LMFDB - Embedded newform 804.2.q.a.265.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(25,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("804.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			265.1
Character	$\chi$	$=$	804.265
Dual form			804.2.q.a.625.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{3} +(-1.58453 - 3.46964i) q^{5} +(-2.06192 - 0.605433i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{3} +(-1.58453 - 3.46964i) q^{5} +(-2.06192 - 0.605433i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(1.84542 + 4.04091i) q^{11} +(1.64348 - 1.89668i) q^{13} +(3.65982 - 1.07462i) q^{15} +(-0.242378 + 0.155767i) q^{17} +(-7.01989 + 2.06123i) q^{19} +(0.892712 - 1.95477i) q^{21} +(-1.26830 + 8.82120i) q^{23} +(-6.25334 + 7.21674i) q^{25} +(0.415415 - 0.909632i) q^{27} -4.60526 q^{29} +(-2.40360 - 2.77390i) q^{31} +(-4.26241 + 1.25156i) q^{33} +(1.16653 + 8.11343i) q^{35} -2.36874 q^{37} +(1.64348 + 1.89668i) q^{39} +(3.31071 - 2.12767i) q^{41} +(-9.43402 + 6.06288i) q^{43} +(0.542836 + 3.77551i) q^{45} +(0.201583 - 1.40204i) q^{47} +(-2.00382 - 1.28778i) q^{49} +(-0.119687 - 0.262079i) q^{51} +(5.80027 + 3.72761i) q^{53} +(11.0964 - 12.8059i) q^{55} +(-1.04121 - 7.24178i) q^{57} +(7.04120 + 8.12597i) q^{59} +(0.0163696 - 0.0358445i) q^{61} +(1.80782 + 1.16182i) q^{63} +(-9.18492 - 2.69693i) q^{65} +(-3.55373 - 7.37367i) q^{67} +(-8.55092 - 2.51078i) q^{69} +(-5.82421 - 3.74299i) q^{71} +(0.452695 - 0.991263i) q^{73} +(-6.25334 - 7.21674i) q^{75} +(-1.35860 - 9.44930i) q^{77} +(4.46588 - 5.15390i) q^{79} +(0.841254 + 0.540641i) q^{81} +(-3.37461 - 7.38938i) q^{83} +(0.924510 + 0.594147i) q^{85} +(0.655397 - 4.55839i) q^{87} +(0.782308 + 5.44107i) q^{89} +(-4.53703 + 2.91577i) q^{91} +(3.08773 - 1.98437i) q^{93} +(18.2749 + 21.0904i) q^{95} -5.98837 q^{97} +(-0.632213 - 4.39714i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9}+O(q^{10}) $ 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9	$ 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9} + 7 q^{11} - 2 q^{13} + 9 q^{15} - 19 q^{17} + 2 q^{19} - 2 q^{21} + 4 q^{23} + 16 q^{25} - 6 q^{27} + 16 q^{29} - 28 q^{31} - 4 q^{33} + 28 q^{35} + 2 q^{37} - 2 q^{39} + 32 q^{41} + 19 q^{43} - 2 q^{45} + 2 q^{47} - 70 q^{49} - 19 q^{51} + 31 q^{53} - 5 q^{55} + 13 q^{57} + 59 q^{59} + 32 q^{61} + 9 q^{63} + 28 q^{65} + 7 q^{67} + 4 q^{69} + 16 q^{71} + 19 q^{73} + 16 q^{75} - 46 q^{77} + 48 q^{79} - 6 q^{81} + 60 q^{83} - 66 q^{85} + 5 q^{87} - 22 q^{89} + 24 q^{91} + 5 q^{93} + 103 q^{95} - 46 q^{97} - 4 q^{99}+O(q^{100}) $ 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9 + 7 * q^11 - 2 * q^13 + 9 * q^15 - 19 * q^17 + 2 * q^19 - 2 * q^21 + 4 * q^23 + 16 * q^25 - 6 * q^27 + 16 * q^29 - 28 * q^31 - 4 * q^33 + 28 * q^35 + 2 * q^37 - 2 * q^39 + 32 * q^41 + 19 * q^43 - 2 * q^45 + 2 * q^47 - 70 * q^49 - 19 * q^51 + 31 * q^53 - 5 * q^55 + 13 * q^57 + 59 * q^59 + 32 * q^61 + 9 * q^63 + 28 * q^65 + 7 * q^67 + 4 * q^69 + 16 * q^71 + 19 * q^73 + 16 * q^75 - 46 * q^77 + 48 * q^79 - 6 * q^81 + 60 * q^83 - 66 * q^85 + 5 * q^87 - 22 * q^89 + 24 * q^91 + 5 * q^93 + 103 * q^95 - 46 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{1}{11}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$4$		0			0
$5$	−1.58453	−	3.46964i	−0.708623	−	1.55167i	−0.829192	−	0.558964i	$-0.811199\pi$
$5$	−1.58453	−	3.46964i	−0.708623	−	1.55167i	0.120569	−	0.992705i	$-0.461528\pi$
$6$		0			0
$7$	−2.06192	−	0.605433i	−0.779331	−	0.228832i	−0.132212	−	0.991221i	$-0.542208\pi$
$7$	−2.06192	−	0.605433i	−0.779331	−	0.228832i	−0.647119	+	0.762389i	$0.724026\pi$
$8$		0			0
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$		0			0
$11$	1.84542	+	4.04091i	0.556416	+	1.21838i	0.953721	+	0.300694i	$0.0972182\pi$
$11$	1.84542	+	4.04091i	0.556416	+	1.21838i	−0.397305	+	0.917687i	$0.630055\pi$
$12$		0			0
$13$	1.64348	−	1.89668i	0.455819	−	0.526043i	−0.480594	−	0.876943i	$-0.659579\pi$
$13$	1.64348	−	1.89668i	0.455819	−	0.526043i	0.936413	+	0.350900i	$0.114124\pi$
$14$		0			0
$15$	3.65982	−	1.07462i	0.944962	−	0.277466i
$16$		0			0
$17$	−0.242378	+	0.155767i	−0.0587853	+	0.0377790i	−0.569703	−	0.821850i	$-0.692942\pi$
$17$	−0.242378	+	0.155767i	−0.0587853	+	0.0377790i	0.510918	+	0.859629i	$0.329306\pi$
$18$		0			0
$19$	−7.01989	+	2.06123i	−1.61047	+	0.472878i	−0.958436	−	0.285309i	$-0.907904\pi$
$19$	−7.01989	+	2.06123i	−1.61047	+	0.472878i	−0.652038	+	0.758187i	$0.726086\pi$
$20$		0			0
$21$	0.892712	−	1.95477i	0.194806	−	0.426565i
$22$		0			0
$23$	−1.26830	+	8.82120i	−0.264458	+	1.83935i	0.233758	+	0.972295i	$0.424898\pi$
$23$	−1.26830	+	8.82120i	−0.264458	+	1.83935i	−0.498216	+	0.867053i	$0.666011\pi$
$24$		0			0
$25$	−6.25334	+	7.21674i	−1.25067	+	1.44335i
$26$		0			0
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$		0			0
$29$	−4.60526			−0.855175			−0.427588	−	0.903974i	$-0.640636\pi$
$29$	−4.60526			−0.855175			−0.427588	+	0.903974i	$0.640636\pi$
$30$		0			0
$31$	−2.40360	−	2.77390i	−0.431699	−	0.498207i	0.497666	−	0.867369i	$-0.334190\pi$
$31$	−2.40360	−	2.77390i	−0.431699	−	0.498207i	−0.929365	+	0.369161i	$0.879645\pi$
$32$		0			0
$33$	−4.26241	+	1.25156i	−0.741991	+	0.217868i
$34$		0			0
$35$	1.16653	+	8.11343i	0.197180	+	1.37142i
$36$		0			0
$37$	−2.36874			−0.389419			−0.194710	−	0.980861i	$-0.562376\pi$
$37$	−2.36874			−0.389419			−0.194710	+	0.980861i	$0.562376\pi$
$38$		0			0
$39$	1.64348	+	1.89668i	0.263167	+	0.303711i
$40$		0			0
$41$	3.31071	−	2.12767i	0.517047	−	0.332286i	−0.255956	−	0.966688i	$-0.582390\pi$
$41$	3.31071	−	2.12767i	0.517047	−	0.332286i	0.773003	+	0.634403i	$0.218754\pi$
$42$		0			0
$43$	−9.43402	+	6.06288i	−1.43868	+	0.924580i	−0.439016	+	0.898479i	$0.644673\pi$
$43$	−9.43402	+	6.06288i	−1.43868	+	0.924580i	−0.999659	+	0.0261012i	$0.991691\pi$
$44$		0			0
$45$	0.542836	+	3.77551i	0.0809212	+	0.562819i
$46$		0			0
$47$	0.201583	−	1.40204i	0.0294039	−	0.204509i	−0.969824	−	0.243808i	$-0.921603\pi$
$47$	0.201583	−	1.40204i	0.0294039	−	0.204509i	0.999227	+	0.0392989i	$0.0125125\pi$
$48$		0			0
$49$	−2.00382	−	1.28778i	−0.286261	−	0.183969i
$50$		0			0
$51$	−0.119687	−	0.262079i	−0.0167596	−	0.0366984i
$52$		0			0
$53$	5.80027	+	3.72761i	0.796729	+	0.512027i	0.874547	−	0.484941i	$-0.161159\pi$
$53$	5.80027	+	3.72761i	0.796729	+	0.512027i	−0.0778179	+	0.996968i	$0.524795\pi$
$54$		0			0
$55$	11.0964	−	12.8059i	1.49623	−	1.72675i
$56$		0			0
$57$	−1.04121	−	7.24178i	−0.137912	−	0.959197i
$58$		0			0
$59$	7.04120	+	8.12597i	0.916686	+	1.05791i	0.998123	+	0.0612331i	$0.0195033\pi$
$59$	7.04120	+	8.12597i	0.916686	+	1.05791i	−0.0814379	+	0.996678i	$0.525951\pi$
$60$		0			0
$61$	0.0163696	−	0.0358445i	0.00209592	−	0.00458942i	−0.908581	−	0.417708i	$-0.862833\pi$
$61$	0.0163696	−	0.0358445i	0.00209592	−	0.00458942i	0.910677	+	0.413119i	$0.135561\pi$
$62$		0			0
$63$	1.80782	+	1.16182i	0.227764	+	0.146375i
$64$		0			0
$65$	−9.18492	−	2.69693i	−1.13925	−	0.334514i
