LMFDB - Embedded newform 2940.2.q.t.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2940,2,Mod(361,2940)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2940, 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("2940.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2940.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:	$23.4760181943$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$-1.32288 + 2.29129i$ of defining polynomial
Character	$\chi$	$=$	2940.361
Dual form			2940.2.q.t.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-1.82288 + 3.15731i) q^{11} -2.64575 q^{13} +1.00000 q^{15} +(1.82288 - 3.15731i) q^{17} +(-1.14575 - 1.98450i) q^{19} +(1.82288 + 3.15731i) q^{23} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} +2.35425 q^{29} +(3.14575 - 5.44860i) q^{31} +(1.82288 + 3.15731i) q^{33} +(2.32288 + 4.02334i) q^{37} +(-1.32288 + 2.29129i) q^{39} +10.9373 q^{41} +9.93725 q^{43} +(0.500000 - 0.866025i) q^{45} +(3.00000 + 5.19615i) q^{47} +(-1.82288 - 3.15731i) q^{51} +(3.64575 - 6.31463i) q^{53} -3.64575 q^{55} -2.29150 q^{57} +(-2.46863 + 4.27579i) q^{59} +(4.00000 + 6.92820i) q^{61} +(-1.32288 - 2.29129i) q^{65} +(2.32288 - 4.02334i) q^{67} +3.64575 q^{69} +8.35425 q^{71} +(-6.61438 + 11.4564i) q^{73} +(0.500000 + 0.866025i) q^{75} +(4.14575 + 7.18065i) q^{79} +(-0.500000 + 0.866025i) q^{81} -4.93725 q^{83} +3.64575 q^{85} +(1.17712 - 2.03884i) q^{87} +(6.11438 + 10.5904i) q^{89} +(-3.14575 - 5.44860i) q^{93} +(1.14575 - 1.98450i) q^{95} -8.00000 q^{97} +3.64575 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{5} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^5 - 2 * q^9	$ 4 q + 2 q^{3} + 2 q^{5} - 2 q^{9} - 2 q^{11} + 4 q^{15} + 2 q^{17} + 6 q^{19} + 2 q^{23} - 2 q^{25} - 4 q^{27} + 20 q^{29} + 2 q^{31} + 2 q^{33} + 4 q^{37} + 12 q^{41} + 8 q^{43} + 2 q^{45} + 12 q^{47} - 2 q^{51} + 4 q^{53} - 4 q^{55} + 12 q^{57} + 6 q^{59} + 16 q^{61} + 4 q^{67} + 4 q^{69} + 44 q^{71} + 2 q^{75} + 6 q^{79} - 2 q^{81} + 12 q^{83} + 4 q^{85} + 10 q^{87} - 2 q^{89} - 2 q^{93} - 6 q^{95} - 32 q^{97} + 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^5 - 2 * q^9 - 2 * q^11 + 4 * q^15 + 2 * q^17 + 6 * q^19 + 2 * q^23 - 2 * q^25 - 4 * q^27 + 20 * q^29 + 2 * q^31 + 2 * q^33 + 4 * q^37 + 12 * q^41 + 8 * q^43 + 2 * q^45 + 12 * q^47 - 2 * q^51 + 4 * q^53 - 4 * q^55 + 12 * q^57 + 6 * q^59 + 16 * q^61 + 4 * q^67 + 4 * q^69 + 44 * q^71 + 2 * q^75 + 6 * q^79 - 2 * q^81 + 12 * q^83 + 4 * q^85 + 10 * q^87 - 2 * q^89 - 2 * q^93 - 6 * q^95 - 32 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times$.

$n$	$1081$	$1177$	$1471$	$1961$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		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
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.82288	+	3.15731i	−0.549618	+	0.951966i	0.448683	+	0.893691i	$0.351893\pi$
$11$	−1.82288	+	3.15731i	−0.549618	+	0.951966i	−0.998301	+	0.0582747i	$0.981440\pi$
$12$		0			0
$13$	−2.64575			−0.733799			−0.366900	−	0.930261i	$-0.619581\pi$
$13$	−2.64575			−0.733799			−0.366900	+	0.930261i	$0.619581\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	1.82288	−	3.15731i	0.442112	−	0.765761i	−0.555734	−	0.831360i	$-0.687563\pi$
$17$	1.82288	−	3.15731i	0.442112	−	0.765761i	0.997846	+	0.0655994i	$0.0208959\pi$
$18$		0			0
$19$	−1.14575	−	1.98450i	−0.262853	−	0.455275i	0.704146	−	0.710056i	$-0.251330\pi$
$19$	−1.14575	−	1.98450i	−0.262853	−	0.455275i	−0.966999	+	0.254780i	$0.917997\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.82288	+	3.15731i	0.380096	+	0.658345i	0.991076	−	0.133301i	$-0.0425577\pi$
$23$	1.82288	+	3.15731i	0.380096	+	0.658345i	−0.610980	+	0.791646i	$0.709224\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	2.35425			0.437173			0.218587	−	0.975818i	$-0.429855\pi$
$29$	2.35425			0.437173			0.218587	+	0.975818i	$0.429855\pi$
$30$		0			0
$31$	3.14575	−	5.44860i	0.564994	−	0.978598i	−0.432057	−	0.901846i	$-0.642212\pi$
$31$	3.14575	−	5.44860i	0.564994	−	0.978598i	0.997050	−	0.0767512i	$-0.0244547\pi$
$32$		0			0
$33$	1.82288	+	3.15731i	0.317322	+	0.549618i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.32288	+	4.02334i	0.381878	+	0.661433i	0.991331	−	0.131390i	$-0.0419440\pi$
$37$	2.32288	+	4.02334i	0.381878	+	0.661433i	−0.609452	+	0.792823i	$0.708611\pi$
$38$		0			0
$39$	−1.32288	+	2.29129i	−0.211830	+	0.366900i
$40$		0			0
$41$	10.9373			1.70811			0.854056	−	0.520181i	$-0.174136\pi$
$41$	10.9373			1.70811			0.854056	+	0.520181i	$0.174136\pi$
$42$		0			0
$43$	9.93725			1.51542			0.757709	−	0.652593i	$-0.226319\pi$
$43$	9.93725			1.51542			0.757709	+	0.652593i	$0.226319\pi$
$44$		0			0
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$		0			0
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−1.82288	−	3.15731i	−0.255254	−	0.442112i
$52$		0			0
$53$	3.64575	−	6.31463i	0.500782	−	0.867381i	−0.499217	−	0.866477i	$-0.666379\pi$
$53$	3.64575	−	6.31463i	0.500782	−	0.867381i	1.00000		0.000903738i	$-0.000287669\pi$
$54$		0			0
$55$	−3.64575			−0.491593
$56$		0			0
$57$	−2.29150			−0.303517
$58$		0			0
$59$	−2.46863	+	4.27579i	−0.321388	+	0.556660i	−0.980775	−	0.195144i	$-0.937483\pi$
$59$	−2.46863	+	4.27579i	−0.321388	+	0.556660i	0.659387	+	0.751804i	$0.270816\pi$
$60$		0			0
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	0.999901	+	0.0140840i	$0.00448323\pi$
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	−0.487753	+	0.872982i	$0.662183\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.32288	−	2.29129i	−0.164083	−	0.284199i
$66$		0			0
$67$	2.32288	−	4.02334i	0.283784	−	0.491529i	−0.688529	−	0.725209i	$-0.741743\pi$
$67$	2.32288	−	4.02334i	0.283784	−	0.491529i	0.972314	+	0.233680i	$0.0750767\pi$
$68$		0			0
$69$	3.64575			0.438897
$70$		0			0
$71$	8.35425			0.991467			0.495733	−	0.868475i	$-0.334899\pi$
$71$	8.35425			0.991467			0.495733	+	0.868475i	$0.334899\pi$
$72$		0			0
$73$	−6.61438	+	11.4564i	−0.774154	+	1.34087i	0.161114	+	0.986936i	$0.448491\pi$
$73$	−6.61438	+	11.4564i	−0.774154	+	1.34087i	−0.935269	+	0.353939i	$0.884842\pi$
$74$		0			0
