LMFDB - Embedded newform 1638.2.p.g.919.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(919,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("1638.919");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.p (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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.6498455769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} + 3x^{5} + 25x^{4} - 3x^{3} + 6x^{2} + x + 1 $ x^8 - x^7 + 6x^6 + 3x^5 + 25x^4 - 3x^3 + 6*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			919.1
Root			$1.33821 - 2.31784i$ of defining polynomial
Character	$\chi$	$=$	1638.919
Dual form			1638.2.p.g.991.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.651388 + 1.12824i) q^{5} +(-2.36323 + 1.18960i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.651388 + 1.12824i) q^{5} +(-2.36323 + 1.18960i) q^{7} +1.00000 q^{8} +1.30278 q^{10} -6.09231 q^{11} +(2.61985 + 2.47718i) q^{13} +(2.21184 + 1.45181i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.74338 - 3.01962i) q^{17} +1.67075 q^{19} +(-0.651388 - 1.12824i) q^{20} +(3.04616 + 5.27610i) q^{22} +(-0.408007 - 0.706688i) q^{23} +(1.65139 + 2.86029i) q^{25} +(0.835374 - 3.50744i) q^{26} +(0.151388 - 2.64142i) q^{28} +(0.243381 - 0.421549i) q^{29} +(0.256619 + 0.444477i) q^{31} +(-0.500000 + 0.866025i) q^{32} -3.48676 q^{34} +(0.197224 - 3.44117i) q^{35} +(-5.38153 - 9.32109i) q^{37} +(-0.835374 - 1.44691i) q^{38} +(-0.651388 + 1.12824i) q^{40} +(-4.81845 + 8.34580i) q^{41} +(-6.00032 - 10.3929i) q^{43} +(3.04616 - 5.27610i) q^{44} +(-0.408007 + 0.706688i) q^{46} +(6.57401 - 11.3865i) q^{47} +(4.16969 - 5.62260i) q^{49} +(1.65139 - 2.86029i) q^{50} +(-3.45522 + 1.03027i) q^{52} +(6.24476 + 10.8162i) q^{53} +(3.96846 - 6.87357i) q^{55} +(-2.36323 + 1.18960i) q^{56} -0.486762 q^{58} +(4.57507 - 7.92425i) q^{59} -2.23758 q^{61} +(0.256619 - 0.444477i) q^{62} +1.00000 q^{64} +(-4.50138 + 1.34220i) q^{65} -2.15540 q^{67} +(1.74338 + 3.01962i) q^{68} +(-3.07876 + 1.54979i) q^{70} +(-5.44093 - 9.42396i) q^{71} +(2.44198 + 4.22964i) q^{73} +(-5.38153 + 9.32109i) q^{74} +(-0.835374 + 1.44691i) q^{76} +(14.3975 - 7.24743i) q^{77} +(5.95628 - 10.3166i) q^{79} +1.30278 q^{80} +9.63690 q^{82} +0.486762 q^{83} +(2.27123 + 3.93389i) q^{85} +(-6.00032 + 10.3929i) q^{86} -6.09231 q^{88} +(-3.84999 - 6.66838i) q^{89} +(-9.13815 - 2.73756i) q^{91} +0.816013 q^{92} -13.1480 q^{94} +(-1.08831 + 1.88500i) q^{95} +(-7.84999 - 13.5966i) q^{97} +(-6.95416 - 0.799757i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 2 q^{5} + 3 q^{7} + 8 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^4 + 2 * q^5 + 3 * q^7 + 8 * q^8	$ 8 q - 4 q^{2} - 4 q^{4} + 2 q^{5} + 3 q^{7} + 8 q^{8} - 4 q^{10} - 4 q^{11} + 7 q^{13} + 3 q^{14} - 4 q^{16} + 6 q^{17} - 4 q^{19} + 2 q^{20} + 2 q^{22} - 4 q^{23} + 6 q^{25} - 2 q^{26} - 6 q^{28} - 6 q^{29} + 10 q^{31} - 4 q^{32} - 12 q^{34} + 16 q^{35} - 12 q^{37} + 2 q^{38} + 2 q^{40} + 6 q^{41} - 4 q^{43} + 2 q^{44} - 4 q^{46} + 17 q^{47} + 17 q^{49} + 6 q^{50} - 5 q^{52} - 3 q^{53} + 25 q^{55} + 3 q^{56} + 12 q^{58} + 8 q^{61} + 10 q^{62} + 8 q^{64} + 9 q^{65} + 14 q^{67} + 6 q^{68} - 8 q^{70} - 6 q^{71} - 19 q^{73} - 12 q^{74} + 2 q^{76} + 10 q^{77} + 24 q^{79} - 4 q^{80} - 12 q^{82} - 12 q^{83} - 3 q^{85} - 4 q^{86} - 4 q^{88} + 7 q^{89} - 50 q^{91} + 8 q^{92} - 34 q^{94} + 12 q^{95} - 25 q^{97} - 34 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 2 * q^5 + 3 * q^7 + 8 * q^8 - 4 * q^10 - 4 * q^11 + 7 * q^13 + 3 * q^14 - 4 * q^16 + 6 * q^17 - 4 * q^19 + 2 * q^20 + 2 * q^22 - 4 * q^23 + 6 * q^25 - 2 * q^26 - 6 * q^28 - 6 * q^29 + 10 * q^31 - 4 * q^32 - 12 * q^34 + 16 * q^35 - 12 * q^37 + 2 * q^38 + 2 * q^40 + 6 * q^41 - 4 * q^43 + 2 * q^44 - 4 * q^46 + 17 * q^47 + 17 * q^49 + 6 * q^50 - 5 * q^52 - 3 * q^53 + 25 * q^55 + 3 * q^56 + 12 * q^58 + 8 * q^61 + 10 * q^62 + 8 * q^64 + 9 * q^65 + 14 * q^67 + 6 * q^68 - 8 * q^70 - 6 * q^71 - 19 * q^73 - 12 * q^74 + 2 * q^76 + 10 * q^77 + 24 * q^79 - 4 * q^80 - 12 * q^82 - 12 * q^83 - 3 * q^85 - 4 * q^86 - 4 * q^88 + 7 * q^89 - 50 * q^91 + 8 * q^92 - 34 * q^94 + 12 * q^95 - 25 * q^97 - 34 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.651388	+	1.12824i	−0.291309	+	0.504563i	−0.974120	−	0.226033i	$-0.927424\pi$
$5$	−0.651388	+	1.12824i	−0.291309	+	0.504563i	0.682810	+	0.730596i	$0.260758\pi$
$6$		0			0
$7$	−2.36323	+	1.18960i	−0.893216	+	0.449628i
$7$	−2.36323	+	1.18960i	−0.893216	+	0.449628i
$8$	1.00000			0.353553
$9$		0			0
$10$	1.30278			0.411974
$11$	−6.09231			−1.83690			−0.918451	−	0.395535i	$-0.870559\pi$
$11$	−6.09231			−1.83690			−0.918451	+	0.395535i	$0.870559\pi$
$12$		0			0
$13$	2.61985	+	2.47718i	0.726615	+	0.687045i
$13$	2.61985	+	2.47718i	0.726615	+	0.687045i
$14$	2.21184	+	1.45181i	0.591139	+	0.388014i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.74338	−	3.01962i	0.422832	−	0.732367i	−0.573383	−	0.819287i	$-0.694369\pi$
$17$	1.74338	−	3.01962i	0.422832	−	0.732367i	0.996215	+	0.0869208i	$0.0277027\pi$
$18$		0			0
$19$	1.67075			0.383296			0.191648	−	0.981464i	$-0.438617\pi$
$19$	1.67075			0.383296			0.191648	+	0.981464i	$0.438617\pi$
$20$	−0.651388	−	1.12824i	−0.145655	−	0.252281i
$21$		0			0
$22$	3.04616	+	5.27610i	0.649443	+	1.12487i
$23$	−0.408007	−	0.706688i	−0.0850753	−	0.147355i	0.820348	−	0.571865i	$-0.193780\pi$
$23$	−0.408007	−	0.706688i	−0.0850753	−	0.147355i	−0.905423	+	0.424510i	$0.860446\pi$
$24$		0			0
$25$	1.65139	+	2.86029i	0.330278	+	0.572058i
$26$	0.835374	−	3.50744i	0.163830	−	0.687866i
$27$		0			0
$28$	0.151388	−	2.64142i	0.0286096	−	0.499181i
$29$	0.243381	−	0.421549i	0.0451947	−	0.0782796i	−0.842543	−	0.538629i	$-0.818942\pi$
$29$	0.243381	−	0.421549i	0.0451947	−	0.0782796i	0.887738	+	0.460349i	$0.152276\pi$
$30$		0			0
$31$	0.256619	+	0.444477i	0.0460901	+	0.0798304i	0.888150	−	0.459553i	$-0.151991\pi$
$31$	0.256619	+	0.444477i	0.0460901	+	0.0798304i	−0.842060	+	0.539384i	$0.818657\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−3.48676			−0.597975
$35$	0.197224	−	3.44117i	0.0333370	−	0.581664i
$36$		0			0
$37$	−5.38153	−	9.32109i	−0.884718	−	1.53238i	−0.846036	−	0.533125i	$-0.821017\pi$
$37$	−5.38153	−	9.32109i	−0.884718	−	1.53238i	−0.0386821	−	0.999252i	$-0.512316\pi$
$38$	−0.835374	−	1.44691i	−0.135516	−	0.234720i
$39$		0			0
$40$	−0.651388	+	1.12824i	−0.102993	+	0.178390i
$41$	−4.81845	+	8.34580i	−0.752515	+	1.30339i	0.194085	+	0.980985i	$0.437826\pi$
$41$	−4.81845	+	8.34580i	−0.752515	+	1.30339i	−0.946600	+	0.322410i	$0.895507\pi$
$42$		0			0
$43$	−6.00032	−	10.3929i	−0.915040	−	1.58490i	−0.806842	−	0.590767i	$-0.798825\pi$
$43$	−6.00032	−	10.3929i	−0.915040	−	1.58490i	−0.108198	−	0.994129i	$-0.534508\pi$
$44$	3.04616	−	5.27610i	0.459225	−	0.795402i
$45$		0			0
$46$	−0.408007	+	0.706688i	−0.0601573	+	0.104196i
$47$	6.57401	−	11.3865i	0.958918	−	1.66089i	0.233782	−	0.972289i	$-0.424890\pi$
$47$	6.57401	−	11.3865i	0.958918	−	1.66089i	0.725136	−	0.688605i	$-0.241777\pi$
$48$		0			0
$49$	4.16969	−	5.62260i	0.595670	−	0.803229i
$50$	1.65139	−	2.86029i	0.233542	−	0.404506i
$51$		0			0
$52$	−3.45522	+	1.03027i	−0.479153	+	0.142872i
$53$	6.24476	+	10.8162i	0.857784	+	1.48572i	0.874038	+	0.485857i	$0.161492\pi$
$53$	6.24476	+	10.8162i	0.857784	+	1.48572i	−0.0162547	+	0.999868i	$0.505174\pi$
$54$		0			0
$55$	3.96846	−	6.87357i	0.535107	−	0.926832i
$56$	−2.36323	+	1.18960i	−0.315800	+	0.158967i
$57$		0			0
$58$	−0.486762			−0.0639150
