LMFDB - Embedded newform 2106.2.e.j.1405.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2106,2,Mod(703,2106)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2106, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("2106.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2106 = 2 \cdot 3^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2106.e (of order $3$, degree $2$, not 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:	$16.8164946657$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1405.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2106.1405
Dual form			2106.2.e.j.703.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +(-2.00000 - 3.46410i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +(-2.00000 - 3.46410i) q^{7} +1.00000 q^{8} -2.00000 q^{10} +(-2.00000 - 3.46410i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(-2.00000 + 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} -2.00000 q^{17} -8.00000 q^{19} +(1.00000 + 1.73205i) q^{20} +(-2.00000 + 3.46410i) q^{22} +(0.500000 + 0.866025i) q^{25} +1.00000 q^{26} +4.00000 q^{28} +(3.00000 + 5.19615i) q^{29} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{34} -8.00000 q^{35} -2.00000 q^{37} +(4.00000 + 6.92820i) q^{38} +(1.00000 - 1.73205i) q^{40} +(-5.00000 + 8.66025i) q^{41} +(-2.00000 - 3.46410i) q^{43} +4.00000 q^{44} +(4.00000 + 6.92820i) q^{47} +(-4.50000 + 7.79423i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.500000 - 0.866025i) q^{52} +10.0000 q^{53} -8.00000 q^{55} +(-2.00000 - 3.46410i) q^{56} +(3.00000 - 5.19615i) q^{58} +(2.00000 - 3.46410i) q^{59} +(1.00000 + 1.73205i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(8.00000 - 13.8564i) q^{67} +(1.00000 - 1.73205i) q^{68} +(4.00000 + 6.92820i) q^{70} +8.00000 q^{71} +2.00000 q^{73} +(1.00000 + 1.73205i) q^{74} +(4.00000 - 6.92820i) q^{76} +(-8.00000 + 13.8564i) q^{77} +(-4.00000 - 6.92820i) q^{79} -2.00000 q^{80} +10.0000 q^{82} +(6.00000 + 10.3923i) q^{83} +(-2.00000 + 3.46410i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(-2.00000 - 3.46410i) q^{88} -14.0000 q^{89} +4.00000 q^{91} +(4.00000 - 6.92820i) q^{94} +(-8.00000 + 13.8564i) q^{95} +(-5.00000 - 8.66025i) q^{97} +9.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8} - 4 q^{10} - 4 q^{11} - q^{13} - 4 q^{14} - q^{16} - 4 q^{17} - 16 q^{19} + 2 q^{20} - 4 q^{22} + q^{25} + 2 q^{26} + 8 q^{28} + 6 q^{29} + 4 q^{31} - q^{32} + 2 q^{34} - 16 q^{35} - 4 q^{37} + 8 q^{38} + 2 q^{40} - 10 q^{41} - 4 q^{43} + 8 q^{44} + 8 q^{47} - 9 q^{49} + q^{50} - q^{52} + 20 q^{53} - 16 q^{55} - 4 q^{56} + 6 q^{58} + 4 q^{59} + 2 q^{61} - 8 q^{62} + 2 q^{64} + 2 q^{65} + 16 q^{67} + 2 q^{68} + 8 q^{70} + 16 q^{71} + 4 q^{73} + 2 q^{74} + 8 q^{76} - 16 q^{77} - 8 q^{79} - 4 q^{80} + 20 q^{82} + 12 q^{83} - 4 q^{85} - 4 q^{86} - 4 q^{88} - 28 q^{89} + 8 q^{91} + 8 q^{94} - 16 q^{95} - 10 q^{97} + 18 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8 - 4 * q^10 - 4 * q^11 - q^13 - 4 * q^14 - q^16 - 4 * q^17 - 16 * q^19 + 2 * q^20 - 4 * q^22 + q^25 + 2 * q^26 + 8 * q^28 + 6 * q^29 + 4 * q^31 - q^32 + 2 * q^34 - 16 * q^35 - 4 * q^37 + 8 * q^38 + 2 * q^40 - 10 * q^41 - 4 * q^43 + 8 * q^44 + 8 * q^47 - 9 * q^49 + q^50 - q^52 + 20 * q^53 - 16 * q^55 - 4 * q^56 + 6 * q^58 + 4 * q^59 + 2 * q^61 - 8 * q^62 + 2 * q^64 + 2 * q^65 + 16 * q^67 + 2 * q^68 + 8 * q^70 + 16 * q^71 + 4 * q^73 + 2 * q^74 + 8 * q^76 - 16 * q^77 - 8 * q^79 - 4 * q^80 + 20 * q^82 + 12 * q^83 - 4 * q^85 - 4 * q^86 - 4 * q^88 - 28 * q^89 + 8 * q^91 + 8 * q^94 - 16 * q^95 - 10 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2106\mathbb{Z}\right)^\times$.

$n$	$1379$	$1783$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	0.998203	+	0.0599153i	$0.0190830\pi$
$6$		0			0
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	0.188982	−	0.981981i	$-0.439481\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−2.00000			−0.632456
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	−2.00000	+	3.46410i	−0.534522	+	0.925820i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$		0			0
$19$	−8.00000			−1.83533			−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000			−1.83533			−0.917663	+	0.397360i	$0.869927\pi$
$20$	1.00000	+	1.73205i	0.223607	+	0.387298i
$21$		0			0
$22$	−2.00000	+	3.46410i	−0.426401	+	0.738549i
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	1.00000			0.196116
$27$		0			0
$28$	4.00000			0.755929
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	1.00000	+	1.73205i	0.171499	+	0.297044i
$35$	−8.00000			−1.35225
$36$		0			0
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	4.00000	+	6.92820i	0.648886	+	1.12390i
$39$		0			0
$40$	1.00000	−	1.73205i	0.158114	−	0.273861i
$41$	−5.00000	+	8.66025i	−0.780869	+	1.35250i	0.150567	+	0.988600i	$0.451890\pi$
$41$	−5.00000	+	8.66025i	−0.780869	+	1.35250i	−0.931436	+	0.363905i	$0.881443\pi$
$42$		0			0
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	0.672264	−	0.740312i	$-0.265322\pi$
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	−0.977261	+	0.212041i	$0.931989\pi$
$44$	4.00000			0.603023
$45$		0			0
$46$		0			0
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	0.995066	+	0.0992202i	$0.0316348\pi$
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	−0.411606	+	0.911362i	$0.635032\pi$
$48$		0			0
$49$	−4.50000	+	7.79423i	−0.642857	+	1.11346i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$		0			0
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	10.0000			1.37361			0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000			1.37361			0.686803	+	0.726844i	$0.259014\pi$
$54$		0			0
$55$	−8.00000			−1.07872
$56$	−2.00000	−	3.46410i	−0.267261	−	0.462910i
$57$		0			0
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$		0			0
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	1.00000	+	1.73205i	0.124035	+	0.214834i
$66$		0			0
$67$	8.00000	−	13.8564i	0.977356	−	1.69283i	0.305424	−	0.952217i	$-0.401202\pi$
$67$	8.00000	−	13.8564i	0.977356	−	1.69283i	0.671932	−	0.740613i	$-0.265465\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$		0			0
$70$	4.00000	+	6.92820i	0.478091	+	0.828079i
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$		0			0
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$		0			0
$76$	4.00000	−	6.92820i	0.458831	−	0.794719i
$77$	−8.00000	+	13.8564i	−0.911685	+	1.57908i
$78$		0			0
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	−2.00000			−0.223607
$81$		0			0
$82$	10.0000			1.10432
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	0.980982	+	0.194099i	$0.0621783\pi$
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	−0.322396	+	0.946605i	$0.604488\pi$
$84$		0			0
$85$	−2.00000	+	3.46410i	−0.216930	+	0.375735i
