LMFDB - Embedded newform 552.2.q.a.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.2
Character	$\chi$	$=$	552.121
Dual form			552.2.q.a.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{3} +(0.191143 - 0.122840i) q^{5} +(0.0348746 - 0.242558i) q^{7} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{3} +(0.191143 - 0.122840i) q^{5} +(0.0348746 - 0.242558i) q^{7} +(0.841254 + 0.540641i) q^{9} +(2.22743 + 4.87739i) q^{11} +(-0.774183 - 5.38456i) q^{13} +(-0.218009 + 0.0640132i) q^{15} +(1.94477 - 2.24438i) q^{17} +(2.94740 + 3.40148i) q^{19} +(-0.101799 + 0.222908i) q^{21} +(4.50411 - 1.64711i) q^{23} +(-2.05563 + 4.50120i) q^{25} +(-0.654861 - 0.755750i) q^{27} +(6.19371 - 7.14792i) q^{29} +(3.39926 - 0.998111i) q^{31} +(-0.763083 - 5.30736i) q^{33} +(-0.0231299 - 0.0506475i) q^{35} +(2.33178 + 1.49854i) q^{37} +(-0.774183 + 5.38456i) q^{39} +(9.56573 - 6.14752i) q^{41} +(-10.0853 - 2.96132i) q^{43} +0.227213 q^{45} +4.29375 q^{47} +(6.65883 + 1.95521i) q^{49} +(-2.49831 + 1.60557i) q^{51} +(-1.70087 + 11.8298i) q^{53} +(1.02490 + 0.658663i) q^{55} +(-1.86970 - 4.09408i) q^{57} +(1.01138 + 7.03434i) q^{59} +(-4.39339 + 1.29002i) q^{61} +(0.160475 - 0.185198i) q^{63} +(-0.809422 - 0.934123i) q^{65} +(1.03113 - 2.25786i) q^{67} +(-4.78571 + 0.311439i) q^{69} +(-1.30743 + 2.86287i) q^{71} +(-10.9079 - 12.5884i) q^{73} +(3.24050 - 3.73973i) q^{75} +(1.26073 - 0.370184i) q^{77} +(-0.659291 - 4.58547i) q^{79} +(0.415415 + 0.909632i) q^{81} +(0.0148972 + 0.00957387i) q^{83} +(0.0960289 - 0.667896i) q^{85} +(-7.95662 + 5.11341i) q^{87} +(4.24524 + 1.24651i) q^{89} -1.33307 q^{91} -3.54276 q^{93} +(0.981216 + 0.288111i) q^{95} +(-6.46026 + 4.15176i) q^{97} +(-0.763083 + 5.30736i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9	$ 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9} - 15 q^{11} + 5 q^{13} - 15 q^{17} + 5 q^{19} + 9 q^{21} + 14 q^{23} + 5 q^{25} - 3 q^{27} + 13 q^{29} - 29 q^{31} - 15 q^{33} + 8 q^{35} - 3 q^{37} + 5 q^{39} + 24 q^{41} + 2 q^{43} + 22 q^{45} + 38 q^{47} + 15 q^{49} + 7 q^{51} - 7 q^{53} + 46 q^{55} - 6 q^{57} - 43 q^{59} - 22 q^{61} - 2 q^{63} + 44 q^{65} + 31 q^{67} + 3 q^{69} + 19 q^{71} - 50 q^{73} + 5 q^{75} + 16 q^{77} - 84 q^{79} - 3 q^{81} - 73 q^{83} - 8 q^{85} + 2 q^{87} + 19 q^{89} + 18 q^{91} + 26 q^{93} - 67 q^{95} - 29 q^{97} - 15 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9 - 15 * q^11 + 5 * q^13 - 15 * q^17 + 5 * q^19 + 9 * q^21 + 14 * q^23 + 5 * q^25 - 3 * q^27 + 13 * q^29 - 29 * q^31 - 15 * q^33 + 8 * q^35 - 3 * q^37 + 5 * q^39 + 24 * q^41 + 2 * q^43 + 22 * q^45 + 38 * q^47 + 15 * q^49 + 7 * q^51 - 7 * q^53 + 46 * q^55 - 6 * q^57 - 43 * q^59 - 22 * q^61 - 2 * q^63 + 44 * q^65 + 31 * q^67 + 3 * q^69 + 19 * q^71 - 50 * q^73 + 5 * q^75 + 16 * q^77 - 84 * q^79 - 3 * q^81 - 73 * q^83 - 8 * q^85 + 2 * q^87 + 19 * q^89 + 18 * q^91 + 26 * q^93 - 67 * q^95 - 29 * q^97 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{9}{11}\right)$	$1$	$1$	$1$

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
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$4$		0			0
$5$	0.191143	−	0.122840i	0.0854820	−	0.0549359i	−0.497202	−	0.867635i	$-0.665639\pi$
$5$	0.191143	−	0.122840i	0.0854820	−	0.0549359i	0.582684	+	0.812699i	$0.302003\pi$
$6$		0			0
$7$	0.0348746	−	0.242558i	0.0131814	−	0.0916785i	−0.982169	−	0.188001i	$-0.939799\pi$
$7$	0.0348746	−	0.242558i	0.0131814	−	0.0916785i	0.995350	+	0.0963229i	$0.0307081\pi$
$8$		0			0
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$		0			0
$11$	2.22743	+	4.87739i	0.671595	+	1.47059i	0.871309	+	0.490734i	$0.163271\pi$
$11$	2.22743	+	4.87739i	0.671595	+	1.47059i	−0.199714	+	0.979854i	$0.564001\pi$
$12$		0			0
$13$	−0.774183	−	5.38456i	−0.214720	−	1.49341i	−0.757113	−	0.653284i	$-0.773391\pi$
$13$	−0.774183	−	5.38456i	−0.214720	−	1.49341i	0.542393	−	0.840125i	$-0.317518\pi$
$14$		0			0
$15$	−0.218009	+	0.0640132i	−0.0562897	+	0.0165281i
$16$		0			0
$17$	1.94477	−	2.24438i	0.471676	−	0.544343i	−0.469201	−	0.883091i	$-0.655458\pi$
$17$	1.94477	−	2.24438i	0.471676	−	0.544343i	0.940877	+	0.338748i	$0.110003\pi$
$18$		0			0
$19$	2.94740	+	3.40148i	0.676180	+	0.780353i	0.985330	−	0.170660i	$-0.0545900\pi$
$19$	2.94740	+	3.40148i	0.676180	+	0.780353i	−0.309150	+	0.951013i	$0.600045\pi$
$20$		0			0
$21$	−0.101799	+	0.222908i	−0.0222143	+	0.0486425i
$22$		0			0
$23$	4.50411	−	1.64711i	0.939172	−	0.343447i
$23$	4.50411	−	1.64711i	0.939172	−	0.343447i
$24$		0			0
$25$	−2.05563	+	4.50120i	−0.411126	+	0.900240i
$26$		0			0
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$		0			0
$29$	6.19371	−	7.14792i	1.15014	−	1.32734i	0.213543	−	0.976934i	$-0.431500\pi$
$29$	6.19371	−	7.14792i	1.15014	−	1.32734i	0.936600	−	0.350401i	$-0.113955\pi$
$30$		0			0
$31$	3.39926	−	0.998111i	0.610524	−	0.179266i	0.0381683	−	0.999271i	$-0.487848\pi$
$31$	3.39926	−	0.998111i	0.610524	−	0.179266i	0.572356	+	0.820005i	$0.306030\pi$
$32$		0			0
$33$	−0.763083	−	5.30736i	−0.132836	−	0.923893i
$34$		0			0
$35$	−0.0231299	−	0.0506475i	−0.00390967	−	0.00856099i
$36$		0			0
$37$	2.33178	+	1.49854i	0.383342	+	0.246359i	0.718092	−	0.695948i	$-0.245016\pi$
$37$	2.33178	+	1.49854i	0.383342	+	0.246359i	−0.334750	+	0.942307i	$0.608652\pi$
$38$		0			0
$39$	−0.774183	+	5.38456i	−0.123968	+	0.862220i
$40$		0			0
$41$	9.56573	−	6.14752i	1.49392	−	0.960081i	0.498254	−	0.867031i	$-0.333975\pi$
$41$	9.56573	−	6.14752i	1.49392	−	0.960081i	0.995661	−	0.0930499i	$-0.0296616\pi$
$42$		0			0
$43$	−10.0853	−	2.96132i	−1.53800	−	0.451597i	−0.600510	−	0.799617i	$-0.705036\pi$
$43$	−10.0853	−	2.96132i	−1.53800	−	0.451597i	−0.937487	+	0.348021i	$0.886854\pi$
$44$		0			0
$45$	0.227213			0.0338709
$46$		0			0
$47$	4.29375			0.626308			0.313154	−	0.949702i	$-0.398614\pi$
$47$	4.29375			0.626308			0.313154	+	0.949702i	$0.398614\pi$
$48$		0			0
$49$	6.65883	+	1.95521i	0.951262	+	0.279316i
$50$		0			0
$51$	−2.49831	+	1.60557i	−0.349833	+	0.224824i
$52$		0			0
$53$	−1.70087	+	11.8298i	−0.233632	+	1.62495i	0.448543	+	0.893761i	$0.351943\pi$
$53$	−1.70087	+	11.8298i	−0.233632	+	1.62495i	−0.682176	+	0.731188i	$0.738966\pi$
$54$		0			0
$55$	1.02490	+	0.658663i	0.138197	+	0.0888141i
$56$		0			0
$57$	−1.86970	−	4.09408i	−0.247648	−	0.542274i
$58$		0			0
$59$	1.01138	+	7.03434i	0.131671	+	0.915793i	0.943376	+	0.331725i	$0.107631\pi$
$59$	1.01138	+	7.03434i	0.131671	+	0.915793i	−0.811705	+	0.584068i	$0.801460\pi$
$60$		0			0
$61$	−4.39339	+	1.29002i	−0.562516	+	0.165170i	−0.550615	−	0.834760i	$-0.685607\pi$
$61$	−4.39339	+	1.29002i	−0.562516	+	0.165170i	−0.0119014	+	0.999929i	$0.503788\pi$
$62$		0			0
$63$	0.160475	−	0.185198i	0.0202180	−	0.0233328i
$64$		0			0
$65$	−0.809422	−	0.934123i	−0.100396	−	0.115864i
$66$		0			0
$67$	1.03113	−	2.25786i	0.125972	−	0.275841i	−0.836129	−	0.548533i	$-0.815187\pi$
$67$	1.03113	−	2.25786i	0.125972	−	0.275841i	0.962101	+	0.272692i	$0.0879139\pi$
$68$		0			0
$69$	−4.78571	+	0.311439i	−0.576132	+	0.0374928i
