LMFDB - Embedded newform 1638.2.p.j.919.2

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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 15x^{8} + 14x^{7} + 110x^{6} + 36x^{5} + 233x^{4} + 164x^{3} + 345x^{2} + 76x + 16 $ x^10 - 2x^9 + 15x^8 + 14x^7 + 110x^6 + 36x^5 + 233x^4 + 164x^3 + 345x^2 + 76*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			919.2
Root			$-0.623307 - 1.07960i$ of defining polynomial
Character	$\chi$	$=$	1638.919
Dual form			1638.2.p.j.991.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.623307 + 1.07960i) q^{5} +(-2.27938 + 1.34329i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.623307 + 1.07960i) q^{5} +(-2.27938 + 1.34329i) q^{7} +1.00000 q^{8} +1.24661 q^{10} +2.49532 q^{11} +(-0.785103 + 3.51904i) q^{13} +(2.30301 + 1.30235i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.247662 - 0.428963i) q^{17} -7.67156 q^{19} +(-0.623307 - 1.07960i) q^{20} +(-1.24766 - 2.16101i) q^{22} +(0.224026 + 0.388024i) q^{23} +(1.72298 + 2.98428i) q^{25} +(3.44013 - 1.07960i) q^{26} +(-0.0236360 - 2.64565i) q^{28} +(3.71142 - 6.42837i) q^{29} +(-4.06448 - 7.03989i) q^{31} +(-0.500000 + 0.866025i) q^{32} -0.495324 q^{34} +(-0.0294650 - 3.29810i) q^{35} +(-1.37097 - 2.37459i) q^{37} +(3.83578 + 6.64376i) q^{38} +(-0.623307 + 1.07960i) q^{40} +(1.87097 - 3.24061i) q^{41} +(1.47532 + 2.55532i) q^{43} +(-1.24766 + 2.16101i) q^{44} +(0.224026 - 0.388024i) q^{46} +(-3.29729 + 5.71107i) q^{47} +(3.39113 - 6.12374i) q^{49} +(1.72298 - 2.98428i) q^{50} +(-2.65502 - 2.43944i) q^{52} +(-3.86750 - 6.69870i) q^{53} +(-1.55535 + 2.69395i) q^{55} +(-2.27938 + 1.34329i) q^{56} -7.42285 q^{58} +(-0.727653 + 1.26033i) q^{59} -4.19934 q^{61} +(-4.06448 + 7.03989i) q^{62} +1.00000 q^{64} +(-3.30979 - 3.04103i) q^{65} +0.0276094 q^{67} +(0.247662 + 0.428963i) q^{68} +(-2.84150 + 1.67457i) q^{70} +(-4.68884 - 8.12130i) q^{71} +(-5.07151 - 8.78412i) q^{73} +(-1.37097 + 2.37459i) q^{74} +(3.83578 - 6.64376i) q^{76} +(-5.68779 + 3.35195i) q^{77} +(-4.93545 + 8.54845i) q^{79} +1.24661 q^{80} -3.74194 q^{82} -7.42285 q^{83} +(0.308739 + 0.534751i) q^{85} +(1.47532 - 2.55532i) q^{86} +2.49532 q^{88} +(-5.74056 - 9.94294i) q^{89} +(-2.93755 - 9.07584i) q^{91} -0.448052 q^{92} +6.59458 q^{94} +(4.78173 - 8.28221i) q^{95} +(-0.509831 - 0.883054i) q^{97} +(-6.99888 + 0.125065i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 5 q^{4} + 2 q^{5} + 4 q^{7} + 10 q^{8}+O(q^{10}) $ 10 * q - 5 * q^2 - 5 * q^4 + 2 * q^5 + 4 * q^7 + 10 * q^8	$ 10 q - 5 q^{2} - 5 q^{4} + 2 q^{5} + 4 q^{7} + 10 q^{8} - 4 q^{10} + 12 q^{11} - 4 q^{13} - 2 q^{14} - 5 q^{16} - 4 q^{17} - 6 q^{19} + 2 q^{20} - 6 q^{22} - 6 q^{23} - q^{25} + 2 q^{26} - 2 q^{28} - 10 q^{31} - 5 q^{32} + 8 q^{34} + 2 q^{35} + q^{37} + 3 q^{38} + 2 q^{40} + 4 q^{41} + 3 q^{43} - 6 q^{44} - 6 q^{46} + 15 q^{47} - 20 q^{49} - q^{50} + 2 q^{52} + 17 q^{53} + 3 q^{55} + 4 q^{56} - 2 q^{59} - 22 q^{61} - 10 q^{62} + 10 q^{64} - 41 q^{65} + 2 q^{67} - 4 q^{68} - 16 q^{70} - 18 q^{71} + 12 q^{73} + q^{74} + 3 q^{76} - 18 q^{77} - 4 q^{79} - 4 q^{80} - 8 q^{82} + q^{85} + 3 q^{86} + 12 q^{88} - 7 q^{89} - 4 q^{91} + 12 q^{92} - 30 q^{94} - 24 q^{95} - 6 q^{97} + 16 q^{98}+O(q^{100}) $ 10 * q - 5 * q^2 - 5 * q^4 + 2 * q^5 + 4 * q^7 + 10 * q^8 - 4 * q^10 + 12 * q^11 - 4 * q^13 - 2 * q^14 - 5 * q^16 - 4 * q^17 - 6 * q^19 + 2 * q^20 - 6 * q^22 - 6 * q^23 - q^25 + 2 * q^26 - 2 * q^28 - 10 * q^31 - 5 * q^32 + 8 * q^34 + 2 * q^35 + q^37 + 3 * q^38 + 2 * q^40 + 4 * q^41 + 3 * q^43 - 6 * q^44 - 6 * q^46 + 15 * q^47 - 20 * q^49 - q^50 + 2 * q^52 + 17 * q^53 + 3 * q^55 + 4 * q^56 - 2 * q^59 - 22 * q^61 - 10 * q^62 + 10 * q^64 - 41 * q^65 + 2 * q^67 - 4 * q^68 - 16 * q^70 - 18 * q^71 + 12 * q^73 + q^74 + 3 * q^76 - 18 * q^77 - 4 * q^79 - 4 * q^80 - 8 * q^82 + q^85 + 3 * q^86 + 12 * q^88 - 7 * q^89 - 4 * q^91 + 12 * q^92 - 30 * q^94 - 24 * q^95 - 6 * q^97 + 16 * 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
$5$	−0.623307	+	1.07960i	−0.278751	+	0.482811i	−0.971075	−	0.238776i	$-0.923254\pi$
$5$	−0.623307	+	1.07960i	−0.278751	+	0.482811i	0.692323	+	0.721587i	$0.256587\pi$
$6$		0			0
$7$	−2.27938	+	1.34329i	−0.861524	+	0.507717i
$7$	−2.27938	+	1.34329i	−0.861524	+	0.507717i
$8$	1.00000			0.353553
$9$		0			0
$10$	1.24661			0.394214
$11$	2.49532			0.752369			0.376184	−	0.926545i	$-0.377236\pi$
$11$	2.49532			0.752369			0.376184	+	0.926545i	$0.377236\pi$
$12$		0			0
$13$	−0.785103	+	3.51904i	−0.217748	+	0.976005i
$13$	−0.785103	+	3.51904i	−0.217748	+	0.976005i
$14$	2.30301	+	1.30235i	0.615506	+	0.348069i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.247662	−	0.428963i	0.0600669	−	0.104039i	−0.834428	−	0.551117i	$-0.814202\pi$
$17$	0.247662	−	0.428963i	0.0600669	−	0.104039i	0.894495	+	0.447078i	$0.147535\pi$
$18$		0			0
$19$	−7.67156			−1.75998			−0.879988	−	0.474996i	$-0.842450\pi$
$19$	−7.67156			−1.75998			−0.879988	+	0.474996i	$0.842450\pi$
$20$	−0.623307	−	1.07960i	−0.139376	−	0.241406i
$21$		0			0
$22$	−1.24766	−	2.16101i	−0.266002	−	0.460730i
$23$	0.224026	+	0.388024i	0.0467127	+	0.0809087i	0.888436	−	0.459000i	$-0.151792\pi$
$23$	0.224026	+	0.388024i	0.0467127	+	0.0809087i	−0.841724	+	0.539909i	$0.818459\pi$
$24$		0			0
$25$	1.72298	+	2.98428i	0.344595	+	0.596857i
$26$	3.44013	−	1.07960i	0.674664	−	0.211727i
$27$		0			0
$28$	−0.0236360	−	2.64565i	−0.00446679	−	0.499980i
$29$	3.71142	−	6.42837i	0.689194	−	1.19372i	−0.282905	−	0.959148i	$-0.591298\pi$
$29$	3.71142	−	6.42837i	0.689194	−	1.19372i	0.972099	−	0.234571i	$-0.0753686\pi$
$30$		0			0
$31$	−4.06448	−	7.03989i	−0.730002	−	1.26440i	−0.956882	−	0.290478i	$-0.906186\pi$
$31$	−4.06448	−	7.03989i	−0.730002	−	1.26440i	0.226879	−	0.973923i	$-0.427148\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−0.495324			−0.0849474
$35$	−0.0294650	−	3.29810i	−0.00498050	−	0.557480i
$36$		0			0
$37$	−1.37097	−	2.37459i	−0.225386	−	0.390380i	0.731049	−	0.682325i	$-0.239031\pi$
$37$	−1.37097	−	2.37459i	−0.225386	−	0.390380i	−0.956435	+	0.291945i	$0.905698\pi$
$38$	3.83578	+	6.64376i	0.622246	+	1.07776i
$39$		0			0
$40$	−0.623307	+	1.07960i	−0.0985534	+	0.170700i
$41$	1.87097	−	3.24061i	0.292196	−	0.506099i	−0.682133	−	0.731229i	$-0.738947\pi$
$41$	1.87097	−	3.24061i	0.292196	−	0.506099i	0.974329	+	0.225130i	$0.0722806\pi$
$42$		0			0
$43$	1.47532	+	2.55532i	0.224983	+	0.389683i	0.956314	−	0.292340i	$-0.0944339\pi$
$43$	1.47532	+	2.55532i	0.224983	+	0.389683i	−0.731331	+	0.682023i	$0.761101\pi$
$44$	−1.24766	+	2.16101i	−0.188092	+	0.325785i
$45$		0			0
$46$	0.224026	−	0.388024i	0.0330308	−	0.0572111i
$47$	−3.29729	+	5.71107i	−0.480959	+	0.833046i	−0.999761	−	0.0218486i	$-0.993045\pi$
$47$	−3.29729	+	5.71107i	−0.480959	+	0.833046i	0.518802	+	0.854894i	$0.326378\pi$
$48$		0			0
$49$	3.39113	−	6.12374i	0.484447	−	0.874820i
$50$	1.72298	−	2.98428i	0.243666	−	0.422042i
$51$		0			0
$52$	−2.65502	−	2.43944i	−0.368185	−	0.338289i
$53$	−3.86750	−	6.69870i	−0.531241	−	0.920137i	−0.999335	−	0.0364583i	$-0.988392\pi$
$53$	−3.86750	−	6.69870i	−0.531241	−	0.920137i	0.468094	−	0.883679i	$-0.344941\pi$
$54$		0			0
$55$	−1.55535	+	2.69395i	−0.209724	+	0.363252i
$56$	−2.27938	+	1.34329i	−0.304595	+	0.179505i
$57$		0			0
$58$	−7.42285			−0.974668
$59$	−0.727653	+	1.26033i	−0.0947324	+	0.164081i	−0.909497	−	0.415711i	$-0.863533\pi$
$59$	−0.727653	+	1.26033i	−0.0947324	+	0.164081i	0.814764	+	0.579792i	$0.196866\pi$
$60$		0			0