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.14575	+	7.18065i	0.466433	+	0.807886i	0.999265	−	0.0383349i	$-0.0122054\pi$
$79$	4.14575	+	7.18065i	0.466433	+	0.807886i	−0.532831	+	0.846221i	$0.678872\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−4.93725			−0.541934			−0.270967	−	0.962589i	$-0.587343\pi$
$83$	−4.93725			−0.541934			−0.270967	+	0.962589i	$0.587343\pi$
$84$		0			0
$85$	3.64575			0.395437
$86$		0			0
$87$	1.17712	−	2.03884i	0.126201	−	0.218587i
$88$		0			0
$89$	6.11438	+	10.5904i	0.648123	+	1.12258i	0.983571	+	0.180523i	$0.0577790\pi$
$89$	6.11438	+	10.5904i	0.648123	+	1.12258i	−0.335448	+	0.942059i	$0.608888\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−3.14575	−	5.44860i	−0.326199	−	0.564994i
$94$		0			0
$95$	1.14575	−	1.98450i	0.117552	−	0.203605i
$96$		0			0
$97$	−8.00000			−0.812277			−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000			−0.812277			−0.406138	+	0.913812i	$0.633125\pi$
$98$		0			0
$99$	3.64575			0.366412
$100$		0			0
$101$	5.46863	−	9.47194i	0.544149	−	0.942493i	−0.454511	−	0.890741i	$-0.650186\pi$
$101$	5.46863	−	9.47194i	0.544149	−	0.942493i	0.998660	−	0.0517522i	$-0.0164806\pi$
$102$		0			0
$103$	7.32288	+	12.6836i	0.721544	+	1.24975i	0.960381	+	0.278692i	$0.0899007\pi$
$103$	7.32288	+	12.6836i	0.721544	+	1.24975i	−0.238836	+	0.971060i	$0.576766\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.531373	+	0.920365i	0.0513698	+	0.0889751i	0.890567	−	0.454852i	$-0.150308\pi$
$107$	0.531373	+	0.920365i	0.0513698	+	0.0889751i	−0.839197	+	0.543827i	$0.816975\pi$
$108$		0			0
$109$	6.50000	−	11.2583i	0.622587	−	1.07835i	−0.366415	−	0.930451i	$-0.619415\pi$
$109$	6.50000	−	11.2583i	0.622587	−	1.07835i	0.989002	−	0.147901i	$-0.0472517\pi$
$110$		0			0
$111$	4.64575			0.440955
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$	−1.82288	+	3.15731i	−0.169984	+	0.294421i
$116$		0			0
$117$	1.32288	+	2.29129i	0.122300	+	0.211830i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−1.14575	−	1.98450i	−0.104159	−	0.180409i
$122$		0			0
$123$	5.46863	−	9.47194i	0.493089	−	0.854056i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−17.9373			−1.59167			−0.795837	−	0.605511i	$-0.792969\pi$
$127$	−17.9373			−1.59167			−0.795837	+	0.605511i	$0.792969\pi$
$128$		0			0
$129$	4.96863	−	8.60591i	0.437463	−	0.757709i
$130$		0			0
$131$	5.35425	+	9.27383i	0.467803	+	0.810258i	0.999323	−	0.0367872i	$-0.0117124\pi$
$131$	5.35425	+	9.27383i	0.467803	+	0.810258i	−0.531520	+	0.847046i	$0.678379\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$		0			0
$137$	−3.11438	+	5.39426i	−0.266079	+	0.460863i	−0.967846	−	0.251544i	$-0.919062\pi$
$137$	−3.11438	+	5.39426i	−0.266079	+	0.460863i	0.701767	+	0.712407i	$0.252395\pi$
$138$		0			0
$139$	−5.00000			−0.424094			−0.212047	−	0.977259i	$-0.568013\pi$
$139$	−5.00000			−0.424094			−0.212047	+	0.977259i	$0.568013\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$		0			0
$143$	4.82288	−	8.35347i	0.403309	−	0.698552i
$144$		0			0
$145$	1.17712	+	2.03884i	0.0977549	+	0.169316i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.29150	−	12.6293i	−0.597343	−	1.03463i	−0.993212	−	0.116321i	$-0.962890\pi$
$149$	−7.29150	−	12.6293i	−0.597343	−	1.03463i	0.395868	−	0.918307i	$-0.370444\pi$
$150$		0			0
$151$	−8.29150	+	14.3613i	−0.674753	+	1.16871i	0.301788	+	0.953375i	$0.402416\pi$
$151$	−8.29150	+	14.3613i	−0.674753	+	1.16871i	−0.976541	+	0.215331i	$0.930917\pi$
$152$		0			0
$153$	−3.64575			−0.294742
$154$		0			0
$155$	6.29150			0.505346
$156$		0			0
$157$	4.64575	−	8.04668i	0.370771	−	0.642195i	−0.618913	−	0.785459i	$-0.712427\pi$
$157$	4.64575	−	8.04668i	0.370771	−	0.642195i	0.989684	+	0.143265i	$0.0457600\pi$
$158$		0			0
$159$	−3.64575	−	6.31463i	−0.289127	−	0.500782i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	0.988227	+	0.152992i	$0.0488907\pi$
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	−0.361619	+	0.932326i	$0.617776\pi$
$164$		0			0
$165$	−1.82288	+	3.15731i	−0.141911	+	0.245797i
$166$		0			0
$167$	−14.3542			−1.11077			−0.555383	−	0.831595i	$-0.687428\pi$
$167$	−14.3542			−1.11077			−0.555383	+	0.831595i	$0.687428\pi$
$168$		0			0
$169$	−6.00000			−0.461538
$170$		0			0
$171$	−1.14575	+	1.98450i	−0.0876178	+	0.151758i
$172$		0			0
$173$	−10.9373	−	18.9439i	−0.831544	−	1.44028i	−0.896813	−	0.442409i	$-0.854124\pi$
$173$	−10.9373	−	18.9439i	−0.831544	−	1.44028i	0.0652695	−	0.997868i	$-0.479209\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.46863	+	4.27579i	0.185553	+	0.321388i
$178$		0			0
$179$	10.2915	−	17.8254i	0.769223	−	1.33233i	−0.168762	−	0.985657i	$-0.553977\pi$
$179$	10.2915	−	17.8254i	0.769223	−	1.33233i	0.937985	−	0.346676i	$-0.112690\pi$
$180$		0			0
$181$	−6.29150			−0.467644			−0.233822	−	0.972279i	$-0.575123\pi$
$181$	−6.29150			−0.467644			−0.233822	+	0.972279i	$0.575123\pi$
$182$		0			0
$183$	8.00000			0.591377
$184$		0			0
$185$	−2.32288	+	4.02334i	−0.170781	+	0.295802i
$186$		0			0
$187$	6.64575	+	11.5108i	0.485985	+	0.841752i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.5830	+	20.0624i	0.838117	+	1.45166i	0.891467	+	0.453085i	$0.149677\pi$
$191$	11.5830	+	20.0624i	0.838117	+	1.45166i	−0.0533504	+	0.998576i	$0.516990\pi$
$192$		0			0
$193$	11.9686	−	20.7303i	0.861521	−	1.49220i	−0.00894034	−	0.999960i	$-0.502846\pi$
$193$	11.9686	−	20.7303i	0.861521	−	1.49220i	0.870461	−	0.492237i	$-0.163821\pi$
$194$		0			0
$195$	−2.64575			−0.189466
$196$		0			0
$197$	10.9373			0.779247			0.389624	−	0.920974i	$-0.372605\pi$
$197$	10.9373			0.779247			0.389624	+	0.920974i	$0.372605\pi$
$198$		0			0
$199$	9.58301	−	16.5983i	0.679321	−	1.17662i	−0.295864	−	0.955230i	$-0.595608\pi$
$199$	9.58301	−	16.5983i	0.679321	−	1.17662i	0.975186	−	0.221389i	$-0.0710590\pi$
$200$		0			0
$201$	−2.32288	−	4.02334i	−0.163843	−	0.283784i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	5.46863	+	9.47194i	0.381945	+	0.661549i
$206$		0			0
$207$	1.82288	−	3.15731i	0.126699	−	0.219448i
$208$		0			0
$209$	8.35425			0.577875
$210$		0			0
$211$	−12.5830			−0.866250			−0.433125	−	0.901334i	$-0.642589\pi$
$211$	−12.5830			−0.866250			−0.433125	+	0.901334i	$0.642589\pi$
$212$		0			0
