LMFDB - Embedded newform 460.2.x.a.217.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(17,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 14]))

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

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

chi := DirichletCharacter("460.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.x (of order $44$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.8
Character	$\chi$	$=$	460.217
Dual form			460.2.x.a.53.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.898100 - 0.195370i) q^{3} +(-1.85310 - 1.25140i) q^{5} +(-2.76379 + 1.50914i) q^{7} +(-1.96048 + 0.895322i) q^{9} +O(q^{10})$	\(q+(0.898100 - 0.195370i) q^{3} +(-1.85310 - 1.25140i) q^{5} +(-2.76379 + 1.50914i) q^{7} +(-1.96048 + 0.895322i) q^{9} +(-2.29022 - 1.98448i) q^{11} +(3.12199 - 5.71749i) q^{13} +(-1.90876 - 0.761845i) q^{15} +(-5.09655 - 3.81523i) q^{17} +(0.831806 - 5.78534i) q^{19} +(-2.18732 + 1.89532i) q^{21} +(1.58599 + 4.52600i) q^{23} +(1.86798 + 4.63796i) q^{25} +(-3.79313 + 2.83950i) q^{27} +(-3.94097 + 0.566627i) q^{29} +(-3.65534 + 2.34915i) q^{31} +(-2.44455 - 1.33483i) q^{33} +(7.01013 + 0.662017i) q^{35} +(7.02292 + 2.61941i) q^{37} +(1.68683 - 5.74482i) q^{39} +(-1.07762 + 2.35966i) q^{41} +(-0.919885 - 4.22864i) q^{43} +(4.75338 + 0.794229i) q^{45} +(3.86747 + 3.86747i) q^{47} +(1.57653 - 2.45313i) q^{49} +(-5.32260 - 2.43075i) q^{51} +(-0.977837 - 1.79077i) q^{53} +(1.76062 + 6.54344i) q^{55} +(-0.383234 - 5.35832i) q^{57} +(-0.122192 - 0.416147i) q^{59} +(-7.48545 - 11.6476i) q^{61} +(4.06719 - 5.43313i) q^{63} +(-12.9403 + 6.68824i) q^{65} +(7.94838 + 0.568479i) q^{67} +(2.30862 + 3.75494i) q^{69} +(7.49397 + 8.64851i) q^{71} +(-1.73886 - 2.32285i) q^{73} +(2.58375 + 3.80040i) q^{75} +(9.32455 + 2.02843i) q^{77} +(2.54388 - 0.746951i) q^{79} +(1.38230 - 1.59526i) q^{81} +(1.38375 - 3.70998i) q^{83} +(4.67005 + 13.4479i) q^{85} +(-3.42869 + 1.27883i) q^{87} +(-11.2419 - 7.22472i) q^{89} +20.5135i q^{91} +(-2.82391 + 2.82391i) q^{93} +(-8.78121 + 9.67990i) q^{95} +(-5.04656 - 13.5304i) q^{97} +(6.26668 + 1.84006i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3}+O(q^{10}) $ 240 * q + 4 * q^3	$ 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) $ 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

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
$3$	0.898100	−	0.195370i	0.518518	−	0.112797i	0.0543122	−	0.998524i	$-0.482703\pi$
$3$	0.898100	−	0.195370i	0.518518	−	0.112797i	0.464206	+	0.885727i	$0.346340\pi$
$4$		0			0
$5$	−1.85310	−	1.25140i	−0.828733	−	0.559644i
$5$	−1.85310	−	1.25140i	−0.828733	−	0.559644i
$6$		0			0
$7$	−2.76379	+	1.50914i	−1.04461	+	0.570403i	−0.907456	−	0.420147i	$-0.861979\pi$
$7$	−2.76379	+	1.50914i	−1.04461	+	0.570403i	−0.137158	+	0.990549i	$0.543797\pi$
$8$		0			0
$9$	−1.96048	+	0.895322i	−0.653494	+	0.298441i
$10$		0			0
$11$	−2.29022	−	1.98448i	−0.690527	−	0.598345i	0.237264	−	0.971445i	$-0.423749\pi$
$11$	−2.29022	−	1.98448i	−0.690527	−	0.598345i	−0.927791	+	0.373100i	$0.878295\pi$
$12$		0			0
$13$	3.12199	−	5.71749i	0.865884	−	1.58575i	0.0565489	−	0.998400i	$-0.481990\pi$
$13$	3.12199	−	5.71749i	0.865884	−	1.58575i	0.809335	−	0.587348i	$-0.199828\pi$
$14$		0			0
$15$	−1.90876	−	0.761845i	−0.492839	−	0.196707i
$16$		0			0
$17$	−5.09655	−	3.81523i	−1.23610	−	0.925330i	−0.237161	−	0.971470i	$-0.576217\pi$
$17$	−5.09655	−	3.81523i	−1.23610	−	0.925330i	−0.998935	+	0.0461404i	$0.985308\pi$
$18$		0			0
$19$	0.831806	−	5.78534i	0.190829	−	1.32725i	−0.638990	−	0.769215i	$-0.720648\pi$
$19$	0.831806	−	5.78534i	0.190829	−	1.32725i	0.829819	−	0.558032i	$-0.188443\pi$
$20$		0			0
$21$	−2.18732	+	1.89532i	−0.477312	+	0.413593i
$22$		0			0
$23$	1.58599	+	4.52600i	0.330702	+	0.943735i
$23$	1.58599	+	4.52600i	0.330702	+	0.943735i
$24$		0			0
$25$	1.86798	+	4.63796i	0.373596	+	0.927591i
$26$		0			0
$27$	−3.79313	+	2.83950i	−0.729989	+	0.546463i
$28$		0			0
$29$	−3.94097	+	0.566627i	−0.731821	+	0.105220i	−0.498144	−	0.867094i	$-0.665985\pi$
$29$	−3.94097	+	0.566627i	−0.731821	+	0.105220i	−0.233677	+	0.972314i	$0.575076\pi$
$30$		0			0
$31$	−3.65534	+	2.34915i	−0.656519	+	0.421919i	−0.826043	−	0.563607i	$-0.809413\pi$
$31$	−3.65534	+	2.34915i	−0.656519	+	0.421919i	0.169524	+	0.985526i	$0.445777\pi$
$32$		0			0
$33$	−2.44455	−	1.33483i	−0.425542	−	0.232363i
$34$		0			0
$35$	7.01013	+	0.662017i	1.18493	+	0.111901i
$36$		0			0
$37$	7.02292	+	2.61941i	1.15456	+	0.430629i	0.852535	−	0.522671i	$-0.175064\pi$
$37$	7.02292	+	2.61941i	1.15456	+	0.430629i	0.302026	+	0.953300i	$0.402337\pi$
$38$		0			0
$39$	1.68683	−	5.74482i	0.270109	−	0.919908i
$40$		0			0
$41$	−1.07762	+	2.35966i	−0.168296	+	0.368517i	−0.974922	−	0.222545i	$-0.928564\pi$
$41$	−1.07762	+	2.35966i	−0.168296	+	0.368517i	0.806627	+	0.591061i	$0.201291\pi$
$42$		0			0
$43$	−0.919885	−	4.22864i	−0.140281	−	0.644862i	−0.992558	−	0.121771i	$-0.961143\pi$
$43$	−0.919885	−	4.22864i	−0.140281	−	0.644862i	0.852277	−	0.523091i	$-0.175221\pi$
$44$		0			0
$45$	4.75338	+	0.794229i	0.708593	+	0.118397i
$46$		0			0
$47$	3.86747	+	3.86747i	0.564129	+	0.564129i	0.930478	−	0.366349i	$-0.119392\pi$
$47$	3.86747	+	3.86747i	0.564129	+	0.564129i	−0.366349	+	0.930478i	$0.619392\pi$
$48$		0			0
$49$	1.57653	−	2.45313i	0.225219	−	0.350448i
$50$		0			0
$51$	−5.32260	−	2.43075i	−0.745312	−	0.340373i
$52$		0			0
$53$	−0.977837	−	1.79077i	−0.134316	−	0.245982i	0.801861	−	0.597511i	$-0.203844\pi$
$53$	−0.977837	−	1.79077i	−0.134316	−	0.245982i	−0.936177	+	0.351529i	$0.885662\pi$
$54$		0			0
$55$	1.76062	+	6.54344i	0.237402	+	0.882317i
$56$		0			0
$57$	−0.383234	−	5.35832i	−0.0507606	−	0.709726i
$58$		0			0
$59$	−0.122192	−	0.416147i	−0.0159080	−	0.0541777i	0.951157	−	0.308709i	$-0.0998970\pi$
$59$	−0.122192	−	0.416147i	−0.0159080	−	0.0541777i	−0.967065	+	0.254531i	$0.918079\pi$
$60$		0			0
$61$	−7.48545	−	11.6476i	−0.958414	−	1.49132i	−0.868691	−	0.495354i	$-0.835038\pi$
$61$	−7.48545	−	11.6476i	−0.958414	−	1.49132i	−0.0897228	−	0.995967i	$-0.528598\pi$
$62$		0			0
$63$	4.06719	−	5.43313i	0.512418	−	0.684510i
$64$		0			0
$65$	−12.9403	+	6.68824i	−1.60504	+	0.829574i
$66$		0			0
$67$	7.94838	+	0.568479i	0.971049	+	0.0694508i	0.547842	−	0.836582i	$-0.315450\pi$
$67$	7.94838	+	0.568479i	0.971049	+	0.0694508i	0.423207	+	0.906033i	$0.360904\pi$
$68$		0			0
$69$	2.30862	+	3.75494i	0.277925	+	0.452042i
$70$		0			0
$71$	7.49397	+	8.64851i	0.889371	+	1.02639i	0.999473	+	0.0324685i	$0.0103369\pi$
$71$	7.49397	+	8.64851i	0.889371	+	1.02639i	−0.110102	+	0.993920i	$0.535118\pi$
$72$		0			0
$73$	−1.73886	−	2.32285i	−0.203518	−	0.271869i	0.687157	−	0.726509i	$-0.258859\pi$
$73$	−1.73886	−	2.32285i	−0.203518	−	0.271869i	−0.890675	+	0.454641i	$0.849768\pi$
$74$		0			0
$75$	2.58375	+	3.80040i	0.298346	+	0.438833i
$76$		0			0
