LMFDB - Embedded newform 585.2.bs.c.334.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(289,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("585.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bs (of order $6$, degree $2$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			334.3
Character	$\chi$	$=$	585.334
Dual form			585.2.bs.c.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57126 - 0.907167i) q^{2} +(0.645904 + 1.11874i) q^{4} +(-1.19685 - 1.88880i) q^{5} +(4.06197 - 2.34518i) q^{7} +1.28490i q^{8} +O(q^{10})$	\(q+(-1.57126 - 0.907167i) q^{2} +(0.645904 + 1.11874i) q^{4} +(-1.19685 - 1.88880i) q^{5} +(4.06197 - 2.34518i) q^{7} +1.28490i q^{8} +(0.167109 + 4.05353i) q^{10} +(-0.270358 + 0.468274i) q^{11} +(-1.34237 - 3.34635i) q^{13} -8.50987 q^{14} +(2.45742 - 4.25638i) q^{16} +(5.92637 - 3.42159i) q^{17} +(2.78100 + 4.81684i) q^{19} +(1.34002 - 2.55894i) q^{20} +(0.849606 - 0.490520i) q^{22} +(-0.0291335 - 0.0168202i) q^{23} +(-2.13510 + 4.52121i) q^{25} +(-0.926492 + 6.47573i) q^{26} +(5.24728 + 3.02952i) q^{28} +(3.40734 - 5.90168i) q^{29} -0.352843 q^{31} +(-5.49700 + 3.17369i) q^{32} -12.4158 q^{34} +(-9.29113 - 4.86540i) q^{35} +(-6.98136 - 4.03069i) q^{37} -10.0913i q^{38} +(2.42691 - 1.53783i) q^{40} +(-3.59880 + 6.23331i) q^{41} +(-6.08901 + 3.51549i) q^{43} -0.698502 q^{44} +(0.0305175 + 0.0528578i) q^{46} -1.99690i q^{47} +(7.49972 - 12.9899i) q^{49} +(7.45629 - 5.16711i) q^{50} +(2.87665 - 3.66318i) q^{52} -8.50859i q^{53} +(1.20805 - 0.0498027i) q^{55} +(3.01331 + 5.21921i) q^{56} +(-10.7076 + 6.18205i) q^{58} +(-6.64864 - 11.5158i) q^{59} +(1.60333 + 2.77705i) q^{61} +(0.554408 + 0.320088i) q^{62} +1.68658 q^{64} +(-4.71396 + 6.54053i) q^{65} +(-8.70757 - 5.02732i) q^{67} +(7.65573 + 4.42004i) q^{68} +(10.1850 + 16.0734i) q^{70} +(4.33383 + 7.50641i) q^{71} -8.05229i q^{73} +(7.31302 + 12.6665i) q^{74} +(-3.59252 + 6.22243i) q^{76} +2.53615i q^{77} -2.29181 q^{79} +(-10.9806 + 0.452682i) q^{80} +(11.3093 - 6.52943i) q^{82} +14.8223i q^{83} +(-13.5557 - 7.09857i) q^{85} +12.7566 q^{86} +(-0.601684 - 0.347382i) q^{88} +(-3.98458 + 6.90149i) q^{89} +(-13.3004 - 10.4447i) q^{91} -0.0434570i q^{92} +(-1.81152 + 3.13764i) q^{94} +(5.76958 - 11.0178i) q^{95} +(0.265973 - 0.153560i) q^{97} +(-23.5680 + 13.6070i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 20 q^{4}+O(q^{10}) $ 32 * q + 20 * q^4	$ 32 q + 20 q^{4} - 6 q^{10} - 28 q^{16} - 8 q^{19} + 28 q^{25} + 8 q^{31} - 8 q^{34} - 20 q^{40} - 8 q^{46} + 44 q^{49} + 20 q^{55} - 56 q^{61} - 136 q^{64} - 80 q^{70} + 88 q^{76} - 72 q^{79} - 50 q^{85} - 28 q^{91} + 48 q^{94}+O(q^{100}) $ 32 * q + 20 * q^4 - 6 * q^10 - 28 * q^16 - 8 * q^19 + 28 * q^25 + 8 * q^31 - 8 * q^34 - 20 * q^40 - 8 * q^46 + 44 * q^49 + 20 * q^55 - 56 * q^61 - 136 * q^64 - 80 * q^70 + 88 * q^76 - 72 * q^79 - 50 * q^85 - 28 * q^91 + 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.57126	−	0.907167i	−1.11105	−	0.641464i	−0.171948	−	0.985106i	$-0.555006\pi$
$2$	−1.57126	−	0.907167i	−1.11105	−	0.641464i	−0.939101	+	0.343642i	$0.888339\pi$
$3$		0			0
$3$		0			0
$4$	0.645904	+	1.11874i	0.322952	+	0.559369i
$5$	−1.19685	−	1.88880i	−0.535248	−	0.844695i
$5$	−1.19685	−	1.88880i	−0.535248	−	0.844695i
$6$		0			0
$7$	4.06197	−	2.34518i	1.53528	−	0.886394i	0.536174	−	0.844108i	$-0.319869\pi$
$7$	4.06197	−	2.34518i	1.53528	−	0.886394i	0.999106	−	0.0422862i	$-0.0134641\pi$
$8$			1.28490i			0.454279i
$9$		0			0
$10$	0.167109	+	4.05353i	0.0528446	+	1.28184i
$11$	−0.270358	+	0.468274i	−0.0815161	+	0.141190i	−0.903901	−	0.427741i	$-0.859310\pi$
$11$	−0.270358	+	0.468274i	−0.0815161	+	0.141190i	0.822385	+	0.568931i	$0.192643\pi$
$12$		0			0
$13$	−1.34237	−	3.34635i	−0.372305	−	0.928110i
$13$	−1.34237	−	3.34635i	−0.372305	−	0.928110i
$14$	−8.50987			−2.27436
$15$		0			0
$16$	2.45742	−	4.25638i	0.614356	−	1.06410i
$17$	5.92637	−	3.42159i	1.43736	−	0.829858i	0.439690	−	0.898150i	$-0.355088\pi$
$17$	5.92637	−	3.42159i	1.43736	−	0.829858i	0.997665	+	0.0682919i	$0.0217549\pi$
$18$		0			0
$19$	2.78100	+	4.81684i	0.638006	+	1.10506i	0.985870	+	0.167513i	$0.0535737\pi$
$19$	2.78100	+	4.81684i	0.638006	+	1.10506i	−0.347864	+	0.937545i	$0.613093\pi$
$20$	1.34002	−	2.55894i	0.299637	−	0.572197i
$21$		0			0
$22$	0.849606	−	0.490520i	0.181137	−	0.104579i
$23$	−0.0291335	−	0.0168202i	−0.00607475	−	0.00350726i	0.496960	−	0.867774i	$-0.334450\pi$
$23$	−0.0291335	−	0.0168202i	−0.00607475	−	0.00350726i	−0.503034	+	0.864266i	$0.667783\pi$
$24$		0			0
$25$	−2.13510	+	4.52121i	−0.427020	+	0.904242i
$26$	−0.926492	+	6.47573i	−0.181700	+	1.27000i
$27$		0			0
$28$	5.24728	+	3.02952i	0.991643	+	0.572526i
$29$	3.40734	−	5.90168i	0.632727	−	1.09591i	−0.354265	−	0.935145i	$-0.615269\pi$
$29$	3.40734	−	5.90168i	0.632727	−	1.09591i	0.986992	−	0.160770i	$-0.0513976\pi$
$30$		0			0
$31$	−0.352843			−0.0633725			−0.0316863	−	0.999498i	$-0.510088\pi$
$31$	−0.352843			−0.0633725			−0.0316863	+	0.999498i	$0.510088\pi$
$32$	−5.49700	+	3.17369i	−0.971741	+	0.561035i
$33$		0			0
$34$	−12.4158			−2.12930
$35$	−9.29113	−	4.86540i	−1.57049	−	0.822402i
$36$		0			0
$37$	−6.98136	−	4.03069i	−1.14773	−	0.662642i	−0.199396	−	0.979919i	$-0.563898\pi$
$37$	−6.98136	−	4.03069i	−1.14773	−	0.662642i	−0.948333	+	0.317277i	$0.897231\pi$
$38$		−	10.0913i		−	1.63703i
$39$		0			0
$40$	2.42691	−	1.53783i	0.383728	−	0.243152i
$41$	−3.59880	+	6.23331i	−0.562038	+	0.973479i	0.435280	+	0.900295i	$0.356649\pi$
$41$	−3.59880	+	6.23331i	−0.562038	+	0.973479i	−0.997318	+	0.0731840i	$0.976684\pi$
$42$		0			0
$43$	−6.08901	+	3.51549i	−0.928566	+	0.536108i	−0.886358	−	0.463001i	$-0.846773\pi$
$43$	−6.08901	+	3.51549i	−0.928566	+	0.536108i	−0.0422080	+	0.999109i	$0.513439\pi$
$44$	−0.698502			−0.105303
$45$		0			0
$46$	0.0305175	+	0.0528578i	0.00449956	+	0.00779346i
$47$		−	1.99690i		−	0.291277i	−0.989338	−	0.145639i	$-0.953476\pi$
$47$		−	1.99690i		−	0.291277i	0.989338	−	0.145639i	$-0.0465237\pi$
$48$		0			0
$49$	7.49972	−	12.9899i	1.07139	−	1.85570i
$50$	7.45629	−	5.16711i	1.05448	−	0.730739i
$51$		0			0
$52$	2.87665	−	3.66318i	0.398920	−	0.507991i
$53$		−	8.50859i		−	1.16875i	−0.811486	−	0.584373i	$-0.801341\pi$
$53$		−	8.50859i		−	1.16875i	0.811486	−	0.584373i	$-0.198659\pi$
$54$		0			0
$55$	1.20805	−	0.0498027i	0.162894	−	0.00671540i
$56$	3.01331	+	5.21921i	0.402670	+	0.697446i
$57$		0			0
$58$	−10.7076	+	6.18205i	−1.40598	+	0.811743i
$59$	−6.64864	−	11.5158i	−0.865579	−	1.49923i	−0.866471	−	0.499227i	$-0.833617\pi$
$59$	−6.64864	−	11.5158i	−0.865579	−	1.49923i	0.000892529	−	1.00000i	$-0.499716\pi$
$60$		0			0
$61$	1.60333	+	2.77705i	0.205285	+	0.355564i	0.950224	−	0.311569i	$-0.100854\pi$
$61$	1.60333	+	2.77705i	0.205285	+	0.355564i	−0.744938	+	0.667133i	$0.767521\pi$
$62$	0.554408	+	0.320088i	0.0704099	+	0.0406512i
$63$		0			0
$64$	1.68658			0.210822
$65$	−4.71396	+	6.54053i	−0.584695	+	0.811254i
$66$		0			0
$67$	−8.70757	−	5.02732i	−1.06380	−	0.614184i	−0.137318	−	0.990527i	$-0.543848\pi$
$67$	−8.70757	−	5.02732i	−1.06380	−	0.614184i	−0.926481	+	0.376343i	$0.877182\pi$
$68$	7.65573	+	4.42004i	0.928394	+	0.536009i
$69$		0			0
$70$	10.1850	+	16.0734i	1.21735	+	1.92114i
$71$	4.33383	+	7.50641i	0.514331	+	0.890847i	0.999862	+	0.0166277i	$0.00529299\pi$
