LMFDB - Embedded newform 315.2.k.c.16.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(16,315)]

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([4, 0, 2]))

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

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

chi := DirichletCharacter("315.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.k (of order $3$, 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:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.14
Character	$\chi$	$=$	315.16
Dual form			315.2.k.c.256.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.792206 + 1.37214i) q^{2} +(-1.71008 + 0.274985i) q^{3} +(-0.255182 + 0.441987i) q^{4} +1.00000 q^{5} +(-1.73206 - 2.12863i) q^{6} +(2.64012 - 0.172564i) q^{7} +2.36020 q^{8} +(2.84877 - 0.940495i) q^{9} +O(q^{10})$	\(q+(0.792206 + 1.37214i) q^{2} +(-1.71008 + 0.274985i) q^{3} +(-0.255182 + 0.441987i) q^{4} +1.00000 q^{5} +(-1.73206 - 2.12863i) q^{6} +(2.64012 - 0.172564i) q^{7} +2.36020 q^{8} +(2.84877 - 0.940495i) q^{9} +(0.792206 + 1.37214i) q^{10} -2.98171 q^{11} +(0.314842 - 0.826006i) q^{12} +(2.53669 + 4.39367i) q^{13} +(2.32830 + 3.48591i) q^{14} +(-1.71008 + 0.274985i) q^{15} +(2.38013 + 4.12250i) q^{16} +(-3.18542 - 5.51731i) q^{17} +(3.54730 + 3.16384i) q^{18} +(-3.69586 + 6.40141i) q^{19} +(-0.255182 + 0.441987i) q^{20} +(-4.46737 + 1.02109i) q^{21} +(-2.36213 - 4.09133i) q^{22} +6.24165 q^{23} +(-4.03614 + 0.649020i) q^{24} +1.00000 q^{25} +(-4.01916 + 6.96138i) q^{26} +(-4.61300 + 2.39169i) q^{27} +(-0.597438 + 1.21093i) q^{28} +(0.418671 - 0.725160i) q^{29} +(-1.73206 - 2.12863i) q^{30} +(0.914722 - 1.58435i) q^{31} +(-1.41091 + 2.44376i) q^{32} +(5.09897 - 0.819927i) q^{33} +(5.04702 - 8.74170i) q^{34} +(2.64012 - 0.172564i) q^{35} +(-0.311265 + 1.49912i) q^{36} +(2.60592 - 4.51358i) q^{37} -11.7115 q^{38} +(-5.54614 - 6.81599i) q^{39} +2.36020 q^{40} +(-1.00698 - 1.74414i) q^{41} +(-4.94016 - 5.32094i) q^{42} +(-1.06988 + 1.85308i) q^{43} +(0.760878 - 1.31788i) q^{44} +(2.84877 - 0.940495i) q^{45} +(4.94468 + 8.56443i) q^{46} +(-4.55885 - 7.89616i) q^{47} +(-5.20384 - 6.39532i) q^{48} +(6.94044 - 0.911178i) q^{49} +(0.792206 + 1.37214i) q^{50} +(6.96451 + 8.55912i) q^{51} -2.58926 q^{52} +(-1.91070 - 3.30943i) q^{53} +(-6.93619 - 4.43498i) q^{54} -2.98171 q^{55} +(6.23120 - 0.407285i) q^{56} +(4.55992 - 11.9632i) q^{57} +1.32670 q^{58} +(-5.50599 + 9.53665i) q^{59} +(0.314842 - 0.826006i) q^{60} +(-5.99864 - 10.3899i) q^{61} +2.89860 q^{62} +(7.35878 - 2.97461i) q^{63} +5.04960 q^{64} +(2.53669 + 4.39367i) q^{65} +(5.16449 + 6.34696i) q^{66} +(-2.39334 + 4.14538i) q^{67} +3.25144 q^{68} +(-10.6737 + 1.71636i) q^{69} +(2.32830 + 3.48591i) q^{70} -15.4212 q^{71} +(6.72366 - 2.21976i) q^{72} +(2.01212 + 3.48510i) q^{73} +8.25770 q^{74} +(-1.71008 + 0.274985i) q^{75} +(-1.88623 - 3.26704i) q^{76} +(-7.87207 + 0.514536i) q^{77} +(4.95881 - 13.0098i) q^{78} +(-5.83603 - 10.1083i) q^{79} +(2.38013 + 4.12250i) q^{80} +(7.23094 - 5.35850i) q^{81} +(1.59547 - 2.76343i) q^{82} +(5.39240 - 9.33991i) q^{83} +(0.688680 - 2.23508i) q^{84} +(-3.18542 - 5.51731i) q^{85} -3.39026 q^{86} +(-0.516554 + 1.35521i) q^{87} -7.03743 q^{88} +(-3.18399 + 5.51484i) q^{89} +(3.54730 + 3.16384i) q^{90} +(7.45534 + 11.1621i) q^{91} +(-1.59275 + 2.75873i) q^{92} +(-1.12858 + 2.96090i) q^{93} +(7.22310 - 12.5108i) q^{94} +(-3.69586 + 6.40141i) q^{95} +(1.74077 - 4.56701i) q^{96} +(-0.444786 + 0.770392i) q^{97} +(6.74853 + 8.80143i) q^{98} +(-8.49420 + 2.80429i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) $ 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.792206	+	1.37214i	0.560174	+	0.970251i	0.997481	+	0.0709379i	$0.0225992\pi$
$2$	0.792206	+	1.37214i	0.560174	+	0.970251i	−0.437306	+	0.899313i	$0.644067\pi$
$3$	−1.71008	+	0.274985i	−0.987317	+	0.158763i
$3$	−1.71008	+	0.274985i	−0.987317	+	0.158763i
$4$	−0.255182	+	0.441987i	−0.127591	+	0.220994i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.73206	−	2.12863i	−0.707109	−	0.869010i
$7$	2.64012	−	0.172564i	0.997871	−	0.0652230i
$7$	2.64012	−	0.172564i	0.997871	−	0.0652230i
$8$	2.36020			0.834456
$9$	2.84877	−	0.940495i	0.949589	−	0.313498i
$10$	0.792206	+	1.37214i	0.250518	+	0.433909i
$11$	−2.98171			−0.899020			−0.449510	−	0.893275i	$-0.648401\pi$
$11$	−2.98171			−0.899020			−0.449510	+	0.893275i	$0.648401\pi$
$12$	0.314842	−	0.826006i	0.0908869	−	0.238447i
$13$	2.53669	+	4.39367i	0.703550	+	1.21858i	0.967212	+	0.253969i	$0.0817362\pi$
$13$	2.53669	+	4.39367i	0.703550	+	1.21858i	−0.263662	+	0.964615i	$0.584930\pi$
$14$	2.32830	+	3.48591i	0.622264	+	0.931648i
$15$	−1.71008	+	0.274985i	−0.441541	+	0.0710009i
$16$	2.38013	+	4.12250i	0.595032	+	1.03063i
$17$	−3.18542	−	5.51731i	−0.772578	−	1.33814i	−0.936146	−	0.351613i	$-0.885633\pi$
$17$	−3.18542	−	5.51731i	−0.772578	−	1.33814i	0.163567	−	0.986532i	$-0.447700\pi$
$18$	3.54730	+	3.16384i	0.836107	+	0.745725i
$19$	−3.69586	+	6.40141i	−0.847887	+	1.46858i	0.0352027	+	0.999380i	$0.488792\pi$
$19$	−3.69586	+	6.40141i	−0.847887	+	1.46858i	−0.883090	+	0.469204i	$0.844541\pi$
$20$	−0.255182	+	0.441987i	−0.0570603	+	0.0988314i
$21$	−4.46737	+	1.02109i	−0.974859	+	0.222821i
$22$	−2.36213	−	4.09133i	−0.503608	−	0.872274i
$23$	6.24165			1.30147			0.650737	−	0.759303i	$-0.274460\pi$
$23$	6.24165			1.30147			0.650737	+	0.759303i	$0.274460\pi$
$24$	−4.03614	+	0.649020i	−0.823873	+	0.132481i
$25$	1.00000			0.200000
$26$	−4.01916	+	6.96138i	−0.788221	+	1.36524i
$27$	−4.61300	+	2.39169i	−0.887773	+	0.460282i
$28$	−0.597438	+	1.21093i	−0.112905	+	0.228845i
$29$	0.418671	−	0.725160i	0.0777453	−	0.134659i	−0.824532	−	0.565816i	$-0.808561\pi$
$29$	0.418671	−	0.725160i	0.0777453	−	0.134659i	0.902277	+	0.431157i	$0.141895\pi$
$30$	−1.73206	−	2.12863i	−0.316229	−	0.388633i
$31$	0.914722	−	1.58435i	0.164289	−	0.284557i	−0.772114	−	0.635485i	$-0.780800\pi$
$31$	0.914722	−	1.58435i	0.164289	−	0.284557i	0.936403	+	0.350928i	$0.114134\pi$
$32$	−1.41091	+	2.44376i	−0.249415	+	0.432000i
$33$	5.09897	−	0.819927i	0.887617	−	0.142731i
$34$	5.04702	−	8.74170i	0.865557	−	1.49919i
$35$	2.64012	−	0.172564i	0.446261	−	0.0291686i
$36$	−0.311265	+	1.49912i	−0.0518776	+	0.249853i
$37$	2.60592	−	4.51358i	0.428410	−	0.742029i	−0.568322	−	0.822806i	$-0.692407\pi$
$37$	2.60592	−	4.51358i	0.428410	−	0.742029i	0.996732	+	0.0807779i	$0.0257404\pi$
$38$	−11.7115			−1.89986
$39$	−5.54614	−	6.81599i	−0.888093	−	1.09143i
$40$	2.36020			0.373180
$41$	−1.00698	−	1.74414i	−0.157263	−	0.272388i	0.776617	−	0.629972i	$-0.216934\pi$
$41$	−1.00698	−	1.74414i	−0.157263	−	0.272388i	−0.933881	+	0.357584i	$0.883601\pi$
$42$	−4.94016	−	5.32094i	−0.762283	−	0.821040i
$43$	−1.06988	+	1.85308i	−0.163155	+	0.282593i	−0.935999	−	0.352004i	$-0.885500\pi$
$43$	−1.06988	+	1.85308i	−0.163155	+	0.282593i	0.772844	+	0.634597i	$0.218834\pi$
$44$	0.760878	−	1.31788i	0.114707	−	0.198678i
$45$	2.84877	−	0.940495i	0.424669	−	0.140201i
$46$	4.94468	+	8.56443i	0.729053	+	1.26276i
$47$	−4.55885	−	7.89616i	−0.664977	−	1.15177i	−0.979292	−	0.202455i	$-0.935108\pi$
$47$	−4.55885	−	7.89616i	−0.664977	−	1.15177i	0.314315	−	0.949319i	$-0.398225\pi$
$48$	−5.20384	−	6.39532i	−0.751110	−	0.923085i
$49$	6.94044	−	0.911178i	0.991492	−	0.130168i
$50$	0.792206	+	1.37214i	0.112035	+	0.194050i
$51$	6.96451	+	8.55912i	0.975227	+	1.19852i
$52$	−2.58926			−0.359066
$53$	−1.91070	−	3.30943i	−0.262455	−	0.454585i	0.704439	−	0.709765i	$-0.251199\pi$
$53$	−1.91070	−	3.30943i	−0.262455	−	0.454585i	−0.966894	+	0.255180i	$0.917865\pi$
$54$	−6.93619	−	4.43498i	−0.943896	−	0.603524i
$55$	−2.98171			−0.402054
$56$	6.23120	−	0.407285i	0.832680	−	0.0544258i
$57$	4.55992	−	11.9632i	0.603977	−	1.58457i
$58$	1.32670			0.174204
$59$	−5.50599	+	9.53665i	−0.716818	+	1.24157i	0.245436	+	0.969413i	$0.421069\pi$
$59$	−5.50599	+	9.53665i	−0.716818	+	1.24157i	−0.962254	+	0.272153i	$0.912264\pi$
$60$	0.314842	−	0.826006i	0.0406459	−	0.106637i
$61$	−5.99864	−	10.3899i	−0.768047	−	1.33030i	−0.938621	−	0.344951i	$-0.887895\pi$
$61$	−5.99864	−	10.3899i	−0.768047	−	1.33030i	0.170574	−	0.985345i	$-0.445438\pi$
$62$	2.89860			0.368122
$63$	7.35878	−	2.97461i	0.927119	−	0.374766i
$64$	5.04960			0.631200
$65$	2.53669	+	4.39367i	0.314637	+	0.544967i
$66$	5.16449	+	6.34696i	0.635705	+	0.781257i
$67$	−2.39334	+	4.14538i	−0.292393	+	0.506439i	−0.974375	−	0.224930i	$-0.927785\pi$
$67$	−2.39334	+	4.14538i	−0.292393	+	0.506439i	0.681982	+	0.731369i	$0.261118\pi$
$68$	3.25144			0.394295
$69$	−10.6737	+	1.71636i	−1.28497	+	0.206626i
$70$	2.32830	+	3.48591i	0.278285	+	0.416646i
$71$	−15.4212			−1.83015			−0.915077	−	0.403279i	$-0.867870\pi$
$71$	−15.4212			−1.83015			−0.915077	+	0.403279i	$0.867870\pi$
$72$	6.72366	−	2.21976i	0.792390	−	0.261601i
