LMFDB - Embedded newform 585.2.j.d.406.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(406,585)]

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, 0, 2]))

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

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

chi := DirichletCharacter("585.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.j (of order $3$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			406.2
Root			$-0.651388 - 1.12824i$ of defining polynomial
Character	$\chi$	$=$	585.406
Dual form			585.2.j.d.451.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.651388 + 1.12824i) q^{2} +(0.151388 - 0.262211i) q^{4} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +(0.651388 + 1.12824i) q^{10} +(-2.80278 - 4.85455i) q^{11} +3.60555 q^{13} +1.30278 q^{14} +(1.65139 + 2.86029i) q^{16} +(0.197224 - 0.341603i) q^{17} +(-0.802776 + 1.39045i) q^{19} +(0.151388 - 0.262211i) q^{20} +(3.65139 - 6.32439i) q^{22} +(-1.50000 - 2.59808i) q^{23} +1.00000 q^{25} +(2.34861 + 4.06792i) q^{26} +(-0.151388 - 0.262211i) q^{28} +(4.10555 + 7.11102i) q^{29} -4.00000 q^{31} +(0.848612 - 1.46984i) q^{32} +0.513878 q^{34} +(0.500000 - 0.866025i) q^{35} +(1.80278 + 3.12250i) q^{37} -2.09167 q^{38} +3.00000 q^{40} +(1.50000 + 2.59808i) q^{41} +(-2.10555 + 3.64692i) q^{43} -1.69722 q^{44} +(1.95416 - 3.38471i) q^{46} +5.21110 q^{47} +(3.00000 + 5.19615i) q^{49} +(0.651388 + 1.12824i) q^{50} +(0.545837 - 0.945417i) q^{52} -11.2111 q^{53} +(-2.80278 - 4.85455i) q^{55} +(1.50000 - 2.59808i) q^{56} +(-5.34861 + 9.26407i) q^{58} +(5.40833 - 9.36750i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-2.60555 - 4.51295i) q^{62} +8.81665 q^{64} +3.60555 q^{65} +(3.50000 + 6.06218i) q^{67} +(-0.0597147 - 0.103429i) q^{68} +1.30278 q^{70} +(-8.40833 + 14.5636i) q^{71} -15.2111 q^{73} +(-2.34861 + 4.06792i) q^{74} +(0.243061 + 0.420994i) q^{76} -5.60555 q^{77} -9.21110 q^{79} +(1.65139 + 2.86029i) q^{80} +(-1.95416 + 3.38471i) q^{82} -5.21110 q^{83} +(0.197224 - 0.341603i) q^{85} -5.48612 q^{86} +(-8.40833 - 14.5636i) q^{88} +(4.10555 + 7.11102i) q^{89} +(1.80278 - 3.12250i) q^{91} -0.908327 q^{92} +(3.39445 + 5.87936i) q^{94} +(-0.802776 + 1.39045i) q^{95} +(7.80278 - 13.5148i) q^{97} +(-3.90833 + 6.76942i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 3 q^{4} + 4 q^{5} + 2 q^{7} + 12 q^{8} - q^{10} - 4 q^{11} - 2 q^{14} + 3 q^{16} + 8 q^{17} + 4 q^{19} - 3 q^{20} + 11 q^{22} - 6 q^{23} + 4 q^{25} + 13 q^{26} + 3 q^{28} + 2 q^{29} - 16 q^{31}+ \cdots + 6 q^{98}+O(q^{100}) $ 4 * q - q^2 - 3 * q^4 + 4 * q^5 + 2 * q^7 + 12 * q^8 - q^10 - 4 * q^11 - 2 * q^14 + 3 * q^16 + 8 * q^17 + 4 * q^19 - 3 * q^20 + 11 * q^22 - 6 * q^23 + 4 * q^25 + 13 * q^26 + 3 * q^28 + 2 * q^29 - 16 * q^31 + 7 * q^32 - 34 * q^34 + 2 * q^35 - 30 * q^38 + 12 * q^40 + 6 * q^41 + 6 * q^43 - 14 * q^44 - 3 * q^46 - 8 * q^47 + 12 * q^49 - q^50 + 13 * q^52 - 16 * q^53 - 4 * q^55 + 6 * q^56 - 25 * q^58 + 2 * q^61 + 4 * q^62 - 8 * q^64 + 14 * q^67 + 25 * q^68 - 2 * q^70 - 12 * q^71 - 32 * q^73 - 13 * q^74 + 19 * q^76 - 8 * q^77 - 8 * q^79 + 3 * q^80 + 3 * q^82 + 8 * q^83 + 8 * q^85 - 58 * q^86 - 12 * q^88 + 2 * q^89 + 18 * q^92 + 28 * q^94 + 4 * q^95 + 24 * q^97 + 6 * q^98

Character values

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

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

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 $

$2$	0.651388	+	1.12824i	0.460601	+	0.797784i	0.998991	−	0.0449118i	$-0.0143007\pi$
$2$	0.651388	+	1.12824i	0.460601	+	0.797784i	−0.538390	+	0.842696i	$0.680967\pi$
$3$		0			0
$3$		0			0
$4$	0.151388	−	0.262211i	0.0756939	−	0.131106i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	0.944911	+	0.327327i	$0.106148\pi$
$8$	3.00000			1.06066
$9$		0			0
$10$	0.651388	+	1.12824i	0.205987	+	0.356780i
$11$	−2.80278	−	4.85455i	−0.845069	−	1.46370i	−0.885562	−	0.464522i	$-0.846226\pi$
$11$	−2.80278	−	4.85455i	−0.845069	−	1.46370i	0.0404929	−	0.999180i	$-0.487107\pi$
$12$		0			0
$13$	3.60555			1.00000
$13$	3.60555			1.00000
$14$	1.30278			0.348181
$15$		0			0
$16$	1.65139	+	2.86029i	0.412847	+	0.715072i
$17$	0.197224	−	0.341603i	0.0478339	−	0.0828508i	−0.841117	−	0.540853i	$-0.818102\pi$
$17$	0.197224	−	0.341603i	0.0478339	−	0.0828508i	0.888951	+	0.458002i	$0.151435\pi$
$18$		0			0
$19$	−0.802776	+	1.39045i	−0.184169	+	0.318991i	−0.943296	−	0.331952i	$-0.892293\pi$
$19$	−0.802776	+	1.39045i	−0.184169	+	0.318991i	0.759127	+	0.650943i	$0.225626\pi$
$20$	0.151388	−	0.262211i	0.0338513	−	0.0586323i
$21$		0			0
$22$	3.65139	−	6.32439i	0.778478	−	1.34836i
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	2.34861	+	4.06792i	0.460601	+	0.797784i
$27$		0			0
$28$	−0.151388	−	0.262211i	−0.0286096	−	0.0495533i
$29$	4.10555	+	7.11102i	0.762382	+	1.32048i	0.941620	+	0.336678i	$0.109303\pi$
$29$	4.10555	+	7.11102i	0.762382	+	1.32048i	−0.179238	+	0.983806i	$0.557363\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.848612	−	1.46984i	0.150015	−	0.259833i
$33$		0			0
$34$	0.513878			0.0881294
$35$	0.500000	−	0.866025i	0.0845154	−	0.146385i
$36$		0			0
$37$	1.80278	+	3.12250i	0.296374	+	0.513336i	0.975304	−	0.220868i	$-0.0708890\pi$
$37$	1.80278	+	3.12250i	0.296374	+	0.513336i	−0.678929	+	0.734204i	$0.737556\pi$
$38$	−2.09167			−0.339314
$39$		0			0
$40$	3.00000			0.474342
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		0			0
$43$	−2.10555	+	3.64692i	−0.321094	+	0.556150i	−0.980714	−	0.195449i	$-0.937384\pi$
$43$	−2.10555	+	3.64692i	−0.321094	+	0.556150i	0.659620	+	0.751599i	$0.270717\pi$
$44$	−1.69722			−0.255866
$45$		0			0
$46$	1.95416	−	3.38471i	0.288126	−	0.499048i
$47$	5.21110			0.760117			0.380059	−	0.924962i	$-0.375904\pi$
$47$	5.21110			0.760117			0.380059	+	0.924962i	$0.375904\pi$
$48$		0			0
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$	0.651388	+	1.12824i	0.0921201	+	0.159557i
$51$		0			0
$52$	0.545837	−	0.945417i	0.0756939	−	0.131106i
$53$	−11.2111			−1.53996			−0.769982	−	0.638066i	$-0.779735\pi$
$53$	−11.2111			−1.53996			−0.769982	+	0.638066i	$0.779735\pi$
$54$		0			0
$55$	−2.80278	−	4.85455i	−0.377926	−	0.654587i
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$		0			0
$58$	−5.34861	+	9.26407i	−0.702307	+	1.21643i
$59$	5.40833	−	9.36750i	0.704104	−	1.21954i	−0.262910	−	0.964820i	$-0.584682\pi$
$59$	5.40833	−	9.36750i	0.704104	−	1.21954i	0.967014	−	0.254724i	$-0.0819845\pi$
$60$		0			0
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$	−2.60555	−	4.51295i	−0.330905	−	0.573145i
$63$		0			0
$64$	8.81665			1.10208
$65$	3.60555			0.447214
$66$		0			0
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	0.996659	−	0.0816792i	$-0.0260283\pi$
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	−0.569066	+	0.822292i	$0.692695\pi$
$68$	−0.0597147	−	0.103429i	−0.00724147	−	0.0125426i
$69$		0			0
$70$	1.30278			0.155711
$71$	−8.40833	+	14.5636i	−0.997885	+	1.72839i	−0.442645	+	0.896697i	$0.645960\pi$
$71$	−8.40833	+	14.5636i	−0.997885	+	1.72839i	−0.555240	+	0.831690i	$0.687374\pi$
$72$		0			0
$73$	−15.2111			−1.78032			−0.890162	−	0.455643i	$-0.849409\pi$
$73$	−15.2111			−1.78032			−0.890162	+	0.455643i	$0.849409\pi$
