LMFDB - Embedded newform 276.2.c.a.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(47,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("276.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.c (of order $2$, degree $1$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.2
Character	$\chi$	$=$	276.47
Dual form			276.2.c.a.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40657 + 0.146847i) q^{2} +(0.169868 - 1.72370i) q^{3} +(1.95687 - 0.413102i) q^{4} +2.76583i q^{5} +(0.0141905 + 2.44945i) q^{6} +3.82694i q^{7} +(-2.69181 + 0.868418i) q^{8} +(-2.94229 - 0.585602i) q^{9} +O(q^{10})$	\(q+(-1.40657 + 0.146847i) q^{2} +(0.169868 - 1.72370i) q^{3} +(1.95687 - 0.413102i) q^{4} +2.76583i q^{5} +(0.0141905 + 2.44945i) q^{6} +3.82694i q^{7} +(-2.69181 + 0.868418i) q^{8} +(-2.94229 - 0.585602i) q^{9} +(-0.406156 - 3.89033i) q^{10} -2.92964 q^{11} +(-0.379655 - 3.44323i) q^{12} -4.70010 q^{13} +(-0.561977 - 5.38286i) q^{14} +(4.76747 + 0.469826i) q^{15} +(3.65869 - 1.61678i) q^{16} +4.06418i q^{17} +(4.22453 + 0.391622i) q^{18} +3.75945i q^{19} +(1.14257 + 5.41238i) q^{20} +(6.59650 + 0.650074i) q^{21} +(4.12074 - 0.430210i) q^{22} +1.00000 q^{23} +(1.03964 + 4.78739i) q^{24} -2.64983 q^{25} +(6.61101 - 0.690197i) q^{26} +(-1.50920 + 4.97215i) q^{27} +(1.58092 + 7.48883i) q^{28} -8.01162i q^{29} +(-6.77476 + 0.0392486i) q^{30} +1.15321i q^{31} +(-4.90878 + 2.81138i) q^{32} +(-0.497651 + 5.04982i) q^{33} +(-0.596814 - 5.71654i) q^{34} -10.5847 q^{35} +(-5.99960 + 0.0695179i) q^{36} +10.9539 q^{37} +(-0.552066 - 5.28793i) q^{38} +(-0.798395 + 8.10156i) q^{39} +(-2.40190 - 7.44510i) q^{40} -1.54300i q^{41} +(-9.37390 + 0.0543063i) q^{42} +2.22457i q^{43} +(-5.73293 + 1.21024i) q^{44} +(1.61968 - 8.13788i) q^{45} +(-1.40657 + 0.146847i) q^{46} +11.5685 q^{47} +(-2.16534 - 6.58113i) q^{48} -7.64548 q^{49} +(3.72717 - 0.389121i) q^{50} +(7.00543 + 0.690372i) q^{51} +(-9.19749 + 1.94162i) q^{52} +6.30409i q^{53} +(1.39265 - 7.21530i) q^{54} -8.10289i q^{55} +(-3.32339 - 10.3014i) q^{56} +(6.48017 + 0.638609i) q^{57} +(1.17649 + 11.2689i) q^{58} -7.03012 q^{59} +(9.52341 - 1.05006i) q^{60} -6.15204 q^{61} +(-0.169346 - 1.62207i) q^{62} +(2.24107 - 11.2600i) q^{63} +(6.49170 - 4.67524i) q^{64} -12.9997i q^{65} +(-0.0415731 - 7.17600i) q^{66} -1.65217i q^{67} +(1.67892 + 7.95307i) q^{68} +(0.169868 - 1.72370i) q^{69} +(14.8881 - 1.55433i) q^{70} +12.6986 q^{71} +(8.42864 - 0.978807i) q^{72} -5.68142 q^{73} +(-15.4075 + 1.60856i) q^{74} +(-0.450120 + 4.56751i) q^{75} +(1.55304 + 7.35676i) q^{76} -11.2116i q^{77} +(-0.0666969 - 11.5126i) q^{78} -3.06335i q^{79} +(4.47173 + 10.1193i) q^{80} +(8.31414 + 3.44602i) q^{81} +(0.226585 + 2.17033i) q^{82} -2.88693 q^{83} +(13.1771 - 1.45292i) q^{84} -11.2408 q^{85} +(-0.326672 - 3.12901i) q^{86} +(-13.8096 - 1.36091i) q^{87} +(7.88604 - 2.54415i) q^{88} +8.17643i q^{89} +(-1.08316 + 11.6843i) q^{90} -17.9870i q^{91} +(1.95687 - 0.413102i) q^{92} +(1.98779 + 0.195893i) q^{93} +(-16.2719 + 1.69880i) q^{94} -10.3980 q^{95} +(4.01213 + 8.93884i) q^{96} -4.28092 q^{97} +(10.7539 - 1.12272i) q^{98} +(8.61985 + 1.71560i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9}+O(q^{10}) $ 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9	$ 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{16} - 14 q^{18} - 14 q^{20} + 2 q^{22} + 22 q^{23} + 22 q^{24} - 18 q^{25} + 27 q^{26} + 12 q^{27} + 6 q^{28} - 24 q^{30} - 20 q^{32} - 8 q^{33} - 6 q^{34} - 8 q^{35} + 3 q^{36} - 4 q^{37} + 22 q^{38} - 24 q^{39} - 4 q^{40} - 38 q^{42} - 56 q^{44} + 8 q^{47} + 17 q^{48} - 14 q^{49} + 20 q^{50} + 16 q^{51} - 19 q^{52} - 54 q^{54} - 18 q^{56} + 12 q^{57} + 3 q^{58} - 72 q^{59} + 64 q^{60} + 12 q^{61} + 63 q^{62} - 20 q^{63} + 3 q^{64} - 18 q^{66} - 20 q^{68} + 40 q^{71} + 48 q^{72} - 4 q^{73} + 28 q^{74} + 48 q^{75} + 26 q^{76} - 46 q^{78} - 84 q^{80} + 10 q^{81} - 29 q^{82} - 8 q^{83} + 76 q^{84} + 8 q^{85} + 28 q^{86} - 48 q^{87} - 30 q^{88} - 26 q^{90} + 12 q^{93} - 13 q^{94} + 32 q^{95} + 18 q^{96} - 4 q^{97} + 64 q^{98} + 20 q^{99}+O(q^{100}) $ 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^16 - 14 * q^18 - 14 * q^20 + 2 * q^22 + 22 * q^23 + 22 * q^24 - 18 * q^25 + 27 * q^26 + 12 * q^27 + 6 * q^28 - 24 * q^30 - 20 * q^32 - 8 * q^33 - 6 * q^34 - 8 * q^35 + 3 * q^36 - 4 * q^37 + 22 * q^38 - 24 * q^39 - 4 * q^40 - 38 * q^42 - 56 * q^44 + 8 * q^47 + 17 * q^48 - 14 * q^49 + 20 * q^50 + 16 * q^51 - 19 * q^52 - 54 * q^54 - 18 * q^56 + 12 * q^57 + 3 * q^58 - 72 * q^59 + 64 * q^60 + 12 * q^61 + 63 * q^62 - 20 * q^63 + 3 * q^64 - 18 * q^66 - 20 * q^68 + 40 * q^71 + 48 * q^72 - 4 * q^73 + 28 * q^74 + 48 * q^75 + 26 * q^76 - 46 * q^78 - 84 * q^80 + 10 * q^81 - 29 * q^82 - 8 * q^83 + 76 * q^84 + 8 * q^85 + 28 * q^86 - 48 * q^87 - 30 * q^88 - 26 * q^90 + 12 * q^93 - 13 * q^94 + 32 * q^95 + 18 * q^96 - 4 * q^97 + 64 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.40657	+	0.146847i	−0.994594	+	0.103837i
$2$	−1.40657	+	0.146847i	−0.994594	+	0.103837i
$3$	0.169868	−	1.72370i	0.0980732	−	0.995179i
$3$	0.169868	−	1.72370i	0.0980732	−	0.995179i
$4$	1.95687	−	0.413102i	0.978436	−	0.206551i
$5$			2.76583i			1.23692i	0.785817	+	0.618459i	$0.212243\pi$
$5$			2.76583i			1.23692i	−0.785817	+	0.618459i	$0.787757\pi$
$6$	0.0141905	+	2.44945i	0.00579326	+	0.999983i
$7$			3.82694i			1.44645i	0.690614	+	0.723224i	$0.257341\pi$
$7$			3.82694i			1.44645i	−0.690614	+	0.723224i	$0.742659\pi$
$8$	−2.69181	+	0.868418i	−0.951699	+	0.307032i
$9$	−2.94229	−	0.585602i	−0.980763	−	0.195201i
$10$	−0.406156	−	3.89033i	−0.128438	−	1.23023i
$11$	−2.92964			−0.883320			−0.441660	−	0.897183i	$-0.645610\pi$
$11$	−2.92964			−0.883320			−0.441660	+	0.897183i	$0.645610\pi$
$12$	−0.379655	−	3.44323i	−0.109597	−	0.993976i
$13$	−4.70010			−1.30357			−0.651786	−	0.758403i	$-0.725980\pi$
$13$	−4.70010			−1.30357			−0.651786	+	0.758403i	$0.725980\pi$
$14$	−0.561977	−	5.38286i	−0.150195	−	1.43863i
$15$	4.76747	+	0.469826i	1.23095	+	0.121308i
$16$	3.65869	−	1.61678i	0.914673	−	0.404194i
$17$			4.06418i			0.985708i	0.870112	+	0.492854i	$0.164046\pi$
$17$			4.06418i			0.985708i	−0.870112	+	0.492854i	$0.835954\pi$
$18$	4.22453	+	0.391622i	0.995731	+	0.0923062i
$19$			3.75945i			0.862477i	0.902238	+	0.431239i	$0.141923\pi$
$19$			3.75945i			0.862477i	−0.902238	+	0.431239i	$0.858077\pi$
$20$	1.14257	+	5.41238i	0.255487	+	1.21024i
$21$	6.59650	+	0.650074i	1.43947	+	0.141858i
$22$	4.12074	−	0.430210i	0.878545	−	0.0917211i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	1.03964	+	4.78739i	0.212216	+	0.977223i
$25$	−2.64983			−0.529966
$26$	6.61101	−	0.690197i	1.29653	−	0.135359i
$27$	−1.50920	+	4.97215i	−0.290446	+	0.956891i
$28$	1.58092	+	7.48883i	0.298765	+	1.41526i
$29$		−	8.01162i		−	1.48772i	−0.668336	−	0.743860i	$-0.732993\pi$
$29$		−	8.01162i		−	1.48772i	0.668336	−	0.743860i	$-0.267007\pi$
$30$	−6.77476	+	0.0392486i	−1.23690	+	0.00716578i
$31$			1.15321i			0.207123i	0.994623	+	0.103561i	$0.0330238\pi$
$31$			1.15321i			0.207123i	−0.994623	+	0.103561i	$0.966976\pi$
$32$	−4.90878	+	2.81138i	−0.867759	+	0.496986i
$33$	−0.497651	+	5.04982i	−0.0866299	+	0.879061i
$34$	−0.596814	−	5.71654i	−0.102353	−	0.980379i
$35$	−10.5847			−1.78914
$36$	−5.99960	+	0.0695179i	−0.999933	+	0.0115863i
$37$	10.9539			1.80082			0.900408	−	0.435046i	$-0.143268\pi$
$37$	10.9539			1.80082			0.900408	+	0.435046i	$0.143268\pi$
$38$	−0.552066	−	5.28793i	−0.0895569	−	0.857815i
$39$	−0.798395	+	8.10156i	−0.127845	+	1.29729i
$40$	−2.40190	−	7.44510i	−0.379774	−	1.17717i
$41$		−	1.54300i		−	0.240976i	−0.992715	−	0.120488i	$-0.961554\pi$
$41$		−	1.54300i		−	0.240976i	0.992715	−	0.120488i	$-0.0384459\pi$
$42$	−9.37390	+	0.0543063i	−1.44642	+	0.00837964i
$43$			2.22457i			0.339243i	0.985509	+	0.169622i	$0.0542545\pi$
$43$			2.22457i			0.339243i	−0.985509	+	0.169622i	$0.945745\pi$
$44$	−5.73293	+	1.21024i	−0.864272	+	0.182451i
$45$	1.61968	−	8.13788i	0.241447	−	1.21312i
$46$	−1.40657	+	0.146847i	−0.207387	+	0.0216515i
$47$	11.5685			1.68744			0.843718	−	0.536787i	$-0.180362\pi$
$47$	11.5685			1.68744			0.843718	+	0.536787i	$0.180362\pi$
$48$	−2.16534	−	6.58113i	−0.312541	−	0.949904i
$49$	−7.64548			−1.09221
$50$	3.72717	−	0.389121i	0.527101	−	0.0550300i
$51$	7.00543	+	0.690372i	0.980956	+	0.0966715i
$52$	−9.19749	+	1.94162i	−1.27546	+	0.269254i
$53$			6.30409i			0.865933i	0.901410	+	0.432966i	$0.142533\pi$
$53$			6.30409i			0.865933i	−0.901410	+	0.432966i	$0.857467\pi$
$54$	1.39265	−	7.21530i	0.189516	−	0.981878i
$55$		−	8.10289i		−	1.09259i