$73$	2.01212	+	3.48510i	0.235501	+	0.407900i	0.959418	−	0.281987i	$-0.0909935\pi$
$73$	2.01212	+	3.48510i	0.235501	+	0.407900i	−0.723917	+	0.689887i	$0.757660\pi$
$74$	8.25770			0.959938
$75$	−1.71008	+	0.274985i	−0.197463	+	0.0317526i
$76$	−1.88623	−	3.26704i	−0.216365	−	0.374756i
$77$	−7.87207	+	0.514536i	−0.897105	+	0.0586368i
$78$	4.95881	−	13.0098i	0.561475	−	1.47306i
$79$	−5.83603	−	10.1083i	−0.656605	−	1.13727i	−0.981489	−	0.191519i	$-0.938659\pi$
$79$	−5.83603	−	10.1083i	−0.656605	−	1.13727i	0.324884	−	0.945754i	$-0.394675\pi$
$80$	2.38013	+	4.12250i	0.266106	+	0.460910i
$81$	7.23094	−	5.35850i	0.803437	−	0.595389i
$82$	1.59547	−	2.76343i	0.176190	−	0.305170i
$83$	5.39240	−	9.33991i	0.591893	−	1.02519i	−0.402084	−	0.915603i	$-0.631714\pi$
$83$	5.39240	−	9.33991i	0.591893	−	1.02519i	0.993977	−	0.109586i	$-0.0349525\pi$
$84$	0.688680	−	2.23508i	0.0751411	−	0.243868i
$85$	−3.18542	−	5.51731i	−0.345507	−	0.598437i
$86$	−3.39026			−0.365581
$87$	−0.516554	+	1.35521i	−0.0553804	+	0.145294i
$88$	−7.03743			−0.750193
$89$	−3.18399	+	5.51484i	−0.337503	+	0.584572i	−0.983962	−	0.178377i	$-0.942915\pi$
$89$	−3.18399	+	5.51484i	−0.337503	+	0.584572i	0.646460	+	0.762948i	$0.276249\pi$
$90$	3.54730	+	3.16384i	0.373919	+	0.333498i
$91$	7.45534	+	11.1621i	0.781532	+	1.17010i
$92$	−1.59275	+	2.75873i	−0.166056	+	0.287618i
$93$	−1.12858	+	2.96090i	−0.117028	+	0.307031i
$94$	7.22310	−	12.5108i	0.745006	−	1.29039i
$95$	−3.69586	+	6.40141i	−0.379187	+	0.656771i
$96$	1.74077	−	4.56701i	0.177666	−	0.466118i
$97$	−0.444786	+	0.770392i	−0.0451612	+	0.0782215i	−0.887722	−	0.460379i	$-0.847713\pi$
$97$	−0.444786	+	0.770392i	−0.0451612	+	0.0782215i	0.842561	+	0.538601i	$0.181047\pi$
$98$	6.74853	+	8.80143i	0.681704	+	0.889079i
$99$	−8.49420	+	2.80429i	−0.853699	+	0.281841i
$100$	−0.255182	+	0.441987i	−0.0255182	+	0.0441987i
$101$	4.27612			0.425489			0.212745	−	0.977108i	$-0.431760\pi$
$101$	4.27612			0.425489			0.212745	+	0.977108i	$0.431760\pi$
$102$	−6.22699	+	16.3369i	−0.616564	+	1.61759i
$103$	−0.0951236			−0.00937280			−0.00468640	−	0.999989i	$-0.501492\pi$
$103$	−0.0951236			−0.00937280			−0.00468640	+	0.999989i	$0.501492\pi$
$104$	5.98708	+	10.3699i	0.587082	+	1.01686i
$105$	−4.46737	+	1.02109i	−0.435970	+	0.0996484i
$106$	3.02734	−	5.24350i	0.294041	−	0.509294i
$107$	0.703963	−	1.21930i	0.0680547	−	0.117874i	−0.829990	−	0.557778i	$-0.811654\pi$
$107$	0.703963	−	1.21930i	0.0680547	−	0.117874i	0.898045	+	0.439904i	$0.144987\pi$
$108$	0.120055	−	2.64921i	0.0115523	−	0.254920i
$109$	−1.09895	−	1.90343i	−0.105260	−	0.182316i	0.808584	−	0.588380i	$-0.200234\pi$
$109$	−1.09895	−	1.90343i	−0.105260	−	0.182316i	−0.913844	+	0.406064i	$0.866901\pi$
$110$	−2.36213	−	4.09133i	−0.225220	−	0.390093i
$111$	−3.21517	+	8.43519i	−0.305170	+	0.800633i
$112$	6.99521	+	10.4732i	0.660985	+	0.989621i
$113$	1.18841	+	2.05838i	0.111796	+	0.193636i	0.916494	−	0.400048i	$-0.131006\pi$
$113$	1.18841	+	2.05838i	0.111796	+	0.193636i	−0.804699	+	0.593684i	$0.797673\pi$
$114$	20.0277	−	3.22050i	1.87576	−	0.301627i
$115$	6.24165			0.582037
$116$	0.213674	+	0.370095i	0.0198392	+	0.0343624i
$117$	11.3586	+	10.1308i	1.05011	+	0.936592i
$118$	−17.4475			−1.60617
$119$	−9.36198	−	14.0167i	−0.858211	−	1.28491i
$120$	−4.03614	+	0.649020i	−0.368447	+	0.0592472i
$121$	−2.10940			−0.191764
$122$	9.50432	−	16.4620i	0.860480	−	1.49040i
$123$	2.20163	+	2.70571i	0.198514	+	0.243966i
$124$	0.466841	+	0.808592i	0.0419235	+	0.0726137i
$125$	1.00000			0.0894427
$126$	9.91126	+	7.74078i	0.882966	+	0.689604i
$127$	7.47856			0.663615			0.331808	−	0.943347i	$-0.392342\pi$
$127$	7.47856			0.663615			0.331808	+	0.943347i	$0.392342\pi$
$128$	6.82213	+	11.8163i	0.602997	+	1.04442i
$129$	1.32001	−	3.46313i	0.116220	−	0.304911i
$130$	−4.01916	+	6.96138i	−0.352503	+	0.610554i
$131$	−4.30130			−0.375807			−0.187903	−	0.982188i	$-0.560169\pi$
$131$	−4.30130			−0.375807			−0.187903	+	0.982188i	$0.560169\pi$
$132$	−0.938766	+	2.46291i	−0.0817091	+	0.214369i
$133$	−8.65284	+	17.5382i	−0.750296	+	1.52076i
$134$	−7.58407			−0.655164
$135$	−4.61300	+	2.39169i	−0.397024	+	0.205844i
$136$	−7.51823	−	13.0220i	−0.644683	−	1.11662i
$137$	−3.37687			−0.288506			−0.144253	−	0.989541i	$-0.546078\pi$
$137$	−3.37687			−0.288506			−0.144253	+	0.989541i	$0.546078\pi$
$138$	−10.8109	−	13.2862i	−0.920285	−	1.13099i
$139$	−6.46198	−	11.1925i	−0.548098	−	0.949333i	−0.998405	−	0.0564596i	$-0.982019\pi$
$139$	−6.46198	−	11.1925i	−0.548098	−	0.949333i	0.450307	−	0.892874i	$-0.351315\pi$
$140$	−0.597438	+	1.21093i	−0.0504928	+	0.102343i
$141$	9.96735	+	12.2495i	0.839402	+	1.03159i
$142$	−12.2167	−	21.1600i	−1.02521	−	1.77571i
$143$	−7.56366	−	13.1006i	−0.632505	−	1.09553i
$144$	10.6576	+	9.50555i	0.888135	+	0.792129i
$145$	0.418671	−	0.725160i	0.0347687	−	0.0602212i
$146$	−3.18803	+	5.52184i	−0.263844	+	0.456991i
$147$	−11.6182	+	3.46671i	−0.958251	+	0.285929i
$148$	1.32996	+	2.30357i	0.109322	+	0.189352i
$149$	−0.605477			−0.0496026			−0.0248013	−	0.999692i	$-0.507895\pi$
$149$	−0.605477			−0.0496026			−0.0248013	+	0.999692i	$0.507895\pi$
$150$	−1.73206	−	2.12863i	−0.141422	−	0.173802i
$151$	−22.7927			−1.85484			−0.927421	−	0.374018i	$-0.877980\pi$
$151$	−22.7927			−1.85484			−0.927421	+	0.374018i	$0.877980\pi$
$152$	−8.72295	+	15.1086i	−0.707525	+	1.22547i
$153$	−14.2635	−	12.7217i	−1.15314	−	1.02849i
$154$	−6.94232	−	10.3940i	−0.559428	−	0.837570i
$155$	0.914722	−	1.58435i	0.0734723	−	0.127258i
$156$	4.42785	−	0.712009i	0.354512	−	0.0570063i
$157$	6.87364	−	11.9055i	0.548576	−	0.950162i	−0.449796	−	0.893131i	$-0.648503\pi$
$157$	6.87364	−	11.9055i	0.548576	−	0.950162i	0.998372	−	0.0570305i	$-0.0181632\pi$
$158$	9.24668	−	16.0157i	0.735627	−	1.27414i
$159$	4.17750	+	5.13398i	0.331297	+	0.407151i
$160$	−1.41091	+	2.44376i	−0.111542	+	0.193196i
$161$	16.4787	−	1.07708i	1.29870	−	0.0848861i
$162$	13.0810	+	5.67683i	1.02774	+	0.446014i
$163$	−4.16743	+	7.21819i	−0.326418	+	0.565373i	−0.981798	−	0.189927i	$-0.939175\pi$
$163$	−4.16743	+	7.21819i	−0.326418	+	0.565373i	0.655380	+	0.755299i	$0.272508\pi$
$164$	1.02785			0.0802615
$165$	5.09897	−	0.819927i	0.396954	−	0.0638312i
$166$	17.0876			1.32625
$167$	3.38452	+	5.86216i	0.261902	+	0.453628i	0.966747	−	0.255733i	$-0.0823169\pi$
$167$	3.38452	+	5.86216i	0.261902	+	0.453628i	−0.704845	+	0.709361i	$0.748984\pi$
$168$	−10.5439	+	2.40998i	−0.813478	+	0.185934i
$169$	−6.36955	+	11.0324i	−0.489965	+	0.848645i
$170$	5.04702	−	8.74170i	0.387089	−	0.670458i
$171$	−4.50813	+	21.7121i	−0.344745	+	1.66036i
$172$	−0.546026	−	0.945746i	−0.0416341	−	0.0721124i
$173$	0.520284	+	0.901158i	0.0395564	+	0.0685138i	0.885126	−	0.465352i	$-0.154072\pi$
$173$	0.520284	+	0.901158i	0.0395564	+	0.0685138i	−0.845569	+	0.533866i	$0.820739\pi$
$174$	−2.26876	+	0.364822i	−0.171994	+	0.0276571i
$175$	2.64012	−	0.172564i	0.199574	−	0.0130446i
$176$	−7.09685	−	12.2921i	−0.534945	−	0.926553i
$177$	6.79325	−	17.8225i	0.510612	−	1.33962i
$178$	−10.0895			−0.756241
$179$	3.69562	+	6.40100i	0.276224	+	0.478433i	0.970443	−	0.241330i	$-0.0775836\pi$
$179$	3.69562	+	6.40100i	0.276224	+	0.478433i	−0.694220	+	0.719763i	$0.744250\pi$
$180$	−0.311265	+	1.49912i	−0.0232004	+	0.111737i
$181$	7.64655			0.568364			0.284182	−	0.958770i	$-0.408278\pi$
$181$	7.64655			0.568364			0.284182	+	0.958770i	$0.408278\pi$
$182$	−9.40976	+	19.0724i	−0.697498	+	1.41374i
$183$	13.1152	+	16.1181i	0.969507	+	1.19149i
$184$	14.7315			1.08602
$185$	2.60592	−	4.51358i	0.191591	−	0.331845i
$186$	−4.95684	+	0.797071i	−0.363453	+	0.0584441i
$187$	9.49801	+	16.4510i	0.694563	+	1.20302i
$188$	4.65334			0.339380
$189$	−11.7662	+	7.11039i	−0.855862	+	0.517205i
$190$	−11.7115			−0.849643
$191$	0.948810	+	1.64339i	0.0686535	+	0.118911i	0.898309	−	0.439365i	$-0.144796\pi$
$191$	0.948810	+	1.64339i	0.0686535	+	0.118911i	−0.829655	+	0.558276i	$0.811463\pi$
$192$	−8.63523	+	1.38857i	−0.623194	+	0.100211i
$193$	−8.50544	+	14.7319i	−0.612235	+	1.06042i	0.378628	+	0.925549i	$0.376396\pi$
$193$	−8.50544	+	14.7319i	−0.612235	+	1.06042i	−0.990863	+	0.134873i	$0.956937\pi$
$194$	−1.40945			−0.101193
$195$	−5.54614	−	6.81599i	−0.397167	−	0.488103i
$196$	−1.36834	+	3.30010i	−0.0977389	+	0.235722i
$197$	4.41217			0.314354			0.157177	−	0.987570i	$-0.449761\pi$
$197$	4.41217			0.314354			0.157177	+	0.987570i	$0.449761\pi$
$198$	−10.5770	−	9.43367i	−0.751677	−	0.670422i
$199$	12.0553	+	20.8804i	0.854576	+	1.48017i	0.877038	+	0.480421i	$0.159516\pi$
$199$	12.0553	+	20.8804i	0.854576	+	1.48017i	−0.0224617	+	0.999748i	$0.507150\pi$
$200$	2.36020			0.166891
$201$	2.95289	−	7.74708i	0.208281	−	0.546437i
$202$	3.38757	+	5.86744i	0.238348	+	0.412831i
$203$	0.980205	−	1.98675i	0.0687969	−	0.139443i
$204$	−5.56024	+	0.894099i	−0.389294	+	0.0625995i