$74$	−2.34861	+	4.06792i	−0.273021	+	0.472886i
$75$		0			0
$76$	0.243061	+	0.420994i	0.0278810	+	0.0482913i
$77$	−5.60555			−0.638812
$78$		0			0
$79$	−9.21110			−1.03633			−0.518165	−	0.855281i	$-0.673385\pi$
$79$	−9.21110			−1.03633			−0.518165	+	0.855281i	$0.673385\pi$
$80$	1.65139	+	2.86029i	0.184631	+	0.319790i
$81$		0			0
$82$	−1.95416	+	3.38471i	−0.215801	+	0.373779i
$83$	−5.21110			−0.571993			−0.285996	−	0.958231i	$-0.592325\pi$
$83$	−5.21110			−0.571993			−0.285996	+	0.958231i	$0.592325\pi$
$84$		0			0
$85$	0.197224	−	0.341603i	0.0213920	−	0.0370520i
$86$	−5.48612			−0.591584
$87$		0			0
$88$	−8.40833	−	14.5636i	−0.896331	−	1.55249i
$89$	4.10555	+	7.11102i	0.435188	+	0.753767i	0.997311	−	0.0732864i	$-0.0233487\pi$
$89$	4.10555	+	7.11102i	0.435188	+	0.753767i	−0.562123	+	0.827053i	$0.690015\pi$
$90$		0			0
$91$	1.80278	−	3.12250i	0.188982	−	0.327327i
$92$	−0.908327			−0.0946996
$93$		0			0
$94$	3.39445	+	5.87936i	0.350111	+	0.606409i
$95$	−0.802776	+	1.39045i	−0.0823630	+	0.142657i
$96$		0			0
$97$	7.80278	−	13.5148i	0.792252	−	1.37222i	−0.132318	−	0.991207i	$-0.542242\pi$
$97$	7.80278	−	13.5148i	0.792252	−	1.37222i	0.924570	−	0.381013i	$-0.124425\pi$
$98$	−3.90833	+	6.76942i	−0.394801	+	0.683815i
$99$		0			0
$100$	0.151388	−	0.262211i	0.0151388	−	0.0262211i
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$		0			0
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$	10.8167			1.06066
$105$		0			0
$106$	−7.30278	−	12.6488i	−0.709308	−	1.22856i
$107$	−4.10555	−	7.11102i	−0.396899	−	0.687449i	0.596443	−	0.802656i	$-0.296580\pi$
$107$	−4.10555	−	7.11102i	−0.396899	−	0.687449i	−0.993342	+	0.115207i	$0.963247\pi$
$108$		0			0
$109$	−4.78890			−0.458693			−0.229347	−	0.973345i	$-0.573659\pi$
$109$	−4.78890			−0.458693			−0.229347	+	0.973345i	$0.573659\pi$
$110$	3.65139	−	6.32439i	0.348146	−	0.603007i
$111$		0			0
$112$	3.30278			0.312083
$113$	2.80278	−	4.85455i	0.263663	−	0.456678i	−0.703550	−	0.710646i	$-0.748403\pi$
$113$	2.80278	−	4.85455i	0.263663	−	0.456678i	0.967212	+	0.253969i	$0.0817360\pi$
$114$		0			0
$115$	−1.50000	−	2.59808i	−0.139876	−	0.242272i
$116$	2.48612			0.230831
$117$		0			0
$118$	14.0917			1.29724
$119$	−0.197224	−	0.341603i	−0.0180795	−	0.0313147i
$120$		0			0
$121$	−10.2111	+	17.6861i	−0.928282	+	1.60783i
$122$	1.30278			0.117948
$123$		0			0
$124$	−0.605551	+	1.04885i	−0.0543801	+	0.0941891i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−5.10555	−	8.84307i	−0.453044	−	0.784696i	0.545529	−	0.838092i	$-0.316329\pi$
$127$	−5.10555	−	8.84307i	−0.453044	−	0.784696i	−0.998573	+	0.0533960i	$0.982995\pi$
$128$	4.04584	+	7.00759i	0.357605	+	0.619390i
$129$		0			0
$130$	2.34861	+	4.06792i	0.205987	+	0.356780i
$131$	6.78890			0.593149			0.296574	−	0.955010i	$-0.404156\pi$
$131$	6.78890			0.593149			0.296574	+	0.955010i	$0.404156\pi$
$132$		0			0
$133$	0.802776	+	1.39045i	0.0696095	+	0.120567i
$134$	−4.55971	+	7.89766i	−0.393899	+	0.682254i
$135$		0			0
$136$	0.591673	−	1.02481i	0.0507355	−	0.0878765i
$137$	2.80278	−	4.85455i	0.239457	−	0.414752i	−0.721101	−	0.692830i	$-0.756364\pi$
$137$	2.80278	−	4.85455i	0.239457	−	0.414752i	0.960559	+	0.278077i	$0.0896972\pi$
$138$		0			0
$139$	−6.80278	+	11.7828i	−0.577004	+	0.999400i	0.418817	+	0.908071i	$0.362445\pi$
$139$	−6.80278	+	11.7828i	−0.577004	+	0.999400i	−0.995821	+	0.0913293i	$0.970888\pi$
$140$	−0.151388	−	0.262211i	−0.0127946	−	0.0221609i
$141$		0			0
$142$	−21.9083			−1.83851
$143$	−10.1056	−	17.5033i	−0.845069	−	1.46370i
$144$		0			0
$145$	4.10555	+	7.11102i	0.340947	+	0.590538i
$146$	−9.90833	−	17.1617i	−0.820019	−	1.42031i
$147$		0			0
$148$	1.09167			0.0897350
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	−0.798019	−	0.602632i	$-0.794119\pi$
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	0.920904	+	0.389789i	$0.127452\pi$
$150$		0			0
$151$	13.2111			1.07510			0.537552	−	0.843231i	$-0.319349\pi$
$151$	13.2111			1.07510			0.537552	+	0.843231i	$0.319349\pi$
$152$	−2.40833	+	4.17134i	−0.195341	+	0.338341i
$153$		0			0
$154$	−3.65139	−	6.32439i	−0.294237	−	0.509634i
$155$	−4.00000			−0.321288
$156$		0			0
$157$	−3.21110			−0.256274			−0.128137	−	0.991756i	$-0.540900\pi$
$157$	−3.21110			−0.256274			−0.128137	+	0.991756i	$0.540900\pi$
$158$	−6.00000	−	10.3923i	−0.477334	−	0.826767i
$159$		0			0
$160$	0.848612	−	1.46984i	0.0670887	−	0.116201i
$161$	−3.00000			−0.236433
$162$		0			0
$163$	9.10555	−	15.7713i	0.713202	−	1.23530i	−0.250447	−	0.968130i	$-0.580578\pi$
$163$	9.10555	−	15.7713i	0.713202	−	1.23530i	0.963649	−	0.267172i	$-0.0860890\pi$
$164$	0.908327			0.0709284
$165$		0			0
$166$	−3.39445	−	5.87936i	−0.263460	−	0.456327i
$167$	4.50000	+	7.79423i	0.348220	+	0.603136i	0.985933	−	0.167139i	$-0.0534527\pi$
$167$	4.50000	+	7.79423i	0.348220	+	0.603136i	−0.637713	+	0.770274i	$0.720119\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$	0.513878			0.0394127
$171$		0			0
$172$	0.637510	+	1.10420i	0.0486097	+	0.0841944i
$173$	−8.40833	+	14.5636i	−0.639273	+	1.10725i	0.346319	+	0.938117i	$0.387431\pi$
$173$	−8.40833	+	14.5636i	−0.639273	+	1.10725i	−0.985593	+	0.169137i	$0.945902\pi$
$174$		0			0
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	9.25694	−	16.0335i	0.697768	−	1.20857i
$177$		0			0
$178$	−5.34861	+	9.26407i	−0.400895	+	0.694371i
$179$	0.591673	+	1.02481i	0.0442237	+	0.0765977i	0.887290	−	0.461212i	$-0.152585\pi$
$179$	0.591673	+	1.02481i	0.0442237	+	0.0765977i	−0.843066	+	0.537810i	$0.819252\pi$
$180$		0			0
$181$	−25.6333			−1.90531			−0.952654	−	0.304055i	$-0.901659\pi$
$181$	−25.6333			−1.90531			−0.952654	+	0.304055i	$0.901659\pi$
$182$	4.69722			0.348181
$183$		0			0
$184$	−4.50000	−	7.79423i	−0.331744	−	0.574598i
$185$	1.80278	+	3.12250i	0.132543	+	0.229571i
$186$		0			0
$187$	−2.21110			−0.161692
$188$	0.788897	−	1.36641i	0.0575363	−	0.0996557i
$189$		0			0
$190$	−2.09167			−0.151746
$191$	−2.40833	+	4.17134i	−0.174260	+	0.301828i	−0.939905	−	0.341436i	$-0.889087\pi$
$191$	−2.40833	+	4.17134i	−0.174260	+	0.301828i	0.765645	+	0.643264i	$0.222420\pi$
$192$		0			0
$193$	−4.19722	−	7.26981i	−0.302123	−	0.523292i	0.674494	−	0.738281i	$-0.264362\pi$
$193$	−4.19722	−	7.26981i	−0.302123	−	0.523292i	−0.976617	+	0.214988i	$0.931029\pi$
$194$	20.3305			1.45965
$195$		0			0
$196$	1.81665			0.129761
$197$	11.4083	+	19.7598i	0.812810	+	1.40783i	0.910890	+	0.412649i	$0.135396\pi$
$197$	11.4083	+	19.7598i	0.812810	+	1.40783i	−0.0980804	+	0.995178i	$0.531270\pi$
$198$		0			0
$199$	4.40833	−	7.63545i	0.312498	−	0.541262i	−0.666404	−	0.745590i	$-0.732168\pi$
$199$	4.40833	−	7.63545i	0.312498	−	0.541262i	0.978902	+	0.204328i	$0.0655009\pi$
$200$	3.00000			0.212132
$201$		0			0
$202$	5.86249	−	10.1541i	0.412483	−	0.714442i
$203$	8.21110			0.576306
$204$		0			0
$205$	1.50000	+	2.59808i	0.104765	+	0.181458i
$206$	−2.60555	−	4.51295i	−0.181537	−	0.314432i
$207$		0			0
$208$	5.95416	+	10.3129i	0.412847	+	0.715072i
$209$	9.00000			0.622543
$210$		0			0
$211$	8.19722	+	14.1980i	0.564320	+	0.977431i	0.997113	+	0.0759376i	$0.0241950\pi$
$211$	8.19722	+	14.1980i	0.564320	+	0.977431i	−0.432792	+	0.901494i	$0.642472\pi$
$212$	−1.69722	+	2.93968i	−0.116566	+	0.201898i
