LMFDB - Embedded newform 552.2.f.d.277.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(277,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("552.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 2 x^{18} - 2 x^{17} + x^{16} - 4 x^{15} + 16 x^{14} - 24 x^{13} + 32 x^{12} + \cdots + 1024 $ x^20 - 2x^19 + 2x^18 - 2x^17 + x^16 - 4x^15 + 16x^14 - 24x^13 + 32x^12 - 16x^11 - 16x^10 - 32x^9 + 128x^8 - 192x^7 + 256x^6 - 128x^5 + 64x^4 - 256x^3 + 512x^2 - 1024x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			277.1
Root			$1.38506 + 0.285679i$ of defining polynomial
Character	$\chi$	$=$	552.277
Dual form			552.2.f.d.277.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38506 - 0.285679i) q^{2} +1.00000i q^{3} +(1.83677 + 0.791365i) q^{4} -2.43947i q^{5} +(0.285679 - 1.38506i) q^{6} -3.50435 q^{7} +(-2.31796 - 1.62082i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.38506 - 0.285679i) q^{2} +1.00000i q^{3} +(1.83677 + 0.791365i) q^{4} -2.43947i q^{5} +(0.285679 - 1.38506i) q^{6} -3.50435 q^{7} +(-2.31796 - 1.62082i) q^{8} -1.00000 q^{9} +(-0.696905 + 3.37881i) q^{10} +2.10475i q^{11} +(-0.791365 + 1.83677i) q^{12} +1.86581i q^{13} +(4.85374 + 1.00112i) q^{14} +2.43947 q^{15} +(2.74748 + 2.90712i) q^{16} +7.45202 q^{17} +(1.38506 + 0.285679i) q^{18} +6.83190i q^{19} +(1.93051 - 4.48075i) q^{20} -3.50435i q^{21} +(0.601283 - 2.91520i) q^{22} +1.00000 q^{23} +(1.62082 - 2.31796i) q^{24} -0.951008 q^{25} +(0.533023 - 2.58426i) q^{26} -1.00000i q^{27} +(-6.43671 - 2.77322i) q^{28} +1.91480i q^{29} +(-3.37881 - 0.696905i) q^{30} +3.05752 q^{31} +(-2.97492 - 4.81143i) q^{32} -2.10475 q^{33} +(-10.3215 - 2.12889i) q^{34} +8.54876i q^{35} +(-1.83677 - 0.791365i) q^{36} +6.64083i q^{37} +(1.95173 - 9.46258i) q^{38} -1.86581 q^{39} +(-3.95393 + 5.65460i) q^{40} +8.85352 q^{41} +(-1.00112 + 4.85374i) q^{42} +1.33057i q^{43} +(-1.66562 + 3.86595i) q^{44} +2.43947i q^{45} +(-1.38506 - 0.285679i) q^{46} -0.423767 q^{47} +(-2.90712 + 2.74748i) q^{48} +5.28050 q^{49} +(1.31720 + 0.271683i) q^{50} +7.45202i q^{51} +(-1.47654 + 3.42708i) q^{52} -5.74482i q^{53} +(-0.285679 + 1.38506i) q^{54} +5.13447 q^{55} +(8.12297 + 5.67991i) q^{56} -6.83190 q^{57} +(0.547020 - 2.65212i) q^{58} +6.88650i q^{59} +(4.48075 + 1.93051i) q^{60} +5.52040i q^{61} +(-4.23485 - 0.873470i) q^{62} +3.50435 q^{63} +(2.74592 + 7.51398i) q^{64} +4.55159 q^{65} +(2.91520 + 0.601283i) q^{66} -5.44309i q^{67} +(13.6877 + 5.89727i) q^{68} +1.00000i q^{69} +(2.44220 - 11.8405i) q^{70} -10.0258 q^{71} +(2.31796 + 1.62082i) q^{72} -3.86198 q^{73} +(1.89715 - 9.19794i) q^{74} -0.951008i q^{75} +(-5.40653 + 12.5487i) q^{76} -7.37579i q^{77} +(2.58426 + 0.533023i) q^{78} +7.55375 q^{79} +(7.09182 - 6.70240i) q^{80} +1.00000 q^{81} +(-12.2626 - 2.52927i) q^{82} +16.3370i q^{83} +(2.77322 - 6.43671i) q^{84} -18.1790i q^{85} +(0.380115 - 1.84291i) q^{86} -1.91480 q^{87} +(3.41141 - 4.87873i) q^{88} +0.143819 q^{89} +(0.696905 - 3.37881i) q^{90} -6.53846i q^{91} +(1.83677 + 0.791365i) q^{92} +3.05752i q^{93} +(0.586943 + 0.121062i) q^{94} +16.6662 q^{95} +(4.81143 - 2.97492i) q^{96} -18.0182 q^{97} +(-7.31380 - 1.50853i) q^{98} -2.10475i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9	$ 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9} - 12 q^{10} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 32 q^{17} + 2 q^{18} + 20 q^{20} + 14 q^{22} + 20 q^{23} + 10 q^{24} - 28 q^{25} + 18 q^{28} - 22 q^{32} + 28 q^{33} - 26 q^{34} + 16 q^{38} + 4 q^{40} - 40 q^{41} + 14 q^{42} + 10 q^{44} - 2 q^{46} + 40 q^{47} + 12 q^{49} - 14 q^{50} + 20 q^{52} - 2 q^{54} - 8 q^{55} + 6 q^{56} - 44 q^{57} - 32 q^{58} - 24 q^{60} + 20 q^{62} + 8 q^{63} - 48 q^{64} + 8 q^{65} + 10 q^{66} + 22 q^{68} + 80 q^{70} - 40 q^{71} + 2 q^{72} - 16 q^{73} - 30 q^{74} + 44 q^{76} - 36 q^{78} - 16 q^{79} + 4 q^{80} + 20 q^{81} - 32 q^{82} + 6 q^{84} - 4 q^{86} + 8 q^{87} - 70 q^{88} - 40 q^{89} + 12 q^{90} + 64 q^{94} - 40 q^{95} + 2 q^{96} + 32 q^{97} - 26 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9 - 12 * q^10 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 32 * q^17 + 2 * q^18 + 20 * q^20 + 14 * q^22 + 20 * q^23 + 10 * q^24 - 28 * q^25 + 18 * q^28 - 22 * q^32 + 28 * q^33 - 26 * q^34 + 16 * q^38 + 4 * q^40 - 40 * q^41 + 14 * q^42 + 10 * q^44 - 2 * q^46 + 40 * q^47 + 12 * q^49 - 14 * q^50 + 20 * q^52 - 2 * q^54 - 8 * q^55 + 6 * q^56 - 44 * q^57 - 32 * q^58 - 24 * q^60 + 20 * q^62 + 8 * q^63 - 48 * q^64 + 8 * q^65 + 10 * q^66 + 22 * q^68 + 80 * q^70 - 40 * q^71 + 2 * q^72 - 16 * q^73 - 30 * q^74 + 44 * q^76 - 36 * q^78 - 16 * q^79 + 4 * q^80 + 20 * q^81 - 32 * q^82 + 6 * q^84 - 4 * q^86 + 8 * q^87 - 70 * q^88 - 40 * q^89 + 12 * q^90 + 64 * q^94 - 40 * q^95 + 2 * q^96 + 32 * q^97 - 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.38506	−	0.285679i	−0.979384	−	0.202006i
$2$	−1.38506	−	0.285679i	−0.979384	−	0.202006i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.83677	+	0.791365i	0.918387	+	0.395682i
$5$		−	2.43947i		−	1.09096i	−0.838123	−	0.545482i	$-0.816347\pi$
$5$		−	2.43947i		−	1.09096i	0.838123	−	0.545482i	$-0.183653\pi$
$6$	0.285679	−	1.38506i	0.116628	−	0.565448i
$7$	−3.50435			−1.32452			−0.662261	−	0.749273i	$-0.730403\pi$
$7$	−3.50435			−1.32452			−0.662261	+	0.749273i	$0.730403\pi$
$8$	−2.31796	−	1.62082i	−0.819524	−	0.573045i
$9$	−1.00000			−0.333333
$10$	−0.696905	+	3.37881i	−0.220381	+	1.06847i
$11$			2.10475i			0.634606i	0.948324	+	0.317303i	$0.102777\pi$
$11$			2.10475i			0.634606i	−0.948324	+	0.317303i	$0.897223\pi$
$12$	−0.791365	+	1.83677i	−0.228447	+	0.530231i
$13$			1.86581i			0.517483i	0.965947	+	0.258741i	$0.0833078\pi$
$13$			1.86581i			0.517483i	−0.965947	+	0.258741i	$0.916692\pi$
$14$	4.85374	+	1.00112i	1.29722	+	0.267561i
$15$	2.43947			0.629868
$16$	2.74748	+	2.90712i	0.686871	+	0.726780i
$17$	7.45202			1.80738			0.903690	−	0.428187i	$-0.140848\pi$
$17$	7.45202			1.80738			0.903690	+	0.428187i	$0.140848\pi$
$18$	1.38506	+	0.285679i	0.326461	+	0.0673352i
$19$			6.83190i			1.56735i	0.621174	+	0.783673i	$0.286656\pi$
$19$			6.83190i			1.56735i	−0.621174	+	0.783673i	$0.713344\pi$
$20$	1.93051	−	4.48075i	0.431675	−	1.00193i
$21$		−	3.50435i		−	0.764713i
$22$	0.601283	−	2.91520i	0.128194	−	0.621523i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	1.62082	−	2.31796i	0.330847	−	0.473152i
$25$	−0.951008			−0.190202
$26$	0.533023	−	2.58426i	0.104535	−	0.506815i
$27$		−	1.00000i		−	0.192450i
$28$	−6.43671	−	2.77322i	−1.21642	−	0.524090i
$29$			1.91480i			0.355570i	0.984069	+	0.177785i	$0.0568932\pi$
$29$			1.91480i			0.355570i	−0.984069	+	0.177785i	$0.943107\pi$
$30$	−3.37881	−	0.696905i	−0.616883	−	0.127237i
$31$	3.05752			0.549147			0.274573	−	0.961566i	$-0.411463\pi$
$31$	3.05752			0.549147			0.274573	+	0.961566i	$0.411463\pi$
$32$	−2.97492	−	4.81143i	−0.525897	−	0.850548i
$33$	−2.10475			−0.366390
