LMFDB - Embedded newform 966.2.h.a.827.5

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			827.5
Character	$\chi$	$=$	966.827
Dual form			966.2.h.a.827.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.529264 - 1.64921i) q^{3} -1.00000 q^{4} -2.93995 q^{5} +(-1.64921 + 0.529264i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(-2.43976 + 1.74573i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.529264 - 1.64921i) q^{3} -1.00000 q^{4} -2.93995 q^{5} +(-1.64921 + 0.529264i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(-2.43976 + 1.74573i) q^{9} +2.93995i q^{10} -2.76188 q^{11} +(0.529264 + 1.64921i) q^{12} +4.19891 q^{13} +1.00000 q^{14} +(1.55601 + 4.84858i) q^{15} +1.00000 q^{16} -1.10783 q^{17} +(1.74573 + 2.43976i) q^{18} +4.25362i q^{19} +2.93995 q^{20} +(1.64921 - 0.529264i) q^{21} +2.76188i q^{22} +(2.65936 - 3.99096i) q^{23} +(1.64921 - 0.529264i) q^{24} +3.64330 q^{25} -4.19891i q^{26} +(4.17035 + 3.09971i) q^{27} -1.00000i q^{28} -0.175217i q^{29} +(4.84858 - 1.55601i) q^{30} +3.49565 q^{31} -1.00000i q^{32} +(1.46176 + 4.55490i) q^{33} +1.10783i q^{34} -2.93995i q^{35} +(2.43976 - 1.74573i) q^{36} -1.18840i q^{37} +4.25362 q^{38} +(-2.22233 - 6.92486i) q^{39} -2.93995i q^{40} +6.45300i q^{41} +(-0.529264 - 1.64921i) q^{42} +5.95249i q^{43} +2.76188 q^{44} +(7.17276 - 5.13236i) q^{45} +(-3.99096 - 2.65936i) q^{46} -6.79656i q^{47} +(-0.529264 - 1.64921i) q^{48} -1.00000 q^{49} -3.64330i q^{50} +(0.586336 + 1.82704i) q^{51} -4.19891 q^{52} +7.44927 q^{53} +(3.09971 - 4.17035i) q^{54} +8.11978 q^{55} -1.00000 q^{56} +(7.01509 - 2.25129i) q^{57} -0.175217 q^{58} +10.5842i q^{59} +(-1.55601 - 4.84858i) q^{60} +5.65397i q^{61} -3.49565i q^{62} +(-1.74573 - 2.43976i) q^{63} -1.00000 q^{64} -12.3446 q^{65} +(4.55490 - 1.46176i) q^{66} -7.63070i q^{67} +1.10783 q^{68} +(-7.98942 - 2.27356i) q^{69} -2.93995 q^{70} +5.46979i q^{71} +(-1.74573 - 2.43976i) q^{72} -5.68482 q^{73} -1.18840 q^{74} +(-1.92827 - 6.00855i) q^{75} -4.25362i q^{76} -2.76188i q^{77} +(-6.92486 + 2.22233i) q^{78} +0.0580516i q^{79} -2.93995 q^{80} +(2.90484 - 8.51833i) q^{81} +6.45300 q^{82} +17.1295 q^{83} +(-1.64921 + 0.529264i) q^{84} +3.25697 q^{85} +5.95249 q^{86} +(-0.288969 + 0.0927362i) q^{87} -2.76188i q^{88} -7.60139 q^{89} +(-5.13236 - 7.17276i) q^{90} +4.19891i q^{91} +(-2.65936 + 3.99096i) q^{92} +(-1.85013 - 5.76505i) q^{93} -6.79656 q^{94} -12.5054i q^{95} +(-1.64921 + 0.529264i) q^{96} +1.20123i q^{97} +1.00000i q^{98} +(6.73831 - 4.82150i) 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
$3$	−0.529264	−	1.64921i	−0.305571	−	0.952169i
$3$	−0.529264	−	1.64921i	−0.305571	−	0.952169i
$4$	−1.00000			−0.500000
$5$	−2.93995			−1.31478			−0.657392	−	0.753548i	$-0.728341\pi$
$5$	−2.93995			−1.31478			−0.657392	+	0.753548i	$0.728341\pi$
$6$	−1.64921	+	0.529264i	−0.673285	+	0.216071i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$			1.00000i			0.353553i
$9$	−2.43976	+	1.74573i	−0.813253	+	0.581911i
$10$			2.93995i			0.929693i
$11$	−2.76188			−0.832738			−0.416369	−	0.909196i	$-0.636697\pi$
$11$	−2.76188			−0.832738			−0.416369	+	0.909196i	$0.636697\pi$
$12$	0.529264	+	1.64921i	0.152785	+	0.476085i
$13$	4.19891			1.16457			0.582284	−	0.812986i	$-0.302159\pi$
$13$	4.19891			1.16457			0.582284	+	0.812986i	$0.302159\pi$
$14$	1.00000			0.267261
$15$	1.55601	+	4.84858i	0.401760	+	1.25190i
$16$	1.00000			0.250000
$17$	−1.10783			−0.268688			−0.134344	−	0.990935i	$-0.542893\pi$
$17$	−1.10783			−0.268688			−0.134344	+	0.990935i	$0.542893\pi$
$18$	1.74573	+	2.43976i	0.411473	+	0.575057i
$19$			4.25362i			0.975847i	0.872886	+	0.487923i	$0.162245\pi$
$19$			4.25362i			0.975847i	−0.872886	+	0.487923i	$0.837755\pi$
$20$	2.93995			0.657392
$21$	1.64921	−	0.529264i	0.359886	−	0.115495i
$22$			2.76188i			0.588834i
$23$	2.65936	−	3.99096i	0.554516	−	0.832173i
$23$	2.65936	−	3.99096i	0.554516	−	0.832173i
$24$	1.64921	−	0.529264i	0.336643	−	0.108036i
$25$	3.64330			0.728660
$26$		−	4.19891i		−	0.823474i
$27$	4.17035	+	3.09971i	0.802584	+	0.596539i
$28$		−	1.00000i		−	0.188982i
$29$		−	0.175217i		−	0.0325370i	−0.999868	−	0.0162685i	$-0.994821\pi$
$29$		−	0.175217i		−	0.0325370i	0.999868	−	0.0162685i	$-0.00517865\pi$
$30$	4.84858	−	1.55601i	0.885225	−	0.284087i
$31$	3.49565			0.627838			0.313919	−	0.949450i	$-0.398358\pi$
$31$	3.49565			0.627838			0.313919	+	0.949450i	$0.398358\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.46176	+	4.55490i	0.254460	+	0.792907i
$34$			1.10783i			0.189991i
$35$		−	2.93995i		−	0.496942i
$36$	2.43976	−	1.74573i	0.406626	−	0.290955i
$37$		−	1.18840i		−	0.195372i	−0.995217	−	0.0976858i	$-0.968856\pi$
$37$		−	1.18840i		−	0.195372i	0.995217	−	0.0976858i	$-0.0311440\pi$
$38$	4.25362			0.690028
$39$	−2.22233	−	6.92486i	−0.355858	−	1.10887i
$40$		−	2.93995i		−	0.464847i
$41$			6.45300i			1.00779i	0.863765	+	0.503894i	$0.168100\pi$
$41$			6.45300i			1.00779i	−0.863765	+	0.503894i	$0.831900\pi$
$42$	−0.529264	−	1.64921i	−0.0816673	−	0.254478i
$43$			5.95249i			0.907746i	0.891066	+	0.453873i	$0.149958\pi$
$43$			5.95249i			0.907746i	−0.891066	+	0.453873i	$0.850042\pi$
$44$	2.76188			0.416369
$45$	7.17276	−	5.13236i	1.06925	−	0.765087i
$46$	−3.99096	−	2.65936i	−0.588435	−	0.392102i
$47$		−	6.79656i		−	0.991380i	−0.868500	−	0.495690i	$-0.834915\pi$
$47$		−	6.79656i		−	0.991380i	0.868500	−	0.495690i	$-0.165085\pi$
$48$	−0.529264	−	1.64921i	−0.0763927	−	0.238042i
$49$	−1.00000			−0.142857
$50$		−	3.64330i		−	0.515240i
$51$	0.586336	+	1.82704i	0.0821034	+	0.255837i
$52$	−4.19891			−0.582284
$53$	7.44927			1.02324			0.511618	−	0.859213i	$-0.329046\pi$
$53$	7.44927			1.02324			0.511618	+	0.859213i	$0.329046\pi$
$54$	3.09971	−	4.17035i	0.421817	−	0.567513i
$55$	8.11978			1.09487
$56$	−1.00000			−0.133631
$57$	7.01509	−	2.25129i	0.929171	−	0.298190i
$58$	−0.175217			−0.0230071
$59$			10.5842i			1.37795i	0.724784	+	0.688976i	$0.241939\pi$
$59$			10.5842i			1.37795i	−0.724784	+	0.688976i	$0.758061\pi$
$60$	−1.55601	−	4.84858i	−0.200880	−	0.625949i
$61$			5.65397i			0.723917i	0.932194	+	0.361958i	$0.117892\pi$
$61$			5.65397i			0.723917i	−0.932194	+	0.361958i	$0.882108\pi$
$62$		−	3.49565i		−	0.443948i
$63$	−1.74573	−	2.43976i	−0.219942	−	0.307381i
$64$	−1.00000			−0.125000
$65$	−12.3446			−1.53116
$66$	4.55490	−	1.46176i	0.560670	−	0.179931i
$67$		−	7.63070i		−	0.932238i	−0.884722	−	0.466119i	$-0.845652\pi$
$67$		−	7.63070i		−	0.932238i	0.884722	−	0.466119i	$-0.154348\pi$
$68$	1.10783			0.134344
$69$	−7.98942	−	2.27356i	−0.961814	−	0.273705i
$70$	−2.93995			−0.351391
$71$			5.46979i			0.649145i	0.945861	+	0.324573i	$0.105220\pi$
$71$			5.46979i			0.649145i	−0.945861	+	0.324573i	$0.894780\pi$
$72$	−1.74573	−	2.43976i	−0.205736	−	0.287528i
$73$	−5.68482			−0.665358			−0.332679	−	0.943040i	$-0.607953\pi$
$73$	−5.68482			−0.665358			−0.332679	+	0.943040i	$0.607953\pi$
$74$	−1.18840			−0.138149
$75$	−1.92827	−	6.00855i	−0.222657	−	0.693807i
$76$		−	4.25362i		−	0.487923i
$77$		−	2.76188i		−	0.314745i
$78$	−6.92486	+	2.22233i	−0.784086	+	0.251630i
$79$			0.0580516i			0.00653132i	0.999995	+	0.00326566i	$0.00103949\pi$
$79$			0.0580516i			0.00653132i	−0.999995	+	0.00326566i	$0.998961\pi$
$80$	−2.93995			−0.328696
