LMFDB - Embedded newform 1638.2.bj.g.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

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, 5]))

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

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

chi := DirichletCharacter("1638.127");

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.bj (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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.4
Root			$0.500000 - 1.73154i$ of defining polynomial
Character	$\chi$	$=$	1638.127
Dual form			1638.2.bj.g.1135.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.71131i q^{5} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.71131i q^{5} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-1.85566 - 3.21409i) q^{10} +(5.00118 - 2.88743i) q^{11} +(2.87757 + 2.17246i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.106098 - 0.183768i) q^{17} +(1.85081 + 1.06857i) q^{19} +(-3.21409 - 1.85566i) q^{20} +(2.88743 - 5.00118i) q^{22} +(-1.23970 - 2.14722i) q^{23} -8.77384 q^{25} +(3.57828 + 0.442616i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(-0.0492830 - 0.0853606i) q^{29} -2.31076i q^{31} +(-0.866025 - 0.500000i) q^{32} -0.212197i q^{34} +(-1.85566 + 3.21409i) q^{35} +(6.81859 - 3.93672i) q^{37} +2.13714 q^{38} -3.71131 q^{40} +(-6.51354 + 3.76060i) q^{41} +(2.28987 - 3.96617i) q^{43} -5.77486i q^{44} +(-2.14722 - 1.23970i) q^{46} +9.15570i q^{47} +(0.500000 + 0.866025i) q^{49} +(-7.59837 + 4.38692i) q^{50} +(3.32019 - 1.40582i) q^{52} -12.0948 q^{53} +(-10.7162 - 18.5609i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-0.0853606 - 0.0492830i) q^{58} +(0.200843 + 0.115957i) q^{59} +(-4.01605 + 6.95601i) q^{61} +(-1.15538 - 2.00118i) q^{62} -1.00000 q^{64} +(8.06267 - 10.6796i) q^{65} +(-11.2323 + 6.48500i) q^{67} +(-0.106098 - 0.183768i) q^{68} +3.71131i q^{70} +(-6.37721 - 3.68188i) q^{71} -5.60414i q^{73} +(3.93672 - 6.81859i) q^{74} +(1.85081 - 1.06857i) q^{76} -5.77486 q^{77} -9.19749 q^{79} +(-3.21409 + 1.85566i) q^{80} +(-3.76060 + 6.51354i) q^{82} +3.17186i q^{83} +(-0.682021 - 0.393765i) q^{85} -4.57973i q^{86} +(-2.88743 - 5.00118i) q^{88} +(10.2335 - 5.90833i) q^{89} +(-1.40582 - 3.32019i) q^{91} -2.47940 q^{92} +(4.57785 + 7.92907i) q^{94} +(3.96579 - 6.86895i) q^{95} +(12.1952 + 7.04093i) q^{97} +(0.866025 + 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4}+O(q^{10}) $ 12 * q + 6 * q^4	$ 12 q + 6 q^{4} - 2 q^{10} + 18 q^{11} - 8 q^{13} - 12 q^{14} - 6 q^{16} - 4 q^{17} + 12 q^{19} - 2 q^{22} + 6 q^{23} - 24 q^{25} + 14 q^{26} + 10 q^{29} - 2 q^{35} - 6 q^{37} - 8 q^{38} - 4 q^{40} + 24 q^{41} + 26 q^{43} - 6 q^{46} + 6 q^{49} + 12 q^{50} - 4 q^{52} - 36 q^{53} - 6 q^{55} - 6 q^{56} + 24 q^{58} - 6 q^{59} - 28 q^{61} + 2 q^{62} - 12 q^{64} + 34 q^{65} - 42 q^{67} + 4 q^{68} - 48 q^{71} + 12 q^{76} + 4 q^{77} + 44 q^{79} + 6 q^{82} + 54 q^{85} + 2 q^{88} - 12 q^{89} - 16 q^{91} + 12 q^{92} + 8 q^{94} - 32 q^{95} + 60 q^{97}+O(q^{100}) $ 12 * q + 6 * q^4 - 2 * q^10 + 18 * q^11 - 8 * q^13 - 12 * q^14 - 6 * q^16 - 4 * q^17 + 12 * q^19 - 2 * q^22 + 6 * q^23 - 24 * q^25 + 14 * q^26 + 10 * q^29 - 2 * q^35 - 6 * q^37 - 8 * q^38 - 4 * q^40 + 24 * q^41 + 26 * q^43 - 6 * q^46 + 6 * q^49 + 12 * q^50 - 4 * q^52 - 36 * q^53 - 6 * q^55 - 6 * q^56 + 24 * q^58 - 6 * q^59 - 28 * q^61 + 2 * q^62 - 12 * q^64 + 34 * q^65 - 42 * q^67 + 4 * q^68 - 48 * q^71 + 12 * q^76 + 4 * q^77 + 44 * q^79 + 6 * q^82 + 54 * q^85 + 2 * q^88 - 12 * q^89 - 16 * q^91 + 12 * q^92 + 8 * q^94 - 32 * q^95 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	3.71131i		−	1.65975i	−0.557950	−	0.829875i	$-0.688412\pi$
$5$		−	3.71131i		−	1.65975i	0.557950	−	0.829875i	$-0.311588\pi$
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.85566	−	3.21409i	−0.586810	−	1.01638i
$11$	5.00118	−	2.88743i	1.50791	−	0.870594i	0.507955	−	0.861384i	$-0.330402\pi$
$11$	5.00118	−	2.88743i	1.50791	−	0.870594i	0.999958	−	0.00920984i	$-0.00293162\pi$
$12$		0			0
$13$	2.87757	+	2.17246i	0.798095	+	0.602531i
$13$	2.87757	+	2.17246i	0.798095	+	0.602531i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.106098	−	0.183768i	0.0257327	−	0.0445703i	−0.852872	−	0.522120i	$-0.825141\pi$
$17$	0.106098	−	0.183768i	0.0257327	−	0.0445703i	0.878605	+	0.477549i	$0.158475\pi$
$18$		0			0
$19$	1.85081	+	1.06857i	0.424606	+	0.245146i	0.697046	−	0.717026i	$-0.254497\pi$
$19$	1.85081	+	1.06857i	0.424606	+	0.245146i	−0.272440	+	0.962173i	$0.587831\pi$
$20$	−3.21409	−	1.85566i	−0.718693	−	0.414937i
$21$		0			0
$22$	2.88743	−	5.00118i	0.615603	−	1.06626i
$23$	−1.23970	−	2.14722i	−0.258495	−	0.447727i	0.707344	−	0.706870i	$-0.249893\pi$
$23$	−1.23970	−	2.14722i	−0.258495	−	0.447727i	−0.965839	+	0.259143i	$0.916560\pi$
$24$		0			0
$25$	−8.77384			−1.75477
$26$	3.57828	+	0.442616i	0.701759	+	0.0868041i
$27$		0			0
$28$	−0.866025	+	0.500000i	−0.163663	+	0.0944911i
$29$	−0.0492830	−	0.0853606i	−0.00915162	−	0.0158511i	0.861413	−	0.507905i	$-0.169580\pi$
$29$	−0.0492830	−	0.0853606i	−0.00915162	−	0.0158511i	−0.870565	+	0.492054i	$0.836246\pi$
$30$		0			0
$31$		−	2.31076i		−	0.415025i	−0.978232	−	0.207513i	$-0.933463\pi$
$31$		−	2.31076i		−	0.415025i	0.978232	−	0.207513i	$-0.0665368\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$		−	0.212197i		−	0.0363915i
$35$	−1.85566	+	3.21409i	−0.313663	+	0.543281i
$36$		0			0
$37$	6.81859	−	3.93672i	1.12097	−	0.647192i	0.179321	−	0.983791i	$-0.442610\pi$
$37$	6.81859	−	3.93672i	1.12097	−	0.647192i	0.941648	+	0.336599i	$0.109277\pi$
$38$	2.13714			0.346689
$39$		0			0
$40$	−3.71131			−0.586810
$41$	−6.51354	+	3.76060i	−1.01724	+	0.587306i	−0.913305	−	0.407277i	$-0.866478\pi$
$41$	−6.51354	+	3.76060i	−1.01724	+	0.587306i	−0.103940	+	0.994584i	$0.533145\pi$
$42$		0			0
$43$	2.28987	−	3.96617i	0.349201	−	0.604835i	−0.636906	−	0.770941i	$-0.719786\pi$
$43$	2.28987	−	3.96617i	0.349201	−	0.604835i	0.986108	+	0.166107i	$0.0531196\pi$
$44$		−	5.77486i		−	0.870594i
$45$		0			0
$46$	−2.14722	−	1.23970i	−0.316591	−	0.182784i
$47$			9.15570i			1.33550i	0.744388	+	0.667748i	$0.232742\pi$
$47$			9.15570i			1.33550i	−0.744388	+	0.667748i	$0.767258\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−7.59837	+	4.38692i	−1.07457	+	0.620404i
$51$		0			0
$52$	3.32019	−	1.40582i	0.460427	−	0.194953i
$53$	−12.0948			−1.66135			−0.830674	−	0.556759i	$-0.812045\pi$
$53$	−12.0948			−1.66135			−0.830674	+	0.556759i	$0.812045\pi$
$54$		0			0
$55$	−10.7162	−	18.5609i	−1.44497	−	2.50276i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		0			0
$58$	−0.0853606	−	0.0492830i	−0.0112084	−	0.00647117i
$59$	0.200843	+	0.115957i	0.0261476	+	0.0150963i	0.513017	−	0.858379i	$-0.328528\pi$
$59$	0.200843	+	0.115957i	0.0261476	+	0.0150963i	−0.486869	+	0.873475i	$0.661861\pi$
$60$		0			0
$61$	−4.01605	+	6.95601i	−0.514203	+	0.890626i	0.485661	+	0.874147i	$0.338579\pi$
$61$	−4.01605	+	6.95601i	−0.514203	+	0.890626i	−0.999864	+	0.0164787i	$0.994754\pi$
$62$	−1.15538	−	2.00118i	−0.146734	−	0.254150i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	8.06267	−	10.6796i	1.00005	−	1.32464i
$66$		0			0
$67$	−11.2323	+	6.48500i	−1.37225	+	0.792269i	−0.991211	−	0.132291i	$-0.957767\pi$
$67$	−11.2323	+	6.48500i	−1.37225	+	0.792269i	−0.381039	+	0.924559i	$0.624433\pi$
$68$	−0.106098	−	0.183768i	−0.0128663	−	0.0222851i
$69$		0			0
$70$			3.71131i			0.443587i
