LMFDB - Embedded newform 1960.2.q.r.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1960,2,Mod(361,1960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1960, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1960.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1960 = 2^{3} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1960.q (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:	$15.6506787962$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$1.68614 - 0.396143i$ of defining polynomial
Character	$\chi$	$=$	1960.361
Dual form			1960.2.q.r.961.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18614 - 2.05446i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.31386 - 2.27567i) q^{9} +O(q^{10})$	\(q+(1.18614 - 2.05446i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.31386 - 2.27567i) q^{9} +(-3.18614 + 5.51856i) q^{11} -4.37228 q^{13} -2.37228 q^{15} +(-0.186141 + 0.322405i) q^{17} +(-2.37228 - 4.10891i) q^{19} +(2.37228 + 4.10891i) q^{23} +(-0.500000 + 0.866025i) q^{25} +0.883156 q^{27} -4.37228 q^{29} +(-4.00000 + 6.92820i) q^{31} +(7.55842 + 13.0916i) q^{33} +(1.00000 + 1.73205i) q^{37} +(-5.18614 + 8.98266i) q^{39} -6.74456 q^{41} -8.74456 q^{43} +(-1.31386 + 2.27567i) q^{45} +(-3.55842 - 6.16337i) q^{47} +(0.441578 + 0.764836i) q^{51} +(-5.37228 + 9.30506i) q^{53} +6.37228 q^{55} -11.2554 q^{57} +(4.00000 - 6.92820i) q^{59} +(-1.37228 - 2.37686i) q^{61} +(2.18614 + 3.78651i) q^{65} +(2.00000 - 3.46410i) q^{67} +11.2554 q^{69} +8.00000 q^{71} +(-3.00000 + 5.19615i) q^{73} +(1.18614 + 2.05446i) q^{75} +(-7.55842 - 13.0916i) q^{79} +(4.98913 - 8.64142i) q^{81} +9.48913 q^{83} +0.372281 q^{85} +(-5.18614 + 8.98266i) q^{87} +(7.37228 + 12.7692i) q^{89} +(9.48913 + 16.4356i) q^{93} +(-2.37228 + 4.10891i) q^{95} +9.86141 q^{97} +16.7446 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} - 2 q^{5} - 11 q^{9}+O(q^{10}) $ 4 * q - q^3 - 2 * q^5 - 11 * q^9	$ 4 q - q^{3} - 2 q^{5} - 11 q^{9} - 7 q^{11} - 6 q^{13} + 2 q^{15} + 5 q^{17} + 2 q^{19} - 2 q^{23} - 2 q^{25} + 38 q^{27} - 6 q^{29} - 16 q^{31} + 13 q^{33} + 4 q^{37} - 15 q^{39} - 4 q^{41} - 12 q^{43} - 11 q^{45} + 3 q^{47} + 19 q^{51} - 10 q^{53} + 14 q^{55} - 68 q^{57} + 16 q^{59} + 6 q^{61} + 3 q^{65} + 8 q^{67} + 68 q^{69} + 32 q^{71} - 12 q^{73} - q^{75} - 13 q^{79} - 26 q^{81} - 8 q^{83} - 10 q^{85} - 15 q^{87} + 18 q^{89} - 8 q^{93} + 2 q^{95} - 18 q^{97} + 44 q^{99}+O(q^{100}) $ 4 * q - q^3 - 2 * q^5 - 11 * q^9 - 7 * q^11 - 6 * q^13 + 2 * q^15 + 5 * q^17 + 2 * q^19 - 2 * q^23 - 2 * q^25 + 38 * q^27 - 6 * q^29 - 16 * q^31 + 13 * q^33 + 4 * q^37 - 15 * q^39 - 4 * q^41 - 12 * q^43 - 11 * q^45 + 3 * q^47 + 19 * q^51 - 10 * q^53 + 14 * q^55 - 68 * q^57 + 16 * q^59 + 6 * q^61 + 3 * q^65 + 8 * q^67 + 68 * q^69 + 32 * q^71 - 12 * q^73 - q^75 - 13 * q^79 - 26 * q^81 - 8 * q^83 - 10 * q^85 - 15 * q^87 + 18 * q^89 - 8 * q^93 + 2 * q^95 - 18 * q^97 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$.

$n$	$981$	$1081$	$1177$	$1471$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.18614	−	2.05446i	0.684819	−	1.18614i	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	1.18614	−	2.05446i	0.684819	−	1.18614i	0.973494	−	0.228714i	$-0.0734519\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.31386	−	2.27567i	−0.437953	−	0.758557i
$10$		0			0
$11$	−3.18614	+	5.51856i	−0.960658	+	1.66391i	−0.239803	+	0.970822i	$0.577083\pi$
$11$	−3.18614	+	5.51856i	−0.960658	+	1.66391i	−0.720855	+	0.693086i	$0.756251\pi$
$12$		0			0
$13$	−4.37228			−1.21265			−0.606326	−	0.795216i	$-0.707357\pi$
$13$	−4.37228			−1.21265			−0.606326	+	0.795216i	$0.707357\pi$
$14$		0			0
$15$	−2.37228			−0.612520
$16$		0			0
$17$	−0.186141	+	0.322405i	−0.0451457	+	0.0781947i	−0.887715	−	0.460393i	$-0.847709\pi$
$17$	−0.186141	+	0.322405i	−0.0451457	+	0.0781947i	0.842570	+	0.538588i	$0.181042\pi$
$18$		0			0
$19$	−2.37228	−	4.10891i	−0.544239	−	0.942649i	−0.998654	−	0.0518593i	$-0.983485\pi$
$19$	−2.37228	−	4.10891i	−0.544239	−	0.942649i	0.454416	−	0.890790i	$-0.349848\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.37228	+	4.10891i	0.494655	+	0.856767i	0.999981	−	0.00616109i	$-0.00196115\pi$
$23$	2.37228	+	4.10891i	0.494655	+	0.856767i	−0.505326	+	0.862928i	$0.668628\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	0.883156			0.169963
$28$		0			0
$29$	−4.37228			−0.811912			−0.405956	−	0.913893i	$-0.633061\pi$
$29$	−4.37228			−0.811912			−0.405956	+	0.913893i	$0.633061\pi$
$30$		0			0
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	0.243204	+	0.969975i	$0.421802\pi$
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	−0.961625	+	0.274367i	$0.911532\pi$
$32$		0			0
$33$	7.55842	+	13.0916i	1.31575	+	2.27895i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$		0			0
$39$	−5.18614	+	8.98266i	−0.830447	+	1.43838i
$40$		0			0
$41$	−6.74456			−1.05332			−0.526662	−	0.850075i	$-0.676557\pi$
$41$	−6.74456			−1.05332			−0.526662	+	0.850075i	$0.676557\pi$
$42$		0			0
$43$	−8.74456			−1.33353			−0.666767	−	0.745267i	$-0.732322\pi$
$43$	−8.74456			−1.33353			−0.666767	+	0.745267i	$0.732322\pi$
$44$		0			0
$45$	−1.31386	+	2.27567i	−0.195859	+	0.339237i
$46$		0			0
$47$	−3.55842	−	6.16337i	−0.519049	−	0.899020i	−0.999755	−	0.0221376i	$-0.992953\pi$
$47$	−3.55842	−	6.16337i	−0.519049	−	0.899020i	0.480706	−	0.876882i	$-0.340381\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	0.441578	+	0.764836i	0.0618333	+	0.107098i
$52$		0			0
$53$	−5.37228	+	9.30506i	−0.737940	+	1.27815i	0.215482	+	0.976508i	$0.430868\pi$
$53$	−5.37228	+	9.30506i	−0.737940	+	1.27815i	−0.953422	+	0.301641i	$0.902466\pi$
$54$		0			0
$55$	6.37228			0.859238
$56$		0			0
$57$	−11.2554			−1.49082
$58$		0			0
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	−0.478953	−	0.877841i	$-0.658984\pi$
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	0.999709	−	0.0241347i	$-0.00768307\pi$
$60$		0			0
$61$	−1.37228	−	2.37686i	−0.175703	−	0.304326i	0.764702	−	0.644385i	$-0.222886\pi$
$61$	−1.37228	−	2.37686i	−0.175703	−	0.304326i	−0.940404	+	0.340059i	$0.889553\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.18614	+	3.78651i	0.271157	+	0.469658i
$66$		0			0
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$		0			0
