LMFDB - Embedded newform 315.2.t.b.101.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(101,315)]

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([1, 0, 1]))

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

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

chi := DirichletCharacter("315.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.t (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:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.6
Character	$\chi$	$=$	315.101
Dual form			315.2.t.b.131.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.929301i q^{2} +(0.479000 + 1.66450i) q^{3} +1.13640 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.54682 - 0.445136i) q^{6} +(0.0655497 + 2.64494i) q^{7} -2.91466i q^{8} +(-2.54112 + 1.59459i) q^{9} +O(q^{10})$	\(q-0.929301i q^{2} +(0.479000 + 1.66450i) q^{3} +1.13640 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.54682 - 0.445136i) q^{6} +(0.0655497 + 2.64494i) q^{7} -2.91466i q^{8} +(-2.54112 + 1.59459i) q^{9} +(-0.804799 - 0.464651i) q^{10} +(4.54030 - 2.62135i) q^{11} +(0.544335 + 1.89154i) q^{12} +(-0.516376 + 0.298130i) q^{13} +(2.45795 - 0.0609154i) q^{14} +(1.68100 + 0.417423i) q^{15} -0.435799 q^{16} +(-1.80401 + 3.12464i) q^{17} +(1.48186 + 2.36146i) q^{18} +(-2.80984 + 1.62226i) q^{19} +(0.568200 - 0.984151i) q^{20} +(-4.37110 + 1.37603i) q^{21} +(-2.43602 - 4.21931i) q^{22} +(2.38642 + 1.37780i) q^{23} +(4.85145 - 1.39612i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.277052 + 0.479869i) q^{26} +(-3.87139 - 3.46588i) q^{27} +(0.0744906 + 3.00571i) q^{28} +(3.53879 + 2.04312i) q^{29} +(0.387912 - 1.56215i) q^{30} -6.39488i q^{31} -5.42433i q^{32} +(6.53803 + 6.30171i) q^{33} +(2.90373 + 1.67647i) q^{34} +(2.32336 + 1.26570i) q^{35} +(-2.88772 + 1.81209i) q^{36} +(0.988179 + 1.71158i) q^{37} +(1.50757 + 2.61119i) q^{38} +(-0.743581 - 0.716703i) q^{39} +(-2.52417 - 1.45733i) q^{40} +(-4.89572 - 8.47964i) q^{41} +(1.27875 + 4.06207i) q^{42} +(0.604036 - 1.04622i) q^{43} +(5.15960 - 2.97889i) q^{44} +(0.110398 + 2.99797i) q^{45} +(1.28039 - 2.21770i) q^{46} -5.73177 q^{47} +(-0.208748 - 0.725387i) q^{48} +(-6.99141 + 0.346750i) q^{49} +(-0.804799 + 0.464651i) q^{50} +(-6.06508 - 1.50607i) q^{51} +(-0.586809 + 0.338794i) q^{52} +(-8.79935 - 5.08031i) q^{53} +(-3.22085 + 3.59769i) q^{54} -5.24269i q^{55} +(7.70910 - 0.191055i) q^{56} +(-4.04617 - 3.89992i) q^{57} +(1.89868 - 3.28860i) q^{58} +1.32833 q^{59} +(1.91029 + 0.474360i) q^{60} +10.0668i q^{61} -5.94277 q^{62} +(-4.38417 - 6.61658i) q^{63} -5.91244 q^{64} +0.596259i q^{65} +(5.85618 - 6.07580i) q^{66} -9.26557 q^{67} +(-2.05007 + 3.55083i) q^{68} +(-1.15025 + 4.63215i) q^{69} +(1.17622 - 2.15910i) q^{70} -11.6581i q^{71} +(4.64769 + 7.40649i) q^{72} +(12.2136 + 7.05152i) q^{73} +(1.59057 - 0.918316i) q^{74} +(1.20200 - 1.24708i) q^{75} +(-3.19310 + 1.84354i) q^{76} +(7.23091 + 11.8370i) q^{77} +(-0.666033 + 0.691011i) q^{78} -12.9669 q^{79} +(-0.217899 + 0.377413i) q^{80} +(3.91456 - 8.10409i) q^{81} +(-7.88014 + 4.54960i) q^{82} +(-5.40645 + 9.36424i) q^{83} +(-4.96732 + 1.56372i) q^{84} +(1.80401 + 3.12464i) q^{85} +(-0.972254 - 0.561331i) q^{86} +(-1.70569 + 6.86897i) q^{87} +(-7.64033 - 13.2334i) q^{88} +(-4.26740 - 7.39135i) q^{89} +(2.78602 - 0.102593i) q^{90} +(-0.822383 - 1.34624i) q^{91} +(2.71192 + 1.56573i) q^{92} +(10.6443 - 3.06315i) q^{93} +5.32654i q^{94} +3.24453i q^{95} +(9.02880 - 2.59826i) q^{96} +(11.2557 + 6.49848i) q^{97} +(0.322235 + 6.49712i) q^{98} +(-7.35747 + 13.9011i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9}+O(q^{10}) $ 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9	$ 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9} + 3 q^{10} + 9 q^{11} + 15 q^{12} - 12 q^{13} - 27 q^{14} - q^{15} + 42 q^{16} - 3 q^{17} - 4 q^{18} - 15 q^{20} + 4 q^{21} + 15 q^{22} + q^{24} - 15 q^{25} + 24 q^{26} - 5 q^{27} + 27 q^{28} - 2 q^{30} - 25 q^{33} + 48 q^{34} - 6 q^{35} + 21 q^{36} - 3 q^{37} - 30 q^{38} - 3 q^{39} + 3 q^{40} - 18 q^{41} - 16 q^{42} + 12 q^{43} + 15 q^{44} - 7 q^{45} + 9 q^{46} - 60 q^{47} - 40 q^{48} - 15 q^{49} + 3 q^{50} - 48 q^{51} - 33 q^{52} - 30 q^{53} + 35 q^{54} + 42 q^{56} - 21 q^{57} + 30 q^{59} + 33 q^{60} + 12 q^{62} - 47 q^{63} - 138 q^{64} + 100 q^{66} + 12 q^{67} - 21 q^{68} + 32 q^{69} - 18 q^{70} + 85 q^{72} + 6 q^{73} + 54 q^{74} - 5 q^{75} - 54 q^{76} - 9 q^{77} - 18 q^{78} + 24 q^{79} + 21 q^{80} - 14 q^{81} + 6 q^{82} - 6 q^{83} - 9 q^{84} + 3 q^{85} - 60 q^{86} - 16 q^{87} - 48 q^{88} - 3 q^{89} + 22 q^{90} + 15 q^{91} - 3 q^{92} + 69 q^{93} - 48 q^{96} + 36 q^{97} + 24 q^{98} - q^{99}+O(q^{100}) $ 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9 + 3 * q^10 + 9 * q^11 + 15 * q^12 - 12 * q^13 - 27 * q^14 - q^15 + 42 * q^16 - 3 * q^17 - 4 * q^18 - 15 * q^20 + 4 * q^21 + 15 * q^22 + q^24 - 15 * q^25 + 24 * q^26 - 5 * q^27 + 27 * q^28 - 2 * q^30 - 25 * q^33 + 48 * q^34 - 6 * q^35 + 21 * q^36 - 3 * q^37 - 30 * q^38 - 3 * q^39 + 3 * q^40 - 18 * q^41 - 16 * q^42 + 12 * q^43 + 15 * q^44 - 7 * q^45 + 9 * q^46 - 60 * q^47 - 40 * q^48 - 15 * q^49 + 3 * q^50 - 48 * q^51 - 33 * q^52 - 30 * q^53 + 35 * q^54 + 42 * q^56 - 21 * q^57 + 30 * q^59 + 33 * q^60 + 12 * q^62 - 47 * q^63 - 138 * q^64 + 100 * q^66 + 12 * q^67 - 21 * q^68 + 32 * q^69 - 18 * q^70 + 85 * q^72 + 6 * q^73 + 54 * q^74 - 5 * q^75 - 54 * q^76 - 9 * q^77 - 18 * q^78 + 24 * q^79 + 21 * q^80 - 14 * q^81 + 6 * q^82 - 6 * q^83 - 9 * q^84 + 3 * q^85 - 60 * q^86 - 16 * q^87 - 48 * q^88 - 3 * q^89 + 22 * q^90 + 15 * q^91 - 3 * q^92 + 69 * q^93 - 48 * q^96 + 36 * q^97 + 24 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	0.929301i		−	0.657115i	−0.944484	−	0.328558i	$-0.893437\pi$
$2$		−	0.929301i		−	0.657115i	0.944484	−	0.328558i	$-0.106563\pi$
$3$	0.479000	+	1.66450i	0.276551	+	0.960999i
$3$	0.479000	+	1.66450i	0.276551	+	0.960999i
$4$	1.13640			0.568200
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	1.54682	−	0.445136i	0.631487	−	0.181726i
$7$	0.0655497	+	2.64494i	0.0247754	+	0.999693i
$7$	0.0655497	+	2.64494i	0.0247754	+	0.999693i
$8$		−	2.91466i		−	1.03049i
$9$	−2.54112	+	1.59459i	−0.847039	+	0.531530i
$10$	−0.804799	−	0.464651i	−0.254500	−	0.146935i
$11$	4.54030	−	2.62135i	1.36895	−	0.790365i	0.378158	−	0.925741i	$-0.376557\pi$
$11$	4.54030	−	2.62135i	1.36895	−	0.790365i	0.990794	+	0.135376i	$0.0432241\pi$
$12$	0.544335	+	1.89154i	0.157136	+	0.546039i
$13$	−0.516376	+	0.298130i	−0.143217	+	0.0826863i	−0.569896	−	0.821717i	$-0.693017\pi$
$13$	−0.516376	+	0.298130i	−0.143217	+	0.0826863i	0.426679	+	0.904403i	$0.359683\pi$
$14$	2.45795	−	0.0609154i	0.656914	−	0.0162803i
$15$	1.68100	+	0.417423i	0.434032	+	0.107778i
$16$	−0.435799			−0.108950
$17$	−1.80401	+	3.12464i	−0.437536	+	0.757835i	−0.997499	−	0.0706826i	$-0.977482\pi$
$17$	−1.80401	+	3.12464i	−0.437536	+	0.757835i	0.559962	+	0.828518i	$0.310816\pi$
$18$	1.48186	+	2.36146i	0.349277	+	0.556602i
$19$	−2.80984	+	1.62226i	−0.644622	+	0.372173i	−0.786393	−	0.617727i	$-0.788054\pi$
$19$	−2.80984	+	1.62226i	−0.644622	+	0.372173i	0.141771	+	0.989900i	$0.454720\pi$
$20$	0.568200	−	0.984151i	0.127053	−	0.220063i
$21$	−4.37110	+	1.37603i	−0.953853	+	0.300275i
$22$	−2.43602	−	4.21931i	−0.519361	−	0.899560i
$23$	2.38642	+	1.37780i	0.497602	+	0.287291i	0.727723	−	0.685871i	$-0.240579\pi$
$23$	2.38642	+	1.37780i	0.497602	+	0.287291i	−0.230121	+	0.973162i	$0.573912\pi$
$24$	4.85145	−	1.39612i	0.990298	−	0.284982i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.277052	+	0.479869i	0.0543344	+	0.0941100i
$27$	−3.87139	−	3.46588i	−0.745050	−	0.667009i
$28$	0.0744906	+	3.00571i	0.0140774	+	0.568025i
$29$	3.53879	+	2.04312i	0.657137	+	0.379398i	0.791185	−	0.611576i	$-0.209464\pi$
$29$	3.53879	+	2.04312i	0.657137	+	0.379398i	−0.134048	+	0.990975i	$0.542798\pi$
$30$	0.387912	−	1.56215i	0.0708227	−	0.285209i
$31$		−	6.39488i		−	1.14855i	−0.818661	−	0.574277i	$-0.805283\pi$
$31$		−	6.39488i		−	1.14855i	0.818661	−	0.574277i	$-0.194717\pi$
$32$		−	5.42433i		−	0.958895i
$33$	6.53803	+	6.30171i	1.13813	+	1.09699i
$34$	2.90373	+	1.67647i	0.497985	+	0.287512i
$35$	2.32336	+	1.26570i	0.392719	+	0.213943i
$36$	−2.88772	+	1.81209i	−0.481287	+	0.302015i
$37$	0.988179	+	1.71158i	0.162456	+	0.281381i	0.935749	−	0.352667i	$-0.114725\pi$
$37$	0.988179	+	1.71158i	0.162456	+	0.281381i	−0.773293	+	0.634049i	$0.781392\pi$
$38$	1.50757	+	2.61119i	0.244560	+	0.423591i
$39$	−0.743581	−	0.716703i	−0.119068	−	0.114764i
$40$	−2.52417	−	1.45733i	−0.399106	−	0.230424i
$41$	−4.89572	−	8.47964i	−0.764583	−	1.32430i	−0.940467	−	0.339886i	$-0.889612\pi$
$41$	−4.89572	−	8.47964i	−0.764583	−	1.32430i	0.175884	−	0.984411i	$-0.443722\pi$
$42$	1.27875	+	4.06207i	0.197315	+	0.626791i
$43$	0.604036	−	1.04622i	0.0921146	−	0.159547i	−0.816286	−	0.577648i	$-0.803971\pi$
$43$	0.604036	−	1.04622i	0.0921146	−	0.159547i	0.908401	+	0.418101i	$0.137304\pi$
$44$	5.15960	−	2.97889i	0.777838	−	0.449085i
$45$	0.110398	+	2.99797i	0.0164571	+	0.446911i
$46$	1.28039	−	2.21770i	0.188783	−	0.326982i
$47$	−5.73177			−0.836064			−0.418032	−	0.908432i	$-0.637280\pi$
$47$	−5.73177			−0.836064			−0.418032	+	0.908432i	$0.637280\pi$
$48$	−0.208748	−	0.725387i	−0.0301301	−	0.104701i
$49$	−6.99141	+	0.346750i	−0.998772	+	0.0495357i
$50$	−0.804799	+	0.464651i	−0.113816	+	0.0657115i