$66$		0			0
$67$	−3.55373	−	7.37367i	−0.434157	−	0.900837i
$67$	−3.55373	−	7.37367i	−0.434157	−	0.900837i
$68$		0			0
$69$	−8.55092	−	2.51078i	−1.02941	−	0.302262i
$70$		0			0
$71$	−5.82421	−	3.74299i	−0.691207	−	0.444212i	0.147308	−	0.989091i	$-0.452939\pi$
$71$	−5.82421	−	3.74299i	−0.691207	−	0.444212i	−0.838515	+	0.544879i	$0.816576\pi$
$72$		0			0
$73$	0.452695	−	0.991263i	0.0529839	−	0.116019i	−0.881288	−	0.472579i	$-0.843323\pi$
$73$	0.452695	−	0.991263i	0.0529839	−	0.116019i	0.934272	+	0.356560i	$0.116051\pi$
$74$		0			0
$75$	−6.25334	−	7.21674i	−0.722074	−	0.833317i
$76$		0			0
$77$	−1.35860	−	9.44930i	−0.154827	−	1.07685i
$78$		0			0
$79$	4.46588	−	5.15390i	0.502450	−	0.579859i	−0.446699	−	0.894684i	$-0.647401\pi$
$79$	4.46588	−	5.15390i	0.502450	−	0.579859i	0.949150	+	0.314826i	$0.101946\pi$
$80$		0			0
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$		0			0
$83$	−3.37461	−	7.38938i	−0.370412	−	0.811089i	−0.999432	−	0.0337002i	$-0.989271\pi$
$83$	−3.37461	−	7.38938i	−0.370412	−	0.811089i	0.629020	−	0.777389i	$-0.283456\pi$
$84$		0			0
$85$	0.924510	+	0.594147i	0.100277	+	0.0644443i
$86$		0			0
$87$	0.655397	−	4.55839i	0.0702659	−	0.488710i
$88$		0			0
$89$	0.782308	+	5.44107i	0.0829244	+	0.576752i	0.988344	+	0.152235i	$0.0486471\pi$
$89$	0.782308	+	5.44107i	0.0829244	+	0.576752i	−0.905420	+	0.424517i	$0.860444\pi$
$90$		0			0
$91$	−4.53703	+	2.91577i	−0.475610	+	0.305656i
$92$		0			0
$93$	3.08773	−	1.98437i	0.320183	−	0.205769i
$94$		0			0
$95$	18.2749	+	21.0904i	1.87497	+	2.16383i
$96$		0			0
$97$	−5.98837			−0.608027			−0.304013	−	0.952668i	$-0.598327\pi$
$97$	−5.98837			−0.608027			−0.304013	+	0.952668i	$0.598327\pi$
$98$		0			0
$99$	−0.632213	−	4.39714i	−0.0635398	−	0.441929i
$100$		0			0
$101$	−14.4954	+	4.25624i	−1.44235	+	0.423512i	−0.907004	−	0.421122i	$-0.861636\pi$
$101$	−14.4954	+	4.25624i	−1.44235	+	0.423512i	−0.535345	+	0.844634i	$0.679818\pi$
$102$		0			0
$103$	4.46627	+	5.15435i	0.440075	+	0.507873i	0.931847	−	0.362850i	$-0.118196\pi$
$103$	4.46627	+	5.15435i	0.440075	+	0.507873i	−0.491773	+	0.870724i	$0.663651\pi$
$104$		0			0
$105$	−8.19686			−0.799932
$106$		0			0
$107$	−5.16603	+	11.3120i	−0.499419	+	1.09357i	0.477239	+	0.878773i	$0.341638\pi$
$107$	−5.16603	+	11.3120i	−0.499419	+	1.09357i	−0.976658	+	0.214801i	$0.931090\pi$
$108$		0			0
$109$	10.1640	−	11.7299i	0.973532	−	1.12352i	−0.0187885	−	0.999823i	$-0.505981\pi$
$109$	10.1640	−	11.7299i	0.973532	−	1.12352i	0.992321	−	0.123692i	$-0.0394736\pi$
$110$		0			0
$111$	0.337108	−	2.34463i	0.0319968	−	0.222543i
$112$		0			0
$113$	−6.51667	+	14.2695i	−0.613037	+	1.34236i	0.307441	+	0.951567i	$0.400527\pi$
$113$	−6.51667	+	14.2695i	−0.613037	+	1.34236i	−0.920477	+	0.390796i	$0.872200\pi$
$114$		0			0
$115$	32.6160	−	9.57693i	3.04146	−	0.893053i
$116$		0			0
$117$	−2.11126	+	1.35683i	−0.195186	+	0.125439i
$118$		0			0
$119$	0.594070	−	0.174435i	0.0544583	−	0.0159904i
$120$		0			0
$121$	−5.71991	+	6.60113i	−0.519992	+	0.600102i
$122$		0			0
$123$	1.63485	+	3.57981i	0.147409	+	0.322781i
$124$		0			0
$125$	16.6490	+	4.88857i	1.48913	+	0.437247i
$126$		0			0
$127$	9.13194	+	2.68138i	0.810328	+	0.237934i	0.660547	−	0.750785i	$-0.270325\pi$
$127$	9.13194	+	2.68138i	0.810328	+	0.237934i	0.149782	+	0.988719i	$0.452143\pi$
$128$		0			0
$129$	−4.65857	−	10.2008i	−0.410164	−	0.898134i
$130$		0			0
$131$	1.71375	−	11.9194i	0.149731	−	1.04140i	−0.766928	−	0.641733i	$-0.778216\pi$
$131$	1.71375	−	11.9194i	0.149731	−	1.04140i	0.916659	−	0.399670i	$-0.130875\pi$
$132$		0			0
$133$	15.7224			1.36330
$134$		0			0
$135$	−3.81433			−0.328285
$136$		0			0
$137$	−0.0303986	+	0.211427i	−0.00259713	+	0.0180634i	−0.991079	−	0.133277i	$-0.957450\pi$
$137$	−0.0303986	+	0.211427i	−0.00259713	+	0.0180634i	0.988482	+	0.151341i	$0.0483590\pi$
$138$		0			0
$139$	−5.55102	−	12.1550i	−0.470832	−	1.03098i	−0.984883	−	0.173218i	$-0.944583\pi$
$139$	−5.55102	−	12.1550i	−0.470832	−	1.03098i	0.514052	−	0.857759i	$-0.328144\pi$
$140$		0			0
$141$	1.35908	+	0.399063i	0.114455	+	0.0336072i
$142$		0			0
$143$	10.6972	+	3.14098i	0.894545	+	0.262662i
$144$		0			0
$145$	7.29717	+	15.9786i	0.605997	+	1.32695i
$146$		0			0
$147$	1.55985	−	1.80016i	0.128654	−	0.148475i
$148$		0			0
$149$	−0.601729	+	0.176683i	−0.0492955	+	0.0144745i	−0.306287	−	0.951939i	$-0.599087\pi$
$149$	−0.601729	+	0.176683i	−0.0492955	+	0.0144745i	0.256992	+	0.966414i	$0.417269\pi$
$150$		0			0
$151$	−11.5940	+	7.45102i	−0.943507	+	0.606355i	−0.919387	−	0.393354i	$-0.871315\pi$
$151$	−11.5940	+	7.45102i	−0.943507	+	0.606355i	−0.0241197	+	0.999709i	$0.507678\pi$
$152$		0			0
$153$	0.276445	−	0.0811715i	0.0223492	−	0.00656233i
$154$		0			0
$155$	−5.81586	+	12.7349i	−0.467141	+	1.02290i
$156$		0			0
$157$	1.32296	−	9.20139i	0.105584	−	0.734351i	−0.866408	−	0.499337i	$-0.833577\pi$
$157$	1.32296	−	9.20139i	0.105584	−	0.734351i	0.971992	−	0.235015i	$-0.0755138\pi$
$158$		0			0
$159$	−4.51513	+	5.21074i	−0.358073	+	0.413239i
$160$		0			0
$161$	7.95577	−	17.4207i	0.627003	−	1.37294i
$162$		0			0
$163$	−14.3226			−1.12184			−0.560918	−	0.827871i	$-0.689552\pi$
$163$	−14.3226			−1.12184			−0.560918	+	0.827871i	$0.689552\pi$
$164$		0			0
$165$	11.0964	+	12.8059i	0.863851	+	0.996937i
$166$		0			0
$167$	19.8198	−	5.81963i	1.53370	−	0.450336i	0.597523	−	0.801852i	$-0.296152\pi$
$167$	19.8198	−	5.81963i	1.53370	−	0.450336i	0.936182	+	0.351515i	$0.114334\pi$
$168$		0			0
$169$	0.953737	+	6.63339i	0.0733644	+	0.510261i
$170$		0			0
$171$	7.31625			0.559488
$172$		0			0
$173$	3.15314	+	3.63892i	0.239729	+	0.276662i	0.862846	−	0.505466i	$-0.168680\pi$
$173$	3.15314	+	3.63892i	0.239729	+	0.276662i	−0.623117	+	0.782128i	$0.714134\pi$
$174$		0			0
$175$	17.2631	−	11.0943i	1.30497	−	0.838653i
$176$		0			0
$177$	−9.04533	+	5.81308i	−0.679889	+	0.436938i
$178$		0			0
$179$	−1.65499	−	11.5107i	−0.123700	−	0.860353i	−0.953306	−	0.302005i	$-0.902344\pi$
$179$	−1.65499	−	11.5107i	−0.123700	−	0.860353i	0.829606	−	0.558349i	$-0.188565\pi$
$180$		0			0
$181$	−2.43858	+	16.9607i	−0.181258	+	1.26068i	0.672535	+	0.740065i	$0.265205\pi$
$181$	−2.43858	+	16.9607i	−0.181258	+	1.26068i	−0.853793	+	0.520612i	$0.825704\pi$
$182$		0			0
$183$	0.0331500	+	0.0213042i	0.00245052	+	0.00157485i
$184$		0			0
$185$	3.75335	+	8.21868i	0.275952	+	0.604250i
$186$		0			0
$187$	−1.07673	−	0.691973i	−0.0787383	−	0.0506021i
$188$		0			0
$189$	−1.40727	+	1.62408i	−0.102364	+	0.118134i
$190$		0			0
$191$	−2.96551	−	20.6256i	−0.214577	−	1.49241i	−0.757612	−	0.652705i	$-0.773634\pi$
$191$	−2.96551	−	20.6256i	−0.214577	−	1.49241i	0.543035	−	0.839710i	$-0.317275\pi$
$192$		0			0
$193$	−5.41270	−	6.24659i	−0.389615	−	0.449639i	0.526728	−	0.850034i	$-0.323419\pi$
$193$	−5.41270	−	6.24659i	−0.389615	−	0.449639i	−0.916343	+	0.400394i	$0.868873\pi$
$194$		0			0
$195$	3.97663	−	8.70761i	0.284773	−	0.623565i
$196$		0			0
$197$	−7.31131	−	4.69870i	−0.520909	−	0.334768i	0.253622	−	0.967303i	$-0.418378\pi$
