LMFDB - Embedded newform 460.2.x.a.33.8

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			33.8
Character	$\chi$	$=$	460.33
Dual form			460.2.x.a.237.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.195370 + 0.898100i) q^{3} +(-2.15927 - 0.580987i) q^{5} +(1.50914 + 2.76379i) q^{7} +(1.96048 - 0.895322i) q^{9} +O(q^{10})$	\(q+(0.195370 + 0.898100i) q^{3} +(-2.15927 - 0.580987i) q^{5} +(1.50914 + 2.76379i) q^{7} +(1.96048 - 0.895322i) q^{9} +(-2.29022 - 1.98448i) q^{11} +(5.71749 + 3.12199i) q^{13} +(0.0999282 - 2.05275i) q^{15} +(-3.81523 + 5.09655i) q^{17} +(-0.831806 + 5.78534i) q^{19} +(-2.18732 + 1.89532i) q^{21} +(-4.52600 + 1.58599i) q^{23} +(4.32491 + 2.50902i) q^{25} +(2.83950 + 3.79313i) q^{27} +(3.94097 - 0.566627i) q^{29} +(-3.65534 + 2.34915i) q^{31} +(1.33483 - 2.44455i) q^{33} +(-1.65292 - 6.84456i) q^{35} +(2.61941 - 7.02292i) q^{37} +(-1.68683 + 5.74482i) q^{39} +(-1.07762 + 2.35966i) q^{41} +(4.22864 - 0.919885i) q^{43} +(-4.75338 + 0.794229i) q^{45} +(3.86747 - 3.86747i) q^{47} +(-1.57653 + 2.45313i) q^{49} +(-5.32260 - 2.43075i) q^{51} +(1.79077 - 0.977837i) q^{53} +(3.79224 + 5.61563i) q^{55} +(-5.35832 + 0.383234i) q^{57} +(0.122192 + 0.416147i) q^{59} +(-7.48545 - 11.6476i) q^{61} +(5.43313 + 4.06719i) q^{63} +(-10.5318 - 10.0630i) q^{65} +(0.568479 - 7.94838i) q^{67} +(-2.30862 - 3.75494i) q^{69} +(7.49397 + 8.64851i) q^{71} +(2.32285 - 1.73886i) q^{73} +(-1.40839 + 4.37438i) q^{75} +(2.02843 - 9.32455i) q^{77} +(-2.54388 + 0.746951i) q^{79} +(1.38230 - 1.59526i) q^{81} +(3.70998 + 1.38375i) q^{83} +(11.1992 - 8.78825i) q^{85} +(1.27883 + 3.42869i) q^{87} +(11.2419 + 7.22472i) q^{89} +20.5135i q^{91} +(-2.82391 - 2.82391i) q^{93} +(5.15730 - 12.0088i) q^{95} +(-13.5304 + 5.04656i) q^{97} +(-6.26668 - 1.84006i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

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

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
$3$	0.195370	+	0.898100i	0.112797	+	0.518518i	0.998524	+	0.0543122i	$0.0172966\pi$
$3$	0.195370	+	0.898100i	0.112797	+	0.518518i	−0.885727	+	0.464206i	$0.846340\pi$
$4$		0			0
$5$	−2.15927	−	0.580987i	−0.965656	−	0.259825i
$5$	−2.15927	−	0.580987i	−0.965656	−	0.259825i
$6$		0			0
$7$	1.50914	+	2.76379i	0.570403	+	1.04461i	0.990549	+	0.137158i	$0.0437968\pi$
$7$	1.50914	+	2.76379i	0.570403	+	1.04461i	−0.420147	+	0.907456i	$0.638021\pi$
$8$		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
$13$	5.71749	+	3.12199i	1.58575	+	0.865884i	0.998400	+	0.0565489i	$0.0180097\pi$
$13$	5.71749	+	3.12199i	1.58575	+	0.865884i	0.587348	+	0.809335i	$0.300172\pi$
$14$		0			0
$15$	0.0999282	−	2.05275i	0.0258013	−	0.530017i
$16$		0			0
$17$	−3.81523	+	5.09655i	−0.925330	+	1.23610i	0.0461404	+	0.998935i	$0.485308\pi$
$17$	−3.81523	+	5.09655i	−0.925330	+	1.23610i	−0.971470	+	0.237161i	$0.923783\pi$
$18$		0			0
$19$	−0.831806	+	5.78534i	−0.190829	+	1.32725i	0.638990	+	0.769215i	$0.279352\pi$
$19$	−0.831806	+	5.78534i	−0.190829	+	1.32725i	−0.829819	+	0.558032i	$0.811557\pi$
$20$		0			0
$21$	−2.18732	+	1.89532i	−0.477312	+	0.413593i
$22$		0			0
$23$	−4.52600	+	1.58599i	−0.943735	+	0.330702i
$23$	−4.52600	+	1.58599i	−0.943735	+	0.330702i
$24$		0			0
$25$	4.32491	+	2.50902i	0.864982	+	0.501804i
$26$		0			0
$27$	2.83950	+	3.79313i	0.546463	+	0.729989i
$28$		0			0
$29$	3.94097	−	0.566627i	0.731821	−	0.105220i	0.233677	−	0.972314i	$-0.424924\pi$
$29$	3.94097	−	0.566627i	0.731821	−	0.105220i	0.498144	+	0.867094i	$0.334015\pi$
$30$		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
$33$	1.33483	−	2.44455i	0.232363	−	0.425542i
$34$		0			0
$35$	−1.65292	−	6.84456i	−0.279395	−	1.15694i
$36$		0			0
$37$	2.61941	−	7.02292i	0.430629	−	1.15456i	−0.522671	−	0.852535i	$-0.675064\pi$
$37$	2.61941	−	7.02292i	0.430629	−	1.15456i	0.953300	−	0.302026i	$-0.0976631\pi$
$38$		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
$43$	4.22864	−	0.919885i	0.644862	−	0.140281i	0.121771	−	0.992558i	$-0.461143\pi$
$43$	4.22864	−	0.919885i	0.644862	−	0.140281i	0.523091	+	0.852277i	$0.324779\pi$
$44$		0			0
$45$	−4.75338	+	0.794229i	−0.708593	+	0.118397i
$46$		0			0
$47$	3.86747	−	3.86747i	0.564129	−	0.564129i	−0.366349	−	0.930478i	$-0.619392\pi$
$47$	3.86747	−	3.86747i	0.564129	−	0.564129i	0.930478	+	0.366349i	$0.119392\pi$
$48$		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
$53$	1.79077	−	0.977837i	0.245982	−	0.134316i	−0.351529	−	0.936177i	$-0.614338\pi$
$53$	1.79077	−	0.977837i	0.245982	−	0.134316i	0.597511	+	0.801861i	$0.296156\pi$
$54$		0			0
$55$	3.79224	+	5.61563i	0.511346	+	0.757211i
$56$		0			0
$57$	−5.35832	+	0.383234i	−0.709726	+	0.0507606i
$58$		0			0
$59$	0.122192	+	0.416147i	0.0159080	+	0.0541777i	0.967065	−	0.254531i	$-0.0819212\pi$
$59$	0.122192	+	0.416147i	0.0159080	+	0.0541777i	−0.951157	+	0.308709i	$0.900103\pi$
$60$		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
$63$	5.43313	+	4.06719i	0.684510	+	0.512418i
$64$		0			0
$65$	−10.5318	−	10.0630i	−1.30631	−	1.24816i
$66$		0			0
$67$	0.568479	−	7.94838i	0.0694508	−	0.971049i	−0.836582	−	0.547842i	$-0.815450\pi$
$67$	0.568479	−	7.94838i	0.0694508	−	0.971049i	0.906033	−	0.423207i	$-0.139096\pi$
$68$		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
$73$	2.32285	−	1.73886i	0.271869	−	0.203518i	−0.454641	−	0.890675i	$-0.650232\pi$
$73$	2.32285	−	1.73886i	0.271869	−	0.203518i	0.726509	+	0.687157i	$0.241141\pi$
$74$		0			0
$75$	−1.40839	+	4.37438i	−0.162627	+	0.505110i
$76$		0			0
