LMFDB - Embedded newform 1100.2.q.b.221.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1100,2,Mod(221,1100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1100.221"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.q (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [52] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$8.78354422234$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			221.3
Character	$\chi$	$=$	1100.221
Dual form			1100.2.q.b.881.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.84339 - 1.33930i) q^{3} +(0.702061 + 2.12300i) q^{5} -3.98140 q^{7} +(0.677309 + 2.08454i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(-1.95146 - 6.00596i) q^{13} +(1.54916 - 4.85378i) q^{15} +(2.73983 - 1.99060i) q^{17} +(-1.03621 + 0.752852i) q^{19} +(7.33928 + 5.33230i) q^{21} +(-0.925011 + 2.84689i) q^{23} +(-4.01422 + 2.98095i) q^{25} +(-0.569051 + 1.75136i) q^{27} +(8.32724 + 6.05009i) q^{29} +(4.95603 - 3.60077i) q^{31} +(1.84339 - 1.33930i) q^{33} +(-2.79519 - 8.45250i) q^{35} +(0.738428 + 2.27265i) q^{37} +(-4.44650 + 13.6849i) q^{39} +(3.07565 + 9.46588i) q^{41} +2.64935 q^{43} +(-3.94996 + 2.90140i) q^{45} +(6.52278 + 4.73907i) q^{47} +8.85157 q^{49} -7.71658 q^{51} +(4.20247 + 3.05327i) q^{53} +(-2.23604 + 0.0116581i) q^{55} +2.91844 q^{57} +(-1.77912 - 5.47556i) q^{59} +(1.10092 - 3.38827i) q^{61} +(-2.69664 - 8.29940i) q^{63} +(11.3806 - 8.35949i) q^{65} +(-2.78520 + 2.02357i) q^{67} +(5.51801 - 4.00907i) q^{69} +(1.92786 + 1.40067i) q^{71} +(4.42905 - 13.6312i) q^{73} +(11.3922 - 0.118795i) q^{75} +(1.23032 - 3.78654i) q^{77} +(-11.3833 - 8.27044i) q^{79} +(8.71424 - 6.33126i) q^{81} +(3.96051 - 2.87748i) q^{83} +(6.14956 + 4.41912i) q^{85} +(-7.24745 - 22.3054i) q^{87} +(-4.45845 + 13.7217i) q^{89} +(7.76953 + 23.9122i) q^{91} -13.9584 q^{93} +(-2.32578 - 1.67132i) q^{95} +(6.43566 + 4.67578i) q^{97} -2.19182 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) $ 52 * q - 3 * q^5 - 9 * q^9 + 13 * q^11 + 12 * q^13 - 15 * q^15 + 8 * q^17 - 10 * q^19 - 6 * q^21 + 22 * q^23 + 5 * q^25 + 21 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^35 + 15 * q^37 - 20 * q^39 - 68 * q^43 - 7 * q^45 + 19 * q^47 + 68 * q^49 + 34 * q^51 + 3 * q^53 - 2 * q^55 - 24 * q^57 - 37 * q^59 + 10 * q^61 - 8 * q^63 + 12 * q^65 + 2 * q^67 + 27 * q^69 - 3 * q^71 + 4 * q^73 + 68 * q^75 - 17 * q^79 - 39 * q^81 + 78 * q^83 + 13 * q^85 + 13 * q^87 - 7 * q^89 - 2 * q^91 - 94 * q^93 + 18 * q^95 + 15 * q^97 - 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.84339	−	1.33930i	−1.06428	−	0.773246i	−0.0894062	−	0.995995i	$-0.528497\pi$
$3$	−1.84339	−	1.33930i	−1.06428	−	0.773246i	−0.974876	+	0.222749i	$0.928497\pi$
$4$		0			0
$5$	0.702061	+	2.12300i	0.313971	+	0.949432i
$5$	0.702061	+	2.12300i	0.313971	+	0.949432i
$6$		0			0
$7$	−3.98140			−1.50483			−0.752414	−	0.658690i	$-0.771111\pi$
$7$	−3.98140			−1.50483			−0.752414	+	0.658690i	$0.771111\pi$
$8$		0			0
$9$	0.677309	+	2.08454i	0.225770	+	0.694848i
$10$		0			0
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$12$		0			0
$13$	−1.95146	−	6.00596i	−0.541236	−	1.66575i	−0.729774	−	0.683689i	$-0.760375\pi$
$13$	−1.95146	−	6.00596i	−0.541236	−	1.66575i	0.188537	−	0.982066i	$-0.439625\pi$
$14$		0			0
$15$	1.54916	−	4.85378i	0.399991	−	1.25324i
$16$		0			0
$17$	2.73983	−	1.99060i	0.664505	−	0.482791i	−0.203676	−	0.979038i	$-0.565289\pi$
$17$	2.73983	−	1.99060i	0.664505	−	0.482791i	0.868181	+	0.496247i	$0.165289\pi$
$18$		0			0
$19$	−1.03621	+	0.752852i	−0.237723	+	0.172716i	−0.700268	−	0.713880i	$-0.746936\pi$
$19$	−1.03621	+	0.752852i	−0.237723	+	0.172716i	0.462545	+	0.886596i	$0.346936\pi$
$20$		0			0
$21$	7.33928	+	5.33230i	1.60156	+	1.16360i
$22$		0			0
$23$	−0.925011	+	2.84689i	−0.192878	+	0.593618i	0.807117	+	0.590392i	$0.201027\pi$
$23$	−0.925011	+	2.84689i	−0.192878	+	0.593618i	−0.999995	+	0.00322604i	$0.998973\pi$
$24$		0			0
$25$	−4.01422	+	2.98095i	−0.802844	+	0.596189i
$26$		0			0
$27$	−0.569051	+	1.75136i	−0.109514	+	0.337049i
$28$		0			0
$29$	8.32724	+	6.05009i	1.54633	+	1.12347i	0.946205	+	0.323568i	$0.104882\pi$
$29$	8.32724	+	6.05009i	1.54633	+	1.12347i	0.600125	+	0.799907i	$0.295118\pi$
$30$		0			0
$31$	4.95603	−	3.60077i	0.890129	−	0.646717i	−0.0457827	−	0.998951i	$-0.514578\pi$
$31$	4.95603	−	3.60077i	0.890129	−	0.646717i	0.935912	+	0.352235i	$0.114578\pi$
$32$		0			0
$33$	1.84339	−	1.33930i	0.320893	−	0.233142i
$34$		0			0
$35$	−2.79519	−	8.45250i	−0.472473	−	1.42873i
$36$		0			0
$37$	0.738428	+	2.27265i	0.121397	+	0.373621i	0.993227	−	0.116187i	$-0.0370671\pi$
$37$	0.738428	+	2.27265i	0.121397	+	0.373621i	−0.871831	+	0.489807i	$0.837067\pi$
$38$		0			0
$39$	−4.44650	+	13.6849i	−0.712010	+	2.19134i
$40$		0			0
$41$	3.07565	+	9.46588i	0.480336	+	1.47832i	0.838624	+	0.544711i	$0.183360\pi$
$41$	3.07565	+	9.46588i	0.480336	+	1.47832i	−0.358288	+	0.933611i	$0.616640\pi$
$42$		0			0
$43$	2.64935			0.404022			0.202011	−	0.979383i	$-0.435252\pi$
$43$	2.64935			0.404022			0.202011	+	0.979383i	$0.435252\pi$
$44$		0			0
$45$	−3.94996	+	2.90140i	−0.588826	+	0.432515i
$46$		0			0
$47$	6.52278	+	4.73907i	0.951445	+	0.691265i	0.951148	−	0.308735i	$-0.0999056\pi$
$47$	6.52278	+	4.73907i	0.951445	+	0.691265i	0.000296464		1.00000i	$0.499906\pi$
$48$		0			0
$49$	8.85157			1.26451
$50$		0			0
$51$	−7.71658			−1.08054
$52$		0			0
$53$	4.20247	+	3.05327i	0.577253	+	0.419399i	0.837733	−	0.546080i	$-0.183881\pi$
$53$	4.20247	+	3.05327i	0.577253	+	0.419399i	−0.260479	+	0.965479i	$0.583881\pi$
$54$		0			0
$55$	−2.23604	+	0.0116581i	−0.301507	+	0.00157198i
$56$		0			0
$57$	2.91844			0.386557
$58$		0			0
$59$	−1.77912	−	5.47556i	−0.231622	−	0.712858i	−0.997552	−	0.0699339i	$-0.977721\pi$
$59$	−1.77912	−	5.47556i	−0.231622	−	0.712858i	0.765930	−	0.642924i	$-0.222279\pi$
$60$		0			0
$61$	1.10092	−	3.38827i	0.140958	−	0.433824i	−0.855511	−	0.517784i	$-0.826757\pi$
$61$	1.10092	−	3.38827i	0.140958	−	0.433824i	0.996469	+	0.0839605i	$0.0267569\pi$
$62$		0			0
$63$	−2.69664	−	8.29940i	−0.339745	−	1.04563i
$64$		0			0
$65$	11.3806	−	8.35949i	1.41159	−	1.03687i
$66$		0			0
$67$	−2.78520	+	2.02357i	−0.340267	+	0.247218i	−0.744774	−	0.667316i	$-0.767443\pi$
$67$	−2.78520	+	2.02357i	−0.340267	+	0.247218i	0.404508	+	0.914535i	$0.367443\pi$
$68$		0			0
$69$	5.51801	−	4.00907i	0.664290	−	0.482635i
$70$		0			0
$71$	1.92786	+	1.40067i	0.228794	+	0.166229i	0.696276	−	0.717774i	$-0.254839\pi$
$71$	1.92786	+	1.40067i	0.228794	+	0.166229i	−0.467482	+	0.884003i	$0.654839\pi$
$72$		0			0
$73$	4.42905	−	13.6312i	0.518382	−	1.59541i	−0.258662	−	0.965968i	$-0.583282\pi$