$56$	−3.32339	−	10.3014i	−0.444106	−	1.37658i
$57$	6.48017	+	0.638609i	0.858319	+	0.0845859i
$58$	1.17649	+	11.2689i	0.154480	+	1.47968i
$59$	−7.03012			−0.915244			−0.457622	−	0.889147i	$-0.651299\pi$
$59$	−7.03012			−0.915244			−0.457622	+	0.889147i	$0.651299\pi$
$60$	9.52341	−	1.05006i	1.22947	−	0.135563i
$61$	−6.15204			−0.787688			−0.393844	−	0.919177i	$-0.628855\pi$
$61$	−6.15204			−0.787688			−0.393844	+	0.919177i	$0.628855\pi$
$62$	−0.169346	−	1.62207i	−0.0215070	−	0.206003i
$63$	2.24107	−	11.2600i	0.282348	−	1.41862i
$64$	6.49170	−	4.67524i	0.811462	−	0.584405i
$65$		−	12.9997i		−	1.61241i
$66$	−0.0415731	−	7.17600i	−0.00511730	−	0.883305i
$67$		−	1.65217i		−	0.201845i	−0.994894	−	0.100922i	$-0.967821\pi$
$67$		−	1.65217i		−	0.201845i	0.994894	−	0.100922i	$-0.0321794\pi$
$68$	1.67892	+	7.95307i	0.203599	+	0.964452i
$69$	0.169868	−	1.72370i	0.0204497	−	0.207509i
$70$	14.8881	−	1.55433i	1.77947	−	0.185778i
$71$	12.6986			1.50704			0.753522	−	0.657423i	$-0.228354\pi$
$71$	12.6986			1.50704			0.753522	+	0.657423i	$0.228354\pi$
$72$	8.42864	−	0.978807i	0.993324	−	0.115354i
$73$	−5.68142			−0.664960			−0.332480	−	0.943110i	$-0.607885\pi$
$73$	−5.68142			−0.664960			−0.332480	+	0.943110i	$0.607885\pi$
$74$	−15.4075	+	1.60856i	−1.79108	+	0.186991i
$75$	−0.450120	+	4.56751i	−0.0519754	+	0.527411i
$76$	1.55304	+	7.35676i	0.178146	+	0.843878i
$77$		−	11.2116i		−	1.27768i
$78$	−0.0666969	−	11.5126i	−0.00755193	−	1.30355i
$79$		−	3.06335i		−	0.344654i	−0.985040	−	0.172327i	$-0.944871\pi$
$79$		−	3.06335i		−	0.344654i	0.985040	−	0.172327i	$-0.0551285\pi$
$80$	4.47173	+	10.1193i	0.499955	+	1.13138i
$81$	8.31414	+	3.44602i	0.923793	+	0.382891i
$82$	0.226585	+	2.17033i	0.0250221	+	0.239673i
$83$	−2.88693			−0.316881			−0.158441	−	0.987369i	$-0.550647\pi$
$83$	−2.88693			−0.316881			−0.158441	+	0.987369i	$0.550647\pi$
$84$	13.1771	−	1.45292i	1.43773	−	0.158526i
$85$	−11.2408			−1.21924
$86$	−0.326672	−	3.12901i	−0.0352259	−	0.337409i
$87$	−13.8096	−	1.36091i	−1.48055	−	0.145905i
$88$	7.88604	−	2.54415i	0.840655	−	0.271208i
$89$			8.17643i			0.866700i	0.901226	+	0.433350i	$0.142669\pi$
$89$			8.17643i			0.866700i	−0.901226	+	0.433350i	$0.857331\pi$
$90$	−1.08316	+	11.6843i	−0.114175	+	1.23164i
$91$		−	17.9870i		−	1.88555i
$92$	1.95687	−	0.413102i	0.204018	−	0.0430689i
$93$	1.98779	+	0.195893i	0.206124	+	0.0203132i
$94$	−16.2719	+	1.69880i	−1.67831	+	0.175218i
$95$	−10.3980			−1.06681
$96$	4.01213	+	8.93884i	0.409486	+	0.912316i
$97$	−4.28092			−0.434661			−0.217331	−	0.976098i	$-0.569735\pi$
$97$	−4.28092			−0.434661			−0.217331	+	0.976098i	$0.569735\pi$
$98$	10.7539	−	1.12272i	1.08631	−	0.113412i
$99$	8.61985	+	1.71560i	0.866327	+	0.172425i
$100$	−5.18537	+	1.09465i	−0.518537	+	0.109465i
$101$		−	0.157064i		−	0.0156284i	−0.999969	−	0.00781422i	$-0.997513\pi$
$101$		−	0.157064i		−	0.0156284i	0.999969	−	0.00781422i	$-0.00248737\pi$
$102$	−9.95499	+	0.0576728i	−0.985691	+	0.00571046i
$103$			0.837604i			0.0825316i	0.999148	+	0.0412658i	$0.0131390\pi$
$103$			0.837604i			0.0825316i	−0.999148	+	0.0412658i	$0.986861\pi$
$104$	12.6518	−	4.08165i	1.24061	−	0.400239i
$105$	−1.79799	+	18.2448i	−0.175466	+	1.78051i
$106$	−0.925739	−	8.86713i	−0.0899157	−	0.861252i
$107$	5.27152			0.509617			0.254808	−	0.966992i	$-0.417988\pi$
$107$	5.27152			0.509617			0.254808	+	0.966992i	$0.417988\pi$
$108$	−0.899310	+	10.3533i	−0.0865361	+	0.996249i
$109$	−3.53593			−0.338680			−0.169340	−	0.985558i	$-0.554164\pi$
$109$	−3.53593			−0.338680			−0.169340	+	0.985558i	$0.554164\pi$
$110$	1.18989	+	11.3973i	0.113451	+	1.08669i
$111$	1.86072	−	18.8813i	0.176612	−	1.79214i
$112$	6.18731	+	14.0016i	0.584645	+	1.32303i
$113$			1.07484i			0.101112i	0.998721	+	0.0505562i	$0.0160994\pi$
$113$			1.07484i			0.101112i	−0.998721	+	0.0505562i	$0.983901\pi$
$114$	−9.20858	+	0.0533486i	−0.862463	+	0.00499655i
$115$			2.76583i			0.257915i
$116$	−3.30962	−	15.6777i	−0.307290	−	1.45564i
$117$	13.8291	+	2.75239i	1.27850	+	0.254458i
$118$	9.88835	−	1.03236i	0.910297	−	0.0950361i
$119$	−15.5534			−1.42577
$120$	−13.2411	+	2.87547i	−1.20874	+	0.262494i
$121$	−2.41721			−0.219746
$122$	8.65327	−	0.903412i	0.783430	−	0.0817911i
$123$	−2.65966	−	0.262105i	−0.239814	−	0.0236332i
$124$	0.476394	+	2.25669i	0.0427815	+	0.202656i
$125$			6.50018i			0.581394i
$126$	−1.49871	+	16.1670i	−0.133516	+	1.44027i
$127$			17.1767i			1.52419i	0.647467	+	0.762093i	$0.275828\pi$
$127$			17.1767i			1.52419i	−0.647467	+	0.762093i	$0.724172\pi$
$128$	−8.44448	+	7.52933i	−0.746393	+	0.665505i
$129$	3.83449	+	0.377882i	0.337608	+	0.0332707i
$130$	1.90897	+	18.2849i	0.167428	+	1.60370i
$131$	1.71808			0.150109			0.0750547	−	0.997179i	$-0.476087\pi$
$131$	1.71808			0.150109			0.0750547	+	0.997179i	$0.476087\pi$
$132$	1.11225	+	10.0874i	0.0968092	+	0.877999i
$133$	−14.3872			−1.24753
$134$	0.242617	+	2.32389i	0.0209589	+	0.200754i
$135$	−13.7521	−	4.17420i	−1.18360	−	0.359258i
$136$	−3.52941	−	10.9400i	−0.302644	−	0.938097i
$137$			19.5809i			1.67291i	0.548039	+	0.836453i	$0.315375\pi$
$137$			19.5809i			1.67291i	−0.548039	+	0.836453i	$0.684625\pi$
$138$	0.0141905	+	2.44945i	0.00120798	+	0.208511i
$139$		−	3.80864i		−	0.323045i	−0.986869	−	0.161522i	$-0.948360\pi$
$139$		−	3.80864i		−	0.323045i	0.986869	−	0.161522i	$-0.0516404\pi$
$140$	−20.7129	+	4.37255i	−1.75056	+	0.369548i
$141$	1.96511	−	19.9406i	0.165492	−	1.67930i
$142$	−17.8614	+	1.86475i	−1.49890	+	0.156487i
$143$	13.7696			1.15147
$144$	−11.7117	+	2.61448i	−0.975977	+	0.217874i
$145$	22.1588			1.84019
$146$	7.99131	−	0.834302i	0.661365	−	0.0690473i
$147$	−1.29872	+	13.1785i	−0.107117	+	1.08695i
$148$	21.4355	−	4.52510i	1.76198	−	0.371961i
$149$		−	18.5848i		−	1.52253i	−0.648444	−	0.761263i	$-0.724580\pi$
$149$		−	18.5848i		−	1.52253i	0.648444	−	0.761263i	$-0.275420\pi$
$150$	−0.0376025	−	6.49062i	−0.00307023	−	0.529957i
$151$			3.58973i			0.292128i	0.989275	+	0.146064i	$0.0466605\pi$
$151$			3.58973i			0.292128i	−0.989275	+	0.146064i	$0.953339\pi$
$152$	−3.26478	−	10.1197i	−0.264808	−	0.820819i
$153$	2.37999	−	11.9580i	0.192411	−	0.966746i
$154$	1.64639	+	15.7698i	0.132670	+	1.27077i
$155$	−3.18959			−0.256194
$156$	1.78442	+	16.1835i	0.142868	+	1.29572i
$157$	−3.64861			−0.291190			−0.145595	−	0.989344i	$-0.546510\pi$
$157$	−3.64861			−0.291190			−0.145595	+	0.989344i	$0.546510\pi$
$158$	0.449845	+	4.30881i	0.0357877	+	0.342791i
$159$	10.8664	+	1.07086i	0.861758	+	0.0849248i
$160$	−7.77580	−	13.5769i	−0.614731	−	1.07335i
$161$			3.82694i			0.301605i
$162$	−12.2004	−	3.62616i	−0.958558	−	0.284898i
$163$		−	19.3261i		−	1.51374i	−0.653566	−	0.756870i	$-0.726728\pi$
$163$		−	19.3261i		−	1.51374i	0.653566	−	0.756870i	$-0.273272\pi$
$164$	−0.637415	−	3.01945i	−0.0497738	−	0.235779i
$165$	−13.9670	−	1.37642i	−1.08733	−	0.107154i
$166$	4.06066	−	0.423938i	0.315168	−	0.0329039i
$167$	6.78412			0.524971			0.262486	−	0.964936i	$-0.415458\pi$
$167$	6.78412			0.524971			0.262486	+	0.964936i	$0.415458\pi$
$168$	−18.3211	+	3.97865i	−1.41350	+	0.306959i
$169$	9.09092			0.699301
$170$	15.8110	−	1.65069i	1.21265	−	0.126602i
$171$	2.20154	−	11.0614i	0.168356	−	0.845886i
$172$	0.918973	+	4.35319i	0.0700710	+	0.331928i
$173$			16.0897i			1.22327i	0.791138	+	0.611637i	$0.209489\pi$
$173$			16.0897i			1.22327i	−0.791138	+	0.611637i	$0.790511\pi$
$174$	19.6240	−	0.113689i	1.48769	−	0.00861874i
$175$		−	10.1407i		−	0.766568i
$176$	−10.7187	+	4.73657i	−0.807949	+	0.357032i
$177$	−1.19419	+	12.1178i	−0.0897609	+	0.910832i
$178$	−1.20069	−	11.5007i	−0.0899953	−	0.862014i
$179$	11.2966			0.844347			0.422174	−	0.906515i	$-0.361267\pi$
$179$	11.2966			0.844347			0.422174	+	0.906515i	$0.361267\pi$
$180$	−0.192275	−	16.5939i	−0.0143313	−	1.23683i
$181$	20.3968			1.51608			0.758041	−	0.652207i	$-0.226157\pi$
$181$	20.3968			1.51608			0.758041	+	0.652207i	$0.226157\pi$
$182$	2.64135	+	25.2999i	0.195790	+	1.87536i
$183$	−1.04503	+	10.6043i	−0.0772511	+	0.783891i
$184$	−2.69181	+	0.868418i	−0.198443	+	0.0640206i
$185$			30.2968i			2.22746i
$186$	−2.82473	+	0.0163647i	−0.207119	+	0.00119992i
$187$		−	11.9066i		−	0.870695i
$188$	22.6380	−	4.77896i	1.65105	−	0.348542i
$189$	−19.0281	−	5.77563i	−1.38409	−	0.420115i
$190$	14.6255	−	1.52692i	1.06105	−	0.110775i
$191$	−5.18504			−0.375176			−0.187588	−	0.982248i	$-0.560067\pi$
$191$	−5.18504			−0.375176			−0.187588	+	0.982248i	$0.560067\pi$
$192$	−6.95598	−	11.9839i	−0.502005	−	0.864865i
$193$	7.73602			0.556851			0.278425	−	0.960458i	$-0.410187\pi$
$193$	7.73602			0.556851			0.278425	+	0.960458i	$0.410187\pi$
