LMFDB - Embedded newform 64.2.i.a.45.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,2,Mod(5,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(16))

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

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

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

chi := DirichletCharacter("64.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	64.i (of order $16$, degree $8$, 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:	$0.511042572936$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			45.7
Character	$\chi$	$=$	64.45
Dual form			64.2.i.a.37.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.998819 + 1.00118i) q^{2} +(-0.477374 - 0.714441i) q^{3} +(-0.00472188 + 1.99999i) q^{4} +(0.0517508 + 0.260169i) q^{5} +(0.238474 - 1.19153i) q^{6} +(-0.515195 - 1.24379i) q^{7} +(-2.00707 + 1.99290i) q^{8} +(0.865510 - 2.08953i) q^{9} +O(q^{10})$	\(q+(0.998819 + 1.00118i) q^{2} +(-0.477374 - 0.714441i) q^{3} +(-0.00472188 + 1.99999i) q^{4} +(0.0517508 + 0.260169i) q^{5} +(0.238474 - 1.19153i) q^{6} +(-0.515195 - 1.24379i) q^{7} +(-2.00707 + 1.99290i) q^{8} +(0.865510 - 2.08953i) q^{9} +(-0.208786 + 0.311673i) q^{10} +(-4.11495 - 2.74952i) q^{11} +(1.43113 - 0.951372i) q^{12} +(-0.650168 + 3.26862i) q^{13} +(0.730672 - 1.75812i) q^{14} +(0.161171 - 0.161171i) q^{15} +(-3.99996 - 0.0188875i) q^{16} +(1.10212 + 1.10212i) q^{17} +(2.95648 - 1.22053i) q^{18} +(2.56547 + 0.510304i) q^{19} +(-0.520580 + 0.102273i) q^{20} +(-0.642674 + 0.961830i) q^{21} +(-1.35733 - 6.86609i) q^{22} +(3.70792 + 1.53587i) q^{23} +(2.38194 + 0.482572i) q^{24} +(4.55439 - 1.88649i) q^{25} +(-3.92187 + 2.61382i) q^{26} +(-4.43424 + 0.882025i) q^{27} +(2.49001 - 1.02451i) q^{28} +(-5.46390 + 3.65086i) q^{29} +(0.322341 + 0.000380515i) q^{30} +8.22961i q^{31} +(-3.97632 - 4.02354i) q^{32} +4.25245i q^{33} +(-0.00260204 + 2.20424i) q^{34} +(0.296934 - 0.198405i) q^{35} +(4.17496 + 1.74088i) q^{36} +(7.58710 - 1.50917i) q^{37} +(2.05154 + 3.07820i) q^{38} +(2.64561 - 1.09585i) q^{39} +(-0.622359 - 0.419042i) q^{40} +(-10.4659 - 4.33512i) q^{41} +(-1.60488 + 0.317262i) q^{42} +(2.31618 - 3.46640i) q^{43} +(5.51846 - 8.21690i) q^{44} +(0.588420 + 0.117044i) q^{45} +(2.16586 + 5.24635i) q^{46} +(2.33317 + 2.33317i) q^{47} +(1.89598 + 2.86675i) q^{48} +(3.66816 - 3.66816i) q^{49} +(6.43772 + 2.67550i) q^{50} +(0.261277 - 1.31353i) q^{51} +(-6.53414 - 1.31577i) q^{52} +(-3.33837 - 2.23063i) q^{53} +(-5.31207 - 3.55849i) q^{54} +(0.502388 - 1.21287i) q^{55} +(3.51279 + 1.46964i) q^{56} +(-0.860108 - 2.07648i) q^{57} +(-9.11262 - 1.82380i) q^{58} +(1.16241 + 5.84382i) q^{59} +(0.321579 + 0.323102i) q^{60} +(-6.89488 - 10.3189i) q^{61} +(-8.23932 + 8.21989i) q^{62} -3.04484 q^{63} +(0.0566621 - 7.99980i) q^{64} -0.884038 q^{65} +(-4.25746 + 4.24742i) q^{66} +(1.94793 + 2.91529i) q^{67} +(-2.20944 + 2.19903i) q^{68} +(-0.672776 - 3.38227i) q^{69} +(0.495222 + 0.0991136i) q^{70} +(-5.39337 - 13.0208i) q^{71} +(2.42709 + 5.91871i) q^{72} +(-0.375531 + 0.906612i) q^{73} +(9.08909 + 6.08867i) q^{74} +(-3.52193 - 2.35328i) q^{75} +(-1.03272 + 5.12852i) q^{76} +(-1.29983 + 6.53468i) q^{77} +(3.73962 + 1.55418i) q^{78} +(1.20158 - 1.20158i) q^{79} +(-0.202087 - 1.04164i) q^{80} +(-2.05082 - 2.05082i) q^{81} +(-6.11331 - 14.8083i) q^{82} +(15.1088 + 3.00532i) q^{83} +(-1.92062 - 1.28989i) q^{84} +(-0.229702 + 0.343773i) q^{85} +(5.78393 - 1.14340i) q^{86} +(5.21666 + 2.16081i) q^{87} +(13.7385 - 2.68222i) q^{88} +(-1.66533 + 0.689803i) q^{89} +(0.470543 + 0.706020i) q^{90} +(4.40044 - 0.875301i) q^{91} +(-3.08924 + 7.40856i) q^{92} +(5.87957 - 3.92860i) q^{93} +(-0.00550847 + 4.66633i) q^{94} +0.693864i q^{95} +(-0.976389 + 4.76158i) q^{96} +15.4207i q^{97} +(7.33631 + 0.00866031i) q^{98} +(-9.30674 + 6.21857i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$1$

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 $

$2$	0.998819	+	1.00118i	0.706272	+	0.707941i
$2$	0.998819	+	1.00118i	0.706272	+	0.707941i
$3$	−0.477374	−	0.714441i	−0.275612	−	0.412483i	0.667679	−	0.744449i	$-0.267288\pi$
$3$	−0.477374	−	0.714441i	−0.275612	−	0.412483i	−0.943291	+	0.331967i	$0.892288\pi$
$4$	−0.00472188	+	1.99999i	−0.00236094	+	0.999997i
$5$	0.0517508	+	0.260169i	0.0231436	+	0.116351i	0.990630	−	0.136571i	$-0.0436083\pi$
$5$	0.0517508	+	0.260169i	0.0231436	+	0.116351i	−0.967487	+	0.252922i	$0.918608\pi$
$6$	0.238474	−	1.19153i	0.0973564	−	0.486442i
$7$	−0.515195	−	1.24379i	−0.194725	−	0.470109i	0.796115	−	0.605145i	$-0.206885\pi$
$7$	−0.515195	−	1.24379i	−0.194725	−	0.470109i	−0.990841	+	0.135036i	$0.956885\pi$
$8$	−2.00707	+	1.99290i	−0.709606	+	0.704598i
$9$	0.865510	−	2.08953i	0.288503	−	0.696509i
$10$	−0.208786	+	0.311673i	−0.0660239	+	0.0985597i
$11$	−4.11495	−	2.74952i	−1.24071	−	0.829013i	−0.250430	−	0.968135i	$-0.580572\pi$
$11$	−4.11495	−	2.74952i	−1.24071	−	0.829013i	−0.990275	+	0.139122i	$0.955572\pi$
$12$	1.43113	−	0.951372i	0.413132	−	0.274638i
$13$	−0.650168	+	3.26862i	−0.180324	+	0.906551i	0.779597	+	0.626281i	$0.215424\pi$
$13$	−0.650168	+	3.26862i	−0.180324	+	0.906551i	−0.959921	+	0.280269i	$0.909576\pi$
$14$	0.730672	−	1.75812i	0.195280	−	0.469879i
$15$	0.161171	−	0.161171i	0.0416141	−	0.0416141i
$16$	−3.99996	−	0.0188875i	−0.999989	−	0.00472187i
$17$	1.10212	+	1.10212i	0.267304	+	0.267304i	0.828013	−	0.560709i	$-0.189471\pi$
$17$	1.10212	+	1.10212i	0.267304	+	0.267304i	−0.560709	+	0.828013i	$0.689471\pi$
$18$	2.95648	−	1.22053i	0.696849	−	0.287681i
$19$	2.56547	+	0.510304i	0.588560	+	0.117072i	0.480381	−	0.877060i	$-0.340498\pi$
$19$	2.56547	+	0.510304i	0.588560	+	0.117072i	0.108178	+	0.994132i	$0.465498\pi$
$20$	−0.520580	+	0.102273i	−0.116405	+	0.0228689i
$21$	−0.642674	+	0.961830i	−0.140243	+	0.209889i
$22$	−1.35733	−	6.86609i	−0.289383	−	1.46385i
$23$	3.70792	+	1.53587i	0.773154	+	0.320251i	0.734149	−	0.678988i	$-0.237581\pi$
$23$	3.70792	+	1.53587i	0.773154	+	0.320251i	0.0390048	+	0.999239i	$0.487581\pi$
$24$	2.38194	+	0.482572i	0.486211	+	0.0985046i
$25$	4.55439	−	1.88649i	0.910878	−	0.377298i
$26$	−3.92187	+	2.61382i	−0.769142	+	0.512612i
$27$	−4.43424	+	0.882025i	−0.853370	+	0.169746i
$28$	2.49001	−	1.02451i	0.470567	−	0.193615i
$29$	−5.46390	+	3.65086i	−1.01462	+	0.677948i	−0.947487	−	0.319795i	$-0.896386\pi$
$29$	−5.46390	+	3.65086i	−1.01462	+	0.677948i	−0.0671349	+	0.997744i	$0.521386\pi$
$30$	0.322341		0.000380515i	0.0588512		6.94721e-5i
$31$			8.22961i			1.47808i	0.673661	+	0.739041i	$0.264721\pi$
$31$			8.22961i			1.47808i	−0.673661	+	0.739041i	$0.735279\pi$
$32$	−3.97632	−	4.02354i	−0.702921	−	0.711268i
$33$			4.25245i			0.740256i
$34$	−0.00260204	+	2.20424i	−0.000446247	+	0.378024i
$35$	0.296934	−	0.198405i	0.0501909	−	0.0335365i
$36$	4.17496	+	1.74088i	0.695826	+	0.290147i
$37$	7.58710	−	1.50917i	1.24731	−	0.248106i	0.473087	−	0.881016i	$-0.343140\pi$
$37$	7.58710	−	1.50917i	1.24731	−	0.248106i	0.774225	+	0.632910i	$0.218140\pi$
$38$	2.05154	+	3.07820i	0.332803	+	0.499350i
$39$	2.64561	−	1.09585i	0.423636	−	0.175476i
$40$	−0.622359	−	0.419042i	−0.0984036	−	0.0662564i
$41$	−10.4659	−	4.33512i	−1.63450	−	0.677032i	−0.638774	−	0.769394i	$-0.720558\pi$
$41$	−10.4659	−	4.33512i	−1.63450	−	0.677032i	−0.995725	+	0.0923624i	$0.970558\pi$
$42$	−1.60488	+	0.317262i	−0.247638	+	0.0489545i
$43$	2.31618	−	3.46640i	0.353213	−	0.528621i	−0.611734	−	0.791063i	$-0.709528\pi$
$43$	2.31618	−	3.46640i	0.353213	−	0.528621i	0.964948	+	0.262442i	$0.0845278\pi$
$44$	5.51846	−	8.21690i	0.831940	−	1.23874i
$45$	0.588420	+	0.117044i	0.0877165	+	0.0174479i
$46$	2.16586	+	5.24635i	0.319338	+	0.773532i
$47$	2.33317	+	2.33317i	0.340328	+	0.340328i	0.856490	−	0.516163i	$-0.172640\pi$
$47$	2.33317	+	2.33317i	0.340328	+	0.340328i	−0.516163	+	0.856490i	$0.672640\pi$
$48$	1.89598	+	2.86675i	0.273661	+	0.413780i
$49$	3.66816	−	3.66816i	0.524023	−	0.524023i
$50$	6.43772	+	2.67550i	0.910432	+	0.378373i
$51$	0.261277	−	1.31353i	0.0365860	−	0.183930i
$52$	−6.53414	−	1.31577i	−0.906122	−	0.182464i
$53$	−3.33837	−	2.23063i	−0.458560	−	0.306400i	0.304750	−	0.952432i	$-0.401427\pi$
$53$	−3.33837	−	2.23063i	−0.458560	−	0.306400i	−0.763310	+	0.646032i	$0.776427\pi$
$54$	−5.31207	−	3.55849i	−0.722881	−	0.484249i
$55$	0.502388	−	1.21287i	0.0677420	−	0.163544i
$56$	3.51279	+	1.46964i	0.469416	+	0.196389i
$57$	−0.860108	−	2.07648i	−0.113924	−	0.275037i
$58$	−9.11262	−	1.82380i	−1.19655	−	0.239476i
$59$	1.16241	+	5.84382i	0.151333	+	0.760800i	0.979677	+	0.200581i	$0.0642830\pi$
$59$	1.16241	+	5.84382i	0.151333	+	0.760800i	−0.828345	+	0.560219i	$0.810717\pi$
$60$	0.321579	+	0.323102i	0.0415157	+	0.0417122i
$61$	−6.89488	−	10.3189i	−0.882799	−	1.32120i	−0.946323	−	0.323222i	$-0.895234\pi$
$61$	−6.89488	−	10.3189i	−0.882799	−	1.32120i	0.0635241	−	0.997980i	$-0.479766\pi$
$62$	−8.23932	+	8.21989i	−1.04639	+	1.04393i
$63$	−3.04484			−0.383614
$64$	0.0566621	−	7.99980i	0.00708277	−	0.999975i
$65$	−0.884038			−0.109651
$66$	−4.25746	+	4.24742i	−0.524057	+	0.522822i
$67$	1.94793	+	2.91529i	0.237978	+	0.356159i	0.931165	−	0.364599i	$-0.118794\pi$
$67$	1.94793	+	2.91529i	0.237978	+	0.356159i	−0.693187	+	0.720758i	$0.743794\pi$
$68$	−2.20944	+	2.19903i	−0.267934	+	0.266672i
$69$	−0.672776	−	3.38227i	−0.0809927	−	0.407178i
$70$	0.495222	+	0.0991136i	0.0591903	+	0.0118463i
$71$	−5.39337	−	13.0208i	−0.640076	−	1.54528i	−0.826577	−	0.562824i	$-0.809715\pi$