$34$	−10.3215	−	2.12889i	−1.77012	−	0.365101i
$35$			8.54876i			1.44500i
$36$	−1.83677	−	0.791365i	−0.306129	−	0.131894i
$37$			6.64083i			1.09175i	0.837868	+	0.545873i	$0.183802\pi$
$37$			6.64083i			1.09175i	−0.837868	+	0.545873i	$0.816198\pi$
$38$	1.95173	−	9.46258i	0.316613	−	1.53503i
$39$	−1.86581			−0.298769
$40$	−3.95393	+	5.65460i	−0.625171	+	0.894071i
$41$	8.85352			1.38269			0.691344	−	0.722526i	$-0.257019\pi$
$41$	8.85352			1.38269			0.691344	+	0.722526i	$0.257019\pi$
$42$	−1.00112	+	4.85374i	−0.154476	+	0.748948i
$43$			1.33057i			0.202909i	0.994840	+	0.101455i	$0.0323497\pi$
$43$			1.33057i			0.202909i	−0.994840	+	0.101455i	$0.967650\pi$
$44$	−1.66562	+	3.86595i	−0.251102	+	0.582814i
$45$			2.43947i			0.363655i
$46$	−1.38506	−	0.285679i	−0.204216	−	0.0421211i
$47$	−0.423767			−0.0618128			−0.0309064	−	0.999522i	$-0.509839\pi$
$47$	−0.423767			−0.0618128			−0.0309064	+	0.999522i	$0.509839\pi$
$48$	−2.90712	+	2.74748i	−0.419606	+	0.396565i
$49$	5.28050			0.754357
$50$	1.31720	+	0.271683i	0.186280	+	0.0384218i
$51$			7.45202i			1.04349i
$52$	−1.47654	+	3.42708i	−0.204759	+	0.475250i
$53$		−	5.74482i		−	0.789111i	−0.918872	−	0.394556i	$-0.870899\pi$
$53$		−	5.74482i		−	0.789111i	0.918872	−	0.394556i	$-0.129101\pi$
$54$	−0.285679	+	1.38506i	−0.0388760	+	0.188483i
$55$	5.13447			0.692332
$56$	8.12297	+	5.67991i	1.08548	+	0.759010i
$57$	−6.83190			−0.904907
$58$	0.547020	−	2.65212i	0.0718272	−	0.348240i
$59$			6.88650i			0.896546i	0.893897	+	0.448273i	$0.147961\pi$
$59$			6.88650i			0.896546i	−0.893897	+	0.448273i	$0.852039\pi$
$60$	4.48075	+	1.93051i	0.578463	+	0.249228i
$61$			5.52040i			0.706815i	0.935470	+	0.353407i	$0.114977\pi$
$61$			5.52040i			0.706815i	−0.935470	+	0.353407i	$0.885023\pi$
$62$	−4.23485	−	0.873470i	−0.537826	−	0.110931i
$63$	3.50435			0.441507
$64$	2.74592	+	7.51398i	0.343240	+	0.939248i
$65$	4.55159			0.564555
$66$	2.91520	+	0.601283i	0.358836	+	0.0740128i
$67$		−	5.44309i		−	0.664979i	−0.943107	−	0.332490i	$-0.892111\pi$
$67$		−	5.44309i		−	0.664979i	0.943107	−	0.332490i	$-0.107889\pi$
$68$	13.6877	+	5.89727i	1.65988	+	0.715149i
$69$			1.00000i			0.120386i
$70$	2.44220	−	11.8405i	0.291899	−	1.41521i
$71$	−10.0258			−1.18984			−0.594922	−	0.803784i	$-0.702817\pi$
$71$	−10.0258			−1.18984			−0.594922	+	0.803784i	$0.702817\pi$
$72$	2.31796	+	1.62082i	0.273175	+	0.191015i
$73$	−3.86198			−0.452011			−0.226005	−	0.974126i	$-0.572567\pi$
$73$	−3.86198			−0.452011			−0.226005	+	0.974126i	$0.572567\pi$
$74$	1.89715	−	9.19794i	0.220539	−	1.06924i
$75$		−	0.951008i		−	0.109813i
$76$	−5.40653	+	12.5487i	−0.620171	+	1.43943i
$77$		−	7.37579i		−	0.840549i
$78$	2.58426	+	0.533023i	0.292610	+	0.0603530i
$79$	7.55375			0.849864			0.424932	−	0.905225i	$-0.360298\pi$
$79$	7.55375			0.849864			0.424932	+	0.905225i	$0.360298\pi$
$80$	7.09182	−	6.70240i	0.792890	−	0.749351i
$81$	1.00000			0.111111
$82$	−12.2626	−	2.52927i	−1.35418	−	0.279311i
$83$			16.3370i			1.79322i	0.442824	+	0.896609i	$0.353977\pi$
$83$			16.3370i			1.79322i	−0.442824	+	0.896609i	$0.646023\pi$
$84$	2.77322	−	6.43671i	0.302583	−	0.702303i
$85$		−	18.1790i		−	1.97179i
$86$	0.380115	−	1.84291i	0.0409889	−	0.198726i
$87$	−1.91480			−0.205289
$88$	3.41141	−	4.87873i	0.363657	−	0.520075i
$89$	0.143819			0.0152448			0.00762241	−	0.999971i	$-0.497574\pi$
$89$	0.143819			0.0152448			0.00762241	+	0.999971i	$0.497574\pi$
$90$	0.696905	−	3.37881i	0.0734603	−	0.356158i
$91$		−	6.53846i		−	0.685417i
$92$	1.83677	+	0.791365i	0.191497	+	0.0825055i
$93$			3.05752i			0.317050i
$94$	0.586943	+	0.121062i	0.0605385	+	0.0124865i
$95$	16.6662			1.70992
$96$	4.81143	−	2.97492i	0.491064	−	0.303627i
$97$	−18.0182			−1.82947			−0.914734	−	0.404057i	$-0.867600\pi$
$97$	−18.0182			−1.82947			−0.914734	+	0.404057i	$0.867600\pi$
$98$	−7.31380	−	1.50853i	−0.738805	−	0.152384i
$99$		−	2.10475i		−	0.211535i
$100$	−1.74679	−	0.752594i	−0.174679	−	0.0752594i
$101$			5.59872i			0.557093i	0.960423	+	0.278547i	$0.0898527\pi$
$101$			5.59872i			0.557093i	−0.960423	+	0.278547i	$0.910147\pi$
$102$	2.12889	−	10.3215i	0.210791	−	1.02198i
$103$	11.5665			1.13968			0.569841	−	0.821755i	$-0.307005\pi$
$103$	11.5665			1.13968			0.569841	+	0.821755i	$0.307005\pi$
$104$	3.02414	−	4.32488i	0.296541	−	0.424090i
$105$	−8.54876			−0.834274
$106$	−1.64117	+	7.95691i	−0.159405	+	0.772843i
$107$		−	17.7588i		−	1.71681i	−0.512972	−	0.858405i	$-0.671455\pi$
$107$		−	17.7588i		−	1.71681i	0.512972	−	0.858405i	$-0.328545\pi$
$108$	0.791365	−	1.83677i	0.0761491	−	0.176744i
$109$			17.4519i			1.67159i	0.549039	+	0.835797i	$0.314994\pi$
$109$			17.4519i			1.67159i	−0.549039	+	0.835797i	$0.685006\pi$
$110$	−7.11154	−	1.46681i	−0.678059	−	0.139855i
$111$	−6.64083			−0.630320
$112$	−9.62815	−	10.1876i	−0.909775	−	0.962635i
$113$	−14.8708			−1.39893			−0.699464	−	0.714668i	$-0.746578\pi$
$113$	−14.8708			−1.39893			−0.699464	+	0.714668i	$0.746578\pi$
$114$	9.46258	+	1.95173i	0.886252	+	0.182796i
$115$		−	2.43947i		−	0.227482i
$116$	−1.51531	+	3.51706i	−0.140693	+	0.326551i
$117$		−	1.86581i		−	0.172494i
$118$	1.96733	−	9.53821i	0.181107	−	0.878063i
$119$	−26.1145			−2.39391
$120$	−5.65460	−	3.95393i	−0.516192	−	0.360943i
$121$	6.57003			0.597276
$122$	1.57706	−	7.64608i	0.142781	−	0.692243i
$123$			8.85352i			0.798295i
$124$	5.61598	+	2.41961i	0.504330	+	0.217288i
$125$		−	9.87739i		−	0.883461i
$126$	−4.85374	−	1.00112i	−0.432405	−	0.0891870i
$127$	−2.68976			−0.238677			−0.119339	−	0.992854i	$-0.538077\pi$
$127$	−2.68976			−0.238677			−0.119339	+	0.992854i	$0.538077\pi$
$128$	−1.65667	−	11.1918i	−0.146430	−	0.989221i
$129$	−1.33057			−0.117150
$130$	−6.30422	−	1.30029i	−0.552916	−	0.114043i
$131$		−	2.06936i		−	0.180801i	−0.995905	−	0.0904005i	$-0.971185\pi$
$131$		−	2.06936i		−	0.180801i	0.995905	−	0.0904005i	$-0.0288147\pi$
$132$	−3.86595	−	1.66562i	−0.336488	−	0.144974i
$133$		−	23.9414i		−	2.07598i
$134$	−1.55498	+	7.53900i	−0.134330	+	0.651271i
$135$	−2.43947			−0.209956
$136$	−17.2735	−	12.0783i	−1.48119	−	1.03571i
$137$	−12.9997			−1.11064			−0.555320	−	0.831637i	$-0.687404\pi$
$137$	−12.9997			−1.11064			−0.555320	+	0.831637i	$0.687404\pi$
$138$	0.285679	−	1.38506i	0.0243186	−	0.117904i
$139$			4.89369i			0.415077i	0.978227	+	0.207539i	$0.0665453\pi$
$139$			4.89369i			0.415077i	−0.978227	+	0.207539i	$0.933455\pi$
$140$	−6.76519	+	15.7022i	−0.571763	+	1.32707i
$141$		−	0.423767i		−	0.0356877i
$142$	13.8863	+	2.86416i	1.16531	+	0.240355i
$143$	−3.92706			−0.328398
$144$	−2.74748	−	2.90712i	−0.228957	−	0.242260i
$145$	4.67110			0.387914
$146$	5.34907	+	1.10329i	0.442692	+	0.0913087i
$147$			5.28050i			0.435528i
$148$	−5.25532	+	12.1977i	−0.431985	+	1.00265i
$149$		−	8.72567i		−	0.714835i	−0.933945	−	0.357417i	$-0.883657\pi$
$149$		−	8.72567i		−	0.714835i	0.933945	−	0.357417i	$-0.116343\pi$
$150$	−0.271683	+	1.31720i	−0.0221828	+	0.107549i
$151$	18.6454			1.51734			0.758670	−	0.651475i	$-0.225850\pi$
