LMFDB - Embedded newform 1638.2.dw.b.719.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(647,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 1, 5]))

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

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

chi := DirichletCharacter("1638.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.dw (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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			719.17
Character	$\chi$	$=$	1638.719
Dual form			1638.2.dw.b.647.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(3.19176 + 1.84276i) q^{5} +(2.56349 - 0.654608i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(3.19176 + 1.84276i) q^{5} +(2.56349 - 0.654608i) q^{7} -1.00000 q^{8} +3.68552i q^{10} -0.360649 q^{11} +(3.09215 + 1.85435i) q^{13} +(1.84865 + 1.89275i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.62495 - 6.27861i) q^{17} -1.02117 q^{19} +(-3.19176 + 1.84276i) q^{20} +(-0.180325 - 0.312331i) q^{22} +(2.16373 - 1.24923i) q^{23} +(4.29155 + 7.43318i) q^{25} +(-0.0598406 + 3.60505i) q^{26} +(-0.714839 + 2.54735i) q^{28} +(1.85395 + 1.07038i) q^{29} +(-0.995345 - 1.72399i) q^{31} +(0.500000 - 0.866025i) q^{32} +7.24991 q^{34} +(9.38833 + 2.63456i) q^{35} +(-5.55479 + 3.20706i) q^{37} +(-0.510587 - 0.884362i) q^{38} +(-3.19176 - 1.84276i) q^{40} +(-6.58538 - 3.80207i) q^{41} +(0.865187 + 1.49855i) q^{43} +(0.180325 - 0.312331i) q^{44} +(2.16373 + 1.24923i) q^{46} +(-5.77041 - 3.33155i) q^{47} +(6.14298 - 3.35616i) q^{49} +(-4.29155 + 7.43318i) q^{50} +(-3.15199 + 1.75070i) q^{52} +(-1.92427 + 1.11098i) q^{53} +(-1.15110 - 0.664591i) q^{55} +(-2.56349 + 0.654608i) q^{56} +2.14076i q^{58} +(-8.42022 - 4.86142i) q^{59} -2.28162i q^{61} +(0.995345 - 1.72399i) q^{62} +1.00000 q^{64} +(6.45226 + 11.6167i) q^{65} -11.2553i q^{67} +(3.62495 + 6.27861i) q^{68} +(2.41257 + 9.44781i) q^{70} +(2.50082 + 4.33155i) q^{71} +(7.65435 + 13.2577i) q^{73} +(-5.55479 - 3.20706i) q^{74} +(0.510587 - 0.884362i) q^{76} +(-0.924521 + 0.236084i) q^{77} +(-4.58586 + 7.94294i) q^{79} -3.68552i q^{80} -7.60414i q^{82} -11.1000i q^{83} +(23.1400 - 13.3599i) q^{85} +(-0.865187 + 1.49855i) q^{86} +0.360649 q^{88} +(-12.6748 + 7.31778i) q^{89} +(9.14057 + 2.72947i) q^{91} +2.49846i q^{92} -6.66309i q^{94} +(-3.25934 - 1.88178i) q^{95} +(7.87790 + 13.6449i) q^{97} +(5.97801 + 3.64189i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{2} - 18 q^{4} - 2 q^{7} - 36 q^{8}+O(q^{10}) $ 36 * q + 18 * q^2 - 18 * q^4 - 2 * q^7 - 36 * q^8	$ 36 q + 18 q^{2} - 18 q^{4} - 2 q^{7} - 36 q^{8} + 2 q^{13} + 2 q^{14} - 18 q^{16} + 28 q^{19} + 12 q^{23} + 14 q^{25} + 4 q^{26} + 4 q^{28} - 4 q^{31} + 18 q^{32} + 24 q^{35} - 30 q^{37} + 14 q^{38} + 24 q^{41} + 14 q^{43} + 12 q^{46} - 36 q^{47} + 6 q^{49} - 14 q^{50} + 2 q^{52} + 24 q^{53} - 24 q^{55} + 2 q^{56} - 12 q^{59} + 4 q^{62} + 36 q^{64} + 12 q^{65} + 2 q^{73} - 30 q^{74} - 14 q^{76} - 16 q^{79} - 24 q^{85} - 14 q^{86} + 16 q^{91} + 12 q^{95} - 2 q^{97} + 24 q^{98}+O(q^{100}) $ 36 * q + 18 * q^2 - 18 * q^4 - 2 * q^7 - 36 * q^8 + 2 * q^13 + 2 * q^14 - 18 * q^16 + 28 * q^19 + 12 * q^23 + 14 * q^25 + 4 * q^26 + 4 * q^28 - 4 * q^31 + 18 * q^32 + 24 * q^35 - 30 * q^37 + 14 * q^38 + 24 * q^41 + 14 * q^43 + 12 * q^46 - 36 * q^47 + 6 * q^49 - 14 * q^50 + 2 * q^52 + 24 * q^53 - 24 * q^55 + 2 * q^56 - 12 * q^59 + 4 * q^62 + 36 * q^64 + 12 * q^65 + 2 * q^73 - 30 * q^74 - 14 * q^76 - 16 * q^79 - 24 * q^85 - 14 * q^86 + 16 * q^91 + 12 * q^95 - 2 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	3.19176	+	1.84276i	1.42740	+	0.824108i	0.996915	−	0.0784903i	$-0.0250100\pi$
$5$	3.19176	+	1.84276i	1.42740	+	0.824108i	0.430483	+	0.902599i	$0.358343\pi$
$6$		0			0
$7$	2.56349	−	0.654608i	0.968909	−	0.247418i
$7$	2.56349	−	0.654608i	0.968909	−	0.247418i
$8$	−1.00000			−0.353553
$9$		0			0
$10$			3.68552i			1.16547i
$11$	−0.360649			−0.108740			−0.0543699	−	0.998521i	$-0.517315\pi$
$11$	−0.360649			−0.108740			−0.0543699	+	0.998521i	$0.517315\pi$
$12$		0			0
$13$	3.09215	+	1.85435i	0.857608	+	0.514304i
$13$	3.09215	+	1.85435i	0.857608	+	0.514304i
$14$	1.84865	+	1.89275i	0.494073	+	0.505857i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.62495	−	6.27861i	0.879181	−	1.52279i	0.0269392	−	0.999637i	$-0.491424\pi$
$17$	3.62495	−	6.27861i	0.879181	−	1.52279i	0.852241	−	0.523149i	$-0.175243\pi$
$18$		0			0
$19$	−1.02117			−0.234273			−0.117137	−	0.993116i	$-0.537372\pi$
$19$	−1.02117			−0.234273			−0.117137	+	0.993116i	$0.537372\pi$
$20$	−3.19176	+	1.84276i	−0.713699	+	0.412054i
$21$		0			0
$22$	−0.180325	−	0.312331i	−0.0384453	−	0.0665892i
$23$	2.16373	−	1.24923i	0.451169	−	0.260482i	−0.257155	−	0.966370i	$-0.582785\pi$
$23$	2.16373	−	1.24923i	0.451169	−	0.260482i	0.708324	+	0.705888i	$0.249452\pi$
$24$		0			0
$25$	4.29155	+	7.43318i	0.858309	+	1.48664i
$26$	−0.0598406	+	3.60505i	−0.0117357	+	0.707009i
$27$		0			0
$28$	−0.714839	+	2.54735i	−0.135092	+	0.481404i
$29$	1.85395	+	1.07038i	0.344270	+	0.198765i	0.662159	−	0.749364i	$-0.269640\pi$
$29$	1.85395	+	1.07038i	0.344270	+	0.198765i	−0.317888	+	0.948128i	$0.602974\pi$
$30$		0			0
$31$	−0.995345	−	1.72399i	−0.178769	−	0.309637i	0.762690	−	0.646764i	$-0.223878\pi$
$31$	−0.995345	−	1.72399i	−0.178769	−	0.309637i	−0.941459	+	0.337127i	$0.890545\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	7.24991			1.24335
$35$	9.38833	+	2.63456i	1.58692	+	0.445321i
$36$		0			0
$37$	−5.55479	+	3.20706i	−0.913201	+	0.527237i	−0.881460	−	0.472259i	$-0.843439\pi$
$37$	−5.55479	+	3.20706i	−0.913201	+	0.527237i	−0.0317416	+	0.999496i	$0.510105\pi$
$38$	−0.510587	−	0.884362i	−0.0828281	−	0.143462i
$39$		0			0
$40$	−3.19176	−	1.84276i	−0.504661	−	0.291366i
$41$	−6.58538	−	3.80207i	−1.02846	−	0.593783i	−0.111919	−	0.993717i	$-0.535700\pi$
$41$	−6.58538	−	3.80207i	−1.02846	−	0.593783i	−0.916544	+	0.399934i	$0.869033\pi$
$42$		0			0
$43$	0.865187	+	1.49855i	0.131940	+	0.228526i	0.924424	−	0.381366i	$-0.124546\pi$
$43$	0.865187	+	1.49855i	0.131940	+	0.228526i	−0.792485	+	0.609892i	$0.791213\pi$
$44$	0.180325	−	0.312331i	0.0271849	−	0.0470857i
$45$		0			0
$46$	2.16373	+	1.24923i	0.319024	+	0.184189i
$47$	−5.77041	−	3.33155i	−0.841701	−	0.485956i	0.0161413	−	0.999870i	$-0.494862\pi$
$47$	−5.77041	−	3.33155i	−0.841701	−	0.485956i	−0.857842	+	0.513914i	$0.828195\pi$
$48$		0			0
$49$	6.14298	−	3.35616i	0.877568	−	0.479452i
$50$	−4.29155	+	7.43318i	−0.606916	+	1.05121i
$51$		0			0
$52$	−3.15199	+	1.75070i	−0.437102	+	0.242779i
$53$	−1.92427	+	1.11098i	−0.264319	+	0.152604i	−0.626303	−	0.779580i	$-0.715433\pi$
$53$	−1.92427	+	1.11098i	−0.264319	+	0.152604i	0.361984	+	0.932184i	$0.382099\pi$
$54$		0			0
$55$	−1.15110	−	0.664591i	−0.155215	−	0.0896134i
$56$	−2.56349	+	0.654608i	−0.342561	+	0.0874756i
$57$		0			0
$58$			2.14076i			0.281096i
$59$	−8.42022	−	4.86142i	−1.09622	−	0.632902i	−0.160994	−	0.986955i	$-0.551470\pi$
$59$	−8.42022	−	4.86142i	−1.09622	−	0.632902i	−0.935225	+	0.354053i	$0.884803\pi$
$60$		0			0
$61$		−	2.28162i		−	0.292132i	−0.989275	−	0.146066i	$-0.953339\pi$
$61$		−	2.28162i		−	0.292132i	0.989275	−	0.146066i	$-0.0466612\pi$
$62$	0.995345	−	1.72399i	0.126409	−	0.218947i
$63$		0			0
$64$	1.00000			0.125000
$65$	6.45226	+	11.6167i	0.800305	+	1.44088i
$66$		0			0
$67$		−	11.2553i		−	1.37505i	−0.726160	−	0.687526i	$-0.758697\pi$
