LMFDB - Embedded newform 966.2.k.a.229.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(229,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("966.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.8
Character	$\chi$	$=$	966.229
Dual form			966.2.k.a.367.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.81715 - 3.14740i) q^{5} -1.00000i q^{6} +(1.58446 - 2.11884i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.81715 - 3.14740i) q^{5} -1.00000i q^{6} +(1.58446 - 2.11884i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.81715 + 3.14740i) q^{10} +(-0.401830 + 0.231997i) q^{11} +(0.866025 + 0.500000i) q^{12} +6.88399i q^{13} +(1.04274 + 2.43160i) q^{14} +3.63431i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.54730 - 2.68000i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.90210 - 5.02659i) q^{19} -3.63431 q^{20} +(-0.312760 + 2.62720i) q^{21} -0.463993i q^{22} +(4.79068 - 0.222148i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-4.10410 - 7.10851i) q^{25} +(-5.96171 - 3.44200i) q^{26} +1.00000i q^{27} +(-2.62720 - 0.312760i) q^{28} +3.72335 q^{29} +(-3.14740 - 1.81715i) q^{30} +(-2.45312 + 1.41631i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.231997 - 0.401830i) q^{33} +3.09460 q^{34} +(-3.78965 - 8.83719i) q^{35} -1.00000 q^{36} +(-6.15851 - 3.55562i) q^{37} +(2.90210 + 5.02659i) q^{38} +(-3.44200 - 5.96171i) q^{39} +(1.81715 - 3.14740i) q^{40} -8.56367i q^{41} +(-2.11884 - 1.58446i) q^{42} -2.69191i q^{43} +(0.401830 + 0.231997i) q^{44} +(-1.81715 - 3.14740i) q^{45} +(-2.20296 + 4.25993i) q^{46} +(-2.16453 - 1.24969i) q^{47} -1.00000i q^{48} +(-1.97899 - 6.71443i) q^{49} +8.20821 q^{50} +(2.68000 + 1.54730i) q^{51} +(5.96171 - 3.44200i) q^{52} +(-4.36472 + 2.51997i) q^{53} +(-0.866025 - 0.500000i) q^{54} +1.68630i q^{55} +(1.58446 - 2.11884i) q^{56} +5.80420i q^{57} +(-1.86167 + 3.22451i) q^{58} +(9.36417 - 5.40640i) q^{59} +(3.14740 - 1.81715i) q^{60} +(-1.47496 + 2.55470i) q^{61} -2.83261i q^{62} +(-1.04274 - 2.43160i) q^{63} +1.00000 q^{64} +(21.6667 + 12.5093i) q^{65} +(0.231997 + 0.401830i) q^{66} +(4.25926 - 2.45909i) q^{67} +(-1.54730 + 2.68000i) q^{68} +(-4.03778 + 2.58773i) q^{69} +(9.54806 + 1.13667i) q^{70} +8.05872 q^{71} +(0.500000 - 0.866025i) q^{72} +(-7.09187 + 4.09450i) q^{73} +(6.15851 - 3.55562i) q^{74} +(7.10851 + 4.10410i) q^{75} -5.80420 q^{76} +(-0.145118 + 1.21900i) q^{77} +6.88399 q^{78} +(9.37510 + 5.41271i) q^{79} +(1.81715 + 3.14740i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.41636 + 4.28184i) q^{82} +0.215097 q^{83} +(2.43160 - 1.04274i) q^{84} -11.2467 q^{85} +(2.33126 + 1.34595i) q^{86} +(-3.22451 + 1.86167i) q^{87} +(-0.401830 + 0.231997i) q^{88} +(5.36505 - 9.29255i) q^{89} +3.63431 q^{90} +(14.5861 + 10.9074i) q^{91} +(-2.58773 - 4.03778i) q^{92} +(1.41631 - 2.45312i) q^{93} +(2.16453 - 1.24969i) q^{94} +(-10.5471 - 18.2682i) q^{95} +(0.866025 + 0.500000i) q^{96} -12.0445 q^{97} +(6.80436 + 1.64336i) q^{98} +0.463993i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 16 * q^9	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 16 q^{9} - 16 q^{16} + 16 q^{18} + 8 q^{23} - 24 q^{25} - 12 q^{26} - 8 q^{29} + 48 q^{31} - 16 q^{32} - 20 q^{35} - 32 q^{36} - 8 q^{39} + 8 q^{46} + 12 q^{47} + 24 q^{49} + 48 q^{50} + 12 q^{52} + 4 q^{58} - 12 q^{59} + 32 q^{64} + 64 q^{70} + 48 q^{71} + 16 q^{72} + 12 q^{73} + 36 q^{75} + 64 q^{77} + 16 q^{78} - 16 q^{81} - 12 q^{82} + 32 q^{85} - 24 q^{87} - 16 q^{92} - 12 q^{94} + 40 q^{95} - 24 q^{98}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 16 * q^9 - 16 * q^16 + 16 * q^18 + 8 * q^23 - 24 * q^25 - 12 * q^26 - 8 * q^29 + 48 * q^31 - 16 * q^32 - 20 * q^35 - 32 * q^36 - 8 * q^39 + 8 * q^46 + 12 * q^47 + 24 * q^49 + 48 * q^50 + 12 * q^52 + 4 * q^58 - 12 * q^59 + 32 * q^64 + 64 * q^70 + 48 * q^71 + 16 * q^72 + 12 * q^73 + 36 * q^75 + 64 * q^77 + 16 * q^78 - 16 * q^81 - 12 * q^82 + 32 * q^85 - 24 * q^87 - 16 * q^92 - 12 * q^94 + 40 * q^95 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.81715	−	3.14740i	0.812656	−	1.40756i	−0.0983423	−	0.995153i	$-0.531354\pi$
$5$	1.81715	−	3.14740i	0.812656	−	1.40756i	0.910999	−	0.412409i	$-0.135313\pi$
$6$		−	1.00000i		−	0.408248i
$7$	1.58446	−	2.11884i	0.598869	−	0.800847i
$7$	1.58446	−	2.11884i	0.598869	−	0.800847i
$8$	1.00000			0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.81715	+	3.14740i	0.574635	+	0.995297i
$11$	−0.401830	+	0.231997i	−0.121156	+	0.0699496i	−0.559353	−	0.828929i	$-0.688951\pi$
$11$	−0.401830	+	0.231997i	−0.121156	+	0.0699496i	0.438197	+	0.898879i	$0.355617\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$			6.88399i			1.90928i	0.297770	+	0.954638i	$0.403757\pi$
$13$			6.88399i			1.90928i	−0.297770	+	0.954638i	$0.596243\pi$
$14$	1.04274	+	2.43160i	0.278685	+	0.649873i
$15$			3.63431i			0.938375i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.54730	−	2.68000i	−0.375276	−	0.649996i	0.615093	−	0.788455i	$-0.289119\pi$
$17$	−1.54730	−	2.68000i	−0.375276	−	0.649996i	−0.990368	+	0.138459i	$0.955785\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	2.90210	−	5.02659i	0.665788	−	1.15318i	−0.313283	−	0.949660i	$-0.601429\pi$
$19$	2.90210	−	5.02659i	0.665788	−	1.15318i	0.979071	−	0.203519i	$-0.0652378\pi$
$20$	−3.63431			−0.812656
$21$	−0.312760	+	2.62720i	−0.0682497	+	0.573302i
$22$		−	0.463993i		−	0.0989237i
$23$	4.79068	−	0.222148i	0.998927	−	0.0463210i
$23$	4.79068	−	0.222148i	0.998927	−	0.0463210i
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	−4.10410	−	7.10851i	−0.820821	−	1.42170i
$26$	−5.96171	−	3.44200i	−1.16919	−	0.675031i
$27$			1.00000i			0.192450i
$28$	−2.62720	−	0.312760i	−0.496494	−	0.0591060i
$29$	3.72335			0.691408			0.345704	−	0.938344i	$-0.387640\pi$
$29$	3.72335			0.691408			0.345704	+	0.938344i	$0.387640\pi$
$30$	−3.14740	−	1.81715i	−0.574635	−	0.331766i
$31$	−2.45312	+	1.41631i	−0.440593	+	0.254376i	−0.703849	−	0.710350i	$-0.748537\pi$
$31$	−2.45312	+	1.41631i	−0.440593	+	0.254376i	0.263256	+	0.964726i	$0.415203\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.231997	−	0.401830i	0.0403854	−	0.0699496i
$34$	3.09460			0.530720
$35$	−3.78965	−	8.83719i	−0.640568	−	1.49376i
$36$	−1.00000			−0.166667
$37$	−6.15851	−	3.55562i	−1.01245	−	0.584540i	−0.100544	−	0.994933i	$-0.532058\pi$
$37$	−6.15851	−	3.55562i	−1.01245	−	0.584540i	−0.911909	+	0.410392i	$0.865392\pi$
$38$	2.90210	+	5.02659i	0.470783	+	0.815420i
$39$	−3.44200	−	5.96171i	−0.551160	−	0.954638i
$40$	1.81715	−	3.14740i	0.287317	−	0.497648i
$41$		−	8.56367i		−	1.33742i	−0.743523	−	0.668711i	$-0.766847\pi$
$41$		−	8.56367i		−	1.33742i	0.743523	−	0.668711i	$-0.233153\pi$
$42$	−2.11884	−	1.58446i	−0.326944	−	0.244487i
$43$		−	2.69191i		−	0.410512i	−0.978708	−	0.205256i	$-0.934197\pi$
$43$		−	2.69191i		−	0.410512i	0.978708	−	0.205256i	$-0.0658027\pi$
$44$	0.401830	+	0.231997i	0.0605782	+	0.0349748i
$45$	−1.81715	−	3.14740i	−0.270885	−	0.469187i
$46$	−2.20296	+	4.25993i	−0.324808	+	0.628092i
$47$	−2.16453	−	1.24969i	−0.315729	−	0.182286i	0.333758	−	0.942659i	$-0.391683\pi$
$47$	−2.16453	−	1.24969i	−0.315729	−	0.182286i	−0.649487	+	0.760372i	$0.725016\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−1.97899	−	6.71443i	−0.282712	−	0.959205i
$50$	8.20821			1.16082
$51$	2.68000	+	1.54730i	0.375276	+	0.216665i
$52$	5.96171	−	3.44200i	0.826740	−	0.477319i
$53$	−4.36472	+	2.51997i	−0.599540	+	0.346145i	−0.768861	−	0.639416i	$-0.779176\pi$
$53$	−4.36472	+	2.51997i	−0.599540	+	0.346145i	0.169320	+	0.985561i	$0.445843\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$			1.68630i			0.227380i
$56$	1.58446	−	2.11884i	0.211732	−	0.283142i
$57$			5.80420i			0.768786i
$58$	−1.86167	+	3.22451i	−0.244450	+	0.423399i
$59$	9.36417	−	5.40640i	1.21911	−	0.703854i	0.254383	−	0.967104i	$-0.418128\pi$
$59$	9.36417	−	5.40640i	1.21911	−	0.703854i	0.964728	+	0.263250i	$0.0847943\pi$
$60$	3.14740	−	1.81715i	0.406328	−	0.234594i
$61$	−1.47496	+	2.55470i	−0.188849	+	0.327095i	−0.944867	−	0.327455i	$-0.893809\pi$
$61$	−1.47496	+	2.55470i	−0.188849	+	0.327095i	0.756018	+	0.654551i	$0.227142\pi$
$62$		−	2.83261i		−	0.359742i
$63$	−1.04274	−	2.43160i	−0.131373	−	0.306353i
$64$	1.00000			0.125000
$65$	21.6667	+	12.5093i	2.68742	+	1.55158i
$66$	0.231997	+	0.401830i	0.0285568	+	0.0494619i
$67$	4.25926	−	2.45909i	0.520352	−	0.300425i	−0.216727	−	0.976232i	$-0.569538\pi$
$67$	4.25926	−	2.45909i	0.520352	−	0.300425i	0.737079	+	0.675807i	$0.236205\pi$
$68$	−1.54730	+	2.68000i	−0.187638	+	0.324998i
$69$	−4.03778	+	2.58773i	−0.486092	+	0.311526i
$70$	9.54806	+	1.13667i	1.14121	+	0.135857i
$71$	8.05872			0.956394			0.478197	−	0.878253i	$-0.341291\pi$
