LMFDB - Embedded newform 315.2.bl.j.41.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(41,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("315.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bl (of order $6$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.5
Character	$\chi$	$=$	315.41
Dual form			315.2.bl.j.146.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.334847 + 0.193324i) q^{2} +(0.454500 + 1.67136i) q^{3} +(-0.925251 + 1.60258i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.475302 - 0.471783i) q^{6} +(1.06999 + 2.41974i) q^{7} -1.48879i q^{8} +(-2.58686 + 1.51926i) q^{9} +O(q^{10})$	\(q+(-0.334847 + 0.193324i) q^{2} +(0.454500 + 1.67136i) q^{3} +(-0.925251 + 1.60258i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.475302 - 0.471783i) q^{6} +(1.06999 + 2.41974i) q^{7} -1.48879i q^{8} +(-2.58686 + 1.51926i) q^{9} -0.386648i q^{10} +(3.67564 - 2.12213i) q^{11} +(-3.09901 - 0.818050i) q^{12} +(-3.15051 - 1.81895i) q^{13} +(-0.826077 - 0.603387i) q^{14} +(-1.67469 - 0.442069i) q^{15} +(-1.56268 - 2.70665i) q^{16} -2.70345 q^{17} +(0.572492 - 1.00882i) q^{18} +5.17685i q^{19} +(-0.925251 - 1.60258i) q^{20} +(-3.55793 + 2.88810i) q^{21} +(-0.820519 + 1.42118i) q^{22} +(3.29639 + 1.90317i) q^{23} +(2.48830 - 0.676656i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.40658 q^{26} +(-3.71496 - 3.63306i) q^{27} +(-4.86784 - 0.524116i) q^{28} +(3.67289 - 2.12054i) q^{29} +(0.646227 - 0.175732i) q^{30} +(-0.652414 - 0.376671i) q^{31} +(3.62518 + 2.09300i) q^{32} +(5.21742 + 5.17879i) q^{33} +(0.905243 - 0.522642i) q^{34} +(-2.63055 - 0.283229i) q^{35} +(-0.0412499 - 5.55136i) q^{36} -4.23308 q^{37} +(-1.00081 - 1.73345i) q^{38} +(1.60820 - 6.09233i) q^{39} +(1.28933 + 0.744395i) q^{40} +(0.143256 - 0.248127i) q^{41} +(0.633022 - 1.65491i) q^{42} +(5.08515 + 8.80773i) q^{43} +7.85402i q^{44} +(-0.0222912 - 2.99992i) q^{45} -1.47172 q^{46} +(4.82756 + 8.36159i) q^{47} +(3.81353 - 3.84197i) q^{48} +(-4.71024 + 5.17819i) q^{49} +(0.334847 + 0.193324i) q^{50} +(-1.22872 - 4.51842i) q^{51} +(5.83002 - 3.36596i) q^{52} +2.71745i q^{53} +(1.94630 + 0.498328i) q^{54} +4.24426i q^{55} +(3.60248 - 1.59299i) q^{56} +(-8.65235 + 2.35288i) q^{57} +(-0.819904 + 1.42012i) q^{58} +(4.44145 - 7.69282i) q^{59} +(2.25796 - 2.27480i) q^{60} +(10.5052 - 6.06518i) q^{61} +0.291279 q^{62} +(-6.44413 - 4.63392i) q^{63} +4.63222 q^{64} +(3.15051 - 1.81895i) q^{65} +(-2.74822 - 0.725452i) q^{66} +(-4.74849 + 8.22463i) q^{67} +(2.50137 - 4.33250i) q^{68} +(-1.68267 + 6.37443i) q^{69} +(0.935587 - 0.413710i) q^{70} -11.7148i q^{71} +(2.26187 + 3.85129i) q^{72} +15.7249i q^{73} +(1.41744 - 0.818357i) q^{74} +(1.22019 - 1.22929i) q^{75} +(-8.29632 - 4.78988i) q^{76} +(9.06790 + 6.62342i) q^{77} +(0.639293 + 2.35090i) q^{78} +(-1.05648 - 1.82988i) q^{79} +3.12537 q^{80} +(4.38368 - 7.86024i) q^{81} +0.110779i q^{82} +(-6.95521 - 12.0468i) q^{83} +(-1.33645 - 8.37410i) q^{84} +(1.35172 - 2.34126i) q^{85} +(-3.40549 - 1.96616i) q^{86} +(5.21351 + 5.17491i) q^{87} +(-3.15941 - 5.47226i) q^{88} +6.28517 q^{89} +(0.587421 + 1.00020i) q^{90} +(1.03036 - 9.56964i) q^{91} +(-6.09998 + 3.52182i) q^{92} +(0.333029 - 1.26161i) q^{93} +(-3.23299 - 1.86657i) q^{94} +(-4.48328 - 2.58842i) q^{95} +(-1.85050 + 7.01024i) q^{96} +(11.7467 - 6.78195i) q^{97} +(0.576143 - 2.64451i) q^{98} +(-6.28429 + 11.0739i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9	$ 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9} + 9 q^{11} - 18 q^{12} + 3 q^{13} + 18 q^{14} + 2 q^{15} - 18 q^{16} + 18 q^{17} + 2 q^{18} + 18 q^{20} + 8 q^{21} - 9 q^{22} + 9 q^{23} - 7 q^{24} - 12 q^{25} - 18 q^{26} - 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} - 42 q^{31} + 18 q^{32} + 13 q^{33} - 39 q^{34} - 9 q^{35} - 21 q^{36} - 12 q^{38} - 21 q^{39} - 6 q^{40} - 33 q^{41} - 65 q^{42} + 18 q^{43} + q^{45} - 30 q^{46} - 17 q^{48} + 9 q^{49} - 6 q^{50} - 12 q^{51} + 129 q^{52} + 52 q^{54} - 9 q^{56} + 6 q^{57} - 15 q^{58} + 12 q^{59} + 15 q^{60} - 15 q^{61} + 12 q^{62} + 46 q^{63} - 60 q^{64} - 3 q^{65} + 29 q^{66} - 15 q^{67} + 9 q^{68} + 61 q^{69} - 9 q^{70} + 61 q^{72} - 18 q^{74} - 7 q^{75} + 54 q^{76} - 45 q^{77} - 66 q^{78} + 21 q^{79} + 36 q^{80} + q^{81} - 30 q^{83} + 15 q^{84} - 9 q^{85} - 102 q^{86} + 10 q^{87} - 9 q^{88} + 102 q^{89} - 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} - 156 q^{94} - 18 q^{95} - 42 q^{96} - 45 q^{97} + 3 q^{98} + 23 q^{99}+O(q^{100}) $ 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9 + 9 * q^11 - 18 * q^12 + 3 * q^13 + 18 * q^14 + 2 * q^15 - 18 * q^16 + 18 * q^17 + 2 * q^18 + 18 * q^20 + 8 * q^21 - 9 * q^22 + 9 * q^23 - 7 * q^24 - 12 * q^25 - 18 * q^26 - 4 * q^27 - 9 * q^28 + 9 * q^29 - 5 * q^30 - 42 * q^31 + 18 * q^32 + 13 * q^33 - 39 * q^34 - 9 * q^35 - 21 * q^36 - 12 * q^38 - 21 * q^39 - 6 * q^40 - 33 * q^41 - 65 * q^42 + 18 * q^43 + q^45 - 30 * q^46 - 17 * q^48 + 9 * q^49 - 6 * q^50 - 12 * q^51 + 129 * q^52 + 52 * q^54 - 9 * q^56 + 6 * q^57 - 15 * q^58 + 12 * q^59 + 15 * q^60 - 15 * q^61 + 12 * q^62 + 46 * q^63 - 60 * q^64 - 3 * q^65 + 29 * q^66 - 15 * q^67 + 9 * q^68 + 61 * q^69 - 9 * q^70 + 61 * q^72 - 18 * q^74 - 7 * q^75 + 54 * q^76 - 45 * q^77 - 66 * q^78 + 21 * q^79 + 36 * q^80 + q^81 - 30 * q^83 + 15 * q^84 - 9 * q^85 - 102 * q^86 + 10 * q^87 - 9 * q^88 + 102 * q^89 - 37 * q^90 + 42 * q^91 - 3 * q^92 - 6 * q^93 - 156 * q^94 - 18 * q^95 - 42 * q^96 - 45 * q^97 + 3 * q^98 + 23 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.334847	+	0.193324i	−0.236773	+	0.136701i	−0.613693	−	0.789545i	$-0.710317\pi$
$2$	−0.334847	+	0.193324i	−0.236773	+	0.136701i	0.376920	+	0.926246i	$0.376983\pi$
$3$	0.454500	+	1.67136i	0.262406	+	0.964958i
$3$	0.454500	+	1.67136i	0.262406	+	0.964958i
$4$	−0.925251	+	1.60258i	−0.462626	+	0.801291i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−0.475302	−	0.471783i	−0.194041	−	0.192605i
$7$	1.06999	+	2.41974i	0.404418	+	0.914574i
$7$	1.06999	+	2.41974i	0.404418	+	0.914574i
$8$		−	1.48879i		−	0.526367i
$9$	−2.58686	+	1.51926i	−0.862286	+	0.506421i
$10$		−	0.386648i		−	0.122269i
$11$	3.67564	−	2.12213i	1.10825	−	0.639847i	0.169873	−	0.985466i	$-0.445664\pi$
$11$	3.67564	−	2.12213i	1.10825	−	0.639847i	0.938375	+	0.345619i	$0.112331\pi$
$12$	−3.09901	−	0.818050i	−0.894608	−	0.236151i
$13$	−3.15051	−	1.81895i	−0.873793	−	0.504485i	−0.00518619	−	0.999987i	$-0.501651\pi$
$13$	−3.15051	−	1.81895i	−0.873793	−	0.504485i	−0.868607	+	0.495502i	$0.834984\pi$
$14$	−0.826077	−	0.603387i	−0.220778	−	0.161262i
$15$	−1.67469	−	0.442069i	−0.432402	−	0.114142i
$16$	−1.56268	−	2.70665i	−0.390671	−	0.676662i
$17$	−2.70345			−0.655683			−0.327841	−	0.944733i	$-0.606321\pi$
$17$	−2.70345			−0.655683			−0.327841	+	0.944733i	$0.606321\pi$
$18$	0.572492	−	1.00882i	0.134938	−	0.237782i
$19$			5.17685i			1.18765i	0.804594	+	0.593825i	$0.202383\pi$
$19$			5.17685i			1.18765i	−0.804594	+	0.593825i	$0.797617\pi$
$20$	−0.925251	−	1.60258i	−0.206893	−	0.358348i
$21$	−3.55793	+	2.88810i	−0.776404	+	0.630236i
$22$	−0.820519	+	1.42118i	−0.174935	+	0.302997i
$23$	3.29639	+	1.90317i	0.687345	+	0.396839i	0.802616	−	0.596495i	$-0.203441\pi$
$23$	3.29639	+	1.90317i	0.687345	+	0.396839i	−0.115272	+	0.993334i	$0.536774\pi$
$24$	2.48830	−	0.676656i	0.507922	−	0.138122i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.40658			0.275854
$27$	−3.71496	−	3.63306i	−0.714944	−	0.699182i
$28$	−4.86784	−	0.524116i	−0.919935	−	0.0990487i
$29$	3.67289	−	2.12054i	0.682038	−	0.393775i	−0.118584	−	0.992944i	$-0.537836\pi$
$29$	3.67289	−	2.12054i	0.682038	−	0.393775i	0.800622	+	0.599169i	$0.204502\pi$
$30$	0.646227	−	0.175732i	0.117984	−	0.0320841i
$31$	−0.652414	−	0.376671i	−0.117177	−	0.0676522i	0.440266	−	0.897867i	$-0.354884\pi$
$31$	−0.652414	−	0.376671i	−0.117177	−	0.0676522i	−0.557443	+	0.830215i	$0.688217\pi$
$32$	3.62518	+	2.09300i	0.640848	+	0.369994i
$33$	5.21742	+	5.17879i	0.908236	+	0.901512i
$34$	0.905243	−	0.522642i	0.155248	−	0.0896324i
$35$	−2.63055	−	0.283229i	−0.444644	−	0.0478745i
$36$	−0.0412499	−	5.55136i	−0.00687498	−	0.925226i
$37$	−4.23308			−0.695914			−0.347957	−	0.937510i	$-0.613124\pi$
$37$	−4.23308			−0.695914			−0.347957	+	0.937510i	$0.613124\pi$
$38$	−1.00081	−	1.73345i	−0.162353	−	0.281203i
$39$	1.60820	−	6.09233i	0.257518	−	0.975553i
$40$	1.28933	+	0.744395i	0.203861	+	0.117699i
$41$	0.143256	−	0.248127i	0.0223728	−	0.0387509i	−0.854622	−	0.519250i	$-0.826211\pi$
$41$	0.143256	−	0.248127i	0.0223728	−	0.0387509i	0.876995	+	0.480499i	$0.159545\pi$
$42$	0.633022	−	1.65491i	0.0976774	−	0.255358i
$43$	5.08515	+	8.80773i	0.775477	+	1.34317i	0.934526	+	0.355895i	$0.115824\pi$
$43$	5.08515	+	8.80773i	0.775477	+	1.34317i	−0.159048	+	0.987271i	$0.550843\pi$
$44$			7.85402i			1.18404i
$45$	−0.0222912	−	2.99992i	−0.00332297	−	0.447201i
$46$	−1.47172			−0.216993
$47$	4.82756	+	8.36159i	0.704173	+	1.21966i	0.966989	+	0.254817i	$0.0820152\pi$
$47$	4.82756	+	8.36159i	0.704173	+	1.21966i	−0.262817	+	0.964846i	$0.584651\pi$
$48$	3.81353	−	3.84197i	0.550436	−	0.554541i
$49$	−4.71024	+	5.17819i	−0.672892	+	0.739741i
$50$	0.334847	+	0.193324i	0.0473546	+	0.0273402i
$51$	−1.22872	−	4.51842i	−0.172055	−	0.632706i
$52$	5.83002	−	3.36596i	0.808478	−	0.466775i
$53$			2.71745i			0.373271i	0.982429	+	0.186635i	$0.0597583\pi$