$59$	4.57507	−	7.92425i	0.595623	−	1.03165i	−0.397836	−	0.917457i	$-0.630239\pi$
$59$	4.57507	−	7.92425i	0.595623	−	1.03165i	0.993459	−	0.114193i	$-0.0364281\pi$
$60$		0			0
$61$	−2.23758			−0.286493			−0.143246	−	0.989687i	$-0.545754\pi$
$61$	−2.23758			−0.286493			−0.143246	+	0.989687i	$0.545754\pi$
$62$	0.256619	−	0.444477i	0.0325906	−	0.0564486i
$63$		0			0
$64$	1.00000			0.125000
$65$	−4.50138	+	1.34220i	−0.558327	+	0.166480i
$66$		0			0
$67$	−2.15540			−0.263324			−0.131662	−	0.991295i	$-0.542031\pi$
$67$	−2.15540			−0.263324			−0.131662	+	0.991295i	$0.542031\pi$
$68$	1.74338	+	3.01962i	0.211416	+	0.366183i
$69$		0			0
$70$	−3.07876	+	1.54979i	−0.367982	+	0.185235i
$71$	−5.44093	−	9.42396i	−0.645719	−	1.11842i	−0.984135	−	0.177422i	$-0.943224\pi$
$71$	−5.44093	−	9.42396i	−0.645719	−	1.11842i	0.338416	−	0.940997i	$-0.390109\pi$
$72$		0			0
$73$	2.44198	+	4.22964i	0.285813	+	0.495042i	0.972806	−	0.231622i	$-0.0744032\pi$
$73$	2.44198	+	4.22964i	0.285813	+	0.495042i	−0.686993	+	0.726664i	$0.741070\pi$
$74$	−5.38153	+	9.32109i	−0.625590	+	1.08355i
$75$		0			0
$76$	−0.835374	+	1.44691i	−0.0958240	+	0.165972i
$77$	14.3975	−	7.24743i	1.64075	−	0.825922i
$78$		0			0
$79$	5.95628	−	10.3166i	0.670134	−	1.16071i	−0.307732	−	0.951473i	$-0.599570\pi$
$79$	5.95628	−	10.3166i	0.670134	−	1.16071i	0.977866	−	0.209233i	$-0.0670966\pi$
$80$	1.30278			0.145655
$81$		0			0
$82$	9.63690			1.06422
$83$	0.486762			0.0534291			0.0267146	−	0.999643i	$-0.491495\pi$
$83$	0.486762			0.0534291			0.0267146	+	0.999643i	$0.491495\pi$
$84$		0			0
$85$	2.27123	+	3.93389i	0.246350	+	0.426691i
$86$	−6.00032	+	10.3929i	−0.647031	+	1.12069i
$87$		0			0
$88$	−6.09231			−0.649443
$89$	−3.84999	−	6.66838i	−0.408098	−	0.706847i	0.586578	−	0.809892i	$-0.300475\pi$
$89$	−3.84999	−	6.66838i	−0.408098	−	0.706847i	−0.994677	+	0.103046i	$0.967141\pi$
$90$		0			0
$91$	−9.13815	−	2.73756i	−0.957938	−	0.286974i
$92$	0.816013			0.0850753
$93$		0			0
$94$	−13.1480			−1.35611
$95$	−1.08831	+	1.88500i	−0.111658	+	0.193397i
$96$		0			0
$97$	−7.84999	−	13.5966i	−0.797046	−	1.38052i	−0.921532	−	0.388302i	$-0.873062\pi$
$97$	−7.84999	−	13.5966i	−0.797046	−	1.38052i	0.124486	−	0.992221i	$-0.460272\pi$
$98$	−6.95416	−	0.799757i	−0.702477	−	0.0807876i
$99$		0			0
$100$	−3.30278			−0.330278
$101$	16.3877			1.63064			0.815319	−	0.579012i	$-0.196561\pi$
$101$	16.3877			1.63064			0.815319	+	0.579012i	$0.196561\pi$
$102$		0			0
$103$	2.45785	−	4.25712i	0.242179	−	0.419467i	−0.719155	−	0.694849i	$-0.755471\pi$
$103$	2.45785	−	4.25712i	0.242179	−	0.419467i	0.961335	+	0.275382i	$0.0888044\pi$
$104$	2.61985	+	2.47718i	0.256897	+	0.242907i
$105$		0			0
$106$	6.24476	−	10.8162i	0.606545	−	1.05057i
$107$	−2.43955	−	4.22542i	−0.235840	−	0.408487i	0.723676	−	0.690139i	$-0.242451\pi$
$107$	−2.43955	−	4.22542i	−0.235840	−	0.408487i	−0.959516	+	0.281653i	$0.909117\pi$
$108$		0			0
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	−0.999512	−	0.0312328i	$-0.990057\pi$
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	0.472708	−	0.881219i	$-0.343277\pi$
$110$	−7.93692			−0.756755
$111$		0			0
$112$	2.21184	+	1.45181i	0.208999	+	0.137184i
$113$	6.36829	+	11.0302i	0.599079	+	1.03763i	0.992957	+	0.118472i	$0.0377997\pi$
$113$	6.36829	+	11.0302i	0.599079	+	1.03763i	−0.393879	+	0.919162i	$0.628867\pi$
$114$		0			0
$115$	1.06308			0.0991329
$116$	0.243381	+	0.421549i	0.0225974	+	0.0391398i
$117$		0			0
$118$	−9.15014			−0.842338
$119$	−0.527853	+	9.20999i	−0.0483882	+	0.844279i
$120$		0			0
$121$	26.1163			2.37421
$122$	1.11879	+	1.93780i	0.101290	+	0.175440i
$123$		0			0
$124$	−0.513238			−0.0460901
$125$	−10.8167			−0.967471
$126$		0			0
$127$	−5.95554	+	10.3153i	−0.528469	+	0.915335i	0.470980	+	0.882144i	$0.343900\pi$
$127$	−5.95554	+	10.3153i	−0.528469	+	0.915335i	−0.999449	+	0.0331911i	$0.989433\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	3.41307	+	3.22721i	0.299346	+	0.283045i
$131$	−4.63340	+	8.02529i	−0.404822	+	0.701173i	−0.994301	−	0.106611i	$-0.966000\pi$
$131$	−4.63340	+	8.02529i	−0.404822	+	0.701173i	0.589478	+	0.807784i	$0.299333\pi$
$132$		0			0
$133$	−3.94836	+	1.98753i	−0.342366	+	0.172340i
$134$	1.07770	+	1.86663i	0.0930989	+	0.161252i
$135$		0			0
$136$	1.74338	−	3.01962i	0.149494	−	0.258931i
$137$	5.15277	−	8.92485i	0.440230	−	0.762502i	−0.557476	−	0.830193i	$-0.688230\pi$
$137$	5.15277	−	8.92485i	0.440230	−	0.762502i	0.997706	+	0.0676916i	$0.0215634\pi$
$138$		0			0
$139$	−0.106609	−	0.184652i	−0.00904245	−	0.0156620i	0.861469	−	0.507811i	$-0.169545\pi$
$139$	−0.106609	−	0.184652i	−0.00904245	−	0.0156620i	−0.870511	+	0.492149i	$0.836212\pi$
$140$	2.88153	+	1.89139i	0.243534	+	0.159851i
$141$		0			0
$142$	−5.44093	+	9.42396i	−0.456592	+	0.790841i
$143$	−15.9609	−	15.0917i	−1.33472	−	1.26203i
$144$		0			0
$145$	0.317071	+	0.549183i	0.0263313	+	0.0456072i
$146$	2.44198	−	4.22964i	0.202100	−	0.350047i
$147$		0			0
$148$	10.7631			0.884718
$149$	−12.0335			−0.985820			−0.492910	−	0.870080i	$-0.664067\pi$
$149$	−12.0335			−0.985820			−0.492910	+	0.870080i	$0.664067\pi$
$150$		0			0
$151$	2.23969	+	3.87926i	0.182264	+	0.315690i	0.942651	−	0.333780i	$-0.108324\pi$
$151$	2.23969	+	3.87926i	0.182264	+	0.315690i	−0.760387	+	0.649470i	$0.774991\pi$
$152$	1.67075			0.135516
$153$		0			0
$154$	−13.4752	−	8.84491i	−1.08586	−	0.712743i
$155$	−0.668634			−0.0537059
$156$		0			0
$157$	−10.2859	−	17.8156i	−0.820900	−	1.42184i	−0.905013	−	0.425385i	$-0.860139\pi$
$157$	−10.2859	−	17.8156i	−0.820900	−	1.42184i	0.0841125	−	0.996456i	$-0.473194\pi$
$158$	−11.9126			−0.947712
$159$		0			0
$160$	−0.651388	−	1.12824i	−0.0514967	−	0.0891950i
$161$	1.80489	+	1.18470i	0.142245	+	0.0933674i
$162$		0			0
$163$	10.5160			0.823676			0.411838	−	0.911257i	$-0.364887\pi$
$163$	10.5160			0.823676			0.411838	+	0.911257i	$0.364887\pi$
$164$	−4.81845	−	8.34580i	−0.376258	−	0.651697i
$165$		0			0
$166$	−0.243381	−	0.421549i	−0.0188900	−	0.0327185i
$167$	3.45416	−	5.98279i	0.267291	−	0.462962i	−0.700870	−	0.713289i	$-0.747205\pi$
$167$	3.45416	−	5.98279i	0.267291	−	0.462962i	0.968161	+	0.250327i	$0.0805381\pi$
$168$		0			0
$169$	0.727193	+	12.9796i	0.0559379	+	0.998434i
$170$	2.27123	−	3.93389i	0.174196	−	0.301716i
$171$		0			0
$172$	12.0006			0.915040
$173$	−5.39656			−0.410293			−0.205147	−	0.978731i	$-0.565767\pi$
$173$	−5.39656			−0.410293			−0.205147	+	0.978731i	$0.565767\pi$
$174$		0			0
$175$	−7.30521	−	4.79502i	−0.552222	−	0.362469i
$176$	3.04616	+	5.27610i	0.229613	+	0.397701i
$177$		0			0
$178$	−3.84999	+	6.66838i	−0.288569	+	0.499816i
$179$	3.12302			0.233425			0.116713	−	0.993166i	$-0.462764\pi$
$179$	3.12302			0.233425			0.116713	+	0.993166i	$0.462764\pi$
$180$		0			0
$181$	−21.0972			−1.56814			−0.784071	−	0.620672i	$-0.786860\pi$
$181$	−21.0972			−1.56814			−0.784071	+	0.620672i	$0.786860\pi$
$182$	2.19828	+	9.28265i	0.162948	+	0.688076i
$183$		0			0
$184$	−0.408007	−	0.706688i	−0.0300787	−	0.0520978i
$185$	14.0219			1.03091
$186$		0			0
$187$	−10.6212	+	18.3965i	−0.776701	+	1.34529i
$188$	6.57401	+	11.3865i	0.479459	+	0.830447i
$189$		0			0
$190$	2.17661			0.157908
$191$	−5.60831			−0.405803			−0.202901	−	0.979199i	$-0.565037\pi$
$191$	−5.60831			−0.405803			−0.202901	+	0.979199i	$0.565037\pi$
$192$		0			0
$193$	7.67075			0.552153			0.276076	−	0.961136i	$-0.410966\pi$
$193$	7.67075			0.552153			0.276076	+	0.961136i	$0.410966\pi$
$194$	−7.84999	+	13.5966i	−0.563596	+	0.976178i
$195$		0			0
