LMFDB - Embedded newform 676.2.f.i.239.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [676,2,Mod(99,676)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(676, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("676.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 676 = 2^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	676.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.39788717664$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.102930383934669717504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 5 x^{14} - 2 x^{13} + 5 x^{12} - 8 x^{11} - 12 x^{10} + 32 x^{9} - 36 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 5x^14 - 2x^13 + 5x^12 - 8x^11 - 12x^10 + 32x^9 - 36x^8 + 64x^7 - 48x^6 - 64x^5 + 80x^4 - 64x^3 + 320x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.5
Root			$1.17605 + 0.785427i$ of defining polynomial
Character	$\chi$	$=$	676.239
Dual form			676.2.f.i.99.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.625780 - 1.26823i) q^{2} -2.09440i q^{3} +(-1.21680 - 1.58726i) q^{4} +(-0.894007 + 0.894007i) q^{5} +(-2.65617 - 1.31063i) q^{6} +(-3.20020 + 3.20020i) q^{7} +(-2.77446 + 0.549903i) q^{8} -1.38651 q^{9} +O(q^{10})$	\(q+(0.625780 - 1.26823i) q^{2} -2.09440i q^{3} +(-1.21680 - 1.58726i) q^{4} +(-0.894007 + 0.894007i) q^{5} +(-2.65617 - 1.31063i) q^{6} +(-3.20020 + 3.20020i) q^{7} +(-2.77446 + 0.549903i) q^{8} -1.38651 q^{9} +(0.574352 + 1.69325i) q^{10} +(-1.10580 + 1.10580i) q^{11} +(-3.32436 + 2.54846i) q^{12} +(2.05596 + 6.06121i) q^{14} +(1.87241 + 1.87241i) q^{15} +(-1.03880 + 3.86276i) q^{16} -0.0559625i q^{17} +(-0.867649 + 1.75841i) q^{18} +(-1.57611 - 1.57611i) q^{19} +(2.50685 + 0.331195i) q^{20} +(6.70250 + 6.70250i) q^{21} +(0.710421 + 2.09440i) q^{22} -1.05782 q^{23} +(1.15172 + 5.81082i) q^{24} +3.40150i q^{25} -3.37929i q^{27} +(8.97356 + 1.18555i) q^{28} -7.34904 q^{29} +(3.54635 - 1.20292i) q^{30} +(-4.52800 - 4.52800i) q^{31} +(4.24880 + 3.73466i) q^{32} +(2.31599 + 2.31599i) q^{33} +(-0.0709732 - 0.0350202i) q^{34} -5.72201i q^{35} +(1.68710 + 2.20075i) q^{36} +(-1.36603 - 1.36603i) q^{37} +(-2.98516 + 1.01257i) q^{38} +(1.98877 - 2.97200i) q^{40} +(-1.09808 + 1.09808i) q^{41} +(12.6946 - 4.30601i) q^{42} +2.08050 q^{43} +(3.10074 + 0.409658i) q^{44} +(1.23955 - 1.23955i) q^{45} +(-0.661960 + 1.34155i) q^{46} +(-5.38281 + 5.38281i) q^{47} +(8.09016 + 2.17565i) q^{48} -13.4826i q^{49} +(4.31388 + 2.12859i) q^{50} -0.117208 q^{51} -4.40150 q^{53} +(-4.28571 - 2.11469i) q^{54} -1.97719i q^{55} +(7.11902 - 10.6386i) q^{56} +(-3.30100 + 3.30100i) q^{57} +(-4.59888 + 9.32026i) q^{58} +(6.35242 - 6.35242i) q^{59} +(0.693654 - 5.25034i) q^{60} -2.01500 q^{61} +(-8.57606 + 2.90900i) q^{62} +(4.43711 - 4.43711i) q^{63} +(7.39521 - 3.05136i) q^{64} +(4.38651 - 1.48790i) q^{66} +(-6.48861 - 6.48861i) q^{67} +(-0.0888271 + 0.0680952i) q^{68} +2.21549i q^{69} +(-7.25680 - 3.58071i) q^{70} +(4.82430 + 4.82430i) q^{71} +(3.84681 - 0.762445i) q^{72} +(5.45504 + 5.45504i) q^{73} +(-2.58726 + 0.877600i) q^{74} +7.12411 q^{75} +(-0.583887 + 4.41950i) q^{76} -7.07759i q^{77} +8.87422i q^{79} +(-2.52464 - 4.38202i) q^{80} -11.2371 q^{81} +(0.705456 + 2.07976i) q^{82} +(6.96160 + 6.96160i) q^{83} +(2.48302 - 18.7942i) q^{84} +(0.0500308 + 0.0500308i) q^{85} +(1.30194 - 2.63855i) q^{86} +15.3918i q^{87} +(2.45992 - 3.67609i) q^{88} +(-11.2076 - 11.2076i) q^{89} +(-0.796345 - 2.34771i) q^{90} +(1.28715 + 1.67903i) q^{92} +(-9.48344 + 9.48344i) q^{93} +(3.45817 + 10.1951i) q^{94} +2.81810 q^{95} +(7.82188 - 8.89868i) q^{96} +(-0.322629 + 0.322629i) q^{97} +(-17.0990 - 8.43714i) q^{98} +(1.53321 - 1.53321i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 12 q^{5} - 4 q^{6} - 10 q^{8} - 8 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 + 12 * q^5 - 4 * q^6 - 10 * q^8 - 8 * q^9	$ 16 q + 2 q^{2} + 12 q^{5} - 4 q^{6} - 10 q^{8} - 8 q^{9} + 8 q^{14} + 4 q^{16} + 6 q^{18} + 22 q^{20} + 28 q^{21} - 4 q^{24} + 36 q^{28} + 16 q^{29} + 2 q^{32} - 28 q^{33} - 14 q^{34} - 8 q^{37} - 40 q^{40} + 24 q^{41} + 56 q^{42} + 8 q^{44} - 20 q^{45} - 56 q^{46} + 20 q^{48} + 32 q^{50} - 32 q^{53} - 44 q^{54} - 12 q^{57} - 30 q^{58} + 24 q^{60} - 8 q^{61} + 56 q^{66} - 32 q^{68} - 28 q^{70} + 46 q^{72} - 20 q^{73} - 8 q^{74} + 8 q^{76} + 22 q^{80} - 96 q^{81} + 48 q^{84} + 52 q^{85} - 16 q^{86} - 44 q^{89} - 12 q^{92} - 112 q^{93} + 76 q^{94} + 72 q^{96} + 52 q^{97} - 70 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 + 12 * q^5 - 4 * q^6 - 10 * q^8 - 8 * q^9 + 8 * q^14 + 4 * q^16 + 6 * q^18 + 22 * q^20 + 28 * q^21 - 4 * q^24 + 36 * q^28 + 16 * q^29 + 2 * q^32 - 28 * q^33 - 14 * q^34 - 8 * q^37 - 40 * q^40 + 24 * q^41 + 56 * q^42 + 8 * q^44 - 20 * q^45 - 56 * q^46 + 20 * q^48 + 32 * q^50 - 32 * q^53 - 44 * q^54 - 12 * q^57 - 30 * q^58 + 24 * q^60 - 8 * q^61 + 56 * q^66 - 32 * q^68 - 28 * q^70 + 46 * q^72 - 20 * q^73 - 8 * q^74 + 8 * q^76 + 22 * q^80 - 96 * q^81 + 48 * q^84 + 52 * q^85 - 16 * q^86 - 44 * q^89 - 12 * q^92 - 112 * q^93 + 76 * q^94 + 72 * q^96 + 52 * q^97 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$.

$n$	$339$	$509$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.625780	−	1.26823i	0.442493	−	0.896772i
$2$	0.625780	−	1.26823i	0.442493	−	0.896772i
$3$		−	2.09440i		−	1.20920i	−0.796528	−	0.604601i	$-0.793333\pi$
$3$		−	2.09440i		−	1.20920i	0.796528	−	0.604601i	$-0.206667\pi$
$4$	−1.21680	−	1.58726i	−0.608400	−	0.793631i
$5$	−0.894007	+	0.894007i	−0.399812	+	0.399812i	−0.878167	−	0.478355i	$-0.841233\pi$
$5$	−0.894007	+	0.894007i	−0.399812	+	0.399812i	0.478355	+	0.878167i	$0.341233\pi$
$6$	−2.65617	−	1.31063i	−1.08438	−	0.535063i
$7$	−3.20020	+	3.20020i	−1.20956	+	1.20956i	−0.238395	+	0.971168i	$0.576621\pi$
$7$	−3.20020	+	3.20020i	−1.20956	+	1.20956i	−0.971168	+	0.238395i	$0.923379\pi$
$8$	−2.77446	+	0.549903i	−0.980918	+	0.194420i
$9$	−1.38651			−0.462170
$10$	0.574352	+	1.69325i	0.181626	+	0.535454i
$11$	−1.10580	+	1.10580i	−0.333412	+	0.333412i	−0.853881	−	0.520469i	$-0.825757\pi$
$11$	−1.10580	+	1.10580i	−0.333412	+	0.333412i	0.520469	+	0.853881i	$0.325757\pi$
$12$	−3.32436	+	2.54846i	−0.959660	+	0.735678i
$13$		0			0
$13$		0			0
$14$	2.05596	+	6.06121i	0.549479	+	1.61993i
$15$	1.87241	+	1.87241i	0.483453	+	0.483453i
$16$	−1.03880	+	3.86276i	−0.259699	+	0.965690i
$17$		−	0.0559625i		−	0.0135729i	−0.999977	−	0.00678645i	$-0.997840\pi$
$17$		−	0.0559625i		−	0.0135729i	0.999977	−	0.00678645i	$-0.00216021\pi$
$18$	−0.867649	+	1.75841i	−0.204507	+	0.414461i
$19$	−1.57611	−	1.57611i	−0.361584	−	0.361584i	0.502812	−	0.864396i	$-0.332299\pi$
$19$	−1.57611	−	1.57611i	−0.361584	−	0.361584i	−0.864396	+	0.502812i	$0.832299\pi$
$20$	2.50685	+	0.331195i	0.560549	+	0.0740574i
$21$	6.70250	+	6.70250i	1.46261	+	1.46261i
$22$	0.710421	+	2.09440i	0.151462	+	0.446527i
$23$	−1.05782			−0.220570			−0.110285	−	0.993900i	$-0.535176\pi$
$23$	−1.05782			−0.220570			−0.110285	+	0.993900i	$0.535176\pi$
$24$	1.15172	+	5.81082i	0.235093	+	1.18613i
$25$			3.40150i			0.680301i
$26$		0			0
$27$		−	3.37929i		−	0.650346i
$28$	8.97356	+	1.18555i	1.69584	+	0.224048i
$29$	−7.34904			−1.36468			−0.682342	−	0.731033i	$-0.739038\pi$
$29$	−7.34904			−1.36468			−0.682342	+	0.731033i	$0.739038\pi$
$30$	3.54635	−	1.20292i	0.647472	−	0.219623i
$31$	−4.52800	−	4.52800i	−0.813253	−	0.813253i	0.171867	−	0.985120i	$-0.445020\pi$
$31$	−4.52800	−	4.52800i	−0.813253	−	0.813253i	−0.985120	+	0.171867i	$0.945020\pi$
$32$	4.24880	+	3.73466i	0.751088	+	0.660202i
$33$	2.31599	+	2.31599i	0.403163	+	0.403163i
$34$	−0.0709732	−	0.0350202i	−0.0121718	−	0.00600591i
$35$		−	5.72201i		−	0.967195i
$36$	1.68710	+	2.20075i	0.281184	+	0.366792i
$37$	−1.36603	−	1.36603i	−0.224573	−	0.224573i	0.585848	−	0.810421i	$-0.300762\pi$
$37$	−1.36603	−	1.36603i	−0.224573	−	0.224573i	−0.810421	+	0.585848i	$0.800762\pi$
$38$	−2.98516	+	1.01257i	−0.484257	+	0.164260i
$39$		0			0
$40$	1.98877	−	2.97200i	0.314451	−	0.469914i
$41$	−1.09808	+	1.09808i	−0.171491	+	0.171491i	−0.787634	−	0.616143i	$-0.788694\pi$
$41$	−1.09808	+	1.09808i	−0.171491	+	0.171491i	0.616143	+	0.787634i	$0.288694\pi$
$42$	12.6946	−	4.30601i	1.95882	−	0.664431i
$43$	2.08050			0.317274			0.158637	−	0.987337i	$-0.449290\pi$
$43$	2.08050			0.317274			0.158637	+	0.987337i	$0.449290\pi$
$44$	3.10074	+	0.409658i	0.467454	+	0.0617582i
$45$	1.23955	−	1.23955i	0.184781	−	0.184781i
$46$	−0.661960	+	1.34155i	−0.0976006	+	0.197801i
$47$	−5.38281	+	5.38281i	−0.785163	+	0.785163i	−0.980697	−	0.195534i	$-0.937356\pi$
$47$	−5.38281	+	5.38281i	−0.785163	+	0.785163i	0.195534	+	0.980697i	$0.437356\pi$
$48$	8.09016	+	2.17565i	1.16771	+	0.314029i
$49$		−	13.4826i		−	1.92609i
$50$	4.31388	+	2.12859i	0.610075	+	0.301028i
$51$	−0.117208			−0.0164124
$52$		0			0
$53$	−4.40150			−0.604593			−0.302297	−	0.953214i	$-0.597753\pi$
$53$	−4.40150			−0.604593			−0.302297	+	0.953214i	$0.597753\pi$