$151$	18.6454			1.51734			0.758670	+	0.651475i	$0.225850\pi$
$152$	11.0732	−	15.8361i	0.898159	−	1.28448i
$153$	−7.45202			−0.602460
$154$	−2.10711	+	10.2159i	−0.169796	+	0.823220i
$155$		−	7.45873i		−	0.599099i
$156$	−3.42708	−	1.47654i	−0.274386	−	0.118218i
$157$		−	20.5209i		−	1.63774i	−0.573977	−	0.818872i	$-0.694600\pi$
$157$		−	20.5209i		−	1.63774i	0.573977	−	0.818872i	$-0.305400\pi$
$158$	−10.4624	−	2.15795i	−0.832343	−	0.171677i
$159$	5.74482			0.455594
$160$	−11.7373	+	7.25723i	−0.927917	+	0.573734i
$161$	−3.50435			−0.276182
$162$	−1.38506	−	0.285679i	−0.108820	−	0.0224451i
$163$			13.6013i			1.06533i	0.846325	+	0.532666i	$0.178810\pi$
$163$			13.6013i			1.06533i	−0.846325	+	0.532666i	$0.821190\pi$
$164$	16.2619	+	7.00636i	1.26984	+	0.547105i
$165$			5.13447i			0.399718i
$166$	4.66714	−	22.6277i	0.362240	−	1.75625i
$167$	−2.18558			−0.169125			−0.0845627	−	0.996418i	$-0.526949\pi$
$167$	−2.18558			−0.169125			−0.0845627	+	0.996418i	$0.526949\pi$
$168$	−5.67991	+	8.12297i	−0.438215	+	0.626701i
$169$	9.51875			0.732211
$170$	−5.19335	+	25.1789i	−0.398312	+	1.93114i
$171$		−	6.83190i		−	0.522449i
$172$	−1.05296	+	2.44395i	−0.0802877	+	0.186349i
$173$		−	9.35591i		−	0.711317i	−0.934616	−	0.355658i	$-0.884257\pi$
$173$		−	9.35591i		−	0.711317i	0.934616	−	0.355658i	$-0.115743\pi$
$174$	2.65212	+	0.547020i	0.201056	+	0.0414694i
$175$	3.33267			0.251926
$176$	−6.11875	+	5.78276i	−0.461218	+	0.435892i
$177$	−6.88650			−0.517621
$178$	−0.199198	−	0.0410862i	−0.0149305	−	0.00307954i
$179$			12.7469i			0.952750i	0.879242	+	0.476375i	$0.158049\pi$
$179$			12.7469i			0.952750i	−0.879242	+	0.476375i	$0.841951\pi$
$180$	−1.93051	+	4.48075i	−0.143892	+	0.333976i
$181$			2.06330i			0.153364i	0.997056	+	0.0766821i	$0.0244326\pi$
$181$			2.06330i			0.153364i	−0.997056	+	0.0766821i	$0.975567\pi$
$182$	−1.86790	+	9.05616i	−0.138458	+	0.671287i
$183$	−5.52040			−0.408080
$184$	−2.31796	−	1.62082i	−0.170883	−	0.119488i
$185$	16.2001			1.19106
$186$	0.873470	−	4.23485i	0.0640459	−	0.310514i
$187$			15.6846i			1.14697i
$188$	−0.778365	−	0.335355i	−0.0567681	−	0.0244582i
$189$			3.50435i			0.254904i
$190$	−23.0837	−	4.76119i	−1.67467	−	0.345413i
$191$	−12.7067			−0.919422			−0.459711	−	0.888069i	$-0.652047\pi$
$191$	−12.7067			−0.919422			−0.459711	+	0.888069i	$0.652047\pi$
$192$	−7.51398	+	2.74592i	−0.542275	+	0.198169i
$193$	18.7174			1.34731			0.673656	−	0.739045i	$-0.264723\pi$
$193$	18.7174			1.34731			0.673656	+	0.739045i	$0.264723\pi$
$194$	24.9562	+	5.14742i	1.79175	+	0.369563i
$195$			4.55159i			0.325946i
$196$	9.69909	+	4.17880i	0.692792	+	0.298486i
$197$			2.85370i			0.203317i	0.994819	+	0.101659i	$0.0324150\pi$
$197$			2.85370i			0.203317i	−0.994819	+	0.101659i	$0.967585\pi$
$198$	−0.601283	+	2.91520i	−0.0427313	+	0.207174i
$199$	−3.67764			−0.260701			−0.130351	−	0.991468i	$-0.541610\pi$
$199$	−3.67764			−0.260701			−0.130351	+	0.991468i	$0.541610\pi$
$200$	2.20440	+	1.54141i	0.155875	+	0.108994i
$201$	5.44309			0.383926
$202$	1.59944	−	7.75455i	0.112536	−	0.545608i
$203$		−	6.71015i		−	0.470960i
$204$	−5.89727	+	13.6877i	−0.412891	+	0.958329i
$205$		−	21.5979i		−	1.50846i
$206$	−16.0203	−	3.30431i	−1.11619	−	0.230222i
$207$	−1.00000			−0.0695048
$208$	−5.42413	+	5.12629i	−0.376096	+	0.355444i
$209$	−14.3794			−0.994646
$210$	11.8405	+	2.44220i	0.817075	+	0.168528i
$211$		−	15.1991i		−	1.04635i	−0.852225	−	0.523175i	$-0.824747\pi$
$211$		−	15.1991i		−	1.04635i	0.852225	−	0.523175i	$-0.175253\pi$
$212$	4.54625	−	10.5519i	0.312238	−	0.724710i
$213$		−	10.0258i		−	0.686956i
$214$	−5.07333	+	24.5970i	−0.346806	+	1.68142i
$215$	3.24587			0.221367
$216$	−1.62082	+	2.31796i	−0.110282	+	0.157717i
$217$	−10.7146			−0.727357
$218$	4.98566	−	24.1720i	0.337671	−	1.63713i
$219$		−	3.86198i		−	0.260968i
$220$	9.43086	+	4.06324i	0.635829	+	0.273943i
$221$			13.9041i			0.935288i
$222$	9.19794	+	1.89715i	0.617325	+	0.127328i
$223$	14.5714			0.975771			0.487885	−	0.872908i	$-0.337768\pi$
$223$	14.5714			0.975771			0.487885	+	0.872908i	$0.337768\pi$
$224$	10.4252	+	16.8609i	0.696562	+	1.12657i
$225$	0.951008			0.0634005
$226$	20.5969	+	4.24828i	1.37009	+	0.282591i
$227$		−	28.9375i		−	1.92065i	−0.278883	−	0.960325i	$-0.589964\pi$
$227$		−	28.9375i		−	1.92065i	0.278883	−	0.960325i	$-0.410036\pi$
$228$	−12.5487	−	5.40653i	−0.831056	−	0.358056i
$229$		−	2.55304i		−	0.168710i	−0.996436	−	0.0843550i	$-0.973117\pi$
$229$		−	2.55304i		−	0.168710i	0.996436	−	0.0843550i	$-0.0268830\pi$
$230$	−0.696905	+	3.37881i	−0.0459526	+	0.222792i
$231$	7.37579			0.485291
$232$	3.10354	−	4.43845i	0.203758	−	0.291398i
$233$	15.9481			1.04479			0.522396	−	0.852703i	$-0.325038\pi$
$233$	15.9481			1.04479			0.522396	+	0.852703i	$0.325038\pi$
$234$	−0.533023	+	2.58426i	−0.0348448	+	0.168938i
$235$			1.03377i			0.0674355i
$236$	−5.44974	+	12.6490i	−0.354748	+	0.823377i
$237$			7.55375i			0.490669i
$238$	36.1701	+	7.46037i	2.34456	+	0.483584i
$239$	17.4340			1.12771			0.563857	−	0.825873i	$-0.309317\pi$
$239$	17.4340			1.12771			0.563857	+	0.825873i	$0.309317\pi$
$240$	6.70240	+	7.09182i	0.432638	+	0.457775i
$241$	−1.01754			−0.0655458			−0.0327729	−	0.999463i	$-0.510434\pi$
$241$	−1.01754			−0.0655458			−0.0327729	+	0.999463i	$0.510434\pi$
$242$	−9.09988	−	1.87692i	−0.584962	−	0.120653i
$243$			1.00000i			0.0641500i
$244$	−4.36865	+	10.1397i	−0.279674	+	0.649130i
$245$		−	12.8816i		−	0.822976i
$246$	2.52927	−	12.2626i	0.161260	−	0.781838i
$247$	−12.7470			−0.811075
$248$	−7.08722	−	4.95568i	−0.450039	−	0.314686i
$249$	−16.3370			−1.03531
$250$	−2.82176	+	13.6808i	−0.178464	+	0.865248i
$251$			15.5488i			0.981433i	0.871319	+	0.490716i	$0.163265\pi$
$251$			15.5488i			0.981433i	−0.871319	+	0.490716i	$0.836735\pi$
$252$	6.43671	+	2.77322i	0.405475	+	0.174697i
$253$			2.10475i			0.132324i
$254$	3.72547	+	0.768407i	0.233757	+	0.0482142i
$255$	18.1790			1.13841
$256$	−0.902671	+	15.9745i	−0.0564170	+	0.998407i
$257$	21.3366			1.33094			0.665469	−	0.746425i	$-0.268231\pi$
$257$	21.3366			1.33094			0.665469	+	0.746425i	$0.268231\pi$
$258$	1.84291	+	0.380115i	0.114735	+	0.0236649i
$259$		−	23.2718i		−	1.44604i
$260$	8.36024	+	3.60197i	0.518480	+	0.223385i
$261$		−	1.91480i		−	0.118523i
$262$	−0.591174	+	2.86619i	−0.0365228	+	0.177074i
$263$	15.1462			0.933956			0.466978	−	0.884269i	$-0.345343\pi$
$263$	15.1462			0.933956			0.466978	+	0.884269i	$0.345343\pi$
$264$	4.87873	+	3.41141i	0.300265	+	0.209958i
$265$	−14.0143			−0.860892
$266$	−6.83956	+	33.1602i	−0.419360	+	2.03319i
$267$			0.143819i			0.00880160i
$268$	4.30747	−	9.99773i	0.263121	−	0.610709i
$269$		−	10.8517i		−	0.661639i	−0.943694	−	0.330819i	$-0.892675\pi$
$269$		−	10.8517i		−	0.661639i	0.943694	−	0.330819i	$-0.107325\pi$
$270$	3.37881	+	0.696905i	0.205628	+	0.0424123i
$271$	−25.7031			−1.56135			−0.780675	−	0.624937i	$-0.785124\pi$
$271$	−25.7031			−1.56135			−0.780675	+	0.624937i	$0.785124\pi$