$67$		−	11.2553i		−	1.37505i	0.726160	−	0.687526i	$-0.241303\pi$
$68$	3.62495	+	6.27861i	0.439590	+	0.761393i
$69$		0			0
$70$	2.41257	+	9.44781i	0.288358	+	1.12923i
$71$	2.50082	+	4.33155i	0.296793	+	0.514060i	0.975400	−	0.220441i	$-0.0707497\pi$
$71$	2.50082	+	4.33155i	0.296793	+	0.514060i	−0.678608	+	0.734501i	$0.737416\pi$
$72$		0			0
$73$	7.65435	+	13.2577i	0.895874	+	1.55170i	0.832719	+	0.553696i	$0.186783\pi$
$73$	7.65435	+	13.2577i	0.895874	+	1.55170i	0.0631552	+	0.998004i	$0.479884\pi$
$74$	−5.55479	−	3.20706i	−0.645731	−	0.372813i
$75$		0			0
$76$	0.510587	−	0.884362i	0.0585683	−	0.101443i
$77$	−0.924521	+	0.236084i	−0.105359	+	0.0269042i
$78$		0			0
$79$	−4.58586	+	7.94294i	−0.515949	+	0.893651i	0.483879	+	0.875135i	$0.339227\pi$
$79$	−4.58586	+	7.94294i	−0.515949	+	0.893651i	−0.999829	+	0.0185157i	$0.994106\pi$
$80$		−	3.68552i		−	0.412054i
$81$		0			0
$82$		−	7.60414i		−	0.839737i
$83$		−	11.1000i		−	1.21839i	−0.793022	−	0.609193i	$-0.791493\pi$
$83$		−	11.1000i		−	1.21839i	0.793022	−	0.609193i	$-0.208507\pi$
$84$		0			0
$85$	23.1400	−	13.3599i	2.50988	−	1.44908i
$86$	−0.865187	+	1.49855i	−0.0932955	+	0.161593i
$87$		0			0
$88$	0.360649			0.0384453
$89$	−12.6748	+	7.31778i	−1.34352	+	0.775683i	−0.987323	−	0.158727i	$-0.949261\pi$
$89$	−12.6748	+	7.31778i	−1.34352	+	0.775683i	−0.356200	+	0.934410i	$0.615928\pi$
$90$		0			0
$91$	9.14057	+	2.72947i	0.958192	+	0.286126i
$92$			2.49846i			0.260482i
$93$		0			0
$94$		−	6.66309i		−	0.687246i
$95$	−3.25934	−	1.88178i	−0.334401	−	0.193067i
$96$		0			0
$97$	7.87790	+	13.6449i	0.799880	+	1.38543i	0.919694	+	0.392636i	$0.128437\pi$
$97$	7.87790	+	13.6449i	0.799880	+	1.38543i	−0.119815	+	0.992796i	$0.538230\pi$
$98$	5.97801	+	3.64189i	0.603870	+	0.367887i
$99$		0			0
$100$	−8.58309			−0.858309
$101$	−8.76556			−0.872206			−0.436103	−	0.899897i	$-0.643642\pi$
$101$	−8.76556			−0.872206			−0.436103	+	0.899897i	$0.643642\pi$
$102$		0			0
$103$	2.72155	+	1.57129i	0.268162	+	0.154824i	0.628052	−	0.778171i	$-0.283852\pi$
$103$	2.72155	+	1.57129i	0.268162	+	0.154824i	−0.359890	+	0.932995i	$0.617186\pi$
$104$	−3.09215	−	1.85435i	−0.303210	−	0.181834i
$105$		0			0
$106$	−1.92427	−	1.11098i	−0.186902	−	0.107908i
$107$	−16.0555	+	9.26964i	−1.55214	+	0.896130i	−0.554175	+	0.832400i	$0.686966\pi$
$107$	−16.0555	+	9.26964i	−1.55214	+	0.896130i	−0.997967	+	0.0637300i	$0.979700\pi$
$108$		0			0
$109$	6.81950	−	3.93724i	0.653189	−	0.377119i	−0.136488	−	0.990642i	$-0.543581\pi$
$109$	6.81950	−	3.93724i	0.653189	−	0.377119i	0.789677	+	0.613523i	$0.210248\pi$
$110$		−	1.32918i		−	0.126732i
$111$		0			0
$112$	−1.84865	−	1.89275i	−0.174681	−	0.178848i
$113$	0.239792	−	0.138444i	0.0225577	−	0.0130237i	−0.488679	−	0.872464i	$-0.662521\pi$
$113$	0.239792	−	0.138444i	0.0225577	−	0.0130237i	0.511236	+	0.859440i	$0.329188\pi$
$114$		0			0
$115$	9.20813			0.858663
$116$	−1.85395	+	1.07038i	−0.172135	+	0.0993823i
$117$		0			0
$118$		−	9.72283i		−	0.895059i
$119$	5.18252	−	18.4681i	0.475081	−	1.69297i
$120$		0			0
$121$	−10.8699			−0.988176
$122$	1.97594	−	1.14081i	0.178894	−	0.103284i
$123$		0			0
$124$	1.99069			0.178769
$125$			13.2056i			1.18114i
$126$		0			0
$127$	−5.18786	+	8.98564i	−0.460348	+	0.797347i	−0.998978	−	0.0451957i	$-0.985609\pi$
$127$	−5.18786	+	8.98564i	−0.460348	+	0.797347i	0.538630	+	0.842543i	$0.318942\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−6.83426	+	11.3962i	−0.599404	+	0.999512i
$131$	−4.14703	+	7.18287i	−0.362328	+	0.627570i	−0.988344	−	0.152240i	$-0.951351\pi$
$131$	−4.14703	+	7.18287i	−0.362328	+	0.627570i	0.626016	+	0.779810i	$0.284685\pi$
$132$		0			0
$133$	−2.61777	+	0.668468i	−0.226989	+	0.0579635i
$134$	9.74737	−	5.62764i	0.842044	−	0.486154i
$135$		0			0
$136$	−3.62495	+	6.27861i	−0.310837	+	0.538386i
$137$	−0.596243	+	1.03272i	−0.0509404	+	0.0882314i	−0.890371	−	0.455235i	$-0.849555\pi$
$137$	−0.596243	+	1.03272i	−0.0509404	+	0.0882314i	0.839431	+	0.543467i	$0.182889\pi$
$138$		0			0
$139$	−16.8421	+	9.72381i	−1.42853	+	0.824763i	−0.997005	−	0.0773371i	$-0.975358\pi$
$139$	−16.8421	+	9.72381i	−1.42853	+	0.824763i	−0.431527	+	0.902100i	$0.642025\pi$
$140$	−6.97576	+	6.81326i	−0.589559	+	0.575825i
$141$		0			0
$142$	−2.50082	+	4.33155i	−0.209864	+	0.363495i
$143$	−1.11518	−	0.668770i	−0.0932561	−	0.0559253i
$144$		0			0
$145$	3.94491	+	6.83279i	0.327607	+	0.567432i
$146$	−7.65435	+	13.2577i	−0.633479	+	1.09722i
$147$		0			0
$148$		−	6.41412i		−	0.527237i
$149$	−7.73438			−0.633625			−0.316812	−	0.948488i	$-0.602613\pi$
$149$	−7.73438			−0.633625			−0.316812	+	0.948488i	$0.602613\pi$
$150$		0			0
$151$	−12.8722	+	7.43180i	−1.04753	+	0.604791i	−0.921956	−	0.387294i	$-0.873410\pi$
$151$	−12.8722	+	7.43180i	−1.04753	+	0.604791i	−0.125572	+	0.992084i	$0.540077\pi$
$152$	1.02117			0.0828281
$153$		0			0
$154$	−0.666715	−	0.682617i	−0.0537254	−	0.0550068i
$155$		−	7.33674i		−	0.589301i
$156$		0			0
$157$	3.75405	−	2.16740i	0.299605	−	0.172977i	−0.342660	−	0.939459i	$-0.611328\pi$
$157$	3.75405	−	2.16740i	0.299605	−	0.172977i	0.642266	+	0.766482i	$0.277995\pi$
$158$	−9.17172			−0.729663
$159$		0			0
$160$	3.19176	−	1.84276i	0.252331	−	0.145683i
$161$	4.72895	−	4.61878i	0.372693	−	0.364011i
$162$		0			0
$163$		−	7.00364i		−	0.548567i	−0.961649	−	0.274284i	$-0.911559\pi$
$163$		−	7.00364i		−	0.548567i	0.961649	−	0.274284i	$-0.0884407\pi$
$164$	6.58538	−	3.80207i	0.514232	−	0.296892i
$165$		0			0
$166$	9.61290	−	5.55001i	0.746106	−	0.430764i
$167$	16.4440	+	9.49393i	1.27247	+	0.734662i	0.975453	−	0.220209i	$-0.0706741\pi$
$167$	16.4440	+	9.49393i	1.27247	+	0.734662i	0.297019	+	0.954871i	$0.404007\pi$
$168$		0			0
$169$	6.12277	+	11.4679i	0.470982	+	0.882143i
$170$	23.1400	+	13.3599i	1.77475	+	1.02465i
$171$		0			0
$172$	−1.73037			−0.131940
$173$	18.1262			1.37811			0.689056	−	0.724708i	$-0.258025\pi$
$173$	18.1262			1.37811			0.689056	+	0.724708i	$0.258025\pi$
$174$		0			0
$175$	15.8672	+	16.2456i	1.19944	+	1.22805i
$176$	0.180325	+	0.312331i	0.0135925	+	0.0235429i
$177$		0			0
$178$	−12.6748	−	7.31778i	−0.950014	−	0.548491i
$179$		−	11.9411i		−	0.892519i	−0.894904	−	0.446259i	$-0.852756\pi$
$179$		−	11.9411i		−	0.892519i	0.894904	−	0.446259i	$-0.147244\pi$
$180$		0			0
$181$		−	6.92887i		−	0.515019i	−0.966276	−	0.257510i	$-0.917098\pi$
$181$		−	6.92887i		−	0.515019i	0.966276	−	0.257510i	$-0.0829019\pi$
$182$	2.20650	+	9.28070i	0.163556	+	0.687931i
$183$		0			0
$184$	−2.16373	+	1.24923i	−0.159512	+	0.0920944i
$185$	−23.6394			−1.73800
$186$		0			0
$187$	−1.30734	+	2.26437i	−0.0956019	+	0.165587i
$188$	5.77041	−	3.33155i	0.420850	−	0.242978i
$189$		0			0
$190$		−	3.76356i		−	0.273037i
$191$		−	0.978510i		−	0.0708025i	−0.999373	−	0.0354012i	$-0.988729\pi$
$191$		−	0.978510i		−	0.0708025i	0.999373	−	0.0354012i	$-0.0112709\pi$
$192$		0			0
$193$		−	5.11260i		−	0.368013i	−0.982925	−	0.184006i	$-0.941093\pi$
$193$		−	5.11260i		−	0.368013i	0.982925	−	0.184006i	$-0.0589067\pi$
$194$	−7.87790	+	13.6449i	−0.565600	+	0.979648i
$195$		0			0
$196$	−0.164967	+	6.99806i	−0.0117834	+	0.499861i
$197$	9.72108	−	16.8374i	0.692598	−	1.19962i	−0.278386	−	0.960469i	$-0.589799\pi$
$197$	9.72108	−	16.8374i	0.692598	−	1.19962i	0.970984	−	0.239146i	$-0.0768673\pi$
$198$		0			0
$199$	16.8671	+	9.73825i	1.19568	+	0.690326i	0.959589	−	0.281405i	$-0.0908005\pi$
$199$	16.8671	+	9.73825i	1.19568	+	0.690326i	0.236091	+	0.971731i	$0.424134\pi$
