LMFDB - Embedded newform 676.2.f.i.99.7

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			99.7
Root			$1.41121 + 0.0921725i$ of defining polynomial
Character	$\chi$	$=$	676.99
Dual form			676.2.f.i.239.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26823 + 0.625780i) q^{2} -2.09440i q^{3} +(1.21680 + 1.58726i) q^{4} +(-0.894007 - 0.894007i) q^{5} +(1.31063 - 2.65617i) q^{6} +(3.20020 + 3.20020i) q^{7} +(0.549903 + 2.77446i) q^{8} -1.38651 q^{9} +O(q^{10})$	\(q+(1.26823 + 0.625780i) q^{2} -2.09440i q^{3} +(1.21680 + 1.58726i) q^{4} +(-0.894007 - 0.894007i) q^{5} +(1.31063 - 2.65617i) q^{6} +(3.20020 + 3.20020i) q^{7} +(0.549903 + 2.77446i) 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} +(-1.75841 - 0.867649i) q^{18} +(1.57611 - 1.57611i) q^{19} +(0.331195 - 2.50685i) q^{20} +(6.70250 - 6.70250i) q^{21} +(0.710421 + 2.09440i) q^{22} +1.05782 q^{23} +(5.81082 - 1.15172i) q^{24} -3.40150i q^{25} -3.37929i q^{27} +(-1.18555 + 8.97356i) q^{28} -7.34904 q^{29} +(-3.54635 + 1.20292i) q^{30} +(4.52800 - 4.52800i) q^{31} +(-3.73466 + 4.24880i) q^{32} +(2.31599 - 2.31599i) q^{33} +(-0.0350202 + 0.0709732i) 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} +(-0.409658 + 3.10074i) q^{44} +(1.23955 + 1.23955i) q^{45} +(1.34155 + 0.661960i) q^{46} +(5.38281 + 5.38281i) q^{47} +(8.09016 + 2.17565i) q^{48} +13.4826i q^{49} +(2.12859 - 4.31388i) q^{50} +0.117208 q^{51} -4.40150 q^{53} +(2.11469 - 4.28571i) q^{54} -1.97719i q^{55} +(-7.11902 + 10.6386i) q^{56} +(-3.30100 - 3.30100i) q^{57} +(-9.32026 - 4.59888i) q^{58} +(-6.35242 - 6.35242i) q^{59} +(-5.25034 - 0.693654i) 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} +(3.58071 - 7.25680i) q^{70} +(-4.82430 + 4.82430i) q^{71} +(-0.762445 - 3.84681i) q^{72} +(5.45504 - 5.45504i) q^{73} +(-2.58726 + 0.877600i) q^{74} -7.12411 q^{75} +(4.41950 + 0.583887i) q^{76} +7.07759i q^{77} +8.87422i q^{79} +(4.38202 - 2.52464i) q^{80} -11.2371 q^{81} +(-0.705456 - 2.07976i) q^{82} +(-6.96160 + 6.96160i) q^{83} +(18.7942 + 2.48302i) q^{84} +(0.0500308 - 0.0500308i) q^{85} +(-2.63855 - 1.30194i) 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} +(8.89868 + 7.82188i) q^{96} +(-0.322629 - 0.322629i) q^{97} +(-8.43714 + 17.0990i) 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 $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.26823	+	0.625780i	0.896772	+	0.442493i
$2$	1.26823	+	0.625780i	0.896772	+	0.442493i
$3$		−	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	0.478355	−	0.878167i	$-0.341233\pi$
$5$	−0.894007	−	0.894007i	−0.399812	−	0.399812i	−0.878167	+	0.478355i	$0.841233\pi$
$6$	1.31063	−	2.65617i	0.535063	−	1.08438i
$7$	3.20020	+	3.20020i	1.20956	+	1.20956i	0.971168	+	0.238395i	$0.0766212\pi$
$7$	3.20020	+	3.20020i	1.20956	+	1.20956i	0.238395	+	0.971168i	$0.423379\pi$
$8$	0.549903	+	2.77446i	0.194420	+	0.980918i
$9$	−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	$-0.174243\pi$
$11$	1.10580	+	1.10580i	0.333412	+	0.333412i	−0.520469	+	0.853881i	$0.674243\pi$
$12$	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	$0.00216021\pi$
$17$			0.0559625i			0.0135729i	−0.999977	+	0.00678645i	$0.997840\pi$
$18$	−1.75841	−	0.867649i	−0.414461	−	0.204507i
$19$	1.57611	−	1.57611i	0.361584	−	0.361584i	−0.502812	−	0.864396i	$-0.667701\pi$
$19$	1.57611	−	1.57611i	0.361584	−	0.361584i	0.864396	+	0.502812i	$0.167701\pi$
$20$	0.331195	−	2.50685i	0.0740574	−	0.560549i
$21$	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	$-0.464824\pi$
$23$	1.05782			0.220570			0.110285	+	0.993900i	$0.464824\pi$
$24$	5.81082	−	1.15172i	1.18613	−	0.235093i
$25$		−	3.40150i		−	0.680301i
$26$		0			0
$27$		−	3.37929i		−	0.650346i
$28$	−1.18555	+	8.97356i	−0.224048	+	1.69584i
$29$	−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	$-0.554980\pi$
$31$	4.52800	−	4.52800i	0.813253	−	0.813253i	0.985120	+	0.171867i	$0.0549801\pi$
$32$	−3.73466	+	4.24880i	−0.660202	+	0.751088i
$33$	2.31599	−	2.31599i	0.403163	−	0.403163i
$34$	−0.0350202	+	0.0709732i	−0.00600591	+	0.0121718i
$35$		−	5.72201i		−	0.967195i
$36$	−1.68710	−	2.20075i	−0.281184	−	0.366792i
$37$	−1.36603	+	1.36603i	−0.224573	+	0.224573i	−0.810421	−	0.585848i	$-0.800762\pi$
$37$	−1.36603	+	1.36603i	−0.224573	+	0.224573i	0.585848	+	0.810421i	$0.300762\pi$
$38$	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	0.616143	−	0.787634i	$-0.288694\pi$
$41$	−1.09808	−	1.09808i	−0.171491	−	0.171491i	−0.787634	+	0.616143i	$0.788694\pi$
$42$	12.6946	−	4.30601i	1.95882	−	0.664431i
$43$	−2.08050			−0.317274			−0.158637	−	0.987337i	$-0.550710\pi$
$43$	−2.08050			−0.317274			−0.158637	+	0.987337i	$0.550710\pi$
$44$	−0.409658	+	3.10074i	−0.0617582	+	0.467454i
$45$	1.23955	+	1.23955i	0.184781	+	0.184781i
$46$	1.34155	+	0.661960i	0.197801	+	0.0976006i
$47$	5.38281	+	5.38281i	0.785163	+	0.785163i	0.980697	−	0.195534i	$-0.0626440\pi$
$47$	5.38281	+	5.38281i	0.785163	+	0.785163i	−0.195534	+	0.980697i	$0.562644\pi$
$48$	8.09016	+	2.17565i	1.16771	+	0.314029i
$49$			13.4826i			1.92609i
$50$	2.12859	−	4.31388i	0.301028	−	0.610075i
$51$	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	$0.597753\pi$
$54$	2.11469	−	4.28571i	0.287773	−	0.583212i
$55$		−	1.97719i		−	0.266604i
$56$	−7.11902	+	10.6386i	−0.951319	+	1.42165i
$57$	−3.30100	−	3.30100i	−0.437228	−	0.437228i
$58$	−9.32026	−	4.59888i	−1.22381	−	0.603863i
$59$	−6.35242	−	6.35242i	−0.827014	−	0.827014i	0.160088	−	0.987103i	$-0.448822\pi$
$59$	−6.35242	−	6.35242i	−0.827014	−	0.827014i	−0.987103	+	0.160088i	$0.948822\pi$
$60$	−5.25034	−	0.693654i	−0.677816	−	0.0895504i
$61$	−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	$-0.560597\pi$
$67$	6.48861	−	6.48861i	0.792710	−	0.792710i	0.981934	+	0.189224i	$0.0605973\pi$
$68$	−0.0888271	+	0.0680952i	−0.0107719	+	0.00825775i
$69$		−	2.21549i		−	0.266714i
$70$	3.58071	−	7.25680i	0.427977	−	0.867354i
$71$	−4.82430	+	4.82430i	−0.572539	+	0.572539i	−0.932837	−	0.360298i	$-0.882675\pi$
$71$	−4.82430	+	4.82430i	−0.572539	+	0.572539i	0.360298	+	0.932837i	$0.382675\pi$
$72$	−0.762445	−	3.84681i	−0.0898550	−	0.453351i
$73$	5.45504	−	5.45504i	0.638464	−	0.638464i	−0.311713	−	0.950176i	$-0.600903\pi$
$73$	5.45504	−	5.45504i	0.638464	−	0.638464i	0.950176	+	0.311713i	$0.100903\pi$
$74$	−2.58726	+	0.877600i	−0.300763	+	0.102019i