$53$			2.71745i			0.373271i	−0.982429	+	0.186635i	$0.940242\pi$
$54$	1.94630	+	0.498328i	0.264858	+	0.0678138i
$55$			4.24426i			0.572296i
$56$	3.60248	−	1.59299i	0.481402	−	0.212872i
$57$	−8.65235	+	2.35288i	−1.14603	+	0.311646i
$58$	−0.819904	+	1.42012i	−0.107659	+	0.186470i
$59$	4.44145	−	7.69282i	0.578228	−	1.00152i	−0.417455	−	0.908698i	$-0.637078\pi$
$59$	4.44145	−	7.69282i	0.578228	−	1.00152i	0.995683	−	0.0928220i	$-0.0295888\pi$
$60$	2.25796	−	2.27480i	0.291501	−	0.293675i
$61$	10.5052	−	6.06518i	1.34505	−	0.776567i	0.357510	−	0.933909i	$-0.383626\pi$
$61$	10.5052	−	6.06518i	1.34505	−	0.776567i	0.987544	+	0.157342i	$0.0502926\pi$
$62$	0.291279			0.0369924
$63$	−6.44413	−	4.63392i	−0.811884	−	0.583819i
$64$	4.63222			0.579028
$65$	3.15051	−	1.81895i	0.390772	−	0.225612i
$66$	−2.74822	−	0.725452i	−0.338283	−	0.0892970i
$67$	−4.74849	+	8.22463i	−0.580120	+	1.00480i	0.415344	+	0.909664i	$0.363661\pi$
$67$	−4.74849	+	8.22463i	−0.580120	+	1.00480i	−0.995465	+	0.0951336i	$0.969672\pi$
$68$	2.50137	−	4.33250i	0.303336	−	0.525393i
$69$	−1.68267	+	6.37443i	−0.202569	+	0.767391i
$70$	0.935587	−	0.413710i	0.111824	−	0.0494478i
$71$		−	11.7148i		−	1.39029i	−0.718869	−	0.695146i	$-0.755340\pi$
$71$		−	11.7148i		−	1.39029i	0.718869	−	0.695146i	$-0.244660\pi$
$72$	2.26187	+	3.85129i	0.266563	+	0.453879i
$73$			15.7249i			1.84046i	0.391381	+	0.920229i	$0.371998\pi$
$73$			15.7249i			1.84046i	−0.391381	+	0.920229i	$0.628002\pi$
$74$	1.41744	−	0.818357i	0.164774	−	0.0951320i
$75$	1.22019	−	1.22929i	0.140895	−	0.141946i
$76$	−8.29632	−	4.78988i	−0.951653	−	0.549437i
$77$	9.06790	+	6.62342i	1.03338	+	0.754809i
$78$	0.639293	+	2.35090i	0.0723857	+	0.266187i
$79$	−1.05648	−	1.82988i	−0.118864	−	0.205878i	0.800454	−	0.599394i	$-0.204592\pi$
$79$	−1.05648	−	1.82988i	−0.118864	−	0.205878i	−0.919318	+	0.393516i	$0.871258\pi$
$80$	3.12537			0.349427
$81$	4.38368	−	7.86024i	0.487075	−	0.873360i
$82$			0.110779i			0.0122335i
$83$	−6.95521	−	12.0468i	−0.763433	−	1.32231i	−0.941071	−	0.338210i	$-0.890179\pi$
$83$	−6.95521	−	12.0468i	−0.763433	−	1.32231i	0.177637	−	0.984096i	$-0.443155\pi$
$84$	−1.33645	−	8.37410i	−0.145818	−	0.913689i
$85$	1.35172	−	2.34126i	0.146615	−	0.253945i
$86$	−3.40549	−	1.96616i	−0.367224	−	0.212017i
$87$	5.21351	+	5.17491i	0.558947	+	0.554809i
$88$	−3.15941	−	5.47226i	−0.336794	−	0.583345i
$89$	6.28517			0.666226			0.333113	−	0.942887i	$-0.391901\pi$
$89$	6.28517			0.666226			0.333113	+	0.942887i	$0.391901\pi$
$90$	0.587421	+	1.00020i	0.0619196	+	0.105431i
$91$	1.03036	−	9.56964i	0.108011	−	1.00317i
$92$	−6.09998	+	3.52182i	−0.635967	+	0.367175i
$93$	0.333029	−	1.26161i	0.0345335	−	0.130823i
$94$	−3.23299	−	1.86657i	−0.333458	−	0.192522i
$95$	−4.48328	−	2.58842i	−0.459975	−	0.265567i
$96$	−1.85050	+	7.01024i	−0.188866	+	0.715479i
$97$	11.7467	−	6.78195i	1.19270	−	0.688603i	0.233778	−	0.972290i	$-0.424891\pi$
$97$	11.7467	−	6.78195i	1.19270	−	0.688603i	0.958917	+	0.283687i	$0.0915577\pi$
$98$	0.576143	−	2.64451i	0.0581993	−	0.267135i
$99$	−6.28429	+	11.0739i	−0.631595	+	1.11297i
$100$	1.85050			0.185050
$101$	9.57767	+	16.5890i	0.953014	+	1.65067i	0.738849	+	0.673871i	$0.235369\pi$
$101$	9.57767	+	16.5890i	0.953014	+	1.65067i	0.214164	+	0.976798i	$0.431297\pi$
$102$	1.28495	+	1.27544i	0.127229	+	0.126288i
$103$	−1.97678	−	1.14129i	−0.194778	−	0.112455i	0.399440	−	0.916759i	$-0.369205\pi$
$103$	−1.97678	−	1.14129i	−0.194778	−	0.112455i	−0.594217	+	0.804305i	$0.702538\pi$
$104$	−2.70803	+	4.69044i	−0.265544	+	0.459936i
$105$	−0.722208	−	4.52531i	−0.0704803	−	0.441625i
$106$	−0.525350	−	0.909932i	−0.0510265	−	0.0883804i
$107$		−	4.49066i		−	0.434128i	−0.976157	−	0.217064i	$-0.930352\pi$
$107$		−	4.49066i		−	0.434128i	0.976157	−	0.217064i	$-0.0696481\pi$
$108$	9.25954	−	2.59204i	0.891000	−	0.249419i
$109$	2.76774			0.265102			0.132551	−	0.991176i	$-0.457683\pi$
$109$	2.76774			0.265102			0.132551	+	0.991176i	$0.457683\pi$
$110$	−0.820519	−	1.42118i	−0.0782334	−	0.135504i
$111$	−1.92394	−	7.07498i	−0.182612	−	0.671527i
$112$	4.87732	−	6.67737i	0.460863	−	0.630952i
$113$	−4.02691	−	2.32494i	−0.378820	−	0.218712i	0.298485	−	0.954414i	$-0.403519\pi$
$113$	−4.02691	−	2.32494i	−0.378820	−	0.218712i	−0.677305	+	0.735702i	$0.736852\pi$
$114$	2.44235	−	2.46056i	0.228747	−	0.230453i
$115$	−3.29639	+	1.90317i	−0.307390	+	0.177472i
$116$			7.84814i			0.728681i
$117$	10.9134	−	0.0810928i	1.00894	−	0.00749703i
$118$			3.43456i			0.316177i
$119$	−2.89266	−	6.54163i	−0.265170	−	0.599670i
$120$	−0.658148	+	2.49326i	−0.0600804	+	0.227602i
$121$	3.50689	−	6.07411i	0.318808	−	0.552192i
$122$	−2.34509	+	4.06182i	−0.212315	+	0.367740i
$123$	0.479818	+	0.126658i	0.0432637	+	0.0114204i
$124$	1.20729	−	0.697032i	0.108418	−	0.0625953i
$125$	1.00000			0.0894427
$126$	3.05365	+	0.305849i	0.272041	+	0.0272472i
$127$	14.6254			1.29779			0.648896	−	0.760877i	$-0.275231\pi$
$127$	14.6254			1.29779			0.648896	+	0.760877i	$0.275231\pi$
$128$	−8.80145	+	5.08152i	−0.777946	+	0.449147i
$129$	−12.4096	+	12.5022i	−1.09261	+	1.10076i
$130$	−0.703292	+	1.21814i	−0.0616828	+	0.106838i
$131$	−5.64780	+	9.78227i	−0.493450	+	0.854681i	−0.999972	−	0.00754645i	$-0.997598\pi$
$131$	−5.64780	+	9.78227i	−0.493450	+	0.854681i	0.506521	+	0.862228i	$0.330931\pi$
$132$	−13.1269	+	3.56966i	−1.14255	+	0.310699i
$133$	−12.5266	+	5.53917i	−1.08619	+	0.480307i
$134$		−	3.67199i		−	0.317212i
$135$	5.00380	−	1.40072i	0.430658	−	0.120555i
$136$			4.02487i			0.345130i
$137$	−14.4550	+	8.34559i	−1.23497	+	0.713012i	−0.968062	−	0.250710i	$-0.919336\pi$
$137$	−14.4550	+	8.34559i	−1.23497	+	0.713012i	−0.266910	+	0.963721i	$0.586003\pi$
$138$	−0.668895	−	2.45976i	−0.0569402	−	0.209389i
$139$	−7.61828	−	4.39842i	−0.646174	−	0.373069i	0.140815	−	0.990036i	$-0.455028\pi$
$139$	−7.61828	−	4.39842i	−0.646174	−	0.373069i	−0.786989	+	0.616967i	$0.788361\pi$
$140$	2.88782	−	3.95361i	0.244065	−	0.334141i
$141$	−11.7811	+	11.8689i	−0.992144	+	0.999543i
$142$	2.26476	+	3.92267i	0.190054	+	0.329183i
$143$	−15.4402			−1.29117
$144$	8.15455	+	4.62759i	0.679546	+	0.385632i
$145$			4.24108i			0.352203i
$146$	−3.04000	−	5.26543i	−0.251592	−	0.435770i
$147$	−10.7954	−	5.51900i	−0.890389	−	0.455200i
$148$	3.91666	−	6.78386i	0.321948	−	0.557630i
$149$	−7.63089	−	4.40570i	−0.625147	−	0.360929i	0.153723	−	0.988114i	$-0.450874\pi$
$149$	−7.63089	−	4.40570i	−0.625147	−	0.360929i	−0.778870	+	0.627185i	$0.784207\pi$
$150$	−0.170925	+	0.647515i	−0.0139560	+	0.0528694i
$151$	0.632340	+	1.09524i	0.0514591	+	0.0891297i	0.890608	−	0.454773i	$-0.150279\pi$
$151$	0.632340	+	1.09524i	0.0514591	+	0.0891297i	−0.839148	+	0.543902i	$0.816946\pi$
$152$	7.70724			0.625140
$153$	6.99344	−	4.10725i	0.565386	−	0.332052i
$154$	−4.31683	−	0.464790i	−0.347860	−	0.0374538i
$155$	0.652414	−	0.376671i	0.0524032	−	0.0302550i
$156$	8.27547	+	8.21421i	0.662568	+	0.657663i
$157$	−0.850530	−	0.491054i	−0.0678797	−	0.0391903i	0.465676	−	0.884955i	$-0.345811\pi$
$157$	−0.850530	−	0.491054i	−0.0678797	−	0.0391903i	−0.533556	+	0.845765i	$0.679145\pi$
$158$	0.707521	+	0.408488i	0.0562874	+	0.0324975i
$159$	−4.54183	+	1.23508i	−0.360191	+	0.0979485i
$160$	−3.62518	+	2.09300i	−0.286596	+	0.165466i
$161$	−1.07807	+	10.0128i	−0.0849636	+	0.789116i
$162$	0.0517116	+	3.47945i	0.00406285	+	0.273372i
$163$	9.90775			0.776035			0.388018	−	0.921652i	$-0.373160\pi$
$163$	9.90775			0.776035			0.388018	+	0.921652i	$0.373160\pi$
$164$	0.265096	+	0.459159i	0.0207005	+	0.0358543i
$165$	−7.09367	+	1.92902i	−0.552242	+	0.150174i
$166$	4.65787	+	2.68922i	0.361521	+	0.208724i
$167$	−0.932410	+	1.61498i	−0.0721521	+	0.124971i	−0.899844	−	0.436211i	$-0.856320\pi$
$167$	−0.932410	+	1.61498i	−0.0721521	+	0.124971i	0.827692	+	0.561182i	$0.189653\pi$
$168$	4.29978	+	5.29701i	0.331736	+	0.408673i
$169$	0.117124	+	0.202864i	0.00900953	+	0.0156050i
$170$			1.04528i			0.0801696i
$171$	−7.86499	−	13.3918i	−0.601451	−	1.02409i
$172$	−18.8202			−1.43502
$173$	−3.93230	−	6.81094i	−0.298967	−	0.517826i	0.676933	−	0.736045i	$-0.263309\pi$
$173$	−3.93230	−	6.81094i	−0.298967	−	0.517826i	−0.975900	+	0.218219i	$0.929975\pi$
$174$	−2.74617	−	0.724908i	−0.208186	−	0.0549552i
$175$	1.56056	−	2.13651i	0.117967	−	0.161505i
$176$	−11.4877	−	6.63244i	−0.865920	−	0.499939i
$177$	14.8761	+	3.92685i	1.11815	+	0.295160i
$178$	−2.10457	+	1.21507i	−0.157744	+	0.0910737i
$179$			4.21069i			0.314722i	0.987541	+	0.157361i	$0.0502986\pi$
$179$			4.21069i			0.314722i	−0.987541	+	0.157361i	$0.949701\pi$
$180$	4.82824	+	2.73995i	0.359876	+	0.204224i
$181$		−	1.38290i		−	0.102790i	−0.998678	−	0.0513951i	$-0.983633\pi$
$181$		−	1.38290i		−	0.102790i	0.998678	−	0.0513951i	$-0.0163668\pi$
$182$	1.50503	+	3.40356i	0.111560	+	0.252289i
$183$	14.9117	+	14.8013i	1.10230	+	1.09414i
$184$	2.83342	−	4.90763i	0.208883	−	0.361796i
$185$	2.11654	−	3.66595i	0.155611	−	0.269526i
$186$	0.132386	+	0.486830i	0.00970704	+	0.0356961i
$187$	−9.93691	+	5.73708i	−0.726659	+	0.419537i
$188$	−17.8668			−1.30307
$189$	4.81607	−	12.8765i	0.350317	−	0.936631i
$190$	2.00162			0.145213
$191$	4.94345	−	2.85410i	0.357695	−	0.206515i	−0.310374	−	0.950614i	$-0.600454\pi$
$191$	4.94345	−	2.85410i	0.357695	−	0.206515i	0.668069	+	0.744099i	$0.267121\pi$
$192$	2.10535	+	7.74209i	0.151940	+	0.558737i
$193$	−0.515538	+	0.892938i	−0.0371093	+	0.0642751i	−0.883984	−	0.467518i	$-0.845148\pi$