$51$	−6.06508	−	1.50607i	−0.849280	−	0.210892i
$52$	−0.586809	+	0.338794i	−0.0813758	+	0.0469823i
$53$	−8.79935	−	5.08031i	−1.20868	−	0.697834i	−0.246212	−	0.969216i	$-0.579186\pi$
$53$	−8.79935	−	5.08031i	−1.20868	−	0.697834i	−0.962472	+	0.271382i	$0.912519\pi$
$54$	−3.22085	+	3.59769i	−0.438302	+	0.489584i
$55$		−	5.24269i		−	0.706924i
$56$	7.70910	−	0.191055i	1.03017	−	0.0255308i
$57$	−4.04617	−	3.89992i	−0.535928	−	0.516556i
$58$	1.89868	−	3.28860i	0.249308	−	0.431815i
$59$	1.32833			0.172934			0.0864668	−	0.996255i	$-0.472442\pi$
$59$	1.32833			0.172934			0.0864668	+	0.996255i	$0.472442\pi$
$60$	1.91029	+	0.474360i	0.246617	+	0.0612396i
$61$			10.0668i			1.28892i	0.764639	+	0.644459i	$0.222917\pi$
$61$			10.0668i			1.28892i	−0.764639	+	0.644459i	$0.777083\pi$
$62$	−5.94277			−0.754732
$63$	−4.38417	−	6.61658i	−0.552353	−	0.833610i
$64$	−5.91244			−0.739054
$65$			0.596259i			0.0739569i
$66$	5.85618	−	6.07580i	0.720847	−	0.747880i
$67$	−9.26557			−1.13197			−0.565985	−	0.824416i	$-0.691504\pi$
$67$	−9.26557			−1.13197			−0.565985	+	0.824416i	$0.691504\pi$
$68$	−2.05007	+	3.55083i	−0.248608	+	0.430602i
$69$	−1.15025	+	4.63215i	−0.138474	+	0.557646i
$70$	1.17622	−	2.15910i	0.140585	−	0.258062i
$71$		−	11.6581i		−	1.38357i	−0.722105	−	0.691784i	$-0.756825\pi$
$71$		−	11.6581i		−	1.38357i	0.722105	−	0.691784i	$-0.243175\pi$
$72$	4.64769	+	7.40649i	0.547736	+	0.872864i
$73$	12.2136	+	7.05152i	1.42949	+	0.825318i	0.997081	−	0.0763575i	$-0.0243290\pi$
$73$	12.2136	+	7.05152i	1.42949	+	0.825318i	0.432413	+	0.901676i	$0.357662\pi$
$74$	1.59057	−	0.918316i	0.184900	−	0.106752i
$75$	1.20200	−	1.24708i	0.138795	−	0.144000i
$76$	−3.19310	+	1.84354i	−0.366274	+	0.211468i
$77$	7.23091	+	11.8370i	0.824039	+	1.34895i
$78$	−0.666033	+	0.691011i	−0.0754134	+	0.0782415i
$79$	−12.9669			−1.45888			−0.729442	−	0.684042i	$-0.760220\pi$
$79$	−12.9669			−1.45888			−0.729442	+	0.684042i	$0.760220\pi$
$80$	−0.217899	+	0.377413i	−0.0243619	+	0.0421960i
$81$	3.91456	−	8.10409i	0.434951	−	0.900454i
$82$	−7.88014	+	4.54960i	−0.870215	+	0.502419i
$83$	−5.40645	+	9.36424i	−0.593435	+	1.02786i	0.400331	+	0.916371i	$0.368895\pi$
$83$	−5.40645	+	9.36424i	−0.593435	+	1.02786i	−0.993766	+	0.111489i	$0.964438\pi$
$84$	−4.96732	+	1.56372i	−0.541979	+	0.170616i
$85$	1.80401	+	3.12464i	0.195672	+	0.338914i
$86$	−0.972254	−	0.561331i	−0.104841	−	0.0605299i
$87$	−1.70569	+	6.86897i	−0.182870	+	0.736431i
$88$	−7.64033	−	13.2334i	−0.814462	−	1.41069i
$89$	−4.26740	−	7.39135i	−0.452343	−	0.783481i	0.546188	−	0.837663i	$-0.316078\pi$
$89$	−4.26740	−	7.39135i	−0.452343	−	0.783481i	−0.998531	+	0.0541814i	$0.982745\pi$
$90$	2.78602	−	0.102593i	0.293672	−	0.0108142i
$91$	−0.822383	−	1.34624i	−0.0862092	−	0.141124i
$92$	2.71192	+	1.56573i	0.282737	+	0.163239i
$93$	10.6443	−	3.06315i	1.10376	−	0.317634i
$94$			5.32654i			0.549390i
$95$			3.24453i			0.332881i
$96$	9.02880	−	2.59826i	0.921498	−	0.265183i
$97$	11.2557	+	6.49848i	1.14284	+	0.659820i	0.947133	−	0.320842i	$-0.103966\pi$
$97$	11.2557	+	6.49848i	1.14284	+	0.659820i	0.195709	+	0.980662i	$0.437299\pi$
$98$	0.322235	+	6.49712i	0.0325507	+	0.656309i
$99$	−7.35747	+	13.9011i	−0.739453	+	1.39711i
$100$	−0.568200	−	0.984151i	−0.0568200	−	0.0984151i
$101$	2.07528	+	3.59450i	0.206498	+	0.357666i	0.950609	−	0.310391i	$-0.100460\pi$
$101$	2.07528	+	3.59450i	0.206498	+	0.357666i	−0.744111	+	0.668056i	$0.767127\pi$
$102$	−1.39959	+	5.63628i	−0.138580	+	0.558075i
$103$	−10.0012	−	5.77417i	−0.985443	−	0.568946i	−0.0815339	−	0.996671i	$-0.525982\pi$
$103$	−10.0012	−	5.77417i	−0.985443	−	0.568946i	−0.903909	+	0.427725i	$0.859315\pi$
$104$	0.868946	+	1.50506i	0.0852072	+	0.147583i
$105$	−0.993871	+	4.47350i	−0.0969918	+	0.436569i
$106$	−4.72114	+	8.17725i	−0.458557	+	0.794245i
$107$	0.875674	−	0.505571i	0.0846546	−	0.0488753i	−0.457075	−	0.889428i	$-0.651103\pi$
$107$	0.875674	−	0.505571i	0.0846546	−	0.0488753i	0.541730	+	0.840553i	$0.317770\pi$
$108$	−4.39945	−	3.93862i	−0.423337	−	0.378994i
$109$	3.13405	−	5.42833i	0.300187	−	0.519940i	−0.675991	−	0.736910i	$-0.736284\pi$
$109$	3.13405	−	5.42833i	0.300187	−	0.519940i	0.976178	+	0.216970i	$0.0696175\pi$
$110$	−4.87204			−0.464531
$111$	−2.37558	+	2.46467i	−0.225480	+	0.233936i
$112$	−0.0285665	−	1.15266i	−0.00269928	−	0.108916i
$113$	−11.5944	+	6.69401i	−1.09071	+	0.629719i	−0.933764	−	0.357888i	$-0.883497\pi$
$113$	−11.5944	+	6.69401i	−1.09071	+	0.629719i	−0.156942	+	0.987608i	$0.550163\pi$
$114$	−3.62420	+	3.76011i	−0.339437	+	0.352167i
$115$	2.38642	−	1.37780i	0.222534	−	0.128480i
$116$	4.02148	+	2.32180i	0.373385	+	0.215574i
$117$	0.836776	−	1.58099i	0.0773600	−	0.146163i
$118$		−	1.23442i		−	0.113637i
$119$	−8.38272	−	4.56668i	−0.768443	−	0.418626i
$120$	1.21665	−	4.89954i	0.111064	−	0.447265i
$121$	8.24290	−	14.2771i	0.749355	−	1.29792i
$122$	9.35507			0.846968
$123$	11.7693	−	12.2107i	1.06120	−	1.10100i
$124$		−	7.26713i		−	0.652608i
$125$	−1.00000			−0.0894427
$126$	−6.14879	+	4.07421i	−0.547778	+	0.362960i
$127$	12.6328			1.12098			0.560488	−	0.828162i	$-0.310613\pi$
$127$	12.6328			1.12098			0.560488	+	0.828162i	$0.310613\pi$
$128$		−	5.35423i		−	0.473251i
$129$	2.03077	+	0.504277i	0.178799	+	0.0443991i
$130$	0.554105			0.0485982
$131$	2.49193	−	4.31615i	0.217721	−	0.377104i	−0.736390	−	0.676557i	$-0.763471\pi$
$131$	2.49193	−	4.31615i	0.217721	−	0.377104i	0.954111	+	0.299454i	$0.0968044\pi$
$132$	7.42982	+	7.16125i	0.646682	+	0.623307i
$133$	−4.47497	−	7.32552i	−0.388029	−	0.635203i
$134$			8.61050i			0.743834i
$135$	−4.93724	+	1.61978i	−0.424930	+	0.139409i
$136$	9.10725	+	5.25807i	0.780940	+	0.450876i
$137$	10.5476	−	6.08968i	0.901145	−	0.520277i	0.0235738	−	0.999722i	$-0.492496\pi$
$137$	10.5476	−	6.08968i	0.901145	−	0.520277i	0.877572	+	0.479446i	$0.159162\pi$
$138$	4.30467	+	1.06893i	0.366438	+	0.0909933i
$139$	14.5703	−	8.41218i	1.23584	−	0.713512i	0.267598	−	0.963531i	$-0.413770\pi$
$139$	14.5703	−	8.41218i	1.23584	−	0.713512i	0.968241	+	0.250019i	$0.0804369\pi$
$140$	2.64026	+	1.43834i	0.223143	+	0.121562i
$141$	−2.74552	−	9.54052i	−0.231214	−	0.803457i
$142$	−10.8339			−0.909163
$143$	−1.56300	+	2.70720i	−0.130705	+	0.226387i
$144$	1.10742	−	0.694921i	0.0922847	−	0.0579101i
$145$	3.53879	−	2.04312i	0.293881	−	0.169672i
$146$	6.55299	−	11.3501i	0.542329	−	0.939342i
$147$	−3.92605	−	11.4711i	−0.323815	−	0.946120i
$148$	1.12297	+	1.94503i	0.0923072	+	0.159881i
$149$	4.10533	+	2.37021i	0.336322	+	0.194175i	0.658644	−	0.752454i	$-0.271130\pi$
$149$	4.10533	+	2.37021i	0.336322	+	0.194175i	−0.322323	+	0.946630i	$0.604464\pi$
$150$	−1.15891	−	1.11702i	−0.0946246	−	0.0912042i
$151$	8.91211	+	15.4362i	0.725257	+	1.25618i	0.958868	+	0.283852i	$0.0916125\pi$
$151$	8.91211	+	15.4362i	0.725257	+	1.25618i	−0.233611	+	0.972330i	$0.575054\pi$
$152$	4.72834	+	8.18973i	0.383519	+	0.664275i
$153$	−0.398317	−	10.8167i	−0.0322021	−	0.874480i
$154$	11.0001	−	6.71970i	0.886416	−	0.541489i
$155$	−5.53812	−	3.19744i	−0.444833	−	0.256824i
$156$	−0.845005	−	0.814461i	−0.0676545	−	0.0652090i
$157$			5.92643i			0.472981i	0.971634	+	0.236490i	$0.0759972\pi$
$157$			5.92643i			0.472981i	−0.971634	+	0.236490i	$0.924003\pi$
$158$			12.0501i			0.958655i
$159$	4.24128	−	17.0800i	0.336355	−	1.35453i
$160$	−4.69761	−	2.71217i	−0.371379	−	0.214416i
$161$	−3.48776	+	6.40224i	−0.274874	+	0.504567i
$162$	−7.53114	−	3.63780i	−0.591702	−	0.285813i
$163$	−7.24254	−	12.5444i	−0.567279	−	0.982556i	−0.996834	−	0.0795155i	$-0.974663\pi$
$163$	−7.24254	−	12.5444i	−0.567279	−	0.982556i	0.429554	−	0.903041i	$-0.358671\pi$
$164$	−5.56349	−	9.63625i	−0.434436	−	0.752465i
$165$	8.72646	−	2.51125i	0.679354	−	0.195501i
$166$	8.70220	+	5.02422i	0.675422	+	0.389955i
$167$	−6.15227	−	10.6560i	−0.476077	−	0.824589i	0.523547	−	0.851997i	$-0.324608\pi$
$167$	−6.15227	−	10.6560i	−0.476077	−	0.824589i	−0.999624	+	0.0274071i	$0.991275\pi$
$168$	4.01067	+	12.7403i	0.309430	+	0.982934i
$169$	−6.32224	+	10.9504i	−0.486326	+	0.842341i
$170$	2.90373	−	1.67647i	0.222706	−	0.128579i
$171$	4.55329	−	8.60291i	0.348199	−	0.657881i
$172$	0.686426	−	1.18892i	0.0523395	−	0.0906546i
$173$	−2.25025			−0.171084			−0.0855418	−	0.996335i	$-0.527262\pi$
$173$	−2.25025			−0.171084			−0.0855418	+	0.996335i	$0.527262\pi$
$174$	6.38335	+	1.58510i	0.483920	+	0.120166i
$175$	2.25781	−	1.37924i	0.170674	−	0.104261i
$176$	−1.97866	+	1.14238i	−0.149147	+	0.0861101i
$177$	0.636269	+	2.21100i	0.0478249	+	0.166189i
$178$	−6.86879	+	3.96570i	−0.514837	+	0.297242i
$179$	11.4279	+	6.59789i	0.854159	+	0.493149i	0.862052	−	0.506820i	$-0.169179\pi$
$179$	11.4279	+	6.59789i	0.854159	+	0.493149i	−0.00789264	+	0.999969i	$0.502512\pi$
$180$	0.125456	+	3.40689i	0.00935094	+	0.253934i
$181$			6.74629i			0.501448i	0.968059	+	0.250724i	$0.0806687\pi$
$181$			6.74629i			0.501448i	−0.968059	+	0.250724i	$0.919331\pi$
$182$	−1.25106	+	0.764242i	−0.0927349	+	0.0566494i
$183$	−16.7561	+	4.82199i	−1.23865	+	0.356452i
$184$	4.01581	−	6.95559i	0.296050	−	0.512773i
$185$	1.97636			0.145305
$186$	−2.84659	−	9.89173i	−0.208722	−	0.725297i
$187$			18.9157i			1.38325i
$188$	−6.51357			−0.475051
$189$	8.91327	−	10.4668i	0.648345	−	0.761347i
$190$	3.01514			0.218741
$191$			9.82110i			0.710630i	0.934747	+	0.355315i	$0.115626\pi$
$191$			9.82110i			0.710630i	−0.934747	+	0.355315i	$0.884374\pi$