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$		0			0
$88$	−2.00000	−	3.46410i	−0.213201	−	0.369274i
$89$	−14.0000			−1.48400			−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000			−1.48400			−0.741999	+	0.670402i	$0.766122\pi$
$90$		0			0
$91$	4.00000			0.419314
$92$		0			0
$93$		0			0
$94$	4.00000	−	6.92820i	0.412568	−	0.714590i
$95$	−8.00000	+	13.8564i	−0.820783	+	1.42164i
$96$		0			0
$97$	−5.00000	−	8.66025i	−0.507673	−	0.879316i	−0.999961	−	0.00888289i	$-0.997172\pi$
$97$	−5.00000	−	8.66025i	−0.507673	−	0.879316i	0.492287	−	0.870433i	$-0.336161\pi$
$98$	9.00000			0.909137
$99$		0			0
$100$	−1.00000			−0.100000
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	0.811976	−	0.583691i	$-0.198392\pi$
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	−0.911479	+	0.411346i	$0.865059\pi$
$102$		0			0
$103$	−8.00000	+	13.8564i	−0.788263	+	1.36531i	0.138767	+	0.990325i	$0.455686\pi$
$103$	−8.00000	+	13.8564i	−0.788263	+	1.36531i	−0.927030	+	0.374987i	$0.877647\pi$
$104$	−0.500000	+	0.866025i	−0.0490290	+	0.0849208i
$105$		0			0
$106$	−5.00000	−	8.66025i	−0.485643	−	0.841158i
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	4.00000	+	6.92820i	0.381385	+	0.660578i
$111$		0			0
$112$	−2.00000	+	3.46410i	−0.188982	+	0.327327i
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	−0.971930	−	0.235269i	$-0.924403\pi$
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	0.689714	+	0.724082i	$0.257736\pi$
$114$		0			0
$115$		0			0
$116$	−6.00000			−0.557086
$117$		0			0
$118$	−4.00000			−0.368230
$119$	4.00000	+	6.92820i	0.366679	+	0.635107i
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	1.00000	−	1.73205i	0.0905357	−	0.156813i
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	12.0000			1.07331
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	1.00000	−	1.73205i	0.0877058	−	0.151911i
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	−0.765331	−	0.643637i	$-0.777425\pi$
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	0.940072	+	0.340977i	$0.110758\pi$
$132$		0			0
$133$	16.0000	+	27.7128i	1.38738	+	2.40301i
$134$	−16.0000			−1.38219
$135$		0			0
$136$	−2.00000			−0.171499
$137$	−5.00000	−	8.66025i	−0.427179	−	0.739895i	0.569442	−	0.822031i	$-0.307159\pi$
$137$	−5.00000	−	8.66025i	−0.427179	−	0.739895i	−0.996621	+	0.0821359i	$0.973826\pi$
$138$		0			0
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	0.491033	+	0.871141i	$0.336619\pi$
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	−0.999947	+	0.0103230i	$0.996714\pi$
$140$	4.00000	−	6.92820i	0.338062	−	0.585540i
$141$		0			0
$142$	−4.00000	−	6.92820i	−0.335673	−	0.581402i
$143$	4.00000			0.334497
$144$		0			0
$145$	12.0000			0.996546
$146$	−1.00000	−	1.73205i	−0.0827606	−	0.143346i
$147$		0			0
$148$	1.00000	−	1.73205i	0.0821995	−	0.142374i
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	−6.00000	−	10.3923i	−0.488273	−	0.845714i	0.511636	−	0.859202i	$-0.329040\pi$
$151$	−6.00000	−	10.3923i	−0.488273	−	0.845714i	−0.999909	+	0.0134886i	$0.995706\pi$
$152$	−8.00000			−0.648886
$153$		0			0
$154$	16.0000			1.28932
$155$	−4.00000	−	6.92820i	−0.321288	−	0.556487i
$156$		0			0
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	−4.00000	+	6.92820i	−0.318223	+	0.551178i
$159$		0			0
$160$	1.00000	+	1.73205i	0.0790569	+	0.136931i
$161$		0			0
$162$		0			0
$163$	−16.0000			−1.25322			−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000			−1.25322			−0.626608	+	0.779334i	$0.715557\pi$
$164$	−5.00000	−	8.66025i	−0.390434	−	0.676252i
$165$		0			0
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$167$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	4.00000			0.306786
$171$		0			0
$172$	4.00000			0.304997
$173$	−5.00000	−	8.66025i	−0.380143	−	0.658427i	0.610939	−	0.791677i	$-0.290792\pi$
$173$	−5.00000	−	8.66025i	−0.380143	−	0.658427i	−0.991082	+	0.133250i	$0.957459\pi$
$174$		0			0
$175$	2.00000	−	3.46410i	0.151186	−	0.261861i
$176$	−2.00000	+	3.46410i	−0.150756	+	0.261116i
$177$		0			0
$178$	7.00000	+	12.1244i	0.524672	+	0.908759i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	−2.00000	−	3.46410i	−0.148250	−	0.256776i
$183$		0			0
$184$		0			0
$185$	−2.00000	+	3.46410i	−0.147043	+	0.254686i
$186$		0			0
$187$	4.00000	+	6.92820i	0.292509	+	0.506640i
$188$	−8.00000			−0.583460
$189$		0			0
$190$	16.0000			1.16076
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	0.684244	−	0.729253i	$-0.260132\pi$
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	−0.973674	+	0.227946i	$0.926799\pi$
$192$		0			0
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	0.999990	−	0.00447566i	$-0.00142465\pi$
$194$	−5.00000	+	8.66025i	−0.358979	+	0.621770i
$195$		0			0
$196$	−4.50000	−	7.79423i	−0.321429	−	0.556731i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	−8.00000			−0.567105			−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000			−0.567105			−0.283552	+	0.958957i	$0.591513\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$		0			0
$202$	−1.00000	+	1.73205i	−0.0703598	+	0.121867i
$203$	12.0000	−	20.7846i	0.842235	−	1.45879i
$204$		0			0
$205$	10.0000	+	17.3205i	0.698430	+	1.20972i
$206$	16.0000			1.11477
$207$		0			0
$208$	1.00000			0.0693375
$209$	16.0000	+	27.7128i	1.10674	+	1.91694i
$210$		0			0
$211$	−6.00000	+	10.3923i	−0.413057	+	0.715436i	−0.995222	−	0.0976347i	$-0.968872\pi$
$211$	−6.00000	+	10.3923i	−0.413057	+	0.715436i	0.582165	+	0.813070i	$0.302206\pi$
$212$	−5.00000	+	8.66025i	−0.343401	+	0.594789i
$213$		0			0
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	−8.00000			−0.545595
$216$		0			0
$217$	−16.0000			−1.08615
$218$	1.00000	+	1.73205i	0.0677285	+	0.117309i
$219$		0			0
$220$	4.00000	−	6.92820i	0.269680	−	0.467099i
$221$	1.00000	−	1.73205i	0.0672673	−	0.116510i
$222$		0			0
$223$	2.00000	+	3.46410i	0.133930	+	0.231973i	0.925188	−	0.379509i	$-0.123907\pi$
$223$	2.00000	+	3.46410i	0.133930	+	0.231973i	−0.791258	+	0.611482i	$0.790574\pi$
$224$	4.00000			0.267261
$225$		0			0
$226$	6.00000			0.399114
$227$	10.0000	+	17.3205i	0.663723	+	1.14960i	0.979630	+	0.200812i	$0.0643581\pi$
$227$	10.0000	+	17.3205i	0.663723	+	1.14960i	−0.315906	+	0.948790i	$0.602309\pi$
$228$		0			0
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	0.231287	+	0.972886i	$0.425707\pi$
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	−0.958187	+	0.286143i	$0.907627\pi$
$230$		0			0
$231$		0			0
$232$	3.00000	+	5.19615i	0.196960	+	0.341144i
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$		0			0
$235$	16.0000			1.04372
$236$	2.00000	+	3.46410i	0.130189	+	0.225494i
$237$		0			0
$238$	4.00000	−	6.92820i	0.259281	−	0.449089i
$239$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$239$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$240$		0			0