$213$		0			0
$214$	5.34861	−	9.26407i	0.365624	−	0.633279i
$215$	−2.10555	+	3.64692i	−0.143597	+	0.248718i
$216$		0			0
$217$	−2.00000	+	3.46410i	−0.135769	+	0.235159i
$218$	−3.11943	−	5.40301i	−0.211274	−	0.365938i
$219$		0			0
$220$	−1.69722			−0.114427
$221$	0.711103	−	1.23167i	0.0478339	−	0.0828508i
$222$		0			0
$223$	−5.10555	−	8.84307i	−0.341893	−	0.592176i	0.642891	−	0.765957i	$-0.277735\pi$
$223$	−5.10555	−	8.84307i	−0.341893	−	0.592176i	−0.984784	+	0.173781i	$0.944401\pi$
$224$	−0.848612	−	1.46984i	−0.0567003	−	0.0982078i
$225$		0			0
$226$	7.30278			0.485773
$227$	0.711103	−	1.23167i	0.0471975	−	0.0817485i	−0.841462	−	0.540317i	$-0.818304\pi$
$227$	0.711103	−	1.23167i	0.0471975	−	0.0817485i	0.888659	+	0.458569i	$0.151638\pi$
$228$		0			0
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$	1.95416	−	3.38471i	0.128854	−	0.223181i
$231$		0			0
$232$	12.3167	+	21.3331i	0.808628	+	1.40058i
$233$	−0.788897			−0.0516824			−0.0258412	−	0.999666i	$-0.508226\pi$
$233$	−0.788897			−0.0516824			−0.0258412	+	0.999666i	$0.508226\pi$
$234$		0			0
$235$	5.21110			0.339935
$236$	−1.63751	−	2.83625i	−0.106593	−	0.184624i
$237$		0			0
$238$	0.256939	−	0.445032i	0.0166549	−	0.0288471i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	−8.10555	+	14.0392i	−0.522124	+	0.904346i	0.477544	+	0.878608i	$0.341527\pi$
$241$	−8.10555	+	14.0392i	−0.522124	+	0.904346i	−0.999669	+	0.0257384i	$0.991806\pi$
$242$	−26.6056			−1.71027
$243$		0			0
$244$	−0.151388	−	0.262211i	−0.00969161	−	0.0167864i
$245$	3.00000	+	5.19615i	0.191663	+	0.331970i
$246$		0			0
$247$	−2.89445	+	5.01333i	−0.184169	+	0.318991i
$248$	−12.0000			−0.762001
$249$		0			0
$250$	0.651388	+	1.12824i	0.0411974	+	0.0713560i
$251$	−14.4083	+	24.9560i	−0.909446	+	1.57521i	−0.0946094	+	0.995514i	$0.530160\pi$
$251$	−14.4083	+	24.9560i	−0.909446	+	1.57521i	−0.814836	+	0.579691i	$0.803173\pi$
$252$		0			0
$253$	−8.40833	+	14.5636i	−0.528627	+	0.915609i
$254$	6.65139	−	11.5205i	0.417345	−	0.722863i
$255$		0			0
$256$	3.54584	−	6.14157i	0.221615	−	0.383848i
$257$	−11.8028	−	20.4430i	−0.736237	−	1.27520i	−0.954179	−	0.299238i	$-0.903268\pi$
$257$	−11.8028	−	20.4430i	−0.736237	−	1.27520i	0.217942	−	0.975962i	$-0.430066\pi$
$258$		0			0
$259$	3.60555			0.224038
$260$	0.545837	−	0.945417i	0.0338513	−	0.0586323i
$261$		0			0
$262$	4.42221	+	7.65948i	0.273205	+	0.473204i
$263$	13.1056	+	22.6995i	0.808123	+	1.39971i	0.914162	+	0.405348i	$0.132850\pi$
$263$	13.1056	+	22.6995i	0.808123	+	1.39971i	−0.106040	+	0.994362i	$0.533817\pi$
$264$		0			0
$265$	−11.2111			−0.688693
$266$	−1.04584	+	1.81144i	−0.0641244	+	0.111067i
$267$		0			0
$268$	2.11943			0.129465
$269$	−4.50000	+	7.79423i	−0.274370	+	0.475223i	−0.969976	−	0.243201i	$-0.921803\pi$
$269$	−4.50000	+	7.79423i	−0.274370	+	0.475223i	0.695606	+	0.718423i	$0.255136\pi$
$270$		0			0
$271$	−0.408327	−	0.707243i	−0.0248041	−	0.0429620i	0.853357	−	0.521327i	$-0.174563\pi$
$271$	−0.408327	−	0.707243i	−0.0248041	−	0.0429620i	−0.878161	+	0.478365i	$0.841230\pi$
$272$	1.30278			0.0789924
$273$		0			0
$274$	7.30278			0.441177
$275$	−2.80278	−	4.85455i	−0.169014	−	0.292740i
$276$		0			0
$277$	−10.1972	+	17.6621i	−0.612692	+	1.06121i	0.378093	+	0.925768i	$0.376580\pi$
$277$	−10.1972	+	17.6621i	−0.612692	+	1.06121i	−0.990785	+	0.135446i	$0.956753\pi$
$278$	−17.7250			−1.06307
$279$		0			0
$280$	1.50000	−	2.59808i	0.0896421	−	0.155265i
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	−2.50000	−	4.33013i	−0.148610	−	0.257399i	0.782104	−	0.623148i	$-0.214146\pi$
$283$	−2.50000	−	4.33013i	−0.148610	−	0.257399i	−0.930714	+	0.365748i	$0.880813\pi$
$284$	2.54584	+	4.40952i	0.151068	+	0.261657i
$285$		0			0
$286$	13.1653	−	22.8029i	0.778478	−	1.34836i
$287$	3.00000			0.177084
$288$		0			0
$289$	8.42221	+	14.5877i	0.495424	+	0.858099i
$290$	−5.34861	+	9.26407i	−0.314081	+	0.544005i
$291$		0			0
$292$	−2.30278	+	3.98852i	−0.134760	+	0.233411i
$293$	8.80278	−	15.2469i	0.514264	−	0.890731i	−0.485599	−	0.874181i	$-0.661399\pi$
$293$	8.80278	−	15.2469i	0.514264	−	0.890731i	0.999863	−	0.0165493i	$-0.00526805\pi$
$294$		0			0
$295$	5.40833	−	9.36750i	0.314885	−	0.545397i
$296$	5.40833	+	9.36750i	0.314353	+	0.544475i
$297$		0			0
$298$	3.90833			0.226403
$299$	−5.40833	−	9.36750i	−0.312772	−	0.541736i
$300$		0			0
$301$	2.10555	+	3.64692i	0.121362	+	0.210205i
$302$	8.60555	+	14.9053i	0.495194	+	0.857701i
$303$		0			0
$304$	−5.30278			−0.304135
$305$	0.500000	−	0.866025i	0.0286299	−	0.0495885i
$306$		0			0
$307$	−16.0000			−0.913168			−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000			−0.913168			−0.456584	+	0.889680i	$0.650927\pi$
$308$	−0.848612	+	1.46984i	−0.0483542	+	0.0837519i
$309$		0			0
$310$	−2.60555	−	4.51295i	−0.147985	−	0.256318i
$311$	−5.21110			−0.295495			−0.147747	−	0.989025i	$-0.547202\pi$
$311$	−5.21110			−0.295495			−0.147747	+	0.989025i	$0.547202\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$	−2.09167	−	3.62288i	−0.118040	−	0.204451i
$315$		0			0
$316$	−1.39445	+	2.41526i	−0.0784439	+	0.135869i
$317$	−6.00000			−0.336994			−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000			−0.336994			−0.168497	+	0.985702i	$0.553891\pi$
$318$		0			0
$319$	23.0139	−	39.8612i	1.28853	−	2.23180i
$320$	8.81665			0.492866
$321$		0			0
$322$	−1.95416	−	3.38471i	−0.108901	−	0.188623i
$323$	0.316654	+	0.548461i	0.0176191	+	0.0305172i
$324$		0			0
$325$	3.60555			0.200000
$326$	23.7250			1.31401
$327$		0			0
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$	2.60555	−	4.51295i	0.143649	−	0.248807i
$330$		0			0
$331$	13.0139	−	22.5407i	0.715307	−	1.23895i	−0.247533	−	0.968879i	$-0.579620\pi$
$331$	13.0139	−	22.5407i	0.715307	−	1.23895i	0.962841	−	0.270069i	$-0.0870467\pi$
$332$	−0.788897	+	1.36641i	−0.0432964	+	0.0749915i
$333$		0			0
$334$	−5.86249	+	10.1541i	−0.320781	+	0.555609i
$335$	3.50000	+	6.06218i	0.191225	+	0.331212i
$336$		0			0
$337$	17.6333			0.960547			0.480274	−	0.877119i	$-0.340537\pi$
$337$	17.6333			0.960547			0.480274	+	0.877119i	$0.340537\pi$
$338$	8.46804	+	14.6671i	0.460601	+	0.797784i
$339$		0			0
$340$	−0.0597147	−	0.103429i	−0.00323849	−	0.00560922i
$341$	11.2111	+	19.4182i	0.607115	+	1.05155i
$342$		0			0
$343$	13.0000			0.701934
$344$	−6.31665	+	10.9408i	−0.340571	+	0.589887i
$345$		0			0
$346$	−21.9083			−1.17780
$347$	10.1056	−	17.5033i	0.542494	−	0.939628i	−0.456266	−	0.889844i	$-0.650813\pi$
$347$	10.1056	−	17.5033i	0.542494	−	0.939628i	0.998760	−	0.0497842i	$-0.0158534\pi$
$348$		0			0
$349$	9.10555	+	15.7713i	0.487409	+	0.844217i	0.999895	−	0.0144783i	$-0.00460876\pi$
$349$	9.10555	+	15.7713i	0.487409	+	0.844217i	−0.512486	+	0.858695i	$0.671275\pi$
$350$	1.30278			0.0696363
$351$		0			0
$352$	−9.51388			−0.507091
$353$	−2.40833	−	4.17134i	−0.128182	−	0.222018i	0.794790	−	0.606884i	$-0.207581\pi$
$353$	−2.40833	−	4.17134i	−0.128182	−	0.222018i	−0.922972	+	0.384866i	$0.874248\pi$
$354$		0			0
$355$	−8.40833	+	14.5636i	−0.446268	+	0.772958i
$356$	2.48612			0.131764
$357$		0			0
$358$	−0.770817	+	1.33509i	−0.0407390	+	0.0705619i
$359$	10.4222			0.550063			0.275031	−	0.961435i	$-0.411312\pi$