$196$	2.78447	+	6.42236i	0.198891	+	0.458740i
$197$	−7.08968	+	12.2797i	−0.505119	+	0.874892i	0.494863	+	0.868971i	$0.335218\pi$
$197$	−7.08968	+	12.2797i	−0.505119	+	0.874892i	−0.999982	+	0.00592106i	$0.998115\pi$
$198$		0			0
$199$	−1.74601	+	3.02418i	−0.123771	+	0.214378i	−0.921252	−	0.388966i	$-0.872832\pi$
$199$	−1.74601	+	3.02418i	−0.123771	+	0.214378i	0.797481	+	0.603345i	$0.206166\pi$
$200$	1.65139	+	2.86029i	0.116771	+	0.202253i
$201$		0			0
$202$	−8.19386	−	14.1922i	−0.576518	−	0.998558i
$203$	−0.0736899	+	1.28574i	−0.00517202	+	0.0902414i
$204$		0			0
$205$	−6.27736	−	10.8727i	−0.438430	−	0.759383i
$206$	−4.91570			−0.342493
$207$		0			0
$208$	0.835374	−	3.50744i	0.0579228	−	0.243197i
$209$	−10.1787			−0.704077
$210$		0			0
$211$	6.56109	−	11.3641i	0.451684	−	0.782340i	−0.546807	−	0.837259i	$-0.684157\pi$
$211$	6.56109	−	11.3641i	0.451684	−	0.782340i	0.998491	+	0.0549189i	$0.0174900\pi$
$212$	−12.4895			−0.857784
$213$		0			0
$214$	−2.43955	+	4.22542i	−0.166764	+	0.288844i
$215$	15.6341			1.06624
$216$		0			0
$217$	−1.13520	−	0.745126i	−0.0770624	−	0.0505824i
$218$	−5.50000	+	9.52628i	−0.372507	+	0.645201i
$219$		0			0
$220$	3.96846	+	6.87357i	0.267553	+	0.463416i
$221$	12.0475	−	3.59229i	0.810405	−	0.241644i
$222$		0			0
$223$	−4.92875	+	8.53684i	−0.330053	+	0.571669i	−0.982522	−	0.186147i	$-0.940400\pi$
$223$	−4.92875	+	8.53684i	−0.330053	+	0.571669i	0.652469	+	0.757816i	$0.273733\pi$
$224$	0.151388	−	2.64142i	0.0101150	−	0.176487i
$225$		0			0
$226$	6.36829	−	11.0302i	0.423613	−	0.733719i
$227$	−3.17956	+	5.50716i	−0.211035	+	0.365523i	−0.952039	−	0.305978i	$-0.901017\pi$
$227$	−3.17956	+	5.50716i	−0.211035	+	0.365523i	0.741004	+	0.671501i	$0.234350\pi$
$228$		0			0
$229$	−5.60767	+	9.71276i	−0.370565	+	0.641837i	−0.989653	−	0.143485i	$-0.954169\pi$
$229$	−5.60767	+	9.71276i	−0.370565	+	0.641837i	0.619088	+	0.785322i	$0.287503\pi$
$230$	−0.531541	−	0.920656i	−0.0350488	−	0.0607063i
$231$		0			0
$232$	0.243381	−	0.421549i	0.0159788	−	0.0276760i
$233$	−4.74845	+	8.22455i	−0.311081	+	0.538808i	−0.978597	−	0.205788i	$-0.934024\pi$
$233$	−4.74845	+	8.22455i	−0.311081	+	0.538808i	0.667516	+	0.744596i	$0.267358\pi$
$234$		0			0
$235$	8.56446	+	14.8341i	0.558684	+	0.967669i
$236$	4.57507	+	7.92425i	0.297812	+	0.515825i
$237$		0			0
$238$	8.24001	−	4.14786i	0.534121	−	0.268866i
$239$	−4.32714			−0.279899			−0.139950	−	0.990159i	$-0.544694\pi$
$239$	−4.32714			−0.279899			−0.139950	+	0.990159i	$0.544694\pi$
$240$		0			0
$241$	−8.58013	+	14.8612i	−0.552695	+	0.957296i	0.445384	+	0.895340i	$0.353067\pi$
$241$	−8.58013	+	14.8612i	−0.552695	+	0.957296i	−0.998079	+	0.0619561i	$0.980266\pi$
$242$	−13.0581	−	22.6174i	−0.839409	−	1.45390i
$243$		0			0
$244$	1.11879	−	1.93780i	0.0716231	−	0.124055i
$245$	3.62754	+	8.36689i	0.231755	+	0.534541i
$246$		0			0
$247$	4.37711	+	4.13874i	0.278509	+	0.263342i
$248$	0.256619	+	0.444477i	0.0162953	+	0.0282243i
$249$		0			0
$250$	5.40833	+	9.36750i	0.342053	+	0.592453i
$251$	−5.56308	−	9.63554i	−0.351139	−	0.608190i	0.635311	−	0.772257i	$-0.280872\pi$
$251$	−5.56308	−	9.63554i	−0.351139	−	0.608190i	−0.986449	+	0.164067i	$0.947539\pi$
$252$		0			0
$253$	2.48570	+	4.30537i	0.156275	+	0.270676i
$254$	11.9111			0.747368
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.15213	+	1.99554i	0.0718676	+	0.124478i	0.899720	−	0.436468i	$-0.143771\pi$
$257$	1.15213	+	1.99554i	0.0718676	+	0.124478i	−0.827852	+	0.560946i	$0.810437\pi$
$258$		0			0
$259$	23.8062	+	15.6260i	1.47924	+	0.970950i
$260$	1.08831	−	4.56941i	0.0674938	−	0.283383i
$261$		0			0
$262$	9.26681			0.572505
$263$	18.7944			1.15891			0.579456	−	0.815003i	$-0.303265\pi$
$263$	18.7944			1.15891			0.579456	+	0.815003i	$0.303265\pi$
$264$		0			0
$265$	−16.2710			−0.999522
$266$	3.69543	+	2.42562i	0.226581	+	0.148724i
$267$		0			0
$268$	1.07770	−	1.86663i	0.0658309	−	0.114022i
$269$	13.8198	−	23.9366i	0.842610	−	1.45944i	−0.0450712	−	0.998984i	$-0.514351\pi$
$269$	13.8198	−	23.9366i	0.842610	−	1.45944i	0.887681	−	0.460459i	$-0.152315\pi$
$270$		0			0
$271$	5.87942	+	10.1834i	0.357149	+	0.618600i	0.987483	−	0.157724i	$-0.0504155\pi$
$271$	5.87942	+	10.1834i	0.357149	+	0.618600i	−0.630334	+	0.776324i	$0.717082\pi$
$272$	−3.48676			−0.211416
$273$		0			0
$274$	−10.3055			−0.622580
$275$	−10.0608	−	17.4258i	−0.606687	−	1.05081i
$276$		0			0
$277$	14.5320	−	25.1701i	0.873142	−	1.51233i	0.0144141	−	0.999896i	$-0.495412\pi$
$277$	14.5320	−	25.1701i	0.873142	−	1.51233i	0.858728	−	0.512431i	$-0.171255\pi$
$278$	−0.106609	+	0.184652i	−0.00639398	+	0.0110747i
$279$		0			0
$280$	0.197224	−	3.44117i	0.0117864	−	0.205649i
$281$	5.76306			0.343795			0.171898	−	0.985115i	$-0.445010\pi$
$281$	5.76306			0.343795			0.171898	+	0.985115i	$0.445010\pi$
$282$		0			0
$283$	−6.72120			−0.399534			−0.199767	−	0.979843i	$-0.564018\pi$
$283$	−6.72120			−0.399534			−0.199767	+	0.979843i	$0.564018\pi$
$284$	10.8819			0.645719
$285$		0			0
$286$	−5.08936	+	21.3684i	−0.300940	+	1.26354i
$287$	1.45891	−	25.4551i	0.0861167	−	1.50256i
$288$		0			0
$289$	2.42124	+	4.19372i	0.142426	+	0.246689i
$290$	0.317071	−	0.549183i	0.0186191	−	0.0322491i
$291$		0			0
$292$	−4.88397			−0.285813
$293$	−2.99769	−	5.19215i	−0.175127	−	0.303329i	0.765078	−	0.643937i	$-0.222700\pi$
$293$	−2.99769	−	5.19215i	−0.175127	−	0.303329i	−0.940205	+	0.340609i	$0.889367\pi$
$294$		0			0
$295$	5.96029	+	10.3235i	0.347021	+	0.601059i
$296$	−5.38153	−	9.32109i	−0.312795	−	0.541777i
$297$		0			0
$298$	6.01673	+	10.4213i	0.348540	+	0.603689i
$299$	0.681677	−	2.86212i	0.0394224	−	0.165521i
$300$		0			0
$301$	26.5435	+	17.4227i	1.52994	+	1.00423i
$302$	2.23969	−	3.87926i	0.128880	−	0.223226i
$303$		0			0
$304$	−0.835374	−	1.44691i	−0.0479120	−	0.0829860i
$305$	1.45753	−	2.52452i	0.0834580	−	0.144553i
$306$		0			0
$307$	9.00340			0.513851			0.256925	−	0.966431i	$-0.417291\pi$
$307$	9.00340			0.513851			0.256925	+	0.966431i	$0.417291\pi$
$308$	−0.922302	+	16.0923i	−0.0525530	+	0.916946i
$309$		0			0
$310$	0.334317	+	0.579054i	0.0189879	+	0.0328880i
$311$	−7.31771	−	12.6746i	−0.414949	−	0.718713i	0.580474	−	0.814279i	$-0.302867\pi$
$311$	−7.31771	−	12.6746i	−0.414949	−	0.718713i	−0.995423	+	0.0955656i	$0.969534\pi$
$312$		0			0
$313$	1.72540	−	2.98848i	0.0975253	−	0.168919i	−0.813134	−	0.582076i	$-0.802241\pi$
$313$	1.72540	−	2.98848i	0.0975253	−	0.168919i	0.910660	+	0.413157i	$0.135574\pi$
$314$	−10.2859	+	17.8156i	−0.580464	+	1.00539i
$315$		0			0
$316$	5.95628	+	10.3166i	0.335067	+	0.580353i
$317$	6.67850	−	11.5675i	0.375102	−	0.649696i	−0.615240	−	0.788340i	$-0.710941\pi$
$317$	6.67850	−	11.5675i	0.375102	−	0.649696i	0.990342	+	0.138644i	$0.0442743\pi$
$318$		0			0
$319$	−1.48275	+	2.56821i	−0.0830183	+	0.143792i
$320$	−0.651388	+	1.12824i	−0.0364137	+	0.0630704i
$321$		0			0
$322$	0.123534	−	2.15543i	0.00688431	−	0.120117i
$323$	2.91275	−	5.04503i	0.162070	−	0.280713i
$324$		0			0
$325$	−2.75905	+	11.5843i	−0.153045	+	0.642581i
$326$	−5.25800	−	9.10712i	−0.291214	−	0.504397i
$327$		0			0
$328$	−4.81845	+	8.34580i	−0.266054	+	0.460820i
$329$	−1.99045	+	34.7294i	−0.109737	+	1.91469i
$330$		0			0
$331$	−3.43381			−0.188739			−0.0943697	−	0.995537i	$-0.530084\pi$
$331$	−3.43381			−0.188739			−0.0943697	+	0.995537i	$0.530084\pi$
$332$	−0.243381	+	0.421549i	−0.0133573	+	0.0231355i
$333$		0			0
$334$	−6.90833			−0.378007
$335$	1.40400	−	2.43180i	0.0767086	−	0.132863i
$336$		0			0
$337$	−6.17386			−0.336311			−0.168156	−	0.985760i	$-0.553781\pi$