$54$	−4.28571	−	2.11469i	−0.583212	−	0.287773i
$55$		−	1.97719i		−	0.266604i
$56$	7.11902	−	10.6386i	0.951319	−	1.42165i
$57$	−3.30100	+	3.30100i	−0.437228	+	0.437228i
$58$	−4.59888	+	9.32026i	−0.603863	+	1.22381i
$59$	6.35242	−	6.35242i	0.827014	−	0.827014i	−0.160088	−	0.987103i	$-0.551178\pi$
$59$	6.35242	−	6.35242i	0.827014	−	0.827014i	0.987103	+	0.160088i	$0.0511779\pi$
$60$	0.693654	−	5.25034i	0.0895504	−	0.677816i
$61$	−2.01500			−0.257994			−0.128997	−	0.991645i	$-0.541176\pi$
$61$	−2.01500			−0.257994			−0.128997	+	0.991645i	$0.541176\pi$
$62$	−8.57606	+	2.90900i	−1.08916	+	0.369444i
$63$	4.43711	−	4.43711i	0.559023	−	0.559023i
$64$	7.39521	−	3.05136i	0.924402	−	0.381420i
$65$		0			0
$66$	4.38651	−	1.48790i	0.539942	−	0.183148i
$67$	−6.48861	−	6.48861i	−0.792710	−	0.792710i	0.189224	−	0.981934i	$-0.439403\pi$
$67$	−6.48861	−	6.48861i	−0.792710	−	0.792710i	−0.981934	+	0.189224i	$0.939403\pi$
$68$	−0.0888271	+	0.0680952i	−0.0107719	+	0.00825775i
$69$			2.21549i			0.266714i
$70$	−7.25680	−	3.58071i	−0.867354	−	0.427977i
$71$	4.82430	+	4.82430i	0.572539	+	0.572539i	0.932837	−	0.360298i	$-0.117325\pi$
$71$	4.82430	+	4.82430i	0.572539	+	0.572539i	−0.360298	+	0.932837i	$0.617325\pi$
$72$	3.84681	−	0.762445i	0.453351	−	0.0898550i
$73$	5.45504	+	5.45504i	0.638464	+	0.638464i	0.950176	−	0.311713i	$-0.100903\pi$
$73$	5.45504	+	5.45504i	0.638464	+	0.638464i	−0.311713	+	0.950176i	$0.600903\pi$
$74$	−2.58726	+	0.877600i	−0.300763	+	0.102019i
$75$	7.12411			0.822621
$76$	−0.583887	+	4.41950i	−0.0669764	+	0.506952i
$77$		−	7.07759i		−	0.806567i
$78$		0			0
$79$			8.87422i			0.998428i	0.866479	+	0.499214i	$0.166378\pi$
$79$			8.87422i			0.998428i	−0.866479	+	0.499214i	$0.833622\pi$
$80$	−2.52464	−	4.38202i	−0.282263	−	0.489925i
$81$	−11.2371			−1.24857
$82$	0.705456	+	2.07976i	0.0779046	+	0.229671i
$83$	6.96160	+	6.96160i	0.764135	+	0.764135i	0.977067	−	0.212932i	$-0.0683014\pi$
$83$	6.96160	+	6.96160i	0.764135	+	0.764135i	−0.212932	+	0.977067i	$0.568301\pi$
$84$	2.48302	−	18.7942i	0.270920	−	2.05062i
$85$	0.0500308	+	0.0500308i	0.00542661	+	0.00542661i
$86$	1.30194	−	2.63855i	0.140391	−	0.284522i
$87$			15.3918i			1.65018i
$88$	2.45992	−	3.67609i	0.262228	−	0.391872i
$89$	−11.2076	−	11.2076i	−1.18800	−	1.18800i	−0.977620	−	0.210381i	$-0.932530\pi$
$89$	−11.2076	−	11.2076i	−1.18800	−	1.18800i	−0.210381	−	0.977620i	$-0.567470\pi$
$90$	−0.796345	−	2.34771i	−0.0839421	−	0.247471i
$91$		0			0
$92$	1.28715	+	1.67903i	0.134195	+	0.175051i
$93$	−9.48344	+	9.48344i	−0.983387	+	0.983387i
$94$	3.45817	+	10.1951i	0.356683	+	1.05154i
$95$	2.81810			0.289131
$96$	7.82188	−	8.89868i	0.798317	−	0.908218i
$97$	−0.322629	+	0.322629i	−0.0327581	+	0.0327581i	−0.723296	−	0.690538i	$-0.757374\pi$
$97$	−0.322629	+	0.322629i	−0.0327581	+	0.0327581i	0.690538	+	0.723296i	$0.257374\pi$
$98$	−17.0990	−	8.43714i	−1.72726	−	0.852279i
$99$	1.53321	−	1.53321i	0.154093	−	0.154093i
$100$	5.39908	−	4.13895i	0.539908	−	0.413895i
$101$			11.0661i			1.10112i	0.834796	+	0.550559i	$0.185585\pi$
$101$			11.0661i			1.10112i	−0.834796	+	0.550559i	$0.814415\pi$
$102$	−0.0733463	+	0.148646i	−0.00726236	+	0.0147182i
$103$	−3.85469			−0.379813			−0.189907	−	0.981802i	$-0.560819\pi$
$103$	−3.85469			−0.379813			−0.189907	+	0.981802i	$0.560819\pi$
$104$		0			0
$105$	−11.9842			−1.16953
$106$	−2.75437	+	5.58211i	−0.267528	+	0.542182i
$107$		−	0.293614i		−	0.0283847i	−0.999899	−	0.0141924i	$-0.995482\pi$
$107$		−	0.293614i		−	0.0283847i	0.999899	−	0.0141924i	$-0.00451772\pi$
$108$	−5.36382	+	4.11192i	−0.516134	+	0.395670i
$109$	1.15289	−	1.15289i	0.110427	−	0.110427i	−0.649734	−	0.760161i	$-0.725120\pi$
$109$	1.15289	−	1.15289i	0.110427	−	0.110427i	0.760161	+	0.649734i	$0.225120\pi$
$110$	−2.50753	−	1.23729i	−0.239083	−	0.117971i
$111$	−2.86100	+	2.86100i	−0.271554	+	0.271554i
$112$	−9.03725	−	15.6860i	−0.853940	−	1.48218i
$113$	−9.13706			−0.859542			−0.429771	−	0.902938i	$-0.641406\pi$
$113$	−9.13706			−0.859542			−0.429771	+	0.902938i	$0.641406\pi$
$114$	2.12072	+	6.25211i	0.198624	+	0.585564i
$115$	0.945695	−	0.945695i	0.0881865	−	0.0881865i
$116$	8.94232	+	11.6649i	0.830273	+	1.08305i
$117$		0			0
$118$	−4.08110	−	12.0315i	−0.375695	−	1.10759i
$119$	0.179091	+	0.179091i	0.0164173	+	0.0164173i
$120$	−6.22455	−	4.16527i	−0.568221	−	0.380235i
$121$			8.55440i			0.777672i
$122$	−1.26094	+	2.55547i	−0.114160	+	0.231362i
$123$	2.29981	+	2.29981i	0.207367	+	0.207367i
$124$	−1.67745	+	12.6968i	−0.150639	+	1.14021i
$125$	−7.51100	−	7.51100i	−0.671804	−	0.671804i
$126$	−2.85061	−	8.40392i	−0.253953	−	0.748680i
$127$	9.43541			0.837258			0.418629	−	0.908157i	$-0.362511\pi$
$127$	9.43541			0.837258			0.418629	+	0.908157i	$0.362511\pi$
$128$	0.757953	−	11.2883i	0.0669942	−	0.997753i
$129$		−	4.35741i		−	0.383648i
$130$		0			0
$131$		−	9.03673i		−	0.789543i	−0.918779	−	0.394771i	$-0.870824\pi$
$131$		−	9.03673i		−	0.789543i	0.918779	−	0.394771i	$-0.129176\pi$
$132$	0.857986	−	6.49419i	0.0746781	−	0.565247i
$133$	10.0877			0.874717
$134$	−12.2895	+	4.16859i	−1.06165	+	0.360111i
$135$	3.02111	+	3.02111i	0.260016	+	0.260016i
$136$	0.0307739	+	0.155265i	0.00263884	+	0.0133139i
$137$	−6.63748	−	6.63748i	−0.567078	−	0.567078i	0.364231	−	0.931309i	$-0.381332\pi$
$137$	−6.63748	−	6.63748i	−0.567078	−	0.567078i	−0.931309	+	0.364231i	$0.881332\pi$
$138$	2.80974	+	1.38641i	0.239181	+	0.118019i
$139$		−	10.3621i		−	0.878904i	−0.898266	−	0.439452i	$-0.855173\pi$
$139$		−	10.3621i		−	0.878904i	0.898266	−	0.439452i	$-0.144827\pi$
$140$	−9.08232	+	6.96254i	−0.767596	+	0.588442i
$141$	11.2737	+	11.2737i	0.949421	+	0.949421i
$142$	9.13725	−	3.09936i	0.766781	−	0.260092i
$143$		0			0
$144$	1.44030	−	5.35575i	0.120025	−	0.446312i
$145$	6.57009	−	6.57009i	0.545617	−	0.545617i
$146$	10.3319	−	3.50458i	0.855072	−	0.290041i
$147$	−28.2379			−2.32903
$148$	−0.506060	+	3.83042i	−0.0415978	+	0.314858i
$149$	7.39116	−	7.39116i	0.605507	−	0.605507i	−0.336261	−	0.941769i	$-0.609163\pi$
$149$	7.39116	−	7.39116i	0.605507	−	0.605507i	0.941769	+	0.336261i	$0.109163\pi$
$150$	4.45812	−	9.03499i	0.364004	−	0.737704i
$151$	−3.84960	+	3.84960i	−0.313276	+	0.313276i	−0.846177	−	0.532901i	$-0.821102\pi$
$151$	−3.84960	+	3.84960i	−0.313276	+	0.313276i	0.532901	+	0.846177i	$0.321102\pi$
$152$	5.23955	+	3.50614i	0.424983	+	0.284385i
$153$			0.0775925i			0.00627298i
$154$	−8.97599	−	4.42901i	−0.723306	−	0.356900i
$155$	8.09612			0.650296
$156$		0			0
$157$	8.76868			0.699817			0.349908	−	0.936784i	$-0.386213\pi$
$157$	8.76868			0.699817			0.349908	+	0.936784i	$0.386213\pi$
$158$	11.2545	+	5.55331i	0.895362	+	0.441797i
$159$			9.21851i			0.731075i
$160$	−7.13727	+	0.459638i	−0.564251	+	0.0363376i
$161$	3.38523	−	3.38523i	0.266793	−	0.266793i
$162$	−7.03196	+	14.2512i	−0.552483	+	1.11968i
$163$	6.21398	−	6.21398i	0.486716	−	0.486716i	−0.420552	−	0.907268i	$-0.638164\pi$
$163$	6.21398	−	6.21398i	0.486716	−	0.486716i	0.907268	+	0.420552i	$0.138164\pi$
$164$	3.07907	+	0.406795i	0.240435	+	0.0317653i
$165$	−4.14103			−0.322379
$166$	13.1853	−	4.47246i	1.02338	−	0.347130i
$167$	−6.14941	+	6.14941i	−0.475856	+	0.475856i	−0.903803	−	0.427948i	$-0.859237\pi$
$167$	−6.14941	+	6.14941i	−0.475856	+	0.475856i	0.427948	+	0.903803i	$0.359237\pi$
$168$	−22.2815	−	14.9101i	−1.71906	−	1.15034i
$169$		0			0
$170$	0.0947588	−	0.0321422i	0.00726766	−	0.00246519i
$171$	2.18529	+	2.18529i	0.167113	+	0.167113i
$172$	−2.53156	−	3.30230i	−0.193029	−	0.251798i
$173$			6.28874i			0.478124i	0.971004	+	0.239062i	$0.0768399\pi$
$173$			6.28874i			0.478124i	−0.971004	+	0.239062i	$0.923160\pi$
$174$	19.5203	+	9.63190i	1.47983	+	0.730192i
$175$	−10.8855	−	10.8855i	−0.822867	−	0.822867i
$176$	−3.12275	−	5.42016i	−0.235386	−	0.408560i
$177$	−13.3045	−	13.3045i	−1.00003	−	1.00003i
$178$	−21.2272	+	7.20028i	−1.59105	+	0.539684i
$179$	−24.1995			−1.80876			−0.904379	−	0.426731i	$-0.859665\pi$
$179$	−24.1995			−1.80876			−0.904379	+	0.426731i	$0.859665\pi$
$180$	−3.47577	−	0.459205i	−0.259069	−	0.0342271i
$181$		−	5.03261i		−	0.374071i	−0.982353	−	0.187035i	$-0.940112\pi$
$181$		−	5.03261i		−	0.374071i	0.982353	−	0.187035i	$-0.0598879\pi$
$182$		0			0
$183$			4.22020i			0.311967i
$184$	2.93486	−	0.581696i	0.216361	−	0.0428832i
$185$	2.44247			0.179574
$186$	6.09261	+	17.9617i	0.446732	+	1.31702i
$187$	0.0618835	+	0.0618835i	0.00452537	+	0.00452537i
$188$	15.0937	+	1.99412i	1.10082	+	0.145436i
$189$	10.8144	+	10.8144i	0.786634	+	0.786634i
$190$	1.76351	−	3.57399i	0.127939	−	0.259285i
$191$		−	19.1366i		−	1.38468i	−0.721572	−	0.692340i	$-0.756580\pi$
$191$		−	19.1366i		−	1.38468i	0.721572	−	0.692340i	$-0.243420\pi$
$192$	−6.39077	−	15.4885i	−0.461214	−	1.11779i
$193$	−6.74819	−	6.74819i	−0.485746	−	0.485746i	0.421215	−	0.906961i	$-0.361604\pi$
$193$	−6.74819	−	6.74819i	−0.485746	−	0.485746i	−0.906961	+	0.421215i	$0.861604\pi$
$194$	0.207272	+	0.611062i	0.0148813	+	0.0438717i