$194$	6.02141	−	0.628642i	0.432312	−	0.0451339i
$195$	−22.4076	−	2.20823i	−1.60464	−	0.158134i
$196$	−14.9612	+	3.15836i	−1.06866	+	0.225597i
$197$			7.64420i			0.544627i	0.962209	+	0.272313i	$0.0877888\pi$
$197$			7.64420i			0.544627i	−0.962209	+	0.272313i	$0.912211\pi$
$198$	−12.3763	−	1.14731i	−0.879548	−	0.0815359i
$199$			13.9093i			0.986005i	0.870028	+	0.493002i	$0.164101\pi$
$199$			13.9093i			0.986005i	−0.870028	+	0.493002i	$0.835899\pi$
$200$	7.13284	−	2.30116i	0.504368	−	0.162717i
$201$	−2.84785	−	0.280650i	−0.200872	−	0.0197955i
$202$	0.0230644	+	0.220921i	0.00162281	+	0.0155439i
$203$	30.6600			2.15191
$204$	13.9939	−	1.54299i	0.979770	−	0.108031i
$205$	4.26767			0.298067
$206$	−0.123000	−	1.17815i	−0.00856982	−	0.0820855i
$207$	−2.94229	−	0.585602i	−0.204503	−	0.0407022i
$208$	−17.1962	+	7.59900i	−1.19234	+	0.526896i
$209$		−	11.0138i		−	0.761843i
$210$	−0.150202	−	25.9266i	−0.0103649	−	1.78911i
$211$		−	11.7202i		−	0.806851i	−0.915012	−	0.403426i	$-0.867819\pi$
$211$		−	11.7202i		−	0.806851i	0.915012	−	0.403426i	$-0.132181\pi$
$212$	2.60423	+	12.3363i	0.178859	+	0.847260i
$213$	2.15708	−	21.8885i	0.147800	−	1.49978i
$214$	−7.41475	+	0.774109i	−0.506862	+	0.0529170i
$215$	−6.15278			−0.419616
$216$	−0.255418	−	14.6947i	−0.0173790	−	0.999849i
$217$	−4.41327			−0.299592
$218$	4.97352	−	0.519242i	0.336850	−	0.0351675i
$219$	−0.965090	+	9.79307i	−0.0652147	+	0.661754i
$220$	−3.34732	−	15.8563i	−0.225676	−	1.06903i
$221$		−	19.1020i		−	1.28494i
$222$	0.155442	+	26.8311i	0.0104326	+	1.80079i
$223$		−	0.154946i		−	0.0103759i	−0.999987	−	0.00518796i	$-0.998349\pi$
$223$		−	0.154946i		−	0.0103759i	0.999987	−	0.00518796i	$-0.00165139\pi$
$224$	−10.7590	−	18.7856i	−0.718864	−	1.25517i
$225$	7.79656	+	1.55175i	0.519771	+	0.103450i
$226$	−0.157838	−	1.51184i	−0.0104992	−	0.100566i
$227$	−4.63743			−0.307797			−0.153898	−	0.988087i	$-0.549183\pi$
$227$	−4.63743			−0.307797			−0.153898	+	0.988087i	$0.549183\pi$
$228$	12.9447	−	1.42730i	0.857282	−	0.0945249i
$229$	−2.69850			−0.178322			−0.0891610	−	0.996017i	$-0.528419\pi$
$229$	−2.69850			−0.178322			−0.0891610	+	0.996017i	$0.528419\pi$
$230$	−0.406156	−	3.89033i	−0.0267811	−	0.256521i
$231$	−19.3254	−	1.90448i	−1.27152	−	0.125306i
$232$	6.95743	+	21.5658i	0.456778	+	1.41586i
$233$		−	2.77392i		−	0.181726i	−0.995863	−	0.0908628i	$-0.971038\pi$
$233$		−	2.77392i		−	0.181726i	0.995863	−	0.0908628i	$-0.0289625\pi$
$234$	−19.8557	−	1.84066i	−1.29801	−	0.120328i
$235$			31.9965i			2.08722i
$236$	−13.7571	+	2.90416i	−0.895508	+	0.189045i
$237$	−5.28030	−	0.520364i	−0.342992	−	0.0338013i
$238$	21.8769	−	2.28397i	1.41807	−	0.148048i
$239$	22.0216			1.42446			0.712229	−	0.701947i	$-0.247686\pi$
$239$	22.0216			1.42446			0.712229	+	0.701947i	$0.247686\pi$
$240$	18.2023	−	5.98898i	1.17495	−	0.386587i
$241$	19.5900			1.26190			0.630951	−	0.775823i	$-0.282665\pi$
$241$	19.5900			1.26190			0.630951	+	0.775823i	$0.282665\pi$
$242$	3.39997	−	0.354961i	0.218559	−	0.0228178i
$243$	7.35222	−	13.7457i	0.471645	−	0.881789i
$244$	−12.0388	+	2.54142i	−0.770702	+	0.162698i
$245$		−	21.1461i		−	1.35098i
$246$	3.77949	−	0.0218959i	0.240972	−	0.00139603i
$247$		−	17.6698i		−	1.12430i
$248$	−1.00147	−	3.10423i	−0.0635934	−	0.197119i
$249$	−0.490395	+	4.97620i	−0.0310775	+	0.315354i
$250$	−0.954535	−	9.14295i	−0.0603701	−	0.578251i
$251$	−23.2116			−1.46510			−0.732550	−	0.680713i	$-0.761670\pi$
$251$	−23.2116			−1.46510			−0.732550	+	0.680713i	$0.761670\pi$
$252$	−0.266041	−	22.9601i	−0.0167590	−	1.44635i
$253$	−2.92964			−0.184185
$254$	−2.52236	−	24.1602i	−0.158267	−	1.51595i
$255$	−1.90945	+	19.3758i	−0.119575	+	1.21336i
$256$	10.7721	−	11.8306i	0.673255	−	0.739411i
$257$		−	12.7553i		−	0.795654i	−0.917461	−	0.397827i	$-0.869764\pi$
$257$		−	12.7553i		−	0.795654i	0.917461	−	0.397827i	$-0.130236\pi$
$258$	−5.44896	+	0.0315678i	−0.339237	+	0.00196532i
$259$			41.9201i			2.60479i
$260$	−5.37020	−	25.4387i	−0.333045	−	1.57764i
$261$	−4.69162	+	23.5725i	−0.290404	+	1.45910i
$262$	−2.41660	+	0.252296i	−0.149298	+	0.0155869i
$263$	−22.4169			−1.38229			−0.691143	−	0.722718i	$-0.742892\pi$
$263$	−22.4169			−1.38229			−0.691143	+	0.722718i	$0.742892\pi$
$264$	−3.04578	−	14.0253i	−0.187455	−	0.863200i
$265$	−17.4360			−1.07109
$266$	20.2366	−	2.11272i	1.24078	−	0.129539i
$267$	14.0937	+	1.38891i	0.862521	+	0.0850000i
$268$	−0.682515	−	3.23308i	−0.0416912	−	0.197492i
$269$		−	20.4277i		−	1.24550i	−0.782422	−	0.622748i	$-0.786016\pi$
$269$		−	20.4277i		−	1.24550i	0.782422	−	0.622748i	$-0.213984\pi$
$270$	19.9563	+	3.85184i	1.21450	+	0.234415i
$271$			31.6158i			1.92053i	0.279097	+	0.960263i	$0.409965\pi$
$271$			31.6158i			1.92053i	−0.279097	+	0.960263i	$0.590035\pi$
$272$	6.57086	+	14.8696i	0.398417	+	0.901601i
$273$	−31.0042	−	3.05541i	−1.87646	−	0.184922i
$274$	−2.87540	−	27.5418i	−0.173709	−	1.66386i
$275$	7.76304			0.468129
$276$	−0.379655	−	3.44323i	−0.0228526	−	0.207258i
$277$	−0.881881			−0.0529871			−0.0264936	−	0.999649i	$-0.508434\pi$
$277$	−0.881881			−0.0529871			−0.0264936	+	0.999649i	$0.508434\pi$
$278$	0.559289	+	5.35712i	0.0335440	+	0.321299i
$279$	0.675323	−	3.39308i	0.0404305	−	0.203139i
$280$	28.4920	−	9.19193i	1.70272	−	0.549323i
$281$		−	10.2646i		−	0.612336i	−0.951978	−	0.306168i	$-0.900953\pi$
$281$		−	10.2646i		−	0.612336i	0.951978	−	0.306168i	$-0.0990469\pi$
$282$	0.164163	+	28.3364i	0.00977575	+	1.68741i
$283$			1.17276i			0.0697136i	0.999392	+	0.0348568i	$0.0110975\pi$
$283$			1.17276i			0.0697136i	−0.999392	+	0.0348568i	$0.988902\pi$
$284$	24.8495	−	5.24581i	1.47454	−	0.311281i
$285$	−1.76629	+	17.9231i	−0.104626	+	1.06167i
$286$	−19.3679	+	2.02203i	−1.14525	+	0.119565i
$287$	5.90496			0.348559
$288$	16.0894	−	5.39729i	0.948078	−	0.318038i
$289$	0.482465			0.0283803
$290$	−31.1679	+	3.25396i	−1.83024	+	0.191079i
$291$	−0.727190	+	7.37902i	−0.0426286	+	0.432566i
$292$	−11.1178	+	2.34701i	−0.650620	+	0.137348i
$293$			11.9709i			0.699349i	0.936871	+	0.349674i	$0.113708\pi$
$293$			11.9709i			0.699349i	−0.936871	+	0.349674i	$0.886292\pi$
$294$	−0.108493	−	18.7272i	−0.00632746	−	1.09219i
$295$		−	19.4441i		−	1.13208i
$296$	−29.4859	+	9.51260i	−1.71384	+	0.552909i
$297$	4.42142	−	14.5666i	0.256557	−	0.845241i
$298$	2.72913	+	26.1408i	0.158094	+	1.51429i
$299$	−4.70010			−0.271814
$300$	1.00602	+	9.12398i	0.0580827	+	0.526773i
$301$	−8.51328			−0.490698
$302$	−0.527143	−	5.04920i	−0.0303336	−	0.290549i
$303$	−0.270731	−	0.0266801i	−0.0155531	−	0.00153273i
$304$	6.07819	+	13.7547i	0.348608	+	0.788885i
$305$		−	17.0155i		−	0.974306i
$306$	−1.59162	+	17.1692i	−0.0909869	+	0.981499i
$307$		−	13.5918i		−	0.775723i	−0.921718	−	0.387861i	$-0.873214\pi$
$307$		−	13.5918i		−	0.775723i	0.921718	−	0.387861i	$-0.126786\pi$
$308$	−4.63152	−	21.9396i	−0.263905	−	1.25012i
$309$	1.44378	+	0.142282i	0.0821337	+	0.00809414i
$310$	4.48638	−	0.468383i	0.254809	−	0.0266024i
$311$	13.5020			0.765626			0.382813	−	0.923826i	$-0.374955\pi$
$311$	13.5020			0.765626			0.382813	+	0.923826i	$0.374955\pi$
$312$	−4.88642	−	22.5012i	−0.276639	−	1.27388i
$313$	−16.2458			−0.918269			−0.459134	−	0.888367i	$-0.651840\pi$
$313$	−16.2458			−0.918269			−0.459134	+	0.888367i	$0.651840\pi$
$314$	5.13202	−	0.535789i	0.289616	−	0.0302363i
$315$	31.1432	+	6.19841i	1.75472	+	0.349241i
$316$	−1.26548	−	5.99458i	−0.0711886	−	0.337221i
$317$			19.5722i			1.09928i	0.835401	+	0.549641i	$0.185235\pi$
$317$			19.5722i			1.09928i	−0.835401	+	0.549641i	$0.814765\pi$
$318$	−15.4415	+	0.0894583i	−0.865918	+	0.00501657i
$319$			23.4711i			1.31413i
$320$	12.9309	+	17.9550i	0.722860	+	1.00371i
$321$	0.895461	−	9.08652i	0.0499797	−	0.507160i
$322$	−0.561977	−	5.38286i	−0.0313177	−	0.299975i
$323$	−15.2791			−0.850150
$324$	17.6933	+	3.30884i	0.982959	+	0.183824i
$325$	12.4545			0.690849
$326$	2.83799	+	27.1835i	0.157182	+	1.50556i
$327$	−0.600640	+	6.09488i	−0.0332155	+	0.337048i
$328$	1.33997	+	4.15346i	0.0739873	+	0.229336i
$329$			44.2719i			2.44079i
$330$	19.8476	−	0.114984i	1.09258	−	0.00632968i
$331$		−	3.40087i		−	0.186928i	−0.995623	−	0.0934642i	$-0.970206\pi$
$331$		−	3.40087i		−	0.186928i	0.995623	−	0.0934642i	$-0.0297941\pi$
$332$	−5.64934	+	1.19260i	−0.310048	+	0.0654522i
$333$	−32.2297	−	6.41465i	−1.76617	−	0.351521i
$334$	−9.54233	+	0.996231i	−0.522133	+	0.0545113i
$335$	4.56963			0.249665
$336$	25.1856	−	8.28664i	1.37399	−	0.452074i
$337$	−21.2328			−1.15662			−0.578312	−	0.815815i	$-0.696288\pi$
$337$	−21.2328			−1.15662			−0.578312	+	0.815815i	$0.696288\pi$
$338$	−12.7870	+	1.33498i	−0.695521	+	0.0726133i
