LMFDB - Embedded newform 966.2.h.a.827.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(827,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("966.827");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.h (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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			827.12
Character	$\chi$	$=$	966.827
Dual form			966.2.h.a.827.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.73197 + 0.0164012i) q^{3} -1.00000 q^{4} -3.75984 q^{5} +(0.0164012 - 1.73197i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(2.99946 + 0.0568128i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.73197 + 0.0164012i) q^{3} -1.00000 q^{4} -3.75984 q^{5} +(0.0164012 - 1.73197i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(2.99946 + 0.0568128i) q^{9} +3.75984i q^{10} -2.91258 q^{11} +(-1.73197 - 0.0164012i) q^{12} -1.96159 q^{13} +1.00000 q^{14} +(-6.51193 - 0.0616657i) q^{15} +1.00000 q^{16} +6.79484 q^{17} +(0.0568128 - 2.99946i) q^{18} +5.60702i q^{19} +3.75984 q^{20} +(-0.0164012 + 1.73197i) q^{21} +2.91258i q^{22} +(-2.47675 + 4.10679i) q^{23} +(-0.0164012 + 1.73197i) q^{24} +9.13636 q^{25} +1.96159i q^{26} +(5.19406 + 0.147593i) q^{27} -1.00000i q^{28} +9.69207i q^{29} +(-0.0616657 + 6.51193i) q^{30} -8.11540 q^{31} -1.00000i q^{32} +(-5.04451 - 0.0477697i) q^{33} -6.79484i q^{34} -3.75984i q^{35} +(-2.99946 - 0.0568128i) q^{36} +1.15756i q^{37} +5.60702 q^{38} +(-3.39742 - 0.0321724i) q^{39} -3.75984i q^{40} -1.92878i q^{41} +(1.73197 + 0.0164012i) q^{42} +6.91669i q^{43} +2.91258 q^{44} +(-11.2775 - 0.213607i) q^{45} +(4.10679 + 2.47675i) q^{46} +10.7687i q^{47} +(1.73197 + 0.0164012i) q^{48} -1.00000 q^{49} -9.13636i q^{50} +(11.7685 + 0.111443i) q^{51} +1.96159 q^{52} +2.59988 q^{53} +(0.147593 - 5.19406i) q^{54} +10.9508 q^{55} -1.00000 q^{56} +(-0.0919617 + 9.71121i) q^{57} +9.69207 q^{58} -6.79727i q^{59} +(6.51193 + 0.0616657i) q^{60} +5.64532i q^{61} +8.11540i q^{62} +(-0.0568128 + 2.99946i) q^{63} -1.00000 q^{64} +7.37525 q^{65} +(-0.0477697 + 5.04451i) q^{66} -12.1031i q^{67} -6.79484 q^{68} +(-4.35702 + 7.07223i) q^{69} -3.75984 q^{70} -4.18407i q^{71} +(-0.0568128 + 2.99946i) q^{72} -11.1705 q^{73} +1.15756 q^{74} +(15.8239 + 0.149847i) q^{75} -5.60702i q^{76} -2.91258i q^{77} +(-0.0321724 + 3.39742i) q^{78} -8.47864i q^{79} -3.75984 q^{80} +(8.99354 + 0.340815i) q^{81} -1.92878 q^{82} -8.52673 q^{83} +(0.0164012 - 1.73197i) q^{84} -25.5475 q^{85} +6.91669 q^{86} +(-0.158961 + 16.7864i) q^{87} -2.91258i q^{88} -5.22396 q^{89} +(-0.213607 + 11.2775i) q^{90} -1.96159i q^{91} +(2.47675 - 4.10679i) q^{92} +(-14.0557 - 0.133102i) q^{93} +10.7687 q^{94} -21.0815i q^{95} +(0.0164012 - 1.73197i) q^{96} -1.81206i q^{97} +1.00000i q^{98} +(-8.73617 - 0.165472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9	$ 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9} - 4 q^{12} + 8 q^{13} + 24 q^{14} - 4 q^{15} + 24 q^{16} + 32 q^{17} + 4 q^{18} + 4 q^{20} - 8 q^{23} - 12 q^{25} + 16 q^{27} - 4 q^{30} - 16 q^{31} + 20 q^{33} + 4 q^{36} - 8 q^{39} + 4 q^{42} + 24 q^{45} - 4 q^{46} + 4 q^{48} - 24 q^{49} + 24 q^{51} - 8 q^{52} + 24 q^{53} - 12 q^{54} + 16 q^{55} - 24 q^{56} + 4 q^{57} + 4 q^{58} + 4 q^{60} - 4 q^{63} - 24 q^{64} - 12 q^{66} - 32 q^{68} - 24 q^{69} - 4 q^{70} - 4 q^{72} - 32 q^{73} - 16 q^{74} + 48 q^{75} + 12 q^{78} - 4 q^{80} - 8 q^{81} - 8 q^{82} + 16 q^{83} - 16 q^{85} + 16 q^{86} + 20 q^{87} + 24 q^{89} - 28 q^{90} + 8 q^{92} + 16 q^{93} + 8 q^{94} - 48 q^{99}+O(q^{100}) $ 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9 - 4 * q^12 + 8 * q^13 + 24 * q^14 - 4 * q^15 + 24 * q^16 + 32 * q^17 + 4 * q^18 + 4 * q^20 - 8 * q^23 - 12 * q^25 + 16 * q^27 - 4 * q^30 - 16 * q^31 + 20 * q^33 + 4 * q^36 - 8 * q^39 + 4 * q^42 + 24 * q^45 - 4 * q^46 + 4 * q^48 - 24 * q^49 + 24 * q^51 - 8 * q^52 + 24 * q^53 - 12 * q^54 + 16 * q^55 - 24 * q^56 + 4 * q^57 + 4 * q^58 + 4 * q^60 - 4 * q^63 - 24 * q^64 - 12 * q^66 - 32 * q^68 - 24 * q^69 - 4 * q^70 - 4 * q^72 - 32 * q^73 - 16 * q^74 + 48 * q^75 + 12 * q^78 - 4 * q^80 - 8 * q^81 - 8 * q^82 + 16 * q^83 - 16 * q^85 + 16 * q^86 + 20 * q^87 + 24 * q^89 - 28 * q^90 + 8 * q^92 + 16 * q^93 + 8 * q^94 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.73197	+	0.0164012i	0.999955	+	0.00946922i
$3$	1.73197	+	0.0164012i	0.999955	+	0.00946922i
$4$	−1.00000			−0.500000
$5$	−3.75984			−1.68145			−0.840725	−	0.541463i	$-0.817871\pi$
$5$	−3.75984			−1.68145			−0.840725	+	0.541463i	$0.817871\pi$
$6$	0.0164012	−	1.73197i	0.00669575	−	0.707075i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$			1.00000i			0.353553i
$9$	2.99946	+	0.0568128i	0.999821	+	0.0189376i
$10$			3.75984i			1.18896i
$11$	−2.91258			−0.878175			−0.439088	−	0.898444i	$-0.644698\pi$
$11$	−2.91258			−0.878175			−0.439088	+	0.898444i	$0.644698\pi$
$12$	−1.73197	−	0.0164012i	−0.499978	−	0.00473461i
$13$	−1.96159			−0.544047			−0.272024	−	0.962291i	$-0.587693\pi$
$13$	−1.96159			−0.544047			−0.272024	+	0.962291i	$0.587693\pi$
$14$	1.00000			0.267261
$15$	−6.51193	−	0.0616657i	−1.68137	−	0.0159220i
$16$	1.00000			0.250000
$17$	6.79484			1.64799			0.823995	−	0.566597i	$-0.191740\pi$
$17$	6.79484			1.64799			0.823995	+	0.566597i	$0.191740\pi$
$18$	0.0568128	−	2.99946i	0.0133909	−	0.706980i
$19$			5.60702i			1.28634i	0.765724	+	0.643170i	$0.222381\pi$
$19$			5.60702i			1.28634i	−0.765724	+	0.643170i	$0.777619\pi$
$20$	3.75984			0.840725
$21$	−0.0164012	+	1.73197i	−0.00357903	+	0.377948i
$22$			2.91258i			0.620964i
$23$	−2.47675	+	4.10679i	−0.516438	+	0.856325i
$23$	−2.47675	+	4.10679i	−0.516438	+	0.856325i
$24$	−0.0164012	+	1.73197i	−0.00334787	+	0.353538i
$25$	9.13636			1.82727
$26$			1.96159i			0.384699i
$27$	5.19406	+	0.147593i	0.999597	+	0.0284043i
$28$		−	1.00000i		−	0.188982i
$29$			9.69207i			1.79977i	0.436125	+	0.899886i	$0.356350\pi$
$29$			9.69207i			1.79977i	−0.436125	+	0.899886i	$0.643650\pi$
$30$	−0.0616657	+	6.51193i	−0.0112586	+	1.18891i
$31$	−8.11540			−1.45757			−0.728785	−	0.684743i	$-0.759915\pi$
$31$	−8.11540			−1.45757			−0.728785	+	0.684743i	$0.759915\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−5.04451	−	0.0477697i	−0.878136	−	0.00831563i
$34$		−	6.79484i		−	1.16530i
$35$		−	3.75984i		−	0.635528i
$36$	−2.99946	−	0.0568128i	−0.499910	−	0.00946879i
$37$			1.15756i			0.190302i	0.995463	+	0.0951510i	$0.0303334\pi$
$37$			1.15756i			0.190302i	−0.995463	+	0.0951510i	$0.969667\pi$
$38$	5.60702			0.909579
$39$	−3.39742	−	0.0321724i	−0.544023	−	0.00515170i
$40$		−	3.75984i		−	0.594482i
$41$		−	1.92878i		−	0.301225i	−0.988593	−	0.150613i	$-0.951875\pi$
$41$		−	1.92878i		−	0.301225i	0.988593	−	0.150613i	$-0.0481246\pi$
$42$	1.73197	+	0.0164012i	0.267249	+	0.00253075i
$43$			6.91669i			1.05479i	0.849621	+	0.527393i	$0.176830\pi$
$43$			6.91669i			1.05479i	−0.849621	+	0.527393i	$0.823170\pi$
$44$	2.91258			0.439088
$45$	−11.2775	−	0.213607i	−1.68115	−	0.0318426i
$46$	4.10679	+	2.47675i	0.605513	+	0.365176i
$47$			10.7687i			1.57077i	0.619008	+	0.785385i	$0.287535\pi$
$47$			10.7687i			1.57077i	−0.619008	+	0.785385i	$0.712465\pi$
$48$	1.73197	+	0.0164012i	0.249989	+	0.00236730i
$49$	−1.00000			−0.142857
$50$		−	9.13636i		−	1.29208i
$51$	11.7685	+	0.111443i	1.64792	+	0.0156052i
$52$	1.96159			0.272024
$53$	2.59988			0.357121			0.178560	−	0.983929i	$-0.442856\pi$
$53$	2.59988			0.357121			0.178560	+	0.983929i	$0.442856\pi$
$54$	0.147593	−	5.19406i	0.0200848	−	0.706821i
$55$	10.9508			1.47661
$56$	−1.00000			−0.133631
$57$	−0.0919617	+	9.71121i	−0.0121806	+	1.28628i
$58$	9.69207			1.27263
$59$		−	6.79727i		−	0.884929i	−0.896786	−	0.442465i	$-0.854104\pi$