$205$	−1.00698	−	1.74414i	−0.0703303	−	0.121816i
$206$	−0.0753575	−	0.130523i	−0.00525040	−	0.00909397i
$207$	17.7810	−	5.87024i	1.23587	−	0.408010i
$208$	−12.0753	+	20.9150i	−0.837269	+	1.45019i
$209$	11.0200	−	19.0872i	0.762267	−	1.32029i
$210$	−4.94016	−	5.32094i	−0.340903	−	0.367180i
$211$	5.44268	+	9.42700i	0.374690	+	0.648981i	0.990281	−	0.139085i	$-0.0444160\pi$
$211$	5.44268	+	9.42700i	0.374690	+	0.648981i	−0.615591	+	0.788066i	$0.711083\pi$
$212$	1.95030			0.133947
$213$	26.3714	−	4.24059i	1.80694	−	0.290561i
$214$	2.23074			0.152490
$215$	−1.06988	+	1.85308i	−0.0729651	+	0.126379i
$216$	−10.8876	+	5.64487i	−0.740808	+	0.384085i
$217$	2.14157	−	4.34071i	0.145380	−	0.294666i
$218$	1.74119	−	3.01582i	0.117928	−	0.204257i
$219$	−4.39925	−	5.40651i	−0.297274	−	0.365338i
$220$	0.760878	−	1.31788i	0.0512984	−	0.0888514i
$221$	16.1608	−	27.9914i	1.08709	−	1.88290i
$222$	−14.1214	+	2.27075i	−0.947763	+	0.152403i
$223$	−0.0421509	+	0.0730076i	−0.00282264	+	0.00488895i	−0.867433	−	0.497554i	$-0.834232\pi$
$223$	−0.0421509	+	0.0730076i	−0.00282264	+	0.00488895i	0.864611	+	0.502442i	$0.167565\pi$
$224$	−3.30325	+	6.69528i	−0.220708	+	0.447347i
$225$	2.84877	−	0.940495i	0.189918	−	0.0626997i
$226$	−1.88292	+	3.26132i	−0.125250	+	0.216940i
$227$	17.5505			1.16487			0.582433	−	0.812879i	$-0.302101\pi$
$227$	17.5505			1.16487			0.582433	+	0.812879i	$0.302101\pi$
$228$	4.12400	+	5.06823i	0.273118	+	0.335652i
$229$	8.26123			0.545918			0.272959	−	0.962026i	$-0.411998\pi$
$229$	8.26123			0.545918			0.272959	+	0.962026i	$0.411998\pi$
$230$	4.94468	+	8.56443i	0.326042	+	0.564722i
$231$	13.3204	−	3.04460i	0.876418	−	0.200320i
$232$	0.988147	−	1.71152i	0.0648750	−	0.112367i
$233$	3.85631	−	6.67933i	0.252635	−	0.437577i	−0.711615	−	0.702569i	$-0.752036\pi$
$233$	3.85631	−	6.67933i	0.252635	−	0.437577i	0.964251	+	0.264992i	$0.0853694\pi$
$234$	−4.90249	+	23.6114i	−0.320486	+	1.54352i
$235$	−4.55885	−	7.89616i	−0.297387	−	0.515089i
$236$	−2.81005	−	4.86715i	−0.182919	−	0.316825i
$237$	12.7597	+	15.6812i	0.828834	+	1.01860i
$238$	11.8162	−	23.9500i	0.765932	−	1.55245i
$239$	3.26325	+	5.65211i	0.211082	+	0.365605i	0.952053	−	0.305932i	$-0.0989680\pi$
$239$	3.26325	+	5.65211i	0.211082	+	0.365605i	−0.740971	+	0.671537i	$0.765635\pi$
$240$	−5.20384	−	6.39532i	−0.335907	−	0.412816i
$241$	24.6280			1.58643			0.793215	−	0.608941i	$-0.208405\pi$
$241$	24.6280			1.58643			0.793215	+	0.608941i	$0.208405\pi$
$242$	−1.67108	−	2.89439i	−0.107421	−	0.186059i
$243$	−10.8920	+	11.1519i	−0.698722	+	0.715394i
$244$	6.12297			0.391983
$245$	6.94044	−	0.911178i	0.443409	−	0.0582130i
$246$	−1.96848	+	5.16443i	−0.125506	+	0.329272i
$247$	−37.5009			−2.38612
$248$	2.15893	−	3.73937i	0.137092	−	0.237450i
$249$	−6.65311	+	17.4549i	−0.421624	+	1.10616i
$250$	0.792206	+	1.37214i	0.0501035	+	0.0867818i
$251$	−3.98640			−0.251620			−0.125810	−	0.992054i	$-0.540153\pi$
$251$	−3.98640			−0.251620			−0.125810	+	0.992054i	$0.540153\pi$
$252$	−0.563084	+	4.01156i	−0.0354710	+	0.252704i
$253$	−18.6108			−1.17005
$254$	5.92457	+	10.2616i	0.371740	+	0.643873i
$255$	6.96451	+	8.55912i	0.436135	+	0.535993i
$256$	−5.75948	+	9.97571i	−0.359967	+	0.623482i
$257$	−10.3533			−0.645820			−0.322910	−	0.946430i	$-0.604661\pi$
$257$	−10.3533			−0.645820			−0.322910	+	0.946430i	$0.604661\pi$
$258$	5.79762	−	0.932271i	0.360944	−	0.0580407i
$259$	6.10105	−	12.3661i	0.379101	−	0.768391i
$260$	−2.58926			−0.160579
$261$	0.510687	−	2.45957i	0.0316107	−	0.152243i
$262$	−3.40752	−	5.90200i	−0.210517	−	0.364627i
$263$	−4.82109			−0.297281			−0.148641	−	0.988891i	$-0.547490\pi$
$263$	−4.82109			−0.297281			−0.148641	+	0.988891i	$0.547490\pi$
$264$	12.0346	−	1.93519i	0.740678	−	0.119103i
$265$	−1.91070	−	3.30943i	−0.117373	−	0.203297i
$266$	−30.9198	+	2.02099i	−1.89581	+	0.123915i
$267$	3.92839	−	10.3064i	0.240414	−	0.630740i
$268$	−1.22147	−	2.11565i	−0.0746132	−	0.129234i
$269$	−15.1340	−	26.2128i	−0.922735	−	1.59822i	−0.795163	−	0.606395i	$-0.792615\pi$
$269$	−15.1340	−	26.2128i	−0.922735	−	1.59822i	−0.127572	−	0.991829i	$-0.540718\pi$
$270$	−6.93619	−	4.43498i	−0.422123	−	0.269904i
$271$	11.4512	−	19.8341i	0.695611	−	1.20483i	−0.274364	−	0.961626i	$-0.588467\pi$
$271$	11.4512	−	19.8341i	0.695611	−	1.20483i	0.969974	−	0.243207i	$-0.0781994\pi$
$272$	15.1634	−	26.2638i	0.919417	−	1.59248i
$273$	−15.8186	−	17.0379i	−0.957388	−	1.03118i
$274$	−2.67518	−	4.63355i	−0.161614	−	0.279923i
$275$	−2.98171			−0.179804
$276$	1.96513	−	5.15564i	0.118287	−	0.310333i
$277$	5.57830			0.335168			0.167584	−	0.985858i	$-0.446404\pi$
$277$	5.57830			0.335168			0.167584	+	0.985858i	$0.446404\pi$
$278$	10.2384	−	17.7335i	0.614061	−	1.06358i
$279$	1.11576	−	5.37372i	0.0667988	−	0.321716i
$280$	6.23120	−	0.407285i	0.372386	−	0.0243399i
$281$	−10.6304	+	18.4123i	−0.634154	+	1.09839i	0.352540	+	0.935797i	$0.385318\pi$
$281$	−10.6304	+	18.4123i	−0.634154	+	1.09839i	−0.986694	+	0.162590i	$0.948015\pi$
$282$	−8.91182	+	23.3807i	−0.530691	+	1.39230i
$283$	−1.42623	+	2.47030i	−0.0847805	+	0.146844i	−0.905298	−	0.424778i	$-0.860352\pi$
$283$	−1.42623	+	2.47030i	−0.0847805	+	0.146844i	0.820517	+	0.571622i	$0.193686\pi$
$284$	3.93519	−	6.81596i	0.233511	−	0.404453i
$285$	4.55992	−	11.9632i	0.270107	−	0.708641i
$286$	11.9840	−	20.7568i	0.708627	−	1.22738i
$287$	−2.95951	−	4.43096i	−0.174695	−	0.261551i
$288$	−1.72099	+	8.28865i	−0.101411	+	0.488413i
$289$	−11.7938	+	20.4275i	−0.693754	+	1.20162i
$290$	1.32670			0.0779062
$291$	0.548775	−	1.43974i	0.0321697	−	0.0843993i
$292$	−2.05383			−0.120191
$293$	13.2450	+	22.9410i	0.773781	+	1.34023i	0.935477	+	0.353387i	$0.114970\pi$
$293$	13.2450	+	22.9410i	0.773781	+	1.34023i	−0.161696	+	0.986841i	$0.551697\pi$
$294$	−13.9608	−	13.1954i	−0.814211	−	0.769573i
$295$	−5.50599	+	9.53665i	−0.320571	+	0.555245i
$296$	6.15049	−	10.6530i	0.357490	−	0.619191i
$297$	13.7546	−	7.13134i	0.798125	−	0.413802i
$298$	−0.479663	−	0.830800i	−0.0277861	−	0.0481269i
$299$	15.8331	+	27.4237i	0.915652	+	1.58596i
$300$	0.314842	−	0.826006i	0.0181774	−	0.0476895i
$301$	−2.50483	+	5.07698i	−0.144376	+	0.292632i
$302$	−18.0565	−	31.2748i	−1.03904	−	1.79966i
$303$	−7.31251	+	1.17587i	−0.420093	+	0.0675519i
$304$	−35.1864			−2.01808
$305$	−5.99864	−	10.3899i	−0.343481	−	0.594926i
$306$	6.15626	−	29.6498i	0.351930	−	1.69496i
$307$	−20.5561			−1.17320			−0.586599	−	0.809877i	$-0.699534\pi$
$307$	−20.5561			−1.17320			−0.586599	+	0.809877i	$0.699534\pi$
$308$	1.78139	−	3.61066i	0.101504	−	0.205736i
$309$	0.162669	−	0.0261576i	0.00925393	−	0.00148805i
$310$	2.89860			0.164629
$311$	3.58105	−	6.20255i	0.203062	−	0.351715i	−0.746451	−	0.665440i	$-0.768244\pi$
$311$	3.58105	−	6.20255i	0.203062	−	0.351715i	0.949514	+	0.313726i	$0.101577\pi$
$312$	−13.0900	−	16.0871i	−0.741075	−	0.910752i
$313$	3.14769	+	5.45197i	0.177918	+	0.308163i	0.941167	−	0.337941i	$-0.109730\pi$
$313$	3.14769	+	5.45197i	0.177918	+	0.308163i	−0.763249	+	0.646104i	$0.776397\pi$
$314$	21.7814			1.22919
$315$	7.35878	−	2.97461i	0.414620	−	0.167600i
$316$	5.95699			0.335107
$317$	−0.379060	−	0.656551i	−0.0212901	−	0.0368756i	0.855184	−	0.518324i	$-0.173444\pi$
$317$	−0.379060	−	0.656551i	−0.0212901	−	0.0368756i	−0.876474	+	0.481449i	$0.840111\pi$
$318$	−3.73511	+	9.79929i	−0.209455	+	0.549517i
$319$	−1.24836	+	2.16222i	−0.0698945	+	0.121061i
$320$	5.04960			0.282281
$321$	−0.868545	+	2.27868i	−0.0484775	+	0.127184i
$322$	14.5324	+	21.7578i	0.809861	+	1.21252i
$323$	47.0914			2.62024
$324$	0.523189	+	4.56337i	0.0290661	+	0.253521i
$325$	2.53669	+	4.39367i	0.140710	+	0.243717i
$326$	−13.2058			−0.731404
$327$	2.40271	+	2.95283i	0.132870	+	0.163292i
$328$	−2.37667	−	4.11651i	−0.131230	−	0.227296i
$329$	−13.3985	−	20.0601i	−0.738683	−	1.10595i
$330$	5.16449	+	6.34696i	0.284296	+	0.349389i
$331$	−11.5784	−	20.0544i	−0.636407	−	1.10229i	−0.986215	−	0.165468i	$-0.947087\pi$
$331$	−11.5784	−	20.0544i	−0.636407	−	1.10229i	0.349809	−	0.936821i	$-0.386247\pi$
$332$	2.75208	+	4.76675i	0.151040	+	0.261609i
$333$	3.17865	−	15.3090i	0.174189	−	0.838928i
$334$	−5.36248	+	9.28809i	−0.293422	+	0.508222i
$335$	−2.39334	+	4.14538i	−0.130762	+	0.226486i
$336$	−14.8424	−	15.9864i	−0.809717	−	0.872130i
$337$	4.20036	+	7.27524i	0.228808	+	0.396308i	0.957455	−	0.288582i	$-0.0931837\pi$
$337$	4.20036	+	7.27524i	0.228808	+	0.396308i	−0.728647	+	0.684890i	$0.759850\pi$
$338$	−20.1840			−1.09786
$339$	−2.59830	−	3.19320i	−0.141120	−	0.173431i
$340$	3.25144			0.176334
$341$	−2.72744	+	4.72406i	−0.147699	+	0.255822i
$342$	−33.3634	+	11.0146i	−1.80408	+	0.595603i
$343$	18.1664	−	3.60329i	0.980891	−	0.194559i
$344$	−2.52513	+	4.37365i	−0.136146	+	0.235811i
$345$	−10.6737	+	1.71636i	−0.574655	+	0.0924059i
$346$	−0.824344	+	1.42781i	−0.0443170	+	0.0767593i