$197$	−7.31131	−	4.69870i	−0.520909	−	0.334768i	−0.774532	+	0.632535i	$0.782014\pi$
$198$		0			0
$199$	7.53107	+	2.21132i	0.533863	+	0.156756i	0.537542	−	0.843237i	$-0.319353\pi$
$199$	7.53107	+	2.21132i	0.533863	+	0.156756i	−0.00367895	+	0.999993i	$0.501171\pi$
$200$		0			0
$201$	7.80437	−	2.46817i	0.550478	−	0.174091i
$202$		0			0
$203$	9.49566	+	2.78818i	0.666465	+	0.195692i
$204$		0			0
$205$	−12.6282	−	8.11562i	−0.881989	−	0.566820i
$206$		0			0
$207$	3.70214	−	8.10656i	0.257317	−	0.563445i
$208$		0			0
$209$	−21.2839	−	24.5629i	−1.47224	−	1.69905i
$210$		0			0
$211$	−2.22742	−	15.4920i	−0.153342	−	1.06651i	−0.910567	−	0.413361i	$-0.864355\pi$
$211$	−2.22742	−	15.4920i	−0.153342	−	1.06651i	0.757226	−	0.653153i	$-0.226554\pi$
$212$		0			0
$213$	4.53377	−	5.23225i	0.310649	−	0.358508i
$214$		0			0
$215$	35.9845	+	23.1258i	2.45412	+	1.57717i
$216$		0			0
$217$	3.27661	+	7.17477i	0.222431	+	0.487055i
$218$		0			0
$219$	0.916748	+	0.589158i	0.0619481	+	0.0398116i
$220$		0			0
$221$	−0.102904	+	0.715712i	−0.00692207	+	0.0481440i
$222$		0			0
$223$	−1.15173	−	8.01048i	−0.0771258	−	0.536422i	−0.991353	−	0.131220i	$-0.958110\pi$
$223$	−1.15173	−	8.01048i	−0.0771258	−	0.536422i	0.914227	−	0.405201i	$-0.132799\pi$
$224$		0			0
$225$	8.03323	−	5.16264i	0.535548	−	0.344176i
$226$		0			0
$227$	−19.5463	+	12.5616i	−1.29733	+	0.833746i	−0.992919	−	0.118794i	$-0.962097\pi$
$227$	−19.5463	+	12.5616i	−1.29733	+	0.833746i	−0.304414	+	0.952540i	$0.598461\pi$
$228$		0			0
$229$	−17.3931	−	20.0727i	−1.14937	−	1.32644i	−0.937031	−	0.349246i	$-0.886438\pi$
$229$	−17.3931	−	20.0727i	−1.14937	−	1.32644i	−0.212337	−	0.977196i	$-0.568108\pi$
$230$		0			0
$231$	9.54647			0.628112
$232$		0			0
$233$	2.77758	+	19.3185i	0.181965	+	1.26560i	0.852109	+	0.523364i	$0.175323\pi$
$233$	2.77758	+	19.3185i	0.181965	+	1.26560i	−0.670144	+	0.742231i	$0.733768\pi$
$234$		0			0
$235$	−5.18399	+	1.52216i	−0.338166	+	0.0992946i
$236$		0			0
$237$	4.46588	+	5.15390i	0.290090	+	0.334782i
$238$		0			0
$239$	21.6916			1.40311			0.701556	−	0.712614i	$-0.252489\pi$
$239$	21.6916			1.40311			0.701556	+	0.712614i	$0.252489\pi$
$240$		0			0
$241$	5.73197	−	12.5513i	0.369229	−	0.808498i	−0.630256	−	0.776388i	$-0.717050\pi$
$241$	5.73197	−	12.5513i	0.369229	−	0.808498i	0.999484	−	0.0321102i	$-0.0102227\pi$
$242$		0			0
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$		0			0
$245$	−1.29301	+	8.99307i	−0.0826073	+	0.574546i
$246$		0			0
$247$	−7.62756	+	16.7020i	−0.485330	+	1.06272i
$248$		0			0
$249$	7.79442	−	2.28865i	0.493951	−	0.145037i
$250$		0			0
$251$	15.0067	−	9.64425i	0.947217	−	0.608740i	0.0267849	−	0.999641i	$-0.491473\pi$
$251$	15.0067	−	9.64425i	0.947217	−	0.608740i	0.920432	+	0.390902i	$0.127837\pi$
$252$		0			0
$253$	−37.9862	+	11.1538i	−2.38817	+	0.701231i
$254$		0			0
$255$	−0.719671	+	0.830544i	−0.0450675	+	0.0520107i
$256$		0			0
$257$	−8.49605	−	18.6038i	−0.529969	−	1.16047i	−0.965525	−	0.260309i	$-0.916176\pi$
$257$	−8.49605	−	18.6038i	−0.529969	−	1.16047i	0.435556	−	0.900162i	$-0.356552\pi$
$258$		0			0
$259$	4.88415	+	1.43412i	0.303487	+	0.0891117i
$260$		0			0
$261$	4.41871	+	1.29745i	0.273512	+	0.0803102i
$262$		0			0
$263$	−8.78370	−	19.2336i	−0.541626	−	1.18600i	−0.960584	−	0.277990i	$-0.910332\pi$
$263$	−8.78370	−	19.2336i	−0.541626	−	1.18600i	0.418958	−	0.908006i	$-0.362396\pi$
$264$		0			0
$265$	3.74274	−	26.0314i	0.229915	−	1.59909i
$266$		0			0
$267$	−5.49702			−0.336412
$268$		0			0
$269$	28.2668			1.72346			0.861729	−	0.507368i	$-0.169382\pi$
$269$	28.2668			1.72346			0.861729	+	0.507368i	$0.169382\pi$
$270$		0			0
$271$	−1.48133	+	10.3029i	−0.0899846	+	0.625857i	0.894062	+	0.447944i	$0.147844\pi$
$271$	−1.48133	+	10.3029i	−0.0899846	+	0.625857i	−0.984046	+	0.177913i	$0.943066\pi$
$272$		0			0
$273$	−2.24041	−	4.90580i	−0.135595	−	0.296913i
$274$		0			0
$275$	−40.7023	−	11.9513i	−2.45444	−	0.720688i
$276$		0			0
$277$	−29.2830	−	8.59827i	−1.75945	−	0.516620i	−0.767254	−	0.641344i	$-0.778377\pi$
$277$	−29.2830	−	8.59827i	−1.75945	−	0.516620i	−0.992191	+	0.124724i	$0.960195\pi$
$278$		0			0
$279$	1.52474	+	3.33871i	0.0912837	+	0.199883i
$280$		0			0
$281$	6.42292	−	7.41244i	0.383159	−	0.442189i	−0.531106	−	0.847305i	$-0.678223\pi$
$281$	6.42292	−	7.41244i	0.383159	−	0.442189i	0.914265	+	0.405116i	$0.132769\pi$
$282$		0			0
$283$	−6.30377	+	1.85095i	−0.374720	+	0.110028i	−0.463669	−	0.886008i	$-0.653467\pi$
$283$	−6.30377	+	1.85095i	−0.374720	+	0.110028i	0.0889491	+	0.996036i	$0.471649\pi$
$284$		0			0
$285$	−23.4765	+	15.0874i	−1.39063	+	0.893703i
$286$		0			0
$287$	−8.11457	+	2.38265i	−0.478988	+	0.140644i
$288$		0			0
$289$	−7.02757	+	15.3882i	−0.413387	+	0.905190i
$290$		0			0
$291$	0.852234	−	5.92742i	0.0499588	−	0.347471i
$292$		0			0
$293$	2.03209	−	2.34516i	0.118716	−	0.137006i	−0.693280	−	0.720668i	$-0.743835\pi$
$293$	2.03209	−	2.34516i	0.118716	−	0.137006i	0.811997	+	0.583662i	$0.198381\pi$
$294$		0			0
$295$	17.0372	−	37.3062i	0.991943	−	2.17205i
$296$		0			0
$297$	4.44236			0.257772
$298$		0			0
$299$	14.6465	+	16.9030i	0.847031	+	0.977526i
$300$		0			0
$301$	23.1228	−	6.78948i	1.33278	−	0.391339i
$302$		0			0
$303$	−2.15000	−	14.9536i	−0.123515	−	0.859062i
$304$		0			0
$305$	−0.150305			−0.00860647
$306$		0			0
$307$	−0.120749	−	0.139352i	−0.00689150	−	0.00795321i	0.752293	−	0.658828i	$-0.228948\pi$
$307$	−0.120749	−	0.139352i	−0.00689150	−	0.00795321i	−0.759185	+	0.650875i	$0.774402\pi$
$308$		0			0
$309$	−5.73750	+	3.68727i	−0.326395	+	0.209761i
$310$		0			0
$311$	−21.3806	+	13.7405i	−1.21238	+	0.779151i	−0.981056	−	0.193726i	$-0.937943\pi$
$311$	−21.3806	+	13.7405i	−1.21238	+	0.779151i	−0.231326	+	0.972876i	$0.574307\pi$
$312$		0			0
$313$	3.72282	+	25.8928i	0.210426	+	1.46355i	0.771738	+	0.635941i	$0.219388\pi$
$313$	3.72282	+	25.8928i	0.210426	+	1.46355i	−0.561312	+	0.827604i	$0.689703\pi$
$314$		0			0
$315$	1.16653	−	8.11343i	0.0657268	−	0.457140i
$316$		0			0
$317$	10.1876	+	6.54720i	0.572195	+	0.367727i	0.794513	−	0.607247i	$-0.207726\pi$
$317$	10.1876	+	6.54720i	0.572195	+	0.367727i	−0.222318	+	0.974974i	$0.571362\pi$
$318$		0			0
$319$	−8.49865	−	18.6094i	−0.475833	−	1.04193i
$320$		0			0
$321$	−10.4617	−	6.72331i	−0.583914	−	0.375259i
$322$		0			0
$323$	1.38040	−	1.59306i	0.0768073	−	0.0886404i
$324$		0			0
$325$	3.41058	+	23.7211i	0.189185	+	1.31581i
$326$		0			0
$327$	10.1640	+	11.7299i	0.562069	+	0.648662i
$328$		0			0
$329$	−1.26449	+	2.76885i	−0.0697137	+	0.152652i
$330$		0			0
$331$	27.7214	+	17.8155i	1.52371	+	0.979228i	0.991137	+	0.132842i	$0.0424103\pi$
$331$	27.7214	+	17.8155i	1.52371	+	0.979228i	0.532571	+	0.846386i	$0.321226\pi$
$332$		0			0
$333$	2.27279	+	0.667353i	0.124548	+	0.0365707i
$334$		0			0
$335$	−19.9530	+	24.0139i	−1.09015	+	1.31202i
$336$		0			0
$337$	17.1830	+	5.04538i	0.936016	+	0.274839i	0.713953	−	0.700193i	$-0.246903\pi$
$337$	17.1830	+	5.04538i	0.936016	+	0.274839i	0.222063	+	0.975032i	$0.428721\pi$