$75$	−7.12411			−0.822621
$76$	4.41950	+	0.583887i	0.506952	+	0.0669764i
$77$			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	$0.833622\pi$
$80$	4.38202	−	2.52464i	0.489925	−	0.282263i
$81$	−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	$-0.931699\pi$
$83$	−6.96160	+	6.96160i	−0.764135	+	0.764135i	0.212932	+	0.977067i	$0.431699\pi$
$84$	18.7942	+	2.48302i	2.05062	+	0.270920i
$85$	0.0500308	−	0.0500308i	0.00542661	−	0.00542661i
$86$	−2.63855	−	1.30194i	−0.284522	−	0.140391i
$87$			15.3918i			1.65018i
$88$	−2.45992	+	3.67609i	−0.262228	+	0.391872i
$89$	−11.2076	+	11.2076i	−1.18800	+	1.18800i	−0.210381	+	0.977620i	$0.567470\pi$
$89$	−11.2076	+	11.2076i	−1.18800	+	1.18800i	−0.977620	+	0.210381i	$0.932530\pi$
$90$	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
$96$	8.89868	+	7.82188i	0.908218	+	0.798317i
$97$	−0.322629	−	0.322629i	−0.0327581	−	0.0327581i	0.690538	−	0.723296i	$-0.257374\pi$
$97$	−0.322629	−	0.322629i	−0.0327581	−	0.0327581i	−0.723296	+	0.690538i	$0.757374\pi$
$98$	−8.43714	+	17.0990i	−0.852279	+	1.72726i
$99$	−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	$-0.814415\pi$
$101$		−	11.0661i		−	1.10112i	0.834796	−	0.550559i	$-0.185585\pi$
$102$	0.148646	+	0.0733463i	0.0147182	+	0.00726236i
$103$	3.85469			0.379813			0.189907	−	0.981802i	$-0.439181\pi$
$103$	3.85469			0.379813			0.189907	+	0.981802i	$0.439181\pi$
$104$		0			0
$105$	−11.9842			−1.16953
$106$	−5.58211	−	2.75437i	−0.542182	−	0.267528i
$107$		−	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	0.760161	−	0.649734i	$-0.225120\pi$
$109$	1.15289	+	1.15289i	0.110427	+	0.110427i	−0.649734	+	0.760161i	$0.725120\pi$
$110$	1.23729	−	2.50753i	0.117971	−	0.239083i
$111$	2.86100	+	2.86100i	0.271554	+	0.271554i
$112$	−15.6860	+	9.03725i	−1.48218	+	0.853940i
$113$	−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
$122$	−2.55547	−	1.26094i	−0.231362	−	0.114160i
$123$	−2.29981	+	2.29981i	−0.207367	+	0.207367i
$124$	12.6968	+	1.67745i	1.14021	+	0.150639i
$125$	−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	$-0.637489\pi$
$127$	−9.43541			−0.837258			−0.418629	+	0.908157i	$0.637489\pi$
$128$	−11.2883	−	0.757953i	−0.997753	−	0.0669942i
$129$			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	$-0.129176\pi$
$132$	6.49419	+	0.857986i	0.565247	+	0.0746781i
$133$	10.0877			0.874717
$134$	12.2895	−	4.16859i	1.06165	−	0.360111i
$135$	−3.02111	+	3.02111i	−0.260016	+	0.260016i
$136$	−0.155265	+	0.0307739i	−0.0133139	+	0.00263884i
$137$	−6.63748	+	6.63748i	−0.567078	+	0.567078i	−0.931309	−	0.364231i	$-0.881332\pi$
$137$	−6.63748	+	6.63748i	−0.567078	+	0.567078i	0.364231	+	0.931309i	$0.381332\pi$
$138$	1.38641	−	2.80974i	0.118019	−	0.239181i
$139$		−	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
$148$	−3.83042	−	0.506060i	−0.314858	−	0.0415978i
$149$	7.39116	+	7.39116i	0.605507	+	0.605507i	0.941769	−	0.336261i	$-0.109163\pi$
$149$	7.39116	+	7.39116i	0.605507	+	0.605507i	−0.336261	+	0.941769i	$0.609163\pi$
$150$	−9.03499	−	4.45812i	−0.737704	−	0.364004i
$151$	3.84960	+	3.84960i	0.313276	+	0.313276i	0.846177	−	0.532901i	$-0.178898\pi$
$151$	3.84960	+	3.84960i	0.313276	+	0.313276i	−0.532901	+	0.846177i	$0.678898\pi$
$152$	5.23955	+	3.50614i	0.424983	+	0.284385i
$153$		−	0.0775925i		−	0.00627298i
$154$	−4.42901	+	8.97599i	−0.356900	+	0.723306i
$155$	−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	$0.386213\pi$
$158$	−5.55331	+	11.2545i	−0.441797	+	0.895362i
$159$			9.21851i			0.731075i
$160$	7.13727	−	0.459638i	0.564251	−	0.0363376i
$161$	3.38523	+	3.38523i	0.266793	+	0.266793i
$162$	−14.2512	−	7.03196i	−1.11968	−	0.552483i
$163$	−6.21398	−	6.21398i	−0.486716	−	0.486716i	0.420552	−	0.907268i	$-0.361836\pi$
$163$	−6.21398	−	6.21398i	−0.486716	−	0.486716i	−0.907268	+	0.420552i	$0.861836\pi$
$164$	0.406795	−	3.07907i	0.0317653	−	0.240435i
$165$	−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	$-0.140763\pi$
$167$	6.14941	+	6.14941i	0.475856	+	0.475856i	−0.427948	+	0.903803i	$0.640763\pi$
$168$	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	$-0.923160\pi$
$173$		−	6.28874i		−	0.478124i	0.971004	−	0.239062i	$-0.0768399\pi$
$174$	−9.63190	+	19.5203i	−0.730192	+	1.47983i
$175$	10.8855	−	10.8855i	0.822867	−	0.822867i
$176$	−5.42016	+	3.12275i	−0.408560	+	0.235386i
$177$	−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	$-0.140335\pi$
$179$	24.1995			1.80876			0.904379	+	0.426731i	$0.140335\pi$
$180$	−0.459205	+	3.47577i	−0.0342271	+	0.259069i
$181$			5.03261i			0.374071i	0.982353	+	0.187035i	$0.0598879\pi$
$181$			5.03261i			0.374071i	−0.982353	+	0.187035i	$0.940112\pi$
$182$		0			0
$183$			4.22020i			0.311967i
$184$	0.581696	+	2.93486i	0.0428832	+	0.216361i
$185$	2.44247			0.179574
$186$	−6.09261	−	17.9617i	−0.446732	−	1.31702i
$187$	−0.0618835	+	0.0618835i	−0.00452537	+	0.00452537i
$188$	−1.99412	+	15.0937i	−0.145436	+	1.10082i
$189$	10.8144	−	10.8144i	0.786634	−	0.786634i
$190$	−3.57399	−	1.76351i	−0.259285	−	0.127939i
$191$		−	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	−0.906961	−	0.421215i	$-0.861604\pi$
$193$	−6.74819	+	6.74819i	−0.485746	+	0.485746i	0.421215	+	0.906961i	$0.361604\pi$
$194$	−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	0.679701	−	0.733490i	$-0.262110\pi$
$197$	−0.754963	−	0.754963i	−0.0537889	−	0.0537889i	−0.733490	+	0.679701i	$0.762110\pi$
$198$	−0.985005	−	2.90390i	−0.0700012	−	0.206371i
$199$	−11.3268			−0.802936			−0.401468	−	0.915873i	$-0.631500\pi$
$199$	−11.3268			−0.802936			−0.401468	+	0.915873i	$0.631500\pi$
$200$	9.43732	−	1.87050i	0.667320	−	0.132264i
$201$	−13.5897	−	13.5897i	−0.958546	−	0.958546i
$202$	6.92494	−	14.0343i	0.487237	−	0.987452i
$203$	−23.5184	−	23.5184i	−1.65067	−	1.65067i
$204$	0.142618	+	0.186039i	0.00998529	+	0.0130254i
$205$			1.96337i			0.137128i
$206$	4.88862	+	2.41218i	0.340606	+	0.168065i
$207$	−1.46667			−0.101941
$208$		0			0
$209$	3.48573			0.241113
$210$	−15.1986	−	7.49945i	−1.04881	−	0.517511i
$211$			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
$214$	0.183737	−	0.372369i	0.0125600	−	0.0254546i
$215$	1.85998	+	1.85998i	0.126850	+	0.126850i
$216$	9.37570	−	1.85828i	0.637936	−	0.126440i
$217$	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	$-0.879486\pi$
