LMFDB - Embedded newform 1638.2.r.z.757.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(757,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 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("1638.757");

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.r (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			757.2
Root			$1.28078 + 2.21837i$ of defining polynomial
Character	$\chi$	$=$	1638.757
Dual form			1638.2.r.z.1387.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.56155 q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.56155 q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.78078 + 3.08440i) q^{10} +(1.28078 + 2.21837i) q^{11} +(-0.500000 + 3.57071i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 + 4.33013i) q^{17} +(-3.84233 + 6.65511i) q^{19} +(-1.78078 + 3.08440i) q^{20} +(-1.28078 + 2.21837i) q^{22} +(-4.56155 - 7.90084i) q^{23} +7.68466 q^{25} +(-3.34233 + 1.35234i) q^{26} +(0.500000 + 0.866025i) q^{28} +(-0.500000 - 0.866025i) q^{29} +5.12311 q^{31} +(0.500000 - 0.866025i) q^{32} -5.00000 q^{34} +(1.78078 - 3.08440i) q^{35} +(4.90388 + 8.49377i) q^{37} -7.68466 q^{38} -3.56155 q^{40} +(2.06155 + 3.57071i) q^{41} +(1.43845 - 2.49146i) q^{43} -2.56155 q^{44} +(4.56155 - 7.90084i) q^{46} +7.68466 q^{47} +(-0.500000 - 0.866025i) q^{49} +(3.84233 + 6.65511i) q^{50} +(-2.84233 - 2.21837i) q^{52} +3.87689 q^{53} +(4.56155 + 7.90084i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(0.500000 - 0.866025i) q^{58} +(6.56155 - 11.3649i) q^{59} +(0.500000 - 0.866025i) q^{61} +(2.56155 + 4.43674i) q^{62} +1.00000 q^{64} +(-1.78078 + 12.7173i) q^{65} +(-0.561553 - 0.972638i) q^{67} +(-2.50000 - 4.33013i) q^{68} +3.56155 q^{70} +(-2.00000 + 3.46410i) q^{71} -2.43845 q^{73} +(-4.90388 + 8.49377i) q^{74} +(-3.84233 - 6.65511i) q^{76} +2.56155 q^{77} +1.43845 q^{79} +(-1.78078 - 3.08440i) q^{80} +(-2.06155 + 3.57071i) q^{82} +10.2462 q^{83} +(-8.90388 + 15.4220i) q^{85} +2.87689 q^{86} +(-1.28078 - 2.21837i) q^{88} +(-4.84233 - 8.38716i) q^{89} +(2.84233 + 2.21837i) q^{91} +9.12311 q^{92} +(3.84233 + 6.65511i) q^{94} +(-13.6847 + 23.7025i) q^{95} +(-6.12311 + 10.6055i) q^{97} +(0.500000 - 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 6 q^{5} + 2 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 + 2 * q^7 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} + 6 q^{5} + 2 q^{7} - 4 q^{8} + 3 q^{10} + q^{11} - 2 q^{13} + 4 q^{14} - 2 q^{16} - 10 q^{17} - 3 q^{19} - 3 q^{20} - q^{22} - 10 q^{23} + 6 q^{25} - q^{26} + 2 q^{28} - 2 q^{29} + 4 q^{31} + 2 q^{32} - 20 q^{34} + 3 q^{35} - q^{37} - 6 q^{38} - 6 q^{40} + 14 q^{43} - 2 q^{44} + 10 q^{46} + 6 q^{47} - 2 q^{49} + 3 q^{50} + q^{52} + 32 q^{53} + 10 q^{55} - 2 q^{56} + 2 q^{58} + 18 q^{59} + 2 q^{61} + 2 q^{62} + 4 q^{64} - 3 q^{65} + 6 q^{67} - 10 q^{68} + 6 q^{70} - 8 q^{71} - 18 q^{73} + q^{74} - 3 q^{76} + 2 q^{77} + 14 q^{79} - 3 q^{80} + 8 q^{83} - 15 q^{85} + 28 q^{86} - q^{88} - 7 q^{89} - q^{91} + 20 q^{92} + 3 q^{94} - 30 q^{95} - 8 q^{97} + 2 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 + 2 * q^7 - 4 * q^8 + 3 * q^10 + q^11 - 2 * q^13 + 4 * q^14 - 2 * q^16 - 10 * q^17 - 3 * q^19 - 3 * q^20 - q^22 - 10 * q^23 + 6 * q^25 - q^26 + 2 * q^28 - 2 * q^29 + 4 * q^31 + 2 * q^32 - 20 * q^34 + 3 * q^35 - q^37 - 6 * q^38 - 6 * q^40 + 14 * q^43 - 2 * q^44 + 10 * q^46 + 6 * q^47 - 2 * q^49 + 3 * q^50 + q^52 + 32 * q^53 + 10 * q^55 - 2 * q^56 + 2 * q^58 + 18 * q^59 + 2 * q^61 + 2 * q^62 + 4 * q^64 - 3 * q^65 + 6 * q^67 - 10 * q^68 + 6 * q^70 - 8 * q^71 - 18 * q^73 + q^74 - 3 * q^76 + 2 * q^77 + 14 * q^79 - 3 * q^80 + 8 * q^83 - 15 * q^85 + 28 * q^86 - q^88 - 7 * q^89 - q^91 + 20 * q^92 + 3 * q^94 - 30 * q^95 - 8 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	3.56155			1.59277			0.796387	−	0.604787i	$-0.206742\pi$
$5$	3.56155			1.59277			0.796387	+	0.604787i	$0.206742\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.78078	+	3.08440i	0.563131	+	0.975371i
$11$	1.28078	+	2.21837i	0.386169	+	0.668864i	0.991931	−	0.126782i	$-0.0404650\pi$
$11$	1.28078	+	2.21837i	0.386169	+	0.668864i	−0.605762	+	0.795646i	$0.707132\pi$
$12$		0			0
$13$	−0.500000	+	3.57071i	−0.138675	+	0.990338i
$13$	−0.500000	+	3.57071i	−0.138675	+	0.990338i
$14$	1.00000			0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	0.385499	+	0.922708i	$0.374029\pi$
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	−0.991838	+	0.127502i	$0.959304\pi$
$18$		0			0
$19$	−3.84233	+	6.65511i	−0.881491	+	1.52679i	−0.0318071	+	0.999494i	$0.510126\pi$
$19$	−3.84233	+	6.65511i	−0.881491	+	1.52679i	−0.849684	+	0.527293i	$0.823207\pi$
$20$	−1.78078	+	3.08440i	−0.398194	+	0.689692i
$21$		0			0
$22$	−1.28078	+	2.21837i	−0.273062	+	0.472958i
$23$	−4.56155	−	7.90084i	−0.951150	−	1.64744i	−0.742943	−	0.669354i	$-0.766571\pi$
$23$	−4.56155	−	7.90084i	−0.951150	−	1.64744i	−0.208206	−	0.978085i	$-0.566763\pi$
$24$		0			0
$25$	7.68466			1.53693
$26$	−3.34233	+	1.35234i	−0.655485	+	0.265217i
$27$		0			0
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	0.815861	−	0.578249i	$-0.196264\pi$
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	−0.908708	+	0.417432i	$0.862930\pi$
$30$		0			0
$31$	5.12311			0.920137			0.460068	−	0.887883i	$-0.347825\pi$
$31$	5.12311			0.920137			0.460068	+	0.887883i	$0.347825\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−5.00000			−0.857493
$35$	1.78078	−	3.08440i	0.301006	−	0.521358i
$36$		0			0
$37$	4.90388	+	8.49377i	0.806193	+	1.39637i	0.915483	+	0.402358i	$0.131809\pi$
$37$	4.90388	+	8.49377i	0.806193	+	1.39637i	−0.109289	+	0.994010i	$0.534857\pi$
$38$	−7.68466			−1.24662
$39$		0			0
$40$	−3.56155			−0.563131
$41$	2.06155	+	3.57071i	0.321960	+	0.557652i	0.980892	−	0.194551i	$-0.0623249\pi$
$41$	2.06155	+	3.57071i	0.321960	+	0.557652i	−0.658932	+	0.752202i	$0.728992\pi$
$42$		0			0
$43$	1.43845	−	2.49146i	0.219361	−	0.379945i	−0.735252	−	0.677794i	$-0.762936\pi$
$43$	1.43845	−	2.49146i	0.219361	−	0.379945i	0.954613	+	0.297850i	$0.0962694\pi$
$44$	−2.56155			−0.386169
$45$		0			0
$46$	4.56155	−	7.90084i	0.672564	−	1.16492i
$47$	7.68466			1.12092			0.560461	−	0.828181i	$-0.310624\pi$
$47$	7.68466			1.12092			0.560461	+	0.828181i	$0.310624\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	3.84233	+	6.65511i	0.543387	+	0.941175i
$51$		0			0
$52$	−2.84233	−	2.21837i	−0.394160	−	0.307633i
$53$	3.87689			0.532532			0.266266	−	0.963900i	$-0.414210\pi$
$53$	3.87689			0.532532			0.266266	+	0.963900i	$0.414210\pi$
$54$		0			0
$55$	4.56155	+	7.90084i	0.615080	+	1.06535i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		0			0
$58$	0.500000	−	0.866025i	0.0656532	−	0.113715i
$59$	6.56155	−	11.3649i	0.854241	−	1.47959i	−0.0231056	−	0.999733i	$-0.507355\pi$
$59$	6.56155	−	11.3649i	0.854241	−	1.47959i	0.877347	−	0.479857i	$-0.159311\pi$
$60$		0			0
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$	2.56155	+	4.43674i	0.325318	+	0.563466i
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.78078	+	12.7173i	−0.220878	+	1.57739i
$66$		0			0
$67$	−0.561553	−	0.972638i	−0.0686046	−	0.118827i	0.829683	−	0.558235i	$-0.188521\pi$
$67$	−0.561553	−	0.972638i	−0.0686046	−	0.118827i	−0.898287	+	0.439409i	$0.855188\pi$