$200$	−4.29155	−	7.43318i	−0.303458	−	0.525605i
$201$		0			0
$202$	−4.38278	−	7.59120i	−0.308371	−	0.534115i
$203$	5.45327	+	1.53030i	0.382745	+	0.107406i
$204$		0			0
$205$	−14.0126	−	24.2706i	−0.978684	−	1.69513i
$206$			3.14257i			0.218954i
$207$		0			0
$208$	0.0598406	−	3.60505i	0.00414920	−	0.249966i
$209$	0.368285			0.0254748
$210$		0			0
$211$	3.41205	−	5.90984i	0.234895	−	0.406850i	−0.724347	−	0.689435i	$-0.757859\pi$
$211$	3.41205	−	5.90984i	0.234895	−	0.406850i	0.959242	+	0.282585i	$0.0911920\pi$
$212$		−	2.22195i		−	0.152604i
$213$		0			0
$214$	−16.0555	−	9.26964i	−1.09753	−	0.633660i
$215$			6.37734i			0.434931i
$216$		0			0
$217$	−3.68009	−	3.76787i	−0.249821	−	0.255780i
$218$	6.81950	+	3.93724i	0.461874	+	0.266663i
$219$		0			0
$220$	1.15110	−	0.664591i	0.0776075	−	0.0448067i
$221$	22.8516	−	12.6924i	1.53717	−	0.853786i
$222$		0			0
$223$	14.2672	−	24.7115i	0.955403	−	1.65481i	0.221960	−	0.975056i	$-0.428755\pi$
$223$	14.2672	−	24.7115i	0.955403	−	1.65481i	0.733443	−	0.679751i	$-0.237912\pi$
$224$	0.714839	−	2.54735i	0.0477622	−	0.170202i
$225$		0			0
$226$	0.239792	+	0.138444i	0.0159507	+	0.00920916i
$227$	−4.48708	−	2.59062i	−0.297818	−	0.171945i	0.343644	−	0.939100i	$-0.388339\pi$
$227$	−4.48708	−	2.59062i	−0.297818	−	0.171945i	−0.641462	+	0.767155i	$0.721672\pi$
$228$		0			0
$229$	−4.39140	+	7.60612i	−0.290192	+	0.502627i	−0.973855	−	0.227171i	$-0.927052\pi$
$229$	−4.39140	+	7.60612i	−0.290192	+	0.502627i	0.683663	+	0.729798i	$0.260386\pi$
$230$	4.60407	+	7.97448i	0.303583	+	0.525821i
$231$		0			0
$232$	−1.85395	−	1.07038i	−0.121718	−	0.0702739i
$233$	2.45840	+	1.41936i	0.161055	+	0.0929852i	0.578361	−	0.815781i	$-0.303692\pi$
$233$	2.45840	+	1.41936i	0.161055	+	0.0929852i	−0.417306	+	0.908766i	$0.637026\pi$
$234$		0			0
$235$	−12.2785	−	21.2670i	−0.800961	−	1.38731i
$236$	8.42022	−	4.86142i	0.548110	−	0.316451i
$237$		0			0
$238$	18.5851	−	4.74585i	1.20469	−	0.307628i
$239$	−19.9601			−1.29111			−0.645555	−	0.763714i	$-0.723374\pi$
$239$	−19.9601			−1.29111			−0.645555	+	0.763714i	$0.723374\pi$
$240$		0			0
$241$	−1.35228	+	2.34221i	−0.0871079	+	0.150875i	−0.906287	−	0.422662i	$-0.861096\pi$
$241$	−1.35228	+	2.34221i	−0.0871079	+	0.150875i	0.819180	+	0.573537i	$0.194429\pi$
$242$	−5.43497	−	9.41364i	−0.349373	−	0.605132i
$243$		0			0
$244$	1.97594	+	1.14081i	0.126497	+	0.0730330i
$245$	25.7915	+	0.607991i	1.64776	+	0.0388431i
$246$		0			0
$247$	−3.15762	−	1.89361i	−0.200915	−	0.120488i
$248$	0.995345	+	1.72399i	0.0632045	+	0.109473i
$249$		0			0
$250$	−11.4364	+	6.60279i	−0.723300	+	0.417597i
$251$	−15.2289	−	26.3773i	−0.961242	−	1.66492i	−0.719389	−	0.694607i	$-0.755578\pi$
$251$	−15.2289	−	26.3773i	−0.961242	−	1.66492i	−0.241853	−	0.970313i	$-0.577755\pi$
$252$		0			0
$253$	−0.780347	+	0.450533i	−0.0490600	+	0.0283248i
$254$	−10.3757			−0.651031
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.66047	+	13.2683i	0.477847	+	0.827655i	0.999678	−	0.0253938i	$-0.00808396\pi$
$257$	7.66047	+	13.2683i	0.477847	+	0.827655i	−0.521830	+	0.853049i	$0.674751\pi$
$258$		0			0
$259$	−12.1403	+	11.8575i	−0.754361	+	0.736787i
$260$	−13.2865	−	0.220544i	−0.823995	−	0.0136776i
$261$		0			0
$262$	−8.29406			−0.512409
$263$		−	8.82779i		−	0.544345i	−0.962248	−	0.272172i	$-0.912258\pi$
$263$		−	8.82779i		−	0.544345i	0.962248	−	0.272172i	$-0.0877421\pi$
$264$		0			0
$265$	−8.18907			−0.503051
$266$	−1.88779	−	1.93282i	−0.115748	−	0.118509i
$267$		0			0
$268$	9.74737	+	5.62764i	0.595415	+	0.343763i
$269$	−6.95223	+	12.0416i	−0.423885	+	0.734190i	−0.996316	−	0.0857629i	$-0.972667\pi$
$269$	−6.95223	+	12.0416i	−0.423885	+	0.734190i	0.572431	+	0.819953i	$0.306001\pi$
$270$		0			0
$271$	−7.75333	−	13.4292i	−0.470981	−	0.815764i	0.528468	−	0.848953i	$-0.322767\pi$
$271$	−7.75333	−	13.4292i	−0.470981	−	0.815764i	−0.999449	+	0.0331898i	$0.989433\pi$
$272$	−7.24991			−0.439590
$273$		0			0
$274$	−1.19249			−0.0720407
$275$	−1.54774	−	2.68077i	−0.0933324	−	0.161656i
$276$		0			0
$277$	2.95010	−	5.10972i	0.177254	−	0.307014i	−0.763685	−	0.645589i	$-0.776612\pi$
$277$	2.95010	−	5.10972i	0.177254	−	0.307014i	0.940939	+	0.338576i	$0.109945\pi$
$278$	−16.8421	−	9.72381i	−1.01012	−	0.583196i
$279$		0			0
$280$	−9.38833	−	2.63456i	−0.561060	−	0.157445i
$281$	8.92253			0.532273			0.266137	−	0.963935i	$-0.414253\pi$
$281$	8.92253			0.532273			0.266137	+	0.963935i	$0.414253\pi$
$282$		0			0
$283$		−	22.9871i		−	1.36644i	−0.730213	−	0.683220i	$-0.760579\pi$
$283$		−	22.9871i		−	1.36644i	0.730213	−	0.683220i	$-0.239421\pi$
$284$	−5.00164			−0.296793
$285$		0			0
$286$	0.0215815	−	1.30016i	0.00127614	−	0.0768800i
$287$	−19.3704	−	5.43573i	−1.14340	−	0.320861i
$288$		0			0
$289$	−17.7806	−	30.7969i	−1.04592	−	1.81158i
$290$	−3.94491	+	6.83279i	−0.231653	+	0.401235i
$291$		0			0
$292$	−15.3087			−0.895874
$293$	3.49834	−	2.01977i	0.204375	−	0.117996i	−0.394319	−	0.918973i	$-0.629020\pi$
$293$	3.49834	−	2.01977i	0.204375	−	0.117996i	0.598695	+	0.800977i	$0.295686\pi$
$294$		0			0
$295$	−17.9169	−	31.0329i	−1.04316	−	1.80681i
$296$	5.55479	−	3.20706i	0.322865	−	0.186406i
$297$		0			0
$298$	−3.86719	−	6.69817i	−0.224020	−	0.388014i
$299$	9.00708	+	0.149509i	0.520893	+	0.00864634i
$300$		0			0
$301$	3.19886	+	3.27516i	0.184379	+	0.188777i
$302$	−12.8722	−	7.43180i	−0.740715	−	0.427652i
$303$		0			0
$304$	0.510587	+	0.884362i	0.0292842	+	0.0507216i
$305$	4.20449	−	7.28239i	0.240748	−	0.416989i
$306$		0			0
$307$	7.12167			0.406455			0.203228	−	0.979132i	$-0.434857\pi$
$307$	7.12167			0.406455			0.203228	+	0.979132i	$0.434857\pi$
$308$	0.257806	−	0.918700i	0.0146899	−	0.0523478i
$309$		0			0
$310$	6.35380	−	3.66837i	0.360872	−	0.208349i
$311$	13.0682	+	22.6348i	0.741030	+	1.28350i	0.952027	+	0.306015i	$0.0989958\pi$
$311$	13.0682	+	22.6348i	0.741030	+	1.28350i	−0.210996	+	0.977487i	$0.567671\pi$
$312$		0			0
$313$	22.3391	+	12.8975i	1.26268	+	0.729009i	0.973592	−	0.228293i	$-0.0733145\pi$
$313$	22.3391	+	12.8975i	1.26268	+	0.729009i	0.289089	+	0.957302i	$0.406648\pi$
$314$	3.75405	+	2.16740i	0.211853	+	0.122313i
$315$		0			0
$316$	−4.58586	−	7.94294i	−0.257975	−	0.446825i
$317$	4.44620	−	7.70104i	0.249723	−	0.432533i	−0.713726	−	0.700425i	$-0.752994\pi$
$317$	4.44620	−	7.70104i	0.249723	−	0.432533i	0.963449	+	0.267892i	$0.0863270\pi$
$318$		0			0
$319$	−0.668626	−	0.386032i	−0.0374359	−	0.0216136i
$320$	3.19176	+	1.84276i	0.178425	+	0.103014i
$321$		0			0
$322$	6.36446	+	1.78600i	0.354677	+	0.0995297i
$323$	−3.70171	+	6.41154i	−0.205968	+	0.356748i
$324$		0			0
$325$	−0.513617	+	30.9425i	−0.0284904	+	1.71638i
$326$	6.06533	−	3.50182i	0.335928	−	0.193948i
$327$		0			0
$328$	6.58538	+	3.80207i	0.363617	+	0.209934i
$329$	−16.9732	−	4.76304i	−0.935766	−	0.262595i
$330$		0			0
$331$		−	8.56960i		−	0.471028i	−0.971871	−	0.235514i	$-0.924323\pi$
$331$		−	8.56960i		−	0.471028i	0.971871	−	0.235514i	$-0.0756773\pi$
$332$	9.61290	+	5.55001i	0.527577	+	0.304596i
$333$		0			0
$334$			18.9879i			1.03897i
$335$	20.7408	−	35.9242i	1.13319	−	1.96275i
$336$		0			0
$337$	−14.9192			−0.812699			−0.406350	−	0.913718i	$-0.633198\pi$
$337$	−14.9192			−0.812699			−0.406350	+	0.913718i	$0.633198\pi$
$338$	−6.87007	+	11.0364i	−0.373683	+	0.600301i
$339$		0			0
$340$			26.7197i			1.44908i
$341$	0.358970	+	0.621755i	0.0194393	+	0.0336699i
$342$		0			0
