LMFDB - Embedded newform 315.2.bl.i.146.5

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			146.5
Character	$\chi$	$=$	315.146
Dual form			315.2.bl.i.41.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.334847 - 0.193324i) q^{2} +(-0.454500 + 1.67136i) q^{3} +(-0.925251 - 1.60258i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.475302 - 0.471783i) q^{6} +(1.56056 - 2.13651i) q^{7} +1.48879i q^{8} +(-2.58686 - 1.51926i) q^{9} +O(q^{10})$	\(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} +(1.56056 - 2.13651i) 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} +(-0.935587 + 0.413710i) 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} +(2.86159 + 3.57929i) 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} +(-0.266232 - 1.75173i) 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} +(-2.12932 - 6.66828i) 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} +(3.18081 + 2.32334i) 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} +(-7.28286 + 3.15594i) 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} +(-0.826077 - 0.603387i) 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} +(10.2700 - 4.54132i) 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} +(3.08842 - 7.89767i) 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} + q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 - 5 * q^3 + 18 * q^4 + 12 * q^5 - q^6 + q^9	$ 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9} + 9 q^{11} + 18 q^{12} - 3 q^{13} + 9 q^{14} + 2 q^{15} - 18 q^{16} - 18 q^{17} + 2 q^{18} - 18 q^{20} + 4 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} + 26 q^{42} + 18 q^{43} - q^{45} - 30 q^{46} + 17 q^{48} - 6 q^{50} - 12 q^{51} - 129 q^{52} - 52 q^{54} + 6 q^{56} + 6 q^{57} - 15 q^{58} - 12 q^{59} + 15 q^{60} + 15 q^{61} - 12 q^{62} - 83 q^{63} - 60 q^{64} - 3 q^{65} - 29 q^{66} - 15 q^{67} - 9 q^{68} - 61 q^{69} + 18 q^{70} + 61 q^{72} - 18 q^{74} + 7 q^{75} - 54 q^{76} - 57 q^{77} - 66 q^{78} + 21 q^{79} - 36 q^{80} + q^{81} + 30 q^{83} - 42 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 + q^9 + 9 * q^11 + 18 * q^12 - 3 * q^13 + 9 * q^14 + 2 * q^15 - 18 * q^16 - 18 * q^17 + 2 * q^18 - 18 * q^20 + 4 * 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 + 26 * q^42 + 18 * q^43 - q^45 - 30 * q^46 + 17 * q^48 - 6 * q^50 - 12 * q^51 - 129 * q^52 - 52 * q^54 + 6 * q^56 + 6 * q^57 - 15 * q^58 - 12 * q^59 + 15 * q^60 + 15 * q^61 - 12 * q^62 - 83 * q^63 - 60 * q^64 - 3 * q^65 - 29 * q^66 - 15 * q^67 - 9 * q^68 - 61 * q^69 + 18 * q^70 + 61 * q^72 - 18 * q^74 + 7 * q^75 - 54 * q^76 - 57 * q^77 - 66 * q^78 + 21 * q^79 - 36 * q^80 + q^81 + 30 * q^83 - 42 * 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

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

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	0.376920	−	0.926246i	$-0.376983\pi$
$2$	−0.334847	−	0.193324i	−0.236773	−	0.136701i	−0.613693	+	0.789545i	$0.710317\pi$
$3$	−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
$7$	1.56056	−	2.13651i	0.589835	−	0.807524i
$7$	1.56056	−	2.13651i	0.589835	−	0.807524i
$8$			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	0.938375	−	0.345619i	$-0.112331\pi$
$11$	3.67564	+	2.12213i	1.10825	+	0.639847i	0.169873	+	0.985466i	$0.445664\pi$
$12$	3.09901	−	0.818050i	0.894608	−	0.236151i
$13$	3.15051	−	1.81895i	0.873793	−	0.504485i	0.00518619	−	0.999987i	$-0.498349\pi$
$13$	3.15051	−	1.81895i	0.873793	−	0.504485i	0.868607	+	0.495502i	$0.165016\pi$
$14$	−0.935587	+	0.413710i	−0.250046	+	0.110569i
$15$	−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	$-0.393679\pi$
$17$	2.70345			0.655683			0.327841	+	0.944733i	$0.393679\pi$
$18$	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
$21$	2.86159	+	3.57929i	0.624450	+	0.781065i
$22$	−0.820519	−	1.42118i	−0.174935	−	0.302997i
$23$	3.29639	−	1.90317i	0.687345	−	0.396839i	−0.115272	−	0.993334i	$-0.536774\pi$
$23$	3.29639	−	1.90317i	0.687345	−	0.396839i	0.802616	+	0.596495i	$0.203441\pi$
$24$	−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	0.800622	−	0.599169i	$-0.204502\pi$
$29$	3.67289	+	2.12054i	0.682038	+	0.393775i	−0.118584	+	0.992944i	$0.537836\pi$
$30$	0.646227	+	0.175732i	0.117984	+	0.0320841i
$31$	0.652414	−	0.376671i	0.117177	−	0.0676522i	−0.440266	−	0.897867i	$-0.645116\pi$
$31$	0.652414	−	0.376671i	0.117177	−	0.0676522i	0.557443	+	0.830215i	$0.311783\pi$
$32$	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	$-0.173789\pi$
$41$	−0.143256	−	0.248127i	−0.0223728	−	0.0387509i	−0.876995	+	0.480499i	$0.840455\pi$
$42$	−0.266232	−	1.75173i	−0.0410805	−	0.270298i
$43$	5.08515	−	8.80773i	0.775477	−	1.34317i	−0.159048	−	0.987271i	$-0.550843\pi$
$43$	5.08515	−	8.80773i	0.775477	−	1.34317i	0.934526	−	0.355895i	$-0.115824\pi$
$44$		−	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	0.262817	+	0.964846i	$0.415349\pi$
$47$	−4.82756	+	8.36159i	−0.704173	+	1.21966i	−0.966989	+	0.254817i	$0.917985\pi$
$48$	−3.81353	−	3.84197i	−0.550436	−	0.554541i
$49$	−2.12932	−	6.66828i	−0.304189	−	0.952612i
$50$	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	$-0.940242\pi$
$53$		−	2.71745i		−	0.373271i	0.982429	−	0.186635i	$-0.0597583\pi$
$54$	−1.94630	+	0.498328i	−0.264858	+	0.0678138i
$55$			4.24426i			0.572296i