$195$		0			0
$196$	−21.4004	+	16.4056i	−1.52860	+	1.17183i
$197$	−0.754963	+	0.754963i	−0.0537889	+	0.0537889i	−0.733490	−	0.679701i	$-0.762110\pi$
$197$	−0.754963	+	0.754963i	−0.0537889	+	0.0537889i	0.679701	+	0.733490i	$0.262110\pi$
$198$	−0.985005	−	2.90390i	−0.0700012	−	0.206371i
$199$	11.3268			0.802936			0.401468	−	0.915873i	$-0.368500\pi$
$199$	11.3268			0.802936			0.401468	+	0.915873i	$0.368500\pi$
$200$	−1.87050	−	9.43732i	−0.132264	−	0.667320i
$201$	−13.5897	+	13.5897i	−0.958546	+	0.958546i
$202$	14.0343	+	6.92494i	0.987452	+	0.487237i
$203$	23.5184	−	23.5184i	1.65067	−	1.65067i
$204$	0.142618	+	0.186039i	0.00998529	+	0.0130254i
$205$		−	1.96337i		−	0.137128i
$206$	−2.41218	+	4.88862i	−0.168065	+	0.340606i
$207$	1.46667			0.101941
$208$		0			0
$209$	3.48573			0.241113
$210$	−7.49945	+	15.1986i	−0.517511	+	1.04881i
$211$			5.37038i			0.369712i	0.982766	+	0.184856i	$0.0591819\pi$
$211$			5.37038i			0.369712i	−0.982766	+	0.184856i	$0.940818\pi$
$212$	5.35575	+	6.98634i	0.367834	+	0.479824i
$213$	10.1040	−	10.1040i	0.692315	−	0.692315i
$214$	−0.372369	−	0.183737i	−0.0254546	−	0.0125600i
$215$	−1.85998	+	1.85998i	−0.126850	+	0.126850i
$216$	1.85828	+	9.37570i	0.126440	+	0.637936i
$217$	28.9810			1.96736
$218$	−0.740673	−	2.18359i	−0.0501647	−	0.147891i
$219$	11.4250	−	11.4250i	0.772032	−	0.772032i
$220$	−3.13832	+	2.40585i	−0.211585	+	0.162202i
$221$		0			0
$222$	1.83804	+	5.41876i	0.123361	+	0.363683i
$223$	8.35593	+	8.35593i	0.559554	+	0.559554i	0.929181	−	0.369626i	$-0.120514\pi$
$223$	8.35593	+	8.35593i	0.559554	+	0.559554i	−0.369626	+	0.929181i	$0.620514\pi$
$224$	−25.5487	+	1.64533i	−1.70704	+	0.109933i
$225$		−	4.71622i		−	0.314414i
$226$	−5.71778	+	11.5879i	−0.380341	+	0.770813i
$227$	−1.24199	−	1.24199i	−0.0824340	−	0.0824340i	0.664687	−	0.747122i	$-0.268565\pi$
$227$	−1.24199	−	1.24199i	−0.0824340	−	0.0824340i	−0.747122	+	0.664687i	$0.768565\pi$
$228$	9.25620	+	1.22289i	0.613007	+	0.0809880i
$229$	7.04097	+	7.04097i	0.465280	+	0.465280i	0.900382	−	0.435101i	$-0.143287\pi$
$229$	7.04097	+	7.04097i	0.465280	+	0.465280i	−0.435101	+	0.900382i	$0.643287\pi$
$230$	−0.607559	−	1.79115i	−0.0400613	−	0.118105i
$231$	−14.8233			−0.975302
$232$	20.3896	−	4.04126i	1.33864	−	0.265322i
$233$			21.3205i			1.39675i	0.715731	+	0.698376i	$0.246094\pi$
$233$			21.3205i			1.39675i	−0.715731	+	0.698376i	$0.753906\pi$
$234$		0			0
$235$		−	9.62453i		−	0.627835i
$236$	−17.8126	−	2.35333i	−1.15950	−	0.153188i
$237$	18.5862			1.20730
$238$	0.339200	−	0.115057i	0.0219871	−	0.00745802i
$239$	−15.1574	−	15.1574i	−0.980452	−	0.980452i	0.0193606	−	0.999813i	$-0.493837\pi$
$239$	−15.1574	−	15.1574i	−0.980452	−	0.980452i	−0.999813	+	0.0193606i	$0.993837\pi$
$240$	−9.17771	+	5.28761i	−0.592418	+	0.341314i
$241$	−14.1907	−	14.1907i	−0.914101	−	0.914101i	0.0824908	−	0.996592i	$-0.473712\pi$
$241$	−14.1907	−	14.1907i	−0.914101	−	0.914101i	−0.996592	+	0.0824908i	$0.973712\pi$
$242$	10.8489	+	5.35317i	0.697395	+	0.344115i
$243$			13.3971i			0.859427i
$244$	2.45185	+	3.19832i	0.156963	+	0.204752i
$245$	12.0535	+	12.0535i	0.770072	+	0.770072i
$246$	4.35586	−	1.47751i	0.277719	−	0.0942024i
$247$		0			0
$248$	15.0527	+	10.0728i	0.955847	+	0.639622i
$249$	14.5804	−	14.5804i	0.923993	−	0.923993i
$250$	−14.2259	+	4.82542i	−0.899724	+	0.305187i
$251$	14.6175			0.922646			0.461323	−	0.887232i	$-0.347375\pi$
$251$	14.6175			0.922646			0.461323	+	0.887232i	$0.347375\pi$
$252$	−12.4419	−	1.64378i	−0.783768	−	0.103548i
$253$	1.16974	−	1.16974i	0.0735407	−	0.0735407i
$254$	5.90449	−	11.9662i	0.370481	−	0.750829i
$255$	0.104785	−	0.104785i	0.00656186	−	0.00656186i
$256$	−13.8418	−	8.02524i	−0.865113	−	0.501577i
$257$			14.0246i			0.874828i	0.899260	+	0.437414i	$0.144106\pi$
$257$			14.0246i			0.874828i	−0.899260	+	0.437414i	$0.855894\pi$
$258$	−5.52618	−	2.72678i	−0.344045	−	0.169762i
$259$	8.74312			0.543271
$260$		0			0
$261$	10.1895			0.630715
$262$	−11.4606	−	5.65500i	−0.708040	−	0.349367i
$263$		−	29.6593i		−	1.82887i	−0.404731	−	0.914436i	$-0.632635\pi$
$263$		−	29.6593i		−	1.82887i	0.404731	−	0.914436i	$-0.367365\pi$
$264$	−7.69920	−	5.15205i	−0.473853	−	0.317087i
$265$	3.93497	−	3.93497i	0.241724	−	0.241724i
$266$	6.31270	−	12.7935i	0.387056	−	0.784422i
$267$	−23.4731	+	23.4731i	−1.43653	+	1.43653i
$268$	−2.40378	+	18.1945i	−0.146834	+	1.11140i
$269$	1.78195			0.108647			0.0543236	−	0.998523i	$-0.482700\pi$
$269$	1.78195			0.108647			0.0543236	+	0.998523i	$0.482700\pi$
$270$	5.72201	−	1.94091i	0.348230	−	0.118120i
$271$	−14.8611	+	14.8611i	−0.902749	+	0.902749i	−0.995673	−	0.0929244i	$-0.970379\pi$
$271$	−14.8611	+	14.8611i	−0.902749	+	0.902749i	0.0929244	+	0.995673i	$0.470379\pi$
$272$	0.216170	+	0.0581336i	0.0131072	+	0.00352487i
$273$		0			0
$274$	−12.5714	+	4.26423i	−0.759468	+	0.257612i
$275$	−3.76140	−	3.76140i	−0.226821	−	0.226821i
$276$	3.51656	−	2.69581i	0.211672	−	0.162269i
$277$		−	15.6320i		−	0.939235i	−0.882870	−	0.469618i	$-0.844392\pi$
$277$		−	15.6320i		−	0.939235i	0.882870	−	0.469618i	$-0.155608\pi$
$278$	−13.1415	−	6.48441i	−0.788177	−	0.388909i
$279$	6.27811	+	6.27811i	0.375861	+	0.375861i
$280$	3.14655	+	15.8755i	0.188042	+	0.948740i
$281$	−17.0835	−	17.0835i	−1.01912	−	1.01912i	−0.999814	−	0.0193039i	$-0.993855\pi$
$281$	−17.0835	−	17.0835i	−1.01912	−	1.01912i	−0.0193039	−	0.999814i	$-0.506145\pi$
$282$	21.3525	−	7.24279i	1.27153	−	0.431302i
$283$	18.8782			1.12219			0.561095	−	0.827751i	$-0.310380\pi$
$283$	18.8782			1.12219			0.561095	+	0.827751i	$0.310380\pi$
$284$	1.78722	−	13.5276i	0.106052	−	0.802717i
$285$		−	5.90223i		−	0.349618i
$286$		0			0
$287$		−	7.02813i		−	0.414858i
$288$	−5.89100	−	5.17815i	−0.347130	−	0.305125i
$289$	16.9969			0.999816
$290$	−4.22094	−	12.4438i	−0.247862	−	0.730725i
$291$	0.675715	+	0.675715i	0.0396111	+	0.0396111i
$292$	2.02088	−	15.2963i	0.118263	−	0.895146i
$293$	0.0487486	+	0.0487486i	0.00284792	+	0.00284792i	0.708529	−	0.705681i	$-0.249359\pi$
$293$	0.0487486	+	0.0487486i	0.00284792	+	0.00284792i	−0.705681	+	0.708529i	$0.749359\pi$
$294$	−17.6707	+	35.8121i	−1.03058	+	2.08861i
$295$			11.3582i			0.661301i
$296$	4.54116	+	3.03880i	0.263949	+	0.176626i
$297$	3.73684	+	3.73684i	0.216833	+	0.216833i
$298$	−4.74843	−	13.9989i	−0.275069	−	0.810935i
$299$		0			0
$300$	−8.66861	−	11.3078i	−0.500483	−	0.652857i
$301$	−6.65803	+	6.65803i	−0.383763	+	0.383763i
$302$	2.47317	+	7.29117i	0.142315	+	0.419559i
$303$	23.1768			1.33147
$304$	7.72538	−	4.45087i	0.443081	−	0.255275i
$305$	1.80142	−	1.80142i	0.103149	−	0.103149i
$306$	0.0984049	+	0.0485558i	0.00562544	+	0.00277575i
$307$	−6.80614	+	6.80614i	−0.388447	+	0.388447i	−0.874133	−	0.485686i	$-0.838570\pi$
$307$	−6.80614	+	6.80614i	−0.388447	+	0.388447i	0.485686	+	0.874133i	$0.338570\pi$
$308$	−11.2340	+	8.61201i	−0.640116	+	0.490715i
$309$			8.07325i			0.459271i
$310$	5.06639	−	10.2677i	0.287752	−	0.583167i
$311$	−26.1979			−1.48555			−0.742775	−	0.669542i	$-0.766491\pi$
$311$	−26.1979			−1.48555			−0.742775	+	0.669542i	$0.766491\pi$
$312$		0			0
$313$	24.8487			1.40453			0.702265	−	0.711915i	$-0.252172\pi$
$313$	24.8487			1.40453			0.702265	+	0.711915i	$0.252172\pi$
$314$	5.48726	−	11.1207i	0.309664	−	0.627576i
$315$			7.93361i			0.447008i
$316$	14.0857	−	10.7982i	0.792383	−	0.607443i
$317$	−24.2717	+	24.2717i	−1.36323	+	1.36323i	−0.493472	+	0.869762i	$0.664273\pi$
$317$	−24.2717	+	24.2717i	−1.36323	+	1.36323i	−0.869762	+	0.493472i	$0.835727\pi$
$318$	11.6912	+	5.76875i	0.655608	+	0.323496i
$319$	8.12660	−	8.12660i	0.455002	−	0.455002i
$320$	−3.88343	+	9.33931i	−0.217090	+	0.522083i
$321$	−0.614944			−0.0343228
$322$	−2.17483	−	6.41164i	−0.121199	−	0.357307i
$323$	−0.0882029	+	0.0882029i	−0.00490774	+	0.00490774i
$324$	13.6733	+	17.8362i	0.759629	+	0.990902i
$325$		0			0
$326$	−3.99215	−	11.7693i	−0.221105	−	0.651842i
$327$	−2.41462	−	2.41462i	−0.133529	−	0.133529i
$328$	2.44273	−	3.65040i	0.134877	−	0.201560i
$329$		−	34.4521i		−	1.89941i
$330$	−2.59137	+	5.25177i	−0.142650	+	0.289100i
$331$	13.4904	+	13.4904i	0.741501	+	0.741501i	0.972867	−	0.231366i	$-0.0743195\pi$
$331$	13.4904	+	13.4904i	0.741501	+	0.741501i	−0.231366	+	0.972867i	$0.574319\pi$
$332$	2.57900	−	19.5207i	0.141541	−	1.07134i
$333$	1.89401	+	1.89401i	0.103791	+	0.103791i
$334$	3.95067	+	11.6470i	0.216171	+	0.637297i
$335$	11.6017			0.633870
$336$	−32.8527	+	18.9276i	−1.79226	+	1.03259i
$337$			28.8443i			1.57125i	0.618702	+	0.785626i	$0.287659\pi$
$337$			28.8443i			1.57125i	−0.618702	+	0.785626i	$0.712341\pi$
$338$		0			0
$339$			19.1366i			1.03936i
$340$	0.0185345	−	0.140290i	0.00100517	−	0.00760827i
$341$	10.0142			0.542297
$342$	4.13895	−	1.40393i	0.223809	−	0.0759160i
$343$	20.7456	+	20.7456i	1.12016	+	1.12016i
$344$	−5.77227	+	1.14407i	−0.311220	+	0.0616844i
$345$	−1.98066	−	1.98066i	−0.106635	−	0.106635i
$346$	7.97555	+	3.93537i	0.428768	+	0.211567i
