LMFDB - Embedded newform 504.2.r.c.169.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(169,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("504.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.r (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			169.3
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	504.169
Dual form			504.2.r.c.337.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11334 - 1.32683i) q^{3} +(1.43969 + 2.49362i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.520945 - 2.95442i) q^{9} +O(q^{10})$	\(q+(1.11334 - 1.32683i) q^{3} +(1.43969 + 2.49362i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.520945 - 2.95442i) q^{9} +(0.592396 - 1.02606i) q^{11} +(2.37939 + 4.12122i) q^{13} +(4.91147 + 0.866025i) q^{15} +5.41147 q^{17} +1.10607 q^{19} +(0.592396 + 1.62760i) q^{21} +(-2.95084 - 5.11100i) q^{23} +(-1.64543 + 2.84997i) q^{25} +(-4.50000 - 2.59808i) q^{27} +(-2.49273 + 4.31753i) q^{29} +(2.78699 + 4.82721i) q^{31} +(-0.701867 - 1.92836i) q^{33} -2.87939 q^{35} -2.42602 q^{37} +(8.11721 + 1.43128i) q^{39} +(-3.81908 - 6.61484i) q^{41} +(3.78699 - 6.55926i) q^{43} +(6.61721 - 5.55250i) q^{45} +(-0.141559 + 0.245188i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(6.02481 - 7.18009i) q^{51} -4.22668 q^{53} +3.41147 q^{55} +(1.23143 - 1.46756i) q^{57} +(-5.86231 - 10.1538i) q^{59} +(-0.992726 + 1.71945i) q^{61} +(2.81908 + 1.02606i) q^{63} +(-6.85117 + 11.8666i) q^{65} +(6.76991 + 11.7258i) q^{67} +(-10.0667 - 1.77503i) q^{69} -5.11381 q^{71} -0.327696 q^{73} +(1.94949 + 5.35619i) q^{75} +(0.592396 + 1.02606i) q^{77} +(5.24763 - 9.08916i) q^{79} +(-8.45723 + 3.07818i) q^{81} +(-3.62701 + 6.28217i) q^{83} +(7.79086 + 13.4942i) q^{85} +(2.95336 + 8.11430i) q^{87} -14.7023 q^{89} -4.75877 q^{91} +(9.50774 + 1.67647i) q^{93} +(1.59240 + 2.75811i) q^{95} +(-9.04710 + 15.6700i) q^{97} +(-3.34002 - 1.21567i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} - 3 q^{7}+O(q^{10}) $ 6 * q + 3 * q^5 - 3 * q^7	$ 6 q + 3 q^{5} - 3 q^{7} + 3 q^{13} + 9 q^{15} + 12 q^{17} - 18 q^{19} - 6 q^{23} + 6 q^{25} - 27 q^{27} + 3 q^{29} + 9 q^{31} - 18 q^{33} - 6 q^{35} - 30 q^{37} + 18 q^{39} - 6 q^{41} + 15 q^{43} + 9 q^{45} - 9 q^{47} - 3 q^{49} + 9 q^{51} - 12 q^{53} + 27 q^{57} - 3 q^{59} + 12 q^{61} - 15 q^{65} + 12 q^{67} - 27 q^{69} + 42 q^{71} + 6 q^{73} + 9 q^{75} + 15 q^{79} + 6 q^{83} + 15 q^{85} - 9 q^{87} - 36 q^{89} - 6 q^{91} + 9 q^{93} + 6 q^{95} - 15 q^{97}+O(q^{100}) $ 6 * q + 3 * q^5 - 3 * q^7 + 3 * q^13 + 9 * q^15 + 12 * q^17 - 18 * q^19 - 6 * q^23 + 6 * q^25 - 27 * q^27 + 3 * q^29 + 9 * q^31 - 18 * q^33 - 6 * q^35 - 30 * q^37 + 18 * q^39 - 6 * q^41 + 15 * q^43 + 9 * q^45 - 9 * q^47 - 3 * q^49 + 9 * q^51 - 12 * q^53 + 27 * q^57 - 3 * q^59 + 12 * q^61 - 15 * q^65 + 12 * q^67 - 27 * q^69 + 42 * q^71 + 6 * q^73 + 9 * q^75 + 15 * q^79 + 6 * q^83 + 15 * q^85 - 9 * q^87 - 36 * q^89 - 6 * q^91 + 9 * q^93 + 6 * q^95 - 15 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.11334	−	1.32683i	0.642788	−	0.766044i
$3$	1.11334	−	1.32683i	0.642788	−	0.766044i
$4$		0			0
$5$	1.43969	+	2.49362i	0.643850	+	1.11518i	0.984566	+	0.175015i	$0.0559973\pi$
$5$	1.43969	+	2.49362i	0.643850	+	1.11518i	−0.340716	+	0.940166i	$0.610669\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$		0			0
$9$	−0.520945	−	2.95442i	−0.173648	−	0.984808i
$10$		0			0
$11$	0.592396	−	1.02606i	0.178614	−	0.309369i	−0.762792	−	0.646644i	$-0.776172\pi$
$11$	0.592396	−	1.02606i	0.178614	−	0.309369i	0.941406	+	0.337275i	$0.109505\pi$
$12$		0			0
$13$	2.37939	+	4.12122i	0.659923	+	1.14302i	0.980635	+	0.195843i	$0.0627443\pi$
$13$	2.37939	+	4.12122i	0.659923	+	1.14302i	−0.320713	+	0.947177i	$0.603922\pi$
$14$		0			0
$15$	4.91147	+	0.866025i	1.26814	+	0.223607i
$16$		0			0
$17$	5.41147			1.31248			0.656238	−	0.754554i	$-0.272147\pi$
$17$	5.41147			1.31248			0.656238	+	0.754554i	$0.272147\pi$
$18$		0			0
$19$	1.10607			0.253749			0.126875	−	0.991919i	$-0.459505\pi$
$19$	1.10607			0.253749			0.126875	+	0.991919i	$0.459505\pi$
$20$		0			0
$21$	0.592396	+	1.62760i	0.129271	+	0.355170i
$22$		0			0
$23$	−2.95084	−	5.11100i	−0.615292	−	1.06572i	−0.990333	−	0.138709i	$-0.955705\pi$
$23$	−2.95084	−	5.11100i	−0.615292	−	1.06572i	0.375041	−	0.927008i	$-0.377629\pi$
$24$		0			0
$25$	−1.64543	+	2.84997i	−0.329086	+	0.569994i
$26$		0			0
$27$	−4.50000	−	2.59808i	−0.866025	−	0.500000i
$28$		0			0
$29$	−2.49273	+	4.31753i	−0.462888	+	0.801745i	−0.999103	−	0.0423361i	$-0.986520\pi$
$29$	−2.49273	+	4.31753i	−0.462888	+	0.801745i	0.536216	+	0.844081i	$0.319853\pi$
$30$		0			0
$31$	2.78699	+	4.82721i	0.500558	+	0.866992i	1.00000		0.000644439i	$0.000205131\pi$
$31$	2.78699	+	4.82721i	0.500558	+	0.866992i	−0.499442	+	0.866347i	$0.666462\pi$
$32$		0			0
$33$	−0.701867	−	1.92836i	−0.122179	−	0.335685i
$34$		0			0
$35$	−2.87939			−0.486705
$36$		0			0
$37$	−2.42602			−0.398836			−0.199418	−	0.979915i	$-0.563905\pi$
$37$	−2.42602			−0.398836			−0.199418	+	0.979915i	$0.563905\pi$
$38$		0			0
$39$	8.11721	+	1.43128i	1.29979	+	0.229189i
$40$		0			0
$41$	−3.81908	−	6.61484i	−0.596440	−	1.03306i	−0.993342	−	0.115203i	$-0.963248\pi$
$41$	−3.81908	−	6.61484i	−0.596440	−	1.03306i	0.396902	−	0.917861i	$-0.370085\pi$
$42$		0			0
$43$	3.78699	−	6.55926i	0.577510	−	1.00028i	−0.418253	−	0.908330i	$-0.637358\pi$
$43$	3.78699	−	6.55926i	0.577510	−	1.00028i	0.995764	−	0.0919470i	$-0.0293090\pi$
$44$		0			0
$45$	6.61721	−	5.55250i	0.986436	−	0.827718i
$46$		0			0
$47$	−0.141559	+	0.245188i	−0.0206485	+	0.0357643i	−0.876165	−	0.482011i	$-0.839906\pi$
$47$	−0.141559	+	0.245188i	−0.0206485	+	0.0357643i	0.855516	+	0.517776i	$0.173240\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$	6.02481	−	7.18009i	0.843643	−	1.00541i
$52$		0			0
$53$	−4.22668			−0.580579			−0.290290	−	0.956939i	$-0.593752\pi$
$53$	−4.22668			−0.580579			−0.290290	+	0.956939i	$0.593752\pi$
$54$		0			0
$55$	3.41147			0.460003
$56$		0			0
$57$	1.23143	−	1.46756i	0.163107	−	0.194383i
$58$		0			0
$59$	−5.86231	−	10.1538i	−0.763208	−	1.32191i	−0.941189	−	0.337881i	$-0.890290\pi$
$59$	−5.86231	−	10.1538i	−0.763208	−	1.32191i	0.177981	−	0.984034i	$-0.443043\pi$
$60$		0			0
$61$	−0.992726	+	1.71945i	−0.127106	+	0.220153i	−0.922554	−	0.385868i	$-0.873902\pi$
$61$	−0.992726	+	1.71945i	−0.127106	+	0.220153i	0.795448	+	0.606021i	$0.207235\pi$
$62$		0			0
$63$	2.81908	+	1.02606i	0.355170	+	0.129271i
$64$		0			0
$65$	−6.85117	+	11.8666i	−0.849783	+	1.47187i
$66$		0			0
$67$	6.76991	+	11.7258i	0.827077	+	1.43254i	0.900322	+	0.435225i	$0.143331\pi$
$67$	6.76991	+	11.7258i	0.827077	+	1.43254i	−0.0732450	+	0.997314i	$0.523336\pi$
$68$		0			0