$73$	4.42905	−	13.6312i	0.518382	−	1.59541i	0.777044	−	0.629447i	$-0.216718\pi$
$74$		0			0
$75$	11.3922	−	0.118795i	1.31545	−	0.0137173i
$76$		0			0
$77$	1.23032	−	3.78654i	0.140208	−	0.431516i
$78$		0			0
$79$	−11.3833	−	8.27044i	−1.28072	−	0.930497i	−0.281145	−	0.959665i	$-0.590714\pi$
$79$	−11.3833	−	8.27044i	−1.28072	−	0.930497i	−0.999575	+	0.0291677i	$0.990714\pi$
$80$		0			0
$81$	8.71424	−	6.33126i	0.968248	−	0.703474i
$82$		0			0
$83$	3.96051	−	2.87748i	0.434723	−	0.315844i	−0.348812	−	0.937193i	$-0.613415\pi$
$83$	3.96051	−	2.87748i	0.434723	−	0.315844i	0.783534	+	0.621348i	$0.213415\pi$
$84$		0			0
$85$	6.14956	+	4.41912i	0.667013	+	0.479320i
$86$		0			0
$87$	−7.24745	−	22.3054i	−0.777009	−	2.39139i
$88$		0			0
$89$	−4.45845	+	13.7217i	−0.472595	+	1.45450i	0.376579	+	0.926385i	$0.377101\pi$
$89$	−4.45845	+	13.7217i	−0.472595	+	1.45450i	−0.849174	+	0.528114i	$0.822899\pi$
$90$		0			0
$91$	7.76953	+	23.9122i	0.814468	+	2.50668i
$92$		0			0
$93$	−13.9584			−1.44742
$94$		0			0
$95$	−2.32578	−	1.67132i	−0.238620	−	0.171474i
$96$		0			0
$97$	6.43566	+	4.67578i	0.653443	+	0.474754i	0.864442	−	0.502732i	$-0.167672\pi$
$97$	6.43566	+	4.67578i	0.653443	+	0.474754i	−0.210999	+	0.977486i	$0.567672\pi$
$98$		0			0
$99$	−2.19182			−0.220286
$100$		0			0
$101$	11.9259			1.18668			0.593338	−	0.804953i	$-0.297810\pi$
$101$	11.9259			1.18668			0.593338	+	0.804953i	$0.297810\pi$
$102$		0			0
$103$	1.29949	+	0.944133i	0.128042	+	0.0930282i	0.649963	−	0.759966i	$-0.274784\pi$
$103$	1.29949	+	0.944133i	0.128042	+	0.0930282i	−0.521921	+	0.852994i	$0.674784\pi$
$104$		0			0
$105$	−6.16782	+	19.3249i	−0.601918	+	1.88591i
$106$		0			0
$107$	9.50503			0.918886			0.459443	−	0.888207i	$-0.348049\pi$
$107$	9.50503			0.918886			0.459443	+	0.888207i	$0.348049\pi$
$108$		0			0
$109$	1.84366	+	5.67420i	0.176590	+	0.543490i	0.999703	−	0.0243894i	$-0.00776416\pi$
$109$	1.84366	+	5.67420i	0.176590	+	0.543490i	−0.823112	+	0.567879i	$0.807764\pi$
$110$		0			0
$111$	1.68255	−	5.17835i	0.159700	−	0.491507i
$112$		0			0
$113$	3.86897	+	11.9075i	0.363962	+	1.12016i	0.950628	+	0.310331i	$0.100440\pi$
$113$	3.86897	+	11.9075i	0.363962	+	1.12016i	−0.586666	+	0.809829i	$0.699560\pi$
$114$		0			0
$115$	−6.69336	+	0.0348975i	−0.624159	+	0.00325421i
$116$		0			0
$117$	11.1979	−	8.13579i	1.03525	−	0.752154i
$118$		0			0
$119$	−10.9084	+	7.92538i	−0.999967	+	0.726518i
$120$		0			0
$121$	−0.809017	−	0.587785i	−0.0735470	−	0.0534350i
$122$		0			0
$123$	7.00804	−	21.5685i	0.631894	−	1.94477i
$124$		0			0
$125$	−9.14676	−	6.42937i	−0.818111	−	0.575060i
$126$		0			0
$127$	−4.46351	+	13.7373i	−0.396072	+	1.21898i	0.532051	+	0.846712i	$0.321421\pi$
$127$	−4.46351	+	13.7373i	−0.396072	+	1.21898i	−0.928123	+	0.372273i	$0.878579\pi$
$128$		0			0
$129$	−4.88379	−	3.54828i	−0.429994	−	0.312409i
$130$		0			0
$131$	0.0531810	−	0.0386383i	0.00464645	−	0.00337584i	−0.585460	−	0.810702i	$-0.699086\pi$
$131$	0.0531810	−	0.0386383i	0.00464645	−	0.00337584i	0.590106	+	0.807326i	$0.299086\pi$
$132$		0			0
$133$	4.12558	−	2.99741i	0.357733	−	0.259908i
$134$		0			0
$135$	−4.11764	+	0.0214683i	−0.354390	+	0.00184770i
$136$		0			0
$137$	−4.65551	−	14.3282i	−0.397747	−	1.22414i	−0.926801	−	0.375552i	$-0.877453\pi$
$137$	−4.65551	−	14.3282i	−0.397747	−	1.22414i	0.529054	−	0.848588i	$-0.322547\pi$
$138$		0			0
$139$	−1.18608	+	3.65038i	−0.100602	+	0.309621i	−0.988673	−	0.150085i	$-0.952045\pi$
$139$	−1.18608	+	3.65038i	−0.100602	+	0.309621i	0.888071	+	0.459706i	$0.152045\pi$
$140$		0			0
$141$	−5.67697	−	17.4719i	−0.478087	−	1.47140i
$142$		0			0
$143$	6.31504			0.528090
$144$		0			0
$145$	−6.99809	+	21.9262i	−0.581160	+	1.82087i
$146$		0			0
$147$	−16.3169	−	11.8549i	−1.34580	−	0.977778i
$148$		0			0
$149$	−13.8400			−1.13382			−0.566909	−	0.823780i	$-0.691861\pi$
$149$	−13.8400			−1.13382			−0.566909	+	0.823780i	$0.691861\pi$
$150$		0			0
$151$	19.4381			1.58185			0.790927	−	0.611911i	$-0.209599\pi$
$151$	19.4381			1.58185			0.790927	+	0.611911i	$0.209599\pi$
$152$		0			0
$153$	6.00520	+	4.36303i	0.485492	+	0.352730i
$154$		0			0
$155$	11.1238	+	7.99367i	0.893489	+	0.642067i
$156$		0			0
$157$	−11.1274			−0.888066			−0.444033	−	0.896011i	$-0.646453\pi$
$157$	−11.1274			−0.888066			−0.444033	+	0.896011i	$0.646453\pi$
$158$		0			0
$159$	−3.65754	−	11.2567i	−0.290062	−	0.892718i
$160$		0			0
$161$	3.68284	−	11.3346i	0.290249	−	0.893294i
$162$		0			0
$163$	1.95871	+	6.02830i	0.153418	+	0.472173i	0.997997	−	0.0632583i	$-0.0201492\pi$
$163$	1.95871	+	6.02830i	0.153418	+	0.472173i	−0.844579	+	0.535431i	$0.820149\pi$
$164$		0			0
$165$	4.13750	+	2.97324i	0.322104	+	0.231466i
$166$		0			0
$167$	7.75942	−	5.63755i	0.600442	−	0.436246i	−0.245594	−	0.969373i	$-0.578983\pi$
$167$	7.75942	−	5.63755i	0.600442	−	0.436246i	0.846036	+	0.533126i	$0.178983\pi$
$168$		0			0
$169$	−21.7462	+	15.7995i	−1.67278	+	1.21535i
$170$		0			0
$171$	−2.27119	−	1.65011i	−0.173682	−	0.126187i
$172$		0			0
$173$	−3.40903	+	10.4919i	−0.259184	+	0.797685i	0.733793	+	0.679373i	$0.237748\pi$
$173$	−3.40903	+	10.4919i	−0.259184	+	0.797685i	−0.992976	+	0.118312i	$0.962252\pi$
$174$		0			0
$175$	15.9822	−	11.8683i	1.20814	−	0.897163i
$176$		0			0
$177$	−4.05382	+	12.4764i	−0.304704	+	0.937782i
$178$		0			0
$179$	−5.59356	−	4.06396i	−0.418083	−	0.303755i	0.358783	−	0.933421i	$-0.383192\pi$
$179$	−5.59356	−	4.06396i	−0.418083	−	0.303755i	−0.776866	+	0.629666i	$0.783192\pi$
$180$		0			0
$181$	15.2279	−	11.0638i	1.13188	−	0.822362i	0.145916	−	0.989297i	$-0.453387\pi$
$181$	15.2279	−	11.0638i	1.13188	−	0.822362i	0.985968	+	0.166935i	$0.0533869\pi$
$182$		0			0
$183$	−6.56734	+	4.77145i	−0.485472	+	0.352716i
$184$		0			0
$185$	−4.30640	+	3.16322i	−0.316613	+	0.232564i
$186$		0			0
$187$	1.04652	+	3.22086i	0.0765291	+	0.235532i
$188$		0			0
$189$	2.26562	−	6.97287i	0.164800	−	0.507202i
$190$		0			0
$191$	7.32981	+	22.5588i	0.530367	+	1.63230i	0.753453	+	0.657502i	$0.228387\pi$
$191$	7.32981	+	22.5588i	0.530367	+	1.63230i	−0.223086	+	0.974799i	$0.571613\pi$
$192$		0			0
$193$	−12.4661			−0.897329			−0.448664	−	0.893700i	$-0.648100\pi$
$193$	−12.4661			−0.897329			−0.448664	+	0.893700i	$0.648100\pi$
$194$		0			0
$195$	−32.1748	+	0.167751i	−2.30408	+	0.0120129i
$196$		0			0
$197$	−13.5407	−	9.83791i	−0.964737	−	0.700922i	−0.0104908	−	0.999945i	$-0.503339\pi$
$197$	−13.5407	−	9.83791i	−0.964737	−	0.700922i	−0.954246	+	0.299023i	$0.903339\pi$
$198$		0			0
$199$	20.9394			1.48436			0.742178	−	0.670203i	$-0.233793\pi$
$199$	20.9394			1.48436			0.742178	+	0.670203i	$0.233793\pi$
$200$		0			0
$201$	7.84439			0.553300
$202$		0			0