$343$	13.5505	−	12.6247i	0.731658	−	0.681671i
$344$	−0.865187	−	1.49855i	−0.0466477	−	0.0807963i
$345$		0			0
$346$	9.06312	+	15.6978i	0.487236	+	0.843918i
$347$	−26.3328	−	15.2032i	−1.41362	−	0.816153i	−0.417891	−	0.908497i	$-0.637231\pi$
$347$	−26.3328	−	15.2032i	−1.41362	−	0.816153i	−0.995727	+	0.0923444i	$0.970564\pi$
$348$		0			0
$349$	−3.00120	+	5.19823i	−0.160651	+	0.278255i	−0.935102	−	0.354378i	$-0.884693\pi$
$349$	−3.00120	+	5.19823i	−0.160651	+	0.278255i	0.774452	+	0.632633i	$0.218026\pi$
$350$	−6.13553	+	21.8642i	−0.327958	+	1.16869i
$351$		0			0
$352$	−0.180325	+	0.312331i	−0.00961133	+	0.0166473i
$353$		−	20.2197i		−	1.07618i	−0.842886	−	0.538092i	$-0.819145\pi$
$353$		−	20.2197i		−	1.07618i	0.842886	−	0.538092i	$-0.180855\pi$
$354$		0			0
$355$			18.4337i			0.978357i
$356$		−	14.6356i		−	0.775683i
$357$		0			0
$358$	10.3413	−	5.97054i	0.546554	−	0.315553i
$359$	14.8473	−	25.7163i	0.783610	−	1.35725i	−0.146216	−	0.989253i	$-0.546709\pi$
$359$	14.8473	−	25.7163i	0.783610	−	1.35725i	0.929826	−	0.368000i	$-0.119957\pi$
$360$		0			0
$361$	−17.9572			−0.945116
$362$	6.00058	−	3.46444i	0.315384	−	0.182087i
$363$		0			0
$364$	−6.93407	+	6.55123i	−0.363444	+	0.343378i
$365$			56.4206i			2.95319i
$366$		0			0
$367$			30.7688i			1.60612i	0.595900	+	0.803058i	$0.296795\pi$
$367$			30.7688i			1.60612i	−0.595900	+	0.803058i	$0.703205\pi$
$368$	−2.16373	−	1.24923i	−0.112792	−	0.0651206i
$369$		0			0
$370$	−11.8197	−	20.4723i	−0.614477	−	1.06430i
$371$	−4.20559	+	4.10762i	−0.218344	+	0.213257i
$372$		0			0
$373$	11.5145			0.596196			0.298098	−	0.954535i	$-0.403648\pi$
$373$	11.5145			0.596196			0.298098	+	0.954535i	$0.403648\pi$
$374$	−2.61467			−0.135202
$375$		0			0
$376$	5.77041	+	3.33155i	0.297586	+	0.171811i
$377$	3.74784	+	6.74765i	0.193023	+	0.347522i
$378$		0			0
$379$	−1.28888	−	0.744135i	−0.0662053	−	0.0382236i	0.466532	−	0.884504i	$-0.345503\pi$
$379$	−1.28888	−	0.744135i	−0.0662053	−	0.0382236i	−0.532737	+	0.846281i	$0.678837\pi$
$380$	3.25934	−	1.88178i	0.167201	−	0.0965333i
$381$		0			0
$382$	0.847414	−	0.489255i	0.0433575	−	0.0250325i
$383$		−	23.9889i		−	1.22578i	−0.790169	−	0.612889i	$-0.790007\pi$
$383$		−	23.9889i		−	1.22578i	0.790169	−	0.612889i	$-0.209993\pi$
$384$		0			0
$385$	−3.38589	−	0.950150i	−0.172561	−	0.0484242i
$386$	4.42764	−	2.55630i	0.225361	−	0.130112i
$387$		0			0
$388$	−15.7558			−0.799880
$389$	18.6504	−	10.7678i	0.945615	−	0.545951i	0.0538987	−	0.998546i	$-0.482835\pi$
$389$	18.6504	−	10.7678i	0.945615	−	0.545951i	0.891716	+	0.452596i	$0.149502\pi$
$390$		0			0
$391$		−	18.1136i		−	0.916044i
$392$	−6.14298	+	3.35616i	−0.310267	+	0.169512i
$393$		0			0
$394$	19.4422			0.979482
$395$	−29.2739	+	16.9013i	−1.47293	+	0.850396i
$396$		0			0
$397$	−3.58264			−0.179807			−0.0899037	−	0.995950i	$-0.528656\pi$
$397$	−3.58264			−0.179807			−0.0899037	+	0.995950i	$0.528656\pi$
$398$			19.4765i			0.976268i
$399$		0			0
$400$	4.29155	−	7.43318i	0.214577	−	0.371659i
$401$	−17.9224	−	31.0425i	−0.895002	−	1.55019i	−0.833802	−	0.552063i	$-0.813841\pi$
$401$	−17.9224	−	31.0425i	−0.895002	−	1.55019i	−0.0611994	−	0.998126i	$-0.519493\pi$
$402$		0			0
$403$	0.119124	−	7.17655i	0.00593399	−	0.357489i
$404$	4.38278	−	7.59120i	0.218051	−	0.377676i
$405$		0			0
$406$	1.40136	+	5.48782i	0.0695482	+	0.272356i
$407$	2.00333	−	1.15662i	0.0993013	−	0.0573316i
$408$		0			0
$409$	−17.1675	+	29.7349i	−0.848877	+	1.47030i	0.0333351	+	0.999444i	$0.489387\pi$
$409$	−17.1675	+	29.7349i	−0.848877	+	1.47030i	−0.882212	+	0.470853i	$0.843946\pi$
$410$	14.0126	−	24.2706i	0.692034	−	1.19864i
$411$		0			0
$412$	−2.72155	+	1.57129i	−0.134081	+	0.0774118i
$413$	−24.7675	−	6.95026i	−1.21873	−	0.342000i
$414$		0			0
$415$	20.4547	−	35.4286i	1.00408	−	1.73912i
$416$	3.15199	−	1.75070i	0.154539	−	0.0858353i
$417$		0			0
$418$	0.184143	+	0.318944i	0.00900671	+	0.0156001i
$419$	10.4886	−	18.1668i	0.512401	−	0.887504i	−0.487496	−	0.873125i	$-0.662090\pi$
$419$	10.4886	−	18.1668i	0.512401	−	0.887504i	0.999897	−	0.0143791i	$-0.00457716\pi$
$420$		0			0
$421$			1.22524i			0.0597146i	0.999554	+	0.0298573i	$0.00950528\pi$
$421$			1.22524i			0.0597146i	−0.999554	+	0.0298573i	$0.990495\pi$
$422$	6.82409			0.332192
$423$		0			0
$424$	1.92427	−	1.11098i	0.0934508	−	0.0539538i
$425$	62.2267			3.01844
$426$		0			0
$427$	−1.49357	−	5.84892i	−0.0722788	−	0.283049i
$428$		−	18.5393i		−	0.896130i
$429$		0			0
$430$	−5.52293	+	3.18867i	−0.266340	+	0.153771i
$431$	−5.89033			−0.283727			−0.141864	−	0.989886i	$-0.545309\pi$
$431$	−5.89033			−0.283727			−0.141864	+	0.989886i	$0.545309\pi$
$432$		0			0
$433$	−34.0327	+	19.6488i	−1.63551	+	0.944259i	−0.653151	+	0.757227i	$0.726553\pi$
$433$	−34.0327	+	19.6488i	−1.63551	+	0.944259i	−0.982354	+	0.187032i	$0.940113\pi$
$434$	1.42302	−	5.07099i	0.0683073	−	0.243415i
$435$		0			0
$436$			7.87447i			0.377119i
$437$	−2.20954	+	1.27568i	−0.105697	+	0.0610240i
$438$		0			0
$439$	14.9305	−	8.62010i	0.712592	−	0.411415i	−0.0994281	−	0.995045i	$-0.531701\pi$
$439$	14.9305	−	8.62010i	0.712592	−	0.411415i	0.812020	+	0.583630i	$0.198368\pi$
$440$	1.15110	+	0.664591i	0.0548768	+	0.0316831i
$441$		0			0
$442$	22.4178	+	13.4439i	1.06631	+	0.639460i
$443$	−0.543112	−	0.313566i	−0.0258040	−	0.0148980i	0.487042	−	0.873378i	$-0.338076\pi$
$443$	−0.543112	−	0.313566i	−0.0258040	−	0.0148980i	−0.512847	+	0.858480i	$0.671409\pi$
$444$		0			0
$445$	−53.9397			−2.55699
$446$	28.5344			1.35114
$447$		0			0
$448$	2.56349	−	0.654608i	0.121114	−	0.0309273i
$449$	13.0921	+	22.6762i	0.617855	+	1.07016i	0.989876	+	0.141932i	$0.0453313\pi$
$449$	13.0921	+	22.6762i	0.617855	+	1.07016i	−0.372022	+	0.928224i	$0.621335\pi$
$450$		0			0
$451$	2.37501	+	1.37121i	0.111835	+	0.0645679i
$452$			0.276888i			0.0130237i
$453$		0			0
$454$		−	5.18123i		−	0.243167i
$455$	24.1447	+	25.5557i	1.13192	+	1.19807i
$456$		0			0
$457$	−20.6258	+	11.9083i	−0.964835	+	0.557047i	−0.897658	−	0.440694i	$-0.854733\pi$
$457$	−20.6258	+	11.9083i	−0.964835	+	0.557047i	−0.0671769	+	0.997741i	$0.521399\pi$
$458$	−8.78280			−0.410393
$459$		0			0
$460$	−4.60407	+	7.97448i	−0.214666	+	0.371812i
$461$	15.9116	−	9.18657i	0.741077	−	0.427861i	−0.0813835	−	0.996683i	$-0.525934\pi$
$461$	15.9116	−	9.18657i	0.741077	−	0.427861i	0.822461	+	0.568822i	$0.192601\pi$
$462$		0			0
$463$		−	11.3462i		−	0.527304i	−0.964618	−	0.263652i	$-0.915073\pi$
$463$		−	11.3462i		−	0.527304i	0.964618	−	0.263652i	$-0.0849271\pi$
$464$		−	2.14076i		−	0.0993823i
$465$		0			0
$466$			2.83871i			0.131501i
$467$	1.12837	−	1.95440i	0.0522149	−	0.0904388i	−0.838737	−	0.544537i	$-0.816705\pi$
$467$	1.12837	−	1.95440i	0.0522149	−	0.0904388i	0.890951	+	0.454099i	$0.150039\pi$
$468$		0			0
$469$	−7.36780	−	28.8528i	−0.340213	−	1.33230i
$470$	12.2785	−	21.2670i	0.566365	−	0.980973i
$471$		0			0
$472$	8.42022	+	4.86142i	0.387572	+	0.223765i
$473$	−0.312029	−	0.540450i	−0.0143471	−	0.0248499i
$474$		0			0
$475$	−4.38241	−	7.59056i	−0.201079	−	0.348279i
$476$	13.4026	+	13.7222i	0.614306	+	0.628957i
$477$		0			0
$478$	−9.98004	−	17.2859i	−0.456476	−	0.790640i
$479$		−	12.4328i		−	0.568068i	−0.958814	−	0.284034i	$-0.908327\pi$
$479$		−	12.4328i		−	0.568068i	0.958814	−	0.284034i	$-0.0916728\pi$
$480$		0			0
$481$	−23.1232	−	0.383824i	−1.05433	−	0.0175009i
$482$	−2.70456			−0.123189
$483$		0			0
$484$	5.43497	−	9.41364i	0.247044	−	0.427893i