$69$	−10.0667	−	1.77503i	−1.21189	−	0.213689i
$70$		0			0
$71$	−5.11381			−0.606897			−0.303449	−	0.952848i	$-0.598138\pi$
$71$	−5.11381			−0.606897			−0.303449	+	0.952848i	$0.598138\pi$
$72$		0			0
$73$	−0.327696			−0.0383539			−0.0191770	−	0.999816i	$-0.506105\pi$
$73$	−0.327696			−0.0383539			−0.0191770	+	0.999816i	$0.506105\pi$
$74$		0			0
$75$	1.94949	+	5.35619i	0.225108	+	0.618479i
$76$		0			0
$77$	0.592396	+	1.02606i	0.0675098	+	0.116930i
$78$		0			0
$79$	5.24763	−	9.08916i	0.590404	−	1.02261i	−0.403774	−	0.914859i	$-0.632302\pi$
$79$	5.24763	−	9.08916i	0.590404	−	1.02261i	0.994178	−	0.107751i	$-0.0343649\pi$
$80$		0			0
$81$	−8.45723	+	3.07818i	−0.939693	+	0.342020i
$82$		0			0
$83$	−3.62701	+	6.28217i	−0.398116	+	0.689558i	−0.993494	−	0.113889i	$-0.963669\pi$
$83$	−3.62701	+	6.28217i	−0.398116	+	0.689558i	0.595377	+	0.803446i	$0.297003\pi$
$84$		0			0
$85$	7.79086	+	13.4942i	0.845037	+	1.46365i
$86$		0			0
$87$	2.95336	+	8.11430i	0.316634	+	0.869944i
$88$		0			0
$89$	−14.7023			−1.55844			−0.779222	−	0.626748i	$-0.784386\pi$
$89$	−14.7023			−1.55844			−0.779222	+	0.626748i	$0.784386\pi$
$90$		0			0
$91$	−4.75877			−0.498855
$92$		0			0
$93$	9.50774	+	1.67647i	0.985907	+	0.173842i
$94$		0			0
$95$	1.59240	+	2.75811i	0.163376	+	0.282976i
$96$		0			0
$97$	−9.04710	+	15.6700i	−0.918594	+	1.59105i	−0.117042	+	0.993127i	$0.537341\pi$
$97$	−9.04710	+	15.6700i	−0.918594	+	1.59105i	−0.801552	+	0.597925i	$0.795992\pi$
$98$		0			0
$99$	−3.34002	−	1.21567i	−0.335685	−	0.122179i
$100$		0			0
$101$	8.84389	−	15.3181i	0.880000	−	1.52421i	0.0286612	−	0.999589i	$-0.490876\pi$
$101$	8.84389	−	15.3181i	0.880000	−	1.52421i	0.851339	−	0.524616i	$-0.175791\pi$
$102$		0			0
$103$	−6.58899	−	11.4125i	−0.649233	−	1.12450i	−0.983306	−	0.181957i	$-0.941757\pi$
$103$	−6.58899	−	11.4125i	−0.649233	−	1.12450i	0.334074	−	0.942547i	$-0.391577\pi$
$104$		0			0
$105$	−3.20574	+	3.82045i	−0.312848	+	0.372838i
$106$		0			0
$107$	−13.9513			−1.34872			−0.674362	−	0.738401i	$-0.735581\pi$
$107$	−13.9513			−1.34872			−0.674362	+	0.738401i	$0.735581\pi$
$108$		0			0
$109$	−10.1702			−0.974133			−0.487066	−	0.873365i	$-0.661933\pi$
$109$	−10.1702			−0.974133			−0.487066	+	0.873365i	$0.661933\pi$
$110$		0			0
$111$	−2.70099	+	3.21891i	−0.256367	+	0.305526i
$112$		0			0
$113$	2.83750	+	4.91469i	0.266929	+	0.462335i	0.968067	−	0.250691i	$-0.0806577\pi$
$113$	2.83750	+	4.91469i	0.266929	+	0.462335i	−0.701138	+	0.713026i	$0.747324\pi$
$114$		0			0
$115$	8.49660	−	14.7165i	0.792312	−	1.37232i
$116$		0			0
$117$	10.9363	−	9.17664i	1.01106	−	0.848380i
$118$		0			0
$119$	−2.70574	+	4.68647i	−0.248035	+	0.429608i
$120$		0			0
$121$	4.79813	+	8.31061i	0.436194	+	0.755510i
$122$		0			0
$123$	−13.0287	−	2.29731i	−1.17476	−	0.207141i
$124$		0			0
$125$	4.92127			0.440172
$126$		0			0
$127$	−20.0915			−1.78283			−0.891417	−	0.453184i	$-0.850288\pi$
$127$	−20.0915			−1.78283			−0.891417	+	0.453184i	$0.850288\pi$
$128$		0			0
$129$	−4.48680	−	12.3274i	−0.395040	−	1.08536i
$130$		0			0
$131$	−3.84002	−	6.65111i	−0.335504	−	0.581111i	0.648077	−	0.761575i	$-0.275573\pi$
$131$	−3.84002	−	6.65111i	−0.335504	−	0.581111i	−0.983582	+	0.180464i	$0.942240\pi$
$132$		0			0
$133$	−0.553033	+	0.957882i	−0.0479541	+	0.0830589i
$134$		0			0
$135$		−	14.9617i		−	1.28770i
$136$		0			0
$137$	7.13429	−	12.3569i	0.609523	−	1.05573i	−0.381796	−	0.924247i	$-0.624694\pi$
$137$	7.13429	−	12.3569i	0.609523	−	1.05573i	0.991319	−	0.131478i	$-0.0419724\pi$
$138$		0			0
$139$	7.63950	+	13.2320i	0.647974	+	1.12232i	0.983606	+	0.180331i	$0.0577168\pi$
$139$	7.63950	+	13.2320i	0.647974	+	1.12232i	−0.335632	+	0.941993i	$0.608950\pi$
$140$		0			0
$141$	0.167718	+	0.460802i	0.0141244	+	0.0388066i
$142$		0			0
$143$	5.63816			0.471486
$144$		0			0
$145$	−14.3550			−1.19212
$146$		0			0
$147$	−1.70574	−	0.300767i	−0.140687	−	0.0248069i
$148$		0			0
$149$	7.20826	+	12.4851i	0.590524	+	1.02282i	0.994162	+	0.107899i	$0.0344122\pi$
$149$	7.20826	+	12.4851i	0.590524	+	1.02282i	−0.403638	+	0.914919i	$0.632254\pi$
$150$		0			0
$151$	−5.90420	+	10.2264i	−0.480477	+	0.832211i	−0.999749	−	0.0223984i	$-0.992870\pi$
$151$	−5.90420	+	10.2264i	−0.480477	+	0.832211i	0.519272	+	0.854609i	$0.326203\pi$
$152$		0			0
$153$	−2.81908	−	15.9878i	−0.227909	−	1.29254i
$154$		0			0
$155$	−8.02481	+	13.8994i	−0.644569	+	1.11643i
$156$		0			0
$157$	−6.76011	−	11.7089i	−0.539516	−	0.934469i	−0.998930	−	0.0462468i	$-0.985274\pi$
$157$	−6.76011	−	11.7089i	−0.539516	−	0.934469i	0.459414	−	0.888222i	$-0.348059\pi$
$158$		0			0
$159$	−4.70574	+	5.60808i	−0.373189	+	0.444750i
$160$		0			0
$161$	5.90167			0.465117
$162$		0			0
$163$	23.9641			1.87701			0.938506	−	0.345262i	$-0.112210\pi$
$163$	23.9641			1.87701			0.938506	+	0.345262i	$0.112210\pi$
$164$		0			0
$165$	3.79813	−	4.52644i	0.295684	−	0.352383i
$166$		0			0
$167$	2.48545	+	4.30493i	0.192330	+	0.333125i	0.946022	−	0.324102i	$-0.105062\pi$
$167$	2.48545	+	4.30493i	0.192330	+	0.333125i	−0.753692	+	0.657228i	$0.771729\pi$
$168$		0			0
$169$	−4.82295	+	8.35359i	−0.370996	+	0.642584i
$170$		0			0
$171$	−0.576199	−	3.26779i	−0.0440631	−	0.249894i
$172$		0			0
$173$	12.6099	−	21.8411i	0.958716	−	1.66054i	0.233090	−	0.972455i	$-0.425116\pi$
$173$	12.6099	−	21.8411i	0.958716	−	1.66054i	0.725626	−	0.688089i	$-0.241550\pi$
$174$		0			0
$175$	−1.64543	−	2.84997i	−0.124383	−	0.215437i
$176$		0			0
$177$	−19.9991	−	3.52638i	−1.50323	−	0.265059i
$178$		0			0
$179$	−9.27362			−0.693143			−0.346572	−	0.938024i	$-0.612654\pi$
$179$	−9.27362			−0.693143			−0.346572	+	0.938024i	$0.612654\pi$
$180$		0			0
$181$	13.3327			0.991015			0.495508	−	0.868604i	$-0.334982\pi$
$181$	13.3327			0.991015			0.495508	+	0.868604i	$0.334982\pi$
$182$		0			0
$183$	1.17617	+	3.23151i	0.0869453	+	0.238880i
$184$		0			0
$185$	−3.49273	−	6.04958i	−0.256790	−	0.444774i
$186$		0			0
$187$	3.20574	−	5.55250i	0.234427	−	0.406039i
$188$		0			0
$189$	4.50000	−	2.59808i	0.327327	−	0.188982i
$190$		0			0
$191$	−4.38326	+	7.59202i	−0.317161	+	0.549339i	−0.979895	−	0.199516i	$-0.936063\pi$
$191$	−4.38326	+	7.59202i	−0.317161	+	0.549339i	0.662733	+	0.748856i	$0.269396\pi$
$192$		0			0
$193$	−7.62108	−	13.2001i	−0.548577	−	0.950164i	−0.998372	−	0.0570321i	$-0.981836\pi$
$193$	−7.62108	−	13.2001i	−0.548577	−	0.950164i	0.449795	−	0.893132i	$-0.351497\pi$
$194$		0			0
$195$	8.11721	+	22.3019i	0.581286	+	1.59707i
$196$		0			0
$197$	−8.64496			−0.615928			−0.307964	−	0.951398i	$-0.599648\pi$
$197$	−8.64496			−0.615928			−0.307964	+	0.951398i	$0.599648\pi$
$198$		0			0
$199$	−13.3746			−0.948103			−0.474051	−	0.880497i	$-0.657209\pi$
$199$	−13.3746			−0.948103			−0.474051	+	0.880497i	$0.657209\pi$