$71$	8.05872			0.956394			0.478197	+	0.878253i	$0.341291\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−7.09187	+	4.09450i	−0.830041	+	0.479224i	−0.853867	−	0.520492i	$-0.825749\pi$
$73$	−7.09187	+	4.09450i	−0.830041	+	0.479224i	0.0238257	+	0.999716i	$0.492415\pi$
$74$	6.15851	−	3.55562i	0.715913	−	0.413332i
$75$	7.10851	+	4.10410i	0.820821	+	0.473901i
$76$	−5.80420			−0.665788
$77$	−0.145118	+	1.21900i	−0.0165378	+	0.138918i
$78$	6.88399			0.779458
$79$	9.37510	+	5.41271i	1.05478	+	0.608978i	0.923984	−	0.382431i	$-0.124913\pi$
$79$	9.37510	+	5.41271i	1.05478	+	0.608978i	0.130797	+	0.991409i	$0.458246\pi$
$80$	1.81715	+	3.14740i	0.203164	+	0.351891i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	7.41636	+	4.28184i	0.819000	+	0.472850i
$83$	0.215097			0.0236099			0.0118050	−	0.999930i	$-0.496242\pi$
$83$	0.215097			0.0236099			0.0118050	+	0.999930i	$0.496242\pi$
$84$	2.43160	−	1.04274i	0.265310	−	0.113773i
$85$	−11.2467			−1.21988
$86$	2.33126	+	1.34595i	0.251386	+	0.145138i
$87$	−3.22451	+	1.86167i	−0.345704	+	0.199592i
$88$	−0.401830	+	0.231997i	−0.0428352	+	0.0247309i
$89$	5.36505	−	9.29255i	0.568695	−	0.985008i	−0.428001	−	0.903778i	$-0.640782\pi$
$89$	5.36505	−	9.29255i	0.568695	−	0.985008i	0.996695	−	0.0812297i	$-0.0258847\pi$
$90$	3.63431			0.383090
$91$	14.5861	+	10.9074i	1.52904	+	1.14341i
$92$	−2.58773	−	4.03778i	−0.269789	−	0.420968i
$93$	1.41631	−	2.45312i	0.146864	−	0.254376i
$94$	2.16453	−	1.24969i	0.223254	−	0.128896i
$95$	−10.5471	−	18.2682i	−1.08211	−	1.87428i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−12.0445			−1.22293			−0.611467	−	0.791270i	$-0.709420\pi$
$97$	−12.0445			−1.22293			−0.611467	+	0.791270i	$0.709420\pi$
$98$	6.80436	+	1.64336i	0.687344	+	0.166005i
$99$			0.463993i			0.0466331i
$100$	−4.10410	+	7.10851i	−0.410410	+	0.710851i
$101$	−6.51092	+	3.75908i	−0.647861	+	0.374043i	−0.787636	−	0.616141i	$-0.788695\pi$
$101$	−6.51092	+	3.75908i	−0.647861	+	0.374043i	0.139775	+	0.990183i	$0.455362\pi$
$102$	−2.68000	+	1.54730i	−0.265360	+	0.153206i
$103$	−2.09604	+	3.63045i	−0.206529	+	0.357719i	−0.950619	−	0.310361i	$-0.899550\pi$
$103$	−2.09604	+	3.63045i	−0.206529	+	0.357719i	0.744090	+	0.668080i	$0.232884\pi$
$104$			6.88399i			0.675031i
$105$	7.70053	+	5.75841i	0.751495	+	0.561963i
$106$		−	5.03994i		−	0.489523i
$107$	6.12168	+	3.53435i	0.591805	+	0.341679i	0.765811	−	0.643066i	$-0.222338\pi$
$107$	6.12168	+	3.53435i	0.591805	+	0.341679i	−0.174006	+	0.984745i	$0.555671\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	−12.9714	+	7.48903i	−1.24243	+	0.717319i	−0.969589	−	0.244739i	$-0.921298\pi$
$109$	−12.9714	+	7.48903i	−1.24243	+	0.717319i	−0.272844	+	0.962058i	$0.587964\pi$
$110$	−1.46037	−	0.843148i	−0.139241	−	0.0803910i
$111$	7.11124			0.674969
$112$	1.04274	+	2.43160i	0.0985299	+	0.229765i
$113$		−	18.3985i		−	1.73078i	−0.501095	−	0.865392i	$-0.667069\pi$
$113$		−	18.3985i		−	1.73078i	0.501095	−	0.865392i	$-0.332931\pi$
$114$	−5.02659	−	2.90210i	−0.470783	−	0.271807i
$115$	8.00623	−	15.4819i	0.746584	−	1.44369i
$116$	−1.86167	−	3.22451i	−0.172852	−	0.299388i
$117$	5.96171	+	3.44200i	0.551160	+	0.318213i
$118$			10.8128i			0.995400i
$119$	−8.13014	−	0.967866i	−0.745288	−	0.0887242i
$120$			3.63431i			0.331766i
$121$	−5.39236	+	9.33983i	−0.490214	+	0.849076i
$122$	−1.47496	−	2.55470i	−0.133536	−	0.231291i
$123$	4.28184	+	7.41636i	0.386080	+	0.668711i
$124$	2.45312	+	1.41631i	0.220296	+	0.127188i
$125$	−11.6596			−1.04287
$126$	2.62720	+	0.312760i	0.234050	+	0.0278628i
$127$	16.4072			1.45590			0.727951	−	0.685629i	$-0.240473\pi$
$127$	16.4072			1.45590			0.727951	+	0.685629i	$0.240473\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	1.34595	+	2.33126i	0.118505	+	0.205256i
$130$	−21.6667	+	12.5093i	−1.90030	+	1.09714i
$131$	−5.28775	−	3.05288i	−0.461993	−	0.266732i	0.250889	−	0.968016i	$-0.419277\pi$
$131$	−5.28775	−	3.05288i	−0.461993	−	0.266732i	−0.712882	+	0.701284i	$0.752610\pi$
$132$	−0.463993			−0.0403854
$133$	−6.05229	−	14.1135i	−0.524800	−	1.22380i
$134$			4.91818i			0.424866i
$135$	3.14740	+	1.81715i	0.270885	+	0.156396i
$136$	−1.54730	−	2.68000i	−0.132680	−	0.229808i
$137$	1.36467	−	0.787893i	0.116592	−	0.0673142i	−0.440570	−	0.897718i	$-0.645224\pi$
$137$	1.36467	−	0.787893i	0.116592	−	0.0673142i	0.557162	+	0.830404i	$0.311890\pi$
$138$	−0.222148	−	4.79068i	−0.0189105	−	0.407810i
$139$		−	15.0361i		−	1.27535i	−0.770307	−	0.637673i	$-0.779897\pi$
$139$		−	15.0361i		−	1.27535i	0.770307	−	0.637673i	$-0.220103\pi$
$140$	−5.75841	+	7.70053i	−0.486675	+	0.650814i
$141$	2.49939			0.210486
$142$	−4.02936	+	6.97905i	−0.338136	+	0.585669i
$143$	−1.59706	−	2.76619i	−0.133553	−	0.231321i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	6.76590	−	11.7189i	0.561877	−	0.973200i
$146$		−	8.18899i		−	0.677726i
$147$	5.07107	+	4.82538i	0.418255	+	0.397990i
$148$			7.11124i			0.584540i
$149$	−2.26983	−	1.31048i	−0.185951	−	0.107359i	0.404134	−	0.914700i	$-0.367573\pi$
$149$	−2.26983	−	1.31048i	−0.185951	−	0.107359i	−0.590086	+	0.807340i	$0.700906\pi$
$150$	−7.10851	+	4.10410i	−0.580408	+	0.335099i
$151$	8.29751	+	14.3717i	0.675242	+	1.16955i	0.976398	+	0.215979i	$0.0692941\pi$
$151$	8.29751	+	14.3717i	0.675242	+	1.16955i	−0.301156	+	0.953575i	$0.597373\pi$
$152$	2.90210	−	5.02659i	0.235392	−	0.407710i
$153$	−3.09460			−0.250184
$154$	−0.983129	−	0.735178i	−0.0792228	−	0.0592423i
$155$			10.2946i			0.826882i
$156$	−3.44200	+	5.96171i	−0.275580	+	0.477319i
$157$	4.19634	+	7.26828i	0.334905	+	0.580072i	0.983467	−	0.181090i	$-0.0579626\pi$
$157$	4.19634	+	7.26828i	0.334905	+	0.580072i	−0.648562	+	0.761162i	$0.724629\pi$
$158$	−9.37510	+	5.41271i	−0.745843	+	0.430612i
$159$	2.51997	−	4.36472i	0.199847	−	0.346145i
$160$	−3.63431			−0.287317
$161$	7.11994	−	10.5027i	0.561130	−	0.827728i
$162$	1.00000			0.0785674
$163$	−8.31297	+	14.3985i	−0.651122	+	1.12778i	0.331729	+	0.943375i	$0.392368\pi$
$163$	−8.31297	+	14.3985i	−0.651122	+	1.12778i	−0.982851	+	0.184402i	$0.940965\pi$
$164$	−7.41636	+	4.28184i	−0.579120	+	0.334355i
$165$	−0.843148	−	1.46037i	−0.0656390	−	0.113690i
$166$	−0.107548	+	0.186279i	−0.00834737	+	0.0144581i
$167$		−	18.8326i		−	1.45731i	−0.684882	−	0.728654i	$-0.740146\pi$
$167$		−	18.8326i		−	1.45731i	0.684882	−	0.728654i	$-0.259854\pi$
$168$	−0.312760	+	2.62720i	−0.0241299	+	0.202693i
$169$	−34.3893			−2.64533
$170$	5.62337	−	9.73996i	0.431293	−	0.747021i
$171$	−2.90210	−	5.02659i	−0.221929	−	0.384393i
$172$	−2.33126	+	1.34595i	−0.177757	+	0.102628i
$173$	12.2025	+	7.04510i	0.927737	+	0.535629i	0.886095	−	0.463503i	$-0.153408\pi$
$173$	12.2025	+	7.04510i	0.927737	+	0.535629i	0.0416419	+	0.999133i	$0.486741\pi$
$174$		−	3.72335i		−	0.282266i
$175$	−21.5646	−	2.56720i	−1.63013	−	0.194062i
$176$		−	0.463993i		−	0.0349748i
$177$	−5.40640	+	9.36417i	−0.406370	+	0.703854i
$178$	5.36505	+	9.29255i	0.402128	+	0.696506i
$179$	7.43963	+	12.8858i	0.556064	+	0.963131i	0.997820	+	0.0659956i	$0.0210223\pi$
$179$	7.43963	+	12.8858i	0.556064	+	0.963131i	−0.441756	+	0.897135i	$0.645644\pi$
$180$	−1.81715	+	3.14740i	−0.135443	+	0.234594i
$181$	7.38879			0.549204			0.274602	−	0.961558i	$-0.411454\pi$
$181$	7.38879			0.549204			0.274602	+	0.961558i	$0.411454\pi$
$182$	−16.7391	+	7.17823i	−1.24079	+	0.532086i
$183$		−	2.94991i		−	0.218064i
$184$	4.79068	−	0.222148i	0.353174	−	0.0163769i
$185$	−22.3819	+	12.9222i	−1.64555	+	0.950061i
$186$	1.41631	+	2.45312i	0.103849	+	0.179871i
$187$	1.24350	+	0.717937i	0.0909340	+	0.0525008i
$188$			2.49939i			0.182286i
$189$	2.11884	+	1.58446i	0.154123	+	0.115252i
$190$	21.0943			1.53034
$191$	1.73467	+	1.00151i	0.125516	+	0.0724669i	0.561444	−	0.827515i	$-0.310246\pi$
$191$	1.73467	+	1.00151i	0.125516	+	0.0724669i	−0.435927	+	0.899982i	$0.643579\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	5.62532	+	9.74334i	0.404919	+	0.701341i	0.994312	−	0.106506i	$-0.0339663\pi$
$193$	5.62532	+	9.74334i	0.404919	+	0.701341i	−0.589393	+	0.807847i	$0.700633\pi$
$194$	6.02225	−	10.4308i	0.432372	−	0.748891i
$195$	−25.0186			−1.79162
$196$	−4.82538	+	5.07107i	−0.344670	+	0.362219i
$197$	19.3223			1.37666			0.688328	−	0.725400i	$-0.258345\pi$
$197$	19.3223			1.37666			0.688328	+	0.725400i	$0.258345\pi$
$198$	−0.401830	−	0.231997i	−0.0285568	−	0.0164873i
$199$	−10.8453	−	18.7846i	−0.768801	−	1.33160i	−0.938214	−	0.346057i	$-0.887520\pi$
$199$	−10.8453	−	18.7846i	−0.768801	−	1.33160i	0.169413	−	0.985545i	$-0.445813\pi$
$200$	−4.10410	−	7.10851i	−0.290204	−	0.502648i
$201$	−2.45909	+	4.25926i	−0.173451	+	0.300425i
$202$		−	7.51817i		−	0.528976i
$203$	5.89949	−	7.88918i	0.414063	−	0.553712i
$204$		−	3.09460i		−	0.216665i
$205$	−26.9533	−	15.5615i	−1.88250	−	1.08686i