$485$			58.0684i			2.63675i
$486$		0			0
$487$	18.9880	+	10.9627i	0.860430	+	0.496769i	0.864156	−	0.503224i	$-0.167853\pi$
$487$	18.9880	+	10.9627i	0.860430	+	0.496769i	−0.00372628	+	0.999993i	$0.501186\pi$
$488$			2.28162i			0.103284i
$489$		0			0
$490$	12.3692	+	22.6401i	0.558784	+	1.02278i
$491$	36.6150	+	21.1397i	1.65241	+	0.954022i	0.976076	+	0.217430i	$0.0697674\pi$
$491$	36.6150	+	21.1397i	1.65241	+	0.954022i	0.676338	+	0.736592i	$0.263566\pi$
$492$		0			0
$493$	13.4410	−	7.76016i	0.605352	−	0.349500i
$494$	0.0611076	−	3.68139i	0.00274936	−	0.165633i
$495$		0			0
$496$	−0.995345	+	1.72399i	−0.0446923	+	0.0774093i
$497$	9.24629	+	9.46682i	0.414753	+	0.424645i
$498$		0			0
$499$	34.5433	+	19.9436i	1.54637	+	0.892797i	0.998415	+	0.0562886i	$0.0179267\pi$
$499$	34.5433	+	19.9436i	1.54637	+	0.892797i	0.547955	+	0.836508i	$0.315407\pi$
$500$	−11.4364	−	6.60279i	−0.511450	−	0.295286i
$501$		0			0
$502$	15.2289	−	26.3773i	0.679701	−	1.17728i
$503$	4.78495	+	8.28777i	0.213350	+	0.369534i	0.952761	−	0.303721i	$-0.0982291\pi$
$503$	4.78495	+	8.28777i	0.213350	+	0.369534i	−0.739411	+	0.673255i	$0.764896\pi$
$504$		0			0
$505$	−27.9775	−	16.1528i	−1.24498	−	0.718792i
$506$	−0.780347	−	0.450533i	−0.0346906	−	0.0200287i
$507$		0			0
$508$	−5.18786	−	8.98564i	−0.230174	−	0.398673i
$509$	32.5760	−	18.8078i	1.44391	−	0.833639i	0.445798	−	0.895133i	$-0.352920\pi$
$509$	32.5760	−	18.8078i	1.44391	−	0.833639i	0.998107	+	0.0614940i	$0.0195865\pi$
$510$		0			0
$511$	28.3005	+	28.9755i	1.25194	+	1.28180i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−7.66047	+	13.2683i	−0.337889	+	0.585241i
$515$	5.79102	+	10.0303i	0.255183	+	0.441989i
$516$		0			0
$517$	2.08109	+	1.20152i	0.0915263	+	0.0528428i
$518$	−16.3390	−	4.58506i	−0.717895	−	0.201456i
$519$		0			0
$520$	−6.45226	−	11.6167i	−0.282950	−	0.509428i
$521$	12.7987	+	22.1681i	0.560723	+	0.971201i	0.997433	+	0.0715991i	$0.0228102\pi$
$521$	12.7987	+	22.1681i	0.560723	+	0.971201i	−0.436710	+	0.899602i	$0.643856\pi$
$522$		0			0
$523$	−13.5507	+	7.82348i	−0.592529	+	0.342097i	−0.766097	−	0.642725i	$-0.777804\pi$
$523$	−13.5507	+	7.82348i	−0.592529	+	0.342097i	0.173568	+	0.984822i	$0.444470\pi$
$524$	−4.14703	−	7.18287i	−0.181164	−	0.313785i
$525$		0			0
$526$	7.64509	−	4.41390i	0.333342	−	0.192455i
$527$	−14.4323			−0.628682
$528$		0			0
$529$	−8.37885	+	14.5126i	−0.364298	+	0.630982i
$530$	−4.09453	−	7.09194i	−0.177855	−	0.308054i
$531$		0			0
$532$	0.729974	−	2.60129i	0.0316484	−	0.112780i
$533$	−13.3126	−	23.9682i	−0.576632	−	1.03818i
$534$		0			0
$535$	−68.3270			−2.95403
$536$			11.2553i			0.486154i
$537$		0			0
$538$	−13.9045			−0.599464
$539$	−2.21546	+	1.21040i	−0.0954266	+	0.0521355i
$540$		0			0
$541$	4.52509	+	2.61256i	0.194549	+	0.112323i	0.594110	−	0.804384i	$-0.297504\pi$
$541$	4.52509	+	2.61256i	0.194549	+	0.112323i	−0.399562	+	0.916706i	$0.630838\pi$
$542$	7.75333	−	13.4292i	0.333034	−	0.576832i
$543$		0			0
$544$	−3.62495	−	6.27861i	−0.155419	−	0.269193i
$545$	29.0216			1.24315
$546$		0			0
$547$	15.9755			0.683065			0.341532	−	0.939870i	$-0.389054\pi$
$547$	15.9755			0.683065			0.341532	+	0.939870i	$0.389054\pi$
$548$	−0.596243	−	1.03272i	−0.0254702	−	0.0441157i
$549$		0			0
$550$	1.54774	−	2.68077i	0.0659960	−	0.114308i
$551$	−1.89321	−	1.09304i	−0.0806533	−	0.0465652i
$552$		0			0
$553$	−6.55630	+	23.3636i	−0.278802	+	0.993521i
$554$	5.90020			0.250675
$555$		0			0
$556$		−	19.4476i		−	0.824763i
$557$	−14.7387			−0.624497			−0.312249	−	0.950000i	$-0.601082\pi$
$557$	−14.7387			−0.624497			−0.312249	+	0.950000i	$0.601082\pi$
$558$		0			0
$559$	−0.103547	+	6.23809i	−0.00437955	+	0.263843i
$560$	−2.41257	−	9.44781i	−0.101950	−	0.399243i
$561$		0			0
$562$	4.46126	+	7.72714i	0.188187	+	0.325950i
$563$	−20.7151	+	35.8796i	−0.873037	+	1.51215i	−0.0141988	+	0.999899i	$0.504520\pi$
$563$	−20.7151	+	35.8796i	−0.873037	+	1.51215i	−0.858839	+	0.512246i	$0.828814\pi$
$564$		0			0
$565$	1.02048			0.0429318
$566$	19.9074	−	11.4935i	0.836770	−	0.483109i
$567$		0			0
$568$	−2.50082	−	4.33155i	−0.104932	−	0.181748i
$569$	21.6943	−	12.5252i	0.909474	−	0.525085i	0.0292120	−	0.999573i	$-0.490700\pi$
$569$	21.6943	−	12.5252i	0.909474	−	0.525085i	0.880262	+	0.474488i	$0.157367\pi$
$570$		0			0
$571$	−5.98475	−	10.3659i	−0.250454	−	0.433799i	0.713197	−	0.700964i	$-0.247247\pi$
$571$	−5.98475	−	10.3659i	−0.250454	−	0.433799i	−0.963651	+	0.267165i	$0.913913\pi$
$572$	1.13676	−	0.631390i	0.0475304	−	0.0263997i
$573$		0			0
$574$	−4.97773	−	19.4931i	−0.207766	−	0.813628i
$575$	18.5715	+	10.7223i	0.774485	+	0.447149i
$576$		0			0
$577$	21.5762	+	37.3711i	0.898230	+	1.55578i	0.829755	+	0.558128i	$0.188480\pi$
$577$	21.5762	+	37.3711i	0.898230	+	1.55578i	0.0684756	+	0.997653i	$0.478186\pi$
$578$	17.7806	−	30.7969i	0.739575	−	1.28098i
$579$		0			0
$580$	−7.88983			−0.327607
$581$	−7.26616	−	28.4548i	−0.301451	−	1.18050i
$582$		0			0
$583$	0.693986	−	0.400673i	0.0287420	−	0.0165942i
$584$	−7.65435	−	13.2577i	−0.316739	−	0.548609i
$585$		0			0
$586$	3.49834	+	2.01977i	0.144515	+	0.0834358i
$587$	−16.7194	−	9.65298i	−0.690085	−	0.398421i	0.113559	−	0.993531i	$-0.463775\pi$
$587$	−16.7194	−	9.65298i	−0.690085	−	0.398421i	−0.803644	+	0.595110i	$0.797108\pi$
$588$		0			0
$589$	1.01642	+	1.76049i	0.0418808	+	0.0725397i
$590$	17.9169	−	31.0329i	0.737626	−	1.27761i
$591$		0			0
$592$	5.55479	+	3.20706i	0.228300	+	0.131809i
$593$	−26.6966	−	15.4133i	−1.09630	−	0.632947i	−0.161051	−	0.986946i	$-0.551488\pi$
$593$	−26.6966	−	15.4133i	−1.09630	−	0.632947i	−0.935246	+	0.353999i	$0.884822\pi$
$594$		0			0
$595$	50.5736	−	49.3955i	2.07332	−	2.02502i
$596$	3.86719	−	6.69817i	0.158406	−	0.274368i
$597$		0			0
$598$	4.37406	+	7.87512i	0.178869	+	0.322037i
$599$	−34.6710	+	20.0173i	−1.41662	+	0.817884i	−0.996000	−	0.0893540i	$-0.971520\pi$
$599$	−34.6710	+	20.0173i	−1.41662	+	0.817884i	−0.420617	+	0.907238i	$0.638186\pi$
$600$		0			0
$601$	19.8183	+	11.4421i	0.808407	+	0.466734i	0.846402	−	0.532544i	$-0.178764\pi$
$601$	19.8183	+	11.4421i	0.808407	+	0.466734i	−0.0379955	+	0.999278i	$0.512097\pi$
$602$	−1.23694	+	4.40787i	−0.0504139	+	0.179651i
$603$		0			0
$604$		−	14.8636i		−	0.604791i
$605$	−34.6942	−	20.0307i	−1.41052	−	0.814364i
$606$		0			0
$607$			15.8910i			0.644997i	0.946570	+	0.322498i	$0.104523\pi$
$607$			15.8910i			0.644997i	−0.946570	+	0.322498i	$0.895477\pi$
$608$	−0.510587	+	0.884362i	−0.0207070	+	0.0358656i
$609$		0			0
$610$	8.40898			0.340470
$611$	−11.6651	−	21.0020i	−0.471920	−	0.849650i
$612$		0			0
$613$		−	29.4647i		−	1.19007i	−0.803701	−	0.595034i	$-0.797139\pi$
$613$		−	29.4647i		−	1.19007i	0.803701	−	0.595034i	$-0.202861\pi$
$614$	3.56084	+	6.16755i	0.143704	+	0.248902i
$615$		0			0
$616$	0.924521	−	0.236084i	0.0372500	−	0.00951208i
$617$	3.71810	+	6.43994i	0.149685	+	0.259262i	0.931111	−	0.364736i	$-0.118841\pi$
$617$	3.71810	+	6.43994i	0.149685	+	0.259262i	−0.781426	+	0.623998i	$0.785507\pi$
$618$		0			0
$619$	−12.8172	−	22.2000i	−0.515167	−	0.892295i	−0.999845	−	0.0176024i	$-0.994397\pi$
$619$	−12.8172	−	22.2000i	−0.515167	−	0.892295i	0.484678	−	0.874692i	$-0.338937\pi$
$620$	6.35380	+	3.66837i	0.255175	+	0.147325i
$621$		0			0
$622$	−13.0682	+	22.6348i	−0.523987	+	0.907573i
$623$	−27.7014	+	27.0561i	−1.10983	+	1.08398i
$624$		0			0
$625$	−2.87702	+	4.98314i	−0.115081	+	0.199326i
$626$			25.7950i			1.03097i