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$	5.00000			0.321412
$243$		0			0
$244$	−2.00000			−0.128037
$245$	9.00000	+	15.5885i	0.574989	+	0.995910i
$246$		0			0
$247$	4.00000	−	6.92820i	0.254514	−	0.440831i
$248$	2.00000	−	3.46410i	0.127000	−	0.219971i
$249$		0			0
$250$	−6.00000	−	10.3923i	−0.379473	−	0.657267i
$251$	−4.00000			−0.252478			−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000			−0.252478			−0.126239	+	0.992000i	$0.540291\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$		0			0
$259$	4.00000	+	6.92820i	0.248548	+	0.430498i
$260$	−2.00000			−0.124035
$261$		0			0
$262$	−4.00000			−0.247121
$263$	4.00000	+	6.92820i	0.246651	+	0.427211i	0.962594	−	0.270947i	$-0.0873367\pi$
$263$	4.00000	+	6.92820i	0.246651	+	0.427211i	−0.715944	+	0.698158i	$0.754003\pi$
$264$		0			0
$265$	10.0000	−	17.3205i	0.614295	−	1.06399i
$266$	16.0000	−	27.7128i	0.981023	−	1.69918i
$267$		0			0
$268$	8.00000	+	13.8564i	0.488678	+	0.846415i
$269$	26.0000			1.58525			0.792624	−	0.609711i	$-0.208714\pi$
$269$	26.0000			1.58525			0.792624	+	0.609711i	$0.208714\pi$
$270$		0			0
$271$	−4.00000			−0.242983			−0.121491	−	0.992592i	$-0.538768\pi$
$271$	−4.00000			−0.242983			−0.121491	+	0.992592i	$0.538768\pi$
$272$	1.00000	+	1.73205i	0.0606339	+	0.105021i
$273$		0			0
$274$	−5.00000	+	8.66025i	−0.302061	+	0.523185i
$275$	2.00000	−	3.46410i	0.120605	−	0.208893i
$276$		0			0
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	−0.980373	−	0.197153i	$-0.936830\pi$
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	0.319447	−	0.947604i	$-0.396503\pi$
$278$	12.0000			0.719712
$279$		0			0
$280$	−8.00000			−0.478091
$281$	−13.0000	−	22.5167i	−0.775515	−	1.34323i	−0.934505	−	0.355951i	$-0.884157\pi$
$281$	−13.0000	−	22.5167i	−0.775515	−	1.34323i	0.158990	−	0.987280i	$-0.449176\pi$
$282$		0			0
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$	−4.00000	+	6.92820i	−0.237356	+	0.411113i
$285$		0			0
$286$	−2.00000	−	3.46410i	−0.118262	−	0.204837i
$287$	40.0000			2.36113
$288$		0			0
$289$	−13.0000			−0.764706
$290$	−6.00000	−	10.3923i	−0.352332	−	0.610257i
$291$		0			0
$292$	−1.00000	+	1.73205i	−0.0585206	+	0.101361i
$293$	13.0000	−	22.5167i	0.759468	−	1.31544i	−0.183654	−	0.982991i	$-0.558793\pi$
$293$	13.0000	−	22.5167i	0.759468	−	1.31544i	0.943122	−	0.332446i	$-0.107874\pi$
$294$		0			0
$295$	−4.00000	−	6.92820i	−0.232889	−	0.403376i
$296$	−2.00000			−0.116248
$297$		0			0
$298$	6.00000			0.347571
$299$		0			0
$300$		0			0
$301$	−8.00000	+	13.8564i	−0.461112	+	0.798670i
$302$	−6.00000	+	10.3923i	−0.345261	+	0.598010i
$303$		0			0
$304$	4.00000	+	6.92820i	0.229416	+	0.397360i
$305$	4.00000			0.229039
$306$		0			0
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$	−8.00000	−	13.8564i	−0.455842	−	0.789542i
$309$		0			0
$310$	−4.00000	+	6.92820i	−0.227185	+	0.393496i
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$		0			0
$313$	3.00000	+	5.19615i	0.169570	+	0.293704i	0.938269	−	0.345907i	$-0.112429\pi$
$313$	3.00000	+	5.19615i	0.169570	+	0.293704i	−0.768699	+	0.639611i	$0.779095\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	8.00000			0.450035
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	0.769395	−	0.638774i	$-0.220558\pi$
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	−0.937892	+	0.346929i	$0.887225\pi$
$318$		0			0
$319$	12.0000	−	20.7846i	0.671871	−	1.16371i
$320$	1.00000	−	1.73205i	0.0559017	−	0.0968246i
$321$		0			0
$322$		0			0
$323$	16.0000			0.890264
$324$		0			0
$325$	−1.00000			−0.0554700
$326$	8.00000	+	13.8564i	0.443079	+	0.767435i
$327$		0			0
$328$	−5.00000	+	8.66025i	−0.276079	+	0.478183i
$329$	16.0000	−	27.7128i	0.882109	−	1.52786i
$330$		0			0
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	0.734905	−	0.678170i	$-0.237227\pi$
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	−0.954765	+	0.297361i	$0.903893\pi$
$332$	−12.0000			−0.658586
$333$		0			0
$334$		0			0
$335$	−16.0000	−	27.7128i	−0.874173	−	1.51411i
$336$		0			0
$337$	−9.00000	+	15.5885i	−0.490261	+	0.849157i	−0.999937	−	0.0112091i	$-0.996432\pi$
$337$	−9.00000	+	15.5885i	−0.490261	+	0.849157i	0.509676	+	0.860366i	$0.329765\pi$
$338$	−0.500000	+	0.866025i	−0.0271964	+	0.0471056i
$339$		0			0
$340$	−2.00000	−	3.46410i	−0.108465	−	0.187867i
$341$	−16.0000			−0.866449
$342$		0			0
$343$	8.00000			0.431959
$344$	−2.00000	−	3.46410i	−0.107833	−	0.186772i
$345$		0			0
$346$	−5.00000	+	8.66025i	−0.268802	+	0.465578i
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	−0.980921	−	0.194409i	$-0.937721\pi$
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	0.658824	+	0.752297i	$0.271054\pi$
$348$		0			0
$349$	−3.00000	−	5.19615i	−0.160586	−	0.278144i	0.774493	−	0.632583i	$-0.218005\pi$
$349$	−3.00000	−	5.19615i	−0.160586	−	0.278144i	−0.935079	+	0.354439i	$0.884672\pi$
$350$	−4.00000			−0.213809
$351$		0			0
$352$	4.00000			0.213201
$353$	7.00000	+	12.1244i	0.372572	+	0.645314i	0.989960	−	0.141344i	$-0.0451425\pi$
$353$	7.00000	+	12.1244i	0.372572	+	0.645314i	−0.617388	+	0.786659i	$0.711809\pi$
$354$		0			0
$355$	8.00000	−	13.8564i	0.424596	−	0.735422i
$356$	7.00000	−	12.1244i	0.370999	−	0.642590i
$357$		0			0
$358$	−6.00000	−	10.3923i	−0.317110	−	0.549250i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	45.0000			2.36842
$362$	5.00000	+	8.66025i	0.262794	+	0.455173i
$363$		0			0
$364$	−2.00000	+	3.46410i	−0.104828	+	0.181568i
$365$	2.00000	−	3.46410i	0.104685	−	0.181319i
$366$		0			0
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	0.578101	−	0.815966i	$-0.303794\pi$
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	−0.995697	+	0.0926670i	$0.970461\pi$
$368$		0			0
$369$		0			0
$370$	4.00000			0.207950
$371$	−20.0000	−	34.6410i	−1.03835	−	1.79847i
$372$		0			0
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	−0.933181	−	0.359408i	$-0.882979\pi$
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	0.777847	+	0.628454i	$0.216312\pi$
$374$	4.00000	−	6.92820i	0.206835	−	0.358249i
$375$		0			0
$376$	4.00000	+	6.92820i	0.206284	+	0.357295i
$377$	−6.00000			−0.309016
$378$		0			0
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$	−8.00000	−	13.8564i	−0.410391	−	0.710819i
$381$		0			0
$382$	−4.00000	+	6.92820i	−0.204658	+	0.354478i
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	0.377531	+	0.925997i	$0.376773\pi$
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	−0.990702	+	0.136047i	$0.956560\pi$
$384$		0			0
$385$	16.0000	+	27.7128i	0.815436	+	1.41238i
$386$	−14.0000			−0.712581
$387$		0			0
$388$	10.0000			0.507673
$389$	−13.0000	−	22.5167i	−0.659126	−	1.14164i	−0.980842	−	0.194804i	$-0.937593\pi$
$389$	−13.0000	−	22.5167i	−0.659126	−	1.14164i	0.321716	−	0.946836i	$-0.395740\pi$
$390$		0			0
$391$		0			0