$338$		0			0
$339$	−13.1969	−	8.48110i	−0.716755	−	0.460630i
$340$		0			0
$341$	6.77343	−	14.8317i	0.366802	−	0.803184i
$342$		0			0
$343$	13.2030	+	15.2370i	0.712893	+	0.822722i
$344$		0			0
$345$	4.83770	+	33.6470i	0.260453	+	1.81149i
$346$		0			0
$347$	−1.92528	+	2.22189i	−0.103355	+	0.119278i	−0.805070	−	0.593180i	$-0.797872\pi$
$347$	−1.92528	+	2.22189i	−0.103355	+	0.119278i	0.701715	+	0.712457i	$0.252418\pi$
$348$		0			0
$349$	−4.13927	−	2.66014i	−0.221570	−	0.142394i	0.425147	−	0.905124i	$-0.360222\pi$
$349$	−4.13927	−	2.66014i	−0.221570	−	0.142394i	−0.646717	+	0.762730i	$0.723859\pi$
$350$		0			0
$351$	−1.04255	−	2.28287i	−0.0556473	−	0.121850i
$352$		0			0
$353$	12.0246	+	7.72772i	0.640003	+	0.411305i	0.820001	−	0.572362i	$-0.193973\pi$
$353$	12.0246	+	7.72772i	0.640003	+	0.411305i	−0.179998	+	0.983667i	$0.557609\pi$
$354$		0			0
$355$	−3.75819	+	26.1388i	−0.199464	+	1.38730i
$356$		0			0
$357$	0.0881142	+	0.612848i	0.00466350	+	0.0324354i
$358$		0			0
$359$	−23.8003	+	15.2955i	−1.25613	+	0.807268i	−0.987750	−	0.156044i	$-0.950126\pi$
$359$	−23.8003	+	15.2955i	−1.25613	+	0.807268i	−0.268383	+	0.963312i	$0.586489\pi$
$360$		0			0
$361$	29.0464	−	18.6670i	1.52876	−	0.982472i
$362$		0			0
$363$	−5.71991	−	6.60113i	−0.300217	−	0.346469i
$364$		0			0
$365$	−4.15663			−0.217568
$366$		0			0
$367$	5.09789	+	35.4566i	0.266108	+	1.85082i	0.484286	+	0.874910i	$0.339079\pi$
$367$	5.09789	+	35.4566i	0.266108	+	1.85082i	−0.218179	+	0.975909i	$0.570012\pi$
$368$		0			0
$369$	−3.77604	+	1.10875i	−0.196573	+	0.0577190i
$370$		0			0
$371$	−9.70286	−	11.1977i	−0.503747	−	0.581356i
$372$		0			0
$373$	−27.4370			−1.42064			−0.710318	−	0.703881i	$-0.751449\pi$
$373$	−27.4370			−1.42064			−0.710318	+	0.703881i	$0.751449\pi$
$374$		0			0
$375$	−7.20821	+	15.7838i	−0.372230	+	0.815071i
$376$		0			0
$377$	−7.56865	+	8.73468i	−0.389805	+	0.449859i
$378$		0			0
$379$	−1.02493	+	7.12856i	−0.0526473	+	0.366170i	0.946418	+	0.322944i	$0.104673\pi$
$379$	−1.02493	+	7.12856i	−0.0526473	+	0.366170i	−0.999065	+	0.0432257i	$0.986237\pi$
$380$		0			0
$381$	−3.95370	+	8.65739i	−0.202554	+	0.443531i
$382$		0			0
$383$	−21.0634	+	6.18477i	−1.07629	+	0.316027i	−0.771393	−	0.636359i	$-0.780440\pi$
$383$	−21.0634	+	6.18477i	−1.07629	+	0.316027i	−0.304896	+	0.952386i	$0.598622\pi$
$384$		0			0
$385$	−30.6329	+	19.6866i	−1.56120	+	1.00332i
$386$		0			0
$387$	10.7600	−	3.15942i	0.546961	−	0.160602i
$388$		0			0
$389$	9.48807	−	10.9498i	0.481064	−	0.555178i	−0.462392	−	0.886676i	$-0.653009\pi$
$389$	9.48807	−	10.9498i	0.481064	−	0.555178i	0.943456	+	0.331498i	$0.107554\pi$
$390$		0			0
$391$	−1.06664	−	2.33563i	−0.0539425	−	0.118118i
$392$		0			0
$393$	11.5542	+	3.39261i	0.582831	+	0.171135i
$394$		0			0
$395$	−24.9585	−	7.32847i	−1.25580	−	0.368735i
$396$		0			0
$397$	−11.5476	−	25.2857i	−0.579557	−	1.26905i	−0.941550	−	0.336873i	$-0.890631\pi$
$397$	−11.5476	−	25.2857i	−0.579557	−	1.26905i	0.361993	−	0.932181i	$-0.382096\pi$
$398$		0			0
$399$	−2.23753	+	15.5623i	−0.112016	+	0.779091i
$400$		0			0
$401$	20.8213			1.03976			0.519882	−	0.854238i	$-0.325976\pi$
$401$	20.8213			1.03976			0.519882	+	0.854238i	$0.325976\pi$
$402$		0			0
$403$	−9.21145			−0.458855
$404$		0			0
$405$	0.542836	−	3.77551i	0.0269737	−	0.187606i
$406$		0			0
$407$	−4.37133	−	9.57189i	−0.216679	−	0.474461i
$408$		0			0
$409$	16.4862	+	4.84078i	0.815189	+	0.239361i	0.662643	−	0.748935i	$-0.269435\pi$
$409$	16.4862	+	4.84078i	0.815189	+	0.239361i	0.152546	+	0.988296i	$0.451253\pi$
$410$		0			0
$411$	−0.204949	−	0.0601785i	−0.0101094	−	0.00296838i
$412$		0			0
$413$	−9.59862	−	21.0181i	−0.472317	−	1.03423i
$414$		0			0
$415$	−20.2913	+	23.4174i	−0.996059	+	1.14951i
$416$		0			0
$417$	12.8213	−	3.76468i	0.627863	−	0.184357i
$418$		0			0
$419$	−12.4686	+	8.01308i	−0.609131	+	0.391465i	−0.808531	−	0.588453i	$-0.799737\pi$
$419$	−12.4686	+	8.01308i	−0.609131	+	0.391465i	0.199400	+	0.979918i	$0.436101\pi$
$420$		0			0
$421$	−16.2188	+	4.76228i	−0.790458	+	0.232099i	−0.651950	−	0.758262i	$-0.726049\pi$
$421$	−16.2188	+	4.76228i	−0.790458	+	0.232099i	−0.138508	+	0.990361i	$0.544231\pi$
$422$		0			0
$423$	−0.588419	+	1.28846i	−0.0286099	+	0.0626469i
$424$		0			0
$425$	0.391543	−	2.72324i	0.0189926	−	0.132097i
$426$		0			0
$427$	−0.0554542	+	0.0639976i	−0.00268362	+	0.00309706i
$428$		0			0
$429$	−4.63138	+	10.1413i	−0.223605	+	0.489627i
$430$		0			0
$431$	36.6855			1.76708			0.883539	−	0.468357i	$-0.155154\pi$
$431$	36.6855			1.76708			0.883539	+	0.468357i	$0.155154\pi$
$432$		0			0
$433$	16.8456	+	19.4409i	0.809549	+	0.934270i	0.998864	−	0.0476468i	$-0.0151722\pi$
$433$	16.8456	+	19.4409i	0.809549	+	0.934270i	−0.189315	+	0.981916i	$0.560627\pi$
$434$		0			0
$435$	−16.8544	+	4.94891i	−0.808108	+	0.237282i
$436$		0			0
$437$	−9.27918	−	64.5381i	−0.443883	−	3.08728i
$438$		0			0
$439$	−16.6959			−0.796850			−0.398425	−	0.917201i	$-0.630443\pi$
$439$	−16.6959			−0.796850			−0.398425	+	0.917201i	$0.630443\pi$
$440$		0			0
$441$	1.55985	+	1.80016i	0.0742784	+	0.0857218i
$442$		0			0
$443$	−4.30167	+	2.76452i	−0.204379	+	0.131346i	−0.638827	−	0.769351i	$-0.720580\pi$
$443$	−4.30167	+	2.76452i	−0.204379	+	0.131346i	0.434448	+	0.900697i	$0.356944\pi$
$444$		0			0
$445$	17.6389	−	11.3359i	0.836166	−	0.537371i
$446$		0			0
$447$	−0.0892502	−	0.620749i	−0.00422139	−	0.0293604i
$448$		0			0
$449$	0.500247	−	3.47929i	0.0236081	−	0.164198i	−0.974607	−	0.223923i	$-0.928113\pi$
$449$	0.500247	−	3.47929i	0.0236081	−	0.164198i	0.998215	+	0.0597254i	$0.0190225\pi$
$450$		0			0
$451$	14.7074	+	9.45185i	0.692543	+	0.445070i
$452$		0			0
$453$	−5.72518	−	12.5364i	−0.268992	−	0.589011i
$454$		0			0
$455$	17.3057	+	11.1217i	0.811305	+	0.521394i
$456$		0			0
$457$	14.5730	−	16.8181i	0.681694	−	0.786717i	−0.304464	−	0.952524i	$-0.598477\pi$
$457$	14.5730	−	16.8181i	0.681694	−	0.786717i	0.986158	+	0.165807i	$0.0530227\pi$
$458$		0			0
$459$	0.0410031	+	0.285183i	0.00191386	+	0.0133112i
$460$		0			0
$461$	−6.53366	−	7.54025i	−0.304303	−	0.351185i	0.582916	−	0.812532i	$-0.301912\pi$
$461$	−6.53366	−	7.54025i	−0.304303	−	0.351185i	−0.887219	+	0.461348i	$0.847366\pi$
$462$		0			0
$463$	−7.96498	+	17.4409i	−0.370164	+	0.810547i	0.629279	+	0.777180i	$0.283350\pi$
$463$	−7.96498	+	17.4409i	−0.370164	+	0.810547i	−0.999443	+	0.0333671i	$0.989377\pi$
$464$		0			0
$465$	−11.7776	−	7.56903i	−0.546175	−	0.351005i
$466$		0			0
$467$	−38.2683	−	11.2366i	−1.77084	−	0.519967i	−0.776878	−	0.629651i	$-0.783198\pi$
$467$	−38.2683	−	11.2366i	−1.77084	−	0.519967i	−0.993966	+	0.109684i	$0.965016\pi$
$468$		0			0
$469$	2.86322	+	17.3554i	0.132211	+	0.801400i
$470$		0			0
$471$	8.91946	+	2.61899i	0.410987	+	0.120677i
$472$		0			0
$473$	−41.9093	−	26.9335i	−1.92699	−	1.23840i
$474$		0			0
$475$	29.0224	−	63.5503i	1.33164	−	2.91589i
$476$		0			0
$477$	−4.51513	−	5.21074i	−0.206734	−	0.238583i
$478$		0			0
$479$	−0.234458	−	1.63069i	−0.0107127	−	0.0745082i	0.983764	−	0.179468i	$-0.0574377\pi$