$192$	−2.83206	−	9.84125i	−0.204386	−	0.710231i
$193$	9.36496			0.674105			0.337052	−	0.941486i	$-0.390570\pi$
$193$	9.36496			0.674105			0.337052	+	0.941486i	$0.390570\pi$
$194$	6.03904	−	10.4599i	0.433578	−	0.750979i
$195$	−0.992473	+	0.285608i	−0.0710725	+	0.0204528i
$196$	−7.94503	+	0.394046i	−0.567502	+	0.0281462i
$197$			4.31693i			0.307569i	0.988104	+	0.153784i	$0.0491461\pi$
$197$			4.31693i			0.307569i	−0.988104	+	0.153784i	$0.950854\pi$
$198$	12.9183	+	6.83731i	0.918063	+	0.485906i
$199$	14.8590	+	8.57887i	1.05333	+	0.608140i	0.923579	−	0.383407i	$-0.125249\pi$
$199$	14.8590	+	8.57887i	1.05333	+	0.608140i	0.129749	+	0.991547i	$0.458583\pi$
$200$	−2.52417	+	1.45733i	−0.178486	+	0.103049i
$201$	−4.43821	−	15.4225i	−0.313047	−	1.08782i
$202$	3.34037	−	1.92856i	0.235028	−	0.135693i
$203$	−5.17197	+	9.49382i	−0.363001	+	0.666335i
$204$	−6.89235	−	1.71150i	−0.482561	−	0.119829i
$205$	−9.79144			−0.683864
$206$	−5.36594	+	9.29408i	−0.373863	+	0.647549i
$207$	−8.26119	+	0.304212i	−0.574192	+	0.0211442i
$208$	0.225036	−	0.129925i	0.0156034	−	0.00900864i
$209$	−8.50502	+	14.7311i	−0.588305	+	1.01897i
$210$	4.15723	+	0.923605i	0.286876	+	0.0637348i
$211$	10.0158	+	17.3479i	0.689519	+	1.19428i	0.971994	+	0.235007i	$0.0755113\pi$
$211$	10.0158	+	17.3479i	0.689519	+	1.19428i	−0.282475	+	0.959275i	$0.591155\pi$
$212$	−9.99958	−	5.77326i	−0.686774	−	0.396509i
$213$	19.4050	−	5.58425i	1.32961	−	0.382627i
$214$	−0.469827	−	0.813765i	−0.0321167	−	0.0556278i
$215$	−0.604036	−	1.04622i	−0.0411949	−	0.0713517i
$216$	−10.1019	+	11.2838i	−0.687344	+	0.767765i
$217$	16.9141	−	0.419182i	1.14820	−	0.0284559i
$218$	−5.04455	−	2.91247i	−0.341660	−	0.197258i
$219$	−5.88694	+	23.7072i	−0.397803	+	1.60198i
$220$		−	5.95779i		−	0.401674i
$221$		−	2.15131i		−	0.144713i
$222$	2.29042	+	2.20763i	0.153723	+	0.148166i
$223$	13.5808	+	7.84086i	0.909435	+	0.525063i	0.880249	−	0.474511i	$-0.157375\pi$
$223$	13.5808	+	7.84086i	0.909435	+	0.525063i	0.0291859	+	0.999574i	$0.490709\pi$
$224$	14.3470	−	0.355563i	0.958601	−	0.0237571i
$225$	2.65152	+	1.40338i	0.176768	+	0.0935584i
$226$	6.22075	+	10.7747i	0.413798	+	0.716720i
$227$	−2.14698	−	3.71868i	−0.142500	−	0.246817i	0.785937	−	0.618306i	$-0.212181\pi$
$227$	−2.14698	−	3.71868i	−0.142500	−	0.246817i	−0.928437	+	0.371489i	$0.878847\pi$
$228$	−4.59806	−	4.43186i	−0.304514	−	0.293507i
$229$	−7.29434	−	4.21139i	−0.482024	−	0.278297i	0.239236	−	0.970962i	$-0.423103\pi$
$229$	−7.29434	−	4.21139i	−0.482024	−	0.278297i	−0.721259	+	0.692665i	$0.756436\pi$
$230$	−1.28039	−	2.21770i	−0.0844264	−	0.146231i
$231$	−16.2391	+	17.7058i	−1.06845	+	1.16495i
$232$	5.95501	−	10.3144i	0.390965	−	0.677172i
$233$	13.0808	−	7.55221i	0.856953	−	0.494762i	−0.00603784	−	0.999982i	$-0.501922\pi$
$233$	13.0808	−	7.55221i	0.856953	−	0.494762i	0.862991	+	0.505220i	$0.168589\pi$
$234$	−1.46922	−	0.777617i	−0.0960457	−	0.0508344i
$235$	−2.86588	+	4.96386i	−0.186950	+	0.323806i
$236$	1.50951			0.0982608
$237$	−6.21113	−	21.5833i	−0.403456	−	1.40199i
$238$	−4.24382	+	7.79008i	−0.275086	+	0.504956i
$239$	−7.72892	+	4.46229i	−0.499942	+	0.288642i	−0.728690	−	0.684844i	$-0.759870\pi$
$239$	−7.72892	+	4.46229i	−0.499942	+	0.288642i	0.228748	+	0.973486i	$0.426537\pi$
$240$	−0.732577	−	0.181913i	−0.0472877	−	0.0117424i
$241$	26.4082	−	15.2468i	1.70110	−	0.982132i	0.756454	−	0.654046i	$-0.226930\pi$
$241$	26.4082	−	15.2468i	1.70110	−	0.982132i	0.944648	−	0.328085i	$-0.106403\pi$
$242$	−13.2677	−	7.66014i	−0.852883	−	0.492412i
$243$	15.3643	+	2.63392i	0.985622	+	0.168966i
$244$			11.4399i			0.732363i
$245$	−3.19541	+	6.22811i	−0.204147	+	0.397899i
$246$	−11.3474	−	10.9372i	−0.723483	−	0.697332i
$247$	0.967289	−	1.67539i	0.0615471	−	0.106603i
$248$	−18.6389			−1.18357
$249$	−18.1765	−	4.51356i	−1.15189	−	0.286035i
$250$			0.929301i			0.0587742i
$251$	9.76019			0.616058			0.308029	−	0.951377i	$-0.400331\pi$
$251$	9.76019			0.616058			0.308029	+	0.951377i	$0.400331\pi$
$252$	−4.98216	−	7.51907i	−0.313847	−	0.473657i
$253$	14.4467			0.908259
$254$		−	11.7396i		−	0.736611i
$255$	−4.33683	+	4.49947i	−0.271583	+	0.281768i
$256$	−16.8006			−1.05004
$257$	−5.21004	+	9.02405i	−0.324993	+	0.562905i	−0.981511	−	0.191406i	$-0.938695\pi$
$257$	−5.21004	+	9.02405i	−0.324993	+	0.562905i	0.656518	+	0.754311i	$0.272029\pi$
$258$	0.468626	−	1.88719i	0.0291754	−	0.117492i
$259$	−4.46224	+	2.72587i	−0.277270	+	0.169377i
$260$			0.677589i			0.0420223i
$261$	−12.2504	+	0.451113i	−0.758283	+	0.0279232i
$262$	−4.01100	−	2.31575i	−0.247801	−	0.143068i
$263$	−20.0438	+	11.5723i	−1.23596	+	0.713579i	−0.968265	−	0.249926i	$-0.919594\pi$
$263$	−20.0438	+	11.5723i	−1.23596	+	0.713579i	−0.267690	+	0.963505i	$0.586260\pi$
$264$	18.3673	−	19.0561i	1.13043	−	1.17282i
$265$	−8.79935	+	5.08031i	−0.540540	+	0.312081i
$266$	−6.80762	+	4.15860i	−0.417402	+	0.254980i
$267$	10.2588	−	10.6435i	0.627829	−	0.651374i
$268$	−10.5294			−0.643184
$269$	−15.6437	+	27.0957i	−0.953815	+	1.65206i	−0.216759	+	0.976225i	$0.569549\pi$
$269$	−15.6437	+	27.0957i	−0.953815	+	1.65206i	−0.737056	+	0.675831i	$0.763785\pi$
$270$	1.50527	+	4.58818i	0.0916077	+	0.279228i
$271$	−16.0145	+	9.24600i	−0.972814	+	0.561654i	−0.900093	−	0.435698i	$-0.856502\pi$
$271$	−16.0145	+	9.24600i	−0.972814	+	0.561654i	−0.0727211	+	0.997352i	$0.523168\pi$
$272$	0.786185	−	1.36171i	0.0476695	−	0.0825659i
$273$	1.84689	−	2.01371i	0.111779	−	0.121875i
$274$	−5.65915	−	9.80193i	−0.341882	−	0.592156i
$275$	−4.54030	−	2.62135i	−0.273791	−	0.158073i
$276$	−1.30714	+	5.26398i	−0.0786808	+	0.316854i
$277$	8.73371	+	15.1272i	0.524758	+	0.908907i	0.999584	+	0.0288279i	$0.00917746\pi$
$277$	8.73371	+	15.1272i	0.524758	+	0.908907i	−0.474827	+	0.880079i	$0.657489\pi$
$278$	−7.81745	−	13.5402i	−0.468859	−	0.812088i
$279$	10.1972	+	16.2501i	0.610491	+	0.972870i
$280$	3.68909	−	6.77180i	0.220465	−	0.404693i
$281$	17.7776	+	10.2639i	1.06052	+	0.612292i	0.925576	−	0.378561i	$-0.123581\pi$
$281$	17.7776	+	10.2639i	1.06052	+	0.612292i	0.134945	+	0.990853i	$0.456914\pi$
$282$	−8.86602	+	2.55141i	−0.527964	+	0.151934i
$283$		−	22.8794i		−	1.36004i	−0.733193	−	0.680021i	$-0.761971\pi$
$283$		−	22.8794i		−	1.36004i	0.733193	−	0.680021i	$-0.238029\pi$
$284$		−	13.2483i		−	0.786142i
$285$	−5.40051	+	1.55413i	−0.319899	+	0.0920586i
$286$	2.51580	+	1.45250i	0.148763	+	0.0858881i
$287$	22.1072	−	13.5047i	1.30495	−	0.797158i
$288$	8.64959	+	13.7839i	0.509682	+	0.812222i
$289$	1.99110	+	3.44869i	0.117124	+	0.202864i
$290$	−1.89868	−	3.28860i	−0.111494	−	0.193113i
$291$	−5.42523	+	21.8479i	−0.318033	+	1.28074i
$292$	13.8795	+	8.01334i	0.812237	+	0.468945i
$293$	6.87701	+	11.9113i	0.401759	+	0.695868i	0.993938	−	0.109939i	$-0.0350655\pi$
$293$	6.87701	+	11.9113i	0.401759	+	0.695868i	−0.592179	+	0.805806i	$0.701732\pi$
$294$	−10.6601	+	3.64848i	−0.621710	+	0.212784i
$295$	0.664164	−	1.15037i	0.0386691	−	0.0669769i
$296$	4.98866	−	2.88020i	0.289960	−	0.167409i
$297$	−26.6626	−	5.58789i	−1.54712	−	0.324242i
$298$	2.20264	−	3.81509i	0.127596	−	0.221002i
$299$	−1.64305			−0.0950200
$300$	1.36595	−	1.41718i	0.0788632	−	0.0818207i
$301$	2.80678	+	1.52906i	0.161780	+	0.0881335i
$302$	14.3449	−	8.28203i	0.825457	−	0.476578i
$303$	−4.98898	+	5.17607i	−0.286609	+	0.297358i
$304$	1.22453	−	0.706980i	0.0702313	−	0.0405481i
$305$	8.71808	+	5.03339i	0.499196	+	0.288211i
$306$	−10.0520	+	0.370157i	−0.574634	+	0.0211605i
$307$		−	21.7512i		−	1.24141i	−0.784046	−	0.620703i	$-0.786847\pi$
$307$		−	21.7512i		−	1.24141i	0.784046	−	0.620703i	$-0.213153\pi$
$308$	8.21720	+	13.4516i	0.468219	+	0.766473i
$309$	4.82055	−	19.4127i	0.274231	−	1.10435i
$310$	−2.97138	+	5.14659i	−0.168763	+	0.292306i
$311$	−11.4895			−0.651507			−0.325754	−	0.945455i	$-0.605618\pi$
$311$	−11.4895			−0.651507			−0.325754	+	0.945455i	$0.605618\pi$
$312$	−2.08895	+	2.16728i	−0.118263	+	0.122698i
$313$		−	28.3691i		−	1.60352i	−0.597648	−	0.801758i	$-0.703898\pi$
$313$		−	28.3691i		−	1.60352i	0.597648	−	0.801758i	$-0.296102\pi$
$314$	5.50744			0.310803
$315$	−7.92221	+	0.488511i	−0.446366	+	0.0275245i
$316$	−14.7355			−0.828938
$317$		−	13.6208i		−	0.765022i	−0.923951	−	0.382511i	$-0.875059\pi$
$317$		−	13.6208i		−	0.765022i	0.923951	−	0.382511i	$-0.124941\pi$
$318$	−15.8725	−	3.94143i	−0.890083	−	0.221024i
$319$	21.4229			1.19945
$320$	−2.95622	+	5.12032i	−0.165258	+	0.286235i
$321$	1.26097	+	1.21539i	0.0703805	+	0.0678365i
$322$	5.94961	+	3.24118i	0.331559	+	0.180624i
$323$		−	11.7063i		−	0.651356i
$324$	4.44850	−	9.20948i	0.247139	−	0.511638i
$325$	0.516376	+	0.298130i	0.0286434	+	0.0165373i
$326$	−11.6576	+	6.73050i	−0.645653	+	0.372768i
$327$	10.5367	+	2.61645i	0.582679	+	0.144690i
$328$	−24.7153	+	14.2694i	−1.36467	+	0.787893i
$329$	−0.375715	−	15.1602i	−0.0207139	−	0.835807i
$330$	−2.33371	−	8.10951i	−0.128466	−	0.446414i
$331$	−23.0252			−1.26558			−0.632789	−	0.774325i	$-0.718090\pi$
$331$	−23.0252			−1.26558			−0.632789	+	0.774325i	$0.718090\pi$
$332$	−6.14388	+	10.6415i	−0.337189	+	0.584029i
$333$	−5.24034	−	2.77357i	−0.287169	−	0.151991i
$334$	−9.90268	+	5.71731i	−0.541850	+	0.312837i
$335$	−4.63278	+	8.02422i	−0.253116	+	0.438410i
$336$	1.90492	−	0.599674i	0.103922	−	0.0327149i
$337$	5.15757	+	8.93317i	0.280951	+	0.486621i	0.971619	−	0.236551i	$-0.0760169\pi$
$337$	5.15757	+	8.93317i	0.280951	+	0.486621i	−0.690668	+	0.723172i	$0.742684\pi$
