LMFDB - Embedded newform 1710.2.t.c.919.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(919,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1710.919");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 49 x^{16} - 8 x^{15} + 72 x^{13} + 2145 x^{12} - 648 x^{11} + 32 x^{10} - 7056 x^{9} + \cdots + 1024 $ x^20 - 49x^16 - 8x^15 + 72x^13 + 2145x^12 - 648x^11 + 32x^10 - 7056x^9 - 11968x^8 + 10368x^7 + 9344x^6 + 18176x^5 + 56320x^4 + 28160x^3 + 8192x^2 + 4096*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			919.1
Root			$0.320085 + 1.19457i$ of defining polynomial
Character	$\chi$	$=$	1710.919
Dual form			1710.2.t.c.1189.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.21950 + 0.271659i) q^{5} +4.03495i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.21950 + 0.271659i) q^{5} +4.03495i q^{7} +1.00000i q^{8} +(1.78632 - 1.34502i) q^{10} +1.47054 q^{11} +(4.38320 + 2.53064i) q^{13} +(-2.01747 - 3.49437i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.0812933 + 0.0469347i) q^{17} +(-4.00172 + 1.72807i) q^{19} +(-0.874489 + 2.05798i) q^{20} +(-1.27352 + 0.735269i) q^{22} +(-2.22178 - 1.28274i) q^{23} +(4.85240 - 1.20590i) q^{25} -5.06128 q^{26} +(3.49437 + 2.01747i) q^{28} +(-2.10491 + 3.64581i) q^{29} +4.26558 q^{31} +(0.866025 + 0.500000i) q^{32} +(0.0469347 - 0.0812933i) q^{34} +(-1.09613 - 8.95558i) q^{35} +1.53807i q^{37} +(2.60156 - 3.49741i) q^{38} +(-0.271659 - 2.21950i) q^{40} +(3.88123 + 6.72248i) q^{41} +(3.97202 - 2.29325i) q^{43} +(0.735269 - 1.27352i) q^{44} +2.56549 q^{46} +(3.49530 + 2.01801i) q^{47} -9.28080 q^{49} +(-3.59936 + 3.47054i) q^{50} +(4.38320 - 2.53064i) q^{52} +(-9.22964 - 5.32873i) q^{53} +(-3.26387 + 0.399485i) q^{55} -4.03495 q^{56} -4.20982i q^{58} +(3.07599 + 5.32777i) q^{59} +(0.653722 - 1.13228i) q^{61} +(-3.69410 + 2.13279i) q^{62} -1.00000 q^{64} +(-10.4160 - 4.42603i) q^{65} +(-9.31187 - 5.37621i) q^{67} +0.0938694i q^{68} +(5.42707 + 7.20770i) q^{70} +(-4.33806 - 7.51373i) q^{71} +(-11.0108 + 6.35711i) q^{73} +(-0.769037 - 1.33201i) q^{74} +(-0.504306 + 4.32963i) q^{76} +5.93355i q^{77} +(-6.48112 - 11.2256i) q^{79} +(1.34502 + 1.78632i) q^{80} +(-6.72248 - 3.88123i) q^{82} +2.06328i q^{83} +(0.167681 - 0.126256i) q^{85} +(-2.29325 + 3.97202i) q^{86} +1.47054i q^{88} +(0.813846 - 1.40962i) q^{89} +(-10.2110 + 17.6860i) q^{91} +(-2.22178 + 1.28274i) q^{92} -4.03603 q^{94} +(8.41239 - 4.92257i) q^{95} +(-10.3479 + 5.97438i) q^{97} +(8.03741 - 4.64040i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{4}+O(q^{10}) $ 20 * q + 10 * q^4	$ 20 q + 10 q^{4} - 2 q^{10} - 12 q^{11} - 10 q^{14} - 10 q^{16} + 6 q^{19} + 14 q^{25} - 8 q^{29} + 40 q^{31} + 12 q^{34} - 2 q^{35} + 2 q^{40} + 14 q^{41} - 6 q^{44} + 44 q^{46} - 8 q^{49} + 8 q^{50} - 20 q^{56} - 8 q^{59} + 16 q^{61} - 20 q^{64} - 40 q^{65} + 8 q^{70} + 4 q^{71} - 26 q^{74} + 8 q^{79} - 16 q^{85} + 20 q^{86} + 2 q^{89} - 44 q^{91} - 32 q^{94} + 80 q^{95}+O(q^{100}) $ 20 * q + 10 * q^4 - 2 * q^10 - 12 * q^11 - 10 * q^14 - 10 * q^16 + 6 * q^19 + 14 * q^25 - 8 * q^29 + 40 * q^31 + 12 * q^34 - 2 * q^35 + 2 * q^40 + 14 * q^41 - 6 * q^44 + 44 * q^46 - 8 * q^49 + 8 * q^50 - 20 * q^56 - 8 * q^59 + 16 * q^61 - 20 * q^64 - 40 * q^65 + 8 * q^70 + 4 * q^71 - 26 * q^74 + 8 * q^79 - 16 * q^85 + 20 * q^86 + 2 * q^89 - 44 * q^91 - 32 * q^94 + 80 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.21950	+	0.271659i	−0.992593	+	0.121490i
$5$	−2.21950	+	0.271659i	−0.992593	+	0.121490i
$6$		0			0
$7$			4.03495i			1.52507i	0.646949	+	0.762533i	$0.276045\pi$
$7$			4.03495i			1.52507i	−0.646949	+	0.762533i	$0.723955\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	1.78632	−	1.34502i	0.564883	−	0.425331i
$11$	1.47054			0.443384			0.221692	−	0.975117i	$-0.428842\pi$
$11$	1.47054			0.443384			0.221692	+	0.975117i	$0.428842\pi$
$12$		0			0
$13$	4.38320	+	2.53064i	1.21568	+	0.701874i	0.963991	−	0.265934i	$-0.0856805\pi$
$13$	4.38320	+	2.53064i	1.21568	+	0.701874i	0.251690	+	0.967808i	$0.419014\pi$
$14$	−2.01747	−	3.49437i	−0.539192	−	0.933909i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.0812933	+	0.0469347i	−0.0197165	+	0.0113833i	−0.509826	−	0.860278i	$-0.670290\pi$
$17$	−0.0812933	+	0.0469347i	−0.0197165	+	0.0113833i	0.490109	+	0.871661i	$0.336957\pi$
$18$		0			0
$19$	−4.00172	+	1.72807i	−0.918058	+	0.396447i
$19$	−4.00172	+	1.72807i	−0.918058	+	0.396447i
$20$	−0.874489	+	2.05798i	−0.195542	+	0.460178i
$21$		0			0
$22$	−1.27352	+	0.735269i	−0.271516	+	0.156760i
$23$	−2.22178	−	1.28274i	−0.463273	−	0.267471i	0.250147	−	0.968208i	$-0.419521\pi$
$23$	−2.22178	−	1.28274i	−0.463273	−	0.267471i	−0.713419	+	0.700737i	$0.752855\pi$
$24$		0			0
$25$	4.85240	−	1.20590i	0.970481	−	0.241179i
$26$	−5.06128			−0.992599
$27$		0			0
$28$	3.49437	+	2.01747i	0.660373	+	0.381267i
$29$	−2.10491	+	3.64581i	−0.390872	+	0.677011i	−0.992565	−	0.121717i	$-0.961160\pi$
$29$	−2.10491	+	3.64581i	−0.390872	+	0.677011i	0.601693	+	0.798728i	$0.294493\pi$
$30$		0			0
$31$	4.26558			0.766120			0.383060	−	0.923723i	$-0.374870\pi$
$31$	4.26558			0.766120			0.383060	+	0.923723i	$0.374870\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	0.0469347	−	0.0812933i	0.00804924	−	0.0139417i
$35$	−1.09613	−	8.95558i	−0.185280	−	1.51377i
$36$		0			0
$37$			1.53807i			0.252858i	0.991976	+	0.126429i	$0.0403515\pi$
$37$			1.53807i			0.252858i	−0.991976	+	0.126429i	$0.959648\pi$
$38$	2.60156	−	3.49741i	0.422028	−	0.567356i
$39$		0			0
$40$	−0.271659	−	2.21950i	−0.0429531	−	0.350935i
$41$	3.88123	+	6.72248i	0.606146	+	1.04987i	0.991869	+	0.127261i	$0.0406184\pi$
$41$	3.88123	+	6.72248i	0.606146	+	1.04987i	−0.385724	+	0.922614i	$0.626048\pi$
$42$		0			0
$43$	3.97202	−	2.29325i	0.605727	−	0.349717i	−0.165564	−	0.986199i	$-0.552944\pi$
$43$	3.97202	−	2.29325i	0.605727	−	0.349717i	0.771291	+	0.636482i	$0.219611\pi$
$44$	0.735269	−	1.27352i	0.110846	−	0.191991i
$45$		0			0
$46$	2.56549			0.378261
$47$	3.49530	+	2.01801i	0.509842	+	0.294358i	0.732769	−	0.680478i	$-0.238228\pi$
$47$	3.49530	+	2.01801i	0.509842	+	0.294358i	−0.222927	+	0.974835i	$0.571561\pi$
$48$		0			0
$49$	−9.28080			−1.32583
$50$	−3.59936	+	3.47054i	−0.509026	+	0.490808i
$51$		0			0
$52$	4.38320	−	2.53064i	0.607840	−	0.350937i
$53$	−9.22964	−	5.32873i	−1.26779	−	0.731958i	−0.293219	−	0.956045i	$-0.594727\pi$
$53$	−9.22964	−	5.32873i	−1.26779	−	0.731958i	−0.974569	+	0.224087i	$0.928060\pi$
$54$		0			0
$55$	−3.26387	+	0.399485i	−0.440100	+	0.0538666i
$56$	−4.03495			−0.539192
$57$		0			0
$58$		−	4.20982i		−	0.552777i
$59$	3.07599	+	5.32777i	0.400460	+	0.693617i	0.993781	−	0.111349i	$-0.0355170\pi$
$59$	3.07599	+	5.32777i	0.400460	+	0.693617i	−0.593321	+	0.804966i	$0.702184\pi$
$60$		0			0
$61$	0.653722	−	1.13228i	0.0837005	−	0.144974i	−0.821136	−	0.570732i	$-0.806659\pi$
$61$	0.653722	−	1.13228i	0.0837005	−	0.144974i	0.904837	+	0.425759i	$0.139993\pi$
$62$	−3.69410	+	2.13279i	−0.469151	+	0.270864i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−10.4160	−	4.42603i	−1.29195	−	0.548982i
$66$		0			0
$67$	−9.31187	−	5.37621i	−1.13763	−	0.656808i	−0.191784	−	0.981437i	$-0.561427\pi$
$67$	−9.31187	−	5.37621i	−1.13763	−	0.656808i	−0.945842	+	0.324629i	$0.894761\pi$
$68$			0.0938694i			0.0113833i
$69$		0			0
$70$	5.42707	+	7.20770i	0.648659	+	0.861485i
