LMFDB - Embedded newform 1100.2.n.f.301.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1100,2,Mod(201,1100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1100, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("1100.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.n (of order $5$, degree $4$, 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:	$8.78354422234$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 220)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.4
Character	$\chi$	$=$	1100.301
Dual form			1100.2.n.f.201.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.321419 - 0.989226i) q^{3} +(0.699249 + 2.15207i) q^{7} +(1.55179 + 1.12744i) q^{9} +(-2.50847 + 2.16969i) q^{11} +(-0.217017 - 0.157672i) q^{13} +(-4.79272 + 3.48212i) q^{17} +(-1.77525 + 5.46367i) q^{19} +2.35363 q^{21} -2.92836 q^{23} +(4.13853 - 3.00682i) q^{27} +(2.00268 + 6.16362i) q^{29} +(-0.202293 - 0.146974i) q^{31} +(1.34004 + 3.17883i) q^{33} +(-3.18410 - 9.79964i) q^{37} +(-0.225727 + 0.164000i) q^{39} +(-0.730277 + 2.24756i) q^{41} -7.56763 q^{43} +(-0.349982 + 1.07714i) q^{47} +(1.52068 - 1.10484i) q^{49} +(1.90413 + 5.86031i) q^{51} +(8.25291 + 5.99609i) q^{53} +(4.83421 + 3.51226i) q^{57} +(3.52502 + 10.8489i) q^{59} +(3.73924 - 2.71672i) q^{61} +(-1.34124 + 4.12792i) q^{63} +6.11229 q^{67} +(-0.941231 + 2.89681i) q^{69} +(-4.11807 + 2.99195i) q^{71} +(-2.52055 - 7.75747i) q^{73} +(-6.42337 - 3.88125i) q^{77} +(6.71777 + 4.88074i) q^{79} +(0.133975 + 0.412332i) q^{81} +(13.2894 - 9.65532i) q^{83} +6.74092 q^{87} -5.73205 q^{89} +(0.187572 - 0.577288i) q^{91} +(-0.210411 + 0.152873i) q^{93} +(3.65106 + 2.65265i) q^{97} +(-6.33883 + 0.538749i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 14 q^{9} - 2 q^{11} - 8 q^{19} - 28 q^{21} + 16 q^{29} - 26 q^{31} - 12 q^{39} + 10 q^{41} + 46 q^{49} - 12 q^{51} + 48 q^{59} - 10 q^{61} + 58 q^{69} + 42 q^{71} + 64 q^{79} + 36 q^{81} - 72 q^{89}+ \cdots - 156 q^{99}+O(q^{100}) $ 24 * q - 14 * q^9 - 2 * q^11 - 8 * q^19 - 28 * q^21 + 16 * q^29 - 26 * q^31 - 12 * q^39 + 10 * q^41 + 46 * q^49 - 12 * q^51 + 48 * q^59 - 10 * q^61 + 58 * q^69 + 42 * q^71 + 64 * q^79 + 36 * q^81 - 72 * q^89 + 10 * q^91 - 156 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.321419	−	0.989226i	0.185571	−	0.571130i	−0.814386	−	0.580323i	$-0.802926\pi$
$3$	0.321419	−	0.989226i	0.185571	−	0.571130i	0.999958	+	0.00919303i	$0.00292627\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.699249	+	2.15207i	0.264291	+	0.813405i	0.991856	+	0.127365i	$0.0406521\pi$
$7$	0.699249	+	2.15207i	0.264291	+	0.813405i	−0.727565	+	0.686039i	$0.759348\pi$
$8$		0			0
$9$	1.55179	+	1.12744i	0.517264	+	0.375814i
$10$		0			0
$11$	−2.50847	+	2.16969i	−0.756333	+	0.654187i
$11$	−2.50847	+	2.16969i	−0.756333	+	0.654187i
$12$		0			0
$13$	−0.217017	−	0.157672i	−0.0601897	−	0.0437304i	0.557284	−	0.830322i	$-0.311844\pi$
$13$	−0.217017	−	0.157672i	−0.0601897	−	0.0437304i	−0.617473	+	0.786592i	$0.711844\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.79272	+	3.48212i	−1.16241	+	0.844537i	−0.990080	−	0.140503i	$-0.955128\pi$
$17$	−4.79272	+	3.48212i	−1.16241	+	0.844537i	−0.172326	+	0.985040i	$0.555128\pi$
$18$		0			0
$19$	−1.77525	+	5.46367i	−0.407271	+	1.25345i	0.511712	+	0.859157i	$0.329011\pi$
$19$	−1.77525	+	5.46367i	−0.407271	+	1.25345i	−0.918984	+	0.394296i	$0.870989\pi$
$20$		0			0
$21$	2.35363			0.513605
$22$		0			0
$23$	−2.92836			−0.610605			−0.305303	−	0.952255i	$-0.598758\pi$
$23$	−2.92836			−0.610605			−0.305303	+	0.952255i	$0.598758\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	4.13853	−	3.00682i	0.796461	−	0.578663i
$28$		0			0
$29$	2.00268	+	6.16362i	0.371889	+	1.14456i	0.945554	+	0.325466i	$0.105521\pi$
$29$	2.00268	+	6.16362i	0.371889	+	1.14456i	−0.573665	+	0.819090i	$0.694479\pi$
$30$		0			0
$31$	−0.202293	−	0.146974i	−0.0363328	−	0.0263973i	0.569471	−	0.822012i	$-0.307148\pi$
$31$	−0.202293	−	0.146974i	−0.0363328	−	0.0263973i	−0.605803	+	0.795614i	$0.707148\pi$
$32$		0			0
$33$	1.34004	+	3.17883i	0.233272	+	0.553363i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.18410	−	9.79964i	−0.523462	−	1.61105i	−0.767337	−	0.641244i	$-0.778418\pi$
$37$	−3.18410	−	9.79964i	−0.523462	−	1.61105i	0.243874	−	0.969807i	$-0.421582\pi$
$38$		0			0
$39$	−0.225727	+	0.164000i	−0.0361452	+	0.0262611i
$40$		0			0
$41$	−0.730277	+	2.24756i	−0.114050	+	0.351010i	−0.991748	−	0.128205i	$-0.959079\pi$
$41$	−0.730277	+	2.24756i	−0.114050	+	0.351010i	0.877698	+	0.479215i	$0.159079\pi$
$42$		0			0
$43$	−7.56763			−1.15405			−0.577027	−	0.816725i	$-0.695787\pi$
$43$	−7.56763			−1.15405			−0.577027	+	0.816725i	$0.695787\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.349982	+	1.07714i	−0.0510502	+	0.157116i	−0.973332	−	0.229403i	$-0.926323\pi$
$47$	−0.349982	+	1.07714i	−0.0510502	+	0.157116i	0.922281	+	0.386519i	$0.126323\pi$
$48$		0			0
$49$	1.52068	−	1.10484i	0.217240	−	0.157834i
$50$		0			0
$51$	1.90413	+	5.86031i	0.266631	+	0.820607i
$52$		0			0
$53$	8.25291	+	5.99609i	1.13362	+	0.823627i	0.986218	−	0.165449i	$-0.0529075\pi$
$53$	8.25291	+	5.99609i	1.13362	+	0.823627i	0.147406	+	0.989076i	$0.452907\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	4.83421	+	3.51226i	0.640306	+	0.465210i
$58$		0			0
$59$	3.52502	+	10.8489i	0.458919	+	1.41241i	0.866473	+	0.499225i	$0.166382\pi$
$59$	3.52502	+	10.8489i	0.458919	+	1.41241i	−0.407554	+	0.913181i	$0.633618\pi$
$60$		0			0
$61$	3.73924	−	2.71672i	0.478761	−	0.347840i	−0.322085	−	0.946711i	$-0.604384\pi$
$61$	3.73924	−	2.71672i	0.478761	−	0.347840i	0.800846	+	0.598871i	$0.204384\pi$
$62$		0			0
$63$	−1.34124	+	4.12792i	−0.168981	+	0.520069i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6.11229			0.746735			0.373368	−	0.927683i	$-0.378203\pi$
$67$	6.11229			0.746735			0.373368	+	0.927683i	$0.378203\pi$
$68$		0			0
$69$	−0.941231	+	2.89681i	−0.113311	+	0.348735i
$70$		0			0
$71$	−4.11807	+	2.99195i	−0.488725	+	0.355079i	−0.804694	−	0.593690i	$-0.797670\pi$
$71$	−4.11807	+	2.99195i	−0.488725	+	0.355079i	0.315969	+	0.948770i	$0.397670\pi$
$72$		0			0
$73$	−2.52055	−	7.75747i	−0.295009	−	0.907943i	−0.983219	−	0.182432i	$-0.941603\pi$
$73$	−2.52055	−	7.75747i	−0.295009	−	0.907943i	0.688210	−	0.725512i	$-0.258397\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−6.42337	−	3.88125i	−0.732011	−	0.442309i