$71$	−5.39337	−	13.0208i	−0.640076	−	1.54528i	0.186501	−	0.982455i	$-0.440285\pi$
$72$	2.42709	+	5.91871i	0.286035	+	0.697526i
$73$	−0.375531	+	0.906612i	−0.0439526	+	0.106111i	−0.944331	−	0.328996i	$-0.893290\pi$
$73$	−0.375531	+	0.906612i	−0.0439526	+	0.106111i	0.900379	+	0.435107i	$0.143290\pi$
$74$	9.08909	+	6.08867i	1.05659	+	0.707793i
$75$	−3.52193	−	2.35328i	−0.406678	−	0.271733i
$76$	−1.03272	+	5.12852i	−0.118461	+	0.588282i
$77$	−1.29983	+	6.53468i	−0.148129	+	0.744696i
$78$	3.73962	+	1.55418i	0.423429	+	0.175976i
$79$	1.20158	−	1.20158i	0.135189	−	0.135189i	−0.636274	−	0.771463i	$-0.719525\pi$
$79$	1.20158	−	1.20158i	0.135189	−	0.135189i	0.771463	+	0.636274i	$0.219525\pi$
$80$	−0.202087	−	1.04164i	−0.0225940	−	0.116459i
$81$	−2.05082	−	2.05082i	−0.227869	−	0.227869i
$82$	−6.11331	−	14.8083i	−0.675102	−	1.63530i
$83$	15.1088	+	3.00532i	1.65840	+	0.329877i	0.933392	−	0.358859i	$-0.116834\pi$
$83$	15.1088	+	3.00532i	1.65840	+	0.329877i	0.725012	+	0.688736i	$0.241834\pi$
$84$	−1.92062	−	1.28989i	−0.209557	−	0.140738i
$85$	−0.229702	+	0.343773i	−0.0249147	+	0.0372874i
$86$	5.78393	−	1.14340i	0.623697	−	0.123296i
$87$	5.21666	+	2.16081i	0.559284	+	0.231663i
$88$	13.7385	−	2.68222i	1.46453	−	0.285926i
$89$	−1.66533	+	0.689803i	−0.176525	+	0.0731189i	−0.469195	−	0.883094i	$-0.655456\pi$
$89$	−1.66533	+	0.689803i	−0.176525	+	0.0731189i	0.292671	+	0.956213i	$0.405456\pi$
$90$	0.470543	+	0.706020i	0.0495996	+	0.0744211i
$91$	4.40044	−	0.875301i	0.461291	−	0.0917565i
$92$	−3.08924	+	7.40856i	−0.322075	+	0.772396i
$93$	5.87957	−	3.92860i	0.609683	−	0.407377i
$94$	−0.00550847	+	4.66633i	−0.000568156	+	0.481296i
$95$			0.693864i			0.0711889i
$96$	−0.976389	+	4.76158i	−0.0996523	+	0.485977i
$97$			15.4207i			1.56574i	0.622188	+	0.782868i	$0.286244\pi$
$97$			15.4207i			1.56574i	−0.622188	+	0.782868i	$0.713756\pi$
$98$	7.33631	+	0.00866031i	0.741079	+	0.000874823i
$99$	−9.30674	+	6.21857i	−0.935363	+	0.624989i
$100$	3.75146	+	9.11766i	0.375146	+	0.911766i
$101$	8.24786	−	1.64060i	0.820692	−	0.163246i	0.233152	−	0.972440i	$-0.425096\pi$
$101$	8.24786	−	1.64060i	0.820692	−	0.163246i	0.587541	+	0.809195i	$0.300096\pi$
$102$	1.57604	−	1.05039i	0.156052	−	0.104004i
$103$	−9.41219	+	3.89866i	−0.927410	+	0.384146i	−0.794695	−	0.607008i	$-0.792369\pi$
$103$	−9.41219	+	3.89866i	−0.927410	+	0.384146i	−0.132715	+	0.991154i	$0.542369\pi$
$104$	−5.20911	−	7.85606i	−0.510795	−	0.770350i
$105$	−0.283497	−	0.117428i	−0.0276665	−	0.0114598i
$106$	−1.10117	−	5.57030i	−0.106955	−	0.541035i
$107$	1.05984	−	1.58616i	0.102459	−	0.153340i	−0.776698	−	0.629873i	$-0.783107\pi$
$107$	1.05984	−	1.58616i	0.102459	−	0.153340i	0.879156	+	0.476533i	$0.158107\pi$
$108$	−1.74311	−	8.87262i	−0.167731	−	0.853768i
$109$	4.24989	+	0.845355i	0.407065	+	0.0809704i	0.394376	−	0.918949i	$-0.370961\pi$
$109$	4.24989	+	0.845355i	0.407065	+	0.0809704i	0.0126894	+	0.999919i	$0.495961\pi$
$110$	1.71610	−	0.708459i	0.163623	−	0.0675489i
$111$	−4.70010	−	4.70010i	−0.446114	−	0.446114i
$112$	2.03727	+	4.98484i	0.192503	+	0.471023i
$113$	1.13449	−	1.13449i	0.106724	−	0.106724i	−0.651728	−	0.758453i	$-0.725956\pi$
$113$	1.13449	−	1.13449i	0.106724	−	0.106724i	0.758453	+	0.651728i	$0.225956\pi$
$114$	1.21984	−	2.93516i	0.114249	−	0.274902i
$115$	−0.207698	+	1.04417i	−0.0193679	+	0.0973690i
$116$	−7.27591	−	10.9450i	−0.675551	−	1.01622i
$117$	6.26713	+	4.18756i	0.579397	+	0.387140i
$118$	−4.68968	+	7.00069i	−0.431720	+	0.644466i
$119$	0.803001	−	1.93862i	0.0736110	−	0.177713i
$120$	−0.00228308	+	0.644679i	−0.000208416	+	0.0588508i
$121$	5.16345	+	12.4657i	0.469404	+	1.13324i
$122$	3.44436	−	17.2097i	0.311837	−	1.55810i
$123$	1.89897	+	9.54675i	0.171224	+	0.860801i
$124$	−16.4592	−	0.0388592i	−1.47808	−	0.00348966i
$125$	1.46337	+	2.19008i	0.130888	+	0.195887i
$126$	−3.04124	−	3.04843i	−0.270936	−	0.271576i
$127$	−18.1894			−1.61405			−0.807025	−	0.590517i	$-0.798924\pi$
$127$	−18.1894			−1.61405			−0.807025	+	0.590517i	$0.798924\pi$
$128$	8.06583	−	7.93362i	0.712926	−	0.701240i
$129$	−3.58222			−0.315397
$130$	−0.882994	−	0.885081i	−0.0774437	−	0.0776267i
$131$	−5.01304	−	7.50254i	−0.437991	−	0.655500i	0.545152	−	0.838337i	$-0.316472\pi$
$131$	−5.01304	−	7.50254i	−0.437991	−	0.655500i	−0.983143	+	0.182837i	$0.941472\pi$
$132$	−8.50487	−	0.0200795i	−0.740254	−	0.00174770i
$133$	−0.687007	−	3.45382i	−0.0595711	−	0.299484i
$134$	−0.973095	+	4.86208i	−0.0840626	+	0.420019i
$135$	−0.458950	−	1.10800i	−0.0395002	−	0.0953618i
$136$	−4.40846	−	0.0156122i	−0.378022	−	0.00133874i
$137$	−2.99585	+	7.23263i	−0.255953	+	0.617925i	−0.998663	−	0.0516877i	$-0.983540\pi$
$137$	−2.99585	+	7.23263i	−0.255953	+	0.617925i	0.742710	+	0.669613i	$0.233540\pi$
$138$	2.71428	−	4.05185i	0.231055	−	0.344916i
$139$	2.95817	+	1.97658i	0.250908	+	0.167652i	0.674664	−	0.738125i	$-0.264288\pi$
$139$	2.95817	+	1.97658i	0.250908	+	0.167652i	−0.423756	+	0.905777i	$0.639288\pi$
$140$	0.395406	+	0.594802i	0.0334179	+	0.0502700i
$141$	0.553117	−	2.78071i	0.0465808	−	0.234178i
$142$	7.64911	−	18.4051i	0.641899	−	1.54452i
$143$	11.6625	−	11.6625i	0.975271	−	0.975271i
$144$	−3.50147	+	8.34167i	−0.291789	+	0.695139i
$145$	−1.23260	−	1.23260i	−0.102362	−	0.102362i
$146$	−1.28277	+	0.529567i	−0.106163	+	0.0438273i
$147$	−4.37177	−	0.869599i	−0.360577	−	0.0717233i
$148$	2.98250	+	15.1813i	0.245160	+	1.24789i
$149$	−4.93832	+	7.39072i	−0.404563	+	0.605472i	−0.976680	−	0.214701i	$-0.931122\pi$
$149$	−4.93832	+	7.39072i	−0.404563	+	0.605472i	0.572117	+	0.820172i	$0.306122\pi$
$150$	−1.16172	−	5.87659i	−0.0948538	−	0.479822i
$151$	−3.73549	−	1.54729i	−0.303990	−	0.125917i	0.225474	−	0.974249i	$-0.427607\pi$
$151$	−3.73549	−	1.54729i	−0.303990	−	0.125917i	−0.529464	+	0.848332i	$0.677607\pi$
$152$	−6.16607	+	4.08853i	−0.500134	+	0.331623i
$153$	3.25681	−	1.34902i	0.263298	−	0.109061i
$154$	−7.84069	+	5.22560i	−0.631821	+	0.421091i
$155$	−2.14109	+	0.425888i	−0.171976	+	0.0342082i
$156$	2.17919	+	5.29637i	0.174475	+	0.424049i
$157$	9.49118	−	6.34180i	0.757478	−	0.506131i	−0.115848	−	0.993267i	$-0.536958\pi$
$157$	9.49118	−	6.34180i	0.757478	−	0.506131i	0.873326	+	0.487136i	$0.161958\pi$
$158$	2.40317	+	0.00283687i	0.191186	+	0.000225689i
$159$			3.44991i			0.273596i
$160$	0.841021	−	1.24274i	0.0664886	−	0.0982468i
$161$		−	5.40314i		−	0.425827i
$162$	0.00484186	−	4.10163i	0.000380412	−	0.322255i
$163$	0.00315871	−	0.00211058i	0.000247409	−	0.000165314i	−0.555447	−	0.831552i	$-0.687453\pi$
$163$	0.00315871	−	0.00211058i	0.000247409	−	0.000165314i	0.555694	+	0.831387i	$0.312453\pi$
$164$	8.71963	−	20.9113i	0.680889	−	1.63290i
$165$	−1.10635	+	0.220067i	−0.0861295	+	0.0171322i
$166$	12.0821	+	18.1284i	0.937750	+	1.40704i
$167$	−4.28839	+	1.77631i	−0.331846	+	0.137455i	−0.542384	−	0.840131i	$-0.682478\pi$
$167$	−4.28839	+	1.77631i	−0.331846	+	0.137455i	0.210538	+	0.977586i	$0.432478\pi$
$168$	−0.626943	−	3.21125i	−0.0483697	−	0.247753i
$169$	1.74931	+	0.724587i	0.134562	+	0.0557374i
$170$	−0.573609	+	0.113394i	−0.0439938	+	0.00869694i
$171$	3.28674	−	4.91895i	0.251343	−	0.376161i
$172$	6.92185	+	4.64871i	0.527786	+	0.354461i
$173$	7.26821	+	1.44574i	0.552592	+	0.109917i	0.463485	−	0.886105i	$-0.346599\pi$
$173$	7.26821	+	1.44574i	0.552592	+	0.109917i	0.0891066	+	0.996022i	$0.471599\pi$
$174$	3.04713	+	7.38107i	0.231003	+	0.559557i
$175$	−4.69280	−	4.69280i	−0.354742	−	0.354742i
$176$	16.4077	+	11.0757i	1.23678	+	0.834862i
$177$	3.62016	−	3.62016i	0.272108	−	0.272108i
$178$	−2.35398	−	0.978308i	−0.176438	−	0.0733273i
$179$	2.46773	−	12.4061i	0.184447	−	0.927277i	−0.772056	−	0.635554i	$-0.780772\pi$
$179$	2.46773	−	12.4061i	0.184447	−	0.927277i	0.956503	−	0.291722i	$-0.0942283\pi$
$180$	−0.236866	+	1.17628i	−0.0176549	+	0.0876751i
$181$	−13.4674	−	8.99863i	−1.00102	−	0.668863i	−0.0568753	−	0.998381i	$-0.518114\pi$
$181$	−13.4674	−	8.99863i	−1.00102	−	0.668863i	−0.944149	+	0.329518i	$0.893114\pi$
$182$	5.27157	+	3.53136i	0.390755	+	0.261762i
$183$	−4.08082	+	9.85197i	−0.301663	+	0.728279i
$184$	−10.5029	+	4.30693i	−0.774283	+	0.317511i
$185$	0.785277	+	1.89583i	0.0577347	+	0.139384i
$186$	9.80586	+	1.96254i	0.719001	+	0.143901i
$187$	−1.50487	−	7.56549i	−0.110047	−	0.553244i
$188$	−4.67734	+	4.65531i	−0.341130	+	0.339523i
$189$	3.38155	+	5.06085i	0.245972	+	0.368123i
$190$	−0.694683	+	0.693044i	−0.0503976	+	0.0502787i
$191$	17.2169			1.24577			0.622885	−	0.782313i	$-0.285960\pi$
$191$	17.2169			1.24577			0.622885	+	0.782313i	$0.285960\pi$
$192$	−5.74243	+	3.77842i	−0.414425	+	0.272684i
$193$	−12.7608			−0.918541			−0.459270	−	0.888296i	$-0.651889\pi$
$193$	−12.7608			−0.918541			−0.459270	+	0.888296i	$0.651889\pi$
$194$	−15.4389	+	15.4025i	−1.10845	+	1.10583i
$195$	0.422017	+	0.631593i	0.0302213	+	0.0452293i
$196$	7.31897	+	7.35362i	0.522784	+	0.525258i
$197$	−0.972213	−	4.88764i	−0.0692673	−	0.348230i	0.930573	−	0.366107i	$-0.119309\pi$
$197$	−0.972213	−	4.88764i	−0.0692673	−	0.348230i	−0.999840	+	0.0178765i	$0.994309\pi$
$198$	−15.5217	−	3.10650i	−1.10308	−	0.220769i
$199$	8.85562	+	21.3794i	0.627758	+	1.51554i	0.842402	+	0.538850i	$0.181141\pi$
$199$	8.85562	+	21.3794i	0.627758	+	1.51554i	−0.214643	+	0.976692i	$0.568859\pi$
$200$	−5.38138	+	12.8628i	−0.380521	+	0.909536i
$201$	1.15291	−	2.78337i	0.0813199	−	0.196324i
$202$	9.88065	+	6.61892i	0.695200	+	0.465706i