$223$	−8.35593	+	8.35593i	−0.559554	+	0.559554i	0.369626	+	0.929181i	$0.379486\pi$
$224$	−25.5487	+	1.64533i	−1.70704	+	0.109933i
$225$			4.71622i			0.314414i
$226$	−11.5879	−	5.71778i	−0.770813	−	0.380341i
$227$	1.24199	−	1.24199i	0.0824340	−	0.0824340i	−0.664687	−	0.747122i	$-0.731435\pi$
$227$	1.24199	−	1.24199i	0.0824340	−	0.0824340i	0.747122	+	0.664687i	$0.231435\pi$
$228$	1.22289	−	9.25620i	0.0809880	−	0.613007i
$229$	7.04097	−	7.04097i	0.465280	−	0.465280i	−0.435101	−	0.900382i	$-0.643287\pi$
$229$	7.04097	−	7.04097i	0.465280	−	0.465280i	0.900382	+	0.435101i	$0.143287\pi$
$230$	−0.607559	−	1.79115i	−0.0400613	−	0.118105i
$231$	14.8233			0.975302
$232$	−4.04126	−	20.3896i	−0.265322	−	1.33864i
$233$		−	21.3205i		−	1.39675i	−0.715731	−	0.698376i	$-0.753906\pi$
$233$		−	21.3205i		−	1.39675i	0.715731	−	0.698376i	$-0.246094\pi$
$234$		0			0
$235$		−	9.62453i		−	0.627835i
$236$	2.35333	−	17.8126i	0.153188	−	1.15950i
$237$	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	$-0.506163\pi$
$239$	15.1574	−	15.1574i	0.980452	−	0.980452i	0.999813	+	0.0193606i	$0.00616305\pi$
$240$	−5.28761	−	9.17771i	−0.341314	−	0.592418i
$241$	−14.1907	+	14.1907i	−0.914101	+	0.914101i	−0.996592	−	0.0824908i	$-0.973712\pi$
$241$	−14.1907	+	14.1907i	−0.914101	+	0.914101i	0.0824908	+	0.996592i	$0.473712\pi$
$242$	5.35317	−	10.8489i	0.344115	−	0.697395i
$243$			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	$-0.652625\pi$
$251$	−14.6175			−0.922646			−0.461323	+	0.887232i	$0.652625\pi$
$252$	1.64378	−	12.4419i	0.103548	−	0.783768i
$253$	1.16974	+	1.16974i	0.0735407	+	0.0735407i
$254$	−11.9662	−	5.90449i	−0.750829	−	0.370481i
$255$	−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	$-0.855894\pi$
$257$		−	14.0246i		−	0.874828i	0.899260	−	0.437414i	$-0.144106\pi$
$258$	−2.72678	+	5.52618i	−0.169762	+	0.344045i
$259$	−8.74312			−0.543271
$260$		0			0
$261$	10.1895			0.630715
$262$	5.65500	−	11.4606i	0.349367	−	0.708040i
$263$		−	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
$266$	12.7935	+	6.31270i	0.784422	+	0.387056i
$267$	23.4731	+	23.4731i	1.43653	+	1.43653i
$268$	18.1945	+	2.40378i	1.11140	+	0.146834i
$269$	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	$-0.0296215\pi$
$271$	14.8611	+	14.8611i	0.902749	+	0.902749i	−0.0929244	+	0.995673i	$0.529621\pi$
$272$	−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	$0.155608\pi$
$277$			15.6320i			0.939235i	−0.882870	+	0.469618i	$0.844392\pi$
$278$	6.48441	−	13.1415i	0.388909	−	0.788177i
$279$	−6.27811	+	6.27811i	−0.375861	+	0.375861i
$280$	15.8755	−	3.14655i	0.948740	−	0.188042i
$281$	−17.0835	+	17.0835i	−1.01912	+	1.01912i	−0.0193039	+	0.999814i	$0.506145\pi$
$281$	−17.0835	+	17.0835i	−1.01912	+	1.01912i	−0.999814	+	0.0193039i	$0.993855\pi$
$282$	21.3525	−	7.24279i	1.27153	−	0.431302i
$283$	−18.8782			−1.12219			−0.561095	−	0.827751i	$-0.689620\pi$
$283$	−18.8782			−1.12219			−0.561095	+	0.827751i	$0.689620\pi$
$284$	−13.5276	−	1.78722i	−0.802717	−	0.106052i
$285$			5.90223i			0.349618i
$286$		0			0
$287$		−	7.02813i		−	0.414858i
$288$	5.17815	−	5.89100i	0.305125	−	0.347130i
$289$	16.9969			0.999816
$290$	4.22094	+	12.4438i	0.247862	+	0.730725i
$291$	−0.675715	+	0.675715i	−0.0396111	+	0.0396111i
$292$	15.2963	+	2.02088i	0.895146	+	0.118263i
$293$	0.0487486	−	0.0487486i	0.00284792	−	0.00284792i	−0.705681	−	0.708529i	$-0.749359\pi$
$293$	0.0487486	−	0.0487486i	0.00284792	−	0.00284792i	0.708529	+	0.705681i	$0.249359\pi$
$294$	35.8121	+	17.6707i	2.08861	+	1.03058i
$295$			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
$304$	4.45087	+	7.72538i	0.255275	+	0.443081i
$305$	1.80142	+	1.80142i	0.103149	+	0.103149i
$306$	0.0485558	−	0.0984049i	0.00277575	−	0.00562544i
$307$	6.80614	+	6.80614i	0.388447	+	0.388447i	0.874133	−	0.485686i	$-0.161430\pi$
$307$	6.80614	+	6.80614i	0.388447	+	0.388447i	−0.485686	+	0.874133i	$0.661430\pi$
$308$	−11.2340	+	8.61201i	−0.640116	+	0.490715i
$309$		−	8.07325i		−	0.459271i
$310$	−10.2677	−	5.06639i	−0.583167	−	0.287752i
$311$	26.1979			1.48555			0.742775	−	0.669542i	$-0.233509\pi$
$311$	26.1979			1.48555			0.742775	+	0.669542i	$0.233509\pi$
$312$		0			0
$313$	24.8487			1.40453			0.702265	−	0.711915i	$-0.252172\pi$
$313$	24.8487			1.40453			0.702265	+	0.711915i	$0.252172\pi$
$314$	11.1207	+	5.48726i	0.627576	+	0.309664i
$315$			7.93361i			0.447008i
$316$	−14.0857	+	10.7982i	−0.792383	+	0.607443i
$317$	−24.2717	−	24.2717i	−1.36323	−	1.36323i	−0.869762	−	0.493472i	$-0.835727\pi$
$317$	−24.2717	−	24.2717i	−1.36323	−	1.36323i	−0.493472	−	0.869762i	$-0.664273\pi$
$318$	−5.76875	+	11.6912i	−0.323496	+	0.655608i
$319$	−8.12660	−	8.12660i	−0.455002	−	0.455002i
$320$	9.33931	+	3.88343i	0.522083	+	0.217090i
$321$	−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
$330$	−5.25177	−	2.59137i	−0.289100	−	0.142650i
$331$	−13.4904	+	13.4904i	−0.741501	+	0.741501i	−0.972867	−	0.231366i	$-0.925681\pi$
$331$	−13.4904	+	13.4904i	−0.741501	+	0.741501i	0.231366	+	0.972867i	$0.425681\pi$
$332$	−19.5207	−	2.57900i	−1.07134	−	0.141541i
$333$	1.89401	−	1.89401i	0.103791	−	0.103791i
$334$	3.95067	+	11.6470i	0.216171	+	0.637297i
$335$	−11.6017			−0.633870
$336$	18.9276	+	32.8527i	1.03259	+	1.79226i
$337$		−	28.8443i		−	1.57125i	−0.618702	−	0.785626i	$-0.712341\pi$
$337$		−	28.8443i		−	1.57125i	0.618702	−	0.785626i	$-0.287659\pi$
$338$		0			0
$339$			19.1366i			1.03936i
$340$	0.140290	+	0.0185345i	0.00760827	+	0.00100517i
$341$	10.0142			0.542297
$342$	−4.13895	+	1.40393i	−0.223809	+	0.0759160i
$343$	−20.7456	+	20.7456i	−1.12016	+	1.12016i
$344$	−1.14407	−	5.77227i	−0.0616844	−	0.311220i
$345$	−1.98066	+	1.98066i	−0.106635	+	0.106635i
$346$	3.93537	−	7.97555i	0.211567	−	0.428768i
$347$			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	−0.120659	−	0.992694i	$-0.538501\pi$
$349$	16.2910	−	16.2910i	0.872035	−	0.872035i	0.992694	+	0.120659i	$0.0385007\pi$
$350$	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	0.972064	−	0.234717i	$-0.0754164\pi$
$353$	13.8535	+	13.8535i	0.737346	+	0.737346i	−0.234717	+	0.972064i	$0.575416\pi$
$354$	−25.1988	+	8.54744i	−1.33930	+	0.454292i
$355$	8.62591			0.457816
$356$	−31.4267	−	4.15197i	−1.66561	−	0.220054i
$357$	0.375089	+	0.375089i	0.0198518	+	0.0198518i
$358$	30.6905	+	15.1436i	1.62204	+	0.800362i
