LMFDB - Embedded newform 585.2.j.d.406.1

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			406.1
Root			$1.15139 + 1.99426i$ of defining polynomial
Character	$\chi$	$=$	585.406
Dual form			585.2.j.d.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.15139 - 1.99426i) q^{2} +(-1.65139 + 2.86029i) q^{4} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +(-1.15139 - 1.99426i) q^{10} +(0.802776 + 1.39045i) q^{11} -3.60555 q^{13} -2.30278 q^{14} +(-0.151388 - 0.262211i) q^{16} +(3.80278 - 6.58660i) q^{17} +(2.80278 - 4.85455i) q^{19} +(-1.65139 + 2.86029i) q^{20} +(1.84861 - 3.20189i) q^{22} +(-1.50000 - 2.59808i) q^{23} +1.00000 q^{25} +(4.15139 + 7.19041i) q^{26} +(1.65139 + 2.86029i) q^{28} +(-3.10555 - 5.37897i) q^{29} -4.00000 q^{31} +(2.65139 - 4.59234i) q^{32} -17.5139 q^{34} +(0.500000 - 0.866025i) q^{35} +(-1.80278 - 3.12250i) q^{37} -12.9083 q^{38} +3.00000 q^{40} +(1.50000 + 2.59808i) q^{41} +(5.10555 - 8.84307i) q^{43} -5.30278 q^{44} +(-3.45416 + 5.98279i) q^{46} -9.21110 q^{47} +(3.00000 + 5.19615i) q^{49} +(-1.15139 - 1.99426i) q^{50} +(5.95416 - 10.3129i) q^{52} +3.21110 q^{53} +(0.802776 + 1.39045i) q^{55} +(1.50000 - 2.59808i) q^{56} +(-7.15139 + 12.3866i) q^{58} +(-5.40833 + 9.36750i) q^{59} +(0.500000 - 0.866025i) q^{61} +(4.60555 + 7.97705i) q^{62} -12.8167 q^{64} -3.60555 q^{65} +(3.50000 + 6.06218i) q^{67} +(12.5597 + 21.7541i) q^{68} -2.30278 q^{70} +(2.40833 - 4.17134i) q^{71} -0.788897 q^{73} +(-4.15139 + 7.19041i) q^{74} +(9.25694 + 16.0335i) q^{76} +1.60555 q^{77} +5.21110 q^{79} +(-0.151388 - 0.262211i) q^{80} +(3.45416 - 5.98279i) q^{82} +9.21110 q^{83} +(3.80278 - 6.58660i) q^{85} -23.5139 q^{86} +(2.40833 + 4.17134i) q^{88} +(-3.10555 - 5.37897i) q^{89} +(-1.80278 + 3.12250i) q^{91} +9.90833 q^{92} +(10.6056 + 18.3694i) q^{94} +(2.80278 - 4.85455i) q^{95} +(4.19722 - 7.26981i) q^{97} +(6.90833 - 11.9656i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.15139	−	1.99426i	−0.814154	−	1.41016i	−0.909934	−	0.414754i	$-0.863868\pi$
$2$	−1.15139	−	1.99426i	−0.814154	−	1.41016i	0.0957796	−	0.995403i	$-0.469466\pi$
$3$		0			0
$3$		0			0
$4$	−1.65139	+	2.86029i	−0.825694	+	1.43014i
$5$	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
$10$	−1.15139	−	1.99426i	−0.364101	−	0.630641i
$11$	0.802776	+	1.39045i	0.242046	+	0.419236i	0.961297	−	0.275514i	$-0.0888482\pi$
$11$	0.802776	+	1.39045i	0.242046	+	0.419236i	−0.719251	+	0.694750i	$0.755515\pi$
$12$		0			0
$13$	−3.60555			−1.00000
$13$	−3.60555			−1.00000
$14$	−2.30278			−0.615443
$15$		0			0
$16$	−0.151388	−	0.262211i	−0.0378470	−	0.0655528i
$17$	3.80278	−	6.58660i	0.922309	−	1.59749i	0.126475	−	0.991970i	$-0.459634\pi$
$17$	3.80278	−	6.58660i	0.922309	−	1.59749i	0.795834	−	0.605516i	$-0.207033\pi$
$18$		0			0
$19$	2.80278	−	4.85455i	0.643001	−	1.11371i	−0.341759	−	0.939788i	$-0.611023\pi$
$19$	2.80278	−	4.85455i	0.643001	−	1.11371i	0.984759	−	0.173922i	$-0.0556442\pi$
$20$	−1.65139	+	2.86029i	−0.369262	+	0.639580i
$21$		0			0
$22$	1.84861	−	3.20189i	0.394125	−	0.682645i
$23$	−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
$26$	4.15139	+	7.19041i	0.814154	+	1.41016i
$27$		0			0
$28$	1.65139	+	2.86029i	0.312083	+	0.540544i
$29$	−3.10555	−	5.37897i	−0.576686	−	0.998850i	−0.995856	−	0.0909423i	$-0.971012\pi$
$29$	−3.10555	−	5.37897i	−0.576686	−	0.998850i	0.419170	−	0.907908i	$-0.362321\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	2.65139	−	4.59234i	0.468704	−	0.811818i
$33$		0			0
$34$	−17.5139			−3.00361
$35$	0.500000	−	0.866025i	0.0845154	−	0.146385i
$36$		0			0
$37$	−1.80278	−	3.12250i	−0.296374	−	0.513336i	0.678929	−	0.734204i	$-0.262444\pi$
$37$	−1.80278	−	3.12250i	−0.296374	−	0.513336i	−0.975304	+	0.220868i	$0.929111\pi$
$38$	−12.9083			−2.09401
$39$		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
$43$	5.10555	−	8.84307i	0.778589	−	1.34856i	−0.154166	−	0.988045i	$-0.549269\pi$
$43$	5.10555	−	8.84307i	0.778589	−	1.34856i	0.932755	−	0.360511i	$-0.117398\pi$
$44$	−5.30278			−0.799424
$45$		0			0
$46$	−3.45416	+	5.98279i	−0.509289	+	0.882114i
$47$	−9.21110			−1.34358			−0.671789	−	0.740743i	$-0.734474\pi$
$47$	−9.21110			−1.34358			−0.671789	+	0.740743i	$0.734474\pi$
$48$		0			0
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$	−1.15139	−	1.99426i	−0.162831	−	0.282031i
$51$		0			0
$52$	5.95416	−	10.3129i	0.825694	−	1.43014i
$53$	3.21110			0.441079			0.220539	−	0.975378i	$-0.429218\pi$
$53$	3.21110			0.441079			0.220539	+	0.975378i	$0.429218\pi$
$54$		0			0
$55$	0.802776	+	1.39045i	0.108246	+	0.187488i
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$		0			0
$58$	−7.15139	+	12.3866i	−0.939023	+	1.62644i
$59$	−5.40833	+	9.36750i	−0.704104	+	1.21954i	0.262910	+	0.964820i	$0.415318\pi$
$59$	−5.40833	+	9.36750i	−0.704104	+	1.21954i	−0.967014	+	0.254724i	$0.918015\pi$
$60$		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	$0.146275\pi$
$62$	4.60555	+	7.97705i	0.584906	+	1.01309i
$63$		0			0
$64$	−12.8167			−1.60208
$65$	−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	$0.692695\pi$
$68$	12.5597	+	21.7541i	1.52309	+	2.63807i
$69$		0			0
$70$	−2.30278			−0.275234
$71$	2.40833	−	4.17134i	0.285816	−	0.495048i	−0.686991	−	0.726666i	$-0.741069\pi$
$71$	2.40833	−	4.17134i	0.285816	−	0.495048i	0.972807	+	0.231619i	$0.0744021\pi$
$72$		0			0
$73$	−0.788897			−0.0923335			−0.0461667	−	0.998934i	$-0.514701\pi$
$73$	−0.788897			−0.0923335			−0.0461667	+	0.998934i	$0.514701\pi$
$74$	−4.15139	+	7.19041i	−0.482589	+	0.835869i
$75$		0			0
$76$	9.25694	+	16.0335i	1.06184	+	1.83917i
$77$	1.60555			0.182970
$78$		0			0
$79$	5.21110			0.586295			0.293147	−	0.956067i	$-0.405297\pi$
$79$	5.21110			0.586295			0.293147	+	0.956067i	$0.405297\pi$
$80$	−0.151388	−	0.262211i	−0.0169257	−	0.0293161i
$81$		0			0
$82$	3.45416	−	5.98279i	0.381449	−	0.660688i
$83$	9.21110			1.01105			0.505525	−	0.862812i	$-0.331299\pi$
$83$	9.21110			1.01105			0.505525	+	0.862812i	$0.331299\pi$
$84$		0			0
$85$	3.80278	−	6.58660i	0.412469	−	0.714417i
$86$	−23.5139			−2.53557
$87$		0			0
$88$	2.40833	+	4.17134i	0.256729	+	0.444667i
$89$	−3.10555	−	5.37897i	−0.329188	−	0.570170i	0.653163	−	0.757217i	$-0.273442\pi$
$89$	−3.10555	−	5.37897i	−0.329188	−	0.570170i	−0.982351	+	0.187047i	$0.940108\pi$
$90$		0			0
$91$	−1.80278	+	3.12250i	−0.188982	+	0.327327i
$92$	9.90833			1.03301
$93$		0			0
$94$	10.6056	+	18.3694i	1.09388	+	1.89465i
$95$	2.80278	−	4.85455i	0.287559	−	0.498066i
$96$		0			0
$97$	4.19722	−	7.26981i	0.426164	−	0.738137i	−0.570365	−	0.821392i	$-0.693198\pi$
$97$	4.19722	−	7.26981i	0.426164	−	0.738137i	0.996528	+	0.0832546i	$0.0265315\pi$