$213$	4.17712	−	7.23499i	0.286212	−	0.495733i
$214$		0			0
$215$	4.96863	+	8.60591i	0.338858	+	0.586918i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	6.61438	+	11.4564i	0.446958	+	0.774154i
$220$		0			0
$221$	−4.82288	+	8.35347i	−0.324422	+	0.561915i
$222$		0			0
$223$	13.8745			0.929106			0.464553	−	0.885545i	$-0.346215\pi$
$223$	13.8745			0.929106			0.464553	+	0.885545i	$0.346215\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	7.17712	−	12.4311i	0.476362	−	0.825084i	−0.523271	−	0.852167i	$-0.675288\pi$
$227$	7.17712	−	12.4311i	0.476362	−	0.825084i	0.999633	+	0.0270825i	$0.00862168\pi$
$228$		0			0
$229$	−3.50000	−	6.06218i	−0.231287	−	0.400600i	0.726900	−	0.686743i	$-0.240960\pi$
$229$	−3.50000	−	6.06218i	−0.231287	−	0.400600i	−0.958187	+	0.286143i	$0.907627\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.35425	−	9.27383i	−0.350768	−	0.607549i	0.635616	−	0.772006i	$-0.280746\pi$
$233$	−5.35425	−	9.27383i	−0.350768	−	0.607549i	−0.986384	+	0.164457i	$0.947413\pi$
$234$		0			0
$235$	−3.00000	+	5.19615i	−0.195698	+	0.338960i
$236$		0			0
$237$	8.29150			0.538591
$238$		0			0
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		0			0
$241$	−11.6458	+	20.1710i	−0.750169	+	1.29933i	0.197572	+	0.980288i	$0.436694\pi$
$241$	−11.6458	+	20.1710i	−0.750169	+	1.29933i	−0.947741	+	0.319042i	$0.896639\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.03137	+	5.25049i	0.192882	+	0.334081i
$248$		0			0
$249$	−2.46863	+	4.27579i	−0.156443	+	0.270967i
$250$		0			0
$251$	−4.93725			−0.311637			−0.155818	−	0.987786i	$-0.549801\pi$
$251$	−4.93725			−0.311637			−0.155818	+	0.987786i	$0.549801\pi$
$252$		0			0
$253$	−13.2915			−0.835630
$254$		0			0
$255$	1.82288	−	3.15731i	0.114153	−	0.197719i
$256$		0			0
$257$	−15.7601	−	27.2973i	−0.983090	−	1.70276i	−0.650135	−	0.759819i	$-0.725288\pi$
$257$	−15.7601	−	27.2973i	−0.983090	−	1.70276i	−0.332955	−	0.942943i	$-0.608046\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.17712	−	2.03884i	−0.0728622	−	0.126201i
$262$		0			0
$263$	−12.2288	+	21.1808i	−0.754057	+	1.30607i	0.191784	+	0.981437i	$0.438573\pi$
$263$	−12.2288	+	21.1808i	−0.754057	+	1.30607i	−0.945842	+	0.324629i	$0.894761\pi$
$264$		0			0
$265$	7.29150			0.447913
$266$		0			0
$267$	12.2288			0.748388
$268$		0			0
$269$	−1.93725	+	3.35542i	−0.118116	+	0.204584i	−0.919021	−	0.394208i	$-0.871019\pi$
$269$	−1.93725	+	3.35542i	−0.118116	+	0.204584i	0.800905	+	0.598792i	$0.204352\pi$
$270$		0			0
$271$	14.2915	+	24.7536i	0.868147	+	1.50367i	0.863888	+	0.503684i	$0.168022\pi$
$271$	14.2915	+	24.7536i	0.868147	+	1.50367i	0.00425882	+	0.999991i	$0.498644\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.82288	−	3.15731i	−0.109924	−	0.190393i
$276$		0			0
$277$	7.67712	−	13.2972i	0.461274	−	0.798949i	−0.537751	−	0.843104i	$-0.680726\pi$
$277$	7.67712	−	13.2972i	0.461274	−	0.798949i	0.999025	+	0.0441542i	$0.0140593\pi$
$278$		0			0
$279$	−6.29150			−0.376662
$280$		0			0
$281$	24.0000			1.43172			0.715860	−	0.698244i	$-0.246035\pi$
$281$	24.0000			1.43172			0.715860	+	0.698244i	$0.246035\pi$
$282$		0			0
$283$	−4.67712	+	8.10102i	−0.278026	+	0.481555i	−0.970894	−	0.239509i	$-0.923014\pi$
$283$	−4.67712	+	8.10102i	−0.278026	+	0.481555i	0.692868	+	0.721064i	$0.256347\pi$
$284$		0			0
$285$	−1.14575	−	1.98450i	−0.0678685	−	0.117552i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	1.85425	+	3.21165i	0.109073	+	0.188921i
$290$		0			0
$291$	−4.00000	+	6.92820i	−0.234484	+	0.406138i
$292$		0			0
$293$		0			0			−	1.00000i	$-0.5\pi$
$293$		0			0				1.00000i	$0.5\pi$
$294$		0			0
$295$	−4.93725			−0.287458
$296$		0			0
$297$	1.82288	−	3.15731i	0.105774	−	0.183206i
$298$		0			0
$299$	−4.82288	−	8.35347i	−0.278914	−	0.483093i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−5.46863	−	9.47194i	−0.314164	−	0.544149i
$304$		0			0
$305$	−4.00000	+	6.92820i	−0.229039	+	0.396708i
$306$		0			0
$307$	−12.0627			−0.688457			−0.344229	−	0.938886i	$-0.611860\pi$
$307$	−12.0627			−0.688457			−0.344229	+	0.938886i	$0.611860\pi$
$308$		0			0
$309$	14.6458			0.833168
$310$		0			0
$311$	4.17712	−	7.23499i	0.236863	−	0.410259i	−0.722949	−	0.690901i	$-0.757214\pi$
$311$	4.17712	−	7.23499i	0.236863	−	0.410259i	0.959812	+	0.280642i	$0.0905474\pi$
$312$		0			0
$313$	2.61438	+	4.52824i	0.147773	+	0.255951i	0.930404	−	0.366535i	$-0.119456\pi$
$313$	2.61438	+	4.52824i	0.147773	+	0.255951i	−0.782631	+	0.622486i	$0.786123\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.76013	+	11.7089i	0.379687	+	0.657637i	0.991017	−	0.133739i	$-0.0426985\pi$
$317$	6.76013	+	11.7089i	0.379687	+	0.657637i	−0.611330	+	0.791376i	$0.709365\pi$
$318$		0			0
$319$	−4.29150	+	7.43310i	−0.240278	+	0.416174i
$320$		0			0
$321$	1.06275			0.0593167
$322$		0			0
$323$	−8.35425			−0.464843
$324$		0			0
$325$	1.32288	−	2.29129i	0.0733799	−	0.127098i
$326$		0			0
$327$	−6.50000	−	11.2583i	−0.359451	−	0.622587i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−11.0830	−	19.1963i	−0.609177	−	1.05513i	−0.991376	−	0.131046i	$-0.958167\pi$
$331$	−11.0830	−	19.1963i	−0.609177	−	1.05513i	0.382199	−	0.924080i	$-0.375167\pi$
$332$		0			0
$333$	2.32288	−	4.02334i	0.127293	−	0.220478i
$334$		0			0
$335$	4.64575			0.253825
$336$		0			0
$337$	−6.77124			−0.368853			−0.184427	−	0.982846i	$-0.559043\pi$
$337$	−6.77124			−0.368853			−0.184427	+	0.982846i	$0.559043\pi$
$338$		0			0
$339$	3.00000	−	5.19615i	0.162938	−	0.282216i
$340$		0			0
$341$	11.4686	+	19.8642i	0.621061	+	1.07571i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	1.82288	+	3.15731i	0.0981403	+	0.169984i
$346$		0			0
$347$	14.5830	−	25.2585i	0.782857	−	1.35595i	−0.147414	−	0.989075i	$-0.547095\pi$
$347$	14.5830	−	25.2585i	0.782857	−	1.35595i	0.930271	−	0.366873i	$-0.119572\pi$
$348$		0			0
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$		0			0
$351$	2.64575			0.141220
$352$		0			0
$353$	11.0516	−	19.1420i	0.588219	−	1.01883i	−0.406247	−	0.913763i	$-0.633163\pi$
$353$	11.0516	−	19.1420i	0.588219	−	1.01883i	0.994466	−	0.105062i	$-0.0335040\pi$
$354$		0			0
$355$	4.17712	+	7.23499i	0.221699	+	0.383993i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−13.4059	−	23.2197i	−0.707535	−	1.22549i	−0.965769	−	0.259405i	$-0.916474\pi$