$359$	10.7783	+	10.7783i	0.568858	+	0.568858i	0.931808	−	0.362951i	$-0.118231\pi$
$359$	10.7783	+	10.7783i	0.568858	+	0.568858i	−0.362951	+	0.931808i	$0.618231\pi$
$360$	−2.75744	+	4.12070i	−0.145330	+	0.217180i
$361$			14.0318i			0.738514i
$362$	−3.14930	+	6.38249i	−0.165524	+	0.335456i
$363$	−17.9163			−0.940363
$364$		0			0
$365$	−9.75368			−0.510531
$366$	−2.64092	+	5.35218i	−0.138043	+	0.279763i
$367$			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
$370$	3.09761	+	1.52845i	0.161037	+	0.0794603i
$371$	−14.0857	−	14.0857i	−0.731293	−	0.731293i
$372$	3.51325	−	26.5921i	0.182153	−	1.37874i
$373$	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	$-0.884290\pi$
$379$	−11.2737	+	11.2737i	−0.579093	+	0.579093i	0.355561	+	0.934653i	$0.384290\pi$
$380$	−3.42907	−	4.47306i	−0.175907	−	0.229463i
$381$			19.7615i			1.01241i
$382$	11.9753	−	24.2696i	0.612711	−	1.24174i
$383$	16.5568	−	16.5568i	0.846015	−	0.846015i	−0.143618	−	0.989633i	$-0.545874\pi$
$383$	16.5568	−	16.5568i	0.846015	−	0.846015i	0.989633	+	0.143618i	$0.0458738\pi$
$384$	−1.58746	+	23.6422i	−0.0810095	+	1.20649i
$385$	6.32741	−	6.32741i	0.322475	−	0.322475i
$386$	−12.7811	+	4.33536i	−0.650542	+	0.220664i
$387$	2.88464			0.146634
$388$	0.119522	−	0.904673i	0.00606780	−	0.0459278i
$389$			39.2161i			1.98834i	0.107845	+	0.994168i	$0.465605\pi$
$389$			39.2161i			1.98834i	−0.107845	+	0.994168i	$0.534395\pi$
$390$		0			0
$391$			0.0591980i			0.00299377i
$392$	−37.4069	+	7.41412i	−1.88933	+	0.374470i
$393$	−18.9265			−0.954717
$394$	−0.485024	−	1.42991i	−0.0244352	−	0.0720376i
$395$	7.93361	−	7.93361i	0.399183	−	0.399183i
$396$	0.567994	−	4.29921i	0.0285428	−	0.216043i
$397$	7.68317	−	7.68317i	0.385607	−	0.385607i	−0.487510	−	0.873117i	$-0.662095\pi$
$397$	7.68317	−	7.68317i	0.385607	−	0.385607i	0.873117	+	0.487510i	$0.162095\pi$
$398$	−14.3650	−	7.08808i	−0.720050	−	0.355293i
$399$		−	21.1277i		−	1.05771i
$400$	13.1392	+	3.53347i	0.656959	+	0.176673i
$401$	−1.08972	+	1.08972i	−0.0544178	+	0.0544178i	−0.733792	−	0.679374i	$-0.762251\pi$
$401$	−1.08972	+	1.08972i	−0.0544178	+	0.0544178i	0.679374	+	0.733792i	$0.262251\pi$
$402$	−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
$408$	0.0644529	+	0.325188i	0.00319090	+	0.0160992i
$409$	−0.481082	−	0.481082i	−0.0237880	−	0.0237880i	0.695113	−	0.718901i	$-0.255354\pi$
$409$	−0.481082	−	0.481082i	−0.0237880	−	0.0237880i	−0.718901	+	0.695113i	$0.755354\pi$
$410$	−1.22864	+	2.49001i	−0.0606782	+	0.122973i
$411$	13.9015	+	13.9015i	0.685712	+	0.685712i
$412$	4.69038	+	6.11839i	0.231078	+	0.301432i
$413$		−	40.6581i		−	2.00065i
$414$	−1.86007	−	0.917813i	−0.0914176	−	0.0451081i
$415$	12.4474			0.611020
$416$		0			0
$417$	−21.7024			−1.06277
$418$	4.42070	+	2.18130i	0.216223	+	0.106691i
$419$			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	0.978341	−	0.207002i	$-0.0663705\pi$
$421$	15.8266	+	15.8266i	0.771339	+	0.771339i	−0.207002	+	0.978341i	$0.566371\pi$
$422$	−3.36068	+	6.81086i	−0.163595	+	0.331548i
$423$	−7.46331	−	7.46331i	−0.362878	−	0.362878i
$424$	−2.42040	−	12.2118i	−0.117545	−	0.593056i
$425$	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	$-0.685931\pi$
$431$	5.86969	−	5.86969i	0.282733	−	0.282733i	0.834198	+	0.551465i	$0.185931\pi$
$432$	13.0534	+	3.51040i	0.628032	+	0.168894i
$433$		−	24.3482i		−	1.17010i	−0.810997	−	0.585050i	$-0.801075\pi$
$433$		−	24.3482i		−	1.17010i	0.810997	−	0.585050i	$-0.198925\pi$
$434$	36.7545	+	18.1357i	1.76427	+	0.870543i
$435$	13.7604	−	13.7604i	0.659761	−	0.659761i
$436$	−0.427102	+	3.23278i	−0.0204545	+	0.154822i
$437$	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	$-0.507701\pi$
$439$	−1.01370			−0.0483814			−0.0241907	+	0.999707i	$0.507701\pi$
$440$	5.48563	−	1.08726i	0.261517	−	0.0518332i
$441$		−	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	$0.620115\pi$
$444$	−1.05989	+	8.02243i	−0.0503002	+	0.380728i
$445$	20.0393			0.949953
$446$	−15.8262	+	5.36825i	−0.749392	+	0.254194i
$447$	15.4800	−	15.4800i	0.732181	−	0.732181i
$448$	−33.4312	−	13.9012i	−1.57947	−	0.656770i
$449$	17.8770	−	17.8770i	0.843669	−	0.843669i	−0.145665	−	0.989334i	$-0.546532\pi$
$449$	17.8770	−	17.8770i	0.843669	−	0.843669i	0.989334	+	0.145665i	$0.0465322\pi$
$450$	−2.95131	+	5.98123i	−0.139126	+	0.281958i
$451$		−	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	0.188524	−	0.982069i	$-0.439630\pi$
$457$	−16.9641	−	16.9641i	−0.793545	−	0.793545i	−0.982069	+	0.188524i	$0.939630\pi$
$458$	13.3356	−	4.52345i	0.623133	−	0.211367i
$459$	0.189114			0.00882707
$460$	0.350343	−	2.65179i	0.0163348	−	0.123640i
$461$	−3.55288	−	3.55288i	−0.165474	−	0.165474i	0.619513	−	0.784987i	$-0.287330\pi$
$461$	−3.55288	−	3.55288i	−0.165474	−	0.165474i	−0.784987	+	0.619513i	$0.787330\pi$
$462$	18.7993	+	9.27612i	0.874623	+	0.431564i
$463$	1.18158	+	1.18158i	0.0549128	+	0.0549128i	0.734030	−	0.679117i	$-0.237637\pi$
$463$	1.18158	+	1.18158i	0.0549128	+	0.0549128i	−0.679117	+	0.734030i	$0.737637\pi$
$464$	7.63416	−	28.3876i	0.354407	−	1.31786i
$465$			16.9565i			0.786340i
$466$	13.3419	−	27.0392i	0.618053	−	1.25257i
$467$	24.9759			1.15575			0.577873	−	0.816127i	$-0.303883\pi$
$467$	24.9759			1.15575			0.577873	+	0.816127i	$0.303883\pi$
$468$		0			0
$469$	41.5297			1.91766
$470$	6.02283	−	12.2061i	0.277813	−	0.563025i
$471$		−	18.3651i		−	0.846220i
$472$	14.1313	−	21.1177i	0.650446	−	0.972022i
$473$	−2.30063	−	2.30063i	−0.105783	−	0.105783i
$474$	23.5715	+	11.6308i	1.08267	+	0.534222i
$475$	−5.36114	−	5.36114i	−0.245986	−	0.245986i
$476$	−0.502183	−	0.0663464i	−0.0230175	−	0.00304098i
$477$	6.10273			0.279425
$478$	28.7083	−	9.73785i	1.31308	−	0.445399i
$479$	−22.1427	−	22.1427i	−1.01172	−	1.01172i	−0.999930	−	0.0117932i	$-0.996246\pi$
$479$	−22.1427	−	22.1427i	−1.01172	−	1.01172i	−0.0117932	−	0.999930i	$-0.503754\pi$
$480$	−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
$486$	−8.38365	+	16.9906i	−0.380290	+	0.770710i
$487$	−12.0339	+	12.0339i	−0.545309	+	0.545309i	−0.925080	−	0.379771i	$-0.876003\pi$
$487$	−12.0339	+	12.0339i	−0.545309	+	0.545309i	0.379771	+	0.925080i	$0.376003\pi$
$488$	−1.10805	−	5.59052i	−0.0501591	−	0.253071i
$489$	−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	$-0.418548\pi$
$491$	11.2169			0.506213			0.253107	+	0.967438i	$0.418548\pi$