$347$			27.5142i			1.47704i	0.674230	+	0.738521i	$0.264475\pi$
$347$			27.5142i			1.47704i	−0.674230	+	0.738521i	$0.735525\pi$
$348$	24.4309	−	18.7288i	1.30963	−	1.00397i
$349$	16.2910	+	16.2910i	0.872035	+	0.872035i	0.992694	−	0.120659i	$-0.0385007\pi$
$349$	16.2910	+	16.2910i	0.872035	+	0.872035i	−0.120659	+	0.992694i	$0.538501\pi$
$350$	−20.6172	+	6.99337i	−1.10204	+	0.373811i
$351$		0			0
$352$	−8.82814	+	0.568530i	−0.470542	+	0.0303027i
$353$	13.8535	−	13.8535i	0.737346	−	0.737346i	−0.234717	−	0.972064i	$-0.575416\pi$
$353$	13.8535	−	13.8535i	0.737346	−	0.737346i	0.972064	+	0.234717i	$0.0754164\pi$
$354$	−25.1988	+	8.54744i	−1.33930	+	0.454292i
$355$	−8.62591			−0.457816
$356$	−4.15197	+	31.4267i	−0.220054	+	1.66561i
$357$	0.375089	−	0.375089i	0.0198518	−	0.0198518i
$358$	−15.1436	+	30.6905i	−0.800362	+	1.62204i
$359$	−10.7783	+	10.7783i	−0.568858	+	0.568858i	−0.931808	−	0.362951i	$-0.881769\pi$
$359$	−10.7783	+	10.7783i	−0.568858	+	0.568858i	0.362951	+	0.931808i	$0.381769\pi$
$360$	−2.75744	+	4.12070i	−0.145330	+	0.217180i
$361$		−	14.0318i		−	0.738514i
$362$	−6.38249	−	3.14930i	−0.335456	−	0.165524i
$363$	17.9163			0.940363
$364$		0			0
$365$	−9.75368			−0.510531
$366$	5.35218	+	2.64092i	0.279763	+	0.138043i
$367$			33.8566i			1.76730i	0.468146	+	0.883651i	$0.344922\pi$
$367$			33.8566i			1.76730i	−0.468146	+	0.883651i	$0.655078\pi$
$368$	1.09886	−	4.08609i	0.0572818	−	0.213002i
$369$	1.52249	−	1.52249i	0.0792578	−	0.0792578i
$370$	1.52845	−	3.09761i	0.0794603	−	0.161037i
$371$	14.0857	−	14.0857i	0.731293	−	0.731293i
$372$	26.5921	+	3.51325i	1.37874	+	0.182153i
$373$	11.9652			0.619535			0.309767	−	0.950812i	$-0.399749\pi$
$373$	11.9652			0.619535			0.309767	+	0.950812i	$0.399749\pi$
$374$	0.117208	−	0.0397569i	0.00606067	−	0.00205578i
$375$	−15.7310	+	15.7310i	−0.812347	+	0.812347i
$376$	11.9743	−	17.8944i	0.617529	−	0.922832i
$377$		0			0
$378$	20.4826	−	6.94770i	1.05351	−	0.357351i
$379$	11.2737	+	11.2737i	0.579093	+	0.579093i	0.934653	−	0.355561i	$-0.115710\pi$
$379$	11.2737	+	11.2737i	0.579093	+	0.579093i	−0.355561	+	0.934653i	$0.615710\pi$
$380$	−3.42907	−	4.47306i	−0.175907	−	0.229463i
$381$		−	19.7615i		−	1.01241i
$382$	−24.2696	−	11.9753i	−1.24174	−	0.612711i
$383$	−16.5568	−	16.5568i	−0.846015	−	0.846015i	0.143618	−	0.989633i	$-0.454126\pi$
$383$	−16.5568	−	16.5568i	−0.846015	−	0.846015i	−0.989633	+	0.143618i	$0.954126\pi$
$384$	−23.6422	−	1.58746i	−1.20649	−	0.0810095i
$385$	6.32741	+	6.32741i	0.322475	+	0.322475i
$386$	−12.7811	+	4.33536i	−0.650542	+	0.220664i
$387$	−2.88464			−0.146634
$388$	0.904673	+	0.119522i	0.0459278	+	0.00606780i
$389$		−	39.2161i		−	1.98834i	−0.107845	−	0.994168i	$-0.534395\pi$
$389$		−	39.2161i		−	1.98834i	0.107845	−	0.994168i	$-0.465605\pi$
$390$		0			0
$391$			0.0591980i			0.00299377i
$392$	7.41412	+	37.4069i	0.374470	+	1.88933i
$393$	−18.9265			−0.954717
$394$	0.485024	+	1.42991i	0.0244352	+	0.0720376i
$395$	−7.93361	−	7.93361i	−0.399183	−	0.399183i
$396$	−4.29921	−	0.567994i	−0.216043	−	0.0285428i
$397$	7.68317	+	7.68317i	0.385607	+	0.385607i	0.873117	−	0.487510i	$-0.162095\pi$
$397$	7.68317	+	7.68317i	0.385607	+	0.385607i	−0.487510	+	0.873117i	$0.662095\pi$
$398$	7.08808	−	14.3650i	0.355293	−	0.720050i
$399$		−	21.1277i		−	1.05771i
$400$	−13.1392	−	3.53347i	−0.656959	−	0.176673i
$401$	−1.08972	−	1.08972i	−0.0544178	−	0.0544178i	0.679374	−	0.733792i	$-0.262251\pi$
$401$	−1.08972	−	1.08972i	−0.0544178	−	0.0544178i	−0.733792	+	0.679374i	$0.762251\pi$
$402$	8.73069	+	25.7391i	0.435447	+	1.28375i
$403$		0			0
$404$	17.5648	−	13.4652i	0.873881	−	0.669920i
$405$	10.0461	−	10.0461i	0.499193	−	0.499193i
$406$	−15.1094	−	44.5441i	−0.749865	−	2.21069i
$407$	3.02111			0.149751
$408$	0.325188	−	0.0644529i	0.0160992	−	0.00319090i
$409$	−0.481082	+	0.481082i	−0.0237880	+	0.0237880i	−0.718901	−	0.695113i	$-0.755354\pi$
$409$	−0.481082	+	0.481082i	−0.0237880	+	0.0237880i	0.695113	+	0.718901i	$0.255354\pi$
$410$	−2.49001	−	1.22864i	−0.122973	−	0.0606782i
$411$	−13.9015	+	13.9015i	−0.685712	+	0.685712i
$412$	4.69038	+	6.11839i	0.231078	+	0.301432i
$413$			40.6581i			2.00065i
$414$	0.917813	−	1.86007i	0.0451081	−	0.0914176i
$415$	−12.4474			−0.611020
$416$		0			0
$417$	−21.7024			−1.06277
$418$	2.18130	−	4.42070i	0.106691	−	0.216223i
$419$			24.0945i			1.17709i	0.808464	+	0.588546i	$0.200299\pi$
$419$			24.0945i			1.17709i	−0.808464	+	0.588546i	$0.799701\pi$
$420$	14.5823	+	19.0220i	0.711545	+	0.928179i
$421$	15.8266	−	15.8266i	0.771339	−	0.771339i	−0.207002	−	0.978341i	$-0.566371\pi$
$421$	15.8266	−	15.8266i	0.771339	−	0.771339i	0.978341	+	0.207002i	$0.0663705\pi$
$422$	6.81086	+	3.36068i	0.331548	+	0.163595i
$423$	7.46331	−	7.46331i	0.362878	−	0.362878i
$424$	12.2118	−	2.42040i	0.593056	−	0.117545i
$425$	0.190357			0.00923366
$426$	−6.49129	−	19.1371i	−0.314504	−	0.927193i
$427$	6.44839	−	6.44839i	0.312060	−	0.312060i
$428$	−0.466042	+	0.357269i	−0.0225270	+	0.0172693i
$429$		0			0
$430$	1.19494	+	3.52282i	0.0576252	+	0.169886i
$431$	−5.86969	−	5.86969i	−0.282733	−	0.282733i	0.551465	−	0.834198i	$-0.314069\pi$
$431$	−5.86969	−	5.86969i	−0.282733	−	0.282733i	−0.834198	+	0.551465i	$0.814069\pi$
$432$	13.0534	+	3.51040i	0.628032	+	0.168894i
$433$			24.3482i			1.17010i	0.810997	+	0.585050i	$0.198925\pi$
$433$			24.3482i			1.17010i	−0.810997	+	0.585050i	$0.801075\pi$
$434$	18.1357	−	36.7545i	0.870543	−	1.76427i
$435$	−13.7604	−	13.7604i	−0.659761	−	0.659761i
$436$	−3.23278	−	0.427102i	−0.154822	−	0.0204545i
$437$	1.66723	+	1.66723i	0.0797545	+	0.0797545i
$438$	−7.33998	−	21.6391i	−0.350718	−	1.03396i
$439$	1.01370			0.0483814			0.0241907	−	0.999707i	$-0.492299\pi$
$439$	1.01370			0.0483814			0.0241907	+	0.999707i	$0.492299\pi$
$440$	1.08726	+	5.48563i	0.0518332	+	0.261517i
$441$			18.6937i			0.890178i
$442$		0			0
$443$			39.1335i			1.85929i	0.368460	+	0.929644i	$0.379885\pi$
$443$			39.1335i			1.85929i	−0.368460	+	0.929644i	$0.620115\pi$
$444$	8.02243	+	1.05989i	0.380728	+	0.0503002i
$445$	20.0393			0.949953
$446$	15.8262	−	5.36825i	0.749392	−	0.254194i
$447$	−15.4800	−	15.4800i	−0.732181	−	0.732181i
$448$	−13.9012	+	33.4312i	−0.656770	+	1.57947i
$449$	17.8770	+	17.8770i	0.843669	+	0.843669i	0.989334	−	0.145665i	$-0.0465322\pi$
$449$	17.8770	+	17.8770i	0.843669	+	0.843669i	−0.145665	+	0.989334i	$0.546532\pi$
$450$	−5.98123	−	2.95131i	−0.281958	−	0.139126i
$451$		−	2.42851i		−	0.114354i
$452$	11.1180	+	14.5029i	0.522945	+	0.682159i
$453$	8.06260	+	8.06260i	0.378814	+	0.378814i
$454$	−2.35234	+	0.797916i	−0.110401	+	0.0374480i
$455$		0			0
$456$	7.34325	−	10.9737i	0.343879	−	0.513891i
$457$	−16.9641	+	16.9641i	−0.793545	+	0.793545i	−0.982069	−	0.188524i	$-0.939630\pi$
$457$	−16.9641	+	16.9641i	−0.793545	+	0.793545i	0.188524	+	0.982069i	$0.439630\pi$
$458$	13.3356	−	4.52345i	0.623133	−	0.211367i
$459$	−0.189114			−0.00882707
$460$	−2.65179	−	0.350343i	−0.123640	−	0.0163348i
$461$	−3.55288	+	3.55288i	−0.165474	+	0.165474i	−0.784987	−	0.619513i	$-0.787330\pi$
$461$	−3.55288	+	3.55288i	−0.165474	+	0.165474i	0.619513	+	0.784987i	$0.287330\pi$
$462$	−9.27612	+	18.7993i	−0.431564	+	0.874623i
$463$	−1.18158	+	1.18158i	−0.0549128	+	0.0549128i	−0.734030	−	0.679117i	$-0.762363\pi$
$463$	−1.18158	+	1.18158i	−0.0549128	+	0.0549128i	0.679117	+	0.734030i	$0.262363\pi$
$464$	7.63416	−	28.3876i	0.354407	−	1.31786i
$465$		−	16.9565i		−	0.786340i
$466$	27.0392	+	13.3419i	1.25257	+	0.618053i
$467$	−24.9759			−1.15575			−0.577873	−	0.816127i	$-0.696117\pi$
$467$	−24.9759			−1.15575			−0.577873	+	0.816127i	$0.696117\pi$
$468$		0			0
$469$	41.5297			1.91766
$470$	−12.2061	−	6.02283i	−0.563025	−	0.277813i
$471$		−	18.3651i		−	0.846220i
$472$	−14.1313	+	21.1177i	−0.650446	+	0.972022i
$473$	−2.30063	+	2.30063i	−0.105783	+	0.105783i
$474$	11.6308	−	23.5715i	0.534222	−	1.08267i
$475$	5.36114	−	5.36114i	0.245986	−	0.245986i
$476$	0.0663464	−	0.502183i	0.00304098	−	0.0230175i
$477$	6.10273			0.279425
$478$	−28.7083	+	9.73785i	−1.31308	+	0.445399i
$479$	22.1427	−	22.1427i	1.01172	−	1.01172i	0.0117932	−	0.999930i	$-0.496246\pi$
$479$	22.1427	−	22.1427i	1.01172	−	1.01172i	0.999930	−	0.0117932i	$-0.00375397\pi$
$480$	0.962665	+	14.9483i	0.0439395	+	0.682293i
$481$		0			0
$482$	−26.8772	+	9.11676i	−1.22422	+	0.415257i
$483$	−7.09002	−	7.09002i	−0.322607	−	0.322607i
$484$	13.5781	−	10.4090i	0.617185	−	0.473136i
$485$		−	0.576866i		−	0.0261941i
$486$	16.9906	+	8.38365i	0.770710	+	0.380290i
$487$	12.0339	+	12.0339i	0.545309	+	0.545309i	0.925080	−	0.379771i	$-0.123997\pi$
$487$	12.0339	+	12.0339i	0.545309	+	0.545309i	−0.379771	+	0.925080i	$0.623997\pi$
$488$	5.59052	−	1.10805i	0.253071	−	0.0501591i
$489$	−13.0146	−	13.0146i	−0.588538	−	0.588538i
$490$	22.8295	−	7.74376i	1.03133	−	0.349828i
$491$	−11.2169			−0.506213			−0.253107	−	0.967438i	$-0.581452\pi$
$491$	−11.2169			−0.506213			−0.253107	+	0.967438i	$0.581452\pi$
$492$	0.851991	−	6.44881i	0.0384107	−	0.290735i