$203$	7.35589	+	4.91505i	0.516282	+	0.344969i
$204$	2.62581	+	0.528754i	0.183843	+	0.0370202i
$205$	0.586244	−	2.94725i	0.0409450	−	0.205845i
$206$	−13.3043	−	5.52924i	−0.926956	−	0.385240i
$207$	6.41848	−	6.41848i	0.446115	−	0.446115i
$208$	2.66238	−	13.0620i	0.184603	−	0.905689i
$209$	−9.15371	−	9.15371i	−0.633175	−	0.633175i
$210$	−0.165595	−	0.401121i	−0.0114272	−	0.0276800i
$211$	−3.65496	−	0.727017i	−0.251618	−	0.0500499i	0.0676697	−	0.997708i	$-0.478444\pi$
$211$	−3.65496	−	0.727017i	−0.251618	−	0.0500499i	−0.319288	+	0.947658i	$0.603444\pi$
$212$	4.47700	−	6.66618i	0.307482	−	0.457835i
$213$	−6.72790	+	10.0690i	−0.460988	+	0.689918i
$214$	2.64662	−	0.523199i	0.180919	−	0.0357651i
$215$	1.02171	+	0.423207i	0.0696802	+	0.0288625i
$216$	7.14204	−	10.6073i	0.485954	−	0.721735i
$217$	10.2359	−	4.23985i	0.694859	−	0.287820i
$218$	3.39852	+	5.09926i	0.230177	+	0.345365i
$219$	0.826990	−	0.164498i	0.0558828	−	0.0111158i
$220$	2.42337	+	1.01050i	0.163383	+	0.0681279i
$221$	−4.31898	+	2.88585i	−0.290526	+	0.194123i
$222$	0.0110967	−	9.40019i	0.000744759	−	0.630900i
$223$		−	23.7016i		−	1.58718i	−0.608456	−	0.793588i	$-0.708211\pi$
$223$		−	23.7016i		−	1.58718i	0.608456	−	0.793588i	$-0.291789\pi$
$224$	−2.95586	+	7.01862i	−0.197497	+	0.468951i
$225$		−	11.1493i		−	0.743286i
$226$	2.26899	+	0.00267847i	0.150931	+	0.000178169i
$227$	−8.78436	+	5.86952i	−0.583039	+	0.389574i	−0.811823	−	0.583903i	$-0.801525\pi$
$227$	−8.78436	+	5.86952i	−0.583039	+	0.389574i	0.228785	+	0.973477i	$0.426525\pi$
$228$	4.15702	−	1.71041i	0.275305	−	0.113274i
$229$	−14.0985	+	2.80436i	−0.931653	+	0.185317i	−0.637508	−	0.770444i	$-0.720035\pi$
$229$	−14.0985	+	2.80436i	−0.931653	+	0.185317i	−0.294145	+	0.955761i	$0.595035\pi$
$230$	−1.25285	+	0.834990i	−0.0826105	+	0.0550576i
$231$	5.28915	−	2.19084i	0.348001	−	0.144147i
$232$	3.69062	−	18.2166i	0.242301	−	1.19598i
$233$	5.04386	+	2.08924i	0.330435	+	0.136870i	0.541732	−	0.840551i	$-0.317769\pi$
$233$	5.04386	+	2.08924i	0.330435	+	0.136870i	−0.211297	+	0.977422i	$0.567769\pi$
$234$	2.06723	+	10.4571i	0.135139	+	0.683605i
$235$	−0.486274	+	0.727761i	−0.0317210	+	0.0474739i
$236$	−11.6931	+	2.29721i	−0.761155	+	0.149536i
$237$	−1.43207	−	0.284856i	−0.0930228	−	0.0185034i
$238$	2.74296	−	1.13238i	0.177799	−	0.0734012i
$239$	13.6816	+	13.6816i	0.884992	+	0.884992i	0.994037	−	0.109045i	$-0.0347793\pi$
$239$	13.6816	+	13.6816i	0.884992	+	0.884992i	−0.109045	+	0.994037i	$0.534779\pi$
$240$	−0.647720	+	0.641631i	−0.0418101	+	0.0414171i
$241$	2.22031	−	2.22031i	0.143023	−	0.143023i	−0.631970	−	0.774993i	$-0.717753\pi$
$241$	2.22031	−	2.22031i	0.143023	−	0.143023i	0.774993	+	0.631970i	$0.217753\pi$
$242$	−7.32302	+	17.6205i	−0.470742	+	1.13269i
$243$	−3.13226	+	15.7469i	−0.200934	+	1.01016i
$244$	20.6703	−	13.7410i	1.32328	−	0.879677i
$245$	1.14417	+	0.764510i	0.0730983	+	0.0488427i
$246$	−7.66129	+	11.4367i	−0.488466	+	0.729176i
$247$	−3.33598	+	8.05376i	−0.212263	+	0.512448i
$248$	−16.4008	−	16.5174i	−1.04145	−	1.04886i
$249$	−5.06542	−	12.2290i	−0.321008	−	0.774981i
$250$	−0.731029	+	3.65259i	−0.0462343	+	0.231010i
$251$	0.729724	+	3.66857i	0.0460598	+	0.231558i	0.996957	−	0.0779471i	$-0.0248365\pi$
$251$	0.729724	+	3.66857i	0.0460598	+	0.231558i	−0.950898	+	0.309505i	$0.899837\pi$
$252$	0.0143774	−	6.08967i	0.000905689	−	0.383613i
$253$	−11.0350	−	16.5150i	−0.693764	−	1.03829i
$254$	−18.1679	−	18.2109i	−1.13996	−	1.14265i
$255$	0.355259			0.0222472
$256$	15.9993	+	0.151098i	0.999955	+	0.00944363i
$257$	17.3864			1.08453			0.542267	−	0.840206i	$-0.317566\pi$
$257$	17.3864			1.08453			0.542267	+	0.840206i	$0.317566\pi$
$258$	−3.57799	−	3.58645i	−0.222756	−	0.223283i
$259$	−5.78593	−	8.65925i	−0.359520	−	0.538060i
$260$	0.00417432	−	1.76807i	0.000258880	−	0.109651i
$261$	2.89951	+	14.5768i	0.179475	+	0.902283i
$262$	2.50428	−	12.5126i	0.154715	−	0.773033i
$263$	0.656941	+	1.58600i	0.0405087	+	0.0977967i	0.942839	−	0.333249i	$-0.108145\pi$
$263$	0.656941	+	1.58600i	0.0405087	+	0.0977967i	−0.902330	+	0.431045i	$0.858145\pi$
$264$	−8.47472	−	8.53496i	−0.521583	−	0.525290i
$265$	0.407576	−	0.983975i	0.0250372	−	0.0604451i
$266$	2.77170	−	4.13755i	0.169944	−	0.253690i
$267$	1.28781	+	0.860487i	0.0788127	+	0.0526609i
$268$	−5.83976	+	3.88209i	−0.356720	+	0.237136i
$269$	−1.25541	+	6.31135i	−0.0765434	+	0.384810i	0.923456	+	0.383704i	$0.125352\pi$
$269$	−1.25541	+	6.31135i	−0.0765434	+	0.384810i	−0.999999	+	0.00110539i	$0.999648\pi$
$270$	0.650903	−	1.56619i	0.0396127	−	0.0953151i
$271$	−17.1048	+	17.1048i	−1.03904	+	1.03904i	−0.0398353	+	0.999206i	$0.512683\pi$
$271$	−17.1048	+	17.1048i	−1.03904	+	1.03904i	−0.999206	+	0.0398353i	$0.987317\pi$
$272$	−4.38762	−	4.42925i	−0.266039	−	0.268563i
$273$	−2.72601	−	2.72601i	−0.164985	−	0.164985i
$274$	−10.2335	+	4.22470i	−0.618227	+	0.255223i
$275$	−23.9280	−	4.75958i	−1.44292	−	0.287014i
$276$	6.76770	−	1.32958i	0.407368	−	0.0800311i
$277$	−4.08114	+	6.10786i	−0.245212	+	0.366985i	−0.933576	−	0.358380i	$-0.883329\pi$
$277$	−4.08114	+	6.10786i	−0.245212	+	0.366985i	0.688364	+	0.725365i	$0.258329\pi$
$278$	0.975757	+	4.93591i	0.0585220	+	0.296036i
$279$	17.1960	+	7.12281i	1.02950	+	0.426432i
$280$	−0.200565	+	0.989973i	−0.0119861	+	0.0591622i
$281$	−16.8252	+	6.96925i	−1.00371	+	0.415750i	−0.823156	−	0.567815i	$-0.807789\pi$
$281$	−16.8252	+	6.96925i	−1.00371	+	0.415750i	−0.180554	+	0.983565i	$0.557789\pi$
$282$	3.33645	−	2.22365i	0.198683	−	0.132417i
$283$	22.3174	−	4.43920i	1.32663	−	0.263883i	0.519608	−	0.854405i	$-0.326078\pi$
$283$	22.3174	−	4.43920i	1.32663	−	0.263883i	0.807022	+	0.590522i	$0.201078\pi$
$284$	26.0669	−	10.7252i	1.54679	−	0.636425i
$285$	0.495725	−	0.331233i	0.0293642	−	0.0196205i
$286$	23.3251	+	0.0275346i	1.37924	+	0.00162815i
$287$			15.2508i			0.900228i
$288$	−11.8488	+	4.82621i	−0.698200	+	0.284387i
$289$		−	14.5707i		−	0.857097i
$290$	0.00291010	−	2.46520i	0.000170887	−	0.144762i
$291$	11.0172	−	7.36145i	0.645839	−	0.431536i
$292$	−1.81145	−	0.755341i	−0.106007	−	0.0442030i
$293$	−23.6486	+	4.70399i	−1.38156	+	0.274810i	−0.829274	−	0.558842i	$-0.811246\pi$
$293$	−23.6486	+	4.70399i	−1.38156	+	0.274810i	−0.552290	+	0.833652i	$0.686246\pi$
$294$	−3.49598	−	5.24550i	−0.203890	−	0.305924i
$295$	−1.46022	+	0.604844i	−0.0850174	+	0.0352154i
$296$	−12.2202	+	18.1494i	−0.710286	+	1.05491i
$297$	20.6718	+	8.56256i	1.19950	+	0.496850i
$298$	−12.3319	+	2.43784i	−0.714370	+	0.141220i
$299$	−7.43093	+	11.1212i	−0.429742	+	0.643154i
$300$	4.72318	−	7.03274i	0.272693	−	0.406035i
$301$	−5.50476	−	1.09497i	−0.317289	−	0.0631127i
$302$	−2.18196	−	5.28536i	−0.125558	−	0.304139i
$303$	−5.10943	−	5.10943i	−0.293529	−	0.293529i
$304$	−10.2521	−	2.08965i	−0.588000	−	0.119850i
$305$	2.32784	−	2.32784i	0.133292	−	0.133292i
$306$	4.60357	+	1.91323i	0.263169	+	0.109372i
$307$	1.72081	−	8.65108i	0.0982116	−	0.493743i	−0.900101	−	0.435681i	$-0.856508\pi$
$307$	1.72081	−	8.65108i	0.0982116	−	0.493743i	0.998313	−	0.0580626i	$-0.0184923\pi$
$308$	−13.0632	−	2.63051i	−0.744345	−	0.149887i
$309$	7.27850	+	4.86334i	0.414059	+	0.276666i
$310$	−2.56495	−	1.71823i	−0.145679	−	0.0975887i
$311$	1.49356	−	3.60578i	0.0846923	−	0.204465i	−0.875860	−	0.482566i	$-0.839705\pi$
$311$	1.49356	−	3.60578i	0.0846923	−	0.204465i	0.960552	+	0.278101i	$0.0897049\pi$
$312$	−3.12600	+	7.47188i	−0.176975	+	0.423012i
$313$	8.26474	+	19.9529i	0.467151	+	1.12780i	0.965401	+	0.260769i	$0.0839760\pi$
$313$	8.26474	+	19.9529i	0.467151	+	1.12780i	−0.498250	+	0.867033i	$0.666024\pi$
$314$	15.8292	+	3.16806i	0.893296	+	0.178784i
$315$	−0.157573	−	0.792172i	−0.00887822	−	0.0446338i
$316$	2.39749	+	2.40884i	0.134869	+	0.135508i
$317$	16.4821	+	24.6672i	0.925727	+	1.38545i	0.922728	+	0.385452i	$0.125955\pi$
$317$	16.4821	+	24.6672i	0.925727	+	1.38545i	0.00299906	+	0.999996i	$0.499045\pi$
$318$	−3.45398	+	3.44583i	−0.193690	+	0.193233i
$319$	32.5219			1.82087
$320$	2.08423	−	0.399254i	0.116512	−	0.0223190i
$321$	−1.63916			−0.0914890
$322$	5.40952	−	5.39676i	0.301461	−	0.300750i
$323$	2.26505	+	3.38988i	0.126030	+	0.188618i
$324$	4.11131	−	4.09194i	0.228406	−	0.227330i
$325$	3.20509	+	16.1131i	0.177786	+	0.893793i
$326$	0.00526805	+	0.00105435i	0.000291770	+	5.83949e-5i
$327$	−1.42483	−	3.43985i	−0.0787933	−	0.190224i
$328$	29.6453	−	12.1567i	1.63689	−	0.671239i
$329$	1.69994	−	4.10401i	0.0937206	−	0.226261i
$330$	−1.32537	−	0.887851i	−0.0729594	−	0.0488746i
$331$	−0.162367	−	0.108490i	−0.00892448	−	0.00596315i	0.551100	−	0.834439i	$-0.314208\pi$
$331$	−0.162367	−	0.108490i	−0.00892448	−	0.00596315i	−0.560024	+	0.828476i	$0.689208\pi$
$332$	−6.08197	+	30.2033i	−0.333792	+	1.65762i
$333$	3.41327	−	17.1597i	0.187046	−	0.940343i
$334$	−6.06174	−	2.51924i	−0.331683	−	0.137847i
$335$	−0.657660	+	0.657660i	−0.0359318	+	0.0359318i
$336$	2.58884	−	3.83514i	0.141233	−	0.209224i
$337$	6.58517	+	6.58517i	0.358717	+	0.358717i	0.863340	−	0.504623i	$-0.168368\pi$
$337$	6.58517	+	6.58517i	0.358717	+	0.358717i	−0.504623	+	0.863340i	$0.668368\pi$
$338$	1.02180	+	2.47510i	0.0555786	+	0.134628i
$339$	−1.35211	−	0.268951i	−0.0734364	−	0.0146074i
$340$	−0.686460	−	0.461026i	−0.0372285	−	0.0250026i
$341$	22.6275	−	33.8645i	1.22535	−	1.83386i
$342$	8.20761	−	1.62252i	0.443817	−	0.0877361i
$343$	−15.1588	−	6.27897i	−0.818497	−	0.339032i
$344$	2.25948	+	11.5732i	0.121823	+	0.623987i
$345$	0.845145	−	0.350070i	0.0455011	−	0.0188472i