$492$	−6.44881	−	0.851991i	−0.290735	−	0.0384107i
$493$		−	0.411271i		−	0.0185227i
$494$		0			0
$495$			2.74139i			0.123217i
$496$	12.7869	+	22.1942i	0.574149	+	0.996551i
$497$	−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	$-0.819862\pi$
$499$	−6.87805	+	6.87805i	−0.307904	+	0.307904i	0.536192	+	0.844096i	$0.319862\pi$
$500$	−21.0613	−	2.78254i	−0.941890	−	0.124439i
$501$	12.8793	−	12.8793i	0.575406	−	0.575406i
$502$	−18.5383	−	9.14731i	−0.827403	−	0.408264i
$503$		−	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	0.843371	−	0.537331i	$-0.180567\pi$
$509$	6.90459	+	6.90459i	0.306040	+	0.306040i	−0.537331	+	0.843371i	$0.680567\pi$
$510$	−0.0673186	−	0.198463i	−0.00298092	−	0.00878808i
$511$	34.9145			1.54452
$512$	−12.5325	−	18.8397i	−0.553864	−	0.832607i
$513$	−5.32613	−	5.32613i	−0.235154	−	0.235154i
$514$	8.77629	−	17.7863i	0.387105	−	0.784522i
$515$	−3.44611	−	3.44611i	−0.151854	−	0.151854i
$516$	−6.91634	+	5.30209i	−0.304475	+	0.233411i
$517$			11.9047i			0.523566i
$518$	−11.0883	−	5.47126i	−0.487190	−	0.240394i
$519$	−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	$0.641067\pi$
$522$	12.9226	+	6.37639i	0.565608	+	0.279087i
$523$		−	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
$526$	18.5602	−	37.6148i	0.809263	−	1.64008i
$527$	0.253398	+	0.253398i	0.0110382	+	0.0110382i
$528$	6.54028	+	11.3520i	0.284629	+	0.494031i
$529$	−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
$538$	2.25991	+	1.11511i	0.0974317	+	0.0480756i
$539$	−14.9091	+	14.9091i	−0.642181	+	0.642181i
$540$	−8.47138	−	1.11921i	−0.364550	−	0.0481629i
$541$	12.3423	−	12.3423i	0.530636	−	0.530636i	−0.390126	−	0.920762i	$-0.627568\pi$
$541$	12.3423	−	12.3423i	0.530636	−	0.530636i	0.920762	+	0.390126i	$0.127568\pi$
$542$	9.54749	+	28.1471i	0.410100	+	1.20902i
$543$	10.5403			0.452327
$544$	−0.237773	−	0.209001i	−0.0101944	−	0.00896085i
$545$		−	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	$-0.0375041\pi$
$548$	−18.6119	−	2.45893i	−0.795061	−	0.105040i
$549$	2.79381			0.119237
$550$	7.12411	−	2.41650i	0.303773	−	0.103040i
$551$	−11.5829	+	11.5829i	−0.493448	+	0.493448i
$552$	6.14678	−	1.21830i	0.261624	−	0.0518545i
$553$	−28.3993	+	28.3993i	−1.20766	+	1.20766i
$554$	−9.78218	+	19.8249i	−0.415605	+	0.842280i
$555$		−	5.11551i		−	0.217141i
$556$	16.4474	−	12.6086i	0.697525	−	0.534725i
$557$	−2.42633	+	2.42633i	−0.102807	+	0.102807i	−0.756639	−	0.653832i	$-0.773160\pi$
$557$	−2.42633	+	2.42633i	−0.102807	+	0.102807i	0.653832	+	0.756639i	$0.273160\pi$
$558$	−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	$-0.563031\pi$
$563$	−9.33572			−0.393454			−0.196727	+	0.980458i	$0.563031\pi$
$564$	31.6123	+	4.17649i	1.33112	+	0.175862i
$565$	8.16859	+	8.16859i	0.343655	+	0.343655i
$566$	−23.9418	−	11.8136i	−1.00635	−	0.496561i
$567$	−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	$0.253790\pi$
$569$			34.1336i			1.43095i	−0.698637	+	0.715477i	$0.746210\pi$
$570$	−3.69350	+	7.48537i	−0.154704	+	0.313528i
$571$	30.2446			1.26570			0.632848	−	0.774276i	$-0.281886\pi$
$571$	30.2446			1.26570			0.632848	+	0.774276i	$0.281886\pi$
$572$		0			0
$573$	−40.0798			−1.67436
$574$	4.39806	−	8.91327i	0.183572	−	0.372033i
$575$		−	3.59817i		−	0.150054i
$576$	10.2535	−	4.23074i	0.427230	−	0.176281i
$577$	24.5041	+	24.5041i	1.02012	+	1.02012i	0.999793	+	0.0203254i	$0.00647021\pi$
$577$	24.5041	+	24.5041i	1.02012	+	1.02012i	0.0203254	+	0.999793i	$0.493530\pi$
$578$	21.5559	+	10.6363i	0.896607	+	0.442411i
$579$	14.1334	+	14.1334i	0.587364	+	0.587364i
$580$	−2.43397	+	18.4229i	−0.101065	+	0.764971i
$581$	−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	$-0.975772\pi$
$587$	−22.3156	+	22.3156i	−0.921064	+	0.921064i	0.0760405	+	0.997105i	$0.475772\pi$
$588$	34.3599	+	44.8210i	1.41698	+	1.84839i
$589$		−	14.2732i		−	0.588118i
$590$	−7.10774	+	14.4048i	−0.292621	+	0.593036i
$591$	−1.58119	+	1.58119i	−0.0650416	+	0.0650416i
$592$	−3.85760	−	6.69565i	−0.158547	−	0.275189i
$593$	11.3864	−	11.3864i	0.467582	−	0.467582i	−0.433548	−	0.901130i	$-0.642739\pi$
$593$	11.3864	−	11.3864i	0.467582	−	0.467582i	0.901130	+	0.433548i	$0.142739\pi$
$594$	7.07759	−	2.40072i	0.290397	−	0.0985028i
$595$	0.320218			0.0131276
$596$	−2.73814	+	20.7253i	−0.112159	+	0.848940i
$597$			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	$-0.276976\pi$
$600$	−3.91757	−	19.7655i	−0.159934	−	0.806924i
$601$	−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
$604$	−1.42613	+	10.7945i	−0.0580283	+	0.439222i
$605$	−7.64769	+	7.64769i	−0.310923	+	0.310923i
$606$	−29.3935	−	14.5036i	−1.19403	−	0.589168i
$607$			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	0.0336005	−	0.999435i	$-0.489303\pi$
$613$	−23.9129	−	23.9129i	−0.965835	−	0.965835i	−0.999435	+	0.0336005i	$0.989303\pi$
$614$	4.37259	+	12.8909i	0.176463	+	0.520233i
$615$	4.11209			0.165816
$616$	−19.6365	+	3.89199i	−0.791176	+	0.156813i
$617$	−12.9438	−	12.9438i	−0.521099	−	0.521099i	0.396804	−	0.917903i	$-0.370119\pi$
$617$	−12.9438	−	12.9438i	−0.521099	−	0.521099i	−0.917903	+	0.396804i	$0.870119\pi$
$618$	5.05208	−	10.2387i	0.203224	−	0.411862i
$619$	5.55216	+	5.55216i	0.223160	+	0.223160i	0.809828	−	0.586668i	$-0.199561\pi$
$619$	5.55216	+	5.55216i	0.223160	+	0.223160i	−0.586668	+	0.809828i	$0.699561\pi$
$620$	−9.85136	−	12.8507i	−0.395640	−	0.516095i
$621$		−	3.57467i		−	0.143447i
$622$	33.2249	+	16.3941i	1.33220	+	0.657345i
$623$	−71.7330			−2.87392
$624$		0			0
$625$	−3.57775			−0.143110
$626$	31.5138	+	15.5498i	1.25954	+	0.621495i
$627$		−	7.30051i		−	0.291554i
$628$	10.6697	+	13.9182i	0.425768	+	0.555396i
$629$	−0.0764462	−	0.0764462i	−0.00304811	−	0.00304811i
$630$	−4.96469	+	10.0616i	−0.197798	+	0.400865i
$631$	16.7460	+	16.7460i	0.666646	+	0.666646i	0.956938	−	0.290292i	$-0.0937525\pi$
$631$	16.7460	+	16.7460i	0.666646	+	0.666646i	−0.290292	+	0.956938i	$0.593753\pi$
$632$	−24.6211	+	4.87996i	−0.979376	+	0.194114i
$633$	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	$0.0629490\pi$
$641$			9.94862i			0.392947i	−0.980509	+	0.196473i	$0.937051\pi$
$642$	−0.779889	−	0.384820i	−0.0307798	−	0.0151876i
$643$	17.1393	−	17.1393i	0.675907	−	0.675907i	−0.283165	−	0.959071i	$-0.591384\pi$
$643$	17.1393	−	17.1393i	0.675907	−	0.675907i	0.959071	+	0.283165i	$0.0913843\pi$
$644$	−1.25410	+	9.49238i	−0.0494183	+	0.374052i