$70$		0			0
$71$	−1.30743	+	2.86287i	−0.155163	+	0.339760i	−0.971210	−	0.238226i	$-0.923434\pi$
$71$	−1.30743	+	2.86287i	−0.155163	+	0.339760i	0.816046	+	0.577986i	$0.196161\pi$
$72$		0			0
$73$	−10.9079	−	12.5884i	−1.27667	−	1.47336i	−0.807040	−	0.590497i	$-0.798932\pi$
$73$	−10.9079	−	12.5884i	−1.27667	−	1.47336i	−0.469633	−	0.882862i	$-0.655614\pi$
$74$		0			0
$75$	3.24050	−	3.73973i	0.374180	−	0.431827i
$76$		0			0
$77$	1.26073	−	0.370184i	0.143674	−	0.0421864i
$78$		0			0
$79$	−0.659291	−	4.58547i	−0.0741760	−	0.515905i	−0.992707	−	0.120556i	$-0.961532\pi$
$79$	−0.659291	−	4.58547i	−0.0741760	−	0.515905i	0.918531	−	0.395350i	$-0.129377\pi$
$80$		0			0
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$		0			0
$83$	0.0148972	+	0.00957387i	0.00163518	+	0.00105087i	0.541458	−	0.840728i	$-0.317872\pi$
$83$	0.0148972	+	0.00957387i	0.00163518	+	0.00105087i	−0.539823	+	0.841779i	$0.681509\pi$
$84$		0			0
$85$	0.0960289	−	0.667896i	0.0104158	−	0.0724435i
$86$		0			0
$87$	−7.95662	+	5.11341i	−0.853039	+	0.548215i
$88$		0			0
$89$	4.24524	+	1.24651i	0.449994	+	0.132130i	0.498874	−	0.866674i	$-0.333747\pi$
$89$	4.24524	+	1.24651i	0.449994	+	0.132130i	−0.0488799	+	0.998805i	$0.515565\pi$
$90$		0			0
$91$	−1.33307			−0.139744
$92$		0			0
$93$	−3.54276			−0.367367
$94$		0			0
$95$	0.981216	+	0.288111i	0.100671	+	0.0295596i
$96$		0			0
$97$	−6.46026	+	4.15176i	−0.655940	+	0.421547i	−0.825832	−	0.563916i	$-0.809294\pi$
$97$	−6.46026	+	4.15176i	−0.655940	+	0.421547i	0.169893	+	0.985463i	$0.445658\pi$
$98$		0			0
$99$	−0.763083	+	5.30736i	−0.0766927	+	0.533410i
$100$		0			0
$101$	−2.93004	−	1.88303i	−0.291550	−	0.187368i	0.386687	−	0.922211i	$-0.373619\pi$
$101$	−2.93004	−	1.88303i	−0.291550	−	0.187368i	−0.678237	+	0.734843i	$0.737256\pi$
$102$		0			0
$103$	−0.432143	−	0.946261i	−0.0425803	−	0.0932379i	0.887146	−	0.461488i	$-0.152684\pi$
$103$	−0.432143	−	0.946261i	−0.0425803	−	0.0932379i	−0.929727	+	0.368250i	$0.879957\pi$
$104$		0			0
$105$	0.00792396	+	0.0551123i	0.000773299	+	0.00537841i
$106$		0			0
$107$	−17.6938	+	5.19537i	−1.71052	+	0.502255i	−0.982966	−	0.183790i	$-0.941163\pi$
$107$	−17.6938	+	5.19537i	−1.71052	+	0.502255i	−0.727559	+	0.686045i	$0.759345\pi$
$108$		0			0
$109$	−9.92462	+	11.4536i	−0.950606	+	1.09706i	0.0445750	+	0.999006i	$0.485807\pi$
$109$	−9.92462	+	11.4536i	−0.950606	+	1.09706i	−0.995181	+	0.0980521i	$0.968739\pi$
$110$		0			0
$111$	−1.81514	−	2.09478i	−0.172285	−	0.198828i
$112$		0			0
$113$	3.40587	−	7.45782i	0.320398	−	0.701573i	−0.679074	−	0.734070i	$-0.737619\pi$
$113$	3.40587	−	7.45782i	0.320398	−	0.701573i	0.999472	+	0.0324966i	$0.0103458\pi$
$114$		0			0
$115$	0.658599	−	0.868122i	0.0614147	−	0.0809528i
$116$		0			0
$117$	2.25983	−	4.94834i	0.208921	−	0.457474i
$118$		0			0
$119$	−0.476571	−	0.549992i	−0.0436872	−	0.0504177i
$120$		0			0
$121$	−11.6240	+	13.4148i	−1.05673	+	1.21953i
$122$		0			0
$123$	−10.9102	+	3.20352i	−0.983740	+	0.288852i
$124$		0			0
$125$	0.321688	+	2.23739i	0.0287726	+	0.200118i
$126$		0			0
$127$	5.03577	+	11.0268i	0.446852	+	0.978469i	0.990290	+	0.139020i	$0.0443951\pi$
$127$	5.03577	+	11.0268i	0.446852	+	0.978469i	−0.543438	+	0.839450i	$0.682878\pi$
$128$		0			0
$129$	8.84249	+	5.68273i	0.778538	+	0.500336i
$130$		0			0
$131$	−0.294034	+	2.04505i	−0.0256898	+	0.178677i	−0.998626	−	0.0523956i	$-0.983314\pi$
$131$	−0.294034	+	2.04505i	−0.0256898	+	0.178677i	0.972937	+	0.231072i	$0.0742234\pi$
$132$		0			0
$133$	0.927847	−	0.596291i	0.0804546	−	0.0517050i
$134$		0			0
$135$	−0.218009	−	0.0640132i	−0.0187632	−	0.00550938i
$136$		0			0
$137$	−1.62105			−0.138496			−0.0692478	−	0.997599i	$-0.522060\pi$
$137$	−1.62105			−0.138496			−0.0692478	+	0.997599i	$0.522060\pi$
$138$		0			0
$139$	−18.2519			−1.54811			−0.774054	−	0.633120i	$-0.781774\pi$
$139$	−18.2519			−1.54811			−0.774054	+	0.633120i	$0.781774\pi$
$140$		0			0
$141$	−4.11983	−	1.20969i	−0.346952	−	0.101874i
$142$		0			0
$143$	24.5382	−	15.7697i	2.05198	−	1.31873i
$144$		0			0
$145$	0.305833	−	2.12712i	0.0253981	−	0.176647i
$146$		0			0
$147$	−5.83826	−	3.75202i	−0.481531	−	0.309461i
$148$		0			0
$149$	−0.798982	−	1.74953i	−0.0654551	−	0.143327i	0.874077	−	0.485787i	$-0.161467\pi$
$149$	−0.798982	−	1.74953i	−0.0654551	−	0.143327i	−0.939532	+	0.342460i	$0.888740\pi$
$150$		0			0
$151$	−2.62827	−	18.2800i	−0.213886	−	1.48761i	−0.760015	−	0.649906i	$-0.774808\pi$
$151$	−2.62827	−	18.2800i	−0.213886	−	1.48761i	0.546129	−	0.837701i	$-0.316101\pi$
$152$		0			0
$153$	2.84945	−	0.836674i	0.230364	−	0.0676411i
$154$		0			0
$155$	0.527137	−	0.608349i	0.0423407	−	0.0488637i
$156$		0			0
$157$	4.29881	+	4.96109i	0.343082	+	0.395938i	0.900901	−	0.434025i	$-0.142907\pi$
$157$	4.29881	+	4.96109i	0.343082	+	0.395938i	−0.557819	+	0.829963i	$0.688361\pi$
$158$		0			0
$159$	4.96481	−	10.8714i	0.393735	−	0.862160i
$160$		0			0
$161$	−0.242442	−	1.14995i	−0.0191071	−	0.0906290i
$162$		0			0
$163$	4.47265	−	9.79374i	0.350325	−	0.767105i	−0.649651	−	0.760232i	$-0.725085\pi$
$163$	4.47265	−	9.79374i	0.350325	−	0.767105i	0.999976	−	0.00687245i	$-0.00218758\pi$
$164$		0			0
$165$	−0.797817	−	0.920730i	−0.0621100	−	0.0716787i
$166$		0			0
$167$	−5.26520	+	6.07636i	−0.407433	+	0.470203i	−0.921968	−	0.387267i	$-0.873419\pi$
$167$	−5.26520	+	6.07636i	−0.407433	+	0.470203i	0.514535	+	0.857470i	$0.327965\pi$
$168$		0			0
$169$	−15.9207	+	4.67475i	−1.22467	+	0.359596i
$170$		0			0
$171$	0.640531	+	4.45499i	0.0489826	+	0.340682i
$172$		0			0
$173$	−0.345508	−	0.756557i	−0.0262685	−	0.0575199i	0.896043	−	0.443967i	$-0.146429\pi$
$173$	−0.345508	−	0.756557i	−0.0262685	−	0.0575199i	−0.922311	+	0.386447i	$0.873702\pi$
$174$		0			0
$175$	1.02011	+	0.655588i	0.0771134	+	0.0495578i
$176$		0			0
$177$	1.01138	−	7.03434i	0.0760203	−	0.528733i
$178$		0			0
$179$	−13.9313	+	8.95312i	−1.04128	+	0.669188i	−0.945302	−	0.326196i	$-0.894233\pi$
$179$	−13.9313	+	8.95312i	−1.04128	+	0.669188i	−0.0959745	+	0.995384i	$0.530597\pi$
$180$		0			0
$181$	18.7047	+	5.49220i	1.39031	+	0.408232i	0.889346	−	0.457235i	$-0.151160\pi$
$181$	18.7047	+	5.49220i	1.39031	+	0.408232i	0.500965	+	0.865467i	$0.332978\pi$
$182$		0			0
$183$	4.57887			0.338480
$184$		0			0
$185$	0.629786			0.0463028
$186$		0			0
$187$	15.2786	+	4.48619i	1.11728	+	0.328063i
$188$		0			0
$189$	−0.206151	+	0.132485i	−0.0149953	+	0.00963690i
$190$		0			0
$191$	−2.18996	+	15.2315i	−0.158460	+	1.10211i	0.743013	+	0.669276i	$0.233396\pi$
$191$	−2.18996	+	15.2315i	−0.158460	+	1.10211i	−0.901473	+	0.432835i	$0.857513\pi$
$192$		0			0
$193$	5.79614	+	3.72495i	0.417215	+	0.268128i	0.732363	−	0.680915i	$-0.238418\pi$
$193$	5.79614	+	3.72495i	0.417215	+	0.268128i	−0.315148	+	0.949043i	$0.602054\pi$
$194$		0			0
$195$	0.513462	+	1.12432i	0.0367698	+	0.0805146i
$196$		0			0
$197$	−2.12847	−	14.8038i	−0.151647	−	1.05473i	−0.913459	−	0.406931i	$-0.866599\pi$
$197$	−2.12847	−	14.8038i	−0.151647	−	1.05473i	0.761812	−	0.647798i	$-0.224310\pi$
$198$		0			0