$339$	1.85270	+	0.182581i	0.100625	+	0.00991642i
$340$	−21.9969	+	4.64361i	−1.19295	+	0.251835i
$341$		−	3.37849i		−	0.182956i
$342$	−1.47228	+	15.8819i	−0.0796120	+	0.858795i
$343$		−	2.47021i		−	0.133379i
$344$	−1.93185	−	5.98811i	−0.104159	−	0.322857i
$345$	4.76747	+	0.469826i	0.256672	+	0.0252946i
$346$	−2.36273	−	22.6312i	−0.127021	−	1.21666i
$347$	0.708313			0.0380242			0.0190121	−	0.999819i	$-0.493948\pi$
$347$	0.708313			0.0380242			0.0190121	+	0.999819i	$0.493948\pi$
$348$	−27.5859	+	3.04165i	−1.47876	+	0.163050i
$349$	33.9476			1.81717			0.908585	−	0.417699i	$-0.137163\pi$
$349$	33.9476			1.81717			0.908585	+	0.417699i	$0.137163\pi$
$350$	1.48914	+	14.2636i	0.0795980	+	0.762424i
$351$	7.09340	−	23.3696i	0.378618	−	1.24738i
$352$	14.3810	−	8.23632i	0.766508	−	0.438997i
$353$		−	25.5647i		−	1.36067i	−0.732901	−	0.680336i	$-0.761834\pi$
$353$		−	25.5647i		−	1.36067i	0.732901	−	0.680336i	$-0.238166\pi$
$354$	−0.0997611	−	17.2199i	−0.00530225	−	0.915229i
$355$			35.1221i			1.86409i
$356$	3.37770	+	16.0002i	0.179018	+	0.848010i
$357$	−2.64201	+	26.8094i	−0.139830	+	1.41890i
$358$	−15.8894	+	1.65888i	−0.839783	+	0.0876743i
$359$	18.0586			0.953098			0.476549	−	0.879148i	$-0.341887\pi$
$359$	18.0586			0.953098			0.476549	+	0.879148i	$0.341887\pi$
$360$	2.70722	+	23.3122i	0.142683	+	1.22866i
$361$	4.86653			0.256133
$362$	−28.6895	+	2.99522i	−1.50789	+	0.157425i
$363$	−0.410606	+	4.16655i	−0.0215512	+	0.218687i
$364$	−7.43047	−	35.1982i	−0.389462	−	1.84489i
$365$		−	15.7139i		−	0.822501i
$366$	−0.0873007	−	15.0691i	−0.00456328	−	0.787675i
$367$		−	3.67268i		−	0.191712i	−0.995395	−	0.0958561i	$-0.969441\pi$
$367$		−	3.67268i		−	0.191712i	0.995395	−	0.0958561i	$-0.0305589\pi$
$368$	3.65869	−	1.61678i	0.190723	−	0.0842803i
$369$	−0.903582	+	4.53994i	−0.0470386	+	0.236340i
$370$	−4.44900	−	42.6145i	−0.231293	−	2.21542i
$371$	−24.1254			−1.25253
$372$	3.97078	−	0.437823i	0.205875	−	0.0227001i
$373$	33.8717			1.75381			0.876904	−	0.480666i	$-0.159605\pi$
$373$	33.8717			1.75381			0.876904	+	0.480666i	$0.159605\pi$
$374$	1.74845	+	16.7474i	0.0904102	+	0.865988i
$375$	11.2044	+	1.10417i	0.578591	+	0.0570191i
$376$	−31.1402	+	10.0463i	−1.60593	+	0.518097i
$377$			37.6554i			1.93935i
$378$	27.6125	+	5.32959i	1.42023	+	0.274124i
$379$		−	12.4131i		−	0.637618i	−0.947819	−	0.318809i	$-0.896717\pi$
$379$		−	12.4131i		−	0.637618i	0.947819	−	0.318809i	$-0.103283\pi$
$380$	−20.3476	+	4.29544i	−1.04381	+	0.220351i
$381$	29.6075	+	2.91777i	1.51684	+	0.149482i
$382$	7.29311	−	0.761410i	0.373148	−	0.0389571i
$383$	−11.2227			−0.573453			−0.286727	−	0.958012i	$-0.592567\pi$
$383$	−11.2227			−0.573453			−0.286727	+	0.958012i	$0.592567\pi$
$384$	11.5439	+	15.8347i	0.589096	+	0.808063i
$385$	31.0093			1.58038
$386$	−10.8812	+	1.13602i	−0.553841	+	0.0578216i
$387$	1.30271	−	6.54532i	0.0662205	−	0.332717i
$388$	−8.37721	+	1.76846i	−0.425288	+	0.0897798i
$389$		−	27.6485i		−	1.40183i	−0.713242	−	0.700917i	$-0.752774\pi$
$389$		−	27.6485i		−	1.40183i	0.713242	−	0.700917i	$-0.247226\pi$
$390$	31.8421	−	0.184472i	1.61239	−	0.00934112i
$391$			4.06418i			0.205534i
$392$	20.5802	−	6.63947i	1.03946	−	0.335344i
$393$	0.291846	−	2.96146i	0.0147217	−	0.149386i
$394$	−1.12253	−	10.7521i	−0.0565523	−	0.541683i
$395$	8.47271			0.426308
$396$	17.5767	−	0.203662i	0.883260	−	0.0102344i
$397$	6.01909			0.302089			0.151045	−	0.988527i	$-0.451736\pi$
$397$	6.01909			0.302089			0.151045	+	0.988527i	$0.451736\pi$
$398$	−2.04255	−	19.5644i	−0.102384	−	0.980675i
$399$	−2.44392	+	24.7992i	−0.122349	+	1.24151i
$400$	−9.69491	+	4.28418i	−0.484746	+	0.214209i
$401$			30.9437i			1.54525i	0.634860	+	0.772627i	$0.281058\pi$
$401$			30.9437i			1.54525i	−0.634860	+	0.772627i	$0.718942\pi$
$402$	4.04691	−	0.0234452i	0.201841	−	0.00116934i
$403$		−	5.42021i		−	0.270000i
$404$	−0.0648834	−	0.307354i	−0.00322807	−	0.0152914i
$405$	−9.53112	+	22.9955i	−0.473605	+	1.14266i
$406$	−43.1254	+	4.50234i	−2.14028	+	0.223447i
$407$	−32.0911			−1.59070
$408$	−19.4568	+	4.22529i	−0.963256	+	0.209183i
$409$	12.6880			0.627382			0.313691	−	0.949525i	$-0.398434\pi$
$409$	12.6880			0.627382			0.313691	+	0.949525i	$0.398434\pi$
$410$	−6.00277	+	0.626697i	−0.296456	+	0.0309503i
$411$	33.7515	+	3.32616i	1.66484	+	0.164067i
$412$	0.346016	+	1.63908i	0.0170470	+	0.0807519i
$413$		−	26.9039i		−	1.32385i
$414$	4.22453	+	0.391622i	0.207624	+	0.0192472i
$415$		−	7.98475i		−	0.391956i
$416$	23.0718	−	13.2137i	1.13119	−	0.647857i
$417$	−6.56496	−	0.646965i	−0.321487	−	0.0316820i
$418$	1.61735	+	15.4917i	0.0791074	+	0.757725i
$419$	−25.9784			−1.26913			−0.634565	−	0.772870i	$-0.718821\pi$
$419$	−25.9784			−1.26913			−0.634565	+	0.772870i	$0.718821\pi$
$420$	4.01853	+	36.4455i	0.196084	+	1.77836i
$421$	−32.0298			−1.56104			−0.780519	−	0.625131i	$-0.785045\pi$
$421$	−32.0298			−1.56104			−0.780519	+	0.625131i	$0.785045\pi$
$422$	1.72108	+	16.4853i	0.0837809	+	0.802490i
$423$	−34.0378	−	6.77453i	−1.65497	−	0.329389i
$424$	−5.47458	−	16.9694i	−0.265869	−	0.824107i
$425$		−	10.7694i		−	0.522391i
$426$	0.180199	+	31.1045i	0.00873069	+	1.50702i
$427$		−	23.5435i		−	1.13935i
$428$	10.3157	−	2.17768i	0.498627	−	0.105262i
$429$	2.33901	−	23.7347i	0.112928	−	1.14592i
$430$	8.65430	−	0.903520i	0.417348	−	0.0435716i
$431$	4.13323			0.199091			0.0995453	−	0.995033i	$-0.468261\pi$
$431$	4.13323			0.199091			0.0995453	+	0.995033i	$0.468261\pi$
$432$	2.51715	+	20.6316i	0.121106	+	0.992640i
$433$	35.0851			1.68608			0.843041	−	0.537850i	$-0.180763\pi$
$433$	35.0851			1.68608			0.843041	+	0.537850i	$0.180763\pi$
$434$	6.20757	−	0.648078i	0.297973	−	0.0311087i
$435$	3.76406	−	38.1951i	0.180473	−	1.83132i
$436$	−6.91935	+	1.46070i	−0.331377	+	0.0699548i
$437$			3.75945i			0.179839i
$438$	−0.0806223	−	13.9163i	−0.00385228	−	0.664949i
$439$		−	23.3061i		−	1.11234i	−0.831069	−	0.556170i	$-0.812270\pi$
$439$		−	23.3061i		−	1.11234i	0.831069	−	0.556170i	$-0.187730\pi$
$440$	7.03670	+	21.8115i	0.335462	+	1.03982i
$441$	22.4952	+	4.47721i	1.07120	+	0.213200i
$442$	2.80508	+	26.8683i	0.133424	+	1.27800i
$443$	4.29971			0.204286			0.102143	−	0.994770i	$-0.467430\pi$
$443$	4.29971			0.204286			0.102143	+	0.994770i	$0.467430\pi$
$444$	−4.15872	−	37.7170i	−0.197364	−	1.78997i
$445$	−22.6146			−1.07204
$446$	0.0227534	+	0.217942i	0.00107740	+	0.0103198i
$447$	−32.0346	−	3.15695i	−1.51519	−	0.149319i
$448$	17.8919	+	24.8434i	0.845311	+	1.17374i
$449$			14.5626i			0.687252i	0.939107	+	0.343626i	$0.111655\pi$
$449$			14.5626i			0.687252i	−0.939107	+	0.343626i	$0.888345\pi$
$450$	−11.1943	−	1.03773i	−0.527703	−	0.0489191i
$451$			4.52042i			0.212858i
$452$	0.444019	+	2.10332i	0.0208849	+	0.0989321i
$453$	6.18762	+	0.609779i	0.290720	+	0.0286499i
$454$	6.52286	−	0.680994i	0.306133	−	0.0319606i
$455$	49.7490			2.33227
$456$	−17.9980	+	3.90848i	−0.842832	+	0.183031i
$457$	−12.4801			−0.583793			−0.291897	−	0.956450i	$-0.594286\pi$
$457$	−12.4801			−0.583793			−0.291897	+	0.956450i	$0.594286\pi$
$458$	3.79563	−	0.396268i	0.177358	−	0.0185164i
$459$	−20.2077	−	6.13367i	−0.943215	−	0.286295i
$460$	1.14257	+	5.41238i	0.0532727	+	0.252353i
$461$			27.9790i			1.30311i	0.758600	+	0.651557i	$0.225884\pi$
$461$			27.9790i			1.30311i	−0.758600	+	0.651557i	$0.774116\pi$
$462$	27.4621	−	0.159098i	1.27765	−	0.00740190i
$463$		−	41.9201i		−	1.94819i	−0.226138	−	0.974095i	$-0.572610\pi$
$463$		−	41.9201i		−	1.94819i	0.226138	−	0.974095i	$-0.427390\pi$
$464$	−12.9530	−	29.3120i	−0.601327	−	1.36078i
$465$	−0.541808	+	5.49790i	−0.0251258	+	0.254959i
$466$	0.407343	+	3.90171i	0.0188698	+	0.180743i
$467$	−6.56355			−0.303725			−0.151862	−	0.988402i	$-0.548527\pi$
$467$	−6.56355			−0.303725			−0.151862	+	0.988402i	$0.548527\pi$
$468$	28.1987	−	0.326741i	1.30349	−	0.0151036i
$469$	6.32276			0.291958
$470$	−4.69860	−	45.0052i	−0.216730	−	2.07594i
$471$	−0.619780	+	6.28911i	−0.0285580	+	0.289787i
$472$	18.9238	−	6.10509i	0.871037	−	0.281009i
$473$		−	6.51718i		−	0.299660i
$474$	7.50351	−	0.0434705i	0.344648	−	0.00199667i
$475$		−	9.96190i		−	0.457083i
$476$	−30.4359	+	6.42513i	−1.39503	+	0.294495i
$477$	3.69169	−	18.5484i	0.169031	−	0.849275i
$478$	−30.9749	+	3.23381i	−1.41676	+	0.147911i
$479$	−25.7395			−1.17607			−0.588034	−	0.808836i	$-0.700098\pi$
$479$	−25.7395			−1.17607			−0.588034	+	0.808836i	$0.700098\pi$
$480$	−24.7233	+	11.0969i	−1.12846	+	0.506501i
$481$	−51.4846			−2.34750
$482$	−27.5547	+	2.87674i	−1.25508	+	0.131032i
$483$	6.59650	+	0.650074i	0.300151	+	0.0295794i
$484$	−4.73017	+	0.998555i	−0.215008	+	0.0453889i