$77$	2.02843	−	9.32455i	0.231161	−	1.06263i
$78$		0			0
$79$	−2.54388	+	0.746951i	−0.286209	+	0.0840385i	−0.421686	−	0.906742i	$-0.638561\pi$
$79$	−2.54388	+	0.746951i	−0.286209	+	0.0840385i	0.135477	+	0.990780i	$0.456743\pi$
$80$		0			0
$81$	1.38230	−	1.59526i	0.153589	−	0.177251i
$82$		0			0
$83$	3.70998	+	1.38375i	0.407224	+	0.151887i	0.544724	−	0.838615i	$-0.316634\pi$
$83$	3.70998	+	1.38375i	0.407224	+	0.151887i	−0.137501	+	0.990502i	$0.543907\pi$
$84$		0			0
$85$	11.1992	−	8.78825i	1.21472	−	0.953219i
$86$		0			0
$87$	1.27883	+	3.42869i	0.137105	+	0.367594i
$88$		0			0
$89$	11.2419	+	7.22472i	1.19164	+	0.765818i	0.977490	−	0.210983i	$-0.0676665\pi$
$89$	11.2419	+	7.22472i	1.19164	+	0.765818i	0.214147	+	0.976801i	$0.431303\pi$
$90$		0			0
$91$			20.5135i			2.15040i
$92$		0			0
$93$	−2.82391	−	2.82391i	−0.292826	−	0.292826i
$94$		0			0
$95$	5.15730	−	12.0088i	0.529128	−	1.23208i
$96$		0			0
$97$	−13.5304	+	5.04656i	−1.37380	+	0.512401i	−0.924569	−	0.381015i	$-0.875575\pi$
$97$	−13.5304	+	5.04656i	−1.37380	+	0.512401i	−0.449231	+	0.893416i	$0.648302\pi$
$98$		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
$103$	0.753221	+	10.5314i	0.0742171	+	1.03769i	0.888995	+	0.457917i	$0.151404\pi$
$103$	0.753221	+	10.5314i	0.0742171	+	1.03769i	−0.814778	+	0.579773i	$0.803141\pi$
$104$		0			0
$105$	5.82417	−	2.82171i	0.568381	−	0.275371i
$106$		0			0
$107$	2.01059	+	0.437378i	0.194371	+	0.0422829i	0.308697	−	0.951160i	$-0.400107\pi$
$107$	2.01059	+	0.437378i	0.194371	+	0.0422829i	−0.114326	+	0.993443i	$0.536471\pi$
$108$		0			0
$109$	−2.15599	−	14.9952i	−0.206506	−	1.43628i	−0.784444	−	0.620200i	$-0.787052\pi$
$109$	−2.15599	−	14.9952i	−0.206506	−	1.43628i	0.577938	−	0.816081i	$-0.303858\pi$
$110$		0			0
$111$	6.81904	+	0.980430i	0.647234	+	0.0930583i
$112$		0			0
$113$	7.81956	+	0.559266i	0.735602	+	0.0526113i	0.434113	−	0.900858i	$-0.357062\pi$
$113$	7.81956	+	0.559266i	0.735602	+	0.0526113i	0.301489	+	0.953470i	$0.402516\pi$
$114$		0			0
$115$	10.6943	−	0.795039i	0.997248	−	0.0741378i
$116$		0			0
$117$	14.0042	+	1.00160i	1.29469	+	0.0925982i
$118$		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
$123$	−2.32974	−	0.506804i	−0.210066	−	0.0456970i
$124$		0			0
$125$	−7.88094	−	7.93037i	−0.704893	−	0.709314i
$126$		0			0
$127$	−1.60141	−	22.3906i	−0.142102	−	1.98684i	−0.160623	−	0.987016i	$-0.551350\pi$
$127$	−1.60141	−	22.3906i	−0.142102	−	1.98684i	0.0185215	−	0.999828i	$-0.494104\pi$
$128$		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
$133$	−17.2448	+	6.43196i	−1.49531	+	0.557722i
$134$		0			0
$135$	−3.92750	−	9.84012i	−0.338025	−	0.846902i
$136$		0			0
$137$	4.79265	+	4.79265i	0.409464	+	0.409464i	0.881552	−	0.472088i	$-0.156499\pi$
$137$	4.79265	+	4.79265i	0.409464	+	0.409464i	−0.472088	+	0.881552i	$0.656499\pi$
$138$		0			0
$139$			1.21383i			0.102956i	0.998674	+	0.0514779i	$0.0163932\pi$
$139$			1.21383i			0.102956i	−0.998674	+	0.0514779i	$0.983607\pi$
$140$		0			0
$141$	4.22896	+	2.71779i	0.356143	+	0.228879i
$142$		0			0
$143$	−6.89877	−	18.4963i	−0.576904	−	1.54674i
$144$		0			0
$145$	−8.83884	−	1.06615i	−0.734026	−	0.0885393i
$146$		0			0
$147$	−2.51116	−	0.936616i	−0.207117	−	0.0772508i
$148$		0			0
$149$	−0.540235	+	0.623464i	−0.0442577	+	0.0510762i	−0.777447	−	0.628949i	$-0.783486\pi$
$149$	−0.540235	+	0.623464i	−0.0442577	+	0.0510762i	0.733189	+	0.680025i	$0.238031\pi$
$150$		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
$153$	−2.91664	+	13.4076i	−0.235796	+	1.08394i
$154$		0			0
$155$	9.25770	−	2.94874i	0.743596	−	0.236848i
$156$		0			0
$157$	10.7909	−	8.07800i	0.861211	−	0.644694i	−0.0745936	−	0.997214i	$-0.523766\pi$
$157$	10.7909	−	8.07800i	0.861211	−	0.644694i	0.935804	+	0.352520i	$0.114675\pi$
$158$		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
$163$	−0.566558	+	7.92152i	−0.0443763	+	0.620461i	0.925793	+	0.378032i	$0.123399\pi$
$163$	−0.566558	+	7.92152i	−0.0443763	+	0.620461i	−0.970169	+	0.242430i	$0.922056\pi$
$164$		0			0
$165$	−4.30251	+	4.50293i	−0.334950	+	0.350553i
$166$		0			0
$167$	1.35467	+	1.01409i	0.104827	+	0.0784727i	0.650405	−	0.759587i	$-0.274599\pi$
$167$	1.35467	+	1.01409i	0.104827	+	0.0784727i	−0.545578	+	0.838060i	$0.683690\pi$
$168$		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
$173$	13.6743	−	0.978006i	1.03964	−	0.0743564i	0.458933	−	0.888471i	$-0.348232\pi$
$173$	13.6743	−	0.978006i	1.03964	−	0.0743564i	0.580705	+	0.814114i	$0.302777\pi$
$174$		0			0
$175$	−0.407491	+	15.7396i	−0.0308034	+	1.18980i
$176$		0			0
$177$	−0.349869	+	0.191043i	−0.0262977	+	0.0143597i
$178$		0			0
$179$	11.9629	+	5.46328i	0.894150	+	0.408345i	0.808853	−	0.588011i	$-0.200089\pi$
$179$	11.9629	+	5.46328i	0.894150	+	0.408345i	0.0852973	+	0.996356i	$0.472816\pi$
$180$		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
$187$	18.8517	−	4.10095i	1.37858	−	0.299891i
$188$		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
$193$	−1.08356	+	2.90515i	−0.0779966	+	0.209117i	−0.970096	−	0.242723i	$-0.921959\pi$
$193$	−1.08356	+	2.90515i	−0.0779966	+	0.209117i	0.892099	+	0.451840i	$0.149232\pi$
$194$		0			0
$195$	6.97999	−	11.4246i	0.499848	−	0.818133i
$196$		0			0
$197$	3.39340	−	6.21455i	0.241770	−	0.442768i	−0.728414	−	0.685137i	$-0.759742\pi$
$197$	3.39340	−	6.21455i	0.241770	−	0.442768i	0.970184	+	0.242368i	$0.0779243\pi$
$198$		0			0
$199$	10.1722	−	6.53727i	0.721088	−	0.463415i	−0.127927	−	0.991784i	$-0.540832\pi$
$199$	10.1722	−	6.53727i	0.721088	−	0.463415i	0.849015	+	0.528369i	$0.177196\pi$