$56$	3.18081	+	2.32334i	0.425054	+	0.310470i
$57$	−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	−0.995683	−	0.0928220i	$-0.970411\pi$
$59$	−4.44145	−	7.69282i	−0.578228	−	1.00152i	0.417455	−	0.908698i	$-0.362922\pi$
$60$	2.25796	+	2.27480i	0.291501	+	0.293675i
$61$	−10.5052	−	6.06518i	−1.34505	−	0.776567i	−0.357510	−	0.933909i	$-0.616374\pi$
$61$	−10.5052	−	6.06518i	−1.34505	−	0.776567i	−0.987544	+	0.157342i	$0.949707\pi$
$62$	−0.291279			−0.0369924
$63$	−7.28286	+	3.15594i	−0.917554	+	0.397611i
$64$	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	−0.995465	−	0.0951336i	$-0.969672\pi$
$67$	−4.74849	−	8.22463i	−0.580120	−	1.00480i	0.415344	−	0.909664i	$-0.363661\pi$
$68$	−2.50137	−	4.33250i	−0.303336	−	0.525393i
$69$	1.68267	+	6.37443i	0.202569	+	0.767391i
$70$	−0.826077	−	0.603387i	−0.0987351	−	0.0721186i
$71$			11.7148i			1.39029i	0.718869	+	0.695146i	$0.244660\pi$
$71$			11.7148i			1.39029i	−0.718869	+	0.695146i	$0.755340\pi$
$72$	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
$77$	10.2700	−	4.54132i	1.17037	−	0.517532i
$78$	0.639293	−	2.35090i	0.0723857	−	0.266187i
$79$	−1.05648	+	1.82988i	−0.118864	+	0.205878i	−0.919318	−	0.393516i	$-0.871258\pi$
$79$	−1.05648	+	1.82988i	−0.118864	+	0.205878i	0.800454	+	0.599394i	$0.204592\pi$
$80$	−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	−0.177637	−	0.984096i	$-0.556845\pi$
$83$	6.95521	−	12.0468i	0.763433	−	1.32231i	0.941071	−	0.338210i	$-0.109821\pi$
$84$	3.08842	−	7.89767i	0.336974	−	0.861707i
$85$	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	$-0.608099\pi$
$89$	−6.28517			−0.666226			−0.333113	+	0.942887i	$0.608099\pi$
$90$	−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	$-0.575109\pi$
$97$	−11.7467	−	6.78195i	−1.19270	−	0.688603i	−0.958917	+	0.283687i	$0.908442\pi$
$98$	−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	−0.214164	+	0.976798i	$0.568703\pi$
$101$	−9.57767	+	16.5890i	−0.953014	+	1.65067i	−0.738849	+	0.673871i	$0.764631\pi$
$102$	1.28495	−	1.27544i	0.127229	−	0.126288i
$103$	1.97678	−	1.14129i	0.194778	−	0.112455i	−0.399440	−	0.916759i	$-0.630795\pi$
$103$	1.97678	−	1.14129i	0.194778	−	0.112455i	0.594217	+	0.804305i	$0.297462\pi$
$104$	2.70803	+	4.69044i	0.265544	+	0.459936i
$105$	−1.66896	+	4.26785i	−0.162874	+	0.416500i
$106$	−0.525350	+	0.909932i	−0.0510265	+	0.0883804i
$107$			4.49066i			0.434128i	0.976157	+	0.217064i	$0.0696481\pi$
$107$			4.49066i			0.434128i	−0.976157	+	0.217064i	$0.930352\pi$
$108$	−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
$112$	3.34411	+	7.56256i	0.315989	+	0.714595i
$113$	−4.02691	+	2.32494i	−0.378820	+	0.218712i	−0.677305	−	0.735702i	$-0.736852\pi$
$113$	−4.02691	+	2.32494i	−0.378820	+	0.218712i	0.298485	+	0.954414i	$0.403519\pi$
$114$	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
$119$	4.21889	−	5.77594i	0.386745	−	0.529479i
$120$	−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
$126$	3.04877	+	0.351194i	0.271606	+	0.0312868i
$127$	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	$-0.00240213\pi$
$131$	5.64780	+	9.78227i	0.493450	+	0.854681i	−0.506521	+	0.862228i	$0.669069\pi$
$132$	13.1269	+	3.56966i	1.14255	+	0.310699i
$133$	11.0604	+	8.07877i	0.959055	+	0.700518i
$134$			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	−0.266910	−	0.963721i	$-0.586003\pi$
$137$	−14.4550	−	8.34559i	−1.23497	−	0.713012i	−0.968062	+	0.250710i	$0.919336\pi$
$138$	0.668895	−	2.45976i	0.0569402	−	0.209389i
$139$	7.61828	−	4.39842i	0.646174	−	0.373069i	−0.140815	−	0.990036i	$-0.544972\pi$
$139$	7.61828	−	4.39842i	0.646174	−	0.373069i	0.786989	+	0.616967i	$0.211639\pi$
$140$	−1.98002	−	4.47773i	−0.167342	−	0.378437i
$141$	−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
$147$	12.1128	−	0.528115i	0.999051	−	0.0435582i
$148$	3.91666	+	6.78386i	0.321948	+	0.557630i
$149$	−7.63089	+	4.40570i	−0.625147	+	0.360929i	−0.778870	−	0.627185i	$-0.784207\pi$
$149$	−7.63089	+	4.40570i	−0.625147	+	0.360929i	0.153723	+	0.988114i	$0.450874\pi$
$150$	0.170925	+	0.647515i	0.0139560	+	0.0528694i
$151$	0.632340	−	1.09524i	0.0514591	−	0.0891297i	−0.839148	−	0.543902i	$-0.816946\pi$
$151$	0.632340	−	1.09524i	0.0514591	−	0.0891297i	0.890608	+	0.454773i	$0.150279\pi$
$152$	−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	$-0.654189\pi$
$157$	0.850530	−	0.491054i	0.0678797	−	0.0391903i	0.533556	+	0.845765i	$0.320855\pi$
$158$	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	$-0.143680\pi$
$167$	0.932410	+	1.61498i	0.0721521	+	0.124971i	−0.827692	+	0.561182i	$0.810347\pi$
$168$	−5.32881	+	4.26031i	−0.411127	+	0.328690i
$169$	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	$-0.736691\pi$
$173$	3.93230	−	6.81094i	0.298967	−	0.517826i	0.975900	+	0.218219i	$0.0700246\pi$
$174$	2.74617	−	0.724908i	0.208186	−	0.0549552i
$175$	1.06999	+	2.41974i	0.0808837	+	0.182915i
$176$	−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	$-0.949701\pi$
$179$		−	4.21069i		−	0.314722i	0.987541	−	0.157361i	$-0.0502986\pi$
$180$	−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	$-0.0163668\pi$
$182$	−2.19506	+	3.00518i	−0.162708	+	0.222759i
$183$	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
$189$	−1.96464	−	13.6066i	−0.142907	−	0.989736i
$190$	2.00162			0.145213
