LMFDB - Embedded newform 2940.2.bb.f.949.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2940,2,Mod(949,2940)]

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, 3, 4]))

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

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

chi := DirichletCharacter("2940.949");

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.bb (of order $6$, 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 $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			949.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2940.949
Dual form			2940.2.bb.f.1549.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{3} +(1.86603 + 1.23205i) q^{5} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{3} +(1.86603 + 1.23205i) q^{5} +(0.500000 + 0.866025i) q^{9} +(-2.00000 + 3.46410i) q^{11} +2.00000i q^{13} +(1.00000 + 2.00000i) q^{15} +(1.73205 + 1.00000i) q^{17} +(1.00000 + 1.73205i) q^{19} +(5.19615 - 3.00000i) q^{23} +(1.96410 + 4.59808i) q^{25} +1.00000i q^{27} -6.00000 q^{29} +(3.00000 - 5.19615i) q^{31} +(-3.46410 + 2.00000i) q^{33} +(-3.46410 + 2.00000i) q^{37} +(-1.00000 + 1.73205i) q^{39} +4.00000i q^{43} +(-0.133975 + 2.23205i) q^{45} +(-3.46410 + 2.00000i) q^{47} +(1.00000 + 1.73205i) q^{51} +(-1.73205 - 1.00000i) q^{53} +(-8.00000 + 4.00000i) q^{55} +2.00000i q^{57} +(-2.00000 + 3.46410i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(-2.46410 + 3.73205i) q^{65} +(10.3923 + 6.00000i) q^{67} +6.00000 q^{69} -8.00000 q^{71} +(-12.1244 - 7.00000i) q^{73} +(-0.598076 + 4.96410i) q^{75} +(8.00000 + 13.8564i) q^{79} +(-0.500000 + 0.866025i) q^{81} +16.0000i q^{83} +(2.00000 + 4.00000i) q^{85} +(-5.19615 - 3.00000i) q^{87} +(-8.00000 - 13.8564i) q^{89} +(5.19615 - 3.00000i) q^{93} +(-0.267949 + 4.46410i) q^{95} +14.0000i q^{97} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{5} + 2 q^{9}+O(q^{10}) $ 4 * q + 4 * q^5 + 2 * q^9	$ 4 q + 4 q^{5} + 2 q^{9} - 8 q^{11} + 4 q^{15} + 4 q^{19} - 6 q^{25} - 24 q^{29} + 12 q^{31} - 4 q^{39} - 4 q^{45} + 4 q^{51} - 32 q^{55} - 8 q^{59} - 4 q^{61} + 4 q^{65} + 24 q^{69} - 32 q^{71} + 8 q^{75} + 32 q^{79} - 2 q^{81} + 8 q^{85} - 32 q^{89} - 8 q^{95} - 16 q^{99}+O(q^{100}) $ 4 * q + 4 * q^5 + 2 * q^9 - 8 * q^11 + 4 * q^15 + 4 * q^19 - 6 * q^25 - 24 * q^29 + 12 * q^31 - 4 * q^39 - 4 * q^45 + 4 * q^51 - 32 * q^55 - 8 * q^59 - 4 * q^61 + 4 * q^65 + 24 * q^69 - 32 * q^71 + 8 * q^75 + 32 * q^79 - 2 * q^81 + 8 * q^85 - 32 * q^89 - 8 * q^95 - 16 * 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
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$		0			0
$5$	1.86603	+	1.23205i	0.834512	+	0.550990i
$5$	1.86603	+	1.23205i	0.834512	+	0.550990i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	0.389338	+	0.921095i	$0.372704\pi$
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	−0.992361	+	0.123371i	$0.960630\pi$
$12$		0			0
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$		0			0
$15$	1.00000	+	2.00000i	0.258199	+	0.516398i
$16$		0			0
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	0.695113	−	0.718900i	$-0.255354\pi$
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	−0.275029	+	0.961436i	$0.588688\pi$
$18$		0			0
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.151642	−	0.988436i	$-0.451544\pi$
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.931831	+	0.362892i	$0.118211\pi$
$24$		0			0
$25$	1.96410	+	4.59808i	0.392820	+	0.919615i
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	−0.460152	−	0.887840i	$-0.652205\pi$
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	0.998968	−	0.0454165i	$-0.0144615\pi$
$32$		0			0
$33$	−3.46410	+	2.00000i	−0.603023	+	0.348155i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.46410	+	2.00000i	−0.569495	+	0.328798i	−0.756948	−	0.653476i	$-0.773310\pi$
$37$	−3.46410	+	2.00000i	−0.569495	+	0.328798i	0.187453	+	0.982274i	$0.439977\pi$
$38$		0			0
$39$	−1.00000	+	1.73205i	−0.160128	+	0.277350i
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$		0			0
$45$	−0.133975	+	2.23205i	−0.0199718	+	0.332734i
$46$		0			0
$47$	−3.46410	+	2.00000i	−0.505291	+	0.291730i	−0.730896	−	0.682489i	$-0.760898\pi$
$47$	−3.46410	+	2.00000i	−0.505291	+	0.291730i	0.225605	+	0.974219i	$0.427564\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	1.00000	+	1.73205i	0.140028	+	0.242536i
$52$		0			0
$53$	−1.73205	−	1.00000i	−0.237915	−	0.137361i	0.376303	−	0.926497i	$-0.377195\pi$
$53$	−1.73205	−	1.00000i	−0.237915	−	0.137361i	−0.614218	+	0.789136i	$0.710529\pi$
$54$		0			0
$55$	−8.00000	+	4.00000i	−1.07872	+	0.539360i
$56$		0			0
$57$			2.00000i			0.264906i
$58$		0			0
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.46410	+	3.73205i	−0.305634	+	0.462904i
$66$		0			0
$67$	10.3923	+	6.00000i	1.26962	+	0.733017i	0.974916	−	0.222571i	$-0.0714450\pi$
$67$	10.3923	+	6.00000i	1.26962	+	0.733017i	0.294706	+	0.955588i	$0.404778\pi$
$68$		0			0
$69$	6.00000			0.722315
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	−12.1244	−	7.00000i	−1.41905	−	0.819288i	−0.422833	−	0.906208i	$-0.638964\pi$
$73$	−12.1244	−	7.00000i	−1.41905	−	0.819288i	−0.996215	+	0.0869195i	$0.972298\pi$
$74$		0			0
$75$	−0.598076	+	4.96410i	−0.0690599	+	0.573205i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	8.00000	+	13.8564i	0.900070	+	1.55897i	0.827401	+	0.561611i	$0.189818\pi$
$79$	8.00000	+	13.8564i	0.900070	+	1.55897i	0.0726692	+	0.997356i	$0.476848\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			16.0000i			1.75623i	0.478451	+	0.878114i	$0.341198\pi$
$83$			16.0000i			1.75623i	−0.478451	+	0.878114i	$0.658802\pi$
$84$		0			0
$85$	2.00000	+	4.00000i	0.216930	+	0.433861i
$86$		0			0
$87$	−5.19615	−	3.00000i	−0.557086	−	0.321634i
$88$		0			0
$89$	−8.00000	−	13.8564i	−0.847998	−	1.46878i	−0.882992	−	0.469389i	$-0.844474\pi$