$98$	6.90833	−	11.9656i	0.697846	−	1.20871i
$99$		0			0
$100$	−1.65139	+	2.86029i	−0.165139	+	0.286029i
$101$	−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
$106$	−3.69722	−	6.40378i	−0.359106	−	0.621990i
$107$	3.10555	+	5.37897i	0.300225	+	0.520005i	0.976187	−	0.216932i	$-0.0696049\pi$
$107$	3.10555	+	5.37897i	0.300225	+	0.520005i	−0.675962	+	0.736937i	$0.736272\pi$
$108$		0			0
$109$	−19.2111			−1.84009			−0.920045	−	0.391813i	$-0.871848\pi$
$109$	−19.2111			−1.84009			−0.920045	+	0.391813i	$0.871848\pi$
$110$	1.84861	−	3.20189i	0.176258	−	0.305288i
$111$		0			0
$112$	−0.302776			−0.0286096
$113$	−0.802776	+	1.39045i	−0.0755188	+	0.130802i	−0.901312	−	0.433171i	$-0.857395\pi$
$113$	−0.802776	+	1.39045i	−0.0755188	+	0.130802i	0.825793	+	0.563973i	$0.190728\pi$
$114$		0			0
$115$	−1.50000	−	2.59808i	−0.139876	−	0.242272i
$116$	20.5139			1.90467
$117$		0			0
$118$	24.9083			2.29300
$119$	−3.80278	−	6.58660i	−0.348600	−	0.603793i
$120$		0			0
$121$	4.21110	−	7.29384i	0.382828	−	0.663077i
$122$	−2.30278			−0.208484
$123$		0			0
$124$	6.60555	−	11.4412i	0.593196	−	1.02745i
$125$	1.00000			0.0894427
$126$		0			0
$127$	2.10555	+	3.64692i	0.186837	+	0.323612i	0.944194	−	0.329389i	$-0.106843\pi$
$127$	2.10555	+	3.64692i	0.186837	+	0.323612i	−0.757357	+	0.653001i	$0.773510\pi$
$128$	9.45416	+	16.3751i	0.835638	+	1.44737i
$129$		0			0
$130$	4.15139	+	7.19041i	0.364101	+	0.630641i
$131$	21.2111			1.85322			0.926611	−	0.376021i	$-0.122708\pi$
$131$	21.2111			1.85322			0.926611	+	0.376021i	$0.122708\pi$
$132$		0			0
$133$	−2.80278	−	4.85455i	−0.243031	−	0.420943i
$134$	8.05971	−	13.9598i	0.696253	−	1.20595i
$135$		0			0
$136$	11.4083	−	19.7598i	0.978256	−	1.69439i
$137$	−0.802776	+	1.39045i	−0.0685858	+	0.118794i	−0.898279	−	0.439426i	$-0.855182\pi$
$137$	−0.802776	+	1.39045i	−0.0685858	+	0.118794i	0.829693	+	0.558220i	$0.188515\pi$
$138$		0			0
$139$	−3.19722	+	5.53776i	−0.271185	+	0.469706i	−0.969166	−	0.246410i	$-0.920749\pi$
$139$	−3.19722	+	5.53776i	−0.271185	+	0.469706i	0.697981	+	0.716117i	$0.254082\pi$
$140$	1.65139	+	2.86029i	0.139568	+	0.241738i
$141$		0			0
$142$	−11.0917			−0.930793
$143$	−2.89445	−	5.01333i	−0.242046	−	0.419236i
$144$		0			0
$145$	−3.10555	−	5.37897i	−0.257902	−	0.446699i
$146$	0.908327	+	1.57327i	0.0751737	+	0.130205i
$147$		0			0
$148$	11.9083			0.978858
$149$	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
$151$	−1.21110			−0.0985581			−0.0492791	−	0.998785i	$-0.515692\pi$
$151$	−1.21110			−0.0985581			−0.0492791	+	0.998785i	$0.515692\pi$
$152$	8.40833	−	14.5636i	0.682005	−	1.18127i
$153$		0			0
$154$	−1.84861	−	3.20189i	−0.148965	−	0.258016i
$155$	−4.00000			−0.321288
$156$		0			0
$157$	11.2111			0.894743			0.447372	−	0.894348i	$-0.352360\pi$
$157$	11.2111			0.894743			0.447372	+	0.894348i	$0.352360\pi$
$158$	−6.00000	−	10.3923i	−0.477334	−	0.826767i
$159$		0			0
$160$	2.65139	−	4.59234i	0.209611	−	0.363056i
$161$	−3.00000			−0.236433
$162$		0			0
$163$	1.89445	−	3.28128i	0.148385	−	0.257010i	−0.782246	−	0.622970i	$-0.785926\pi$
$163$	1.89445	−	3.28128i	0.148385	−	0.257010i	0.930631	+	0.365960i	$0.119259\pi$
$164$	−9.90833			−0.773710
$165$		0			0
$166$	−10.6056	−	18.3694i	−0.823150	−	1.42574i
$167$	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
$170$	−17.5139			−1.34325
$171$		0			0
$172$	16.8625	+	29.2067i	1.28575	+	2.22699i
$173$	2.40833	−	4.17134i	0.183102	−	0.317141i	−0.759834	−	0.650118i	$-0.774720\pi$
$173$	2.40833	−	4.17134i	0.183102	−	0.317141i	0.942935	+	0.332976i	$0.108053\pi$
$174$		0			0
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	0.243061	−	0.420994i	0.0183214	−	0.0317336i
$177$		0			0
$178$	−7.15139	+	12.3866i	−0.536019	+	0.928412i
$179$	11.4083	+	19.7598i	0.852698	+	1.47692i	0.878764	+	0.477257i	$0.158369\pi$
$179$	11.4083	+	19.7598i	0.852698	+	1.47692i	−0.0260655	+	0.999660i	$0.508298\pi$
$180$		0			0
$181$	17.6333			1.31067			0.655337	−	0.755337i	$-0.272527\pi$
$181$	17.6333			1.31067			0.655337	+	0.755337i	$0.272527\pi$
$182$	8.30278			0.615443
$183$		0			0
$184$	−4.50000	−	7.79423i	−0.331744	−	0.574598i
$185$	−1.80278	−	3.12250i	−0.132543	−	0.229571i
$186$		0			0
$187$	12.2111			0.892964
$188$	15.2111	−	26.3464i	1.10938	−	1.92151i
$189$		0			0
$190$	−12.9083			−0.936468
$191$	8.40833	−	14.5636i	0.608405	−	1.05379i	−0.383098	−	0.923708i	$-0.625143\pi$
$191$	8.40833	−	14.5636i	0.608405	−	1.05379i	0.991503	−	0.130081i	$-0.0415238\pi$
$192$		0			0
$193$	−7.80278	−	13.5148i	−0.561656	−	0.972817i	−0.997352	−	0.0727230i	$-0.976831\pi$
$193$	−7.80278	−	13.5148i	−0.561656	−	0.972817i	0.435696	−	0.900094i	$-0.356502\pi$
$194$	−19.3305			−1.38785
$195$		0			0
$196$	−19.8167			−1.41548
$197$	0.591673	+	1.02481i	0.0421550	+	0.0730145i	0.886333	−	0.463048i	$-0.153244\pi$
$197$	0.591673	+	1.02481i	0.0421550	+	0.0730145i	−0.844178	+	0.536063i	$0.819911\pi$
$198$		0			0
$199$	−6.40833	+	11.0995i	−0.454274	+	0.786826i	−0.998646	−	0.0520179i	$-0.983435\pi$
$199$	−6.40833	+	11.0995i	−0.454274	+	0.786826i	0.544372	+	0.838844i	$0.316768\pi$
$200$	3.00000			0.212132
$201$		0			0
$202$	−10.3625	+	17.9484i	−0.729102	+	1.26284i
$203$	−6.21110			−0.435934
$204$		0			0
$205$	1.50000	+	2.59808i	0.104765	+	0.181458i
$206$	4.60555	+	7.97705i	0.320884	+	0.555787i
$207$		0			0
$208$	0.545837	+	0.945417i	0.0378470	+	0.0655528i
$209$	9.00000			0.622543
$210$		0			0
$211$	11.8028	+	20.4430i	0.812537	+	1.40735i	0.911083	+	0.412222i	$0.135247\pi$
$211$	11.8028	+	20.4430i	0.812537	+	1.40735i	−0.0985467	+	0.995132i	$0.531419\pi$
$212$	−5.30278	+	9.18468i	−0.364196	+	0.630806i
$213$		0			0
$214$	7.15139	−	12.3866i	0.488859	−	0.846728i
$215$	5.10555	−	8.84307i	0.348196	−	0.603093i
$216$		0			0
$217$	−2.00000	+	3.46410i	−0.135769	+	0.235159i
$218$	22.1194	+	38.3120i	1.49812	+	2.59481i
$219$		0			0
$220$	−5.30278			−0.357513
$221$	−13.7111	+	23.7483i	−0.922309	+	1.59749i
$222$		0			0
$223$	2.10555	+	3.64692i	0.140998	+	0.244216i	0.927873	−	0.372897i	$-0.121636\pi$
$223$	2.10555	+	3.64692i	0.140998	+	0.244216i	−0.786875	+	0.617113i	$0.788302\pi$
$224$	−2.65139	−	4.59234i	−0.177153	−	0.306839i
$225$		0			0
$226$	3.69722			0.245936
$227$	−13.7111	+	23.7483i	−0.910038	+	1.57623i	−0.0960296	+	0.995378i	$0.530614\pi$
$227$	−13.7111	+	23.7483i	−0.910038	+	1.57623i	−0.814008	+	0.580853i	$0.802719\pi$
$228$		0			0
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$	−3.45416	+	5.98279i	−0.227761	+	0.394493i
$231$		0			0
$232$	−9.31665	−	16.1369i	−0.611668	−	1.05944i
$233$	−15.2111			−0.996512			−0.498256	−	0.867030i	$-0.666026\pi$