$272$	20.4743	+	21.6639i	1.24144	+	1.31357i
$273$	6.53846			0.395726
$274$	18.0053	+	3.71374i	1.08774	+	0.224356i
$275$		−	2.00163i		−	0.120703i
$276$	−0.791365	+	1.83677i	−0.0476346	+	0.110561i
$277$			30.7532i			1.84778i	0.382656	+	0.923891i	$0.375009\pi$
$277$			30.7532i			1.84778i	−0.382656	+	0.923891i	$0.624991\pi$
$278$	1.39802	−	6.77805i	0.0838480	−	0.406520i
$279$	−3.05752			−0.183049
$280$	13.8560	−	19.8157i	0.828052	−	1.18422i
$281$	−12.1680			−0.725883			−0.362942	−	0.931812i	$-0.618228\pi$
$281$	−12.1680			−0.725883			−0.362942	+	0.931812i	$0.618228\pi$
$282$	−0.121062	+	0.586943i	−0.00720911	+	0.0349519i
$283$		−	6.04776i		−	0.359502i	−0.983712	−	0.179751i	$-0.942471\pi$
$283$		−	6.04776i		−	0.359502i	0.983712	−	0.179751i	$-0.0575292\pi$
$284$	−18.4151	−	7.93407i	−1.09274	−	0.470800i
$285$			16.6662i			0.987221i
$286$	5.43921	+	1.12188i	0.321627	+	0.0663382i
$287$	−31.0259			−1.83140
$288$	2.97492	+	4.81143i	0.175299	+	0.283516i
$289$	38.5326			2.26662
$290$	−6.46975	−	1.33444i	−0.379917	−	0.0783608i
$291$		−	18.0182i		−	1.05624i
$292$	−7.09359	−	3.05624i	−0.415121	−	0.178853i
$293$			17.7870i			1.03913i	0.854432	+	0.519564i	$0.173906\pi$
$293$			17.7870i			1.03913i	−0.854432	+	0.519564i	$0.826094\pi$
$294$	1.50853	−	7.31380i	0.0879792	−	0.426550i
$295$	16.7994			0.978099
$296$	10.7636	−	15.3932i	0.625619	−	0.894712i
$297$	2.10475			0.122130
$298$	−2.49274	+	12.0856i	−0.144401	+	0.700098i
$299$			1.86581i			0.107903i
$300$	0.752594	−	1.74679i	0.0434510	−	0.100851i
$301$		−	4.66277i		−	0.268758i
$302$	−25.8250	−	5.32660i	−1.48606	−	0.306511i
$303$	−5.59872			−0.321638
$304$	−19.8611	+	18.7705i	−1.13911	+	1.07656i
$305$	13.4668			0.771109
$306$	10.3215	+	2.12889i	0.590040	+	0.121700i
$307$		−	3.02852i		−	0.172847i	−0.996258	−	0.0864235i	$-0.972456\pi$
$307$		−	3.02852i		−	0.172847i	0.996258	−	0.0864235i	$-0.0275438\pi$
$308$	5.83694	−	13.5477i	0.332590	−	0.771949i
$309$			11.5665i			0.657996i
$310$	−2.13080	+	10.3308i	−0.121021	+	0.586748i
$311$	−17.6413			−1.00034			−0.500172	−	0.865926i	$-0.666730\pi$
$311$	−17.6413			−1.00034			−0.500172	+	0.865926i	$0.666730\pi$
$312$	4.32488	+	3.02414i	0.244848	+	0.171208i
$313$	2.79695			0.158093			0.0790465	−	0.996871i	$-0.474812\pi$
$313$	2.79695			0.158093			0.0790465	+	0.996871i	$0.474812\pi$
$314$	−5.86238	+	28.4226i	−0.330833	+	1.60398i
$315$		−	8.54876i		−	0.481668i
$316$	13.8745	+	5.97778i	0.780504	+	0.336276i
$317$			29.1832i			1.63909i	0.573013	+	0.819547i	$0.305775\pi$
$317$			29.1832i			1.63909i	−0.573013	+	0.819547i	$0.694225\pi$
$318$	−7.95691	−	1.64117i	−0.446201	−	0.0920325i
$319$	−4.03018			−0.225647
$320$	18.3301	−	6.69858i	1.02469	−	0.374462i
$321$	17.7588			0.991201
$322$	4.85374	+	1.00112i	0.270488	+	0.0557903i
$323$			50.9115i			2.83279i
$324$	1.83677	+	0.791365i	0.102043	+	0.0439647i
$325$		−	1.77440i		−	0.0984260i
$326$	3.88560	−	18.8385i	0.215203	−	1.04337i
$327$	−17.4519			−0.965095
$328$	−20.5221	−	14.3499i	−1.13315	−	0.792342i
$329$	1.48503			0.0818724
$330$	1.46681	−	7.11154i	0.0807453	−	0.391477i
$331$		−	15.1651i		−	0.833547i	−0.909010	−	0.416774i	$-0.863161\pi$
$331$		−	15.1651i		−	0.833547i	0.909010	−	0.416774i	$-0.136839\pi$
$332$	−12.9285	+	30.0074i	−0.709545	+	1.64687i
$333$		−	6.64083i		−	0.363915i
$334$	3.02716	+	0.624375i	0.165639	+	0.0341643i
$335$	−13.2783			−0.725468
$336$	10.1876	−	9.62815i	0.555778	−	0.525259i
$337$	−35.3117			−1.92355			−0.961775	−	0.273839i	$-0.911706\pi$
$337$	−35.3117			−1.92355			−0.961775	+	0.273839i	$0.911706\pi$
$338$	−13.1840	−	2.71931i	−0.717116	−	0.147911i
$339$		−	14.8708i		−	0.807671i
$340$	14.3862	−	33.3907i	0.780201	−	1.81086i
$341$			6.43531i			0.348492i
$342$	−1.95173	+	9.46258i	−0.105538	+	0.511678i
$343$	6.02574			0.325359
$344$	2.15660	−	3.08420i	0.116276	−	0.166289i
$345$	2.43947			0.131337
$346$	−2.67279	+	12.9585i	−0.143690	+	0.696653i
$347$		−	9.36723i		−	0.502859i	−0.967876	−	0.251430i	$-0.919099\pi$
$347$		−	9.36723i		−	0.502859i	0.967876	−	0.251430i	$-0.0809007\pi$
$348$	−3.51706	−	1.51531i	−0.188534	−	0.0812291i
$349$			8.71267i			0.466379i	0.972431	+	0.233189i	$0.0749162\pi$
$349$			8.71267i			0.466379i	−0.972431	+	0.233189i	$0.925084\pi$
$350$	−4.61594	−	0.952074i	−0.246732	−	0.0508905i
$351$	1.86581			0.0995896
$352$	10.1268	−	6.26146i	0.539763	−	0.333737i
$353$	8.78408			0.467529			0.233765	−	0.972293i	$-0.424895\pi$
$353$	8.78408			0.467529			0.233765	+	0.972293i	$0.424895\pi$
$354$	9.53821	+	1.96733i	0.506950	+	0.104562i
$355$			24.4576i			1.29808i
$356$	0.264164	+	0.113814i	0.0140006	+	0.00603210i
$357$		−	26.1145i		−	1.38213i
$358$	3.64153	−	17.6552i	0.192461	−	0.933108i
$359$	−33.7678			−1.78220			−0.891098	−	0.453811i	$-0.850064\pi$
$359$	−33.7678			−1.78220			−0.891098	+	0.453811i	$0.850064\pi$
$360$	3.95393	−	5.65460i	0.208390	−	0.298024i
$361$	−27.6749			−1.45657
$362$	0.589443	−	2.85780i	0.0309804	−	0.150202i
$363$			6.57003i			0.344837i
$364$	5.17431	−	12.0097i	0.271208	−	0.629479i
$365$			9.42118i			0.493127i
$366$	7.64608	+	1.57706i	0.399667	+	0.0824344i
$367$	−6.02489			−0.314496			−0.157248	−	0.987559i	$-0.550262\pi$
$367$	−6.02489			−0.314496			−0.157248	+	0.987559i	$0.550262\pi$
$368$	2.74748	+	2.90712i	0.143222	+	0.151544i
$369$	−8.85352			−0.460896
$370$	−22.4381	−	4.62803i	−1.16650	−	0.240600i
$371$			20.1319i			1.04519i
$372$	−2.41961	+	5.61598i	−0.125451	+	0.291175i
$373$			23.3674i			1.20992i	0.796257	+	0.604959i	$0.206811\pi$
$373$			23.3674i			1.20992i	−0.796257	+	0.604959i	$0.793189\pi$
$374$	4.48077	−	21.7241i	0.231695	−	1.12333i
$375$	9.87739			0.510066
$376$	0.982278	+	0.686849i	0.0506571	+	0.0354215i
$377$	−3.57266			−0.184001
$378$	1.00112	−	4.85374i	0.0514921	−	0.249649i
$379$		−	23.7951i		−	1.22227i	−0.791526	−	0.611135i	$-0.790713\pi$
$379$		−	23.7951i		−	1.22227i	0.791526	−	0.611135i	$-0.209287\pi$
$380$	30.6121	+	13.1891i	1.57037	+	0.676584i
$381$		−	2.68976i		−	0.137800i
$382$	17.5995	+	3.63003i	0.900468	+	0.185729i
$383$	−12.4565			−0.636498			−0.318249	−	0.948007i	$-0.603095\pi$
$383$	−12.4565			−0.636498			−0.318249	+	0.948007i	$0.603095\pi$
$384$	11.1918	−	1.65667i	0.571127	−	0.0845414i
$385$	−17.9930			−0.917008
$386$	−25.9248	−	5.34718i	−1.31954	−	0.272165i
$387$		−	1.33057i		−	0.0676365i
$388$	−33.0953	−	14.2589i	−1.68016	−	0.723888i
$389$			27.2072i			1.37946i	0.724066	+	0.689731i	$0.242271\pi$
$389$			27.2072i			1.37946i	−0.724066	+	0.689731i	$0.757729\pi$
$390$	1.30029	−	6.30422i	0.0658430	−	0.319226i
$391$	7.45202			0.376865
$392$	−12.2400	−	8.55871i	−0.618214	−	0.432280i
$393$	2.06936			0.104385
$394$	0.815242	−	3.95254i	0.0410713	−	0.199126i
$395$		−	18.4271i		−	0.927170i
$396$	1.66562	−	3.86595i	0.0837008	−	0.194271i
$397$		−	5.64764i		−	0.283447i	−0.989906	−	0.141724i	$-0.954736\pi$
$397$		−	5.64764i		−	0.283447i	0.989906	−	0.141724i	$-0.0452644\pi$
$398$	5.09375	+	1.05063i	0.255327	+	0.0526631i
$399$	23.9414			1.19857