$485$		−	11.8403i		−	0.537641i
$486$	−8.32287	+	20.4140i	−0.377533	+	0.925996i
$487$			27.5408i			1.24799i	0.781427	+	0.623996i	$0.214492\pi$
$487$			27.5408i			1.24799i	−0.781427	+	0.623996i	$0.785508\pi$
$488$	16.5601	−	5.34255i	0.749642	−	0.241846i
$489$	−33.3125	−	3.28289i	−1.50644	−	0.148457i
$490$	3.10525	+	29.7435i	0.140281	+	1.34367i
$491$	−31.6626			−1.42891			−0.714456	−	0.699680i	$-0.753326\pi$
$491$	−31.6626			−1.42891			−0.714456	+	0.699680i	$0.753326\pi$
$492$	−5.31290	+	0.585807i	−0.239524	+	0.0264102i
$493$	32.5606			1.46646
$494$	2.59476	+	24.8538i	0.116744	+	1.11822i
$495$	−4.74507	+	23.8411i	−0.213275	+	1.07158i
$496$	1.86448	+	4.21925i	0.0837178	+	0.189450i
$497$			48.5967i			2.17986i
$498$	−0.0409670	−	7.07138i	−0.00183577	−	0.316876i
$499$			23.9814i			1.07356i	0.843723	+	0.536778i	$0.180359\pi$
$499$			23.9814i			1.07356i	−0.843723	+	0.536778i	$0.819641\pi$
$500$	2.68524	+	12.7200i	0.120088	+	0.568856i
$501$	1.15240	−	11.6938i	0.0514856	−	0.522440i
$502$	32.6487	−	3.40856i	1.45718	−	0.152131i
$503$	−4.85746			−0.216583			−0.108292	−	0.994119i	$-0.534538\pi$
$503$	−4.85746			−0.216583			−0.108292	+	0.994119i	$0.534538\pi$
$504$	3.74584	+	32.2559i	0.166853	+	1.43679i
$505$	0.434412			0.0193311
$506$	4.12074	−	0.430210i	0.183189	−	0.0191252i
$507$	1.54425	−	15.6700i	0.0685827	−	0.695930i
$508$	7.09574	+	33.6126i	0.314822	+	1.49132i
$509$			1.85806i			0.0823571i	0.999152	+	0.0411785i	$0.0131112\pi$
$509$			1.85806i			0.0823571i	−0.999152	+	0.0411785i	$0.986889\pi$
$510$	−0.159513	−	27.5338i	−0.00706337	−	1.21922i
$511$		−	21.7425i		−	0.961830i
$512$	−13.4144	+	18.2224i	−0.592837	+	0.805322i
$513$	−18.6926	−	5.67377i	−0.825297	−	0.250503i
$514$	1.87308	+	17.9412i	0.0826182	+	0.791353i
$515$	−2.31667			−0.102085
$516$	7.65970	−	0.844568i	0.337200	−	0.0371800i
$517$	−33.8915			−1.49054
$518$	−6.15586	−	58.9635i	−0.270473	−	2.59071i
$519$	27.7338	+	2.73312i	1.21738	+	0.119970i
$520$	11.2892	+	34.9927i	0.495062	+	1.53453i
$521$			13.6172i			0.596579i	0.954475	+	0.298290i	$0.0964161\pi$
$521$			13.6172i			0.596579i	−0.954475	+	0.298290i	$0.903584\pi$
$522$	3.13753	−	33.8453i	0.137326	−	1.48137i
$523$		−	6.26762i		−	0.274064i	−0.990567	−	0.137032i	$-0.956244\pi$
$523$		−	6.26762i		−	0.274064i	0.990567	−	0.137032i	$-0.0437563\pi$
$524$	3.36206	−	0.709743i	0.146872	−	0.0310053i
$525$	−17.4796	−	1.72258i	−0.762872	−	0.0751797i
$526$	31.5309	−	3.29187i	1.37481	−	0.143532i
$527$	−4.68685			−0.204163
$528$	6.34368	+	19.2803i	0.276073	+	0.839069i
$529$	1.00000			0.0434783
$530$	24.5250	−	2.56044i	1.06530	−	0.111218i
$531$	20.6847	+	4.11686i	0.897638	+	0.178656i
$532$	−28.1539	+	5.94338i	−1.22063	+	0.257678i
$533$			7.25224i			0.314129i
$534$	−20.0277	+	0.116028i	−0.866685	+	0.00502101i
$535$			14.5801i			0.630354i
$536$	1.43477	+	4.44733i	0.0619728	+	0.192095i
$537$	1.91893	−	19.4720i	0.0828078	−	0.840277i
$538$	2.99975	+	28.7329i	0.129328	+	1.23876i
$539$	22.3985			0.964772
$540$	−28.6355	−	2.48734i	−1.23228	−	0.107038i
$541$	23.0200			0.989707			0.494853	−	0.868977i	$-0.335222\pi$
$541$	23.0200			0.989707			0.494853	+	0.868977i	$0.335222\pi$
$542$	−4.64271	−	44.4699i	−0.199421	−	1.91014i
$543$	3.46476	−	35.1580i	0.148687	−	1.50877i
$544$	−11.4259	−	19.9502i	−0.489883	−	0.855356i
$545$		−	9.77978i		−	0.418920i
$546$	44.0582	−	0.255245i	1.88552	−	0.0109235i
$547$		−	18.5034i		−	0.791149i	−0.918434	−	0.395574i	$-0.870546\pi$
$547$		−	18.5034i		−	0.791149i	0.918434	−	0.395574i	$-0.129454\pi$
$548$	8.08890	+	38.3172i	0.345540	+	1.63683i
$549$	18.1011	+	3.60265i	0.772536	+	0.153757i
$550$	−10.9193	+	1.13998i	−0.465599	+	0.0486091i
$551$	30.1193			1.28312
$552$	1.03964	+	4.78739i	0.0442501	+	0.203765i
$553$	11.7233			0.498523
$554$	1.24043	−	0.129502i	0.0527007	−	0.00550201i
$555$	52.2226	+	5.14644i	2.21672	+	0.218454i
$556$	−1.57336	−	7.45302i	−0.0667252	−	0.316079i
$557$		−	24.4347i		−	1.03533i	−0.855583	−	0.517665i	$-0.826801\pi$
$557$		−	24.4347i		−	1.03533i	0.855583	−	0.517665i	$-0.173199\pi$
$558$	−0.451623	+	4.87177i	−0.0191187	+	0.206239i
$559$		−	10.4557i		−	0.442228i
$560$	−38.7261	+	17.1131i	−1.63648	+	0.723158i
$561$	−20.5234	−	2.02254i	−0.866498	−	0.0853918i
$562$	1.50733	+	14.4379i	0.0635830	+	0.609026i
$563$	24.8835			1.04872			0.524358	−	0.851498i	$-0.324305\pi$
$563$	24.8835			1.04872			0.524358	+	0.851498i	$0.324305\pi$
$564$	−4.39203	−	39.8330i	−0.184938	−	1.67727i
$565$	−2.97283			−0.125068
$566$	−0.172217	−	1.64957i	−0.00723884	−	0.0693368i
$567$	−13.1877	+	31.8177i	−0.553832	+	1.33622i
$568$	−34.1822	+	11.0277i	−1.43425	+	0.462711i
$569$		−	15.8518i		−	0.664541i	−0.943184	−	0.332270i	$-0.892185\pi$
$569$		−	15.8518i		−	0.664541i	0.943184	−	0.332270i	$-0.107815\pi$
$570$	−0.147553	−	25.4694i	−0.00618032	−	1.06680i
$571$			26.5847i			1.11254i	0.831003	+	0.556268i	$0.187767\pi$
$571$			26.5847i			1.11254i	−0.831003	+	0.556268i	$0.812233\pi$
$572$	26.9453	−	5.68825i	1.12664	−	0.237838i
$573$	−0.880770	+	8.93745i	−0.0367947	+	0.373367i
$574$	−8.30573	+	0.867128i	−0.346674	+	0.0361932i
$575$	−2.64983			−0.110505
$576$	−21.8383	+	9.95435i	−0.909929	+	0.414765i
$577$	−20.5093			−0.853814			−0.426907	−	0.904295i	$-0.640397\pi$
$577$	−20.5093			−0.853814			−0.426907	+	0.904295i	$0.640397\pi$
$578$	−0.678620	+	0.0708487i	−0.0282269	+	0.00294692i
$579$	1.31410	−	13.3346i	0.0546121	−	0.554166i
$580$	43.3619	−	9.15384i	1.80051	−	0.380093i
$581$		−	11.0481i		−	0.458352i
$582$	−0.0607485	−	10.4859i	−0.00251811	−	0.434654i
$583$		−	18.4687i		−	0.764895i
$584$	15.2933	−	4.93385i	0.632842	−	0.204164i
$585$	−7.61264	+	38.2488i	−0.314744	+	1.58139i
$586$	−1.75790	−	16.8379i	−0.0726182	−	0.695568i
$587$	6.83308			0.282031			0.141016	−	0.990007i	$-0.454963\pi$
$587$	6.83308			0.282031			0.141016	+	0.990007i	$0.454963\pi$
$588$	2.90265	+	26.3252i	0.119703	+	1.08563i
$589$	−4.33544			−0.178639
$590$	2.85532	+	27.3495i	0.117552	+	1.12596i
$591$	13.1763	+	1.29850i	0.542001	+	0.0534133i
$592$	40.0771	−	17.7101i	1.64716	−	0.727879i
$593$		−	33.6825i		−	1.38317i	−0.722293	−	0.691587i	$-0.756912\pi$
$593$		−	33.6825i		−	1.38317i	0.722293	−	0.691587i	$-0.243088\pi$
$594$	−4.07996	+	21.1382i	−0.167403	+	0.867312i
$595$		−	43.0180i		−	1.76357i
$596$	−7.67742	−	36.3680i	−0.314479	−	1.48969i
$597$	23.9755	+	2.36274i	0.981252	+	0.0967006i
$598$	6.61101	−	0.690197i	0.270344	−	0.0282243i
$599$	22.2688			0.909878			0.454939	−	0.890523i	$-0.349661\pi$
$599$	22.2688			0.909878			0.454939	+	0.890523i	$0.349661\pi$
$600$	−2.75487	−	12.6858i	−0.112467	−	0.517895i
$601$	45.1209			1.84052			0.920259	−	0.391310i	$-0.127978\pi$
$601$	45.1209			1.84052			0.920259	+	0.391310i	$0.127978\pi$
$602$	11.9745	−	1.25015i	0.488045	−	0.0509525i
$603$	−0.967514	+	4.86116i	−0.0394002	+	0.197962i
$604$	1.48292	+	7.02464i	0.0603393	+	0.285828i
$605$		−	6.68560i		−	0.271808i
$606$	0.384720	−	0.00222882i	0.0156282	−	9.05395e-5i
$607$			0.224796i			0.00912420i	0.999990	+	0.00456210i	$0.00145217\pi$
$607$			0.224796i			0.00912420i	−0.999990	+	0.00456210i	$0.998548\pi$
$608$	−10.5692	−	18.4543i	−0.428639	−	0.748422i
$609$	5.20814	−	52.8486i	0.211045	−	2.14154i
$610$	2.49869	+	23.9335i	0.101169	+	0.969039i
$611$	−54.3730			−2.19969
$612$	−0.282533	−	24.3834i	−0.0114207	−	0.985642i
$613$	17.6004			0.710875			0.355438	−	0.934700i	$-0.384332\pi$
$613$	17.6004			0.710875			0.355438	+	0.934700i	$0.384332\pi$
$614$	1.99592	+	19.1177i	0.0805486	+	0.771529i
$615$	0.724939	−	7.35619i	0.0292324	−	0.296630i
$616$	9.73632	+	30.1794i	0.392288	+	1.21596i
$617$		−	28.8321i		−	1.16074i	−0.814354	−	0.580368i	$-0.802909\pi$
$617$		−	28.8321i		−	1.16074i	0.814354	−	0.580368i	$-0.197091\pi$
$618$	−2.05167	+	0.0118860i	−0.0825302	+	0.000478127i
$619$			14.4966i			0.582667i	0.956621	+	0.291334i	$0.0940990\pi$
$619$			14.4966i			0.582667i	−0.956621	+	0.291334i	$0.905901\pi$
$620$	−6.24162	+	1.31763i	−0.250669	+	0.0529171i
$621$	−1.50920	+	4.97215i	−0.0605622	+	0.199526i
$622$	−18.9914	+	1.98273i	−0.761487	+	0.0795002i
$623$	−31.2907			−1.25364
$624$	10.1773	+	30.9320i	0.407419	+	1.23827i
$625$	−31.2276			−1.24910
$626$	22.8509	−	2.38566i	0.913305	−	0.0953501i
$627$	−18.9846	−	1.87089i	−0.758170	−	0.0747163i
$628$	−7.13985	+	1.50725i	−0.284911	+	0.0601457i
$629$			44.5188i			1.77508i
$630$	−44.7153	−	4.14519i	−1.78150	−	0.165148i
$631$		−	12.7856i		−	0.508987i	−0.967074	−	0.254494i	$-0.918091\pi$
$631$		−	12.7856i		−	0.508987i	0.967074	−	0.254494i	$-0.0819088\pi$
$632$	2.66027	+	8.24596i	0.105820	+	0.328007i
$633$	−20.2021	−	1.99088i	−0.802962	−	0.0791305i
