LMFDB - Embedded newform 1008.2.r.i.673.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(337,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("1008.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.r (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
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:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			673.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	1008.673
Dual form			1008.2.r.i.337.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11334 + 1.32683i) q^{3} +(1.43969 + 2.49362i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-0.520945 - 2.95442i) q^{9} +O(q^{10})$	\(q+(-1.11334 + 1.32683i) q^{3} +(1.43969 + 2.49362i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-0.520945 - 2.95442i) q^{9} +(-0.592396 + 1.02606i) q^{11} +(2.37939 + 4.12122i) q^{13} +(-4.91147 - 0.866025i) q^{15} +5.41147 q^{17} -1.10607 q^{19} +(0.592396 + 1.62760i) q^{21} +(2.95084 + 5.11100i) q^{23} +(-1.64543 + 2.84997i) q^{25} +(4.50000 + 2.59808i) q^{27} +(-2.49273 + 4.31753i) q^{29} +(-2.78699 - 4.82721i) q^{31} +(-0.701867 - 1.92836i) q^{33} +2.87939 q^{35} -2.42602 q^{37} +(-8.11721 - 1.43128i) q^{39} +(-3.81908 - 6.61484i) q^{41} +(-3.78699 + 6.55926i) q^{43} +(6.61721 - 5.55250i) q^{45} +(0.141559 - 0.245188i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-6.02481 + 7.18009i) q^{51} -4.22668 q^{53} -3.41147 q^{55} +(1.23143 - 1.46756i) q^{57} +(5.86231 + 10.1538i) q^{59} +(-0.992726 + 1.71945i) q^{61} +(-2.81908 - 1.02606i) q^{63} +(-6.85117 + 11.8666i) q^{65} +(-6.76991 - 11.7258i) q^{67} +(-10.0667 - 1.77503i) q^{69} +5.11381 q^{71} -0.327696 q^{73} +(-1.94949 - 5.35619i) q^{75} +(0.592396 + 1.02606i) q^{77} +(-5.24763 + 9.08916i) q^{79} +(-8.45723 + 3.07818i) q^{81} +(3.62701 - 6.28217i) q^{83} +(7.79086 + 13.4942i) q^{85} +(-2.95336 - 8.11430i) q^{87} -14.7023 q^{89} +4.75877 q^{91} +(9.50774 + 1.67647i) q^{93} +(-1.59240 - 2.75811i) q^{95} +(-9.04710 + 15.6700i) q^{97} +(3.34002 + 1.21567i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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	−0.941406	−	0.337275i	$-0.890495\pi$
$11$	−0.592396	+	1.02606i	−0.178614	+	0.309369i	0.762792	+	0.646644i	$0.223828\pi$
$12$		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	$-0.540495\pi$
$19$	−1.10607			−0.253749			−0.126875	+	0.991919i	$0.540495\pi$
$20$		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	$0.0442952\pi$
$23$	2.95084	+	5.11100i	0.615292	+	1.06572i	−0.375041	+	0.927008i	$0.622371\pi$
$24$		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	$-0.999795\pi$
$31$	−2.78699	−	4.82721i	−0.500558	−	0.866992i	0.499442	−	0.866347i	$-0.333538\pi$
$32$		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	$0.362642\pi$
$43$	−3.78699	+	6.55926i	−0.577510	+	1.00028i	−0.995764	+	0.0919470i	$0.970691\pi$
$44$		0			0
$45$	6.61721	−	5.55250i	0.986436	−	0.827718i
$46$		0			0
$47$	0.141559	−	0.245188i	0.0206485	−	0.0357643i	−0.855516	−	0.517776i	$-0.826760\pi$
$47$	0.141559	−	0.245188i	0.0206485	−	0.0357643i	0.876165	+	0.482011i	$0.160094\pi$
$48$		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	$0.109710\pi$
$59$	5.86231	+	10.1538i	0.763208	+	1.32191i	−0.177981	+	0.984034i	$0.556957\pi$
$60$		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	$-0.856669\pi$
$67$	−6.76991	−	11.7258i	−0.827077	−	1.43254i	0.0732450	−	0.997314i	$-0.476664\pi$
$68$		0			0
$69$	−10.0667	−	1.77503i	−1.21189	−	0.213689i
$70$		0			0
$71$	5.11381			0.606897			0.303449	−	0.952848i	$-0.401862\pi$
