LMFDB - Embedded newform 64.2.i.a.37.7

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			37.7
Character	$\chi$	$=$	64.37
Dual form			64.2.i.a.45.7

$q$-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 $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{9}{16}\right)$	$1$

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	−0.943291	−	0.331967i	$-0.892288\pi$
$3$	−0.477374	+	0.714441i	−0.275612	+	0.412483i	0.667679	+	0.744449i	$0.267288\pi$
$4$	−0.00472188	−	1.99999i	−0.00236094	−	0.999997i
$5$	0.0517508	−	0.260169i	0.0231436	−	0.116351i	−0.967487	−	0.252922i	$-0.918608\pi$
$5$	0.0517508	−	0.260169i	0.0231436	−	0.116351i	0.990630	+	0.136571i	$0.0436083\pi$
$6$	0.238474	+	1.19153i	0.0973564	+	0.486442i
$7$	−0.515195	+	1.24379i	−0.194725	+	0.470109i	−0.990841	−	0.135036i	$-0.956885\pi$
$7$	−0.515195	+	1.24379i	−0.194725	+	0.470109i	0.796115	+	0.605145i	$0.206885\pi$
$8$	−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	−0.990275	−	0.139122i	$-0.955572\pi$
$11$	−4.11495	+	2.74952i	−1.24071	+	0.829013i	−0.250430	+	0.968135i	$0.580572\pi$
$12$	1.43113	+	0.951372i	0.413132	+	0.274638i
$13$	−0.650168	−	3.26862i	−0.180324	−	0.906551i	−0.959921	−	0.280269i	$-0.909576\pi$
$13$	−0.650168	−	3.26862i	−0.180324	−	0.906551i	0.779597	−	0.626281i	$-0.215424\pi$
$14$	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	−0.560709	−	0.828013i	$-0.689471\pi$
$17$	1.10212	−	1.10212i	0.267304	−	0.267304i	0.828013	+	0.560709i	$0.189471\pi$
$18$	2.95648	+	1.22053i	0.696849	+	0.287681i
$19$	2.56547	−	0.510304i	0.588560	−	0.117072i	0.108178	−	0.994132i	$-0.465498\pi$
$19$	2.56547	−	0.510304i	0.588560	−	0.117072i	0.480381	+	0.877060i	$0.340498\pi$
$20$	−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	0.0390048	−	0.999239i	$-0.487581\pi$
$23$	3.70792	−	1.53587i	0.773154	−	0.320251i	0.734149	+	0.678988i	$0.237581\pi$
$24$	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	−0.0671349	−	0.997744i	$-0.521386\pi$
$29$	−5.46390	−	3.65086i	−1.01462	−	0.677948i	−0.947487	+	0.319795i	$0.896386\pi$
$30$	0.322341		0.000380515i	0.0588512		6.94721e-5i
$31$		−	8.22961i		−	1.47808i	−0.673661	−	0.739041i	$-0.735279\pi$
$31$		−	8.22961i		−	1.47808i	0.673661	−	0.739041i	$-0.264721\pi$
$32$	−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	0.774225	−	0.632910i	$-0.218140\pi$
$37$	7.58710	+	1.50917i	1.24731	+	0.248106i	0.473087	+	0.881016i	$0.343140\pi$
$38$	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	−0.995725	−	0.0923624i	$-0.970558\pi$
$41$	−10.4659	+	4.33512i	−1.63450	+	0.677032i	−0.638774	+	0.769394i	$0.720558\pi$
$42$	−1.60488	−	0.317262i	−0.247638	−	0.0489545i
$43$	2.31618	+	3.46640i	0.353213	+	0.528621i	0.964948	−	0.262442i	$-0.0845278\pi$
$43$	2.31618	+	3.46640i	0.353213	+	0.528621i	−0.611734	+	0.791063i	$0.709528\pi$
$44$	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	−0.516163	−	0.856490i	$-0.672640\pi$
$47$	2.33317	−	2.33317i	0.340328	−	0.340328i	0.856490	+	0.516163i	$0.172640\pi$
$48$	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	−0.763310	−	0.646032i	$-0.776427\pi$
$53$	−3.33837	+	2.23063i	−0.458560	+	0.306400i	0.304750	+	0.952432i	$0.401427\pi$
$54$	−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	−0.828345	−	0.560219i	$-0.810717\pi$
$59$	1.16241	−	5.84382i	0.151333	−	0.760800i	0.979677	−	0.200581i	$-0.0642830\pi$
$60$	0.321579	−	0.323102i	0.0415157	−	0.0417122i
$61$	−6.89488	+	10.3189i	−0.882799	+	1.32120i	0.0635241	+	0.997980i	$0.479766\pi$
$61$	−6.89488	+	10.3189i	−0.882799	+	1.32120i	−0.946323	+	0.323222i	$0.895234\pi$
$62$	−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	−0.693187	−	0.720758i	$-0.743794\pi$
$67$	1.94793	−	2.91529i	0.237978	−	0.356159i	0.931165	+	0.364599i	$0.118794\pi$
$68$	−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	0.186501	+	0.982455i	$0.440285\pi$