$71$	−6.37721	−	3.68188i	−0.756836	−	0.436959i	0.0713229	−	0.997453i	$-0.477278\pi$
$71$	−6.37721	−	3.68188i	−0.756836	−	0.436959i	−0.828158	+	0.560494i	$0.810611\pi$
$72$		0			0
$73$		−	5.60414i		−	0.655915i	−0.944692	−	0.327958i	$-0.893640\pi$
$73$		−	5.60414i		−	0.655915i	0.944692	−	0.327958i	$-0.106360\pi$
$74$	3.93672	−	6.81859i	0.457634	−	0.792645i
$75$		0			0
$76$	1.85081	−	1.06857i	0.212303	−	0.122573i
$77$	−5.77486			−0.658107
$78$		0			0
$79$	−9.19749			−1.03480			−0.517399	−	0.855744i	$-0.673100\pi$
$79$	−9.19749			−1.03480			−0.517399	+	0.855744i	$0.673100\pi$
$80$	−3.21409	+	1.85566i	−0.359346	+	0.207469i
$81$		0			0
$82$	−3.76060	+	6.51354i	−0.415288	+	0.719301i
$83$			3.17186i			0.348157i	0.984732	+	0.174078i	$0.0556946\pi$
$83$			3.17186i			0.348157i	−0.984732	+	0.174078i	$0.944305\pi$
$84$		0			0
$85$	−0.682021	−	0.393765i	−0.0739755	−	0.0427098i
$86$		−	4.57973i		−	0.493845i
$87$		0			0
$88$	−2.88743	−	5.00118i	−0.307801	−	0.533128i
$89$	10.2335	−	5.90833i	1.08475	−	0.626282i	0.152577	−	0.988292i	$-0.451243\pi$
$89$	10.2335	−	5.90833i	1.08475	−	0.626282i	0.932174	+	0.362010i	$0.117909\pi$
$90$		0			0
$91$	−1.40582	−	3.32019i	−0.147370	−	0.348050i
$92$	−2.47940			−0.258495
$93$		0			0
$94$	4.57785	+	7.92907i	0.472169	+	0.817821i
$95$	3.96579	−	6.86895i	0.406882	−	0.704740i
$96$		0			0
$97$	12.1952	+	7.04093i	1.23824	+	0.714898i	0.968734	−	0.248101i	$-0.0798064\pi$
$97$	12.1952	+	7.04093i	1.23824	+	0.714898i	0.269506	+	0.962999i	$0.413140\pi$
$98$	0.866025	+	0.500000i	0.0874818	+	0.0505076i
$99$		0			0
$100$	−4.38692	+	7.59837i	−0.438692	+	0.759837i
$101$	3.07622	+	5.32816i	0.306095	+	0.530172i	0.977505	−	0.210914i	$-0.0676441\pi$
$101$	3.07622	+	5.32816i	0.306095	+	0.530172i	−0.671410	+	0.741087i	$0.734311\pi$
$102$		0			0
$103$	19.3491			1.90652			0.953260	−	0.302152i	$-0.0977050\pi$
$103$	19.3491			1.90652			0.953260	+	0.302152i	$0.0977050\pi$
$104$	2.17246	−	2.87757i	0.213027	−	0.282169i
$105$		0			0
$106$	−10.4744	+	6.04740i	−1.01736	+	0.587375i
$107$	5.82506	+	10.0893i	0.563130	+	0.975369i	0.997221	+	0.0745005i	$0.0237362\pi$
$107$	5.82506	+	10.0893i	0.563130	+	0.975369i	−0.434091	+	0.900869i	$0.642930\pi$
$108$		0			0
$109$			5.73307i			0.549129i	0.961569	+	0.274564i	$0.0885336\pi$
$109$			5.73307i			0.549129i	−0.961569	+	0.274564i	$0.911466\pi$
$110$	−18.5609	−	10.7162i	−1.76972	−	1.02175i
$111$		0			0
$112$			1.00000i			0.0944911i
$113$	8.25971	−	14.3062i	0.777008	−	1.34582i	−0.156650	−	0.987654i	$-0.550070\pi$
$113$	8.25971	−	14.3062i	0.777008	−	1.34582i	0.933659	−	0.358164i	$-0.116597\pi$
$114$		0			0
$115$	−7.96901	+	4.60091i	−0.743114	+	0.429037i
$116$	−0.0985660			−0.00915162
$117$		0			0
$118$	0.231914			0.0213494
$119$	−0.183768	+	0.106098i	−0.0168460	+	0.00972603i
$120$		0			0
$121$	11.1745	−	19.3549i	1.01587	−	1.75953i
$122$			8.03211i			0.727193i
$123$		0			0
$124$	−2.00118	−	1.15538i	−0.179711	−	0.103756i
$125$			14.0059i			1.25273i
$126$		0			0
$127$	−5.89420	−	10.2090i	−0.523025	−	0.905907i	−0.999641	−	0.0267947i	$-0.991470\pi$
$127$	−5.89420	−	10.2090i	−0.523025	−	0.905907i	0.476616	−	0.879112i	$-0.341863\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	1.64269	−	13.2801i	0.144073	−	1.16474i
$131$	5.12859			0.448087			0.224043	−	0.974579i	$-0.428074\pi$
$131$	5.12859			0.448087			0.224043	+	0.974579i	$0.428074\pi$
$132$		0			0
$133$	−1.06857	−	1.85081i	−0.0926566	−	0.160486i
$134$	−6.48500	+	11.2323i	−0.560219	+	0.970327i
$135$		0			0
$136$	−0.183768	−	0.106098i	−0.0157580	−	0.00909787i
$137$	8.13482	+	4.69664i	0.695005	+	0.401261i	0.805484	−	0.592617i	$-0.201905\pi$
$137$	8.13482	+	4.69664i	0.695005	+	0.401261i	−0.110479	+	0.993878i	$0.535239\pi$
$138$		0			0
$139$	−7.57063	+	13.1127i	−0.642133	+	1.11221i	0.342823	+	0.939400i	$0.388617\pi$
$139$	−7.57063	+	13.1127i	−0.642133	+	1.11221i	−0.984956	+	0.172806i	$0.944717\pi$
$140$	1.85566	+	3.21409i	0.156832	+	0.271640i
$141$		0			0
$142$	−7.36377			−0.617954
$143$	20.6641	+	2.55605i	1.72802	+	0.213747i
$144$		0			0
$145$	−0.316800	+	0.182905i	−0.0263088	+	0.0151894i
$146$	−2.80207	−	4.85333i	−0.231901	−	0.401664i
$147$		0			0
$148$		−	7.87343i		−	0.647192i
$149$	17.8425	+	10.3013i	1.46171	+	0.843919i	0.999091	−	0.0426374i	$-0.0135760\pi$
$149$	17.8425	+	10.3013i	1.46171	+	0.843919i	0.462620	+	0.886557i	$0.346909\pi$
$150$		0			0
$151$		−	11.9407i		−	0.971721i	−0.874036	−	0.485861i	$-0.838506\pi$
$151$		−	11.9407i		−	0.971721i	0.874036	−	0.485861i	$-0.161494\pi$
$152$	1.06857	−	1.85081i	0.0866723	−	0.150121i
$153$		0			0
$154$	−5.00118	+	2.88743i	−0.403007	+	0.232676i
$155$	−8.57596			−0.688838
$156$		0			0
$157$	9.34022			0.745431			0.372715	−	0.927946i	$-0.378427\pi$
$157$	9.34022			0.745431			0.372715	+	0.927946i	$0.378427\pi$
$158$	−7.96526	+	4.59875i	−0.633682	+	0.365857i
$159$		0			0
$160$	−1.85566	+	3.21409i	−0.146703	+	0.254096i
$161$			2.47940i			0.195404i
$162$		0			0
$163$	3.87746	+	2.23865i	0.303706	+	0.175345i	0.644106	−	0.764936i	$-0.277229\pi$
$163$	3.87746	+	2.23865i	0.303706	+	0.175345i	−0.340401	+	0.940280i	$0.610563\pi$
$164$			7.52119i			0.587306i
$165$		0			0
$166$	1.58593	+	2.74691i	0.123092	+	0.213202i
$167$	−12.7365	+	7.35342i	−0.985579	+	0.569025i	−0.903950	−	0.427638i	$-0.859346\pi$
$167$	−12.7365	+	7.35342i	−0.985579	+	0.569025i	−0.0816295	+	0.996663i	$0.526012\pi$
$168$		0			0
$169$	3.56086	+	12.5028i	0.273912	+	0.961755i
$170$	−0.787529			−0.0604008
$171$		0			0
$172$	−2.28987	−	3.96617i	−0.174601	−	0.302417i
$173$	−6.88286	+	11.9215i	−0.523294	+	0.906372i	0.476339	+	0.879262i	$0.341964\pi$
$173$	−6.88286	+	11.9215i	−0.523294	+	0.906372i	−0.999632	+	0.0271097i	$0.991370\pi$
$174$		0			0
$175$	7.59837	+	4.38692i	0.574383	+	0.331620i
$176$	−5.00118	−	2.88743i	−0.376978	−	0.217648i
$177$		0			0
$178$	5.90833	−	10.2335i	0.442848	−	0.767035i
$179$	−7.63936	−	13.2318i	−0.570992	−	0.988988i	−0.996464	−	0.0840164i	$-0.973225\pi$
$179$	−7.63936	−	13.2318i	−0.570992	−	0.988988i	0.425472	−	0.904972i	$-0.360108\pi$
$180$		0			0
$181$	−1.66748			−0.123943			−0.0619713	−	0.998078i	$-0.519739\pi$
$181$	−1.66748			−0.123943			−0.0619713	+	0.998078i	$0.519739\pi$
$182$	−2.87757	−	2.17246i	−0.213300	−	0.161033i
$183$		0			0
$184$	−2.14722	+	1.23970i	−0.158295	+	0.0913919i
$185$	−14.6104	−	25.3059i	−1.07418	−	1.86053i
$186$		0			0
$187$		−	1.22541i		−	0.0896108i
$188$	7.92907	+	4.57785i	0.578287	+	0.333874i
$189$		0			0
$190$		−	7.93158i		−	0.575418i
$191$	0.0604880	−	0.104768i	0.00437676	−	0.00758076i	−0.863829	−	0.503786i	$-0.831940\pi$
$191$	0.0604880	−	0.104768i	0.00437676	−	0.00758076i	0.868205	+	0.496205i	$0.165273\pi$
$192$		0			0
$193$	−2.38633	+	1.37775i	−0.171772	+	0.0991725i	−0.583421	−	0.812170i	$-0.698286\pi$
$193$	−2.38633	+	1.37775i	−0.171772	+	0.0991725i	0.411649	+	0.911342i	$0.364953\pi$
$194$	14.0819			1.01102
$195$		0			0
$196$	1.00000			0.0714286
$197$	13.0989	−	7.56267i	0.933260	−	0.538818i	0.0454187	−	0.998968i	$-0.485538\pi$
$197$	13.0989	−	7.56267i	0.933260	−	0.538818i	0.887841	+	0.460150i	$0.152204\pi$
$198$		0			0
$199$	2.65320	−	4.59548i	0.188080	−	0.325765i	−0.756530	−	0.653959i	$-0.773107\pi$
$199$	2.65320	−	4.59548i	0.188080	−	0.325765i	0.944610	+	0.328194i	$0.106440\pi$
$200$			8.77384i			0.620404i
$201$		0			0
$202$	5.32816	+	3.07622i	0.374888	+	0.216442i
$203$			0.0985660i			0.00691798i
$204$		0			0
$205$	13.9567	+	24.1738i	0.974782	+	1.68837i
$206$	16.7568	−	9.67453i	1.16750	−	0.674056i