$71$	−4.33806	−	7.51373i	−0.514833	−	0.891716i	−0.999852	−	0.0172126i	$-0.994521\pi$
$71$	−4.33806	−	7.51373i	−0.514833	−	0.891716i	0.485019	−	0.874503i	$-0.338813\pi$
$72$		0			0
$73$	−11.0108	+	6.35711i	−1.28872	+	0.744044i	−0.978426	−	0.206596i	$-0.933761\pi$
$73$	−11.0108	+	6.35711i	−1.28872	+	0.744044i	−0.310296	+	0.950640i	$0.600428\pi$
$74$	−0.769037	−	1.33201i	−0.0893987	−	0.154843i
$75$		0			0
$76$	−0.504306	+	4.32963i	−0.0578479	+	0.496642i
$77$			5.93355i			0.676190i
$78$		0			0
$79$	−6.48112	−	11.2256i	−0.729183	−	1.26298i	−0.957229	−	0.289332i	$-0.906567\pi$
$79$	−6.48112	−	11.2256i	−0.729183	−	1.26298i	0.228046	−	0.973650i	$-0.426766\pi$
$80$	1.34502	+	1.78632i	0.150377	+	0.199716i
$81$		0			0
$82$	−6.72248	−	3.88123i	−0.742374	−	0.428610i
$83$			2.06328i			0.226475i	0.993568	+	0.113237i	$0.0361221\pi$
$83$			2.06328i			0.226475i	−0.993568	+	0.113237i	$0.963878\pi$
$84$		0			0
$85$	0.167681	−	0.126256i	0.0181875	−	0.0136944i
$86$	−2.29325	+	3.97202i	−0.247287	+	0.428314i
$87$		0			0
$88$			1.47054i			0.156760i
$89$	0.813846	−	1.40962i	0.0862675	−	0.149420i	−0.819663	−	0.572846i	$-0.805839\pi$
$89$	0.813846	−	1.40962i	0.0862675	−	0.149420i	0.905931	+	0.423426i	$0.139173\pi$
$90$		0			0
$91$	−10.2110	+	17.6860i	−1.07040	+	1.85399i
$92$	−2.22178	+	1.28274i	−0.231636	+	0.133735i
$93$		0			0
$94$	−4.03603			−0.416285
$95$	8.41239	−	4.92257i	0.863093	−	0.505045i
$96$		0			0
$97$	−10.3479	+	5.97438i	−1.05067	+	0.606607i	−0.922838	−	0.385188i	$-0.874136\pi$
$97$	−10.3479	+	5.97438i	−1.05067	+	0.606607i	−0.127836	+	0.991795i	$0.540803\pi$
$98$	8.03741	−	4.64040i	0.811901	−	0.468751i
$99$		0			0
$100$	1.38186	−	4.80525i	0.138186	−	0.480525i
$101$	0.252103	−	0.436656i	0.0250852	−	0.0434489i	−0.853210	−	0.521567i	$-0.825348\pi$
$101$	0.252103	−	0.436656i	0.0250852	−	0.0434489i	0.878295	+	0.478118i	$0.158681\pi$
$102$		0			0
$103$			5.33797i			0.525966i	0.964800	+	0.262983i	$0.0847063\pi$
$103$			5.33797i			0.525966i	−0.964800	+	0.262983i	$0.915294\pi$
$104$	−2.53064	+	4.38320i	−0.248150	+	0.429808i
$105$		0			0
$106$	10.6575			1.03514
$107$			17.9275i			1.73312i	0.499076	+	0.866558i	$0.333673\pi$
$107$			17.9275i			1.73312i	−0.499076	+	0.866558i	$0.666327\pi$
$108$		0			0
$109$	−4.43631	−	7.68392i	−0.424922	−	0.735986i	0.571492	−	0.820608i	$-0.306365\pi$
$109$	−4.43631	−	7.68392i	−0.424922	−	0.735986i	−0.996413	+	0.0846222i	$0.973032\pi$
$110$	2.62685	−	1.97790i	0.250460	−	0.188585i
$111$		0			0
$112$	3.49437	−	2.01747i	0.330187	−	0.190633i
$113$			15.8667i			1.49261i	0.665603	+	0.746306i	$0.268174\pi$
$113$			15.8667i			1.49261i	−0.665603	+	0.746306i	$0.731826\pi$
$114$		0			0
$115$	5.27972	+	2.24349i	0.492336	+	0.209207i
$116$	2.10491	+	3.64581i	0.195436	+	0.338505i
$117$		0			0
$118$	−5.32777	−	3.07599i	−0.490461	−	0.283168i
$119$	−0.189379	−	0.328014i	−0.0173604	−	0.0300690i
$120$		0			0
$121$	−8.83752			−0.803410
$122$			1.30744i			0.118370i
$123$		0			0
$124$	2.13279	−	3.69410i	0.191530	−	0.331740i
$125$	−10.4423	+	3.99469i	−0.933991	+	0.357296i
$126$		0			0
$127$	−5.77290	−	3.33298i	−0.512262	−	0.295755i	0.221501	−	0.975160i	$-0.428904\pi$
$127$	−5.77290	−	3.33298i	−0.512262	−	0.295755i	−0.733763	+	0.679406i	$0.762238\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	11.2335	−	1.37494i	0.985247	−	0.120590i
$131$	3.53784	+	6.12771i	0.309102	+	0.535381i	0.978166	−	0.207824i	$-0.0666381\pi$
$131$	3.53784	+	6.12771i	0.309102	+	0.535381i	−0.669064	+	0.743205i	$0.733305\pi$
$132$		0			0
$133$	−6.97268	−	16.1467i	−0.604608	−	1.40010i
$134$	10.7524			0.928867
$135$		0			0
$136$	−0.0469347	−	0.0812933i	−0.00402462	−	0.00697084i
$137$	16.3302	+	9.42826i	1.39519	+	0.805511i	0.993883	−	0.110435i	$-0.0352245\pi$
$137$	16.3302	+	9.42826i	1.39519	+	0.805511i	0.401302	+	0.915946i	$0.368558\pi$
$138$		0			0
$139$	−9.99616	+	17.3139i	−0.847864	+	1.46854i	0.0352474	+	0.999379i	$0.488778\pi$
$139$	−9.99616	+	17.3139i	−0.847864	+	1.46854i	−0.883111	+	0.469164i	$0.844555\pi$
$140$	−8.30383	−	3.52852i	−0.701802	−	0.298214i
$141$		0			0
$142$	7.51373	+	4.33806i	0.630538	+	0.364042i
$143$	6.44566	+	3.72141i	0.539014	+	0.311200i
$144$		0			0
$145$	3.68144	−	8.66372i	0.305727	−	0.719483i
$146$	6.35711	−	11.0108i	0.526119	−	0.911264i
$147$		0			0
$148$	1.33201	+	0.769037i	0.109491	+	0.0632144i
$149$	−6.10397	−	10.5724i	−0.500056	−	0.866123i	−1.00000		6.51503e-5i	$-0.999979\pi$
$149$	−6.10397	−	10.5724i	−0.500056	−	0.866123i	0.499944	−	0.866058i	$-0.333354\pi$
$150$		0			0
$151$	19.9109			1.62032			0.810161	−	0.586207i	$-0.199380\pi$
$151$	19.9109			1.62032			0.810161	+	0.586207i	$0.199380\pi$
$152$	−1.72807	−	4.00172i	−0.140165	−	0.324582i
$153$		0			0
$154$	−2.96677	−	5.13860i	−0.239069	−	0.414080i
$155$	−9.46747	+	1.15878i	−0.760445	+	0.0930756i
$156$		0			0
$157$	−14.0594	+	8.11721i	−1.12206	+	0.647824i	−0.941927	−	0.335817i	$-0.890988\pi$
$157$	−14.0594	+	8.11721i	−1.12206	+	0.647824i	−0.180137	+	0.983641i	$0.557654\pi$
$158$	11.2256	+	6.48112i	0.893063	+	0.515610i
$159$		0			0
$160$	−2.05798	−	0.874489i	−0.162697	−	0.0691344i
$161$	5.17581	−	8.96476i	0.407911	−	0.706522i
$162$		0			0
$163$		−	2.05750i		−	0.161156i	−0.996748	−	0.0805780i	$-0.974323\pi$
$163$		−	2.05750i		−	0.161156i	0.996748	−	0.0805780i	$-0.0256766\pi$
$164$	7.76245			0.606146
$165$		0			0
$166$	−1.03164	−	1.78686i	−0.0800709	−	0.138687i
$167$	−18.8169	−	10.8639i	−1.45609	−	0.840676i	−0.457278	−	0.889324i	$-0.651176\pi$
$167$	−18.8169	−	10.8639i	−1.45609	−	0.840676i	−0.998816	+	0.0486476i	$0.984509\pi$
$168$		0			0
$169$	6.30829	+	10.9263i	0.485253	+	0.840483i
$170$	−0.0820878	+	0.193181i	−0.00629584	+	0.0148163i
$171$		0			0
$172$		−	4.58649i		−	0.349717i
$173$	−20.0963	+	11.6026i	−1.52790	+	0.882132i	−0.528447	+	0.848966i	$0.677226\pi$
$173$	−20.0963	+	11.6026i	−1.52790	+	0.882132i	−0.999450	+	0.0331655i	$0.989441\pi$
$174$		0			0
$175$	4.86573	+	19.5792i	0.367815	+	1.48005i
$176$	−0.735269	−	1.27352i	−0.0554230	−	0.0959955i
$177$		0			0
$178$			1.62769i			0.122001i
$179$	6.37559			0.476534			0.238267	−	0.971200i	$-0.423421\pi$
$179$	6.37559			0.476534			0.238267	+	0.971200i	$0.423421\pi$
$180$		0			0
$181$	4.39603	−	7.61415i	0.326755	−	0.565955i	−0.655111	−	0.755532i	$-0.727378\pi$
$181$	4.39603	−	7.61415i	0.326755	−	0.565955i	0.981866	+	0.189577i	$0.0607116\pi$
$182$		−	20.4220i		−	1.51378i
$183$		0			0
$184$	1.28274	−	2.22178i	0.0945652	−	0.163792i
$185$	−0.417831	−	3.41376i	−0.0307196	−	0.250985i
$186$		0			0
$187$	−0.119545	+	0.0690193i	−0.00874200	+	0.00504719i
$188$	3.49530	−	2.01801i	0.254921	−	0.147179i
$189$		0			0
$190$	−4.82406	+	8.46926i	−0.349974	+	0.614425i
$191$	−12.9659			−0.938177			−0.469088	−	0.883151i	$-0.655417\pi$
$191$	−12.9659			−0.938177			−0.469088	+	0.883151i	$0.655417\pi$
$192$		0			0
$193$	5.29710	−	3.05828i	0.381294	−	0.220140i	−0.297087	−	0.954850i	$-0.596015\pi$
$193$	5.29710	−	3.05828i	0.381294	−	0.220140i	0.678381	+	0.734710i	$0.262682\pi$
$194$	5.97438	−	10.3479i	0.428936	−	0.742939i
$195$		0			0
$196$	−4.64040	+	8.03741i	−0.331457	+	0.574101i
$197$		−	7.34941i		−	0.523624i	−0.965119	−	0.261812i	$-0.915680\pi$
$197$		−	7.34941i		−	0.523624i	0.965119	−	0.261812i	$-0.0843200\pi$
$198$		0			0
$199$	1.71780	−	2.97531i	0.121771	−	0.210914i	−0.798695	−	0.601736i	$-0.794476\pi$
$199$	1.71780	−	2.97531i	0.121771	−	0.210914i	0.920466	+	0.390822i	$0.127809\pi$