$359$	10.4222			0.550063			0.275031	+	0.961435i	$0.411312\pi$
$360$		0			0
$361$	8.21110	+	14.2220i	0.432163	+	0.748529i
$362$	−16.6972	−	28.9204i	−0.877587	−	1.52002i
$363$		0			0
$364$	−0.545837	−	0.945417i	−0.0286096	−	0.0495533i
$365$	−15.2111			−0.796185
$366$		0			0
$367$	8.71110	+	15.0881i	0.454716	+	0.787591i	0.998672	−	0.0515228i	$-0.0164075\pi$
$367$	8.71110	+	15.0881i	0.454716	+	0.787591i	−0.543956	+	0.839114i	$0.683074\pi$
$368$	4.95416	−	8.58086i	0.258254	−	0.447308i
$369$		0			0
$370$	−2.34861	+	4.06792i	−0.122099	+	0.211481i
$371$	−5.60555	+	9.70910i	−0.291026	+	0.504071i
$372$		0			0
$373$	13.8028	−	23.9071i	0.714681	−	1.23786i	−0.248402	−	0.968657i	$-0.579905\pi$
$373$	13.8028	−	23.9071i	0.714681	−	1.23786i	0.963083	−	0.269206i	$-0.0867613\pi$
$374$	−1.44029	−	2.49465i	−0.0744754	−	0.128995i
$375$		0			0
$376$	15.6333			0.806226
$377$	14.8028	+	25.6392i	0.762382	+	1.32048i
$378$		0			0
$379$	−1.19722	−	2.07365i	−0.0614973	−	0.106516i	0.833638	−	0.552312i	$-0.186254\pi$
$379$	−1.19722	−	2.07365i	−0.0614973	−	0.106516i	−0.895135	+	0.445795i	$0.852921\pi$
$380$	0.243061	+	0.420994i	0.0124688	+	0.0215965i
$381$		0			0
$382$	−6.27502			−0.321058
$383$	9.31665	−	16.1369i	0.476059	−	0.824558i	−0.523565	−	0.851986i	$-0.675398\pi$
$383$	9.31665	−	16.1369i	0.476059	−	0.824558i	0.999624	+	0.0274277i	$0.00873162\pi$
$384$		0			0
$385$	−5.60555			−0.285685
$386$	5.46804	−	9.47093i	0.278316	−	0.482057i
$387$		0			0
$388$	−2.36249	−	4.09195i	−0.119937	−	0.207737i
$389$	0.788897			0.0399987			0.0199993	−	0.999800i	$-0.493634\pi$
$389$	0.788897			0.0399987			0.0199993	+	0.999800i	$0.493634\pi$
$390$		0			0
$391$	−1.18335			−0.0598444
$392$	9.00000	+	15.5885i	0.454569	+	0.787336i
$393$		0			0
$394$	−14.8625	+	25.7426i	−0.748761	+	1.29689i
$395$	−9.21110			−0.463461
$396$		0			0
$397$	7.01388	−	12.1484i	0.352016	−	0.609710i	−0.634586	−	0.772852i	$-0.718829\pi$
$397$	7.01388	−	12.1484i	0.352016	−	0.609710i	0.986603	+	0.163142i	$0.0521628\pi$
$398$	11.4861			0.575747
$399$		0			0
$400$	1.65139	+	2.86029i	0.0825694	+	0.143014i
$401$	−1.10555	−	1.91487i	−0.0552086	−	0.0956241i	0.837100	−	0.547049i	$-0.184249\pi$
$401$	−1.10555	−	1.91487i	−0.0552086	−	0.0956241i	−0.892309	+	0.451425i	$0.850916\pi$
$402$		0			0
$403$	−14.4222			−0.718421
$404$	−2.72498			−0.135573
$405$		0			0
$406$	5.34861	+	9.26407i	0.265447	+	0.459768i
$407$	10.1056	−	17.5033i	0.500914	−	0.867608i
$408$		0			0
$409$	3.10555	−	5.37897i	0.153560	−	0.265973i	−0.778974	−	0.627056i	$-0.784260\pi$
$409$	3.10555	−	5.37897i	0.153560	−	0.265973i	0.932534	+	0.361083i	$0.117593\pi$
$410$	−1.95416	+	3.38471i	−0.0965093	+	0.167159i
$411$		0			0
$412$	−0.605551	+	1.04885i	−0.0298334	+	0.0516729i
$413$	−5.40833	−	9.36750i	−0.266126	−	0.460944i
$414$		0			0
$415$	−5.21110			−0.255803
$416$	3.05971	−	5.29958i	0.150015	−	0.259833i
$417$		0			0
$418$	5.86249	+	10.1541i	0.286744	+	0.496655i
$419$	−16.6194	−	28.7857i	−0.811912	−	1.40627i	−0.911524	−	0.411247i	$-0.865093\pi$
$419$	−16.6194	−	28.7857i	−0.811912	−	1.40627i	0.0996117	−	0.995026i	$-0.468240\pi$
$420$		0			0
$421$	3.57779			0.174371			0.0871855	−	0.996192i	$-0.472213\pi$
$421$	3.57779			0.174371			0.0871855	+	0.996192i	$0.472213\pi$
$422$	−10.6791	+	18.4968i	−0.519853	+	0.900411i
$423$		0			0
$424$	−33.6333			−1.63338
$425$	0.197224	−	0.341603i	0.00956679	−	0.0165702i
$426$		0			0
$427$	−0.500000	−	0.866025i	−0.0241967	−	0.0419099i
$428$	−2.48612			−0.120171
$429$		0			0
$430$	−5.48612			−0.264564
$431$	−10.6194	−	18.3934i	−0.511520	−	0.885978i	−0.999911	−	0.0133535i	$-0.995749\pi$
$431$	−10.6194	−	18.3934i	−0.511520	−	0.885978i	0.488391	−	0.872625i	$-0.337584\pi$
$432$		0			0
$433$	1.80278	−	3.12250i	0.0866359	−	0.150058i	−0.819451	−	0.573149i	$-0.805722\pi$
$433$	1.80278	−	3.12250i	0.0866359	−	0.150058i	0.906087	+	0.423091i	$0.139055\pi$
$434$	−5.21110			−0.250141
$435$		0			0
$436$	−0.724981	+	1.25570i	−0.0347203	+	0.0601373i
$437$	4.81665			0.230412
$438$		0			0
$439$	−11.6194	−	20.1254i	−0.554565	−	0.960535i	−0.997937	−	0.0641973i	$-0.979551\pi$
$439$	−11.6194	−	20.1254i	−0.554565	−	0.960535i	0.443372	−	0.896338i	$-0.353782\pi$
$440$	−8.40833	−	14.5636i	−0.400851	−	0.694295i
$441$		0			0
$442$	1.85281			0.0881294
$443$	22.4222			1.06531			0.532656	−	0.846332i	$-0.321194\pi$
$443$	22.4222			1.06531			0.532656	+	0.846332i	$0.321194\pi$
$444$		0			0
$445$	4.10555	+	7.11102i	0.194622	+	0.337095i
$446$	6.65139	−	11.5205i	0.314952	−	0.545513i
$447$		0			0
$448$	4.40833	−	7.63545i	0.208274	−	0.360741i
$449$	−6.31665	+	10.9408i	−0.298101	+	0.516327i	−0.975702	−	0.219104i	$-0.929687\pi$
$449$	−6.31665	+	10.9408i	−0.298101	+	0.516327i	0.677600	+	0.735430i	$0.263020\pi$
$450$		0			0
$451$	8.40833	−	14.5636i	0.395933	−	0.685775i
$452$	−0.848612	−	1.46984i	−0.0399154	−	0.0691354i
$453$		0			0
$454$	1.85281			0.0869569
$455$	1.80278	−	3.12250i	0.0845154	−	0.146385i
$456$		0			0
$457$	2.59167	+	4.48891i	0.121233	+	0.209982i	0.920254	−	0.391321i	$-0.127982\pi$
$457$	2.59167	+	4.48891i	0.121233	+	0.209982i	−0.799021	+	0.601303i	$0.794648\pi$
$458$	9.11943	+	15.7953i	0.426123	+	0.738067i
$459$		0			0
$460$	−0.908327			−0.0423510
$461$	10.8944	−	18.8697i	0.507405	−	0.878851i	−0.492558	−	0.870280i	$-0.663938\pi$
$461$	10.8944	−	18.8697i	0.507405	−	0.878851i	0.999963	−	0.00857184i	$-0.00272854\pi$
$462$		0			0
$463$	−5.57779			−0.259222			−0.129611	−	0.991565i	$-0.541373\pi$
$463$	−5.57779			−0.259222			−0.129611	+	0.991565i	$0.541373\pi$
$464$	−13.5597	+	23.4861i	−0.629494	+	1.09032i
$465$		0			0
$466$	−0.513878	−	0.890063i	−0.0238049	−	0.0412314i
$467$	−17.2111			−0.796435			−0.398217	−	0.917291i	$-0.630371\pi$
$467$	−17.2111			−0.796435			−0.398217	+	0.917291i	$0.630371\pi$
$468$		0			0
$469$	7.00000			0.323230
$470$	3.39445	+	5.87936i	0.156574	+	0.271195i
$471$		0			0
$472$	16.2250	−	28.1025i	0.746815	−	1.29352i
$473$	23.6056			1.08538
$474$		0			0
$475$	−0.802776	+	1.39045i	−0.0368339	+	0.0637981i
$476$	−0.119429			−0.00547404
$477$		0			0
$478$		0			0
$479$	−3.59167	−	6.22096i	−0.164108	−	0.284243i	0.772230	−	0.635343i	$-0.219141\pi$
$479$	−3.59167	−	6.22096i	−0.164108	−	0.284243i	−0.936338	+	0.351100i	$0.885808\pi$
$480$		0			0
$481$	6.50000	+	11.2583i	0.296374	+	0.513336i
$482$	−21.1194			−0.961964
$483$		0			0
$484$	3.09167	+	5.35493i	0.140531	+	0.243406i
$485$	7.80278	−	13.5148i	0.354306	−	0.613676i
$486$		0			0
$487$	0.500000	−	0.866025i	0.0226572	−	0.0392434i	−0.854475	−	0.519493i	$-0.826121\pi$
$487$	0.500000	−	0.866025i	0.0226572	−	0.0392434i	0.877132	+	0.480250i	$0.159454\pi$
$488$	1.50000	−	2.59808i	0.0679018	−	0.117609i
$489$		0			0
$490$	−3.90833	+	6.76942i	−0.176560	+	0.305811i
$491$	2.40833	+	4.17134i	0.108686	+	0.188250i	0.915238	−	0.402913i	$-0.132002\pi$
$491$	2.40833	+	4.17134i	0.108686	+	0.188250i	−0.806552	+	0.591163i	$0.798669\pi$
$492$		0			0
$493$	3.23886			0.145871
$494$	−7.54163			−0.339314
$495$		0			0
$496$	−6.60555	−	11.4412i	−0.296598	−	0.513723i
$497$	8.40833	+	14.5636i	0.377165	+	0.653269i
$498$		0			0
$499$	−26.4222			−1.18282			−0.591410	−	0.806371i	$-0.701429\pi$
$499$	−26.4222			−1.18282			−0.591410	+	0.806371i	$0.701429\pi$