$71$	−5.39337	+	13.0208i	−0.640076	+	1.54528i	−0.826577	+	0.562824i	$0.809715\pi$
$72$	2.42709	−	5.91871i	0.286035	−	0.697526i
$73$	−0.375531	−	0.906612i	−0.0439526	−	0.106111i	0.900379	−	0.435107i	$-0.143290\pi$
$73$	−0.375531	−	0.906612i	−0.0439526	−	0.106111i	−0.944331	+	0.328996i	$0.893290\pi$
$74$	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	0.771463	−	0.636274i	$-0.219525\pi$
$79$	1.20158	+	1.20158i	0.135189	+	0.135189i	−0.636274	+	0.771463i	$0.719525\pi$
$80$	−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	0.725012	−	0.688736i	$-0.241834\pi$
$83$	15.1088	−	3.00532i	1.65840	−	0.329877i	0.933392	+	0.358859i	$0.116834\pi$
$84$	−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	0.292671	−	0.956213i	$-0.405456\pi$
$89$	−1.66533	−	0.689803i	−0.176525	−	0.0731189i	−0.469195	+	0.883094i	$0.655456\pi$
$90$	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	$-0.713756\pi$
$97$		−	15.4207i		−	1.56574i	0.622188	−	0.782868i	$-0.286244\pi$
$98$	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	0.587541	−	0.809195i	$-0.300096\pi$
$101$	8.24786	+	1.64060i	0.820692	+	0.163246i	0.233152	+	0.972440i	$0.425096\pi$
$102$	1.57604	+	1.05039i	0.156052	+	0.104004i
$103$	−9.41219	−	3.89866i	−0.927410	−	0.384146i	−0.132715	−	0.991154i	$-0.542369\pi$
$103$	−9.41219	−	3.89866i	−0.927410	−	0.384146i	−0.794695	+	0.607008i	$0.792369\pi$
$104$	−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	0.879156	−	0.476533i	$-0.158107\pi$
$107$	1.05984	+	1.58616i	0.102459	+	0.153340i	−0.776698	+	0.629873i	$0.783107\pi$
$108$	−1.74311	+	8.87262i	−0.167731	+	0.853768i
$109$	4.24989	−	0.845355i	0.407065	−	0.0809704i	0.0126894	−	0.999919i	$-0.495961\pi$
$109$	4.24989	−	0.845355i	0.407065	−	0.0809704i	0.394376	+	0.918949i	$0.370961\pi$
$110$	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	0.758453	−	0.651728i	$-0.225956\pi$
$113$	1.13449	+	1.13449i	0.106724	+	0.106724i	−0.651728	+	0.758453i	$0.725956\pi$
$114$	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	−0.983143	−	0.182837i	$-0.941472\pi$
$131$	−5.01304	+	7.50254i	−0.437991	+	0.655500i	0.545152	+	0.838337i	$0.316472\pi$
$132$	−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	0.742710	−	0.669613i	$-0.233540\pi$
$137$	−2.99585	−	7.23263i	−0.255953	−	0.617925i	−0.998663	+	0.0516877i	$0.983540\pi$
$138$	2.71428	+	4.05185i	0.231055	+	0.344916i
$139$	2.95817	−	1.97658i	0.250908	−	0.167652i	−0.423756	−	0.905777i	$-0.639288\pi$
$139$	2.95817	−	1.97658i	0.250908	−	0.167652i	0.674664	+	0.738125i	$0.264288\pi$
$140$	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	0.572117	−	0.820172i	$-0.306122\pi$
$149$	−4.93832	−	7.39072i	−0.404563	−	0.605472i	−0.976680	+	0.214701i	$0.931122\pi$
$150$	−1.16172	+	5.87659i	−0.0948538	+	0.479822i
$151$	−3.73549	+	1.54729i	−0.303990	+	0.125917i	−0.529464	−	0.848332i	$-0.677607\pi$
$151$	−3.73549	+	1.54729i	−0.303990	+	0.125917i	0.225474	+	0.974249i	$0.427607\pi$
$152$	−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	0.873326	−	0.487136i	$-0.161958\pi$
$157$	9.49118	+	6.34180i	0.757478	+	0.506131i	−0.115848	+	0.993267i	$0.536958\pi$
$158$	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	0.555694	−	0.831387i	$-0.312453\pi$
$163$	0.00315871	+	0.00211058i	0.000247409	+	0.000165314i	−0.555447	+	0.831552i	$0.687453\pi$
$164$	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	0.210538	−	0.977586i	$-0.432478\pi$
$167$	−4.28839	−	1.77631i	−0.331846	−	0.137455i	−0.542384	+	0.840131i	$0.682478\pi$
$168$	−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	0.0891066	−	0.996022i	$-0.471599\pi$
$173$	7.26821	−	1.44574i	0.552592	−	0.109917i	0.463485	+	0.886105i	$0.346599\pi$
$174$	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	0.956503	+	0.291722i	$0.0942283\pi$
$179$	2.46773	+	12.4061i	0.184447	+	0.927277i	−0.772056	+	0.635554i	$0.780772\pi$