$61$	−4.19934			−0.537671			−0.268835	−	0.963186i	$-0.586639\pi$
$61$	−4.19934			−0.537671			−0.268835	+	0.963186i	$0.586639\pi$
$62$	−4.06448	+	7.03989i	−0.516190	+	0.894067i
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.30979	−	3.04103i	−0.410529	−	0.377194i
$66$		0			0
$67$	0.0276094			0.00337303			0.00168652	−	0.999999i	$-0.499463\pi$
$67$	0.0276094			0.00337303			0.00168652	+	0.999999i	$0.499463\pi$
$68$	0.247662	+	0.428963i	0.0300334	+	0.0520194i
$69$		0			0
$70$	−2.84150	+	1.67457i	−0.339625	+	0.200149i
$71$	−4.68884	−	8.12130i	−0.556463	−	0.963821i	−0.997788	−	0.0664743i	$-0.978825\pi$
$71$	−4.68884	−	8.12130i	−0.556463	−	0.963821i	0.441326	−	0.897347i	$-0.354508\pi$
$72$		0			0
$73$	−5.07151	−	8.78412i	−0.593576	−	1.02810i	−0.993746	−	0.111663i	$-0.964382\pi$
$73$	−5.07151	−	8.78412i	−0.593576	−	1.02810i	0.400170	−	0.916441i	$-0.368951\pi$
$74$	−1.37097	+	2.37459i	−0.159372	+	0.276040i
$75$		0			0
$76$	3.83578	−	6.64376i	0.439994	−	0.762092i
$77$	−5.68779	+	3.35195i	−0.648184	+	0.381990i
$78$		0			0
$79$	−4.93545	+	8.54845i	−0.555282	+	0.961776i	0.442600	+	0.896719i	$0.354056\pi$
$79$	−4.93545	+	8.54845i	−0.555282	+	0.961776i	−0.997882	+	0.0650567i	$0.979277\pi$
$80$	1.24661			0.139376
$81$		0			0
$82$	−3.74194			−0.413228
$83$	−7.42285			−0.814763			−0.407382	−	0.913258i	$-0.633558\pi$
$83$	−7.42285			−0.814763			−0.407382	+	0.913258i	$0.633558\pi$
$84$		0			0
$85$	0.308739	+	0.534751i	0.0334874	+	0.0580019i
$86$	1.47532	−	2.55532i	0.159087	−	0.275547i
$87$		0			0
$88$	2.49532			0.266002
$89$	−5.74056	−	9.94294i	−0.608498	−	1.05395i	−0.991488	−	0.130197i	$-0.958439\pi$
$89$	−5.74056	−	9.94294i	−0.608498	−	1.05395i	0.382990	−	0.923753i	$-0.374894\pi$
$90$		0			0
$91$	−2.93755	−	9.07584i	−0.307939	−	0.951406i
$92$	−0.448052			−0.0467127
$93$		0			0
$94$	6.59458			0.680179
$95$	4.78173	−	8.28221i	0.490596	−	0.849736i
$96$		0			0
$97$	−0.509831	−	0.883054i	−0.0517655	−	0.0896605i	0.838982	−	0.544160i	$-0.183152\pi$
$97$	−0.509831	−	0.883054i	−0.0517655	−	0.0896605i	−0.890747	+	0.454499i	$0.849818\pi$
$98$	−6.99888	+	0.125065i	−0.706994	+	0.0126335i
$99$		0			0
$100$	−3.44595			−0.344595
$101$	−17.9425			−1.78535			−0.892675	−	0.450701i	$-0.851174\pi$
$101$	−17.9425			−1.78535			−0.892675	+	0.450701i	$0.851174\pi$
$102$		0			0
$103$	0.524685	−	0.908780i	0.0516987	−	0.0895448i	−0.839018	−	0.544104i	$-0.816870\pi$
$103$	0.524685	−	0.908780i	0.0516987	−	0.0895448i	0.890717	+	0.454559i	$0.150203\pi$
$104$	−0.785103	+	3.51904i	−0.0769857	+	0.345070i
$105$		0			0
$106$	−3.86750	+	6.69870i	−0.375644	+	0.650635i
$107$	−5.09152	−	8.81877i	−0.492216	−	0.852543i	0.507744	−	0.861508i	$-0.330480\pi$
$107$	−5.09152	−	8.81877i	−0.492216	−	0.852543i	−0.999960	+	0.00896501i	$0.997146\pi$
$108$		0			0
$109$	9.92285	+	17.1869i	0.950436	+	1.64620i	0.744482	+	0.667643i	$0.232697\pi$
$109$	9.92285	+	17.1869i	0.950436	+	1.64620i	0.205955	+	0.978562i	$0.433970\pi$
$110$	3.11070			0.296594
$111$		0			0
$112$	2.30301	+	1.30235i	0.217614	+	0.123061i
$113$	7.93440	+	13.7428i	0.746406	+	1.29281i	0.949535	+	0.313661i	$0.101555\pi$
$113$	7.93440	+	13.7428i	0.746406	+	1.29281i	−0.203129	+	0.979152i	$0.565111\pi$
$114$		0			0
$115$	−0.558548			−0.0520848
$116$	3.71142	+	6.42837i	0.344597	+	0.596860i
$117$		0			0
$118$	1.45531			0.133972
$119$	0.0117075	+	1.31045i	0.00107322	+	0.120129i
$120$		0			0
$121$	−4.77336			−0.433942
$122$	2.09967	+	3.63674i	0.190095	+	0.329255i
$123$		0			0
$124$	8.12896			0.730002
$125$	−10.5288			−0.941728
$126$		0			0
$127$	4.23846	−	7.34124i	0.376103	−	0.651429i	−0.614389	−	0.789004i	$-0.710597\pi$
$127$	4.23846	−	7.34124i	0.376103	−	0.651429i	0.990491	+	0.137574i	$0.0439306\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−0.978720	+	4.38688i	−0.0858394	+	0.384755i
$131$	8.26678	−	14.3185i	0.722272	−	1.25101i	−0.237816	−	0.971310i	$-0.576431\pi$
$131$	8.26678	−	14.3185i	0.722272	−	1.25101i	0.960087	−	0.279701i	$-0.0902353\pi$
$132$		0			0
$133$	17.4864	−	10.3051i	1.51626	−	0.893569i
$134$	−0.0138047	−	0.0239105i	−0.00119255	−	0.00206555i
$135$		0			0
$136$	0.247662	−	0.428963i	0.0212368	−	0.0367833i
$137$	−0.428418	+	0.742042i	−0.0366023	+	0.0633970i	−0.883746	−	0.467966i	$-0.844987\pi$
$137$	−0.428418	+	0.742042i	−0.0366023	+	0.0633970i	0.847144	+	0.531363i	$0.178320\pi$
$138$		0			0
$139$	4.74886	+	8.22528i	0.402793	+	0.697659i	0.994062	−	0.108816i	$-0.0347060\pi$
$139$	4.74886	+	8.22528i	0.402793	+	0.697659i	−0.591268	+	0.806475i	$0.701373\pi$
$140$	2.87097	+	1.62353i	0.242641	+	0.137213i
$141$		0			0
$142$	−4.68884	+	8.12130i	−0.393478	+	0.681525i
$143$	−1.95909	+	8.78114i	−0.163827	+	0.734315i
$144$		0			0
$145$	4.62671	+	8.01370i	0.384227	+	0.665501i
$146$	−5.07151	+	8.78412i	−0.419721	+	0.726979i
$147$		0			0
$148$	2.74194			0.225386
$149$	4.73744			0.388106			0.194053	−	0.980991i	$-0.437837\pi$
$149$	4.73744			0.388106			0.194053	+	0.980991i	$0.437837\pi$
$150$		0			0
$151$	−3.56085	−	6.16758i	−0.289778	−	0.501911i	0.683978	−	0.729502i	$-0.260248\pi$
$151$	−3.56085	−	6.16758i	−0.289778	−	0.501911i	−0.973757	+	0.227592i	$0.926915\pi$
$152$	−7.67156			−0.622246
$153$		0			0
$154$	5.74677	+	3.24979i	0.463088	+	0.261876i
$155$	10.1337			0.813956
$156$		0			0
$157$	−7.52147	−	13.0276i	−0.600279	−	1.03971i	−0.992779	−	0.119961i	$-0.961723\pi$
$157$	−7.52147	−	13.0276i	−0.600279	−	1.03971i	0.392500	−	0.919752i	$-0.371610\pi$
$158$	9.87090			0.785287
$159$		0			0
$160$	−0.623307	−	1.07960i	−0.0492767	−	0.0853498i
$161$	−1.03187	−	0.583522i	−0.0813228	−	0.0459880i
$162$		0			0
$163$	−9.02971			−0.707261			−0.353631	−	0.935385i	$-0.615053\pi$
$163$	−9.02971			−0.707261			−0.353631	+	0.935385i	$0.615053\pi$
$164$	1.87097	+	3.24061i	0.146098	+	0.253049i
$165$		0			0
$166$	3.71142	+	6.42837i	0.288062	+	0.498939i
$167$	−1.42442	+	2.46716i	−0.110225	+	0.190915i	−0.915861	−	0.401496i	$-0.868490\pi$
$167$	−1.42442	+	2.46716i	−0.110225	+	0.190915i	0.805636	+	0.592411i	$0.201824\pi$
$168$		0			0
$169$	−11.7672	−	5.52561i	−0.905171	−	0.425047i
$170$	0.308739	−	0.534751i	0.0236792	−	0.0410136i
$171$		0			0
$172$	−2.95063			−0.224983
$173$	25.4875			1.93778			0.968891	−	0.247487i	$-0.0796048\pi$
$173$	25.4875			1.93778			0.968891	+	0.247487i	$0.0796048\pi$
$174$		0			0
$175$	−7.93608	−	4.48785i	−0.599912	−	0.339250i
$176$	−1.24766	−	2.16101i	−0.0940461	−	0.162893i
$177$		0			0
$178$	−5.74056	+	9.94294i	−0.430273	+	0.745255i
$179$	−18.2006			−1.36038			−0.680189	−	0.733037i	$-0.738102\pi$
$179$	−18.2006			−1.36038			−0.680189	+	0.733037i	$0.738102\pi$
$180$		0			0
$181$	−13.7305			−1.02058			−0.510290	−	0.860003i	$-0.670462\pi$
$181$	−13.7305			−1.02058			−0.510290	+	0.860003i	$0.670462\pi$
$182$	−6.39113	+	7.08191i	−0.473742	+	0.524946i
$183$		0			0
$184$	0.224026	+	0.388024i	0.0165154	+	0.0286055i
$185$	3.41814			0.251306
$186$		0			0
$187$	0.617997	−	1.07040i	0.0451924	−	0.0782756i
$188$	−3.29729	−	5.71107i	−0.240480	−	0.416523i
$189$		0			0
$190$	−9.56347			−0.693807
$191$	−5.28588			−0.382473			−0.191236	−	0.981544i	$-0.561250\pi$
$191$	−5.28588			−0.382473			−0.191236	+	0.981544i	$0.561250\pi$
$192$		0			0
$193$	4.81197			0.346373			0.173187	−	0.984889i	$-0.444594\pi$
$193$	4.81197			0.346373			0.173187	+	0.984889i	$0.444594\pi$
$194$	−0.509831	+	0.883054i	−0.0366038	+	0.0633996i
$195$		0			0
$196$	3.60775	+	5.99868i	0.257696	+	0.428477i
$197$	−11.7743	+	20.3937i	−0.838883	+	1.45299i	0.0519458	+	0.998650i	$0.483458\pi$