$71$	5.11381			0.606897			0.303449	+	0.952848i	$0.401862\pi$
$72$		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	$0.367698\pi$
$79$	−5.24763	+	9.08916i	−0.590404	+	1.02261i	−0.994178	+	0.107751i	$0.965635\pi$
$80$		0			0
$81$	−8.45723	+	3.07818i	−0.939693	+	0.342020i
$82$		0			0
$83$	3.62701	−	6.28217i	0.398116	−	0.689558i	−0.595377	−	0.803446i	$-0.702997\pi$
$83$	3.62701	−	6.28217i	0.398116	−	0.689558i	0.993494	+	0.113889i	$0.0363307\pi$
$84$		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	$0.0582432\pi$
$103$	6.58899	+	11.4125i	0.649233	+	1.12450i	−0.334074	+	0.942547i	$0.608423\pi$
$104$		0			0
$105$	−3.20574	+	3.82045i	−0.312848	+	0.372838i
$106$		0			0
$107$	13.9513			1.34872			0.674362	−	0.738401i	$-0.264419\pi$
$107$	13.9513			1.34872			0.674362	+	0.738401i	$0.264419\pi$
$108$		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	$-0.149712\pi$
$127$	20.0915			1.78283			0.891417	+	0.453184i	$0.149712\pi$
$128$		0			0
$129$	−4.48680	−	12.3274i	−0.395040	−	1.08536i
$130$		0			0
$131$	3.84002	+	6.65111i	0.335504	+	0.581111i	0.983582	−	0.180464i	$-0.0577600\pi$
$131$	3.84002	+	6.65111i	0.335504	+	0.581111i	−0.648077	+	0.761575i	$0.724427\pi$
$132$		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	$-0.942283\pi$
$139$	−7.63950	−	13.2320i	−0.647974	−	1.12232i	0.335632	−	0.941993i	$-0.391050\pi$
$140$		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	−0.519272	−	0.854609i	$-0.673797\pi$
$151$	5.90420	−	10.2264i	0.480477	−	0.832211i	0.999749	+	0.0223984i	$0.00713022\pi$
$152$		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	$-0.887790\pi$
$163$	−23.9641			−1.87701			−0.938506	+	0.345262i	$0.887790\pi$
$164$		0			0
$165$	3.79813	−	4.52644i	0.295684	−	0.352383i
$166$		0			0
$167$	−2.48545	−	4.30493i	−0.192330	−	0.333125i	0.753692	−	0.657228i	$-0.228271\pi$
$167$	−2.48545	−	4.30493i	−0.192330	−	0.333125i	−0.946022	+	0.324102i	$0.894938\pi$
$168$		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	$-0.387346\pi$
$179$	9.27362			0.693143			0.346572	+	0.938024i	$0.387346\pi$
$180$		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	−0.662733	−	0.748856i	$-0.730604\pi$
$191$	4.38326	−	7.59202i	0.317161	−	0.549339i	0.979895	+	0.199516i	$0.0639370\pi$
$192$		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	$-0.342791\pi$
$199$	13.3746			0.948103			0.474051	+	0.880497i	$0.342791\pi$
$200$		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	0.712955	−	0.701210i	$-0.247356\pi$
$211$	−3.64290	−	6.30969i	−0.250788	−	0.434377i	−0.963743	+	0.266832i	$0.914023\pi$
$212$		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	−0.875753	−	0.482759i	$-0.839635\pi$
$223$	−0.295607	+	0.512007i	−0.0197953	+	0.0342865i	0.855958	+	0.517045i	$0.172968\pi$
$224$		0			0
$225$	9.27719	+	3.37662i	0.618479	+	0.225108i
$226$		0			0
$227$	−1.74170	+	3.01671i	−0.115600	+	0.200226i	−0.918020	−	0.396535i	$-0.870213\pi$
$227$	−1.74170	+	3.01671i	−0.115600	+	0.200226i	0.802419	+	0.596761i	$0.203546\pi$
$228$		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	0.924596	−	0.380950i	$-0.124403\pi$
$239$	2.04664	+	3.54488i	0.132386	+	0.229299i	−0.792210	+	0.610249i	$0.791070\pi$
$240$		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	$-0.552469\pi$
$251$	−5.19934			−0.328179			−0.164090	+	0.986445i	$0.552469\pi$
$252$		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	−0.984715	−	0.174175i	$-0.944274\pi$
$263$	−5.53849	+	9.59294i	−0.341518	+	0.591526i	0.643197	+	0.765701i	$0.277608\pi$