$180$	−0.236866	−	1.17628i	−0.0176549	−	0.0876751i
$181$	−13.4674	+	8.99863i	−1.00102	+	0.668863i	−0.944149	−	0.329518i	$-0.893114\pi$
$181$	−13.4674	+	8.99863i	−1.00102	+	0.668863i	−0.0568753	+	0.998381i	$0.518114\pi$
$182$	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	−0.999840	−	0.0178765i	$-0.994309\pi$
$197$	−0.972213	+	4.88764i	−0.0692673	+	0.348230i	0.930573	+	0.366107i	$0.119309\pi$
$198$	−15.5217	+	3.10650i	−1.10308	+	0.220769i
$199$	8.85562	−	21.3794i	0.627758	−	1.51554i	−0.214643	−	0.976692i	$-0.568859\pi$
$199$	8.85562	−	21.3794i	0.627758	−	1.51554i	0.842402	−	0.538850i	$-0.181141\pi$
$200$	−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	−0.319288	−	0.947658i	$-0.603444\pi$
$211$	−3.65496	+	0.727017i	−0.251618	+	0.0500499i	0.0676697	+	0.997708i	$0.478444\pi$
$212$	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	$0.291789\pi$
$223$			23.7016i			1.58718i	−0.608456	+	0.793588i	$0.708211\pi$
$224$	−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	0.228785	−	0.973477i	$-0.426525\pi$
$227$	−8.78436	−	5.86952i	−0.583039	−	0.389574i	−0.811823	+	0.583903i	$0.801525\pi$
$228$	4.15702	+	1.71041i	0.275305	+	0.113274i
$229$	−14.0985	−	2.80436i	−0.931653	−	0.185317i	−0.294145	−	0.955761i	$-0.595035\pi$
$229$	−14.0985	−	2.80436i	−0.931653	−	0.185317i	−0.637508	+	0.770444i	$0.720035\pi$
$230$	−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	−0.211297	−	0.977422i	$-0.567769\pi$
$233$	5.04386	−	2.08924i	0.330435	−	0.136870i	0.541732	+	0.840551i	$0.317769\pi$
$234$	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	−0.109045	−	0.994037i	$-0.534779\pi$
$239$	13.6816	−	13.6816i	0.884992	−	0.884992i	0.994037	+	0.109045i	$0.0347793\pi$
$240$	−0.647720	−	0.641631i	−0.0418101	−	0.0414171i
$241$	2.22031	+	2.22031i	0.143023	+	0.143023i	0.774993	−	0.631970i	$-0.217753\pi$
$241$	2.22031	+	2.22031i	0.143023	+	0.143023i	−0.631970	+	0.774993i	$0.717753\pi$
$242$	−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	−0.950898	−	0.309505i	$-0.899837\pi$
$251$	0.729724	−	3.66857i	0.0460598	−	0.231558i	0.996957	+	0.0779471i	$0.0248365\pi$
$252$	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	−0.902330	−	0.431045i	$-0.858145\pi$
$263$	0.656941	−	1.58600i	0.0405087	−	0.0977967i	0.942839	+	0.333249i	$0.108145\pi$
$264$	−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	−0.999999	−	0.00110539i	$-0.999648\pi$
$269$	−1.25541	−	6.31135i	−0.0765434	−	0.384810i	0.923456	−	0.383704i	$-0.125352\pi$
$270$	0.650903	+	1.56619i	0.0396127	+	0.0953151i
$271$	−17.1048	−	17.1048i	−1.03904	−	1.03904i	−0.999206	−	0.0398353i	$-0.987317\pi$
$271$	−17.1048	−	17.1048i	−1.03904	−	1.03904i	−0.0398353	−	0.999206i	$-0.512683\pi$
$272$	−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	0.688364	−	0.725365i	$-0.258329\pi$
$277$	−4.08114	−	6.10786i	−0.245212	−	0.366985i	−0.933576	+	0.358380i	$0.883329\pi$
$278$	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	−0.180554	−	0.983565i	$-0.557789\pi$
$281$	−16.8252	−	6.96925i	−1.00371	−	0.415750i	−0.823156	+	0.567815i	$0.807789\pi$
$282$	3.33645	+	2.22365i	0.198683	+	0.132417i
$283$	22.3174	+	4.43920i	1.32663	+	0.263883i	0.807022	−	0.590522i	$-0.201078\pi$
$283$	22.3174	+	4.43920i	1.32663	+	0.263883i	0.519608	+	0.854405i	$0.326078\pi$
$284$	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	−0.552290	−	0.833652i	$-0.686246\pi$
$293$	−23.6486	−	4.70399i	−1.38156	−	0.274810i	−0.829274	+	0.558842i	$0.811246\pi$
$294$	−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	0.998313	+	0.0580626i	$0.0184923\pi$
$307$	1.72081	+	8.65108i	0.0982116	+	0.493743i	−0.900101	+	0.435681i	$0.856508\pi$
$308$	−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	0.960552	−	0.278101i	$-0.0897049\pi$
$311$	1.49356	+	3.60578i	0.0846923	+	0.204465i	−0.875860	+	0.482566i	$0.839705\pi$