$206$	−2.09604	−	3.63045i	−0.146038	−	0.252946i
$207$	2.20296	−	4.25993i	0.153116	−	0.296085i
$208$	−5.96171	−	3.44200i	−0.413370	−	0.238659i
$209$			2.69311i			0.186286i
$210$	−8.83719	+	3.78965i	−0.609824	+	0.261511i
$211$	−22.9385			−1.57915			−0.789576	−	0.613653i	$-0.789699\pi$
$211$	−22.9385			−1.57915			−0.789576	+	0.613653i	$0.789699\pi$
$212$	4.36472	+	2.51997i	0.299770	+	0.173072i
$213$	−6.97905	+	4.02936i	−0.478197	+	0.276087i
$214$	−6.12168	+	3.53435i	−0.418469	+	0.241603i
$215$	−8.47252	−	4.89161i	−0.577821	−	0.333605i
$216$			1.00000i			0.0680414i
$217$	−0.885927	+	7.44184i	−0.0601406	+	0.505185i
$218$		−	14.9781i		−	1.01444i
$219$	4.09450	−	7.09187i	0.276680	−	0.479224i
$220$	1.46037	−	0.843148i	0.0984584	−	0.0568450i
$221$	18.4491	−	10.6516i	1.24102	−	0.716504i
$222$	−3.55562	+	6.15851i	−0.238638	+	0.413332i
$223$			6.73457i			0.450980i	0.974245	+	0.225490i	$0.0723983\pi$
$223$			6.73457i			0.450980i	−0.974245	+	0.225490i	$0.927602\pi$
$224$	−2.62720	−	0.312760i	−0.175537	−	0.0208971i
$225$	−8.20821			−0.547214
$226$	15.9336	+	9.19925i	1.05988	+	0.611925i
$227$	5.07341	+	8.78741i	0.336734	+	0.583241i	0.983816	−	0.179179i	$-0.0573442\pi$
$227$	5.07341	+	8.78741i	0.336734	+	0.583241i	−0.647082	+	0.762420i	$0.724011\pi$
$228$	5.02659	−	2.90210i	0.332894	−	0.192196i
$229$	11.6550	−	20.1871i	0.770187	−	1.33400i	−0.167273	−	0.985911i	$-0.553496\pi$
$229$	11.6550	−	20.1871i	0.770187	−	1.33400i	0.937460	−	0.348092i	$-0.113170\pi$
$230$	9.40460	+	14.6745i	0.620121	+	0.967611i
$231$	−0.483826	−	1.12825i	−0.0318334	−	0.0742332i
$232$	3.72335			0.244450
$233$	−6.44413	+	11.1616i	−0.422169	+	0.731219i	−0.996151	−	0.0876492i	$-0.972065\pi$
$233$	−6.44413	+	11.1616i	−0.422169	+	0.731219i	0.573982	+	0.818868i	$0.305398\pi$
$234$	−5.96171	+	3.44200i	−0.389729	+	0.225010i
$235$	−7.86658	+	4.54177i	−0.513159	+	0.296273i
$236$	−9.36417	−	5.40640i	−0.609555	−	0.351927i
$237$	−10.8254			−0.703187
$238$	4.90327	−	6.55697i	0.317831	−	0.425025i
$239$	−19.7335			−1.27645			−0.638227	−	0.769849i	$-0.720332\pi$
$239$	−19.7335			−1.27645			−0.638227	+	0.769849i	$0.720332\pi$
$240$	−3.14740	−	1.81715i	−0.203164	−	0.117297i
$241$	1.94609	+	3.37072i	0.125359	+	0.217127i	0.921873	−	0.387492i	$-0.126659\pi$
$241$	1.94609	+	3.37072i	0.125359	+	0.217127i	−0.796514	+	0.604619i	$0.793325\pi$
$242$	−5.39236	−	9.33983i	−0.346634	−	0.600387i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	2.94991			0.188849
$245$	−24.7292	−	5.97249i	−1.57989	−	0.381569i
$246$	−8.56367			−0.546000
$247$	34.6030	+	19.9780i	2.20174	+	1.27117i
$248$	−2.45312	+	1.41631i	−0.155773	+	0.0899356i
$249$	−0.186279	+	0.107548i	−0.0118050	+	0.00681560i
$250$	5.82981	−	10.0975i	0.368709	−	0.638623i
$251$	26.5603			1.67647			0.838237	−	0.545306i	$-0.183587\pi$
$251$	26.5603			1.67647			0.838237	+	0.545306i	$0.183587\pi$
$252$	−1.58446	+	2.11884i	−0.0998115	+	0.133475i
$253$	−1.87350	+	1.20069i	−0.117786	+	0.0754866i
$254$	−8.20359	+	14.2090i	−0.514739	+	0.891554i
$255$	9.73996	−	5.62337i	0.609940	−	0.352149i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.55458	+	4.36164i	0.471242	+	0.272072i	0.716760	−	0.697320i	$-0.245625\pi$
$257$	7.55458	+	4.36164i	0.471242	+	0.272072i	−0.245517	+	0.969392i	$0.578958\pi$
$258$	−2.69191			−0.167591
$259$	−17.2917	+	7.41519i	−1.07445	+	0.460758i
$260$		−	25.0186i		−	1.55158i
$261$	1.86167	−	3.22451i	0.115235	−	0.199592i
$262$	5.28775	−	3.05288i	0.326678	−	0.188608i
$263$	−10.3409	+	5.97033i	−0.637649	+	0.368147i	−0.783708	−	0.621129i	$-0.786674\pi$
$263$	−10.3409	+	5.97033i	−0.637649	+	0.368147i	0.146060	+	0.989276i	$0.453341\pi$
$264$	0.231997	−	0.401830i	0.0142784	−	0.0247309i
$265$			18.3167i			1.12519i
$266$	15.2488	+	1.81532i	0.934964	+	0.111304i
$267$			10.7301i			0.656672i
$268$	−4.25926	−	2.45909i	−0.260176	−	0.150213i
$269$	−1.29245	+	0.746198i	−0.0788022	+	0.0454965i	−0.538883	−	0.842380i	$-0.681154\pi$
$269$	−1.29245	+	0.746198i	−0.0788022	+	0.0454965i	0.460081	+	0.887877i	$0.347820\pi$
$270$	−3.14740	+	1.81715i	−0.191545	+	0.110589i
$271$	14.1697	+	8.18090i	0.860750	+	0.496954i	0.864263	−	0.503040i	$-0.167785\pi$
$271$	14.1697	+	8.18090i	0.860750	+	0.496954i	−0.00351337	+	0.999994i	$0.501118\pi$
$272$	3.09460			0.187638
$273$	−18.0856	−	2.15303i	−1.09459	−	0.130308i
$274$			1.57579i			0.0951967i
$275$	3.29830	+	1.90428i	0.198895	+	0.114832i
$276$	4.25993	+	2.20296i	0.256418	+	0.132602i
$277$	14.2549	+	24.6903i	0.856496	+	1.48349i	0.875250	+	0.483670i	$0.160696\pi$
$277$	14.2549	+	24.6903i	0.856496	+	1.48349i	−0.0187547	+	0.999824i	$0.505970\pi$
$278$	13.0217	+	7.51805i	0.780987	+	0.450903i
$279$			2.83261i			0.169584i
$280$	−3.78965	−	8.83719i	−0.226475	−	0.528123i
$281$			28.1607i			1.67993i	0.542644	+	0.839963i	$0.317423\pi$
$281$			28.1607i			1.67993i	−0.542644	+	0.839963i	$0.682577\pi$
$282$	−1.24969	+	2.16453i	−0.0744181	+	0.128896i
$283$	3.85474	+	6.67660i	0.229140	+	0.396883i	0.957554	−	0.288255i	$-0.0930752\pi$
$283$	3.85474	+	6.67660i	0.229140	+	0.396883i	−0.728413	+	0.685138i	$0.759742\pi$
$284$	−4.02936	−	6.97905i	−0.239098	−	0.414131i
$285$	18.2682	+	10.5471i	1.08211	+	0.624759i
$286$	3.19413			0.188873
$287$	−18.1451	−	13.5688i	−1.07107	−	0.800940i
$288$	−1.00000			−0.0589256
$289$	3.71172	−	6.42889i	0.218337	−	0.378170i
$290$	6.76590	+	11.7189i	0.397307	+	0.688156i
$291$	10.4308	−	6.02225i	0.611467	−	0.353030i
$292$	7.09187	+	4.09450i	0.415021	+	0.239612i
$293$	0.631689			0.0369036			0.0184518	−	0.999830i	$-0.494126\pi$
$293$	0.631689			0.0369036			0.0184518	+	0.999830i	$0.494126\pi$
$294$	−6.71443	+	1.97899i	−0.391594	+	0.115417i
$295$		−	39.2971i		−	2.28797i
$296$	−6.15851	−	3.55562i	−0.357956	−	0.206666i
$297$	−0.231997	−	0.401830i	−0.0134618	−	0.0233165i
$298$	2.26983	−	1.31048i	0.131487	−	0.0759143i
$299$	1.52926	+	32.9790i	0.0884395	+	1.90723i
$300$		−	8.20821i		−	0.473901i
$301$	−5.70373	−	4.26522i	−0.328757	−	0.245843i
$302$	−16.5950			−0.954936
$303$	3.75908	−	6.51092i	0.215954	−	0.374043i
$304$	2.90210	+	5.02659i	0.166447	+	0.288295i
$305$	5.36044	+	9.28456i	0.306938	+	0.531632i
$306$	1.54730	−	2.68000i	0.0884533	−	0.153206i
$307$		−	6.66420i		−	0.380346i	−0.981751	−	0.190173i	$-0.939095\pi$
$307$		−	6.66420i		−	0.380346i	0.981751	−	0.190173i	$-0.0609049\pi$
$308$	1.12825	−	0.483826i	0.0642879	−	0.0275685i
$309$		−	4.19209i		−	0.238479i
$310$	−8.91538	−	5.14730i	−0.506360	−	0.292347i
$311$	−2.42439	+	1.39972i	−0.137475	+	0.0793710i	−0.567160	−	0.823608i	$-0.691958\pi$
$311$	−2.42439	+	1.39972i	−0.137475	+	0.0793710i	0.429685	+	0.902979i	$0.358625\pi$
$312$	−3.44200	−	5.96171i	−0.194865	−	0.337515i
$313$	2.29678	−	3.97815i	0.129822	−	0.224858i	−0.793786	−	0.608198i	$-0.791893\pi$
$313$	2.29678	−	3.97815i	0.129822	−	0.224858i	0.923607	+	0.383340i	$0.125226\pi$
$314$	−8.39269			−0.473627
$315$	−9.54806	−	1.13667i	−0.537972	−	0.0640438i
$316$		−	10.8254i		−	0.608978i
$317$	−7.58603	+	13.1394i	−0.426074	+	0.737981i	−0.996520	−	0.0833535i	$-0.973437\pi$
$317$	−7.58603	+	13.1394i	−0.426074	+	0.737981i	0.570446	+	0.821335i	$0.306770\pi$
$318$	2.51997	+	4.36472i	0.141313	+	0.244761i
$319$	−1.49615	+	0.863804i	−0.0837685	+	0.0483637i
$320$	1.81715	−	3.14740i	0.101582	−	0.175945i
$321$	−7.06871			−0.394537
$322$	5.53562	+	11.4174i	0.308488	+	0.636266i
$323$	−17.9617			−0.999416
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	48.9349	−	28.2526i	2.71442	−	1.56717i
$326$	−8.31297	−	14.3985i	−0.460413	−	0.797459i
$327$	7.48903	−	12.9714i	0.414144	−	0.717319i
$328$		−	8.56367i		−	0.472850i
$329$	−6.07751	+	2.60622i	−0.335064	+	0.143685i
$330$	1.68630			0.0928275
$331$	13.7644	−	23.8407i	0.756561	−	1.31040i	−0.188033	−	0.982163i	$-0.560211\pi$
$331$	13.7644	−	23.8407i	0.756561	−	1.31040i	0.944594	−	0.328240i	$-0.106456\pi$
$332$	−0.107548	−	0.186279i	−0.00590248	−	0.0102234i
$333$	−6.15851	+	3.55562i	−0.337485	+	0.194847i
$334$	16.3095	+	9.41629i	0.892416	+	0.515236i
$335$		−	17.8742i		−	0.976570i
$336$	−2.11884	−	1.58446i	−0.115592	−	0.0864393i
$337$			27.0942i			1.47591i	0.674848	+	0.737957i	$0.264209\pi$
$337$			27.0942i			1.47591i	−0.674848	+	0.737957i	$0.735791\pi$
$338$	17.1947	−	29.7820i	0.935266	−	1.61993i
$339$	9.19925	+	15.9336i	0.499634	+	0.865392i
$340$	5.62337	+	9.73996i	0.304970	+	0.528224i
$341$	0.657157	−	1.13823i	0.0355870	−	0.0616386i
$342$	5.80420			0.313855
$343$	−17.3624	−	6.44558i	−0.937484	−	0.348028i
$344$		−	2.69191i		−	0.145138i
$345$	0.807353	+	17.4108i	0.0434664	+	0.937367i
$346$	−12.2025	+	7.04510i	−0.656009	+	0.378747i
$347$	−4.73729	−	8.20522i	−0.254311	−	0.440479i	0.710397	−	0.703801i	$-0.248515\pi$
$347$	−4.73729	−	8.20522i	−0.254311	−	0.440479i	−0.964708	+	0.263322i	$0.915182\pi$