$200$		0			0
$201$	7.24950	−	1.04232i	0.511340	−	0.0735196i
$202$		0			0
$203$	7.51353	+	10.0369i	0.527347	+	0.704453i
$204$		0			0
$205$	3.69780	−	4.46906i	0.258266	−	0.312133i
$206$		0			0
$207$	−7.45316	+	7.16153i	−0.518031	+	0.497761i
$208$		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
$213$	−6.30313	+	8.41999i	−0.431883	+	0.576928i
$214$		0			0
$215$	−9.66523	−	0.470505i	−0.659163	−	0.0320882i
$216$		0			0
$217$	−12.0090	−	6.55740i	−0.815223	−	0.445145i
$218$		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
$223$	−1.84060	−	3.37081i	−0.123256	−	0.225726i	0.808764	−	0.588133i	$-0.200137\pi$
$223$	−1.84060	−	3.37081i	−0.123256	−	0.225726i	−0.932020	+	0.362407i	$0.881955\pi$
$224$		0			0
$225$	10.7253	+	1.04670i	0.715019	+	0.0697799i
$226$		0			0
$227$	4.00756	+	18.4225i	0.265991	+	1.22274i	0.895256	+	0.445551i	$0.146992\pi$
$227$	4.00756	+	18.4225i	0.265991	+	1.22274i	−0.629265	+	0.777191i	$0.716644\pi$
$228$		0			0
$229$	16.2428			1.07335			0.536677	−	0.843787i	$-0.319679\pi$
$229$	16.2428			1.07335			0.536677	+	0.843787i	$0.319679\pi$
$230$		0			0
$231$	8.77067			0.577068
$232$		0			0
$233$	0.737031	+	3.38808i	0.0482845	+	0.221960i	0.994966	−	0.100210i	$-0.0319513\pi$
$233$	0.737031	+	3.38808i	0.0482845	+	0.221960i	−0.946682	+	0.322170i	$0.895588\pi$
$234$		0			0
$235$	−10.5979	+	6.10397i	−0.691329	+	0.398179i
$236$		0			0
$237$	−1.16783	−	2.13873i	−0.0758589	−	0.138925i
$238$		0			0
$239$	−23.2470	+	10.6166i	−1.50373	+	0.686729i	−0.985680	−	0.168624i	$-0.946067\pi$
$239$	−23.2470	+	10.6166i	−1.50373	+	0.686729i	−0.518046	+	0.855353i	$0.673340\pi$
$240$		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
$243$	14.1786	+	7.74213i	0.909561	+	0.496658i
$244$		0			0
$245$	4.82940	−	4.38104i	0.308539	−	0.279894i
$246$		0			0
$247$	−22.8176	+	30.4807i	−1.45185	+	1.93944i
$248$		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
$253$	13.5129	+	5.34951i	0.849548	+	0.336321i
$254$		0			0
$255$	10.0807	+	8.34100i	0.631278	+	0.522334i
$256$		0			0
$257$	−4.21514	−	5.63077i	−0.262934	−	0.351238i	0.649574	−	0.760299i	$-0.274947\pi$
$257$	−4.21514	−	5.63077i	−0.262934	−	0.351238i	−0.912507	+	0.409061i	$0.865856\pi$
$258$		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
$263$	11.5521	−	21.1561i	0.712334	−	1.30454i	−0.231083	−	0.972934i	$-0.574227\pi$
$263$	11.5521	−	21.1561i	0.712334	−	1.30454i	0.943417	−	0.331608i	$-0.107591\pi$
$264$		0			0
$265$	−4.43488	+	1.07100i	−0.272432	+	0.0657909i
$266$		0			0
$267$	−4.29219	+	11.5078i	−0.262678	+	0.704267i
$268$		0			0
$269$	−2.34135	+	7.97392i	−0.142755	+	0.486178i	−0.999566	−	0.0294517i	$-0.990624\pi$
$269$	−2.34135	+	7.97392i	−0.142755	+	0.486178i	0.856811	+	0.515630i	$0.172442\pi$
$270$		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
$273$	−18.4231	+	4.00771i	−1.11502	+	0.242558i
$274$		0			0
$275$	−4.92587	−	14.3289i	−0.297041	−	0.864066i
$276$		0			0
$277$	−8.11966	+	8.11966i	−0.487863	+	0.487863i	−0.907631	−	0.419768i	$-0.862111\pi$
$277$	−8.11966	+	8.11966i	−0.487863	+	0.487863i	0.419768	+	0.907631i	$0.362111\pi$
$278$		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
$283$	−8.21743	+	4.48706i	−0.488476	+	0.266728i	−0.704557	−	0.709647i	$-0.748854\pi$
$283$	−8.21743	+	4.48706i	−0.488476	+	0.266728i	0.216081	+	0.976375i	$0.430672\pi$
$284$		0			0
$285$	11.7927	+	2.28561i	0.698540	+	0.135388i
$286$		0			0
$287$	−8.14788	+	0.582748i	−0.480954	+	0.0343985i
$288$		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
$293$	−11.1891	−	8.37607i	−0.653676	−	0.489335i	0.220219	−	0.975450i	$-0.429323\pi$
$293$	−11.1891	−	8.37607i	−0.653676	−	0.489335i	−0.873895	+	0.486115i	$0.838414\pi$
$294$		0			0
$295$	−0.0220692	−	0.969566i	−0.00128492	−	0.0564503i
$296$		0			0
$297$	1.02433	−	14.3220i	0.0594378	−	0.831049i
$298$		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
$303$	12.7740	−	9.56246i	0.733844	−	0.549349i
$304$		0			0
$305$	9.39602	+	29.4993i	0.538015	+	1.68912i
$306$		0			0
$307$	−0.697879	+	3.20810i	−0.0398301	+	0.183096i	−0.992764	−	0.120082i	$-0.961684\pi$
$307$	−0.697879	+	3.20810i	−0.0398301	+	0.183096i	0.952934	+	0.303178i	$0.0980477\pi$
$308$		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
$313$	−9.33818	−	3.48296i	−0.527825	−	0.196869i	0.0714020	−	0.997448i	$-0.477253\pi$
$313$	−9.33818	−	3.48296i	−0.527825	−	0.196869i	−0.599227	+	0.800579i	$0.704525\pi$
$314$		0			0
$315$	−9.36862	−	11.9387i	−0.527862	−	0.672672i
$316$		0			0
$317$	4.47967	+	12.0105i	0.251603	+	0.674575i	0.999937	+	0.0112518i	$0.00358163\pi$
$317$	4.47967	+	12.0105i	0.251603	+	0.674575i	−0.748333	+	0.663323i	$0.769146\pi$
$318$		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
$325$	16.8945	+	27.8476i	0.937139	+	1.54471i
$326$		0			0
$327$	13.0460	−	4.86590i	0.721444	−	0.269085i
$328$		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
$333$	−1.15246	−	16.1135i	−0.0631546	−	0.883016i
$334$		0			0
$335$	−5.84541	+	16.8324i	−0.319369	+	0.919654i
$336$		0			0
$337$	−16.2468	−	3.53428i	−0.885020	−	0.192524i	−0.252991	−	0.967469i	$-0.581414\pi$
$337$	−16.2468	−	3.53428i	−0.885020	−	0.192524i	−0.632029	+	0.774944i	$0.717778\pi$
$338$		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
$343$	12.8275	+	0.917441i	0.692620	+	0.0495372i
$344$		0			0
$345$	2.80336	+	9.44922i	0.150928	+	0.508729i
$346$		0			0
$347$	−9.58856	−	0.685787i	−0.514741	−	0.0368150i	−0.188447	−	0.982083i	$-0.560345\pi$
$347$	−9.58856	−	0.685787i	−0.514741	−	0.0368150i	−0.326294	+	0.945268i	$0.605800\pi$