$197$	−11.7743	+	20.3937i	−0.838883	+	1.45299i	−0.890829	+	0.454339i	$0.849876\pi$
$198$		0			0
$199$	−5.63984	+	9.76849i	−0.399798	+	0.692470i	−0.993701	−	0.112067i	$-0.964253\pi$
$199$	−5.63984	+	9.76849i	−0.399798	+	0.692470i	0.593903	+	0.804537i	$0.297586\pi$
$200$	1.72298	+	2.98428i	0.121833	+	0.211021i
$201$		0			0
$202$	8.97127	+	15.5387i	0.631217	+	1.09330i
$203$	0.175447	+	19.6382i	0.0123139	+	1.37833i
$204$		0			0
$205$	2.33237	+	4.03979i	0.162900	+	0.282151i
$206$	−1.04937			−0.0731130
$207$		0			0
$208$	3.44013	−	1.07960i	0.238530	−	0.0748567i
$209$	−19.1430			−1.32415
$210$		0			0
$211$	−6.22021	+	10.7737i	−0.428217	+	0.741693i	−0.996715	−	0.0809915i	$-0.974191\pi$
$211$	−6.22021	+	10.7737i	−0.428217	+	0.741693i	0.568498	+	0.822685i	$0.307525\pi$
$212$	7.73499			0.531241
$213$		0			0
$214$	−5.09152	+	8.81877i	−0.348049	+	0.602839i
$215$	−3.67830			−0.250858
$216$		0			0
$217$	18.7211	+	10.5868i	1.27087	+	0.718678i
$218$	9.92285	−	17.1869i	0.672060	−	1.16404i
$219$		0			0
$220$	−1.55535	−	2.69395i	−0.104862	−	0.181626i
$221$	1.31510	+	1.20831i	0.0884630	+	0.0812799i
$222$		0			0
$223$	−10.4651	+	18.1260i	−0.700793	+	1.21381i	0.267396	+	0.963587i	$0.413837\pi$
$223$	−10.4651	+	18.1260i	−0.700793	+	1.21381i	−0.968188	+	0.250222i	$0.919496\pi$
$224$	−0.0236360	−	2.64565i	−0.00157925	−	0.176770i
$225$		0			0
$226$	7.93440	−	13.7428i	0.527789	−	0.914157i
$227$	8.79052	−	15.2256i	0.583447	−	1.01056i	−0.411620	−	0.911356i	$-0.635037\pi$
$227$	8.79052	−	15.2256i	0.583447	−	1.01056i	0.995067	−	0.0992044i	$-0.0316298\pi$
$228$		0			0
$229$	7.24620	−	12.5508i	0.478842	−	0.829379i	−0.520863	−	0.853640i	$-0.674390\pi$
$229$	7.24620	−	12.5508i	0.478842	−	0.829379i	0.999706	+	0.0242609i	$0.00772324\pi$
$230$	0.279274	+	0.483717i	0.0184148	+	0.0318953i
$231$		0			0
$232$	3.71142	−	6.42837i	0.243667	−	0.422043i
$233$	7.24897	−	12.5556i	0.474896	−	0.822544i	−0.524691	−	0.851293i	$-0.675819\pi$
$233$	7.24897	−	12.5556i	0.474896	−	0.822544i	0.999587	+	0.0287492i	$0.00915242\pi$
$234$		0			0
$235$	−4.11045	−	7.11950i	−0.268136	−	0.464425i
$236$	−0.727653	−	1.26033i	−0.0473662	−	0.0820407i
$237$		0			0
$238$	1.12903	−	0.665365i	0.0731842	−	0.0431292i
$239$	−3.15093			−0.203817			−0.101908	−	0.994794i	$-0.532495\pi$
$239$	−3.15093			−0.203817			−0.101908	+	0.994794i	$0.532495\pi$
$240$		0			0
$241$	12.4223	−	21.5160i	0.800189	−	1.38597i	−0.119302	−	0.992858i	$-0.538066\pi$
$241$	12.4223	−	21.5160i	0.800189	−	1.38597i	0.919491	−	0.393111i	$-0.128601\pi$
$242$	2.38668	+	4.13385i	0.153422	+	0.265734i
$243$		0			0
$244$	2.09967	−	3.63674i	0.134418	−	0.232818i
$245$	4.49747	+	7.47803i	0.287333	+	0.477754i
$246$		0			0
$247$	6.02296	−	26.9965i	0.383232	−	1.71775i
$248$	−4.06448	−	7.03989i	−0.258095	−	0.447033i
$249$		0			0
$250$	5.26442	+	9.11824i	0.332951	+	0.576688i
$251$	3.69421	+	6.39857i	0.233177	+	0.403874i	0.958741	−	0.284280i	$-0.0917546\pi$
$251$	3.69421	+	6.39857i	0.233177	+	0.403874i	−0.725564	+	0.688154i	$0.758421\pi$
$252$		0			0
$253$	0.559018	+	0.968247i	0.0351451	+	0.0608732i
$254$	−8.47693			−0.531890
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	13.4446	+	23.2867i	0.838650	+	1.45258i	0.891024	+	0.453957i	$0.149988\pi$
$257$	13.4446	+	23.2867i	0.838650	+	1.45258i	−0.0523740	+	0.998628i	$0.516679\pi$
$258$		0			0
$259$	6.31472	+	3.57097i	0.392378	+	0.221889i
$260$	4.28851	−	1.34584i	0.265962	−	0.0834656i
$261$		0			0
$262$	−16.5336			−1.02145
$263$	2.93123			0.180748			0.0903738	−	0.995908i	$-0.471194\pi$
$263$	2.93123			0.180748			0.0903738	+	0.995908i	$0.471194\pi$
$264$		0			0
$265$	9.64254			0.592337
$266$	−17.6677	−	9.99108i	−1.08328	−	0.612592i
$267$		0			0
$268$	−0.0138047	+	0.0239105i	−0.000843258	+	0.00146056i
$269$	1.07222	−	1.85713i	0.0653741	−	0.113231i	−0.831486	−	0.555546i	$-0.812509\pi$
$269$	1.07222	−	1.85713i	0.0653741	−	0.113231i	0.896860	+	0.442315i	$0.145843\pi$
$270$		0			0
$271$	−8.64220	−	14.9687i	−0.524976	−	0.909285i	−0.999577	−	0.0290842i	$-0.990741\pi$
$271$	−8.64220	−	14.9687i	−0.524976	−	0.909285i	0.474601	−	0.880201i	$-0.342592\pi$
$272$	−0.495324			−0.0300334
$273$		0			0
$274$	0.856837			0.0517634
$275$	4.29939	+	7.44676i	0.259263	+	0.449056i
$276$		0			0
$277$	1.41690	−	2.45415i	0.0851336	−	0.147456i	−0.820315	−	0.571913i	$-0.806202\pi$
$277$	1.41690	−	2.45415i	0.0851336	−	0.147456i	0.905448	+	0.424457i	$0.139535\pi$
$278$	4.74886	−	8.22528i	0.284818	−	0.493319i
$279$		0			0
$280$	−0.0294650	−	3.29810i	−0.00176087	−	0.197099i
$281$	28.5254			1.70168			0.850842	−	0.525422i	$-0.176093\pi$
$281$	28.5254			1.70168			0.850842	+	0.525422i	$0.176093\pi$
$282$		0			0
$283$	−4.59802			−0.273324			−0.136662	−	0.990618i	$-0.543637\pi$
$283$	−4.59802			−0.273324			−0.136662	+	0.990618i	$0.543637\pi$
$284$	9.37767			0.556463
$285$		0			0
$286$	8.58423	−	2.69395i	0.507596	−	0.159297i
$287$	0.0884446	+	9.89984i	0.00522072	+	0.584369i
$288$		0			0
$289$	8.37733	+	14.5100i	0.492784	+	0.853527i
$290$	4.62671	−	8.01370i	0.271690	−	0.470581i
$291$		0			0
$292$	10.1430			0.593576
$293$	−3.19384	−	5.53189i	−0.186586	−	0.323177i	0.757524	−	0.652808i	$-0.226409\pi$
$293$	−3.19384	−	5.53189i	−0.186586	−	0.323177i	−0.944110	+	0.329631i	$0.893076\pi$
$294$		0			0
$295$	−0.907102	−	1.57115i	−0.0528135	−	0.0914757i
$296$	−1.37097	−	2.37459i	−0.0796859	−	0.138020i
$297$		0			0
$298$	−2.36872	−	4.10274i	−0.137216	−	0.237665i
$299$	−1.54136	+	0.483717i	−0.0891389	+	0.0279740i
$300$		0			0
$301$	−6.79535	−	3.84276i	−0.391677	−	0.221493i
$302$	−3.56085	+	6.16758i	−0.204904	+	0.354904i
$303$		0			0
$304$	3.83578	+	6.64376i	0.219997	+	0.381046i
$305$	2.61748	−	4.53360i	0.149876	−	0.259593i
$306$		0			0
$307$	−1.39899			−0.0798446			−0.0399223	−	0.999203i	$-0.512711\pi$
$307$	−1.39899			−0.0798446			−0.0399223	+	0.999203i	$0.512711\pi$
$308$	−0.0589796	−	6.60174i	−0.00336067	−	0.376169i
$309$		0			0
$310$	−5.06684	−	8.77602i	−0.287777	−	0.498444i
$311$	8.55183	+	14.8122i	0.484930	+	0.839923i	0.999850	−	0.0173150i	$-0.00551183\pi$
$311$	8.55183	+	14.8122i	0.484930	+	0.839923i	−0.514920	+	0.857238i	$0.672178\pi$
$312$		0			0
$313$	−5.81247	+	10.0675i	−0.328540	+	0.569048i	−0.982222	−	0.187721i	$-0.939890\pi$
$313$	−5.81247	+	10.0675i	−0.328540	+	0.569048i	0.653682	+	0.756769i	$0.273223\pi$
$314$	−7.52147	+	13.0276i	−0.424461	+	0.735188i
$315$		0			0
$316$	−4.93545	−	8.54845i	−0.277641	−	0.480888i
$317$	3.29277	−	5.70324i	0.184940	−	0.320326i	−0.758616	−	0.651538i	$-0.774124\pi$
$317$	3.29277	−	5.70324i	0.184940	−	0.320326i	0.943556	+	0.331212i	$0.107457\pi$
$318$		0			0
$319$	9.26121	−	16.0409i	0.518528	−	0.898117i
$320$	−0.623307	+	1.07960i	−0.0348439	+	0.0603514i
$321$		0			0
$322$	0.0105902	+	1.18539i	0.000590168	+	0.0660590i
$323$	−1.89995	+	3.29082i	−0.105716	+	0.183106i
$324$		0			0
$325$	−11.8545	+	3.72025i	−0.657570	+	0.206362i
$326$	4.51485	+	7.81996i	0.250055	+	0.433107i
$327$		0			0
$328$	1.87097	−	3.24061i	0.103307	−	0.178933i
$329$	−0.155870	−	17.4469i	−0.00859338	−	0.961880i
$330$		0			0
$331$	−23.2685			−1.27895			−0.639477	−	0.768810i	$-0.720849\pi$
$331$	−23.2685			−1.27895			−0.639477	+	0.768810i	$0.720849\pi$
$332$	3.71142	−	6.42837i	0.203691	−	0.352803i
$333$		0			0
$334$	2.84883			0.155881
$335$	−0.0172092	+	0.0298071i	−0.000940236	+	0.00162854i
$336$		0			0
$337$	19.4320			1.05853			0.529263	−	0.848458i	$-0.322468\pi$
$337$	19.4320			1.05853			0.529263	+	0.848458i	$0.322468\pi$