$89$	−8.00000	−	13.8564i	−0.847998	−	1.46878i	0.0349934	−	0.999388i	$-0.488859\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	5.19615	−	3.00000i	0.538816	−	0.311086i
$94$		0			0
$95$	−0.267949	+	4.46410i	−0.0274910	+	0.458007i
$96$		0			0
$97$			14.0000i			1.42148i	0.703452	+	0.710742i	$0.251641\pi$
$97$			14.0000i			1.42148i	−0.703452	+	0.710742i	$0.748359\pi$
$98$		0			0
$99$	−4.00000			−0.402015
$100$		0			0
$101$	4.00000	−	6.92820i	0.398015	−	0.689382i	−0.595466	−	0.803380i	$-0.703033\pi$
$101$	4.00000	−	6.92820i	0.398015	−	0.689382i	0.993481	+	0.113998i	$0.0363659\pi$
$102$		0			0
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	15.5885	−	9.00000i	1.50699	−	0.870063i	0.507026	−	0.861931i	$-0.330745\pi$
$107$	15.5885	−	9.00000i	1.50699	−	0.870063i	0.999967	−	0.00813215i	$-0.00258857\pi$
$108$		0			0
$109$	9.00000	−	15.5885i	0.862044	−	1.49310i	−0.00790932	−	0.999969i	$-0.502518\pi$
$109$	9.00000	−	15.5885i	0.862044	−	1.49310i	0.869953	−	0.493135i	$-0.164149\pi$
$110$		0			0
$111$	−4.00000			−0.379663
$112$		0			0
$113$			6.00000i			0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$		0			0
$115$	13.3923	+	0.803848i	1.24884	+	0.0749592i
$116$		0			0
$117$	−1.73205	+	1.00000i	−0.160128	+	0.0924500i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$		0			0
$129$	−2.00000	+	3.46410i	−0.176090	+	0.304997i
$130$		0			0
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	0.940072	−	0.340977i	$-0.110758\pi$
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	−0.765331	+	0.643637i	$0.777425\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−1.23205	+	1.86603i	−0.106038	+	0.160602i
$136$		0			0
$137$	−8.66025	−	5.00000i	−0.739895	−	0.427179i	0.0821359	−	0.996621i	$-0.473826\pi$
$137$	−8.66025	−	5.00000i	−0.739895	−	0.427179i	−0.822031	+	0.569442i	$0.807159\pi$
$138$		0			0
$139$	−14.0000			−1.18746			−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000			−1.18746			−0.593732	+	0.804663i	$0.702346\pi$
$140$		0			0
$141$	−4.00000			−0.336861
$142$		0			0
$143$	−6.92820	−	4.00000i	−0.579365	−	0.334497i
$144$		0			0
$145$	−11.1962	−	7.39230i	−0.929790	−	0.613898i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$		0			0
$153$			2.00000i			0.161690i
$154$		0			0
$155$	12.0000	−	6.00000i	0.963863	−	0.481932i
$156$		0			0
$157$	1.73205	+	1.00000i	0.138233	+	0.0798087i	0.567521	−	0.823359i	$-0.307902\pi$
$157$	1.73205	+	1.00000i	0.138233	+	0.0798087i	−0.429289	+	0.903167i	$0.641236\pi$
$158$		0			0
$159$	−1.00000	−	1.73205i	−0.0793052	−	0.137361i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	20.7846	−	12.0000i	1.62798	−	0.939913i	0.643280	−	0.765631i	$-0.277573\pi$
$163$	20.7846	−	12.0000i	1.62798	−	0.939913i	0.984696	−	0.174282i	$-0.0557604\pi$
$164$		0			0
$165$	−8.92820	−	0.535898i	−0.695060	−	0.0417196i
$166$		0			0
$167$			8.00000i			0.619059i	0.950890	+	0.309529i	$0.100171\pi$
$167$			8.00000i			0.619059i	−0.950890	+	0.309529i	$0.899829\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$		0			0
$171$	−1.00000	+	1.73205i	−0.0764719	+	0.132453i
$172$		0			0
$173$	12.1244	−	7.00000i	0.921798	−	0.532200i	0.0375896	−	0.999293i	$-0.488032\pi$
$173$	12.1244	−	7.00000i	0.921798	−	0.532200i	0.884208	+	0.467093i	$0.154699\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.46410	+	2.00000i	−0.260378	+	0.150329i
$178$		0			0
$179$	−10.0000	+	17.3205i	−0.747435	+	1.29460i	0.201613	+	0.979465i	$0.435382\pi$
$179$	−10.0000	+	17.3205i	−0.747435	+	1.29460i	−0.949048	+	0.315130i	$0.897952\pi$
$180$		0			0
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$		0			0
$183$		−	2.00000i		−	0.147844i
$184$		0			0
$185$	−8.92820	−	0.535898i	−0.656415	−	0.0394000i
$186$		0			0
$187$	−6.92820	+	4.00000i	−0.506640	+	0.292509i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	0.684244	−	0.729253i	$-0.260132\pi$
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	−0.973674	+	0.227946i	$0.926799\pi$
$192$		0			0
$193$	20.7846	+	12.0000i	1.49611	+	0.863779i	0.999990	−	0.00447566i	$-0.00142465\pi$
$193$	20.7846	+	12.0000i	1.49611	+	0.863779i	0.496119	+	0.868255i	$0.334758\pi$
$194$		0			0
$195$	−4.00000	+	2.00000i	−0.286446	+	0.143223i
$196$		0			0
$197$			18.0000i			1.28245i	0.767354	+	0.641223i	$0.221573\pi$
$197$			18.0000i			1.28245i	−0.767354	+	0.641223i	$0.778427\pi$
$198$		0			0
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	−0.987022	−	0.160585i	$-0.948662\pi$
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	0.632581	+	0.774494i	$0.281995\pi$
$200$		0			0
$201$	6.00000	+	10.3923i	0.423207	+	0.733017i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	5.19615	+	3.00000i	0.361158	+	0.208514i
$208$		0			0
$209$	−8.00000			−0.553372
$210$		0			0
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$		0			0
$213$	−6.92820	−	4.00000i	−0.474713	−	0.274075i
$214$		0			0
$215$	−4.92820	+	7.46410i	−0.336101	+	0.509048i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−7.00000	−	12.1244i	−0.473016	−	0.819288i
$220$		0			0
$221$	−2.00000	+	3.46410i	−0.134535	+	0.233021i
$222$		0			0
$223$		−	16.0000i		−	1.07144i	−0.844396	−	0.535720i	$-0.820040\pi$
$223$		−	16.0000i		−	1.07144i	0.844396	−	0.535720i	$-0.179960\pi$
$224$		0			0
$225$	−3.00000	+	4.00000i	−0.200000	+	0.266667i
$226$		0			0
$227$	3.46410	+	2.00000i	0.229920	+	0.132745i	0.610535	−	0.791989i	$-0.290954\pi$
$227$	3.46410	+	2.00000i	0.229920	+	0.132745i	−0.380615	+	0.924734i	$0.624288\pi$
$228$		0			0
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	0.831092	−	0.556136i	$-0.187717\pi$
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	−0.897173	+	0.441679i	$0.854383\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	15.5885	−	9.00000i	1.02123	−	0.589610i	0.106773	−	0.994283i	$-0.465948\pi$
$233$	15.5885	−	9.00000i	1.02123	−	0.589610i	0.914461	+	0.404674i	$0.132615\pi$
$234$		0			0
$235$	−8.92820	−	0.535898i	−0.582412	−	0.0349582i