$193$	−0.515538	+	0.892938i	−0.0371093	+	0.0642751i	0.846874	+	0.531793i	$0.178482\pi$
$194$	−2.62223	+	4.54184i	−0.188265	+	0.326085i
$195$	4.47201	+	4.43890i	0.320247	+	0.317877i
$196$	−3.94031	−	12.3397i	−0.281451	−	0.881406i
$197$		−	16.2023i		−	1.15437i	−0.816615	−	0.577183i	$-0.804152\pi$
$197$		−	16.2023i		−	1.15437i	0.816615	−	0.577183i	$-0.195848\pi$
$198$	−0.0365807	−	4.92298i	−0.00259967	−	0.349861i
$199$		−	17.6156i		−	1.24874i	−0.781129	−	0.624370i	$-0.785356\pi$
$199$		−	17.6156i		−	1.24874i	0.781129	−	0.624370i	$-0.214644\pi$
$200$	−1.28933	+	0.744395i	−0.0911695	+	0.0526367i
$201$	−15.9045	−	4.19832i	−1.12181	−	0.296127i
$202$	−6.41411	−	3.70319i	−0.451296	−	0.260556i
$203$	9.06110	+	6.61846i	0.635965	+	0.464525i
$204$	8.37802	+	2.21156i	0.586579	+	0.154840i
$205$	0.143256	+	0.248127i	0.0100054	+	0.0173299i
$206$	0.882558			0.0614907
$207$	−11.4187	+	0.0848478i	−0.793655	+	0.00589733i
$208$			11.3697i			0.788350i
$209$	10.9860	+	19.0282i	0.759914	+	1.31621i
$210$	1.11668	+	1.37567i	0.0770583	+	0.0949301i
$211$	3.36761	−	5.83288i	0.231836	−	0.401552i	−0.726512	−	0.687153i	$-0.758860\pi$
$211$	3.36761	−	5.83288i	0.231836	−	0.401552i	0.958348	+	0.285602i	$0.0921934\pi$
$212$	−4.35494	−	2.51433i	−0.299099	−	0.172685i
$213$	19.5796	−	5.32438i	1.34157	−	0.364821i
$214$	0.868153	+	1.50368i	0.0593457	+	0.102790i
$215$	−10.1703			−0.693608
$216$	−5.40886	+	5.53079i	−0.368026	+	0.376323i
$217$	0.213369	−	1.98170i	0.0144844	−	0.134527i
$218$	−0.926771	+	0.535072i	−0.0627689	+	0.0362396i
$219$	−26.2819	+	7.14696i	−1.77596	+	0.482947i
$220$	−6.80178	−	3.92701i	−0.458576	−	0.264759i
$221$	8.51723	+	4.91743i	0.572931	+	0.330782i
$222$	2.01199	+	1.99710i	0.135036	+	0.134036i
$223$	4.86430	−	2.80840i	0.325737	−	0.188065i	−0.328210	−	0.944605i	$-0.606445\pi$
$223$	4.86430	−	2.80840i	0.325737	−	0.188065i	0.653947	+	0.756540i	$0.273112\pi$
$224$	−1.18560	+	11.0115i	−0.0792161	+	0.735735i
$225$	2.60915	+	1.48065i	0.173943	+	0.0987103i
$226$	1.79787			0.119592
$227$	−7.27122	−	12.5941i	−0.482608	−	0.835901i	0.517193	−	0.855869i	$-0.326977\pi$
$227$	−7.27122	−	12.5941i	−0.482608	−	0.835901i	−0.999801	+	0.0199678i	$0.993644\pi$
$228$	4.23492	−	16.0431i	0.280464	−	1.06248i
$229$	18.6640	+	10.7757i	1.23335	+	0.712076i	0.967727	−	0.252001i	$-0.0810886\pi$
$229$	18.6640	+	10.7757i	1.23335	+	0.712076i	0.265624	+	0.964077i	$0.414422\pi$
$230$	0.735858	−	1.27454i	0.0485210	−	0.0840409i
$231$	−6.94872	+	18.1660i	−0.457193	+	1.19524i
$232$	−3.15704	−	5.46816i	−0.207270	−	0.359002i
$233$		−	8.01672i		−	0.525193i	−0.964906	−	0.262596i	$-0.915421\pi$
$233$		−	8.01672i		−	0.525193i	0.964906	−	0.262596i	$-0.0845788\pi$
$234$	−3.63864	+	2.13697i	−0.237865	+	0.139698i
$235$	−9.65513			−0.629831
$236$	8.21892	+	14.2356i	0.535006	+	0.926657i
$237$	2.57821	−	2.59744i	0.167473	−	0.168722i
$238$	2.23326	+	1.63123i	0.144761	+	0.105737i
$239$	−24.4549	−	14.1190i	−1.58185	−	0.913284i	−0.994589	−	0.103889i	$-0.966871\pi$
$239$	−24.4549	−	14.1190i	−1.58185	−	0.913284i	−0.587265	−	0.809395i	$-0.699795\pi$
$240$	1.42048	+	5.22360i	0.0916916	+	0.337182i
$241$	12.4500	−	7.18803i	0.801977	−	0.463022i	−0.0421850	−	0.999110i	$-0.513432\pi$
$241$	12.4500	−	7.18803i	0.801977	−	0.463022i	0.844162	+	0.536088i	$0.180099\pi$
$242$			2.71187i			0.174325i
$243$	15.1296	+	3.75420i	0.970567	+	0.240832i
$244$			22.4473i			1.43704i
$245$	−2.12932	−	6.66828i	−0.136037	−	0.426021i
$246$	−0.185152	+	0.0503493i	−0.0118048	+	0.00321015i
$247$	9.41640	−	16.3097i	0.599151	−	1.03776i
$248$	−0.560785	+	0.971308i	−0.0356099	+	0.0616781i
$249$	16.9733	−	17.0999i	1.07564	−	1.08366i
$250$	−0.334847	+	0.193324i	−0.0211776	+	0.0122269i
$251$	28.7546			1.81498			0.907488	−	0.420078i	$-0.137997\pi$
$251$	28.7546			1.81498			0.907488	+	0.420078i	$0.137997\pi$
$252$	13.3887	−	6.03971i	0.843407	−	0.380466i
$253$	16.1551			1.01566
$254$	−4.89727	+	2.82744i	−0.307282	+	0.177409i
$255$	4.52743	+	1.19511i	0.283519	+	0.0748407i
$256$	−2.66746	+	4.62018i	−0.166716	+	0.288761i
$257$	7.94503	−	13.7612i	0.495598	−	0.858400i	−0.504390	−	0.863476i	$-0.668282\pi$
$257$	7.94503	−	13.7612i	0.495598	−	0.858400i	0.999987	+	0.00507607i	$0.00161577\pi$
$258$	1.73836	−	6.58541i	0.108226	−	0.409990i
$259$	−4.52935	−	10.2429i	−0.281440	−	0.636465i
$260$			6.73193i			0.417496i
$261$	−6.27958	+	11.0656i	−0.388696	+	0.684945i
$262$		−	4.36742i		−	0.269820i
$263$	−1.02433	+	0.591398i	−0.0631629	+	0.0364671i	−0.531249	−	0.847216i	$-0.678277\pi$
$263$	−1.02433	+	0.591398i	−0.0631629	+	0.0364671i	0.468086	+	0.883683i	$0.344944\pi$
$264$	7.71014	−	7.76764i	0.474526	−	0.478065i
$265$	−2.35338	−	1.35873i	−0.144567	−	0.0834659i
$266$	3.12364	−	4.27647i	0.191523	−	0.262207i
$267$	2.85661	+	10.5047i	0.174822	+	0.642880i
$268$	−8.78710	−	15.2197i	−0.536757	−	0.929691i
$269$	10.8395			0.660895			0.330448	−	0.943824i	$-0.392800\pi$
$269$	10.8395			0.660895			0.330448	+	0.943824i	$0.392800\pi$
$270$	−1.40472	+	1.43638i	−0.0854882	+	0.0874155i
$271$		−	21.6099i		−	1.31271i	−0.754453	−	0.656354i	$-0.772098\pi$
$271$		−	21.6099i		−	1.31271i	0.754453	−	0.656354i	$-0.227902\pi$
$272$	4.22464	+	7.31728i	0.256156	+	0.443675i
$273$	16.4626	−	2.62731i	0.996360	−	0.159012i
$274$	3.22681	−	5.58900i	0.194939	−	0.337644i
$275$	−3.67564	−	2.12213i	−0.221649	−	0.127969i
$276$	−8.65866	−	8.59456i	−0.521190	−	0.517332i
$277$	−2.76756	−	4.79355i	−0.166286	−	0.288017i	0.770825	−	0.637047i	$-0.219844\pi$
$277$	−2.76756	−	4.79355i	−0.166286	−	0.288017i	−0.937111	+	0.349030i	$0.886511\pi$
$278$	3.40128			0.203995
$279$	2.25997	−	0.0167929i	0.135301	−	0.00100536i
$280$	−0.421669	+	3.91634i	−0.0251995	+	0.234046i
$281$	−15.4759	+	8.93502i	−0.923215	+	0.533019i	−0.884659	−	0.466238i	$-0.845609\pi$
$281$	−15.4759	+	8.93502i	−0.923215	+	0.533019i	−0.0385558	+	0.999256i	$0.512276\pi$
$282$	1.65031	−	6.25184i	0.0982743	−	0.372292i
$283$	6.12953	+	3.53888i	0.364363	+	0.210365i	0.670993	−	0.741464i	$-0.265868\pi$
$283$	6.12953	+	3.53888i	0.364363	+	0.210365i	−0.306630	+	0.951829i	$0.599201\pi$
$284$	18.7739	+	10.8391i	1.11403	+	0.643185i
$285$	2.28852	−	8.66959i	0.135560	−	0.513542i
$286$	5.17010	−	2.98496i	0.305714	−	0.176504i
$287$	0.753683	+	0.0811485i	0.0444885	+	0.00479005i
$288$	−12.5577	+	0.0933108i	−0.739967	+	0.00549839i
$289$	−9.69137			−0.570080
$290$	−0.819904	−	1.42012i	−0.0481464	−	0.0833921i
$291$	16.6739	+	16.5505i	0.977443	+	0.970207i
$292$	−25.2004	−	14.5495i	−1.47474	−	0.851443i
$293$	7.41171	−	12.8375i	0.432997	−	0.749972i	−0.564133	−	0.825684i	$-0.690790\pi$
$293$	7.41171	−	12.8375i	0.432997	−	0.749972i	0.997130	+	0.0757117i	$0.0241229\pi$
$294$	4.68177	−	0.238989i	0.273046	−	0.0139381i
$295$	4.44145	+	7.69282i	0.258591	+	0.447893i
$296$			6.30217i			0.366306i
$297$	−21.3647	−	5.47018i	−1.23970	−	0.317412i
$298$	3.40691			0.197357
$299$	−6.92353	−	11.9919i	−0.400398	−	0.693510i
$300$	0.841054	+	3.09285i	0.0485583	+	0.178566i
$301$	−15.8713	+	21.7289i	−0.914808	+	1.25243i
$302$	−0.423475	−	0.244493i	−0.0243682	−	0.0140690i
$303$	−23.3731	+	23.5474i	−1.34275	+	1.35276i
$304$	14.0119	−	8.08977i	0.803637	−	0.463980i
$305$			12.1304i			0.694583i
$306$	−1.54770	+	2.72730i	−0.0884764	+	0.155910i
$307$			6.07854i			0.346921i	0.984841	+	0.173460i	$0.0554949\pi$
$307$			6.07854i			0.346921i	−0.984841	+	0.173460i	$0.944505\pi$
$308$	−19.0047	+	8.40373i	−1.08289	+	0.478847i
$309$	1.00906	−	3.82261i	0.0574034	−	0.217461i
$310$	−0.145639	+	0.252255i	−0.00827176	+	0.0143271i
$311$	−5.13664	+	8.89692i	−0.291272	+	0.504498i	−0.974111	−	0.226071i	$-0.927412\pi$
$311$	−5.13664	+	8.89692i	−0.291272	+	0.504498i	0.682839	+	0.730569i	$0.260745\pi$
$312$	−9.07020	−	2.39427i	−0.513499	−	0.135549i
$313$	−14.0962	+	8.13844i	−0.796764	+	0.460012i	−0.842338	−	0.538949i	$-0.818821\pi$
$313$	−14.0962	+	8.13844i	−0.796764	+	0.460012i	0.0455747	+	0.998961i	$0.485488\pi$
$314$	0.379730			0.0214294
$315$	7.23516	−	3.26382i	0.407655	−	0.183895i
$316$	3.91005			0.219958
$317$	28.8682	−	16.6671i	1.62140	−	0.936115i	0.634853	−	0.772633i	$-0.281061\pi$
$317$	28.8682	−	16.6671i	1.62140	−	0.936115i	0.986546	−	0.163482i	$-0.0522725\pi$
$318$	1.28205	−	1.29161i	0.0718937	−	0.0724299i
$319$	9.00014	−	15.5887i	0.503911	−	0.872800i
$320$	−2.31611	+	4.01162i	−0.129475	+	0.224257i
$321$	7.50549	−	2.04101i	0.418915	−	0.113918i
$322$	−1.57472	−	3.56116i	−0.0877558	−	0.198456i
$323$		−	13.9953i		−	0.778721i
$324$	8.54068	+	14.2979i	0.474482	+	0.794328i
$325$			3.63789i			0.201794i
$326$	−3.31758	+	1.91541i	−0.183744	+	0.106085i
$327$	1.25794	+	4.62588i	0.0695642	+	0.255812i
$328$	−0.369409	−	0.213278i	−0.0203972	−	0.0117763i
$329$	−15.0674	+	20.6282i	−0.830692	+	1.13727i
$330$	2.00237	−	2.01731i	0.110227	−	0.111049i
$331$	12.9962	+	22.5101i	0.714336	+	1.23727i	0.963215	+	0.268732i	$0.0866046\pi$
$331$	12.9962	+	22.5101i	0.714336	+	1.23727i	−0.248879	+	0.968535i	$0.580062\pi$
$332$	25.7413			1.41274
$333$	10.9504	−	6.43116i	0.600077	−	0.352426i
$334$		−	0.721030i		−	0.0394530i
$335$	−4.74849	−	8.22463i	−0.259438	−	0.449359i
$336$	13.3770	+	5.11686i	0.729775	+	0.279148i
$337$	2.76544	−	4.78989i	0.150643	−	0.260922i	−0.780821	−	0.624755i	$-0.785199\pi$
$337$	2.76544	−	4.78989i	0.150643	−	0.260922i	0.931464	+	0.363833i	$0.118532\pi$
$338$	−0.0784372	−	0.0452858i	−0.00426642	−	0.00246322i