$81$	2.90484	−	8.51833i	0.322760	−	0.946481i
$82$	6.45300			0.712614
$83$	17.1295			1.88020			0.940102	−	0.340892i	$-0.110729\pi$
$83$	17.1295			1.88020			0.940102	+	0.340892i	$0.110729\pi$
$84$	−1.64921	+	0.529264i	−0.179943	+	0.0577475i
$85$	3.25697			0.353268
$86$	5.95249			0.641873
$87$	−0.288969	+	0.0927362i	−0.0309807	+	0.00994236i
$88$		−	2.76188i		−	0.294417i
$89$	−7.60139			−0.805746			−0.402873	−	0.915256i	$-0.631988\pi$
$89$	−7.60139			−0.805746			−0.402873	+	0.915256i	$0.631988\pi$
$90$	−5.13236	−	7.17276i	−0.540998	−	0.756076i
$91$			4.19891i			0.440165i
$92$	−2.65936	+	3.99096i	−0.277258	+	0.416087i
$93$	−1.85013	−	5.76505i	−0.191849	−	0.597808i
$94$	−6.79656			−0.701011
$95$		−	12.5054i		−	1.28303i
$96$	−1.64921	+	0.529264i	−0.168321	+	0.0540178i
$97$			1.20123i			0.121967i	0.998139	+	0.0609833i	$0.0194236\pi$
$97$			1.20123i			0.121967i	−0.998139	+	0.0609833i	$0.980576\pi$
$98$			1.00000i			0.101015i
$99$	6.73831	−	4.82150i	0.677226	−	0.484579i
$100$	−3.64330			−0.364330
$101$			17.5633i			1.74761i	0.486273	+	0.873807i	$0.338356\pi$
$101$			17.5633i			1.74761i	−0.486273	+	0.873807i	$0.661644\pi$
$102$	1.82704	−	0.586336i	0.180904	−	0.0580559i
$103$			20.1540i			1.98583i	0.118806	+	0.992917i	$0.462093\pi$
$103$			20.1540i			1.98583i	−0.118806	+	0.992917i	$0.537907\pi$
$104$			4.19891i			0.411737i
$105$	−4.84858	+	1.55601i	−0.473173	+	0.151851i
$106$		−	7.44927i		−	0.723537i
$107$	5.02539			0.485823			0.242911	−	0.970048i	$-0.421898\pi$
$107$	5.02539			0.485823			0.242911	+	0.970048i	$0.421898\pi$
$108$	−4.17035	−	3.09971i	−0.401292	−	0.298270i
$109$			0.467060i			0.0447363i	0.999750	+	0.0223681i	$0.00712059\pi$
$109$			0.467060i			0.0447363i	−0.999750	+	0.0223681i	$0.992879\pi$
$110$		−	8.11978i		−	0.774191i
$111$	−1.95991	+	0.628977i	−0.186027	+	0.0596999i
$112$			1.00000i			0.0944911i
$113$	1.09365			0.102882			0.0514411	−	0.998676i	$-0.483619\pi$
$113$	1.09365			0.102882			0.0514411	+	0.998676i	$0.483619\pi$
$114$	−2.25129	−	7.01509i	−0.210853	−	0.657023i
$115$	−7.81839	+	11.7332i	−0.729069	+	1.09413i
$116$			0.175217i			0.0162685i
$117$	−10.2443	+	7.33017i	−0.947088	+	0.677674i
$118$	10.5842			0.974359
$119$		−	1.10783i		−	0.101555i
$120$	−4.84858	+	1.55601i	−0.442613	+	0.142044i
$121$	−3.37203			−0.306548
$122$	5.65397			0.511887
$123$	10.6423	−	3.41534i	0.959585	−	0.307951i
$124$	−3.49565			−0.313919
$125$	3.98864			0.356754
$126$	−2.43976	+	1.74573i	−0.217351	+	0.155522i
$127$	5.30179			0.470458			0.235229	−	0.971940i	$-0.424416\pi$
$127$	5.30179			0.470458			0.235229	+	0.971940i	$0.424416\pi$
$128$			1.00000i			0.0883883i
$129$	9.81688	−	3.15044i	0.864328	−	0.277381i
$130$			12.3446i			1.08269i
$131$		−	1.94272i		−	0.169736i	−0.996392	−	0.0848682i	$-0.972953\pi$
$131$		−	1.94272i		−	0.169736i	0.996392	−	0.0848682i	$-0.0270469\pi$
$132$	−1.46176	−	4.55490i	−0.127230	−	0.396454i
$133$	−4.25362			−0.368835
$134$	−7.63070			−0.659192
$135$	−12.2606	−	9.11298i	−1.05523	−	0.784321i
$136$		−	1.10783i		−	0.0949957i
$137$	−18.6531			−1.59364			−0.796821	−	0.604216i	$-0.793487\pi$
$137$	−18.6531			−1.59364			−0.796821	+	0.604216i	$0.793487\pi$
$138$	−2.27356	+	7.98942i	−0.193539	+	0.680105i
$139$	16.5936			1.40745			0.703723	−	0.710474i	$-0.251519\pi$
$139$	16.5936			1.40745			0.703723	+	0.710474i	$0.251519\pi$
$140$			2.93995i			0.248471i
$141$	−11.2089	+	3.59718i	−0.943961	+	0.302937i
$142$	5.46979			0.459015
$143$	−11.5969			−0.969779
$144$	−2.43976	+	1.74573i	−0.203313	+	0.145478i
$145$			0.515129i			0.0427792i
$146$			5.68482i			0.470479i
$147$	0.529264	+	1.64921i	0.0436530	+	0.136024i
$148$			1.18840i			0.0976858i
$149$	2.34195			0.191860			0.0959300	−	0.995388i	$-0.469417\pi$
$149$	2.34195			0.191860			0.0959300	+	0.995388i	$0.469417\pi$
$150$	−6.00855	+	1.92827i	−0.490596	+	0.157442i
$151$	−5.80992			−0.472805			−0.236402	−	0.971655i	$-0.575968\pi$
$151$	−5.80992			−0.472805			−0.236402	+	0.971655i	$0.575968\pi$
$152$	−4.25362			−0.345014
$153$	2.70284	−	1.93398i	0.218512	−	0.156353i
$154$	−2.76188			−0.222558
$155$	−10.2770			−0.825472
$156$	2.22233	+	6.92486i	0.177929	+	0.554433i
$157$			1.93235i			0.154218i	0.997023	+	0.0771091i	$0.0245690\pi$
$157$			1.93235i			0.154218i	−0.997023	+	0.0771091i	$0.975431\pi$
$158$	0.0580516			0.00461834
$159$	−3.94264	−	12.2854i	−0.312671	−	0.974294i
$160$			2.93995i			0.232423i
$161$	3.99096	+	2.65936i	0.314532	+	0.209587i
$162$	−8.51833	−	2.90484i	−0.669263	−	0.228226i
$163$	18.1179			1.41910			0.709552	−	0.704653i	$-0.248897\pi$
$163$	18.1179			1.41910			0.709552	+	0.704653i	$0.248897\pi$
$164$		−	6.45300i		−	0.503894i
$165$	−4.29751	−	13.3912i	−0.334561	−	1.04250i
$166$		−	17.1295i		−	1.32951i
$167$			23.9731i			1.85509i	0.373707	+	0.927547i	$0.378087\pi$
$167$			23.9731i			1.85509i	−0.373707	+	0.927547i	$0.621913\pi$
$168$	0.529264	+	1.64921i	0.0408336	+	0.127239i
$169$	4.63084			0.356218
$170$		−	3.25697i		−	0.249798i
$171$	−7.42568	−	10.3778i	−0.567856	−	0.793610i
$172$		−	5.95249i		−	0.453873i
$173$			14.4444i			1.09819i	0.835761	+	0.549094i	$0.185027\pi$
$173$			14.4444i			1.09819i	−0.835761	+	0.549094i	$0.814973\pi$
$174$	0.0927362	+	0.288969i	0.00703031	+	0.0219067i
$175$			3.64330i			0.275407i
$176$	−2.76188			−0.208184
$177$	17.4556	−	5.60187i	1.31204	−	0.421062i
$178$			7.60139i			0.569749i
$179$		−	2.52408i		−	0.188659i	−0.995541	−	0.0943293i	$-0.969929\pi$
$179$		−	2.52408i		−	0.188659i	0.995541	−	0.0943293i	$-0.0300707\pi$
$180$	−7.17276	+	5.13236i	−0.534626	+	0.382544i
$181$		−	5.19145i		−	0.385877i	−0.981211	−	0.192939i	$-0.938198\pi$
$181$		−	5.19145i		−	0.385877i	0.981211	−	0.192939i	$-0.0618018\pi$
$182$	4.19891			0.311244
$183$	9.32456	−	2.99245i	0.689291	−	0.221208i
$184$	3.99096	+	2.65936i	0.294218	+	0.196051i
$185$			3.49383i			0.256872i
$186$	−5.76505	+	1.85013i	−0.422714	+	0.135658i
$187$	3.05969			0.223747
$188$			6.79656i			0.495690i
$189$	−3.09971	+	4.17035i	−0.225471	+	0.303348i
$190$	−12.5054			−0.907238
$191$	−19.8064			−1.43314			−0.716569	−	0.697516i	$-0.754288\pi$
$191$	−19.8064			−1.43314			−0.716569	+	0.697516i	$0.754288\pi$
$192$	0.529264	+	1.64921i	0.0381964	+	0.119021i
$193$	14.8163			1.06650			0.533250	−	0.845957i	$-0.320970\pi$
$193$	14.8163			1.06650			0.533250	+	0.845957i	$0.320970\pi$
$194$	1.20123			0.0862434
$195$	6.53355	+	20.3587i	0.467877	+	1.45792i
$196$	1.00000			0.0714286
$197$			9.11484i			0.649405i	0.945816	+	0.324703i	$0.105264\pi$
$197$			9.11484i			0.649405i	−0.945816	+	0.324703i	$0.894736\pi$
$198$	−4.82150	−	6.73831i	−0.342649	−	0.478871i
$199$			22.7356i			1.61169i	0.592129	+	0.805843i	$0.298288\pi$
$199$			22.7356i			1.61169i	−0.592129	+	0.805843i	$0.701712\pi$
$200$			3.64330i			0.257620i
$201$	−12.5846	+	4.03866i	−0.887649	+	0.284865i
$202$	17.5633			1.23575
$203$	0.175217			0.0122978
$204$	−0.586336	−	1.82704i	−0.0410517	−	0.127918i
$205$		−	18.9715i		−	1.32503i
$206$	20.1540			1.40420
$207$	0.478944	+	14.3795i	0.0332889	+	0.999446i
$208$	4.19891			0.291142
$209$		−	11.7480i		−	0.812624i
$210$	1.55601	+	4.84858i	0.107375	+	0.334584i
$211$	21.4366			1.47576			0.737878	−	0.674934i	$-0.235828\pi$
$211$	21.4366			1.47576			0.737878	+	0.674934i	$0.235828\pi$
$212$	−7.44927			−0.511618