$78$		0			0
$79$	6.71777	+	4.88074i	0.755808	+	0.549127i	0.897622	−	0.440767i	$-0.145293\pi$
$79$	6.71777	+	4.88074i	0.755808	+	0.549127i	−0.141814	+	0.989893i	$0.545293\pi$
$80$		0			0
$81$	0.133975	+	0.412332i	0.0148861	+	0.0458147i
$82$		0			0
$83$	13.2894	−	9.65532i	1.45870	−	1.05981i	0.475003	−	0.879984i	$-0.342447\pi$
$83$	13.2894	−	9.65532i	1.45870	−	1.05981i	0.983699	−	0.179824i	$-0.0575529\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	6.74092			0.722702
$88$		0			0
$89$	−5.73205			−0.607596			−0.303798	−	0.952736i	$-0.598255\pi$
$89$	−5.73205			−0.607596			−0.303798	+	0.952736i	$0.598255\pi$
$90$		0			0
$91$	0.187572	−	0.577288i	0.0196629	−	0.0605162i
$92$		0			0
$93$	−0.210411	+	0.152873i	−0.0218186	+	0.0158522i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	3.65106	+	2.65265i	0.370709	+	0.269336i	0.757505	−	0.652830i	$-0.226418\pi$
$97$	3.65106	+	2.65265i	0.370709	+	0.269336i	−0.386796	+	0.922165i	$0.626418\pi$
$98$		0			0
$99$	−6.33883	+	0.538749i	−0.637077	+	0.0541464i
$100$		0			0
$101$	7.58271	+	5.50916i	0.754508	+	0.548182i	0.897221	−	0.441582i	$-0.145583\pi$
$101$	7.58271	+	5.50916i	0.754508	+	0.548182i	−0.142713	+	0.989764i	$0.545583\pi$
$102$		0			0
$103$	2.03183	+	6.25332i	0.200202	+	0.616158i	0.999876	+	0.0157244i	$0.00500544\pi$
$103$	2.03183	+	6.25332i	0.200202	+	0.616158i	−0.799674	+	0.600434i	$0.794995\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.14454	+	6.60021i	−0.207320	+	0.638066i	0.792290	+	0.610145i	$0.208889\pi$
$107$	−2.14454	+	6.60021i	−0.207320	+	0.638066i	−0.999610	+	0.0279214i	$0.991111\pi$
$108$		0			0
$109$	10.0676			0.964299			0.482150	−	0.876089i	$-0.339856\pi$
$109$	10.0676			0.964299			0.482150	+	0.876089i	$0.339856\pi$
$110$		0			0
$111$	−10.7175			−1.01726
$112$		0			0
$113$	5.80293	−	17.8596i	0.545894	−	1.68009i	−0.172962	−	0.984928i	$-0.555334\pi$
$113$	5.80293	−	17.8596i	0.545894	−	1.68009i	0.718856	−	0.695159i	$-0.244666\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.158999	−	0.489349i	−0.0146995	−	0.0452403i
$118$		0			0
$119$	−10.8450	−	7.87939i	−0.994164	−	0.722302i
$120$		0			0
$121$	1.58488	−	10.8852i	0.144080	−	0.989566i
$122$		0			0
$123$	1.98862	+	1.44482i	0.179308	+	0.130275i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−15.4444	+	11.2210i	−1.37047	+	0.995707i	−0.372773	+	0.927922i	$0.621593\pi$
$127$	−15.4444	+	11.2210i	−1.37047	+	0.995707i	−0.997700	+	0.0677847i	$0.978407\pi$
$128$		0			0
$129$	−2.43238	+	7.48610i	−0.214159	+	0.659115i
$130$		0			0
$131$	−1.78426			−0.155891			−0.0779457	−	0.996958i	$-0.524836\pi$
$131$	−1.78426			−0.155891			−0.0779457	+	0.996958i	$0.524836\pi$
$132$		0			0
$133$	−12.9995			−1.12720
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.12592	+	4.45074i	−0.523372	+	0.380252i	−0.817873	−	0.575399i	$-0.804847\pi$
$137$	−6.12592	+	4.45074i	−0.523372	+	0.380252i	0.294500	+	0.955651i	$0.404847\pi$
$138$		0			0
$139$	−3.41970	−	10.5248i	−0.290055	−	0.892698i	−0.984838	−	0.173478i	$-0.944499\pi$
$139$	−3.41970	−	10.5248i	−0.290055	−	0.892698i	0.694783	−	0.719220i	$-0.255501\pi$
$140$		0			0
$141$	0.953039	+	0.692424i	0.0802604	+	0.0583126i
$142$		0			0
$143$	0.886482	−	0.0753438i	0.0741313	−	0.00630056i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.604159	−	1.85941i	−0.0498302	−	0.153362i
$148$		0			0
$149$	9.43314	−	6.85358i	0.772793	−	0.561467i	−0.130015	−	0.991512i	$-0.541502\pi$
$149$	9.43314	−	6.85358i	0.772793	−	0.561467i	0.902807	+	0.430045i	$0.141502\pi$
$150$		0			0
$151$	−0.0749733	+	0.230744i	−0.00610124	+	0.0187777i	−0.954061	−	0.299613i	$-0.903142\pi$
$151$	−0.0749733	+	0.230744i	−0.00610124	+	0.0187777i	0.947960	+	0.318391i	$0.103142\pi$
$152$		0			0
$153$	−11.3632			−0.918660
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.912183	−	2.80741i	0.0728001	−	0.224056i	−0.908035	−	0.418894i	$-0.862418\pi$
$157$	0.912183	−	2.80741i	0.0728001	−	0.224056i	0.980835	+	0.194838i	$0.0624180\pi$
$158$		0			0
$159$	8.58414	−	6.23674i	0.680766	−	0.494606i
$160$		0			0
$161$	−2.04765	−	6.30203i	−0.161378	−	0.496669i
$162$		0			0
$163$	8.40964	+	6.10996i	0.658694	+	0.478569i	0.866222	−	0.499660i	$-0.166542\pi$
$163$	8.40964	+	6.10996i	0.658694	+	0.478569i	−0.207528	+	0.978229i	$0.566542\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.99932	−	5.81185i	−0.619006	−	0.449734i	0.233568	−	0.972340i	$-0.424960\pi$
$167$	−7.99932	−	5.81185i	−0.619006	−	0.449734i	−0.852574	+	0.522606i	$0.824960\pi$
$168$		0			0
$169$	−3.99498	−	12.2953i	−0.307307	−	0.945792i
$170$		0			0
$171$	−8.91481	+	6.47699i	−0.681732	+	0.495308i
$172$		0			0
$173$	−4.87981	+	15.0185i	−0.371005	+	1.14184i	0.575129	+	0.818063i	$0.304952\pi$
$173$	−4.87981	+	15.0185i	−0.371005	+	1.14184i	−0.946134	+	0.323774i	$0.895048\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	11.8650			0.891830
$178$		0			0
$179$	1.81268	−	5.57884i	0.135486	−	0.416982i	−0.860180	−	0.509991i	$-0.829649\pi$
$179$	1.81268	−	5.57884i	0.135486	−	0.416982i	0.995665	+	0.0930092i	$0.0296486\pi$
$180$		0			0
$181$	18.2792	−	13.2806i	1.35868	−	0.987138i	0.360151	−	0.932894i	$-0.382725\pi$
$181$	18.2792	−	13.2806i	1.35868	−	0.987138i	0.998528	−	0.0542444i	$-0.0172750\pi$
$182$		0			0
$183$	−1.48559	−	4.57216i	−0.109818	−	0.337984i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	4.46730	−	19.1335i	0.326681	−	1.39918i
$188$		0			0
$189$	9.36473	+	6.80388i	0.681184	+	0.494909i
$190$		0			0
$191$	3.42585	+	10.5437i	0.247886	+	0.762914i	0.995148	+	0.0983854i	$0.0313678\pi$
$191$	3.42585	+	10.5437i	0.247886	+	0.762914i	−0.747262	+	0.664529i	$0.768632\pi$
$192$		0			0
$193$	−5.18527	+	3.76732i	−0.373244	+	0.271178i	−0.758555	−	0.651609i	$-0.774094\pi$
$193$	−5.18527	+	3.76732i	−0.373244	+	0.271178i	0.385311	+	0.922787i	$0.374094\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	9.15141			0.652011			0.326005	−	0.945368i	$-0.394297\pi$
$197$	9.15141			0.652011			0.326005	+	0.945368i	$0.394297\pi$
$198$		0			0
$199$	−14.6653			−1.03960			−0.519798	−	0.854289i	$-0.673993\pi$
$199$	−14.6653			−1.03960			−0.519798	+	0.854289i	$0.673993\pi$
$200$		0			0
$201$	1.96461	−	6.04644i	0.138573	−	0.426483i
$202$		0			0
$203$	−11.8642	+	8.61981i	−0.832700	+	0.604992i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−4.54421	−	3.30156i	−0.315844	−	0.229474i