$500$	0.151388	−	0.262211i	0.00677027	−	0.0117265i
$501$		0			0
$502$	−37.5416			−1.67557
$503$	1.50000	−	2.59808i	0.0668817	−	0.115842i	−0.830645	−	0.556802i	$-0.812028\pi$
$503$	1.50000	−	2.59808i	0.0668817	−	0.115842i	0.897527	+	0.440959i	$0.145362\pi$
$504$		0			0
$505$	−4.50000	−	7.79423i	−0.200247	−	0.346839i
$506$	−21.9083			−0.973944
$507$		0			0
$508$	−3.09167			−0.137171
$509$	1.50000	+	2.59808i	0.0664863	+	0.115158i	0.897352	−	0.441315i	$-0.145488\pi$
$509$	1.50000	+	2.59808i	0.0664863	+	0.115158i	−0.830866	+	0.556473i	$0.812154\pi$
$510$		0			0
$511$	−7.60555	+	13.1732i	−0.336450	+	0.582748i
$512$	25.4222			1.12351
$513$		0			0
$514$	15.3764	−	26.6327i	0.678223	−	1.17472i
$515$	−4.00000			−0.176261
$516$		0			0
$517$	−14.6056	−	25.2976i	−0.642351	−	1.11259i
$518$	2.34861	+	4.06792i	0.103192	+	0.178734i
$519$		0			0
$520$	10.8167			0.474342
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$		0			0
$523$	−13.7111	−	23.7483i	−0.599545	−	1.03844i	−0.992888	−	0.119050i	$-0.962015\pi$
$523$	−13.7111	−	23.7483i	−0.599545	−	1.03844i	0.393344	−	0.919392i	$-0.371318\pi$
$524$	1.02776	−	1.78013i	0.0448977	−	0.0777652i
$525$		0			0
$526$	−17.0736	+	29.5723i	−0.744444	+	1.28941i
$527$	−0.788897	+	1.36641i	−0.0343649	+	0.0595218i
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	−7.30278	−	12.6488i	−0.317212	−	0.549428i
$531$		0			0
$532$	0.486122			0.0210761
$533$	5.40833	+	9.36750i	0.234261	+	0.405751i
$534$		0			0
$535$	−4.10555	−	7.11102i	−0.177498	−	0.307436i
$536$	10.5000	+	18.1865i	0.453531	+	0.785539i
$537$		0			0
$538$	−11.7250			−0.505500
$539$	16.8167	−	29.1273i	0.724345	−	1.25460i
$540$		0			0
$541$	17.6333			0.758115			0.379058	−	0.925373i	$-0.376248\pi$
$541$	17.6333			0.758115			0.379058	+	0.925373i	$0.376248\pi$
$542$	0.531958	−	0.921379i	0.0228496	−	0.0395766i
$543$		0			0
$544$	−0.334734	−	0.579776i	−0.0143516	−	0.0248577i
$545$	−4.78890			−0.205134
$546$		0			0
$547$	−24.8444			−1.06227			−0.531135	−	0.847287i	$-0.678234\pi$
$547$	−24.8444			−1.06227			−0.531135	+	0.847287i	$0.678234\pi$
$548$	−0.848612	−	1.46984i	−0.0362509	−	0.0627884i
$549$		0			0
$550$	3.65139	−	6.32439i	0.155696	−	0.269673i
$551$	−13.1833			−0.561629
$552$		0			0
$553$	−4.60555	+	7.97705i	−0.195848	+	0.339219i
$554$	−26.5694			−1.12883
$555$		0			0
$556$	2.05971	+	3.56753i	0.0873514	+	0.151297i
$557$	2.80278	+	4.85455i	0.118757	+	0.205694i	0.919276	−	0.393615i	$-0.128776\pi$
$557$	2.80278	+	4.85455i	0.118757	+	0.205694i	−0.800518	+	0.599309i	$0.795442\pi$
$558$		0			0
$559$	−7.59167	+	13.1492i	−0.321094	+	0.556150i
$560$	3.30278			0.139568
$561$		0			0
$562$	3.90833	+	6.76942i	0.164863	+	0.285551i
$563$	−9.71110	+	16.8201i	−0.409274	+	0.708884i	−0.994809	−	0.101764i	$-0.967551\pi$
$563$	−9.71110	+	16.8201i	−0.409274	+	0.708884i	0.585534	+	0.810648i	$0.300885\pi$
$564$		0			0
$565$	2.80278	−	4.85455i	0.117914	−	0.204232i
$566$	3.25694	−	5.64118i	0.136899	−	0.237117i
$567$		0			0
$568$	−25.2250	+	43.6909i	−1.05842	+	1.83323i
$569$	0.711103	+	1.23167i	0.0298110	+	0.0516341i	0.880546	−	0.473961i	$-0.157176\pi$
$569$	0.711103	+	1.23167i	0.0298110	+	0.0516341i	−0.850735	+	0.525595i	$0.823843\pi$
$570$		0			0
$571$	−36.8444			−1.54189			−0.770945	−	0.636901i	$-0.780216\pi$
$571$	−36.8444			−1.54189			−0.770945	+	0.636901i	$0.780216\pi$
$572$	−6.11943			−0.255866
$573$		0			0
$574$	1.95416	+	3.38471i	0.0815652	+	0.141275i
$575$	−1.50000	−	2.59808i	−0.0625543	−	0.108347i
$576$		0			0
$577$	29.6333			1.23365			0.616825	−	0.787100i	$-0.288418\pi$
$577$	29.6333			1.23365			0.616825	+	0.787100i	$0.288418\pi$
$578$	−10.9722	+	19.0045i	−0.456385	+	0.790482i
$579$		0			0
$580$	2.48612			0.103231
$581$	−2.60555	+	4.51295i	−0.108096	+	0.187229i
$582$		0			0
$583$	31.4222	+	54.4249i	1.30137	+	2.25405i
$584$	−45.6333			−1.88832
$585$		0			0
$586$	22.9361			0.947481
$587$	−2.28890	−	3.96449i	−0.0944729	−	0.163632i	0.814916	−	0.579580i	$-0.196783\pi$
$587$	−2.28890	−	3.96449i	−0.0944729	−	0.163632i	−0.909389	+	0.415948i	$0.863450\pi$
$588$		0			0
$589$	3.21110	−	5.56179i	0.132311	−	0.229170i
$590$	14.0917			0.580145
$591$		0			0
$592$	−5.95416	+	10.3129i	−0.244715	+	0.423858i
$593$	−35.2111			−1.44595			−0.722973	−	0.690876i	$-0.757225\pi$
$593$	−35.2111			−1.44595			−0.722973	+	0.690876i	$0.757225\pi$
$594$		0			0
$595$	−0.197224	−	0.341603i	−0.00808541	−	0.0140043i
$596$	−0.454163	−	0.786634i	−0.0186033	−	0.0322218i
$597$		0			0
$598$	7.04584	−	12.2037i	0.288126	−	0.499048i
$599$	6.78890			0.277387			0.138693	−	0.990335i	$-0.455710\pi$
$599$	6.78890			0.277387			0.138693	+	0.990335i	$0.455710\pi$
$600$		0			0
$601$	−14.1056	−	24.4315i	−0.575377	−	0.996583i	−0.996001	−	0.0893475i	$-0.971522\pi$
$601$	−14.1056	−	24.4315i	−0.575377	−	0.996583i	0.420623	−	0.907235i	$-0.361811\pi$
$602$	−2.74306	+	4.75112i	−0.111799	+	0.193641i
$603$		0			0
$604$	2.00000	−	3.46410i	0.0813788	−	0.140952i
$605$	−10.2111	+	17.6861i	−0.415140	+	0.719044i
$606$		0			0
$607$	9.89445	−	17.1377i	0.401603	−	0.695597i	−0.592316	−	0.805706i	$-0.701786\pi$
$607$	9.89445	−	17.1377i	0.401603	−	0.695597i	0.993920	+	0.110108i	$0.0351197\pi$
$608$	1.36249	+	2.35990i	0.0552563	+	0.0957067i
$609$		0			0
$610$	1.30278			0.0527478
$611$	18.7889			0.760117
$612$		0			0
$613$	−0.802776	−	1.39045i	−0.0324238	−	0.0561597i	0.849358	−	0.527817i	$-0.176989\pi$
$613$	−0.802776	−	1.39045i	−0.0324238	−	0.0561597i	−0.881782	+	0.471657i	$0.843656\pi$
$614$	−10.4222	−	18.0518i	−0.420606	−	0.728511i
$615$		0			0
$616$	−16.8167			−0.677562
$617$	13.2250	−	22.9063i	0.532418	−	0.922174i	−0.466866	−	0.884328i	$-0.654617\pi$
$617$	13.2250	−	22.9063i	0.532418	−	0.922174i	0.999284	−	0.0378463i	$-0.0120497\pi$
$618$		0			0
$619$	−14.4222			−0.579677			−0.289839	−	0.957076i	$-0.593602\pi$
$619$	−14.4222			−0.579677			−0.289839	+	0.957076i	$0.593602\pi$
$620$	−0.605551	+	1.04885i	−0.0243195	+	0.0421227i
$621$		0			0
$622$	−3.39445	−	5.87936i	−0.136105	−	0.235741i
$623$	8.21110			0.328971
$624$		0			0
$625$	1.00000			0.0400000
$626$	9.11943	+	15.7953i	0.364486	+	0.631308i
$627$		0			0
$628$	−0.486122	+	0.841988i	−0.0193984	+	0.0335990i
$629$	1.42221			0.0567070
$630$		0			0
$631$	−0.0138782	+	0.0240377i	−0.000552482	+	0.000956927i	−0.866302	−	0.499521i	$-0.833509\pi$
$631$	−0.0138782	+	0.0240377i	−0.000552482	+	0.000956927i	0.865749	+	0.500478i	$0.166843\pi$
$632$	−27.6333			−1.09919
$633$		0			0
$634$	−3.90833	−	6.76942i	−0.155219	−	0.268848i
$635$	−5.10555	−	8.84307i	−0.202608	−	0.350927i
$636$		0			0
$637$	10.8167	+	18.7350i	0.428571	+	0.742307i
$638$	59.9638			2.37399
$639$		0			0
$640$	4.04584	+	7.00759i	0.159926	+	0.276999i
$641$	−9.71110	+	16.8201i	−0.383565	+	0.664355i	−0.991569	−	0.129579i	$-0.958637\pi$
$641$	−9.71110	+	16.8201i	−0.383565	+	0.664355i	0.608004	+	0.793934i	$0.291971\pi$
$642$		0			0
$643$	20.3167	−	35.1895i	0.801211	−	1.38774i	−0.117609	−	0.993060i	$-0.537523\pi$
$643$	20.3167	−	35.1895i	0.801211	−	1.38774i	0.918820	−	0.394678i	$-0.129144\pi$
$644$	−0.454163	+	0.786634i	−0.0178965	+	0.0309977i
$645$		0			0
$646$	−0.412529	+	0.714521i	−0.0162307	+	0.0281125i
$647$	5.28890	+	9.16064i	0.207928	+	0.360142i	0.951062	−	0.309001i	$-0.0999947\pi$