$392$	−4.50000	+	7.79423i	−0.227284	+	0.393668i
$393$		0			0
$394$	9.00000	+	15.5885i	0.453413	+	0.785335i
$395$	−16.0000			−0.805047
$396$		0			0
$397$	6.00000			0.301131			0.150566	−	0.988600i	$-0.451890\pi$
$397$	6.00000			0.301131			0.150566	+	0.988600i	$0.451890\pi$
$398$	4.00000	+	6.92820i	0.200502	+	0.347279i
$399$		0			0
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	0.931158	+	0.364615i	$0.118800\pi$
$402$		0			0
$403$	2.00000	+	3.46410i	0.0996271	+	0.172559i
$404$	2.00000			0.0995037
$405$		0			0
$406$	−24.0000			−1.19110
$407$	4.00000	+	6.92820i	0.198273	+	0.343418i
$408$		0			0
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	−0.889689	−	0.456566i	$-0.849079\pi$
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	0.840243	+	0.542211i	$0.182412\pi$
$410$	10.0000	−	17.3205i	0.493865	−	0.855399i
$411$		0			0
$412$	−8.00000	−	13.8564i	−0.394132	−	0.682656i
$413$	−16.0000			−0.787309
$414$		0			0
$415$	24.0000			1.17811
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$		0			0
$418$	16.0000	−	27.7128i	0.782586	−	1.35548i
$419$	2.00000	−	3.46410i	0.0977064	−	0.169232i	−0.813029	−	0.582224i	$-0.802183\pi$
$419$	2.00000	−	3.46410i	0.0977064	−	0.169232i	0.910735	+	0.412991i	$0.135516\pi$
$420$		0			0
$421$	−11.0000	−	19.0526i	−0.536107	−	0.928565i	−0.999109	−	0.0422075i	$-0.986561\pi$
$421$	−11.0000	−	19.0526i	−0.536107	−	0.928565i	0.463002	−	0.886357i	$-0.346772\pi$
$422$	12.0000			0.584151
$423$		0			0
$424$	10.0000			0.485643
$425$	−1.00000	−	1.73205i	−0.0485071	−	0.0840168i
$426$		0			0
$427$	4.00000	−	6.92820i	0.193574	−	0.335279i
$428$	6.00000	−	10.3923i	0.290021	−	0.502331i
$429$		0			0
$430$	4.00000	+	6.92820i	0.192897	+	0.334108i
$431$	8.00000			0.385346			0.192673	−	0.981263i	$-0.438284\pi$
$431$	8.00000			0.385346			0.192673	+	0.981263i	$0.438284\pi$
$432$		0			0
$433$	−30.0000			−1.44171			−0.720854	−	0.693087i	$-0.756250\pi$
$433$	−30.0000			−1.44171			−0.720854	+	0.693087i	$0.756250\pi$
$434$	8.00000	+	13.8564i	0.384012	+	0.665129i
$435$		0			0
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$		0			0
$438$		0			0
$439$	−8.00000	−	13.8564i	−0.381819	−	0.661330i	0.609503	−	0.792784i	$-0.291369\pi$
$439$	−8.00000	−	13.8564i	−0.381819	−	0.661330i	−0.991322	+	0.131453i	$0.958036\pi$
$440$	−8.00000			−0.381385
$441$		0			0
$442$	−2.00000			−0.0951303
$443$	−2.00000	−	3.46410i	−0.0950229	−	0.164584i	0.814595	−	0.580030i	$-0.196959\pi$
$443$	−2.00000	−	3.46410i	−0.0950229	−	0.164584i	−0.909618	+	0.415445i	$0.863626\pi$
$444$		0			0
$445$	−14.0000	+	24.2487i	−0.663664	+	1.14950i
$446$	2.00000	−	3.46410i	0.0947027	−	0.164030i
$447$		0			0
$448$	−2.00000	−	3.46410i	−0.0944911	−	0.163663i
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$		0			0
$451$	40.0000			1.88353
$452$	−3.00000	−	5.19615i	−0.141108	−	0.244406i
$453$		0			0
$454$	10.0000	−	17.3205i	0.469323	−	0.812892i
$455$	4.00000	−	6.92820i	0.187523	−	0.324799i
$456$		0			0
$457$	15.0000	+	25.9808i	0.701670	+	1.21533i	0.967880	+	0.251414i	$0.0808954\pi$
$457$	15.0000	+	25.9808i	0.701670	+	1.21533i	−0.266209	+	0.963915i	$0.585771\pi$
$458$	22.0000			1.02799
$459$		0			0
$460$		0			0
$461$	−3.00000	−	5.19615i	−0.139724	−	0.242009i	0.787668	−	0.616100i	$-0.211288\pi$
$461$	−3.00000	−	5.19615i	−0.139724	−	0.242009i	−0.927392	+	0.374091i	$0.877955\pi$
$462$		0			0
$463$	10.0000	−	17.3205i	0.464739	−	0.804952i	−0.534450	−	0.845200i	$-0.679481\pi$
$463$	10.0000	−	17.3205i	0.464739	−	0.804952i	0.999190	+	0.0402476i	$0.0128147\pi$
$464$	3.00000	−	5.19615i	0.139272	−	0.241225i
$465$		0			0
$466$	9.00000	+	15.5885i	0.416917	+	0.722121i
$467$	4.00000			0.185098			0.0925490	−	0.995708i	$-0.470499\pi$
$467$	4.00000			0.185098			0.0925490	+	0.995708i	$0.470499\pi$
$468$		0			0
$469$	−64.0000			−2.95525
$470$	−8.00000	−	13.8564i	−0.369012	−	0.639148i
$471$		0			0
$472$	2.00000	−	3.46410i	0.0920575	−	0.159448i
$473$	−8.00000	+	13.8564i	−0.367840	+	0.637118i
$474$		0			0
$475$	−4.00000	−	6.92820i	−0.183533	−	0.317888i
$476$	−8.00000			−0.366679
$477$		0			0
$478$		0			0
$479$	−8.00000	−	13.8564i	−0.365529	−	0.633115i	0.623332	−	0.781958i	$-0.285779\pi$
$479$	−8.00000	−	13.8564i	−0.365529	−	0.633115i	−0.988861	+	0.148842i	$0.952445\pi$
$480$		0			0
$481$	1.00000	−	1.73205i	0.0455961	−	0.0789747i
$482$	−5.00000	+	8.66025i	−0.227744	+	0.394464i
$483$		0			0
$484$	−2.50000	−	4.33013i	−0.113636	−	0.196824i
$485$	−20.0000			−0.908153
$486$		0			0
$487$	4.00000			0.181257			0.0906287	−	0.995885i	$-0.471112\pi$
$487$	4.00000			0.181257			0.0906287	+	0.995885i	$0.471112\pi$
$488$	1.00000	+	1.73205i	0.0452679	+	0.0784063i
$489$		0			0
$490$	9.00000	−	15.5885i	0.406579	−	0.704215i
$491$	18.0000	−	31.1769i	0.812329	−	1.40699i	−0.0989017	−	0.995097i	$-0.531533\pi$
$491$	18.0000	−	31.1769i	0.812329	−	1.40699i	0.911230	−	0.411897i	$-0.135134\pi$
$492$		0			0
$493$	−6.00000	−	10.3923i	−0.270226	−	0.468046i
$494$	−8.00000			−0.359937
$495$		0			0
$496$	−4.00000			−0.179605
$497$	−16.0000	−	27.7128i	−0.717698	−	1.24309i
$498$		0			0
$499$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$499$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$500$	−6.00000	+	10.3923i	−0.268328	+	0.464758i
$501$		0			0
$502$	2.00000	+	3.46410i	0.0892644	+	0.154610i
$503$	−40.0000			−1.78351			−0.891756	−	0.452517i	$-0.850526\pi$
$503$	−40.0000			−1.78351			−0.891756	+	0.452517i	$0.850526\pi$
$504$		0			0
$505$	−4.00000			−0.177998
$506$		0			0
$507$		0			0
$508$		0			0
$509$	21.0000	−	36.3731i	0.930809	−	1.61221i	0.148866	−	0.988857i	$-0.452438\pi$
$509$	21.0000	−	36.3731i	0.930809	−	1.61221i	0.781943	−	0.623350i	$-0.214229\pi$
$510$		0			0
$511$	−4.00000	−	6.92820i	−0.176950	−	0.306486i
$512$	1.00000			0.0441942
$513$		0			0
$514$	6.00000			0.264649
$515$	16.0000	+	27.7128i	0.705044	+	1.22117i
$516$		0			0
$517$	16.0000	−	27.7128i	0.703679	−	1.21881i
$518$	4.00000	−	6.92820i	0.175750	−	0.304408i
$519$		0			0
$520$	1.00000	+	1.73205i	0.0438529	+	0.0759555i
$521$	14.0000			0.613351			0.306676	−	0.951814i	$-0.400783\pi$
$521$	14.0000			0.613351			0.306676	+	0.951814i	$0.400783\pi$
$522$		0			0
$523$	−20.0000			−0.874539			−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000			−0.874539			−0.437269	+	0.899331i	$0.644054\pi$
$524$	2.00000	+	3.46410i	0.0873704	+	0.151330i
$525$		0			0
$526$	4.00000	−	6.92820i	0.174408	−	0.302084i
$527$	−4.00000	+	6.92820i	−0.174243	+	0.301797i
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	−20.0000			−0.868744
$531$		0			0
$532$	−32.0000			−1.38738
$533$	−5.00000	−	8.66025i	−0.216574	−	0.375117i
$534$		0			0
$535$	−12.0000	+	20.7846i	−0.518805	+	0.898597i
$536$	8.00000	−	13.8564i	0.345547	−	0.598506i
$537$		0			0
$538$	−13.0000	−	22.5167i	−0.560470	−	0.970762i
$539$	36.0000			1.55063