$236$		0			0
$237$			16.0000i			1.03931i
$238$		0			0
$239$	−8.00000			−0.517477			−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000			−0.517477			−0.258738	+	0.965947i	$0.583307\pi$
$240$		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
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.46410	+	2.00000i	−0.220416	+	0.127257i
$248$		0			0
$249$	−8.00000	+	13.8564i	−0.506979	+	0.878114i
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$			24.0000i			1.50887i
$254$		0			0
$255$	−0.267949	+	4.46410i	−0.0167796	+	0.279553i
$256$		0			0
$257$	−19.0526	+	11.0000i	−1.18847	+	0.686161i	−0.957958	−	0.286909i	$-0.907372\pi$
$257$	−19.0526	+	11.0000i	−1.18847	+	0.686161i	−0.230508	+	0.973070i	$0.574039\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.00000	−	5.19615i	−0.185695	−	0.321634i
$262$		0			0
$263$	25.9808	+	15.0000i	1.60204	+	0.924940i	0.991078	+	0.133281i	$0.0425514\pi$
$263$	25.9808	+	15.0000i	1.60204	+	0.924940i	0.610964	+	0.791658i	$0.290782\pi$
$264$		0			0
$265$	−2.00000	−	4.00000i	−0.122859	−	0.245718i
$266$		0			0
$267$		−	16.0000i		−	0.979184i
$268$		0			0
$269$	2.00000	−	3.46410i	0.121942	−	0.211210i	−0.798591	−	0.601874i	$-0.794421\pi$
$269$	2.00000	−	3.46410i	0.121942	−	0.211210i	0.920534	+	0.390664i	$0.127754\pi$
$270$		0			0
$271$	−11.0000	−	19.0526i	−0.668202	−	1.15736i	−0.978406	−	0.206691i	$-0.933731\pi$
$271$	−11.0000	−	19.0526i	−0.668202	−	1.15736i	0.310204	−	0.950670i	$-0.399603\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−19.8564	−	2.39230i	−1.19739	−	0.144261i
$276$		0			0
$277$	−3.46410	−	2.00000i	−0.208138	−	0.120168i	0.392308	−	0.919834i	$-0.371677\pi$
$277$	−3.46410	−	2.00000i	−0.208138	−	0.120168i	−0.600446	+	0.799666i	$0.705010\pi$
$278$		0			0
$279$	6.00000			0.359211
$280$		0			0
$281$	10.0000			0.596550			0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000			0.596550			0.298275	+	0.954480i	$0.403589\pi$
$282$		0			0
$283$	17.3205	+	10.0000i	1.02960	+	0.594438i	0.916869	−	0.399188i	$-0.130708\pi$
$283$	17.3205	+	10.0000i	1.02960	+	0.594438i	0.112728	+	0.993626i	$0.464041\pi$
$284$		0			0
$285$	−2.46410	+	3.73205i	−0.145961	+	0.221068i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−6.50000	−	11.2583i	−0.382353	−	0.662255i
$290$		0			0
$291$	−7.00000	+	12.1244i	−0.410347	+	0.710742i
$292$		0			0
$293$		−	22.0000i		−	1.28525i	−0.766179	−	0.642627i	$-0.777845\pi$
$293$		−	22.0000i		−	1.28525i	0.766179	−	0.642627i	$-0.222155\pi$
$294$		0			0
$295$	−8.00000	+	4.00000i	−0.465778	+	0.232889i
$296$		0			0
$297$	−3.46410	−	2.00000i	−0.201008	−	0.116052i
$298$		0			0
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	6.92820	−	4.00000i	0.398015	−	0.229794i
$304$		0			0
$305$	0.267949	−	4.46410i	0.0153427	−	0.255614i
$306$		0			0
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−10.0000	+	17.3205i	−0.567048	+	0.982156i	0.429808	+	0.902920i	$0.358581\pi$
$311$	−10.0000	+	17.3205i	−0.567048	+	0.982156i	−0.996856	+	0.0792356i	$0.974752\pi$
$312$		0			0
$313$	19.0526	−	11.0000i	1.07691	−	0.621757i	0.146852	−	0.989158i	$-0.453086\pi$
$313$	19.0526	−	11.0000i	1.07691	−	0.621757i	0.930062	+	0.367402i	$0.119753\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−22.5167	+	13.0000i	−1.26466	+	0.730153i	−0.973973	−	0.226665i	$-0.927218\pi$
$317$	−22.5167	+	13.0000i	−1.26466	+	0.730153i	−0.290689	+	0.956818i	$0.593884\pi$
$318$		0			0
$319$	12.0000	−	20.7846i	0.671871	−	1.16371i
$320$		0			0
$321$	18.0000			1.00466
$322$		0			0
$323$			4.00000i			0.222566i
$324$		0			0
$325$	−9.19615	+	3.92820i	−0.510111	+	0.217898i
$326$		0			0
$327$	15.5885	−	9.00000i	0.862044	−	0.497701i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	12.0000	+	20.7846i	0.659580	+	1.14243i	0.980725	+	0.195395i	$0.0625990\pi$
$331$	12.0000	+	20.7846i	0.659580	+	1.14243i	−0.321145	+	0.947030i	$0.604068\pi$
$332$		0			0
$333$	−3.46410	−	2.00000i	−0.189832	−	0.109599i
$334$		0			0
$335$	12.0000	+	24.0000i	0.655630	+	1.31126i
$336$		0			0
$337$			8.00000i			0.435788i	0.975972	+	0.217894i	$0.0699187\pi$
$337$			8.00000i			0.435788i	−0.975972	+	0.217894i	$0.930081\pi$
$338$		0			0
$339$	−3.00000	+	5.19615i	−0.162938	+	0.282216i
$340$		0			0
$341$	12.0000	+	20.7846i	0.649836	+	1.12555i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	11.1962	+	7.39230i	0.602781	+	0.397988i
$346$		0			0
$347$	−8.66025	−	5.00000i	−0.464907	−	0.268414i	0.249198	−	0.968452i	$-0.419833\pi$
$347$	−8.66025	−	5.00000i	−0.464907	−	0.268414i	−0.714105	+	0.700038i	$0.753166\pi$
$348$		0			0
$349$	6.00000			0.321173			0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000			0.321173			0.160586	+	0.987022i	$0.448662\pi$
$350$		0			0
$351$	−2.00000			−0.106752
$352$		0			0
$353$	−25.9808	−	15.0000i	−1.38282	−	0.798369i	−0.390324	−	0.920677i	$-0.627637\pi$
$353$	−25.9808	−	15.0000i	−1.38282	−	0.798369i	−0.992492	+	0.122308i	$0.960970\pi$
$354$		0			0
$355$	−14.9282	−	9.85641i	−0.792307	−	0.523124i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.00000	+	6.92820i	0.211112	+	0.365657i	0.952063	−	0.305903i	$-0.0989582\pi$
$359$	4.00000	+	6.92820i	0.211112	+	0.365657i	−0.740951	+	0.671559i	$0.765625\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$		0			0
$363$		−	5.00000i		−	0.262432i
$364$		0			0
$365$	−14.0000	−	28.0000i	−0.732793	−	1.46559i
$366$		0			0
$367$	13.8564	+	8.00000i	0.723299	+	0.417597i	0.815966	−	0.578101i	$-0.196206\pi$
$367$	13.8564	+	8.00000i	0.723299	+	0.417597i	−0.0926670	+	0.995697i	$0.529539\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	20.7846	−	12.0000i	1.07619	−	0.621336i	0.146321	−	0.989237i	$-0.453257\pi$
$373$	20.7846	−	12.0000i	1.07619	−	0.621336i	0.929865	+	0.367901i	$0.119923\pi$
$374$		0			0
$375$	−7.23205	+	8.52628i	−0.373461	+	0.440295i
$376$		0			0
$377$		−	12.0000i		−	0.618031i
$378$		0			0