$69$	11.2554			1.35500
$70$		0			0
$71$	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
$73$	−3.00000	+	5.19615i	−0.351123	+	0.608164i	−0.986447	−	0.164083i	$-0.947534\pi$
$73$	−3.00000	+	5.19615i	−0.351123	+	0.608164i	0.635323	+	0.772246i	$0.280867\pi$
$74$		0			0
$75$	1.18614	+	2.05446i	0.136964	+	0.237228i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−7.55842	−	13.0916i	−0.850389	−	1.47292i	−0.880858	−	0.473381i	$-0.843033\pi$
$79$	−7.55842	−	13.0916i	−0.850389	−	1.47292i	0.0304688	−	0.999536i	$-0.490300\pi$
$80$		0			0
$81$	4.98913	−	8.64142i	0.554347	−	0.960158i
$82$		0			0
$83$	9.48913			1.04157			0.520783	−	0.853689i	$-0.325640\pi$
$83$	9.48913			1.04157			0.520783	+	0.853689i	$0.325640\pi$
$84$		0			0
$85$	0.372281			0.0403796
$86$		0			0
$87$	−5.18614	+	8.98266i	−0.556013	+	0.963042i
$88$		0			0
$89$	7.37228	+	12.7692i	0.781460	+	1.35353i	0.931091	+	0.364787i	$0.118858\pi$
$89$	7.37228	+	12.7692i	0.781460	+	1.35353i	−0.149631	+	0.988742i	$0.547808\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	9.48913	+	16.4356i	0.983976	+	1.70430i
$94$		0			0
$95$	−2.37228	+	4.10891i	−0.243391	+	0.421565i
$96$		0			0
$97$	9.86141			1.00127			0.500637	−	0.865657i	$-0.333099\pi$
$97$	9.86141			1.00127			0.500637	+	0.865657i	$0.333099\pi$
$98$		0			0
$99$	16.7446			1.68289
$100$		0			0
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$		0			0
$103$	−2.81386	−	4.87375i	−0.277258	−	0.480225i	0.693444	−	0.720510i	$-0.256092\pi$
$103$	−2.81386	−	4.87375i	−0.277258	−	0.480225i	−0.970702	+	0.240285i	$0.922759\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.37228	−	7.57301i	−0.422684	−	0.732111i	0.573517	−	0.819194i	$-0.305579\pi$
$107$	−4.37228	−	7.57301i	−0.422684	−	0.732111i	−0.996201	+	0.0870831i	$0.972245\pi$
$108$		0			0
$109$	−0.186141	+	0.322405i	−0.0178290	+	0.0308808i	−0.874802	−	0.484480i	$-0.839009\pi$
$109$	−0.186141	+	0.322405i	−0.0178290	+	0.0308808i	0.856973	+	0.515361i	$0.172342\pi$
$110$		0			0
$111$	4.74456			0.450334
$112$		0			0
$113$	2.00000			0.188144			0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000			0.188144			0.0940721	+	0.995565i	$0.470012\pi$
$114$		0			0
$115$	2.37228	−	4.10891i	0.221216	−	0.383158i
$116$		0			0
$117$	5.74456	+	9.94987i	0.531085	+	0.919866i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−14.8030	−	25.6395i	−1.34573	−	2.33087i
$122$		0			0
$123$	−8.00000	+	13.8564i	−0.721336	+	1.24939i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$		0			0
$129$	−10.3723	+	17.9653i	−0.913228	+	1.58176i
$130$		0			0
$131$	−2.37228	−	4.10891i	−0.207267	−	0.358997i	0.743586	−	0.668641i	$-0.233124\pi$
$131$	−2.37228	−	4.10891i	−0.207267	−	0.358997i	−0.950853	+	0.309644i	$0.899790\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.441578	−	0.764836i	−0.0380050	−	0.0658266i
$136$		0			0
$137$	−7.37228	+	12.7692i	−0.629857	+	1.09094i	0.357724	+	0.933827i	$0.383553\pi$
$137$	−7.37228	+	12.7692i	−0.629857	+	1.09094i	−0.987580	+	0.157116i	$0.949780\pi$
$138$		0			0
$139$	4.74456			0.402429			0.201214	−	0.979547i	$-0.435511\pi$
$139$	4.74456			0.402429			0.201214	+	0.979547i	$0.435511\pi$
$140$		0			0
$141$	−16.8832			−1.42182
$142$		0			0
$143$	13.9307	−	24.1287i	1.16494	−	2.01774i
$144$		0			0
$145$	2.18614	+	3.78651i	0.181549	+	0.314452i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.74456	−	13.4140i	−0.634459	−	1.09892i	−0.986629	−	0.162980i	$-0.947889\pi$
$149$	−7.74456	−	13.4140i	−0.634459	−	1.09892i	0.352170	−	0.935936i	$-0.385444\pi$
$150$		0			0
$151$	−7.55842	+	13.0916i	−0.615096	+	1.06538i	0.375272	+	0.926915i	$0.377549\pi$
$151$	−7.55842	+	13.0916i	−0.615096	+	1.06538i	−0.990368	+	0.138462i	$0.955784\pi$
$152$		0			0
$153$	0.978251			0.0790869
$154$		0			0
$155$	8.00000			0.642575
$156$		0			0
$157$	−7.74456	+	13.4140i	−0.618083	+	1.07055i	0.371752	+	0.928332i	$0.378757\pi$
$157$	−7.74456	+	13.4140i	−0.618083	+	1.07055i	−0.989835	+	0.142220i	$0.954576\pi$
$158$		0			0
$159$	12.7446	+	22.0742i	1.01071	+	1.75060i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	8.37228	+	14.5012i	0.655768	+	1.13582i	0.981701	+	0.190430i	$0.0609883\pi$
$163$	8.37228	+	14.5012i	0.655768	+	1.13582i	−0.325933	+	0.945393i	$0.605678\pi$
$164$		0			0
$165$	7.55842	−	13.0916i	0.588422	−	1.01918i
$166$		0			0
$167$	5.62772			0.435486			0.217743	−	0.976006i	$-0.430131\pi$
$167$	5.62772			0.435486			0.217743	+	0.976006i	$0.430131\pi$
$168$		0			0
$169$	6.11684			0.470526
$170$		0			0
$171$	−6.23369	+	10.7971i	−0.476702	+	0.825672i
$172$		0			0
$173$	−0.186141	−	0.322405i	−0.0141520	−	0.0245120i	0.858863	−	0.512206i	$-0.171172\pi$
$173$	−0.186141	−	0.322405i	−0.0141520	−	0.0245120i	−0.873015	+	0.487694i	$0.837838\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−9.48913	−	16.4356i	−0.713246	−	1.23538i
$178$		0			0
$179$	11.4891	−	19.8997i	0.858738	−	1.48738i	−0.0143962	−	0.999896i	$-0.504583\pi$
$179$	11.4891	−	19.8997i	0.858738	−	1.48738i	0.873134	−	0.487481i	$-0.162084\pi$
$180$		0			0
$181$	−16.2337			−1.20664			−0.603320	−	0.797499i	$-0.706156\pi$
$181$	−16.2337			−1.20664			−0.603320	+	0.797499i	$0.706156\pi$
$182$		0			0
$183$	−6.51087			−0.481298
$184$		0			0
$185$	1.00000	−	1.73205i	0.0735215	−	0.127343i
$186$		0			0
$187$	−1.18614	−	2.05446i	−0.0867392	−	0.150237i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.93070	−	3.34408i	−0.139701	−	0.241969i	0.787683	−	0.616081i	$-0.211281\pi$
$191$	−1.93070	−	3.34408i	−0.139701	−	0.241969i	−0.927383	+	0.374112i	$0.877947\pi$
$192$		0			0
$193$	−3.37228	+	5.84096i	−0.242742	+	0.420442i	−0.961494	−	0.274825i	$-0.911380\pi$
$193$	−3.37228	+	5.84096i	−0.242742	+	0.420442i	0.718752	+	0.695266i	$0.244714\pi$
$194$		0			0
$195$	10.3723			0.742774
$196$		0			0
$197$	−8.23369			−0.586626			−0.293313	−	0.956016i	$-0.594758\pi$
$197$	−8.23369			−0.586626			−0.293313	+	0.956016i	$0.594758\pi$
$198$		0			0
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	0.429745	+	0.902950i	$0.358603\pi$
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	−0.996850	+	0.0793045i	$0.974730\pi$
$200$		0			0
$201$	−4.74456	−	8.21782i	−0.334656	−	0.579641i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	3.37228	+	5.84096i	0.235530	+	0.407951i
$206$		0			0
