LMFDB - Embedded newform 966.2.h.b.827.17

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

$q$-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} +(-5.17441 - 6.49811i) 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	$-0.271659\pi$
$5$	2.93995			1.31478			0.657392	+	0.753548i	$0.271659\pi$
$6$	−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	$-0.363303\pi$
$11$	2.76188			0.832738			0.416369	+	0.909196i	$0.363303\pi$
$12$	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	$-0.457107\pi$
$17$	1.10783			0.268688			0.134344	+	0.990935i	$0.457107\pi$
$18$	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	$0.00517865\pi$
$29$			0.175217i			0.0325370i	−0.999868	+	0.0162685i	$0.994821\pi$
$30$	−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	$-0.831900\pi$
$41$		−	6.45300i		−	1.00779i	0.863765	−	0.503894i	$-0.168100\pi$
$42$	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	$0.165085\pi$
$47$			6.79656i			0.991380i	−0.868500	+	0.495690i	$0.834915\pi$
$48$	−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	$-0.670954\pi$
$53$	−7.44927			−1.02324			−0.511618	+	0.859213i	$0.670954\pi$
$54$	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	$-0.758061\pi$
$59$		−	10.5842i		−	1.37795i	0.724784	−	0.688976i	$-0.241939\pi$
$60$	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
$69$	−5.17441	−	6.49811i	−0.622926	−	0.782281i
$70$	−2.93995			−0.351391
$71$		−	5.46979i		−	0.649145i	−0.945861	−	0.324573i	$-0.894780\pi$
$71$		−	5.46979i		−	0.649145i	0.945861	−	0.324573i	$-0.105220\pi$
$72$	−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	$-0.889271\pi$
$83$	−17.1295			−1.88020			−0.940102	+	0.340892i	$0.889271\pi$
$84$	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	$-0.368012\pi$
$89$	7.60139			0.805746			0.402873	+	0.915256i	$0.368012\pi$
$90$	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	$-0.661644\pi$
$101$		−	17.5633i		−	1.74761i	0.486273	−	0.873807i	$-0.338356\pi$
$102$	−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	$-0.578102\pi$
$107$	−5.02539			−0.485823			−0.242911	+	0.970048i	$0.578102\pi$
$108$	−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	$-0.516381\pi$
$113$	−1.09365			−0.102882			−0.0514411	+	0.998676i	$0.516381\pi$
$114$	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	$0.0270469\pi$
$131$			1.94272i			0.169736i	−0.996392	+	0.0848682i	$0.972953\pi$
$132$	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	$-0.206513\pi$
$137$	18.6531			1.59364			0.796821	+	0.604216i	$0.206513\pi$
$138$	6.49811	−	5.17441i	0.553156	−	0.440475i
$139$	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	$-0.530583\pi$
$149$	−2.34195			−0.191860			−0.0959300	+	0.995388i	$0.530583\pi$
$150$	−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	$-0.621913\pi$
$167$		−	23.9731i		−	1.85509i	0.373707	−	0.927547i	$-0.378087\pi$
$168$	−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	$-0.814973\pi$
$173$		−	14.4444i		−	1.09819i	0.835761	−	0.549094i	$-0.185027\pi$
$174$	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	$0.0300707\pi$
$179$			2.52408i			0.188659i	−0.995541	+	0.0943293i	$0.969929\pi$
$180$	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	$-0.245712\pi$
$191$	19.8064			1.43314			0.716569	+	0.697516i	$0.245712\pi$
$192$	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	$-0.894736\pi$
$197$		−	9.11484i		−	0.649405i	0.945816	−	0.324703i	$-0.105264\pi$
$198$	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
$207$	13.4554	−	5.09445i	0.935212	−	0.354088i
$208$	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	$-0.376966\pi$
$227$	11.3592			0.753938			0.376969	+	0.926226i	$0.376966\pi$
$228$	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	$0.120064\pi$
$233$			11.2440i			0.736621i	−0.929703	+	0.368310i	$0.879936\pi$
$234$	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	$-0.836945\pi$
$239$		−	15.1549i		−	0.980286i	0.871642	−	0.490143i	$-0.163055\pi$
$240$	−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	$-0.715376\pi$
$251$	−19.8406			−1.25233			−0.626165	+	0.779691i	$0.715376\pi$
$252$	−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	$-0.962041\pi$
$257$		−	3.81449i		−	0.237941i	0.992898	−	0.118971i	$-0.0379595\pi$
$258$	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	$-0.301254\pi$
$263$	18.9610			1.16919			0.584594	+	0.811326i	$0.301254\pi$
$264$	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	$0.0507605\pi$
$269$			5.20882i			0.317588i	−0.987312	+	0.158794i	$0.949239\pi$
$270$	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
$276$	5.17441	+	6.49811i	0.311463	+	0.391140i
$277$	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	$-0.321336\pi$