$346$	5.81218	+	8.72081i	0.312465	+	0.468834i
$347$	−24.8134	+	4.93570i	−1.33206	+	0.264962i	−0.809237	−	0.587482i	$-0.800119\pi$
$347$	−24.8134	+	4.93570i	−1.33206	+	0.264962i	−0.522818	+	0.852444i	$0.675119\pi$
$348$	−4.34624	+	10.4231i	−0.232983	+	0.558736i
$349$	−10.7430	+	7.17827i	−0.575062	+	0.384244i	−0.808825	−	0.588050i	$-0.799896\pi$
$349$	−10.7430	+	7.17827i	−0.575062	+	0.384244i	0.233763	+	0.972294i	$0.424896\pi$
$350$	0.0110794	−	9.38559i	0.000592220	−	0.501681i
$351$		−	15.0673i		−	0.804232i
$352$	5.29956	+	27.4897i	0.282467	+	1.46520i
$353$		−	15.3080i		−	0.814764i	−0.913258	−	0.407382i	$-0.866442\pi$
$353$		−	15.3080i		−	0.814764i	0.913258	−	0.407382i	$-0.133558\pi$
$354$	7.24032	+	0.00854699i	0.384818	+	0.000454267i
$355$	3.10848	−	2.07702i	0.164981	−	0.110237i
$356$	−1.37174	−	3.33391i	−0.0727020	−	0.176697i
$357$	−1.76836	+	0.351749i	−0.0935915	+	0.0186165i
$358$	14.8856	−	9.92082i	0.786727	−	0.524332i
$359$	7.28425	−	3.01723i	0.384448	−	0.159243i	−0.182085	−	0.983283i	$-0.558285\pi$
$359$	7.28425	−	3.01723i	0.384448	−	0.159243i	0.566533	+	0.824039i	$0.308285\pi$
$360$	−1.41426	+	0.937750i	−0.0745380	+	0.0494237i
$361$	−11.2325	−	4.65264i	−0.591183	−	0.244876i
$362$	−4.44225	−	22.4713i	−0.233479	−	1.18107i
$363$	6.44108	−	9.63976i	0.338069	−	0.505956i
$364$	1.72982	+	8.80498i	0.0906672	+	0.461506i
$365$	−0.255306	−	0.0507835i	−0.0133633	−	0.00265813i
$366$	−13.9396	+	5.75470i	−0.728634	+	0.300803i
$367$	−9.38201	−	9.38201i	−0.489737	−	0.489737i	0.418486	−	0.908223i	$-0.362561\pi$
$367$	−9.38201	−	9.38201i	−0.489737	−	0.489737i	−0.908223	+	0.418486i	$0.862561\pi$
$368$	−14.8025	−	6.21344i	−0.771633	−	0.323898i
$369$	−18.1167	+	18.1167i	−0.943118	+	0.943118i
$370$	−1.11371	+	2.67979i	−0.0578992	+	0.139316i
$371$	−1.05452	+	5.30144i	−0.0547480	+	0.275237i
$372$	7.82942	+	11.7777i	0.405937	+	0.610643i
$373$	1.73641	+	1.16023i	0.0899078	+	0.0600745i	0.599712	−	0.800216i	$-0.295282\pi$
$373$	1.73641	+	1.16023i	0.0899078	+	0.0600745i	−0.509804	+	0.860291i	$0.670282\pi$
$374$	6.07132	−	9.06320i	0.313941	−	0.468647i
$375$	0.866112	−	2.09098i	0.0447258	−	0.107978i
$376$	−9.33262	−	0.0330508i	−0.481293	−	0.00170446i
$377$	−8.38081	−	20.2331i	−0.431634	−	1.04206i
$378$	−1.68926	+	8.44042i	−0.0868863	+	0.434128i
$379$	−6.02722	−	30.3009i	−0.309597	−	1.55645i	−0.751711	−	0.659492i	$-0.770771\pi$
$379$	−6.02722	−	30.3009i	−0.309597	−	1.55645i	0.442114	−	0.896959i	$-0.354229\pi$
$380$	−1.38772	−	0.00327634i	−0.0711887	−	0.000168073i
$381$	8.68317	+	12.9953i	0.444852	+	0.665768i
$382$	17.1966	+	17.2372i	0.879852	+	0.881932i
$383$	−28.6473			−1.46381			−0.731904	−	0.681408i	$-0.761368\pi$
$383$	−28.6473			−1.46381			−0.731904	+	0.681408i	$0.761368\pi$
$384$	−9.51853	−	1.97526i	−0.485740	−	0.100799i
$385$	−1.76739			−0.0900744
$386$	−12.7457	−	12.7758i	−0.648739	−	0.650273i
$387$	−5.23847	−	7.83992i	−0.266286	−	0.398525i
$388$	−30.8413	−	0.0728147i	−1.56573	−	0.00369661i
$389$	−1.69036	−	8.49804i	−0.0857049	−	0.430868i	−0.999685	−	0.0251080i	$-0.992007\pi$
$389$	−1.69036	−	8.49804i	−0.0857049	−	0.430868i	0.913980	−	0.405760i	$-0.132993\pi$
$390$	−0.210820	+	1.05336i	−0.0106753	+	0.0533391i
$391$	2.39386	+	5.77929i	0.121063	+	0.292271i
$392$	−0.0519617	+	14.6725i	−0.00262446	+	0.741075i
$393$	−2.96703	+	7.16304i	−0.149667	+	0.361328i
$394$	3.92234	−	5.85523i	0.197605	−	0.294982i
$395$	0.374798	+	0.250432i	0.0188581	+	0.0126006i
$396$	−12.3932	−	18.6428i	−0.622779	−	0.936836i
$397$	3.77514	−	18.9789i	0.189469	−	0.952525i	−0.762653	−	0.646808i	$-0.776104\pi$
$397$	3.77514	−	18.9789i	0.189469	−	0.952525i	0.952122	−	0.305718i	$-0.0988963\pi$
$398$	−12.5594	+	30.2202i	−0.629547	+	1.51480i
$399$	−2.13959	+	2.13959i	−0.107113	+	0.107113i
$400$	−18.2530	+	7.45985i	−0.912649	+	0.372993i
$401$	22.1086	+	22.1086i	1.10405	+	1.10405i	0.993917	+	0.110133i	$0.0351275\pi$
$401$	22.1086	+	22.1086i	1.10405	+	1.10405i	0.110133	+	0.993917i	$0.464872\pi$
$402$	3.93820	−	1.62581i	0.196419	−	0.0810881i
$403$	−26.8994	−	5.35063i	−1.33996	−	0.266534i
$404$	3.24225	+	16.5034i	0.161308	+	0.821076i
$405$	0.427427	−	0.639690i	0.0212390	−	0.0317864i
$406$	2.42635	+	12.2738i	0.120418	+	0.609139i
$407$	−35.3701	−	14.6508i	−1.75323	−	0.726212i
$408$	2.09333	+	3.15704i	0.103635	+	0.156297i
$409$	−0.412610	+	0.170909i	−0.0204023	+	0.00845089i	−0.392861	−	0.919598i	$-0.628515\pi$
$409$	−0.412610	+	0.170909i	−0.0204023	+	0.00845089i	0.372459	+	0.928049i	$0.378515\pi$
$410$	3.53627	−	2.35683i	0.174644	−	0.116395i
$411$	6.59743	−	1.31231i	0.325427	−	0.0647315i
$412$	−7.75285	−	18.8427i	−0.381955	−	0.928315i
$413$	6.66962	−	4.45650i	0.328191	−	0.219290i
$414$	12.8370	+	0.0151537i	0.630902	+	0.000744762i
$415$			4.08636i			0.200591i
$416$	15.7367	−	10.3811i	0.771554	−	0.508975i
$417$		−	3.05701i		−	0.149702i
$418$	0.0216114	−	18.3074i	0.00105705	−	0.895444i
$419$	24.9030	−	16.6397i	1.21659	−	0.812901i	0.229541	−	0.973299i	$-0.426278\pi$
$419$	24.9030	−	16.6397i	1.21659	−	0.812901i	0.987052	+	0.160398i	$0.0512776\pi$
$420$	0.236195	−	0.566438i	0.0115251	−	0.0276393i
$421$	27.6476	−	5.49946i	1.34746	−	0.268027i	0.531955	−	0.846772i	$-0.321457\pi$
$421$	27.6476	−	5.49946i	1.34746	−	0.268027i	0.815508	+	0.578745i	$0.196457\pi$
$422$	−2.92277	−	4.38543i	−0.142278	−	0.213479i
$423$	6.89460	−	2.85584i	0.335227	−	0.138856i
$424$	11.1458	−	2.17602i	0.541286	−	0.105677i
$425$	7.09863	+	2.94035i	0.344334	+	0.142628i
$426$	−16.8009	+	3.32129i	−0.814004	+	0.160917i
$427$	−9.28237	+	13.8920i	−0.449205	+	0.672283i
$428$	3.16731	+	2.12716i	0.153098	+	0.102820i
$429$	−13.8996	−	2.76480i	−0.671079	−	0.133486i
$430$	0.596799	+	1.44563i	0.0287802	+	0.0697143i
$431$	5.47861	+	5.47861i	0.263896	+	0.263896i	0.826635	−	0.562739i	$-0.190252\pi$
$431$	5.47861	+	5.47861i	0.263896	+	0.263896i	−0.562739	+	0.826635i	$0.690252\pi$
$432$	17.7534	−	3.44431i	0.854162	−	0.165714i
$433$	−13.9653	+	13.9653i	−0.671130	+	0.671130i	−0.957977	−	0.286847i	$-0.907393\pi$
$433$	−13.9653	+	13.9653i	−0.671130	+	0.671130i	0.286847	+	0.957977i	$0.407393\pi$
$434$	14.4687	+	6.01314i	0.694519	+	0.288640i
$435$	−0.292209	+	1.46903i	−0.0140103	+	0.0704348i
$436$	−1.71077	+	8.49576i	−0.0819312	+	0.406873i
$437$	8.72880	+	5.83240i	0.417555	+	0.279001i
$438$	0.990705	+	0.663661i	0.0473377	+	0.0317110i
$439$	7.32429	−	17.6824i	0.349569	−	0.843935i	−0.647102	−	0.762404i	$-0.724019\pi$
$439$	7.32429	−	17.6824i	0.349569	−	0.843935i	0.996671	−	0.0815308i	$-0.0259809\pi$
$440$	1.40881	+	3.43553i	0.0671624	+	0.163783i
$441$	−4.48989	−	10.8395i	−0.213804	−	0.516169i
$442$	−7.20313	−	1.44163i	−0.342618	−	0.0685715i
$443$	1.03061	+	5.18121i	0.0489656	+	0.246167i	0.997514	−	0.0704647i	$-0.0224482\pi$
$443$	1.03061	+	5.18121i	0.0489656	+	0.246167i	−0.948549	+	0.316631i	$0.897448\pi$
$444$	9.42237	−	9.37798i	0.447166	−	0.445059i
$445$	−0.265647	−	0.397569i	−0.0125929	−	0.0188466i
$446$	23.7295	−	23.6736i	1.12363	−	1.12098i
$447$	7.63766			0.361249
$448$	−9.97927	+	4.05098i	−0.471476	+	0.191391i
$449$	25.4195			1.19962			0.599809	−	0.800143i	$-0.295243\pi$
$449$	25.4195			1.19962			0.599809	+	0.800143i	$0.295243\pi$
$450$	11.1624	−	11.1361i	0.526203	−	0.524962i
$451$	31.1472	+	46.6151i	1.46666	+	2.19502i
$452$	2.26362	+	2.27434i	0.106472	+	0.106976i
$453$	0.677779	+	3.40743i	0.0318449	+	0.160095i
$454$	−14.6504	−	2.93214i	−0.687579	−	0.137612i
$455$	0.455452	+	1.09956i	0.0213519	+	0.0515481i
$456$	5.86453	+	2.45354i	0.274632	+	0.114897i
$457$	0.410387	−	0.990763i	0.0191971	−	0.0463459i	−0.913990	−	0.405736i	$-0.867015\pi$
$457$	0.410387	−	0.990763i	0.0191971	−	0.0463459i	0.933187	+	0.359390i	$0.117015\pi$
$458$	−16.8895	−	11.3140i	−0.789193	−	0.528671i
$459$	−5.85917	−	3.91497i	−0.273483	−	0.182735i
$460$	−2.08735	−	0.420324i	−0.0973230	−	0.0195977i
$461$	−0.499040	+	2.50885i	−0.0232426	+	0.116849i	−0.990665	−	0.136320i	$-0.956473\pi$
$461$	−0.499040	+	2.50885i	−0.0232426	+	0.116849i	0.967422	+	0.253168i	$0.0814726\pi$
$462$	7.47633	+	3.10714i	0.347830	+	0.144557i
$463$	−23.9046	+	23.9046i	−1.11094	+	1.11094i	−0.117915	+	0.993024i	$0.537621\pi$
$463$	−23.9046	+	23.9046i	−1.11094	+	1.11094i	−0.993024	+	0.117915i	$0.962379\pi$
$464$	21.9243	−	14.5001i	1.01781	−	0.673150i
$465$	1.32637	+	1.32637i	0.0615090	+	0.0615090i
$466$	2.94620	+	7.13658i	0.136480	+	0.330596i
$467$	32.9221	+	6.54862i	1.52345	+	0.303034i	0.884621	−	0.466311i	$-0.154417\pi$
$467$	32.9221	+	6.54862i	1.52345	+	0.303034i	0.638833	+	0.769345i	$0.279417\pi$
$468$	−8.40470	+	12.5145i	−0.388507	+	0.578481i
$469$	2.62244	−	3.92476i	0.121093	−	0.181229i
$470$	−1.21432	+	0.240053i	−0.0560124	+	0.0110728i
$471$	−9.06169	−	3.75347i	−0.417540	−	0.172951i
$472$	−13.9792	−	9.41238i	−0.643445	−	0.433240i
$473$	−19.0619	+	7.89570i	−0.876468	+	0.363045i
$474$	−1.14518	−	1.71828i	−0.0526000	−	0.0789230i
$475$	12.6468	−	2.51561i	0.580277	−	0.115424i
$476$	3.87343	+	1.61515i	0.177538	+	0.0740304i
$477$	−7.55034	+	5.04498i	−0.345706	+	0.230994i
$478$	−0.0323016	+	27.3633i	−0.00147744	+	1.25157i
$479$		−	17.7201i		−	0.809654i	−0.914393	−	0.404827i	$-0.867332\pi$
$479$		−	17.7201i		−	0.809654i	0.914393	−	0.404827i	$-0.132668\pi$
$480$	−1.28934	−	0.00761025i	−0.0588502	−	0.000347359i
$481$			25.7805i			1.17549i
$482$	4.44062	+	0.00524203i	0.202265	+	0.000238768i
$483$	−3.86023	+	2.57932i	−0.175647	+	0.117363i
$484$	−24.9556	+	10.2680i	−1.13435	+	0.466727i