$71$	4.33383	+	7.50641i	0.514331	+	0.890847i	−0.485531	+	0.874220i	$0.661374\pi$
$72$		0			0
$73$		−	8.05229i		−	0.942449i	−0.882013	−	0.471225i	$-0.843812\pi$
$73$		−	8.05229i		−	0.942449i	0.882013	−	0.471225i	$-0.156188\pi$
$74$	7.31302	+	12.6665i	0.850121	+	1.47245i
$75$		0			0
$76$	−3.59252	+	6.22243i	−0.412091	+	0.713762i
$77$			2.53615i			0.289021i
$78$		0			0
$79$	−2.29181			−0.257849			−0.128924	−	0.991654i	$-0.541152\pi$
$79$	−2.29181			−0.257849			−0.128924	+	0.991654i	$0.541152\pi$
$80$	−10.9806	+	0.452682i	−1.22767	+	0.0506114i
$81$		0			0
$82$	11.3093	−	6.52943i	1.24890	−	0.721055i
$83$			14.8223i			1.62696i	0.581591	+	0.813481i	$0.302430\pi$
$83$			14.8223i			1.62696i	−0.581591	+	0.813481i	$0.697570\pi$
$84$		0			0
$85$	−13.5557	−	7.09857i	−1.47032	−	0.769948i
$86$	12.7566			1.37557
$87$		0			0
$88$	−0.601684	−	0.347382i	−0.0641397	−	0.0370311i
$89$	−3.98458	+	6.90149i	−0.422364	+	0.731557i	−0.996170	−	0.0874348i	$-0.972133\pi$
$89$	−3.98458	+	6.90149i	−0.422364	+	0.731557i	0.573806	+	0.818991i	$0.305466\pi$
$90$		0			0
$91$	−13.3004	−	10.4447i	−1.39426	−	1.09490i
$92$		−	0.0434570i		−	0.00453070i
$93$		0			0
$94$	−1.81152	+	3.13764i	−0.186844	+	0.323623i
$95$	5.76958	−	11.0178i	0.591946	−	1.13040i
$96$		0			0
$97$	0.265973	−	0.153560i	0.0270055	−	0.0155916i	−0.486436	−	0.873716i	$-0.661703\pi$
$97$	0.265973	−	0.153560i	0.0270055	−	0.0155916i	0.513442	+	0.858124i	$0.328370\pi$
$98$	−23.5680	+	13.6070i	−2.38073	+	1.37451i
$99$		0			0
$100$	−6.43712	+	0.531652i	−0.643712	+	0.0531652i
$101$	0.577241	−	0.999811i	0.0574377	−	0.0994849i	−0.835877	−	0.548917i	$-0.815040\pi$
$101$	0.577241	−	0.999811i	0.0574377	−	0.0994849i	0.893315	+	0.449432i	$0.148374\pi$
$102$		0			0
$103$			2.34973i			0.231525i	0.993277	+	0.115763i	$0.0369312\pi$
$103$			2.34973i			0.231525i	−0.993277	+	0.115763i	$0.963069\pi$
$104$	4.29971	−	1.72480i	0.421621	−	0.169131i
$105$		0			0
$106$	−7.71871	+	13.3692i	−0.749708	+	1.29853i
$107$	6.04684	+	3.49114i	0.584570	+	0.337502i	0.762947	−	0.646461i	$-0.223751\pi$
$107$	6.04684	+	3.49114i	0.584570	+	0.337502i	−0.178378	+	0.983962i	$0.557085\pi$
$108$		0			0
$109$	11.0821			1.06147			0.530735	−	0.847538i	$-0.321916\pi$
$109$	11.0821			1.06147			0.530735	+	0.847538i	$0.321916\pi$
$110$	−1.94334	−	1.01765i	−0.185291	−	0.0970294i
$111$		0			0
$112$		−	23.0524i		−	2.17825i
$113$	6.41401	−	3.70313i	0.603379	−	0.348361i	−0.166991	−	0.985958i	$-0.553405\pi$
$113$	6.41401	−	3.70313i	0.603379	−	0.348361i	0.770370	+	0.637597i	$0.220072\pi$
$114$		0			0
$115$	0.00309845	+	0.0751584i	0.000288932	+	0.00700856i
$116$	8.80325			0.817361
$117$		0			0
$118$			24.1257i			2.22095i
$119$	16.0485	−	27.7968i	1.47116	−	2.54813i
$120$		0			0
$121$	5.35381	+	9.27308i	0.486710	+	0.843007i
$122$		−	5.81795i		−	0.526732i
$123$		0			0
$124$	−0.227903	−	0.394740i	−0.0204663	−	0.0354487i
$125$	11.0950	−	1.37845i	0.992370	−	0.123292i
$126$		0			0
$127$	8.96566	+	5.17633i	0.795574	+	0.459325i	0.841921	−	0.539601i	$-0.181425\pi$
$127$	8.96566	+	5.17633i	0.795574	+	0.459325i	−0.0463472	+	0.998925i	$0.514758\pi$
$128$	8.34394	+	4.81737i	0.737507	+	0.425800i
$129$		0			0
$130$	13.3402	−	6.00053i	1.17001	−	0.526281i
$131$	8.12694			0.710054			0.355027	−	0.934856i	$-0.384472\pi$
$131$	8.12694			0.710054			0.355027	+	0.934856i	$0.384472\pi$
$132$		0			0
$133$	22.5927	+	13.0439i	1.95903	+	1.13105i
$134$	9.12123	+	15.7984i	0.787954	+	1.36478i
$135$		0			0
$136$	4.39639	+	7.61477i	0.376987	+	0.652961i
$137$	−6.21344	+	3.58733i	−0.530850	+	0.306487i	−0.741363	−	0.671105i	$-0.765820\pi$
$137$	−6.21344	+	3.58733i	−0.530850	+	0.306487i	0.210512	+	0.977591i	$0.432487\pi$
$138$		0			0
$139$	3.31277	+	5.73789i	0.280986	+	0.486681i	0.971628	−	0.236515i	$-0.0760053\pi$
$139$	3.31277	+	5.73789i	0.280986	+	0.486681i	−0.690642	+	0.723197i	$0.742672\pi$
$140$	−0.558068	−	13.5369i	−0.0471654	−	1.14408i
$141$		0			0
$142$		−	15.7260i		−	1.31970i
$143$	1.92993	+	0.276118i	0.161389	+	0.0230901i
$144$		0			0
$145$	−15.2251	+	0.627666i	−1.26438	+	0.0521248i
$146$	−7.30477	+	12.6522i	−0.604547	+	1.04711i
$147$		0			0
$148$		−	10.4138i		−	0.856006i
$149$	−0.926492	−	1.60473i	−0.0759012	−	0.131465i	0.825577	−	0.564290i	$-0.190850\pi$
$149$	−0.926492	−	1.60473i	−0.0759012	−	0.131465i	−0.901478	+	0.432825i	$0.857517\pi$
$150$		0			0
$151$	−4.08459			−0.332399			−0.166199	−	0.986092i	$-0.553150\pi$
$151$	−4.08459			−0.332399			−0.166199	+	0.986092i	$0.553150\pi$
$152$	−6.18914	+	3.57330i	−0.502005	+	0.289833i
$153$		0			0
$154$	2.30071	−	3.98495i	0.185397	−	0.321117i
$155$	0.422301	+	0.666449i	0.0339200	+	0.0535305i
$156$		0			0
$157$		−	17.0544i		−	1.36109i	−0.732705	−	0.680547i	$-0.761742\pi$
$157$		−	17.0544i		−	1.36109i	0.732705	−	0.680547i	$-0.238258\pi$
$158$	3.60103	+	2.07905i	0.286482	+	0.165401i
$159$		0			0
$160$	12.5735	+	6.58427i	0.994025	+	0.520532i
$161$	−0.157786			−0.0124352
$162$		0			0
$163$	11.5842	−	6.68815i	0.907346	−	0.523856i	0.0277697	−	0.999614i	$-0.491160\pi$
$163$	11.5842	−	6.68815i	0.907346	−	0.523856i	0.879576	+	0.475758i	$0.157826\pi$
$164$	−9.29793			−0.726046
$165$		0			0
$166$	13.4463	−	23.2897i	1.04364	−	1.80763i
$167$	−1.96756	−	1.13597i	−0.152255	−	0.0879042i	0.421937	−	0.906625i	$-0.361350\pi$
$167$	−1.96756	−	1.13597i	−0.152255	−	0.0879042i	−0.574192	+	0.818721i	$0.694684\pi$
$168$		0			0
$169$	−9.39611	+	8.98405i	−0.722777	+	0.691081i
$170$	14.8599	+	23.4509i	1.13970	+	1.79861i
$171$		0			0
$172$	−7.86584	−	4.54134i	−0.599764	−	0.346274i
$173$	1.95817	−	1.13055i	0.148877	−	0.0859542i	−0.423711	−	0.905797i	$-0.639273\pi$
$173$	1.95817	−	1.13055i	0.148877	−	0.0859542i	0.572588	+	0.819843i	$0.305939\pi$
$174$		0			0
$175$	1.93035	+	23.3722i	0.145921	+	1.76677i
$176$	1.32877	+	2.30150i	0.100160	+	0.173482i
$177$		0			0
$178$	12.5216	−	7.22936i	0.938534	−	0.541863i
$179$	−1.59088	+	2.75548i	−0.118908	+	0.205954i	−0.919335	−	0.393476i	$-0.871273\pi$
$179$	−1.59088	+	2.75548i	−0.118908	+	0.205954i	0.800427	+	0.599430i	$0.204606\pi$
$180$		0			0
$181$	3.93646			0.292595			0.146297	−	0.989241i	$-0.453264\pi$
$181$	3.93646			0.292595			0.146297	+	0.989241i	$0.453264\pi$
$182$	11.4234	+	28.4770i	0.846756	+	2.11086i
$183$		0			0
$184$	0.0216122	−	0.0374335i	0.00159327	−	0.00275963i
$185$	0.742494	+	18.0105i	0.0545893	+	1.32416i
$186$		0			0
$187$			3.70022i			0.270587i
$188$	2.23401	−	1.28980i	0.162932	−	0.0940687i
$189$		0			0
$190$	−19.0605	+	12.0778i	−1.38279	+	0.876217i
$191$	−5.06601	−	8.77459i	−0.366564	−	0.634907i	0.622462	−	0.782650i	$-0.286132\pi$
$191$	−5.06601	−	8.77459i	−0.366564	−	0.634907i	−0.989026	+	0.147743i	$0.952799\pi$
$192$		0			0
$193$	7.82309	+	4.51666i	0.563118	+	0.325117i	0.754396	−	0.656419i	$-0.227930\pi$
$193$	7.82309	+	4.51666i	0.563118	+	0.325117i	−0.191278	+	0.981536i	$0.561263\pi$
$194$	−0.557218			−0.0400059
$195$		0			0
$196$	19.3764			1.38403
$197$	−13.0568	−	7.53836i	−0.930260	−	0.537086i	−0.0433665	−	0.999059i	$-0.513808\pi$
$197$	−13.0568	−	7.53836i	−0.930260	−	0.537086i	−0.886894	+	0.461973i	$0.847142\pi$
$198$		0			0
$199$	6.21871	+	10.7711i	0.440833	+	0.763545i	0.997751	−	0.0670220i	$-0.0213498\pi$
$199$	6.21871	+	10.7711i	0.440833	+	0.763545i	−0.556918	+	0.830567i	$0.688016\pi$
$200$	−5.80929	−	2.74338i	−0.410779	−	0.193986i
$201$		0			0
$202$	−1.81399	+	1.04731i	−0.127632	+	0.0736884i