$68$	−2.50000	−	4.33013i	−0.303170	−	0.525105i
$69$		0			0
$70$	3.56155			0.425687
$71$	−2.00000	+	3.46410i	−0.237356	+	0.411113i	−0.959955	−	0.280155i	$-0.909614\pi$
$71$	−2.00000	+	3.46410i	−0.237356	+	0.411113i	0.722599	+	0.691268i	$0.242948\pi$
$72$		0			0
$73$	−2.43845			−0.285399			−0.142699	−	0.989766i	$-0.545578\pi$
$73$	−2.43845			−0.285399			−0.142699	+	0.989766i	$0.545578\pi$
$74$	−4.90388	+	8.49377i	−0.570065	+	0.987381i
$75$		0			0
$76$	−3.84233	−	6.65511i	−0.440745	−	0.763393i
$77$	2.56155			0.291916
$78$		0			0
$79$	1.43845			0.161838			0.0809190	−	0.996721i	$-0.474214\pi$
$79$	1.43845			0.161838			0.0809190	+	0.996721i	$0.474214\pi$
$80$	−1.78078	−	3.08440i	−0.199097	−	0.344846i
$81$		0			0
$82$	−2.06155	+	3.57071i	−0.227660	+	0.394319i
$83$	10.2462			1.12467			0.562334	−	0.826910i	$-0.309904\pi$
$83$	10.2462			1.12467			0.562334	+	0.826910i	$0.309904\pi$
$84$		0			0
$85$	−8.90388	+	15.4220i	−0.965762	+	1.67275i
$86$	2.87689			0.310223
$87$		0			0
$88$	−1.28078	−	2.21837i	−0.136531	−	0.236479i
$89$	−4.84233	−	8.38716i	−0.513286	−	0.889037i	−0.999881	−	0.0154098i	$-0.995095\pi$
$89$	−4.84233	−	8.38716i	−0.513286	−	0.889037i	0.486595	−	0.873627i	$-0.338239\pi$
$90$		0			0
$91$	2.84233	+	2.21837i	0.297957	+	0.232548i
$92$	9.12311			0.951150
$93$		0			0
$94$	3.84233	+	6.65511i	0.396306	+	0.686422i
$95$	−13.6847	+	23.7025i	−1.40402	+	2.43183i
$96$		0			0
$97$	−6.12311	+	10.6055i	−0.621707	+	1.07683i	0.367461	+	0.930039i	$0.380227\pi$
$97$	−6.12311	+	10.6055i	−0.621707	+	1.07683i	−0.989168	+	0.146789i	$0.953106\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$		0			0
$100$	−3.84233	+	6.65511i	−0.384233	+	0.665511i
$101$	−9.78078	−	16.9408i	−0.973224	−	1.68567i	−0.685677	−	0.727906i	$-0.740494\pi$
$101$	−9.78078	−	16.9408i	−0.973224	−	1.68567i	−0.287547	−	0.957767i	$-0.592840\pi$
$102$		0			0
$103$	−11.3693			−1.12025			−0.560126	−	0.828407i	$-0.689247\pi$
$103$	−11.3693			−1.12025			−0.560126	+	0.828407i	$0.689247\pi$
$104$	0.500000	−	3.57071i	0.0490290	−	0.350137i
$105$		0			0
$106$	1.93845	+	3.35749i	0.188279	+	0.326108i
$107$	−4.71922	−	8.17394i	−0.456225	−	0.790204i	0.542533	−	0.840034i	$-0.317465\pi$
$107$	−4.71922	−	8.17394i	−0.456225	−	0.790204i	−0.998758	+	0.0498303i	$0.984132\pi$
$108$		0			0
$109$	0.876894			0.0839912			0.0419956	−	0.999118i	$-0.486628\pi$
$109$	0.876894			0.0839912			0.0419956	+	0.999118i	$0.486628\pi$
$110$	−4.56155	+	7.90084i	−0.434927	+	0.753316i
$111$		0			0
$112$	−1.00000			−0.0944911
$113$	8.46543	−	14.6626i	0.796361	−	1.37934i	−0.125610	−	0.992080i	$-0.540089\pi$
$113$	8.46543	−	14.6626i	0.796361	−	1.37934i	0.921971	−	0.387258i	$-0.126578\pi$
$114$		0			0
$115$	−16.2462	−	28.1393i	−1.51497	−	2.62400i
$116$	1.00000			0.0928477
$117$		0			0
$118$	13.1231			1.20808
$119$	2.50000	+	4.33013i	0.229175	+	0.396942i
$120$		0			0
$121$	2.21922	−	3.84381i	0.201748	−	0.349437i
$122$	1.00000			0.0905357
$123$		0			0
$124$	−2.56155	+	4.43674i	−0.230034	+	0.398431i
$125$	9.56155			0.855211
$126$		0			0
$127$	−1.12311	−	1.94528i	−0.0996595	−	0.172615i	0.811884	−	0.583818i	$-0.198442\pi$
$127$	−1.12311	−	1.94528i	−0.0996595	−	0.172615i	−0.911544	+	0.411203i	$0.865109\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−11.9039	+	4.81645i	−1.04404	+	0.422430i
$131$	16.4924			1.44095			0.720475	−	0.693481i	$-0.243924\pi$
$131$	16.4924			1.44095			0.720475	+	0.693481i	$0.243924\pi$
$132$		0			0
$133$	3.84233	+	6.65511i	0.333172	+	0.577071i
$134$	0.561553	−	0.972638i	0.0485108	−	0.0840231i
$135$		0			0
$136$	2.50000	−	4.33013i	0.214373	−	0.371305i
$137$	−2.90388	+	5.02967i	−0.248095	+	0.429714i	−0.962997	−	0.269511i	$-0.913138\pi$
$137$	−2.90388	+	5.02967i	−0.248095	+	0.429714i	0.714902	+	0.699225i	$0.246471\pi$
$138$		0			0
$139$	3.84233	−	6.65511i	0.325902	−	0.564479i	−0.655792	−	0.754941i	$-0.727665\pi$
$139$	3.84233	−	6.65511i	0.325902	−	0.564479i	0.981695	+	0.190462i	$0.0609987\pi$
$140$	1.78078	+	3.08440i	0.150503	+	0.260679i
$141$		0			0
$142$	−4.00000			−0.335673
$143$	−8.56155	+	3.46410i	−0.715953	+	0.289683i
$144$		0			0
$145$	−1.78078	−	3.08440i	−0.147885	−	0.256145i
$146$	−1.21922	−	2.11176i	−0.100904	−	0.174770i
$147$		0			0
$148$	−9.80776			−0.806193
$149$	−8.90388	+	15.4220i	−0.729434	+	1.26342i	0.227688	+	0.973734i	$0.426883\pi$
$149$	−8.90388	+	15.4220i	−0.729434	+	1.26342i	−0.957123	+	0.289683i	$0.906450\pi$
$150$		0			0
$151$	−17.4384			−1.41912			−0.709560	−	0.704645i	$-0.751106\pi$
$151$	−17.4384			−1.41912			−0.709560	+	0.704645i	$0.751106\pi$
$152$	3.84233	−	6.65511i	0.311654	−	0.539801i
$153$		0			0
$154$	1.28078	+	2.21837i	0.103208	+	0.178761i
$155$	18.2462			1.46557
$156$		0			0
$157$	−5.80776			−0.463510			−0.231755	−	0.972774i	$-0.574447\pi$
$157$	−5.80776			−0.463510			−0.231755	+	0.972774i	$0.574447\pi$
$158$	0.719224	+	1.24573i	0.0572184	+	0.0991051i
$159$		0			0
$160$	1.78078	−	3.08440i	0.140783	−	0.243843i
$161$	−9.12311			−0.719001
$162$		0			0
$163$	0.561553	−	0.972638i	0.0439842	−	0.0761829i	−0.843195	−	0.537608i	$-0.819328\pi$
$163$	0.561553	−	0.972638i	0.0439842	−	0.0761829i	0.887179	+	0.461425i	$0.152662\pi$
$164$	−4.12311			−0.321960
$165$		0			0
$166$	5.12311	+	8.87348i	0.397630	+	0.688716i
$167$	10.2462	+	17.7470i	0.792876	+	1.37330i	0.924179	+	0.381959i	$0.124750\pi$
$167$	10.2462	+	17.7470i	0.792876	+	1.37330i	−0.131304	+	0.991342i	$0.541916\pi$
$168$		0			0
$169$	−12.5000	−	3.57071i	−0.961538	−	0.274670i
$170$	−17.8078			−1.36579
$171$		0			0
$172$	1.43845	+	2.49146i	0.109681	+	0.189972i
$173$	−2.43845	+	4.22351i	−0.185392	+	0.321108i	−0.943708	−	0.330778i	$-0.892689\pi$
$173$	−2.43845	+	4.22351i	−0.185392	+	0.321108i	0.758317	+	0.651886i	$0.226022\pi$
$174$		0			0
$175$	3.84233	−	6.65511i	0.290453	−	0.503079i
$176$	1.28078	−	2.21837i	0.0965422	−	0.167216i
$177$		0			0
$178$	4.84233	−	8.38716i	0.362948	−	0.628644i
$179$	−8.24621	−	14.2829i	−0.616351	−	1.06755i	−0.990146	−	0.140040i	$-0.955277\pi$
$179$	−8.24621	−	14.2829i	−0.616351	−	1.06755i	0.373795	−	0.927511i	$-0.378056\pi$
$180$		0			0
$181$	13.2462			0.984583			0.492292	−	0.870430i	$-0.336159\pi$
$181$	13.2462			0.984583			0.492292	+	0.870430i	$0.336159\pi$
$182$	−0.500000	+	3.57071i	−0.0370625	+	0.264679i
$183$		0			0
$184$	4.56155	+	7.90084i	0.336282	+	0.582458i
$185$	17.4654	+	30.2510i	1.28408	+	2.22410i
$186$		0			0
$187$	−12.8078			−0.936596
$188$	−3.84233	+	6.65511i	−0.280231	+	0.485374i
$189$		0			0
$190$	−27.3693			−1.98558
$191$	2.87689	−	4.98293i	0.208165	−	0.360552i	−0.742972	−	0.669323i	$-0.766584\pi$
$191$	2.87689	−	4.98293i	0.208165	−	0.360552i	0.951136	+	0.308771i	$0.0999176\pi$
$192$		0			0
$193$	10.1847	+	17.6403i	0.733108	+	1.26978i	0.955549	+	0.294834i	$0.0952642\pi$
$193$	10.1847	+	17.6403i	0.733108	+	1.26978i	−0.222441	+	0.974946i	$0.571402\pi$
$194$	−12.2462			−0.879227
$195$		0			0
$196$	1.00000			0.0714286
$197$	−0.280776	−	0.486319i	−0.0200045	−	0.0346488i	0.855850	−	0.517224i	$-0.173035\pi$
$197$	−0.280776	−	0.486319i	−0.0200045	−	0.0346488i	−0.875854	+	0.482576i	$0.839701\pi$
$198$		0			0
$199$	8.80776	−	15.2555i	0.624366	−	1.08143i	−0.364297	−	0.931283i	$-0.618691\pi$
$199$	8.80776	−	15.2555i	0.624366	−	1.08143i	0.988663	−	0.150151i	$-0.0479759\pi$