$200$	1.20590	+	4.85240i	0.0852698	+	0.343117i
$201$		0			0
$202$			0.504207i			0.0354759i
$203$	−14.7107	−	8.49321i	−1.03249	−	0.596106i
$204$		0			0
$205$	−10.4406	−	13.8662i	−0.729205	−	0.968458i
$206$	−2.66899	−	4.62282i	−0.185957	−	0.322087i
$207$		0			0
$208$		−	5.06128i		−	0.350937i
$209$	−5.88469	+	2.54120i	−0.407052	+	0.175778i
$210$		0			0
$211$	2.01970	+	3.49822i	0.139042	+	0.240827i	0.927134	−	0.374730i	$-0.122264\pi$
$211$	2.01970	+	3.49822i	0.139042	+	0.240827i	−0.788092	+	0.615557i	$0.788931\pi$
$212$	−9.22964	+	5.32873i	−0.633894	+	0.365979i
$213$		0			0
$214$	−8.96375	−	15.5257i	−0.612749	−	1.06131i
$215$	−8.19293	+	6.16891i	−0.558754	+	0.420716i
$216$		0			0
$217$			17.2114i			1.16838i
$218$	7.68392	+	4.43631i	0.520421	+	0.300465i
$219$		0			0
$220$	−1.28597	+	3.02634i	−0.0867001	+	0.204035i
$221$	−0.475100			−0.0319587
$222$		0			0
$223$	15.6334	−	9.02593i	1.04689	−	0.604421i	0.125111	−	0.992143i	$-0.460071\pi$
$223$	15.6334	−	9.02593i	1.04689	−	0.604421i	0.921776	+	0.387722i	$0.126738\pi$
$224$	−2.01747	+	3.49437i	−0.134798	+	0.233477i
$225$		0			0
$226$	−7.93334	−	13.7409i	−0.527718	−	0.914034i
$227$		−	26.8513i		−	1.78219i	−0.453820	−	0.891093i	$-0.649939\pi$
$227$		−	26.8513i		−	1.78219i	0.453820	−	0.891093i	$-0.350061\pi$
$228$		0			0
$229$	13.7131			0.906190			0.453095	−	0.891462i	$-0.350320\pi$
$229$	13.7131			0.906190			0.453095	+	0.891462i	$0.350320\pi$
$230$	−5.69412	+	0.696938i	−0.375459	+	0.0459548i
$231$		0			0
$232$	−3.64581	−	2.10491i	−0.239359	−	0.138194i
$233$	−0.00572506	+	0.00330537i	−0.000375061	+	0.000216542i	−0.500188	−	0.865917i	$-0.666736\pi$
$233$	−0.00572506	+	0.00330537i	−0.000375061	+	0.000216542i	0.499812	+	0.866134i	$0.333402\pi$
$234$		0			0
$235$	−8.30605	−	3.52946i	−0.541827	−	0.230237i
$236$	6.15198			0.400460
$237$		0			0
$238$	0.328014	+	0.189379i	0.0212620	+	0.0122756i
$239$	−4.67499			−0.302400			−0.151200	−	0.988503i	$-0.548314\pi$
$239$	−4.67499			−0.302400			−0.151200	+	0.988503i	$0.548314\pi$
$240$		0			0
$241$	13.9044	−	24.0831i	0.895659	−	1.55133i	0.0626717	−	0.998034i	$-0.480038\pi$
$241$	13.9044	−	24.0831i	0.895659	−	1.55133i	0.832987	−	0.553292i	$-0.186629\pi$
$242$	7.65351	−	4.41876i	0.491986	−	0.284049i
$243$		0			0
$244$	−0.653722	−	1.13228i	−0.0418503	−	0.0724868i
$245$	20.5988	−	2.52121i	1.31601	−	0.161074i
$246$		0			0
$247$	−21.9135	−	2.55244i	−1.39432	−	0.162408i
$248$			4.26558i			0.270864i
$249$		0			0
$250$	7.04598	−	8.68068i	0.445627	−	0.549014i
$251$	−3.03259	+	5.25259i	−0.191415	+	0.331541i	−0.945719	−	0.324984i	$-0.894641\pi$
$251$	−3.03259	+	5.25259i	−0.191415	+	0.331541i	0.754304	+	0.656525i	$0.227974\pi$
$252$		0			0
$253$	−3.26721	−	1.88633i	−0.205408	−	0.118592i
$254$	6.66597			0.418260
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.11707	−	0.644941i	−0.0696809	−	0.0402303i	0.464755	−	0.885439i	$-0.346142\pi$
$257$	−1.11707	−	0.644941i	−0.0696809	−	0.0402303i	−0.534436	+	0.845209i	$0.679476\pi$
$258$		0			0
$259$	−6.20604			−0.385625
$260$	−9.04106	+	6.80751i	−0.560703	+	0.422184i
$261$		0			0
$262$	−6.12771	−	3.53784i	−0.378571	−	0.218568i
$263$	24.4863	−	14.1372i	1.50989	−	0.871737i	0.509959	−	0.860199i	$-0.329661\pi$
$263$	24.4863	−	14.1372i	1.50989	−	0.871737i	0.999933	−	0.0115378i	$-0.00367269\pi$
$264$		0			0
$265$	21.9328	+	9.31984i	1.34732	+	0.572513i
$266$	14.1119	+	10.4971i	0.865255	+	0.643621i
$267$		0			0
$268$	−9.31187	+	5.37621i	−0.568813	+	0.328404i
$269$	13.8782	+	24.0377i	0.846169	+	1.46561i	0.884602	+	0.466346i	$0.154430\pi$
$269$	13.8782	+	24.0377i	0.846169	+	1.46561i	−0.0384337	+	0.999261i	$0.512237\pi$
$270$		0			0
$271$	−5.42826	−	9.40202i	−0.329743	−	0.571132i	0.652718	−	0.757601i	$-0.273629\pi$
$271$	−5.42826	−	9.40202i	−0.329743	−	0.571132i	−0.982461	+	0.186469i	$0.940296\pi$
$272$	0.0812933	+	0.0469347i	0.00492913	+	0.00284584i
$273$		0			0
$274$	−18.8565			−1.13916
$275$	7.13565	−	1.77332i	0.430296	−	0.106935i
$276$		0			0
$277$			24.5237i			1.47349i	0.676173	+	0.736743i	$0.263637\pi$
$277$			24.5237i			1.47349i	−0.676173	+	0.736743i	$0.736363\pi$
$278$		−	19.9923i		−	1.19906i
$279$		0			0
$280$	8.95558	−	1.09613i	0.535199	−	0.0655063i
$281$	−3.29709	+	5.71073i	−0.196688	+	0.340674i	−0.947453	−	0.319896i	$-0.896352\pi$
$281$	−3.29709	+	5.71073i	−0.196688	+	0.340674i	0.750765	+	0.660570i	$0.229685\pi$
$282$		0			0
$283$	20.4709	−	11.8189i	1.21687	−	0.702559i	0.252621	−	0.967565i	$-0.418707\pi$
$283$	20.4709	−	11.8189i	1.21687	−	0.702559i	0.964247	+	0.265006i	$0.0853740\pi$
$284$	−8.67611			−0.514833
$285$		0			0
$286$	−7.44281			−0.440103
$287$	−27.1248	+	15.6605i	−1.60113	+	0.924412i
$288$		0			0
$289$	−8.49559	+	14.7148i	−0.499741	+	0.865577i
$290$	1.14364	+	9.34372i	0.0671567	+	0.548682i
$291$		0			0
$292$			12.7142i			0.744044i
$293$		−	23.0123i		−	1.34439i	−0.740374	−	0.672195i	$-0.765352\pi$
$293$		−	23.0123i		−	1.34439i	0.740374	−	0.672195i	$-0.234648\pi$
$294$		0			0
$295$	−8.27451	−	10.9894i	−0.481761	−	0.639827i
$296$	−1.53807			−0.0893987
$297$		0			0
$298$	10.5724	+	6.10397i	0.612442	+	0.353593i
$299$	−6.49233	−	11.2451i	−0.375461	−	0.650318i
$300$		0			0
$301$	9.25313	+	16.0269i	0.533341	+	0.923774i
$302$	−17.2433	+	9.95543i	−0.992241	+	0.572870i
$303$		0			0
$304$	3.49741	+	2.60156i	0.200590	+	0.149209i
$305$	−1.14335	+	2.69069i	−0.0654678	+	0.154068i
$306$		0			0
$307$	22.0807	−	12.7483i	1.26021	−	0.727584i	0.287097	−	0.957902i	$-0.407310\pi$
$307$	22.0807	−	12.7483i	1.26021	−	0.727584i	0.973116	+	0.230318i	$0.0739765\pi$
$308$	5.13860	+	2.96677i	0.292799	+	0.169048i
$309$		0			0
$310$	7.61968	−	5.73727i	0.432768	−	0.325855i
$311$	30.3172			1.71913			0.859565	−	0.511027i	$-0.170735\pi$
$311$	30.3172			1.71913			0.859565	+	0.511027i	$0.170735\pi$
$312$		0			0
$313$	−6.54063	−	3.77623i	−0.369698	−	0.213445i	0.303628	−	0.952791i	$-0.401802\pi$
$313$	−6.54063	−	3.77623i	−0.369698	−	0.213445i	−0.673327	+	0.739345i	$0.735135\pi$
$314$	8.11721	−	14.0594i	0.458081	−	0.793419i
$315$		0			0
$316$	−12.9622			−0.729183
$317$	−12.1344	−	7.00579i	−0.681535	−	0.393484i	0.118898	−	0.992906i	$-0.462064\pi$
$317$	−12.1344	−	7.00579i	−0.681535	−	0.393484i	−0.800433	+	0.599422i	$0.795397\pi$
$318$		0			0
$319$	−3.09535	+	5.36131i	−0.173307	+	0.300176i
$320$	2.21950	−	0.271659i	0.124074	−	0.0151862i
$321$		0			0
$322$			10.3516i			0.576873i
$323$	0.244207	−	0.328300i	0.0135880	−	0.0182671i
$324$		0			0
$325$	24.3207	+	6.99400i	1.34907	+	0.387957i
$326$	1.02875	+	1.78185i	0.0569773	+	0.0986875i
$327$		0			0
$328$	−6.72248	+	3.88123i	−0.371187	+	0.214305i
$329$	−8.14258	+	14.1034i	−0.448915	+	0.777544i
$330$		0			0
$331$	−2.20541			−0.121220			−0.0606102	−	0.998162i	$-0.519305\pi$
$331$	−2.20541			−0.121220			−0.0606102	+	0.998162i	$0.519305\pi$
$332$	1.78686	+	1.03164i	0.0980665	+	0.0566187i
$333$		0			0
$334$	21.7279			1.18890
$335$	22.1282	+	9.40287i	1.20899	+	0.513734i
$336$		0			0
$337$	3.35026	−	1.93428i	0.182500	−	0.105367i	−0.405966	−	0.913888i	$-0.633065\pi$
$337$	3.35026	−	1.93428i	0.182500	−	0.105367i	0.588467	+	0.808521i	$0.299732\pi$
$338$	−10.9263	−	6.30829i	−0.594311	−	0.343126i
$339$		0			0
$340$	−0.0255005	−	0.208344i	−0.00138296	−	0.0112990i
$341$	6.27270			0.339685
$342$		0			0
$343$		−	9.20290i		−	0.496910i
$344$	2.29325	+	3.97202i	0.123644	+	0.214157i
$345$		0			0