$203$		−	31.9632i		−	2.24338i
$204$		0			0
$205$	16.0807	−	0.662936i	1.12312	−	0.0463014i
$206$	2.13159	−	3.69203i	0.148515	−	0.257236i
$207$		0			0
$208$	−17.5421	−	2.50977i	−1.21633	−	0.174022i
$209$	−3.00747			−0.208031
$210$		0			0
$211$	6.48891	−	11.2391i	0.446715	−	0.773733i	−0.551455	−	0.834205i	$-0.685927\pi$
$211$	6.48891	−	11.2391i	0.446715	−	0.773733i	0.998170	+	0.0604716i	$0.0192604\pi$
$212$	9.51889	−	5.49574i	0.653760	−	0.377449i
$213$		0			0
$214$	−6.33410	−	10.9710i	−0.432990	−	0.749961i
$215$	13.9277	+	7.29338i	0.949860	+	0.497404i
$216$		0			0
$217$	−1.43324	+	0.827480i	−0.0972945	+	0.0561730i
$218$	−17.4128	−	10.0533i	−1.17935	−	0.680895i
$219$		0			0
$220$	0.836002	+	1.31933i	0.0563633	+	0.0889490i
$221$	−19.4052	−	15.2387i	−1.30533	−	1.02506i
$222$		0			0
$223$	7.20459	+	4.15957i	0.482455	+	0.278546i	0.721439	−	0.692478i	$-0.243481\pi$
$223$	7.20459	+	4.15957i	0.482455	+	0.278546i	−0.238984	+	0.971024i	$0.576814\pi$
$224$	−14.8857	+	25.7829i	−0.994596	+	1.72269i
$225$		0			0
$226$	−13.4374			−0.893845
$227$	2.58811	−	1.49425i	0.171779	−	0.0991766i	−0.411645	−	0.911344i	$-0.635046\pi$
$227$	2.58811	−	1.49425i	0.171779	−	0.0991766i	0.583424	+	0.812167i	$0.301712\pi$
$228$		0			0
$229$	−12.2067			−0.806639			−0.403319	−	0.915059i	$-0.632144\pi$
$229$	−12.2067			−0.806639			−0.403319	+	0.915059i	$0.632144\pi$
$230$	0.0633128	−	0.120904i	0.00417472	−	0.00797219i
$231$		0			0
$232$	7.58305	+	4.37807i	0.497851	+	0.287435i
$233$			10.9631i			0.718217i	0.933296	+	0.359108i	$0.116919\pi$
$233$			10.9631i			0.718217i	−0.933296	+	0.359108i	$0.883081\pi$
$234$		0			0
$235$	−3.77173	+	2.38999i	−0.246041	+	0.155906i
$236$	8.58876	−	14.8762i	0.559081	−	0.968357i
$237$		0			0
$238$	−50.4326	+	29.1173i	−3.26906	+	1.88739i
$239$	17.8760			1.15630			0.578152	−	0.815929i	$-0.303774\pi$
$239$	17.8760			1.15630			0.578152	+	0.815929i	$0.303774\pi$
$240$		0			0
$241$	1.44815	+	2.50827i	0.0932837	+	0.161572i	0.908891	−	0.417034i	$-0.136930\pi$
$241$	1.44815	+	2.50827i	0.0932837	+	0.161572i	−0.815607	+	0.578606i	$0.803597\pi$
$242$		−	19.4272i		−	1.24883i
$243$		0			0
$244$	−2.07119	+	3.58741i	−0.132595	+	0.229660i
$245$	−33.5113	+	1.38152i	−2.14096	+	0.0882623i
$246$		0			0
$247$	12.3857	−	15.7722i	0.788083	−	1.00356i
$248$		−	0.453367i		−	0.0287888i
$249$		0			0
$250$	−18.6837	−	7.89915i	−1.18166	−	0.499586i
$251$	1.96556	+	3.40444i	0.124065	+	0.214887i	0.921367	−	0.388694i	$-0.127074\pi$
$251$	1.96556	+	3.40444i	0.124065	+	0.214887i	−0.797302	+	0.603580i	$0.793740\pi$
$252$		0			0
$253$	0.0157529	−	0.00909497i	0.000990379	−	0.000571796i
$254$	−9.39159	−	16.2667i	−0.589281	−	1.02066i
$255$		0			0
$256$	−10.4269	−	18.0599i	−0.651682	−	1.12875i
$257$	0.404805	+	0.233714i	0.0252511	+	0.0145787i	0.512572	−	0.858644i	$-0.328693\pi$
$257$	0.404805	+	0.233714i	0.0252511	+	0.0145787i	−0.487321	+	0.873223i	$0.662026\pi$
$258$		0			0
$259$	−37.8108			−2.34945
$260$	−10.3619	−	1.04913i	−0.642619	−	0.0650642i
$261$		0			0
$262$	−12.7695	−	7.37249i	−0.788904	−	0.455474i
$263$	12.5607	+	7.25191i	0.774525	+	0.447172i	0.834486	−	0.551028i	$-0.185764\pi$
$263$	12.5607	+	7.25191i	0.774525	+	0.447172i	−0.0599614	+	0.998201i	$0.519098\pi$
$264$		0			0
$265$	−16.0710	+	10.1835i	−0.987233	+	0.625568i
$266$	−23.6660	−	40.9907i	−1.45105	−	2.51330i
$267$		0			0
$268$		−	12.9887i		−	0.793409i
$269$	−1.39941	−	2.42385i	−0.0853236	−	0.147785i	0.820205	−	0.572069i	$-0.193859\pi$
$269$	−1.39941	−	2.42385i	−0.0853236	−	0.147785i	−0.905529	+	0.424284i	$0.860526\pi$
$270$		0			0
$271$	12.4889	−	21.6314i	0.758647	−	1.31402i	−0.184893	−	0.982759i	$-0.559194\pi$
$271$	12.4889	−	21.6314i	0.758647	−	1.31402i	0.943541	−	0.331257i	$-0.107473\pi$
$272$		−	33.6332i		−	2.03931i
$273$		0			0
$274$	13.0172			0.786401
$275$	−1.53993	−	2.22216i	−0.0928610	−	0.134001i
$276$		0			0
$277$	−18.5735	+	10.7234i	−1.11597	+	0.644306i	−0.940369	−	0.340155i	$-0.889520\pi$
$277$	−18.5735	+	10.7234i	−1.11597	+	0.644306i	−0.175602	+	0.984461i	$0.556187\pi$
$278$		−	12.0210i		−	0.720969i
$279$		0			0
$280$	6.25153	−	11.9381i	0.373601	−	0.713440i
$281$	−19.0470			−1.13625			−0.568125	−	0.822942i	$-0.692331\pi$
$281$	−19.0470			−1.13625			−0.568125	+	0.822942i	$0.692331\pi$
$282$		0			0
$283$	6.68052	+	3.85700i	0.397116	+	0.229275i	0.685239	−	0.728319i	$-0.259698\pi$
$283$	6.68052	+	3.85700i	0.397116	+	0.229275i	−0.288123	+	0.957593i	$0.593031\pi$
$284$	−5.59848	+	9.69685i	−0.332208	+	0.575402i
$285$		0			0
$286$	−2.78193	−	2.18462i	−0.164499	−	0.129179i
$287$			33.7593i			1.99275i
$288$		0			0
$289$	14.9146	−	25.8328i	0.877327	−	1.51958i
$290$	24.4920	+	12.8255i	1.43822	+	0.753140i
$291$		0			0
$292$	9.00841	−	5.20101i	0.527177	−	0.304366i
$293$	−27.3147	+	15.7701i	−1.59574	+	0.921302i	−0.603447	+	0.797403i	$0.706206\pi$
$293$	−27.3147	+	15.7701i	−1.59574	+	0.921302i	−0.992295	+	0.123898i	$0.960460\pi$
$294$		0			0
$295$	−13.7935	+	26.3406i	−0.803090	+	1.53361i
$296$	5.17902	−	8.97033i	0.301024	−	0.521390i
$297$		0			0
$298$			3.36193i			0.194752i
$299$	−0.0171785	+	0.120070i	−0.000993460	+	0.00694381i
$300$		0			0
$301$	−16.4889	+	28.5596i	−0.950405	+	1.64615i
$302$	6.41794	+	3.70540i	0.369311	+	0.213222i
$303$		0			0
$304$	27.3364			1.56785
$305$	3.32633	−	6.35207i	0.190465	−	0.363718i
$306$		0			0
$307$			26.0969i			1.48943i	0.667384	+	0.744714i	$0.267414\pi$
$307$			26.0969i			1.48943i	−0.667384	+	0.744714i	$0.732586\pi$
$308$	−2.83729	+	1.63811i	−0.161670	+	0.0933401i
$309$		0			0
$310$	−0.0589634	−	1.43026i	−0.00334890	−	0.0812334i
$311$	4.26319			0.241743			0.120872	−	0.992668i	$-0.461431\pi$
$311$	4.26319			0.241743			0.120872	+	0.992668i	$0.461431\pi$
$312$		0			0
$313$			6.66418i			0.376682i	0.982104	+	0.188341i	$0.0603110\pi$
$313$			6.66418i			0.376682i	−0.982104	+	0.188341i	$0.939689\pi$
$314$	−15.4712	+	26.7970i	−0.873092	+	1.51224i
$315$		0			0
$316$	−1.48029	−	2.56394i	−0.0832727	−	0.144233i
$317$		−	23.3982i		−	1.31417i	−0.753815	−	0.657087i	$-0.771788\pi$
$317$		−	23.3982i		−	1.31417i	0.753815	−	0.657087i	$-0.228212\pi$
$318$		0			0
$319$	1.84240	+	3.19114i	0.103155	+	0.178669i
$320$	−2.01858	−	3.18560i	−0.112842	−	0.178081i
$321$		0			0
$322$	0.247922	+	0.143138i	0.0138162	+	0.00797676i
$323$	32.9625	+	19.0309i	1.83408	+	1.05891i
$324$		0			0
$325$	17.9956	+	1.07566i	0.998218	+	0.0596670i
$326$	−24.2691			−1.34414
$327$		0			0
$328$	−8.00915	−	4.62409i	−0.442232	−	0.255322i
$329$	−4.68308	−	8.11133i	−0.258187	−	0.447192i
$330$		0			0
$331$	4.83285	+	8.37074i	0.265637	+	0.460097i	0.967730	−	0.251988i	$-0.0810843\pi$
$331$	4.83285	+	8.37074i	0.265637	+	0.460097i	−0.702093	+	0.712085i	$0.747751\pi$
$332$	−16.5823	+	9.57381i	−0.910073	+	0.525431i
$333$		0			0
$334$	2.06103	+	3.56982i	0.112775	+	0.195332i
$335$	0.926082	+	22.4638i	0.0505973	+	1.22733i
$336$		0			0
$337$			0.725932i			0.0395440i	0.999805	+	0.0197720i	$0.00629404\pi$
$337$			0.725932i			0.0395440i	−0.999805	+	0.0197720i	$0.993706\pi$
$338$	22.9138	−	5.59244i	1.24634	−	0.304189i
$339$		0			0
$340$	−0.814216	−	19.7502i	−0.0441571	−	1.07111i
$341$	0.0953941	−	0.165227i	0.00516588	−	0.00894757i
$342$		0			0
$343$		−	37.5202i		−	2.02590i
$344$	−4.51704	−	7.82375i	−0.243543	−	0.421828i
$345$		0			0
$346$	−4.10240			−0.220546