$77$	9.32455	+	2.02843i	1.06263	+	0.231161i
$78$		0			0
$79$	2.54388	−	0.746951i	0.286209	−	0.0840385i	−0.135477	−	0.990780i	$-0.543257\pi$
$79$	2.54388	−	0.746951i	0.286209	−	0.0840385i	0.421686	+	0.906742i	$0.361439\pi$
$80$		0			0
$81$	1.38230	−	1.59526i	0.153589	−	0.177251i
$82$		0			0
$83$	1.38375	−	3.70998i	0.151887	−	0.407224i	−0.838615	−	0.544724i	$-0.816634\pi$
$83$	1.38375	−	3.70998i	0.151887	−	0.407224i	0.990502	+	0.137501i	$0.0439070\pi$
$84$		0			0
$85$	4.67005	+	13.4479i	0.506538	+	1.45863i
$86$		0			0
$87$	−3.42869	+	1.27883i	−0.367594	+	0.137105i
$88$		0			0
$89$	−11.2419	−	7.22472i	−1.19164	−	0.765818i	−0.214147	−	0.976801i	$-0.568697\pi$
$89$	−11.2419	−	7.22472i	−1.19164	−	0.765818i	−0.977490	+	0.210983i	$0.932334\pi$
$90$		0			0
$91$			20.5135i			2.15040i
$92$		0			0
$93$	−2.82391	+	2.82391i	−0.292826	+	0.292826i
$94$		0			0
$95$	−8.78121	+	9.67990i	−0.900933	+	0.993137i
$96$		0			0
$97$	−5.04656	−	13.5304i	−0.512401	−	1.37380i	−0.893416	−	0.449231i	$-0.851698\pi$
$97$	−5.04656	−	13.5304i	−0.512401	−	1.37380i	0.381015	−	0.924569i	$-0.375575\pi$
$98$		0			0
$99$	6.26668	+	1.84006i	0.629825	+	0.184933i
$100$		0			0
$101$	−7.21205	−	15.7922i	−0.717626	−	1.57138i	−0.817201	−	0.576352i	$-0.804476\pi$
$101$	−7.21205	−	15.7922i	−0.717626	−	1.57138i	0.0995750	−	0.995030i	$-0.468252\pi$
$102$		0			0
$103$	10.5314	−	0.753221i	1.03769	−	0.0742171i	0.457917	−	0.888995i	$-0.348596\pi$
$103$	10.5314	−	0.753221i	1.03769	−	0.0742171i	0.579773	+	0.814778i	$0.303141\pi$
$104$		0			0
$105$	6.42514	−	0.775010i	0.627029	−	0.0756332i
$106$		0			0
$107$	−0.437378	+	2.01059i	−0.0422829	+	0.194371i	−0.993443	−	0.114326i	$-0.963529\pi$
$107$	−0.437378	+	2.01059i	−0.0422829	+	0.194371i	0.951160	+	0.308697i	$0.0998929\pi$
$108$		0			0
$109$	2.15599	+	14.9952i	0.206506	+	1.43628i	0.784444	+	0.620200i	$0.212948\pi$
$109$	2.15599	+	14.9952i	0.206506	+	1.43628i	−0.577938	+	0.816081i	$0.696142\pi$
$110$		0			0
$111$	6.81904	+	0.980430i	0.647234	+	0.0930583i
$112$		0			0
$113$	0.559266	−	7.81956i	0.0526113	−	0.735602i	−0.900858	−	0.434113i	$-0.857062\pi$
$113$	0.559266	−	7.81956i	0.0526113	−	0.735602i	0.953470	−	0.301489i	$-0.0974837\pi$
$114$		0			0
$115$	2.72484	−	10.3718i	0.254093	−	0.967180i
$116$		0			0
$117$	−1.00160	+	14.0042i	−0.0925982	+	1.29469i
$118$		0			0
$119$	19.8435	+	2.85307i	1.81905	+	0.261540i
$120$		0			0
$121$	−0.258547	−	1.79823i	−0.0235043	−	0.163476i
$122$		0			0
$123$	−0.506804	+	2.32974i	−0.0456970	+	0.210066i
$124$		0			0
$125$	2.34239	−	10.9322i	0.209510	−	0.977807i
$126$		0			0
$127$	22.3906	−	1.60141i	1.98684	−	0.142102i	0.987016	−	0.160623i	$-0.0513505\pi$
$127$	22.3906	−	1.60141i	1.98684	−	0.142102i	0.999828	+	0.0185215i	$0.00589591\pi$
$128$		0			0
$129$	−1.65230	−	3.61803i	−0.145477	−	0.318549i
$130$		0			0
$131$	−17.0710	−	5.01249i	−1.49150	−	0.437943i	−0.568479	−	0.822698i	$-0.692468\pi$
$131$	−17.0710	−	5.01249i	−1.49150	−	0.437943i	−0.923019	+	0.384754i	$0.874286\pi$
$132$		0			0
$133$	6.43196	+	17.2448i	0.557722	+	1.49531i
$134$		0			0
$135$	10.5824	−	0.515155i	0.910790	−	0.0443374i
$136$		0			0
$137$	−4.79265	+	4.79265i	−0.409464	+	0.409464i	−0.881552	−	0.472088i	$-0.843501\pi$
$137$	−4.79265	+	4.79265i	−0.409464	+	0.409464i	0.472088	+	0.881552i	$0.343501\pi$
$138$		0			0
$139$		−	1.21383i		−	0.102956i	−0.998674	−	0.0514779i	$-0.983607\pi$
$139$		−	1.21383i		−	0.102956i	0.998674	−	0.0514779i	$-0.0163932\pi$
$140$		0			0
$141$	4.22896	+	2.71779i	0.356143	+	0.228879i
$142$		0			0
$143$	−18.4963	+	6.89877i	−1.54674	+	0.576904i
$144$		0			0
$145$	8.01211	+	3.88173i	0.665370	+	0.322360i
$146$		0			0
$147$	0.936616	−	2.51116i	0.0772508	−	0.207117i
$148$		0			0
$149$	0.540235	−	0.623464i	0.0442577	−	0.0510762i	−0.733189	−	0.680025i	$-0.761969\pi$
$149$	0.540235	−	0.623464i	0.0442577	−	0.0510762i	0.777447	+	0.628949i	$0.216514\pi$
$150$		0			0
$151$	−17.7226	+	5.20384i	−1.44225	+	0.423482i	−0.906971	−	0.421194i	$-0.861611\pi$
$151$	−17.7226	+	5.20384i	−1.44225	+	0.423482i	−0.535278	+	0.844676i	$0.679793\pi$
$152$		0			0
$153$	13.4076	+	2.91664i	1.08394	+	0.235796i
$154$		0			0
$155$	9.71345	+	0.221097i	0.780203	+	0.0177590i
$156$		0			0
$157$	8.07800	+	10.7909i	0.644694	+	0.861211i	0.997214	−	0.0745936i	$-0.0237659\pi$
$157$	8.07800	+	10.7909i	0.644694	+	0.861211i	−0.352520	+	0.935804i	$0.614675\pi$
$158$		0			0
$159$	−1.22806	−	1.41725i	−0.0973913	−	0.112396i
$160$		0			0
$161$	−11.2137	−	10.1154i	−0.883765	−	0.797206i
$162$		0			0
$163$	7.92152	+	0.566558i	0.620461	+	0.0443763i	0.378032	−	0.925793i	$-0.376601\pi$
$163$	7.92152	+	0.566558i	0.620461	+	0.0443763i	0.242430	+	0.970169i	$0.422056\pi$
$164$		0			0
$165$	2.85960	+	5.53269i	0.222620	+	0.430719i
$166$		0			0
$167$	−1.01409	+	1.35467i	−0.0784727	+	0.104827i	−0.838060	−	0.545578i	$-0.816310\pi$
$167$	−1.01409	+	1.35467i	−0.0784727	+	0.104827i	0.759587	+	0.650405i	$0.225401\pi$
$168$		0			0
$169$	−15.9146	−	24.7636i	−1.22420	−	1.90489i
$170$		0			0
$171$	3.54900	+	12.0868i	0.271399	+	0.924299i
$172$		0			0
$173$	−0.978006	−	13.6743i	−0.0743564	−	1.03964i	−0.888471	−	0.458933i	$-0.848232\pi$
$173$	−0.978006	−	13.6743i	−0.0743564	−	1.03964i	0.814114	−	0.580705i	$-0.197223\pi$
$174$		0			0
$175$	−12.1620	−	9.99929i	−0.919364	−	0.755875i
$176$		0			0
$177$	−0.191043	−	0.349869i	−0.0143597	−	0.0262977i
$178$		0			0
$179$	−11.9629	−	5.46328i	−0.894150	−	0.408345i	−0.0852973	−	0.996356i	$-0.527184\pi$
$179$	−11.9629	−	5.46328i	−0.894150	−	0.408345i	−0.808853	+	0.588011i	$0.799911\pi$
$180$		0			0
$181$	−2.16002	+	3.36105i	−0.160553	+	0.249825i	−0.912204	−	0.409735i	$-0.865621\pi$
$181$	−2.16002	+	3.36105i	−0.160553	+	0.249825i	0.751652	+	0.659560i	$0.229257\pi$
$182$		0			0
$183$	−8.99827	−	8.99827i	−0.665171	−	0.665171i
$184$		0			0
$185$	−9.73625	−	13.6425i	−0.715824	−	1.00302i
$186$		0			0
$187$	4.10095	+	18.8517i	0.299891	+	1.37858i
$188$		0			0
$189$	6.19820	−	13.5722i	0.450853	−	0.987230i
$190$		0			0
$191$	−1.09095	+	3.71542i	−0.0789381	+	0.268839i	−0.989500	−	0.144535i	$-0.953831\pi$
$191$	−1.09095	+	3.71542i	−0.0789381	+	0.268839i	0.910562	+	0.413373i	$0.135650\pi$
$192$		0			0
$193$	2.90515	+	1.08356i	0.209117	+	0.0779966i	0.451840	−	0.892099i	$-0.350768\pi$
$193$	2.90515	+	1.08356i	0.209117	+	0.0779966i	−0.242723	+	0.970096i	$0.578041\pi$
$194$		0			0
$195$	−10.3150	+	8.53484i	−0.738670	+	0.611192i
$196$		0			0
$197$	6.21455	+	3.39340i	0.442768	+	0.241770i	0.685137	−	0.728414i	$-0.259742\pi$
$197$	6.21455	+	3.39340i	0.442768	+	0.241770i	−0.242368	+	0.970184i	$0.577924\pi$
$198$		0			0
$199$	−10.1722	+	6.53727i	−0.721088	+	0.463415i	−0.849015	−	0.528369i	$-0.822804\pi$
$199$	−10.1722	+	6.53727i	−0.721088	+	0.463415i	0.127927	+	0.991784i	$0.459168\pi$
$200$		0			0
$201$	7.24950	−	1.04232i	0.511340	−	0.0735196i
$202$		0			0
$203$	10.0369	−	7.51353i	0.704453	−	0.527347i