$400$	−2.61288	−	2.76469i	−0.130644	−	0.138235i
$401$	14.4501			0.721604			0.360802	−	0.932643i	$-0.382503\pi$
$401$	14.4501			0.721604			0.360802	+	0.932643i	$0.382503\pi$
$402$	−7.53900	−	1.55498i	−0.376011	−	0.0775553i
$403$			5.70476i			0.284174i
$404$	−4.43063	+	10.2836i	−0.220432	+	0.511628i
$405$		−	2.43947i		−	0.121218i
$406$	−1.91695	+	9.29395i	−0.0951367	+	0.461251i
$407$	−13.9773			−0.692828
$408$	12.0783	−	17.2735i	0.597967	−	0.855166i
$409$	12.9968			0.642649			0.321324	−	0.946969i	$-0.395872\pi$
$409$	12.9968			0.642649			0.321324	+	0.946969i	$0.395872\pi$
$410$	−6.17007	+	29.9143i	−0.304718	+	1.47736i
$411$		−	12.9997i		−	0.641228i
$412$	21.2451	+	9.15333i	1.04667	+	0.450952i
$413$		−	24.1327i		−	1.18749i
$414$	1.38506	+	0.285679i	0.0680719	+	0.0140404i
$415$	39.8536			1.95633
$416$	8.97722	−	5.55064i	0.440144	−	0.272143i
$417$	−4.89369			−0.239645
$418$	19.9164	+	4.10791i	0.974141	+	0.200924i
$419$		−	22.7844i		−	1.11309i	−0.830818	−	0.556544i	$-0.812127\pi$
$419$		−	22.7844i		−	1.11309i	0.830818	−	0.556544i	$-0.187873\pi$
$420$	−15.7022	−	6.76519i	−0.766187	−	0.330107i
$421$		−	37.5304i		−	1.82912i	−0.404453	−	0.914559i	$-0.632538\pi$
$421$		−	37.5304i		−	1.82912i	0.404453	−	0.914559i	$-0.367462\pi$
$422$	−4.34207	+	21.0517i	−0.211369	+	1.02478i
$423$	0.423767			0.0206043
$424$	−9.31129	+	13.3163i	−0.452196	+	0.646696i
$425$	−7.08693			−0.343766
$426$	−2.86416	+	13.8863i	−0.138769	+	0.672794i
$427$		−	19.3454i		−	0.936191i
$428$	14.0537	−	32.6190i	0.679312	−	1.57670i
$429$		−	3.92706i		−	0.189600i
$430$	−4.49573	−	0.927279i	−0.216803	−	0.0447173i
$431$	18.8438			0.907675			0.453838	−	0.891084i	$-0.350055\pi$
$431$	18.8438			0.907675			0.453838	+	0.891084i	$0.350055\pi$
$432$	2.90712	−	2.74748i	0.139869	−	0.132188i
$433$	−13.4600			−0.646848			−0.323424	−	0.946254i	$-0.604834\pi$
$433$	−13.4600			−0.646848			−0.323424	+	0.946254i	$0.604834\pi$
$434$	14.8404	+	3.06095i	0.712362	+	0.146930i
$435$			4.67110i			0.223962i
$436$	−13.8109	+	32.0553i	−0.661420	+	1.53517i
$437$			6.83190i			0.326814i
$438$	−1.10329	+	5.34907i	−0.0527171	+	0.255588i
$439$	35.1120			1.67580			0.837902	−	0.545821i	$-0.183782\pi$
$439$	35.1120			1.67580			0.837902	+	0.545821i	$0.183782\pi$
$440$	−11.9015	−	8.32202i	−0.567382	−	0.396737i
$441$	−5.28050			−0.251452
$442$	3.97210	−	19.2579i	0.188934	−	0.916007i
$443$		−	17.5372i		−	0.833218i	−0.909086	−	0.416609i	$-0.863218\pi$
$443$		−	17.5372i		−	0.833218i	0.909086	−	0.416609i	$-0.136782\pi$
$444$	−12.1977	−	5.25532i	−0.578878	−	0.249407i
$445$		−	0.350843i		−	0.0166315i
$446$	−20.1822	−	4.16274i	−0.955655	−	0.197111i
$447$	8.72567			0.412710
$448$	−9.62267	−	26.3317i	−0.454628	−	1.24405i
$449$	−7.52810			−0.355273			−0.177637	−	0.984096i	$-0.556845\pi$
$449$	−7.52810			−0.355273			−0.177637	+	0.984096i	$0.556845\pi$
$450$	−1.31720	−	0.271683i	−0.0620935	−	0.0128073i
$451$			18.6344i			0.877461i
$452$	−27.3143	−	11.7682i	−1.28476	−	0.553531i
$453$			18.6454i			0.876037i
$454$	−8.26684	+	40.0801i	−0.387982	+	1.88105i
$455$	−15.9504			−0.747765
$456$	15.8361	+	11.0732i	0.741593	+	0.518552i
$457$	17.7971			0.832514			0.416257	−	0.909247i	$-0.363342\pi$
$457$	17.7971			0.832514			0.416257	+	0.909247i	$0.363342\pi$
$458$	−0.729352	+	3.53612i	−0.0340804	+	0.165232i
$459$		−	7.45202i		−	0.347830i
$460$	1.93051	−	4.48075i	0.0900105	−	0.208916i
$461$		−	12.1020i		−	0.563648i	−0.959466	−	0.281824i	$-0.909061\pi$
$461$		−	12.1020i		−	0.563648i	0.959466	−	0.281824i	$-0.0909394\pi$
$462$	−10.2159	−	2.10711i	−0.475286	−	0.0980316i
$463$	−30.9375			−1.43779			−0.718893	−	0.695121i	$-0.755351\pi$
$463$	−30.9375			−1.43779			−0.718893	+	0.695121i	$0.755351\pi$
$464$	−5.56656	+	5.26089i	−0.258421	+	0.244231i
$465$	7.45873			0.345890
$466$	−22.0890	−	4.55603i	−1.02325	−	0.211054i
$467$			28.6153i			1.32416i	0.749434	+	0.662079i	$0.230326\pi$
$467$			28.6153i			1.32416i	−0.749434	+	0.662079i	$0.769674\pi$
$468$	1.47654	−	3.42708i	0.0682530	−	0.158417i
$469$			19.0745i			0.880780i
$470$	0.295326	−	1.43183i	0.0136224	−	0.0660453i
$471$	20.5209			0.945551
$472$	11.1617	−	15.9627i	0.513761	−	0.734741i
$473$	−2.80051			−0.128767
$474$	2.15795	−	10.4624i	0.0991179	−	0.480554i
$475$		−	6.49719i		−	0.298112i
$476$	−47.9665	−	20.6661i	−2.19854	−	0.947230i
$477$			5.74482i			0.263037i
$478$	−24.1472	−	4.98054i	−1.10447	−	0.227805i
$479$	−22.0195			−1.00610			−0.503048	−	0.864258i	$-0.667788\pi$
$479$	−22.0195			−1.00610			−0.503048	+	0.864258i	$0.667788\pi$
$480$	−7.25723	−	11.7373i	−0.331246	−	0.535733i
$481$	−12.3905			−0.564960
$482$	1.40936	+	0.290691i	0.0641945	+	0.0132406i
$483$		−	3.50435i		−	0.159454i
$484$	12.0677	+	5.19929i	0.548530	+	0.236331i
$485$			43.9548i			1.99588i
$486$	0.285679	−	1.38506i	0.0129587	−	0.0628275i
$487$	−0.693324			−0.0314175			−0.0157087	−	0.999877i	$-0.505000\pi$
$487$	−0.693324			−0.0314175			−0.0157087	+	0.999877i	$0.505000\pi$
$488$	8.94755	−	12.7961i	0.405036	−	0.579252i
$489$	−13.6013			−0.615070
$490$	−3.68001	+	17.8418i	−0.166246	+	0.806010i
$491$		−	39.1608i		−	1.76730i	−0.468145	−	0.883652i	$-0.655077\pi$
$491$		−	39.1608i		−	1.76730i	0.468145	−	0.883652i	$-0.344923\pi$
$492$	−7.00636	+	16.2619i	−0.315871	+	0.733144i
$493$			14.2692i			0.642650i
$494$	17.6554	+	3.64156i	0.794354	+	0.163842i
$495$	−5.13447			−0.230777
$496$	8.40049	+	8.88857i	0.377193	+	0.399109i
$497$	35.1340			1.57597
$498$	22.6277	+	4.66714i	1.01397	+	0.209139i
$499$			18.6419i			0.834527i	0.908786	+	0.417264i	$0.137011\pi$
$499$			18.6419i			0.834527i	−0.908786	+	0.417264i	$0.862989\pi$
$500$	7.81662	−	18.1425i	0.349570	−	0.811359i
$501$		−	2.18558i		−	0.0976446i
$502$	4.44197	−	21.5360i	0.198255	−	0.961200i
$503$	5.99584			0.267341			0.133671	−	0.991026i	$-0.457324\pi$
$503$	5.99584			0.267341			0.133671	+	0.991026i	$0.457324\pi$
$504$	−8.12297	−	5.67991i	−0.361826	−	0.253003i
$505$	13.6579			0.607769
$506$	0.601283	−	2.91520i	0.0267303	−	0.129596i
$507$			9.51875i			0.422742i
$508$	−4.94048	−	2.12858i	−0.219198	−	0.0944404i
$509$		−	33.9929i		−	1.50671i	−0.657614	−	0.753355i	$-0.728434\pi$
$509$		−	33.9929i		−	1.50671i	0.657614	−	0.753355i	$-0.271566\pi$
$510$	−25.1789	−	5.19335i	−1.11494	−	0.229966i
$511$	13.5337			0.598698
$512$	5.81384	−	21.8678i	0.256938	−	0.966428i
$513$	6.83190			0.301636
$514$	−29.5524	−	6.09542i	−1.30350	−	0.268857i
$515$		−	28.2161i		−	1.24335i
$516$	−2.44395	−	1.05296i	−0.107589	−	0.0463541i
$517$		−	0.891924i		−	0.0392268i
$518$	−6.64828	+	32.2328i	−0.292109	+	1.41623i
$519$	9.35591			0.410679
$520$	−10.5504	−	7.37728i	−0.462666	−	0.323515i
$521$	−19.3660			−0.848439			−0.424219	−	0.905559i	$-0.639451\pi$
$521$	−19.3660			−0.848439			−0.424219	+	0.905559i	$0.639451\pi$
$522$	−0.547020	+	2.65212i	−0.0239424	+	0.116080i
$523$		−	22.0024i		−	0.962100i	−0.876693	−	0.481050i	$-0.840256\pi$
$523$		−	22.0024i		−	0.962100i	0.876693	−	0.481050i	$-0.159744\pi$
$524$	1.63762	−	3.80095i	0.0715398	−	0.166045i