$338$	10.1763	+	5.87526i	0.553515	+	0.319572i
$339$	−16.6959	−	16.0924i	−0.906796	−	0.874018i
$340$	2.05007	+	3.55083i	0.111181	+	0.192571i
$341$	−16.7632	−	29.0347i	−0.907777	−	1.57232i
$342$	−7.99469	−	4.23138i	−0.432304	−	0.228807i
$343$	−1.37542	−	18.4691i	−0.0742655	−	0.997239i
$344$	−3.04938	−	1.76056i	−0.164411	−	0.0949230i
$345$	3.43644	+	3.31222i	0.185012	+	0.178324i
$346$			2.09116i			0.112422i
$347$		−	25.0448i		−	1.34447i	−0.740336	−	0.672237i	$-0.765333\pi$
$347$		−	25.0448i		−	1.34447i	0.740336	−	0.672237i	$-0.234667\pi$
$348$	−1.93835	+	7.80590i	−0.103906	+	0.418440i
$349$	2.42311	+	1.39898i	0.129706	+	0.0748859i	0.563449	−	0.826151i	$-0.309474\pi$
$349$	2.42311	+	1.39898i	0.129706	+	0.0748859i	−0.433743	+	0.901037i	$0.642807\pi$
$350$	−1.28173	−	2.09819i	−0.0685112	−	0.112153i
$351$	3.03237	+	0.635519i	0.161856	+	0.0339215i
$352$	−14.2190	−	24.6281i	−0.757878	−	1.31268i
$353$	−0.393817	−	0.682111i	−0.0209608	−	0.0363051i	0.855355	−	0.518043i	$-0.173339\pi$
$353$	−0.393817	−	0.682111i	−0.0209608	−	0.0363051i	−0.876316	+	0.481738i	$0.840006\pi$
$354$	2.05469	−	0.591286i	0.109205	−	0.0314265i
$355$	−10.0963	−	5.82907i	−0.535853	−	0.309375i
$356$	−4.84946	−	8.39952i	−0.257021	−	0.445174i
$357$	3.58590	−	16.1405i	0.189786	−	0.854245i
$358$	6.13142	−	10.6199i	0.324056	−	0.561281i
$359$	−3.14705	+	1.81695i	−0.166095	+	0.0958950i	−0.580743	−	0.814087i	$-0.697238\pi$
$359$	−3.14705	+	1.81695i	−0.166095	+	0.0958950i	0.414648	+	0.909982i	$0.363905\pi$
$360$	8.73806	−	0.321772i	0.460536	−	0.0169589i
$361$	−4.23653	+	7.33788i	−0.222975	+	0.386204i
$362$	6.26934			0.329509
$363$	27.7126	+	6.88156i	1.45454	+	0.361188i
$364$	−0.934555	−	1.52987i	−0.0489840	−	0.0801868i
$365$	12.2136	−	7.05152i	0.639289	−	0.369094i
$366$	4.48108	+	15.5715i	0.234230	+	0.813935i
$367$	−10.7930	+	6.23132i	−0.563388	+	0.325272i	−0.754504	−	0.656295i	$-0.772123\pi$
$367$	−10.7930	+	6.23132i	−0.563388	+	0.325272i	0.191116	+	0.981567i	$0.438789\pi$
$368$	−1.04000	−	0.600443i	−0.0542136	−	0.0313002i
$369$	25.9622	+	13.7411i	1.35154	+	0.715332i
$370$		−	1.83663i		−	0.0954819i
$371$	12.8603	−	23.6068i	0.667674	−	1.22560i
$372$	12.0961	−	3.48096i	0.627155	−	0.180479i
$373$	−5.13308	+	8.89076i	−0.265781	+	0.460346i	−0.967768	−	0.251844i	$-0.918963\pi$
$373$	−5.13308	+	8.89076i	−0.265781	+	0.460346i	0.701987	+	0.712190i	$0.252296\pi$
$374$	17.5784			0.908958
$375$	−0.479000	−	1.66450i	−0.0247355	−	0.0859544i
$376$			16.7061i			0.861554i
$377$	−2.43646			−0.125484
$378$	−9.72680	−	8.28311i	−0.500292	−	0.426037i
$379$	−21.1937			−1.08864			−0.544322	−	0.838876i	$-0.683213\pi$
$379$	−21.1937			−1.08864			−0.544322	+	0.838876i	$0.683213\pi$
$380$			3.68708i			0.189143i
$381$	6.05110	+	21.0272i	0.310007	+	1.07726i
$382$	9.12676			0.466966
$383$	−3.48642	+	6.03866i	−0.178148	+	0.308561i	−0.941246	−	0.337721i	$-0.890344\pi$
$383$	−3.48642	+	6.03866i	−0.178148	+	0.308561i	0.763098	+	0.646282i	$0.223677\pi$
$384$	8.91211	−	2.56468i	0.454794	−	0.130878i
$385$	13.8666	−	0.343657i	0.706707	−	0.0175144i
$386$		−	8.70287i		−	0.442964i
$387$	0.133368	+	3.62176i	0.00677950	+	0.184104i
$388$	12.7910	+	7.38486i	0.649362	+	0.374910i
$389$	−16.4420	+	9.49282i	−0.833645	+	0.481305i	−0.855099	−	0.518465i	$-0.826504\pi$
$389$	−16.4420	+	9.49282i	−0.833645	+	0.481305i	0.0214542	+	0.999770i	$0.493170\pi$
$390$	0.265416	+	0.922307i	0.0134399	+	0.0467028i
$391$	−8.61023	+	4.97112i	−0.435438	+	0.251400i
$392$	1.01066	+	20.3776i	0.0510459	+	1.02922i
$393$	8.37787	+	2.08038i	0.422607	+	0.104941i
$394$	4.01173			0.202108
$395$	−6.48343	+	11.2296i	−0.326217	+	0.565024i
$396$	−8.36102	+	15.7972i	−0.420157	+	0.793838i
$397$	−20.5199	+	11.8472i	−1.02987	+	0.594593i	−0.916946	−	0.399011i	$-0.869353\pi$
$397$	−20.5199	+	11.8472i	−1.02987	+	0.594593i	−0.112919	+	0.993604i	$0.536020\pi$
$398$	7.97235	−	13.8085i	0.399618	−	0.692158i
$399$	10.0498	−	10.9575i	0.503120	−	0.548562i
$400$	0.217899	+	0.377413i	0.0108950	+	0.0188706i
$401$	23.5407	+	13.5912i	1.17557	+	0.678714i	0.954985	−	0.296654i	$-0.0958709\pi$
$401$	23.5407	+	13.5912i	1.17557	+	0.678714i	0.220582	+	0.975368i	$0.429204\pi$
$402$	−14.3322	+	4.12443i	−0.714824	+	0.205708i
$403$	1.90650	+	3.30216i	0.0949696	+	0.164492i
$404$	2.35835	+	4.08478i	0.117332	+	0.203226i
$405$	−5.06107	−	7.44215i	−0.251486	−	0.369803i
$406$	8.82262	+	4.80632i	0.437859	+	0.238533i
$407$	8.97326	+	5.18072i	0.444788	+	0.256799i
$408$	−4.38969	+	17.6776i	−0.217322	+	0.875173i
$409$			3.46525i			0.171346i	0.996323	+	0.0856729i	$0.0273040\pi$
$409$			3.46525i			0.171346i	−0.996323	+	0.0856729i	$0.972696\pi$
$410$			9.09920i			0.449377i
$411$	15.1886	+	14.6396i	0.749198	+	0.722117i
$412$	−11.3653	−	6.56176i	−0.559928	−	0.323275i
$413$	0.0870715	+	3.51335i	0.00428451	+	0.172880i
$414$	0.282705	+	7.67713i	0.0138942	+	0.377311i
$415$	5.40645	+	9.36424i	0.265392	+	0.459673i
$416$	1.61715	+	2.80099i	0.0792875	+	0.137330i
$417$	20.9813	+	20.2229i	1.02746	+	0.990318i
$418$	13.6897	+	7.90373i	0.669583	+	0.386584i
$419$	0.596980	+	1.03400i	0.0291644	+	0.0505142i	0.880239	−	0.474530i	$-0.157382\pi$
$419$	0.596980	+	1.03400i	0.0291644	+	0.0505142i	−0.851075	+	0.525044i	$0.824049\pi$
$420$	−1.12943	+	5.08368i	−0.0551107	+	0.248058i
$421$	15.3249	−	26.5435i	0.746889	−	1.29365i	−0.202417	−	0.979299i	$-0.564880\pi$
$421$	15.3249	−	26.5435i	0.746889	−	1.29365i	0.949307	−	0.314351i	$-0.101787\pi$
$422$	16.1215	−	9.30773i	0.784781	−	0.453093i
$423$	14.5651	−	9.13982i	0.708179	−	0.444393i
$424$	−14.8074	+	25.6471i	−0.719109	+	1.24553i
$425$	3.60802			0.175015
$426$	−5.18946	−	18.0331i	−0.251430	−	0.873705i
$427$	−26.6260	+	0.659874i	−1.28852	+	0.0319335i
$428$	0.995115	−	0.574530i	0.0481007	−	0.0277710i
$429$	−5.25481	−	1.30487i	−0.253705	−	0.0629996i
$430$	−0.972254	+	0.561331i	−0.0468863	+	0.0270698i
$431$	21.2265	+	12.2551i	1.02244	+	0.590307i	0.914811	−	0.403883i	$-0.132340\pi$
$431$	21.2265	+	12.2551i	1.02244	+	0.590307i	0.107632	+	0.994191i	$0.465673\pi$
$432$	1.68715	+	1.51043i	0.0811729	+	0.0726704i
$433$		−	21.7966i		−	1.04748i	−0.851879	−	0.523739i	$-0.824537\pi$
$433$		−	21.7966i		−	1.04748i	0.851879	−	0.523739i	$-0.175463\pi$
$434$	−0.389546	−	15.7183i	−0.0186988	−	0.754500i
$435$	5.09586	+	4.91166i	0.244328	+	0.235496i
$436$	3.56153	−	6.16875i	0.170566	−	0.295429i
$437$	−8.94060			−0.427687
$438$	22.0311	+	5.47074i	1.05269	+	0.261402i
$439$		−	0.765213i		−	0.0365216i	−0.999833	−	0.0182608i	$-0.994187\pi$
$439$		−	0.765213i		−	0.0365216i	0.999833	−	0.0182608i	$-0.00581292\pi$
$440$	−15.2807			−0.728477
$441$	17.2131	−	12.0296i	0.819670	−	0.572837i
$442$	−1.99922			−0.0950932
$443$			0.552046i			0.0262285i	0.999914	+	0.0131142i	$0.00417451\pi$
$443$			0.552046i			0.0262285i	−0.999914	+	0.0131142i	$0.995825\pi$
$444$	−2.69961	+	2.80085i	−0.128118	+	0.132922i
$445$	−8.53479			−0.404588
$446$	7.28652	−	12.6206i	0.345027	−	0.597604i
$447$	−1.97876	+	7.96865i	−0.0935924	+	0.376904i
$448$	−0.387558	−	15.6380i	−0.0183104	−	0.738828i
$449$			38.0738i			1.79681i	0.439164	+	0.898407i	$0.355275\pi$
$449$			38.0738i			1.79681i	−0.439164	+	0.898407i	$0.644725\pi$
$450$	1.30416	−	2.46406i	0.0614787	−	0.116157i
$451$	−44.4561	−	25.6667i	−2.09336	−	1.20860i
$452$	−13.1758	+	7.60707i	−0.619739	+	0.357806i
$453$	−21.4247	+	22.2282i	−1.00662	+	1.04437i
$454$	−3.45577	+	1.99519i	−0.162187	+	0.0936389i
$455$	−1.57707	+	0.0390846i	−0.0739342	+	0.00183231i
$456$	−11.3669	+	11.7932i	−0.532305	+	0.552268i
$457$	30.5432			1.42875			0.714375	−	0.699763i	$-0.246711\pi$
$457$	30.5432			1.42875			0.714375	+	0.699763i	$0.246711\pi$
$458$	−3.91365	+	6.77864i	−0.182873	+	0.316745i
$459$	17.8136	−	5.84421i	0.831469	−	0.272784i
$460$	2.71192	−	1.56573i	0.126444	−	0.0730025i
$461$	−16.1726	+	28.0117i	−0.753232	+	1.30464i	0.193016	+	0.981196i	$0.438173\pi$
$461$	−16.1726	+	28.0117i	−0.753232	+	1.30464i	−0.946248	+	0.323441i	$0.895160\pi$
$462$	16.4540	+	15.0910i	0.765509	+	0.702096i
$463$	−0.0238247	−	0.0412655i	−0.00110723	−	0.00191777i	0.865471	−	0.500959i	$-0.167019\pi$
$463$	−0.0238247	−	0.0412655i	−0.00110723	−	0.00191777i	−0.866578	+	0.499041i	$0.833686\pi$
$464$	−1.54220	−	0.890390i	−0.0715949	−	0.0413353i
$465$	2.66937	−	10.7498i	0.123789	−	0.498509i
$466$	−7.01828	−	12.1560i	−0.325116	−	0.563117i
$467$	−8.92449	−	15.4577i	−0.412976	−	0.715296i	0.582237	−	0.813019i	$-0.302177\pi$
$467$	−8.92449	−	15.4577i	−0.412976	−	0.715296i	−0.995214	+	0.0977230i	$0.968844\pi$
$468$	0.950912	−	1.79664i	0.0439559	−	0.0830495i
$469$	−0.607355	−	24.5069i	−0.0280450	−	1.13162i
$470$	4.61292	+	2.66327i	0.212778	+	0.122847i
$471$	−9.86454	+	2.83876i	−0.454534	+	0.130803i
$472$		−	3.87162i		−	0.178206i
$473$		−	6.33354i		−	0.291217i
$474$	−20.0574	+	5.77201i	−0.921267	+	0.265117i
$475$	2.80984	+	1.62226i	0.128924	+	0.0744345i
$476$	−9.52612	−	5.18957i	−0.436629	−	0.237863i
$477$	30.4612	−	1.12171i	1.39472	−	0.0513596i
$478$	4.14681	+	7.18249i	0.189671	+	0.328520i
$479$	−0.406721	−	0.704461i	−0.0185835	−	0.0321877i	0.856584	−	0.516007i	$-0.172582\pi$
$479$	−0.406721	−	0.704461i	−0.0185835	−	0.0321877i	−0.875168	+	0.483820i	$0.839249\pi$
$480$	2.26424	−	9.11830i	0.103348	−	0.416191i
$481$	−1.02054	−	0.589211i	−0.0465328	−	0.0268657i
$482$	−14.1689	−	24.5412i	−0.645374	−	1.11782i
$483$	−12.3272	−	2.73871i	−0.560905	−	0.124615i