$645$	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	$-0.603004\pi$
$647$	−16.1764			−0.635959			−0.317980	+	0.948098i	$0.603004\pi$
$648$	−6.17932	−	31.1769i	−0.242747	−	1.22474i
$649$		−	14.0491i		−	0.551474i
$650$		0			0
$651$		−	60.6979i		−	2.37894i
$652$	2.30204	−	17.4244i	0.0901548	−	0.682391i
$653$	−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
$656$	5.38228	−	3.10093i	0.210143	−	0.121071i
$657$	−7.56346	+	7.56346i	−0.295079	+	0.295079i
$658$	−21.5594	+	43.6931i	−0.840475	+	1.70334i
$659$		−	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	−0.817855	−	0.575425i	$-0.804837\pi$
$661$	−6.23284	+	6.23284i	−0.242429	+	0.242429i	0.575425	+	0.817855i	$0.304837\pi$
$662$	−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
$668$	−2.27812	+	17.2433i	−0.0881430	+	0.667164i
$669$	17.5007	+	17.5007i	0.676614	+	0.676614i
$670$	−14.7136	−	7.26012i	−0.568437	−	0.280483i
$671$	−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	$-0.871430\pi$
$673$		−	20.3917i		−	0.786044i	0.919529	−	0.393022i	$-0.128570\pi$
$674$	18.0502	−	36.5812i	0.695268	−	1.40905i
$675$	−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	$0.506200\pi$
$678$	−11.9753	+	24.2696i	−0.459910	+	0.932069i
$679$		−	2.06496i		−	0.0792459i
$680$	0.166320	+	0.111296i	0.00637810	+	0.00426802i
$681$	−2.60123	−	2.60123i	−0.0996794	−	0.0996794i
$682$	12.7002	+	6.26665i	0.486317	+	0.239963i
$683$	17.8559	+	17.8559i	0.683238	+	0.683238i	0.960728	−	0.277491i	$-0.0895028\pi$
$683$	17.8559	+	17.8559i	0.683238	+	0.683238i	−0.277491	+	0.960728i	$0.589503\pi$
$684$	−6.12768	−	0.809565i	−0.234298	−	0.0309545i
$685$	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	$-0.510670\pi$
$691$	25.3911	−	25.3911i	0.965924	−	0.965924i	0.999438	+	0.0335142i	$0.0106699\pi$
$692$	9.98187	−	7.65214i	0.379454	−	0.290891i
$693$		−	9.81315i		−	0.372771i
$694$	−17.2179	+	34.8943i	−0.653581	+	1.32457i
$695$	−9.26381	+	9.26381i	−0.351396	+	0.351396i
$696$	−42.7040	+	8.46401i	−1.61869	+	0.320828i
$697$	0.0614511	−	0.0614511i	0.00232763	−	0.00232763i
$698$	30.8552	−	10.4661i	1.16789	−	0.396147i
$699$	−44.6537			−1.68896
$700$	30.5236	+	4.03266i	1.15368	+	0.152420i
$701$			16.0203i			0.605077i	0.953137	+	0.302539i	$0.0978342\pi$
$701$			16.0203i			0.605077i	−0.953137	+	0.302539i	$0.902166\pi$
$702$		0			0
$703$			4.30601i			0.162404i
$704$	−11.5519	−	4.80345i	−0.435377	−	0.181037i
$705$	−20.1576			−0.759179
$706$	8.90014	+	26.2386i	0.334961	+	0.987502i
$707$	35.4138	−	35.4138i	1.33187	−	1.33187i
$708$	−37.3066	−	4.92880i	−1.40207	−	0.185236i
$709$	−16.6393	+	16.6393i	−0.624900	+	0.624900i	−0.946780	−	0.321880i	$-0.895685\pi$
$709$	−16.6393	+	16.6393i	−0.624900	+	0.624900i	0.321880	+	0.946780i	$0.395685\pi$
$710$	10.9396	+	5.39792i	0.410556	+	0.202580i
$711$		−	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	$-0.159982\pi$
$719$	46.9964			1.75267			0.876334	+	0.481703i	$0.159982\pi$
$720$	−6.07571	+	3.50044i	−0.226428	+	0.130454i
$721$	12.3358	+	12.3358i	0.459408	+	0.459408i
$722$	−8.78079	+	17.7955i	−0.326787	+	0.662279i
$723$	29.7209	+	29.7209i	1.10533	+	1.10533i
$724$	−7.98806	+	6.12368i	−0.296874	+	0.227585i
$725$			24.9978i			0.928395i
$726$	−22.7220	−	11.2117i	−0.843291	−	0.416104i
$727$	−20.0985			−0.745412			−0.372706	−	0.927950i	$-0.621570\pi$
$727$	−20.0985			−0.745412			−0.372706	+	0.927950i	$0.621570\pi$
$728$		0			0
$729$	−5.65241			−0.209348
$730$	−12.3699	−	6.10365i	−0.457830	−	0.225906i
$731$		−	0.116430i		−	0.00430633i
$732$	−6.69857	+	5.13514i	−0.247586	+	0.189800i
$733$	13.3827	+	13.3827i	0.494300	+	0.494300i	0.909658	−	0.415358i	$-0.136344\pi$
$733$	13.3827	+	13.3827i	0.494300	+	0.494300i	−0.415358	+	0.909658i	$0.636344\pi$
$734$	−21.1868	+	42.9379i	−0.782019	+	1.58487i
$735$	−25.2449	−	25.2449i	−0.931173	−	0.931173i
$736$	−3.95059	+	4.49445i	−0.145621	+	0.165668i
$737$	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	$-0.236684\pi$
$739$	1.60780	+	1.60780i	0.0591438	+	0.0591438i	−0.676916	+	0.736060i	$0.736684\pi$
$740$	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	$-0.656042\pi$
$743$	11.2142	−	11.2142i	0.411411	−	0.411411i	0.882230	+	0.470819i	$0.156042\pi$
$744$	21.0964	−	31.5264i	0.773432	−	1.15581i
$745$		−	13.2155i		−	0.484178i
$746$	15.1746	+	7.48758i	0.555581	+	0.274140i
$747$	9.65232	−	9.65232i	0.353160	−	0.353160i
$748$	−0.173525	−	0.0229255i	−0.00634471	−	0.000838238i
$749$	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	$-0.307357\pi$
$751$	31.1824			1.13786			0.568930	+	0.822386i	$0.307357\pi$
$752$	−26.3841	+	15.2008i	−0.962130	+	0.554318i
$753$			30.6148i			1.11567i
$754$		0			0
$755$		−	6.88313i		−	0.250503i
$756$	30.3243	+	4.00633i	1.10288	+	0.145709i
$757$	−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
$760$	−1.54968	−	7.81870i	−0.0562129	−	0.283614i
$761$	7.83377	−	7.83377i	0.283974	−	0.283974i	−0.550718	−	0.834692i	$-0.685646\pi$
$761$	7.83377	−	7.83377i	0.283974	−	0.283974i	0.834692	+	0.550718i	$0.185646\pi$
$762$	−12.3664	+	25.0621i	−0.447986	+	0.907904i
$763$			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	0.996470	−	0.0839527i	$-0.0267545\pi$
$769$	25.3049	+	25.3049i	0.912517	+	0.912517i	−0.0839527	+	0.996470i	$0.526754\pi$
$770$	11.9842	−	4.06503i	0.431879	−	0.146494i
$771$	−29.3730			−1.05784
$772$	−18.9223	−	2.49994i	−0.681030	−	0.0899750i
$773$	34.6449	+	34.6449i	1.24609	+	1.24609i	0.957433	+	0.288656i	$0.0932085\pi$
$773$	34.6449	+	34.6449i	1.24609	+	1.24609i	0.288656	+	0.957433i	$0.406792\pi$
$774$	3.65837	+	1.80515i	0.131498	+	0.0648847i
$775$	−15.4020	−	15.4020i	−0.553256	−	0.553256i
$776$	0.717706	−	1.07254i	0.0257642	−	0.0385018i
$777$			18.3116i			0.656924i
$778$	−24.5406	+	49.7349i	−0.879824	+	1.78308i
$779$	−3.46137			−0.124017
$780$		0			0
$781$	−10.6695			−0.381783
$782$	−0.0370449	+	0.0750766i	−0.00132472	+	0.00268473i
$783$			24.8346i			0.887516i
$784$	−52.0800	−	14.0057i	−1.86000	−	0.500203i
$785$	−7.83925	−	7.83925i	−0.279795	−	0.279795i
$786$	−24.0031	−	11.8438i	−0.856163	−	0.422456i
$787$	−25.7703	−	25.7703i	−0.918611	−	0.918611i	0.0783179	−	0.996928i	$-0.475045\pi$
$787$	−25.7703	−	25.7703i	−0.918611	−	0.918611i	−0.996928	+	0.0783179i	$0.975045\pi$
$788$	0.279685	−	2.11696i	0.00996335	−	0.0754137i
