LMFDB - Embedded newform 1008.2.q.h.529.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(529,1008)]

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, 4, 4]))

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

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

chi := DirichletCharacter("1008.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.2
Root			$0.500000 - 2.05195i$ of defining polynomial
Character	$\chi$	$=$	1008.529
Dual form			1008.2.q.h.625.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.796790 + 1.53790i) q^{3} +(0.230252 - 0.398809i) q^{5} +(-0.0665372 + 2.64491i) q^{7} +(-1.73025 + 2.45076i) q^{9} +O(q^{10})$	\(q+(0.796790 + 1.53790i) q^{3} +(0.230252 - 0.398809i) q^{5} +(-0.0665372 + 2.64491i) q^{7} +(-1.73025 + 2.45076i) q^{9} +(-1.82383 - 3.15897i) q^{11} +(0.730252 + 1.26483i) q^{13} +(0.796790 + 0.0363376i) q^{15} +(-1.86693 + 3.23361i) q^{17} +(2.02704 + 3.51094i) q^{19} +(-4.12062 + 2.00511i) q^{21} +(0.566537 - 0.981271i) q^{23} +(2.39397 + 4.14647i) q^{25} +(-5.14766 - 0.708209i) q^{27} +(-4.48755 + 7.77266i) q^{29} +0.514589 q^{31} +(3.40496 - 5.32190i) q^{33} +(1.03950 + 0.635534i) q^{35} +(-4.55408 - 7.88791i) q^{37} +(-1.36333 + 2.13086i) q^{39} +(-0.472958 - 0.819187i) q^{41} +(-4.66372 + 8.07779i) q^{43} +(0.578990 + 1.25433i) q^{45} -2.32743 q^{47} +(-6.99115 - 0.351971i) q^{49} +(-6.46050 - 0.294632i) q^{51} +(6.21780 - 10.7695i) q^{53} -1.67977 q^{55} +(-3.78434 + 5.91486i) q^{57} +12.8961 q^{59} +12.0833 q^{61} +(-6.36693 - 4.73944i) q^{63} +0.672570 q^{65} +2.32023 q^{67} +(1.96050 + 0.0894089i) q^{69} -1.67977 q^{71} +(-6.62062 + 11.4673i) q^{73} +(-4.46936 + 6.98554i) q^{75} +(8.47656 - 4.61369i) q^{77} +5.00720 q^{79} +(-3.01245 - 8.48087i) q^{81} +(-3.32383 + 5.75705i) q^{83} +(0.859728 + 1.48909i) q^{85} +(-15.5292 - 0.708209i) q^{87} +(-1.36333 - 2.36135i) q^{89} +(-3.39397 + 1.84730i) q^{91} +(0.410019 + 0.791385i) q^{93} +1.86693 q^{95} +(-5.59358 + 9.68836i) q^{97} +(10.8976 + 0.996040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{3} - 5 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 6 * q + 2 * q^3 - 5 * q^5 - 4 * q^7 - 4 * q^9	$ 6 q + 2 q^{3} - 5 q^{5} - 4 q^{7} - 4 q^{9} + q^{11} - 2 q^{13} + 2 q^{15} - 4 q^{17} + 3 q^{19} - 10 q^{21} + 7 q^{23} - 2 q^{25} - 7 q^{27} - 5 q^{29} - 28 q^{31} - 19 q^{33} + 19 q^{35} - 9 q^{37} - 9 q^{39} - 12 q^{41} - 18 q^{43} + 29 q^{45} + 6 q^{47} - 12 q^{49} - 26 q^{51} + 9 q^{53} - 14 q^{55} + 2 q^{57} + 8 q^{59} - 8 q^{61} - 31 q^{63} + 24 q^{65} + 10 q^{67} - q^{69} - 14 q^{71} - 25 q^{73} - 44 q^{75} + 52 q^{77} + 14 q^{79} - 40 q^{81} - 8 q^{83} + 14 q^{85} - 31 q^{87} - 9 q^{89} - 4 q^{91} + 4 q^{95} - 28 q^{97} + 41 q^{99}+O(q^{100}) $ 6 * q + 2 * q^3 - 5 * q^5 - 4 * q^7 - 4 * q^9 + q^11 - 2 * q^13 + 2 * q^15 - 4 * q^17 + 3 * q^19 - 10 * q^21 + 7 * q^23 - 2 * q^25 - 7 * q^27 - 5 * q^29 - 28 * q^31 - 19 * q^33 + 19 * q^35 - 9 * q^37 - 9 * q^39 - 12 * q^41 - 18 * q^43 + 29 * q^45 + 6 * q^47 - 12 * q^49 - 26 * q^51 + 9 * q^53 - 14 * q^55 + 2 * q^57 + 8 * q^59 - 8 * q^61 - 31 * q^63 + 24 * q^65 + 10 * q^67 - q^69 - 14 * q^71 - 25 * q^73 - 44 * q^75 + 52 * q^77 + 14 * q^79 - 40 * q^81 - 8 * q^83 + 14 * q^85 - 31 * q^87 - 9 * q^89 - 4 * q^91 + 4 * q^95 - 28 * q^97 + 41 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

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

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
$3$	0.796790	+	1.53790i	0.460027	+	0.887905i
$3$	0.796790	+	1.53790i	0.460027	+	0.887905i
$4$		0			0
$5$	0.230252	−	0.398809i	0.102972	−	0.178353i	−0.809936	−	0.586519i	$-0.800498\pi$
$5$	0.230252	−	0.398809i	0.102972	−	0.178353i	0.912908	+	0.408166i	$0.133831\pi$
$6$		0			0
$7$	−0.0665372	+	2.64491i	−0.0251487	+	0.999684i
$7$	−0.0665372	+	2.64491i	−0.0251487	+	0.999684i
$8$		0			0
$9$	−1.73025	+	2.45076i	−0.576751	+	0.816920i
$10$		0			0
$11$	−1.82383	−	3.15897i	−0.549906	−	0.952465i	−0.998280	−	0.0586193i	$-0.981330\pi$
$11$	−1.82383	−	3.15897i	−0.549906	−	0.952465i	0.448374	−	0.893846i	$-0.352003\pi$
$12$		0			0
$13$	0.730252	+	1.26483i	0.202536	+	0.350802i	0.949345	−	0.314236i	$-0.101748\pi$
$13$	0.730252	+	1.26483i	0.202536	+	0.350802i	−0.746809	+	0.665038i	$0.768415\pi$
$14$		0			0
$15$	0.796790	+	0.0363376i	0.205730	+	0.00938234i
$16$		0			0
$17$	−1.86693	+	3.23361i	−0.452796	+	0.784266i	−0.998558	−	0.0536743i	$-0.982907\pi$
$17$	−1.86693	+	3.23361i	−0.452796	+	0.784266i	0.545763	+	0.837940i	$0.316240\pi$
$18$		0			0
$19$	2.02704	+	3.51094i	0.465035	+	0.805465i	0.999203	−	0.0399136i	$-0.0127083\pi$
$19$	2.02704	+	3.51094i	0.465035	+	0.805465i	−0.534168	+	0.845378i	$0.679375\pi$
$20$		0			0
$21$	−4.12062	+	2.00511i	−0.899193	+	0.437552i
$22$		0			0
$23$	0.566537	−	0.981271i	0.118131	−	0.204609i	−0.800896	−	0.598804i	$-0.795643\pi$
$23$	0.566537	−	0.981271i	0.118131	−	0.204609i	0.919027	+	0.394194i	$0.128976\pi$
$24$		0			0
$25$	2.39397	+	4.14647i	0.478794	+	0.829295i
$26$		0			0
$27$	−5.14766	−	0.708209i	−0.990668	−	0.136295i
$28$		0			0
$29$	−4.48755	+	7.77266i	−0.833317	+	1.44335i	0.0620772	+	0.998071i	$0.480228\pi$
$29$	−4.48755	+	7.77266i	−0.833317	+	1.44335i	−0.895394	+	0.445275i	$0.853106\pi$
$30$		0			0
$31$	0.514589			0.0924229			0.0462115	−	0.998932i	$-0.485285\pi$
$31$	0.514589			0.0924229			0.0462115	+	0.998932i	$0.485285\pi$
$32$		0			0
$33$	3.40496	−	5.32190i	0.592727	−	0.926424i
$34$		0			0
$35$	1.03950	+	0.635534i	0.175707	+	0.107425i
$36$		0			0
$37$	−4.55408	−	7.88791i	−0.748687	−	1.29676i	−0.948452	−	0.316920i	$-0.897351\pi$
$37$	−4.55408	−	7.88791i	−0.748687	−	1.29676i	0.199765	−	0.979844i	$-0.435982\pi$
$38$		0			0
$39$	−1.36333	+	2.13086i	−0.218307	+	0.341211i
$40$		0			0
$41$	−0.472958	−	0.819187i	−0.0738636	−	0.127936i	0.826728	−	0.562602i	$-0.190200\pi$
$41$	−0.472958	−	0.819187i	−0.0738636	−	0.127936i	−0.900592	+	0.434666i	$0.856866\pi$
$42$		0			0
$43$	−4.66372	+	8.07779i	−0.711210	+	1.23185i	0.253193	+	0.967416i	$0.418519\pi$
$43$	−4.66372	+	8.07779i	−0.711210	+	1.23185i	−0.964403	+	0.264436i	$0.914814\pi$
$44$		0			0
$45$	0.578990	+	1.25433i	0.0863108	+	0.186985i
$46$		0			0
$47$	−2.32743			−0.339491			−0.169745	−	0.985488i	$-0.554295\pi$
$47$	−2.32743			−0.339491			−0.169745	+	0.985488i	$0.554295\pi$
$48$		0			0
$49$	−6.99115	−	0.351971i	−0.998735	−	0.0502815i
$50$		0			0
$51$	−6.46050	−	0.294632i	−0.904652	−	0.0412567i
$52$		0			0
$53$	6.21780	−	10.7695i	0.854080	−	1.47931i	−0.0234151	−	0.999726i	$-0.507454\pi$
$53$	6.21780	−	10.7695i	0.854080	−	1.47931i	0.877495	−	0.479585i	$-0.159213\pi$
$54$		0			0
$55$	−1.67977			−0.226500
$56$		0			0
$57$	−3.78434	+	5.91486i	−0.501248	+	0.783443i
$58$		0			0
$59$	12.8961			1.67893			0.839465	−	0.543414i	$-0.182869\pi$
$59$	12.8961			1.67893			0.839465	+	0.543414i	$0.182869\pi$
$60$		0			0
$61$	12.0833			1.54710			0.773552	−	0.633733i	$-0.218478\pi$
$61$	12.0833			1.54710			0.773552	+	0.633733i	$0.218478\pi$
$62$		0			0
$63$	−6.36693	−	4.73944i	−0.802157	−	0.597113i
$64$		0			0
$65$	0.672570			0.0834220
$66$		0			0
$67$	2.32023			0.283462			0.141731	−	0.989905i	$-0.454733\pi$