$493$			0.411271i			0.0185227i
$494$		0			0
$495$			2.74139i			0.123217i
$496$	22.1942	−	12.7869i	0.996551	−	0.574149i
$497$	−30.8775			−1.38504
$498$	−9.36712	−	27.6153i	−0.419751	−	1.23747i
$499$	6.87805	+	6.87805i	0.307904	+	0.307904i	0.844096	−	0.536192i	$-0.180138\pi$
$499$	6.87805	+	6.87805i	0.307904	+	0.307904i	−0.536192	+	0.844096i	$0.680138\pi$
$500$	−2.78254	+	21.0613i	−0.124439	+	0.941890i
$501$	12.8793	+	12.8793i	0.575406	+	0.575406i
$502$	9.14731	−	18.5383i	0.408264	−	0.827403i
$503$		−	7.54030i		−	0.336205i	−0.985769	−	0.168103i	$-0.946236\pi$
$503$		−	7.54030i		−	0.336205i	0.985769	−	0.168103i	$-0.0537640\pi$
$504$	−9.87059	+	14.7505i	−0.439671	+	0.657042i
$505$	−9.89317	−	9.89317i	−0.440240	−	0.440240i
$506$	−0.751495	−	2.21549i	−0.0334080	−	0.0984905i
$507$		0			0
$508$	−11.4810	−	14.9765i	−0.509387	−	0.664473i
$509$	6.90459	−	6.90459i	0.306040	−	0.306040i	−0.537331	−	0.843371i	$-0.680567\pi$
$509$	6.90459	−	6.90459i	0.306040	−	0.306040i	0.843371	+	0.537331i	$0.180567\pi$
$510$	−0.0673186	−	0.198463i	−0.00298092	−	0.00878808i
$511$	−34.9145			−1.54452
$512$	−18.8397	+	12.5325i	−0.832607	+	0.553864i
$513$	−5.32613	+	5.32613i	−0.235154	+	0.235154i
$514$	17.7863	+	8.77629i	0.784522	+	0.387105i
$515$	3.44611	−	3.44611i	0.151854	−	0.151854i
$516$	−6.91634	+	5.30209i	−0.304475	+	0.233411i
$517$		−	11.9047i		−	0.523566i
$518$	5.47126	−	11.0883i	0.240394	−	0.487190i
$519$	13.1711			0.578149
$520$		0			0
$521$	−19.5755			−0.857619			−0.428809	−	0.903395i	$-0.641067\pi$
$521$	−19.5755			−0.857619			−0.428809	+	0.903395i	$0.641067\pi$
$522$	6.37639	−	12.9226i	0.279087	−	0.565608i
$523$		−	35.8199i		−	1.56630i	−0.621835	−	0.783148i	$-0.713613\pi$
$523$		−	35.8199i		−	1.56630i	0.621835	−	0.783148i	$-0.286387\pi$
$524$	−14.3437	+	10.9959i	−0.626605	+	0.480358i
$525$	−22.7986	+	22.7986i	−0.995012	+	0.995012i
$526$	−37.6148	−	18.5602i	−1.64008	−	0.809263i
$527$	−0.253398	+	0.253398i	−0.0110382	+	0.0110382i
$528$	−11.3520	+	6.54028i	−0.494031	+	0.284629i
$529$	−21.8810			−0.951349
$530$	−2.52801	−	7.45287i	−0.109810	−	0.323732i
$531$	−8.80769	+	8.80769i	−0.382221	+	0.382221i
$532$	−12.2747	−	16.0119i	−0.532178	−	0.694202i
$533$		0			0
$534$	15.0803	+	44.4583i	0.652587	+	1.92390i
$535$	0.262493	+	0.262493i	0.0113485	+	0.0113485i
$536$	21.5705	+	14.4343i	0.931702	+	0.623465i
$537$			50.6835i			2.18715i
$538$	1.11511	−	2.25991i	0.0480756	−	0.0974317i
$539$	14.9091	+	14.9091i	0.642181	+	0.642181i
$540$	1.11921	−	8.47138i	0.0481629	−	0.364550i
$541$	12.3423	+	12.3423i	0.530636	+	0.530636i	0.920762	−	0.390126i	$-0.127568\pi$
$541$	12.3423	+	12.3423i	0.530636	+	0.530636i	−0.390126	+	0.920762i	$0.627568\pi$
$542$	9.54749	+	28.1471i	0.410100	+	1.20902i
$543$	−10.5403			−0.452327
$544$	0.209001	−	0.237773i	0.00896085	−	0.0101944i
$545$			2.06139i			0.0883001i
$546$		0			0
$547$		−	5.49854i		−	0.235101i	−0.993067	−	0.117550i	$-0.962496\pi$
$547$		−	5.49854i		−	0.235101i	0.993067	−	0.117550i	$-0.0375041\pi$
$548$	−2.45893	+	18.6119i	−0.105040	+	0.795061i
$549$	2.79381			0.119237
$550$	−7.12411	+	2.41650i	−0.303773	+	0.103040i
$551$	11.5829	+	11.5829i	0.493448	+	0.493448i
$552$	−1.21830	−	6.14678i	−0.0518545	−	0.261624i
$553$	−28.3993	−	28.3993i	−1.20766	−	1.20766i
$554$	−19.8249	−	9.78218i	−0.842280	−	0.415605i
$555$		−	5.11551i		−	0.217141i
$556$	−16.4474	+	12.6086i	−0.697525	+	0.534725i
$557$	−2.42633	−	2.42633i	−0.102807	−	0.102807i	0.653832	−	0.756639i	$-0.273160\pi$
$557$	−2.42633	−	2.42633i	−0.102807	−	0.102807i	−0.756639	+	0.653832i	$0.773160\pi$
$558$	11.8908	−	4.03336i	0.503377	−	0.170746i
$559$		0			0
$560$	22.1027	+	5.94400i	0.934011	+	0.251180i
$561$	0.129609	−	0.129609i	0.00547209	−	0.00547209i
$562$	−32.3563	+	10.9753i	−1.36487	+	0.462964i
$563$	9.33572			0.393454			0.196727	−	0.980458i	$-0.436969\pi$
$563$	9.33572			0.393454			0.196727	+	0.980458i	$0.436969\pi$
$564$	4.17649	−	31.6123i	0.175862	−	1.33112i
$565$	8.16859	−	8.16859i	0.343655	−	0.343655i
$566$	11.8136	−	23.9418i	0.496561	−	1.00635i
$567$	35.9611	−	35.9611i	1.51022	−	1.51022i
$568$	−16.0377	−	10.7319i	−0.672927	−	0.450301i
$569$		−	34.1336i		−	1.43095i	−0.698637	−	0.715477i	$-0.746210\pi$
$569$		−	34.1336i		−	1.43095i	0.698637	−	0.715477i	$-0.253790\pi$
$570$	−7.48537	−	3.69350i	−0.313528	−	0.154704i
$571$	−30.2446			−1.26570			−0.632848	−	0.774276i	$-0.718114\pi$
$571$	−30.2446			−1.26570			−0.632848	+	0.774276i	$0.718114\pi$
$572$		0			0
$573$	−40.0798			−1.67436
$574$	−8.91327	−	4.39806i	−0.372033	−	0.183572i
$575$		−	3.59817i		−	0.150054i
$576$	−10.2535	+	4.23074i	−0.427230	+	0.176281i
$577$	24.5041	−	24.5041i	1.02012	−	1.02012i	0.0203254	−	0.999793i	$-0.493530\pi$
$577$	24.5041	−	24.5041i	1.02012	−	1.02012i	0.999793	−	0.0203254i	$-0.00647021\pi$
$578$	10.6363	−	21.5559i	0.442411	−	0.896607i
$579$	−14.1334	+	14.1334i	−0.587364	+	0.587364i
$580$	−18.4229	−	2.43397i	−0.764971	−	0.101065i
$581$	−44.5571			−1.84854
$582$	1.27981	−	0.434111i	0.0530498	−	0.0179945i
$583$	4.86720	−	4.86720i	0.201579	−	0.201579i
$584$	−18.1345	−	12.1350i	−0.750411	−	0.502151i
$585$		0			0
$586$	0.0923302	−	0.0313184i	0.00381413	−	0.00129375i
$587$	22.3156	+	22.3156i	0.921064	+	0.921064i	0.997105	−	0.0760405i	$-0.0242278\pi$
$587$	22.3156	+	22.3156i	0.921064	+	0.921064i	−0.0760405	+	0.997105i	$0.524228\pi$
$588$	34.3599	+	44.8210i	1.41698	+	1.84839i
$589$			14.2732i			0.588118i
$590$	14.4048	+	7.10774i	0.593036	+	0.292621i
$591$	1.58119	+	1.58119i	0.0650416	+	0.0650416i
$592$	6.69565	−	3.85760i	0.275189	−	0.158547i
$593$	11.3864	+	11.3864i	0.467582	+	0.467582i	0.901130	−	0.433548i	$-0.142739\pi$
$593$	11.3864	+	11.3864i	0.467582	+	0.467582i	−0.433548	+	0.901130i	$0.642739\pi$
$594$	7.07759	−	2.40072i	0.290397	−	0.0985028i
$595$	−0.320218			−0.0131276
$596$	−20.7253	−	2.73814i	−0.848940	−	0.112159i
$597$		−	23.7229i		−	0.970912i
$598$		0			0
$599$		−	37.4177i		−	1.52885i	−0.644715	−	0.764423i	$-0.723024\pi$
$599$		−	37.4177i		−	1.52885i	0.644715	−	0.764423i	$-0.276976\pi$
$600$	−19.7655	+	3.91757i	−0.806924	+	0.159934i
$601$	−13.8847			−0.566368			−0.283184	−	0.959066i	$-0.591391\pi$
$601$	−13.8847			−0.566368			−0.283184	+	0.959066i	$0.591391\pi$
$602$	4.27744	+	12.6104i	0.174335	+	0.513960i
$603$	8.99652	+	8.99652i	0.366366	+	0.366366i
$604$	10.7945	+	1.42613i	0.439222	+	0.0580283i
$605$	−7.64769	−	7.64769i	−0.310923	−	0.310923i
$606$	14.5036	−	29.3935i	0.589168	−	1.19403i
$607$			20.1684i			0.818611i	0.912397	+	0.409306i	$0.134229\pi$
$607$			20.1684i			0.818611i	−0.912397	+	0.409306i	$0.865771\pi$
$608$	−0.810328	−	12.5828i	−0.0328631	−	0.510300i
$609$	−49.2570	−	49.2570i	−1.99599	−	1.99599i
$610$	−1.15732	−	3.41190i	−0.0468584	−	0.138144i
$611$		0			0
$612$	0.123160	−	0.0944146i	0.00497843	−	0.00381648i
$613$	−23.9129	+	23.9129i	−0.965835	+	0.965835i	−0.999435	−	0.0336005i	$-0.989303\pi$
$613$	−23.9129	+	23.9129i	−0.965835	+	0.965835i	0.0336005	+	0.999435i	$0.489303\pi$
$614$	4.37259	+	12.8909i	0.176463	+	0.520233i
$615$	−4.11209			−0.165816
$616$	3.89199	+	19.6365i	0.156813	+	0.791176i
$617$	−12.9438	+	12.9438i	−0.521099	+	0.521099i	−0.917903	−	0.396804i	$-0.870119\pi$
$617$	−12.9438	+	12.9438i	−0.521099	+	0.521099i	0.396804	+	0.917903i	$0.370119\pi$
$618$	10.2387	+	5.05208i	0.411862	+	0.203224i
$619$	−5.55216	+	5.55216i	−0.223160	+	0.223160i	−0.809828	−	0.586668i	$-0.800439\pi$
$619$	−5.55216	+	5.55216i	−0.223160	+	0.223160i	0.586668	+	0.809828i	$0.300439\pi$
$620$	−9.85136	−	12.8507i	−0.395640	−	0.516095i
$621$			3.57467i			0.143447i
$622$	−16.3941	+	33.2249i	−0.657345	+	1.33220i
$623$	71.7330			2.87392
$624$		0			0
$625$	−3.57775			−0.143110
$626$	15.5498	−	31.5138i	0.621495	−	1.25954i
$627$		−	7.30051i		−	0.291554i
$628$	−10.6697	−	13.9182i	−0.425768	−	0.555396i
$629$	−0.0764462	+	0.0764462i	−0.00304811	+	0.00304811i
$630$	10.0616	+	4.96469i	0.400865	+	0.197798i
$631$	−16.7460	+	16.7460i	−0.666646	+	0.666646i	−0.956938	−	0.290292i	$-0.906247\pi$
$631$	−16.7460	+	16.7460i	−0.666646	+	0.666646i	0.290292	+	0.956938i	$0.406247\pi$
$632$	−4.87996	−	24.6211i	−0.194114	−	0.979376i
$633$	11.2477			0.447057
$634$	15.5933	+	45.9707i	0.619288	+	1.82573i
$635$	−8.43532	+	8.43532i	−0.334746	+	0.334746i
$636$	14.6322	−	11.2171i	0.580204	−	0.444786i
$637$		0			0
$638$	−5.22091	−	15.3918i	−0.206698	−	0.609369i
$639$	−6.68893	−	6.68893i	−0.264610	−	0.264610i
$640$	9.41419	+	10.7694i	0.372129	+	0.425699i
$641$		−	9.94862i		−	0.392947i	−0.980509	−	0.196473i	$-0.937051\pi$
$641$		−	9.94862i		−	0.392947i	0.980509	−	0.196473i	$-0.0629490\pi$
$642$	−0.384820	+	0.779889i	−0.0151876	+	0.0307798i
$643$	−17.1393	−	17.1393i	−0.675907	−	0.675907i	0.283165	−	0.959071i	$-0.408616\pi$
$643$	−17.1393	−	17.1393i	−0.675907	−	0.675907i	−0.959071	+	0.283165i	$0.908616\pi$
$644$	−9.49238	−	1.25410i	−0.374052	−	0.0494183i
$645$	3.89555	+	3.89555i	0.153387	+	0.153387i