$347$	0.262943	−	0.455430i	0.0141155	−	0.0244488i	−0.858881	−	0.512175i	$-0.828840\pi$
$347$	0.262943	−	0.455430i	0.0141155	−	0.0244488i	0.872997	+	0.487726i	$0.162173\pi$
$348$	−0.467171	−	0.574135i	−0.0250430	−	0.0307769i
$349$	−0.0741161	+	0.128373i	−0.00396734	+	0.00687164i	−0.868002	−	0.496560i	$-0.834596\pi$
$349$	−0.0741161	+	0.128373i	−0.00396734	+	0.00687164i	0.864035	+	0.503432i	$0.167930\pi$
$350$	2.32830	+	3.48591i	0.124453	+	0.186330i
$351$	−22.2100	−	14.2010i	−1.18548	−	0.757995i
$352$	4.20691	−	7.28658i	0.224229	−	0.388376i
$353$	−21.3874			−1.13834			−0.569168	−	0.822221i	$-0.692735\pi$
$353$	−21.3874			−1.13834			−0.569168	+	0.822221i	$0.692735\pi$
$354$	29.8367	−	4.79781i	1.58580	−	0.255001i
$355$	−15.4212			−0.818470
$356$	−1.62499	−	2.81457i	−0.0861244	−	0.149172i
$357$	19.8641	+	21.3953i	1.05132	+	1.13236i
$358$	−5.85539	+	10.1418i	−0.309467	+	0.536012i
$359$	5.86037	−	10.1505i	0.309298	−	0.535720i	−0.668911	−	0.743343i	$-0.733239\pi$
$359$	5.86037	−	10.1505i	0.309298	−	0.535720i	0.978209	+	0.207622i	$0.0665725\pi$
$360$	6.72366	−	2.21976i	0.354368	−	0.116991i
$361$	−17.8187	−	30.8629i	−0.937826	−	1.62436i
$362$	6.05765	+	10.4922i	0.318383	+	0.551455i
$363$	3.60725	−	0.580054i	0.189331	−	0.0304449i
$364$	−6.83596	+	0.446813i	−0.358301	+	0.0234194i
$365$	2.01212	+	3.48510i	0.105319	+	0.182419i
$366$	−11.7264	+	30.7649i	−0.612947	+	1.60810i
$367$	27.3542			1.42788			0.713939	−	0.700207i	$-0.246909\pi$
$367$	27.3542			1.42788			0.713939	+	0.700207i	$0.246909\pi$
$368$	14.8559	+	25.7312i	0.774419	+	1.34133i
$369$	−4.50899	−	4.02158i	−0.234729	−	0.209355i
$370$	8.25770			0.429297
$371$	−5.61556	−	8.40756i	−0.291545	−	0.436499i
$372$	−1.02069	−	1.25438i	−0.0529201	−	0.0650368i
$373$	25.1643			1.30296			0.651479	−	0.758667i	$-0.274149\pi$
$373$	25.1643			1.30296			0.651479	+	0.758667i	$0.274149\pi$
$374$	−15.0488	+	26.0652i	−0.778153	+	1.34780i
$375$	−1.71008	+	0.274985i	−0.0883083	+	0.0142002i
$376$	−10.7598	−	18.6365i	−0.554894	−	0.961105i
$377$	4.24815			0.218791
$378$	−19.0777	−	10.5119i	−0.981250	−	0.540675i
$379$	15.4889			0.795613			0.397806	−	0.917469i	$-0.369772\pi$
$379$	15.4889			0.795613			0.397806	+	0.917469i	$0.369772\pi$
$380$	−1.88623	−	3.26704i	−0.0967615	−	0.167596i
$381$	−12.7890	+	2.05650i	−0.655198	+	0.105357i
$382$	−1.50331	+	2.60380i	−0.0769159	+	0.133222i
$383$	−2.81736			−0.143960			−0.0719802	−	0.997406i	$-0.522932\pi$
$383$	−2.81736			−0.143960			−0.0719802	+	0.997406i	$0.522932\pi$
$384$	−14.9157	−	18.3308i	−0.761165	−	0.935442i
$385$	−7.87207	+	0.514536i	−0.401198	+	0.0262232i
$386$	−26.9523			−1.37183
$387$	−1.30502	+	6.28522i	−0.0663377	+	0.319496i
$388$	−0.227003	−	0.393180i	−0.0115243	−	0.0199607i
$389$	−6.58114			−0.333677			−0.166839	−	0.985984i	$-0.553356\pi$
$389$	−6.58114			−0.333677			−0.166839	+	0.985984i	$0.553356\pi$
$390$	4.95881	−	13.0098i	0.251099	−	0.658774i
$391$	−19.8823	−	34.4371i	−1.00549	−	1.74156i
$392$	16.3808	−	2.15056i	0.827357	−	0.108620i
$393$	7.35558	−	1.18280i	0.371040	−	0.0596641i
$394$	3.49535	+	6.05412i	0.176093	+	0.305002i
$395$	−5.83603	−	10.1083i	−0.293643	−	0.508604i
$396$	0.928104	−	4.46993i	0.0466390	−	0.224622i
$397$	−1.55980	+	2.70166i	−0.0782843	+	0.135592i	−0.902510	−	0.430669i	$-0.858278\pi$
$397$	−1.55980	+	2.70166i	−0.0782843	+	0.135592i	0.824225	+	0.566262i	$0.191611\pi$
$398$	−19.1005	+	33.0831i	−0.957423	+	1.65831i
$399$	9.97431	−	32.3713i	0.499340	−	1.62059i
$400$	2.38013	+	4.12250i	0.119006	+	0.206125i
$401$	−7.27041			−0.363067			−0.181533	−	0.983385i	$-0.558106\pi$
$401$	−7.27041			−0.363067			−0.181533	+	0.983385i	$0.558106\pi$
$402$	12.9694	−	2.08551i	0.646854	−	0.104016i
$403$	9.28145			0.462342
$404$	−1.09119	+	1.88999i	−0.0542885	+	0.0940305i
$405$	7.23094	−	5.35850i	0.359308	−	0.266266i
$406$	3.50263	−	0.228940i	0.173833	−	0.0113621i
$407$	−7.77010	+	13.4582i	−0.385149	+	0.667098i
$408$	16.4376	+	20.2012i	0.813785	+	1.00011i
$409$	−11.5769	+	20.0517i	−0.572440	+	0.991495i	0.423875	+	0.905721i	$0.360670\pi$
$409$	−11.5769	+	20.0517i	−0.572440	+	0.991495i	−0.996315	+	0.0857741i	$0.972664\pi$
$410$	1.59547	−	2.76343i	0.0787945	−	0.136476i
$411$	5.77473	−	0.928591i	0.284847	−	0.0458040i
$412$	0.0242738	−	0.0420434i	0.00119588	−	0.00207133i
$413$	−12.8908	+	26.1280i	−0.634313	+	1.28568i
$414$	22.1410	+	19.7476i	1.08817	+	0.970542i
$415$	5.39240	−	9.33991i	0.264703	−	0.458478i
$416$	−14.3161			−0.701904
$417$	14.1283	+	17.3631i	0.691865	+	0.850275i
$418$	34.9204			1.70801
$419$	−4.03007	−	6.98028i	−0.196882	−	0.341009i	0.750634	−	0.660718i	$-0.229748\pi$
$419$	−4.03007	−	6.98028i	−0.196882	−	0.341009i	−0.947516	+	0.319709i	$0.896415\pi$
$420$	0.688680	−	2.23508i	0.0336041	−	0.109061i
$421$	−6.28682	+	10.8891i	−0.306401	+	0.530702i	−0.977572	−	0.210600i	$-0.932458\pi$
$421$	−6.28682	+	10.8891i	−0.306401	+	0.530702i	0.671171	+	0.741302i	$0.265792\pi$
$422$	−8.62345	+	14.9363i	−0.419783	+	0.727085i
$423$	−20.4134	−	18.2067i	−0.992534	−	0.885242i
$424$	−4.50963	−	7.81091i	−0.219007	−	0.379331i
$425$	−3.18542	−	5.51731i	−0.154516	−	0.267629i
$426$	26.7103	+	32.8259i	1.29412	+	1.59042i
$427$	−17.6300	−	26.3955i	−0.853177	−	1.27737i
$428$	0.359277	+	0.622286i	0.0173663	+	0.0300793i
$429$	16.5370	+	20.3233i	0.798413	+	0.981218i
$430$	−3.39026			−0.163493
$431$	12.2367	+	21.1945i	0.589419	+	1.02090i	0.994309	+	0.106538i	$0.0339766\pi$
$431$	12.2367	+	21.1945i	0.589419	+	1.02090i	−0.404890	+	0.914366i	$0.632690\pi$
$432$	−20.8393	−	13.3246i	−1.00263	−	0.641079i
$433$	32.8481			1.57858			0.789289	−	0.614023i	$-0.210450\pi$
$433$	32.8481			1.57858			0.789289	+	0.614023i	$0.210450\pi$
$434$	7.65263	−	0.500193i	0.367338	−	0.0240100i
$435$	−0.516554	+	1.35521i	−0.0247669	+	0.0649774i
$436$	1.12172			0.0537209
$437$	−23.0682	+	39.9554i	−1.10350	+	1.91132i
$438$	3.93338	−	10.3195i	0.187944	−	0.493083i
$439$	2.16462	+	3.74924i	0.103312	+	0.178941i	0.913047	−	0.407854i	$-0.133723\pi$
$439$	2.16462	+	3.74924i	0.103312	+	0.178941i	−0.809735	+	0.586795i	$0.800389\pi$
$440$	−7.03743			−0.335496
$441$	18.9147	−	9.12319i	0.900702	−	0.434438i
$442$	51.2108			2.43585
$443$	12.1878	+	21.1100i	0.579062	+	1.00297i	0.995587	+	0.0938408i	$0.0299145\pi$
$443$	12.1878	+	21.1100i	0.579062	+	1.00297i	−0.416525	+	0.909124i	$0.636752\pi$
$444$	−2.90780	−	3.57357i	−0.137998	−	0.169594i
$445$	−3.18399	+	5.51484i	−0.150936	+	0.261428i
$446$	−0.133569			−0.00632467
$447$	1.03542	−	0.166497i	0.0489735	−	0.00787505i
$448$	13.3315	−	0.871379i	0.629856	−	0.0411688i
$449$	−27.1112			−1.27946			−0.639728	−	0.768601i	$-0.720953\pi$
$449$	−27.1112			−1.27946			−0.639728	+	0.768601i	$0.720953\pi$
$450$	3.54730	+	3.16384i	0.167221	+	0.149145i
$451$	3.00252	+	5.20051i	0.141383	+	0.244882i
$452$	−1.21304			−0.0570565
$453$	38.9774	−	6.26766i	1.83132	−	0.294480i
$454$	13.9036	+	24.0817i	0.652528	+	1.13021i
$455$	7.45534	+	11.1621i	0.349512	+	0.523286i
$456$	10.7623	−	28.2356i	0.503992	−	1.32226i
$457$	0.498731	+	0.863828i	0.0233297	+	0.0404082i	0.877455	−	0.479660i	$-0.159240\pi$
$457$	0.498731	+	0.863828i	0.0233297	+	0.0404082i	−0.854125	+	0.520068i	$0.825907\pi$
$458$	6.54460	+	11.3356i	0.305809	+	0.529677i
$459$	27.8901	+	17.8328i	1.30180	+	0.832365i
$460$	−1.59275	+	2.75873i	−0.0742626	+	0.128627i
$461$	1.71437	−	2.96938i	0.0798464	−	0.138298i	−0.823337	−	0.567553i	$-0.807890\pi$
$461$	1.71437	−	2.96938i	0.0798464	−	0.138298i	0.903184	+	0.429255i	$0.141224\pi$
$462$	14.7301	+	15.8655i	0.685308	+	0.738131i
$463$	−16.7701	−	29.0466i	−0.779370	−	1.34991i	−0.932305	−	0.361673i	$-0.882206\pi$
$463$	−16.7701	−	29.0466i	−0.779370	−	1.34991i	0.152935	−	0.988236i	$-0.451128\pi$
$464$	3.98596			0.185044
$465$	−1.12858	+	2.96090i	−0.0523366	+	0.137308i
$466$	12.2200			0.566079
$467$	−10.9969	+	19.0472i	−0.508875	+	0.881397i	0.491072	+	0.871119i	$0.336605\pi$
$467$	−10.9969	+	19.0472i	−0.508875	+	0.881397i	−0.999947	+	0.0102783i	$0.996728\pi$
$468$	−7.37620	+	2.43519i	−0.340965	+	0.112567i
$469$	−5.60335	+	11.3573i	−0.258739	+	0.524432i
$470$	7.22310	−	12.5108i	0.333177	−	0.577079i
$471$	−8.48066	+	22.2495i	−0.390768	+	1.02520i
$472$	−12.9952	+	22.5084i	−0.598154	+	1.03603i
$473$	3.19007	−	5.52536i	0.146680	−	0.254056i
$474$	−11.4085	+	29.9309i	−0.524010	+	1.37477i
$475$	−3.69586	+	6.40141i	−0.169577	+	0.293717i
$476$	8.58419	−	0.561082i	0.393456	−	0.0257171i
$477$	−8.55564	−	7.63078i	−0.391736	−	0.349390i
$478$	−5.17033	+	8.95528i	−0.236485	+	0.409605i
$479$	22.6209			1.03358			0.516788	−	0.856113i	$-0.327127\pi$
$479$	22.6209			1.03358			0.516788	+	0.856113i	$0.327127\pi$
$480$	1.74077	−	4.56701i	0.0794548	−	0.208454i
$481$	26.4416			1.20563
$482$	19.5105	+	33.7931i	0.888678	+	1.53924i
$483$	−27.8837	+	6.37330i	−1.26875	+	0.289995i
$484$	0.538280	−	0.932328i	0.0244673	−	0.0423785i