$339$	2.05557	−	7.78709i	0.111643	−	0.422937i
$340$	2.50137	+	4.33250i	0.135656	+	0.234963i
$341$	−3.19739			−0.173148
$342$	5.22252	+	2.96371i	0.282402	+	0.160259i
$343$	−17.5698	−	5.85693i	−0.948678	−	0.316245i
$344$	13.1129	−	7.57072i	0.706998	−	0.408186i
$345$	−4.67909	−	4.64445i	−0.251913	−	0.250049i
$346$	2.63344	+	1.52042i	0.141575	+	0.0817381i
$347$	−16.1976	−	9.35170i	−0.869534	−	0.502026i	−0.00234075	−	0.999997i	$-0.500745\pi$
$347$	−16.1976	−	9.35170i	−0.869534	−	0.502026i	−0.867193	+	0.497971i	$0.834078\pi$
$348$	−13.1170	+	3.56698i	−0.703147	+	0.191210i
$349$	17.6313	−	10.1794i	0.943780	−	0.544892i	0.0526367	−	0.998614i	$-0.483237\pi$
$349$	17.6313	−	10.1794i	0.943780	−	0.544892i	0.891143	+	0.453722i	$0.149904\pi$
$350$	−0.109510	+	1.01710i	−0.00585356	+	0.0543661i
$351$	5.09567	+	18.2033i	0.271986	+	0.971618i
$352$	17.7665			0.946957
$353$	−3.80931	−	6.59791i	−0.202749	−	0.351171i	0.746664	−	0.665201i	$-0.231654\pi$
$353$	−3.80931	−	6.59791i	−0.202749	−	0.351171i	−0.949413	+	0.314030i	$0.898321\pi$
$354$	−5.74037	+	1.56101i	−0.305097	+	0.0829667i
$355$	10.1453	+	5.85740i	0.538458	+	0.310879i
$356$	−5.81536	+	10.0725i	−0.308213	+	0.533841i
$357$	9.61868	−	7.80784i	0.509074	−	0.413235i
$358$	−0.814028	−	1.40994i	−0.0430227	−	0.0745175i
$359$		−	13.5305i		−	0.714114i	−0.934083	−	0.357057i	$-0.883780\pi$
$359$		−	13.5305i		−	0.714114i	0.934083	−	0.357057i	$-0.116220\pi$
$360$	−4.46625	+	0.0331869i	−0.235392	+	0.00174910i
$361$	−7.79973			−0.410512
$362$	0.267348	+	0.463061i	0.0140515	+	0.0243379i
$363$	11.7459	+	3.10057i	0.616499	+	0.162738i
$364$	14.3828	+	10.5056i	0.753864	+	0.550641i
$365$	−13.6181	−	7.86244i	−0.712806	−	0.411539i
$366$	−7.85459	−	2.07339i	−0.410566	−	0.108378i
$367$	−1.03813	+	0.599366i	−0.0541901	+	0.0312867i	−0.526850	−	0.849958i	$-0.676627\pi$
$367$	−1.03813	+	0.599366i	−0.0541901	+	0.0312867i	0.472660	+	0.881245i	$0.343294\pi$
$368$		−	11.8962i		−	0.620133i
$369$	0.00638668	+	0.859512i	0.000332478	+	0.0447444i
$370$			1.63671i			0.0850887i
$371$	−6.57552	+	2.90765i	−0.341384	+	0.150958i
$372$	1.71370	+	1.70102i	0.0888514	+	0.0881936i
$373$	−14.2091	+	24.6109i	−0.735721	+	1.27431i	0.218685	+	0.975795i	$0.429823\pi$
$373$	−14.2091	+	24.6109i	−0.735721	+	1.27431i	−0.954406	+	0.298511i	$0.903510\pi$
$374$	2.21823	−	3.84209i	0.114702	−	0.198670i
$375$	0.454500	+	1.67136i	0.0234703	+	0.0863084i
$376$	12.4487	−	7.18723i	0.641990	−	0.370653i
$377$	−15.4286			−0.794613
$378$	0.876702	+	5.24274i	0.0450927	+	0.269657i
$379$	23.8261			1.22386			0.611931	−	0.790911i	$-0.290393\pi$
$379$	23.8261			1.22386			0.611931	+	0.790911i	$0.290393\pi$
$380$	8.29632	−	4.78988i	0.425592	−	0.245716i
$381$	6.64724	+	24.4442i	0.340548	+	1.25231i
$382$	−1.10353	+	1.91138i	−0.0564617	+	0.0977945i
$383$	7.72665	−	13.3830i	0.394813	−	0.683837i	−0.598264	−	0.801299i	$-0.704143\pi$
$383$	7.72665	−	13.3830i	0.394813	−	0.683837i	0.993077	+	0.117462i	$0.0374759\pi$
$384$	−12.4933	−	12.4008i	−0.637546	−	0.632826i
$385$	−10.2700	+	4.54132i	−0.523408	+	0.231447i
$386$		−	0.398664i		−	0.0202915i
$387$	−26.5358	−	15.0587i	−1.34889	−	0.765476i
$388$			25.1000i			1.27426i
$389$	32.5077	−	18.7683i	1.64821	−	0.951593i	0.670423	−	0.741979i	$-0.266113\pi$
$389$	32.5077	−	18.7683i	1.64821	−	0.951593i	0.977784	−	0.209614i	$-0.0672207\pi$
$390$	−2.35559	−	0.621807i	−0.119280	−	0.0314864i
$391$	−8.91162	−	5.14512i	−0.450680	−	0.260200i
$392$	7.70924	+	7.01257i	0.389375	+	0.354188i
$393$	−18.9166	−	4.99343i	−0.954215	−	0.251885i
$394$	3.13229	+	5.42529i	0.157803	+	0.273322i
$395$	2.11297			0.106315
$396$	−11.9323	−	20.3173i	−0.599622	−	1.02098i
$397$		−	12.7223i		−	0.638513i	−0.947668	−	0.319257i	$-0.896567\pi$
$397$		−	12.7223i		−	0.638513i	0.947668	−	0.319257i	$-0.103433\pi$
$398$	3.40553	+	5.89855i	0.170704	+	0.295668i
$399$	−14.9513	−	18.4188i	−0.748500	−	0.922095i
$400$	−1.56268	+	2.70665i	−0.0781342	+	0.135332i
$401$	12.6232	+	7.28802i	0.630374	+	0.363946i	0.780897	−	0.624660i	$-0.214762\pi$
$401$	12.6232	+	7.28802i	0.630374	+	0.363946i	−0.150523	+	0.988607i	$0.548096\pi$
$402$	6.13720	−	1.66892i	0.306096	−	0.0832383i
$403$	1.37029	+	2.37341i	0.0682590	+	0.118228i
$404$	−35.4470			−1.76355
$405$	4.61533	+	7.72650i	0.229338	+	0.383933i
$406$	−4.31359	−	0.464442i	−0.214080	−	0.0230499i
$407$	−15.5593	+	8.98315i	−0.771245	+	0.445278i
$408$	−6.72699	+	1.82930i	−0.333036	+	0.0905641i
$409$	−32.7144	−	18.8877i	−1.61762	−	0.933936i	−0.987532	−	0.157415i	$-0.949684\pi$
$409$	−32.7144	−	18.8877i	−1.61762	−	0.933936i	−0.630092	−	0.776520i	$-0.716983\pi$
$410$	−0.0959378	−	0.0553897i	−0.00473803	−	0.00273550i
$411$	−20.5182	−	20.3663i	−1.01209	−	1.00460i
$412$	3.65803	−	2.11196i	0.180218	−	0.104049i
$413$	23.3669	+	2.51590i	1.14981	+	0.123799i
$414$	3.80712	−	2.23592i	0.187110	−	0.109890i
$415$	13.9104			0.682836
$416$	−7.61411	−	13.1880i	−0.373312	−	0.646596i
$417$	3.88881	−	14.7319i	0.190436	−	0.721426i
$418$	−7.35723	−	4.24770i	−0.359854	−	0.207762i
$419$	0.454552	−	0.787307i	0.0222063	−	0.0384625i	−0.854709	−	0.519108i	$-0.826264\pi$
$419$	0.454552	−	0.787307i	0.0222063	−	0.0384625i	0.876915	+	0.480645i	$0.159598\pi$
$420$	7.92040	+	3.02965i	0.386476	+	0.147832i
$421$	2.13949	+	3.70571i	0.104273	+	0.180605i	0.913441	−	0.406972i	$-0.133415\pi$
$421$	2.13949	+	3.70571i	0.104273	+	0.180605i	−0.809168	+	0.587577i	$0.800082\pi$
$422$			2.60416i			0.126769i
$423$	−25.1917	−	14.2959i	−1.22486	−	0.695091i
$424$	4.04572			0.196478
$425$	1.35172	+	2.34126i	0.0655683	+	0.113568i
$426$	−5.52685	+	5.56807i	−0.267777	+	0.269774i
$427$	25.9166	+	18.9301i	1.25419	+	0.916093i
$428$	7.19665	+	4.15499i	0.347863	+	0.200839i
$429$	−7.01756	−	25.8060i	−0.338811	−	1.24593i
$430$	3.40549	−	1.96616i	0.164228	−	0.0948168i
$431$		−	11.8641i		−	0.571471i	−0.958308	−	0.285736i	$-0.907762\pi$
$431$		−	11.8641i		−	0.571471i	0.958308	−	0.285736i	$-0.0922380\pi$
$432$	−4.02810	+	15.7324i	−0.193802	+	0.756925i
$433$			15.0802i			0.724709i	0.932040	+	0.362354i	$0.118027\pi$
$433$			15.0802i			0.724709i	−0.932040	+	0.362354i	$0.881973\pi$
$434$	0.311665	+	0.704818i	0.0149604	+	0.0338323i
$435$	−7.08836	+	1.92757i	−0.339861	+	0.0924201i
$436$	−2.56086	+	4.43554i	−0.122643	+	0.212424i
$437$	−9.85242	+	17.0649i	−0.471305	+	0.816325i
$438$	7.41873	−	7.47406i	0.354481	−	0.357124i
$439$	−33.8067	+	19.5183i	−1.61350	+	0.931557i	−0.624955	+	0.780661i	$0.714883\pi$
$439$	−33.8067	+	19.5183i	−1.61350	+	0.931557i	−0.988550	+	0.150897i	$0.951784\pi$
$440$	6.31882			0.301238
$441$	4.31770	−	20.5513i	0.205605	−	0.978635i
$442$	−3.80263			−0.180873
$443$	−15.6110	+	9.01300i	−0.741700	+	0.428220i	−0.822687	−	0.568495i	$-0.807526\pi$
$443$	−15.6110	+	9.01300i	−0.741700	+	0.428220i	0.0809874	+	0.996715i	$0.474193\pi$
$444$	13.1184	+	3.46287i	0.622570	+	0.164341i
$445$	−3.14258	+	5.44311i	−0.148973	+	0.258028i
$446$	−1.08586	+	1.88077i	−0.0514172	+	0.0890572i
$447$	3.89524	−	14.7563i	0.184239	−	0.697950i
$448$	4.95643	+	11.2088i	0.234170	+	0.529564i
$449$			17.5843i			0.829856i	0.909854	+	0.414928i	$0.136193\pi$
$449$			17.5843i			0.829856i	−0.909854	+	0.414928i	$0.863807\pi$
$450$	−1.15991	+	0.00861884i	−0.0546788	+	0.000406296i
$451$		−	1.21603i		−	0.0572607i
$452$	7.45182	−	4.30231i	0.350504	−	0.202364i
$453$	−1.54314	+	1.55465i	−0.0725033	+	0.0730440i
$454$	4.86950	+	2.81140i	0.228537	+	0.131946i
$455$	7.77238	+	5.67714i	0.364375	+	0.266148i
$456$	3.50294	+	12.8815i	0.164040	+	0.603233i
$457$	3.96531	+	6.86813i	0.185490	+	0.321277i	0.943741	−	0.330684i	$-0.107280\pi$
$457$	3.96531	+	6.86813i	0.185490	+	0.321277i	−0.758252	+	0.651962i	$0.773946\pi$
$458$	−8.33279			−0.389365
$459$	10.0432	+	9.82178i	0.468776	+	0.458441i
$460$		−	7.04365i		−	0.328412i
$461$	4.02115	+	6.96483i	0.187284	+	0.324385i	0.944344	−	0.328961i	$-0.106698\pi$
$461$	4.02115	+	6.96483i	0.187284	+	0.324385i	−0.757060	+	0.653345i	$0.773365\pi$
$462$	−1.18517	−	7.42620i	−0.0551391	−	0.345498i
$463$	9.70541	−	16.8103i	0.451049	−	0.781239i	−0.547403	−	0.836869i	$-0.684383\pi$
$463$	9.70541	−	16.8103i	0.451049	−	0.781239i	0.998451	+	0.0556301i	$0.0177168\pi$
$464$	−11.4791	−	6.62747i	−0.532905	−	0.307673i
$465$	0.926074	+	0.919218i	0.0429457	+	0.0426277i
$466$	1.54983	+	2.68438i	0.0717943	+	0.124351i
$467$	−15.5234			−0.718337			−0.359169	−	0.933273i	$-0.616940\pi$
$467$	−15.5234			−0.718337			−0.359169	+	0.933273i	$0.616940\pi$
$468$	−9.96765	+	17.5646i	−0.460755	+	0.811924i
$469$	−24.9823	−	2.68982i	−1.15357	−	0.124204i
$470$	3.23299	−	1.86657i	0.149127	−	0.0860985i
$471$	0.434159	−	1.64472i	0.0200050	−	0.0757848i
$472$	−11.4530	−	6.61239i	−0.527167	−	0.304360i
$473$	37.3823	+	21.5827i	1.71884	+	0.992374i
$474$	−0.361159	+	1.36818i	−0.0165886	+	0.0628425i
$475$	4.48328	−	2.58842i	0.205707	−	0.118765i
$476$	13.1599	+	1.41692i	0.603185	+	0.0649445i
$477$	−4.12853	−	7.02967i	−0.189032	−	0.321866i
$478$	10.9182			0.499387
$479$	4.74982	+	8.22692i	0.217025	+	0.375898i	0.953897	−	0.300134i	$-0.0970315\pi$
$479$	4.74982	+	8.22692i	0.217025	+	0.375898i	−0.736872	+	0.676032i	$0.763698\pi$
$480$	−5.14579	−	5.10770i	−0.234872	−	0.233134i
$481$	13.3363	+	7.69974i	0.608085	+	0.351078i
$482$	−2.77924	+	4.81378i	−0.126591	+	0.219262i
$483$	−17.2249	+	2.74897i	−0.783759	+	0.125083i
$484$	6.48951	+	11.2402i	0.294978	+	0.510916i
$485$			13.5639i			0.615905i
