LMFDB - Embedded newform 966.2.k.a.367.8

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			367.8
Character	$\chi$	$=$	966.367
Dual form			966.2.k.a.229.8

$q$-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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

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

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	0.910999	+	0.412409i	$0.135313\pi$
$5$	1.81715	+	3.14740i	0.812656	+	1.40756i	−0.0983423	+	0.995153i	$0.531354\pi$
$6$			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	0.438197	−	0.898879i	$-0.355617\pi$
$11$	−0.401830	−	0.231997i	−0.121156	−	0.0699496i	−0.559353	+	0.828929i	$0.688951\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$		−	6.88399i		−	1.90928i	−0.297770	−	0.954638i	$-0.596243\pi$
$13$		−	6.88399i		−	1.90928i	0.297770	−	0.954638i	$-0.403757\pi$
$14$	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	−0.990368	−	0.138459i	$-0.955785\pi$
$17$	−1.54730	+	2.68000i	−0.375276	+	0.649996i	0.615093	+	0.788455i	$0.289119\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	2.90210	+	5.02659i	0.665788	+	1.15318i	0.979071	+	0.203519i	$0.0652378\pi$
$19$	2.90210	+	5.02659i	0.665788	+	1.15318i	−0.313283	+	0.949660i	$0.601429\pi$
$20$	−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	0.263256	−	0.964726i	$-0.415203\pi$
$31$	−2.45312	−	1.41631i	−0.440593	−	0.254376i	−0.703849	+	0.710350i	$0.748537\pi$
$32$	−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	−0.911909	−	0.410392i	$-0.865392\pi$
$37$	−6.15851	+	3.55562i	−1.01245	+	0.584540i	−0.100544	+	0.994933i	$0.532058\pi$
$38$	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	$0.233153\pi$
$41$			8.56367i			1.33742i	−0.743523	+	0.668711i	$0.766847\pi$
$42$	−2.11884	+	1.58446i	−0.326944	+	0.244487i
$43$			2.69191i			0.410512i	0.978708	+	0.205256i	$0.0658027\pi$
$43$			2.69191i			0.410512i	−0.978708	+	0.205256i	$0.934197\pi$
$44$	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	−0.649487	−	0.760372i	$-0.725016\pi$
$47$	−2.16453	+	1.24969i	−0.315729	+	0.182286i	0.333758	+	0.942659i	$0.391683\pi$
$48$			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	0.169320	−	0.985561i	$-0.445843\pi$
$53$	−4.36472	−	2.51997i	−0.599540	−	0.346145i	−0.768861	+	0.639416i	$0.779176\pi$
$54$	−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	0.964728	−	0.263250i	$-0.0847943\pi$
$59$	9.36417	+	5.40640i	1.21911	+	0.703854i	0.254383	+	0.967104i	$0.418128\pi$
$60$	3.14740	+	1.81715i	0.406328	+	0.234594i
$61$	−1.47496	−	2.55470i	−0.188849	−	0.327095i	0.756018	−	0.654551i	$-0.227142\pi$
$61$	−1.47496	−	2.55470i	−0.188849	−	0.327095i	−0.944867	+	0.327455i	$0.893809\pi$
$62$			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	0.737079	−	0.675807i	$-0.236205\pi$
$67$	4.25926	+	2.45909i	0.520352	+	0.300425i	−0.216727	+	0.976232i	$0.569538\pi$
$68$	−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	0.0238257	−	0.999716i	$-0.492415\pi$
$73$	−7.09187	−	4.09450i	−0.830041	−	0.479224i	−0.853867	+	0.520492i	$0.825749\pi$
$74$	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	0.130797	−	0.991409i	$-0.458246\pi$