$264$		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	$-0.369157\pi$
$271$	13.1557			0.799152			0.399576	+	0.916700i	$0.369157\pi$
$272$		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	0.998612	−	0.0526741i	$-0.0167745\pi$
$283$	7.63223	+	13.2194i	0.453689	+	0.785812i	−0.544923	+	0.838486i	$0.683441\pi$
$284$		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	$-0.642117\pi$
$307$	−15.1310			−0.863574			−0.431787	+	0.901976i	$0.642117\pi$
$308$		0			0
$309$	−22.4782	−	3.96351i	−1.27874	−	0.225476i
$310$		0			0
$311$	−2.49407	−	4.31986i	−0.141426	−	0.244957i	0.786608	−	0.617453i	$-0.211835\pi$
$311$	−2.49407	−	4.31986i	−0.141426	−	0.244957i	−0.928034	+	0.372496i	$0.878502\pi$
$312$		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	−0.917348	−	0.398085i	$-0.869675\pi$
$331$	−2.07263	+	3.58991i	−0.113922	+	0.197319i	0.803426	+	0.595404i	$0.203008\pi$
$332$		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	0.983330	−	0.181832i	$-0.0582027\pi$
$347$	6.22534	+	10.7826i	0.334194	+	0.578840i	−0.649136	+	0.760672i	$0.724869\pi$
$348$		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	$-0.342886\pi$
$359$	17.9540			0.947575			0.473788	+	0.880639i	$0.342886\pi$
$360$		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	$-0.648509\pi$
$367$	10.5089	−	18.2020i	0.548561	−	0.950136i	0.998373	−	0.0570129i	$-0.0181576\pi$
$368$		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	$-0.508057\pi$
$379$	−0.985452			−0.0506193			−0.0253096	+	0.999680i	$0.508057\pi$
$380$		0			0
$381$	−22.3687	+	26.6580i	−1.14598	+	1.36573i
$382$		0			0
$383$	−0.994070	−	1.72178i	−0.0507946	−	0.0879789i	0.839510	−	0.543344i	$-0.182842\pi$
$383$	−0.994070	−	1.72178i	−0.0507946	−	0.0879789i	−0.890305	+	0.455365i	$0.849509\pi$
$384$		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	0.624812	−	0.780775i	$-0.285176\pi$
$419$	−7.44609	−	12.8970i	−0.363765	−	0.630060i	−0.988577	+	0.150715i	$0.951842\pi$
$420$		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	$-0.711303\pi$
$431$	−25.5827			−1.23227			−0.616137	+	0.787639i	$0.711303\pi$
$432$		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	−0.728999	−	0.684515i	$-0.760014\pi$
$439$	4.78359	−	8.28541i	0.228308	−	0.395441i	0.957307	+	0.289074i	$0.0933473\pi$
$440$		0			0
$441$	−2.29813	+	1.92836i	−0.109435	+	0.0918268i
$442$		0			0
$443$	−7.92902	+	13.7335i	−0.376719	+	0.652496i	−0.990583	−	0.136916i	$-0.956281\pi$
$443$	−7.92902	+	13.7335i	−0.376719	+	0.652496i	0.613864	+	0.789412i	$0.289614\pi$
$444$		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	0.736558	−	0.676374i	$-0.236450\pi$
$463$	−4.67958	−	8.10527i	−0.217478	−	0.376684i	−0.954036	+	0.299691i	$0.903117\pi$
$464$		0			0
$465$	9.50774	+	26.1223i	0.440911	+	1.21139i
$466$		0			0
$467$	−24.7273			−1.14424			−0.572122	−	0.820169i	$-0.693880\pi$
$467$	−24.7273			−1.14424			−0.572122	+	0.820169i	$0.693880\pi$
$468$		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	$-0.494429\pi$
$479$	19.1425	−	33.1558i	0.874643	−	1.51493i	0.857143	−	0.515079i	$-0.172237\pi$
$480$		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	$-0.509341\pi$
$487$	−1.29498			−0.0586811			−0.0293405	+	0.999569i	$0.509341\pi$
$488$		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	$0.0106671\pi$
$491$	11.7160	+	20.2927i	0.528736	+	0.915797i	−0.470703	+	0.882292i	$0.656000\pi$
$492$		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	$-0.882944\pi$
$499$	−17.3773	−	30.0984i	−0.777916	−	1.34739i	0.155225	−	0.987879i	$-0.450390\pi$
$500$		0			0