$346$	11.6026	−	20.0963i	0.623761	−	1.08039i
$347$	−10.6406	+	6.14337i	−0.571219	+	0.329793i	−0.757636	−	0.652677i	$-0.773646\pi$
$347$	−10.6406	+	6.14337i	−0.571219	+	0.329793i	0.186417	+	0.982471i	$0.440312\pi$
$348$		0			0
$349$	23.1329			1.23828			0.619139	−	0.785282i	$-0.287482\pi$
$349$	23.1329			1.23828			0.619139	+	0.785282i	$0.287482\pi$
$350$	−14.0034	−	14.5232i	−0.748515	−	0.776298i
$351$		0			0
$352$	1.27352	+	0.735269i	0.0678791	+	0.0391900i
$353$			2.27216i			0.120935i	0.998170	+	0.0604674i	$0.0192591\pi$
$353$			2.27216i			0.120935i	−0.998170	+	0.0604674i	$0.980741\pi$
$354$		0			0
$355$	11.6695	+	15.4983i	0.619353	+	0.822564i
$356$	−0.813846	−	1.40962i	−0.0431338	−	0.0747098i
$357$		0			0
$358$	−5.52142	+	3.18779i	−0.291816	+	0.168480i
$359$	10.3404	+	17.9101i	0.545746	+	0.945260i	0.998560	+	0.0536549i	$0.0170871\pi$
$359$	10.3404	+	17.9101i	0.545746	+	0.945260i	−0.452813	+	0.891605i	$0.649580\pi$
$360$		0			0
$361$	13.0275	−	13.8305i	0.685660	−	0.727922i
$362$			8.79207i			0.462101i
$363$		0			0
$364$	10.2110	+	17.6860i	0.535202	+	0.926997i
$365$	22.7117	−	17.1008i	1.18878	−	0.895099i
$366$		0			0
$367$	−31.7744	−	18.3450i	−1.65861	−	0.957600i	−0.973357	−	0.229296i	$-0.926358\pi$
$367$	−31.7744	−	18.3450i	−1.65861	−	0.957600i	−0.685255	−	0.728304i	$-0.740309\pi$
$368$			2.56549i			0.133735i
$369$		0			0
$370$	2.06873	+	2.74749i	0.107548	+	0.142835i
$371$	21.5012	−	37.2411i	1.11628	−	1.93346i
$372$		0			0
$373$			19.5380i			1.01164i	0.862640	+	0.505819i	$0.168810\pi$
$373$			19.5380i			1.01164i	−0.862640	+	0.505819i	$0.831190\pi$
$374$	0.0690193	−	0.119545i	0.00356890	−	0.00618152i
$375$		0			0
$376$	−2.01801	+	3.49530i	−0.104071	+	0.180256i
$377$	−18.4525	+	10.6536i	−0.950352	+	0.548686i
$378$		0			0
$379$	−3.46802			−0.178140			−0.0890701	−	0.996025i	$-0.528390\pi$
$379$	−3.46802			−0.178140			−0.0890701	+	0.996025i	$0.528390\pi$
$380$	−0.0568730	−	9.74663i	−0.00291752	−	0.499991i
$381$		0			0
$382$	11.2288	−	6.48293i	0.574514	−	0.331696i
$383$	21.7388	−	12.5509i	1.11080	−	0.641322i	0.171765	−	0.985138i	$-0.445053\pi$
$383$	21.7388	−	12.5509i	1.11080	−	0.641322i	0.939037	+	0.343816i	$0.111720\pi$
$384$		0			0
$385$	−1.61190	−	13.1695i	−0.0821501	−	0.671182i
$386$	−3.05828	+	5.29710i	−0.155662	+	0.269615i
$387$		0			0
$388$			11.9488i			0.606607i
$389$	−7.02074	+	12.1603i	−0.355965	+	0.616550i	−0.987283	−	0.158974i	$-0.949181\pi$
$389$	−7.02074	+	12.1603i	−0.355965	+	0.616550i	0.631317	+	0.775525i	$0.282515\pi$
$390$		0			0
$391$	0.240821			0.0121788
$392$		−	9.28080i		−	0.468751i
$393$		0			0
$394$	3.67471	+	6.36478i	0.185129	+	0.320653i
$395$	17.4344	+	23.1547i	0.877221	+	1.16504i
$396$		0			0
$397$	−26.6267	+	15.3729i	−1.33635	+	0.771544i	−0.986265	−	0.165172i	$-0.947182\pi$
$397$	−26.6267	+	15.3729i	−1.33635	+	0.771544i	−0.350089	+	0.936716i	$0.613849\pi$
$398$			3.43559i			0.172211i
$399$		0			0
$400$	−3.47054	−	3.59936i	−0.173527	−	0.179968i
$401$	19.3518	+	33.5183i	0.966381	+	1.67382i	0.705857	+	0.708355i	$0.250562\pi$
$401$	19.3518	+	33.5183i	0.966381	+	1.67382i	0.260525	+	0.965467i	$0.416104\pi$
$402$		0			0
$403$	18.6969	+	10.7946i	0.931357	+	0.537719i
$404$	−0.252103	−	0.436656i	−0.0125426	−	0.0217244i
$405$		0			0
$406$	16.9864			0.843022
$407$			2.26180i			0.112113i
$408$		0			0
$409$	−10.3920	+	17.9994i	−0.513850	+	0.890014i	0.486021	+	0.873947i	$0.338448\pi$
$409$	−10.3920	+	17.9994i	−0.513850	+	0.890014i	−0.999871	+	0.0160671i	$0.994885\pi$
$410$	15.9749	+	6.78818i	0.788946	+	0.335244i
$411$		0			0
$412$	4.62282	+	2.66899i	0.227750	+	0.131491i
$413$	−21.4973	+	12.4115i	−1.05781	+	0.610728i
$414$		0			0
$415$	−0.560510	−	4.57947i	−0.0275143	−	0.224797i
$416$	2.53064	+	4.38320i	0.124075	+	0.214904i
$417$		0			0
$418$	3.82569	−	5.14308i	0.187121	−	0.251556i
$419$	−36.2672			−1.77177			−0.885883	−	0.463908i	$-0.846447\pi$
$419$	−36.2672			−1.77177			−0.885883	+	0.463908i	$0.846447\pi$
$420$		0			0
$421$	10.7212	+	18.5697i	0.522519	+	0.905030i	0.999657	+	0.0262013i	$0.00834109\pi$
$421$	10.7212	+	18.5697i	0.522519	+	0.905030i	−0.477137	+	0.878829i	$0.658326\pi$
$422$	−3.49822	−	2.01970i	−0.170291	−	0.0983174i
$423$		0			0
$424$	5.32873	−	9.22964i	0.258786	−	0.448231i
$425$	−0.337869	+	0.325778i	−0.0163891	+	0.0158025i
$426$		0			0
$427$	4.56869	+	2.63773i	0.221094	+	0.127649i
$428$	15.5257	+	8.96375i	0.750461	+	0.433279i
$429$		0			0
$430$	4.01084	−	9.43890i	0.193420	−	0.455184i
$431$	−2.91216	+	5.04400i	−0.140274	+	0.242961i	−0.927600	−	0.373576i	$-0.878132\pi$
$431$	−2.91216	+	5.04400i	−0.140274	+	0.242961i	0.787326	+	0.616537i	$0.211465\pi$
$432$		0			0
$433$	27.3690	+	15.8015i	1.31527	+	0.759371i	0.982963	−	0.183801i	$-0.0588403\pi$
$433$	27.3690	+	15.8015i	1.31527	+	0.759371i	0.332305	+	0.943172i	$0.392174\pi$
$434$	−8.60569	−	14.9055i	−0.413086	−	0.715486i
$435$		0			0
$436$	−8.87262			−0.424922
$437$	11.1076	+	1.29379i	0.531349	+	0.0618904i
$438$		0			0
$439$	−0.932951	−	1.61592i	−0.0445273	−	0.0771236i	0.842903	−	0.538066i	$-0.180845\pi$
$439$	−0.932951	−	1.61592i	−0.0445273	−	0.0771236i	−0.887430	+	0.460942i	$0.847512\pi$
$440$	−0.399485	−	3.26387i	−0.0190447	−	0.155599i
$441$		0			0
$442$	0.411448	−	0.237550i	0.0195706	−	0.0112991i
$443$	13.6368	+	7.87318i	0.647902	+	0.374066i	0.787652	−	0.616121i	$-0.211297\pi$
$443$	13.6368	+	7.87318i	0.647902	+	0.374066i	−0.139750	+	0.990187i	$0.544630\pi$
$444$		0			0
$445$	−1.42340	+	3.34975i	−0.0674755	+	0.158794i
$446$	−9.02593	+	15.6334i	−0.427390	+	0.740262i
$447$		0			0
$448$		−	4.03495i		−	0.190633i
$449$	29.7436			1.40369			0.701845	−	0.712330i	$-0.252360\pi$
$449$	29.7436			1.40369			0.701845	+	0.712330i	$0.252360\pi$
$450$		0			0
$451$	5.70749	+	9.88567i	0.268755	+	0.465498i
$452$	13.7409	+	7.93334i	0.646320	+	0.373153i
$453$		0			0
$454$	13.4257	+	23.2539i	0.630098	+	1.09136i
$455$	17.8588	−	42.0280i	0.837234	−	1.97030i
$456$		0			0
$457$		−	12.7891i		−	0.598250i	−0.954214	−	0.299125i	$-0.903305\pi$
$457$		−	12.7891i		−	0.598250i	0.954214	−	0.299125i	$-0.0966948\pi$
$458$	−11.8759	+	6.85657i	−0.554926	+	0.320387i
$459$		0			0
$460$	4.58278	−	3.45062i	0.213673	−	0.160886i
$461$	−5.96303	−	10.3283i	−0.277726	−	0.481035i	0.693093	−	0.720848i	$-0.256247\pi$
$461$	−5.96303	−	10.3283i	−0.277726	−	0.481035i	−0.970819	+	0.239813i	$0.922914\pi$
$462$		0			0
$463$		−	19.3208i		−	0.897913i	−0.893554	−	0.448956i	$-0.851796\pi$
$463$		−	19.3208i		−	0.897913i	0.893554	−	0.448956i	$-0.148204\pi$
$464$	4.20982			0.195436
$465$		0			0
$466$	0.00330537	−	0.00572506i	0.000153118	−	0.000265208i
$467$		−	26.7009i		−	1.23557i	−0.786347	−	0.617785i	$-0.788030\pi$
$467$		−	26.7009i		−	1.23557i	0.786347	−	0.617785i	$-0.211970\pi$
$468$		0			0
$469$	21.6927	−	37.5729i	1.00168	−	1.73496i
$470$	8.95798	−	1.09642i	0.413201	−	0.0505742i
$471$		0			0
$472$	−5.32777	+	3.07599i	−0.245231	+	0.141584i
$473$	5.84101	−	3.37231i	0.268570	−	0.155059i
$474$		0			0
$475$	−17.3341	+	13.2110i	−0.795342	+	0.606161i
$476$	−0.378758			−0.0173604
$477$		0			0
$478$	4.04866	−	2.33750i	0.185182	−	0.106915i
$479$	6.79124	−	11.7628i	0.310299	−	0.537454i	−0.668128	−	0.744047i	$-0.732904\pi$
$479$	6.79124	−	11.7628i	0.310299	−	0.537454i	0.978427	+	0.206592i	$0.0662373\pi$
$480$		0			0
$481$	−3.89231	+	6.74168i	−0.177474	+	0.307394i
$482$			27.8087i			1.26665i
$483$		0			0