$207$		0			0
$208$	0.442616	−	3.57828i	0.0306899	−	0.248109i
$209$	12.3417			0.853691
$210$		0			0
$211$	−8.94910	−	15.5003i	−0.616081	−	1.06708i	−0.990194	−	0.139701i	$-0.955386\pi$
$211$	−8.94910	−	15.5003i	−0.616081	−	1.06708i	0.374112	−	0.927383i	$-0.377947\pi$
$212$	−6.04740	+	10.4744i	−0.415337	+	0.719385i
$213$		0			0
$214$	10.0893	+	5.82506i	0.689690	+	0.398193i
$215$	−14.7197	−	8.49841i	−1.00387	−	0.579587i
$216$		0			0
$217$	−1.15538	+	2.00118i	−0.0784324	+	0.135849i
$218$	2.86654	+	4.96499i	0.194146	+	0.336271i
$219$		0			0
$220$	−21.4323			−1.44497
$221$	0.704534	−	0.298312i	0.0473921	−	0.0200666i
$222$		0			0
$223$	−14.2362	+	8.21925i	−0.953324	+	0.550402i	−0.894112	−	0.447844i	$-0.852192\pi$
$223$	−14.2362	+	8.21925i	−0.953324	+	0.550402i	−0.0592118	+	0.998245i	$0.518859\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$		0			0
$226$		−	16.5194i		−	1.09886i
$227$	4.87655	+	2.81547i	0.323668	+	0.186870i	0.653026	−	0.757335i	$-0.273499\pi$
$227$	4.87655	+	2.81547i	0.323668	+	0.186870i	−0.329359	+	0.944205i	$0.606832\pi$
$228$		0			0
$229$		−	27.7225i		−	1.83196i	−0.401228	−	0.915978i	$-0.631416\pi$
$229$		−	27.7225i		−	1.83196i	0.401228	−	0.915978i	$-0.368584\pi$
$230$	−4.60091	+	7.96901i	−0.303375	+	0.525461i
$231$		0			0
$232$	−0.0853606	+	0.0492830i	−0.00560420	+	0.00323559i
$233$	20.1104			1.31747			0.658737	−	0.752374i	$-0.271091\pi$
$233$	20.1104			1.31747			0.658737	+	0.752374i	$0.271091\pi$
$234$		0			0
$235$	33.9797			2.21659
$236$	0.200843	−	0.115957i	0.0130738	−	0.00754816i
$237$		0			0
$238$	−0.106098	+	0.183768i	−0.00687734	+	0.0119119i
$239$			6.62968i			0.428838i	0.976742	+	0.214419i	$0.0687858\pi$
$239$			6.62968i			0.428838i	−0.976742	+	0.214419i	$0.931214\pi$
$240$		0			0
$241$	1.40025	+	0.808433i	0.0901978	+	0.0520757i	0.544420	−	0.838812i	$-0.316750\pi$
$241$	1.40025	+	0.808433i	0.0901978	+	0.0520757i	−0.454223	+	0.890888i	$0.650083\pi$
$242$		−	22.3491i		−	1.43665i
$243$		0			0
$244$	4.01605	+	6.95601i	0.257102	+	0.445313i
$245$	3.21409	−	1.85566i	0.205341	−	0.118554i
$246$		0			0
$247$	3.00444	+	7.09570i	0.191168	+	0.451489i
$248$	−2.31076			−0.146734
$249$		0			0
$250$	7.00296	+	12.1295i	0.442906	+	0.767136i
$251$	−0.253506	+	0.439085i	−0.0160011	+	0.0277148i	−0.873915	−	0.486079i	$-0.838427\pi$
$251$	−0.253506	+	0.439085i	−0.0160011	+	0.0277148i	0.857914	+	0.513793i	$0.171760\pi$
$252$		0			0
$253$	−12.3999	−	7.15910i	−0.779576	−	0.450089i
$254$	−10.2090	−	5.89420i	−0.640573	−	0.369835i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.82032	+	8.34903i	0.300683	+	0.520798i	0.976291	−	0.216463i	$-0.0694520\pi$
$257$	4.82032	+	8.34903i	0.300683	+	0.520798i	−0.675608	+	0.737261i	$0.736119\pi$
$258$		0			0
$259$	−7.87343			−0.489231
$260$	−5.21745	−	12.3223i	−0.323573	−	0.764194i
$261$		0			0
$262$	4.44149	−	2.56429i	0.274396	−	0.158423i
$263$	−3.67309	−	6.36197i	−0.226492	−	0.392296i	0.730274	−	0.683155i	$-0.239392\pi$
$263$	−3.67309	−	6.36197i	−0.226492	−	0.392296i	−0.956766	+	0.290858i	$0.906059\pi$
$264$		0			0
$265$			44.8876i			2.75742i
$266$	−1.85081	−	1.06857i	−0.113481	−	0.0655181i
$267$		0			0
$268$			12.9700i			0.792269i
$269$	11.1770	−	19.3592i	0.681476	−	1.18035i	−0.293055	−	0.956096i	$-0.594672\pi$
$269$	11.1770	−	19.3592i	0.681476	−	1.18035i	0.974530	−	0.224255i	$-0.0719949\pi$
$270$		0			0
$271$	−8.32891	+	4.80870i	−0.505945	+	0.292108i	−0.731165	−	0.682200i	$-0.761023\pi$
$271$	−8.32891	+	4.80870i	−0.505945	+	0.292108i	0.225220	+	0.974308i	$0.427690\pi$
$272$	−0.212197			−0.0128663
$273$		0			0
$274$	9.39328			0.567469
$275$	−43.8796	+	25.3339i	−2.64604	+	1.52769i
$276$		0			0
$277$	5.08945	−	8.81518i	0.305795	−	0.529653i	−0.671643	−	0.740875i	$-0.734411\pi$
$277$	5.08945	−	8.81518i	0.305795	−	0.529653i	0.977438	+	0.211222i	$0.0677444\pi$
$278$			15.1413i			0.908113i
$279$		0			0
$280$	3.21409	+	1.85566i	0.192079	+	0.110897i
$281$			14.1692i			0.845265i	0.906301	+	0.422633i	$0.138894\pi$
$281$			14.1692i			0.845265i	−0.906301	+	0.422633i	$0.861106\pi$
$282$		0			0
$283$	9.46631	+	16.3961i	0.562714	+	0.974649i	0.997258	+	0.0739986i	$0.0235760\pi$
$283$	9.46631	+	16.3961i	0.562714	+	0.974649i	−0.434545	+	0.900650i	$0.643091\pi$
$284$	−6.37721	+	3.68188i	−0.378418	+	0.218480i
$285$		0			0
$286$	19.1736	−	8.11844i	1.13376	−	0.480053i
$287$	7.52119			0.443962
$288$		0			0
$289$	8.47749	+	14.6834i	0.498676	+	0.863732i
$290$	−0.182905	+	0.316800i	−0.0107405	+	0.0186031i
$291$		0			0
$292$	−4.85333	−	2.80207i	−0.284020	−	0.163979i
$293$	−3.16950	−	1.82991i	−0.185164	−	0.106905i	0.404553	−	0.914515i	$-0.367427\pi$
$293$	−3.16950	−	1.82991i	−0.185164	−	0.106905i	−0.589717	+	0.807610i	$0.700761\pi$
$294$		0			0
$295$	0.430353	−	0.745393i	0.0250561	−	0.0433985i
$296$	−3.93672	−	6.81859i	−0.228817	−	0.396323i
$297$		0			0
$298$	20.6027			1.19348
$299$	1.09742	−	8.87198i	0.0634655	−	0.513080i
$300$		0			0
$301$	−3.96617	+	2.28987i	−0.228606	+	0.131986i
$302$	−5.97036	−	10.3410i	−0.343555	−	0.595055i
$303$		0			0
$304$		−	2.13714i		−	0.122573i
$305$	25.8159	+	14.9048i	1.47822	+	0.853448i
$306$		0			0
$307$			19.6987i			1.12426i	0.827048	+	0.562132i	$0.190019\pi$
$307$			19.6987i			1.12426i	−0.827048	+	0.562132i	$0.809981\pi$
$308$	−2.88743	+	5.00118i	−0.164527	+	0.284969i
$309$		0			0
$310$	−7.42700	+	4.28798i	−0.421825	+	0.243541i
$311$	−16.9685			−0.962195			−0.481098	−	0.876667i	$-0.659762\pi$
$311$	−16.9685			−0.962195			−0.481098	+	0.876667i	$0.659762\pi$
$312$		0			0
$313$	−4.53794			−0.256500			−0.128250	−	0.991742i	$-0.540936\pi$
$313$	−4.53794			−0.256500			−0.128250	+	0.991742i	$0.540936\pi$
$314$	8.08887	−	4.67011i	0.456481	−	0.263550i
$315$		0			0
$316$	−4.59875	+	7.96526i	−0.258700	+	0.448081i
$317$			29.1866i			1.63928i	0.572877	+	0.819641i	$0.305827\pi$
$317$			29.1866i			1.63928i	−0.572877	+	0.819641i	$0.694173\pi$
$318$		0			0
$319$	−0.492946	−	0.284603i	−0.0275997	−	0.0159347i
$320$			3.71131i			0.207469i
$321$		0			0
$322$	1.23970	+	2.14722i	0.0690857	+	0.119660i
$323$	0.392737	−	0.226747i	0.0218525	−	0.0126165i
$324$		0			0
$325$	−25.2474	−	19.0608i	−1.40047	−	1.05730i
$326$	4.47730			0.247975
$327$		0			0
$328$	3.76060	+	6.51354i	0.207644	+	0.359650i
$329$	4.57785	−	7.92907i	0.252385	−	0.437144i
$330$		0			0
$331$	4.16161	+	2.40271i	0.228743	+	0.132065i	0.609992	−	0.792408i	$-0.291173\pi$
$331$	4.16161	+	2.40271i	0.228743	+	0.132065i	−0.381249	+	0.924472i	$0.624506\pi$
$332$	2.74691	+	1.58593i	0.150756	+	0.0870392i
$333$		0			0
$334$	−7.35342	+	12.7365i	−0.402361	+	0.696910i
$335$	24.0679	+	41.6868i	1.31497	+	2.27759i
$336$		0			0
$337$	17.7312			0.965883			0.482941	−	0.875653i	$-0.339568\pi$
$337$	17.7312			0.965883			0.482941	+	0.875653i	$0.339568\pi$
$338$	9.33520	+	9.04732i	0.507768	+	0.492109i
$339$		0			0
$340$	−0.682021	+	0.393765i	−0.0369878	+	0.0213549i
$341$	−6.67217	−	11.5565i	−0.361318	−	0.625822i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−3.96617	−	2.28987i	−0.213841	−	0.123461i
$345$		0			0
$346$			13.7657i			0.740049i
$347$	−8.35240	+	14.4668i	−0.448380	+	0.776617i	−0.998281	−	0.0586128i	$-0.981332\pi$
$347$	−8.35240	+	14.4668i	−0.448380	+	0.776617i	0.549901	+	0.835230i	$0.314666\pi$
$348$		0			0
$349$	0.0173616	−	0.0100237i	0.000929347	−	0.000536559i	−0.499535	−	0.866294i	$-0.666496\pi$
$349$	0.0173616	−	0.0100237i	0.000929347	−	0.000536559i	0.500465	+	0.865757i	$0.333163\pi$