$208$		0			0
$209$	−7.40130	−	17.5572i	−0.511959	−	1.21446i
$210$		0			0
$211$	−10.0758	−	7.32046i	−0.693644	−	0.503962i	0.184212	−	0.982886i	$-0.441027\pi$
$211$	−10.0758	−	7.32046i	−0.693644	−	0.503962i	−0.877856	+	0.478925i	$0.841027\pi$
$212$		0			0
$213$	1.63609	+	5.03537i	0.112103	+	0.345018i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.174845	−	0.538118i	0.0118693	−	0.0365299i
$218$		0			0
$219$	−8.48405			−0.573299
$220$		0			0
$221$	1.58914			0.106897
$222$		0			0
$223$	−3.76756	+	11.5954i	−0.252295	+	0.776483i	0.742056	+	0.670338i	$0.233851\pi$
$223$	−3.76756	+	11.5954i	−0.252295	+	0.776483i	−0.994351	+	0.106145i	$0.966149\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.38109	+	7.32825i	0.158039	+	0.486393i	0.998456	−	0.0555464i	$-0.0176901\pi$
$227$	2.38109	+	7.32825i	0.158039	+	0.486393i	−0.840417	+	0.541940i	$0.817690\pi$
$228$		0			0
$229$	−14.7494	−	10.7160i	−0.974666	−	0.708136i	−0.0181560	−	0.999835i	$-0.505780\pi$
$229$	−14.7494	−	10.7160i	−0.974666	−	0.708136i	−0.956510	+	0.291699i	$0.905780\pi$
$230$		0			0
$231$	−5.90402	+	5.10666i	−0.388456	+	0.335993i
$232$		0			0
$233$	−4.00263	−	2.90808i	−0.262221	−	0.190515i	0.448905	−	0.893580i	$-0.351814\pi$
$233$	−4.00263	−	2.90808i	−0.262221	−	0.190515i	−0.711126	+	0.703065i	$0.751814\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	6.98738	−	5.07663i	0.453879	−	0.329762i
$238$		0			0
$239$	−5.24855	+	16.1534i	−0.339501	+	1.04488i	0.624962	+	0.780655i	$0.285115\pi$
$239$	−5.24855	+	16.1534i	−0.339501	+	1.04488i	−0.964462	+	0.264220i	$0.914885\pi$
$240$		0			0
$241$	6.72951			0.433486			0.216743	−	0.976229i	$-0.430457\pi$
$241$	6.72951			0.433486			0.216743	+	0.976229i	$0.430457\pi$
$242$		0			0
$243$	15.7975			1.01341
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.24673	−	0.905803i	0.0793275	−	0.0576348i
$248$		0			0
$249$	−5.27982	−	16.2496i	−0.334595	−	1.02978i
$250$		0			0
$251$	−15.9920	−	11.6188i	−1.00940	−	0.733374i	−0.0453193	−	0.998973i	$-0.514431\pi$
$251$	−15.9920	−	11.6188i	−1.00940	−	0.733374i	−0.964084	+	0.265598i	$0.914431\pi$
$252$		0			0
$253$	7.34571	−	6.35364i	0.461821	−	0.399450i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.97616	−	6.08199i	−0.123269	−	0.379384i	0.870312	−	0.492500i	$-0.163917\pi$
$257$	−1.97616	−	6.08199i	−0.123269	−	0.379384i	−0.993582	+	0.113116i	$0.963917\pi$
$258$		0			0
$259$	18.8630	−	13.7048i	1.17209	−	0.851573i
$260$		0			0
$261$	−3.84139	+	11.8226i	−0.237776	+	0.731799i
$262$		0			0
$263$	−14.6417			−0.902843			−0.451422	−	0.892311i	$-0.649083\pi$
$263$	−14.6417			−0.902843			−0.451422	+	0.892311i	$0.649083\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.84239	+	5.67029i	−0.112752	+	0.347016i
$268$		0			0
$269$	16.0781	−	11.6814i	0.980299	−	0.712229i	0.0225237	−	0.999746i	$-0.492830\pi$
$269$	16.0781	−	11.6814i	0.980299	−	0.712229i	0.957775	+	0.287517i	$0.0928299\pi$
$270$		0			0
$271$	−5.93702	−	18.2723i	−0.360648	−	1.10996i	−0.952662	−	0.304033i	$-0.901667\pi$
$271$	−5.93702	−	18.2723i	−0.360648	−	1.10996i	0.592014	−	0.805928i	$-0.298333\pi$
$272$		0			0
$273$	−0.510779	−	0.371102i	−0.0309137	−	0.0224601i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	19.2825	+	14.0095i	1.15857	+	0.841751i	0.989597	−	0.143870i	$-0.0459547\pi$
$277$	19.2825	+	14.0095i	1.15857	+	0.841751i	0.168974	+	0.985621i	$0.445955\pi$
$278$		0			0
$279$	−0.148211	−	0.456147i	−0.00887316	−	0.0273088i
$280$		0			0
$281$	14.5045	−	10.5382i	0.865267	−	0.628654i	−0.0640454	−	0.997947i	$-0.520400\pi$
$281$	14.5045	−	10.5382i	0.865267	−	0.628654i	0.929313	+	0.369293i	$0.120400\pi$
$282$		0			0
$283$	6.49760	−	19.9975i	0.386242	−	1.18873i	−0.549333	−	0.835603i	$-0.685118\pi$
$283$	6.49760	−	19.9975i	0.386242	−	1.18873i	0.935575	−	0.353127i	$-0.114882\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5.34755			−0.315656
$288$		0			0
$289$	5.59176	−	17.2097i	0.328927	−	1.01233i
$290$		0			0
$291$	3.79759	−	2.75911i	0.222619	−	0.161742i
$292$		0			0
$293$	6.57220	+	20.2271i	0.383952	+	1.18168i	0.937238	+	0.348691i	$0.113374\pi$
$293$	6.57220	+	20.2271i	0.383952	+	1.18168i	−0.553286	+	0.832991i	$0.686626\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−3.85753	+	16.5219i	−0.223836	+	0.958696i
$298$		0			0
$299$	0.635505	+	0.461721i	0.0367522	+	0.0267020i
$300$		0			0
$301$	−5.29166	−	16.2861i	−0.305006	−	0.938712i
$302$		0			0
$303$	7.88704	−	5.73027i	0.453098	−	0.329195i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−32.6823			−1.86528			−0.932639	−	0.360812i	$-0.882500\pi$
$307$	−32.6823			−1.86528			−0.932639	+	0.360812i	$0.882500\pi$
$308$		0			0
$309$	6.83902			0.389058
$310$		0			0
$311$	−5.84842	+	17.9996i	−0.331634	+	1.02066i	0.636723	+	0.771093i	$0.280289\pi$
$311$	−5.84842	+	17.9996i	−0.331634	+	1.02066i	−0.968357	+	0.249571i	$0.919711\pi$
$312$		0			0
$313$	9.73292	−	7.07138i	0.550137	−	0.399698i	−0.277699	−	0.960668i	$-0.589572\pi$
$313$	9.73292	−	7.07138i	0.550137	−	0.399698i	0.827836	+	0.560970i	$0.189572\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.25258	−	5.99585i	−0.463511	−	0.336761i	0.331396	−	0.943492i	$-0.392480\pi$
$317$	−8.25258	−	5.99585i	−0.463511	−	0.336761i	−0.794907	+	0.606731i	$0.792480\pi$
$318$		0			0
$319$	−18.3968	−	11.1161i	−1.03003	−	0.622381i
$320$		0			0
$321$	5.83981	+	4.24287i	0.325946	+	0.236814i
$322$		0			0
$323$	−10.5168	−	32.3675i	−0.585173	−	1.80098i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.23591	−	9.95911i	0.178946	−	0.550740i
$328$		0			0
$329$	−2.56279			−0.141291
$330$		0			0
$331$	11.8942			0.653763			0.326882	−	0.945065i	$-0.394002\pi$
$331$	11.8942			0.653763			0.326882	+	0.945065i	$0.394002\pi$
$332$		0			0
$333$	6.10748	−	18.7969i	0.334688	−	1.03006i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	3.10572	+	9.55843i	0.169179	+	0.520681i	0.999320	−	0.0368735i	$-0.0117399\pi$
$337$	3.10572	+	9.55843i	0.169179	+	0.520681i	−0.830141	+	0.557554i	$0.811740\pi$
$338$		0			0
$339$	−15.8020	−	11.4808i	−0.858246	−	0.623552i
$340$		0			0
$341$	0.826334	−	0.0702317i	0.0447485	−	0.00380326i
$342$		0			0
$343$	16.2556	+	11.8104i	0.877721	+	0.637701i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	18.7685	−	13.6361i	1.00755	−	0.732025i	0.0438535	−	0.999038i	$-0.486037\pi$
$347$	18.7685	−	13.6361i	1.00755	−	0.732025i	0.963693	+	0.267013i	$0.0860365\pi$