$200$		0			0
$201$	23.0954	+	4.07234i	1.62902	+	0.287241i
$202$		0			0
$203$	−2.49273	−	4.31753i	−0.174955	−	0.303031i
$204$		0			0
$205$	10.9966	−	19.0467i	0.768036	−	1.33028i
$206$		0			0
$207$	−13.5628	+	11.3806i	−0.942682	+	0.791004i
$208$		0			0
$209$	0.655230	−	1.13489i	0.0453232	−	0.0785021i
$210$		0			0
$211$	3.64290	+	6.30969i	0.250788	+	0.434377i	0.963743	−	0.266832i	$-0.0859770\pi$
$211$	3.64290	+	6.30969i	0.250788	+	0.434377i	−0.712955	+	0.701210i	$0.752644\pi$
$212$		0			0
$213$	−5.69341	+	6.78514i	−0.390106	+	0.464910i
$214$		0			0
$215$	21.8084			1.48732
$216$		0			0
$217$	−5.57398			−0.378386
$218$		0			0
$219$	−0.364837	+	0.434796i	−0.0246534	+	0.0293808i
$220$		0			0
$221$	12.8760	+	22.3019i	0.866132	+	1.50019i
$222$		0			0
$223$	0.295607	−	0.512007i	0.0197953	−	0.0342865i	−0.855958	−	0.517045i	$-0.827032\pi$
$223$	0.295607	−	0.512007i	0.0197953	−	0.0342865i	0.875753	+	0.482759i	$0.160365\pi$
$224$		0			0
$225$	9.27719	+	3.37662i	0.618479	+	0.225108i
$226$		0			0
$227$	1.74170	−	3.01671i	0.115600	−	0.200226i	−0.802419	−	0.596761i	$-0.796454\pi$
$227$	1.74170	−	3.01671i	0.115600	−	0.200226i	0.918020	+	0.396535i	$0.129787\pi$
$228$		0			0
$229$	12.3007	+	21.3054i	0.812850	+	1.40790i	0.910861	+	0.412713i	$0.135419\pi$
$229$	12.3007	+	21.3054i	0.812850	+	1.40790i	−0.0980107	+	0.995185i	$0.531248\pi$
$230$		0			0
$231$	2.02094	+	0.356347i	0.132968	+	0.0234459i
$232$		0			0
$233$	11.4165			0.747922			0.373961	−	0.927445i	$-0.377999\pi$
$233$	11.4165			0.747922			0.373961	+	0.927445i	$0.377999\pi$
$234$		0			0
$235$	−0.815207			−0.0531783
$236$		0			0
$237$	−6.21735	−	17.0820i	−0.403860	−	1.10960i
$238$		0			0
$239$	−2.04664	−	3.54488i	−0.132386	−	0.229299i	0.792210	−	0.610249i	$-0.208930\pi$
$239$	−2.04664	−	3.54488i	−0.132386	−	0.229299i	−0.924596	+	0.380950i	$0.875597\pi$
$240$		0			0
$241$	3.60354	−	6.24152i	0.232124	−	0.402051i	−0.726309	−	0.687369i	$-0.758766\pi$
$241$	3.60354	−	6.24152i	0.232124	−	0.402051i	0.958433	+	0.285317i	$0.0920990\pi$
$242$		0			0
$243$	−5.33157	+	14.6484i	−0.342020	+	0.939693i
$244$		0			0
$245$	1.43969	−	2.49362i	0.0919786	−	0.159312i
$246$		0			0
$247$	2.63176	+	4.55834i	0.167455	+	0.290040i
$248$		0			0
$249$	4.29726	+	11.8066i	0.272328	+	0.748214i
$250$		0			0
$251$	5.19934			0.328179			0.164090	−	0.986445i	$-0.447531\pi$
$251$	5.19934			0.328179			0.164090	+	0.986445i	$0.447531\pi$
$252$		0			0
$253$	−6.99226			−0.439600
$254$		0			0
$255$	26.5783	+	4.68647i	1.66440	+	0.293478i
$256$		0			0
$257$	6.71688	+	11.6340i	0.418988	+	0.725708i	0.995838	−	0.0911421i	$-0.0290518\pi$
$257$	6.71688	+	11.6340i	0.418988	+	0.725708i	−0.576850	+	0.816850i	$0.695718\pi$
$258$		0			0
$259$	1.21301	−	2.10100i	0.0753728	−	0.130550i
$260$		0			0
$261$	14.0544	+	5.11538i	0.869944	+	0.316634i
$262$		0			0
$263$	5.53849	−	9.59294i	0.341518	−	0.591526i	−0.643197	−	0.765701i	$-0.722392\pi$
$263$	5.53849	−	9.59294i	0.341518	−	0.591526i	0.984715	+	0.174175i	$0.0557258\pi$
$264$		0			0
$265$	−6.08512	−	10.5397i	−0.373806	−	0.647451i
$266$		0			0
$267$	−16.3687	+	19.5075i	−1.00175	+	1.19384i
$268$		0			0
$269$	18.1489			1.10656			0.553279	−	0.832996i	$-0.313376\pi$
$269$	18.1489			1.10656			0.553279	+	0.832996i	$0.313376\pi$
$270$		0			0
$271$	−13.1557			−0.799152			−0.399576	−	0.916700i	$-0.630843\pi$
$271$	−13.1557			−0.799152			−0.399576	+	0.916700i	$0.630843\pi$
$272$		0			0
$273$	−5.29813	+	6.31407i	−0.320658	+	0.382145i
$274$		0			0
$275$	1.94949	+	3.37662i	0.117559	+	0.203618i
$276$		0			0
$277$	11.8983	−	20.6084i	0.714898	−	1.23824i	−0.248101	−	0.968734i	$-0.579807\pi$
$277$	11.8983	−	20.6084i	0.714898	−	1.23824i	0.962999	−	0.269505i	$-0.0868601\pi$
$278$		0			0
$279$	12.8097	−	10.7487i	0.766899	−	0.643505i
$280$		0			0
$281$	−5.99660	+	10.3864i	−0.357727	+	0.619601i	−0.987581	−	0.157112i	$-0.949781\pi$
$281$	−5.99660	+	10.3864i	−0.357727	+	0.619601i	0.629854	+	0.776714i	$0.283115\pi$
$282$		0			0
$283$	−7.63223	−	13.2194i	−0.453689	−	0.785812i	0.544923	−	0.838486i	$-0.316559\pi$
$283$	−7.63223	−	13.2194i	−0.453689	−	0.785812i	−0.998612	+	0.0526741i	$0.983226\pi$
$284$		0			0
$285$	5.43242	+	0.957882i	0.321789	+	0.0567400i
$286$		0			0
$287$	7.63816			0.450866
$288$		0			0
$289$	12.2841			0.722591
$290$		0			0
$291$	10.7189	+	29.4500i	0.628355	+	1.72639i
$292$		0			0
$293$	2.50727	+	4.34273i	0.146477	+	0.253705i	0.929923	−	0.367755i	$-0.119873\pi$
$293$	2.50727	+	4.34273i	0.146477	+	0.253705i	−0.783446	+	0.621459i	$0.786540\pi$
$294$		0			0
$295$	16.8799	−	29.2368i	0.982783	−	1.70223i
$296$		0			0
$297$	−5.33157	+	3.07818i	−0.309369	+	0.178614i
$298$		0			0
$299$	14.0424	−	24.3221i	0.812090	−	1.40658i
$300$		0			0
$301$	3.78699	+	6.55926i	0.218278	+	0.378069i
$302$		0			0
$303$	−10.4782	−	28.7886i	−0.601956	−	1.65386i
$304$		0			0
$305$	−5.71688			−0.327348
$306$		0			0
$307$	15.1310			0.863574			0.431787	−	0.901976i	$-0.357883\pi$
$307$	15.1310			0.863574			0.431787	+	0.901976i	$0.357883\pi$
$308$		0			0
$309$	−22.4782	−	3.96351i	−1.27874	−	0.225476i
$310$		0			0
$311$	2.49407	+	4.31986i	0.141426	+	0.244957i	0.928034	−	0.372496i	$-0.121498\pi$
$311$	2.49407	+	4.31986i	0.141426	+	0.244957i	−0.786608	+	0.617453i	$0.788165\pi$
$312$		0			0
$313$	12.7640	−	22.1079i	0.721463	−	1.24961i	−0.238950	−	0.971032i	$-0.576803\pi$
$313$	12.7640	−	22.1079i	0.721463	−	1.24961i	0.960413	−	0.278579i	$-0.0898634\pi$
$314$		0			0
$315$	1.50000	+	8.50692i	0.0845154	+	0.479311i
$316$		0			0
$317$	2.60694	−	4.51536i	0.146421	−	0.253608i	−0.783481	−	0.621415i	$-0.786558\pi$
$317$	2.60694	−	4.51536i	0.146421	−	0.253608i	0.929902	+	0.367807i	$0.119891\pi$
$318$		0			0
$319$	2.95336	+	5.11538i	0.165357	+	0.286406i
$320$		0			0
$321$	−15.5326	+	18.5110i	−0.866943	+	1.03318i
$322$		0			0
$323$	5.98545			0.333039
$324$		0			0
$325$	−15.6604			−0.868685
$326$		0			0
$327$	−11.3229	+	13.4942i	−0.626160	+	0.746229i
$328$		0			0
$329$	−0.141559	−	0.245188i	−0.00780442	−	0.0135176i
$330$		0			0
$331$	2.07263	−	3.58991i	0.113922	−	0.197319i	−0.803426	−	0.595404i	$-0.796992\pi$
$331$	2.07263	−	3.58991i	0.113922	−	0.197319i	0.917348	+	0.398085i	$0.130325\pi$
$332$		0			0
$333$	1.26382	+	7.16750i	0.0692571	+	0.392776i
$334$		0			0
$335$	−19.4932	+	33.7632i	−1.06503	+	1.84468i
$336$		0			0
$337$	−1.96064	−	3.39592i	−0.106803	−	0.184988i	0.807671	−	0.589634i	$-0.200728\pi$
$337$	−1.96064	−	3.39592i	−0.106803	−	0.184988i	−0.914473	+	0.404646i	$0.867395\pi$
$338$		0			0
$339$	9.68004	+	1.70685i	0.525748	+	0.0927035i
$340$		0			0
$341$	6.60401			0.357627
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	−10.0667	−	27.6580i	−0.541973	−	1.48906i
$346$		0			0