$199$	11.8691	−	3.48507i	0.841376	−	0.247050i	0.167479	−	0.985876i	$-0.446437\pi$
$199$	11.8691	−	3.48507i	0.841376	−	0.247050i	0.673897	+	0.738825i	$0.264619\pi$
$200$		0			0
$201$	−1.62547	+	1.87590i	−0.114652	+	0.132315i
$202$		0			0
$203$	−1.51778	−	1.75162i	−0.106528	−	0.122939i
$204$		0			0
$205$	1.07326	−	2.35012i	0.0749599	−	0.164139i
$206$		0			0
$207$	4.67960	+	1.04947i	0.325254	+	0.0729430i
$208$		0			0
$209$	−10.0252	+	21.9522i	−0.693459	+	1.51846i
$210$		0			0
$211$	−1.05251	−	1.21466i	−0.0724576	−	0.0836206i	0.718363	−	0.695668i	$-0.244892\pi$
$211$	−1.05251	−	1.21466i	−0.0724576	−	0.0836206i	−0.790821	+	0.612048i	$0.790346\pi$
$212$		0			0
$213$	2.06103	−	2.37856i	0.141220	−	0.162976i
$214$		0			0
$215$	−2.29151	+	0.672849i	−0.156280	+	0.0458879i
$216$		0			0
$217$	−0.123553	−	0.859327i	−0.00838729	−	0.0583349i
$218$		0			0
$219$	6.91949	+	15.1516i	0.467576	+	1.02385i
$220$		0			0
$221$	−13.5906	−	8.73417i	−0.914205	−	0.587524i
$222$		0			0
$223$	4.04706	−	28.1479i	0.271011	−	1.88492i	−0.167005	−	0.985956i	$-0.553410\pi$
$223$	4.04706	−	28.1479i	0.271011	−	1.88492i	0.438016	−	0.898967i	$-0.355681\pi$
$224$		0			0
$225$	−4.16284	+	2.67529i	−0.277522	+	0.178353i
$226$		0			0
$227$	15.2063	+	4.46496i	1.00928	+	0.296350i	0.744257	−	0.667893i	$-0.232804\pi$
$227$	15.2063	+	4.46496i	1.00928	+	0.296350i	0.265018	+	0.964243i	$0.414622\pi$
$228$		0			0
$229$	−15.2999			−1.01105			−0.505523	−	0.862813i	$-0.668700\pi$
$229$	−15.2999			−1.01105			−0.505523	+	0.862813i	$0.668700\pi$
$230$		0			0
$231$	−1.31396			−0.0864520
$232$		0			0
$233$	12.6931	+	3.72702i	0.831550	+	0.244165i	0.669683	−	0.742647i	$-0.266430\pi$
$233$	12.6931	+	3.72702i	0.831550	+	0.244165i	0.161868	+	0.986812i	$0.448248\pi$
$234$		0			0
$235$	0.820723	−	0.527447i	0.0535381	−	0.0344068i
$236$		0			0
$237$	−0.659291	+	4.58547i	−0.0428255	+	0.297858i
$238$		0			0
$239$	−0.306216	−	0.196793i	−0.0198075	−	0.0127295i	0.530700	−	0.847560i	$-0.321929\pi$
$239$	−0.306216	−	0.196793i	−0.0198075	−	0.0127295i	−0.550507	+	0.834830i	$0.685566\pi$
$240$		0			0
$241$	−2.25048	−	4.92786i	−0.144966	−	0.317432i	0.823195	−	0.567758i	$-0.192189\pi$
$241$	−2.25048	−	4.92786i	−0.144966	−	0.317432i	−0.968161	+	0.250327i	$0.919462\pi$
$242$		0			0
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$		0			0
$245$	1.51297	−	0.444248i	0.0966602	−	0.0283820i
$246$		0			0
$247$	16.0337	−	18.5038i	1.02020	−	1.17737i
$248$		0			0
$249$	−0.0115965	−	0.0133831i	−0.000734900	−	0.000848119i
$250$		0			0
$251$	10.5010	−	22.9939i	0.662815	−	1.45136i	−0.217061	−	0.976158i	$-0.569647\pi$
$251$	10.5010	−	22.9939i	0.662815	−	1.45136i	0.879876	−	0.475204i	$-0.157626\pi$
$252$		0			0
$253$	18.0662	+	18.2995i	1.13581	+	1.15048i
$254$		0			0
$255$	−0.280307	+	0.613787i	−0.0175535	+	0.0384368i
$256$		0			0
$257$	12.2926	+	14.1865i	0.766794	+	0.884928i	0.996082	−	0.0884309i	$-0.0281852\pi$
$257$	12.2926	+	14.1865i	0.766794	+	0.884928i	−0.229288	+	0.973359i	$0.573640\pi$
$258$		0			0
$259$	0.444804	−	0.513331i	0.0276388	−	0.0318969i
$260$		0			0
$261$	9.07493	−	2.66464i	0.561724	−	0.164937i
$262$		0			0
$263$	−3.24554	−	22.5733i	−0.200129	−	1.39193i	−0.803898	−	0.594767i	$-0.797244\pi$
$263$	−3.24554	−	22.5733i	−0.200129	−	1.39193i	0.603769	−	0.797159i	$-0.293665\pi$
$264$		0			0
$265$	1.12807	+	2.47013i	0.0692967	+	0.151739i
$266$		0			0
$267$	−3.72209	−	2.39204i	−0.227788	−	0.146391i
$268$		0			0
$269$	1.25327	−	8.71665i	0.0764129	−	0.531464i	−0.915278	−	0.402822i	$-0.868029\pi$
$269$	1.25327	−	8.71665i	0.0764129	−	0.531464i	0.991691	−	0.128641i	$-0.0410616\pi$
$270$		0			0
$271$	−12.2221	+	7.85464i	−0.742437	+	0.477136i	−0.856376	−	0.516352i	$-0.827290\pi$
$271$	−12.2221	+	7.85464i	−0.742437	+	0.477136i	0.113939	+	0.993488i	$0.463653\pi$
$272$		0			0
$273$	1.27907	+	0.375569i	0.0774129	+	0.0227305i
$274$		0			0
$275$	−26.5329			−1.59999
$276$		0			0
$277$	15.1413			0.909755			0.454877	−	0.890554i	$-0.349683\pi$
$277$	15.1413			0.909755			0.454877	+	0.890554i	$0.349683\pi$
$278$		0			0
$279$	3.39926	+	0.998111i	0.203508	+	0.0597554i
$280$		0			0
$281$	4.83470	−	3.10707i	0.288414	−	0.185352i	−0.388431	−	0.921478i	$-0.626983\pi$
$281$	4.83470	−	3.10707i	0.288414	−	0.185352i	0.676845	+	0.736125i	$0.263347\pi$
$282$		0			0
$283$	−2.76461	+	19.2283i	−0.164339	+	1.14300i	0.725996	+	0.687699i	$0.241379\pi$
$283$	−2.76461	+	19.2283i	−0.164339	+	1.14300i	−0.890335	+	0.455306i	$0.849530\pi$
$284$		0			0
$285$	−0.860299	−	0.552881i	−0.0509597	−	0.0327498i
$286$		0			0
$287$	−1.15753	−	2.53464i	−0.0683269	−	0.149615i
$288$		0			0
$289$	1.16422	+	8.09734i	0.0684836	+	0.476314i
$290$		0			0
$291$	7.36826	−	2.16352i	0.431935	−	0.126828i
$292$		0			0
$293$	−11.1620	+	12.8817i	−0.652094	+	0.752556i	−0.981464	−	0.191644i	$-0.938618\pi$
$293$	−11.1620	+	12.8817i	−0.652094	+	0.752556i	0.329371	+	0.944201i	$0.393163\pi$
$294$		0			0
$295$	1.05742	+	1.22033i	0.0615654	+	0.0710503i
$296$		0			0
$297$	2.22743	−	4.87739i	0.129249	−	0.283015i
$298$		0			0
$299$	−12.3560	−	22.9775i	−0.714565	−	1.32882i
$300$		0			0
$301$	−1.07001	+	2.34300i	−0.0616746	+	0.135049i
$302$		0			0
$303$	2.28085	+	2.63224i	0.131031	+	0.151218i
$304$		0			0
$305$	−0.681302	+	0.786264i	−0.0390112	+	0.0450214i
$306$		0			0
$307$	−0.789220	+	0.231736i	−0.0450431	+	0.0132259i	−0.304177	−	0.952616i	$-0.598381\pi$
$307$	−0.789220	+	0.231736i	−0.0450431	+	0.0132259i	0.259133	+	0.965842i	$0.416563\pi$
$308$		0			0
$309$	0.148046	+	1.02968i	0.00842202	+	0.0585764i
$310$		0			0
$311$	1.80067	+	3.94293i	0.102107	+	0.223583i	0.953790	−	0.300474i	$-0.0971450\pi$
$311$	1.80067	+	3.94293i	0.102107	+	0.223583i	−0.851683	+	0.524057i	$0.824418\pi$
$312$		0			0
$313$	3.31001	+	2.12722i	0.187093	+	0.120237i	0.630834	−	0.775918i	$-0.282713\pi$
$313$	3.31001	+	2.12722i	0.187093	+	0.120237i	−0.443741	+	0.896155i	$0.646349\pi$
$314$		0			0
$315$	0.00792396	−	0.0551123i	0.000446465	−	0.00310523i
$316$		0			0
$317$	−13.9011	+	8.93370i	−0.780764	+	0.501766i	−0.869287	−	0.494308i	$-0.835422\pi$
$317$	−13.9011	+	8.93370i	−0.780764	+	0.501766i	0.0885232	+	0.996074i	$0.471785\pi$
$318$		0			0
$319$	48.6592	+	14.2876i	2.72439	+	0.799954i
$320$		0			0
$321$	18.4408			1.02926
$322$		0			0
$323$	13.3662			0.743718
$324$		0			0
$325$	25.8284	+	7.58391i	1.43270	+	0.420679i
$326$		0			0
$327$	12.7495	−	8.19358i	0.705047	−	0.453106i
$328$		0			0
$329$	0.149743	−	1.04149i	0.00825560	−	0.0574190i
$330$		0			0
$331$	−18.0645	−	11.6093i	−0.992914	−	0.638107i	−0.0599972	−	0.998199i	$-0.519109\pi$
$331$	−18.0645	−	11.6093i	−0.992914	−	0.638107i	−0.932917	+	0.360091i	$0.882746\pi$
$332$		0			0
$333$	1.15144	+	2.52131i	0.0630987	+	0.138167i
$334$		0			0
$335$	−0.0802626	−	0.558239i	−0.00438522	−	0.0304998i
$336$		0			0
$337$	−30.6363	+	8.99562i	−1.66886	+	0.490022i	−0.973510	−	0.228645i	$-0.926570\pi$
$337$	−30.6363	+	8.99562i	−1.66886	+	0.490022i	−0.695354	+	0.718668i	$0.744752\pi$
$338$		0			0
$339$	−5.36902	+	6.19618i	−0.291605	+	0.336531i