$213$	9.02082	−	2.89497i	0.618096	−	0.198360i
$214$		−	5.02539i		−	0.343529i
$215$		−	17.5000i		−	1.19349i
$216$	−3.09971	+	4.17035i	−0.210908	+	0.283756i
$217$			3.49565i			0.237300i
$218$	0.467060			0.0316333
$219$	3.00878	+	9.37544i	0.203314	+	0.633534i
$220$	−8.11978			−0.547435
$221$	−4.65168			−0.312906
$222$	0.628977	+	1.95991i	0.0422142	+	0.131541i
$223$	−12.4533			−0.833936			−0.416968	−	0.908921i	$-0.636907\pi$
$223$	−12.4533			−0.833936			−0.416968	+	0.908921i	$0.636907\pi$
$224$	1.00000			0.0668153
$225$	−8.88877	+	6.36022i	−0.592584	+	0.424015i
$226$		−	1.09365i		−	0.0727487i
$227$	−11.3592			−0.753938			−0.376969	−	0.926226i	$-0.623034\pi$
$227$	−11.3592			−0.753938			−0.376969	+	0.926226i	$0.623034\pi$
$228$	−7.01509	+	2.25129i	−0.464586	+	0.149095i
$229$		−	14.2353i		−	0.940696i	−0.882481	−	0.470348i	$-0.844128\pi$
$229$		−	14.2353i		−	0.940696i	0.882481	−	0.470348i	$-0.155872\pi$
$230$	11.7332	+	7.81839i	0.773666	+	0.515530i
$231$	−4.55490	+	1.46176i	−0.299691	+	0.0961770i
$232$	0.175217			0.0115036
$233$		−	11.2440i		−	0.736621i	−0.929703	−	0.368310i	$-0.879936\pi$
$233$		−	11.2440i		−	0.736621i	0.929703	−	0.368310i	$-0.120064\pi$
$234$	7.33017	+	10.2443i	0.479188	+	0.669692i
$235$			19.9815i			1.30345i
$236$		−	10.5842i		−	0.688976i
$237$	0.0957390	−	0.0307247i	0.00621892	−	0.00199578i
$238$	−1.10783			−0.0718100
$239$			15.1549i			0.980286i	0.871642	+	0.490143i	$0.163055\pi$
$239$			15.1549i			0.980286i	−0.871642	+	0.490143i	$0.836945\pi$
$240$	1.55601	+	4.84858i	0.100440	+	0.312974i
$241$		−	16.6422i		−	1.07202i	−0.844213	−	0.536008i	$-0.819932\pi$
$241$		−	16.6422i		−	1.07202i	0.844213	−	0.536008i	$-0.180068\pi$
$242$			3.37203i			0.216762i
$243$	−15.5859	−	0.282230i	−0.999836	−	0.0181051i
$244$		−	5.65397i		−	0.361958i
$245$	2.93995			0.187826
$246$	−3.41534	−	10.6423i	−0.217754	−	0.678529i
$247$			17.8606i			1.13644i
$248$			3.49565i			0.221974i
$249$	−9.06602	−	28.2500i	−0.574536	−	1.79027i
$250$		−	3.98864i		−	0.252263i
$251$	19.8406			1.25233			0.626165	−	0.779691i	$-0.284624\pi$
$251$	19.8406			1.25233			0.626165	+	0.779691i	$0.284624\pi$
$252$	1.74573	+	2.43976i	0.109971	+	0.153690i
$253$	−7.34484	+	11.0226i	−0.461766	+	0.692982i
$254$		−	5.30179i		−	0.332664i
$255$	−1.72380	−	5.37141i	−0.107948	−	0.336370i
$256$	1.00000			0.0625000
$257$			3.81449i			0.237941i	0.992898	+	0.118971i	$0.0379595\pi$
$257$			3.81449i			0.237941i	−0.992898	+	0.118971i	$0.962041\pi$
$258$	−3.15044	−	9.81688i	−0.196138	−	0.611172i
$259$	1.18840			0.0738435
$260$	12.3446			0.765578
$261$	0.305882	+	0.427487i	0.0189336	+	0.0264608i
$262$	−1.94272			−0.120022
$263$	−18.9610			−1.16919			−0.584594	−	0.811326i	$-0.698746\pi$
$263$	−18.9610			−1.16919			−0.584594	+	0.811326i	$0.698746\pi$
$264$	−4.55490	+	1.46176i	−0.280335	+	0.0899654i
$265$	−21.9005			−1.34534
$266$			4.25362i			0.260806i
$267$	4.02315	+	12.5363i	0.246213	+	0.767207i
$268$			7.63070i			0.466119i
$269$		−	5.20882i		−	0.317588i	−0.987312	−	0.158794i	$-0.949239\pi$
$269$		−	5.20882i		−	0.317588i	0.987312	−	0.158794i	$-0.0507605\pi$
$270$	−9.11298	+	12.2606i	−0.554599	+	0.746157i
$271$	−26.4064			−1.60407			−0.802036	−	0.597275i	$-0.796250\pi$
$271$	−26.4064			−1.60407			−0.802036	+	0.597275i	$0.796250\pi$
$272$	−1.10783			−0.0671721
$273$	6.92486	−	2.22233i	0.419112	−	0.134502i
$274$			18.6531i			1.12687i
$275$	−10.0623			−0.606782
$276$	7.98942	+	2.27356i	0.480907	+	0.136852i
$277$	6.42416			0.385991			0.192995	−	0.981200i	$-0.438180\pi$
$277$	6.42416			0.385991			0.192995	+	0.981200i	$0.438180\pi$
$278$		−	16.5936i		−	0.995215i
$279$	−8.52855	+	6.10247i	−0.510591	+	0.365346i
$280$	2.93995			0.175696
$281$	−17.8452			−1.06456			−0.532279	−	0.846569i	$-0.678664\pi$
$281$	−17.8452			−1.06456			−0.532279	+	0.846569i	$0.678664\pi$
$282$	3.59718	+	11.2089i	0.214209	+	0.667481i
$283$			17.5725i			1.04457i	0.852770	+	0.522287i	$0.174921\pi$
$283$			17.5725i			1.04457i	−0.852770	+	0.522287i	$0.825079\pi$
$284$		−	5.46979i		−	0.324573i
$285$	−20.6240	+	6.61867i	−1.22166	+	0.392056i
$286$			11.5969i			0.685738i
$287$	−6.45300			−0.380908
$288$	1.74573	+	2.43976i	0.102868	+	0.143764i
$289$	−15.7727			−0.927807
$290$	0.515129			0.0302494
$291$	1.98108	−	0.635770i	0.116133	−	0.0372695i
$292$	5.68482			0.332679
$293$	−22.0435			−1.28780			−0.643899	−	0.765111i	$-0.722684\pi$
$293$	−22.0435			−1.28780			−0.643899	+	0.765111i	$0.722684\pi$
$294$	1.64921	−	0.529264i	0.0961836	−	0.0308673i
$295$		−	31.1171i		−	1.81171i
$296$	1.18840			0.0690743
$297$	−11.5180	−	8.56102i	−0.668342	−	0.496761i
$298$		−	2.34195i		−	0.135666i
$299$	11.1664	−	16.7577i	0.645771	−	0.969122i
$300$	1.92827	+	6.00855i	0.111329	+	0.346904i
$301$	−5.95249			−0.343096
$302$			5.80992i			0.334323i
$303$	28.9655	−	9.29563i	1.66402	−	0.534020i
$304$			4.25362i			0.243962i
$305$		−	16.6224i		−	0.951795i
$306$	−1.93398	−	2.70284i	−0.110558	−	0.154511i
$307$	−21.7371			−1.24060			−0.620300	−	0.784365i	$-0.712989\pi$
$307$	−21.7371			−1.24060			−0.620300	+	0.784365i	$0.712989\pi$
$308$			2.76188i			0.157373i
$309$	33.2381	−	10.6668i	1.89085	−	0.606814i
$310$			10.2770i			0.583697i
$311$			16.8422i			0.955034i	0.878623	+	0.477517i	$0.158463\pi$
$311$			16.8422i			0.955034i	−0.878623	+	0.477517i	$0.841537\pi$
$312$	6.92486	−	2.22233i	0.392043	−	0.125815i
$313$		−	31.1434i		−	1.76033i	−0.474668	−	0.880165i	$-0.657432\pi$
$313$		−	31.1434i		−	1.76033i	0.474668	−	0.880165i	$-0.342568\pi$
$314$	1.93235			0.109049
$315$	5.13236	+	7.17276i	0.289176	+	0.404139i
$316$		−	0.0580516i		−	0.00326566i
$317$		−	14.0232i		−	0.787619i	−0.919192	−	0.393810i	$-0.871157\pi$
$317$		−	14.0232i		−	0.787619i	0.919192	−	0.393810i	$-0.128843\pi$
$318$	−12.2854	+	3.94264i	−0.688930	+	0.221092i
$319$			0.483928i			0.0270948i
$320$	2.93995			0.164348
$321$	−2.65976	−	8.28790i	−0.148453	−	0.462585i
$322$	2.65936	−	3.99096i	0.148201	−	0.222408i
$323$		−	4.71229i		−	0.262199i
$324$	−2.90484	+	8.51833i	−0.161380	+	0.473240i
$325$	15.2979			0.848573
$326$		−	18.1179i		−	1.00346i
$327$	0.770279	−	0.247198i	0.0425965	−	0.0136701i
$328$	−6.45300			−0.356307
$329$	6.79656			0.374706
$330$	−13.3912	+	4.29751i	−0.737161	+	0.236570i
$331$	−4.89731			−0.269180			−0.134590	−	0.990901i	$-0.542972\pi$
$331$	−4.89731			−0.269180			−0.134590	+	0.990901i	$0.542972\pi$
$332$	−17.1295			−0.940102
$333$	2.07463	+	2.89941i	0.113689	+	0.158886i
$334$	23.9731			1.31175
$335$			22.4339i			1.22569i
$336$	1.64921	−	0.529264i	0.0899715	−	0.0288737i
$337$			7.89252i			0.429933i	0.976621	+	0.214967i	$0.0689642\pi$
$337$			7.89252i			0.429933i	−0.976621	+	0.214967i	$0.931036\pi$
$338$		−	4.63084i		−	0.251884i
$339$	−0.578832	−	1.80366i	−0.0314378	−	0.0979613i
$340$	−3.25697			−0.176634
$341$	−9.65457			−0.522824
$342$	−10.3778	+	7.42568i	−0.561167	+	0.401535i
$343$		−	1.00000i		−	0.0539949i
$344$	−5.95249			−0.320937
$345$	23.4885	+	6.68416i	1.26458	+	0.359863i
$346$	14.4444			0.776536
$347$			10.0714i			0.540664i	0.962767	+	0.270332i	$0.0871334\pi$
$347$			10.0714i			0.540664i	−0.962767	+	0.270332i	$0.912867\pi$
$348$	0.288969	−	0.0927362i	0.0154904	−	0.00497118i
$349$	−27.5013			−1.47211			−0.736056	−	0.676921i	$-0.763314\pi$