$233$	−15.2111			−0.996512			−0.498256	+	0.867030i	$0.666026\pi$
$234$		0			0
$235$	−9.21110			−0.600866
$236$	−17.8625	−	30.9387i	−1.16275	−	2.01394i
$237$		0			0
$238$	−8.75694	+	15.1675i	−0.567628	+	0.983161i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	−0.894449	+	1.54923i	−0.0576165	+	0.0997947i	−0.893395	−	0.449272i	$-0.851683\pi$
$241$	−0.894449	+	1.54923i	−0.0576165	+	0.0997947i	0.835778	+	0.549067i	$0.185017\pi$
$242$	−19.3944			−1.24672
$243$		0			0
$244$	1.65139	+	2.86029i	0.105719	+	0.183111i
$245$	3.00000	+	5.19615i	0.191663	+	0.331970i
$246$		0			0
$247$	−10.1056	+	17.5033i	−0.643001	+	1.11371i
$248$	−12.0000			−0.762001
$249$		0			0
$250$	−1.15139	−	1.99426i	−0.0728202	−	0.126128i
$251$	−3.59167	+	6.22096i	−0.226704	+	0.392664i	−0.956829	−	0.290650i	$-0.906128\pi$
$251$	−3.59167	+	6.22096i	−0.226704	+	0.392664i	0.730125	+	0.683314i	$0.239462\pi$
$252$		0			0
$253$	2.40833	−	4.17134i	0.151410	−	0.262250i
$254$	4.84861	−	8.39804i	0.304229	−	0.526940i
$255$		0			0
$256$	8.95416	−	15.5091i	0.559635	−	0.969317i
$257$	−8.19722	−	14.1980i	−0.511329	−	0.885647i	−0.999914	−	0.0131312i	$-0.995820\pi$
$257$	−8.19722	−	14.1980i	−0.511329	−	0.885647i	0.488585	−	0.872516i	$-0.337513\pi$
$258$		0			0
$259$	−3.60555			−0.224038
$260$	5.95416	−	10.3129i	0.369262	−	0.639580i
$261$		0			0
$262$	−24.4222	−	42.3005i	−1.50881	−	2.61333i
$263$	5.89445	+	10.2095i	0.363467	+	0.629544i	0.988529	−	0.151032i	$-0.0482595\pi$
$263$	5.89445	+	10.2095i	0.363467	+	0.629544i	−0.625062	+	0.780575i	$0.714926\pi$
$264$		0			0
$265$	3.21110			0.197256
$266$	−6.45416	+	11.1789i	−0.395730	+	0.685425i
$267$		0			0
$268$	−23.1194			−1.41224
$269$	−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
$271$	10.4083	+	18.0278i	0.632261	+	1.09511i	0.987088	+	0.160176i	$0.0512062\pi$
$271$	10.4083	+	18.0278i	0.632261	+	1.09511i	−0.354828	+	0.934932i	$0.615460\pi$
$272$	−2.30278			−0.139626
$273$		0			0
$274$	3.69722			0.223357
$275$	0.802776	+	1.39045i	0.0484092	+	0.0838472i
$276$		0			0
$277$	−13.8028	+	23.9071i	−0.829328	+	1.43644i	0.0692374	+	0.997600i	$0.477943\pi$
$277$	−13.8028	+	23.9071i	−0.829328	+	1.43644i	−0.898566	+	0.438839i	$0.855390\pi$
$278$	14.7250			0.883146
$279$		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	$0.880813\pi$
$284$	7.95416	+	13.7770i	0.471993	+	0.817515i
$285$		0			0
$286$	−6.66527	+	11.5446i	−0.394125	+	0.682645i
$287$	3.00000			0.177084
$288$		0			0
$289$	−20.4222	−	35.3723i	−1.20131	−	2.08072i
$290$	−7.15139	+	12.3866i	−0.419944	+	0.727364i
$291$		0			0
$292$	1.30278	−	2.25647i	0.0762392	−	0.132050i
$293$	5.19722	−	9.00186i	0.303625	−	0.525894i	−0.673329	−	0.739343i	$-0.735136\pi$
$293$	5.19722	−	9.00186i	0.303625	−	0.525894i	0.976954	+	0.213449i	$0.0684696\pi$
$294$		0			0
$295$	−5.40833	+	9.36750i	−0.314885	+	0.545397i
$296$	−5.40833	−	9.36750i	−0.314353	−	0.544475i
$297$		0			0
$298$	−6.90833			−0.400189
$299$	5.40833	+	9.36750i	0.312772	+	0.541736i
$300$		0			0
$301$	−5.10555	−	8.84307i	−0.294279	−	0.509706i
$302$	1.39445	+	2.41526i	0.0802415	+	0.138982i
$303$		0			0
$304$	−1.69722			−0.0973425
$305$	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	$0.650927\pi$
$308$	−2.65139	+	4.59234i	−0.151077	+	0.261673i
$309$		0			0
$310$	4.60555	+	7.97705i	0.261578	+	0.453066i
$311$	9.21110			0.522314			0.261157	−	0.965296i	$-0.415896\pi$
$311$	9.21110			0.522314			0.261157	+	0.965296i	$0.415896\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$	−12.9083	−	22.3579i	−0.728459	−	1.26173i
$315$		0			0
$316$	−8.60555	+	14.9053i	−0.484100	+	0.838486i
$317$	−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
$319$	4.98612	−	8.63622i	0.279169	−	0.483535i
$320$	−12.8167			−0.716473
$321$		0			0
$322$	3.45416	+	5.98279i	0.192493	+	0.333408i
$323$	−21.3167	−	36.9215i	−1.18609	−	2.05437i
$324$		0			0
$325$	−3.60555			−0.200000
$326$	−8.72498			−0.483232
$327$		0			0
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$	−4.60555	+	7.97705i	−0.253912	+	0.439789i
$330$		0			0
$331$	−5.01388	+	8.68429i	−0.275588	+	0.477332i	−0.970283	−	0.241972i	$-0.922206\pi$
$331$	−5.01388	+	8.68429i	−0.275588	+	0.477332i	0.694696	+	0.719304i	$0.255539\pi$
$332$	−15.2111	+	26.3464i	−0.834818	+	1.44595i
$333$		0			0
$334$	10.3625	−	17.9484i	0.567010	−	0.982091i
$335$	3.50000	+	6.06218i	0.191225	+	0.331212i
$336$		0			0
$337$	−25.6333			−1.39634			−0.698168	−	0.715934i	$-0.746001\pi$
$337$	−25.6333			−1.39634			−0.698168	+	0.715934i	$0.746001\pi$
$338$	−14.9680	−	25.9254i	−0.814154	−	1.41016i
$339$		0			0
$340$	12.5597	+	21.7541i	0.681146	+	1.17978i
$341$	−3.21110	−	5.56179i	−0.173891	−	0.301188i
$342$		0			0
$343$	13.0000			0.701934
$344$	15.3167	−	26.5292i	0.825819	−	1.43036i
$345$		0			0
$346$	−11.0917			−0.596292
$347$	2.89445	−	5.01333i	0.155382	−	0.269130i	−0.777816	−	0.628492i	$-0.783672\pi$
$347$	2.89445	−	5.01333i	0.155382	−	0.269130i	0.933198	+	0.359362i	$0.117006\pi$
$348$		0			0
$349$	1.89445	+	3.28128i	0.101408	+	0.175643i	0.912265	−	0.409601i	$-0.134332\pi$
$349$	1.89445	+	3.28128i	0.101408	+	0.175643i	−0.810857	+	0.585244i	$0.800999\pi$
$350$	−2.30278			−0.123089
$351$		0			0
$352$	8.51388			0.453791
$353$	8.40833	+	14.5636i	0.447530	+	0.775145i	0.998225	−	0.0595620i	$-0.0189704\pi$
$353$	8.40833	+	14.5636i	0.447530	+	0.775145i	−0.550695	+	0.834707i	$0.685637\pi$
$354$		0			0
$355$	2.40833	−	4.17134i	0.127821	−	0.221392i
$356$	20.5139			1.08723
$357$		0			0
$358$	26.2708	−	45.5024i	1.38846	−	2.40488i
$359$	−18.4222			−0.972287			−0.486143	−	0.873879i	$-0.661597\pi$
$359$	−18.4222			−0.972287			−0.486143	+	0.873879i	$0.661597\pi$
$360$		0			0
$361$	−6.21110	−	10.7579i	−0.326900	−	0.566208i
$362$	−20.3028	−	35.1654i	−1.06709	−	1.84825i
$363$		0			0
$364$	−5.95416	−	10.3129i	−0.312083	−	0.540544i
$365$	−0.788897			−0.0412928
$366$		0			0
$367$	−5.71110	−	9.89192i	−0.298117	−	0.516354i	0.677588	−	0.735442i	$-0.263025\pi$
$367$	−5.71110	−	9.89192i	−0.298117	−	0.516354i	−0.975705	+	0.219088i	$0.929692\pi$
$368$	−0.454163	+	0.786634i	−0.0236749	+	0.0410061i
$369$		0			0
$370$	−4.15139	+	7.19041i	−0.215820	+	0.373812i
$371$	1.60555	−	2.78090i	0.0833561	−	0.144377i
$372$		0			0
$373$	10.1972	−	17.6621i	0.527992	−	0.914509i	−0.471475	−	0.881879i	$-0.656278\pi$
$373$	10.1972	−	17.6621i	0.527992	−	0.914509i	0.999467	−	0.0326301i	$-0.0103883\pi$
$374$	−14.0597	−	24.3521i	−0.727011	−	1.25922i
$375$		0			0
$376$	−27.6333			−1.42508
$377$	11.1972	+	19.3942i	0.576686	+	0.998850i
$378$		0			0
$379$	−4.80278	−	8.31865i	−0.246702	−	0.427300i	0.715907	−	0.698196i	$-0.246014\pi$
$379$	−4.80278	−	8.31865i	−0.246702	−	0.427300i	−0.962609	+	0.270895i	$0.912680\pi$