$485$	−4.01198	+	0.798033i	−0.182175	+	0.0362368i
$486$	−18.8940	+	12.5924i	−0.857051	+	0.571201i
$487$	22.3630	−	9.26304i	1.01336	−	0.419749i	0.186682	−	0.982420i	$-0.440227\pi$
$487$	22.3630	−	9.26304i	1.01336	−	0.419749i	0.826680	+	0.562672i	$0.190227\pi$
$488$	34.4031	+	6.96995i	1.55736	+	0.315515i
$489$	−0.00301577	−	0.00124917i	−0.000136378	−	5.64896e-5i
$490$	0.377406	+	1.90913i	0.0170495	+	0.0862455i
$491$	−16.5333	+	24.7438i	−0.746136	+	1.11667i	0.243051	+	0.970013i	$0.421852\pi$
$491$	−16.5333	+	24.7438i	−0.746136	+	1.11667i	−0.989187	+	0.146658i	$0.953148\pi$
$492$	−19.1024	+	3.75284i	−0.861203	+	0.169191i
$493$	−10.0456	−	1.99819i	−0.452430	−	0.0899940i
$494$	−11.3953	+	4.70433i	−0.512699	+	0.211658i
$495$	−2.09951	−	2.09951i	−0.0943658	−	0.0943658i
$496$	0.155436	−	32.9181i	0.00697930	−	1.47806i
$497$	−13.4165	+	13.4165i	−0.601810	+	0.601810i
$498$	7.18399	−	17.2859i	0.321922	−	0.774602i
$499$	−5.85555	+	29.4378i	−0.262130	+	1.31782i	0.595419	+	0.803416i	$0.296986\pi$
$499$	−5.85555	+	29.4378i	−0.262130	+	1.31782i	−0.857549	+	0.514402i	$0.828014\pi$
$500$	−4.38706	+	2.91638i	−0.196195	+	0.130425i
$501$	3.31624	+	2.21584i	0.148159	+	0.0989964i
$502$	−2.94404	+	4.39482i	−0.131399	+	0.196151i
$503$	2.73931	−	6.61328i	0.122140	−	0.294871i	−0.850970	−	0.525215i	$-0.823985\pi$
$503$	2.73931	−	6.61328i	0.122140	−	0.294871i	0.973109	+	0.230343i	$0.0739849\pi$
$504$	6.11121	−	6.06808i	0.272215	−	0.270294i
$505$	0.853666	+	2.06093i	0.0379876	+	0.0917102i
$506$	5.51256	−	27.5435i	0.245063	−	1.22446i
$507$	−0.317400	−	1.59568i	−0.0140962	−	0.0708665i
$508$	0.0858883	−	36.3788i	0.00381068	−	1.61405i
$509$	3.41939	+	5.11748i	0.151562	+	0.226829i	0.899479	−	0.436963i	$-0.143946\pi$
$509$	3.41939	+	5.11748i	0.151562	+	0.226829i	−0.747917	+	0.663792i	$0.768946\pi$
$510$	0.354840	+	0.355679i	0.0157126	+	0.0157497i
$511$	1.32111			0.0584423
$512$	15.8291	+	16.1691i	0.699555	+	0.714579i
$513$	−11.8260			−0.522131
$514$	17.3659	+	17.4069i	0.765976	+	0.767787i
$515$	−1.50140	−	2.24700i	−0.0661594	−	0.0990145i
$516$	0.0169148	−	7.16443i	0.000744634	−	0.315396i
$517$	−3.18578	−	16.0160i	−0.140110	−	0.704382i
$518$	2.89038	−	14.4418i	0.126996	−	0.634535i
$519$	−2.43676	−	5.88286i	−0.106962	−	0.258229i
$520$	1.77433	−	1.76180i	0.0778093	−	0.0772602i
$521$	5.10532	−	12.3253i	0.223668	−	0.539983i	−0.771715	−	0.635969i	$-0.780601\pi$
$521$	5.10532	−	12.3253i	0.223668	−	0.539983i	0.995383	+	0.0959866i	$0.0306006\pi$
$522$	−11.6979	+	17.4626i	−0.512005	+	0.764315i
$523$	22.7053	+	15.1712i	0.992835	+	0.663391i	0.942104	−	0.335321i	$-0.108845\pi$
$523$	22.7053	+	15.1712i	0.992835	+	0.663391i	0.0507311	+	0.998712i	$0.483845\pi$
$524$	15.0287	−	9.99062i	0.656532	−	0.436442i
$525$	−1.11251	+	5.59295i	−0.0485538	+	0.244096i
$526$	−0.931702	+	2.24184i	−0.0406241	+	0.0977488i
$527$	−9.07003	+	9.07003i	−0.395097	+	0.395097i
$528$	0.0803179	−	17.0096i	0.00349539	−	0.740247i
$529$	−4.87371	−	4.87371i	−0.211900	−	0.211900i
$530$	1.39223	−	0.574756i	0.0604746	−	0.0249658i
$531$	13.2169	+	2.62900i	0.573564	+	0.114089i
$532$	6.91086	−	1.35770i	0.299624	−	0.0588638i
$533$	20.9744	−	31.3905i	0.908504	−	1.35967i
$534$	0.424786	+	2.14880i	0.0183823	+	0.0929877i
$535$	0.467517	+	0.193652i	0.0202125	+	0.00837231i
$536$	−9.71953	−	1.96914i	−0.419820	−	0.0850540i
$537$	−10.0415	+	4.15931i	−0.433321	+	0.179488i
$538$	−7.57272	+	5.04701i	−0.326483	+	0.217592i
$539$	−25.1800	+	5.00861i	−1.08458	+	0.215736i
$540$	2.21817	−	0.912666i	0.0954548	−	0.0392749i
$541$	−1.36491	+	0.912006i	−0.0586822	+	0.0392102i	−0.584565	−	0.811347i	$-0.698735\pi$
$541$	−1.36491	+	0.912006i	−0.0586822	+	0.0392102i	0.525883	+	0.850557i	$0.323735\pi$
$542$	−34.2095	−	0.0403834i	−1.46943	−	0.00173462i
$543$			13.9174i			0.597252i
$544$	0.0520406	−	8.81682i	0.00223122	−	0.378018i
$545$			1.14944i			0.0492364i
$546$	0.00643594	−	5.45201i	0.000275433	−	0.233324i
$547$	35.6558	−	23.8244i	1.52453	−	1.01866i	0.540361	−	0.841434i	$-0.318288\pi$
$547$	35.6558	−	23.8244i	1.52453	−	1.01866i	0.984170	−	0.177225i	$-0.0567122\pi$
$548$	−14.4511	−	6.02584i	−0.617319	−	0.257411i
$549$	−27.5292	+	5.47591i	−1.17492	+	0.233706i
$550$	−19.1346	−	28.7102i	−0.815901	−	1.22421i
$551$	−15.8805	+	6.57794i	−0.676534	+	0.280230i
$552$	8.09086	+	5.44768i	0.344370	+	0.231869i
$553$	−2.11357	−	0.875469i	−0.0898782	−	0.0372287i
$554$	−10.1914	+	2.01469i	−0.432990	+	0.0855959i
$555$	0.979585	−	1.46605i	0.0415811	−	0.0622305i
$556$	−3.96713	+	5.90699i	−0.168244	+	0.250512i
$557$	−2.38952	−	0.475305i	−0.101247	−	0.0201393i	0.144207	−	0.989548i	$-0.453937\pi$
$557$	−2.38952	−	0.475305i	−0.101247	−	0.0201393i	−0.245454	+	0.969408i	$0.578937\pi$
$558$	10.0445	+	24.3307i	0.425216	+	1.03000i
$559$	9.82443	+	9.82443i	0.415529	+	0.415529i
$560$	−1.19147	+	0.788002i	−0.0503487	+	0.0332991i
$561$	−4.68671	+	4.68671i	−0.197873	+	0.197873i
$562$	−23.7828	−	9.88408i	−1.00322	−	0.416935i
$563$	2.89115	−	14.5348i	0.121847	−	0.612567i	−0.870811	−	0.491617i	$-0.836406\pi$
$563$	2.89115	−	14.5348i	0.121847	−	0.612567i	0.992659	−	0.120950i	$-0.0385941\pi$
$564$	5.55879	+	1.11936i	0.234067	+	0.0471336i
$565$	0.353871	+	0.236449i	0.0148874	+	0.00994748i
$566$	26.7354	+	17.9097i	1.12377	+	0.752802i
$567$	−1.49422	+	3.60736i	−0.0627512	+	0.151495i
$568$	36.7740	+	15.3851i	1.54300	+	0.645544i
$569$	−13.6164	−	32.8729i	−0.570829	−	1.37810i	−0.900851	−	0.434129i	$-0.857056\pi$
$569$	−13.6164	−	32.8729i	−0.570829	−	1.37810i	0.330022	−	0.943973i	$-0.392944\pi$
$570$	0.826763	+	0.165468i	0.0346293	+	0.00693070i
$571$	−4.08279	−	20.5256i	−0.170859	−	0.858968i	−0.967180	−	0.254093i	$-0.918223\pi$
$571$	−4.08279	−	20.5256i	−0.170859	−	0.858968i	0.796321	−	0.604875i	$-0.206777\pi$
$572$	23.2700	+	23.3801i	0.972966	+	0.977571i
$573$	−8.21890	−	12.3005i	−0.343350	−	0.513859i
$574$	−15.2688	+	15.2328i	−0.637308	+	0.635805i
$575$	19.7847			0.825079
$576$	−16.6668	−	7.04231i	−0.694448	−	0.293429i
$577$	−13.2749			−0.552640			−0.276320	−	0.961066i	$-0.589115\pi$
$577$	−13.2749			−0.552640			−0.276320	+	0.961066i	$0.589115\pi$
$578$	14.5878	−	14.5534i	0.606774	−	0.605344i
$579$	6.09167	+	9.11682i	0.253161	+	0.378882i
$580$	2.47102	−	2.45938i	0.102603	−	0.102120i
$581$	−4.04598	−	20.3405i	−0.167855	−	0.843866i
$582$	18.3743	+	3.67743i	0.761639	+	0.152434i
$583$	7.60407	+	18.3578i	0.314928	+	0.760304i
$584$	−1.05307	−	2.56803i	−0.0435765	−	0.106266i
$585$	−0.765144	+	1.84722i	−0.0316348	+	0.0763732i
$586$	−28.3302	−	18.9780i	−1.17031	−	0.783975i
$587$	−5.72679	−	3.82652i	−0.236370	−	0.157937i	0.431744	−	0.901996i	$-0.357898\pi$
$587$	−5.72679	−	3.82652i	−0.236370	−	0.157937i	−0.668114	+	0.744059i	$0.732898\pi$
$588$	1.75984	−	8.73940i	0.0725744	−	0.360407i
$589$	−4.19960	+	21.1128i	−0.173042	+	0.869939i
$590$	−2.06406	−	0.857816i	−0.0849758	−	0.0353157i
$591$	−3.02782	+	3.02782i	−0.124548	+	0.124548i
$592$	−30.3766	+	5.89331i	−1.24847	+	0.242213i
$593$	5.93109	+	5.93109i	0.243561	+	0.243561i	0.818321	−	0.574761i	$-0.194905\pi$
$593$	5.93109	+	5.93109i	0.243561	+	0.243561i	−0.574761	+	0.818321i	$0.694905\pi$
$594$	12.0748	+	29.2487i	0.495434	+	1.20009i
$595$	0.545923	+	0.108591i	0.0223807	+	0.00445179i
$596$	−14.7581	−	9.91152i	−0.604515	−	0.405991i
$597$	11.0468	−	16.5328i	0.452117	−	0.676642i
$598$	−18.5565	+	3.66834i	−0.758830	+	0.150010i
$599$	8.60956	+	3.56620i	0.351777	+	0.145711i	0.551573	−	0.834127i	$-0.314028\pi$
$599$	8.60956	+	3.56620i	0.351777	+	0.145711i	−0.199796	+	0.979838i	$0.564028\pi$
$600$	11.7586	−	2.29568i	0.480044	−	0.0937207i
$601$	−9.04530	+	3.74668i	−0.368965	+	0.152830i	−0.559459	−	0.828858i	$-0.688991\pi$
$601$	−9.04530	+	3.74668i	−0.368965	+	0.152830i	0.190494	+	0.981688i	$0.438991\pi$
$602$	−4.40200	−	6.60493i	−0.179412	−	0.269197i
$603$	7.77753	−	1.54705i	0.316725	−	0.0630006i
$604$	3.11221	−	7.46366i	0.126634	−	0.303692i
$605$	−2.97596	+	1.98847i	−0.120990	+	0.0808430i
$606$	0.0120631	−	10.2188i	0.000490028	−	0.415112i
$607$		−	34.8085i		−	1.41283i	−0.707796	−	0.706417i	$-0.750311\pi$
$607$		−	34.8085i		−	1.41283i	0.707796	−	0.706417i	$-0.249689\pi$
$608$	−8.14791	−	12.3514i	−0.330441	−	0.500916i
$609$		−	7.60167i		−	0.308035i
$610$	4.65568	+	0.00549590i	0.188503	+	0.000222523i
$611$	−9.14318	+	6.10928i	−0.369894	+	0.247155i
$612$	2.68264	+	6.51997i	0.108439	+	0.263554i
$613$	14.7093	−	2.92585i	0.594101	−	0.118174i	0.111123	−	0.993807i	$-0.464555\pi$
$613$	14.7093	−	2.92585i	0.594101	−	0.118174i	0.482978	+	0.875632i	$0.339555\pi$
$614$	10.3801	−	6.91802i	0.418905	−	0.279189i
$615$	−2.38549	+	0.988103i	−0.0961923	+	0.0398442i
$616$	−10.4142	−	15.7060i	−0.419598	−	0.632813i
$617$	7.99200	+	3.31040i	0.321746	+	0.133272i	0.537710	−	0.843130i	$-0.319289\pi$
$617$	7.99200	+	3.31040i	0.321746	+	0.133272i	−0.215964	+	0.976401i	$0.569289\pi$
$618$	2.40083	+	12.1447i	0.0965754	+	0.488530i
$619$	−4.66067	+	6.97519i	−0.187328	+	0.280356i	−0.913232	−	0.407440i	$-0.866422\pi$
$619$	−4.66067	+	6.97519i	−0.187328	+	0.280356i	0.725904	+	0.687796i	$0.241422\pi$
$620$	−0.841665	−	4.28417i	−0.0338021	−	0.172056i
$621$	−17.7965	−	3.53994i	−0.714147	−	0.142053i
$622$	5.10184	−	2.10620i	0.204565	−	0.0844509i
$623$	1.71594	+	1.71594i	0.0687477	+	0.0687477i
$624$	−10.6030	+	4.33337i	−0.424460	+	0.173474i
$625$	16.9348	−	16.9348i	0.677393	−	0.677393i
$626$	−11.7214	+	28.2038i	−0.468482	+	1.12725i