$501$	8.47906	+	1.49509i	0.378816	+	0.0667955i
$502$		0			0
$503$	−8.61318			−0.384043			−0.192021	−	0.981391i	$-0.561504\pi$
$503$	−8.61318			−0.384043			−0.192021	+	0.981391i	$0.561504\pi$
$504$		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	$-0.416349\pi$
$523$	11.8821			0.519567			0.259783	+	0.965667i	$0.416349\pi$
$524$		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	−0.847731	−	0.530427i	$-0.822032\pi$
$547$	0.830222	−	1.43799i	0.0354977	−	0.0614839i	0.883228	+	0.468943i	$0.155365\pi$
$548$		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	$0.0292354\pi$
$563$	13.6985	+	23.7264i	0.577321	+	0.999950i	−0.418464	+	0.908233i	$0.637431\pi$
$564$		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	0.913957	−	0.405812i	$-0.133011\pi$
$571$	2.52182	+	4.36792i	0.105535	+	0.182792i	−0.808422	+	0.588604i	$0.799678\pi$
$572$		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	$-0.487057\pi$
$587$	21.4572	−	37.1650i	0.885635	−	1.53396i	0.844984	−	0.534791i	$-0.179610\pi$
$588$		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	0.566572	−	0.824012i	$-0.308269\pi$
$599$	−10.5321	−	18.2421i	−0.430329	−	0.745353i	−0.996902	+	0.0786597i	$0.974936\pi$
$600$		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	$-0.910383\pi$
$607$	−17.7618	−	30.7643i	−0.720928	−	1.24868i	0.239701	−	0.970847i	$-0.422951\pi$
$608$		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	−0.976690	−	0.214655i	$-0.931137\pi$
$619$	−7.52481	+	13.0334i	−0.302448	+	0.523855i	0.674242	+	0.738510i	$0.264470\pi$
$620$		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	$-0.505414\pi$
$631$	−0.854408			−0.0340135			−0.0170067	+	0.999855i	$0.505414\pi$
$632$		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	$0.0631169\pi$
$643$	16.7562	+	29.0227i	0.660802	+	1.14454i	−0.319604	+	0.947551i	$0.603550\pi$
$644$		0			0
$645$	24.2802	−	28.9360i	0.956031	−	1.13935i
$646$		0			0
$647$	20.0966			0.790078			0.395039	−	0.918664i	$-0.370731\pi$
$647$	20.0966			0.790078			0.395039	+	0.918664i	$0.370731\pi$
$648$		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	−0.712340	−	0.701835i	$-0.752365\pi$
$659$	6.45976	−	11.1886i	0.251637	−	0.435847i	0.963977	+	0.265987i	$0.0856979\pi$
$660$		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	$-0.660191\pi$
$683$	−25.2080			−0.964558			−0.482279	+	0.876018i	$0.660191\pi$
$684$		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	−0.633287	−	0.773917i	$-0.718295\pi$
$691$	9.29473	−	16.0989i	0.353588	−	0.612433i	0.986875	+	0.161484i	$0.0516281\pi$
$692$		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	$-0.563875\pi$
$719$	−10.6895			−0.398653			−0.199326	+	0.979933i	$0.563875\pi$
$720$		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	$-0.436994\pi$
$727$	25.5458	−	44.2466i	0.947440	−	1.64101i	0.750791	−	0.660540i	$-0.229673\pi$
$728$		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	$-0.780503\pi$
$739$	−41.9469			−1.54304			−0.771520	+	0.636205i	$0.780503\pi$
$740$		0			0
$741$	8.97818	+	1.58310i	0.329822	+	0.0581564i
$742$		0			0
$743$	−8.05809	−	13.9570i	−0.295622	−	0.512033i	0.679507	−	0.733669i	$-0.262194\pi$
$743$	−8.05809	−	13.9570i	−0.295622	−	0.512033i	−0.975130	+	0.221636i	$0.928860\pi$
$744$		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	$-0.780368\pi$
$751$	−25.6746	−	44.4697i	−0.936879	−	1.62272i	−0.165630	−	0.986188i	$-0.552966\pi$
$752$		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	0.533311	−	0.845919i	$-0.320948\pi$