$479$	−0.234458	−	1.63069i	−0.0107127	−	0.0745082i	−0.994476	+	0.104960i	$0.966529\pi$
$480$		0			0
$481$	−3.89298	+	4.49274i	−0.177505	+	0.204851i
$482$		0			0
$483$	16.1112	+	10.3540i	0.733084	+	0.471124i
$484$		0			0
$485$	9.48875	+	20.7775i	0.430862	+	0.943456i
$486$		0			0
$487$	−20.6030	−	13.2407i	−0.933611	−	0.599995i	−0.0170347	−	0.999855i	$-0.505423\pi$
$487$	−20.6030	−	13.2407i	−0.933611	−	0.599995i	−0.916576	+	0.399859i	$0.869059\pi$
$488$		0			0
$489$	2.03832	−	14.1769i	0.0921762	−	0.641100i
$490$		0			0
$491$	0.659560	+	4.58734i	0.0297655	+	0.207024i	0.999277	−	0.0380227i	$-0.0121059\pi$
$491$	0.659560	+	4.58734i	0.0297655	+	0.207024i	−0.969511	+	0.245046i	$0.921197\pi$
$492$		0			0
$493$	1.11621	−	0.717348i	0.0502718	−	0.0323077i
$494$		0			0
$495$	−14.2547	+	9.16095i	−0.640702	+	0.411754i
$496$		0			0
$497$	9.74290	+	11.2439i	0.437029	+	0.504358i
$498$		0			0
$499$	−18.7038			−0.837298			−0.418649	−	0.908148i	$-0.637496\pi$
$499$	−18.7038			−0.837298			−0.418649	+	0.908148i	$0.637496\pi$
$500$		0			0
$501$	2.93974	+	20.4463i	0.131338	+	0.913474i
$502$		0			0
$503$	−21.9353	+	6.44079i	−0.978048	+	0.287181i	−0.731418	−	0.681929i	$-0.761141\pi$
$503$	−21.9353	+	6.44079i	−0.978048	+	0.287181i	−0.246630	+	0.969110i	$0.579323\pi$
$504$		0			0
$505$	37.7360	+	43.5497i	1.67923	+	1.93794i
$506$		0			0
$507$	−6.70160			−0.297629
$508$		0			0
$509$	1.41033	−	3.08820i	0.0625120	−	0.136882i	−0.875798	−	0.482679i	$-0.839664\pi$
$509$	1.41033	−	3.08820i	0.0625120	−	0.136882i	0.938310	+	0.345796i	$0.112391\pi$
$510$		0			0
$511$	−1.53356	+	1.76983i	−0.0678408	+	0.0782925i
$512$		0			0
$513$	−1.04121	+	7.24178i	−0.0459706	+	0.319732i
$514$		0			0
$515$	10.8068	−	23.6636i	0.476204	−	1.04274i
$516$		0			0
$517$	6.03753	−	1.77278i	0.265530	−	0.0779668i
$518$		0			0
$519$	−4.05062	+	2.60317i	−0.177802	+	0.114267i
$520$		0			0
$521$	−27.1528	+	7.97279i	−1.18959	+	0.349294i	−0.815863	−	0.578245i	$-0.803738\pi$
$521$	−27.1528	+	7.97279i	−1.18959	+	0.349294i	−0.373724	+	0.927540i	$0.621919\pi$
$522$		0			0
$523$	0.998762	−	1.15263i	0.0436728	−	0.0504011i	−0.733493	−	0.679697i	$-0.762111\pi$
$523$	0.998762	−	1.15263i	0.0436728	−	0.0504011i	0.777166	+	0.629296i	$0.216657\pi$
$524$		0			0
$525$	8.52461	+	18.6663i	0.372045	+	0.814664i
$526$		0			0
$527$	1.01466	+	0.297932i	0.0441994	+	0.0129781i
$528$		0			0
$529$	−54.1367	−	15.8960i	−2.35377	−	0.691129i
$530$		0			0
$531$	−4.46663	−	9.78055i	−0.193835	−	0.424440i
$532$		0			0
$533$	1.40559	−	9.77612i	0.0608830	−	0.423451i
$534$		0			0
$535$	47.4343			2.05076
$536$		0			0
$537$	11.6291			0.501833
$538$		0			0
$539$	1.50590	−	10.4738i	0.0648638	−	0.451137i
$540$		0			0
$541$	−12.4820	−	27.3319i	−0.536645	−	1.17509i	−0.962744	−	0.270413i	$-0.912840\pi$
$541$	−12.4820	−	27.3319i	−0.536645	−	1.17509i	0.426099	−	0.904676i	$-0.359887\pi$
$542$		0			0
$543$	−16.4410	−	4.82751i	−0.705551	−	0.207168i
$544$		0			0
$545$	−56.8034	−	16.6790i	−2.43319	−	0.714450i
$546$		0			0
$547$	5.88845	+	12.8939i	0.251772	+	0.551304i	0.992746	−	0.120230i	$-0.0383632\pi$
$547$	5.88845	+	12.8939i	0.251772	+	0.551304i	−0.740974	+	0.671534i	$0.765636\pi$
$548$		0			0
$549$	−0.0258051	+	0.0297807i	−0.00110133	+	0.00127101i
$550$		0			0
$551$	32.3284	−	9.49248i	1.37724	−	0.404393i
$552$		0			0
$553$	−12.3286	+	7.92311i	−0.524266	+	0.336925i
$554$		0			0
$555$	−8.66919	+	2.54550i	−0.367986	+	0.108051i
$556$		0			0
$557$	−5.40193	+	11.8286i	−0.228887	+	0.501193i	−0.988876	−	0.148743i	$-0.952477\pi$
$557$	−5.40193	+	11.8286i	−0.228887	+	0.501193i	0.759989	+	0.649936i	$0.225204\pi$
$558$		0			0
$559$	−4.00530	+	27.8575i	−0.169406	+	1.17825i
$560$		0			0
$561$	0.838164	−	0.967293i	0.0353873	−	0.0408391i
$562$		0			0
$563$	−3.81828	+	8.36087i	−0.160921	+	0.352369i	−0.972867	−	0.231364i	$-0.925681\pi$
$563$	−3.81828	+	8.36087i	−0.160921	+	0.352369i	0.811946	+	0.583733i	$0.198408\pi$
$564$		0			0
$565$	59.8359			2.51732
$566$		0			0
$567$	−1.40727	−	1.62408i	−0.0590999	−	0.0682049i
$568$		0			0
$569$	27.1321	−	7.96670i	1.13744	−	0.333981i	0.341810	−	0.939769i	$-0.388960\pi$
$569$	27.1321	−	7.96670i	1.13744	−	0.333981i	0.795626	+	0.605788i	$0.207142\pi$
$570$		0			0
$571$	−4.87619	−	33.9147i	−0.204062	−	1.41929i	−0.792070	−	0.610430i	$-0.790997\pi$
$571$	−4.87619	−	33.9147i	−0.204062	−	1.41929i	0.588008	−	0.808855i	$-0.299912\pi$
$572$		0			0
$573$	20.8377			0.870507
$574$		0			0
$575$	−55.7292	−	64.3149i	−2.32407	−	2.68212i
$576$		0			0
$577$	−20.9322	+	13.4523i	−0.871417	+	0.560026i	−0.898186	−	0.439616i	$-0.855115\pi$
$577$	−20.9322	+	13.4523i	−0.871417	+	0.560026i	0.0267687	+	0.999642i	$0.491478\pi$
$578$		0			0
$579$	6.95332	−	4.46863i	0.288970	−	0.185710i
$580$		0			0
$581$	2.48440	+	17.2794i	0.103070	+	0.716870i
$582$		0			0
$583$	−4.35898	+	30.3174i	−0.180531	+	1.25562i
$584$		0			0
$585$	8.05305	+	5.17538i	0.332953	+	0.213976i
$586$		0			0
$587$	5.09072	+	11.1471i	0.210117	+	0.460091i	0.985120	−	0.171865i	$-0.0549794\pi$
$587$	5.09072	+	11.1471i	0.210117	+	0.460091i	−0.775004	+	0.631957i	$0.782252\pi$
$588$		0			0
$589$	22.5906	+	14.5181i	0.930831	+	0.598209i
$590$		0			0
$591$	5.69138	−	6.56820i	0.234112	−	0.270180i
$592$		0			0
$593$	3.81250	+	26.5165i	0.156561	+	1.08890i	0.904912	+	0.425600i	$0.139937\pi$
$593$	3.81250	+	26.5165i	0.156561	+	1.08890i	−0.748351	+	0.663303i	$0.769154\pi$
$594$		0			0
$595$	−1.54655	−	1.78481i	−0.0634022	−	0.0731701i
$596$		0			0
$597$	−3.26060	+	7.13971i	−0.133447	+	0.292209i
$598$		0			0
$599$	25.4501	+	16.3558i	1.03986	+	0.668280i	0.944953	−	0.327206i	$-0.106107\pi$
$599$	25.4501	+	16.3558i	1.03986	+	0.668280i	0.0949108	+	0.995486i	$0.469743\pi$
$600$		0			0
$601$	37.6035	+	11.0414i	1.53388	+	0.450388i	0.936235	−	0.351374i	$-0.114285\pi$
$601$	37.6035	+	11.0414i	1.53388	+	0.450388i	0.597644	+	0.801761i	$0.296103\pi$
$602$		0			0
$603$	1.33237	+	8.07619i	0.0542584	+	0.328888i
$604$		0			0
$605$	31.9669	+	9.38632i	1.29964	+	0.381608i
$606$		0			0
$607$	12.0142	+	7.72104i	0.487640	+	0.313387i	0.761256	−	0.648452i	$-0.224583\pi$
$607$	12.0142	+	7.72104i	0.487640	+	0.313387i	−0.273616	+	0.961839i	$0.588220\pi$
$608$		0			0
$609$	−4.11117	+	9.00221i	−0.166593	+	0.364788i
$610$		0			0
$611$	−2.32792	−	2.68657i	−0.0941776	−	0.108687i
$612$		0			0
$613$	0.271701	+	1.88972i	0.0109739	+	0.0763251i	0.994572	−	0.104046i	$-0.0331791\pi$
$613$	0.271701	+	1.88972i	0.0109739	+	0.0763251i	−0.983599	+	0.180372i	$0.942270\pi$
$614$		0			0
$615$	9.83019	−	11.3446i	0.396392	−	0.457460i
$616$		0			0
$617$	6.59692	+	4.23959i	0.265582	+	0.170679i	0.666654	−	0.745367i	$-0.267726\pi$
$617$	6.59692	+	4.23959i	0.265582	+	0.170679i	−0.401072	+	0.916047i	$0.631362\pi$
$618$		0			0
$619$	−14.3733	−	31.4732i	−0.577712	−	1.26501i	−0.942588	−	0.333957i	$-0.891616\pi$
$619$	−14.3733	−	31.4732i	−0.577712	−	1.26501i	0.364876	−	0.931056i	$-0.381111\pi$
$620$		0			0
$621$	7.49718	+	4.81814i	0.300851	+	0.193345i