$340$		0			0
$341$	12.4398	+	14.3563i	0.673652	+	0.777436i
$342$		0			0
$343$	1.41907	−	3.10732i	0.0766224	−	0.167780i
$344$		0			0
$345$	−0.876500	+	0.647408i	−0.0471892	+	0.0348553i
$346$		0			0
$347$	1.31212	−	2.87313i	0.0704381	−	0.154238i	−0.871138	−	0.491038i	$-0.836617\pi$
$347$	1.31212	−	2.87313i	0.0704381	−	0.154238i	0.941576	+	0.336800i	$0.109345\pi$
$348$		0			0
$349$	−17.8914	−	20.6477i	−0.957702	−	1.10525i	−0.994375	−	0.105920i	$-0.966221\pi$
$349$	−17.8914	−	20.6477i	−0.957702	−	1.10525i	0.0366723	−	0.999327i	$-0.488324\pi$
$350$		0			0
$351$	−3.56240	+	4.11123i	−0.190147	+	0.219441i
$352$		0			0
$353$	0.644694	−	0.189299i	0.0343136	−	0.0100754i	−0.264531	−	0.964377i	$-0.585217\pi$
$353$	0.644694	−	0.189299i	0.0343136	−	0.0100754i	0.298844	+	0.954302i	$0.403399\pi$
$354$		0			0
$355$	0.101770	+	0.707825i	0.00540138	+	0.0375674i
$356$		0			0
$357$	0.302316	+	0.661979i	0.0160003	+	0.0350357i
$358$		0			0
$359$	13.0694	+	8.39920i	0.689777	+	0.443293i	0.838007	−	0.545660i	$-0.183721\pi$
$359$	13.0694	+	8.39920i	0.689777	+	0.443293i	−0.148229	+	0.988953i	$0.547357\pi$
$360$		0			0
$361$	−0.178924	+	1.24444i	−0.00941705	+	0.0654970i
$362$		0			0
$363$	14.9326	−	9.59657i	0.783756	−	0.503689i
$364$		0			0
$365$	−3.63134	−	1.06626i	−0.190073	−	0.0558104i
$366$		0			0
$367$	7.23366			0.377594			0.188797	−	0.982016i	$-0.439541\pi$
$367$	7.23366			0.377594			0.188797	+	0.982016i	$0.439541\pi$
$368$		0			0
$369$	11.3708			0.591940
$370$		0			0
$371$	2.81010	+	0.825121i	0.145893	+	0.0428381i
$372$		0			0
$373$	31.6491	−	20.3397i	1.63873	−	1.05315i	0.696839	−	0.717227i	$-0.254589\pi$
$373$	31.6491	−	20.3397i	1.63873	−	1.05315i	0.941890	−	0.335920i	$-0.109047\pi$
$374$		0			0
$375$	0.321688	−	2.23739i	0.0166119	−	0.115538i
$376$		0			0
$377$	−43.2835	−	27.8166i	−2.22921	−	1.43263i
$378$		0			0
$379$	−1.29428	−	2.83408i	−0.0664828	−	0.145577i	0.873474	−	0.486871i	$-0.161862\pi$
$379$	−1.29428	−	2.83408i	−0.0664828	−	0.145577i	−0.939956	+	0.341294i	$0.889135\pi$
$380$		0			0
$381$	−1.72518	−	11.9989i	−0.0883835	−	0.614720i
$382$		0			0
$383$	−23.2961	+	6.84035i	−1.19038	+	0.349526i	−0.816165	−	0.577818i	$-0.803904\pi$
$383$	−23.2961	+	6.84035i	−1.19038	+	0.349526i	−0.374210	+	0.927344i	$0.622086\pi$
$384$		0			0
$385$	0.195507	−	0.225627i	0.00996397	−	0.0114990i
$386$		0			0
$387$	−6.88330	−	7.94375i	−0.349898	−	0.403804i
$388$		0			0
$389$	−2.42757	+	5.31564i	−0.123083	+	0.269514i	−0.961136	−	0.276074i	$-0.910966\pi$
$389$	−2.42757	+	5.31564i	−0.123083	+	0.269514i	0.838054	+	0.545588i	$0.183694\pi$
$390$		0			0
$391$	5.06271	−	13.3122i	0.256032	−	0.673228i
$392$		0			0
$393$	0.858280	−	1.87937i	0.0432945	−	0.0948018i
$394$		0			0
$395$	−0.689300	−	0.795495i	−0.0346824	−	0.0400257i
$396$		0			0
$397$	9.06012	−	10.4559i	0.454714	−	0.524768i	−0.481382	−	0.876511i	$-0.659865\pi$
$397$	9.06012	−	10.4559i	0.454714	−	0.524768i	0.936097	+	0.351742i	$0.114411\pi$
$398$		0			0
$399$	−1.05826	+	0.310733i	−0.0529792	+	0.0155561i
$400$		0			0
$401$	−1.70325	−	11.8464i	−0.0850562	−	0.591579i	−0.987121	−	0.159977i	$-0.948858\pi$
$401$	−1.70325	−	11.8464i	−0.0850562	−	0.591579i	0.902064	−	0.431601i	$-0.142051\pi$
$402$		0			0
$403$	−8.00604	−	17.5308i	−0.398809	−	0.873270i
$404$		0			0
$405$	0.191143	+	0.122840i	0.00949800	+	0.00610399i
$406$		0			0
$407$	−2.11511	+	14.7109i	−0.104842	+	0.729192i
$408$		0			0
$409$	0.726443	−	0.466856i	0.0359203	−	0.0230846i	−0.522557	−	0.852604i	$-0.675022\pi$
$409$	0.726443	−	0.466856i	0.0359203	−	0.0230846i	0.558478	+	0.829520i	$0.311386\pi$
$410$		0			0
$411$	1.55539	+	0.456703i	0.0767216	+	0.0225275i
$412$		0			0
$413$	1.74151			0.0856941
$414$		0			0
$415$	0.00402357			0.000197509
$416$		0			0
$417$	17.5126	+	5.14216i	0.857595	+	0.251813i
$418$		0			0
$419$	−21.7851	+	14.0005i	−1.06427	+	0.683967i	−0.950873	−	0.309582i	$-0.899811\pi$
$419$	−21.7851	+	14.0005i	−1.06427	+	0.683967i	−0.113401	+	0.993549i	$0.536175\pi$
$420$		0			0
$421$	−0.521780	+	3.62906i	−0.0254300	+	0.176870i	−0.998578	−	0.0533109i	$-0.983023\pi$
$421$	−0.521780	+	3.62906i	−0.0254300	+	0.176870i	0.973148	+	0.230181i	$0.0739317\pi$
$422$		0			0
$423$	3.61214	+	2.32138i	0.175628	+	0.112869i
$424$		0			0
$425$	6.10470	+	13.3674i	0.296121	+	0.648415i
$426$		0			0
$427$	0.159686	+	1.11064i	0.00772776	+	0.0537478i
$428$		0			0
$429$	−27.9870	+	8.21773i	−1.35123	+	0.396756i
$430$		0			0
$431$	−1.23446	+	1.42465i	−0.0594620	+	0.0686228i	−0.784701	−	0.619874i	$-0.787184\pi$
$431$	−1.23446	+	1.42465i	−0.0594620	+	0.0686228i	0.725239	+	0.688497i	$0.241729\pi$
$432$		0			0
$433$	18.5840	+	21.4471i	0.893090	+	1.03068i	0.999339	+	0.0363417i	$0.0115705\pi$
$433$	18.5840	+	21.4471i	0.893090	+	1.03068i	−0.106249	+	0.994340i	$0.533884\pi$
$434$		0			0
$435$	−0.892722	+	1.95479i	−0.0428028	+	0.0937250i
$436$		0			0
$437$	18.8780	+	10.4659i	0.903059	+	0.500654i
$438$		0			0
$439$	−14.2972	+	31.3064i	−0.682366	+	1.49417i	0.177750	+	0.984076i	$0.443118\pi$
$439$	−14.2972	+	31.3064i	−0.682366	+	1.49417i	−0.860116	+	0.510098i	$0.829609\pi$
$440$		0			0
$441$	4.54470	+	5.24486i	0.216414	+	0.249755i
$442$		0			0
$443$	4.63229	−	5.34595i	0.220087	−	0.253994i	−0.634959	−	0.772545i	$-0.718983\pi$
$443$	4.63229	−	5.34595i	0.220087	−	0.253994i	0.855046	+	0.518552i	$0.173529\pi$
$444$		0			0
$445$	0.964572	−	0.283224i	0.0457251	−	0.0134261i
$446$		0			0
$447$	0.273719	+	1.90376i	0.0129465	+	0.0900446i
$448$		0			0
$449$	4.35180	+	9.52911i	0.205374	+	0.449706i	0.984090	−	0.177670i	$-0.0568560\pi$
$449$	4.35180	+	9.52911i	0.205374	+	0.449706i	−0.778716	+	0.627376i	$0.784129\pi$
$450$		0			0
$451$	51.2908	+	32.9626i	2.41519	+	1.55215i
$452$		0			0
$453$	−2.62827	+	18.2800i	−0.123487	+	0.858870i
$454$		0			0
$455$	−0.254808	+	0.163755i	−0.0119456	+	0.00767695i
$456$		0			0
$457$	−39.0361	−	11.4620i	−1.82603	−	0.536171i	−0.826393	−	0.563094i	$-0.809611\pi$
$457$	−39.0361	−	11.4620i	−1.82603	−	0.536171i	−0.999637	+	0.0269235i	$0.991429\pi$
$458$		0			0
$459$	−2.96975			−0.138616
$460$		0			0
$461$	−25.4025			−1.18311			−0.591556	−	0.806264i	$-0.701486\pi$
$461$	−25.4025			−1.18311			−0.591556	+	0.806264i	$0.701486\pi$
$462$		0			0
$463$	−31.6924	−	9.30573i	−1.47287	−	0.432474i	−0.555840	−	0.831289i	$-0.687603\pi$
$463$	−31.6924	−	9.30573i	−1.47287	−	0.432474i	−0.917031	+	0.398815i	$0.869421\pi$
$464$		0			0
$465$	−0.677176	+	0.435195i	−0.0314033	+	0.0201817i
$466$		0			0
$467$	−2.72729	+	18.9687i	−0.126204	+	0.877768i	0.824100	+	0.566444i	$0.191681\pi$
$467$	−2.72729	+	18.9687i	−0.126204	+	0.877768i	−0.950304	+	0.311324i	$0.899228\pi$
$468$		0			0
$469$	−0.511702	−	0.328851i	−0.0236282	−	0.0151849i
$470$		0			0
$471$	−2.72698	−	5.97125i	−0.125652	−	0.275141i
$472$		0			0
$473$	−8.02084	−	55.7861i	−0.368798	−	2.56505i
$474$		0			0
$475$	−21.3695	+	6.27465i	−0.980500	+	0.287901i
$476$		0			0
$477$	−7.82654	+	9.03231i	−0.358353	+	0.413561i
$478$		0			0