$484$	−4.41876	+	7.65351i	−0.200853	+	0.347887i
$485$	21.3443	−	16.0713i	0.969195	−	0.729760i
$486$		0			0
$487$			8.03640i			0.364164i	0.983283	+	0.182082i	$0.0582837\pi$
$487$			8.03640i			0.364164i	−0.983283	+	0.182082i	$0.941716\pi$
$488$	1.13228	+	0.653722i	0.0512559	+	0.0295926i
$489$		0			0
$490$	−16.5785	+	12.4828i	−0.748938	+	0.563916i
$491$	−10.3390	−	17.9077i	−0.466593	−	0.808163i	0.532679	−	0.846317i	$-0.321185\pi$
$491$	−10.3390	−	17.9077i	−0.466593	−	0.808163i	−0.999272	+	0.0381546i	$0.987852\pi$
$492$		0			0
$493$		−	0.395174i		−	0.0177977i
$494$	20.2538	−	8.74626i	0.911263	−	0.393513i
$495$		0			0
$496$	−2.13279	−	3.69410i	−0.0957650	−	0.165870i
$497$	30.3175	−	17.5038i	1.35993	−	0.785154i
$498$		0			0
$499$	−0.551160	−	0.954638i	−0.0246733	−	0.0427355i	0.853425	−	0.521216i	$-0.174521\pi$
$499$	−0.551160	−	0.954638i	−0.0246733	−	0.0427355i	−0.878098	+	0.478480i	$0.841188\pi$
$500$	−1.76166	+	11.0407i	−0.0787840	+	0.493754i
$501$		0			0
$502$		−	6.06517i		−	0.270702i
$503$	−21.0518	−	12.1543i	−0.938653	−	0.541932i	−0.0491154	−	0.998793i	$-0.515640\pi$
$503$	−21.0518	−	12.1543i	−0.938653	−	0.541932i	−0.889538	+	0.456861i	$0.848974\pi$
$504$		0			0
$505$	−0.440923	+	1.03765i	−0.0196208	+	0.0461746i
$506$	3.77265			0.167715
$507$		0			0
$508$	−5.77290	+	3.33298i	−0.256131	+	0.147877i
$509$	4.96728	−	8.60358i	0.220171	−	0.381347i	−0.734689	−	0.678404i	$-0.762672\pi$
$509$	4.96728	−	8.60358i	0.220171	−	0.381347i	0.954860	+	0.297057i	$0.0960052\pi$
$510$		0			0
$511$	−25.6506	−	44.4282i	−1.13472	−	1.96539i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	1.28988			0.0568942
$515$	−1.45011	−	11.8477i	−0.0638994	−	0.522070i
$516$		0			0
$517$	5.13998	+	2.96757i	0.226056	+	0.130513i
$518$	5.37459	−	3.10302i	0.236146	−	0.136339i
$519$		0			0
$520$	4.42603	−	10.4160i	0.194094	−	0.456772i
$521$	20.9057			0.915895			0.457947	−	0.888979i	$-0.348585\pi$
$521$	20.9057			0.915895			0.457947	+	0.888979i	$0.348585\pi$
$522$		0			0
$523$	27.3676	+	15.8007i	1.19670	+	0.690916i	0.959818	−	0.280622i	$-0.0905408\pi$
$523$	27.3676	+	15.8007i	1.19670	+	0.690916i	0.236883	+	0.971538i	$0.423874\pi$
$524$	7.07568			0.309102
$525$		0			0
$526$	−14.1372	+	24.4863i	−0.616411	+	1.06766i
$527$	−0.346763	+	0.200204i	−0.0151052	+	0.00872101i
$528$		0			0
$529$	−8.20913	−	14.2186i	−0.356919	−	0.618202i
$530$	−23.6543	+	2.89520i	−1.02748	+	0.125759i
$531$		0			0
$532$	−17.4698	−	2.03485i	−0.757413	−	0.0882218i
$533$			39.2880i			1.70175i
$534$		0			0
$535$	−4.87017	−	39.7902i	−0.210556	−	1.72028i
$536$	5.37621	−	9.31187i	0.232217	−	0.402211i
$537$		0			0
$538$	−24.0377	−	13.8782i	−1.03634	−	0.598332i
$539$	−13.6478			−0.587851
$540$		0			0
$541$	−2.50615	+	4.34078i	−0.107748	+	0.186625i	−0.914858	−	0.403777i	$-0.867697\pi$
$541$	−2.50615	+	4.34078i	−0.107748	+	0.186625i	0.807110	+	0.590402i	$0.201031\pi$
$542$	9.40202	+	5.42826i	0.403851	+	0.233164i
$543$		0			0
$544$	−0.0938694			−0.00402462
$545$	11.9338	+	15.8493i	0.511189	+	0.678911i
$546$		0			0
$547$	−30.7554	−	17.7566i	−1.31500	−	0.759218i	−0.332084	−	0.943250i	$-0.607752\pi$
$547$	−30.7554	−	17.7566i	−1.31500	−	0.759218i	−0.982920	+	0.184032i	$0.941085\pi$
$548$	16.3302	−	9.42826i	0.697593	−	0.402755i
$549$		0			0
$550$	−5.29299	+	5.10356i	−0.225694	+	0.217617i
$551$	2.12304	−	18.2270i	0.0904445	−	0.776495i
$552$		0			0
$553$	45.2948	−	26.1510i	1.92613	−	1.11205i
$554$	−12.2618	−	21.2381i	−0.520956	−	0.902322i
$555$		0			0
$556$	9.99616	+	17.3139i	0.423932	+	0.734271i
$557$	8.45640	+	4.88231i	0.358309	+	0.206870i	0.668339	−	0.743857i	$-0.267006\pi$
$557$	8.45640	+	4.88231i	0.358309	+	0.206870i	−0.310030	+	0.950727i	$0.600339\pi$
$558$		0			0
$559$	23.2135			0.981828
$560$	−7.20770	+	5.42707i	−0.304581	+	0.229336i
$561$		0			0
$562$		−	6.59418i		−	0.278159i
$563$		−	11.5237i		−	0.485665i	−0.970068	−	0.242833i	$-0.921923\pi$
$563$		−	11.5237i		−	0.485665i	0.970068	−	0.242833i	$-0.0780766\pi$
$564$		0			0
$565$	−4.31033	−	35.2162i	−0.181337	−	1.48156i
$566$	−11.8189	+	20.4709i	−0.496784	+	0.860456i
$567$		0			0
$568$	7.51373	−	4.33806i	0.315269	−	0.182021i
$569$	1.93925			0.0812978			0.0406489	−	0.999173i	$-0.487057\pi$
$569$	1.93925			0.0812978			0.0406489	+	0.999173i	$0.487057\pi$
$570$		0			0
$571$	−38.0052			−1.59047			−0.795235	−	0.606301i	$-0.792652\pi$
$571$	−38.0052			−1.59047			−0.795235	+	0.606301i	$0.792652\pi$
$572$	6.44566	−	3.72141i	0.269507	−	0.155600i
$573$		0			0
$574$	15.6605	−	27.1248i	0.653658	−	1.13217i
$575$	−12.3278	−	3.54516i	−0.514106	−	0.147843i
$576$		0			0
$577$			28.3094i			1.17854i	0.807938	+	0.589268i	$0.200584\pi$
$577$			28.3094i			1.17854i	−0.807938	+	0.589268i	$0.799416\pi$
$578$		−	16.9912i		−	0.706740i
$579$		0			0
$580$	−5.66228	−	7.52008i	−0.235113	−	0.312254i
$581$	−8.32524			−0.345389
$582$		0			0
$583$	−13.5725	−	7.83611i	−0.562117	−	0.324539i
$584$	−6.35711	−	11.0108i	−0.263059	−	0.455632i
$585$		0			0
$586$	11.5061	+	19.9292i	0.475314	+	0.823267i
$587$	−9.39980	+	5.42698i	−0.387971	+	0.223995i	−0.681281	−	0.732022i	$-0.738577\pi$
$587$	−9.39980	+	5.42698i	−0.387971	+	0.223995i	0.293309	+	0.956018i	$0.405243\pi$
$588$		0			0
$589$	−17.0696	+	7.37122i	−0.703342	+	0.303726i
$590$	12.6606	+	5.37984i	0.521230	+	0.221484i
$591$		0			0
$592$	1.33201	−	0.769037i	0.0547453	−	0.0316072i
$593$	24.0190	+	13.8674i	0.986341	+	0.569464i	0.904179	−	0.427155i	$-0.140484\pi$
$593$	24.0190	+	13.8674i	0.986341	+	0.569464i	0.0821625	+	0.996619i	$0.473817\pi$
$594$		0			0
$595$	0.509436	+	0.676583i	0.0208848	+	0.0277372i
$596$	−12.2079			−0.500056
$597$		0			0
$598$	11.2451	+	6.49233i	0.459844	+	0.265491i
$599$	−15.6071	+	27.0323i	−0.637690	+	1.10451i	0.348248	+	0.937402i	$0.386777\pi$
$599$	−15.6071	+	27.0323i	−0.637690	+	1.10451i	−0.985938	+	0.167109i	$0.946557\pi$
$600$		0			0
$601$	42.3271			1.72656			0.863280	−	0.504726i	$-0.168406\pi$
$601$	42.3271			1.72656			0.863280	+	0.504726i	$0.168406\pi$
$602$	−16.0269	−	9.25313i	−0.653207	−	0.377129i
$603$		0			0
$604$	9.95543	−	17.2433i	0.405081	−	0.701620i
$605$	19.6149	−	2.40079i	0.797459	−	0.0976060i
$606$		0			0
$607$			12.9882i			0.527176i	0.964635	+	0.263588i	$0.0849059\pi$
$607$			12.9882i			0.527176i	−0.964635	+	0.263588i	$0.915094\pi$
$608$	−4.32963	−	0.504306i	−0.175590	−	0.0204523i
$609$		0			0
$610$	−0.355179	−	2.90188i	−0.0143808	−	0.117494i
$611$	10.2137	+	17.6907i	0.413204	+	0.715690i
$612$		0			0
$613$	−23.2303	+	13.4120i	−0.938264	+	0.541707i	−0.889416	−	0.457099i	$-0.848888\pi$
$613$	−23.2303	+	13.4120i	−0.938264	+	0.541707i	−0.0488484	+	0.998806i	$0.515555\pi$
$614$	−12.7483	+	22.0807i	−0.514480	+	0.891105i
$615$		0			0
$616$	−5.93355			−0.239069
$617$	−11.9663	−	6.90877i	−0.481747	−	0.278136i	0.239398	−	0.970922i	$-0.423050\pi$
$617$	−11.9663	−	6.90877i	−0.481747	−	0.278136i	−0.721144	+	0.692785i	$0.756383\pi$
$618$		0			0
$619$	36.2091			1.45537			0.727684	−	0.685912i	$-0.240597\pi$
$619$	36.2091			1.45537			0.727684	+	0.685912i	$0.240597\pi$
$620$	−3.73020	+	8.77846i	−0.149808	+	0.352551i
$621$		0			0
$622$	−26.2555	+	15.1586i	−1.05275	+	0.607804i
$623$	5.68775	+	3.28383i	0.227875	+	0.131564i
$624$		0			0
$625$	22.0916	−	11.7030i	0.883665	−	0.468120i
$626$	7.55247			0.301857
$627$		0			0
$628$			16.2344i			0.647824i
$629$	−0.0721890	−	0.125035i	−0.00287837	−	0.00498547i