$380$	9.25694	+	16.0335i	0.474871	+	0.822501i
$381$		0			0
$382$	−38.7250			−1.98134
$383$	−12.3167	+	21.3331i	−0.629352	+	1.09007i	0.358330	+	0.933595i	$0.383346\pi$
$383$	−12.3167	+	21.3331i	−0.629352	+	1.09007i	−0.987682	+	0.156474i	$0.949987\pi$
$384$		0			0
$385$	1.60555			0.0818265
$386$	−17.9680	+	31.1216i	−0.914549	+	1.58405i
$387$		0			0
$388$	13.8625	+	24.0105i	0.703761	+	1.21895i
$389$	15.2111			0.771234			0.385617	−	0.922659i	$-0.373989\pi$
$389$	15.2111			0.771234			0.385617	+	0.922659i	$0.373989\pi$
$390$		0			0
$391$	−22.8167			−1.15389
$392$	9.00000	+	15.5885i	0.454569	+	0.787336i
$393$		0			0
$394$	1.36249	−	2.35990i	0.0686413	−	0.118890i
$395$	5.21110			0.262199
$396$		0			0
$397$	−11.0139	+	19.0766i	−0.552771	+	0.957427i	0.445303	+	0.895380i	$0.353096\pi$
$397$	−11.0139	+	19.0766i	−0.552771	+	0.957427i	−0.998073	+	0.0620468i	$0.980237\pi$
$398$	29.5139			1.47940
$399$		0			0
$400$	−0.151388	−	0.262211i	−0.00756939	−	0.0131106i
$401$	6.10555	+	10.5751i	0.304897	+	0.528097i	0.977238	−	0.212144i	$-0.0680447\pi$
$401$	6.10555	+	10.5751i	0.304897	+	0.528097i	−0.672342	+	0.740241i	$0.734711\pi$
$402$		0			0
$403$	14.4222			0.718421
$404$	29.7250			1.47887
$405$		0			0
$406$	7.15139	+	12.3866i	0.354917	+	0.614735i
$407$	2.89445	−	5.01333i	0.143472	−	0.248502i
$408$		0			0
$409$	−4.10555	+	7.11102i	−0.203006	+	0.351617i	−0.949496	−	0.313780i	$-0.898405\pi$
$409$	−4.10555	+	7.11102i	−0.203006	+	0.351617i	0.746489	+	0.665397i	$0.231738\pi$
$410$	3.45416	−	5.98279i	0.170589	−	0.295469i
$411$		0			0
$412$	6.60555	−	11.4412i	0.325432	−	0.563665i
$413$	5.40833	+	9.36750i	0.266126	+	0.460944i
$414$		0			0
$415$	9.21110			0.452155
$416$	−9.55971	+	16.5579i	−0.468704	+	0.811818i
$417$		0			0
$418$	−10.3625	−	17.9484i	−0.506846	−	0.877883i
$419$	8.61943	+	14.9293i	0.421087	+	0.729344i	0.996046	−	0.0888384i	$-0.0283155\pi$
$419$	8.61943	+	14.9293i	0.421087	+	0.729344i	−0.574959	+	0.818182i	$0.694982\pi$
$420$		0			0
$421$	32.4222			1.58016			0.790081	−	0.613003i	$-0.210039\pi$
$421$	32.4222			1.58016			0.790081	+	0.613003i	$0.210039\pi$
$422$	27.1791	−	47.0757i	1.32306	−	2.29161i
$423$		0			0
$424$	9.63331			0.467835
$425$	3.80278	−	6.58660i	0.184462	−	0.319497i
$426$		0			0
$427$	−0.500000	−	0.866025i	−0.0241967	−	0.0419099i
$428$	−20.5139			−0.991576
$429$		0			0
$430$	−23.5139			−1.13394
$431$	14.6194	+	25.3216i	0.704193	+	1.21970i	0.966982	+	0.254845i	$0.0820244\pi$
$431$	14.6194	+	25.3216i	0.704193	+	1.21970i	−0.262789	+	0.964853i	$0.584642\pi$
$432$		0			0
$433$	−1.80278	+	3.12250i	−0.0866359	+	0.150058i	−0.906087	−	0.423091i	$-0.860945\pi$
$433$	−1.80278	+	3.12250i	−0.0866359	+	0.150058i	0.819451	+	0.573149i	$0.194278\pi$
$434$	9.21110			0.442147
$435$		0			0
$436$	31.7250	−	54.9493i	1.51935	−	2.63159i
$437$	−16.8167			−0.804450
$438$		0			0
$439$	13.6194	+	23.5895i	0.650020	+	1.12587i	0.983118	+	0.182975i	$0.0585728\pi$
$439$	13.6194	+	23.5895i	0.650020	+	1.12587i	−0.333098	+	0.942892i	$0.608094\pi$
$440$	2.40833	+	4.17134i	0.114812	+	0.198861i
$441$		0			0
$442$	63.1472			3.00361
$443$	−6.42221			−0.305128			−0.152564	−	0.988294i	$-0.548753\pi$
$443$	−6.42221			−0.305128			−0.152564	+	0.988294i	$0.548753\pi$
$444$		0			0
$445$	−3.10555	−	5.37897i	−0.147217	−	0.254988i
$446$	4.84861	−	8.39804i	0.229588	−	0.397659i
$447$		0			0
$448$	−6.40833	+	11.0995i	−0.302765	+	0.524404i
$449$	15.3167	−	26.5292i	0.722838	−	1.25199i	−0.237020	−	0.971505i	$-0.576171\pi$
$449$	15.3167	−	26.5292i	0.722838	−	1.25199i	0.959858	−	0.280487i	$-0.0904959\pi$
$450$		0			0
$451$	−2.40833	+	4.17134i	−0.113404	+	0.196421i
$452$	−2.65139	−	4.59234i	−0.124711	−	0.216005i
$453$		0			0
$454$	63.1472			2.96364
$455$	−1.80278	+	3.12250i	−0.0845154	+	0.146385i
$456$		0			0
$457$	13.4083	+	23.2239i	0.627215	+	1.08637i	0.988108	+	0.153761i	$0.0491386\pi$
$457$	13.4083	+	23.2239i	0.627215	+	1.08637i	−0.360893	+	0.932607i	$0.617528\pi$
$458$	−16.1194	−	27.9197i	−0.753211	−	1.30460i
$459$		0			0
$460$	9.90833			0.461978
$461$	18.1056	−	31.3597i	0.843260	−	1.46057i	−0.0438645	−	0.999037i	$-0.513967\pi$
$461$	18.1056	−	31.3597i	0.843260	−	1.46057i	0.887124	−	0.461531i	$-0.152700\pi$
$462$		0			0
$463$	−34.4222			−1.59974			−0.799868	−	0.600176i	$-0.795097\pi$
$463$	−34.4222			−1.59974			−0.799868	+	0.600176i	$0.795097\pi$
$464$	−0.940285	+	1.62862i	−0.0436516	+	0.0756069i
$465$		0			0
$466$	17.5139	+	30.3349i	0.811315	+	1.40524i
$467$	−2.78890			−0.129055			−0.0645274	−	0.997916i	$-0.520554\pi$
$467$	−2.78890			−0.129055			−0.0645274	+	0.997916i	$0.520554\pi$
$468$		0			0
$469$	7.00000			0.323230
$470$	10.6056	+	18.3694i	0.489198	+	0.847315i
$471$		0			0
$472$	−16.2250	+	28.1025i	−0.746815	+	1.29352i
$473$	16.3944			0.753818
$474$		0			0
$475$	2.80278	−	4.85455i	0.128600	−	0.222742i
$476$	25.1194			1.15135
$477$		0			0
$478$		0			0
$479$	−14.4083	−	24.9560i	−0.658333	−	1.14027i	−0.981047	−	0.193770i	$-0.937928\pi$
$479$	−14.4083	−	24.9560i	−0.658333	−	1.14027i	0.322714	−	0.946497i	$-0.395405\pi$
$480$		0			0
$481$	6.50000	+	11.2583i	0.296374	+	0.513336i
$482$	4.11943			0.187635
$483$		0			0
$484$	13.9083	+	24.0899i	0.632197	+	1.09500i
$485$	4.19722	−	7.26981i	0.190586	−	0.330105i
$486$		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
$490$	6.90833	−	11.9656i	0.312086	−	0.540549i
$491$	−8.40833	−	14.5636i	−0.379462	−	0.657248i	0.611522	−	0.791228i	$-0.290558\pi$
$491$	−8.40833	−	14.5636i	−0.379462	−	0.657248i	−0.990984	+	0.133979i	$0.957224\pi$
$492$		0			0
$493$	−47.2389			−2.12753
$494$	46.5416			2.09401
$495$		0			0
$496$	0.605551	+	1.04885i	0.0271901	+	0.0470946i
$497$	−2.40833	−	4.17134i	−0.108028	−	0.187110i
$498$		0			0
$499$	2.42221			0.108433			0.0542164	−	0.998529i	$-0.482734\pi$
$499$	2.42221			0.108433			0.0542164	+	0.998529i	$0.482734\pi$
$500$	−1.65139	+	2.86029i	−0.0738523	+	0.127916i
$501$		0			0
$502$	16.5416			0.738289
$503$	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
$506$	−11.0917			−0.493085
$507$		0			0
$508$	−13.9083			−0.617082
$509$	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
$511$	−0.394449	+	0.683205i	−0.0174494	+	0.0302232i
$512$	−3.42221			−0.151242
$513$		0			0
$514$	−18.8764	+	32.6948i	−0.832601	+	1.44211i
$515$	−4.00000			−0.176261
$516$		0			0
$517$	−7.39445	−	12.8076i	−0.325207	−	0.563276i
$518$	4.15139	+	7.19041i	0.182402	+	0.315929i
$519$		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
$523$	0.711103	+	1.23167i	0.0310943	+	0.0538570i	0.881154	−	0.472830i	$-0.156767\pi$
$523$	0.711103	+	1.23167i	0.0310943	+	0.0538570i	−0.850059	+	0.526687i	$0.823434\pi$