$348$		0			0
$349$	7.27680	+	1.04625i	0.389518	+	0.0560042i	0.334292	−	0.942470i	$-0.391503\pi$
$349$	7.27680	+	1.04625i	0.389518	+	0.0560042i	0.0552262	+	0.998474i	$0.482412\pi$
$350$		0			0
$351$	4.39273	+	30.5521i	0.234467	+	1.63075i
$352$		0			0
$353$	−3.12393	−	0.679570i	−0.166270	−	0.0361699i	0.128659	−	0.991689i	$-0.458933\pi$
$353$	−3.12393	−	0.679570i	−0.166270	−	0.0361699i	−0.294930	+	0.955519i	$0.595296\pi$
$354$		0			0
$355$	−11.1569	−	23.0284i	−0.592144	−	1.22222i
$356$		0			0
$357$	−1.31448	−	18.3789i	−0.0695698	−	0.972713i
$358$		0			0
$359$	−8.93003	−	19.5540i	−0.471309	−	1.03202i	−0.984762	−	0.173905i	$-0.944361\pi$
$359$	−8.93003	−	19.5540i	−0.471309	−	1.03202i	0.513454	−	0.858117i	$-0.328366\pi$
$360$		0			0
$361$	−14.5478	−	4.27163i	−0.765676	−	0.224823i
$362$		0			0
$363$	1.56448	−	0.583521i	0.0821140	−	0.0306269i
$364$		0			0
$365$	−6.02591	+	2.40513i	−0.315411	+	0.125890i
$366$		0			0
$367$	20.6026	+	20.6026i	1.07545	+	1.07545i	0.996911	+	0.0785338i	$0.0250238\pi$
$367$	20.6026	+	20.6026i	1.07545	+	1.07545i	0.0785338	+	0.996911i	$0.474976\pi$
$368$		0			0
$369$			5.59088i			0.291050i
$370$		0			0
$371$	5.40507	+	3.47363i	0.280617	+	0.180342i
$372$		0			0
$373$	4.65947	+	12.4925i	0.241258	+	0.646839i	0.999990	−	0.00456504i	$-0.00145310\pi$
$373$	4.65947	+	12.4925i	0.241258	+	0.646839i	−0.758731	+	0.651404i	$0.774180\pi$
$374$		0			0
$375$	5.58256	−	8.62723i	0.288282	−	0.445508i
$376$		0			0
$377$	24.3015	+	9.06399i	1.25159	+	0.466819i
$378$		0			0
$379$	0.649283	−	0.749313i	0.0333514	−	0.0384896i	−0.738829	−	0.673893i	$-0.764621\pi$
$379$	0.649283	−	0.749313i	0.0333514	−	0.0384896i	0.772180	+	0.635404i	$0.219166\pi$
$380$		0			0
$381$	19.7961	−	5.81267i	1.01419	−	0.297792i
$382$		0			0
$383$	−3.38470	+	15.5592i	−0.172950	+	0.795039i	0.806158	+	0.591700i	$0.201543\pi$
$383$	−3.38470	+	15.5592i	−0.172950	+	0.795039i	−0.979108	+	0.203339i	$0.934821\pi$
$384$		0			0
$385$	−9.79738	+	18.9557i	−0.499321	+	0.966074i
$386$		0			0
$387$	7.46659	−	5.58942i	0.379548	−	0.284126i
$388$		0			0
$389$	−16.4320	−	18.9636i	−0.833136	−	0.961490i	0.166563	−	0.986031i	$-0.446733\pi$
$389$	−16.4320	−	18.9636i	−0.833136	−	0.961490i	−0.999699	+	0.0245405i	$0.992188\pi$
$390$		0			0
$391$	9.18464	−	29.1179i	0.464487	−	1.47256i
$392$		0			0
$393$	1.16657	−	16.3107i	0.0588455	−	0.822768i
$394$		0			0
$395$	5.92690	−	0.134908i	0.298215	−	0.00678795i
$396$		0			0
$397$	−5.37438	−	4.02321i	−0.269732	−	0.201919i	0.455846	−	0.890059i	$-0.349337\pi$
$397$	−5.37438	−	4.02321i	−0.269732	−	0.201919i	−0.725578	+	0.688140i	$0.758428\pi$
$398$		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
$403$	−28.2334	+	2.01929i	−1.40641	+	0.100588i
$404$		0			0
$405$	−3.91159	+	2.64151i	−0.194369	+	0.131257i
$406$		0			0
$407$	−19.9359	+	10.8858i	−0.988186	+	0.539590i
$408$		0			0
$409$	−29.5798	−	13.5086i	−1.46263	−	0.667958i	−0.484275	−	0.874916i	$-0.660917\pi$
$409$	−29.5798	−	13.5086i	−1.46263	−	0.667958i	−0.978350	+	0.206957i	$0.933644\pi$
$410$		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
$417$	−1.09014	+	0.237146i	−0.0533844	+	0.0116131i
$418$		0			0
$419$	6.25980	−	13.7070i	0.305811	−	0.669633i	−0.692865	−	0.721067i	$-0.743652\pi$
$419$	6.25980	−	13.7070i	0.305811	−	0.669633i	0.998676	+	0.0514342i	$0.0163792\pi$
$420$		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
$423$	4.11948	−	11.0447i	0.200296	−	0.537014i
$424$		0			0
$425$	−29.2879	+	12.4696i	−1.42067	+	0.604867i
$426$		0			0
$427$	20.8949	−	38.2661i	1.01117	−	1.85183i
$428$		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
$433$	19.1268	+	25.5505i	0.919178	+	1.22788i	0.973345	+	0.229346i	$0.0736587\pi$
$433$	19.1268	+	25.5505i	0.919178	+	1.22788i	−0.0541673	+	0.998532i	$0.517250\pi$
$434$		0			0
$435$	−0.769328	−	8.14645i	−0.0368864	−	0.390592i
$436$		0			0
$437$	−5.41074	−	27.5036i	−0.258831	−	1.31568i
$438$		0			0
$439$	12.2439	−	10.6094i	0.584368	−	0.506358i	−0.311756	−	0.950162i	$-0.600917\pi$
$439$	12.2439	−	10.6094i	0.584368	−	0.506358i	0.896124	+	0.443805i	$0.146372\pi$
$440$		0			0
$441$	−0.894420	+	6.22083i	−0.0425914	+	0.296230i
$442$		0			0
$443$	1.75875	−	2.34941i	0.0835606	−	0.111624i	−0.756813	−	0.653631i	$-0.773245\pi$
$443$	1.75875	−	2.34941i	0.0835606	−	0.111624i	0.840374	+	0.542008i	$0.182336\pi$
$444$		0			0
$445$	−20.0768	−	22.1315i	−0.951732	−	1.04913i
$446$		0			0
$447$	−0.665478	−	0.363379i	−0.0314760	−	0.0171872i
$448$		0			0
$449$	10.1923	+	8.83172i	0.481006	+	0.416795i	0.861320	−	0.508063i	$-0.169638\pi$
$449$	10.1923	+	8.83172i	0.481006	+	0.416795i	−0.380313	+	0.924858i	$0.624184\pi$
$450$		0			0
$451$	7.15069	−	3.26561i	0.336713	−	0.153772i
$452$		0			0
$453$	−8.13603	−	14.9000i	−0.382264	−	0.700065i
$454$		0			0
$455$	11.9181	−	44.2942i	0.558727	−	2.07654i
$456$		0			0
$457$	2.68971	+	12.3644i	0.125820	+	0.578383i	0.996282	+	0.0861488i	$0.0274561\pi$
$457$	2.68971	+	12.3644i	0.125820	+	0.578383i	−0.870463	+	0.492234i	$0.836180\pi$
$458$		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
$463$	0.311227	+	1.43069i	0.0144639	+	0.0664896i	0.983813	−	0.179197i	$-0.0573501\pi$
$463$	0.311227	+	1.43069i	0.0144639	+	0.0664896i	−0.969349	+	0.245687i	$0.920986\pi$
$464$		0			0
$465$	4.45693	+	7.73824i	0.206685	+	0.358852i
$466$		0			0
$467$	−0.713552	−	1.30677i	−0.0330193	−	0.0604703i	0.860648	−	0.509200i	$-0.170059\pi$
$467$	−0.713552	−	1.30677i	−0.0330193	−	0.0604703i	−0.893668	+	0.448729i	$0.851877\pi$