$79$	9.37510	−	5.41271i	1.05478	−	0.608978i	0.923984	+	0.382431i	$0.124913\pi$
$80$	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	0.996695	+	0.0812297i	$0.0258847\pi$
$89$	5.36505	+	9.29255i	0.568695	+	0.985008i	−0.428001	+	0.903778i	$0.640782\pi$
$90$	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	0.139775	−	0.990183i	$-0.455362\pi$
$101$	−6.51092	−	3.75908i	−0.647861	−	0.374043i	−0.787636	+	0.616141i	$0.788695\pi$
$102$	−2.68000	−	1.54730i	−0.265360	−	0.153206i
$103$	−2.09604	−	3.63045i	−0.206529	−	0.357719i	0.744090	−	0.668080i	$-0.232884\pi$
$103$	−2.09604	−	3.63045i	−0.206529	−	0.357719i	−0.950619	+	0.310361i	$0.899550\pi$
$104$		−	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	−0.174006	−	0.984745i	$-0.555671\pi$
$107$	6.12168	−	3.53435i	0.591805	−	0.341679i	0.765811	+	0.643066i	$0.222338\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	−12.9714	−	7.48903i	−1.24243	−	0.717319i	−0.272844	−	0.962058i	$-0.587964\pi$
$109$	−12.9714	−	7.48903i	−1.24243	−	0.717319i	−0.969589	+	0.244739i	$0.921298\pi$
$110$	−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	$0.332931\pi$
$113$			18.3985i			1.73078i	−0.501095	+	0.865392i	$0.667069\pi$
$114$	−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	−0.712882	−	0.701284i	$-0.752610\pi$
$131$	−5.28775	+	3.05288i	−0.461993	+	0.266732i	0.250889	+	0.968016i	$0.419277\pi$
$132$	−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	0.557162	−	0.830404i	$-0.311890\pi$
$137$	1.36467	+	0.787893i	0.116592	+	0.0673142i	−0.440570	+	0.897718i	$0.645224\pi$
$138$	−0.222148	+	4.79068i	−0.0189105	+	0.407810i
$139$			15.0361i			1.27535i	0.770307	+	0.637673i	$0.220103\pi$
$139$			15.0361i			1.27535i	−0.770307	+	0.637673i	$0.779897\pi$
$140$	−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	−0.590086	−	0.807340i	$-0.700906\pi$
$149$	−2.26983	+	1.31048i	−0.185951	+	0.107359i	0.404134	+	0.914700i	$0.367573\pi$
$150$	−7.10851	−	4.10410i	−0.580408	−	0.335099i
$151$	8.29751	−	14.3717i	0.675242	−	1.16955i	−0.301156	−	0.953575i	$-0.597373\pi$
$151$	8.29751	−	14.3717i	0.675242	−	1.16955i	0.976398	−	0.215979i	$-0.0692941\pi$
$152$	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	−0.648562	−	0.761162i	$-0.724629\pi$
$157$	4.19634	−	7.26828i	0.334905	−	0.580072i	0.983467	+	0.181090i	$0.0579626\pi$
$158$	−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	−0.982851	−	0.184402i	$-0.940965\pi$
$163$	−8.31297	−	14.3985i	−0.651122	−	1.12778i	0.331729	−	0.943375i	$-0.392368\pi$
$164$	−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	$0.259854\pi$
$167$			18.8326i			1.45731i	−0.684882	+	0.728654i	$0.740146\pi$
$168$	−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	0.0416419	−	0.999133i	$-0.486741\pi$
$173$	12.2025	−	7.04510i	0.927737	−	0.535629i	0.886095	+	0.463503i	$0.153408\pi$
$174$			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	−0.441756	−	0.897135i	$-0.645644\pi$
$179$	7.43963	−	12.8858i	0.556064	−	0.963131i	0.997820	−	0.0659956i	$-0.0210223\pi$
$180$	−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	−0.435927	−	0.899982i	$-0.643579\pi$