$59$		−	6.79727i		−	0.884929i	0.896786	−	0.442465i	$-0.145896\pi$
$60$	6.51193	+	0.0616657i	0.840687	+	0.00796101i
$61$			5.64532i			0.722809i	0.932409	+	0.361405i	$0.117703\pi$
$61$			5.64532i			0.722809i	−0.932409	+	0.361405i	$0.882297\pi$
$62$			8.11540i			1.03066i
$63$	−0.0568128	+	2.99946i	−0.00715773	+	0.377897i
$64$	−1.00000			−0.125000
$65$	7.37525			0.914788
$66$	−0.0477697	+	5.04451i	−0.00588004	+	0.620936i
$67$		−	12.1031i		−	1.47863i	−0.673357	−	0.739317i	$-0.735148\pi$
$67$		−	12.1031i		−	1.47863i	0.673357	−	0.739317i	$-0.264852\pi$
$68$	−6.79484			−0.823995
$69$	−4.35702	+	7.07223i	−0.524523	+	0.851396i
$70$	−3.75984			−0.449386
$71$		−	4.18407i		−	0.496557i	−0.968689	−	0.248279i	$-0.920135\pi$
$71$		−	4.18407i		−	0.496557i	0.968689	−	0.248279i	$-0.0798648\pi$
$72$	−0.0568128	+	2.99946i	−0.00669545	+	0.353490i
$73$	−11.1705			−1.30740			−0.653702	−	0.756752i	$-0.726785\pi$
$73$	−11.1705			−1.30740			−0.653702	+	0.756752i	$0.726785\pi$
$74$	1.15756			0.134564
$75$	15.8239	+	0.149847i	1.82719	+	0.0173028i
$76$		−	5.60702i		−	0.643170i
$77$		−	2.91258i		−	0.331919i
$78$	−0.0321724	+	3.39742i	−0.00364280	+	0.384682i
$79$		−	8.47864i		−	0.953922i	−0.878925	−	0.476961i	$-0.841738\pi$
$79$		−	8.47864i		−	0.953922i	0.878925	−	0.476961i	$-0.158262\pi$
$80$	−3.75984			−0.420362
$81$	8.99354	+	0.340815i	0.999283	+	0.0378684i
$82$	−1.92878			−0.212999
$83$	−8.52673			−0.935931			−0.467965	−	0.883747i	$-0.655013\pi$
$83$	−8.52673			−0.935931			−0.467965	+	0.883747i	$0.655013\pi$
$84$	0.0164012	−	1.73197i	0.00178951	−	0.188974i
$85$	−25.5475			−2.77101
$86$	6.91669			0.745846
$87$	−0.158961	+	16.7864i	−0.0170424	+	1.79969i
$88$		−	2.91258i		−	0.310482i
$89$	−5.22396			−0.553739			−0.276869	−	0.960908i	$-0.589297\pi$
$89$	−5.22396			−0.553739			−0.276869	+	0.960908i	$0.589297\pi$
$90$	−0.213607	+	11.2775i	−0.0225161	+	1.18875i
$91$		−	1.96159i		−	0.205630i
$92$	2.47675	−	4.10679i	0.258219	−	0.428162i
$93$	−14.0557	−	0.133102i	−1.45750	−	0.0138020i
$94$	10.7687			1.11070
$95$		−	21.0815i		−	2.16291i
$96$	0.0164012	−	1.73197i	0.00167394	−	0.176769i
$97$		−	1.81206i		−	0.183986i	−0.995760	−	0.0919932i	$-0.970676\pi$
$97$		−	1.81206i		−	0.183986i	0.995760	−	0.0919932i	$-0.0293238\pi$
$98$			1.00000i			0.101015i
$99$	−8.73617	−	0.165472i	−0.878018	−	0.0166305i
$100$	−9.13636			−0.913636
$101$		−	16.3857i		−	1.63043i	−0.579156	−	0.815217i	$-0.696618\pi$
$101$		−	16.3857i		−	1.63043i	0.579156	−	0.815217i	$-0.303382\pi$
$102$	0.111443	−	11.7685i	0.0110345	−	1.16525i
$103$		−	0.710537i		−	0.0700113i	−0.999387	−	0.0350057i	$-0.988855\pi$
$103$		−	0.710537i		−	0.0700113i	0.999387	−	0.0350057i	$-0.0111449\pi$
$104$		−	1.96159i		−	0.192350i
$105$	0.0616657	−	6.51193i	0.00601795	−	0.635500i
$106$		−	2.59988i		−	0.252522i
$107$	−0.517068			−0.0499869			−0.0249934	−	0.999688i	$-0.507956\pi$
$107$	−0.517068			−0.0499869			−0.0249934	+	0.999688i	$0.507956\pi$
$108$	−5.19406	−	0.147593i	−0.499798	−	0.0142021i
$109$			16.9889i			1.62724i	0.581396	+	0.813620i	$0.302507\pi$
$109$			16.9889i			1.62724i	−0.581396	+	0.813620i	$0.697493\pi$
$110$		−	10.9508i		−	1.04412i
$111$	−0.0189854	+	2.00487i	−0.00180201	+	0.190294i
$112$			1.00000i			0.0944911i
$113$	8.98903			0.845617			0.422809	−	0.906219i	$-0.361044\pi$
$113$	8.98903			0.845617			0.422809	+	0.906219i	$0.361044\pi$
$114$	9.71121	+	0.0919617i	0.909539	+	0.00861301i
$115$	9.31216	−	15.4409i	0.868364	−	1.43987i
$116$		−	9.69207i		−	0.899886i
$117$	−5.88371	−	0.111443i	−0.543950	−	0.0103029i
$118$	−6.79727			−0.625740
$119$			6.79484i			0.622882i
$120$	0.0616657	−	6.51193i	0.00562928	−	0.594455i
$121$	−2.51689			−0.228808
$122$	5.64532			0.511103
$123$	0.0316343	−	3.34060i	0.00285237	−	0.301212i
$124$	8.11540			0.728785
$125$	−15.5520			−1.39102
$126$	2.99946	+	0.0568128i	0.267213	+	0.00506128i
$127$	8.90582			0.790263			0.395132	−	0.918624i	$-0.370699\pi$
$127$	8.90582			0.790263			0.395132	+	0.918624i	$0.370699\pi$
$128$			1.00000i			0.0883883i
$129$	−0.113442	+	11.9795i	−0.00998800	+	1.05474i
$130$		−	7.37525i		−	0.646853i
$131$			0.909360i			0.0794512i	0.999211	+	0.0397256i	$0.0126484\pi$
$131$			0.909360i			0.0794512i	−0.999211	+	0.0397256i	$0.987352\pi$
$132$	5.04451	+	0.0477697i	0.439068	+	0.00415782i
$133$	−5.60702			−0.486191
$134$	−12.1031			−1.04555
$135$	−19.5288	−	0.554925i	−1.68077	−	0.0477603i
$136$			6.79484i			0.582652i
$137$	15.6538			1.33739			0.668696	−	0.743536i	$-0.266853\pi$
$137$	15.6538			1.33739			0.668696	+	0.743536i	$0.266853\pi$
$138$	7.07223	+	4.35702i	0.602028	+	0.370894i
$139$	−13.5378			−1.14827			−0.574133	−	0.818762i	$-0.694661\pi$
$139$	−13.5378			−1.14827			−0.574133	+	0.818762i	$0.694661\pi$
$140$			3.75984i			0.317764i
$141$	−0.176619	+	18.6510i	−0.0148740	+	1.57070i
$142$	−4.18407			−0.351119
$143$	5.71328			0.477769
$144$	2.99946	+	0.0568128i	0.249955	+	0.00473440i
$145$		−	36.4406i		−	3.02623i
$146$			11.1705i			0.924474i
$147$	−1.73197	−	0.0164012i	−0.142851	−	0.00135275i
$148$		−	1.15756i		−	0.0951510i
$149$	0.967034			0.0792225			0.0396113	−	0.999215i	$-0.487388\pi$
$149$	0.967034			0.0792225			0.0396113	+	0.999215i	$0.487388\pi$
$150$	0.149847	−	15.8239i	0.0122350	−	1.29202i
$151$	12.6440			1.02895			0.514477	−	0.857504i	$-0.327986\pi$
$151$	12.6440			1.02895			0.514477	+	0.857504i	$0.327986\pi$
$152$	−5.60702			−0.454790
$153$	20.3809	+	0.386033i	1.64769	+	0.0312090i
$154$	−2.91258			−0.234702
$155$	30.5126			2.45083
$156$	3.39742	+	0.0321724i	0.272011	+	0.00257585i
$157$		−	10.6369i		−	0.848913i	−0.905448	−	0.424457i	$-0.860465\pi$
$157$		−	10.6369i		−	0.848913i	0.905448	−	0.424457i	$-0.139535\pi$
$158$	−8.47864			−0.674524
$159$	4.50292	+	0.0426410i	0.357105	+	0.00338165i
$160$			3.75984i			0.297241i
$161$	−4.10679	−	2.47675i	−0.323660	−	0.195195i
$162$	0.340815	−	8.99354i	0.0267770	−	0.706600i
$163$	6.65727			0.521438			0.260719	−	0.965415i	$-0.416040\pi$
$163$	6.65727			0.521438			0.260719	+	0.965415i	$0.416040\pi$
$164$			1.92878i			0.150613i
$165$	18.9665	+	0.179606i	1.47654	+	0.0139823i
$166$			8.52673i			0.661803i
$167$			4.68669i			0.362667i	0.983422	+	0.181333i	$0.0580413\pi$
$167$			4.68669i			0.362667i	−0.983422	+	0.181333i	$0.941959\pi$
$168$	−1.73197	−	0.0164012i	−0.133625	−	0.00126538i
$169$	−9.15217			−0.704013
$170$			25.5475i			1.95940i
$171$	−0.318551	+	16.8181i	−0.0243602	+	1.28611i
$172$		−	6.91669i		−	0.527393i
$173$			8.43183i			0.641060i	0.947238	+	0.320530i	$0.103861\pi$
$173$			8.43183i			0.641060i	−0.947238	+	0.320530i	$0.896139\pi$
$174$	16.7864	+	0.158961i	1.27257	+	0.0120508i
$175$			9.13636i			0.690644i
$176$	−2.91258			−0.219544
$177$	0.111483	−	11.7727i	0.00837959	−	0.884890i
$178$			5.22396i			0.391552i
$179$			22.4042i			1.67457i	0.546769	+	0.837283i	$0.315857\pi$
$179$			22.4042i			1.67457i	−0.546769	+	0.837283i	$0.684143\pi$
$180$	11.2775	+	0.213607i	0.840574	+	0.0159213i
$181$			18.3842i			1.36649i	0.730190	+	0.683244i	$0.239432\pi$
$181$			18.3842i			1.36649i	−0.730190	+	0.683244i	$0.760568\pi$
$182$	−1.96159			−0.145403
$183$	−0.0925898	+	9.77754i	−0.00684444	+	0.722777i
$184$	−4.10679	−	2.47675i	−0.302757	−	0.182588i
$185$		−	4.35224i		−	0.319983i
$186$	−0.133102	+	14.0557i	−0.00975952	+	1.03061i
$187$	−19.7905			−1.44722
$188$		−	10.7687i		−	0.785385i
$189$	−0.147593	+	5.19406i	−0.0107358	+	0.377812i
$190$	−21.0815			−1.52941
$191$	1.89418			0.137058			0.0685292	−	0.997649i	$-0.478169\pi$
$191$	1.89418			0.137058			0.0685292	+	0.997649i	$0.478169\pi$
$192$	−1.73197	−	0.0164012i	−0.124994	−	0.00118365i
$193$	20.2323			1.45635			0.728175	−	0.685391i	$-0.240369\pi$
$193$	20.2323			1.45635			0.728175	+	0.685391i	$0.240369\pi$
$194$	−1.81206			−0.130098
$195$	12.7737	+	0.120963i	0.914747	+	0.00866232i