$484$	9.36722	−	16.2245i	0.425783	−	0.737478i
$485$	11.2557	−	6.49848i	0.511095	−	0.295081i
$486$	2.44770	−	14.2781i	0.111030	−	0.647667i
$487$	−1.30232	+	2.25568i	−0.0590137	+	0.102215i	−0.894023	−	0.448021i	$-0.852129\pi$
$487$	−1.30232	+	2.25568i	−0.0590137	+	0.102215i	0.835009	+	0.550236i	$0.185462\pi$
$488$	29.3412			1.32821
$489$	17.4110	−	18.0640i	0.787354	−	0.816882i
$490$	5.78779	+	2.96950i	0.261466	+	0.134148i
$491$	14.8669	−	8.58341i	0.670934	−	0.387364i	−0.125496	−	0.992094i	$-0.540052\pi$
$491$	14.8669	−	8.58341i	0.670934	−	0.387364i	0.796430	+	0.604730i	$0.206719\pi$
$492$	13.3746	−	13.8762i	0.602974	−	0.625587i
$493$	−12.7680	+	7.37162i	−0.575043	+	0.332001i
$494$	−1.55695	−	0.898903i	−0.0700503	−	0.0404436i
$495$	8.35995	+	13.3223i	0.375752	+	0.598793i
$496$			2.78688i			0.125135i
$497$	30.8351	−	0.764188i	1.38314	−	0.0342785i
$498$	−4.19445	+	16.8914i	−0.187958	+	0.756923i
$499$	1.79117	−	3.10240i	0.0801840	−	0.138883i	−0.823145	−	0.567831i	$-0.807783\pi$
$499$	1.79117	−	3.10240i	0.0801840	−	0.138883i	0.903329	+	0.428949i	$0.141116\pi$
$500$	−1.13640			−0.0508213
$501$	14.7900	−	15.3447i	0.660770	−	0.685551i
$502$		−	9.07015i		−	0.404821i
$503$	9.90167			0.441494			0.220747	−	0.975331i	$-0.429151\pi$
$503$	9.90167			0.441494			0.220747	+	0.975331i	$0.429151\pi$
$504$	−19.2851	+	12.7784i	−0.859025	+	0.569193i
$505$	4.15057			0.184698
$506$		−	13.4254i		−	0.596831i
$507$	−21.2553	−	5.27810i	−0.943983	−	0.234409i
$508$	14.3559			0.636938
$509$	16.7467	−	29.0061i	0.742283	−	1.28567i	−0.209170	−	0.977879i	$-0.567076\pi$
$509$	16.7467	−	29.0061i	0.742283	−	1.28567i	0.951453	−	0.307793i	$-0.0995904\pi$
$510$	4.18137	+	4.03022i	0.185154	+	0.178461i
$511$	−17.8503	+	32.7664i	−0.789649	+	1.44950i
$512$			4.90433i			0.216743i
$513$	16.5006	+	3.45816i	0.728518	+	0.152681i
$514$	8.38606	+	4.84170i	0.369893	+	0.213558i
$515$	−10.0012	+	5.77417i	−0.440703	+	0.254440i
$516$	2.30776	+	0.573060i	0.101594	+	0.0252276i
$517$	−26.0240	+	15.0249i	−1.14453	+	0.660796i
$518$	2.53315	+	4.14676i	0.111300	+	0.182198i
$519$	−1.07787	−	3.74554i	−0.0473133	−	0.164411i
$520$	1.73789			0.0762116
$521$	−1.46842	+	2.54339i	−0.0643329	+	0.111428i	−0.896398	−	0.443250i	$-0.853825\pi$
$521$	−1.46842	+	2.54339i	−0.0643329	+	0.111428i	0.832065	+	0.554678i	$0.187159\pi$
$522$	0.419220	+	11.3843i	0.0183487	+	0.498279i
$523$	−6.60049	+	3.81080i	−0.288619	+	0.166634i	−0.637319	−	0.770600i	$-0.719957\pi$
$523$	−6.60049	+	3.81080i	−0.288619	+	0.166634i	0.348700	+	0.937234i	$0.386623\pi$
$524$	2.83183	−	4.90487i	0.123709	−	0.214270i
$525$	3.37723	+	3.09747i	0.147394	+	0.135185i
$526$	10.7542	+	18.6268i	0.468904	+	0.812165i
$527$	19.9817	+	11.5364i	0.870415	+	0.502534i
$528$	−2.84927	−	2.74628i	−0.123998	−	0.119516i
$529$	−7.70334	−	13.3426i	−0.334928	−	0.580112i
$530$	4.72114	+	8.17725i	0.205073	+	0.355197i
$531$	−3.37544	+	2.11814i	−0.146481	+	0.0919195i
$532$	−5.08535	−	8.32472i	−0.220478	−	0.360922i
$533$	5.05606	+	2.91912i	0.219002	+	0.126441i
$534$	−9.89105	−	9.53352i	−0.428028	−	0.412556i
$535$		−	1.01114i		−	0.0437154i
$536$			27.0060i			1.16648i
$537$	−5.50822	+	22.1821i	−0.237697	+	0.957227i
$538$	25.1801	+	14.5377i	1.08559	+	0.626767i
$539$	−30.8342	+	19.9012i	−1.32812	+	0.857207i
$540$	−5.61067	+	1.84072i	−0.241445	+	0.0792121i
$541$	2.00276	+	3.46888i	0.0861053	+	0.149139i	0.905862	−	0.423574i	$-0.139225\pi$
$541$	2.00276	+	3.46888i	0.0861053	+	0.149139i	−0.819756	+	0.572712i	$0.805891\pi$
$542$	8.59232	+	14.8823i	0.369072	+	0.639251i
$543$	−11.2292	+	3.23148i	−0.481891	+	0.138676i
$544$	16.9491	+	9.78554i	0.726685	+	0.419552i
$545$	−3.13405	−	5.42833i	−0.134248	−	0.232524i
$546$	−1.87134	−	1.71632i	−0.0800859	−	0.0734518i
$547$	19.4542	−	33.6956i	0.831800	−	1.44072i	−0.0648089	−	0.997898i	$-0.520644\pi$
$547$	19.4542	−	33.6956i	0.831800	−	1.44072i	0.896609	−	0.442823i	$-0.146023\pi$
$548$	11.9863	−	6.92031i	0.512030	−	0.295621i
$549$	−16.0524	−	25.5809i	−0.685099	−	1.09176i
$550$	−2.43602	+	4.21931i	−0.103872	+	0.179912i
$551$	−13.2579			−0.564807
$552$	13.5012	+	3.35259i	0.574647	+	0.142696i
$553$	−0.849973	−	34.2965i	−0.0361445	−	1.45844i
$554$	14.0578	−	8.11625i	0.597257	−	0.344826i
$555$	0.946676	+	3.28965i	0.0401841	+	0.139638i
$556$	16.5577	−	9.55959i	0.702203	−	0.405417i
$557$	6.65261	+	3.84089i	0.281880	+	0.162744i	0.634274	−	0.773108i	$-0.281299\pi$
$557$	6.65261	+	3.84089i	0.281880	+	0.162744i	−0.352394	+	0.935852i	$0.614632\pi$
$558$	15.1013	−	9.47628i	0.639288	−	0.401163i
$559$			0.720324i			0.0304665i
$560$	−1.01252	−	0.551591i	−0.0427867	−	0.0233090i
$561$	−31.4852	+	9.06064i	−1.32931	+	0.382540i
$562$	9.53825	−	16.5207i	0.402347	−	0.696885i
$563$	34.6123			1.45873			0.729367	−	0.684122i	$-0.239815\pi$
$563$	34.6123			1.45873			0.729367	+	0.684122i	$0.239815\pi$
$564$	−3.12000	−	10.8418i	−0.131376	−	0.456524i
$565$			13.3880i			0.563238i
$566$	−21.2619			−0.893704
$567$	21.6914	+	9.82254i	0.910954	+	0.412508i
$568$	−33.9795			−1.42575
$569$			11.4349i			0.479374i	0.970850	+	0.239687i	$0.0770449\pi$
$569$			11.4349i			0.479374i	−0.970850	+	0.239687i	$0.922955\pi$
$570$	1.44425	+	5.01870i	0.0604931	+	0.210210i
$571$	−33.5597			−1.40443			−0.702215	−	0.711965i	$-0.747805\pi$
$571$	−33.5597			−1.40443			−0.702215	+	0.711965i	$0.747805\pi$
$572$	−1.77619	+	3.07646i	−0.0742664	+	0.128633i
$573$	−16.3472	+	4.70431i	−0.682915	+	0.196525i
$574$	−12.5500	−	20.5443i	−0.523825	−	0.857501i
$575$		−	2.75560i		−	0.114916i
$576$	15.0242	−	9.42792i	0.626008	−	0.392830i
$577$	11.4056	+	6.58501i	0.474820	+	0.274137i	0.718255	−	0.695780i	$-0.244941\pi$
$577$	11.4056	+	6.58501i	0.474820	+	0.274137i	−0.243435	+	0.969917i	$0.578274\pi$
$578$	3.20487	−	1.85033i	0.133305	−	0.0769637i
$579$	4.48582	+	15.5880i	0.186424	+	0.647814i
$580$	4.02148	−	2.32180i	0.166983	−	0.0964076i
$581$	−25.1222	−	13.6859i	−1.04225	−	0.567787i
$582$	20.3032	+	5.04168i	0.841597	+	0.208984i
$583$	−53.2690			−2.20618
$584$	20.5528	−	35.5985i	0.850480	−	1.47308i
$585$	−0.950790	−	1.51516i	−0.0393103	−	0.0626444i
$586$	11.0692	−	6.39082i	0.457265	−	0.264002i
$587$	14.3135	−	24.7917i	0.590781	−	1.02326i	−0.403346	−	0.915047i	$-0.632153\pi$
$587$	14.3135	−	24.7917i	0.590781	−	1.02326i	0.994127	−	0.108215i	$-0.0345136\pi$
$588$	−4.46156	−	13.0357i	−0.183992	−	0.537585i
$589$	10.3742	+	17.9686i	0.427460	+	0.740383i
$590$	−1.06904	−	0.617208i	−0.0440115	−	0.0254101i
$591$	−7.18553	+	2.06781i	−0.295573	+	0.0850584i
$592$	−0.430647	−	0.745903i	−0.0176995	−	0.0306564i
$593$	−10.6177	−	18.3904i	−0.436016	−	0.755202i	0.561362	−	0.827571i	$-0.310278\pi$
$593$	−10.6177	−	18.3904i	−0.436016	−	0.755202i	−0.997378	+	0.0723683i	$0.976944\pi$
$594$	−5.19283	+	24.7776i	−0.213064	+	1.01664i
$595$	−8.14622	+	4.97631i	−0.333962	+	0.204009i
$596$	4.66529	+	2.69351i	0.191098	+	0.110330i
$597$	−7.16204	+	28.8421i	−0.293123	+	1.18043i
$598$			1.52689i			0.0624391i
$599$		−	48.2385i		−	1.97097i	−0.169757	−	0.985486i	$-0.554298\pi$
$599$		−	48.2385i		−	1.97097i	0.169757	−	0.985486i	$-0.445702\pi$
$600$	−3.63480	−	3.50342i	−0.148390	−	0.143026i
$601$	14.1137	+	8.14853i	0.575708	+	0.332385i	0.759426	−	0.650594i	$-0.225480\pi$
$601$	14.1137	+	8.14853i	0.575708	+	0.332385i	−0.183718	+	0.982979i	$0.558813\pi$
$602$	1.42096	−	2.60835i	0.0579138	−	0.106308i
$603$	23.5449	−	14.7748i	0.958822	−	0.601676i
$604$	10.1277	+	17.5417i	0.412091	+	0.713762i
$605$	−8.24290	−	14.2771i	−0.335122	−	0.580448i
$606$	4.81013	+	4.63626i	0.195398	+	0.188335i
$607$	−7.01397	−	4.04952i	−0.284688	−	0.164365i	0.350856	−	0.936430i	$-0.385891\pi$
$607$	−7.01397	−	4.04952i	−0.284688	−	0.164365i	−0.635544	+	0.772065i	$0.719224\pi$
$608$	8.79969	+	15.2415i	0.356875	+	0.618125i
$609$	−18.2798	−	4.06120i	−0.740736	−	0.164568i
$610$	4.67753	−	8.10172i	0.189388	−	0.328029i
$611$	2.95974	−	1.70881i	0.119738	−	0.0691310i
$612$	−0.452648	−	12.2921i	−0.0182972	−	0.496879i
$613$	−18.0545	+	31.2713i	−0.729215	+	1.26304i	0.228001	+	0.973661i	$0.426781\pi$
$613$	−18.0545	+	31.2713i	−0.729215	+	1.26304i	−0.957215	+	0.289376i	$0.906552\pi$
$614$	−20.2134			−0.815746
$615$	−4.69010	−	16.2978i	−0.189123	−	0.657193i
$616$	34.5008	−	21.0757i	1.39008	−	0.849162i
$617$	−34.0805	+	19.6764i	−1.37203	+	0.792141i	−0.991183	−	0.132499i	$-0.957700\pi$
$617$	−34.0805	+	19.6764i	−1.37203	+	0.792141i	−0.380844	+	0.924639i	$0.624367\pi$
$618$	−18.0403	−	4.47974i	−0.725687	−	0.180202i
$619$	5.33493	−	3.08013i	0.214429	−	0.123801i	−0.388939	−	0.921264i	$-0.627158\pi$
$619$	5.33493	−	3.08013i	0.214429	−	0.123801i	0.603368	+	0.797463i	$0.293825\pi$
$620$	−6.29352	−	3.63357i	−0.252754	−	0.145927i
$621$	−4.46347	−	13.6050i	−0.179113	−	0.545951i
$622$			10.6772i			0.428115i
$623$	19.2699	−	11.7715i	0.772034	−	0.471615i
$624$	0.324052	+	0.312338i	0.0129724	+	0.0125035i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−26.3634			−1.05370
$627$	−28.5939	−	7.10039i	−1.14193	−	0.283562i
$628$			6.73479i			0.268747i
$629$	−7.13073			−0.284321
$630$	0.453974	+	7.36212i	0.0180868	+	0.293314i
$631$	22.3970			0.891610			0.445805	−	0.895130i	$-0.352917\pi$
$631$	22.3970			0.891610			0.445805	+	0.895130i	$0.352917\pi$
$632$			37.7940i			1.50336i
$633$	−24.0781	+	24.9810i	−0.957017	+	0.992907i
$634$	−12.6579			−0.502708
$635$	6.31638	−	10.9403i	0.250658	−	0.434152i
$636$	4.81979	−	19.4097i	0.191117	−	0.769644i