$204$		0			0
$205$	4.94982	−	3.02415i	0.345711	−	0.211216i
$206$		0			0
$207$	−7.16153	−	7.45316i	−0.497761	−	0.518031i
$208$		0			0
$209$	−13.3859	+	11.5990i	−0.925924	+	0.802317i
$210$		0			0
$211$	1.28497	−	8.93714i	0.0884607	−	0.615258i	−0.896573	−	0.442896i	$-0.853951\pi$
$211$	1.28497	−	8.93714i	0.0884607	−	0.615258i	0.985034	−	0.172362i	$-0.0551398\pi$
$212$		0			0
$213$	8.41999	+	6.30313i	0.576928	+	0.431883i
$214$		0			0
$215$	−3.58710	+	8.98726i	−0.244638	+	0.612926i
$216$		0			0
$217$	6.55740	−	12.0090i	0.445145	−	0.815223i
$218$		0			0
$219$	−2.01548	−	1.74643i	−0.136194	−	0.118013i
$220$		0			0
$221$	−37.7250	+	17.2284i	−2.53766	+	1.15891i
$222$		0			0
$223$	−3.37081	+	1.84060i	−0.225726	+	0.123256i	−0.588133	−	0.808764i	$-0.700137\pi$
$223$	−3.37081	+	1.84060i	−0.225726	+	0.123256i	0.362407	+	0.932020i	$0.381955\pi$
$224$		0			0
$225$	−7.81461	−	7.42019i	−0.520974	−	0.494679i
$226$		0			0
$227$	−18.4225	+	4.00756i	−1.22274	+	0.265991i	−0.777191	−	0.629265i	$-0.783356\pi$
$227$	−18.4225	+	4.00756i	−1.22274	+	0.265991i	−0.445551	+	0.895256i	$0.646992\pi$
$228$		0			0
$229$	−16.2428			−1.07335			−0.536677	−	0.843787i	$-0.680321\pi$
$229$	−16.2428			−1.07335			−0.536677	+	0.843787i	$0.680321\pi$
$230$		0			0
$231$	8.77067			0.577068
$232$		0			0
$233$	3.38808	−	0.737031i	0.221960	−	0.0482845i	−0.100210	−	0.994966i	$-0.531951\pi$
$233$	3.38808	−	0.737031i	0.221960	−	0.0482845i	0.322170	+	0.946682i	$0.395588\pi$
$234$		0			0
$235$	−2.32706	−	12.0066i	−0.151801	−	0.783224i
$236$		0			0
$237$	2.13873	−	1.16783i	0.138925	−	0.0758589i
$238$		0			0
$239$	23.2470	−	10.6166i	1.50373	−	0.686729i	0.518046	−	0.855353i	$-0.326660\pi$
$239$	23.2470	−	10.6166i	1.50373	−	0.686729i	0.985680	+	0.168624i	$0.0539325\pi$
$240$		0			0
$241$	4.27822	+	3.70710i	0.275584	+	0.238795i	0.781676	−	0.623684i	$-0.214365\pi$
$241$	4.27822	+	3.70710i	0.275584	+	0.238795i	−0.506092	+	0.862479i	$0.668910\pi$
$242$		0			0
$243$	7.74213	−	14.1786i	0.496658	−	0.909561i
$244$		0			0
$245$	−5.99134	+	2.57303i	−0.382772	+	0.164385i
$246$		0			0
$247$	−30.4807	−	22.8176i	−1.93944	−	1.45185i
$248$		0			0
$249$	0.517929	−	3.60228i	0.0328224	−	0.228285i
$250$		0			0
$251$	6.85689	−	5.94153i	0.432803	−	0.375026i	−0.411039	−	0.911618i	$-0.634834\pi$
$251$	6.85689	−	5.94153i	0.432803	−	0.375026i	0.843842	+	0.536592i	$0.180288\pi$
$252$		0			0
$253$	5.34951	−	13.5129i	0.336321	−	0.849548i
$254$		0			0
$255$	6.82147	+	11.1651i	0.427177	+	0.699188i
$256$		0			0
$257$	5.63077	−	4.21514i	0.351238	−	0.262934i	−0.409061	−	0.912507i	$-0.634144\pi$
$257$	5.63077	−	4.21514i	0.351238	−	0.262934i	0.760299	+	0.649574i	$0.225053\pi$
$258$		0			0
$259$	−23.3629	+	3.35908i	−1.45170	+	0.208723i
$260$		0			0
$261$	7.21890	−	4.63930i	0.446839	−	0.287166i
$262$		0			0
$263$	−21.1561	−	11.5521i	−1.30454	−	0.712334i	−0.331608	−	0.943417i	$-0.607591\pi$
$263$	−21.1561	−	11.5521i	−1.30454	−	0.712334i	−0.972934	+	0.231083i	$0.925773\pi$
$264$		0			0
$265$	−0.428948	+	4.54216i	−0.0263501	+	0.279023i
$266$		0			0
$267$	−11.5078	−	4.29219i	−0.704267	−	0.262678i
$268$		0			0
$269$	2.34135	−	7.97392i	0.142755	−	0.486178i	−0.856811	−	0.515630i	$-0.827558\pi$
$269$	2.34135	−	7.97392i	0.142755	−	0.486178i	0.999566	+	0.0294517i	$0.00937613\pi$
$270$		0			0
$271$	4.66374	−	10.2122i	0.283302	−	0.620345i	−0.713465	−	0.700691i	$-0.752875\pi$
$271$	4.66374	−	10.2122i	0.283302	−	0.620345i	0.996767	+	0.0803459i	$0.0256025\pi$
$272$		0			0
$273$	4.00771	+	18.4231i	0.242558	+	1.11502i
$274$		0			0
$275$	4.92587	−	14.3289i	0.297041	−	0.864066i
$276$		0			0
$277$	−8.11966	−	8.11966i	−0.487863	−	0.487863i	0.419768	−	0.907631i	$-0.362111\pi$
$277$	−8.11966	−	8.11966i	−0.487863	−	0.487863i	−0.907631	+	0.419768i	$0.862111\pi$
$278$		0			0
$279$	5.06299	−	7.87817i	0.303113	−	0.471654i
$280$		0			0
$281$	14.3275	+	6.54314i	0.854705	+	0.390331i	0.794068	−	0.607829i	$-0.207959\pi$
$281$	14.3275	+	6.54314i	0.854705	+	0.390331i	0.0606373	+	0.998160i	$0.480687\pi$
$282$		0			0
$283$	4.48706	+	8.21743i	0.266728	+	0.488476i	0.976375	−	0.216081i	$-0.0693276\pi$
$283$	4.48706	+	8.21743i	0.266728	+	0.488476i	−0.709647	+	0.704557i	$0.751146\pi$
$284$		0			0
$285$	−5.99524	+	10.4091i	−0.355127	+	0.616582i
$286$		0			0
$287$	−0.582748	−	8.14788i	−0.0343985	−	0.480954i
$288$		0			0
$289$	6.62941	+	22.5777i	0.389966	+	1.32810i
$290$		0			0
$291$	−7.17574	−	11.1657i	−0.420649	−	0.654543i
$292$		0			0
$293$	−8.37607	+	11.1891i	−0.489335	+	0.653676i	−0.975450	−	0.220219i	$-0.929323\pi$
$293$	−8.37607	+	11.1891i	−0.489335	+	0.653676i	0.486115	+	0.873895i	$0.338414\pi$
$294$		0			0
$295$	−0.294333	+	0.924074i	−0.0171368	+	0.0538017i
$296$		0			0
$297$	14.3220	+	1.02433i	0.831049	+	0.0594378i
$298$		0			0
$299$	30.8288	+	5.06221i	1.78288	+	0.292755i
$300$		0			0
$301$	8.92400	+	10.2988i	0.514371	+	0.593615i
$302$		0			0
$303$	−9.56246	−	12.7740i	−0.549349	−	0.733844i
$304$		0			0
$305$	−0.704517	+	30.9515i	−0.0403405	+	1.77228i
$306$		0			0
$307$	−3.20810	−	0.697879i	−0.183096	−	0.0398301i	0.120082	−	0.992764i	$-0.461684\pi$
$307$	−3.20810	−	0.697879i	−0.183096	−	0.0398301i	−0.303178	+	0.952934i	$0.598048\pi$
$308$		0			0
$309$	9.31110	−	2.73399i	0.529690	−	0.155531i
$310$		0			0
$311$	20.4873	−	23.6436i	1.16173	−	1.34070i	0.231884	−	0.972743i	$-0.425511\pi$
$311$	20.4873	−	23.6436i	1.16173	−	1.34070i	0.929842	−	0.367960i	$-0.119944\pi$
$312$		0			0
$313$	−3.48296	+	9.33818i	−0.196869	+	0.527825i	−0.997448	−	0.0714020i	$-0.977253\pi$
$313$	−3.48296	+	9.33818i	−0.196869	+	0.527825i	0.800579	+	0.599227i	$0.204525\pi$
$314$		0			0
$315$	−14.3360	+	4.97846i	−0.807740	+	0.280504i
$316$		0			0
$317$	−12.0105	+	4.47967i	−0.674575	+	0.251603i	−0.663323	−	0.748333i	$-0.730854\pi$
$317$	−12.0105	+	4.47967i	−0.674575	+	0.251603i	−0.0112518	+	0.999937i	$0.503582\pi$
$318$		0			0
$319$	10.1502	+	6.52311i	0.568299	+	0.365224i
$320$		0			0
$321$			1.89116i			0.105554i
$322$		0			0
$323$	−26.3117	+	26.3117i	−1.46402	+	1.46402i
$324$		0			0
$325$	32.3493	+	3.79948i	1.79442	+	0.210757i
$326$		0			0
$327$	4.86590	+	13.0460i	0.269085	+	0.721444i
$328$		0			0
$329$	−16.5255	−	4.85231i	−0.911078	−	0.267517i
$330$		0			0
$331$	6.35597	+	13.9176i	0.349356	+	0.764983i	0.999984	+	0.00558644i	$0.00177823\pi$
$331$	6.35597	+	13.9176i	0.349356	+	0.764983i	−0.650629	+	0.759396i	$0.725494\pi$
$332$		0			0
$333$	−16.1135	+	1.15246i	−0.883016	+	0.0631546i
$334$		0			0
$335$	−14.0178	−	11.0001i	−0.765873	−	0.600998i
$336$		0			0
$337$	3.53428	−	16.2468i	0.192524	−	0.885020i	−0.774944	−	0.632029i	$-0.782222\pi$
$337$	3.53428	−	16.2468i	0.192524	−	0.885020i	0.967469	−	0.252991i	$-0.0814141\pi$
$338$		0			0
$339$	−1.02543	−	7.13201i	−0.0556936	−	0.387358i
$340$		0			0
$341$	13.0334	+	1.87392i	0.705797	+	0.101478i
$342$		0			0