$196$	1.00000			0.0714286
$197$			3.73420i			0.266051i	0.991113	+	0.133025i	$0.0424691\pi$
$197$			3.73420i			0.266051i	−0.991113	+	0.133025i	$0.957531\pi$
$198$	−0.165472	+	8.73617i	−0.0117596	+	0.620852i
$199$		−	23.8313i		−	1.68936i	−0.535275	−	0.844678i	$-0.679792\pi$
$199$		−	23.8313i		−	1.68936i	0.535275	−	0.844678i	$-0.320208\pi$
$200$			9.13636i			0.646038i
$201$	0.198506	−	20.9623i	0.0140015	−	1.47857i
$202$	−16.3857			−1.15289
$203$	−9.69207			−0.680250
$204$	−11.7685	−	0.111443i	−0.823958	−	0.00780259i
$205$			7.25191i			0.506495i
$206$	−0.710537			−0.0495055
$207$	−7.66223	+	12.1774i	−0.532562	+	0.846391i
$208$	−1.96159			−0.136012
$209$		−	16.3309i		−	1.12963i
$210$	−6.51193	−	0.0616657i	−0.449366	−	0.00425534i
$211$	−18.5758			−1.27881			−0.639405	−	0.768870i	$-0.720819\pi$
$211$	−18.5758			−1.27881			−0.639405	+	0.768870i	$0.720819\pi$
$212$	−2.59988			−0.178560
$213$	0.0686236	−	7.24669i	0.00470201	−	0.496535i
$214$			0.517068i			0.0353461i
$215$		−	26.0056i		−	1.77357i
$216$	−0.147593	+	5.19406i	−0.0100424	+	0.353411i
$217$		−	8.11540i		−	0.550910i
$218$	16.9889			1.15063
$219$	−19.3469	−	0.183209i	−1.30735	−	0.0123801i
$220$	−10.9508			−0.738304
$221$	−13.3287			−0.896584
$222$	2.00487	+	0.0189854i	0.134558	+	0.00127421i
$223$	14.5055			0.971360			0.485680	−	0.874137i	$-0.338572\pi$
$223$	14.5055			0.971360			0.485680	+	0.874137i	$0.338572\pi$
$224$	1.00000			0.0668153
$225$	27.4042	+	0.519062i	1.82694	+	0.0346041i
$226$		−	8.98903i		−	0.597942i
$227$	−21.7024			−1.44044			−0.720219	−	0.693746i	$-0.755959\pi$
$227$	−21.7024			−1.44044			−0.720219	+	0.693746i	$0.755959\pi$
$228$	0.0919617	−	9.71121i	0.00609031	−	0.643141i
$229$		−	3.74644i		−	0.247572i	−0.992309	−	0.123786i	$-0.960496\pi$
$229$		−	3.74644i		−	0.247572i	0.992309	−	0.123786i	$-0.0395036\pi$
$230$	−15.4409	−	9.31216i	−1.01814	−	0.614026i
$231$	0.0477697	−	5.04451i	0.00314301	−	0.331904i
$232$	−9.69207			−0.636315
$233$			27.9410i			1.83047i	0.402917	+	0.915237i	$0.367996\pi$
$233$			27.9410i			1.83047i	−0.402917	+	0.915237i	$0.632004\pi$
$234$	−0.111443	+	5.88371i	−0.00728528	+	0.384630i
$235$		−	40.4884i		−	2.64117i
$236$			6.79727i			0.442465i
$237$	0.139060	−	14.6848i	0.00903289	−	0.953879i
$238$	6.79484			0.440444
$239$			3.61062i			0.233552i	0.993158	+	0.116776i	$0.0372559\pi$
$239$			3.61062i			0.233552i	−0.993158	+	0.116776i	$0.962744\pi$
$240$	−6.51193	−	0.0616657i	−0.420343	−	0.00398050i
$241$		−	2.48966i		−	0.160373i	−0.996780	−	0.0801864i	$-0.974448\pi$
$241$		−	2.48966i		−	0.160373i	0.996780	−	0.0801864i	$-0.0255516\pi$
$242$			2.51689i			0.161792i
$243$	15.5710	+	0.737788i	0.998879	+	0.0473291i
$244$		−	5.64532i		−	0.361405i
$245$	3.75984			0.240207
$246$	−3.34060	−	0.0316343i	−0.212989	−	0.00201693i
$247$		−	10.9987i		−	0.699829i
$248$		−	8.11540i		−	0.515329i
$249$	−14.7681	−	0.139848i	−0.935889	−	0.00886253i
$250$			15.5520i			0.983597i
$251$	12.2344			0.772229			0.386115	−	0.922451i	$-0.373817\pi$
$251$	12.2344			0.772229			0.386115	+	0.922451i	$0.373817\pi$
$252$	0.0568128	−	2.99946i	0.00357887	−	0.188948i
$253$	7.21372	−	11.9613i	0.453523	−	0.752003i
$254$		−	8.90582i		−	0.558801i
$255$	−44.2475	−	0.419008i	−2.77089	−	0.0262393i
$256$	1.00000			0.0625000
$257$			4.65565i			0.290411i	0.989402	+	0.145206i	$0.0463844\pi$
$257$			4.65565i			0.290411i	−0.989402	+	0.145206i	$0.953616\pi$
$258$	11.9795	+	0.113442i	0.745813	+	0.00706258i
$259$	−1.15756			−0.0719274
$260$	−7.37525			−0.457394
$261$	−0.550633	+	29.0710i	−0.0340833	+	1.79945i
$262$	0.909360			0.0561805
$263$	−15.6351			−0.964104			−0.482052	−	0.876143i	$-0.660108\pi$
$263$	−15.6351			−0.964104			−0.482052	+	0.876143i	$0.660108\pi$
$264$	0.0477697	−	5.04451i	0.00294002	−	0.310468i
$265$	−9.77511			−0.600480
$266$			5.60702i			0.343789i
$267$	−9.04776	−	0.0856790i	−0.553714	−	0.00524347i
$268$			12.1031i			0.739317i
$269$			3.86709i			0.235781i	0.993027	+	0.117890i	$0.0376131\pi$
$269$			3.86709i			0.235781i	−0.993027	+	0.117890i	$0.962387\pi$
$270$	−0.554925	+	19.5288i	−0.0337716	+	1.18848i
$271$	5.44131			0.330536			0.165268	−	0.986249i	$-0.447151\pi$
$271$	5.44131			0.330536			0.165268	+	0.986249i	$0.447151\pi$
$272$	6.79484			0.411998
$273$	0.0321724	−	3.39742i	0.00194716	−	0.205621i
$274$		−	15.6538i		−	0.945680i
$275$	−26.6104			−1.60467
$276$	4.35702	−	7.07223i	0.262262	−	0.425698i
$277$	9.86313			0.592618			0.296309	−	0.955092i	$-0.404244\pi$
$277$	9.86313			0.592618			0.296309	+	0.955092i	$0.404244\pi$
$278$			13.5378i			0.811946i
$279$	−24.3418	−	0.461058i	−1.45731	−	0.0276028i
$280$	3.75984			0.224693
$281$	7.85778			0.468756			0.234378	−	0.972146i	$-0.424695\pi$
$281$	7.85778			0.468756			0.234378	+	0.972146i	$0.424695\pi$
$282$	18.6510	+	0.176619i	1.11065	+	0.0105175i
$283$			32.4964i			1.93171i	0.259080	+	0.965856i	$0.416581\pi$
$283$			32.4964i			1.93171i	−0.259080	+	0.965856i	$0.583419\pi$
$284$			4.18407i			0.248279i
$285$	0.345761	−	36.5126i	0.0204811	−	2.16282i
$286$		−	5.71328i		−	0.337834i
$287$	1.92878			0.113852
$288$	0.0568128	−	2.99946i	0.00334772	−	0.176745i
$289$	29.1698			1.71587
$290$	−36.4406			−2.13986
$291$	0.0297198	−	3.13843i	0.00174221	−	0.183978i
$292$	11.1705			0.653702
$293$	14.9756			0.874885			0.437443	−	0.899246i	$-0.355884\pi$
$293$	14.9756			0.874885			0.437443	+	0.899246i	$0.355884\pi$
$294$	−0.0164012	+	1.73197i	−0.000956535	+	0.101011i
$295$			25.5566i			1.48796i
$296$	−1.15756			−0.0672819
$297$	−15.1281	−	0.429876i	−0.877821	−	0.0249439i
$298$		−	0.967034i		−	0.0560188i
$299$	4.85836	−	8.05584i	0.280966	−	0.465881i
$300$	−15.8239	−	0.149847i	−0.913595	−	0.00865142i
$301$	−6.91669			−0.398672
$302$		−	12.6440i		−	0.727580i
$303$	0.268744	−	28.3795i	0.0154389	−	1.63036i
$304$			5.60702i			0.321585i
$305$		−	21.2255i		−	1.21537i
$306$	0.386033	−	20.3809i	0.0220681	−	1.16510i
$307$	−17.7202			−1.01135			−0.505674	−	0.862725i	$-0.668756\pi$
$307$	−17.7202			−1.01135			−0.505674	+	0.862725i	$0.668756\pi$
$308$			2.91258i			0.165960i
$309$	0.0116536	−	1.23063i	0.000662952	−	0.0700082i
$310$		−	30.5126i		−	1.73300i
$311$		−	3.26065i		−	0.184894i	−0.995718	−	0.0924471i	$-0.970531\pi$
$311$		−	3.26065i		−	0.184894i	0.995718	−	0.0924471i	$-0.0294689\pi$
$312$	0.0321724	−	3.39742i	0.00182140	−	0.192341i
$313$			7.67726i			0.433944i	0.976178	+	0.216972i	$0.0696181\pi$
$313$			7.67726i			0.433944i	−0.976178	+	0.216972i	$0.930382\pi$
$314$	−10.6369			−0.600272
$315$	0.213607	−	11.2775i	0.0120354	−	0.635414i
$316$			8.47864i			0.476961i
$317$		−	26.9273i		−	1.51239i	−0.654348	−	0.756194i	$-0.727057\pi$
$317$		−	26.9273i		−	1.51239i	0.654348	−	0.756194i	$-0.272943\pi$
$318$	0.0426410	−	4.50292i	0.00239119	−	0.252511i
$319$		−	28.2289i		−	1.58052i
$320$	3.75984			0.210181
$321$	−0.895548	−	0.00848052i	−0.0499846	−	0.000473337i
$322$	−2.47675	+	4.10679i	−0.138024	+	0.228862i
$323$			38.0988i			2.11987i
$324$	−8.99354	−	0.340815i	−0.499641	−	0.0189342i
$325$	−17.9218			−0.994122
$326$		−	6.65727i		−	0.368712i
$327$	−0.278638	+	29.4243i	−0.0154087	+	1.62717i
$328$	1.92878			0.106499
$329$	−10.7687			−0.593695
$330$	0.179606	−	18.9665i	0.00988699	−	1.04407i
$331$	−1.61003			−0.0884950			−0.0442475	−	0.999021i	$-0.514089\pi$
$331$	−1.61003			−0.0884950			−0.0442475	+	0.999021i	$0.514089\pi$
$332$	8.52673			0.467965
$333$	−0.0657643	+	3.47206i	−0.00360386	+	0.190268i
$334$	4.68669			0.256444
$335$			45.5058i			2.48625i
$336$	−0.0164012	+	1.73197i	−0.000894757	+	0.0944869i
$337$		−	28.5956i		−	1.55770i	−0.627211	−	0.778849i	$-0.715804\pi$
$337$		−	28.5956i		−	1.55770i	0.627211	−	0.778849i	$-0.284196\pi$
$338$			9.15217i			0.497812i
$339$	15.5688	+	0.147431i	0.845579	+	0.00800733i
