LMFDB - Embedded newform 1710.2.l.q.1531.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1261,1710)]

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, 0, 2]))

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

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

chi := DirichletCharacter("1710.1261");

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.l (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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.29654208.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 14x^{4} + 49x^{2} + 12 $ x^6 + 14x^4 + 49x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1531.1
Root			$2.35084i$ of defining polynomial
Character	$\chi$	$=$	1710.1531
Dual form			1710.2.l.q.1261.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -4.59821 q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -4.59821 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} -0.473560 q^{11} +(0.263220 + 0.455910i) q^{13} +(-2.29911 + 3.98217i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.27267 + 3.93637i) q^{17} +(2.56233 - 3.52626i) q^{19} -1.00000 q^{20} +(-0.236780 + 0.410115i) q^{22} +(-0.236780 - 0.410115i) q^{23} +(-0.500000 - 0.866025i) q^{25} +0.526440 q^{26} +(2.29911 + 3.98217i) q^{28} +(4.32555 + 7.49206i) q^{29} -0.526440 q^{31} +(0.500000 + 0.866025i) q^{32} +(2.27267 + 3.93637i) q^{34} +(-2.29911 + 3.98217i) q^{35} -1.00000 q^{37} +(-1.77267 - 3.98217i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(-5.63410 + 9.75854i) q^{41} +(-6.33499 + 10.9725i) q^{43} +(0.236780 + 0.410115i) q^{44} -0.473560 q^{46} +(4.07177 + 7.05251i) q^{47} +14.1435 q^{49} -1.00000 q^{50} +(0.263220 - 0.455910i) q^{52} +(0.964114 + 1.66990i) q^{53} +(-0.236780 + 0.410115i) q^{55} +4.59821 q^{56} +8.65109 q^{58} +(3.00000 - 5.19615i) q^{59} +(-1.53589 - 2.66023i) q^{61} +(-0.263220 + 0.455910i) q^{62} +1.00000 q^{64} +0.526440 q^{65} +(-4.53589 - 7.85638i) q^{67} +4.54533 q^{68} +(2.29911 + 3.98217i) q^{70} +(-2.27267 + 3.93637i) q^{71} +(1.46411 - 2.53592i) q^{73} +(-0.500000 + 0.866025i) q^{74} +(-4.33499 - 0.455910i) q^{76} +2.17753 q^{77} +(0.736780 - 1.27614i) q^{79} +(0.500000 + 0.866025i) q^{80} +(5.63410 + 9.75854i) q^{82} -4.10576 q^{83} +(2.27267 + 3.93637i) q^{85} +(6.33499 + 10.9725i) q^{86} +0.473560 q^{88} +(-0.964114 - 1.66990i) q^{89} +(-1.21034 - 2.09637i) q^{91} +(-0.236780 + 0.410115i) q^{92} +8.14354 q^{94} +(-1.77267 - 3.98217i) q^{95} +(-8.79911 + 15.2405i) q^{97} +(7.07177 - 12.2487i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} + 2 q^{7} - 6 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 + 2 * q^7 - 6 * q^8	$ 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} + 2 q^{7} - 6 q^{8} - 3 q^{10} - 8 q^{11} - q^{13} + q^{14} - 3 q^{16} - 4 q^{17} - 2 q^{19} - 6 q^{20} - 4 q^{22} - 4 q^{23} - 3 q^{25} - 2 q^{26} - q^{28} + 6 q^{29} + 2 q^{31} + 3 q^{32} + 4 q^{34} + q^{35} - 6 q^{37} - q^{38} - 3 q^{40} + 8 q^{41} - 11 q^{43} + 4 q^{44} - 8 q^{46} + 36 q^{49} - 6 q^{50} - q^{52} + 18 q^{53} - 4 q^{55} - 2 q^{56} + 12 q^{58} + 18 q^{59} + 3 q^{61} + q^{62} + 6 q^{64} - 2 q^{65} - 15 q^{67} + 8 q^{68} - q^{70} - 4 q^{71} + 21 q^{73} - 3 q^{74} + q^{76} - 32 q^{77} + 7 q^{79} + 3 q^{80} - 8 q^{82} - 4 q^{83} + 4 q^{85} + 11 q^{86} + 8 q^{88} - 18 q^{89} - 15 q^{91} - 4 q^{92} - q^{95} - 38 q^{97} + 18 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 + 2 * q^7 - 6 * q^8 - 3 * q^10 - 8 * q^11 - q^13 + q^14 - 3 * q^16 - 4 * q^17 - 2 * q^19 - 6 * q^20 - 4 * q^22 - 4 * q^23 - 3 * q^25 - 2 * q^26 - q^28 + 6 * q^29 + 2 * q^31 + 3 * q^32 + 4 * q^34 + q^35 - 6 * q^37 - q^38 - 3 * q^40 + 8 * q^41 - 11 * q^43 + 4 * q^44 - 8 * q^46 + 36 * q^49 - 6 * q^50 - q^52 + 18 * q^53 - 4 * q^55 - 2 * q^56 + 12 * q^58 + 18 * q^59 + 3 * q^61 + q^62 + 6 * q^64 - 2 * q^65 - 15 * q^67 + 8 * q^68 - q^70 - 4 * q^71 + 21 * q^73 - 3 * q^74 + q^76 - 32 * q^77 + 7 * q^79 + 3 * q^80 - 8 * q^82 - 4 * q^83 + 4 * q^85 + 11 * q^86 + 8 * q^88 - 18 * q^89 - 15 * q^91 - 4 * q^92 - q^95 - 38 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	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
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−4.59821			−1.73796			−0.868980	−	0.494847i	$-0.835224\pi$
$7$	−4.59821			−1.73796			−0.868980	+	0.494847i	$0.835224\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−0.473560			−0.142784			−0.0713919	−	0.997448i	$-0.522744\pi$
$11$	−0.473560			−0.142784			−0.0713919	+	0.997448i	$0.522744\pi$
$12$		0			0
$13$	0.263220	+	0.455910i	0.0730041	+	0.126447i	0.900217	−	0.435442i	$-0.143408\pi$
$13$	0.263220	+	0.455910i	0.0730041	+	0.126447i	−0.827213	+	0.561889i	$0.810075\pi$
$14$	−2.29911	+	3.98217i	−0.614462	+	1.06428i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.27267	+	3.93637i	−0.551202	+	0.954711i	0.446986	+	0.894541i	$0.352497\pi$
$17$	−2.27267	+	3.93637i	−0.551202	+	0.954711i	−0.998188	+	0.0601695i	$0.980836\pi$
$18$		0			0
$19$	2.56233	−	3.52626i	0.587838	−	0.808979i
$19$	2.56233	−	3.52626i	0.587838	−	0.808979i
$20$	−1.00000			−0.223607
$21$		0			0
$22$	−0.236780	+	0.410115i	−0.0504817	+	0.0874369i
$23$	−0.236780	−	0.410115i	−0.0493721	−	0.0855149i	0.840283	−	0.542148i	$-0.182389\pi$
$23$	−0.236780	−	0.410115i	−0.0493721	−	0.0855149i	−0.889655	+	0.456633i	$0.849055\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.526440			0.103243
$27$		0			0
$28$	2.29911	+	3.98217i	0.434490	+	0.752559i
$29$	4.32555	+	7.49206i	0.803234	+	1.39124i	0.917477	+	0.397789i	$0.130222\pi$
$29$	4.32555	+	7.49206i	0.803234	+	1.39124i	−0.114244	+	0.993453i	$0.536444\pi$
$30$		0			0
$31$	−0.526440			−0.0945514			−0.0472757	−	0.998882i	$-0.515054\pi$
$31$	−0.526440			−0.0945514			−0.0472757	+	0.998882i	$0.515054\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	2.27267	+	3.93637i	0.389759	+	0.675082i
$35$	−2.29911	+	3.98217i	−0.388620	+	0.673109i
$36$		0			0
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−1.77267	−	3.98217i	−0.287564	−	0.645993i
$39$		0			0
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−5.63410	+	9.75854i	−0.879898	+	1.52403i	−0.0284461	+	0.999595i	$0.509056\pi$
$41$	−5.63410	+	9.75854i	−0.879898	+	1.52403i	−0.851452	+	0.524433i	$0.824277\pi$
$42$		0			0
$43$	−6.33499	+	10.9725i	−0.966077	+	1.67329i	−0.259384	+	0.965774i	$0.583520\pi$
$43$	−6.33499	+	10.9725i	−0.966077	+	1.67329i	−0.706693	+	0.707520i	$0.749814\pi$
$44$	0.236780	+	0.410115i	0.0356959	+	0.0618272i
$45$		0			0
$46$	−0.473560			−0.0698227
$47$	4.07177	+	7.05251i	0.593929	+	1.02871i	0.993697	+	0.112099i	$0.0357573\pi$
$47$	4.07177	+	7.05251i	0.593929	+	1.02871i	−0.399768	+	0.916616i	$0.630909\pi$
$48$		0			0
$49$	14.1435			2.02051
$50$	−1.00000			−0.141421
$51$		0			0
$52$	0.263220	−	0.455910i	0.0365020	−	0.0632234i
$53$	0.964114	+	1.66990i	0.132431	+	0.229378i	0.924613	−	0.380907i	$-0.124388\pi$
$53$	0.964114	+	1.66990i	0.132431	+	0.229378i	−0.792182	+	0.610285i	$0.791055\pi$
$54$		0			0
$55$	−0.236780	+	0.410115i	−0.0319274	+	0.0552999i
$56$	4.59821			0.614462
$57$		0			0
$58$	8.65109			1.13594
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$		0			0
$61$	−1.53589	−	2.66023i	−0.196650	−	0.340608i	0.750790	−	0.660541i	$-0.229673\pi$