$479$	−23.9295	−	27.6161i	−1.09337	−	1.26181i	−0.962754	−	0.270378i	$-0.912851\pi$
$479$	−23.9295	−	27.6161i	−1.09337	−	1.26181i	−0.130612	−	0.991434i	$-0.541694\pi$
$480$		0			0
$481$	6.26377	−	13.7157i	0.285603	−	0.625384i
$482$		0			0
$483$	−0.0913577	+	1.17168i	−0.00415692	+	0.0533131i
$484$		0			0
$485$	−0.724832	+	1.58716i	−0.0329129	+	0.0720693i
$486$		0			0
$487$	−11.5725	−	13.3554i	−0.524401	−	0.605191i	0.430326	−	0.902673i	$-0.358398\pi$
$487$	−11.5725	−	13.3554i	−0.524401	−	0.605191i	−0.954727	+	0.297482i	$0.903853\pi$
$488$		0			0
$489$	−7.05069	+	8.13693i	−0.318843	+	0.367965i
$490$		0			0
$491$	−16.1490	+	4.74177i	−0.728794	+	0.213993i	−0.625021	−	0.780608i	$-0.714910\pi$
$491$	−16.1490	+	4.74177i	−0.728794	+	0.213993i	−0.103773	+	0.994601i	$0.533091\pi$
$492$		0			0
$493$	−3.99734	−	27.8021i	−0.180031	−	1.25214i
$494$		0			0
$495$	0.506100	+	1.10820i	0.0227475	+	0.0498101i
$496$		0			0
$497$	0.648818	+	0.416970i	0.0291034	+	0.0187036i
$498$		0			0
$499$	−2.31818	+	16.1233i	−0.103776	+	0.721777i	0.869798	+	0.493407i	$0.164249\pi$
$499$	−2.31818	+	16.1233i	−0.103776	+	0.721777i	−0.973574	+	0.228370i	$0.926660\pi$
$500$		0			0
$501$	6.76383	−	4.34685i	0.302186	−	0.194203i
$502$		0			0
$503$	−21.6174	−	6.34745i	−0.963874	−	0.283019i	−0.238322	−	0.971186i	$-0.576597\pi$
$503$	−21.6174	−	6.34745i	−0.963874	−	0.283019i	−0.725552	+	0.688167i	$0.758416\pi$
$504$		0			0
$505$	−0.791371			−0.0352155
$506$		0			0
$507$	16.5929			0.736914
$508$		0			0
$509$	21.8838	+	6.42567i	0.969983	+	0.284813i	0.728084	−	0.685488i	$-0.240411\pi$
$509$	21.8838	+	6.42567i	0.969983	+	0.284813i	0.241900	+	0.970301i	$0.422229\pi$
$510$		0			0
$511$	−3.43383	+	2.20679i	−0.151904	+	0.0976225i
$512$		0			0
$513$	0.640531	−	4.45499i	0.0282801	−	0.196693i
$514$		0			0
$515$	−0.198840	−	0.127787i	−0.00876196	−	0.00563097i
$516$		0			0
$517$	9.56403	+	20.9423i	0.420626	+	0.921042i
$518$		0			0
$519$	0.118366	+	0.823252i	0.00519568	+	0.0361367i
$520$		0			0
$521$	−20.3345	+	5.97075i	−0.890871	+	0.261583i	−0.694969	−	0.719040i	$-0.744582\pi$
$521$	−20.3345	+	5.97075i	−0.890871	+	0.261583i	−0.195902	+	0.980623i	$0.562764\pi$
$522$		0			0
$523$	11.6596	−	13.4559i	0.509837	−	0.588384i	−0.441220	−	0.897399i	$-0.645454\pi$
$523$	11.6596	−	13.4559i	0.509837	−	0.588384i	0.951057	+	0.309016i	$0.0999995\pi$
$524$		0			0
$525$	−0.794092	−	0.916431i	−0.0346570	−	0.0399963i
$526$		0			0
$527$	4.37062	−	9.57033i	0.190387	−	0.416890i
$528$		0			0
$529$	17.5740	−	14.8376i	0.764088	−	0.645111i
$530$		0			0
$531$	−2.95222	+	6.46446i	−0.128115	+	0.280533i
$532$		0			0
$533$	−40.5073	−	46.7479i	−1.75457	−	2.02488i
$534$		0			0
$535$	−2.74385	+	3.16658i	−0.118627	+	0.136903i
$536$		0			0
$537$	15.8894	−	4.66555i	0.685678	−	0.201333i
$538$		0			0
$539$	5.29576	+	36.8328i	0.228104	+	1.58650i
$540$		0			0
$541$	−11.1520	−	24.4195i	−0.479463	−	1.04988i	−0.982611	−	0.185677i	$-0.940552\pi$
$541$	−11.1520	−	24.4195i	−0.479463	−	1.04988i	0.503148	−	0.864200i	$-0.332175\pi$
$542$		0			0
$543$	−16.3997	−	10.5395i	−0.703779	−	0.452291i
$544$		0			0
$545$	−0.490058	+	3.40843i	−0.0209918	+	0.146001i
$546$		0			0
$547$	−27.3428	+	17.5722i	−1.16909	+	0.751331i	−0.973350	−	0.229324i	$-0.926348\pi$
$547$	−27.3428	+	17.5722i	−1.16909	+	0.751331i	−0.195744	+	0.980655i	$0.562712\pi$
$548$		0			0
$549$	−4.39339	−	1.29002i	−0.187505	−	0.0550565i
$550$		0			0
$551$	42.5688			1.81349
$552$		0			0
$553$	−1.13524			−0.0482752
$554$		0			0
$555$	−0.604275	−	0.177431i	−0.0256500	−	0.00753153i
$556$		0			0
$557$	−29.4532	+	18.9284i	−1.24797	+	0.802022i	−0.986591	−	0.163214i	$-0.947814\pi$
$557$	−29.4532	+	18.9284i	−1.24797	+	0.802022i	−0.261380	+	0.965236i	$0.584178\pi$
$558$		0			0
$559$	−8.13751	+	56.5976i	−0.344180	+	2.39382i
$560$		0			0
$561$	−13.3958	−	8.60894i	−0.565570	−	0.363470i
$562$		0			0
$563$	−6.45207	−	14.1281i	−0.271922	−	0.595427i	0.723572	−	0.690249i	$-0.242499\pi$
$563$	−6.45207	−	14.1281i	−0.271922	−	0.595427i	−0.995494	+	0.0948223i	$0.969772\pi$
$564$		0			0
$565$	−0.265112	−	1.84389i	−0.0111533	−	0.0775732i
$566$		0			0
$567$	0.235126	−	0.0690393i	0.00987438	−	0.00289938i
$568$		0			0
$569$	−15.7011	+	18.1200i	−0.658225	+	0.759632i	−0.982486	−	0.186336i	$-0.940339\pi$
$569$	−15.7011	+	18.1200i	−0.658225	+	0.759632i	0.324261	+	0.945968i	$0.394884\pi$
$570$		0			0
$571$	3.92922	+	4.53456i	0.164433	+	0.189766i	0.831986	−	0.554796i	$-0.187204\pi$
$571$	3.92922	+	4.53456i	0.164433	+	0.189766i	−0.667553	+	0.744562i	$0.732658\pi$
$572$		0			0
$573$	6.39245	−	13.9975i	0.267049	−	0.584755i
$574$		0			0
$575$	−1.84480	+	23.6598i	−0.0769333	+	0.986680i
$576$		0			0
$577$	−4.62053	+	10.1175i	−0.192355	+	0.421199i	−0.981095	−	0.193529i	$-0.938007\pi$
$577$	−4.62053	+	10.1175i	−0.192355	+	0.421199i	0.788740	+	0.614727i	$0.210734\pi$
$578$		0			0
$579$	−4.51191	−	5.20702i	−0.187509	−	0.216397i
$580$		0			0
$581$	0.00284176	−	0.00327956i	0.000117896	−	0.000136059i
$582$		0			0
$583$	−61.4871	+	18.0543i	−2.54654	+	0.747731i
$584$		0			0
$585$	−0.175904	−	1.22344i	−0.00727274	−	0.0505830i
$586$		0			0
$587$	11.3137	+	24.7736i	0.466967	+	1.02251i	0.985844	+	0.167666i	$0.0536229\pi$
$587$	11.3137	+	24.7736i	0.466967	+	1.02251i	−0.518877	+	0.854849i	$0.673650\pi$
$588$		0			0
$589$	13.4140	+	8.62067i	0.552715	+	0.355208i
$590$		0			0
$591$	−2.12847	+	14.8038i	−0.0875535	+	0.608948i
$592$		0			0
$593$	9.78731	−	6.28992i	0.401917	−	0.258296i	−0.324031	−	0.946047i	$-0.605038\pi$
$593$	9.78731	−	6.28992i	0.401917	−	0.258296i	0.725947	+	0.687751i	$0.241402\pi$
$594$		0			0
$595$	−0.158655	−	0.0465852i	−0.00650421	−	0.00190981i
$596$		0			0
$597$	−12.3701			−0.506276
$598$		0			0
$599$	11.6868			0.477508			0.238754	−	0.971080i	$-0.423261\pi$
$599$	11.6868			0.477508			0.238754	+	0.971080i	$0.423261\pi$
$600$		0			0
$601$	−7.92012	−	2.32556i	−0.323068	−	0.0948615i	0.116177	−	0.993229i	$-0.462936\pi$
$601$	−7.92012	−	2.32556i	−0.323068	−	0.0948615i	−0.439246	+	0.898367i	$0.644754\pi$
$602$		0			0
$603$	2.08813	−	1.34196i	0.0850352	−	0.0546488i
$604$		0			0
$605$	−0.573971	+	3.99206i	−0.0233352	+	0.162300i
$606$		0			0
$607$	17.0136	+	10.9340i	0.690561	+	0.443797i	0.838285	−	0.545232i	$-0.183558\pi$
$607$	17.0136	+	10.9340i	0.690561	+	0.443797i	−0.147724	+	0.989029i	$0.547195\pi$
$608$		0			0
$609$	0.962816	+	2.10827i	0.0390153	+	0.0854315i
$610$		0			0
$611$	−3.32415	−	23.1200i	−0.134481	−	0.935334i
$612$		0			0
$613$	11.4687	−	3.36752i	0.463217	−	0.136013i	−0.0417930	−	0.999126i	$-0.513307\pi$
$613$	11.4687	−	3.36752i	0.463217	−	0.136013i	0.505010	+	0.863114i	$0.331489\pi$
$614$		0			0
$615$	−1.69189	+	1.95255i	−0.0682237	+	0.0787343i
$616$		0			0
$617$	23.2599	+	26.8434i	0.936408	+	1.08067i	0.996592	+	0.0824854i	$0.0262858\pi$
$617$	23.2599	+	26.8434i	0.936408	+	1.08067i	−0.0601840	+	0.998187i	$0.519169\pi$
$618$		0			0
$619$	−4.45193	+	9.74837i	−0.178938	+	0.391820i	−0.977754	−	0.209756i	$-0.932733\pi$
$619$	−4.45193	+	9.74837i	−0.178938	+	0.391820i	0.798816	+	0.601576i	$0.205460\pi$