$525$			3.33267i			0.145450i
$526$	−20.9784	−	4.32696i	−0.914702	−	0.188664i
$527$	22.7847			0.992517
$528$	−5.78276	−	6.11875i	−0.251662	−	0.266285i
$529$	1.00000			0.0434783
$530$	19.4106	+	4.00359i	0.843144	+	0.173905i
$531$		−	6.88650i		−	0.298849i
$532$	18.9464	−	43.9750i	0.821430	−	1.90656i
$533$			16.5190i			0.715517i
$534$	0.0410862	−	0.199198i	0.00177797	−	0.00862014i
$535$	−43.3221			−1.87298
$536$	−8.82225	+	12.6169i	−0.381063	+	0.544967i
$537$	−12.7469			−0.550070
$538$	−3.10010	+	15.0302i	−0.133655	+	0.647998i
$539$			11.1141i			0.478719i
$540$	−4.48075	−	1.93051i	−0.192821	−	0.0830759i
$541$			17.9533i			0.771872i	0.922525	+	0.385936i	$0.126122\pi$
$541$			17.9533i			0.771872i	−0.922525	+	0.385936i	$0.873878\pi$
$542$	35.6002	+	7.34283i	1.52916	+	0.315402i
$543$	−2.06330			−0.0885448
$544$	−22.1692	−	35.8549i	−0.950496	−	1.53726i
$545$	42.5735			1.82365
$546$	−9.05616	−	1.86790i	−0.387568	−	0.0799389i
$547$		−	9.02010i		−	0.385672i	−0.981231	−	0.192836i	$-0.938232\pi$
$547$		−	9.02010i		−	0.385672i	0.981231	−	0.192836i	$-0.0617685\pi$
$548$	−23.8775	−	10.2875i	−1.02000	−	0.439461i
$549$		−	5.52040i		−	0.235605i
$550$	−0.571825	+	2.77238i	−0.0243827	+	0.118215i
$551$	−13.0817			−0.557301
$552$	1.62082	−	2.31796i	0.0689865	−	0.0986591i
$553$	−26.4710			−1.12566
$554$	8.78555	−	42.5950i	0.373262	−	1.80969i
$555$			16.2001i			0.687656i
$556$	−3.87269	+	8.98860i	−0.164239	+	0.381202i
$557$		−	6.12352i		−	0.259462i	−0.991549	−	0.129731i	$-0.958589\pi$
$557$		−	6.12352i		−	0.259462i	0.991549	−	0.129731i	$-0.0414114\pi$
$558$	4.23485	+	0.873470i	0.179275	+	0.0369769i
$559$	−2.48258			−0.105002
$560$	−24.8523	+	23.4876i	−1.05020	+	0.992532i
$561$	−15.6846			−0.662206
$562$	16.8534	+	3.47615i	0.710919	+	0.146633i
$563$			12.7882i			0.538958i	0.963006	+	0.269479i	$0.0868514\pi$
$563$			12.7882i			0.538958i	−0.963006	+	0.269479i	$0.913149\pi$
$564$	0.335355	−	0.778365i	0.0141210	−	0.0327751i
$565$			36.2769i			1.52618i
$566$	−1.72772	+	8.37650i	−0.0726215	+	0.352091i
$567$	−3.50435			−0.147169
$568$	23.2394	+	16.2500i	0.975105	+	0.681833i
$569$	21.6667			0.908316			0.454158	−	0.890921i	$-0.349940\pi$
$569$	21.6667			0.908316			0.454158	+	0.890921i	$0.349940\pi$
$570$	4.76119	−	23.0837i	0.199424	−	0.966869i
$571$			1.05770i			0.0442633i	0.999755	+	0.0221316i	$0.00704529\pi$
$571$			1.05770i			0.0442633i	−0.999755	+	0.0221316i	$0.992955\pi$
$572$	−7.21313	−	3.10774i	−0.301596	−	0.129941i
$573$		−	12.7067i		−	0.530829i
$574$	42.9726	+	8.86345i	1.79364	+	0.369953i
$575$	−0.951008			−0.0396598
$576$	−2.74592	−	7.51398i	−0.114413	−	0.313083i
$577$	19.8796			0.827600			0.413800	−	0.910368i	$-0.364201\pi$
$577$	19.8796			0.827600			0.413800	+	0.910368i	$0.364201\pi$
$578$	−53.3699	−	11.0080i	−2.21989	−	0.457871i
$579$			18.7174i			0.777870i
$580$	8.57977	+	3.69655i	0.356255	+	0.153491i
$581$		−	57.2506i		−	2.37515i
$582$	−5.14742	+	24.9562i	−0.213367	+	1.03447i
$583$	12.0914			0.500775
$584$	8.95193	+	6.25956i	0.370434	+	0.259022i
$585$	−4.55159			−0.188185
$586$	5.08138	−	24.6360i	0.209910	−	1.01771i
$587$		−	27.8120i		−	1.14793i	−0.818881	−	0.573963i	$-0.805405\pi$
$587$		−	27.8120i		−	1.14793i	0.818881	−	0.573963i	$-0.194595\pi$
$588$	−4.17880	+	9.69909i	−0.172331	+	0.399984i
$589$			20.8887i			0.860703i
$590$	−23.2682	−	4.79924i	−0.957935	−	0.197582i
$591$	−2.85370			−0.117385
$592$	−19.3057	+	18.2456i	−0.793459	+	0.749888i
$593$	9.94717			0.408481			0.204241	−	0.978921i	$-0.434528\pi$
$593$	9.94717			0.408481			0.204241	+	0.978921i	$0.434528\pi$
$594$	−2.91520	−	0.601283i	−0.119612	−	0.0246709i
$595$			63.7055i			2.61167i
$596$	6.90519	−	16.0271i	0.282847	−	0.656495i
$597$		−	3.67764i		−	0.150516i
$598$	0.533023	−	2.58426i	0.0217970	−	0.105678i
$599$	29.8074			1.21790			0.608948	−	0.793210i	$-0.291592\pi$
$599$	29.8074			1.21790			0.608948	+	0.793210i	$0.291592\pi$
$600$	−1.54141	+	2.20440i	−0.0629277	+	0.0899943i
$601$	32.6825			1.33315			0.666574	−	0.745439i	$-0.267760\pi$
$601$	32.6825			1.33315			0.666574	+	0.745439i	$0.267760\pi$
$602$	−1.33206	+	6.45822i	−0.0542906	+	0.263217i
$603$			5.44309i			0.221660i
$604$	34.2474	+	14.7553i	1.39351	+	0.600385i
$605$		−	16.0274i		−	0.651606i
$606$	7.75455	+	1.59944i	0.315007	+	0.0649727i
$607$	−31.9226			−1.29570			−0.647848	−	0.761769i	$-0.724331\pi$
$607$	−31.9226			−1.29570			−0.647848	+	0.761769i	$0.724331\pi$
$608$	32.8712	−	20.3244i	1.33310	−	0.824262i
$609$	6.71015			0.271909
$610$	−18.6524	−	3.84720i	−0.755212	−	0.155768i
$611$		−	0.790670i		−	0.0319871i
$612$	−13.6877	−	5.89727i	−0.553292	−	0.238383i
$613$			1.80263i			0.0728075i	0.999337	+	0.0364038i	$0.0115902\pi$
$613$			1.80263i			0.0728075i	−0.999337	+	0.0364038i	$0.988410\pi$
$614$	−0.865186	+	4.19468i	−0.0349161	+	0.169284i
$615$	21.5979			0.870911
$616$	−11.9548	+	17.0968i	−0.481672	+	0.688850i
$617$	18.3876			0.740257			0.370129	−	0.928980i	$-0.379314\pi$
$617$	18.3876			0.740257			0.370129	+	0.928980i	$0.379314\pi$
$618$	3.30431	−	16.0203i	0.132919	−	0.644431i
$619$		−	16.4632i		−	0.661714i	−0.943681	−	0.330857i	$-0.892662\pi$
$619$		−	16.4632i		−	0.661714i	0.943681	−	0.330857i	$-0.107338\pi$
$620$	5.90257	−	13.7000i	0.237053	−	0.550205i
$621$		−	1.00000i		−	0.0401286i
$622$	24.4342	+	5.03974i	0.979721	+	0.202075i
$623$	−0.503994			−0.0201921
$624$	−5.12629	−	5.42413i	−0.205216	−	0.217139i
$625$	−28.8506			−1.15402
$626$	−3.87394	−	0.799031i	−0.154834	−	0.0319357i
$627$		−	14.3794i		−	0.574259i
$628$	16.2395	−	37.6922i	0.648026	−	1.50408i
$629$			49.4876i			1.97320i
$630$	−2.44220	+	11.8405i	−0.0972997	+	0.471738i
$631$	−43.6375			−1.73718			−0.868591	−	0.495530i	$-0.834974\pi$
$631$	−43.6375			−1.73718			−0.868591	+	0.495530i	$0.834974\pi$
$632$	−17.5093	−	12.2432i	−0.696484	−	0.487010i
$633$	15.1991			0.604111
$634$	8.33704	−	40.4205i	0.331106	−	1.60530i
$635$			6.56158i			0.260388i
$636$	10.5519	+	4.54625i	0.418411	+	0.180270i
$637$			9.85241i			0.390367i
$638$	5.58204	+	1.15134i	0.220995	+	0.0455819i
$639$	10.0258			0.396614
$640$	−27.3019	+	4.04139i	−1.07920	+	0.159750i
$641$	29.7301			1.17427			0.587134	−	0.809490i	$-0.300256\pi$
$641$	29.7301			1.17427			0.587134	+	0.809490i	$0.300256\pi$
$642$	−24.5970	−	5.07333i	−0.970767	−	0.200228i
$643$		−	18.9426i		−	0.747022i	−0.927626	−	0.373511i	$-0.878154\pi$
$643$		−	18.9426i		−	0.747022i	0.927626	−	0.373511i	$-0.121846\pi$
$644$	−6.43671	−	2.77322i	−0.253642	−	0.109280i
$645$			3.24587i			0.127806i
$646$	14.5443	−	70.5154i	0.572240	−	2.77439i
$647$	30.4025			1.19525			0.597623	−	0.801777i	$-0.296112\pi$
$647$	30.4025			1.19525			0.597623	+	0.801777i	$0.296112\pi$
$648$	−2.31796	−	1.62082i	−0.0910582	−	0.0636716i
$649$	−14.4944			−0.568953
$650$	−0.506909	+	2.45765i	−0.0198826	+	0.0963969i
$651$		−	10.7146i		−	0.419940i
$652$	−10.7636	+	24.9824i	−0.421533	+	0.978388i
$653$			13.2129i			0.517059i	0.966003	+	0.258530i	$0.0832379\pi$