$348$		0			0
$349$	−7.82954	+	24.0968i	−0.419106	+	1.28987i	0.489421	+	0.872048i	$0.337208\pi$
$349$	−7.82954	+	24.0968i	−0.419106	+	1.28987i	−0.908527	+	0.417827i	$0.862792\pi$
$350$		0			0
$351$	−1.37222			−0.0732439
$352$		0			0
$353$	−1.08185			−0.0575813			−0.0287907	−	0.999585i	$-0.509166\pi$
$353$	−1.08185			−0.0575813			−0.0287907	+	0.999585i	$0.509166\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−11.2803	+	8.19562i	−0.597017	+	0.433758i
$358$		0			0
$359$	2.84200	+	8.74677i	0.149995	+	0.461637i	0.997619	−	0.0689595i	$-0.0219679\pi$
$359$	2.84200	+	8.74677i	0.149995	+	0.461637i	−0.847624	+	0.530597i	$0.821968\pi$
$360$		0			0
$361$	−11.3289	−	8.23090i	−0.596256	−	0.433205i
$362$		0			0
$363$	−10.2585	−	5.06652i	−0.538434	−	0.265924i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	6.00182	+	18.4717i	0.313292	+	0.964215i	0.976452	+	0.215737i	$0.0692153\pi$
$367$	6.00182	+	18.4717i	0.313292	+	0.964215i	−0.663159	+	0.748478i	$0.730785\pi$
$368$		0			0
$369$	−3.66724	+	2.66440i	−0.190909	+	0.138703i
$370$		0			0
$371$	−7.13315	+	21.9536i	−0.370335	+	1.13977i
$372$		0			0
$373$	25.8608			1.33902			0.669510	−	0.742803i	$-0.266504\pi$
$373$	25.8608			1.33902			0.669510	+	0.742803i	$0.266504\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.537216	−	1.65338i	0.0276680	−	0.0851534i
$378$		0			0
$379$	23.2283	−	16.8764i	1.19316	−	0.866881i	0.199564	−	0.979885i	$-0.436047\pi$
$379$	23.2283	−	16.8764i	1.19316	−	0.866881i	0.993595	+	0.113004i	$0.0360473\pi$
$380$		0			0
$381$	6.13602	+	18.8847i	0.314358	+	0.967493i
$382$		0			0
$383$	−9.04156	−	6.56908i	−0.462002	−	0.335664i	0.332314	−	0.943169i	$-0.392171\pi$
$383$	−9.04156	−	6.56908i	−0.462002	−	0.335664i	−0.794316	+	0.607505i	$0.792171\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−11.7434	−	8.53208i	−0.596951	−	0.433710i
$388$		0			0
$389$	9.32498	+	28.6994i	0.472795	+	1.45511i	0.848908	+	0.528541i	$0.177261\pi$
$389$	9.32498	+	28.6994i	0.472795	+	1.45511i	−0.376112	+	0.926574i	$0.622739\pi$
$390$		0			0
$391$	14.0348	−	10.1969i	0.709771	−	0.515679i
$392$		0			0
$393$	−0.573495	+	1.76504i	−0.0289290	+	0.0890343i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−28.3518			−1.42293			−0.711467	−	0.702719i	$-0.751969\pi$
$397$	−28.3518			−1.42293			−0.711467	+	0.702719i	$0.751969\pi$
$398$		0			0
$399$	−4.17830	+	12.8595i	−0.209176	+	0.643779i
$400$		0			0
$401$	−11.2850	+	8.19906i	−0.563548	+	0.409442i	−0.832756	−	0.553641i	$-0.813238\pi$
$401$	−11.2850	+	8.19906i	−0.563548	+	0.409442i	0.269208	+	0.963082i	$0.413238\pi$
$402$		0			0
$403$	0.0207272	+	0.0637918i	0.00103250	+	0.00317770i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	29.2494	+	17.6736i	1.44984	+	0.876050i
$408$		0			0
$409$	10.4677	+	7.60522i	0.517594	+	0.376054i	0.815697	−	0.578480i	$-0.196354\pi$
$409$	10.4677	+	7.60522i	0.517594	+	0.376054i	−0.298103	+	0.954534i	$0.596354\pi$
$410$		0			0
$411$	2.43380	+	7.49047i	0.120051	+	0.369478i
$412$		0			0
$413$	−20.8827	+	15.1722i	−1.02757	+	0.746573i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−11.5105			−0.563673
$418$		0			0
$419$	−26.6889			−1.30384			−0.651920	−	0.758288i	$-0.726036\pi$
$419$	−26.6889			−1.30384			−0.651920	+	0.758288i	$0.726036\pi$
$420$		0			0
$421$	8.25641	−	25.4106i	0.402393	−	1.23844i	−0.520660	−	0.853764i	$-0.674314\pi$
$421$	8.25641	−	25.4106i	0.402393	−	1.23844i	0.923053	−	0.384673i	$-0.125686\pi$
$422$		0			0
$423$	−1.75751	+	1.27690i	−0.0854530	+	0.0620852i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	8.46122	+	6.14743i	0.409467	+	0.297495i
$428$		0			0
$429$	0.210400	−	0.901148i	0.0101582	−	0.0435078i
$430$		0			0
$431$	12.0756	+	8.77343i	0.581661	+	0.422601i	0.839322	−	0.543634i	$-0.182952\pi$
$431$	12.0756	+	8.77343i	0.581661	+	0.422601i	−0.257662	+	0.966235i	$0.582952\pi$
$432$		0			0
$433$	6.12475	+	18.8500i	0.294337	+	0.905875i	0.983443	+	0.181215i	$0.0580030\pi$
$433$	6.12475	+	18.8500i	0.294337	+	0.905875i	−0.689107	+	0.724660i	$0.741997\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.19859	−	15.9996i	0.248682	−	0.765365i
$438$		0			0
$439$	34.4507			1.64424			0.822122	−	0.569312i	$-0.192790\pi$
$439$	34.4507			1.64424			0.822122	+	0.569312i	$0.192790\pi$
$440$		0			0
$441$	3.60542			0.171687
$442$		0			0
$443$	−8.39080	+	25.8242i	−0.398659	+	1.22695i	0.527416	+	0.849607i	$0.323161\pi$
$443$	−8.39080	+	25.8242i	−0.398659	+	1.22695i	−0.926075	+	0.377339i	$0.876839\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−3.74775	−	11.5344i	−0.177262	−	0.545557i
$448$		0			0
$449$	−22.1399	−	16.0856i	−1.04485	−	0.759125i	−0.0736198	−	0.997286i	$-0.523455\pi$
$449$	−22.1399	−	16.0856i	−1.04485	−	0.759125i	−0.971225	+	0.238162i	$0.923455\pi$
$450$		0			0
$451$	−3.04464	−	7.22243i	−0.143366	−	0.340091i
$452$		0			0
$453$	0.204160	+	0.148331i	0.00959229	+	0.00696921i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	31.1955	−	22.6649i	1.45926	−	1.06022i	0.475711	−	0.879601i	$-0.342191\pi$
$457$	31.1955	−	22.6649i	1.45926	−	1.06022i	0.983554	−	0.180617i	$-0.0578093\pi$
$458$		0			0
$459$	−9.36473	+	28.8217i	−0.437108	+	1.34528i
$460$		0			0
$461$	−27.7494			−1.29242			−0.646208	−	0.763161i	$-0.723646\pi$
$461$	−27.7494			−1.29242			−0.646208	+	0.763161i	$0.723646\pi$
$462$		0			0
$463$	10.9962			0.511035			0.255518	−	0.966804i	$-0.417754\pi$
$463$	10.9962			0.511035			0.255518	+	0.966804i	$0.417754\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	25.9219	−	18.8334i	1.19952	−	0.871504i	0.205285	−	0.978702i	$-0.434188\pi$
$467$	25.9219	−	18.8334i	1.19952	−	0.871504i	0.994238	+	0.107198i	$0.0341878\pi$
$468$		0			0
$469$	4.27401	+	13.1541i	0.197356	+	0.607398i
$470$		0			0
$471$	−2.48397	−	1.80471i	−0.114455	−	0.0831567i
$472$		0			0
$473$	18.9832	−	16.4194i	0.872849	−	0.754966i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	6.04655	+	18.6094i	0.276853	+	0.852065i
$478$		0			0
$479$	12.4714	−	9.06097i	0.569831	−	0.414006i	−0.265213	−	0.964190i	$-0.585442\pi$
$479$	12.4714	−	9.06097i	0.569831	−	0.414006i	0.835044	+	0.550184i	$0.185442\pi$
$480$		0			0
$481$	−0.854128	+	2.62873i	−0.0389449	+	0.119860i
$482$		0			0
$483$	−6.89228			−0.313610
$484$		0			0
$485$		0			0
$486$		0			0
$487$	8.09158	−	24.9033i	0.366664	−	1.12848i	−0.582268	−	0.812997i	$-0.697834\pi$