$347$	24.7184	−	14.2712i	1.32695	−	0.766117i	0.342126	−	0.939654i	$-0.388853\pi$
$347$	24.7184	−	14.2712i	1.32695	−	0.766117i	0.984827	+	0.173538i	$0.0555199\pi$
$348$		0			0
$349$	−8.35256	+	14.4671i	−0.447102	+	0.774404i	−0.998196	−	0.0600395i	$-0.980877\pi$
$349$	−8.35256	+	14.4671i	−0.447102	+	0.774404i	0.551094	+	0.834443i	$0.314211\pi$
$350$	18.1694	−	38.4749i	0.971196	−	2.05657i
$351$		0			0
$352$		−	3.43213i		−	0.182933i
$353$	4.98961	+	2.88075i	0.265570	+	0.153327i	0.626873	−	0.779122i	$-0.284335\pi$
$353$	4.98961	+	2.88075i	0.265570	+	0.153327i	−0.361303	+	0.932449i	$0.617668\pi$
$354$		0			0
$355$	8.99113	−	17.1698i	0.477200	−	0.911277i
$356$	−10.2946			−0.545614
$357$		0			0
$358$	4.99936	−	2.88638i	0.264224	−	0.152550i
$359$	21.0921			1.11320			0.556600	−	0.830780i	$-0.312105\pi$
$359$	21.0921			1.11320			0.556600	+	0.830780i	$0.312105\pi$
$360$		0			0
$361$	−5.96795	+	10.3368i	−0.314102	+	0.544041i
$362$	−6.18520	−	3.57103i	−0.325087	−	0.187689i
$363$		0			0
$364$	3.09406	−	21.6260i	0.162173	−	1.13351i
$365$	−15.2091	+	9.63738i	−0.796082	+	0.504444i
$366$		0			0
$367$	−4.92175	−	2.84157i	−0.256913	−	0.148329i	0.366012	−	0.930610i	$-0.380723\pi$
$367$	−4.92175	−	2.84157i	−0.256913	−	0.148329i	−0.622926	+	0.782281i	$0.714056\pi$
$368$	−0.143187	+	0.0826688i	−0.00746412	+	0.00430941i
$369$		0			0
$370$	15.1719	−	28.9727i	0.788749	−	1.50622i
$371$	−19.9542	−	34.5616i	−1.03597	−	1.79435i
$372$		0			0
$373$	−1.22018	+	0.704474i	−0.0631788	+	0.0364763i	−0.531257	−	0.847211i	$-0.678280\pi$
$373$	−1.22018	+	0.704474i	−0.0631788	+	0.0364763i	0.468078	+	0.883687i	$0.344947\pi$
$374$	3.35672	−	5.81401i	0.173572	−	0.300635i
$375$		0			0
$376$	2.56581			0.132321
$377$	−24.3230	−	3.47992i	−1.25270	−	0.179225i
$378$		0			0
$379$	−2.12429	+	3.67938i	−0.109118	+	0.188997i	−0.915413	−	0.402516i	$-0.868136\pi$
$379$	−2.12429	+	3.67938i	−0.109118	+	0.188997i	0.806295	+	0.591513i	$0.201469\pi$
$380$	16.0526	−	0.661779i	0.823482	−	0.0339485i
$381$		0			0
$382$			18.3829i			0.940550i
$383$	−17.6210	+	10.1735i	−0.900391	+	0.519841i	−0.877327	−	0.479893i	$-0.840676\pi$
$383$	−17.6210	+	10.1735i	−0.900391	+	0.519841i	−0.0230641	+	0.999734i	$0.507342\pi$
$384$		0			0
$385$	4.79027	−	3.03539i	0.244135	−	0.154698i
$386$	−8.19474	−	14.1937i	−0.417101	−	0.722440i
$387$		0			0
$388$	0.343587	+	0.198370i	0.0174430	+	0.0100707i
$389$	22.1170			1.12138			0.560689	−	0.828027i	$-0.310536\pi$
$389$	22.1170			1.12138			0.560689	+	0.828027i	$0.310536\pi$
$390$		0			0
$391$	−0.230208			−0.0116421
$392$	16.6907	+	9.63636i	0.843006	+	0.486710i
$393$		0			0
$394$	13.6771	+	23.6894i	0.689043	+	1.19346i
$395$	2.74295	+	4.32876i	0.138013	+	0.217803i
$396$		0			0
$397$	1.16956	−	0.675248i	0.0586987	−	0.0338897i	−0.470363	−	0.882473i	$-0.655877\pi$
$397$	1.16956	−	0.675248i	0.0586987	−	0.0338897i	0.529062	+	0.848583i	$0.322544\pi$
$398$		−	22.5657i		−	1.13111i
$399$		0			0
$400$	13.9972	+	20.1983i	0.699858	+	1.00992i
$401$	−9.70672	+	16.8125i	−0.484731	+	0.839578i	−0.999846	−	0.0175428i	$-0.994416\pi$
$401$	−9.70672	+	16.8125i	−0.484731	+	0.839578i	0.515116	+	0.857121i	$0.327749\pi$
$402$		0			0
$403$	0.473645	+	1.18074i	0.0235939	+	0.0588167i
$404$	1.49137			0.0741984
$405$		0			0
$406$	−28.9960	+	50.2225i	−1.43905	+	2.49250i
$407$	3.77494	−	2.17946i	0.187117	−	0.108032i
$408$		0			0
$409$	4.60583	+	7.97754i	0.227744	+	0.394464i	0.957139	−	0.289629i	$-0.0935318\pi$
$409$	4.60583	+	7.97754i	0.227744	+	0.394464i	−0.729395	+	0.684092i	$0.760198\pi$
$410$	−25.8683	−	13.5462i	−1.27754	−	0.669000i
$411$		0			0
$412$	−2.62873	+	1.51770i	−0.129508	+	0.0747716i
$413$	−54.0131	−	31.1845i	−2.65781	−	1.53449i
$414$		0			0
$415$	27.9964	−	17.7401i	1.37429	−	0.870828i
$416$	17.9993	+	14.1346i	0.882486	+	0.693006i
$417$		0			0
$418$	4.72551	+	2.72828i	0.231132	+	0.133444i
$419$	−10.8164	+	18.7346i	−0.528417	+	0.915245i	0.471034	+	0.882115i	$0.343881\pi$
$419$	−10.8164	+	18.7346i	−0.528417	+	0.915245i	−0.999451	+	0.0331302i	$0.989452\pi$
$420$		0			0
$421$	4.97532			0.242482			0.121241	−	0.992623i	$-0.461313\pi$
$421$	4.97532			0.242482			0.121241	+	0.992623i	$0.461313\pi$
$422$	−20.3915	+	11.7731i	−0.992644	+	0.573103i
$423$		0			0
$424$	10.9327			0.530937
$425$	2.81636	+	34.0998i	0.136613	+	1.65408i
$426$		0			0
$427$	13.0253	+	7.52018i	0.630340	+	0.363927i
$428$			9.01978i			0.435987i
$429$		0			0
$430$	−15.2677	−	24.0945i	−0.736273	−	1.16194i
$431$	−3.60990	+	6.25253i	−0.173883	+	0.301174i	−0.939774	−	0.341796i	$-0.888965\pi$
$431$	−3.60990	+	6.25253i	−0.173883	+	0.301174i	0.765891	+	0.642970i	$0.222298\pi$
$432$		0			0
$433$	19.4152	−	11.2094i	0.933034	−	0.538688i	0.0452643	−	0.998975i	$-0.485587\pi$
$433$	19.4152	−	11.2094i	0.933034	−	0.538688i	0.887770	+	0.460287i	$0.152254\pi$
$434$	3.00265			0.144132
$435$		0			0
$436$	7.15796	+	12.3980i	0.342804	+	0.593754i
$437$		−	0.187108i		−	0.00895060i
$438$		0			0
$439$	18.1123	−	31.3715i	0.864454	−	1.49728i	−0.00313495	−	0.999995i	$-0.500998\pi$
$439$	18.1123	−	31.3715i	0.864454	−	1.49728i	0.867589	−	0.497283i	$-0.165669\pi$
$440$	0.0639913	+	1.55222i	0.00305067	+	0.0739993i
$441$		0			0
$442$	16.6666	+	41.5477i	0.792748	+	1.97622i
$443$		−	30.7382i		−	1.46042i	−0.683225	−	0.730208i	$-0.739423\pi$
$443$		−	30.7382i		−	1.46042i	0.683225	−	0.730208i	$-0.260577\pi$
$444$		0			0
$445$	17.8045	−	0.733999i	0.844012	−	0.0347949i
$446$	−7.54685	−	13.0715i	−0.357354	−	0.618955i
$447$		0			0
$448$	6.85083	−	3.95533i	0.323671	−	0.186872i
$449$	16.2145	+	28.0844i	0.765210	+	1.32538i	0.940135	+	0.340801i	$0.110698\pi$
$449$	16.2145	+	28.0844i	0.765210	+	1.32538i	−0.174925	+	0.984582i	$0.555968\pi$
$450$		0			0
$451$	−1.94593	−	3.37045i	−0.0916303	−	0.158708i
$452$	8.28567	+	4.78373i	0.389725	+	0.225008i
$453$		0			0
$454$	−5.42212			−0.254473
$455$	−3.80923	+	37.6225i	−0.178579	+	1.76377i
$456$		0			0
$457$	4.16657	+	2.40557i	0.194904	+	0.112528i	0.594276	−	0.804261i	$-0.297439\pi$
$457$	4.16657	+	2.40557i	0.194904	+	0.112528i	−0.399372	+	0.916789i	$0.630772\pi$
$458$	19.1798	+	11.0735i	0.896214	+	0.517430i
$459$		0			0
$460$	−0.0820814	+	0.0520115i	−0.00382706	+	0.00242505i
$461$	14.2320	+	24.6506i	0.662851	+	1.14809i	0.979863	+	0.199670i	$0.0639871\pi$
$461$	14.2320	+	24.6506i	0.662851	+	1.14809i	−0.317012	+	0.948422i	$0.602680\pi$
$462$		0			0
$463$		−	4.02553i		−	0.187082i	−0.995615	−	0.0935411i	$-0.970181\pi$
$463$		−	4.02553i		−	0.187082i	0.995615	−	0.0935411i	$-0.0298187\pi$
$464$	−16.7465	−	29.0059i	−0.777439	−	1.34656i
$465$		0			0
$466$	9.94537	−	17.2259i	0.460710	−	0.797973i
$467$			4.45595i			0.206197i	0.994671	+	0.103098i	$0.0328757\pi$
$467$			4.45595i			0.206197i	−0.994671	+	0.103098i	$0.967124\pi$
$468$		0			0
$469$	−47.1598			−2.17764
$470$	8.09449	−	0.333700i	0.373371	−	0.0153924i
$471$		0			0
$472$	14.7966	−	8.54281i	0.681068	−	0.393215i
$473$		−	3.80177i		−	0.174806i
$474$		0			0
$475$	−27.7157	+	2.28908i	−1.27168	+	0.105030i
$476$	41.4631			1.90046
$477$		0			0
$478$	−28.0879	−	16.2165i	−1.28471	−	0.741728i
$479$	16.8596	−	29.2016i	0.770333	−	1.33426i	−0.167048	−	0.985949i	$-0.553424\pi$
$479$	16.8596	−	29.2016i	0.770333	−	1.33426i	0.937381	−	0.348306i	$-0.113243\pi$
$480$		0			0
$481$	−4.11656	+	28.7727i	−0.187699	+	1.31192i
$482$		−	5.25487i		−	0.239353i
$483$		0			0