$468$		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
$473$	−11.5100	−	6.28494i	−0.529231	−	0.288982i
$474$		0			0
$475$	−18.1130	+	22.9340i	−0.831081	+	1.05229i
$476$		0			0
$477$	2.63530	−	3.52035i	0.120662	−	0.161186i
$478$		0			0
$479$	4.65702	−	32.3903i	0.212785	−	1.47995i	−0.551014	−	0.834496i	$-0.685759\pi$
$479$	4.65702	−	32.3903i	0.212785	−	1.47995i	0.763799	−	0.645454i	$-0.223332\pi$
$480$		0			0
$481$	36.9020	−	31.9757i	1.68258	−	1.45797i
$482$		0			0
$483$	6.89383	−	12.0473i	0.313680	−	0.548170i
$484$		0			0
$485$	32.1477	−	3.03594i	1.45975	−	0.137855i
$486$		0			0
$487$	19.8171	+	26.4726i	0.898000	+	1.19959i	0.979202	+	0.202890i	$0.0650334\pi$
$487$	19.8171	+	26.4726i	0.898000	+	1.19959i	−0.0812015	+	0.996698i	$0.525876\pi$
$488$		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
$493$	−12.1479	+	22.2472i	−0.547114	+	1.00196i
$494$		0			0
$495$	12.4624	+	7.61406i	0.560144	+	0.342227i
$496$		0			0
$497$	−12.5932	+	33.7636i	−0.564881	+	1.51450i
$498$		0			0
$499$	−3.68916	+	12.5641i	−0.165149	+	0.562447i	0.834780	+	0.550583i	$0.185595\pi$
$499$	−3.68916	+	12.5641i	−0.165149	+	0.562447i	−0.999930	+	0.0118638i	$0.996224\pi$
$500$		0			0
$501$	−0.646094	+	1.41475i	−0.0288653	+	0.0632063i
$502$		0			0
$503$	15.1051	−	3.28592i	0.673505	−	0.146512i	0.137209	−	0.990542i	$-0.456187\pi$
$503$	15.1051	−	3.28592i	0.673505	−	0.146512i	0.536296	+	0.844030i	$0.319823\pi$
$504$		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	−0.676733	−	0.736229i	$-0.736605\pi$
$509$	6.18374	−	9.62209i	0.274090	−	0.426492i	0.950822	+	0.309737i	$0.100241\pi$
$510$		0			0
$511$	8.31135	+	3.79567i	0.367673	+	0.167910i
$512$		0			0
$513$	−24.3065	+	13.2723i	−1.07316	+	0.585988i
$514$		0			0
$515$	4.49220	−	23.1778i	0.197950	−	1.02134i
$516$		0			0
$517$	−16.5323	+	1.18241i	−0.727090	+	0.0520025i
$518$		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
$523$	−8.26995	−	6.19081i	−0.361620	−	0.270705i	0.402982	−	0.915208i	$-0.367974\pi$
$523$	−8.26995	−	6.19081i	−0.361620	−	0.270705i	−0.764602	+	0.644503i	$0.777065\pi$
$524$		0			0
$525$	−14.2153	+	2.70907i	−0.620408	+	0.118234i
$526$		0			0
$527$	1.97343	−	27.5922i	0.0859641	−	1.20193i
$528$		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
$533$	−13.5281	+	10.1270i	−0.585967	+	0.438650i
$534$		0			0
$535$	−4.08730	−	2.11255i	−0.176710	−	0.0913333i
$536$		0			0
$537$	−2.56938	+	11.8113i	−0.110877	+	0.509693i
$538$		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
$543$	−3.44056	−	1.28326i	−0.147649	−	0.0550701i
$544$		0			0
$545$	−4.05666	+	33.6313i	−0.173768	+	1.44061i
$546$		0			0
$547$	0.0453060	+	0.121470i	0.00193714	+	0.00519368i	0.937915	−	0.346866i	$-0.112754\pi$
$547$	0.0453060	+	0.121470i	0.00193714	+	0.00519368i	−0.935978	+	0.352060i	$0.885481\pi$
$548$		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
$555$	−14.1545	−	6.07879i	−0.600827	−	0.258030i
$556$		0			0
$557$	−24.4288	+	9.11148i	−1.03508	+	0.386066i	−0.808855	−	0.588009i	$-0.799912\pi$
$557$	−24.4288	+	9.11148i	−1.03508	+	0.386066i	−0.226228	+	0.974074i	$0.572639\pi$
$558$		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
$563$	−1.44936	−	20.2646i	−0.0610830	−	0.854052i	−0.931962	−	0.362555i	$-0.881904\pi$
$563$	−1.44936	−	20.2646i	−0.0610830	−	0.854052i	0.870879	−	0.491497i	$-0.163550\pi$
$564$		0			0
$565$	−16.5596	−	5.75067i	−0.696669	−	0.241933i
$566$		0			0
$567$	6.49506	+	1.41291i	0.272767	+	0.0593368i
$568$		0			0
$569$	0.592821	+	4.12316i	0.0248524	+	0.172852i	0.998467	−	0.0553453i	$-0.0176260\pi$
$569$	0.592821	+	4.12316i	0.0248524	+	0.172852i	−0.973615	+	0.228197i	$0.926717\pi$
$570$		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
$573$	−3.54996	−	0.253898i	−0.148302	−	0.0106067i
$574$		0			0
$575$	−23.5538	−	4.49654i	−0.982261	−	0.187519i
$576$		0			0
$577$	−14.2864	−	1.02178i	−0.594750	−	0.0425373i	−0.229280	−	0.973361i	$-0.573637\pi$
$577$	−14.2864	−	1.02178i	−0.594750	−	0.0425373i	−0.365470	+	0.930823i	$0.619092\pi$
$578$		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
$583$	−6.04176	−	1.31431i	−0.250224	−	0.0544330i
$584$		0			0
$585$	−29.6570	−	10.2990i	−1.22617	−	0.425812i
$586$		0			0
$587$	−0.0151677	−	0.212072i	−0.000626039	−	0.00875317i	0.997129	−	0.0757151i	$-0.0241239\pi$
$587$	−0.0151677	−	0.212072i	−0.000626039	−	0.00875317i	−0.997756	+	0.0669619i	$0.978669\pi$
$588$		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
$593$	0.578195	−	0.215655i	0.0237436	−	0.00885591i	−0.337564	−	0.941302i	$-0.609603\pi$
$593$	0.578195	−	0.215655i	0.0237436	−	0.00885591i	0.361308	+	0.932447i	$0.382330\pi$
$594$		0			0
$595$	41.1900	+	17.6894i	1.68862	+	0.725194i
$596$		0			0
$597$	7.85846	+	7.85846i	0.321625	+	0.321625i
$598$		0			0
$599$			28.7217i			1.17354i	0.809755	+	0.586769i	$0.199600\pi$
$599$			28.7217i			1.17354i	−0.809755	+	0.586769i	$0.800400\pi$
$600$		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
$603$	−6.00187	−	16.0916i	−0.244415	−	0.655302i
$604$		0			0
$605$	−0.486477	+	4.03309i	−0.0197781	+	0.163968i
$606$		0			0
$607$	−26.8056	−	9.99798i	−1.08801	−	0.405806i	−0.259476	−	0.965749i	$-0.583550\pi$
$607$	−26.8056	−	9.99798i	−1.08801	−	0.405806i	−0.828531	+	0.559944i	$0.810823\pi$
$608$		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
$613$	4.23691	−	19.4768i	0.171127	−	0.786660i	−0.808924	−	0.587914i	$-0.799949\pi$
$613$	4.23691	−	19.4768i	0.171127	−	0.786660i	0.980051	−	0.198746i	$-0.0636869\pi$
$614$		0			0
$615$	4.73610	+	2.44788i	0.190978	+	0.0987080i
$616$		0			0