$281$	17.8452			1.06456			0.532279	+	0.846569i	$0.321336\pi$
$282$	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	$-0.277316\pi$
$293$	22.0435			1.28780			0.643899	+	0.765111i	$0.277316\pi$
$294$	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	$-0.841537\pi$
$311$		−	16.8422i		−	0.955034i	0.878623	−	0.477517i	$-0.158463\pi$
$312$	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	$0.128843\pi$
$317$			14.0232i			0.787619i	−0.919192	+	0.393810i	$0.871157\pi$
$318$	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
$345$	−15.2125	−	19.1041i	−0.819013	−	1.02853i
$346$	14.4444			0.776536
$347$		−	10.0714i		−	0.540664i	−0.962767	−	0.270332i	$-0.912867\pi$
$347$		−	10.0714i		−	0.540664i	0.962767	−	0.270332i	$-0.0871334\pi$
$348$	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	$0.123884\pi$
$353$			14.2582i			0.758887i	−0.925215	+	0.379443i	$0.876116\pi$
$354$	−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	$-0.865305\pi$
$359$	−34.5522			−1.82359			−0.911797	+	0.410641i	$0.865305\pi$
$360$	−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	$-0.771898\pi$
$383$	−29.5137			−1.50808			−0.754041	+	0.656827i	$0.771898\pi$
$384$	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	$-0.675536\pi$
$389$	−20.6672			−1.04787			−0.523933	+	0.851759i	$0.675536\pi$
$390$	−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	$-0.529754\pi$
$401$	−3.73823			−0.186678			−0.0933392	+	0.995634i	$0.529754\pi$
$402$	−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
$414$	5.09445	+	13.4554i	0.250378	+	0.661295i
$415$	−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	$-0.621809\pi$
$419$	−15.2868			−0.746807			−0.373404	+	0.927669i	$0.621809\pi$
$420$	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	$-0.133607\pi$
$431$	37.9168			1.82639			0.913195	+	0.407523i	$0.133607\pi$
$432$	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	$-0.820779\pi$
$443$		−	22.4686i		−	1.06752i	0.845637	−	0.533758i	$-0.179221\pi$
$444$	−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	$0.118364\pi$
$449$			15.3982i			0.726685i	−0.931656	+	0.363342i	$0.881636\pi$
$450$	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	$-0.875147\pi$
$461$		−	16.4149i		−	0.764516i	0.924056	−	0.382258i	$-0.124853\pi$
$462$	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	$-0.423027\pi$
$467$	10.3499			0.478938			0.239469	+	0.970904i	$0.423027\pi$
$468$	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	$-0.719075\pi$
$479$	−27.8033			−1.27037			−0.635183	+	0.772362i	$0.719075\pi$
$480$	−4.84858	−	1.55601i	−0.221306	−	0.0710218i
$481$		−	4.98998i		−	0.227523i
$482$	16.6422			0.758030
$483$	6.49811	−	5.17441i	0.295674	−	0.235444i
$484$	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	$0.0176853\pi$
$491$			2.46099i			0.111063i	−0.998457	+	0.0555315i	$0.982315\pi$
$492$	−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	$-0.483103\pi$
$503$	2.37989			0.106114			0.0530570	+	0.998591i	$0.483103\pi$
$504$	−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	$0.142907\pi$
$509$			19.5840i			0.868047i	−0.900902	+	0.434024i	$0.857093\pi$
$510$	−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	$-0.899681\pi$
$521$	−43.4024			−1.90149			−0.950746	+	0.309970i	$0.899681\pi$
$522$	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
$552$	−6.49811	+	5.17441i	−0.276578	+	0.220238i
$553$	−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	$-0.361371\pi$
$557$	19.9134			0.843758			0.421879	+	0.906652i	$0.361371\pi$
$558$	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	$-0.921306\pi$
$563$	−46.0124			−1.93919			−0.969596	+	0.244712i	$0.921306\pi$
$564$	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	$-0.525690\pi$
$569$	−3.84617			−0.161240			−0.0806200	+	0.996745i	$0.525690\pi$
$570$	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	$-0.960747\pi$
$587$		−	5.96032i		−	0.246009i	0.992406	−	0.123004i	$-0.0392529\pi$
$588$	−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	$-0.783295\pi$
$593$		−	30.6544i		−	1.25883i	0.777071	−	0.629413i	$-0.216705\pi$
$594$	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	$-0.934442\pi$
$599$		−	10.0103i		−	0.409010i	0.978866	−	0.204505i	$-0.0655584\pi$
$600$	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	$-0.452469\pi$
$617$	7.39063			0.297536			0.148768	+	0.988872i	$0.452469\pi$
$618$	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
$621$	1.28035	+	24.8870i	0.0513785	+	0.998679i
$622$	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	$-0.620928\pi$
$641$	−18.7775			−0.741665			−0.370833	+	0.928700i	$0.620928\pi$
$642$	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	$-0.758971\pi$