$486$	−5.79190	+	1.66784i	−0.262726	+	0.0756548i
$487$	−36.0106			−1.63179			−0.815897	−	0.578197i	$-0.803756\pi$
$487$	−36.0106			−1.63179			−0.815897	+	0.578197i	$0.803756\pi$
$488$	−9.02979	−	15.6401i	−0.408759	−	0.707992i
$489$	4.50308	+	16.5594i	0.203636	+	0.748841i
$490$	2.00214	+	1.82121i	0.0904474	+	0.0822738i
$491$	26.0433	+	15.0361i	1.17532	+	0.678571i	0.954927	−	0.296840i	$-0.0959328\pi$
$491$	26.0433	+	15.0361i	1.17532	+	0.678571i	0.220393	+	0.975411i	$0.429266\pi$
$492$	−0.646932	+	0.651757i	−0.0291659	+	0.0293835i
$493$	−9.92946	+	5.73278i	−0.447200	+	0.258191i
$494$			7.28167i			0.327618i
$495$	−6.44816	−	10.9793i	−0.289823	−	0.493483i
$496$			2.35447i			0.105719i
$497$	28.3467	−	12.5347i	1.27152	−	0.562259i
$498$	−2.37764	+	9.00720i	−0.106545	+	0.403622i
$499$	−20.8184	+	36.0586i	−0.931961	+	1.61420i	−0.151994	+	0.988381i	$0.548570\pi$
$499$	−20.8184	+	36.0586i	−0.931961	+	1.61420i	−0.779966	+	0.625822i	$0.784764\pi$
$500$	−0.925251	+	1.60258i	−0.0413785	+	0.0716697i
$501$	−3.12299	−	0.824379i	−0.139525	−	0.0368306i
$502$	−9.62841	+	5.55897i	−0.429737	+	0.248109i
$503$	1.37222			0.0611841			0.0305920	−	0.999532i	$-0.490261\pi$
$503$	1.37222			0.0611841			0.0305920	+	0.999532i	$0.490261\pi$
$504$	−6.89894	+	9.59396i	−0.307303	+	0.427349i
$505$	−19.1553			−0.852401
$506$	−5.40950	+	3.12318i	−0.240482	+	0.138842i
$507$	−0.285826	+	0.287958i	−0.0126940	+	0.0127886i
$508$	−13.5321	+	23.4384i	−0.600392	+	1.03991i
$509$	9.47184	−	16.4057i	0.419832	−	0.727170i	−0.576090	−	0.817386i	$-0.695422\pi$
$509$	9.47184	−	16.4057i	0.419832	−	0.727170i	0.995922	+	0.0902160i	$0.0287557\pi$
$510$	−1.74704	+	0.475082i	−0.0773603	+	0.0210370i
$511$	−38.0500	+	16.8255i	−1.68324	+	0.744315i
$512$		−	22.3888i		−	0.989456i
$513$	18.8078	−	19.2318i	0.830383	−	0.849103i
$514$			6.14387i			0.270994i
$515$	1.97678	−	1.14129i	0.0871072	−	0.0502914i
$516$	−8.55377	−	31.4552i	−0.376559	−	1.38474i
$517$	35.4888	+	20.4895i	1.56079	+	0.901125i
$518$	3.49685	+	2.55419i	0.153643	+	0.112224i
$519$	9.59627	−	9.66784i	0.421229	−	0.424371i
$520$	−2.70803	−	4.69044i	−0.118755	−	0.205690i
$521$	−32.4326			−1.42090			−0.710448	−	0.703750i	$-0.751508\pi$
$521$	−32.4326			−1.42090			−0.710448	+	0.703750i	$0.751508\pi$
$522$	−0.0365532	−	4.91929i	−0.00159989	−	0.215311i
$523$		−	40.2111i		−	1.75831i	−0.476537	−	0.879154i	$-0.658108\pi$
$523$		−	40.2111i		−	1.75831i	0.476537	−	0.879154i	$-0.341892\pi$
$524$	−10.4513	−	18.1021i	−0.456566	−	0.790795i
$525$	4.28014	+	1.63720i	0.186800	+	0.0714534i
$526$	0.228663	−	0.396056i	0.00997018	−	0.0172689i
$527$	1.76377	+	1.01831i	0.0768309	+	0.0443584i
$528$	5.86399	−	22.2145i	0.255198	−	0.966763i
$529$	−4.25588	−	7.37140i	−0.185038	−	0.320496i
$530$	1.05070			0.0456395
$531$	0.198010	+	26.6480i	0.00859291	+	1.15642i
$532$	2.71327	−	25.2000i	0.117635	−	1.09256i
$533$	−0.902657	+	0.521149i	−0.0390984	+	0.0225735i
$534$	−2.98735	−	2.96523i	−0.129275	−	0.128318i
$535$	3.88902	+	2.24533i	0.168137	+	0.0970740i
$536$	12.2447	+	7.06951i	0.528893	+	0.305356i
$537$	−7.03756	+	1.91376i	−0.303693	+	0.0825848i
$538$	−3.62957	+	2.09553i	−0.156482	+	0.0903449i
$539$	−6.32436	+	29.0289i	−0.272409	+	1.25036i
$540$	−2.38500	+	9.31502i	−0.102634	+	0.400854i
$541$	−23.5961			−1.01448			−0.507239	−	0.861806i	$-0.669334\pi$
$541$	−23.5961			−1.01448			−0.507239	+	0.861806i	$0.669334\pi$
$542$	4.17772	+	7.23602i	0.179448	+	0.310813i
$543$	2.31132	−	0.628529i	0.0991883	−	0.0269728i
$544$	−9.80049	−	5.65832i	−0.420193	−	0.242598i
$545$	−1.38387	+	2.39694i	−0.0592785	+	0.102673i
$546$	−5.00453	+	4.06236i	−0.214174	+	0.173853i
$547$	4.43140	+	7.67540i	0.189473	+	0.328176i	0.945075	−	0.326855i	$-0.105989\pi$
$547$	4.43140	+	7.67540i	0.189473	+	0.328176i	−0.755602	+	0.655031i	$0.772655\pi$
$548$		−	30.8871i		−	1.31943i
$549$	−17.9609	+	31.6499i	−0.766551	+	1.35079i
$550$	1.64104			0.0699741
$551$	10.9777	+	19.0140i	0.467667	+	0.810022i
$552$	9.49019	+	2.50514i	0.403929	+	0.106626i
$553$	3.29741	−	4.51437i	0.140220	−	0.191970i
$554$	1.85342	+	1.07007i	0.0787442	+	0.0454630i
$555$	7.08908	+	1.87131i	0.300915	+	0.0794328i
$556$	14.0977	−	8.13928i	0.597874	−	0.345182i
$557$			40.1442i			1.70096i	0.526005	+	0.850481i	$0.323689\pi$
$557$			40.1442i			1.70096i	−0.526005	+	0.850481i	$0.676311\pi$
$558$	−0.753497	+	0.442529i	−0.0318981	+	0.0187338i
$559$		−	36.9984i		−	1.56487i
$560$	3.34411	+	7.56256i	0.141315	+	0.319577i
$561$	−14.1050	−	14.0006i	−0.595514	−	0.591106i
$562$	3.45471	−	5.98374i	0.145728	−	0.252409i
$563$	−1.30952	+	2.26815i	−0.0551895	+	0.0955910i	−0.892300	−	0.451442i	$-0.850910\pi$
$563$	−1.30952	+	2.26815i	−0.0551895	+	0.0955910i	0.837111	+	0.547033i	$0.184243\pi$
$564$	−8.12049	−	29.8618i	−0.341934	−	1.25741i
$565$	4.02691	−	2.32494i	0.169414	−	0.0978110i
$566$	−2.73661			−0.115028
$567$	23.7102	+	2.19696i	0.995735	+	0.0922638i
$568$	−17.4409			−0.731804
$569$	−5.42169	+	3.13021i	−0.227289	+	0.131225i	−0.609321	−	0.792924i	$-0.708558\pi$
$569$	−5.42169	+	3.13021i	−0.227289	+	0.131225i	0.382032	+	0.924149i	$0.375224\pi$
$570$	0.909737	+	3.34542i	0.0381047	+	0.140124i
$571$	0.966490	−	1.67401i	0.0404464	−	0.0700552i	−0.845094	−	0.534618i	$-0.820455\pi$
$571$	0.966490	−	1.67401i	0.0404464	−	0.0700552i	0.885540	+	0.464563i	$0.153789\pi$
$572$	14.2860	−	24.7441i	0.597329	−	1.03460i
$573$	7.01701	+	6.96507i	0.293140	+	0.290970i
$574$	−0.268057	+	0.118533i	−0.0111885	+	0.00494747i
$575$		−	3.80634i		−	0.158735i
$576$	−11.9829	+	7.03757i	−0.499288	+	0.293232i
$577$			27.0058i			1.12427i	0.827047	+	0.562133i	$0.190019\pi$
$577$			27.0058i			1.12427i	−0.827047	+	0.562133i	$0.809981\pi$
$578$	3.24513	−	1.87358i	0.134980	−	0.0779305i
$579$	−1.72673	−	0.455807i	−0.0717604	−	0.0189427i
$580$	−6.79669	−	3.92407i	−0.282217	−	0.162938i
$581$	21.7080	−	29.7197i	0.900600	−	1.23298i
$582$	−8.78283	−	2.31841i	−0.364060	−	0.0961014i
$583$	5.76680	+	9.98838i	0.238836	+	0.413677i
$584$	23.4111			0.968756
$585$	−5.38646	+	9.49180i	−0.222703	+	0.392438i
$586$			5.73145i			0.236764i
$587$	13.2537	+	22.9561i	0.547038	+	0.947498i	0.998476	+	0.0551950i	$0.0175780\pi$
$587$	13.2537	+	22.9561i	0.547038	+	0.947498i	−0.451438	+	0.892303i	$0.649089\pi$
$588$	18.8331	−	12.1941i	0.776665	−	0.502874i
$589$	1.94997	−	3.37745i	0.0803471	−	0.139165i
$590$	−2.97442	−	1.71728i	−0.122455	−	0.0706993i
$591$	27.0798	−	7.36394i	1.11391	−	0.302912i
$592$	6.61496	+	11.4575i	0.271873	+	0.470898i
$593$	−9.48706			−0.389587			−0.194793	−	0.980844i	$-0.562404\pi$
$593$	−9.48706			−0.389587			−0.194793	+	0.980844i	$0.562404\pi$
$594$	8.21142	−	2.29863i	0.336919	−	0.0943141i
$595$	7.11155	+	0.765696i	0.291545	+	0.0313905i
$596$	14.1210	−	8.15275i	0.578418	−	0.333950i
$597$	29.4420	−	8.00632i	1.20498	−	0.327677i
$598$	4.63665	+	2.67697i	0.189607	+	0.109469i
$599$	−24.3866	−	14.0796i	−0.996408	−	0.575276i	−0.0892244	−	0.996012i	$-0.528439\pi$
$599$	−24.3866	−	14.0796i	−0.996408	−	0.575276i	−0.907184	+	0.420735i	$0.861772\pi$
$600$	−1.83015	−	1.81660i	−0.0747156	−	0.0741625i
$601$	−31.7370	+	18.3234i	−1.29458	+	0.747425i	−0.979462	−	0.201628i	$-0.935377\pi$
$601$	−31.7370	+	18.3234i	−1.29458	+	0.747425i	−0.315116	+	0.949053i	$0.602043\pi$
$602$	1.11375	−	10.3442i	0.0453930	−	0.421597i
$603$	−0.211699	−	28.4902i	−0.00862104	−	1.16021i
$604$	−2.34029			−0.0952252
$605$	3.50689	+	6.07411i	0.142575	+	0.246948i
$606$	3.27413	−	12.4034i	0.133003	−	0.503852i
$607$	21.6527	+	12.5012i	0.878855	+	0.507407i	0.870281	−	0.492556i	$-0.163937\pi$
$607$	21.6527	+	12.5012i	0.878855	+	0.507407i	0.00857405	+	0.999963i	$0.497271\pi$
$608$	−10.8351	+	18.7670i	−0.439423	+	0.761103i
$609$	−6.94352	+	18.1524i	−0.281366	+	0.735573i
$610$	−2.34509	−	4.06182i	−0.0949501	−	0.164458i
$611$		−	35.1243i		−	1.42098i
$612$	0.111517	+	15.0078i	0.00450780	+	0.606655i
$613$	12.4336			0.502188			0.251094	−	0.967963i	$-0.419210\pi$
$613$	12.4336			0.502188			0.251094	+	0.967963i	$0.419210\pi$
$614$	−1.17513	−	2.03538i	−0.0474244	−	0.0821414i
$615$	−0.349598	+	0.352205i	−0.0140971	+	0.0142023i
$616$	9.86089	−	13.5002i	0.397306	−	0.543939i
$617$	4.00794	+	2.31398i	0.161353	+	0.0931575i	0.578502	−	0.815681i	$-0.303637\pi$
$617$	4.00794	+	2.31398i	0.161353	+	0.0931575i	−0.417149	+	0.908838i	$0.636971\pi$
$618$	0.401123	+	1.47507i	0.0161355	+	0.0593359i
$619$	−18.3309	+	10.5834i	−0.736783	+	0.425382i	−0.820898	−	0.571074i	$-0.806527\pi$
$619$	−18.3309	+	10.5834i	−0.736783	+	0.425382i	0.0841156	+	0.996456i	$0.473193\pi$
$620$			1.39406i			0.0559869i
$621$	−5.33162	−	19.0462i	−0.213950	−	0.764296i
$622$		−	3.97215i		−	0.159269i
$623$	6.72506	+	15.2084i	0.269434	+	0.609313i
$624$	−19.0029	+	5.16755i	−0.760724	+	0.206868i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	3.14671	−	5.45027i	0.125768	−	0.217837i
$627$	−26.8098	+	27.0098i	−1.07068	+	1.07867i
$628$	1.57391	−	0.908696i	0.0628058	−	0.0362609i
$629$	11.4439			0.456299
$630$	−1.79170	+	2.49161i	−0.0713829	+	0.0992682i
$631$	28.3793			1.12976			0.564882	−	0.825172i	$-0.308922\pi$
$631$	28.3793			1.12976			0.564882	+	0.825172i	$0.308922\pi$
$632$	−2.72431	+	1.57288i	−0.108367	+	0.0625659i
$633$	11.2794	+	2.97743i	0.448316	+	0.118342i
$634$	−6.44429	+	11.1618i	−0.255935	+	0.443293i
$635$	−7.31269	+	12.6659i	−0.290195	+	0.502633i
$636$	2.22301	−	8.42142i	0.0881482	−	0.333931i
$637$	24.2585	−	7.74623i	0.961156	−	0.306917i