$540$		0			0
$541$	−34.0000			−1.46177			−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000			−1.46177			−0.730887	+	0.682498i	$0.760893\pi$
$542$	2.00000	+	3.46410i	0.0859074	+	0.148796i
$543$		0			0
$544$	1.00000	−	1.73205i	0.0428746	−	0.0742611i
$545$	−2.00000	+	3.46410i	−0.0856706	+	0.148386i
$546$		0			0
$547$	14.0000	+	24.2487i	0.598597	+	1.03680i	0.993028	+	0.117875i	$0.0376081\pi$
$547$	14.0000	+	24.2487i	0.598597	+	1.03680i	−0.394432	+	0.918925i	$0.629059\pi$
$548$	10.0000			0.427179
$549$		0			0
$550$	−4.00000			−0.170561
$551$	−24.0000	−	41.5692i	−1.02243	−	1.77091i
$552$		0			0
$553$	−16.0000	+	27.7128i	−0.680389	+	1.17847i
$554$	−11.0000	+	19.0526i	−0.467345	+	0.809466i
$555$		0			0
$556$	−6.00000	−	10.3923i	−0.254457	−	0.440732i
$557$	−18.0000			−0.762684			−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000			−0.762684			−0.381342	+	0.924434i	$0.624538\pi$
$558$		0			0
$559$	4.00000			0.169182
$560$	4.00000	+	6.92820i	0.169031	+	0.292770i
$561$		0			0
$562$	−13.0000	+	22.5167i	−0.548372	+	0.949808i
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	−0.820798	−	0.571218i	$-0.806471\pi$
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	0.905088	+	0.425223i	$0.139804\pi$
$564$		0			0
$565$	6.00000	+	10.3923i	0.252422	+	0.437208i
$566$	−4.00000			−0.168133
$567$		0			0
$568$	8.00000			0.335673
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	−0.987786	−	0.155815i	$-0.950200\pi$
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	0.358954	−	0.933355i	$-0.383134\pi$
$570$		0			0
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	−0.577301	−	0.816532i	$-0.695894\pi$
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	0.995788	+	0.0916910i	$0.0292272\pi$
$572$	−2.00000	+	3.46410i	−0.0836242	+	0.144841i
$573$		0			0
$574$	−20.0000	−	34.6410i	−0.834784	−	1.44589i
$575$		0			0
$576$		0			0
$577$	18.0000			0.749350			0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000			0.749350			0.374675	+	0.927156i	$0.377754\pi$
$578$	6.50000	+	11.2583i	0.270364	+	0.468285i
$579$		0			0
$580$	−6.00000	+	10.3923i	−0.249136	+	0.431517i
$581$	24.0000	−	41.5692i	0.995688	−	1.72458i
$582$		0			0
$583$	−20.0000	−	34.6410i	−0.828315	−	1.43468i
$584$	2.00000			0.0827606
$585$		0			0
$586$	−26.0000			−1.07405
$587$	2.00000	+	3.46410i	0.0825488	+	0.142979i	0.904344	−	0.426804i	$-0.140361\pi$
$587$	2.00000	+	3.46410i	0.0825488	+	0.142979i	−0.821795	+	0.569783i	$0.807027\pi$
$588$		0			0
$589$	−16.0000	+	27.7128i	−0.659269	+	1.14189i
$590$	−4.00000	+	6.92820i	−0.164677	+	0.285230i
$591$		0			0
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	42.0000			1.72473			0.862367	−	0.506284i	$-0.168981\pi$
$593$	42.0000			1.72473			0.862367	+	0.506284i	$0.168981\pi$
$594$		0			0
$595$	16.0000			0.655936
$596$	−3.00000	−	5.19615i	−0.122885	−	0.212843i
$597$		0			0
$598$		0			0
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	−0.999938	−	0.0111569i	$-0.996449\pi$
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	0.509631	+	0.860393i	$0.329782\pi$
$600$		0			0
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	0.469095	−	0.883148i	$-0.344580\pi$
$602$	16.0000			0.652111
$603$		0			0
$604$	12.0000			0.488273
$605$	5.00000	+	8.66025i	0.203279	+	0.352089i
$606$		0			0
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	−0.656744	−	0.754114i	$-0.728067\pi$
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	0.981454	+	0.191700i	$0.0614000\pi$
$608$	4.00000	−	6.92820i	0.162221	−	0.280976i
$609$		0			0
$610$	−2.00000	−	3.46410i	−0.0809776	−	0.140257i
$611$	−8.00000			−0.323645
$612$		0			0
$613$	−2.00000			−0.0807792			−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000			−0.0807792			−0.0403896	+	0.999184i	$0.512860\pi$
$614$	4.00000	+	6.92820i	0.161427	+	0.279600i
$615$		0			0
$616$	−8.00000	+	13.8564i	−0.322329	+	0.558291i
$617$	3.00000	−	5.19615i	0.120775	−	0.209189i	−0.799298	−	0.600935i	$-0.794795\pi$
$617$	3.00000	−	5.19615i	0.120775	−	0.209189i	0.920074	+	0.391745i	$0.128129\pi$
$618$		0			0
$619$	−16.0000	−	27.7128i	−0.643094	−	1.11387i	−0.984738	−	0.174042i	$-0.944317\pi$
$619$	−16.0000	−	27.7128i	−0.643094	−	1.11387i	0.341644	−	0.939829i	$-0.389016\pi$
$620$	8.00000			0.321288
$621$		0			0
$622$		0			0
$623$	28.0000	+	48.4974i	1.12180	+	1.94301i
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	3.00000	−	5.19615i	0.119904	−	0.207680i
$627$		0			0
$628$	−7.00000	−	12.1244i	−0.279330	−	0.483814i
$629$	4.00000			0.159490
$630$		0			0
$631$	−36.0000			−1.43314			−0.716569	−	0.697517i	$-0.754288\pi$
$631$	−36.0000			−1.43314			−0.716569	+	0.697517i	$0.754288\pi$
$632$	−4.00000	−	6.92820i	−0.159111	−	0.275589i
$633$		0			0
$634$	−3.00000	+	5.19615i	−0.119145	+	0.206366i
$635$		0			0
$636$		0			0
$637$	−4.50000	−	7.79423i	−0.178296	−	0.308819i
$638$	−24.0000			−0.950169
$639$		0			0
$640$	−2.00000			−0.0790569
$641$	1.00000	+	1.73205i	0.0394976	+	0.0684119i	0.885098	−	0.465404i	$-0.154091\pi$
$641$	1.00000	+	1.73205i	0.0394976	+	0.0684119i	−0.845601	+	0.533816i	$0.820758\pi$
$642$		0			0
$643$	8.00000	−	13.8564i	0.315489	−	0.546443i	−0.664052	−	0.747686i	$-0.731165\pi$
$643$	8.00000	−	13.8564i	0.315489	−	0.546443i	0.979541	+	0.201243i	$0.0644981\pi$
$644$		0			0
$645$		0			0
$646$	−8.00000	−	13.8564i	−0.314756	−	0.545173i
$647$	−24.0000			−0.943537			−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000			−0.943537			−0.471769	+	0.881722i	$0.656384\pi$
$648$		0			0
$649$	−16.0000			−0.628055
$650$	0.500000	+	0.866025i	0.0196116	+	0.0339683i
$651$		0			0
$652$	8.00000	−	13.8564i	0.313304	−	0.542659i
$653$	−5.00000	+	8.66025i	−0.195665	+	0.338902i	−0.947118	−	0.320884i	$-0.896020\pi$
$653$	−5.00000	+	8.66025i	−0.195665	+	0.338902i	0.751453	+	0.659786i	$0.229353\pi$
$654$		0			0
$655$	−4.00000	−	6.92820i	−0.156293	−	0.270707i
$656$	10.0000			0.390434
$657$		0			0
$658$	−32.0000			−1.24749
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	−0.968052	−	0.250748i	$-0.919323\pi$
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	0.266872	−	0.963732i	$-0.414010\pi$
$660$		0			0
$661$	1.00000	−	1.73205i	0.0388955	−	0.0673690i	−0.845922	−	0.533306i	$-0.820949\pi$
$661$	1.00000	−	1.73205i	0.0388955	−	0.0673690i	0.884818	+	0.465937i	$0.154283\pi$
$662$	−4.00000	+	6.92820i	−0.155464	+	0.269272i
$663$		0			0
$664$	6.00000	+	10.3923i	0.232845	+	0.403300i
$665$	64.0000			2.48181
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$	−16.0000	+	27.7128i	−0.618134	+	1.07064i
$671$	4.00000	−	6.92820i	0.154418	−	0.267460i
$672$		0			0
$673$	7.00000	+	12.1244i	0.269830	+	0.467360i	0.968818	−	0.247774i	$-0.0796991\pi$
$673$	7.00000	+	12.1244i	0.269830	+	0.467360i	−0.698988	+	0.715134i	$0.746366\pi$
$674$	18.0000			0.693334
$675$		0			0