$337$	−6.17386			−0.336311			−0.168156	+	0.985760i	$0.553781\pi$
$338$	10.8771	−	7.11959i	0.591637	−	0.387255i
$339$		0			0
$340$	−4.54247			−0.246350
$341$	−1.56340	−	2.70789i	−0.0846630	−	0.146641i
$342$		0			0
$343$	−3.16527	+	18.2478i	−0.170908	+	0.985287i
$344$	−6.00032	−	10.3929i	−0.323516	−	0.560345i
$345$		0			0
$346$	2.69828	+	4.67356i	0.145061	+	0.251252i
$347$	−0.0723120	+	0.125248i	−0.00388191	+	0.00672367i	−0.867960	−	0.496634i	$-0.834569\pi$
$347$	−0.0723120	+	0.125248i	−0.00388191	+	0.00672367i	0.864078	+	0.503358i	$0.167902\pi$
$348$		0			0
$349$	13.8792	−	24.0395i	0.742938	−	1.28681i	−0.208214	−	0.978083i	$-0.566765\pi$
$349$	13.8792	−	24.0395i	0.742938	−	1.28681i	0.951152	−	0.308723i	$-0.0999015\pi$
$350$	−0.500000	+	8.72401i	−0.0267261	+	0.466318i
$351$		0			0
$352$	3.04616	−	5.27610i	0.162361	−	0.281217i
$353$	0.967179			0.0514777			0.0257389	−	0.999669i	$-0.491806\pi$
$353$	0.967179			0.0514777			0.0257389	+	0.999669i	$0.491806\pi$
$354$		0			0
$355$	14.1766			0.752416
$356$	7.69998			0.408098
$357$		0			0
$358$	−1.56151	−	2.70461i	−0.0825284	−	0.142943i
$359$	7.57507	−	13.1204i	0.399797	−	0.692468i	−0.593904	−	0.804536i	$-0.702414\pi$
$359$	7.57507	−	13.1204i	0.399797	−	0.692468i	0.993701	+	0.112068i	$0.0357474\pi$
$360$		0			0
$361$	−16.2086			−0.853084
$362$	10.5486	+	18.2707i	0.554422	+	0.960287i
$363$		0			0
$364$	6.93987	−	6.54509i	0.363748	−	0.343056i
$365$	−6.36271			−0.333040
$366$		0			0
$367$	−4.83352			−0.252308			−0.126154	−	0.992011i	$-0.540263\pi$
$367$	−4.83352			−0.252308			−0.126154	+	0.992011i	$0.540263\pi$
$368$	−0.408007	+	0.706688i	−0.0212688	+	0.0368387i
$369$		0			0
$370$	−7.01093	−	12.1433i	−0.364481	−	0.631299i
$371$	−27.6248	−	18.1325i	−1.43421	−	0.941390i
$372$		0			0
$373$	8.56157			0.443301			0.221651	−	0.975126i	$-0.428856\pi$
$373$	8.56157			0.443301			0.221651	+	0.975126i	$0.428856\pi$
$374$	21.2424			1.09842
$375$		0			0
$376$	6.57401	−	11.3865i	0.339029	−	0.587215i
$377$	1.68187	−	0.501494i	0.0866208	−	0.0258283i
$378$		0			0
$379$	−16.3161	+	28.2604i	−0.838104	+	1.45164i	0.0533744	+	0.998575i	$0.483002\pi$
$379$	−16.3161	+	28.2604i	−0.838104	+	1.45164i	−0.891478	+	0.453064i	$0.850331\pi$
$380$	−1.08831	−	1.88500i	−0.0558289	−	0.0966985i
$381$		0			0
$382$	2.80415	+	4.85694i	0.143473	+	0.248502i
$383$	−19.2439			−0.983319			−0.491659	−	0.870788i	$-0.663609\pi$
$383$	−19.2439			−0.983319			−0.491659	+	0.870788i	$0.663609\pi$
$384$		0			0
$385$	−1.20155	+	20.9647i	−0.0612368	+	1.06846i
$386$	−3.83537	−	6.64306i	−0.195215	−	0.338123i
$387$		0			0
$388$	15.7000			0.797046
$389$	6.40570	+	11.0950i	0.324782	+	0.562538i	0.981468	−	0.191625i	$-0.0613758\pi$
$389$	6.40570	+	11.0950i	0.324782	+	0.562538i	−0.656686	+	0.754164i	$0.728042\pi$
$390$		0			0
$391$	−2.84524			−0.143890
$392$	4.16969	−	5.62260i	0.210601	−	0.283984i
$393$		0			0
$394$	14.1794			0.714346
$395$	7.75969	+	13.4402i	0.390433	+	0.676249i
$396$		0			0
$397$	−4.43529			−0.222601			−0.111300	−	0.993787i	$-0.535502\pi$
$397$	−4.43529			−0.222601			−0.111300	+	0.993787i	$0.535502\pi$
$398$	3.49202			0.175039
$399$		0			0
$400$	1.65139	−	2.86029i	0.0825694	−	0.143014i
$401$	11.5491	+	20.0036i	0.576735	+	0.998934i	0.995851	+	0.0910014i	$0.0290068\pi$
$401$	11.5491	+	20.0036i	0.576735	+	0.998934i	−0.419116	+	0.907933i	$0.637660\pi$
$402$		0			0
$403$	−0.428746	+	1.80015i	−0.0213573	+	0.0896719i
$404$	−8.19386	+	14.1922i	−0.407660	+	0.706087i
$405$		0			0
$406$	1.15033	−	0.579054i	0.0570899	−	0.0287380i
$407$	32.7860	+	56.7870i	1.62514	+	2.81483i
$408$		0			0
$409$	9.96772	−	17.2646i	0.492872	−	0.853680i	−0.507094	−	0.861891i	$-0.669280\pi$
$409$	9.96772	−	17.2646i	0.492872	−	0.853680i	0.999966	+	0.00821112i	$0.00261371\pi$
$410$	−6.27736	+	10.8727i	−0.310017	+	0.536965i
$411$		0			0
$412$	2.45785	+	4.25712i	0.121090	+	0.209733i
$413$	−1.38522	+	24.1693i	−0.0681622	+	1.18929i
$414$		0			0
$415$	−0.317071	+	0.549183i	−0.0155644	+	0.0269583i
$416$	−3.45522	+	1.03027i	−0.169406	+	0.0505129i
$417$		0			0
$418$	5.08936	+	8.81504i	0.248929	+	0.431157i
$419$	−3.23489	+	5.60299i	−0.158035	+	0.273724i	−0.934160	−	0.356855i	$-0.883849\pi$
$419$	−3.23489	+	5.60299i	−0.158035	+	0.273724i	0.776125	+	0.630579i	$0.217182\pi$
$420$		0			0
$421$	−6.65600			−0.324393			−0.162197	−	0.986758i	$-0.551858\pi$
$421$	−6.65600			−0.324393			−0.162197	+	0.986758i	$0.551858\pi$
$422$	−13.1222			−0.638778
$423$		0			0
$424$	6.24476	+	10.8162i	0.303272	+	0.525283i
$425$	11.5160			0.558608
$426$		0			0
$427$	5.28791	−	2.66183i	0.255900	−	0.128815i
$428$	4.87910			0.235840
$429$		0			0
$430$	−7.81707	−	13.5396i	−0.376973	−	0.652936i
$431$	−13.3299			−0.642078			−0.321039	−	0.947066i	$-0.604032\pi$
$431$	−13.3299			−0.642078			−0.321039	+	0.947066i	$0.604032\pi$
$432$		0			0
$433$	3.01693	+	5.22547i	0.144984	+	0.251120i	0.929367	−	0.369157i	$-0.120354\pi$
$433$	3.01693	+	5.22547i	0.144984	+	0.251120i	−0.784383	+	0.620277i	$0.787020\pi$
$434$	−0.0776979	+	1.35567i	−0.00372962	+	0.0650745i
$435$		0			0
$436$	11.0000			0.526804
$437$	−0.681677	−	1.18070i	−0.0326090	−	0.0564805i
$438$		0			0
$439$	−3.82662	−	6.62790i	−0.182635	−	0.316332i	0.760142	−	0.649757i	$-0.225129\pi$
$439$	−3.82662	−	6.62790i	−0.182635	−	0.316332i	−0.942777	+	0.333424i	$0.891796\pi$
$440$	3.96846	−	6.87357i	0.189189	−	0.327685i
$441$		0			0
$442$	−9.13478	−	8.63733i	−0.434497	−	0.410836i
$443$	−13.2991	+	23.0347i	−0.631859	+	1.09441i	0.355313	+	0.934747i	$0.384374\pi$
$443$	−13.2991	+	23.0347i	−0.631859	+	1.09441i	−0.987171	+	0.159664i	$0.948959\pi$
$444$		0			0
$445$	10.0313			0.475531
$446$	9.85749			0.466766
$447$		0			0
$448$	−2.36323	+	1.18960i	−0.111652	+	0.0562034i
$449$	0.721905	+	1.25038i	0.0340688	+	0.0590089i	0.882557	−	0.470205i	$-0.155820\pi$
$449$	0.721905	+	1.25038i	0.0340688	+	0.0590089i	−0.848488	+	0.529214i	$0.822487\pi$
$450$		0			0
$451$	29.3555	−	50.8452i	1.38230	−	2.39421i
$452$	−12.7366			−0.599079
$453$		0			0
$454$	6.35912			0.298448
$455$	9.04109	−	8.52679i	0.423853	−	0.399742i
$456$		0			0
$457$	11.6902	+	20.2480i	0.546843	+	0.947160i	0.998488	+	0.0549624i	$0.0175039\pi$
$457$	11.6902	+	20.2480i	0.546843	+	0.947160i	−0.451645	+	0.892198i	$0.649163\pi$
$458$	11.2153			0.524058
$459$		0			0
$460$	−0.531541	+	0.920656i	−0.0247832	+	0.0429258i
$461$	−4.69123	−	8.12544i	−0.218492	−	0.378440i	0.735855	−	0.677139i	$-0.236780\pi$
$461$	−4.69123	−	8.12544i	−0.218492	−	0.378440i	−0.954347	+	0.298700i	$0.903447\pi$
$462$		0			0
$463$	16.0637			0.746545			0.373272	−	0.927722i	$-0.378236\pi$
$463$	16.0637			0.746545			0.373272	+	0.927722i	$0.378236\pi$
$464$	−0.486762			−0.0225974
$465$		0			0
$466$	9.49689			0.439935
$467$	13.3195	−	23.0701i	0.616353	−	1.06756i	−0.373792	−	0.927512i	$-0.621943\pi$
$467$	13.3195	−	23.0701i	0.616353	−	1.06756i	0.990145	−	0.140043i	$-0.0447240\pi$
$468$		0			0
$469$	5.09369	−	2.56406i	0.235205	−	0.118398i
$470$	8.56446	−	14.8341i	0.395049	−	0.684245i
$471$		0			0
$472$	4.57507	−	7.92425i	0.210585	−	0.364743i
$473$	36.5558	+	63.3166i	1.68084	+	2.91130i
$474$		0			0
$475$	2.75905	+	4.77882i	0.126594	+	0.219267i
$476$	−7.71216	−	5.06213i	−0.353486	−	0.232022i
$477$		0			0
$478$	2.16357	+	3.74741i	0.0989593	+	0.171403i
$479$	−9.57529			−0.437506			−0.218753	−	0.975780i	$-0.570199\pi$
$479$	−9.57529			−0.437506			−0.218753	+	0.975780i	$0.570199\pi$
$480$		0			0
$481$	8.99119	−	37.7508i	0.409963	−	1.72129i
$482$	17.1603			0.781629