$207$	6.23369	−	10.7971i	0.433271	−	0.750448i
$208$		0			0
$209$	30.2337			2.09131
$210$		0			0
$211$	−14.3723			−0.989429			−0.494714	−	0.869056i	$-0.664727\pi$
$211$	−14.3723			−0.989429			−0.494714	+	0.869056i	$0.664727\pi$
$212$		0			0
$213$	9.48913	−	16.4356i	0.650184	−	1.12615i
$214$		0			0
$215$	4.37228	+	7.57301i	0.298187	+	0.516475i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	7.11684	+	12.3267i	0.480912	+	0.832964i
$220$		0			0
$221$	0.813859	−	1.40965i	0.0547461	−	0.0948230i
$222$		0			0
$223$	5.62772			0.376860			0.188430	−	0.982087i	$-0.439660\pi$
$223$	5.62772			0.376860			0.188430	+	0.982087i	$0.439660\pi$
$224$		0			0
$225$	2.62772			0.175181
$226$		0			0
$227$	9.93070	−	17.2005i	0.659124	−	1.14164i	−0.321719	−	0.946835i	$-0.604261\pi$
$227$	9.93070	−	17.2005i	0.659124	−	1.14164i	0.980843	−	0.194801i	$-0.0624061\pi$
$228$		0			0
$229$	−6.11684	−	10.5947i	−0.404212	−	0.700116i	0.590017	−	0.807391i	$-0.299121\pi$
$229$	−6.11684	−	10.5947i	−0.404212	−	0.700116i	−0.994229	+	0.107274i	$0.965788\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.627719	+	1.08724i	0.0411232	+	0.0712275i	0.885854	−	0.463963i	$-0.153573\pi$
$233$	0.627719	+	1.08724i	0.0411232	+	0.0712275i	−0.844731	+	0.535191i	$0.820240\pi$
$234$		0			0
$235$	−3.55842	+	6.16337i	−0.232126	+	0.402054i
$236$		0			0
$237$	−35.8614			−2.32945
$238$		0			0
$239$	13.6277			0.881504			0.440752	−	0.897629i	$-0.354712\pi$
$239$	13.6277			0.881504			0.440752	+	0.897629i	$0.354712\pi$
$240$		0			0
$241$	13.0000	−	22.5167i	0.837404	−	1.45043i	−0.0546547	−	0.998505i	$-0.517406\pi$
$241$	13.0000	−	22.5167i	0.837404	−	1.45043i	0.892058	−	0.451920i	$-0.149261\pi$
$242$		0			0
$243$	−10.5109	−	18.2054i	−0.674273	−	1.16787i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	10.3723	+	17.9653i	0.659972	+	1.14311i
$248$		0			0
$249$	11.2554	−	19.4950i	0.713284	−	1.23544i
$250$		0			0
$251$	−4.74456			−0.299474			−0.149737	−	0.988726i	$-0.547843\pi$
$251$	−4.74456			−0.299474			−0.149737	+	0.988726i	$0.547843\pi$
$252$		0			0
$253$	−30.2337			−1.90078
$254$		0			0
$255$	0.441578	−	0.764836i	0.0276527	−	0.0478959i
$256$		0			0
$257$	−11.7446	−	20.3422i	−0.732606	−	1.26891i	−0.955766	−	0.294128i	$-0.904971\pi$
$257$	−11.7446	−	20.3422i	−0.732606	−	1.26891i	0.223160	−	0.974782i	$-0.428363\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	5.74456	+	9.94987i	0.355580	+	0.615882i
$262$		0			0
$263$	−11.1168	+	19.2549i	−0.685494	+	1.18731i	0.287787	+	0.957694i	$0.407080\pi$
$263$	−11.1168	+	19.2549i	−0.685494	+	1.18731i	−0.973281	+	0.229616i	$0.926253\pi$
$264$		0			0
$265$	10.7446			0.660033
$266$		0			0
$267$	34.9783			2.14063
$268$		0			0
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	−0.942871	−	0.333157i	$-0.891886\pi$
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	0.759958	+	0.649972i	$0.225219\pi$
$270$		0			0
$271$	4.74456	+	8.21782i	0.288212	+	0.499197i	0.973383	−	0.229185i	$-0.0736060\pi$
$271$	4.74456	+	8.21782i	0.288212	+	0.499197i	−0.685171	+	0.728382i	$0.740273\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.18614	−	5.51856i	−0.192132	−	0.332782i
$276$		0			0
$277$	−12.4891	+	21.6318i	−0.750399	+	1.29973i	0.197231	+	0.980357i	$0.436805\pi$
$277$	−12.4891	+	21.6318i	−0.750399	+	1.29973i	−0.947630	+	0.319372i	$0.896528\pi$
$278$		0			0
$279$	21.0217			1.25854
$280$		0			0
$281$	18.6060			1.10994			0.554970	−	0.831871i	$-0.312730\pi$
$281$	18.6060			1.10994			0.554970	+	0.831871i	$0.312730\pi$
$282$		0			0
$283$	−4.44158	+	7.69304i	−0.264024	+	0.457304i	−0.967308	−	0.253606i	$-0.918383\pi$
$283$	−4.44158	+	7.69304i	−0.264024	+	0.457304i	0.703283	+	0.710910i	$0.251717\pi$
$284$		0			0
$285$	5.62772	+	9.74749i	0.333357	+	0.577392i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.43070	+	14.6024i	0.495924	+	0.858965i
$290$		0			0
$291$	11.6970	−	20.2598i	0.685691	−	1.18765i
$292$		0			0
$293$	−25.1168			−1.46734			−0.733671	−	0.679505i	$-0.762195\pi$
$293$	−25.1168			−1.46734			−0.733671	+	0.679505i	$0.762195\pi$
$294$		0			0
$295$	−8.00000			−0.465778
$296$		0			0
$297$	−2.81386	+	4.87375i	−0.163277	+	0.282804i
$298$		0			0
$299$	−10.3723	−	17.9653i	−0.599845	−	1.03896i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	7.11684	+	12.3267i	0.408852	+	0.708152i
$304$		0			0
$305$	−1.37228	+	2.37686i	−0.0785766	+	0.136099i
$306$		0			0
$307$	−31.1168			−1.77593			−0.887966	−	0.459909i	$-0.847882\pi$
$307$	−31.1168			−1.77593			−0.887966	+	0.459909i	$0.847882\pi$
$308$		0			0
$309$	−13.3505			−0.759485
$310$		0			0
$311$	−6.37228	+	11.0371i	−0.361339	+	0.625857i	−0.988181	−	0.153289i	$-0.951014\pi$
$311$	−6.37228	+	11.0371i	−0.361339	+	0.625857i	0.626843	+	0.779146i	$0.284347\pi$
$312$		0			0
$313$	1.44158	+	2.49689i	0.0814828	+	0.141132i	0.903887	−	0.427771i	$-0.140701\pi$
$313$	1.44158	+	2.49689i	0.0814828	+	0.141132i	−0.822404	+	0.568904i	$0.807368\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.00000	−	12.1244i	−0.393159	−	0.680972i	0.599705	−	0.800221i	$-0.295285\pi$
$317$	−7.00000	−	12.1244i	−0.393159	−	0.680972i	−0.992864	+	0.119249i	$0.961951\pi$
$318$		0			0
$319$	13.9307	−	24.1287i	0.779970	−	1.35095i
$320$		0			0
$321$	−20.7446			−1.15785
$322$		0			0
$323$	1.76631			0.0982802
$324$		0			0
$325$	2.18614	−	3.78651i	0.121265	−	0.210038i
$326$		0			0
$327$	0.441578	+	0.764836i	0.0244193	+	0.0422955i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−6.00000	−	10.3923i	−0.329790	−	0.571213i	0.652680	−	0.757634i	$-0.273645\pi$
$331$	−6.00000	−	10.3923i	−0.329790	−	0.571213i	−0.982470	+	0.186421i	$0.940311\pi$
$332$		0			0
$333$	2.62772	−	4.55134i	0.143998	−	0.249412i
$334$		0			0
$335$	−4.00000			−0.218543
$336$		0			0
$337$	−7.48913			−0.407959			−0.203979	−	0.978975i	$-0.565388\pi$
$337$	−7.48913			−0.407959			−0.203979	+	0.978975i	$0.565388\pi$
$338$		0			0
$339$	2.37228	−	4.10891i	0.128845	−	0.223165i
$340$		0			0
$341$	−25.4891	−	44.1485i	−1.38031	−	2.39077i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−5.62772	−	9.74749i	−0.302986	−	0.524787i
$346$		0			0
$347$	12.3723	−	21.4294i	0.664179	−	1.15039i	−0.315328	−	0.948983i	$-0.602115\pi$
$347$	12.3723	−	21.4294i	0.664179	−	1.15039i	0.979507	−	0.201409i	$-0.0645520\pi$
$348$		0			0