$61$	−1.53589	−	2.66023i	−0.196650	−	0.340608i	−0.947440	+	0.319933i	$0.896340\pi$
$62$	−0.263220	+	0.455910i	−0.0334290	+	0.0579007i
$63$		0			0
$64$	1.00000			0.125000
$65$	0.526440			0.0652968
$66$		0			0
$67$	−4.53589	−	7.85638i	−0.554147	−	0.959810i	−0.997969	−	0.0636955i	$-0.979711\pi$
$67$	−4.53589	−	7.85638i	−0.554147	−	0.959810i	0.443823	−	0.896115i	$-0.353622\pi$
$68$	4.54533			0.551202
$69$		0			0
$70$	2.29911	+	3.98217i	0.274796	+	0.475960i
$71$	−2.27267	+	3.93637i	−0.269716	+	0.467161i	−0.968788	−	0.247889i	$-0.920263\pi$
$71$	−2.27267	+	3.93637i	−0.269716	+	0.467161i	0.699073	+	0.715051i	$0.253596\pi$
$72$		0			0
$73$	1.46411	−	2.53592i	0.171362	−	0.296807i	−0.767535	−	0.641008i	$-0.778517\pi$
$73$	1.46411	−	2.53592i	0.171362	−	0.296807i	0.938896	+	0.344201i	$0.111850\pi$
$74$	−0.500000	+	0.866025i	−0.0581238	+	0.100673i
$75$		0			0
$76$	−4.33499	−	0.455910i	−0.497258	−	0.0522965i
$77$	2.17753			0.248153
$78$		0			0
$79$	0.736780	−	1.27614i	0.0828942	−	0.143577i	−0.821598	−	0.570068i	$-0.806917\pi$
$79$	0.736780	−	1.27614i	0.0828942	−	0.143577i	0.904492	+	0.426491i	$0.140250\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$		0			0
$82$	5.63410	+	9.75854i	0.622182	+	1.07765i
$83$	−4.10576			−0.450666			−0.225333	−	0.974282i	$-0.572347\pi$
$83$	−4.10576			−0.450666			−0.225333	+	0.974282i	$0.572347\pi$
$84$		0			0
$85$	2.27267	+	3.93637i	0.246505	+	0.426960i
$86$	6.33499	+	10.9725i	0.683120	+	1.18320i
$87$		0			0
$88$	0.473560			0.0504817
$89$	−0.964114	−	1.66990i	−0.102196	−	0.177009i	0.810393	−	0.585886i	$-0.199254\pi$
$89$	−0.964114	−	1.66990i	−0.102196	−	0.177009i	−0.912589	+	0.408878i	$0.865920\pi$
$90$		0			0
$91$	−1.21034	−	2.09637i	−0.126878	−	0.219759i
$92$	−0.236780	+	0.410115i	−0.0246860	+	0.0427575i
$93$		0			0
$94$	8.14354			0.839942
$95$	−1.77267	−	3.98217i	−0.181872	−	0.408562i
$96$		0			0
$97$	−8.79911	+	15.2405i	−0.893414	+	1.54744i	−0.0576582	+	0.998336i	$0.518363\pi$
$97$	−8.79911	+	15.2405i	−0.893414	+	1.54744i	−0.835756	+	0.549102i	$0.814970\pi$
$98$	7.07177	−	12.2487i	0.714357	−	1.23730i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	6.59821	+	11.4284i	0.656547	+	1.13717i	0.981504	+	0.191443i	$0.0613168\pi$
$101$	6.59821	+	11.4284i	0.656547	+	1.13717i	−0.324957	+	0.945729i	$0.605350\pi$
$102$		0			0
$103$	−12.7418			−1.25548			−0.627741	−	0.778422i	$-0.716020\pi$
$103$	−12.7418			−1.25548			−0.627741	+	0.778422i	$0.716020\pi$
$104$	−0.263220	−	0.455910i	−0.0258108	−	0.0447057i
$105$		0			0
$106$	1.92823			0.187286
$107$	10.7946			1.04356			0.521778	−	0.853081i	$-0.325269\pi$
$107$	10.7946			1.04356			0.521778	+	0.853081i	$0.325269\pi$
$108$		0			0
$109$	−3.27267	+	5.66842i	−0.313465	+	0.542936i	−0.979110	−	0.203332i	$-0.934823\pi$
$109$	−3.27267	+	5.66842i	−0.313465	+	0.542936i	0.665645	+	0.746268i	$0.268156\pi$
$110$	0.236780	+	0.410115i	0.0225761	+	0.0391030i
$111$		0			0
$112$	2.29911	−	3.98217i	0.217245	−	0.376279i
$113$	−16.7946			−1.57991			−0.789953	−	0.613167i	$-0.789895\pi$
$113$	−16.7946			−1.57991			−0.789953	+	0.613167i	$0.789895\pi$
$114$		0			0
$115$	−0.473560			−0.0441597
$116$	4.32555	−	7.49206i	0.401617	−	0.695621i
$117$		0			0
$118$	−3.00000	−	5.19615i	−0.276172	−	0.478345i
$119$	10.4502	−	18.1003i	0.957968	−	1.65925i
$120$		0			0
$121$	−10.7757			−0.979613
$122$	−3.07177			−0.278105
$123$		0			0
$124$	0.263220	+	0.455910i	0.0236378	+	0.0409419i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−7.10766	−	12.3108i	−0.630703	−	1.09241i	−0.987408	−	0.158192i	$-0.949433\pi$
$127$	−7.10766	−	12.3108i	−0.630703	−	1.09241i	0.356706	−	0.934217i	$-0.383900\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	0.263220	−	0.455910i	0.0230859	−	0.0399860i
$131$	7.43320	−	12.8747i	0.649442	−	1.12487i	−0.333815	−	0.942639i	$-0.608336\pi$
$131$	7.43320	−	12.8747i	0.649442	−	1.12487i	0.983256	−	0.182227i	$-0.0583307\pi$
$132$		0			0
$133$	−11.7821	+	16.2145i	−1.02164	+	1.40597i
$134$	−9.07177			−0.783682
$135$		0			0
$136$	2.27267	−	3.93637i	0.194879	−	0.337541i
$137$	4.66998	+	8.08865i	0.398983	+	0.691060i	0.993601	−	0.112949i	$-0.0360297\pi$
$137$	4.66998	+	8.08865i	0.398983	+	0.691060i	−0.594617	+	0.804009i	$0.702696\pi$
$138$		0			0
$139$	−2.26322	−	3.92001i	−0.191964	−	0.332491i	0.753937	−	0.656947i	$-0.228152\pi$
$139$	−2.26322	−	3.92001i	−0.191964	−	0.332491i	−0.945901	+	0.324455i	$0.894819\pi$
$140$	4.59821			0.388620
$141$		0			0
$142$	2.27267	+	3.93637i	0.190718	+	0.330333i
$143$	−0.124650	−	0.215901i	−0.0104238	−	0.0180545i
$144$		0			0
$145$	8.65109			0.718434
$146$	−1.46411	−	2.53592i	−0.121171	−	0.209874i
$147$		0			0
$148$	0.500000	+	0.866025i	0.0410997	+	0.0711868i
$149$	−1.20089	+	2.08001i	−0.0983811	+	0.170401i	−0.911015	−	0.412374i	$-0.864700\pi$
$149$	−1.20089	+	2.08001i	−0.0983811	+	0.170401i	0.812634	+	0.582775i	$0.198033\pi$
$150$		0			0
$151$	−15.7418			−1.28105			−0.640523	−	0.767939i	$-0.721282\pi$
$151$	−15.7418			−1.28105			−0.640523	+	0.767939i	$0.721282\pi$
$152$	−2.56233	+	3.52626i	−0.207832	+	0.286017i
$153$		0			0
$154$	1.08876	−	1.88580i	0.0877352	−	0.151962i
$155$	−0.263220	+	0.455910i	−0.0211423	+	0.0366196i
$156$		0			0
$157$	4.09821	−	7.09831i	0.327073	−	0.566507i	−0.654857	−	0.755753i	$-0.727271\pi$
$157$	4.09821	−	7.09831i	0.327073	−	0.566507i	0.981930	+	0.189246i	$0.0606044\pi$
$158$	−0.736780	−	1.27614i	−0.0586151	−	0.101524i
$159$		0			0
$160$	1.00000			0.0790569
$161$	1.08876	+	1.88580i	0.0858067	+	0.148622i
$162$		0			0
$163$	15.5793			1.22027			0.610133	−	0.792299i	$-0.291116\pi$
$163$	15.5793			1.22027			0.610133	+	0.792299i	$0.291116\pi$
$164$	11.2682			0.879898
$165$		0			0
$166$	−2.05288	+	3.55569i	−0.159334	+	0.275975i
$167$	6.23678	+	10.8024i	0.482617	+	0.835916i	0.999801	−	0.0199577i	$-0.00635316\pi$
$167$	6.23678	+	10.8024i	0.482617	+	0.835916i	−0.517184	+	0.855874i	$0.673020\pi$
$168$		0			0
$169$	6.36143	−	11.0183i	0.489341	−	0.847563i
$170$	4.54533			0.348611
$171$		0			0
$172$	12.6700			0.966077
$173$	7.56233	−	13.0983i	0.574953	−	0.995848i	−0.421094	−	0.907017i	$-0.638354\pi$
$173$	7.56233	−	13.0983i	0.574953	−	0.995848i	0.996047	−	0.0888306i	$-0.0283130\pi$
$174$		0			0
$175$	2.29911	+	3.98217i	0.173796	+	0.301024i
$176$	0.236780	−	0.410115i	0.0178480	−	0.0309136i
$177$		0			0
$178$	−1.92823			−0.144527
$179$	1.42068			0.106187			0.0530933	−	0.998590i	$-0.483092\pi$
$179$	1.42068			0.106187			0.0530933	+	0.998590i	$0.483092\pi$
$180$		0			0
$181$	4.39732	+	7.61637i	0.326850	+	0.566121i	0.981885	−	0.189478i	$-0.0606795\pi$
$181$	4.39732	+	7.61637i	0.326850	+	0.566121i	−0.655035	+	0.755598i	$0.727346\pi$
$182$	−2.42068			−0.179433
$183$		0			0
$184$	0.236780	+	0.410115i	0.0174557	+	0.0302341i
$185$	−0.500000	+	0.866025i	−0.0367607	+	0.0636715i
$186$		0			0
$187$	1.07624	−	1.86411i	0.0787028	−	0.136317i
$188$	4.07177	−	7.05251i	0.296964	−	0.514357i
$189$		0			0
$190$	−4.33499	−	0.455910i	−0.314493	−	0.0330752i
$191$	−9.15864			−0.662696			−0.331348	−	0.943509i	$-0.607503\pi$
$191$	−9.15864			−0.662696			−0.331348	+	0.943509i	$0.607503\pi$
$192$		0			0
$193$	−0.588765	+	1.01977i	−0.0423802	+	0.0734047i	−0.886437	−	0.462848i	$-0.846827\pi$
$193$	−0.588765	+	1.01977i	−0.0423802	+	0.0734047i	0.844057	+	0.536253i	$0.180161\pi$
$194$	8.79911	+	15.2405i	0.631739	+	1.09420i