$338$	1.09829	+	12.9535i	0.0597394	+	0.704579i
$339$		0			0
$340$	−0.617478			−0.0334874
$341$	−10.1422	−	17.5668i	−0.549231	−	0.951296i
$342$		0			0
$343$	0.496304	+	18.5136i	0.0267979	+	0.999641i
$344$	1.47532	+	2.55532i	0.0795437	+	0.137774i
$345$		0			0
$346$	−12.7438	−	22.0729i	−0.685110	−	1.18664i
$347$	14.8354	−	25.6956i	0.796404	−	1.37941i	−0.125540	−	0.992089i	$-0.540066\pi$
$347$	14.8354	−	25.6956i	0.796404	−	1.37941i	0.921944	−	0.387324i	$-0.126600\pi$
$348$		0			0
$349$	−13.3023	+	23.0403i	−0.712058	+	1.23332i	0.252025	+	0.967721i	$0.418904\pi$
$349$	−13.3023	+	23.0403i	−0.712058	+	1.23332i	−0.964083	+	0.265600i	$0.914430\pi$
$350$	0.0814487	+	9.11678i	0.00435362	+	0.487312i
$351$		0			0
$352$	−1.24766	+	2.16101i	−0.0665006	+	0.115182i
$353$	13.8188			0.735499			0.367750	−	0.929925i	$-0.380128\pi$
$353$	13.8188			0.735499			0.367750	+	0.929925i	$0.380128\pi$
$354$		0			0
$355$	11.6903			0.620458
$356$	11.4811			0.608498
$357$		0			0
$358$	9.10030	+	15.7622i	0.480966	+	0.833058i
$359$	−1.38095	+	2.39188i	−0.0728840	+	0.126239i	−0.900164	−	0.435551i	$-0.856554\pi$
$359$	−1.38095	+	2.39188i	−0.0728840	+	0.126239i	0.827280	+	0.561790i	$0.189887\pi$
$360$		0			0
$361$	39.8528			2.09752
$362$	6.86524	+	11.8910i	0.360829	+	0.624975i
$363$		0			0
$364$	9.32868	+	1.99393i	0.488956	+	0.104510i
$365$	12.6444			0.661840
$366$		0			0
$367$	−10.9230			−0.570177			−0.285089	−	0.958501i	$-0.592023\pi$
$367$	−10.9230			−0.570177			−0.285089	+	0.958501i	$0.592023\pi$
$368$	0.224026	−	0.388024i	0.0116782	−	0.0202272i
$369$		0			0
$370$	−1.70907	−	2.96019i	−0.0888502	−	0.153893i
$371$	17.8138	+	10.0737i	0.924846	+	0.523000i
$372$		0			0
$373$	19.6861			1.01931			0.509653	−	0.860380i	$-0.329774\pi$
$373$	19.6861			1.01931			0.509653	+	0.860380i	$0.329774\pi$
$374$	−1.23599			−0.0639117
$375$		0			0
$376$	−3.29729	+	5.71107i	−0.170045	+	0.294526i
$377$	19.7078	+	18.1076i	1.01501	+	0.932587i
$378$		0			0
$379$	−8.31713	+	14.4057i	−0.427222	+	0.739970i	−0.996625	−	0.0820882i	$-0.973841\pi$
$379$	−8.31713	+	14.4057i	−0.427222	+	0.739970i	0.569403	+	0.822059i	$0.307174\pi$
$380$	4.78173	+	8.28221i	0.245298	+	0.424868i
$381$		0			0
$382$	2.64294	+	4.57771i	0.135225	+	0.234216i
$383$	−36.3667			−1.85825			−0.929127	−	0.369761i	$-0.879440\pi$
$383$	−36.3667			−1.85825			−0.929127	+	0.369761i	$0.879440\pi$
$384$		0			0
$385$	−0.0735247	−	8.22982i	−0.00374717	−	0.419431i
$386$	−2.40599	−	4.16729i	−0.122461	−	0.212109i
$387$		0			0
$388$	1.01966			0.0517655
$389$	−8.89008	−	15.3981i	−0.450745	−	0.780713i	0.547687	−	0.836683i	$-0.315508\pi$
$389$	−8.89008	−	15.3981i	−0.450745	−	0.780713i	−0.998432	+	0.0559696i	$0.982175\pi$
$390$		0			0
$391$	0.221931			0.0112235
$392$	3.39113	−	6.12374i	0.171278	−	0.309296i
$393$		0			0
$394$	23.5486			1.18636
$395$	−6.15260	−	10.6566i	−0.309571	−	0.536192i
$396$		0			0
$397$	8.87904			0.445626			0.222813	−	0.974861i	$-0.428476\pi$
$397$	8.87904			0.445626			0.222813	+	0.974861i	$0.428476\pi$
$398$	11.2797			0.565400
$399$		0			0
$400$	1.72298	−	2.98428i	0.0861489	−	0.149214i
$401$	−15.0815	−	26.1219i	−0.753134	−	1.30447i	−0.946297	−	0.323300i	$-0.895208\pi$
$401$	−15.0815	−	26.1219i	−0.753134	−	1.30447i	0.193163	−	0.981167i	$-0.438126\pi$
$402$		0			0
$403$	27.9647	−	8.77602i	1.39302	−	0.437165i
$404$	8.97127	−	15.5387i	0.446338	−	0.773079i
$405$		0			0
$406$	16.9195	−	9.97105i	0.839700	−	0.494855i
$407$	−3.42101	−	5.92537i	−0.169573	−	0.293709i
$408$		0			0
$409$	−8.38601	+	14.5250i	−0.414662	+	0.718215i	−0.995393	−	0.0958804i	$-0.969433\pi$
$409$	−8.38601	+	14.5250i	−0.414662	+	0.718215i	0.580731	+	0.814095i	$0.302767\pi$
$410$	2.33237	−	4.03979i	0.115188	−	0.199511i
$411$		0			0
$412$	0.524685	+	0.908780i	0.0258494	+	0.0447724i
$413$	−0.0343977	−	3.85023i	−0.00169260	−	0.189457i
$414$		0			0
$415$	4.62671	−	8.01370i	0.227116	−	0.393377i
$416$	−2.65502	−	2.43944i	−0.130173	−	0.119603i
$417$		0			0
$418$	9.57151	+	16.5783i	0.468158	+	0.810873i
$419$	19.8098	−	34.3115i	0.967770	−	1.67623i	0.265788	−	0.964031i	$-0.414368\pi$
$419$	19.8098	−	34.3115i	0.967770	−	1.67623i	0.701982	−	0.712195i	$-0.252299\pi$
$420$		0			0
$421$	−32.2271			−1.57065			−0.785326	−	0.619083i	$-0.787505\pi$
$421$	−32.2271			−1.57065			−0.785326	+	0.619083i	$0.787505\pi$
$422$	12.4404			0.605590
$423$		0			0
$424$	−3.86750	−	6.69870i	−0.187822	−	0.325318i
$425$	1.70686			0.0827951
$426$		0			0
$427$	9.57189	−	5.64094i	0.463216	−	0.272984i
$428$	10.1830			0.492216
$429$		0			0
$430$	1.83915	+	3.18550i	0.0886916	+	0.153618i
$431$	−11.0013			−0.529912			−0.264956	−	0.964260i	$-0.585358\pi$
$431$	−11.0013			−0.529912			−0.264956	+	0.964260i	$0.585358\pi$
$432$		0			0
$433$	15.9643	+	27.6509i	0.767193	+	1.32882i	0.939079	+	0.343701i	$0.111681\pi$
$433$	15.9643	+	27.6509i	0.767193	+	1.32882i	−0.171886	+	0.985117i	$0.554986\pi$
$434$	−0.192136	−	21.5064i	−0.00922285	−	1.03234i
$435$		0			0
$436$	−19.8457			−0.950436
$437$	−1.71863	−	2.97675i	−0.0822132	−	0.142397i
$438$		0			0
$439$	0.717628	+	1.24297i	0.0342505	+	0.0593236i	0.882643	−	0.470045i	$-0.155762\pi$
$439$	0.717628	+	1.24297i	0.0342505	+	0.0593236i	−0.848392	+	0.529368i	$0.822429\pi$
$440$	−1.55535	+	2.69395i	−0.0741485	+	0.128429i
$441$		0			0
$442$	0.388880	−	1.74306i	0.0184972	−	0.0829091i
$443$	−5.72758	+	9.92047i	−0.272126	+	0.471336i	−0.969406	−	0.245463i	$-0.921060\pi$
$443$	−5.72758	+	9.92047i	−0.272126	+	0.471336i	0.697280	+	0.716799i	$0.254393\pi$
$444$		0			0
$445$	14.3125			0.678479
$446$	20.9301			0.991071
$447$		0			0
$448$	−2.27938	+	1.34329i	−0.107691	+	0.0634646i
$449$	17.3713	+	30.0880i	0.819803	+	1.41994i	0.905827	+	0.423647i	$0.139250\pi$
$449$	17.3713	+	30.0880i	0.819803	+	1.41994i	−0.0860243	+	0.996293i	$0.527416\pi$
$450$		0			0
$451$	4.66867	−	8.08638i	0.219839	−	0.380773i
$452$	−15.8688			−0.746406
$453$		0			0
$454$	−17.5810			−0.825119
$455$	11.6293	+	2.48566i	0.545188	+	0.116529i
$456$		0			0
$457$	−18.4024	−	31.8739i	−0.860829	−	1.49100i	−0.871130	−	0.491053i	$-0.836612\pi$
$457$	−18.4024	−	31.8739i	−0.860829	−	1.49100i	0.0103007	−	0.999947i	$-0.496721\pi$
$458$	−14.4924			−0.677185
$459$		0			0
$460$	0.279274	−	0.483717i	0.0130212	−	0.0225534i
$461$	3.99129	+	6.91311i	0.185893	+	0.321976i	0.943877	−	0.330297i	$-0.107149\pi$
$461$	3.99129	+	6.91311i	0.185893	+	0.321976i	−0.757984	+	0.652273i	$0.773816\pi$
$462$		0			0
$463$	26.4799			1.23063			0.615314	−	0.788282i	$-0.289029\pi$
$463$	26.4799			1.23063			0.615314	+	0.788282i	$0.289029\pi$
$464$	−7.42285			−0.344597
$465$		0			0
$466$	−14.4979			−0.671604
$467$	3.12210	−	5.40764i	0.144474	−	0.250236i	−0.784703	−	0.619872i	$-0.787184\pi$
$467$	3.12210	−	5.40764i	0.144474	−	0.250236i	0.929176	+	0.369636i	$0.120518\pi$
$468$		0			0
$469$	−0.0629324	+	0.0370876i	−0.00290595	+	0.00171254i
$470$	−4.11045	+	7.11950i	−0.189601	+	0.328398i
$471$		0			0
$472$	−0.727653	+	1.26033i	−0.0334930	+	0.0580115i
$473$	3.68139	+	6.37635i	0.169270	+	0.293185i
$474$		0			0
$475$	−13.2179	−	22.8941i	−0.606480	−	1.05045i
$476$	−1.14074	−	0.645087i	−0.0522857	−	0.0295675i
$477$		0			0
$478$	1.57547	+	2.72879i	0.0720601	+	0.124812i
$479$	−21.5725			−0.985671			−0.492836	−	0.870122i	$-0.664040\pi$
$479$	−21.5725			−0.985671			−0.492836	+	0.870122i	$0.664040\pi$
$480$		0			0
$481$	9.43261	−	2.96019i	0.430090	−	0.134973i
$482$	−24.8446			−1.13164
$483$		0			0
$484$	2.38668	−	4.13385i	0.108485	−	0.187902i