$349$	−19.4891			−1.04323			−0.521614	−	0.853181i	$-0.674670\pi$
$349$	−19.4891			−1.04323			−0.521614	+	0.853181i	$0.674670\pi$
$350$		0			0
$351$	−3.86141			−0.206107
$352$		0			0
$353$	−0.930703	+	1.61203i	−0.0495363	+	0.0857995i	−0.889730	−	0.456486i	$-0.849108\pi$
$353$	−0.930703	+	1.61203i	−0.0495363	+	0.0857995i	0.840194	+	0.542286i	$0.182441\pi$
$354$		0			0
$355$	−4.00000	−	6.92820i	−0.212298	−	0.367711i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$359$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$360$		0			0
$361$	−1.75544	+	3.04051i	−0.0923914	+	0.160027i
$362$		0			0
$363$	−70.2337			−3.68631
$364$		0			0
$365$	6.00000			0.314054
$366$		0			0
$367$	9.93070	−	17.2005i	0.518378	−	0.897858i	−0.481393	−	0.876505i	$-0.659869\pi$
$367$	9.93070	−	17.2005i	0.518378	−	0.897858i	0.999772	−	0.0213533i	$-0.00679748\pi$
$368$		0			0
$369$	8.86141	+	15.3484i	0.461306	+	0.799006i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	15.3723	+	26.6256i	0.795947	+	1.37862i	0.922236	+	0.386626i	$0.126360\pi$
$373$	15.3723	+	26.6256i	0.795947	+	1.37862i	−0.126290	+	0.991993i	$0.540307\pi$
$374$		0			0
$375$	1.18614	−	2.05446i	0.0612520	−	0.106092i
$376$		0			0
$377$	19.1168			0.984568
$378$		0			0
$379$	12.0000			0.616399			0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000			0.616399			0.308199	+	0.951322i	$0.400274\pi$
$380$		0			0
$381$	9.48913	−	16.4356i	0.486143	−	0.842024i
$382$		0			0
$383$	−8.74456	−	15.1460i	−0.446826	−	0.773926i	0.551351	−	0.834273i	$-0.314112\pi$
$383$	−8.74456	−	15.1460i	−0.446826	−	0.773926i	−0.998177	+	0.0603475i	$0.980779\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	11.4891	+	19.8997i	0.584025	+	1.01156i
$388$		0			0
$389$	−8.93070	+	15.4684i	−0.452805	+	0.784281i	−0.998559	−	0.0536646i	$-0.982910\pi$
$389$	−8.93070	+	15.4684i	−0.452805	+	0.784281i	0.545754	+	0.837945i	$0.316243\pi$
$390$		0			0
$391$	−1.76631			−0.0893262
$392$		0			0
$393$	−11.2554			−0.567762
$394$		0			0
$395$	−7.55842	+	13.0916i	−0.380305	+	0.658708i
$396$		0			0
$397$	15.8139	+	27.3904i	0.793675	+	1.37469i	0.923677	+	0.383171i	$0.125168\pi$
$397$	15.8139	+	27.3904i	0.793675	+	1.37469i	−0.130002	+	0.991514i	$0.541498\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	19.3030	+	33.4338i	0.963945	+	1.66960i	0.712423	+	0.701750i	$0.247598\pi$
$401$	19.3030	+	33.4338i	0.963945	+	1.66960i	0.251522	+	0.967852i	$0.419069\pi$
$402$		0			0
$403$	17.4891	−	30.2921i	0.871195	−	1.50895i
$404$		0			0
$405$	−9.97825			−0.495823
$406$		0			0
$407$	−12.7446			−0.631725
$408$		0			0
$409$	5.74456	−	9.94987i	0.284050	−	0.491990i	−0.688328	−	0.725399i	$-0.741655\pi$
$409$	5.74456	−	9.94987i	0.284050	−	0.491990i	0.972378	+	0.233410i	$0.0749884\pi$
$410$		0			0
$411$	17.4891	+	30.2921i	0.862675	+	1.49420i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−4.74456	−	8.21782i	−0.232901	−	0.403397i
$416$		0			0
$417$	5.62772	−	9.74749i	0.275591	−	0.477337i
$418$		0			0
$419$	14.5109			0.708903			0.354451	−	0.935074i	$-0.384668\pi$
$419$	14.5109			0.708903			0.354451	+	0.935074i	$0.384668\pi$
$420$		0			0
$421$	−18.6060			−0.906799			−0.453400	−	0.891307i	$-0.649789\pi$
$421$	−18.6060			−0.906799			−0.453400	+	0.891307i	$0.649789\pi$
$422$		0			0
$423$	−9.35053	+	16.1956i	−0.454638	+	0.787457i
$424$		0			0
$425$	−0.186141	−	0.322405i	−0.00902915	−	0.0156389i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−33.0475	−	57.2400i	−1.59555	−	2.76357i
$430$		0			0
$431$	−9.18614	+	15.9109i	−0.442481	+	0.766399i	−0.997873	−	0.0651893i	$-0.979235\pi$
$431$	−9.18614	+	15.9109i	−0.442481	+	0.766399i	0.555392	+	0.831589i	$0.312568\pi$
$432$		0			0
$433$	−28.9783			−1.39261			−0.696303	−	0.717748i	$-0.745173\pi$
$433$	−28.9783			−1.39261			−0.696303	+	0.717748i	$0.745173\pi$
$434$		0			0
$435$	10.3723			0.497313
$436$		0			0
$437$	11.2554	−	19.4950i	0.538421	−	0.932572i
$438$		0			0
$439$	−3.11684	−	5.39853i	−0.148759	−	0.257658i	0.782010	−	0.623266i	$-0.214194\pi$
$439$	−3.11684	−	5.39853i	−0.148759	−	0.257658i	−0.930769	+	0.365608i	$0.880861\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	8.37228	+	14.5012i	0.397779	+	0.688974i	0.993452	−	0.114254i	$-0.0364477\pi$
$443$	8.37228	+	14.5012i	0.397779	+	0.688974i	−0.595673	+	0.803227i	$0.703114\pi$
$444$		0			0
$445$	7.37228	−	12.7692i	0.349480	−	0.605317i
$446$		0			0
$447$	−36.7446			−1.73796
$448$		0			0
$449$	17.1168			0.807794			0.403897	−	0.914805i	$-0.367655\pi$
$449$	17.1168			0.807794			0.403897	+	0.914805i	$0.367655\pi$
$450$		0			0
$451$	21.4891	−	37.2203i	1.01188	−	1.75263i
$452$		0			0
$453$	17.9307	+	31.0569i	0.842458	+	1.45918i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−2.62772	−	4.55134i	−0.122919	−	0.212903i	0.797998	−	0.602660i	$-0.205892\pi$
$457$	−2.62772	−	4.55134i	−0.122919	−	0.212903i	−0.920918	+	0.389757i	$0.872559\pi$
$458$		0			0
$459$	−0.164391	+	0.284734i	−0.00767313	+	0.0132902i
$460$		0			0
$461$	1.25544			0.0584715			0.0292358	−	0.999573i	$-0.490693\pi$
$461$	1.25544			0.0584715			0.0292358	+	0.999573i	$0.490693\pi$
$462$		0			0
$463$	−6.51087			−0.302586			−0.151293	−	0.988489i	$-0.548344\pi$
$463$	−6.51087			−0.302586			−0.151293	+	0.988489i	$0.548344\pi$
$464$		0			0
$465$	9.48913	−	16.4356i	0.440048	−	0.762185i
$466$		0			0
$467$	4.30298	+	7.45299i	0.199118	+	0.344883i	0.948243	−	0.317546i	$-0.102859\pi$
$467$	4.30298	+	7.45299i	0.199118	+	0.344883i	−0.749124	+	0.662429i	$0.769526\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	18.3723	+	31.8217i	0.846550	+	1.46627i
$472$		0			0
$473$	27.8614	−	48.2574i	1.28107	−	2.21888i
$474$		0			0
$475$	4.74456			0.217695
$476$		0			0
$477$	28.2337			1.29273
$478$		0			0
$479$	11.1168	−	19.2549i	0.507942	−	0.879781i	−0.492016	−	0.870586i	$-0.663740\pi$
$479$	11.1168	−	19.2549i	0.507942	−	0.879781i	0.999958	−	0.00919454i	$-0.00292675\pi$
$480$		0			0
$481$	−4.37228	−	7.57301i	−0.199359	−	0.345300i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.93070	−	8.54023i	−0.223892	−	0.387792i
$486$		0			0
$487$	−15.1168	+	26.1831i	−0.685010	+	1.18647i	0.288424	+	0.957503i	$0.406869\pi$
$487$	−15.1168	+	26.1831i	−0.685010	+	1.18647i	−0.973434	+	0.228969i	$0.926465\pi$
$488$		0			0
$489$	39.7228			1.79633
$490$		0			0