$191$	1.73467	−	1.00151i	0.125516	−	0.0724669i	0.561444	+	0.827515i	$0.310246\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	5.62532	−	9.74334i	0.404919	−	0.701341i	−0.589393	−	0.807847i	$-0.700633\pi$
$193$	5.62532	−	9.74334i	0.404919	−	0.701341i	0.994312	+	0.106506i	$0.0339663\pi$
$194$	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	0.169413	+	0.985545i	$0.445813\pi$
$199$	−10.8453	+	18.7846i	−0.768801	+	1.33160i	−0.938214	+	0.346057i	$0.887520\pi$
$200$	−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	$-0.927602\pi$
$223$		−	6.73457i		−	0.450980i	0.974245	−	0.225490i	$-0.0723983\pi$
$224$	−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	−0.647082	−	0.762420i	$-0.724011\pi$
$227$	5.07341	−	8.78741i	0.336734	−	0.583241i	0.983816	+	0.179179i	$0.0573442\pi$
$228$	5.02659	+	2.90210i	0.332894	+	0.192196i
$229$	11.6550	+	20.1871i	0.770187	+	1.33400i	0.937460	+	0.348092i	$0.113170\pi$
$229$	11.6550	+	20.1871i	0.770187	+	1.33400i	−0.167273	+	0.985911i	$0.553496\pi$
$230$	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	0.573982	−	0.818868i	$-0.305398\pi$
$233$	−6.44413	−	11.1616i	−0.422169	−	0.731219i	−0.996151	+	0.0876492i	$0.972065\pi$
$234$	−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	−0.796514	−	0.604619i	$-0.793325\pi$
$241$	1.94609	−	3.37072i	0.125359	−	0.217127i	0.921873	+	0.387492i	$0.126659\pi$
$242$	−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	−0.245517	−	0.969392i	$-0.578958\pi$
$257$	7.55458	−	4.36164i	0.471242	−	0.272072i	0.716760	+	0.697320i	$0.245625\pi$
$258$	−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	0.146060	−	0.989276i	$-0.453341\pi$
$263$	−10.3409	−	5.97033i	−0.637649	−	0.368147i	−0.783708	+	0.621129i	$0.786674\pi$
$264$	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	0.460081	−	0.887877i	$-0.347820\pi$
$269$	−1.29245	−	0.746198i	−0.0788022	−	0.0454965i	−0.538883	+	0.842380i	$0.681154\pi$
$270$	−3.14740	−	1.81715i	−0.191545	−	0.110589i
$271$	14.1697	−	8.18090i	0.860750	−	0.496954i	−0.00351337	−	0.999994i	$-0.501118\pi$
$271$	14.1697	−	8.18090i	0.860750	−	0.496954i	0.864263	+	0.503040i	$0.167785\pi$
$272$	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	−0.0187547	−	0.999824i	$-0.505970\pi$
$277$	14.2549	−	24.6903i	0.856496	−	1.48349i	0.875250	−	0.483670i	$-0.160696\pi$
$278$	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	$-0.682577\pi$
$281$		−	28.1607i		−	1.67993i	0.542644	−	0.839963i	$-0.317423\pi$
$282$	−1.24969	−	2.16453i	−0.0744181	−	0.128896i
$283$	3.85474	−	6.67660i	0.229140	−	0.396883i	−0.728413	−	0.685138i	$-0.759742\pi$
$283$	3.85474	−	6.67660i	0.229140	−	0.396883i	0.957554	+	0.288255i	$0.0930752\pi$
$284$	−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	$0.0609049\pi$
$307$			6.66420i			0.380346i	−0.981751	+	0.190173i	$0.939095\pi$
$308$	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	0.429685	−	0.902979i	$-0.358625\pi$
$311$	−2.42439	−	1.39972i	−0.137475	−	0.0793710i	−0.567160	+	0.823608i	$0.691958\pi$
$312$	−3.44200	+	5.96171i	−0.194865	+	0.337515i
$313$	2.29678	+	3.97815i	0.129822	+	0.224858i	0.923607	−	0.383340i	$-0.125226\pi$
$313$	2.29678	+	3.97815i	0.129822	+	0.224858i	−0.793786	+	0.608198i	$0.791893\pi$