$647$	5.28890	+	9.16064i	0.207928	+	0.360142i	−0.743134	+	0.669143i	$0.766661\pi$
$648$		0			0
$649$	−60.6333			−2.38007
$650$	2.34861	+	4.06792i	0.0921201	+	0.159557i
$651$		0			0
$652$	−2.75694	−	4.77516i	−0.107970	−	0.187010i
$653$	−14.4083	−	24.9560i	−0.563841	−	0.976602i	−0.997156	−	0.0753594i	$-0.975990\pi$
$653$	−14.4083	−	24.9560i	−0.563841	−	0.976602i	0.433315	−	0.901243i	$-0.357344\pi$
$654$		0			0
$655$	6.78890			0.265264
$656$	−4.95416	+	8.58086i	−0.193428	+	0.335026i
$657$		0			0
$658$	6.78890			0.264659
$659$	−6.59167	+	11.4171i	−0.256775	+	0.444748i	−0.965376	−	0.260862i	$-0.915993\pi$
$659$	−6.59167	+	11.4171i	−0.256775	+	0.444748i	0.708601	+	0.705609i	$0.249327\pi$
$660$		0			0
$661$	−19.3167	−	33.4574i	−0.751331	−	1.30134i	−0.947178	−	0.320709i	$-0.896079\pi$
$661$	−19.3167	−	33.4574i	−0.751331	−	1.30134i	0.195847	−	0.980634i	$-0.437254\pi$
$662$	33.9083			1.31788
$663$		0			0
$664$	−15.6333			−0.606690
$665$	0.802776	+	1.39045i	0.0311303	+	0.0539193i
$666$		0			0
$667$	12.3167	−	21.3331i	0.476903	−	0.826020i
$668$	2.72498			0.105433
$669$		0			0
$670$	−4.55971	+	7.89766i	−0.176157	+	0.305113i
$671$	−5.60555			−0.216400
$672$		0			0
$673$	5.19722	+	9.00186i	0.200338	+	0.346996i	0.948637	−	0.316365i	$-0.102463\pi$
$673$	5.19722	+	9.00186i	0.200338	+	0.346996i	−0.748299	+	0.663361i	$0.769129\pi$
$674$	11.4861	+	19.8945i	0.442429	+	0.766309i
$675$		0			0
$676$	1.96804	−	3.40875i	0.0756939	−	0.131106i
$677$	−33.6333			−1.29263			−0.646317	−	0.763069i	$-0.723691\pi$
$677$	−33.6333			−1.29263			−0.646317	+	0.763069i	$0.723691\pi$
$678$		0			0
$679$	−7.80278	−	13.5148i	−0.299443	−	0.518651i
$680$	0.591673	−	1.02481i	0.0226896	−	0.0392996i
$681$		0			0
$682$	−14.6056	+	25.2976i	−0.559275	+	0.968694i
$683$	10.8944	−	18.8697i	0.416864	−	0.722030i	−0.578758	−	0.815500i	$-0.696462\pi$
$683$	10.8944	−	18.8697i	0.416864	−	0.722030i	0.995622	+	0.0934691i	$0.0297956\pi$
$684$		0			0
$685$	2.80278	−	4.85455i	0.107089	−	0.185483i
$686$	8.46804	+	14.6671i	0.323311	+	0.559992i
$687$		0			0
$688$	−13.9083			−0.530250
$689$	−40.4222			−1.53996
$690$		0			0
$691$	−3.01388	−	5.22019i	−0.114653	−	0.198585i	0.802988	−	0.595995i	$-0.203242\pi$
$691$	−3.01388	−	5.22019i	−0.114653	−	0.198585i	−0.917641	+	0.397410i	$0.869909\pi$
$692$	2.54584	+	4.40952i	0.0967782	+	0.167625i
$693$		0			0
$694$	26.3305			0.999493
$695$	−6.80278	+	11.7828i	−0.258044	+	0.446945i
$696$		0			0
$697$	1.18335			0.0448224
$698$	−11.8625	+	20.5464i	−0.449002	+	0.777694i
$699$		0			0
$700$	−0.151388	−	0.262211i	−0.00572192	−	0.00991066i
$701$	7.57779			0.286209			0.143105	−	0.989708i	$-0.454291\pi$
$701$	7.57779			0.286209			0.143105	+	0.989708i	$0.454291\pi$
$702$		0			0
$703$	−5.78890			−0.218332
$704$	−24.7111	−	42.8009i	−0.931335	−	1.61312i
$705$		0			0
$706$	3.13751	−	5.43433i	0.118082	−	0.204524i
$707$	−9.00000			−0.338480
$708$		0			0
$709$	−21.9222	+	37.9704i	−0.823306	+	1.42601i	0.0799016	+	0.996803i	$0.474539\pi$
$709$	−21.9222	+	37.9704i	−0.823306	+	1.42601i	−0.903207	+	0.429205i	$0.858794\pi$
$710$	−21.9083			−0.822205
$711$		0			0
$712$	12.3167	+	21.3331i	0.461586	+	0.799491i
$713$	6.00000	+	10.3923i	0.224702	+	0.389195i
$714$		0			0
$715$	−10.1056	−	17.5033i	−0.377926	−	0.654587i
$716$	0.358288			0.0133899
$717$		0			0
$718$	6.78890	+	11.7587i	0.253359	+	0.438831i
$719$	−9.19722	+	15.9301i	−0.342999	+	0.594091i	−0.984988	−	0.172622i	$-0.944776\pi$
$719$	−9.19722	+	15.9301i	−0.342999	+	0.594091i	0.641989	+	0.766713i	$0.278109\pi$
$720$		0			0
$721$	−2.00000	+	3.46410i	−0.0744839	+	0.129010i
$722$	−10.6972	+	18.5281i	−0.398109	+	0.689546i
$723$		0			0
$724$	−3.88057	+	6.72135i	−0.144220	+	0.249797i
$725$	4.10555	+	7.11102i	0.152476	+	0.264097i
$726$		0			0
$727$	42.4222			1.57335			0.786676	−	0.617366i	$-0.211800\pi$
$727$	42.4222			1.57335			0.786676	+	0.617366i	$0.211800\pi$
$728$	5.40833	−	9.36750i	0.200446	−	0.347183i
$729$		0			0
$730$	−9.90833	−	17.1617i	−0.366724	−	0.635184i
$731$	0.830532	+	1.43852i	0.0307183	+	0.0532057i
$732$		0			0
$733$	10.8444			0.400547			0.200274	−	0.979740i	$-0.435817\pi$
$733$	10.8444			0.400547			0.200274	+	0.979740i	$0.435817\pi$
$734$	−11.3486	+	19.6564i	−0.418885	+	0.725530i
$735$		0			0
$736$	−5.09167			−0.187682
$737$	19.6194	−	33.9818i	0.722691	−	1.25174i
$738$		0			0
$739$	14.1972	+	24.5903i	0.522253	+	0.904569i	0.999665	+	0.0258895i	$0.00824179\pi$
$739$	14.1972	+	24.5903i	0.522253	+	0.904569i	−0.477411	+	0.878680i	$0.658425\pi$
$740$	1.09167			0.0401307
$741$		0			0
$742$	−14.6056			−0.536187
$743$	−3.31665	−	5.74461i	−0.121676	−	0.210749i	0.798753	−	0.601660i	$-0.205494\pi$
$743$	−3.31665	−	5.74461i	−0.121676	−	0.210749i	−0.920429	+	0.390910i	$0.872160\pi$
$744$		0			0
$745$	1.50000	−	2.59808i	0.0549557	−	0.0951861i
$746$	35.9638			1.31673
$747$		0			0
$748$	−0.334734	+	0.579776i	−0.0122391	+	0.0211987i
$749$	−8.21110			−0.300027
$750$		0			0
$751$	9.22498	+	15.9781i	0.336624	+	0.583050i	0.983795	−	0.179294i	$-0.0573814\pi$
$751$	9.22498	+	15.9781i	0.336624	+	0.583050i	−0.647171	+	0.762345i	$0.724048\pi$
$752$	8.60555	+	14.9053i	0.313812	+	0.543539i
$753$		0			0
$754$	−19.2847	+	33.4021i	−0.702307	+	1.21643i
$755$	13.2111			0.480801
$756$		0			0
$757$	10.4083	+	18.0278i	0.378297	+	0.655230i	0.990815	−	0.135227i	$-0.0431764\pi$
$757$	10.4083	+	18.0278i	0.378297	+	0.655230i	−0.612518	+	0.790457i	$0.709843\pi$
$758$	1.55971	−	2.70151i	0.0566514	−	0.0981231i
$759$		0			0
$760$	−2.40833	+	4.17134i	−0.0873592	+	0.151311i
$761$	−12.3167	+	21.3331i	−0.446478	+	0.773323i	−0.998154	−	0.0607356i	$-0.980655\pi$
$761$	−12.3167	+	21.3331i	−0.446478	+	0.773323i	0.551676	+	0.834059i	$0.313989\pi$
$762$		0			0
$763$	−2.39445	+	4.14731i	−0.0866849	+	0.150143i
$764$	0.729183	+	1.26298i	0.0263809	+	0.0456931i
$765$		0			0
$766$	24.2750			0.877092
$767$	19.5000	−	33.7750i	0.704104	−	1.21954i
$768$		0			0
$769$	−5.50000	−	9.52628i	−0.198335	−	0.343526i	0.749654	−	0.661830i	$-0.230220\pi$
$769$	−5.50000	−	9.52628i	−0.198335	−	0.343526i	−0.947989	+	0.318304i	$0.896887\pi$
$770$	−3.65139	−	6.32439i	−0.131587	−	0.227915i
$771$		0			0
$772$	−2.54163			−0.0914754
$773$	14.8028	−	25.6392i	0.532419	−	0.922176i	−0.466865	−	0.884329i	$-0.654616\pi$
$773$	14.8028	−	25.6392i	0.532419	−	0.922176i	0.999284	−	0.0378477i	$-0.0120502\pi$
$774$		0			0
$775$	−4.00000			−0.143684
$776$	23.4083	−	40.5444i	0.840310	−	1.45546i
$777$		0			0
$778$	0.513878	+	0.890063i	0.0184234	+	0.0319103i
$779$	−4.81665			−0.172575
$780$		0			0
$781$	94.2666			3.37312
$782$	−0.770817	−	1.33509i	−0.0275644	−	0.0477429i
$783$		0			0
$784$	−9.90833	+	17.1617i	−0.353869	+	0.612919i
$785$	−3.21110			−0.114609
$786$		0			0
$787$	14.3167	−	24.7972i	0.510334	−	0.883924i	−0.489595	−	0.871950i	$-0.662855\pi$
$787$	14.3167	−	24.7972i	0.510334	−	0.883924i	0.999928	−	0.0119736i	$-0.00381140\pi$
$788$	6.90833			0.246099
$789$		0			0
$790$	−6.00000	−	10.3923i	−0.213470	−	0.369742i
$791$	−2.80278	−	4.85455i	−0.0996552	−	0.172608i
$792$		0			0
$793$	1.80278	−	3.12250i	0.0640184	−	0.110883i
$794$	18.2750			0.648556
$795$		0			0
$796$	−1.33473	−	2.31183i	−0.0473084	−	0.0819405i