$485$	−0.444786	+	0.770392i	−0.0201967	+	0.0349817i
$486$	−23.9307	−	6.11076i	−1.08552	−	0.277190i
$487$	−3.95353	−	6.84772i	−0.179152	−	0.310300i	0.762439	−	0.647061i	$-0.224002\pi$
$487$	−3.95353	−	6.84772i	−0.179152	−	0.310300i	−0.941590	+	0.336761i	$0.890669\pi$
$488$	−14.1580	−	24.5223i	−0.640902	−	1.11007i
$489$	5.14175	−	13.4897i	0.232518	−	0.610025i
$490$	6.74853	+	8.80143i	0.304867	+	0.397608i
$491$	18.7554	+	32.4854i	0.846421	+	1.46604i	0.884381	+	0.466765i	$0.154581\pi$
$491$	18.7554	+	32.4854i	0.846421	+	1.46604i	−0.0379603	+	0.999279i	$0.512086\pi$
$492$	−1.75771	+	0.282643i	−0.0792435	+	0.0127425i
$493$	−5.33458			−0.240257
$494$	−29.7084	−	51.4565i	−1.33665	−	2.31514i
$495$	−8.49420	+	2.80429i	−0.381786	+	0.126043i
$496$	8.70863			0.391029
$497$	−40.7137	+	2.66113i	−1.82626	+	0.119368i
$498$	−29.2212	+	4.69883i	−1.30943	+	0.210560i
$499$	−16.2672			−0.728219			−0.364109	−	0.931356i	$-0.618627\pi$
$499$	−16.2672			−0.728219			−0.364109	+	0.931356i	$0.618627\pi$
$500$	−0.255182	+	0.441987i	−0.0114121	+	0.0197663i
$501$	−7.39982	−	9.09409i	−0.330600	−	0.406294i
$502$	−3.15805	−	5.46991i	−0.140951	−	0.244134i
$503$	35.0647			1.56346			0.781730	−	0.623617i	$-0.214338\pi$
$503$	35.0647			1.56346			0.781730	+	0.623617i	$0.214338\pi$
$504$	17.3682	−	7.02068i	0.773641	−	0.312726i
$505$	4.27612			0.190285
$506$	−14.7436	−	25.5367i	−0.655433	−	1.13524i
$507$	7.85871	−	20.6178i	0.349018	−	0.915669i
$508$	−1.90839	+	3.30543i	−0.0846712	+	0.146655i
$509$	−13.4731			−0.597184			−0.298592	−	0.954381i	$-0.596517\pi$
$509$	−13.4731			−0.597184			−0.298592	+	0.954381i	$0.596517\pi$
$510$	−6.22699	+	16.3369i	−0.275736	+	0.723409i
$511$	5.91365	+	8.85386i	0.261604	+	0.391672i
$512$	9.03777			0.399417
$513$	1.73878	−	38.3691i	0.0767691	−	1.69404i
$514$	−8.20194	−	14.2062i	−0.361772	−	0.626608i
$515$	−0.0951236			−0.00419164
$516$	1.19382	+	1.46715i	0.0525548	+	0.0645879i
$517$	13.5932	+	23.5441i	0.597827	+	1.03547i
$518$	21.8013	−	1.42498i	0.957894	−	0.0626101i
$519$	−1.13753	−	1.39798i	−0.0499322	−	0.0613647i
$520$	5.98708	+	10.3699i	0.262551	+	0.454752i
$521$	12.6099	+	21.8409i	0.552449	+	0.956869i	0.998097	+	0.0616610i	$0.0196398\pi$
$521$	12.6099	+	21.8409i	0.552449	+	0.956869i	−0.445649	+	0.895208i	$0.647027\pi$
$522$	3.77945	−	1.24775i	0.165422	−	0.0546126i
$523$	3.84924	−	6.66707i	0.168315	−	0.291531i	−0.769512	−	0.638632i	$-0.779501\pi$
$523$	3.84924	−	6.66707i	0.168315	−	0.291531i	0.937828	+	0.347101i	$0.112834\pi$
$524$	1.09761	−	1.90112i	0.0479495	−	0.0830509i
$525$	−4.46737	+	1.02109i	−0.194972	+	0.0445641i
$526$	−3.81930	−	6.61522i	−0.166529	−	0.288437i
$527$	−11.6551			−0.507704
$528$	15.5164	+	19.0690i	0.675263	+	0.829872i
$529$	15.9582			0.693835
$530$	3.02734	−	5.24350i	0.131499	−	0.227763i
$531$	−6.71609	+	32.3460i	−0.291454	+	1.40370i
$532$	−5.54364	−	8.29988i	−0.240347	−	0.359846i
$533$	5.10877	−	8.84865i	0.221285	−	0.383278i
$534$	17.2539	−	2.77447i	0.746650	−	0.120063i
$535$	0.703963	−	1.21930i	0.0304350	−	0.0527149i
$536$	−5.64876	+	9.78393i	−0.243989	+	0.422601i
$537$	−8.08000	−	9.93000i	−0.348678	−	0.428511i
$538$	23.9785	−	41.5319i	1.03379	−	1.79057i
$539$	−20.6944	+	2.71687i	−0.891371	+	0.117024i
$540$	0.120055	−	2.64921i	0.00516633	−	0.114004i
$541$	−6.88974	+	11.9334i	−0.296213	+	0.513056i	−0.975266	−	0.221033i	$-0.929057\pi$
$541$	−6.88974	+	11.9334i	−0.296213	+	0.513056i	0.679053	+	0.734089i	$0.262391\pi$
$542$	36.2868			1.55865
$543$	−13.0762	+	2.10269i	−0.561155	+	0.0902350i
$544$	17.9773			0.770771
$545$	−1.09895	−	1.90343i	−0.0470737	−	0.0815341i
$546$	10.8468	−	35.2030i	0.464202	−	1.50655i
$547$	0.623256	−	1.07951i	0.0266485	−	0.0461566i	−0.852394	−	0.522901i	$-0.824850\pi$
$547$	0.623256	−	1.07951i	0.0266485	−	0.0461566i	0.879042	+	0.476744i	$0.158183\pi$
$548$	0.861716	−	1.49254i	0.0368107	−	0.0637580i
$549$	−26.8604	−	23.9568i	−1.14637	−	1.02245i
$550$	−2.36213	−	4.09133i	−0.100722	−	0.174455i
$551$	3.09470	+	5.36017i	0.131838	+	0.228351i
$552$	−25.1922	+	4.05096i	−1.07225	+	0.172420i
$553$	−17.1521	−	25.6800i	−0.729383	−	1.09203i
$554$	4.41916	+	7.65422i	0.187752	+	0.325196i
$555$	−3.21517	+	8.43519i	−0.136476	+	0.358054i
$556$	6.59591			0.279729
$557$	−8.07396	−	13.9845i	−0.342105	−	0.592542i	0.642719	−	0.766102i	$-0.277806\pi$
$557$	−8.07396	−	13.9845i	−0.342105	−	0.592542i	−0.984823	+	0.173560i	$0.944473\pi$
$558$	8.25742	−	2.72612i	0.349564	−	0.115406i
$559$	−10.8558			−0.459151
$560$	6.99521	+	10.4732i	0.295602	+	0.442572i
$561$	−20.7662	−	25.5208i	−0.876748	−	1.07749i
$562$	−33.6857			−1.42095
$563$	0.652846	−	1.13076i	0.0275142	−	0.0476560i	−0.851940	−	0.523639i	$-0.824574\pi$
$563$	0.652846	−	1.13076i	0.0275142	−	0.0476560i	0.879455	+	0.475983i	$0.157908\pi$
$564$	−7.95760	+	1.27960i	−0.335075	+	0.0538809i
$565$	1.18841	+	2.05838i	0.0499966	+	0.0865967i
$566$	−4.51947			−0.189967
$567$	18.1658	−	15.3949i	0.762894	−	0.646524i
$568$	−36.3970			−1.52718
$569$	13.0638	+	22.6272i	0.547664	+	0.948581i	0.998434	+	0.0559413i	$0.0178160\pi$
$569$	13.0638	+	22.6272i	0.547664	+	0.948581i	−0.450770	+	0.892640i	$0.648851\pi$
$570$	20.0277	−	3.22050i	0.838867	−	0.134892i
$571$	−11.1437	+	19.3014i	−0.466349	+	0.807740i	−0.999261	−	0.0384303i	$-0.987764\pi$
$571$	−11.1437	+	19.3014i	−0.466349	+	0.807740i	0.532912	+	0.846170i	$0.321098\pi$
$572$	7.72043			0.322807
$573$	−2.07445	−	2.54942i	−0.0866615	−	0.106504i
$574$	3.73535	−	7.57110i	0.155911	−	0.316012i
$575$	6.24165			0.260295
$576$	14.3851	−	4.74913i	0.599380	−	0.197880i
$577$	−15.9190	−	27.5724i	−0.662715	−	1.14786i	−0.979899	−	0.199492i	$-0.936071\pi$
$577$	−15.9190	−	27.5724i	−0.662715	−	1.14786i	0.317184	−	0.948364i	$-0.397263\pi$
$578$	−37.3726			−1.55449
$579$	10.4940	−	27.5316i	0.436114	−	1.14417i
$580$	0.213674	+	0.370095i	0.00887234	+	0.0153673i
$581$	12.6248	−	25.5890i	0.523767	−	1.06161i
$582$	2.41028	−	0.387578i	0.0999092	−	0.0160656i
$583$	5.69715	+	9.86776i	0.235952	+	0.408681i
$584$	4.74901	+	8.22553i	0.196516	+	0.340375i
$585$	11.3586	+	10.1308i	0.469622	+	0.418857i
$586$	−20.9855	+	36.3480i	−0.866904	+	1.50152i
$587$	−9.02806	+	15.6371i	−0.372628	+	0.645411i	−0.989969	−	0.141285i	$-0.954877\pi$
$587$	−9.02806	+	15.6371i	−0.372628	+	0.645411i	0.617341	+	0.786696i	$0.288210\pi$
$588$	1.43250	−	6.01973i	0.0590753	−	0.248249i
$589$	6.76136	+	11.7110i	0.278597	+	0.482544i
$590$	−17.4475			−0.718303
$591$	−7.54518	+	1.21328i	−0.310367	+	0.0499078i
$592$	24.8097			1.01967
$593$	−16.4678	+	28.5231i	−0.676253	+	1.17130i	0.299848	+	0.953987i	$0.403064\pi$
$593$	−16.4678	+	28.5231i	−0.676253	+	1.17130i	−0.976101	+	0.217317i	$0.930269\pi$
$594$	20.6817	+	13.2238i	0.848581	+	0.542580i
$595$	−9.36198	−	14.0167i	−0.383804	−	0.574627i
$596$	0.154507	−	0.267613i	0.00632883	−	0.0109619i
$597$	−26.3573	−	32.3921i	−1.07873	−	1.32572i
$598$	−25.0862	+	43.4505i	−1.02585	+	1.77682i
$599$	−2.88523	+	4.99737i	−0.117887	+	0.204187i	−0.918930	−	0.394420i	$-0.870946\pi$
$599$	−2.88523	+	4.99737i	−0.117887	+	0.204187i	0.801043	+	0.598607i	$0.204279\pi$
$600$	−4.03614	+	0.649020i	−0.164775	+	0.0264961i
$601$	−2.08906	+	3.61836i	−0.0852147	+	0.147596i	−0.905483	−	0.424383i	$-0.860491\pi$
$601$	−2.08906	+	3.61836i	−0.0852147	+	0.147596i	0.820268	+	0.571979i	$0.193824\pi$
$602$	−8.95068	+	0.585036i	−0.364802	+	0.0238443i
$603$	−2.91935	+	14.0602i	−0.118885	+	0.572574i
$604$	5.81627	−	10.0741i	0.236661	−	0.409909i
$605$	−2.10940			−0.0857593
$606$	−7.40648	−	9.10227i	−0.300868	−	0.369754i
$607$	18.6699			0.757789			0.378895	−	0.925440i	$-0.376304\pi$
$607$	18.6699			0.757789			0.378895	+	0.925440i	$0.376304\pi$
$608$	−10.4290	−	18.0636i	−0.422952	−	0.732574i
$609$	−1.12990	+	3.66706i	−0.0457860	+	0.148597i
$610$	9.50432	−	16.4620i	0.384819	−	0.666525i
$611$	23.1288	−	40.0602i	0.935689	−	1.62066i
$612$	9.26260	−	3.05797i	0.374418	−	0.123611i
$613$	3.56314	+	6.17154i	0.143914	+	0.249266i	0.928967	−	0.370162i	$-0.120698\pi$
$613$	3.56314	+	6.17154i	0.143914	+	0.249266i	−0.785053	+	0.619428i	$0.787364\pi$
$614$	−16.2847	−	28.2059i	−0.657196	−	1.13830i
$615$	2.20163	+	2.70571i	0.0887781	+	0.109105i
$616$	−18.5797	+	1.21441i	−0.748595	+	0.0489298i
$617$	5.44924	+	9.43837i	0.219378	+	0.379974i	0.954618	−	0.297833i	$-0.0962638\pi$
$617$	5.44924	+	9.43837i	0.219378	+	0.379974i	−0.735240	+	0.677807i	$0.762930\pi$
$618$	0.164759	+	0.202483i	0.00662760	+	0.00814506i
$619$	−38.3335			−1.54076			−0.770378	−	0.637588i	$-0.779932\pi$
$619$	−38.3335			−1.54076			−0.770378	+	0.637588i	$0.779932\pi$
$620$	0.466841	+	0.808592i	0.0187488	+	0.0324738i
$621$	−28.7928	+	14.9281i	−1.15541	+	0.599045i
$622$	11.3477			0.455002
$623$	−7.45445	+	15.1093i	−0.298656	+	0.605340i
$624$	14.8984	−	39.0869i	0.596413	−	1.56473i
$625$	1.00000			0.0400000