$195$		0			0
$196$	−7.07177	−	12.2487i	−0.505127	−	0.874905i
$197$	−12.2153			−0.870305			−0.435153	−	0.900357i	$-0.643306\pi$
$197$	−12.2153			−0.870305			−0.435153	+	0.900357i	$0.643306\pi$
$198$		0			0
$199$	−1.06233	−	1.84000i	−0.0753062	−	0.130434i	0.825913	−	0.563797i	$-0.190660\pi$
$199$	−1.06233	−	1.84000i	−0.0753062	−	0.130434i	−0.901219	+	0.433363i	$0.857327\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$		0			0
$202$	13.1964			0.928497
$203$	−19.8898	−	34.4501i	−1.39599	−	2.41792i
$204$		0			0
$205$	5.63410	+	9.75854i	0.393502	+	0.681566i
$206$	−6.37088	+	11.0347i	−0.443880	+	0.768823i
$207$		0			0
$208$	−0.526440			−0.0365020
$209$	−1.21342	+	1.66990i	−0.0839337	+	0.115509i
$210$		0			0
$211$	9.49553	−	16.4467i	0.653699	−	1.13224i	−0.328519	−	0.944497i	$-0.606550\pi$
$211$	9.49553	−	16.4467i	0.653699	−	1.13224i	0.982218	−	0.187743i	$-0.0601171\pi$
$212$	0.964114	−	1.66990i	0.0662157	−	0.114689i
$213$		0			0
$214$	5.39732	−	9.34843i	0.368953	−	0.639045i
$215$	6.33499	+	10.9725i	0.432043	+	0.748320i
$216$		0			0
$217$	2.42068			0.164327
$218$	3.27267	+	5.66842i	0.221653	+	0.383914i
$219$		0			0
$220$	0.473560			0.0319274
$221$	−2.39284			−0.160960
$222$		0			0
$223$	−10.4238	+	18.0545i	−0.698026	+	1.20902i	0.271123	+	0.962545i	$0.412605\pi$
$223$	−10.4238	+	18.0545i	−0.698026	+	1.20902i	−0.969150	+	0.246472i	$0.920729\pi$
$224$	−2.29911	−	3.98217i	−0.153615	−	0.266070i
$225$		0			0
$226$	−8.39732	+	14.5446i	−0.558581	+	0.967491i
$227$	−4.79463			−0.318231			−0.159115	−	0.987260i	$-0.550864\pi$
$227$	−4.79463			−0.318231			−0.159115	+	0.987260i	$0.550864\pi$
$228$		0			0
$229$	−18.5264			−1.22426			−0.612131	−	0.790757i	$-0.709687\pi$
$229$	−18.5264			−1.22426			−0.612131	+	0.790757i	$0.709687\pi$
$230$	−0.236780	+	0.410115i	−0.0156128	+	0.0270422i
$231$		0			0
$232$	−4.32555	−	7.49206i	−0.283986	−	0.491878i
$233$	−12.7229	+	22.0366i	−0.833502	+	1.44367i	0.0617416	+	0.998092i	$0.480335\pi$
$233$	−12.7229	+	22.0366i	−0.833502	+	1.44367i	−0.895244	+	0.445576i	$0.852999\pi$
$234$		0			0
$235$	8.14354			0.531226
$236$	−6.00000			−0.390567
$237$		0			0
$238$	−10.4502	−	18.1003i	−0.677386	−	1.17327i
$239$	9.33996			0.604152			0.302076	−	0.953284i	$-0.402320\pi$
$239$	9.33996			0.604152			0.302076	+	0.953284i	$0.402320\pi$
$240$		0			0
$241$	7.21034	+	12.4887i	0.464459	+	0.804466i	0.999177	−	0.0405642i	$-0.0129155\pi$
$241$	7.21034	+	12.4887i	0.464459	+	0.804466i	−0.534718	+	0.845031i	$0.679582\pi$
$242$	−5.38787	+	9.33207i	−0.346345	+	0.599888i
$243$		0			0
$244$	−1.53589	+	2.66023i	−0.0983250	+	0.170304i
$245$	7.07177	−	12.2487i	0.451799	−	0.782539i
$246$		0			0
$247$	2.28211	+	0.240009i	0.145207	+	0.0152714i
$248$	0.526440			0.0334290
$249$		0			0
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−11.6171	−	20.1214i	−0.733265	−	1.27005i	−0.955480	−	0.295055i	$-0.904662\pi$
$251$	−11.6171	−	20.1214i	−0.733265	−	1.27005i	0.222215	−	0.974998i	$-0.428671\pi$
$252$		0			0
$253$	0.112130	+	0.194214i	0.00704953	+	0.0122101i
$254$	−14.2153			−0.891948
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$		0			0
$259$	4.59821			0.285719
$260$	−0.263220	−	0.455910i	−0.0163242	−	0.0282743i
$261$		0			0
$262$	−7.43320	−	12.8747i	−0.459225	−	0.795401i
$263$	−11.2897	+	19.5543i	−0.696150	+	1.20577i	0.273641	+	0.961832i	$0.411772\pi$
$263$	−11.2897	+	19.5543i	−0.696150	+	1.20577i	−0.969791	+	0.243936i	$0.921561\pi$
$264$		0			0
$265$	1.92823			0.118450
$266$	8.15109	+	18.3108i	0.499775	+	1.12271i
$267$		0			0
$268$	−4.53589	+	7.85638i	−0.277073	+	0.479905i
$269$	−0.253774	+	0.439550i	−0.0154729	+	0.0267998i	−0.873658	−	0.486540i	$-0.838259\pi$
$269$	−0.253774	+	0.439550i	−0.0154729	+	0.0267998i	0.858185	+	0.513340i	$0.171592\pi$
$270$		0			0
$271$	−13.1247	+	22.7326i	−0.797266	+	1.38090i	0.124125	+	0.992267i	$0.460388\pi$
$271$	−13.1247	+	22.7326i	−0.797266	+	1.38090i	−0.921390	+	0.388638i	$0.872946\pi$
$272$	−2.27267	−	3.93637i	−0.137801	−	0.238678i
$273$		0			0
$274$	9.33996			0.564248
$275$	0.236780	+	0.410115i	0.0142784	+	0.0247309i
$276$		0			0
$277$	32.2493			1.93767			0.968836	−	0.247702i	$-0.0796753\pi$
$277$	32.2493			1.93767			0.968836	+	0.247702i	$0.0796753\pi$
$278$	−4.52644			−0.271478
$279$		0			0
$280$	2.29911	−	3.98217i	0.137398	−	0.237980i
$281$	−0.107657	−	0.186467i	−0.00642225	−	0.0111237i	0.862796	−	0.505552i	$-0.168711\pi$
$281$	−0.107657	−	0.186467i	−0.00642225	−	0.0111237i	−0.869219	+	0.494428i	$0.835378\pi$
$282$		0			0
$283$	14.2153	−	24.6216i	0.845013	−	1.46360i	−0.0405976	−	0.999176i	$-0.512926\pi$
$283$	14.2153	−	24.6216i	0.845013	−	1.46360i	0.885610	−	0.464429i	$-0.153741\pi$
$284$	4.54533			0.269716
$285$		0			0
$286$	−0.249301			−0.0147415
$287$	25.9068	−	44.8718i	1.52923	−	2.64870i
$288$		0			0
$289$	−1.83002	−	3.16968i	−0.107648	−	0.186452i
$290$	4.32555	−	7.49206i	0.254005	−	0.439949i
$291$		0			0
$292$	−2.92823			−0.171362
$293$	−23.2682			−1.35934			−0.679671	−	0.733517i	$-0.737878\pi$
$293$	−23.2682			−1.35934			−0.679671	+	0.733517i	$0.737878\pi$
$294$		0			0
$295$	−3.00000	−	5.19615i	−0.174667	−	0.302532i
$296$	1.00000			0.0581238
$297$		0			0
$298$	1.20089	+	2.08001i	0.0695660	+	0.120492i
$299$	0.124650	−	0.215901i	0.00720872	−	0.0124859i
$300$		0			0
$301$	29.1296	−	50.4540i	1.67900	−	2.90812i
$302$	−7.87088	+	13.6328i	−0.452918	+	0.784477i
$303$		0			0
$304$	1.77267	+	3.98217i	0.101669	+	0.228393i
$305$	−3.07177			−0.175889
$306$		0			0
$307$	−6.99553	+	12.1166i	−0.399256	+	0.691531i	−0.993634	−	0.112654i	$-0.964065\pi$
$307$	−6.99553	+	12.1166i	−0.399256	+	0.691531i	0.594378	+	0.804185i	$0.297398\pi$
$308$	−1.08876	−	1.88580i	−0.0620381	−	0.107453i
$309$		0			0
$310$	0.263220	+	0.455910i	0.0149499	+	0.0258940i
$311$	−31.4457			−1.78312			−0.891562	−	0.452899i	$-0.850390\pi$
$311$	−31.4457			−1.78312			−0.891562	+	0.452899i	$0.850390\pi$
$312$		0			0
$313$	−15.6171	−	27.0496i	−0.882731	−	1.52893i	−0.848293	−	0.529528i	$-0.822369\pi$
$313$	−15.6171	−	27.0496i	−0.882731	−	1.52893i	−0.0344382	−	0.999407i	$-0.510964\pi$
$314$	−4.09821	−	7.09831i	−0.231275	−	0.400581i
$315$		0			0
$316$	−1.47356			−0.0828942
$317$	10.1794	+	17.6313i	0.571734	+	0.990272i	0.996388	+	0.0849162i	$0.0270622\pi$
$317$	10.1794	+	17.6313i	0.571734	+	0.990272i	−0.424654	+	0.905355i	$0.639604\pi$
$318$		0			0
$319$	−2.04841	−	3.54794i	−0.114689	−	0.198647i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$		0			0
$322$	2.17753			0.121349
$323$	8.05735	+	18.1003i	0.448323	+	1.00713i
$324$		0			0
$325$	0.263220	−	0.455910i	0.0146008	−	0.0252893i
$326$	7.78966	−	13.4921i	0.431429	−	0.747258i
$327$		0			0
$328$	5.63410	−	9.75854i	0.311091	−	0.538825i
$329$	−18.7229	−	32.4289i	−1.03222	−	1.78787i
$330$		0			0
$331$	−3.40179			−0.186979			−0.0934896	−	0.995620i	$-0.529802\pi$
$331$	−3.40179			−0.186979			−0.0934896	+	0.995620i	$0.529802\pi$
$332$	2.05288	+	3.55569i	0.112666	+	0.195144i
$333$		0			0
$334$	12.4736			0.682523
$335$	−9.07177			−0.495644
$336$		0			0
$337$	5.40676	−	9.36479i	0.294525	−	0.510132i	−0.680349	−	0.732888i	$-0.738172\pi$
$337$	5.40676	−	9.36479i	0.294525	−	0.510132i	0.974874	+	0.222756i	$0.0715052\pi$
$338$	−6.36143	−	11.0183i	−0.346016	−	0.599318i
$339$		0			0