$200$	−7.68466			−0.543387
$201$		0			0
$202$	9.78078	−	16.9408i	0.688173	−	1.19195i
$203$	−1.00000			−0.0701862
$204$		0			0
$205$	7.34233	+	12.7173i	0.512811	+	0.888214i
$206$	−5.68466	−	9.84612i	−0.396069	−	0.686011i
$207$		0			0
$208$	3.34233	−	1.35234i	0.231749	−	0.0937682i
$209$	−19.6847			−1.36162
$210$		0			0
$211$	1.43845	+	2.49146i	0.0990268	+	0.171519i	0.911282	−	0.411783i	$-0.135094\pi$
$211$	1.43845	+	2.49146i	0.0990268	+	0.171519i	−0.812255	+	0.583302i	$0.801760\pi$
$212$	−1.93845	+	3.35749i	−0.133133	+	0.230593i
$213$		0			0
$214$	4.71922	−	8.17394i	0.322599	−	0.558759i
$215$	5.12311	−	8.87348i	0.349393	−	0.605166i
$216$		0			0
$217$	2.56155	−	4.43674i	0.173890	−	0.301186i
$218$	0.438447	+	0.759413i	0.0296954	+	0.0514339i
$219$		0			0
$220$	−9.12311			−0.615080
$221$	−14.2116	−	11.0918i	−0.955979	−	0.746119i
$222$		0			0
$223$	8.24621	+	14.2829i	0.552207	+	0.956451i	0.998115	+	0.0613719i	$0.0195476\pi$
$223$	8.24621	+	14.2829i	0.552207	+	0.956451i	−0.445908	+	0.895079i	$0.647119\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$		0			0
$226$	16.9309			1.12622
$227$	6.56155	−	11.3649i	0.435506	−	0.754318i	−0.561831	−	0.827252i	$-0.689903\pi$
$227$	6.56155	−	11.3649i	0.435506	−	0.754318i	0.997337	+	0.0729341i	$0.0232363\pi$
$228$		0			0
$229$	22.8078			1.50718			0.753590	−	0.657345i	$-0.228321\pi$
$229$	22.8078			1.50718			0.753590	+	0.657345i	$0.228321\pi$
$230$	16.2462	−	28.1393i	1.07124	−	1.85545i
$231$		0			0
$232$	0.500000	+	0.866025i	0.0328266	+	0.0568574i
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$	27.3693			1.78538
$236$	6.56155	+	11.3649i	0.427121	+	0.739795i
$237$		0			0
$238$	−2.50000	+	4.33013i	−0.162051	+	0.280680i
$239$	−4.00000			−0.258738			−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000			−0.258738			−0.129369	+	0.991596i	$0.541295\pi$
$240$		0			0
$241$	−5.65767	+	9.79937i	−0.364443	+	0.631233i	−0.988687	−	0.149996i	$-0.952074\pi$
$241$	−5.65767	+	9.79937i	−0.364443	+	0.631233i	0.624244	+	0.781229i	$0.285407\pi$
$242$	4.43845			0.285314
$243$		0			0
$244$	0.500000	+	0.866025i	0.0320092	+	0.0554416i
$245$	−1.78078	−	3.08440i	−0.113770	−	0.197055i
$246$		0			0
$247$	−21.8423	−	17.0474i	−1.38979	−	1.08470i
$248$	−5.12311			−0.325318
$249$		0			0
$250$	4.78078	+	8.28055i	0.302363	+	0.523708i
$251$	4.24621	−	7.35465i	0.268018	−	0.464222i	−0.700332	−	0.713818i	$-0.746965\pi$
$251$	4.24621	−	7.35465i	0.268018	−	0.464222i	0.968350	+	0.249596i	$0.0802978\pi$
$252$		0			0
$253$	11.6847	−	20.2384i	0.734608	−	1.27238i
$254$	1.12311	−	1.94528i	0.0704699	−	0.122057i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.37689	−	12.7772i	−0.460158	−	0.797017i	0.538810	−	0.842427i	$-0.318874\pi$
$257$	−7.37689	−	12.7772i	−0.460158	−	0.797017i	−0.998968	+	0.0454100i	$0.985541\pi$
$258$		0			0
$259$	9.80776			0.609425
$260$	−10.1231	−	7.90084i	−0.627808	−	0.489989i
$261$		0			0
$262$	8.24621	+	14.2829i	0.509453	+	0.882398i
$263$	−10.2462	−	17.7470i	−0.631808	−	1.09432i	−0.987182	−	0.159600i	$-0.948980\pi$
$263$	−10.2462	−	17.7470i	−0.631808	−	1.09432i	0.355373	−	0.934724i	$-0.384354\pi$
$264$		0			0
$265$	13.8078			0.848204
$266$	−3.84233	+	6.65511i	−0.235588	+	0.408051i
$267$		0			0
$268$	1.12311			0.0686046
$269$	−2.43845	+	4.22351i	−0.148675	+	0.257512i	−0.930738	−	0.365687i	$-0.880834\pi$
$269$	−2.43845	+	4.22351i	−0.148675	+	0.257512i	0.782063	+	0.623199i	$0.214167\pi$
$270$		0			0
$271$	−6.56155	−	11.3649i	−0.398586	−	0.690371i	0.594966	−	0.803751i	$-0.297166\pi$
$271$	−6.56155	−	11.3649i	−0.398586	−	0.690371i	−0.993552	+	0.113380i	$0.963832\pi$
$272$	5.00000			0.303170
$273$		0			0
$274$	−5.80776			−0.350860
$275$	9.84233	+	17.0474i	0.593515	+	1.02800i
$276$		0			0
$277$	1.78078	−	3.08440i	0.106996	−	0.185323i	−0.807556	−	0.589791i	$-0.799210\pi$
$277$	1.78078	−	3.08440i	0.106996	−	0.185323i	0.914552	+	0.404468i	$0.132543\pi$
$278$	7.68466			0.460895
$279$		0			0
$280$	−1.78078	+	3.08440i	−0.106422	+	0.184328i
$281$	−7.80776			−0.465772			−0.232886	−	0.972504i	$-0.574817\pi$
$281$	−7.80776			−0.465772			−0.232886	+	0.972504i	$0.574817\pi$
$282$		0			0
$283$	−4.24621	−	7.35465i	−0.252411	−	0.437189i	0.711778	−	0.702404i	$-0.247890\pi$
$283$	−4.24621	−	7.35465i	−0.252411	−	0.437189i	−0.964189	+	0.265216i	$0.914557\pi$
$284$	−2.00000	−	3.46410i	−0.118678	−	0.205557i
$285$		0			0
$286$	−7.28078	−	5.68247i	−0.430521	−	0.336012i
$287$	4.12311			0.243379
$288$		0			0
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$	1.78078	−	3.08440i	0.104571	−	0.181122i
$291$		0			0
$292$	1.21922	−	2.11176i	0.0713497	−	0.123581i
$293$	−2.34233	+	4.05703i	−0.136840	+	0.237014i	−0.926299	−	0.376789i	$-0.877028\pi$
$293$	−2.34233	+	4.05703i	−0.136840	+	0.237014i	0.789459	+	0.613804i	$0.210361\pi$
$294$		0			0
$295$	23.3693	−	40.4768i	1.36061	−	2.35665i
$296$	−4.90388	−	8.49377i	−0.285032	−	0.493691i
$297$		0			0
$298$	−17.8078			−1.03158
$299$	30.4924	−	12.3376i	1.76342	−	0.713501i
$300$		0			0
$301$	−1.43845	−	2.49146i	−0.0829107	−	0.143606i
$302$	−8.71922	−	15.1021i	−0.501735	−	0.869030i
$303$		0			0
$304$	7.68466			0.440745
$305$	1.78078	−	3.08440i	0.101967	−	0.176612i
$306$		0			0
$307$	−33.9309			−1.93654			−0.968269	−	0.249912i	$-0.919598\pi$
$307$	−33.9309			−1.93654			−0.968269	+	0.249912i	$0.919598\pi$
$308$	−1.28078	+	2.21837i	−0.0729790	+	0.126403i
$309$		0			0
$310$	9.12311	+	15.8017i	0.518158	+	0.897475i
$311$	−22.5616			−1.27935			−0.639674	−	0.768646i	$-0.720931\pi$
$311$	−22.5616			−1.27935			−0.639674	+	0.768646i	$0.720931\pi$
$312$		0			0
$313$	27.6155			1.56092			0.780461	−	0.625205i	$-0.214984\pi$
$313$	27.6155			1.56092			0.780461	+	0.625205i	$0.214984\pi$
$314$	−2.90388	−	5.02967i	−0.163876	−	0.283841i
$315$		0			0
$316$	−0.719224	+	1.24573i	−0.0404595	+	0.0700779i
$317$	11.5616			0.649362			0.324681	−	0.945824i	$-0.394743\pi$
$317$	11.5616			0.649362			0.324681	+	0.945824i	$0.394743\pi$
$318$		0			0
$319$	1.28078	−	2.21837i	0.0717097	−	0.124205i
$320$	3.56155			0.199097
$321$		0			0
$322$	−4.56155	−	7.90084i	−0.254205	−	0.440297i
$323$	−19.2116	−	33.2755i	−1.06896	−	1.85150i
$324$		0			0
$325$	−3.84233	+	27.4397i	−0.213134	+	1.52208i
$326$	1.12311			0.0622031
$327$		0			0
$328$	−2.06155	−	3.57071i	−0.113830	−	0.197160i
$329$	3.84233	−	6.65511i	0.211834	−	0.366908i
$330$		0			0
$331$	17.6847	−	30.6307i	0.972037	−	1.68362i	0.282651	−	0.959223i	$-0.408786\pi$
$331$	17.6847	−	30.6307i	0.972037	−	1.68362i	0.689386	−	0.724394i	$-0.257880\pi$
$332$	−5.12311	+	8.87348i	−0.281167	+	0.486995i
$333$		0			0
$334$	−10.2462	+	17.7470i	−0.560648	+	0.971070i
$335$	−2.00000	−	3.46410i	−0.109272	−	0.189264i
$336$		0			0
$337$	−29.4924			−1.60655			−0.803277	−	0.595605i	$-0.796912\pi$
$337$	−29.4924			−1.60655			−0.803277	+	0.595605i	$0.796912\pi$
$338$	−3.15767	−	12.6107i	−0.171755	−	0.685930i
$339$		0			0
$340$	−8.90388	−	15.4220i	−0.482881	−	0.836374i
$341$	6.56155	+	11.3649i	0.355328	+	0.615446i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	−1.43845	+	2.49146i	−0.0775559	+	0.134331i
$345$		0			0
$346$	−4.87689			−0.262183
$347$	−0.157671	+	0.273094i	−0.00846421	+	0.0146604i	−0.870226	−	0.492652i	$-0.836028\pi$