$524$	−35.0278	+	60.6699i	−1.53019	+	2.65037i
$525$		0			0
$526$	13.5736	−	23.5102i	0.591837	−	1.02509i
$527$	−15.2111	+	26.3464i	−0.662606	+	1.14767i
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	−3.69722	−	6.40378i	−0.160597	−	0.278162i
$531$		0			0
$532$	18.5139			0.802678
$533$	−5.40833	−	9.36750i	−0.234261	−	0.405751i
$534$		0			0
$535$	3.10555	+	5.37897i	0.134265	+	0.232553i
$536$	10.5000	+	18.1865i	0.453531	+	0.785539i
$537$		0			0
$538$	20.7250			0.893517
$539$	−4.81665	+	8.34269i	−0.207468	+	0.359345i
$540$		0			0
$541$	−25.6333			−1.10206			−0.551031	−	0.834485i	$-0.685765\pi$
$541$	−25.6333			−1.10206			−0.551031	+	0.834485i	$0.685765\pi$
$542$	23.9680	−	41.5139i	1.02952	−	1.78317i
$543$		0			0
$544$	−20.1653	−	34.9273i	−0.864579	−	1.49749i
$545$	−19.2111			−0.822913
$546$		0			0
$547$	32.8444			1.40433			0.702163	−	0.712016i	$-0.252218\pi$
$547$	32.8444			1.40433			0.702163	+	0.712016i	$0.252218\pi$
$548$	−2.65139	−	4.59234i	−0.113262	−	0.196175i
$549$		0			0
$550$	1.84861	−	3.20189i	0.0788251	−	0.136529i
$551$	−34.8167			−1.48324
$552$		0			0
$553$	2.60555	−	4.51295i	0.110799	−	0.191910i
$554$	63.5694			2.70080
$555$		0			0
$556$	−10.5597	−	18.2900i	−0.447832	−	0.775667i
$557$	−0.802776	−	1.39045i	−0.0340147	−	0.0589152i	0.848517	−	0.529168i	$-0.177496\pi$
$557$	−0.802776	−	1.39045i	−0.0340147	−	0.0589152i	−0.882532	+	0.470253i	$0.844163\pi$
$558$		0			0
$559$	−18.4083	+	31.8842i	−0.778589	+	1.34856i
$560$	−0.302776			−0.0127946
$561$		0			0
$562$	−6.90833	−	11.9656i	−0.291410	−	0.504737i
$563$	4.71110	−	8.15987i	0.198549	−	0.343897i	−0.749509	−	0.661994i	$-0.769710\pi$
$563$	4.71110	−	8.15987i	0.198549	−	0.343897i	0.948058	+	0.318097i	$0.103044\pi$
$564$		0			0
$565$	−0.802776	+	1.39045i	−0.0337730	+	0.0584966i
$566$	−5.75694	+	9.97131i	−0.241982	+	0.419125i
$567$		0			0
$568$	7.22498	−	12.5140i	0.303153	−	0.525077i
$569$	−13.7111	−	23.7483i	−0.574799	−	0.995582i	−0.996063	−	0.0886436i	$-0.971747\pi$
$569$	−13.7111	−	23.7483i	−0.574799	−	0.995582i	0.421264	−	0.906938i	$-0.361587\pi$
$570$		0			0
$571$	20.8444			0.872311			0.436156	−	0.899871i	$-0.356340\pi$
$571$	20.8444			0.872311			0.436156	+	0.899871i	$0.356340\pi$
$572$	19.1194			0.799424
$573$		0			0
$574$	−3.45416	−	5.98279i	−0.144174	−	0.249717i
$575$	−1.50000	−	2.59808i	−0.0625543	−	0.108347i
$576$		0			0
$577$	−13.6333			−0.567562			−0.283781	−	0.958889i	$-0.591589\pi$
$577$	−13.6333			−0.567562			−0.283781	+	0.958889i	$0.591589\pi$
$578$	−47.0278	+	81.4545i	−1.95610	+	3.38806i
$579$		0			0
$580$	20.5139			0.851792
$581$	4.60555	−	7.97705i	0.191070	−	0.330944i
$582$		0			0
$583$	2.57779	+	4.46487i	0.106761	+	0.184916i
$584$	−2.36669			−0.0979344
$585$		0			0
$586$	−23.9361			−0.988790
$587$	−16.7111	−	28.9445i	−0.689741	−	1.19467i	−0.971922	−	0.235305i	$-0.924391\pi$
$587$	−16.7111	−	28.9445i	−0.689741	−	1.19467i	0.282181	−	0.959361i	$-0.408942\pi$
$588$		0			0
$589$	−11.2111	+	19.4182i	−0.461945	+	0.800113i
$590$	24.9083			1.02546
$591$		0			0
$592$	−0.545837	+	0.945417i	−0.0224337	+	0.0388564i
$593$	−20.7889			−0.853698			−0.426849	−	0.904323i	$-0.640376\pi$
$593$	−20.7889			−0.853698			−0.426849	+	0.904323i	$0.640376\pi$
$594$		0			0
$595$	−3.80278	−	6.58660i	−0.155899	−	0.270024i
$596$	4.95416	+	8.58086i	0.202930	+	0.351486i
$597$		0			0
$598$	12.4542	−	21.5712i	0.509289	−	0.882114i
$599$	21.2111			0.866662			0.433331	−	0.901235i	$-0.357338\pi$
$599$	21.2111			0.866662			0.433331	+	0.901235i	$0.357338\pi$
$600$		0			0
$601$	−6.89445	−	11.9415i	−0.281230	−	0.487105i	0.690458	−	0.723373i	$-0.257409\pi$
$601$	−6.89445	−	11.9415i	−0.281230	−	0.487105i	−0.971688	+	0.236267i	$0.924076\pi$
$602$	−11.7569	+	20.3636i	−0.479177	+	0.829959i
$603$		0			0
$604$	2.00000	−	3.46410i	0.0813788	−	0.140952i
$605$	4.21110	−	7.29384i	0.171206	−	0.296537i
$606$		0			0
$607$	17.1056	−	29.6277i	0.694293	−	1.20255i	−0.276126	−	0.961122i	$-0.589051\pi$
$607$	17.1056	−	29.6277i	0.694293	−	1.20255i	0.970418	−	0.241429i	$-0.0776161\pi$
$608$	−14.8625	−	25.7426i	−0.602754	−	1.04400i
$609$		0			0
$610$	−2.30278			−0.0932367
$611$	33.2111			1.34358
$612$		0			0
$613$	2.80278	+	4.85455i	0.113203	+	0.196073i	0.917060	−	0.398749i	$-0.130556\pi$
$613$	2.80278	+	4.85455i	0.113203	+	0.196073i	−0.803857	+	0.594823i	$0.797222\pi$
$614$	18.4222	+	31.9082i	0.743460	+	1.28771i
$615$		0			0
$616$	4.81665			0.194069
$617$	−19.2250	+	33.2986i	−0.773969	+	1.34055i	0.161404	+	0.986888i	$0.448398\pi$
$617$	−19.2250	+	33.2986i	−0.773969	+	1.34055i	−0.935372	+	0.353664i	$0.884935\pi$
$618$		0			0
$619$	14.4222			0.579677			0.289839	−	0.957076i	$-0.406398\pi$
$619$	14.4222			0.579677			0.289839	+	0.957076i	$0.406398\pi$
$620$	6.60555	−	11.4412i	0.265285	−	0.459488i
$621$		0			0
$622$	−10.6056	−	18.3694i	−0.425244	−	0.736544i
$623$	−6.21110			−0.248843
$624$		0			0
$625$	1.00000			0.0400000
$626$	−16.1194	−	27.9197i	−0.644262	−	1.11589i
$627$		0			0
$628$	−18.5139	+	32.0670i	−0.738784	+	1.27961i
$629$	−27.4222			−1.09339
$630$		0			0
$631$	18.0139	−	31.2010i	0.717121	−	1.24209i	−0.245015	−	0.969519i	$-0.578793\pi$
$631$	18.0139	−	31.2010i	0.717121	−	1.24209i	0.962136	−	0.272571i	$-0.0878739\pi$
$632$	15.6333			0.621860
$633$		0			0
$634$	6.90833	+	11.9656i	0.274365	+	0.475214i
$635$	2.10555	+	3.64692i	0.0835563	+	0.144724i
$636$		0			0
$637$	−10.8167	−	18.7350i	−0.428571	−	0.742307i
$638$	−22.9638			−0.909147
$639$		0			0
$640$	9.45416	+	16.3751i	0.373709	+	0.647282i
$641$	4.71110	−	8.15987i	0.186077	−	0.322295i	−0.757862	−	0.652415i	$-0.773756\pi$
$641$	4.71110	−	8.15987i	0.186077	−	0.322295i	0.943939	+	0.330120i	$0.107089\pi$
$642$		0			0
$643$	−1.31665	+	2.28051i	−0.0519238	+	0.0899346i	−0.890819	−	0.454358i	$-0.849869\pi$
$643$	−1.31665	+	2.28051i	−0.0519238	+	0.0899346i	0.838895	+	0.544293i	$0.183202\pi$
$644$	4.95416	−	8.58086i	0.195221	−	0.338133i
$645$		0			0
$646$	−49.0875	+	85.0220i	−1.93132	+	3.34515i
$647$	19.7111	+	34.1406i	0.774923	+	1.34221i	0.934838	+	0.355076i	$0.115545\pi$
$647$	19.7111	+	34.1406i	0.774923	+	1.34221i	−0.159914	+	0.987131i	$0.551122\pi$
$648$		0			0
$649$	−17.3667			−0.681702
$650$	4.15139	+	7.19041i	0.162831	+	0.282031i
$651$		0			0
$652$	6.25694	+	10.8373i	0.245041	+	0.424423i
$653$	−3.59167	−	6.22096i	−0.140553	−	0.243445i	0.787152	−	0.616759i	$-0.211555\pi$
$653$	−3.59167	−	6.22096i	−0.140553	−	0.243445i	−0.927705	+	0.373314i	$0.878221\pi$
$654$		0			0
$655$	21.2111			0.828786
$656$	0.454163	−	0.786634i	0.0177321	−	0.0307129i
$657$		0			0
$658$	21.2111			0.826895
$659$	−17.4083	+	30.1521i	−0.678132	+	1.17456i	0.297411	+	0.954750i	$0.403877\pi$