$349$	−27.5013			−1.47211			−0.736056	+	0.676921i	$0.763314\pi$
$350$	3.64330			0.194742
$351$	17.5109	+	13.0154i	0.934663	+	0.694710i
$352$			2.76188i			0.147209i
$353$		−	14.2582i		−	0.758887i	−0.925215	−	0.379443i	$-0.876116\pi$
$353$		−	14.2582i		−	0.758887i	0.925215	−	0.379443i	$-0.123884\pi$
$354$	−5.60187	−	17.4556i	−0.297736	−	0.927754i
$355$		−	16.0809i		−	0.853486i
$356$	7.60139			0.402873
$357$	−1.82704	+	0.586336i	−0.0966973	+	0.0310322i
$358$	−2.52408			−0.133402
$359$	34.5522			1.82359			0.911797	−	0.410641i	$-0.134695\pi$
$359$	34.5522			1.82359			0.911797	+	0.410641i	$0.134695\pi$
$360$	5.13236	+	7.17276i	0.270499	+	0.378038i
$361$	0.906736			0.0477229
$362$	−5.19145			−0.272856
$363$	1.78470	+	5.56117i	0.0936722	+	0.291886i
$364$		−	4.19891i		−	0.220083i
$365$	16.7131			0.874803
$366$	−2.99245	−	9.32456i	−0.156418	−	0.487403i
$367$		−	19.9066i		−	1.03912i	−0.854435	−	0.519559i	$-0.826096\pi$
$367$		−	19.9066i		−	1.03912i	0.854435	−	0.519559i	$-0.173904\pi$
$368$	2.65936	−	3.99096i	0.138629	−	0.208043i
$369$	−11.2652	−	15.7437i	−0.586443	−	0.819587i
$370$	3.49383			0.181636
$371$			7.44927i			0.386747i
$372$	1.85013	+	5.76505i	0.0959245	+	0.298904i
$373$			2.54169i			0.131604i	0.997833	+	0.0658018i	$0.0209605\pi$
$373$			2.54169i			0.131604i	−0.997833	+	0.0658018i	$0.979039\pi$
$374$		−	3.05969i		−	0.158213i
$375$	−2.11104	−	6.57808i	−0.109014	−	0.339691i
$376$	6.79656			0.350506
$377$		−	0.735721i		−	0.0378915i
$378$	4.17035	+	3.09971i	0.214500	+	0.159432i
$379$		−	15.6116i		−	0.801916i	−0.916096	−	0.400958i	$-0.868677\pi$
$379$		−	15.6116i		−	0.801916i	0.916096	−	0.400958i	$-0.131323\pi$
$380$			12.5054i			0.641514i
$381$	−2.80605	−	8.74374i	−0.143758	−	0.447955i
$382$			19.8064i			1.01338i
$383$	29.5137			1.50808			0.754041	−	0.656827i	$-0.228102\pi$
$383$	29.5137			1.50808			0.754041	+	0.656827i	$0.228102\pi$
$384$	1.64921	−	0.529264i	0.0841607	−	0.0270089i
$385$			8.11978i			0.413822i
$386$		−	14.8163i		−	0.754130i
$387$	−10.3915	−	14.5226i	−0.528227	−	0.738227i
$388$		−	1.20123i		−	0.0609833i
$389$	20.6672			1.04787			0.523933	−	0.851759i	$-0.324464\pi$
$389$	20.6672			1.04787			0.523933	+	0.851759i	$0.324464\pi$
$390$	20.3587	−	6.53355i	1.03091	−	0.330839i
$391$	−2.94613	+	4.42131i	−0.148992	+	0.223595i
$392$		−	1.00000i		−	0.0505076i
$393$	−3.20395	+	1.02821i	−0.161618	+	0.0518665i
$394$	9.11484			0.459199
$395$		−	0.170669i		−	0.00858728i
$396$	−6.73831	+	4.82150i	−0.338613	+	0.242289i
$397$	26.9895			1.35457			0.677283	−	0.735722i	$-0.263157\pi$
$397$	26.9895			1.35457			0.677283	+	0.735722i	$0.263157\pi$
$398$	22.7356			1.13963
$399$	2.25129	+	7.01509i	0.112705	+	0.351194i
$400$	3.64330			0.182165
$401$	3.73823			0.186678			0.0933392	−	0.995634i	$-0.470246\pi$
$401$	3.73823			0.186678			0.0933392	+	0.995634i	$0.470246\pi$
$402$	4.03866	+	12.5846i	0.201430	+	0.627662i
$403$	14.6779			0.731160
$404$		−	17.5633i		−	0.873807i
$405$	−8.54008	+	25.0434i	−0.424360	+	1.24442i
$406$		−	0.175217i		−	0.00869588i
$407$			3.28221i			0.162693i
$408$	−1.82704	+	0.586336i	−0.0904520	+	0.0290279i
$409$	−13.4666			−0.665880			−0.332940	−	0.942948i	$-0.608041\pi$
$409$	−13.4666			−0.665880			−0.332940	+	0.942948i	$0.608041\pi$
$410$	−18.9715			−0.936934
$411$	9.87242	+	30.7628i	0.486971	+	1.51742i
$412$		−	20.1540i		−	0.992917i
$413$	−10.5842			−0.520817
$414$	14.3795	−	0.478944i	0.706715	−	0.0235388i
$415$	−50.3598			−2.47206
$416$		−	4.19891i		−	0.205868i
$417$	−8.78238	−	27.3662i	−0.430075	−	1.34013i
$418$	−11.7480			−0.574612
$419$	15.2868			0.746807			0.373404	−	0.927669i	$-0.378191\pi$
$419$	15.2868			0.746807			0.373404	+	0.927669i	$0.378191\pi$
$420$	4.84858	−	1.55601i	0.236586	−	0.0759255i
$421$		−	23.3600i		−	1.13849i	−0.822166	−	0.569247i	$-0.807235\pi$
$421$		−	23.3600i		−	1.13849i	0.822166	−	0.569247i	$-0.192765\pi$
$422$		−	21.4366i		−	1.04352i
$423$	11.8650	+	16.5820i	0.576894	+	0.806242i
$424$			7.44927i			0.361769i
$425$	−4.03616			−0.195782
$426$	−2.89497	−	9.02082i	−0.140262	−	0.437060i
$427$	−5.65397			−0.273615
$428$	−5.02539			−0.242911
$429$	6.13781	+	19.1256i	0.296336	+	0.923394i
$430$	−17.5000			−0.843926
$431$	−37.9168			−1.82639			−0.913195	−	0.407523i	$-0.866393\pi$
$431$	−37.9168			−1.82639			−0.913195	+	0.407523i	$0.866393\pi$
$432$	4.17035	+	3.09971i	0.200646	+	0.149135i
$433$		−	31.4169i		−	1.50980i	−0.655840	−	0.754900i	$-0.727685\pi$
$433$		−	31.4169i		−	1.50980i	0.655840	−	0.754900i	$-0.272315\pi$
$434$	3.49565			0.167797
$435$	0.849554	−	0.272640i	0.0407330	−	0.0130721i
$436$		−	0.467060i		−	0.0223681i
$437$	16.9760	+	11.3119i	0.812074	+	0.541123i
$438$	9.37544	−	3.00878i	0.447976	−	0.143765i
$439$	31.5071			1.50375			0.751877	−	0.659304i	$-0.229149\pi$
$439$	31.5071			1.50375			0.751877	+	0.659304i	$0.229149\pi$
$440$			8.11978i			0.387095i
$441$	2.43976	−	1.74573i	0.116179	−	0.0831301i
$442$			4.65168i			0.221258i
$443$			22.4686i			1.06752i	0.845637	+	0.533758i	$0.179221\pi$
$443$			22.4686i			1.06752i	−0.845637	+	0.533758i	$0.820779\pi$
$444$	1.95991	−	0.628977i	0.0930134	−	0.0298499i
$445$	22.3477			1.05938
$446$			12.4533i			0.589682i
$447$	−1.23951	−	3.86236i	−0.0586269	−	0.182683i
$448$		−	1.00000i		−	0.0472456i
$449$		−	15.3982i		−	0.726685i	−0.931656	−	0.363342i	$-0.881636\pi$
$449$		−	15.3982i		−	0.726685i	0.931656	−	0.363342i	$-0.118364\pi$
$450$	6.36022	+	8.88877i	0.299824	+	0.419020i
$451$		−	17.8224i		−	0.839223i
$452$	−1.09365			−0.0514411
$453$	3.07498	+	9.58175i	0.144475	+	0.450190i
$454$			11.3592i			0.533114i
$455$		−	12.3446i		−	0.578723i
$456$	2.25129	+	7.01509i	0.105426	+	0.328512i
$457$			12.4120i			0.580609i	0.956934	+	0.290305i	$0.0937566\pi$
$457$			12.4120i			0.580609i	−0.956934	+	0.290305i	$0.906243\pi$
$458$	−14.2353			−0.665173
$459$	−4.62004	−	3.43395i	−0.215645	−	0.160283i
$460$	7.81839	−	11.7332i	0.364535	−	0.547064i
$461$			16.4149i			0.764516i	0.924056	+	0.382258i	$0.124853\pi$
$461$			16.4149i			0.764516i	−0.924056	+	0.382258i	$0.875147\pi$
$462$	1.46176	+	4.55490i	0.0680074	+	0.211913i
$463$	25.3435			1.17781			0.588906	−	0.808202i	$-0.299559\pi$
$463$	25.3435			1.17781			0.588906	+	0.808202i	$0.299559\pi$
$464$		−	0.175217i		−	0.00813425i
$465$	5.43927	+	16.9490i	0.252240	+	0.785989i
$466$	−11.2440			−0.520870
$467$	−10.3499			−0.478938			−0.239469	−	0.970904i	$-0.576973\pi$
$467$	−10.3499			−0.478938			−0.239469	+	0.970904i	$0.576973\pi$
$468$	10.2443	−	7.33017i	0.473544	−	0.338837i
$469$	7.63070			0.352353
$470$	19.9815			0.921679
$471$	3.18684	−	1.02272i	0.146842	−	0.0471246i
$472$	−10.5842			−0.487179
$473$		−	16.4401i		−	0.755914i
$474$	−0.0307247	−	0.0957390i	−0.00141123	−	0.00439744i
$475$			15.4972i			0.711060i
$476$			1.10783i			0.0507773i
$477$	−18.1744	+	13.0044i	−0.832150	+	0.595432i
$478$	15.1549			0.693167
$479$	27.8033			1.27037			0.635183	−	0.772362i	$-0.280925\pi$
$479$	27.8033			1.27037			0.635183	+	0.772362i	$0.280925\pi$
$480$	4.84858	−	1.55601i	0.221306	−	0.0710218i
$481$		−	4.98998i		−	0.227523i
$482$	−16.6422			−0.758030
$483$	2.27356	−	7.98942i	0.103451	−	0.363531i
$484$	3.37203			0.153274
$485$		−	3.53156i		−	0.160360i
$486$	−0.282230	+	15.5859i	−0.0128022	+	0.706991i
$487$	−41.0490			−1.86011			−0.930054	−	0.367423i	$-0.880240\pi$