$491$	35.1168			1.58480			0.792400	−	0.610001i	$-0.208831\pi$
$491$	35.1168			1.58480			0.792400	+	0.610001i	$0.208831\pi$
$492$		0			0
$493$	0.813859	−	1.40965i	0.0366544	−	0.0634873i
$494$		0			0
$495$	−8.37228	−	14.5012i	−0.376306	−	0.651781i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−15.9307	−	27.5928i	−0.713156	−	1.23522i	−0.963666	−	0.267109i	$-0.913932\pi$
$499$	−15.9307	−	27.5928i	−0.713156	−	1.23522i	0.250510	−	0.968114i	$-0.419402\pi$
$500$		0			0
$501$	6.67527	−	11.5619i	0.298229	−	0.516548i
$502$		0			0
$503$	18.3723			0.819180			0.409590	−	0.912270i	$-0.365672\pi$
$503$	18.3723			0.819180			0.409590	+	0.912270i	$0.365672\pi$
$504$		0			0
$505$	6.00000			0.266996
$506$		0			0
$507$	7.25544	−	12.5668i	0.322225	−	0.558111i
$508$		0			0
$509$	−20.4891	−	35.4882i	−0.908165	−	1.57299i	−0.816612	−	0.577187i	$-0.804150\pi$
$509$	−20.4891	−	35.4882i	−0.908165	−	1.57299i	−0.0915524	−	0.995800i	$-0.529183\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−2.09509	−	3.62881i	−0.0925007	−	0.160216i
$514$		0			0
$515$	−2.81386	+	4.87375i	−0.123993	+	0.214763i
$516$		0			0
$517$	45.3505			1.99451
$518$		0			0
$519$	−0.883156			−0.0387662
$520$		0			0
$521$	−15.0000	+	25.9808i	−0.657162	+	1.13824i	0.324185	+	0.945994i	$0.394910\pi$
$521$	−15.0000	+	25.9808i	−0.657162	+	1.13824i	−0.981347	+	0.192244i	$0.938423\pi$
$522$		0			0
$523$	−18.2337	−	31.5817i	−0.797304	−	1.38097i	−0.921366	−	0.388696i	$-0.872926\pi$
$523$	−18.2337	−	31.5817i	−0.797304	−	1.38097i	0.124063	−	0.992274i	$-0.460408\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.48913	−	2.57924i	−0.0648673	−	0.112353i
$528$		0			0
$529$	0.244563	−	0.423595i	0.0106332	−	0.0184172i
$530$		0			0
$531$	−21.0217			−0.912266
$532$		0			0
$533$	29.4891			1.27732
$534$		0			0
$535$	−4.37228	+	7.57301i	−0.189030	+	0.327410i
$536$		0			0
$537$	−27.2554	−	47.2078i	−1.17616	−	2.03717i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	15.6753	+	27.1504i	0.673932	+	1.16729i	0.976780	+	0.214246i	$0.0687294\pi$
$541$	15.6753	+	27.1504i	0.673932	+	1.16729i	−0.302847	+	0.953039i	$0.597937\pi$
$542$		0			0
$543$	−19.2554	+	33.3514i	−0.826330	+	1.43125i
$544$		0			0
$545$	0.372281			0.0159468
$546$		0			0
$547$	−30.9783			−1.32453			−0.662267	−	0.749268i	$-0.730406\pi$
$547$	−30.9783			−1.32453			−0.662267	+	0.749268i	$0.730406\pi$
$548$		0			0
$549$	−3.60597	+	6.24572i	−0.153899	+	0.266561i
$550$		0			0
$551$	10.3723	+	17.9653i	0.441874	+	0.765348i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−2.37228	−	4.10891i	−0.100698	−	0.174414i
$556$		0			0
$557$	1.88316	−	3.26172i	0.0797919	−	0.138204i	−0.823368	−	0.567508i	$-0.807908\pi$
$557$	1.88316	−	3.26172i	0.0797919	−	0.138204i	0.903160	+	0.429304i	$0.141241\pi$
$558$		0			0
$559$	38.2337			1.61711
$560$		0			0
$561$	−5.62772			−0.237602
$562$		0			0
$563$	8.74456	−	15.1460i	0.368539	−	0.638329i	−0.620798	−	0.783971i	$-0.713191\pi$
$563$	8.74456	−	15.1460i	0.368539	−	0.638329i	0.989337	+	0.145642i	$0.0465246\pi$
$564$		0			0
$565$	−1.00000	−	1.73205i	−0.0420703	−	0.0728679i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	12.4891	+	21.6318i	0.523571	+	0.906852i	0.999624	+	0.0274352i	$0.00873399\pi$
$569$	12.4891	+	21.6318i	0.523571	+	0.906852i	−0.476052	+	0.879417i	$0.657933\pi$
$570$		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	$0.0292272\pi$
$572$		0			0
$573$	−9.16034			−0.382679
$574$		0			0
$575$	−4.74456			−0.197862
$576$		0			0
$577$	−11.3030	+	19.5773i	−0.470549	+	0.815015i	−0.999433	−	0.0336791i	$-0.989278\pi$
$577$	−11.3030	+	19.5773i	−0.470549	+	0.815015i	0.528883	+	0.848695i	$0.322611\pi$
$578$		0			0
$579$	8.00000	+	13.8564i	0.332469	+	0.575853i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−34.2337	−	59.2945i	−1.41781	−	2.45573i
$584$		0			0
$585$	5.74456	−	9.94987i	0.237508	−	0.411377i
$586$		0			0
$587$	34.9783			1.44371			0.721853	−	0.692046i	$-0.243290\pi$
$587$	34.9783			1.44371			0.721853	+	0.692046i	$0.243290\pi$
$588$		0			0
$589$	37.9565			1.56397
$590$		0			0
$591$	−9.76631	+	16.9157i	−0.401732	+	0.695821i
$592$		0			0
$593$	−9.81386	−	16.9981i	−0.403007	−	0.698028i	0.591080	−	0.806613i	$-0.298702\pi$
$593$	−9.81386	−	16.9981i	−0.403007	−	0.698028i	−0.994087	+	0.108584i	$0.965368\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	18.9783	+	32.8713i	0.776728	+	1.34533i
$598$		0			0
$599$	16.3030	−	28.2376i	0.666122	−	1.15376i	−0.312858	−	0.949800i	$-0.601286\pi$
$599$	16.3030	−	28.2376i	0.666122	−	1.15376i	0.978980	−	0.203957i	$-0.0653803\pi$
$600$		0			0
$601$	−16.5109			−0.673493			−0.336746	−	0.941595i	$-0.609326\pi$
$601$	−16.5109			−0.673493			−0.336746	+	0.941595i	$0.609326\pi$
$602$		0			0
$603$	−10.5109			−0.428036
$604$		0			0
$605$	−14.8030	+	25.6395i	−0.601827	+	1.04239i
$606$		0			0
$607$	12.3030	+	21.3094i	0.499363	+	0.864922i	1.00000		0.000735686i	$-0.000234176\pi$
$607$	12.3030	+	21.3094i	0.499363	+	0.864922i	−0.500637	+	0.865657i	$0.666901\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	15.5584	+	26.9480i	0.629426	+	1.09020i
$612$		0			0
$613$	4.25544	−	7.37063i	0.171875	−	0.297697i	−0.767200	−	0.641408i	$-0.778351\pi$
$613$	4.25544	−	7.37063i	0.171875	−	0.297697i	0.939076	+	0.343711i	$0.111684\pi$
$614$		0			0
$615$	16.0000			0.645182
$616$		0			0
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$		0			0
$619$	−6.37228	+	11.0371i	−0.256124	+	0.443619i	−0.965200	−	0.261512i	$-0.915779\pi$
$619$	−6.37228	+	11.0371i	−0.256124	+	0.443619i	0.709076	+	0.705132i	$0.249112\pi$
$620$		0			0
$621$	2.09509	+	3.62881i	0.0840732	+	0.145619i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	35.8614	−	62.1138i	1.43217	−	2.48059i
$628$		0			0
$629$	−0.744563			−0.0296877
$630$		0			0
$631$	2.37228			0.0944390			0.0472195	−	0.998885i	$-0.484964\pi$
$631$	2.37228			0.0944390			0.0472195	+	0.998885i	$0.484964\pi$
$632$		0			0
$633$	−17.0475	+	29.5272i	−0.677579	+	1.17360i
$634$		0			0
$635$	−4.00000	−	6.92820i	−0.158735	−	0.274937i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−10.5109	−	18.2054i	−0.415804	−	0.720193i
$640$		0			0
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	−0.885098	−	0.465404i	$-0.845909\pi$
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	0.845601	+	0.533816i	$0.179242\pi$