$484$	−6.91610	+	11.9790i	−0.314368	+	0.544502i
$485$	−0.608374	−	0.318581i	−0.0276248	−	0.0144660i
$486$		0			0
$487$	−16.7539	+	9.67286i	−0.759191	+	0.438319i	−0.829005	−	0.559241i	$-0.811093\pi$
$487$	−16.7539	+	9.67286i	−0.759191	+	0.438319i	0.0698142	+	0.997560i	$0.477759\pi$
$488$	−3.56822	+	2.06011i	−0.161526	+	0.0932568i
$489$		0			0
$490$	53.9082	+	28.2296i	2.43532	+	1.27528i
$491$	15.3500	−	26.5869i	0.692735	−	1.19985i	−0.278204	−	0.960522i	$-0.589739\pi$
$491$	15.3500	−	26.5869i	0.692735	−	1.19985i	0.970938	−	0.239330i	$-0.0769276\pi$
$492$		0			0
$493$		−	46.6340i		−	2.10029i
$494$	−33.7691	+	13.5463i	−1.51934	+	0.609475i
$495$		0			0
$496$	−0.867086	+	1.50184i	−0.0389333	+	0.0674344i
$497$	35.2077	+	20.3272i	1.57928	+	0.911799i
$498$		0			0
$499$	−2.87413			−0.128664			−0.0643318	−	0.997929i	$-0.520492\pi$
$499$	−2.87413			−0.128664			−0.0643318	+	0.997929i	$0.520492\pi$
$500$	8.70846	+	11.5221i	0.389454	+	0.515284i
$501$		0			0
$502$		−	7.13235i		−	0.318333i
$503$	13.9368	−	8.04644i	0.621413	−	0.358773i	−0.156006	−	0.987756i	$-0.549862\pi$
$503$	13.9368	−	8.04644i	0.621413	−	0.358773i	0.777419	+	0.628983i	$0.216529\pi$
$504$		0			0
$505$	−2.57931	+	0.106334i	−0.114778	+	0.00473179i
$506$	−0.0330026			−0.00146715
$507$		0			0
$508$			13.3736i			0.593360i
$509$	−13.8573	+	24.0016i	−0.614216	+	1.06385i	0.376306	+	0.926495i	$0.377194\pi$
$509$	−13.8573	+	24.0016i	−0.614216	+	1.06385i	−0.990522	+	0.137357i	$0.956139\pi$
$510$		0			0
$511$	−18.8840	−	32.7081i	−0.835381	−	1.44692i
$512$			18.5663i			0.820522i
$513$		0			0
$514$	−0.424036	−	0.734452i	−0.0187034	−	0.0323953i
$515$	4.43815	−	2.81227i	0.195568	−	0.123923i
$516$		0			0
$517$	0.935095	+	0.539878i	0.0411255	+	0.0237438i
$518$	59.4105	+	34.3007i	2.61035	+	1.50708i
$519$		0			0
$520$	−8.40391	−	6.05695i	−0.368536	−	0.265615i
$521$	−9.59699			−0.420452			−0.210226	−	0.977653i	$-0.567420\pi$
$521$	−9.59699			−0.420452			−0.210226	+	0.977653i	$0.567420\pi$
$522$		0			0
$523$	12.1083	+	6.99072i	0.529458	+	0.305683i	0.740796	−	0.671730i	$-0.234449\pi$
$523$	12.1083	+	6.99072i	0.529458	+	0.305683i	−0.211337	+	0.977413i	$0.567782\pi$
$524$	5.24923	+	9.09192i	0.229313	+	0.397183i
$525$		0			0
$526$	−13.1574	−	22.7893i	−0.573690	−	0.993660i
$527$	−2.09108	+	1.20729i	−0.0910889	+	0.0525902i
$528$		0			0
$529$	−11.4994	−	19.9176i	−0.499975	−	0.865983i
$530$	34.4898	−	1.42187i	1.49814	−	0.0617619i
$531$		0			0
$532$			33.7004i			1.46110i
$533$	25.6897	+	3.67547i	1.11275	+	0.159202i
$534$		0			0
$535$	−0.643104	−	15.5996i	−0.0278038	−	0.674430i
$536$	6.45958	−	11.1883i	0.279011	−	0.483262i
$537$		0			0
$538$			5.07800i			0.218928i
$539$	4.05522	+	7.02385i	0.174671	+	0.302539i
$540$		0			0
$541$	43.8366			1.88468			0.942342	−	0.334651i	$-0.108618\pi$
$541$	43.8366			1.88468			0.942342	+	0.334651i	$0.108618\pi$
$542$	−39.2466	+	22.6591i	−1.68579	+	0.973290i
$543$		0			0
$544$	−21.7181	+	37.6169i	−0.931158	+	1.61281i
$545$	−13.2636	−	20.9318i	−0.568150	−	0.896619i
$546$		0			0
$547$			11.7486i			0.502335i	0.967944	+	0.251167i	$0.0808145\pi$
$547$			11.7486i			0.502335i	−0.967944	+	0.251167i	$0.919186\pi$
$548$	−8.02658	−	4.63415i	−0.342878	−	0.197961i
$549$		0			0
$550$	0.403754	+	4.88856i	0.0172161	+	0.208449i
$551$	37.9032			1.61473
$552$		0			0
$553$	−9.30925	+	5.37470i	−0.395870	+	0.228555i
$554$	38.9116			1.65320
$555$		0			0
$556$	−4.27947	+	7.41225i	−0.181490	+	0.314350i
$557$	−17.2830	−	9.97832i	−0.732303	−	0.422795i	0.0869613	−	0.996212i	$-0.472284\pi$
$557$	−17.2830	−	9.97832i	−0.732303	−	0.422795i	−0.819264	+	0.573417i	$0.805618\pi$
$558$		0			0
$559$	19.9378	+	15.6569i	0.843277	+	0.662216i
$560$	−43.5412	+	27.5903i	−1.83995	+	1.16590i
$561$		0			0
$562$	29.9278	+	17.2788i	1.26243	+	0.728863i
$563$	−33.2872	+	19.2184i	−1.40289	+	0.809958i	−0.994688	−	0.102935i	$-0.967177\pi$
$563$	−33.2872	+	19.2184i	−1.40289	+	0.809958i	−0.408200	+	0.912892i	$0.633843\pi$
$564$		0			0
$565$	−14.6711	−	7.68266i	−0.617216	−	0.323212i
$566$	−6.99789	−	12.1207i	−0.294143	−	0.509471i
$567$		0			0
$568$	−9.64496	+	5.56852i	−0.404694	+	0.233650i
$569$	14.8151	−	25.6605i	0.621081	−	1.07574i	−0.368203	−	0.929745i	$-0.620027\pi$
$569$	14.8151	−	25.6605i	0.621081	−	1.07574i	0.989285	−	0.145999i	$-0.0466397\pi$
$570$		0			0
$571$	8.27270			0.346202			0.173101	−	0.984904i	$-0.444621\pi$
$571$	8.27270			0.346202			0.173101	+	0.984904i	$0.444621\pi$
$572$	0.937645	+	2.33743i	0.0392049	+	0.0977329i
$573$		0			0
$574$	30.6253	−	53.0447i	1.27828	−	2.21404i
$575$	0.138251	−	0.0958058i	0.00576545	−	0.00399538i
$576$		0			0
$577$		−	6.98163i		−	0.290649i	−0.989384	−	0.145324i	$-0.953577\pi$
$577$		−	6.98163i		−	0.290649i	0.989384	−	0.145324i	$-0.0464226\pi$
$578$	−46.8693	+	27.0600i	−1.94951	+	1.12555i
$579$		0			0
$580$	−10.5362	−	16.6275i	−0.437491	−	0.690421i
$581$	34.7610	+	60.2078i	1.44213	+	2.49784i
$582$		0			0
$583$	3.98435	+	2.30037i	0.165015	+	0.0952715i
$584$	10.3464			0.428135
$585$		0			0
$586$	57.2246			2.36393
$587$	−19.4660	−	11.2387i	−0.803448	−	0.463871i	0.0412272	−	0.999150i	$-0.486873\pi$
$587$	−19.4660	−	11.2387i	−0.803448	−	0.463871i	−0.844675	+	0.535279i	$0.820207\pi$
$588$		0			0
$589$	−0.981258	−	1.69959i	−0.0404320	−	0.0700303i
$590$	45.5685	−	28.8749i	1.87603	−	1.18876i
$591$		0			0
$592$	−34.3123	+	19.8102i	−1.41023	+	0.814196i
$593$			22.5363i			0.925453i	0.886501	+	0.462727i	$0.153129\pi$
$593$			22.5363i			0.925453i	−0.886501	+	0.462727i	$0.846871\pi$
$594$		0			0
$595$	−71.7101	+	2.95629i	−2.93983	+	0.121196i
$596$	1.19685	−	2.07301i	0.0490249	−	0.0849136i
$597$		0			0
$598$	0.135915	−	0.173077i	0.00555798	−	0.00707763i
$599$	22.7143			0.928081			0.464040	−	0.885814i	$-0.346399\pi$
$599$	22.7143			0.928081			0.464040	+	0.885814i	$0.346399\pi$
$600$		0			0
$601$	6.14687	−	10.6467i	0.250736	−	0.434288i	−0.712993	−	0.701172i	$-0.752661\pi$
$601$	6.14687	−	10.6467i	0.250736	−	0.434288i	0.963729	+	0.266884i	$0.0859940\pi$
$602$	51.8167	−	29.9164i	2.11189	−	1.21930i
$603$		0			0
$604$	−2.63825	−	4.56959i	−0.107349	−	0.185934i
$605$	11.1072	−	21.2107i	0.451573	−	0.862339i
$606$		0			0
$607$	−31.2486	+	18.0414i	−1.26834	+	0.732276i	−0.974674	−	0.223632i	$-0.928209\pi$
$607$	−31.2486	+	18.0414i	−1.26834	+	0.732276i	−0.293666	+	0.955908i	$0.594875\pi$
$608$	−30.5743	−	17.6521i	−1.23995	−	0.715887i
$609$		0			0
$610$	−10.9889	+	6.96321i	−0.444928	+	0.281932i
$611$	−6.68232	+	2.68057i	−0.270338	+	0.108444i
$612$		0			0
$613$	19.6890	+	11.3675i	0.795233	+	0.459128i	0.841801	−	0.539787i	$-0.181495\pi$
$613$	19.6890	+	11.3675i	0.795233	+	0.459128i	−0.0465688	+	0.998915i	$0.514829\pi$
$614$	23.6742	−	41.0050i	0.955414	−	1.65483i
$615$		0			0
$616$	−3.25869			−0.131296
$617$	−3.90143	+	2.25249i	−0.157066	+	0.0906818i	−0.576473	−	0.817116i	$-0.695571\pi$
$617$	−3.90143	+	2.25249i	−0.157066	+	0.0906818i	0.419407	+	0.907798i	$0.362238\pi$
$618$		0			0
$619$	31.6213			1.27097			0.635485	−	0.772114i	$-0.280800\pi$
$619$	31.6213			1.27097			0.635485	+	0.772114i	$0.280800\pi$
$620$	−0.472817	+	0.902906i	−0.0189888	+	0.0362616i
$621$		0			0
$622$	−6.69857	−	3.86742i	−0.268588	−	0.155070i
$623$			37.3782i			1.49752i
$624$		0			0
$625$	−15.8827	−	19.3065i	−0.635308	−	0.772258i
$626$	6.04553	−	10.4712i	0.241628	−	0.418512i
$627$		0			0