$340$	2.27267	−	3.93637i	0.123253	−	0.213480i
$341$	0.249301			0.0135004
$342$		0			0
$343$	−32.8475			−1.77360
$344$	6.33499	−	10.9725i	0.341560	−	0.591599i
$345$		0			0
$346$	−7.56233	−	13.0983i	−0.406553	−	0.704171i
$347$	−4.57932	+	7.93161i	−0.245831	+	0.425791i	−0.962365	−	0.271761i	$-0.912394\pi$
$347$	−4.57932	+	7.93161i	−0.245831	+	0.425791i	0.716534	+	0.697552i	$0.245727\pi$
$348$		0			0
$349$	4.08687			0.218765			0.109382	−	0.994000i	$-0.465113\pi$
$349$	4.08687			0.218765			0.109382	+	0.994000i	$0.465113\pi$
$350$	4.59821			0.245785
$351$		0			0
$352$	−0.236780	−	0.410115i	−0.0126204	−	0.0218592i
$353$	17.8097			0.947916			0.473958	−	0.880547i	$-0.342825\pi$
$353$	17.8097			0.947916			0.473958	+	0.880547i	$0.342825\pi$
$354$		0			0
$355$	2.27267	+	3.93637i	0.120621	+	0.208921i
$356$	−0.964114	+	1.66990i	−0.0510980	+	0.0885043i
$357$		0			0
$358$	0.710340	−	1.23035i	0.0375427	−	0.0650258i
$359$	−4.79911	+	8.31229i	−0.253287	+	0.438706i	−0.964429	−	0.264343i	$-0.914845\pi$
$359$	−4.79911	+	8.31229i	−0.253287	+	0.438706i	0.711142	+	0.703049i	$0.248178\pi$
$360$		0			0
$361$	−5.86898	−	18.0708i	−0.308894	−	0.951097i
$362$	8.79463			0.462236
$363$		0			0
$364$	−1.21034	+	2.09637i	−0.0634391	+	0.109880i
$365$	−1.46411	−	2.53592i	−0.0766353	−	0.132736i
$366$		0			0
$367$	−0.683901	−	1.18455i	−0.0356993	−	0.0618330i	0.847624	−	0.530598i	$-0.178033\pi$
$367$	−0.683901	−	1.18455i	−0.0356993	−	0.0618330i	−0.883323	+	0.468765i	$0.844699\pi$
$368$	0.473560			0.0246860
$369$		0			0
$370$	0.500000	+	0.866025i	0.0259938	+	0.0450225i
$371$	−4.43320	−	7.67853i	−0.230160	−	0.398649i
$372$		0			0
$373$	−24.6171			−1.27463			−0.637313	−	0.770605i	$-0.719954\pi$
$373$	−24.6171			−1.27463			−0.637313	+	0.770605i	$0.719954\pi$
$374$	−1.07624	−	1.86411i	−0.0556513	−	0.0963908i
$375$		0			0
$376$	−4.07177	−	7.05251i	−0.209986	−	0.363706i
$377$	−2.27714	+	3.94412i	−0.117279	+	0.203133i
$378$		0			0
$379$	15.7606			0.809570			0.404785	−	0.914412i	$-0.367346\pi$
$379$	15.7606			0.809570			0.404785	+	0.914412i	$0.367346\pi$
$380$	−2.56233	+	3.52626i	−0.131445	+	0.180893i
$381$		0			0
$382$	−4.57932	+	7.93161i	−0.234298	+	0.405817i
$383$	10.0718	−	17.4448i	0.514643	−	0.891389i	−0.485212	−	0.874396i	$-0.661258\pi$
$383$	10.0718	−	17.4448i	0.514643	−	0.891389i	0.999856	−	0.0169922i	$-0.00540903\pi$
$384$		0			0
$385$	1.08876	−	1.88580i	0.0554886	−	0.0961091i
$386$	0.588765	+	1.01977i	0.0299673	+	0.0519050i
$387$		0			0
$388$	17.5982			0.893414
$389$	−10.3255	−	17.8844i	−0.523526	−	0.906773i	−0.999625	−	0.0273819i	$-0.991283\pi$
$389$	−10.3255	−	17.8844i	−0.523526	−	0.906773i	0.476099	−	0.879392i	$-0.342050\pi$
$390$		0			0
$391$	2.15249			0.108856
$392$	−14.1435			−0.714357
$393$		0			0
$394$	−6.10766	+	10.5788i	−0.307699	+	0.532951i
$395$	−0.736780	−	1.27614i	−0.0370714	−	0.0642096i
$396$		0			0
$397$	−13.6435	+	23.6313i	−0.684750	+	1.18602i	0.288766	+	0.957400i	$0.406755\pi$
$397$	−13.6435	+	23.6313i	−0.684750	+	1.18602i	−0.973515	+	0.228622i	$0.926578\pi$
$398$	−2.12465			−0.106499
$399$		0			0
$400$	1.00000			0.0500000
$401$	17.1435	−	29.6935i	0.856108	−	1.48282i	−0.0195060	−	0.999810i	$-0.506209\pi$
$401$	17.1435	−	29.6935i	0.856108	−	1.48282i	0.875614	−	0.483012i	$-0.160457\pi$
$402$		0			0
$403$	−0.138569	−	0.240009i	−0.00690263	−	0.0119557i
$404$	6.59821	−	11.4284i	0.328273	−	0.568586i
$405$		0			0
$406$	−39.7795			−1.97423
$407$	0.473560			0.0234735
$408$		0			0
$409$	10.3803	+	17.9792i	0.513274	+	0.889016i	0.999881	+	0.0153958i	$0.00490083\pi$
$409$	10.3803	+	17.9792i	0.513274	+	0.889016i	−0.486608	+	0.873621i	$0.661766\pi$
$410$	11.2682			0.556496
$411$		0			0
$412$	6.37088	+	11.0347i	0.313871	+	0.543640i
$413$	−13.7946	+	23.8930i	−0.678789	+	1.17570i
$414$		0			0
$415$	−2.05288	+	3.55569i	−0.100772	+	0.174542i
$416$	−0.263220	+	0.455910i	−0.0129054	+	0.0223528i
$417$		0			0
$418$	0.839464	+	1.88580i	0.0410595	+	0.0922373i
$419$	27.5642			1.34660			0.673300	−	0.739369i	$-0.264876\pi$
$419$	27.5642			1.34660			0.673300	+	0.739369i	$0.264876\pi$
$420$		0			0
$421$	2.72733	−	4.72388i	0.132922	−	0.230228i	−0.791880	−	0.610677i	$-0.790897\pi$
$421$	2.72733	−	4.72388i	0.132922	−	0.230228i	0.924802	+	0.380449i	$0.124231\pi$
$422$	−9.49553	−	16.4467i	−0.462235	−	0.800615i
$423$		0			0
$424$	−0.964114	−	1.66990i	−0.0468215	−	0.0810973i
$425$	4.54533			0.220481
$426$		0			0
$427$	7.06233	+	12.2323i	0.341770	+	0.591963i
$428$	−5.39732	−	9.34843i	−0.260889	−	0.451873i
$429$		0			0
$430$	12.6700			0.611001
$431$	−20.0484	−	34.7249i	−0.965698	−	1.67264i	−0.707729	−	0.706484i	$-0.750280\pi$
$431$	−20.0484	−	34.7249i	−0.965698	−	1.67264i	−0.257969	−	0.966153i	$-0.583053\pi$
$432$		0			0
$433$	−5.60766	−	9.71275i	−0.269487	−	0.466765i	0.699243	−	0.714884i	$-0.253521\pi$
$433$	−5.60766	−	9.71275i	−0.269487	−	0.466765i	−0.968729	+	0.248120i	$0.920187\pi$
$434$	1.21034	−	2.09637i	0.0580982	−	0.100629i
$435$		0			0
$436$	6.54533			0.313465
$437$	−2.05288	−	0.215901i	−0.0982025	−	0.0103279i
$438$		0			0
$439$	−7.18698	+	12.4482i	−0.343016	+	0.594121i	−0.984991	−	0.172605i	$-0.944782\pi$
$439$	−7.18698	+	12.4482i	−0.343016	+	0.594121i	0.641976	+	0.766725i	$0.278115\pi$
$440$	0.236780	−	0.410115i	0.0112881	−	0.0195515i
$441$		0			0
$442$	−1.19642	+	2.07226i	−0.0569080	+	0.0985675i
$443$	−3.25377	−	5.63570i	−0.154591	−	0.267760i	0.778319	−	0.627869i	$-0.216073\pi$
$443$	−3.25377	−	5.63570i	−0.154591	−	0.267760i	−0.932910	+	0.360109i	$0.882739\pi$
$444$		0			0
$445$	−1.92823			−0.0914068
$446$	10.4238	+	18.0545i	0.493579	+	0.854904i
$447$		0			0
$448$	−4.59821			−0.217245
$449$	1.92823			0.0909988			0.0454994	−	0.998964i	$-0.485512\pi$
$449$	1.92823			0.0909988			0.0454994	+	0.998964i	$0.485512\pi$
$450$		0			0
$451$	2.66808	−	4.62126i	0.125635	−	0.217607i
$452$	8.39732	+	14.5446i	0.394977	+	0.684119i
$453$		0			0
$454$	−2.39732	+	4.15227i	−0.112512	+	0.194876i
$455$	−2.42068			−0.113483
$456$		0			0
$457$	−29.2531			−1.36840			−0.684201	−	0.729293i	$-0.739849\pi$
$457$	−29.2531			−1.36840			−0.684201	+	0.729293i	$0.739849\pi$
$458$	−9.26322	+	16.0444i	−0.432842	+	0.749704i
$459$		0			0
$460$	0.236780	+	0.410115i	0.0110399	+	0.0191217i
$461$	−0.473560	+	0.820230i	−0.0220559	+	0.0382019i	−0.876843	−	0.480777i	$-0.840355\pi$
$461$	−0.473560	+	0.820230i	−0.0220559	+	0.0382019i	0.854787	+	0.518979i	$0.173688\pi$
$462$		0			0
$463$	16.7418			0.778055			0.389028	−	0.921226i	$-0.372811\pi$
$463$	16.7418			0.778055			0.389028	+	0.921226i	$0.372811\pi$
$464$	−8.65109			−0.401617
$465$		0			0
$466$	12.7229	+	22.0366i	0.589375	+	1.02083i
$467$	−19.7040			−0.911791			−0.455895	−	0.890033i	$-0.650681\pi$
$467$	−19.7040			−0.911791			−0.455895	+	0.890033i	$0.650681\pi$
$468$		0			0
$469$	20.8570	+	36.1253i	0.963085	+	1.66811i
$470$	4.07177	−	7.05251i	0.187817	−	0.325308i
$471$		0			0
$472$	−3.00000	+	5.19615i	−0.138086	+	0.239172i
$473$	3.00000	−	5.19615i	0.137940	−	0.238919i
$474$		0			0
$475$	−4.33499	−	0.455910i	−0.198903	−	0.0209186i
$476$	−20.9004			−0.957968
$477$		0			0
$478$	4.66998	−	8.08865i	0.213600	−	0.369966i
$479$	15.3444	+	26.5773i	0.701105	+	1.21435i	0.968079	+	0.250646i	$0.0806430\pi$
$479$	15.3444	+	26.5773i	0.701105	+	1.21435i	−0.266974	+	0.963704i	$0.586024\pi$
$480$		0			0