$642$		0			0
$643$	−18.3723			−0.724532			−0.362266	−	0.932075i	$-0.617997\pi$
$643$	−18.3723			−0.724532			−0.362266	+	0.932075i	$0.617997\pi$
$644$		0			0
$645$	20.7446			0.816816
$646$		0			0
$647$	−8.00000	+	13.8564i	−0.314512	+	0.544752i	−0.979334	−	0.202251i	$-0.935174\pi$
$647$	−8.00000	+	13.8564i	−0.314512	+	0.544752i	0.664821	+	0.747002i	$0.268508\pi$
$648$		0			0
$649$	25.4891	+	44.1485i	1.00054	+	1.73298i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.00000	−	5.19615i	−0.117399	−	0.203341i	0.801337	−	0.598213i	$-0.204122\pi$
$653$	−3.00000	−	5.19615i	−0.117399	−	0.203341i	−0.918736	+	0.394872i	$0.870789\pi$
$654$		0			0
$655$	−2.37228	+	4.10891i	−0.0926927	+	0.160548i
$656$		0			0
$657$	15.7663			0.615102
$658$		0			0
$659$	−11.1168			−0.433051			−0.216525	−	0.976277i	$-0.569472\pi$
$659$	−11.1168			−0.433051			−0.216525	+	0.976277i	$0.569472\pi$
$660$		0			0
$661$	7.37228	−	12.7692i	0.286749	−	0.496663i	−0.686283	−	0.727334i	$-0.740759\pi$
$661$	7.37228	−	12.7692i	0.286749	−	0.496663i	0.973032	+	0.230671i	$0.0740923\pi$
$662$		0			0
$663$	−1.93070	−	3.34408i	−0.0749823	−	0.129873i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−10.3723	−	17.9653i	−0.401616	−	0.695620i
$668$		0			0
$669$	6.67527	−	11.5619i	0.258081	−	0.447009i
$670$		0			0
$671$	17.4891			0.675160
$672$		0			0
$673$	25.7228			0.991542			0.495771	−	0.868453i	$-0.334886\pi$
$673$	25.7228			0.991542			0.495771	+	0.868453i	$0.334886\pi$
$674$		0			0
$675$	−0.441578	+	0.764836i	−0.0169963	+	0.0294385i
$676$		0			0
$677$	7.67527	+	13.2940i	0.294984	+	0.510928i	0.974981	−	0.222287i	$-0.0713522\pi$
$677$	7.67527	+	13.2940i	0.294984	+	0.510928i	−0.679997	+	0.733215i	$0.738019\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−23.5584	−	40.8044i	−0.902761	−	1.56363i
$682$		0			0
$683$	−18.0000	+	31.1769i	−0.688751	+	1.19295i	0.283491	+	0.958975i	$0.408507\pi$
$683$	−18.0000	+	31.1769i	−0.688751	+	1.19295i	−0.972242	+	0.233977i	$0.924826\pi$
$684$		0			0
$685$	14.7446			0.563361
$686$		0			0
$687$	−29.0217			−1.10725
$688$		0			0
$689$	23.4891	−	40.6844i	0.894864	−	1.54995i
$690$		0			0
$691$	−4.74456	−	8.21782i	−0.180492	−	0.312621i	0.761556	−	0.648099i	$-0.224436\pi$
$691$	−4.74456	−	8.21782i	−0.180492	−	0.312621i	−0.942048	+	0.335478i	$0.891102\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.37228	−	4.10891i	−0.0899858	−	0.155860i
$696$		0			0
$697$	1.25544	−	2.17448i	0.0475531	−	0.0823644i
$698$		0			0
$699$	2.97825			0.112648
$700$		0			0
$701$	2.13859			0.0807736			0.0403868	−	0.999184i	$-0.487141\pi$
$701$	2.13859			0.0807736			0.0403868	+	0.999184i	$0.487141\pi$
$702$		0			0
$703$	4.74456	−	8.21782i	0.178945	−	0.309941i
$704$		0			0
$705$	8.44158	+	14.6212i	0.317928	+	0.550668i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−3.30298	−	5.72094i	−0.124046	−	0.214854i	0.797314	−	0.603565i	$-0.206254\pi$
$709$	−3.30298	−	5.72094i	−0.124046	−	0.214854i	−0.921360	+	0.388711i	$0.872920\pi$
$710$		0			0
$711$	−19.8614	+	34.4010i	−0.744861	+	1.29014i
$712$		0			0
$713$	−37.9565			−1.42148
$714$		0			0
$715$	−27.8614			−1.04196
$716$		0			0
$717$	16.1644	−	27.9975i	0.603670	−	1.04559i
$718$		0			0
$719$	1.62772	+	2.81929i	0.0607037	+	0.105142i	0.894780	−	0.446507i	$-0.147332\pi$
$719$	1.62772	+	2.81929i	0.0607037	+	0.105142i	−0.834076	+	0.551649i	$0.813999\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−30.8397	−	53.4159i	−1.14694	−	1.98656i
$724$		0			0
$725$	2.18614	−	3.78651i	0.0811912	−	0.140627i
$726$		0			0
$727$	−32.0000			−1.18681			−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000			−1.18681			−0.593407	+	0.804902i	$0.702218\pi$
$728$		0			0
$729$	−19.9348			−0.738324
$730$		0			0
$731$	1.62772	−	2.81929i	0.0602034	−	0.104275i
$732$		0			0
$733$	−5.06930	−	8.78028i	−0.187239	−	0.324307i	0.757090	−	0.653311i	$-0.226620\pi$
$733$	−5.06930	−	8.78028i	−0.187239	−	0.324307i	−0.944329	+	0.329004i	$0.893287\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	12.7446	+	22.0742i	0.469452	+	0.813115i
$738$		0			0
$739$	10.3030	−	17.8453i	0.379001	−	0.656450i	−0.611916	−	0.790923i	$-0.709601\pi$
$739$	10.3030	−	17.8453i	0.379001	−	0.656450i	0.990917	+	0.134473i	$0.0429342\pi$
$740$		0			0
$741$	49.2119			1.80785
$742$		0			0
$743$	−6.51087			−0.238861			−0.119430	−	0.992843i	$-0.538107\pi$
$743$	−6.51087			−0.238861			−0.119430	+	0.992843i	$0.538107\pi$
$744$		0			0
$745$	−7.74456	+	13.4140i	−0.283739	+	0.491450i
$746$		0			0
$747$	−12.4674	−	21.5941i	−0.456157	−	0.790088i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−10.0693	−	17.4405i	−0.367434	−	0.636414i	0.621730	−	0.783232i	$-0.286430\pi$
$751$	−10.0693	−	17.4405i	−0.367434	−	0.636414i	−0.989164	+	0.146818i	$0.953097\pi$
$752$		0			0
$753$	−5.62772	+	9.74749i	−0.205085	+	0.355218i
$754$		0			0
$755$	15.1168			0.550158
$756$		0			0
$757$	−3.76631			−0.136889			−0.0684445	−	0.997655i	$-0.521804\pi$
$757$	−3.76631			−0.136889			−0.0684445	+	0.997655i	$0.521804\pi$
$758$		0			0
$759$	−35.8614	+	62.1138i	−1.30169	+	2.25459i
$760$		0			0
$761$	2.48913	+	4.31129i	0.0902307	+	0.156284i	0.907608	−	0.419818i	$-0.137906\pi$
$761$	2.48913	+	4.31129i	0.0902307	+	0.156284i	−0.817377	+	0.576103i	$0.804573\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.489125	−	0.847190i	−0.0176844	−	0.0306302i
$766$		0			0
$767$	−17.4891	+	30.2921i	−0.631496	+	1.09378i
$768$		0			0
$769$	−3.48913			−0.125821			−0.0629105	−	0.998019i	$-0.520038\pi$
$769$	−3.48913			−0.125821			−0.0629105	+	0.998019i	$0.520038\pi$
$770$		0			0
$771$	−55.7228			−2.00681
$772$		0			0
$773$	2.18614	−	3.78651i	0.0786300	−	0.136191i	−0.824029	−	0.566548i	$-0.808279\pi$
$773$	2.18614	−	3.78651i	0.0786300	−	0.136191i	0.902659	+	0.430356i	$0.141612\pi$
$774$		0			0
$775$	−4.00000	−	6.92820i	−0.143684	−	0.248868i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	16.0000	+	27.7128i	0.573259	+	0.992915i
$780$		0			0
$781$	−25.4891	+	44.1485i	−0.912073	+	1.57976i
$782$		0			0
$783$	−3.86141			−0.137995
$784$		0			0
$785$	15.4891			0.552831
$786$		0			0
$787$	−15.5584	+	26.9480i	−0.554598	+	0.960592i	0.443337	+	0.896355i	$0.353795\pi$
$787$	−15.5584	+	26.9480i	−0.554598	+	0.960592i	−0.997935	+	0.0642366i	$0.979539\pi$
$788$		0			0