$350$	8.77384			0.468982
$351$		0			0
$352$	−5.77486			−0.307801
$353$	−25.8299	+	14.9129i	−1.37479	+	0.793734i	−0.991526	−	0.129905i	$-0.958533\pi$
$353$	−25.8299	+	14.9129i	−1.37479	+	0.793734i	−0.383262	+	0.923640i	$0.625199\pi$
$354$		0			0
$355$	−13.6646	+	23.6678i	−0.725243	+	1.25616i
$356$		−	11.8167i		−	0.626282i
$357$		0			0
$358$	−13.2318	−	7.63936i	−0.699320	−	0.403753i
$359$		−	18.3351i		−	0.967687i	−0.875154	−	0.483844i	$-0.839240\pi$
$359$		−	18.3351i		−	0.967687i	0.875154	−	0.483844i	$-0.160760\pi$
$360$		0			0
$361$	−7.21632	−	12.4990i	−0.379806	−	0.657844i
$362$	−1.44408	+	0.833739i	−0.0758991	+	0.0438204i
$363$		0			0
$364$	−3.57828	−	0.442616i	−0.187553	−	0.0231994i
$365$	−20.7987			−1.08866
$366$		0			0
$367$	−0.672426	−	1.16468i	−0.0351004	−	0.0607956i	0.847942	−	0.530090i	$-0.177842\pi$
$367$	−0.672426	−	1.16468i	−0.0351004	−	0.0607956i	−0.883042	+	0.469294i	$0.844508\pi$
$368$	−1.23970	+	2.14722i	−0.0646238	+	0.111932i
$369$		0			0
$370$	−25.3059	−	14.6104i	−1.31559	−	0.759558i
$371$	10.4744	+	6.04740i	0.543804	+	0.313965i
$372$		0			0
$373$	5.53575	−	9.58821i	0.286630	−	0.496458i	−0.686373	−	0.727250i	$-0.740798\pi$
$373$	5.53575	−	9.58821i	0.286630	−	0.496458i	0.973003	+	0.230791i	$0.0741315\pi$
$374$	−0.612704	−	1.06124i	−0.0316822	−	0.0548752i
$375$		0			0
$376$	9.15570			0.472169
$377$	0.0436269	−	0.352697i	0.00224690	−	0.0181648i
$378$		0			0
$379$	14.5583	−	8.40523i	0.747808	−	0.431747i	−0.0770930	−	0.997024i	$-0.524564\pi$
$379$	14.5583	−	8.40523i	0.747808	−	0.431747i	0.824902	+	0.565276i	$0.191231\pi$
$380$	−3.96579	−	6.86895i	−0.203441	−	0.352370i
$381$		0			0
$382$		−	0.120976i		−	0.00618967i
$383$	−14.3562	−	8.28855i	−0.733567	−	0.423525i	0.0861585	−	0.996281i	$-0.472541\pi$
$383$	−14.3562	−	8.28855i	−0.733567	−	0.423525i	−0.819726	+	0.572756i	$0.805874\pi$
$384$		0			0
$385$			21.4323i			1.09229i
$386$	−1.37775	+	2.38633i	−0.0701256	+	0.121461i
$387$		0			0
$388$	12.1952	−	7.04093i	0.619120	−	0.357449i
$389$	1.17013			0.0593280			0.0296640	−	0.999560i	$-0.490556\pi$
$389$	1.17013			0.0593280			0.0296640	+	0.999560i	$0.490556\pi$
$390$		0			0
$391$	−0.526121			−0.0266071
$392$	0.866025	−	0.500000i	0.0437409	−	0.0252538i
$393$		0			0
$394$	7.56267	−	13.0989i	0.381002	−	0.659914i
$395$			34.1348i			1.71751i
$396$		0			0
$397$	22.6877	+	13.0987i	1.13866	+	0.657406i	0.946099	−	0.323878i	$-0.104987\pi$
$397$	22.6877	+	13.0987i	1.13866	+	0.657406i	0.192562	+	0.981285i	$0.438320\pi$
$398$		−	5.30640i		−	0.265986i
$399$		0			0
$400$	4.38692	+	7.59837i	0.219346	+	0.379919i
$401$	9.84559	−	5.68436i	0.491665	−	0.283863i	−0.233600	−	0.972333i	$-0.575051\pi$
$401$	9.84559	−	5.68436i	0.491665	−	0.283863i	0.725265	+	0.688470i	$0.241717\pi$
$402$		0			0
$403$	5.02003	−	6.64939i	0.250066	−	0.331230i
$404$	6.15243			0.306095
$405$		0			0
$406$	0.0492830	+	0.0853606i	0.00244587	+	0.00423638i
$407$	22.7340	−	39.3764i	1.12688	−	1.95182i
$408$		0			0
$409$	−20.2056	−	11.6657i	−0.999102	−	0.576832i	−0.0911196	−	0.995840i	$-0.529045\pi$
$409$	−20.2056	−	11.6657i	−0.999102	−	0.576832i	−0.907982	+	0.419008i	$0.862378\pi$
$410$	24.1738	+	13.9567i	1.19386	+	0.689275i
$411$		0			0
$412$	9.67453	−	16.7568i	0.476630	−	0.825547i
$413$	−0.115957	−	0.200843i	−0.00570587	−	0.00988286i
$414$		0			0
$415$	11.7718			0.577853
$416$	−1.40582	−	3.32019i	−0.0689262	−	0.162786i
$417$		0			0
$418$	10.6882	−	6.17084i	0.522777	−	0.301826i
$419$	−6.33402	−	10.9709i	−0.309437	−	0.535961i	0.668802	−	0.743441i	$-0.266807\pi$
$419$	−6.33402	−	10.9709i	−0.309437	−	0.535961i	−0.978239	+	0.207479i	$0.933474\pi$
$420$		0			0
$421$		−	27.6625i		−	1.34819i	−0.738646	−	0.674094i	$-0.764534\pi$
$421$		−	27.6625i		−	1.34819i	0.738646	−	0.674094i	$-0.235466\pi$
$422$	−15.5003	−	8.94910i	−0.754543	−	0.435635i
$423$		0			0
$424$			12.0948i			0.587375i
$425$	−0.930892	+	1.61235i	−0.0451549	+	0.0782105i
$426$		0			0
$427$	6.95601	−	4.01605i	0.336625	−	0.194351i
$428$	11.6501			0.563130
$429$		0			0
$430$	−16.9968			−0.819660
$431$	−5.55462	+	3.20696i	−0.267557	+	0.154474i	−0.627777	−	0.778393i	$-0.716035\pi$
$431$	−5.55462	+	3.20696i	−0.267557	+	0.154474i	0.360220	+	0.932867i	$0.382702\pi$
$432$		0			0
$433$	−0.0325135	+	0.0563150i	−0.00156250	+	0.00270633i	−0.866806	−	0.498646i	$-0.833831\pi$
$433$	−0.0325135	+	0.0563150i	−0.00156250	+	0.00270633i	0.865243	+	0.501353i	$0.167164\pi$
$434$			2.31076i			0.110920i
$435$		0			0
$436$	4.96499	+	2.86654i	0.237780	+	0.137282i
$437$		−	5.29881i		−	0.253477i
$438$		0			0
$439$	18.3889	+	31.8505i	0.877655	+	1.52014i	0.853908	+	0.520424i	$0.174226\pi$
$439$	18.3889	+	31.8505i	0.877655	+	1.52014i	0.0237469	+	0.999718i	$0.492440\pi$
$440$	−18.5609	+	10.7162i	−0.884858	+	0.510873i
$441$		0			0
$442$	0.460989	−	0.610613i	0.0219270	−	0.0290439i
$443$	8.46383			0.402129			0.201064	−	0.979578i	$-0.435560\pi$
$443$	8.46383			0.402129			0.201064	+	0.979578i	$0.435560\pi$
$444$		0			0
$445$	−21.9277	−	37.9798i	−1.03947	−	1.80042i
$446$	−8.21925	+	14.2362i	−0.389193	+	0.674102i
$447$		0			0
$448$	0.866025	+	0.500000i	0.0409159	+	0.0236228i
$449$	19.5984	+	11.3152i	0.924907	+	0.533995i	0.885197	−	0.465216i	$-0.154023\pi$
$449$	19.5984	+	11.3152i	0.924907	+	0.533995i	0.0397096	+	0.999211i	$0.487357\pi$
$450$		0			0
$451$	−21.7169	+	37.6148i	−1.02261	+	1.77121i
$452$	−8.25971	−	14.3062i	−0.388504	−	0.672909i
$453$		0			0
$454$	5.63095			0.264274
$455$	−12.3223	+	5.21745i	−0.577677	+	0.244598i
$456$		0			0
$457$	−14.1310	+	8.15851i	−0.661018	+	0.381639i	−0.792665	−	0.609658i	$-0.791307\pi$
$457$	−14.1310	+	8.15851i	−0.661018	+	0.381639i	0.131647	+	0.991297i	$0.457974\pi$
$458$	−13.8613	−	24.0084i	−0.647694	−	1.12184i
$459$		0			0
$460$			9.20183i			0.429037i
$461$	−16.6951	−	9.63892i	−0.777568	−	0.448929i	0.0579996	−	0.998317i	$-0.481528\pi$
$461$	−16.6951	−	9.63892i	−0.777568	−	0.448929i	−0.835568	+	0.549387i	$0.814861\pi$
$462$		0			0
$463$			2.70218i			0.125581i	0.998027	+	0.0627904i	$0.0200000\pi$
$463$			2.70218i			0.125581i	−0.998027	+	0.0627904i	$0.980000\pi$
$464$	−0.0492830	+	0.0853606i	−0.00228791	+	0.00396277i
$465$		0			0
$466$	17.4161	−	10.0552i	0.806784	−	0.465797i
$467$	18.3906			0.851014			0.425507	−	0.904955i	$-0.360096\pi$
$467$	18.3906			0.851014			0.425507	+	0.904955i	$0.360096\pi$
$468$		0			0
$469$	12.9700			0.598899
$470$	29.4272	−	16.9898i	1.35738	−	0.783682i
$471$		0			0
$472$	0.115957	−	0.200843i	0.00533735	−	0.00924457i
$473$		−	26.4473i		−	1.21605i
$474$		0			0
$475$	−16.2388	−	9.37545i	−0.745085	−	0.430175i
$476$			0.212197i			0.00972603i
$477$		0			0
$478$	3.31484	+	5.74147i	0.151617	+	0.262609i
$479$	−35.3951	+	20.4354i	−1.61725	+	0.933717i	−0.629617	+	0.776906i	$0.716788\pi$
$479$	−35.3951	+	20.4354i	−1.61725	+	0.933717i	−0.987629	+	0.156811i	$0.949879\pi$
$480$		0			0
$481$	28.1733	+	3.48491i	1.28459	+	0.158898i
$482$	1.61687			0.0736462
$483$		0			0
$484$	−11.1745	−	19.3549i	−0.507933	−	0.879766i
$485$	26.1311	−	45.2604i	1.18655	−	2.05517i
$486$		0			0
$487$	15.2674	+	8.81466i	0.691834	+	0.399430i	0.804299	−	0.594225i	$-0.202541\pi$
$487$	15.2674	+	8.81466i	0.691834	+	0.399430i	−0.112465	+	0.993656i	$0.535875\pi$
$488$	6.95601	+	4.01605i	0.314884	+	0.181798i
$489$		0			0
$490$	1.85566	−	3.21409i	0.0838300	−	0.145198i
$491$	9.42997	+	16.3332i	0.425569	+	0.737106i	0.996473	−	0.0839098i	$-0.0267408\pi$
$491$	9.42997	+	16.3332i	0.425569	+	0.737106i	−0.570905	+	0.821016i	$0.693407\pi$