$634$	−2.87412	−	27.5296i	−0.114146	−	1.09334i
$635$	−47.5079			−1.88529
$636$	21.7064	−	2.39338i	0.860716	−	0.0949037i
$637$	35.9345			1.42378
$638$	−3.44668	−	33.0138i	−0.136455	−	1.30703i
$639$	−37.3629	−	7.43631i	−1.47805	−	0.294176i
$640$	−20.8249	−	23.3560i	−0.823175	−	0.923227i
$641$		−	38.0942i		−	1.50463i	−0.658803	−	0.752315i	$-0.728937\pi$
$641$		−	38.0942i		−	1.50463i	0.658803	−	0.752315i	$-0.271063\pi$
$642$	0.0748056	+	12.9123i	0.00295234	+	0.509608i
$643$		−	15.2375i		−	0.600909i	−0.953796	−	0.300455i	$-0.902862\pi$
$643$		−	15.2375i		−	0.600909i	0.953796	−	0.300455i	$-0.0971384\pi$
$644$	1.58092	+	7.48883i	0.0622969	+	0.295101i
$645$	−1.04516	+	10.6055i	−0.0411531	+	0.417593i
$646$	21.4911	−	2.24369i	0.845555	−	0.0882769i
$647$	19.6466			0.772386			0.386193	−	0.922418i	$-0.373790\pi$
$647$	19.6466			0.772386			0.386193	+	0.922418i	$0.373790\pi$
$648$	−25.3727	−	2.05589i	−0.996733	−	0.0807631i
$649$	20.5957			0.808453
$650$	−17.5180	+	1.82891i	−0.687114	+	0.0717356i
$651$	−0.749672	+	7.60716i	−0.0293820	+	0.298148i
$652$	−7.98367	−	37.8188i	−0.312665	−	1.48110i
$653$			34.6146i			1.35457i	0.735719	+	0.677287i	$0.236844\pi$
$653$			34.6146i			1.35457i	−0.735719	+	0.677287i	$0.763156\pi$
$654$	−0.0501767	−	8.66107i	−0.00196206	−	0.338675i
$655$			4.75192i			0.185673i
$656$	−2.49468	−	5.64535i	−0.0974009	−	0.220414i
$657$	16.7164	+	3.32705i	0.652168	+	0.129801i
$658$	−6.50121	−	62.2714i	−0.253444	−	2.42759i
$659$	30.7950			1.19960			0.599802	−	0.800149i	$-0.295246\pi$
$659$	30.7950			1.19960			0.599802	+	0.800149i	$0.295246\pi$
$660$	−27.9002	+	3.07631i	−1.08601	+	0.119745i
$661$	−8.69254			−0.338101			−0.169050	−	0.985607i	$-0.554070\pi$
$661$	−8.69254			−0.338101			−0.169050	+	0.985607i	$0.554070\pi$
$662$	0.499408	+	4.78355i	0.0194101	+	0.185918i
$663$	−32.9262	−	3.24482i	−1.27875	−	0.126018i
$664$	7.77106	−	2.50706i	0.301576	−	0.0972928i
$665$		−	39.7926i		−	1.54309i
$666$	46.2752	+	4.28980i	1.79313	+	0.166227i
$667$		−	8.01162i		−	0.310211i
$668$	13.2757	−	2.80253i	0.513650	−	0.108433i
$669$	−0.267080	−	0.0263203i	−0.0103259	−	0.00101760i
$670$	−6.42749	+	0.671038i	−0.248316	+	0.0259245i
$671$	18.0233			0.695780
$672$	−34.2084	+	15.3542i	−1.31962	+	0.592300i
$673$	−28.1174			−1.08384			−0.541922	−	0.840429i	$-0.682303\pi$
$673$	−28.1174			−1.08384			−0.541922	+	0.840429i	$0.682303\pi$
$674$	29.8654	−	3.11798i	1.15037	−	0.120100i
$675$	3.99913	−	13.1754i	0.153927	−	0.507120i
$676$	17.7898	−	3.75548i	0.684222	−	0.144441i
$677$			39.5123i			1.51858i	0.650752	+	0.759290i	$0.274454\pi$
$677$			39.5123i			1.51858i	−0.650752	+	0.759290i	$0.725546\pi$
$678$	−2.63277	+	0.0152525i	−0.101111	+	0.000585771i
$679$		−	16.3828i		−	0.628715i
$680$	30.2582	−	9.76174i	1.16035	−	0.374346i
$681$	−0.787749	+	7.99353i	−0.0301866	+	0.306313i
$682$	0.496123	+	4.75208i	0.0189975	+	0.181967i
$683$	3.49594			0.133768			0.0668842	−	0.997761i	$-0.478694\pi$
$683$	3.49594			0.133768			0.0668842	+	0.997761i	$0.478694\pi$
$684$	−0.261349	−	22.5552i	−0.00999294	−	0.862419i
$685$	−54.1574			−2.06925
$686$	0.362744	+	3.47452i	0.0138496	+	0.132658i
$687$	−0.458388	+	4.65141i	−0.0174886	+	0.177462i
$688$	3.59662	+	8.13901i	0.137120	+	0.310297i
$689$		−	29.6298i		−	1.12881i
$690$	−6.77476	+	0.0392486i	−0.257911	+	0.00149417i
$691$			42.5349i			1.61810i	0.587737	+	0.809052i	$0.300019\pi$
$691$			42.5349i			1.61810i	−0.587737	+	0.809052i	$0.699981\pi$
$692$	6.64668	+	31.4854i	0.252669	+	1.19690i
$693$	−6.56551	+	32.9877i	−0.249403	+	1.25310i
$694$	−0.996290	+	0.104014i	−0.0378187	+	0.00394831i
$695$	10.5341			0.399580
$696$	38.3548	−	8.32921i	1.45383	−	0.315718i
$697$	6.27101			0.237532
$698$	−47.7496	+	4.98511i	−1.80735	+	0.188689i
$699$	−4.78141	−	0.471200i	−0.180850	−	0.0178224i
$700$	−4.18916	−	19.8441i	−0.158335	−	0.750037i
$701$		−	40.9215i		−	1.54558i	−0.634660	−	0.772791i	$-0.718860\pi$
$701$		−	40.9215i		−	1.54558i	0.634660	−	0.772791i	$-0.281140\pi$
$702$	−6.54559	+	33.9126i	−0.247047	+	1.27995i
$703$			41.1808i			1.55316i
$704$	−19.0183	+	13.6968i	−0.716781	+	0.516216i
$705$	55.1523	+	5.43517i	2.07716	+	0.204700i
$706$	3.75411	+	35.9585i	0.141288	+	1.35332i
$707$	0.601074			0.0226057
$708$	2.66902	+	24.2064i	0.100308	+	0.909731i
$709$	−20.3138			−0.762899			−0.381449	−	0.924390i	$-0.624575\pi$
$709$	−20.3138			−0.762899			−0.381449	+	0.924390i	$0.624575\pi$
$710$	−5.15759	−	49.4017i	−0.193561	−	1.85401i
$711$	−1.79390	+	9.01326i	−0.0672766	+	0.338024i
$712$	−7.10056	−	22.0094i	−0.266105	−	0.824837i
$713$			1.15321i			0.0431881i
$714$	−0.220710	−	38.0972i	−0.00825988	−	1.42575i
$715$			38.0844i			1.42428i
$716$	22.1060	−	4.66665i	0.826140	−	0.174401i
$717$	3.74076	−	37.9586i	0.139701	−	1.41759i
$718$	−25.4007	+	2.65186i	−0.947946	+	0.0989667i
$719$	19.5609			0.729497			0.364749	−	0.931106i	$-0.381155\pi$
$719$	19.5609			0.729497			0.364749	+	0.931106i	$0.381155\pi$
$720$	−7.23123	−	32.3927i	−0.269492	−	1.20720i
$721$	−3.20546			−0.119378
$722$	−6.84511	+	0.714638i	−0.254749	+	0.0265961i
$723$	3.32770	−	33.7673i	0.123759	−	1.25582i
$724$	39.9139	−	8.42596i	1.48339	−	0.313148i
$725$			21.2294i			0.788441i
$726$	−0.0343015	−	5.92083i	−0.00127305	−	0.219743i
$727$			11.4558i			0.424871i	0.977175	+	0.212436i	$0.0681396\pi$
$727$			11.4558i			0.424871i	−0.977175	+	0.212436i	$0.931860\pi$
$728$	15.6202	+	48.4176i	0.578925	+	1.79448i
$729$	−22.4446	−	15.0080i	−0.831282	−	0.555851i
$730$	2.30754	+	22.1026i	0.0854059	+	0.818054i
$731$	−9.04103			−0.334395
$732$	2.33566	+	21.1829i	0.0863283	+	0.782943i
$733$	4.31889			0.159522			0.0797610	−	0.996814i	$-0.474584\pi$
$733$	4.31889			0.159522			0.0797610	+	0.996814i	$0.474584\pi$
$734$	0.539323	+	5.16587i	0.0199068	+	0.190676i
$735$	−36.4496	−	3.59204i	−1.34446	−	0.132494i
$736$	−4.90878	+	2.81138i	−0.180940	+	0.103629i
$737$			4.84026i			0.178293i
$738$	0.604271	−	6.51843i	0.0222435	−	0.239947i
$739$			31.1659i			1.14646i	0.819396	+	0.573228i	$0.194309\pi$
$739$			31.1659i			1.14646i	−0.819396	+	0.573228i	$0.805691\pi$
$740$	12.5157	+	59.2869i	0.460085	+	2.17943i
$741$	−30.4574	−	3.00153i	−1.11888	−	0.110264i
$742$	33.9340	−	3.54275i	1.24576	−	0.130058i
$743$	−16.9547			−0.622007			−0.311004	−	0.950409i	$-0.600665\pi$
$743$	−16.9547			−0.622007			−0.311004	+	0.950409i	$0.600665\pi$
$744$	−5.52088	+	1.19893i	−0.202405	+	0.0439548i
$745$	51.4024			1.88324
$746$	−47.6428	+	4.97397i	−1.74433	+	0.182110i
$747$	8.49417	+	1.69059i	0.310785	+	0.0618555i
$748$	−4.91863	−	23.2996i	−0.179843	−	0.851919i
$749$			20.1738i			0.737134i
$750$	−15.9219	+	0.0922410i	−0.581384	+	0.00336816i
$751$		−	32.8289i		−	1.19794i	−0.800770	−	0.598972i	$-0.795576\pi$
$751$		−	32.8289i		−	1.19794i	0.800770	−	0.598972i	$-0.204424\pi$
$752$	42.3255	−	18.7036i	1.54345	−	0.682051i
$753$	−3.94289	+	40.0098i	−0.143687	+	1.45804i
$754$	−5.52960	−	52.9649i	−0.201376	−	1.92887i
$755$	−9.92859			−0.361338
$756$	−39.6215	−	3.44161i	−1.44102	−	0.125170i
$757$	−1.34070			−0.0487287			−0.0243644	−	0.999703i	$-0.507756\pi$
$757$	−1.34070			−0.0487287			−0.0243644	+	0.999703i	$0.507756\pi$
$758$	1.82283	+	17.4599i	0.0662082	+	0.634171i
$759$	−0.497651	+	5.04982i	−0.0180636	+	0.183297i
$760$	27.9895	−	9.02982i	1.01529	−	0.327546i
$761$			27.4549i			0.995238i	0.867396	+	0.497619i	$0.165792\pi$
$761$			27.4549i			0.995238i	−0.867396	+	0.497619i	$0.834208\pi$
$762$	−42.0735	+	0.243747i	−1.52416	+	0.00883001i
$763$		−	13.5318i		−	0.489883i
$764$	−10.1465	+	2.14195i	−0.367086	+	0.0774930i
$765$	33.0738	+	6.58266i	1.19579	+	0.237996i
$766$	15.7855	−	1.64803i	0.570353	−	0.0595456i
$767$	33.0423			1.19309
$768$	−18.5625	−	20.5775i	−0.669818	−	0.742525i
$769$	−4.77966			−0.172359			−0.0861795	−	0.996280i	$-0.527466\pi$
$769$	−4.77966			−0.172359			−0.0861795	+	0.996280i	$0.527466\pi$
$770$	−43.6167	+	4.55364i	−1.57184	+	0.164102i
$771$	−21.9863	−	2.16671i	−0.791818	−	0.0780323i
$772$	15.1384	−	3.19577i	0.544843	−	0.115018i
$773$			26.8417i			0.965429i	0.875778	+	0.482714i	$0.160349\pi$
$773$			26.8417i			0.965429i	−0.875778	+	0.482714i	$0.839651\pi$
$774$	−0.871189	+	9.39774i	−0.0313142	+	0.337795i
$775$		−	3.05581i		−	0.109768i
$776$	11.5234	−	3.71763i	0.413667	−	0.133455i
$777$	72.2577	+	7.12087i	2.59223	+	0.255460i
$778$	4.06011	+	38.8895i	0.145562	+	1.39426i
$779$	5.80082			0.207836
$780$	−44.7610	+	4.93540i	−1.60270	+	0.176716i
$781$	−37.2022			−1.33120
$782$	−0.596814	−	5.71654i	−0.0213420	−	0.204423i
$783$	39.8350	+	12.0912i	1.42359	+	0.432103i
$784$	−27.9725	+	12.3610i	−0.999016	+	0.441465i