$630$		0			0
$631$	−1.00438	+	1.73963i	−0.0399836	+	0.0692536i	−0.885325	−	0.464973i	$-0.846064\pi$
$631$	−1.00438	+	1.73963i	−0.0399836	+	0.0692536i	0.845341	+	0.534227i	$0.179397\pi$
$632$	11.2256	−	6.48112i	0.446532	−	0.257805i
$633$		0			0
$634$	14.0116			0.556471
$635$	13.7184	+	5.82932i	0.544399	+	0.231329i
$636$		0			0
$637$	−40.6796	−	23.4864i	−1.61178	−	0.930564i
$638$		−	6.19071i		−	0.245093i
$639$		0			0
$640$	−1.78632	+	1.34502i	−0.0706104	+	0.0531664i
$641$	8.04795	+	13.9395i	0.317875	+	0.550575i	0.980044	−	0.198779i	$-0.0636975\pi$
$641$	8.04795	+	13.9395i	0.317875	+	0.550575i	−0.662170	+	0.749354i	$0.730364\pi$
$642$		0			0
$643$	−34.6016	+	19.9773i	−1.36455	+	0.787826i	−0.990226	−	0.139470i	$-0.955460\pi$
$643$	−34.6016	+	19.9773i	−1.36455	+	0.787826i	−0.374328	+	0.927296i	$0.622127\pi$
$644$	−5.17581	−	8.96476i	−0.203955	−	0.353261i
$645$		0			0
$646$	−0.0473389	+	0.406420i	−0.00186252	+	0.0159904i
$647$			32.2985i			1.26979i	0.772600	+	0.634893i	$0.218956\pi$
$647$			32.2985i			1.26979i	−0.772600	+	0.634893i	$0.781044\pi$
$648$		0			0
$649$	4.52336	+	7.83470i	0.177558	+	0.307539i
$650$	−24.5594	+	6.10339i	−0.963298	+	0.239394i
$651$		0			0
$652$	−1.78185	−	1.02875i	−0.0697826	−	0.0402890i
$653$			25.3382i			0.991559i	0.868448	+	0.495780i	$0.165118\pi$
$653$			25.3382i			0.991559i	−0.868448	+	0.495780i	$0.834882\pi$
$654$		0			0
$655$	−9.51690	−	12.6394i	−0.371856	−	0.493862i
$656$	3.88123	−	6.72248i	0.151536	−	0.262469i
$657$		0			0
$658$		−	16.2852i		−	0.634862i
$659$	−2.44914	+	4.24204i	−0.0954051	+	0.165247i	−0.909778	−	0.415096i	$-0.863748\pi$
$659$	−2.44914	+	4.24204i	−0.0954051	+	0.165247i	0.814372	+	0.580343i	$0.197081\pi$
$660$		0			0
$661$	−24.1271	+	41.7893i	−0.938435	+	1.62542i	−0.170044	+	0.985437i	$0.554391\pi$
$661$	−24.1271	+	41.7893i	−0.938435	+	1.62542i	−0.768391	+	0.639980i	$0.778942\pi$
$662$	1.90994	−	1.10271i	0.0742320	−	0.0428579i
$663$		0			0
$664$	−2.06328			−0.0800709
$665$	19.8623	+	33.9436i	0.770227	+	1.31627i
$666$		0			0
$667$	9.35330	−	5.40013i	0.362161	−	0.209094i
$668$	−18.8169	+	10.8639i	−0.728047	+	0.420338i
$669$		0			0
$670$	−23.8650	+	2.92099i	−0.921987	+	0.112848i
$671$	0.961324	−	1.66506i	0.0371115	−	0.0642790i
$672$		0			0
$673$			11.3374i			0.437025i	0.975834	+	0.218512i	$0.0701204\pi$
$673$			11.3374i			0.437025i	−0.975834	+	0.218512i	$0.929880\pi$
$674$	−1.93428	+	3.35026i	−0.0745055	+	0.129047i
$675$		0			0
$676$	12.6166			0.485253
$677$		−	30.8182i		−	1.18444i	−0.805776	−	0.592220i	$-0.798252\pi$
$677$		−	30.8182i		−	1.18444i	0.805776	−	0.592220i	$-0.201748\pi$
$678$		0			0
$679$	−24.1063	−	41.7534i	−0.925116	−	1.60235i
$680$	0.126256	+	0.167681i	0.00484169	+	0.00643026i
$681$		0			0
$682$	−5.43231	+	3.13635i	−0.208014	+	0.120097i
$683$			10.5683i			0.404386i	0.979346	+	0.202193i	$0.0648069\pi$
$683$			10.5683i			0.404386i	−0.979346	+	0.202193i	$0.935193\pi$
$684$		0			0
$685$	−38.8063	−	16.4898i	−1.48271	−	0.630043i
$686$	4.60145	+	7.96995i	0.175684	+	0.304294i
$687$		0			0
$688$	−3.97202	−	2.29325i	−0.151432	−	0.0874292i
$689$	−26.9702	−	46.7138i	−1.02748	−	1.77965i
$690$		0			0
$691$	−0.570970			−0.0217207			−0.0108604	−	0.999941i	$-0.503457\pi$
$691$	−0.570970			−0.0217207			−0.0108604	+	0.999941i	$0.503457\pi$
$692$			23.2053i			0.882132i
$693$		0			0
$694$	6.14337	−	10.6406i	0.233199	−	0.403913i
$695$	17.4831	−	41.1438i	0.663171	−	1.56067i
$696$		0			0
$697$	−0.631035	−	0.364328i	−0.0239022	−	0.0137999i
$698$	−20.0337	+	11.5665i	−0.758287	+	0.437797i
$699$		0			0
$700$	19.3889	+	5.57575i	0.732833	+	0.210743i
$701$	−3.36247	−	5.82398i	−0.126999	−	0.219969i	0.795514	−	0.605936i	$-0.207201\pi$
$701$	−3.36247	−	5.82398i	−0.126999	−	0.219969i	−0.922513	+	0.385967i	$0.873868\pi$
$702$		0			0
$703$	−2.65790	−	6.15494i	−0.100245	−	0.232138i
$704$	−1.47054			−0.0554230
$705$		0			0
$706$	−1.13608	−	1.96775i	−0.0427569	−	0.0740571i
$707$	1.76188	+	1.01722i	0.0662625	+	0.0382566i
$708$		0			0
$709$	−15.4517	+	26.7632i	−0.580302	+	1.00511i	0.415141	+	0.909757i	$0.363732\pi$
$709$	−15.4517	+	26.7632i	−0.580302	+	1.00511i	−0.995443	+	0.0953554i	$0.969601\pi$
$710$	−17.8552	−	7.58716i	−0.670095	−	0.284741i
$711$		0			0
$712$	1.40962	+	0.813846i	0.0528278	+	0.0305002i
$713$	−9.47717	−	5.47164i	−0.354923	−	0.204915i
$714$		0			0
$715$	−15.3171	−	6.50866i	−0.572828	−	0.243410i
$716$	3.18779	−	5.52142i	0.119133	−	0.206345i
$717$		0			0
$718$	−17.9101	−	10.3404i	−0.668400	−	0.385901i
$719$	11.7185	+	20.2970i	0.437025	+	0.756949i	0.997458	−	0.0712504i	$-0.0226989\pi$
$719$	11.7185	+	20.2970i	0.437025	+	0.756949i	−0.560434	+	0.828199i	$0.689366\pi$
$720$		0			0
$721$	−21.5384			−0.802133
$722$	−4.36691	+	18.4914i	−0.162520	+	0.688177i
$723$		0			0
$724$	−4.39603	−	7.61415i	−0.163377	−	0.282978i
$725$	−5.81740	+	20.2293i	−0.216053	+	0.751296i
$726$		0			0
$727$	34.0238	−	19.6436i	1.26187	−	0.728543i	0.288436	−	0.957499i	$-0.406865\pi$
$727$	34.0238	−	19.6436i	1.26187	−	0.728543i	0.973437	+	0.228957i	$0.0735314\pi$
$728$	−17.6860	−	10.2110i	−0.655486	−	0.378445i
$729$		0			0
$730$	−11.1184	+	26.1656i	−0.411512	+	0.968432i
$731$	−0.215266	+	0.372851i	−0.00796189	+	0.0137904i
$732$		0			0
$733$			45.2875i			1.67273i	0.548171	+	0.836366i	$0.315324\pi$
$733$			45.2875i			1.67273i	−0.548171	+	0.836366i	$0.684676\pi$
$734$	36.6899			1.35425
$735$		0			0
$736$	−1.28274	−	2.22178i	−0.0472826	−	0.0818959i
$737$	−13.6935	−	7.90592i	−0.504405	−	0.291218i
$738$		0			0
$739$	15.7422	+	27.2663i	0.579086	+	1.00301i	0.995585	+	0.0938695i	$0.0299237\pi$
$739$	15.7422	+	27.2663i	0.579086	+	1.00301i	−0.416499	+	0.909136i	$0.636743\pi$
$740$	−3.16532	−	1.34503i	−0.116359	−	0.0494442i
$741$		0			0
$742$			43.0023i			1.57866i
$743$	40.4415	−	23.3489i	1.48365	−	0.856587i	0.483826	−	0.875164i	$-0.339247\pi$
$743$	40.4415	−	23.3489i	1.48365	−	0.856587i	0.999827	+	0.0185770i	$0.00591359\pi$
$744$		0			0
$745$	16.4199	+	21.8073i	0.601577	+	0.798956i
$746$	−9.76898	−	16.9204i	−0.357668	−	0.619499i
$747$		0			0
$748$			0.138039i			0.00504719i
$749$	−72.3365			−2.64312
$750$		0			0
$751$	−14.8807	+	25.7741i	−0.543004	+	0.940510i	0.455726	+	0.890120i	$0.349380\pi$
$751$	−14.8807	+	25.7741i	−0.543004	+	0.940510i	−0.998730	+	0.0503901i	$0.983954\pi$
$752$		−	4.03603i		−	0.147179i
$753$		0			0
$754$	10.6536	−	18.4525i	0.387980	−	0.672000i
$755$	−44.1922	+	5.40896i	−1.60832	+	0.196852i
$756$		0			0
$757$	−11.2784	+	6.51161i	−0.409922	+	0.236668i	−0.690756	−	0.723088i	$-0.742722\pi$
$757$	−11.2784	+	6.51161i	−0.409922	+	0.236668i	0.280834	+	0.959756i	$0.409389\pi$
$758$	3.00339	−	1.73401i	0.109088	−	0.0629820i
$759$		0			0
$760$	4.92257	+	8.41239i	0.178560	+	0.305150i
$761$	−43.4538			−1.57520			−0.787600	−	0.616187i	$-0.788676\pi$
$761$	−43.4538			−1.57520			−0.787600	+	0.616187i	$0.788676\pi$
$762$		0			0
$763$	31.0042	−	17.9003i	1.12243	−	0.648034i
$764$	−6.48293	+	11.2288i	−0.234544	+	0.406242i
$765$		0			0
$766$	−12.5509	+	21.7388i	−0.453483	+	0.785456i
$767$			31.1369i			1.12429i
$768$		0			0
$769$	−23.6418	+	40.9487i	−0.852544	+	1.47665i	0.0263617	+	0.999652i	$0.491608\pi$
$769$	−23.6418	+	40.9487i	−0.852544	+	1.47665i	−0.878905	+	0.476996i	$0.841725\pi$
$770$	7.98072	+	10.5992i	0.287605	+	0.381969i
$771$		0			0
$772$		−	6.11656i		−	0.220140i
$773$	−11.4692	−	6.62172i	−0.412517	−	0.238167i	0.279354	−	0.960188i	$-0.409880\pi$