$487$	−41.0490			−1.86011			−0.930054	+	0.367423i	$0.880240\pi$
$488$	−5.65397			−0.255943
$489$	−9.58917	−	29.8802i	−0.433637	−	1.35123i
$490$		−	2.93995i		−	0.132813i
$491$		−	2.46099i		−	0.111063i	−0.998457	−	0.0555315i	$-0.982315\pi$
$491$		−	2.46099i		−	0.111063i	0.998457	−	0.0555315i	$-0.0176853\pi$
$492$	−10.6423	+	3.41534i	−0.479793	+	0.153975i
$493$			0.194111i			0.00874231i
$494$	17.8606			0.803584
$495$	−19.8103	+	14.1750i	−0.890407	+	0.637117i
$496$	3.49565			0.156959
$497$	−5.46979			−0.245354
$498$	−28.2500	+	9.06602i	−1.26591	+	0.406258i
$499$	25.0436			1.12110			0.560552	−	0.828119i	$-0.310589\pi$
$499$	25.0436			1.12110			0.560552	+	0.828119i	$0.310589\pi$
$500$	−3.98864			−0.178377
$501$	39.5366	−	12.6881i	1.76636	−	0.566863i
$502$		−	19.8406i		−	0.885531i
$503$	−2.37989			−0.106114			−0.0530570	−	0.998591i	$-0.516897\pi$
$503$	−2.37989			−0.106114			−0.0530570	+	0.998591i	$0.516897\pi$
$504$	2.43976	−	1.74573i	0.108675	−	0.0777611i
$505$		−	51.6352i		−	2.29774i
$506$	11.0226	+	7.34484i	0.490012	+	0.326518i
$507$	−2.45094	−	7.63720i	−0.108850	−	0.339180i
$508$	−5.30179			−0.235229
$509$		−	19.5840i		−	0.868047i	−0.900902	−	0.434024i	$-0.857093\pi$
$509$		−	19.5840i		−	0.868047i	0.900902	−	0.434024i	$-0.142907\pi$
$510$	−5.37141	+	1.72380i	−0.237850	+	0.0763310i
$511$		−	5.68482i		−	0.251482i
$512$		−	1.00000i		−	0.0441942i
$513$	−13.1850	+	17.7391i	−0.582131	+	0.783199i
$514$	3.81449			0.168250
$515$		−	59.2518i		−	2.61095i
$516$	−9.81688	+	3.15044i	−0.432164	+	0.138690i
$517$			18.7713i			0.825559i
$518$		−	1.18840i		−	0.0522153i
$519$	23.8218	−	7.64491i	1.04566	−	0.335574i
$520$		−	12.3446i		−	0.541345i
$521$	43.4024			1.90149			0.950746	−	0.309970i	$-0.100319\pi$
$521$	43.4024			1.90149			0.950746	+	0.309970i	$0.100319\pi$
$522$	0.427487	−	0.305882i	0.0187106	−	0.0133881i
$523$			33.7817i			1.47717i	0.674161	+	0.738584i	$0.264505\pi$
$523$			33.7817i			1.47717i	−0.674161	+	0.738584i	$0.735495\pi$
$524$			1.94272i			0.0848682i
$525$	6.00855	−	1.92827i	0.262234	−	0.0841565i
$526$			18.9610i			0.826741i
$527$	−3.87259			−0.168693
$528$	1.46176	+	4.55490i	0.0636151	+	0.198227i
$529$	−8.85556	−	21.2268i	−0.385024	−	0.922906i
$530$			21.9005i			0.951296i
$531$	−18.4773	−	25.8230i	−0.801845	−	1.12062i
$532$	4.25362			0.184418
$533$			27.0955i			1.17364i
$534$	12.5363	−	4.02315i	0.542497	−	0.174099i
$535$	−14.7744			−0.638752
$536$	7.63070			0.329596
$537$	−4.16273	+	1.33591i	−0.179635	+	0.0576486i
$538$	−5.20882			−0.224568
$539$	2.76188			0.118963
$540$	12.2606	+	9.11298i	0.527613	+	0.392160i
$541$	−11.8851			−0.510979			−0.255489	−	0.966812i	$-0.582237\pi$
$541$	−11.8851			−0.510979			−0.255489	+	0.966812i	$0.582237\pi$
$542$			26.4064i			1.13425i
$543$	−8.56176	+	2.74765i	−0.367420	+	0.117913i
$544$			1.10783i			0.0474979i
$545$		−	1.37313i		−	0.0588186i
$546$	−2.22233	−	6.92486i	−0.0951071	−	0.296357i
$547$	−18.6555			−0.797651			−0.398825	−	0.917027i	$-0.630582\pi$
$547$	−18.6555			−0.797651			−0.398825	+	0.917027i	$0.630582\pi$
$548$	18.6531			0.796821
$549$	−9.87032	−	13.7943i	−0.421255	−	0.588727i
$550$			10.0623i			0.429060i
$551$	0.745306			0.0317511
$552$	2.27356	−	7.98942i	0.0967693	−	0.340052i
$553$	−0.0580516			−0.00246861
$554$		−	6.42416i		−	0.272937i
$555$	5.76205	−	1.84916i	0.244585	−	0.0784925i
$556$	−16.5936			−0.703723
$557$	−19.9134			−0.843758			−0.421879	−	0.906652i	$-0.638629\pi$
$557$	−19.9134			−0.843758			−0.421879	+	0.906652i	$0.638629\pi$
$558$	6.10247	+	8.52855i	0.258338	+	0.361042i
$559$			24.9940i			1.05713i
$560$		−	2.93995i		−	0.124236i
$561$	−1.61939	−	5.04606i	−0.0683706	−	0.213045i
$562$			17.8452i			0.752756i
$563$	46.0124			1.93919			0.969596	−	0.244712i	$-0.0786936\pi$
$563$	46.0124			1.93919			0.969596	+	0.244712i	$0.0786936\pi$
$564$	11.2089	−	3.59718i	0.471981	−	0.151468i
$565$	−3.21528			−0.135268
$566$	17.5725			0.738626
$567$	8.51833	+	2.90484i	0.357736	+	0.121992i
$568$	−5.46979			−0.229507
$569$	3.84617			0.161240			0.0806200	−	0.996745i	$-0.474310\pi$
$569$	3.84617			0.161240			0.0806200	+	0.996745i	$0.474310\pi$
$570$	6.61867	+	20.6240i	0.277226	+	0.863844i
$571$		−	20.4977i		−	0.857803i	−0.903351	−	0.428901i	$-0.858901\pi$
$571$		−	20.4977i		−	0.857803i	0.903351	−	0.428901i	$-0.141099\pi$
$572$	11.5969			0.484890
$573$	10.4828	+	32.6648i	0.437925	+	1.36459i
$574$			6.45300i			0.269343i
$575$	9.68886	−	14.5403i	0.404053	−	0.606371i
$576$	2.43976	−	1.74573i	0.101657	−	0.0727388i
$577$	3.68789			0.153529			0.0767645	−	0.997049i	$-0.475541\pi$
$577$	3.68789			0.153529			0.0767645	+	0.997049i	$0.475541\pi$
$578$			15.7727i			0.656058i
$579$	−7.84174	−	24.4351i	−0.325892	−	1.01549i
$580$		−	0.515129i		−	0.0213896i
$581$			17.1295i			0.710651i
$582$	−0.635770	−	1.98108i	−0.0263535	−	0.0821184i
$583$	−20.5740			−0.852087
$584$		−	5.68482i		−	0.235240i
$585$	30.1178	−	21.5503i	1.24522	−	0.890996i
$586$			22.0435i			0.910610i
$587$			5.96032i			0.246009i	0.992406	+	0.123004i	$0.0392529\pi$
$587$			5.96032i			0.246009i	−0.992406	+	0.123004i	$0.960747\pi$
$588$	−0.529264	−	1.64921i	−0.0218265	−	0.0680121i
$589$			14.8692i			0.612674i
$590$	−31.1171			−1.28107
$591$	15.0322	−	4.82416i	0.618344	−	0.198439i
$592$		−	1.18840i		−	0.0488429i
$593$			30.6544i			1.25883i	0.777071	+	0.629413i	$0.216705\pi$
$593$			30.6544i			1.25883i	−0.777071	+	0.629413i	$0.783295\pi$
$594$	−8.56102	+	11.5180i	−0.351263	+	0.472589i
$595$			3.25697i			0.133523i
$596$	−2.34195			−0.0959300
$597$	37.4957	−	12.0332i	1.53460	−	0.492485i
$598$	−16.7577	−	11.1664i	−0.685273	−	0.456629i
$599$			10.0103i			0.409010i	0.978866	+	0.204505i	$0.0655584\pi$
$599$			10.0103i			0.409010i	−0.978866	+	0.204505i	$0.934442\pi$
$600$	6.00855	−	1.92827i	0.245298	−	0.0787212i
$601$	−20.3400			−0.829686			−0.414843	−	0.909893i	$-0.636164\pi$
$601$	−20.3400			−0.829686			−0.414843	+	0.909893i	$0.636164\pi$
$602$			5.95249i			0.242605i
$603$	13.3212	+	18.6171i	0.542479	+	0.758145i
$604$	5.80992			0.236402
$605$	9.91359			0.403045
$606$	−9.29563	−	28.9655i	−0.377609	−	1.17664i
$607$	37.1546			1.50806			0.754028	−	0.656842i	$-0.228108\pi$
$607$	37.1546			1.50806			0.754028	+	0.656842i	$0.228108\pi$
$608$	4.25362			0.172507
$609$	−0.0927362	−	0.288969i	−0.00375786	−	0.0117096i
$610$	−16.6224			−0.673021
$611$		−	28.5381i		−	1.15453i
$612$	−2.70284	+	1.93398i	−0.109256	+	0.0781763i
$613$			37.1898i			1.50208i	0.660256	+	0.751040i	$0.270448\pi$
$613$			37.1898i			1.50208i	−0.660256	+	0.751040i	$0.729552\pi$
$614$			21.7371i			0.877236i
$615$	−31.2879	+	10.0409i	−1.26165	+	0.404889i
$616$	2.76188			0.111279
$617$	−7.39063			−0.297536			−0.148768	−	0.988872i	$-0.547531\pi$
$617$	−7.39063			−0.297536			−0.148768	+	0.988872i	$0.547531\pi$
$618$	−10.6668	−	33.2381i	−0.429082	−	1.33703i
$619$		−	16.4033i		−	0.659302i	−0.944103	−	0.329651i	$-0.893069\pi$
$619$		−	16.4033i		−	0.659302i	0.944103	−	0.329651i	$-0.106931\pi$
$620$	10.2770			0.412736
$621$	23.4613	−	8.40045i	0.941469	−	0.337098i
$622$	16.8422			0.675311
$623$		−	7.60139i		−	0.304543i
$624$	−2.22233	−	6.92486i	−0.0889645	−	0.277216i
$625$	−29.9429			−1.19771
$626$	−31.1434			−1.24474
$627$	−19.3748	+	6.21779i	−0.773756	+	0.248314i