$626$	−4.98725	+	8.63816i	−0.199330	+	0.345250i
$627$	−13.5964	+	35.6709i	−0.542987	+	1.42456i
$628$	3.50805	+	6.07612i	0.139987	+	0.242464i
$629$	−33.2038			−1.32392
$630$	9.91126	+	7.74078i	0.394874	+	0.308400i
$631$	38.1566			1.51899			0.759495	−	0.650513i	$-0.225446\pi$
$631$	38.1566			1.51899			0.759495	+	0.650513i	$0.225446\pi$
$632$	−13.7742	−	23.8576i	−0.547908	−	0.949005i
$633$	−11.8997	−	14.6243i	−0.472971	−	0.581263i
$634$	0.600587	−	1.04025i	0.0238524	−	0.0413135i
$635$	7.47856			0.296778
$636$	−3.33518	+	0.536304i	−0.132248	+	0.0212658i
$637$	21.6091	+	28.1826i	0.856185	+	1.11664i
$638$	−3.95582			−0.156613
$639$	−43.9313	+	14.5035i	−1.73789	+	0.573751i
$640$	6.82213	+	11.8163i	0.269669	+	0.467080i
$641$	30.6726			1.21150			0.605748	−	0.795656i	$-0.292874\pi$
$641$	30.6726			1.21150			0.605748	+	0.795656i	$0.292874\pi$
$642$	−3.81474	+	0.613420i	−0.150556	+	0.0242097i
$643$	−2.16495	−	3.74980i	−0.0853773	−	0.147878i	0.820175	−	0.572113i	$-0.193876\pi$
$643$	−2.16495	−	3.74980i	−0.0853773	−	0.147878i	−0.905552	+	0.424235i	$0.860543\pi$
$644$	−3.72900	+	7.55823i	−0.146943	+	0.297836i
$645$	1.32001	−	3.46313i	0.0519753	−	0.136361i
$646$	37.3061	+	64.6161i	1.46779	+	2.54229i
$647$	2.33724	+	4.04821i	0.0918862	+	0.159152i	0.908305	−	0.418309i	$-0.137377\pi$
$647$	2.33724	+	4.04821i	0.0918862	+	0.159152i	−0.816419	+	0.577461i	$0.804044\pi$
$648$	17.0665	−	12.6471i	0.670434	−	0.496826i
$649$	16.4173	−	28.4355i	0.644434	−	1.11619i
$650$	−4.01916	+	6.96138i	−0.157644	+	0.273048i
$651$	−2.46864	+	8.01187i	−0.0967536	+	0.314010i
$652$	−2.12690	−	3.68390i	−0.0832958	−	0.144273i
$653$	6.77024			0.264940			0.132470	−	0.991187i	$-0.457709\pi$
$653$	6.77024			0.264940			0.132470	+	0.991187i	$0.457709\pi$
$654$	−2.14827	+	5.63611i	−0.0840038	+	0.220389i
$655$	−4.30130			−0.168066
$656$	4.79347	−	8.30253i	0.187154	−	0.324159i
$657$	9.00979	+	8.03585i	0.351506	+	0.313508i
$658$	16.9109	−	34.2764i	0.659257	−	1.33623i
$659$	20.9047	−	36.2080i	0.814332	−	1.41046i	−0.0954745	−	0.995432i	$-0.530437\pi$
$659$	20.9047	−	36.2080i	0.814332	−	1.41046i	0.909807	−	0.415033i	$-0.136230\pi$
$660$	−0.938766	+	2.46291i	−0.0365414	+	0.0958687i
$661$	5.30838	−	9.19439i	0.206472	−	0.357620i	−0.744129	−	0.668036i	$-0.767135\pi$
$661$	5.30838	−	9.19439i	0.206472	−	0.357620i	0.950601	+	0.310416i	$0.100468\pi$
$662$	18.3450	−	31.7744i	0.712998	−	1.23495i
$663$	−19.9391	+	52.3116i	−0.774372	+	2.03161i
$664$	12.7271	−	22.0441i	0.493909	−	0.855475i
$665$	−8.65284	+	17.5382i	−0.335543	+	0.680104i
$666$	23.5243	−	7.76633i	0.911546	−	0.300939i
$667$	2.61320	−	4.52619i	0.101183	−	0.175255i
$668$	−3.45467			−0.133665
$669$	0.0520056	−	0.136440i	0.00201065	−	0.00527507i
$670$	−7.58407			−0.292998
$671$	17.8862	+	30.9798i	0.690489	+	1.19596i
$672$	3.80773	−	12.3578i	0.146886	−	0.476714i
$673$	4.10449	−	7.10918i	0.158216	−	0.274039i	−0.776009	−	0.630722i	$-0.782759\pi$
$673$	4.10449	−	7.10918i	0.158216	−	0.274039i	0.934226	+	0.356683i	$0.116092\pi$
$674$	−6.65511	+	11.5270i	−0.256345	+	0.444003i
$675$	−4.61300	+	2.39169i	−0.177555	+	0.0920563i
$676$	−3.25078	−	5.63052i	−0.125030	−	0.216558i
$677$	−3.28767	−	5.69440i	−0.126355	−	0.218854i	0.795907	−	0.605419i	$-0.206995\pi$
$677$	−3.28767	−	5.69440i	−0.126355	−	0.218854i	−0.922262	+	0.386566i	$0.873661\pi$
$678$	2.32314	−	6.09491i	0.0892197	−	0.234073i
$679$	−1.04135	+	2.11068i	−0.0399632	+	0.0810005i
$680$	−7.51823	−	13.0220i	−0.288311	−	0.499369i
$681$	−30.0128	+	4.82612i	−1.15009	+	0.184937i
$682$	−8.64277			−0.330949
$683$	−22.0222	−	38.1435i	−0.842655	−	1.45952i	−0.887642	−	0.460533i	$-0.847658\pi$
$683$	−22.0222	−	38.1435i	−0.842655	−	1.45952i	0.0449876	−	0.998988i	$-0.485675\pi$
$684$	−8.44606	−	7.53305i	−0.322943	−	0.288033i
$685$	−3.37687			−0.129024
$686$	19.3357	+	22.0723i	0.738241	+	0.842723i
$687$	−14.1274	+	2.27172i	−0.538994	+	0.0866715i
$688$	−10.1858			−0.388330
$689$	9.69369	−	16.7900i	0.369300	−	0.639647i
$690$	−10.8109	−	13.2862i	−0.411564	−	0.505796i
$691$	−10.5834	−	18.3311i	−0.402613	−	0.697346i	0.591427	−	0.806358i	$-0.298565\pi$
$691$	−10.5834	−	18.3311i	−0.402613	−	0.697346i	−0.994040	+	0.109012i	$0.965231\pi$
$692$	−0.531067			−0.0201882
$693$	−21.9418	+	8.86944i	−0.833499	+	0.336922i
$694$	0.833220			0.0316286
$695$	−6.46198	−	11.1925i	−0.245117	−	0.424555i
$696$	−1.21917	+	3.19857i	−0.0462125	+	0.121241i
$697$	−6.41530	+	11.1116i	−0.242997	+	0.420883i
$698$	−0.234861			−0.00888962
$699$	−4.75789	+	12.4826i	−0.179960	+	0.472136i
$700$	−0.597438	+	1.21093i	−0.0225810	+	0.0457690i
$701$	−15.0260			−0.567523			−0.283761	−	0.958895i	$-0.591582\pi$
$701$	−15.0260			−0.567523			−0.283761	+	0.958895i	$0.591582\pi$
$702$	1.89088	−	41.7255i	0.0713668	−	1.57483i
$703$	19.2622	+	33.3631i	0.726487	+	1.25831i
$704$	−15.0564			−0.567461
$705$	9.96735	+	12.2495i	0.375392	+	0.461342i
$706$	−16.9432	−	29.3465i	−0.637667	−	1.10447i
$707$	11.2894	−	0.737903i	0.424583	−	0.0277517i
$708$	6.14382	+	7.55051i	0.230899	+	0.283766i
$709$	3.10931	+	5.38548i	0.116773	+	0.202256i	0.918487	−	0.395451i	$-0.129412\pi$
$709$	3.10931	+	5.38548i	0.116773	+	0.202256i	−0.801714	+	0.597707i	$0.796078\pi$
$710$	−12.2167	−	21.1600i	−0.458486	−	0.794121i
$711$	−26.1323	−	23.3074i	−0.980038	−	0.874097i
$712$	−7.51486	+	13.0161i	−0.281631	+	0.487800i
$713$	5.70938	−	9.88893i	0.213818	−	0.370343i
$714$	−13.6208	+	44.2059i	−0.509746	+	1.65436i
$715$	−7.56366	−	13.1006i	−0.282865	−	0.489937i
$716$	−3.77222			−0.140974
$717$	−7.13467	−	8.76823i	−0.266449	−	0.327456i
$718$	18.5705			0.693044
$719$	17.6967	−	30.6516i	0.659976	−	1.14311i	−0.320646	−	0.947199i	$-0.603900\pi$
$719$	17.6967	−	30.6516i	0.659976	−	1.14311i	0.980621	−	0.195912i	$-0.0627667\pi$
$720$	10.6576	+	9.50555i	0.397186	+	0.354251i
$721$	−0.251137	+	0.0164149i	−0.00935285	+	0.000611322i
$722$	28.2322	−	48.8995i	1.05069	−	1.81985i
$723$	−42.1160	+	6.77235i	−1.56631	+	0.251866i
$724$	−1.95126	+	3.37968i	−0.0725180	+	0.125605i
$725$	0.418671	−	0.725160i	0.0155491	−	0.0269318i
$726$	3.65360	+	4.49013i	0.135598	+	0.166644i
$727$	0.465536	−	0.806331i	0.0172658	−	0.0299052i	−0.857263	−	0.514878i	$-0.827837\pi$
$727$	0.465536	−	0.806331i	0.0172658	−	0.0299052i	0.874529	+	0.484973i	$0.161171\pi$
$728$	17.5961	+	26.3447i	0.652154	+	0.976399i
$729$	15.5596	−	22.0658i	0.576281	−	0.817251i
$730$	−3.18803	+	5.52184i	−0.117994	+	0.204372i
$731$	13.6321			0.504200
$732$	−10.4708	+	1.68373i	−0.387011	+	0.0622323i
$733$	−51.5444			−1.90384			−0.951918	−	0.306351i	$-0.900892\pi$
$733$	−51.5444			−1.90384			−0.951918	+	0.306351i	$0.900892\pi$
$734$	21.6702	+	37.5339i	0.799861	+	1.38540i
$735$	−11.6182	+	3.46671i	−0.428543	+	0.127872i
$736$	−8.80638	+	15.2531i	−0.324607	+	0.562236i
$737$	7.13624	−	12.3603i	0.262867	−	0.455299i
$738$	1.94612	−	9.37290i	0.0716377	−	0.345021i
$739$	−5.73042	−	9.92538i	−0.210797	−	0.365111i	0.741167	−	0.671320i	$-0.234273\pi$
$739$	−5.73042	−	9.92538i	−0.210797	−	0.365111i	−0.951964	+	0.306209i	$0.900939\pi$
$740$	1.32996	+	2.30357i	0.0488905	+	0.0846808i
$741$	64.1296	−	10.3122i	2.35586	−	0.378828i
$742$	7.08769	−	14.3659i	0.260197	−	0.527388i
$743$	−11.0067	−	19.0642i	−0.403797	−	0.699396i	0.590384	−	0.807123i	$-0.298976\pi$
$743$	−11.0067	−	19.0642i	−0.403797	−	0.699396i	−0.994181	+	0.107726i	$0.965643\pi$
$744$	−2.66367	+	6.98831i	−0.0976549	+	0.256204i
$745$	−0.605477			−0.0221830
$746$	19.9353	+	34.5290i	0.729883	+	1.26419i
$747$	6.57755	−	31.6788i	0.240660	−	1.15907i
$748$	−9.69486			−0.354479
$749$	1.64814	−	3.34057i	0.0602217	−	0.122062i
$750$	−1.73206	−	2.12863i	−0.0632458	−	0.0777266i
$751$	26.7542			0.976276			0.488138	−	0.872767i	$-0.337676\pi$
$751$	26.7542			0.976276			0.488138	+	0.872767i	$0.337676\pi$
$752$	21.7013	−	37.5878i	0.791365	−	1.37068i
$753$	6.81708	−	1.09620i	0.248428	−	0.0399479i
$754$	3.36541	+	5.82906i	0.122561	+	0.212282i
$755$	−22.7927			−0.829511
$756$	−0.140199	−	7.01493i	−0.00509897	−	0.255131i
$757$	−28.4008			−1.03224			−0.516122	−	0.856515i	$-0.672625\pi$
$757$	−28.4008			−1.03224			−0.516122	+	0.856515i	$0.672625\pi$
$758$	12.2704	+	21.2530i	0.445682	+	0.771943i
$759$	31.8260	−	5.11770i	1.15521	−	0.185761i
$760$	−8.72295	+	15.1086i	−0.316415	+	0.548047i
$761$	−1.19374			−0.0432731			−0.0216366	−	0.999766i	$-0.506888\pi$
$761$	−1.19374			−0.0432731			−0.0216366	+	0.999766i	$0.506888\pi$
$762$	−12.9533	−	15.9191i	−0.469249	−	0.576688i
$763$	−3.22981	−	4.83565i	−0.116927	−	0.175062i
$764$	−0.968476			−0.0350382
$765$	−14.2635	−	12.7217i	−0.515699	−	0.459953i
$766$	−2.23193	−	3.86582i	−0.0806430	−	0.139678i
$767$	−55.8678			−2.01727
$768$	7.10601	−	18.6431i	0.256416	−	0.672723i
$769$	−1.05507	−	1.82744i	−0.0380469	−	0.0658992i	0.846375	−	0.532588i	$-0.178780\pi$