$67$	2.32023			0.283462			0.141731	+	0.989905i	$0.454733\pi$
$68$		0			0
$69$	1.96050	+	0.0894089i	0.236017	+	0.0107636i
$70$		0			0
$71$	−1.67977			−0.199352			−0.0996758	−	0.995020i	$-0.531781\pi$
$71$	−1.67977			−0.199352			−0.0996758	+	0.995020i	$0.531781\pi$
$72$		0			0
$73$	−6.62062	+	11.4673i	−0.774885	+	1.34214i	0.159974	+	0.987121i	$0.448859\pi$
$73$	−6.62062	+	11.4673i	−0.774885	+	1.34214i	−0.934859	+	0.355019i	$0.884474\pi$
$74$		0			0
$75$	−4.46936	+	6.98554i	−0.516077	+	0.806621i
$76$		0			0
$77$	8.47656	−	4.61369i	0.965993	−	0.525779i
$78$		0			0
$79$	5.00720			0.563354			0.281677	−	0.959509i	$-0.409109\pi$
$79$	5.00720			0.563354			0.281677	+	0.959509i	$0.409109\pi$
$80$		0			0
$81$	−3.01245	−	8.48087i	−0.334717	−	0.942319i
$82$		0			0
$83$	−3.32383	+	5.75705i	−0.364838	+	0.631918i	−0.988750	−	0.149577i	$-0.952209\pi$
$83$	−3.32383	+	5.75705i	−0.364838	+	0.631918i	0.623912	+	0.781494i	$0.285542\pi$
$84$		0			0
$85$	0.859728	+	1.48909i	0.0932506	+	0.161515i
$86$		0			0
$87$	−15.5292	−	0.708209i	−1.66490	−	0.0759280i
$88$		0			0
$89$	−1.36333	−	2.36135i	−0.144512	−	0.250303i	0.784679	−	0.619903i	$-0.212828\pi$
$89$	−1.36333	−	2.36135i	−0.144512	−	0.250303i	−0.929191	+	0.369600i	$0.879495\pi$
$90$		0			0
$91$	−3.39397	+	1.84730i	−0.355784	+	0.193649i
$92$		0			0
$93$	0.410019	+	0.791385i	0.0425170	+	0.0820628i
$94$		0			0
$95$	1.86693			0.191543
$96$		0			0
$97$	−5.59358	+	9.68836i	−0.567942	+	0.983704i	0.428827	+	0.903386i	$0.358927\pi$
$97$	−5.59358	+	9.68836i	−0.567942	+	0.983704i	−0.996769	+	0.0803178i	$0.974406\pi$
$98$		0			0
$99$	10.8976	+	0.996040i	1.09525	+	0.100106i
$100$		0			0
$101$	−6.87792	−	11.9129i	−0.684378	−	1.18538i	−0.973632	−	0.228125i	$-0.926740\pi$
$101$	−6.87792	−	11.9129i	−0.684378	−	1.18538i	0.289254	−	0.957253i	$-0.406593\pi$
$102$		0			0
$103$	5.58113	−	9.66679i	0.549925	−	0.952498i	−0.448354	−	0.893856i	$-0.647990\pi$
$103$	5.58113	−	9.66679i	0.549925	−	0.952498i	0.998279	−	0.0586417i	$-0.0186769\pi$
$104$		0			0
$105$	−0.149126	+	2.10502i	−0.0145532	+	0.205429i
$106$		0			0
$107$	3.89037	+	6.73832i	0.376096	+	0.651418i	0.990490	−	0.137581i	$-0.0439329\pi$
$107$	3.89037	+	6.73832i	0.376096	+	0.651418i	−0.614394	+	0.788999i	$0.710600\pi$
$108$		0			0
$109$	−3.75729	+	6.50783i	−0.359884	+	0.623337i	−0.987941	−	0.154830i	$-0.950517\pi$
$109$	−3.75729	+	6.50783i	−0.359884	+	0.623337i	0.628058	+	0.778167i	$0.283850\pi$
$110$		0			0
$111$	8.50214	−	13.2887i	0.806987	−	1.26131i
$112$		0			0
$113$	3.03064	+	5.24922i	0.285099	+	0.493805i	0.972633	−	0.232346i	$-0.0746403\pi$
$113$	3.03064	+	5.24922i	0.285099	+	0.493805i	−0.687534	+	0.726152i	$0.741307\pi$
$114$		0			0
$115$	−0.260893	−	0.451880i	−0.0243284	−	0.0421380i
$116$		0			0
$117$	−4.36333	−	0.398809i	−0.403390	−	0.0368699i
$118$		0			0
$119$	−8.42840	−	5.15301i	−0.772630	−	0.472376i
$120$		0			0
$121$	−1.15272	+	1.99658i	−0.104793	+	0.181507i
$122$		0			0
$123$	0.882977	−	1.38008i	0.0796154	−	0.124438i
$124$		0			0
$125$	4.50739			0.403153
$126$		0			0
$127$	−8.80992			−0.781754			−0.390877	−	0.920443i	$-0.627828\pi$
$127$	−8.80992			−0.781754			−0.390877	+	0.920443i	$0.627828\pi$
$128$		0			0
$129$	−16.1388	−	0.736011i	−1.42094	−	0.0648022i
$130$		0			0
$131$	10.5687	−	18.3055i	0.923389	−	1.59936i	0.129258	−	0.991611i	$-0.458740\pi$
$131$	10.5687	−	18.3055i	0.923389	−	1.59936i	0.794131	−	0.607746i	$-0.207926\pi$
$132$		0			0
$133$	−9.42101	+	5.12774i	−0.816905	+	0.444632i
$134$		0			0
$135$	−1.46770	+	1.88987i	−0.126320	+	0.162654i
$136$		0			0
$137$	2.20321	+	3.81607i	0.188233	+	0.326029i	0.944661	−	0.328048i	$-0.106391\pi$
$137$	2.20321	+	3.81607i	0.188233	+	0.326029i	−0.756428	+	0.654077i	$0.773057\pi$
$138$		0			0
$139$	1.01245	+	1.75362i	0.0858751	+	0.148740i	0.905764	−	0.423783i	$-0.139298\pi$
$139$	1.01245	+	1.75362i	0.0858751	+	0.148740i	−0.819889	+	0.572523i	$0.805965\pi$
$140$		0			0
$141$	−1.85447	−	3.57935i	−0.156175	−	0.301435i
$142$		0			0
$143$	2.66372	−	4.61369i	0.222751	−	0.385816i
$144$		0			0
$145$	2.06654	+	3.57935i	0.171617	+	0.297249i
$146$		0			0
$147$	−5.02918	−	11.0321i	−0.414800	−	0.909913i
$148$		0			0
$149$	4.58113	−	7.93474i	0.375300	−	0.650040i	−0.615071	−	0.788471i	$-0.710873\pi$
$149$	4.58113	−	7.93474i	0.375300	−	0.650040i	0.990372	+	0.138432i	$0.0442062\pi$
$150$		0			0
$151$	−0.0519482	−	0.0899768i	−0.00422748	−	0.00732221i	0.863904	−	0.503657i	$-0.168012\pi$
$151$	−0.0519482	−	0.0899768i	−0.00422748	−	0.00732221i	−0.868131	+	0.496334i	$0.834679\pi$
$152$		0			0
$153$	−4.69455	−	10.1703i	−0.379532	−	0.822224i
$154$		0			0
$155$	0.118485	−	0.205223i	0.00951698	−	0.0164839i
$156$		0			0
$157$	20.9823			1.67457			0.837285	−	0.546767i	$-0.184142\pi$
$157$	20.9823			1.67457			0.837285	+	0.546767i	$0.184142\pi$
$158$		0			0
$159$	21.5167	+	0.981271i	1.70639	+	0.0778199i
$160$		0			0
$161$	2.55768	+	1.56373i	0.201574	+	0.123239i
$162$		0			0
$163$	11.5182	+	19.9501i	0.902174	+	1.56261i	0.824666	+	0.565620i	$0.191363\pi$
$163$	11.5182	+	19.9501i	0.902174	+	1.56261i	0.0775078	+	0.996992i	$0.475304\pi$
$164$		0			0
$165$	−1.33842	−	2.58331i	−0.104196	−	0.201110i
$166$		0			0
$167$	5.31498	+	9.20581i	0.411285	+	0.712367i	0.995031	−	0.0995698i	$-0.0317467\pi$
$167$	5.31498	+	9.20581i	0.411285	+	0.712367i	−0.583745	+	0.811937i	$0.698413\pi$
$168$		0			0
$169$	5.43346	−	9.41103i	0.417959	−	0.723926i
$170$		0			0
$171$	−12.1118	−	1.10702i	−0.926210	−	0.0846558i
$172$		0			0
$173$	2.93872			0.223427			0.111713	−	0.993740i	$-0.464366\pi$
$173$	2.93872			0.223427			0.111713	+	0.993740i	$0.464366\pi$
$174$		0			0
$175$	−11.1264	+	6.05594i	−0.841073	+	0.457786i
$176$		0			0
$177$	10.2755	+	19.8329i	0.772353	+	1.49073i
$178$		0			0
$179$	4.58113	−	7.93474i	0.342409	−	0.593071i	−0.642470	−	0.766311i	$-0.722090\pi$
$179$	4.58113	−	7.93474i	0.342409	−	0.593071i	0.984880	+	0.173240i	$0.0554237\pi$
$180$		0			0
$181$	22.4284			1.66709			0.833545	−	0.552452i	$-0.186308\pi$
$181$	22.4284			1.66709			0.833545	+	0.552452i	$0.186308\pi$
$182$		0			0
$183$	9.62782	+	18.5828i	0.711709	+	1.37368i
$184$		0			0
$185$	−4.19436			−0.308375
$186$		0			0
$187$	13.6198			0.995981
$188$		0			0
$189$	2.21566	−	13.5680i	0.161166	−	0.986927i
$190$		0			0
$191$	−2.48968			−0.180147			−0.0900736	−	0.995935i	$-0.528710\pi$
$191$	−2.48968			−0.180147			−0.0900736	+	0.995935i	$0.528710\pi$
$192$		0			0
$193$	4.48968			0.323174			0.161587	−	0.986858i	$-0.448339\pi$
$193$	4.48968			0.323174			0.161587	+	0.986858i	$0.448339\pi$
$194$		0			0
$195$	0.535897	+	1.03434i	0.0383763	+	0.0740708i
$196$		0			0
$197$	12.7339			0.907249			0.453625	−	0.891193i	$-0.350131\pi$
$197$	12.7339			0.907249			0.453625	+	0.891193i	$0.350131\pi$
$198$		0			0
$199$	1.47296	−	2.55124i	0.104415	−	0.180852i	−0.809084	−	0.587693i	$-0.800036\pi$
$199$	1.47296	−	2.55124i	0.104415	−	0.180852i	0.913499	+	0.406841i	$0.133370\pi$
$200$		0			0
$201$	1.84874	+	3.56828i	0.130400	+	0.251687i
$202$		0			0
$203$	−20.2594	−	12.3863i	−1.42193	−	0.869351i
$204$		0			0
$205$	−0.435599			−0.0304235
$206$		0			0