$483$		0			0
$484$	−13.0581	+	22.6174i	−0.593552	+	1.02806i
$485$	20.4536			0.928748
$486$		0			0
$487$	−14.1616	+	24.5286i	−0.641722	+	1.11150i	0.343326	+	0.939216i	$0.388447\pi$
$487$	−14.1616	+	24.5286i	−0.641722	+	1.11150i	−0.985048	+	0.172279i	$0.944887\pi$
$488$	−2.23758			−0.101290
$489$		0			0
$490$	5.43217	−	7.32499i	0.245401	−	0.330909i
$491$	16.2403	−	28.1291i	0.732916	−	1.26945i	−0.222716	−	0.974883i	$-0.571492\pi$
$491$	16.2403	−	28.1291i	0.732916	−	1.26945i	0.955632	−	0.294564i	$-0.0951745\pi$
$492$		0			0
$493$	−0.848612	−	1.46984i	−0.0382196	−	0.0661982i
$494$	1.39570	−	5.86005i	0.0627956	−	0.263656i
$495$		0			0
$496$	0.256619	−	0.444477i	0.0115225	−	0.0199576i
$497$	24.0689	+	15.7984i	1.07964	+	0.708656i
$498$		0			0
$499$	5.41650	−	9.38165i	0.242476	−	0.419980i	−0.718943	−	0.695069i	$-0.755374\pi$
$499$	5.41650	−	9.38165i	0.242476	−	0.419980i	0.961419	+	0.275089i	$0.0887072\pi$
$500$	5.40833	−	9.36750i	0.241868	−	0.418927i
$501$		0			0
$502$	−5.56308	+	9.63554i	−0.248293	+	0.430055i
$503$	−7.43429	−	12.8766i	−0.331478	−	0.574138i	0.651323	−	0.758800i	$-0.274214\pi$
$503$	−7.43429	−	12.8766i	−0.331478	−	0.574138i	−0.982802	+	0.184663i	$0.940881\pi$
$504$		0			0
$505$	−10.6748	+	18.4892i	−0.475020	+	0.822760i
$506$	2.48570	−	4.30537i	0.110503	−	0.191397i
$507$		0			0
$508$	−5.95554	−	10.3153i	−0.264234	−	0.457667i
$509$	9.84682	+	17.0552i	0.436452	+	0.755958i	0.997413	−	0.0718847i	$-0.0229014\pi$
$509$	9.84682	+	17.0552i	0.436452	+	0.755958i	−0.560960	+	0.827843i	$0.689568\pi$
$510$		0			0
$511$	−10.8026	−	7.09061i	−0.477877	−	0.313670i
$512$	1.00000			0.0441942
$513$		0			0
$514$	1.15213	−	1.99554i	0.0508181	−	0.0880195i
$515$	3.20203	+	5.54608i	0.141098	+	0.244389i
$516$		0			0
$517$	−40.0509	+	69.3702i	−1.76144	+	3.05090i
$518$	1.62940	−	28.4297i	0.0715916	−	1.24913i
$519$		0			0
$520$	−4.50138	+	1.34220i	−0.197398	+	0.0588596i
$521$	−16.9583	−	29.3726i	−0.742956	−	1.28684i	−0.951143	−	0.308749i	$-0.900090\pi$
$521$	−16.9583	−	29.3726i	−0.742956	−	1.28684i	0.208187	−	0.978089i	$-0.433244\pi$
$522$		0			0
$523$	−5.96634	−	10.3340i	−0.260890	−	0.451875i	0.705589	−	0.708622i	$-0.250683\pi$
$523$	−5.96634	−	10.3340i	−0.260890	−	0.451875i	−0.966479	+	0.256747i	$0.917349\pi$
$524$	−4.63340	−	8.02529i	−0.202411	−	0.350587i
$525$		0			0
$526$	−9.39720	−	16.2764i	−0.409738	−	0.709686i
$527$	1.78954			0.0779535
$528$		0			0
$529$	11.1671	−	19.3419i	0.485524	−	0.840953i
$530$	8.13552	+	14.0911i	0.353384	+	0.612080i
$531$		0			0
$532$	0.252931	−	4.41314i	0.0109660	−	0.191334i
$533$	−33.2976	+	9.92856i	−1.44228	+	0.430054i
$534$		0			0
$535$	6.35637			0.274810
$536$	−2.15540			−0.0930989
$537$		0			0
$538$	−27.6397			−1.19163
$539$	−25.4031	+	34.2547i	−1.09419	+	1.47545i
$540$		0			0
$541$	13.3341	−	23.0954i	0.573279	−	0.992948i	−0.422948	−	0.906154i	$-0.639005\pi$
$541$	13.3341	−	23.0954i	0.573279	−	0.992948i	0.996226	−	0.0867937i	$-0.0276621\pi$
$542$	5.87942	−	10.1834i	0.252543	−	0.437417i
$543$		0			0
$544$	1.74338	+	3.01962i	0.0747468	+	0.129465i
$545$	14.3305			0.613853
$546$		0			0
$547$	−19.9689			−0.853809			−0.426904	−	0.904297i	$-0.640396\pi$
$547$	−19.9689			−0.853809			−0.426904	+	0.904297i	$0.640396\pi$
$548$	5.15277	+	8.92485i	0.220115	+	0.381251i
$549$		0			0
$550$	−10.0608	+	17.4258i	−0.428993	+	0.743037i
$551$	0.406629	−	0.704302i	0.0173230	−	0.0300043i
$552$		0			0
$553$	−1.80342	+	31.4660i	−0.0766891	+	1.33807i
$554$	−29.0640			−1.23481
$555$		0			0
$556$	0.213218			0.00904245
$557$	−28.3395			−1.20078			−0.600392	−	0.799706i	$-0.704989\pi$
$557$	−28.3395			−1.20078			−0.600392	+	0.799706i	$0.704989\pi$
$558$		0			0
$559$	10.0250	−	42.0916i	0.424014	−	1.78028i
$560$	−3.07876	+	1.54979i	−0.130101	+	0.0654904i
$561$		0			0
$562$	−2.88153	−	4.99096i	−0.121550	−	0.210531i
$563$	−16.2164	+	28.0876i	−0.683439	+	1.18375i	0.290485	+	0.956880i	$0.406183\pi$
$563$	−16.2164	+	28.0876i	−0.683439	+	1.18375i	−0.973925	+	0.226872i	$0.927150\pi$
$564$		0			0
$565$	−16.5929			−0.698069
$566$	3.36060	+	5.82073i	0.141256	+	0.244663i
$567$		0			0
$568$	−5.44093	−	9.42396i	−0.228296	−	0.395421i
$569$	−12.4881	−	21.6301i	−0.523530	−	0.906781i	−0.999625	−	0.0273867i	$-0.991281\pi$
$569$	−12.4881	−	21.6301i	−0.523530	−	0.906781i	0.476095	−	0.879394i	$-0.342052\pi$
$570$		0			0
$571$	0.0710597	+	0.123079i	0.00297376	+	0.00515070i	0.867508	−	0.497422i	$-0.165720\pi$
$571$	0.0710597	+	0.123079i	0.00297376	+	0.00515070i	−0.864535	+	0.502573i	$0.832387\pi$
$572$	21.0503	−	6.27670i	0.880157	−	0.262442i
$573$		0			0
$574$	−22.7742	+	11.4641i	−0.950576	+	0.478501i
$575$	1.34755	−	2.33403i	0.0561969	−	0.0973359i
$576$		0			0
$577$	17.0033	+	29.4505i	0.707855	+	1.22604i	0.965651	+	0.259842i	$0.0836705\pi$
$577$	17.0033	+	29.4505i	0.707855	+	1.22604i	−0.257796	+	0.966199i	$0.582996\pi$
$578$	2.42124	−	4.19372i	0.100710	−	0.174436i
$579$		0			0
$580$	−0.634142			−0.0263313
$581$	−1.15033	+	0.579054i	−0.0477237	+	0.0240232i
$582$		0			0
$583$	−38.0450	−	65.8959i	−1.57566	−	2.72913i
$584$	2.44198	+	4.22964i	0.101050	+	0.175024i
$585$		0			0
$586$	−2.99769	+	5.19215i	−0.123833	+	0.214486i
$587$	−10.8444	+	18.7831i	−0.447598	+	0.775263i	−0.998229	−	0.0594859i	$-0.981054\pi$
$587$	−10.8444	+	18.7831i	−0.447598	+	0.775263i	0.550631	+	0.834749i	$0.314387\pi$
$588$		0			0
$589$	0.428746	+	0.742609i	0.0176662	+	0.0305987i
$590$	5.96029	−	10.3235i	0.245381	−	0.425013i
$591$		0			0
$592$	−5.38153	+	9.32109i	−0.221180	+	0.383094i
$593$	1.39002	−	2.40759i	0.0570814	−	0.0988679i	−0.836073	−	0.548619i	$-0.815154\pi$
$593$	1.39002	−	2.40759i	0.0570814	−	0.0988679i	0.893154	+	0.449751i	$0.148487\pi$
$594$		0			0
$595$	−10.0472	−	6.59482i	−0.411896	−	0.270361i
$596$	6.01673	−	10.4213i	0.246455	−	0.426872i
$597$		0			0
$598$	−2.81951	+	0.840710i	−0.115298	+	0.0343792i
$599$	8.54173	+	14.7947i	0.349006	+	0.604496i	0.986073	−	0.166313i	$-0.0531861\pi$
$599$	8.54173	+	14.7947i	0.349006	+	0.604496i	−0.637067	+	0.770808i	$0.719853\pi$
$600$		0			0
$601$	17.7386	−	30.7242i	0.723574	−	1.25327i	−0.235984	−	0.971757i	$-0.575831\pi$
$601$	17.7386	−	30.7242i	0.723574	−	1.25327i	0.959558	−	0.281510i	$-0.0908353\pi$
$602$	1.81675	−	31.6987i	0.0740452	−	1.29194i
$603$		0			0
$604$	−4.47939			−0.182264
$605$	−17.0118	+	29.4654i	−0.691629	+	1.19794i
$606$		0			0
$607$	−20.8892			−0.847868			−0.423934	−	0.905693i	$-0.639351\pi$
$607$	−20.8892			−0.847868			−0.423934	+	0.905693i	$0.639351\pi$
$608$	−0.835374	+	1.44691i	−0.0338789	+	0.0586800i
$609$		0			0
$610$	−2.91506			−0.118027
$611$	45.4293	−	13.5460i	1.83787	−	0.548011i
$612$		0			0
$613$	39.0667			1.57789			0.788945	−	0.614464i	$-0.210628\pi$
$613$	39.0667			1.57789			0.788945	+	0.614464i	$0.210628\pi$
$614$	−4.50170	−	7.79717i	−0.181674	−	0.314668i
$615$		0			0
$616$	14.3975	−	7.24743i	0.580093	−	0.292007i
$617$	−5.75569	−	9.96914i	−0.231715	−	0.401343i	0.726598	−	0.687063i	$-0.241100\pi$
$617$	−5.75569	−	9.96914i	−0.231715	−	0.401343i	−0.958313	+	0.285721i	$0.907767\pi$
$618$		0			0
$619$	−17.6738	−	30.6120i	−0.710371	−	1.23040i	−0.964718	−	0.263286i	$-0.915194\pi$
$619$	−17.6738	−	30.6120i	−0.710371	−	1.23040i	0.254347	−	0.967113i	$-0.418139\pi$
$620$	0.334317	−	0.579054i	0.0134265	−	0.0232554i
$621$		0			0
$622$	−7.31771	+	12.6746i	−0.293413	+	0.508207i
$623$	17.0311	+	11.1789i	0.682338	+	0.447875i
$624$		0			0
$625$	−1.21110	+	2.09769i	−0.0484441	+	0.0839076i
$626$	−3.45080			−0.137922
$627$		0			0
