0.400748i) q^{3} +(-3.92969 + 0.375240i) q^{5} +(-0.614617 + 2.57337i) q^{7} +(1.62226 - 2.27814i) q^{9} +(0.784113 - 0.271384i) q^{11} +(-0.984024 - 3.35128i) q^{13} +(-0.962249 - 1.49729i) q^{15} +(-4.14039 - 1.65756i) q^{17} +(5.45682 - 2.18458i) q^{19} +(-1.15825 + 0.285352i) q^{21} +(-3.94103 - 2.73282i) q^{23} +(10.3920 - 2.00289i) q^{25} +(2.58695 + 0.371948i) q^{27} +(-1.38222 - 9.61357i) q^{29} +(-5.34673 + 0.254696i) q^{31} +(0.270754 + 0.258163i) q^{33} +(1.44962 - 10.3432i) q^{35} +(-2.15028 - 1.53121i) q^{37} +(1.13972 - 1.08672i) q^{39} +(-3.07836 - 1.40584i) q^{41} +(2.66242 - 4.14280i) q^{43} +(-5.52011 + 9.56111i) q^{45} +(-2.49473 + 1.44033i) q^{47} +(-6.24449 - 3.16328i) q^{49} +(-0.191140 - 2.00170i) q^{51} +(9.87470 + 10.3563i) q^{53} +(-2.97948 + 1.36068i) q^{55} +(2.00284 + 1.73547i) q^{57} +(0.928157 + 0.225169i) q^{59} +(-4.28630 - 2.20974i) q^{61} +(4.86543 + 5.57485i) q^{63} +(5.12444 + 12.8002i) q^{65} +(2.44546 + 12.6883i) q^{67} +(0.280954 - 2.14396i) q^{69} +(-8.80089 - 10.1568i) q^{71} +(-4.12935 + 5.25090i) q^{73} +(2.94964 + 3.75077i) q^{75} +(0.216443 + 2.18461i) q^{77} +(3.89653 - 4.08656i) q^{79} +(-2.35874 - 6.81514i) q^{81} +(-4.78253 - 10.4723i) q^{83} +(16.8924 + 4.96006i) q^{85} +(3.56705 - 2.54008i) q^{87} +(-0.388686 + 8.15953i) q^{89} +(9.22888 - 0.472507i) q^{91} +(-1.20670 - 2.09007i) q^{93} +(-20.6239 + 10.6323i) q^{95} +(0.200937 - 0.439990i) q^{97} +(0.653780 - 2.22657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 20 q^{9}+O(q^{10}) \) 320 * q - 20 * q^9	\( 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) \) 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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