$343$	0.917441	−	12.8275i	0.0495372	−	0.692620i
$344$		0			0
$345$	0.420835	−	9.84731i	0.0226570	−	0.530161i
$346$		0			0
$347$	0.685787	−	9.58856i	0.0368150	−	0.514741i	−0.945268	−	0.326294i	$-0.894200\pi$
$347$	0.685787	−	9.58856i	0.0368150	−	0.514741i	0.982083	−	0.188447i	$-0.0603453\pi$
$348$		0			0
$349$	−7.27680	−	1.04625i	−0.389518	−	0.0560042i	−0.0552262	−	0.998474i	$-0.517588\pi$
$349$	−7.27680	−	1.04625i	−0.389518	−	0.0560042i	−0.334292	+	0.942470i	$0.608497\pi$
$350$		0			0
$351$	4.39273	+	30.5521i	0.234467	+	1.63075i
$352$		0			0
$353$	−0.679570	+	3.12393i	−0.0361699	+	0.166270i	−0.991689	−	0.128659i	$-0.958933\pi$
$353$	−0.679570	+	3.12393i	−0.0361699	+	0.166270i	0.955519	+	0.294930i	$0.0952962\pi$
$354$		0			0
$355$	−3.06434	−	25.4046i	−0.162638	−	1.34833i
$356$		0			0
$357$	18.3789	−	1.31448i	0.972713	−	0.0695698i
$358$		0			0
$359$	8.93003	+	19.5540i	0.471309	+	1.03202i	0.984762	+	0.173905i	$0.0556386\pi$
$359$	8.93003	+	19.5540i	0.471309	+	1.03202i	−0.513454	+	0.858117i	$0.671634\pi$
$360$		0			0
$361$	−14.5478	−	4.27163i	−0.765676	−	0.224823i
$362$		0			0
$363$	−0.583521	−	1.56448i	−0.0306269	−	0.0821140i
$364$		0			0
$365$	0.315471	+	6.48049i	0.0165125	+	0.339204i
$366$		0			0
$367$	−20.6026	+	20.6026i	−1.07545	+	1.07545i	−0.0785338	+	0.996911i	$0.525024\pi$
$367$	−20.6026	+	20.6026i	−1.07545	+	1.07545i	−0.996911	+	0.0785338i	$0.974976\pi$
$368$		0			0
$369$		−	5.59088i		−	0.291050i
$370$		0			0
$371$	5.40507	+	3.47363i	0.280617	+	0.180342i
$372$		0			0
$373$	12.4925	−	4.65947i	0.646839	−	0.241258i	−0.00456504	−	0.999990i	$-0.501453\pi$
$373$	12.4925	−	4.65947i	0.646839	−	0.241258i	0.651404	+	0.758731i	$0.274180\pi$
$374$		0			0
$375$	−0.0321194	−	10.2758i	−0.00165864	−	0.530642i
$376$		0			0
$377$	−9.06399	+	24.3015i	−0.466819	+	1.25159i
$378$		0			0
$379$	−0.649283	+	0.749313i	−0.0333514	+	0.0384896i	−0.772180	−	0.635404i	$-0.780834\pi$
$379$	−0.649283	+	0.749313i	−0.0333514	+	0.0384896i	0.738829	+	0.673893i	$0.235379\pi$
$380$		0			0
$381$	19.7961	−	5.81267i	1.01419	−	0.297792i
$382$		0			0
$383$	15.5592	+	3.38470i	0.795039	+	0.172950i	0.591700	−	0.806158i	$-0.298457\pi$
$383$	15.5592	+	3.38470i	0.795039	+	0.172950i	0.203339	+	0.979108i	$0.434821\pi$
$384$		0			0
$385$	−14.7410	−	15.4277i	−0.751269	−	0.786266i
$386$		0			0
$387$	5.58942	+	7.46659i	0.284126	+	0.379548i
$388$		0			0
$389$	16.4320	+	18.9636i	0.833136	+	0.961490i	0.999699	−	0.0245405i	$-0.00781227\pi$
$389$	16.4320	+	18.9636i	0.833136	+	0.961490i	−0.166563	+	0.986031i	$0.553267\pi$
$390$		0			0
$391$	9.18464	−	29.1179i	0.464487	−	1.47256i
$392$		0			0
$393$	−16.3107	−	1.16657i	−0.822768	−	0.0588455i
$394$		0			0
$395$	−5.64881	−	1.79924i	−0.284222	−	0.0905297i
$396$		0			0
$397$	4.02321	−	5.37438i	0.201919	−	0.269732i	−0.688140	−	0.725578i	$-0.741572\pi$
$397$	4.02321	−	5.37438i	0.201919	−	0.269732i	0.890059	+	0.455846i	$0.150663\pi$
$398$		0			0
$399$	9.14565	+	14.2309i	0.457855	+	0.712436i
$400$		0			0
$401$	−2.31225	−	7.87481i	−0.115468	−	0.393249i	0.881396	−	0.472378i	$-0.156604\pi$
$401$	−2.31225	−	7.87481i	−0.115468	−	0.393249i	−0.996864	+	0.0791290i	$0.974786\pi$
$402$		0			0
$403$	2.01929	+	28.2334i	0.100588	+	1.40641i
$404$		0			0
$405$	−4.55787	+	1.22637i	−0.226482	+	0.0609387i
$406$		0			0
$407$	−10.8858	−	19.9359i	−0.539590	−	0.988186i
$408$		0			0
$409$	29.5798	+	13.5086i	1.46263	+	0.667958i	0.978350	−	0.206957i	$-0.0663561\pi$
$409$	29.5798	+	13.5086i	1.46263	+	0.667958i	0.484275	+	0.874916i	$0.339083\pi$
$410$		0			0
$411$	−3.36794	+	5.24062i	−0.166128	+	0.258501i
$412$		0			0
$413$	0.965737	+	0.965737i	0.0475208	+	0.0475208i
$414$		0			0
$415$	−7.20692	+	5.14335i	−0.353774	+	0.252477i
$416$		0			0
$417$	−0.237146	−	1.09014i	−0.0116131	−	0.0533844i
$418$		0			0
$419$	−6.25980	+	13.7070i	−0.305811	+	0.669633i	−0.998676	−	0.0514342i	$-0.983621\pi$
$419$	−6.25980	+	13.7070i	−0.305811	+	0.669633i	0.692865	+	0.721067i	$0.256348\pi$
$420$		0			0
$421$	4.37007	−	14.8831i	0.212984	−	0.725358i	−0.781816	−	0.623510i	$-0.785706\pi$
$421$	4.37007	−	14.8831i	0.212984	−	0.725358i	0.994800	−	0.101848i	$-0.0324756\pi$
$422$		0			0
$423$	−11.0447	−	4.11948i	−0.537014	−	0.200296i
$424$		0			0
$425$	8.17462	−	30.7644i	0.396527	−	1.49229i
$426$		0			0
$427$	38.2661	+	20.8949i	1.85183	+	1.01117i
$428$		0			0
$429$	−15.2637	+	9.80940i	−0.736939	+	0.473602i
$430$		0			0
$431$	−33.7876	+	4.85792i	−1.62749	+	0.233998i	−0.894769	−	0.446530i	$-0.852660\pi$
$431$	−33.7876	+	4.85792i	−1.62749	+	0.233998i	−0.732722	+	0.680528i	$0.761750\pi$
$432$		0			0
$433$	25.5505	−	19.1268i	1.22788	−	0.919178i	0.229346	−	0.973345i	$-0.426341\pi$
$433$	25.5505	−	19.1268i	1.22788	−	0.919178i	0.998532	+	0.0541673i	$0.0172504\pi$
$434$		0			0
$435$	7.95405	+	1.92086i	0.381367	+	0.0920981i
$436$		0			0
$437$	27.5036	−	5.41074i	1.31568	−	0.258831i
$438$		0			0
$439$	−12.2439	+	10.6094i	−0.584368	+	0.506358i	−0.896124	−	0.443805i	$-0.853628\pi$
$439$	−12.2439	+	10.6094i	−0.584368	+	0.506358i	0.311756	+	0.950162i	$0.399083\pi$
$440$		0			0
$441$	−0.894420	+	6.22083i	−0.0425914	+	0.296230i
$442$		0			0
$443$	−2.34941	−	1.75875i	−0.111624	−	0.0835606i	0.542008	−	0.840374i	$-0.317664\pi$
$443$	−2.34941	−	1.75875i	−0.111624	−	0.0835606i	−0.653631	+	0.756813i	$0.726755\pi$
$444$		0			0
$445$	11.7913	+	27.4563i	0.558962	+	1.30155i
$446$		0			0
$447$	0.363379	−	0.665478i	0.0171872	−	0.0314760i
$448$		0			0
$449$	−10.1923	−	8.83172i	−0.481006	−	0.416795i	0.380313	−	0.924858i	$-0.375816\pi$
$449$	−10.1923	−	8.83172i	−0.481006	−	0.416795i	−0.861320	+	0.508063i	$0.830362\pi$
$450$		0			0
$451$	7.15069	−	3.26561i	0.336713	−	0.153772i
$452$		0			0
$453$	−14.9000	+	8.13603i	−0.700065	+	0.382264i
$454$		0			0
$455$	25.6706	−	38.0136i	1.20346	−	1.78210i
$456$		0			0
$457$	−12.3644	+	2.68971i	−0.578383	+	0.125820i	−0.492234	−	0.870463i	$-0.663820\pi$
$457$	−12.3644	+	2.68971i	−0.578383	+	0.125820i	−0.0861488	+	0.996282i	$0.527456\pi$
$458$		0			0
$459$	30.1653			1.40799
$460$		0			0
$461$	21.3051			0.992279			0.496140	−	0.868243i	$-0.334750\pi$
$461$	21.3051			0.992279			0.496140	+	0.868243i	$0.334750\pi$
$462$		0			0
$463$	1.43069	−	0.311227i	0.0664896	−	0.0144639i	−0.179197	−	0.983813i	$-0.557350\pi$
$463$	1.43069	−	0.311227i	0.0664896	−	0.0144639i	0.245687	+	0.969349i	$0.420986\pi$
$464$		0			0
$465$	8.76684	−	1.69915i	0.406553	−	0.0787960i
$466$		0			0
$467$	1.30677	−	0.713552i	0.0604703	−	0.0330193i	−0.448729	−	0.893668i	$-0.648123\pi$
$467$	1.30677	−	0.713552i	0.0604703	−	0.0330193i	0.509200	+	0.860648i	$0.329941\pi$
$468$		0			0
$469$	−22.8256	+	10.4241i	−1.05399	+	0.481340i
$470$		0			0
$471$	9.36307	+	8.11315i	0.431427	+	0.373834i
$472$		0			0
$473$	−6.28494	+	11.5100i	−0.288982	+	0.529231i
$474$		0			0
$475$	28.3859	−	6.94902i	1.30244	−	0.318843i
$476$		0			0
$477$	3.52035	+	2.63530i	0.161186	+	0.120662i