$617$	13.8146	−	10.3415i	0.556155	−	0.416333i	−0.283884	−	0.958859i	$-0.591623\pi$
$617$	13.8146	−	10.3415i	0.556155	−	0.416333i	0.840039	+	0.542526i	$0.182532\pi$
$618$		0			0
$619$	−3.92665	−	4.53160i	−0.157826	−	0.182140i	0.671330	−	0.741159i	$-0.265724\pi$
$619$	−3.92665	−	4.53160i	−0.157826	−	0.182140i	−0.829155	+	0.559019i	$0.811178\pi$
$620$		0			0
$621$	−18.8674	−	12.6643i	−0.757125	−	0.508200i
$622$		0			0
$623$	−3.00199	+	41.9733i	−0.120272	+	1.68163i
$624$		0			0
$625$	12.4097	+	21.7025i	0.496386	+	0.868102i
$626$		0			0
$627$	13.0322	+	9.75581i	0.520457	+	0.389609i
$628$		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
$633$	8.27748	−	0.592017i	0.329000	−	0.0235306i
$634$		0			0
$635$	−9.55077	+	49.2778i	−0.379011	+	1.95553i
$636$		0			0
$637$	−16.6725	+	9.10386i	−0.660587	+	0.360708i
$638$		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	$-0.889624\pi$
$643$	−15.2304	+	15.2304i	−0.600629	+	0.600629i	0.339850	+	0.940480i	$0.389624\pi$
$644$		0			0
$645$	−1.46573	−	8.77226i	−0.0577131	−	0.345408i
$646$		0			0
$647$	26.5718	−	5.78035i	1.04465	−	0.227249i	0.342675	−	0.939454i	$-0.388667\pi$
$647$	26.5718	−	5.78035i	1.04465	−	0.227249i	0.701971	+	0.712205i	$0.252303\pi$
$648$		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
$653$	−9.02800	+	24.2050i	−0.353293	+	0.947215i	0.631791	+	0.775139i	$0.282320\pi$
$653$	−9.02800	+	24.2050i	−0.353293	+	0.947215i	−0.985084	+	0.172076i	$0.944952\pi$
$654$		0			0
$655$	33.9487	+	20.7414i	1.32649	+	0.810432i
$656$		0			0
$657$	2.99706	−	5.48870i	0.116926	−	0.214135i
$658$		0			0
$659$	−23.6015	+	15.1678i	−0.919385	+	0.590853i	−0.912479	−	0.409124i	$-0.865834\pi$
$659$	−23.6015	+	15.1678i	−0.919385	+	0.590853i	−0.00690556	+	0.999976i	$0.502198\pi$
$660$		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
$663$	−22.8431	−	30.5149i	−0.887154	−	1.18510i
$664$		0			0
$665$	40.9730	−	3.86937i	1.58887	−	0.150048i
$666$		0			0
$667$	−16.9382	+	8.81490i	−0.655849	+	0.341314i
$668$		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
$673$	23.1861	−	30.9730i	0.893757	−	1.19392i	−0.0865113	−	0.996251i	$-0.527572\pi$
$673$	23.1861	−	30.9730i	0.893757	−	1.19392i	0.980269	−	0.197669i	$-0.0633372\pi$
$674$		0			0
$675$	2.76355	+	23.5293i	0.106369	+	0.905644i
$676$		0			0
$677$	30.5092	+	16.6593i	1.17256	+	0.640268i	0.942924	−	0.333008i	$-0.108064\pi$
$677$	30.5092	+	16.6593i	1.17256	+	0.640268i	0.229639	+	0.973276i	$0.426246\pi$
$678$		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
$683$	−0.950329	−	1.74040i	−0.0363633	−	0.0665945i	0.858865	−	0.512201i	$-0.171170\pi$
$683$	−0.950329	−	1.74040i	−0.0363633	−	0.0665945i	−0.895229	+	0.445607i	$0.852988\pi$
$684$		0			0
$685$	−7.56417	−	13.1331i	−0.289012	−	0.501790i
$686$		0			0
$687$	3.17335	+	14.5877i	0.121071	+	0.556554i
$688$		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
$693$	−4.37177	−	20.0967i	−0.166070	−	0.763411i
$694$		0			0
$695$	0.705220	−	2.62099i	0.0267505	−	0.0994198i
$696$		0			0
$697$	−7.91475	−	14.4948i	−0.299793	−	0.549029i
$698$		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
$703$	38.4511	+	20.9959i	1.45021	+	0.791875i
$704$		0			0
$705$	−7.55248	−	8.32542i	−0.284443	−	0.313553i
$706$		0			0
$707$	32.7623	−	43.7653i	1.23215	−	1.64596i
$708$		0			0
$709$	−2.64211	+	18.3763i	−0.0992264	+	0.690135i	0.878112	+	0.478454i	$0.158803\pi$
$709$	−2.64211	+	18.3763i	−0.0992264	+	0.690135i	−0.977339	+	0.211681i	$0.932106\pi$
$710$		0			0
$711$	−4.31847	+	3.74198i	−0.161955	+	0.140335i
$712$		0			0
$713$	12.8183	−	16.4296i	0.480051	−	0.615292i
$714$		0			0
$715$	4.15020	+	43.9466i	0.155209	+	1.64351i
$716$		0			0
$717$	−14.0765	−	18.8040i	−0.525697	−	0.702248i
$718$		0			0
$719$	−24.4979	+	3.52227i	−0.913619	+	0.131359i	−0.583062	−	0.812427i	$-0.698146\pi$
$719$	−24.4979	+	3.52227i	−0.913619	+	0.131359i	−0.330557	+	0.943786i	$0.607237\pi$
$720$		0			0
$721$	−27.9699	+	17.9752i	−1.04165	+	0.669430i
$722$		0			0
$723$	−2.49351	+	4.56652i	−0.0927346	+	0.169831i
$724$		0			0
$725$	18.4660	+	7.43737i	0.685811	+	0.276217i
$726$		0			0
$727$	−4.68500	+	12.5610i	−0.173757	+	0.465861i	−0.994413	−	0.105562i	$-0.966336\pi$
$727$	−4.68500	+	12.5610i	−0.173757	+	0.465861i	0.820656	+	0.571423i	$0.193608\pi$
$728$		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
$733$	−28.4803	+	6.19552i	−1.05195	+	0.228837i	−0.705116	−	0.709092i	$-0.749105\pi$
$733$	−28.4803	+	6.19552i	−1.05195	+	0.228837i	−0.346829	+	0.937928i	$0.612742\pi$
$734$		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	$-0.540063\pi$
$739$	22.5374	−	35.0689i	0.829053	−	1.29003i	0.954584	−	0.297942i	$-0.0963003\pi$
$740$		0			0
$741$	−31.8326	−	14.5375i	−1.16940	−	0.534047i
$742$		0			0
$743$	−5.33158	+	2.91126i	−0.195597	+	0.106804i	−0.574063	−	0.818811i	$-0.694633\pi$
$743$	−5.33158	+	2.91126i	−0.195597	+	0.106804i	0.378466	+	0.925615i	$0.376452\pi$
$744$		0			0
$745$	1.52874	−	1.03236i	0.0560086	−	0.0378227i
$746$		0			0
$747$	8.51226	−	0.608809i	0.311447	−	0.0222752i
$748$		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
$753$	6.67572	+	4.99738i	0.243277	+	0.182115i
$754$		0			0
$755$	41.2914	−	0.939873i	1.50275	−	0.0342055i
$756$		0			0
$757$	0.225052	−	3.14663i	0.00817964	−	0.114366i	−0.991722	−	0.128405i	$-0.959014\pi$
$757$	0.225052	−	3.14663i	0.00817964	−	0.114366i	0.999901	+	0.0140387i	$0.00446880\pi$
$758$		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
$763$	38.1899	−	28.5886i	1.38257	−	1.03498i
$764$		0			0