$314$	−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	0.570446	−	0.821335i	$-0.306770\pi$
$317$	−7.58603	−	13.1394i	−0.426074	−	0.737981i	−0.996520	+	0.0833535i	$0.973437\pi$
$318$	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	0.944594	+	0.328240i	$0.106456\pi$
$331$	13.7644	+	23.8407i	0.756561	+	1.31040i	−0.188033	+	0.982163i	$0.560211\pi$
$332$	−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	$-0.735791\pi$
$337$		−	27.0942i		−	1.47591i	0.674848	−	0.737957i	$-0.264209\pi$
$338$	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	−0.964708	−	0.263322i	$-0.915182\pi$
$347$	−4.73729	+	8.20522i	−0.254311	+	0.440479i	0.710397	+	0.703801i	$0.248515\pi$
$348$	3.22451	−	1.86167i	0.172852	−	0.0997962i
$349$		−	4.84804i		−	0.259510i	−0.991546	−	0.129755i	$-0.958581\pi$
$349$		−	4.84804i		−	0.259510i	0.991546	−	0.129755i	$-0.0414191\pi$
$350$	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	−0.142493	−	0.989796i	$-0.545512\pi$
$353$	−20.1209	−	11.6168i	−1.07093	−	0.618300i	−0.928435	+	0.371496i	$0.878845\pi$
$354$	−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	−0.259215	−	0.965820i	$-0.583464\pi$
$359$	8.48083	−	4.89641i	0.447601	−	0.258423i	0.706817	+	0.707397i	$0.250131\pi$
$360$	−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	−0.651200	−	0.758906i	$-0.725734\pi$
$367$	6.35316	−	11.0040i	0.331632	−	0.574404i	0.982832	+	0.184502i	$0.0590674\pi$
$368$	−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	0.136937	−	0.990580i	$-0.456274\pi$
$373$	20.5352	−	11.8560i	1.06327	−	0.613881i	0.926336	+	0.376699i	$0.122941\pi$
$374$	−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	$-0.933893\pi$
$379$		−	8.02828i		−	0.412385i	0.978511	−	0.206193i	$-0.0661073\pi$
$380$	−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	−0.828912	−	0.559379i	$-0.811040\pi$
$383$	−17.5917	−	30.4697i	−0.898892	−	1.55693i	−0.0699801	−	0.997548i	$-0.522294\pi$
$384$			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	0.368004	−	0.929824i	$-0.380041\pi$
$389$	−4.99478	−	2.88374i	−0.253245	−	0.146211i	−0.621249	+	0.783613i	$0.713375\pi$
$390$	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	0.619654	−	0.784875i	$-0.287273\pi$
$397$	32.0631	−	18.5117i	1.60920	−	0.929074i	0.989549	−	0.144198i	$-0.0460604\pi$
$398$	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	−0.819712	−	0.572776i	$-0.805866\pi$
$401$	−14.6889	+	8.48064i	−0.733529	+	0.423503i	0.0861829	+	0.996279i	$0.472533\pi$
$402$	−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	0.0524709	−	0.998622i	$-0.483290\pi$
$409$	−15.8984	−	9.17895i	−0.786126	−	0.453870i	−0.838597	+	0.544752i	$0.816624\pi$
$410$	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	$-0.946694\pi$
$421$		−	6.84009i		−	0.333366i	0.986011	−	0.166683i	$-0.0533056\pi$
$422$	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	−0.0892984	−	0.996005i	$-0.528462\pi$
$431$	−20.6882	−	11.9443i	−0.996513	−	0.575337i	−0.907215	+	0.420668i	$0.861796\pi$
$432$	−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	−0.286889	−	0.957964i	$-0.592621\pi$
$439$	8.36598	−	4.83010i	0.399287	−	0.230528i	0.686176	+	0.727435i	$0.259288\pi$