$628$	20.5717			0.820900
$629$	−37.5282			−1.49635
$630$		0			0
$631$	−13.8346	−	23.9623i	−0.550748	−	0.953924i	−0.998221	−	0.0596262i	$-0.981009\pi$
$631$	−13.8346	−	23.9623i	−0.550748	−	0.953924i	0.447473	−	0.894298i	$-0.352324\pi$
$632$	5.95628	−	10.3166i	0.236928	−	0.410371i
$633$		0			0
$634$	−13.3570			−0.530475
$635$	−7.75873	−	13.4385i	−0.307896	−	0.533291i
$636$		0			0
$637$	24.8521	−	4.40130i	0.984677	−	0.174386i
$638$	2.96551			0.117406
$639$		0			0
$640$	1.30278			0.0514967
$641$	15.0064	−	25.9919i	0.592719	−	1.02662i	−0.401146	−	0.916014i	$-0.631388\pi$
$641$	15.0064	−	25.9919i	0.592719	−	1.02662i	0.993864	−	0.110605i	$-0.0352788\pi$
$642$		0			0
$643$	17.4779	+	30.2725i	0.689259	+	1.19383i	0.972078	+	0.234659i	$0.0753972\pi$
$643$	17.4779	+	30.2725i	0.689259	+	1.19383i	−0.282819	+	0.959173i	$0.591269\pi$
$644$	−1.92843	+	0.970732i	−0.0759906	+	0.0382522i
$645$		0			0
$646$	−5.82550			−0.229201
$647$	−25.0653			−0.985419			−0.492710	−	0.870194i	$-0.663994\pi$
$647$	−25.0653			−0.985419			−0.492710	+	0.870194i	$0.663994\pi$
$648$		0			0
$649$	−27.8727	+	48.2770i	−1.09410	+	1.89504i
$650$	11.4118	−	3.40274i	0.447608	−	0.133466i
$651$		0			0
$652$	−5.25800	+	9.10712i	−0.205919	+	0.356662i
$653$	−0.0580833	−	0.100603i	−0.00227298	−	0.00393691i	0.864887	−	0.501967i	$-0.167390\pi$
$653$	−0.0580833	−	0.100603i	−0.00227298	−	0.00393691i	−0.867160	+	0.498030i	$0.834057\pi$
$654$		0			0
$655$	−6.03629	−	10.4552i	−0.235857	−	0.408517i
$656$	9.63690			0.376258
$657$		0			0
$658$	31.0718	−	15.6409i	1.21130	−	0.609747i
$659$	−6.83643	−	11.8410i	−0.266310	−	0.461262i	0.701596	−	0.712575i	$-0.252471\pi$
$659$	−6.83643	−	11.8410i	−0.266310	−	0.461262i	−0.967906	+	0.251313i	$0.919138\pi$
$660$		0			0
$661$	−50.9824			−1.98299			−0.991493	−	0.130157i	$-0.958452\pi$
$661$	−50.9824			−1.98299			−0.991493	+	0.130157i	$0.958452\pi$
$662$	1.71691	+	2.97377i	0.0667294	+	0.115579i
$663$		0			0
$664$	0.486762			0.0188900
$665$	0.329512	−	5.74934i	0.0127779	−	0.222950i
$666$		0			0
$667$	−0.397205			−0.0153798
$668$	3.45416	+	5.98279i	0.133646	+	0.231481i
$669$		0			0
$670$	−2.80800			−0.108482
$671$	13.6320			0.526259
$672$		0			0
$673$	17.2877	−	29.9432i	0.666394	−	1.15423i	−0.312512	−	0.949914i	$-0.601170\pi$
$673$	17.2877	−	29.9432i	0.666394	−	1.15423i	0.978905	−	0.204314i	$-0.0654962\pi$
$674$	3.08693	+	5.34672i	0.118904	+	0.205948i
$675$		0			0
$676$	−11.6043	−	5.86005i	−0.446319	−	0.225387i
$677$	−6.93750	+	12.0161i	−0.266630	+	0.461816i	−0.967989	−	0.250991i	$-0.919243\pi$
$677$	−6.93750	+	12.0161i	−0.266630	+	0.461816i	0.701360	+	0.712808i	$0.252577\pi$
$678$		0			0
$679$	34.7258	+	22.7935i	1.33266	+	0.874732i
$680$	2.27123	+	3.93389i	0.0870979	+	0.150858i
$681$		0			0
$682$	−1.56340	+	2.70789i	−0.0598658	+	0.103691i
$683$	5.42875	−	9.40286i	0.207725	−	0.359791i	−0.743272	−	0.668989i	$-0.766727\pi$
$683$	5.42875	−	9.40286i	0.207725	−	0.359791i	0.950998	+	0.309198i	$0.100061\pi$
$684$		0			0
$685$	6.71290	+	11.6271i	0.256487	+	0.444248i
$686$	17.3857	−	6.38268i	0.663788	−	0.243692i
$687$		0			0
$688$	−6.00032	+	10.3929i	−0.228760	+	0.396224i
$689$	−10.4334	+	43.8063i	−0.397482	+	1.66889i
$690$		0			0
$691$	−3.39201	−	5.87514i	−0.129038	−	0.223501i	0.794266	−	0.607570i	$-0.207856\pi$
$691$	−3.39201	−	5.87514i	−0.129038	−	0.223501i	−0.923304	+	0.384069i	$0.874522\pi$
$692$	2.69828	−	4.67356i	0.102573	−	0.177662i
$693$		0			0
$694$	0.144624			0.00548985
$695$	0.277775			0.0105366
$696$		0			0
$697$	16.8008	+	29.0998i	0.636375	+	1.10223i
$698$	−27.7584			−1.05067
$699$		0			0
$700$	7.80521	−	3.92899i	0.295009	−	0.148502i
$701$	−19.3000			−0.728952			−0.364476	−	0.931213i	$-0.618752\pi$
$701$	−19.3000			−0.728952			−0.364476	+	0.931213i	$0.618752\pi$
$702$		0			0
$703$	−8.99119	−	15.5732i	−0.339109	−	0.587354i
$704$	−6.09231			−0.229613
$705$		0			0
$706$	−0.483589	−	0.837601i	−0.0182001	−	0.0315235i
$707$	−38.7279	+	19.4949i	−1.45651	+	0.733180i
$708$		0			0
$709$	4.84524			0.181967			0.0909835	−	0.995852i	$-0.470999\pi$
$709$	4.84524			0.181967			0.0909835	+	0.995852i	$0.470999\pi$
$710$	−7.08831	−	12.2773i	−0.266019	−	0.460759i
$711$		0			0
$712$	−3.84999	−	6.66838i	−0.144284	−	0.249908i
$713$	0.209404	−	0.362699i	0.00784226	−	0.0135832i
$714$		0			0
$715$	27.4238	−	8.17713i	1.02559	−	0.305807i
$716$	−1.56151	+	2.70461i	−0.0583564	+	0.101076i
$717$		0			0
$718$	−15.1501			−0.565398
$719$	−11.3499			−0.423280			−0.211640	−	0.977348i	$-0.567880\pi$
$719$	−11.3499			−0.423280			−0.211640	+	0.977348i	$0.567880\pi$
$720$		0			0
$721$	−0.744177	+	12.9844i	−0.0277146	+	0.483565i
$722$	8.10430	+	14.0371i	0.301611	+	0.522405i
$723$		0			0
$724$	10.5486	−	18.2707i	0.392035	−	0.679025i
$725$	1.60767			0.0597072
$726$		0			0
$727$	−3.52009			−0.130553			−0.0652765	−	0.997867i	$-0.520793\pi$
$727$	−3.52009			−0.130553			−0.0652765	+	0.997867i	$0.520793\pi$
$728$	−9.13815	−	2.73756i	−0.338682	−	0.101461i
$729$		0			0
$730$	3.18136	+	5.51027i	0.117747	+	0.203944i
$731$	−41.8434			−1.54763
$732$		0			0
$733$	−11.7071	+	20.2773i	−0.432411	+	0.748959i	−0.997080	−	0.0763590i	$-0.975671\pi$
$733$	−11.7071	+	20.2773i	−0.432411	+	0.748959i	0.564669	+	0.825317i	$0.309004\pi$
$734$	2.41676	+	4.18595i	0.0892042	+	0.154506i
$735$		0			0
$736$	0.816013			0.0300787
$737$	13.1313			0.483699
$738$		0			0
$739$	−41.9994			−1.54497			−0.772487	−	0.635031i	$-0.780987\pi$
$739$	−41.9994			−1.54497			−0.772487	+	0.635031i	$0.780987\pi$
$740$	−7.01093	+	12.1433i	−0.257727	+	0.446396i
$741$		0			0
$742$	−1.89076	+	32.9900i	−0.0694120	+	1.21110i
$743$	3.47141	−	6.01266i	0.127354	−	0.220583i	−0.795297	−	0.606220i	$-0.792685\pi$
$743$	3.47141	−	6.01266i	0.127354	−	0.220583i	0.922651	+	0.385637i	$0.126018\pi$
$744$		0			0
$745$	7.83845	−	13.5766i	0.287179	−	0.497408i
$746$	−4.28078	−	7.41454i	−0.156731	−	0.271465i
$747$		0			0
$748$	−10.6212	−	18.3965i	−0.388350	−	0.672643i
$749$	10.7918	+	7.08354i	0.394323	+	0.258827i
$750$		0			0
$751$	−19.2663	−	33.3702i	−0.703037	−	1.21770i	−0.967395	−	0.253271i	$-0.918493\pi$
$751$	−19.2663	−	33.3702i	−0.703037	−	1.21770i	0.264358	−	0.964425i	$-0.414840\pi$
$752$	−13.1480			−0.479459
$753$		0			0
$754$	−1.27524	−	1.20580i	−0.0464416	−	0.0439125i
$755$	−5.83564			−0.212381
$756$		0			0
$757$	−16.9857	+	29.4201i	−0.617356	+	1.06929i	0.372610	+	0.927988i	$0.378463\pi$
$757$	−16.9857	+	29.4201i	−0.617356	+	1.06929i	−0.989966	+	0.141304i	$0.954871\pi$
$758$	32.6323			1.18526
$759$		0			0
$760$	−1.08831	+	1.88500i	−0.0394770	+	0.0683762i
$761$	10.7418			0.389392			0.194696	−	0.980864i	$-0.437628\pi$
$761$	10.7418			0.389392			0.194696	+	0.980864i	$0.437628\pi$
$762$		0			0
$763$	24.3302	+	15.9700i	0.880814	+	0.578151i
$764$	2.80415	−	4.85694i	0.101451	−	0.175718i
$765$		0			0
$766$	9.62196	+	16.6657i	0.347656	+	0.602157i
$767$	31.6157	−	9.42707i	1.14158	−	0.340392i
$768$		0			0
$769$	14.3203	−	24.8036i	0.516405	−	0.894439i	−0.483414	−	0.875392i	$-0.660603\pi$
$769$	14.3203	−	24.8036i	0.516405	−	0.894439i	0.999819	−	0.0190473i	$-0.00606331\pi$
$770$	18.7567	−	9.44178i	0.675946	−	0.340258i
$771$		0			0
$772$	−3.83537	+	6.64306i	−0.138038	+	0.239089i
$773$	23.7869	−	41.2001i	0.855556	−	1.48187i	−0.0205730	−	0.999788i	$-0.506549\pi$
$773$	23.7869	−	41.2001i	0.855556	−	1.48187i	0.876129	−	0.482077i	$-0.160118\pi$
$774$		0			0
$775$	−0.847555	+	1.46801i	−0.0304451	+	0.0527324i
$776$	−7.84999	−	13.5966i	−0.281798	−	0.488089i
$777$		0			0