$347$	−6.22534	−	10.7826i	−0.334194	−	0.578840i	0.649136	−	0.760672i	$-0.275131\pi$
$347$	−6.22534	−	10.7826i	−0.334194	−	0.578840i	−0.983330	+	0.181832i	$0.941797\pi$
$348$		0			0
$349$	18.1976	−	31.5191i	0.974094	−	1.68718i	0.291203	−	0.956661i	$-0.405945\pi$
$349$	18.1976	−	31.5191i	0.974094	−	1.68718i	0.682892	−	0.730520i	$-0.260722\pi$
$350$		0			0
$351$		−	24.7273i		−	1.31985i
$352$		0			0
$353$	14.9217	−	25.8452i	0.794204	−	1.37560i	−0.129139	−	0.991626i	$-0.541221\pi$
$353$	14.9217	−	25.8452i	0.794204	−	1.37560i	0.923343	−	0.383975i	$-0.125445\pi$
$354$		0			0
$355$	−7.36231	−	12.7519i	−0.390751	−	0.676800i
$356$		0			0
$357$	3.20574	+	8.80769i	0.169666	+	0.466152i
$358$		0			0
$359$	−17.9540			−0.947575			−0.473788	−	0.880639i	$-0.657114\pi$
$359$	−17.9540			−0.947575			−0.473788	+	0.880639i	$0.657114\pi$
$360$		0			0
$361$	−17.7766			−0.935611
$362$		0			0
$363$	16.3687	+	2.88624i	0.859134	+	0.151489i
$364$		0			0
$365$	−0.471782	−	0.817150i	−0.0246942	−	0.0427716i
$366$		0			0
$367$	−10.5089	+	18.2020i	−0.548561	+	0.950136i	0.449812	+	0.893123i	$0.351491\pi$
$367$	−10.5089	+	18.2020i	−0.548561	+	0.950136i	−0.998373	+	0.0570129i	$0.981842\pi$
$368$		0			0
$369$	−17.5535	+	14.7291i	−0.913799	+	0.766768i
$370$		0			0
$371$	2.11334	−	3.66041i	0.109719	−	0.190039i
$372$		0			0
$373$	14.9376	+	25.8727i	0.773441	+	1.33964i	0.935666	+	0.352886i	$0.114800\pi$
$373$	14.9376	+	25.8727i	0.773441	+	1.33964i	−0.162225	+	0.986754i	$0.551867\pi$
$374$		0			0
$375$	5.47906	−	6.52968i	0.282937	−	0.337191i
$376$		0			0
$377$	−23.7246			−1.22188
$378$		0			0
$379$	0.985452			0.0506193			0.0253096	−	0.999680i	$-0.491943\pi$
$379$	0.985452			0.0506193			0.0253096	+	0.999680i	$0.491943\pi$
$380$		0			0
$381$	−22.3687	+	26.6580i	−1.14598	+	1.36573i
$382$		0			0
$383$	0.994070	+	1.72178i	0.0507946	+	0.0879789i	0.890305	−	0.455365i	$-0.150491\pi$
$383$	0.994070	+	1.72178i	0.0507946	+	0.0879789i	−0.839510	+	0.543344i	$0.817158\pi$
$384$		0			0
$385$	−1.70574	+	2.95442i	−0.0869324	+	0.150571i
$386$		0			0
$387$	−21.3516	−	7.77136i	−1.08536	−	0.395040i
$388$		0			0
$389$	−7.04323	+	12.1992i	−0.357106	+	0.618526i	−0.987476	−	0.157769i	$-0.949570\pi$
$389$	−7.04323	+	12.1992i	−0.357106	+	0.618526i	0.630370	+	0.776295i	$0.282903\pi$
$390$		0			0
$391$	−15.9684	−	27.6580i	−0.807556	−	1.39873i
$392$		0			0
$393$	−13.1001	−	2.30991i	−0.660815	−	0.116519i
$394$		0			0
$395$	30.2199			1.52053
$396$		0			0
$397$	−17.3874			−0.872650			−0.436325	−	0.899789i	$-0.643720\pi$
$397$	−17.3874			−0.872650			−0.436325	+	0.899789i	$0.643720\pi$
$398$		0			0
$399$	0.655230	+	1.80023i	0.0328025	+	0.0901242i
$400$		0			0
$401$	5.86871	+	10.1649i	0.293069	+	0.507611i	0.974534	−	0.224240i	$-0.0719900\pi$
$401$	5.86871	+	10.1649i	0.293069	+	0.507611i	−0.681465	+	0.731851i	$0.738657\pi$
$402$		0			0
$403$	−13.2626	+	22.9716i	−0.660659	+	1.14430i
$404$		0			0
$405$	−19.8516	−	16.6575i	−0.986436	−	0.827718i
$406$		0			0
$407$	−1.43717	+	2.48925i	−0.0712377	+	0.123387i
$408$		0			0
$409$	2.26352	+	3.92053i	0.111924	+	0.193858i	0.916546	−	0.399930i	$-0.130965\pi$
$409$	2.26352	+	3.92053i	0.111924	+	0.193858i	−0.804622	+	0.593787i	$0.797632\pi$
$410$		0			0
$411$	−8.45265	−	23.2235i	−0.416938	−	1.14553i
$412$		0			0
$413$	11.7246			0.576931
$414$		0			0
$415$	−20.8871			−1.02531
$416$		0			0
$417$	26.0620	+	4.59543i	1.27626	+	0.225039i
$418$		0			0
$419$	7.44609	+	12.8970i	0.363765	+	0.630060i	0.988577	−	0.150715i	$-0.0481577\pi$
$419$	7.44609	+	12.8970i	0.363765	+	0.630060i	−0.624812	+	0.780775i	$0.714824\pi$
$420$		0			0
$421$	−13.7875	+	23.8806i	−0.671959	+	1.16387i	0.305388	+	0.952228i	$0.401214\pi$
$421$	−13.7875	+	23.8806i	−0.671959	+	1.16387i	−0.977348	+	0.211640i	$0.932120\pi$
$422$		0			0
$423$	0.798133	+	0.290497i	0.0388066	+	0.0141244i
$424$		0			0
$425$	−8.90420	+	15.4225i	−0.431917	+	0.748102i
$426$		0			0
$427$	−0.992726	−	1.71945i	−0.0480414	−	0.0832101i
$428$		0			0
$429$	6.27719	−	7.48086i	0.303066	−	0.361179i
$430$		0			0
$431$	25.5827			1.23227			0.616137	−	0.787639i	$-0.288697\pi$
$431$	25.5827			1.23227			0.616137	+	0.787639i	$0.288697\pi$
$432$		0			0
$433$	−19.5425			−0.939153			−0.469577	−	0.882892i	$-0.655593\pi$
$433$	−19.5425			−0.939153			−0.469577	+	0.882892i	$0.655593\pi$
$434$		0			0
$435$	−15.9820	+	19.0467i	−0.766281	+	0.913218i
$436$		0			0
$437$	−3.26382	−	5.65311i	−0.156130	−	0.270425i
$438$		0			0
$439$	−4.78359	+	8.28541i	−0.228308	+	0.395441i	−0.957307	−	0.289074i	$-0.906653\pi$
$439$	−4.78359	+	8.28541i	−0.228308	+	0.395441i	0.728999	+	0.684515i	$0.239986\pi$
$440$		0			0
$441$	−2.29813	+	1.92836i	−0.109435	+	0.0918268i
$442$		0			0
$443$	7.92902	−	13.7335i	0.376719	−	0.652496i	−0.613864	−	0.789412i	$-0.710386\pi$
$443$	7.92902	−	13.7335i	0.376719	−	0.652496i	0.990583	+	0.136916i	$0.0437189\pi$
$444$		0			0
$445$	−21.1668	−	36.6620i	−1.00340	−	1.73795i
$446$		0			0
$447$	24.5908	+	4.33602i	1.16311	+	0.205087i
$448$		0			0
$449$	30.0223			1.41684			0.708420	−	0.705791i	$-0.249408\pi$
$449$	30.0223			1.41684			0.708420	+	0.705791i	$0.249408\pi$
$450$		0			0
$451$	−9.04963			−0.426130
$452$		0			0
$453$	6.99525	+	19.2193i	0.328666	+	0.903001i
$454$		0			0
$455$	−6.85117	−	11.8666i	−0.321188	−	0.556313i
$456$		0			0
$457$	8.71554	−	15.0958i	0.407696	−	0.706150i	−0.586935	−	0.809634i	$-0.699666\pi$
$457$	8.71554	−	15.0958i	0.407696	−	0.706150i	0.994631	+	0.103484i	$0.0329991\pi$
$458$		0			0
$459$	−24.3516	−	14.0594i	−1.13664	−	0.656238i
$460$		0			0
$461$	−5.16684	+	8.94923i	−0.240644	+	0.416807i	−0.960898	−	0.276903i	$-0.910692\pi$
$461$	−5.16684	+	8.94923i	−0.240644	+	0.416807i	0.720254	+	0.693710i	$0.244025\pi$
$462$		0			0
$463$	4.67958	+	8.10527i	0.217478	+	0.376684i	0.954036	−	0.299691i	$-0.0968835\pi$
$463$	4.67958	+	8.10527i	0.217478	+	0.376684i	−0.736558	+	0.676374i	$0.763550\pi$
$464$		0			0
$465$	9.50774	+	26.1223i	0.440911	+	1.21139i
$466$		0			0
$467$	24.7273			1.14424			0.572122	−	0.820169i	$-0.306120\pi$
$467$	24.7273			1.14424			0.572122	+	0.820169i	$0.306120\pi$
$468$		0			0
$469$	−13.5398			−0.625211
$470$		0			0
$471$	−23.0620	−	4.06645i	−1.06264	−	0.187372i
$472$		0			0
$473$	−4.48680	−	7.77136i	−0.206303	−	0.357327i
$474$		0			0
$475$	−1.81996	+	3.15225i	−0.0835053	+	0.144635i
$476$		0			0
$477$	2.20187	+	12.4874i	0.100817	+	0.571759i
$478$		0			0
$479$	−19.1425	+	33.1558i	−0.874643	+	1.51493i	−0.0175001	+	0.999847i	$0.505571\pi$
$479$	−19.1425	+	33.1558i	−0.874643	+	1.51493i	−0.857143	+	0.515079i	$0.827763\pi$
$480$		0			0
$481$	−5.77244	−	9.99816i	−0.263201	−	0.455877i
$482$		0			0
$483$	6.57057	−	7.83051i	0.298971	−	0.356300i
$484$		0			0
$485$	−52.1002			−2.36575
$486$		0			0