$769$	−1.05507	−	1.82744i	−0.0380469	−	0.0658992i	−0.884422	+	0.466688i	$0.845447\pi$
$770$	−6.94232	−	10.3940i	−0.250184	−	0.374573i
$771$	17.7050	−	2.84700i	0.637629	−	0.102532i
$772$	−4.34086	−	7.51860i	−0.156231	−	0.270600i
$773$	11.4342	+	19.8047i	0.411261	+	0.712325i	0.995028	−	0.0995966i	$-0.0317552\pi$
$773$	11.4342	+	19.8047i	0.411261	+	0.712325i	−0.583767	+	0.811921i	$0.698422\pi$
$774$	−9.65805	+	3.18852i	−0.347151	+	0.114609i
$775$	0.914722	−	1.58435i	0.0328578	−	0.0569114i
$776$	−1.04978	+	1.81828i	−0.0376851	+	0.0652724i
$777$	−7.03281	+	22.8247i	−0.252301	+	0.818832i
$778$	−5.21362	−	9.03026i	−0.186917	−	0.323751i
$779$	14.8866			0.533367
$780$	4.42785	−	0.712009i	0.158543	−	0.0254940i
$781$	45.9814			1.64534
$782$	31.5018	−	54.5626i	1.12650	−	1.95116i
$783$	−0.196971	+	4.34650i	−0.00703918	+	0.155331i
$784$	20.2755	+	26.4433i	0.724124	+	0.944403i
$785$	6.87364	−	11.9055i	0.245331	−	0.424925i
$786$	7.45010	+	9.15588i	0.265736	+	0.326580i
$787$	18.0318	−	31.2319i	0.642763	−	1.11330i	−0.342051	−	0.939681i	$-0.611121\pi$
$787$	18.0318	−	31.2319i	0.642763	−	1.11330i	0.984813	−	0.173616i	$-0.0555452\pi$
$788$	−1.12590	+	1.95012i	−0.0401087	+	0.0694703i
$789$	8.24446	−	1.32573i	0.293511	−	0.0471972i
$790$	9.24668	−	16.0157i	0.328982	−	0.569814i
$791$	3.49273	+	5.22929i	0.124187	+	0.185932i
$792$	−20.0480	+	6.61867i	−0.712375	+	0.235184i
$793$	30.4333	−	52.7120i	1.08072	−	1.87186i
$794$	−4.94275			−0.175412
$795$	4.17750	+	5.13398i	0.148161	+	0.182084i
$796$	−12.3051			−0.436144
$797$	0.527738	+	0.914069i	0.0186934	+	0.0323780i	0.875221	−	0.483724i	$-0.160716\pi$
$797$	0.527738	+	0.914069i	0.0186934	+	0.0323780i	−0.856527	+	0.516102i	$0.827383\pi$
$798$	52.3197	−	11.9585i	1.85210	−	0.423328i
$799$	−29.0437	+	50.3052i	−1.02749	+	1.77967i
$800$	−1.41091	+	2.44376i	−0.0498830	+	0.0863999i
$801$	−3.88377	+	18.7050i	−0.137226	+	0.660909i
$802$	−5.75966	−	9.97603i	−0.203381	−	0.352266i
$803$	−5.99957	−	10.3916i	−0.211720	−	0.366710i
$804$	2.67059	+	3.28205i	0.0941845	+	0.115749i
$805$	16.4787	−	1.07708i	0.580798	−	0.0379622i
$806$	7.35283	+	12.7355i	0.258992	+	0.448588i
$807$	33.0885	+	40.6645i	1.16477	+	1.43146i
$808$	10.0925			0.355052
$809$	18.5684	+	32.1615i	0.652832	+	1.13074i	0.982433	+	0.186617i	$0.0597525\pi$
$809$	18.5684	+	32.1615i	0.652832	+	1.13074i	−0.329601	+	0.944120i	$0.606914\pi$
$810$	13.0810	+	5.67683i	0.459620	+	0.199463i
$811$	−42.7365			−1.50068			−0.750341	−	0.661051i	$-0.770110\pi$
$811$	−42.7365			−1.50068			−0.750341	+	0.661051i	$0.770110\pi$
$812$	0.627990	+	0.940221i	0.0220381	+	0.0329953i
$813$	−14.1284	+	37.0668i	−0.495505	+	1.29999i
$814$	−24.6221			−0.863003
$815$	−4.16743	+	7.21819i	−0.145979	+	0.252842i
$816$	−18.7085	+	49.0830i	−0.654930	+	1.71825i
$817$	−7.90823	−	13.6975i	−0.276674	−	0.479213i
$818$	−36.6851			−1.28266
$819$	31.7364	+	24.7864i	1.10896	+	0.866107i
$820$	1.02785			0.0358940
$821$	−14.2633	−	24.7047i	−0.497791	−	0.862200i	0.502205	−	0.864748i	$-0.332522\pi$
$821$	−14.2633	−	24.7047i	−0.497791	−	0.862200i	−0.999997	+	0.00254842i	$0.999189\pi$
$822$	5.84894	+	7.18812i	0.204005	+	0.250714i
$823$	25.4471	−	44.0756i	0.887029	−	1.53638i	0.0436594	−	0.999046i	$-0.486098\pi$
$823$	25.4471	−	44.0756i	0.887029	−	1.53638i	0.843370	−	0.537333i	$-0.180568\pi$
$824$	−0.224511			−0.00782120
$825$	5.09897	−	0.819927i	0.177523	−	0.0285462i
$826$	−46.0635	+	3.01081i	−1.60275	+	0.104759i
$827$	16.5397			0.575142			0.287571	−	0.957759i	$-0.407152\pi$
$827$	16.5397			0.575142			0.287571	+	0.957759i	$0.407152\pi$
$828$	−1.94281	+	9.35696i	−0.0675173	+	0.325177i
$829$	16.8527	+	29.1897i	0.585318	+	1.01380i	0.994836	+	0.101498i	$0.0323637\pi$
$829$	16.8527	+	29.1897i	0.585318	+	1.01380i	−0.409518	+	0.912302i	$0.634303\pi$
$830$	17.0876			0.593118
$831$	−9.53935	+	1.53395i	−0.330917	+	0.0532122i
$832$	12.8092	+	22.1863i	0.444081	+	0.769170i
$833$	−27.1355	−	35.3901i	−0.940189	−	1.22619i
$834$	−12.6321	+	33.1412i	−0.437415	+	1.14758i
$835$	3.38452	+	5.86216i	0.117126	+	0.202869i
$836$	5.62419	+	9.74138i	0.194517	+	0.336913i
$837$	−0.430348	+	9.49633i	−0.0148750	+	0.328241i
$838$	6.38529	−	11.0596i	0.220576	−	0.382049i
$839$	17.6803	−	30.6231i	0.610391	−	1.05723i	−0.380784	−	0.924664i	$-0.624346\pi$
$839$	17.6803	−	30.6231i	0.610391	−	1.05723i	0.991174	−	0.132564i	$-0.0423210\pi$
$840$	−10.5439	+	2.40998i	−0.363798	+	0.0831523i
$841$	14.1494	+	24.5075i	0.487911	+	0.845087i
$842$	−19.9218			−0.686552
$843$	13.1157	−	34.4098i	0.451727	−	1.18514i
$844$	−5.55549			−0.191228
$845$	−6.36955	+	11.0324i	−0.219119	+	0.379525i
$846$	8.81060	−	42.4336i	0.302915	−	1.45890i
$847$	−5.56906	+	0.364006i	−0.191355	+	0.0125074i
$848$	9.09542	−	15.7537i	0.312338	−	0.540985i
$849$	1.75967	−	4.61661i	0.0603918	−	0.158442i
$850$	5.04702	−	8.74170i	0.173111	−	0.299838i
$851$	16.2652	−	28.1722i	0.557565	−	0.965731i
$852$	−4.85522	+	12.7380i	−0.166337	+	0.436396i
$853$	−22.0172	+	38.1350i	−0.753856	+	1.30572i	0.192085	+	0.981378i	$0.438475\pi$
$853$	−22.0172	+	38.1350i	−0.753856	+	1.30572i	−0.945941	+	0.324338i	$0.894858\pi$
$854$	22.2518	−	45.1016i	0.761440	−	1.54335i
$855$	−4.50813	+	21.7121i	−0.154175	+	0.742536i
$856$	1.66149	−	2.87779i	0.0567887	−	0.0983608i
$857$	43.1730			1.47476			0.737381	−	0.675477i	$-0.236062\pi$
$857$	43.1730			1.47476			0.737381	+	0.675477i	$0.236062\pi$
$858$	−14.7857	+	38.7913i	−0.504777	+	1.32431i
$859$	15.6175			0.532861			0.266431	−	0.963854i	$-0.414156\pi$
$859$	15.6175			0.532861			0.266431	+	0.963854i	$0.414156\pi$
$860$	−0.546026	−	0.945746i	−0.0186193	−	0.0322497i
$861$	6.27946	+	6.76348i	0.214003	+	0.230499i
$862$	−19.3879	+	33.5808i	−0.660355	+	1.14377i
$863$	−9.96733	+	17.2639i	−0.339292	+	0.587671i	−0.984300	−	0.176505i	$-0.943521\pi$
$863$	−9.96733	+	17.2639i	−0.339292	+	0.587671i	0.645008	+	0.764176i	$0.276854\pi$
$864$	0.663786	−	14.6475i	0.0225824	−	0.498319i
$865$	0.520284	+	0.901158i	0.0176902	+	0.0306403i
$866$	26.0224	+	45.0722i	0.884278	+	1.53162i
$867$	14.5511	−	38.1758i	0.494183	−	1.29652i
$868$	1.37205	+	2.05422i	0.0465703	+	0.0697247i
$869$	17.4014	+	30.1400i	0.590301	+	1.02243i
$870$	−2.26876	+	0.364822i	−0.0769181	+	0.0123686i
$871$	−24.2846			−0.822852
$872$	−2.59374	−	4.49248i	−0.0878350	−	0.152135i
$873$	−0.542542	+	2.61299i	−0.0183623	+	0.0884362i
$874$	−73.0992			−2.47262
$875$	2.64012	−	0.172564i	0.0892523	−	0.00583372i
$876$	3.51222	−	0.564773i	0.118667	−	0.0190819i
$877$	32.7385			1.10550			0.552750	−	0.833347i	$-0.313578\pi$
$877$	32.7385			1.10550			0.552750	+	0.833347i	$0.313578\pi$
$878$	−3.42966	+	5.94034i	−0.115745	+	0.200477i
$879$	−28.9585	−	35.5888i	−0.976745	−	1.20038i
$880$	−7.09685	−	12.2921i	−0.239235	−	0.414367i
$881$	−25.7844			−0.868697			−0.434349	−	0.900745i	$-0.643021\pi$
$881$	−25.7844			−0.868697			−0.434349	+	0.900745i	$0.643021\pi$
$882$	27.5027	+	18.7263i	0.926063	+	0.630546i
$883$	0.944502			0.0317850			0.0158925	−	0.999874i	$-0.494941\pi$
$883$	0.944502			0.0317850			0.0158925	+	0.999874i	$0.494941\pi$
$884$	8.24789	+	14.2858i	0.277407	+	0.480482i
$885$	6.79325	−	17.8225i	0.228353	−	0.599098i
$886$	−19.3106	+	33.4469i	−0.648752	+	1.12367i
$887$	8.89581			0.298692			0.149346	−	0.988785i	$-0.452283\pi$
$887$	8.89581			0.298692			0.149346	+	0.988785i	$0.452283\pi$
$888$	−7.58844	+	19.9087i	−0.254651	+	0.668093i
$889$	19.7443	−	1.29053i	0.662202	−	0.0432830i
$890$	−10.0895			−0.338201
$891$	−21.5606	+	15.9775i	−0.722306	+	0.535267i
$892$	−0.0215123	−	0.0372604i	−0.000720285	−	0.00124757i
$893$	67.3954			2.25530
$894$	1.04872	+	1.28884i	0.0350745	+	0.0431051i
$895$	3.69562	+	6.40100i	0.123531	+	0.213962i
$896$	20.0503	+	30.0191i	0.669834	+	1.00287i
$897$	−34.6171	−	42.5430i	−1.15583	−	1.42047i
$898$	−21.4777	−	37.2004i	−0.716719	−	1.24139i
$899$	−0.765936	−	1.32664i	−0.0255454	−	0.0442459i
$900$	−0.311265	+	1.49912i	−0.0103755	+	0.0499705i
$901$	−12.1728	+	21.0839i	−0.405534	+	0.702405i
$902$	−4.75722	+	8.23975i	−0.158398	+	0.274354i
$903$	2.88737	−	9.37085i	0.0960857	−	0.311842i
$904$	2.80487	+	4.85819i	0.0932887	+	0.161581i
$905$	7.64655			0.254180
$906$	39.4782	+	48.5172i	1.31158	+	1.61188i
$907$	−41.0205			−1.36206			−0.681032	−	0.732254i	$-0.738469\pi$
$907$	−41.0205			−1.36206			−0.681032	+	0.732254i	$0.738469\pi$
$908$	−4.47856	+	7.75709i	−0.148626	+	0.257428i
$909$	12.1817	−	4.02167i	0.404040	−	0.133390i
$910$	−9.40976	+	19.0724i	−0.311931	+	0.632245i
$911$	−17.7611	+	30.7632i	−0.588453	+	1.01923i	0.405982	+	0.913881i	$0.366930\pi$
$911$	−17.7611	+	30.7632i	−0.588453	+	1.01923i	−0.994435	+	0.105350i	$0.966404\pi$
$912$	60.1717	−	9.67575i	1.99248	−	0.320396i
$913$	−16.0786	+	27.8489i	−0.532123	+	0.921665i
$914$	−0.790196	+	1.36866i	−0.0261374	+	0.0452712i
$915$	13.1152	+	16.1181i	0.433577	+	0.532849i
$916$	−2.10811	+	3.65136i	−0.0696541	+	0.120644i