$646$	0.0566658	+	0.167057i	0.00222948	+	0.00657277i
$647$	16.1764			0.635959			0.317980	−	0.948098i	$-0.396996\pi$
$647$	16.1764			0.635959			0.317980	+	0.948098i	$0.396996\pi$
$648$	31.1769	−	6.17932i	1.22474	−	0.242747i
$649$			14.0491i			0.551474i
$650$		0			0
$651$		−	60.6979i		−	2.37894i
$652$	−17.4244	−	2.30204i	−0.682391	−	0.0901548i
$653$	−19.4504			−0.761152			−0.380576	−	0.924750i	$-0.624274\pi$
$653$	−19.4504			−0.761152			−0.380576	+	0.924750i	$0.624274\pi$
$654$	−4.57330	+	1.55126i	−0.178830	+	0.0606593i
$655$	8.07890	+	8.07890i	0.315669	+	0.315669i
$656$	−3.10093	−	5.38228i	−0.121071	−	0.210143i
$657$	−7.56346	−	7.56346i	−0.295079	−	0.295079i
$658$	−43.6931	−	21.5594i	−1.70334	−	0.840475i
$659$		−	33.7847i		−	1.31607i	−0.752989	−	0.658033i	$-0.771389\pi$
$659$		−	33.7847i		−	1.31607i	0.752989	−	0.658033i	$-0.228611\pi$
$660$	5.03880	+	6.57289i	0.196135	+	0.255850i
$661$	−6.23284	−	6.23284i	−0.242429	−	0.242429i	0.575425	−	0.817855i	$-0.304837\pi$
$661$	−6.23284	−	6.23284i	−0.242429	−	0.242429i	−0.817855	+	0.575425i	$0.804837\pi$
$662$	25.5510	−	8.66689i	0.993066	−	0.336848i
$663$		0			0
$664$	−23.1429	−	15.4864i	−0.898117	−	0.600991i
$665$	−9.01850	+	9.01850i	−0.349722	+	0.349722i
$666$	3.58726	−	1.21680i	0.139004	−	0.0471500i
$667$	7.77394			0.301008
$668$	17.2433	+	2.27812i	0.667164	+	0.0881430i
$669$	17.5007	−	17.5007i	0.676614	−	0.676614i
$670$	7.26012	−	14.7136i	0.280483	−	0.568437i
$671$	2.22819	−	2.22819i	0.0860183	−	0.0860183i
$672$	3.44597	+	53.5092i	0.132931	+	2.06416i
$673$			20.3917i			0.786044i	0.919529	+	0.393022i	$0.128570\pi$
$673$			20.3917i			0.786044i	−0.919529	+	0.393022i	$0.871430\pi$
$674$	36.5812	+	18.0502i	1.40905	+	0.695268i
$675$	11.4947			0.442431
$676$		0			0
$677$	−1.01359			−0.0389554			−0.0194777	−	0.999810i	$-0.506200\pi$
$677$	−1.01359			−0.0389554			−0.0194777	+	0.999810i	$0.506200\pi$
$678$	24.2696	+	11.9753i	0.932069	+	0.459910i
$679$		−	2.06496i		−	0.0792459i
$680$	−0.166320	−	0.111296i	−0.00637810	−	0.00426802i
$681$	−2.60123	+	2.60123i	−0.0996794	+	0.0996794i
$682$	6.26665	−	12.7002i	0.239963	−	0.486317i
$683$	−17.8559	+	17.8559i	−0.683238	+	0.683238i	−0.960728	−	0.277491i	$-0.910497\pi$
$683$	−17.8559	+	17.8559i	−0.683238	+	0.683238i	0.277491	+	0.960728i	$0.410497\pi$
$684$	0.809565	−	6.12768i	0.0309545	−	0.234298i
$685$	11.8679			0.453449
$686$	39.2924	−	13.3280i	1.50019	−	0.508865i
$687$	14.7466	−	14.7466i	0.562618	−	0.562618i
$688$	−2.16122	+	8.03648i	−0.0823957	+	0.306388i
$689$		0			0
$690$	−3.75139	+	1.27247i	−0.142813	+	0.0484422i
$691$	−25.3911	−	25.3911i	−0.965924	−	0.965924i	0.0335142	−	0.999438i	$-0.489330\pi$
$691$	−25.3911	−	25.3911i	−0.965924	−	0.965924i	−0.999438	+	0.0335142i	$0.989330\pi$
$692$	9.98187	−	7.65214i	0.379454	−	0.290891i
$693$			9.81315i			0.372771i
$694$	34.8943	+	17.2179i	1.32457	+	0.653581i
$695$	9.26381	+	9.26381i	0.351396	+	0.351396i
$696$	−8.46401	−	42.7040i	−0.320828	−	1.61869i
$697$	0.0614511	+	0.0614511i	0.00232763	+	0.00232763i
$698$	30.8552	−	10.4661i	1.16789	−	0.396147i
$699$	44.6537			1.68896
$700$	−4.03266	+	30.5236i	−0.152420	+	1.15368i
$701$		−	16.0203i		−	0.605077i	−0.953137	−	0.302539i	$-0.902166\pi$
$701$		−	16.0203i		−	0.605077i	0.953137	−	0.302539i	$-0.0978342\pi$
$702$		0			0
$703$			4.30601i			0.162404i
$704$	−4.80345	+	11.5519i	−0.181037	+	0.435377i
$705$	−20.1576			−0.759179
$706$	−8.90014	−	26.2386i	−0.334961	−	0.987502i
$707$	−35.4138	−	35.4138i	−1.33187	−	1.33187i
$708$	−4.92880	+	37.3066i	−0.185236	+	1.40207i
$709$	−16.6393	−	16.6393i	−0.624900	−	0.624900i	0.321880	−	0.946780i	$-0.395685\pi$
$709$	−16.6393	−	16.6393i	−0.624900	−	0.624900i	−0.946780	+	0.321880i	$0.895685\pi$
$710$	−5.39792	+	10.9396i	−0.202580	+	0.410556i
$711$		−	12.3042i		−	0.461443i
$712$	37.2580	+	24.9318i	1.39630	+	0.934360i
$713$	4.78979	+	4.78979i	0.179379	+	0.179379i
$714$	−0.240975	−	0.710421i	−0.00901826	−	0.0265868i
$715$		0			0
$716$	29.4460	+	38.4110i	1.10045	+	1.43549i
$717$	−31.7457	+	31.7457i	−1.18556	+	1.18556i
$718$	6.92450	+	20.4142i	0.258420	+	0.761851i
$719$	−46.9964			−1.75267			−0.876334	−	0.481703i	$-0.840018\pi$
$719$	−46.9964			−1.75267			−0.876334	+	0.481703i	$0.840018\pi$
$720$	3.50044	+	6.07571i	0.130454	+	0.226428i
$721$	12.3358	−	12.3358i	0.459408	−	0.459408i
$722$	−17.7955	−	8.78079i	−0.662279	−	0.326787i
$723$	−29.7209	+	29.7209i	−1.10533	+	1.10533i
$724$	−7.98806	+	6.12368i	−0.296874	+	0.227585i
$725$		−	24.9978i		−	0.928395i
$726$	11.2117	−	22.7220i	0.416104	−	0.843291i
$727$	20.0985			0.745412			0.372706	−	0.927950i	$-0.378430\pi$
$727$	20.0985			0.745412			0.372706	+	0.927950i	$0.378430\pi$
$728$		0			0
$729$	−5.65241			−0.209348
$730$	−6.10365	+	12.3699i	−0.225906	+	0.457830i
$731$		−	0.116430i		−	0.00430633i
$732$	6.69857	−	5.13514i	0.247586	−	0.189800i
$733$	13.3827	−	13.3827i	0.494300	−	0.494300i	−0.415358	−	0.909658i	$-0.636344\pi$
$733$	13.3827	−	13.3827i	0.494300	−	0.494300i	0.909658	+	0.415358i	$0.136344\pi$
$734$	42.9379	+	21.1868i	1.58487	+	0.782019i
$735$	25.2449	−	25.2449i	0.931173	−	0.931173i
$736$	−4.49445	−	3.95059i	−0.165668	−	0.145621i
$737$	14.3503			0.528598
$738$	−0.978122	−	2.88361i	−0.0360052	−	0.106147i
$739$	−1.60780	+	1.60780i	−0.0591438	+	0.0591438i	−0.736060	−	0.676916i	$-0.763316\pi$
$739$	−1.60780	+	1.60780i	−0.0591438	+	0.0591438i	0.676916	+	0.736060i	$0.263316\pi$
$740$	−2.97200	−	3.87684i	−0.109253	−	0.142515i
$741$		0			0
$742$	−9.04933	−	26.6784i	−0.332211	−	0.979396i
$743$	−11.2142	−	11.2142i	−0.411411	−	0.411411i	0.470819	−	0.882230i	$-0.343958\pi$
$743$	−11.2142	−	11.2142i	−0.411411	−	0.411411i	−0.882230	+	0.470819i	$0.843958\pi$
$744$	21.0964	−	31.5264i	0.773432	−	1.15581i
$745$			13.2155i			0.484178i
$746$	7.48758	−	15.1746i	0.274140	−	0.555581i
$747$	−9.65232	−	9.65232i	−0.353160	−	0.353160i
$748$	0.0229255	−	0.173525i	0.000838238	−	0.00634471i
$749$	0.939623	+	0.939623i	0.0343331	+	0.0343331i
$750$	10.1064	+	29.7947i	0.369032	+	1.08795i
$751$	−31.1824			−1.13786			−0.568930	−	0.822386i	$-0.692643\pi$
$751$	−31.1824			−1.13786			−0.568930	+	0.822386i	$0.692643\pi$
$752$	−15.2008	−	26.3841i	−0.554318	−	0.962130i
$753$		−	30.6148i		−	1.11567i
$754$		0			0
$755$		−	6.88313i		−	0.250503i
$756$	4.00633	−	30.3243i	0.145709	−	1.10288i
$757$	−12.7672			−0.464033			−0.232016	−	0.972712i	$-0.574532\pi$
$757$	−12.7672			−0.464033			−0.232016	+	0.972712i	$0.574532\pi$
$758$	21.3525	−	7.24278i	0.775558	−	0.263070i
$759$	−2.44990	−	2.44990i	−0.0889256	−	0.0889256i
$760$	−7.81870	+	1.54968i	−0.283614	+	0.0562129i
$761$	7.83377	+	7.83377i	0.283974	+	0.283974i	0.834692	−	0.550718i	$-0.185646\pi$
$761$	7.83377	+	7.83377i	0.283974	+	0.283974i	−0.550718	+	0.834692i	$0.685646\pi$
$762$	−25.0621	−	12.3664i	−0.907904	−	0.447986i
$763$			7.37898i			0.267137i
$764$	−30.3749	+	23.2855i	−1.09892	+	0.842439i
$765$	−0.0693682	−	0.0693682i	−0.00250801	−	0.00250801i
$766$	−31.3588	+	10.6369i	−1.13304	+	0.384327i
$767$		0			0
$768$	−16.8081	+	28.9903i	−0.606508	+	1.04610i
$769$	25.3049	−	25.3049i	0.912517	−	0.912517i	−0.0839527	−	0.996470i	$-0.526754\pi$
$769$	25.3049	−	25.3049i	0.912517	−	0.912517i	0.996470	+	0.0839527i	$0.0267545\pi$
$770$	11.9842	−	4.06503i	0.431879	−	0.146494i
$771$	29.3730			1.05784
$772$	−2.49994	+	18.9223i	−0.0899750	+	0.681030i
$773$	34.6449	−	34.6449i	1.24609	−	1.24609i	0.288656	−	0.957433i	$-0.406792\pi$
$773$	34.6449	−	34.6449i	1.24609	−	1.24609i	0.957433	−	0.288656i	$-0.0932085\pi$
$774$	−1.80515	+	3.65837i	−0.0648847	+	0.131498i
$775$	15.4020	−	15.4020i	0.553256	−	0.553256i
$776$	0.717706	−	1.07254i	0.0257642	−	0.0385018i
$777$		−	18.3116i		−	0.656924i
$778$	−49.7349	−	24.5406i	−1.78308	−	0.879824i
$779$	3.46137			0.124017
$780$		0			0
$781$	−10.6695			−0.381783
$782$	0.0750766	+	0.0370449i	0.00268473	+	0.00132472i
$783$			24.8346i			0.887516i
$784$	52.0800	+	14.0057i	1.86000	+	0.500203i
$785$	−7.83925	+	7.83925i	−0.279795	+	0.279795i
$786$	−11.8438	+	24.0031i	−0.422456	+	0.856163i
$787$	25.7703	−	25.7703i	0.918611	−	0.918611i	−0.0783179	−	0.996928i	$-0.524955\pi$
$787$	25.7703	−	25.7703i	0.918611	−	0.918611i	0.996928	+	0.0783179i	$0.0249549\pi$
$788$	2.11696	+	0.279685i	0.0754137	+	0.00996335i
$789$	−62.1185			−2.21148
$790$	−15.0263	+	5.09693i	−0.534612	+	0.181341i
$791$	29.2404	−	29.2404i	1.03967	−	1.03967i
$792$	−3.41070	+	5.09693i	−0.121194	+	0.181112i
$793$		0			0
$794$	14.5520	−	4.93603i	0.516430	−	0.175173i
$795$	−8.24141	−	8.24141i	−0.292293	−	0.292293i
$796$	−13.7825	−	17.9786i	−0.488506	−	0.637234i
$797$			19.8118i			0.701770i	0.936419	+	0.350885i	$0.114119\pi$
$797$			19.8118i			0.701770i	−0.936419	+	0.350885i	$0.885881\pi$
$798$	−26.7948	−	13.2213i	−0.948525	−	0.468029i
$799$	0.301235	+	0.301235i	0.0106569	+	0.0106569i
$800$	−12.7035	+	14.4523i	−0.449136	+	0.510966i
$801$	15.5394	+	15.5394i	0.549058	+	0.549058i
$802$	−2.06393	+	0.700085i	−0.0728799	+	0.0247209i