$627$	−2.17004	+	10.9095i	−0.0866631	+	0.435685i
$628$	12.6387	+	19.0122i	0.504341	+	0.758671i
$629$	10.0252	+	6.69862i	0.399731	+	0.267092i
$630$	0.635720	−	0.948995i	0.0253277	−	0.0378089i
$631$	12.6693	−	30.5864i	0.504358	−	1.21763i	−0.442731	−	0.896654i	$-0.645990\pi$
$631$	12.6693	−	30.5864i	0.504358	−	1.21763i	0.947089	−	0.320972i	$-0.104010\pi$
$632$	−0.0170212	+	4.80631i	−0.000677067	+	0.191185i
$633$	1.22537	+	2.95831i	0.0487042	+	0.117582i
$634$	−8.23367	+	41.1396i	−0.327001	+	1.63386i
$635$	−0.941317	−	4.73232i	−0.0373550	−	0.187796i
$636$	−6.89980	−	0.0162901i	−0.273595	−	0.000645943i
$637$	9.60488	+	14.3747i	0.380559	+	0.569547i
$638$	32.4834	+	32.5602i	1.28603	+	1.28907i
$639$	−31.8752			−1.26096
$640$	2.48149	+	1.68791i	0.0980896	+	0.0667203i
$641$	10.2292			0.404030			0.202015	−	0.979382i	$-0.435251\pi$
$641$	10.2292			0.404030			0.202015	+	0.979382i	$0.435251\pi$
$642$	−1.63722	−	1.64109i	−0.0646161	−	0.0647688i
$643$	−4.22568	−	6.32418i	−0.166645	−	0.249401i	0.738743	−	0.673987i	$-0.235420\pi$
$643$	−4.22568	−	6.32418i	−0.166645	−	0.249401i	−0.905388	+	0.424586i	$0.860420\pi$
$644$	10.8063	+	0.0255130i	0.425826	+	0.00100535i
$645$	−0.185383	−	0.931982i	−0.00729944	−	0.0366968i
$646$	−1.13151	+	5.65359i	−0.0445186	+	0.222438i
$647$	−7.05188	−	17.0247i	−0.277238	−	0.669311i	0.722519	−	0.691351i	$-0.242984\pi$
$647$	−7.05188	−	17.0247i	−0.277238	−	0.669311i	−0.999757	+	0.0220394i	$0.992984\pi$
$648$	8.20322	+	0.0290511i	0.322253	+	0.00114124i
$649$	11.2845	−	27.2431i	0.442954	−	1.06939i
$650$	−12.9308	+	19.3029i	−0.507187	+	0.757123i
$651$	−7.91549	−	5.28896i	−0.310232	−	0.207291i
$652$	0.00420624	+	0.00632737i	0.000164729	+	0.000247799i
$653$	5.75170	−	28.9158i	0.225081	−	1.13156i	−0.688604	−	0.725138i	$-0.741776\pi$
$653$	5.75170	−	28.9158i	0.225081	−	1.13156i	0.913685	−	0.406423i	$-0.133224\pi$
$654$	2.02076	−	4.86230i	0.0790178	−	0.190131i
$655$	1.69250	−	1.69250i	0.0661314	−	0.0661314i
$656$	41.7813	+	17.5380i	1.63128	+	0.684742i
$657$	1.56936	+	1.56936i	0.0612267	+	0.0612267i
$658$	5.80678	−	2.39722i	0.226372	−	0.0934534i
$659$	−4.76397	−	0.947613i	−0.185578	−	0.0369138i	0.101426	−	0.994843i	$-0.467659\pi$
$659$	−4.76397	−	0.947613i	−0.185578	−	0.0369138i	−0.287004	+	0.957929i	$0.592659\pi$
$660$	−0.434909	−	2.21374i	−0.0169288	−	0.0861697i
$661$	−14.3165	+	21.4261i	−0.556846	+	0.833378i	−0.997945	−	0.0640799i	$-0.979589\pi$
$661$	−14.3165	+	21.4261i	−0.556846	+	0.833378i	0.441099	+	0.897458i	$0.354589\pi$
$662$	−0.0535570	−	0.270920i	−0.00208155	−	0.0105296i
$663$	4.12354	+	1.70802i	0.160145	+	0.0663342i
$664$	−36.3137	+	24.0785i	−1.40925	+	0.934426i
$665$	0.863022	−	0.357475i	0.0334665	−	0.0138623i
$666$	20.5891	−	13.7221i	0.797813	−	0.531720i
$667$	−25.8670	+	5.14526i	−1.00157	+	0.199225i
$668$	−3.53236	−	8.58515i	−0.136671	−	0.332169i
$669$	−16.9334	+	11.3145i	−0.654683	+	0.437445i
$670$	−1.31532	−	0.00155270i	−0.0508152	−	5.99859e-5i
$671$			61.4195i			2.37107i
$672$	6.42544	−	1.23872i	0.247867	−	0.0477847i
$673$			7.18022i			0.276777i	0.990378	+	0.138389i	$0.0441923\pi$
$673$			7.18022i			0.276777i	−0.990378	+	0.138389i	$0.955808\pi$
$674$	−0.0155472	+	13.1703i	−0.000598856	+	0.507302i
$675$	−18.5313	+	12.3822i	−0.713271	+	0.476592i
$676$	−1.45743	+	3.49518i	−0.0560550	+	0.134430i
$677$	0.516673	−	0.102773i	0.0198574	−	0.00394987i	−0.185152	−	0.982710i	$-0.559278\pi$
$677$	0.516673	−	0.102773i	0.0198574	−	0.00394987i	0.205009	+	0.978760i	$0.434278\pi$
$678$	−1.08124	−	1.62234i	−0.0415249	−	0.0623054i
$679$	19.1801	−	7.94467i	0.736066	−	0.304888i
$680$	−0.224079	−	1.14775i	−0.00859305	−	0.0440142i
$681$	8.38686	+	3.47395i	0.321385	+	0.133122i
$682$	56.5052	−	11.1703i	2.16370	−	0.427731i
$683$	10.6617	−	15.9564i	0.407960	−	0.610555i	−0.569420	−	0.822047i	$-0.692832\pi$
$683$	10.6617	−	15.9564i	0.407960	−	0.610555i	0.977380	+	0.211492i	$0.0678322\pi$
$684$	9.82235	+	6.59668i	0.375567	+	0.252230i
$685$	−2.03674	−	0.405133i	−0.0778199	−	0.0154793i
$686$	−8.85449	−	21.4482i	−0.338066	−	0.818896i
$687$	8.73379	+	8.73379i	0.333215	+	0.333215i
$688$	−9.33007	+	13.8217i	−0.355706	+	0.526948i
$689$	9.46156	−	9.46156i	0.360457	−	0.360457i
$690$	1.19463	+	0.496485i	0.0454788	+	0.0189009i
$691$	8.09941	−	40.7185i	0.308116	−	1.54901i	−0.447677	−	0.894195i	$-0.647749\pi$
$691$	8.09941	−	40.7185i	0.308116	−	1.54901i	0.755794	−	0.654810i	$-0.227251\pi$
$692$	−2.92578	+	14.5295i	−0.111222	+	0.552331i
$693$	12.5294	+	8.37187i	0.475952	+	0.318021i
$694$	−29.7257	−	19.9128i	−1.12837	−	0.755881i
$695$	−0.361158	+	0.871912i	−0.0136995	+	0.0330735i
$696$	−14.7765	+	6.05940i	−0.560101	+	0.229681i
$697$	−6.75687	−	16.3125i	−0.255935	−	0.617881i
$698$	−17.9171	−	3.58592i	−0.678172	−	0.135729i
$699$	−0.915174	−	4.60089i	−0.0346151	−	0.174022i
$700$	9.40773	−	9.36341i	0.355579	−	0.353904i
$701$	2.87333	+	4.30025i	0.108524	+	0.162418i	0.881756	−	0.471705i	$-0.156361\pi$
$701$	2.87333	+	4.30025i	0.108524	+	0.162418i	−0.773232	+	0.634123i	$0.781361\pi$
$702$	15.0851	−	15.0495i	0.569349	−	0.568006i
$703$	20.2346			0.763164
$704$	−22.2288	+	32.7630i	−0.837780	+	1.23480i
$705$	0.752077			0.0283249
$706$	15.3261	−	15.2899i	0.576805	−	0.575445i
$707$	−6.28982	−	9.41338i	−0.236553	−	0.354027i
$708$	7.22321	+	7.25739i	0.271465	+	0.272750i
$709$	8.49385	+	42.7015i	0.318993	+	1.60369i	0.724286	+	0.689500i	$0.242170\pi$
$709$	8.49385	+	42.7015i	0.318993	+	1.60369i	−0.405292	+	0.914187i	$0.632830\pi$
$710$	5.18428	+	1.03758i	0.194563	+	0.0389397i
$711$	−1.47076	−	3.55073i	−0.0551578	−	0.133163i
$712$	1.96773	−	4.70333i	0.0737436	−	0.176265i
$713$	−12.6396	+	30.5147i	−0.473357	+	1.14278i
$714$	−2.11843	−	1.41911i	−0.0792804	−	0.0531090i
$715$	3.63778	+	2.43068i	0.136045	+	0.0909024i
$716$	24.8005	+	4.99403i	0.926838	+	0.186635i
$717$	3.24346	−	16.3060i	0.121129	−	0.608958i
$718$	10.2964	+	4.27917i	0.384260	+	0.159697i
$719$	4.80412	−	4.80412i	0.179163	−	0.179163i	−0.611828	−	0.790991i	$-0.709565\pi$
$719$	4.80412	−	4.80412i	0.179163	−	0.179163i	0.790991	+	0.611828i	$0.209565\pi$
$720$	−2.35144	−	0.479285i	−0.0876331	−	0.0178619i
$721$	9.69822	+	9.69822i	0.361181	+	0.361181i
$722$	−6.56107	−	15.8929i	−0.244178	−	0.591472i
$723$	−2.64620	−	0.526363i	−0.0984134	−	0.0195756i
$724$	18.0608	−	26.8923i	0.671225	−	0.999443i
$725$	−17.9974	+	26.9350i	−0.668408	+	1.00034i
$726$	16.0846	−	3.17969i	0.596956	−	0.118010i
$727$	3.79111	+	1.57033i	0.140604	+	0.0582402i	0.451876	−	0.892081i	$-0.350755\pi$
$727$	3.79111	+	1.57033i	0.140604	+	0.0582402i	−0.311272	+	0.950321i	$0.600755\pi$
$728$	−7.08759	+	10.5264i	−0.262684	+	0.390136i
$729$	4.70693	−	1.94968i	0.174331	−	0.0722102i
$730$	−0.204161	−	0.306331i	−0.00755634	−	0.0113378i
$731$	6.37310	−	1.26769i	0.235718	−	0.0468872i
$732$	−19.6846	−	8.20814i	−0.727565	−	0.303382i
$733$	37.2568	−	24.8942i	1.37611	−	0.919488i	0.376136	−	0.926564i	$-0.377253\pi$
$733$	37.2568	−	24.8942i	1.37611	−	0.919488i	0.999975	+	0.00707651i	$0.00225254\pi$
$734$	0.0221504	−	18.7640i	0.000817585	−	0.692592i
$735$		−	1.18240i		−	0.0436134i
$736$	−8.56424	−	21.0261i	−0.315682	−	0.775031i
$737$		−	17.3522i		−	0.639175i
$738$	−36.2334	−	0.0427725i	−1.33377	−	0.00157448i
$739$	−29.8791	+	19.9646i	−1.09912	+	0.734409i	−0.966477	−	0.256754i	$-0.917347\pi$
$739$	−29.8791	+	19.9646i	−1.09912	+	0.734409i	−0.132645	+	0.991164i	$0.542347\pi$
$740$	−3.79535	+	1.56160i	−0.139520	+	0.0574055i
$741$	7.34645	−	1.46130i	0.269878	−	0.0536822i
$742$	−6.36097	+	4.23941i	−0.233518	+	0.155634i
$743$	−18.9414	+	7.84578i	−0.694892	+	0.287834i	−0.702037	−	0.712141i	$-0.747726\pi$
$743$	−18.9414	+	7.84578i	−0.694892	+	0.287834i	0.00714476	+	0.999974i	$0.497726\pi$
$744$	−3.97138	+	19.6024i	−0.145598	+	0.718659i
$745$	−2.17840	−	0.902321i	−0.0798102	−	0.0330585i
$746$	0.572757	+	2.89732i	0.0209701	+	0.106078i
$747$	19.3565	−	28.9691i	0.708218	−	1.05992i
$748$	15.1380	−	2.97401i	0.553502	−	0.108740i
$749$	−2.51888	−	0.501036i	−0.0920379	−	0.0183075i
$750$	2.95853	−	1.22138i	0.108030	−	0.0445983i
$751$	−5.62839	−	5.62839i	−0.205383	−	0.205383i	0.596919	−	0.802302i	$-0.296391\pi$
$751$	−5.62839	−	5.62839i	−0.205383	−	0.205383i	−0.802302	+	0.596919i	$0.796391\pi$
$752$	−9.28850	−	9.37664i	−0.338717	−	0.341931i
$753$	2.27263	−	2.27263i	0.0828191	−	0.0828191i
$754$	11.8860	−	28.5999i	0.432864	−	1.04155i
$755$	0.209242	−	1.05193i	0.00761510	−	0.0382837i
$756$	−10.1376	+	6.73919i	−0.368702	+	0.245102i
$757$	−17.5865	−	11.7509i	−0.639192	−	0.427095i	0.193293	−	0.981141i	$-0.438083\pi$
$757$	−17.5865	−	11.7509i	−0.639192	−	0.427095i	−0.832486	+	0.554046i	$0.813083\pi$
$758$	24.3165	−	36.2994i	0.883216	−	1.31845i
$759$	−6.53120	+	15.7677i	−0.237068	+	0.572332i
$760$	−1.38280	−	1.39263i	−0.0501596	−	0.0505161i
$761$	8.96561	+	21.6449i	0.325003	+	0.784627i	0.998949	+	0.0458456i	$0.0145982\pi$
$761$	8.96561	+	21.6449i	0.325003	+	0.784627i	−0.673946	+	0.738781i	$0.735402\pi$
$762$	−4.33770	+	21.6733i	−0.157138	+	0.785142i
$763$	−1.13808	−	5.72150i	−0.0412011	−	0.207132i
$764$	−0.0812961	+	34.4337i	−0.00294119	+	1.24577i
$765$	0.519514	+	0.777507i	0.0187831	+	0.0281108i
$766$	−28.6135	−	28.6811i	−1.03385	−	1.03629i
$767$	−19.8570			−0.716993
$768$	−7.52970	−	11.5027i	−0.271705	−	0.415067i
$769$	6.14218			0.221493			0.110746	−	0.993849i	$-0.464676\pi$
$769$	6.14218			0.221493			0.110746	+	0.993849i	$0.464676\pi$
$770$	−1.76530	−	1.76947i	−0.0636170	−	0.0637673i