$340$	25.5475			1.38551
$341$	23.6367			1.28000
$342$	16.8181	+	0.318551i	0.909416	+	0.0172252i
$343$		−	1.00000i		−	0.0539949i
$344$	−6.91669			−0.372923
$345$	16.3817	−	26.5904i	0.881959	−	1.43158i
$346$	8.43183			0.453298
$347$			1.97141i			0.105831i	0.998599	+	0.0529155i	$0.0168514\pi$
$347$			1.97141i			0.105831i	−0.998599	+	0.0529155i	$0.983149\pi$
$348$	0.158961	−	16.7864i	0.00852122	−	0.899846i
$349$	−31.4579			−1.68390			−0.841952	−	0.539552i	$-0.818594\pi$
$349$	−31.4579			−1.68390			−0.841952	+	0.539552i	$0.818594\pi$
$350$	9.13636			0.488359
$351$	−10.1886	−	0.289517i	−0.543828	−	0.0154533i
$352$			2.91258i			0.155241i
$353$		−	6.46986i		−	0.344356i	−0.985066	−	0.172178i	$-0.944920\pi$
$353$		−	6.46986i		−	0.344356i	0.985066	−	0.172178i	$-0.0550804\pi$
$354$	−11.7727	−	0.111483i	−0.625711	−	0.00592526i
$355$			15.7314i			0.834936i
$356$	5.22396			0.276869
$357$	−0.111443	+	11.7685i	−0.00589820	+	0.622854i
$358$	22.4042			1.18410
$359$	−6.78424			−0.358059			−0.179029	−	0.983844i	$-0.557296\pi$
$359$	−6.78424			−0.358059			−0.179029	+	0.983844i	$0.557296\pi$
$360$	0.213607	−	11.2775i	0.0112581	−	0.594376i
$361$	−12.4387			−0.654669
$362$	18.3842			0.966254
$363$	−4.35918	−	0.0412799i	−0.228798	−	0.00216663i
$364$			1.96159i			0.102815i
$365$	41.9991			2.19833
$366$	9.77754	+	0.0925898i	0.511080	+	0.00483975i
$367$		−	14.5298i		−	0.758449i	−0.925305	−	0.379224i	$-0.876191\pi$
$367$		−	14.5298i		−	0.758449i	0.925305	−	0.379224i	$-0.123809\pi$
$368$	−2.47675	+	4.10679i	−0.129109	+	0.214081i
$369$	0.109580	−	5.78531i	0.00570448	−	0.301171i
$370$	−4.35224			−0.226262
$371$			2.59988i			0.134979i
$372$	14.0557	+	0.133102i	0.728752	+	0.00690102i
$373$		−	4.17907i		−	0.216384i	−0.994130	−	0.108192i	$-0.965494\pi$
$373$		−	4.17907i		−	0.216384i	0.994130	−	0.108192i	$-0.0345061\pi$
$374$			19.7905i			1.02334i
$375$	−26.9357	−	0.255071i	−1.39095	−	0.0131718i
$376$	−10.7687			−0.555351
$377$		−	19.0119i		−	0.979161i
$378$	5.19406	+	0.147593i	0.267153	+	0.00759136i
$379$			32.6880i			1.67907i	0.543304	+	0.839536i	$0.317173\pi$
$379$			32.6880i			1.67907i	−0.543304	+	0.839536i	$0.682827\pi$
$380$			21.0815i			1.08146i
$381$	15.4246	+	0.146066i	0.790228	+	0.00748318i
$382$		−	1.89418i		−	0.0969149i
$383$	−20.2555			−1.03501			−0.517503	−	0.855681i	$-0.673138\pi$
$383$	−20.2555			−1.03501			−0.517503	+	0.855681i	$0.673138\pi$
$384$	−0.0164012	+	1.73197i	−0.000836969	+	0.0883844i
$385$			10.9508i			0.558105i
$386$		−	20.2323i		−	1.02980i
$387$	−0.392956	+	20.7464i	−0.0199751	+	1.05460i
$388$			1.81206i			0.0919932i
$389$	13.4755			0.683235			0.341618	−	0.939839i	$-0.389025\pi$
$389$	13.4755			0.683235			0.341618	+	0.939839i	$0.389025\pi$
$390$	0.120963	−	12.7737i	0.00612519	−	0.646824i
$391$	−16.8291	+	27.9050i	−0.851084	+	1.41121i
$392$		−	1.00000i		−	0.0505076i
$393$	−0.0149146	+	1.57499i	−0.000752340	+	0.0794476i
$394$	3.73420			0.188126
$395$			31.8783i			1.60397i
$396$	8.73617	+	0.165472i	0.439009	+	0.00831526i
$397$	−2.44902			−0.122913			−0.0614564	−	0.998110i	$-0.519575\pi$
$397$	−2.44902			−0.122913			−0.0614564	+	0.998110i	$0.519575\pi$
$398$	−23.8313			−1.19455
$399$	−9.71121	−	0.0919617i	−0.486169	−	0.00460385i
$400$	9.13636			0.456818
$401$	33.8855			1.69216			0.846081	−	0.533054i	$-0.178956\pi$
$401$	33.8855			1.69216			0.846081	+	0.533054i	$0.178956\pi$
$402$	−20.9623	−	0.198506i	−1.04551	−	0.00990057i
$403$	15.9191			0.792986
$404$			16.3857i			0.815217i
$405$	−33.8142	−	1.28141i	−1.68024	−	0.0636738i
$406$			9.69207i			0.481009i
$407$		−	3.37149i		−	0.167119i
$408$	−0.111443	+	11.7685i	−0.00551726	+	0.582626i
$409$	10.9939			0.543616			0.271808	−	0.962352i	$-0.412378\pi$
$409$	10.9939			0.543616			0.271808	+	0.962352i	$0.412378\pi$
$410$	7.25191			0.358146
$411$	27.1119	+	0.256740i	1.33733	+	0.0126641i
$412$			0.710537i			0.0350057i
$413$	6.79727			0.334472
$414$	12.1774	+	7.66223i	0.598489	+	0.376578i
$415$	32.0591			1.57372
$416$			1.96159i			0.0961748i
$417$	−23.4472	−	0.222037i	−1.14821	−	0.0108732i
$418$	−16.3309			−0.798770
$419$	−8.56363			−0.418361			−0.209180	−	0.977877i	$-0.567080\pi$
$419$	−8.56363			−0.418361			−0.209180	+	0.977877i	$0.567080\pi$
$420$	−0.0616657	+	6.51193i	−0.00300898	+	0.317750i
$421$		−	1.24130i		−	0.0604972i	−0.999542	−	0.0302486i	$-0.990370\pi$
$421$		−	1.24130i		−	0.0604972i	0.999542	−	0.0302486i	$-0.00962989\pi$
$422$			18.5758i			0.904256i
$423$	−0.611797	+	32.3002i	−0.0297466	+	1.57049i
$424$			2.59988i			0.126261i
$425$	62.0801			3.01133
$426$	−7.24669	−	0.0686236i	−0.351103	−	0.00332482i
$427$	−5.64532			−0.273196
$428$	0.517068			0.0249934
$429$	9.89525	+	0.0937045i	0.477747	+	0.00452410i
$430$	−26.0056			−1.25410
$431$	5.92872			0.285576			0.142788	−	0.989753i	$-0.454393\pi$
$431$	5.92872			0.285576			0.142788	+	0.989753i	$0.454393\pi$
$432$	5.19406	+	0.147593i	0.249899	+	0.00710106i
$433$			15.7746i			0.758077i	0.925381	+	0.379039i	$0.123745\pi$
$433$			15.7746i			0.758077i	−0.925381	+	0.379039i	$0.876255\pi$
$434$	−8.11540			−0.389552
$435$	0.597668	−	63.1141i	0.0286560	−	3.02609i
$436$		−	16.9889i		−	0.813620i
$437$	−23.0269	−	13.8872i	−1.10152	−	0.664314i
$438$	−0.183209	+	19.3469i	−0.00875405	+	0.924433i
$439$	22.0533			1.05255			0.526274	−	0.850315i	$-0.323589\pi$
$439$	22.0533			1.05255			0.526274	+	0.850315i	$0.323589\pi$
$440$			10.9508i			0.522060i
$441$	−2.99946	−	0.0568128i	−0.142832	−	0.00270537i
$442$			13.3287i			0.633981i
$443$		−	38.0996i		−	1.81017i	−0.425235	−	0.905083i	$-0.639809\pi$
$443$		−	38.0996i		−	1.81017i	0.425235	−	0.905083i	$-0.360191\pi$
$444$	0.0189854	−	2.00487i	0.000901006	−	0.0951468i
$445$	19.6412			0.931084
$446$		−	14.5055i		−	0.686855i
$447$	1.67488	+	0.0158605i	0.0792190	+	0.000750176i
$448$		−	1.00000i		−	0.0472456i
$449$		−	5.51144i		−	0.260101i	−0.991507	−	0.130050i	$-0.958486\pi$
$449$		−	5.51144i		−	0.260101i	0.991507	−	0.130050i	$-0.0415139\pi$
$450$	0.519062	−	27.4042i	0.0244688	−	1.29184i
$451$			5.61773i			0.264529i
$452$	−8.98903			−0.422809
$453$	21.8991	+	0.207376i	1.02891	+	0.00974339i
$454$			21.7024i			1.01854i
$455$			7.37525i			0.345757i
$456$	−9.71121	−	0.0919617i	−0.454769	−	0.00430650i
$457$			36.2557i			1.69597i	0.530019	+	0.847986i	$0.322185\pi$
$457$			36.2557i			1.69597i	−0.530019	+	0.847986i	$0.677815\pi$
$458$	−3.74644			−0.175060
$459$	35.2928	+	1.00287i	1.64733	+	0.0468099i
$460$	−9.31216	+	15.4409i	−0.434182	+	0.719933i
$461$		−	19.0070i		−	0.885245i	−0.896708	−	0.442623i	$-0.854048\pi$
$461$		−	19.0070i		−	0.885245i	0.896708	−	0.442623i	$-0.145952\pi$
$462$	−5.04451	−	0.0477697i	−0.234692	−	0.00222245i
$463$	35.5863			1.65384			0.826918	−	0.562322i	$-0.190092\pi$
$463$	35.5863			1.65384			0.826918	+	0.562322i	$0.190092\pi$
$464$			9.69207i			0.449943i
$465$	52.8470	+	0.500442i	2.45072	+	0.0232074i
$466$	27.9410			1.29434
$467$	−23.2621			−1.07644			−0.538220	−	0.842804i	$-0.680903\pi$
$467$	−23.2621			−1.07644			−0.538220	+	0.842804i	$0.680903\pi$
$468$	5.88371	+	0.111443i	0.271975	+	0.00515147i
$469$	12.1031			0.558871
$470$	−40.4884			−1.86759
$471$	0.174457	−	18.4227i	0.00803855	−	0.848875i
$472$	6.79727			0.312870
$473$		−	20.1454i		−	0.926287i
$474$	−14.6848	−	0.139060i	−0.674494	−	0.00638722i
$475$			51.2278i			2.35049i
$476$		−	6.79484i		−	0.311441i
$477$	7.79823	+	0.147706i	0.357056	+	0.00676300i
$478$	3.61062			0.165146
$479$	7.28129			0.332690			0.166345	−	0.986068i	$-0.446803\pi$
$479$	7.28129			0.332690			0.166345	+	0.986068i	$0.446803\pi$
$480$	−0.0616657	+	6.51193i	−0.00281464	+	0.297228i
$481$		−	2.27066i		−	0.103533i
$482$	−2.48966			−0.113401
$483$	−7.07223	−	4.35702i	−0.321798	−	0.198251i
$484$	2.51689			0.114404