$348$	3.22451	+	1.86167i	0.172852	+	0.0997962i
$349$			4.84804i			0.259510i	0.991546	+	0.129755i	$0.0414191\pi$
$349$			4.84804i			0.259510i	−0.991546	+	0.129755i	$0.958581\pi$
$350$	13.0056	−	17.3919i	0.695176	−	0.929636i
$351$	−6.88399			−0.367440
$352$	0.401830	+	0.231997i	0.0214176	+	0.0123655i
$353$	−20.1209	+	11.6168i	−1.07093	+	0.618300i	−0.928435	−	0.371496i	$-0.878845\pi$
$353$	−20.1209	+	11.6168i	−1.07093	+	0.618300i	−0.142493	+	0.989796i	$0.545512\pi$
$354$	−5.40640	−	9.36417i	−0.287347	−	0.497700i
$355$	14.6439	−	25.3640i	0.777220	−	1.34618i
$356$	−10.7301			−0.568695
$357$	7.52484	−	3.22687i	0.398257	−	0.170784i
$358$	−14.8793			−0.786393
$359$	8.48083	+	4.89641i	0.447601	+	0.258423i	0.706817	−	0.707397i	$-0.250131\pi$
$359$	8.48083	+	4.89641i	0.447601	+	0.258423i	−0.259215	+	0.965820i	$0.583464\pi$
$360$	−1.81715	−	3.14740i	−0.0957725	−	0.165883i
$361$	−7.34440	−	12.7209i	−0.386547	−	0.669519i
$362$	−3.69439	+	6.39888i	−0.194173	+	0.336318i
$363$		−	10.7847i		−	0.566050i
$364$	2.15303	−	18.0856i	0.112850	−	0.947944i
$365$			29.7613i			1.55778i
$366$	2.55470	+	1.47496i	0.133536	+	0.0770971i
$367$	6.35316	+	11.0040i	0.331632	+	0.574404i	0.982832	−	0.184502i	$-0.0590674\pi$
$367$	6.35316	+	11.0040i	0.331632	+	0.574404i	−0.651200	+	0.758906i	$0.725734\pi$
$368$	−2.20296	+	4.25993i	−0.114837	+	0.222064i
$369$	−7.41636	−	4.28184i	−0.386080	−	0.222904i
$370$		−	25.8444i		−	1.34359i
$371$	−1.57629	+	13.2409i	−0.0818369	+	0.687436i
$372$	−2.83261			−0.146864
$373$	20.5352	+	11.8560i	1.06327	+	0.613881i	0.926336	−	0.376699i	$-0.122941\pi$
$373$	20.5352	+	11.8560i	1.06327	+	0.613881i	0.136937	+	0.990580i	$0.456274\pi$
$374$	−1.24350	+	0.717937i	−0.0643001	+	0.0371237i
$375$	10.0975	−	5.82981i	0.521434	−	0.301050i
$376$	−2.16453	−	1.24969i	−0.111627	−	0.0644480i
$377$			25.6315i			1.32009i
$378$	−2.43160	+	1.04274i	−0.125068	+	0.0536329i
$379$			8.02828i			0.412385i	0.978511	+	0.206193i	$0.0661073\pi$
$379$			8.02828i			0.412385i	−0.978511	+	0.206193i	$0.933893\pi$
$380$	−10.5471	+	18.2682i	−0.541057	+	0.937138i
$381$	−14.2090	+	8.20359i	−0.727951	+	0.420283i
$382$	−1.73467	+	1.00151i	−0.0887535	+	0.0512419i
$383$	−17.5917	+	30.4697i	−0.898892	+	1.55693i	−0.0699801	+	0.997548i	$0.522294\pi$
$383$	−17.5917	+	30.4697i	−0.898892	+	1.55693i	−0.828912	+	0.559379i	$0.811040\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	3.57299	+	2.67186i	0.182097	+	0.136171i
$386$	−11.2506			−0.572642
$387$	−2.33126	−	1.34595i	−0.118505	−	0.0684187i
$388$	6.02225	+	10.4308i	0.305733	+	0.529546i
$389$	−4.99478	+	2.88374i	−0.253245	+	0.146211i	−0.621249	−	0.783613i	$-0.713375\pi$
$389$	−4.99478	+	2.88374i	−0.253245	+	0.146211i	0.368004	+	0.929824i	$0.380041\pi$
$390$	12.5093	−	21.6667i	0.633432	−	1.09714i
$391$	−8.00798	−	12.4953i	−0.404981	−	0.631915i
$392$	−1.97899	−	6.71443i	−0.0999539	−	0.339130i
$393$	6.10577			0.307995
$394$	−9.66114	+	16.7336i	−0.486721	+	0.843026i
$395$	34.0720	−	19.6715i	1.71435	−	0.989780i
$396$	0.401830	−	0.231997i	0.0201927	−	0.0116583i
$397$	32.0631	+	18.5117i	1.60920	+	0.929074i	0.989549	+	0.144198i	$0.0460604\pi$
$397$	32.0631	+	18.5117i	1.60920	+	0.929074i	0.619654	+	0.784875i	$0.287273\pi$
$398$	21.6905			1.08725
$399$	12.2982	+	9.19652i	0.615680	+	0.460402i
$400$	8.20821			0.410410
$401$	−14.6889	−	8.48064i	−0.733529	−	0.423503i	0.0861829	−	0.996279i	$-0.472533\pi$
$401$	−14.6889	−	8.48064i	−0.733529	−	0.423503i	−0.819712	+	0.572776i	$0.805866\pi$
$402$	−2.45909	−	4.25926i	−0.122648	−	0.212433i
$403$	−9.74984	−	16.8872i	−0.485674	−	0.841212i
$404$	6.51092	+	3.75908i	0.323930	+	0.187021i
$405$	−3.63431			−0.180590
$406$	3.88249	+	9.05370i	0.192685	+	0.449327i
$407$	3.29957			0.163554
$408$	2.68000	+	1.54730i	0.132680	+	0.0766028i
$409$	−15.8984	+	9.17895i	−0.786126	+	0.453870i	−0.838597	−	0.544752i	$-0.816624\pi$
$409$	−15.8984	+	9.17895i	−0.786126	+	0.453870i	0.0524709	+	0.998622i	$0.483290\pi$
$410$	26.9533	−	15.5615i	1.33113	−	0.768529i
$411$	−0.787893	+	1.36467i	−0.0388639	+	0.0673142i
$412$	4.19209			0.206529
$413$	3.38181	−	28.4074i	0.166408	−	1.39784i
$414$	2.58773	+	4.03778i	0.127180	+	0.198446i
$415$	0.390864	−	0.676996i	0.0191868	−	0.0332324i
$416$	5.96171	−	3.44200i	0.292297	−	0.168758i
$417$	7.51805	+	13.0217i	0.368161	+	0.637673i
$418$	−2.33230	−	1.34656i	−0.114077	−	0.0658622i
$419$	−1.03154			−0.0503940			−0.0251970	−	0.999683i	$-0.508021\pi$
$419$	−1.03154			−0.0503940			−0.0251970	+	0.999683i	$0.508021\pi$
$420$	1.13667	−	9.54806i	0.0554636	−	0.465898i
$421$			6.84009i			0.333366i	0.986011	+	0.166683i	$0.0533056\pi$
$421$			6.84009i			0.333366i	−0.986011	+	0.166683i	$0.946694\pi$
$422$	11.4692	−	19.8653i	0.558314	−	0.967029i
$423$	−2.16453	+	1.24969i	−0.105243	+	0.0607622i
$424$	−4.36472	+	2.51997i	−0.211970	+	0.122381i
$425$	−12.7006	+	21.9980i	−0.616068	+	1.06706i
$426$		−	8.05872i		−	0.390446i
$427$	3.07600	+	7.17301i	0.148858	+	0.347126i
$428$		−	7.06871i		−	0.341679i
$429$	2.76619	+	1.59706i	0.133553	+	0.0771069i
$430$	8.47252	−	4.89161i	0.408581	−	0.235895i
$431$	−20.6882	+	11.9443i	−0.996513	+	0.575337i	−0.907215	−	0.420668i	$-0.861796\pi$
$431$	−20.6882	+	11.9443i	−0.996513	+	0.575337i	−0.0892984	+	0.996005i	$0.528462\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	20.4049			0.980599			0.490299	−	0.871554i	$-0.336887\pi$
$433$	20.4049			0.980599			0.490299	+	0.871554i	$0.336887\pi$
$434$	−6.00186	−	4.48816i	−0.288099	−	0.215438i
$435$			13.5318i			0.648800i
$436$	12.9714	+	7.48903i	0.621217	+	0.358660i
$437$	12.7864	−	24.7255i	0.611657	−	1.18278i
$438$	4.09450	+	7.09187i	0.195643	+	0.338863i
$439$	8.36598	+	4.83010i	0.399287	+	0.230528i	0.686176	−	0.727435i	$-0.259288\pi$
$439$	8.36598	+	4.83010i	0.399287	+	0.230528i	−0.286889	+	0.957964i	$0.592621\pi$
$440$			1.68630i			0.0803910i
$441$	−6.80436	−	1.64336i	−0.324017	−	0.0782554i
$442$			21.3032i			1.01329i
$443$	−14.0208	+	24.2848i	−0.666149	+	1.15380i	0.312823	+	0.949811i	$0.398725\pi$
$443$	−14.0208	+	24.2848i	−0.666149	+	1.15380i	−0.978972	+	0.203993i	$0.934608\pi$
$444$	−3.55562	−	6.15851i	−0.168742	−	0.292270i
$445$	−19.4983	−	33.7720i	−0.924307	−	1.60095i
$446$	−5.83231	−	3.36728i	−0.276168	−	0.159446i
$447$	2.62097			0.123968
$448$	1.58446	−	2.11884i	0.0748586	−	0.100106i
$449$	10.8438			0.511749			0.255874	−	0.966710i	$-0.417637\pi$
$449$	10.8438			0.511749			0.255874	+	0.966710i	$0.417637\pi$
$450$	4.10410	−	7.10851i	0.193469	−	0.335099i
$451$	1.98674	+	3.44114i	0.0935521	+	0.162037i
$452$	−15.9336	+	9.19925i	−0.749452	+	0.432696i
$453$	−14.3717	−	8.29751i	−0.675242	−	0.389851i
$454$	−10.1468			−0.476214
$455$	60.8352	−	26.0879i	2.85200	−	1.22302i
$456$			5.80420i			0.271807i
$457$	−0.341377	−	0.197094i	−0.0159689	−	0.00921966i	0.491994	−	0.870598i	$-0.336268\pi$
$457$	−0.341377	−	0.197094i	−0.0159689	−	0.00921966i	−0.507963	+	0.861379i	$0.669601\pi$
$458$	11.6550	+	20.1871i	0.544604	+	0.943283i
$459$	2.68000	−	1.54730i	0.125092	−	0.0722218i
$460$	−17.4108	+	0.807353i	−0.811784	+	0.0376430i
$461$		−	33.4721i		−	1.55895i	−0.626432	−	0.779476i	$-0.715485\pi$
$461$		−	33.4721i		−	1.55895i	0.626432	−	0.779476i	$-0.284515\pi$
$462$	1.21900	+	0.145118i	0.0567132	+	0.00675152i
$463$	−15.0091			−0.697533			−0.348766	−	0.937210i	$-0.613399\pi$
$463$	−15.0091			−0.697533			−0.348766	+	0.937210i	$0.613399\pi$
$464$	−1.86167	+	3.22451i	−0.0864260	+	0.149694i
$465$	−5.14730	−	8.91538i	−0.238700	−	0.413441i
$466$	−6.44413	−	11.1616i	−0.298519	−	0.517050i
$467$	−14.4988	+	25.1127i	−0.670925	+	1.16208i	0.306717	+	0.951801i	$0.400770\pi$
$467$	−14.4988	+	25.1127i	−0.670925	+	1.16208i	−0.977642	+	0.210276i	$0.932564\pi$
$468$		−	6.88399i		−	0.318213i
$469$	1.53821	−	12.9210i	0.0710278	−	0.596638i
$470$		−	9.08354i		−	0.418993i
$471$	−7.26828	−	4.19634i	−0.334905	−	0.193357i
$472$	9.36417	−	5.40640i	0.431021	−	0.248850i
$473$	0.624514	+	1.08169i	0.0287152	+	0.0497361i
$474$	5.41271	−	9.37510i	0.248614	−	0.430612i
$475$	−47.6421			−2.18597
$476$	3.22687	+	7.52484i	0.147903	+	0.344900i
$477$			5.03994i			0.230763i
$478$	9.86674	−	17.0897i	0.451294	−	0.781665i
$479$	−18.8516	−	32.6519i	−0.861350	−	1.49190i	−0.870626	−	0.491946i	$-0.836286\pi$
$479$	−18.8516	−	32.6519i	−0.861350	−	1.49190i	0.00927537	−	0.999957i	$-0.497048\pi$
$480$	3.14740	−	1.81715i	0.143659	−	0.0829414i
$481$	24.4769	−	42.3952i	1.11605	−	1.93305i
$482$	−3.89218			−0.177284
$483$	−0.914706	+	12.6556i	−0.0416206	+	0.575848i
$484$	10.7847			0.490214
$485$	−21.8867	+	37.9089i	−0.993824	+	1.72135i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	−11.3256	−	19.6165i	−0.513211	−	0.888907i	−0.999883	−	0.0153220i	$-0.995123\pi$
$487$	−11.3256	−	19.6165i	−0.513211	−	0.888907i	0.486672	−	0.873585i	$-0.338211\pi$