$191$	4.94345	+	2.85410i	0.357695	+	0.206515i	0.668069	−	0.744099i	$-0.267121\pi$
$191$	4.94345	+	2.85410i	0.357695	+	0.206515i	−0.310374	+	0.950614i	$0.600454\pi$
$192$	−2.10535	+	7.74209i	−0.151940	+	0.558737i
$193$	−0.515538	−	0.892938i	−0.0371093	−	0.0642751i	0.846874	−	0.531793i	$-0.178482\pi$
$193$	−0.515538	−	0.892938i	−0.0371093	−	0.0642751i	−0.883984	+	0.467518i	$0.845148\pi$
$194$	2.62223	+	4.54184i	0.188265	+	0.326085i
$195$	−4.47201	+	4.43890i	−0.320247	+	0.317877i
$196$	−8.71632	+	9.58225i	−0.622594	+	0.684446i
$197$			16.2023i			1.15437i	0.816615	+	0.577183i	$0.195848\pi$
$197$			16.2023i			1.15437i	−0.816615	+	0.577183i	$0.804152\pi$
$198$	−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
$203$	10.2623	−	4.53792i	0.720272	−	0.318499i
$204$	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
$210$	1.38393	−	1.10643i	0.0955000	−	0.0763508i
$211$	3.36761	+	5.83288i	0.231836	+	0.401552i	0.958348	−	0.285602i	$-0.0921934\pi$
$211$	3.36761	+	5.83288i	0.231836	+	0.401552i	−0.726512	+	0.687153i	$0.758860\pi$
$212$	−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	$-0.393555\pi$
$223$	−4.86430	−	2.80840i	−0.325737	−	0.188065i	−0.653947	+	0.756540i	$0.726888\pi$
$224$	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	$-0.673023\pi$
$227$	7.27122	−	12.5941i	0.482608	−	0.835901i	0.999801	+	0.0199678i	$0.00635638\pi$
$228$	4.23492	+	16.0431i	0.280464	+	1.06248i
$229$	−18.6640	+	10.7757i	−1.23335	+	0.712076i	−0.967727	−	0.252001i	$-0.918911\pi$
$229$	−18.6640	+	10.7757i	−1.23335	+	0.712076i	−0.265624	+	0.964077i	$0.585578\pi$
$230$	−0.735858	−	1.27454i	−0.0485210	−	0.0840409i
$231$	2.92244	+	19.2289i	0.192283	+	1.26517i
$232$	−3.15704	+	5.46816i	−0.207270	+	0.359002i
$233$			8.01672i			0.525193i	0.964906	+	0.262596i	$0.0845788\pi$
$233$			8.01672i			0.525193i	−0.964906	+	0.262596i	$0.915421\pi$
$234$	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
$238$	−2.52931	+	1.11844i	−0.163951	+	0.0724979i
$239$	−24.4549	+	14.1190i	−1.58185	+	0.913284i	−0.587265	+	0.809395i	$0.699795\pi$
$239$	−24.4549	+	14.1190i	−1.58185	+	0.913284i	−0.994589	+	0.103889i	$0.966871\pi$
$240$	1.42048	−	5.22360i	0.0916916	−	0.337182i
$241$	−12.4500	−	7.18803i	−0.801977	−	0.463022i	0.0421850	−	0.999110i	$-0.486568\pi$
$241$	−12.4500	−	7.18803i	−0.801977	−	0.463022i	−0.844162	+	0.536088i	$0.819901\pi$
$242$		−	2.71187i		−	0.174325i
$243$	−15.1296	+	3.75420i	−0.970567	+	0.240832i
$244$			22.4473i			1.43704i
$245$	4.71024	−	5.17819i	0.300926	−	0.330822i
$246$	−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	$-0.862003\pi$
$251$	−28.7546			−1.81498			−0.907488	+	0.420078i	$0.862003\pi$
$252$	11.7961	+	8.75134i	0.743087	+	0.551283i
$253$	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	$-0.331718\pi$
$257$	−7.94503	−	13.7612i	−0.495598	−	0.858400i	−0.999987	+	0.00507607i	$0.998384\pi$
$258$	−1.73836	−	6.58541i	−0.108226	−	0.409990i
$259$	−6.60596	+	9.04400i	−0.410475	+	0.561967i
$260$		−	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	0.468086	−	0.883683i	$-0.344944\pi$
$263$	−1.02433	−	0.591398i	−0.0631629	−	0.0364671i	−0.531249	+	0.847216i	$0.678277\pi$
$264$	−7.71014	−	7.76764i	−0.474526	−	0.478065i
$265$	2.35338	−	1.35873i	0.144567	−	0.0834659i
$266$	−2.14171	−	4.84339i	−0.131317	−	0.296967i
$267$	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	$-0.607200\pi$
$269$	−10.8395			−0.660895			−0.330448	+	0.943824i	$0.607200\pi$
$270$	−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
$273$	15.5260	+	6.07150i	0.939675	+	0.367464i
$274$	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	−0.937111	−	0.349030i	$-0.886511\pi$
$277$	−2.76756	+	4.79355i	−0.166286	+	0.288017i	0.770825	+	0.637047i	$0.219844\pi$
$278$	−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	−0.0385558	−	0.999256i	$-0.512276\pi$
$281$	−15.4759	−	8.93502i	−0.923215	−	0.533019i	−0.884659	+	0.466238i	$0.845609\pi$
$282$	1.65031	+	6.25184i	0.0982743	+	0.372292i
$283$	−6.12953	+	3.53888i	−0.364363	+	0.210365i	−0.670993	−	0.741464i	$-0.734132\pi$
$283$	−6.12953	+	3.53888i	−0.364363	+	0.210365i	0.306630	+	0.951829i	$0.400799\pi$
$284$	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	$-0.309210\pi$
$293$	−7.41171	−	12.8375i	−0.432997	−	0.749972i	−0.997130	+	0.0757117i	$0.975877\pi$
$294$	−4.15805	−	2.16487i	−0.242503	−	0.126258i
$295$	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
$301$	−10.8821	−	24.6094i	−0.627234	−	1.41846i
$302$	−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	$0.944505\pi$
$308$	−16.7802	−	12.2567i	−0.956139	−	0.698388i
$309$	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	$-0.0725881\pi$
$311$	5.13664	+	8.89692i	0.291272	+	0.504498i	−0.682839	+	0.730569i	$0.739255\pi$
$312$	−9.07020	+	2.39427i	−0.513499	+	0.135549i
$313$	14.0962	+	8.13844i	0.796764	+	0.460012i	0.842338	−	0.538949i	$-0.181179\pi$
$313$	14.0962	+	8.13844i	0.796764	+	0.460012i	−0.0455747	+	0.998961i	$0.514512\pi$
$314$	−0.379730			−0.0214294
$315$	−6.37456	−	4.72917i	−0.359166	−	0.266458i
$316$	3.91005			0.219958
$317$	28.8682	+	16.6671i	1.62140	+	0.936115i	0.986546	+	0.163482i	$0.0522725\pi$
$317$	28.8682	+	16.6671i	1.62140	+	0.936115i	0.634853	+	0.772633i	$0.281061\pi$
$318$	−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
$322$	−2.29670	+	3.14433i	−0.127990	+	0.175227i