$440$		−	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	−0.978972	−	0.203993i	$-0.934608\pi$
$443$	−14.0208	−	24.2848i	−0.666149	−	1.15380i	0.312823	−	0.949811i	$-0.398725\pi$
$444$	−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	−0.507963	−	0.861379i	$-0.669601\pi$
$457$	−0.341377	+	0.197094i	−0.0159689	+	0.00921966i	0.491994	+	0.870598i	$0.336268\pi$
$458$	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	$0.284515\pi$
$461$			33.4721i			1.55895i	−0.626432	+	0.779476i	$0.715485\pi$
$462$	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	−0.977642	−	0.210276i	$-0.932564\pi$
$467$	−14.4988	−	25.1127i	−0.670925	−	1.16208i	0.306717	−	0.951801i	$-0.400770\pi$
$468$			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	0.00927537	+	0.999957i	$0.497048\pi$
$479$	−18.8516	+	32.6519i	−0.861350	+	1.49190i	−0.870626	+	0.491946i	$0.836286\pi$
$480$	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	0.486672	+	0.873585i	$0.338211\pi$
$487$	−11.3256	+	19.6165i	−0.513211	+	0.888907i	−0.999883	+	0.0153220i	$0.995123\pi$
$488$	−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	−0.978388	−	0.206778i	$-0.933702\pi$
$499$	−14.9280	−	25.8560i	−0.668269	−	1.15748i	0.310119	−	0.950698i	$-0.399631\pi$
$500$	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	−0.743694	−	0.668521i	$-0.766928\pi$
$509$	−12.1059	+	6.98934i	−0.536585	+	0.309797i	0.207109	+	0.978318i	$0.433594\pi$
$510$		−	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	−0.981112	−	0.193439i	$-0.938036\pi$
$521$	−7.37338	+	12.7711i	−0.323033	+	0.559510i	0.658079	+	0.752949i	$0.271369\pi$
$522$	1.86167	−	3.22451i	0.0814832	−	0.141133i
$523$	−8.32378	−	14.4172i	−0.363974	−	0.630421i	0.624637	−	0.780915i	$-0.285247\pi$
$523$	−8.32378	−	14.4172i	−0.363974	−	0.630421i	−0.988611	+	0.150494i	$0.951913\pi$
$524$		−	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	0.971373	−	0.237558i	$-0.0763470\pi$
$541$	6.51160	+	11.2784i	0.279955	+	0.484897i	−0.691418	+	0.722455i	$0.743014\pi$
$542$	−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	0.983467	−	0.181086i	$-0.0579613\pi$
$557$	31.1148	+	17.9641i	1.31838	+	0.761164i	0.334908	+	0.942251i	$0.391295\pi$
$558$	−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	−0.280147	−	0.959957i	$-0.590383\pi$
$563$	16.4023	−	28.4096i	0.691274	−	1.19732i	0.971421	−	0.237364i	$-0.0762835\pi$
$564$	−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	0.185046	−	0.982730i	$-0.440757\pi$
$569$	26.9222	−	15.5435i	1.12864	−	0.651619i	0.943592	+	0.331111i	$0.107423\pi$
$570$	−18.2682	−	10.5471i	−0.765170	−	0.441771i
$571$	33.6805	+	19.4454i	1.40948	+	0.813766i	0.995338	−	0.0964438i	$-0.0307468\pi$
$571$	33.6805	+	19.4454i	1.40948	+	0.813766i	0.414146	+	0.910210i	$0.364080\pi$
$572$	−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	0.405830	−	0.913949i	$-0.366983\pi$
$577$	−4.39001	−	2.53457i	−0.182758	−	0.105516i	−0.588588	+	0.808433i	$0.700316\pi$
$578$	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	$0.0599798\pi$
$587$			9.07676i			0.374638i	−0.982299	+	0.187319i	$0.940020\pi$
$588$	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	−0.621752	−	0.783214i	$-0.713579\pi$