$917$	−11.3559	+	0.742250i	−0.375006	+	0.0245112i
$918$	−2.37446	+	52.3964i	−0.0783689	+	1.72934i
$919$	22.1441	−	38.3548i	0.730468	−	1.26521i	−0.226215	−	0.974077i	$-0.572635\pi$
$919$	22.1441	−	38.3548i	0.730468	−	1.26521i	0.956683	−	0.291130i	$-0.0940313\pi$
$920$	14.7315			0.485685
$921$	35.1526	−	5.65263i	1.15832	−	0.186260i
$922$	5.43255			0.178912
$923$	−39.1186	−	67.7554i	−1.28761	−	2.23020i
$924$	−2.05344	+	6.66437i	−0.0675534	+	0.219242i
$925$	2.60592	−	4.51358i	0.0856821	−	0.148406i
$926$	26.5707	−	46.0218i	0.873167	−	1.51237i
$927$	−0.270985	+	0.0894633i	−0.00890031	+	0.00293836i
$928$	1.18141	+	2.04626i	0.0387817	+	0.0671719i
$929$	−8.85216	−	15.3324i	−0.290430	−	0.503040i	0.683481	−	0.729968i	$-0.260465\pi$
$929$	−8.85216	−	15.3324i	−0.290430	−	0.503040i	−0.973911	+	0.226928i	$0.927132\pi$
$930$	−4.95684	+	0.797071i	−0.162541	+	0.0261370i
$931$	−19.8181	+	47.7962i	−0.649510	+	1.56646i
$932$	1.96812	+	3.40888i	0.0644679	+	0.111662i
$933$	−4.41827	+	11.5916i	−0.144648	+	0.379492i
$934$	−34.8472			−1.14023
$935$	9.49801	+	16.4510i	0.310618	+	0.538006i
$936$	26.8087	+	23.9107i	0.876269	+	0.781545i
$937$	−5.67975			−0.185549			−0.0927746	−	0.995687i	$-0.529574\pi$
$937$	−5.67975			−0.185549			−0.0927746	+	0.995687i	$0.529574\pi$
$938$	−20.0228	+	1.30874i	−0.653769	+	0.0427318i
$939$	−6.88203	−	8.45774i	−0.224586	−	0.276008i
$940$	4.65334			0.151775
$941$	7.96868	−	13.8022i	0.259772	−	0.449938i	−0.706409	−	0.707804i	$-0.749686\pi$
$941$	7.96868	−	13.8022i	0.259772	−	0.449938i	0.966181	+	0.257866i	$0.0830194\pi$
$942$	−37.2479	+	5.98955i	−1.21360	+	0.195150i
$943$	−6.28520	−	10.8863i	−0.204674	−	0.354506i
$944$	−52.4198			−1.70612
$945$	−11.7662	+	7.11039i	−0.382753	+	0.231301i
$946$	10.1088			0.328664
$947$	6.59184	+	11.4174i	0.214206	+	0.371016i	0.953027	−	0.302886i	$-0.0979503\pi$
$947$	6.59184	+	11.4174i	0.214206	+	0.371016i	−0.738821	+	0.673902i	$0.764617\pi$
$948$	−10.1869	+	1.63809i	−0.330857	+	0.0532025i
$949$	−10.2083	+	17.6812i	−0.331374	+	0.573956i
$950$	−11.7115			−0.379972
$951$	0.828766	+	1.01852i	0.0268746	+	0.0330278i
$952$	−22.0961	−	33.0821i	−0.716140	−	1.07220i
$953$	−41.2678			−1.33680			−0.668398	−	0.743803i	$-0.733020\pi$
$953$	−41.2678			−1.33680			−0.668398	+	0.743803i	$0.733020\pi$
$954$	3.69269	−	17.7847i	0.119555	−	0.575801i
$955$	0.948810	+	1.64339i	0.0307028	+	0.0531788i
$956$	−3.33088			−0.107728
$957$	1.54021	−	4.04085i	0.0497881	−	0.130622i
$958$	17.9204	+	31.0391i	0.578983	+	1.00283i
$959$	−8.91534	+	0.582726i	−0.287891	+	0.0188172i
$960$	−8.63523	+	1.38857i	−0.278701	+	0.0448158i
$961$	13.8266	+	23.9483i	0.446018	+	0.772526i
$962$	20.9472	+	36.2816i	0.675365	+	1.16977i
$963$	0.858680	−	4.13557i	0.0276706	−	0.133267i
$964$	−6.28462	+	10.8853i	−0.202414	+	0.350591i
$965$	−8.50544	+	14.7319i	−0.273800	+	0.474235i
$966$	−30.8348	−	33.2115i	−0.992092	−	1.06856i
$967$	−13.2481	−	22.9464i	−0.426030	−	0.737906i	0.570486	−	0.821307i	$-0.306755\pi$
$967$	−13.2481	−	22.9464i	−0.426030	−	0.737906i	−0.996516	+	0.0834017i	$0.973422\pi$
$968$	−4.97860			−0.160018
$969$	−80.5302	+	12.9495i	−2.58700	+	0.415996i
$970$	−1.40945			−0.0452547
$971$	−27.8291	+	48.2013i	−0.893077	+	1.54685i	−0.0569100	+	0.998379i	$0.518125\pi$
$971$	−27.8291	+	48.2013i	−0.893077	+	1.54685i	−0.836167	+	0.548475i	$0.815209\pi$
$972$	−2.14956	−	7.65988i	−0.0689471	−	0.245691i
$973$	−18.9918	−	28.4344i	−0.608849	−	0.911563i
$974$	6.26403	−	10.8496i	0.200712	−	0.347644i
$975$	−5.54614	−	6.81599i	−0.177619	−	0.218286i
$976$	28.5550	−	49.4588i	0.914025	−	1.58314i
$977$	−7.30999	+	12.6613i	−0.233867	+	0.405070i	−0.958943	−	0.283599i	$-0.908472\pi$
$977$	−7.30999	+	12.6613i	−0.233867	+	0.405070i	0.725076	+	0.688669i	$0.241805\pi$
$978$	22.5831	−	3.63141i	0.722127	−	0.116120i
$979$	9.49375	−	16.4437i	0.303421	−	0.525541i
$980$	−1.36834	+	3.30010i	−0.0437101	+	0.105418i
$981$	−4.92081	−	4.38888i	−0.157110	−	0.140126i
$982$	−29.7164	+	51.4702i	−0.948287	+	1.64248i
$983$	−44.6189			−1.42312			−0.711561	−	0.702625i	$-0.752011\pi$
$983$	−44.6189			−1.42312			−0.711561	+	0.702625i	$0.752011\pi$
$984$	5.19628	+	6.38602i	0.165651	+	0.203579i
$985$	4.41217			0.140583
$986$	−4.22608	−	7.31979i	−0.134586	−	0.233110i
$987$	28.4288	+	30.6201i	0.904898	+	0.974647i
$988$	9.56954	−	16.5749i	0.304447	−	0.527318i
$989$	−6.67781	+	11.5663i	−0.212342	+	0.367787i
$990$	−10.5770	−	9.43367i	−0.336160	−	0.299822i
$991$	−9.86169	−	17.0809i	−0.313267	−	0.542594i	0.665801	−	0.746130i	$-0.268090\pi$
$991$	−9.86169	−	17.0809i	−0.313267	−	0.542594i	−0.979068	+	0.203536i	$0.934757\pi$
$992$	2.58117	+	4.47072i	0.0819523	+	0.141946i
$993$	25.3147	+	31.1108i	0.803338	+	0.987270i
$994$	−35.9051	−	53.7567i	−1.13884	−	1.70506i
$995$	12.0553	+	20.8804i	0.382178	+	0.661952i
$996$	−6.01708	−	7.39475i	−0.190658	−	0.234312i
$997$	−23.8837			−0.756406			−0.378203	−	0.925723i	$-0.623458\pi$
$997$	−23.8837			−0.756406			−0.378203	+	0.925723i	$0.623458\pi$
$998$	−12.8870	−	22.3209i	−0.407929	−	0.706555i
$999$	−1.22600	+	27.0537i	−0.0387890	+	0.855942i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.c.16.14	✓	36
3.2	odd	2		945.2.k.c.856.5		36
7.4	even	3		315.2.l.c.151.5	yes	36
9.4	even	3		315.2.l.c.121.5	yes	36
9.5	odd	6		945.2.l.c.226.14		36
21.11	odd	6		945.2.l.c.46.14		36
63.4	even	3	inner	315.2.k.c.256.14	yes	36
63.32	odd	6		945.2.k.c.361.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.14	✓	36	1.1	even	1	trivial
315.2.k.c.256.14	yes	36	63.4	even	3	inner
315.2.l.c.121.5	yes	36	9.4	even	3
315.2.l.c.151.5	yes	36	7.4	even	3
945.2.k.c.361.5		36	63.32	odd	6
945.2.k.c.856.5		36	3.2	odd	2
945.2.l.c.46.14		36	21.11	odd	6
945.2.l.c.226.14		36	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.792206 + 1.37214i) q^{2} +(-1.71008 + 0.274985i) q^{3} +(-0.255182 + 0.441987i) q^{4} +1.00000 q^{5} +(-1.73206 - 2.12863i) q^{6} +(2.64012 - 0.172564i) q^{7} +2.36020 q^{8} +(2.84877 - 0.940495i) q^{9} +O(q^{10})\)	\(q+(0.792206 + 1.37214i) q^{2} +(-1.71008 + 0.274985i) q^{3} +(-0.255182 + 0.441987i) q^{4} +1.00000 q^{5} +(-1.73206 - 2.12863i) q^{6} +(2.64012 - 0.172564i) q^{7} +2.36020 q^{8} +(2.84877 - 0.940495i) q^{9} +(0.792206 + 1.37214i) q^{10} -2.98171 q^{11} +(0.314842 - 0.826006i) q^{12} +(2.53669 + 4.39367i) q^{13} +(2.32830 + 3.48591i) q^{14} +(-1.71008 + 0.274985i) q^{15} +(2.38013 + 4.12250i) q^{16} +(-3.18542 - 5.51731i) q^{17} +(3.54730 + 3.16384i) q^{18} +(-3.69586 + 6.40141i) q^{19} +(-0.255182 + 0.441987i) q^{20} +(-4.46737 + 1.02109i) q^{21} +(-2.36213 - 4.09133i) q^{22} +6.24165 q^{23} +(-4.03614 + 0.649020i) q^{24} +1.00000 q^{25} +(-4.01916 + 6.96138i) q^{26} +(-4.61300 + 2.39169i) q^{27} +(-0.597438 + 1.21093i) q^{28} +(0.418671 - 0.725160i) q^{29} +(-1.73206 - 2.12863i) q^{30} +(0.914722 - 1.58435i) q^{31} +(-1.41091 + 2.44376i) q^{32} +(5.09897 - 0.819927i) q^{33} +(5.04702 - 8.74170i) q^{34} +(2.64012 - 0.172564i) q^{35} +(-0.311265 + 1.49912i) q^{36} +(2.60592 - 4.51358i) q^{37} -11.7115 q^{38} +(-5.54614 - 6.81599i) q^{39} +2.36020 q^{40} +(-1.00698 - 1.74414i) q^{41} +(-4.94016 - 5.32094i) q^{42} +(-1.06988 + 1.85308i) q^{43} +(0.760878 - 1.31788i) q^{44} +(2.84877 - 0.940495i) q^{45} +(4.94468 + 8.56443i) q^{46} +(-4.55885 - 7.89616i) q^{47} +(-5.20384 - 6.39532i) q^{48} +(6.94044 - 0.911178i) q^{49} +(0.792206 + 1.37214i) q^{50} +(6.96451 + 8.55912i) q^{51} -2.58926 q^{52} +(-1.91070 - 3.30943i) q^{53} +(-6.93619 - 4.43498i) q^{54} -2.98171 q^{55} +(6.23120 - 0.407285i) q^{56} +(4.55992 - 11.9632i) q^{57} +1.32670 q^{58} +(-5.50599 + 9.53665i) q^{59} +(0.314842 - 0.826006i) q^{60} +(-5.99864 - 10.3899i) q^{61} +2.89860 q^{62} +(7.35878 - 2.97461i) q^{63} +5.04960 q^{64} +(2.53669 + 4.39367i) q^{65} +(5.16449 + 6.34696i) q^{66} +(-2.39334 + 4.14538i) q^{67} +3.25144 q^{68} +(-10.6737 + 1.71636i) q^{69} +(2.32830 + 3.48591i) q^{70} -15.4212 q^{71} +(6.72366 - 2.21976i) q^{72} +(2.01212 + 3.48510i) q^{73} +8.25770 q^{74} +(-1.71008 + 0.274985i) q^{75} +(-1.88623 - 3.26704i) q^{76} +(-7.87207 + 0.514536i) q^{77} +(4.95881 - 13.0098i) q^{78} +(-5.83603 - 10.1083i) q^{79} +(2.38013 + 4.12250i) q^{80} +(7.23094 - 5.35850i) q^{81} +(1.59547 - 2.76343i) q^{82} +(5.39240 - 9.33991i) q^{83} +(0.688680 - 2.23508i) q^{84} +(-3.18542 - 5.51731i) q^{85} -3.39026 q^{86} +(-0.516554 + 1.35521i) q^{87} -7.03743 q^{88} +(-3.18399 + 5.51484i) q^{89} +(3.54730 + 3.16384i) q^{90} +(7.45534 + 11.1621i) q^{91} +(-1.59275 + 2.75873i) q^{92} +(-1.12858 + 2.96090i) q^{93} +(7.22310 - 12.5108i) q^{94} +(-3.69586 + 6.40141i) q^{95} +(1.74077 - 4.56701i) q^{96} +(-0.444786 + 0.770392i) q^{97} +(6.74853 + 8.80143i) q^{98} +(-8.49420 + 2.80429i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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