$207$	1.42461	+	3.08629i	0.0990171	+	0.214512i
$208$		0			0
$209$	7.39397	−	12.8067i	0.511451	−	0.885860i
$210$		0			0
$211$	0.608168	+	1.05338i	0.0418680	+	0.0725176i	0.886200	−	0.463303i	$-0.153336\pi$
$211$	0.608168	+	1.05338i	0.0418680	+	0.0725176i	−0.844332	+	0.535820i	$0.820002\pi$
$212$		0			0
$213$	−1.33842	−	2.58331i	−0.0917071	−	0.177005i
$214$		0			0
$215$	2.14766	+	3.71986i	0.146469	+	0.253693i
$216$		0			0
$217$	−0.0342393	+	1.36104i	−0.00232432	+	0.0923937i
$218$		0			0
$219$	−22.9107	−	1.04484i	−1.54816	−	0.0706040i
$220$		0			0
$221$	−5.45331			−0.366829
$222$		0			0
$223$	0.445916	−	0.772349i	0.0298607	−	0.0517203i	−0.850709	−	0.525637i	$-0.823827\pi$
$223$	0.445916	−	0.772349i	0.0298607	−	0.0517203i	0.880570	+	0.473917i	$0.157160\pi$
$224$		0			0
$225$	−14.3042	−	1.30740i	−0.953612	−	0.0871603i
$226$		0			0
$227$	−7.32597	−	12.6889i	−0.486242	−	0.842195i	0.513633	−	0.858010i	$-0.328299\pi$
$227$	−7.32597	−	12.6889i	−0.486242	−	0.842195i	−0.999875	+	0.0158147i	$0.994966\pi$
$228$		0			0
$229$	4.78794	−	8.29295i	0.316396	−	0.548013i	−0.663338	−	0.748320i	$-0.730861\pi$
$229$	4.78794	−	8.29295i	0.316396	−	0.548013i	0.979733	+	0.200307i	$0.0641939\pi$
$230$		0			0
$231$	13.8494	+	9.35993i	0.911224	+	0.615838i
$232$		0			0
$233$	7.21420	+	12.4954i	0.472618	+	0.818598i	0.999509	−	0.0313345i	$-0.00997571\pi$
$233$	7.21420	+	12.4954i	0.472618	+	0.818598i	−0.526891	+	0.849933i	$0.676642\pi$
$234$		0			0
$235$	−0.535897	+	0.928200i	−0.0349580	+	0.0605491i
$236$		0			0
$237$	3.98968	+	7.70055i	0.259158	+	0.500205i
$238$		0			0
$239$	9.15486	+	15.8567i	0.592179	+	1.02568i	0.993938	+	0.109938i	$0.0350654\pi$
$239$	9.15486	+	15.8567i	0.592179	+	1.02568i	−0.401760	+	0.915745i	$0.631601\pi$
$240$		0			0
$241$	−0.0466924	−	0.0808735i	−0.00300772	−	0.00520952i	0.864518	−	0.502602i	$-0.167624\pi$
$241$	−0.0466924	−	0.0808735i	−0.00300772	−	0.00520952i	−0.867525	+	0.497393i	$0.834291\pi$
$242$		0			0
$243$	10.6424	−	11.3903i	0.682711	−	0.730689i
$244$		0			0
$245$	−1.75010	+	2.70709i	−0.111810	+	0.172950i
$246$		0			0
$247$	−2.96050	+	5.12774i	−0.188372	+	0.326271i
$248$		0			0
$249$	−11.5021	−	0.524555i	−0.728918	−	0.0332424i
$250$		0			0
$251$	18.2733			1.15340			0.576702	−	0.816955i	$-0.304339\pi$
$251$	18.2733			1.15340			0.576702	+	0.816955i	$0.304339\pi$
$252$		0			0
$253$	−4.13307			−0.259844
$254$		0			0
$255$	−1.60505	+	2.50867i	−0.100512	+	0.157099i
$256$		0			0
$257$	10.5256	−	18.2308i	0.656568	−	1.13721i	−0.324931	−	0.945738i	$-0.605341\pi$
$257$	10.5256	−	18.2308i	0.656568	−	1.13721i	0.981498	−	0.191471i	$-0.0613257\pi$
$258$		0			0
$259$	21.1659	−	11.5203i	1.31518	−	0.715838i
$260$		0			0
$261$	−11.2843	−	24.4466i	−0.698483	−	1.51320i
$262$		0			0
$263$	−2.58259	−	4.47318i	−0.159249	−	0.275828i	0.775349	−	0.631533i	$-0.217574\pi$
$263$	−2.58259	−	4.47318i	−0.159249	−	0.275828i	−0.934598	+	0.355705i	$0.884241\pi$
$264$		0			0
$265$	−2.86333	−	4.95943i	−0.175893	−	0.304655i
$266$		0			0
$267$	2.54523	−	3.97816i	0.155766	−	0.243459i
$268$		0			0
$269$	8.42840	−	14.5984i	0.513889	−	0.890081i	−0.485981	−	0.873969i	$-0.661538\pi$
$269$	8.42840	−	14.5984i	0.513889	−	0.890081i	0.999870	−	0.0161123i	$-0.00512891\pi$
$270$		0			0
$271$	−12.5562	−	21.7480i	−0.762736	−	1.32110i	−0.941435	−	0.337194i	$-0.890522\pi$
$271$	−12.5562	−	21.7480i	−0.762736	−	1.32110i	0.178699	−	0.983904i	$-0.442811\pi$
$272$		0			0
$273$	−5.54523	−	3.74766i	−0.335613	−	0.226819i
$274$		0			0
$275$	8.73239	−	15.1249i	0.526583	−	0.912068i
$276$		0			0
$277$	−1.69076	−	2.92848i	−0.101588	−	0.175955i	0.810751	−	0.585391i	$-0.199059\pi$
$277$	−1.69076	−	2.92848i	−0.101588	−	0.175955i	−0.912339	+	0.409436i	$0.865726\pi$
$278$		0			0
$279$	−0.890369	+	1.26113i	−0.0533050	+	0.0755022i
$280$		0			0
$281$	−10.1388	+	17.5609i	−0.604831	+	1.04760i	0.387248	+	0.921976i	$0.373426\pi$
$281$	−10.1388	+	17.5609i	−0.604831	+	1.04760i	−0.992078	+	0.125622i	$0.959907\pi$
$282$		0			0
$283$	−17.3494			−1.03132			−0.515658	−	0.856795i	$-0.672452\pi$
$283$	−17.3494			−1.03132			−0.515658	+	0.856795i	$0.672452\pi$
$284$		0			0
$285$	1.48755	+	2.87114i	0.0881147	+	0.170072i
$286$		0			0
$287$	2.19815	−	1.19643i	0.129753	−	0.0706228i
$288$		0			0
$289$	1.52918	+	2.64861i	0.0899517	+	0.155801i
$290$		0			0
$291$	−19.3566	−	0.882759i	−1.13470	−	0.0517483i
$292$		0			0
$293$	−4.93560	−	8.54871i	−0.288341	−	0.499421i	0.685073	−	0.728474i	$-0.259770\pi$
$293$	−4.93560	−	8.54871i	−0.288341	−	0.499421i	−0.973414	+	0.229054i	$0.926437\pi$
$294$		0			0
$295$	2.96936	−	5.14308i	0.172883	−	0.299442i
$296$		0			0
$297$	7.15126	+	17.5530i	0.414958	+	1.01853i
$298$		0			0
$299$	1.65486			0.0957031
$300$		0			0
$301$	−21.0548	−	12.8726i	−1.21358	−	0.741964i
$302$		0			0
$303$	12.8406	−	20.0696i	0.737671	−	1.15297i
$304$		0			0
$305$	2.78220	−	4.81891i	0.159308	−	0.275930i
$306$		0			0
$307$	−7.78794			−0.444481			−0.222240	−	0.974992i	$-0.571337\pi$
$307$	−7.78794			−0.444481			−0.222240	+	0.974992i	$0.571337\pi$
$308$		0			0
$309$	19.3135	+	0.880794i	1.09871	+	0.0501066i
$310$		0			0
$311$	−15.4107			−0.873860			−0.436930	−	0.899495i	$-0.643934\pi$
$311$	−15.4107			−0.873860			−0.436930	+	0.899495i	$0.643934\pi$
$312$		0			0
$313$	8.49688			0.480272			0.240136	−	0.970739i	$-0.422808\pi$
$313$	8.49688			0.480272			0.240136	+	0.970739i	$0.422808\pi$
$314$		0			0
$315$	−3.35613	+	1.44792i	−0.189096	+	0.0815810i
$316$		0			0
$317$	−14.1052			−0.792229			−0.396115	−	0.918201i	$-0.629642\pi$
$317$	−14.1052			−0.792229			−0.396115	+	0.918201i	$0.629642\pi$
$318$		0			0
$319$	32.7381			1.83298
$320$		0			0
$321$	−7.26303	+	11.3520i	−0.405383	+	0.633607i
$322$		0			0
$323$	−15.1373			−0.842264
$324$		0			0
$325$	−3.49640	+	6.05594i	−0.193945	+	0.335923i
$326$		0			0
$327$	−13.0021	−	0.592963i	−0.719020	−	0.0327909i
$328$		0			0
$329$	0.154861	−	6.15585i	0.00853775	−	0.339383i
$330$		0			0
$331$	−27.5438			−1.51394			−0.756971	−	0.653448i	$-0.773322\pi$
$331$	−27.5438			−1.51394			−0.756971	+	0.653448i	$0.773322\pi$
$332$		0			0
$333$	27.2111	+	2.48710i	1.49116	+	0.136292i
$334$		0			0
$335$	0.534239	−	0.925330i	0.0291886	−	0.0505562i
$336$		0			0
$337$	0.748440	+	1.29634i	0.0407701	+	0.0706159i	0.885690	−	0.464276i	$-0.153686\pi$
$337$	0.748440	+	1.29634i	0.0407701	+	0.0706159i	−0.844920	+	0.534892i	$0.820352\pi$
$338$		0			0
$339$	−5.65798	+	8.84334i	−0.307299	+	0.480304i
$340$		0			0
$341$	−0.938524	−	1.62557i	−0.0508239	−	0.0880296i
$342$		0			0
$343$	1.39610	−	18.4676i	0.0753825	−	0.997155i
$344$		0			0
$345$	0.487068	−	0.761280i	0.0262229	−	0.0409859i
$346$		0			0
$347$	18.2881			0.981758			0.490879	−	0.871228i	$-0.336676\pi$
$347$	18.2881			0.981758			0.490879	+	0.871228i	$0.336676\pi$
$348$		0			0
$349$	−3.90136	+	6.75735i	−0.208835	+	0.361713i	−0.951348	−	0.308119i	$-0.900300\pi$
$349$	−3.90136	+	6.75735i	−0.208835	+	0.361713i	0.742513	+	0.669832i	$0.233634\pi$
$350$		0			0
$351$	−2.86333	−	7.02811i	−0.152833	−	0.375133i
$352$		0			0
$353$	−13.4626	−	23.3180i	−0.716544	−	1.24109i	−0.962361	−	0.271774i	$-0.912390\pi$