$659$	−17.4083	+	30.1521i	−0.678132	+	1.17456i	−0.975543	+	0.219810i	$0.929456\pi$
$660$		0			0
$661$	2.31665	+	4.01256i	0.0901074	+	0.156071i	0.907556	−	0.419931i	$-0.137946\pi$
$661$	2.31665	+	4.01256i	0.0901074	+	0.156071i	−0.817449	+	0.576001i	$0.804612\pi$
$662$	23.0917			0.897483
$663$		0			0
$664$	27.6333			1.07238
$665$	−2.80278	−	4.85455i	−0.108687	−	0.188251i
$666$		0			0
$667$	−9.31665	+	16.1369i	−0.360742	+	0.624824i
$668$	−29.7250			−1.15009
$669$		0			0
$670$	8.05971	−	13.9598i	0.311374	−	0.539315i
$671$	1.60555			0.0619816
$672$		0			0
$673$	8.80278	+	15.2469i	0.339322	+	0.587723i	0.984305	−	0.176474i	$-0.0564690\pi$
$673$	8.80278	+	15.2469i	0.339322	+	0.587723i	−0.644983	+	0.764197i	$0.723136\pi$
$674$	29.5139	+	51.1195i	1.13683	+	1.96905i
$675$		0			0
$676$	−21.4680	+	37.1837i	−0.825694	+	1.43014i
$677$	9.63331			0.370238			0.185119	−	0.982716i	$-0.440733\pi$
$677$	9.63331			0.370238			0.185119	+	0.982716i	$0.440733\pi$
$678$		0			0
$679$	−4.19722	−	7.26981i	−0.161075	−	0.278990i
$680$	11.4083	−	19.7598i	0.437489	−	0.757754i
$681$		0			0
$682$	−7.39445	+	12.8076i	−0.283148	+	0.490427i
$683$	18.1056	−	31.3597i	0.692790	−	1.19995i	−0.278130	−	0.960543i	$-0.589715\pi$
$683$	18.1056	−	31.3597i	0.692790	−	1.19995i	0.970920	−	0.239404i	$-0.0769519\pi$
$684$		0			0
$685$	−0.802776	+	1.39045i	−0.0306725	+	0.0531263i
$686$	−14.9680	−	25.9254i	−0.571482	−	0.989837i
$687$		0			0
$688$	−3.09167			−0.117869
$689$	−11.5778			−0.441079
$690$		0			0
$691$	15.0139	+	26.0048i	0.571155	+	0.989269i	0.996448	+	0.0842134i	$0.0268378\pi$
$691$	15.0139	+	26.0048i	0.571155	+	0.989269i	−0.425293	+	0.905056i	$0.639829\pi$
$692$	7.95416	+	13.7770i	0.302372	+	0.523724i
$693$		0			0
$694$	−13.3305			−0.506020
$695$	−3.19722	+	5.53776i	−0.121278	+	0.210059i
$696$		0			0
$697$	22.8167			0.864242
$698$	4.36249	−	7.55605i	0.165123	−	0.286001i
$699$		0			0
$700$	1.65139	+	2.86029i	0.0624166	+	0.108109i
$701$	36.4222			1.37565			0.687824	−	0.725878i	$-0.258566\pi$
$701$	36.4222			1.37565			0.687824	+	0.725878i	$0.258566\pi$
$702$		0			0
$703$	−20.2111			−0.762276
$704$	−10.2889	−	17.8209i	−0.387777	−	0.671650i
$705$		0			0
$706$	19.3625	−	33.5368i	0.728717	−	1.26217i
$707$	−9.00000			−0.338480
$708$		0			0
$709$	6.92221	−	11.9896i	0.259969	−	0.450279i	−0.706264	−	0.707948i	$-0.749621\pi$
$709$	6.92221	−	11.9896i	0.259969	−	0.450279i	0.966233	+	0.257669i	$0.0829544\pi$
$710$	−11.0917			−0.416263
$711$		0			0
$712$	−9.31665	−	16.1369i	−0.349156	−	0.604757i
$713$	6.00000	+	10.3923i	0.224702	+	0.389195i
$714$		0			0
$715$	−2.89445	−	5.01333i	−0.108246	−	0.187488i
$716$	−75.3583			−2.81627
$717$		0			0
$718$	21.2111	+	36.7387i	0.791591	+	1.37108i
$719$	−12.8028	+	22.1751i	−0.477463	+	0.826990i	−0.999666	−	0.0258309i	$-0.991777\pi$
$719$	−12.8028	+	22.1751i	−0.477463	+	0.826990i	0.522203	+	0.852821i	$0.325110\pi$
$720$		0			0
$721$	−2.00000	+	3.46410i	−0.0744839	+	0.129010i
$722$	−14.3028	+	24.7731i	−0.532294	+	0.921961i
$723$		0			0
$724$	−29.1194	+	50.4363i	−1.08222	+	1.87445i
$725$	−3.10555	−	5.37897i	−0.115337	−	0.199770i
$726$		0			0
$727$	13.5778			0.503573			0.251786	−	0.967783i	$-0.418982\pi$
$727$	13.5778			0.503573			0.251786	+	0.967783i	$0.418982\pi$
$728$	−5.40833	+	9.36750i	−0.200446	+	0.347183i
$729$		0			0
$730$	0.908327	+	1.57327i	0.0336187	+	0.0582293i
$731$	−38.8305	−	67.2565i	−1.43620	−	2.48757i
$732$		0			0
$733$	−46.8444			−1.73024			−0.865119	−	0.501567i	$-0.832757\pi$
$733$	−46.8444			−1.73024			−0.865119	+	0.501567i	$0.832757\pi$
$734$	−13.1514	+	22.7789i	−0.485427	+	0.840784i
$735$		0			0
$736$	−15.9083			−0.586389
$737$	−5.61943	+	9.73314i	−0.206994	+	0.358525i
$738$		0			0
$739$	17.8028	+	30.8353i	0.654886	+	1.13430i	0.981922	+	0.189284i	$0.0606166\pi$
$739$	17.8028	+	30.8353i	0.654886	+	1.13430i	−0.327037	+	0.945012i	$0.606050\pi$
$740$	11.9083			0.437759
$741$		0			0
$742$	−7.39445			−0.271459
$743$	18.3167	+	31.7254i	0.671973	+	1.16389i	0.977344	+	0.211658i	$0.0678862\pi$
$743$	18.3167	+	31.7254i	0.671973	+	1.16389i	−0.305371	+	0.952233i	$0.598780\pi$
$744$		0			0
$745$	1.50000	−	2.59808i	0.0549557	−	0.0951861i
$746$	−46.9638			−1.71947
$747$		0			0
$748$	−20.1653	+	34.9273i	−0.737315	+	1.27707i
$749$	6.21110			0.226949
$750$		0			0
$751$	−23.2250	−	40.2268i	−0.847492	−	1.46790i	−0.883440	−	0.468545i	$-0.844778\pi$
$751$	−23.2250	−	40.2268i	−0.847492	−	1.46790i	0.0359481	−	0.999354i	$-0.488555\pi$
$752$	1.39445	+	2.41526i	0.0508503	+	0.0880753i
$753$		0			0
$754$	25.7847	−	44.6604i	0.939023	−	1.62644i
$755$	−1.21110			−0.0440765
$756$		0			0
$757$	−0.408327	−	0.707243i	−0.0148409	−	0.0257052i	0.858510	−	0.512798i	$-0.171391\pi$
$757$	−0.408327	−	0.707243i	−0.0148409	−	0.0257052i	−0.873350	+	0.487092i	$0.838058\pi$
$758$	−11.0597	+	19.1560i	−0.401707	+	0.695777i
$759$		0			0
$760$	8.40833	−	14.5636i	0.305002	−	0.528279i
$761$	9.31665	−	16.1369i	0.337728	−	0.584963i	−0.646277	−	0.763103i	$-0.723675\pi$
$761$	9.31665	−	16.1369i	0.337728	−	0.584963i	0.984005	+	0.178140i	$0.0570081\pi$
$762$		0			0
$763$	−9.60555	+	16.6373i	−0.347744	+	0.602311i
$764$	27.7708	+	48.1005i	1.00471	+	1.74021i
$765$		0			0
$766$	56.7250			2.04956
$767$	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	$0.896887\pi$
$770$	−1.84861	−	3.20189i	−0.0666194	−	0.115388i
$771$		0			0
$772$	51.5416			1.85502
$773$	11.1972	−	19.3942i	0.402736	−	0.697560i	−0.591319	−	0.806438i	$-0.701393\pi$
$773$	11.1972	−	19.3942i	0.402736	−	0.697560i	0.994055	+	0.108878i	$0.0347259\pi$
$774$		0			0
$775$	−4.00000			−0.143684
$776$	12.5917	−	21.8094i	0.452015	−	0.782912i
$777$		0			0
$778$	−17.5139	−	30.3349i	−0.627903	−	1.08756i
$779$	16.8167			0.602519
$780$		0			0
$781$	7.73338			0.276722
$782$	26.2708	+	45.5024i	0.939443	+	1.62716i
$783$		0			0
$784$	0.908327	−	1.57327i	0.0324402	−	0.0561882i
$785$	11.2111			0.400141
$786$		0			0
$787$	−7.31665	+	12.6728i	−0.260811	+	0.451737i	−0.966458	−	0.256826i	$-0.917323\pi$
$787$	−7.31665	+	12.6728i	−0.260811	+	0.451737i	0.705647	+	0.708564i	$0.250656\pi$
$788$	−3.90833			−0.139228
$789$		0			0
$790$	−6.00000	−	10.3923i	−0.213470	−	0.369742i
$791$	0.802776	+	1.39045i	0.0285434	+	0.0494386i
$792$		0			0
$793$	−1.80278	+	3.12250i	−0.0640184	+	0.110883i
$794$	50.7250			1.80016
$795$		0			0
$796$	−21.1653	−	36.6593i	−0.750183	−	1.29936i
$797$	−7.22498	+	12.5140i	−0.255922	+	0.443270i	−0.965146	−	0.261714i	$-0.915712\pi$
$797$	−7.22498	+	12.5140i	−0.255922	+	0.443270i	0.709224	+	0.704984i	$0.249046\pi$
$798$		0			0
$799$	−35.0278	+	60.6699i	−1.23919	+	2.14635i
$800$	2.65139	−	4.59234i	0.0937407	−	0.162364i