$203$	−33.1541	−	24.0879i	−2.32696	−	1.69064i
$204$		0			0
$205$	−17.9367	+	13.1752i	−1.25275	+	0.920197i
$206$		0			0
$207$	−6.56099			−0.456020
$208$		0			0
$209$	−0.395798	−	1.21814i	−0.0273779	−	0.0842605i
$210$		0			0
$211$	6.32495	−	19.4662i	0.435427	−	1.34011i	−0.457221	−	0.889353i	$-0.651155\pi$
$211$	6.32495	−	19.4662i	0.435427	−	1.34011i	0.892648	−	0.450754i	$-0.148845\pi$
$212$		0			0
$213$	−1.67787	−	5.16396i	−0.114966	−	0.353829i
$214$		0			0
$215$	1.86001	+	5.62456i	0.126851	+	0.383592i
$216$		0			0
$217$	−19.7319	+	14.3361i	−1.33949	+	0.973198i
$218$		0			0
$219$	−26.4208	+	19.1958i	−1.78535	+	1.29713i
$220$		0			0
$221$	−17.3021	−	12.5707i	−1.16387	−	0.845599i
$222$		0			0
$223$	−0.753633	+	2.31944i	−0.0504670	+	0.155322i	−0.973114	−	0.230324i	$-0.926021\pi$
$223$	−0.753633	+	2.31944i	−0.0504670	+	0.155322i	0.922647	+	0.385646i	$0.126021\pi$
$224$		0			0
$225$	−8.93278	−	6.34879i	−0.595518	−	0.423253i
$226$		0			0
$227$	−1.32427	+	4.07570i	−0.0878952	+	0.270514i	−0.985337	−	0.170619i	$-0.945423\pi$
$227$	−1.32427	+	4.07570i	−0.0878952	+	0.270514i	0.897442	+	0.441133i	$0.145423\pi$
$228$		0			0
$229$	−16.3255	−	11.8612i	−1.07882	−	0.783810i	−0.101345	−	0.994851i	$-0.532315\pi$
$229$	−16.3255	−	11.8612i	−1.07882	−	0.783810i	−0.977477	+	0.211041i	$0.932315\pi$
$230$		0			0
$231$	−7.33928	+	5.33230i	−0.482889	+	0.350840i
$232$		0			0
$233$	5.15555	−	3.74573i	0.337751	−	0.245391i	−0.405961	−	0.913890i	$-0.633063\pi$
$233$	5.15555	−	3.74573i	0.337751	−	0.245391i	0.743712	+	0.668500i	$0.233063\pi$
$234$		0			0
$235$	−5.48164	+	17.1749i	−0.357583	+	1.12037i
$236$		0			0
$237$	9.90723	+	30.4913i	0.643544	+	1.98062i
$238$		0			0
$239$	0.0753449	−	0.231888i	0.00487366	−	0.0149996i	−0.948590	−	0.316507i	$-0.897490\pi$
$239$	0.0753449	−	0.231888i	0.00487366	−	0.0149996i	0.953464	+	0.301508i	$0.0974899\pi$
$240$		0			0
$241$	4.61927	+	14.2166i	0.297553	+	0.915774i	0.982352	+	0.187042i	$0.0598901\pi$
$241$	4.61927	+	14.2166i	0.297553	+	0.915774i	−0.684799	+	0.728732i	$0.740110\pi$
$242$		0			0
$243$	−19.0187			−1.22005
$244$		0			0
$245$	6.21434	+	18.7918i	0.397020	+	1.20057i
$246$		0			0
$247$	6.54372	+	4.75429i	0.416367	+	0.302508i
$248$		0			0
$249$	−11.1546			−0.706893
$250$		0			0
$251$	−19.7970			−1.24958			−0.624788	−	0.780795i	$-0.714815\pi$
$251$	−19.7970			−1.24958			−0.624788	+	0.780795i	$0.714815\pi$
$252$		0			0
$253$	−2.42171	−	1.75948i	−0.152252	−	0.110617i
$254$		0			0
$255$	−5.41751	−	16.3823i	−0.339258	−	1.02590i
$256$		0			0
$257$	−11.3290			−0.706683			−0.353342	−	0.935494i	$-0.614955\pi$
$257$	−11.3290			−0.706683			−0.353342	+	0.935494i	$0.614955\pi$
$258$		0			0
$259$	−2.93998	−	9.04832i	−0.182681	−	0.562235i
$260$		0			0
$261$	−6.97156	+	21.4563i	−0.431529	+	1.32811i
$262$		0			0
$263$	1.05655	+	3.25172i	0.0651495	+	0.200510i	0.978332	−	0.207041i	$-0.0663832\pi$
$263$	1.05655	+	3.25172i	0.0651495	+	0.200510i	−0.913183	+	0.407550i	$0.866383\pi$
$264$		0			0
$265$	−3.53169	+	11.0654i	−0.216950	+	0.679742i
$266$		0			0
$267$	26.5962	−	19.3233i	1.62766	−	1.18256i
$268$		0			0
$269$	17.2215	−	12.5121i	1.05001	−	0.762878i	0.0777973	−	0.996969i	$-0.475211\pi$
$269$	17.2215	−	12.5121i	1.05001	−	0.762878i	0.972215	+	0.234091i	$0.0752113\pi$
$270$		0			0
$271$	13.5826	+	9.86835i	0.825086	+	0.599460i	0.918165	−	0.396199i	$-0.129671\pi$
$271$	13.5826	+	9.86835i	0.825086	+	0.599460i	−0.0930791	+	0.995659i	$0.529671\pi$
$272$		0			0
$273$	17.7033	−	54.4852i	1.07145	−	3.29759i
$274$		0			0
$275$	−1.59459	−	4.73891i	−0.0961571	−	0.285767i
$276$		0			0
$277$	4.83464	−	14.8795i	0.290485	−	0.894022i	−0.694215	−	0.719768i	$-0.744248\pi$
$277$	4.83464	−	14.8795i	0.290485	−	0.894022i	0.984701	−	0.174255i	$-0.0557516\pi$
$278$		0			0
$279$	10.8627	+	7.89222i	0.650333	+	0.472495i
$280$		0			0
$281$	−0.632829	+	0.459777i	−0.0377514	+	0.0274280i	−0.606501	−	0.795083i	$-0.707427\pi$
$281$	−0.632829	+	0.459777i	−0.0377514	+	0.0274280i	0.568750	+	0.822511i	$0.307427\pi$
$282$		0			0
$283$	−12.3846	+	8.99796i	−0.736190	+	0.534873i	−0.891516	−	0.452990i	$-0.850357\pi$
$283$	−12.3846	+	8.99796i	−0.736190	+	0.534873i	0.155326	+	0.987863i	$0.450357\pi$
$284$		0			0
$285$	2.04892	+	6.19583i	0.121368	+	0.367009i
$286$		0			0
$287$	−12.2454	−	37.6875i	−0.722823	−	2.22462i
$288$		0			0
$289$	−1.70913	+	5.26017i	−0.100537	+	0.309422i
$290$		0			0
$291$	−5.60116	−	17.2386i	−0.328346	−	1.01054i
$292$		0			0
$293$	10.3378			0.603940			0.301970	−	0.953317i	$-0.402356\pi$
$293$	10.3378			0.603940			0.301970	+	0.953317i	$0.402356\pi$
$294$		0			0
$295$	10.3755	−	7.62124i	0.604088	−	0.443726i
$296$		0			0
$297$	−1.48980	−	1.08240i	−0.0864467	−	0.0628072i
$298$		0			0
$299$	18.9035			1.09321
$300$		0			0
$301$	−10.5481			−0.607985
$302$		0			0
$303$	−21.9842	−	15.9724i	−1.26296	−	0.917593i
$304$		0			0
$305$	7.96620	−	0.0415338i	0.456143	−	0.00237822i
$306$		0			0
$307$	14.9141			0.851193			0.425597	−	0.904913i	$-0.360064\pi$
$307$	14.9141			0.851193			0.425597	+	0.904913i	$0.360064\pi$
$308$		0			0
$309$	−1.13098	−	3.48081i	−0.0643395	−	0.198017i
$310$		0			0
$311$	−6.97205	+	21.4578i	−0.395349	+	1.21676i	0.533341	+	0.845900i	$0.320936\pi$
$311$	−6.97205	+	21.4578i	−0.395349	+	1.21676i	−0.928690	+	0.370858i	$0.879064\pi$
$312$		0			0
$313$	9.70561	+	29.8708i	0.548594	+	1.68840i	0.712288	+	0.701887i	$0.247659\pi$
$313$	9.70561	+	29.8708i	0.548594	+	1.68840i	−0.163695	+	0.986511i	$0.552341\pi$
$314$		0			0
$315$	15.7264	−	11.5516i	0.886082	−	0.650861i
$316$		0			0
$317$	18.3049	−	13.2993i	1.02811	−	0.746964i	0.0601787	−	0.998188i	$-0.480833\pi$
$317$	18.3049	−	13.2993i	1.02811	−	0.746964i	0.967929	+	0.251224i	$0.0808329\pi$
$318$		0			0
$319$	−8.32724	+	6.05009i	−0.466236	+	0.338740i
$320$		0			0
$321$	−17.5215	−	12.7301i	−0.977954	−	0.710525i
$322$		0			0
$323$	−1.34041	+	4.12537i	−0.0745825	+	0.229541i
$324$		0			0
$325$	25.7370	+	18.2921i	1.42763	+	1.01466i
$326$		0			0
$327$	4.20088	−	12.9290i	0.232309	−	0.714974i
$328$		0			0
$329$	−25.9698	−	18.8682i	−1.43176	−	1.04024i
$330$		0			0
$331$	6.88210	−	5.00014i	0.378275	−	0.274833i	−0.382359	−	0.924014i	$-0.624888\pi$
$331$	6.88210	−	5.00014i	0.378275	−	0.274833i	0.760634	+	0.649181i	$0.224888\pi$
$332$		0			0
$333$	−4.23728	+	3.07857i	−0.232202	+	0.168704i
$334$		0			0
$335$	−6.25141	−	4.49231i	−0.341551	−	0.245441i
$336$		0			0
$337$	2.57087	+	7.91233i	0.140044	+	0.431012i	0.996340	−	0.0854731i	$-0.0272402\pi$
$337$	2.57087	+	7.91233i	0.140044	+	0.431012i	−0.856296	+	0.516485i	$0.827240\pi$
$338$		0			0
$339$	8.81566	−	27.1318i	0.478801	−	1.47360i
$340$		0			0