$353$	−13.4626	−	23.3180i	−0.716544	−	1.24109i	0.245817	−	0.969316i	$-0.420944\pi$
$354$		0			0
$355$	−0.386770	+	0.669906i	−0.0205276	+	0.0355549i
$356$		0			0
$357$	1.20914	−	17.0679i	0.0639945	−	0.903328i
$358$		0			0
$359$	3.13161	+	5.42411i	0.165280	+	0.286274i	0.936755	−	0.349987i	$-0.113814\pi$
$359$	3.13161	+	5.42411i	0.165280	+	0.286274i	−0.771475	+	0.636260i	$0.780481\pi$
$360$		0			0
$361$	1.28220	−	2.22084i	0.0674842	−	0.116886i
$362$		0			0
$363$	−3.98901	−	0.181919i	−0.209369	−	0.00954827i
$364$		0			0
$365$	3.04883	+	5.28073i	0.159583	+	0.276406i
$366$		0			0
$367$	14.6367	+	25.3515i	0.764028	+	1.32334i	0.940759	+	0.339076i	$0.110114\pi$
$367$	14.6367	+	25.3515i	0.764028	+	1.32334i	−0.176731	+	0.984259i	$0.556552\pi$
$368$		0			0
$369$	2.82597	+	0.258294i	0.147114	+	0.0134462i
$370$		0			0
$371$	28.0708	+	17.1621i	1.45736	+	0.891013i
$372$		0			0
$373$	−8.92986	+	15.4670i	−0.462371	+	0.800850i	−0.999079	−	0.0429184i	$-0.986334\pi$
$373$	−8.92986	+	15.4670i	−0.462371	+	0.800850i	0.536708	+	0.843768i	$0.319668\pi$
$374$		0			0
$375$	3.59144	+	6.93190i	0.185461	+	0.357962i
$376$		0			0
$377$	−13.1082			−0.675105
$378$		0			0
$379$	22.4255			1.15192			0.575960	−	0.817478i	$-0.304629\pi$
$379$	22.4255			1.15192			0.575960	+	0.817478i	$0.304629\pi$
$380$		0			0
$381$	−7.01965	−	13.5487i	−0.359628	−	0.694123i
$382$		0			0
$383$	−7.07014	+	12.2458i	−0.361267	+	0.625733i	−0.988170	−	0.153365i	$-0.950989\pi$
$383$	−7.07014	+	12.2458i	−0.361267	+	0.625733i	0.626903	+	0.779098i	$0.284322\pi$
$384$		0			0
$385$	0.111767	−	4.44284i	0.00569618	−	0.226428i
$386$		0			0
$387$	−11.7273	−	25.4063i	−0.596134	−	1.29147i
$388$		0			0
$389$	11.5651	+	20.0313i	0.586373	+	1.01563i	0.994703	+	0.102793i	$0.0327779\pi$
$389$	11.5651	+	20.0313i	0.586373	+	1.01563i	−0.408330	+	0.912834i	$0.633889\pi$
$390$		0			0
$391$	2.11537	+	3.66392i	0.106979	+	0.185292i
$392$		0			0
$393$	36.5729	+	1.66791i	1.84486	+	0.0841350i
$394$		0			0
$395$	1.15292	−	1.99691i	0.0580097	−	0.100476i
$396$		0			0
$397$	−5.13307	−	8.89075i	−0.257622	−	0.446214i	0.707983	−	0.706230i	$-0.249605\pi$
$397$	−5.13307	−	8.89075i	−0.257622	−	0.446214i	−0.965604	+	0.260016i	$0.916272\pi$
$398$		0			0
$399$	−15.3925	−	10.4028i	−0.770589	−	0.520792i
$400$		0			0
$401$	−17.0167	+	29.4738i	−0.849775	+	1.47185i	0.0316345	+	0.999500i	$0.489929\pi$
$401$	−17.0167	+	29.4738i	−0.849775	+	1.47185i	−0.881409	+	0.472353i	$0.843405\pi$
$402$		0			0
$403$	0.375780	+	0.650870i	0.0187189	+	0.0324221i
$404$		0			0
$405$	−4.07587	−	0.751347i	−0.202532	−	0.0373348i
$406$		0			0
$407$	−16.6118	+	28.7724i	−0.823415	+	1.42620i
$408$		0			0
$409$	−3.48968			−0.172554			−0.0862769	−	0.996271i	$-0.527497\pi$
$409$	−3.48968			−0.172554			−0.0862769	+	0.996271i	$0.527497\pi$
$410$		0			0
$411$	−4.11323	+	6.42892i	−0.202891	+	0.317115i
$412$		0			0
$413$	−0.858071	+	34.1091i	−0.0422229	+	1.67840i
$414$		0			0
$415$	1.53064	+	2.65115i	0.0751362	+	0.130140i
$416$		0			0
$417$	−1.89017	+	2.95431i	−0.0925622	+	0.144673i
$418$		0			0
$419$	−14.4897	−	25.0969i	−0.707867	−	1.22606i	−0.965647	−	0.259858i	$-0.916324\pi$
$419$	−14.4897	−	25.0969i	−0.707867	−	1.22606i	0.257779	−	0.966204i	$-0.417009\pi$
$420$		0			0
$421$	−1.06128	+	1.83819i	−0.0517237	+	0.0895881i	−0.890728	−	0.454537i	$-0.849805\pi$
$421$	−1.06128	+	1.83819i	−0.0517237	+	0.0895881i	0.839004	+	0.544125i	$0.183138\pi$
$422$		0			0
$423$	4.02704	−	5.70397i	0.195801	−	0.277337i
$424$		0			0
$425$	−17.8774			−0.867183
$426$		0			0
$427$	−0.803987	+	31.9592i	−0.0389077	+	1.54661i
$428$		0			0
$429$	9.21780	+	0.420378i	0.445040	+	0.0202960i
$430$		0			0
$431$	−10.9356	+	18.9410i	−0.526749	+	0.912356i	0.472765	+	0.881189i	$0.343256\pi$
$431$	−10.9356	+	18.9410i	−0.526749	+	0.912356i	−0.999514	+	0.0311679i	$0.990077\pi$
$432$		0			0
$433$	−13.0512			−0.627199			−0.313599	−	0.949555i	$-0.601535\pi$
$433$	−13.0512			−0.627199			−0.313599	+	0.949555i	$0.601535\pi$
$434$		0			0
$435$	−3.85807	+	6.03011i	−0.184980	+	0.289122i
$436$		0			0
$437$	4.59358			0.219741
$438$		0			0
$439$	−4.86400			−0.232146			−0.116073	−	0.993241i	$-0.537031\pi$
$439$	−4.86400			−0.232146			−0.116073	+	0.993241i	$0.537031\pi$
$440$		0			0
$441$	12.9590	−	16.5246i	0.617097	−	0.786887i
$442$		0			0
$443$	11.5395			0.548258			0.274129	−	0.961693i	$-0.411610\pi$
$443$	11.5395			0.548258			0.274129	+	0.961693i	$0.411610\pi$
$444$		0			0
$445$	−1.25564			−0.0595229
$446$		0			0
$447$	15.8530	+	0.722977i	0.749822	+	0.0341957i
$448$		0			0
$449$	−26.4251			−1.24708			−0.623538	−	0.781793i	$-0.714306\pi$
$449$	−26.4251			−1.24708			−0.623538	+	0.781793i	$0.714306\pi$
$450$		0			0
$451$	−1.72519	+	2.98812i	−0.0812361	+	0.140705i
$452$		0			0
$453$	0.0969833	−	0.151584i	0.00455667	−	0.00712201i
$454$		0			0
$455$	−0.0447509	+	1.77889i	−0.00209796	+	0.0833956i
$456$		0			0
$457$	−3.73812			−0.174862			−0.0874310	−	0.996171i	$-0.527866\pi$
$457$	−3.73812			−0.174862			−0.0874310	+	0.996171i	$0.527866\pi$
$458$		0			0
$459$	11.9004	−	15.3234i	0.555462	−	0.715233i
$460$		0			0
$461$	−7.90496	+	13.6918i	−0.368171	+	0.637690i	−0.989280	−	0.146034i	$-0.953349\pi$
$461$	−7.90496	+	13.6918i	−0.368171	+	0.637690i	0.621109	+	0.783724i	$0.286682\pi$
$462$		0			0
$463$	−19.1965	−	33.2493i	−0.892137	−	1.54523i	−0.837309	−	0.546730i	$-0.815872\pi$
$463$	−19.1965	−	33.2493i	−0.892137	−	1.54523i	−0.0548278	−	0.998496i	$-0.517461\pi$
$464$		0			0
$465$	0.410019	+	0.0186989i	0.0190142	+	0.000867143i
$466$		0			0
$467$	−3.15652	−	5.46725i	−0.146066	−	0.252994i	0.783704	−	0.621134i	$-0.213328\pi$
$467$	−3.15652	−	5.46725i	−0.146066	−	0.252994i	−0.929770	+	0.368140i	$0.879995\pi$
$468$		0			0
$469$	−0.154382	+	6.13682i	−0.00712869	+	0.283372i
$470$		0			0
$471$	16.7185	+	32.2686i	0.770347	+	1.48686i
$472$		0			0
$473$	34.0233			1.56439
$474$		0			0
$475$	−9.70535	+	16.8102i	−0.445312	+	0.771303i
$476$		0			0
$477$	15.6352	+	33.8724i	0.715887	+	1.55091i
$478$		0			0
$479$	−10.2068	−	17.6787i	−0.466361	−	0.807761i	0.532901	−	0.846178i	$-0.321102\pi$
$479$	−10.2068	−	17.6787i	−0.466361	−	0.807761i	−0.999262	+	0.0384168i	$0.987769\pi$
$480$		0			0
$481$	6.65126	−	11.5203i	0.303271	−	0.525282i
$482$		0			0
$483$	−0.366926	+	5.17942i	−0.0166957	+	0.235672i
$484$		0			0
$485$	2.57587	+	4.46154i	0.116964	+	0.202588i
$486$		0			0
$487$	−6.18190	+	10.7074i	−0.280129	+	0.485197i	−0.971416	−	0.237383i	$-0.923710\pi$
$487$	−6.18190	+	10.7074i	−0.280129	+	0.485197i	0.691287	+	0.722580i	$0.257044\pi$
$488$		0			0
$489$	−21.5036	+	33.6098i	−0.972426	+	1.51989i
$490$		0			0
$491$	−0.207004	−	0.358541i	−0.00934194	−	0.0161807i	0.861317	−	0.508069i	$-0.169640\pi$
$491$	−0.207004	−	0.358541i	−0.00934194	−	0.0161807i	−0.870659	+	0.491888i	$0.836307\pi$
$492$		0			0
$493$	−16.7558	−	29.0220i	−0.754645	−	1.30708i
$494$		0			0
$495$	2.90642	−	4.11671i	0.130634	−	0.185032i
$496$		0			0
$497$	0.111767	−	4.44284i	0.00501344	−	0.199289i
$498$		0			0
$499$	−0.461967	+	0.800151i	−0.0206805	+	0.0358197i	−0.876180	−	0.481983i	$-0.839917\pi$
$499$	−0.461967	+	0.800151i	−0.0206805	+	0.0358197i	0.855500	+	0.517803i	$0.173250\pi$