$620$		0			0
$621$	−4.19437	−	2.32535i	−0.168314	−	0.0933131i
$622$		0			0
$623$	0.450404	−	0.986247i	0.0180450	−	0.0395131i
$624$		0			0
$625$	−15.8661	−	18.3105i	−0.634646	−	0.732421i
$626$		0			0
$627$	15.8038	−	18.2385i	0.631142	−	0.728377i
$628$		0			0
$629$	7.89808	−	2.31908i	0.314917	−	0.0924680i
$630$		0			0
$631$	0.930747	+	6.47349i	0.0370525	+	0.257706i	0.999925	−	0.0122510i	$-0.00389972\pi$
$631$	0.930747	+	6.47349i	0.0370525	+	0.257706i	−0.962872	+	0.269957i	$0.912991\pi$
$632$		0			0
$633$	0.667665	+	1.46198i	0.0265373	+	0.0581086i
$634$		0			0
$635$	2.31709	+	1.48910i	0.0919509	+	0.0590932i
$636$		0			0
$637$	5.37279	−	37.3686i	0.212878	−	1.48060i
$638$		0			0
$639$	−2.64767	+	1.70155i	−0.104740	+	0.0673123i
$640$		0			0
$641$	28.7947	+	8.45489i	1.13732	+	0.333948i	0.795582	−	0.605846i	$-0.207165\pi$
$641$	28.7947	+	8.45489i	1.13732	+	0.333948i	0.341741	+	0.939794i	$0.388983\pi$
$642$		0			0
$643$	−30.1282			−1.18814			−0.594071	−	0.804413i	$-0.702480\pi$
$643$	−30.1282			−1.18814			−0.594071	+	0.804413i	$0.702480\pi$
$644$		0			0
$645$	2.38825			0.0940374
$646$		0			0
$647$	−12.7561	−	3.74553i	−0.501494	−	0.147252i	0.0211949	−	0.999775i	$-0.493253\pi$
$647$	−12.7561	−	3.74553i	−0.501494	−	0.147252i	−0.522689	+	0.852523i	$0.675071\pi$
$648$		0			0
$649$	−32.0564	+	20.6014i	−1.25832	+	0.808676i
$650$		0			0
$651$	−0.123553	+	0.859327i	−0.00484241	+	0.0336797i
$652$		0			0
$653$	−3.03032	−	1.94747i	−0.118586	−	0.0762104i	0.480003	−	0.877267i	$-0.340635\pi$
$653$	−3.03032	−	1.94747i	−0.118586	−	0.0762104i	−0.598589	+	0.801056i	$0.704272\pi$
$654$		0			0
$655$	0.195012	+	0.427017i	0.00761976	+	0.0166849i
$656$		0			0
$657$	−2.37051	−	16.4873i	−0.0924825	−	0.643230i
$658$		0			0
$659$	23.3477	−	6.85552i	0.909499	−	0.267053i	0.206669	−	0.978411i	$-0.433738\pi$
$659$	23.3477	−	6.85552i	0.909499	−	0.267053i	0.702830	+	0.711358i	$0.251919\pi$
$660$		0			0
$661$	24.3080	−	28.0529i	0.945470	−	1.09113i	−0.0502521	−	0.998737i	$-0.516002\pi$
$661$	24.3080	−	28.0529i	0.945470	−	1.09113i	0.995722	−	0.0923944i	$-0.0294521\pi$
$662$		0			0
$663$	10.5794	+	12.2093i	0.410870	+	0.474170i
$664$		0			0
$665$	0.104103	−	0.227954i	0.00403695	−	0.00883969i
$666$		0			0
$667$	16.1237	−	42.3968i	0.624313	−	1.64161i
$668$		0			0
$669$	−11.8133	+	25.8675i	−0.456729	+	1.00010i
$670$		0			0
$671$	−16.0779	−	18.5549i	−0.620680	−	0.716302i
$672$		0			0
$673$	5.05564	−	5.83452i	0.194881	−	0.224904i	−0.649896	−	0.760023i	$-0.725188\pi$
$673$	5.05564	−	5.83452i	0.194881	−	0.224904i	0.844777	+	0.535119i	$0.179733\pi$
$674$		0			0
$675$	4.74793	−	1.39412i	0.182748	−	0.0536596i
$676$		0			0
$677$	−1.98300	−	13.7921i	−0.0762128	−	0.530072i	−0.991785	−	0.127918i	$-0.959171\pi$
$677$	−1.98300	−	13.7921i	−0.0762128	−	0.530072i	0.915572	−	0.402154i	$-0.131738\pi$
$678$		0			0
$679$	0.781744	+	1.71178i	0.0300006	+	0.0656921i
$680$		0			0
$681$	−13.3324	−	8.56820i	−0.510898	−	0.328334i
$682$		0			0
$683$	−0.382916	+	2.66324i	−0.0146519	+	0.101906i	−0.995835	−	0.0911731i	$-0.970938\pi$
$683$	−0.382916	+	2.66324i	−0.0146519	+	0.101906i	0.981183	+	0.193079i	$0.0618474\pi$
$684$		0			0
$685$	−0.309853	+	0.199131i	−0.0118389	+	0.00760839i
$686$		0			0
$687$	14.6802	+	4.31048i	0.560083	+	0.164455i
$688$		0			0
$689$	65.0151			2.47688
$690$		0			0
$691$	18.7277			0.712434			0.356217	−	0.934403i	$-0.384066\pi$
$691$	18.7277			0.712434			0.356217	+	0.934403i	$0.384066\pi$
$692$		0			0
$693$	1.26073	+	0.370184i	0.0478913	+	0.0140621i
$694$		0			0
$695$	−3.48873	+	2.24207i	−0.132335	+	0.0850467i
$696$		0			0
$697$	4.80574	−	33.4247i	0.182030	−	1.26605i
$698$		0			0
$699$	−11.1289	−	7.15210i	−0.420933	−	0.270517i
$700$		0			0
$701$	−17.2976	−	37.8764i	−0.653320	−	1.43057i	−0.888618	−	0.458649i	$-0.848334\pi$
$701$	−17.2976	−	37.8764i	−0.653320	−	1.43057i	0.235297	−	0.971923i	$-0.424394\pi$
$702$		0			0
$703$	1.77542	+	12.3483i	0.0669612	+	0.465725i
$704$		0			0
$705$	−0.936077	+	0.274857i	−0.0352547	+	0.0103517i
$706$		0			0
$707$	−0.558928	+	0.645037i	−0.0210206	+	0.0242591i
$708$		0			0
$709$	−6.20570	−	7.16176i	−0.233060	−	0.268966i	0.627158	−	0.778892i	$-0.284218\pi$
$709$	−6.20570	−	7.16176i	−0.233060	−	0.268966i	−0.860218	+	0.509927i	$0.829673\pi$
$710$		0			0
$711$	1.92446	−	4.21398i	0.0721729	−	0.158037i
$712$		0			0
$713$	13.6666	−	10.0946i	0.511819	−	0.378044i
$714$		0			0
$715$	2.75315	−	6.02856i	0.102962	−	0.225455i
$716$		0			0
$717$	0.238369	+	0.275093i	0.00890206	+	0.0102735i
$718$		0			0
$719$	8.30889	−	9.58897i	0.309869	−	0.357608i	−0.579359	−	0.815073i	$-0.696697\pi$
$719$	8.30889	−	9.58897i	0.309869	−	0.357608i	0.889228	+	0.457465i	$0.151242\pi$
$720$		0			0
$721$	−0.244594	+	0.0718194i	−0.00910917	+	0.00267469i
$722$		0			0
$723$	0.770980	+	5.36229i	0.0286731	+	0.199426i
$724$		0			0
$725$	19.4422	+	42.5726i	0.722067	+	1.58111i
$726$		0			0
$727$	5.34636	+	3.43590i	0.198286	+	0.127430i	0.636016	−	0.771676i	$-0.280581\pi$
$727$	5.34636	+	3.43590i	0.198286	+	0.127430i	−0.437730	+	0.899106i	$0.644218\pi$
$728$		0			0
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$		0			0
$731$	−26.2600	+	16.8763i	−0.971260	+	0.624191i
$732$		0			0
$733$	37.6756	+	11.0625i	1.39158	+	0.408604i	0.889784	−	0.456382i	$-0.150855\pi$
$733$	37.6756	+	11.0625i	1.39158	+	0.408604i	0.501795	+	0.864987i	$0.332673\pi$
$734$		0			0
$735$	−1.57684			−0.0581628
$736$		0			0
$737$	13.3092			0.490251
$738$		0			0
$739$	18.2287	+	5.35242i	0.670552	+	0.196892i	0.599249	−	0.800563i	$-0.295466\pi$
$739$	18.2287	+	5.35242i	0.670552	+	0.196892i	0.0713034	+	0.997455i	$0.477284\pi$
$740$		0			0
$741$	−20.5973	+	13.2371i	−0.756661	+	0.486277i
$742$		0			0
$743$	−1.64803	+	11.4623i	−0.0604603	+	0.420510i	0.937003	+	0.349322i	$0.113588\pi$
$743$	−1.64803	+	11.4623i	−0.0604603	+	0.420510i	−0.997463	+	0.0711881i	$0.977321\pi$
$744$		0			0
$745$	−0.367633	−	0.236263i	−0.0134690	−	0.00865601i
$746$		0			0
$747$	0.00735633	+	0.0161081i	0.000269154	+	0.000589365i
$748$		0			0
$749$	0.643116	+	4.47297i	0.0234989	+	0.163439i
$750$		0			0
$751$	−0.762637	+	0.223930i	−0.0278290	+	0.00817133i	−0.295617	−	0.955306i	$-0.595525\pi$
$751$	−0.762637	+	0.223930i	−0.0278290	+	0.00817133i	0.267788	+	0.963478i	$0.413707\pi$
$752$		0			0
$753$	−16.5537	+	19.1040i	−0.603252	+	0.696189i
$754$		0			0
$755$	−2.74790	−	3.17125i	−0.100006	−	0.115414i
$756$		0			0
$757$	1.52729	−	3.34430i	0.0555103	−	0.121551i	−0.879844	−	0.475262i	$-0.842353\pi$
$757$	1.52729	−	3.34430i	0.0555103	−	0.121551i	0.935355	+	0.353712i	$0.115081\pi$
$758$		0			0
$759$	−12.1788	−	22.6481i	−0.442064	−	0.822072i
$760$		0			0
$761$	2.31026	−	5.05877i	0.0837470	−	0.183380i	−0.863126	−	0.504989i	$-0.831496\pi$
$761$	2.31026	−	5.05877i	0.0837470	−	0.183380i	0.946873	+	0.321609i	$0.104224\pi$
$762$		0			0
$763$	2.43206	+	2.80674i	0.0880463	+	0.101611i
$764$		0			0
$765$	0.441876	−	0.509953i	0.0159761	−	0.0184374i
$766$		0			0
$767$	37.0938	−	10.8917i	1.33938	−	0.393277i