$638$			6.95978i			0.275540i
$639$	17.7979	+	30.3045i	0.704073	+	1.19883i
$640$		−	10.1630i		−	0.401730i
$641$	−23.6678	+	13.6646i	−0.934821	+	0.539719i	−0.888333	−	0.459200i	$-0.848136\pi$
$641$	−23.6678	+	13.6646i	−0.934821	+	0.539719i	−0.0464877	+	0.998919i	$0.514803\pi$
$642$	−2.11862	+	2.13442i	−0.0836151	+	0.0842387i
$643$	33.1113	+	19.1168i	1.30578	+	0.753894i	0.981389	−	0.192029i	$-0.0615067\pi$
$643$	33.1113	+	19.1168i	1.30578	+	0.753894i	0.324393	+	0.945922i	$0.394840\pi$
$644$	−15.0488	−	10.9920i	−0.593006	−	0.433146i
$645$	−4.62240	−	16.9982i	−0.182007	−	0.669302i
$646$	2.70564	+	4.68630i	0.106452	+	0.184380i
$647$	−14.5947			−0.573775			−0.286887	−	0.957964i	$-0.592621\pi$
$647$	−14.5947			−0.573775			−0.286887	+	0.957964i	$0.592621\pi$
$648$	−11.7023	−	6.52638i	−0.459708	−	0.256380i
$649$		−	37.7014i		−	1.47991i
$650$	−0.703292	−	1.21814i	−0.0275854	−	0.0477793i
$651$	3.40911	−	0.544070i	0.133613	−	0.0213238i
$652$	−9.16716	+	15.8780i	−0.359014	+	0.621830i
$653$	14.2573	+	8.23145i	0.557931	+	0.322122i	0.752315	−	0.658804i	$-0.228937\pi$
$653$	14.2573	+	8.23145i	0.557931	+	0.322122i	−0.194384	+	0.980926i	$0.562271\pi$
$654$	−1.31551	−	1.30577i	−0.0514406	−	0.0510598i
$655$	−5.64780	−	9.78227i	−0.220678	−	0.382225i
$656$	−0.895455			−0.0349616
$657$	−23.8902	−	40.6780i	−0.932047	−	1.58700i
$658$	1.05733	−	9.82020i	0.0412192	−	0.382831i
$659$	15.9994	−	9.23728i	0.623249	−	0.359833i	−0.154884	−	0.987933i	$-0.549500\pi$
$659$	15.9994	−	9.23728i	0.623249	−	0.359833i	0.778133	+	0.628100i	$0.216167\pi$
$660$	3.47202	−	13.1530i	0.135148	−	0.511981i
$661$	19.0057	+	10.9729i	0.739234	+	0.426797i	0.821791	−	0.569789i	$-0.192975\pi$
$661$	19.0057	+	10.9729i	0.739234	+	0.426797i	−0.0825565	+	0.996586i	$0.526308\pi$
$662$	−8.70349	−	5.02496i	−0.338271	−	0.195301i
$663$	−4.34768	+	16.4703i	−0.168850	+	0.639653i
$664$	−17.9351	+	10.3549i	−0.696018	+	0.401846i
$665$	1.46623	−	13.6179i	0.0568581	−	0.528081i
$666$	−2.42341	+	4.27043i	−0.0939051	+	0.165476i
$667$	16.1430			0.625060
$668$	−1.72543	−	2.98853i	−0.0667588	−	0.115630i
$669$	6.90467	+	6.85355i	0.266950	+	0.264974i
$670$	3.18004	+	1.83600i	0.122856	+	0.0709307i
$671$	25.7422	−	44.5869i	0.993768	−	1.72126i
$672$	−18.9429	+	3.02316i	−0.730740	+	0.116621i
$673$	−6.33688	−	10.9758i	−0.244269	−	0.423086i	0.717657	−	0.696397i	$-0.245215\pi$
$673$	−6.33688	−	10.9758i	−0.244269	−	0.423086i	−0.961926	+	0.273311i	$0.911881\pi$
$674$			2.13851i			0.0823722i
$675$	−1.28884	+	5.03378i	−0.0496075	+	0.193750i
$676$	−0.433476			−0.0166722
$677$	−24.0294	−	41.6202i	−0.923526	−	1.59959i	−0.793915	−	0.608028i	$-0.791961\pi$
$677$	−24.0294	−	41.6202i	−0.923526	−	1.59959i	−0.129610	−	0.991565i	$-0.541373\pi$
$678$	0.817132	+	3.00488i	0.0313818	+	0.115402i
$679$	28.9794	+	21.1673i	1.11213	+	0.812325i
$680$	−3.48564	−	2.01243i	−0.133668	−	0.0771734i
$681$	17.7445	−	17.8768i	0.679970	−	0.685041i
$682$	1.07064	−	0.618132i	0.0409968	−	0.0236695i
$683$		−	16.8700i		−	0.645512i	−0.946482	−	0.322756i	$-0.895391\pi$
$683$		−	16.8700i		−	0.645512i	0.946482	−	0.322756i	$-0.104609\pi$
$684$	28.7385	−	0.213544i	1.09884	−	0.00816507i
$685$		−	16.6912i		−	0.637737i
$686$	7.01547	−	1.43548i	0.267852	−	0.0548069i
$687$	−9.52717	+	36.0917i	−0.363484	+	1.37698i
$688$	15.8929	−	27.5274i	0.605913	−	1.04947i
$689$	4.94290	−	8.56135i	0.188309	−	0.326162i
$690$	2.46466	+	0.650600i	0.0938281	+	0.0247679i
$691$	−17.7426	+	10.2437i	−0.674959	+	0.389688i	−0.797953	−	0.602720i	$-0.794084\pi$
$691$	−17.7426	+	10.2437i	−0.674959	+	0.389688i	0.122994	+	0.992407i	$0.460750\pi$
$692$	14.5535			0.553239
$693$	−33.5201	−	3.35732i	−1.27332	−	0.127534i
$694$	7.23164			0.274509
$695$	7.61828	−	4.39842i	0.288978	−	0.166841i
$696$	7.70436	−	7.76182i	0.292033	−	0.294211i
$697$	−0.387285	+	0.670798i	−0.0146695	+	0.0254083i
$698$	−3.93585	+	6.81710i	−0.148974	+	0.258031i
$699$	13.3988	−	3.64360i	0.506789	−	0.137814i
$700$	1.98002	+	4.47773i	0.0748377	+	0.169242i
$701$		−	21.3800i		−	0.807513i	−0.914867	−	0.403756i	$-0.867704\pi$
$701$		−	21.3800i		−	0.807513i	0.914867	−	0.403756i	$-0.132296\pi$
$702$	−5.22540	−	5.11020i	−0.197220	−	0.192872i
$703$		−	21.9140i		−	0.826502i
$704$	17.0264	−	9.83019i	0.641706	−	0.370489i
$705$	−4.38826	−	16.1372i	−0.165271	−	0.607760i
$706$	2.55107	+	1.47286i	0.0960109	+	0.0554319i
$707$	−29.8930	+	40.9255i	−1.12424	+	1.53916i
$708$	−20.0572	+	20.2068i	−0.753796	+	0.759418i
$709$	−11.1926	−	19.3862i	−0.420349	−	0.728065i	0.575625	−	0.817714i	$-0.304759\pi$
$709$	−11.1926	−	19.3862i	−0.420349	−	0.728065i	−0.995973	+	0.0896487i	$0.971426\pi$
$710$	−4.52951			−0.169990
$711$	5.51305	+	3.12857i	0.206755	+	0.117331i
$712$		−	9.35730i		−	0.350680i
$713$	−1.43374	−	2.48331i	−0.0536940	−	0.0930007i
$714$	−1.71134	+	4.47396i	−0.0640454	+	0.167434i
$715$	7.72008	−	13.3716i	0.288715	−	0.500069i
$716$	−6.74798	−	3.89595i	−0.252184	−	0.145598i
$717$	12.4832	−	47.2899i	0.466192	−	1.76607i
$718$	2.61578	+	4.53066i	0.0976201	+	0.169083i
$719$	29.8224			1.11219			0.556095	−	0.831119i	$-0.312299\pi$
$719$	29.8224			1.11219			0.556095	+	0.831119i	$0.312299\pi$
$720$	−8.08488	+	4.74826i	−0.301306	+	0.176957i
$721$	0.646495	−	6.00445i	0.0240767	−	0.223617i
$722$	2.61172	−	1.50788i	0.0971981	−	0.0561174i
$723$	17.6723	+	17.5415i	0.657240	+	0.652374i
$724$	2.21621	+	1.27953i	0.0823650	+	0.0475534i
$725$	−3.67289	−	2.12054i	−0.136408	−	0.0787550i
$726$	−4.53249	+	1.23254i	−0.168217	+	0.0457440i
$727$	−6.90885	+	3.98882i	−0.256235	+	0.147937i	−0.622616	−	0.782528i	$-0.713930\pi$
$727$	−6.90885	+	3.98882i	−0.256235	+	0.147937i	0.366381	+	0.930465i	$0.380597\pi$
$728$	−14.2472	−	1.53399i	−0.528036	−	0.0568533i
$729$	0.601817	+	26.9933i	0.0222895	+	0.999752i
$730$	6.08000			0.225031
$731$	−13.7474	−	23.8112i	−0.508467	−	0.880691i
$732$	−37.5174	+	10.2023i	−1.38668	+	0.377088i
$733$	4.66110	+	2.69109i	0.172162	+	0.0993975i	0.583605	−	0.812038i	$-0.301642\pi$
$733$	4.66110	+	2.69109i	0.172162	+	0.0993975i	−0.411443	+	0.911435i	$0.634975\pi$
$734$	0.231744	−	0.401392i	0.00855383	−	0.0148157i
$735$	10.1773	−	6.58959i	0.375395	−	0.243061i
$736$	7.96667	+	13.7987i	0.293655	+	0.508626i
$737$			40.3077i			1.48475i
$738$	−0.168303	−	0.286571i	−0.00619532	−	0.0105488i
$739$	7.85381			0.288907			0.144453	−	0.989512i	$-0.453858\pi$
$739$	7.85381			0.288907			0.144453	+	0.989512i	$0.453858\pi$
$740$	3.91666	+	6.78386i	0.143979	+	0.249380i
$741$	31.5390	+	8.32540i	1.15862	+	0.305841i
$742$	1.63968	−	2.24483i	0.0601944	−	0.0824101i
$743$	−40.8901	−	23.6079i	−1.50011	−	0.866089i	−1.00000		0.000128167i	$-0.999959\pi$
$743$	−40.8901	−	23.6079i	−1.50011	−	0.866089i	−0.500111	−	0.865961i	$-0.666707\pi$
$744$	−1.87828	−	0.495811i	−0.0688610	−	0.0181773i
$745$	7.63089	−	4.40570i	0.279574	−	0.161412i
$746$		−	10.9879i		−	0.402295i
$747$	36.2944	+	20.5965i	1.32794	+	0.753587i
$748$		−	21.2330i		−	0.776354i
$749$	10.8662	−	4.80496i	0.397042	−	0.175569i
$750$	−0.475302	−	0.471783i	−0.0173556	−	0.0172271i
$751$	17.4591	−	30.2400i	0.637090	−	1.10347i	−0.348978	−	0.937131i	$-0.613471\pi$
$751$	17.4591	−	30.2400i	0.637090	−	1.10347i	0.986068	−	0.166342i	$-0.0531956\pi$
$752$	15.0879	−	26.1330i	0.550199	−	0.952973i
$753$	13.0690	+	48.0592i	0.476261	+	1.75138i
$754$	5.16623	−	2.98272i	0.188143	−	0.108624i
$755$	−1.26468			−0.0460264
$756$	16.1797	+	19.6322i	0.588449	+	0.714016i
$757$	−11.7811			−0.428190			−0.214095	−	0.976813i	$-0.568680\pi$
$757$	−11.7811			−0.428190			−0.214095	+	0.976813i	$0.568680\pi$
$758$	−7.97809	+	4.60615i	−0.289777	+	0.167303i
$759$	7.34251	+	27.0010i	0.266516	+	0.980072i
$760$	−3.85362	+	6.67467i	−0.139786	+	0.242116i
$761$	−25.6257	+	44.3849i	−0.928929	+	1.60895i	−0.143813	+	0.989605i	$0.545936\pi$
$761$	−25.6257	+	44.3849i	−0.928929	+	1.60895i	−0.785117	+	0.619348i	$0.787397\pi$
$762$	−6.95147	−	6.90000i	−0.251825	−	0.249961i
$763$	2.96146	+	6.69721i	0.107212	+	0.242455i
$764$			10.5630i			0.382157i
$765$	0.0602630	+	8.11012i	0.00217881	+	0.293222i
$766$			5.97499i			0.215885i
$767$	−27.9856	+	16.1575i	−1.01050	+	0.583414i
$768$	−8.93433	−	2.35840i	−0.322390	−	0.0851016i
$769$	−3.05041	−	1.76116i	−0.110001	−	0.0635089i	0.443990	−	0.896032i	$-0.353562\pi$
$769$	−3.05041	−	1.76116i	−0.110001	−	0.0635089i	−0.553991	+	0.832523i	$0.686896\pi$
$770$	2.56093	−	3.50609i	0.0922897	−	0.126351i
$771$	26.6109	+	7.02451i	0.958367	+	0.252981i
$772$	−0.954005	−	1.65239i	−0.0343354	−	0.0594706i
$773$	36.9128			1.32766			0.663831	−	0.747882i	$-0.268929\pi$
$773$	36.9128			1.32766			0.663831	+	0.747882i	$0.268929\pi$
$774$	11.7967	−	0.0876561i	0.424022	−	0.00315074i
$775$			0.753343i			0.0270609i
$776$	−10.0969	−	17.4884i	−0.362458	−	0.627796i
$777$	15.0610	−	12.2256i	0.540310	−	0.438590i
$778$	−7.25675	+	12.5691i	−0.260167	+	0.450623i
$779$	1.28451	+	0.741614i	0.0460225	+	0.0265711i
$780$	−11.2514	+	3.05966i	−0.402866	+	0.109554i
$781$	−24.8604	−	43.0594i	−0.889574	−	1.54079i
$782$	3.97871			0.142278
$783$	−21.3487	−	5.46608i	−0.762939	−	0.195342i
$784$	21.3761	+	4.65710i	0.763434	+	0.166325i
$785$	0.850530	−	0.491054i	0.0303567	−	0.0175265i
$786$	7.29952	−	1.98500i	0.260365	−	0.0708024i
$787$	−20.1637	−	11.6415i	−0.718759	−	0.414976i	0.0955367	−	0.995426i	$-0.469543\pi$
$787$	−20.1637	−	11.6415i	−0.718759	−	0.414976i	−0.814296	+	0.580450i	$0.802877\pi$