$628$		−	1.93235i		−	0.0771091i
$629$			1.31654i			0.0524941i
$630$	7.17276	−	5.13236i	0.285770	−	0.204478i
$631$		−	37.5093i		−	1.49322i	−0.665261	−	0.746611i	$-0.731680\pi$
$631$		−	37.5093i		−	1.49322i	0.665261	−	0.746611i	$-0.268320\pi$
$632$	−0.0580516			−0.00230917
$633$	−11.3456	−	35.3534i	−0.450948	−	1.40517i
$634$	−14.0232			−0.556931
$635$	−15.5870			−0.618550
$636$	3.94264	+	12.2854i	0.156336	+	0.487147i
$637$	−4.19891			−0.166367
$638$	0.483928			0.0191589
$639$	−9.54879	−	13.3450i	−0.377744	−	0.527919i
$640$		−	2.93995i		−	0.116212i
$641$	18.7775			0.741665			0.370833	−	0.928700i	$-0.379072\pi$
$641$	18.7775			0.741665			0.370833	+	0.928700i	$0.379072\pi$
$642$	−8.28790	+	2.65976i	−0.327097	+	0.104972i
$643$			0.582778i			0.0229825i	0.999934	+	0.0114913i	$0.00365786\pi$
$643$			0.582778i			0.0229825i	−0.999934	+	0.0114913i	$0.996342\pi$
$644$	−3.99096	−	2.65936i	−0.157266	−	0.104794i
$645$	−28.8611	+	9.26214i	−1.13641	+	0.364696i
$646$	−4.71229			−0.185403
$647$			34.9442i			1.37380i	0.726753	+	0.686899i	$0.241029\pi$
$647$			34.9442i			1.37380i	−0.726753	+	0.686899i	$0.758971\pi$
$648$	8.51833	+	2.90484i	0.334632	+	0.114113i
$649$		−	29.2324i		−	1.14747i
$650$		−	15.2979i		−	0.600032i
$651$	5.76505	−	1.85013i	0.225950	−	0.0725121i
$652$	−18.1179			−0.709552
$653$		−	21.0363i		−	0.823215i	−0.911361	−	0.411607i	$-0.864968\pi$
$653$		−	21.0363i		−	0.823215i	0.911361	−	0.411607i	$-0.135032\pi$
$654$	−0.247198	−	0.770279i	−0.00966622	−	0.0301203i
$655$			5.71151i			0.223167i
$656$			6.45300i			0.251947i
$657$	13.8696	−	9.92418i	0.541105	−	0.387179i
$658$		−	6.79656i		−	0.264957i
$659$	−11.5595			−0.450296			−0.225148	−	0.974325i	$-0.572287\pi$
$659$	−11.5595			−0.450296			−0.225148	+	0.974325i	$0.572287\pi$
$660$	4.29751	+	13.3912i	0.167280	+	0.521251i
$661$			40.0139i			1.55636i	0.628040	+	0.778181i	$0.283857\pi$
$661$			40.0139i			1.55636i	−0.628040	+	0.778181i	$0.716143\pi$
$662$			4.89731i			0.190339i
$663$	2.46197	+	7.67158i	0.0956150	+	0.297939i
$664$			17.1295i			0.664753i
$665$	12.5054			0.484939
$666$	2.89941	−	2.07463i	0.112350	−	0.0803901i
$667$	−0.699285	−	0.465966i	−0.0270764	−	0.0180423i
$668$		−	23.9731i		−	0.927547i
$669$	6.59110	+	20.5381i	0.254827	+	0.794049i
$670$	22.4339			0.866696
$671$		−	15.6156i		−	0.602833i
$672$	−0.529264	−	1.64921i	−0.0204168	−	0.0636195i
$673$	35.1052			1.35320			0.676602	−	0.736349i	$-0.263452\pi$
$673$	35.1052			1.35320			0.676602	+	0.736349i	$0.263452\pi$
$674$	7.89252			0.304009
$675$	15.1938	+	11.2932i	0.584810	+	0.434674i
$676$	−4.63084			−0.178109
$677$	−38.7134			−1.48788			−0.743939	−	0.668248i	$-0.767045\pi$
$677$	−38.7134			−1.48788			−0.743939	+	0.668248i	$0.767045\pi$
$678$	−1.80366	+	0.578832i	−0.0692691	+	0.0222299i
$679$	−1.20123			−0.0460991
$680$			3.25697i			0.124899i
$681$	6.01203	+	18.7337i	0.230381	+	0.717876i
$682$			9.65457i			0.369693i
$683$			0.865276i			0.0331089i	0.999863	+	0.0165544i	$0.00526968\pi$
$683$			0.865276i			0.0331089i	−0.999863	+	0.0165544i	$0.994730\pi$
$684$	7.42568	+	10.3778i	0.283928	+	0.396805i
$685$	54.8391			2.09530
$686$	−1.00000			−0.0381802
$687$	−23.4770	+	7.53425i	−0.895702	+	0.287450i
$688$			5.95249i			0.226937i
$689$	31.2788			1.19163
$690$	6.68416	−	23.4885i	0.254462	−	0.894192i
$691$	24.9830			0.950397			0.475199	−	0.879879i	$-0.342376\pi$
$691$	24.9830			0.950397			0.475199	+	0.879879i	$0.342376\pi$
$692$		−	14.4444i		−	0.549094i
$693$	4.82150	+	6.73831i	0.183154	+	0.255967i
$694$	10.0714			0.382307
$695$	−48.7842			−1.85049
$696$	−0.0927362	−	0.288969i	−0.00351516	−	0.0109533i
$697$		−	7.14883i		−	0.270781i
$698$			27.5013i			1.04094i
$699$	−18.5437	+	5.95107i	−0.701388	+	0.225090i
$700$		−	3.64330i		−	0.137704i
$701$	−7.10954			−0.268524			−0.134262	−	0.990946i	$-0.542866\pi$
$701$	−7.10954			−0.268524			−0.134262	+	0.990946i	$0.542866\pi$
$702$	13.0154	−	17.5109i	0.491234	−	0.660907i
$703$	5.05499			0.190653
$704$	2.76188			0.104092
$705$	32.9536	−	10.5755i	1.24111	−	0.398297i
$706$	−14.2582			−0.536614
$707$	−17.5633			−0.660536
$708$	−17.4556	+	5.60187i	−0.656021	+	0.210531i
$709$		−	29.7875i		−	1.11869i	−0.828933	−	0.559347i	$-0.811052\pi$
$709$		−	29.7875i		−	1.11869i	0.828933	−	0.559347i	$-0.188948\pi$
$710$	−16.0809			−0.603506
$711$	−0.101343	−	0.141632i	−0.00380064	−	0.00531161i
$712$		−	7.60139i		−	0.284874i
$713$	9.29622	−	13.9510i	0.348146	−	0.522470i
$714$	0.586336	+	1.82704i	0.0219431	+	0.0683753i
$715$	34.0942			1.27505
$716$			2.52408i			0.0943293i
$717$	24.9935	−	8.02093i	0.933398	−	0.299547i
$718$		−	34.5522i		−	1.28948i
$719$		−	17.2944i		−	0.644971i	−0.946574	−	0.322485i	$-0.895482\pi$
$719$		−	17.2944i		−	0.644971i	0.946574	−	0.322485i	$-0.104518\pi$
$720$	7.17276	−	5.13236i	0.267313	−	0.191272i
$721$	−20.1540			−0.750575
$722$		−	0.906736i		−	0.0337452i
$723$	−27.4464	+	8.80811i	−1.02074	+	0.327577i
$724$			5.19145i			0.192939i
$725$		−	0.638368i		−	0.0237084i
$726$	5.56117	−	1.78470i	0.206394	−	0.0662363i
$727$		−	46.5047i		−	1.72477i	−0.506257	−	0.862383i	$-0.668971\pi$
$727$		−	46.5047i		−	1.72477i	0.506257	−	0.862383i	$-0.331029\pi$
$728$	−4.19891			−0.155622
$729$	7.78361	+	25.8537i	0.288282	+	0.957546i
$730$		−	16.7131i		−	0.618579i
$731$		−	6.59435i		−	0.243901i
$732$	−9.32456	+	2.99245i	−0.344646	+	0.110604i
$733$			21.5744i			0.796869i	0.917197	+	0.398434i	$0.130446\pi$
$733$			21.5744i			0.796869i	−0.917197	+	0.398434i	$0.869554\pi$
$734$	−19.9066			−0.734767
$735$	−1.55601	−	4.84858i	−0.0573943	−	0.178843i
$736$	−3.99096	−	2.65936i	−0.147109	−	0.0980255i
$737$			21.0751i			0.776310i
$738$	−15.7437	+	11.2652i	−0.579535	+	0.414678i
$739$	−32.6888			−1.20248			−0.601238	−	0.799070i	$-0.705326\pi$
$739$	−32.6888			−1.20248			−0.601238	+	0.799070i	$0.705326\pi$
$740$		−	3.49383i		−	0.128436i
$741$	29.4557	−	9.45296i	1.08208	−	0.347263i
$742$	7.44927			0.273471
$743$	34.2279			1.25570			0.627849	−	0.778335i	$-0.283936\pi$
$743$	34.2279			1.25570			0.627849	+	0.778335i	$0.283936\pi$
$744$	5.76505	−	1.85013i	0.211357	−	0.0678289i
$745$	−6.88521			−0.252255
$746$	2.54169			0.0930579
$747$	−41.7918	+	29.9035i	−1.52908	+	1.09411i
$748$	−3.05969			−0.111873
$749$			5.02539i			0.183624i
$750$	−6.57808	+	2.11104i	−0.240198	+	0.0770844i
$751$			13.5272i			0.493614i	0.969065	+	0.246807i	$0.0793814\pi$
$751$			13.5272i			0.493614i	−0.969065	+	0.246807i	$0.920619\pi$
$752$		−	6.79656i		−	0.247845i
$753$	−10.5009	−	32.7213i	−0.382676	−	1.19243i
$754$	−0.735721			−0.0267934
$755$	17.0809			0.621636
$756$	3.09971	−	4.17035i	0.112735	−	0.151674i
$757$			29.2886i			1.06451i	0.846584	+	0.532256i	$0.178656\pi$
$757$			29.2886i			1.06451i	−0.846584	+	0.532256i	$0.821344\pi$
$758$	−15.6116			−0.567040
$759$	22.0658	+	6.27931i	0.800938	+	0.227924i
$760$	12.5054			0.453619
$761$			21.6592i			0.785147i	0.919721	+	0.392574i	$0.128415\pi$
$761$			21.6592i			0.785147i	−0.919721	+	0.392574i	$0.871585\pi$
$762$	−8.74374	+	2.80605i	−0.316752	+	0.101652i
$763$	−0.467060			−0.0169087
$764$	19.8064			0.716569
$765$	−7.94621	+	5.68579i	−0.287296	+	0.205570i
$766$		−	29.5137i		−	1.06638i
$767$			44.4423i			1.60472i
$768$	−0.529264	−	1.64921i	−0.0190982	−	0.0595106i
$769$		−	4.23708i		−	0.152793i	−0.997078	−	0.0763966i	$-0.975658\pi$