$627$		0			0
$628$			4.33480i			0.172977i
$629$			46.5018i			1.85415i
$630$		0			0
$631$	28.3328	−	16.3579i	1.12791	−	0.651199i	0.184501	−	0.982832i	$-0.440933\pi$
$631$	28.3328	−	16.3579i	1.12791	−	0.651199i	0.943408	+	0.331633i	$0.107600\pi$
$632$	4.58586	−	7.94294i	0.182416	−	0.315953i
$633$		0			0
$634$	8.89239			0.353162
$635$	−33.1168	+	19.1200i	−1.31420	+	0.758754i
$636$		0			0
$637$	25.2185	+	1.01348i	0.999193	+	0.0401557i
$638$		−	0.772063i		−	0.0305663i
$639$		0			0
$640$			3.68552i			0.145683i
$641$	13.5226	+	7.80726i	0.534110	+	0.308368i	0.742688	−	0.669637i	$-0.233550\pi$
$641$	13.5226	+	7.80726i	0.534110	+	0.308368i	−0.208579	+	0.978006i	$0.566884\pi$
$642$		0			0
$643$	17.1247	+	29.6609i	0.675333	+	1.16971i	0.976371	+	0.216099i	$0.0693335\pi$
$643$	17.1247	+	29.6609i	0.675333	+	1.16971i	−0.301038	+	0.953612i	$0.597333\pi$
$644$	1.63551	+	6.40478i	0.0644481	+	0.252384i
$645$		0			0
$646$	−7.40341			−0.291283
$647$	8.83242			0.347238			0.173619	−	0.984813i	$-0.444454\pi$
$647$	8.83242			0.347238			0.173619	+	0.984813i	$0.444454\pi$
$648$		0			0
$649$	3.03674	+	1.75326i	0.119203	+	0.0688217i
$650$	−27.0538	+	15.0265i	−1.06114	+	0.589386i
$651$		0			0
$652$	6.06533	+	3.50182i	0.237537	+	0.137142i
$653$	10.8809	−	6.28208i	0.425802	−	0.245837i	−0.271755	−	0.962367i	$-0.587604\pi$
$653$	10.8809	−	6.28208i	0.425802	−	0.245837i	0.697557	+	0.716530i	$0.254271\pi$
$654$		0			0
$655$	−26.4726	+	15.2840i	−1.03437	+	0.597195i
$656$			7.60414i			0.296892i
$657$		0			0
$658$	−4.36171	−	17.0808i	−0.170037	−	0.665878i
$659$	14.1612	−	8.17598i	0.551643	−	0.318491i	−0.198142	−	0.980173i	$-0.563491\pi$
$659$	14.1612	−	8.17598i	0.551643	−	0.318491i	0.749784	+	0.661682i	$0.230157\pi$
$660$		0			0
$661$	13.0677			0.508274			0.254137	−	0.967168i	$-0.418209\pi$
$661$	13.0677			0.508274			0.254137	+	0.967168i	$0.418209\pi$
$662$	7.42149	−	4.28480i	0.288445	−	0.166534i
$663$		0			0
$664$			11.1000i			0.430764i
$665$	−9.58711	−	2.69034i	−0.371772	−	0.104327i
$666$		0			0
$667$	5.34860			0.207099
$668$	−16.4440	+	9.49393i	−0.636236	+	0.367331i
$669$		0			0
$670$	41.4817			1.60258
$671$			0.822866i			0.0317664i
$672$		0			0
$673$	3.74139	−	6.48028i	0.144220	−	0.249796i	−0.784862	−	0.619671i	$-0.787266\pi$
$673$	3.74139	−	6.48028i	0.144220	−	0.249796i	0.929082	+	0.369875i	$0.120599\pi$
$674$	−7.45959	−	12.9204i	−0.287333	−	0.497674i
$675$		0			0
$676$	−12.9928	−	0.431457i	−0.499725	−	0.0165945i
$677$	−10.4566	+	18.1114i	−0.401880	+	0.696077i	−0.993953	−	0.109808i	$-0.964976\pi$
$677$	−10.4566	+	18.1114i	−0.401880	+	0.696077i	0.592073	+	0.805885i	$0.298310\pi$
$678$		0			0
$679$	29.1270	+	29.8217i	1.11779	+	1.14445i
$680$	−23.1400	+	13.3599i	−0.887377	+	0.512327i
$681$		0			0
$682$	−0.358970	+	0.621755i	−0.0137457	+	0.0238082i
$683$	12.8107	−	22.1887i	0.490186	−	0.849027i	−0.509750	−	0.860322i	$-0.670262\pi$
$683$	12.8107	−	22.1887i	0.490186	−	0.849027i	0.999936	+	0.0112954i	$0.00359551\pi$
$684$		0			0
$685$	−3.80612	+	2.19747i	−0.145425	+	0.0839609i
$686$	17.7086	+	5.42271i	0.676117	+	0.207040i
$687$		0			0
$688$	0.865187	−	1.49855i	0.0329849	−	0.0571316i
$689$	−8.01027	−	0.132963i	−0.305167	−	0.00506549i
$690$		0			0
$691$	−10.4560	−	18.1103i	−0.397764	−	0.688947i	0.595686	−	0.803217i	$-0.296880\pi$
$691$	−10.4560	−	18.1103i	−0.397764	−	0.688947i	−0.993450	+	0.114270i	$0.963547\pi$
$692$	−9.06312	+	15.6978i	−0.344528	+	0.596740i
$693$		0			0
$694$		−	30.4065i		−	1.15421i
$695$	−71.6747			−2.71878
$696$		0			0
$697$	−47.7434	+	27.5647i	−1.80841	+	1.04409i
$698$	−6.00240			−0.227194
$699$		0			0
$700$	−22.0027	+	5.61856i	−0.831624	+	0.212362i
$701$			35.9194i			1.35666i	0.734759	+	0.678328i	$0.237295\pi$
$701$			35.9194i			1.35666i	−0.734759	+	0.678328i	$0.762705\pi$
$702$		0			0
$703$	5.67240	−	3.27496i	0.213939	−	0.123518i
$704$	−0.360649			−0.0135925
$705$		0			0
$706$	17.5107	−	10.1098i	0.659025	−	0.380488i
$707$	−22.4704	+	5.73800i	−0.845088	+	0.215800i
$708$		0			0
$709$		−	43.6381i		−	1.63886i	−0.573178	−	0.819431i	$-0.694290\pi$
$709$		−	43.6381i		−	1.63886i	0.573178	−	0.819431i	$-0.305710\pi$
$710$	−15.9640	+	9.21683i	−0.599119	+	0.345901i
$711$		0			0
$712$	12.6748	−	7.31778i	0.475007	−	0.274245i
$713$	−4.30731	−	2.48683i	−0.161310	−	0.0931325i
$714$		0			0
$715$	−2.32700	−	4.18956i	−0.0870250	−	0.156681i
$716$	10.3413	+	5.97054i	0.386472	+	0.223130i
$717$		0			0
$718$	29.6946			1.10819
$719$	−29.2896			−1.09232			−0.546160	−	0.837681i	$-0.683911\pi$
$719$	−29.2896			−1.09232			−0.546160	+	0.837681i	$0.683911\pi$
$720$		0			0
$721$	8.00524	+	2.24643i	0.298131	+	0.0836616i
$722$	−8.97860	−	15.5514i	−0.334149	−	0.578763i
$723$		0			0
$724$	6.00058	+	3.46444i	0.223010	+	0.128755i
$725$			18.3743i			0.682406i
$726$		0			0
$727$			48.0240i			1.78111i	0.454873	+	0.890556i	$0.349685\pi$
$727$			48.0240i			1.78111i	−0.454873	+	0.890556i	$0.650315\pi$
$728$	−9.14057	−	2.72947i	−0.338772	−	0.101161i
$729$		0			0
$730$	−48.8617	+	28.2103i	−1.80845	+	1.04411i
$731$	12.5451			0.463996
$732$		0			0
$733$	23.0396	−	39.9058i	0.850989	−	1.47396i	−0.0293284	−	0.999570i	$-0.509337\pi$
$733$	23.0396	−	39.9058i	0.850989	−	1.47396i	0.880317	−	0.474386i	$-0.157330\pi$
$734$	−26.6465	+	15.3844i	−0.983542	+	0.567848i
$735$		0			0
$736$		−	2.49846i		−	0.0920944i
$737$			4.05921i			0.149523i
$738$		0			0
$739$		−	31.6517i		−	1.16433i	−0.813071	−	0.582164i	$-0.802206\pi$
$739$		−	31.6517i		−	1.16433i	0.813071	−	0.582164i	$-0.197794\pi$
$740$	11.8197	−	20.4723i	0.434501	−	0.752577i
$741$		0			0
$742$	−5.66010	−	1.58834i	−0.207789	−	0.0583098i
$743$	−16.6091	+	28.7678i	−0.609329	+	1.05539i	0.382023	+	0.924153i	$0.375228\pi$
$743$	−16.6091	+	28.7678i	−0.609329	+	1.05539i	−0.991351	+	0.131235i	$0.958106\pi$
$744$		0			0
$745$	−24.6863	−	14.2526i	−0.904435	−	0.522176i
$746$	5.75723	+	9.97181i	0.210787	+	0.365094i
$747$		0			0
$748$	−1.30734	−	2.26437i	−0.0478010	−	0.0827937i
$749$	−35.0901	+	34.2727i	−1.28217	+	1.25230i
$750$		0			0
$751$	−2.65279	−	4.59476i	−0.0968016	−	0.167665i	0.813557	−	0.581485i	$-0.197528\pi$
$751$	−2.65279	−	4.59476i	−0.0968016	−	0.167665i	−0.910359	+	0.413819i	$0.864195\pi$
$752$			6.66309i			0.242978i
$753$		0			0
$754$	−3.96972	+	6.61955i	−0.144569	+	0.241070i
$755$	−54.7801			−1.99365
$756$		0			0
$757$	−6.36478	+	11.0241i	−0.231332	+	0.400678i	−0.958200	−	0.286098i	$-0.907642\pi$
$757$	−6.36478	+	11.0241i	−0.231332	+	0.400678i	0.726869	+	0.686777i	$0.240975\pi$
$758$		−	1.48827i		−	0.0540564i
$759$		0			0
$760$	3.25934	+	1.88178i	0.118229	+	0.0682593i
$761$			14.2329i			0.515944i	0.966152	+	0.257972i	$0.0830542\pi$
$761$			14.2329i			0.515944i	−0.966152	+	0.257972i	$0.916946\pi$
$762$		0			0
$763$	14.9044	−	14.5572i	0.539575	−	0.527005i
$764$	0.847414	+	0.489255i	0.0306584	+	0.0177006i
$765$		0			0
$766$	20.7750	−	11.9945i	0.750632	−	0.433378i
$767$	−17.0218	−	30.6463i	−0.614621	−	1.10657i
$768$		0			0
$769$	−21.1003	+	36.5468i	−0.760896	+	1.31791i	0.181494	+	0.983392i	$0.441907\pi$
$769$	−21.1003	+	36.5468i	−0.760896	+	1.31791i	−0.942389	+	0.334518i	$0.891427\pi$
$770$	−0.870092	−	3.40734i	−0.0313559	−	0.122792i
$771$		0			0
$772$	4.42764	+	2.55630i	0.159354	+	0.0920032i
$773$	−0.673439	−	0.388810i	−0.0242219	−	0.0139845i	0.487840	−	0.872933i	$-0.337785\pi$
$773$	−0.673439	−	0.388810i	−0.0242219	−	0.0139845i	−0.512062	+	0.858948i	$0.671118\pi$