$341$	1.89303	+	5.82616i	0.102514	+	0.315504i
$342$		0			0
$343$	−7.37185			−0.398042
$344$		0			0
$345$	12.3852	+	8.90009i	0.666797	+	0.479165i
$346$		0			0
$347$	15.2286	+	11.0642i	0.817515	+	0.593959i	0.916000	−	0.401179i	$-0.131400\pi$
$347$	15.2286	+	11.0642i	0.817515	+	0.593959i	−0.0984845	+	0.995139i	$0.531400\pi$
$348$		0			0
$349$	29.5799			1.58337			0.791687	−	0.610927i	$-0.209203\pi$
$349$	29.5799			1.58337			0.791687	+	0.610927i	$0.209203\pi$
$350$		0			0
$351$	11.6291			0.620714
$352$		0			0
$353$	−7.52140	−	5.46462i	−0.400324	−	0.290852i	0.369349	−	0.929291i	$-0.379581\pi$
$353$	−7.52140	−	5.46462i	−0.400324	−	0.290852i	−0.769673	+	0.638438i	$0.779581\pi$
$354$		0			0
$355$	−1.62014	+	5.07618i	−0.0859882	+	0.269416i
$356$		0			0
$357$	30.7228			1.62602
$358$		0			0
$359$	1.90912	+	5.87565i	0.100759	+	0.310105i	0.988712	−	0.149830i	$-0.0478727\pi$
$359$	1.90912	+	5.87565i	0.100759	+	0.310105i	−0.887953	+	0.459935i	$0.847873\pi$
$360$		0			0
$361$	−5.36437	+	16.5098i	−0.282335	+	0.868939i
$362$		0			0
$363$	0.704113	+	2.16704i	0.0369563	+	0.113740i
$364$		0			0
$365$	32.0485	−	0.167093i	1.67750	−	0.00874604i
$366$		0			0
$367$	17.0951	−	12.4204i	0.892359	−	0.648337i	−0.0441327	−	0.999026i	$-0.514052\pi$
$367$	17.0951	−	12.4204i	0.892359	−	0.648337i	0.936492	+	0.350689i	$0.114052\pi$
$368$		0			0
$369$	−17.6489	+	12.8226i	−0.918763	+	0.667520i
$370$		0			0
$371$	−16.7317	−	12.1563i	−0.868668	−	0.631124i
$372$		0			0
$373$	−6.10998	+	18.8046i	−0.316363	+	0.973665i	0.658827	+	0.752295i	$0.271053\pi$
$373$	−6.10998	+	18.8046i	−0.316363	+	0.973665i	−0.975190	+	0.221370i	$0.928947\pi$
$374$		0			0
$375$	8.25020	+	24.1021i	0.426038	+	1.24463i
$376$		0			0
$377$	20.0864	−	61.8196i	1.03450	−	3.18387i
$378$		0			0
$379$	2.33045	+	1.69317i	0.119707	+	0.0869724i	0.646028	−	0.763314i	$-0.276429\pi$
$379$	2.33045	+	1.69317i	0.119707	+	0.0869724i	−0.526321	+	0.850286i	$0.676429\pi$
$380$		0			0
$381$	26.6263	−	19.3452i	1.36411	−	0.991082i
$382$		0			0
$383$	1.70617	−	1.23960i	0.0871810	−	0.0633407i	−0.543341	−	0.839512i	$-0.682841\pi$
$383$	1.70617	−	1.23960i	0.0871810	−	0.0633407i	0.630522	+	0.776171i	$0.282841\pi$
$384$		0			0
$385$	8.90257	−	0.0464158i	0.453717	−	0.00236557i
$386$		0			0
$387$	1.79443	+	5.52269i	0.0912160	+	0.280734i
$388$		0			0
$389$	3.88719	−	11.9635i	0.197088	−	0.606575i	−0.802858	−	0.596171i	$-0.796688\pi$
$389$	3.88719	−	11.9635i	0.197088	−	0.606575i	0.999946	−	0.0104043i	$-0.00331184\pi$
$390$		0			0
$391$	3.13265	+	9.64132i	0.158425	+	0.487582i
$392$		0			0
$393$	−0.149782			−0.00755549
$394$		0			0
$395$	9.56635	−	29.9730i	0.481335	−	1.50811i
$396$		0			0
$397$	−7.12989	−	5.18017i	−0.357839	−	0.259985i	0.394311	−	0.918977i	$-0.370983\pi$
$397$	−7.12989	−	5.18017i	−0.357839	−	0.259985i	−0.752150	+	0.658992i	$0.770983\pi$
$398$		0			0
$399$	−11.6195			−0.581702
$400$		0			0
$401$	18.2018			0.908955			0.454477	−	0.890758i	$-0.349826\pi$
$401$	18.2018			0.908955			0.454477	+	0.890758i	$0.349826\pi$
$402$		0			0
$403$	−31.2975	−	22.7390i	−1.55904	−	1.13271i
$404$		0			0
$405$	19.5592	+	14.0554i	0.971903	+	0.698416i
$406$		0			0
$407$	−2.38960			−0.118448
$408$		0			0
$409$	6.18803	+	19.0448i	0.305978	+	0.941704i	0.979310	+	0.202364i	$0.0648624\pi$
$409$	6.18803	+	19.0448i	0.305978	+	0.941704i	−0.673332	+	0.739340i	$0.735138\pi$
$410$		0			0
$411$	−10.6078	+	32.6476i	−0.523246	+	1.61039i
$412$		0			0
$413$	7.08339	+	21.8004i	0.348551	+	1.07273i
$414$		0			0
$415$	8.88940	+	6.38798i	0.436363	+	0.313574i
$416$		0			0
$417$	7.07536	−	5.14055i	0.346482	−	0.251734i
$418$		0			0
$419$	−25.5580	+	18.5690i	−1.24859	+	0.907153i	−0.998139	−	0.0609763i	$-0.980579\pi$
$419$	−25.5580	+	18.5690i	−1.24859	+	0.907153i	−0.250450	+	0.968130i	$0.580579\pi$
$420$		0			0
$421$	−29.0811	−	21.1287i	−1.41733	−	1.02975i	−0.992205	−	0.124612i	$-0.960231\pi$
$421$	−29.0811	−	21.1287i	−1.41733	−	1.02975i	−0.425122	−	0.905136i	$-0.639769\pi$
$422$		0			0
$423$	−5.46087	+	16.8068i	−0.265516	+	0.817176i
$424$		0			0
$425$	−5.06439	+	16.1580i	−0.245659	+	0.783777i
$426$		0			0
$427$	−4.38319	+	13.4901i	−0.212118	+	0.652831i
$428$		0			0
$429$	−11.6411	−	8.45775i	−0.562037	−	0.408344i
$430$		0			0
$431$	14.6781	−	10.6642i	0.707018	−	0.513679i	−0.175192	−	0.984534i	$-0.556055\pi$
$431$	14.6781	−	10.6642i	0.707018	−	0.513679i	0.882210	+	0.470855i	$0.156055\pi$
$432$		0			0
$433$	−27.5255	+	19.9984i	−1.32279	+	0.961063i	−0.322897	+	0.946434i	$0.604657\pi$
$433$	−27.5255	+	19.9984i	−1.32279	+	0.961063i	−0.999893	+	0.0146286i	$0.995343\pi$
$434$		0			0
$435$	42.2660	−	31.0460i	2.02650	−	1.48854i
$436$		0			0
$437$	−1.18478	−	3.64638i	−0.0566757	−	0.174430i
$438$		0			0
$439$	4.12582	−	12.6980i	0.196915	−	0.606041i	−0.803034	−	0.595933i	$-0.796782\pi$
$439$	4.12582	−	12.6980i	0.196915	−	0.606041i	0.999949	−	0.0101080i	$-0.00321754\pi$
$440$		0			0
$441$	5.99525	+	18.4515i	0.285488	+	0.878642i
$442$		0			0
$443$	−25.0208			−1.18878			−0.594388	−	0.804179i	$-0.702605\pi$
$443$	−25.0208			−1.18878			−0.594388	+	0.804179i	$0.702605\pi$
$444$		0			0
$445$	−32.2612	+	0.168202i	−1.52933	+	0.00797354i
$446$		0			0
$447$	25.5125	+	18.5360i	1.20670	+	0.876720i
$448$		0			0
$449$	−32.4949			−1.53353			−0.766765	−	0.641927i	$-0.778135\pi$
$449$	−32.4949			−1.53353			−0.766765	+	0.641927i	$0.778135\pi$
$450$		0			0
$451$	−9.95301			−0.468669
$452$		0			0
$453$	−35.8321	−	26.0335i	−1.68354	−	1.22316i
$454$		0			0
$455$	−45.3107	+	33.2825i	−2.12420	+	1.56031i
$456$		0			0
$457$	−19.2253			−0.899323			−0.449662	−	0.893199i	$-0.648455\pi$
$457$	−19.2253			−0.899323			−0.449662	+	0.893199i	$0.648455\pi$
$458$		0			0
$459$	1.92716	+	5.93117i	0.0899519	+	0.276843i
$460$		0			0
$461$	−6.68841	+	20.5848i	−0.311510	+	0.958730i	0.665657	+	0.746258i	$0.268151\pi$
$461$	−6.68841	+	20.5848i	−0.311510	+	0.958730i	−0.977167	+	0.212472i	$0.931849\pi$
$462$		0			0
$463$	11.3958	+	35.0726i	0.529606	+	1.62996i	0.755023	+	0.655699i	$0.227626\pi$
$463$	11.3958	+	35.0726i	0.529606	+	1.62996i	−0.225416	+	0.974263i	$0.572374\pi$
$464$		0			0
$465$	−9.79965	−	29.6336i	−0.454448	−	1.37423i
$466$		0			0
$467$	10.5887	−	7.69317i	0.489988	−	0.355997i	−0.315191	−	0.949028i	$-0.602069\pi$
$467$	10.5887	−	7.69317i	0.489988	−	0.355997i	0.805180	+	0.593031i	$0.202069\pi$
$468$		0			0
$469$	11.0890	−	8.05664i	0.512043	−	0.372021i
$470$		0			0
$471$	20.5122	+	14.9030i	0.945152	+	0.686693i
$472$		0			0
$473$	−0.818695	+	2.51968i	−0.0376436	+	0.115855i
$474$		0			0
$475$	1.91537	−	6.11100i	0.0878833	−	0.280392i
$476$		0			0
$477$	−3.51831	+	10.8282i	−0.161092	+	0.495791i
$478$		0			0