$487$	1.29498			0.0586811			0.0293405	−	0.999569i	$-0.490659\pi$
$487$	1.29498			0.0586811			0.0293405	+	0.999569i	$0.490659\pi$
$488$		0			0
$489$	26.6802	−	31.7962i	1.20652	−	1.43788i
$490$		0			0
$491$	−11.7160	−	20.2927i	−0.528736	−	0.915797i	−0.999439	−	0.0335055i	$-0.989333\pi$
$491$	−11.7160	−	20.2927i	−0.528736	−	0.915797i	0.470703	−	0.882292i	$-0.344000\pi$
$492$		0			0
$493$	−13.4893	+	23.3642i	−0.607529	+	1.05227i
$494$		0			0
$495$	−1.77719	−	10.0789i	−0.0798787	−	0.453015i
$496$		0			0
$497$	2.55690	−	4.42869i	0.114693	−	0.198654i
$498$		0			0
$499$	17.3773	+	30.0984i	0.777916	+	1.34739i	0.933141	+	0.359511i	$0.117056\pi$
$499$	17.3773	+	30.0984i	0.777916	+	1.34739i	−0.155225	+	0.987879i	$0.549610\pi$
$500$		0			0
$501$	8.47906	+	1.49509i	0.378816	+	0.0667955i
$502$		0			0
$503$	8.61318			0.384043			0.192021	−	0.981391i	$-0.438496\pi$
$503$	8.61318			0.384043			0.192021	+	0.981391i	$0.438496\pi$
$504$		0			0
$505$	50.9299			2.26635
$506$		0			0
$507$	5.71419	+	15.6996i	0.253776	+	0.697244i
$508$		0			0
$509$	4.58125	+	7.93496i	0.203060	+	0.351711i	0.949513	−	0.313728i	$-0.101578\pi$
$509$	4.58125	+	7.93496i	0.203060	+	0.351711i	−0.746453	+	0.665439i	$0.768245\pi$
$510$		0			0
$511$	0.163848	−	0.283793i	0.00724821	−	0.0125543i
$512$		0			0
$513$	−4.97730	−	2.87365i	−0.219753	−	0.126875i
$514$		0			0
$515$	18.9722	−	32.8609i	0.836017	−	1.44802i
$516$		0			0
$517$	0.167718	+	0.290497i	0.00737625	+	0.0127760i
$518$		0			0
$519$	−14.9402	−	41.0478i	−0.655800	−	1.80180i
$520$		0			0
$521$	−9.13846			−0.400363			−0.200182	−	0.979759i	$-0.564153\pi$
$521$	−9.13846			−0.400363			−0.200182	+	0.979759i	$0.564153\pi$
$522$		0			0
$523$	−11.8821			−0.519567			−0.259783	−	0.965667i	$-0.583651\pi$
$523$	−11.8821			−0.519567			−0.259783	+	0.965667i	$0.583651\pi$
$524$		0			0
$525$	−5.61334	−	0.989783i	−0.244986	−	0.0431977i
$526$		0			0
$527$	15.0817	+	26.1223i	0.656970	+	1.13791i
$528$		0			0
$529$	−5.91488	+	10.2449i	−0.257169	+	0.445429i
$530$		0			0
$531$	−26.9447	+	22.6093i	−1.16930	+	0.981161i
$532$		0			0
$533$	18.1741	−	31.4785i	0.787208	−	1.36348i
$534$		0			0
$535$	−20.0856	−	34.7893i	−0.868376	−	1.50407i
$536$		0			0
$537$	−10.3247	+	12.3045i	−0.445544	+	0.530978i
$538$		0			0
$539$	−1.18479			−0.0510326
$540$		0			0
$541$	16.9763			0.729867			0.364934	−	0.931034i	$-0.381092\pi$
$541$	16.9763			0.729867			0.364934	+	0.931034i	$0.381092\pi$
$542$		0			0
$543$	14.8439	−	17.6903i	0.637012	−	0.759162i
$544$		0			0
$545$	−14.6420	−	25.3607i	−0.627195	−	1.08633i
$546$		0			0
$547$	−0.830222	+	1.43799i	−0.0354977	+	0.0614839i	−0.883228	−	0.468943i	$-0.844635\pi$
$547$	−0.830222	+	1.43799i	−0.0354977	+	0.0614839i	0.847731	+	0.530427i	$0.177968\pi$
$548$		0			0
$549$	5.59714	+	2.03719i	0.238880	+	0.0869453i
$550$		0			0
$551$	−2.75712	+	4.77547i	−0.117457	+	0.203442i
$552$		0			0
$553$	5.24763	+	9.08916i	0.223152	+	0.386510i
$554$		0			0
$555$	−11.9153	−	2.10100i	−0.505778	−	0.0891823i
$556$		0			0
$557$	−23.0455			−0.976470			−0.488235	−	0.872712i	$-0.662359\pi$
$557$	−23.0455			−0.976470			−0.488235	+	0.872712i	$0.662359\pi$
$558$		0			0
$559$	36.0428			1.52445
$560$		0			0
$561$	−3.79813	−	10.4353i	−0.160357	−	0.440578i
$562$		0			0
$563$	−13.6985	−	23.7264i	−0.577321	−	0.999950i	−0.995785	−	0.0917165i	$-0.970765\pi$
$563$	−13.6985	−	23.7264i	−0.577321	−	0.999950i	0.418464	−	0.908233i	$-0.362569\pi$
$564$		0			0
$565$	−8.17024	+	14.1513i	−0.343725	+	0.595349i
$566$		0			0
$567$	1.56283	−	8.86327i	0.0656328	−	0.372222i
$568$		0			0
$569$	−20.1732	+	34.9411i	−0.845706	+	1.46481i	0.0393005	+	0.999227i	$0.487487\pi$
$569$	−20.1732	+	34.9411i	−0.845706	+	1.46481i	−0.885007	+	0.465579i	$0.845846\pi$
$570$		0			0
$571$	−2.52182	−	4.36792i	−0.105535	−	0.182792i	0.808422	−	0.588604i	$-0.200322\pi$
$571$	−2.52182	−	4.36792i	−0.105535	−	0.182792i	−0.913957	+	0.405812i	$0.866989\pi$
$572$		0			0
$573$	5.19325	+	14.2683i	0.216951	+	0.596068i
$574$		0			0
$575$	19.4216			0.809936
$576$		0			0
$577$	8.95037			0.372609			0.186304	−	0.982492i	$-0.440349\pi$
$577$	8.95037			0.372609			0.186304	+	0.982492i	$0.440349\pi$
$578$		0			0
$579$	−25.9991	−	4.58435i	−1.08049	−	0.190519i
$580$		0			0
$581$	−3.62701	−	6.28217i	−0.150474	−	0.260628i
$582$		0			0
$583$	−2.50387	+	4.33683i	−0.103700	+	0.179613i
$584$		0			0
$585$	38.6279	+	14.0594i	1.59707	+	0.581286i
$586$		0			0
$587$	−21.4572	+	37.1650i	−0.885635	+	1.53396i	−0.0406505	+	0.999173i	$0.512943\pi$
$587$	−21.4572	+	37.1650i	−0.885635	+	1.53396i	−0.844984	+	0.534791i	$0.820390\pi$
$588$		0			0
$589$	3.08260	+	5.33921i	0.127016	+	0.219998i
$590$		0			0
$591$	−9.62479	+	11.4704i	−0.395911	+	0.471828i
$592$		0			0
$593$	−20.6081			−0.846274			−0.423137	−	0.906066i	$-0.639071\pi$
$593$	−20.6081			−0.846274			−0.423137	+	0.906066i	$0.639071\pi$
$594$		0			0
$595$	−15.5817			−0.638788
$596$		0			0
$597$	−14.8905	+	17.7458i	−0.609429	+	0.726289i
$598$		0			0
$599$	10.5321	+	18.2421i	0.430329	+	0.745353i	0.996902	−	0.0786597i	$-0.0250640\pi$
$599$	10.5321	+	18.2421i	0.430329	+	0.745353i	−0.566572	+	0.824012i	$0.691731\pi$
$600$		0			0
$601$	−8.95424	+	15.5092i	−0.365251	+	0.632633i	−0.988816	−	0.149138i	$-0.952350\pi$
$601$	−8.95424	+	15.5092i	−0.365251	+	0.632633i	0.623565	+	0.781771i	$0.285684\pi$
$602$		0			0
$603$	31.1163	−	26.1097i	1.26716	−	1.06327i
$604$		0			0
$605$	−13.8157	+	23.9294i	−0.561687	+	0.972870i
$606$		0			0
$607$	17.7618	+	30.7643i	0.720928	+	1.24868i	0.960628	+	0.277837i	$0.0896174\pi$
$607$	17.7618	+	30.7643i	0.720928	+	1.24868i	−0.239701	+	0.970847i	$0.577049\pi$
$608$		0			0
$609$	−8.50387	−	1.49946i	−0.344594	−	0.0607613i
$610$		0			0
$611$	−1.34730			−0.0545058
$612$		0			0
$613$	−2.19253			−0.0885556			−0.0442778	−	0.999019i	$-0.514099\pi$
$613$	−2.19253			−0.0885556			−0.0442778	+	0.999019i	$0.514099\pi$
$614$		0			0
$615$	−13.0287	−	35.7960i	−0.525367	−	1.44343i
$616$		0			0
$617$	11.7258	+	20.3097i	0.472063	+	0.817637i	0.999489	−	0.0319637i	$-0.0101761\pi$
$617$	11.7258	+	20.3097i	0.472063	+	0.817637i	−0.527426	+	0.849601i	$0.676843\pi$
$618$		0			0
$619$	7.52481	−	13.0334i	0.302448	−	0.523855i	−0.674242	−	0.738510i	$-0.735530\pi$
$619$	7.52481	−	13.0334i	0.302448	−	0.523855i	0.976690	+	0.214655i	$0.0688629\pi$
$620$		0			0
$621$			30.6660i			1.23058i
$622$		0			0
$623$	7.35117	−	12.7326i	0.294518	−	0.510121i
$624$		0			0
$625$	15.3123	+	26.5216i	0.612491	+	1.06087i
$626$		0			0
$627$	−0.776311	−	2.13290i	−0.0310029	−	0.0851797i
$628$		0			0
$629$	−13.1284			−0.523462
$630$		0			0
$631$	0.854408			0.0340135			0.0170067	−	0.999855i	$-0.494586\pi$
$631$	0.854408			0.0340135			0.0170067	+	0.999855i	$0.494586\pi$