$347$	−0.157671	+	0.273094i	−0.00846421	+	0.0146604i	0.861762	+	0.507312i	$0.169361\pi$
$348$		0			0
$349$	3.24621	+	5.62260i	0.173766	+	0.300971i	0.939733	−	0.341908i	$-0.111073\pi$
$349$	3.24621	+	5.62260i	0.173766	+	0.300971i	−0.765968	+	0.642879i	$0.777740\pi$
$350$	7.68466			0.410762
$351$		0			0
$352$	2.56155			0.136531
$353$	−4.90388	−	8.49377i	−0.261007	−	0.452078i	0.705503	−	0.708707i	$-0.250721\pi$
$353$	−4.90388	−	8.49377i	−0.261007	−	0.452078i	−0.966510	+	0.256629i	$0.917388\pi$
$354$		0			0
$355$	−7.12311	+	12.3376i	−0.378055	+	0.654811i
$356$	9.68466			0.513286
$357$		0			0
$358$	8.24621	−	14.2829i	0.435826	−	0.754872i
$359$	4.63068			0.244398			0.122199	−	0.992506i	$-0.461005\pi$
$359$	4.63068			0.244398			0.122199	+	0.992506i	$0.461005\pi$
$360$		0			0
$361$	−20.0270	−	34.6878i	−1.05405	−	1.82567i
$362$	6.62311	+	11.4716i	0.348103	+	0.602932i
$363$		0			0
$364$	−3.34233	+	1.35234i	−0.175186	+	0.0708821i
$365$	−8.68466			−0.454576
$366$		0			0
$367$	−5.68466	−	9.84612i	−0.296737	−	0.513963i	0.678651	−	0.734461i	$-0.262565\pi$
$367$	−5.68466	−	9.84612i	−0.296737	−	0.513963i	−0.975387	+	0.220498i	$0.929232\pi$
$368$	−4.56155	+	7.90084i	−0.237787	+	0.411860i
$369$		0			0
$370$	−17.4654	+	30.2510i	−0.907985	+	1.57268i
$371$	1.93845	−	3.35749i	0.100639	−	0.174312i
$372$		0			0
$373$	−10.7808	+	18.6729i	−0.558207	+	0.966844i	0.439439	+	0.898273i	$0.355177\pi$
$373$	−10.7808	+	18.6729i	−0.558207	+	0.966844i	−0.997646	+	0.0685711i	$0.978156\pi$
$374$	−6.40388	−	11.0918i	−0.331137	−	0.573546i
$375$		0			0
$376$	−7.68466			−0.396306
$377$	3.34233	−	1.35234i	0.172139	−	0.0696493i
$378$		0			0
$379$	−0.246211	−	0.426450i	−0.0126470	−	0.0219053i	0.859633	−	0.510913i	$-0.170692\pi$
$379$	−0.246211	−	0.426450i	−0.0126470	−	0.0219053i	−0.872280	+	0.489007i	$0.837359\pi$
$380$	−13.6847	−	23.7025i	−0.702008	−	1.21591i
$381$		0			0
$382$	5.75379			0.294389
$383$	4.15767	−	7.20130i	0.212447	−	0.367969i	−0.740033	−	0.672571i	$-0.765190\pi$
$383$	4.15767	−	7.20130i	0.212447	−	0.367969i	0.952480	+	0.304602i	$0.0985234\pi$
$384$		0			0
$385$	9.12311			0.464957
$386$	−10.1847	+	17.6403i	−0.518385	+	0.897870i
$387$		0			0
$388$	−6.12311	−	10.6055i	−0.310854	−	0.538414i
$389$	−18.6847			−0.947350			−0.473675	−	0.880700i	$-0.657073\pi$
$389$	−18.6847			−0.947350			−0.473675	+	0.880700i	$0.657073\pi$
$390$		0			0
$391$	45.6155			2.30688
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$		0			0
$394$	0.280776	−	0.486319i	0.0141453	−	0.0245004i
$395$	5.12311			0.257771
$396$		0			0
$397$	−0.842329	+	1.45896i	−0.0422753	+	0.0732230i	−0.886389	−	0.462942i	$-0.846794\pi$
$397$	−0.842329	+	1.45896i	−0.0422753	+	0.0732230i	0.844114	+	0.536164i	$0.180127\pi$
$398$	17.6155			0.882987
$399$		0			0
$400$	−3.84233	−	6.65511i	−0.192116	−	0.332755i
$401$	7.58854	+	13.1437i	0.378954	+	0.656367i	0.990910	−	0.134524i	$-0.0429507\pi$
$401$	7.58854	+	13.1437i	0.378954	+	0.656367i	−0.611957	+	0.790891i	$0.709617\pi$
$402$		0			0
$403$	−2.56155	+	18.2931i	−0.127600	+	0.911247i
$404$	19.5616			0.973224
$405$		0			0
$406$	−0.500000	−	0.866025i	−0.0248146	−	0.0429801i
$407$	−12.5616	+	21.7572i	−0.622653	+	1.07847i
$408$		0			0
$409$	15.2192	−	26.3605i	0.752542	−	1.30344i	−0.194045	−	0.980993i	$-0.562161\pi$
$409$	15.2192	−	26.3605i	0.752542	−	1.30344i	0.946587	−	0.322449i	$-0.104506\pi$
$410$	−7.34233	+	12.7173i	−0.362612	+	0.628062i
$411$		0			0
$412$	5.68466	−	9.84612i	0.280063	−	0.485083i
$413$	−6.56155	−	11.3649i	−0.322873	−	0.559232i
$414$		0			0
$415$	36.4924			1.79134
$416$	2.84233	+	2.21837i	0.139357	+	0.108765i
$417$		0			0
$418$	−9.84233	−	17.0474i	−0.481404	−	0.833816i
$419$	11.3693	+	19.6922i	0.555427	+	0.962029i	0.997870	+	0.0652318i	$0.0207787\pi$
$419$	11.3693	+	19.6922i	0.555427	+	0.962029i	−0.442443	+	0.896797i	$0.645888\pi$
$420$		0			0
$421$	8.43845			0.411265			0.205632	−	0.978629i	$-0.434075\pi$
$421$	8.43845			0.411265			0.205632	+	0.978629i	$0.434075\pi$
$422$	−1.43845	+	2.49146i	−0.0700225	+	0.121283i
$423$		0			0
$424$	−3.87689			−0.188279
$425$	−19.2116	+	33.2755i	−0.931902	+	1.61410i
$426$		0			0
$427$	−0.500000	−	0.866025i	−0.0241967	−	0.0419099i
$428$	9.43845			0.456225
$429$		0			0
$430$	10.2462			0.494116
$431$	−9.36932	−	16.2281i	−0.451304	−	0.781682i	0.547163	−	0.837026i	$-0.315708\pi$
$431$	−9.36932	−	16.2281i	−0.451304	−	0.781682i	−0.998467	+	0.0553443i	$0.982374\pi$
$432$		0			0
$433$	2.65767	−	4.60322i	0.127720	−	0.221217i	−0.795073	−	0.606514i	$-0.792568\pi$
$433$	2.65767	−	4.60322i	0.127720	−	0.221217i	0.922793	+	0.385297i	$0.125901\pi$
$434$	5.12311			0.245917
$435$		0			0
$436$	−0.438447	+	0.759413i	−0.0209978	+	0.0363693i
$437$	70.1080			3.35372
$438$		0			0
$439$	14.2462	+	24.6752i	0.679935	+	1.17768i	0.975000	+	0.222204i	$0.0713252\pi$
$439$	14.2462	+	24.6752i	0.679935	+	1.17768i	−0.295066	+	0.955477i	$0.595342\pi$
$440$	−4.56155	−	7.90084i	−0.217463	−	0.376658i
$441$		0			0
$442$	2.50000	−	17.8536i	0.118913	−	0.849208i
$443$	34.4233			1.63550			0.817750	−	0.575574i	$-0.195221\pi$
$443$	34.4233			1.63550			0.817750	+	0.575574i	$0.195221\pi$
$444$		0			0
$445$	−17.2462	−	29.8713i	−0.817549	−	1.41604i
$446$	−8.24621	+	14.2829i	−0.390469	+	0.676313i
$447$		0			0
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	9.00000	−	15.5885i	0.424736	−	0.735665i	−0.571660	−	0.820491i	$-0.693700\pi$
$449$	9.00000	−	15.5885i	0.424736	−	0.735665i	0.996396	+	0.0848262i	$0.0270335\pi$
$450$		0			0
$451$	−5.28078	+	9.14657i	−0.248662	+	0.430695i
$452$	8.46543	+	14.6626i	0.398181	+	0.689669i
$453$		0			0
$454$	13.1231			0.615898
$455$	10.1231	+	7.90084i	0.474579	+	0.370397i
$456$		0			0
$457$	6.65767	+	11.5314i	0.311433	+	0.539417i	0.978673	−	0.205425i	$-0.0658578\pi$
$457$	6.65767	+	11.5314i	0.311433	+	0.539417i	−0.667240	+	0.744843i	$0.732524\pi$
$458$	11.4039	+	19.7521i	0.532868	+	0.922955i
$459$		0			0
$460$	32.4924			1.51497
$461$	15.0270	−	26.0275i	0.699877	−	1.21222i	−0.268632	−	0.963243i	$-0.586572\pi$
$461$	15.0270	−	26.0275i	0.699877	−	1.21222i	0.968509	−	0.248979i	$-0.0800950\pi$
$462$		0			0
$463$	−11.6847			−0.543032			−0.271516	−	0.962434i	$-0.587525\pi$
$463$	−11.6847			−0.543032			−0.271516	+	0.962434i	$0.587525\pi$
$464$	−0.500000	+	0.866025i	−0.0232119	+	0.0402042i
$465$		0			0
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	−28.0000			−1.29569			−0.647843	−	0.761774i	$-0.724329\pi$
$467$	−28.0000			−1.29569			−0.647843	+	0.761774i	$0.724329\pi$
$468$		0			0
$469$	−1.12311			−0.0518602
$470$	13.6847	+	23.7025i	0.631226	+	1.09332i
$471$		0			0
$472$	−6.56155	+	11.3649i	−0.302020	+	0.523114i
$473$	7.36932			0.338842
$474$		0			0
$475$	−29.5270	+	51.1422i	−1.35479	+	2.34657i
$476$	−5.00000			−0.229175
$477$		0			0
$478$	−2.00000	−	3.46410i	−0.0914779	−	0.158444i
$479$	−1.28078	−	2.21837i	−0.0585202	−	0.101360i	0.835281	−	0.549823i	$-0.185305\pi$
$479$	−1.28078	−	2.21837i	−0.0585202	−	0.101360i	−0.893801	+	0.448463i	$0.851972\pi$
$480$		0			0
$481$	−32.7808	+	13.2635i	−1.49467	+	0.604762i
$482$	−11.3153			−0.515400
$483$		0			0
$484$	2.21922	+	3.84381i	0.100874	+	0.174719i
$485$	−21.8078	+	37.7722i	−0.990240	+	1.71515i
$486$		0			0
$487$	−11.8423	+	20.5115i	−0.536627	+	0.929466i	0.462456	+	0.886642i	$0.346968\pi$