$797$	25.2250	−	43.6909i	0.893515	−	1.54761i	0.0578825	−	0.998323i	$-0.481565\pi$
$797$	25.2250	−	43.6909i	0.893515	−	1.54761i	0.835632	−	0.549289i	$-0.185102\pi$
$798$		0			0
$799$	1.02776	−	1.78013i	0.0363594	−	0.0629763i
$800$	0.848612	−	1.46984i	0.0300030	−	0.0519667i
$801$		0			0
$802$	1.44029	−	2.49465i	0.0508582	−	0.0880891i
$803$	42.6333	+	73.8431i	1.50450	+	2.60586i
$804$		0			0
$805$	−3.00000			−0.105736
$806$	−9.39445	−	16.2717i	−0.330905	−	0.573145i
$807$		0			0
$808$	−13.5000	−	23.3827i	−0.474928	−	0.822600i
$809$	8.52776	+	14.7705i	0.299820	+	0.519303i	0.976095	−	0.217346i	$-0.0697401\pi$
$809$	8.52776	+	14.7705i	0.299820	+	0.519303i	−0.676275	+	0.736650i	$0.736407\pi$
$810$		0			0
$811$	−17.5778			−0.617240			−0.308620	−	0.951185i	$-0.599867\pi$
$811$	−17.5778			−0.617240			−0.308620	+	0.951185i	$0.599867\pi$
$812$	1.24306	−	2.15304i	0.0436229	−	0.0755571i
$813$		0			0
$814$	26.3305			0.922885
$815$	9.10555	−	15.7713i	0.318954	−	0.552444i
$816$		0			0
$817$	−3.38057	−	5.85532i	−0.118271	−	0.204852i
$818$	8.09167			0.282919
$819$		0			0
$820$	0.908327			0.0317202
$821$	−3.71110	−	6.42782i	−0.129518	−	0.224332i	0.793972	−	0.607955i	$-0.208010\pi$
$821$	−3.71110	−	6.42782i	−0.129518	−	0.224332i	−0.923490	+	0.383622i	$0.874676\pi$
$822$		0			0
$823$	−13.3167	+	23.0651i	−0.464189	+	0.804000i	−0.999165	−	0.0408682i	$-0.986988\pi$
$823$	−13.3167	+	23.0651i	−0.464189	+	0.804000i	0.534975	+	0.844868i	$0.320321\pi$
$824$	−12.0000			−0.418040
$825$		0			0
$826$	7.04584	−	12.2037i	0.245156	−	0.424623i
$827$	13.5778			0.472146			0.236073	−	0.971735i	$-0.424140\pi$
$827$	13.5778			0.472146			0.236073	+	0.971735i	$0.424140\pi$
$828$		0			0
$829$	−0.288897	−	0.500385i	−0.0100338	−	0.0173791i	0.860965	−	0.508664i	$-0.169861\pi$
$829$	−0.288897	−	0.500385i	−0.0100338	−	0.0173791i	−0.870999	+	0.491285i	$0.836527\pi$
$830$	−3.39445	−	5.87936i	−0.117823	−	0.204075i
$831$		0			0
$832$	31.7889			1.10208
$833$	2.36669			0.0820010
$834$		0			0
$835$	4.50000	+	7.79423i	0.155729	+	0.269730i
$836$	1.36249	−	2.35990i	0.0471227	−	0.0816189i
$837$		0			0
$838$	21.6514	−	37.5013i	0.747935	−	1.29546i
$839$	8.01388	−	13.8804i	0.276670	−	0.479206i	−0.693885	−	0.720086i	$-0.744103\pi$
$839$	8.01388	−	13.8804i	0.276670	−	0.479206i	0.970555	+	0.240879i	$0.0774358\pi$
$840$		0			0
$841$	−19.2111	+	33.2746i	−0.662452	+	1.14740i
$842$	2.33053	+	4.03660i	0.0803154	+	0.139110i
$843$		0			0
$844$	4.96384			0.170862
$845$	13.0000			0.447214
$846$		0			0
$847$	10.2111	+	17.6861i	0.350858	+	0.607703i
$848$	−18.5139	−	32.0670i	−0.635769	−	1.10118i
$849$		0			0
$850$	0.513878			0.0176259
$851$	5.40833	−	9.36750i	0.185395	−	0.321114i
$852$		0			0
$853$	32.7889			1.12267			0.561335	−	0.827589i	$-0.310288\pi$
$853$	32.7889			1.12267			0.561335	+	0.827589i	$0.310288\pi$
$854$	0.651388	−	1.12824i	0.0222900	−	0.0386075i
$855$		0			0
$856$	−12.3167	−	21.3331i	−0.420975	−	0.729149i
$857$	−6.00000			−0.204956			−0.102478	−	0.994735i	$-0.532677\pi$
$857$	−6.00000			−0.204956			−0.102478	+	0.994735i	$0.532677\pi$
$858$		0			0
$859$	25.2111			0.860192			0.430096	−	0.902783i	$-0.358480\pi$
$859$	25.2111			0.860192			0.430096	+	0.902783i	$0.358480\pi$
$860$	0.637510	+	1.10420i	0.0217389	+	0.0376529i
$861$		0			0
$862$	13.8347	−	23.9625i	0.471213	−	0.816165i
$863$	−36.0000			−1.22545			−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000			−1.22545			−0.612727	+	0.790295i	$0.709928\pi$
$864$		0			0
$865$	−8.40833	+	14.5636i	−0.285892	+	0.495179i
$866$	4.69722			0.159618
$867$		0			0
$868$	0.605551	+	1.04885i	0.0205537	+	0.0356001i
$869$	25.8167	+	44.7158i	0.875770	+	1.51688i
$870$		0			0
$871$	12.6194	+	21.8575i	0.427593	+	0.740613i
$872$	−14.3667			−0.486518
$873$		0			0
$874$	3.13751	+	5.43433i	0.106128	+	0.183819i
$875$	0.500000	−	0.866025i	0.0169031	−	0.0292770i
$876$		0			0
$877$	19.0139	−	32.9330i	0.642053	−	1.11207i	−0.342921	−	0.939364i	$-0.611416\pi$
$877$	19.0139	−	32.9330i	0.642053	−	1.11207i	0.984974	−	0.172704i	$-0.0552504\pi$
$878$	15.1375	−	26.2189i	0.510866	−	0.884846i
$879$		0			0
$880$	9.25694	−	16.0335i	0.312051	−	0.540489i
$881$	17.9222	+	31.0422i	0.603814	+	1.04584i	0.992238	+	0.124356i	$0.0396865\pi$
$881$	17.9222	+	31.0422i	0.603814	+	1.04584i	−0.388423	+	0.921481i	$0.626980\pi$
$882$		0			0
$883$	−31.6333			−1.06455			−0.532273	−	0.846573i	$-0.678662\pi$
$883$	−31.6333			−1.06455			−0.532273	+	0.846573i	$0.678662\pi$
$884$	−0.215305	−	0.372918i	−0.00724147	−	0.0125426i
$885$		0			0
$886$	14.6056	+	25.2976i	0.490683	+	0.849888i
$887$	17.5278	+	30.3590i	0.588524	+	1.01935i	0.994426	+	0.105437i	$0.0336243\pi$
$887$	17.5278	+	30.3590i	0.588524	+	1.01935i	−0.405901	+	0.913917i	$0.633042\pi$
$888$		0			0
$889$	−10.2111			−0.342469
$890$	−5.34861	+	9.26407i	−0.179286	+	0.310532i
$891$		0			0
$892$	−3.09167			−0.103517
$893$	−4.18335	+	7.24577i	−0.139990	+	0.242470i
$894$		0			0
$895$	0.591673	+	1.02481i	0.0197775	+	0.0342555i
$896$	8.09167			0.270324
$897$		0			0
$898$	−16.4584			−0.549223
$899$	−16.4222	−	28.4441i	−0.547711	−	0.948664i
$900$		0			0
$901$	−2.21110	+	3.82974i	−0.0736625	+	0.127587i
$902$	21.9083			0.729467
$903$		0			0
$904$	8.40833	−	14.5636i	0.279657	−	0.484380i
$905$	−25.6333			−0.852080
$906$		0			0
$907$	−24.1333	−	41.8001i	−0.801333	−	1.38795i	−0.918739	−	0.394866i	$-0.870791\pi$
$907$	−24.1333	−	41.8001i	−0.801333	−	1.38795i	0.117405	−	0.993084i	$-0.462542\pi$
$908$	−0.215305	−	0.372918i	−0.00714513	−	0.0123757i
$909$		0			0
$910$	4.69722			0.155711
$911$	36.0000			1.19273			0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000			1.19273			0.596367	+	0.802712i	$0.296610\pi$
$912$		0			0
$913$	14.6056	+	25.2976i	0.483373	+	0.837227i
$914$	−3.37637	+	5.84804i	−0.111680	+	0.193436i
$915$		0			0
$916$	2.11943	−	3.67096i	0.0700279	−	0.121292i
$917$	3.39445	−	5.87936i	0.112095	−	0.194153i
$918$		0			0
$919$	8.59167	−	14.8812i	0.283413	−	0.490886i	−0.688810	−	0.724942i	$-0.741867\pi$
$919$	8.59167	−	14.8812i	0.283413	−	0.490886i	0.972223	+	0.234056i	$0.0751999\pi$
$920$	−4.50000	−	7.79423i	−0.148361	−	0.256968i
$921$		0			0
$922$	28.3860			0.934845
$923$	−30.3167	+	52.5100i	−0.997885	+	1.72839i
$924$		0			0
$925$	1.80278	+	3.12250i	0.0592749	+	0.102667i
$926$	−3.63331	−	6.29307i	−0.119398	−	0.206803i
$927$		0			0
$928$	13.9361			0.457474
$929$	6.71110	−	11.6240i	0.220184	−	0.381370i	−0.734680	−	0.678414i	$-0.762668\pi$
$929$	6.71110	−	11.6240i	0.220184	−	0.381370i	0.954864	+	0.297044i	$0.0960008\pi$
$930$		0			0
$931$	−9.63331			−0.315719
$932$	−0.119429	+	0.206858i	−0.00391204	+	0.00677586i
$933$		0			0
$934$	−11.2111	−	19.4182i	−0.366838	−	0.635383i
$935$	−2.21110			−0.0723108
$936$		0			0
$937$	−46.4777			−1.51836			−0.759180	−	0.650880i	$-0.774400\pi$
$937$	−46.4777			−1.51836			−0.759180	+	0.650880i	$0.774400\pi$
$938$	4.55971	+	7.89766i	0.148880	+	0.257868i
$939$		0			0
$940$	0.788897	−	1.36641i	0.0257310	−	0.0445674i
$941$	−33.6333			−1.09641			−0.548207	−	0.836343i	$-0.684689\pi$
$941$	−33.6333			−1.09641			−0.548207	+	0.836343i	$0.684689\pi$
$942$		0			0
$943$	4.50000	−	7.79423i	0.146540	−	0.253815i
$944$	35.7250			1.16275
$945$		0			0
$946$	15.3764	+	26.6327i	0.499929	+	0.865902i