$487$	8.09158	−	24.9033i	0.366664	−	1.12848i	0.948932	−	0.315480i	$-0.102166\pi$
$488$		0			0
$489$	8.74716	−	6.35518i	0.395560	−	0.287391i
$490$		0			0
$491$	−2.00100	−	6.15846i	−0.0903040	−	0.277927i	0.895697	−	0.444664i	$-0.146677\pi$
$491$	−2.00100	−	6.15846i	−0.0903040	−	0.277927i	−0.986001	+	0.166737i	$0.946677\pi$
$492$		0			0
$493$	−31.0608	−	22.5670i	−1.39891	−	1.01636i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.31843	−	6.77024i	−0.417989	−	0.303687i
$498$		0			0
$499$	7.11586	+	21.9004i	0.318549	+	0.980395i	0.974269	+	0.225390i	$0.0723655\pi$
$499$	7.11586	+	21.9004i	0.318549	+	0.980395i	−0.655719	+	0.755005i	$0.727634\pi$
$500$		0			0
$501$	−8.32036	+	6.04510i	−0.371726	+	0.270075i
$502$		0			0
$503$	−8.51361	+	26.2022i	−0.379603	+	1.16830i	0.560717	+	0.828007i	$0.310525\pi$
$503$	−8.51361	+	26.2022i	−0.379603	+	1.16830i	−0.940320	+	0.340291i	$0.889475\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−13.4469			−0.597198
$508$		0			0
$509$	−3.01438	+	9.27730i	−0.133610	+	0.411209i	−0.995371	−	0.0961049i	$-0.969362\pi$
$509$	−3.01438	+	9.27730i	−0.133610	+	0.411209i	0.861761	+	0.507314i	$0.169362\pi$
$510$		0			0
$511$	14.9321	−	10.8488i	0.660557	−	0.479923i
$512$		0			0
$513$	9.08132	+	27.9494i	0.400950	+	1.23400i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−1.45913	−	3.46132i	−0.0641724	−	0.152229i
$518$		0			0
$519$	13.2882	+	9.65448i	0.583289	+	0.423784i
$520$		0			0
$521$	6.24278	+	19.2133i	0.273501	+	0.841749i	0.989612	+	0.143763i	$0.0459204\pi$
$521$	6.24278	+	19.2133i	0.273501	+	0.841749i	−0.716111	+	0.697986i	$0.754080\pi$
$522$		0			0
$523$	−18.5316	+	13.4640i	−0.810330	+	0.588739i	−0.913926	−	0.405881i	$-0.866965\pi$
$523$	−18.5316	+	13.4640i	−0.810330	+	0.588739i	0.103597	+	0.994619i	$0.466965\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.48131			0.0645270
$528$		0			0
$529$	−14.4247			−0.627161
$530$		0			0
$531$	−6.76141	+	20.8095i	−0.293420	+	0.903055i
$532$		0			0
$533$	0.512861	−	0.372615i	0.0222145	−	0.0161398i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−4.93611	−	3.58629i	−0.213009	−	0.154760i
$538$		0			0
$539$	−1.41743	+	6.07086i	−0.0610528	+	0.261490i
$540$		0			0
$541$	29.0419	+	21.1002i	1.24861	+	0.907168i	0.998140	−	0.0609571i	$-0.0194153\pi$
$541$	29.0419	+	21.1002i	1.24861	+	0.907168i	0.250469	+	0.968125i	$0.419415\pi$
$542$		0			0
$543$	−7.26223	−	22.3509i	−0.311652	−	0.959167i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−11.8996	+	36.6231i	−0.508789	+	1.56589i	0.285517	+	0.958373i	$0.407835\pi$
$547$	−11.8996	+	36.6231i	−0.508789	+	1.56589i	−0.794306	+	0.607517i	$0.792165\pi$
$548$		0			0
$549$	8.86547			0.378369
$550$		0			0
$551$	−37.2313			−1.58611
$552$		0			0
$553$	−5.80629	+	17.8699i	−0.246909	+	0.759907i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.93543	−	15.1897i	−0.209121	−	0.643608i	−0.999519	−	0.0310143i	$-0.990126\pi$
$557$	−4.93543	−	15.1897i	−0.209121	−	0.643608i	0.790398	−	0.612594i	$-0.209874\pi$
$558$		0			0
$559$	1.64231	+	1.19321i	0.0694622	+	0.0504672i
$560$		0			0
$561$	−17.4915	−	10.5690i	−0.738492	−	0.446226i
$562$		0			0
$563$	0.461423	+	0.335243i	0.0194467	+	0.0141288i	0.597466	−	0.801894i	$-0.296174\pi$
$563$	0.461423	+	0.335243i	0.0194467	+	0.0141288i	−0.578019	+	0.816023i	$0.696174\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.793684	+	0.576645i	−0.0333316	+	0.0242168i
$568$		0			0
$569$	−14.5218	+	44.6936i	−0.608786	+	1.87365i	−0.140485	+	0.990083i	$0.544866\pi$
$569$	−14.5218	+	44.6936i	−0.608786	+	1.87365i	−0.468301	+	0.883569i	$0.655134\pi$
$570$		0			0
$571$	39.8308			1.66687			0.833434	−	0.552619i	$-0.186372\pi$
$571$	39.8308			1.66687			0.833434	+	0.552619i	$0.186372\pi$
$572$		0			0
$573$	11.5312			0.481724
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−27.7974	+	20.1960i	−1.15722	+	0.840770i	−0.989424	−	0.145052i	$-0.953665\pi$
$577$	−27.7974	+	20.1960i	−1.15722	+	0.840770i	−0.167797	+	0.985822i	$0.553665\pi$
$578$		0			0
$579$	2.06009	+	6.34029i	0.0856143	+	0.263494i
$580$		0			0
$581$	30.0715	+	21.8482i	1.24758	+	0.906416i
$582$		0			0
$583$	−33.7119	+	2.86524i	−1.39620	+	0.118666i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	10.0233	+	30.8485i	0.413705	+	1.27325i	0.913404	+	0.407054i	$0.133444\pi$
$587$	10.0233	+	30.8485i	0.413705	+	1.27325i	−0.499699	+	0.866199i	$0.666556\pi$
$588$		0			0
$589$	1.16214	−	0.844343i	0.0478851	−	0.0347906i
$590$		0			0
$591$	2.94144	−	9.05281i	0.120995	−	0.372383i
$592$		0			0
$593$	19.9594			0.819635			0.409817	−	0.912168i	$-0.365592\pi$
$593$	19.9594			0.819635			0.409817	+	0.912168i	$0.365592\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4.71371	+	14.5073i	−0.192919	+	0.593744i
$598$		0			0
$599$	−9.52358	+	6.91929i	−0.389123	+	0.282714i	−0.765096	−	0.643916i	$-0.777309\pi$
$599$	−9.52358	+	6.91929i	−0.389123	+	0.282714i	0.375973	+	0.926631i	$0.377309\pi$
$600$		0			0
$601$	−1.71529	−	5.27913i	−0.0699683	−	0.215340i	0.909958	−	0.414700i	$-0.136114\pi$
$601$	−1.71529	−	5.27913i	−0.0699683	−	0.215340i	−0.979926	+	0.199360i	$0.936114\pi$
$602$		0			0
$603$	9.48501	+	6.89126i	0.386259	+	0.280634i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−11.4984	−	8.35410i	−0.466707	−	0.339083i	0.329449	−	0.944173i	$-0.393137\pi$
$607$	−11.4984	−	8.35410i	−0.466707	−	0.339083i	−0.796157	+	0.605091i	$0.793137\pi$
$608$		0			0
$609$	4.71358	+	14.5069i	0.191004	+	0.587849i
$610$		0			0
$611$	0.245787	−	0.178574i	0.00994346	−	0.00722435i
$612$		0			0
$613$	13.5125	−	41.5872i	0.545764	−	1.67969i	−0.173401	−	0.984851i	$-0.555476\pi$
$613$	13.5125	−	41.5872i	0.545764	−	1.67969i	0.719165	−	0.694839i	$-0.244524\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.0295713			−0.00119050			−0.000595249	−	1.00000i	$-0.500189\pi$
$617$	−0.0295713			−0.00119050			−0.000595249		1.00000i	$0.500189\pi$
$618$		0			0
$619$	−2.92169	+	8.99204i	−0.117433	+	0.361421i	−0.992447	−	0.122677i	$-0.960852\pi$
$619$	−2.92169	+	8.99204i	−0.117433	+	0.361421i	0.875014	+	0.484098i	$0.160852\pi$
$620$		0			0
$621$	−12.1191	+	8.80505i	−0.486323	+	0.353334i
$622$		0			0
$623$	−4.00813	−	12.3358i	−0.160582	−	0.494221i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−19.7470	+	1.67833i	−0.788619	+	0.0670262i
$628$		0			0
$629$	49.3840	+	35.8796i	1.96907	+	1.43061i
$630$		0			0