$323$			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
$329$	10.3309	+	23.3629i	0.569561	+	1.28804i
$330$	2.00237	+	2.01731i	0.110227	+	0.111049i
$331$	12.9962	−	22.5101i	0.714336	−	1.23727i	−0.248879	−	0.968535i	$-0.580062\pi$
$331$	12.9962	−	22.5101i	0.714336	−	1.23727i	0.963215	−	0.268732i	$-0.0866046\pi$
$332$	−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
$336$	−14.1596	+	2.15201i	−0.772471	+	0.117402i
$337$	2.76544	+	4.78989i	0.150643	+	0.260922i	0.931464	−	0.363833i	$-0.118532\pi$
$337$	2.76544	+	4.78989i	0.150643	+	0.260922i	−0.780821	+	0.624755i	$0.785199\pi$
$338$	−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	−0.867193	−	0.497971i	$-0.834078\pi$
$347$	−16.1976	+	9.35170i	−0.869534	+	0.502026i	−0.00234075	+	0.999997i	$0.500745\pi$
$348$	13.1170	+	3.56698i	0.703147	+	0.191210i
$349$	−17.6313	−	10.1794i	−0.943780	−	0.544892i	−0.0526367	−	0.998614i	$-0.516763\pi$
$349$	−17.6313	−	10.1794i	−0.943780	−	0.544892i	−0.891143	+	0.453722i	$0.850096\pi$
$350$	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	$-0.768346\pi$
$353$	3.80931	−	6.59791i	0.202749	−	0.351171i	0.949413	+	0.314030i	$0.101679\pi$
$354$	−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
$357$	7.73616	+	9.67643i	0.409441	+	0.512131i
$358$	−0.814028	+	1.40994i	−0.0430227	+	0.0745175i
$359$			13.5305i			0.714114i	0.934083	+	0.357057i	$0.116220\pi$
$359$			13.5305i			0.714114i	−0.934083	+	0.357057i	$0.883780\pi$
$360$	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
$364$	−16.2895	+	7.20310i	−0.853801	+	0.377545i
$365$	−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	$-0.323373\pi$
$367$	1.03813	+	0.599366i	0.0541901	+	0.0312867i	−0.472660	+	0.881245i	$0.656706\pi$
$368$			11.8962i			0.620133i
$369$	−0.00638668	+	0.859512i	−0.000332478	+	0.0447444i
$370$			1.63671i			0.0850887i
$371$	−5.80586	−	4.24074i	−0.301425	−	0.220168i
$372$	1.71370	−	1.70102i	0.0888514	−	0.0881936i
$373$	−14.2091	−	24.6109i	−0.735721	−	1.27431i	−0.954406	−	0.298511i	$-0.903510\pi$
$373$	−14.2091	−	24.6109i	−0.735721	−	1.27431i	0.218685	−	0.975795i	$-0.429823\pi$
$374$	−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
$378$	−1.97263	+	4.93595i	−0.101461	+	0.253878i
$379$	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	$-0.295857\pi$
$383$	−7.72665	−	13.3830i	−0.394813	−	0.683837i	−0.993077	+	0.117462i	$0.962524\pi$
$384$	12.4933	−	12.4008i	0.637546	−	0.632826i
$385$	9.06790	+	6.62342i	0.462143	+	0.337561i
$386$			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	0.977784	+	0.209614i	$0.0672207\pi$
$389$	32.5077	+	18.7683i	1.64821	+	0.951593i	0.670423	+	0.741979i	$0.266113\pi$
$390$	2.35559	−	0.621807i	0.119280	−	0.0314864i
$391$	8.91162	−	5.14512i	0.450680	−	0.260200i
$392$	9.92768	−	3.17011i	0.501424	−	0.160115i
$393$	−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
$399$	−18.5294	+	14.8140i	−0.927632	+	0.741628i
$400$	−1.56268	−	2.70665i	−0.0781342	−	0.135332i
$401$	12.6232	−	7.28802i	0.630374	−	0.363946i	−0.150523	−	0.988607i	$-0.548096\pi$
$401$	12.6232	−	7.28802i	0.630374	−	0.363946i	0.780897	+	0.624660i	$0.214762\pi$
$402$	−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	0.630092	−	0.776520i	$-0.283017\pi$
$409$	32.7144	−	18.8877i	1.61762	−	0.933936i	0.987532	−	0.157415i	$-0.0503162\pi$
$410$	−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	$-0.173736\pi$
$419$	−0.454552	−	0.787307i	−0.0222063	−	0.0384625i	−0.876915	+	0.480645i	$0.840402\pi$
$420$	8.38380	−	1.27419i	0.409087	−	0.0621740i
$421$	2.13949	−	3.70571i	0.104273	−	0.180605i	−0.809168	−	0.587577i	$-0.800082\pi$
$421$	2.13949	−	3.70571i	0.104273	−	0.180605i	0.913441	+	0.406972i	$0.133415\pi$
$422$		−	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
$427$	−29.3523	+	12.9794i	−1.42046	+	0.628116i
$428$	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	$0.0922380\pi$
$431$			11.8641i			0.571471i	−0.958308	+	0.285736i	$0.907762\pi$
$432$	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	$0.881973\pi$
$434$	−0.454557	+	0.622319i	−0.0218195	+	0.0298723i
$435$	−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	0.988550	+	0.150897i	$0.0482161\pi$
$439$	33.8067	+	19.5183i	1.61350	+	0.931557i	0.624955	+	0.780661i	$0.285117\pi$
$440$	−6.31882			−0.301238
$441$	−4.62263	+	20.4849i	−0.220125	+	0.975472i
$442$	−3.80263			−0.180873
$443$	−15.6110	−	9.01300i	−0.741700	−	0.428220i	0.0809874	−	0.996715i	$-0.474193\pi$
$443$	−15.6110	−	9.01300i	−0.741700	−	0.428220i	−0.822687	+	0.568495i	$0.807526\pi$
$444$	−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
$448$	7.22885	−	9.89678i	0.341531	−	0.467579i
$449$		−	17.5843i		−	0.829856i	−0.909854	−	0.414928i	$-0.863807\pi$
$449$		−	17.5843i		−	0.829856i	0.909854	−	0.414928i	$-0.136193\pi$
$450$	−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
$455$	8.80273	−	3.89251i	0.412679	−	0.182484i
$456$	3.50294	−	12.8815i	0.164040	−	0.603233i
$457$	3.96531	−	6.86813i	0.185490	−	0.321277i	−0.758252	−	0.651962i	$-0.773946\pi$
$457$	3.96531	−	6.86813i	0.185490	−	0.321277i	0.943741	+	0.330684i	$0.107280\pi$
$458$	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	$-0.893302\pi$
$461$	−4.02115	+	6.96483i	−0.187284	+	0.324385i	0.757060	+	0.653345i	$0.226635\pi$
$462$	2.73883	−	7.00371i	0.127422	−	0.325842i