$488$	−1.47496	+	2.55470i	−0.0667681	+	0.115646i
$489$		−	16.6259i		−	0.751851i
$490$	17.5369	−	18.4298i	0.792237	−	0.832575i
$491$	30.6005			1.38098			0.690490	−	0.723342i	$-0.257395\pi$
$491$	30.6005			1.38098			0.690490	+	0.723342i	$0.257395\pi$
$492$	4.28184	−	7.41636i	0.193040	−	0.334355i
$493$	−5.76114	−	9.97858i	−0.259469	−	0.449413i
$494$	−34.6030	+	19.9780i	−1.55686	+	0.898855i
$495$	1.46037	+	0.843148i	0.0656390	+	0.0378967i
$496$		−	2.83261i		−	0.127188i
$497$	12.7687	−	17.0752i	0.572754	−	0.765925i
$498$		−	0.215097i		−	0.00963871i
$499$	−14.9280	+	25.8560i	−0.668269	+	1.15748i	0.310119	+	0.950698i	$0.399631\pi$
$499$	−14.9280	+	25.8560i	−0.668269	+	1.15748i	−0.978388	+	0.206778i	$0.933702\pi$
$500$	5.82981	+	10.0975i	0.260717	+	0.451575i
$501$	9.41629	+	16.3095i	0.420689	+	0.728654i
$502$	−13.2802	+	23.0019i	−0.592723	+	1.02663i
$503$	31.0395			1.38398			0.691992	−	0.721905i	$-0.256733\pi$
$503$	31.0395			1.38398			0.691992	+	0.721905i	$0.256733\pi$
$504$	−1.04274	−	2.43160i	−0.0464474	−	0.108312i
$505$			27.3233i			1.21587i
$506$	−0.103075	−	2.22285i	−0.00458224	−	0.0988175i
$507$	29.7820	−	17.1947i	1.32267	−	0.763642i
$508$	−8.20359	−	14.2090i	−0.363976	−	0.630424i
$509$	−12.1059	−	6.98934i	−0.536585	−	0.309797i	0.207109	−	0.978318i	$-0.433594\pi$
$509$	−12.1059	−	6.98934i	−0.536585	−	0.309797i	−0.743694	+	0.668521i	$0.766928\pi$
$510$			11.2467i			0.498014i
$511$	−2.56119	+	21.5141i	−0.113300	+	0.951729i
$512$	1.00000			0.0441942
$513$	5.02659	+	2.90210i	0.221929	+	0.128131i
$514$	−7.55458	+	4.36164i	−0.333218	+	0.192384i
$515$	7.61767	+	13.1942i	0.335675	+	0.581406i
$516$	1.34595	−	2.33126i	0.0592523	−	0.102628i
$517$	1.15970			0.0510035
$518$	2.22411	−	18.6827i	0.0977217	−	0.820869i
$519$	−14.0902			−0.618491
$520$	21.6667	+	12.5093i	0.950148	+	0.548568i
$521$	−7.37338	−	12.7711i	−0.323033	−	0.559510i	0.658079	−	0.752949i	$-0.271369\pi$
$521$	−7.37338	−	12.7711i	−0.323033	−	0.559510i	−0.981112	+	0.193439i	$0.938036\pi$
$522$	1.86167	+	3.22451i	0.0814832	+	0.141133i
$523$	−8.32378	+	14.4172i	−0.363974	+	0.630421i	−0.988611	−	0.150494i	$-0.951913\pi$
$523$	−8.32378	+	14.4172i	−0.363974	+	0.630421i	0.624637	+	0.780915i	$0.285247\pi$
$524$			6.10577i			0.266732i
$525$	19.9591	−	8.55904i	0.871086	−	0.373547i
$526$		−	11.9407i		−	0.520638i
$527$	7.59141	+	4.38290i	0.330687	+	0.190922i
$528$	0.231997	+	0.401830i	0.0100964	+	0.0174874i
$529$	22.9013	−	2.12848i	0.995709	−	0.0925425i
$530$	−15.8627	−	9.15836i	−0.689034	−	0.397814i
$531$		−	10.8128i		−	0.469236i
$532$	−9.19652	+	12.2982i	−0.398720	+	0.533194i
$533$	58.9522			2.55351
$534$	−9.29255	−	5.36505i	−0.402128	−	0.232169i
$535$	22.2481	−	12.8449i	0.961868	−	0.555335i
$536$	4.25926	−	2.45909i	0.183972	−	0.106216i
$537$	−12.8858	−	7.43963i	−0.556064	−	0.321044i
$538$		−	1.49240i		−	0.0643417i
$539$	2.35294	+	2.23894i	0.101348	+	0.0964381i
$540$		−	3.63431i		−	0.156396i
$541$	6.51160	−	11.2784i	0.279955	−	0.484897i	−0.691418	−	0.722455i	$-0.743014\pi$
$541$	6.51160	−	11.2784i	0.279955	−	0.484897i	0.971373	+	0.237558i	$0.0763470\pi$
$542$	−14.1697	+	8.18090i	−0.608642	+	0.351400i
$543$	−6.39888	+	3.69439i	−0.274602	+	0.158542i
$544$	−1.54730	+	2.68000i	−0.0663400	+	0.114904i
$545$			54.4349i			2.33174i
$546$	10.9074	−	14.5861i	0.466793	−	0.624227i
$547$	0.952418			0.0407224			0.0203612	−	0.999793i	$-0.493518\pi$
$547$	0.952418			0.0407224			0.0203612	+	0.999793i	$0.493518\pi$
$548$	−1.36467	−	0.787893i	−0.0582958	−	0.0336571i
$549$	1.47496	+	2.55470i	0.0629496	+	0.109032i
$550$	−3.29830	+	1.90428i	−0.140640	+	0.0811986i
$551$	10.8055	−	18.7157i	0.460331	−	0.797317i
$552$	−4.03778	+	2.58773i	−0.171859	+	0.110141i
$553$	26.3231	−	11.2881i	1.11937	−	0.480020i
$554$	−28.5099			−1.21127
$555$	12.9222	−	22.3819i	0.548518	−	0.950061i
$556$	−13.0217	+	7.51805i	−0.552241	+	0.318836i
$557$	31.1148	−	17.9641i	1.31838	−	0.761164i	0.334908	−	0.942251i	$-0.391295\pi$
$557$	31.1148	−	17.9641i	1.31838	−	0.761164i	0.983467	+	0.181086i	$0.0579613\pi$
$558$	−2.45312	−	1.41631i	−0.103849	−	0.0599570i
$559$	18.5311			0.783781
$560$	9.54806	+	1.13667i	0.403479	+	0.0480329i
$561$	−1.43587			−0.0606227
$562$	−24.3879	−	14.0803i	−1.02874	−	0.593943i
$563$	16.4023	+	28.4096i	0.691274	+	1.19732i	0.971421	+	0.237364i	$0.0762835\pi$
$563$	16.4023	+	28.4096i	0.691274	+	1.19732i	−0.280147	+	0.959957i	$0.590383\pi$
$564$	−1.24969	−	2.16453i	−0.0526216	−	0.0911432i
$565$	−57.9075	−	33.4329i	−2.43619	−	1.40653i
$566$	−7.70948			−0.324054
$567$	−2.62720	−	0.312760i	−0.110332	−	0.0131347i
$568$	8.05872			0.338136
$569$	26.9222	+	15.5435i	1.12864	+	0.651619i	0.943592	−	0.331111i	$-0.107423\pi$
$569$	26.9222	+	15.5435i	1.12864	+	0.651619i	0.185046	+	0.982730i	$0.440757\pi$
$570$	−18.2682	+	10.5471i	−0.765170	+	0.441771i
$571$	33.6805	−	19.4454i	1.40948	−	0.813766i	0.414146	−	0.910210i	$-0.364080\pi$
$571$	33.6805	−	19.4454i	1.40948	−	0.813766i	0.995338	+	0.0964438i	$0.0307468\pi$
$572$	−1.59706	+	2.76619i	−0.0667766	+	0.115660i
$573$	−2.00303			−0.0836776
$574$	20.8234	−	8.92971i	0.869154	−	0.372719i
$575$	−21.2406	−	33.1429i	−0.885794	−	1.38216i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−4.39001	+	2.53457i	−0.182758	+	0.105516i	−0.588588	−	0.808433i	$-0.700316\pi$
$577$	−4.39001	+	2.53457i	−0.182758	+	0.105516i	0.405830	+	0.913949i	$0.366983\pi$
$578$	3.71172	+	6.42889i	0.154387	+	0.267407i
$579$	−9.74334	−	5.62532i	−0.404919	−	0.233780i
$580$	−13.5318			−0.561877
$581$	0.340812	−	0.455756i	0.0141393	−	0.0189079i
$582$			12.0445i			0.499260i
$583$	1.16925	−	2.02520i	0.0484254	−	0.0838753i
$584$	−7.09187	+	4.09450i	−0.293464	+	0.169431i
$585$	21.6667	−	12.5093i	0.895808	−	0.517195i
$586$	−0.315844	+	0.547058i	−0.0130474	+	0.0225988i
$587$		−	9.07676i		−	0.374638i	−0.982299	−	0.187319i	$-0.940020\pi$
$587$		−	9.07676i		−	0.374638i	0.982299	−	0.187319i	$-0.0599798\pi$
$588$	1.64336	−	6.80436i	0.0677712	−	0.280607i
$589$			16.4411i			0.677442i
$590$	34.0323	+	19.6485i	1.40109	+	0.808918i
$591$	−16.7336	+	9.66114i	−0.688328	+	0.397406i
$592$	6.15851	−	3.55562i	0.253113	−	0.146135i
$593$	−6.19369	−	3.57593i	−0.254345	−	0.146846i	0.367407	−	0.930060i	$-0.380245\pi$
$593$	−6.19369	−	3.57593i	−0.254345	−	0.146846i	−0.621752	+	0.783214i	$0.713579\pi$
$594$	0.463993			0.0190379
$595$	−17.8200	+	23.8301i	−0.730548	+	0.976938i
$596$			2.62097i			0.107359i
$597$	18.7846	+	10.8453i	0.768801	+	0.443867i
$598$	−29.3253	−	15.1651i	−1.19920	−	0.620148i
$599$	7.97624	+	13.8152i	0.325900	+	0.564476i	0.981694	−	0.190464i	$-0.0609993\pi$
$599$	7.97624	+	13.8152i	0.325900	+	0.564476i	−0.655794	+	0.754940i	$0.727666\pi$
$600$	7.10851	+	4.10410i	0.290204	+	0.167549i
$601$		−	5.80649i		−	0.236852i	−0.992963	−	0.118426i	$-0.962215\pi$
$601$		−	5.80649i		−	0.236852i	0.992963	−	0.118426i	$-0.0377848\pi$
$602$	6.54565	−	2.80697i	0.266781	−	0.114403i
$603$		−	4.91818i		−	0.200284i
$604$	8.29751	−	14.3717i	0.337621	−	0.584777i
$605$	19.5975	+	33.9438i	0.796751	+	1.38001i
$606$	3.75908	+	6.51092i	0.152702	+	0.264488i
$607$	−16.4330	−	9.48757i	−0.666993	−	0.385089i	0.127943	−	0.991781i	$-0.459162\pi$
$607$	−16.4330	−	9.48757i	−0.666993	−	0.385089i	−0.794936	+	0.606693i	$0.792496\pi$
$608$	−5.80420			−0.235392
$609$	−1.16451	+	9.78198i	−0.0471884	+	0.396386i
$610$	−10.7209			−0.434076
$611$	8.60288	−	14.9006i	0.348035	−	0.602814i
$612$	1.54730	+	2.68000i	0.0625459	+	0.108333i
$613$	−13.7109	+	7.91598i	−0.553777	+	0.319723i	−0.750644	−	0.660707i	$-0.770257\pi$
$613$	−13.7109	+	7.91598i	−0.553777	+	0.319723i	0.196867	+	0.980430i	$0.436923\pi$
$614$	5.77137	+	3.33210i	0.232913	+	0.134473i
$615$	31.1230			1.25500
$616$	−0.145118	+	1.21900i	−0.00584699	+	0.0491151i
$617$			1.93272i			0.0778085i	0.999243	+	0.0389042i	$0.0123867\pi$
$617$			1.93272i			0.0778085i	−0.999243	+	0.0389042i	$0.987613\pi$
$618$	3.63045	+	2.09604i	0.146038	+	0.0843152i
$619$	−15.1832	−	26.2980i	−0.610263	−	1.05701i	−0.991196	−	0.132404i	$-0.957730\pi$
$619$	−15.1832	−	26.2980i	−0.610263	−	1.05701i	0.380933	−	0.924603i	$-0.375603\pi$
$620$	8.91538	−	5.14730i	0.358050	−	0.206720i
$621$	0.222148	+	4.79068i	0.00891447	+	0.192244i
$622$		−	2.79945i		−	0.112248i
$623$	−11.1887	−	26.0914i	−0.448267	−	1.04533i
$624$	6.88399			0.275580
$625$	−0.666808	+	1.15495i	−0.0266723	+	0.0461978i
$626$	2.29678	+	3.97815i	0.0917979	+	0.158999i
$627$	−1.34656	−	2.33230i	−0.0537763	−	0.0931432i
$628$	4.19634	−	7.26828i	0.167452	−	0.290036i
$629$			22.0065i			0.877455i
$630$	5.75841	−	7.70053i	0.229421	−	0.306796i
$631$			46.5963i			1.85497i	0.373862	+	0.927484i	$0.378033\pi$
$631$			46.5963i			1.85497i	−0.373862	+	0.927484i	$0.621967\pi$