$771$	−8.29983	−	12.4216i	−0.298911	−	0.447352i
$772$	0.0602549	−	25.5215i	0.00216862	−	0.918538i
$773$	3.65565	+	18.3782i	0.131485	+	0.661018i	0.989162	+	0.146830i	$0.0469069\pi$
$773$	3.65565	+	18.3782i	0.131485	+	0.661018i	−0.857677	+	0.514189i	$0.828093\pi$
$774$	2.61689	−	13.0753i	0.0940621	−	0.469982i
$775$	15.5251	+	37.4808i	0.557677	+	1.34635i
$776$	−30.7320	−	30.9504i	−1.10321	−	1.11106i
$777$	−3.42447	+	8.26741i	−0.122852	+	0.296592i
$778$	6.81970	−	10.1804i	0.244498	−	0.364984i
$779$	−24.6378	−	16.4624i	−0.882739	−	0.589827i
$780$	−1.26518	+	0.841049i	−0.0453005	+	0.0301144i
$781$	−13.6074	+	68.4090i	−0.486911	+	2.44787i
$782$	−3.39508	+	8.16915i	−0.121408	+	0.292128i
$783$	21.0081	−	21.0081i	0.750768	−	0.750768i
$784$	−14.7417	+	14.6032i	−0.526491	+	0.521542i
$785$	2.14111	+	2.14111i	0.0764196	+	0.0764196i
$786$	−10.1350	+	4.18405i	−0.361504	+	0.149240i
$787$	−43.2635	−	8.60564i	−1.54218	−	0.306758i	−0.650526	−	0.759484i	$-0.725452\pi$
$787$	−43.2635	−	8.60564i	−1.54218	−	0.306758i	−0.891650	+	0.452726i	$0.850452\pi$
$788$	9.77985	−	1.92134i	0.348393	−	0.0684449i
$789$	0.819494	−	1.22646i	0.0291747	−	0.0436631i
$790$	0.123628	+	0.625376i	0.00439848	+	0.0222499i
$791$	−1.99556	−	0.826587i	−0.0709539	−	0.0293901i
$792$	6.28628	−	31.0285i	0.223373	−	1.10255i
$793$	38.2114	−	15.8277i	1.35693	−	0.562058i
$794$	22.7720	−	15.1769i	0.808148	−	0.538609i
$795$	−0.897558	+	0.178535i	−0.0318331	+	0.00633200i
$796$	−42.8004	+	17.6102i	−1.51702	+	0.624178i
$797$	−39.2600	+	26.2327i	−1.39066	+	0.929211i	−0.390700	+	0.920518i	$0.627767\pi$
$797$	−39.2600	+	26.2327i	−1.39066	+	0.929211i	−0.999962	+	0.00869271i	$0.997233\pi$
$798$	−4.27918	−	0.00505145i	−0.151481	−	0.000178819i
$799$			5.14287i			0.181942i
$800$	−25.7001	−	10.8235i	−0.908635	−	0.382668i
$801$			4.07679i			0.144046i
$802$	−0.0521970	+	44.2171i	−0.00184314	+	1.56136i
$803$	4.03804	−	2.69813i	0.142499	−	0.0952151i
$804$	5.56128	+	2.31895i	0.196131	+	0.0817832i
$805$	1.40573	−	0.279617i	0.0495454	−	0.00985520i
$806$	−21.5107	−	32.2755i	−0.757682	−	1.13685i
$807$	5.10839	−	2.11596i	0.179824	−	0.0744854i
$808$	−13.2845	+	19.7300i	−0.467346	+	0.694099i
$809$	−14.5037	−	6.00764i	−0.509924	−	0.211217i	0.112861	−	0.993611i	$-0.463999\pi$
$809$	−14.5037	−	6.00764i	−0.509924	−	0.211217i	−0.622784	+	0.782394i	$0.713999\pi$
$810$	1.06737	−	0.211003i	0.0375034	−	0.00741388i
$811$	−15.8735	+	23.7564i	−0.557395	+	0.834200i	−0.997981	−	0.0635100i	$-0.979771\pi$
$811$	−15.8735	+	23.7564i	−0.557395	+	0.834200i	0.440586	+	0.897710i	$0.354771\pi$
$812$	−9.86480	+	14.6885i	−0.346187	+	0.515466i
$813$	20.3857	+	4.05498i	0.714959	+	0.142214i
$814$	−20.6603	−	50.0453i	−0.724141	−	1.75409i
$815$	0.000712573	0	0.000712573i	2.49603e−5	0	2.49603e-5i
$816$	−1.06990	+	5.24911i	−0.0374541	+	0.183756i
$817$	7.71100	−	7.71100i	0.269774	−	0.269774i
$818$	−0.583233	−	0.242390i	−0.0203923	−	0.00847497i
$819$	1.97966	−	9.95241i	0.0691749	−	0.347765i
$820$	5.89171	+	1.18640i	0.205747	+	0.0414309i
$821$	−10.7690	−	7.19563i	−0.375842	−	0.251129i	0.353274	−	0.935520i	$-0.385068\pi$
$821$	−10.7690	−	7.19563i	−0.375842	−	0.251129i	−0.729116	+	0.684391i	$0.760068\pi$
$822$	7.90350	+	5.29445i	0.275666	+	0.184665i
$823$	−5.78447	+	13.9649i	−0.201634	+	0.486788i	−0.992059	−	0.125771i	$-0.959860\pi$
$823$	−5.78447	+	13.9649i	−0.201634	+	0.486788i	0.790425	+	0.612558i	$0.209860\pi$
$824$	11.1213	−	26.5825i	0.387428	−	0.926044i
$825$	8.02219	+	19.3673i	0.279297	+	0.674282i
$826$	11.1235	+	2.22625i	0.387036	+	0.0774613i
$827$	6.95283	+	34.9542i	0.241774	+	1.21548i	0.890687	+	0.454616i	$0.150224\pi$
$827$	6.95283	+	34.9542i	0.241774	+	1.21548i	−0.648914	+	0.760862i	$0.724776\pi$
$828$	12.8066	+	12.8672i	0.445061	+	0.447167i
$829$	−15.3694	−	23.0020i	−0.533802	−	0.798891i	0.462335	−	0.886705i	$-0.347012\pi$
$829$	−15.3694	−	23.0020i	−0.533802	−	0.798891i	−0.996137	+	0.0878145i	$0.972012\pi$
$830$	−4.09118	+	4.08153i	−0.142007	+	0.141672i
$831$	6.31193			0.218959
$832$	26.1114	+	5.38642i	0.905251	+	0.186741i
$833$	8.08551			0.280146
$834$	3.06061	−	3.05340i	0.105980	−	0.105730i
$835$	−0.684068	−	1.02378i	−0.0236732	−	0.0354294i
$836$	18.3506	−	18.2641i	0.634668	−	0.631678i
$837$	−7.25872	−	36.4920i	−0.250898	−	1.26135i
$838$	41.5329	+	8.31239i	1.43473	+	0.287147i
$839$	−11.8401	−	28.5844i	−0.408764	−	0.986844i	−0.985463	−	0.169887i	$-0.945660\pi$
$839$	−11.8401	−	28.5844i	−0.408764	−	0.986844i	0.576699	−	0.816956i	$-0.304340\pi$
$840$	0.803022	−	0.329296i	0.0277069	−	0.0113618i
$841$	5.42762	−	13.1034i	0.187159	−	0.451843i
$842$	33.1209	+	22.1873i	1.14142	+	0.764625i
$843$	13.0111	+	8.69371i	0.448125	+	0.299427i
$844$	1.47129	−	7.30647i	0.0506438	−	0.251499i
$845$	−0.0979868	+	0.492613i	−0.00337085	+	0.0169464i
$846$	9.74566	+	4.05027i	0.335063	+	0.139251i
$847$	12.8445	−	12.8445i	0.441342	−	0.441342i
$848$	13.3112	+	8.98546i	0.457108	+	0.308562i
$849$	−13.8253	−	13.8253i	−0.474482	−	0.474482i
$850$	4.14643	+	10.0439i	0.142221	+	0.344502i
$851$	30.4502	+	6.05693i	1.04382	+	0.207629i
$852$	−20.1062	−	13.5033i	−0.688828	−	0.462616i
$853$	−25.8867	+	38.7421i	−0.886343	+	1.32651i	0.0582640	+	0.998301i	$0.481443\pi$
$853$	−25.8867	+	38.7421i	−0.886343	+	1.32651i	−0.944607	+	0.328204i	$0.893557\pi$
$854$	−23.1798	+	4.58232i	−0.793198	+	0.156804i
$855$	1.44985	+	0.600546i	0.0495837	+	0.0205383i
$856$	1.03390	+	5.29570i	0.0353379	+	0.181003i
$857$	11.6236	−	4.81466i	0.397055	−	0.164466i	−0.175216	−	0.984530i	$-0.556062\pi$
$857$	11.6236	−	4.81466i	0.397055	−	0.164466i	0.572271	+	0.820064i	$0.306062\pi$
$858$	−11.1151	−	16.6775i	−0.379464	−	0.569362i
$859$	7.21770	−	1.43569i	0.246265	−	0.0489851i	−0.0704144	−	0.997518i	$-0.522432\pi$
$859$	7.21770	−	1.43569i	0.246265	−	0.0489851i	0.316679	+	0.948533i	$0.397432\pi$
$860$	−0.851237	+	2.04142i	−0.0290269	+	0.0696119i
$861$	10.8958	−	7.28035i	0.371329	−	0.248114i
$862$	−0.0129347	+	10.9572i	−0.000440557	+	0.373204i
$863$		−	51.3234i		−	1.74707i	−0.486761	−	0.873535i	$-0.661822\pi$
$863$		−	51.3234i		−	1.74707i	0.486761	−	0.873535i	$-0.338178\pi$
$864$	21.1808	+	14.3341i	0.720586	+	0.487657i
$865$			1.96578i			0.0668384i
$866$	−27.9306	−	0.0329713i	−0.949121	−	0.00112041i
$867$	−10.4099	+	6.95566i	−0.353538	+	0.236226i
$868$	8.43135	+	20.4918i	0.286179	+	0.695536i
$869$	−8.24825	+	1.64068i	−0.279803	+	0.0556562i
$870$	−1.76263	+	1.17474i	−0.0597588	+	0.0398276i
$871$	−10.7954	+	4.47162i	−0.365790	+	0.151515i
$872$	−10.2145	+	6.77294i	−0.345908	+	0.229361i
$873$	32.2220	+	13.3468i	1.09055	+	0.451720i
$874$	2.87921	+	14.5646i	0.0973907	+	0.492655i
$875$	1.97009	−	2.94844i	0.0666011	−	0.0996755i
$876$	0.325091	+	1.65475i	0.0109838	+	0.0559089i
$877$	41.5765	+	8.27007i	1.40394	+	0.279260i	0.838217	−	0.545337i	$-0.183598\pi$
$877$	41.5765	+	8.27007i	1.40394	+	0.279260i	0.565720	+	0.824597i	$0.308598\pi$
$878$	25.0189	−	10.3286i	0.844347	−	0.348573i
$879$	14.6499	+	14.6499i	0.494130	+	0.494130i
$880$	−2.03244	+	4.84195i	−0.0685135	+	0.163222i
$881$	19.0362	−	19.0362i	0.641347	−	0.641347i	−0.309539	−	0.950887i	$-0.600175\pi$
$881$	19.0362	−	19.0362i	0.641347	−	0.641347i	0.950887	+	0.309539i	$0.100175\pi$
$882$	6.36775	−	15.3219i	0.214413	−	0.515916i
$883$	−6.24157	+	31.3785i	−0.210046	+	1.05597i	0.721519	+	0.692395i	$0.243444\pi$
$883$	−6.24157	+	31.3785i	−0.210046	+	1.05597i	−0.931565	+	0.363576i	$0.881556\pi$
$884$	−5.75129	−	8.65155i	−0.193437	−	0.290983i
$885$	1.12920	+	0.754506i	0.0379576	+	0.0253624i
$886$	−4.15793	+	6.20691i	−0.139688	+	0.208525i
$887$	−17.9162	+	43.2535i	−0.601567	+	1.45231i	0.270401	+	0.962748i	$0.412844\pi$
$887$	−17.9162	+	43.2535i	−0.601567	+	1.45231i	−0.871968	+	0.489563i	$0.837156\pi$
$888$	18.8003	+	0.0665799i	0.630896	+	0.00223427i
$889$	9.37110	+	22.6238i	0.314297	+	0.758779i
$890$	0.132705	−	0.663060i	0.00444827	−	0.0222258i
$891$	2.80025	+	14.0778i	0.0938118	+	0.471624i
$892$	47.4030	+	0.111916i	1.58717	+	0.00374723i
$893$	4.79505	+	7.17630i	0.160460	+	0.240146i
$894$	7.62864	+	7.64667i	0.255140	+	0.255743i
$895$	3.35539			0.112158
$896$	−14.0232	−	5.94485i	−0.468484	−	0.198603i
$897$	11.4928			0.383732
$898$	25.3894	+	25.4495i	0.847257	+	0.849259i
$899$	−30.0452	−	44.9658i	−1.00206	−	1.49969i
$900$	22.2985	+	0.0526456i	0.743284	+	0.00175485i
$901$	−1.22087	−	6.13771i	−0.0406729	−	0.204477i
$902$	−15.5597	+	77.7440i	−0.518080	+	2.58859i
$903$	1.84554	+	4.45554i	0.0614158	+	0.148271i
$904$	−0.0160708	+	4.53795i	−0.000534507	+	0.150930i
$905$	1.64421	−	3.96948i	0.0546555	−	0.131950i
$906$	−2.73447	+	4.08198i	−0.0908466	+	0.135615i
$907$	−6.59470	−	4.40644i	−0.218974	−	0.146313i	0.441246	−	0.897386i	$-0.354537\pi$
$907$	−6.59470	−	4.40644i	−0.218974	−	0.146313i	−0.660219	+	0.751073i	$0.729537\pi$
$908$	−11.6975	−	17.5964i	−0.388196	−	0.583957i
$909$	3.71053	−	18.6541i	0.123070	−	0.618717i
$910$	−0.645941	+	1.55425i	−0.0214128	+	0.0515228i
$911$	−0.693019	+	0.693019i	−0.0229608	+	0.0229608i	−0.718494	−	0.695533i	$-0.755168\pi$
$911$	−0.693019	+	0.693019i	−0.0229608	+	0.0229608i	0.695533	+	0.718494i	$0.255168\pi$
$912$	3.40118	+	8.32209i	0.112624	+	0.275572i
$913$	−53.9087	−	53.9087i	−1.78412	−	1.78412i
$914$	1.40183	−	0.578721i	0.0463686	−	0.0191424i
$915$	−2.77436	−	0.551855i	−0.0917175	−	0.0182437i
$916$	−5.54213	−	28.2101i	−0.183117	−	0.932088i
$917$	−6.74890	+	10.1004i	−0.222868	+	0.333546i