$676$	1.00000			0.0384615
$677$	19.0000	+	32.9090i	0.730229	+	1.26479i	0.956785	+	0.290796i	$0.0939201\pi$
$677$	19.0000	+	32.9090i	0.730229	+	1.26479i	−0.226556	+	0.973998i	$0.572747\pi$
$678$		0			0
$679$	−20.0000	+	34.6410i	−0.767530	+	1.32940i
$680$	−2.00000	+	3.46410i	−0.0766965	+	0.132842i
$681$		0			0
$682$	8.00000	+	13.8564i	0.306336	+	0.530589i
$683$	−44.0000			−1.68361			−0.841807	−	0.539779i	$-0.818508\pi$
$683$	−44.0000			−1.68361			−0.841807	+	0.539779i	$0.818508\pi$
$684$		0			0
$685$	−20.0000			−0.764161
$686$	−4.00000	−	6.92820i	−0.152721	−	0.264520i
$687$		0			0
$688$	−2.00000	+	3.46410i	−0.0762493	+	0.132068i
$689$	−5.00000	+	8.66025i	−0.190485	+	0.329929i
$690$		0			0
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	0.991460	+	0.130410i	$0.0416295\pi$
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	−0.382791	+	0.923835i	$0.625037\pi$
$692$	10.0000			0.380143
$693$		0			0
$694$	12.0000			0.455514
$695$	12.0000	+	20.7846i	0.455186	+	0.788405i
$696$		0			0
$697$	10.0000	−	17.3205i	0.378777	−	0.656061i
$698$	−3.00000	+	5.19615i	−0.113552	+	0.196677i
$699$		0			0
$700$	2.00000	+	3.46410i	0.0755929	+	0.130931i
$701$	50.0000			1.88847			0.944237	−	0.329267i	$-0.106802\pi$
$701$	50.0000			1.88847			0.944237	+	0.329267i	$0.106802\pi$
$702$		0			0
$703$	16.0000			0.603451
$704$	−2.00000	−	3.46410i	−0.0753778	−	0.130558i
$705$		0			0
$706$	7.00000	−	12.1244i	0.263448	−	0.456306i
$707$	−4.00000	+	6.92820i	−0.150435	+	0.260562i
$708$		0			0
$709$	−3.00000	−	5.19615i	−0.112667	−	0.195146i	0.804178	−	0.594389i	$-0.202606\pi$
$709$	−3.00000	−	5.19615i	−0.112667	−	0.195146i	−0.916845	+	0.399244i	$0.869273\pi$
$710$	−16.0000			−0.600469
$711$		0			0
$712$	−14.0000			−0.524672
$713$		0			0
$714$		0			0
$715$	4.00000	−	6.92820i	0.149592	−	0.259100i
$716$	−6.00000	+	10.3923i	−0.224231	+	0.388379i
$717$		0			0
$718$		0			0
$719$	24.0000			0.895049			0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000			0.895049			0.447524	+	0.894272i	$0.352306\pi$
$720$		0			0
$721$	64.0000			2.38348
$722$	−22.5000	−	38.9711i	−0.837363	−	1.45036i
$723$		0			0
$724$	5.00000	−	8.66025i	0.185824	−	0.321856i
$725$	−3.00000	+	5.19615i	−0.111417	+	0.192980i
$726$		0			0
$727$	20.0000	+	34.6410i	0.741759	+	1.28476i	0.951694	+	0.307049i	$0.0993415\pi$
$727$	20.0000	+	34.6410i	0.741759	+	1.28476i	−0.209935	+	0.977715i	$0.567325\pi$
$728$	4.00000			0.148250
$729$		0			0
$730$	−4.00000			−0.148047
$731$	4.00000	+	6.92820i	0.147945	+	0.256249i
$732$		0			0
$733$	1.00000	−	1.73205i	0.0369358	−	0.0639748i	−0.846967	−	0.531646i	$-0.821574\pi$
$733$	1.00000	−	1.73205i	0.0369358	−	0.0639748i	0.883902	+	0.467671i	$0.154907\pi$
$734$	−8.00000	+	13.8564i	−0.295285	+	0.511449i
$735$		0			0
$736$		0			0
$737$	−64.0000			−2.35747
$738$		0			0
$739$	40.0000			1.47142			0.735712	−	0.677295i	$-0.236848\pi$
$739$	40.0000			1.47142			0.735712	+	0.677295i	$0.236848\pi$
$740$	−2.00000	−	3.46410i	−0.0735215	−	0.127343i
$741$		0			0
$742$	−20.0000	+	34.6410i	−0.734223	+	1.27171i
$743$	−12.0000	+	20.7846i	−0.440237	+	0.762513i	−0.997707	−	0.0676840i	$-0.978439\pi$
$743$	−12.0000	+	20.7846i	−0.440237	+	0.762513i	0.557470	+	0.830197i	$0.311772\pi$
$744$		0			0
$745$	6.00000	+	10.3923i	0.219823	+	0.380745i
$746$	6.00000			0.219676
$747$		0			0
$748$	−8.00000			−0.292509
$749$	24.0000	+	41.5692i	0.876941	+	1.51891i
$750$		0			0
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	−0.227153	−	0.973859i	$-0.572942\pi$
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	0.956963	−	0.290209i	$-0.0937250\pi$
$752$	4.00000	−	6.92820i	0.145865	−	0.252646i
$753$		0			0
$754$	3.00000	+	5.19615i	0.109254	+	0.189233i
$755$	−24.0000			−0.873449
$756$		0			0
$757$	54.0000			1.96266			0.981332	−	0.192323i	$-0.0616021\pi$
$757$	54.0000			1.96266			0.981332	+	0.192323i	$0.0616021\pi$
$758$		0			0
$759$		0			0
$760$	−8.00000	+	13.8564i	−0.290191	+	0.502625i
$761$	−13.0000	+	22.5167i	−0.471250	+	0.816228i	−0.999459	−	0.0328858i	$-0.989530\pi$
$761$	−13.0000	+	22.5167i	−0.471250	+	0.816228i	0.528209	+	0.849114i	$0.322864\pi$
$762$		0			0
$763$	4.00000	+	6.92820i	0.144810	+	0.250818i
$764$	8.00000			0.289430
$765$		0			0
$766$	24.0000			0.867155
$767$	2.00000	+	3.46410i	0.0722158	+	0.125081i
$768$		0			0
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	0.847432	+	0.530904i	$0.178148\pi$
$770$	16.0000	−	27.7128i	0.576600	−	0.998700i
$771$		0			0
$772$	7.00000	+	12.1244i	0.251936	+	0.436365i
$773$	54.0000			1.94225			0.971123	−	0.238581i	$-0.0766824\pi$
$773$	54.0000			1.94225			0.971123	+	0.238581i	$0.0766824\pi$
$774$		0			0
$775$	4.00000			0.143684
$776$	−5.00000	−	8.66025i	−0.179490	−	0.310885i
$777$		0			0
$778$	−13.0000	+	22.5167i	−0.466073	+	0.807261i
$779$	40.0000	−	69.2820i	1.43315	−	2.48229i
$780$		0			0
$781$	−16.0000	−	27.7128i	−0.572525	−	0.991642i
$782$		0			0
$783$		0			0
$784$	9.00000			0.321429
$785$	14.0000	+	24.2487i	0.499681	+	0.865474i
$786$		0			0
$787$	−20.0000	+	34.6410i	−0.712923	+	1.23482i	0.250832	+	0.968031i	$0.419296\pi$
$787$	−20.0000	+	34.6410i	−0.712923	+	1.23482i	−0.963755	+	0.266788i	$0.914038\pi$
$788$	9.00000	−	15.5885i	0.320612	−	0.555316i
$789$		0			0
$790$	8.00000	+	13.8564i	0.284627	+	0.492989i
$791$	24.0000			0.853342
$792$		0			0
$793$	−2.00000			−0.0710221
$794$	−3.00000	−	5.19615i	−0.106466	−	0.184405i
$795$		0			0
$796$	4.00000	−	6.92820i	0.141776	−	0.245564i
$797$	−1.00000	+	1.73205i	−0.0354218	+	0.0613524i	−0.883193	−	0.469010i	$-0.844611\pi$
$797$	−1.00000	+	1.73205i	−0.0354218	+	0.0613524i	0.847771	+	0.530362i	$0.177944\pi$
$798$		0			0
$799$	−8.00000	−	13.8564i	−0.283020	−	0.490204i
$800$	−1.00000			−0.0353553
$801$		0			0
$802$	−6.00000			−0.211867
$803$	−4.00000	−	6.92820i	−0.141157	−	0.244491i
$804$		0			0
$805$		0			0
$806$	2.00000	−	3.46410i	0.0704470	−	0.122018i
$807$		0			0
$808$	−1.00000	−	1.73205i	−0.0351799	−	0.0609333i
$809$	−2.00000			−0.0703163			−0.0351581	−	0.999382i	$-0.511193\pi$
$809$	−2.00000			−0.0703163			−0.0351581	+	0.999382i	$0.511193\pi$
$810$		0			0
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$	12.0000	+	20.7846i	0.421117	+	0.729397i
$813$		0			0
$814$	4.00000	−	6.92820i	0.140200	−	0.242833i
$815$	−16.0000	+	27.7128i	−0.560456	+	0.970737i
$816$		0			0
$817$	16.0000	+	27.7128i	0.559769	+	0.969549i
$818$	2.00000			0.0699284
$819$		0			0
$820$	−20.0000			−0.698430
$821$	21.0000	+	36.3731i	0.732905	+	1.26943i	0.955636	+	0.294549i	$0.0951694\pi$
$821$	21.0000	+	36.3731i	0.732905	+	1.26943i	−0.222731	+	0.974880i	$0.571497\pi$
$822$		0			0
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	−0.692240	−	0.721668i	$-0.743376\pi$
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	0.971102	+	0.238664i	$0.0767093\pi$