$622$		0			0
$623$	1.68115	−	11.6927i	0.0673539	−	0.468457i
$624$		0			0
$625$	−2.62429	−	18.2523i	−0.104972	−	0.730093i
$626$		0			0
$627$	27.3419	−	17.5716i	1.09193	−	0.701741i
$628$		0			0
$629$	0.574132	−	0.368972i	0.0228921	−	0.0147119i
$630$		0			0
$631$	−14.8152	−	17.0977i	−0.589784	−	0.680647i	0.379895	−	0.925030i	$-0.375960\pi$
$631$	−14.8152	−	17.0977i	−0.589784	−	0.680647i	−0.969679	+	0.244383i	$0.921415\pi$
$632$		0			0
$633$	15.6513			0.622084
$634$		0			0
$635$	−5.16642	−	35.9332i	−0.205023	−	1.42597i
$636$		0			0
$637$	−5.73574	+	1.68417i	−0.227258	+	0.0667291i
$638$		0			0
$639$	4.53377	+	5.23225i	0.179353	+	0.206984i
$640$		0			0
$641$	3.80412			0.150254			0.0751269	−	0.997174i	$-0.476064\pi$
$641$	3.80412			0.150254			0.0751269	+	0.997174i	$0.476064\pi$
$642$		0			0
$643$	−13.0186	+	28.5068i	−0.513404	+	1.12420i	0.458473	+	0.888709i	$0.348397\pi$
$643$	−13.0186	+	28.5068i	−0.513404	+	1.12420i	−0.971877	+	0.235490i	$0.924331\pi$
$644$		0			0
$645$	−28.0116	+	32.3271i	−1.10295	+	1.27288i
$646$		0			0
$647$	1.88639	−	13.1201i	0.0741616	−	0.515806i	−0.918551	−	0.395302i	$-0.870640\pi$
$647$	1.88639	−	13.1201i	0.0741616	−	0.515806i	0.992713	−	0.120504i	$-0.0384509\pi$
$648$		0			0
$649$	−19.8424	+	43.4487i	−0.778880	+	1.70551i
$650$		0			0
$651$	−7.56805	+	2.22218i	−0.296615	+	0.0870941i
$652$		0			0
$653$	21.4999	−	13.8172i	0.841357	−	0.540707i	−0.0475113	−	0.998871i	$-0.515129\pi$
$653$	21.4999	−	13.8172i	0.841357	−	0.540707i	0.888868	+	0.458164i	$0.151493\pi$
$654$		0			0
$655$	−44.0715	+	12.9405i	−1.72201	+	0.505629i
$656$		0			0
$657$	−0.713629	+	0.823571i	−0.0278413	+	0.0321306i
$658$		0			0
$659$	5.67877	+	12.4348i	0.221214	+	0.484390i	0.987403	−	0.158224i	$-0.0505770\pi$
$659$	5.67877	+	12.4348i	0.221214	+	0.484390i	−0.766190	+	0.642615i	$0.777850\pi$
$660$		0			0
$661$	−15.7942	−	4.63761i	−0.614325	−	0.180382i	−0.0402565	−	0.999189i	$-0.512817\pi$
$661$	−15.7942	−	4.63761i	−0.614325	−	0.180382i	−0.574068	+	0.818807i	$0.694636\pi$
$662$		0			0
$663$	−0.693783	−	0.203713i	−0.0269443	−	0.00791156i
$664$		0			0
$665$	−24.9126	−	54.5509i	−0.966067	−	2.11539i
$666$		0			0
$667$	5.84084	−	40.6239i	0.226158	−	1.57296i
$668$		0			0
$669$	8.09286			0.312888
$670$		0			0
$671$	0.175053			0.00675785
$672$		0			0
$673$	−0.295203	+	2.05318i	−0.0113792	+	0.0791444i	−0.994720	−	0.102629i	$-0.967275\pi$
$673$	−0.295203	+	2.05318i	−0.0113792	+	0.0791444i	0.983340	+	0.181773i	$0.0581837\pi$
$674$		0			0
$675$	3.96685	+	8.68618i	0.152684	+	0.334331i
$676$		0			0
$677$	5.43195	+	1.59496i	0.208767	+	0.0612995i	0.384444	−	0.923148i	$-0.374393\pi$
$677$	5.43195	+	1.59496i	0.208767	+	0.0612995i	−0.175677	+	0.984448i	$0.556211\pi$
$678$		0			0
$679$	12.3475	+	3.62556i	0.473854	+	0.139136i
$680$		0			0
$681$	−9.65206	−	21.1351i	−0.369868	−	0.809897i
$682$		0			0
$683$	−6.79783	+	7.84511i	−0.260112	+	0.300185i	−0.870751	−	0.491724i	$-0.836367\pi$
$683$	−6.79783	+	7.84511i	−0.260112	+	0.300185i	0.610640	+	0.791909i	$0.290912\pi$
$684$		0			0
$685$	0.781743	−	0.229540i	0.0298689	−	0.00877029i
$686$		0			0
$687$	22.3437	−	14.3594i	0.852465	−	0.547846i
$688$		0			0
$689$	16.6027	−	4.87499i	0.632512	−	0.185722i
$690$		0			0
$691$	−1.45502	+	3.18606i	−0.0553517	+	0.121203i	−0.935287	−	0.353890i	$-0.884859\pi$
$691$	−1.45502	+	3.18606i	−0.0553517	+	0.121203i	0.879935	+	0.475094i	$0.157586\pi$
$692$		0			0
$693$	−1.35860	+	9.44930i	−0.0516091	+	0.358949i
$694$		0			0
$695$	−33.3778	+	38.5201i	−1.26609	+	1.46115i
$696$		0			0
$697$	−0.471024	+	1.03140i	−0.0178413	+	0.0390670i
$698$		0			0
$699$	−19.5171			−0.738206
$700$		0			0
$701$	9.63414	+	11.1184i	0.363877	+	0.419936i	0.907935	−	0.419112i	$-0.137658\pi$
$701$	9.63414	+	11.1184i	0.363877	+	0.419936i	−0.544058	+	0.839047i	$0.683113\pi$
$702$		0			0
$703$	16.6283	−	4.88252i	0.627149	−	0.184148i
$704$		0			0
$705$	−0.768905	−	5.34785i	−0.0289586	−	0.201412i
$706$		0			0
$707$	32.4652			1.22098
$708$		0			0
$709$	15.8138	+	18.2501i	0.593899	+	0.685397i	0.970534	−	0.240966i	$-0.0774641\pi$
$709$	15.8138	+	18.2501i	0.593899	+	0.685397i	−0.376634	+	0.926362i	$0.622919\pi$
$710$		0			0
$711$	−5.73700	+	3.68694i	−0.215154	+	0.138271i
$712$		0			0
$713$	27.5176	−	17.6845i	1.03054	−	0.662290i
$714$		0			0
$715$	−6.05197	−	42.0924i	−0.226331	−	1.57417i
$716$		0			0
$717$	−3.08703	+	21.4708i	−0.115287	+	0.801841i
$718$		0			0
$719$	8.56301	+	5.50311i	0.319346	+	0.205231i	0.690486	−	0.723346i	$-0.257397\pi$
$719$	8.56301	+	5.50311i	0.319346	+	0.205231i	−0.371140	+	0.928577i	$0.621033\pi$
$720$		0			0
$721$	−6.08846	−	13.3319i	−0.226746	−	0.496505i
$722$		0			0
$723$	11.6078	+	7.45986i	0.431697	+	0.277435i
$724$		0			0
$725$	28.7983	−	33.2350i	1.06954	−	1.23432i
$726$		0			0
$727$	1.15361	+	8.02354i	0.0427850	+	0.297577i	0.999967	+	0.00809045i	$0.00257530\pi$
$727$	1.15361	+	8.02354i	0.0427850	+	0.297577i	−0.957182	+	0.289486i	$0.906516\pi$
$728$		0			0
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$		0			0
$731$	1.34221	−	2.93902i	0.0496432	−	0.108704i
$732$		0			0
$733$	27.3317	+	17.5650i	1.00952	+	0.648778i	0.937269	−	0.348608i	$-0.113346\pi$
$733$	27.3317	+	17.5650i	1.00952	+	0.648778i	0.0722502	+	0.997387i	$0.476982\pi$
$734$		0			0
$735$	−8.71752	−	2.55969i	−0.321551	−	0.0944158i
$736$		0			0
$737$	23.2382	−	27.9678i	0.855991	−	1.03021i
$738$		0			0
$739$	46.6785	+	13.7060i	1.71710	+	0.504185i	0.984336	−	0.176302i	$-0.0564136\pi$
$739$	46.6785	+	13.7060i	1.71710	+	0.504185i	0.732760	+	0.680487i	$0.238232\pi$
$740$		0			0
$741$	−15.4465	−	9.92687i	−0.567442	−	0.364673i
$742$		0			0
$743$	−16.0041	+	35.0441i	−0.587134	+	1.28564i	0.350025	+	0.936740i	$0.386173\pi$
$743$	−16.0041	+	35.0441i	−0.587134	+	1.28564i	−0.937159	+	0.348904i	$0.886554\pi$
$744$		0			0
$745$	1.56648	+	1.80782i	0.0573916	+	0.0662334i
$746$		0			0
$747$	1.15609	+	8.04079i	0.0422992	+	0.294197i
$748$		0			0
$749$	17.5006	−	20.1968i	0.639458	−	0.737973i
$750$		0			0
$751$	−25.9297	−	16.6640i	−0.946187	−	0.608077i	−0.0260441	−	0.999661i	$-0.508291\pi$
$751$	−25.9297	−	16.6640i	−0.946187	−	0.608077i	−0.920143	+	0.391584i	$0.871927\pi$
$752$		0			0
$753$	7.41040	+	16.2265i	0.270050	+	0.591327i
$754$		0			0
$755$	44.2234	+	28.4206i	1.60945	+	1.03433i
$756$		0			0
$757$	−4.15522	+	28.9002i	−0.151024	+	1.05040i	0.763484	+	0.645827i	$0.223487\pi$
$757$	−4.15522	+	28.9002i	−0.151024	+	1.05040i	−0.914508	+	0.404568i	$0.867422\pi$
$758$		0			0
$759$	−5.63423	−	39.1869i	−0.204510	−	1.42240i
$760$		0			0
$761$	−10.5944	+	6.80859i	−0.384046	+	0.246811i	−0.718391	−	0.695639i	$-0.755121\pi$
$761$	−10.5944	+	6.80859i	−0.384046	+	0.246811i	0.334345	+	0.942451i	$0.391485\pi$
$762$		0			0
$763$	−28.0589	+	18.0324i	−1.01580	+	0.652815i
$764$		0			0
$765$	−0.719671	−	0.830544i	−0.0260197	−	0.0300284i
$766$		0			0
$767$	26.9844			0.974350
$768$		0			0
$769$	−4.90208	−	34.0947i	−0.176773	−	1.22949i	−0.864168	−	0.503203i	$-0.832155\pi$