$593$	−6.19369	+	3.57593i	−0.254345	+	0.146846i	0.367407	+	0.930060i	$0.380245\pi$
$594$	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	−0.655794	−	0.754940i	$-0.727666\pi$
$599$	7.97624	−	13.8152i	0.325900	−	0.564476i	0.981694	+	0.190464i	$0.0609993\pi$
$600$	7.10851	−	4.10410i	0.290204	−	0.167549i
$601$			5.80649i			0.236852i	0.992963	+	0.118426i	$0.0377848\pi$
$601$			5.80649i			0.236852i	−0.992963	+	0.118426i	$0.962215\pi$
$602$	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	−0.794936	−	0.606693i	$-0.792496\pi$
$607$	−16.4330	+	9.48757i	−0.666993	+	0.385089i	0.127943	+	0.991781i	$0.459162\pi$
$608$	−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	0.196867	−	0.980430i	$-0.436923\pi$
$613$	−13.7109	−	7.91598i	−0.553777	−	0.319723i	−0.750644	+	0.660707i	$0.770257\pi$
$614$	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	$-0.987613\pi$
$617$		−	1.93272i		−	0.0778085i	0.999243	−	0.0389042i	$-0.0123867\pi$
$618$	3.63045	−	2.09604i	0.146038	−	0.0843152i
$619$	−15.1832	+	26.2980i	−0.610263	+	1.05701i	0.380933	+	0.924603i	$0.375603\pi$
$619$	−15.1832	+	26.2980i	−0.610263	+	1.05701i	−0.991196	+	0.132404i	$0.957730\pi$
$620$	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	$-0.621967\pi$
$631$		−	46.5963i		−	1.85497i	0.373862	−	0.927484i	$-0.378033\pi$
$632$	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	0.0103803	−	0.999946i	$-0.496696\pi$
$641$	−21.5306	−	12.4307i	−0.850408	−	0.490983i	−0.860789	+	0.508963i	$0.830029\pi$
$642$	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	0.303755	−	0.952750i	$-0.401760\pi$
$647$	−9.39800	−	5.42594i	−0.369473	−	0.213316i	−0.673228	+	0.739435i	$0.735093\pi$
$648$	−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	−0.994343	−	0.106216i	$-0.966126\pi$
$653$	−15.0552	−	26.0765i	−0.589157	−	1.02045i	0.405186	−	0.914234i	$-0.367207\pi$
$654$	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	$0.0331308\pi$
$659$			5.33421i			0.207791i	−0.994588	+	0.103896i	$0.966869\pi$
$660$	−0.843148	−	1.46037i	−0.0328195	−	0.0568450i
$661$	−23.3926	+	40.5172i	−0.909868	+	1.57594i	−0.0956209	+	0.995418i	$0.530484\pi$
$661$	−23.3926	+	40.5172i	−0.909868	+	1.57594i	−0.814247	+	0.580519i	$0.802850\pi$
$662$	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	0.988097	−	0.153835i	$-0.0491623\pi$
$677$	9.38835	+	16.2611i	0.360824	+	0.624965i	−0.627273	+	0.778799i	$0.715829\pi$
$678$	−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	−0.749882	−	0.661571i	$-0.769890\pi$
$683$	5.17449	−	8.96248i	0.197996	−	0.342940i	0.947879	+	0.318632i	$0.103223\pi$
$684$	−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	−0.0469602	−	0.998897i	$-0.514953\pi$
$691$	20.8883	−	12.0599i	0.794630	−	0.458780i	0.841590	+	0.540117i	$0.181620\pi$
$692$			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	$0.00723951\pi$
$701$			1.20423i			0.0454833i	−0.999741	+	0.0227416i	$0.992760\pi$
$702$	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	0.00266782	−	0.999996i	$-0.499151\pi$
$709$	23.1662	−	13.3750i	0.870024	−	0.502309i	0.867356	+	0.497688i	$0.165817\pi$
$710$	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	−0.788343	−	0.615236i	$-0.789061\pi$