$628$	19.0795	−	11.0155i	0.761354	−	0.439568i
$629$	−55.1655			−2.19959
$630$		0			0
$631$	−11.2910	−	19.5565i	−0.449486	−	0.778533i	0.548867	−	0.835910i	$-0.315060\pi$
$631$	−11.2910	−	19.5565i	−0.449486	−	0.778533i	−0.998353	+	0.0573774i	$0.981726\pi$
$632$		−	2.94474i		−	0.117135i
$633$		0			0
$634$	−21.2261	+	36.7647i	−0.842996	+	1.46011i
$635$	−0.953532	−	23.1296i	−0.0378398	−	0.917870i
$636$		0			0
$637$	−53.5361	−	7.65948i	−2.12118	−	0.303480i
$638$		−	6.68547i		−	0.264680i
$639$		0			0
$640$	−0.887409	−	21.5257i	−0.0350779	−	0.850877i
$641$	18.2955	+	31.6887i	0.722628	+	1.25163i	0.959943	+	0.280196i	$0.0903995\pi$
$641$	18.2955	+	31.6887i	0.722628	+	1.25163i	−0.237314	+	0.971433i	$0.576267\pi$
$642$		0			0
$643$	−14.2185	+	8.20907i	−0.560724	+	0.323734i	−0.753436	−	0.657521i	$-0.771605\pi$
$643$	−14.2185	+	8.20907i	−0.560724	+	0.323734i	0.192712	+	0.981255i	$0.438272\pi$
$644$	−0.101914	−	0.176521i	−0.00401599	−	0.00695590i
$645$		0			0
$646$	−34.5284	−	59.8050i	−1.35850	−	2.35300i
$647$	6.27654	+	3.62376i	0.246756	+	0.142465i	0.618278	−	0.785959i	$-0.287831\pi$
$647$	6.27654	+	3.62376i	0.246756	+	0.142465i	−0.371522	+	0.928424i	$0.621164\pi$
$648$		0			0
$649$	7.19005			0.282234
$650$	−27.3000	−	18.0152i	−1.07079	−	0.706614i
$651$		0			0
$652$	14.9646	+	8.63981i	0.586059	+	0.338361i
$653$	19.4951	+	11.2555i	0.762904	+	0.440463i	0.830337	−	0.557261i	$-0.188148\pi$
$653$	19.4951	+	11.2555i	0.762904	+	0.440463i	−0.0674335	+	0.997724i	$0.521481\pi$
$654$		0			0
$655$	−9.72673	−	15.3501i	−0.380055	−	0.599779i
$656$	17.6876	+	30.6358i	0.690583	+	1.19613i
$657$		0			0
$658$			16.9933i			0.662469i
$659$	−3.00747	−	5.20909i	−0.117154	−	0.202917i	0.801485	−	0.598015i	$-0.204044\pi$
$659$	−3.00747	−	5.20909i	−0.117154	−	0.202917i	−0.918639	+	0.395098i	$0.870711\pi$
$660$		0			0
$661$	16.3208	−	28.2684i	0.634805	−	1.09951i	−0.351751	−	0.936094i	$-0.614414\pi$
$661$	16.3208	−	28.2684i	0.634805	−	1.09951i	0.986556	−	0.163421i	$-0.0522530\pi$
$662$		−	17.5368i		−	0.681587i
$663$		0			0
$664$	−19.0452			−0.739096
$665$	−2.40282	−	58.2845i	−0.0931772	−	2.26018i
$666$		0			0
$667$	−0.198535	+	0.114624i	−0.00768731	+	0.00443827i
$668$		−	2.93492i		−	0.113555i
$669$		0			0
$670$	18.9233	−	36.1365i	0.731070	−	1.39607i
$671$	−1.73389			−0.0669361
$672$		0			0
$673$	7.68362	+	4.43614i	0.296182	+	0.171001i	0.640726	−	0.767769i	$-0.278633\pi$
$673$	7.68362	+	4.43614i	0.296182	+	0.171001i	−0.344545	+	0.938770i	$0.611967\pi$
$674$	0.658542	−	1.14063i	0.0253661	−	0.0439353i
$675$		0			0
$676$	−16.1198	−	4.70895i	−0.619992	−	0.181114i
$677$			23.2731i			0.894458i	0.894419	+	0.447229i	$0.147589\pi$
$677$			23.2731i			0.894458i	−0.894419	+	0.447229i	$0.852411\pi$
$678$		0			0
$679$	0.720250	−	1.24751i	0.0276407	−	0.0478750i
$680$	9.12092	−	17.4176i	0.349771	−	0.667935i
$681$		0			0
$682$	−0.299778	+	0.173077i	−0.0114791	+	0.00662745i
$683$	−15.0835	+	8.70849i	−0.577156	+	0.333221i	−0.760002	−	0.649920i	$-0.774802\pi$
$683$	−15.0835	+	8.70849i	−0.577156	+	0.333221i	0.182846	+	0.983141i	$0.441469\pi$
$684$		0			0
$685$	14.2123	+	7.44242i	0.543024	+	0.284360i
$686$	−34.0371	+	58.9540i	−1.29954	+	2.25087i
$687$		0			0
$688$			34.5562i			1.31744i
$689$	−28.4727	+	11.4216i	−1.08472	+	0.435130i
$690$		0			0
$691$	−6.74790	+	11.6877i	−0.256702	+	0.444621i	−0.965356	−	0.260935i	$-0.915969\pi$
$691$	−6.74790	+	11.6877i	−0.256702	+	0.444621i	0.708654	+	0.705556i	$0.249303\pi$
$692$	2.52958	+	1.46046i	0.0961604	+	0.0555182i
$693$		0			0
$694$	−51.7853			−1.96574
$695$	6.87281	−	13.1245i	0.260700	−	0.497842i
$696$		0			0
$697$			49.2545i			1.86565i
$698$	26.2481	−	15.1543i	0.993504	−	0.573600i
$699$		0			0
$700$	−24.9006	+	17.2558i	−0.941153	+	0.652206i
$701$	−21.3455			−0.806207			−0.403104	−	0.915154i	$-0.632069\pi$
$701$	−21.3455			−0.806207			−0.403104	+	0.915154i	$0.632069\pi$
$702$		0			0
$703$		−	44.8375i		−	1.69108i
$704$	−0.455981	+	0.789781i	−0.0171854	+	0.0297660i
$705$		0			0
$706$	−5.22665	−	9.05282i	−0.196708	−	0.340708i
$707$		−	5.41493i		−	0.203650i
$708$		0			0
$709$	19.5294	+	33.8259i	0.733441	+	1.27036i	0.955404	+	0.295303i	$0.0954205\pi$
$709$	19.5294	+	33.8259i	0.733441	+	1.27036i	−0.221962	+	0.975055i	$0.571246\pi$
$710$	−29.7033	+	18.8217i	−1.11474	+	0.706366i
$711$		0			0
$712$	−8.86770	−	5.11977i	−0.332331	−	0.191871i
$713$	0.0102795	+	0.00593490i	0.000384972	+	0.000222264i
$714$		0			0
$715$	−1.78831	−	3.97571i	−0.0668789	−	0.148683i
$716$	−4.11022			−0.153606
$717$		0			0
$718$	−33.1412	−	19.1341i	−1.23682	−	0.714078i
$719$	−14.5784	−	25.2506i	−0.543683	−	0.941687i	−0.998688	−	0.0511985i	$-0.983696\pi$
$719$	−14.5784	−	25.2506i	−0.543683	−	0.941687i	0.455005	−	0.890489i	$-0.349637\pi$
$720$		0			0
$721$	5.51052	+	9.54451i	0.205223	+	0.355456i
$722$	18.7544	−	10.8279i	0.697966	−	0.402971i
$723$		0			0
$724$	2.54258	+	4.40387i	0.0944941	+	0.163669i
$725$	19.4077	+	28.0060i	0.720786	+	1.04012i
$726$		0			0
$727$			35.4958i			1.31647i	0.752815	+	0.658233i	$0.228696\pi$
$727$			35.4958i			1.31647i	−0.752815	+	0.658233i	$0.771304\pi$
$728$	13.4203	−	17.0897i	0.497390	−	0.633385i
$729$		0			0
$730$	32.6402	−	1.34561i	1.20807	−	0.0498034i
$731$	−24.0572	+	41.6682i	−0.889786	+	1.54115i
$732$		0			0
$733$			16.0916i			0.594357i	0.954822	+	0.297178i	$0.0960456\pi$
$733$			16.0916i			0.594357i	−0.954822	+	0.297178i	$0.903954\pi$
$734$	5.15556	+	8.92969i	0.190295	+	0.329601i
$735$		0			0
$736$	0.213529			0.00787077
$737$	4.70832	−	2.71835i	0.173433	−	0.100132i
$738$		0			0
$739$	3.46795	−	6.00666i	0.127570	−	0.220959i	−0.795164	−	0.606394i	$-0.792615\pi$
$739$	3.46795	−	6.00666i	0.127570	−	0.220959i	0.922735	+	0.385435i	$0.125949\pi$
$740$	−19.6695	+	12.4637i	−0.723064	+	0.458175i
$741$		0			0
$742$			72.4070i			2.65815i
$743$	−13.7526	−	7.94009i	−0.504536	−	0.291294i	0.226049	−	0.974116i	$-0.427419\pi$
$743$	−13.7526	−	7.94009i	−0.504536	−	0.291294i	−0.730585	+	0.682822i	$0.760752\pi$
$744$		0			0
$745$	−1.92214	+	3.67058i	−0.0704217	+	0.134480i
$746$	2.55630			0.0935929
$747$		0			0
$748$	−4.13958	+	2.38999i	−0.151358	+	0.0873866i
$749$	32.7494			1.19664
$750$		0			0
$751$	−13.8110	+	23.9213i	−0.503969	+	0.872900i	0.496021	+	0.868311i	$0.334794\pi$
$751$	−13.8110	+	23.9213i	−0.503969	+	0.872900i	−0.999989	+	0.00458893i	$0.998539\pi$
$752$	−8.49956	−	4.90722i	−0.309947	−	0.178948i
$753$		0			0
$754$	35.0608	+	27.5329i	1.27684	+	1.00269i
$755$	4.88864	+	7.71495i	0.177916	+	0.280776i
$756$		0			0
$757$	−37.6733	−	21.7507i	−1.36926	−	0.790542i	−0.378425	−	0.925632i	$-0.623534\pi$
$757$	−37.6733	−	21.7507i	−1.36926	−	0.790542i	−0.990833	+	0.135090i	$0.956868\pi$
$758$	6.67563	−	3.85418i	0.242470	−	0.139990i
$759$		0			0
$760$	14.1567	+	7.41331i	0.513518	+	0.268909i
$761$	16.6763	+	28.8843i	0.604517	+	1.04705i	0.992128	+	0.125231i	$0.0399671\pi$
$761$	16.6763	+	28.8843i	0.604517	+	1.04705i	−0.387611	+	0.921823i	$0.626700\pi$
$762$		0			0
$763$	45.0150	−	25.9895i	1.62965	−	0.940881i
$764$	6.54431	−	11.3351i	0.236765	−	0.410089i
$765$		0			0
$766$	36.9162			1.33384
$767$	−29.6109	+	37.7071i	−1.06919	+	1.36152i
$768$		0			0
$769$	22.4645	−	38.9097i	0.810091	−	1.40312i	−0.102709	−	0.994711i	$-0.532751\pi$
$769$	22.4645	−	38.9097i	0.810091	−	1.40312i	0.912800	−	0.408407i	$-0.133916\pi$