$478$		0			0
$479$	−4.65702	+	32.3903i	−0.212785	+	1.47995i	0.551014	+	0.834496i	$0.314241\pi$
$479$	−4.65702	+	32.3903i	−0.212785	+	1.47995i	−0.763799	+	0.645454i	$0.776668\pi$
$480$		0			0
$481$	36.9020	−	31.9757i	1.68258	−	1.45797i
$482$		0			0
$483$	−12.0473	−	6.89383i	−0.548170	−	0.313680i
$484$		0			0
$485$	−7.58013	+	31.3884i	−0.344196	+	1.42528i
$486$		0			0
$487$	−26.4726	+	19.8171i	−1.19959	+	0.898000i	−0.996698	−	0.0812015i	$-0.974124\pi$
$487$	−26.4726	+	19.8171i	−1.19959	+	0.898000i	−0.202890	+	0.979202i	$0.565033\pi$
$488$		0			0
$489$	7.22500	−	1.03880i	0.326726	−	0.0469761i
$490$		0			0
$491$	20.6481	−	13.2697i	0.931836	−	0.598855i	0.0157673	−	0.999876i	$-0.494981\pi$
$491$	20.6481	−	13.2697i	0.931836	−	0.598855i	0.916069	+	0.401021i	$0.131345\pi$
$492$		0			0
$493$	22.2472	+	12.1479i	1.00196	+	0.547114i
$494$		0			0
$495$	−9.31015	−	11.2520i	−0.418460	−	0.505739i
$496$		0			0
$497$	−33.7636	−	12.5932i	−1.51450	−	0.564881i
$498$		0			0
$499$	3.68916	−	12.5641i	0.165149	−	0.562447i	−0.834780	−	0.550583i	$-0.814405\pi$
$499$	3.68916	−	12.5641i	0.165149	−	0.562447i	0.999930	−	0.0118638i	$-0.00377647\pi$
$500$		0			0
$501$	−0.646094	+	1.41475i	−0.0288653	+	0.0632063i
$502$		0			0
$503$	−3.28592	−	15.1051i	−0.146512	−	0.673505i	−0.990542	−	0.137209i	$-0.956187\pi$
$503$	−3.28592	−	15.1051i	−0.146512	−	0.673505i	0.844030	−	0.536296i	$-0.180177\pi$
$504$		0			0
$505$	−6.39772	+	38.2898i	−0.284695	+	1.70387i
$506$		0			0
$507$	−19.1309	−	19.1309i	−0.849635	−	0.849635i
$508$		0			0
$509$	−6.18374	+	9.62209i	−0.274090	+	0.426492i	−0.950822	−	0.309737i	$-0.899759\pi$
$509$	−6.18374	+	9.62209i	−0.274090	+	0.426492i	0.676733	+	0.736229i	$0.263395\pi$
$510$		0			0
$511$	8.31135	+	3.79567i	0.367673	+	0.167910i
$512$		0			0
$513$	13.2723	+	24.3065i	0.585988	+	1.07316i
$514$		0			0
$515$	−20.4584	−	11.7832i	−0.901504	−	0.519232i
$516$		0			0
$517$	−1.18241	−	16.5323i	−0.0520025	−	0.727090i
$518$		0			0
$519$	−3.54989	−	12.0898i	−0.155823	−	0.530684i
$520$		0			0
$521$	5.28563	+	8.22459i	0.231567	+	0.360326i	0.937519	−	0.347934i	$-0.113117\pi$
$521$	5.28563	+	8.22459i	0.231567	+	0.360326i	−0.705951	+	0.708260i	$0.749480\pi$
$522$		0			0
$523$	−6.19081	+	8.26995i	−0.270705	+	0.361620i	−0.915208	−	0.402982i	$-0.867974\pi$
$523$	−6.19081	+	8.26995i	−0.270705	+	0.361620i	0.644503	+	0.764602i	$0.277065\pi$
$524$		0			0
$525$	−12.8763	−	6.60426i	−0.561967	−	0.288234i
$526$		0			0
$527$	27.5922	+	1.97343i	1.20193	+	0.0859641i
$528$		0			0
$529$	−17.9693	+	14.3564i	−0.781273	+	0.624190i
$530$		0			0
$531$	0.612140	+	0.706447i	0.0265646	+	0.0306572i
$532$		0			0
$533$	10.1270	+	13.5281i	0.438650	+	0.585967i
$534$		0			0
$535$	3.32657	−	3.17850i	0.143820	−	0.137418i
$536$		0			0
$537$	−11.8113	−	2.56938i	−0.509693	−	0.110877i
$538$		0			0
$539$	−8.47881	+	2.48960i	−0.365208	+	0.107235i
$540$		0			0
$541$	14.9183	−	17.2167i	0.641389	−	0.740203i	−0.338230	−	0.941063i	$-0.609828\pi$
$541$	14.9183	−	17.2167i	0.641389	−	0.740203i	0.979620	+	0.200861i	$0.0643738\pi$
$542$		0			0
$543$	−1.28326	+	3.44056i	−0.0550701	+	0.147649i
$544$		0			0
$545$	14.7698	−	30.4857i	0.632668	−	1.30586i
$546$		0			0
$547$	−0.121470	+	0.0453060i	−0.00519368	+	0.00193714i	−0.352060	−	0.935978i	$-0.614519\pi$
$547$	−0.121470	+	0.0453060i	−0.00519368	+	0.00193714i	0.346866	+	0.937915i	$0.387246\pi$
$548$		0			0
$549$	25.1034	+	16.1330i	1.07139	+	0.688540i
$550$		0			0
$551$			23.2712i			0.991386i
$552$		0			0
$553$	−5.90349	+	5.90349i	−0.251042	+	0.251042i
$554$		0			0
$555$	−11.4095	−	10.3502i	−0.484305	−	0.439342i
$556$		0			0
$557$	−9.11148	−	24.4288i	−0.386066	−	1.03508i	−0.974074	−	0.226228i	$-0.927361\pi$
$557$	−9.11148	−	24.4288i	−0.386066	−	1.03508i	0.588009	−	0.808855i	$-0.299912\pi$
$558$		0			0
$559$	−27.0491	−	7.94234i	−1.14406	−	0.335925i
$560$		0			0
$561$	7.36612	+	16.1295i	0.310998	+	0.680990i
$562$		0			0
$563$	−20.2646	+	1.44936i	−0.854052	+	0.0610830i	−0.491497	−	0.870879i	$-0.663550\pi$
$563$	−20.2646	+	1.44936i	−0.854052	+	0.0610830i	−0.362555	+	0.931962i	$0.618096\pi$
$564$		0			0
$565$	−10.8218	+	13.7906i	−0.455277	+	0.580174i
$566$		0			0
$567$	−1.41291	+	6.49506i	−0.0593368	+	0.272767i
$568$		0			0
$569$	−0.592821	−	4.12316i	−0.0248524	−	0.172852i	0.973615	−	0.228197i	$-0.0732831\pi$
$569$	−0.592821	−	4.12316i	−0.0248524	−	0.172852i	−0.998467	+	0.0553453i	$0.982374\pi$
$570$		0			0
$571$	−18.5290	−	2.66407i	−0.775416	−	0.111488i	−0.256765	−	0.966474i	$-0.582657\pi$
$571$	−18.5290	−	2.66407i	−0.775416	−	0.111488i	−0.518651	+	0.854986i	$0.673566\pi$
$572$		0			0
$573$	−0.253898	+	3.54996i	−0.0106067	+	0.148302i
$574$		0			0
$575$	−18.0288	+	15.8102i	−0.751852	+	0.659332i
$576$		0			0
$577$	1.02178	−	14.2864i	0.0425373	−	0.594750i	−0.930823	−	0.365470i	$-0.880908\pi$
$577$	1.02178	−	14.2864i	0.0425373	−	0.594750i	0.973361	−	0.229280i	$-0.0736371\pi$
$578$		0			0
$579$	2.82081	+	0.405571i	0.117229	+	0.0168549i
$580$		0			0
$581$	1.77450	+	12.3419i	0.0736185	+	0.512028i
$582$		0			0
$583$	−1.31431	+	6.04176i	−0.0544330	+	0.250224i
$584$		0			0
$585$	19.3810	−	24.6979i	0.801306	−	1.02113i
$586$		0			0
$587$	0.212072	−	0.0151677i	0.00875317	−	0.000626039i	−0.0669619	−	0.997756i	$-0.521331\pi$
$587$	0.212072	−	0.0151677i	0.00875317	−	0.000626039i	0.0757151	+	0.997129i	$0.475876\pi$
$588$		0			0
$589$	10.5501	+	23.1014i	0.434708	+	0.951877i
$590$		0			0
$591$	6.24425	+	1.83348i	0.256854	+	0.0754192i
$592$		0			0
$593$	−0.215655	−	0.578195i	−0.00885591	−	0.0237436i	0.932447	−	0.361308i	$-0.117670\pi$
$593$	−0.215655	−	0.578195i	−0.00885591	−	0.0237436i	−0.941302	+	0.337564i	$0.890397\pi$
$594$		0			0
$595$	−33.2018	−	30.1193i	−1.36114	−	1.23477i
$596$		0			0
$597$	−7.85846	+	7.85846i	−0.321625	+	0.321625i
$598$		0			0
$599$		−	28.7217i		−	1.17354i	−0.809755	−	0.586769i	$-0.800400\pi$
$599$		−	28.7217i		−	1.17354i	0.809755	−	0.586769i	$-0.199600\pi$
$600$		0			0
$601$	8.41450	+	5.40767i	0.343235	+	0.220584i	0.700889	−	0.713271i	$-0.252787\pi$
$601$	8.41450	+	5.40767i	0.343235	+	0.220584i	−0.357654	+	0.933854i	$0.616423\pi$
$602$		0			0
$603$	−16.0916	+	6.00187i	−0.655302	+	0.244415i
$604$		0			0
$605$	−1.77120	+	3.65586i	−0.0720096	+	0.148632i
$606$		0			0
$607$	9.99798	−	26.8056i	0.405806	−	1.08801i	−0.559944	−	0.828531i	$-0.689177\pi$
$607$	9.99798	−	26.8056i	0.405806	−	1.08801i	0.965749	−	0.259476i	$-0.0835500\pi$
$608$		0			0
$609$	7.54622	−	8.70881i	0.305788	−	0.352899i
$610$		0			0
$611$	34.1865	−	10.0381i	1.38304	−	0.406096i
$612$		0			0
$613$	−19.4768	−	4.23691i	−0.786660	−	0.171127i	−0.198746	−	0.980051i	$-0.563687\pi$
$613$	−19.4768	−	4.23691i	−0.786660	−	0.171127i	−0.587914	+	0.808924i	$0.700051\pi$
$614$		0			0
$615$	3.85461	−	3.68304i	0.155433	−	0.148514i
$616$		0			0