$463$	9.70541	+	16.8103i	0.451049	+	0.781239i	0.998451	−	0.0556301i	$-0.0177168\pi$
$463$	9.70541	+	16.8103i	0.451049	+	0.781239i	−0.547403	+	0.836869i	$0.684383\pi$
$464$	−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	$-0.383060\pi$
$467$	15.5234			0.718337			0.359169	+	0.933273i	$0.383060\pi$
$468$	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	$-0.902969\pi$
$479$	−4.74982	+	8.22692i	−0.217025	+	0.375898i	0.736872	+	0.676032i	$0.236302\pi$
$480$	−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
$483$	16.2449	+	6.35264i	0.739169	+	0.289055i
$484$	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
$490$	−2.57828	+	0.823298i	−0.116475	+	0.0371928i
$491$	26.0433	−	15.0361i	1.17532	−	0.678571i	0.220393	−	0.975411i	$-0.429266\pi$
$491$	26.0433	−	15.0361i	1.17532	−	0.678571i	0.954927	+	0.296840i	$0.0959328\pi$
$492$	−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
$497$	25.0288	+	18.2816i	1.12269	+	0.820043i
$498$	−2.37764	−	9.00720i	−0.106545	−	0.403622i
$499$	−20.8184	−	36.0586i	−0.931961	−	1.61420i	−0.779966	−	0.625822i	$-0.784764\pi$
$499$	−20.8184	−	36.0586i	−0.931961	−	1.61420i	−0.151994	−	0.988381i	$-0.548570\pi$
$500$	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	$-0.509739\pi$
$503$	−1.37222			−0.0611841			−0.0305920	+	0.999532i	$0.509739\pi$
$504$	−4.69854	−	10.8427i	−0.209290	−	0.482970i
$505$	−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	$-0.304578\pi$
$509$	−9.47184	−	16.4057i	−0.419832	−	0.727170i	−0.995922	+	0.0902160i	$0.971244\pi$
$510$	1.74704	+	0.475082i	0.0773603	+	0.0210370i
$511$	33.5963	+	24.5396i	1.48621	+	1.08557i
$512$			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
$518$	3.96041	−	1.75127i	0.174011	−	0.0769463i
$519$	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	$-0.248492\pi$
$521$	32.4326			1.42090			0.710448	+	0.703750i	$0.248492\pi$
$522$	−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
$525$	−4.53055	+	0.688563i	−0.197729	+	0.0300514i
$526$	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
$546$	−4.02507	−	5.03457i	−0.172257	−	0.215460i
$547$	4.43140	−	7.67540i	0.189473	−	0.328176i	−0.755602	−	0.655031i	$-0.772655\pi$
$547$	4.43140	−	7.67540i	0.189473	−	0.328176i	0.945075	+	0.326855i	$0.105989\pi$
$548$			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
$553$	2.26085	+	5.11282i	0.0961413	+	0.217419i
$554$	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	$-0.676311\pi$
$557$		−	40.1442i		−	1.70096i	0.526005	−	0.850481i	$-0.323689\pi$
$558$	0.753497	+	0.442529i	0.0318981	+	0.0187338i
$559$		−	36.9984i		−	1.56487i
$560$	−4.87732	+	6.67737i	−0.206104	+	0.282170i
$561$	−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	$-0.149090\pi$
$563$	1.30952	+	2.26815i	0.0551895	+	0.0955910i	−0.837111	+	0.547033i	$0.815757\pi$
$564$	−8.12049	+	29.8618i	−0.341934	+	1.25741i
$565$	−4.02691	−	2.32494i	−0.169414	−	0.0978110i
$566$	2.73661			0.115028
$567$	23.6344	+	2.90060i	0.992553	+	0.121814i
$568$	−17.4409			−0.731804
$569$	−5.42169	−	3.13021i	−0.227289	−	0.131225i	0.382032	−	0.924149i	$-0.375224\pi$
$569$	−5.42169	−	3.13021i	−0.227289	−	0.131225i	−0.609321	+	0.792924i	$0.708558\pi$
$570$	−0.909737	+	3.34542i	−0.0381047	+	0.140124i
$571$	0.966490	+	1.67401i	0.0404464	+	0.0700552i	0.885540	−	0.464563i	$-0.153789\pi$
$571$	0.966490	+	1.67401i	0.0404464	+	0.0700552i	−0.845094	+	0.534618i	$0.820455\pi$
$572$	−14.2860	−	24.7441i	−0.597329	−	1.03460i
$573$	−7.01701	+	6.96507i	−0.293140	+	0.290970i
$574$	0.236681	+	0.172878i	0.00987887	+	0.00721577i
$575$			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
$581$	−14.8840	−	33.6595i	−0.617493	−	1.39643i
$582$	−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	0.451438	+	0.892303i	$0.350911\pi$
$587$	−13.2537	+	22.9561i	−0.547038	+	0.947498i	−0.998476	+	0.0551950i	$0.982422\pi$
$588$	−12.0538	−	18.9232i	−0.497089	−	0.780380i
$589$	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	$-0.437596\pi$
$593$	9.48706			0.389587			0.194793	+	0.980844i	$0.437596\pi$
$594$	−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	−0.907184	−	0.420735i	$-0.861772\pi$
$599$	−24.3866	+	14.0796i	−0.996408	+	0.575276i	−0.0892244	+	0.996012i	$0.528439\pi$
$600$	1.83015	−	1.81660i	0.0747156	−	0.0741625i
$601$	31.7370	+	18.3234i	1.29458	+	0.747425i	0.979462	−	0.201628i	$-0.0646232\pi$
$601$	31.7370	+	18.3234i	1.29458	+	0.747425i	0.315116	+	0.949053i	$0.397957\pi$
$602$	−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	$-0.836063\pi$
$607$	−21.6527	+	12.5012i	−0.878855	+	0.507407i	−0.00857405	+	0.999963i	$0.502729\pi$
$608$	10.8351	+	18.7670i	0.439423	+	0.761103i
$609$	2.92026	+	19.2144i	0.118335	+	0.778609i
$610$	−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
$616$	6.76108	+	15.2899i	0.272412	+	0.616047i
$617$	4.00794	−	2.31398i	0.161353	−	0.0931575i	−0.417149	−	0.908838i	$-0.636971\pi$
$617$	4.00794	−	2.31398i	0.161353	−	0.0931575i	0.578502	+	0.815681i	$0.303637\pi$
$618$	0.401123	−	1.47507i	0.0161355	−	0.0593359i
$619$	18.3309	+	10.5834i	0.736783	+	0.425382i	0.820898	−	0.571074i	$-0.193473\pi$
$619$	18.3309	+	10.5834i	0.736783	+	0.425382i	−0.0841156	+	0.996456i	$0.526807\pi$
$620$		−	1.39406i		−	0.0559869i
$621$	5.33162	−	19.0462i	0.213950	−	0.764296i