$785$		−	10.0914i		−	0.360179i
$786$	0.0243805	+	4.20835i	0.000869623	+	0.150107i
$787$			21.8772i			0.779837i	0.920849	+	0.389919i	$0.127497\pi$
$787$			21.8772i			0.779837i	−0.920849	+	0.389919i	$0.872503\pi$
$788$	3.15784	+	14.9587i	0.112493	+	0.532882i
$789$	−3.80791	+	38.6400i	−0.135565	+	1.37562i
$790$	−11.9174	+	1.24420i	−0.424004	+	0.0442665i
$791$	−4.11335			−0.146254
$792$	−24.6929	+	2.86755i	−0.877423	+	0.101894i
$793$	28.9152			1.02681
$794$	−8.46626	+	0.883888i	−0.300456	+	0.0313680i
$795$	−2.96182	+	30.0545i	−0.105045	+	1.06592i
$796$	5.74597	+	27.2187i	0.203660	+	0.964743i
$797$		−	21.7837i		−	0.771618i	−0.922579	−	0.385809i	$-0.873922\pi$
$797$		−	21.7837i		−	0.771618i	0.922579	−	0.385809i	$-0.126078\pi$
$798$	−0.204162	−	35.2407i	−0.00722725	−	1.24751i
$799$			47.0163i			1.66332i
$800$	13.0074	−	7.44967i	0.459882	−	0.263385i
$801$	4.78813	−	24.0574i	0.169180	−	0.850027i
$802$	−4.54400	−	43.5244i	−0.160454	−	1.53690i
$803$	16.6445			0.587372
$804$	−5.68881	+	0.627255i	−0.200629	+	0.0221216i
$805$	−10.5847			−0.373061
$806$	0.795944	+	7.62389i	0.0280359	+	0.268540i
$807$	−35.2112	−	3.47000i	−1.23949	−	0.122150i
$808$	0.136397	+	0.422786i	0.00479843	+	0.0148736i
$809$		−	4.38781i		−	0.154267i	−0.997021	−	0.0771335i	$-0.975423\pi$
$809$		−	4.38781i		−	0.154267i	0.997021	−	0.0771335i	$-0.0245768\pi$
$810$	10.0293	−	33.7444i	0.352395	−	1.18566i
$811$		−	24.3428i		−	0.854792i	−0.904065	−	0.427396i	$-0.859431\pi$
$811$		−	24.3428i		−	0.854792i	0.904065	−	0.427396i	$-0.140569\pi$
$812$	59.9977	−	12.6657i	2.10550	−	0.444479i
$813$	54.4963	+	5.37051i	1.91127	+	0.188352i
$814$	45.1383	−	4.71250i	1.58210	−	0.165173i
$815$	53.4529			1.87237
$816$	26.7469	−	8.80034i	0.936328	−	0.308074i
$817$	−8.36315			−0.292589
$818$	−17.8466	+	1.86320i	−0.623990	+	0.0651454i
$819$	−10.5332	+	52.9230i	−0.368061	+	1.84928i
$820$	8.35128	−	1.76298i	0.291639	−	0.0615661i
$821$			48.1971i			1.68209i	0.540964	+	0.841046i	$0.318060\pi$
$821$			48.1971i			1.68209i	−0.540964	+	0.841046i	$0.681940\pi$
$822$	−47.9623	+	0.277863i	−1.67288	+	0.00969157i
$823$		−	4.99654i		−	0.174169i	−0.996201	−	0.0870843i	$-0.972245\pi$
$823$		−	4.99654i		−	0.174169i	0.996201	−	0.0870843i	$-0.0277549\pi$
$824$	−0.727391	−	2.25467i	−0.0253399	−	0.0785453i
$825$	1.31869	−	13.3812i	0.0459109	−	0.465872i
$826$	3.95077	+	37.8421i	0.137465	+	1.31670i
$827$	19.6028			0.681657			0.340829	−	0.940125i	$-0.389292\pi$
$827$	19.6028			0.681657			0.340829	+	0.940125i	$0.389292\pi$
$828$	−5.99960	+	0.0695179i	−0.208500	+	0.00241591i
$829$	−9.07466			−0.315176			−0.157588	−	0.987505i	$-0.550372\pi$
$829$	−9.07466			−0.315176			−0.157588	+	0.987505i	$0.550372\pi$
$830$	1.17254	+	11.2311i	0.0406995	+	0.389837i
$831$	−0.149803	+	1.52010i	−0.00519661	+	0.0527317i
$832$	−30.5116	+	21.9741i	−1.05780	+	0.761814i
$833$		−	31.0726i		−	1.07660i
$834$	9.32907	−	0.0540466i	0.323039	−	0.00187148i
$835$			18.7637i			0.649346i
$836$	−4.54984	−	21.5527i	−0.157359	−	0.745414i
$837$	−5.73394	−	1.74043i	−0.198194	−	0.0601581i
$838$	36.5405	−	3.81487i	1.26227	−	0.131782i
$839$	51.3597			1.77313			0.886567	−	0.462600i	$-0.153083\pi$
$839$	51.3597			1.77313			0.886567	+	0.462600i	$0.153083\pi$
$840$	−11.0043	−	50.6730i	−0.379683	−	1.74839i
$841$	−35.1860			−1.21331
$842$	45.0522	−	4.70350i	1.55260	−	0.162093i
$843$	−17.6931	−	1.74363i	−0.609384	−	0.0600537i
$844$	−4.84164	−	22.9349i	−0.166656	−	0.789452i
$845$			25.1440i			0.864978i
$846$	48.8713	+	4.53047i	1.68023	+	0.155761i
$847$		−	9.25052i		−	0.317852i
$848$	10.1923	+	23.0647i	0.350005	+	0.792046i
$849$	2.02150	+	0.199215i	0.0693775	+	0.00683703i
$850$	1.58146	+	15.1479i	0.0542435	+	0.519567i
$851$	10.9539			0.375496
$852$	−4.82108	−	43.7242i	−0.165167	−	1.49796i
$853$	6.08280			0.208271			0.104136	−	0.994563i	$-0.466792\pi$
$853$	6.08280			0.208271			0.104136	+	0.994563i	$0.466792\pi$
$854$	3.45730	+	33.1156i	0.118306	+	1.13319i
$855$	30.5940	+	6.08910i	1.04629	+	0.208243i
$856$	−14.1899	+	4.57788i	−0.485002	+	0.156469i
$857$		−	14.7712i		−	0.504576i	−0.967652	−	0.252288i	$-0.918817\pi$
$857$		−	14.7712i		−	0.504576i	0.967652	−	0.252288i	$-0.0811830\pi$
$858$	0.195398	+	33.7279i	0.00667077	+	1.15145i
$859$			28.2794i			0.964879i	0.875929	+	0.482440i	$0.160249\pi$
$859$			28.2794i			0.964879i	−0.875929	+	0.482440i	$0.839751\pi$
$860$	−12.0402	+	2.54173i	−0.410567	+	0.0866721i
$861$	1.00306	−	10.1784i	0.0341842	−	0.346878i
$862$	−5.81367	+	0.606954i	−0.198014	+	0.0206729i
$863$	9.72692			0.331108			0.165554	−	0.986201i	$-0.447059\pi$
$863$	9.72692			0.331108			0.165554	+	0.986201i	$0.447059\pi$
$864$	−6.57024	−	28.6502i	−0.223524	−	0.974698i
$865$	−44.5013			−1.51309
$866$	−49.3496	+	5.15215i	−1.67697	+	0.175077i
$867$	0.0819551	−	0.831625i	0.00278334	−	0.0282435i
$868$	−8.63621	+	1.82313i	−0.293132	+	0.0618811i
$869$			8.97451i			0.304439i
$870$	0.314445	+	54.2768i	0.0106607	+	1.84016i
$871$			7.76536i			0.263119i
$872$	9.51805	−	3.07066i	0.322322	−	0.103986i
$873$	12.5957	+	2.50692i	0.426300	+	0.0848462i
$874$	−0.552066	−	5.28793i	−0.0186739	−	0.178867i
$875$	−24.8758			−0.840956
$876$	2.15698	+	19.5625i	0.0728776	+	0.660954i
$877$	−22.7188			−0.767161			−0.383580	−	0.923508i	$-0.625309\pi$
$877$	−22.7188			−0.767161			−0.383580	+	0.923508i	$0.625309\pi$
$878$	3.42244	+	32.7816i	0.115502	+	1.10633i
$879$	20.6343	+	2.03347i	0.695977	+	0.0685873i
$880$	−13.1006	−	29.6460i	−0.441620	−	0.999366i
$881$		−	8.36445i		−	0.281805i	−0.990023	−	0.140903i	$-0.955000\pi$
$881$		−	8.36445i		−	0.281805i	0.990023	−	0.140903i	$-0.0450005\pi$
$882$	−32.2985	−	2.99414i	−1.08755	−	0.100818i
$883$			32.6837i			1.09989i	0.835199	+	0.549947i	$0.185352\pi$
$883$			32.6837i			1.09989i	−0.835199	+	0.549947i	$0.814648\pi$
$884$	−7.89109	−	37.3802i	−0.265406	−	1.25723i
$885$	−33.5159	−	3.30293i	−1.12662	−	0.111027i
$886$	−6.04784	+	0.631402i	−0.203181	+	0.0212124i
$887$	11.7634			0.394977			0.197488	−	0.980305i	$-0.436722\pi$
$887$	11.7634			0.394977			0.197488	+	0.980305i	$0.436722\pi$
$888$	11.3882	+	52.4408i	0.382162	+	1.75980i
$889$	−65.7343			−2.20466
$890$	31.8090	−	3.32090i	1.06624	−	0.111317i
$891$	−24.3574	−	10.0956i	−0.816005	−	0.338216i
$892$	−0.0640084	−	0.303209i	−0.00214316	−	0.0101522i
$893$			43.4911i			1.45537i
$894$	45.5225	−	0.263728i	1.52250	−	0.00882038i
$895$			31.2445i			1.04439i
$896$	−28.8143	−	32.3165i	−0.962619	−	1.07962i
$897$	−0.798395	+	8.10156i	−0.0266576	+	0.270503i
$898$	−2.13848	−	20.4833i	−0.0713621	−	0.683537i
$899$	9.23909			0.308141
$900$	15.8979	−	0.184211i	0.529930	−	0.00614035i
$901$	−25.6209			−0.853557
$902$	−0.663813	−	6.35829i	−0.0221026	−	0.211708i
$903$	−1.44613	+	14.6744i	−0.0481243	+	0.488332i
$904$	−0.933411	−	2.89327i	−0.0310448	−	0.0962287i
$905$			56.4141i			1.87527i
$906$	−8.79285	+	0.0509401i	−0.292123	+	0.00169237i
$907$		−	42.5544i		−	1.41300i	−0.707715	−	0.706498i	$-0.750274\pi$
$907$		−	42.5544i		−	1.41300i	0.707715	−	0.706498i	$-0.249726\pi$
$908$	−9.07485	+	1.91573i	−0.301159	+	0.0635758i
$909$	−0.0919769	+	0.462127i	−0.00305068	+	0.0153278i
$910$	−69.9754	+	7.30552i	−2.31966	+	0.242176i
$911$	−35.8044			−1.18625			−0.593126	−	0.805110i	$-0.702106\pi$
$911$	−35.8044			−1.18625			−0.593126	+	0.805110i	$0.702106\pi$
$912$	24.7414	−	8.14050i	0.819271	−	0.269559i
$913$	8.45765			0.279907
$914$	17.5541	−	1.83267i	0.580637	−	0.0606193i
$915$	−29.3297	−	2.89039i	−0.969609	−	0.0955532i
$916$	−5.28062	+	1.11476i	−0.174477	+	0.0368326i
$917$			6.57500i			0.217125i
$918$	29.3242	+	5.65998i	0.967844	+	0.186807i
$919$		−	5.15225i		−	0.169957i	−0.996383	−	0.0849785i	$-0.972918\pi$
$919$		−	5.15225i		−	0.169957i	0.996383	−	0.0849785i	$-0.0270821\pi$
$920$	−2.40190	−	7.44510i	−0.0791883	−	0.245458i
$921$	−23.4281	−	2.30880i	−0.771983	−	0.0760776i
$922$	−4.10865	−	39.3544i	−0.135311	−	1.29607i
$923$	−59.6845			−1.96454
$924$	−38.6040	+	4.25653i	−1.26998	+	0.140029i
$925$	−29.0261			−0.954371
$926$	6.15586	+	58.9634i	0.202294	+	1.93766i
$927$	0.490503	−	2.46447i	0.0161102	−	0.0809440i
$928$	22.5237	+	39.3273i	0.739376	+	1.29098i
$929$		−	37.5078i		−	1.23059i	−0.788297	−	0.615295i	$-0.789037\pi$
$929$		−	37.5078i		−	1.23059i	0.788297	−	0.615295i	$-0.210963\pi$
$930$	−0.0452619	−	7.81273i	−0.00148420	−	0.256190i
$931$		−	28.7428i		−	0.942007i
$932$	−1.14591	−	5.42821i	−0.0375356	−	0.177807i
$933$	2.29355	−	23.2733i	0.0750873	−	0.761935i
$934$	9.23208	−	0.963841i	0.302083	−	0.0315378i
$935$	32.9316			1.07698
$936$	−39.6154	+	4.60049i	−1.29487	+	0.150372i
$937$	−7.90116			−0.258120			−0.129060	−	0.991637i	$-0.541196\pi$