$312$	−3.12600	−	7.47188i	−0.176975	−	0.423012i
$313$	8.26474	−	19.9529i	0.467151	−	1.12780i	−0.498250	−	0.867033i	$-0.666024\pi$
$313$	8.26474	−	19.9529i	0.467151	−	1.12780i	0.965401	−	0.260769i	$-0.0839760\pi$
$314$	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	0.00299906	−	0.999996i	$-0.499045\pi$
$317$	16.4821	−	24.6672i	0.925727	−	1.38545i	0.922728	−	0.385452i	$-0.125955\pi$
$318$	−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	−0.560024	−	0.828476i	$-0.689208\pi$
$331$	−0.162367	+	0.108490i	−0.00892448	+	0.00596315i	0.551100	+	0.834439i	$0.314208\pi$
$332$	−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	−0.504623	−	0.863340i	$-0.668368\pi$
$337$	6.58517	−	6.58517i	0.358717	−	0.358717i	0.863340	+	0.504623i	$0.168368\pi$
$338$	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	−0.522818	−	0.852444i	$-0.675119\pi$
$347$	−24.8134	−	4.93570i	−1.33206	−	0.264962i	−0.809237	+	0.587482i	$0.800119\pi$
$348$	−4.34624	−	10.4231i	−0.232983	−	0.558736i
$349$	−10.7430	−	7.17827i	−0.575062	−	0.384244i	0.233763	−	0.972294i	$-0.424896\pi$
$349$	−10.7430	−	7.17827i	−0.575062	−	0.384244i	−0.808825	+	0.588050i	$0.799896\pi$
$350$	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	$0.133558\pi$
$353$			15.3080i			0.814764i	−0.913258	+	0.407382i	$0.866442\pi$
$354$	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	0.566533	−	0.824039i	$-0.308285\pi$
$359$	7.28425	+	3.01723i	0.384448	+	0.159243i	−0.182085	+	0.983283i	$0.558285\pi$
$360$	−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	−0.908223	−	0.418486i	$-0.862561\pi$
$367$	−9.38201	+	9.38201i	−0.489737	+	0.489737i	0.418486	+	0.908223i	$0.362561\pi$
$368$	−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	−0.509804	−	0.860291i	$-0.670282\pi$
$373$	1.73641	−	1.16023i	0.0899078	−	0.0600745i	0.599712	+	0.800216i	$0.295282\pi$
$374$	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	0.442114	+	0.896959i	$0.354229\pi$
$379$	−6.02722	+	30.3009i	−0.309597	+	1.55645i	−0.751711	+	0.659492i	$0.770771\pi$
$380$	−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	0.913980	+	0.405760i	$0.132993\pi$
$389$	−1.69036	+	8.49804i	−0.0857049	+	0.430868i	−0.999685	+	0.0251080i	$0.992007\pi$
$390$	−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	0.952122	+	0.305718i	$0.0988963\pi$
$397$	3.77514	+	18.9789i	0.189469	+	0.952525i	−0.762653	+	0.646808i	$0.776104\pi$
$398$	−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	0.110133	−	0.993917i	$-0.464872\pi$
$401$	22.1086	−	22.1086i	1.10405	−	1.10405i	0.993917	−	0.110133i	$-0.0351275\pi$
$402$	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	0.372459	−	0.928049i	$-0.378515\pi$
$409$	−0.412610	−	0.170909i	−0.0204023	−	0.00845089i	−0.392861	+	0.919598i	$0.628515\pi$
$410$	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	0.987052	−	0.160398i	$-0.0512776\pi$
$419$	24.9030	+	16.6397i	1.21659	+	0.812901i	0.229541	+	0.973299i	$0.426278\pi$
$420$	0.236195	+	0.566438i	0.0115251	+	0.0276393i
$421$	27.6476	+	5.49946i	1.34746	+	0.268027i	0.815508	−	0.578745i	$-0.196457\pi$
$421$	27.6476	+	5.49946i	1.34746	+	0.268027i	0.531955	+	0.846772i	$0.321457\pi$
$422$	−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	−0.562739	−	0.826635i	$-0.690252\pi$
$431$	5.47861	−	5.47861i	0.263896	−	0.263896i	0.826635	+	0.562739i	$0.190252\pi$
$432$	17.7534	+	3.44431i	0.854162	+	0.165714i
$433$	−13.9653	−	13.9653i	−0.671130	−	0.671130i	0.286847	−	0.957977i	$-0.407393\pi$
$433$	−13.9653	−	13.9653i	−0.671130	−	0.671130i	−0.957977	+	0.286847i	$0.907393\pi$
$434$	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	0.996671	+	0.0815308i	$0.0259809\pi$
$439$	7.32429	+	17.6824i	0.349569	+	0.843935i	−0.647102	+	0.762404i	$0.724019\pi$
$440$	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	−0.948549	−	0.316631i	$-0.897448\pi$