$769$		−	4.23708i		−	0.152793i	0.997078	−	0.0763966i	$-0.0243415\pi$
$770$	8.11978			0.292617
$771$	6.29088	−	2.01887i	0.226560	−	0.0727080i
$772$	−14.8163			−0.533250
$773$	−44.4144			−1.59747			−0.798737	−	0.601680i	$-0.794498\pi$
$773$	−44.4144			−1.59747			−0.798737	+	0.601680i	$0.794498\pi$
$774$	−14.5226	+	10.3915i	−0.522005	+	0.373513i
$775$	12.7357			0.457480
$776$	−1.20123			−0.0431217
$777$	−0.628977	−	1.95991i	−0.0225644	−	0.0703115i
$778$		−	20.6672i		−	0.740954i
$779$	−27.4486			−0.983447
$780$	−6.53355	−	20.3587i	−0.233938	−	0.728960i
$781$		−	15.1069i		−	0.540568i
$782$	4.42131	+	2.94613i	0.158106	+	0.105353i
$783$	0.543122	−	0.730716i	0.0194096	−	0.0261137i
$784$	−1.00000			−0.0357143
$785$		−	5.68101i		−	0.202764i
$786$	1.02821	+	3.20395i	0.0366752	+	0.114281i
$787$			15.9821i			0.569700i	0.958572	+	0.284850i	$0.0919438\pi$
$787$			15.9821i			0.569700i	−0.958572	+	0.284850i	$0.908056\pi$
$788$		−	9.11484i		−	0.324703i
$789$	10.0354	+	31.2707i	0.357270	+	1.11326i
$790$	−0.170669			−0.00607212
$791$			1.09365i			0.0388858i
$792$	4.82150	+	6.73831i	0.171324	+	0.239436i
$793$			23.7405i			0.843050i
$794$		−	26.9895i		−	0.957823i
$795$	11.5911	+	36.1184i	0.411096	+	1.28099i
$796$		−	22.7356i		−	0.805843i
$797$	−38.9173			−1.37852			−0.689260	−	0.724514i	$-0.742064\pi$
$797$	−38.9173			−1.37852			−0.689260	+	0.724514i	$0.742064\pi$
$798$	7.01509	−	2.25129i	0.248332	−	0.0796948i
$799$			7.52943i			0.266372i
$800$		−	3.64330i		−	0.128810i
$801$	18.5456	−	13.2700i	0.655275	−	0.468872i
$802$		−	3.73823i		−	0.132002i
$803$	15.7008			0.554069
$804$	12.5846	−	4.03866i	0.443824	−	0.142432i
$805$	−11.7332	−	7.81839i	−0.413542	−	0.275562i
$806$		−	14.6779i		−	0.517008i
$807$	−8.59042	+	2.75685i	−0.302397	+	0.0970456i
$808$	−17.5633			−0.617875
$809$			9.43426i			0.331691i	0.986152	+	0.165846i	$0.0530353\pi$
$809$			9.43426i			0.331691i	−0.986152	+	0.165846i	$0.946965\pi$
$810$	25.0434	+	8.54008i	0.879937	+	0.300068i
$811$	2.45961			0.0863685			0.0431842	−	0.999067i	$-0.486250\pi$
$811$	2.45961			0.0863685			0.0431842	+	0.999067i	$0.486250\pi$
$812$	−0.175217			−0.00614891
$813$	13.9760	+	43.5495i	0.490158	+	1.52735i
$814$	3.28221			0.115042
$815$	−53.2657			−1.86582
$816$	0.586336	+	1.82704i	0.0205258	+	0.0639592i
$817$	−25.3196			−0.885821
$818$			13.4666i			0.470848i
$819$	−7.33017	−	10.2443i	−0.256137	−	0.357966i
$820$			18.9715i			0.662513i
$821$			21.2303i			0.740941i	0.928844	+	0.370471i	$0.120804\pi$
$821$			21.2303i			0.740941i	−0.928844	+	0.370471i	$0.879196\pi$
$822$	30.7628	−	9.87242i	1.07298	−	0.344340i
$823$	−13.6539			−0.475945			−0.237972	−	0.971272i	$-0.576483\pi$
$823$	−13.6539			−0.475945			−0.237972	+	0.971272i	$0.576483\pi$
$824$	−20.1540			−0.702099
$825$	5.32564	+	16.5949i	0.185415	+	0.577759i
$826$			10.5842i			0.368273i
$827$	−15.7090			−0.546254			−0.273127	−	0.961978i	$-0.588058\pi$
$827$	−15.7090			−0.546254			−0.273127	+	0.961978i	$0.588058\pi$
$828$	−0.478944	−	14.3795i	−0.0166445	−	0.499723i
$829$	32.6964			1.13559			0.567796	−	0.823170i	$-0.307796\pi$
$829$	32.6964			1.13559			0.567796	+	0.823170i	$0.307796\pi$
$830$			50.3598i			1.74801i
$831$	−3.40008	−	10.5948i	−0.117948	−	0.367528i
$832$	−4.19891			−0.145571
$833$	1.10783			0.0383841
$834$	−27.3662	+	8.78238i	−0.947613	+	0.304109i
$835$		−	70.4797i		−	2.43905i
$836$			11.7480i			0.406312i
$837$	14.5781	+	10.8355i	0.503893	+	0.374530i
$838$		−	15.2868i		−	0.528073i
$839$	−26.5679			−0.917227			−0.458613	−	0.888636i	$-0.651654\pi$
$839$	−26.5679			−0.917227			−0.458613	+	0.888636i	$0.651654\pi$
$840$	−1.55601	−	4.84858i	−0.0536875	−	0.167292i
$841$	28.9693			0.998941
$842$	−23.3600			−0.805037
$843$	9.44485	+	29.4305i	0.325298	+	1.01364i
$844$	−21.4366			−0.737878
$845$	−13.6144			−0.468350
$846$	16.5820	−	11.8650i	0.570099	−	0.407926i
$847$		−	3.37203i		−	0.115864i
$848$	7.44927			0.255809
$849$	28.9806	−	9.30048i	0.994612	−	0.319192i
$850$			4.03616i			0.138439i
$851$	−4.74286	−	3.16039i	−0.162583	−	0.108337i
$852$	−9.02082	+	2.89497i	−0.309048	+	0.0991800i
$853$	−32.7862			−1.12258			−0.561289	−	0.827620i	$-0.689695\pi$
$853$	−32.7862			−1.12258			−0.561289	+	0.827620i	$0.689695\pi$
$854$			5.65397i			0.193475i
$855$	21.8311	+	30.5102i	0.746608	+	1.04343i
$856$			5.02539i			0.171764i
$857$			40.2730i			1.37570i	0.725853	+	0.687850i	$0.241445\pi$
$857$			40.2730i			1.37570i	−0.725853	+	0.687850i	$0.758555\pi$
$858$	19.1256	−	6.13781i	0.652938	−	0.209542i
$859$	−3.29511			−0.112428			−0.0562138	−	0.998419i	$-0.517903\pi$
$859$	−3.29511			−0.112428			−0.0562138	+	0.998419i	$0.517903\pi$
$860$			17.5000i			0.596746i
$861$	3.41534	+	10.6423i	0.116395	+	0.362689i
$862$			37.9168i			1.29145i
$863$		−	40.0237i		−	1.36242i	−0.732087	−	0.681211i	$-0.761454\pi$
$863$		−	40.0237i		−	1.36242i	0.732087	−	0.681211i	$-0.238546\pi$
$864$	3.09971	−	4.17035i	0.105454	−	0.141878i
$865$		−	42.4658i		−	1.44388i
$866$	−31.4169			−1.06759
$867$	8.34794	+	26.0124i	0.283511	+	0.883429i
$868$		−	3.49565i		−	0.118650i
$869$		−	0.160331i		−	0.00543887i
$870$	−0.272640	−	0.849554i	−0.00924335	−	0.0288026i
$871$		−	32.0406i		−	1.08565i
$872$	−0.467060			−0.0158167
$873$	−2.09703	−	2.93072i	−0.0709737	−	0.0991897i
$874$	11.3119	−	16.9760i	0.382631	−	0.574223i
$875$			3.98864i			0.134840i
$876$	−3.00878	−	9.37544i	−0.101657	−	0.316767i
$877$	−19.3436			−0.653186			−0.326593	−	0.945165i	$-0.605901\pi$
$877$	−19.3436			−0.653186			−0.326593	+	0.945165i	$0.605901\pi$
$878$		−	31.5071i		−	1.06331i
$879$	11.6669	+	36.3543i	0.393514	+	1.22620i
$880$	8.11978			0.273718
$881$	−33.0950			−1.11500			−0.557499	−	0.830177i	$-0.688239\pi$
$881$	−33.0950			−1.11500			−0.557499	+	0.830177i	$0.688239\pi$
$882$	−1.74573	−	2.43976i	−0.0587819	−	0.0821509i
$883$	−5.62661			−0.189351			−0.0946753	−	0.995508i	$-0.530181\pi$
$883$	−5.62661			−0.189351			−0.0946753	+	0.995508i	$0.530181\pi$
$884$	4.65168			0.156453
$885$	−51.3186	+	16.4692i	−1.72505	+	0.553606i
$886$	22.4686			0.754848
$887$		−	36.8419i		−	1.23703i	−0.785774	−	0.618514i	$-0.787735\pi$
$887$		−	36.8419i		−	1.23703i	0.785774	−	0.618514i	$-0.212265\pi$
$888$	−0.628977	−	1.95991i	−0.0211071	−	0.0657704i
$889$			5.30179i			0.177816i
$890$		−	22.3477i		−	0.749097i
$891$	−8.02281	+	23.5266i	−0.268774	+	0.788170i
$892$	12.4533			0.416968
$893$	28.9100			0.967435
$894$	−3.86236	+	1.23951i	−0.129177	+	0.0414555i
$895$			7.42067i			0.248046i
$896$	−1.00000			−0.0334077
$897$	−33.5469	−	9.54649i	−1.12010	−	0.318748i
$898$	−15.3982			−0.513844
$899$		−	0.612498i		−	0.0204280i
$900$	8.88877	−	6.36022i	0.296292	−	0.212007i
$901$	−8.25253			−0.274932
$902$	−17.8224			−0.593421
$903$	3.15044	+	9.81688i	0.104840	+	0.326685i
$904$			1.09365i			0.0363744i
$905$			15.2626i			0.507346i
$906$	9.58175	−	3.07498i	0.318332	−	0.102160i
$907$			47.8418i			1.58856i	0.607551	+	0.794281i	$0.292152\pi$
$907$			47.8418i			1.58856i	−0.607551	+	0.794281i	$0.707848\pi$
$908$	11.3592			0.376969
$909$	−30.6608	−	42.8502i	−1.01696	−	1.42125i
$910$	−12.3446			−0.409219
$911$	−12.4208			−0.411519			−0.205760	−	0.978603i	$-0.565967\pi$
$911$	−12.4208			−0.411519			−0.205760	+	0.978603i	$0.565967\pi$
$912$	7.01509	−	2.25129i	0.232293	−	0.0745476i