$632$	9.37510	+	5.41271i	0.372921	+	0.215306i
$633$	19.8653	−	11.4692i	0.789576	−	0.455862i
$634$	−7.58603	−	13.1394i	−0.301280	−	0.521832i
$635$	29.8144	−	51.6400i	1.18315	−	2.04927i
$636$	−5.03994			−0.199847
$637$	46.2221	−	13.6233i	1.83139	−	0.539776i
$638$		−	1.72761i		−	0.0683967i
$639$	4.02936	−	6.97905i	0.159399	−	0.276087i
$640$	1.81715	+	3.14740i	0.0718293	+	0.124412i
$641$	−21.5306	+	12.4307i	−0.850408	+	0.490983i	−0.860789	−	0.508963i	$-0.830029\pi$
$641$	−21.5306	+	12.4307i	−0.850408	+	0.490983i	0.0103803	+	0.999946i	$0.496696\pi$
$642$	3.53435	−	6.12168i	0.139490	−	0.241603i
$643$	−2.25138			−0.0887857			−0.0443928	−	0.999014i	$-0.514135\pi$
$643$	−2.25138			−0.0887857			−0.0443928	+	0.999014i	$0.514135\pi$
$644$	−12.6556	−	0.914706i	−0.498699	−	0.0360445i
$645$	9.78323			0.385214
$646$	8.98085	−	15.5553i	0.353347	−	0.612015i
$647$	−9.39800	+	5.42594i	−0.369473	+	0.213316i	−0.673228	−	0.739435i	$-0.735093\pi$
$647$	−9.39800	+	5.42594i	−0.369473	+	0.213316i	0.303755	+	0.952750i	$0.401760\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−2.50854	+	4.34491i	−0.0984687	+	0.170553i
$650$			56.5052i			2.21632i
$651$	−2.95369	−	6.88779i	−0.115764	−	0.269954i
$652$	16.6259			0.651122
$653$	−15.0552	+	26.0765i	−0.589157	+	1.02045i	0.405186	+	0.914234i	$0.367207\pi$
$653$	−15.0552	+	26.0765i	−0.589157	+	1.02045i	−0.994343	+	0.106216i	$0.966126\pi$
$654$	7.48903	+	12.9714i	0.292844	+	0.507221i
$655$	−19.2173	+	11.0951i	−0.750883	+	0.433522i
$656$	7.41636	+	4.28184i	0.289560	+	0.167178i
$657$			8.18899i			0.319483i
$658$	0.781707	−	6.56639i	0.0304741	−	0.255984i
$659$		−	5.33421i		−	0.207791i	−0.994588	−	0.103896i	$-0.966869\pi$
$659$		−	5.33421i		−	0.207791i	0.994588	−	0.103896i	$-0.0331308\pi$
$660$	−0.843148	+	1.46037i	−0.0328195	+	0.0568450i
$661$	−23.3926	−	40.5172i	−0.909868	−	1.57594i	−0.814247	−	0.580519i	$-0.802850\pi$
$661$	−23.3926	−	40.5172i	−0.909868	−	1.57594i	−0.0956209	−	0.995418i	$-0.530484\pi$
$662$	13.7644	+	23.8407i	0.534970	+	0.926595i
$663$	−10.6516	+	18.4491i	−0.413674	+	0.716504i
$664$	0.215097			0.00834737
$665$	−55.4189	−	6.59744i	−2.14905	−	0.255838i
$666$		−	7.11124i		−	0.275555i
$667$	17.8374	−	0.827132i	0.690666	−	0.0320267i
$668$	−16.3095	+	9.41629i	−0.631033	+	0.364327i
$669$	−3.36728	−	5.83231i	−0.130187	−	0.225490i
$670$	15.4795	+	8.93709i	0.598025	+	0.345270i
$671$		−	1.36874i		−	0.0528396i
$672$	2.43160	−	1.04274i	0.0938011	−	0.0402247i
$673$	−25.3950			−0.978905			−0.489453	−	0.872030i	$-0.662803\pi$
$673$	−25.3950			−0.978905			−0.489453	+	0.872030i	$0.662803\pi$
$674$	−23.4642	−	13.5471i	−0.903809	−	0.521814i
$675$	7.10851	−	4.10410i	0.273607	−	0.157967i
$676$	17.1947	+	29.7820i	0.661333	+	1.14546i
$677$	9.38835	−	16.2611i	0.360824	−	0.624965i	−0.627273	−	0.778799i	$-0.715829\pi$
$677$	9.38835	−	16.2611i	0.360824	−	0.624965i	0.988097	+	0.153835i	$0.0491623\pi$
$678$	−18.3985			−0.706590
$679$	−19.0840	+	25.5204i	−0.732376	+	0.979383i
$680$	−11.2467			−0.431293
$681$	−8.78741	−	5.07341i	−0.336734	−	0.194414i
$682$	0.657157	+	1.13823i	0.0251638	+	0.0435850i
$683$	5.17449	+	8.96248i	0.197996	+	0.342940i	0.947879	−	0.318632i	$-0.103223\pi$
$683$	5.17449	+	8.96248i	0.197996	+	0.342940i	−0.749882	+	0.661571i	$0.769890\pi$
$684$	−2.90210	+	5.02659i	−0.110965	+	0.192196i
$685$		−	5.72689i		−	0.218813i
$686$	14.2633	−	11.8135i	0.544574	−	0.451043i
$687$			23.3101i			0.889335i
$688$	2.33126	+	1.34595i	0.0888785	+	0.0513140i
$689$	−17.3475	−	30.0467i	−0.660886	−	1.14469i
$690$	−15.4819	−	8.00623i	−0.589386	−	0.304792i
$691$	20.8883	+	12.0599i	0.794630	+	0.458780i	0.841590	−	0.540117i	$-0.181620\pi$
$691$	20.8883	+	12.0599i	0.794630	+	0.458780i	−0.0469602	+	0.998897i	$0.514953\pi$
$692$		−	14.0902i		−	0.535629i
$693$	0.983129	+	0.735178i	0.0373460	+	0.0279271i
$694$	9.47457			0.359650
$695$	−47.3247	−	27.3229i	−1.79513	−	1.03642i
$696$	−3.22451	+	1.86167i	−0.122225	+	0.0705665i
$697$	−22.9507	+	13.2506i	−0.869319	+	0.501901i
$698$	−4.19853	−	2.42402i	−0.158917	−	0.0917506i
$699$		−	12.8883i		−	0.487479i
$700$	8.55904	+	19.9591i	0.323501	+	0.754383i
$701$		−	1.20423i		−	0.0454833i	−0.999741	−	0.0227416i	$-0.992760\pi$
$701$		−	1.20423i		−	0.0454833i	0.999741	−	0.0227416i	$-0.00723951\pi$
$702$	3.44200	−	5.96171i	0.129910	−	0.225010i
$703$	−35.7453	+	20.6375i	−1.34816	+	0.778360i
$704$	−0.401830	+	0.231997i	−0.0151445	+	0.00874370i
$705$	4.54177	−	7.86658i	0.171053	−	0.296273i
$706$		−	23.2336i		−	0.874408i
$707$	−2.35138	+	19.7517i	−0.0884327	+	0.742840i
$708$	10.8128			0.406370
$709$	23.1662	+	13.3750i	0.870024	+	0.502309i	0.867356	−	0.497688i	$-0.165817\pi$
$709$	23.1662	+	13.3750i	0.870024	+	0.502309i	0.00266782	+	0.999996i	$0.499151\pi$
$710$	14.6439	+	25.3640i	0.549577	+	0.951896i
$711$	9.37510	−	5.41271i	0.351594	−	0.202993i
$712$	5.36505	−	9.29255i	0.201064	−	0.348253i
$713$	−11.4375	+	7.33003i	−0.428337	+	0.274512i
$714$	−0.967866	+	8.13014i	−0.0362215	+	0.304263i
$715$	−11.6084			−0.434131
$716$	7.43963	−	12.8858i	0.278032	−	0.481565i
$717$	17.0897	−	9.86674i	0.638227	−	0.368480i
$718$	−8.48083	+	4.89641i	−0.316502	+	0.182732i
$719$	−17.4213	−	10.0582i	−0.649705	−	0.375107i	0.138638	−	0.990343i	$-0.455727\pi$
$719$	−17.4213	−	10.0582i	−0.649705	−	0.375107i	−0.788343	+	0.615236i	$0.789061\pi$
$720$	3.63431			0.135443
$721$	4.37127	+	10.1935i	0.162794	+	0.379625i
$722$	14.6888			0.546660
$723$	−3.37072	−	1.94609i	−0.125359	−	0.0723758i
$724$	−3.69439	−	6.39888i	−0.137301	−	0.237812i
$725$	−15.2810	−	26.4675i	−0.567522	−	0.982977i
$726$	9.33983	+	5.39236i	0.346634	+	0.200129i
$727$	37.4039			1.38723			0.693617	−	0.720344i	$-0.256016\pi$
$727$	37.4039			1.38723			0.693617	+	0.720344i	$0.256016\pi$
$728$	14.5861	+	10.9074i	0.540596	+	0.404255i
$729$	−1.00000			−0.0370370
$730$	−25.7741	−	14.8807i	−0.953941	−	0.550758i
$731$	−7.21432	+	4.16519i	−0.266831	+	0.154055i
$732$	−2.55470	+	1.47496i	−0.0944243	+	0.0545159i
$733$	17.4883	−	30.2907i	0.645946	−	1.11881i	−0.338136	−	0.941097i	$-0.609796\pi$
$733$	17.4883	−	30.2907i	0.645946	−	1.11881i	0.984082	−	0.177714i	$-0.0568703\pi$
$734$	−12.7063			−0.468999
$735$	24.4023	−	7.19225i	0.900093	−	0.265290i
$736$	−2.58773	−	4.03778i	−0.0953849	−	0.148835i
$737$	−1.14100	+	1.97627i	−0.0420293	+	0.0727969i
$738$	7.41636	−	4.28184i	0.273000	−	0.157617i
$739$	−12.1514	−	21.0469i	−0.446998	−	0.774223i	0.551191	−	0.834379i	$-0.314173\pi$
$739$	−12.1514	−	21.0469i	−0.446998	−	0.774223i	−0.998189	+	0.0601562i	$0.980840\pi$
$740$	22.3819	+	12.9222i	0.822777	+	0.475030i
$741$	−39.9561			−1.46782
$742$	−10.6788	−	7.98558i	−0.392033	−	0.293160i
$743$		−	40.1537i		−	1.47310i	−0.676386	−	0.736548i	$-0.736455\pi$
$743$		−	40.1537i		−	1.47310i	0.676386	−	0.736548i	$-0.263545\pi$
$744$	1.41631	−	2.45312i	0.0519243	−	0.0899356i
$745$	−8.24925	+	4.76271i	−0.302229	+	0.174492i
$746$	−20.5352	+	11.8560i	−0.751847	+	0.434079i
$747$	0.107548	−	0.186279i	0.00393499	−	0.00681560i
$748$		−	1.43587i		−	0.0525008i
$749$	17.1883	−	7.37084i	0.628046	−	0.269325i
$750$			11.6596i			0.425749i
$751$	−12.6550	−	7.30634i	−0.461786	−	0.266612i	0.251009	−	0.967985i	$-0.419238\pi$
$751$	−12.6550	−	7.30634i	−0.461786	−	0.266612i	−0.712795	+	0.701373i	$0.752571\pi$
$752$	2.16453	−	1.24969i	0.0789324	−	0.0455716i
$753$	−23.0019	+	13.2802i	−0.838237	+	0.483956i
$754$	−22.1975	−	12.8157i	−0.808386	−	0.466722i
$755$	60.3115			2.19496
$756$	0.312760	−	2.62720i	0.0113750	−	0.0955504i
$757$			26.2448i			0.953883i	0.878935	+	0.476941i	$0.158255\pi$
$757$			26.2448i			0.953883i	−0.878935	+	0.476941i	$0.841745\pi$
$758$	−6.95269	−	4.01414i	−0.252533	−	0.145800i
$759$	1.02216	−	1.97658i	0.0371020	−	0.0717452i
$760$	−10.5471	−	18.2682i	−0.382585	−	0.662657i
$761$	−35.6370	−	20.5750i	−1.29184	−	0.745844i	−0.312859	−	0.949800i	$-0.601287\pi$
$761$	−35.6370	−	20.5750i	−1.29184	−	0.745844i	−0.978980	+	0.203956i	$0.934620\pi$
$762$		−	16.4072i		−	0.594370i
$763$	−4.68453	+	39.3504i	−0.169591	+	1.42458i
$764$		−	2.00303i		−	0.0724669i
$765$	−5.62337	+	9.73996i	−0.203313	+	0.352149i
$766$	−17.5917	−	30.4697i	−0.635613	−	1.10091i
$767$	37.2176	+	64.4628i	1.34385	+	2.32762i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−10.7651			−0.388199			−0.194099	−	0.980982i	$-0.562178\pi$
$769$	−10.7651			−0.388199			−0.194099	+	0.980982i	$0.562178\pi$
$770$	−4.10040	+	1.75837i	−0.147768	+	0.0633673i
$771$	−8.72328			−0.314161
$772$	5.62532	−	9.74334i	0.202460	−	0.350670i
$773$	13.9324	+	24.1317i	0.501114	+	0.867956i	0.999999	+	0.00128738i	$0.000409786\pi$
$773$	13.9324	+	24.1317i	0.501114	+	0.867956i	−0.498885	+	0.866668i	$0.666257\pi$
$774$	2.33126	−	1.34595i	0.0837954	−	0.0483793i
$775$	20.1357	+	11.6253i	0.723295	+	0.417594i