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	10.3923	−	6.00000i	0.531022	−	0.306586i	−0.210411	−	0.977613i	$-0.567480\pi$
$383$	10.3923	−	6.00000i	0.531022	−	0.306586i	0.741433	+	0.671027i	$0.234147\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.46410	+	2.00000i	−0.176090	+	0.101666i
$388$		0			0
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	0.182047	+	0.983290i	$0.441728\pi$
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	−0.942578	+	0.333987i	$0.891606\pi$
$390$		0			0
$391$	12.0000			0.606866
$392$		0			0
$393$			4.00000i			0.201773i
$394$		0			0
$395$	−2.14359	+	35.7128i	−0.107856	+	1.79691i
$396$		0			0
$397$	29.4449	−	17.0000i	1.47780	−	0.853206i	0.478110	−	0.878300i	$-0.341322\pi$
$397$	29.4449	−	17.0000i	1.47780	−	0.853206i	0.999685	+	0.0250943i	$0.00798860\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	0.781345	−	0.624099i	$-0.214534\pi$
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	−0.931158	+	0.364615i	$0.881200\pi$
$402$		0			0
$403$	10.3923	+	6.00000i	0.517678	+	0.298881i
$404$		0			0
$405$	−2.00000	+	1.00000i	−0.0993808	+	0.0496904i
$406$		0			0
$407$		−	16.0000i		−	0.793091i
$408$		0			0
$409$	13.0000	−	22.5167i	0.642809	−	1.11338i	−0.341994	−	0.939702i	$-0.611102\pi$
$409$	13.0000	−	22.5167i	0.642809	−	1.11338i	0.984803	−	0.173675i	$-0.0555643\pi$
$410$		0			0
$411$	−5.00000	−	8.66025i	−0.246632	−	0.427179i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−19.7128	+	29.8564i	−0.967664	+	1.46559i
$416$		0			0
$417$	−12.1244	−	7.00000i	−0.593732	−	0.342791i
$418$		0			0
$419$	−24.0000			−1.17248			−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000			−1.17248			−0.586238	+	0.810139i	$0.699392\pi$
$420$		0			0
$421$	−2.00000			−0.0974740			−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000			−0.0974740			−0.0487370	+	0.998812i	$0.515520\pi$
$422$		0			0
$423$	−3.46410	−	2.00000i	−0.168430	−	0.0972433i
$424$		0			0
$425$	−1.19615	+	9.92820i	−0.0580219	+	0.481589i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−4.00000	−	6.92820i	−0.193122	−	0.334497i
$430$		0			0
$431$	12.0000	−	20.7846i	0.578020	−	1.00116i	−0.417687	−	0.908591i	$-0.637159\pi$
$431$	12.0000	−	20.7846i	0.578020	−	1.00116i	0.995706	−	0.0925683i	$-0.0295076\pi$
$432$		0			0
$433$		−	34.0000i		−	1.63394i	−0.576683	−	0.816968i	$-0.695653\pi$
$433$		−	34.0000i		−	1.63394i	0.576683	−	0.816968i	$-0.304347\pi$
$434$		0			0
$435$	−6.00000	−	12.0000i	−0.287678	−	0.575356i
$436$		0			0
$437$	10.3923	+	6.00000i	0.497131	+	0.287019i
$438$		0			0
$439$	3.00000	+	5.19615i	0.143182	+	0.247999i	0.928693	−	0.370849i	$-0.120933\pi$
$439$	3.00000	+	5.19615i	0.143182	+	0.247999i	−0.785511	+	0.618848i	$0.787600\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.19615	−	3.00000i	0.246877	−	0.142534i	−0.371457	−	0.928450i	$-0.621142\pi$
$443$	5.19615	−	3.00000i	0.246877	−	0.142534i	0.618333	+	0.785916i	$0.287808\pi$
$444$		0			0
$445$	2.14359	−	35.7128i	0.101616	−	1.69295i
$446$		0			0
$447$			6.00000i			0.283790i
$448$		0			0
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	13.8564	−	8.00000i	0.651031	−	0.375873i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−24.2487	+	14.0000i	−1.13431	+	0.654892i	−0.945015	−	0.327028i	$-0.893953\pi$
$457$	−24.2487	+	14.0000i	−1.13431	+	0.654892i	−0.189292	+	0.981921i	$0.560619\pi$
$458$		0			0
$459$	−1.00000	+	1.73205i	−0.0466760	+	0.0808452i
$460$		0			0
$461$	24.0000			1.11779			0.558896	−	0.829238i	$-0.311225\pi$
$461$	24.0000			1.11779			0.558896	+	0.829238i	$0.311225\pi$
$462$		0			0
$463$		−	24.0000i		−	1.11537i	−0.830051	−	0.557687i	$-0.811689\pi$
$463$		−	24.0000i		−	1.11537i	0.830051	−	0.557687i	$-0.188311\pi$
$464$		0			0
$465$	13.3923	+	0.803848i	0.621053	+	0.0372775i
$466$		0			0
$467$	−24.2487	+	14.0000i	−1.12210	+	0.647843i	−0.941935	−	0.335794i	$-0.890995\pi$
$467$	−24.2487	+	14.0000i	−1.12210	+	0.647843i	−0.180161	+	0.983637i	$0.557662\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	1.00000	+	1.73205i	0.0460776	+	0.0798087i
$472$		0			0
$473$	−13.8564	−	8.00000i	−0.637118	−	0.367840i
$474$		0			0
$475$	−6.00000	+	8.00000i	−0.275299	+	0.367065i
$476$		0			0
$477$		−	2.00000i		−	0.0915737i
$478$		0			0
$479$	2.00000	−	3.46410i	0.0913823	−	0.158279i	−0.816711	−	0.577047i	$-0.804205\pi$
$479$	2.00000	−	3.46410i	0.0913823	−	0.158279i	0.908093	+	0.418769i	$0.137538\pi$
$480$		0			0
$481$	−4.00000	−	6.92820i	−0.182384	−	0.315899i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−17.2487	+	26.1244i	−0.783224	+	1.18625i
$486$		0			0
$487$	10.3923	+	6.00000i	0.470920	+	0.271886i	0.716625	−	0.697459i	$-0.245686\pi$
$487$	10.3923	+	6.00000i	0.470920	+	0.271886i	−0.245705	+	0.969345i	$0.579019\pi$
$488$		0			0
$489$	24.0000			1.08532
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$		0			0
$493$	−10.3923	−	6.00000i	−0.468046	−	0.270226i
$494$		0			0
$495$	−7.46410	−	4.92820i	−0.335486	−	0.221506i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	0.817781	−	0.575529i	$-0.195204\pi$
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	−0.907314	+	0.420455i	$0.861871\pi$
$500$		0			0
$501$	−4.00000	+	6.92820i	−0.178707	+	0.309529i
$502$		0			0
$503$		−	12.0000i		−	0.535054i	−0.963550	−	0.267527i	$-0.913794\pi$
$503$		−	12.0000i		−	0.535054i	0.963550	−	0.267527i	$-0.0862064\pi$
$504$		0			0
$505$	16.0000	−	8.00000i	0.711991	−	0.355995i
$506$		0			0
$507$	7.79423	+	4.50000i	0.346154	+	0.199852i
$508$		0			0
$509$	14.0000	+	24.2487i	0.620539	+	1.07481i	0.989385	+	0.145315i	$0.0464195\pi$
$509$	14.0000	+	24.2487i	0.620539	+	1.07481i	−0.368846	+	0.929490i	$0.620247\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−1.73205	+	1.00000i	−0.0764719	+	0.0441511i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	16.0000i		−	0.703679i
$518$		0			0
$519$	14.0000			0.614532
$520$		0			0
$521$	6.00000	−	10.3923i	0.262865	−	0.455295i	−0.704137	−	0.710064i	$-0.748666\pi$