$913$	−47.3095			−1.56572
$914$	12.4120			0.410553
$915$	−27.4137	+	8.79764i	−0.906270	+	0.290841i
$916$			14.2353i			0.470348i
$917$	1.94272			0.0641544
$918$	−3.43395	+	4.62004i	−0.113337	+	0.152484i
$919$			55.4768i			1.83001i	0.403441	+	0.915006i	$0.367814\pi$
$919$			55.4768i			1.83001i	−0.403441	+	0.915006i	$0.632186\pi$
$920$	−11.7332	−	7.81839i	−0.386833	−	0.257765i
$921$	11.5047	+	35.8489i	0.379091	+	1.18126i
$922$	16.4149			0.540595
$923$			22.9672i			0.755974i
$924$	4.55490	−	1.46176i	0.149845	−	0.0480885i
$925$		−	4.32969i		−	0.142359i
$926$		−	25.3435i		−	0.832839i
$927$	−35.1835	−	49.1709i	−1.15558	−	1.61499i
$928$	−0.175217			−0.00575178
$929$		−	12.2005i		−	0.400286i	−0.979767	−	0.200143i	$-0.935859\pi$
$929$		−	12.2005i		−	0.400286i	0.979767	−	0.200143i	$-0.0641406\pi$
$930$	16.9490	−	5.43927i	0.555778	−	0.178361i
$931$		−	4.25362i		−	0.139407i
$932$			11.2440i			0.368310i
$933$	27.7763	−	8.91398i	0.909354	−	0.291831i
$934$			10.3499i			0.338660i
$935$	−8.99534			−0.294179
$936$	−7.33017	−	10.2443i	−0.239594	−	0.334846i
$937$			17.3670i			0.567355i	0.958920	+	0.283677i	$0.0915545\pi$
$937$			17.3670i			0.567355i	−0.958920	+	0.283677i	$0.908445\pi$
$938$		−	7.63070i		−	0.249151i
$939$	−51.3619	+	16.4831i	−1.67613	+	0.537906i
$940$		−	19.9815i		−	0.651726i
$941$	−15.8935			−0.518115			−0.259057	−	0.965862i	$-0.583412\pi$
$941$	−15.8935			−0.518115			−0.259057	+	0.965862i	$0.583412\pi$
$942$	−1.02272	−	3.18684i	−0.0333221	−	0.103833i
$943$	25.7537	+	17.1609i	0.838655	+	0.558835i
$944$			10.5842i			0.344488i
$945$	9.11298	−	12.2606i	0.296445	−	0.398838i
$946$	−16.4401			−0.534512
$947$			38.0104i			1.23517i	0.786503	+	0.617587i	$0.211889\pi$
$947$			38.0104i			1.23517i	−0.786503	+	0.617587i	$0.788111\pi$
$948$	−0.0957390	+	0.0307247i	−0.00310946	+	0.000997890i
$949$	−23.8701			−0.774855
$950$	15.4972			0.502795
$951$	−23.1271	+	7.42196i	−0.749947	+	0.240674i
$952$	1.10783			0.0359050
$953$	12.1161			0.392479			0.196240	−	0.980556i	$-0.437127\pi$
$953$	12.1161			0.392479			0.196240	+	0.980556i	$0.437127\pi$
$954$	13.0044	+	18.1744i	0.421034	+	0.588419i
$955$	58.2297			1.88427
$956$		−	15.1549i		−	0.490143i
$957$	0.798097	−	0.256126i	0.0257988	−	0.00827938i
$958$		−	27.8033i		−	0.898284i
$959$		−	18.6531i		−	0.602340i
$960$	−1.55601	−	4.84858i	−0.0502200	−	0.156487i
$961$	−18.7804			−0.605819
$962$	−4.98998			−0.160883
$963$	−12.2607	+	8.77298i	−0.395097	+	0.282705i
$964$			16.6422i			0.536008i
$965$	−43.5592			−1.40222
$966$	−7.98942	−	2.27356i	−0.257056	−	0.0731507i
$967$	0.0915790			0.00294498			0.00147249	−	0.999999i	$-0.499531\pi$
$967$	0.0915790			0.00294498			0.00147249	+	0.999999i	$0.499531\pi$
$968$		−	3.37203i		−	0.108381i
$969$	−7.77153	+	2.49405i	−0.249658	+	0.0801203i
$970$	−3.53156			−0.113392
$971$	−0.0960486			−0.00308235			−0.00154117	−	0.999999i	$-0.500491\pi$
$971$	−0.0960486			−0.00308235			−0.00154117	+	0.999999i	$0.500491\pi$
$972$	15.5859	+	0.282230i	0.499918	+	0.00905254i
$973$			16.5936i			0.531965i
$974$			41.0490i			1.31529i
$975$	−8.09662	−	25.2293i	−0.259299	−	0.807986i
$976$			5.65397i			0.180979i
$977$	−10.7657			−0.344427			−0.172213	−	0.985060i	$-0.555092\pi$
$977$	−10.7657			−0.344427			−0.172213	+	0.985060i	$0.555092\pi$
$978$	−29.8802	+	9.58917i	−0.955462	+	0.306628i
$979$	20.9941			0.670975
$980$	−2.93995			−0.0939132
$981$	−0.815362	−	1.13951i	−0.0260325	−	0.0363819i
$982$	−2.46099			−0.0785334
$983$	58.4794			1.86520			0.932602	−	0.360907i	$-0.117533\pi$
$983$	58.4794			1.86520			0.932602	+	0.360907i	$0.117533\pi$
$984$	3.41534	+	10.6423i	0.108877	+	0.339265i
$985$		−	26.7972i		−	0.853828i
$986$	0.194111			0.00618175
$987$	−3.59718	−	11.2089i	−0.114499	−	0.356784i
$988$		−	17.8606i		−	0.568220i
$989$	23.7562	+	15.8298i	0.755402	+	0.503360i
$990$	14.1750	+	19.8103i	0.450510	+	0.629613i
$991$	−16.2677			−0.516761			−0.258380	−	0.966043i	$-0.583189\pi$
$991$	−16.2677			−0.516761			−0.258380	+	0.966043i	$0.583189\pi$
$992$		−	3.49565i		−	0.110987i
$993$	2.59197	+	8.07667i	0.0822537	+	0.256305i
$994$			5.46979i			0.173491i
$995$		−	66.8416i		−	2.11902i
$996$	9.06602	+	28.2500i	0.287268	+	0.895137i
$997$	−10.7821			−0.341472			−0.170736	−	0.985317i	$-0.554614\pi$
$997$	−10.7821			−0.341472			−0.170736	+	0.985317i	$0.554614\pi$
$998$		−	25.0436i		−	0.792741i
$999$	3.68369	−	4.95604i	0.116547	−	0.156802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.h.a.827.5	✓	24
3.2	odd	2		966.2.h.b.827.17	yes	24
23.22	odd	2		966.2.h.b.827.5	yes	24
69.68	even	2	inner	966.2.h.a.827.17	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.h.a.827.5	✓	24	1.1	even	1	trivial
966.2.h.a.827.17	yes	24	69.68	even	2	inner
966.2.h.b.827.5	yes	24	23.22	odd	2
966.2.h.b.827.17	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.529264 - 1.64921i) q^{3} -1.00000 q^{4} -2.93995 q^{5} +(-1.64921 + 0.529264i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(-2.43976 + 1.74573i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.529264 - 1.64921i) q^{3} -1.00000 q^{4} -2.93995 q^{5} +(-1.64921 + 0.529264i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(-2.43976 + 1.74573i) q^{9} +2.93995i q^{10} -2.76188 q^{11} +(0.529264 + 1.64921i) q^{12} +4.19891 q^{13} +1.00000 q^{14} +(1.55601 + 4.84858i) q^{15} +1.00000 q^{16} -1.10783 q^{17} +(1.74573 + 2.43976i) q^{18} +4.25362i q^{19} +2.93995 q^{20} +(1.64921 - 0.529264i) q^{21} +2.76188i q^{22} +(2.65936 - 3.99096i) q^{23} +(1.64921 - 0.529264i) q^{24} +3.64330 q^{25} -4.19891i q^{26} +(4.17035 + 3.09971i) q^{27} -1.00000i q^{28} -0.175217i q^{29} +(4.84858 - 1.55601i) q^{30} +3.49565 q^{31} -1.00000i q^{32} +(1.46176 + 4.55490i) q^{33} +1.10783i q^{34} -2.93995i q^{35} +(2.43976 - 1.74573i) q^{36} -1.18840i q^{37} +4.25362 q^{38} +(-2.22233 - 6.92486i) q^{39} -2.93995i q^{40} +6.45300i q^{41} +(-0.529264 - 1.64921i) q^{42} +5.95249i q^{43} +2.76188 q^{44} +(7.17276 - 5.13236i) q^{45} +(-3.99096 - 2.65936i) q^{46} -6.79656i q^{47} +(-0.529264 - 1.64921i) q^{48} -1.00000 q^{49} -3.64330i q^{50} +(0.586336 + 1.82704i) q^{51} -4.19891 q^{52} +7.44927 q^{53} +(3.09971 - 4.17035i) q^{54} +8.11978 q^{55} -1.00000 q^{56} +(7.01509 - 2.25129i) q^{57} -0.175217 q^{58} +10.5842i q^{59} +(-1.55601 - 4.84858i) q^{60} +5.65397i q^{61} -3.49565i q^{62} +(-1.74573 - 2.43976i) q^{63} -1.00000 q^{64} -12.3446 q^{65} +(4.55490 - 1.46176i) q^{66} -7.63070i q^{67} +1.10783 q^{68} +(-7.98942 - 2.27356i) q^{69} -2.93995 q^{70} +5.46979i q^{71} +(-1.74573 - 2.43976i) q^{72} -5.68482 q^{73} -1.18840 q^{74} +(-1.92827 - 6.00855i) q^{75} -4.25362i q^{76} -2.76188i q^{77} +(-6.92486 + 2.22233i) q^{78} +0.0580516i q^{79} -2.93995 q^{80} +(2.90484 - 8.51833i) q^{81} +6.45300 q^{82} +17.1295 q^{83} +(-1.64921 + 0.529264i) q^{84} +3.25697 q^{85} +5.95249 q^{86} +(-0.288969 + 0.0927362i) q^{87} -2.76188i q^{88} -7.60139 q^{89} +(-5.13236 - 7.17276i) q^{90} +4.19891i q^{91} +(-2.65936 + 3.99096i) q^{92} +(-1.85013 - 5.76505i) q^{93} -6.79656 q^{94} -12.5054i q^{95} +(-1.64921 + 0.529264i) q^{96} +1.20123i q^{97} +1.00000i q^{98} +(6.73831 - 4.82150i) 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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