$359$	−13.4059	−	23.2197i	−0.707535	−	1.22549i	0.258233	−	0.966083i	$-0.416860\pi$
$360$		0			0
$361$	6.87451	−	11.9070i	0.361816	−	0.626684i
$362$		0			0
$363$	−2.29150			−0.120273
$364$		0			0
$365$	−13.2288			−0.692425
$366$		0			0
$367$	−9.61438	+	16.6526i	−0.501866	+	0.869258i	0.498131	+	0.867102i	$0.334020\pi$
$367$	−9.61438	+	16.6526i	−0.501866	+	0.869258i	−0.999998	+	0.00215655i	$0.999314\pi$
$368$		0			0
$369$	−5.46863	−	9.47194i	−0.284685	−	0.493089i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−7.96863	−	13.8021i	−0.412600	−	0.714644i	0.582573	−	0.812778i	$-0.302046\pi$
$373$	−7.96863	−	13.8021i	−0.412600	−	0.714644i	−0.995173	+	0.0981342i	$0.968713\pi$
$374$		0			0
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$		0			0
$377$	−6.22876			−0.320797
$378$		0			0
$379$	−26.2915			−1.35050			−0.675252	−	0.737587i	$-0.735965\pi$
$379$	−26.2915			−1.35050			−0.675252	+	0.737587i	$0.735965\pi$
$380$		0			0
$381$	−8.96863	+	15.5341i	−0.459477	+	0.795837i
$382$		0			0
$383$	−8.35425	−	14.4700i	−0.426882	−	0.739382i	0.569712	−	0.821844i	$-0.307055\pi$
$383$	−8.35425	−	14.4700i	−0.426882	−	0.739382i	−0.996594	+	0.0824628i	$0.973721\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−4.96863	−	8.60591i	−0.252570	−	0.437463i
$388$		0			0
$389$	18.7601	−	32.4935i	0.951176	−	1.64749i	0.208291	−	0.978067i	$-0.433210\pi$
$389$	18.7601	−	32.4935i	0.951176	−	1.64749i	0.742885	−	0.669419i	$-0.233457\pi$
$390$		0			0
$391$	13.2915			0.672180
$392$		0			0
$393$	10.7085			0.540172
$394$		0			0
$395$	−4.14575	+	7.18065i	−0.208595	+	0.361298i
$396$		0			0
$397$	−8.32288	−	14.4156i	−0.417713	−	0.723500i	0.577996	−	0.816040i	$-0.303835\pi$
$397$	−8.32288	−	14.4156i	−0.417713	−	0.723500i	−0.995709	+	0.0925393i	$0.970502\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.64575	−	16.7069i	−0.481686	−	0.834304i	0.518093	−	0.855324i	$-0.326642\pi$
$401$	−9.64575	−	16.7069i	−0.481686	−	0.834304i	−0.999779	+	0.0210198i	$0.993309\pi$
$402$		0			0
$403$	−8.32288	+	14.4156i	−0.414592	+	0.718094i
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−16.9373			−0.839549
$408$		0			0
$409$	−18.0830	+	31.3207i	−0.894147	+	1.54871i	−0.0592904	+	0.998241i	$0.518884\pi$
$409$	−18.0830	+	31.3207i	−0.894147	+	1.54871i	−0.834857	+	0.550467i	$0.814450\pi$
$410$		0			0
$411$	3.11438	+	5.39426i	0.153621	+	0.266079i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2.46863	−	4.27579i	−0.121180	−	0.209890i
$416$		0			0
$417$	−2.50000	+	4.33013i	−0.122426	+	0.212047i
$418$		0			0
$419$	−10.7085			−0.523144			−0.261572	−	0.965184i	$-0.584241\pi$
$419$	−10.7085			−0.523144			−0.261572	+	0.965184i	$0.584241\pi$
$420$		0			0
$421$	1.58301			0.0771510			0.0385755	−	0.999256i	$-0.487718\pi$
$421$	1.58301			0.0771510			0.0385755	+	0.999256i	$0.487718\pi$
$422$		0			0
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$		0			0
$425$	1.82288	+	3.15731i	0.0884225	+	0.153152i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−4.82288	−	8.35347i	−0.232851	−	0.403309i
$430$		0			0
$431$	−4.06275	+	7.03688i	−0.195696	+	0.338955i	−0.947128	−	0.320855i	$-0.896030\pi$
$431$	−4.06275	+	7.03688i	−0.195696	+	0.338955i	0.751433	+	0.659810i	$0.229363\pi$
$432$		0			0
$433$	−8.64575			−0.415488			−0.207744	−	0.978183i	$-0.566612\pi$
$433$	−8.64575			−0.415488			−0.207744	+	0.978183i	$0.566612\pi$
$434$		0			0
$435$	2.35425			0.112878
$436$		0			0
$437$	4.17712	−	7.23499i	0.199819	−	0.346097i
$438$		0			0
$439$	−2.64575	−	4.58258i	−0.126275	−	0.218714i	0.795956	−	0.605355i	$-0.206969\pi$
$439$	−2.64575	−	4.58258i	−0.126275	−	0.218714i	−0.922231	+	0.386640i	$0.873635\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.9373	+	18.9439i	0.519645	+	0.900051i	0.999739	+	0.0228342i	$0.00726898\pi$
$443$	10.9373	+	18.9439i	0.519645	+	0.900051i	−0.480095	+	0.877217i	$0.659398\pi$
$444$		0			0
$445$	−6.11438	+	10.5904i	−0.289849	+	0.502034i
$446$		0			0
$447$	−14.5830			−0.689752
$448$		0			0
$449$	8.58301			0.405057			0.202529	−	0.979276i	$-0.435084\pi$
$449$	8.58301			0.405057			0.202529	+	0.979276i	$0.435084\pi$
$450$		0			0
$451$	−19.9373	+	34.5323i	−0.938809	+	1.62606i
$452$		0			0
$453$	8.29150	+	14.3613i	0.389569	+	0.674753i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	4.67712	+	8.10102i	0.218787	+	0.378950i	0.954437	−	0.298412i	$-0.0964568\pi$
$457$	4.67712	+	8.10102i	0.218787	+	0.378950i	−0.735651	+	0.677361i	$0.763123\pi$
$458$		0			0
$459$	−1.82288	+	3.15731i	−0.0850845	+	0.147371i
$460$		0			0
$461$	14.3542			0.668544			0.334272	−	0.942477i	$-0.391510\pi$
$461$	14.3542			0.668544			0.334272	+	0.942477i	$0.391510\pi$
$462$		0			0
$463$	−26.5203			−1.23250			−0.616250	−	0.787550i	$-0.711349\pi$
$463$	−26.5203			−1.23250			−0.616250	+	0.787550i	$0.711349\pi$
$464$		0			0
$465$	3.14575	−	5.44860i	0.145881	−	0.252673i
$466$		0			0
$467$	12.8745	+	22.2993i	0.595761	+	1.03189i	0.993439	+	0.114363i	$0.0364829\pi$
$467$	12.8745	+	22.2993i	0.595761	+	1.03189i	−0.397678	+	0.917525i	$0.630184\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−4.64575	−	8.04668i	−0.214065	−	0.370771i
$472$		0			0
$473$	−18.1144	+	31.3750i	−0.832900	+	1.44263i
$474$		0			0
$475$	2.29150			0.105141
$476$		0			0
$477$	−7.29150			−0.333855
$478$		0			0
$479$	7.29150	−	12.6293i	0.333157	−	0.577045i	−0.649972	−	0.759958i	$-0.725219\pi$
$479$	7.29150	−	12.6293i	0.333157	−	0.577045i	0.983129	+	0.182913i	$0.0585527\pi$
$480$		0			0
$481$	−6.14575	−	10.6448i	−0.280222	−	0.485359i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.00000	−	6.92820i	−0.181631	−	0.314594i
$486$		0			0
$487$	−1.32288	+	2.29129i	−0.0599452	+	0.103828i	−0.894441	−	0.447187i	$-0.852426\pi$
$487$	−1.32288	+	2.29129i	−0.0599452	+	0.103828i	0.834495	+	0.551015i	$0.185759\pi$
$488$		0			0
$489$	16.0000			0.723545
$490$		0			0
$491$	33.8745			1.52874			0.764368	−	0.644781i	$-0.223051\pi$
$491$	33.8745			1.52874			0.764368	+	0.644781i	$0.223051\pi$
$492$		0			0
$493$	4.29150	−	7.43310i	0.193280	−	0.334770i
$494$		0			0