$776$	−12.0445			−0.432372
$777$	11.2675	−	15.0676i	0.404218	−	0.540547i
$778$		−	5.76747i		−	0.206774i
$779$	−43.0461	−	24.8527i	−1.54229	−	0.890439i
$780$	12.5093	+	21.6667i	0.447904	+	0.775792i
$781$	−3.23824	+	1.86960i	−0.115873	+	0.0668994i
$782$	14.8253	−	0.687458i	0.530150	−	0.0245835i
$783$			3.72335i			0.133062i
$784$	6.80436	+	1.64336i	0.243013	+	0.0586916i
$785$	30.5016			1.08865
$786$	−3.05288	+	5.28775i	−0.108893	+	0.188608i
$787$	−4.89963	−	8.48641i	−0.174653	−	0.302508i	0.765388	−	0.643569i	$-0.222547\pi$
$787$	−4.89963	−	8.48641i	−0.174653	−	0.302508i	−0.940041	+	0.341061i	$0.889214\pi$
$788$	−9.66114	−	16.7336i	−0.344164	−	0.596110i
$789$	5.97033	−	10.3409i	0.212550	−	0.368147i
$790$			39.3430i			1.39976i
$791$	−38.9835	−	29.1516i	−1.38609	−	1.03651i
$792$			0.463993i			0.0164873i
$793$	−17.5865	−	10.1536i	−0.624515	−	0.360564i
$794$	−32.0631	+	18.5117i	−1.13788	+	0.656954i
$795$	−9.15836	−	15.8627i	−0.324814	−	0.562594i
$796$	−10.8453	+	18.7846i	−0.384400	+	0.665801i
$797$	−47.3960			−1.67885			−0.839426	−	0.543474i	$-0.817109\pi$
$797$	−47.3960			−1.67885			−0.839426	+	0.543474i	$0.817109\pi$
$798$	−14.1135	+	6.05229i	−0.499613	+	0.214249i
$799$			7.73460i			0.273631i
$800$	−4.10410	+	7.10851i	−0.145102	+	0.251324i
$801$	−5.36505	−	9.29255i	−0.189565	−	0.328336i
$802$	14.6889	−	8.48064i	0.518683	−	0.299462i
$803$	1.89982	−	3.29058i	0.0670431	−	0.116122i
$804$	4.91818			0.173451
$805$	−20.1182	−	41.4943i	−0.709072	−	1.46248i
$806$	19.4997			0.686847
$807$	0.746198	−	1.29245i	0.0262674	−	0.0454965i
$808$	−6.51092	+	3.75908i	−0.229053	+	0.132244i
$809$	−1.66172	−	2.87818i	−0.0584230	−	0.101192i	0.835335	−	0.549742i	$-0.185274\pi$
$809$	−1.66172	−	2.87818i	−0.0584230	−	0.101192i	−0.893758	+	0.448550i	$0.851941\pi$
$810$	1.81715	−	3.14740i	0.0638483	−	0.110589i
$811$			30.9763i			1.08773i	0.839174	+	0.543863i	$0.183039\pi$
$811$			30.9763i			1.08773i	−0.839174	+	0.543863i	$0.816961\pi$
$812$	−9.78198	−	1.16451i	−0.343280	−	0.0408664i
$813$	−16.3618			−0.573833
$814$	−1.64978	+	2.85751i	−0.0578249	+	0.100156i
$815$	30.2119	+	52.3286i	1.05828	+	1.83299i
$816$	−2.68000	+	1.54730i	−0.0938189	+	0.0541664i
$817$	−13.5311	−	7.81219i	−0.473394	−	0.273314i
$818$		−	18.3579i		−	0.641869i
$819$	16.7391	−	7.17823i	0.584912	−	0.250828i
$820$			31.1230i			1.08686i
$821$	13.1260	−	22.7350i	0.458102	−	0.793456i	−0.540759	−	0.841178i	$-0.681863\pi$
$821$	13.1260	−	22.7350i	0.458102	−	0.793456i	0.998861	+	0.0477219i	$0.0151961\pi$
$822$	−0.787893	−	1.36467i	−0.0274809	−	0.0475983i
$823$	8.71050	+	15.0870i	0.303629	+	0.525901i	0.976955	−	0.213445i	$-0.0684684\pi$
$823$	8.71050	+	15.0870i	0.303629	+	0.525901i	−0.673326	+	0.739345i	$0.735135\pi$
$824$	−2.09604	+	3.63045i	−0.0730191	+	0.126473i
$825$	−3.80855			−0.132597
$826$	22.9106	+	17.1324i	0.797163	+	0.596114i
$827$			7.46593i			0.259616i	0.991539	+	0.129808i	$0.0414361\pi$
$827$			7.46593i			0.259616i	−0.991539	+	0.129808i	$0.958564\pi$
$828$	−4.79068	+	0.222148i	−0.166488	+	0.00772016i
$829$	−35.5742	+	20.5388i	−1.23554	+	0.713341i	−0.968180	−	0.250255i	$-0.919486\pi$
$829$	−35.5742	+	20.5388i	−1.23554	+	0.713341i	−0.267363	+	0.963596i	$0.586152\pi$
$830$	0.390864	+	0.676996i	0.0135671	+	0.0234989i
$831$	−24.6903	−	14.2549i	−0.856496	−	0.494498i
$832$			6.88399i			0.238659i
$833$	−14.9326	+	15.6929i	−0.517385	+	0.543728i
$834$	−15.0361			−0.520658
$835$	−59.2737	−	34.2217i	−2.05125	−	1.18429i
$836$	2.33230	−	1.34656i	0.0806644	−	0.0465716i
$837$	−1.41631	−	2.45312i	−0.0489547	−	0.0847921i
$838$	0.515770	−	0.893340i	0.0178170	−	0.0308599i
$839$	15.1631			0.523490			0.261745	−	0.965137i	$-0.415702\pi$
$839$	15.1631			0.523490			0.261745	+	0.965137i	$0.415702\pi$
$840$	7.70053	+	5.75841i	0.265694	+	0.198684i
$841$	−15.1367			−0.521955
$842$	−5.92369	−	3.42004i	−0.204144	−	0.117863i
$843$	−14.0803	−	24.3879i	−0.484953	−	0.839963i
$844$	11.4692	+	19.8653i	0.394788	+	0.683793i
$845$	−62.4907	+	108.237i	−2.14975	+	3.72347i
$846$		−	2.49939i		−	0.0859307i
$847$	11.2457	+	26.2241i	0.386406	+	0.901072i
$848$		−	5.03994i		−	0.173072i
$849$	−6.67660	−	3.85474i	−0.229140	−	0.132294i
$850$	−12.7006	−	21.9980i	−0.435626	−	0.754526i
$851$	−30.2934	−	15.6658i	−1.03844	−	0.537015i
$852$	6.97905	+	4.02936i	0.239098	+	0.138044i
$853$			31.2352i			1.06947i	0.845018	+	0.534737i	$0.179589\pi$
$853$			31.2352i			1.06947i	−0.845018	+	0.534737i	$0.820411\pi$
$854$	−7.75001	−	0.922613i	−0.265200	−	0.0315712i
$855$	−21.0943			−0.721409
$856$	6.12168	+	3.53435i	0.209235	+	0.120802i
$857$	19.4780	−	11.2456i	0.665356	−	0.384143i	−0.128959	−	0.991650i	$-0.541163\pi$
$857$	19.4780	−	11.2456i	0.665356	−	0.384143i	0.794315	+	0.607506i	$0.207830\pi$
$858$	−2.76619	+	1.59706i	−0.0944363	+	0.0545228i
$859$	32.4994	+	18.7636i	1.10887	+	0.640204i	0.938536	−	0.345183i	$-0.112183\pi$
$859$	32.4994	+	18.7636i	1.10887	+	0.640204i	0.170331	+	0.985387i	$0.445516\pi$
$860$			9.78323i			0.333605i
$861$	22.4985	+	2.67837i	0.766746	+	0.0912786i
$862$		−	23.8886i		−	0.813650i
$863$	−8.44445	+	14.6262i	−0.287452	+	0.497882i	−0.973201	−	0.229956i	$-0.926142\pi$
$863$	−8.44445	+	14.6262i	−0.287452	+	0.497882i	0.685749	+	0.727838i	$0.259475\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	44.3476	−	25.6041i	1.50786	−	0.870565i
$866$	−10.2025	+	17.6712i	−0.346694	+	0.600492i
$867$			7.42344i			0.252113i
$868$	6.88779	−	2.95369i	0.233787	−	0.100255i
$869$	−5.02293			−0.170391
$870$	−11.7189	−	6.76590i	−0.397307	−	0.229385i
$871$	16.9283	+	29.3207i	0.573595	+	0.993495i
$872$	−12.9714	+	7.48903i	−0.439266	+	0.253611i
$873$	−6.02225	+	10.4308i	−0.203822	+	0.353030i
$874$	15.0197	+	23.4361i	0.508049	+	0.792738i
$875$	−18.4742	+	24.7049i	−0.624541	+	0.835178i
$876$	−8.18899			−0.276680
$877$	0.862433	−	1.49378i	0.0291223	−	0.0504413i	−0.851097	−	0.525009i	$-0.824062\pi$
$877$	0.862433	−	1.49378i	0.0291223	−	0.0504413i	0.880219	+	0.474567i	$0.157395\pi$
$878$	−8.36598	+	4.83010i	−0.282338	+	0.163008i
$879$	−0.547058	+	0.315844i	−0.0184518	+	0.0106532i
$880$	−1.46037	−	0.843148i	−0.0492292	−	0.0284225i
$881$	−29.5084			−0.994163			−0.497082	−	0.867704i	$-0.665595\pi$
$881$	−29.5084			−0.994163			−0.497082	+	0.867704i	$0.665595\pi$
$882$	4.82538	−	5.07107i	0.162479	−	0.170752i
$883$	58.2690			1.96091			0.980455	−	0.196746i	$-0.0630373\pi$
$883$	58.2690			1.96091			0.980455	+	0.196746i	$0.0630373\pi$
$884$	−18.4491	−	10.6516i	−0.620511	−	0.358252i
$885$	19.6485	+	34.0323i	0.660479	+	1.14398i
$886$	−14.0208	−	24.2848i	−0.471039	−	0.815863i
$887$	15.0333	+	8.67946i	0.504768	+	0.291428i	0.730680	−	0.682720i	$-0.239203\pi$
$887$	15.0333	+	8.67946i	0.504768	+	0.291428i	−0.225913	+	0.974148i	$0.572536\pi$
$888$	7.11124			0.238638
$889$	25.9965	−	34.7642i	0.871894	−	1.16596i
$890$	38.9965			1.30717
$891$	0.401830	+	0.231997i	0.0134618	+	0.00777218i
$892$	5.83231	−	3.36728i	0.195280	−	0.112745i
$893$	−12.5634	+	7.25347i	−0.420418	+	0.242728i
$894$	−1.31048	+	2.26983i	−0.0438292	+	0.0759143i
$895$	54.0758			1.80756
$896$	1.04274	+	2.43160i	0.0348356	+	0.0812341i
$897$	−17.8139	−	27.7960i	−0.594788	−	0.928083i
$898$	−5.42188	+	9.39098i	−0.180931	+	0.313381i
$899$	−9.13380	+	5.27340i	−0.304629	+	0.175878i
$900$	4.10410	+	7.10851i	0.136803	+	0.236950i
$901$	13.5071	+	7.79831i	0.449986	+	0.259799i
$902$	−3.97349			−0.132303
$903$	7.07218	+	0.841920i	0.235347	+	0.0280173i
$904$		−	18.3985i		−	0.611925i
$905$	13.4266	−	23.2555i	0.446314	−	0.773039i
$906$	14.3717	−	8.29751i	0.477468	−	0.275666i
$907$	26.0509	−	15.0405i	0.865008	−	0.499412i	−0.000678457	−	1.00000i	$-0.500216\pi$
$907$	26.0509	−	15.0405i	0.865008	−	0.499412i	0.865686	+	0.500587i	$0.166883\pi$
$908$	5.07341	−	8.78741i	0.168367	−	0.291621i
$909$			7.51817i			0.249362i
$910$	−7.82479	+	65.7287i	−0.259389	+	2.17889i
$911$		−	46.6938i		−	1.54704i	−0.633775	−	0.773518i	$-0.718495\pi$
$911$		−	46.6938i		−	1.54704i	0.633775	−	0.773518i	$-0.281505\pi$
$912$	−5.02659	−	2.90210i	−0.166447	−	0.0960982i
$913$	−0.0864323	+	0.0499017i	−0.00286049	+	0.00165151i
$914$	0.341377	−	0.197094i	0.0112917	−	0.00651929i
$915$	−9.28456	−	5.36044i	−0.306938	−	0.177211i
$916$	−23.3101			−0.770187
$917$	−14.8468	+	6.36674i	−0.490284	+	0.210248i
$918$			3.09460i			0.102137i
$919$	9.53303	+	5.50390i	0.314466	+	0.181557i	0.648923	−	0.760854i	$-0.275220\pi$
$919$	9.53303	+	5.50390i	0.314466	+	0.181557i	−0.334457	+	0.942411i	$0.608553\pi$
$920$	8.00623	−	15.4819i	0.263957	−	0.510423i
$921$	3.33210	+	5.77137i	0.109796	+	0.190173i
$922$	28.9877	+	16.7361i	0.954660	+	0.551173i
$923$			55.4761i			1.82602i
$924$	−0.735178	+	0.983129i	−0.0241856	+	0.0323426i
$925$			58.3705i			1.91921i
$926$	7.50456	−	12.9983i	0.246615	−	0.427150i