$500$		0			0
$501$	−9.92267	+	15.5090i	−0.443312	+	0.692890i
$502$		0			0
$503$	23.8142			1.06182			0.530911	−	0.847428i	$-0.321850\pi$
$503$	23.8142			1.06182			0.530911	+	0.847428i	$0.321850\pi$
$504$		0			0
$505$	−6.33463			−0.281887
$506$		0			0
$507$	18.8025	+	0.857490i	0.835049	+	0.0380825i
$508$		0			0
$509$	15.3171	−	26.5300i	0.678919	−	1.17592i	−0.296388	−	0.955068i	$-0.595782\pi$
$509$	15.3171	−	26.5300i	0.678919	−	1.17592i	0.975307	−	0.220855i	$-0.0708846\pi$
$510$		0			0
$511$	−29.8894	−	18.2740i	−1.32223	−	0.808393i
$512$		0			0
$513$	−7.94805	−	19.5087i	−0.350915	−	0.861330i
$514$		0			0
$515$	−2.57014	−	4.45161i	−0.113254	−	0.196161i
$516$		0			0
$517$	4.24484	+	7.35228i	0.186688	+	0.323353i
$518$		0			0
$519$	2.34154	+	4.51945i	0.102782	+	0.198382i
$520$		0			0
$521$	−13.4518	+	23.2993i	−0.589336	+	1.02076i	0.404984	+	0.914324i	$0.367277\pi$
$521$	−13.4518	+	23.2993i	−0.589336	+	1.02076i	−0.994320	+	0.106436i	$0.966056\pi$
$522$		0			0
$523$	7.85301	+	13.6018i	0.343388	+	0.594766i	0.985060	−	0.172214i	$-0.0550920\pi$
$523$	7.85301	+	13.6018i	0.343388	+	0.594766i	−0.641671	+	0.766980i	$0.721759\pi$
$524$		0			0
$525$	−18.1788	−	12.2859i	−0.793387	−	0.536199i
$526$		0			0
$527$	−0.960699	+	1.66398i	−0.0418487	+	0.0724841i
$528$		0			0
$529$	10.8581	+	18.8067i	0.472090	+	0.817684i
$530$		0			0
$531$	−22.3135	+	31.6053i	−0.968324	+	1.37155i
$532$		0			0
$533$	0.690757	−	1.19643i	0.0299200	−	0.0518230i
$534$		0			0
$535$	3.58307			0.154910
$536$		0			0
$537$	15.8530	+	0.722977i	0.684108	+	0.0311988i
$538$		0			0
$539$	11.6388	+	22.7267i	0.501319	+	0.978910i
$540$		0			0
$541$	−2.05934	−	3.56688i	−0.0885379	−	0.153352i	0.818355	−	0.574713i	$-0.194886\pi$
$541$	−2.05934	−	3.56688i	−0.0885379	−	0.153352i	−0.906893	+	0.421360i	$0.861553\pi$
$542$		0			0
$543$	17.8707	+	34.4926i	0.766906	+	1.48022i
$544$		0			0
$545$	1.73025	+	2.99689i	0.0741159	+	0.128372i
$546$		0			0
$547$	11.8602	−	20.5425i	0.507106	−	0.878333i	−0.492860	−	0.870108i	$-0.664049\pi$
$547$	11.8602	−	20.5425i	0.507106	−	0.878333i	0.999966	−	0.00822465i	$-0.00261802\pi$
$548$		0			0
$549$	−20.9071	+	29.6132i	−0.892293	+	1.26386i
$550$		0			0
$551$	−36.3858			−1.55009
$552$		0			0
$553$	−0.333165	+	13.2436i	−0.0141676	+	0.563176i
$554$		0			0
$555$	−3.34202	−	6.45049i	−0.141861	−	0.273808i
$556$		0			0
$557$	−21.0313	+	36.4273i	−0.891125	+	1.54347i	−0.0525975	+	0.998616i	$0.516750\pi$
$557$	−21.0313	+	36.4273i	−0.891125	+	1.54347i	−0.838528	+	0.544859i	$0.816583\pi$
$558$		0			0
$559$	−13.6228			−0.576181
$560$		0			0
$561$	10.8521	+	20.9459i	0.458178	+	0.884336i
$562$		0			0
$563$	−11.8243			−0.498335			−0.249168	−	0.968460i	$-0.580157\pi$
$563$	−11.8243			−0.498335			−0.249168	+	0.968460i	$0.580157\pi$
$564$		0			0
$565$	2.79125			0.117429
$566$		0			0
$567$	22.6316	−	7.40339i	0.950438	−	0.310913i
$568$		0			0
$569$	14.2016			0.595360			0.297680	−	0.954666i	$-0.403787\pi$
$569$	14.2016			0.595360			0.297680	+	0.954666i	$0.403787\pi$
$570$		0			0
$571$	−11.9574			−0.500401			−0.250200	−	0.968194i	$-0.580497\pi$
$571$	−11.9574			−0.500401			−0.250200	+	0.968194i	$0.580497\pi$
$572$		0			0
$573$	−1.98375	−	3.82888i	−0.0828725	−	0.159954i
$574$		0			0
$575$	5.42509			0.226242
$576$		0			0
$577$	21.3135	−	36.9161i	0.887293	−	1.53684i	0.0442307	−	0.999021i	$-0.485916\pi$
$577$	21.3135	−	36.9161i	0.887293	−	1.53684i	0.843062	−	0.537816i	$-0.180750\pi$
$578$		0			0
$579$	3.57733	+	6.90467i	0.148669	+	0.286948i
$580$		0			0
$581$	−15.0057	−	9.17431i	−0.622543	−	0.380614i
$582$		0			0
$583$	−45.3609			−1.87866
$584$		0			0
$585$	−1.16372	+	1.64831i	−0.0481137	+	0.0681491i
$586$		0			0
$587$	−20.5328	+	35.5638i	−0.847478	+	1.46788i	0.0359730	+	0.999353i	$0.488547\pi$
$587$	−20.5328	+	35.5638i	−0.847478	+	1.46788i	−0.883451	+	0.468523i	$0.844786\pi$
$588$		0			0
$589$	1.04309	+	1.80669i	0.0429799	+	0.0744434i
$590$		0			0
$591$	10.1462	+	19.5833i	0.417359	+	0.805551i
$592$		0			0
$593$	16.1008	+	27.8874i	0.661180	+	1.14520i	0.980306	+	0.197485i	$0.0632772\pi$
$593$	16.1008	+	27.8874i	0.661180	+	1.14520i	−0.319126	+	0.947712i	$0.603389\pi$
$594$		0			0
$595$	−3.99573	+	2.17483i	−0.163809	+	0.0891592i
$596$		0			0
$597$	5.09718	+	0.232457i	0.208614	+	0.00951383i
$598$		0			0
$599$	−19.0718			−0.779252			−0.389626	−	0.920973i	$-0.627396\pi$
$599$	−19.0718			−0.779252			−0.389626	+	0.920973i	$0.627396\pi$
$600$		0			0
$601$	4.27188	−	7.39912i	0.174254	−	0.301816i	−0.765649	−	0.643259i	$-0.777582\pi$
$601$	4.27188	−	7.39912i	0.174254	−	0.301816i	0.939903	+	0.341442i	$0.110915\pi$
$602$		0			0
$603$	−4.01459	+	5.68634i	−0.163487	+	0.231565i
$604$		0			0
$605$	0.530835	+	0.919434i	0.0215815	+	0.0373803i
$606$		0			0
$607$	19.0057	−	32.9189i	0.771419	−	1.33614i	−0.165366	−	0.986232i	$-0.552881\pi$
$607$	19.0057	−	32.9189i	0.771419	−	1.33614i	0.936785	−	0.349905i	$-0.113786\pi$
$608$		0			0
$609$	2.90642	−	41.0262i	0.117774	−	1.66247i
$610$		0			0
$611$	−1.69961	−	2.94381i	−0.0687589	−	0.119094i
$612$		0			0
$613$	11.3296	−	19.6234i	0.457597	−	0.792581i	−0.541237	−	0.840870i	$-0.682044\pi$
$613$	11.3296	−	19.6234i	0.457597	−	0.792581i	0.998833	+	0.0482894i	$0.0153770\pi$
$614$		0			0
$615$	−0.347081	−	0.669906i	−0.0139956	−	0.0270132i
$616$		0			0
$617$	−10.1388	−	17.5609i	−0.408173	−	0.706977i	0.586512	−	0.809941i	$-0.300501\pi$
$617$	−10.1388	−	17.5609i	−0.408173	−	0.706977i	−0.994685	+	0.102964i	$0.967167\pi$
$618$		0			0
$619$	1.03064	+	1.78512i	0.0414249	+	0.0717501i	0.885994	−	0.463696i	$-0.153477\pi$
$619$	1.03064	+	1.78512i	0.0414249	+	0.0717501i	−0.844570	+	0.535446i	$0.820144\pi$
$620$		0			0
$621$	−3.61129	+	4.65003i	−0.144916	+	0.186599i
$622$		0			0
$623$	6.33628	−	3.44877i	0.253858	−	0.138172i
$624$		0			0
$625$	−10.9320	+	18.9348i	−0.437280	+	0.757391i
$626$		0			0
$627$	25.5869	+	1.16689i	1.02184	+	0.0466011i
$628$		0			0
$629$	34.0085			1.35601
$630$		0			0
$631$	−1.63715			−0.0651740			−0.0325870	−	0.999469i	$-0.510375\pi$
$631$	−1.63715			−0.0651740			−0.0325870	+	0.999469i	$0.510375\pi$
$632$		0			0
$633$	−1.13541	+	1.77462i	−0.0451283	+	0.0705349i
$634$		0			0
$635$	−2.02850	+	3.51347i	−0.0804988	+	0.139428i
$636$		0			0
$637$	−4.66012	−	9.09967i	−0.184641	−	0.360542i
$638$		0			0
$639$	2.90642	−	4.11671i	0.114976	−	0.162854i
$640$		0			0
$641$	−10.9662	−	18.9941i	−0.433140	−	0.750221i	0.564001	−	0.825774i	$-0.309261\pi$
$641$	−10.9662	−	18.9941i	−0.433140	−	0.750221i	−0.997142	+	0.0755526i	$0.975928\pi$
$642$		0			0
$643$	14.1819	+	24.5638i	0.559280	+	0.968701i	0.997557	+	0.0698609i	$0.0222555\pi$
$643$	14.1819	+	24.5638i	0.559280	+	0.968701i	−0.438277	+	0.898840i	$0.644411\pi$
$644$		0			0
$645$	−4.00953	+	6.26683i	−0.157875	+	0.246756i
$646$		0			0
$647$	−17.3904	+	30.1210i	−0.683686	+	1.18418i	0.290162	+	0.956978i	$0.406291\pi$
$647$	−17.3904	+	30.1210i	−0.683686	+	1.18418i	−0.973848	+	0.227201i	$0.927042\pi$
$648$		0			0
$649$	−23.5203	−	40.7384i	−0.923253	−	1.59912i
$650$		0			0
$651$	−2.12043	+	1.03181i	−0.0831061	+	0.0404398i
$652$		0			0
$653$	1.59931	−	2.77009i	0.0625860	−	0.108402i	−0.833035	−	0.553221i	$-0.813399\pi$