$768$		0			0
$769$	5.13550	+	35.7182i	0.185191	+	1.28803i	0.844254	+	0.535944i	$0.180044\pi$
$769$	5.13550	+	35.7182i	0.185191	+	1.28803i	−0.659063	+	0.752088i	$0.729047\pi$
$770$		0			0
$771$	−7.79792	−	17.0751i	−0.280835	−	0.614943i
$772$		0			0
$773$	36.1393	+	23.2253i	1.29984	+	0.835357i	0.993195	−	0.116467i	$-0.0371569\pi$
$773$	36.1393	+	23.2253i	1.29984	+	0.835357i	0.306646	+	0.951824i	$0.400793\pi$
$774$		0			0
$775$	−2.49491	+	17.3525i	−0.0896198	+	0.623319i
$776$		0			0
$777$	−0.571408	+	0.367222i	−0.0204992	+	0.0131740i
$778$		0			0
$779$	49.1047	+	14.4184i	1.75936	+	0.516594i
$780$		0			0
$781$	−16.8755			−0.603855
$782$		0			0
$783$	−9.45805			−0.338003
$784$		0			0
$785$	1.43111	+	0.420213i	0.0510786	+	0.0149980i
$786$		0			0
$787$	27.7166	−	17.8124i	0.987989	−	0.634942i	0.0563824	−	0.998409i	$-0.482043\pi$
$787$	27.7166	−	17.8124i	0.987989	−	0.634942i	0.931607	+	0.363467i	$0.118407\pi$
$788$		0			0
$789$	−3.24554	+	22.5733i	−0.115544	+	0.803629i
$790$		0			0
$791$	−1.69018	−	1.08621i	−0.0600959	−	0.0386213i
$792$		0			0
$793$	10.3475	+	22.6578i	0.367449	+	0.804601i
$794$		0			0
$795$	−0.386459	−	2.68788i	−0.0137063	−	0.0953294i
$796$		0			0
$797$	−26.0430	+	7.64693i	−0.922492	+	0.270868i	−0.708290	−	0.705921i	$-0.750533\pi$
$797$	−26.0430	+	7.64693i	−0.922492	+	0.270868i	−0.214202	+	0.976789i	$0.568715\pi$
$798$		0			0
$799$	8.35036	−	9.63683i	0.295415	−	0.340927i
$800$		0			0
$801$	2.89740	+	3.34378i	0.102375	+	0.118147i
$802$		0			0
$803$	37.1019	−	81.2418i	1.30930	−	2.86696i
$804$		0			0
$805$	−0.187602	−	0.190024i	−0.00661210	−	0.00669747i
$806$		0			0
$807$	−3.65826	+	8.01048i	−0.128777	+	0.281982i
$808$		0			0
$809$	−0.935245	−	1.07933i	−0.0328815	−	0.0379472i	0.739071	−	0.673628i	$-0.235265\pi$
$809$	−0.935245	−	1.07933i	−0.0328815	−	0.0379472i	−0.771952	+	0.635681i	$0.780719\pi$
$810$		0			0
$811$	−3.03034	+	3.49720i	−0.106410	+	0.122803i	−0.806456	−	0.591294i	$-0.798617\pi$
$811$	−3.03034	+	3.49720i	−0.106410	+	0.122803i	0.700046	+	0.714098i	$0.253163\pi$
$812$		0			0
$813$	13.9399	−	4.09312i	0.488893	−	0.143552i
$814$		0			0
$815$	−0.348149	−	2.42143i	−0.0121951	−	0.0848190i
$816$		0			0
$817$	−19.6526	−	43.0332i	−0.687558	−	1.50554i
$818$		0			0
$819$	−1.12145	−	0.720712i	−0.0391866	−	0.0251837i
$820$		0			0
$821$	−5.26765	+	36.6373i	−0.183842	+	1.27865i	0.663731	+	0.747971i	$0.268972\pi$
$821$	−5.26765	+	36.6373i	−0.183842	+	1.27865i	−0.847573	+	0.530679i	$0.821937\pi$
$822$		0			0
$823$	−15.0942	+	9.70047i	−0.526151	+	0.338137i	−0.776601	−	0.629993i	$-0.783058\pi$
$823$	−15.0942	+	9.70047i	−0.526151	+	0.338137i	0.250450	+	0.968130i	$0.419422\pi$
$824$		0			0
$825$	25.4581	+	7.47517i	0.886337	+	0.260252i
$826$		0			0
$827$	29.3163			1.01943			0.509714	−	0.860344i	$-0.329751\pi$
$827$	29.3163			1.01943			0.509714	+	0.860344i	$0.329751\pi$
$828$		0			0
$829$	6.26141			0.217468			0.108734	−	0.994071i	$-0.465320\pi$
$829$	6.26141			0.217468			0.108734	+	0.994071i	$0.465320\pi$
$830$		0			0
$831$	−14.5280	−	4.26581i	−0.503971	−	0.147979i
$832$		0			0
$833$	17.3381	−	11.1425i	0.600731	−	0.386066i
$834$		0			0
$835$	−0.259985	+	1.80824i	−0.00899715	+	0.0625766i
$836$		0			0
$837$	−2.98036	−	1.91536i	−0.103016	−	0.0662046i
$838$		0			0
$839$	6.01438	+	13.1697i	0.207639	+	0.454667i	0.984586	−	0.174899i	$-0.0559599\pi$
$839$	6.01438	+	13.1697i	0.207639	+	0.454667i	−0.776947	+	0.629566i	$0.783233\pi$
$840$		0			0
$841$	−8.60361	−	59.8394i	−0.296676	−	2.06343i
$842$		0			0
$843$	−5.51422	+	1.61912i	−0.189920	+	0.0557655i
$844$		0			0
$845$	−2.46889	+	2.84926i	−0.0849326	+	0.0980174i
$846$		0			0
$847$	2.84850	+	3.28734i	0.0978755	+	0.112954i
$848$		0			0
$849$	8.06987	−	17.6705i	0.276957	−	0.606452i
$850$		0			0
$851$	12.9709	+	2.90890i	0.444635	+	0.0997158i
$852$		0			0
$853$	−4.41548	+	9.66856i	−0.151183	+	0.331045i	−0.970037	−	0.242957i	$-0.921883\pi$
$853$	−4.41548	+	9.66856i	−0.151183	+	0.331045i	0.818854	+	0.574002i	$0.194610\pi$
$854$		0			0
$855$	0.669687	+	0.772860i	0.0229028	+	0.0264312i
$856$		0			0
$857$	−25.1051	+	28.9729i	−0.857575	+	0.989694i	−1.00000		0.000111584i	$-0.999964\pi$
$857$	−25.1051	+	28.9729i	−0.857575	+	0.989694i	0.142425	+	0.989806i	$0.454510\pi$
$858$		0			0
$859$	−39.7626	+	11.6754i	−1.35668	+	0.398358i	−0.877592	−	0.479408i	$-0.840852\pi$
$859$	−39.7626	+	11.6754i	−1.35668	+	0.398358i	−0.479090	+	0.877766i	$0.659033\pi$
$860$		0			0
$861$	0.396553	+	2.75808i	0.0135145	+	0.0939952i
$862$		0			0
$863$	−7.66784	−	16.7902i	−0.261016	−	0.571546i	0.733068	−	0.680155i	$-0.238088\pi$
$863$	−7.66784	−	16.7902i	−0.261016	−	0.571546i	−0.994085	+	0.108609i	$0.965360\pi$
$864$		0			0
$865$	−0.158977	−	0.102169i	−0.00540539	−	0.00347383i
$866$		0			0
$867$	1.16422	−	8.09734i	0.0395391	−	0.275000i
$868$		0			0
$869$	20.8966	−	13.4294i	0.708868	−	0.455562i
$870$		0			0
$871$	−12.9558	−	3.80418i	−0.438992	−	0.128900i
$872$		0			0
$873$	−7.67932			−0.259906
$874$		0			0
$875$	0.553916			0.0187258
$876$		0			0
$877$	25.7387	+	7.55757i	0.869134	+	0.255201i	0.685747	−	0.727840i	$-0.259476\pi$
$877$	25.7387	+	7.55757i	0.869134	+	0.255201i	0.183387	+	0.983041i	$0.441294\pi$
$878$		0			0
$879$	14.3391	−	9.21518i	0.483646	−	0.310820i
$880$		0			0
$881$	5.82427	−	40.5087i	0.196225	−	1.36477i	−0.618892	−	0.785476i	$-0.712418\pi$
$881$	5.82427	−	40.5087i	0.196225	−	1.36477i	0.815117	−	0.579296i	$-0.196673\pi$
$882$		0			0
$883$	−3.19692	−	2.05454i	−0.107585	−	0.0691406i	0.485742	−	0.874102i	$-0.338549\pi$
$883$	−3.19692	−	2.05454i	−0.107585	−	0.0691406i	−0.593327	+	0.804962i	$0.702186\pi$
$884$		0			0
$885$	−0.670781	−	1.46881i	−0.0225481	−	0.0493734i
$886$		0			0
$887$	1.33488	+	9.28431i	0.0448210	+	0.311737i	0.999883	+	0.0153291i	$0.00487961\pi$
$887$	1.33488	+	9.28431i	0.0448210	+	0.311737i	−0.955062	+	0.296408i	$0.904211\pi$
$888$		0			0
$889$	2.85026	−	0.836912i	0.0955947	−	0.0280691i
$890$		0			0
$891$	−3.51132	+	4.05228i	−0.117634	+	0.135757i
$892$		0			0
$893$	12.6554	+	14.6051i	0.423497	+	0.488742i
$894$		0			0
$895$	−1.56308	+	3.42266i	−0.0522479	+	0.114407i
$896$		0			0
$897$	5.38198	+	25.5278i	0.179699	+	0.852349i
$898$		0			0
$899$	13.9196	−	30.4796i	0.464244	−	1.01655i
$900$		0			0
$901$	23.2428	+	26.8237i	0.774331	+	0.893626i
$902$		0			0
$903$	1.68677	−	1.94664i	0.0561322	−	0.0647801i
$904$		0			0
$905$	4.24995	−	1.24790i	0.141273	−	0.0414815i
$906$		0			0
$907$	−4.27678	−	29.7457i	−0.142008	−	0.987688i	−0.928829	−	0.370507i	$-0.879184\pi$
$907$	−4.27678	−	29.7457i	−0.142008	−	0.987688i	0.786821	−	0.617181i	$-0.211725\pi$
$908$		0			0
$909$	−1.44687	−	3.16820i	−0.0479896	−	0.105083i
$910$		0			0
$911$	23.2568	+	14.9462i	0.770531	+	0.495190i	0.865879	−	0.500254i	$-0.166760\pi$
$911$	23.2568	+	14.9462i	0.770531	+	0.495190i	−0.0953480	+	0.995444i	$0.530396\pi$
$912$		0			0
$913$	−0.0135130	+	0.0939847i	−0.000447214	+	0.00311044i
$914$		0			0
$915$	0.875221	−	0.562470i	0.0289339	−	0.0185947i
$916$		0			0