$927$	2.09604	+	3.63045i	0.0688431	+	0.119240i
$928$	−1.86167	−	3.22451i	−0.0611124	−	0.105850i
$929$	−45.9015	−	26.5012i	−1.50598	−	0.869478i	−0.999976	−	0.00694636i	$-0.997789\pi$
$929$	−45.9015	−	26.5012i	−1.50598	−	0.869478i	−0.506004	−	0.862531i	$-0.668878\pi$
$930$	10.2946			0.337573
$931$	−39.4939	−	9.53842i	−1.29436	−	0.312609i
$932$	12.8883			0.422169
$933$	1.39972	−	2.42439i	0.0458249	−	0.0793710i
$934$	−14.4988	−	25.1127i	−0.474416	−	0.821712i
$935$	4.51928	−	2.60921i	0.147796	−	0.0853302i
$936$	5.96171	+	3.44200i	0.194865	+	0.112505i
$937$	−30.0548			−0.981847			−0.490923	−	0.871203i	$-0.663340\pi$
$937$	−30.0548			−0.981847			−0.490923	+	0.871203i	$0.663340\pi$
$938$	10.4208	+	7.79264i	0.340252	+	0.254439i
$939$			4.59357i			0.149905i
$940$	7.86658	+	4.54177i	0.256580	+	0.148136i
$941$	5.83177	+	10.1009i	0.190110	+	0.329281i	0.945287	−	0.326241i	$-0.105782\pi$
$941$	5.83177	+	10.1009i	0.190110	+	0.329281i	−0.755176	+	0.655522i	$0.772449\pi$
$942$	7.26828	−	4.19634i	0.236813	−	0.136724i
$943$	−1.90240	−	41.0259i	−0.0619506	−	1.33599i
$944$			10.8128i			0.351927i
$945$	8.83719	−	3.78965i	0.287474	−	0.123277i
$946$	−1.24903			−0.0406094
$947$	1.08204	−	1.87415i	0.0351616	−	0.0609017i	−0.847909	−	0.530142i	$-0.822139\pi$
$947$	1.08204	−	1.87415i	0.0351616	−	0.0609017i	0.883071	+	0.469240i	$0.155472\pi$
$948$	5.41271	+	9.37510i	0.175797	+	0.304489i
$949$	−28.1865	−	48.8204i	−0.914971	−	1.58478i
$950$	23.8211	−	41.2593i	0.772857	−	1.33863i
$951$		−	15.1721i		−	0.491988i
$952$	−8.13014	−	0.967866i	−0.263499	−	0.0313687i
$953$		−	1.06473i		−	0.0344900i	−0.999851	−	0.0172450i	$-0.994510\pi$
$953$		−	1.06473i		−	0.0344900i	0.999851	−	0.0172450i	$-0.00548953\pi$
$954$	−4.36472	−	2.51997i	−0.141313	−	0.0815871i
$955$	6.30433	−	3.63981i	0.204003	−	0.117781i
$956$	9.86674	+	17.0897i	0.319113	+	0.552720i
$957$	0.863804	−	1.49615i	0.0279228	−	0.0483637i
$958$	37.7032			1.21813
$959$	0.492842	−	4.13990i	0.0159147	−	0.133684i
$960$			3.63431i			0.117297i
$961$	−11.4882	+	19.8981i	−0.370585	+	0.641873i
$962$	24.4769	+	42.3952i	0.789165	+	1.36687i
$963$	6.12168	−	3.53435i	0.197268	−	0.113893i
$964$	1.94609	−	3.37072i	0.0626793	−	0.108564i
$965$	40.8883			1.31624
$966$	−10.5027	−	7.11994i	−0.337918	−	0.229080i
$967$	7.59233			0.244153			0.122076	−	0.992521i	$-0.461045\pi$
$967$	7.59233			0.244153			0.122076	+	0.992521i	$0.461045\pi$
$968$	−5.39236	+	9.33983i	−0.173317	+	0.300194i
$969$	15.5553	−	8.98085i	0.499708	−	0.288506i
$970$	−21.8867	−	37.9089i	−0.702740	−	1.21718i
$971$	9.30947	−	16.1245i	0.298755	−	0.517459i	−0.677096	−	0.735894i	$-0.736762\pi$
$971$	9.30947	−	16.1245i	0.298755	−	0.517459i	0.975851	+	0.218435i	$0.0700953\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	−31.8591	−	23.8241i	−1.02136	−	0.763765i
$974$	22.6511			0.725789
$975$	−28.2526	+	48.9349i	−0.904808	+	1.56717i
$976$	−1.47496	−	2.55470i	−0.0472122	−	0.0817739i
$977$	−15.5782	+	8.99409i	−0.498391	+	0.287746i	−0.728049	−	0.685525i	$-0.759573\pi$
$977$	−15.5782	+	8.99409i	−0.498391	+	0.287746i	0.229658	+	0.973271i	$0.426239\pi$
$978$	14.3985	+	8.31297i	0.460413	+	0.265820i
$979$			4.97870i			0.159120i
$980$	7.19225	+	24.4023i	0.229748	+	0.779504i
$981$			14.9781i			0.478213i
$982$	−15.3002	+	26.5008i	−0.488250	+	0.845675i
$983$	−22.3934	−	38.7865i	−0.714239	−	1.23710i	−0.963252	−	0.268598i	$-0.913440\pi$
$983$	−22.3934	−	38.7865i	−0.714239	−	1.23710i	0.249014	−	0.968500i	$-0.419894\pi$
$984$	4.28184	+	7.41636i	0.136500	+	0.236425i
$985$	35.1116	−	60.8151i	1.11875	−	1.93773i
$986$	11.5223			0.366944
$987$	3.96017	−	5.29581i	0.126054	−	0.168567i
$988$		−	39.9561i		−	1.27117i
$989$	−0.598001	−	12.8961i	−0.0190153	−	0.410072i
$990$	−1.46037	+	0.843148i	−0.0464138	+	0.0267970i
$991$	18.4963	+	32.0366i	0.587556	+	1.01768i	0.994551	+	0.104247i	$0.0332431\pi$
$991$	18.4963	+	32.0366i	0.587556	+	1.01768i	−0.406996	+	0.913430i	$0.633424\pi$
$992$	2.45312	+	1.41631i	0.0778865	+	0.0449678i
$993$			27.5289i			0.873602i
$994$	8.40317	+	19.5956i	0.266532	+	0.621535i
$995$	−78.8301			−2.49908
$996$	0.186279	+	0.107548i	0.00590248	+	0.00340780i
$997$	48.1387	−	27.7929i	1.52457	−	0.880209i	0.524991	−	0.851108i	$-0.324069\pi$
$997$	48.1387	−	27.7929i	1.52457	−	0.880209i	0.999576	−	0.0291014i	$-0.00926458\pi$
$998$	−14.9280	−	25.8560i	−0.472537	−	0.818459i
$999$	3.55562	−	6.15851i	0.112495	−	0.194847i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.k.a.229.8	yes	32
7.3	odd	6	inner	966.2.k.a.367.1	yes	32
23.22	odd	2	inner	966.2.k.a.229.1	✓	32
161.45	even	6	inner	966.2.k.a.367.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.k.a.229.1	✓	32	23.22	odd	2	inner
966.2.k.a.229.8	yes	32	1.1	even	1	trivial
966.2.k.a.367.1	yes	32	7.3	odd	6	inner
966.2.k.a.367.8	yes	32	161.45	even	6	inner

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.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.81715 - 3.14740i) q^{5} -1.00000i q^{6} +(1.58446 - 2.11884i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.81715 - 3.14740i) q^{5} -1.00000i q^{6} +(1.58446 - 2.11884i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.81715 + 3.14740i) q^{10} +(-0.401830 + 0.231997i) q^{11} +(0.866025 + 0.500000i) q^{12} +6.88399i q^{13} +(1.04274 + 2.43160i) q^{14} +3.63431i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.54730 - 2.68000i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.90210 - 5.02659i) q^{19} -3.63431 q^{20} +(-0.312760 + 2.62720i) q^{21} -0.463993i q^{22} +(4.79068 - 0.222148i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-4.10410 - 7.10851i) q^{25} +(-5.96171 - 3.44200i) q^{26} +1.00000i q^{27} +(-2.62720 - 0.312760i) q^{28} +3.72335 q^{29} +(-3.14740 - 1.81715i) q^{30} +(-2.45312 + 1.41631i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.231997 - 0.401830i) q^{33} +3.09460 q^{34} +(-3.78965 - 8.83719i) q^{35} -1.00000 q^{36} +(-6.15851 - 3.55562i) q^{37} +(2.90210 + 5.02659i) q^{38} +(-3.44200 - 5.96171i) q^{39} +(1.81715 - 3.14740i) q^{40} -8.56367i q^{41} +(-2.11884 - 1.58446i) q^{42} -2.69191i q^{43} +(0.401830 + 0.231997i) q^{44} +(-1.81715 - 3.14740i) q^{45} +(-2.20296 + 4.25993i) q^{46} +(-2.16453 - 1.24969i) q^{47} -1.00000i q^{48} +(-1.97899 - 6.71443i) q^{49} +8.20821 q^{50} +(2.68000 + 1.54730i) q^{51} +(5.96171 - 3.44200i) q^{52} +(-4.36472 + 2.51997i) q^{53} +(-0.866025 - 0.500000i) q^{54} +1.68630i q^{55} +(1.58446 - 2.11884i) q^{56} +5.80420i q^{57} +(-1.86167 + 3.22451i) q^{58} +(9.36417 - 5.40640i) q^{59} +(3.14740 - 1.81715i) q^{60} +(-1.47496 + 2.55470i) q^{61} -2.83261i q^{62} +(-1.04274 - 2.43160i) q^{63} +1.00000 q^{64} +(21.6667 + 12.5093i) q^{65} +(0.231997 + 0.401830i) q^{66} +(4.25926 - 2.45909i) q^{67} +(-1.54730 + 2.68000i) q^{68} +(-4.03778 + 2.58773i) q^{69} +(9.54806 + 1.13667i) q^{70} +8.05872 q^{71} +(0.500000 - 0.866025i) q^{72} +(-7.09187 + 4.09450i) q^{73} +(6.15851 - 3.55562i) q^{74} +(7.10851 + 4.10410i) q^{75} -5.80420 q^{76} +(-0.145118 + 1.21900i) q^{77} +6.88399 q^{78} +(9.37510 + 5.41271i) q^{79} +(1.81715 + 3.14740i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.41636 + 4.28184i) q^{82} +0.215097 q^{83} +(2.43160 - 1.04274i) q^{84} -11.2467 q^{85} +(2.33126 + 1.34595i) q^{86} +(-3.22451 + 1.86167i) q^{87} +(-0.401830 + 0.231997i) q^{88} +(5.36505 - 9.29255i) q^{89} +3.63431 q^{90} +(14.5861 + 10.9074i) q^{91} +(-2.58773 - 4.03778i) q^{92} +(1.41631 - 2.45312i) q^{93} +(2.16453 - 1.24969i) q^{94} +(-10.5471 - 18.2682i) q^{95} +(0.866025 + 0.500000i) q^{96} -12.0445 q^{97} +(6.80436 + 1.64336i) q^{98} +0.463993i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 16 * q^9	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 16 q^{9} - 16 q^{16} + 16 q^{18} + 8 q^{23} - 24 q^{25} - 12 q^{26} - 8 q^{29} + 48 q^{31} - 16 q^{32} - 20 q^{35} - 32 q^{36} - 8 q^{39} + 8 q^{46} + 12 q^{47} + 24 q^{49} + 48 q^{50} + 12 q^{52} + 4 q^{58} - 12 q^{59} + 32 q^{64} + 64 q^{70} + 48 q^{71} + 16 q^{72} + 12 q^{73} + 36 q^{75} + 64 q^{77} + 16 q^{78} - 16 q^{81} - 12 q^{82} + 32 q^{85} - 24 q^{87} - 16 q^{92} - 12 q^{94} + 40 q^{95} - 24 q^{98}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 16 * q^9 - 16 * q^16 + 16 * q^18 + 8 * q^23 - 24 * q^25 - 12 * q^26 - 8 * q^29 + 48 * q^31 - 16 * q^32 - 20 * q^35 - 32 * q^36 - 8 * q^39 + 8 * q^46 + 12 * q^47 + 24 * q^49 + 48 * q^50 + 12 * q^52 + 4 * q^58 - 12 * q^59 + 32 * q^64 + 64 * q^70 + 48 * q^71 + 16 * q^72 + 12 * q^73 + 36 * q^75 + 64 * q^77 + 16 * q^78 - 16 * q^81 - 12 * q^82 + 32 * q^85 - 24 * q^87 - 16 * q^92 - 12 * q^94 + 40 * q^95 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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