$801$		0			0
$802$	14.0597	−	24.3521i	0.496466	−	0.859904i
$803$	−0.633308	−	1.09692i	−0.0223489	−	0.0387095i
$804$		0			0
$805$	−3.00000			−0.105736
$806$	−16.6056	−	28.7617i	−0.584906	−	1.01309i
$807$		0			0
$808$	−13.5000	−	23.3827i	−0.474928	−	0.822600i
$809$	−27.5278	−	47.6795i	−0.967824	−	1.67632i	−0.701827	−	0.712347i	$-0.747632\pi$
$809$	−27.5278	−	47.6795i	−0.967824	−	1.67632i	−0.265997	−	0.963974i	$-0.585701\pi$
$810$		0			0
$811$	−46.4222			−1.63010			−0.815052	−	0.579388i	$-0.803292\pi$
$811$	−46.4222			−1.63010			−0.815052	+	0.579388i	$0.803292\pi$
$812$	10.2569	−	17.7655i	0.359948	−	0.623448i
$813$		0			0
$814$	−13.3305			−0.467235
$815$	1.89445	−	3.28128i	0.0663596	−	0.114938i
$816$		0			0
$817$	−28.6194	−	49.5703i	−1.00127	−	1.73425i
$818$	18.9083			0.661114
$819$		0			0
$820$	−9.90833			−0.346014
$821$	10.7111	+	18.5522i	0.373820	+	0.647475i	0.990150	−	0.140013i	$-0.0447144\pi$
$821$	10.7111	+	18.5522i	0.373820	+	0.647475i	−0.616330	+	0.787488i	$0.711381\pi$
$822$		0			0
$823$	8.31665	−	14.4049i	0.289900	−	0.502122i	−0.683885	−	0.729589i	$-0.739711\pi$
$823$	8.31665	−	14.4049i	0.289900	−	0.502122i	0.973786	+	0.227467i	$0.0730445\pi$
$824$	−12.0000			−0.418040
$825$		0			0
$826$	12.4542	−	21.5712i	0.433336	−	0.750560i
$827$	42.4222			1.47516			0.737582	−	0.675257i	$-0.235967\pi$
$827$	42.4222			1.47516			0.737582	+	0.675257i	$0.235967\pi$
$828$		0			0
$829$	−14.7111	−	25.4804i	−0.510938	−	0.884970i	−0.999920	−	0.0126762i	$-0.995965\pi$
$829$	−14.7111	−	25.4804i	−0.510938	−	0.884970i	0.488982	−	0.872294i	$-0.337368\pi$
$830$	−10.6056	−	18.3694i	−0.368124	−	0.637610i
$831$		0			0
$832$	46.2111			1.60208
$833$	45.6333			1.58110
$834$		0			0
$835$	4.50000	+	7.79423i	0.155729	+	0.269730i
$836$	−14.8625	+	25.7426i	−0.514030	+	0.890326i
$837$		0			0
$838$	19.8486	−	34.3788i	0.685659	−	1.18760i
$839$	−10.0139	+	17.3445i	−0.345717	+	0.598800i	−0.985484	−	0.169769i	$-0.945698\pi$
$839$	−10.0139	+	17.3445i	−0.345717	+	0.598800i	0.639766	+	0.768569i	$0.279031\pi$
$840$		0			0
$841$	−4.78890	+	8.29461i	−0.165134	+	0.286021i
$842$	−37.3305	−	64.6584i	−1.28650	−	2.22827i
$843$		0			0
$844$	−77.9638			−2.68363
$845$	13.0000			0.447214
$846$		0			0
$847$	−4.21110	−	7.29384i	−0.144695	−	0.250619i
$848$	−0.486122	−	0.841988i	−0.0166935	−	0.0289140i
$849$		0			0
$850$	−17.5139			−0.600721
$851$	−5.40833	+	9.36750i	−0.185395	+	0.321114i
$852$		0			0
$853$	47.2111			1.61648			0.808239	−	0.588855i	$-0.200421\pi$
$853$	47.2111			1.61648			0.808239	+	0.588855i	$0.200421\pi$
$854$	−1.15139	+	1.99426i	−0.0393997	+	0.0682422i
$855$		0			0
$856$	9.31665	+	16.1369i	0.318437	+	0.551548i
$857$	−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
$859$	10.7889			0.368112			0.184056	−	0.982916i	$-0.441077\pi$
$859$	10.7889			0.368112			0.184056	+	0.982916i	$0.441077\pi$
$860$	16.8625	+	29.2067i	0.575006	+	0.995940i
$861$		0			0
$862$	33.6653	−	58.3100i	1.14664	−	1.98604i
$863$	−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
$865$	2.40833	−	4.17134i	0.0818856	−	0.141830i
$866$	8.30278			0.282140
$867$		0			0
$868$	−6.60555	−	11.4412i	−0.224207	−	0.388338i
$869$	4.18335	+	7.24577i	0.141910	+	0.245796i
$870$		0			0
$871$	−12.6194	−	21.8575i	−0.427593	−	0.740613i
$872$	−57.6333			−1.95171
$873$		0			0
$874$	19.3625	+	33.5368i	0.654946	+	1.13440i
$875$	0.500000	−	0.866025i	0.0169031	−	0.0292770i
$876$		0			0
$877$	0.986122	−	1.70801i	0.0332990	−	0.0576755i	−0.848896	−	0.528560i	$-0.822732\pi$
$877$	0.986122	−	1.70801i	0.0332990	−	0.0576755i	0.882195	+	0.470885i	$0.156065\pi$
$878$	31.3625	−	54.3214i	1.05843	−	1.83326i
$879$		0			0
$880$	0.243061	−	0.420994i	0.00819358	−	0.0141917i
$881$	−10.9222	−	18.9178i	−0.367978	−	0.637357i	0.621271	−	0.783596i	$-0.286617\pi$
$881$	−10.9222	−	18.9178i	−0.367978	−	0.637357i	−0.989249	+	0.146238i	$0.953283\pi$
$882$		0			0
$883$	11.6333			0.391492			0.195746	−	0.980655i	$-0.437287\pi$
$883$	11.6333			0.391492			0.195746	+	0.980655i	$0.437287\pi$
$884$	−45.2847	−	78.4354i	−1.52309	−	2.63807i
$885$		0			0
$886$	7.39445	+	12.8076i	0.248421	+	0.430278i
$887$	−18.5278	−	32.0910i	−0.622101	−	1.07751i	−0.989094	−	0.147287i	$-0.952946\pi$
$887$	−18.5278	−	32.0910i	−0.622101	−	1.07751i	0.366993	−	0.930224i	$-0.380387\pi$
$888$		0			0
$889$	4.21110			0.141236
$890$	−7.15139	+	12.3866i	−0.239715	+	0.415199i
$891$		0			0
$892$	−13.9083			−0.465685
$893$	−25.8167	+	44.7158i	−0.863921	+	1.49636i
$894$		0			0
$895$	11.4083	+	19.7598i	0.381338	+	0.660497i
$896$	18.9083			0.631683
$897$		0			0
$898$	−70.5416			−2.35400
$899$	12.4222	+	21.5159i	0.414304	+	0.717595i
$900$		0			0
$901$	12.2111	−	21.1503i	0.406811	−	0.704617i
$902$	11.0917			0.369312
$903$		0			0
$904$	−2.40833	+	4.17134i	−0.0800998	+	0.138737i
$905$	17.6333			0.586151
$906$		0			0
$907$	19.1333	+	33.1399i	0.635311	+	1.10039i	0.986449	+	0.164067i	$0.0524614\pi$
$907$	19.1333	+	33.1399i	0.635311	+	1.10039i	−0.351138	+	0.936324i	$0.614205\pi$
$908$	−45.2847	−	78.4354i	−1.50283	−	2.60297i
$909$		0			0
$910$	8.30278			0.275234
$911$	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
$913$	7.39445	+	12.8076i	0.244721	+	0.423868i
$914$	30.8764	−	53.4794i	1.02130	−	1.76894i
$915$		0			0
$916$	−23.1194	+	40.0440i	−0.763887	+	1.32309i
$917$	10.6056	−	18.3694i	0.350226	−	0.606610i
$918$		0			0
$919$	19.4083	−	33.6162i	0.640222	−	1.10890i	−0.345161	−	0.938543i	$-0.612176\pi$
$919$	19.4083	−	33.6162i	0.640222	−	1.10890i	0.985383	−	0.170353i	$-0.0544908\pi$
$920$	−4.50000	−	7.79423i	−0.148361	−	0.256968i
$921$		0			0
$922$	−83.3860			−2.74617
$923$	−8.68335	+	15.0400i	−0.285816	+	0.495048i
$924$		0			0
$925$	−1.80278	−	3.12250i	−0.0592749	−	0.102667i
$926$	39.6333	+	68.6469i	1.30243	+	2.25588i
$927$		0			0
$928$	−32.9361			−1.08118
$929$	−7.71110	+	13.3560i	−0.252993	+	0.438197i	−0.964348	−	0.264636i	$-0.914748\pi$
$929$	−7.71110	+	13.3560i	−0.252993	+	0.438197i	0.711355	+	0.702832i	$0.248082\pi$
$930$		0			0
$931$	33.6333			1.10229
$932$	25.1194	−	43.5081i	0.822814	−	1.42516i
$933$		0			0
$934$	3.21110	+	5.56179i	0.105070	+	0.181987i
$935$	12.2111			0.399346
$936$		0			0
$937$	54.4777			1.77971			0.889855	−	0.456244i	$-0.150806\pi$
$937$	54.4777			1.77971			0.889855	+	0.456244i	$0.150806\pi$
$938$	−8.05971	−	13.9598i	−0.263159	−	0.455805i
$939$		0			0
$940$	15.2111	−	26.3464i	0.496131	−	0.859325i
$941$	9.63331			0.314037			0.157018	−	0.987596i	$-0.449812\pi$
$941$	9.63331			0.314037			0.157018	+	0.987596i	$0.449812\pi$
$942$		0			0
$943$	4.50000	−	7.79423i	0.146540	−	0.253815i
$944$	3.27502			0.106593
$945$		0			0