$492$		0			0
$493$	−0.0209154			−0.000941982
$494$	6.14977	+	4.64284i	0.276691	+	0.208891i
$495$		0			0
$496$	−2.00118	+	1.15538i	−0.0898556	+	0.0518782i
$497$	3.68188	+	6.37721i	0.165155	+	0.286057i
$498$		0			0
$499$		−	2.10742i		−	0.0943410i	−0.998887	−	0.0471705i	$-0.984980\pi$
$499$		−	2.10742i		−	0.0943410i	0.998887	−	0.0471705i	$-0.0150204\pi$
$500$	12.1295	+	7.00296i	0.542447	+	0.313182i
$501$		0			0
$502$			0.507011i			0.0226290i
$503$	10.8942	−	18.8693i	0.485749	−	0.841342i	−0.514117	−	0.857720i	$-0.671880\pi$
$503$	10.8942	−	18.8693i	0.485749	−	0.841342i	0.999866	+	0.0163784i	$0.00521363\pi$
$504$		0			0
$505$	19.7745	−	11.4168i	0.879953	−	0.508041i
$506$	−14.3182			−0.636521
$507$		0			0
$508$	−11.7884			−0.523025
$509$	10.5636	−	6.09887i	0.468221	−	0.270328i	−0.247273	−	0.968946i	$-0.579535\pi$
$509$	10.5636	−	6.09887i	0.468221	−	0.270328i	0.715495	+	0.698618i	$0.246201\pi$
$510$		0			0
$511$	−2.80207	+	4.85333i	−0.123956	+	0.214699i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	8.34903	+	4.82032i	0.368260	+	0.212615i
$515$		−	71.8104i		−	3.16435i
$516$		0			0
$517$	26.4365	+	45.7893i	1.16267	+	2.01381i
$518$	−6.81859	+	3.93672i	−0.299592	+	0.172969i
$519$		0			0
$520$	−10.6796	−	8.06267i	−0.468330	−	0.353571i
$521$	26.9765			1.18186			0.590932	−	0.806722i	$-0.298760\pi$
$521$	26.9765			1.18186			0.590932	+	0.806722i	$0.298760\pi$
$522$		0			0
$523$	1.87683	+	3.25076i	0.0820679	+	0.142146i	0.904138	−	0.427241i	$-0.140514\pi$
$523$	1.87683	+	3.25076i	0.0820679	+	0.142146i	−0.822070	+	0.569386i	$0.807181\pi$
$524$	2.56429	−	4.44149i	0.112022	−	0.194027i
$525$		0			0
$526$	−6.36197	−	3.67309i	−0.277395	−	0.160154i
$527$	−0.424644	−	0.245168i	−0.0184978	−	0.0106797i
$528$		0			0
$529$	8.42629	−	14.5948i	0.366360	−	0.634555i
$530$	22.4438	+	38.8738i	0.974896	+	1.68857i
$531$		0			0
$532$	−2.13714			−0.0926566
$533$	−26.9129	−	3.32900i	−1.16573	−	0.144195i
$534$		0			0
$535$	37.4445	−	21.6186i	1.61887	−	0.934654i
$536$	6.48500	+	11.2323i	0.280109	+	0.485163i
$537$		0			0
$538$		−	22.3541i		−	0.963752i
$539$	5.00118	+	2.88743i	0.215416	+	0.124371i
$540$		0			0
$541$			0.0135705i			0.000583440i	1.00000		0.000291720i	$9.28574e-5\pi$
$541$			0.0135705i			0.000583440i	−1.00000		0.000291720i	$0.999907\pi$
$542$	−4.80870	+	8.32891i	−0.206551	+	0.357757i
$543$		0			0
$544$	−0.183768	+	0.106098i	−0.00787899	+	0.00454894i
$545$	21.2772			0.911416
$546$		0			0
$547$	−9.66115			−0.413081			−0.206540	−	0.978438i	$-0.566220\pi$
$547$	−9.66115			−0.413081			−0.206540	+	0.978438i	$0.566220\pi$
$548$	8.13482	−	4.69664i	0.347502	−	0.200631i
$549$		0			0
$550$	−25.3339	+	43.8796i	−1.08024	+	1.87103i
$551$		−	0.210649i		−	0.00897395i
$552$		0			0
$553$	7.96526	+	4.59875i	0.338717	+	0.195559i
$554$		−	10.1789i		−	0.432460i
$555$		0			0
$556$	7.57063	+	13.1127i	0.321066	+	0.556103i
$557$	21.6145	−	12.4791i	0.915834	−	0.528757i	0.0335307	−	0.999438i	$-0.489325\pi$
$557$	21.6145	−	12.4791i	0.915834	−	0.528757i	0.882304	+	0.470680i	$0.155992\pi$
$558$		0			0
$559$	15.2056	−	6.43830i	0.643128	−	0.272311i
$560$	3.71131			0.156832
$561$		0			0
$562$	7.08461	+	12.2709i	0.298846	+	0.517617i
$563$	−7.94970	+	13.7693i	−0.335040	+	0.580306i	−0.983492	−	0.180949i	$-0.942083\pi$
$563$	−7.94970	+	13.7693i	−0.335040	+	0.580306i	0.648453	+	0.761255i	$0.275416\pi$
$564$		0			0
$565$	−53.0949	−	30.6544i	−2.23372	−	1.28964i
$566$	16.3961	+	9.46631i	0.689181	+	0.397899i
$567$		0			0
$568$	−3.68188	+	6.37721i	−0.154488	+	0.267582i
$569$	8.95465	+	15.5099i	0.375398	+	0.650209i	0.990387	−	0.138327i	$-0.0441725\pi$
$569$	8.95465	+	15.5099i	0.375398	+	0.650209i	−0.614988	+	0.788536i	$0.710839\pi$
$570$		0			0
$571$	−12.5123			−0.523623			−0.261812	−	0.965119i	$-0.584320\pi$
$571$	−12.5123			−0.523623			−0.261812	+	0.965119i	$0.584320\pi$
$572$	12.5456	−	16.6176i	0.524560	−	0.694817i
$573$		0			0
$574$	6.51354	−	3.76060i	0.271870	−	0.156964i
$575$	10.8769	+	18.8394i	0.453599	+	0.785657i
$576$		0			0
$577$		−	22.0910i		−	0.919662i	−0.888007	−	0.459831i	$-0.847910\pi$
$577$		−	22.0910i		−	0.919662i	0.888007	−	0.459831i	$-0.152090\pi$
$578$	14.6834	+	8.47749i	0.610750	+	0.352617i
$579$		0			0
$580$			0.365809i			0.0151894i
$581$	1.58593	−	2.74691i	0.0657954	−	0.113961i
$582$		0			0
$583$	−60.4883	+	34.9229i	−2.50517	+	1.44636i
$584$	−5.60414			−0.231901
$585$		0			0
$586$	−3.65982			−0.151186
$587$	18.3007	−	10.5659i	0.755352	−	0.436102i	−0.0722727	−	0.997385i	$-0.523025\pi$
$587$	18.3007	−	10.5659i	0.755352	−	0.436102i	0.827624	+	0.561282i	$0.189692\pi$
$588$		0			0
$589$	2.46921	−	4.27679i	0.101742	−	0.176222i
$590$		−	0.860706i		−	0.0354347i
$591$		0			0
$592$	−6.81859	−	3.93672i	−0.280242	−	0.161798i
$593$		−	8.95493i		−	0.367735i	−0.982951	−	0.183867i	$-0.941138\pi$
$593$		−	8.95493i		−	0.367735i	0.982951	−	0.183867i	$-0.0588617\pi$
$594$		0			0
$595$	0.393765	+	0.682021i	0.0161428	+	0.0279601i
$596$	17.8425	−	10.3013i	0.730855	−	0.421960i
$597$		0			0
$598$	−3.48560	−	8.23207i	−0.142537	−	0.336635i
$599$	−41.7996			−1.70788			−0.853942	−	0.520368i	$-0.825795\pi$
$599$	−41.7996			−1.70788			−0.853942	+	0.520368i	$0.825795\pi$
$600$		0			0
$601$	−7.64481	−	13.2412i	−0.311838	−	0.540120i	0.666922	−	0.745127i	$-0.267611\pi$
$601$	−7.64481	−	13.2412i	−0.311838	−	0.540120i	−0.978760	+	0.205008i	$0.934278\pi$
$602$	−2.28987	+	3.96617i	−0.0933280	+	0.161649i
$603$		0			0
$604$	−10.3410	−	5.97036i	−0.420768	−	0.242930i
$605$	−71.8319	−	41.4722i	−2.92038	−	1.68608i
$606$		0			0
$607$	−7.30434	+	12.6515i	−0.296474	+	0.513508i	−0.975327	−	0.220766i	$-0.929144\pi$
$607$	−7.30434	+	12.6515i	−0.296474	+	0.513508i	0.678853	+	0.734275i	$0.262478\pi$
$608$	−1.06857	−	1.85081i	−0.0433362	−	0.0750604i
$609$		0			0
$610$	29.8097			1.20696
$611$	−19.8904	+	26.3462i	−0.804678	+	1.06585i
$612$		0			0
$613$	−33.9623	+	19.6081i	−1.37172	+	0.791965i	−0.991145	−	0.132783i	$-0.957609\pi$
$613$	−33.9623	+	19.6081i	−1.37172	+	0.791965i	−0.380579	+	0.924748i	$0.624275\pi$
$614$	9.84935	+	17.0596i	0.397487	+	0.688468i
$615$		0			0
$616$			5.77486i			0.232676i
$617$	−8.10486	−	4.67934i	−0.326289	−	0.188383i	0.327903	−	0.944711i	$-0.393658\pi$
$617$	−8.10486	−	4.67934i	−0.326289	−	0.188383i	−0.654192	+	0.756328i	$0.726991\pi$
$618$		0			0
$619$		−	43.7075i		−	1.75675i	−0.477970	−	0.878376i	$-0.658627\pi$
$619$		−	43.7075i		−	1.75675i	0.477970	−	0.878376i	$-0.341373\pi$
$620$	−4.28798	+	7.42700i	−0.172210	+	0.298276i
$621$		0			0
$622$	−14.6952	+	8.48425i	−0.589222	+	0.340187i
$623$	−11.8167			−0.473424
$624$		0			0
$625$	8.11112			0.324445
$626$	−3.92997	+	2.26897i	−0.157073	+	0.0906863i
$627$		0			0
$628$	4.67011	−	8.08887i	0.186358	−	0.322781i
$629$		−	1.67072i		−	0.0666159i
$630$		0			0
$631$	−18.0096	−	10.3978i	−0.716951	−	0.413932i	0.0966785	−	0.995316i	$-0.469178\pi$
$631$	−18.0096	−	10.3978i	−0.716951	−	0.413932i	−0.813629	+	0.581384i	$0.802511\pi$
$632$			9.19749i			0.365857i
$633$		0			0
$634$	14.5933	+	25.2763i	0.579574	+	1.00385i
$635$	−37.8890	+	21.8752i	−1.50358	+	0.868091i
$636$		0			0
$637$	−0.442616	+	3.57828i	−0.0175371	+	0.141777i
$638$	−0.569205			−0.0225350
$639$		0			0
$640$	1.85566	+	3.21409i	0.0733513	+	0.127048i
$641$	3.61897	−	6.26824i	0.142941	−	0.247581i	−0.785662	−	0.618656i	$-0.787677\pi$
$641$	3.61897	−	6.26824i	0.142941	−	0.247581i	0.928603	+	0.371075i	$0.121011\pi$
$642$		0			0