$653$	1.59931	−	2.77009i	0.0625860	−	0.108402i	0.895621	+	0.444819i	$0.146732\pi$
$654$		0			0
$655$	−4.86693	−	8.42976i	−0.190167	−	0.329378i
$656$		0			0
$657$	−16.6481	−	36.0668i	−0.649506	−	1.40710i
$658$		0			0
$659$	−5.30418	+	9.18711i	−0.206622	+	0.357879i	−0.950648	−	0.310271i	$-0.899580\pi$
$659$	−5.30418	+	9.18711i	−0.206622	+	0.357879i	0.744027	+	0.668150i	$0.232914\pi$
$660$		0			0
$661$	10.1301			0.394017			0.197009	−	0.980402i	$-0.436877\pi$
$661$	10.1301			0.394017			0.197009	+	0.980402i	$0.436877\pi$
$662$		0			0
$663$	−4.34514	−	8.38662i	−0.168751	−	0.325709i
$664$		0			0
$665$	−0.124220	+	4.93786i	−0.00481705	+	0.191482i
$666$		0			0
$667$	5.08472	+	8.80700i	0.196881	+	0.341008i
$668$		0			0
$669$	1.54309	+	0.0703729i	0.0596595	+	0.00272077i
$670$		0			0
$671$	−22.0378	−	38.1707i	−0.850761	−	1.47356i
$672$		0			0
$673$	1.60817	−	2.78543i	0.0619903	−	0.107370i	−0.833365	−	0.552724i	$-0.813589\pi$
$673$	1.60817	−	2.78543i	0.0619903	−	0.107370i	0.895355	+	0.445353i	$0.146922\pi$
$674$		0			0
$675$	−9.38677	−	23.0401i	−0.361297	−	0.886813i
$676$		0			0
$677$	−29.3638			−1.12854			−0.564271	−	0.825589i	$-0.690843\pi$
$677$	−29.3638			−1.12854			−0.564271	+	0.825589i	$0.690843\pi$
$678$		0			0
$679$	−25.2527	−	15.4392i	−0.969110	−	0.592501i
$680$		0			0
$681$	13.6770	−	21.3770i	0.524105	−	0.819169i
$682$		0			0
$683$	−12.6278	+	21.8720i	−0.483190	+	0.836910i	−0.999814	−	0.0193029i	$-0.993855\pi$
$683$	−12.6278	+	21.8720i	−0.483190	+	0.836910i	0.516624	+	0.856213i	$0.327189\pi$
$684$		0			0
$685$	2.02918			0.0775309
$686$		0			0
$687$	16.5687	+	0.755615i	0.632134	+	0.0288285i
$688$		0			0
$689$	18.1623			0.691927
$690$		0			0
$691$	15.3638			0.584467			0.292233	−	0.956347i	$-0.405602\pi$
$691$	15.3638			0.584467			0.292233	+	0.956347i	$0.405602\pi$
$692$		0			0
$693$	−3.35953	+	28.7569i	−0.127618	+	1.09238i
$694$		0			0
$695$	0.932479			0.0353709
$696$		0			0
$697$	3.53191			0.133781
$698$		0			0
$699$	−13.4684	+	21.0509i	−0.509421	+	0.796217i
$700$		0			0
$701$	−13.3700			−0.504980			−0.252490	−	0.967600i	$-0.581249\pi$
$701$	−13.3700			−0.504980			−0.252490	+	0.967600i	$0.581249\pi$
$702$		0			0
$703$	18.4626	−	31.9782i	0.696332	−	1.20608i
$704$		0			0
$705$	−1.85447	−	0.0845733i	−0.0698435	−	0.00318522i
$706$		0			0
$707$	31.9662	−	17.3988i	1.20221	−	0.654351i
$708$		0			0
$709$	−1.12588			−0.0422832			−0.0211416	−	0.999776i	$-0.506730\pi$
$709$	−1.12588			−0.0422832			−0.0211416	+	0.999776i	$0.506730\pi$
$710$		0			0
$711$	−8.66372	+	12.2714i	−0.324915	+	0.460215i
$712$		0			0
$713$	0.291534	−	0.504951i	0.0109180	−	0.0189106i
$714$		0			0
$715$	−1.22665	−	2.12463i	−0.0458743	−	0.0794565i
$716$		0			0
$717$	−17.0914	+	26.7137i	−0.638292	+	0.997640i
$718$		0			0
$719$	−9.13667	−	15.8252i	−0.340740	−	0.590180i	0.643830	−	0.765169i	$-0.277344\pi$
$719$	−9.13667	−	15.8252i	−0.340740	−	0.590180i	−0.984570	+	0.174989i	$0.944011\pi$
$720$		0			0
$721$	25.1965	+	15.4048i	0.938366	+	0.573705i
$722$		0			0
$723$	0.0871712	−	0.136247i	0.00324193	−	0.00506709i
$724$		0			0
$725$	−42.9722			−1.59595
$726$		0			0
$727$	14.8478	−	25.7171i	0.550673	−	0.953793i	−0.447553	−	0.894257i	$-0.647705\pi$
$727$	14.8478	−	25.7171i	0.550673	−	0.953793i	0.998226	−	0.0595359i	$-0.0189621\pi$
$728$		0			0
$729$	25.9969	+	7.29124i	0.962847	+	0.270046i
$730$		0			0
$731$	−17.4136	−	30.1613i	−0.644066	−	1.11555i
$732$		0			0
$733$	−9.61390	+	16.6518i	−0.355098	+	0.615047i	−0.987135	−	0.159891i	$-0.948886\pi$
$733$	−9.61390	+	16.6518i	−0.355098	+	0.615047i	0.632037	+	0.774938i	$0.282219\pi$
$734$		0			0
$735$	−5.55768	−	0.534488i	−0.204998	−	0.0197149i
$736$		0			0
$737$	−4.23171	−	7.32955i	−0.155877	−	0.269987i
$738$		0			0
$739$	15.1336	−	26.2121i	0.556697	−	0.964227i	−0.441073	−	0.897471i	$-0.645402\pi$
$739$	15.1336	−	26.2121i	0.556697	−	0.964227i	0.997769	−	0.0667556i	$-0.0212648\pi$
$740$		0			0
$741$	−10.2448	−	0.467216i	−0.376354	−	0.0171636i
$742$		0			0
$743$	11.8815	+	20.5794i	0.435890	+	0.754984i	0.997368	−	0.0725076i	$-0.0231002\pi$
$743$	11.8815	+	20.5794i	0.435890	+	0.754984i	−0.561477	+	0.827492i	$0.689767\pi$
$744$		0			0
$745$	−2.10963	−	3.65399i	−0.0772909	−	0.133872i
$746$		0			0
$747$	−8.35807	−	18.1071i	−0.305806	−	0.662503i
$748$		0			0
$749$	−18.0811	+	9.84134i	−0.660670	+	0.359595i
$750$		0			0
$751$	6.33415	−	10.9711i	0.231136	−	0.400340i	−0.727006	−	0.686631i	$-0.759089\pi$
$751$	6.33415	−	10.9711i	0.231136	−	0.400340i	0.958143	+	0.286291i	$0.0924223\pi$
$752$		0			0
$753$	14.5600	+	28.1025i	0.530596	+	1.02411i
$754$		0			0
$755$	−0.0478448			−0.00174125
$756$		0			0
$757$	−29.0799			−1.05693			−0.528464	−	0.848955i	$-0.677232\pi$
$757$	−29.0799			−1.05693			−0.528464	+	0.848955i	$0.677232\pi$
$758$		0			0
$759$	−3.29319	−	6.35624i	−0.119535	−	0.230717i
$760$		0			0
$761$	−14.6015	+	25.2905i	−0.529302	+	0.916778i	0.470114	+	0.882606i	$0.344213\pi$
$761$	−14.6015	+	25.2905i	−0.529302	+	0.916778i	−0.999416	+	0.0341724i	$0.989120\pi$
$762$		0			0
$763$	−16.9626	−	10.3707i	−0.614089	−	0.375446i
$764$		0			0
$765$	−5.13696	−	0.469519i	−0.185727	−	0.0169755i
$766$		0			0
$767$	9.41741	+	16.3114i	0.340043	+	0.588972i
$768$		0			0
$769$	12.5869	+	21.8011i	0.453894	+	0.786167i	0.998624	−	0.0524443i	$-0.0167012\pi$
$769$	12.5869	+	21.8011i	0.453894	+	0.786167i	−0.544730	+	0.838611i	$0.683368\pi$
$770$		0			0
$771$	36.4238	+	1.66111i	1.31177	+	0.0598234i
$772$		0			0
$773$	−0.752039	+	1.30257i	−0.0270490	+	0.0468502i	−0.879233	−	0.476392i	$-0.841944\pi$
$773$	−0.752039	+	1.30257i	−0.0270490	+	0.0468502i	0.852184	+	0.523242i	$0.175278\pi$
$774$		0			0
$775$	1.23191	+	2.13373i	0.0442515	+	0.0766458i
$776$		0			0
$777$	34.5818	+	23.3716i	1.24062	+	0.838452i
$778$		0			0
$779$	1.91741	−	3.32105i	0.0686984	−	0.118989i
$780$		0			0
$781$	3.06361	+	5.30633i	0.109625	+	0.189875i
$782$		0			0
$783$	28.6050	−	36.8329i	1.02226	−	1.31630i
$784$		0			0
$785$	4.83122	−	8.36792i	0.172434	−	0.298664i
$786$		0			0
$787$	14.9531			0.533021			0.266510	−	0.963832i	$-0.414129\pi$
$787$	14.9531			0.533021			0.266510	+	0.963832i	$0.414129\pi$
$788$		0			0
$789$	4.82150	−	7.53593i	0.171650	−	0.268286i
$790$		0			0
$791$	−14.0854	+	7.66652i	−0.500819	+	0.272590i
$792$		0			0
$793$	8.82383	+	15.2833i	0.313343	+	0.542727i
$794$		0			0
$795$	5.34562	−	8.35512i	0.189590	−	0.296326i
$796$		0			0
$797$	−4.56294	−	7.90324i	−0.161628	−	0.279947i	0.773825	−	0.633400i	$-0.218341\pi$
$797$	−4.56294	−	7.90324i	−0.161628	−	0.279947i	−0.935453	+	0.353452i	$0.885008\pi$
$798$		0			0
$799$	4.34514	−	7.52600i	0.153720	−	0.266251i
$800$		0			0
$801$	8.14601	+	0.744547i	0.287825	+	0.0263073i
$802$		0			0
$803$	48.2996			1.70446
$804$		0			0
$805$	1.21254	−	0.659973i	0.0427365	−	0.0232610i
$806$		0			0
$807$	29.1665	+	1.33014i	1.02671	+	0.0468232i
$808$		0			0
$809$	17.7755	−	30.7880i	0.624953	−	1.08245i	−0.363597	−	0.931556i	$-0.618452\pi$
$809$	17.7755	−	30.7880i	0.624953	−	1.08245i	0.988550	−	0.150894i	$-0.0482151\pi$
$810$		0			0
$811$	13.5070			0.474295			0.237148	−	0.971474i	$-0.423788\pi$