$719$	−17.4213	+	10.0582i	−0.649705	+	0.375107i	0.138638	+	0.990343i	$0.455727\pi$
$720$	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	0.984082	+	0.177714i	$0.0568703\pi$
$733$	17.4883	+	30.2907i	0.645946	+	1.11881i	−0.338136	+	0.941097i	$0.609796\pi$
$734$	−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	−0.998189	−	0.0601562i	$-0.980840\pi$
$739$	−12.1514	+	21.0469i	−0.446998	+	0.774223i	0.551191	+	0.834379i	$0.314173\pi$
$740$	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	$0.263545\pi$
$743$			40.1537i			1.47310i	−0.676386	+	0.736548i	$0.736455\pi$
$744$	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	−0.712795	−	0.701373i	$-0.752571\pi$
$751$	−12.6550	+	7.30634i	−0.461786	+	0.266612i	0.251009	+	0.967985i	$0.419238\pi$
$752$	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	$-0.841745\pi$
$757$		−	26.2448i		−	0.953883i	0.878935	−	0.476941i	$-0.158255\pi$
$758$	−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	−0.978980	−	0.203956i	$-0.934620\pi$
$761$	−35.6370	+	20.5750i	−1.29184	+	0.745844i	−0.312859	+	0.949800i	$0.601287\pi$
$762$			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	−0.498885	−	0.866668i	$-0.666257\pi$
$773$	13.9324	−	24.1317i	0.501114	−	0.867956i	0.999999	−	0.00128738i	$-0.000409786\pi$
$774$	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	−0.940041	−	0.341061i	$-0.889214\pi$
$787$	−4.89963	+	8.48641i	−0.174653	+	0.302508i	0.765388	+	0.643569i	$0.222547\pi$
$788$	−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	−0.893758	−	0.448550i	$-0.851941\pi$
$809$	−1.66172	+	2.87818i	−0.0584230	+	0.101192i	0.835335	+	0.549742i	$0.185274\pi$
$810$	1.81715	+	3.14740i	0.0638483	+	0.110589i
$811$		−	30.9763i		−	1.08773i	−0.839174	−	0.543863i	$-0.816961\pi$
$811$		−	30.9763i		−	1.08773i	0.839174	−	0.543863i	$-0.183039\pi$
$812$	−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	0.998861	−	0.0477219i	$-0.0151961\pi$
$821$	13.1260	+	22.7350i	0.458102	+	0.793456i	−0.540759	+	0.841178i	$0.681863\pi$
$822$	−0.787893	+	1.36467i	−0.0274809	+	0.0475983i
$823$	8.71050	−	15.0870i	0.303629	−	0.525901i	−0.673326	−	0.739345i	$-0.735135\pi$
$823$	8.71050	−	15.0870i	0.303629	−	0.525901i	0.976955	+	0.213445i	$0.0684684\pi$
$824$	−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	$-0.958564\pi$
$827$		−	7.46593i		−	0.259616i	0.991539	−	0.129808i	$-0.0414361\pi$
$828$	−4.79068	−	0.222148i	−0.166488	−	0.00772016i
$829$	−35.5742	−	20.5388i	−1.23554	−	0.713341i	−0.267363	−	0.963596i	$-0.586152\pi$
$829$	−35.5742	−	20.5388i	−1.23554	−	0.713341i	−0.968180	+	0.250255i	$0.919486\pi$
$830$	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	$-0.820411\pi$
$853$		−	31.2352i		−	1.06947i	0.845018	−	0.534737i	$-0.179589\pi$
$854$	−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	0.794315	−	0.607506i	$-0.207830\pi$
$857$	19.4780	+	11.2456i	0.665356	+	0.384143i	−0.128959	+	0.991650i	$0.541163\pi$
$858$	−2.76619	−	1.59706i	−0.0944363	−	0.0545228i
$859$	32.4994	−	18.7636i	1.10887	−	0.640204i	0.170331	−	0.985387i	$-0.445516\pi$
$859$	32.4994	−	18.7636i	1.10887	−	0.640204i	0.938536	+	0.345183i	$0.112183\pi$