$481$	−0.263220	−	0.455910i	−0.0120018	−	0.0207877i
$482$	14.4207			0.656844
$483$		0			0
$484$	5.38787	+	9.33207i	0.244903	+	0.424185i
$485$	8.79911	+	15.2405i	0.399547	+	0.692035i
$486$		0			0
$487$	−41.9103			−1.89914			−0.949569	−	0.313557i	$-0.898479\pi$
$487$	−41.9103			−1.89914			−0.949569	+	0.313557i	$0.898479\pi$
$488$	1.53589	+	2.66023i	0.0695263	+	0.120423i
$489$		0			0
$490$	−7.07177	−	12.2487i	−0.319470	−	0.553338i
$491$	−7.81610	+	13.5379i	−0.352736	+	0.610956i	−0.986728	−	0.162384i	$-0.948082\pi$
$491$	−7.81610	+	13.5379i	−0.352736	+	0.610956i	0.633992	+	0.773340i	$0.281415\pi$
$492$		0			0
$493$	−39.3221			−1.77098
$494$	1.34891	−	1.85636i	0.0606903	−	0.0835217i
$495$		0			0
$496$	0.263220	−	0.455910i	0.0118189	−	0.0204710i
$497$	10.4502	−	18.1003i	0.468755	−	0.811908i
$498$		0			0
$499$	−0.102684	+	0.177854i	−0.00459676	+	0.00796183i	−0.868315	−	0.496014i	$-0.834797\pi$
$499$	−0.102684	+	0.177854i	−0.00459676	+	0.00796183i	0.863718	+	0.503976i	$0.168130\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		0			0
$502$	−23.2342			−1.03699
$503$	1.81610	+	3.14558i	0.0809759	+	0.140254i	0.903669	−	0.428231i	$-0.140863\pi$
$503$	1.81610	+	3.14558i	0.0809759	+	0.140254i	−0.822693	+	0.568485i	$0.807530\pi$
$504$		0			0
$505$	13.1964			0.587233
$506$	0.224259			0.00996954
$507$		0			0
$508$	−7.10766	+	12.3108i	−0.315351	+	0.546204i
$509$	5.01889	+	8.69298i	0.222458	+	0.385309i	0.955554	−	0.294816i	$-0.0952585\pi$
$509$	5.01889	+	8.69298i	0.222458	+	0.385309i	−0.733095	+	0.680126i	$0.761925\pi$
$510$		0			0
$511$	−6.73231	+	11.6607i	−0.297820	+	0.515839i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	6.00000			0.264649
$515$	−6.37088	+	11.0347i	−0.280734	+	0.486246i
$516$		0			0
$517$	−1.92823	−	3.33979i	−0.0848034	−	0.146884i
$518$	2.29911	−	3.98217i	0.101017	−	0.174966i
$519$		0			0
$520$	−0.526440			−0.0230859
$521$	6.24930			0.273787			0.136893	−	0.990586i	$-0.456288\pi$
$521$	6.24930			0.273787			0.136893	+	0.990586i	$0.456288\pi$
$522$		0			0
$523$	−13.2776	−	22.9975i	−0.580591	−	1.00561i	−0.995409	−	0.0957084i	$-0.969488\pi$
$523$	−13.2776	−	22.9975i	−0.580591	−	1.00561i	0.414819	−	0.909904i	$-0.363845\pi$
$524$	−14.8664			−0.649442
$525$		0			0
$526$	11.2897	+	19.5543i	0.492253	+	0.852606i
$527$	1.19642	−	2.07226i	0.0521169	−	0.0902692i
$528$		0			0
$529$	11.3879	−	19.7244i	0.495125	−	0.857581i
$530$	0.964114	−	1.66990i	0.0418785	−	0.0725356i
$531$		0			0
$532$	19.9332	+	2.09637i	0.864214	+	0.0908892i
$533$	−5.93202			−0.256944
$534$		0			0
$535$	5.39732	−	9.34843i	0.233346	−	0.404168i
$536$	4.53589	+	7.85638i	0.195920	+	0.339344i
$537$		0			0
$538$	0.253774	+	0.439550i	0.0109410	+	0.0189503i
$539$	−6.69782			−0.288496
$540$		0			0
$541$	15.0390	+	26.0482i	0.646575	+	1.11990i	0.983935	+	0.178526i	$0.0571328\pi$
$541$	15.0390	+	26.0482i	0.646575	+	1.11990i	−0.337360	+	0.941376i	$0.609534\pi$
$542$	13.1247	+	22.7326i	0.563752	+	0.976447i
$543$		0			0
$544$	−4.54533			−0.194879
$545$	3.27267	+	5.66842i	0.140186	+	0.242809i
$546$		0			0
$547$	3.26322	+	5.65206i	0.139525	+	0.241665i	0.927317	−	0.374277i	$-0.122109\pi$
$547$	3.26322	+	5.65206i	0.139525	+	0.241665i	−0.787792	+	0.615942i	$0.788776\pi$
$548$	4.66998	−	8.08865i	0.199492	−	0.345530i
$549$		0			0
$550$	0.473560			0.0201927
$551$	37.5024	+	3.94412i	1.59766	+	0.168025i
$552$		0			0
$553$	−3.38787	+	5.86796i	−0.144067	+	0.249531i
$554$	16.1247	−	27.9287i	0.685071	−	1.18658i
$555$		0			0
$556$	−2.26322	+	3.92001i	−0.0959819	+	0.166246i
$557$	−15.1077	−	26.1672i	−0.640132	−	1.10874i	−0.985403	−	0.170238i	$-0.945546\pi$
$557$	−15.1077	−	26.1672i	−0.640132	−	1.10874i	0.345271	−	0.938503i	$-0.387787\pi$
$558$		0			0
$559$	−6.66998			−0.282110
$560$	−2.29911	−	3.98217i	−0.0971549	−	0.168277i
$561$		0			0
$562$	−0.215313			−0.00908243
$563$	−11.2342			−0.473465			−0.236733	−	0.971575i	$-0.576077\pi$
$563$	−11.2342			−0.473465			−0.236733	+	0.971575i	$0.576077\pi$
$564$		0			0
$565$	−8.39732	+	14.5446i	−0.353278	+	0.611895i
$566$	−14.2153	−	24.6216i	−0.597514	−	1.03492i
$567$		0			0
$568$	2.27267	−	3.93637i	0.0953589	−	0.165167i
$569$	15.3740			0.644510			0.322255	−	0.946653i	$-0.395559\pi$
$569$	15.3740			0.644510			0.322255	+	0.946653i	$0.395559\pi$
$570$		0			0
$571$	18.8513			0.788903			0.394451	−	0.918917i	$-0.370935\pi$
$571$	18.8513			0.788903			0.394451	+	0.918917i	$0.370935\pi$
$572$	−0.124650	+	0.215901i	−0.00521190	+	0.00902727i
$573$		0			0
$574$	−25.9068	−	44.8718i	−1.08133	−	1.87291i
$575$	−0.236780	+	0.410115i	−0.00987441	+	0.0171030i
$576$		0			0
$577$	−19.3489			−0.805506			−0.402753	−	0.915309i	$-0.631947\pi$
$577$	−19.3489			−0.805506			−0.402753	+	0.915309i	$0.631947\pi$
$578$	−3.66004			−0.152237
$579$		0			0
$580$	−4.32555	−	7.49206i	−0.179608	−	0.311091i
$581$	18.8791			0.783239
$582$		0			0
$583$	−0.456566	−	0.790796i	−0.0189090	−	0.0327514i
$584$	−1.46411	+	2.53592i	−0.0605855	+	0.104937i
$585$		0			0
$586$	−11.6341	+	20.1508i	−0.480600	+	0.832424i
$587$	8.01889	−	13.8891i	0.330975	−	0.573266i	−0.651728	−	0.758453i	$-0.725956\pi$
$587$	8.01889	−	13.8891i	0.330975	−	0.573266i	0.982703	+	0.185187i	$0.0592891\pi$
$588$		0			0
$589$	−1.34891	+	1.85636i	−0.0555809	+	0.0764901i
$590$	−6.00000			−0.247016
$591$		0			0
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	14.4880	+	25.0939i	0.594950	+	1.03048i	0.993554	+	0.113360i	$0.0361615\pi$
$593$	14.4880	+	25.0939i	0.594950	+	1.03048i	−0.398604	+	0.917123i	$0.630505\pi$
$594$		0			0
$595$	−10.4502	−	18.1003i	−0.428416	−	0.742039i
$596$	2.40179			0.0983811
$597$		0			0
$598$	−0.124650	−	0.215901i	−0.00509734	−	0.00882885i
$599$	23.1391	+	40.0780i	0.945437	+	1.63754i	0.754874	+	0.655869i	$0.227698\pi$
$599$	23.1391	+	40.0780i	0.945437	+	1.63754i	0.190562	+	0.981675i	$0.438969\pi$
$600$		0			0
$601$	−10.6072			−0.432675			−0.216337	−	0.976319i	$-0.569411\pi$
$601$	−10.6072			−0.432675			−0.216337	+	0.976319i	$0.569411\pi$
$602$	−29.1296	−	50.4540i	−1.18723	−	2.05635i
$603$		0			0
$604$	7.87088	+	13.6328i	0.320261	+	0.554709i
$605$	−5.38787	+	9.33207i	−0.219048	+	0.379402i
$606$		0			0
$607$	28.0439			1.13827			0.569134	−	0.822245i	$-0.307279\pi$
$607$	28.0439			1.13827			0.569134	+	0.822245i	$0.307279\pi$
$608$	4.33499	+	0.455910i	0.175807	+	0.0184896i
$609$		0			0
$610$	−1.53589	+	2.66023i	−0.0621862	+	0.107710i
$611$	−2.14354	+	3.71272i	−0.0867184	+	0.150201i
$612$		0			0
$613$	−12.4143	+	21.5022i	−0.501409	+	0.868466i	0.498589	+	0.866838i	$0.333852\pi$
$613$	−12.4143	+	21.5022i	−0.501409	+	0.868466i	−0.999999	+	0.00162804i	$0.999482\pi$
$614$	6.99553	+	12.1166i	0.282316	+	0.488987i
$615$		0			0
$616$	−2.17753			−0.0877352
$617$	−6.00000	−	10.3923i	−0.241551	−	0.418378i	0.719605	−	0.694383i	$-0.244323\pi$
$617$	−6.00000	−	10.3923i	−0.241551	−	0.418378i	−0.961156	+	0.276005i	$0.910989\pi$
$618$		0			0
$619$	33.7946			1.35832			0.679160	−	0.733990i	$-0.262344\pi$
$619$	33.7946			1.35832			0.679160	+	0.733990i	$0.262344\pi$
$620$	0.526440			0.0211423
$621$		0			0
$622$	−15.7229	+	27.2328i	−0.630429	+	1.09194i
$623$	4.43320	+	7.67853i	0.177612	+	0.307634i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−31.2342			−1.24837
$627$		0			0
$628$	−8.19642			−0.327073
$629$	2.27267	−	3.93637i	0.0906171	−	0.156953i