$617$	10.3415	+	13.8146i	0.416333	+	0.556155i	0.958859	−	0.283884i	$-0.0916230\pi$
$617$	10.3415	+	13.8146i	0.416333	+	0.556155i	−0.542526	+	0.840039i	$0.682532\pi$
$618$		0			0
$619$	3.92665	+	4.53160i	0.157826	+	0.182140i	0.829155	−	0.559019i	$-0.188822\pi$
$619$	3.92665	+	4.53160i	0.157826	+	0.182140i	−0.671330	+	0.741159i	$0.734276\pi$
$620$		0			0
$621$	−18.8674	−	12.6643i	−0.757125	−	0.508200i
$622$		0			0
$623$	41.9733	+	3.00199i	1.68163	+	0.120272i
$624$		0			0
$625$	−18.0213	+	17.3272i	−0.720852	+	0.693089i
$626$		0			0
$627$	−9.75581	+	13.0322i	−0.389609	+	0.520457i
$628$		0			0
$629$	−25.7990	−	40.1441i	−1.02867	−	1.60065i
$630$		0			0
$631$	−9.87356	−	33.6263i	−0.393060	−	1.33864i	−0.884016	−	0.467456i	$-0.845171\pi$
$631$	−9.87356	−	33.6263i	−0.393060	−	1.33864i	0.490956	−	0.871184i	$-0.336647\pi$
$632$		0			0
$633$	−0.592017	−	8.27748i	−0.0235306	−	0.329000i
$634$		0			0
$635$	−43.4961	−	25.0521i	−1.72609	−	0.994162i
$636$		0			0
$637$	−9.10386	−	16.6725i	−0.360708	−	0.660587i
$638$		0			0
$639$	−22.4350	−	10.2457i	−0.887515	−	0.405314i
$640$		0			0
$641$	13.1251	−	20.4231i	0.518410	−	0.806662i	−0.479057	−	0.877784i	$-0.659021\pi$
$641$	13.1251	−	20.4231i	0.518410	−	0.806662i	0.997468	+	0.0711215i	$0.0226578\pi$
$642$		0			0
$643$	15.2304	+	15.2304i	0.600629	+	0.600629i	0.940480	−	0.339850i	$-0.110376\pi$
$643$	15.2304	+	15.2304i	0.600629	+	0.600629i	−0.339850	+	0.940480i	$0.610376\pi$
$644$		0			0
$645$	−1.46573	+	8.77226i	−0.0577131	+	0.345408i
$646$		0			0
$647$	5.78035	+	26.5718i	0.227249	+	1.04465i	0.939454	+	0.342675i	$0.111333\pi$
$647$	5.78035	+	26.5718i	0.227249	+	1.04465i	−0.712205	+	0.701971i	$0.752303\pi$
$648$		0			0
$649$	−0.545991	+	1.19555i	−0.0214320	+	0.0469296i
$650$		0			0
$651$	3.54301	−	12.0664i	0.138861	−	0.472919i
$652$		0			0
$653$	24.2050	+	9.02800i	0.947215	+	0.353293i	0.775139	−	0.631791i	$-0.217680\pi$
$653$	24.2050	+	9.02800i	0.947215	+	0.353293i	0.172076	+	0.985084i	$0.444952\pi$
$654$		0			0
$655$	25.3616	+	30.6513i	0.990961	+	1.19765i
$656$		0			0
$657$	5.48870	+	2.99706i	0.214135	+	0.116926i
$658$		0			0
$659$	23.6015	−	15.1678i	0.919385	−	0.590853i	0.00690556	−	0.999976i	$-0.497802\pi$
$659$	23.6015	−	15.1678i	0.919385	−	0.590853i	0.912479	+	0.409124i	$0.134166\pi$
$660$		0			0
$661$	−14.9326	+	2.14699i	−0.580811	+	0.0835081i	−0.426458	−	0.904508i	$-0.640239\pi$
$661$	−14.9326	+	2.14699i	−0.580811	+	0.0835081i	−0.154354	+	0.988016i	$0.549330\pi$
$662$		0			0
$663$	−30.5149	+	22.8431i	−1.18510	+	0.887154i
$664$		0			0
$665$	9.66106	−	40.0053i	0.374640	−	1.55134i
$666$		0			0
$667$	−8.81490	−	16.9382i	−0.341314	−	0.655849i
$668$		0			0
$669$	−2.66773	+	2.31160i	−0.103140	+	0.0893717i
$670$		0			0
$671$	−5.97115	+	41.5303i	−0.230514	+	1.60326i
$672$		0			0
$673$	−30.9730	−	23.1861i	−1.19392	−	0.893757i	−0.197669	−	0.980269i	$-0.563337\pi$
$673$	−30.9730	−	23.1861i	−1.19392	−	0.893757i	−0.996251	+	0.0865113i	$0.972428\pi$
$674$		0			0
$675$	−20.2550	−	12.2882i	−0.779615	−	0.472975i
$676$		0			0
$677$	−16.6593	+	30.5092i	−0.640268	+	1.17256i	0.333008	+	0.942924i	$0.391936\pi$
$677$	−16.6593	+	30.5092i	−0.640268	+	1.17256i	−0.973276	+	0.229639i	$0.926246\pi$
$678$		0			0
$679$	34.3669	+	29.7791i	1.31888	+	1.14282i
$680$		0			0
$681$	−15.7623	+	7.19838i	−0.604011	+	0.275843i
$682$		0			0
$683$	−1.74040	+	0.950329i	−0.0665945	+	0.0363633i	−0.512201	−	0.858865i	$-0.671170\pi$
$683$	−1.74040	+	0.950329i	−0.0665945	+	0.0363633i	0.445607	+	0.895229i	$0.352988\pi$
$684$		0			0
$685$	14.8788	−	2.88374i	0.568490	−	0.110182i
$686$		0			0
$687$	−14.5877	+	3.17335i	−0.556554	+	0.121071i
$688$		0			0
$689$	−13.2915			−0.506367
$690$		0			0
$691$	−37.4791			−1.42577			−0.712885	−	0.701280i	$-0.752612\pi$
$691$	−37.4791			−1.42577			−0.712885	+	0.701280i	$0.752612\pi$
$692$		0			0
$693$	−20.0967	+	4.37177i	−0.763411	+	0.166070i
$694$		0			0
$695$	−1.51899	+	2.24935i	−0.0576186	+	0.0853228i
$696$		0			0
$697$	14.4948	−	7.91475i	0.549029	−	0.299793i
$698$		0			0
$699$	2.89884	−	1.32386i	0.109644	−	0.0500728i
$700$		0			0
$701$	37.8577	+	32.8039i	1.42986	+	1.23898i	0.927234	+	0.374483i	$0.122180\pi$
$701$	37.8577	+	32.8039i	1.42986	+	1.23898i	0.502630	+	0.864501i	$0.332366\pi$
$702$		0			0
$703$	20.9959	−	38.4511i	0.791875	−	1.45021i
$704$		0			0
$705$	−4.43566	−	10.3285i	−0.167056	−	0.388993i
$706$		0			0
$707$	43.7653	+	32.7623i	1.64596	+	1.23215i
$708$		0			0
$709$	2.64211	−	18.3763i	0.0992264	−	0.690135i	−0.878112	−	0.478454i	$-0.841197\pi$
$709$	2.64211	−	18.3763i	0.0992264	−	0.690135i	0.977339	−	0.211681i	$-0.0678937\pi$
$710$		0			0
$711$	−4.31847	+	3.74198i	−0.161955	+	0.140335i
$712$		0			0
$713$	−16.4296	−	12.8183i	−0.615292	−	0.480051i
$714$		0			0
$715$	42.9087	+	10.3622i	1.60469	+	0.387525i
$716$		0			0
$717$	18.8040	−	14.0765i	0.702248	−	0.525697i
$718$		0			0
$719$	24.4979	−	3.52227i	0.913619	−	0.131359i	0.330557	−	0.943786i	$-0.392763\pi$
$719$	24.4979	−	3.52227i	0.913619	−	0.131359i	0.583062	+	0.812427i	$0.301854\pi$
$720$		0			0
$721$	−27.9699	+	17.9752i	−1.04165	+	0.669430i
$722$		0			0
$723$	4.56652	+	2.49351i	0.169831	+	0.0927346i
$724$		0			0
$725$	−9.98966	−	17.2196i	−0.371007	−	0.639521i
$726$		0			0
$727$	−12.5610	−	4.68500i	−0.465861	−	0.173757i	0.105562	−	0.994413i	$-0.466336\pi$
$727$	−12.5610	−	4.68500i	−0.465861	−	0.173757i	−0.571423	+	0.820656i	$0.693608\pi$
$728$		0			0
$729$	2.39905	−	8.17042i	0.0888538	−	0.302608i
$730$		0			0
$731$	−11.4450	+	25.0611i	−0.423309	+	0.926918i
$732$		0			0
$733$	6.19552	+	28.4803i	0.228837	+	1.05195i	0.937928	+	0.346829i	$0.112742\pi$
$733$	6.19552	+	28.4803i	0.228837	+	1.05195i	−0.709092	+	0.705116i	$0.750895\pi$
$734$		0			0
$735$	−4.87813	+	3.48136i	−0.179932	+	0.128412i
$736$		0			0
$737$	−17.0754	−	17.0754i	−0.628980	−	0.628980i
$738$		0			0
$739$	−22.5374	+	35.0689i	−0.829053	+	1.29003i	0.125531	+	0.992090i	$0.459937\pi$
$739$	−22.5374	+	35.0689i	−0.829053	+	1.29003i	−0.954584	+	0.297942i	$0.903700\pi$
$740$		0			0
$741$	−31.8326	−	14.5375i	−1.16940	−	0.534047i
$742$		0			0
$743$	2.91126	+	5.33158i	0.106804	+	0.195597i	0.925615	−	0.378466i	$-0.123548\pi$
$743$	2.91126	+	5.33158i	0.106804	+	0.195597i	−0.818811	+	0.574063i	$0.805367\pi$
$744$		0			0
$745$	−1.78131	+	0.479292i	−0.0652623	+	0.0175599i
$746$		0			0
$747$	0.608809	+	8.51226i	0.0222752	+	0.311447i
$748$		0			0
$749$	−1.82545	−	6.21692i	−0.0667006	−	0.227161i
$750$		0			0
$751$	−11.3991	−	17.7373i	−0.415959	−	0.647245i	0.568536	−	0.822658i	$-0.307510\pi$
$751$	−11.3991	−	17.7373i	−0.415959	−	0.647245i	−0.984495	+	0.175414i	$0.943874\pi$
$752$		0			0
$753$	4.99738	−	6.67572i	0.182115	−	0.243277i
$754$		0			0
$755$	39.3540	+	12.5349i	1.43224	+	0.456193i
$756$		0			0
$757$	3.14663	+	0.225052i	0.114366	+	0.00817964i	0.128405	−	0.991722i	$-0.459014\pi$
$757$	3.14663	+	0.225052i	0.114366	+	0.00817964i	−0.0140387	+	0.999901i	$0.504469\pi$