$824$	−8.00000	+	13.8564i	−0.278693	+	0.482711i
$825$		0			0
$826$	8.00000	+	13.8564i	0.278356	+	0.482126i
$827$	−28.0000			−0.973655			−0.486828	−	0.873498i	$-0.661846\pi$
$827$	−28.0000			−0.973655			−0.486828	+	0.873498i	$0.661846\pi$
$828$		0			0
$829$	−2.00000			−0.0694629			−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000			−0.0694629			−0.0347314	+	0.999397i	$0.511058\pi$
$830$	−12.0000	−	20.7846i	−0.416526	−	0.721444i
$831$		0			0
$832$	−0.500000	+	0.866025i	−0.0173344	+	0.0300240i
$833$	9.00000	−	15.5885i	0.311832	−	0.540108i
$834$		0			0
$835$		0			0
$836$	−32.0000			−1.10674
$837$		0			0
$838$	−4.00000			−0.138178
$839$	−20.0000	−	34.6410i	−0.690477	−	1.19594i	−0.971682	−	0.236293i	$-0.924067\pi$
$839$	−20.0000	−	34.6410i	−0.690477	−	1.19594i	0.281205	−	0.959648i	$-0.409266\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	−11.0000	+	19.0526i	−0.379085	+	0.656595i
$843$		0			0
$844$	−6.00000	−	10.3923i	−0.206529	−	0.357718i
$845$	−2.00000			−0.0688021
$846$		0			0
$847$	20.0000			0.687208
$848$	−5.00000	−	8.66025i	−0.171701	−	0.297394i
$849$		0			0
$850$	−1.00000	+	1.73205i	−0.0342997	+	0.0594089i
$851$		0			0
$852$		0			0
$853$	1.00000	+	1.73205i	0.0342393	+	0.0593043i	0.882637	−	0.470055i	$-0.155766\pi$
$853$	1.00000	+	1.73205i	0.0342393	+	0.0593043i	−0.848398	+	0.529359i	$0.822432\pi$
$854$	−8.00000			−0.273754
$855$		0			0
$856$	−12.0000			−0.410152
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	0.977800	−	0.209539i	$-0.0671963\pi$
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	−0.670366	+	0.742030i	$0.733863\pi$
$858$		0			0
$859$	22.0000	−	38.1051i	0.750630	−	1.30013i	−0.196887	−	0.980426i	$-0.563083\pi$
$859$	22.0000	−	38.1051i	0.750630	−	1.30013i	0.947518	−	0.319704i	$-0.103583\pi$
$860$	4.00000	−	6.92820i	0.136399	−	0.236250i
$861$		0			0
$862$	−4.00000	−	6.92820i	−0.136241	−	0.235976i
$863$	−40.0000			−1.36162			−0.680808	−	0.732462i	$-0.738371\pi$
$863$	−40.0000			−1.36162			−0.680808	+	0.732462i	$0.738371\pi$
$864$		0			0
$865$	−20.0000			−0.680020
$866$	15.0000	+	25.9808i	0.509721	+	0.882862i
$867$		0			0
$868$	8.00000	−	13.8564i	0.271538	−	0.470317i
$869$	−16.0000	+	27.7128i	−0.542763	+	0.940093i
$870$		0			0
$871$	8.00000	+	13.8564i	0.271070	+	0.469506i
$872$	−2.00000			−0.0677285
$873$		0			0
$874$		0			0
$875$	−24.0000	−	41.5692i	−0.811348	−	1.40530i
$876$		0			0
$877$	−11.0000	+	19.0526i	−0.371444	+	0.643359i	−0.989788	−	0.142548i	$-0.954470\pi$
$877$	−11.0000	+	19.0526i	−0.371444	+	0.643359i	0.618344	+	0.785907i	$0.287804\pi$
$878$	−8.00000	+	13.8564i	−0.269987	+	0.467631i
$879$		0			0
$880$	4.00000	+	6.92820i	0.134840	+	0.233550i
$881$	−26.0000			−0.875962			−0.437981	−	0.898984i	$-0.644306\pi$
$881$	−26.0000			−0.875962			−0.437981	+	0.898984i	$0.644306\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$	1.00000	+	1.73205i	0.0336336	+	0.0582552i
$885$		0			0
$886$	−2.00000	+	3.46410i	−0.0671913	+	0.116379i
$887$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$887$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$888$		0			0
$889$		0			0
$890$	28.0000			0.938562
$891$		0			0
$892$	−4.00000			−0.133930
$893$	−32.0000	−	55.4256i	−1.07084	−	1.85475i
$894$		0			0
$895$	12.0000	−	20.7846i	0.401116	−	0.694753i
$896$	−2.00000	+	3.46410i	−0.0668153	+	0.115728i
$897$		0			0
$898$	3.00000	+	5.19615i	0.100111	+	0.173398i
$899$	24.0000			0.800445
$900$		0			0
$901$	−20.0000			−0.666297
$902$	−20.0000	−	34.6410i	−0.665927	−	1.15342i
$903$		0			0
$904$	−3.00000	+	5.19615i	−0.0997785	+	0.172821i
$905$	−10.0000	+	17.3205i	−0.332411	+	0.575753i
$906$		0			0
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	0.534333	−	0.845274i	$-0.320563\pi$
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	−0.999195	+	0.0401089i	$0.987230\pi$
$908$	−20.0000			−0.663723
$909$		0			0
$910$	−8.00000			−0.265197
$911$	20.0000	+	34.6410i	0.662630	+	1.14771i	0.979922	+	0.199380i	$0.0638929\pi$
$911$	20.0000	+	34.6410i	0.662630	+	1.14771i	−0.317293	+	0.948328i	$0.602774\pi$
$912$		0			0
$913$	24.0000	−	41.5692i	0.794284	−	1.37574i
$914$	15.0000	−	25.9808i	0.496156	−	0.859367i
$915$		0			0
$916$	−11.0000	−	19.0526i	−0.363450	−	0.629514i
$917$	−16.0000			−0.528367
$918$		0			0
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$		0			0
$921$		0			0
$922$	−3.00000	+	5.19615i	−0.0987997	+	0.171126i
$923$	−4.00000	+	6.92820i	−0.131662	+	0.228045i
$924$		0			0
$925$	−1.00000	−	1.73205i	−0.0328798	−	0.0569495i
$926$	−20.0000			−0.657241
$927$		0			0
$928$	−6.00000			−0.196960
$929$	23.0000	+	39.8372i	0.754606	+	1.30702i	0.945570	+	0.325418i	$0.105505\pi$
$929$	23.0000	+	39.8372i	0.754606	+	1.30702i	−0.190965	+	0.981597i	$0.561162\pi$
$930$		0			0
$931$	36.0000	−	62.3538i	1.17985	−	2.04356i
$932$	9.00000	−	15.5885i	0.294805	−	0.510617i
$933$		0			0
$934$	−2.00000	−	3.46410i	−0.0654420	−	0.113349i
$935$	16.0000			0.523256
$936$		0			0
$937$	26.0000			0.849383			0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000			0.849383			0.424691	+	0.905338i	$0.360383\pi$
$938$	32.0000	+	55.4256i	1.04484	+	1.80971i
$939$		0			0
$940$	−8.00000	+	13.8564i	−0.260931	+	0.451946i
$941$	−23.0000	+	39.8372i	−0.749779	+	1.29865i	0.198150	+	0.980172i	$0.436507\pi$
$941$	−23.0000	+	39.8372i	−0.749779	+	1.29865i	−0.947929	+	0.318483i	$0.896827\pi$
$942$		0			0
$943$		0			0
$944$	−4.00000			−0.130189
$945$		0			0
$946$	16.0000			0.520205
$947$	−2.00000	−	3.46410i	−0.0649913	−	0.112568i	0.831699	−	0.555227i	$-0.187369\pi$
$947$	−2.00000	−	3.46410i	−0.0649913	−	0.112568i	−0.896690	+	0.442659i	$0.854035\pi$
$948$		0			0
$949$	−1.00000	+	1.73205i	−0.0324614	+	0.0562247i
$950$	−4.00000	+	6.92820i	−0.129777	+	0.224781i
$951$		0			0
$952$	4.00000	+	6.92820i	0.129641	+	0.224544i
$953$	30.0000			0.971795			0.485898	−	0.874016i	$-0.338493\pi$
$953$	30.0000			0.971795			0.485898	+	0.874016i	$0.338493\pi$
$954$		0			0
$955$	−16.0000			−0.517748
$956$		0			0
$957$		0			0
$958$	−8.00000	+	13.8564i	−0.258468	+	0.447680i
$959$	−20.0000	+	34.6410i	−0.645834	+	1.11862i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	−2.00000			−0.0644826
$963$		0			0
$964$	10.0000			0.322078
$965$	−14.0000	−	24.2487i	−0.450676	−	0.780594i
$966$		0			0
$967$	−2.00000	+	3.46410i	−0.0643157	+	0.111398i	−0.896390	−	0.443266i	$-0.853820\pi$
$967$	−2.00000	+	3.46410i	−0.0643157	+	0.111398i	0.832075	+	0.554664i	$0.187153\pi$
$968$	−2.50000	+	4.33013i	−0.0803530	+	0.139176i
$969$		0			0
$970$	10.0000	+	17.3205i	0.321081	+	0.556128i
$971$	28.0000			0.898563			0.449281	−	0.893390i	$-0.351680\pi$
$971$	28.0000			0.898563			0.449281	+	0.893390i	$0.351680\pi$
$972$		0			0
$973$	48.0000			1.53881
$974$	−2.00000	−	3.46410i	−0.0640841	−	0.110997i
$975$		0			0
$976$	1.00000	−	1.73205i	0.0320092	−	0.0554416i