$485$	1.27113			0.0577188
$486$		0			0
$487$	−6.80757	+	11.7911i	−0.308481	+	0.534304i	−0.978030	−	0.208463i	$-0.933154\pi$
$487$	−6.80757	+	11.7911i	−0.308481	+	0.534304i	0.669550	+	0.742767i	$0.266487\pi$
$488$	−4.19934			−0.190095
$489$		0			0
$490$	4.22743	−	7.63394i	0.190976	−	0.344866i
$491$	−6.14512	+	10.6437i	−0.277326	+	0.480342i	−0.970719	−	0.240217i	$-0.922781\pi$
$491$	−6.14512	+	10.6437i	−0.277326	+	0.480342i	0.693394	+	0.720559i	$0.256115\pi$
$492$		0			0
$493$	−1.83836	−	3.18413i	−0.0827955	−	0.143406i
$494$	−26.3911	+	8.28221i	−1.18739	+	0.372634i
$495$		0			0
$496$	−4.06448	+	7.03989i	−0.182501	+	0.316100i
$497$	21.5969	+	12.2130i	0.968754	+	0.547830i
$498$		0			0
$499$	−7.11789	+	12.3285i	−0.318640	+	0.551901i	−0.980205	−	0.197987i	$-0.936560\pi$
$499$	−7.11789	+	12.3285i	−0.318640	+	0.551901i	0.661564	+	0.749889i	$0.269893\pi$
$500$	5.26442	−	9.11824i	0.235432	−	0.407780i
$501$		0			0
$502$	3.69421	−	6.39857i	0.164881	−	0.285582i
$503$	−10.4692	−	18.1332i	−0.466798	−	0.808518i	0.532482	−	0.846441i	$-0.321259\pi$
$503$	−10.4692	−	18.1332i	−0.466798	−	0.808518i	−0.999281	+	0.0379227i	$0.987926\pi$
$504$		0			0
$505$	11.1837	−	19.3708i	0.497669	−	0.861987i
$506$	0.559018	−	0.968247i	0.0248514	−	0.0430438i
$507$		0			0
$508$	4.23846	+	7.34124i	0.188051	+	0.325715i
$509$	6.96485	+	12.0635i	0.308711	+	0.534704i	0.978081	−	0.208226i	$-0.0667689\pi$
$509$	6.96485	+	12.0635i	0.308711	+	0.534704i	−0.669369	+	0.742930i	$0.733436\pi$
$510$		0			0
$511$	23.3595	+	13.2098i	1.03336	+	0.584367i
$512$	1.00000			0.0441942
$513$		0			0
$514$	13.4446	−	23.2867i	0.593015	−	1.02713i
$515$	0.654079	+	1.13290i	0.0288222	+	0.0499214i
$516$		0			0
$517$	−8.22781	+	14.2510i	−0.361859	+	0.626757i
$518$	−0.0648086	−	7.25420i	−0.00284752	−	0.318731i
$519$		0			0
$520$	−3.30979	−	3.04103i	−0.145144	−	0.133358i
$521$	−11.1502	−	19.3128i	−0.488501	−	0.846109i	0.511412	−	0.859336i	$-0.329123\pi$
$521$	−11.1502	−	19.3128i	−0.488501	−	0.846109i	−0.999913	+	0.0132274i	$0.995789\pi$
$522$		0			0
$523$	13.8516	+	23.9917i	0.605689	+	1.04908i	0.991942	+	0.126691i	$0.0404357\pi$
$523$	13.8516	+	23.9917i	0.605689	+	1.04908i	−0.386254	+	0.922393i	$0.626231\pi$
$524$	8.26678	+	14.3185i	0.361136	+	0.625506i
$525$		0			0
$526$	−1.46562	−	2.53852i	−0.0639040	−	0.110685i
$527$	−4.02647			−0.175396
$528$		0			0
$529$	11.3996	−	19.7447i	0.495636	−	0.858466i
$530$	−4.82127	−	8.35069i	−0.209423	−	0.362731i
$531$		0			0
$532$	0.181325	+	20.2962i	0.00786145	+	0.879953i
$533$	9.93493	+	9.12822i	0.430330	+	0.395387i
$534$		0			0
$535$	12.6943			0.548823
$536$	0.0276094			0.00119255
$537$		0			0
$538$	−2.14443			−0.0924530
$539$	8.46197	−	15.2807i	0.364483	−	0.658187i
$540$		0			0
$541$	7.32108	−	12.6805i	0.314758	−	0.545177i	−0.664628	−	0.747174i	$-0.731410\pi$
$541$	7.32108	−	12.6805i	0.314758	−	0.545177i	0.979386	+	0.201998i	$0.0647434\pi$
$542$	−8.64220	+	14.9687i	−0.371214	+	0.642962i
$543$		0			0
$544$	0.247662	+	0.428963i	0.0106184	+	0.0183916i
$545$	−24.7399			−1.05974
$546$		0			0
$547$	21.7401			0.929542			0.464771	−	0.885431i	$-0.346137\pi$
$547$	21.7401			0.929542			0.464771	+	0.885431i	$0.346137\pi$
$548$	−0.428418	−	0.742042i	−0.0183011	−	0.0316985i
$549$		0			0
$550$	4.29939	−	7.44676i	0.183326	−	0.317531i
$551$	−28.4724	+	49.3157i	−1.21297	+	2.10092i
$552$		0			0
$553$	−0.233309	−	26.1149i	−0.00992131	−	1.11052i
$554$	−2.83381			−0.120397
$555$		0			0
$556$	−9.49773			−0.402793
$557$	−4.47177			−0.189475			−0.0947375	−	0.995502i	$-0.530201\pi$
$557$	−4.47177			−0.189475			−0.0947375	+	0.995502i	$0.530201\pi$
$558$		0			0
$559$	−10.1505	+	3.18550i	−0.429322	+	0.134732i
$560$	−2.84150	+	1.67457i	−0.120075	+	0.0707633i
$561$		0			0
$562$	−14.2627	−	24.7037i	−0.601636	−	1.04206i
$563$	−5.57899	+	9.66309i	−0.235126	+	0.407251i	−0.959309	−	0.282357i	$-0.908884\pi$
$563$	−5.57899	+	9.66309i	−0.235126	+	0.407251i	0.724183	+	0.689608i	$0.242217\pi$
$564$		0			0
$565$	−19.7823			−0.832246
$566$	2.29901	+	3.98201i	0.0966347	+	0.167376i
$567$		0			0
$568$	−4.68884	−	8.12130i	−0.196739	−	0.340762i
$569$	−18.4409	−	31.9406i	−0.773083	−	1.33902i	−0.935865	−	0.352358i	$-0.885380\pi$
$569$	−18.4409	−	31.9406i	−0.773083	−	1.33902i	0.162782	−	0.986662i	$-0.447953\pi$
$570$		0			0
$571$	0.101526	+	0.175849i	0.00424874	+	0.00735904i	0.868142	−	0.496316i	$-0.165314\pi$
$571$	0.101526	+	0.175849i	0.00424874	+	0.00735904i	−0.863893	+	0.503675i	$0.831981\pi$
$572$	−6.62514	−	6.08719i	−0.277011	−	0.254518i
$573$		0			0
$574$	8.52929	−	5.02652i	0.356006	−	0.209803i
$575$	−0.771984	+	1.33711i	−0.0321939	+	0.0557615i
$576$		0			0
$577$	10.4151	+	18.0396i	0.433588	+	0.750997i	0.997179	−	0.0750570i	$-0.0239139\pi$
$577$	10.4151	+	18.0396i	0.433588	+	0.750997i	−0.563591	+	0.826054i	$0.690581\pi$
$578$	8.37733	−	14.5100i	0.348451	−	0.603535i
$579$		0			0
$580$	−9.25342			−0.384227
$581$	16.9195	−	9.97105i	0.701938	−	0.413669i
$582$		0			0
$583$	−9.65066	−	16.7154i	−0.399689	−	0.692282i
$584$	−5.07151	−	8.78412i	−0.209861	−	0.363489i
$585$		0			0
$586$	−3.19384	+	5.53189i	−0.131936	+	0.228520i
$587$	8.25511	−	14.2983i	0.340725	−	0.590153i	−0.643843	−	0.765158i	$-0.722661\pi$
$587$	8.25511	−	14.2983i	0.340725	−	0.590153i	0.984568	+	0.175005i	$0.0559942\pi$
$588$		0			0
$589$	31.1809	+	54.0069i	1.28479	+	2.22532i
$590$	−0.907102	+	1.57115i	−0.0373448	+	0.0646831i
$591$		0			0
$592$	−1.37097	+	2.37459i	−0.0563465	+	0.0975950i
$593$	−5.86959	+	10.1664i	−0.241035	+	0.417485i	−0.961009	−	0.276515i	$-0.910820\pi$
$593$	−5.86959	+	10.1664i	−0.241035	+	0.417485i	0.719974	+	0.694001i	$0.244154\pi$
$594$		0			0
$595$	−1.42206	−	0.804174i	−0.0582988	−	0.0329679i
$596$	−2.36872	+	4.10274i	−0.0970264	+	0.168055i
$597$		0			0
$598$	1.18959	+	1.09299i	0.0486459	+	0.0446959i
$599$	21.8486	+	37.8430i	0.892711	+	1.54622i	0.836612	+	0.547796i	$0.184533\pi$
$599$	21.8486	+	37.8430i	0.892711	+	1.54622i	0.0560993	+	0.998425i	$0.482134\pi$
$600$		0			0
$601$	2.84613	−	4.92964i	0.116096	−	0.201084i	−0.802121	−	0.597161i	$-0.796295\pi$
$601$	2.84613	−	4.92964i	0.116096	−	0.201084i	0.918217	+	0.396077i	$0.129629\pi$
$602$	0.0697412	+	7.80632i	0.00284244	+	0.318162i
$603$		0			0
$604$	7.12171			0.289778
$605$	2.97527	−	5.15331i	0.120962	−	0.209512i
$606$		0			0
$607$	−25.0986			−1.01872			−0.509360	−	0.860553i	$-0.670118\pi$
$607$	−25.0986			−1.01872			−0.509360	+	0.860553i	$0.670118\pi$
$608$	3.83578	−	6.64376i	0.155561	−	0.269440i
$609$		0			0
$610$	−5.23496			−0.211957
$611$	−17.5088	−	16.0871i	−0.708329	−	0.650813i
$612$		0			0
$613$	2.59331			0.104743			0.0523715	−	0.998628i	$-0.483322\pi$
$613$	2.59331			0.104743			0.0523715	+	0.998628i	$0.483322\pi$
$614$	0.699495	+	1.21156i	0.0282293	+	0.0488947i
$615$		0			0
$616$	−5.68779	+	3.35195i	−0.229168	+	0.135054i
$617$	−8.83438	−	15.3016i	−0.355659	−	0.616019i	0.631572	−	0.775318i	$-0.282410\pi$
$617$	−8.83438	−	15.3016i	−0.355659	−	0.616019i	−0.987231	+	0.159298i	$0.949077\pi$
$618$		0			0
$619$	20.4642	+	35.4450i	0.822525	+	1.42465i	0.903797	+	0.427962i	$0.140768\pi$
$619$	20.4642	+	35.4450i	0.822525	+	1.42465i	−0.0812719	+	0.996692i	$0.525898\pi$
$620$	−5.06684	+	8.77602i	−0.203489	+	0.352453i
$621$		0			0
$622$	8.55183	−	14.8122i	0.342897	−	0.593915i
$623$	26.4412	+	14.9525i	1.05934	+	0.599058i
$624$		0			0
$625$	−2.05219	+	3.55450i	−0.0820876	+	0.142180i
$626$	11.6249			0.464626
$627$		0			0
$628$	15.0429			0.600279