$811$	13.5070			0.474295			0.237148	+	0.971474i	$0.423788\pi$
$812$		0			0
$813$	23.4415	−	36.6388i	0.822130	−	1.28498i
$814$		0			0
$815$	10.6084			0.371595
$816$		0			0
$817$	−37.8142			−1.32295
$818$		0			0
$819$	1.34514	−	11.5141i	0.0470030	−	0.402335i
$820$		0			0
$821$	21.6228			0.754639			0.377320	−	0.926083i	$-0.376846\pi$
$821$	21.6228			0.754639			0.377320	+	0.926083i	$0.376846\pi$
$822$		0			0
$823$	1.50700			0.0525308			0.0262654	−	0.999655i	$-0.491639\pi$
$823$	1.50700			0.0525308			0.0262654	+	0.999655i	$0.491639\pi$
$824$		0			0
$825$	30.2185	+	1.37811i	1.05207	+	0.0479798i
$826$		0			0
$827$	−23.3786			−0.812953			−0.406477	−	0.913661i	$-0.633243\pi$
$827$	−23.3786			−0.812953			−0.406477	+	0.913661i	$0.633243\pi$
$828$		0			0
$829$	−11.0095	+	19.0691i	−0.382377	+	0.662296i	−0.991401	−	0.130855i	$-0.958228\pi$
$829$	−11.0095	+	19.0691i	−0.382377	+	0.662296i	0.609025	+	0.793151i	$0.291561\pi$
$830$		0			0
$831$	3.15652	−	4.93359i	0.109498	−	0.171144i
$832$		0			0
$833$	14.1901	−	21.9495i	0.491657	−	0.760506i
$834$		0			0
$835$	4.89515			0.169404
$836$		0			0
$837$	−2.64893	−	0.364437i	−0.0915605	−	0.0125968i
$838$		0			0
$839$	1.06507	−	1.84476i	0.0367705	−	0.0636883i	−0.847055	−	0.531506i	$-0.821626\pi$
$839$	1.06507	−	1.84476i	0.0367705	−	0.0636883i	0.883825	+	0.467818i	$0.154960\pi$
$840$		0			0
$841$	−25.7762	−	44.6456i	−0.888833	−	1.53950i
$842$		0			0
$843$	−35.0854	−	1.60007i	−1.20841	−	0.0551094i
$844$		0			0
$845$	−2.50214	−	4.33383i	−0.0860761	−	0.149088i
$846$		0			0
$847$	−5.20408	−	3.18171i	−0.178814	−	0.109325i
$848$		0			0
$849$	−13.8238	−	26.6816i	−0.474433	−	0.915710i
$850$		0			0
$851$	−10.3202			−0.353773
$852$		0			0
$853$	−3.50146	+	6.06471i	−0.119888	+	0.207652i	−0.919723	−	0.392568i	$-0.871587\pi$
$853$	−3.50146	+	6.06471i	−0.119888	+	0.207652i	0.799835	+	0.600220i	$0.204920\pi$
$854$		0			0
$855$	−3.23025	+	4.57539i	−0.110472	+	0.156475i
$856$		0			0
$857$	−5.46410	−	9.46410i	−0.186650	−	0.323288i	0.757481	−	0.652857i	$-0.226430\pi$
$857$	−5.46410	−	9.46410i	−0.186650	−	0.323288i	−0.944131	+	0.329569i	$0.893096\pi$
$858$		0			0
$859$	−6.95379	+	12.0443i	−0.237260	+	0.410947i	−0.959927	−	0.280250i	$-0.909583\pi$
$859$	−6.95379	+	12.0443i	−0.237260	+	0.410947i	0.722667	+	0.691196i	$0.242916\pi$
$860$		0			0
$861$	3.59144	+	2.42723i	0.122396	+	0.0827196i
$862$		0			0
$863$	18.4231	+	31.9098i	0.627131	+	1.08622i	0.988125	+	0.153655i	$0.0491043\pi$
$863$	18.4231	+	31.9098i	0.627131	+	1.08622i	−0.360993	+	0.932568i	$0.617562\pi$
$864$		0			0
$865$	0.676647	−	1.17199i	0.0230067	−	0.0398488i
$866$		0			0
$867$	−2.85486	+	4.46211i	−0.0969562	+	0.151541i
$868$		0			0
$869$	−9.13229	−	15.8176i	−0.309792	−	0.536575i
$870$		0			0
$871$	1.69436	+	2.93471i	0.0574111	+	0.0994389i
$872$		0			0
$873$	−14.0656	−	30.4718i	−0.476047	−	1.03132i
$874$		0			0
$875$	−0.299909	+	11.9217i	−0.0101388	+	0.403026i
$876$		0			0
$877$	5.17977	−	8.97162i	0.174908	−	0.302950i	−0.765221	−	0.643767i	$-0.777370\pi$
$877$	5.17977	−	8.97162i	0.174908	−	0.302950i	0.940130	+	0.340817i	$0.110704\pi$
$878$		0			0
$879$	9.21440	−	14.4020i	0.310794	−	0.485766i
$880$		0			0
$881$	9.34806			0.314944			0.157472	−	0.987523i	$-0.449666\pi$
$881$	9.34806			0.314944			0.157472	+	0.987523i	$0.449666\pi$
$882$		0			0
$883$	−2.29494			−0.0772308			−0.0386154	−	0.999254i	$-0.512295\pi$
$883$	−2.29494			−0.0772308			−0.0386154	+	0.999254i	$0.512295\pi$
$884$		0			0
$885$	10.2755	+	0.468614i	0.345407	+	0.0157523i
$886$		0			0
$887$	−13.8363	+	23.9651i	−0.464577	+	0.804671i	−0.999182	−	0.0404309i	$-0.987127\pi$
$887$	−13.8363	+	23.9651i	−0.464577	+	0.804671i	0.534605	+	0.845102i	$0.320460\pi$
$888$		0			0
$889$	0.586187	−	23.3015i	0.0196601	−	0.781506i
$890$		0			0
$891$	−21.2966	+	24.9839i	−0.713463	+	0.836993i
$892$		0			0
$893$	−4.71780	−	8.17147i	−0.157875	−	0.273448i
$894$		0			0
$895$	−2.10963	−	3.65399i	−0.0705172	−	0.122139i
$896$		0			0
$897$	1.31858	+	2.54500i	0.0440260	+	0.0849752i
$898$		0			0
$899$	−2.30924	+	3.99973i	−0.0770176	+	0.133398i
$900$		0			0
$901$	23.2163	+	40.2119i	0.773448	+	1.33965i
$902$		0			0
$903$	3.02052	−	42.6368i	0.100517	−	1.41886i
$904$		0			0
$905$	5.16419	−	8.94465i	0.171664	−	0.297330i
$906$		0			0
$907$	−1.46576	−	2.53877i	−0.0486698	−	0.0842985i	0.840664	−	0.541557i	$-0.182165\pi$
$907$	−1.46576	−	2.53877i	−0.0486698	−	0.0842985i	−0.889334	+	0.457258i	$0.848832\pi$
$908$		0			0
$909$	41.0962	+	3.75620i	1.36307	+	0.124585i
$910$		0			0
$911$	−15.3171	+	26.5300i	−0.507479	+	0.878979i	0.492484	+	0.870322i	$0.336089\pi$
$911$	−15.3171	+	26.5300i	−0.507479	+	0.878979i	−0.999963	+	0.00865719i	$0.997244\pi$
$912$		0			0
$913$	24.2484			0.802506
$914$		0			0
$915$	9.62782	+	0.439077i	0.318286	+	0.0145154i
$916$		0			0
$917$	47.7132	+	29.1712i	1.57563	+	0.963319i
$918$		0			0
$919$	−13.1857	−	22.8383i	−0.434956	−	0.753366i	0.562336	−	0.826909i	$-0.309903\pi$
$919$	−13.1857	−	22.8383i	−0.434956	−	0.753366i	−0.997292	+	0.0735429i	$0.976569\pi$
$920$		0			0
$921$	−6.20535	−	11.9770i	−0.204473	−	0.394657i
$922$		0			0
$923$	−1.22665	−	2.12463i	−0.0403758	−	0.0699329i
$924$		0			0
$925$	21.8047	−	37.7668i	0.716933	−	1.24176i
$926$		0			0
$927$	14.0342	+	30.4040i	0.460945	+	0.998598i
$928$		0			0
$929$	17.8741			0.586431			0.293215	−	0.956046i	$-0.405275\pi$
$929$	17.8741			0.586431			0.293215	+	0.956046i	$0.405275\pi$
$930$		0			0
$931$	−12.9356	−	25.2590i	−0.423947	−	0.827829i
$932$		0			0
$933$	−12.2791	−	23.7001i	−0.401999	−	0.775905i
$934$		0			0
$935$	3.13600	−	5.43171i	0.102558	−	0.177636i
$936$		0			0
$937$	15.9134			0.519869			0.259934	−	0.965626i	$-0.416299\pi$
$937$	15.9134			0.519869			0.259934	+	0.965626i	$0.416299\pi$
$938$		0			0
$939$	6.77023	+	13.0673i	0.220938	+	0.426436i
$940$		0			0
$941$	−16.2805			−0.530731			−0.265365	−	0.964148i	$-0.585493\pi$
$941$	−16.2805			−0.530731			−0.265365	+	0.964148i	$0.585493\pi$
$942$		0			0
$943$	−1.07179			−0.0349024
$944$		0			0
$945$	−4.90088	−	4.00769i	−0.159426	−	0.130370i
$946$		0			0
$947$	28.5903			0.929059			0.464529	−	0.885558i	$-0.346224\pi$
$947$	28.5903			0.929059			0.464529	+	0.885558i	$0.346224\pi$
$948$		0			0
$949$	−19.3389			−0.627767
$950$		0			0
$951$	−11.2389	−	21.6924i	−0.364447	−	0.703424i
$952$		0			0
$953$	−29.3537			−0.950859			−0.475430	−	0.879754i	$-0.657707\pi$
$953$	−29.3537			−0.950859			−0.475430	+	0.879754i	$0.657707\pi$
$954$		0			0
$955$	−0.573256	+	0.992908i	−0.0185501	+	0.0321297i
$956$		0			0
$957$	26.0854	+	50.3479i	0.843221	+	1.62751i
$958$		0			0
$959$	−10.2398	+	5.57339i	−0.330660	+	0.179974i
$960$		0			0
$961$	−30.7352			−0.991458
$962$		0			0
$963$	−23.2453	−	2.12463i	−0.749070	−	0.0684651i
$964$		0			0
$965$	1.03376	−	1.79053i	0.0332779	−	0.0576391i
$966$		0			0
$967$	4.69815	+	8.13743i	0.151082	+	0.261682i	0.931626	−	0.363419i	$-0.118391\pi$
$967$	4.69815	+	8.13743i	0.151082	+	0.261682i	−0.780543	+	0.625102i	$0.785057\pi$
$968$		0			0
$969$	−12.0613	−	23.2797i	−0.387464	−	0.747851i
$970$		0			0
$971$	−7.77335	−	13.4638i	−0.249459	−	0.432075i	0.713917	−	0.700230i	$-0.246919\pi$