$758$		0			0
$759$	2.16438	−	13.1811i	0.0785621	−	0.478442i
$760$		0			0
$761$	5.18202	+	5.98038i	0.187848	+	0.216788i	0.841860	−	0.539696i	$-0.181461\pi$
$761$	5.18202	+	5.98038i	0.187848	+	0.216788i	−0.654012	+	0.756484i	$0.726915\pi$
$762$		0			0
$763$	−28.5886	−	38.1899i	−1.03498	−	1.38257i
$764$		0			0
$765$	−21.1957	−	22.1831i	−0.766333	−	0.802032i
$766$		0			0
$767$	−2.76080	−	0.600575i	−0.0996866	−	0.0216855i
$768$		0			0
$769$	−11.1214	+	3.26554i	−0.401048	+	0.117758i	−0.476035	−	0.879426i	$-0.657927\pi$
$769$	−11.1214	+	3.26554i	−0.401048	+	0.117758i	0.0749874	+	0.997184i	$0.476108\pi$
$770$		0			0
$771$	4.23349	−	4.88570i	0.152465	−	0.175954i
$772$		0			0
$773$	17.4410	−	46.7610i	0.627308	−	1.68188i	−0.0995007	−	0.995037i	$-0.531725\pi$
$773$	17.4410	−	46.7610i	0.627308	−	1.68188i	0.726809	−	0.686840i	$-0.241003\pi$
$774$		0			0
$775$	−17.7233	−	12.5652i	−0.636641	−	0.451354i
$776$		0			0
$777$	−20.3260	+	7.58120i	−0.729191	+	0.271974i
$778$		0			0
$779$	12.7550	+	8.19717i	0.456997	+	0.293694i
$780$		0			0
$781$		−	34.6786i		−	1.24090i
$782$		0			0
$783$	13.3397	−	13.3397i	0.476722	−	0.476722i
$784$		0			0
$785$	−1.46554	−	30.1056i	−0.0523075	−	1.07451i
$786$		0			0
$787$	−18.6402	−	49.9763i	−0.664451	−	1.78146i	−0.622869	−	0.782326i	$-0.714033\pi$
$787$	−18.6402	−	49.9763i	−0.664451	−	1.78146i	−0.0415812	−	0.999135i	$-0.513240\pi$
$788$		0			0
$789$	−21.2572	−	6.24169i	−0.756778	−	0.222210i
$790$		0			0
$791$	10.2551	+	22.4556i	0.364631	+	0.798430i
$792$		0			0
$793$	−89.9645	+	6.43439i	−3.19473	+	0.228492i
$794$		0			0
$795$	0.502161	+	4.16311i	0.0178098	+	0.147650i
$796$		0			0
$797$	5.59543	−	25.7218i	0.198200	−	0.911113i	−0.765356	−	0.643607i	$-0.777437\pi$
$797$	5.59543	−	25.7218i	0.198200	−	0.911113i	0.963556	−	0.267505i	$-0.0861993\pi$
$798$		0			0
$799$	−4.95548	−	34.4661i	−0.175312	−	1.21932i
$800$		0			0
$801$	28.5079	+	4.09882i	1.00728	+	0.144825i
$802$		0			0
$803$	−0.627283	+	8.77056i	−0.0221363	+	0.309506i
$804$		0			0
$805$	8.12172	+	32.7778i	0.286253	+	1.15526i
$806$		0			0
$807$	0.544907	−	7.61880i	0.0191816	−	0.268194i
$808$		0			0
$809$	6.31101	+	0.907386i	0.221883	+	0.0319020i	0.252360	−	0.967633i	$-0.418793\pi$
$809$	6.31101	+	0.907386i	0.221883	+	0.0319020i	−0.0304765	+	0.999535i	$0.509702\pi$
$810$		0			0
$811$	6.73776	+	46.8621i	0.236595	+	1.64555i	0.668558	+	0.743660i	$0.266912\pi$
$811$	6.73776	+	46.8621i	0.236595	+	1.64555i	−0.431963	+	0.901891i	$0.642179\pi$
$812$		0			0
$813$	2.19336	−	10.0827i	0.0769244	−	0.353616i
$814$		0			0
$815$	−13.9704	−	10.9629i	−0.489362	−	0.384014i
$816$		0			0
$817$	−25.2293	+	1.80443i	−0.882661	+	0.0631291i
$818$		0			0
$819$	−18.3662	−	40.2163i	−0.641766	−	1.40527i
$820$		0			0
$821$	−4.57170	−	1.34237i	−0.159553	−	0.0468491i	0.200980	−	0.979595i	$-0.435587\pi$
$821$	−4.57170	−	1.34237i	−0.159553	−	0.0468491i	−0.360534	+	0.932746i	$0.617405\pi$
$822$		0			0
$823$	7.05153	+	18.9059i	0.245801	+	0.659018i	0.999997	+	0.00236885i	$0.000754030\pi$
$823$	7.05153	+	18.9059i	0.245801	+	0.659018i	−0.754196	+	0.656649i	$0.771973\pi$
$824$		0			0
$825$	1.62449	−	13.8312i	0.0565575	−	0.481539i
$826$		0			0
$827$	−26.4769	+	26.4769i	−0.920691	+	0.920691i	−0.997078	−	0.0763875i	$-0.975661\pi$
$827$	−26.4769	+	26.4769i	−0.920691	+	0.920691i	0.0763875	+	0.997078i	$0.475661\pi$
$828$		0			0
$829$		−	45.6929i		−	1.58698i	−0.608583	−	0.793490i	$-0.708262\pi$
$829$		−	45.6929i		−	1.58698i	0.608583	−	0.793490i	$-0.291738\pi$
$830$		0			0
$831$	−8.87860	−	5.70593i	−0.307995	−	0.197936i
$832$		0			0
$833$	−17.3942	+	6.48769i	−0.602672	+	0.224785i
$834$		0			0
$835$	3.57445	−	1.24130i	0.123699	−	0.0429570i
$836$		0			0
$837$	7.19479	−	19.2900i	0.248688	−	0.666759i
$838$		0			0
$839$	−1.73722	+	2.00486i	−0.0599756	+	0.0692156i	−0.784945	−	0.619566i	$-0.787309\pi$
$839$	−1.73722	+	2.00486i	−0.0599756	+	0.0692156i	0.724969	+	0.688782i	$0.241854\pi$
$840$		0			0
$841$	−12.6151	+	3.70412i	−0.435003	+	0.127728i
$842$		0			0
$843$	14.1458	+	3.07724i	0.487208	+	0.105986i
$844$		0			0
$845$	−1.49785	+	65.8051i	−0.0515277	+	2.26376i
$846$		0			0
$847$	3.42836	+	4.57976i	0.117800	+	0.157362i
$848$		0			0
$849$	5.63526	+	6.50344i	0.193402	+	0.223198i
$850$		0			0
$851$	−0.717173	+	35.9401i	−0.0245844	+	1.23201i
$852$		0			0
$853$	28.2565	+	2.02094i	0.967484	+	0.0691958i	0.546130	−	0.837701i	$-0.316101\pi$
$853$	28.2565	+	2.02094i	0.967484	+	0.0691958i	0.421354	+	0.906896i	$0.361555\pi$
$854$		0			0
$855$	8.54877	−	26.8393i	0.292362	−	0.917884i
$856$		0			0
$857$	−5.79782	+	7.74498i	−0.198050	+	0.264563i	−0.888561	−	0.458758i	$-0.848295\pi$
$857$	−5.79782	+	7.74498i	−0.198050	+	0.264563i	0.690512	+	0.723321i	$0.257385\pi$
$858$		0			0
$859$	26.0459	+	40.5282i	0.888674	+	1.38280i	0.923577	+	0.383414i	$0.125252\pi$
$859$	26.0459	+	40.5282i	0.888674	+	1.38280i	−0.0349023	+	0.999391i	$0.511112\pi$
$860$		0			0
$861$	−2.11521	−	7.20376i	−0.0720863	−	0.245503i
$862$		0			0
$863$	2.99979	+	41.9425i	0.102114	+	1.42774i	0.747692	+	0.664046i	$0.231162\pi$
$863$	2.99979	+	41.9425i	0.102114	+	1.42774i	−0.645578	+	0.763695i	$0.723383\pi$
$864$		0			0
$865$	−15.2997	+	26.5638i	−0.520206	+	0.903195i
$866$		0			0
$867$	10.3649	+	18.9818i	0.352010	+	0.644657i
$868$		0			0
$869$	−7.30835	−	3.33761i	−0.247919	−	0.113221i
$870$		0			0
$871$	28.0650	−	43.6700i	0.950947	−	1.47970i
$872$		0			0
$873$	22.0077	+	22.0077i	0.744849	+	0.744849i
$874$		0			0
$875$	10.0244	+	33.7493i	0.338886	+	1.14094i
$876$		0			0
$877$	2.21938	+	10.2023i	0.0749432	+	0.344508i	0.999316	−	0.0369823i	$-0.0117745\pi$
$877$	2.21938	+	10.2023i	0.0749432	+	0.344508i	−0.924373	+	0.381491i	$0.875411\pi$
$878$		0			0
$879$	−5.33653	+	11.6854i	−0.179997	+	0.394138i
$880$		0			0
$881$	4.12308	−	14.0419i	0.138910	−	0.473084i	−0.860424	−	0.509579i	$-0.829801\pi$
$881$	4.12308	−	14.0419i	0.138910	−	0.473084i	0.999334	+	0.0364948i	$0.0116192\pi$
$882$		0			0
$883$	−7.59872	−	2.83417i	−0.255717	−	0.0953776i	0.218336	−	0.975874i	$-0.429937\pi$
$883$	−7.59872	−	2.83417i	−0.255717	−	0.0953776i	−0.474054	+	0.880496i	$0.657210\pi$
$884$		0			0
$885$	−0.0838049	+	0.887414i	−0.00281707	+	0.0298301i
$886$		0			0
$887$	25.7674	+	14.0701i	0.865185	+	0.472427i	0.849585	−	0.527452i	$-0.176852\pi$
$887$	25.7674	+	14.0701i	0.865185	+	0.472427i	0.0155999	+	0.999878i	$0.495034\pi$
$888$		0			0
$889$	−59.4661	+	38.2166i	−1.99443	+	1.28174i
$890$		0			0
$891$	−6.33155	+	0.910339i	−0.212115	+	0.0304975i
$892$		0			0
$893$	25.5916	−	19.1576i	0.856391	−	0.641086i
$894$		0			0
$895$	15.3318	+	25.0945i	0.512484	+	0.838815i
$896$		0			0
$897$	28.6763	−	1.47664i	0.957475	−	0.0493035i
$898$		0			0
$899$	13.0745	−	11.3291i	0.436060	−	0.377848i
$900$		0			0
$901$	−1.84862	+	12.8575i	−0.0615866	+	0.428344i
$902$		0			0