$789$	−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	$-0.885881\pi$
$797$		−	19.8118i		−	0.701770i	0.936419	−	0.350885i	$-0.114119\pi$
$798$	13.2213	−	26.7948i	0.468029	−	0.948525i
$799$	−0.301235	+	0.301235i	−0.0106569	+	0.0106569i
$800$	14.4523	+	12.7035i	0.510966	+	0.449136i
$801$	15.5394	−	15.5394i	0.549058	−	0.549058i
$802$	−2.06393	+	0.700085i	−0.0728799	+	0.0247209i
$803$	12.0644			0.425744
$804$	5.03447	−	38.1065i	0.177552	−	1.34391i
$805$		−	6.05283i		−	0.213334i
$806$		0			0
$807$		−	3.73211i		−	0.131376i
$808$	30.7024	−	6.08528i	1.08011	−	0.214079i
$809$	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	$-0.658444\pi$
$811$	11.4250	−	11.4250i	0.401187	−	0.401187i	0.878651	+	0.477464i	$0.158444\pi$
$812$	8.71267	−	65.9471i	0.305755	−	2.31429i
$813$	31.1251	−	31.1251i	1.09161	−	1.09161i
$814$	−3.83146	−	1.89055i	−0.134292	−	0.0662637i
$815$			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	0.157816	−	0.987468i	$-0.449555\pi$
$821$	−23.7721	−	23.7721i	−0.829652	−	0.829652i	−0.987468	+	0.157816i	$0.949555\pi$
$822$	8.93100	+	26.3296i	0.311505	+	0.918350i
$823$	18.6013			0.648400			0.324200	−	0.945989i	$-0.394905\pi$
$823$	18.6013			0.648400			0.324200	+	0.945989i	$0.394905\pi$
$824$	2.11970	+	10.6947i	0.0738433	+	0.372566i
$825$	−7.87787	−	7.87787i	−0.274272	−	0.274272i
$826$	25.4430	−	51.5637i	0.885275	−	1.79413i
$827$	1.07171	+	1.07171i	0.0372671	+	0.0372671i	0.725495	−	0.688228i	$-0.241611\pi$
$827$	1.07171	+	1.07171i	0.0372671	+	0.0372671i	−0.688228	+	0.725495i	$0.741611\pi$
$828$	−1.78465	−	2.32799i	−0.0620207	−	0.0809033i
$829$			30.0497i			1.04367i	0.853047	+	0.521835i	$0.174752\pi$
$829$			30.0497i			1.04367i	−0.853047	+	0.521835i	$0.825248\pi$
$830$	15.7862	+	7.78935i	0.547946	+	0.270372i
$831$	32.7396			1.13573
$832$		0			0
$833$	−0.754520			−0.0261426
$834$	−27.5236	−	13.5809i	−0.953065	−	0.470269i
$835$		−	10.9952i		−	0.380505i
$836$	4.24144	+	5.53277i	0.146693	+	0.191355i
$837$	−15.3014	−	15.3014i	−0.528895	−	0.528895i
$838$	−15.0778	+	30.5572i	−0.520855	+	1.05558i
$839$	26.3923	+	26.3923i	0.911163	+	0.911163i	0.996364	−	0.0852005i	$-0.0271531\pi$
$839$	26.3923	+	26.3923i	0.911163	+	0.911163i	−0.0852005	+	0.996364i	$0.527153\pi$
$840$	−6.59013	−	33.2495i	−0.227381	−	1.14722i
$841$	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
$850$	0.241415	+	0.119121i	0.00828048	+	0.00408583i
$851$	−1.44500	+	1.44500i	−0.0495341	+	0.0495341i
$852$	−3.74314	+	28.3323i	−0.128238	+	0.970647i
$853$	36.7666	−	36.7666i	1.25887	−	1.25887i	0.307230	−	0.951635i	$-0.400598\pi$
$853$	36.7666	−	36.7666i	1.25887	−	1.25887i	0.951635	−	0.307230i	$-0.0994020\pi$
$854$	−4.14275	−	12.2133i	−0.141762	−	0.417931i
$855$	3.90732			0.133628
$856$	0.814618	−	0.161459i	0.0278431	−	0.00551856i
$857$		−	23.1948i		−	0.792319i	−0.918182	−	0.396160i	$-0.870343\pi$
$857$		−	23.1948i		−	0.792319i	0.918182	−	0.396160i	$-0.129657\pi$
$858$		0			0
$859$			53.8518i			1.83740i	0.394956	+	0.918700i	$0.370760\pi$
$859$			53.8518i			1.83740i	−0.394956	+	0.918700i	$0.629240\pi$
$860$	−0.689052	+	5.21551i	−0.0234965	+	0.177847i
$861$	−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	$-0.938332\pi$
$863$	−23.1715	+	23.1715i	−0.788766	+	0.788766i	0.192526	+	0.981292i	$0.438332\pi$
$864$	14.3579	+	12.6205i	0.488467	+	0.429359i
$865$	−5.62218	+	5.62218i	−0.191160	+	0.191160i
$866$	15.2366	−	30.8791i	0.517761	−	1.04931i
$867$		−	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
$876$	4.23253	−	32.0365i	0.143004	−	1.08241i
$877$	−25.3413	−	25.3413i	−0.855714	−	0.855714i	0.135116	−	0.990830i	$-0.456859\pi$
$877$	−25.3413	−	25.3413i	−0.855714	−	0.855714i	−0.990830	+	0.135116i	$0.956859\pi$
$878$	−1.28561	−	0.634354i	−0.0433871	−	0.0214084i
$879$	−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	$0.00881557\pi$
$881$			1.64385i			0.0553828i	−0.999617	+	0.0276914i	$0.991184\pi$
$882$	11.6982	−	23.7079i	0.393898	−	0.798287i
$883$	15.1271			0.509067			0.254534	−	0.967064i	$-0.418078\pi$
$883$	15.1271			0.509067			0.254534	+	0.967064i	$0.418078\pi$
$884$		0			0
$885$	23.7886			0.799646
$886$	−24.4889	+	49.6301i	−0.822722	+	1.66736i
$887$		−	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
$890$	25.4144	+	12.5402i	0.851892	+	0.420348i
$891$	−12.4260	−	12.4260i	−0.416288	−	0.416288i
$892$	−23.4305	−	3.09555i	−0.784512	−	0.103647i
$893$	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
$902$	1.51971	−	3.07991i	0.0506009	−	0.102550i
$903$	−13.9446	+	13.9446i	−0.464047	+	0.464047i
$904$	−5.02449	−	25.3504i	−0.167112	−	0.843141i
$905$	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	$-0.237899\pi$
$907$	44.1790			1.46694			0.733471	+	0.679721i	$0.237899\pi$
$908$	3.48263	+	0.460111i	0.115575	+	0.0152693i
$909$			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	$0.873596\pi$
$912$	16.1800	−	9.32190i	0.535774	−	0.308679i
$913$	−15.3963			−0.509544
$914$	−10.8985	−	32.1300i	−0.360491	−	1.06277i
$915$	3.77289	−	3.77289i	0.124728	−	0.124728i
$916$	19.7433	+	2.60841i	0.652337	+	0.0861842i
$917$	28.9194	−	28.9194i	0.955002	−	0.955002i
$918$	0.239839	+	0.118344i	0.00791587	+	0.00390592i
$919$			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
$928$	27.4462	−	31.2246i	0.900966	−	1.02500i
$929$	−37.1594	−	37.1594i	−1.21916	−	1.21916i	−0.967927	−	0.251233i	$-0.919164\pi$
$929$	−37.1594	−	37.1594i	−1.21916	−	1.21916i	−0.251233	−	0.967927i	$-0.580836\pi$
$930$	−10.6110	+	21.5047i	−0.347950	+	0.705167i
$931$	21.2500	+	21.2500i	0.696442	+	0.696442i
$932$	33.8412	−	25.9428i	1.10851	−	0.849784i
$933$		−	54.8690i		−	1.79633i
$934$	31.6751	+	15.6294i	1.03644	+	0.511409i
$935$	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	$0.703175\pi$
$938$	52.6691	+	25.9885i	1.71971	+	0.848553i
$939$		−	52.0431i		−	1.69836i
$940$	15.2766	−	11.7111i	0.498269	−	0.381975i
$941$	15.2238	+	15.2238i	0.496283	+	0.496283i	0.910279	−	0.413996i	$-0.135867\pi$
$941$	15.2238	+	15.2238i	0.496283	+	0.496283i	−0.413996	+	0.910279i	$0.635867\pi$
$942$	11.4925	−	23.2911i	0.374446	−	0.758866i
$943$	−1.16156	−	1.16156i	−0.0378257	−	0.0378257i
$944$	31.1367	−	17.9390i	1.01341	−	0.583864i
$945$	−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	$-0.159313\pi$
$947$	12.2318	+	12.2318i	0.397482	+	0.397482i	−0.479862	+	0.877344i	$0.659313\pi$