$643$	34.7898	+	20.0859i	1.37198	+	0.792111i	0.991177	−	0.132547i	$-0.0423154\pi$
$643$	34.7898	+	20.0859i	1.37198	+	0.792111i	0.380800	+	0.924658i	$0.375649\pi$
$644$	2.14722	+	1.23970i	0.0846124	+	0.0488510i
$645$		0			0
$646$	0.226747	−	0.392737i	0.00892124	−	0.0154520i
$647$	−7.27561	−	12.6017i	−0.286034	−	0.495425i	0.686826	−	0.726822i	$-0.259004\pi$
$647$	−7.27561	−	12.6017i	−0.286034	−	0.495425i	−0.972859	+	0.231397i	$0.925670\pi$
$648$		0			0
$649$	1.33927			0.0525710
$650$	−31.3953	−	3.88344i	−1.23142	−	0.152321i
$651$		0			0
$652$	3.87746	−	2.23865i	0.151853	−	0.0876723i
$653$	−24.8634	−	43.0646i	−0.972978	−	1.68525i	−0.686451	−	0.727176i	$-0.740832\pi$
$653$	−24.8634	−	43.0646i	−0.972978	−	1.68525i	−0.286527	−	0.958072i	$-0.592501\pi$
$654$		0			0
$655$		−	19.0338i		−	0.743712i
$656$	6.51354	+	3.76060i	0.254311	+	0.146827i
$657$		0			0
$658$		−	9.15570i		−	0.356926i
$659$	−15.7988	+	27.3644i	−0.615436	+	1.06597i	0.374872	+	0.927076i	$0.377687\pi$
$659$	−15.7988	+	27.3644i	−0.615436	+	1.06597i	−0.990308	+	0.138889i	$0.955647\pi$
$660$		0			0
$661$	−21.5391	+	12.4356i	−0.837775	+	0.483689i	−0.856507	−	0.516135i	$-0.827370\pi$
$661$	−21.5391	+	12.4356i	−0.837775	+	0.483689i	0.0187325	+	0.999825i	$0.494037\pi$
$662$	4.80542			0.186768
$663$		0			0
$664$	3.17186			0.123092
$665$	−6.86895	+	3.96579i	−0.266367	+	0.153787i
$666$		0			0
$667$	−0.122192	+	0.211643i	−0.00473130	+	0.00819485i
$668$			14.7068i			0.569025i
$669$		0			0
$670$	41.6868	+	24.0679i	1.61050	+	0.929822i
$671$			46.3843i			1.79065i
$672$		0			0
$673$	−10.8245	−	18.7486i	−0.417254	−	0.722705i	0.578408	−	0.815748i	$-0.303674\pi$
$673$	−10.8245	−	18.7486i	−0.417254	−	0.722705i	−0.995662	+	0.0930423i	$0.970341\pi$
$674$	15.3557	−	8.86562i	0.591480	−	0.341491i
$675$		0			0
$676$	12.6082	+	3.16761i	0.484930	+	0.121831i
$677$	−14.3935			−0.553187			−0.276594	−	0.960987i	$-0.589206\pi$
$677$	−14.3935			−0.553187			−0.276594	+	0.960987i	$0.589206\pi$
$678$		0			0
$679$	−7.04093	−	12.1952i	−0.270206	−	0.468011i
$680$	−0.393765	+	0.682021i	−0.0151002	+	0.0261543i
$681$		0			0
$682$	−11.5565	−	6.67217i	−0.442523	−	0.255491i
$683$	36.6968	+	21.1869i	1.40416	+	0.810694i	0.994817	−	0.101686i	$-0.0324235\pi$
$683$	36.6968	+	21.1869i	1.40416	+	0.810694i	0.409346	+	0.912379i	$0.365757\pi$
$684$		0			0
$685$	17.4307	−	30.1909i	0.665993	−	1.15353i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$		0			0
$688$	−4.57973			−0.174601
$689$	−34.8037	−	26.2754i	−1.32591	−	1.00101i
$690$		0			0
$691$	−19.8651	+	11.4691i	−0.755703	+	0.436305i	−0.827751	−	0.561096i	$-0.810380\pi$
$691$	−19.8651	+	11.4691i	−0.755703	+	0.436305i	0.0720480	+	0.997401i	$0.477047\pi$
$692$	6.88286	+	11.9215i	0.261647	+	0.453186i
$693$		0			0
$694$			16.7048i			0.634105i
$695$	48.6654	+	28.0970i	1.84598	+	1.06578i
$696$		0			0
$697$			1.59597i			0.0604518i
$698$	0.0100237	−	0.0173616i	0.000379404	−	0.000657147i
$699$		0			0
$700$	7.59837	−	4.38692i	0.287191	−	0.165810i
$701$	−1.70699			−0.0644723			−0.0322361	−	0.999480i	$-0.510263\pi$
$701$	−1.70699			−0.0644723			−0.0322361	+	0.999480i	$0.510263\pi$
$702$		0			0
$703$	16.8266			0.634627
$704$	−5.00118	+	2.88743i	−0.188489	+	0.108824i
$705$		0			0
$706$	−14.9129	+	25.8299i	−0.561255	+	0.972122i
$707$		−	6.15243i		−	0.231386i
$708$		0			0
$709$	−15.7730	−	9.10657i	−0.592369	−	0.342005i	0.173665	−	0.984805i	$-0.444439\pi$
$709$	−15.7730	−	9.10657i	−0.592369	−	0.342005i	−0.766034	+	0.642800i	$0.777772\pi$
$710$			27.3292i			1.02565i
$711$		0			0
$712$	−5.90833	−	10.2335i	−0.221424	−	0.383518i
$713$	−4.96172	+	2.86465i	−0.185818	+	0.107282i
$714$		0			0
$715$	9.48629	−	76.6909i	0.354767	−	2.86808i
$716$	−15.2787			−0.570992
$717$		0			0
$718$	−9.16753	−	15.8786i	−0.342129	−	0.592585i
$719$	−1.79107	+	3.10222i	−0.0667956	+	0.115693i	−0.897489	−	0.441037i	$-0.854611\pi$
$719$	−1.79107	+	3.10222i	−0.0667956	+	0.115693i	0.830694	+	0.556730i	$0.187944\pi$
$720$		0			0
$721$	−16.7568	−	9.67453i	−0.624055	−	0.360298i
$722$	−12.4990	−	7.21632i	−0.465166	−	0.268564i
$723$		0			0
$724$	−0.833739	+	1.44408i	−0.0309857	+	0.0536688i
$725$	0.432401	+	0.748941i	0.0160590	+	0.0278150i
$726$		0			0
$727$	3.21747			0.119329			0.0596647	−	0.998218i	$-0.480997\pi$
$727$	3.21747			0.119329			0.0596647	+	0.998218i	$0.480997\pi$
$728$	−3.32019	+	1.40582i	−0.123054	+	0.0521033i
$729$		0			0
$730$	−18.0122	+	10.3994i	−0.666662	+	0.384898i
$731$	−0.485903	−	0.841608i	−0.0179718	−	0.0311280i
$732$		0			0
$733$			4.79233i			0.177009i	0.996076	+	0.0885043i	$0.0282087\pi$
$733$			4.79233i			0.177009i	−0.996076	+	0.0885043i	$0.971791\pi$
$734$	−1.16468	−	0.672426i	−0.0429890	−	0.0248197i
$735$		0			0
$736$			2.47940i			0.0913919i
$737$	−37.4500	+	64.8653i	−1.37949	+	2.38934i
$738$		0			0
$739$	9.69853	−	5.59945i	0.356766	−	0.205979i	−0.310895	−	0.950444i	$-0.600629\pi$
$739$	9.69853	−	5.59945i	0.356766	−	0.205979i	0.667661	+	0.744465i	$0.267295\pi$
$740$	−29.2208			−1.07418
$741$		0			0
$742$	12.0948			0.444014
$743$	33.1315	−	19.1285i	1.21548	−	0.701757i	0.251531	−	0.967849i	$-0.419066\pi$
$743$	33.1315	−	19.1285i	1.21548	−	0.701757i	0.963947	+	0.266093i	$0.0857328\pi$
$744$		0			0
$745$	38.2315	−	66.2189i	1.40069	−	2.42607i
$746$		−	11.0715i		−	0.405357i
$747$		0			0
$748$	−1.06124	−	0.612704i	−0.0388026	−	0.0224027i
$749$		−	11.6501i		−	0.425686i
$750$		0			0
$751$	−0.920125	−	1.59370i	−0.0335758	−	0.0581551i	0.848749	−	0.528796i	$-0.177356\pi$
$751$	−0.920125	−	1.59370i	−0.0335758	−	0.0581551i	−0.882325	+	0.470641i	$0.844023\pi$
$752$	7.92907	−	4.57785i	0.289143	−	0.166937i
$753$		0			0
$754$	−0.138566	−	0.327258i	−0.00504629	−	0.0119180i
$755$	−44.3157			−1.61281
$756$		0			0
$757$	10.5961	+	18.3529i	0.385120	+	0.667048i	0.991786	−	0.127909i	$-0.0408266\pi$
$757$	10.5961	+	18.3529i	0.385120	+	0.667048i	−0.606666	+	0.794957i	$0.707493\pi$
$758$	8.40523	−	14.5583i	0.305292	−	0.528780i
$759$		0			0
$760$	−6.86895	−	3.96579i	−0.249163	−	0.143854i
$761$	12.2381	+	7.06566i	0.443630	+	0.256130i	0.705136	−	0.709072i	$-0.250886\pi$
$761$	12.2381	+	7.06566i	0.443630	+	0.256130i	−0.261506	+	0.965202i	$0.584219\pi$
$762$		0			0
$763$	2.86654	−	4.96499i	0.103776	−	0.179745i
$764$	−0.0604880	−	0.104768i	−0.00218838	−	0.00379038i
$765$		0			0
$766$	−16.5771			−0.598955
$767$	0.326030	+	0.769999i	0.0117723	+	0.0278030i
$768$		0			0
$769$	−26.5219	+	15.3124i	−0.956405	+	0.552181i	−0.895065	−	0.445936i	$-0.852871\pi$
$769$	−26.5219	+	15.3124i	−0.956405	+	0.552181i	−0.0613401	+	0.998117i	$0.519537\pi$
$770$	10.7162	+	18.5609i	0.386184	+	0.668890i
$771$		0			0
$772$			2.75550i			0.0991725i
$773$	8.48254	+	4.89740i	0.305096	+	0.176147i	0.644730	−	0.764411i	$-0.276970\pi$
$773$	8.48254	+	4.89740i	0.305096	+	0.176147i	−0.339634	+	0.940558i	$0.610303\pi$
$774$		0			0
$775$			20.2743i			0.728273i
$776$	7.04093	−	12.1952i	0.252755	−	0.437784i
$777$		0			0
$778$	1.01336	−	0.585065i	0.0363308	−	0.0209756i
$779$	−16.0738			−0.575904
$780$		0			0
$781$	−42.5248			−1.52166
$782$	−0.455634	+	0.263061i	−0.0162934	+	0.00940702i
$783$		0			0
$784$	0.500000	−	0.866025i	0.0178571	−	0.0309295i
$785$		−	34.6645i		−	1.23723i
$786$		0			0
$787$	17.8665	+	10.3152i	0.636873	+	0.367699i	0.783409	−	0.621507i	$-0.213479\pi$
$787$	17.8665	+	10.3152i	0.636873	+	0.367699i	−0.146536	+	0.989205i	$0.546812\pi$
$788$		−	15.1253i		−	0.538818i
$789$		0			0
$790$	17.0674	+	29.5616i	0.607230	+	1.05175i