$647$		−	34.9442i		−	1.37380i	0.726753	−	0.686899i	$-0.241029\pi$
$648$	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	$0.135032\pi$
$653$			21.0363i			0.823215i	−0.911361	+	0.411607i	$0.864968\pi$
$654$	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	$-0.427713\pi$
$659$	11.5595			0.450296			0.225148	+	0.974325i	$0.427713\pi$
$660$	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	$-0.232955\pi$
$677$	38.7134			1.48788			0.743939	+	0.668248i	$0.232955\pi$
$678$	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	$-0.994730\pi$
$683$		−	0.865276i		−	0.0331089i	0.999863	−	0.0165544i	$-0.00526968\pi$
$684$	−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
$690$	19.1041	−	15.2125i	0.727281	−	0.579130i
$691$	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	$-0.457134\pi$
$701$	7.10954			0.268524			0.134262	+	0.990946i	$0.457134\pi$
$702$	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	$0.104518\pi$
$719$			17.2944i			0.644971i	−0.946574	+	0.322485i	$0.895482\pi$
$720$	−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	$-0.716064\pi$
$743$	−34.2279			−1.25570			−0.627849	+	0.778335i	$0.716064\pi$
$744$	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
$759$	−14.2911	−	17.9470i	−0.518734	−	0.651435i
$760$	12.5054			0.453619
$761$		−	21.6592i		−	0.785147i	−0.919721	−	0.392574i	$-0.871585\pi$
$761$		−	21.6592i		−	0.785147i	0.919721	−	0.392574i	$-0.128415\pi$
$762$	−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	$-0.205502\pi$
$773$	44.4144			1.59747			0.798737	+	0.601680i	$0.205502\pi$
$774$	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	$-0.257936\pi$
$797$	38.9173			1.37852			0.689260	+	0.724514i	$0.257936\pi$
$798$	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	$-0.946965\pi$
$809$		−	9.43426i		−	0.331691i	0.986152	−	0.165846i	$-0.0530353\pi$
$810$	−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	$-0.879196\pi$
$821$		−	21.2303i		−	0.740941i	0.928844	−	0.370471i	$-0.120804\pi$
$822$	−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	$-0.411942\pi$
$827$	15.7090			0.546254			0.273127	+	0.961978i	$0.411942\pi$
$828$	−13.4554	+	5.09445i	−0.467606	+	0.177044i
$829$	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	$-0.348346\pi$
$839$	26.5679			0.917227			0.458613	+	0.888636i	$0.348346\pi$
$840$	−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	$-0.758555\pi$
$857$		−	40.2730i		−	1.37570i	0.725853	−	0.687850i	$-0.241445\pi$
$858$	−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	$0.238546\pi$
$863$			40.0237i			1.36242i	−0.732087	+	0.681211i	$0.761454\pi$
$864$	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	$-0.311761\pi$
$881$	33.0950			1.11500			0.557499	+	0.830177i	$0.311761\pi$
$882$	−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	$0.212265\pi$
$887$			36.8419i			1.23703i	−0.785774	+	0.618514i	$0.787735\pi$
$888$	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
$897$	−21.7269	−	27.2850i	−0.725439	−	0.911019i
$898$	−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	$-0.434033\pi$
$911$	12.4208			0.411519			0.205760	+	0.978603i	$0.434033\pi$
$912$	−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	$0.0641406\pi$
$929$			12.2005i			0.400286i	−0.979767	+	0.200143i	$0.935859\pi$
$930$	−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	$-0.416588\pi$
$941$	15.8935			0.518115			0.259057	+	0.965862i	$0.416588\pi$
$942$	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	$-0.788111\pi$
$947$		−	38.0104i		−	1.23517i	0.786503	−	0.617587i	$-0.211889\pi$
$948$	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	$-0.562873\pi$
$953$	−12.1161			−0.392479			−0.196240	+	0.980556i	$0.562873\pi$
$954$	−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
$966$	5.17441	+	6.49811i	0.166484	+	0.209073i
$967$	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	$-0.499509\pi$
$971$	0.0960486			0.00308235			0.00154117	+	0.999999i	$0.499509\pi$
$972$	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	$-0.444908\pi$
$977$	10.7657			0.344427			0.172213	+	0.985060i	$0.444908\pi$
$978$	−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	$-0.882467\pi$
$983$	−58.4794			−1.86520			−0.932602	+	0.360907i	$0.882467\pi$
$984$	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.b.827.17	yes	24
3.2	odd	2		966.2.h.a.827.5	✓	24
23.22	odd	2		966.2.h.a.827.17	yes	24
69.68	even	2	inner	966.2.h.b.827.5	yes	24

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

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} +(-5.17441 - 6.49811i) 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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