$485$			6.81303i			0.309364i
$486$	0.737788	−	15.5710i	0.0334667	−	0.706314i
$487$	1.34485			0.0609410			0.0304705	−	0.999536i	$-0.490299\pi$
$487$	1.34485			0.0609410			0.0304705	+	0.999536i	$0.490299\pi$
$488$	−5.64532			−0.255552
$489$	11.5302	+	0.109187i	0.521415	+	0.00493761i
$490$		−	3.75984i		−	0.169852i
$491$		−	14.3278i		−	0.646606i	−0.946296	−	0.323303i	$-0.895207\pi$
$491$		−	14.3278i		−	0.646606i	0.946296	−	0.323303i	$-0.104793\pi$
$492$	−0.0316343	+	3.34060i	−0.00142618	+	0.150606i
$493$			65.8560i			2.96601i
$494$	−10.9987			−0.494854
$495$	32.8466	+	0.622146i	1.47634	+	0.0279634i
$496$	−8.11540			−0.364392
$497$	4.18407			0.187681
$498$	−0.139848	+	14.7681i	−0.00626676	+	0.661773i
$499$	8.37270			0.374814			0.187407	−	0.982282i	$-0.439992\pi$
$499$	8.37270			0.374814			0.187407	+	0.982282i	$0.439992\pi$
$500$	15.5520			0.695508
$501$	−0.0768671	+	8.11721i	−0.00343417	+	0.362650i
$502$		−	12.2344i		−	0.546048i
$503$	−9.66661			−0.431013			−0.215506	−	0.976502i	$-0.569140\pi$
$503$	−9.66661			−0.431013			−0.215506	+	0.976502i	$0.569140\pi$
$504$	−2.99946	−	0.0568128i	−0.133607	−	0.00253064i
$505$			61.6073i			2.74149i
$506$	−11.9613	−	7.21372i	−0.531747	−	0.320689i
$507$	−15.8513	−	0.150106i	−0.703981	−	0.00666645i
$508$	−8.90582			−0.395132
$509$		−	5.79201i		−	0.256726i	−0.991727	−	0.128363i	$-0.959028\pi$
$509$		−	5.79201i		−	0.256726i	0.991727	−	0.128363i	$-0.0409723\pi$
$510$	−0.419008	+	44.2475i	−0.0185540	+	1.95931i
$511$		−	11.1705i		−	0.494152i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.827557	+	29.1232i	−0.0365375	+	1.28582i
$514$	4.65565			0.205352
$515$			2.67150i			0.117720i
$516$	0.113442	−	11.9795i	0.00499400	−	0.527369i
$517$		−	31.3646i		−	1.37941i
$518$			1.15756i			0.0508604i
$519$	−0.138292	+	14.6037i	−0.00607034	+	0.641032i
$520$			7.37525i			0.323426i
$521$	15.2658			0.668809			0.334404	−	0.942430i	$-0.391465\pi$
$521$	15.2658			0.668809			0.334404	+	0.942430i	$0.391465\pi$
$522$	29.0710	+	0.550633i	1.27240	+	0.0241006i
$523$		−	8.11525i		−	0.354855i	−0.984134	−	0.177427i	$-0.943222\pi$
$523$		−	8.11525i		−	0.354855i	0.984134	−	0.177427i	$-0.0567775\pi$
$524$		−	0.909360i		−	0.0397256i
$525$	−0.149847	+	15.8239i	−0.00653986	+	0.690613i
$526$			15.6351i			0.681725i
$527$	−55.1428			−2.40206
$528$	−5.04451	−	0.0477697i	−0.219534	−	0.00207891i
$529$	−10.7314	−	20.3430i	−0.466585	−	0.884477i
$530$			9.77511i			0.424604i
$531$	0.386172	−	20.3882i	0.0167584	−	0.884771i
$532$	5.60702			0.243095
$533$			3.78348i			0.163881i
$534$	−0.0856790	+	9.04776i	−0.00370769	+	0.391535i
$535$	1.94409			0.0840504
$536$	12.1031			0.522776
$537$	−0.367455	+	38.8034i	−0.0158568	+	1.67449i
$538$	3.86709			0.166722
$539$	2.91258			0.125454
$540$	19.5288	+	0.554925i	0.840385	+	0.0238802i
$541$	30.7808			1.32337			0.661685	−	0.749782i	$-0.269841\pi$
$541$	30.7808			1.32337			0.661685	+	0.749782i	$0.269841\pi$
$542$		−	5.44131i		−	0.233724i
$543$	−0.301523	+	31.8410i	−0.0129396	+	1.36643i
$544$		−	6.79484i		−	0.291326i
$545$		−	63.8754i		−	2.73612i
$546$	−3.39742	−	0.0321724i	−0.145396	−	0.00137685i
$547$	−11.9413			−0.510574			−0.255287	−	0.966865i	$-0.582170\pi$
$547$	−11.9413			−0.510574			−0.255287	+	0.966865i	$0.582170\pi$
$548$	−15.6538			−0.668696
$549$	−0.320726	+	16.9329i	−0.0136883	+	0.722680i
$550$			26.6104i			1.13467i
$551$	−54.3437			−2.31512
$552$	−7.07223	−	4.35702i	−0.301014	−	0.185447i
$553$	8.47864			0.360548
$554$		−	9.86313i		−	0.419044i
$555$	0.0713819	−	7.53797i	0.00302999	−	0.319969i
$556$	13.5378			0.574133
$557$	26.5274			1.12400			0.562001	−	0.827136i	$-0.310032\pi$
$557$	26.5274			1.12400			0.562001	+	0.827136i	$0.310032\pi$
$558$	−0.461058	+	24.3418i	−0.0195182	+	1.03047i
$559$		−	13.5677i		−	0.573853i
$560$		−	3.75984i		−	0.158882i
$561$	−34.2766	−	0.324587i	−1.44716	−	0.0137041i
$562$		−	7.85778i		−	0.331460i
$563$	42.7093			1.79998			0.899991	−	0.435908i	$-0.143573\pi$
$563$	42.7093			1.79998			0.899991	+	0.435908i	$0.143573\pi$
$564$	0.176619	−	18.6510i	0.00743698	−	0.785350i
$565$	−33.7973			−1.42186
$566$	32.4964			1.36593
$567$	−0.340815	+	8.99354i	−0.0143129	+	0.377693i
$568$	4.18407			0.175559
$569$	22.2739			0.933770			0.466885	−	0.884318i	$-0.345376\pi$
$569$	22.2739			0.933770			0.466885	+	0.884318i	$0.345376\pi$
$570$	−36.5126	−	0.345761i	−1.52934	−	0.0144823i
$571$			18.0521i			0.755456i	0.925917	+	0.377728i	$0.123295\pi$
$571$			18.0521i			0.755456i	−0.925917	+	0.377728i	$0.876705\pi$
$572$	−5.71328			−0.238884
$573$	3.28068	+	0.0310668i	0.137052	+	0.00129783i
$574$		−	1.92878i		−	0.0805059i
$575$	−22.6285	+	37.5211i	−0.943672	+	1.56474i
$576$	−2.99946	−	0.0568128i	−0.124978	−	0.00236720i
$577$	39.2815			1.63531			0.817655	−	0.575709i	$-0.195274\pi$
$577$	39.2815			1.63531			0.817655	+	0.575709i	$0.195274\pi$
$578$		−	29.1698i		−	1.21330i
$579$	35.0417	+	0.331833i	1.45629	+	0.0137905i
$580$			36.4406i			1.51311i
$581$		−	8.52673i		−	0.353749i
$582$	−3.13843	−	0.0297198i	−0.130092	−	0.00123193i
$583$	−7.57234			−0.313614
$584$		−	11.1705i		−	0.462237i
$585$	22.1218	+	0.419009i	0.914624	+	0.0173239i
$586$		−	14.9756i		−	0.618637i
$587$		−	17.3027i		−	0.714159i	−0.934074	−	0.357079i	$-0.883773\pi$
$587$		−	17.3027i		−	0.714159i	0.934074	−	0.357079i	$-0.116227\pi$
$588$	1.73197	+	0.0164012i	0.0714254	+	0.000676373i
$589$		−	45.5033i		−	1.87493i
$590$	25.5566			1.05215
$591$	−0.0612452	+	6.46753i	−0.00251929	+	0.266039i
$592$			1.15756i			0.0475755i
$593$		−	16.9101i		−	0.694415i	−0.937788	−	0.347207i	$-0.887130\pi$
$593$		−	16.9101i		−	0.694415i	0.937788	−	0.347207i	$-0.112870\pi$
$594$	−0.429876	+	15.1281i	−0.0176380	+	0.620713i
$595$		−	25.5475i		−	1.04734i
$596$	−0.967034			−0.0396113
$597$	0.390861	−	41.2752i	0.0159969	−	1.68928i
$598$	−8.05584	−	4.85836i	−0.329428	−	0.198673i
$599$		−	0.394692i		−	0.0161267i	−0.999967	−	0.00806334i	$-0.997433\pi$
$599$		−	0.394692i		−	0.0161267i	0.999967	−	0.00806334i	$-0.00256667\pi$
$600$	−0.149847	+	15.8239i	−0.00611748	+	0.646009i
$601$	29.2241			1.19208			0.596038	−	0.802956i	$-0.296741\pi$
$601$	29.2241			1.19208			0.596038	+	0.802956i	$0.296741\pi$
$602$			6.91669i			0.281903i
$603$	0.687613	−	36.3029i	0.0280018	−	1.47837i
$604$	−12.6440			−0.514477
$605$	9.46308			0.384729
$606$	−28.3795	−	0.268744i	−1.15284	−	0.0109170i
$607$	−13.0539			−0.529842			−0.264921	−	0.964270i	$-0.585346\pi$
$607$	−13.0539			−0.529842			−0.264921	+	0.964270i	$0.585346\pi$
$608$	5.60702			0.227395
$609$	−16.7864	−	0.158961i	−0.680219	−	0.00644143i
$610$	−21.2255			−0.859394
$611$		−	21.1237i		−	0.854573i
$612$	−20.3809	−	0.386033i	−0.823847	−	0.0156045i
$613$			12.5943i			0.508679i	0.967115	+	0.254340i	$0.0818581\pi$
$613$			12.5943i			0.508679i	−0.967115	+	0.254340i	$0.918142\pi$
$614$			17.7202i			0.715131i
$615$	−0.118940	+	12.5601i	−0.00479611	+	0.506473i
$616$	2.91258			0.117351
$617$	1.60987			0.0648110			0.0324055	−	0.999475i	$-0.489683\pi$
$617$	1.60987			0.0648110			0.0324055	+	0.999475i	$0.489683\pi$
$618$	−1.23063	−	0.0116536i	−0.0495033	−	0.000468778i
$619$			26.9583i			1.08354i	0.840526	+	0.541772i	$0.182246\pi$
$619$			26.9583i			1.08354i	−0.840526	+	0.541772i	$0.817754\pi$
$620$	−30.5126			−1.22541
$621$	−13.4705	+	20.9653i	−0.540552	+	0.841310i
$622$	−3.26065			−0.130740
$623$		−	5.22396i		−	0.209294i
$624$	−3.39742	−	0.0321724i	−0.136006	−	0.00128793i
$625$	12.7913			0.511651
$626$	7.67726			0.306845
$627$	0.267846	−	28.2847i	0.0106967	−	1.12958i
$628$			10.6369i			0.424457i
$629$			7.86545i			0.313616i
$630$	−11.2775	−	0.213607i	−0.449306	−	0.00851029i
$631$		−	9.47949i		−	0.377373i	−0.982037	−	0.188686i	$-0.939577\pi$
$631$		−	9.47949i		−	0.377373i	0.982037	−	0.188686i	$-0.0604229\pi$