$632$		0			0
$633$	12.4277	+	2.19133i	0.493956	+	0.0870977i
$634$		0			0
$635$	−28.9256	−	50.1006i	−1.14788	−	1.98818i
$636$		0			0
$637$	2.37939	−	4.12122i	0.0942747	−	0.163289i
$638$		0			0
$639$	2.66401	+	15.1084i	0.105387	+	0.597677i
$640$		0			0
$641$	−9.58630	+	16.6040i	−0.378636	+	0.655817i	−0.990864	−	0.134864i	$-0.956940\pi$
$641$	−9.58630	+	16.6040i	−0.378636	+	0.655817i	0.612228	+	0.790681i	$0.290274\pi$
$642$		0			0
$643$	−16.7562	−	29.0227i	−0.660802	−	1.14454i	−0.980405	−	0.196991i	$-0.936883\pi$
$643$	−16.7562	−	29.0227i	−0.660802	−	1.14454i	0.319604	−	0.947551i	$-0.396450\pi$
$644$		0			0
$645$	24.2802	−	28.9360i	0.956031	−	1.13935i
$646$		0			0
$647$	−20.0966			−0.790078			−0.395039	−	0.918664i	$-0.629269\pi$
$647$	−20.0966			−0.790078			−0.395039	+	0.918664i	$0.629269\pi$
$648$		0			0
$649$	−13.8912			−0.545279
$650$		0			0
$651$	−6.20574	+	7.39571i	−0.243222	+	0.289861i
$652$		0			0
$653$	−9.16179	−	15.8687i	−0.358528	−	0.620990i	0.629187	−	0.777254i	$-0.283388\pi$
$653$	−9.16179	−	15.8687i	−0.358528	−	0.620990i	−0.987715	+	0.156265i	$0.950055\pi$
$654$		0			0
$655$	11.0569	−	19.1511i	0.432029	−	0.748296i
$656$		0			0
$657$	0.170711	+	0.968153i	0.00666009	+	0.0377712i
$658$		0			0
$659$	−6.45976	+	11.1886i	−0.251637	+	0.435847i	−0.963977	−	0.265987i	$-0.914302\pi$
$659$	−6.45976	+	11.1886i	−0.251637	+	0.435847i	0.712340	+	0.701835i	$0.247635\pi$
$660$		0			0
$661$	−1.91101	−	3.30996i	−0.0743296	−	0.128743i	0.826465	−	0.562988i	$-0.190348\pi$
$661$	−1.91101	−	3.30996i	−0.0743296	−	0.128743i	−0.900795	+	0.434246i	$0.857015\pi$
$662$		0			0
$663$	43.9261	+	7.74535i	1.70595	+	0.300805i
$664$		0			0
$665$	−3.18479			−0.123501
$666$		0			0
$667$	29.4225			1.13924
$668$		0			0
$669$	−0.350233	−	0.962258i	−0.0135408	−	0.0372030i
$670$		0			0
$671$	1.17617	+	2.03719i	0.0454057	+	0.0786450i
$672$		0			0
$673$	19.8045	−	34.3025i	0.763409	−	1.32226i	−0.177675	−	0.984089i	$-0.556858\pi$
$673$	19.8045	−	34.3025i	0.763409	−	1.32226i	0.941084	−	0.338173i	$-0.109809\pi$
$674$		0			0
$675$	14.8089	−	8.54990i	0.569994	−	0.329086i
$676$		0			0
$677$	13.1600	−	22.7937i	0.505779	−	0.876035i	−0.494199	−	0.869349i	$-0.664538\pi$
$677$	13.1600	−	22.7937i	0.505779	−	0.876035i	0.999978	−	0.00668595i	$-0.00212822\pi$
$678$		0			0
$679$	−9.04710	−	15.6700i	−0.347196	−	0.601361i
$680$		0			0
$681$	−2.06355	−	5.66955i	−0.0790754	−	0.217258i
$682$		0			0
$683$	25.2080			0.964558			0.482279	−	0.876018i	$-0.339809\pi$
$683$	25.2080			0.964558			0.482279	+	0.876018i	$0.339809\pi$
$684$		0			0
$685$	41.0847			1.56977
$686$		0			0
$687$	41.9634	+	7.39928i	1.60100	+	0.282300i
$688$		0			0
$689$	−10.0569	−	17.4191i	−0.383138	−	0.663614i
$690$		0			0
$691$	−9.29473	+	16.0989i	−0.353588	+	0.612433i	−0.986875	−	0.161484i	$-0.948372\pi$
$691$	−9.29473	+	16.0989i	−0.353588	+	0.612433i	0.633287	+	0.773917i	$0.281705\pi$
$692$		0			0
$693$	2.72281	−	2.28471i	0.103431	−	0.0867890i
$694$		0			0
$695$	−21.9971	+	38.1000i	−0.834396	+	1.44522i
$696$		0			0
$697$	−20.6668	−	35.7960i	−0.782812	−	1.35587i
$698$		0			0
$699$	12.7105	−	15.1478i	0.480755	−	0.572941i
$700$		0			0
$701$	−47.8580			−1.80757			−0.903786	−	0.427984i	$-0.859224\pi$
$701$	−47.8580			−1.80757			−0.903786	+	0.427984i	$0.859224\pi$
$702$		0			0
$703$	−2.68334			−0.101204
$704$		0			0
$705$	−0.907604	+	1.08164i	−0.0341823	+	0.0407369i
$706$		0			0
$707$	8.84389	+	15.3181i	0.332609	+	0.576095i
$708$		0			0
$709$	4.69965	−	8.14002i	0.176499	−	0.305705i	−0.764180	−	0.645003i	$-0.776856\pi$
$709$	4.69965	−	8.14002i	0.176499	−	0.305705i	0.940679	+	0.339298i	$0.110189\pi$
$710$		0			0
$711$	−29.5869	−	10.7688i	−1.10960	−	0.403860i
$712$		0			0
$713$	16.4479	−	28.4886i	0.615979	−	1.06691i
$714$		0			0
$715$	8.11721	+	14.0594i	0.303566	+	0.525793i
$716$		0			0
$717$	−6.98205	−	1.23112i	−0.260749	−	0.0459772i
$718$		0			0
$719$	10.6895			0.398653			0.199326	−	0.979933i	$-0.436125\pi$
$719$	10.6895			0.398653			0.199326	+	0.979933i	$0.436125\pi$
$720$		0			0
$721$	13.1780			0.490774
$722$		0			0
$723$	−4.26945	−	11.7302i	−0.158782	−	0.436251i
$724$		0			0
$725$	−8.20321	−	14.2084i	−0.304660	−	0.527686i
$726$		0			0
$727$	−25.5458	+	44.2466i	−0.947440	+	1.64101i	−0.196649	+	0.980474i	$0.563006\pi$
$727$	−25.5458	+	44.2466i	−0.947440	+	1.64101i	−0.750791	+	0.660540i	$0.770327\pi$
$728$		0			0
$729$	13.5000	+	23.3827i	0.500000	+	0.866025i
$730$		0			0
$731$	20.4932	−	35.4953i	0.757968	−	1.31284i
$732$		0			0
$733$	−17.3949	−	30.1288i	−0.642494	−	1.11283i	−0.984874	−	0.173271i	$-0.944566\pi$
$733$	−17.3949	−	30.1288i	−0.642494	−	1.11283i	0.342380	−	0.939562i	$-0.388767\pi$
$734$		0			0
$735$	−1.70574	−	4.68647i	−0.0629171	−	0.172863i
$736$		0			0
$737$	16.0419			0.590911
$738$		0			0
$739$	41.9469			1.54304			0.771520	−	0.636205i	$-0.219497\pi$
$739$	41.9469			1.54304			0.771520	+	0.636205i	$0.219497\pi$
$740$		0			0
$741$	8.97818	+	1.58310i	0.329822	+	0.0581564i
$742$		0			0
$743$	8.05809	+	13.9570i	0.295622	+	0.512033i	0.975130	−	0.221636i	$-0.0711396\pi$
$743$	8.05809	+	13.9570i	0.295622	+	0.512033i	−0.679507	+	0.733669i	$0.737806\pi$
$744$		0			0
$745$	−20.7554	+	35.9494i	−0.760418	+	1.31708i
$746$		0			0
$747$	20.4497	+	7.44307i	0.748214	+	0.272328i
$748$		0			0
$749$	6.97565	−	12.0822i	0.254885	−	0.441473i
$750$		0			0
$751$	25.6746	+	44.4697i	0.936879	+	1.62272i	0.771249	+	0.636534i	$0.219632\pi$
$751$	25.6746	+	44.4697i	0.936879	+	1.62272i	0.165630	+	0.986188i	$0.447034\pi$
$752$		0			0
$753$	5.78864	−	6.89863i	0.210950	−	0.251400i
$754$		0			0
$755$	−34.0009			−1.23742
$756$		0			0
$757$	16.8553			0.612618			0.306309	−	0.951932i	$-0.400906\pi$
$757$	16.8553			0.612618			0.306309	+	0.951932i	$0.400906\pi$
$758$		0			0
$759$	−7.78477	+	9.27752i	−0.282569	+	0.336753i
$760$		0			0
$761$	1.42333	+	2.46529i	0.0515958	+	0.0893666i	0.890670	−	0.454651i	$-0.150236\pi$
$761$	1.42333	+	2.46529i	0.0515958	+	0.0893666i	−0.839074	+	0.544017i	$0.816903\pi$
$762$		0			0
$763$	5.08512	−	8.80769i	0.184094	−	0.318860i
$764$		0			0
$765$	35.8089	−	30.0472i	1.29467	−	1.08636i
$766$		0			0
$767$	27.8974	−	48.3197i	1.00732	−	1.74472i
$768$		0			0
$769$	18.9149	+	32.7616i	0.682090	+	1.18141i	0.974342	+	0.225073i	$0.0722621\pi$
$769$	18.9149	+	32.7616i	0.682090	+	1.18141i	−0.292252	+	0.956341i	$0.594405\pi$
$770$		0			0
$771$	22.9145	+	4.04044i	0.825244	+	0.145513i
$772$		0			0
$773$	2.87702			0.103479			0.0517396	−	0.998661i	$-0.483523\pi$
$773$	2.87702			0.103479			0.0517396	+	0.998661i	$0.483523\pi$
$774$		0			0
$775$	−18.3432			−0.658906
$776$		0			0
$777$	−1.43717	−	3.94858i	−0.0515581	−	0.141655i
$778$		0			0
$779$	−4.22416	−	7.31645i	−0.151346	−	0.262139i