$803$	−12.0644			−0.425744
$804$	38.1065	+	5.03447i	1.34391	+	0.177552i
$805$			6.05283i			0.213334i
$806$		0			0
$807$		−	3.73211i		−	0.131376i
$808$	−6.08528	−	30.7024i	−0.214079	−	1.08011i
$809$	13.4958			0.474488			0.237244	−	0.971450i	$-0.423756\pi$
$809$	13.4958			0.474488			0.237244	+	0.971450i	$0.423756\pi$
$810$	−6.45407	−	19.0273i	−0.226773	−	0.668551i
$811$	−11.4250	−	11.4250i	−0.401187	−	0.401187i	0.477464	−	0.878651i	$-0.341556\pi$
$811$	−11.4250	−	11.4250i	−0.401187	−	0.401187i	−0.878651	+	0.477464i	$0.841556\pi$
$812$	−65.9471	−	8.71267i	−2.31429	−	0.305755i
$813$	31.1251	+	31.1251i	1.09161	+	1.09161i
$814$	1.89055	−	3.83146i	0.0662637	−	0.134292i
$815$			11.1107i			0.389190i
$816$	0.121755	−	0.452746i	0.00426228	−	0.0158493i
$817$	−3.27910	−	3.27910i	−0.114721	−	0.114721i
$818$	0.309070	+	0.911173i	0.0108064	+	0.0318584i
$819$		0			0
$820$	−3.11639	+	2.38903i	−0.108829	+	0.0834287i
$821$	−23.7721	+	23.7721i	−0.829652	+	0.829652i	−0.987468	−	0.157816i	$-0.949555\pi$
$821$	−23.7721	+	23.7721i	−0.829652	+	0.829652i	0.157816	+	0.987468i	$0.449555\pi$
$822$	8.93100	+	26.3296i	0.311505	+	0.918350i
$823$	−18.6013			−0.648400			−0.324200	−	0.945989i	$-0.605095\pi$
$823$	−18.6013			−0.648400			−0.324200	+	0.945989i	$0.605095\pi$
$824$	10.6947	−	2.11970i	0.372566	−	0.0738433i
$825$	−7.87787	+	7.87787i	−0.274272	+	0.274272i
$826$	51.5637	+	25.4430i	1.79413	+	0.885275i
$827$	−1.07171	+	1.07171i	−0.0372671	+	0.0372671i	−0.725495	−	0.688228i	$-0.758389\pi$
$827$	−1.07171	+	1.07171i	−0.0372671	+	0.0372671i	0.688228	+	0.725495i	$0.258389\pi$
$828$	−1.78465	−	2.32799i	−0.0620207	−	0.0809033i
$829$		−	30.0497i		−	1.04367i	−0.853047	−	0.521835i	$-0.825248\pi$
$829$		−	30.0497i		−	1.04367i	0.853047	−	0.521835i	$-0.174752\pi$
$830$	−7.78935	+	15.7862i	−0.270372	+	0.547946i
$831$	−32.7396			−1.13573
$832$		0			0
$833$	−0.754520			−0.0261426
$834$	−13.5809	+	27.5236i	−0.470269	+	0.953065i
$835$		−	10.9952i		−	0.380505i
$836$	−4.24144	−	5.53277i	−0.146693	−	0.191355i
$837$	−15.3014	+	15.3014i	−0.528895	+	0.528895i
$838$	30.5572	+	15.0778i	1.05558	+	0.520855i
$839$	−26.3923	+	26.3923i	−0.911163	+	0.911163i	−0.996364	−	0.0852005i	$-0.972847\pi$
$839$	−26.3923	+	26.3923i	−0.911163	+	0.911163i	0.0852005	+	0.996364i	$0.472847\pi$
$840$	33.2495	−	6.59013i	1.14722	−	0.227381i
$841$	25.0085			0.862361
$842$	−10.1677	−	29.9756i	−0.350403	−	1.03303i
$843$	−35.7797	+	35.7797i	−1.23232	+	1.23232i
$844$	8.52420	−	6.53468i	0.293415	−	0.224933i
$845$		0			0
$846$	−4.79478	−	14.1356i	−0.164848	−	0.485990i
$847$	−27.3758	−	27.3758i	−0.940644	−	0.940644i
$848$	4.57227	−	17.0019i	0.157012	−	0.583849i
$849$		−	39.5384i		−	1.35696i
$850$	0.119121	−	0.241415i	0.00408583	−	0.00828048i
$851$	1.44500	+	1.44500i	0.0495341	+	0.0495341i
$852$	−28.3323	−	3.74314i	−0.970647	−	0.128238i
$853$	36.7666	+	36.7666i	1.25887	+	1.25887i	0.951635	+	0.307230i	$0.0994020\pi$
$853$	36.7666	+	36.7666i	1.25887	+	1.25887i	0.307230	+	0.951635i	$0.400598\pi$
$854$	−4.14275	−	12.2133i	−0.141762	−	0.417931i
$855$	−3.90732			−0.133628
$856$	0.161459	+	0.814618i	0.00551856	+	0.0278431i
$857$			23.1948i			0.792319i	0.918182	+	0.396160i	$0.129657\pi$
$857$			23.1948i			0.792319i	−0.918182	+	0.396160i	$0.870343\pi$
$858$		0			0
$859$			53.8518i			1.83740i	0.394956	+	0.918700i	$0.370760\pi$
$859$			53.8518i			1.83740i	−0.394956	+	0.918700i	$0.629240\pi$
$860$	5.21551	+	0.689052i	0.177847	+	0.0234965i
$861$	−14.7197			−0.501647
$862$	−11.1172	+	3.77097i	−0.378655	+	0.128440i
$863$	23.1715	+	23.1715i	0.788766	+	0.788766i	0.981292	−	0.192526i	$-0.0616680\pi$
$863$	23.1715	+	23.1715i	0.788766	+	0.788766i	−0.192526	+	0.981292i	$0.561668\pi$
$864$	12.6205	−	14.3579i	0.429359	−	0.488467i
$865$	−5.62218	−	5.62218i	−0.191160	−	0.191160i
$866$	30.8791	+	15.2366i	1.04931	+	0.517761i
$867$		−	35.5982i		−	1.20898i
$868$	−35.2641	−	46.0005i	−1.19694	−	1.56136i
$869$	−9.81315	−	9.81315i	−0.332888	−	0.332888i
$870$	−26.0623	+	8.84034i	−0.883595	+	0.299715i
$871$		0			0
$872$	−2.56467	+	3.83263i	−0.0868507	+	0.129789i
$873$	0.447329	−	0.447329i	0.0151398	−	0.0151398i
$874$	3.15775	−	1.07111i	0.106812	−	0.0362308i
$875$	48.0735			1.62518
$876$	−32.0365	−	4.23253i	−1.08241	−	0.143004i
$877$	−25.3413	+	25.3413i	−0.855714	+	0.855714i	−0.990830	−	0.135116i	$-0.956859\pi$
$877$	−25.3413	+	25.3413i	−0.855714	+	0.855714i	0.135116	+	0.990830i	$0.456859\pi$
$878$	0.634354	−	1.28561i	0.0214084	−	0.0433871i
$879$	0.102099	−	0.102099i	0.00344372	−	0.00344372i
$880$	7.63741	+	2.05390i	0.257457	+	0.0692369i
$881$		−	1.64385i		−	0.0553828i	−0.999617	−	0.0276914i	$-0.991184\pi$
$881$		−	1.64385i		−	0.0553828i	0.999617	−	0.0276914i	$-0.00881557\pi$
$882$	23.7079	+	11.6982i	0.798287	+	0.393898i
$883$	−15.1271			−0.509067			−0.254534	−	0.967064i	$-0.581922\pi$
$883$	−15.1271			−0.509067			−0.254534	+	0.967064i	$0.581922\pi$
$884$		0			0
$885$	23.7886			0.799646
$886$	49.6301	+	24.4889i	1.66736	+	0.822722i
$887$		−	3.73211i		−	0.125312i	−0.998035	−	0.0626559i	$-0.980043\pi$
$887$		−	3.73211i		−	0.125312i	0.998035	−	0.0626559i	$-0.0199571\pi$
$888$	6.36445	−	9.51100i	0.213577	−	0.319168i
$889$	−30.1952	+	30.1952i	−1.01272	+	1.01272i
$890$	12.5402	−	25.4144i	0.420348	−	0.851892i
$891$	12.4260	−	12.4260i	0.416288	−	0.416288i
$892$	3.09555	−	23.4305i	0.103647	−	0.784512i
$893$	16.9678			0.567805
$894$	−29.3193	+	9.94511i	−0.980584	+	0.332614i
$895$	21.6345	−	21.6345i	0.723163	−	0.723163i
$896$	33.6992	+	38.5504i	1.12581	+	1.28788i
$897$		0			0
$898$	33.8592	−	11.4851i	1.12990	−	0.383261i
$899$	33.2765	+	33.2765i	1.10983	+	1.10983i
$900$	−7.48587	+	5.73869i	−0.249529	+	0.191290i
$901$			0.246319i			0.00820608i
$902$	−3.07991	−	1.51971i	−0.102550	−	0.0506009i
$903$	13.9446	+	13.9446i	0.464047	+	0.464047i
$904$	25.3504	−	5.02449i	0.843141	−	0.167112i
$905$	4.49918	+	4.49918i	0.149558	+	0.149558i
$906$	15.2706	−	5.17980i	0.507332	−	0.172087i
$907$	−44.1790			−1.46694			−0.733471	−	0.679721i	$-0.762101\pi$
$907$	−44.1790			−1.46694			−0.733471	+	0.679721i	$0.762101\pi$
$908$	−0.460111	+	3.48263i	−0.0152693	+	0.115575i
$909$		−	15.3432i		−	0.508903i
$910$		0			0
$911$			23.3467i			0.773510i	0.922182	+	0.386755i	$0.126404\pi$
$911$			23.3467i			0.773510i	−0.922182	+	0.386755i	$0.873596\pi$
$912$	−9.32190	−	16.1800i	−0.308679	−	0.535774i
$913$	−15.3963			−0.509544
$914$	10.8985	+	32.1300i	0.360491	+	1.06277i
$915$	−3.77289	−	3.77289i	−0.124728	−	0.124728i
$916$	2.60841	−	19.7433i	0.0861842	−	0.652337i
$917$	28.9194	+	28.9194i	0.955002	+	0.955002i
$918$	−0.118344	+	0.239839i	−0.00390592	+	0.00791587i
$919$			42.3984i			1.39859i	0.714831	+	0.699297i	$0.246504\pi$
$919$			42.3984i			1.39859i	−0.714831	+	0.699297i	$0.753496\pi$
$920$	−2.10375	+	3.14383i	−0.0693585	+	0.103649i
$921$	14.2548	+	14.2548i	0.469711	+	0.469711i
$922$	2.28254	+	6.72918i	0.0751714	+	0.221614i
$923$		0			0
$924$	18.0370	+	23.5285i	0.593374	+	0.774029i
$925$	4.64654	−	4.64654i	0.152777	−	0.152777i
$926$	0.759105	+	2.23793i	0.0249457	+	0.0735428i
$927$	5.34456			0.175538
$928$	−31.2246	−	27.4462i	−1.02500	−	0.900966i
$929$	−37.1594	+	37.1594i	−1.21916	+	1.21916i	−0.251233	+	0.967927i	$0.580836\pi$
$929$	−37.1594	+	37.1594i	−1.21916	+	1.21916i	−0.967927	+	0.251233i	$0.919164\pi$
$930$	−21.5047	−	10.6110i	−0.705167	−	0.347950i
$931$	−21.2500	+	21.2500i	−0.696442	+	0.696442i
$932$	33.8412	−	25.9428i	1.10851	−	0.849784i
$933$			54.8690i			1.79633i
$934$	−15.6294	+	31.6751i	−0.511409	+	1.03644i
$935$	−0.110649			−0.00361860
$936$		0			0
$937$	−36.4769			−1.19165			−0.595824	−	0.803115i	$-0.703175\pi$
$937$	−36.4769			−1.19165			−0.595824	+	0.803115i	$0.703175\pi$
$938$	25.9885	−	52.6691i	0.848553	−	1.71971i
$939$		−	52.0431i		−	1.69836i
$940$	−15.2766	+	11.7111i	−0.498269	+	0.381975i
$941$	15.2238	−	15.2238i	0.496283	−	0.496283i	−0.413996	−	0.910279i	$-0.635867\pi$
$941$	15.2238	−	15.2238i	0.496283	−	0.496283i	0.910279	+	0.413996i	$0.135867\pi$
$942$	−23.2911	−	11.4925i	−0.758866	−	0.374446i
$943$	1.16156	−	1.16156i	0.0378257	−	0.0378257i
$944$	17.9390	+	31.1367i	0.583864	+	1.01341i
$945$	−19.3363			−0.629011
$946$	1.47803	+	4.35741i	0.0480550	+	0.141671i
$947$	−12.2318	+	12.2318i	−0.397482	+	0.397482i	−0.877344	−	0.479862i	$-0.840687\pi$
$947$	−12.2318	+	12.2318i	−0.397482	+	0.397482i	0.479862	+	0.877344i	$0.340687\pi$
$948$	−22.6156	−	29.5011i	−0.734522	−	0.958151i
$949$		0			0
$950$	−3.44425	−	10.1540i	−0.111746	−	0.329440i
$951$	50.8346	+	50.8346i	1.64843	+	1.64843i
$952$	−0.595364	−	0.398398i	−0.0192959	−	0.0129122i
$953$			15.4425i			0.500231i	0.968216	+	0.250115i	$0.0804685\pi$
$953$			15.4425i			0.500231i	−0.968216	+	0.250115i	$0.919531\pi$
$954$	3.81896	−	7.73964i	0.123643	−	0.250580i
$955$	17.1083	+	17.1083i	0.553611	+	0.553611i
$956$	−5.61524	+	42.5023i	−0.181610	+	1.37462i
$957$	−17.0203	−	17.0203i	−0.550190	−	0.550190i
$958$	−14.2255	−	41.9383i	−0.459605	−	1.35497i