$789$	26.3723	+	45.6781i	0.938878	+	1.62618i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	6.00000	+	10.3923i	0.213066	+	0.369042i
$794$		0			0
$795$	12.7446	−	22.0742i	0.452003	−	0.782892i
$796$		0			0
$797$	−15.6277			−0.553562			−0.276781	−	0.960933i	$-0.589268\pi$
$797$	−15.6277			−0.553562			−0.276781	+	0.960933i	$0.589268\pi$
$798$		0			0
$799$	2.64947			0.0937314
$800$		0			0
$801$	19.3723	−	33.5538i	0.684486	−	1.18556i
$802$		0			0
$803$	−19.1168	−	33.1113i	−0.674619	−	1.16847i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	7.11684	+	12.3267i	0.250525	+	0.433922i
$808$		0			0
$809$	−10.1861	+	17.6429i	−0.358126	+	0.620292i	−0.987648	−	0.156691i	$-0.949917\pi$
$809$	−10.1861	+	17.6429i	−0.358126	+	0.620292i	0.629522	+	0.776983i	$0.283251\pi$
$810$		0			0
$811$	−12.7446			−0.447522			−0.223761	−	0.974644i	$-0.571834\pi$
$811$	−12.7446			−0.447522			−0.223761	+	0.974644i	$0.571834\pi$
$812$		0			0
$813$	22.5109			0.789491
$814$		0			0
$815$	8.37228	−	14.5012i	0.293268	−	0.507955i
$816$		0			0
$817$	20.7446	+	35.9306i	0.725760	+	1.25705i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	12.5584	+	21.7518i	0.438292	+	0.759144i	0.997558	−	0.0698444i	$-0.0222503\pi$
$821$	12.5584	+	21.7518i	0.438292	+	0.759144i	−0.559266	+	0.828988i	$0.688917\pi$
$822$		0			0
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	−0.787850	−	0.615867i	$-0.788806\pi$
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	0.927281	+	0.374365i	$0.122139\pi$
$824$		0			0
$825$	−15.1168			−0.526301
$826$		0			0
$827$	24.7446			0.860453			0.430226	−	0.902721i	$-0.358434\pi$
$827$	24.7446			0.860453			0.430226	+	0.902721i	$0.358434\pi$
$828$		0			0
$829$	−6.11684	+	10.5947i	−0.212447	+	0.367969i	−0.952480	−	0.304602i	$-0.901477\pi$
$829$	−6.11684	+	10.5947i	−0.212447	+	0.367969i	0.740033	+	0.672571i	$0.234810\pi$
$830$		0			0
$831$	29.6277	+	51.3167i	1.02777	+	1.78016i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−2.81386	−	4.87375i	−0.0973776	−	0.168663i
$836$		0			0
$837$	−3.53262	+	6.11868i	−0.122105	+	0.211493i
$838$		0			0
$839$	11.2554			0.388581			0.194290	−	0.980944i	$-0.437760\pi$
$839$	11.2554			0.388581			0.194290	+	0.980944i	$0.437760\pi$
$840$		0			0
$841$	−9.88316			−0.340798
$842$		0			0
$843$	22.0693	−	38.2251i	0.760107	−	1.31654i
$844$		0			0
$845$	−3.05842	−	5.29734i	−0.105213	−	0.182234i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	10.5367	+	18.2501i	0.361618	+	0.626340i
$850$		0			0
$851$	−4.74456	+	8.21782i	−0.162642	+	0.281703i
$852$		0			0
$853$	39.4891			1.35208			0.676041	−	0.736864i	$-0.263694\pi$
$853$	39.4891			1.35208			0.676041	+	0.736864i	$0.263694\pi$
$854$		0			0
$855$	12.4674			0.426375
$856$		0			0
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$		0			0
$859$	22.2337	+	38.5099i	0.758604	+	1.31394i	0.943563	+	0.331194i	$0.107451\pi$
$859$	22.2337	+	38.5099i	0.758604	+	1.31394i	−0.184959	+	0.982746i	$0.559215\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−12.7446	−	22.0742i	−0.433830	−	0.751416i	0.563369	−	0.826205i	$-0.309505\pi$
$863$	−12.7446	−	22.0742i	−0.433830	−	0.751416i	−0.997199	+	0.0747896i	$0.976171\pi$
$864$		0			0
$865$	−0.186141	+	0.322405i	−0.00632897	+	0.0109621i
$866$		0			0
$867$	40.0000			1.35847
$868$		0			0
$869$	96.3288			3.26773
$870$		0			0
$871$	−8.74456	+	15.1460i	−0.296298	+	0.513204i
$872$		0			0
$873$	−12.9565	−	22.4413i	−0.438511	−	0.759524i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	3.51087	+	6.08101i	0.118554	+	0.205341i	0.919195	−	0.393803i	$-0.128841\pi$
$877$	3.51087	+	6.08101i	0.118554	+	0.205341i	−0.800641	+	0.599144i	$0.795508\pi$
$878$		0			0
$879$	−29.7921	+	51.6014i	−1.00486	+	1.74047i
$880$		0			0
$881$	25.2554			0.850877			0.425439	−	0.904987i	$-0.360120\pi$
$881$	25.2554			0.850877			0.425439	+	0.904987i	$0.360120\pi$
$882$		0			0
$883$	−10.5109			−0.353719			−0.176860	−	0.984236i	$-0.556594\pi$
$883$	−10.5109			−0.353719			−0.176860	+	0.984236i	$0.556594\pi$
$884$		0			0
$885$	−9.48913	+	16.4356i	−0.318973	+	0.552478i
$886$		0			0
$887$	−6.51087	−	11.2772i	−0.218614	−	0.378650i	0.735771	−	0.677231i	$-0.236820\pi$
$887$	−6.51087	−	11.2772i	−0.218614	−	0.378650i	−0.954384	+	0.298581i	$0.903487\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	31.7921	+	55.0655i	1.06508	+	1.84477i
$892$		0			0
$893$	−16.8832	+	29.2425i	−0.564973	+	0.978562i
$894$		0			0
$895$	−22.9783			−0.768078
$896$		0			0
$897$	−49.2119			−1.64314
$898$		0			0
$899$	17.4891	−	30.2921i	0.583295	−	1.01030i
$900$		0			0
$901$	−2.00000	−	3.46410i	−0.0666297	−	0.115406i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	8.11684	+	14.0588i	0.269813	+	0.467330i
$906$		0			0
$907$	−5.86141	+	10.1523i	−0.194625	+	0.337100i	−0.946777	−	0.321889i	$-0.895682\pi$
$907$	−5.86141	+	10.1523i	−0.194625	+	0.337100i	0.752153	+	0.658989i	$0.229016\pi$
$908$		0			0
$909$	15.7663			0.522936
$910$		0			0
$911$	−45.9565			−1.52261			−0.761303	−	0.648396i	$-0.775440\pi$
$911$	−45.9565			−1.52261			−0.761303	+	0.648396i	$0.775440\pi$
$912$		0			0
$913$	−30.2337	+	52.3663i	−1.00059	+	1.73307i
$914$		0			0
$915$	3.25544	+	5.63858i	0.107621	+	0.186406i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−6.81386	−	11.8020i	−0.224768	−	0.389310i	0.731481	−	0.681861i	$-0.238829\pi$
$919$	−6.81386	−	11.8020i	−0.224768	−	0.389310i	−0.956250	+	0.292551i	$0.905496\pi$
$920$		0			0
$921$	−36.9090	+	63.9282i	−1.21619	+	2.10651i
$922$		0			0
$923$	−34.9783			−1.15132
$924$		0			0
$925$	−2.00000			−0.0657596
$926$		0			0
$927$	−7.39403	+	12.8068i	−0.242852	+	0.420632i
$928$		0			0
$929$	−3.88316	−	6.72582i	−0.127402	−	0.220667i	0.795267	−	0.606259i	$-0.207331\pi$
$929$	−3.88316	−	6.72582i	−0.127402	−	0.220667i	−0.922669	+	0.385592i	$0.873997\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	15.1168	+	26.1831i	0.494903	+	0.857198i
$934$		0			0
$935$	−1.18614	+	2.05446i	−0.0387909	+	0.0671879i
$936$		0			0
$937$	−28.0951			−0.917827			−0.458913	−	0.888481i	$-0.651761\pi$
$937$	−28.0951			−0.917827			−0.458913	+	0.888481i	$0.651761\pi$
$938$		0			0
$939$	6.83966			0.223204
$940$		0			0
$941$	16.1168	−	27.9152i	0.525394	−	0.910009i	−0.474168	−	0.880434i	$-0.657251\pi$
$941$	16.1168	−	27.9152i	0.525394	−	0.910009i	0.999563	−	0.0295751i	$-0.00941543\pi$