$791$	−14.3062	+	8.25971i	−0.508671	+	0.293682i
$792$		0			0
$793$	−26.6681	+	11.2917i	−0.947013	+	0.400981i
$794$	26.1975			0.929713
$795$		0			0
$796$	−2.65320	−	4.59548i	−0.0940402	−	0.162882i
$797$	−3.88584	+	6.73047i	−0.137643	+	0.238405i	−0.926604	−	0.376038i	$-0.877286\pi$
$797$	−3.88584	+	6.73047i	−0.137643	+	0.238405i	0.788961	+	0.614444i	$0.210619\pi$
$798$		0			0
$799$	1.68252	+	0.971406i	0.0595234	+	0.0343659i
$800$	7.59837	+	4.38692i	0.268643	+	0.155101i
$801$		0			0
$802$	5.68436	−	9.84559i	0.200722	−	0.347660i
$803$	−16.1816	−	28.0273i	−0.571036	−	0.989063i
$804$		0			0
$805$	9.20183			0.324322
$806$	1.02278	−	8.26856i	0.0360259	−	0.291248i
$807$		0			0
$808$	5.32816	−	3.07622i	0.187444	−	0.108221i
$809$	21.2715	+	36.8433i	0.747866	+	1.29534i	0.948844	+	0.315746i	$0.102255\pi$
$809$	21.2715	+	36.8433i	0.747866	+	1.29534i	−0.200977	+	0.979596i	$0.564412\pi$
$810$		0			0
$811$		−	22.1131i		−	0.776494i	−0.921555	−	0.388247i	$-0.873081\pi$
$811$		−	22.1131i		−	0.776494i	0.921555	−	0.388247i	$-0.126919\pi$
$812$	0.0853606	+	0.0492830i	0.00299557	+	0.00172949i
$813$		0			0
$814$		−	45.4680i		−	1.59365i
$815$	8.30833	−	14.3905i	0.291028	−	0.504076i
$816$		0			0
$817$	8.47624	−	4.89376i	0.296546	−	0.171211i
$818$	−23.3314			−0.815763
$819$		0			0
$820$	27.9135			0.974782
$821$	−21.0920	+	12.1775i	−0.736115	+	0.424996i	−0.820655	−	0.571424i	$-0.806391\pi$
$821$	−21.0920	+	12.1775i	−0.736115	+	0.424996i	0.0845401	+	0.996420i	$0.473058\pi$
$822$		0			0
$823$	−2.37957	+	4.12153i	−0.0829465	+	0.143668i	−0.904514	−	0.426443i	$-0.859766\pi$
$823$	−2.37957	+	4.12153i	−0.0829465	+	0.143668i	0.821568	+	0.570111i	$0.193100\pi$
$824$		−	19.3491i		−	0.674056i
$825$		0			0
$826$	−0.200843	−	0.115957i	−0.00698824	−	0.00403466i
$827$		−	7.00333i		−	0.243530i	−0.992559	−	0.121765i	$-0.961145\pi$
$827$		−	7.00333i		−	0.243530i	0.992559	−	0.121765i	$-0.0388554\pi$
$828$		0			0
$829$	−2.87619	−	4.98170i	−0.0998941	−	0.173022i	0.811747	−	0.584010i	$-0.198517\pi$
$829$	−2.87619	−	4.98170i	−0.0998941	−	0.173022i	−0.911641	+	0.410988i	$0.865184\pi$
$830$	10.1946	−	5.88588i	0.353861	−	0.204302i
$831$		0			0
$832$	−2.87757	−	2.17246i	−0.0997619	−	0.0753164i
$833$	0.212197			0.00735219
$834$		0			0
$835$	27.2908	+	47.2691i	0.944438	+	1.63582i
$836$	6.17084	−	10.6882i	0.213423	−	0.369659i
$837$		0			0
$838$	−10.9709	−	6.33402i	−0.378982	−	0.218805i
$839$	35.6863	+	20.6035i	1.23203	+	0.711311i	0.967452	−	0.253054i	$-0.0814350\pi$
$839$	35.6863	+	20.6035i	1.23203	+	0.711311i	0.264575	+	0.964365i	$0.414768\pi$
$840$		0			0
$841$	14.4951	−	25.1063i	0.499832	−	0.865735i
$842$	−13.8312	−	23.9564i	−0.476656	−	0.825593i
$843$		0			0
$844$	−17.8982			−0.616081
$845$	46.4018	−	13.2155i	1.59627	−	0.454626i
$846$		0			0
$847$	−19.3549	+	11.1745i	−0.665041	+	0.383961i
$848$	6.04740	+	10.4744i	0.207669	+	0.359692i
$849$		0			0
$850$			1.86178i			0.0638586i
$851$	−16.9060	−	9.76069i	−0.579530	−	0.334592i
$852$		0			0
$853$		−	2.38939i		−	0.0818113i	−0.999163	−	0.0409056i	$-0.986976\pi$
$853$		−	2.38939i		−	0.0818113i	0.999163	−	0.0409056i	$-0.0130243\pi$
$854$	4.01605	−	6.95601i	0.137427	−	0.238030i
$855$		0			0
$856$	10.0893	−	5.82506i	0.344845	−	0.199096i
$857$	13.8037			0.471526			0.235763	−	0.971811i	$-0.424241\pi$
$857$	13.8037			0.471526			0.235763	+	0.971811i	$0.424241\pi$
$858$		0			0
$859$	−37.7276			−1.28725			−0.643624	−	0.765342i	$-0.722570\pi$
$859$	−37.7276			−1.28725			−0.643624	+	0.765342i	$0.722570\pi$
$860$	−14.7197	+	8.49841i	−0.501937	+	0.289793i
$861$		0			0
$862$	−3.20696	+	5.55462i	−0.109230	+	0.189191i
$863$		−	25.5180i		−	0.868643i	−0.900758	−	0.434322i	$-0.856988\pi$
$863$		−	25.5180i		−	0.868643i	0.900758	−	0.434322i	$-0.143012\pi$
$864$		0			0
$865$	44.2443	+	25.5444i	1.50435	+	0.868537i
$866$			0.0650270i			0.00220971i
$867$		0			0
$868$	1.15538	+	2.00118i	0.0392162	+	0.0679245i
$869$	−45.9983	+	26.5571i	−1.56039	+	0.900889i
$870$		0			0
$871$	−46.4103	−	5.74073i	−1.57255	−	0.194517i
$872$	5.73307			0.194146
$873$		0			0
$874$	−2.64941	−	4.58891i	−0.0896175	−	0.155222i
$875$	7.00296	−	12.1295i	0.236743	−	0.410051i
$876$		0			0
$877$	10.7726	+	6.21955i	0.363764	+	0.210019i	0.670731	−	0.741701i	$-0.265981\pi$
$877$	10.7726	+	6.21955i	0.363764	+	0.210019i	−0.306966	+	0.951720i	$0.599314\pi$
$878$	31.8505	+	18.3889i	1.07490	+	0.620596i
$879$		0			0
$880$	−10.7162	+	18.5609i	−0.361242	+	0.625689i
$881$	11.2710	+	19.5219i	0.379728	+	0.657709i	0.991023	−	0.133694i	$-0.0426841\pi$
$881$	11.2710	+	19.5219i	0.379728	+	0.657709i	−0.611294	+	0.791404i	$0.709351\pi$
$882$		0			0
$883$	−15.1548			−0.509998			−0.254999	−	0.966941i	$-0.582075\pi$
$883$	−15.1548			−0.509998			−0.254999	+	0.966941i	$0.582075\pi$
$884$	0.0939218	−	0.759300i	0.00315893	−	0.0255380i
$885$		0			0
$886$	7.32989	−	4.23191i	0.246252	−	0.142174i
$887$	20.8875	+	36.1781i	0.701332	+	1.21474i	0.967999	+	0.250954i	$0.0807443\pi$
$887$	20.8875	+	36.1781i	0.701332	+	1.21474i	−0.266667	+	0.963789i	$0.585922\pi$
$888$		0			0
$889$			11.7884i			0.395370i
$890$	−37.9798	−	21.9277i	−1.27309	−	0.735017i
$891$		0			0
$892$			16.4385i			0.550402i
$893$	−9.78349	+	16.9455i	−0.327392	+	0.567060i
$894$		0			0
$895$	−49.1072	+	28.3521i	−1.64147	+	0.947705i
$896$	1.00000			0.0334077
$897$		0			0
$898$	22.6303			0.755183
$899$	−0.197248	+	0.113881i	−0.00657860	+	0.00379815i
$900$		0			0
$901$	−1.28324	+	2.22264i	−0.0427509	+	0.0740468i
$902$			43.4339i			1.44619i
$903$		0			0
$904$	−14.3062	−	8.25971i	−0.475818	−	0.274714i
$905$			6.18853i			0.205714i
$906$		0			0
$907$	2.14376	+	3.71310i	0.0711823	+	0.123291i	0.899420	−	0.437086i	$-0.143989\pi$
$907$	2.14376	+	3.71310i	0.0711823	+	0.123291i	−0.828237	+	0.560377i	$0.810656\pi$
$908$	4.87655	−	2.81547i	0.161834	−	0.0934348i
$909$		0			0
$910$	−8.06267	+	10.6796i	−0.267275	+	0.354025i
$911$	3.87618			0.128423			0.0642117	−	0.997936i	$-0.479547\pi$
$911$	3.87618			0.128423			0.0642117	+	0.997936i	$0.479547\pi$
$912$		0			0
$913$	9.15853	+	15.8630i	0.303103	+	0.524990i
$914$	−8.15851	+	14.1310i	−0.269859	+	0.467410i
$915$		0			0
$916$	−24.0084	−	13.8613i	−0.793260	−	0.457989i
$917$	−4.44149	−	2.56429i	−0.146671	−	0.0846805i
$918$		0			0
$919$	−22.9524	+	39.7547i	−0.757129	+	1.31139i	0.187180	+	0.982326i	$0.440065\pi$
$919$	−22.9524	+	39.7547i	−0.757129	+	1.31139i	−0.944309	+	0.329060i	$0.893268\pi$
$920$	4.60091	+	7.96901i	0.151688	+	0.262731i
$921$		0			0
$922$	−19.2778			−0.634882
$923$	−10.3522	−	24.4491i	−0.340745	−	0.804752i
$924$		0			0
$925$	−59.8253	+	34.5401i	−1.96704	+	1.13567i
$926$	1.35109	+	2.34015i	0.0443995	+	0.0769022i
$927$		0			0
$928$			0.0985660i			0.00323559i
$929$	−8.51833	−	4.91806i	−0.279477	−	0.161356i	0.353709	−	0.935355i	$-0.384920\pi$
$929$	−8.51833	−	4.91806i	−0.279477	−	0.161356i	−0.633187	+	0.773999i	$0.718254\pi$
$930$		0			0
$931$			2.13714i			0.0700418i
$932$	10.0552	−	17.4161i	0.329368	−	0.570483i
$933$		0			0
$934$	15.9267	−	9.19528i	0.521137	−	0.300879i
$935$	−4.54788			−0.148731
$936$		0			0
$937$	21.5135			0.702815			0.351407	−	0.936223i	$-0.385703\pi$
$937$	21.5135			0.702815			0.351407	+	0.936223i	$0.385703\pi$
$938$	11.2323	−	6.48500i	0.366749	−	0.211743i
$939$		0			0
$940$	16.9898	−	29.4272i	0.554147	−	0.959811i
$941$		−	6.41845i		−	0.209236i	−0.994513	−	0.104618i	$-0.966638\pi$
$941$		−	6.41845i		−	0.209236i	0.994513	−	0.104618i	$-0.0333619\pi$