$622$		−	3.97215i		−	0.159269i
$623$	−9.80836	+	13.4283i	−0.392964	+	0.537993i
$624$	−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
$630$	1.22024	+	2.81591i	0.0486155	+	0.112188i
$631$	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
$637$	−18.8377	−	17.1353i	−0.746376	−	0.678927i
$638$		−	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	−0.0464877	−	0.998919i	$-0.514803\pi$
$641$	−23.6678	−	13.6646i	−0.934821	−	0.539719i	−0.888333	+	0.459200i	$0.848136\pi$
$642$	2.11862	+	2.13442i	0.0836151	+	0.0842387i
$643$	−33.1113	+	19.1168i	−1.30578	+	0.753894i	−0.981389	−	0.192029i	$-0.938493\pi$
$643$	−33.1113	+	19.1168i	−1.30578	+	0.753894i	−0.324393	+	0.945922i	$0.605160\pi$
$644$	−17.0438	+	7.53663i	−0.671618	+	0.296985i
$645$	−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	$-0.407379\pi$
$647$	14.5947			0.573775			0.286887	+	0.957964i	$0.407379\pi$
$648$	−11.7023	+	6.52638i	−0.459708	+	0.256380i
$649$		−	37.7014i		−	1.47991i
$650$	0.703292	−	1.21814i	0.0275854	−	0.0477793i
$651$	3.21516	+	1.25730i	0.126012	+	0.0492775i
$652$	−9.16716	−	15.8780i	−0.359014	−	0.621830i
$653$	14.2573	−	8.23145i	0.557931	−	0.322122i	−0.194384	−	0.980926i	$-0.562271\pi$
$653$	14.2573	−	8.23145i	0.557931	−	0.322122i	0.752315	+	0.658804i	$0.228937\pi$
$654$	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	0.778133	−	0.628100i	$-0.216167\pi$
$659$	15.9994	+	9.23728i	0.623249	+	0.359833i	−0.154884	+	0.987933i	$0.549500\pi$
$660$	3.47202	+	13.1530i	0.135148	+	0.511981i
$661$	−19.0057	+	10.9729i	−0.739234	+	0.426797i	−0.821791	−	0.569789i	$-0.807025\pi$
$661$	−19.0057	+	10.9729i	−0.739234	+	0.426797i	0.0825565	+	0.996586i	$0.473692\pi$
$662$	−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
$672$	17.8652	+	6.98627i	0.689166	+	0.269501i
$673$	−6.33688	+	10.9758i	−0.244269	+	0.423086i	−0.961926	−	0.273311i	$-0.911881\pi$
$673$	−6.33688	+	10.9758i	−0.244269	+	0.423086i	0.717657	+	0.696397i	$0.245215\pi$
$674$		−	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	0.129610	−	0.991565i	$-0.458627\pi$
$677$	24.0294	−	41.6202i	0.923526	−	1.59959i	0.793915	−	0.608028i	$-0.208039\pi$
$678$	−0.817132	+	3.00488i	−0.0313818	+	0.115402i
$679$	−32.8211	+	14.5132i	−1.25956	+	0.556967i
$680$	−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	$0.104609\pi$
$683$			16.8700i			0.645512i	−0.946482	+	0.322756i	$0.895391\pi$
$684$	−28.7385	−	0.213544i	−1.09884	−	0.00816507i
$685$		−	16.6912i		−	0.637737i
$686$	4.75090	+	5.35784i	0.181390	+	0.204563i
$687$	−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	$-0.205916\pi$
$691$	17.7426	+	10.2437i	0.674959	+	0.389688i	−0.122994	+	0.992407i	$0.539250\pi$
$692$	−14.5535			−0.553239
$693$	−33.4665	−	3.85507i	−1.27129	−	0.146442i
$694$	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
$700$	2.88782	−	3.95361i	0.109149	−	0.149432i
$701$			21.3800i			0.807513i	0.914867	+	0.403756i	$0.132296\pi$
$701$			21.3800i			0.807513i	−0.914867	+	0.403756i	$0.867704\pi$
$702$	−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
$707$	20.4960	+	46.3509i	0.770832	+	1.74320i
$708$	−20.0572	−	20.2068i	−0.753796	−	0.759418i
$709$	−11.1926	+	19.3862i	−0.420349	+	0.728065i	−0.995973	−	0.0896487i	$-0.971426\pi$
$709$	−11.1926	+	19.3862i	−0.420349	+	0.728065i	0.575625	+	0.817714i	$0.304759\pi$
$710$	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
$714$	−0.719744	−	4.73571i	−0.0269358	−	0.177230i
$715$	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	$-0.687701\pi$
$719$	−29.8224			−1.11219			−0.556095	+	0.831119i	$0.687701\pi$
$720$	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	$-0.286070\pi$
$727$	6.90885	+	3.98882i	0.256235	+	0.147937i	−0.366381	+	0.930465i	$0.619403\pi$
$728$	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	$-0.698358\pi$
$733$	−4.66110	+	2.69109i	−0.172162	+	0.0993975i	0.411443	+	0.911435i	$0.365025\pi$
$734$	−0.231744	−	0.401392i	−0.00855383	−	0.0148157i
$735$	6.51379	+	10.2260i	0.240265	+	0.377191i
$736$	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
$742$	1.12424	+	2.54241i	0.0412721	+	0.0933350i
$743$	−40.8901	+	23.6079i	−1.50011	+	0.866089i	−0.500111	+	0.865961i	$0.666707\pi$
$743$	−40.8901	+	23.6079i	−1.50011	+	0.866089i	−1.00000		0.000128167i	$0.999959\pi$
$744$	−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
$749$	9.59432	+	7.00793i	0.350569	+	0.256064i
$750$	−0.475302	+	0.471783i	−0.0173556	+	0.0172271i
$751$	17.4591	+	30.2400i	0.637090	+	1.10347i	0.986068	+	0.166342i	$0.0531956\pi$
$751$	17.4591	+	30.2400i	0.637090	+	1.10347i	−0.348978	+	0.937131i	$0.613471\pi$
$752$	−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
$756$	−19.9879	+	15.7380i	−0.726955	+	0.572387i
$757$	−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	0.785117	+	0.619348i	$0.212603\pi$
$761$	25.6257	+	44.3849i	0.928929	+	1.60895i	0.143813	+	0.989605i	$0.454064\pi$
$762$	6.95147	−	6.90000i	0.251825	−	0.249961i
$763$	4.31922	−	5.91330i	0.156366	−	0.214076i
$764$		−	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	$-0.646438\pi$
$769$	3.05041	−	1.76116i	0.110001	−	0.0635089i	0.553991	+	0.832523i	$0.313104\pi$
$770$	−1.75589	−	3.97088i	−0.0632781	−	0.143101i
$771$	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	$-0.731071\pi$
$773$	−36.9128			−1.32766			−0.663831	+	0.747882i	$0.731071\pi$