$765$	14.0874	−	27.2561i	0.509332	−	0.985445i
$766$		0			0
$767$	−0.600575	+	2.76080i	−0.0216855	+	0.0996866i
$768$		0			0
$769$	11.1214	−	3.26554i	0.401048	−	0.117758i	−0.0749874	−	0.997184i	$-0.523892\pi$
$769$	11.1214	−	3.26554i	0.401048	−	0.117758i	0.476035	+	0.879426i	$0.342073\pi$
$770$		0			0
$771$	4.23349	−	4.88570i	0.152465	−	0.175954i
$772$		0			0
$773$	46.7610	+	17.4410i	1.68188	+	0.627308i	0.995037	−	0.0995007i	$-0.0317246\pi$
$773$	46.7610	+	17.4410i	1.68188	+	0.627308i	0.686840	+	0.726809i	$0.258997\pi$
$774$		0			0
$775$	−21.7031	+	0.988521i	−0.779597	+	0.0355087i
$776$		0			0
$777$	7.58120	+	20.3260i	0.271974	+	0.729191i
$778$		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
$785$	−27.9938	+	11.1732i	−0.999141	+	0.398788i
$786$		0			0
$787$	−49.9763	+	18.6402i	−1.78146	+	0.664451i	−0.782326	+	0.622869i	$0.785967\pi$
$787$	−49.9763	+	18.6402i	−1.78146	+	0.664451i	−0.999135	+	0.0415812i	$0.986760\pi$
$788$		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
$793$	−6.43439	−	89.9645i	−0.228492	−	3.19473i
$794$		0			0
$795$	−1.82830	−	3.77372i	−0.0648433	−	0.133840i
$796$		0			0
$797$	−25.7218	−	5.59543i	−0.911113	−	0.198200i	−0.267505	−	0.963556i	$-0.586199\pi$
$797$	−25.7218	−	5.59543i	−0.911113	−	0.198200i	−0.643607	+	0.765356i	$0.722563\pi$
$798$		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
$803$	−8.77056	−	0.627283i	−0.309506	−	0.0221363i
$804$		0			0
$805$	18.3365	+	28.3569i	0.646278	+	0.999451i
$806$		0			0
$807$	−7.61880	−	0.544907i	−0.268194	−	0.0191816i
$808$		0			0
$809$	−6.31101	−	0.907386i	−0.221883	−	0.0319020i	0.0304765	−	0.999535i	$-0.490298\pi$
$809$	−6.31101	−	0.907386i	−0.221883	−	0.0319020i	−0.252360	+	0.967633i	$0.581207\pi$
$810$		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
$813$	10.0827	+	2.19336i	0.353616	+	0.0769244i
$814$		0			0
$815$	5.82565	−	16.7755i	0.204064	−	0.587622i
$816$		0			0
$817$	1.80443	+	25.2293i	0.0631291	+	0.882661i
$818$		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
$823$	−18.9059	+	7.05153i	−0.659018	+	0.245801i	−0.656649	−	0.754196i	$-0.728027\pi$
$823$	−18.9059	+	7.05153i	−0.659018	+	0.245801i	−0.00236885	+	0.999997i	$0.500754\pi$
$824$		0			0
$825$	11.9064	−	7.22336i	0.414528	−	0.251485i
$826$		0			0
$827$	26.4769	+	26.4769i	0.920691	+	0.920691i	0.997078	−	0.0763875i	$-0.0243386\pi$
$827$	26.4769	+	26.4769i	0.920691	+	0.920691i	−0.0763875	+	0.997078i	$0.524339\pi$
$828$		0			0
$829$			45.6929i			1.58698i	0.608583	+	0.793490i	$0.291738\pi$
$829$			45.6929i			1.58698i	−0.608583	+	0.793490i	$0.708262\pi$
$830$		0			0
$831$	−8.87860	−	5.70593i	−0.307995	−	0.197936i
$832$		0			0
$833$	−6.48769	−	17.3942i	−0.224785	−	0.602672i
$834$		0			0
$835$	−2.33592	−	2.97674i	−0.0808378	−	0.103014i
$836$		0			0
$837$	−19.2900	−	7.19479i	−0.666759	−	0.248688i
$838$		0			0
$839$	1.73722	−	2.00486i	0.0599756	−	0.0692156i	−0.724969	−	0.688782i	$-0.758146\pi$
$839$	1.73722	−	2.00486i	0.0599756	−	0.0692156i	0.784945	+	0.619566i	$0.212691\pi$
$840$		0			0
$841$	−12.6151	+	3.70412i	−0.435003	+	0.127728i
$842$		0			0
$843$	−3.07724	+	14.1458i	−0.105986	+	0.487208i
$844$		0			0
$845$	−19.9766	−	62.7175i	−0.687216	−	2.15755i
$846$		0			0
$847$	4.57976	−	3.42836i	0.157362	−	0.117800i
$848$		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
$853$	−2.02094	+	28.2565i	−0.0691958	+	0.967484i	0.837701	+	0.546130i	$0.183899\pi$
$853$	−2.02094	+	28.2565i	−0.0691958	+	0.967484i	−0.906896	+	0.421354i	$0.861555\pi$
$854$		0			0
$855$	−0.640990	−	28.1606i	−0.0219214	−	0.963071i
$856$		0			0
$857$	7.74498	+	5.79782i	0.264563	+	0.198050i	0.723321	−	0.690512i	$-0.242615\pi$
$857$	7.74498	+	5.79782i	0.264563	+	0.198050i	−0.458758	+	0.888561i	$0.651705\pi$
$858$		0			0
$859$	−26.0459	−	40.5282i	−0.888674	−	1.38280i	−0.923577	−	0.383414i	$-0.874748\pi$
$859$	−26.0459	−	40.5282i	−0.888674	−	1.38280i	0.0349023	−	0.999391i	$-0.488888\pi$
$860$		0			0
$861$	−2.11521	−	7.20376i	−0.0720863	−	0.245503i
$862$		0			0
$863$	−41.9425	+	2.99979i	−1.42774	+	0.102114i	−0.763695	−	0.645578i	$-0.776617\pi$
$863$	−41.9425	+	2.99979i	−1.42774	+	0.102114i	−0.664046	+	0.747692i	$0.731162\pi$
$864$		0			0
$865$	−30.0947	−	5.83281i	−1.02325	−	0.198322i
$866$		0			0
$867$	18.9818	−	10.3649i	0.644657	−	0.352010i
$868$		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
$877$	10.2023	−	2.21938i	0.344508	−	0.0749432i	−0.0369823	−	0.999316i	$-0.511775\pi$
$877$	10.2023	−	2.21938i	0.344508	−	0.0749432i	0.381491	+	0.924373i	$0.375411\pi$
$878$		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
$883$	2.83417	−	7.59872i	0.0953776	−	0.255717i	−0.880496	−	0.474054i	$-0.842790\pi$
$883$	2.83417	−	7.59872i	0.0953776	−	0.255717i	0.975874	+	0.218336i	$0.0700630\pi$
$884$		0			0
$885$	0.866455	−	0.209244i	0.0291256	−	0.00703366i
$886$		0			0
$887$	14.0701	−	25.7674i	0.472427	−	0.865185i	−0.527452	−	0.849585i	$-0.676852\pi$
$887$	14.0701	−	25.7674i	0.472427	−	0.865185i	0.999878	−	0.0155999i	$-0.00496581\pi$
$888$		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
$893$	19.1576	+	25.5916i	0.641086	+	0.856391i
$894$		0			0
$895$	−22.6571	−	18.7470i	−0.757343	−	0.626643i
$896$		0			0
$897$	−1.47664	−	28.6763i	−0.0493035	−	0.957475i
$898$		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
$903$	−7.50591	+	10.0267i	−0.249781	+	0.333668i
$904$		0			0
$905$	6.61679	−	6.00248i	0.219949	−	0.199529i
$906$		0			0
$907$	1.68978	+	0.922692i	0.0561084	+	0.0306375i	0.507058	−	0.861912i	$-0.330733\pi$