$495$	1.82288	+	3.15731i	0.0819322	+	0.141911i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	12.7288	+	22.0469i	0.569817	+	0.986953i	0.996584	+	0.0825907i	$0.0263194\pi$
$499$	12.7288	+	22.0469i	0.569817	+	0.986953i	−0.426766	+	0.904362i	$0.640347\pi$
$500$		0			0
$501$	−7.17712	+	12.4311i	−0.320650	+	0.555383i
$502$		0			0
$503$	30.4575			1.35803			0.679017	−	0.734123i	$-0.262406\pi$
$503$	30.4575			1.35803			0.679017	+	0.734123i	$0.262406\pi$
$504$		0			0
$505$	10.9373			0.486701
$506$		0			0
$507$	−3.00000	+	5.19615i	−0.133235	+	0.230769i
$508$		0			0
$509$	1.93725	+	3.35542i	0.0858673	+	0.148726i	0.905760	−	0.423790i	$-0.139301\pi$
$509$	1.93725	+	3.35542i	0.0858673	+	0.148726i	−0.819893	+	0.572517i	$0.805967\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	1.14575	+	1.98450i	0.0505862	+	0.0876178i
$514$		0			0
$515$	−7.32288	+	12.6836i	−0.322684	+	0.558906i
$516$		0			0
$517$	−21.8745			−0.962040
$518$		0			0
$519$	−21.8745			−0.960184
$520$		0			0
$521$	−16.9373	+	29.3362i	−0.742035	+	1.28524i	0.209533	+	0.977802i	$0.432806\pi$
$521$	−16.9373	+	29.3362i	−0.742035	+	1.28524i	−0.951567	+	0.307440i	$0.900528\pi$
$522$		0			0
$523$	2.38562	+	4.13202i	0.104316	+	0.180681i	0.913459	−	0.406932i	$-0.133401\pi$
$523$	2.38562	+	4.13202i	0.104316	+	0.180681i	−0.809143	+	0.587612i	$0.800068\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−11.4686	−	19.8642i	−0.499581	−	0.865300i
$528$		0			0
$529$	4.85425	−	8.40781i	0.211054	−	0.365557i
$530$		0			0
$531$	4.93725			0.214259
$532$		0			0
$533$	−28.9373			−1.25341
$534$		0			0
$535$	−0.531373	+	0.920365i	−0.0229733	+	0.0397909i
$536$		0			0
$537$	−10.2915	−	17.8254i	−0.444111	−	0.769223i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	13.3745	+	23.1653i	0.575015	+	0.995955i	0.996040	+	0.0889062i	$0.0283371\pi$
$541$	13.3745	+	23.1653i	0.575015	+	0.995955i	−0.421025	+	0.907049i	$0.638330\pi$
$542$		0			0
$543$	−3.14575	+	5.44860i	−0.134997	+	0.233822i
$544$		0			0
$545$	13.0000			0.556859
$546$		0			0
$547$	−32.7085			−1.39851			−0.699257	−	0.714870i	$-0.746486\pi$
$547$	−32.7085			−1.39851			−0.699257	+	0.714870i	$0.746486\pi$
$548$		0			0
$549$	4.00000	−	6.92820i	0.170716	−	0.295689i
$550$		0			0
$551$	−2.69738	−	4.67201i	−0.114912	−	0.199034i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	2.32288	+	4.02334i	0.0986006	+	0.170781i
$556$		0			0
$557$	9.00000	−	15.5885i	0.381342	−	0.660504i	−0.609912	−	0.792469i	$-0.708795\pi$
$557$	9.00000	−	15.5885i	0.381342	−	0.660504i	0.991254	+	0.131965i	$0.0421286\pi$
$558$		0			0
$559$	−26.2915			−1.11201
$560$		0			0
$561$	13.2915			0.561168
$562$		0			0
$563$	−7.70850	+	13.3515i	−0.324874	+	0.562699i	−0.981487	−	0.191529i	$-0.938655\pi$
$563$	−7.70850	+	13.3515i	−0.324874	+	0.562699i	0.656613	+	0.754228i	$0.271989\pi$
$564$		0			0
$565$	3.00000	+	5.19615i	0.126211	+	0.218604i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	15.1144	+	26.1789i	0.633628	+	1.09748i	0.986804	+	0.161919i	$0.0517682\pi$
$569$	15.1144	+	26.1789i	0.633628	+	1.09748i	−0.353176	+	0.935557i	$0.614898\pi$
$570$		0			0
$571$	−16.8542	+	29.1924i	−0.705328	+	1.22166i	0.261245	+	0.965273i	$0.415867\pi$
$571$	−16.8542	+	29.1924i	−0.705328	+	1.22166i	−0.966573	+	0.256392i	$0.917466\pi$
$572$		0			0
$573$	23.1660			0.967774
$574$		0			0
$575$	−3.64575			−0.152038
$576$		0			0
$577$	−2.73987	+	4.74559i	−0.114062	+	0.197562i	−0.917405	−	0.397956i	$-0.869720\pi$
$577$	−2.73987	+	4.74559i	−0.114062	+	0.197562i	0.803342	+	0.595518i	$0.203053\pi$
$578$		0			0
$579$	−11.9686	−	20.7303i	−0.497399	−	0.861521i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	13.2915	+	23.0216i	0.550478	+	0.953456i
$584$		0			0
$585$	−1.32288	+	2.29129i	−0.0546942	+	0.0947331i
$586$		0			0
$587$	−1.06275			−0.0438642			−0.0219321	−	0.999759i	$-0.506982\pi$
$587$	−1.06275			−0.0438642			−0.0219321	+	0.999759i	$0.506982\pi$
$588$		0			0
$589$	−14.4170			−0.594042
$590$		0			0
$591$	5.46863	−	9.47194i	0.224949	−	0.389624i
$592$		0			0
$593$	−20.4686	−	35.4527i	−0.840546	−	1.45587i	−0.889434	−	0.457064i	$-0.848901\pi$
$593$	−20.4686	−	35.4527i	−0.840546	−	1.45587i	0.0488882	−	0.998804i	$-0.484432\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−9.58301	−	16.5983i	−0.392206	−	0.679321i
$598$		0			0
$599$	−16.9373	+	29.3362i	−0.692037	+	1.19864i	0.279132	+	0.960253i	$0.409953\pi$
$599$	−16.9373	+	29.3362i	−0.692037	+	1.19864i	−0.971169	+	0.238391i	$0.923380\pi$
$600$		0			0
$601$	16.4170			0.669663			0.334832	−	0.942278i	$-0.391321\pi$
$601$	16.4170			0.669663			0.334832	+	0.942278i	$0.391321\pi$
$602$		0			0
$603$	−4.64575			−0.189190
$604$		0			0
$605$	1.14575	−	1.98450i	0.0465814	−	0.0806814i
$606$		0			0
$607$	−21.6144	−	37.4372i	−0.877301	−	1.51953i	−0.854292	−	0.519794i	$-0.826009\pi$
$607$	−21.6144	−	37.4372i	−0.877301	−	1.51953i	−0.0230088	−	0.999735i	$-0.507325\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−7.93725	−	13.7477i	−0.321107	−	0.556174i
$612$		0			0
$613$	−0.583005	+	1.00979i	−0.0235474	+	0.0407852i	−0.877559	−	0.479469i	$-0.840829\pi$
$613$	−0.583005	+	1.00979i	−0.0235474	+	0.0407852i	0.854012	+	0.520254i	$0.174163\pi$
$614$		0			0
$615$	10.9373			0.441033
$616$		0			0
$617$	−1.29150			−0.0519939			−0.0259970	−	0.999662i	$-0.508276\pi$
$617$	−1.29150			−0.0519939			−0.0259970	+	0.999662i	$0.508276\pi$
$618$		0			0
$619$	−9.50000	+	16.4545i	−0.381837	+	0.661361i	−0.991325	−	0.131434i	$-0.958042\pi$
$619$	−9.50000	+	16.4545i	−0.381837	+	0.661361i	0.609488	+	0.792796i	$0.291375\pi$
$620$		0			0
$621$	−1.82288	−	3.15731i	−0.0731495	−	0.126699i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	4.17712	−	7.23499i	0.166818	−	0.288938i
$628$		0			0
$629$	16.9373			0.675333
$630$		0			0
$631$	27.7490			1.10467			0.552335	−	0.833622i	$-0.313737\pi$
$631$	27.7490			1.10467			0.552335	+	0.833622i	$0.313737\pi$
$632$		0			0
$633$	−6.29150	+	10.8972i	−0.250065	+	0.433125i
$634$		0			0
$635$	−8.96863	−	15.5341i	−0.355909	−	0.616453i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−4.17712	−	7.23499i	−0.165244	−	0.286212i
$640$		0			0
$641$	−23.0516	+	39.9266i	−0.910485	+	1.57701i	−0.0971039	+	0.995274i	$0.530958\pi$