$630$		0			0
$631$	7.11520	+	12.3239i	0.283252	+	0.490607i	0.972184	−	0.234220i	$-0.0752534\pi$
$631$	7.11520	+	12.3239i	0.283252	+	0.490607i	−0.688932	+	0.724826i	$0.741920\pi$
$632$	−0.736780	+	1.27614i	−0.0293075	+	0.0507621i
$633$		0			0
$634$	20.3589			0.808553
$635$	−14.2153			−0.564117
$636$		0			0
$637$	3.72286	+	6.44818i	0.147505	+	0.255486i
$638$	−4.09681			−0.162194
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	13.1624	−	22.7980i	0.519885	−	0.900467i	−0.479848	−	0.877352i	$-0.659308\pi$
$641$	13.1624	−	22.7980i	0.519885	−	0.900467i	0.999733	−	0.0231153i	$-0.00735849\pi$
$642$		0			0
$643$	−8.25875	+	14.3046i	−0.325693	+	0.564117i	−0.981652	−	0.190679i	$-0.938931\pi$
$643$	−8.25875	+	14.3046i	−0.325693	+	0.564117i	0.655959	+	0.754796i	$0.272264\pi$
$644$	1.08876	−	1.88580i	0.0429033	−	0.0743108i
$645$		0			0
$646$	19.7040	+	2.07226i	0.775242	+	0.0815321i
$647$	−29.2592			−1.15030			−0.575150	−	0.818048i	$-0.695056\pi$
$647$	−29.2592			−1.15030			−0.575150	+	0.818048i	$0.695056\pi$
$648$		0			0
$649$	−1.42068	+	2.46069i	−0.0557666	+	0.0965906i
$650$	−0.263220	−	0.455910i	−0.0103243	−	0.0178823i
$651$		0			0
$652$	−7.78966	−	13.4921i	−0.305067	−	0.528391i
$653$	41.7668			1.63446			0.817230	−	0.576311i	$-0.195508\pi$
$653$	41.7668			1.63446			0.817230	+	0.576311i	$0.195508\pi$
$654$		0			0
$655$	−7.43320	−	12.8747i	−0.290439	−	0.503055i
$656$	−5.63410	−	9.75854i	−0.219975	−	0.381007i
$657$		0			0
$658$	−37.4457			−1.45979
$659$	12.9596	+	22.4468i	0.504836	+	0.874402i	0.999984	+	0.00559311i	$0.00178035\pi$
$659$	12.9596	+	22.4468i	0.504836	+	0.874402i	−0.495148	+	0.868808i	$0.664886\pi$
$660$		0			0
$661$	14.8135	+	25.6578i	0.576179	+	0.997972i	0.995912	+	0.0903242i	$0.0287903\pi$
$661$	14.8135	+	25.6578i	0.576179	+	0.997972i	−0.419733	+	0.907648i	$0.637876\pi$
$662$	−1.70089	+	2.94604i	−0.0661071	+	0.114501i
$663$		0			0
$664$	4.10576			0.159334
$665$	8.15109	+	18.3108i	0.316086	+	0.710064i
$666$		0			0
$667$	2.04841	−	3.54794i	0.0793146	−	0.137377i
$668$	6.23678	−	10.8024i	0.241308	−	0.417958i
$669$		0			0
$670$	−4.53589	+	7.85638i	−0.175237	+	0.303519i
$671$	0.727334	+	1.25978i	0.0280784	+	0.0486333i
$672$		0			0
$673$	39.7606			1.53266			0.766330	−	0.642447i	$-0.222081\pi$
$673$	39.7606			1.53266			0.766330	+	0.642447i	$0.222081\pi$
$674$	−5.40676	−	9.36479i	−0.208261	−	0.360718i
$675$		0			0
$676$	−12.7229			−0.489341
$677$	14.3589			0.551856			0.275928	−	0.961178i	$-0.411015\pi$
$677$	14.3589			0.551856			0.275928	+	0.961178i	$0.411015\pi$
$678$		0			0
$679$	40.4601	−	70.0790i	1.55272	−	2.68939i
$680$	−2.27267	−	3.93637i	−0.0871527	−	0.150953i
$681$		0			0
$682$	0.124650	−	0.215901i	0.00477311	−	0.00826727i
$683$	−10.7946			−0.413045			−0.206523	−	0.978442i	$-0.566215\pi$
$683$	−10.7946			−0.413045			−0.206523	+	0.978442i	$0.566215\pi$
$684$		0			0
$685$	9.33996			0.356862
$686$	−16.4238	+	28.4468i	−0.627062	+	1.08610i
$687$		0			0
$688$	−6.33499	−	10.9725i	−0.241519	−	0.418324i
$689$	−0.507548	+	0.879099i	−0.0193360	+	0.0334910i
$690$		0			0
$691$	−28.4646			−1.08284			−0.541422	−	0.840751i	$-0.682114\pi$
$691$	−28.4646			−1.08284			−0.541422	+	0.840751i	$0.682114\pi$
$692$	−15.1247			−0.574953
$693$		0			0
$694$	4.57932	+	7.93161i	0.173829	+	0.301080i
$695$	−4.52644			−0.171698
$696$		0			0
$697$	−25.6088	−	44.3558i	−0.970004	−	1.68010i
$698$	2.04343	−	3.53933i	0.0773451	−	0.133966i
$699$		0			0
$700$	2.29911	−	3.98217i	0.0868980	−	0.150512i
$701$	−16.7606	+	29.0303i	−0.633041	+	1.09646i	0.353886	+	0.935289i	$0.384860\pi$
$701$	−16.7606	+	29.0303i	−0.633041	+	1.09646i	−0.986927	+	0.161170i	$0.948473\pi$
$702$		0			0
$703$	−2.56233	+	3.52626i	−0.0966399	+	0.132995i
$704$	−0.473560			−0.0178480
$705$		0			0
$706$	8.90486	−	15.4237i	0.335139	−	0.580478i
$707$	−30.3400	−	52.5504i	−1.14105	−	1.97636i
$708$		0			0
$709$	20.8758	+	36.1580i	0.784009	+	1.35794i	0.929589	+	0.368597i	$0.120162\pi$
$709$	20.8758	+	36.1580i	0.784009	+	1.35794i	−0.145580	+	0.989346i	$0.546505\pi$
$710$	4.54533			0.170583
$711$		0			0
$712$	0.964114	+	1.66990i	0.0361317	+	0.0625820i
$713$	0.124650	+	0.215901i	0.00466820	+	0.00808555i
$714$		0			0
$715$	−0.249301			−0.00932333
$716$	−0.710340	−	1.23035i	−0.0265467	−	0.0459802i
$717$		0			0
$718$	4.79911	+	8.31229i	0.179101	+	0.310212i
$719$	3.03399	−	5.25502i	0.113149	−	0.195979i	−0.803890	−	0.594779i	$-0.797240\pi$
$719$	3.03399	−	5.25502i	0.113149	−	0.195979i	0.917038	+	0.398799i	$0.130573\pi$
$720$		0			0
$721$	58.5893			2.18198
$722$	−18.5843	−	3.95273i	−0.691636	−	0.147105i
$723$		0			0
$724$	4.39732	−	7.61637i	0.163425	−	0.283060i
$725$	4.32555	−	7.49206i	0.160647	−	0.278248i
$726$		0			0
$727$	7.80855	−	13.5248i	0.289603	−	0.501607i	−0.684112	−	0.729377i	$-0.739810\pi$
$727$	7.80855	−	13.5248i	0.289603	−	0.501607i	0.973715	+	0.227770i	$0.0731433\pi$
$728$	1.21034	+	2.09637i	0.0448582	+	0.0776967i
$729$		0			0
$730$	−2.92823			−0.108379
$731$	−28.7946	−	49.8738i	−1.06501	−	1.84465i
$732$		0			0
$733$	20.4736			0.756208			0.378104	−	0.925763i	$-0.376576\pi$
$733$	20.4736			0.756208			0.378104	+	0.925763i	$0.376576\pi$
$734$	−1.36780			−0.0504865
$735$		0			0
$736$	0.236780	−	0.410115i	0.00872783	−	0.0151170i
$737$	2.14802	+	3.72047i	0.0791232	+	0.137045i
$738$		0			0
$739$	14.8973	−	25.8029i	0.548007	−	0.949175i	−0.450404	−	0.892825i	$-0.648720\pi$
$739$	14.8973	−	25.8029i	0.548007	−	0.949175i	0.998411	−	0.0563507i	$-0.0179465\pi$
$740$	1.00000			0.0367607
$741$		0			0
$742$	−8.86640			−0.325496
$743$	−15.5767	+	26.9797i	−0.571455	+	0.989790i	0.424962	+	0.905211i	$0.360288\pi$
$743$	−15.5767	+	26.9797i	−0.571455	+	0.989790i	−0.996417	+	0.0845782i	$0.973046\pi$
$744$		0			0
$745$	1.20089	+	2.08001i	0.0439974	+	0.0762057i
$746$	−12.3086	+	21.3190i	−0.450648	+	0.780545i
$747$		0			0
$748$	−2.15249			−0.0787028
$749$	−49.6360			−1.81366
$750$		0			0
$751$	−14.3879	−	24.9205i	−0.525021	−	0.909363i	−0.999575	−	0.0291367i	$-0.990724\pi$
$751$	−14.3879	−	24.9205i	−0.525021	−	0.909363i	0.474555	−	0.880226i	$-0.342609\pi$
$752$	−8.14354			−0.296964
$753$		0			0
$754$	2.27714	+	3.94412i	0.0829285	+	0.143636i
$755$	−7.87088	+	13.6328i	−0.286451	+	0.496147i
$756$		0			0
$757$	11.2040	−	19.4058i	0.407215	−	0.705317i	−0.587361	−	0.809325i	$-0.699833\pi$
$757$	11.2040	−	19.4058i	0.407215	−	0.705317i	0.994577	+	0.104007i	$0.0331666\pi$
$758$	7.88032	−	13.6491i	0.286226	−	0.495758i
$759$		0			0
$760$	1.77267	+	3.98217i	0.0643013	+	0.144448i
$761$	17.5175			0.635009			0.317504	−	0.948257i	$-0.397155\pi$
$761$	17.5175			0.635009			0.317504	+	0.948257i	$0.397155\pi$
$762$		0			0
$763$	15.0484	−	26.0646i	0.544789	−	0.943602i
$764$	4.57932	+	7.93161i	0.165674	+	0.286956i
$765$		0			0
$766$	−10.0718	−	17.4448i	−0.363908	−	0.630307i
$767$	3.15864			0.114052
$768$		0			0
$769$	20.2821	+	35.1296i	0.731392	+	1.26681i	0.956288	+	0.292425i	$0.0944622\pi$
$769$	20.2821	+	35.1296i	0.731392	+	1.26681i	−0.224897	+	0.974383i	$0.572205\pi$
$770$	−1.08876	−	1.88580i	−0.0392364	−	0.0679594i
$771$		0			0
$772$	1.17753			0.0423802
$773$	7.30408	+	12.6510i	0.262709	+	0.455026i	0.966961	−	0.254924i	$-0.0820506\pi$
$773$	7.30408	+	12.6510i	0.262709	+	0.455026i	−0.704252	+	0.709951i	$0.748717\pi$
$774$		0			0