$778$	6.40570	−	11.0950i	0.229655	−	0.397775i
$779$	−8.05042	+	13.9437i	−0.288436	+	0.499586i
$780$		0			0
$781$	33.1478	+	57.4137i	1.18612	+	2.05442i
$782$	1.42262	+	2.46405i	0.0508729	+	0.0881144i
$783$		0			0
$784$	−6.95416	−	0.799757i	−0.248363	−	0.0285627i
$785$	26.8003			0.956544
$786$		0			0
$787$	8.80015	−	15.2423i	0.313691	−	0.543329i	−0.665467	−	0.746427i	$-0.731768\pi$
$787$	8.80015	−	15.2423i	0.313691	−	0.543329i	0.979158	+	0.203098i	$0.0651010\pi$
$788$	−7.08968	−	12.2797i	−0.252560	−	0.437446i
$789$		0			0
$790$	7.75969	−	13.4402i	0.276078	−	0.478180i
$791$	−28.1713	−	18.4912i	−1.00166	−	0.657470i
$792$		0			0
$793$	−5.86211	−	5.54288i	−0.208170	−	0.196833i
$794$	2.21764	+	3.84107i	0.0787012	+	0.136314i
$795$		0			0
$796$	−1.74601	−	3.02418i	−0.0618857	−	0.107189i
$797$	6.78755	+	11.7564i	0.240427	+	0.416432i	0.960836	−	0.277117i	$-0.0893791\pi$
$797$	6.78755	+	11.7564i	0.240427	+	0.416432i	−0.720409	+	0.693550i	$0.756046\pi$
$798$		0			0
$799$	−22.9220	−	39.7021i	−0.810922	−	1.40456i
$800$	−3.30278			−0.116771
$801$		0			0
$802$	11.5491	−	20.0036i	0.407813	−	0.706353i
$803$	−14.8773	−	25.7683i	−0.525010	−	0.909343i
$804$		0			0
$805$	−2.51231	+	1.26465i	−0.0885471	+	0.0445729i
$806$	1.77335	−	0.528771i	0.0624636	−	0.0186252i
$807$		0			0
$808$	16.3877			0.576518
$809$	−22.4268			−0.788485			−0.394243	−	0.919006i	$-0.628993\pi$
$809$	−22.4268			−0.788485			−0.394243	+	0.919006i	$0.628993\pi$
$810$		0			0
$811$	21.9668			0.771358			0.385679	−	0.922633i	$-0.373967\pi$
$811$	21.9668			0.771358			0.385679	+	0.922633i	$0.373967\pi$
$812$	−1.07664	−	0.706688i	−0.0377827	−	0.0247999i
$813$		0			0
$814$	32.7860	−	56.7870i	1.14915	−	1.99038i
$815$	−6.84999	+	11.8645i	−0.239945	+	0.415596i
$816$		0			0
$817$	−10.0250	−	17.3639i	−0.350731	−	0.607485i
$818$	−19.9354			−0.697026
$819$		0			0
$820$	12.5547			0.438430
$821$	−14.9314	−	25.8619i	−0.521109	−	0.902587i	−0.999699	−	0.0245481i	$-0.992185\pi$
$821$	−14.9314	−	25.8619i	−0.521109	−	0.902587i	0.478590	−	0.878038i	$-0.341148\pi$
$822$		0			0
$823$	−10.4953	+	18.1783i	−0.365842	+	0.633656i	−0.988911	−	0.148510i	$-0.952552\pi$
$823$	−10.4953	+	18.1783i	−0.365842	+	0.633656i	0.623069	+	0.782167i	$0.285885\pi$
$824$	2.45785	−	4.25712i	0.0856233	−	0.148304i
$825$		0			0
$826$	21.6239	−	10.8850i	0.752390	−	0.378738i
$827$	−18.3637			−0.638570			−0.319285	−	0.947659i	$-0.603443\pi$
$827$	−18.3637			−0.638570			−0.319285	+	0.947659i	$0.603443\pi$
$828$		0			0
$829$	−10.5818			−0.367522			−0.183761	−	0.982971i	$-0.558827\pi$
$829$	−10.5818			−0.367522			−0.183761	+	0.982971i	$0.558827\pi$
$830$	0.634142			0.0220114
$831$		0			0
$832$	2.61985	+	2.47718i	0.0908268	+	0.0858806i
$833$	−9.70879	−	22.3932i	−0.336390	−	0.775880i
$834$		0			0
$835$	4.50000	+	7.79423i	0.155729	+	0.269730i
$836$	5.08936	−	8.81504i	0.176019	−	0.304874i
$837$		0			0
$838$	6.46978			0.223495
$839$	−21.7428	−	37.6596i	−0.750644	−	1.30015i	−0.947511	−	0.319723i	$-0.896410\pi$
$839$	−21.7428	−	37.6596i	−0.750644	−	1.30015i	0.196867	−	0.980430i	$-0.436923\pi$
$840$		0			0
$841$	14.3815	+	24.9095i	0.495915	+	0.858950i
$842$	3.32800	+	5.76426i	0.114690	+	0.198650i
$843$		0			0
$844$	6.56109	+	11.3641i	0.225842	+	0.391170i
$845$	−15.1178	−	7.63434i	−0.520068	−	0.262629i
$846$		0			0
$847$	−61.7187	+	31.0680i	−2.12068	+	1.06751i
$848$	6.24476	−	10.8162i	0.214446	−	0.371431i
$849$		0			0
$850$	−5.75800	−	9.97314i	−0.197498	−	0.342076i
$851$	−4.39140	+	7.60613i	−0.150535	+	0.260735i
$852$		0			0
$853$	−46.4055			−1.58889			−0.794447	−	0.607334i	$-0.792239\pi$
$853$	−46.4055			−1.58889			−0.794447	+	0.607334i	$0.792239\pi$
$854$	−4.94916	−	3.24855i	−0.169357	−	0.111163i
$855$		0			0
$856$	−2.43955	−	4.22542i	−0.0833820	−	0.144422i
$857$	−9.30499	−	16.1167i	−0.317852	−	0.550536i	0.662187	−	0.749338i	$-0.269628\pi$
$857$	−9.30499	−	16.1167i	−0.317852	−	0.550536i	−0.980040	+	0.198802i	$0.936295\pi$
$858$		0			0
$859$	−3.56395	+	6.17293i	−0.121600	+	0.210618i	−0.920399	−	0.390981i	$-0.872136\pi$
$859$	−3.56395	+	6.17293i	−0.121600	+	0.210618i	0.798799	+	0.601598i	$0.205469\pi$
$860$	−7.81707	+	13.5396i	−0.266560	+	0.461695i
$861$		0			0
$862$	6.66495	+	11.5440i	0.227009	+	0.393191i
$863$	0.989392	−	1.71368i	0.0336793	−	0.0583343i	−0.848694	−	0.528883i	$-0.822611\pi$
$863$	0.989392	−	1.71368i	0.0336793	−	0.0583343i	0.882374	+	0.470549i	$0.155944\pi$
$864$		0			0
$865$	3.51526	−	6.08860i	0.119522	−	0.207019i
$866$	3.01693	−	5.22547i	0.102519	−	0.177569i
$867$		0			0
$868$	1.21290	−	0.610549i	0.0411684	−	0.0207234i
$869$	−36.2875	+	62.8518i	−1.23097	+	2.13210i
$870$		0			0
$871$	−5.64681	−	5.33930i	−0.191335	−	0.180915i
$872$	−5.50000	−	9.52628i	−0.186254	−	0.322601i
$873$		0			0
$874$	−0.681677	+	1.18070i	−0.0230581	+	0.0399377i
$875$	25.5622	−	12.8675i	0.864161	−	0.435002i
$876$		0			0
$877$	−30.3024			−1.02324			−0.511619	−	0.859212i	$-0.670954\pi$
$877$	−30.3024			−1.02324			−0.511619	+	0.859212i	$0.670954\pi$
$878$	−3.82662	+	6.62790i	−0.129142	+	0.223681i
$879$		0			0
$880$	−7.93692			−0.267553
$881$	4.15581	−	7.19808i	0.140013	−	0.242509i	−0.787488	−	0.616330i	$-0.788619\pi$
$881$	4.15581	−	7.19808i	0.140013	−	0.242509i	0.927501	+	0.373820i	$0.121952\pi$
$882$		0			0
$883$	−48.4829			−1.63158			−0.815790	−	0.578348i	$-0.803698\pi$
$883$	−48.4829			−1.63158			−0.815790	+	0.578348i	$0.803698\pi$
$884$	−2.91275	+	12.2296i	−0.0979665	+	0.411327i
$885$		0			0
$886$	26.5982			0.893583
$887$	−6.95080	−	12.0391i	−0.233385	−	0.404234i	0.725417	−	0.688309i	$-0.241647\pi$
$887$	−6.95080	−	12.0391i	−0.233385	−	0.404234i	−0.958802	+	0.284075i	$0.908314\pi$
$888$		0			0
$889$	1.80319	−	31.4621i	0.0604771	−	1.05521i
$890$	−5.01567	−	8.68740i	−0.168126	−	0.291202i
$891$		0			0
$892$	−4.92875	−	8.53684i	−0.165027	−	0.285834i
$893$	10.9835	−	19.0240i	0.367549	−	0.636614i
$894$		0			0
$895$	−2.03430	+	3.52351i	−0.0679990	+	0.117778i
$896$	2.21184	+	1.45181i	0.0738924	+	0.0485017i
$897$		0			0
$898$	0.721905	−	1.25038i	0.0240903	−	0.0417256i
$899$	0.249825			0.00833212
$900$		0			0
$901$	43.5480			1.45079
$902$	−58.7110			−1.95486
$903$		0			0
$904$	6.36829	+	11.0302i	0.211806	+	0.366859i
$905$	13.7424	−	23.8026i	0.456814	−	0.791226i
$906$		0			0
$907$	35.4156			1.17596			0.587978	−	0.808877i	$-0.299924\pi$
$907$	35.4156			1.17596			0.587978	+	0.808877i	$0.299924\pi$
$908$	−3.17956	−	5.50716i	−0.105517	−	0.182762i
$909$		0			0
$910$	−11.9050	−	3.56642i	−0.394646	−	0.118226i
$911$	19.0938			0.632605			0.316303	−	0.948658i	$-0.397558\pi$
$911$	19.0938			0.632605			0.316303	+	0.948658i	$0.397558\pi$
$912$		0			0
$913$	−2.96551			−0.0981440
$914$	11.6902	−	20.2480i	0.386676	−	0.669743i
$915$		0			0
$916$	−5.60767	−	9.71276i	−0.185283	−	0.320919i
$917$	1.40288	−	24.4775i	0.0463272	−	0.808318i
$918$		0			0
$919$	−25.0309			−0.825693			−0.412847	−	0.910801i	$-0.635465\pi$
$919$	−25.0309			−0.825693			−0.412847	+	0.910801i	$0.635465\pi$
$920$	1.06308			0.0350488
$921$		0			0
$922$	−4.69123	+	8.12544i	−0.154497	+	0.267597i
$923$	9.09042	−	38.1675i	0.299215	−	1.25630i
$924$		0			0
$925$	17.7740	−	30.7855i	0.584405	−	1.01222i
$926$	−8.03186	−	13.9116i	−0.263943	−	0.457163i
$927$		0			0
$928$	0.243381	+	0.421549i	0.00798938	+	0.0138380i
$929$	−57.8169			−1.89691			−0.948456	−	0.316910i	$-0.897355\pi$
$929$	−57.8169			−1.89691			−0.948456	+	0.316910i	$0.897355\pi$
$930$		0			0
$931$	6.96651	−	9.39396i	0.228318	−	0.307875i
$932$	−4.74845	−	8.22455i	−0.155541	−	0.269404i