$653$			13.2129i			0.517059i	−0.966003	+	0.258530i	$0.916762\pi$
$654$	24.1720	+	4.98566i	0.945199	+	0.194955i
$655$	−5.04814			−0.197247
$656$	24.3249	+	25.7382i	0.949728	+	1.00491i
$657$	3.86198			0.150670
$658$	−2.05685	−	0.424242i	−0.0801846	−	0.0165387i
$659$			37.1381i			1.44669i	0.690485	+	0.723347i	$0.257397\pi$
$659$			37.1381i			1.44669i	−0.690485	+	0.723347i	$0.742603\pi$
$660$	−4.06324	+	9.43086i	−0.158161	+	0.367096i
$661$			22.7186i			0.883652i	0.897101	+	0.441826i	$0.145669\pi$
$661$			22.7186i			0.883652i	−0.897101	+	0.441826i	$0.854331\pi$
$662$	−4.33234	+	21.0045i	−0.168381	+	0.816363i
$663$	−13.9041			−0.539989
$664$	26.4792	−	37.8686i	1.02759	−	1.46959i
$665$	−58.4043			−2.26482
$666$	−1.89715	+	9.19794i	−0.0735130	+	0.356413i
$667$			1.91480i			0.0741415i
$668$	−4.01442	−	1.72959i	−0.155323	−	0.0669199i
$669$			14.5714i			0.563362i
$670$	18.3912	+	3.79332i	0.710512	+	0.146549i
$671$	−11.6191			−0.448549
$672$	−16.8609	+	10.4252i	−0.650425	+	0.402160i
$673$	−25.5120			−0.983414			−0.491707	−	0.870761i	$-0.663627\pi$
$673$	−25.5120			−0.983414			−0.491707	+	0.870761i	$0.663627\pi$
$674$	48.9088	+	10.0878i	1.88390	+	0.388568i
$675$			0.951008i			0.0366043i
$676$	17.4838	+	7.53280i	0.672454	+	0.289723i
$677$			27.8185i			1.06915i	0.845121	+	0.534575i	$0.179528\pi$
$677$			27.8185i			1.06915i	−0.845121	+	0.534575i	$0.820472\pi$
$678$	−4.24828	+	20.5969i	−0.163154	+	0.791020i
$679$	63.1420			2.42317
$680$	−29.4647	+	42.1382i	−1.12992	+	1.61593i
$681$	28.9375			1.10889
$682$	1.83843	−	8.91329i	0.0703973	−	0.341307i
$683$		−	10.3298i		−	0.395259i	−0.980277	−	0.197630i	$-0.936676\pi$
$683$		−	10.3298i		−	0.395259i	0.980277	−	0.197630i	$-0.0633243\pi$
$684$	5.40653	−	12.5487i	0.206724	−	0.479810i
$685$			31.7124i			1.21167i
$686$	−8.34600	−	1.72143i	−0.318652	−	0.0657245i
$687$	2.55304			0.0974047
$688$	−3.86811	+	3.65571i	−0.147470	+	0.139373i
$689$	10.7187			0.408352
$690$	−3.37881	−	0.696905i	−0.128629	−	0.0265307i
$691$			35.1256i			1.33624i	0.744053	+	0.668121i	$0.232901\pi$
$691$			35.1256i			1.33624i	−0.744053	+	0.668121i	$0.767099\pi$
$692$	7.40394	−	17.1847i	0.281456	−	0.653264i
$693$			7.37579i			0.280183i
$694$	−2.67602	+	12.9742i	−0.101580	+	0.492492i
$695$	11.9380			0.452834
$696$	4.43845	+	3.10354i	0.168239	+	0.117639i
$697$	65.9766			2.49904
$698$	2.48903	−	12.0676i	0.0942112	−	0.456764i
$699$			15.9481i			0.603211i
$700$	6.12136	+	2.63736i	0.231366	+	0.0996827i
$701$		−	22.1212i		−	0.835506i	−0.908561	−	0.417753i	$-0.862818\pi$
$701$		−	22.1212i		−	0.835506i	0.908561	−	0.417753i	$-0.137182\pi$
$702$	−2.58426	−	0.533023i	−0.0975365	−	0.0201177i
$703$	−45.3695			−1.71114
$704$	−15.8150	+	5.77947i	−0.596052	+	0.217822i
$705$	−1.03377			−0.0389339
$706$	−12.1665	−	2.50943i	−0.457891	−	0.0944436i
$707$		−	19.6199i		−	0.737882i
$708$	−12.6490	−	5.44974i	−0.475377	−	0.204814i
$709$		−	10.2955i		−	0.386654i	−0.981134	−	0.193327i	$-0.938072\pi$
$709$		−	10.2955i		−	0.386654i	0.981134	−	0.193327i	$-0.0619279\pi$
$710$	6.98703	−	33.8752i	0.262219	−	1.27132i
$711$	−7.55375			−0.283288
$712$	−0.333368	−	0.233104i	−0.0124935	−	0.00873596i
$713$	3.05752			0.114505
$714$	−7.46037	+	36.1701i	−0.279197	+	1.35363i
$715$			9.57995i			0.358270i
$716$	−10.0875	+	23.4132i	−0.376986	+	0.874993i
$717$			17.4340i			0.651086i
$718$	46.7704	+	9.64675i	1.74545	+	0.360014i
$719$	−9.26687			−0.345596			−0.172798	−	0.984957i	$-0.555281\pi$
$719$	−9.26687			−0.345596			−0.172798	+	0.984957i	$0.555281\pi$
$720$	−7.09182	+	6.70240i	−0.264297	+	0.249784i
$721$	−40.5332			−1.50953
$722$	38.3313	+	7.90613i	1.42654	+	0.294236i
$723$		−	1.01754i		−	0.0378429i
$724$	−1.63283	+	3.78982i	−0.0606835	+	0.140848i
$725$		−	1.82099i		−	0.0676300i
$726$	1.87692	−	9.09988i	0.0696591	−	0.337728i
$727$	−18.3266			−0.679694			−0.339847	−	0.940481i	$-0.610375\pi$
$727$	−18.3266			−0.679694			−0.339847	+	0.940481i	$0.610375\pi$
$728$	−10.5976	+	15.1559i	−0.392775	+	0.561716i
$729$	−1.00000			−0.0370370
$730$	2.69144	−	13.0489i	0.0996145	−	0.482961i
$731$			9.91540i			0.366734i
$732$	−10.1397	−	4.36865i	−0.374775	−	0.161470i
$733$			52.1723i			1.92703i	0.267658	+	0.963514i	$0.413750\pi$
$733$			52.1723i			1.92703i	−0.267658	+	0.963514i	$0.586250\pi$
$734$	8.34482	+	1.72118i	0.308013	+	0.0635301i
$735$	12.8816			0.475145
$736$	−2.97492	−	4.81143i	−0.109657	−	0.177352i
$737$	11.4563			0.422000
$738$	12.2626	+	2.52927i	0.451394	+	0.0931036i
$739$		−	4.24559i		−	0.156177i	−0.996946	−	0.0780883i	$-0.975118\pi$
$739$		−	4.24559i		−	0.156177i	0.996946	−	0.0780883i	$-0.0248816\pi$
$740$	29.7559	+	12.8202i	1.09385	+	0.471280i
$741$		−	12.7470i		−	0.468274i
$742$	5.75126	−	27.8838i	0.211135	−	1.02365i
$743$	−3.29573			−0.120909			−0.0604544	−	0.998171i	$-0.519255\pi$
$743$	−3.29573			−0.120909			−0.0604544	+	0.998171i	$0.519255\pi$
$744$	4.95568	−	7.08722i	0.181684	−	0.259830i
$745$	−21.2860			−0.779859
$746$	6.67558	−	32.3652i	0.244410	−	1.18497i
$747$		−	16.3370i		−	0.597739i
$748$	−12.4123	+	28.8091i	−0.453837	+	1.05337i
$749$			62.2332i			2.27395i
$750$	−13.6808	−	2.82176i	−0.499551	−	0.103036i
$751$	−17.7152			−0.646435			−0.323218	−	0.946325i	$-0.604765\pi$
$751$	−17.7152			−0.646435			−0.323218	+	0.946325i	$0.604765\pi$
$752$	−1.16429	−	1.23194i	−0.0424574	−	0.0449243i
$753$	−15.5488			−0.566630
$754$	4.94835	+	1.02064i	0.180208	+	0.0371693i
$755$		−	45.4848i		−	1.65536i
$756$	−2.77322	+	6.43671i	−0.100861	+	0.234101i
$757$		−	41.5244i		−	1.50923i	−0.656169	−	0.754614i	$-0.727824\pi$
$757$		−	41.5244i		−	1.50923i	0.656169	−	0.754614i	$-0.272176\pi$
$758$	−6.79775	+	32.9576i	−0.246906	+	1.19707i
$759$	−2.10475			−0.0763975
$760$	−38.6317	−	27.0128i	−1.40132	−	0.979859i
$761$	−11.0635			−0.401051			−0.200526	−	0.979688i	$-0.564265\pi$
$761$	−11.0635			−0.401051			−0.200526	+	0.979688i	$0.564265\pi$
$762$	−0.768407	+	3.72547i	−0.0278365	+	0.134960i
$763$		−	61.1578i		−	2.21406i
$764$	−23.3393	−	10.0556i	−0.844386	−	0.363799i
$765$			18.1790i			0.657262i
$766$	17.2530	+	3.55857i	0.623377	+	0.128576i
$767$	−12.8489			−0.463947
$768$	−15.9745	−	0.902671i	−0.576431	−	0.0325723i
$769$	−15.7762			−0.568905			−0.284452	−	0.958690i	$-0.591812\pi$
$769$	−15.7762			−0.568905			−0.284452	+	0.958690i	$0.591812\pi$
$770$	24.9214	+	5.14023i	0.898103	+	0.185241i
$771$			21.3366i			0.768418i
$772$	34.3797	+	14.8123i	1.23735	+	0.533107i
$773$		−	35.3398i		−	1.27108i	−0.772067	−	0.635542i	$-0.780777\pi$
$773$		−	35.3398i		−	1.27108i	0.772067	−	0.635542i	$-0.219223\pi$
$774$	−0.380115	+	1.84291i	−0.0136630	+	0.0662421i
$775$	−2.90773			−0.104449
$776$	41.7655	+	29.2041i	1.49929	+	1.04837i
$777$	23.2718			0.834872
$778$	7.77254	−	37.6836i	0.278659	−	1.35102i
$779$			60.4864i			2.16715i
$780$	−3.60197	+	8.36024i	−0.128971	+	0.299345i
$781$		−	21.1018i		−	0.755081i
$782$	−10.3215	−	2.12889i	−0.369095	−	0.0761288i
$783$	1.91480			0.0684295