$487$	−11.8423	+	20.5115i	−0.536627	+	0.929466i	−0.999083	+	0.0428230i	$0.986365\pi$
$488$	−0.500000	+	0.866025i	−0.0226339	+	0.0392031i
$489$		0			0
$490$	1.78078	−	3.08440i	0.0804473	−	0.139339i
$491$	−0.876894	−	1.51883i	−0.0395737	−	0.0685436i	0.845560	−	0.533880i	$-0.179267\pi$
$491$	−0.876894	−	1.51883i	−0.0395737	−	0.0685436i	−0.885134	+	0.465337i	$0.845933\pi$
$492$		0			0
$493$	5.00000			0.225189
$494$	3.84233	−	27.4397i	0.172875	−	1.23457i
$495$		0			0
$496$	−2.56155	−	4.43674i	−0.115017	−	0.199215i
$497$	2.00000	+	3.46410i	0.0897123	+	0.155386i
$498$		0			0
$499$	−27.3693			−1.22522			−0.612609	−	0.790386i	$-0.709880\pi$
$499$	−27.3693			−1.22522			−0.612609	+	0.790386i	$0.709880\pi$
$500$	−4.78078	+	8.28055i	−0.213803	+	0.370317i
$501$		0			0
$502$	8.49242			0.379035
$503$	10.2462	−	17.7470i	0.456856	−	0.791298i	−0.541937	−	0.840419i	$-0.682309\pi$
$503$	10.2462	−	17.7470i	0.456856	−	0.791298i	0.998793	+	0.0491215i	$0.0156421\pi$
$504$		0			0
$505$	−34.8348	−	60.3356i	−1.55013	−	2.68490i
$506$	23.3693			1.03889
$507$		0			0
$508$	2.24621			0.0996595
$509$	13.6577	+	23.6558i	0.605366	+	1.04852i	0.991994	+	0.126288i	$0.0403064\pi$
$509$	13.6577	+	23.6558i	0.605366	+	1.04852i	−0.386628	+	0.922236i	$0.626360\pi$
$510$		0			0
$511$	−1.21922	+	2.11176i	−0.0539353	+	0.0934186i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	7.37689	−	12.7772i	0.325381	−	0.563576i
$515$	−40.4924			−1.78431
$516$		0			0
$517$	9.84233	+	17.0474i	0.432865	+	0.749744i
$518$	4.90388	+	8.49377i	0.215464	+	0.373195i
$519$		0			0
$520$	1.78078	−	12.7173i	0.0780922	−	0.557690i
$521$	17.0000			0.744784			0.372392	−	0.928076i	$-0.378538\pi$
$521$	17.0000			0.744784			0.372392	+	0.928076i	$0.378538\pi$
$522$		0			0
$523$	−7.59612	−	13.1569i	−0.332155	−	0.575309i	0.650779	−	0.759267i	$-0.274442\pi$
$523$	−7.59612	−	13.1569i	−0.332155	−	0.575309i	−0.982934	+	0.183958i	$0.941109\pi$
$524$	−8.24621	+	14.2829i	−0.360237	+	0.623949i
$525$		0			0
$526$	10.2462	−	17.7470i	0.446756	−	0.773804i
$527$	−12.8078	+	22.1837i	−0.557915	+	0.966337i
$528$		0			0
$529$	−30.1155	+	52.1616i	−1.30937	+	2.26790i
$530$	6.90388	+	11.9579i	0.299885	+	0.519417i
$531$		0			0
$532$	−7.68466			−0.333172
$533$	−13.7808	+	5.57586i	−0.596912	+	0.241517i
$534$		0			0
$535$	−16.8078	−	29.1119i	−0.726663	−	1.25862i
$536$	0.561553	+	0.972638i	0.0242554	+	0.0420116i
$537$		0			0
$538$	−4.87689			−0.210258
$539$	1.28078	−	2.21837i	0.0551669	−	0.0955520i
$540$		0			0
$541$	1.56155			0.0671364			0.0335682	−	0.999436i	$-0.489313\pi$
$541$	1.56155			0.0671364			0.0335682	+	0.999436i	$0.489313\pi$
$542$	6.56155	−	11.3649i	0.281843	−	0.488166i
$543$		0			0
$544$	2.50000	+	4.33013i	0.107187	+	0.185653i
$545$	3.12311			0.133779
$546$		0			0
$547$	−22.7386			−0.972234			−0.486117	−	0.873894i	$-0.661587\pi$
$547$	−22.7386			−0.972234			−0.486117	+	0.873894i	$0.661587\pi$
$548$	−2.90388	−	5.02967i	−0.124048	−	0.214857i
$549$		0			0
$550$	−9.84233	+	17.0474i	−0.419678	+	0.726904i
$551$	7.68466			0.327377
$552$		0			0
$553$	0.719224	−	1.24573i	0.0305845	−	0.0529739i
$554$	3.56155			0.151316
$555$		0			0
$556$	3.84233	+	6.65511i	0.162951	+	0.282240i
$557$	10.8693	+	18.8262i	0.460548	+	0.797692i	0.998988	−	0.0449714i	$-0.0143197\pi$
$557$	10.8693	+	18.8262i	0.460548	+	0.797692i	−0.538441	+	0.842664i	$0.680986\pi$
$558$		0			0
$559$	8.17708	+	6.38202i	0.345854	+	0.269930i
$560$	−3.56155			−0.150503
$561$		0			0
$562$	−3.90388	−	6.76172i	−0.164675	−	0.285226i
$563$	−0.315342	+	0.546188i	−0.0132901	+	0.0230191i	−0.872594	−	0.488446i	$-0.837564\pi$
$563$	−0.315342	+	0.546188i	−0.0132901	+	0.0230191i	0.859304	+	0.511465i	$0.170897\pi$
$564$		0			0
$565$	30.1501	−	52.2215i	1.26842	−	2.19697i
$566$	4.24621	−	7.35465i	0.178482	−	0.309139i
$567$		0			0
$568$	2.00000	−	3.46410i	0.0839181	−	0.145350i
$569$	5.80776	+	10.0593i	0.243474	+	0.421710i	0.961702	−	0.274099i	$-0.0883796\pi$
$569$	5.80776	+	10.0593i	0.243474	+	0.421710i	−0.718227	+	0.695808i	$0.755046\pi$
$570$		0			0
$571$	13.7538			0.575578			0.287789	−	0.957694i	$-0.407080\pi$
$571$	13.7538			0.575578			0.287789	+	0.957694i	$0.407080\pi$
$572$	1.28078	−	9.14657i	0.0535520	−	0.382437i
$573$		0			0
$574$	2.06155	+	3.57071i	0.0860476	+	0.149039i
$575$	−35.0540	−	60.7153i	−1.46185	−	2.53200i
$576$		0			0
$577$	31.3153			1.30367			0.651837	−	0.758359i	$-0.273998\pi$
$577$	31.3153			1.30367			0.651837	+	0.758359i	$0.273998\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$		0			0
$580$	3.56155			0.147885
$581$	5.12311	−	8.87348i	0.212542	−	0.368134i
$582$		0			0
$583$	4.96543	+	8.60039i	0.205647	+	0.356192i
$584$	2.43845			0.100904
$585$		0			0
$586$	−4.68466			−0.193521
$587$	15.6847	+	27.1666i	0.647375	+	1.12129i	0.983747	+	0.179558i	$0.0574666\pi$
$587$	15.6847	+	27.1666i	0.647375	+	1.12129i	−0.336372	+	0.941729i	$0.609200\pi$
$588$		0			0
$589$	−19.6847	+	34.0948i	−0.811092	+	1.40485i
$590$	46.7386			1.92420
$591$		0			0
$592$	4.90388	−	8.49377i	0.201548	−	0.349092i
$593$	−32.6155			−1.33936			−0.669680	−	0.742650i	$-0.733569\pi$
$593$	−32.6155			−1.33936			−0.669680	+	0.742650i	$0.733569\pi$
$594$		0			0
$595$	8.90388	+	15.4220i	0.365024	+	0.632239i
$596$	−8.90388	−	15.4220i	−0.364717	−	0.631709i
$597$		0			0
$598$	25.9309	+	20.2384i	1.06039	+	0.827611i
$599$	22.8769			0.934725			0.467362	−	0.884066i	$-0.345204\pi$
$599$	22.8769			0.934725			0.467362	+	0.884066i	$0.345204\pi$
$600$		0			0
$601$	−18.4654	−	31.9831i	−0.753221	−	1.30462i	−0.946254	−	0.323424i	$-0.895166\pi$
$601$	−18.4654	−	31.9831i	−0.753221	−	1.30462i	0.193033	−	0.981192i	$-0.438167\pi$
$602$	1.43845	−	2.49146i	0.0586267	−	0.101544i
$603$		0			0
$604$	8.71922	−	15.1021i	0.354780	−	0.614497i
$605$	7.90388	−	13.6899i	0.321339	−	0.556575i
$606$		0			0
$607$	−10.5616	+	18.2931i	−0.428680	+	0.742496i	−0.996756	−	0.0804802i	$-0.974355\pi$
$607$	−10.5616	+	18.2931i	−0.428680	+	0.742496i	0.568076	+	0.822976i	$0.307688\pi$
$608$	3.84233	+	6.65511i	0.155827	+	0.269900i
$609$		0			0
$610$	3.56155			0.144203
$611$	−3.84233	+	27.4397i	−0.155444	+	1.11009i
$612$		0			0
$613$	−18.1501	−	31.4369i	−0.733075	−	1.26972i	−0.955563	−	0.294788i	$-0.904751\pi$
$613$	−18.1501	−	31.4369i	−0.733075	−	1.26972i	0.222487	−	0.974936i	$-0.428582\pi$
$614$	−16.9654	−	29.3850i	−0.684669	−	1.18588i
$615$		0			0
$616$	−2.56155			−0.103208
$617$	−13.7116	+	23.7493i	−0.552010	+	0.956110i	0.446119	+	0.894973i	$0.352806\pi$
$617$	−13.7116	+	23.7493i	−0.552010	+	0.956110i	−0.998129	+	0.0611360i	$0.980528\pi$
$618$		0			0
$619$	4.31534			0.173448			0.0867241	−	0.996232i	$-0.472360\pi$
$619$	4.31534			0.173448			0.0867241	+	0.996232i	$0.472360\pi$
$620$	−9.12311	+	15.8017i	−0.366393	+	0.634611i
$621$		0			0
$622$	−11.2808	−	19.5389i	−0.452318	−	0.783438i
$623$	−9.68466			−0.388008
$624$		0			0
$625$	−4.36932			−0.174773
$626$	13.8078	+	23.9157i	0.551869	+	0.955866i
$627$		0			0
$628$	2.90388	−	5.02967i	0.115878	−	0.200706i
$629$	−49.0388			−1.95531
$630$		0			0
$631$	−11.5961	+	20.0851i	−0.461634	+	0.799574i	−0.999043	−	0.0437483i	$-0.986070\pi$
$631$	−11.5961	+	20.0851i	−0.461634	+	0.799574i	0.537408	+	0.843322i	$0.319403\pi$
$632$	−1.43845			−0.0572184
$633$		0			0
$634$	5.78078	+	10.0126i	0.229584	+	0.397651i