$942$		0			0
$943$	−16.0000	−	27.7128i	−0.521032	−	0.902453i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	14.0000	+	24.2487i	0.454939	+	0.787977i	0.998685	−	0.0512727i	$-0.0163278\pi$
$947$	14.0000	+	24.2487i	0.454939	+	0.787977i	−0.543746	+	0.839250i	$0.682994\pi$
$948$		0			0
$949$	13.1168	−	22.7190i	0.425791	−	0.737491i
$950$		0			0
$951$	−33.2119			−1.07697
$952$		0			0
$953$	37.2554			1.20682			0.603411	−	0.797430i	$-0.293808\pi$
$953$	37.2554			1.20682			0.603411	+	0.797430i	$0.293808\pi$
$954$		0			0
$955$	−1.93070	+	3.34408i	−0.0624761	+	0.108212i
$956$		0			0
$957$	−33.0475	−	57.2400i	−1.06828	−	1.85031i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$		0			0
$963$	−11.4891	+	19.8997i	−0.370232	+	0.641260i
$964$		0			0
$965$	6.74456			0.217115
$966$		0			0
$967$	1.76631			0.0568008			0.0284004	−	0.999597i	$-0.490959\pi$
$967$	1.76631			0.0568008			0.0284004	+	0.999597i	$0.490959\pi$
$968$		0			0
$969$	2.09509	−	3.62881i	0.0673041	−	0.116574i
$970$		0			0
$971$	16.7446	+	29.0024i	0.537359	+	0.930732i	0.999045	+	0.0436893i	$0.0139111\pi$
$971$	16.7446	+	29.0024i	0.537359	+	0.930732i	−0.461687	+	0.887043i	$0.652756\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−5.18614	−	8.98266i	−0.166089	−	0.287675i
$976$		0			0
$977$	−26.4891	+	45.8805i	−0.847462	+	1.46785i	0.0360035	+	0.999352i	$0.488537\pi$
$977$	−26.4891	+	45.8805i	−0.847462	+	1.46785i	−0.883466	+	0.468496i	$0.844796\pi$
$978$		0			0
$979$	−93.9565			−3.00286
$980$		0			0
$981$	0.978251			0.0312331
$982$		0			0
$983$	−5.18614	+	8.98266i	−0.165412	+	0.286502i	−0.936802	−	0.349861i	$-0.886229\pi$
$983$	−5.18614	+	8.98266i	−0.165412	+	0.286502i	0.771389	+	0.636363i	$0.219562\pi$
$984$		0			0
$985$	4.11684	+	7.13058i	0.131174	+	0.227199i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−20.7446	−	35.9306i	−0.659639	−	1.14253i
$990$		0			0
$991$	18.9783	−	32.8713i	0.602864	−	1.04419i	−0.389521	−	0.921018i	$-0.627359\pi$
$991$	18.9783	−	32.8713i	0.602864	−	1.04419i	0.992385	−	0.123174i	$-0.0393072\pi$
$992$		0			0
$993$	−28.4674			−0.903385
$994$		0			0
$995$	16.0000			0.507234
$996$		0			0
$997$	−3.44158	+	5.96099i	−0.108996	+	0.188786i	−0.915364	−	0.402628i	$-0.868097\pi$
$997$	−3.44158	+	5.96099i	−0.108996	+	0.188786i	0.806368	+	0.591414i	$0.201430\pi$
$998$		0			0
$999$	0.883156	+	1.52967i	0.0279418	+	0.0483967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1960.2.q.r.361.2		4
7.2	even	3	inner	1960.2.q.r.961.2		4
7.3	odd	6		280.2.a.c.1.2	✓	2
7.4	even	3		1960.2.a.s.1.1		2
7.5	odd	6		1960.2.q.t.961.1		4
7.6	odd	2		1960.2.q.t.361.1		4
21.17	even	6		2520.2.a.x.1.1		2
28.3	even	6		560.2.a.h.1.1		2
28.11	odd	6		3920.2.a.bt.1.2		2
35.3	even	12		1400.2.g.i.449.3		4
35.4	even	6		9800.2.a.bu.1.2		2
35.17	even	12		1400.2.g.i.449.2		4
35.24	odd	6		1400.2.a.r.1.1		2
56.3	even	6		2240.2.a.bg.1.2		2
56.45	odd	6		2240.2.a.bk.1.1		2
84.59	odd	6		5040.2.a.by.1.2		2
140.3	odd	12		2800.2.g.r.449.2		4
140.59	even	6		2800.2.a.bk.1.2		2
140.87	odd	12		2800.2.g.r.449.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.a.c.1.2	✓	2	7.3	odd	6
560.2.a.h.1.1		2	28.3	even	6
1400.2.a.r.1.1		2	35.24	odd	6
1400.2.g.i.449.2		4	35.17	even	12
1400.2.g.i.449.3		4	35.3	even	12
1960.2.a.s.1.1		2	7.4	even	3
1960.2.q.r.361.2		4	1.1	even	1	trivial
1960.2.q.r.961.2		4	7.2	even	3	inner
1960.2.q.t.361.1		4	7.6	odd	2
1960.2.q.t.961.1		4	7.5	odd	6
2240.2.a.bg.1.2		2	56.3	even	6
2240.2.a.bk.1.1		2	56.45	odd	6
2520.2.a.x.1.1		2	21.17	even	6
2800.2.a.bk.1.2		2	140.59	even	6
2800.2.g.r.449.2		4	140.3	odd	12
2800.2.g.r.449.3		4	140.87	odd	12
3920.2.a.bt.1.2		2	28.11	odd	6
5040.2.a.by.1.2		2	84.59	odd	6
9800.2.a.bu.1.2		2	35.4	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:	\( N \)	\(=\)	\( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1960.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.18614 - 2.05446i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.31386 - 2.27567i) q^{9} +O(q^{10})\)	\(q+(1.18614 - 2.05446i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.31386 - 2.27567i) q^{9} +(-3.18614 + 5.51856i) q^{11} -4.37228 q^{13} -2.37228 q^{15} +(-0.186141 + 0.322405i) q^{17} +(-2.37228 - 4.10891i) q^{19} +(2.37228 + 4.10891i) q^{23} +(-0.500000 + 0.866025i) q^{25} +0.883156 q^{27} -4.37228 q^{29} +(-4.00000 + 6.92820i) q^{31} +(7.55842 + 13.0916i) q^{33} +(1.00000 + 1.73205i) q^{37} +(-5.18614 + 8.98266i) q^{39} -6.74456 q^{41} -8.74456 q^{43} +(-1.31386 + 2.27567i) q^{45} +(-3.55842 - 6.16337i) q^{47} +(0.441578 + 0.764836i) q^{51} +(-5.37228 + 9.30506i) q^{53} +6.37228 q^{55} -11.2554 q^{57} +(4.00000 - 6.92820i) q^{59} +(-1.37228 - 2.37686i) q^{61} +(2.18614 + 3.78651i) q^{65} +(2.00000 - 3.46410i) q^{67} +11.2554 q^{69} +8.00000 q^{71} +(-3.00000 + 5.19615i) q^{73} +(1.18614 + 2.05446i) q^{75} +(-7.55842 - 13.0916i) q^{79} +(4.98913 - 8.64142i) q^{81} +9.48913 q^{83} +0.372281 q^{85} +(-5.18614 + 8.98266i) q^{87} +(7.37228 + 12.7692i) q^{89} +(9.48913 + 16.4356i) q^{93} +(-2.37228 + 4.10891i) q^{95} +9.86141 q^{97} +16.7446 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} - 2 q^{5} - 11 q^{9}+O(q^{10}) \) 4 * q - q^3 - 2 * q^5 - 11 * q^9	\( 4 q - q^{3} - 2 q^{5} - 11 q^{9} - 7 q^{11} - 6 q^{13} + 2 q^{15} + 5 q^{17} + 2 q^{19} - 2 q^{23} - 2 q^{25} + 38 q^{27} - 6 q^{29} - 16 q^{31} + 13 q^{33} + 4 q^{37} - 15 q^{39} - 4 q^{41} - 12 q^{43} - 11 q^{45} + 3 q^{47} + 19 q^{51} - 10 q^{53} + 14 q^{55} - 68 q^{57} + 16 q^{59} + 6 q^{61} + 3 q^{65} + 8 q^{67} + 68 q^{69} + 32 q^{71} - 12 q^{73} - q^{75} - 13 q^{79} - 26 q^{81} - 8 q^{83} - 10 q^{85} - 15 q^{87} + 18 q^{89} - 8 q^{93} + 2 q^{95} - 18 q^{97} + 44 q^{99}+O(q^{100}) \) 4 * q - q^3 - 2 * q^5 - 11 * q^9 - 7 * q^11 - 6 * q^13 + 2 * q^15 + 5 * q^17 + 2 * q^19 - 2 * q^23 - 2 * q^25 + 38 * q^27 - 6 * q^29 - 16 * q^31 + 13 * q^33 + 4 * q^37 - 15 * q^39 - 4 * q^41 - 12 * q^43 - 11 * q^45 + 3 * q^47 + 19 * q^51 - 10 * q^53 + 14 * q^55 - 68 * q^57 + 16 * q^59 + 6 * q^61 + 3 * q^65 + 8 * q^67 + 68 * q^69 + 32 * q^71 - 12 * q^73 - q^75 - 13 * q^79 - 26 * q^81 - 8 * q^83 - 10 * q^85 - 15 * q^87 + 18 * q^89 - 8 * q^93 + 2 * q^95 - 18 * q^97 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more