$521$	6.00000	−	10.3923i	0.262865	−	0.455295i	0.967002	+	0.254769i	$0.0819994\pi$
$522$		0			0
$523$	10.3923	−	6.00000i	0.454424	−	0.262362i	−0.255273	−	0.966869i	$-0.582165\pi$
$523$	10.3923	−	6.00000i	0.454424	−	0.262362i	0.709697	+	0.704507i	$0.248832\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	10.3923	−	6.00000i	0.452696	−	0.261364i
$528$		0			0
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$		0			0
$531$	−4.00000			−0.173585
$532$		0			0
$533$		0			0
$534$		0			0
$535$	40.1769	+	2.41154i	1.73700	+	0.104260i
$536$		0			0
$537$	−17.3205	+	10.0000i	−0.747435	+	0.431532i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−5.00000	−	8.66025i	−0.214967	−	0.372333i	0.738296	−	0.674477i	$-0.235631\pi$
$541$	−5.00000	−	8.66025i	−0.214967	−	0.372333i	−0.953262	+	0.302144i	$0.902298\pi$
$542$		0			0
$543$	−19.0526	−	11.0000i	−0.817624	−	0.472055i
$544$		0			0
$545$	36.0000	−	18.0000i	1.54207	−	0.771035i
$546$		0			0
$547$		−	28.0000i		−	1.19719i	−0.801050	−	0.598597i	$-0.795725\pi$
$547$		−	28.0000i		−	1.19719i	0.801050	−	0.598597i	$-0.204275\pi$
$548$		0			0
$549$	1.00000	−	1.73205i	0.0426790	−	0.0739221i
$550$		0			0
$551$	−6.00000	−	10.3923i	−0.255609	−	0.442727i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−7.46410	−	4.92820i	−0.316833	−	0.209191i
$556$		0			0
$557$	−25.9808	−	15.0000i	−1.10084	−	0.635570i	−0.164399	−	0.986394i	$-0.552568\pi$
$557$	−25.9808	−	15.0000i	−1.10084	−	0.635570i	−0.936442	+	0.350824i	$0.885902\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$		0			0
$561$	−8.00000			−0.337760
$562$		0			0
$563$	−20.7846	−	12.0000i	−0.875967	−	0.505740i	−0.00664037	−	0.999978i	$-0.502114\pi$
$563$	−20.7846	−	12.0000i	−0.875967	−	0.505740i	−0.869326	+	0.494238i	$0.835447\pi$
$564$		0			0
$565$	−7.39230	+	11.1962i	−0.310997	+	0.471026i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$		0			0
$571$	4.00000	−	6.92820i	0.167395	−	0.289936i	−0.770108	−	0.637913i	$-0.779798\pi$
$571$	4.00000	−	6.92820i	0.167395	−	0.289936i	0.937503	+	0.347977i	$0.113131\pi$
$572$		0			0
$573$		−	8.00000i		−	0.334205i
$574$		0			0
$575$	24.0000	+	18.0000i	1.00087	+	0.750652i
$576$		0			0
$577$	−15.5885	−	9.00000i	−0.648956	−	0.374675i	0.139100	−	0.990278i	$-0.455579\pi$
$577$	−15.5885	−	9.00000i	−0.648956	−	0.374675i	−0.788056	+	0.615603i	$0.788912\pi$
$578$		0			0
$579$	12.0000	+	20.7846i	0.498703	+	0.863779i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	6.92820	−	4.00000i	0.286937	−	0.165663i
$584$		0			0
$585$	−4.46410	−	0.267949i	−0.184568	−	0.0110783i
$586$		0			0
$587$		−	16.0000i		−	0.660391i	−0.943913	−	0.330195i	$-0.892885\pi$
$587$		−	16.0000i		−	0.660391i	0.943913	−	0.330195i	$-0.107115\pi$
$588$		0			0
$589$	12.0000			0.494451
$590$		0			0
$591$	−9.00000	+	15.5885i	−0.370211	+	0.641223i
$592$		0			0
$593$	−12.1244	+	7.00000i	−0.497888	+	0.287456i	−0.727841	−	0.685746i	$-0.759476\pi$
$593$	−12.1244	+	7.00000i	−0.497888	+	0.287456i	0.229953	+	0.973202i	$0.426143\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−8.66025	+	5.00000i	−0.354441	+	0.204636i
$598$		0			0
$599$	4.00000	−	6.92820i	0.163436	−	0.283079i	−0.772663	−	0.634816i	$-0.781076\pi$
$599$	4.00000	−	6.92820i	0.163436	−	0.283079i	0.936099	+	0.351738i	$0.114409\pi$
$600$		0			0
$601$	−30.0000			−1.22373			−0.611863	−	0.790964i	$-0.709580\pi$
$601$	−30.0000			−1.22373			−0.611863	+	0.790964i	$0.709580\pi$
$602$		0			0
$603$			12.0000i			0.488678i
$604$		0			0
$605$	0.669873	−	11.1603i	0.0272342	−	0.453729i
$606$		0			0
$607$	−6.92820	+	4.00000i	−0.281207	+	0.162355i	−0.633970	−	0.773358i	$-0.718576\pi$
$607$	−6.92820	+	4.00000i	−0.281207	+	0.162355i	0.352763	+	0.935713i	$0.385242\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.00000	−	6.92820i	−0.161823	−	0.280285i
$612$		0			0
$613$	−3.46410	−	2.00000i	−0.139914	−	0.0807792i	0.428409	−	0.903585i	$-0.359074\pi$
$613$	−3.46410	−	2.00000i	−0.139914	−	0.0807792i	−0.568323	+	0.822806i	$0.692408\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			6.00000i			0.241551i	0.992680	+	0.120775i	$0.0385381\pi$
$617$			6.00000i			0.241551i	−0.992680	+	0.120775i	$0.961462\pi$
$618$		0			0
$619$	15.0000	−	25.9808i	0.602901	−	1.04425i	−0.389479	−	0.921036i	$-0.627345\pi$
$619$	15.0000	−	25.9808i	0.602901	−	1.04425i	0.992379	−	0.123219i	$-0.0393219\pi$
$620$		0			0
$621$	3.00000	+	5.19615i	0.120386	+	0.208514i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$		0			0
$627$	−6.92820	−	4.00000i	−0.276686	−	0.159745i
$628$		0			0
$629$	−8.00000			−0.318981
$630$		0			0
$631$	24.0000			0.955425			0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000			0.955425			0.477712	+	0.878516i	$0.341466\pi$
$632$		0			0
$633$	−6.92820	−	4.00000i	−0.275371	−	0.158986i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−4.00000	−	6.92820i	−0.158238	−	0.274075i
$640$		0			0
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	−0.987200	−	0.159489i	$-0.949015\pi$
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	0.631721	+	0.775196i	$0.282349\pi$
$642$		0			0
$643$			4.00000i			0.157745i	0.996885	+	0.0788723i	$0.0251319\pi$
$643$			4.00000i			0.157745i	−0.996885	+	0.0788723i	$0.974868\pi$
$644$		0			0
$645$	−8.00000	+	4.00000i	−0.315000	+	0.157500i
$646$		0			0
$647$	34.6410	+	20.0000i	1.36188	+	0.786281i	0.989874	−	0.141950i	$-0.0453371\pi$
$647$	34.6410	+	20.0000i	1.36188	+	0.786281i	0.372005	+	0.928231i	$0.378670\pi$
$648$		0			0
$649$	−8.00000	−	13.8564i	−0.314027	−	0.543912i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	22.5167	−	13.0000i	0.881145	−	0.508729i	0.0101092	−	0.999949i	$-0.496782\pi$
$653$	22.5167	−	13.0000i	0.881145	−	0.508729i	0.871036	+	0.491220i	$0.163449\pi$
$654$		0			0
$655$	−0.535898	+	8.92820i	−0.0209393	+	0.348854i
$656$		0			0
$657$		−	14.0000i		−	0.546192i
$658$		0			0