$631$	0.713746	+	2.19668i	0.0284138	+	0.0874486i	0.964258	−	0.264966i	$-0.0853607\pi$
$631$	0.713746	+	2.19668i	0.0284138	+	0.0874486i	−0.935844	+	0.352415i	$0.885361\pi$
$632$		0			0
$633$	−10.4801	+	7.61427i	−0.416548	+	0.302640i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−0.504216			−0.0199778
$638$		0			0
$639$	−9.76364			−0.386244
$640$		0			0
$641$	0.489578	−	1.50677i	0.0193372	−	0.0595137i	−0.940922	−	0.338623i	$-0.890039\pi$
$641$	0.489578	−	1.50677i	0.0193372	−	0.0595137i	0.960259	+	0.279109i	$0.0900390\pi$
$642$		0			0
$643$	9.09170	−	6.60550i	0.358542	−	0.260496i	−0.393902	−	0.919152i	$-0.628875\pi$
$643$	9.09170	−	6.60550i	0.358542	−	0.260496i	0.752444	+	0.658657i	$0.228875\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	9.24348	+	6.71578i	0.363399	+	0.264025i	0.754468	−	0.656336i	$-0.227895\pi$
$647$	9.24348	+	6.71578i	0.363399	+	0.264025i	−0.391070	+	0.920361i	$0.627895\pi$
$648$		0			0
$649$	−32.3812	−	19.5660i	−1.27107	−	0.768031i
$650$		0			0
$651$	−0.476122	−	0.345923i	−0.0186607	−	0.0135578i
$652$		0			0
$653$	−4.56675	−	14.0550i	−0.178711	−	0.550015i	0.821073	−	0.570823i	$-0.193376\pi$
$653$	−4.56675	−	14.0550i	−0.178711	−	0.550015i	−0.999783	+	0.0208086i	$0.993376\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	4.83473	−	14.8798i	0.188621	−	0.580515i
$658$		0			0
$659$	14.3223			0.557918			0.278959	−	0.960303i	$-0.410011\pi$
$659$	14.3223			0.557918			0.278959	+	0.960303i	$0.410011\pi$
$660$		0			0
$661$	−17.1886			−0.668561			−0.334280	−	0.942474i	$-0.608493\pi$
$661$	−17.1886			−0.668561			−0.334280	+	0.942474i	$0.608493\pi$
$662$		0			0
$663$	0.510779	−	1.57202i	0.0198370	−	0.0610520i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−5.86458	−	18.0493i	−0.227077	−	0.698872i
$668$		0			0
$669$	10.2595	+	7.45394i	0.396654	+	0.288186i
$670$		0			0
$671$	−3.48535	+	14.9278i	−0.134550	+	0.576282i
$672$		0			0
$673$	−27.8865	−	20.2607i	−1.07495	−	0.780994i	−0.0981513	−	0.995172i	$-0.531293\pi$
$673$	−27.8865	−	20.2607i	−1.07495	−	0.780994i	−0.976795	+	0.214177i	$0.931293\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1.56724	−	1.13867i	0.0602339	−	0.0437625i	−0.557261	−	0.830337i	$-0.688148\pi$
$677$	1.56724	−	1.13867i	0.0602339	−	0.0437625i	0.617495	+	0.786575i	$0.288148\pi$
$678$		0			0
$679$	−3.15568	+	9.71218i	−0.121104	+	0.372719i
$680$		0			0
$681$	8.01463			0.307121
$682$		0			0
$683$	19.1445			0.732543			0.366271	−	0.930508i	$-0.380634\pi$
$683$	19.1445			0.732543			0.366271	+	0.930508i	$0.380634\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−15.3413	+	11.1461i	−0.585308	+	0.425251i
$688$		0			0
$689$	−0.845607	−	2.60251i	−0.0322151	−	0.0991477i
$690$		0			0
$691$	−17.7129	−	12.8692i	−0.673832	−	0.489568i	0.197473	−	0.980308i	$-0.436726\pi$
$691$	−17.7129	−	12.8692i	−0.673832	−	0.489568i	−0.871306	+	0.490740i	$0.836726\pi$
$692$		0			0
$693$	−5.59185	−	13.2649i	−0.212417	−	0.503891i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−4.32626	−	13.3149i	−0.163869	−	0.504336i
$698$		0			0
$699$	−4.16327	+	3.02480i	−0.157469	+	0.114408i
$700$		0			0
$701$	−8.50288	+	26.1692i	−0.321149	+	0.988396i	0.652000	+	0.758219i	$0.273930\pi$
$701$	−8.50288	+	26.1692i	−0.321149	+	0.988396i	−0.973149	+	0.230176i	$0.926070\pi$
$702$		0			0
$703$	59.1946			2.23257
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−6.55388	+	20.1708i	−0.246484	+	0.758600i
$708$		0			0
$709$	22.8733	−	16.6185i	0.859026	−	0.624119i	−0.0685937	−	0.997645i	$-0.521851\pi$
$709$	22.8733	−	16.6185i	0.859026	−	0.624119i	0.927620	+	0.373526i	$0.121851\pi$
$710$		0			0
$711$	4.92182	+	15.1478i	0.184583	+	0.568087i
$712$		0			0
$713$	0.592385	+	0.430393i	0.0221850	+	0.0161184i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	14.2924	+	10.3840i	0.533758	+	0.387798i
$718$		0			0
$719$	−3.38471	−	10.4171i	−0.126228	−	0.388491i	0.867894	−	0.496749i	$-0.165473\pi$
$719$	−3.38471	−	10.4171i	−0.126228	−	0.388491i	−0.994123	+	0.108258i	$0.965473\pi$
$720$		0			0
$721$	−12.0368	+	8.74526i	−0.448274	+	0.325690i
$722$		0			0
$723$	2.16299	−	6.65701i	0.0804426	−	0.247577i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	26.1233			0.968860			0.484430	−	0.874830i	$-0.339027\pi$
$727$	26.1233			0.968860			0.484430	+	0.874830i	$0.339027\pi$
$728$		0			0
$729$	4.67568	−	14.3903i	0.173173	−	0.532973i
$730$		0			0
$731$	36.2696	−	26.3514i	1.34148	−	0.974641i
$732$		0			0
$733$	−0.852648	−	2.62418i	−0.0314933	−	0.0969264i	0.934074	−	0.357079i	$-0.116227\pi$
$733$	−0.852648	−	2.62418i	−0.0314933	−	0.0969264i	−0.965568	+	0.260152i	$0.916227\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−15.3325	+	13.2618i	−0.564781	+	0.488504i
$738$		0			0
$739$	15.6217	+	11.3498i	0.574654	+	0.417511i	0.836793	−	0.547519i	$-0.184428\pi$
$739$	15.6217	+	11.3498i	0.574654	+	0.417511i	−0.262139	+	0.965030i	$0.584428\pi$
$740$		0			0
$741$	−0.495321	−	1.52444i	−0.0181961	−	0.0560017i
$742$		0			0
$743$	2.43304	−	1.76771i	0.0892596	−	0.0648509i	−0.542260	−	0.840211i	$-0.682431\pi$
$743$	2.43304	−	1.76771i	0.0892596	−	0.0648509i	0.631520	+	0.775360i	$0.282431\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	31.5082			1.15283
$748$		0			0
$749$	−15.7037			−0.573799
$750$		0			0
$751$	2.86179	−	8.80767i	0.104428	−	0.321397i	−0.885168	−	0.465272i	$-0.845956\pi$
$751$	2.86179	−	8.80767i	0.104428	−	0.321397i	0.989596	+	0.143876i	$0.0459565\pi$
$752$		0			0
$753$	−16.6338	+	12.0851i	−0.606168	+	0.440407i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	34.0522	+	24.7403i	1.23765	+	0.899203i	0.997439	−	0.0715183i	$-0.0227844\pi$
$757$	34.0522	+	24.7403i	1.23765	+	0.899203i	0.240208	+	0.970722i	$0.422784\pi$
$758$		0			0
$759$	−3.92413	−	9.30875i	−0.142437	−	0.337886i
$760$		0			0
$761$	−36.5243	−	26.5364i	−1.32400	−	0.961945i	−0.999873	−	0.0159331i	$-0.994928\pi$
$761$	−36.5243	−	26.5364i	−1.32400	−	0.961945i	−0.324131	−	0.946012i	$-0.605072\pi$
$762$		0			0
$763$	7.03974	+	21.6661i	0.254856	+	0.784365i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.945580	−	2.91019i	0.0341429	−	0.105081i
$768$		0			0
$769$	−45.9031			−1.65531			−0.827655	−	0.561237i	$-0.810325\pi$
$769$	−45.9031			−1.65531			−0.827655	+	0.561237i	$0.810325\pi$
$770$		0			0
$771$	−6.65164			−0.239553
$772$		0			0
$773$	−2.62450	+	8.07738i	−0.0943967	+	0.290523i	−0.987096	−	0.160130i	$-0.948809\pi$