$443$	1.03061	−	5.18121i	0.0489656	−	0.246167i	0.997514	+	0.0704647i	$0.0224482\pi$
$444$	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	0.933187	−	0.359390i	$-0.117015\pi$
$457$	0.410387	+	0.990763i	0.0191971	+	0.0463459i	−0.913990	+	0.405736i	$0.867015\pi$
$458$	−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	0.967422	−	0.253168i	$-0.0814726\pi$
$461$	−0.499040	−	2.50885i	−0.0232426	−	0.116849i	−0.990665	+	0.136320i	$0.956473\pi$
$462$	7.47633	−	3.10714i	0.347830	−	0.144557i
$463$	−23.9046	−	23.9046i	−1.11094	−	1.11094i	−0.993024	−	0.117915i	$-0.962379\pi$
$463$	−23.9046	−	23.9046i	−1.11094	−	1.11094i	−0.117915	−	0.993024i	$-0.537621\pi$
$464$	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	0.638833	−	0.769345i	$-0.279417\pi$
$467$	32.9221	−	6.54862i	1.52345	−	0.303034i	0.884621	+	0.466311i	$0.154417\pi$
$468$	−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	$0.132668\pi$
$479$			17.7201i			0.809654i	−0.914393	+	0.404827i	$0.867332\pi$
$480$	−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	0.826680	−	0.562672i	$-0.190227\pi$
$487$	22.3630	+	9.26304i	1.01336	+	0.419749i	0.186682	+	0.982420i	$0.440227\pi$
$488$	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	−0.989187	−	0.146658i	$-0.953148\pi$
$491$	−16.5333	−	24.7438i	−0.746136	−	1.11667i	0.243051	−	0.970013i	$-0.421852\pi$
$492$	−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	−0.857549	−	0.514402i	$-0.828014\pi$
$499$	−5.85555	−	29.4378i	−0.262130	−	1.31782i	0.595419	−	0.803416i	$-0.296986\pi$
$500$	−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	0.973109	−	0.230343i	$-0.0739849\pi$
$503$	2.73931	+	6.61328i	0.122140	+	0.294871i	−0.850970	+	0.525215i	$0.823985\pi$
$504$	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	−0.747917	−	0.663792i	$-0.768946\pi$
$509$	3.41939	−	5.11748i	0.151562	−	0.226829i	0.899479	+	0.436963i	$0.143946\pi$
$510$	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	0.995383	−	0.0959866i	$-0.0306006\pi$
$521$	5.10532	+	12.3253i	0.223668	+	0.539983i	−0.771715	+	0.635969i	$0.780601\pi$
$522$	−11.6979	−	17.4626i	−0.512005	−	0.764315i
$523$	22.7053	−	15.1712i	0.992835	−	0.663391i	0.0507311	−	0.998712i	$-0.483845\pi$
$523$	22.7053	−	15.1712i	0.992835	−	0.663391i	0.942104	+	0.335321i	$0.108845\pi$
$524$	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	0.525883	−	0.850557i	$-0.323735\pi$
$541$	−1.36491	−	0.912006i	−0.0586822	−	0.0392102i	−0.584565	+	0.811347i	$0.698735\pi$
$542$	−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	0.984170	+	0.177225i	$0.0567122\pi$
$547$	35.6558	+	23.8244i	1.52453	+	1.01866i	0.540361	+	0.841434i	$0.318288\pi$
$548$	−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	−0.245454	−	0.969408i	$-0.578937\pi$
$557$	−2.38952	+	0.475305i	−0.101247	+	0.0201393i	0.144207	+	0.989548i	$0.453937\pi$
$558$	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	0.992659	+	0.120950i	$0.0385941\pi$
$563$	2.89115	+	14.5348i	0.121847	+	0.612567i	−0.870811	+	0.491617i	$0.836406\pi$
$564$	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	0.330022	+	0.943973i	$0.392944\pi$
$569$	−13.6164	+	32.8729i	−0.570829	+	1.37810i	−0.900851	+	0.434129i	$0.857056\pi$
$570$	0.826763	−	0.165468i	0.0346293	−	0.00693070i
$571$	−4.08279	+	20.5256i	−0.170859	+	0.858968i	0.796321	+	0.604875i	$0.206777\pi$
$571$	−4.08279	+	20.5256i	−0.170859	+	0.858968i	−0.967180	+	0.254093i	$0.918223\pi$
$572$	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	−0.668114	−	0.744059i	$-0.732898\pi$
$587$	−5.72679	+	3.82652i	−0.236370	+	0.157937i	0.431744	+	0.901996i	$0.357898\pi$
$588$	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	−0.574761	−	0.818321i	$-0.694905\pi$
$593$	5.93109	−	5.93109i	0.243561	−	0.243561i	0.818321	+	0.574761i	$0.194905\pi$