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$		0			0
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	−0.884818	−	0.465937i	$-0.845717\pi$
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	0.845922	+	0.533306i	$0.179051\pi$
$662$		0			0
$663$	−3.46410	+	2.00000i	−0.134535	+	0.0776736i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−31.1769	+	18.0000i	−1.20717	+	0.696963i
$668$		0			0
$669$	8.00000	−	13.8564i	0.309298	−	0.535720i
$670$		0			0
$671$	8.00000			0.308837
$672$		0			0
$673$		−	12.0000i		−	0.462566i	−0.972887	−	0.231283i	$-0.925708\pi$
$673$		−	12.0000i		−	0.462566i	0.972887	−	0.231283i	$-0.0742923\pi$
$674$		0			0
$675$	−4.59808	+	1.96410i	−0.176980	+	0.0755983i
$676$		0			0
$677$	36.3731	−	21.0000i	1.39793	−	0.807096i	0.403755	−	0.914867i	$-0.367705\pi$
$677$	36.3731	−	21.0000i	1.39793	−	0.807096i	0.994176	+	0.107772i	$0.0343715\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	2.00000	+	3.46410i	0.0766402	+	0.132745i
$682$		0			0
$683$	−12.1244	−	7.00000i	−0.463926	−	0.267848i	0.249768	−	0.968306i	$-0.419646\pi$
$683$	−12.1244	−	7.00000i	−0.463926	−	0.267848i	−0.713693	+	0.700458i	$0.752979\pi$
$684$		0			0
$685$	−10.0000	−	20.0000i	−0.382080	−	0.764161i
$686$		0			0
$687$		−	2.00000i		−	0.0763048i
$688$		0			0
$689$	2.00000	−	3.46410i	0.0761939	−	0.131972i
$690$		0			0
$691$	11.0000	+	19.0526i	0.418460	+	0.724793i	0.995785	−	0.0917209i	$-0.0292368\pi$
$691$	11.0000	+	19.0526i	0.418460	+	0.724793i	−0.577325	+	0.816514i	$0.695903\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−26.1244	−	17.2487i	−0.990953	−	0.654281i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	18.0000			0.680823
$700$		0			0
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$		0			0
$703$	−6.92820	−	4.00000i	−0.261302	−	0.150863i
$704$		0			0
$705$	−7.46410	−	4.92820i	−0.281114	−	0.185607i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	−0.963512	−	0.267664i	$-0.913748\pi$
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	0.249952	−	0.968258i	$-0.419585\pi$
$710$		0			0
$711$	−8.00000	+	13.8564i	−0.300023	+	0.519656i
$712$		0			0
$713$		−	36.0000i		−	1.34821i
$714$		0			0
$715$	−8.00000	−	16.0000i	−0.299183	−	0.598366i
$716$		0			0
$717$	−6.92820	−	4.00000i	−0.258738	−	0.149383i
$718$		0			0
$719$	−14.0000	−	24.2487i	−0.522112	−	0.904324i	−0.999669	−	0.0257237i	$-0.991811\pi$
$719$	−14.0000	−	24.2487i	−0.522112	−	0.904324i	0.477557	−	0.878601i	$-0.341522\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	22.5167	−	13.0000i	0.837404	−	0.483475i
$724$		0			0
$725$	−11.7846	−	27.5885i	−0.437669	−	1.02461i
$726$		0			0
$727$		−	16.0000i		−	0.593407i	−0.954970	−	0.296704i	$-0.904113\pi$
$727$		−	16.0000i		−	0.593407i	0.954970	−	0.296704i	$-0.0958873\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−4.00000	+	6.92820i	−0.147945	+	0.256249i
$732$		0			0
$733$	36.3731	−	21.0000i	1.34347	−	0.775653i	0.356155	−	0.934427i	$-0.384088\pi$
$733$	36.3731	−	21.0000i	1.34347	−	0.775653i	0.987315	+	0.158774i	$0.0507542\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−41.5692	+	24.0000i	−1.53122	+	0.884051i
$738$		0			0
$739$	−8.00000	+	13.8564i	−0.294285	+	0.509716i	−0.974818	−	0.223001i	$-0.928415\pi$
$739$	−8.00000	+	13.8564i	−0.294285	+	0.509716i	0.680534	+	0.732717i	$0.261748\pi$
$740$		0			0
$741$	−4.00000			−0.146944
$742$		0			0
$743$		−	34.0000i		−	1.24734i	−0.781688	−	0.623670i	$-0.785641\pi$
$743$		−	34.0000i		−	1.24734i	0.781688	−	0.623670i	$-0.214359\pi$
$744$		0			0
$745$	−0.803848	+	13.3923i	−0.0294507	+	0.490656i
$746$		0			0
$747$	−13.8564	+	8.00000i	−0.506979	+	0.292705i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	0.827225	−	0.561870i	$-0.189918\pi$
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	−0.900207	+	0.435463i	$0.856585\pi$
$752$		0			0
$753$	10.3923	+	6.00000i	0.378717	+	0.218652i
$754$		0			0
$755$	32.0000	−	16.0000i	1.16460	−	0.582300i
$756$		0			0
$757$			8.00000i			0.290765i	0.989376	+	0.145382i	$0.0464413\pi$
$757$			8.00000i			0.290765i	−0.989376	+	0.145382i	$0.953559\pi$
$758$		0			0
$759$	−12.0000	+	20.7846i	−0.435572	+	0.754434i
$760$		0			0
$761$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$761$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−2.46410	+	3.73205i	−0.0890898	+	0.134933i
$766$		0			0
$767$	−6.92820	−	4.00000i	−0.250163	−	0.144432i
$768$		0			0
$769$	30.0000			1.08183			0.540914	−	0.841078i	$-0.318079\pi$
$769$	30.0000			1.08183			0.540914	+	0.841078i	$0.318079\pi$
$770$		0			0
$771$	−22.0000			−0.792311
$772$		0			0
$773$	−8.66025	−	5.00000i	−0.311488	−	0.179838i	0.336104	−	0.941825i	$-0.390891\pi$
$773$	−8.66025	−	5.00000i	−0.311488	−	0.179838i	−0.647592	+	0.761987i	$0.724224\pi$
$774$		0			0
$775$	29.7846	+	3.58846i	1.06989	+	0.128901i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$	16.0000	−	27.7128i	0.572525	−	0.991642i
$782$		0			0
$783$		−	6.00000i		−	0.214423i
$784$		0			0
$785$	2.00000	+	4.00000i	0.0713831	+	0.142766i
$786$		0			0
$787$	24.2487	+	14.0000i	0.864373	+	0.499046i	0.865474	−	0.500953i	$-0.167017\pi$
$787$	24.2487	+	14.0000i	0.864373	+	0.499046i	−0.00110111	+	0.999999i	$0.500350\pi$
$788$		0			0
$789$	15.0000	+	25.9808i	0.534014	+	0.924940i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	3.46410	−	2.00000i	0.123014	−	0.0710221i
$794$		0			0
$795$	0.267949	−	4.46410i	0.00950318	−	0.158325i
$796$		0			0
$797$			18.0000i			0.637593i	0.947823	+	0.318796i	$0.103279\pi$
$797$			18.0000i			0.637593i	−0.947823	+	0.318796i	$0.896721\pi$
$798$		0			0
$799$	−8.00000			−0.283020
$800$		0			0
$801$	8.00000	−	13.8564i	0.282666	−	0.489592i
$802$		0			0
$803$	48.4974	−	28.0000i	1.71144	−	0.988099i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	3.46410	−	2.00000i	0.121942	−	0.0704033i
$808$		0			0
$809$	−9.00000	+	15.5885i	−0.316423	+	0.548061i	−0.979739	−	0.200279i	$-0.935815\pi$