$946$	−18.8764	−	32.6948i	−0.613724	−	1.06300i
$947$	−9.31665	−	16.1369i	−0.302751	−	0.524379i	0.674007	−	0.738725i	$-0.264572\pi$
$947$	−9.31665	−	16.1369i	−0.302751	−	0.524379i	−0.976758	+	0.214345i	$0.931238\pi$
$948$		0			0
$949$	2.84441			0.0923335
$950$	−12.9083			−0.418801
$951$		0			0
$952$	−11.4083	−	19.7598i	−0.369746	−	0.640419i
$953$	−7.22498	+	12.5140i	−0.234040	+	0.405369i	−0.958993	−	0.283429i	$-0.908528\pi$
$953$	−7.22498	+	12.5140i	−0.234040	+	0.405369i	0.724953	+	0.688798i	$0.241861\pi$
$954$		0			0
$955$	8.40833	−	14.5636i	0.272087	−	0.471269i
$956$		0			0
$957$		0			0
$958$	−33.1791	+	57.4680i	−1.07197	+	1.85671i
$959$	0.802776	+	1.39045i	0.0259230	+	0.0448999i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	14.9680	−	25.9254i	0.482589	−	0.835869i
$963$		0			0
$964$	−2.95416	−	5.11676i	−0.0951472	−	0.164800i
$965$	−7.80278	−	13.5148i	−0.251180	−	0.435057i
$966$		0			0
$967$	−44.4777			−1.43031			−0.715153	−	0.698967i	$-0.753643\pi$
$967$	−44.4777			−1.43031			−0.715153	+	0.698967i	$0.753643\pi$
$968$	12.6333	−	21.8815i	0.406050	−	0.703299i
$969$		0			0
$970$	−19.3305			−0.620666
$971$	−22.0139	+	38.1292i	−0.706459	+	1.22362i	0.259703	+	0.965688i	$0.416375\pi$
$971$	−22.0139	+	38.1292i	−0.706459	+	1.22362i	−0.966162	+	0.257934i	$0.916958\pi$
$972$		0			0
$973$	3.19722	+	5.53776i	0.102498	+	0.177532i
$974$	−2.30278			−0.0737857
$975$		0			0
$976$	−0.302776			−0.00969161
$977$	14.4083	+	24.9560i	0.460963	+	0.798412i	0.999009	−	0.0445038i	$-0.0141707\pi$
$977$	14.4083	+	24.9560i	0.460963	+	0.798412i	−0.538046	+	0.842915i	$0.680837\pi$
$978$		0			0
$979$	4.98612	−	8.63622i	0.159357	−	0.276015i
$980$	−19.8167			−0.633020
$981$		0			0
$982$	−19.3625	+	33.5368i	−0.617882	+	1.07020i
$983$	−18.4222			−0.587577			−0.293789	−	0.955870i	$-0.594916\pi$
$983$	−18.4222			−0.587577			−0.293789	+	0.955870i	$0.594916\pi$
$984$		0			0
$985$	0.591673	+	1.02481i	0.0188523	+	0.0326531i
$986$	54.3902	+	94.2067i	1.73214	+	3.00015i
$987$		0			0
$988$	−33.3764	−	57.8096i	−1.06184	−	1.83917i
$989$	−30.6333			−0.974083
$990$		0			0
$991$	−20.0139	−	34.6651i	−0.635762	−	1.10117i	−0.986353	−	0.164643i	$-0.947353\pi$
$991$	−20.0139	−	34.6651i	−0.635762	−	1.10117i	0.350591	−	0.936529i	$-0.385981\pi$
$992$	−10.6056	+	18.3694i	−0.336727	+	0.583228i
$993$		0			0
$994$	−5.54584	+	9.60567i	−0.175903	+	0.304673i
$995$	−6.40833	+	11.0995i	−0.203158	+	0.351879i
$996$		0			0
$997$	9.22498	−	15.9781i	0.292158	−	0.506033i	−0.682162	−	0.731201i	$-0.738960\pi$
$997$	9.22498	−	15.9781i	0.292158	−	0.506033i	0.974320	+	0.225169i	$0.0722933\pi$
$998$	−2.78890	−	4.83051i	−0.0882810	−	0.152907i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.j.d.406.1		4
3.2	odd	2		65.2.e.b.16.2	✓	4
12.11	even	2		1040.2.q.o.81.2		4
13.3	even	3		7605.2.a.bg.1.2		2
13.9	even	3	inner	585.2.j.d.451.1		4
13.10	even	6		7605.2.a.bb.1.1		2
15.2	even	4		325.2.o.b.224.1		8
15.8	even	4		325.2.o.b.224.4		8
15.14	odd	2		325.2.e.a.276.1		4
39.2	even	12		845.2.c.d.506.4		4
39.5	even	4		845.2.m.d.361.4		8
39.8	even	4		845.2.m.d.361.1		8
39.11	even	12		845.2.c.d.506.1		4
39.17	odd	6		845.2.e.d.191.1		4
39.20	even	12		845.2.m.d.316.4		8
39.23	odd	6		845.2.a.f.1.2		2
39.29	odd	6		845.2.a.c.1.1		2
39.32	even	12		845.2.m.d.316.1		8
39.35	odd	6		65.2.e.b.61.2	yes	4
39.38	odd	2		845.2.e.d.146.1		4
156.35	even	6		1040.2.q.o.321.2		4
195.29	odd	6		4225.2.a.x.1.2		2
195.74	odd	6		325.2.e.a.126.1		4
195.113	even	12		325.2.o.b.74.1		8
195.152	even	12		325.2.o.b.74.4		8
195.179	odd	6		4225.2.a.t.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.e.b.16.2	✓	4	3.2	odd	2
65.2.e.b.61.2	yes	4	39.35	odd	6
325.2.e.a.126.1		4	195.74	odd	6
325.2.e.a.276.1		4	15.14	odd	2
325.2.o.b.74.1		8	195.113	even	12
325.2.o.b.74.4		8	195.152	even	12
325.2.o.b.224.1		8	15.2	even	4
325.2.o.b.224.4		8	15.8	even	4
585.2.j.d.406.1		4	1.1	even	1	trivial
585.2.j.d.451.1		4	13.9	even	3	inner
845.2.a.c.1.1		2	39.29	odd	6
845.2.a.f.1.2		2	39.23	odd	6
845.2.c.d.506.1		4	39.11	even	12
845.2.c.d.506.4		4	39.2	even	12
845.2.e.d.146.1		4	39.38	odd	2
845.2.e.d.191.1		4	39.17	odd	6
845.2.m.d.316.1		8	39.32	even	12
845.2.m.d.316.4		8	39.20	even	12
845.2.m.d.361.1		8	39.8	even	4
845.2.m.d.361.4		8	39.5	even	4
1040.2.q.o.81.2		4	12.11	even	2
1040.2.q.o.321.2		4	156.35	even	6
4225.2.a.t.1.1		2	195.179	odd	6
4225.2.a.x.1.2		2	195.29	odd	6
7605.2.a.bb.1.1		2	13.10	even	6
7605.2.a.bg.1.2		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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15139 - 1.99426i) q^{2} +(-1.65139 + 2.86029i) q^{4} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +(-1.15139 - 1.99426i) q^{10} +(0.802776 + 1.39045i) q^{11} -3.60555 q^{13} -2.30278 q^{14} +(-0.151388 - 0.262211i) q^{16} +(3.80278 - 6.58660i) q^{17} +(2.80278 - 4.85455i) q^{19} +(-1.65139 + 2.86029i) q^{20} +(1.84861 - 3.20189i) q^{22} +(-1.50000 - 2.59808i) q^{23} +1.00000 q^{25} +(4.15139 + 7.19041i) q^{26} +(1.65139 + 2.86029i) q^{28} +(-3.10555 - 5.37897i) q^{29} -4.00000 q^{31} +(2.65139 - 4.59234i) q^{32} -17.5139 q^{34} +(0.500000 - 0.866025i) q^{35} +(-1.80278 - 3.12250i) q^{37} -12.9083 q^{38} +3.00000 q^{40} +(1.50000 + 2.59808i) q^{41} +(5.10555 - 8.84307i) q^{43} -5.30278 q^{44} +(-3.45416 + 5.98279i) q^{46} -9.21110 q^{47} +(3.00000 + 5.19615i) q^{49} +(-1.15139 - 1.99426i) q^{50} +(5.95416 - 10.3129i) q^{52} +3.21110 q^{53} +(0.802776 + 1.39045i) q^{55} +(1.50000 - 2.59808i) q^{56} +(-7.15139 + 12.3866i) q^{58} +(-5.40833 + 9.36750i) q^{59} +(0.500000 - 0.866025i) q^{61} +(4.60555 + 7.97705i) q^{62} -12.8167 q^{64} -3.60555 q^{65} +(3.50000 + 6.06218i) q^{67} +(12.5597 + 21.7541i) q^{68} -2.30278 q^{70} +(2.40833 - 4.17134i) q^{71} -0.788897 q^{73} +(-4.15139 + 7.19041i) q^{74} +(9.25694 + 16.0335i) q^{76} +1.60555 q^{77} +5.21110 q^{79} +(-0.151388 - 0.262211i) q^{80} +(3.45416 - 5.98279i) q^{82} +9.21110 q^{83} +(3.80278 - 6.58660i) q^{85} -23.5139 q^{86} +(2.40833 + 4.17134i) q^{88} +(-3.10555 - 5.37897i) q^{89} +(-1.80278 + 3.12250i) q^{91} +9.90833 q^{92} +(10.6056 + 18.3694i) q^{94} +(2.80278 - 4.85455i) q^{95} +(4.19722 - 7.26981i) q^{97} +(6.90833 - 11.9656i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 3 q^{4} + 4 q^{5} + 2 q^{7} + 12 q^{8} - q^{10} - 4 q^{11} - 2 q^{14} + 3 q^{16} + 8 q^{17} + 4 q^{19} - 3 q^{20} + 11 q^{22} - 6 q^{23} + 4 q^{25} + 13 q^{26} + 3 q^{28} + 2 q^{29} - 16 q^{31}+ \cdots + 6 q^{98}+O(q^{100}) \) 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

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Database

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