$907$	1.68978	+	0.922692i	0.0561084	+	0.0306375i	−0.450950	+	0.892549i	$0.648915\pi$
$908$		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
$913$	−5.75063	−	10.5315i	−0.190318	−	0.348542i
$914$		0			0
$915$	−24.6576	+	14.2018i	−0.815154	+	0.469498i
$916$		0			0
$917$	−11.9091	−	54.7452i	−0.393273	−	1.80784i
$918$		0			0
$919$	13.5293			0.446290			0.223145	−	0.974785i	$-0.428368\pi$
$919$	13.5293			0.446290			0.223145	+	0.974785i	$0.428368\pi$
$920$		0			0
$921$	−3.01754			−0.0994312
$922$		0			0
$923$	15.8462	+	72.8439i	0.521584	+	2.39769i
$924$		0			0
$925$	28.9494	−	23.8013i	0.951849	−	0.782583i
$926$		0			0
$927$	10.9057	+	19.9723i	0.358190	+	0.655975i
$928$		0			0
$929$	−47.3567	+	21.6271i	−1.55372	+	0.709561i	−0.992964	−	0.118418i	$-0.962218\pi$
$929$	−47.3567	+	21.6271i	−1.55372	+	0.709561i	−0.560759	+	0.827979i	$0.689491\pi$
$930$		0			0
$931$	−12.8808	−	11.1613i	−0.422152	−	0.365797i
$932$		0			0
$933$	25.2369	+	13.7804i	0.826218	+	0.451149i
$934$		0			0
$935$	−43.0886	−	2.09756i	−1.40915	−	0.0685977i
$936$		0			0
$937$	3.82201	−	5.10561i	0.124860	−	0.166793i	−0.733756	−	0.679414i	$-0.762234\pi$
$937$	3.82201	−	5.10561i	0.124860	−	0.166793i	0.858615	+	0.512620i	$0.171325\pi$
$938$		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
$943$	1.13491	−	12.3889i	0.0369577	−	0.403438i
$944$		0			0
$945$	21.2689	−	25.7049i	0.691876	−	0.836181i
$946$		0			0
$947$	−29.0827	−	38.8500i	−0.945062	−	1.26245i	−0.964891	−	0.262651i	$-0.915403\pi$
$947$	−29.0827	−	38.8500i	−0.945062	−	1.26245i	0.0198290	−	0.999803i	$-0.493688\pi$
$948$		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
$953$	−19.5098	+	35.7296i	−0.631986	+	1.15740i	0.343878	+	0.939014i	$0.388259\pi$
$953$	−19.5098	+	35.7296i	−0.631986	+	1.15740i	−0.975864	+	0.218381i	$0.929922\pi$
$954$		0			0
$955$	4.51426	−	7.38878i	0.146078	−	0.239095i
$956$		0			0
$957$	3.87537	−	10.3903i	0.125273	−	0.335870i
$958$		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
$963$	4.33332	−	0.942657i	0.139639	−	0.0303767i
$964$		0			0
$965$	4.02756	−	5.64346i	0.129652	−	0.181669i
$966$		0			0
$967$	14.9921	−	14.9921i	0.482112	−	0.482112i	−0.423693	−	0.905806i	$-0.639267\pi$
$967$	14.9921	−	14.9921i	0.482112	−	0.482112i	0.905806	+	0.423693i	$0.139267\pi$
$968$		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
$973$	−3.35477	+	1.83184i	−0.107549	+	0.0587262i
$974$		0			0
$975$	−21.7093	+	20.6135i	−0.695252	+	0.660161i
$976$		0			0
$977$	9.04901	−	0.647198i	0.289503	−	0.0207057i	0.0741677	−	0.997246i	$-0.476370\pi$
$977$	9.04901	−	0.647198i	0.289503	−	0.0207057i	0.215336	+	0.976540i	$0.430915\pi$
$978$		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
$983$	20.4973	+	15.3441i	0.653761	+	0.489399i	0.873923	−	0.486064i	$-0.161568\pi$
$983$	20.4973	+	15.3441i	0.653761	+	0.489399i	−0.220162	+	0.975463i	$0.570659\pi$
$984$		0			0
$985$	−10.9378	+	11.4474i	−0.348509	+	0.364744i
$986$		0			0
$987$	−1.12929	+	15.7895i	−0.0359456	+	0.502585i
$988$		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
$993$	−11.2577	+	8.42738i	−0.357251	+	0.267435i
$994$		0			0
$995$	−25.7626	+	8.20583i	−0.816729	+	0.260142i
$996$		0			0
$997$	7.50997	−	34.5228i	0.237843	−	1.09335i	−0.690994	−	0.722860i	$-0.742827\pi$
$997$	7.50997	−	34.5228i	0.237843	−	1.09335i	0.928838	−	0.370487i	$-0.120809\pi$
$998$		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.33.8	✓	240
5.2	odd	4	inner	460.2.x.a.217.8	yes	240
23.7	odd	22	inner	460.2.x.a.53.8	yes	240
115.7	even	44	inner	460.2.x.a.237.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.33.8	✓	240	1.1	even	1	trivial
460.2.x.a.53.8	yes	240	23.7	odd	22	inner
460.2.x.a.217.8	yes	240	5.2	odd	4	inner
460.2.x.a.237.8	yes	240	115.7	even	44	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)

\(f(q)\)	\(=\)	\(q+(0.195370 + 0.898100i) q^{3} +(-2.15927 - 0.580987i) q^{5} +(1.50914 + 2.76379i) q^{7} +(1.96048 - 0.895322i) q^{9} +O(q^{10})\)	\(q+(0.195370 + 0.898100i) q^{3} +(-2.15927 - 0.580987i) q^{5} +(1.50914 + 2.76379i) q^{7} +(1.96048 - 0.895322i) q^{9} +(-2.29022 - 1.98448i) q^{11} +(5.71749 + 3.12199i) q^{13} +(0.0999282 - 2.05275i) q^{15} +(-3.81523 + 5.09655i) q^{17} +(-0.831806 + 5.78534i) q^{19} +(-2.18732 + 1.89532i) q^{21} +(-4.52600 + 1.58599i) q^{23} +(4.32491 + 2.50902i) q^{25} +(2.83950 + 3.79313i) q^{27} +(3.94097 - 0.566627i) q^{29} +(-3.65534 + 2.34915i) q^{31} +(1.33483 - 2.44455i) q^{33} +(-1.65292 - 6.84456i) q^{35} +(2.61941 - 7.02292i) q^{37} +(-1.68683 + 5.74482i) q^{39} +(-1.07762 + 2.35966i) q^{41} +(4.22864 - 0.919885i) q^{43} +(-4.75338 + 0.794229i) q^{45} +(3.86747 - 3.86747i) q^{47} +(-1.57653 + 2.45313i) q^{49} +(-5.32260 - 2.43075i) q^{51} +(1.79077 - 0.977837i) q^{53} +(3.79224 + 5.61563i) q^{55} +(-5.35832 + 0.383234i) q^{57} +(0.122192 + 0.416147i) q^{59} +(-7.48545 - 11.6476i) q^{61} +(5.43313 + 4.06719i) q^{63} +(-10.5318 - 10.0630i) q^{65} +(0.568479 - 7.94838i) q^{67} +(-2.30862 - 3.75494i) q^{69} +(7.49397 + 8.64851i) q^{71} +(2.32285 - 1.73886i) q^{73} +(-1.40839 + 4.37438i) q^{75} +(2.02843 - 9.32455i) q^{77} +(-2.54388 + 0.746951i) q^{79} +(1.38230 - 1.59526i) q^{81} +(3.70998 + 1.38375i) q^{83} +(11.1992 - 8.78825i) q^{85} +(1.27883 + 3.42869i) q^{87} +(11.2419 + 7.22472i) q^{89} +20.5135i q^{91} +(-2.82391 - 2.82391i) q^{93} +(5.15730 - 12.0088i) q^{95} +(-13.5304 + 5.04656i) q^{97} +(-6.26668 - 1.84006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 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

Related objects

Downloads

Learn more