$641$	−23.0516	+	39.9266i	−0.910485	+	1.57701i	−0.813381	+	0.581732i	$0.802375\pi$
$642$		0			0
$643$	−25.8118			−1.01792			−0.508958	−	0.860791i	$-0.669969\pi$
$643$	−25.8118			−1.01792			−0.508958	+	0.860791i	$0.669969\pi$
$644$		0			0
$645$	9.93725			0.391279
$646$		0			0
$647$	3.53137	−	6.11652i	0.138833	−	0.240465i	−0.788222	−	0.615390i	$-0.788998\pi$
$647$	3.53137	−	6.11652i	0.138833	−	0.240465i	0.927055	+	0.374925i	$0.122332\pi$
$648$		0			0
$649$	−9.00000	−	15.5885i	−0.353281	−	0.611900i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−16.8229	−	29.1381i	−0.658330	−	1.14026i	−0.981048	−	0.193766i	$-0.937930\pi$
$653$	−16.8229	−	29.1381i	−0.658330	−	1.14026i	0.322718	−	0.946495i	$-0.395404\pi$
$654$		0			0
$655$	−5.35425	+	9.27383i	−0.209208	+	0.362359i
$656$		0			0
$657$	13.2288			0.516103
$658$		0			0
$659$	−24.0000			−0.934907			−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000			−0.934907			−0.467454	+	0.884018i	$0.654829\pi$
$660$		0			0
$661$	−4.56275	+	7.90291i	−0.177470	+	0.307387i	−0.941013	−	0.338369i	$-0.890125\pi$
$661$	−4.56275	+	7.90291i	−0.177470	+	0.307387i	0.763543	+	0.645757i	$0.223458\pi$
$662$		0			0
$663$	4.82288	+	8.35347i	0.187305	+	0.324422i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4.29150	+	7.43310i	0.166168	+	0.287811i
$668$		0			0
$669$	6.93725	−	12.0157i	0.268210	−	0.464553i
$670$		0			0
$671$	−29.1660			−1.12594
$672$		0			0
$673$	−10.6458			−0.410364			−0.205182	−	0.978724i	$-0.565779\pi$
$673$	−10.6458			−0.410364			−0.205182	+	0.978724i	$0.565779\pi$
$674$		0			0
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$		0			0
$677$	−13.8229	−	23.9419i	−0.531256	−	0.920163i	−0.999335	−	0.0364758i	$-0.988387\pi$
$677$	−13.8229	−	23.9419i	−0.531256	−	0.920163i	0.468078	−	0.883687i	$-0.344947\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−7.17712	−	12.4311i	−0.275028	−	0.476362i
$682$		0			0
$683$	5.46863	−	9.47194i	0.209251	−	0.362434i	−0.742228	−	0.670148i	$-0.766231\pi$
$683$	5.46863	−	9.47194i	0.209251	−	0.362434i	0.951479	+	0.307714i	$0.0995640\pi$
$684$		0			0
$685$	−6.22876			−0.237989
$686$		0			0
$687$	−7.00000			−0.267067
$688$		0			0
$689$	−9.64575	+	16.7069i	−0.367474	+	0.636483i
$690$		0			0
$691$	1.20850	+	2.09318i	0.0459734	+	0.0796283i	0.888096	−	0.459657i	$-0.152028\pi$
$691$	1.20850	+	2.09318i	0.0459734	+	0.0796283i	−0.842123	+	0.539285i	$0.818694\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.50000	−	4.33013i	−0.0948304	−	0.164251i
$696$		0			0
$697$	19.9373	−	34.5323i	0.755177	−	1.30801i
$698$		0			0
$699$	−10.7085			−0.405033
$700$		0			0
$701$	19.0627			0.719990			0.359995	−	0.932954i	$-0.382778\pi$
$701$	19.0627			0.719990			0.359995	+	0.932954i	$0.382778\pi$
$702$		0			0
$703$	5.32288	−	9.21949i	0.200756	−	0.347720i
$704$		0			0
$705$	3.00000	+	5.19615i	0.112987	+	0.195698i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.708497	+	1.22715i	0.0266082	+	0.0460867i	0.879023	−	0.476780i	$-0.158196\pi$
$709$	0.708497	+	1.22715i	0.0266082	+	0.0460867i	−0.852415	+	0.522866i	$0.824863\pi$
$710$		0			0
$711$	4.14575	−	7.18065i	0.155478	−	0.269295i
$712$		0			0
$713$	22.9373			0.859007
$714$		0			0
$715$	9.64575			0.360731
$716$		0			0
$717$	3.00000	−	5.19615i	0.112037	−	0.194054i
$718$		0			0
$719$	−12.6458	−	21.9031i	−0.471607	−	0.816847i	0.527865	−	0.849328i	$-0.322993\pi$
$719$	−12.6458	−	21.9031i	−0.471607	−	0.816847i	−0.999472	+	0.0324808i	$0.989659\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	11.6458	+	20.1710i	0.433110	+	0.750169i
$724$		0			0
$725$	−1.17712	+	2.03884i	−0.0437173	+	0.0757206i
$726$		0			0
$727$	−13.8118			−0.512250			−0.256125	−	0.966644i	$-0.582446\pi$
$727$	−13.8118			−0.512250			−0.256125	+	0.966644i	$0.582446\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	18.1144	−	31.3750i	0.669984	−	1.16045i
$732$		0			0
$733$	−9.61438	−	16.6526i	−0.355115	−	0.615078i	0.632023	−	0.774950i	$-0.282225\pi$
$733$	−9.61438	−	16.6526i	−0.355115	−	0.615078i	−0.987138	+	0.159873i	$0.948892\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8.46863	+	14.6681i	0.311946	+	0.540306i
$738$		0			0
$739$	−14.5000	+	25.1147i	−0.533391	+	0.923861i	0.465848	+	0.884865i	$0.345749\pi$
$739$	−14.5000	+	25.1147i	−0.533391	+	0.923861i	−0.999239	+	0.0389959i	$0.987584\pi$
$740$		0			0
$741$	6.06275			0.222721
$742$		0			0
$743$	−28.9373			−1.06160			−0.530802	−	0.847496i	$-0.678109\pi$
$743$	−28.9373			−1.06160			−0.530802	+	0.847496i	$0.678109\pi$
$744$		0			0
$745$	7.29150	−	12.6293i	0.267140	−	0.462700i
$746$		0			0
$747$	2.46863	+	4.27579i	0.0903223	+	0.156443i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	9.08301	+	15.7322i	0.331444	+	0.574077i	0.982795	−	0.184699i	$-0.0591310\pi$
$751$	9.08301	+	15.7322i	0.331444	+	0.574077i	−0.651352	+	0.758776i	$0.725798\pi$
$752$		0			0
$753$	−2.46863	+	4.27579i	−0.0899618	+	0.155818i
$754$		0			0
$755$	−16.5830			−0.603517
$756$		0			0
$757$	−51.1660			−1.85966			−0.929830	−	0.367989i	$-0.880046\pi$
$757$	−51.1660			−1.85966			−0.929830	+	0.367989i	$0.880046\pi$
$758$		0			0
$759$	−6.64575	+	11.5108i	−0.241225	+	0.417815i
$760$		0			0
$761$	23.0516	+	39.9266i	0.835621	+	1.44734i	0.893524	+	0.449016i	$0.148225\pi$
$761$	23.0516	+	39.9266i	0.835621	+	1.44734i	−0.0579028	+	0.998322i	$0.518441\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.82288	−	3.15731i	−0.0659062	−	0.114153i
$766$		0			0
$767$	6.53137	−	11.3127i	0.235834	−	0.408477i
$768$		0			0
$769$	14.2915			0.515365			0.257682	−	0.966230i	$-0.417041\pi$
$769$	14.2915			0.515365			0.257682	+	0.966230i	$0.417041\pi$
$770$		0			0
$771$	−31.5203			−1.13517
$772$		0			0
$773$	−20.6974	+	35.8489i	−0.744433	+	1.28940i	0.206026	+	0.978547i	$0.433947\pi$
$773$	−20.6974	+	35.8489i	−0.744433	+	1.28940i	−0.950459	+	0.310850i	$0.899386\pi$
$774$		0			0
$775$	3.14575	+	5.44860i	0.112999	+	0.195720i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−12.5314	−	21.7050i	−0.448983	−	0.777661i
$780$		0			0
$781$	−15.2288	+	26.3770i	−0.544928	+	0.943843i
$782$		0			0
$783$	−2.35425			−0.0841340
$784$		0			0
$785$	9.29150			0.331628
$786$		0			0