$635$	−4.00000	−	6.92820i	−0.158735	−	0.274937i
$636$		0			0
$637$	3.34233	−	1.35234i	0.132428	−	0.0535818i
$638$	2.56155			0.101413
$639$		0			0
$640$	1.78078	+	3.08440i	0.0703914	+	0.121921i
$641$	18.4654	−	31.9831i	0.729341	−	1.26326i	−0.227821	−	0.973703i	$-0.573160\pi$
$641$	18.4654	−	31.9831i	0.729341	−	1.26326i	0.957162	−	0.289552i	$-0.0935065\pi$
$642$		0			0
$643$	13.2808	−	23.0030i	0.523743	−	0.907149i	−0.475875	−	0.879513i	$-0.657869\pi$
$643$	13.2808	−	23.0030i	0.523743	−	0.907149i	0.999618	−	0.0276362i	$-0.00879800\pi$
$644$	4.56155	−	7.90084i	0.179750	−	0.311337i
$645$		0			0
$646$	19.2116	−	33.2755i	0.755872	−	1.30921i
$647$	−10.4039	−	18.0201i	−0.409019	−	0.708441i	0.585761	−	0.810484i	$-0.300796\pi$
$647$	−10.4039	−	18.0201i	−0.409019	−	0.708441i	−0.994780	+	0.102042i	$0.967462\pi$
$648$		0			0
$649$	33.6155			1.31952
$650$	−25.6847	+	10.3923i	−1.00744	+	0.407620i
$651$		0			0
$652$	0.561553	+	0.972638i	0.0219921	+	0.0380914i
$653$	−9.40388	−	16.2880i	−0.368002	−	0.637399i	0.621251	−	0.783612i	$-0.286625\pi$
$653$	−9.40388	−	16.2880i	−0.368002	−	0.637399i	−0.989253	+	0.146213i	$0.953291\pi$
$654$		0			0
$655$	58.7386			2.29511
$656$	2.06155	−	3.57071i	0.0804901	−	0.139413i
$657$		0			0
$658$	7.68466			0.299579
$659$	−14.1577	+	24.5218i	−0.551505	+	0.955234i	0.446662	+	0.894703i	$0.352613\pi$
$659$	−14.1577	+	24.5218i	−0.551505	+	0.955234i	−0.998166	+	0.0605310i	$0.980721\pi$
$660$		0			0
$661$	4.90388	+	8.49377i	0.190739	+	0.330369i	0.945495	−	0.325636i	$-0.105578\pi$
$661$	4.90388	+	8.49377i	0.190739	+	0.330369i	−0.754756	+	0.656005i	$0.772245\pi$
$662$	35.3693			1.37467
$663$		0			0
$664$	−10.2462			−0.397630
$665$	13.6847	+	23.7025i	0.530668	+	0.919144i
$666$		0			0
$667$	−4.56155	+	7.90084i	−0.176624	+	0.305922i
$668$	−20.4924			−0.792876
$669$		0			0
$670$	2.00000	−	3.46410i	0.0772667	−	0.133830i
$671$	2.56155			0.0988876
$672$		0			0
$673$	−4.37689	−	7.58100i	−0.168717	−	0.292226i	0.769252	−	0.638945i	$-0.220629\pi$
$673$	−4.37689	−	7.58100i	−0.168717	−	0.292226i	−0.937969	+	0.346719i	$0.887296\pi$
$674$	−14.7462	−	25.5412i	−0.568003	−	0.983810i
$675$		0			0
$676$	9.34233	−	9.03996i	0.359320	−	0.347691i
$677$	8.38447			0.322241			0.161121	−	0.986935i	$-0.448489\pi$
$677$	8.38447			0.322241			0.161121	+	0.986935i	$0.448489\pi$
$678$		0			0
$679$	6.12311	+	10.6055i	0.234983	+	0.407003i
$680$	8.90388	−	15.4220i	0.341448	−	0.591406i
$681$		0			0
$682$	−6.56155	+	11.3649i	−0.251255	+	0.435186i
$683$	2.00000	−	3.46410i	0.0765279	−	0.132550i	−0.825222	−	0.564809i	$-0.808950\pi$
$683$	2.00000	−	3.46410i	0.0765279	−	0.132550i	0.901750	+	0.432259i	$0.142283\pi$
$684$		0			0
$685$	−10.3423	+	17.9134i	−0.395160	+	0.684437i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$		0			0
$688$	−2.87689			−0.109681
$689$	−1.93845	+	13.8433i	−0.0738490	+	0.527387i
$690$		0			0
$691$	14.2462	+	24.6752i	0.541951	+	0.938687i	0.998792	+	0.0491388i	$0.0156477\pi$
$691$	14.2462	+	24.6752i	0.541951	+	0.938687i	−0.456841	+	0.889549i	$0.651019\pi$
$692$	−2.43845	−	4.22351i	−0.0926959	−	0.160554i
$693$		0			0
$694$	−0.315342			−0.0119702
$695$	13.6847	−	23.7025i	0.519089	−	0.899088i
$696$		0			0
$697$	−20.6155			−0.780869
$698$	−3.24621	+	5.62260i	−0.122871	+	0.212819i
$699$		0			0
$700$	3.84233	+	6.65511i	0.145226	+	0.251539i
$701$	−9.05398			−0.341964			−0.170982	−	0.985274i	$-0.554694\pi$
$701$	−9.05398			−0.341964			−0.170982	+	0.985274i	$0.554694\pi$
$702$		0			0
$703$	−75.3693			−2.84261
$704$	1.28078	+	2.21837i	0.0482711	+	0.0836080i
$705$		0			0
$706$	4.90388	−	8.49377i	0.184560	−	0.319667i
$707$	−19.5616			−0.735688
$708$		0			0
$709$	−10.1501	+	17.5805i	−0.381195	+	0.660249i	−0.991233	−	0.132123i	$-0.957821\pi$
$709$	−10.1501	+	17.5805i	−0.381195	+	0.660249i	0.610039	+	0.792372i	$0.291154\pi$
$710$	−14.2462			−0.534651
$711$		0			0
$712$	4.84233	+	8.38716i	0.181474	+	0.314322i
$713$	−23.3693	−	40.4768i	−0.875188	−	1.51587i
$714$		0			0
$715$	−30.4924	+	12.3376i	−1.14035	+	0.461399i
$716$	16.4924			0.616351
$717$		0			0
$718$	2.31534	+	4.01029i	0.0864078	+	0.149663i
$719$	10.9654	−	18.9927i	0.408942	−	0.708308i	−0.585830	−	0.810434i	$-0.699231\pi$
$719$	10.9654	−	18.9927i	0.408942	−	0.708308i	0.994771	+	0.102126i	$0.0325646\pi$
$720$		0			0
$721$	−5.68466	+	9.84612i	−0.211708	+	0.366689i
$722$	20.0270	−	34.6878i	0.745327	−	1.29094i
$723$		0			0
$724$	−6.62311	+	11.4716i	−0.246146	+	0.426337i
$725$	−3.84233	−	6.65511i	−0.142701	−	0.247165i
$726$		0			0
$727$	50.2462			1.86353			0.931764	−	0.363063i	$-0.118269\pi$
$727$	50.2462			1.86353			0.931764	+	0.363063i	$0.118269\pi$
$728$	−2.84233	−	2.21837i	−0.105344	−	0.0822183i
$729$		0			0
$730$	−4.34233	−	7.52113i	−0.160717	−	0.278370i
$731$	7.19224	+	12.4573i	0.266014	+	0.460751i
$732$		0			0
$733$	32.6155			1.20468			0.602341	−	0.798239i	$-0.294235\pi$
$733$	32.6155			1.20468			0.602341	+	0.798239i	$0.294235\pi$
$734$	5.68466	−	9.84612i	0.209825	−	0.363427i
$735$		0			0
$736$	−9.12311			−0.336282
$737$	1.43845	−	2.49146i	0.0529859	−	0.0917742i
$738$		0			0
$739$	−23.6847	−	41.0230i	−0.871254	−	1.50906i	−0.860700	−	0.509112i	$-0.829974\pi$
$739$	−23.6847	−	41.0230i	−0.871254	−	1.50906i	−0.0105542	−	0.999944i	$-0.503360\pi$
$740$	−34.9309			−1.28408
$741$		0			0
$742$	3.87689			0.142325
$743$	4.31534	+	7.47439i	0.158315	+	0.274209i	0.934261	−	0.356590i	$-0.116061\pi$
$743$	4.31534	+	7.47439i	0.158315	+	0.274209i	−0.775946	+	0.630799i	$0.782727\pi$
$744$		0			0
$745$	−31.7116	+	54.9262i	−1.16182	+	2.01234i
$746$	−21.5616			−0.789425
$747$		0			0
$748$	6.40388	−	11.0918i	0.234149	−	0.405558i
$749$	−9.43845			−0.344873
$750$		0			0
$751$	0.403882	+	0.699544i	0.0147379	+	0.0255267i	0.873300	−	0.487182i	$-0.161975\pi$
$751$	0.403882	+	0.699544i	0.0147379	+	0.0255267i	−0.858562	+	0.512709i	$0.828642\pi$
$752$	−3.84233	−	6.65511i	−0.140115	−	0.242687i
$753$		0			0
$754$	2.84233	+	2.21837i	0.103512	+	0.0807883i
$755$	−62.1080			−2.26034
$756$		0			0
$757$	3.56155	+	6.16879i	0.129447	+	0.224209i	0.923462	−	0.383689i	$-0.125347\pi$
$757$	3.56155	+	6.16879i	0.129447	+	0.224209i	−0.794016	+	0.607897i	$0.792013\pi$
$758$	0.246211	−	0.426450i	0.00894280	−	0.0154894i
$759$		0			0
$760$	13.6847	−	23.7025i	0.496395	−	0.859781i
$761$	−21.2462	+	36.7995i	−0.770175	+	1.33398i	0.167292	+	0.985907i	$0.446498\pi$
$761$	−21.2462	+	36.7995i	−0.770175	+	1.33398i	−0.937467	+	0.348074i	$0.886836\pi$
$762$		0			0
$763$	0.438447	−	0.759413i	0.0158729	−	0.0274926i
$764$	2.87689	+	4.98293i	0.104082	+	0.180276i
$765$		0			0
$766$	8.31534			0.300446
$767$	37.3002	+	29.1119i	1.34683	+	1.05117i
$768$		0			0
$769$	11.4924	+	19.9055i	0.414427	+	0.717809i	0.995368	−	0.0961366i	$-0.0306486\pi$
$769$	11.4924	+	19.9055i	0.414427	+	0.717809i	−0.580941	+	0.813946i	$0.697315\pi$
$770$	4.56155	+	7.90084i	0.164387	+	0.284727i
$771$		0			0
$772$	−20.3693			−0.733108
$773$	13.2462	−	22.9431i	0.476433	−	0.825206i	−0.523202	−	0.852209i	$-0.675263\pi$
$773$	13.2462	−	22.9431i	0.476433	−	0.825206i	0.999635	+	0.0270022i	$0.00859611\pi$
$774$		0			0
$775$	39.3693			1.41419
$776$	6.12311	−	10.6055i	0.219807	−	0.380716i
$777$		0			0
$778$	−9.34233	−	16.1814i	−0.334939	−	0.580131i