$775$	0.263220	+	0.455910i	0.00945514	+	0.0163768i
$776$	8.79911	−	15.2405i	0.315869	−	0.547102i
$777$		0			0
$778$	−20.6511			−0.740377
$779$	19.9747	+	44.8718i	0.715669	+	1.60770i
$780$		0			0
$781$	1.07624	−	1.86411i	0.0385110	−	0.0667031i
$782$	1.07624	−	1.86411i	0.0384864	−	0.0666604i
$783$		0			0
$784$	−7.07177	+	12.2487i	−0.252563	+	0.437452i
$785$	−4.09821	−	7.09831i	−0.146271	−	0.253350i
$786$		0			0
$787$	9.25310			0.329837			0.164919	−	0.986307i	$-0.447264\pi$
$787$	9.25310			0.329837			0.164919	+	0.986307i	$0.447264\pi$
$788$	6.10766	+	10.5788i	0.217576	+	0.376853i
$789$		0			0
$790$	−1.47356			−0.0524269
$791$	77.2253			2.74581
$792$		0			0
$793$	0.808551	−	1.40045i	0.0287125	−	0.0497315i
$794$	13.6435	+	23.6313i	0.484191	+	0.838644i
$795$		0			0
$796$	−1.06233	+	1.84000i	−0.0376531	+	0.0652171i
$797$	17.9660			0.636389			0.318194	−	0.948025i	$-0.396924\pi$
$797$	17.9660			0.636389			0.318194	+	0.948025i	$0.396924\pi$
$798$		0			0
$799$	−37.0151			−1.30950
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$		0			0
$802$	−17.1435	−	29.6935i	−0.605360	−	1.04851i
$803$	−0.693346	+	1.20091i	−0.0244677	+	0.0423792i
$804$		0			0
$805$	2.17753			0.0767478
$806$	−0.277139			−0.00976180
$807$		0			0
$808$	−6.59821	−	11.4284i	−0.232124	−	0.402051i
$809$	21.8565			0.768432			0.384216	−	0.923243i	$-0.374472\pi$
$809$	21.8565			0.768432			0.384216	+	0.923243i	$0.374472\pi$
$810$		0			0
$811$	−10.2323	−	17.7229i	−0.359305	−	0.622334i	0.628540	−	0.777777i	$-0.283653\pi$
$811$	−10.2323	−	17.7229i	−0.359305	−	0.622334i	−0.987845	+	0.155443i	$0.950320\pi$
$812$	−19.8898	+	34.4501i	−0.697994	+	1.20896i
$813$		0			0
$814$	0.236780	−	0.410115i	0.00829914	−	0.0143745i
$815$	7.78966	−	13.4921i	0.272860	−	0.472607i
$816$		0			0
$817$	22.4596	+	50.4540i	0.785763	+	1.76516i
$818$	20.7606			0.725879
$819$		0			0
$820$	5.63410	−	9.75854i	0.196751	−	0.340783i
$821$	−15.9471	−	27.6212i	−0.556558	−	0.963987i	−0.997780	−	0.0665894i	$-0.978788\pi$
$821$	−15.9471	−	27.6212i	−0.556558	−	0.963987i	0.441222	−	0.897398i	$-0.354545\pi$
$822$		0			0
$823$	8.01699	+	13.8858i	0.279455	+	0.484030i	0.971249	−	0.238064i	$-0.0765129\pi$
$823$	8.01699	+	13.8858i	0.279455	+	0.484030i	−0.691795	+	0.722094i	$0.743180\pi$
$824$	12.7418			0.443880
$825$		0			0
$826$	13.7946	+	23.8930i	0.479977	+	0.831344i
$827$	19.4502	+	33.6887i	0.676350	+	1.17147i	0.976072	+	0.217446i	$0.0697724\pi$
$827$	19.4502	+	33.6887i	0.676350	+	1.17147i	−0.299723	+	0.954026i	$0.596894\pi$
$828$		0			0
$829$	0.602006			0.0209085			0.0104543	−	0.999945i	$-0.496672\pi$
$829$	0.602006			0.0209085			0.0104543	+	0.999945i	$0.496672\pi$
$830$	2.05288	+	3.55569i	0.0712565	+	0.123420i
$831$		0			0
$832$	0.263220	+	0.455910i	0.00912551	+	0.0158058i
$833$	−32.1435	+	55.6742i	−1.11371	+	1.92900i
$834$		0			0
$835$	12.4736			0.431665
$836$	2.05288	+	0.215901i	0.0710003	+	0.00746709i
$837$		0			0
$838$	13.7821	−	23.8713i	0.476095	−	0.824621i
$839$	0.0339879	−	0.0588688i	0.00117339	−	0.00203238i	−0.865438	−	0.501016i	$-0.832960\pi$
$839$	0.0339879	−	0.0588688i	0.00117339	−	0.00203238i	0.866612	+	0.498983i	$0.166293\pi$
$840$		0			0
$841$	−22.9207	+	39.6998i	−0.790368	+	1.36896i
$842$	−2.72733	−	4.72388i	−0.0939901	−	0.162796i
$843$		0			0
$844$	−18.9911			−0.653699
$845$	−6.36143	−	11.0183i	−0.218840	−	0.379042i
$846$		0			0
$847$	49.5491			1.70253
$848$	−1.92823			−0.0662157
$849$		0			0
$850$	2.27267	−	3.93637i	0.0779518	−	0.135016i
$851$	0.236780	+	0.410115i	0.00811672	+	0.0140586i
$852$		0			0
$853$	−1.28211	+	2.22068i	−0.0438987	+	0.0760347i	−0.887140	−	0.461501i	$-0.847311\pi$
$853$	−1.28211	+	2.22068i	−0.0438987	+	0.0760347i	0.843241	+	0.537535i	$0.180645\pi$
$854$	14.1247			0.483336
$855$		0			0
$856$	−10.7946			−0.368953
$857$	9.85646	−	17.0719i	0.336690	−	0.583165i	−0.647118	−	0.762390i	$-0.724026\pi$
$857$	9.85646	−	17.0719i	0.336690	−	0.583165i	0.983808	+	0.179225i	$0.0573592\pi$
$858$		0			0
$859$	−5.75377	−	9.96583i	−0.196316	−	0.340030i	0.751015	−	0.660285i	$-0.229565\pi$
$859$	−5.75377	−	9.96583i	−0.196316	−	0.340030i	−0.947331	+	0.320255i	$0.896231\pi$
$860$	6.33499	−	10.9725i	0.216021	−	0.374160i
$861$		0			0
$862$	−40.0968			−1.36570
$863$	33.1157			1.12727			0.563636	−	0.826023i	$-0.309402\pi$
$863$	33.1157			1.12727			0.563636	+	0.826023i	$0.309402\pi$
$864$		0			0
$865$	−7.56233	−	13.0983i	−0.257127	−	0.445357i
$866$	−11.2153			−0.381112
$867$		0			0
$868$	−1.21034	−	2.09637i	−0.0410816	−	0.0711555i
$869$	−0.348910	+	0.604330i	−0.0118360	+	0.0205005i
$870$		0			0
$871$	2.38787	−	4.13591i	0.0809099	−	0.140140i
$872$	3.27267	−	5.66842i	0.110826	−	0.191957i
$873$		0			0
$874$	−1.21342	+	1.66990i	−0.0410444	+	0.0564851i
$875$	4.59821			0.155448
$876$		0			0
$877$	20.1700	−	34.9354i	0.681092	−	1.17969i	−0.293556	−	0.955942i	$-0.594839\pi$
$877$	20.1700	−	34.9354i	0.681092	−	1.17969i	0.974648	−	0.223744i	$-0.0718279\pi$
$878$	7.18698	+	12.4482i	0.242549	+	0.420107i
$879$		0			0
$880$	−0.236780	−	0.410115i	−0.00798186	−	0.0138250i
$881$	5.51749			0.185889			0.0929445	−	0.995671i	$-0.470372\pi$
$881$	5.51749			0.185889			0.0929445	+	0.995671i	$0.470372\pi$
$882$		0			0
$883$	−23.2927	−	40.3442i	−0.783863	−	1.35769i	−0.929676	−	0.368378i	$-0.879913\pi$
$883$	−23.2927	−	40.3442i	−0.783863	−	1.35769i	0.145813	−	0.989312i	$-0.453420\pi$
$884$	1.19642	+	2.07226i	0.0402400	+	0.0696977i
$885$		0			0
$886$	−6.50755			−0.218625
$887$	10.5793	+	18.3239i	0.355219	+	0.615257i	0.987155	−	0.159763i	$-0.0510730\pi$
$887$	10.5793	+	18.3239i	0.355219	+	0.615257i	−0.631937	+	0.775020i	$0.717740\pi$
$888$		0			0
$889$	32.6825	+	56.6078i	1.09614	+	1.89856i
$890$	−0.964114	+	1.66990i	−0.0323172	+	0.0559750i
$891$		0			0
$892$	20.8475			0.698026
$893$	35.3022	+	3.71272i	1.18134	+	0.124242i
$894$		0			0
$895$	0.710340	−	1.23035i	0.0237441	−	0.0411259i
$896$	−2.29911	+	3.98217i	−0.0768077	+	0.133035i
$897$		0			0
$898$	0.964114	−	1.66990i	0.0321729	−	0.0557251i
$899$	−2.27714	−	3.94412i	−0.0759468	−	0.131544i
$900$		0			0
$901$	−8.76444			−0.291986
$902$	−2.66808	−	4.62126i	−0.0888375	−	0.153871i
$903$		0			0
$904$	16.7946			0.558581
$905$	8.79463			0.292343
$906$		0			0
$907$	−1.38290	+	2.39525i	−0.0459184	+	0.0795329i	−0.888071	−	0.459706i	$-0.847955\pi$
$907$	−1.38290	+	2.39525i	−0.0459184	+	0.0795329i	0.842153	+	0.539239i	$0.181288\pi$
$908$	2.39732	+	4.15227i	0.0795577	+	0.137798i
$909$		0			0
$910$	−1.21034	+	2.09637i	−0.0401224	+	0.0694940i
$911$	7.37775			0.244436			0.122218	−	0.992503i	$-0.460999\pi$
$911$	7.37775			0.244436			0.122218	+	0.992503i	$0.460999\pi$
$912$		0			0
$913$	1.94432			0.0643477
$914$	−14.6265	+	25.3339i	−0.483803	+	0.837972i
$915$		0			0
$916$	9.26322	+	16.0444i	0.306065	+	0.530121i
$917$	−34.1794	+	59.2005i	−1.12870	+	1.95497i
$918$		0			0
$919$	10.0189			0.330493			0.165246	−	0.986252i	$-0.447158\pi$
$919$	10.0189			0.330493			0.165246	+	0.986252i	$0.447158\pi$
$920$	0.473560			0.0156128
$921$		0			0
$922$	0.473560	+	0.820230i	0.0155959	+	0.0270129i
$923$	−2.39284			−0.0787614
$924$		0			0
$925$	0.500000	+	0.866025i	0.0164399	+	0.0284747i
$926$	8.37088	−	14.4988i	0.275084	−	0.476460i
$927$		0			0
$928$	−4.32555	+	7.49206i	−0.141993	+	0.245939i
$929$	−20.4098	+	35.3509i	−0.669625	+	1.15982i	0.308384	+	0.951262i	$0.400212\pi$