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	−0.814038	−	0.580812i	$-0.802735\pi$
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	0.910017	+	0.414572i	$0.136069\pi$
$978$		0			0
$979$	28.0000	+	48.4974i	0.894884	+	1.54998i
$980$	−18.0000			−0.574989
$981$		0			0
$982$	−36.0000			−1.14881
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	0.991453	−	0.130465i	$-0.0416470\pi$
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	−0.608712	+	0.793391i	$0.708314\pi$
$984$		0			0
$985$	−18.0000	+	31.1769i	−0.573528	+	0.993379i
$986$	−6.00000	+	10.3923i	−0.191079	+	0.330958i
$987$		0			0
$988$	4.00000	+	6.92820i	0.127257	+	0.220416i
$989$		0			0
$990$		0			0
$991$	−48.0000			−1.52477			−0.762385	−	0.647124i	$-0.775972\pi$
$991$	−48.0000			−1.52477			−0.762385	+	0.647124i	$0.775972\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$		0			0
$994$	−16.0000	+	27.7128i	−0.507489	+	0.878997i
$995$	−8.00000	+	13.8564i	−0.253617	+	0.439278i
$996$		0			0
$997$	13.0000	+	22.5167i	0.411714	+	0.713110i	0.995077	−	0.0991016i	$-0.0315969\pi$
$997$	13.0000	+	22.5167i	0.411714	+	0.713110i	−0.583363	+	0.812211i	$0.698264\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2106.2.e.j.1405.1		2
3.2	odd	2		2106.2.e.q.1405.1		2
9.2	odd	6		2106.2.e.q.703.1		2
9.4	even	3		234.2.a.c.1.1		1
9.5	odd	6		78.2.a.a.1.1	✓	1
9.7	even	3	inner	2106.2.e.j.703.1		2
36.23	even	6		624.2.a.h.1.1		1
36.31	odd	6		1872.2.a.c.1.1		1
45.4	even	6		5850.2.a.d.1.1		1
45.13	odd	12		5850.2.e.bb.5149.1		2
45.14	odd	6		1950.2.a.w.1.1		1
45.22	odd	12		5850.2.e.bb.5149.2		2
45.23	even	12		1950.2.e.i.1249.2		2
45.32	even	12		1950.2.e.i.1249.1		2
63.41	even	6		3822.2.a.j.1.1		1
72.5	odd	6		2496.2.a.t.1.1		1
72.13	even	6		7488.2.a.bz.1.1		1
72.59	even	6		2496.2.a.b.1.1		1
72.67	odd	6		7488.2.a.bk.1.1		1
99.32	even	6		9438.2.a.t.1.1		1
117.5	even	12		1014.2.b.b.337.2		2
117.23	odd	6		1014.2.e.c.529.1		2
117.31	odd	12		3042.2.b.g.1351.1		2
117.32	even	12		1014.2.i.d.361.2		4
117.41	even	12		1014.2.i.d.823.1		4
117.50	even	12		1014.2.i.d.823.2		4
117.59	even	12		1014.2.i.d.361.1		4
117.68	odd	6		1014.2.e.f.529.1		2
117.77	odd	6		1014.2.a.d.1.1		1
117.86	even	12		1014.2.b.b.337.1		2
117.95	odd	6		1014.2.e.c.991.1		2
117.103	even	6		3042.2.a.f.1.1		1
117.112	odd	12		3042.2.b.g.1351.2		2
117.113	odd	6		1014.2.e.f.991.1		2
468.311	even	6		8112.2.a.v.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.a.a.1.1	✓	1	9.5	odd	6
234.2.a.c.1.1		1	9.4	even	3
624.2.a.h.1.1		1	36.23	even	6
1014.2.a.d.1.1		1	117.77	odd	6
1014.2.b.b.337.1		2	117.86	even	12
1014.2.b.b.337.2		2	117.5	even	12
1014.2.e.c.529.1		2	117.23	odd	6
1014.2.e.c.991.1		2	117.95	odd	6
1014.2.e.f.529.1		2	117.68	odd	6
1014.2.e.f.991.1		2	117.113	odd	6
1014.2.i.d.361.1		4	117.59	even	12
1014.2.i.d.361.2		4	117.32	even	12
1014.2.i.d.823.1		4	117.41	even	12
1014.2.i.d.823.2		4	117.50	even	12
1872.2.a.c.1.1		1	36.31	odd	6
1950.2.a.w.1.1		1	45.14	odd	6
1950.2.e.i.1249.1		2	45.32	even	12
1950.2.e.i.1249.2		2	45.23	even	12
2106.2.e.j.703.1		2	9.7	even	3	inner
2106.2.e.j.1405.1		2	1.1	even	1	trivial
2106.2.e.q.703.1		2	9.2	odd	6
2106.2.e.q.1405.1		2	3.2	odd	2
2496.2.a.b.1.1		1	72.59	even	6
2496.2.a.t.1.1		1	72.5	odd	6
3042.2.a.f.1.1		1	117.103	even	6
3042.2.b.g.1351.1		2	117.31	odd	12
3042.2.b.g.1351.2		2	117.112	odd	12
3822.2.a.j.1.1		1	63.41	even	6
5850.2.a.d.1.1		1	45.4	even	6
5850.2.e.bb.5149.1		2	45.13	odd	12
5850.2.e.bb.5149.2		2	45.22	odd	12
7488.2.a.bk.1.1		1	72.67	odd	6
7488.2.a.bz.1.1		1	72.13	even	6
8112.2.a.v.1.1		1	468.311	even	6
9438.2.a.t.1.1		1	99.32	even	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:	\( N \)	\(=\)	\( 2106 = 2 \cdot 3^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2106.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +(-2.00000 - 3.46410i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +(-2.00000 - 3.46410i) q^{7} +1.00000 q^{8} -2.00000 q^{10} +(-2.00000 - 3.46410i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(-2.00000 + 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} -2.00000 q^{17} -8.00000 q^{19} +(1.00000 + 1.73205i) q^{20} +(-2.00000 + 3.46410i) q^{22} +(0.500000 + 0.866025i) q^{25} +1.00000 q^{26} +4.00000 q^{28} +(3.00000 + 5.19615i) q^{29} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{34} -8.00000 q^{35} -2.00000 q^{37} +(4.00000 + 6.92820i) q^{38} +(1.00000 - 1.73205i) q^{40} +(-5.00000 + 8.66025i) q^{41} +(-2.00000 - 3.46410i) q^{43} +4.00000 q^{44} +(4.00000 + 6.92820i) q^{47} +(-4.50000 + 7.79423i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.500000 - 0.866025i) q^{52} +10.0000 q^{53} -8.00000 q^{55} +(-2.00000 - 3.46410i) q^{56} +(3.00000 - 5.19615i) q^{58} +(2.00000 - 3.46410i) q^{59} +(1.00000 + 1.73205i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(8.00000 - 13.8564i) q^{67} +(1.00000 - 1.73205i) q^{68} +(4.00000 + 6.92820i) q^{70} +8.00000 q^{71} +2.00000 q^{73} +(1.00000 + 1.73205i) q^{74} +(4.00000 - 6.92820i) q^{76} +(-8.00000 + 13.8564i) q^{77} +(-4.00000 - 6.92820i) q^{79} -2.00000 q^{80} +10.0000 q^{82} +(6.00000 + 10.3923i) q^{83} +(-2.00000 + 3.46410i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(-2.00000 - 3.46410i) q^{88} -14.0000 q^{89} +4.00000 q^{91} +(4.00000 - 6.92820i) q^{94} +(-8.00000 + 13.8564i) q^{95} +(-5.00000 - 8.66025i) q^{97} +9.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8} - 4 q^{10} - 4 q^{11} - q^{13} - 4 q^{14} - q^{16} - 4 q^{17} - 16 q^{19} + 2 q^{20} - 4 q^{22} + q^{25} + 2 q^{26} + 8 q^{28} + 6 q^{29} + 4 q^{31} - q^{32} + 2 q^{34} - 16 q^{35} - 4 q^{37} + 8 q^{38} + 2 q^{40} - 10 q^{41} - 4 q^{43} + 8 q^{44} + 8 q^{47} - 9 q^{49} + q^{50} - q^{52} + 20 q^{53} - 16 q^{55} - 4 q^{56} + 6 q^{58} + 4 q^{59} + 2 q^{61} - 8 q^{62} + 2 q^{64} + 2 q^{65} + 16 q^{67} + 2 q^{68} + 8 q^{70} + 16 q^{71} + 4 q^{73} + 2 q^{74} + 8 q^{76} - 16 q^{77} - 8 q^{79} - 4 q^{80} + 20 q^{82} + 12 q^{83} - 4 q^{85} - 4 q^{86} - 4 q^{88} - 28 q^{89} + 8 q^{91} + 8 q^{94} - 16 q^{95} - 10 q^{97} + 18 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8 - 4 * q^10 - 4 * q^11 - q^13 - 4 * q^14 - q^16 - 4 * q^17 - 16 * q^19 + 2 * q^20 - 4 * q^22 + q^25 + 2 * q^26 + 8 * q^28 + 6 * q^29 + 4 * q^31 - q^32 + 2 * q^34 - 16 * q^35 - 4 * q^37 + 8 * q^38 + 2 * q^40 - 10 * q^41 - 4 * q^43 + 8 * q^44 + 8 * q^47 - 9 * q^49 + q^50 - q^52 + 20 * q^53 - 16 * q^55 - 4 * q^56 + 6 * q^58 + 4 * q^59 + 2 * q^61 - 8 * q^62 + 2 * q^64 + 2 * q^65 + 16 * q^67 + 2 * q^68 + 8 * q^70 + 16 * q^71 + 4 * q^73 + 2 * q^74 + 8 * q^76 - 16 * q^77 - 8 * q^79 - 4 * q^80 + 20 * q^82 + 12 * q^83 - 4 * q^85 - 4 * q^86 - 4 * q^88 - 28 * q^89 + 8 * q^91 + 8 * q^94 - 16 * q^95 - 10 * q^97 + 18 * q^98

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