$779$	−31.6847			−1.13522
$780$		0			0
$781$	−10.2462			−0.366638
$782$	22.8078	+	39.5042i	0.815604	+	1.41267i
$783$		0			0
$784$	−0.500000	+	0.866025i	−0.0178571	+	0.0309295i
$785$	−20.6847			−0.738267
$786$		0			0
$787$	−0.403882	+	0.699544i	−0.0143968	+	0.0249361i	−0.873134	−	0.487480i	$-0.837916\pi$
$787$	−0.403882	+	0.699544i	−0.0143968	+	0.0249361i	0.858737	+	0.512416i	$0.171249\pi$
$788$	0.561553			0.0200045
$789$		0			0
$790$	2.56155	+	4.43674i	0.0911360	+	0.157852i
$791$	−8.46543	−	14.6626i	−0.300996	−	0.521341i
$792$		0			0
$793$	2.84233	+	2.21837i	0.100934	+	0.0787766i
$794$	−1.68466			−0.0597863
$795$		0			0
$796$	8.80776	+	15.2555i	0.312183	+	0.540717i
$797$	−12.0540	+	20.8781i	−0.426974	+	0.739540i	−0.996602	−	0.0823619i	$-0.973754\pi$
$797$	−12.0540	+	20.8781i	−0.426974	+	0.739540i	0.569629	+	0.821902i	$0.307087\pi$
$798$		0			0
$799$	−19.2116	+	33.2755i	−0.679659	+	1.17720i
$800$	3.84233	−	6.65511i	0.135847	−	0.235294i
$801$		0			0
$802$	−7.58854	+	13.1437i	−0.267961	+	0.464122i
$803$	−3.12311	−	5.40938i	−0.110212	−	0.190893i
$804$		0			0
$805$	−32.4924			−1.14521
$806$	−17.1231	+	6.92820i	−0.603136	+	0.244036i
$807$		0			0
$808$	9.78078	+	16.9408i	0.344087	+	0.595975i
$809$	−5.46543	−	9.46641i	−0.192154	−	0.332821i	0.753810	−	0.657093i	$-0.228214\pi$
$809$	−5.46543	−	9.46641i	−0.192154	−	0.332821i	−0.945964	+	0.324272i	$0.894881\pi$
$810$		0			0
$811$	5.75379			0.202043			0.101021	−	0.994884i	$-0.467789\pi$
$811$	5.75379			0.202043			0.101021	+	0.994884i	$0.467789\pi$
$812$	0.500000	−	0.866025i	0.0175466	−	0.0303915i
$813$		0			0
$814$	−25.1231			−0.880564
$815$	2.00000	−	3.46410i	0.0700569	−	0.121342i
$816$		0			0
$817$	11.0540	+	19.1460i	0.386730	+	0.669835i
$818$	30.4384			1.06426
$819$		0			0
$820$	−14.6847			−0.512811
$821$	−6.03457	−	10.4522i	−0.210608	−	0.364783i	0.741297	−	0.671177i	$-0.234211\pi$
$821$	−6.03457	−	10.4522i	−0.210608	−	0.364783i	−0.951905	+	0.306394i	$0.900878\pi$
$822$		0			0
$823$	−7.12311	+	12.3376i	−0.248296	+	0.430061i	−0.963053	−	0.269312i	$-0.913204\pi$
$823$	−7.12311	+	12.3376i	−0.248296	+	0.430061i	0.714757	+	0.699373i	$0.246537\pi$
$824$	11.3693			0.396069
$825$		0			0
$826$	6.56155	−	11.3649i	0.228306	−	0.395437i
$827$	11.5076			0.400158			0.200079	−	0.979780i	$-0.435880\pi$
$827$	11.5076			0.400158			0.200079	+	0.979780i	$0.435880\pi$
$828$		0			0
$829$	−14.5540	−	25.2082i	−0.505480	−	0.875518i	−0.999980	−	0.00633989i	$-0.997982\pi$
$829$	−14.5540	−	25.2082i	−0.505480	−	0.875518i	0.494499	−	0.869178i	$-0.335351\pi$
$830$	18.2462	+	31.6034i	0.633335	+	1.09697i
$831$		0			0
$832$	−0.500000	+	3.57071i	−0.0173344	+	0.123792i
$833$	5.00000			0.173240
$834$		0			0
$835$	36.4924	+	63.2067i	1.26287	+	2.18736i
$836$	9.84233	−	17.0474i	0.340404	−	0.589597i
$837$		0			0
$838$	−11.3693	+	19.6922i	−0.392747	+	0.680257i
$839$	4.00000	−	6.92820i	0.138095	−	0.239188i	−0.788680	−	0.614804i	$-0.789235\pi$
$839$	4.00000	−	6.92820i	0.138095	−	0.239188i	0.926776	+	0.375615i	$0.122569\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	4.21922	+	7.30791i	0.145404	+	0.251847i
$843$		0			0
$844$	−2.87689			−0.0990268
$845$	−44.5194	−	12.7173i	−1.53151	−	0.437488i
$846$		0			0
$847$	−2.21922	−	3.84381i	−0.0762534	−	0.132075i
$848$	−1.93845	−	3.35749i	−0.0665665	−	0.115297i
$849$		0			0
$850$	−38.4233			−1.31791
$851$	44.7386	−	77.4896i	1.53362	−	2.65631i
$852$		0			0
$853$	−0.369317			−0.0126452			−0.00632258	−	0.999980i	$-0.502013\pi$
$853$	−0.369317			−0.0126452			−0.00632258	+	0.999980i	$0.502013\pi$
$854$	0.500000	−	0.866025i	0.0171096	−	0.0296348i
$855$		0			0
$856$	4.71922	+	8.17394i	0.161300	+	0.279379i
$857$	22.3002			0.761760			0.380880	−	0.924625i	$-0.375621\pi$
$857$	22.3002			0.761760			0.380880	+	0.924625i	$0.375621\pi$
$858$		0			0
$859$	−36.8078			−1.25586			−0.627932	−	0.778268i	$-0.716099\pi$
$859$	−36.8078			−1.25586			−0.627932	+	0.778268i	$0.716099\pi$
$860$	5.12311	+	8.87348i	0.174696	+	0.302583i
$861$		0			0
$862$	9.36932	−	16.2281i	0.319120	−	0.552732i
$863$	−26.1080			−0.888725			−0.444362	−	0.895847i	$-0.646570\pi$
$863$	−26.1080			−0.888725			−0.444362	+	0.895847i	$0.646570\pi$
$864$		0			0
$865$	−8.68466	+	15.0423i	−0.295287	+	0.511453i
$866$	5.31534			0.180623
$867$		0			0
$868$	2.56155	+	4.43674i	0.0869448	+	0.150593i
$869$	1.84233	+	3.19101i	0.0624967	+	0.108248i
$870$		0			0
$871$	3.75379	−	1.51883i	0.127192	−	0.0514634i
$872$	−0.876894			−0.0296954
$873$		0			0
$874$	35.0540	+	60.7153i	1.18572	+	2.05372i
$875$	4.78078	−	8.28055i	0.161620	−	0.279934i
$876$		0			0
$877$	−4.15009	+	7.18817i	−0.140139	+	0.242727i	−0.927549	−	0.373702i	$-0.878088\pi$
$877$	−4.15009	+	7.18817i	−0.140139	+	0.242727i	0.787410	+	0.616430i	$0.211422\pi$
$878$	−14.2462	+	24.6752i	−0.480786	+	0.832746i
$879$		0			0
$880$	4.56155	−	7.90084i	0.153770	−	0.266337i
$881$	23.5885	+	40.8566i	0.794718	+	1.37649i	0.923018	+	0.384757i	$0.125715\pi$
$881$	23.5885	+	40.8566i	0.794718	+	1.37649i	−0.128300	+	0.991735i	$0.540952\pi$
$882$		0			0
$883$	17.1231			0.576238			0.288119	−	0.957595i	$-0.406970\pi$
$883$	17.1231			0.576238			0.288119	+	0.957595i	$0.406970\pi$
$884$	16.7116	−	6.76172i	0.562073	−	0.227421i
$885$		0			0
$886$	17.2116	+	29.8114i	0.578237	+	1.00154i
$887$	2.71922	+	4.70983i	0.0913026	+	0.158141i	0.908059	−	0.418841i	$-0.137564\pi$
$887$	2.71922	+	4.70983i	0.0913026	+	0.158141i	−0.816757	+	0.576982i	$0.804230\pi$
$888$		0			0
$889$	−2.24621			−0.0753355
$890$	17.2462	−	29.8713i	0.578094	−	1.00129i
$891$		0			0
$892$	−16.4924			−0.552207
$893$	−29.5270	+	51.1422i	−0.988083	+	1.71141i
$894$		0			0
$895$	−29.3693	−	50.8691i	−0.981708	−	1.70037i
$896$	1.00000			0.0334077
$897$		0			0
$898$	18.0000			0.600668
$899$	−2.56155	−	4.43674i	−0.0854326	−	0.147974i
$900$		0			0
$901$	−9.69224	+	16.7874i	−0.322895	+	0.559271i
$902$	−10.5616			−0.351661
$903$		0			0
$904$	−8.46543	+	14.6626i	−0.281556	+	0.487670i
$905$	47.1771			1.56822
$906$		0			0
$907$	−11.4384	−	19.8120i	−0.379807	−	0.657846i	0.611227	−	0.791456i	$-0.290676\pi$
$907$	−11.4384	−	19.8120i	−0.379807	−	0.657846i	−0.991034	+	0.133610i	$0.957343\pi$
$908$	6.56155	+	11.3649i	0.217753	+	0.377159i
$909$		0			0
$910$	−1.78078	+	12.7173i	−0.0590322	+	0.421574i
$911$	5.26137			0.174317			0.0871584	−	0.996194i	$-0.472221\pi$
$911$	5.26137			0.174317			0.0871584	+	0.996194i	$0.472221\pi$
$912$		0			0
$913$	13.1231	+	22.7299i	0.434311	+	0.752249i
$914$	−6.65767	+	11.5314i	−0.220216	+	0.381426i
$915$		0			0
$916$	−11.4039	+	19.7521i	−0.376795	+	0.652628i
$917$	8.24621	−	14.2829i	0.272314	−	0.471661i
$918$		0			0
$919$	−3.28078	+	5.68247i	−0.108223	+	0.187447i	−0.915050	−	0.403340i	$-0.867849\pi$
$919$	−3.28078	+	5.68247i	−0.108223	+	0.187447i	0.806828	+	0.590787i	$0.201183\pi$
$920$	16.2462	+	28.1393i	0.535622	+	0.927724i
$921$		0			0
$922$	30.0540			0.989775
$923$	−11.3693	−	8.87348i	−0.374226	−	0.292074i
$924$		0			0
$925$	37.6847	+	65.2717i	1.23906	+	2.14612i
$926$	−5.84233	−	10.1192i	−0.191991	−	0.332538i
$927$		0			0
$928$	−1.00000			−0.0328266
$929$	−3.30776	+	5.72922i	−0.108524	+	0.187969i	−0.915173	−	0.403062i	$-0.867946\pi$
$929$	−3.30776	+	5.72922i	−0.108524	+	0.187969i	0.806648	+	0.591032i	$0.201279\pi$