$629$	−1.35815			−0.0541529
$630$		0			0
$631$	3.58097	+	6.20242i	0.142556	+	0.246914i	0.928459	−	0.371436i	$-0.121135\pi$
$631$	3.58097	+	6.20242i	0.142556	+	0.246914i	−0.785902	+	0.618351i	$0.787801\pi$
$632$	−4.93545	+	8.54845i	−0.196322	+	0.340039i
$633$		0			0
$634$	−6.58554			−0.261545
$635$	5.28373	+	9.15168i	0.209678	+	0.363173i
$636$		0			0
$637$	18.8873	+	16.7413i	0.748341	+	0.663314i
$638$	−18.5224			−0.733309
$639$		0			0
$640$	1.24661			0.0492767
$641$	1.62960	−	2.82254i	0.0643652	−	0.111484i	−0.832047	−	0.554705i	$-0.812831\pi$
$641$	1.62960	−	2.82254i	0.0643652	−	0.111484i	0.896412	+	0.443221i	$0.146164\pi$
$642$		0			0
$643$	−9.17027	−	15.8834i	−0.361640	−	0.626379i	0.626591	−	0.779348i	$-0.284450\pi$
$643$	−9.17027	−	15.8834i	−0.361640	−	0.626379i	−0.988231	+	0.152969i	$0.951116\pi$
$644$	1.02128	−	0.601865i	0.0402441	−	0.0237168i
$645$		0			0
$646$	3.79991			0.149505
$647$	−43.8685			−1.72465			−0.862325	−	0.506355i	$-0.830992\pi$
$647$	−43.8685			−1.72465			−0.862325	+	0.506355i	$0.830992\pi$
$648$		0			0
$649$	−1.81573	+	3.14494i	−0.0712737	+	0.123450i
$650$	9.14909	+	8.40619i	0.358857	+	0.329718i
$651$		0			0
$652$	4.51485	−	7.81996i	0.176815	−	0.306253i
$653$	6.64022	+	11.5012i	0.259852	+	0.450077i	0.966202	−	0.257786i	$-0.0829930\pi$
$653$	6.64022	+	11.5012i	0.259852	+	0.450077i	−0.706350	+	0.707863i	$0.749660\pi$
$654$		0			0
$655$	10.3055	+	17.8496i	0.402668	+	0.697442i
$656$	−3.74194			−0.146098
$657$		0			0
$658$	−15.0315	+	8.85845i	−0.585991	+	0.345338i
$659$	−1.53479	−	2.65834i	−0.0597871	−	0.103554i	0.834583	−	0.550883i	$-0.185709\pi$
$659$	−1.53479	−	2.65834i	−0.0597871	−	0.103554i	−0.894370	+	0.447328i	$0.852376\pi$
$660$		0			0
$661$	−29.6068			−1.15157			−0.575785	−	0.817601i	$-0.695304\pi$
$661$	−29.6068			−1.15157			−0.575785	+	0.817601i	$0.695304\pi$
$662$	11.6343	+	20.1512i	0.452179	+	0.783197i
$663$		0			0
$664$	−7.42285			−0.288062
$665$	0.226043	+	25.3015i	0.00876555	+	0.981152i
$666$		0			0
$667$	3.32582			0.128776
$668$	−1.42442	−	2.46716i	−0.0551123	−	0.0954573i
$669$		0			0
$670$	0.0344183			0.00132970
$671$	−10.4787			−0.404526
$672$		0			0
$673$	−4.54511	+	7.87235i	−0.175201	+	0.303457i	−0.940231	−	0.340538i	$-0.889391\pi$
$673$	−4.54511	+	7.87235i	−0.175201	+	0.303457i	0.765030	+	0.643995i	$0.222724\pi$
$674$	−9.71598	−	16.8286i	−0.374246	−	0.648212i
$675$		0			0
$676$	10.6689	−	7.42791i	0.410344	−	0.285689i
$677$	−8.92163	+	15.4527i	−0.342886	+	0.593896i	−0.984967	−	0.172741i	$-0.944738\pi$
$677$	−8.92163	+	15.4527i	−0.342886	+	0.593896i	0.642081	+	0.766636i	$0.278071\pi$
$678$		0			0
$679$	2.34830	+	1.32796i	0.0901194	+	0.0509625i
$680$	0.308739	+	0.534751i	0.0118396	+	0.0205068i
$681$		0			0
$682$	−10.1422	+	17.5668i	−0.388365	+	0.672668i
$683$	−6.15898	+	10.6677i	−0.235667	+	0.408187i	−0.959466	−	0.281824i	$-0.909061\pi$
$683$	−6.15898	+	10.6677i	−0.235667	+	0.408187i	0.723800	+	0.690010i	$0.242394\pi$
$684$		0			0
$685$	−0.534072	−	0.925040i	−0.0204058	−	0.0353440i
$686$	15.7851	−	9.68662i	0.602678	−	0.369837i
$687$		0			0
$688$	1.47532	−	2.55532i	0.0562459	−	0.0974207i
$689$	26.6093	−	8.35069i	1.01374	−	0.318136i
$690$		0			0
$691$	13.5881	+	23.5353i	0.516916	+	0.895325i	0.999807	+	0.0196447i	$0.00625351\pi$
$691$	13.5881	+	23.5353i	0.516916	+	0.895325i	−0.482891	+	0.875681i	$0.660413\pi$
$692$	−12.7438	+	22.0729i	−0.484446	+	0.839084i
$693$		0			0
$694$	−29.6707			−1.12629
$695$	−11.8400			−0.449117
$696$		0			0
$697$	−0.926736	−	1.60515i	−0.0351026	−	0.0607995i
$698$	26.6047			1.00700
$699$		0			0
$700$	7.85464	−	4.62892i	0.296877	−	0.174957i
$701$	−38.0704			−1.43790			−0.718950	−	0.695062i	$-0.755377\pi$
$701$	−38.0704			−1.43790			−0.718950	+	0.695062i	$0.755377\pi$
$702$		0			0
$703$	10.5175	+	18.2168i	0.396674	+	0.687059i
$704$	2.49532			0.0940461
$705$		0			0
$706$	−6.90939	−	11.9674i	−0.260038	−	0.450400i
$707$	40.8979	−	24.1021i	1.53812	−	0.906452i
$708$		0			0
$709$	−41.5249			−1.55950			−0.779750	−	0.626091i	$-0.784654\pi$
$709$	−41.5249			−1.55950			−0.779750	+	0.626091i	$0.784654\pi$
$710$	−5.84517	−	10.1241i	−0.219365	−	0.379952i
$711$		0			0
$712$	−5.74056	−	9.94294i	−0.215137	−	0.372628i
$713$	1.82110	−	3.15424i	0.0682007	−	0.118127i
$714$		0			0
$715$	−8.25899	−	7.58837i	−0.308869	−	0.283789i
$716$	9.10030	−	15.7622i	0.340094	−	0.589061i
$717$		0			0
$718$	2.76191			0.103074
$719$	−16.6093			−0.619421			−0.309710	−	0.950831i	$-0.600232\pi$
$719$	−16.6093			−0.619421			−0.309710	+	0.950831i	$0.600232\pi$
$720$		0			0
$721$	0.0248029	+	2.77626i	0.000923710	+	0.103393i
$722$	−19.9264	−	34.5135i	−0.741584	−	1.28446i
$723$		0			0
$724$	6.86524	−	11.8910i	0.255145	−	0.441924i
$725$	25.5788			0.949973
$726$		0			0
$727$	−20.2421			−0.750737			−0.375368	−	0.926876i	$-0.622484\pi$
$727$	−20.2421			−0.750737			−0.375368	+	0.926876i	$0.622484\pi$
$728$	−2.93755	−	9.07584i	−0.108873	−	0.336373i
$729$		0			0
$730$	−6.32222	−	10.9504i	−0.233996	−	0.405292i
$731$	1.46152			0.0540562
$732$		0			0
$733$	−8.42173	+	14.5869i	−0.311064	+	0.538778i	−0.978593	−	0.205805i	$-0.934019\pi$
$733$	−8.42173	+	14.5869i	−0.311064	+	0.538778i	0.667529	+	0.744584i	$0.267352\pi$
$734$	5.46151	+	9.45961i	0.201588	+	0.349161i
$735$		0			0
$736$	−0.448052			−0.0165154
$737$	0.0688945			0.00253776
$738$		0			0
$739$	−48.1193			−1.77010			−0.885049	−	0.465498i	$-0.845875\pi$
$739$	−48.1193			−1.77010			−0.885049	+	0.465498i	$0.845875\pi$
$740$	−1.70907	+	2.96019i	−0.0628266	+	0.108819i
$741$		0			0
$742$	−0.182825	−	20.4640i	−0.00671170	−	0.751259i
$743$	−2.98460	+	5.16948i	−0.109494	+	0.189650i	−0.915566	−	0.402169i	$-0.868256\pi$
$743$	−2.98460	+	5.16948i	−0.109494	+	0.189650i	0.806071	+	0.591819i	$0.201590\pi$
$744$		0			0
$745$	−2.95288	+	5.11453i	−0.108185	+	0.187382i
$746$	−9.84303	−	17.0486i	−0.360379	−	0.624195i
$747$		0			0
$748$	0.617997	+	1.07040i	0.0225962	+	0.0391378i
$749$	23.4517	+	13.2619i	0.856906	+	0.484580i
$750$		0			0
$751$	−18.1527	−	31.4414i	−0.662401	−	1.14731i	−0.979983	−	0.199081i	$-0.936204\pi$
$751$	−18.1527	−	31.4414i	−0.662401	−	1.14731i	0.317582	−	0.948231i	$-0.397129\pi$
$752$	6.59458			0.240480
$753$		0			0
$754$	5.82770	−	26.1213i	0.212232	−	0.951280i
$755$	8.87802			0.323104
$756$		0			0
$757$	−3.48399	+	6.03445i	−0.126628	+	0.219326i	−0.922368	−	0.386312i	$-0.873749\pi$
$757$	−3.48399	+	6.03445i	−0.126628	+	0.219326i	0.795740	+	0.605638i	$0.207082\pi$
$758$	16.6343			0.604183
$759$		0			0
$760$	4.78173	−	8.28221i	0.173452	−	0.300427i
$761$	2.95124			0.106982			0.0534912	−	0.998568i	$-0.482965\pi$
$761$	2.95124			0.106982			0.0534912	+	0.998568i	$0.482965\pi$
$762$		0			0
$763$	−45.7049	−	25.8461i	−1.65463	−	0.935692i
$764$	2.64294	−	4.57771i	0.0956182	−	0.165616i
$765$		0			0
$766$	18.1834	+	31.4945i	0.656992	+	1.13794i
$767$	−3.86387	−	3.55013i	−0.139516	−	0.128188i
$768$		0			0
$769$	−21.0168	+	36.4022i	−0.757885	+	1.31270i	0.186042	+	0.982542i	$0.440434\pi$
$769$	−21.0168	+	36.4022i	−0.757885	+	1.31270i	−0.943927	+	0.330154i	$0.892899\pi$
$770$	−7.09047	+	4.17859i	−0.255523	+	0.150586i
$771$		0			0
$772$	−2.40599	+	4.16729i	−0.0865933	+	0.149984i
$773$	−21.8155	+	37.7856i	−0.784650	+	1.35905i	0.144559	+	0.989496i	$0.453824\pi$
$773$	−21.8155	+	37.7856i	−0.784650	+	1.35905i	−0.929208	+	0.369557i	$0.879510\pi$
$774$		0			0
$775$	14.0060	−	24.2591i	0.503111	−	0.871414i
$776$	−0.509831	−	0.883054i	−0.0183019	−	0.0316998i
$777$		0			0