$770$	−10.2804	+	0.423815i	−0.370479	+	0.0152732i
$771$		0			0
$772$			11.6693i			0.419988i
$773$	39.9425	−	23.0608i	1.43663	−	0.829439i	0.439016	−	0.898479i	$-0.355327\pi$
$773$	39.9425	−	23.0608i	1.43663	−	0.829439i	0.997614	+	0.0690402i	$0.0219937\pi$
$774$		0			0
$775$	0.753355	−	1.59528i	0.0270613	−	0.0573041i
$776$	0.197308	+	0.341748i	0.00708296	+	0.0122680i
$777$		0			0
$778$	−34.7516	−	20.0638i	−1.24590	−	0.719323i
$779$	−40.0331			−1.43433
$780$		0			0
$781$	−4.68674			−0.167705
$782$	0.361716	+	0.208837i	0.0129349	+	0.00746799i
$783$		0			0
$784$	−36.8600	−	63.8433i	−1.31643	−	2.28012i
$785$	−32.2124	+	20.4116i	−1.14971	+	0.728522i
$786$		0			0
$787$	46.7143	−	26.9705i	1.66518	−	0.961394i	0.695004	−	0.719006i	$-0.255402\pi$
$787$	46.7143	−	26.9705i	1.66518	−	0.961394i	0.970179	−	0.242389i	$-0.0779309\pi$
$788$		−	19.4762i		−	0.693812i
$789$		0			0
$790$	−0.382983	−	9.28992i	−0.0136259	−	0.330520i
$791$	17.3690	−	30.0840i	0.617570	−	1.06966i
$792$		0			0
$793$	7.14071	−	9.09311i	0.253574	−	0.322906i
$794$	−2.45025			−0.0869561
$795$		0			0
$796$	−8.03339	+	13.9142i	−0.284736	+	0.493177i
$797$	−38.4000	+	22.1703i	−1.36020	+	0.785311i	−0.989650	−	0.143502i	$-0.954164\pi$
$797$	−38.4000	+	22.1703i	−1.36020	+	0.785311i	−0.370549	+	0.928813i	$0.620830\pi$
$798$		0			0
$799$	−6.83257	−	11.8344i	−0.241719	−	0.418669i
$800$	−2.61231	−	31.6292i	−0.0923591	−	1.11826i
$801$		0			0
$802$	30.5036	−	17.6112i	1.07712	−	0.621874i
$803$	3.77068	+	2.17700i	0.133064	+	0.0768247i
$804$		0			0
$805$	0.188846	+	0.298025i	0.00665594	+	0.0105040i
$806$	0.326907	−	2.28492i	0.0115148	−	0.0804829i
$807$		0			0
$808$	1.28465	+	0.741695i	0.0451940	+	0.0260927i
$809$	−14.0718	+	24.3731i	−0.494739	+	0.856913i	−0.999982	−	0.00606430i	$-0.998070\pi$
$809$	−14.0718	+	24.3731i	−0.494739	+	0.856913i	0.505243	+	0.862977i	$0.331403\pi$
$810$		0			0
$811$	−40.1018			−1.40817			−0.704083	−	0.710118i	$-0.748642\pi$
$811$	−40.1018			−1.40817			−0.704083	+	0.710118i	$0.748642\pi$
$812$	35.7585	−	20.6452i	1.25488	−	0.724504i
$813$		0			0
$814$	−7.90854			−0.277194
$815$	−26.4971	−	13.8755i	−0.928154	−	0.486038i
$816$		0			0
$817$	−33.8671	−	19.5532i	−1.18486	−	0.684079i
$818$		−	16.7130i		−	0.584358i
$819$		0			0
$820$	11.1282	+	17.5619i	0.388614	+	0.613287i
$821$	8.07107	−	13.9795i	0.281682	−	0.487888i	−0.690117	−	0.723698i	$-0.742441\pi$
$821$	8.07107	−	13.9795i	0.281682	−	0.487888i	0.971799	+	0.235810i	$0.0757743\pi$
$822$		0			0
$823$	46.6209	−	26.9166i	1.62510	−	0.938253i	0.639576	−	0.768728i	$-0.279110\pi$
$823$	46.6209	−	26.9166i	1.62510	−	0.938253i	0.985526	−	0.169526i	$-0.0542236\pi$
$824$	−3.01915			−0.105177
$825$		0			0
$826$	56.5790	+	97.9978i	1.96864	+	3.40978i
$827$		−	15.1352i		−	0.526303i	−0.964755	−	0.263152i	$-0.915238\pi$
$827$		−	15.1352i		−	0.526303i	0.964755	−	0.263152i	$-0.0847619\pi$
$828$		0			0
$829$	−17.1978	+	29.7874i	−0.597304	+	1.03456i	0.395913	+	0.918288i	$0.370428\pi$
$829$	−17.1978	+	29.7874i	−0.597304	+	1.03456i	−0.993217	+	0.116273i	$0.962905\pi$
$830$	−60.0828	+	2.47695i	−2.08550	+	0.0859762i
$831$		0			0
$832$	−2.26401	−	5.64388i	−0.0784903	−	0.195666i
$833$		−	102.644i		−	3.55640i
$834$		0			0
$835$	0.209258	+	5.07592i	0.00724166	+	0.175659i
$836$	−1.94254	−	3.36457i	−0.0671840	−	0.116366i
$837$		0			0
$838$	33.9908	−	19.6246i	1.17419	−	0.677921i
$839$	4.01001	+	6.94554i	0.138441	+	0.239787i	0.926907	−	0.375292i	$-0.122458\pi$
$839$	4.01001	+	6.94554i	0.138441	+	0.239787i	−0.788466	+	0.615079i	$0.789124\pi$
$840$		0			0
$841$	−8.71988	−	15.1033i	−0.300686	−	0.520803i
$842$	−7.81751	−	4.51344i	−0.269409	−	0.155544i
$843$		0			0
$844$	16.7649			0.577070
$845$	28.2148	+	6.99476i	0.970618	+	0.240627i
$846$		0			0
$847$	43.4940	+	25.1113i	1.49447	+	0.862834i
$848$	−36.2158	−	20.9092i	−1.24366	−	0.718026i
$849$		0			0
$850$	26.5090	−	56.1345i	0.909251	−	1.92540i
$851$	0.135594	+	0.234856i	0.00464811	+	0.00805076i
$852$		0			0
$853$			26.7150i			0.914704i	0.889286	+	0.457352i	$0.151202\pi$
$853$			26.7150i			0.914704i	−0.889286	+	0.457352i	$0.848798\pi$
$854$	−13.6441	−	23.6323i	−0.466892	−	0.808681i
$855$		0			0
$856$	−4.48576	+	7.76956i	−0.153320	+	0.265558i
$857$		−	25.4722i		−	0.870114i	−0.900403	−	0.435057i	$-0.856728\pi$
$857$		−	25.4722i		−	0.870114i	0.900403	−	0.435057i	$-0.143272\pi$
$858$		0			0
$859$	−0.462113			−0.0157671			−0.00788354	−	0.999969i	$-0.502509\pi$
$859$	−0.462113			−0.0157671			−0.00788354	+	0.999969i	$0.502509\pi$
$860$	0.836561	+	20.2923i	0.0285265	+	0.691961i
$861$		0			0
$862$	11.3442	−	6.54956i	0.386384	−	0.223079i
$863$			46.2533i			1.57448i	0.616647	+	0.787240i	$0.288491\pi$
$863$			46.2533i			1.57448i	−0.616647	+	0.787240i	$0.711509\pi$
$864$		0			0
$865$	−4.47902	−	2.34549i	−0.152291	−	0.0797490i
$866$	−40.6751			−1.38219
$867$		0			0
$868$	−1.85147	−	1.06895i	−0.0628429	−	0.0362824i
$869$	0.619609	−	1.07319i	0.0210188	−	0.0364056i
$870$		0			0
$871$	−5.13441	+	35.8871i	−0.173973	+	1.21599i
$872$			14.2393i			0.482204i
$873$		0			0
$874$	−0.169738	+	0.293996i	−0.00574149	+	0.00994455i
$875$	41.8350	−	31.6191i	1.41428	−	1.06892i
$876$		0			0
$877$	21.1966	−	12.2379i	0.715759	−	0.413243i	−0.0974310	−	0.995242i	$-0.531063\pi$
$877$	21.1966	−	12.2379i	0.715759	−	0.413243i	0.813190	+	0.581999i	$0.197729\pi$
$878$	−56.9183	+	32.8618i	−1.92090	+	1.10903i
$879$		0			0
$880$	2.75672	−	5.26432i	0.0929289	−	0.177460i
$881$	8.24236	−	14.2762i	0.277692	−	0.480977i	−0.693119	−	0.720823i	$-0.743764\pi$
$881$	8.24236	−	14.2762i	0.277692	−	0.480977i	0.970811	+	0.239847i	$0.0770972\pi$
$882$		0			0
$883$			54.3195i			1.82800i	0.405717	+	0.913999i	$0.367022\pi$
$883$			54.3195i			1.82800i	−0.405717	+	0.913999i	$0.632978\pi$
$884$	4.51420	−	31.5521i	0.151829	−	1.06121i
$885$		0			0
$886$	−27.8847	+	48.2977i	−0.936805	+	1.62259i
$887$	−23.5134	−	13.5755i	−0.789503	−	0.455820i	0.0502845	−	0.998735i	$-0.483987\pi$
$887$	−23.5134	−	13.5755i	−0.789503	−	0.455820i	−0.839788	+	0.542915i	$0.817321\pi$
$888$		0			0
$889$	48.5576			1.62857
$890$	−28.6413	−	14.9983i	−0.960058	−	0.502744i
$891$		0			0
$892$			10.7467i			0.359828i
$893$	9.61873	−	5.55338i	0.321879	−	0.185837i
$894$		0			0
$895$	7.10858	−	0.293056i	0.237614	−	0.00979577i
$896$	45.1904			1.50971
$897$		0			0
$898$		−	58.8371i		−	1.96342i
$899$	−1.20226	+	2.08237i	−0.0400975	+	0.0694509i
$900$		0			0
$901$	−29.1129	−	50.4251i	−0.969892	−	1.67990i
$902$			7.06114i			0.235110i
$903$		0			0
$904$	4.75814	+	8.24134i	0.158253	+	0.274103i
$905$	−4.71135	−	7.43517i	−0.156611	−	0.247153i
$906$		0			0
$907$	11.0703	+	6.39145i	0.367584	+	0.212225i	0.672402	−	0.740186i	$-0.265262\pi$
$907$	11.0703	+	6.39145i	0.367584	+	0.212225i	−0.304818	+	0.952410i	$0.598596\pi$
$908$	3.34334	+	1.93028i	0.110953	+	0.0640586i
$909$		0			0
$910$	40.1152	−	55.6591i	1.32981	−	1.84508i
$911$	25.8287			0.855743			0.427871	−	0.903840i	$-0.359264\pi$
$911$	25.8287			0.855743			0.427871	+	0.903840i	$0.359264\pi$
$912$		0			0
$913$	−6.94092	−	4.00734i	−0.229711	−	0.132624i
$914$	−4.36451	−	7.55955i	−0.144365	−	0.250048i
$915$		0			0
$916$	−7.88433	−	13.6561i	−0.260506	−	0.451209i
$917$	33.0114	−	19.0591i	1.09013	−	0.629388i
$918$		0			0
$919$	25.9355	+	44.9217i	0.855534	+	1.48183i	0.876149	+	0.482041i	$0.160104\pi$