$930$		0			0
$931$	7.68466			0.251855
$932$	−3.00000	+	5.19615i	−0.0982683	+	0.170206i
$933$		0			0
$934$	−14.0000	−	24.2487i	−0.458094	−	0.793442i
$935$	−45.6155			−1.49179
$936$		0			0
$937$	13.5616			0.443037			0.221518	−	0.975156i	$-0.428899\pi$
$937$	13.5616			0.443037			0.221518	+	0.975156i	$0.428899\pi$
$938$	−0.561553	−	0.972638i	−0.0183353	−	0.0317578i
$939$		0			0
$940$	−13.6847	+	23.7025i	−0.446344	+	0.773091i
$941$	−53.3693			−1.73979			−0.869895	−	0.493237i	$-0.835814\pi$
$941$	−53.3693			−1.73979			−0.869895	+	0.493237i	$0.835814\pi$
$942$		0			0
$943$	18.8078	−	32.5760i	0.612465	−	1.06082i
$944$	−13.1231			−0.427121
$945$		0			0
$946$	3.68466	+	6.38202i	0.119799	+	0.207497i
$947$	−0.157671	−	0.273094i	−0.00512361	−	0.00887436i	0.863452	−	0.504431i	$-0.168298\pi$
$947$	−0.157671	−	0.273094i	−0.00512361	−	0.00887436i	−0.868576	+	0.495556i	$0.834964\pi$
$948$		0			0
$949$	1.21922	−	8.70700i	0.0395777	−	0.282641i
$950$	−59.0540			−1.91596
$951$		0			0
$952$	−2.50000	−	4.33013i	−0.0810255	−	0.140340i
$953$	−26.3693	+	45.6730i	−0.854186	+	1.47949i	0.0232122	+	0.999731i	$0.492611\pi$
$953$	−26.3693	+	45.6730i	−0.854186	+	1.47949i	−0.877398	+	0.479763i	$0.840723\pi$
$954$		0			0
$955$	10.2462	−	17.7470i	0.331560	−	0.574278i
$956$	2.00000	−	3.46410i	0.0646846	−	0.112037i
$957$		0			0
$958$	1.28078	−	2.21837i	0.0413800	−	0.0716723i
$959$	2.90388	+	5.02967i	0.0937712	+	0.162417i
$960$		0			0
$961$	−4.75379			−0.153348
$962$	−27.8769	−	21.7572i	−0.898787	−	0.701482i
$963$		0			0
$964$	−5.65767	−	9.79937i	−0.182221	−	0.315617i
$965$	36.2732	+	62.8270i	1.16768	+	2.02247i
$966$		0			0
$967$	−4.49242			−0.144467			−0.0722333	−	0.997388i	$-0.523013\pi$
$967$	−4.49242			−0.144467			−0.0722333	+	0.997388i	$0.523013\pi$
$968$	−2.21922	+	3.84381i	−0.0713285	+	0.123545i
$969$		0			0
$970$	−43.6155			−1.40041
$971$	−5.43845	+	9.41967i	−0.174528	+	0.302291i	−0.939998	−	0.341180i	$-0.889173\pi$
$971$	−5.43845	+	9.41967i	−0.174528	+	0.302291i	0.765470	+	0.643472i	$0.222507\pi$
$972$		0			0
$973$	−3.84233	−	6.65511i	−0.123179	−	0.213353i
$974$	−23.6847			−0.758905
$975$		0			0
$976$	−1.00000			−0.0320092
$977$	1.02699	+	1.77879i	0.0328562	+	0.0569087i	0.881986	−	0.471276i	$-0.156206\pi$
$977$	1.02699	+	1.77879i	0.0328562	+	0.0569087i	−0.849130	+	0.528184i	$0.822873\pi$
$978$		0			0
$979$	12.4039	−	21.4842i	0.396430	−	0.686637i
$980$	3.56155			0.113770
$981$		0			0
$982$	0.876894	−	1.51883i	0.0279828	−	0.0484677i
$983$	−55.2311			−1.76160			−0.880799	−	0.473491i	$-0.842994\pi$
$983$	−55.2311			−1.76160			−0.880799	+	0.473491i	$0.842994\pi$
$984$		0			0
$985$	−1.00000	−	1.73205i	−0.0318626	−	0.0551877i
$986$	2.50000	+	4.33013i	0.0796162	+	0.137899i
$987$		0			0
$988$	25.6847	−	10.3923i	0.817138	−	0.330623i
$989$	−26.2462			−0.834581
$990$		0			0
$991$	0.719224	+	1.24573i	0.0228469	+	0.0395720i	0.877223	−	0.480084i	$-0.159394\pi$
$991$	0.719224	+	1.24573i	0.0228469	+	0.0395720i	−0.854376	+	0.519655i	$0.826060\pi$
$992$	2.56155	−	4.43674i	0.0813294	−	0.140867i
$993$		0			0
$994$	−2.00000	+	3.46410i	−0.0634361	+	0.109875i
$995$	31.3693	−	54.3333i	0.994474	−	1.72248i
$996$		0			0
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	−0.699457	−	0.714675i	$-0.746575\pi$
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	0.968655	+	0.248410i	$0.0799082\pi$
$998$	−13.6847	−	23.7025i	−0.433180	−	0.750290i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.r.z.757.2		4
3.2	odd	2		546.2.l.i.211.1	✓	4
13.9	even	3	inner	1638.2.r.z.1387.2		4
39.23	odd	6		7098.2.a.bq.1.2		2
39.29	odd	6		7098.2.a.bw.1.1		2
39.35	odd	6		546.2.l.i.295.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.i.211.1	✓	4	3.2	odd	2
546.2.l.i.295.1	yes	4	39.35	odd	6
1638.2.r.z.757.2		4	1.1	even	1	trivial
1638.2.r.z.1387.2		4	13.9	even	3	inner
7098.2.a.bq.1.2		2	39.23	odd	6
7098.2.a.bw.1.1		2	39.29	odd	6

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.56155 q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.56155 q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.78078 + 3.08440i) q^{10} +(1.28078 + 2.21837i) q^{11} +(-0.500000 + 3.57071i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 + 4.33013i) q^{17} +(-3.84233 + 6.65511i) q^{19} +(-1.78078 + 3.08440i) q^{20} +(-1.28078 + 2.21837i) q^{22} +(-4.56155 - 7.90084i) q^{23} +7.68466 q^{25} +(-3.34233 + 1.35234i) q^{26} +(0.500000 + 0.866025i) q^{28} +(-0.500000 - 0.866025i) q^{29} +5.12311 q^{31} +(0.500000 - 0.866025i) q^{32} -5.00000 q^{34} +(1.78078 - 3.08440i) q^{35} +(4.90388 + 8.49377i) q^{37} -7.68466 q^{38} -3.56155 q^{40} +(2.06155 + 3.57071i) q^{41} +(1.43845 - 2.49146i) q^{43} -2.56155 q^{44} +(4.56155 - 7.90084i) q^{46} +7.68466 q^{47} +(-0.500000 - 0.866025i) q^{49} +(3.84233 + 6.65511i) q^{50} +(-2.84233 - 2.21837i) q^{52} +3.87689 q^{53} +(4.56155 + 7.90084i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(0.500000 - 0.866025i) q^{58} +(6.56155 - 11.3649i) q^{59} +(0.500000 - 0.866025i) q^{61} +(2.56155 + 4.43674i) q^{62} +1.00000 q^{64} +(-1.78078 + 12.7173i) q^{65} +(-0.561553 - 0.972638i) q^{67} +(-2.50000 - 4.33013i) q^{68} +3.56155 q^{70} +(-2.00000 + 3.46410i) q^{71} -2.43845 q^{73} +(-4.90388 + 8.49377i) q^{74} +(-3.84233 - 6.65511i) q^{76} +2.56155 q^{77} +1.43845 q^{79} +(-1.78078 - 3.08440i) q^{80} +(-2.06155 + 3.57071i) q^{82} +10.2462 q^{83} +(-8.90388 + 15.4220i) q^{85} +2.87689 q^{86} +(-1.28078 - 2.21837i) q^{88} +(-4.84233 - 8.38716i) q^{89} +(2.84233 + 2.21837i) q^{91} +9.12311 q^{92} +(3.84233 + 6.65511i) q^{94} +(-13.6847 + 23.7025i) q^{95} +(-6.12311 + 10.6055i) q^{97} +(0.500000 - 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 6 q^{5} + 2 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 + 2 * q^7 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} + 6 q^{5} + 2 q^{7} - 4 q^{8} + 3 q^{10} + q^{11} - 2 q^{13} + 4 q^{14} - 2 q^{16} - 10 q^{17} - 3 q^{19} - 3 q^{20} - q^{22} - 10 q^{23} + 6 q^{25} - q^{26} + 2 q^{28} - 2 q^{29} + 4 q^{31} + 2 q^{32} - 20 q^{34} + 3 q^{35} - q^{37} - 6 q^{38} - 6 q^{40} + 14 q^{43} - 2 q^{44} + 10 q^{46} + 6 q^{47} - 2 q^{49} + 3 q^{50} + q^{52} + 32 q^{53} + 10 q^{55} - 2 q^{56} + 2 q^{58} + 18 q^{59} + 2 q^{61} + 2 q^{62} + 4 q^{64} - 3 q^{65} + 6 q^{67} - 10 q^{68} + 6 q^{70} - 8 q^{71} - 18 q^{73} + q^{74} - 3 q^{76} + 2 q^{77} + 14 q^{79} - 3 q^{80} + 8 q^{83} - 15 q^{85} + 28 q^{86} - q^{88} - 7 q^{89} - q^{91} + 20 q^{92} + 3 q^{94} - 30 q^{95} - 8 q^{97} + 2 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 + 2 * q^7 - 4 * q^8 + 3 * q^10 + q^11 - 2 * q^13 + 4 * q^14 - 2 * q^16 - 10 * q^17 - 3 * q^19 - 3 * q^20 - q^22 - 10 * q^23 + 6 * q^25 - q^26 + 2 * q^28 - 2 * q^29 + 4 * q^31 + 2 * q^32 - 20 * q^34 + 3 * q^35 - q^37 - 6 * q^38 - 6 * q^40 + 14 * q^43 - 2 * q^44 + 10 * q^46 + 6 * q^47 - 2 * q^49 + 3 * q^50 + q^52 + 32 * q^53 + 10 * q^55 - 2 * q^56 + 2 * q^58 + 18 * q^59 + 2 * q^61 + 2 * q^62 + 4 * q^64 - 3 * q^65 + 6 * q^67 - 10 * q^68 + 6 * q^70 - 8 * q^71 - 18 * q^73 + q^74 - 3 * q^76 + 2 * q^77 + 14 * q^79 - 3 * q^80 + 8 * q^83 - 15 * q^85 + 28 * q^86 - q^88 - 7 * q^89 - q^91 + 20 * q^92 + 3 * q^94 - 30 * q^95 - 8 * q^97 + 2 * q^98

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