$780$		0			0
$781$	−3.02940	+	5.24708i	−0.108400	+	0.187755i
$782$		0			0
$783$	22.4345	−	12.9526i	0.801745	−	0.462888i
$784$		0			0
$785$	19.4650	−	33.7143i	0.694735	−	1.20332i
$786$		0			0
$787$	13.0710	+	22.6397i	0.465932	+	0.807018i	0.999243	−	0.0389010i	$-0.0123857\pi$
$787$	13.0710	+	22.6397i	0.465932	+	0.807018i	−0.533311	+	0.845919i	$0.679052\pi$
$788$		0			0
$789$	−6.56196	−	18.0288i	−0.233612	−	0.641843i
$790$		0			0
$791$	−5.67499			−0.201779
$792$		0			0
$793$	−9.44831			−0.335519
$794$		0			0
$795$	−20.7592	−	3.66041i	−0.736254	−	0.129821i
$796$		0			0
$797$	13.4568	+	23.3078i	0.476663	+	0.825605i	0.999642	−	0.0267406i	$-0.00851282\pi$
$797$	13.4568	+	23.3078i	0.476663	+	0.825605i	−0.522979	+	0.852345i	$0.675179\pi$
$798$		0			0
$799$	−0.766044	+	1.32683i	−0.0271007	+	0.0469398i
$800$		0			0
$801$	7.65910	+	43.4369i	0.270621	+	1.53477i
$802$		0			0
$803$	−0.194126	+	0.336236i	−0.00685055	+	0.0118655i
$804$		0			0
$805$	8.49660	+	14.7165i	0.299466	+	0.518690i
$806$		0			0
$807$	20.2059	−	24.0805i	0.711281	−	0.847672i
$808$		0			0
$809$	−32.4228			−1.13993			−0.569963	−	0.821670i	$-0.693043\pi$
$809$	−32.4228			−1.13993			−0.569963	+	0.821670i	$0.693043\pi$
$810$		0			0
$811$	21.2754			0.747080			0.373540	−	0.927614i	$-0.378144\pi$
$811$	21.2754			0.747080			0.373540	+	0.927614i	$0.378144\pi$
$812$		0			0
$813$	−14.6468	+	17.4553i	−0.513685	+	0.612186i
$814$		0			0
$815$	34.5009	+	59.7574i	1.20851	+	2.09321i
$816$		0			0
$817$	4.18866	−	7.25498i	0.146543	−	0.253820i
$818$		0			0
$819$	2.47906	+	14.0594i	0.0866252	+	0.491276i
$820$		0			0
$821$	−24.9354	+	43.1894i	−0.870252	+	1.50732i	−0.00851573	+	0.999964i	$0.502711\pi$
$821$	−24.9354	+	43.1894i	−0.870252	+	1.50732i	−0.861736	+	0.507357i	$0.830623\pi$
$822$		0			0
$823$	9.47296	+	16.4077i	0.330207	+	0.571935i	0.982552	−	0.185987i	$-0.0595482\pi$
$823$	9.47296	+	16.4077i	0.330207	+	0.571935i	−0.652345	+	0.757922i	$0.726215\pi$
$824$		0			0
$825$	6.65064	+	1.17269i	0.231546	+	0.0408278i
$826$		0			0
$827$	−12.1489			−0.422458			−0.211229	−	0.977437i	$-0.567747\pi$
$827$	−12.1489			−0.422458			−0.211229	+	0.977437i	$0.567747\pi$
$828$		0			0
$829$	11.2189			0.389650			0.194825	−	0.980838i	$-0.437586\pi$
$829$	11.2189			0.389650			0.194825	+	0.980838i	$0.437586\pi$
$830$		0			0
$831$	−14.0970	−	38.7311i	−0.489019	−	1.34357i
$832$		0			0
$833$	−2.70574	−	4.68647i	−0.0937482	−	0.162377i
$834$		0			0
$835$	−7.15657	+	12.3955i	−0.247663	+	0.428966i
$836$		0			0
$837$		−	28.9632i		−	1.00112i
$838$		0			0
$839$	2.63516	−	4.56424i	0.0909759	−	0.157575i	−0.816946	−	0.576714i	$-0.804335\pi$
$839$	2.63516	−	4.56424i	0.0909759	−	0.157575i	0.907922	+	0.419139i	$0.137668\pi$
$840$		0			0
$841$	2.07263	+	3.58991i	0.0714701	+	0.123790i
$842$		0			0
$843$	7.10472	+	19.5201i	0.244700	+	0.672307i
$844$		0			0
$845$	−27.7743			−0.955463
$846$		0			0
$847$	−9.59627			−0.329732
$848$		0			0
$849$	−26.0371	−	4.59105i	−0.893592	−	0.157564i
$850$		0			0
$851$	7.15880	+	12.3994i	0.245400	+	0.425046i
$852$		0			0
$853$	1.94222	−	3.36402i	0.0665003	−	0.115182i	−0.830858	−	0.556484i	$-0.812150\pi$
$853$	1.94222	−	3.36402i	0.0665003	−	0.115182i	0.897359	+	0.441302i	$0.145483\pi$
$854$		0			0
$855$	7.31908	−	6.14144i	0.250307	−	0.210033i
$856$		0			0
$857$	−9.50253	+	16.4589i	−0.324600	+	0.562224i	−0.981431	−	0.191814i	$-0.938563\pi$
$857$	−9.50253	+	16.4589i	−0.324600	+	0.562224i	0.656831	+	0.754038i	$0.271896\pi$
$858$		0			0
$859$	25.4513	+	44.0830i	0.868387	+	1.50409i	0.863644	+	0.504102i	$0.168176\pi$
$859$	25.4513	+	44.0830i	0.868387	+	1.50409i	0.00474324	+	0.999989i	$0.498490\pi$
$860$		0			0
$861$	8.50387	−	10.1345i	0.289811	−	0.345383i
$862$		0			0
$863$	12.7615			0.434405			0.217203	−	0.976127i	$-0.430307\pi$
$863$	12.7615			0.434405			0.217203	+	0.976127i	$0.430307\pi$
$864$		0			0
$865$	72.6177			2.46908
$866$		0			0
$867$	13.6763	−	16.2988i	0.464473	−	0.553537i
$868$		0			0
$869$	−6.21735	−	10.7688i	−0.210909	−	0.365305i
$870$		0			0
$871$	−32.2165	+	55.8006i	−1.09161	+	1.89073i
$872$		0			0
$873$	51.0090	+	18.5658i	1.72639	+	0.628355i
$874$		0			0
$875$	−2.46064	+	4.26195i	−0.0831847	+	0.144080i
$876$		0			0
$877$	−7.12226	−	12.3361i	−0.240502	−	0.416561i	0.720356	−	0.693605i	$-0.243979\pi$
$877$	−7.12226	−	12.3361i	−0.240502	−	0.416561i	−0.960857	+	0.277044i	$0.910645\pi$
$878$		0			0
$879$	8.55350	+	1.50821i	0.288502	+	0.0508708i
$880$		0			0
$881$	38.3286			1.29132			0.645662	−	0.763623i	$-0.276581\pi$
$881$	38.3286			1.29132			0.645662	+	0.763623i	$0.276581\pi$
$882$		0			0
$883$	−42.6483			−1.43523			−0.717614	−	0.696441i	$-0.754766\pi$
$883$	−42.6483			−1.43523			−0.717614	+	0.696441i	$0.754766\pi$
$884$		0			0
$885$	−19.9991	−	54.9471i	−0.672263	−	1.84703i
$886$		0			0
$887$	−11.2117	−	19.4192i	−0.376451	−	0.652032i	0.614092	−	0.789234i	$-0.289522\pi$
$887$	−11.2117	−	19.4192i	−0.376451	−	0.652032i	−0.990543	+	0.137202i	$0.956189\pi$
$888$		0			0
$889$	10.0458	−	17.3998i	0.336924	−	0.583569i
$890$		0			0
$891$	−1.85163	+	10.5011i	−0.0620321	+	0.351801i
$892$		0			0
$893$	−0.156574	+	0.271194i	−0.00523955	+	0.00907517i
$894$		0			0
$895$	−13.3512	−	23.1249i	−0.446280	−	0.772980i
$896$		0			0
$897$	−16.6373	−	45.7105i	−0.555503	−	1.52623i
$898$		0			0
$899$	−27.7888			−0.926808
$900$		0			0
$901$	−22.8726			−0.761996
$902$		0			0
$903$	12.9192	+	2.27801i	0.429925	+	0.0758073i
$904$		0			0
$905$	19.1951	+	33.2468i	0.638065	+	1.10516i
$906$		0			0
$907$	−21.6584	+	37.5134i	−0.719155	+	1.24561i	0.242180	+	0.970231i	$0.422137\pi$
$907$	−21.6584	+	37.5134i	−0.719155	+	1.24561i	−0.961335	+	0.275381i	$0.911196\pi$
$908$		0			0
$909$	−49.8632	−	18.1487i	−1.65386	−	0.601956i
$910$		0			0
$911$	−4.44310	+	7.69567i	−0.147206	+	0.254969i	−0.930194	−	0.367068i	$-0.880361\pi$
$911$	−4.44310	+	7.69567i	−0.147206	+	0.254969i	0.782988	+	0.622037i	$0.213695\pi$
$912$		0			0
$913$	4.29726	+	7.44307i	0.142218	+	0.246330i
$914$		0			0
$915$	−6.36484	+	7.58532i	−0.210415	+	0.250763i
$916$		0			0
$917$	7.68004			0.253617
$918$		0			0
$919$	−8.57398			−0.282829			−0.141415	−	0.989950i	$-0.545165\pi$
$919$	−8.57398			−0.282829			−0.141415	+	0.989950i	$0.545165\pi$
$920$		0			0
$921$	16.8460	−	20.0763i	0.555095	−	0.661536i
$922$		0			0
$923$	−12.1677	−	21.0751i	−0.400505	−	0.693696i
$924$		0			0
$925$	3.99185	−	6.91408i	0.131251	−	0.227334i
$926$		0			0
$927$	−30.2848	+	25.4119i	−0.994682	+	0.834638i
$928$		0			0
$929$	−0.825474	+	1.42976i	−0.0270829	+	0.0469090i	−0.879249	−	0.476362i	$-0.841955\pi$
$929$	−0.825474	+	1.42976i	−0.0270829	+	0.0469090i	0.852166	+	0.523271i	$0.175288\pi$
$930$		0			0
$931$	−0.553033	−	0.957882i	−0.0181249	−	0.0313933i