$479$	−6.42518	−	4.66817i	−0.293574	−	0.213294i	0.431242	−	0.902236i	$-0.358075\pi$
$479$	−6.42518	−	4.66817i	−0.293574	−	0.213294i	−0.724816	+	0.688942i	$0.758075\pi$
$480$		0			0
$481$	12.2084	−	8.86994i	0.556656	−	0.404434i
$482$		0			0
$483$	−21.9694	+	15.9617i	−0.999643	+	0.726283i
$484$		0			0
$485$	−5.40844	+	16.9456i	−0.245585	+	0.769459i
$486$		0			0
$487$	−5.47442	−	16.8485i	−0.248070	−	0.763480i	−0.995116	−	0.0987086i	$-0.968529\pi$
$487$	−5.47442	−	16.8485i	−0.248070	−	0.763480i	0.747047	−	0.664772i	$-0.231471\pi$
$488$		0			0
$489$	4.46304	−	13.7358i	0.201825	−	0.621155i
$490$		0			0
$491$	−9.01132	−	27.7340i	−0.406675	−	1.25162i	−0.919488	−	0.393117i	$-0.871397\pi$
$491$	−9.01132	−	27.7340i	−0.406675	−	1.25162i	0.512813	−	0.858500i	$-0.328603\pi$
$492$		0			0
$493$	34.8585			1.56995
$494$		0			0
$495$	−1.53879	−	4.65322i	−0.0691635	−	0.209147i
$496$		0			0
$497$	−7.67557	−	5.57663i	−0.344296	−	0.250146i
$498$		0			0
$499$	13.7573			0.615863			0.307932	−	0.951408i	$-0.400363\pi$
$499$	13.7573			0.615863			0.307932	+	0.951408i	$0.400363\pi$
$500$		0			0
$501$	−21.8540			−0.976365
$502$		0			0
$503$	29.1242	+	21.1600i	1.29858	+	0.943476i	0.999941	−	0.0108894i	$-0.00346626\pi$
$503$	29.1242	+	21.1600i	1.29858	+	0.943476i	0.298642	+	0.954365i	$0.403466\pi$
$504$		0			0
$505$	8.37274	+	25.3187i	0.372582	+	1.12667i
$506$		0			0
$507$	61.2471			2.72008
$508$		0			0
$509$	−4.86462	−	14.9718i	−0.215621	−	0.663612i	−0.999109	−	0.0422057i	$-0.986562\pi$
$509$	−4.86462	−	14.9718i	−0.215621	−	0.663612i	0.783488	−	0.621407i	$-0.213438\pi$
$510$		0			0
$511$	−17.6339	+	54.2714i	−0.780076	+	2.40083i
$512$		0			0
$513$	−0.728857	−	2.24319i	−0.0321798	−	0.0990393i
$514$		0			0
$515$	−1.09207	+	3.42165i	−0.0481224	+	0.150776i
$516$		0			0
$517$	−6.52278	+	4.73907i	−0.286871	+	0.208424i
$518$		0			0
$519$	20.3360	−	14.7750i	0.892651	−	0.648549i
$520$		0			0
$521$	−3.94146	−	2.86364i	−0.172678	−	0.125458i	0.498089	−	0.867126i	$-0.334035\pi$
$521$	−3.94146	−	2.86364i	−0.172678	−	0.125458i	−0.670768	+	0.741668i	$0.734035\pi$
$522$		0			0
$523$	8.19292	−	25.2152i	0.358251	−	1.10258i	−0.595849	−	0.803097i	$-0.703184\pi$
$523$	8.19292	−	25.2152i	0.358251	−	1.10258i	0.954100	−	0.299488i	$-0.0968158\pi$
$524$		0			0
$525$	−45.3568	+	0.472971i	−1.97953	+	0.0206421i
$526$		0			0
$527$	6.41097	−	19.7309i	0.279266	−	0.859493i
$528$		0			0
$529$	11.3582	+	8.25224i	0.493836	+	0.358793i
$530$		0			0
$531$	10.2090	−	7.41730i	0.443034	−	0.321883i
$532$		0			0
$533$	50.8497	−	36.9445i	2.20255	−	1.60024i
$534$		0			0
$535$	6.67311	+	20.1791i	0.288504	+	0.872420i
$536$		0			0
$537$	4.86825	+	14.9829i	0.210081	+	0.646562i
$538$		0			0
$539$	−2.73529	+	8.41834i	−0.117817	+	0.362604i
$540$		0			0
$541$	−8.73538	−	26.8847i	−0.375563	−	1.15587i	−0.943098	−	0.332516i	$-0.892103\pi$
$541$	−8.73538	−	26.8847i	−0.375563	−	1.15587i	0.567534	−	0.823350i	$-0.307897\pi$
$542$		0			0
$543$	−42.8888			−1.84053
$544$		0			0
$545$	−10.7519	+	7.89771i	−0.460562	+	0.338301i
$546$		0			0
$547$	32.4180	+	23.5531i	1.38609	+	1.00706i	0.996281	+	0.0861618i	$0.0274602\pi$
$547$	32.4180	+	23.5531i	1.38609	+	1.00706i	0.389813	+	0.920894i	$0.372540\pi$
$548$		0			0
$549$	7.80866			0.333266
$550$		0			0
$551$	−13.1836			−0.561640
$552$		0			0
$553$	45.3215	+	32.9280i	1.92726	+	1.40024i
$554$		0			0
$555$	12.1749	−	0.0634767i	0.516794	−	0.00269444i
$556$		0			0
$557$	−0.0888659			−0.00376537			−0.00188268	−	0.999998i	$-0.500599\pi$
$557$	−0.0888659			−0.00376537			−0.00188268	+	0.999998i	$0.500599\pi$
$558$		0			0
$559$	−5.17009	−	15.9119i	−0.218672	−	0.673002i
$560$		0			0
$561$	2.38456	−	7.33891i	0.100676	−	0.309849i
$562$		0			0
$563$	9.48207	+	29.1828i	0.399621	+	1.22991i	0.925304	+	0.379227i	$0.123810\pi$
$563$	9.48207	+	29.1828i	0.399621	+	1.22991i	−0.525682	+	0.850681i	$0.676190\pi$
$564$		0			0
$565$	−22.5632	+	16.5736i	−0.949243	+	0.697255i
$566$		0			0
$567$	−34.6949	+	25.2073i	−1.45705	+	1.05861i
$568$		0			0
$569$	11.8016	−	8.57439i	0.494750	−	0.359457i	−0.312258	−	0.949997i	$-0.601085\pi$
$569$	11.8016	−	8.57439i	0.494750	−	0.359457i	0.807008	+	0.590540i	$0.201085\pi$
$570$		0			0
$571$	−20.2271	−	14.6959i	−0.846479	−	0.615003i	0.0776941	−	0.996977i	$-0.475244\pi$
$571$	−20.2271	−	14.6959i	−0.846479	−	0.615003i	−0.924173	+	0.381974i	$0.875244\pi$
$572$		0			0
$573$	16.7014	−	51.4016i	0.697711	−	2.14733i
$574$		0			0
$575$	−4.77323	−	14.1855i	−0.199058	−	0.591575i
$576$		0			0
$577$	−5.20745	+	16.0269i	−0.216789	+	0.667208i	0.782233	+	0.622986i	$0.214081\pi$
$577$	−5.20745	+	16.0269i	−0.216789	+	0.667208i	−0.999022	+	0.0442219i	$0.985919\pi$
$578$		0			0
$579$	22.9799	+	16.6959i	0.955011	+	0.693856i
$580$		0			0
$581$	−15.7684	+	11.4564i	−0.654183	+	0.475292i
$582$		0			0
$583$	−4.20247	+	3.05327i	−0.174048	+	0.126454i
$584$		0			0
$585$	25.1339	+	18.0614i	1.03916	+	0.746746i
$586$		0			0
$587$	11.7865	+	36.2751i	0.486481	+	1.49723i	0.829824	+	0.558024i	$0.188440\pi$
$587$	11.7865	+	36.2751i	0.486481	+	1.49723i	−0.343344	+	0.939210i	$0.611560\pi$
$588$		0			0
$589$	−2.42465	+	7.46231i	−0.0999060	+	0.307479i
$590$		0			0
$591$	11.7849	+	36.2702i	0.484767	+	1.49196i
$592$		0			0
$593$	37.4808			1.53915			0.769576	−	0.638556i	$-0.220468\pi$
$593$	37.4808			1.53915			0.769576	+	0.638556i	$0.220468\pi$
$594$		0			0
$595$	−24.4839	−	17.5943i	−1.00374	−	0.721295i
$596$		0			0
$597$	−38.5995	−	28.0442i	−1.57977	−	1.14777i
$598$		0			0
$599$	−17.3143			−0.707444			−0.353722	−	0.935351i	$-0.615084\pi$
$599$	−17.3143			−0.707444			−0.353722	+	0.935351i	$0.615084\pi$
$600$		0			0
$601$	−3.59867			−0.146793			−0.0733965	−	0.997303i	$-0.523384\pi$
$601$	−3.59867			−0.146793			−0.0733965	+	0.997303i	$0.523384\pi$
$602$		0			0
$603$	−6.10466	−	4.43529i	−0.248601	−	0.180619i
$604$		0			0
$605$	0.679886	−	2.13020i	0.0276413	−	0.0866050i
$606$		0			0
$607$	−15.8314			−0.642577			−0.321289	−	0.946981i	$-0.604116\pi$
$607$	−15.8314			−0.642577			−0.321289	+	0.946981i	$0.604116\pi$
$608$		0			0
$609$	28.8550	+	88.8067i	1.16927	+	3.59863i
$610$		0			0
$611$	15.7338	−	48.4236i	0.636521	−	1.95901i
$612$		0			0
$613$	−9.74603	−	29.9952i	−0.393639	−	1.21150i	−0.930017	−	0.367517i	$-0.880208\pi$
$613$	−9.74603	−	29.9952i	−0.393639	−	1.21150i	0.536378	−	0.843978i	$-0.319792\pi$
$614$		0			0
$615$	50.7100	−	0.264389i	2.04482	−	0.0106612i
$616$		0			0
$617$	−23.3896	+	16.9935i	−0.941628	+	0.684133i	−0.948812	−	0.315841i	$-0.897713\pi$
$617$	−23.3896	+	16.9935i	−0.941628	+	0.684133i	0.00718392	+	0.999974i	$0.497713\pi$
$618$		0			0
$619$	19.1568	−	13.9183i	0.769978	−	0.559422i	−0.131976	−	0.991253i	$-0.542132\pi$