$787$	−13.0710	−	22.6397i	−0.465932	−	0.807018i	−0.999243	+	0.0389010i	$0.987614\pi$
$788$		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	$-0.621856\pi$
$811$	−21.2754			−0.747080			−0.373540	+	0.927614i	$0.621856\pi$
$812$		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	0.652345	−	0.757922i	$-0.273785\pi$
$823$	−9.47296	−	16.4077i	−0.330207	−	0.571935i	−0.982552	+	0.185987i	$0.940452\pi$
$824$		0			0
$825$	6.65064	+	1.17269i	0.231546	+	0.0408278i
$826$		0			0
$827$	12.1489			0.422458			0.211229	−	0.977437i	$-0.432253\pi$
$827$	12.1489			0.422458			0.211229	+	0.977437i	$0.432253\pi$
$828$		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	−0.907922	−	0.419139i	$-0.862332\pi$
$839$	−2.63516	+	4.56424i	−0.0909759	+	0.157575i	0.816946	+	0.576714i	$0.195665\pi$
$840$		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	$-0.831824\pi$
$859$	−25.4513	−	44.0830i	−0.868387	−	1.50409i	−0.00474324	−	0.999989i	$-0.501510\pi$
$860$		0			0
$861$	8.50387	−	10.1345i	0.289811	−	0.345383i
$862$		0			0
$863$	−12.7615			−0.434405			−0.217203	−	0.976127i	$-0.569693\pi$
$863$	−12.7615			−0.434405			−0.217203	+	0.976127i	$0.569693\pi$
$864$		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	$-0.245234\pi$
$883$	42.6483			1.43523			0.717614	+	0.696441i	$0.245234\pi$
$884$		0			0
$885$	−19.9991	−	54.9471i	−0.672263	−	1.84703i
$886$		0			0
$887$	11.2117	+	19.4192i	0.376451	+	0.652032i	0.990543	−	0.137202i	$-0.0438110\pi$
$887$	11.2117	+	19.4192i	0.376451	+	0.652032i	−0.614092	+	0.789234i	$0.710478\pi$
$888$		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	$-0.577863\pi$
$907$	21.6584	−	37.5134i	0.719155	−	1.24561i	0.961335	−	0.275381i	$-0.0888042\pi$
$908$		0			0
$909$	−49.8632	−	18.1487i	−1.65386	−	0.601956i
$910$		0			0
$911$	4.44310	−	7.69567i	0.147206	−	0.254969i	−0.782988	−	0.622037i	$-0.786305\pi$
$911$	4.44310	−	7.69567i	0.147206	−	0.254969i	0.930194	+	0.367068i	$0.119639\pi$
$912$		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	$-0.454835\pi$
$919$	8.57398			0.282829			0.141415	+	0.989950i	$0.454835\pi$
$920$		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	−0.832356	−	0.554242i	$-0.813008\pi$
$947$	1.96363	−	3.40111i	0.0638094	−	0.110521i	0.896165	+	0.443720i	$0.146342\pi$
$948$		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	0.949965	−	0.312357i	$-0.101118\pi$
$967$	6.35844	+	11.0131i	0.204474	+	0.354159i	−0.745491	+	0.666515i	$0.767785\pi$
$968$		0			0
$969$	6.66385	−	7.94166i	0.214074	−	0.255123i
$970$		0			0
$971$	25.6236			0.822301			0.411150	−	0.911568i	$-0.365127\pi$
$971$	25.6236			0.822301			0.411150	+	0.911568i	$0.365127\pi$
$972$		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	−0.843482	−	0.537157i	$-0.819498\pi$
$983$	1.36231	−	2.35959i	0.0434510	−	0.0752593i	0.886933	+	0.461898i	$0.152831\pi$
$984$		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	$-0.205992\pi$
$991$	50.2303			1.59562			0.797809	+	0.602910i	$0.205992\pi$
$992$		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	1008.2.r.i.673.1		6
3.2	odd	2		3024.2.r.h.2017.1		6
4.3	odd	2		504.2.r.c.169.3	✓	6
9.2	odd	6		9072.2.a.cc.1.3		3
9.4	even	3	inner	1008.2.r.i.337.1		6
9.5	odd	6		3024.2.r.h.1009.1		6
9.7	even	3		9072.2.a.br.1.1		3
12.11	even	2		1512.2.r.c.505.1		6
36.7	odd	6		4536.2.a.s.1.1		3
36.11	even	6		4536.2.a.v.1.3		3
36.23	even	6		1512.2.r.c.1009.1		6
36.31	odd	6		504.2.r.c.337.3	yes	6

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.r (of order \(3\), degree \(2\), not 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more