$774$	11.7967	+	0.0876561i	0.424022	+	0.00315074i
$775$			0.753343i			0.0270609i
$776$	10.0969	−	17.4884i	0.362458	−	0.627796i
$777$	−12.1133	−	15.1514i	−0.434563	−	0.543554i
$778$	−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	$-0.530457\pi$
$787$	20.1637	−	11.6415i	0.718759	−	0.414976i	0.814296	+	0.580450i	$0.197123\pi$
$788$	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	0.999096	+	0.0425225i	$0.0135394\pi$
$797$	15.1425	+	26.2275i	0.536373	+	0.929026i	−0.462722	+	0.886503i	$0.653127\pi$
$798$	9.06844	−	1.37824i	0.321019	−	0.0487892i
$799$	−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
$805$	9.21034	−	4.07275i	0.324622	−	0.143546i
$806$	−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	$-0.832323\pi$
$809$		−	28.5991i		−	1.00549i	0.864434	−	0.502746i	$-0.167677\pi$
$810$	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	$0.822470\pi$
$812$	−16.7676	−	12.2475i	−0.588427	−	0.429802i
$813$	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
$819$	−17.2042	+	23.1899i	−0.601163	+	0.810322i
$820$	−0.530191			−0.0185151
$821$	−32.7300	−	18.8967i	−1.14229	−	0.659499i	−0.195290	−	0.980745i	$-0.562565\pi$
$821$	−32.7300	−	18.8967i	−1.14229	−	0.659499i	−0.946996	+	0.321246i	$0.895898\pi$
$822$	−10.8078	+	2.85294i	−0.376965	+	0.0995078i
$823$	25.9752	+	44.9904i	0.905439	+	1.56827i	0.820327	+	0.571895i	$0.193792\pi$
$823$	25.9752	+	44.9904i	0.905439	+	1.56827i	0.0851124	+	0.996371i	$0.472875\pi$
$824$	1.69915	+	2.94301i	0.0591925	+	0.102524i
$825$	−1.87626	−	7.10781i	−0.0653229	−	0.247462i
$826$	7.33796	+	5.35983i	0.255320	+	0.186492i
$827$		−	16.7067i		−	0.580949i	−0.956883	−	0.290475i	$-0.906187\pi$
$827$		−	16.7067i		−	0.580949i	0.956883	−	0.290475i	$-0.0938132\pi$
$828$	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
$833$	−5.75651	−	18.0274i	−0.199451	−	0.624611i
$834$	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	$-0.795549\pi$
$839$	3.43018	−	5.94125i	0.118423	−	0.205115i	0.919143	+	0.393924i	$0.128883\pi$
$840$	−6.35394	−	2.48473i	−0.219232	−	0.0857315i
$841$	−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	$-0.434608\pi$
$853$	−15.8246	−	9.13635i	−0.541825	−	0.312823i	−0.745818	+	0.666150i	$0.767941\pi$
$854$	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	$-0.765319\pi$
$857$	6.20774	−	10.7521i	0.212052	−	0.367285i	0.952357	+	0.304986i	$0.0986519\pi$
$858$	7.33874	−	7.28441i	0.250540	−	0.248686i
$859$	3.69582	−	2.13378i	0.126100	−	0.0728038i	−0.435623	−	0.900129i	$-0.643472\pi$
$859$	3.69582	−	2.13378i	0.126100	−	0.0728038i	0.561723	+	0.827325i	$0.310139\pi$
$860$	−9.41008	−	16.2987i	−0.320881	−	0.555782i
$861$	0.478177	−	1.22279i	0.0162962	−	0.0416726i
$862$	2.29361	−	3.97265i	0.0781206	−	0.135309i
$863$		−	16.8919i		−	0.575008i	−0.957779	−	0.287504i	$-0.907175\pi$
$863$		−	16.8919i		−	0.575008i	0.957779	−	0.287504i	$-0.0928255\pi$
$864$	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
$868$	−3.37326	+	1.49163i	−0.114496	+	0.0506294i
$869$	−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
$875$	−1.56056	+	2.13651i	−0.0527565	+	0.0722271i
$876$	12.8637	+	48.7316i	0.434625	+	1.64649i
$877$	5.91368	+	10.2428i	0.199691	+	0.345875i	0.948428	−	0.316992i	$-0.102673\pi$
$877$	5.91368	+	10.2428i	0.199691	+	0.345875i	−0.748737	+	0.662867i	$0.769340\pi$
$878$	−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	$-0.487191\pi$
$881$	2.38825			0.0804622			0.0402311	+	0.999190i	$0.487191\pi$
$882$	5.50810	−	5.96565i	0.185467	−	0.200874i
$883$	−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	$-0.316846\pi$
$887$	−13.5359	−	23.4449i	−0.454492	−	0.787203i	−0.998659	+	0.0517739i	$0.983512\pi$
$888$	10.5332	+	2.86434i	0.353470	+	0.0961209i
$889$	22.8237	−	31.2472i	0.765484	−	1.04800i
$890$			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
$896$	−24.5919	+	10.8744i	−0.821557	+	0.363287i
$897$	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
$903$	46.0770	−	7.00289i	1.53335	−	0.233042i
$904$	−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	−0.985381	−	0.170364i	$-0.945506\pi$
$907$	−10.3947	+	18.0042i	−0.345151	+	0.597820i	0.640230	+	0.768183i	$0.278839\pi$
$908$	−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	−0.180396	−	0.983594i	$-0.557738\pi$
$911$	−33.8775	−	19.5592i	−1.12241	−	0.648024i	−0.942015	+	0.335570i	$0.891071\pi$
$912$	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
$924$	28.1118	−	22.4750i	0.924811	−	0.739373i
$925$	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	$-0.832109\pi$
$929$	0.117189	−	0.202978i	0.00384486	−	0.00665950i	0.867941	+	0.496667i	$0.165443\pi$
$930$	0.487801	−	0.128765i	0.0159956	−	0.00422238i
$931$	34.5207	−	11.0232i	1.13137	−	0.361270i
$932$	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	$0.904083\pi$
$938$	7.84524	+	5.73036i	0.256156	+	0.187103i
$939$	−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	$-0.163795\pi$
$941$	0.276744	+	0.479335i	0.00902160	+	0.0156259i	−0.861479	+	0.507793i	$0.830462\pi$
$942$	0.172587	−	0.634664i	0.00562320	−	0.0206785i
$943$	−0.944455	−	0.545281i	−0.0307557	−	0.0177568i
$944$	27.7623			0.903587
$945$	10.8014	−	8.50474i	0.351368	−	0.276659i
$946$	−16.6898			−0.542633
$947$	20.8441	+	12.0343i	0.677341	+	0.391063i	0.798852	−	0.601527i	$-0.205441\pi$