$918$	−1.93266	−	9.77643i	−0.0637872	−	0.322670i
$919$	24.9456	+	10.3328i	0.822879	+	0.340848i	0.754080	−	0.656783i	$-0.228083\pi$
$919$	24.9456	+	10.3328i	0.822879	+	0.340848i	0.0687992	+	0.997631i	$0.478083\pi$
$920$	−1.66406	−	2.50964i	−0.0548624	−	0.0827402i
$921$	−7.00216	+	2.90039i	−0.230729	+	0.0955710i
$922$	−3.01026	+	2.00625i	−0.0991375	+	0.0660724i
$923$	46.0664	−	9.16318i	1.51630	−	0.301610i
$924$	4.35669	+	10.5886i	0.143325	+	0.348340i
$925$	31.7076	−	21.1863i	1.04254	−	0.696602i
$926$	−47.8091	−	0.0564373i	−1.57110	−	0.00185464i
$927$			23.0413i			0.756777i
$928$	36.4156	+	7.46723i	1.19540	+	0.245124i
$929$			12.4630i			0.408898i	0.978877	+	0.204449i	$0.0655402\pi$
$929$			12.4630i			0.408898i	−0.978877	+	0.204449i	$0.934460\pi$
$930$	−0.00313149	+	2.65274i	−0.000102685	+	0.0869868i
$931$	11.2824	−	7.53868i	0.369767	−	0.247070i
$932$	−4.20228	+	10.0778i	−0.137650	+	0.330110i
$933$	−3.28911	+	0.654245i	−0.107681	+	0.0214190i
$934$	26.3269	+	39.5018i	0.861442	+	1.29254i
$935$	1.89043	−	0.783040i	0.0618235	−	0.0256081i
$936$	−20.9240	+	4.08506i	−0.683922	+	0.133524i
$937$	−53.2713	−	22.0657i	−1.74030	−	0.720855i	−0.998752	−	0.0499537i	$-0.984093\pi$
$937$	−53.2713	−	22.0657i	−1.74030	−	0.720855i	−0.741547	−	0.670901i	$-0.765907\pi$
$938$	6.54874	−	1.29459i	0.213824	−	0.0422699i
$939$	10.3098	−	15.4297i	0.336446	−	0.503528i
$940$	−1.45322	−	0.975982i	−0.0473988	−	0.0318330i
$941$	−15.5300	−	3.08911i	−0.506264	−	0.100702i	−0.0646512	−	0.997908i	$-0.520593\pi$
$941$	−15.5300	−	3.08911i	−0.506264	−	0.100702i	−0.441613	+	0.897206i	$0.645593\pi$
$942$	−5.29308	−	12.8214i	−0.172458	−	0.417744i
$943$	−32.1485	−	32.1485i	−1.04690	−	1.04690i
$944$	−4.53920	−	23.3970i	−0.147738	−	0.761506i
$945$	−1.14168	+	1.14168i	−0.0371387	+	0.0371387i
$946$	−26.9444	−	11.1980i	−0.876039	−	0.364079i
$947$	−2.16365	+	10.8774i	−0.0703092	+	0.353468i	−0.999885	−	0.0151628i	$-0.995173\pi$
$947$	−2.16365	+	10.8774i	−0.0703092	+	0.353468i	0.929576	+	0.368631i	$0.120173\pi$
$948$	0.576472	−	2.86278i	0.0187229	−	0.0929788i
$949$	−2.71921	−	1.81692i	−0.0882692	−	0.0589796i
$950$	15.1505	+	10.1491i	0.491547	+	0.329281i
$951$	9.75513	−	23.5510i	0.316332	−	0.763693i
$952$	2.25180	+	5.49124i	0.0729812	+	0.177972i
$953$	13.7909	+	33.2942i	0.446731	+	1.07850i	0.973539	+	0.228520i	$0.0733887\pi$
$953$	13.7909	+	33.2942i	0.446731	+	1.07850i	−0.526808	+	0.849984i	$0.676611\pi$
$954$	−12.5924	−	2.52023i	−0.407693	−	0.0815955i
$955$	0.890987	+	4.47929i	0.0288317	+	0.144947i
$956$	−27.4278	+	27.2986i	−0.887079	+	0.882900i
$957$	−15.5251	−	23.2350i	−0.501855	−	0.751079i
$958$	17.7410	−	17.6992i	0.573187	−	0.571835i
$959$	10.5393			0.340333
$960$	−1.28020	−	1.29847i	−0.0413183	−	0.0419078i
$961$	−36.7264			−1.18472
$962$	−25.8110	+	25.7501i	−0.832178	+	0.830216i
$963$	−2.39703	−	3.58741i	−0.0772431	−	0.115603i
$964$	4.43013	+	4.45110i	0.142685	+	0.143360i
$965$	−0.660380	−	3.31995i	−0.0212584	−	0.106873i
$966$	−6.43804	−	1.28851i	−0.207140	−	0.0414570i
$967$	−9.21382	−	22.2441i	−0.296296	−	0.715323i	−0.999988	−	0.00481755i	$-0.998467\pi$
$967$	−9.21382	−	22.2441i	−0.296296	−	0.715323i	0.703692	−	0.710505i	$-0.251533\pi$
$968$	−35.2063	−	14.7292i	−1.13157	−	0.473414i
$969$	1.34060	−	3.23648i	0.0430661	−	0.103971i
$970$	−4.80622	−	3.21963i	−0.154318	−	0.103376i
$971$	11.1713	+	7.46439i	0.358503	+	0.239544i	0.721757	−	0.692146i	$-0.243335\pi$
$971$	11.1713	+	7.46439i	0.358503	+	0.239544i	−0.363255	+	0.931690i	$0.618335\pi$
$972$	−31.4789	−	6.33885i	−1.00969	−	0.203319i
$973$	0.934424	−	4.69767i	0.0299563	−	0.150600i
$974$	31.6105	+	13.1372i	1.01287	+	0.420944i
$975$	9.98182	−	9.98182i	0.319674	−	0.319674i
$976$	27.3843	+	41.4054i	0.876551	+	1.32536i
$977$	−7.40597	−	7.40597i	−0.236938	−	0.236938i	0.578643	−	0.815581i	$-0.303582\pi$
$977$	−7.40597	−	7.40597i	−0.236938	−	0.236938i	−0.815581	+	0.578643i	$0.803582\pi$
$978$	−0.00176156	−	0.00426703i	−5.63286e−5	−	0.000136445i
$979$	8.74939	+	1.74036i	0.279632	+	0.0556222i
$980$	−1.53442	+	2.28472i	−0.0490152	+	0.0729828i
$981$	5.44472	−	8.14859i	0.173836	−	0.260165i
$982$	−41.2867	+	8.16179i	−1.31751	+	0.260453i
$983$	46.6330	+	19.3160i	1.48736	+	0.616085i	0.970741	−	0.240129i	$-0.0771899\pi$
$983$	46.6330	+	19.3160i	1.48736	+	0.616085i	0.516620	+	0.856215i	$0.327190\pi$
$984$	−22.8371	−	15.3765i	−0.728021	−	0.490186i
$985$	1.22130	−	0.505878i	0.0389138	−	0.0161186i
$986$	−8.03317	−	12.0533i	−0.255828	−	0.383854i
$987$	−3.74358	+	0.744644i	−0.119159	+	0.0237023i
$988$	−16.0917	−	6.70996i	−0.511946	−	0.213472i
$989$	13.9121	−	9.29579i	0.442380	−	0.295589i
$990$	0.00495681	−	4.19901i	0.000157538	−	0.133453i
$991$			12.4779i			0.396374i	0.980164	+	0.198187i	$0.0635053\pi$
$991$			12.4779i			0.396374i	−0.980164	+	0.198187i	$0.936495\pi$
$992$	33.1122	−	32.7236i	1.05131	−	1.03897i
$993$			0.167792i			0.00532471i
$994$	−26.8329	−	0.0316755i	−0.851088	−	0.00100468i
$995$	−5.10395	+	3.41035i	−0.161806	+	0.108115i
$996$	24.4818	−	10.0731i	0.775737	−	0.319177i
$997$	1.42739	−	0.283926i	0.0452060	−	0.00899203i	−0.172436	−	0.985021i	$-0.555164\pi$
$997$	1.42739	−	0.283926i	0.0452060	−	0.00899203i	0.217642	+	0.976029i	$0.430164\pi$
$998$	−35.3212	+	23.5406i	−1.11807	+	0.745165i
$999$	−32.3119	+	13.3840i	−1.02230	+	0.423452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.45.7	yes	56
3.2	odd	2		576.2.bd.a.109.1		56
4.3	odd	2		256.2.i.a.17.4		56
8.3	odd	2		512.2.i.a.289.4		56
8.5	even	2		512.2.i.b.289.4		56
64.5	even	16		512.2.i.b.225.4		56
64.27	odd	16		256.2.i.a.241.4		56
64.37	even	16	inner	64.2.i.a.37.7	✓	56
64.59	odd	16		512.2.i.a.225.4		56
192.101	odd	16		576.2.bd.a.37.1		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.37.7	✓	56	64.37	even	16	inner
64.2.i.a.45.7	yes	56	1.1	even	1	trivial
256.2.i.a.17.4		56	4.3	odd	2
256.2.i.a.241.4		56	64.27	odd	16
512.2.i.a.225.4		56	64.59	odd	16
512.2.i.a.289.4		56	8.3	odd	2
512.2.i.b.225.4		56	64.5	even	16
512.2.i.b.289.4		56	8.5	even	2
576.2.bd.a.37.1		56	192.101	odd	16
576.2.bd.a.109.1		56	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	64.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.998819 + 1.00118i) q^{2} +(-0.477374 - 0.714441i) q^{3} +(-0.00472188 + 1.99999i) q^{4} +(0.0517508 + 0.260169i) q^{5} +(0.238474 - 1.19153i) q^{6} +(-0.515195 - 1.24379i) q^{7} +(-2.00707 + 1.99290i) q^{8} +(0.865510 - 2.08953i) q^{9} +O(q^{10})\)	\(q+(0.998819 + 1.00118i) q^{2} +(-0.477374 - 0.714441i) q^{3} +(-0.00472188 + 1.99999i) q^{4} +(0.0517508 + 0.260169i) q^{5} +(0.238474 - 1.19153i) q^{6} +(-0.515195 - 1.24379i) q^{7} +(-2.00707 + 1.99290i) q^{8} +(0.865510 - 2.08953i) q^{9} +(-0.208786 + 0.311673i) q^{10} +(-4.11495 - 2.74952i) q^{11} +(1.43113 - 0.951372i) q^{12} +(-0.650168 + 3.26862i) q^{13} +(0.730672 - 1.75812i) q^{14} +(0.161171 - 0.161171i) q^{15} +(-3.99996 - 0.0188875i) q^{16} +(1.10212 + 1.10212i) q^{17} +(2.95648 - 1.22053i) q^{18} +(2.56547 + 0.510304i) q^{19} +(-0.520580 + 0.102273i) q^{20} +(-0.642674 + 0.961830i) q^{21} +(-1.35733 - 6.86609i) q^{22} +(3.70792 + 1.53587i) q^{23} +(2.38194 + 0.482572i) q^{24} +(4.55439 - 1.88649i) q^{25} +(-3.92187 + 2.61382i) q^{26} +(-4.43424 + 0.882025i) q^{27} +(2.49001 - 1.02451i) q^{28} +(-5.46390 + 3.65086i) q^{29} +(0.322341 + 0.000380515i) q^{30} +8.22961i q^{31} +(-3.97632 - 4.02354i) q^{32} +4.25245i q^{33} +(-0.00260204 + 2.20424i) q^{34} +(0.296934 - 0.198405i) q^{35} +(4.17496 + 1.74088i) q^{36} +(7.58710 - 1.50917i) q^{37} +(2.05154 + 3.07820i) q^{38} +(2.64561 - 1.09585i) q^{39} +(-0.622359 - 0.419042i) q^{40} +(-10.4659 - 4.33512i) q^{41} +(-1.60488 + 0.317262i) q^{42} +(2.31618 - 3.46640i) q^{43} +(5.51846 - 8.21690i) q^{44} +(0.588420 + 0.117044i) q^{45} +(2.16586 + 5.24635i) q^{46} +(2.33317 + 2.33317i) q^{47} +(1.89598 + 2.86675i) q^{48} +(3.66816 - 3.66816i) q^{49} +(6.43772 + 2.67550i) q^{50} +(0.261277 - 1.31353i) q^{51} +(-6.53414 - 1.31577i) q^{52} +(-3.33837 - 2.23063i) q^{53} +(-5.31207 - 3.55849i) q^{54} +(0.502388 - 1.21287i) q^{55} +(3.51279 + 1.46964i) q^{56} +(-0.860108 - 2.07648i) q^{57} +(-9.11262 - 1.82380i) q^{58} +(1.16241 + 5.84382i) q^{59} +(0.321579 + 0.323102i) q^{60} +(-6.89488 - 10.3189i) q^{61} +(-8.23932 + 8.21989i) q^{62} -3.04484 q^{63} +(0.0566621 - 7.99980i) q^{64} -0.884038 q^{65} +(-4.25746 + 4.24742i) q^{66} +(1.94793 + 2.91529i) q^{67} +(-2.20944 + 2.19903i) q^{68} +(-0.672776 - 3.38227i) q^{69} +(0.495222 + 0.0991136i) q^{70} +(-5.39337 - 13.0208i) q^{71} +(2.42709 + 5.91871i) q^{72} +(-0.375531 + 0.906612i) q^{73} +(9.08909 + 6.08867i) q^{74} +(-3.52193 - 2.35328i) q^{75} +(-1.03272 + 5.12852i) q^{76} +(-1.29983 + 6.53468i) q^{77} +(3.73962 + 1.55418i) q^{78} +(1.20158 - 1.20158i) q^{79} +(-0.202087 - 1.04164i) q^{80} +(-2.05082 - 2.05082i) q^{81} +(-6.11331 - 14.8083i) q^{82} +(15.1088 + 3.00532i) q^{83} +(-1.92062 - 1.28989i) q^{84} +(-0.229702 + 0.343773i) q^{85} +(5.78393 - 1.14340i) q^{86} +(5.21666 + 2.16081i) q^{87} +(13.7385 - 2.68222i) q^{88} +(-1.66533 + 0.689803i) q^{89} +(0.470543 + 0.706020i) q^{90} +(4.40044 - 0.875301i) q^{91} +(-3.08924 + 7.40856i) q^{92} +(5.87957 - 3.92860i) q^{93} +(-0.00550847 + 4.66633i) q^{94} +0.693864i q^{95} +(-0.976389 + 4.76158i) q^{96} +15.4207i q^{97} +(7.33631 + 0.00866031i) q^{98} +(-9.30674 + 6.21857i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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