$917$	0.485790	+	0.142641i	0.0160422	+	0.00471041i
$918$		0			0
$919$	−35.0421			−1.15593			−0.577966	−	0.816061i	$-0.696153\pi$
$919$	−35.0421			−1.15593			−0.577966	+	0.816061i	$0.696153\pi$
$920$		0			0
$921$	0.822538			0.0271036
$922$		0			0
$923$	16.4275	+	4.82355i	0.540718	+	0.158769i
$924$		0			0
$925$	−11.5385	+	7.41535i	−0.379384	+	0.243815i
$926$		0			0
$927$	0.148046	−	1.02968i	0.00486245	−	0.0338191i
$928$		0			0
$929$	−5.05432	−	3.24821i	−0.165827	−	0.106570i	0.455095	−	0.890443i	$-0.349605\pi$
$929$	−5.05432	−	3.24821i	−0.165827	−	0.106570i	−0.620922	+	0.783872i	$0.713242\pi$
$930$		0			0
$931$	12.9756	+	28.4127i	0.425259	+	0.931188i
$932$		0			0
$933$	−0.616884	−	4.29052i	−0.0201959	−	0.140465i
$934$		0			0
$935$	3.47149	−	1.01932i	0.113530	−	0.0333353i
$936$		0			0
$937$	12.3208	−	14.2189i	0.402502	−	0.464512i	−0.517925	−	0.855426i	$-0.673295\pi$
$937$	12.3208	−	14.2189i	0.402502	−	0.464512i	0.920427	+	0.390914i	$0.127841\pi$
$938$		0			0
$939$	−2.57663	−	2.97359i	−0.0840851	−	0.0970394i
$940$		0			0
$941$	9.58498	−	20.9882i	0.312462	−	0.684195i	−0.686621	−	0.727015i	$-0.740907\pi$
$941$	9.58498	−	20.9882i	0.312462	−	0.684195i	0.999083	+	0.0428199i	$0.0136342\pi$
$942$		0			0
$943$	32.9594	−	43.4449i	1.07331	−	1.41476i
$944$		0			0
$945$	−0.0231299	+	0.0506475i	−0.000752417	+	0.00164756i
$946$		0			0
$947$	27.3952	+	31.6157i	0.890224	+	1.02737i	0.999444	+	0.0333551i	$0.0106192\pi$
$947$	27.3952	+	31.6157i	0.890224	+	1.02737i	−0.109220	+	0.994018i	$0.534835\pi$
$948$		0			0
$949$	−59.3382	+	68.4799i	−1.92620	+	2.22295i
$950$		0			0
$951$	15.8549	−	4.65543i	0.514131	−	0.150963i
$952$		0			0
$953$	6.36580	+	44.2751i	0.206208	+	1.43421i	0.785385	+	0.619008i	$0.212465\pi$
$953$	6.36580	+	44.2751i	0.206208	+	1.43421i	−0.579176	+	0.815202i	$0.696626\pi$
$954$		0			0
$955$	1.45245	+	3.18041i	0.0470001	+	0.102916i
$956$		0			0
$957$	−42.6629	−	27.4178i	−1.37910	−	0.886291i
$958$		0			0
$959$	−0.0565335	+	0.393199i	−0.00182556	+	0.0126971i
$960$		0			0
$961$	−15.5201	+	9.97419i	−0.500650	+	0.321748i
$962$		0			0
$963$	−17.6938	−	5.19537i	−0.570175	−	0.167418i
$964$		0			0
$965$	1.56547			0.0503942
$966$		0			0
$967$	−54.1383			−1.74097			−0.870485	−	0.492195i	$-0.836195\pi$
$967$	−54.1383			−1.74097			−0.870485	+	0.492195i	$0.836195\pi$
$968$		0			0
$969$	−12.8248	−	3.76571i	−0.411993	−	0.120972i
$970$		0			0
$971$	45.0105	−	28.9265i	1.44446	−	0.928295i	0.444992	−	0.895535i	$-0.353207\pi$
$971$	45.0105	−	28.9265i	1.44446	−	0.928295i	0.999463	−	0.0327605i	$-0.0104299\pi$
$972$		0			0
$973$	−0.636529	+	4.42716i	−0.0204062	+	0.141928i
$974$		0			0
$975$	−22.6455	−	14.5534i	−0.725238	−	0.466082i
$976$		0			0
$977$	−11.8613	−	25.9726i	−0.379477	−	0.830938i	−0.998945	−	0.0459168i	$-0.985379\pi$
$977$	−11.8613	−	25.9726i	−0.379477	−	0.830938i	0.619468	−	0.785022i	$-0.287348\pi$
$978$		0			0
$979$	3.37623	+	23.4822i	0.107905	+	0.750494i
$980$		0			0
$981$	−14.5414	+	4.26975i	−0.464272	+	0.136322i
$982$		0			0
$983$	−14.9771	+	17.2845i	−0.477696	+	0.551290i	−0.942536	−	0.334104i	$-0.891566\pi$
$983$	−14.9771	+	17.2845i	−0.477696	+	0.551290i	0.464841	+	0.885394i	$0.346112\pi$
$984$		0			0
$985$	−2.22535	−	2.56819i	−0.0709056	−	0.0818295i
$986$		0			0
$987$	−0.437098	+	0.957111i	−0.0139130	+	0.0304652i
$988$		0			0
$989$	−50.3030	+	3.27356i	−1.59954	+	0.104093i
$990$		0			0
$991$	1.21961	−	2.67057i	0.0387422	−	0.0848335i	−0.889271	−	0.457380i	$-0.848788\pi$
$991$	1.21961	−	2.67057i	0.0387422	−	0.0848335i	0.928014	+	0.372546i	$0.121515\pi$
$992$		0			0
$993$	14.0620	+	16.2284i	0.446245	+	0.514994i
$994$		0			0
$995$	1.84059	−	2.12415i	0.0583505	−	0.0673401i
$996$		0			0
$997$	36.4844	−	10.7128i	1.15547	−	0.339278i	0.352802	−	0.935698i	$-0.385229\pi$
$997$	36.4844	−	10.7128i	1.15547	−	0.339278i	0.802672	+	0.596420i	$0.203411\pi$
$998$		0			0
$999$	−0.394467	−	2.74358i	−0.0124804	−	0.0868029i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.a.121.2	yes	30
23.4	even	11	inner	552.2.q.a.73.2	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.a.73.2	✓	30	23.4	even	11	inner
552.2.q.a.121.2	yes	30	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{3} +(0.191143 - 0.122840i) q^{5} +(0.0348746 - 0.242558i) q^{7} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{3} +(0.191143 - 0.122840i) q^{5} +(0.0348746 - 0.242558i) q^{7} +(0.841254 + 0.540641i) q^{9} +(2.22743 + 4.87739i) q^{11} +(-0.774183 - 5.38456i) q^{13} +(-0.218009 + 0.0640132i) q^{15} +(1.94477 - 2.24438i) q^{17} +(2.94740 + 3.40148i) q^{19} +(-0.101799 + 0.222908i) q^{21} +(4.50411 - 1.64711i) q^{23} +(-2.05563 + 4.50120i) q^{25} +(-0.654861 - 0.755750i) q^{27} +(6.19371 - 7.14792i) q^{29} +(3.39926 - 0.998111i) q^{31} +(-0.763083 - 5.30736i) q^{33} +(-0.0231299 - 0.0506475i) q^{35} +(2.33178 + 1.49854i) q^{37} +(-0.774183 + 5.38456i) q^{39} +(9.56573 - 6.14752i) q^{41} +(-10.0853 - 2.96132i) q^{43} +0.227213 q^{45} +4.29375 q^{47} +(6.65883 + 1.95521i) q^{49} +(-2.49831 + 1.60557i) q^{51} +(-1.70087 + 11.8298i) q^{53} +(1.02490 + 0.658663i) q^{55} +(-1.86970 - 4.09408i) q^{57} +(1.01138 + 7.03434i) q^{59} +(-4.39339 + 1.29002i) q^{61} +(0.160475 - 0.185198i) q^{63} +(-0.809422 - 0.934123i) q^{65} +(1.03113 - 2.25786i) q^{67} +(-4.78571 + 0.311439i) q^{69} +(-1.30743 + 2.86287i) q^{71} +(-10.9079 - 12.5884i) q^{73} +(3.24050 - 3.73973i) q^{75} +(1.26073 - 0.370184i) q^{77} +(-0.659291 - 4.58547i) q^{79} +(0.415415 + 0.909632i) q^{81} +(0.0148972 + 0.00957387i) q^{83} +(0.0960289 - 0.667896i) q^{85} +(-7.95662 + 5.11341i) q^{87} +(4.24524 + 1.24651i) q^{89} -1.33307 q^{91} -3.54276 q^{93} +(0.981216 + 0.288111i) q^{95} +(-6.46026 + 4.15176i) q^{97} +(-0.763083 + 5.30736i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9	\( 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9} - 15 q^{11} + 5 q^{13} - 15 q^{17} + 5 q^{19} + 9 q^{21} + 14 q^{23} + 5 q^{25} - 3 q^{27} + 13 q^{29} - 29 q^{31} - 15 q^{33} + 8 q^{35} - 3 q^{37} + 5 q^{39} + 24 q^{41} + 2 q^{43} + 22 q^{45} + 38 q^{47} + 15 q^{49} + 7 q^{51} - 7 q^{53} + 46 q^{55} - 6 q^{57} - 43 q^{59} - 22 q^{61} - 2 q^{63} + 44 q^{65} + 31 q^{67} + 3 q^{69} + 19 q^{71} - 50 q^{73} + 5 q^{75} + 16 q^{77} - 84 q^{79} - 3 q^{81} - 73 q^{83} - 8 q^{85} + 2 q^{87} + 19 q^{89} + 18 q^{91} + 26 q^{93} - 67 q^{95} - 29 q^{97} - 15 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9 - 15 * q^11 + 5 * q^13 - 15 * q^17 + 5 * q^19 + 9 * q^21 + 14 * q^23 + 5 * q^25 - 3 * q^27 + 13 * q^29 - 29 * q^31 - 15 * q^33 + 8 * q^35 - 3 * q^37 + 5 * q^39 + 24 * q^41 + 2 * q^43 + 22 * q^45 + 38 * q^47 + 15 * q^49 + 7 * q^51 - 7 * q^53 + 46 * q^55 - 6 * q^57 - 43 * q^59 - 22 * q^61 - 2 * q^63 + 44 * q^65 + 31 * q^67 + 3 * q^69 + 19 * q^71 - 50 * q^73 + 5 * q^75 + 16 * q^77 - 84 * q^79 - 3 * q^81 - 73 * q^83 - 8 * q^85 + 2 * q^87 + 19 * q^89 + 18 * q^91 + 26 * q^93 - 67 * q^95 - 29 * q^97 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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