$778$	−8.89008	+	15.3981i	−0.318725	+	0.552048i
$779$	−14.3532	+	24.8606i	−0.514258	+	0.890722i
$780$		0			0
$781$	−11.7002	−	20.2653i	−0.418665	−	0.725149i
$782$	−0.110966	−	0.192198i	−0.00396812	−	0.00687298i
$783$		0			0
$784$	−6.99888	+	0.125065i	−0.249960	+	0.00446661i
$785$	18.7527			0.669314
$786$		0			0
$787$	−12.1660	+	21.0721i	−0.433671	+	0.751140i	−0.997186	−	0.0749659i	$-0.976115\pi$
$787$	−12.1660	+	21.0721i	−0.433671	+	0.751140i	0.563515	+	0.826106i	$0.309449\pi$
$788$	−11.7743	−	20.3937i	−0.419442	−	0.726494i
$789$		0			0
$790$	−6.15260	+	10.6566i	−0.218900	+	0.379145i
$791$	−36.5461	−	20.6668i	−1.29943	−	0.734826i
$792$		0			0
$793$	3.29691	−	14.7776i	0.117077	−	0.524769i
$794$	−4.43952	−	7.68948i	−0.157553	−	0.272889i
$795$		0			0
$796$	−5.63984	−	9.76849i	−0.199899	−	0.346235i
$797$	13.8223	+	23.9408i	0.489609	+	0.848028i	0.999929	−	0.0119569i	$-0.00380609\pi$
$797$	13.8223	+	23.9408i	0.489609	+	0.848028i	−0.510319	+	0.859985i	$0.670473\pi$
$798$		0			0
$799$	1.63323	+	2.82883i	0.0577794	+	0.100077i
$800$	−3.44595			−0.121833
$801$		0			0
$802$	−15.0815	+	26.1219i	−0.532546	+	0.922397i
$803$	−12.6551	−	21.9192i	−0.446588	−	0.773513i
$804$		0			0
$805$	1.27314	−	0.750293i	0.0448723	−	0.0264443i
$806$	−21.5826	−	19.8301i	−0.760214	−	0.698485i
$807$		0			0
$808$	−17.9425			−0.631217
$809$	46.7670			1.64424			0.822119	−	0.569315i	$-0.192792\pi$
$809$	46.7670			1.64424			0.822119	+	0.569315i	$0.192792\pi$
$810$		0			0
$811$	−33.4037			−1.17296			−0.586481	−	0.809963i	$-0.699487\pi$
$811$	−33.4037			−1.17296			−0.586481	+	0.809963i	$0.699487\pi$
$812$	−17.0949	−	9.66717i	−0.599914	−	0.339251i
$813$		0			0
$814$	−3.42101	+	5.92537i	−0.119906	+	0.207684i
$815$	5.62828	−	9.74846i	0.197150	−	0.341474i
$816$		0			0
$817$	−11.3180	−	19.6033i	−0.395966	−	0.685833i
$818$	16.7720			0.586420
$819$		0			0
$820$	−4.66475			−0.162900
$821$	18.7437	+	32.4651i	0.654160	+	1.13304i	0.982104	+	0.188342i	$0.0603112\pi$
$821$	18.7437	+	32.4651i	0.654160	+	1.13304i	−0.327943	+	0.944697i	$0.606355\pi$
$822$		0			0
$823$	24.8772	−	43.0886i	0.867166	−	1.50198i	0.00228512	−	0.999997i	$-0.499273\pi$
$823$	24.8772	−	43.0886i	0.867166	−	1.50198i	0.864881	−	0.501978i	$-0.167394\pi$
$824$	0.524685	−	0.908780i	0.0182783	−	0.0316589i
$825$		0			0
$826$	−3.31719	+	1.95490i	−0.115420	+	0.0680197i
$827$	−3.32250			−0.115534			−0.0577672	−	0.998330i	$-0.518398\pi$
$827$	−3.32250			−0.115534			−0.0577672	+	0.998330i	$0.518398\pi$
$828$		0			0
$829$	−16.5097			−0.573405			−0.286703	−	0.958020i	$-0.592559\pi$
$829$	−16.5097			−0.573405			−0.286703	+	0.958020i	$0.592559\pi$
$830$	−9.25342			−0.321191
$831$		0			0
$832$	−0.785103	+	3.51904i	−0.0272185	+	0.122001i
$833$	−1.78701	−	2.97129i	−0.0619161	−	0.102949i
$834$		0			0
$835$	−1.77570	−	3.07560i	−0.0614505	−	0.106435i
$836$	9.57151	−	16.5783i	0.331038	−	0.573374i
$837$		0			0
$838$	−39.6195			−1.36863
$839$	−8.35299	−	14.4678i	−0.288377	−	0.499484i	0.685045	−	0.728500i	$-0.259782\pi$
$839$	−8.35299	−	14.4678i	−0.288377	−	0.499484i	−0.973423	+	0.229016i	$0.926449\pi$
$840$		0			0
$841$	−13.0493	−	22.6021i	−0.449977	−	0.779383i
$842$	16.1135	+	27.9095i	0.555309	+	0.961824i
$843$		0			0
$844$	−6.22021	−	10.7737i	−0.214108	−	0.370847i
$845$	13.3000	−	9.25974i	0.457535	−	0.318545i
$846$		0			0
$847$	10.8803	−	6.41201i	0.373851	−	0.220319i
$848$	−3.86750	+	6.69870i	−0.132810	+	0.230034i
$849$		0			0
$850$	−0.853432	−	1.47819i	−0.0292725	−	0.0507014i
$851$	0.614265	−	1.06394i	0.0210567	−	0.0364714i
$852$		0			0
$853$	27.5476			0.943212			0.471606	−	0.881809i	$-0.343674\pi$
$853$	27.5476			0.943212			0.471606	+	0.881809i	$0.343674\pi$
$854$	−9.67114	−	5.46903i	−0.330940	−	0.187146i
$855$		0			0
$856$	−5.09152	−	8.81877i	−0.174025	−	0.301419i
$857$	9.17302	+	15.8881i	0.313344	+	0.542729i	0.979084	−	0.203455i	$-0.0652172\pi$
$857$	9.17302	+	15.8881i	0.313344	+	0.542729i	−0.665740	+	0.746184i	$0.731884\pi$
$858$		0			0
$859$	−21.5684	+	37.3575i	−0.735903	+	1.27462i	0.218423	+	0.975854i	$0.429909\pi$
$859$	−21.5684	+	37.3575i	−0.735903	+	1.27462i	−0.954326	+	0.298767i	$0.903425\pi$
$860$	1.83915	−	3.18550i	0.0627144	−	0.108625i
$861$		0			0
$862$	5.50063	+	9.52738i	0.187352	+	0.324504i
$863$	−22.5095	+	38.9876i	−0.766233	+	1.32715i	0.173359	+	0.984859i	$0.444538\pi$
$863$	−22.5095	+	38.9876i	−0.766233	+	1.32715i	−0.939592	+	0.342296i	$0.888796\pi$
$864$		0			0
$865$	−15.8866	+	27.5163i	−0.540159	+	0.935583i
$866$	15.9643	−	27.6509i	0.542488	−	0.939616i
$867$		0			0
$868$	−18.5290	+	10.9196i	−0.628915	+	0.370634i
$869$	−12.3155	+	21.3312i	−0.417776	+	0.723610i
$870$		0			0
$871$	−0.0216763	+	0.0971586i	−0.000734472	+	0.00329209i
$872$	9.92285	+	17.1869i	0.336030	+	0.582021i
$873$		0			0
$874$	−1.71863	+	2.97675i	−0.0581335	+	0.100690i
$875$	23.9992	−	14.1433i	0.811321	−	0.478131i
$876$		0			0
$877$	−21.8595			−0.738142			−0.369071	−	0.929401i	$-0.620324\pi$
$877$	−21.8595			−0.738142			−0.369071	+	0.929401i	$0.620324\pi$
$878$	0.717628	−	1.24297i	0.0242188	−	0.0419481i
$879$		0			0
$880$	3.11070			0.104862
$881$	−0.975574	+	1.68974i	−0.0328679	+	0.0569289i	−0.881991	−	0.471265i	$-0.843797\pi$
$881$	−0.975574	+	1.68974i	−0.0328679	+	0.0569289i	0.849124	+	0.528194i	$0.177131\pi$
$882$		0			0
$883$	−20.9397			−0.704677			−0.352338	−	0.935873i	$-0.614613\pi$
$883$	−20.9397			−0.704677			−0.352338	+	0.935873i	$0.614613\pi$
$884$	−1.70398	+	0.534751i	−0.0573110	+	0.0179856i
$885$		0			0
$886$	11.4552			0.384844
$887$	11.7886	+	20.4185i	0.395823	+	0.685586i	0.993206	−	0.116370i	$-0.0371260\pi$
$887$	11.7886	+	20.4185i	0.395823	+	0.685586i	−0.597383	+	0.801956i	$0.703793\pi$
$888$		0			0
$889$	0.200361	+	22.4270i	0.00671989	+	0.752176i
$890$	−7.15626	−	12.3950i	−0.239878	−	0.415482i
$891$		0			0
$892$	−10.4651	−	18.1260i	−0.350396	−	0.606904i
$893$	25.2954	−	43.8128i	0.846477	−	1.46614i
$894$		0			0
$895$	11.3446	−	19.6494i	0.379207	−	0.656806i
$896$	2.30301	+	1.30235i	0.0769383	+	0.0435086i
$897$		0			0
$898$	17.3713	−	30.0880i	0.579688	−	1.00405i
$899$	−60.3401			−2.01245
$900$		0			0
$901$	−3.83133			−0.127640
$902$	−9.33735			−0.310900
$903$		0			0
$904$	7.93440	+	13.7428i	0.263894	+	0.457078i
$905$	8.55831	−	14.8234i	0.284488	−	0.492747i
$906$		0			0
$907$	0.141508			0.00469870			0.00234935	−	0.999997i	$-0.499252\pi$
$907$	0.141508			0.00469870			0.00234935	+	0.999997i	$0.499252\pi$
$908$	8.79052	+	15.2256i	0.291724	+	0.505280i
$909$		0			0
$910$	−3.66199	−	11.3141i	−0.121394	−	0.375057i
$911$	−48.1769			−1.59617			−0.798086	−	0.602543i	$-0.794154\pi$
$911$	−48.1769			−1.59617			−0.798086	+	0.602543i	$0.794154\pi$
$912$		0			0
$913$	−18.5224			−0.613002
$914$	−18.4024	+	31.8739i	−0.608698	+	1.05430i
$915$		0			0
$916$	7.24620	+	12.5508i	0.239421	+	0.414690i
$917$	0.390788	+	43.7419i	0.0129049	+	1.44449i
$918$		0			0
$919$	39.6180			1.30688			0.653439	−	0.756980i	$-0.273326\pi$
$919$	39.6180			1.30688			0.653439	+	0.756980i	$0.273326\pi$
$920$	−0.558548			−0.0184148
$921$		0			0
$922$	3.99129	−	6.91311i	0.131446	−	0.227671i
$923$	32.2604	−	10.1241i	1.06186	−	0.333240i
$924$		0			0
$925$	4.72430	−	8.18272i	0.155334	−	0.269046i
$926$	−13.2400	−	22.9323i	−0.435093	−	0.753602i
$927$		0			0
$928$	3.71142	+	6.42837i	0.121833	+	0.211022i
$929$	−36.0334			−1.18222			−0.591109	−	0.806592i	$-0.701310\pi$
$929$	−36.0334			−1.18222			−0.591109	+	0.806592i	$0.701310\pi$
$930$		0			0
$931$	−26.0153	+	46.9787i	−0.852616	+	1.53966i