$942$		0			0
$943$	16.1497	+	9.32402i	0.525906	+	0.303632i
$944$		−	0.231914i		−	0.00754816i
$945$		0			0
$946$	−13.2237	−	22.9041i	−0.429939	−	0.744675i
$947$	−6.55812	+	3.78633i	−0.213110	+	0.123039i	−0.602756	−	0.797926i	$-0.705931\pi$
$947$	−6.55812	+	3.78633i	−0.213110	+	0.123039i	0.389646	+	0.920965i	$0.372597\pi$
$948$		0			0
$949$	12.1748	−	16.1263i	0.395209	−	0.523483i
$950$	−18.7509			−0.608360
$951$		0			0
$952$	0.106098	+	0.183768i	0.00343867	+	0.00595595i
$953$	17.9022	−	31.0075i	0.579909	−	1.00443i	−0.415580	−	0.909557i	$-0.636421\pi$
$953$	17.9022	−	31.0075i	0.579909	−	1.00443i	0.995489	−	0.0948754i	$-0.0302453\pi$
$954$		0			0
$955$	−0.388828	−	0.224490i	−0.0125822	−	0.00726432i
$956$	5.74147	+	3.31484i	0.185692	+	0.107210i
$957$		0			0
$958$	−20.4354	+	35.3951i	−0.660238	+	1.14357i
$959$	−4.69664	−	8.13482i	−0.151662	−	0.262687i
$960$		0			0
$961$	25.6604			0.827754
$962$	26.1413	−	11.0687i	0.842829	−	0.356868i
$963$		0			0
$964$	1.40025	−	0.808433i	0.0450989	−	0.0260379i
$965$	5.11326	+	8.85642i	0.164602	+	0.285098i
$966$		0			0
$967$		−	32.3876i		−	1.04152i	−0.853704	−	0.520758i	$-0.825649\pi$
$967$		−	32.3876i		−	1.04152i	0.853704	−	0.520758i	$-0.174351\pi$
$968$	−19.3549	−	11.1745i	−0.622089	−	0.359163i
$969$		0			0
$970$		−	52.2622i		−	1.67804i
$971$	17.2033	−	29.7969i	0.552079	−	0.956229i	−0.446045	−	0.895010i	$-0.647168\pi$
$971$	17.2033	−	29.7969i	0.552079	−	0.956229i	0.998124	−	0.0612186i	$-0.0194987\pi$
$972$		0			0
$973$	13.1127	−	7.57063i	0.420374	−	0.242703i
$974$	17.6293			0.564880
$975$		0			0
$976$	8.03211			0.257102
$977$	−20.0471	+	11.5742i	−0.641364	+	0.370291i	−0.785140	−	0.619319i	$-0.787409\pi$
$977$	−20.0471	+	11.5742i	−0.641364	+	0.370291i	0.143776	+	0.989610i	$0.454076\pi$
$978$		0			0
$979$	34.1198	−	59.0972i	1.09047	−	1.88876i
$980$		−	3.71131i		−	0.118554i
$981$		0			0
$982$	16.3332	+	9.42997i	0.521213	+	0.300922i
$983$		−	47.0579i		−	1.50092i	−0.660919	−	0.750458i	$-0.729833\pi$
$983$		−	47.0579i		−	1.50092i	0.660919	−	0.750458i	$-0.270167\pi$
$984$		0			0
$985$	−28.0674	−	48.6142i	−0.894303	−	1.54898i
$986$	−0.0181133	+	0.0104577i	−0.000576844	+	0.000333041i
$987$		0			0
$988$	7.64727	+	0.945931i	0.243292	+	0.0300941i
$989$	−11.3550			−0.361068
$990$		0			0
$991$	5.95052	+	10.3066i	0.189025	+	0.327400i	0.944925	−	0.327286i	$-0.106134\pi$
$991$	5.95052	+	10.3066i	0.189025	+	0.327400i	−0.755901	+	0.654686i	$0.772801\pi$
$992$	−1.15538	+	2.00118i	−0.0366834	+	0.0635375i
$993$		0			0
$994$	6.37721	+	3.68188i	0.202273	+	0.116782i
$995$	−17.0553	−	9.84686i	−0.540688	−	0.312167i
$996$		0			0
$997$	−6.50714	+	11.2707i	−0.206083	+	0.356946i	−0.950477	−	0.310794i	$-0.899405\pi$
$997$	−6.50714	+	11.2707i	−0.206083	+	0.356946i	0.744394	+	0.667740i	$0.232738\pi$
$998$	−1.05371	−	1.82508i	−0.0333546	−	0.0577718i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.bj.g.127.4		12
3.2	odd	2		182.2.m.b.127.3	yes	12
12.11	even	2		1456.2.cc.d.673.2		12
13.4	even	6	inner	1638.2.bj.g.1135.6		12
21.2	odd	6		1274.2.v.e.361.4		12
21.5	even	6		1274.2.v.d.361.6		12
21.11	odd	6		1274.2.o.d.569.3		12
21.17	even	6		1274.2.o.e.569.1		12
21.20	even	2		1274.2.m.c.491.1		12
39.2	even	12		2366.2.a.bf.1.2		6
39.11	even	12		2366.2.a.bh.1.2		6
39.17	odd	6		182.2.m.b.43.3	✓	12
39.23	odd	6		2366.2.d.r.337.8		12
39.29	odd	6		2366.2.d.r.337.2		12
156.95	even	6		1456.2.cc.d.225.2		12
273.17	even	6		1274.2.v.d.667.6		12
273.95	odd	6		1274.2.v.e.667.4		12
273.173	even	6		1274.2.o.e.459.4		12
273.212	odd	6		1274.2.o.d.459.6		12
273.251	even	6		1274.2.m.c.589.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.3	✓	12	39.17	odd	6
182.2.m.b.127.3	yes	12	3.2	odd	2
1274.2.m.c.491.1		12	21.20	even	2
1274.2.m.c.589.1		12	273.251	even	6
1274.2.o.d.459.6		12	273.212	odd	6
1274.2.o.d.569.3		12	21.11	odd	6
1274.2.o.e.459.4		12	273.173	even	6
1274.2.o.e.569.1		12	21.17	even	6
1274.2.v.d.361.6		12	21.5	even	6
1274.2.v.d.667.6		12	273.17	even	6
1274.2.v.e.361.4		12	21.2	odd	6
1274.2.v.e.667.4		12	273.95	odd	6
1456.2.cc.d.225.2		12	156.95	even	6
1456.2.cc.d.673.2		12	12.11	even	2
1638.2.bj.g.127.4		12	1.1	even	1	trivial
1638.2.bj.g.1135.6		12	13.4	even	6	inner
2366.2.a.bf.1.2		6	39.2	even	12
2366.2.a.bh.1.2		6	39.11	even	12
2366.2.d.r.337.2		12	39.29	odd	6
2366.2.d.r.337.8		12	39.23	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.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.71131i q^{5} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.71131i q^{5} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-1.85566 - 3.21409i) q^{10} +(5.00118 - 2.88743i) q^{11} +(2.87757 + 2.17246i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.106098 - 0.183768i) q^{17} +(1.85081 + 1.06857i) q^{19} +(-3.21409 - 1.85566i) q^{20} +(2.88743 - 5.00118i) q^{22} +(-1.23970 - 2.14722i) q^{23} -8.77384 q^{25} +(3.57828 + 0.442616i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(-0.0492830 - 0.0853606i) q^{29} -2.31076i q^{31} +(-0.866025 - 0.500000i) q^{32} -0.212197i q^{34} +(-1.85566 + 3.21409i) q^{35} +(6.81859 - 3.93672i) q^{37} +2.13714 q^{38} -3.71131 q^{40} +(-6.51354 + 3.76060i) q^{41} +(2.28987 - 3.96617i) q^{43} -5.77486i q^{44} +(-2.14722 - 1.23970i) q^{46} +9.15570i q^{47} +(0.500000 + 0.866025i) q^{49} +(-7.59837 + 4.38692i) q^{50} +(3.32019 - 1.40582i) q^{52} -12.0948 q^{53} +(-10.7162 - 18.5609i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-0.0853606 - 0.0492830i) q^{58} +(0.200843 + 0.115957i) q^{59} +(-4.01605 + 6.95601i) q^{61} +(-1.15538 - 2.00118i) q^{62} -1.00000 q^{64} +(8.06267 - 10.6796i) q^{65} +(-11.2323 + 6.48500i) q^{67} +(-0.106098 - 0.183768i) q^{68} +3.71131i q^{70} +(-6.37721 - 3.68188i) q^{71} -5.60414i q^{73} +(3.93672 - 6.81859i) q^{74} +(1.85081 - 1.06857i) q^{76} -5.77486 q^{77} -9.19749 q^{79} +(-3.21409 + 1.85566i) q^{80} +(-3.76060 + 6.51354i) q^{82} +3.17186i q^{83} +(-0.682021 - 0.393765i) q^{85} -4.57973i q^{86} +(-2.88743 - 5.00118i) q^{88} +(10.2335 - 5.90833i) q^{89} +(-1.40582 - 3.32019i) q^{91} -2.47940 q^{92} +(4.57785 + 7.92907i) q^{94} +(3.96579 - 6.86895i) q^{95} +(12.1952 + 7.04093i) q^{97} +(0.866025 + 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4}+O(q^{10}) \) 12 * q + 6 * q^4	\( 12 q + 6 q^{4} - 2 q^{10} + 18 q^{11} - 8 q^{13} - 12 q^{14} - 6 q^{16} - 4 q^{17} + 12 q^{19} - 2 q^{22} + 6 q^{23} - 24 q^{25} + 14 q^{26} + 10 q^{29} - 2 q^{35} - 6 q^{37} - 8 q^{38} - 4 q^{40} + 24 q^{41} + 26 q^{43} - 6 q^{46} + 6 q^{49} + 12 q^{50} - 4 q^{52} - 36 q^{53} - 6 q^{55} - 6 q^{56} + 24 q^{58} - 6 q^{59} - 28 q^{61} + 2 q^{62} - 12 q^{64} + 34 q^{65} - 42 q^{67} + 4 q^{68} - 48 q^{71} + 12 q^{76} + 4 q^{77} + 44 q^{79} + 6 q^{82} + 54 q^{85} + 2 q^{88} - 12 q^{89} - 16 q^{91} + 12 q^{92} + 8 q^{94} - 32 q^{95} + 60 q^{97}+O(q^{100}) \) 12 * q + 6 * q^4 - 2 * q^10 + 18 * q^11 - 8 * q^13 - 12 * q^14 - 6 * q^16 - 4 * q^17 + 12 * q^19 - 2 * q^22 + 6 * q^23 - 24 * q^25 + 14 * q^26 + 10 * q^29 - 2 * q^35 - 6 * q^37 - 8 * q^38 - 4 * q^40 + 24 * q^41 + 26 * q^43 - 6 * q^46 + 6 * q^49 + 12 * q^50 - 4 * q^52 - 36 * q^53 - 6 * q^55 - 6 * q^56 + 24 * q^58 - 6 * q^59 - 28 * q^61 + 2 * q^62 - 12 * q^64 + 34 * q^65 - 42 * q^67 + 4 * q^68 - 48 * q^71 + 12 * q^76 + 4 * q^77 + 44 * q^79 + 6 * q^82 + 54 * q^85 + 2 * q^88 - 12 * q^89 - 16 * q^91 + 12 * q^92 + 8 * q^94 - 32 * q^95 + 60 * q^97

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