$788$	25.9655	+	14.9912i	0.924983	+	0.534039i
$789$	−1.45399	−	1.44323i	−0.0517636	−	0.0513804i
$790$	−0.707521	+	0.408488i	−0.0251725	+	0.0145333i
$791$	1.31698	−	12.2317i	0.0468265	−	0.434910i
$792$	16.4868	+	9.35599i	0.585831	+	0.332451i
$793$	−44.1289			−1.56706
$794$	2.45953	+	4.26002i	0.0872853	+	0.151183i
$795$	1.20130	−	4.55088i	0.0426058	−	0.161403i
$796$	28.2305	+	16.2989i	1.00060	+	0.577699i
$797$	−15.1425	+	26.2275i	−0.536373	+	0.929026i	0.462722	+	0.886503i	$0.346873\pi$
$797$	−15.1425	+	26.2275i	−0.536373	+	0.929026i	−0.999096	+	0.0425225i	$0.986461\pi$
$798$	8.56720	+	3.27706i	0.303276	+	0.116007i
$799$	−13.0511	−	22.6051i	−0.461714	−	0.799712i
$800$		−	4.18600i		−	0.147997i
$801$	−16.2588	+	9.54882i	−0.574478	+	0.337391i
$802$	−5.63580			−0.199007
$803$	33.3703	+	57.7990i	1.17761	+	2.03968i
$804$	21.4438	−	21.6037i	0.756264	−	0.761904i
$805$	−8.13227	−	5.94002i	−0.286625	−	0.209358i
$806$	−0.917676	−	0.529820i	−0.0323237	−	0.0186621i
$807$	4.92655	+	18.1166i	0.173423	+	0.637736i
$808$	24.6976	−	14.2591i	0.868857	−	0.501635i
$809$			28.5991i			1.00549i	0.864434	+	0.502746i	$0.167677\pi$
$809$			28.5991i			1.00549i	−0.864434	+	0.502746i	$0.832323\pi$
$810$	−3.03915	−	1.69494i	−0.106785	−	0.0595542i
$811$			30.1445i			1.05852i	0.848461	+	0.529258i	$0.177530\pi$
$811$			30.1445i			1.05852i	−0.848461	+	0.529258i	$0.822470\pi$
$812$	−18.9904	+	8.39743i	−0.666433	+	0.294692i
$813$	36.1178	−	9.82170i	1.26671	−	0.344462i
$814$	3.47332	−	6.01597i	0.121740	−	0.210860i
$815$	−4.95388	+	8.58036i	−0.173527	+	0.300557i
$816$	−10.3097	+	10.3866i	−0.360911	+	0.363603i
$817$	−45.5963	+	26.3250i	−1.59521	+	0.920996i
$818$	14.6058			0.510679
$819$	11.8734	+	26.3207i	0.414891	+	0.919720i
$820$	−0.530191			−0.0185151
$821$	−32.7300	+	18.8967i	−1.14229	+	0.659499i	−0.946996	−	0.321246i	$-0.895898\pi$
$821$	−32.7300	+	18.8967i	−1.14229	+	0.659499i	−0.195290	+	0.980745i	$0.562565\pi$
$822$	10.8078	+	2.85294i	0.376965	+	0.0995078i
$823$	25.9752	−	44.9904i	0.905439	−	1.56827i	0.0851124	−	0.996371i	$-0.472875\pi$
$823$	25.9752	−	44.9904i	0.905439	−	1.56827i	0.820327	−	0.571895i	$-0.193792\pi$
$824$	−1.69915	+	2.94301i	−0.0591925	+	0.102524i
$825$	1.87626	−	7.10781i	0.0653229	−	0.247462i
$826$	−8.31073	+	3.67494i	−0.289167	+	0.127868i
$827$			16.7067i			0.580949i	0.956883	+	0.290475i	$0.0938132\pi$
$827$			16.7067i			0.580949i	−0.956883	+	0.290475i	$0.906187\pi$
$828$	10.4292	−	18.3779i	0.362440	−	0.638677i
$829$			43.0971i			1.49682i	0.663235	+	0.748411i	$0.269183\pi$
$829$			43.0971i			1.49682i	−0.663235	+	0.748411i	$0.730817\pi$
$830$	−4.65787	+	2.68922i	−0.161677	+	0.0933442i
$831$	6.75387	−	6.80424i	0.234289	−	0.236037i
$832$	−14.5938	−	8.42576i	−0.505951	−	0.292111i
$833$	12.7339	−	13.9990i	0.441203	−	0.485035i
$834$	1.54588	+	5.68475i	0.0535296	+	0.196847i
$835$	−0.932410	−	1.61498i	−0.0322674	−	0.0558888i
$836$	−40.6591			−1.40622
$837$	1.05522	+	3.76957i	0.0364738	+	0.130296i
$838$			0.351504i			0.0121425i
$839$	−3.43018	−	5.94125i	−0.118423	−	0.205115i	0.800720	−	0.599039i	$-0.204451\pi$
$839$	−3.43018	−	5.94125i	−0.118423	−	0.205115i	−0.919143	+	0.393924i	$0.871117\pi$
$840$	−6.73724	+	1.07522i	−0.232457	+	0.0370985i
$841$	−5.50660	+	9.53771i	−0.189883	+	0.328887i
$842$	−1.43281	−	0.827232i	−0.0493778	−	0.0285083i
$843$	−21.9674	−	21.8048i	−0.756597	−	0.750996i
$844$	6.23178	+	10.7938i	0.214507	+	0.371536i
$845$	−0.234248			−0.00805837
$846$	11.1991	−	0.0832160i	0.385033	−	0.00286103i
$847$	18.4501	+	1.98651i	0.633952	+	0.0682572i
$848$	7.35519	−	4.24652i	0.252578	−	0.145826i
$849$	−3.12886	+	11.8530i	−0.107382	+	0.406795i
$850$	−0.905243	−	0.522642i	−0.0310496	−	0.0179265i
$851$	−13.9539	−	8.05627i	−0.478333	−	0.276166i
$852$	−9.58330	+	36.3043i	−0.328318	+	1.24377i
$853$	15.8246	−	9.13635i	0.541825	−	0.312823i	−0.203994	−	0.978972i	$-0.565392\pi$
$853$	15.8246	−	9.13635i	0.541825	−	0.312823i	0.745818	+	0.666150i	$0.232059\pi$
$854$	−12.3378	−	1.32840i	−0.422189	−	0.0454568i
$855$	15.5301	−	0.115398i	0.531118	−	0.00394653i
$856$	−6.68565			−0.228511
$857$	−6.20774	−	10.7521i	−0.212052	−	0.367285i	0.740304	−	0.672272i	$-0.234681\pi$
$857$	−6.20774	−	10.7521i	−0.212052	−	0.367285i	−0.952357	+	0.304986i	$0.901348\pi$
$858$	7.33874	+	7.28441i	0.250540	+	0.248686i
$859$	−3.69582	−	2.13378i	−0.126100	−	0.0728038i	0.435623	−	0.900129i	$-0.356528\pi$
$859$	−3.69582	−	2.13378i	−0.126100	−	0.0728038i	−0.561723	+	0.827325i	$0.689861\pi$
$860$	9.41008	−	16.2987i	0.320881	−	0.555782i
$861$	0.206921	+	1.29655i	0.00705186	+	0.0441865i
$862$	2.29361	+	3.97265i	0.0781206	+	0.135309i
$863$			16.8919i			0.575008i	0.957779	+	0.287504i	$0.0928255\pi$
$863$			16.8919i			0.575008i	−0.957779	+	0.287504i	$0.907175\pi$
$864$	−5.86341	−	20.9459i	−0.199477	−	0.712594i
$865$	7.86459			0.267404
$866$	−2.91537	−	5.04957i	−0.0990683	−	0.171591i
$867$	−4.40473	−	16.1977i	−0.149592	−	0.550103i
$868$	2.97842	+	2.17552i	0.101094	+	0.0738418i
$869$	−7.76651	−	4.48400i	−0.263461	−	0.152109i
$870$	2.00087	−	2.01579i	0.0678359	−	0.0683418i
$871$	29.9203	−	17.2745i	1.01381	−	0.585324i
$872$		−	4.12059i		−	0.139541i
$873$	−20.0834	+	35.3903i	−0.679722	+	1.19778i
$874$		−	7.61885i		−	0.257711i
$875$	1.06999	+	2.41974i	0.0361723	+	0.0818020i
$876$	12.8637	−	48.7316i	0.434625	−	1.64649i
$877$	5.91368	−	10.2428i	0.199691	−	0.345875i	−0.748737	−	0.662867i	$-0.769340\pi$
$877$	5.91368	−	10.2428i	0.199691	−	0.345875i	0.948428	+	0.316992i	$0.102673\pi$
$878$	7.54672	−	13.0713i	0.254689	−	0.441135i
$879$	24.8246	+	6.55297i	0.837312	+	0.221026i
$880$	11.4877	−	6.63244i	0.387251	−	0.223580i
$881$	−2.38825			−0.0804622			−0.0402311	−	0.999190i	$-0.512809\pi$
$881$	−2.38825			−0.0804622			−0.0402311	+	0.999190i	$0.512809\pi$
$882$	2.52730	+	7.71628i	0.0850986	+	0.259821i
$883$	−6.82573			−0.229704			−0.114852	−	0.993383i	$-0.536639\pi$
$883$	−6.82573			−0.229704			−0.114852	+	0.993383i	$0.536639\pi$
$884$	−15.7612	+	9.09971i	−0.530105	+	0.306056i
$885$	−10.8388	+	10.9196i	−0.364342	+	0.367059i
$886$	3.48486	−	6.03596i	0.117076	−	0.202782i
$887$	13.5359	−	23.4449i	0.454492	−	0.787203i	−0.544167	−	0.838977i	$-0.683154\pi$
$887$	13.5359	−	23.4449i	0.454492	−	0.787203i	0.998659	+	0.0517739i	$0.0164875\pi$
$888$	−10.5332	+	2.86434i	−0.353470	+	0.0961209i
$889$	15.6490	+	35.3895i	0.524851	+	1.18693i
$890$		−	2.43015i		−	0.0814588i
$891$	−0.567642	−	38.1942i	−0.0190167	−	1.27955i
$892$			10.3939i			0.348014i
$893$	−43.2866	+	24.9916i	−1.44853	+	0.836310i
$894$	1.54844	+	5.69416i	0.0517877	+	0.190441i
$895$	−3.64656	−	2.10534i	−0.121891	−	0.0703739i
$896$	−21.7134	−	15.8600i	−0.725394	−	0.529846i
$897$	16.8960	−	17.0220i	0.564141	−	0.568348i
$898$	−3.39948	−	5.88807i	−0.113442	−	0.196487i
$899$	−3.19499			−0.106559
$900$	−4.78699	+	2.81140i	−0.159566	+	0.0937134i
$901$		−	7.34650i		−	0.244747i
$902$	0.235088	+	0.407185i	0.00782759	+	0.0135578i
$903$	−43.5302	−	16.6508i	−1.44860	−	0.554105i
$904$	−3.46135	+	5.99523i	−0.115123	+	0.199398i
$905$	1.19763	+	0.691451i	0.0398105	+	0.0229846i
$906$	0.216166	−	0.818899i	0.00718162	−	0.0272061i
$907$	−10.3947	−	18.0042i	−0.345151	−	0.597820i	0.640230	−	0.768183i	$-0.278839\pi$
$907$	−10.3947	−	18.0042i	−0.345151	−	0.597820i	−0.985381	+	0.170364i	$0.945506\pi$
$908$	26.9108			0.893067
$909$	−49.9792	−	28.3624i	−1.65770	−	0.940722i
$910$	−3.70009	−	0.398386i	−0.122657	−	0.0132064i
$911$	−33.8775	+	19.5592i	−1.12241	+	0.648024i	−0.942015	−	0.335570i	$-0.891071\pi$
$911$	−33.8775	+	19.5592i	−1.12241	+	0.648024i	−0.180396	+	0.983594i	$0.557738\pi$
$912$	19.8893	+	19.7421i	0.658600	+	0.653725i
$913$	−51.1297	−	29.5198i	−1.69215	−	0.976961i
$914$	−2.65555	−	1.53318i	−0.0878378	−	0.0507132i
$915$	−20.2742	+	5.51326i	−0.670243	+	0.182263i
$916$	−34.5378	+	19.9404i	−1.14116	+	0.658849i
$917$	−29.7136	−	3.19924i	−0.981230	−	0.105648i
$918$	−5.26173	−	1.34720i	−0.173663	−	0.0444643i
$919$	0.643554			0.0212289			0.0106144	−	0.999944i	$-0.496621\pi$
$919$	0.643554			0.0212289			0.0106144	+	0.999944i	$0.496621\pi$
$920$	2.83342	+	4.90763i	0.0934152	+	0.161800i
$921$	−10.1594	+	2.76270i	−0.334764	+	0.0910341i
$922$	−2.69294	−	1.55477i	−0.0886873	−	0.0512036i
$923$	−21.3086	+	36.9076i	−0.701381	+	1.21483i
$924$	−22.6832	−	27.9441i	−0.746224	−	0.919292i
$925$	2.11654	+	3.66595i	0.0695914	+	0.120536i
$926$			7.50516i			0.246635i
$927$	6.84757	−	0.0508815i	0.224904	−	0.00167117i
$928$	17.7532			0.582777
$929$	−0.117189	−	0.202978i	−0.00384486	−	0.00665950i	0.864097	−	0.503326i	$-0.167891\pi$
$929$	−0.117189	−	0.202978i	−0.00384486	−	0.00665950i	−0.867941	+	0.496667i	$0.834557\pi$
$930$	−0.487801	−	0.128765i	−0.0159956	−	0.00422238i
$931$	−26.8067	−	24.3842i	−0.878553	−	0.799160i
$932$	12.8475	+	7.41748i	0.420832	+	0.242968i
$933$	−17.2045	−	4.54150i	−0.563251	−	0.148682i
$934$	5.19797	−	3.00105i	0.170083	−	0.0981973i
$935$		−	11.4742i		−	0.375245i
$936$	−0.120730	−	16.2477i	−0.00394619	−	0.531074i
$937$			18.1699i			0.593584i	0.954942	+	0.296792i	$0.0959167\pi$
$937$			18.1699i			0.593584i	−0.954942	+	0.296792i	$0.904083\pi$
$938$	8.88525	−	3.92900i	0.290114	−	0.128286i
$939$	−20.0089	−	19.8608i	−0.652967	−	0.648133i
$940$	8.93342	−	15.4731i	0.291376	−	0.504678i
$941$	−0.276744	+	0.479335i	−0.00902160	+	0.0156259i	−0.870501	−	0.492167i	$-0.836205\pi$
$941$	−0.276744	+	0.479335i	−0.00902160	+	0.0156259i	0.861479	+	0.507793i	$0.169538\pi$