$773$	−2.62450	+	8.07738i	−0.0943967	+	0.290523i	0.892699	+	0.450653i	$0.148809\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−7.49419	−	23.0648i	−0.268853	−	0.827443i
$778$		0			0
$779$	−10.9835	−	7.97999i	−0.393525	−	0.285913i
$780$		0			0
$781$	3.83845	−	16.4402i	0.137351	−	0.588276i
$782$		0			0
$783$	26.8211	+	19.4866i	0.958507	+	0.696396i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−13.0842	+	9.50620i	−0.466400	+	0.338859i	−0.796037	−	0.605248i	$-0.793074\pi$
$787$	−13.0842	+	9.50620i	−0.466400	+	0.338859i	0.329637	+	0.944108i	$0.393074\pi$
$788$		0			0
$789$	−4.70611	+	14.4839i	−0.167542	+	0.515641i
$790$		0			0
$791$	42.4927			1.51087
$792$		0			0
$793$	−1.23983			−0.0440277
$794$		0			0
$795$		0			0
$796$		0			0
$797$	5.18298	−	3.76565i	0.183591	−	0.133386i	−0.492194	−	0.870486i	$-0.663805\pi$
$797$	5.18298	−	3.76565i	0.183591	−	0.133386i	0.675785	+	0.737099i	$0.263805\pi$
$798$		0			0
$799$	−2.07334	−	6.38109i	−0.0733495	−	0.225747i
$800$		0			0
$801$	−8.89495	−	6.46256i	−0.314288	−	0.228343i
$802$		0			0
$803$	23.1541	+	13.9906i	0.817089	+	0.493717i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−6.38776	−	19.6595i	−0.224860	−	0.692048i
$808$		0			0
$809$	38.2518	−	27.7915i	1.34486	−	0.977098i	0.345610	−	0.938378i	$-0.387672\pi$
$809$	38.2518	−	27.7915i	1.34486	−	0.977098i	0.999250	−	0.0387198i	$-0.0123280\pi$
$810$		0			0
$811$	7.00564	−	21.5611i	0.246001	−	0.757114i	−0.749469	−	0.662040i	$-0.769691\pi$
$811$	7.00564	−	21.5611i	0.246001	−	0.757114i	0.995470	−	0.0950744i	$-0.0303089\pi$
$812$		0			0
$813$	−19.9837			−0.700858
$814$		0			0
$815$		0			0
$816$		0			0
$817$	13.4345	−	41.3471i	0.470013	−	1.44655i
$818$		0			0
$819$	0.941932	−	0.684354i	0.0329138	−	0.0239132i
$820$		0			0
$821$	6.32207	+	19.4573i	0.220642	+	0.679066i	0.998705	+	0.0508794i	$0.0162024\pi$
$821$	6.32207	+	19.4573i	0.220642	+	0.679066i	−0.778063	+	0.628186i	$0.783798\pi$
$822$		0			0
$823$	−21.8405	−	15.8680i	−0.761311	−	0.553125i	0.138001	−	0.990432i	$-0.455932\pi$
$823$	−21.8405	−	15.8680i	−0.761311	−	0.553125i	−0.899312	+	0.437307i	$0.855932\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−15.0038	−	10.9009i	−0.521732	−	0.379060i	0.295524	−	0.955335i	$-0.404506\pi$
$827$	−15.0038	−	10.9009i	−0.521732	−	0.379060i	−0.817256	+	0.576275i	$0.804506\pi$
$828$		0			0
$829$	2.16168	+	6.65296i	0.0750781	+	0.231067i	0.981552	−	0.191195i	$-0.0612363\pi$
$829$	2.16168	+	6.65296i	0.0750781	+	0.231067i	−0.906474	+	0.422262i	$0.861236\pi$
$830$		0			0
$831$	20.0563	−	14.5718i	0.695747	−	0.505490i
$832$		0			0
$833$	−3.44102	+	10.5904i	−0.119224	+	0.366934i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.27912			−0.0442128
$838$		0			0
$839$	4.22625	−	13.0071i	0.145906	−	0.449053i	−0.851220	−	0.524809i	$-0.824137\pi$
$839$	4.22625	−	13.0071i	0.145906	−	0.449053i	0.997126	+	0.0757554i	$0.0241368\pi$
$840$		0			0
$841$	−10.5180	+	7.64180i	−0.362691	+	0.263510i
$842$		0			0
$843$	−5.76259	−	17.7354i	−0.198474	−	0.610840i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	24.5340	−	4.20072i	0.842997	−	0.144338i
$848$		0			0
$849$	−17.6936	−	12.8552i	−0.607244	−	0.441189i
$850$		0			0
$851$	9.32418	+	28.6969i	0.319629	+	0.983716i
$852$		0			0
$853$	−2.68304	+	1.94934i	−0.0918656	+	0.0667442i	−0.632770	−	0.774340i	$-0.718082\pi$
$853$	−2.68304	+	1.94934i	−0.0918656	+	0.0667442i	0.540904	+	0.841084i	$0.318082\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	29.2111			0.997831			0.498915	−	0.866651i	$-0.333732\pi$
$857$	29.2111			0.997831			0.498915	+	0.866651i	$0.333732\pi$
$858$		0			0
$859$	32.2591			1.10067			0.550334	−	0.834945i	$-0.314501\pi$
$859$	32.2591			1.10067			0.550334	+	0.834945i	$0.314501\pi$
$860$		0			0
$861$	−1.71880	+	5.28994i	−0.0585767	+	0.180281i
$862$		0			0
$863$	22.3598	−	16.2453i	0.761136	−	0.552998i	−0.138122	−	0.990415i	$-0.544107\pi$
$863$	22.3598	−	16.2453i	0.761136	−	0.552998i	0.899259	+	0.437417i	$0.144107\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−15.2270	−	11.0630i	−0.517135	−	0.375720i
$868$		0			0
$869$	−27.4411	+	2.33227i	−0.930874	+	0.0791167i
$870$		0			0
$871$	−1.32647	−	0.963739i	−0.0449458	−	0.0326550i
$872$		0			0
$873$	2.67497	+	8.23272i	0.0905341	+	0.278635i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.264053	+	0.812673i	−0.00891645	+	0.0274420i	−0.955416	−	0.295264i	$-0.904592\pi$
$877$	−0.264053	+	0.812673i	−0.00891645	+	0.0274420i	0.946499	+	0.322706i	$0.104592\pi$
$878$		0			0
$879$	22.1216			0.746145
$880$		0			0
$881$	−7.22437			−0.243395			−0.121698	−	0.992567i	$-0.538834\pi$
$881$	−7.22437			−0.243395			−0.121698	+	0.992567i	$0.538834\pi$
$882$		0			0
$883$	−3.51446	+	10.8164i	−0.118271	+	0.364000i	−0.992615	−	0.121306i	$-0.961292\pi$
$883$	−3.51446	+	10.8164i	−0.118271	+	0.364000i	0.874344	+	0.485306i	$0.161292\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.36528	−	7.27958i	−0.0794183	−	0.244424i	0.903462	−	0.428667i	$-0.141017\pi$
$887$	−2.36528	−	7.27958i	−0.0794183	−	0.244424i	−0.982881	+	0.184243i	$0.941017\pi$
$888$		0			0
$889$	−34.9480	−	25.3912i	−1.17212	−	0.851593i
$890$		0			0
$891$	−1.23071	−	0.743640i	−0.0412302	−	0.0249129i
$892$		0			0
$893$	−5.26381	−	3.82438i	−0.176147	−	0.127978i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.661010	−	0.480252i	0.0220705	−	0.0160351i
$898$		0			0
$899$	0.500765	−	1.54120i	0.0167015	−	0.0514018i
$900$		0			0
$901$	−60.4330			−2.01332
$902$		0			0
$903$	−17.8114			−0.592727
$904$		0			0
$905$		0			0
$906$		0			0
$907$	43.9489	−	31.9307i	1.45930	−	1.06024i	0.475755	−	0.879578i	$-0.342175\pi$
$907$	43.9489	−	31.9307i	1.45930	−	1.06024i	0.983545	−	0.180665i	$-0.0578249\pi$
$908$		0			0
$909$	5.55553	+	17.0982i	0.184265	+	0.567110i
$910$		0			0
$911$	−24.1715	−	17.5616i	−0.800836	−	0.581842i	0.110323	−	0.993896i	$-0.464811\pi$
$911$	−24.1715	−	17.5616i	−0.800836	−	0.581842i	−0.911159	+	0.412054i	$0.864811\pi$
$912$		0			0
$913$	−12.3871	+	53.0540i	−0.409952	+	1.75583i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.24764	−	3.83984i	−0.0412007	−	0.126803i
$918$		0			0
$919$	14.3024	−	10.3913i	0.471793	−	0.342778i	−0.326347	−	0.945250i	$-0.605818\pi$
$919$	14.3024	−	10.3913i	0.471793	−	0.342778i	0.798140	+	0.602473i	$0.205818\pi$
$920$		0			0
$921$	−10.5047	+	32.3302i	−0.346142	+	1.06532i