$637$	3.50682	−	2.26340i	0.138945	−	0.0896791i
$638$		−	19.9083i		−	0.788179i
$639$	18.5900	+	29.6247i	0.735408	+	1.17194i
$640$	−4.63690	−	2.67711i	−0.183289	−	0.105822i
$641$	38.4524	−	22.2005i	1.51878	−	0.876868i	0.519024	−	0.854760i	$-0.326295\pi$
$641$	38.4524	−	22.2005i	1.51878	−	0.876868i	0.999756	−	0.0221082i	$-0.00703784\pi$
$642$	1.12946	−	1.17182i	0.0445764	−	0.0462481i
$643$	−3.06913	+	1.77196i	−0.121035	+	0.0698794i	−0.559295	−	0.828969i	$-0.688928\pi$
$643$	−3.06913	+	1.77196i	−0.121035	+	0.0698794i	0.438260	+	0.898848i	$0.355595\pi$
$644$	−3.96349	+	7.27550i	−0.156183	+	0.286695i
$645$	1.45210	−	1.50656i	0.0571764	−	0.0593206i
$646$	−10.8787			−0.428016
$647$	10.3018	−	17.8432i	0.405005	−	0.701489i	−0.589317	−	0.807902i	$-0.700603\pi$
$647$	10.3018	−	17.8432i	0.405005	−	0.701489i	0.994322	+	0.106413i	$0.0339366\pi$
$648$	−23.6207	−	11.4096i	−0.927907	−	0.448211i
$649$	6.03101	−	3.48201i	0.236738	−	0.136681i
$650$	0.277052	−	0.479869i	0.0108669	−	0.0188220i
$651$	8.79957	+	27.9527i	0.344882	+	1.09555i
$652$	−8.23041	−	14.2555i	−0.322328	−	0.558288i
$653$	−36.9882	−	21.3551i	−1.44746	−	0.835691i	−0.449130	−	0.893466i	$-0.648266\pi$
$653$	−36.9882	−	21.3551i	−1.44746	−	0.835691i	−0.998330	+	0.0577754i	$0.981599\pi$
$654$	2.43147	−	9.79173i	0.0950780	−	0.382887i
$655$	−2.49193	−	4.31615i	−0.0973678	−	0.168646i
$656$	2.13355	+	3.69541i	0.0833011	+	0.144282i
$657$	−42.2805	+	1.55695i	−1.64952	+	0.0607422i
$658$	−14.0884	+	0.349153i	−0.549222	+	0.0136114i
$659$	−25.4695	−	14.7048i	−0.992152	−	0.572819i	−0.0862351	−	0.996275i	$-0.527484\pi$
$659$	−25.4695	−	14.7048i	−0.992152	−	0.572819i	−0.905917	+	0.423456i	$0.860817\pi$
$660$	9.91674	−	2.85378i	0.386008	−	0.111083i
$661$		−	7.69973i		−	0.299485i	−0.988725	−	0.149742i	$-0.952156\pi$
$661$		−	7.69973i		−	0.299485i	0.988725	−	0.149742i	$-0.0478444\pi$
$662$			21.3973i			0.831630i
$663$	3.58086	−	1.03048i	0.139069	−	0.0400205i
$664$	27.2936	+	15.7580i	1.05920	+	0.611527i
$665$	−8.58157	+	0.212678i	−0.332779	+	0.00824728i
$666$	−2.57749	+	4.86986i	−0.0998756	+	0.188703i
$667$	5.63002	+	9.75148i	0.217995	+	0.377579i
$668$	−6.99143	−	12.1095i	−0.270507	−	0.468531i
$669$	−6.54592	+	26.3610i	−0.253080	+	1.01917i
$670$	7.45691	+	4.30525i	0.288086	+	0.166326i
$671$	26.3885	+	45.7062i	1.01872	+	1.76447i
$672$	7.46406	+	23.7103i	0.287932	+	0.914645i
$673$	−15.3084	+	26.5148i	−0.590094	+	1.02207i	0.404126	+	0.914703i	$0.367576\pi$
$673$	−15.3084	+	26.5148i	−0.590094	+	1.02207i	−0.994219	+	0.107369i	$0.965757\pi$
$674$	8.30161	−	4.79294i	0.319766	−	0.184617i
$675$	−1.06584	+	5.08566i	−0.0410243	+	0.195747i
$676$	−7.18459	+	12.4441i	−0.276330	+	0.478618i
$677$	−28.6137			−1.09971			−0.549857	−	0.835259i	$-0.685318\pi$
$677$	−28.6137			−1.09971			−0.549857	+	0.835259i	$0.685318\pi$
$678$	−14.9547	+	15.5155i	−0.574331	+	0.595869i
$679$	−16.4503	+	30.1966i	−0.631303	+	1.15884i
$680$	9.10725	−	5.25807i	0.349247	−	0.201638i
$681$	5.16133	−	5.35489i	0.197783	−	0.205200i
$682$	−26.9820	+	15.5780i	−1.03319	+	0.596514i
$683$	−12.4676	−	7.19817i	−0.477059	−	0.275430i	0.242131	−	0.970244i	$-0.422154\pi$
$683$	−12.4676	−	7.19817i	−0.477059	−	0.275430i	−0.719190	+	0.694813i	$0.755487\pi$
$684$	5.17436	−	9.77634i	0.197846	−	0.373808i
$685$		−	12.1794i		−	0.465349i
$686$	−17.1634	+	1.27818i	−0.655301	+	0.0488010i
$687$	3.51587	−	14.1587i	0.134139	−	0.540188i
$688$	−0.263238	+	0.455942i	−0.0100359	+	0.0173826i
$689$	6.05836			0.230805
$690$	3.07805	−	3.19349i	0.117179	−	0.121574i
$691$		−	10.3429i		−	0.393464i	−0.980457	−	0.196732i	$-0.936967\pi$
$691$		−	10.3429i		−	0.393464i	0.980457	−	0.196732i	$-0.0630328\pi$
$692$	−2.55718			−0.0972096
$693$	−37.2498	−	18.5488i	−1.41500	−	0.704612i
$694$	−23.2742			−0.883475
$695$		−	16.8244i		−	0.638184i
$696$	20.0207	+	4.97152i	0.758884	+	0.188445i
$697$	35.3277			1.33813
$698$	1.30008	−	2.25180i	0.0492087	−	0.0852319i
$699$	18.8364	+	18.1555i	0.712457	+	0.686704i
$700$	2.56577	−	1.56736i	0.0969771	−	0.0592408i
$701$			13.7649i			0.519894i	0.965623	+	0.259947i	$0.0837052\pi$
$701$			13.7649i			0.519894i	−0.965623	+	0.259947i	$0.916295\pi$
$702$	0.590589	−	2.81799i	0.0222903	−	0.106358i
$703$	−5.55325	−	3.20617i	−0.209445	−	0.120923i
$704$	−26.8442	+	15.4985i	−1.01173	+	0.584123i
$705$	−9.63509	−	2.39257i	−0.362879	−	0.0901095i
$706$	−0.633886	+	0.365974i	−0.0238566	+	0.0137736i
$707$	−9.37119	+	5.72462i	−0.352440	+	0.215296i
$708$	0.723056	+	2.51258i	0.0271741	+	0.0944285i
$709$	35.2193			1.32269			0.661345	−	0.750082i	$-0.269986\pi$
$709$	35.2193			1.32269			0.661345	+	0.750082i	$0.269986\pi$
$710$	−5.41697	+	9.38246i	−0.203295	+	0.352117i
$711$	32.9503	−	20.6768i	1.23573	−	0.775442i
$712$	−21.5433	+	12.4380i	−0.807368	+	0.466134i
$713$	8.81085	−	15.2608i	0.329969	−	0.571523i
$714$	−14.9994	−	3.33238i	−0.561337	−	0.124711i
$715$	1.56300	+	2.70720i	0.0584529	+	0.101243i
$716$	12.9866	+	7.49783i	0.485333	+	0.280207i
$717$	−11.1296	−	10.7273i	−0.415644	−	0.400620i
$718$	1.68849	+	2.92456i	0.0630141	+	0.109144i
$719$	4.86513	+	8.42665i	0.181439	+	0.314261i	0.942371	−	0.334571i	$-0.108591\pi$
$719$	4.86513	+	8.42665i	0.181439	+	0.314261i	−0.760932	+	0.648832i	$0.775258\pi$
$720$	−0.0481112	−	1.30651i	−0.00179300	−	0.0486908i
$721$	14.6168	−	26.8309i	0.544356	−	0.999236i
$722$	6.81910	+	3.93701i	0.253781	+	0.146520i
$723$	38.0278	+	36.6532i	1.41427	+	1.36315i
$724$			7.66648i			0.284923i
$725$		−	4.08625i		−	0.151759i
$726$	6.39504	−	25.7534i	0.237342	−	0.955797i
$727$	−25.3316	−	14.6252i	−0.939495	−	0.542418i	−0.0496933	−	0.998765i	$-0.515824\pi$
$727$	−25.3316	−	14.6252i	−0.939495	−	0.542418i	−0.889802	+	0.456347i	$0.849158\pi$
$728$	−3.92383	+	2.39697i	−0.145427	+	0.0888375i
$729$	2.97536	+	26.8356i	0.110199	+	0.993910i
$730$	−6.55299	−	11.3501i	−0.242537	−	0.420086i
$731$	2.17937	+	3.77478i	0.0806070	+	0.139615i
$732$	−19.0417	+	5.47970i	−0.703800	+	0.202536i
$733$	−6.16201	−	3.55764i	−0.227599	−	0.131404i	0.381865	−	0.924218i	$-0.375282\pi$
$733$	−6.16201	−	3.55764i	−0.227599	−	0.131404i	−0.609464	+	0.792814i	$0.708615\pi$
$734$	5.79078	+	10.0299i	0.213741	+	0.370211i
$735$	−11.8973	−	2.33549i	−0.438838	−	0.0861459i
$736$	7.47363	−	12.9447i	0.275482	−	0.477148i
$737$	−42.0685	+	24.2882i	−1.54961	+	0.894669i
$738$	12.7696	−	24.1267i	0.470056	−	0.888115i
$739$	5.44572	−	9.43227i	0.200324	−	0.346972i	−0.748309	−	0.663351i	$-0.769134\pi$
$739$	5.44572	−	9.43227i	0.200324	−	0.346972i	0.948633	+	0.316379i	$0.102467\pi$
$740$	2.24593			0.0825621
$741$	3.25202	+	0.807538i	0.119466	+	0.0296657i
$742$	−21.9378	−	11.9511i	−0.805362	−	0.438739i
$743$	−43.0548	+	24.8577i	−1.57953	+	0.911941i	−0.584604	+	0.811319i	$0.698750\pi$
$743$	−43.0548	+	24.8577i	−1.57953	+	0.911941i	−0.994925	+	0.100623i	$0.967917\pi$
$744$	−8.92803	−	31.0244i	−0.327317	−	1.13741i
$745$	4.10533	−	2.37021i	0.150408	−	0.0868379i
$746$	8.26219	+	4.77018i	0.302500	+	0.174649i
$747$	−1.19372	−	32.4167i	−0.0436760	−	1.18607i
$748$			21.4958i			0.785965i
$749$	1.39460	+	2.28296i	0.0509577	+	0.0834177i
$750$	−1.54682	+	0.445136i	−0.0564819	+	0.0162541i
$751$	−6.10616	+	10.5762i	−0.222817	+	0.385930i	−0.955662	−	0.294465i	$-0.904859\pi$
$751$	−6.10616	+	10.5762i	−0.222817	+	0.385930i	0.732845	+	0.680395i	$0.238192\pi$
$752$	2.49790			0.0910889
$753$	4.67513	+	16.2458i	0.170371	+	0.592031i
$754$			2.26421i			0.0824576i
$755$	17.8242			0.648690
$756$	10.1290	−	11.8944i	0.368389	−	0.432597i
$757$	−27.4472			−0.997587			−0.498794	−	0.866721i	$-0.666223\pi$
$757$	−27.4472			−0.997587			−0.498794	+	0.866721i	$0.666223\pi$
$758$			19.6953i			0.715365i
$759$	6.91999	+	24.0466i	0.251180	+	0.872836i
$760$	9.45669			0.343030
$761$	3.03983	−	5.26515i	0.110194	−	0.190861i	−0.805654	−	0.592386i	$-0.798186\pi$
$761$	3.03983	−	5.26515i	0.110194	−	0.190861i	0.915848	+	0.401524i	$0.131519\pi$
$762$	19.5406	−	5.62329i	0.707882	−	0.203710i
$763$	14.5630	+	7.93354i	0.527217	+	0.287213i
$764$			11.1607i			0.403780i
$765$	−9.56672	−	5.06341i	−0.345885	−	0.183068i
$766$	5.61173	+	3.23994i	0.202760	+	0.117064i
$767$	−0.685916	+	0.396014i	−0.0247670	+	0.0142992i
$768$	−8.04747	−	27.9645i	−0.290388	−	1.00908i
$769$	−14.1929	+	8.19430i	−0.511811	+	0.295494i	−0.733578	−	0.679606i	$-0.762151\pi$
$769$	−14.1929	+	8.19430i	−0.511811	+	0.295494i	0.221767	+	0.975100i	$0.428818\pi$
$770$	−0.319361	−	12.8862i	−0.0115090	−	0.464388i
$771$	−17.5161	−	4.34958i	−0.630828	−	0.156646i
$772$	10.6423			0.383026
$773$	8.90571	−	15.4251i	0.320316	−	0.554804i	−0.660237	−	0.751057i	$-0.729544\pi$
$773$	8.90571	−	15.4251i	0.320316	−	0.554804i	0.980553	+	0.196253i	$0.0628775\pi$
$774$	3.36571	−	0.123940i	0.120978	−	0.00445491i
$775$	−5.53812	+	3.19744i	−0.198935	+	0.114855i
$776$	18.9408	−	32.8065i	0.679937	−	1.17769i
$777$	−6.67462	−	6.12170i	−0.239451	−	0.219615i
$778$	8.82169	+	15.2796i	0.316273	+	0.547801i
$779$	27.5124	+	15.8843i	0.985734	+	0.569114i
$780$	−1.12785	+	0.324565i	−0.0403834	+	0.0116213i
$781$	−30.5600	−	52.9315i	−1.09352	−	1.89404i
$782$	4.61967	+	8.00150i	0.165199	+	0.286133i
$783$	−6.61884	−	20.1748i	−0.236538	−	0.720987i
$784$	3.04685	−	0.151113i	0.108816	−	0.00539690i
$785$	5.13244	+	2.96322i	0.183185	+	0.105762i
$786$	1.93330	−	7.78556i	0.0689585	−	0.277702i
$787$			47.4740i			1.69227i	0.532972	+	0.846133i	$0.321075\pi$
$787$			47.4740i			1.69227i	−0.532972	+	0.846133i	$0.678925\pi$