$932$		0			0
$933$	8.50846	+	1.50027i	0.278554	+	0.0491166i
$934$		0			0
$935$	18.4611			0.603743
$936$		0			0
$937$	47.4953			1.55160			0.775801	−	0.630978i	$-0.217346\pi$
$937$	47.4953			1.55160			0.775801	+	0.630978i	$0.217346\pi$
$938$		0			0
$939$	−15.1227	−	41.5492i	−0.493510	−	1.35591i
$940$		0			0
$941$	11.6964	+	20.2588i	0.381292	+	0.660417i	0.991247	−	0.132019i	$-0.0421460\pi$
$941$	11.6964	+	20.2588i	0.381292	+	0.660417i	−0.609955	+	0.792436i	$0.708813\pi$
$942$		0			0
$943$	−22.5390	+	39.0386i	−0.733969	+	1.27127i
$944$		0			0
$945$	12.9572	+	7.48086i	0.421499	+	0.243352i
$946$		0			0
$947$	−1.96363	+	3.40111i	−0.0638094	+	0.110521i	−0.896165	−	0.443720i	$-0.853658\pi$
$947$	−1.96363	+	3.40111i	−0.0638094	+	0.110521i	0.832356	+	0.554242i	$0.186992\pi$
$948$		0			0
$949$	−0.779715	−	1.35051i	−0.0253106	−	0.0438393i
$950$		0			0
$951$	−3.08869	−	8.48610i	−0.100158	−	0.275181i
$952$		0			0
$953$	2.42427			0.0785297			0.0392649	−	0.999229i	$-0.487498\pi$
$953$	2.42427			0.0785297			0.0392649	+	0.999229i	$0.487498\pi$
$954$		0			0
$955$	−25.2422			−0.816817
$956$		0			0
$957$	10.0753	+	1.77655i	0.325689	+	0.0574277i
$958$		0			0
$959$	7.13429	+	12.3569i	0.230378	+	0.399027i
$960$		0			0
$961$	−0.0346151	+	0.0599551i	−0.00111662	+	0.00193404i
$962$		0			0
$963$	7.26786	+	41.2181i	0.234203	+	1.32823i
$964$		0			0
$965$	21.9440	−	38.0082i	0.706403	−	1.22353i
$966$		0			0
$967$	−6.35844	−	11.0131i	−0.204474	−	0.354159i	0.745491	−	0.666515i	$-0.232215\pi$
$967$	−6.35844	−	11.0131i	−0.204474	−	0.354159i	−0.949965	+	0.312357i	$0.898882\pi$
$968$		0			0
$969$	6.66385	−	7.94166i	0.214074	−	0.255123i
$970$		0			0
$971$	−25.6236			−0.822301			−0.411150	−	0.911568i	$-0.634873\pi$
$971$	−25.6236			−0.822301			−0.411150	+	0.911568i	$0.634873\pi$
$972$		0			0
$973$	−15.2790			−0.489822
$974$		0			0
$975$	−17.4354	+	20.7787i	−0.558380	+	0.665451i
$976$		0			0
$977$	−22.9979	−	39.8336i	−0.735769	−	1.27439i	−0.954385	−	0.298579i	$-0.903487\pi$
$977$	−22.9979	−	39.8336i	−0.735769	−	1.27439i	0.218616	−	0.975811i	$-0.429846\pi$
$978$		0			0
$979$	−8.70961	+	15.0855i	−0.278360	+	0.482134i
$980$		0			0
$981$	5.29813	+	30.0472i	0.169156	+	0.959333i
$982$		0			0
$983$	−1.36231	+	2.35959i	−0.0434510	+	0.0752593i	−0.886933	−	0.461898i	$-0.847169\pi$
$983$	−1.36231	+	2.35959i	−0.0434510	+	0.0752593i	0.843482	+	0.537157i	$0.180502\pi$
$984$		0			0
$985$	−12.4461	−	21.5573i	−0.396565	−	0.686871i
$986$		0			0
$987$	−0.482926	−	0.0851529i	−0.0153717	−	0.00271045i
$988$		0			0
$989$	−44.6991			−1.42135
$990$		0			0
$991$	−50.2303			−1.59562			−0.797809	−	0.602910i	$-0.794008\pi$
$991$	−50.2303			−1.59562			−0.797809	+	0.602910i	$0.794008\pi$
$992$		0			0
$993$	−2.45564	−	6.74682i	−0.0779274	−	0.214104i
$994$		0			0
$995$	−19.2554	−	33.3513i	−0.610436	−	1.05731i
$996$		0			0
$997$	−21.6263	+	37.4578i	−0.684912	+	1.18630i	0.288553	+	0.957464i	$0.406826\pi$
$997$	−21.6263	+	37.4578i	−0.684912	+	1.18630i	−0.973465	+	0.228838i	$0.926507\pi$
$998$		0			0
$999$	10.9171	+	6.30299i	0.345402	+	0.199418i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.r.c.169.3	✓	6
3.2	odd	2		1512.2.r.c.505.1		6
4.3	odd	2		1008.2.r.i.673.1		6
9.2	odd	6		4536.2.a.v.1.3		3
9.4	even	3	inner	504.2.r.c.337.3	yes	6
9.5	odd	6		1512.2.r.c.1009.1		6
9.7	even	3		4536.2.a.s.1.1		3
12.11	even	2		3024.2.r.h.2017.1		6
36.7	odd	6		9072.2.a.br.1.1		3
36.11	even	6		9072.2.a.cc.1.3		3
36.23	even	6		3024.2.r.h.1009.1		6
36.31	odd	6		1008.2.r.i.337.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.r.c.169.3	✓	6	1.1	even	1	trivial
504.2.r.c.337.3	yes	6	9.4	even	3	inner
1008.2.r.i.337.1		6	36.31	odd	6
1008.2.r.i.673.1		6	4.3	odd	2
1512.2.r.c.505.1		6	3.2	odd	2
1512.2.r.c.1009.1		6	9.5	odd	6
3024.2.r.h.1009.1		6	36.23	even	6
3024.2.r.h.2017.1		6	12.11	even	2
4536.2.a.s.1.1		3	9.7	even	3
4536.2.a.v.1.3		3	9.2	odd	6
9072.2.a.br.1.1		3	36.7	odd	6
9072.2.a.cc.1.3		3	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.r (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11334 - 1.32683i) q^{3} +(1.43969 + 2.49362i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.520945 - 2.95442i) q^{9} +O(q^{10})\)	\(q+(1.11334 - 1.32683i) q^{3} +(1.43969 + 2.49362i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.520945 - 2.95442i) q^{9} +(0.592396 - 1.02606i) q^{11} +(2.37939 + 4.12122i) q^{13} +(4.91147 + 0.866025i) q^{15} +5.41147 q^{17} +1.10607 q^{19} +(0.592396 + 1.62760i) q^{21} +(-2.95084 - 5.11100i) q^{23} +(-1.64543 + 2.84997i) q^{25} +(-4.50000 - 2.59808i) q^{27} +(-2.49273 + 4.31753i) q^{29} +(2.78699 + 4.82721i) q^{31} +(-0.701867 - 1.92836i) q^{33} -2.87939 q^{35} -2.42602 q^{37} +(8.11721 + 1.43128i) q^{39} +(-3.81908 - 6.61484i) q^{41} +(3.78699 - 6.55926i) q^{43} +(6.61721 - 5.55250i) q^{45} +(-0.141559 + 0.245188i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(6.02481 - 7.18009i) q^{51} -4.22668 q^{53} +3.41147 q^{55} +(1.23143 - 1.46756i) q^{57} +(-5.86231 - 10.1538i) q^{59} +(-0.992726 + 1.71945i) q^{61} +(2.81908 + 1.02606i) q^{63} +(-6.85117 + 11.8666i) q^{65} +(6.76991 + 11.7258i) q^{67} +(-10.0667 - 1.77503i) q^{69} -5.11381 q^{71} -0.327696 q^{73} +(1.94949 + 5.35619i) q^{75} +(0.592396 + 1.02606i) q^{77} +(5.24763 - 9.08916i) q^{79} +(-8.45723 + 3.07818i) q^{81} +(-3.62701 + 6.28217i) q^{83} +(7.79086 + 13.4942i) q^{85} +(2.95336 + 8.11430i) q^{87} -14.7023 q^{89} -4.75877 q^{91} +(9.50774 + 1.67647i) q^{93} +(1.59240 + 2.75811i) q^{95} +(-9.04710 + 15.6700i) q^{97} +(-3.34002 - 1.21567i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} - 3 q^{7}+O(q^{10}) \) 6 * q + 3 * q^5 - 3 * q^7	\( 6 q + 3 q^{5} - 3 q^{7} + 3 q^{13} + 9 q^{15} + 12 q^{17} - 18 q^{19} - 6 q^{23} + 6 q^{25} - 27 q^{27} + 3 q^{29} + 9 q^{31} - 18 q^{33} - 6 q^{35} - 30 q^{37} + 18 q^{39} - 6 q^{41} + 15 q^{43} + 9 q^{45} - 9 q^{47} - 3 q^{49} + 9 q^{51} - 12 q^{53} + 27 q^{57} - 3 q^{59} + 12 q^{61} - 15 q^{65} + 12 q^{67} - 27 q^{69} + 42 q^{71} + 6 q^{73} + 9 q^{75} + 15 q^{79} + 6 q^{83} + 15 q^{85} - 9 q^{87} - 36 q^{89} - 6 q^{91} + 9 q^{93} + 6 q^{95} - 15 q^{97}+O(q^{100}) \) 6 * q + 3 * q^5 - 3 * q^7 + 3 * q^13 + 9 * q^15 + 12 * q^17 - 18 * q^19 - 6 * q^23 + 6 * q^25 - 27 * q^27 + 3 * q^29 + 9 * q^31 - 18 * q^33 - 6 * q^35 - 30 * q^37 + 18 * q^39 - 6 * q^41 + 15 * q^43 + 9 * q^45 - 9 * q^47 - 3 * q^49 + 9 * q^51 - 12 * q^53 + 27 * q^57 - 3 * q^59 + 12 * q^61 - 15 * q^65 + 12 * q^67 - 27 * q^69 + 42 * q^71 + 6 * q^73 + 9 * q^75 + 15 * q^79 + 6 * q^83 + 15 * q^85 - 9 * q^87 - 36 * q^89 - 6 * q^91 + 9 * q^93 + 6 * q^95 - 15 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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