$632$	8.47864			0.337262
$633$	−32.1728	−	0.304665i	−1.27875	−	0.0121093i
$634$	−26.9273			−1.06942
$635$	−33.4844			−1.32879
$636$	−4.50292	−	0.0426410i	−0.178552	−	0.00169083i
$637$	1.96159			0.0777210
$638$	−28.2289			−1.11759
$639$	0.237708	−	12.5499i	0.00940360	−	0.496468i
$640$		−	3.75984i		−	0.148621i
$641$	−0.963336			−0.0380495			−0.0190247	−	0.999819i	$-0.506056\pi$
$641$	−0.963336			−0.0380495			−0.0190247	+	0.999819i	$0.506056\pi$
$642$	−0.00848052	+	0.895548i	−0.000334700	+	0.0353445i
$643$			24.8074i			0.978307i	0.872198	+	0.489154i	$0.162694\pi$
$643$			24.8074i			0.978307i	−0.872198	+	0.489154i	$0.837306\pi$
$644$	4.10679	+	2.47675i	0.161830	+	0.0975975i
$645$	0.426523	−	45.0411i	0.0167943	−	1.77349i
$646$	38.0988			1.49898
$647$			10.2055i			0.401219i	0.979671	+	0.200610i	$0.0642923\pi$
$647$			10.2055i			0.401219i	−0.979671	+	0.200610i	$0.935708\pi$
$648$	−0.340815	+	8.99354i	−0.0133885	+	0.353300i
$649$			19.7976i			0.777123i
$650$			17.9218i			0.702950i
$651$	0.133102	−	14.0557i	0.00521668	−	0.550885i
$652$	−6.65727			−0.260719
$653$		−	2.93164i		−	0.114724i	−0.998353	−	0.0573620i	$-0.981731\pi$
$653$		−	2.93164i		−	0.114724i	0.998353	−	0.0573620i	$-0.0182689\pi$
$654$	29.4243	+	0.278638i	1.15058	+	0.0108956i
$655$		−	3.41904i		−	0.133593i
$656$		−	1.92878i		−	0.0753063i
$657$	−33.5054	−	0.634625i	−1.30717	−	0.0247591i
$658$			10.7687i			0.419806i
$659$	20.2258			0.787885			0.393943	−	0.919135i	$-0.371111\pi$
$659$	20.2258			0.787885			0.393943	+	0.919135i	$0.371111\pi$
$660$	−18.9665	−	0.179606i	−0.738271	−	0.00699116i
$661$		−	16.2897i		−	0.633595i	−0.948493	−	0.316797i	$-0.897392\pi$
$661$		−	16.2897i		−	0.633595i	0.948493	−	0.316797i	$-0.102608\pi$
$662$			1.61003i			0.0625754i
$663$	−23.0849	−	0.218606i	−0.896544	−	0.00848995i
$664$		−	8.52673i		−	0.330901i
$665$	21.0815			0.817505
$666$	3.47206	+	0.0657643i	0.134540	+	0.00254831i
$667$	−39.8033	−	24.0048i	−1.54119	−	0.929470i
$668$		−	4.68669i		−	0.181333i
$669$	25.1231	+	0.237907i	0.971316	+	0.00919802i
$670$	45.5058			1.75804
$671$		−	16.4424i		−	0.634753i
$672$	1.73197	+	0.0164012i	0.0668123	+	0.000632689i
$673$	13.0727			0.503917			0.251959	−	0.967738i	$-0.418925\pi$
$673$	13.0727			0.503917			0.251959	+	0.967738i	$0.418925\pi$
$674$	−28.5956			−1.10146
$675$	47.4548	+	1.34846i	1.82653	+	0.0519023i
$676$	9.15217			0.352006
$677$	−33.0653			−1.27080			−0.635402	−	0.772181i	$-0.719166\pi$
$677$	−33.0653			−1.27080			−0.635402	+	0.772181i	$0.719166\pi$
$678$	0.147431	−	15.5688i	0.00566204	−	0.597915i
$679$	1.81206			0.0695403
$680$		−	25.5475i		−	0.979701i
$681$	−37.5880	−	0.355945i	−1.44037	−	0.0136398i
$682$		−	23.6367i		−	0.905098i
$683$			9.41997i			0.360445i	0.983626	+	0.180223i	$0.0576818\pi$
$683$			9.41997i			0.360445i	−0.983626	+	0.180223i	$0.942318\pi$
$684$	0.318551	−	16.8181i	0.0121801	−	0.643054i
$685$	−58.8556			−2.24876
$686$	−1.00000			−0.0381802
$687$	0.0614460	−	6.48873i	0.00234431	−	0.247561i
$688$			6.91669i			0.263696i
$689$	−5.09989			−0.194290
$690$	−26.5904	−	16.3817i	−1.01228	−	0.623639i
$691$	48.2614			1.83595			0.917976	−	0.396636i	$-0.129822\pi$
$691$	48.2614			1.83595			0.917976	+	0.396636i	$0.129822\pi$
$692$		−	8.43183i		−	0.320530i
$693$	0.165472	−	8.73617i	0.00628575	−	0.331860i
$694$	1.97141			0.0748339
$695$	50.9001			1.93075
$696$	−16.7864	−	0.158961i	−0.636287	−	0.00602541i
$697$		−	13.1058i		−	0.496416i
$698$			31.4579i			1.19070i
$699$	−0.458264	+	48.3930i	−0.0173332	+	1.83039i
$700$		−	9.13636i		−	0.345322i
$701$	−15.6081			−0.589509			−0.294754	−	0.955573i	$-0.595238\pi$
$701$	−15.6081			−0.589509			−0.294754	+	0.955573i	$0.595238\pi$
$702$	−0.289517	+	10.1886i	−0.0109271	+	0.384544i
$703$	−6.49048			−0.244793
$704$	2.91258			0.109772
$705$	0.664057	−	70.1248i	0.0250098	−	2.64105i
$706$	−6.46986			−0.243496
$707$	16.3857			0.616246
$708$	−0.111483	+	11.7727i	−0.00418979	+	0.442445i
$709$			14.0086i			0.526102i	0.964782	+	0.263051i	$0.0847288\pi$
$709$			14.0086i			0.526102i	−0.964782	+	0.263051i	$0.915271\pi$
$710$	15.7314			0.590389
$711$	0.481695	−	25.4314i	0.0180650	−	0.953751i
$712$		−	5.22396i		−	0.195776i
$713$	20.0998	−	33.3283i	0.752744	−	1.24815i
$714$	11.7685	+	0.111443i	0.440424	+	0.00417066i
$715$	−21.4810			−0.803344
$716$		−	22.4042i		−	0.837283i
$717$	−0.0592184	+	6.25350i	−0.00221155	+	0.233541i
$718$			6.78424i			0.253186i
$719$		−	31.1483i		−	1.16164i	−0.814034	−	0.580818i	$-0.802733\pi$
$719$		−	31.1483i		−	1.16164i	0.814034	−	0.580818i	$-0.197267\pi$
$720$	−11.2775	−	0.213607i	−0.420287	−	0.00796065i
$721$	0.710537			0.0264618
$722$			12.4387i			0.462921i
$723$	0.0408332	−	4.31202i	0.00151860	−	0.160366i
$724$		−	18.3842i		−	0.683244i
$725$			88.5502i			3.28867i
$726$	−0.0412799	+	4.35918i	−0.00153204	+	0.161784i
$727$		−	13.2332i		−	0.490791i	−0.969423	−	0.245396i	$-0.921082\pi$
$727$		−	13.2332i		−	0.490791i	0.969423	−	0.245396i	$-0.0789179\pi$
$728$	1.96159			0.0727013
$729$	26.9564	+	1.53321i	0.998386	+	0.0567856i
$730$		−	41.9991i		−	1.55446i
$731$			46.9978i			1.73828i
$732$	0.0925898	−	9.77754i	0.00342222	−	0.361388i
$733$			34.3034i			1.26703i	0.773732	+	0.633513i	$0.218388\pi$
$733$			34.3034i			1.26703i	−0.773732	+	0.633513i	$0.781612\pi$
$734$	−14.5298			−0.536304
$735$	6.51193	+	0.0616657i	0.240196	+	0.00227457i
$736$	4.10679	+	2.47675i	0.151378	+	0.0912941i
$737$			35.2514i			1.29850i
$738$	−5.78531	−	0.109580i	−0.212960	−	0.00403368i
$739$	23.4020			0.860857			0.430428	−	0.902625i	$-0.358362\pi$
$739$	23.4020			0.860857			0.430428	+	0.902625i	$0.358362\pi$
$740$			4.35224i			0.159992i
$741$	0.180391	−	19.0494i	0.00662684	−	0.699798i
$742$	2.59988			0.0954445
$743$	8.95189			0.328413			0.164206	−	0.986426i	$-0.447494\pi$
$743$	8.95189			0.328413			0.164206	+	0.986426i	$0.447494\pi$
$744$	0.133102	−	14.0557i	0.00487976	−	0.515306i
$745$	−3.63589			−0.133209
$746$	−4.17907			−0.153007
$747$	−25.5756	−	0.484427i	−0.935763	−	0.0177243i
$748$	19.7905			0.723612
$749$		−	0.517068i		−	0.0188933i
$750$	−0.255071	+	26.9357i	−0.00931389	+	0.983553i
$751$			6.78470i			0.247577i	0.992309	+	0.123789i	$0.0395045\pi$
$751$			6.78470i			0.247577i	−0.992309	+	0.123789i	$0.960496\pi$
$752$			10.7687i			0.392692i
$753$	21.1897	+	0.200659i	0.772194	+	0.00731241i
$754$	−19.0119			−0.692371
$755$	−47.5393			−1.73013
$756$	0.147593	−	5.19406i	0.00536790	−	0.188906i
$757$		−	29.8050i		−	1.08328i	−0.840610	−	0.541640i	$-0.817803\pi$
$757$		−	29.8050i		−	1.08328i	0.840610	−	0.541640i	$-0.182197\pi$
$758$	32.6880			1.18728
$759$	12.6902	−	20.5984i	0.460623	−	0.747675i
$760$	21.0815			0.764706
$761$			37.6477i			1.36473i	0.731013	+	0.682364i	$0.239048\pi$
$761$			37.6477i			1.36473i	−0.731013	+	0.682364i	$0.760952\pi$
$762$	0.146066	−	15.4246i	0.00529140	−	0.558776i
$763$	−16.9889			−0.615039
$764$	−1.89418			−0.0685292
$765$	−76.6287	−	1.45142i	−2.77051	−	0.0524763i
$766$			20.2555i			0.731860i
$767$			13.3335i			0.481443i
$768$	1.73197	+	0.0164012i	0.0624972	+	0.000591826i
$769$			1.52339i			0.0549349i	0.999623	+	0.0274675i	$0.00874427\pi$
$769$			1.52339i			0.0549349i	−0.999623	+	0.0274675i	$0.991256\pi$
$770$	10.9508			0.394640
$771$	−0.0763580	+	8.06345i	−0.00274997	+	0.290398i
$772$	−20.2323			−0.728175
$773$	−1.17579			−0.0422902			−0.0211451	−	0.999776i	$-0.506731\pi$
$773$	−1.17579			−0.0422902			−0.0211451	+	0.999776i	$0.506731\pi$
$774$	20.7464	+	0.392956i	0.745713	+	0.0141245i
$775$	−74.1452			−2.66338
$776$	1.81206			0.0650490
$777$	−2.00487	−	0.0189854i	−0.0719242	−	0.000681096i
$778$		−	13.4755i		−	0.483120i
$779$	10.8147			0.387478
$780$	−12.7737	−	0.120963i	−0.457373	−	0.00433116i