$809$	−9.00000	+	15.5885i	−0.316423	+	0.548061i	0.663316	+	0.748340i	$0.269149\pi$
$810$		0			0
$811$	22.0000			0.772524			0.386262	−	0.922389i	$-0.373766\pi$
$811$	22.0000			0.772524			0.386262	+	0.922389i	$0.373766\pi$
$812$		0			0
$813$		−	22.0000i		−	0.771574i
$814$		0			0
$815$	53.5692	+	3.21539i	1.87645	+	0.112630i
$816$		0			0
$817$	−6.92820	+	4.00000i	−0.242387	+	0.139942i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	0.913616	−	0.406578i	$-0.133278\pi$
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	−0.808915	+	0.587925i	$0.799945\pi$
$822$		0			0
$823$	6.92820	+	4.00000i	0.241502	+	0.139431i	0.615867	−	0.787850i	$-0.288806\pi$
$823$	6.92820	+	4.00000i	0.241502	+	0.139431i	−0.374365	+	0.927281i	$0.622139\pi$
$824$		0			0
$825$	−16.0000	−	12.0000i	−0.557048	−	0.417786i
$826$		0			0
$827$		−	30.0000i		−	1.04320i	−0.853189	−	0.521601i	$-0.825335\pi$
$827$		−	30.0000i		−	1.04320i	0.853189	−	0.521601i	$-0.174665\pi$
$828$		0			0
$829$	−19.0000	+	32.9090i	−0.659897	+	1.14298i	0.320745	+	0.947166i	$0.396067\pi$
$829$	−19.0000	+	32.9090i	−0.659897	+	1.14298i	−0.980642	+	0.195810i	$0.937266\pi$
$830$		0			0
$831$	−2.00000	−	3.46410i	−0.0693792	−	0.120168i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−9.85641	+	14.9282i	−0.341095	+	0.516612i
$836$		0			0
$837$	5.19615	+	3.00000i	0.179605	+	0.103695i
$838$		0			0
$839$	−16.0000			−0.552381			−0.276191	−	0.961103i	$-0.589072\pi$
$839$	−16.0000			−0.552381			−0.276191	+	0.961103i	$0.589072\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	8.66025	+	5.00000i	0.298275	+	0.172209i
$844$		0			0
$845$	16.7942	+	11.0885i	0.577739	+	0.381455i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	10.0000	+	17.3205i	0.343199	+	0.594438i
$850$		0			0
$851$	−12.0000	+	20.7846i	−0.411355	+	0.712487i
$852$		0			0
$853$		−	26.0000i		−	0.890223i	−0.895475	−	0.445112i	$-0.853164\pi$
$853$		−	26.0000i		−	0.890223i	0.895475	−	0.445112i	$-0.146836\pi$
$854$		0			0
$855$	−4.00000	+	2.00000i	−0.136797	+	0.0683986i
$856$		0			0
$857$	−8.66025	−	5.00000i	−0.295829	−	0.170797i	0.344739	−	0.938699i	$-0.387967\pi$
$857$	−8.66025	−	5.00000i	−0.295829	−	0.170797i	−0.640567	+	0.767902i	$0.721301\pi$
$858$		0			0
$859$	3.00000	+	5.19615i	0.102359	+	0.177290i	0.912656	−	0.408729i	$-0.134028\pi$
$859$	3.00000	+	5.19615i	0.102359	+	0.177290i	−0.810297	+	0.586019i	$0.800694\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	46.7654	−	27.0000i	1.59191	−	0.919091i	0.598933	−	0.800799i	$-0.295592\pi$
$863$	46.7654	−	27.0000i	1.59191	−	0.919091i	0.992979	−	0.118291i	$-0.0377417\pi$
$864$		0			0
$865$	31.2487	+	1.87564i	1.06249	+	0.0637738i
$866$		0			0
$867$		−	13.0000i		−	0.441503i
$868$		0			0
$869$	−64.0000			−2.17105
$870$		0			0
$871$	−12.0000	+	20.7846i	−0.406604	+	0.704260i
$872$		0			0
$873$	−12.1244	+	7.00000i	−0.410347	+	0.236914i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	31.1769	−	18.0000i	1.05277	−	0.607817i	0.129346	−	0.991600i	$-0.458712\pi$
$877$	31.1769	−	18.0000i	1.05277	−	0.607817i	0.923423	+	0.383783i	$0.125379\pi$
$878$		0			0
$879$	11.0000	−	19.0526i	0.371021	−	0.642627i
$880$		0			0
$881$	36.0000			1.21287			0.606435	−	0.795133i	$-0.292599\pi$
$881$	36.0000			1.21287			0.606435	+	0.795133i	$0.292599\pi$
$882$		0			0
$883$			56.0000i			1.88455i	0.334840	+	0.942275i	$0.391318\pi$
$883$			56.0000i			1.88455i	−0.334840	+	0.942275i	$0.608682\pi$
$884$		0			0
$885$	−8.92820	−	0.535898i	−0.300118	−	0.0180140i
$886$		0			0
$887$	−10.3923	+	6.00000i	−0.348939	+	0.201460i	−0.664218	−	0.747539i	$-0.731235\pi$
$887$	−10.3923	+	6.00000i	−0.348939	+	0.201460i	0.315279	+	0.948999i	$0.397902\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−2.00000	−	3.46410i	−0.0670025	−	0.116052i
$892$		0			0
$893$	−6.92820	−	4.00000i	−0.231843	−	0.133855i
$894$		0			0
$895$	−40.0000	+	20.0000i	−1.33705	+	0.668526i
$896$		0			0
$897$			12.0000i			0.400668i
$898$		0			0
$899$	−18.0000	+	31.1769i	−0.600334	+	1.03981i
$900$		0			0
$901$	−2.00000	−	3.46410i	−0.0666297	−	0.115406i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−41.0526	−	27.1051i	−1.36463	−	0.901005i
$906$		0			0
$907$	6.92820	+	4.00000i	0.230047	+	0.132818i	0.610594	−	0.791944i	$-0.290931\pi$
$907$	6.92820	+	4.00000i	0.230047	+	0.132818i	−0.380547	+	0.924762i	$0.624264\pi$
$908$		0			0
$909$	8.00000			0.265343
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$		0			0
$913$	−55.4256	−	32.0000i	−1.83432	−	1.05905i
$914$		0			0
$915$	2.46410	−	3.73205i	0.0814607	−	0.123378i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	10.0000	+	17.3205i	0.329870	+	0.571351i	0.982486	−	0.186338i	$-0.0596619\pi$
$919$	10.0000	+	17.3205i	0.329870	+	0.571351i	−0.652616	+	0.757689i	$0.726329\pi$
$920$		0			0
$921$	2.00000	−	3.46410i	0.0659022	−	0.114146i
$922$		0			0
$923$		−	16.0000i		−	0.526646i
$924$		0			0
$925$	−16.0000	−	12.0000i	−0.526077	−	0.394558i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−24.0000	−	41.5692i	−0.787414	−	1.36384i	−0.927546	−	0.373709i	$-0.878086\pi$
$929$	−24.0000	−	41.5692i	−0.787414	−	1.36384i	0.140132	−	0.990133i	$-0.455247\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−17.3205	+	10.0000i	−0.567048	+	0.327385i
$934$		0			0
$935$	−17.8564	−	1.07180i	−0.583967	−	0.0350515i
$936$		0			0
$937$		−	10.0000i		−	0.326686i	−0.986569	−	0.163343i	$-0.947772\pi$
$937$		−	10.0000i		−	0.326686i	0.986569	−	0.163343i	$-0.0522277\pi$
$938$		0			0
$939$	22.0000			0.717943
$940$		0			0
$941$	−30.0000	+	51.9615i	−0.977972	+	1.69390i	−0.308215	+	0.951317i	$0.599732\pi$
$941$	−30.0000	+	51.9615i	−0.977972	+	1.69390i	−0.669757	+	0.742581i	$0.733602\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−15.5885	+	9.00000i	−0.506557	+	0.292461i	−0.731417	−	0.681930i	$-0.761141\pi$
$947$	−15.5885	+	9.00000i	−0.506557	+	0.292461i	0.224860	+	0.974391i	$0.427807\pi$
$948$		0			0