$774$		0			0
$775$	8.54314	−	14.7972i	0.306879	−	0.531529i
$776$	−7.87790	−	13.6449i	−0.282800	−	0.489824i
$777$		0			0
$778$	18.6504	+	10.7678i	0.668651	+	0.386046i
$779$	6.72481	+	3.88257i	0.240941	+	0.139108i
$780$		0			0
$781$	−0.901918	−	1.56217i	−0.0322732	−	0.0558988i
$782$	15.6868	−	9.05680i	0.560960	−	0.323871i
$783$		0			0
$784$	−5.97801	−	3.64189i	−0.213500	−	0.130068i
$785$	15.9760			0.570208
$786$		0			0
$787$	−6.93992	+	12.0203i	−0.247382	+	0.428477i	−0.962799	−	0.270220i	$-0.912903\pi$
$787$	−6.93992	+	12.0203i	−0.247382	+	0.428477i	0.715417	+	0.698698i	$0.246237\pi$
$788$	9.72108	+	16.8374i	0.346299	+	0.599808i
$789$		0			0
$790$	−29.2739	−	16.9013i	−1.04152	−	0.601321i
$791$	0.524079	−	0.511870i	0.0186341	−	0.0182000i
$792$		0			0
$793$	4.23093	−	7.05512i	0.150245	−	0.250535i
$794$	−1.79132	−	3.10265i	−0.0635715	−	0.110109i
$795$		0			0
$796$	−16.8671	+	9.73825i	−0.597840	+	0.345163i
$797$	14.8879	+	25.7865i	0.527355	+	0.913406i	0.999492	+	0.0318802i	$0.0101495\pi$
$797$	14.8879	+	25.7865i	0.527355	+	0.913406i	−0.472137	+	0.881525i	$0.656517\pi$
$798$		0			0
$799$	−41.8349	+	24.1534i	−1.48001	+	0.854486i
$800$	8.58309			0.303458
$801$		0			0
$802$	17.9224	−	31.0425i	0.632862	−	1.09615i
$803$	−2.76054	−	4.78139i	−0.0974172	−	0.168731i
$804$		0			0
$805$	23.6050	−	6.02771i	0.831966	−	0.212449i
$806$	6.27463	−	3.48511i	0.221015	−	0.122758i
$807$		0			0
$808$	8.76556			0.308371
$809$		−	23.1677i		−	0.814533i	−0.913309	−	0.407267i	$-0.866482\pi$
$809$		−	23.1677i		−	0.814533i	0.913309	−	0.407267i	$-0.133518\pi$
$810$		0			0
$811$	−11.4847			−0.403283			−0.201642	−	0.979459i	$-0.564628\pi$
$811$	−11.4847			−0.403283			−0.201642	+	0.979459i	$0.564628\pi$
$812$	−4.05191	+	3.95752i	−0.142194	+	0.138882i
$813$		0			0
$814$	2.00333	+	1.15662i	0.0702166	+	0.0405396i
$815$	12.9060	−	22.3539i	0.452079	−	0.783024i
$816$		0			0
$817$	−0.883506	−	1.53028i	−0.0309100	−	0.0535376i
$818$	−34.3349			−1.20049
$819$		0			0
$820$	28.0252			0.978684
$821$	6.98796	+	12.1035i	0.243881	+	0.422415i	0.961817	−	0.273695i	$-0.0882459\pi$
$821$	6.98796	+	12.1035i	0.243881	+	0.422415i	−0.717935	+	0.696110i	$0.754913\pi$
$822$		0			0
$823$	0.708385	−	1.22696i	0.0246928	−	0.0427691i	−0.853415	−	0.521232i	$-0.825473\pi$
$823$	0.708385	−	1.22696i	0.0246928	−	0.0427691i	0.878108	+	0.478463i	$0.158806\pi$
$824$	−2.72155	−	1.57129i	−0.0948097	−	0.0547384i
$825$		0			0
$826$	−6.36464	−	24.9244i	−0.221454	−	0.867231i
$827$	29.2756			1.01801			0.509007	−	0.860762i	$-0.330013\pi$
$827$	29.2756			1.01801			0.509007	+	0.860762i	$0.330013\pi$
$828$		0			0
$829$			25.6948i			0.892418i	0.894929	+	0.446209i	$0.147226\pi$
$829$			25.6948i			0.892418i	−0.894929	+	0.446209i	$0.852774\pi$
$830$	40.9094			1.41999
$831$		0			0
$832$	3.09215	+	1.85435i	0.107201	+	0.0642880i
$833$	1.19600	−	50.7353i	0.0414389	−	1.75787i
$834$		0			0
$835$	34.9901	+	60.6046i	1.21088	+	2.09731i
$836$	−0.184143	+	0.318944i	−0.00636870	+	0.0110309i
$837$		0			0
$838$	20.9772			0.724644
$839$	31.8591	−	18.3939i	1.09990	−	0.635027i	0.163704	−	0.986509i	$-0.447656\pi$
$839$	31.8591	−	18.3939i	1.09990	−	0.635027i	0.936194	+	0.351483i	$0.114322\pi$
$840$		0			0
$841$	−12.2086	−	21.1459i	−0.420985	−	0.729168i
$842$	−1.06109	+	0.612620i	−0.0365676	+	0.0211123i
$843$		0			0
$844$	3.41205	+	5.90984i	0.117448	+	0.203425i
$845$	−1.59015	+	47.8854i	−0.0547027	+	1.64731i
$846$		0			0
$847$	−27.8650	+	7.11554i	−0.957452	+	0.244493i
$848$	1.92427	+	1.11098i	0.0660797	+	0.0381511i
$849$		0			0
$850$	31.1133	+	53.8899i	1.06718	+	1.84841i
$851$	−8.01270	+	13.8784i	−0.274672	+	0.475746i
$852$		0			0
$853$	11.0484			0.378291			0.189145	−	0.981949i	$-0.439428\pi$
$853$	11.0484			0.378291			0.189145	+	0.981949i	$0.439428\pi$
$854$	4.31853	−	4.21793i	0.147777	−	0.144335i
$855$		0			0
$856$	16.0555	−	9.26964i	0.548765	−	0.316830i
$857$	−5.51419	−	9.55086i	−0.188361	−	0.326251i	0.756343	−	0.654175i	$-0.226984\pi$
$857$	−5.51419	−	9.55086i	−0.188361	−	0.326251i	−0.944704	+	0.327924i	$0.893651\pi$
$858$		0			0
$859$	2.38511	+	1.37704i	0.0813789	+	0.0469841i	0.540137	−	0.841577i	$-0.318372\pi$
$859$	2.38511	+	1.37704i	0.0813789	+	0.0469841i	−0.458758	+	0.888561i	$0.651706\pi$
$860$	−5.52293	−	3.18867i	−0.188331	−	0.108733i
$861$		0			0
$862$	−2.94517	−	5.10118i	−0.100313	−	0.173747i
$863$	−20.8604	+	36.1313i	−0.710097	+	1.22992i	0.254723	+	0.967014i	$0.418016\pi$
$863$	−20.8604	+	36.1313i	−0.710097	+	1.22992i	−0.964820	+	0.262910i	$0.915318\pi$
$864$		0			0
$865$	57.8546	+	33.4024i	1.96711	+	1.13571i
$866$	−34.0327	−	19.6488i	−1.15648	−	0.667692i
$867$		0			0
$868$	5.10312	−	1.30312i	0.173211	−	0.0442308i
$869$	1.65389	−	2.86461i	0.0561042	−	0.0971754i
$870$		0			0
$871$	20.8713	−	34.8030i	0.707195	−	1.17926i
$872$	−6.81950	+	3.93724i	−0.230937	+	0.133332i
$873$		0			0
$874$	−2.20954	−	1.27568i	−0.0747389	−	0.0431505i
$875$	8.64448	+	33.8524i	0.292237	+	1.14442i
$876$		0			0
$877$		−	36.5369i		−	1.23376i	−0.787056	−	0.616881i	$-0.788396\pi$
$877$		−	36.5369i		−	1.23376i	0.787056	−	0.616881i	$-0.211604\pi$
$878$	14.9305	+	8.62010i	0.503879	+	0.290914i
$879$		0			0
$880$			1.32918i			0.0448067i
$881$	16.5800	−	28.7174i	0.558594	−	0.967512i	−0.439021	−	0.898477i	$-0.644674\pi$
$881$	16.5800	−	28.7174i	0.558594	−	0.967512i	0.997614	−	0.0690355i	$-0.0219922\pi$
$882$		0			0
$883$	58.2306			1.95962			0.979808	−	0.199941i	$-0.0640750\pi$
$883$	58.2306			1.95962			0.979808	+	0.199941i	$0.0640750\pi$
$884$	−0.433839	+	26.1363i	−0.0145916	+	0.879060i
$885$		0			0
$886$		−	0.627132i		−	0.0210689i
$887$	20.1713	+	34.9378i	0.677287	+	1.17310i	0.975795	+	0.218688i	$0.0701778\pi$
$887$	20.1713	+	34.9378i	0.677287	+	1.17310i	−0.298508	+	0.954407i	$0.596489\pi$
$888$		0			0
$889$	−7.41697	+	26.4306i	−0.248757	+	0.886455i
$890$	−26.9699	−	46.7132i	−0.904032	−	1.56583i
$891$		0			0
$892$	14.2672	+	24.7115i	0.477702	+	0.827403i
$893$	5.89259	+	3.40209i	0.197188	+	0.113846i
$894$		0			0
$895$	22.0046	−	38.1131i	0.735532	−	1.27398i
$896$	1.84865	+	1.89275i	0.0617591	+	0.0632322i
$897$		0			0
$898$	−13.0921	+	22.6762i	−0.436889	+	0.756714i
$899$		−	4.26159i		−	0.142132i
$900$		0			0
$901$			16.1090i			0.536668i
$902$			2.74243i			0.0913128i
$903$		0			0
$904$	−0.239792	+	0.138444i	−0.00797537	+	0.00460458i
$905$	12.7683	−	22.1153i	0.424432	−	0.735137i
$906$		0			0
$907$	−18.0242			−0.598485			−0.299243	−	0.954177i	$-0.596734\pi$
$907$	−18.0242			−0.598485			−0.299243	+	0.954177i	$0.596734\pi$
$908$	4.48708	−	2.59062i	0.148909	−	0.0859726i
$909$		0			0
$910$	−10.0595	+	33.6878i	−0.333470	+	1.11674i
$911$		−	6.01179i		−	0.199180i	−0.995029	−	0.0995898i	$-0.968247\pi$
$911$		−	6.01179i		−	0.199180i	0.995029	−	0.0995898i	$-0.0317530\pi$
$912$		0			0
$913$			4.00321i			0.132487i
$914$	−20.6258	−	11.9083i	−0.682241	−	0.393892i
$915$		0			0
$916$	−4.39140	−	7.60612i	−0.145096	−	0.251313i
$917$	−5.92892	+	21.1279i	−0.195790	+	0.697705i
$918$		0			0
$919$	−16.8597			−0.556150			−0.278075	−	0.960559i	$-0.589696\pi$
$919$	−16.8597			−0.556150			−0.278075	+	0.960559i	$0.589696\pi$
$920$	−9.20813			−0.303583
$921$		0			0
$922$	15.9116	+	9.18657i	0.524021	+	0.302544i
$923$	−0.299301	+	18.0312i	−0.00985161	+	0.593503i
$924$		0			0
$925$	−47.6773	−	27.5265i	−1.56762	−	0.905065i
$926$	9.82613	−	5.67312i	0.322907	−	0.186430i
$927$		0			0
$928$	1.85395	−	1.07038i	0.0608590	−	0.0351370i