$769$	−4.90208	−	34.0947i	−0.176773	−	1.22949i	0.687395	−	0.726284i	$-0.258754\pi$
$770$		0			0
$771$	19.6235	−	5.76198i	0.706724	−	0.207513i
$772$		0			0
$773$	−0.828003	−	0.955566i	−0.0297812	−	0.0343693i	0.740664	−	0.671876i	$-0.234511\pi$
$773$	−0.828003	−	0.955566i	−0.0297812	−	0.0343693i	−0.770445	+	0.637507i	$0.779966\pi$
$774$		0			0
$775$	35.0490			1.25900
$776$		0			0
$777$	−2.11461	+	4.63034i	−0.0758611	+	0.166113i
$778$		0			0
$779$	−18.8552	+	21.7601i	−0.675559	+	0.779637i
$780$		0			0
$781$	4.37697	−	30.4425i	0.156620	−	1.08932i
$782$		0			0
$783$	−1.91309	+	4.18909i	−0.0683684	+	0.149706i
$784$		0			0
$785$	−34.0218	+	9.98969i	−1.21429	+	0.356547i
$786$		0			0
$787$	−5.68350	+	3.65257i	−0.202595	+	0.130200i	−0.638005	−	0.770033i	$-0.720240\pi$
$787$	−5.68350	+	3.65257i	−0.202595	+	0.130200i	0.435410	+	0.900232i	$0.356604\pi$
$788$		0			0
$789$	20.2879	−	5.95707i	0.722268	−	0.212077i
$790$		0			0
$791$	22.0761	−	25.4771i	0.784935	−	0.905863i
$792$		0			0
$793$	−0.0410822	−	0.0899575i	−0.00145887	−	0.00319448i
$794$		0			0
$795$	25.2337	+	7.40930i	0.894949	+	0.262781i
$796$		0			0
$797$	−26.6284	−	7.81881i	−0.943227	−	0.276957i	−0.226263	−	0.974066i	$-0.572651\pi$
$797$	−26.6284	−	7.81881i	−0.943227	−	0.276957i	−0.716964	+	0.697110i	$0.754469\pi$
$798$		0			0
$799$	0.169533	+	0.371225i	0.00599763	+	0.0131330i
$800$		0			0
$801$	0.782308	−	5.44107i	0.0276415	−	0.192251i
$802$		0			0
$803$	4.84102			0.170836
$804$		0			0
$805$	−73.0497			−2.57466
$806$		0			0
$807$	−4.02279	+	27.9791i	−0.141609	+	0.984911i
$808$		0			0
$809$	16.7253	+	36.6232i	0.588029	+	1.28760i	0.936626	+	0.350331i	$0.113931\pi$
$809$	16.7253	+	36.6232i	0.588029	+	1.28760i	−0.348597	+	0.937273i	$0.613342\pi$
$810$		0			0
$811$	−19.6528	−	5.77057i	−0.690102	−	0.202632i	−0.0821662	−	0.996619i	$-0.526184\pi$
$811$	−19.6528	−	5.77057i	−0.690102	−	0.202632i	−0.607935	+	0.793987i	$0.708002\pi$
$812$		0			0
$813$	−9.98722	−	2.93251i	−0.350267	−	0.102848i
$814$		0			0
$815$	22.6947	+	49.6944i	0.794959	+	1.74072i
$816$		0			0
$817$	53.7288	−	62.0064i	1.87973	−	2.16933i
$818$		0			0
$819$	5.17471	−	1.51943i	0.180819	−	0.0530933i
$820$		0			0
$821$	5.71939	−	3.67563i	0.199608	−	0.128280i	−0.437019	−	0.899453i	$-0.643966\pi$
$821$	5.71939	−	3.67563i	0.199608	−	0.128280i	0.636627	+	0.771172i	$0.280329\pi$
$822$		0			0
$823$	44.7836	−	13.1496i	1.56106	−	0.458368i	0.616675	−	0.787218i	$-0.288479\pi$
$823$	44.7836	−	13.1496i	1.56106	−	0.458368i	0.944382	+	0.328851i	$0.106661\pi$
$824$		0			0
$825$	17.6221	−	38.5871i	0.613524	−	1.34343i
$826$		0			0
$827$	−0.490171	+	3.40922i	−0.0170449	+	0.118550i	−0.996567	−	0.0827844i	$-0.973619\pi$
$827$	−0.490171	+	3.40922i	−0.0170449	+	0.118550i	0.979523	+	0.201334i	$0.0645278\pi$
$828$		0			0
$829$	−4.36698	+	5.03977i	−0.151672	+	0.175038i	−0.826501	−	0.562936i	$-0.809672\pi$
$829$	−4.36698	+	5.03977i	−0.151672	+	0.175038i	0.674829	+	0.737974i	$0.264217\pi$
$830$		0			0
$831$	12.6782	−	27.7613i	0.439800	−	0.963028i
$832$		0			0
$833$	0.686277			0.0237781
$834$		0			0
$835$	−51.5971	−	59.5463i	−1.78559	−	2.06068i
$836$		0			0
$837$	−3.52172	+	1.03407i	−0.121728	+	0.0357427i
$838$		0			0
$839$	−3.03243	−	21.0910i	−0.104691	−	0.728142i	−0.972780	−	0.231732i	$-0.925561\pi$
$839$	−3.03243	−	21.0910i	−0.104691	−	0.728142i	0.868089	−	0.496409i	$-0.165348\pi$
$840$		0			0
$841$	−7.79158			−0.268675
$842$		0			0
$843$	6.42292	+	7.41244i	0.221217	+	0.255298i
$844$		0			0
$845$	21.5042	−	13.8199i	0.739768	−	0.475420i
$846$		0			0
$847$	15.7905	−	10.1479i	0.542568	−	0.348688i
$848$		0			0
$849$	−0.934993	−	6.50302i	−0.0320889	−	0.223183i
$850$		0			0
$851$	3.00427	−	20.8952i	0.102985	−	0.716277i
$852$		0			0
$853$	34.4689	+	22.1518i	1.18019	+	0.758463i	0.975422	−	0.220347i	$-0.0707189\pi$
$853$	34.4689	+	22.1518i	1.18019	+	0.758463i	0.204770	+	0.978810i	$0.434355\pi$
$854$		0			0
$855$	−11.5928	−	25.3847i	−0.396466	−	0.868139i
$856$		0			0
$857$	−11.9552	−	7.68314i	−0.408382	−	0.262451i	0.320282	−	0.947322i	$-0.396222\pi$
$857$	−11.9552	−	7.68314i	−0.408382	−	0.262451i	−0.728664	+	0.684871i	$0.759859\pi$
$858$		0			0
$859$	4.06951	−	4.69647i	0.138850	−	0.160241i	−0.682066	−	0.731291i	$-0.738918\pi$
$859$	4.06951	−	4.69647i	0.138850	−	0.160241i	0.820916	+	0.571050i	$0.193464\pi$
$860$		0			0
$861$	−1.20358	−	8.37107i	−0.0410178	−	0.285285i
$862$		0			0
$863$	−18.3762	−	21.2073i	−0.625535	−	0.721905i	0.351214	−	0.936295i	$-0.385769\pi$
$863$	−18.3762	−	21.2073i	−0.625535	−	0.721905i	−0.976748	+	0.214390i	$0.931224\pi$
$864$		0			0
$865$	7.62948	−	16.7062i	0.259410	−	0.568029i
$866$		0			0
$867$	−14.2315	−	9.14602i	−0.483326	−	0.310615i
$868$		0			0
$869$	29.0679	+	8.53509i	0.986060	+	0.289533i
$870$		0			0
$871$	−19.8259	−	5.37821i	−0.671776	−	0.182234i
$872$		0			0
$873$	5.74580	+	1.68712i	0.194466	+	0.0571003i
$874$		0			0
$875$	−31.3691	−	20.1597i	−1.06047	−	0.681521i
$876$		0			0
$877$	−17.4564	+	38.2241i	−0.589460	+	1.29074i	0.346308	+	0.938121i	$0.387435\pi$
$877$	−17.4564	+	38.2241i	−0.589460	+	1.29074i	−0.935768	+	0.352616i	$0.885292\pi$
$878$		0			0
$879$	2.03209	+	2.34516i	0.0685408	+	0.0791003i
$880$		0			0
$881$	−3.68676	−	25.6420i	−0.124210	−	0.863900i	−0.952704	−	0.303901i	$-0.901711\pi$
$881$	−3.68676	−	25.6420i	−0.124210	−	0.863900i	0.828493	−	0.559999i	$-0.189198\pi$
$882$		0			0
$883$	−8.15554	+	9.41199i	−0.274456	+	0.316739i	−0.876198	−	0.481952i	$-0.839928\pi$
$883$	−8.15554	+	9.41199i	−0.274456	+	0.316739i	0.601742	+	0.798690i	$0.294474\pi$
$884$		0			0
$885$	34.5019	+	22.1730i	1.15977	+	0.745337i
$886$		0			0
$887$	1.53605	+	3.36349i	0.0515757	+	0.112935i	0.933665	−	0.358146i	$-0.116591\pi$
$887$	1.53605	+	3.36349i	0.0515757	+	0.112935i	−0.882090	+	0.471081i	$0.843864\pi$
$888$		0			0
$889$	−17.2059	−	11.0576i	−0.577067	−	0.370859i
$890$		0			0
$891$	−0.632213	+	4.39714i	−0.0211799	+	0.147310i
$892$		0			0
$893$	1.47483	+	10.2577i	0.0493534	+	0.343261i
$894$		0			0
$895$	−37.3157	+	23.9813i	−1.24733	+	0.801608i
$896$		0			0
$897$	−18.8154	+	12.0919i	−0.628227	+	0.403737i
$898$		0			0
$899$	11.0692	+	12.7745i	0.369178	+	0.426055i
$900$		0			0
$901$	−1.98650			−0.0661799
$902$		0			0
$903$	3.42965	+	23.8537i	0.114132	+	0.793802i
$904$		0			0
$905$	62.7114	−	18.4137i	2.08460	−	0.612093i
$906$		0			0
$907$	1.85978	+	2.14630i	0.0617531	+	0.0712669i	0.785786	−	0.618499i	$-0.212259\pi$
$907$	1.85978	+	2.14630i	0.0617531	+	0.0712669i	−0.724033	+	0.689766i	$0.757713\pi$
$908$		0			0
$909$	15.1074			0.501080
$910$		0			0
$911$	−11.7540	+	25.7376i	−0.389426	+	0.852724i	0.608808	+	0.793318i	$0.291648\pi$
$911$	−11.7540	+	25.7376i	−0.389426	+	0.852724i	−0.998234	+	0.0594066i	$0.981079\pi$
$912$		0			0
$913$	23.6322	−	27.2730i	0.782112	−	0.902606i
$914$		0			0
$915$	0.0213907	−	0.148776i	0.000707155	−	0.00491837i
$916$		0			0
$917$	−10.7500	+	23.5392i	−0.354997	+	0.777334i
$918$		0			0
$919$	20.6528	−	6.06422i	0.681274	−	0.200040i	0.0772568	−	0.997011i	$-0.475384\pi$