$933$		0			0
$934$	−26.6390			−0.871655
$935$	−13.8371	−	23.9665i	−0.452521	−	0.783789i
$936$		0			0
$937$	−18.2900			−0.597509			−0.298754	−	0.954330i	$-0.596571\pi$
$937$	−18.2900			−0.597509			−0.298754	+	0.954330i	$0.596571\pi$
$938$	−4.76739	−	3.12923i	−0.155661	−	0.102173i
$939$		0			0
$940$	−17.1289			−0.558684
$941$	−3.43923	−	5.95692i	−0.112116	−	0.194190i	0.804507	−	0.593943i	$-0.202429\pi$
$941$	−3.43923	−	5.95692i	−0.112116	−	0.194190i	−0.916623	+	0.399753i	$0.869096\pi$
$942$		0			0
$943$	7.86384			0.256082
$944$	−9.15014			−0.297812
$945$		0			0
$946$	36.5558	−	63.3166i	1.18853	−	2.05860i
$947$	−25.8534	−	44.7794i	−0.840122	−	1.45513i	−0.889791	−	0.456369i	$-0.849150\pi$
$947$	−25.8534	−	44.7794i	−0.840122	−	1.45513i	0.0496687	−	0.998766i	$-0.484183\pi$
$948$		0			0
$949$	−4.07994	+	17.1302i	−0.132440	+	0.556071i
$950$	2.75905	−	4.77882i	0.0895155	−	0.155045i
$951$		0			0
$952$	−0.527853	+	9.20999i	−0.0171078	+	0.298498i
$953$	6.62427	+	11.4736i	0.214581	+	0.371666i	0.953143	−	0.302520i	$-0.0978280\pi$
$953$	6.62427	+	11.4736i	0.214581	+	0.371666i	−0.738562	+	0.674186i	$0.764495\pi$
$954$		0			0
$955$	3.65318	−	6.32750i	0.118214	−	0.204753i
$956$	2.16357	−	3.74741i	0.0699748	−	0.121200i
$957$		0			0
$958$	4.78765	+	8.29244i	0.154682	+	0.267917i
$959$	−1.56013	+	27.2212i	−0.0503793	+	0.879018i
$960$		0			0
$961$	15.3683	−	26.6187i	0.495751	−	0.858667i
$962$	−37.1888	+	11.0888i	−1.19901	+	0.357518i
$963$		0			0
$964$	−8.58013	−	14.8612i	−0.276347	−	0.478648i
$965$	−4.99663	+	8.65442i	−0.160847	+	0.278596i
$966$		0			0
$967$	−7.83352			−0.251909			−0.125955	−	0.992036i	$-0.540199\pi$
$967$	−7.83352			−0.251909			−0.125955	+	0.992036i	$0.540199\pi$
$968$	26.1163			0.839409
$969$		0			0
$970$	−10.2268	−	17.7133i	−0.328362	−	0.568740i
$971$	−24.5268			−0.787101			−0.393551	−	0.919303i	$-0.628753\pi$
$971$	−24.5268			−0.787101			−0.393551	+	0.919303i	$0.628753\pi$
$972$		0			0
$973$	0.471604	+	0.309553i	0.0151189	+	0.00992380i
$974$	28.3232			0.907532
$975$		0			0
$976$	1.11879	+	1.93780i	0.0358116	+	0.0620274i
$977$	19.4975			0.623781			0.311891	−	0.950118i	$-0.399038\pi$
$977$	19.4975			0.623781			0.311891	+	0.950118i	$0.399038\pi$
$978$		0			0
$979$	23.4553	+	40.6259i	0.749636	+	1.29841i
$980$	−9.05971	−	1.04190i	−0.289402	−	0.0332824i
$981$		0			0
$982$	−32.4807			−1.03650
$983$	30.1235	+	52.1754i	0.960789	+	1.66414i	0.720526	+	0.693428i	$0.243901\pi$
$983$	30.1235	+	52.1754i	0.960789	+	1.66414i	0.240264	+	0.970708i	$0.422766\pi$
$984$		0			0
$985$	−9.23627	−	15.9977i	−0.294292	−	0.509729i
$986$	−0.848612	+	1.46984i	−0.0270253	+	0.0468092i
$987$		0			0
$988$	−5.77281	+	1.72131i	−0.183657	+	0.0547623i
$989$	−4.89634	+	8.48071i	−0.155695	+	0.269671i
$990$		0			0
$991$	29.5909			0.939987			0.469993	−	0.882670i	$-0.344256\pi$
$991$	29.5909			0.939987			0.469993	+	0.882670i	$0.344256\pi$
$992$	−0.513238			−0.0162953
$993$		0			0
$994$	1.64738	−	28.7435i	0.0522517	−	0.911689i
$995$	−2.27466	−	3.93983i	−0.0721116	−	0.124901i
$996$		0			0
$997$	−20.6532	+	35.7723i	−0.654092	+	1.13292i	0.328029	+	0.944668i	$0.393616\pi$
$997$	−20.6532	+	35.7723i	−0.654092	+	1.13292i	−0.982121	+	0.188253i	$0.939718\pi$
$998$	−10.8330			−0.342913
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.p.g.919.1		8
3.2	odd	2		546.2.k.d.373.3	yes	8
7.4	even	3		1638.2.m.i.1621.2		8
13.3	even	3		1638.2.m.i.289.2		8
21.11	odd	6		546.2.j.b.529.4	yes	8
39.29	odd	6		546.2.j.b.289.4	✓	8
91.81	even	3	inner	1638.2.p.g.991.1		8
273.263	odd	6		546.2.k.d.445.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.b.289.4	✓	8	39.29	odd	6
546.2.j.b.529.4	yes	8	21.11	odd	6
546.2.k.d.373.3	yes	8	3.2	odd	2
546.2.k.d.445.3	yes	8	273.263	odd	6
1638.2.m.i.289.2		8	13.3	even	3
1638.2.m.i.1621.2		8	7.4	even	3
1638.2.p.g.919.1		8	1.1	even	1	trivial
1638.2.p.g.991.1		8	91.81	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.p (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.651388 + 1.12824i) q^{5} +(-2.36323 + 1.18960i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.651388 + 1.12824i) q^{5} +(-2.36323 + 1.18960i) q^{7} +1.00000 q^{8} +1.30278 q^{10} -6.09231 q^{11} +(2.61985 + 2.47718i) q^{13} +(2.21184 + 1.45181i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.74338 - 3.01962i) q^{17} +1.67075 q^{19} +(-0.651388 - 1.12824i) q^{20} +(3.04616 + 5.27610i) q^{22} +(-0.408007 - 0.706688i) q^{23} +(1.65139 + 2.86029i) q^{25} +(0.835374 - 3.50744i) q^{26} +(0.151388 - 2.64142i) q^{28} +(0.243381 - 0.421549i) q^{29} +(0.256619 + 0.444477i) q^{31} +(-0.500000 + 0.866025i) q^{32} -3.48676 q^{34} +(0.197224 - 3.44117i) q^{35} +(-5.38153 - 9.32109i) q^{37} +(-0.835374 - 1.44691i) q^{38} +(-0.651388 + 1.12824i) q^{40} +(-4.81845 + 8.34580i) q^{41} +(-6.00032 - 10.3929i) q^{43} +(3.04616 - 5.27610i) q^{44} +(-0.408007 + 0.706688i) q^{46} +(6.57401 - 11.3865i) q^{47} +(4.16969 - 5.62260i) q^{49} +(1.65139 - 2.86029i) q^{50} +(-3.45522 + 1.03027i) q^{52} +(6.24476 + 10.8162i) q^{53} +(3.96846 - 6.87357i) q^{55} +(-2.36323 + 1.18960i) q^{56} -0.486762 q^{58} +(4.57507 - 7.92425i) q^{59} -2.23758 q^{61} +(0.256619 - 0.444477i) q^{62} +1.00000 q^{64} +(-4.50138 + 1.34220i) q^{65} -2.15540 q^{67} +(1.74338 + 3.01962i) q^{68} +(-3.07876 + 1.54979i) q^{70} +(-5.44093 - 9.42396i) q^{71} +(2.44198 + 4.22964i) q^{73} +(-5.38153 + 9.32109i) q^{74} +(-0.835374 + 1.44691i) q^{76} +(14.3975 - 7.24743i) q^{77} +(5.95628 - 10.3166i) q^{79} +1.30278 q^{80} +9.63690 q^{82} +0.486762 q^{83} +(2.27123 + 3.93389i) q^{85} +(-6.00032 + 10.3929i) q^{86} -6.09231 q^{88} +(-3.84999 - 6.66838i) q^{89} +(-9.13815 - 2.73756i) q^{91} +0.816013 q^{92} -13.1480 q^{94} +(-1.08831 + 1.88500i) q^{95} +(-7.84999 - 13.5966i) q^{97} +(-6.95416 - 0.799757i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 2 q^{5} + 3 q^{7} + 8 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 + 2 * q^5 + 3 * q^7 + 8 * q^8	\( 8 q - 4 q^{2} - 4 q^{4} + 2 q^{5} + 3 q^{7} + 8 q^{8} - 4 q^{10} - 4 q^{11} + 7 q^{13} + 3 q^{14} - 4 q^{16} + 6 q^{17} - 4 q^{19} + 2 q^{20} + 2 q^{22} - 4 q^{23} + 6 q^{25} - 2 q^{26} - 6 q^{28} - 6 q^{29} + 10 q^{31} - 4 q^{32} - 12 q^{34} + 16 q^{35} - 12 q^{37} + 2 q^{38} + 2 q^{40} + 6 q^{41} - 4 q^{43} + 2 q^{44} - 4 q^{46} + 17 q^{47} + 17 q^{49} + 6 q^{50} - 5 q^{52} - 3 q^{53} + 25 q^{55} + 3 q^{56} + 12 q^{58} + 8 q^{61} + 10 q^{62} + 8 q^{64} + 9 q^{65} + 14 q^{67} + 6 q^{68} - 8 q^{70} - 6 q^{71} - 19 q^{73} - 12 q^{74} + 2 q^{76} + 10 q^{77} + 24 q^{79} - 4 q^{80} - 12 q^{82} - 12 q^{83} - 3 q^{85} - 4 q^{86} - 4 q^{88} + 7 q^{89} - 50 q^{91} + 8 q^{92} - 34 q^{94} + 12 q^{95} - 25 q^{97} - 34 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 2 * q^5 + 3 * q^7 + 8 * q^8 - 4 * q^10 - 4 * q^11 + 7 * q^13 + 3 * q^14 - 4 * q^16 + 6 * q^17 - 4 * q^19 + 2 * q^20 + 2 * q^22 - 4 * q^23 + 6 * q^25 - 2 * q^26 - 6 * q^28 - 6 * q^29 + 10 * q^31 - 4 * q^32 - 12 * q^34 + 16 * q^35 - 12 * q^37 + 2 * q^38 + 2 * q^40 + 6 * q^41 - 4 * q^43 + 2 * q^44 - 4 * q^46 + 17 * q^47 + 17 * q^49 + 6 * q^50 - 5 * q^52 - 3 * q^53 + 25 * q^55 + 3 * q^56 + 12 * q^58 + 8 * q^61 + 10 * q^62 + 8 * q^64 + 9 * q^65 + 14 * q^67 + 6 * q^68 - 8 * q^70 - 6 * q^71 - 19 * q^73 - 12 * q^74 + 2 * q^76 + 10 * q^77 + 24 * q^79 - 4 * q^80 - 12 * q^82 - 12 * q^83 - 3 * q^85 - 4 * q^86 - 4 * q^88 + 7 * q^89 - 50 * q^91 + 8 * q^92 - 34 * q^94 + 12 * q^95 - 25 * q^97 - 34 * q^98

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