$594$	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	−0.199796	−	0.979838i	$-0.564028\pi$
$599$	8.60956	−	3.56620i	0.351777	−	0.145711i	0.551573	+	0.834127i	$0.314028\pi$
$600$	11.7586	+	2.29568i	0.480044	+	0.0937207i
$601$	−9.04530	−	3.74668i	−0.368965	−	0.152830i	0.190494	−	0.981688i	$-0.438991\pi$
$601$	−9.04530	−	3.74668i	−0.368965	−	0.152830i	−0.559459	+	0.828858i	$0.688991\pi$
$602$	−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	$0.249689\pi$
$607$			34.8085i			1.41283i	−0.707796	+	0.706417i	$0.750311\pi$
$608$	−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	0.482978	−	0.875632i	$-0.339555\pi$
$613$	14.7093	+	2.92585i	0.594101	+	0.118174i	0.111123	+	0.993807i	$0.464555\pi$
$614$	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	−0.215964	−	0.976401i	$-0.569289\pi$
$617$	7.99200	−	3.31040i	0.321746	−	0.133272i	0.537710	+	0.843130i	$0.319289\pi$
$618$	2.40083	−	12.1447i	0.0965754	−	0.488530i
$619$	−4.66067	−	6.97519i	−0.187328	−	0.280356i	0.725904	−	0.687796i	$-0.241422\pi$
$619$	−4.66067	−	6.97519i	−0.187328	−	0.280356i	−0.913232	+	0.407440i	$0.866422\pi$
$620$	−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	0.947089	+	0.320972i	$0.104010\pi$
$631$	12.6693	+	30.5864i	0.504358	+	1.21763i	−0.442731	+	0.896654i	$0.645990\pi$
$632$	−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	−0.905388	−	0.424586i	$-0.860420\pi$
$643$	−4.22568	+	6.32418i	−0.166645	+	0.249401i	0.738743	+	0.673987i	$0.235420\pi$
$644$	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	−0.999757	−	0.0220394i	$-0.992984\pi$
$647$	−7.05188	+	17.0247i	−0.277238	+	0.669311i	0.722519	+	0.691351i	$0.242984\pi$
$648$	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	0.913685	+	0.406423i	$0.133224\pi$
$653$	5.75170	+	28.9158i	0.225081	+	1.13156i	−0.688604	+	0.725138i	$0.741776\pi$
$654$	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	−0.287004	−	0.957929i	$-0.592659\pi$
$659$	−4.76397	+	0.947613i	−0.185578	+	0.0369138i	0.101426	+	0.994843i	$0.467659\pi$
$660$	−0.434909	+	2.21374i	−0.0169288	+	0.0861697i
$661$	−14.3165	−	21.4261i	−0.556846	−	0.833378i	0.441099	−	0.897458i	$-0.354589\pi$
$661$	−14.3165	−	21.4261i	−0.556846	−	0.833378i	−0.997945	+	0.0640799i	$0.979589\pi$
$662$	−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	$-0.955808\pi$
$673$		−	7.18022i		−	0.276777i	0.990378	−	0.138389i	$-0.0441923\pi$
$674$	−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	0.205009	−	0.978760i	$-0.434278\pi$
$677$	0.516673	+	0.102773i	0.0198574	+	0.00394987i	−0.185152	+	0.982710i	$0.559278\pi$
$678$	−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	0.977380	−	0.211492i	$-0.0678322\pi$
$683$	10.6617	+	15.9564i	0.407960	+	0.610555i	−0.569420	+	0.822047i	$0.692832\pi$
$684$	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	0.755794	+	0.654810i	$0.227251\pi$
$691$	8.09941	+	40.7185i	0.308116	+	1.54901i	−0.447677	+	0.894195i	$0.647749\pi$
$692$	−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	−0.773232	−	0.634123i	$-0.781361\pi$
$701$	2.87333	−	4.30025i	0.108524	−	0.162418i	0.881756	+	0.471705i	$0.156361\pi$
$702$	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	−0.405292	−	0.914187i	$-0.632830\pi$
$709$	8.49385	−	42.7015i	0.318993	−	1.60369i	0.724286	−	0.689500i	$-0.242170\pi$
$710$	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	0.790991	−	0.611828i	$-0.209565\pi$
$719$	4.80412	+	4.80412i	0.179163	+	0.179163i	−0.611828	+	0.790991i	$0.709565\pi$
$720$	−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	−0.311272	−	0.950321i	$-0.600755\pi$
$727$	3.79111	−	1.57033i	0.140604	−	0.0582402i	0.451876	+	0.892081i	$0.350755\pi$
$728$	−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	0.999975	−	0.00707651i	$-0.00225254\pi$
$733$	37.2568	+	24.8942i	1.37611	+	0.919488i	0.376136	+	0.926564i	$0.377253\pi$