$903$	10.0267	+	7.50591i	0.333668	+	0.249781i
$904$		0			0
$905$	8.20876	−	3.52532i	0.272868	−	0.117186i
$906$		0			0
$907$	−0.922692	+	1.68978i	−0.0306375	+	0.0561084i	−0.892549	−	0.450950i	$-0.851085\pi$
$907$	−0.922692	+	1.68978i	−0.0306375	+	0.0561084i	0.861912	+	0.507058i	$0.169267\pi$
$908$		0			0
$909$	28.2782	+	24.5032i	0.937929	+	0.812720i
$910$		0			0
$911$	30.1060	−	13.7489i	0.997455	−	0.455523i	0.151317	−	0.988485i	$-0.451649\pi$
$911$	30.1060	−	13.7489i	0.997455	−	0.455523i	0.846139	+	0.532963i	$0.178921\pi$
$912$		0			0
$913$	−10.5315	+	5.75063i	−0.348542	+	0.190318i
$914$		0			0
$915$	5.41426	+	27.9352i	0.178990	+	0.923508i
$916$		0			0
$917$	54.7452	−	11.9091i	1.80784	−	0.393273i
$918$		0			0
$919$	−13.5293			−0.446290			−0.223145	−	0.974785i	$-0.571632\pi$
$919$	−13.5293			−0.446290			−0.223145	+	0.974785i	$0.571632\pi$
$920$		0			0
$921$	−3.01754			−0.0994312
$922$		0			0
$923$	72.8439	−	15.8462i	2.39769	−	0.521584i
$924$		0			0
$925$	0.969952	+	37.4650i	0.0318918	+	1.23184i
$926$		0			0
$927$	−19.9723	+	10.9057i	−0.655975	+	0.358190i
$928$		0			0
$929$	47.3567	−	21.6271i	1.55372	−	0.709561i	0.560759	−	0.827979i	$-0.310509\pi$
$929$	47.3567	−	21.6271i	1.55372	−	0.709561i	0.992964	+	0.118418i	$0.0377822\pi$
$930$		0			0
$931$	−12.8808	−	11.1613i	−0.422152	−	0.365797i
$932$		0			0
$933$	13.7804	−	25.2369i	0.451149	−	0.826218i
$934$		0			0
$935$	15.9917	−	40.0662i	0.522983	−	1.31030i
$936$		0			0
$937$	5.10561	+	3.82201i	0.166793	+	0.124860i	0.679414	−	0.733756i	$-0.262234\pi$
$937$	5.10561	+	3.82201i	0.166793	+	0.124860i	−0.512620	+	0.858615i	$0.671325\pi$
$938$		0			0
$939$	−1.30365	+	9.06708i	−0.0425430	+	0.295893i
$940$		0			0
$941$	−26.6258	+	23.0714i	−0.867977	+	0.752106i	−0.970110	−	0.242664i	$-0.921979\pi$
$941$	−26.6258	+	23.0714i	−0.867977	+	0.752106i	0.102133	+	0.994771i	$0.467433\pi$
$942$		0			0
$943$	−12.3889	−	1.13491i	−0.403438	−	0.0369577i
$944$		0			0
$945$	−28.4702	+	17.3942i	−0.926134	+	0.565833i
$946$		0			0
$947$	38.8500	−	29.0827i	1.26245	−	0.945062i	0.262651	−	0.964891i	$-0.415403\pi$
$947$	38.8500	−	29.0827i	1.26245	−	0.945062i	0.999803	+	0.0198290i	$0.00631219\pi$
$948$		0			0
$949$	−18.7096	+	2.69003i	−0.607338	+	0.0873220i
$950$		0			0
$951$	−9.91140	+	6.36967i	−0.321399	+	0.206551i
$952$		0			0
$953$	35.7296	+	19.5098i	1.15740	+	0.631986i	0.939014	−	0.343878i	$-0.111741\pi$
$953$	35.7296	+	19.5098i	1.15740	+	0.631986i	0.218381	+	0.975864i	$0.429922\pi$
$954$		0			0
$955$	6.67113	−	5.51985i	0.215873	−	0.178618i
$956$		0			0
$957$	10.3903	+	3.87537i	0.335870	+	0.125273i
$958$		0			0
$959$	6.01308	−	20.4787i	0.194173	−	0.661291i
$960$		0			0
$961$	−5.03483	+	11.0247i	−0.162414	+	0.355636i
$962$		0			0
$963$	−0.942657	−	4.33332i	−0.0303767	−	0.139639i
$964$		0			0
$965$	−4.02756	−	5.64346i	−0.129652	−	0.181669i
$966$		0			0
$967$	14.9921	+	14.9921i	0.482112	+	0.482112i	0.905806	−	0.423693i	$-0.139267\pi$
$967$	14.9921	+	14.9921i	0.482112	+	0.482112i	−0.423693	+	0.905806i	$0.639267\pi$
$968$		0			0
$969$	−18.4901	+	28.7711i	−0.593986	+	0.924260i
$970$		0			0
$971$	−7.51822	−	3.43346i	−0.241271	−	0.110185i	0.291110	−	0.956690i	$-0.405975\pi$
$971$	−7.51822	−	3.43346i	−0.241271	−	0.110185i	−0.532381	+	0.846505i	$0.678703\pi$
$972$		0			0
$973$	1.83184	+	3.35477i	0.0587262	+	0.107549i
$974$		0			0
$975$	29.7952	−	2.90776i	0.954210	−	0.0931229i
$976$		0			0
$977$	0.647198	+	9.04901i	0.0207057	+	0.289503i	0.997246	+	0.0741677i	$0.0236300\pi$
$977$	0.647198	+	9.04901i	0.0207057	+	0.289503i	−0.976540	+	0.215336i	$0.930915\pi$
$978$		0			0
$979$	11.4090	+	38.8555i	0.364633	+	1.24183i
$980$		0			0
$981$	−17.6523	−	27.4675i	−0.563595	−	0.876971i
$982$		0			0
$983$	15.3441	−	20.4973i	0.489399	−	0.653761i	−0.486064	−	0.873923i	$-0.661568\pi$
$983$	15.3441	−	20.4973i	0.489399	−	0.653761i	0.975463	+	0.220162i	$0.0706587\pi$
$984$		0			0
$985$	−7.26969	−	14.0652i	−0.231632	−	0.448155i
$986$		0			0
$987$	−15.7895	−	1.12929i	−0.502585	−	0.0359456i
$988$		0			0
$989$	17.6799	−	10.8700i	0.562188	−	0.345645i
$990$		0			0
$991$	7.85883	+	9.06957i	0.249644	+	0.288105i	0.866716	−	0.498802i	$-0.166227\pi$
$991$	7.85883	+	9.06957i	0.249644	+	0.288105i	−0.617072	+	0.786907i	$0.711681\pi$
$992$		0			0
$993$	8.42738	+	11.2577i	0.267435	+	0.357251i
$994$		0			0
$995$	27.0309	+	0.615276i	0.856936	+	0.0195056i
$996$		0			0
$997$	34.5228	+	7.50997i	1.09335	+	0.237843i	0.722860	−	0.690994i	$-0.242827\pi$
$997$	34.5228	+	7.50997i	1.09335	+	0.237843i	0.370487	+	0.928838i	$0.379191\pi$
$998$		0			0
$999$	−34.0767	+	10.0058i	−1.07814	+	0.316570i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.217.8	yes	240
5.3	odd	4	inner	460.2.x.a.33.8	✓	240
23.7	odd	22	inner	460.2.x.a.237.8	yes	240
115.53	even	44	inner	460.2.x.a.53.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.33.8	✓	240	5.3	odd	4	inner
460.2.x.a.53.8	yes	240	115.53	even	44	inner
460.2.x.a.217.8	yes	240	1.1	even	1	trivial
460.2.x.a.237.8	yes	240	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.898100 - 0.195370i) q^{3} +(-1.85310 - 1.25140i) q^{5} +(-2.76379 + 1.50914i) q^{7} +(-1.96048 + 0.895322i) q^{9} +O(q^{10})\)	\(q+(0.898100 - 0.195370i) q^{3} +(-1.85310 - 1.25140i) q^{5} +(-2.76379 + 1.50914i) q^{7} +(-1.96048 + 0.895322i) q^{9} +(-2.29022 - 1.98448i) q^{11} +(3.12199 - 5.71749i) q^{13} +(-1.90876 - 0.761845i) q^{15} +(-5.09655 - 3.81523i) q^{17} +(0.831806 - 5.78534i) q^{19} +(-2.18732 + 1.89532i) q^{21} +(1.58599 + 4.52600i) q^{23} +(1.86798 + 4.63796i) q^{25} +(-3.79313 + 2.83950i) q^{27} +(-3.94097 + 0.566627i) q^{29} +(-3.65534 + 2.34915i) q^{31} +(-2.44455 - 1.33483i) q^{33} +(7.01013 + 0.662017i) q^{35} +(7.02292 + 2.61941i) q^{37} +(1.68683 - 5.74482i) q^{39} +(-1.07762 + 2.35966i) q^{41} +(-0.919885 - 4.22864i) q^{43} +(4.75338 + 0.794229i) q^{45} +(3.86747 + 3.86747i) q^{47} +(1.57653 - 2.45313i) q^{49} +(-5.32260 - 2.43075i) q^{51} +(-0.977837 - 1.79077i) q^{53} +(1.76062 + 6.54344i) q^{55} +(-0.383234 - 5.35832i) q^{57} +(-0.122192 - 0.416147i) q^{59} +(-7.48545 - 11.6476i) q^{61} +(4.06719 - 5.43313i) q^{63} +(-12.9403 + 6.68824i) q^{65} +(7.94838 + 0.568479i) q^{67} +(2.30862 + 3.75494i) q^{69} +(7.49397 + 8.64851i) q^{71} +(-1.73886 - 2.32285i) q^{73} +(2.58375 + 3.80040i) q^{75} +(9.32455 + 2.02843i) q^{77} +(2.54388 - 0.746951i) q^{79} +(1.38230 - 1.59526i) q^{81} +(1.38375 - 3.70998i) q^{83} +(4.67005 + 13.4479i) q^{85} +(-3.42869 + 1.27883i) q^{87} +(-11.2419 - 7.22472i) q^{89} +20.5135i q^{91} +(-2.82391 + 2.82391i) q^{93} +(-8.78121 + 9.67990i) q^{95} +(-5.04656 - 13.5304i) q^{97} +(6.26668 + 1.84006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 240 * q + 4 * q^3	\( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) \) 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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