$919$	20.6528	−	6.06422i	0.681274	−	0.200040i	0.604018	+	0.796971i	$0.293566\pi$
$920$		0			0
$921$	0.155118	−	0.0996880i	0.00511130	−	0.00328483i
$922$		0			0
$923$	−16.6712	+	4.89511i	−0.548740	+	0.161124i
$924$		0			0
$925$	14.8126	−	17.0946i	0.487034	−	0.562067i
$926$		0			0
$927$	−2.83321	−	6.20386i	−0.0930547	−	0.203761i
$928$		0			0
$929$	29.7920	+	8.74772i	0.977444	+	0.287004i	0.731169	−	0.682196i	$-0.238975\pi$
$929$	29.7920	+	8.74772i	0.977444	+	0.287004i	0.246275	+	0.969200i	$0.420793\pi$
$930$		0			0
$931$	16.7210	+	4.90974i	0.548010	+	0.160910i
$932$		0			0
$933$	−10.5578	−	23.1184i	−0.345648	−	0.756864i
$934$		0			0
$935$	−0.694782	+	4.83232i	−0.0227218	+	0.158034i
$936$		0			0
$937$	43.0039			1.40488			0.702438	−	0.711745i	$-0.252095\pi$
$937$	43.0039			1.40488			0.702438	+	0.711745i	$0.252095\pi$
$938$		0			0
$939$	−26.1590			−0.853667
$940$		0			0
$941$	−3.78461	+	26.3226i	−0.123375	+	0.858091i	0.830314	+	0.557296i	$0.188161\pi$
$941$	−3.78461	+	26.3226i	−0.123375	+	0.858091i	−0.953689	+	0.300795i	$0.902748\pi$
$942$		0			0
$943$	14.5696	+	31.9030i	0.474452	+	1.03890i
$944$		0			0
$945$	7.86483	+	2.30932i	0.255843	+	0.0751223i
$946$		0			0
$947$	−21.6065	−	6.34423i	−0.702115	−	0.206160i	−0.0888598	−	0.996044i	$-0.528322\pi$
$947$	−21.6065	−	6.34423i	−0.702115	−	0.206160i	−0.613256	+	0.789884i	$0.710140\pi$
$948$		0			0
$949$	−1.13611	−	2.48773i	−0.0368797	−	0.0807553i
$950$		0			0
$951$	−7.93041	+	9.15219i	−0.257161	+	0.296780i
$952$		0			0
$953$	5.58335	−	1.63942i	0.180862	−	0.0531060i	−0.190047	−	0.981775i	$-0.560864\pi$
$953$	5.58335	−	1.63942i	0.180862	−	0.0531060i	0.370910	+	0.928669i	$0.379046\pi$
$954$		0			0
$955$	−66.8643	+	42.9711i	−2.16368	+	1.39051i
$956$		0			0
$957$	19.6295	−	5.76374i	0.634532	−	0.186315i
$958$		0			0
$959$	0.190685	−	0.417541i	0.00615752	−	0.0134831i
$960$		0			0
$961$	2.49452	−	17.3498i	0.0804684	−	0.559670i
$962$		0			0
$963$	8.14373	−	9.39837i	0.262428	−	0.302858i
$964$		0			0
$965$	−13.0968	+	28.6780i	−0.421601	+	0.923178i
$966$		0			0
$967$	46.5712			1.49763			0.748814	−	0.662780i	$-0.230624\pi$
$967$	46.5712			1.49763			0.748814	+	0.662780i	$0.230624\pi$
$968$		0			0
$969$	1.38040	+	1.59306i	0.0443447	+	0.0511766i
$970$		0			0
$971$	−25.3179	+	7.43399i	−0.812489	+	0.238568i	−0.661479	−	0.749964i	$-0.730071\pi$
$971$	−25.3179	+	7.43399i	−0.812489	+	0.238568i	−0.151010	+	0.988532i	$0.548253\pi$
$972$		0			0
$973$	4.08668	+	28.4235i	0.131013	+	0.911214i
$974$		0			0
$975$	−23.9650			−0.767496
$976$		0			0
$977$	22.6981	+	26.1950i	0.726178	+	0.838054i	0.992035	−	0.125959i	$-0.0402007\pi$
$977$	22.6981	+	26.1950i	0.726178	+	0.838054i	−0.265858	+	0.964012i	$0.585655\pi$
$978$		0			0
$979$	−20.5432	+	13.2023i	−0.656563	+	0.421947i
$980$		0			0
$981$	−13.0569	+	8.39119i	−0.416876	+	0.267910i
$982$		0			0
$983$	7.94878	+	55.2850i	0.253527	+	1.76332i	0.576681	+	0.816970i	$0.304348\pi$
$983$	7.94878	+	55.2850i	0.253527	+	1.76332i	−0.323154	+	0.946346i	$0.604743\pi$
$984$		0			0
$985$	−4.71777	+	32.8128i	−0.150321	+	1.04550i
$986$		0			0
$987$	−2.56071	−	1.64567i	−0.0815083	−	0.0523822i
$988$		0			0
$989$	−41.5167	−	90.9090i	−1.32016	−	2.89074i
$990$		0			0
$991$	10.8393	+	6.96600i	0.344322	+	0.221282i	0.701359	−	0.712808i	$-0.252577\pi$
$991$	10.8393	+	6.96600i	0.344322	+	0.221282i	−0.357038	+	0.934090i	$0.616213\pi$
$992$		0			0
$993$	−21.5793	+	24.9039i	−0.684799	+	0.790300i
$994$		0			0
$995$	−4.26072	−	29.6340i	−0.135074	−	0.939460i
$996$		0			0
$997$	19.3695	+	22.3536i	0.613438	+	0.707945i	0.974447	−	0.224617i	$-0.0721131\pi$
$997$	19.3695	+	22.3536i	0.613438	+	0.707945i	−0.361009	+	0.932562i	$0.617568\pi$
$998$		0			0
$999$	−0.984012	+	2.15469i	−0.0311328	+	0.0681712i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.q.a.265.1	✓	60
67.22	even	11	inner	804.2.q.a.625.1	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.a.265.1	✓	60	1.1	even	1	trivial
804.2.q.a.625.1	yes	60	67.22	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{3} +(-1.58453 - 3.46964i) q^{5} +(-2.06192 - 0.605433i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{3} +(-1.58453 - 3.46964i) q^{5} +(-2.06192 - 0.605433i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(1.84542 + 4.04091i) q^{11} +(1.64348 - 1.89668i) q^{13} +(3.65982 - 1.07462i) q^{15} +(-0.242378 + 0.155767i) q^{17} +(-7.01989 + 2.06123i) q^{19} +(0.892712 - 1.95477i) q^{21} +(-1.26830 + 8.82120i) q^{23} +(-6.25334 + 7.21674i) q^{25} +(0.415415 - 0.909632i) q^{27} -4.60526 q^{29} +(-2.40360 - 2.77390i) q^{31} +(-4.26241 + 1.25156i) q^{33} +(1.16653 + 8.11343i) q^{35} -2.36874 q^{37} +(1.64348 + 1.89668i) q^{39} +(3.31071 - 2.12767i) q^{41} +(-9.43402 + 6.06288i) q^{43} +(0.542836 + 3.77551i) q^{45} +(0.201583 - 1.40204i) q^{47} +(-2.00382 - 1.28778i) q^{49} +(-0.119687 - 0.262079i) q^{51} +(5.80027 + 3.72761i) q^{53} +(11.0964 - 12.8059i) q^{55} +(-1.04121 - 7.24178i) q^{57} +(7.04120 + 8.12597i) q^{59} +(0.0163696 - 0.0358445i) q^{61} +(1.80782 + 1.16182i) q^{63} +(-9.18492 - 2.69693i) q^{65} +(-3.55373 - 7.37367i) q^{67} +(-8.55092 - 2.51078i) q^{69} +(-5.82421 - 3.74299i) q^{71} +(0.452695 - 0.991263i) q^{73} +(-6.25334 - 7.21674i) q^{75} +(-1.35860 - 9.44930i) q^{77} +(4.46588 - 5.15390i) q^{79} +(0.841254 + 0.540641i) q^{81} +(-3.37461 - 7.38938i) q^{83} +(0.924510 + 0.594147i) q^{85} +(0.655397 - 4.55839i) q^{87} +(0.782308 + 5.44107i) q^{89} +(-4.53703 + 2.91577i) q^{91} +(3.08773 - 1.98437i) q^{93} +(18.2749 + 21.0904i) q^{95} -5.98837 q^{97} +(-0.632213 - 4.39714i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9}+O(q^{10}) \) 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9	\( 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9} + 7 q^{11} - 2 q^{13} + 9 q^{15} - 19 q^{17} + 2 q^{19} - 2 q^{21} + 4 q^{23} + 16 q^{25} - 6 q^{27} + 16 q^{29} - 28 q^{31} - 4 q^{33} + 28 q^{35} + 2 q^{37} - 2 q^{39} + 32 q^{41} + 19 q^{43} - 2 q^{45} + 2 q^{47} - 70 q^{49} - 19 q^{51} + 31 q^{53} - 5 q^{55} + 13 q^{57} + 59 q^{59} + 32 q^{61} + 9 q^{63} + 28 q^{65} + 7 q^{67} + 4 q^{69} + 16 q^{71} + 19 q^{73} + 16 q^{75} - 46 q^{77} + 48 q^{79} - 6 q^{81} + 60 q^{83} - 66 q^{85} + 5 q^{87} - 22 q^{89} + 24 q^{91} + 5 q^{93} + 103 q^{95} - 46 q^{97} - 4 q^{99}+O(q^{100}) \) 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9 + 7 * q^11 - 2 * q^13 + 9 * q^15 - 19 * q^17 + 2 * q^19 - 2 * q^21 + 4 * q^23 + 16 * q^25 - 6 * q^27 + 16 * q^29 - 28 * q^31 - 4 * q^33 + 28 * q^35 + 2 * q^37 - 2 * q^39 + 32 * q^41 + 19 * q^43 - 2 * q^45 + 2 * q^47 - 70 * q^49 - 19 * q^51 + 31 * q^53 - 5 * q^55 + 13 * q^57 + 59 * q^59 + 32 * q^61 + 9 * q^63 + 28 * q^65 + 7 * q^67 + 4 * q^69 + 16 * q^71 + 19 * q^73 + 16 * q^75 - 46 * q^77 + 48 * q^79 - 6 * q^81 + 60 * q^83 - 66 * q^85 + 5 * q^87 - 22 * q^89 + 24 * q^91 + 5 * q^93 + 103 * q^95 - 46 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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