$860$		−	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	0.685749	−	0.727838i	$-0.259475\pi$
$863$	−8.44445	−	14.6262i	−0.287452	−	0.497882i	−0.973201	+	0.229956i	$0.926142\pi$
$864$	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	0.880219	−	0.474567i	$-0.157395\pi$
$877$	0.862433	+	1.49378i	0.0291223	+	0.0504413i	−0.851097	+	0.525009i	$0.824062\pi$
$878$	−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	−0.225913	−	0.974148i	$-0.572536\pi$
$887$	15.0333	−	8.67946i	0.504768	−	0.291428i	0.730680	+	0.682720i	$0.239203\pi$
$888$	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	0.865686	−	0.500587i	$-0.166883\pi$
$907$	26.0509	+	15.0405i	0.865008	+	0.499412i	−0.000678457		1.00000i	$0.500216\pi$
$908$	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	$0.281505\pi$
$911$			46.6938i			1.54704i	−0.633775	+	0.773518i	$0.718495\pi$
$912$	−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	−0.334457	−	0.942411i	$-0.608553\pi$
$919$	9.53303	−	5.50390i	0.314466	−	0.181557i	0.648923	+	0.760854i	$0.275220\pi$
$920$	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	−0.506004	+	0.862531i	$0.668878\pi$
$929$	−45.9015	+	26.5012i	−1.50598	+	0.869478i	−0.999976	+	0.00694636i	$0.997789\pi$
$930$	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	−0.755176	−	0.655522i	$-0.772449\pi$
$941$	5.83177	−	10.1009i	0.190110	−	0.329281i	0.945287	+	0.326241i	$0.105782\pi$
$942$	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	0.883071	−	0.469240i	$-0.155472\pi$
$947$	1.08204	+	1.87415i	0.0351616	+	0.0609017i	−0.847909	+	0.530142i	$0.822139\pi$
$948$	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	$0.00548953\pi$
$953$			1.06473i			0.0344900i	−0.999851	+	0.0172450i	$0.994510\pi$
$954$	−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	0.975851	−	0.218435i	$-0.0700953\pi$
$971$	9.30947	+	16.1245i	0.298755	+	0.517459i	−0.677096	+	0.735894i	$0.736762\pi$
$972$			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	0.229658	−	0.973271i	$-0.426239\pi$
$977$	−15.5782	−	8.99409i	−0.498391	−	0.287746i	−0.728049	+	0.685525i	$0.759573\pi$
$978$	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	0.249014	+	0.968500i	$0.419894\pi$
$983$	−22.3934	+	38.7865i	−0.714239	+	1.23710i	−0.963252	+	0.268598i	$0.913440\pi$
$984$	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	−0.406996	−	0.913430i	$-0.633424\pi$
$991$	18.4963	−	32.0366i	0.587556	−	1.01768i	0.994551	−	0.104247i	$-0.0332431\pi$
$992$	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	0.999576	+	0.0291014i	$0.00926458\pi$
$997$	48.1387	+	27.7929i	1.52457	+	0.880209i	0.524991	+	0.851108i	$0.324069\pi$
$998$	−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.367.8	yes	32
7.5	odd	6	inner	966.2.k.a.229.1	✓	32
23.22	odd	2	inner	966.2.k.a.367.1	yes	32
161.68	even	6	inner	966.2.k.a.229.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.k.a.229.1	✓	32	7.5	odd	6	inner
966.2.k.a.229.8	yes	32	161.68	even	6	inner
966.2.k.a.367.1	yes	32	23.22	odd	2	inner
966.2.k.a.367.8	yes	32	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.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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