$929$	−20.4098	+	35.3509i	−0.669625	+	1.15982i	−0.978009	+	0.208563i	$0.933121\pi$
$930$		0			0
$931$	36.2404	−	49.8738i	1.18773	−	1.63455i
$932$	25.4457			0.833502
$933$		0			0
$934$	−9.85198	+	17.0641i	−0.322367	+	0.558356i
$935$	−1.07624	−	1.86411i	−0.0351969	−	0.0609629i
$936$		0			0
$937$	−14.6983	−	25.4582i	−0.480173	−	0.831684i	0.519568	−	0.854429i	$-0.326093\pi$
$937$	−14.6983	−	25.4582i	−0.480173	−	0.831684i	−0.999741	+	0.0227447i	$0.992760\pi$
$938$	41.7139			1.36201
$939$		0			0
$940$	−4.07177	−	7.05251i	−0.132807	−	0.230028i
$941$	29.0144	+	50.2544i	0.945843	+	1.63825i	0.754054	+	0.656812i	$0.228095\pi$
$941$	29.0144	+	50.2544i	0.945843	+	1.63825i	0.191789	+	0.981436i	$0.438571\pi$
$942$		0			0
$943$	5.33617			0.173770
$944$	3.00000	+	5.19615i	0.0976417	+	0.169120i
$945$		0			0
$946$	−3.00000	−	5.19615i	−0.0975384	−	0.168941i
$947$	−14.8709	+	25.7571i	−0.483239	+	0.836994i	−0.999815	−	0.0192475i	$-0.993873\pi$
$947$	−14.8709	+	25.7571i	−0.483239	+	0.836994i	0.516576	+	0.856241i	$0.327206\pi$
$948$		0			0
$949$	1.54154			0.0500404
$950$	−2.56233	+	3.52626i	−0.0831328	+	0.114407i
$951$		0			0
$952$	−10.4502	+	18.1003i	−0.338693	+	0.586633i
$953$	−20.3928	+	35.3214i	−0.660589	+	1.14417i	0.319872	+	0.947461i	$0.396360\pi$
$953$	−20.3928	+	35.3214i	−0.660589	+	1.14417i	−0.980461	+	0.196713i	$0.936973\pi$
$954$		0			0
$955$	−4.57932	+	7.93161i	−0.148183	+	0.256661i
$956$	−4.66998	−	8.08865i	−0.151038	−	0.261605i
$957$		0			0
$958$	30.6889			0.991512
$959$	−21.4736	−	37.1933i	−0.693417	−	1.20103i
$960$		0			0
$961$	−30.7229			−0.991060
$962$	−0.526440			−0.0169731
$963$		0			0
$964$	7.21034	−	12.4887i	0.232229	−	0.402233i
$965$	0.588765	+	1.01977i	0.0189530	+	0.0328276i
$966$		0			0
$967$	−17.7368	+	30.7210i	−0.570376	+	0.987921i	0.426151	+	0.904652i	$0.359869\pi$
$967$	−17.7368	+	30.7210i	−0.570376	+	0.987921i	−0.996527	+	0.0832687i	$0.973464\pi$
$968$	10.7757			0.346345
$969$		0			0
$970$	17.5982			0.565044
$971$	−12.2153	+	21.1575i	−0.392008	+	0.678978i	−0.992714	−	0.120492i	$-0.961553\pi$
$971$	−12.2153	+	21.1575i	−0.392008	+	0.678978i	0.600706	+	0.799470i	$0.294886\pi$
$972$		0			0
$973$	10.4068	+	18.0250i	0.333625	+	0.577856i
$974$	−20.9552	+	36.2954i	−0.671447	+	1.16298i
$975$		0			0
$976$	3.07177			0.0983250
$977$	45.0137			1.44012			0.720059	−	0.693913i	$-0.244115\pi$
$977$	45.0137			1.44012			0.720059	+	0.693913i	$0.244115\pi$
$978$		0			0
$979$	0.456566	+	0.790796i	0.0145919	+	0.0252740i
$980$	−14.1435			−0.451799
$981$		0			0
$982$	7.81610	+	13.5379i	0.249422	+	0.432011i
$983$	−18.3614	+	31.8029i	−0.585639	+	1.01436i	0.409157	+	0.912464i	$0.365823\pi$
$983$	−18.3614	+	31.8029i	−0.585639	+	1.01436i	−0.994795	+	0.101892i	$0.967510\pi$
$984$		0			0
$985$	−6.10766	+	10.5788i	−0.194606	+	0.337068i
$986$	−19.6610	+	34.0539i	−0.626135	+	1.08450i
$987$		0			0
$988$	−0.933202	−	2.09637i	−0.0296891	−	0.0666944i
$989$	6.00000			0.190789
$990$		0			0
$991$	−17.0005	+	29.4457i	−0.540039	+	0.935374i	0.458862	+	0.888507i	$0.348257\pi$
$991$	−17.0005	+	29.4457i	−0.540039	+	0.935374i	−0.998901	+	0.0468671i	$0.985076\pi$
$992$	−0.263220	−	0.455910i	−0.00835724	−	0.0144752i
$993$		0			0
$994$	−10.4502	−	18.1003i	−0.331460	−	0.574106i
$995$	−2.12465			−0.0673559
$996$		0			0
$997$	8.60955	+	14.9122i	0.272667	+	0.472274i	0.969544	−	0.244917i	$-0.0787608\pi$
$997$	8.60955	+	14.9122i	0.272667	+	0.472274i	−0.696877	+	0.717191i	$0.745428\pi$
$998$	0.102684	+	0.177854i	0.00325040	+	0.00562986i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.l.q.1531.1		6
3.2	odd	2		570.2.i.j.391.1	yes	6
19.7	even	3	inner	1710.2.l.q.1261.1		6
57.26	odd	6		570.2.i.j.121.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.j.121.1	✓	6	57.26	odd	6
570.2.i.j.391.1	yes	6	3.2	odd	2
1710.2.l.q.1261.1		6	19.7	even	3	inner
1710.2.l.q.1531.1		6	1.1	even	1	trivial

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -4.59821 q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -4.59821 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} -0.473560 q^{11} +(0.263220 + 0.455910i) q^{13} +(-2.29911 + 3.98217i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.27267 + 3.93637i) q^{17} +(2.56233 - 3.52626i) q^{19} -1.00000 q^{20} +(-0.236780 + 0.410115i) q^{22} +(-0.236780 - 0.410115i) q^{23} +(-0.500000 - 0.866025i) q^{25} +0.526440 q^{26} +(2.29911 + 3.98217i) q^{28} +(4.32555 + 7.49206i) q^{29} -0.526440 q^{31} +(0.500000 + 0.866025i) q^{32} +(2.27267 + 3.93637i) q^{34} +(-2.29911 + 3.98217i) q^{35} -1.00000 q^{37} +(-1.77267 - 3.98217i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(-5.63410 + 9.75854i) q^{41} +(-6.33499 + 10.9725i) q^{43} +(0.236780 + 0.410115i) q^{44} -0.473560 q^{46} +(4.07177 + 7.05251i) q^{47} +14.1435 q^{49} -1.00000 q^{50} +(0.263220 - 0.455910i) q^{52} +(0.964114 + 1.66990i) q^{53} +(-0.236780 + 0.410115i) q^{55} +4.59821 q^{56} +8.65109 q^{58} +(3.00000 - 5.19615i) q^{59} +(-1.53589 - 2.66023i) q^{61} +(-0.263220 + 0.455910i) q^{62} +1.00000 q^{64} +0.526440 q^{65} +(-4.53589 - 7.85638i) q^{67} +4.54533 q^{68} +(2.29911 + 3.98217i) q^{70} +(-2.27267 + 3.93637i) q^{71} +(1.46411 - 2.53592i) q^{73} +(-0.500000 + 0.866025i) q^{74} +(-4.33499 - 0.455910i) q^{76} +2.17753 q^{77} +(0.736780 - 1.27614i) q^{79} +(0.500000 + 0.866025i) q^{80} +(5.63410 + 9.75854i) q^{82} -4.10576 q^{83} +(2.27267 + 3.93637i) q^{85} +(6.33499 + 10.9725i) q^{86} +0.473560 q^{88} +(-0.964114 - 1.66990i) q^{89} +(-1.21034 - 2.09637i) q^{91} +(-0.236780 + 0.410115i) q^{92} +8.14354 q^{94} +(-1.77267 - 3.98217i) q^{95} +(-8.79911 + 15.2405i) q^{97} +(7.07177 - 12.2487i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} + 2 q^{7} - 6 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 + 2 * q^7 - 6 * q^8	\( 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} + 2 q^{7} - 6 q^{8} - 3 q^{10} - 8 q^{11} - q^{13} + q^{14} - 3 q^{16} - 4 q^{17} - 2 q^{19} - 6 q^{20} - 4 q^{22} - 4 q^{23} - 3 q^{25} - 2 q^{26} - q^{28} + 6 q^{29} + 2 q^{31} + 3 q^{32} + 4 q^{34} + q^{35} - 6 q^{37} - q^{38} - 3 q^{40} + 8 q^{41} - 11 q^{43} + 4 q^{44} - 8 q^{46} + 36 q^{49} - 6 q^{50} - q^{52} + 18 q^{53} - 4 q^{55} - 2 q^{56} + 12 q^{58} + 18 q^{59} + 3 q^{61} + q^{62} + 6 q^{64} - 2 q^{65} - 15 q^{67} + 8 q^{68} - q^{70} - 4 q^{71} + 21 q^{73} - 3 q^{74} + q^{76} - 32 q^{77} + 7 q^{79} + 3 q^{80} - 8 q^{82} - 4 q^{83} + 4 q^{85} + 11 q^{86} + 8 q^{88} - 18 q^{89} - 15 q^{91} - 4 q^{92} - q^{95} - 38 q^{97} + 18 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 + 2 * q^7 - 6 * q^8 - 3 * q^10 - 8 * q^11 - q^13 + q^14 - 3 * q^16 - 4 * q^17 - 2 * q^19 - 6 * q^20 - 4 * q^22 - 4 * q^23 - 3 * q^25 - 2 * q^26 - q^28 + 6 * q^29 + 2 * q^31 + 3 * q^32 + 4 * q^34 + q^35 - 6 * q^37 - q^38 - 3 * q^40 + 8 * q^41 - 11 * q^43 + 4 * q^44 - 8 * q^46 + 36 * q^49 - 6 * q^50 - q^52 + 18 * q^53 - 4 * q^55 - 2 * q^56 + 12 * q^58 + 18 * q^59 + 3 * q^61 + q^62 + 6 * q^64 - 2 * q^65 - 15 * q^67 + 8 * q^68 - q^70 - 4 * q^71 + 21 * q^73 - 3 * q^74 + q^76 - 32 * q^77 + 7 * q^79 + 3 * q^80 - 8 * q^82 - 4 * q^83 + 4 * q^85 + 11 * q^86 + 8 * q^88 - 18 * q^89 - 15 * q^91 - 4 * q^92 - q^95 - 38 * q^97 + 18 * q^98

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