$787$	−12.9373	+	22.4080i	−0.461163	+	0.798758i	−0.999019	−	0.0442785i	$-0.985901\pi$
$787$	−12.9373	+	22.4080i	−0.461163	+	0.798758i	0.537856	+	0.843037i	$0.319234\pi$
$788$		0			0
$789$	12.2288	+	21.1808i	0.435355	+	0.754057i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−10.5830	−	18.3303i	−0.375814	−	0.650928i
$794$		0			0
$795$	3.64575	−	6.31463i	0.129301	−	0.223957i
$796$		0			0
$797$	10.9373			0.387417			0.193709	−	0.981059i	$-0.437948\pi$
$797$	10.9373			0.387417			0.193709	+	0.981059i	$0.437948\pi$
$798$		0			0
$799$	21.8745			0.773864
$800$		0			0
$801$	6.11438	−	10.5904i	0.216041	−	0.374194i
$802$		0			0
$803$	−24.1144	−	41.7673i	−0.850978	−	1.47394i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.93725	+	3.35542i	0.0681946	+	0.118116i
$808$		0			0
$809$	11.5830	−	20.0624i	0.407237	−	0.705355i	−0.587342	−	0.809339i	$-0.699826\pi$
$809$	11.5830	−	20.0624i	0.407237	−	0.705355i	0.994579	+	0.103984i	$0.0331590\pi$
$810$		0			0
$811$	−6.70850			−0.235567			−0.117784	−	0.993039i	$-0.537579\pi$
$811$	−6.70850			−0.235567			−0.117784	+	0.993039i	$0.537579\pi$
$812$		0			0
$813$	28.5830			1.00245
$814$		0			0
$815$	−8.00000	+	13.8564i	−0.280228	+	0.485369i
$816$		0			0
$817$	−11.3856	−	19.7205i	−0.398332	−	0.689932i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−18.9889	−	32.8897i	−0.662717	−	1.14786i	−0.979899	−	0.199494i	$-0.936070\pi$
$821$	−18.9889	−	32.8897i	−0.662717	−	1.14786i	0.317182	−	0.948365i	$-0.397263\pi$
$822$		0			0
$823$	17.2288	−	29.8411i	0.600557	−	1.04019i	−0.392180	−	0.919888i	$-0.628279\pi$
$823$	17.2288	−	29.8411i	0.600557	−	1.04019i	0.992737	−	0.120306i	$-0.0383877\pi$
$824$		0			0
$825$	−3.64575			−0.126929
$826$		0			0
$827$	−30.4575			−1.05911			−0.529556	−	0.848275i	$-0.677641\pi$
$827$	−30.4575			−1.05911			−0.529556	+	0.848275i	$0.677641\pi$
$828$		0			0
$829$	15.1458	−	26.2332i	0.526034	−	0.911117i	−0.473506	−	0.880790i	$-0.657012\pi$
$829$	15.1458	−	26.2332i	0.526034	−	0.911117i	0.999540	−	0.0303267i	$-0.00965476\pi$
$830$		0			0
$831$	−7.67712	−	13.2972i	−0.266316	−	0.461274i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−7.17712	−	12.4311i	−0.248375	−	0.430197i
$836$		0			0
$837$	−3.14575	+	5.44860i	−0.108733	+	0.188331i
$838$		0			0
$839$	−21.6458			−0.747294			−0.373647	−	0.927571i	$-0.621893\pi$
$839$	−21.6458			−0.747294			−0.373647	+	0.927571i	$0.621893\pi$
$840$		0			0
$841$	−23.4575			−0.808880
$842$		0			0
$843$	12.0000	−	20.7846i	0.413302	−	0.715860i
$844$		0			0
$845$	−3.00000	−	5.19615i	−0.103203	−	0.178753i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	4.67712	+	8.10102i	0.160518	+	0.278026i
$850$		0			0
$851$	−8.46863	+	14.6681i	−0.290301	+	0.502816i
$852$		0			0
$853$	−16.7712			−0.574236			−0.287118	−	0.957895i	$-0.592697\pi$
$853$	−16.7712			−0.574236			−0.287118	+	0.957895i	$0.592697\pi$
$854$		0			0
$855$	−2.29150			−0.0783677
$856$		0			0
$857$	−4.17712	+	7.23499i	−0.142688	+	0.247143i	−0.928508	−	0.371313i	$-0.878908\pi$
$857$	−4.17712	+	7.23499i	−0.142688	+	0.247143i	0.785820	+	0.618455i	$0.212241\pi$
$858$		0			0
$859$	13.2288	+	22.9129i	0.451359	+	0.781777i	0.998471	−	0.0552825i	$-0.0176059\pi$
$859$	13.2288	+	22.9129i	0.451359	+	0.781777i	−0.547111	+	0.837060i	$0.684273\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9.22876	−	15.9847i	−0.314151	−	0.544125i	0.665106	−	0.746749i	$-0.268386\pi$
$863$	−9.22876	−	15.9847i	−0.314151	−	0.544125i	−0.979257	+	0.202624i	$0.935053\pi$
$864$		0			0
$865$	10.9373	−	18.9439i	0.371878	−	0.644111i
$866$		0			0
$867$	3.70850			0.125947
$868$		0			0
$869$	−30.2288			−1.02544
$870$		0			0
$871$	−6.14575	+	10.6448i	−0.208241	+	0.360684i
$872$		0			0
$873$	4.00000	+	6.92820i	0.135379	+	0.234484i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	0.723298	−	0.690536i	$-0.242625\pi$
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	−0.959671	+	0.281126i	$0.909292\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	41.1660			1.38692			0.693459	−	0.720496i	$-0.256086\pi$
$881$	41.1660			1.38692			0.693459	+	0.720496i	$0.256086\pi$
$882$		0			0
$883$	25.8118			0.868635			0.434317	−	0.900760i	$-0.356990\pi$
$883$	25.8118			0.868635			0.434317	+	0.900760i	$0.356990\pi$
$884$		0			0
$885$	−2.46863	+	4.27579i	−0.0829820	+	0.143729i
$886$		0			0
$887$	−7.17712	−	12.4311i	−0.240984	−	0.417397i	0.720011	−	0.693963i	$-0.244137\pi$
$887$	−7.17712	−	12.4311i	−0.240984	−	0.417397i	−0.960995	+	0.276566i	$0.910804\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1.82288	−	3.15731i	−0.0610686	−	0.105774i
$892$		0			0
$893$	6.87451	−	11.9070i	0.230047	−	0.398452i
$894$		0			0
$895$	20.5830			0.688014
$896$		0			0
$897$	−9.64575			−0.322062
$898$		0			0
$899$	7.40588	−	12.8274i	0.247000	−	0.427816i
$900$		0			0
$901$	−13.2915	−	23.0216i	−0.442804	−	0.766959i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−3.14575	−	5.44860i	−0.104568	−	0.181118i
$906$		0			0
$907$	7.67712	−	13.2972i	0.254915	−	0.441525i	−0.709958	−	0.704244i	$-0.751286\pi$
$907$	7.67712	−	13.2972i	0.254915	−	0.441525i	0.964872	+	0.262719i	$0.0846193\pi$
$908$		0			0
$909$	−10.9373			−0.362766
$910$		0			0
$911$	31.5203			1.04431			0.522156	−	0.852850i	$-0.325128\pi$
$911$	31.5203			1.04431			0.522156	+	0.852850i	$0.325128\pi$
$912$		0			0
$913$	9.00000	−	15.5885i	0.297857	−	0.515903i
$914$		0			0
$915$	4.00000	+	6.92820i	0.132236	+	0.229039i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−15.7915	−	27.3517i	−0.520914	−	0.902249i	−0.999704	−	0.0243197i	$-0.992258\pi$
$919$	−15.7915	−	27.3517i	−0.520914	−	0.902249i	0.478791	−	0.877929i	$-0.341075\pi$
$920$		0			0
$921$	−6.03137	+	10.4466i	−0.198740	+	0.344229i
$922$		0			0
$923$	−22.1033			−0.727538
$924$		0			0
$925$	−4.64575			−0.152751
$926$		0			0
$927$	7.32288	−	12.6836i	0.240515	−	0.416584i
$928$		0			0
$929$	−0.760130	−	1.31658i	−0.0249390	−	0.0431957i	0.853287	−	0.521442i	$-0.174606\pi$
$929$	−0.760130	−	1.31658i	−0.0249390	−	0.0431957i	−0.878226	+	0.478247i	$0.841273\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−4.17712	−	7.23499i	−0.136753	−	0.236863i
$934$		0			0
$935$	−6.64575	+	11.5108i	−0.217339	+	0.376443i
$936$		0			0