$971$	−7.77335	−	13.4638i	−0.249459	−	0.432075i	−0.963376	+	0.268155i	$0.913586\pi$
$972$		0			0
$973$	−4.70554	+	2.56117i	−0.150853	+	0.0821074i
$974$		0			0
$975$	−12.0993	−	0.551790i	−0.387488	−	0.0176714i
$976$		0			0
$977$	−9.59785			−0.307062			−0.153531	−	0.988144i	$-0.549065\pi$
$977$	−9.59785			−0.307062			−0.153531	+	0.988144i	$0.549065\pi$
$978$		0			0
$979$	−4.97296	+	8.61342i	−0.158936	+	0.275286i
$980$		0			0
$981$	−9.44805	−	20.4684i	−0.301653	−	0.653506i
$982$		0			0
$983$	−23.4267	−	40.5763i	−0.747197	−	1.29418i	−0.949161	−	0.314790i	$-0.898066\pi$
$983$	−23.4267	−	40.5763i	−0.747197	−	1.29418i	0.201964	−	0.979393i	$-0.435268\pi$
$984$		0			0
$985$	2.93200	−	5.07837i	0.0934213	−	0.161810i
$986$		0			0
$987$	9.59046	−	4.66676i	0.305268	−	0.148545i
$988$		0			0
$989$	5.28434	+	9.15274i	0.168032	+	0.291040i
$990$		0			0
$991$	−10.8260	+	18.7511i	−0.343898	+	0.595649i	−0.985153	−	0.171679i	$-0.945081\pi$
$991$	−10.8260	+	18.7511i	−0.343898	+	0.595649i	0.641255	+	0.767328i	$0.278414\pi$
$992$		0			0
$993$	−21.9466	−	42.3595i	−0.696454	−	1.34424i
$994$		0			0
$995$	−0.678304	−	1.17486i	−0.0215037	−	0.0372455i
$996$		0			0
$997$	28.6190	+	49.5695i	0.906372	+	1.56988i	0.819065	+	0.573700i	$0.194493\pi$
$997$	28.6190	+	49.5695i	0.906372	+	1.56988i	0.0873064	+	0.996182i	$0.472174\pi$
$998$		0			0
$999$	17.8566	+	43.8295i	0.564958	+	1.38670i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.q.h.529.2		6
3.2	odd	2		3024.2.q.h.2881.1		6
4.3	odd	2		126.2.e.d.25.2	✓	6
7.2	even	3		1008.2.t.g.961.1		6
9.4	even	3		1008.2.t.g.193.1		6
9.5	odd	6		3024.2.t.g.1873.3		6
12.11	even	2		378.2.e.c.235.1		6
21.2	odd	6		3024.2.t.g.289.3		6
28.3	even	6		882.2.f.m.295.2		6
28.11	odd	6		882.2.f.l.295.2		6
28.19	even	6		882.2.h.o.79.1		6
28.23	odd	6		126.2.h.c.79.3	yes	6
28.27	even	2		882.2.e.p.655.2		6
36.7	odd	6		1134.2.g.k.487.3		6
36.11	even	6		1134.2.g.n.487.1		6
36.23	even	6		378.2.h.d.361.3		6
36.31	odd	6		126.2.h.c.67.3	yes	6
63.23	odd	6		3024.2.q.h.2305.1		6
63.58	even	3	inner	1008.2.q.h.625.2		6
84.11	even	6		2646.2.f.o.883.1		6
84.23	even	6		378.2.h.d.289.3		6
84.47	odd	6		2646.2.h.p.667.1		6
84.59	odd	6		2646.2.f.n.883.3		6
84.83	odd	2		2646.2.e.o.2125.3		6
252.11	even	6		7938.2.a.bu.1.3		3
252.23	even	6		378.2.e.c.37.1		6
252.31	even	6		882.2.f.m.589.2		6
252.59	odd	6		2646.2.f.n.1765.3		6
252.67	odd	6		882.2.f.l.589.2		6
252.79	odd	6		1134.2.g.k.163.3		6
252.95	even	6		2646.2.f.o.1765.1		6
252.103	even	6		882.2.e.p.373.2		6
252.115	even	6		7938.2.a.by.1.3		3
252.131	odd	6		2646.2.e.o.1549.3		6
252.139	even	6		882.2.h.o.67.1		6
252.151	odd	6		7938.2.a.cb.1.1		3
252.167	odd	6		2646.2.h.p.361.1		6
252.191	even	6		1134.2.g.n.163.1		6
252.227	odd	6		7938.2.a.bx.1.1		3
252.247	odd	6		126.2.e.d.121.2	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.2	✓	6	4.3	odd	2
126.2.e.d.121.2	yes	6	252.247	odd	6
126.2.h.c.67.3	yes	6	36.31	odd	6
126.2.h.c.79.3	yes	6	28.23	odd	6
378.2.e.c.37.1		6	252.23	even	6
378.2.e.c.235.1		6	12.11	even	2
378.2.h.d.289.3		6	84.23	even	6
378.2.h.d.361.3		6	36.23	even	6
882.2.e.p.373.2		6	252.103	even	6
882.2.e.p.655.2		6	28.27	even	2
882.2.f.l.295.2		6	28.11	odd	6
882.2.f.l.589.2		6	252.67	odd	6
882.2.f.m.295.2		6	28.3	even	6
882.2.f.m.589.2		6	252.31	even	6
882.2.h.o.67.1		6	252.139	even	6
882.2.h.o.79.1		6	28.19	even	6
1008.2.q.h.529.2		6	1.1	even	1	trivial
1008.2.q.h.625.2		6	63.58	even	3	inner
1008.2.t.g.193.1		6	9.4	even	3
1008.2.t.g.961.1		6	7.2	even	3
1134.2.g.k.163.3		6	252.79	odd	6
1134.2.g.k.487.3		6	36.7	odd	6
1134.2.g.n.163.1		6	252.191	even	6
1134.2.g.n.487.1		6	36.11	even	6
2646.2.e.o.1549.3		6	252.131	odd	6
2646.2.e.o.2125.3		6	84.83	odd	2
2646.2.f.n.883.3		6	84.59	odd	6
2646.2.f.n.1765.3		6	252.59	odd	6
2646.2.f.o.883.1		6	84.11	even	6
2646.2.f.o.1765.1		6	252.95	even	6
2646.2.h.p.361.1		6	252.167	odd	6
2646.2.h.p.667.1		6	84.47	odd	6
3024.2.q.h.2305.1		6	63.23	odd	6
3024.2.q.h.2881.1		6	3.2	odd	2
3024.2.t.g.289.3		6	21.2	odd	6
3024.2.t.g.1873.3		6	9.5	odd	6
7938.2.a.bu.1.3		3	252.11	even	6
7938.2.a.bx.1.1		3	252.227	odd	6
7938.2.a.by.1.3		3	252.115	even	6
7938.2.a.cb.1.1		3	252.151	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.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.796790 + 1.53790i) q^{3} +(0.230252 - 0.398809i) q^{5} +(-0.0665372 + 2.64491i) q^{7} +(-1.73025 + 2.45076i) q^{9} +O(q^{10})\)	\(q+(0.796790 + 1.53790i) q^{3} +(0.230252 - 0.398809i) q^{5} +(-0.0665372 + 2.64491i) q^{7} +(-1.73025 + 2.45076i) q^{9} +(-1.82383 - 3.15897i) q^{11} +(0.730252 + 1.26483i) q^{13} +(0.796790 + 0.0363376i) q^{15} +(-1.86693 + 3.23361i) q^{17} +(2.02704 + 3.51094i) q^{19} +(-4.12062 + 2.00511i) q^{21} +(0.566537 - 0.981271i) q^{23} +(2.39397 + 4.14647i) q^{25} +(-5.14766 - 0.708209i) q^{27} +(-4.48755 + 7.77266i) q^{29} +0.514589 q^{31} +(3.40496 - 5.32190i) q^{33} +(1.03950 + 0.635534i) q^{35} +(-4.55408 - 7.88791i) q^{37} +(-1.36333 + 2.13086i) q^{39} +(-0.472958 - 0.819187i) q^{41} +(-4.66372 + 8.07779i) q^{43} +(0.578990 + 1.25433i) q^{45} -2.32743 q^{47} +(-6.99115 - 0.351971i) q^{49} +(-6.46050 - 0.294632i) q^{51} +(6.21780 - 10.7695i) q^{53} -1.67977 q^{55} +(-3.78434 + 5.91486i) q^{57} +12.8961 q^{59} +12.0833 q^{61} +(-6.36693 - 4.73944i) q^{63} +0.672570 q^{65} +2.32023 q^{67} +(1.96050 + 0.0894089i) q^{69} -1.67977 q^{71} +(-6.62062 + 11.4673i) q^{73} +(-4.46936 + 6.98554i) q^{75} +(8.47656 - 4.61369i) q^{77} +5.00720 q^{79} +(-3.01245 - 8.48087i) q^{81} +(-3.32383 + 5.75705i) q^{83} +(0.859728 + 1.48909i) q^{85} +(-15.5292 - 0.708209i) q^{87} +(-1.36333 - 2.36135i) q^{89} +(-3.39397 + 1.84730i) q^{91} +(0.410019 + 0.791385i) q^{93} +1.86693 q^{95} +(-5.59358 + 9.68836i) q^{97} +(10.8976 + 0.996040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{3} - 5 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 6 * q + 2 * q^3 - 5 * q^5 - 4 * q^7 - 4 * q^9	\( 6 q + 2 q^{3} - 5 q^{5} - 4 q^{7} - 4 q^{9} + q^{11} - 2 q^{13} + 2 q^{15} - 4 q^{17} + 3 q^{19} - 10 q^{21} + 7 q^{23} - 2 q^{25} - 7 q^{27} - 5 q^{29} - 28 q^{31} - 19 q^{33} + 19 q^{35} - 9 q^{37} - 9 q^{39} - 12 q^{41} - 18 q^{43} + 29 q^{45} + 6 q^{47} - 12 q^{49} - 26 q^{51} + 9 q^{53} - 14 q^{55} + 2 q^{57} + 8 q^{59} - 8 q^{61} - 31 q^{63} + 24 q^{65} + 10 q^{67} - q^{69} - 14 q^{71} - 25 q^{73} - 44 q^{75} + 52 q^{77} + 14 q^{79} - 40 q^{81} - 8 q^{83} + 14 q^{85} - 31 q^{87} - 9 q^{89} - 4 q^{91} + 4 q^{95} - 28 q^{97} + 41 q^{99}+O(q^{100}) \) 6 * q + 2 * q^3 - 5 * q^5 - 4 * q^7 - 4 * q^9 + q^11 - 2 * q^13 + 2 * q^15 - 4 * q^17 + 3 * q^19 - 10 * q^21 + 7 * q^23 - 2 * q^25 - 7 * q^27 - 5 * q^29 - 28 * q^31 - 19 * q^33 + 19 * q^35 - 9 * q^37 - 9 * q^39 - 12 * q^41 - 18 * q^43 + 29 * q^45 + 6 * q^47 - 12 * q^49 - 26 * q^51 + 9 * q^53 - 14 * q^55 + 2 * q^57 + 8 * q^59 - 8 * q^61 - 31 * q^63 + 24 * q^65 + 10 * q^67 - q^69 - 14 * q^71 - 25 * q^73 - 44 * q^75 + 52 * q^77 + 14 * q^79 - 40 * q^81 - 8 * q^83 + 14 * q^85 - 31 * q^87 - 9 * q^89 - 4 * q^91 + 4 * q^95 - 28 * q^97 + 41 * q^99

Introduction

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