$922$		0			0
$923$	1.36544			0.0449440
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−3.89729	+	11.9946i	−0.128004	+	0.393955i
$928$		0			0
$929$	0.732789	−	0.532403i	0.0240420	−	0.0174676i	−0.575699	−	0.817661i	$-0.695270\pi$
$929$	0.732789	−	0.532403i	0.0240420	−	0.0174676i	0.599741	+	0.800194i	$0.295270\pi$
$930$		0			0
$931$	3.33688	+	10.2699i	0.109362	+	0.336581i
$932$		0			0
$933$	15.9259	+	11.5708i	0.521390	+	0.378812i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−10.4195	−	7.57019i	−0.340389	−	0.247307i	0.404437	−	0.914566i	$-0.367468\pi$
$937$	−10.4195	−	7.57019i	−0.340389	−	0.247307i	−0.744826	+	0.667259i	$0.767468\pi$
$938$		0			0
$939$	−3.86685	−	11.9009i	−0.126190	−	0.388373i
$940$		0			0
$941$	24.9136	−	18.1008i	0.812161	−	0.590069i	−0.102295	−	0.994754i	$-0.532619\pi$
$941$	24.9136	−	18.1008i	0.812161	−	0.590069i	0.914456	+	0.404685i	$0.132619\pi$
$942$		0			0
$943$	2.13852	−	6.58167i	0.0696396	−	0.214329i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−27.4841			−0.893112			−0.446556	−	0.894756i	$-0.647350\pi$
$947$	−27.4841			−0.893112			−0.446556	+	0.894756i	$0.647350\pi$
$948$		0			0
$949$	−0.676134	+	2.08093i	−0.0219482	+	0.0675497i
$950$		0			0
$951$	−8.58379	+	6.23649i	−0.278348	+	0.202232i
$952$		0			0
$953$	−4.25565	−	13.0975i	−0.137854	−	0.424271i	0.858169	−	0.513367i	$-0.171602\pi$
$953$	−4.25565	−	13.0975i	−0.137854	−	0.424271i	−0.996023	+	0.0890962i	$0.971602\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−16.9094	+	14.6257i	−0.546604	+	0.472782i
$958$		0			0
$959$	−13.8618	−	10.0712i	−0.447622	−	0.325216i
$960$		0			0
$961$	−9.56021	−	29.4233i	−0.308394	−	0.949138i
$962$		0			0
$963$	−10.7692	+	7.82431i	−0.347034	+	0.252135i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−45.5732			−1.46554			−0.732768	−	0.680478i	$-0.761772\pi$
$967$	−45.5732			−1.46554			−0.732768	+	0.680478i	$0.761772\pi$
$968$		0			0
$969$	−35.3991			−1.13718
$970$		0			0
$971$	14.0933	−	43.3748i	0.452276	−	1.39196i	−0.422028	−	0.906583i	$-0.638682\pi$
$971$	14.0933	−	43.3748i	0.452276	−	1.39196i	0.874304	−	0.485379i	$-0.161318\pi$
$972$		0			0
$973$	20.2587	−	14.7188i	0.649466	−	0.471864i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−13.7078	−	9.95932i	−0.438552	−	0.318627i	0.346507	−	0.938047i	$-0.387368\pi$
$977$	−13.7078	−	9.95932i	−0.438552	−	0.318627i	−0.785059	+	0.619420i	$0.787368\pi$
$978$		0			0
$979$	14.3787	−	12.4368i	0.459545	−	0.397481i
$980$		0			0
$981$	15.6228	+	11.3506i	0.498797	+	0.362397i
$982$		0			0
$983$	4.94660	+	15.2241i	0.157772	+	0.485572i	0.998431	−	0.0559924i	$-0.0178323\pi$
$983$	4.94660	+	15.2241i	0.157772	+	0.485572i	−0.840659	+	0.541564i	$0.817832\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.823730	+	2.53518i	−0.0262196	+	0.0806957i
$988$		0			0
$989$	22.1608			0.704671
$990$		0			0
$991$	57.8601			1.83799			0.918993	−	0.394274i	$-0.129004\pi$
$991$	57.8601			1.83799			0.918993	+	0.394274i	$0.129004\pi$
$992$		0			0
$993$	3.82302	−	11.7660i	0.121320	−	0.373384i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	14.3885	+	44.2832i	0.455688	+	1.40246i	0.870325	+	0.492477i	$0.163908\pi$
$997$	14.3885	+	44.2832i	0.455688	+	1.40246i	−0.414637	+	0.909987i	$0.636092\pi$
$998$		0			0
$999$	−42.6432	−	30.9821i	−1.34917	−	0.980231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.n.f.301.4		24
5.2	odd	4		220.2.t.a.169.3	yes	24
5.3	odd	4		220.2.t.a.169.4	yes	24
5.4	even	2	inner	1100.2.n.f.301.3		24
11.3	even	5	inner	1100.2.n.f.201.4		24
20.3	even	4		880.2.cd.d.609.3		24
20.7	even	4		880.2.cd.d.609.4		24
55.3	odd	20		220.2.t.a.69.3	✓	24
55.14	even	10	inner	1100.2.n.f.201.3		24
55.17	even	20		2420.2.b.h.969.5		12
55.27	odd	20		2420.2.b.i.969.5		12
55.28	even	20		2420.2.b.h.969.8		12
55.38	odd	20		2420.2.b.i.969.8		12
55.47	odd	20		220.2.t.a.69.4	yes	24
220.3	even	20		880.2.cd.d.289.4		24
220.47	even	20		880.2.cd.d.289.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.t.a.69.3	✓	24	55.3	odd	20
220.2.t.a.69.4	yes	24	55.47	odd	20
220.2.t.a.169.3	yes	24	5.2	odd	4
220.2.t.a.169.4	yes	24	5.3	odd	4
880.2.cd.d.289.3		24	220.47	even	20
880.2.cd.d.289.4		24	220.3	even	20
880.2.cd.d.609.3		24	20.3	even	4
880.2.cd.d.609.4		24	20.7	even	4
1100.2.n.f.201.3		24	55.14	even	10	inner
1100.2.n.f.201.4		24	11.3	even	5	inner
1100.2.n.f.301.3		24	5.4	even	2	inner
1100.2.n.f.301.4		24	1.1	even	1	trivial
2420.2.b.h.969.5		12	55.17	even	20
2420.2.b.h.969.8		12	55.28	even	20
2420.2.b.i.969.5		12	55.27	odd	20
2420.2.b.i.969.8		12	55.38	odd	20

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

\(f(q)\)	\(=\)	\(q+(0.321419 - 0.989226i) q^{3} +(0.699249 + 2.15207i) q^{7} +(1.55179 + 1.12744i) q^{9} +(-2.50847 + 2.16969i) q^{11} +(-0.217017 - 0.157672i) q^{13} +(-4.79272 + 3.48212i) q^{17} +(-1.77525 + 5.46367i) q^{19} +2.35363 q^{21} -2.92836 q^{23} +(4.13853 - 3.00682i) q^{27} +(2.00268 + 6.16362i) q^{29} +(-0.202293 - 0.146974i) q^{31} +(1.34004 + 3.17883i) q^{33} +(-3.18410 - 9.79964i) q^{37} +(-0.225727 + 0.164000i) q^{39} +(-0.730277 + 2.24756i) q^{41} -7.56763 q^{43} +(-0.349982 + 1.07714i) q^{47} +(1.52068 - 1.10484i) q^{49} +(1.90413 + 5.86031i) q^{51} +(8.25291 + 5.99609i) q^{53} +(4.83421 + 3.51226i) q^{57} +(3.52502 + 10.8489i) q^{59} +(3.73924 - 2.71672i) q^{61} +(-1.34124 + 4.12792i) q^{63} +6.11229 q^{67} +(-0.941231 + 2.89681i) q^{69} +(-4.11807 + 2.99195i) q^{71} +(-2.52055 - 7.75747i) q^{73} +(-6.42337 - 3.88125i) q^{77} +(6.71777 + 4.88074i) q^{79} +(0.133975 + 0.412332i) q^{81} +(13.2894 - 9.65532i) q^{83} +6.74092 q^{87} -5.73205 q^{89} +(0.187572 - 0.577288i) q^{91} +(-0.210411 + 0.152873i) q^{93} +(3.65106 + 2.65265i) q^{97} +(-6.33883 + 0.538749i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 14 q^{9} - 2 q^{11} - 8 q^{19} - 28 q^{21} + 16 q^{29} - 26 q^{31} - 12 q^{39} + 10 q^{41} + 46 q^{49} - 12 q^{51} + 48 q^{59} - 10 q^{61} + 58 q^{69} + 42 q^{71} + 64 q^{79} + 36 q^{81} - 72 q^{89}+ \cdots - 156 q^{99}+O(q^{100}) \) 24 * q - 14 * q^9 - 2 * q^11 - 8 * q^19 - 28 * q^21 + 16 * q^29 - 26 * q^31 - 12 * q^39 + 10 * q^41 + 46 * q^49 - 12 * q^51 + 48 * q^59 - 10 * q^61 + 58 * q^69 + 42 * q^71 + 64 * q^79 + 36 * q^81 - 72 * q^89 + 10 * q^91 - 156 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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