$937$	−7.90116			−0.258120			−0.129060	+	0.991637i	$0.541196\pi$
$938$	−8.89339	+	0.928481i	−0.290380	+	0.0303160i
$939$	−2.75964	+	28.0030i	−0.0900575	+	0.913842i
$940$	13.2178	+	62.6130i	0.431117	+	2.04221i
$941$		−	24.0997i		−	0.785626i	−0.919618	−	0.392813i	$-0.871502\pi$
$941$		−	24.0997i		−	0.785626i	0.919618	−	0.392813i	$-0.128498\pi$
$942$	−0.0517756	−	8.93707i	−0.00168694	−	0.291186i
$943$		−	1.54300i		−	0.0502469i
$944$	−25.7211	+	11.3661i	−0.837149	+	0.369936i
$945$	15.9744	−	52.6286i	0.519648	−	1.71201i
$946$	0.957031	+	9.16686i	0.0311158	+	0.298040i
$947$	−17.4664			−0.567581			−0.283791	−	0.958886i	$-0.591592\pi$
$947$	−17.4664			−0.567581			−0.283791	+	0.958886i	$0.591592\pi$
$948$	−10.5478	+	1.16302i	−0.342577	+	0.0377730i
$949$	26.7032			0.866823
$950$	1.46288	+	14.0121i	0.0474621	+	0.454612i
$951$	33.7365	+	3.32468i	1.09398	+	0.107810i
$952$	41.8667	−	13.5068i	1.35691	−	0.437759i
$953$		−	15.1513i		−	0.490797i	−0.969422	−	0.245399i	$-0.921081\pi$
$953$		−	15.1513i		−	0.490797i	0.969422	−	0.245399i	$-0.0789189\pi$
$954$	−2.46882	+	26.6318i	−0.0799309	+	0.862236i
$955$		−	14.3409i		−	0.464062i
$956$	43.0934	−	9.09716i	1.39374	−	0.294223i
$957$	40.4572	+	3.98699i	1.30780	+	0.128881i
$958$	36.2044	−	3.77978i	1.16971	−	0.122119i
$959$	−74.9348			−2.41977
$960$	33.1455	−	19.2391i	1.06977	−	0.620938i
$961$	29.6701			0.957100
$962$	72.4166	−	7.56038i	2.33481	−	0.243757i
$963$	−15.5103	−	3.08701i	−0.499814	−	0.0994776i
$964$	38.3351	−	8.09266i	1.23469	−	0.260647i
$965$			21.3965i			0.688779i
$966$	−9.37390	+	0.0543063i	−0.301600	+	0.00174728i
$967$		−	32.6643i		−	1.05041i	−0.850975	−	0.525207i	$-0.823988\pi$
$967$		−	32.6643i		−	1.05041i	0.850975	−	0.525207i	$-0.176012\pi$
$968$	6.50668	−	2.09915i	0.209132	−	0.0674692i
$969$	−2.59542	+	26.3366i	−0.0833769	+	0.846052i
$970$	1.73872	+	16.6542i	0.0558269	+	0.534734i
$971$	−42.7329			−1.37136			−0.685682	−	0.727901i	$-0.740496\pi$
$971$	−42.7329			−1.37136			−0.685682	+	0.727901i	$0.740496\pi$
$972$	8.70896	−	29.9358i	0.279340	−	0.960192i
$973$	14.5754			0.467267
$974$	−4.04430	−	38.7380i	−0.129588	−	1.24125i
$975$	2.11561	−	21.4678i	0.0677537	−	0.687518i
$976$	−22.5084	+	9.94647i	−0.720477	+	0.318379i
$977$		−	7.62392i		−	0.243911i	−0.992536	−	0.121955i	$-0.961084\pi$
$977$		−	7.62392i		−	0.243911i	0.992536	−	0.121955i	$-0.0389165\pi$
$978$	47.3384	−	0.274248i	1.51371	−	0.00876948i
$979$		−	23.9540i		−	0.765573i
$980$	−8.73550	−	41.3802i	−0.279045	−	1.32184i
$981$	10.4037	+	2.07065i	0.332165	+	0.0661107i
$982$	44.5356	−	4.64957i	1.42119	−	0.148374i
$983$	14.3005			0.456115			0.228058	−	0.973648i	$-0.426763\pi$
$983$	14.3005			0.456115			0.228058	+	0.973648i	$0.426763\pi$
$984$	7.38693	−	1.60416i	0.235487	−	0.0511389i
$985$	−21.1426			−0.673659
$986$	−45.7988	+	4.78145i	−1.45853	+	0.152272i
$987$	76.3115	+	7.52036i	2.42902	+	0.239376i
$988$	−7.29943	−	34.5775i	−0.232226	−	1.10006i
$989$			2.22457i			0.0707371i
$990$	3.17327	−	34.2309i	0.100853	−	1.08793i
$991$		−	42.3902i		−	1.34657i	−0.739384	−	0.673284i	$-0.764883\pi$
$991$		−	42.3902i		−	1.34657i	0.739384	−	0.673284i	$-0.235117\pi$
$992$	−3.24211	−	5.66087i	−0.102937	−	0.179733i
$993$	−5.86207	−	0.577697i	−0.186027	−	0.0183327i
$994$	−7.13630	−	68.3546i	−0.226350	−	2.16808i
$995$	−38.4708			−1.21961
$996$	1.09604	+	9.94036i	0.0347292	+	0.314972i
$997$	−44.2526			−1.40149			−0.700746	−	0.713410i	$-0.747150\pi$
$997$	−44.2526			−1.40149			−0.700746	+	0.713410i	$0.747150\pi$
$998$	−3.52161	−	33.7315i	−0.111475	−	1.06775i
$999$	−16.5317	+	54.4647i	−0.523041	+	1.72319i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.c.a.47.2	yes	22
3.2	odd	2		276.2.c.b.47.21	yes	22
4.3	odd	2		276.2.c.b.47.22	yes	22
12.11	even	2	inner	276.2.c.a.47.1	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.c.a.47.1	✓	22	12.11	even	2	inner
276.2.c.a.47.2	yes	22	1.1	even	1	trivial
276.2.c.b.47.21	yes	22	3.2	odd	2
276.2.c.b.47.22	yes	22	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40657 + 0.146847i) q^{2} +(0.169868 - 1.72370i) q^{3} +(1.95687 - 0.413102i) q^{4} +2.76583i q^{5} +(0.0141905 + 2.44945i) q^{6} +3.82694i q^{7} +(-2.69181 + 0.868418i) q^{8} +(-2.94229 - 0.585602i) q^{9} +O(q^{10})\)	\(q+(-1.40657 + 0.146847i) q^{2} +(0.169868 - 1.72370i) q^{3} +(1.95687 - 0.413102i) q^{4} +2.76583i q^{5} +(0.0141905 + 2.44945i) q^{6} +3.82694i q^{7} +(-2.69181 + 0.868418i) q^{8} +(-2.94229 - 0.585602i) q^{9} +(-0.406156 - 3.89033i) q^{10} -2.92964 q^{11} +(-0.379655 - 3.44323i) q^{12} -4.70010 q^{13} +(-0.561977 - 5.38286i) q^{14} +(4.76747 + 0.469826i) q^{15} +(3.65869 - 1.61678i) q^{16} +4.06418i q^{17} +(4.22453 + 0.391622i) q^{18} +3.75945i q^{19} +(1.14257 + 5.41238i) q^{20} +(6.59650 + 0.650074i) q^{21} +(4.12074 - 0.430210i) q^{22} +1.00000 q^{23} +(1.03964 + 4.78739i) q^{24} -2.64983 q^{25} +(6.61101 - 0.690197i) q^{26} +(-1.50920 + 4.97215i) q^{27} +(1.58092 + 7.48883i) q^{28} -8.01162i q^{29} +(-6.77476 + 0.0392486i) q^{30} +1.15321i q^{31} +(-4.90878 + 2.81138i) q^{32} +(-0.497651 + 5.04982i) q^{33} +(-0.596814 - 5.71654i) q^{34} -10.5847 q^{35} +(-5.99960 + 0.0695179i) q^{36} +10.9539 q^{37} +(-0.552066 - 5.28793i) q^{38} +(-0.798395 + 8.10156i) q^{39} +(-2.40190 - 7.44510i) q^{40} -1.54300i q^{41} +(-9.37390 + 0.0543063i) q^{42} +2.22457i q^{43} +(-5.73293 + 1.21024i) q^{44} +(1.61968 - 8.13788i) q^{45} +(-1.40657 + 0.146847i) q^{46} +11.5685 q^{47} +(-2.16534 - 6.58113i) q^{48} -7.64548 q^{49} +(3.72717 - 0.389121i) q^{50} +(7.00543 + 0.690372i) q^{51} +(-9.19749 + 1.94162i) q^{52} +6.30409i q^{53} +(1.39265 - 7.21530i) q^{54} -8.10289i q^{55} +(-3.32339 - 10.3014i) q^{56} +(6.48017 + 0.638609i) q^{57} +(1.17649 + 11.2689i) q^{58} -7.03012 q^{59} +(9.52341 - 1.05006i) q^{60} -6.15204 q^{61} +(-0.169346 - 1.62207i) q^{62} +(2.24107 - 11.2600i) q^{63} +(6.49170 - 4.67524i) q^{64} -12.9997i q^{65} +(-0.0415731 - 7.17600i) q^{66} -1.65217i q^{67} +(1.67892 + 7.95307i) q^{68} +(0.169868 - 1.72370i) q^{69} +(14.8881 - 1.55433i) q^{70} +12.6986 q^{71} +(8.42864 - 0.978807i) q^{72} -5.68142 q^{73} +(-15.4075 + 1.60856i) q^{74} +(-0.450120 + 4.56751i) q^{75} +(1.55304 + 7.35676i) q^{76} -11.2116i q^{77} +(-0.0666969 - 11.5126i) q^{78} -3.06335i q^{79} +(4.47173 + 10.1193i) q^{80} +(8.31414 + 3.44602i) q^{81} +(0.226585 + 2.17033i) q^{82} -2.88693 q^{83} +(13.1771 - 1.45292i) q^{84} -11.2408 q^{85} +(-0.326672 - 3.12901i) q^{86} +(-13.8096 - 1.36091i) q^{87} +(7.88604 - 2.54415i) q^{88} +8.17643i q^{89} +(-1.08316 + 11.6843i) q^{90} -17.9870i q^{91} +(1.95687 - 0.413102i) q^{92} +(1.98779 + 0.195893i) q^{93} +(-16.2719 + 1.69880i) q^{94} -10.3980 q^{95} +(4.01213 + 8.93884i) q^{96} -4.28092 q^{97} +(10.7539 - 1.12272i) q^{98} +(8.61985 + 1.71560i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9}+O(q^{10}) \) 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9	\( 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{16} - 14 q^{18} - 14 q^{20} + 2 q^{22} + 22 q^{23} + 22 q^{24} - 18 q^{25} + 27 q^{26} + 12 q^{27} + 6 q^{28} - 24 q^{30} - 20 q^{32} - 8 q^{33} - 6 q^{34} - 8 q^{35} + 3 q^{36} - 4 q^{37} + 22 q^{38} - 24 q^{39} - 4 q^{40} - 38 q^{42} - 56 q^{44} + 8 q^{47} + 17 q^{48} - 14 q^{49} + 20 q^{50} + 16 q^{51} - 19 q^{52} - 54 q^{54} - 18 q^{56} + 12 q^{57} + 3 q^{58} - 72 q^{59} + 64 q^{60} + 12 q^{61} + 63 q^{62} - 20 q^{63} + 3 q^{64} - 18 q^{66} - 20 q^{68} + 40 q^{71} + 48 q^{72} - 4 q^{73} + 28 q^{74} + 48 q^{75} + 26 q^{76} - 46 q^{78} - 84 q^{80} + 10 q^{81} - 29 q^{82} - 8 q^{83} + 76 q^{84} + 8 q^{85} + 28 q^{86} - 48 q^{87} - 30 q^{88} - 26 q^{90} + 12 q^{93} - 13 q^{94} + 32 q^{95} + 18 q^{96} - 4 q^{97} + 64 q^{98} + 20 q^{99}+O(q^{100}) \) 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^16 - 14 * q^18 - 14 * q^20 + 2 * q^22 + 22 * q^23 + 22 * q^24 - 18 * q^25 + 27 * q^26 + 12 * q^27 + 6 * q^28 - 24 * q^30 - 20 * q^32 - 8 * q^33 - 6 * q^34 - 8 * q^35 + 3 * q^36 - 4 * q^37 + 22 * q^38 - 24 * q^39 - 4 * q^40 - 38 * q^42 - 56 * q^44 + 8 * q^47 + 17 * q^48 - 14 * q^49 + 20 * q^50 + 16 * q^51 - 19 * q^52 - 54 * q^54 - 18 * q^56 + 12 * q^57 + 3 * q^58 - 72 * q^59 + 64 * q^60 + 12 * q^61 + 63 * q^62 - 20 * q^63 + 3 * q^64 - 18 * q^66 - 20 * q^68 + 40 * q^71 + 48 * q^72 - 4 * q^73 + 28 * q^74 + 48 * q^75 + 26 * q^76 - 46 * q^78 - 84 * q^80 + 10 * q^81 - 29 * q^82 - 8 * q^83 + 76 * q^84 + 8 * q^85 + 28 * q^86 - 48 * q^87 - 30 * q^88 - 26 * q^90 + 12 * q^93 - 13 * q^94 + 32 * q^95 + 18 * q^96 - 4 * q^97 + 64 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more