$949$	14.0000	−	24.2487i	0.454459	−	0.787146i
$950$		0			0
$951$	−26.0000			−0.843108
$952$		0			0
$953$			6.00000i			0.194359i	0.995267	+	0.0971795i	$0.0309821\pi$
$953$			6.00000i			0.194359i	−0.995267	+	0.0971795i	$0.969018\pi$
$954$		0			0
$955$	1.07180	−	17.8564i	0.0346825	−	0.577820i
$956$		0			0
$957$	20.7846	−	12.0000i	0.671871	−	0.387905i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$		0			0
$963$	15.5885	+	9.00000i	0.502331	+	0.290021i
$964$		0			0
$965$	24.0000	+	48.0000i	0.772587	+	1.54517i
$966$		0			0
$967$		−	36.0000i		−	1.15768i	−0.815440	−	0.578841i	$-0.803505\pi$
$967$		−	36.0000i		−	1.15768i	0.815440	−	0.578841i	$-0.196495\pi$
$968$		0			0
$969$	−2.00000	+	3.46410i	−0.0642493	+	0.111283i
$970$		0			0
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	0.606685	−	0.794943i	$-0.292499\pi$
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	−0.991783	+	0.127933i	$0.959166\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−9.92820	−	1.19615i	−0.317957	−	0.0383075i
$976$		0			0
$977$	36.3731	+	21.0000i	1.16368	+	0.671850i	0.952183	−	0.305530i	$-0.0988335\pi$
$977$	36.3731	+	21.0000i	1.16368	+	0.671850i	0.211495	+	0.977379i	$0.432167\pi$
$978$		0			0
$979$	64.0000			2.04545
$980$		0			0
$981$	18.0000			0.574696
$982$		0			0
$983$	20.7846	+	12.0000i	0.662926	+	0.382741i	0.793391	−	0.608712i	$-0.208314\pi$
$983$	20.7846	+	12.0000i	0.662926	+	0.382741i	−0.130465	+	0.991453i	$0.541647\pi$
$984$		0			0
$985$	−22.1769	+	33.5885i	−0.706615	+	1.07022i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	12.0000	+	20.7846i	0.381578	+	0.660912i
$990$		0			0
$991$	−18.0000	+	31.1769i	−0.571789	+	0.990367i	0.424594	+	0.905384i	$0.360417\pi$
$991$	−18.0000	+	31.1769i	−0.571789	+	0.990367i	−0.996382	+	0.0849833i	$0.972916\pi$
$992$		0			0
$993$			24.0000i			0.761617i
$994$		0			0
$995$	−20.0000	+	10.0000i	−0.634043	+	0.317021i
$996$		0			0
$997$	19.0526	+	11.0000i	0.603401	+	0.348373i	0.770378	−	0.637587i	$-0.220067\pi$
$997$	19.0526	+	11.0000i	0.603401	+	0.348373i	−0.166978	+	0.985961i	$0.553401\pi$
$998$		0			0
$999$	−2.00000	−	3.46410i	−0.0632772	−	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2940.2.bb.f.949.2		4
5.4	even	2	inner	2940.2.bb.f.949.1		4
7.2	even	3	inner	2940.2.bb.f.1549.1		4
7.3	odd	6		420.2.k.b.169.2	yes	2
7.4	even	3		2940.2.k.b.589.1		2
7.5	odd	6		2940.2.bb.a.1549.2		4
7.6	odd	2		2940.2.bb.a.949.1		4
21.17	even	6		1260.2.k.a.1009.2		2
28.3	even	6		1680.2.t.g.1009.1		2
35.3	even	12		2100.2.a.i.1.1		1
35.4	even	6		2940.2.k.b.589.2		2
35.9	even	6	inner	2940.2.bb.f.1549.2		4
35.17	even	12		2100.2.a.n.1.1		1
35.19	odd	6		2940.2.bb.a.1549.1		4
35.24	odd	6		420.2.k.b.169.1	✓	2
35.34	odd	2		2940.2.bb.a.949.2		4
84.59	odd	6		5040.2.t.d.1009.2		2
105.17	odd	12		6300.2.a.b.1.1		1
105.38	odd	12		6300.2.a.r.1.1		1
105.59	even	6		1260.2.k.a.1009.1		2
140.3	odd	12		8400.2.a.bm.1.1		1
140.59	even	6		1680.2.t.g.1009.2		2
140.87	odd	12		8400.2.a.o.1.1		1
420.59	odd	6		5040.2.t.d.1009.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.k.b.169.1	✓	2	35.24	odd	6
420.2.k.b.169.2	yes	2	7.3	odd	6
1260.2.k.a.1009.1		2	105.59	even	6
1260.2.k.a.1009.2		2	21.17	even	6
1680.2.t.g.1009.1		2	28.3	even	6
1680.2.t.g.1009.2		2	140.59	even	6
2100.2.a.i.1.1		1	35.3	even	12
2100.2.a.n.1.1		1	35.17	even	12
2940.2.k.b.589.1		2	7.4	even	3
2940.2.k.b.589.2		2	35.4	even	6
2940.2.bb.a.949.1		4	7.6	odd	2
2940.2.bb.a.949.2		4	35.34	odd	2
2940.2.bb.a.1549.1		4	35.19	odd	6
2940.2.bb.a.1549.2		4	7.5	odd	6
2940.2.bb.f.949.1		4	5.4	even	2	inner
2940.2.bb.f.949.2		4	1.1	even	1	trivial
2940.2.bb.f.1549.1		4	7.2	even	3	inner
2940.2.bb.f.1549.2		4	35.9	even	6	inner
5040.2.t.d.1009.1		2	420.59	odd	6
5040.2.t.d.1009.2		2	84.59	odd	6
6300.2.a.b.1.1		1	105.17	odd	12
6300.2.a.r.1.1		1	105.38	odd	12
8400.2.a.o.1.1		1	140.87	odd	12
8400.2.a.bm.1.1		1	140.3	odd	12

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.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{3} +(1.86603 + 1.23205i) q^{5} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{3} +(1.86603 + 1.23205i) q^{5} +(0.500000 + 0.866025i) q^{9} +(-2.00000 + 3.46410i) q^{11} +2.00000i q^{13} +(1.00000 + 2.00000i) q^{15} +(1.73205 + 1.00000i) q^{17} +(1.00000 + 1.73205i) q^{19} +(5.19615 - 3.00000i) q^{23} +(1.96410 + 4.59808i) q^{25} +1.00000i q^{27} -6.00000 q^{29} +(3.00000 - 5.19615i) q^{31} +(-3.46410 + 2.00000i) q^{33} +(-3.46410 + 2.00000i) q^{37} +(-1.00000 + 1.73205i) q^{39} +4.00000i q^{43} +(-0.133975 + 2.23205i) q^{45} +(-3.46410 + 2.00000i) q^{47} +(1.00000 + 1.73205i) q^{51} +(-1.73205 - 1.00000i) q^{53} +(-8.00000 + 4.00000i) q^{55} +2.00000i q^{57} +(-2.00000 + 3.46410i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(-2.46410 + 3.73205i) q^{65} +(10.3923 + 6.00000i) q^{67} +6.00000 q^{69} -8.00000 q^{71} +(-12.1244 - 7.00000i) q^{73} +(-0.598076 + 4.96410i) q^{75} +(8.00000 + 13.8564i) q^{79} +(-0.500000 + 0.866025i) q^{81} +16.0000i q^{83} +(2.00000 + 4.00000i) q^{85} +(-5.19615 - 3.00000i) q^{87} +(-8.00000 - 13.8564i) q^{89} +(5.19615 - 3.00000i) q^{93} +(-0.267949 + 4.46410i) q^{95} +14.0000i q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{5} + 2 q^{9}+O(q^{10}) \) 4 * q + 4 * q^5 + 2 * q^9	\( 4 q + 4 q^{5} + 2 q^{9} - 8 q^{11} + 4 q^{15} + 4 q^{19} - 6 q^{25} - 24 q^{29} + 12 q^{31} - 4 q^{39} - 4 q^{45} + 4 q^{51} - 32 q^{55} - 8 q^{59} - 4 q^{61} + 4 q^{65} + 24 q^{69} - 32 q^{71} + 8 q^{75} + 32 q^{79} - 2 q^{81} + 8 q^{85} - 32 q^{89} - 8 q^{95} - 16 q^{99}+O(q^{100}) \) 4 * q + 4 * q^5 + 2 * q^9 - 8 * q^11 + 4 * q^15 + 4 * q^19 - 6 * q^25 - 24 * q^29 + 12 * q^31 - 4 * q^39 - 4 * q^45 + 4 * q^51 - 32 * q^55 - 8 * q^59 - 4 * q^61 + 4 * q^65 + 24 * q^69 - 32 * q^71 + 8 * q^75 + 32 * q^79 - 2 * q^81 + 8 * q^85 - 32 * q^89 - 8 * q^95 - 16 * q^99

Introduction

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