$932$	7.24897	+	12.5556i	0.237448	+	0.411272i
$933$		0			0
$934$	−6.24421			−0.204317
$935$	0.770404	+	1.33438i	0.0251949	+	0.0436388i
$936$		0			0
$937$	−2.37671			−0.0776439			−0.0388219	−	0.999246i	$-0.512361\pi$
$937$	−2.37671			−0.0776439			−0.0388219	+	0.999246i	$0.512361\pi$
$938$	0.0635849	+	0.0359573i	0.00207612	+	0.00117405i
$939$		0			0
$940$	8.22089			0.268136
$941$	19.3411	+	33.4998i	0.630503	+	1.09206i	0.987449	+	0.157938i	$0.0504846\pi$
$941$	19.3411	+	33.4998i	0.630503	+	1.09206i	−0.356946	+	0.934125i	$0.616182\pi$
$942$		0			0
$943$	1.67658			0.0545971
$944$	1.45531			0.0473662
$945$		0			0
$946$	3.68139	−	6.37635i	0.119692	−	0.207313i
$947$	−7.37320	−	12.7708i	−0.239597	−	0.414994i	0.721002	−	0.692933i	$-0.243682\pi$
$947$	−7.37320	−	12.7708i	−0.239597	−	0.414994i	−0.960599	+	0.277939i	$0.910349\pi$
$948$		0			0
$949$	34.8933	−	10.9504i	1.13268	−	0.355465i
$950$	−13.2179	+	22.8941i	−0.428846	+	0.742783i
$951$		0			0
$952$	0.0117075	+	1.31045i	0.000379442	+	0.0424720i
$953$	−8.54843	−	14.8063i	−0.276911	−	0.479623i	0.693705	−	0.720259i	$-0.255977\pi$
$953$	−8.54843	−	14.8063i	−0.276911	−	0.479623i	−0.970615	+	0.240636i	$0.922644\pi$
$954$		0			0
$955$	3.29473	−	5.70663i	0.106615	−	0.184662i
$956$	1.57547	−	2.72879i	0.0509542	−	0.0882553i
$957$		0			0
$958$	10.7862	+	18.6823i	0.348487	+	0.603598i
$959$	−0.0202522	−	2.26689i	−0.000653979	−	0.0732016i
$960$		0			0
$961$	−17.5400	+	30.3802i	−0.565807	+	0.980006i
$962$	−7.27991	−	6.68878i	−0.234714	−	0.215655i
$963$		0			0
$964$	12.4223	+	21.5160i	0.400095	+	0.692984i
$965$	−2.99933	+	5.19500i	−0.0965520	+	0.167233i
$966$		0			0
$967$	−7.90857			−0.254323			−0.127161	−	0.991882i	$-0.540587\pi$
$967$	−7.90857			−0.254323			−0.127161	+	0.991882i	$0.540587\pi$
$968$	−4.77336			−0.153422
$969$		0			0
$970$	−0.635563	−	1.10083i	−0.0204067	−	0.0353454i
$971$	−3.90099			−0.125189			−0.0625944	−	0.998039i	$-0.519937\pi$
$971$	−3.90099			−0.125189			−0.0625944	+	0.998039i	$0.519937\pi$
$972$		0			0
$973$	−21.8734	−	12.3694i	−0.701229	−	0.396545i
$974$	13.6151			0.436257
$975$		0			0
$976$	2.09967	+	3.63674i	0.0672088	+	0.116409i
$977$	51.3897			1.64410			0.822051	−	0.569414i	$-0.192830\pi$
$977$	51.3897			1.64410			0.822051	+	0.569414i	$0.192830\pi$
$978$		0			0
$979$	−14.3246	−	24.8109i	−0.457815	−	0.792959i
$980$	−8.72490	+	0.155908i	−0.278707	+	0.00498030i
$981$		0			0
$982$	12.2902			0.392198
$983$	−7.32146	−	12.6811i	−0.233518	−	0.404465i	0.725323	−	0.688409i	$-0.241690\pi$
$983$	−7.32146	−	12.6811i	−0.233518	−	0.404465i	−0.958841	+	0.283944i	$0.908357\pi$
$984$		0			0
$985$	−14.6780	−	25.4230i	−0.467680	−	0.810045i
$986$	−1.83836	+	3.18413i	−0.0585452	+	0.101403i
$987$		0			0
$988$	20.3682	+	18.7143i	0.647998	+	0.595381i
$989$	−0.661018	+	1.14492i	−0.0210192	+	0.0364062i
$990$		0			0
$991$	−22.5329			−0.715780			−0.357890	−	0.933764i	$-0.616504\pi$
$991$	−22.5329			−0.715780			−0.357890	+	0.933764i	$0.616504\pi$
$992$	8.12896			0.258095
$993$		0			0
$994$	−0.221651	−	24.8100i	−0.00703035	−	0.786925i
$995$	−7.03070	−	12.1775i	−0.222888	−	0.386054i
$996$		0			0
$997$	12.3016	−	21.3071i	0.389597	−	0.674801i	−0.602798	−	0.797893i	$-0.705948\pi$
$997$	12.3016	−	21.3071i	0.389597	−	0.674801i	0.992395	+	0.123092i	$0.0392810\pi$
$998$	14.2358			0.450626
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.p.j.919.2		10
3.2	odd	2		546.2.k.e.373.4	yes	10
7.4	even	3		1638.2.m.k.1621.2		10
13.3	even	3		1638.2.m.k.289.2		10
21.11	odd	6		546.2.j.e.529.4	yes	10
39.29	odd	6		546.2.j.e.289.4	✓	10
91.81	even	3	inner	1638.2.p.j.991.2		10
273.263	odd	6		546.2.k.e.445.4	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.e.289.4	✓	10	39.29	odd	6
546.2.j.e.529.4	yes	10	21.11	odd	6
546.2.k.e.373.4	yes	10	3.2	odd	2
546.2.k.e.445.4	yes	10	273.263	odd	6
1638.2.m.k.289.2		10	13.3	even	3
1638.2.m.k.1621.2		10	7.4	even	3
1638.2.p.j.919.2		10	1.1	even	1	trivial
1638.2.p.j.991.2		10	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.623307 + 1.07960i) q^{5} +(-2.27938 + 1.34329i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.623307 + 1.07960i) q^{5} +(-2.27938 + 1.34329i) q^{7} +1.00000 q^{8} +1.24661 q^{10} +2.49532 q^{11} +(-0.785103 + 3.51904i) q^{13} +(2.30301 + 1.30235i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.247662 - 0.428963i) q^{17} -7.67156 q^{19} +(-0.623307 - 1.07960i) q^{20} +(-1.24766 - 2.16101i) q^{22} +(0.224026 + 0.388024i) q^{23} +(1.72298 + 2.98428i) q^{25} +(3.44013 - 1.07960i) q^{26} +(-0.0236360 - 2.64565i) q^{28} +(3.71142 - 6.42837i) q^{29} +(-4.06448 - 7.03989i) q^{31} +(-0.500000 + 0.866025i) q^{32} -0.495324 q^{34} +(-0.0294650 - 3.29810i) q^{35} +(-1.37097 - 2.37459i) q^{37} +(3.83578 + 6.64376i) q^{38} +(-0.623307 + 1.07960i) q^{40} +(1.87097 - 3.24061i) q^{41} +(1.47532 + 2.55532i) q^{43} +(-1.24766 + 2.16101i) q^{44} +(0.224026 - 0.388024i) q^{46} +(-3.29729 + 5.71107i) q^{47} +(3.39113 - 6.12374i) q^{49} +(1.72298 - 2.98428i) q^{50} +(-2.65502 - 2.43944i) q^{52} +(-3.86750 - 6.69870i) q^{53} +(-1.55535 + 2.69395i) q^{55} +(-2.27938 + 1.34329i) q^{56} -7.42285 q^{58} +(-0.727653 + 1.26033i) q^{59} -4.19934 q^{61} +(-4.06448 + 7.03989i) q^{62} +1.00000 q^{64} +(-3.30979 - 3.04103i) q^{65} +0.0276094 q^{67} +(0.247662 + 0.428963i) q^{68} +(-2.84150 + 1.67457i) q^{70} +(-4.68884 - 8.12130i) q^{71} +(-5.07151 - 8.78412i) q^{73} +(-1.37097 + 2.37459i) q^{74} +(3.83578 - 6.64376i) q^{76} +(-5.68779 + 3.35195i) q^{77} +(-4.93545 + 8.54845i) q^{79} +1.24661 q^{80} -3.74194 q^{82} -7.42285 q^{83} +(0.308739 + 0.534751i) q^{85} +(1.47532 - 2.55532i) q^{86} +2.49532 q^{88} +(-5.74056 - 9.94294i) q^{89} +(-2.93755 - 9.07584i) q^{91} -0.448052 q^{92} +6.59458 q^{94} +(4.78173 - 8.28221i) q^{95} +(-0.509831 - 0.883054i) q^{97} +(-6.99888 + 0.125065i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 5 q^{4} + 2 q^{5} + 4 q^{7} + 10 q^{8}+O(q^{10}) \) 10 * q - 5 * q^2 - 5 * q^4 + 2 * q^5 + 4 * q^7 + 10 * q^8	\( 10 q - 5 q^{2} - 5 q^{4} + 2 q^{5} + 4 q^{7} + 10 q^{8} - 4 q^{10} + 12 q^{11} - 4 q^{13} - 2 q^{14} - 5 q^{16} - 4 q^{17} - 6 q^{19} + 2 q^{20} - 6 q^{22} - 6 q^{23} - q^{25} + 2 q^{26} - 2 q^{28} - 10 q^{31} - 5 q^{32} + 8 q^{34} + 2 q^{35} + q^{37} + 3 q^{38} + 2 q^{40} + 4 q^{41} + 3 q^{43} - 6 q^{44} - 6 q^{46} + 15 q^{47} - 20 q^{49} - q^{50} + 2 q^{52} + 17 q^{53} + 3 q^{55} + 4 q^{56} - 2 q^{59} - 22 q^{61} - 10 q^{62} + 10 q^{64} - 41 q^{65} + 2 q^{67} - 4 q^{68} - 16 q^{70} - 18 q^{71} + 12 q^{73} + q^{74} + 3 q^{76} - 18 q^{77} - 4 q^{79} - 4 q^{80} - 8 q^{82} + q^{85} + 3 q^{86} + 12 q^{88} - 7 q^{89} - 4 q^{91} + 12 q^{92} - 30 q^{94} - 24 q^{95} - 6 q^{97} + 16 q^{98}+O(q^{100}) \) 10 * q - 5 * q^2 - 5 * q^4 + 2 * q^5 + 4 * q^7 + 10 * q^8 - 4 * q^10 + 12 * q^11 - 4 * q^13 - 2 * q^14 - 5 * q^16 - 4 * q^17 - 6 * q^19 + 2 * q^20 - 6 * q^22 - 6 * q^23 - q^25 + 2 * q^26 - 2 * q^28 - 10 * q^31 - 5 * q^32 + 8 * q^34 + 2 * q^35 + q^37 + 3 * q^38 + 2 * q^40 + 4 * q^41 + 3 * q^43 - 6 * q^44 - 6 * q^46 + 15 * q^47 - 20 * q^49 - q^50 + 2 * q^52 + 17 * q^53 + 3 * q^55 + 4 * q^56 - 2 * q^59 - 22 * q^61 - 10 * q^62 + 10 * q^64 - 41 * q^65 + 2 * q^67 - 4 * q^68 - 16 * q^70 - 18 * q^71 + 12 * q^73 + q^74 + 3 * q^76 - 18 * q^77 - 4 * q^79 - 4 * q^80 - 8 * q^82 + q^85 + 3 * q^86 + 12 * q^88 - 7 * q^89 - 4 * q^91 + 12 * q^92 - 30 * q^94 - 24 * q^95 - 6 * q^97 + 16 * q^98

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