$619$	19.1568	−	13.9183i	0.769978	−	0.559422i	0.901955	+	0.431831i	$0.142132\pi$
$620$		0			0
$621$	−4.45955	−	3.24006i	−0.178956	−	0.130019i
$622$		0			0
$623$	17.7509	−	54.6317i	0.711175	−	2.18877i
$624$		0			0
$625$	7.22793	−	23.9323i	0.289117	−	0.957294i
$626$		0			0
$627$	−0.901847	+	2.77560i	−0.0360163	+	0.110847i
$628$		0			0
$629$	6.54709	+	4.75674i	0.261050	+	0.189664i
$630$		0			0
$631$	37.6996	−	27.3904i	1.50080	−	1.09039i	0.530737	−	0.847537i	$-0.321915\pi$
$631$	37.6996	−	27.3904i	1.50080	−	1.09039i	0.970062	−	0.242857i	$-0.0780846\pi$
$632$		0			0
$633$	−37.7304	+	27.4128i	−1.49965	+	1.08956i
$634$		0			0
$635$	−32.2978	+	0.168393i	−1.28170	+	0.00668246i
$636$		0			0
$637$	−17.2734	−	53.1622i	−0.684399	−	2.10636i
$638$		0			0
$639$	−1.61400	+	4.96738i	−0.0638489	+	0.196507i
$640$		0			0
$641$	0.390198	+	1.20091i	0.0154119	+	0.0474330i	0.958467	−	0.285204i	$-0.0920615\pi$
$641$	0.390198	+	1.20091i	0.0154119	+	0.0474330i	−0.943055	+	0.332637i	$0.892061\pi$
$642$		0			0
$643$	−22.1395			−0.873099			−0.436549	−	0.899680i	$-0.643800\pi$
$643$	−22.1395			−0.873099			−0.436549	+	0.899680i	$0.643800\pi$
$644$		0			0
$645$	4.10427	−	12.8594i	0.161605	−	0.506337i
$646$		0			0
$647$	12.6802	+	9.21268i	0.498509	+	0.362188i	0.808447	−	0.588569i	$-0.200308\pi$
$647$	12.6802	+	9.21268i	0.498509	+	0.362188i	−0.309938	+	0.950757i	$0.600308\pi$
$648$		0			0
$649$	5.75735			0.225996
$650$		0			0
$651$	55.5740			2.17812
$652$		0			0
$653$	33.8204	+	24.5720i	1.32350	+	0.961576i	0.999882	+	0.0153866i	$0.00489791\pi$
$653$	33.8204	+	24.5720i	1.32350	+	0.961576i	0.323614	+	0.946189i	$0.395102\pi$
$654$		0			0
$655$	0.119365	+	0.0857767i	0.00466399	+	0.00335157i
$656$		0			0
$657$	31.4147			1.22560
$658$		0			0
$659$	−4.24120	−	13.0531i	−0.165214	−	0.508476i	0.833838	−	0.552009i	$-0.186139\pi$
$659$	−4.24120	−	13.0531i	−0.165214	−	0.508476i	−0.999052	+	0.0435332i	$0.986139\pi$
$660$		0			0
$661$	−3.49706	+	10.7628i	−0.136020	+	0.418626i	−0.995747	−	0.0921274i	$-0.970633\pi$
$661$	−3.49706	+	10.7628i	−0.136020	+	0.418626i	0.859728	+	0.510753i	$0.170633\pi$
$662$		0			0
$663$	15.0586	+	46.3455i	0.584826	+	1.79991i
$664$		0			0
$665$	9.25989	+	6.65422i	0.359083	+	0.258039i
$666$		0			0
$667$	−24.9268	+	18.1104i	−0.965168	+	0.701236i
$668$		0			0
$669$	4.49568	−	3.26630i	0.173813	−	0.126282i
$670$		0			0
$671$	2.88224	+	2.09407i	0.111268	+	0.0808406i
$672$		0			0
$673$	−0.929133	+	2.85958i	−0.0358154	+	0.110229i	−0.967366	−	0.253383i	$-0.918457\pi$
$673$	−0.929133	+	2.85958i	−0.0358154	+	0.110229i	0.931551	+	0.363612i	$0.118457\pi$
$674$		0			0
$675$	−2.93641	−	8.72665i	−0.113022	−	0.335889i
$676$		0			0
$677$	4.92695	−	15.1636i	0.189358	−	0.582785i	−0.810638	−	0.585548i	$-0.800879\pi$
$677$	4.92695	−	15.1636i	0.189358	−	0.582785i	0.999996	+	0.00276301i	$0.000879496\pi$
$678$		0			0
$679$	−25.6230	−	18.6162i	−0.983320	−	0.714423i
$680$		0			0
$681$	7.89974	−	5.73950i	0.302719	−	0.219938i
$682$		0			0
$683$	−21.8813	+	15.8977i	−0.837265	+	0.608308i	−0.921605	−	0.388129i	$-0.873122\pi$
$683$	−21.8813	+	15.8977i	−0.837265	+	0.608308i	0.0843407	+	0.996437i	$0.473122\pi$
$684$		0			0
$685$	27.1502	−	19.9429i	1.03736	−	0.761979i
$686$		0			0
$687$	14.2086	+	43.7297i	0.542093	+	1.66839i
$688$		0			0
$689$	10.1369	−	31.1982i	0.386185	−	1.18856i
$690$		0			0
$691$	9.21239	+	28.3528i	0.350456	+	1.07859i	0.958598	+	0.284764i	$0.0919151\pi$
$691$	9.21239	+	28.3528i	0.350456	+	1.07859i	−0.608142	+	0.793828i	$0.708085\pi$
$692$		0			0
$693$	8.72651			0.331493
$694$		0			0
$695$	−8.58243	+	0.0447467i	−0.325550	+	0.00169734i
$696$		0			0
$697$	27.2695	+	19.8125i	1.03291	+	0.750451i
$698$		0			0
$699$	−14.5204			−0.549210
$700$		0			0
$701$	15.9604			0.602814			0.301407	−	0.953496i	$-0.402544\pi$
$701$	15.9604			0.602814			0.301407	+	0.953496i	$0.402544\pi$
$702$		0			0
$703$	−2.47613	−	1.79902i	−0.0933891	−	0.0678512i
$704$		0			0
$705$	33.1072	−	24.3186i	1.24689	−	0.915890i
$706$		0			0
$707$	−47.4820			−1.78574
$708$		0			0
$709$	0.457954	+	1.40944i	0.0171988	+	0.0529325i	0.959288	−	0.282431i	$-0.0911408\pi$
$709$	0.457954	+	1.40944i	0.0171988	+	0.0529325i	−0.942089	+	0.335364i	$0.891141\pi$
$710$		0			0
$711$	9.53009	−	29.3306i	0.357406	−	1.09998i
$712$		0			0
$713$	5.66661	+	17.4400i	0.212216	+	0.653134i
$714$		0			0
$715$	4.43355	+	13.4068i	0.165805	+	0.501386i
$716$		0			0
$717$	−0.449458	+	0.326550i	−0.0167853	+	0.0121952i
$718$		0			0
$719$	6.06583	−	4.40709i	0.226217	−	0.164357i	−0.468903	−	0.883249i	$-0.655351\pi$
$719$	6.06583	−	4.40709i	0.226217	−	0.164357i	0.695121	+	0.718893i	$0.255351\pi$
$720$		0			0
$721$	−5.17378	−	3.75897i	−0.192682	−	0.139992i
$722$		0			0
$723$	10.5253	−	32.3934i	0.391439	−	1.20472i
$724$		0			0
$725$	−51.4624	+	0.536639i	−1.91126	+	0.0199303i
$726$		0			0
$727$	6.77523	−	20.8520i	0.251279	−	0.773358i	−0.743261	−	0.669002i	$-0.766722\pi$
$727$	6.77523	−	20.8520i	0.251279	−	0.773358i	0.994540	−	0.104356i	$-0.0332782\pi$
$728$		0			0
$729$	8.91627	+	6.47805i	0.330232	+	0.239928i
$730$		0			0
$731$	7.25876	−	5.27380i	0.268475	−	0.195059i
$732$		0			0
$733$	26.2958	−	19.1050i	0.971258	−	0.705660i	0.0155200	−	0.999880i	$-0.495060\pi$
$733$	26.2958	−	19.1050i	0.971258	−	0.705660i	0.955738	+	0.294219i	$0.0950596\pi$
$734$		0			0
$735$	13.7125	−	42.9636i	0.505793	−	1.58474i
$736$		0			0
$737$	−1.06385	−	3.27420i	−0.0391875	−	0.120607i
$738$		0			0
$739$	−9.09359	+	27.9872i	−0.334513	+	1.02953i	0.632448	+	0.774602i	$0.282050\pi$
$739$	−9.09359	+	27.9872i	−0.334513	+	1.02953i	−0.966961	+	0.254923i	$0.917950\pi$
$740$		0			0
$741$	−5.69520	−	17.5280i	−0.209219	−	0.643908i
$742$		0			0
$743$	7.10981			0.260834			0.130417	−	0.991459i	$-0.458368\pi$
$743$	7.10981			0.260834			0.130417	+	0.991459i	$0.458368\pi$
$744$		0			0
$745$	−9.71654	−	29.3823i	−0.355986	−	1.07648i
$746$		0			0
$747$	8.68072	+	6.30691i	0.317611	+	0.230758i
$748$		0			0
$749$	−37.8434			−1.38277
$750$		0			0
$751$	−1.66911			−0.0609067			−0.0304534	−	0.999536i	$-0.509695\pi$
$751$	−1.66911			−0.0609067			−0.0304534	+	0.999536i	$0.509695\pi$
$752$		0			0
$753$	36.4936	+	26.5142i	1.32990	+	0.966230i
$754$		0			0
$755$	13.6468	+	41.2671i	0.496657	+	1.50186i
$756$		0			0
$757$	20.0451			0.728552			0.364276	−	0.931291i	$-0.381316\pi$
$757$	20.0451			0.728552			0.364276	+	0.931291i	$0.381316\pi$
$758$		0			0
$759$	2.10769	+	6.48680i	0.0765043	+	0.235456i
$760$		0			0
$761$	11.4872	−	35.3541i	0.416412	−	1.28158i	−0.494570	−	0.869138i	$-0.664674\pi$
$761$	11.4872	−	35.3541i	0.416412	−	1.28158i	0.910982	−	0.412446i	$-0.135326\pi$