$788$			4.90576i			0.174760i
$789$	−28.8631	−	27.8198i	−1.02755	−	0.990411i
$790$	10.4357	+	6.02506i	0.371286	+	0.214362i
$791$	−18.4653	−	30.2276i	−0.656549	−	1.07477i
$792$	40.5169	+	21.4445i	1.43971	+	0.761998i
$793$	−3.00120	−	5.19824i	−0.106576	−	0.184595i
$794$	11.0096	+	19.0692i	0.390716	+	0.676740i
$795$	−12.6711	−	12.2130i	−0.449396	−	0.433152i
$796$	16.8858	+	9.74902i	0.598501	+	0.345545i
$797$	8.92350	+	15.4560i	0.316087	+	0.547478i	0.979668	−	0.200626i	$-0.0642977\pi$
$797$	8.92350	+	15.4560i	0.316087	+	0.547478i	−0.663581	+	0.748104i	$0.730964\pi$
$798$	−10.1828	−	9.33931i	−0.360468	−	0.330608i
$799$	10.3402	−	17.9097i	0.365809	−	0.633599i
$800$	−4.69761	+	2.71217i	−0.166086	+	0.0958895i
$801$	22.6301	+	11.9775i	0.799596	+	0.423205i
$802$	12.6304	−	21.8764i	0.445993	−	0.772483i
$803$	73.9379			2.60921
$804$	−5.04358	−	17.5262i	−0.177873	−	0.618100i
$805$	3.80062	+	6.22161i	0.133954	+	0.219283i
$806$	3.06870	−	1.77171i	0.108090	−	0.0624060i
$807$	−52.5942	−	13.0601i	−1.85140	−	0.459738i
$808$	10.4767	−	6.04875i	0.368570	−	0.212794i
$809$	−4.88185	−	2.81854i	−0.171637	−	0.0990944i	0.411721	−	0.911310i	$-0.364928\pi$
$809$	−4.88185	−	2.81854i	−0.171637	−	0.0990944i	−0.583357	+	0.812216i	$0.698261\pi$
$810$	−6.91600	+	4.70326i	−0.243003	+	0.165256i
$811$		−	20.3541i		−	0.714729i	−0.933965	−	0.357364i	$-0.883675\pi$
$811$		−	20.3541i		−	0.714729i	0.933965	−	0.357364i	$-0.116325\pi$
$812$	−5.87742	+	10.7888i	−0.206257	+	0.378611i
$813$	−23.0609	−	22.2274i	−0.808782	−	0.779548i
$814$	4.81445	−	8.33886i	0.168746	−	0.292277i
$815$	−14.4851			−0.507390
$816$	2.64315	+	0.656344i	0.0925288	+	0.0229766i
$817$			3.91962i			0.137130i
$818$	3.22027			0.112594
$819$	4.23647	+	2.10959i	0.148034	+	0.0737150i
$820$	−11.1270			−0.388571
$821$			5.83916i			0.203788i	0.994795	+	0.101894i	$0.0324903\pi$
$821$			5.83916i			0.203788i	−0.994795	+	0.101894i	$0.967510\pi$
$822$	13.6046	−	14.1148i	0.474514	−	0.492309i
$823$	47.1354			1.64304			0.821518	−	0.570182i	$-0.193127\pi$
$823$	47.1354			1.64304			0.821518	+	0.570182i	$0.193127\pi$
$824$	−16.8297	+	29.1500i	−0.586292	+	1.01549i
$825$	2.18842	−	8.81296i	0.0761911	−	0.306828i
$826$	3.26496	−	0.0809156i	0.113602	−	0.00281541i
$827$		−	35.6635i		−	1.24014i	−0.784546	−	0.620070i	$-0.787104\pi$
$827$		−	35.6635i		−	1.24014i	0.784546	−	0.620070i	$-0.212896\pi$
$828$	−9.38801	+	0.345706i	−0.326256	+	0.0120141i
$829$	0.0501046	+	0.0289279i	0.00174020	+	0.00100471i	0.500870	−	0.865523i	$-0.333014\pi$
$829$	0.0501046	+	0.0289279i	0.00174020	+	0.00100471i	−0.499130	+	0.866527i	$0.666347\pi$
$830$	8.70220	−	5.02422i	0.302058	−	0.174393i
$831$	−20.9958	+	21.7832i	−0.728337	+	0.755651i
$832$	3.05304	−	1.76267i	0.105845	−	0.0611097i
$833$	11.5291	−	22.4711i	0.399459	−	0.778579i
$834$	18.7931	−	19.4979i	0.650753	−	0.675157i
$835$	−12.3045			−0.425816
$836$	−9.66510	+	16.7404i	−0.334274	+	0.578980i
$837$	−22.1639	+	24.7571i	−0.766095	+	0.855730i
$838$	0.960897	−	0.554774i	0.0331936	−	0.0191644i
$839$	−5.35115	+	9.26846i	−0.184742	+	0.319983i	−0.943490	−	0.331402i	$-0.892478\pi$
$839$	−5.35115	+	9.26846i	−0.184742	+	0.319983i	0.758747	+	0.651385i	$0.225812\pi$
$840$	13.0387	+	2.89679i	0.449879	+	0.0999489i
$841$	−6.15130	−	10.6544i	−0.212114	−	0.367392i
$842$	−24.6669	−	14.2414i	−0.850077	−	0.490792i
$843$	−8.56878	+	34.5072i	−0.295124	+	1.18849i
$844$	11.3820	+	19.7142i	0.391784	+	0.678590i
$845$	6.32224	+	10.9504i	0.217492	+	0.376706i
$846$	−8.49365	−	13.5354i	−0.292018	−	0.465355i
$847$	38.3024	+	20.8661i	1.31609	+	0.716968i
$848$	3.83475	+	2.21399i	0.131686	+	0.0760288i
$849$	38.0828	−	10.9593i	1.30700	−	0.376121i
$850$		−	3.35294i		−	0.115005i
$851$			5.44604i			0.186688i
$852$	22.0518	−	6.34594i	0.755482	−	0.217408i
$853$	26.8003	+	15.4732i	0.917625	+	0.529791i	0.882877	−	0.469605i	$-0.155604\pi$
$853$	26.8003	+	15.4732i	0.917625	+	0.529791i	0.0347485	+	0.999396i	$0.488937\pi$
$854$	0.613221	+	24.7436i	0.0209840	+	0.846708i
$855$	−5.17369	−	8.24472i	−0.176937	−	0.281963i
$856$	−1.47357	−	2.55229i	−0.0503654	−	0.0872355i
$857$	−17.8596	−	30.9337i	−0.610072	−	1.05668i	−0.991228	−	0.132164i	$-0.957807\pi$
$857$	−17.8596	−	30.9337i	−0.610072	−	1.05668i	0.381156	−	0.924511i	$-0.375526\pi$
$858$	−1.21261	+	4.88330i	−0.0413980	+	0.166713i
$859$	0.575613	+	0.332330i	0.0196397	+	0.0113390i	0.509788	−	0.860300i	$-0.329724\pi$
$859$	0.575613	+	0.332330i	0.0196397	+	0.0113390i	−0.490148	+	0.871639i	$0.663057\pi$
$860$	−0.686426	−	1.18892i	−0.0234069	−	0.0405420i
$861$	33.0680	+	30.3287i	1.12695	+	1.03360i
$862$	11.3887	−	19.7258i	0.387900	−	0.671863i
$863$	1.34228	−	0.774964i	0.0456916	−	0.0263801i	−0.476980	−	0.878914i	$-0.658269\pi$
$863$	1.34228	−	0.774964i	0.0456916	−	0.0263801i	0.522672	+	0.852534i	$0.324935\pi$
$864$	−18.8001	+	20.9997i	−0.639592	+	0.714425i
$865$	−1.12513	+	1.94878i	−0.0382554	+	0.0662604i
$866$	−20.2556			−0.688314
$867$	−4.78660	+	4.96611i	−0.162562	+	0.168658i
$868$	19.2211	−	0.476358i	0.652407	−	0.0161686i
$869$	−58.8734	+	33.9906i	−1.99714	+	1.15305i
$870$	4.56441	−	4.73559i	0.154748	−	0.160551i
$871$	4.78451	−	2.76234i	0.162117	−	0.0935983i
$872$	−15.8217	−	9.13468i	−0.535791	−	0.309339i
$873$	−38.9644	+	1.43484i	−1.31875	+	0.0485618i
$874$			8.30851i			0.281040i
$875$	−0.0655497	−	2.64494i	−0.00221598	−	0.0894153i
$876$	−6.68991	+	26.9408i	−0.226031	+	0.910247i
$877$	−3.58733	+	6.21344i	−0.121136	+	0.209813i	−0.920216	−	0.391412i	$-0.871987\pi$
$877$	−3.58733	+	6.21344i	−0.121136	+	0.209813i	0.799080	+	0.601224i	$0.205320\pi$
$878$	−0.711114			−0.0239989
$879$	−16.5323	+	17.1523i	−0.557621	+	0.578533i
$880$			2.28476i			0.0770192i
$881$	28.8710			0.972690			0.486345	−	0.873767i	$-0.338330\pi$
$881$	28.8710			0.972690			0.486345	+	0.873767i	$0.338330\pi$
$882$	−11.1791	−	15.9961i	−0.376420	−	0.538617i
$883$	19.1653			0.644964			0.322482	−	0.946576i	$-0.395483\pi$
$883$	19.1653			0.644964			0.322482	+	0.946576i	$0.395483\pi$
$884$		−	2.44475i		−	0.0822259i
$885$	2.23292	+	0.554475i	0.0750587	+	0.0186385i
$886$	0.513017			0.0172351
$887$	−13.9407	+	24.1460i	−0.468083	+	0.810743i	−0.999335	−	0.0364710i	$-0.988388\pi$
$887$	−13.9407	+	24.1460i	−0.468083	+	0.810743i	0.531252	+	0.847214i	$0.321722\pi$
$888$	7.18367	+	6.92401i	0.241068	+	0.232354i
$889$	0.828074	+	33.4129i	0.0277727	+	1.12063i
$890$			7.93139i			0.265861i
$891$	−3.47034	−	47.0564i	−0.116261	−	1.57645i
$892$	15.4332	+	8.91035i	0.516741	+	0.298340i
$893$	16.1054	−	9.29843i	0.538945	−	0.311160i
$894$	7.40528	+	1.83887i	0.247670	+	0.0615010i
$895$	11.4279	−	6.59789i	0.381992	−	0.220543i
$896$	14.1616	−	0.350968i	0.473106	−	0.0117250i
$897$	−0.787021	−	2.73486i	−0.0262779	−	0.0913142i
$898$	35.3820			1.18071
$899$	13.0655	−	22.6301i	0.435759	−	0.754757i
$900$	3.01318	+	1.59480i	0.100439	+	0.0531599i
$901$	31.7482	−	18.3298i	1.05769	−	0.610656i
$902$	−23.8521	+	41.3131i	−0.794189	+	1.37558i
$903$	−1.20067	+	5.40431i	−0.0399557	+	0.179844i
$904$	19.5108	+	33.7936i	0.648918	+	1.12396i
$905$	5.84246	+	3.37315i	0.194210	+	0.112127i
$906$	20.6567	+	19.9100i	0.686271	+	0.661465i
$907$	5.90855	+	10.2339i	0.196190	+	0.339811i	0.947290	−	0.320377i	$-0.103810\pi$
$907$	5.90855	+	10.2339i	0.196190	+	0.339811i	−0.751100	+	0.660189i	$0.770476\pi$
$908$	−2.43982	−	4.22590i	−0.0809684	−	0.140241i
$909$	−11.0053	−	5.82481i	−0.365023	−	0.193197i
$910$	0.0363214	+	1.46557i	0.00120404	+	0.0485833i
$911$	−8.86875	−	5.12037i	−0.293835	−	0.169646i	0.345835	−	0.938295i	$-0.387596\pi$
$911$	−8.86875	−	5.12037i	−0.293835	−	0.169646i	−0.639670	+	0.768650i	$0.720929\pi$
$912$	1.76332	+	1.69958i	0.0583892	+	0.0562787i
$913$			56.6887i			1.87612i
$914$		−	28.3838i		−	0.938854i
$915$	−4.20211	+	16.9222i	−0.138917	+	0.559432i
$916$	−8.28929	−	4.78582i	−0.273886	−	0.158128i
$917$	11.5793	+	6.30808i	0.382382	+	0.208311i
$918$	−5.43103	−	16.5542i	−0.179251	−	0.546371i
$919$	−7.52608	−	13.0355i	−0.248262	−	0.430003i	0.714781	−	0.699348i	$-0.246526\pi$
$919$	−7.52608	−	13.0355i	−0.248262	−	0.430003i	−0.963044	+	0.269345i	$0.913193\pi$
$920$	−4.01581	−	6.95559i	−0.132397	−	0.229319i
$921$	36.2048	−	10.4188i	1.19299	−	0.343312i
$922$	26.0313	+	15.0292i	0.857297	+	0.494960i
$923$	3.47564	+	6.01998i	0.114402	+	0.198150i
$924$	−18.4541	+	20.1208i	−0.607094	+	0.661927i
$925$	0.988179	−	1.71158i	0.0324911	−	0.0562763i
$926$	−0.0383481	+	0.0221403i	−0.00126020	+	0.000727575i
$927$	34.6215	−	1.27491i	1.13712	−	0.0418736i
$928$	11.0826	−	19.1956i	0.363803	−	0.630126i
$929$	−3.16131			−0.103719			−0.0518596	−	0.998654i	$-0.516515\pi$
$929$	−3.16131			−0.103719			−0.0518596	+	0.998654i	$0.516515\pi$
$930$	−9.98978	−	2.48065i	−0.327578	−	0.0813437i
$931$	19.0822	−	12.3162i	0.625395	−	0.403647i
$932$	14.8650	−	8.58233i	0.486920	−	0.281124i
$933$	−5.50345	−	19.1242i	−0.180175	−	0.626098i
$934$	−14.3648	+	8.29354i	−0.470032	+	0.271373i
$935$	16.3815	+	9.45786i	0.535732	+	0.309305i
$936$	−4.60805	−	2.43892i	−0.150619	−	0.0797185i
$937$		−	25.7818i		−	0.842255i	−0.907001	−	0.421128i	$-0.861634\pi$
$937$		−	25.7818i		−	0.842255i	0.907001	−	0.421128i	$-0.138366\pi$
$938$	−22.7743	+	0.564416i	−0.743606	+	0.0184288i
$939$	47.2204	−	13.5888i	1.54098	−	0.443454i
$940$	−3.25679	+	5.64092i	−0.106225	+	0.183987i
$941$	−53.9501			−1.75872			−0.879362	−	0.476153i	$-0.842031\pi$