$948$	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	$-0.919531\pi$
$953$		−	15.4425i		−	0.500231i	0.968216	−	0.250115i	$-0.0804685\pi$
$954$	7.73964	+	3.81896i	0.250580	+	0.123643i
$955$	−17.1083	+	17.1083i	−0.553611	+	0.553611i
$956$	42.5023	+	5.61524i	1.37462	+	0.181610i
$957$	−17.0203	+	17.0203i	−0.550190	+	0.550190i
$958$	−14.2255	−	41.9383i	−0.459605	−	1.35497i
$959$	−42.4826			−1.37183
$960$	8.13346	−	19.5602i	0.262506	−	0.631304i
$961$		−	10.0056i		−	0.322760i
$962$		0			0
$963$			0.407098i			0.0131186i
$964$	−39.7915	−	5.25709i	−1.28160	−	0.169320i
$965$	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	$-0.684223\pi$
$967$	9.02312	−	9.02312i	0.290164	−	0.290164i	0.837145	+	0.546981i	$0.184223\pi$
$968$	23.7338	−	4.70409i	0.762833	−	0.151195i
$969$	0.184732	−	0.184732i	0.00593445	−	0.00593445i
$970$	−0.360991	+	0.731597i	−0.0115907	+	0.0234902i
$971$			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	0.964647	−	0.263545i	$-0.0848917\pi$
$977$	21.9144	+	21.9144i	0.701102	+	0.701102i	−0.263545	+	0.964647i	$0.584892\pi$
$978$	−24.6496	+	8.36117i	−0.788209	+	0.267361i
$979$	−24.7867			−0.792188
$980$	33.7988	+	4.46537i	1.07966	+	0.142641i
$981$	−1.59850	−	1.59850i	−0.0510360	−	0.0510360i
$982$	14.2256	+	7.01933i	0.453958	+	0.223996i
$983$	15.4374	+	15.4374i	0.492377	+	0.492377i	0.909055	−	0.416677i	$-0.136805\pi$
$983$	15.4374	+	15.4374i	0.492377	+	0.492377i	−0.416677	+	0.909055i	$0.636805\pi$
$984$	−7.64539	−	5.11605i	−0.243726	−	0.163094i
$985$			1.34988i			0.0430109i
$986$	0.257365	−	0.521585i	0.00819617	−	0.0166106i
$987$	72.1565			2.29677
$988$		0			0
$989$	−2.20079			−0.0699811
$990$	−1.71551	+	3.47671i	−0.0545224	+	0.110497i
$991$			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
$994$	−39.1596	−	19.3225i	−1.24207	−	0.612872i
$995$	10.1262	+	10.1262i	0.321023	+	0.321023i
$996$	−5.40146	+	40.8842i	−0.171152	+	1.29547i
$997$	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.99.7		16
4.3	odd	2	inner	676.2.f.i.99.5		16
13.2	odd	12		676.2.l.k.19.3		16
13.3	even	3		676.2.l.i.319.2		16
13.4	even	6		52.2.l.b.11.3	yes	16
13.5	odd	4	inner	676.2.f.i.239.5		16
13.6	odd	12		676.2.l.i.587.1		16
13.7	odd	12		676.2.l.m.587.4		16
13.8	odd	4		676.2.f.h.239.4		16
13.9	even	3		676.2.l.k.427.2		16
13.10	even	6		676.2.l.m.319.3		16
13.11	odd	12		52.2.l.b.19.2	yes	16
13.12	even	2		676.2.f.h.99.2		16
39.11	even	12		468.2.cb.f.19.3		16
39.17	odd	6		468.2.cb.f.271.2		16
52.3	odd	6		676.2.l.i.319.1		16
52.7	even	12		676.2.l.m.587.3		16
52.11	even	12		52.2.l.b.19.3	yes	16
52.15	even	12		676.2.l.k.19.2		16
52.19	even	12		676.2.l.i.587.2		16
52.23	odd	6		676.2.l.m.319.4		16
52.31	even	4	inner	676.2.f.i.239.7		16
52.35	odd	6		676.2.l.k.427.3		16
52.43	odd	6		52.2.l.b.11.2	✓	16
52.47	even	4		676.2.f.h.239.2		16
52.51	odd	2		676.2.f.h.99.4		16
104.11	even	12		832.2.bu.n.383.4		16
104.37	odd	12		832.2.bu.n.383.1		16
104.43	odd	6		832.2.bu.n.63.1		16
104.69	even	6		832.2.bu.n.63.4		16
156.11	odd	12		468.2.cb.f.19.2		16
156.95	even	6		468.2.cb.f.271.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.l.b.11.2	✓	16	52.43	odd	6
52.2.l.b.11.3	yes	16	13.4	even	6
52.2.l.b.19.2	yes	16	13.11	odd	12
52.2.l.b.19.3	yes	16	52.11	even	12
468.2.cb.f.19.2		16	156.11	odd	12
468.2.cb.f.19.3		16	39.11	even	12
468.2.cb.f.271.2		16	39.17	odd	6
468.2.cb.f.271.3		16	156.95	even	6
676.2.f.h.99.2		16	13.12	even	2
676.2.f.h.99.4		16	52.51	odd	2
676.2.f.h.239.2		16	52.47	even	4
676.2.f.h.239.4		16	13.8	odd	4
676.2.f.i.99.5		16	4.3	odd	2	inner
676.2.f.i.99.7		16	1.1	even	1	trivial
676.2.f.i.239.5		16	13.5	odd	4	inner
676.2.f.i.239.7		16	52.31	even	4	inner
676.2.l.i.319.1		16	52.3	odd	6
676.2.l.i.319.2		16	13.3	even	3
676.2.l.i.587.1		16	13.6	odd	12
676.2.l.i.587.2		16	52.19	even	12
676.2.l.k.19.2		16	52.15	even	12
676.2.l.k.19.3		16	13.2	odd	12
676.2.l.k.427.2		16	13.9	even	3
676.2.l.k.427.3		16	52.35	odd	6
676.2.l.m.319.3		16	13.10	even	6
676.2.l.m.319.4		16	52.23	odd	6
676.2.l.m.587.3		16	52.7	even	12
676.2.l.m.587.4		16	13.7	odd	12
832.2.bu.n.63.1		16	104.43	odd	6
832.2.bu.n.63.4		16	104.69	even	6
832.2.bu.n.383.1		16	104.37	odd	12
832.2.bu.n.383.4		16	104.11	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.26823 + 0.625780i) q^{2} -2.09440i q^{3} +(1.21680 + 1.58726i) q^{4} +(-0.894007 - 0.894007i) q^{5} +(1.31063 - 2.65617i) q^{6} +(3.20020 + 3.20020i) q^{7} +(0.549903 + 2.77446i) q^{8} -1.38651 q^{9} +O(q^{10})\)	\(q+(1.26823 + 0.625780i) q^{2} -2.09440i q^{3} +(1.21680 + 1.58726i) q^{4} +(-0.894007 - 0.894007i) q^{5} +(1.31063 - 2.65617i) q^{6} +(3.20020 + 3.20020i) q^{7} +(0.549903 + 2.77446i) 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} +(-1.75841 - 0.867649i) q^{18} +(1.57611 - 1.57611i) q^{19} +(0.331195 - 2.50685i) q^{20} +(6.70250 - 6.70250i) q^{21} +(0.710421 + 2.09440i) q^{22} +1.05782 q^{23} +(5.81082 - 1.15172i) q^{24} -3.40150i q^{25} -3.37929i q^{27} +(-1.18555 + 8.97356i) q^{28} -7.34904 q^{29} +(-3.54635 + 1.20292i) q^{30} +(4.52800 - 4.52800i) q^{31} +(-3.73466 + 4.24880i) q^{32} +(2.31599 - 2.31599i) q^{33} +(-0.0350202 + 0.0709732i) 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} +(-0.409658 + 3.10074i) q^{44} +(1.23955 + 1.23955i) q^{45} +(1.34155 + 0.661960i) q^{46} +(5.38281 + 5.38281i) q^{47} +(8.09016 + 2.17565i) q^{48} +13.4826i q^{49} +(2.12859 - 4.31388i) q^{50} +0.117208 q^{51} -4.40150 q^{53} +(2.11469 - 4.28571i) q^{54} -1.97719i q^{55} +(-7.11902 + 10.6386i) q^{56} +(-3.30100 - 3.30100i) q^{57} +(-9.32026 - 4.59888i) q^{58} +(-6.35242 - 6.35242i) q^{59} +(-5.25034 - 0.693654i) 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} +(3.58071 - 7.25680i) q^{70} +(-4.82430 + 4.82430i) q^{71} +(-0.762445 - 3.84681i) q^{72} +(5.45504 - 5.45504i) q^{73} +(-2.58726 + 0.877600i) q^{74} -7.12411 q^{75} +(4.41950 + 0.583887i) q^{76} +7.07759i q^{77} +8.87422i q^{79} +(4.38202 - 2.52464i) q^{80} -11.2371 q^{81} +(-0.705456 - 2.07976i) q^{82} +(-6.96160 + 6.96160i) q^{83} +(18.7942 + 2.48302i) q^{84} +(0.0500308 - 0.0500308i) q^{85} +(-2.63855 - 1.30194i) 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} +(8.89868 + 7.82188i) q^{96} +(-0.322629 - 0.322629i) q^{97} +(-8.43714 + 17.0990i) 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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