$959$	42.4826			1.37183
$960$	19.5602	+	8.13346i	0.631304	+	0.262506i
$961$			10.0056i			0.322760i
$962$		0			0
$963$			0.407098i			0.0131186i
$964$	−5.25709	+	39.7915i	−0.169320	+	1.28160i
$965$	12.0659			0.388414
$966$	−13.4285	+	4.55496i	−0.432056	+	0.146554i
$967$	−9.02312	−	9.02312i	−0.290164	−	0.290164i	0.546981	−	0.837145i	$-0.315777\pi$
$967$	−9.02312	−	9.02312i	−0.290164	−	0.290164i	−0.837145	+	0.546981i	$0.815777\pi$
$968$	−4.70409	−	23.7338i	−0.151195	−	0.762833i
$969$	0.184732	+	0.184732i	0.00593445	+	0.00593445i
$970$	−0.731597	−	0.360991i	−0.0234902	−	0.0115907i
$971$			26.8535i			0.861769i	0.902407	+	0.430884i	$0.141798\pi$
$971$			26.8535i			0.861769i	−0.902407	+	0.430884i	$0.858202\pi$
$972$	21.2648	−	16.3016i	0.682067	−	0.522875i
$973$	33.1609	+	33.1609i	1.06309	+	1.06309i
$974$	22.7923	−	7.73116i	0.730313	−	0.247722i
$975$		0			0
$976$	2.09317	−	7.78344i	0.0670007	−	0.249142i
$977$	21.9144	−	21.9144i	0.701102	−	0.701102i	−0.263545	−	0.964647i	$-0.584892\pi$
$977$	21.9144	−	21.9144i	0.701102	−	0.701102i	0.964647	+	0.263545i	$0.0848917\pi$
$978$	−24.6496	+	8.36117i	−0.788209	+	0.267361i
$979$	24.7867			0.792188
$980$	4.46537	−	33.7988i	0.142641	−	1.07966i
$981$	−1.59850	+	1.59850i	−0.0510360	+	0.0510360i
$982$	−7.01933	+	14.2256i	−0.223996	+	0.453958i
$983$	−15.4374	+	15.4374i	−0.492377	+	0.492377i	−0.909055	−	0.416677i	$-0.863195\pi$
$983$	−15.4374	+	15.4374i	−0.492377	+	0.492377i	0.416677	+	0.909055i	$0.363195\pi$
$984$	−7.64539	−	5.11605i	−0.243726	−	0.163094i
$985$		−	1.34988i		−	0.0430109i
$986$	0.521585	+	0.257365i	0.0166106	+	0.00819617i
$987$	−72.1565			−2.29677
$988$		0			0
$989$	−2.20079			−0.0699811
$990$	3.47671	+	1.71551i	0.110497	+	0.0545224i
$991$			13.1120i			0.416518i	0.978074	+	0.208259i	$0.0667797\pi$
$991$			13.1120i			0.416518i	−0.978074	+	0.208259i	$0.933220\pi$
$992$	−2.32799	−	36.1491i	−0.0739138	−	1.14774i
$993$	28.2543	−	28.2543i	0.896624	−	0.896624i
$994$	−19.3225	+	39.1596i	−0.612872	+	1.24207i
$995$	−10.1262	+	10.1262i	−0.321023	+	0.321023i
$996$	−40.8842	−	5.40146i	−1.29547	−	0.171152i
$997$	13.8622			0.439021			0.219511	−	0.975610i	$-0.429554\pi$
$997$	13.8622			0.439021			0.219511	+	0.975610i	$0.429554\pi$
$998$	13.0271	−	4.41878i	0.412365	−	0.139874i
$999$	−4.61620	+	4.61620i	−0.146050	+	0.146050i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	676.2.f.i.239.5		16
4.3	odd	2	inner	676.2.f.i.239.7		16
13.2	odd	12		676.2.l.m.319.3		16
13.3	even	3		676.2.l.k.19.3		16
13.4	even	6		676.2.l.m.587.4		16
13.5	odd	4		676.2.f.h.99.2		16
13.6	odd	12		52.2.l.b.11.3	yes	16
13.7	odd	12		676.2.l.k.427.2		16
13.8	odd	4	inner	676.2.f.i.99.7		16
13.9	even	3		676.2.l.i.587.1		16
13.10	even	6		52.2.l.b.19.2	yes	16
13.11	odd	12		676.2.l.i.319.2		16
13.12	even	2		676.2.f.h.239.4		16
39.23	odd	6		468.2.cb.f.19.3		16
39.32	even	12		468.2.cb.f.271.2		16
52.3	odd	6		676.2.l.k.19.2		16
52.7	even	12		676.2.l.k.427.3		16
52.11	even	12		676.2.l.i.319.1		16
52.15	even	12		676.2.l.m.319.4		16
52.19	even	12		52.2.l.b.11.2	✓	16
52.23	odd	6		52.2.l.b.19.3	yes	16
52.31	even	4		676.2.f.h.99.4		16
52.35	odd	6		676.2.l.i.587.2		16
52.43	odd	6		676.2.l.m.587.3		16
52.47	even	4	inner	676.2.f.i.99.5		16
52.51	odd	2		676.2.f.h.239.2		16
104.19	even	12		832.2.bu.n.63.1		16
104.45	odd	12		832.2.bu.n.63.4		16
104.75	odd	6		832.2.bu.n.383.4		16
104.101	even	6		832.2.bu.n.383.1		16
156.23	even	6		468.2.cb.f.19.2		16
156.71	odd	12		468.2.cb.f.271.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.l.b.11.2	✓	16	52.19	even	12
52.2.l.b.11.3	yes	16	13.6	odd	12
52.2.l.b.19.2	yes	16	13.10	even	6
52.2.l.b.19.3	yes	16	52.23	odd	6
468.2.cb.f.19.2		16	156.23	even	6
468.2.cb.f.19.3		16	39.23	odd	6
468.2.cb.f.271.2		16	39.32	even	12
468.2.cb.f.271.3		16	156.71	odd	12
676.2.f.h.99.2		16	13.5	odd	4
676.2.f.h.99.4		16	52.31	even	4
676.2.f.h.239.2		16	52.51	odd	2
676.2.f.h.239.4		16	13.12	even	2
676.2.f.i.99.5		16	52.47	even	4	inner
676.2.f.i.99.7		16	13.8	odd	4	inner
676.2.f.i.239.5		16	1.1	even	1	trivial
676.2.f.i.239.7		16	4.3	odd	2	inner
676.2.l.i.319.1		16	52.11	even	12
676.2.l.i.319.2		16	13.11	odd	12
676.2.l.i.587.1		16	13.9	even	3
676.2.l.i.587.2		16	52.35	odd	6
676.2.l.k.19.2		16	52.3	odd	6
676.2.l.k.19.3		16	13.3	even	3
676.2.l.k.427.2		16	13.7	odd	12
676.2.l.k.427.3		16	52.7	even	12
676.2.l.m.319.3		16	13.2	odd	12
676.2.l.m.319.4		16	52.15	even	12
676.2.l.m.587.3		16	52.43	odd	6
676.2.l.m.587.4		16	13.4	even	6
832.2.bu.n.63.1		16	104.19	even	12
832.2.bu.n.63.4		16	104.45	odd	12
832.2.bu.n.383.1		16	104.101	even	6
832.2.bu.n.383.4		16	104.75	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:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	676.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.625780 - 1.26823i) q^{2} -2.09440i q^{3} +(-1.21680 - 1.58726i) q^{4} +(-0.894007 + 0.894007i) q^{5} +(-2.65617 - 1.31063i) q^{6} +(-3.20020 + 3.20020i) q^{7} +(-2.77446 + 0.549903i) q^{8} -1.38651 q^{9} +O(q^{10})\)	\(q+(0.625780 - 1.26823i) q^{2} -2.09440i q^{3} +(-1.21680 - 1.58726i) q^{4} +(-0.894007 + 0.894007i) q^{5} +(-2.65617 - 1.31063i) q^{6} +(-3.20020 + 3.20020i) q^{7} +(-2.77446 + 0.549903i) q^{8} -1.38651 q^{9} +(0.574352 + 1.69325i) q^{10} +(-1.10580 + 1.10580i) q^{11} +(-3.32436 + 2.54846i) q^{12} +(2.05596 + 6.06121i) q^{14} +(1.87241 + 1.87241i) q^{15} +(-1.03880 + 3.86276i) q^{16} -0.0559625i q^{17} +(-0.867649 + 1.75841i) q^{18} +(-1.57611 - 1.57611i) q^{19} +(2.50685 + 0.331195i) q^{20} +(6.70250 + 6.70250i) q^{21} +(0.710421 + 2.09440i) q^{22} -1.05782 q^{23} +(1.15172 + 5.81082i) q^{24} +3.40150i q^{25} -3.37929i q^{27} +(8.97356 + 1.18555i) q^{28} -7.34904 q^{29} +(3.54635 - 1.20292i) q^{30} +(-4.52800 - 4.52800i) q^{31} +(4.24880 + 3.73466i) q^{32} +(2.31599 + 2.31599i) q^{33} +(-0.0709732 - 0.0350202i) q^{34} -5.72201i q^{35} +(1.68710 + 2.20075i) q^{36} +(-1.36603 - 1.36603i) q^{37} +(-2.98516 + 1.01257i) q^{38} +(1.98877 - 2.97200i) q^{40} +(-1.09808 + 1.09808i) q^{41} +(12.6946 - 4.30601i) q^{42} +2.08050 q^{43} +(3.10074 + 0.409658i) q^{44} +(1.23955 - 1.23955i) q^{45} +(-0.661960 + 1.34155i) q^{46} +(-5.38281 + 5.38281i) q^{47} +(8.09016 + 2.17565i) q^{48} -13.4826i q^{49} +(4.31388 + 2.12859i) q^{50} -0.117208 q^{51} -4.40150 q^{53} +(-4.28571 - 2.11469i) q^{54} -1.97719i q^{55} +(7.11902 - 10.6386i) q^{56} +(-3.30100 + 3.30100i) q^{57} +(-4.59888 + 9.32026i) q^{58} +(6.35242 - 6.35242i) q^{59} +(0.693654 - 5.25034i) q^{60} -2.01500 q^{61} +(-8.57606 + 2.90900i) q^{62} +(4.43711 - 4.43711i) q^{63} +(7.39521 - 3.05136i) q^{64} +(4.38651 - 1.48790i) q^{66} +(-6.48861 - 6.48861i) q^{67} +(-0.0888271 + 0.0680952i) q^{68} +2.21549i q^{69} +(-7.25680 - 3.58071i) q^{70} +(4.82430 + 4.82430i) q^{71} +(3.84681 - 0.762445i) q^{72} +(5.45504 + 5.45504i) q^{73} +(-2.58726 + 0.877600i) q^{74} +7.12411 q^{75} +(-0.583887 + 4.41950i) q^{76} -7.07759i q^{77} +8.87422i q^{79} +(-2.52464 - 4.38202i) q^{80} -11.2371 q^{81} +(0.705456 + 2.07976i) q^{82} +(6.96160 + 6.96160i) q^{83} +(2.48302 - 18.7942i) q^{84} +(0.0500308 + 0.0500308i) q^{85} +(1.30194 - 2.63855i) q^{86} +15.3918i q^{87} +(2.45992 - 3.67609i) q^{88} +(-11.2076 - 11.2076i) q^{89} +(-0.796345 - 2.34771i) q^{90} +(1.28715 + 1.67903i) q^{92} +(-9.48344 + 9.48344i) q^{93} +(3.45817 + 10.1951i) q^{94} +2.81810 q^{95} +(7.82188 - 8.89868i) q^{96} +(-0.322629 + 0.322629i) q^{97} +(-17.0990 - 8.43714i) q^{98} +(1.53321 - 1.53321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 12 q^{5} - 4 q^{6} - 10 q^{8} - 8 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 + 12 * q^5 - 4 * q^6 - 10 * q^8 - 8 * q^9	\( 16 q + 2 q^{2} + 12 q^{5} - 4 q^{6} - 10 q^{8} - 8 q^{9} + 8 q^{14} + 4 q^{16} + 6 q^{18} + 22 q^{20} + 28 q^{21} - 4 q^{24} + 36 q^{28} + 16 q^{29} + 2 q^{32} - 28 q^{33} - 14 q^{34} - 8 q^{37} - 40 q^{40} + 24 q^{41} + 56 q^{42} + 8 q^{44} - 20 q^{45} - 56 q^{46} + 20 q^{48} + 32 q^{50} - 32 q^{53} - 44 q^{54} - 12 q^{57} - 30 q^{58} + 24 q^{60} - 8 q^{61} + 56 q^{66} - 32 q^{68} - 28 q^{70} + 46 q^{72} - 20 q^{73} - 8 q^{74} + 8 q^{76} + 22 q^{80} - 96 q^{81} + 48 q^{84} + 52 q^{85} - 16 q^{86} - 44 q^{89} - 12 q^{92} - 112 q^{93} + 76 q^{94} + 72 q^{96} + 52 q^{97} - 70 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 + 12 * q^5 - 4 * q^6 - 10 * q^8 - 8 * q^9 + 8 * q^14 + 4 * q^16 + 6 * q^18 + 22 * q^20 + 28 * q^21 - 4 * q^24 + 36 * q^28 + 16 * q^29 + 2 * q^32 - 28 * q^33 - 14 * q^34 - 8 * q^37 - 40 * q^40 + 24 * q^41 + 56 * q^42 + 8 * q^44 - 20 * q^45 - 56 * q^46 + 20 * q^48 + 32 * q^50 - 32 * q^53 - 44 * q^54 - 12 * q^57 - 30 * q^58 + 24 * q^60 - 8 * q^61 + 56 * q^66 - 32 * q^68 - 28 * q^70 + 46 * q^72 - 20 * q^73 - 8 * q^74 + 8 * q^76 + 22 * q^80 - 96 * q^81 + 48 * q^84 + 52 * q^85 - 16 * q^86 - 44 * q^89 - 12 * q^92 - 112 * q^93 + 76 * q^94 + 72 * q^96 + 52 * q^97 - 70 * q^98

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