$937$	50.9778			1.66537			0.832686	−	0.553746i	$-0.186802\pi$
$937$	50.9778			1.66537			0.832686	+	0.553746i	$0.186802\pi$
$938$		0			0
$939$	5.22876			0.170634
$940$		0			0
$941$	2.46863	−	4.27579i	0.0804749	−	0.139387i	−0.822979	−	0.568072i	$-0.807690\pi$
$941$	2.46863	−	4.27579i	0.0804749	−	0.139387i	0.903454	+	0.428685i	$0.141023\pi$
$942$		0			0
$943$	19.9373	+	34.5323i	0.649246	+	1.12453i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	22.8229	+	39.5304i	0.741644	+	1.28456i	0.951746	+	0.306885i	$0.0992868\pi$
$947$	22.8229	+	39.5304i	0.741644	+	1.28456i	−0.210103	+	0.977679i	$0.567380\pi$
$948$		0			0
$949$	17.5000	−	30.3109i	0.568074	−	0.983933i
$950$		0			0
$951$	13.5203			0.438424
$952$		0			0
$953$	0.457513			0.0148203			0.00741015	−	0.999973i	$-0.497641\pi$
$953$	0.457513			0.0148203			0.00741015	+	0.999973i	$0.497641\pi$
$954$		0			0
$955$	−11.5830	+	20.0624i	−0.374817	+	0.649203i
$956$		0			0
$957$	4.29150	+	7.43310i	0.138725	+	0.240278i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−4.29150	−	7.43310i	−0.138436	−	0.239777i
$962$		0			0
$963$	0.531373	−	0.920365i	0.0171233	−	0.0296584i
$964$		0			0
$965$	23.9373			0.770567
$966$		0			0
$967$	40.3948			1.29901			0.649504	−	0.760358i	$-0.274977\pi$
$967$	40.3948			1.29901			0.649504	+	0.760358i	$0.274977\pi$
$968$		0			0
$969$	−4.17712	+	7.23499i	−0.134189	+	0.232421i
$970$		0			0
$971$	26.5830	+	46.0431i	0.853089	+	1.47759i	0.878406	+	0.477914i	$0.158607\pi$
$971$	26.5830	+	46.0431i	0.853089	+	1.47759i	−0.0253172	+	0.999679i	$0.508060\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−1.32288	−	2.29129i	−0.0423659	−	0.0733799i
$976$		0			0
$977$	20.4686	−	35.4527i	0.654849	−	1.13423i	−0.327082	−	0.944996i	$-0.606065\pi$
$977$	20.4686	−	35.4527i	0.654849	−	1.13423i	0.981932	−	0.189237i	$-0.0606013\pi$
$978$		0			0
$979$	−44.5830			−1.42488
$980$		0			0
$981$	−13.0000			−0.415058
$982$		0			0
$983$	−27.3431	+	47.3597i	−0.872111	+	1.51054i	−0.0123014	+	0.999924i	$0.503916\pi$
$983$	−27.3431	+	47.3597i	−0.872111	+	1.51054i	−0.859809	+	0.510615i	$0.829418\pi$
$984$		0			0
$985$	5.46863	+	9.47194i	0.174245	+	0.301801i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	18.1144	+	31.3750i	0.576004	+	0.997668i
$990$		0			0
$991$	−16.8542	+	29.1924i	−0.535393	+	0.927328i	0.463751	+	0.885965i	$0.346503\pi$
$991$	−16.8542	+	29.1924i	−0.535393	+	0.927328i	−0.999144	+	0.0413622i	$0.986830\pi$
$992$		0			0
$993$	−22.1660			−0.703417
$994$		0			0
$995$	19.1660			0.607603
$996$		0			0
$997$	8.38562	−	14.5243i	0.265575	−	0.459990i	−0.702139	−	0.712040i	$-0.747771\pi$
$997$	8.38562	−	14.5243i	0.265575	−	0.459990i	0.967714	+	0.252050i	$0.0811048\pi$
$998$		0			0
$999$	−2.32288	−	4.02334i	−0.0734925	−	0.127293i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2940.2.q.t.361.1		4
7.2	even	3	inner	2940.2.q.t.961.1		4
7.3	odd	6		2940.2.a.s.1.2		2
7.4	even	3		2940.2.a.m.1.2		2
7.5	odd	6		420.2.q.c.121.2	✓	4
7.6	odd	2		420.2.q.c.361.2	yes	4
21.5	even	6		1260.2.s.f.541.2		4
21.11	odd	6		8820.2.a.bj.1.1		2
21.17	even	6		8820.2.a.be.1.1		2
21.20	even	2		1260.2.s.f.361.2		4
28.19	even	6		1680.2.bg.q.961.1		4
28.27	even	2		1680.2.bg.q.1201.1		4
35.12	even	12		2100.2.bc.e.1549.2		8
35.13	even	4		2100.2.bc.e.949.2		8
35.19	odd	6		2100.2.q.h.1801.1		4
35.27	even	4		2100.2.bc.e.949.3		8
35.33	even	12		2100.2.bc.e.1549.3		8
35.34	odd	2		2100.2.q.h.1201.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.q.c.121.2	✓	4	7.5	odd	6
420.2.q.c.361.2	yes	4	7.6	odd	2
1260.2.s.f.361.2		4	21.20	even	2
1260.2.s.f.541.2		4	21.5	even	6
1680.2.bg.q.961.1		4	28.19	even	6
1680.2.bg.q.1201.1		4	28.27	even	2
2100.2.q.h.1201.1		4	35.34	odd	2
2100.2.q.h.1801.1		4	35.19	odd	6
2100.2.bc.e.949.2		8	35.13	even	4
2100.2.bc.e.949.3		8	35.27	even	4
2100.2.bc.e.1549.2		8	35.12	even	12
2100.2.bc.e.1549.3		8	35.33	even	12
2940.2.a.m.1.2		2	7.4	even	3
2940.2.a.s.1.2		2	7.3	odd	6
2940.2.q.t.361.1		4	1.1	even	1	trivial
2940.2.q.t.961.1		4	7.2	even	3	inner
8820.2.a.be.1.1		2	21.17	even	6
8820.2.a.bj.1.1		2	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-1.82288 + 3.15731i) q^{11} -2.64575 q^{13} +1.00000 q^{15} +(1.82288 - 3.15731i) q^{17} +(-1.14575 - 1.98450i) q^{19} +(1.82288 + 3.15731i) q^{23} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} +2.35425 q^{29} +(3.14575 - 5.44860i) q^{31} +(1.82288 + 3.15731i) q^{33} +(2.32288 + 4.02334i) q^{37} +(-1.32288 + 2.29129i) q^{39} +10.9373 q^{41} +9.93725 q^{43} +(0.500000 - 0.866025i) q^{45} +(3.00000 + 5.19615i) q^{47} +(-1.82288 - 3.15731i) q^{51} +(3.64575 - 6.31463i) q^{53} -3.64575 q^{55} -2.29150 q^{57} +(-2.46863 + 4.27579i) q^{59} +(4.00000 + 6.92820i) q^{61} +(-1.32288 - 2.29129i) q^{65} +(2.32288 - 4.02334i) q^{67} +3.64575 q^{69} +8.35425 q^{71} +(-6.61438 + 11.4564i) q^{73} +(0.500000 + 0.866025i) q^{75} +(4.14575 + 7.18065i) q^{79} +(-0.500000 + 0.866025i) q^{81} -4.93725 q^{83} +3.64575 q^{85} +(1.17712 - 2.03884i) q^{87} +(6.11438 + 10.5904i) q^{89} +(-3.14575 - 5.44860i) q^{93} +(1.14575 - 1.98450i) q^{95} -8.00000 q^{97} +3.64575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{5} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^5 - 2 * q^9	\( 4 q + 2 q^{3} + 2 q^{5} - 2 q^{9} - 2 q^{11} + 4 q^{15} + 2 q^{17} + 6 q^{19} + 2 q^{23} - 2 q^{25} - 4 q^{27} + 20 q^{29} + 2 q^{31} + 2 q^{33} + 4 q^{37} + 12 q^{41} + 8 q^{43} + 2 q^{45} + 12 q^{47} - 2 q^{51} + 4 q^{53} - 4 q^{55} + 12 q^{57} + 6 q^{59} + 16 q^{61} + 4 q^{67} + 4 q^{69} + 44 q^{71} + 2 q^{75} + 6 q^{79} - 2 q^{81} + 12 q^{83} + 4 q^{85} + 10 q^{87} - 2 q^{89} - 2 q^{93} - 6 q^{95} - 32 q^{97} + 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^5 - 2 * q^9 - 2 * q^11 + 4 * q^15 + 2 * q^17 + 6 * q^19 + 2 * q^23 - 2 * q^25 - 4 * q^27 + 20 * q^29 + 2 * q^31 + 2 * q^33 + 4 * q^37 + 12 * q^41 + 8 * q^43 + 2 * q^45 + 12 * q^47 - 2 * q^51 + 4 * q^53 - 4 * q^55 + 12 * q^57 + 6 * q^59 + 16 * q^61 + 4 * q^67 + 4 * q^69 + 44 * q^71 + 2 * q^75 + 6 * q^79 - 2 * q^81 + 12 * q^83 + 4 * q^85 + 10 * q^87 - 2 * q^89 - 2 * q^93 - 6 * q^95 - 32 * q^97 + 4 * q^99

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