$947$	12.3167	+	21.3331i	0.400237	+	0.693232i	0.993754	−	0.111590i	$-0.0355943\pi$
$947$	12.3167	+	21.3331i	0.400237	+	0.693232i	−0.593517	+	0.804822i	$0.702261\pi$
$948$		0			0
$949$	−54.8444			−1.78032
$950$	−2.09167			−0.0678628
$951$		0			0
$952$	−0.591673	−	1.02481i	−0.0191762	−	0.0332142i
$953$	25.2250	−	43.6909i	0.817117	−	1.41529i	−0.0906803	−	0.995880i	$-0.528904\pi$
$953$	25.2250	−	43.6909i	0.817117	−	1.41529i	0.907798	−	0.419409i	$-0.137763\pi$
$954$		0			0
$955$	−2.40833	+	4.17134i	−0.0779316	+	0.134982i
$956$		0			0
$957$		0			0
$958$	4.67914	−	8.10452i	0.151176	−	0.261845i
$959$	−2.80278	−	4.85455i	−0.0905063	−	0.156762i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−8.46804	+	14.6671i	−0.273021	+	0.472886i
$963$		0			0
$964$	2.45416	+	4.25074i	0.0790433	+	0.136907i
$965$	−4.19722	−	7.26981i	−0.135113	−	0.234023i
$966$		0			0
$967$	56.4777			1.81620			0.908100	−	0.418752i	$-0.137532\pi$
$967$	56.4777			1.81620			0.908100	+	0.418752i	$0.137532\pi$
$968$	−30.6333	+	53.0584i	−0.984592	+	1.70536i
$969$		0			0
$970$	20.3305			0.652774
$971$	−3.98612	+	6.90417i	−0.127921	+	0.221565i	−0.922871	−	0.385110i	$-0.874164\pi$
$971$	−3.98612	+	6.90417i	−0.127921	+	0.221565i	0.794950	+	0.606675i	$0.207497\pi$
$972$		0			0
$973$	6.80278	+	11.7828i	0.218087	+	0.377738i
$974$	1.30278			0.0417436
$975$		0			0
$976$	3.30278			0.105719
$977$	3.59167	+	6.22096i	0.114908	+	0.199026i	0.917743	−	0.397175i	$-0.130009\pi$
$977$	3.59167	+	6.22096i	0.114908	+	0.199026i	−0.802835	+	0.596201i	$0.796676\pi$
$978$		0			0
$979$	23.0139	−	39.8612i	0.735527	−	1.27397i
$980$	1.81665			0.0580309
$981$		0			0
$982$	−3.13751	+	5.43433i	−0.100122	+	0.173416i
$983$	10.4222			0.332417			0.166208	−	0.986091i	$-0.446848\pi$
$983$	10.4222			0.332417			0.166208	+	0.986091i	$0.446848\pi$
$984$		0			0
$985$	11.4083	+	19.7598i	0.363500	+	0.629600i
$986$	2.10975	+	3.65420i	0.0671882	+	0.116373i
$987$		0			0
$988$	0.876369	+	1.51791i	0.0278810	+	0.0482913i
$989$	12.6333			0.401716
$990$		0			0
$991$	−1.98612	−	3.44006i	−0.0630912	−	0.109277i	0.832754	−	0.553642i	$-0.186763\pi$
$991$	−1.98612	−	3.44006i	−0.0630912	−	0.109277i	−0.895846	+	0.444365i	$0.853429\pi$
$992$	−3.39445	+	5.87936i	−0.107774	+	0.186670i
$993$		0			0
$994$	−10.9542	+	18.9732i	−0.347445	+	0.601792i
$995$	4.40833	−	7.63545i	0.139753	−	0.242060i
$996$		0			0
$997$	−23.2250	+	40.2268i	−0.735543	+	1.27400i	0.218942	+	0.975738i	$0.429739\pi$
$997$	−23.2250	+	40.2268i	−0.735543	+	1.27400i	−0.954485	+	0.298259i	$0.903594\pi$
$998$	−17.2111	−	29.8105i	−0.544808	−	0.943635i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.j.d.406.2		4
3.2	odd	2		65.2.e.b.16.1	✓	4
12.11	even	2		1040.2.q.o.81.1		4
13.3	even	3		7605.2.a.bg.1.1		2
13.9	even	3	inner	585.2.j.d.451.2		4
13.10	even	6		7605.2.a.bb.1.2		2
15.2	even	4		325.2.o.b.224.3		8
15.8	even	4		325.2.o.b.224.2		8
15.14	odd	2		325.2.e.a.276.2		4
39.2	even	12		845.2.c.d.506.2		4
39.5	even	4		845.2.m.d.361.2		8
39.8	even	4		845.2.m.d.361.3		8
39.11	even	12		845.2.c.d.506.3		4
39.17	odd	6		845.2.e.d.191.2		4
39.20	even	12		845.2.m.d.316.2		8
39.23	odd	6		845.2.a.f.1.1		2
39.29	odd	6		845.2.a.c.1.2		2
39.32	even	12		845.2.m.d.316.3		8
39.35	odd	6		65.2.e.b.61.1	yes	4
39.38	odd	2		845.2.e.d.146.2		4
156.35	even	6		1040.2.q.o.321.1		4
195.29	odd	6		4225.2.a.x.1.1		2
195.74	odd	6		325.2.e.a.126.2		4
195.113	even	12		325.2.o.b.74.3		8
195.152	even	12		325.2.o.b.74.2		8
195.179	odd	6		4225.2.a.t.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.e.b.16.1	✓	4	3.2	odd	2
65.2.e.b.61.1	yes	4	39.35	odd	6
325.2.e.a.126.2		4	195.74	odd	6
325.2.e.a.276.2		4	15.14	odd	2
325.2.o.b.74.2		8	195.152	even	12
325.2.o.b.74.3		8	195.113	even	12
325.2.o.b.224.2		8	15.8	even	4
325.2.o.b.224.3		8	15.2	even	4
585.2.j.d.406.2		4	1.1	even	1	trivial
585.2.j.d.451.2		4	13.9	even	3	inner
845.2.a.c.1.2		2	39.29	odd	6
845.2.a.f.1.1		2	39.23	odd	6
845.2.c.d.506.2		4	39.2	even	12
845.2.c.d.506.3		4	39.11	even	12
845.2.e.d.146.2		4	39.38	odd	2
845.2.e.d.191.2		4	39.17	odd	6
845.2.m.d.316.2		8	39.20	even	12
845.2.m.d.316.3		8	39.32	even	12
845.2.m.d.361.2		8	39.5	even	4
845.2.m.d.361.3		8	39.8	even	4
1040.2.q.o.81.1		4	12.11	even	2
1040.2.q.o.321.1		4	156.35	even	6
4225.2.a.t.1.2		2	195.179	odd	6
4225.2.a.x.1.1		2	195.29	odd	6
7605.2.a.bb.1.2		2	13.10	even	6
7605.2.a.bg.1.1		2	13.3	even	3

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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.651388 + 1.12824i) q^{2} +(0.151388 - 0.262211i) q^{4} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +(0.651388 + 1.12824i) q^{10} +(-2.80278 - 4.85455i) q^{11} +3.60555 q^{13} +1.30278 q^{14} +(1.65139 + 2.86029i) q^{16} +(0.197224 - 0.341603i) q^{17} +(-0.802776 + 1.39045i) q^{19} +(0.151388 - 0.262211i) q^{20} +(3.65139 - 6.32439i) q^{22} +(-1.50000 - 2.59808i) q^{23} +1.00000 q^{25} +(2.34861 + 4.06792i) q^{26} +(-0.151388 - 0.262211i) q^{28} +(4.10555 + 7.11102i) q^{29} -4.00000 q^{31} +(0.848612 - 1.46984i) q^{32} +0.513878 q^{34} +(0.500000 - 0.866025i) q^{35} +(1.80278 + 3.12250i) q^{37} -2.09167 q^{38} +3.00000 q^{40} +(1.50000 + 2.59808i) q^{41} +(-2.10555 + 3.64692i) q^{43} -1.69722 q^{44} +(1.95416 - 3.38471i) q^{46} +5.21110 q^{47} +(3.00000 + 5.19615i) q^{49} +(0.651388 + 1.12824i) q^{50} +(0.545837 - 0.945417i) q^{52} -11.2111 q^{53} +(-2.80278 - 4.85455i) q^{55} +(1.50000 - 2.59808i) q^{56} +(-5.34861 + 9.26407i) q^{58} +(5.40833 - 9.36750i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-2.60555 - 4.51295i) q^{62} +8.81665 q^{64} +3.60555 q^{65} +(3.50000 + 6.06218i) q^{67} +(-0.0597147 - 0.103429i) q^{68} +1.30278 q^{70} +(-8.40833 + 14.5636i) q^{71} -15.2111 q^{73} +(-2.34861 + 4.06792i) q^{74} +(0.243061 + 0.420994i) q^{76} -5.60555 q^{77} -9.21110 q^{79} +(1.65139 + 2.86029i) q^{80} +(-1.95416 + 3.38471i) q^{82} -5.21110 q^{83} +(0.197224 - 0.341603i) q^{85} -5.48612 q^{86} +(-8.40833 - 14.5636i) q^{88} +(4.10555 + 7.11102i) q^{89} +(1.80278 - 3.12250i) q^{91} -0.908327 q^{92} +(3.39445 + 5.87936i) q^{94} +(-0.802776 + 1.39045i) q^{95} +(7.80278 - 13.5148i) q^{97} +(-3.90833 + 6.76942i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 3 q^{4} + 4 q^{5} + 2 q^{7} + 12 q^{8} - q^{10} - 4 q^{11} - 2 q^{14} + 3 q^{16} + 8 q^{17} + 4 q^{19} - 3 q^{20} + 11 q^{22} - 6 q^{23} + 4 q^{25} + 13 q^{26} + 3 q^{28} + 2 q^{29} - 16 q^{31}+ \cdots + 6 q^{98}+O(q^{100}) \) 4 * q - q^2 - 3 * q^4 + 4 * q^5 + 2 * q^7 + 12 * q^8 - q^10 - 4 * q^11 - 2 * q^14 + 3 * q^16 + 8 * q^17 + 4 * q^19 - 3 * q^20 + 11 * q^22 - 6 * q^23 + 4 * q^25 + 13 * q^26 + 3 * q^28 + 2 * q^29 - 16 * q^31 + 7 * q^32 - 34 * q^34 + 2 * q^35 - 30 * q^38 + 12 * q^40 + 6 * q^41 + 6 * q^43 - 14 * q^44 - 3 * q^46 - 8 * q^47 + 12 * q^49 - q^50 + 13 * q^52 - 16 * q^53 - 4 * q^55 + 6 * q^56 - 25 * q^58 + 2 * q^61 + 4 * q^62 - 8 * q^64 + 14 * q^67 + 25 * q^68 - 2 * q^70 - 12 * q^71 - 32 * q^73 - 13 * q^74 + 19 * q^76 - 8 * q^77 - 8 * q^79 + 3 * q^80 + 3 * q^82 + 8 * q^83 + 8 * q^85 - 58 * q^86 - 12 * q^88 + 2 * q^89 + 18 * q^92 + 28 * q^94 + 4 * q^95 + 24 * q^97 + 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more