$929$			41.0176i			1.34574i	0.739759	+	0.672872i	$0.234940\pi$
$929$			41.0176i			1.34574i	−0.739759	+	0.672872i	$0.765060\pi$
$930$		0			0
$931$	−6.27304	+	3.42722i	−0.205591	+	0.112323i
$932$	−2.45840	+	1.41936i	−0.0805275	+	0.0464926i
$933$		0			0
$934$	2.25675			0.0738430
$935$	−8.34540	+	4.81822i	−0.272924	+	0.157573i
$936$		0			0
$937$		−	13.1635i		−	0.430034i	−0.976610	−	0.215017i	$-0.931019\pi$
$937$		−	13.1635i		−	0.430034i	0.976610	−	0.215017i	$-0.0689806\pi$
$938$	21.3034	−	20.8071i	0.695580	−	0.679377i
$939$		0			0
$940$	24.5570			0.800961
$941$	−46.0080	+	26.5628i	−1.49982	+	0.865921i	−1.00000		0.000208449i	$-0.999934\pi$
$941$	−46.0080	+	26.5628i	−1.49982	+	0.865921i	−0.499819	+	0.866130i	$0.666600\pi$
$942$		0			0
$943$	−18.9986			−0.618680
$944$			9.72283i			0.316451i
$945$		0			0
$946$	0.312029	−	0.540450i	0.0101449	−	0.0175715i
$947$	−5.83806	−	10.1118i	−0.189712	−	0.328590i	0.755442	−	0.655215i	$-0.227422\pi$
$947$	−5.83806	−	10.1118i	−0.189712	−	0.328590i	−0.945154	+	0.326625i	$0.894089\pi$
$948$		0			0
$949$	−0.916082	+	55.1887i	−0.0297373	+	1.79150i
$950$	4.38241	−	7.59056i	0.142184	−	0.246270i
$951$		0			0
$952$	−5.18252	+	18.4681i	−0.167966	+	0.598554i
$953$	11.0895	−	6.40254i	0.359225	−	0.207398i	−0.309516	−	0.950894i	$-0.600167\pi$
$953$	11.0895	−	6.40254i	0.359225	−	0.207398i	0.668741	+	0.743496i	$0.266834\pi$
$954$		0			0
$955$	1.80316	−	3.12317i	0.0583489	−	0.101063i
$956$	9.98004	−	17.2859i	0.322777	−	0.559067i
$957$		0			0
$958$	10.7671	−	6.21638i	0.347869	−	0.200842i
$959$	−0.852435	+	3.03768i	−0.0275266	+	0.0980918i
$960$		0			0
$961$	13.5186	−	23.4149i	0.436083	−	0.755318i
$962$	−11.2292	−	20.2172i	−0.362044	−	0.651829i
$963$		0			0
$964$	−1.35228	−	2.34221i	−0.0435539	−	0.0754376i
$965$	9.42130	−	16.3182i	0.303283	−	0.525301i
$966$		0			0
$967$		−	36.2076i		−	1.16436i	−0.813061	−	0.582179i	$-0.802200\pi$
$967$		−	36.2076i		−	1.16436i	0.813061	−	0.582179i	$-0.197800\pi$
$968$	10.8699			0.349373
$969$		0			0
$970$	−50.2887	+	29.0342i	−1.61467	+	0.932232i
$971$	13.8202			0.443513			0.221756	−	0.975102i	$-0.428821\pi$
$971$	13.8202			0.443513			0.221756	+	0.975102i	$0.428821\pi$
$972$		0			0
$973$	−36.8094	+	35.9519i	−1.18006	+	1.15257i
$974$			21.9255i			0.702538i
$975$		0			0
$976$	−1.97594	+	1.14081i	−0.0632484	+	0.0365165i
$977$	−0.690066			−0.0220772			−0.0110386	−	0.999939i	$-0.503514\pi$
$977$	−0.690066			−0.0220772			−0.0110386	+	0.999939i	$0.503514\pi$
$978$		0			0
$979$	4.57114	−	2.63915i	0.146094	−	0.0843476i
$980$	−13.4223	+	22.0321i	−0.428759	+	0.703790i
$981$		0			0
$982$			42.2794i			1.34919i
$983$	31.6283	−	18.2606i	1.00879	−	0.582423i	0.0979498	−	0.995191i	$-0.468772\pi$
$983$	31.6283	−	18.2606i	1.00879	−	0.582423i	0.910836	+	0.412769i	$0.135438\pi$
$984$		0			0
$985$	62.0547	−	35.8273i	1.97723	−	1.14155i
$986$	13.4410	+	7.76016i	0.428048	+	0.247134i
$987$		0			0
$988$	3.21873	−	1.78777i	0.102401	−	0.0568766i
$989$	3.74406	+	2.16163i	0.119054	+	0.0687360i
$990$		0			0
$991$	−20.2493			−0.643240			−0.321620	−	0.946869i	$-0.604227\pi$
$991$	−20.2493			−0.643240			−0.321620	+	0.946869i	$0.604227\pi$
$992$	−1.99069			−0.0632045
$993$		0			0
$994$	−3.57537	+	12.7409i	−0.113404	+	0.404118i
$995$	35.8905	+	62.1643i	1.13781	+	1.97074i
$996$		0			0
$997$	−7.91405	−	4.56918i	−0.250640	−	0.144707i	0.369417	−	0.929264i	$-0.379557\pi$
$997$	−7.91405	−	4.56918i	−0.250640	−	0.144707i	−0.620057	+	0.784556i	$0.712891\pi$
$998$			39.8871i			1.26261i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.dw.b.719.17	yes	36
3.2	odd	2		1638.2.dw.a.719.2	yes	36
7.3	odd	6		1638.2.dg.a.17.17	✓	36
13.10	even	6		1638.2.dg.b.1349.2	yes	36
21.17	even	6		1638.2.dg.b.17.2	yes	36
39.23	odd	6		1638.2.dg.a.1349.17	yes	36
91.10	odd	6		1638.2.dw.a.647.2	yes	36
273.101	even	6	inner	1638.2.dw.b.647.17	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.dg.a.17.17	✓	36	7.3	odd	6
1638.2.dg.a.1349.17	yes	36	39.23	odd	6
1638.2.dg.b.17.2	yes	36	21.17	even	6
1638.2.dg.b.1349.2	yes	36	13.10	even	6
1638.2.dw.a.647.2	yes	36	91.10	odd	6
1638.2.dw.a.719.2	yes	36	3.2	odd	2
1638.2.dw.b.647.17	yes	36	273.101	even	6	inner
1638.2.dw.b.719.17	yes	36	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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.dw (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(3.19176 + 1.84276i) q^{5} +(2.56349 - 0.654608i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(3.19176 + 1.84276i) q^{5} +(2.56349 - 0.654608i) q^{7} -1.00000 q^{8} +3.68552i q^{10} -0.360649 q^{11} +(3.09215 + 1.85435i) q^{13} +(1.84865 + 1.89275i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.62495 - 6.27861i) q^{17} -1.02117 q^{19} +(-3.19176 + 1.84276i) q^{20} +(-0.180325 - 0.312331i) q^{22} +(2.16373 - 1.24923i) q^{23} +(4.29155 + 7.43318i) q^{25} +(-0.0598406 + 3.60505i) q^{26} +(-0.714839 + 2.54735i) q^{28} +(1.85395 + 1.07038i) q^{29} +(-0.995345 - 1.72399i) q^{31} +(0.500000 - 0.866025i) q^{32} +7.24991 q^{34} +(9.38833 + 2.63456i) q^{35} +(-5.55479 + 3.20706i) q^{37} +(-0.510587 - 0.884362i) q^{38} +(-3.19176 - 1.84276i) q^{40} +(-6.58538 - 3.80207i) q^{41} +(0.865187 + 1.49855i) q^{43} +(0.180325 - 0.312331i) q^{44} +(2.16373 + 1.24923i) q^{46} +(-5.77041 - 3.33155i) q^{47} +(6.14298 - 3.35616i) q^{49} +(-4.29155 + 7.43318i) q^{50} +(-3.15199 + 1.75070i) q^{52} +(-1.92427 + 1.11098i) q^{53} +(-1.15110 - 0.664591i) q^{55} +(-2.56349 + 0.654608i) q^{56} +2.14076i q^{58} +(-8.42022 - 4.86142i) q^{59} -2.28162i q^{61} +(0.995345 - 1.72399i) q^{62} +1.00000 q^{64} +(6.45226 + 11.6167i) q^{65} -11.2553i q^{67} +(3.62495 + 6.27861i) q^{68} +(2.41257 + 9.44781i) q^{70} +(2.50082 + 4.33155i) q^{71} +(7.65435 + 13.2577i) q^{73} +(-5.55479 - 3.20706i) q^{74} +(0.510587 - 0.884362i) q^{76} +(-0.924521 + 0.236084i) q^{77} +(-4.58586 + 7.94294i) q^{79} -3.68552i q^{80} -7.60414i q^{82} -11.1000i q^{83} +(23.1400 - 13.3599i) q^{85} +(-0.865187 + 1.49855i) q^{86} +0.360649 q^{88} +(-12.6748 + 7.31778i) q^{89} +(9.14057 + 2.72947i) q^{91} +2.49846i q^{92} -6.66309i q^{94} +(-3.25934 - 1.88178i) q^{95} +(7.87790 + 13.6449i) q^{97} +(5.97801 + 3.64189i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} - 2 q^{7} - 36 q^{8}+O(q^{10}) \) 36 * q + 18 * q^2 - 18 * q^4 - 2 * q^7 - 36 * q^8	\( 36 q + 18 q^{2} - 18 q^{4} - 2 q^{7} - 36 q^{8} + 2 q^{13} + 2 q^{14} - 18 q^{16} + 28 q^{19} + 12 q^{23} + 14 q^{25} + 4 q^{26} + 4 q^{28} - 4 q^{31} + 18 q^{32} + 24 q^{35} - 30 q^{37} + 14 q^{38} + 24 q^{41} + 14 q^{43} + 12 q^{46} - 36 q^{47} + 6 q^{49} - 14 q^{50} + 2 q^{52} + 24 q^{53} - 24 q^{55} + 2 q^{56} - 12 q^{59} + 4 q^{62} + 36 q^{64} + 12 q^{65} + 2 q^{73} - 30 q^{74} - 14 q^{76} - 16 q^{79} - 24 q^{85} - 14 q^{86} + 16 q^{91} + 12 q^{95} - 2 q^{97} + 24 q^{98}+O(q^{100}) \) 36 * q + 18 * q^2 - 18 * q^4 - 2 * q^7 - 36 * q^8 + 2 * q^13 + 2 * q^14 - 18 * q^16 + 28 * q^19 + 12 * q^23 + 14 * q^25 + 4 * q^26 + 4 * q^28 - 4 * q^31 + 18 * q^32 + 24 * q^35 - 30 * q^37 + 14 * q^38 + 24 * q^41 + 14 * q^43 + 12 * q^46 - 36 * q^47 + 6 * q^49 - 14 * q^50 + 2 * q^52 + 24 * q^53 - 24 * q^55 + 2 * q^56 - 12 * q^59 + 4 * q^62 + 36 * q^64 + 12 * q^65 + 2 * q^73 - 30 * q^74 - 14 * q^76 - 16 * q^79 - 24 * q^85 - 14 * q^86 + 16 * q^91 + 12 * q^95 - 2 * q^97 + 24 * q^98

Introduction

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