$734$	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	−0.132645	−	0.991164i	$-0.542347\pi$
$739$	−29.8791	−	19.9646i	−1.09912	−	0.734409i	−0.966477	+	0.256754i	$0.917347\pi$
$740$	−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	0.00714476	−	0.999974i	$-0.497726\pi$
$743$	−18.9414	−	7.84578i	−0.694892	−	0.287834i	−0.702037	+	0.712141i	$0.747726\pi$
$744$	−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	−0.802302	−	0.596919i	$-0.796391\pi$
$751$	−5.62839	+	5.62839i	−0.205383	+	0.205383i	0.596919	+	0.802302i	$0.296391\pi$
$752$	−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	−0.832486	−	0.554046i	$-0.813083\pi$
$757$	−17.5865	+	11.7509i	−0.639192	+	0.427095i	0.193293	+	0.981141i	$0.438083\pi$
$758$	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	−0.673946	−	0.738781i	$-0.735402\pi$
$761$	8.96561	−	21.6449i	0.325003	−	0.784627i	0.998949	−	0.0458456i	$-0.0145982\pi$
$762$	−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	−0.857677	−	0.514189i	$-0.828093\pi$
$773$	3.65565	−	18.3782i	0.131485	−	0.661018i	0.989162	−	0.146830i	$-0.0469069\pi$
$774$	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	−0.891650	−	0.452726i	$-0.850452\pi$
$787$	−43.2635	+	8.60564i	−1.54218	+	0.306758i	−0.650526	+	0.759484i	$0.725452\pi$
$788$	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	−0.999962	−	0.00869271i	$-0.997233\pi$
$797$	−39.2600	−	26.2327i	−1.39066	−	0.929211i	−0.390700	−	0.920518i	$-0.627767\pi$
$798$	−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	−0.622784	−	0.782394i	$-0.713999\pi$
$809$	−14.5037	+	6.00764i	−0.509924	+	0.211217i	0.112861	+	0.993611i	$0.463999\pi$
$810$	1.06737	+	0.211003i	0.0375034	+	0.00741388i
$811$	−15.8735	−	23.7564i	−0.557395	−	0.834200i	0.440586	−	0.897710i	$-0.354771\pi$
$811$	−15.8735	−	23.7564i	−0.557395	−	0.834200i	−0.997981	+	0.0635100i	$0.979771\pi$
$812$	−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	−0.729116	−	0.684391i	$-0.760068\pi$
$821$	−10.7690	+	7.19563i	−0.375842	+	0.251129i	0.353274	+	0.935520i	$0.385068\pi$
$822$	7.90350	−	5.29445i	0.275666	−	0.184665i
$823$	−5.78447	−	13.9649i	−0.201634	−	0.486788i	0.790425	−	0.612558i	$-0.209860\pi$
$823$	−5.78447	−	13.9649i	−0.201634	−	0.486788i	−0.992059	+	0.125771i	$0.959860\pi$
$824$	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	−0.648914	−	0.760862i	$-0.724776\pi$
$827$	6.95283	−	34.9542i	0.241774	−	1.21548i	0.890687	−	0.454616i	$-0.150224\pi$
$828$	12.8066	−	12.8672i	0.445061	−	0.447167i
$829$	−15.3694	+	23.0020i	−0.533802	+	0.798891i	−0.996137	−	0.0878145i	$-0.972012\pi$
$829$	−15.3694	+	23.0020i	−0.533802	+	0.798891i	0.462335	+	0.886705i	$0.347012\pi$
$830$	−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	0.576699	+	0.816956i	$0.304340\pi$
$839$	−11.8401	+	28.5844i	−0.408764	+	0.986844i	−0.985463	+	0.169887i	$0.945660\pi$
$840$	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	−0.944607	−	0.328204i	$-0.893557\pi$
$853$	−25.8867	−	38.7421i	−0.886343	−	1.32651i	0.0582640	−	0.998301i	$-0.481443\pi$
$854$	−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	0.572271	−	0.820064i	$-0.306062\pi$
$857$	11.6236	+	4.81466i	0.397055	+	0.164466i	−0.175216	+	0.984530i	$0.556062\pi$
$858$	−11.1151	+	16.6775i	−0.379464	+	0.569362i
$859$	7.21770	+	1.43569i	0.246265	+	0.0489851i	0.316679	−	0.948533i	$-0.397432\pi$
$859$	7.21770	+	1.43569i	0.246265	+	0.0489851i	−0.0704144	+	0.997518i	$0.522432\pi$
$860$	−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	$0.338178\pi$
$863$			51.3234i			1.74707i	−0.486761	+	0.873535i	$0.661822\pi$
$864$	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	0.565720	−	0.824597i	$-0.308598\pi$
$877$	41.5765	−	8.27007i	1.40394	−	0.279260i	0.838217	+	0.545337i	$0.183598\pi$
$878$	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	0.950887	−	0.309539i	$-0.100175\pi$