$762$		0			0
$763$	−7.34035	−	22.5913i	−0.265738	−	0.817859i
$764$		0			0
$765$	−5.04668	+	15.8121i	−0.182463	+	0.571689i
$766$		0			0
$767$	−29.4142	+	21.3706i	−1.06208	+	0.771649i
$768$		0			0
$769$	10.8387	−	7.87479i	0.390854	−	0.283972i	−0.374951	−	0.927045i	$-0.622341\pi$
$769$	10.8387	−	7.87479i	0.390854	−	0.283972i	0.765805	+	0.643072i	$0.222341\pi$
$770$		0			0
$771$	20.8838	+	15.1729i	0.752110	+	0.546440i
$772$		0			0
$773$	−2.02806	+	6.24174i	−0.0729444	+	0.224500i	−0.980881	−	0.194607i	$-0.937657\pi$
$773$	−2.02806	+	6.24174i	−0.0729444	+	0.224500i	0.907937	+	0.419107i	$0.137657\pi$
$774$		0			0
$775$	−9.16090	+	29.2279i	−0.329069	+	1.04990i
$776$		0			0
$777$	−6.69890	+	20.6171i	−0.240322	+	0.739635i
$778$		0			0
$779$	−10.3134	−	7.49314i	−0.369517	−	0.268470i
$780$		0			0
$781$	−1.92786	+	1.40067i	−0.0689841	+	0.0501199i
$782$		0			0
$783$	−15.3345	+	11.1412i	−0.548011	+	0.398153i
$784$		0			0
$785$	−7.81214	−	23.6235i	−0.278827	−	0.843158i
$786$		0			0
$787$	−5.17920	−	15.9399i	−0.184619	−	0.568198i	0.815323	−	0.579006i	$-0.196559\pi$
$787$	−5.17920	−	15.9399i	−0.184619	−	0.568198i	−0.999942	+	0.0108087i	$0.996559\pi$
$788$		0			0
$789$	2.40740	−	7.40922i	0.0857058	−	0.263775i
$790$		0			0
$791$	−15.4039	−	47.4084i	−0.547701	−	1.68565i
$792$		0			0
$793$	−22.4982			−0.798936
$794$		0			0
$795$	21.3302	−	15.6679i	0.756504	−	0.555682i
$796$		0			0
$797$	−38.0351	−	27.6341i	−1.34727	−	0.978851i	−0.999142	−	0.0414055i	$-0.986816\pi$
$797$	−38.0351	−	27.6341i	−1.34727	−	0.978851i	−0.348131	−	0.937446i	$-0.613184\pi$
$798$		0			0
$799$	27.3049			0.965977
$800$		0			0
$801$	−31.6232			−1.11735
$802$		0			0
$803$	11.5954	+	8.42456i	0.409193	+	0.297296i
$804$		0			0
$805$	26.6489	−	0.138941i	0.939252	−	0.00489703i
$806$		0			0
$807$	−48.5034			−1.70740
$808$		0			0
$809$	15.1335	+	46.5762i	0.532067	+	1.63753i	0.749903	+	0.661548i	$0.230100\pi$
$809$	15.1335	+	46.5762i	0.532067	+	1.63753i	−0.217836	+	0.975985i	$0.569900\pi$
$810$		0			0
$811$	14.7449	−	45.3800i	0.517762	−	1.59351i	−0.260437	−	0.965491i	$-0.583867\pi$
$811$	14.7449	−	45.3800i	0.517762	−	1.59351i	0.778199	−	0.628017i	$-0.216133\pi$
$812$		0			0
$813$	−11.8214	−	36.3825i	−0.414594	−	1.27599i
$814$		0			0
$815$	−11.4229	+	8.39057i	−0.400127	+	0.293909i
$816$		0			0
$817$	−2.74529	+	1.99457i	−0.0960455	+	0.0697811i
$818$		0			0
$819$	−44.5835	+	32.3918i	−1.55788	+	1.13186i
$820$		0			0
$821$	−21.5962	−	15.6906i	−0.753714	−	0.547605i	0.143262	−	0.989685i	$-0.454241\pi$
$821$	−21.5962	−	15.6906i	−0.753714	−	0.547605i	−0.896976	+	0.442079i	$0.854241\pi$
$822$		0			0
$823$	−4.86603	+	14.9761i	−0.169619	+	0.522034i	−0.999347	−	0.0361339i	$-0.988496\pi$
$823$	−4.86603	+	14.9761i	−0.169619	+	0.522034i	0.829728	+	0.558168i	$0.188496\pi$
$824$		0			0
$825$	−3.40739	+	10.8713i	−0.118630	+	0.378490i
$826$		0			0
$827$	−6.28447	+	19.3416i	−0.218532	+	0.672574i	0.780352	+	0.625341i	$0.215040\pi$
$827$	−6.28447	+	19.3416i	−0.218532	+	0.672574i	−0.998884	+	0.0472324i	$0.984960\pi$
$828$		0			0
$829$	−11.6180	−	8.44100i	−0.403511	−	0.293168i	0.367459	−	0.930040i	$-0.380228\pi$
$829$	−11.6180	−	8.44100i	−0.403511	−	0.293168i	−0.770970	+	0.636872i	$0.780228\pi$
$830$		0			0
$831$	−28.8403	+	20.9537i	−1.00046	+	0.726875i
$832$		0			0
$833$	24.2518	−	17.6199i	0.840274	−	0.610495i
$834$		0			0
$835$	17.4161	+	12.5153i	0.602708	+	0.433110i
$836$		0			0
$837$	3.48600	+	10.7288i	0.120494	+	0.370842i
$838$		0			0
$839$	6.82476	−	21.0045i	0.235617	−	0.725155i	−0.761422	−	0.648257i	$-0.775498\pi$
$839$	6.82476	−	21.0045i	0.235617	−	0.725155i	0.997039	−	0.0768980i	$-0.0245016\pi$
$840$		0			0
$841$	23.7778	+	73.1805i	0.819924	+	2.52347i
$842$		0			0
$843$	1.78233			0.0613868
$844$		0			0
$845$	−48.8095	−	35.0748i	−1.67910	−	1.20661i
$846$		0			0
$847$	3.22102	+	2.34021i	0.110676	+	0.0804106i
$848$		0			0
$849$	34.8807			1.19710
$850$		0			0
$851$	−7.15303			−0.245203
$852$		0			0
$853$	9.78192	+	7.10698i	0.334927	+	0.243339i	0.742518	−	0.669826i	$-0.233631\pi$
$853$	9.78192	+	7.10698i	0.334927	+	0.243339i	−0.407592	+	0.913164i	$0.633631\pi$
$854$		0			0
$855$	1.90867	−	5.98020i	0.0652752	−	0.204519i
$856$		0			0
$857$	−36.6737			−1.25275			−0.626375	−	0.779522i	$-0.715462\pi$
$857$	−36.6737			−1.25275			−0.626375	+	0.779522i	$0.715462\pi$
$858$		0			0
$859$	−9.44350	−	29.0641i	−0.322208	−	0.991655i	−0.972685	−	0.232129i	$-0.925431\pi$
$859$	−9.44350	−	29.0641i	−0.322208	−	0.991655i	0.650477	−	0.759526i	$-0.274569\pi$
$860$		0			0
$861$	−27.9018	+	85.8730i	−0.950892	+	2.92654i
$862$		0			0
$863$	8.55531	+	26.3305i	0.291226	+	0.896302i	0.984463	+	0.175592i	$0.0561839\pi$
$863$	8.55531	+	26.3305i	0.291226	+	0.896302i	−0.693237	+	0.720710i	$0.743816\pi$
$864$		0			0
$865$	−24.6676	+	0.128611i	−0.838724	+	0.00437290i
$866$		0			0
$867$	10.1955	−	7.40750i	0.346259	−	0.251572i
$868$		0			0
$869$	11.3833	−	8.27044i	0.386152	−	0.280556i
$870$		0			0
$871$	17.5887	+	12.7789i	0.595970	+	0.432997i
$872$		0			0
$873$	−5.38794	+	16.5824i	−0.182354	+	0.561228i
$874$		0			0
$875$	36.4169	+	25.5979i	1.23112	+	0.865367i
$876$		0			0
$877$	4.98320	−	15.3367i	0.168271	−	0.517884i	−0.830992	−	0.556285i	$-0.812226\pi$
$877$	4.98320	−	15.3367i	0.168271	−	0.517884i	0.999262	+	0.0384007i	$0.0122263\pi$
$878$		0			0
$879$	−19.0566	−	13.8454i	−0.642763	−	0.466994i
$880$		0			0
$881$	14.8951	−	10.8219i	0.501828	−	0.364599i	−0.307887	−	0.951423i	$-0.599622\pi$
$881$	14.8951	−	10.8219i	0.501828	−	0.364599i	0.809715	+	0.586824i	$0.199622\pi$
$882$		0			0
$883$	39.2762	−	28.5358i	1.32175	−	0.960307i	0.321841	−	0.946794i	$-0.395698\pi$
$883$	39.2762	−	28.5358i	1.32175	−	0.960307i	0.999909	−	0.0135138i	$-0.00430169\pi$
$884$		0			0
$885$	−29.3333	+	0.152937i	−0.986029	+	0.00514091i
$886$		0			0
$887$	4.61158	+	14.1930i	0.154842	+	0.476553i	0.998145	−	0.0608847i	$-0.0193922\pi$
$887$	4.61158	+	14.1930i	0.154842	+	0.476553i	−0.843303	+	0.537438i	$0.819392\pi$
$888$		0			0
$889$	17.7710	−	54.6936i	0.596021	−	1.83436i
$890$		0			0
$891$	3.32854	+	10.2442i	0.111510	+	0.343194i
$892$		0			0
$893$	−10.3268			−0.345573
$894$		0			0
$895$	4.70075	−	14.7283i	0.157129	−	0.492312i
$896$		0			0
$897$	−34.8464	−	25.3174i	−1.16349	−	0.845324i
$898$		0			0
$899$	63.0550			2.10300
$900$		0			0
$901$	17.5919			0.586070
$902$		0			0
$903$	19.4443	+	14.1271i	0.647067	+	0.470122i
$904$		0			0
$905$	34.1792	+	24.5614i	1.13616	+	0.816450i
$906$		0			0
$907$	−49.5167			−1.64418			−0.822088	−	0.569361i	$-0.807191\pi$
$907$	−49.5167			−1.64418			−0.822088	+	0.569361i	$0.807191\pi$
$908$		0			0
$909$	8.07755	+	24.8601i	0.267915	+	0.824559i