$781$			12.1864i			0.436064i
$782$	27.9050	+	16.8291i	0.997880	+	0.601807i
$783$	−1.43048	+	50.3411i	−0.0511212	+	1.79905i
$784$	−1.00000			−0.0357143
$785$			39.9928i			1.42740i
$786$	1.57499	+	0.0149146i	0.0561779	+	0.000531985i
$787$		−	28.3966i		−	1.01223i	−0.862467	−	0.506114i	$-0.831082\pi$
$787$		−	28.3966i		−	1.01223i	0.862467	−	0.506114i	$-0.168918\pi$
$788$		−	3.73420i		−	0.133025i
$789$	−27.0796	−	0.256435i	−0.964061	−	0.00912931i
$790$	31.8783			1.13418
$791$			8.98903i			0.319613i
$792$	0.165472	−	8.73617i	0.00587978	−	0.310426i
$793$		−	11.0738i		−	0.393242i
$794$			2.44902i			0.0869125i
$795$	−16.9302	−	0.160323i	−0.600453	−	0.00568608i
$796$			23.8313i			0.844678i
$797$	1.21400			0.0430020			0.0215010	−	0.999769i	$-0.493155\pi$
$797$	1.21400			0.0430020			0.0215010	+	0.999769i	$0.493155\pi$
$798$	−0.0919617	+	9.71121i	−0.00325541	+	0.343773i
$799$			73.1713i			2.58861i
$800$		−	9.13636i		−	0.323019i
$801$	−15.6691	−	0.296788i	−0.553639	−	0.0104865i
$802$		−	33.8855i		−	1.19654i
$803$	32.5349			1.14813
$804$	−0.198506	+	20.9623i	−0.00700076	+	0.739284i
$805$	15.4409	+	9.31216i	0.544219	+	0.328211i
$806$		−	15.9191i		−	0.560726i
$807$	−0.0634248	+	6.69770i	−0.00223266	+	0.235770i
$808$	16.3857			0.576445
$809$		−	1.77440i		−	0.0623845i	−0.999513	−	0.0311922i	$-0.990070\pi$
$809$		−	1.77440i		−	0.0623845i	0.999513	−	0.0311922i	$-0.00993041\pi$
$810$	−1.28141	+	33.8142i	−0.0450242	+	1.18811i
$811$	15.6730			0.550353			0.275176	−	0.961394i	$-0.411264\pi$
$811$	15.6730			0.550353			0.275176	+	0.961394i	$0.411264\pi$
$812$	9.69207			0.340125
$813$	9.42421	+	0.0892439i	0.330522	+	0.00312992i
$814$	−3.37149			−0.118171
$815$	−25.0303			−0.876771
$816$	11.7685	+	0.111443i	0.411979	+	0.00390129i
$817$	−38.7821			−1.35681
$818$		−	10.9939i		−	0.384394i
$819$	0.111443	−	5.88371i	0.00389414	−	0.205594i
$820$		−	7.25191i		−	0.253248i
$821$		−	7.20251i		−	0.251369i	−0.992070	−	0.125685i	$-0.959887\pi$
$821$		−	7.20251i		−	0.251369i	0.992070	−	0.125685i	$-0.0401128\pi$
$822$	0.256740	−	27.1119i	0.00895485	−	0.945637i
$823$	−18.1083			−0.631215			−0.315608	−	0.948890i	$-0.602208\pi$
$823$	−18.1083			−0.631215			−0.315608	+	0.948890i	$0.602208\pi$
$824$	0.710537			0.0247527
$825$	−46.0884	−	0.436441i	−1.60459	−	0.0151949i
$826$		−	6.79727i		−	0.236507i
$827$	−34.0704			−1.18474			−0.592372	−	0.805664i	$-0.701809\pi$
$827$	−34.0704			−1.18474			−0.592372	+	0.805664i	$0.701809\pi$
$828$	7.66223	−	12.1774i	0.266281	−	0.423196i
$829$	−16.2040			−0.562789			−0.281394	−	0.959592i	$-0.590797\pi$
$829$	−16.2040			−0.562789			−0.281394	+	0.959592i	$0.590797\pi$
$830$		−	32.0591i		−	1.11279i
$831$	17.0827	+	0.161767i	0.592592	+	0.00561163i
$832$	1.96159			0.0680059
$833$	−6.79484			−0.235427
$834$	−0.222037	+	23.4472i	−0.00768850	+	0.811910i
$835$		−	17.6212i		−	0.609806i
$836$			16.3309i			0.564816i
$837$	−42.1519	−	1.19778i	−1.45698	−	0.0414012i
$838$			8.56363i			0.295826i
$839$	31.9430			1.10279			0.551397	−	0.834243i	$-0.314095\pi$
$839$	31.9430			1.10279			0.551397	+	0.834243i	$0.314095\pi$
$840$	6.51193	+	0.0616657i	0.224683	+	0.00212767i
$841$	−64.9362			−2.23918
$842$	−1.24130			−0.0427779
$843$	13.6095	+	0.128877i	0.468735	+	0.00443875i
$844$	18.5758			0.639405
$845$	34.4106			1.18376
$846$	32.3002	+	0.611797i	1.11050	+	0.0210340i
$847$		−	2.51689i		−	0.0864813i
$848$	2.59988			0.0892801
$849$	−0.532979	+	56.2829i	−0.0182918	+	1.93162i
$850$		−	62.0801i		−	2.12933i
$851$	−4.75386	−	2.86699i	−0.162960	−	0.0982791i
$852$	−0.0686236	+	7.24669i	−0.00235100	+	0.248267i
$853$	−8.90089			−0.304761			−0.152380	−	0.988322i	$-0.548694\pi$
$853$	−8.90089			−0.304761			−0.152380	+	0.988322i	$0.548694\pi$
$854$			5.64532i			0.193179i
$855$	1.19770	−	63.2331i	0.0409604	−	2.16253i
$856$		−	0.517068i		−	0.0176730i
$857$			12.2337i			0.417894i	0.977927	+	0.208947i	$0.0670036\pi$
$857$			12.2337i			0.417894i	−0.977927	+	0.208947i	$0.932996\pi$
$858$	0.0937045	−	9.89525i	0.00319902	−	0.337818i
$859$	−28.4355			−0.970207			−0.485103	−	0.874457i	$-0.661218\pi$
$859$	−28.4355			−0.970207			−0.485103	+	0.874457i	$0.661218\pi$
$860$			26.0056i			0.886785i
$861$	3.34060	+	0.0316343i	0.113847	+	0.00107809i
$862$		−	5.92872i		−	0.201933i
$863$			9.56460i			0.325583i	0.986661	+	0.162791i	$0.0520497\pi$
$863$			9.56460i			0.325583i	−0.986661	+	0.162791i	$0.947950\pi$
$864$	0.147593	−	5.19406i	0.00502121	−	0.176705i
$865$		−	31.7023i		−	1.07791i
$866$	15.7746			0.536042
$867$	50.5213	+	0.478419i	1.71579	+	0.0162480i
$868$			8.11540i			0.275455i
$869$			24.6947i			0.837711i
$870$	−63.1141	−	0.597668i	−2.13977	−	0.0202628i
$871$			23.7414i			0.804447i
$872$	−16.9889			−0.575317
$873$	0.102948	−	5.43519i	0.00348426	−	0.183953i
$874$	−13.8872	+	23.0269i	−0.469741	+	0.778895i
$875$		−	15.5520i		−	0.525755i
$876$	19.3469	+	0.183209i	0.653673	+	0.00619005i
$877$	43.0851			1.45488			0.727439	−	0.686172i	$-0.240710\pi$
$877$	43.0851			1.45488			0.727439	+	0.686172i	$0.240710\pi$
$878$		−	22.0533i		−	0.744264i
$879$	25.9374	+	0.245618i	0.874846	+	0.00828448i
$880$	10.9508			0.369152
$881$	−15.8920			−0.535416			−0.267708	−	0.963500i	$-0.586266\pi$
$881$	−15.8920			−0.535416			−0.267708	+	0.963500i	$0.586266\pi$
$882$	−0.0568128	+	2.99946i	−0.00191299	+	0.100997i
$883$	27.2750			0.917876			0.458938	−	0.888468i	$-0.348230\pi$
$883$	27.2750			0.917876			0.458938	+	0.888468i	$0.348230\pi$
$884$	13.3287			0.448292
$885$	−0.419158	+	44.2634i	−0.0140899	+	1.48790i
$886$	−38.0996			−1.27998
$887$			47.4716i			1.59394i	0.604018	+	0.796970i	$0.293565\pi$
$887$			47.4716i			1.59394i	−0.604018	+	0.796970i	$0.706435\pi$
$888$	−2.00487	−	0.0189854i	−0.0672789	−	0.000637107i
$889$			8.90582i			0.298691i
$890$		−	19.6412i		−	0.658375i
$891$	−26.1944	−	0.992652i	−0.877546	−	0.0332551i
$892$	−14.5055			−0.485680
$893$	−60.3801			−2.02054
$894$	0.0158605	−	1.67488i	0.000530454	−	0.0560163i
$895$		−	84.2360i		−	2.81570i
$896$	−1.00000			−0.0334077
$897$	8.54668	−	13.8728i	0.285365	−	0.463200i
$898$	−5.51144			−0.183919
$899$		−	78.6550i		−	2.62329i
$900$	−27.4042	−	0.519062i	−0.913472	−	0.0173021i
$901$	17.6657			0.588531
$902$	5.61773			0.187050
$903$	−11.9795	−	0.113442i	−0.398654	−	0.00377511i
$904$			8.98903i			0.298971i
$905$		−	69.1217i		−	2.29768i
$906$	0.207376	−	21.8991i	0.00688962	−	0.727548i
$907$			17.5002i			0.581084i	0.956862	+	0.290542i	$0.0938356\pi$
$907$			17.5002i			0.581084i	−0.956862	+	0.290542i	$0.906164\pi$
$908$	21.7024			0.720219
$909$	0.930914	−	49.1481i	0.0308765	−	1.63014i
$910$	7.37525			0.244487
$911$	−39.1015			−1.29549			−0.647745	−	0.761857i	$-0.724288\pi$
$911$	−39.1015			−1.29549			−0.647745	+	0.761857i	$0.724288\pi$
$912$	−0.0919617	+	9.71121i	−0.00304516	+	0.321570i
$913$	24.8348			0.821911
$914$	36.2557			1.19923
$915$	0.348123	−	36.7620i	0.0115086	−	1.21531i
$916$			3.74644i			0.123786i
$917$	−0.909360			−0.0300297
$918$	1.00287	−	35.2928i	0.0330996	−	1.16483i
$919$			16.9676i			0.559708i	0.960043	+	0.279854i	$0.0902861\pi$
$919$			16.9676i			0.559708i	−0.960043	+	0.279854i	$0.909714\pi$
$920$	15.4409	+	9.31216i	0.509070	+	0.307013i
$921$	−30.6910	−	0.290633i	−1.01130	−	0.00957667i
$922$	−19.0070			−0.625963
$923$			8.20742i			0.270151i
$924$	−0.0477697	+	5.04451i	−0.00157151	+	0.165952i
$925$			10.5759i			0.347734i
$926$		−	35.5863i		−	1.16944i
$927$	0.0403676	−	2.13123i	0.00132585	−	0.0699988i
$928$	9.69207			0.318158
$929$		−	30.7568i		−	1.00910i	−0.863384	−	0.504548i	$-0.831659\pi$
$929$		−	30.7568i		−	1.00910i	0.863384	−	0.504548i	$-0.168341\pi$
$930$	0.500442	−	52.8470i	0.0164101	−	1.73292i
$931$		−	5.60702i		−	0.183763i
$932$		−	27.9410i		−	0.915237i
$933$	0.0534784	−	5.64735i	0.00175080	−	0.184886i