$919$	25.9355	+	44.9217i	0.855534	+	1.48183i	−0.0206144	+	0.999787i	$0.506562\pi$
$920$	−0.0965708	+	0.00398119i	−0.00318385	+	0.000131256i
$921$		0			0
$922$		−	51.6433i		−	1.70078i
$923$	19.3015	−	24.5789i	0.635316	−	0.809023i
$924$		0			0
$925$	33.1295	−	22.9583i	1.08929	−	0.754864i
$926$	−3.65183	+	6.32515i	−0.120007	+	0.207857i
$927$		0			0
$928$			43.2553i			1.41993i
$929$	−20.7846	−	36.0000i	−0.681920	−	1.18112i	−0.974394	−	0.224847i	$-0.927812\pi$
$929$	−20.7846	−	36.0000i	−0.681920	−	1.18112i	0.292474	−	0.956273i	$-0.405521\pi$
$930$		0			0
$931$	83.4269			2.73421
$932$	−12.2648	+	7.08111i	−0.401748	+	0.231950i
$933$		0			0
$934$	4.04229	−	7.00146i	0.132268	−	0.229095i
$935$	6.98896	−	4.42861i	0.228563	−	0.144831i
$936$		0			0
$937$		−	51.5328i		−	1.68350i	−0.539865	−	0.841752i	$-0.681525\pi$
$937$		−	51.5328i		−	1.68350i	0.539865	−	0.841752i	$-0.318475\pi$
$938$	74.1003	+	42.7818i	2.41946	+	1.39688i
$939$		0			0
$940$	−5.10995	−	2.67588i	−0.166668	−	0.0872776i
$941$	−54.7487			−1.78476			−0.892378	−	0.451288i	$-0.850965\pi$
$941$	−54.7487			−1.78476			−0.892378	+	0.451288i	$0.850965\pi$
$942$		0			0
$943$	0.209691	−	0.121065i	0.00682848	−	0.00394243i
$944$	−65.3541			−2.12709
$945$		0			0
$946$	−3.44884	+	5.97357i	−0.112131	+	0.194217i
$947$	12.4988	+	7.21618i	0.406156	+	0.234494i	0.689137	−	0.724631i	$-0.257990\pi$
$947$	12.4988	+	7.21618i	0.406156	+	0.234494i	−0.282981	+	0.959126i	$0.591323\pi$
$948$		0			0
$949$	−26.9458	+	10.8091i	−0.874697	+	0.350879i
$950$	45.6251	+	21.5460i	1.48027	+	0.699044i
$951$		0			0
$952$	35.7160	+	20.6206i	1.15756	+	0.668318i
$953$	−25.9807	+	15.0000i	−0.841599	+	0.485897i	−0.857807	−	0.513971i	$-0.828174\pi$
$953$	−25.9807	+	15.0000i	−0.841599	+	0.485897i	0.0162085	+	0.999869i	$0.494840\pi$
$954$		0			0
$955$	−10.5101	+	20.0705i	−0.340100	+	0.649467i
$956$	11.5462	+	19.9986i	0.373431	+	0.646801i
$957$		0			0
$958$	−52.9815	+	30.5889i	−1.71175	+	0.988281i
$959$	−16.8259	+	29.1433i	−0.543336	+	0.941085i
$960$		0			0
$961$	−30.8755			−0.995984
$962$	32.5699	−	41.4750i	1.05009	−	1.33721i
$963$		0			0
$964$	−1.87074	+	3.24021i	−0.0602524	+	0.104360i
$965$	−0.832015	−	20.1820i	−0.0267835	−	0.649681i
$966$		0			0
$967$			25.3424i			0.814958i	0.913215	+	0.407479i	$0.133592\pi$
$967$			25.3424i			0.814958i	−0.913215	+	0.407479i	$0.866408\pi$
$968$	−11.9149	+	6.87909i	−0.382961	+	0.221102i
$969$		0			0
$970$	0.666906	+	1.05247i	0.0214131	+	0.0337928i
$971$	−21.6215	−	37.4496i	−0.693868	−	1.20181i	−0.970561	−	0.240856i	$-0.922572\pi$
$971$	−21.6215	−	37.4496i	−0.693868	−	1.20181i	0.276693	−	0.960958i	$-0.410761\pi$
$972$		0			0
$973$	26.9127	+	15.5381i	0.862783	+	0.498128i
$974$	35.0996			1.12466
$975$		0			0
$976$	15.7602			0.504473
$977$	−21.7631	−	12.5649i	−0.696264	−	0.401988i	0.109691	−	0.993966i	$-0.465014\pi$
$977$	−21.7631	−	12.5649i	−0.696264	−	0.401988i	−0.805954	+	0.591978i	$0.798347\pi$
$978$		0			0
$979$	−2.15453	−	3.73175i	−0.0688590	−	0.119267i
$980$	−23.1906	−	36.5981i	−0.740798	−	1.16908i
$981$		0			0
$982$	−48.2376	+	27.8500i	−1.53932	+	0.888729i
$983$		−	37.1662i		−	1.18542i	−0.805417	−	0.592709i	$-0.798058\pi$
$983$		−	37.1662i		−	1.18542i	0.805417	−	0.592709i	$-0.201942\pi$
$984$		0			0
$985$	1.38864	+	33.6840i	0.0442458	+	1.07326i
$986$	−42.3049	+	73.2742i	−1.34726	+	2.33353i
$987$		0			0
$988$	25.6449	+	3.66905i	0.815873	+	0.116728i
$989$	0.236525			0.00752107
$990$		0			0
$991$	−16.0842	+	27.8587i	−0.510932	+	0.884960i	0.488988	+	0.872291i	$0.337366\pi$
$991$	−16.0842	+	27.8587i	−0.510932	+	0.884960i	−0.999920	+	0.0126697i	$0.995967\pi$
$992$	1.93958	−	1.11982i	0.0615817	−	0.0355542i
$993$		0			0
$994$	−36.8803	−	63.8786i	−1.16977	−	2.02611i
$995$	12.9016	−	24.6373i	0.409008	−	0.781055i
$996$		0			0
$997$	14.1083	−	8.14545i	0.446816	−	0.257969i	−0.259669	−	0.965698i	$-0.583613\pi$
$997$	14.1083	−	8.14545i	0.446816	−	0.257969i	0.706484	+	0.707729i	$0.250280\pi$
$998$	4.51600	+	2.60731i	0.142952	+	0.0825331i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bs.c.334.3	yes	32
3.2	odd	2	inner	585.2.bs.c.334.14	yes	32
5.4	even	2	inner	585.2.bs.c.334.13	yes	32
13.3	even	3	inner	585.2.bs.c.289.13	yes	32
15.14	odd	2	inner	585.2.bs.c.334.4	yes	32
39.29	odd	6	inner	585.2.bs.c.289.4	yes	32
65.29	even	6	inner	585.2.bs.c.289.3	✓	32
195.29	odd	6	inner	585.2.bs.c.289.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bs.c.289.3	✓	32	65.29	even	6	inner
585.2.bs.c.289.4	yes	32	39.29	odd	6	inner
585.2.bs.c.289.13	yes	32	13.3	even	3	inner
585.2.bs.c.289.14	yes	32	195.29	odd	6	inner
585.2.bs.c.334.3	yes	32	1.1	even	1	trivial
585.2.bs.c.334.4	yes	32	15.14	odd	2	inner
585.2.bs.c.334.13	yes	32	5.4	even	2	inner
585.2.bs.c.334.14	yes	32	3.2	odd	2	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.57126 - 0.907167i) q^{2} +(0.645904 + 1.11874i) q^{4} +(-1.19685 - 1.88880i) q^{5} +(4.06197 - 2.34518i) q^{7} +1.28490i q^{8} +O(q^{10})\)	\(q+(-1.57126 - 0.907167i) q^{2} +(0.645904 + 1.11874i) q^{4} +(-1.19685 - 1.88880i) q^{5} +(4.06197 - 2.34518i) q^{7} +1.28490i q^{8} +(0.167109 + 4.05353i) q^{10} +(-0.270358 + 0.468274i) q^{11} +(-1.34237 - 3.34635i) q^{13} -8.50987 q^{14} +(2.45742 - 4.25638i) q^{16} +(5.92637 - 3.42159i) q^{17} +(2.78100 + 4.81684i) q^{19} +(1.34002 - 2.55894i) q^{20} +(0.849606 - 0.490520i) q^{22} +(-0.0291335 - 0.0168202i) q^{23} +(-2.13510 + 4.52121i) q^{25} +(-0.926492 + 6.47573i) q^{26} +(5.24728 + 3.02952i) q^{28} +(3.40734 - 5.90168i) q^{29} -0.352843 q^{31} +(-5.49700 + 3.17369i) q^{32} -12.4158 q^{34} +(-9.29113 - 4.86540i) q^{35} +(-6.98136 - 4.03069i) q^{37} -10.0913i q^{38} +(2.42691 - 1.53783i) q^{40} +(-3.59880 + 6.23331i) q^{41} +(-6.08901 + 3.51549i) q^{43} -0.698502 q^{44} +(0.0305175 + 0.0528578i) q^{46} -1.99690i q^{47} +(7.49972 - 12.9899i) q^{49} +(7.45629 - 5.16711i) q^{50} +(2.87665 - 3.66318i) q^{52} -8.50859i q^{53} +(1.20805 - 0.0498027i) q^{55} +(3.01331 + 5.21921i) q^{56} +(-10.7076 + 6.18205i) q^{58} +(-6.64864 - 11.5158i) q^{59} +(1.60333 + 2.77705i) q^{61} +(0.554408 + 0.320088i) q^{62} +1.68658 q^{64} +(-4.71396 + 6.54053i) q^{65} +(-8.70757 - 5.02732i) q^{67} +(7.65573 + 4.42004i) q^{68} +(10.1850 + 16.0734i) q^{70} +(4.33383 + 7.50641i) q^{71} -8.05229i q^{73} +(7.31302 + 12.6665i) q^{74} +(-3.59252 + 6.22243i) q^{76} +2.53615i q^{77} -2.29181 q^{79} +(-10.9806 + 0.452682i) q^{80} +(11.3093 - 6.52943i) q^{82} +14.8223i q^{83} +(-13.5557 - 7.09857i) q^{85} +12.7566 q^{86} +(-0.601684 - 0.347382i) q^{88} +(-3.98458 + 6.90149i) q^{89} +(-13.3004 - 10.4447i) q^{91} -0.0434570i q^{92} +(-1.81152 + 3.13764i) q^{94} +(5.76958 - 11.0178i) q^{95} +(0.265973 - 0.153560i) q^{97} +(-23.5680 + 13.6070i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 20 q^{4}+O(q^{10}) \) 32 * q + 20 * q^4	\( 32 q + 20 q^{4} - 6 q^{10} - 28 q^{16} - 8 q^{19} + 28 q^{25} + 8 q^{31} - 8 q^{34} - 20 q^{40} - 8 q^{46} + 44 q^{49} + 20 q^{55} - 56 q^{61} - 136 q^{64} - 80 q^{70} + 88 q^{76} - 72 q^{79} - 50 q^{85} - 28 q^{91} + 48 q^{94}+O(q^{100}) \) 32 * q + 20 * q^4 - 6 * q^10 - 28 * q^16 - 8 * q^19 + 28 * q^25 + 8 * q^31 - 8 * q^34 - 20 * q^40 - 8 * q^46 + 44 * q^49 + 20 * q^55 - 56 * q^61 - 136 * q^64 - 80 * q^70 + 88 * q^76 - 72 * q^79 - 50 * q^85 - 28 * q^91 + 48 * q^94

Introduction

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