$881$	19.0362	+	19.0362i	0.641347	+	0.641347i	−0.309539	+	0.950887i	$0.600175\pi$
$882$	6.36775	+	15.3219i	0.214413	+	0.515916i
$883$	−6.24157	−	31.3785i	−0.210046	−	1.05597i	−0.931565	−	0.363576i	$-0.881556\pi$
$883$	−6.24157	−	31.3785i	−0.210046	−	1.05597i	0.721519	−	0.692395i	$-0.243444\pi$
$884$	−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	−0.871968	−	0.489563i	$-0.837156\pi$
$887$	−17.9162	−	43.2535i	−0.601567	−	1.45231i	0.270401	−	0.962748i	$-0.412844\pi$
$888$	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	−0.660219	−	0.751073i	$-0.729537\pi$
$907$	−6.59470	+	4.40644i	−0.218974	+	0.146313i	0.441246	+	0.897386i	$0.354537\pi$
$908$	−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	0.695533	−	0.718494i	$-0.255168\pi$
$911$	−0.693019	−	0.693019i	−0.0229608	−	0.0229608i	−0.718494	+	0.695533i	$0.755168\pi$
$912$	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	0.0687992	−	0.997631i	$-0.478083\pi$
$919$	24.9456	−	10.3328i	0.822879	−	0.340848i	0.754080	+	0.656783i	$0.228083\pi$
$920$	−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	$-0.934460\pi$
$929$		−	12.4630i		−	0.408898i	0.978877	−	0.204449i	$-0.0655402\pi$
$930$	−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	−0.741547	+	0.670901i	$0.765907\pi$
$937$	−53.2713	+	22.0657i	−1.74030	+	0.720855i	−0.998752	+	0.0499537i	$0.984093\pi$
$938$	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	−0.441613	−	0.897206i	$-0.645593\pi$
$941$	−15.5300	+	3.08911i	−0.506264	+	0.100702i	−0.0646512	+	0.997908i	$0.520593\pi$
$942$	−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	0.929576	−	0.368631i	$-0.120173\pi$
$947$	−2.16365	−	10.8774i	−0.0703092	−	0.353468i	−0.999885	+	0.0151628i	$0.995173\pi$
$948$	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	−0.526808	−	0.849984i	$-0.676611\pi$
$953$	13.7909	−	33.2942i	0.446731	−	1.07850i	0.973539	−	0.228520i	$-0.0733887\pi$
$954$	−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	0.703692	+	0.710505i	$0.251533\pi$
$967$	−9.21382	+	22.2441i	−0.296296	+	0.715323i	−0.999988	+	0.00481755i	$0.998467\pi$
$968$	−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	−0.363255	−	0.931690i	$-0.618335\pi$
$971$	11.1713	−	7.46439i	0.358503	−	0.239544i	0.721757	+	0.692146i	$0.243335\pi$
$972$	−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	−0.815581	−	0.578643i	$-0.803582\pi$
$977$	−7.40597	+	7.40597i	−0.236938	+	0.236938i	0.578643	+	0.815581i	$0.303582\pi$
$978$	−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	0.516620	−	0.856215i	$-0.327190\pi$
$983$	46.6330	−	19.3160i	1.48736	−	0.616085i	0.970741	+	0.240129i	$0.0771899\pi$
$984$	−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	$-0.936495\pi$
$991$		−	12.4779i		−	0.396374i	0.980164	−	0.198187i	$-0.0635053\pi$
$992$	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	0.217642	−	0.976029i	$-0.430164\pi$
$997$	1.42739	+	0.283926i	0.0452060	+	0.00899203i	−0.172436	+	0.985021i	$0.555164\pi$
$998$	−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.37.7	✓	56
3.2	odd	2		576.2.bd.a.37.1		56
4.3	odd	2		256.2.i.a.241.4		56
8.3	odd	2		512.2.i.a.225.4		56
8.5	even	2		512.2.i.b.225.4		56
64.13	even	16		512.2.i.b.289.4		56
64.19	odd	16		256.2.i.a.17.4		56
64.45	even	16	inner	64.2.i.a.45.7	yes	56
64.51	odd	16		512.2.i.a.289.4		56
192.173	odd	16		576.2.bd.a.109.1		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.37.7	✓	56	1.1	even	1	trivial
64.2.i.a.45.7	yes	56	64.45	even	16	inner
256.2.i.a.17.4		56	64.19	odd	16
256.2.i.a.241.4		56	4.3	odd	2
512.2.i.a.225.4		56	8.3	odd	2
512.2.i.a.289.4		56	64.51	odd	16
512.2.i.b.225.4		56	8.5	even	2
512.2.i.b.289.4		56	64.13	even	16
576.2.bd.a.37.1		56	3.2	odd	2
576.2.bd.a.109.1		56	192.173	odd	16

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

Properties

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