$941$	−53.9501			−1.75872			−0.879362	+	0.476153i	$0.842031\pi$
$942$	2.63806	+	9.16713i	0.0859528	+	0.298681i
$943$		−	26.9813i		−	0.878631i
$944$	−0.578884			−0.0188411
$945$	−4.60787	−	12.9525i	−0.149894	−	0.421345i
$946$	−5.88577			−0.191363
$947$			6.07648i			0.197459i	0.995114	+	0.0987296i	$0.0314779\pi$
$947$			6.07648i			0.197459i	−0.995114	+	0.0987296i	$0.968522\pi$
$948$	−7.05832	−	24.5273i	−0.229243	−	0.796609i
$949$	−8.40907			−0.272970
$950$	1.50757	−	2.61119i	0.0489121	−	0.0847182i
$951$	22.6719	−	6.52438i	0.735186	−	0.211568i
$952$	−13.3103	+	24.4328i	−0.431389	+	0.791871i
$953$			32.7280i			1.06016i	0.847947	+	0.530082i	$0.177839\pi$
$953$			32.7280i			1.06016i	−0.847947	+	0.530082i	$0.822161\pi$
$954$	−1.04241	−	28.3076i	−0.0337492	−	0.916494i
$955$	8.50532	+	4.91055i	0.275226	+	0.158902i
$956$	−8.78313	+	5.07094i	−0.284067	+	0.164006i
$957$	10.2616	+	35.6584i	0.331710	+	1.15267i
$958$	−0.654657	+	0.377966i	−0.0211510	+	0.0122115i
$959$	16.7982	+	27.4987i	0.542443	+	0.887979i
$960$	−9.93880	−	2.46799i	−0.320773	−	0.0796540i
$961$	−9.89443			−0.319175
$962$	−0.547554	+	0.948392i	−0.0176539	+	0.0305774i
$963$	−1.41901	+	2.68106i	−0.0457270	+	0.0863958i
$964$	30.0103	−	17.3264i	0.966566	−	0.558047i
$965$	4.68248	−	8.11029i	0.150734	−	0.261080i
$966$	−2.54508	+	11.4557i	−0.0818867	+	0.368580i
$967$	−10.6606	−	18.4646i	−0.342821	−	0.593783i	0.642135	−	0.766592i	$-0.278049\pi$
$967$	−10.6606	−	18.4646i	−0.342821	−	0.593783i	−0.984955	+	0.172809i	$0.944716\pi$
$968$	−41.6130	−	24.0253i	−1.33749	−	0.772201i
$969$	19.4851	−	5.60732i	0.625953	−	0.180133i
$970$	−6.03904	−	10.4599i	−0.193902	−	0.335848i
$971$	−0.486914	−	0.843360i	−0.0156258	−	0.0270647i	0.858107	−	0.513471i	$-0.171641\pi$
$971$	−0.486914	−	0.843360i	−0.0156258	−	0.0270647i	−0.873733	+	0.486407i	$0.838307\pi$
$972$	17.4600	+	2.99318i	0.560030	+	0.0960064i
$973$	23.2048	+	37.9862i	0.743911	+	1.21778i
$974$	2.09621	+	1.21025i	0.0671669	+	0.0387788i
$975$	−0.248893	+	1.00231i	−0.00797094	+	0.0320997i
$976$		−	4.38709i		−	0.140427i
$977$			21.5288i			0.688767i	0.938829	+	0.344383i	$0.111912\pi$
$977$			21.5288i			0.688767i	−0.938829	+	0.344383i	$0.888088\pi$
$978$	−16.7869	−	16.1801i	−0.536786	−	0.517383i
$979$	−38.7505	−	22.3726i	−1.23847	−	0.715033i
$980$	−3.63126	+	7.07762i	−0.115996	+	0.226086i
$981$	0.691984	+	18.7915i	0.0220933	+	0.599968i
$982$	−7.97658	−	13.8158i	−0.254543	−	0.440881i
$983$	4.03870	+	6.99523i	0.128814	+	0.223113i	0.923218	−	0.384278i	$-0.125550\pi$
$983$	4.03870	+	6.99523i	0.128814	+	0.223113i	−0.794403	+	0.607391i	$0.792216\pi$
$984$	−35.5899	−	34.3035i	−1.13457	−	1.09356i
$985$	3.73857	+	2.15847i	0.119121	+	0.0687744i
$986$	6.85046	+	11.8653i	0.218163	+	0.377870i
$987$	25.0541	−	7.88710i	0.797482	−	0.251049i
$988$	1.09923	−	1.90392i	0.0349711	−	0.0605716i
$989$	2.88296	−	1.66448i	0.0916729	−	0.0529273i
$990$	12.3804	−	7.76891i	0.393476	−	0.246912i
$991$	19.8268	−	34.3411i	0.629820	−	1.09088i	−0.357767	−	0.933811i	$-0.616462\pi$
$991$	19.8268	−	34.3411i	0.629820	−	1.09088i	0.987587	−	0.157070i	$-0.0502049\pi$
$992$	−34.6879			−1.10134
$993$	−11.0291	−	38.3254i	−0.349997	−	1.21622i
$994$	−0.710161	−	28.6551i	−0.0225249	−	0.908884i
$995$	14.8590	−	8.57887i	0.471063	−	0.271968i
$996$	−20.6557	−	5.12920i	−0.654502	−	0.162525i
$997$	19.0187	−	10.9805i	0.602329	−	0.347755i	−0.167628	−	0.985850i	$-0.553611\pi$
$997$	19.0187	−	10.9805i	0.602329	−	0.347755i	0.769957	+	0.638096i	$0.220278\pi$
$998$	−2.88307	−	1.66454i	−0.0912619	−	0.0526901i
$999$	2.10649	−	10.0511i	0.0666463	−	0.318002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.t.b.101.6	✓	30
3.2	odd	2		945.2.t.b.521.10		30
7.5	odd	6		315.2.be.b.236.6	yes	30
9.4	even	3		945.2.be.b.206.10		30
9.5	odd	6		315.2.be.b.311.6	yes	30
21.5	even	6		945.2.be.b.656.10		30
63.5	even	6	inner	315.2.t.b.131.10	yes	30
63.40	odd	6		945.2.t.b.341.6		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.b.101.6	✓	30	1.1	even	1	trivial
315.2.t.b.131.10	yes	30	63.5	even	6	inner
315.2.be.b.236.6	yes	30	7.5	odd	6
315.2.be.b.311.6	yes	30	9.5	odd	6
945.2.t.b.341.6		30	63.40	odd	6
945.2.t.b.521.10		30	3.2	odd	2
945.2.be.b.206.10		30	9.4	even	3
945.2.be.b.656.10		30	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.929301i q^{2} +(0.479000 + 1.66450i) q^{3} +1.13640 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.54682 - 0.445136i) q^{6} +(0.0655497 + 2.64494i) q^{7} -2.91466i q^{8} +(-2.54112 + 1.59459i) q^{9} +O(q^{10})\)	\(q-0.929301i q^{2} +(0.479000 + 1.66450i) q^{3} +1.13640 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.54682 - 0.445136i) q^{6} +(0.0655497 + 2.64494i) q^{7} -2.91466i q^{8} +(-2.54112 + 1.59459i) q^{9} +(-0.804799 - 0.464651i) q^{10} +(4.54030 - 2.62135i) q^{11} +(0.544335 + 1.89154i) q^{12} +(-0.516376 + 0.298130i) q^{13} +(2.45795 - 0.0609154i) q^{14} +(1.68100 + 0.417423i) q^{15} -0.435799 q^{16} +(-1.80401 + 3.12464i) q^{17} +(1.48186 + 2.36146i) q^{18} +(-2.80984 + 1.62226i) q^{19} +(0.568200 - 0.984151i) q^{20} +(-4.37110 + 1.37603i) q^{21} +(-2.43602 - 4.21931i) q^{22} +(2.38642 + 1.37780i) q^{23} +(4.85145 - 1.39612i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.277052 + 0.479869i) q^{26} +(-3.87139 - 3.46588i) q^{27} +(0.0744906 + 3.00571i) q^{28} +(3.53879 + 2.04312i) q^{29} +(0.387912 - 1.56215i) q^{30} -6.39488i q^{31} -5.42433i q^{32} +(6.53803 + 6.30171i) q^{33} +(2.90373 + 1.67647i) q^{34} +(2.32336 + 1.26570i) q^{35} +(-2.88772 + 1.81209i) q^{36} +(0.988179 + 1.71158i) q^{37} +(1.50757 + 2.61119i) q^{38} +(-0.743581 - 0.716703i) q^{39} +(-2.52417 - 1.45733i) q^{40} +(-4.89572 - 8.47964i) q^{41} +(1.27875 + 4.06207i) q^{42} +(0.604036 - 1.04622i) q^{43} +(5.15960 - 2.97889i) q^{44} +(0.110398 + 2.99797i) q^{45} +(1.28039 - 2.21770i) q^{46} -5.73177 q^{47} +(-0.208748 - 0.725387i) q^{48} +(-6.99141 + 0.346750i) q^{49} +(-0.804799 + 0.464651i) q^{50} +(-6.06508 - 1.50607i) q^{51} +(-0.586809 + 0.338794i) q^{52} +(-8.79935 - 5.08031i) q^{53} +(-3.22085 + 3.59769i) q^{54} -5.24269i q^{55} +(7.70910 - 0.191055i) q^{56} +(-4.04617 - 3.89992i) q^{57} +(1.89868 - 3.28860i) q^{58} +1.32833 q^{59} +(1.91029 + 0.474360i) q^{60} +10.0668i q^{61} -5.94277 q^{62} +(-4.38417 - 6.61658i) q^{63} -5.91244 q^{64} +0.596259i q^{65} +(5.85618 - 6.07580i) q^{66} -9.26557 q^{67} +(-2.05007 + 3.55083i) q^{68} +(-1.15025 + 4.63215i) q^{69} +(1.17622 - 2.15910i) q^{70} -11.6581i q^{71} +(4.64769 + 7.40649i) q^{72} +(12.2136 + 7.05152i) q^{73} +(1.59057 - 0.918316i) q^{74} +(1.20200 - 1.24708i) q^{75} +(-3.19310 + 1.84354i) q^{76} +(7.23091 + 11.8370i) q^{77} +(-0.666033 + 0.691011i) q^{78} -12.9669 q^{79} +(-0.217899 + 0.377413i) q^{80} +(3.91456 - 8.10409i) q^{81} +(-7.88014 + 4.54960i) q^{82} +(-5.40645 + 9.36424i) q^{83} +(-4.96732 + 1.56372i) q^{84} +(1.80401 + 3.12464i) q^{85} +(-0.972254 - 0.561331i) q^{86} +(-1.70569 + 6.86897i) q^{87} +(-7.64033 - 13.2334i) q^{88} +(-4.26740 - 7.39135i) q^{89} +(2.78602 - 0.102593i) q^{90} +(-0.822383 - 1.34624i) q^{91} +(2.71192 + 1.56573i) q^{92} +(10.6443 - 3.06315i) q^{93} +5.32654i q^{94} +3.24453i q^{95} +(9.02880 - 2.59826i) q^{96} +(11.2557 + 6.49848i) q^{97} +(0.322235 + 6.49712i) q^{98} +(-7.35747 + 13.9011i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9}+O(q^{10}) \) 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9	\( 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9} + 3 q^{10} + 9 q^{11} + 15 q^{12} - 12 q^{13} - 27 q^{14} - q^{15} + 42 q^{16} - 3 q^{17} - 4 q^{18} - 15 q^{20} + 4 q^{21} + 15 q^{22} + q^{24} - 15 q^{25} + 24 q^{26} - 5 q^{27} + 27 q^{28} - 2 q^{30} - 25 q^{33} + 48 q^{34} - 6 q^{35} + 21 q^{36} - 3 q^{37} - 30 q^{38} - 3 q^{39} + 3 q^{40} - 18 q^{41} - 16 q^{42} + 12 q^{43} + 15 q^{44} - 7 q^{45} + 9 q^{46} - 60 q^{47} - 40 q^{48} - 15 q^{49} + 3 q^{50} - 48 q^{51} - 33 q^{52} - 30 q^{53} + 35 q^{54} + 42 q^{56} - 21 q^{57} + 30 q^{59} + 33 q^{60} + 12 q^{62} - 47 q^{63} - 138 q^{64} + 100 q^{66} + 12 q^{67} - 21 q^{68} + 32 q^{69} - 18 q^{70} + 85 q^{72} + 6 q^{73} + 54 q^{74} - 5 q^{75} - 54 q^{76} - 9 q^{77} - 18 q^{78} + 24 q^{79} + 21 q^{80} - 14 q^{81} + 6 q^{82} - 6 q^{83} - 9 q^{84} + 3 q^{85} - 60 q^{86} - 16 q^{87} - 48 q^{88} - 3 q^{89} + 22 q^{90} + 15 q^{91} - 3 q^{92} + 69 q^{93} - 48 q^{96} + 36 q^{97} + 24 q^{98} - q^{99}+O(q^{100}) \) 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9 + 3 * q^10 + 9 * q^11 + 15 * q^12 - 12 * q^13 - 27 * q^14 - q^15 + 42 * q^16 - 3 * q^17 - 4 * q^18 - 15 * q^20 + 4 * q^21 + 15 * q^22 + q^24 - 15 * q^25 + 24 * q^26 - 5 * q^27 + 27 * q^28 - 2 * q^30 - 25 * q^33 + 48 * q^34 - 6 * q^35 + 21 * q^36 - 3 * q^37 - 30 * q^38 - 3 * q^39 + 3 * q^40 - 18 * q^41 - 16 * q^42 + 12 * q^43 + 15 * q^44 - 7 * q^45 + 9 * q^46 - 60 * q^47 - 40 * q^48 - 15 * q^49 + 3 * q^50 - 48 * q^51 - 33 * q^52 - 30 * q^53 + 35 * q^54 + 42 * q^56 - 21 * q^57 + 30 * q^59 + 33 * q^60 + 12 * q^62 - 47 * q^63 - 138 * q^64 + 100 * q^66 + 12 * q^67 - 21 * q^68 + 32 * q^69 - 18 * q^70 + 85 * q^72 + 6 * q^73 + 54 * q^74 - 5 * q^75 - 54 * q^76 - 9 * q^77 - 18 * q^78 + 24 * q^79 + 21 * q^80 - 14 * q^81 + 6 * q^82 - 6 * q^83 - 9 * q^84 + 3 * q^85 - 60 * q^86 - 16 * q^87 - 48 * q^88 - 3 * q^89 + 22 * q^90 + 15 * q^91 - 3 * q^92 + 69 * q^93 - 48 * q^96 + 36 * q^97 + 24 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more