$773$	−11.4692	−	6.62172i	−0.412517	−	0.238167i	−0.691871	+	0.722022i	$0.743213\pi$
$774$		0			0
$775$	20.6983	−	5.14385i	0.743505	−	0.184772i
$776$	−5.97438	−	10.3479i	−0.214468	−	0.371469i
$777$		0			0
$778$		−	14.0415i		−	0.503411i
$779$	−27.1485	−	20.1944i	−0.972696	−	0.723541i
$780$		0			0
$781$	−6.37928	−	11.0492i	−0.228269	−	0.395373i
$782$	−0.208557	+	0.120411i	−0.00745799	+	0.00430587i
$783$		0			0
$784$	4.64040	+	8.03741i	0.165729	+	0.287050i
$785$	28.9999	−	21.8356i	1.03505	−	0.779345i
$786$		0			0
$787$		−	21.7913i		−	0.776775i	−0.921496	−	0.388388i	$-0.873032\pi$
$787$		−	21.7913i		−	0.776775i	0.921496	−	0.388388i	$-0.126968\pi$
$788$	−6.36478	−	3.67471i	−0.226736	−	0.130906i
$789$		0			0
$790$	−26.6760	−	11.3353i	−0.949089	−	0.403293i
$791$	−64.0212			−2.27633
$792$		0			0
$793$	5.73079	−	3.30867i	0.203506	−	0.117494i
$794$	15.3729	−	26.6267i	0.545564	−	0.944945i
$795$		0			0
$796$	−1.71780	−	2.97531i	−0.0608857	−	0.105457i
$797$		−	14.8524i		−	0.526099i	−0.964782	−	0.263049i	$-0.915272\pi$
$797$		−	14.8524i		−	0.526099i	0.964782	−	0.263049i	$-0.0847283\pi$
$798$		0			0
$799$	−0.378860			−0.0134031
$800$	4.80525	+	1.38186i	0.169891	+	0.0488563i
$801$		0			0
$802$	−33.5183	−	19.3518i	−1.18357	−	0.683335i
$803$	−16.1919	+	9.34838i	−0.571399	+	0.329897i
$804$		0			0
$805$	−9.05237	+	21.3034i	−0.319054	+	0.750846i
$806$	−21.5893			−0.760450
$807$		0			0
$808$	0.436656	+	0.252103i	0.0153615	+	0.00886897i
$809$	−0.338772			−0.0119106			−0.00595530	−	0.999982i	$-0.501896\pi$
$809$	−0.338772			−0.0119106			−0.00595530	+	0.999982i	$0.501896\pi$
$810$		0			0
$811$	−2.04652	+	3.54467i	−0.0718629	+	0.124470i	−0.899718	−	0.436472i	$-0.856228\pi$
$811$	−2.04652	+	3.54467i	−0.0718629	+	0.124470i	0.827855	+	0.560942i	$0.189561\pi$
$812$	−14.7107	+	8.49321i	−0.516243	+	0.298053i
$813$		0			0
$814$	−1.13090	−	1.95877i	−0.0396380	−	0.0686550i
$815$	0.558939	+	4.56664i	0.0195788	+	0.159962i
$816$		0			0
$817$	−11.9320	+	16.0409i	−0.417448	+	0.561199i
$818$		−	20.7839i		−	0.726694i
$819$		0			0
$820$	−17.2288	+	2.10874i	−0.601656	+	0.0736404i
$821$	−17.2054	+	29.8007i	−0.600474	+	1.04005i	0.392275	+	0.919848i	$0.371688\pi$
$821$	−17.2054	+	29.8007i	−0.600474	+	1.04005i	−0.992749	+	0.120203i	$0.961645\pi$
$822$		0			0
$823$	10.3009	+	5.94720i	0.359065	+	0.207306i	0.668671	−	0.743559i	$-0.266864\pi$
$823$	10.3009	+	5.94720i	0.359065	+	0.207306i	−0.309605	+	0.950865i	$0.600197\pi$
$824$	−5.33797			−0.185957
$825$		0			0
$826$	12.4115	−	21.4973i	0.431850	−	0.747986i
$827$	10.5632	+	6.09865i	0.367318	+	0.212071i	0.672286	−	0.740292i	$-0.265313\pi$
$827$	10.5632	+	6.09865i	0.367318	+	0.212071i	−0.304968	+	0.952363i	$0.598646\pi$
$828$		0			0
$829$	33.0048			1.14631			0.573153	−	0.819449i	$-0.305720\pi$
$829$	33.0048			1.14631			0.573153	+	0.819449i	$0.305720\pi$
$830$	2.77515	+	3.68568i	0.0963268	+	0.127932i
$831$		0			0
$832$	−4.38320	−	2.53064i	−0.151960	−	0.0877342i
$833$	0.754467	−	0.435592i	0.0261407	−	0.0150924i
$834$		0			0
$835$	44.7154	+	19.0008i	1.54744	+	0.657549i
$836$	−0.741602	+	6.36689i	−0.0256488	+	0.220203i
$837$		0			0
$838$	31.4083	−	18.1336i	1.08498	−	0.626414i
$839$	8.97119	+	15.5386i	0.309720	+	0.536451i	0.978301	−	0.207189i	$-0.0664314\pi$
$839$	8.97119	+	15.5386i	0.309720	+	0.536451i	−0.668581	+	0.743639i	$0.733098\pi$
$840$		0			0
$841$	5.63869	+	9.76650i	0.194438	+	0.336776i
$842$	−18.5697	−	10.7212i	−0.639953	−	0.369477i
$843$		0			0
$844$	4.03940			0.139042
$845$	−16.9695	−	22.5372i	−0.583769	−	0.775304i
$846$		0			0
$847$		−	35.6589i		−	1.22525i
$848$			10.6575i			0.365979i
$849$		0			0
$850$	0.129715	−	0.451066i	0.00444918	−	0.0154714i
$851$	1.97295	−	3.41726i	0.0676320	−	0.117142i
$852$		0			0
$853$	19.4891	−	11.2520i	0.667295	−	0.385263i	−0.127756	−	0.991806i	$-0.540777\pi$
$853$	19.4891	−	11.2520i	0.667295	−	0.385263i	0.795051	+	0.606543i	$0.207444\pi$
$854$	−5.27547			−0.180523
$855$		0			0
$856$	−17.9275			−0.612749
$857$	1.71631	−	0.990914i	0.0586281	−	0.0338490i	−0.470399	−	0.882454i	$-0.655890\pi$
$857$	1.71631	−	0.990914i	0.0586281	−	0.0338490i	0.529028	+	0.848605i	$0.322557\pi$
$858$		0			0
$859$	−16.4673	+	28.5223i	−0.561858	+	0.973167i	0.435476	+	0.900200i	$0.356580\pi$
$859$	−16.4673	+	28.5223i	−0.561858	+	0.973167i	−0.997334	+	0.0729670i	$0.976753\pi$
$860$	1.24596	+	10.1797i	0.0424870	+	0.347126i
$861$		0			0
$862$		−	5.82431i		−	0.198377i
$863$			1.13901i			0.0387723i	0.999812	+	0.0193862i	$0.00617119\pi$
$863$			1.13901i			0.0387723i	−0.999812	+	0.0193862i	$0.993829\pi$
$864$		0			0
$865$	41.4520	−	31.2114i	1.40941	−	1.06122i
$866$	−31.6030			−1.07391
$867$		0			0
$868$	14.9055	+	8.60569i	0.505925	+	0.292096i
$869$	−9.53074	−	16.5077i	−0.323308	−	0.559986i
$870$		0			0
$871$	−27.2105	−	47.1300i	−0.921993	−	1.59694i
$872$	7.68392	−	4.43631i	0.260210	−	0.150232i
$873$		0			0
$874$	−10.2664	+	4.43335i	−0.347265	+	0.149960i
$875$	−16.1184	−	42.1343i	−0.544901	−	1.42440i
$876$		0			0
$877$	19.9508	−	11.5186i	0.673692	−	0.388956i	−0.123782	−	0.992309i	$-0.539502\pi$
$877$	19.9508	−	11.5186i	0.673692	−	0.388956i	0.797474	+	0.603353i	$0.206169\pi$
$878$	1.61592	+	0.932951i	0.0545346	+	0.0314856i
$879$		0			0
$880$	1.97790	+	2.62685i	0.0666749	+	0.0885511i
$881$	6.22555			0.209744			0.104872	−	0.994486i	$-0.466557\pi$
$881$	6.22555			0.209744			0.104872	+	0.994486i	$0.466557\pi$
$882$		0			0
$883$	−28.2402	−	16.3045i	−0.950360	−	0.548691i	−0.0571672	−	0.998365i	$-0.518207\pi$
$883$	−28.2402	−	16.3045i	−0.950360	−	0.548691i	−0.893193	+	0.449674i	$0.851540\pi$
$884$	−0.237550	+	0.411448i	−0.00798967	+	0.0138385i
$885$		0			0
$886$	−15.7464			−0.529009
$887$	3.26261	+	1.88367i	0.109548	+	0.0632474i	0.553773	−	0.832668i	$-0.313188\pi$
$887$	3.26261	+	1.88367i	0.109548	+	0.0632474i	−0.444225	+	0.895915i	$0.646521\pi$
$888$		0			0
$889$	13.4484	−	23.2933i	0.451045	−	0.781234i
$890$	−0.442177	−	3.61267i	−0.0148218	−	0.121097i
$891$		0			0
$892$		−	18.0519i		−	0.604421i
$893$	−17.4745	−	2.03539i	−0.584762	−	0.0681118i
$894$		0			0
$895$	−14.1506	+	1.73199i	−0.473004	+	0.0578939i
$896$	2.01747	+	3.49437i	0.0673991	+	0.116739i
$897$		0			0
$898$	−25.7588	+	14.8718i	−0.859581	+	0.496279i
$899$	−8.97866	+	15.5515i	−0.299455	+	0.518671i
$900$		0			0
$901$	1.00041			0.0333285
$902$	−9.88567	−	5.70749i	−0.329157	−	0.190039i
$903$		0			0
$904$	−15.8667			−0.527718
$905$	−7.68856	+	18.0939i	−0.255576	+	0.601461i
$906$		0			0
$907$	−8.85151	+	5.11042i	−0.293910	+	0.169689i	−0.639704	−	0.768622i	$-0.720943\pi$
$907$	−8.85151	+	5.11042i	−0.293910	+	0.169689i	0.345794	+	0.938310i	$0.387610\pi$
$908$	−23.2539	−	13.4257i	−0.771709	−	0.445547i
$909$		0			0
$910$	5.54782	+	45.3267i	0.183909	+	1.50257i
$911$	18.6042			0.616383			0.308192	−	0.951324i	$-0.400276\pi$
$911$	18.6042			0.616383			0.308192	+	0.951324i	$0.400276\pi$
$912$		0			0
$913$			3.03414i			0.100415i
$914$	6.39456	+	11.0757i	0.211513	+	0.366352i
$915$		0			0
$916$	6.85657	−	11.8759i	0.226548	−	0.392392i
$917$	−24.7250	+	14.2750i	−0.816492	+	0.471402i
$918$		0			0
$919$	35.5145			1.17152			0.585758	−	0.810486i	$-0.300797\pi$
$919$	35.5145			1.17152			0.585758	+	0.810486i	$0.300797\pi$
$920$	−2.24349	+	5.27972i	−0.0739657	+	0.174067i
$921$		0			0
$922$	10.3283	+	5.96303i	0.340143	+	0.196382i