$947$	20.8441	+	12.0343i	0.677341	+	0.391063i	−0.121511	+	0.992590i	$0.538774\pi$
$948$	−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
$952$	8.59916	+	6.28104i	0.278700	+	0.203570i
$953$		−	10.9096i		−	0.353398i	−0.984265	−	0.176699i	$-0.943458\pi$
$953$		−	10.9096i		−	0.353398i	0.984265	−	0.176699i	$-0.0565418\pi$
$954$	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
$959$	−40.3882	+	17.8594i	−1.30420	+	0.576710i
$960$	−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
$966$	−4.21145	−	5.26770i	−0.135501	−	0.169485i
$967$	−8.30830	−	14.3904i	−0.267177	−	0.462764i	0.700955	−	0.713206i	$-0.252757\pi$
$967$	−8.30830	−	14.3904i	−0.267177	−	0.462764i	−0.968132	+	0.250442i	$0.919424\pi$
$968$	−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	$-0.331011\pi$
$971$	31.5538			1.01261			0.506305	+	0.862354i	$0.331011\pi$
$972$	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	−0.766208	−	0.642593i	$-0.777859\pi$
$977$	−18.5295	+	10.6980i	−0.592810	+	0.342259i	0.173398	+	0.984852i	$0.444525\pi$
$978$	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	0.321787	+	0.946812i	$0.395716\pi$
$983$	−20.6637	+	35.7906i	−0.659070	+	1.14154i	−0.980857	+	0.194730i	$0.937617\pi$
$984$	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
$987$	−43.7430	+	6.64817i	−1.39236	+	0.211613i
$988$	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
$994$	−4.84653	−	10.9602i	−0.153723	−	0.347637i
$995$	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	$-0.332762\pi$
$997$	0.0982245	+	0.0567099i	0.00311080	+	0.00179602i	−0.498444	+	0.866922i	$0.666095\pi$
$998$			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.i.146.5	yes	24
3.2	odd	2		945.2.bl.i.251.8		24
7.6	odd	2		315.2.bl.j.146.5	yes	24
9.4	even	3		945.2.bl.j.881.8		24
9.5	odd	6		315.2.bl.j.41.5	yes	24
21.20	even	2		945.2.bl.j.251.8		24
63.13	odd	6		945.2.bl.i.881.8		24
63.41	even	6	inner	315.2.bl.i.41.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bl.i.41.5	✓	24	63.41	even	6	inner
315.2.bl.i.146.5	yes	24	1.1	even	1	trivial
315.2.bl.j.41.5	yes	24	9.5	odd	6
315.2.bl.j.146.5	yes	24	7.6	odd	2
945.2.bl.i.251.8		24	3.2	odd	2
945.2.bl.i.881.8		24	63.13	odd	6
945.2.bl.j.251.8		24	21.20	even	2
945.2.bl.j.881.8		24	9.4	even	3

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)

\(f(q)\)	\(=\)	\(q+(-0.334847 - 0.193324i) q^{2} +(-0.454500 + 1.67136i) q^{3} +(-0.925251 - 1.60258i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.475302 - 0.471783i) q^{6} +(1.56056 - 2.13651i) q^{7} +1.48879i q^{8} +(-2.58686 - 1.51926i) q^{9} +O(q^{10})\)	\(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} +(1.56056 - 2.13651i) 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} +(-0.935587 + 0.413710i) 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} +(2.86159 + 3.57929i) 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} +(-0.266232 - 1.75173i) 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} +(-2.12932 - 6.66828i) 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} +(3.18081 + 2.32334i) 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} +(-7.28286 + 3.15594i) 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} +(-0.826077 - 0.603387i) 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} +(10.2700 - 4.54132i) 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} +(3.08842 - 7.89767i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 - 5 * q^3 + 18 * q^4 + 12 * q^5 - q^6 + q^9	\( 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9} + 9 q^{11} + 18 q^{12} - 3 q^{13} + 9 q^{14} + 2 q^{15} - 18 q^{16} - 18 q^{17} + 2 q^{18} - 18 q^{20} + 4 q^{21} - 9 q^{22} + 9 q^{23} + 7 q^{24} - 12 q^{25} + 18 q^{26} + 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} + 42 q^{31} + 18 q^{32} - 13 q^{33} + 39 q^{34} + 9 q^{35} - 21 q^{36} + 12 q^{38} - 21 q^{39} + 6 q^{40} + 33 q^{41} + 26 q^{42} + 18 q^{43} - q^{45} - 30 q^{46} + 17 q^{48} - 6 q^{50} - 12 q^{51} - 129 q^{52} - 52 q^{54} + 6 q^{56} + 6 q^{57} - 15 q^{58} - 12 q^{59} + 15 q^{60} + 15 q^{61} - 12 q^{62} - 83 q^{63} - 60 q^{64} - 3 q^{65} - 29 q^{66} - 15 q^{67} - 9 q^{68} - 61 q^{69} + 18 q^{70} + 61 q^{72} - 18 q^{74} + 7 q^{75} - 54 q^{76} - 57 q^{77} - 66 q^{78} + 21 q^{79} - 36 q^{80} + q^{81} + 30 q^{83} - 42 q^{84} - 9 q^{85} - 102 q^{86} - 10 q^{87} - 9 q^{88} - 102 q^{89} + 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} + 156 q^{94} - 18 q^{95} + 42 q^{96} + 45 q^{97} - 3 q^{98} + 23 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 - 5 * q^3 + 18 * q^4 + 12 * q^5 - q^6 + q^9 + 9 * q^11 + 18 * q^12 - 3 * q^13 + 9 * q^14 + 2 * q^15 - 18 * q^16 - 18 * q^17 + 2 * q^18 - 18 * q^20 + 4 * 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 + 26 * q^42 + 18 * q^43 - q^45 - 30 * q^46 + 17 * q^48 - 6 * q^50 - 12 * q^51 - 129 * q^52 - 52 * q^54 + 6 * q^56 + 6 * q^57 - 15 * q^58 - 12 * q^59 + 15 * q^60 + 15 * q^61 - 12 * q^62 - 83 * q^63 - 60 * q^64 - 3 * q^65 - 29 * q^66 - 15 * q^67 - 9 * q^68 - 61 * q^69 + 18 * q^70 + 61 * q^72 - 18 * q^74 + 7 * q^75 - 54 * q^76 - 57 * q^77 - 66 * q^78 + 21 * q^79 - 36 * q^80 + q^81 + 30 * q^83 - 42 * 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

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