$934$			23.2621i			0.761159i
$935$	74.4090			2.43343
$936$	0.111443	−	5.88371i	0.00364264	−	0.192315i
$937$			3.88226i			0.126828i	0.997987	+	0.0634139i	$0.0201988\pi$
$937$			3.88226i			0.126828i	−0.997987	+	0.0634139i	$0.979801\pi$
$938$		−	12.1031i		−	0.395182i
$939$	−0.125916	+	13.2968i	−0.00410911	+	0.433925i
$940$			40.4884i			1.32059i
$941$	13.3044			0.433711			0.216856	−	0.976204i	$-0.430420\pi$
$941$	13.3044			0.433711			0.216856	+	0.976204i	$0.430420\pi$
$942$	−18.4227	−	0.174457i	−0.600245	−	0.00568411i
$943$	7.92111	+	4.77711i	0.257947	+	0.155564i
$944$		−	6.79727i		−	0.221232i
$945$	0.554925	−	19.5288i	0.0180517	−	0.635272i
$946$	−20.1454			−0.654984
$947$			15.5661i			0.505831i	0.967488	+	0.252915i	$0.0813894\pi$
$947$			15.5661i			0.505831i	−0.967488	+	0.252915i	$0.918611\pi$
$948$	−0.139060	+	14.6848i	−0.00451645	+	0.476939i
$949$	21.9119			0.711289
$950$	51.2278			1.66205
$951$	0.441639	−	46.6373i	0.0143211	−	1.51232i
$952$	−6.79484			−0.220222
$953$	−47.8577			−1.55026			−0.775132	−	0.631800i	$-0.782317\pi$
$953$	−47.8577			−1.55026			−0.775132	+	0.631800i	$0.782317\pi$
$954$	0.147706	−	7.79823i	0.00478216	−	0.252477i
$955$	−7.12182			−0.230457
$956$		−	3.61062i		−	0.116776i
$957$	0.462987	−	48.8917i	0.0149662	−	1.58044i
$958$		−	7.28129i		−	0.235248i
$959$			15.6538i			0.505487i
$960$	6.51193	+	0.0616657i	0.210172	+	0.00199025i
$961$	34.8598			1.12451
$962$	−2.27066			−0.0732091
$963$	−1.55093	−	0.0293761i	−0.0499779	−	0.000946631i
$964$			2.48966i			0.0801864i
$965$	−76.0700			−2.44878
$966$	−4.35702	+	7.07223i	−0.140185	+	0.227545i
$967$	−47.2500			−1.51946			−0.759729	−	0.650240i	$-0.774668\pi$
$967$	−47.2500			−1.51946			−0.759729	+	0.650240i	$0.774668\pi$
$968$		−	2.51689i		−	0.0808958i
$969$	−0.624865	+	65.9861i	−0.0200736	+	2.11978i
$970$	6.81303			0.218753
$971$	−20.1037			−0.645157			−0.322579	−	0.946543i	$-0.604550\pi$
$971$	−20.1037			−0.645157			−0.322579	+	0.946543i	$0.604550\pi$
$972$	−15.5710	−	0.737788i	−0.499440	−	0.0236646i
$973$		−	13.5378i		−	0.434004i
$974$		−	1.34485i		−	0.0430918i
$975$	−31.0401	−	0.293938i	−0.994077	−	0.00941356i
$976$			5.64532i			0.180702i
$977$	39.0200			1.24836			0.624179	−	0.781281i	$-0.285433\pi$
$977$	39.0200			1.24836			0.624179	+	0.781281i	$0.285433\pi$
$978$	0.109187	−	11.5302i	0.00349142	−	0.368696i
$979$	15.2152			0.486280
$980$	−3.75984			−0.120104
$981$	−0.965186	+	50.9575i	−0.0308160	+	1.62695i
$982$	−14.3278			−0.457219
$983$	−48.4332			−1.54478			−0.772389	−	0.635149i	$-0.780939\pi$
$983$	−48.4332			−1.54478			−0.772389	+	0.635149i	$0.780939\pi$
$984$	3.34060	+	0.0316343i	0.106494	+	0.00100846i
$985$		−	14.0400i		−	0.447350i
$986$	65.8560			2.09728
$987$	−18.6510	−	0.176619i	−0.593669	−	0.00562183i
$988$			10.9987i			0.349915i
$989$	−28.4054	−	17.1309i	−0.903239	−	0.544731i
$990$	0.622146	−	32.8466i	0.0197731	−	1.04393i
$991$	39.5830			1.25739			0.628697	−	0.777650i	$-0.283589\pi$
$991$	39.5830			1.25739			0.628697	+	0.777650i	$0.283589\pi$
$992$			8.11540i			0.257664i
$993$	−2.78852	−	0.0264063i	−0.0884911	−	0.000837979i
$994$		−	4.18407i		−	0.132710i
$995$			89.6017i			2.84057i
$996$	14.7681	+	0.139848i	0.467944	+	0.00443127i
$997$	29.0363			0.919588			0.459794	−	0.888025i	$-0.347923\pi$
$997$	29.0363			0.919588			0.459794	+	0.888025i	$0.347923\pi$
$998$		−	8.37270i		−	0.265033i
$999$	−0.170848	+	6.01244i	−0.00540539	+	0.190225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.h.a.827.12	✓	24
3.2	odd	2		966.2.h.b.827.24	yes	24
23.22	odd	2		966.2.h.b.827.12	yes	24
69.68	even	2	inner	966.2.h.a.827.24	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.h.a.827.12	✓	24	1.1	even	1	trivial
966.2.h.a.827.24	yes	24	69.68	even	2	inner
966.2.h.b.827.12	yes	24	23.22	odd	2
966.2.h.b.827.24	yes	24	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.73197 + 0.0164012i) q^{3} -1.00000 q^{4} -3.75984 q^{5} +(0.0164012 - 1.73197i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(2.99946 + 0.0568128i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.73197 + 0.0164012i) q^{3} -1.00000 q^{4} -3.75984 q^{5} +(0.0164012 - 1.73197i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(2.99946 + 0.0568128i) q^{9} +3.75984i q^{10} -2.91258 q^{11} +(-1.73197 - 0.0164012i) q^{12} -1.96159 q^{13} +1.00000 q^{14} +(-6.51193 - 0.0616657i) q^{15} +1.00000 q^{16} +6.79484 q^{17} +(0.0568128 - 2.99946i) q^{18} +5.60702i q^{19} +3.75984 q^{20} +(-0.0164012 + 1.73197i) q^{21} +2.91258i q^{22} +(-2.47675 + 4.10679i) q^{23} +(-0.0164012 + 1.73197i) q^{24} +9.13636 q^{25} +1.96159i q^{26} +(5.19406 + 0.147593i) q^{27} -1.00000i q^{28} +9.69207i q^{29} +(-0.0616657 + 6.51193i) q^{30} -8.11540 q^{31} -1.00000i q^{32} +(-5.04451 - 0.0477697i) q^{33} -6.79484i q^{34} -3.75984i q^{35} +(-2.99946 - 0.0568128i) q^{36} +1.15756i q^{37} +5.60702 q^{38} +(-3.39742 - 0.0321724i) q^{39} -3.75984i q^{40} -1.92878i q^{41} +(1.73197 + 0.0164012i) q^{42} +6.91669i q^{43} +2.91258 q^{44} +(-11.2775 - 0.213607i) q^{45} +(4.10679 + 2.47675i) q^{46} +10.7687i q^{47} +(1.73197 + 0.0164012i) q^{48} -1.00000 q^{49} -9.13636i q^{50} +(11.7685 + 0.111443i) q^{51} +1.96159 q^{52} +2.59988 q^{53} +(0.147593 - 5.19406i) q^{54} +10.9508 q^{55} -1.00000 q^{56} +(-0.0919617 + 9.71121i) q^{57} +9.69207 q^{58} -6.79727i q^{59} +(6.51193 + 0.0616657i) q^{60} +5.64532i q^{61} +8.11540i q^{62} +(-0.0568128 + 2.99946i) q^{63} -1.00000 q^{64} +7.37525 q^{65} +(-0.0477697 + 5.04451i) q^{66} -12.1031i q^{67} -6.79484 q^{68} +(-4.35702 + 7.07223i) q^{69} -3.75984 q^{70} -4.18407i q^{71} +(-0.0568128 + 2.99946i) q^{72} -11.1705 q^{73} +1.15756 q^{74} +(15.8239 + 0.149847i) q^{75} -5.60702i q^{76} -2.91258i q^{77} +(-0.0321724 + 3.39742i) q^{78} -8.47864i q^{79} -3.75984 q^{80} +(8.99354 + 0.340815i) q^{81} -1.92878 q^{82} -8.52673 q^{83} +(0.0164012 - 1.73197i) q^{84} -25.5475 q^{85} +6.91669 q^{86} +(-0.158961 + 16.7864i) q^{87} -2.91258i q^{88} -5.22396 q^{89} +(-0.213607 + 11.2775i) q^{90} -1.96159i q^{91} +(2.47675 - 4.10679i) q^{92} +(-14.0557 - 0.133102i) q^{93} +10.7687 q^{94} -21.0815i q^{95} +(0.0164012 - 1.73197i) q^{96} -1.81206i q^{97} +1.00000i q^{98} +(-8.73617 - 0.165472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9	\( 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9} - 4 q^{12} + 8 q^{13} + 24 q^{14} - 4 q^{15} + 24 q^{16} + 32 q^{17} + 4 q^{18} + 4 q^{20} - 8 q^{23} - 12 q^{25} + 16 q^{27} - 4 q^{30} - 16 q^{31} + 20 q^{33} + 4 q^{36} - 8 q^{39} + 4 q^{42} + 24 q^{45} - 4 q^{46} + 4 q^{48} - 24 q^{49} + 24 q^{51} - 8 q^{52} + 24 q^{53} - 12 q^{54} + 16 q^{55} - 24 q^{56} + 4 q^{57} + 4 q^{58} + 4 q^{60} - 4 q^{63} - 24 q^{64} - 12 q^{66} - 32 q^{68} - 24 q^{69} - 4 q^{70} - 4 q^{72} - 32 q^{73} - 16 q^{74} + 48 q^{75} + 12 q^{78} - 4 q^{80} - 8 q^{81} - 8 q^{82} + 16 q^{83} - 16 q^{85} + 16 q^{86} + 20 q^{87} + 24 q^{89} - 28 q^{90} + 8 q^{92} + 16 q^{93} + 8 q^{94} - 48 q^{99}+O(q^{100}) \) 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9 - 4 * q^12 + 8 * q^13 + 24 * q^14 - 4 * q^15 + 24 * q^16 + 32 * q^17 + 4 * q^18 + 4 * q^20 - 8 * q^23 - 12 * q^25 + 16 * q^27 - 4 * q^30 - 16 * q^31 + 20 * q^33 + 4 * q^36 - 8 * q^39 + 4 * q^42 + 24 * q^45 - 4 * q^46 + 4 * q^48 - 24 * q^49 + 24 * q^51 - 8 * q^52 + 24 * q^53 - 12 * q^54 + 16 * q^55 - 24 * q^56 + 4 * q^57 + 4 * q^58 + 4 * q^60 - 4 * q^63 - 24 * q^64 - 12 * q^66 - 32 * q^68 - 24 * q^69 - 4 * q^70 - 4 * q^72 - 32 * q^73 - 16 * q^74 + 48 * q^75 + 12 * q^78 - 4 * q^80 - 8 * q^81 - 8 * q^82 + 16 * q^83 - 16 * q^85 + 16 * q^86 + 20 * q^87 + 24 * q^89 - 28 * q^90 + 8 * q^92 + 16 * q^93 + 8 * q^94 - 48 * q^99

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