$942$	0.172587	+	0.634664i	0.00562320	+	0.0206785i
$943$	0.944455	−	0.545281i	0.0307557	−	0.0177568i
$944$	−27.7623			−0.903587
$945$	8.74339	+	10.6091i	0.284422	+	0.345114i
$946$	−16.6898			−0.542633
$947$	20.8441	−	12.0343i	0.677341	−	0.391063i	−0.121511	−	0.992590i	$-0.538774\pi$
$947$	20.8441	−	12.0343i	0.677341	−	0.391063i	0.798852	+	0.601527i	$0.205441\pi$
$948$	1.77712	+	6.53509i	0.0577182	+	0.212250i
$949$	28.6027	−	49.5413i	0.928483	−	1.60818i
$950$	−1.00081	+	1.73345i	−0.0324706	+	0.0562406i
$951$	40.9772	+	40.6738i	1.32878	+	1.31894i
$952$	−9.73912	+	4.30657i	−0.315647	+	0.139577i
$953$			10.9096i			0.353398i	0.984265	+	0.176699i	$0.0565418\pi$
$953$			10.9096i			0.353398i	−0.984265	+	0.176699i	$0.943458\pi$
$954$	2.74143	+	1.55572i	0.0887571	+	0.0503684i
$955$			5.70820i			0.184713i
$956$	45.2538	−	26.1273i	1.46361	−	0.845017i
$957$	30.1448	+	7.95737i	0.974444	+	0.257225i
$958$	−3.18093	−	1.83651i	−0.102771	−	0.0593349i
$959$	−35.6608	−	26.0475i	−1.15155	−	0.841119i
$960$	−7.75752	−	2.04776i	−0.250373	−	0.0660913i
$961$	−15.2162	−	26.3553i	−0.490846	−	0.850171i
$962$	−5.95418			−0.191971
$963$	6.82249	+	11.6167i	0.219852	+	0.374343i
$964$			26.6029i			0.856823i
$965$	−0.515538	−	0.892938i	−0.0165958	−	0.0287447i
$966$	5.23626	−	4.25047i	0.168474	−	0.136757i
$967$	−8.30830	+	14.3904i	−0.267177	+	0.462764i	−0.968132	−	0.250442i	$-0.919424\pi$
$967$	−8.30830	+	14.3904i	−0.267177	+	0.462764i	0.700955	+	0.713206i	$0.252757\pi$
$968$	−9.04308	−	5.22103i	−0.290656	−	0.167810i
$969$	23.3912	−	6.36088i	0.751433	−	0.204341i
$970$	−2.62223	−	4.54184i	−0.0841948	−	0.145830i
$971$	−31.5538			−1.01261			−0.506305	−	0.862354i	$-0.668989\pi$
$971$	−31.5538			−1.01261			−0.506305	+	0.862354i	$0.668989\pi$
$972$	−20.0151	+	20.7729i	−0.641986	+	0.666292i
$973$	2.49152	−	23.1405i	0.0798745	−	0.741850i
$974$	12.0580	−	6.96171i	0.386365	−	0.223068i
$975$	−6.08021	+	1.65342i	−0.194723	+	0.0529519i
$976$	−32.8326	−	18.9559i	−1.05095	−	0.606764i
$977$	−18.5295	−	10.6980i	−0.592810	−	0.342259i	0.173398	−	0.984852i	$-0.444525\pi$
$977$	−18.5295	−	10.6980i	−0.592810	−	0.342259i	−0.766208	+	0.642593i	$0.777859\pi$
$978$	−4.70917	−	4.67431i	−0.150583	−	0.149468i
$979$	23.1020	−	13.3380i	0.738343	−	0.426283i
$980$	12.6566	+	2.75743i	0.404301	+	0.0880828i
$981$	−7.15976	+	4.20493i	−0.228594	+	0.134253i
$982$	−11.6274			−0.371045
$983$	20.6637	+	35.7906i	0.659070	+	1.14154i	0.980857	+	0.194730i	$0.0623830\pi$
$983$	20.6637	+	35.7906i	0.659070	+	1.14154i	−0.321787	+	0.946812i	$0.604284\pi$
$984$	0.188567	−	0.714348i	0.00601131	−	0.0227726i
$985$	14.0316	+	8.10114i	0.447084	+	0.258124i
$986$	2.21657	−	3.83921i	0.0705899	−	0.122265i
$987$	−41.3253	−	15.8074i	−1.31540	−	0.503155i
$988$	17.4251	+	30.1811i	0.554365	+	0.960189i
$989$			38.7116i			1.23096i
$990$	4.28171	+	2.42981i	0.136082	+	0.0772244i
$991$	50.6454			1.60880			0.804402	−	0.594085i	$-0.202486\pi$
$991$	50.6454			1.60880			0.804402	+	0.594085i	$0.202486\pi$
$992$	−1.57675	−	2.73101i	−0.0500618	−	0.0867095i
$993$	−31.7156	+	31.9521i	−1.00646	+	1.01397i
$994$	−7.06856	+	9.67733i	−0.224201	+	0.306946i
$995$	15.2556	+	8.80782i	0.483635	+	0.279227i
$996$	11.6994	+	43.0228i	0.370710	+	1.36323i
$997$	−0.0982245	+	0.0567099i	−0.00311080	+	0.00179602i	−0.501555	−	0.865126i	$-0.667238\pi$
$997$	−0.0982245	+	0.0567099i	−0.00311080	+	0.00179602i	0.498444	+	0.866922i	$0.333905\pi$
$998$		−	16.0988i		−	0.509599i
$999$	15.7257	+	15.3790i	0.497539	+	0.486570i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bl.j.41.5	yes	24
3.2	odd	2		945.2.bl.j.881.8		24
7.6	odd	2		315.2.bl.i.41.5	✓	24
9.2	odd	6		315.2.bl.i.146.5	yes	24
9.7	even	3		945.2.bl.i.251.8		24
21.20	even	2		945.2.bl.i.881.8		24
63.20	even	6	inner	315.2.bl.j.146.5	yes	24
63.34	odd	6		945.2.bl.j.251.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bl.i.41.5	✓	24	7.6	odd	2
315.2.bl.i.146.5	yes	24	9.2	odd	6
315.2.bl.j.41.5	yes	24	1.1	even	1	trivial
315.2.bl.j.146.5	yes	24	63.20	even	6	inner
945.2.bl.i.251.8		24	9.7	even	3
945.2.bl.i.881.8		24	21.20	even	2
945.2.bl.j.251.8		24	63.34	odd	6
945.2.bl.j.881.8		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.334847 + 0.193324i) q^{2} +(0.454500 + 1.67136i) q^{3} +(-0.925251 + 1.60258i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.475302 - 0.471783i) q^{6} +(1.06999 + 2.41974i) q^{7} -1.48879i q^{8} +(-2.58686 + 1.51926i) q^{9} +O(q^{10})\)	\(q+(-0.334847 + 0.193324i) q^{2} +(0.454500 + 1.67136i) q^{3} +(-0.925251 + 1.60258i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.475302 - 0.471783i) q^{6} +(1.06999 + 2.41974i) q^{7} -1.48879i q^{8} +(-2.58686 + 1.51926i) q^{9} -0.386648i q^{10} +(3.67564 - 2.12213i) q^{11} +(-3.09901 - 0.818050i) q^{12} +(-3.15051 - 1.81895i) q^{13} +(-0.826077 - 0.603387i) q^{14} +(-1.67469 - 0.442069i) q^{15} +(-1.56268 - 2.70665i) q^{16} -2.70345 q^{17} +(0.572492 - 1.00882i) q^{18} +5.17685i q^{19} +(-0.925251 - 1.60258i) q^{20} +(-3.55793 + 2.88810i) q^{21} +(-0.820519 + 1.42118i) q^{22} +(3.29639 + 1.90317i) q^{23} +(2.48830 - 0.676656i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.40658 q^{26} +(-3.71496 - 3.63306i) q^{27} +(-4.86784 - 0.524116i) q^{28} +(3.67289 - 2.12054i) q^{29} +(0.646227 - 0.175732i) q^{30} +(-0.652414 - 0.376671i) q^{31} +(3.62518 + 2.09300i) q^{32} +(5.21742 + 5.17879i) q^{33} +(0.905243 - 0.522642i) q^{34} +(-2.63055 - 0.283229i) q^{35} +(-0.0412499 - 5.55136i) q^{36} -4.23308 q^{37} +(-1.00081 - 1.73345i) q^{38} +(1.60820 - 6.09233i) q^{39} +(1.28933 + 0.744395i) q^{40} +(0.143256 - 0.248127i) q^{41} +(0.633022 - 1.65491i) q^{42} +(5.08515 + 8.80773i) q^{43} +7.85402i q^{44} +(-0.0222912 - 2.99992i) q^{45} -1.47172 q^{46} +(4.82756 + 8.36159i) q^{47} +(3.81353 - 3.84197i) q^{48} +(-4.71024 + 5.17819i) q^{49} +(0.334847 + 0.193324i) q^{50} +(-1.22872 - 4.51842i) q^{51} +(5.83002 - 3.36596i) q^{52} +2.71745i q^{53} +(1.94630 + 0.498328i) q^{54} +4.24426i q^{55} +(3.60248 - 1.59299i) q^{56} +(-8.65235 + 2.35288i) q^{57} +(-0.819904 + 1.42012i) q^{58} +(4.44145 - 7.69282i) q^{59} +(2.25796 - 2.27480i) q^{60} +(10.5052 - 6.06518i) q^{61} +0.291279 q^{62} +(-6.44413 - 4.63392i) q^{63} +4.63222 q^{64} +(3.15051 - 1.81895i) q^{65} +(-2.74822 - 0.725452i) q^{66} +(-4.74849 + 8.22463i) q^{67} +(2.50137 - 4.33250i) q^{68} +(-1.68267 + 6.37443i) q^{69} +(0.935587 - 0.413710i) q^{70} -11.7148i q^{71} +(2.26187 + 3.85129i) q^{72} +15.7249i q^{73} +(1.41744 - 0.818357i) q^{74} +(1.22019 - 1.22929i) q^{75} +(-8.29632 - 4.78988i) q^{76} +(9.06790 + 6.62342i) q^{77} +(0.639293 + 2.35090i) q^{78} +(-1.05648 - 1.82988i) q^{79} +3.12537 q^{80} +(4.38368 - 7.86024i) q^{81} +0.110779i q^{82} +(-6.95521 - 12.0468i) q^{83} +(-1.33645 - 8.37410i) q^{84} +(1.35172 - 2.34126i) q^{85} +(-3.40549 - 1.96616i) q^{86} +(5.21351 + 5.17491i) q^{87} +(-3.15941 - 5.47226i) q^{88} +6.28517 q^{89} +(0.587421 + 1.00020i) q^{90} +(1.03036 - 9.56964i) q^{91} +(-6.09998 + 3.52182i) q^{92} +(0.333029 - 1.26161i) q^{93} +(-3.23299 - 1.86657i) q^{94} +(-4.48328 - 2.58842i) q^{95} +(-1.85050 + 7.01024i) q^{96} +(11.7467 - 6.78195i) q^{97} +(0.576143 - 2.64451i) q^{98} +(-6.28429 + 11.0739i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9	\( 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9} + 9 q^{11} - 18 q^{12} + 3 q^{13} + 18 q^{14} + 2 q^{15} - 18 q^{16} + 18 q^{17} + 2 q^{18} + 18 q^{20} + 8 q^{21} - 9 q^{22} + 9 q^{23} - 7 q^{24} - 12 q^{25} - 18 q^{26} - 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} - 42 q^{31} + 18 q^{32} + 13 q^{33} - 39 q^{34} - 9 q^{35} - 21 q^{36} - 12 q^{38} - 21 q^{39} - 6 q^{40} - 33 q^{41} - 65 q^{42} + 18 q^{43} + q^{45} - 30 q^{46} - 17 q^{48} + 9 q^{49} - 6 q^{50} - 12 q^{51} + 129 q^{52} + 52 q^{54} - 9 q^{56} + 6 q^{57} - 15 q^{58} + 12 q^{59} + 15 q^{60} - 15 q^{61} + 12 q^{62} + 46 q^{63} - 60 q^{64} - 3 q^{65} + 29 q^{66} - 15 q^{67} + 9 q^{68} + 61 q^{69} - 9 q^{70} + 61 q^{72} - 18 q^{74} - 7 q^{75} + 54 q^{76} - 45 q^{77} - 66 q^{78} + 21 q^{79} + 36 q^{80} + q^{81} - 30 q^{83} + 15 q^{84} - 9 q^{85} - 102 q^{86} + 10 q^{87} - 9 q^{88} + 102 q^{89} - 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} - 156 q^{94} - 18 q^{95} - 42 q^{96} - 45 q^{97} + 3 q^{98} + 23 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9 + 9 * q^11 - 18 * q^12 + 3 * q^13 + 18 * q^14 + 2 * q^15 - 18 * q^16 + 18 * q^17 + 2 * q^18 + 18 * q^20 + 8 * q^21 - 9 * q^22 + 9 * q^23 - 7 * q^24 - 12 * q^25 - 18 * q^26 - 4 * q^27 - 9 * q^28 + 9 * q^29 - 5 * q^30 - 42 * q^31 + 18 * q^32 + 13 * q^33 - 39 * q^34 - 9 * q^35 - 21 * q^36 - 12 * q^38 - 21 * q^39 - 6 * q^40 - 33 * q^41 - 65 * q^42 + 18 * q^43 + q^45 - 30 * q^46 - 17 * q^48 + 9 * q^49 - 6 * q^50 - 12 * q^51 + 129 * q^52 + 52 * q^54 - 9 * q^56 + 6 * q^57 - 15 * q^58 + 12 * q^59 + 15 * q^60 - 15 * q^61 + 12 * q^62 + 46 * q^63 - 60 * q^64 - 3 * q^65 + 29 * q^66 - 15 * q^67 + 9 * q^68 + 61 * q^69 - 9 * q^70 + 61 * q^72 - 18 * q^74 - 7 * q^75 + 54 * q^76 - 45 * q^77 - 66 * q^78 + 21 * q^79 + 36 * q^80 + q^81 - 30 * q^83 + 15 * q^84 - 9 * q^85 - 102 * q^86 + 10 * q^87 - 9 * q^88 + 102 * q^89 - 37 * q^90 + 42 * q^91 - 3 * q^92 - 6 * q^93 - 156 * q^94 - 18 * q^95 - 42 * q^96 - 45 * q^97 + 3 * q^98 + 23 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more