$923$		−	43.9123i		−	1.44539i
$924$		0			0
$925$	1.85476	+	7.46335i	0.0609841	+	0.245393i
$926$	9.66039	+	16.7323i	0.317460	+	0.549857i
$927$		0			0
$928$	−3.64581	+	2.10491i	−0.119680	+	0.0690971i
$929$	−2.13612	−	3.69987i	−0.0700838	−	0.121389i	0.828854	−	0.559465i	$-0.188993\pi$
$929$	−2.13612	−	3.69987i	−0.0700838	−	0.121389i	−0.898938	+	0.438076i	$0.855660\pi$
$930$		0			0
$931$	37.1392	−	16.0379i	1.21719	−	0.525621i
$932$			0.00661073i			0.000216542i
$933$		0			0
$934$	13.3504	+	23.1237i	0.436840	+	0.756629i
$935$	0.246581	−	0.185664i	0.00806406	−	0.00607187i
$936$		0			0
$937$	44.5676	+	25.7311i	1.45596	+	0.840599i	0.998809	−	0.0487891i	$-0.0155362\pi$
$937$	44.5676	+	25.7311i	1.45596	+	0.840599i	0.457152	+	0.889389i	$0.348870\pi$
$938$			43.3854i			1.41658i
$939$		0			0
$940$	−7.20963	+	5.42852i	−0.235152	+	0.177059i
$941$	30.2442	−	52.3845i	0.985934	−	1.70769i	0.348222	−	0.937412i	$-0.386786\pi$
$941$	30.2442	−	52.3845i	0.985934	−	1.70769i	0.637712	−	0.770275i	$-0.279881\pi$
$942$		0			0
$943$		−	19.9145i		−	0.648505i
$944$	3.07599	−	5.32777i	0.100115	−	0.173404i
$945$		0			0
$946$	−3.37231	+	5.84101i	−0.109643	+	0.189908i
$947$	−10.0415	+	5.79749i	−0.326306	+	0.188393i	−0.654200	−	0.756322i	$-0.726995\pi$
$947$	−10.0415	+	5.79749i	−0.326306	+	0.188393i	0.327894	+	0.944715i	$0.393661\pi$
$948$		0			0
$949$	−64.3503			−2.08890
$950$	8.40627	−	20.1081i	0.272736	−	0.652392i
$951$		0			0
$952$	0.328014	−	0.189379i	0.0106310	−	0.00613781i
$953$	22.5443	−	13.0160i	0.730282	−	0.421629i	−0.0882433	−	0.996099i	$-0.528125\pi$
$953$	22.5443	−	13.0160i	0.730282	−	0.421629i	0.818525	+	0.574470i	$0.194792\pi$
$954$		0			0
$955$	28.7778	−	3.52229i	0.931227	−	0.113979i
$956$	−2.33750	+	4.04866i	−0.0756000	+	0.130943i
$957$		0			0
$958$			13.5825i			0.438830i
$959$	−38.0425	+	65.8916i	−1.22846	+	2.12775i
$960$		0			0
$961$	−12.8049			−0.413060
$962$		−	7.78462i		−	0.250986i
$963$		0			0
$964$	−13.9044	−	24.0831i	−0.447829	−	0.775663i
$965$	−10.9261	+	8.22688i	−0.351725	+	0.264833i
$966$		0			0
$967$	14.9595	−	8.63685i	0.481064	−	0.277743i	−0.239796	−	0.970823i	$-0.577080\pi$
$967$	14.9595	−	8.63685i	0.481064	−	0.277743i	0.720860	+	0.693081i	$0.243747\pi$
$968$		−	8.83752i		−	0.284049i
$969$		0			0
$970$	−10.4491	+	24.5903i	−0.335499	+	0.789547i
$971$	−5.47052	−	9.47522i	−0.175557	−	0.304074i	0.764797	−	0.644272i	$-0.222839\pi$
$971$	−5.47052	−	9.47522i	−0.175557	−	0.304074i	−0.940354	+	0.340198i	$0.889506\pi$
$972$		0			0
$973$	−69.8605	−	40.3340i	−2.23963	−	1.29305i
$974$	−4.01820	−	6.95973i	−0.128752	−	0.223004i
$975$		0			0
$976$	−1.30744			−0.0418503
$977$			9.01488i			0.288412i	0.989548	+	0.144206i	$0.0460627\pi$
$977$			9.01488i			0.288412i	−0.989548	+	0.144206i	$0.953937\pi$
$978$		0			0
$979$	1.19679	−	2.07290i	0.0382496	−	0.0662503i
$980$	8.11595	−	19.0997i	0.259255	−	0.610117i
$981$		0			0
$982$	17.9077	+	10.3390i	0.571457	+	0.329931i
$983$	12.8956	−	7.44527i	0.411305	−	0.237467i	−0.280045	−	0.959987i	$-0.590349\pi$
$983$	12.8956	−	7.44527i	0.411305	−	0.237467i	0.691350	+	0.722520i	$0.257016\pi$
$984$		0			0
$985$	1.99653	+	16.3121i	0.0636149	+	0.519745i
$986$	0.197587	+	0.342231i	0.00629245	+	0.0108988i
$987$		0			0
$988$	−13.1672	+	17.7014i	−0.418905	+	0.563157i
$989$	−11.7666			−0.374156
$990$		0			0
$991$	−23.1717	−	40.1346i	−0.736075	−	1.27492i	−0.954250	−	0.299009i	$-0.903344\pi$
$991$	−23.1717	−	40.1346i	−0.736075	−	1.27492i	0.218176	−	0.975910i	$-0.429989\pi$
$992$	3.69410	+	2.13279i	0.117288	+	0.0677161i
$993$		0			0
$994$	−17.5038	+	30.3175i	−0.555188	+	0.961613i
$995$	−3.00439	+	7.07037i	−0.0952454	+	0.224146i
$996$		0			0
$997$	26.1990	+	15.1260i	0.829730	+	0.479045i	0.853760	−	0.520667i	$-0.174317\pi$
$997$	26.1990	+	15.1260i	0.829730	+	0.479045i	−0.0240304	+	0.999711i	$0.507650\pi$
$998$	0.954638	+	0.551160i	0.0302185	+	0.0174467i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.t.c.919.1		20
3.2	odd	2		570.2.q.c.349.10	yes	20
5.4	even	2	inner	1710.2.t.c.919.9		20
15.14	odd	2		570.2.q.c.349.2	yes	20
19.11	even	3	inner	1710.2.t.c.1189.9		20
57.11	odd	6		570.2.q.c.49.2	✓	20
95.49	even	6	inner	1710.2.t.c.1189.1		20
285.239	odd	6		570.2.q.c.49.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.q.c.49.2	✓	20	57.11	odd	6
570.2.q.c.49.10	yes	20	285.239	odd	6
570.2.q.c.349.2	yes	20	15.14	odd	2
570.2.q.c.349.10	yes	20	3.2	odd	2
1710.2.t.c.919.1		20	1.1	even	1	trivial
1710.2.t.c.919.9		20	5.4	even	2	inner
1710.2.t.c.1189.1		20	95.49	even	6	inner
1710.2.t.c.1189.9		20	19.11	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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.21950 + 0.271659i) q^{5} +4.03495i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.21950 + 0.271659i) q^{5} +4.03495i q^{7} +1.00000i q^{8} +(1.78632 - 1.34502i) q^{10} +1.47054 q^{11} +(4.38320 + 2.53064i) q^{13} +(-2.01747 - 3.49437i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.0812933 + 0.0469347i) q^{17} +(-4.00172 + 1.72807i) q^{19} +(-0.874489 + 2.05798i) q^{20} +(-1.27352 + 0.735269i) q^{22} +(-2.22178 - 1.28274i) q^{23} +(4.85240 - 1.20590i) q^{25} -5.06128 q^{26} +(3.49437 + 2.01747i) q^{28} +(-2.10491 + 3.64581i) q^{29} +4.26558 q^{31} +(0.866025 + 0.500000i) q^{32} +(0.0469347 - 0.0812933i) q^{34} +(-1.09613 - 8.95558i) q^{35} +1.53807i q^{37} +(2.60156 - 3.49741i) q^{38} +(-0.271659 - 2.21950i) q^{40} +(3.88123 + 6.72248i) q^{41} +(3.97202 - 2.29325i) q^{43} +(0.735269 - 1.27352i) q^{44} +2.56549 q^{46} +(3.49530 + 2.01801i) q^{47} -9.28080 q^{49} +(-3.59936 + 3.47054i) q^{50} +(4.38320 - 2.53064i) q^{52} +(-9.22964 - 5.32873i) q^{53} +(-3.26387 + 0.399485i) q^{55} -4.03495 q^{56} -4.20982i q^{58} +(3.07599 + 5.32777i) q^{59} +(0.653722 - 1.13228i) q^{61} +(-3.69410 + 2.13279i) q^{62} -1.00000 q^{64} +(-10.4160 - 4.42603i) q^{65} +(-9.31187 - 5.37621i) q^{67} +0.0938694i q^{68} +(5.42707 + 7.20770i) q^{70} +(-4.33806 - 7.51373i) q^{71} +(-11.0108 + 6.35711i) q^{73} +(-0.769037 - 1.33201i) q^{74} +(-0.504306 + 4.32963i) q^{76} +5.93355i q^{77} +(-6.48112 - 11.2256i) q^{79} +(1.34502 + 1.78632i) q^{80} +(-6.72248 - 3.88123i) q^{82} +2.06328i q^{83} +(0.167681 - 0.126256i) q^{85} +(-2.29325 + 3.97202i) q^{86} +1.47054i q^{88} +(0.813846 - 1.40962i) q^{89} +(-10.2110 + 17.6860i) q^{91} +(-2.22178 + 1.28274i) q^{92} -4.03603 q^{94} +(8.41239 - 4.92257i) q^{95} +(-10.3479 + 5.97438i) q^{97} +(8.03741 - 4.64040i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{4}+O(q^{10}) \) 20 * q + 10 * q^4	\( 20 q + 10 q^{4} - 2 q^{10} - 12 q^{11} - 10 q^{14} - 10 q^{16} + 6 q^{19} + 14 q^{25} - 8 q^{29} + 40 q^{31} + 12 q^{34} - 2 q^{35} + 2 q^{40} + 14 q^{41} - 6 q^{44} + 44 q^{46} - 8 q^{49} + 8 q^{50} - 20 q^{56} - 8 q^{59} + 16 q^{61} - 20 q^{64} - 40 q^{65} + 8 q^{70} + 4 q^{71} - 26 q^{74} + 8 q^{79} - 16 q^{85} + 20 q^{86} + 2 q^{89} - 44 q^{91} - 32 q^{94} + 80 q^{95}+O(q^{100}) \) 20 * q + 10 * q^4 - 2 * q^10 - 12 * q^11 - 10 * q^14 - 10 * q^16 + 6 * q^19 + 14 * q^25 - 8 * q^29 + 40 * q^31 + 12 * q^34 - 2 * q^35 + 2 * q^40 + 14 * q^41 - 6 * q^44 + 44 * q^46 - 8 * q^49 + 8 * q^50 - 20 * q^56 - 8 * q^59 + 16 * q^61 - 20 * q^64 - 40 * q^65 + 8 * q^70 + 4 * q^71 - 26 * q^74 + 8 * q^79 - 16 * q^85 + 20 * q^86 + 2 * q^89 - 44 * q^91 - 32 * q^94 + 80 * q^95

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