$910$		0			0
$911$	9.80029	−	30.1622i	0.324698	−	0.999318i	−0.646879	−	0.762593i	$-0.723926\pi$
$911$	9.80029	−	30.1622i	0.324698	−	0.999318i	0.971577	−	0.236725i	$-0.0760740\pi$
$912$		0			0
$913$	1.51278	+	4.65586i	0.0500657	+	0.154086i
$914$		0			0
$915$	−14.7404	−	10.5926i	−0.487304	−	0.350180i
$916$		0			0
$917$	−0.211735	+	0.153835i	−0.00699211	+	0.00508007i
$918$		0			0
$919$	−31.8703	+	23.1551i	−1.05130	+	0.763817i	−0.972460	−	0.233070i	$-0.925123\pi$
$919$	−31.8703	+	23.1551i	−1.05130	+	0.763817i	−0.0788443	+	0.996887i	$0.525123\pi$
$920$		0			0
$921$	−27.4925	−	19.9745i	−0.905910	−	0.658182i
$922$		0			0
$923$	4.65024	−	14.3120i	0.153065	−	0.471084i
$924$		0			0
$925$	−9.73885	−	6.92169i	−0.320211	−	0.227584i
$926$		0			0
$927$	−1.08793	+	3.34831i	−0.0357323	+	0.109973i
$928$		0			0
$929$	29.7677	+	21.6275i	0.976646	+	0.709575i	0.956957	−	0.290231i	$-0.0937321\pi$
$929$	29.7677	+	21.6275i	0.976646	+	0.709575i	0.0196898	+	0.999806i	$0.493732\pi$
$930$		0			0
$931$	−9.17210	+	6.66392i	−0.300603	+	0.218401i
$932$		0			0
$933$	41.5906	−	30.2174i	1.36162	−	0.989272i
$934$		0			0
$935$	−6.10315	+	4.48300i	−0.199594	+	0.146610i
$936$		0			0
$937$	13.7521	+	42.3247i	0.449262	+	1.38269i	0.877741	+	0.479135i	$0.159050\pi$
$937$	13.7521	+	42.3247i	0.449262	+	1.38269i	−0.428479	+	0.903552i	$0.640950\pi$
$938$		0			0
$939$	22.1148	−	68.0623i	0.721689	−	2.22113i
$940$		0			0
$941$	−4.10444	−	12.6322i	−0.133801	−	0.411797i	0.861601	−	0.507587i	$-0.169462\pi$
$941$	−4.10444	−	12.6322i	−0.133801	−	0.411797i	−0.995402	+	0.0957900i	$0.969462\pi$
$942$		0			0
$943$	−29.7933			−0.970205
$944$		0			0
$945$	16.3940	−	0.0854741i	0.533296	−	0.00278047i
$946$		0			0
$947$	−13.1727	−	9.57051i	−0.428054	−	0.311000i	0.352816	−	0.935693i	$-0.385224\pi$
$947$	−13.1727	−	9.57051i	−0.428054	−	0.311000i	−0.780870	+	0.624693i	$0.785224\pi$
$948$		0			0
$949$	−90.5118			−2.93814
$950$		0			0
$951$	−51.5549			−1.67178
$952$		0			0
$953$	−6.81156	−	4.94889i	−0.220648	−	0.160310i	0.471970	−	0.881614i	$-0.343543\pi$
$953$	−6.81156	−	4.94889i	−0.220648	−	0.160310i	−0.692618	+	0.721304i	$0.743543\pi$
$954$		0			0
$955$	−42.7464	+	31.3989i	−1.38324	+	1.01604i
$956$		0			0
$957$	23.4533			0.758136
$958$		0			0
$959$	18.5355	+	57.0463i	0.598541	+	1.84212i
$960$		0			0
$961$	2.01718	−	6.20823i	0.0650702	−	0.200266i
$962$		0			0
$963$	6.43784	+	19.8136i	0.207457	+	0.638486i
$964$		0			0
$965$	−8.75196	−	26.4655i	−0.281735	−	0.851953i
$966$		0			0
$967$	30.2632	−	21.9875i	0.973199	−	0.707070i	0.0170206	−	0.999855i	$-0.494582\pi$
$967$	30.2632	−	21.9875i	0.973199	−	0.707070i	0.956178	+	0.292785i	$0.0945819\pi$
$968$		0			0
$969$	7.99601	−	5.80944i	0.256869	−	0.186626i
$970$		0			0
$971$	18.5002	+	13.4412i	0.593700	+	0.431349i	0.843637	−	0.536914i	$-0.180410\pi$
$971$	18.5002	+	13.4412i	0.593700	+	0.431349i	−0.249937	+	0.968262i	$0.580410\pi$
$972$		0			0
$973$	4.72226	−	14.5336i	0.151389	−	0.465926i
$974$		0			0
$975$	−22.9448	−	68.1891i	−0.734821	−	2.18380i
$976$		0			0
$977$	−1.49568	+	4.60323i	−0.0478511	+	0.147270i	−0.972127	−	0.234454i	$-0.924670\pi$
$977$	−1.49568	+	4.60323i	−0.0478511	+	0.147270i	0.924276	+	0.381725i	$0.124670\pi$
$978$		0			0
$979$	−11.6724	−	8.48048i	−0.373051	−	0.271037i
$980$		0			0
$981$	−10.5794	+	7.68637i	−0.337774	+	0.245407i
$982$		0			0
$983$	−6.33747	+	4.60444i	−0.202134	+	0.146859i	−0.684248	−	0.729250i	$-0.739869\pi$
$983$	−6.33747	+	4.60444i	−0.202134	+	0.146859i	0.482114	+	0.876109i	$0.339869\pi$
$984$		0			0
$985$	11.3794	−	35.6537i	0.362579	−	1.13602i
$986$		0			0
$987$	22.6023	+	69.5628i	0.719440	+	2.21421i
$988$		0			0
$989$	−2.45068	+	7.54242i	−0.0779271	+	0.239835i
$990$		0			0
$991$	12.0156	+	36.9803i	0.381689	+	1.17472i	0.938853	+	0.344317i	$0.111889\pi$
$991$	12.0156	+	36.9803i	0.381689	+	1.17472i	−0.557164	+	0.830402i	$0.688111\pi$
$992$		0			0
$993$	−19.3831			−0.615104
$994$		0			0
$995$	14.7008	+	44.4543i	0.466045	+	1.40930i
$996$		0			0
$997$	−2.25673	−	1.63961i	−0.0714714	−	0.0519270i	0.551476	−	0.834191i	$-0.314065\pi$
$997$	−2.25673	−	1.63961i	−0.0714714	−	0.0519270i	−0.622947	+	0.782264i	$0.714065\pi$
$998$		0			0
$999$	−4.40042			−0.139223

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.q.b.221.3	✓	52
25.6	even	5	inner	1100.2.q.b.881.3	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.2.q.b.221.3	✓	52	1.1	even	1	trivial
1100.2.q.b.881.3	yes	52	25.6	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.q (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.84339 - 1.33930i) q^{3} +(0.702061 + 2.12300i) q^{5} -3.98140 q^{7} +(0.677309 + 2.08454i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(-1.95146 - 6.00596i) q^{13} +(1.54916 - 4.85378i) q^{15} +(2.73983 - 1.99060i) q^{17} +(-1.03621 + 0.752852i) q^{19} +(7.33928 + 5.33230i) q^{21} +(-0.925011 + 2.84689i) q^{23} +(-4.01422 + 2.98095i) q^{25} +(-0.569051 + 1.75136i) q^{27} +(8.32724 + 6.05009i) q^{29} +(4.95603 - 3.60077i) q^{31} +(1.84339 - 1.33930i) q^{33} +(-2.79519 - 8.45250i) q^{35} +(0.738428 + 2.27265i) q^{37} +(-4.44650 + 13.6849i) q^{39} +(3.07565 + 9.46588i) q^{41} +2.64935 q^{43} +(-3.94996 + 2.90140i) q^{45} +(6.52278 + 4.73907i) q^{47} +8.85157 q^{49} -7.71658 q^{51} +(4.20247 + 3.05327i) q^{53} +(-2.23604 + 0.0116581i) q^{55} +2.91844 q^{57} +(-1.77912 - 5.47556i) q^{59} +(1.10092 - 3.38827i) q^{61} +(-2.69664 - 8.29940i) q^{63} +(11.3806 - 8.35949i) q^{65} +(-2.78520 + 2.02357i) q^{67} +(5.51801 - 4.00907i) q^{69} +(1.92786 + 1.40067i) q^{71} +(4.42905 - 13.6312i) q^{73} +(11.3922 - 0.118795i) q^{75} +(1.23032 - 3.78654i) q^{77} +(-11.3833 - 8.27044i) q^{79} +(8.71424 - 6.33126i) q^{81} +(3.96051 - 2.87748i) q^{83} +(6.14956 + 4.41912i) q^{85} +(-7.24745 - 22.3054i) q^{87} +(-4.45845 + 13.7217i) q^{89} +(7.76953 + 23.9122i) q^{91} -13.9584 q^{93} +(-2.32578 - 1.67132i) q^{95} +(6.43566 + 4.67578i) q^{97} -2.19182 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) \) 52 * q - 3 * q^5 - 9 * q^9 + 13 * q^11 + 12 * q^13 - 15 * q^15 + 8 * q^17 - 10 * q^19 - 6 * q^21 + 22 * q^23 + 5 * q^25 + 21 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^35 + 15 * q^37 - 20 * q^39 - 68 * q^43 - 7 * q^45 + 19 * q^47 + 68 * q^49 + 34 * q^51 + 3 * q^53 - 2 * q^55 - 24 * q^57 - 37 * q^59 + 10 * q^61 - 8 * q^63 + 12 * q^65 + 2 * q^67 + 27 * q^69 - 3 * q^71 + 4 * q^73 + 68 * q^75 - 17 * q^79 - 39 * q^81 + 78 * q^83 + 13 * q^85 + 13 * q^87 - 7 * q^89 - 2 * q^91 - 94 * q^93 + 18 * q^95 + 15 * q^97 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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