$784$	14.5081	+	15.3510i	0.518146	+	0.548251i
$785$	−50.0600			−1.78672
$786$	−2.86619	−	0.591174i	−0.102234	−	0.0210865i
$787$		−	36.7870i		−	1.31131i	−0.755059	−	0.655657i	$-0.772392\pi$
$787$		−	36.7870i		−	1.31131i	0.755059	−	0.655657i	$-0.227608\pi$
$788$	−2.25832	+	5.24160i	−0.0804491	+	0.186724i
$789$			15.1462i			0.539220i
$790$	−5.26425	+	25.5227i	−0.187294	+	0.908056i
$791$	52.1126			1.85291
$792$	−3.41141	+	4.87873i	−0.121219	+	0.173358i
$793$	−10.3000			−0.365765
$794$	−1.61341	+	7.82232i	−0.0572579	+	0.277604i
$795$		−	14.0143i		−	0.497036i
$796$	−6.75500	−	2.91036i	−0.239425	−	0.103155i
$797$		−	51.8879i		−	1.83797i	−0.394298	−	0.918983i	$-0.629012\pi$
$797$		−	51.8879i		−	1.83797i	0.394298	−	0.918983i	$-0.370988\pi$
$798$	−33.1602	−	6.83956i	−1.17386	−	0.242118i
$799$	−3.15792			−0.111719
$800$	2.82917	+	4.57570i	0.100026	+	0.161776i
$801$	−0.143819			−0.00508160
$802$	−20.0142	−	4.12809i	−0.706727	−	0.145768i
$803$		−	8.12850i		−	0.286849i
$804$	9.99773	+	4.30747i	0.352593	+	0.151913i
$805$			8.54876i			0.301304i
$806$	1.62973	−	7.90142i	0.0574048	−	0.278316i
$807$	10.8517			0.381997
$808$	9.07449	−	12.9776i	0.319239	−	0.456551i
$809$	−14.2273			−0.500207			−0.250103	−	0.968219i	$-0.580465\pi$
$809$	−14.2273			−0.500207			−0.250103	+	0.968219i	$0.580465\pi$
$810$	−0.696905	+	3.37881i	−0.0244868	+	0.118719i
$811$		−	21.3336i		−	0.749124i	−0.927202	−	0.374562i	$-0.877793\pi$
$811$		−	21.3336i		−	0.749124i	0.927202	−	0.374562i	$-0.122207\pi$
$812$	5.31018	−	12.3250i	0.186351	−	0.432524i
$813$		−	25.7031i		−	0.901446i
$814$	19.3594	+	3.99302i	0.678545	+	0.139955i
$815$	33.1798			1.16224
$816$	−21.6639	+	20.4743i	−0.758388	+	0.716744i
$817$	−9.09029			−0.318029
$818$	−18.0013	−	3.71291i	−0.629400	−	0.129819i
$819$			6.53846i			0.228472i
$820$	17.0918	−	39.6704i	0.596872	−	1.38535i
$821$		−	15.8978i		−	0.554836i	−0.960749	−	0.277418i	$-0.910521\pi$
$821$		−	15.8978i		−	0.554836i	0.960749	−	0.277418i	$-0.0894786\pi$
$822$	−3.71374	+	18.0053i	−0.129532	+	0.628009i
$823$	15.9516			0.556037			0.278019	−	0.960576i	$-0.410322\pi$
$823$	15.9516			0.556037			0.278019	+	0.960576i	$0.410322\pi$
$824$	−26.8108	−	18.7472i	−0.933997	−	0.653089i
$825$	2.00163			0.0696879
$826$	−6.89422	+	33.4253i	−0.239881	+	1.16301i
$827$			6.73209i			0.234098i	0.993126	+	0.117049i	$0.0373434\pi$
$827$			6.73209i			0.234098i	−0.993126	+	0.117049i	$0.962657\pi$
$828$	−1.83677	−	0.791365i	−0.0638323	−	0.0275018i
$829$		−	53.8360i		−	1.86980i	−0.354910	−	0.934900i	$-0.615489\pi$
$829$		−	53.8360i		−	1.86980i	0.354910	−	0.934900i	$-0.384511\pi$
$830$	−55.1995	−	11.3853i	−1.91600	−	0.395191i
$831$	−30.7532			−1.06682
$832$	−14.0197	+	5.12336i	−0.486045	+	0.177621i
$833$	39.3504			1.36341
$834$	6.77805	+	1.39802i	0.234705	+	0.0484096i
$835$			5.33166i			0.184510i
$836$	−26.4118	−	11.3794i	−0.913471	−	0.393564i
$837$		−	3.05752i		−	0.105683i
$838$	−6.50902	+	31.5577i	−0.224850	+	1.09014i
$839$	23.0617			0.796177			0.398088	−	0.917347i	$-0.369674\pi$
$839$	23.0617			0.796177			0.398088	+	0.917347i	$0.369674\pi$
$840$	19.8157	+	13.8560i	0.683708	+	0.478076i
$841$	25.3335			0.873570
$842$	−10.7216	+	51.9817i	−0.369492	+	1.79141i
$843$		−	12.1680i		−	0.419089i
$844$	12.0280	−	27.9173i	0.414022	−	0.960955i
$845$		−	23.2207i		−	0.798816i
$846$	−0.586943	−	0.121062i	−0.0201795	−	0.00416218i
$847$	−23.0237			−0.791104
$848$	16.7009	−	15.7838i	0.573510	−	0.542018i
$849$	6.04776			0.207559
$850$	9.81581	+	2.02459i	0.336679	+	0.0694428i
$851$			6.64083i			0.227645i
$852$	7.93407	−	18.4151i	0.271817	−	0.630892i
$853$			32.2842i			1.10539i	0.833383	+	0.552695i	$0.186401\pi$
$853$			32.2842i			1.10539i	−0.833383	+	0.552695i	$0.813599\pi$
$854$	−5.52659	+	26.7946i	−0.189116	+	0.916891i
$855$	−16.6662			−0.569972
$856$	−28.7838	+	41.1643i	−0.983809	+	1.40697i
$857$	−10.1707			−0.347424			−0.173712	−	0.984797i	$-0.555576\pi$
$857$	−10.1707			−0.347424			−0.173712	+	0.984797i	$0.555576\pi$
$858$	−1.12188	+	5.43921i	−0.0383004	+	0.185692i
$859$		−	36.0645i		−	1.23050i	−0.788330	−	0.615252i	$-0.789054\pi$
$859$		−	36.0645i		−	1.23050i	0.788330	−	0.615252i	$-0.210946\pi$
$860$	5.96194	+	2.56867i	0.203300	+	0.0875909i
$861$		−	31.0259i		−	1.05736i
$862$	−26.0998	−	5.38329i	−0.888963	−	0.183356i
$863$	−19.6392			−0.668525			−0.334262	−	0.942480i	$-0.608487\pi$
$863$	−19.6392			−0.668525			−0.334262	+	0.942480i	$0.608487\pi$
$864$	−4.81143	+	2.97492i	−0.163688	+	0.101209i
$865$	−22.8235			−0.776021
$866$	18.6429	+	3.84525i	0.633513	+	0.130667i
$867$			38.5326i			1.30864i
$868$	−19.6804	−	8.47919i	−0.667995	−	0.287802i
$869$			15.8988i			0.539328i
$870$	1.33444	−	6.46975i	0.0452417	−	0.219345i
$871$	10.1558			0.344116
$872$	28.2864	−	40.4530i	0.957898	−	1.36991i
$873$	18.0182			0.609823
$874$	1.95173	−	9.46258i	0.0660183	−	0.320077i
$875$			34.6139i			1.17016i
$876$	3.05624	−	7.09359i	0.103261	−	0.239670i
$877$			45.1149i			1.52342i	0.647916	+	0.761712i	$0.275641\pi$
$877$			45.1149i			1.52342i	−0.647916	+	0.761712i	$0.724359\pi$
$878$	−48.6322	−	10.0308i	−1.64126	−	0.338522i
$879$	−17.7870			−0.599941
$880$	14.1069	+	14.9265i	0.475542	+	0.503172i
$881$	−49.3854			−1.66384			−0.831919	−	0.554897i	$-0.812757\pi$
$881$	−49.3854			−1.66384			−0.831919	+	0.554897i	$0.812757\pi$
$882$	7.31380	+	1.50853i	0.246268	+	0.0507948i
$883$			43.2358i			1.45500i	0.686108	+	0.727500i	$0.259318\pi$
$883$			43.2358i			1.45500i	−0.686108	+	0.727500i	$0.740682\pi$
$884$	−11.0032	+	25.5386i	−0.370077	+	0.858957i
$885$			16.7994i			0.564706i
$886$	−5.01002	+	24.2901i	−0.168315	+	0.816041i
$887$	−31.3782			−1.05358			−0.526788	−	0.849997i	$-0.676604\pi$
$887$	−31.3782			−1.05358			−0.526788	+	0.849997i	$0.676604\pi$
$888$	15.3932	+	10.7636i	0.516562	+	0.361201i
$889$	9.42586			0.316133
$890$	−0.100228	+	0.485938i	−0.00335966	+	0.0162887i
$891$			2.10475i			0.0705117i
$892$	26.7643	+	11.5313i	0.896136	+	0.386095i
$893$		−	2.89514i		−	0.0968821i
$894$	−12.0856	−	2.49274i	−0.404202	−	0.0833698i
$895$	31.0957			1.03942
$896$	5.80555	+	39.2199i	0.193950	+	1.31024i
$897$	−1.86581			−0.0622976
$898$	10.4269	+	2.15062i	0.347949	+	0.0717672i
$899$			5.85455i			0.195260i
$900$	1.74679	+	0.752594i	0.0582262	+	0.0250865i
$901$		−	42.8105i		−	1.42622i
$902$	5.32347	−	25.8098i	0.177252	−	0.859372i
$903$	4.66277			0.155167
$904$	34.4700	+	24.1028i	1.14645	+	0.801648i
$905$	5.03336			0.167315
$906$	5.32660	−	25.8250i	0.176964	−	0.857977i
$907$			9.25110i			0.307178i	0.988135	+	0.153589i	$0.0490831\pi$
$907$			9.25110i			0.307178i	−0.988135	+	0.153589i	$0.950917\pi$
$908$	22.9001	−	53.1517i	0.759967	−	1.76390i
$909$		−	5.59872i		−	0.185698i
$910$	22.0922	+	4.55669i	0.732350	+	0.151053i
$911$	54.6183			1.80959			0.904793	−	0.425852i	$-0.140026\pi$
$911$	54.6183			1.80959			0.904793	+	0.425852i	$0.140026\pi$
$912$	−18.7705	−	19.8611i	−0.621554	−	0.657668i
$913$	−34.3853			−1.13799
$914$	−24.6501	−	5.08427i	−0.815351	−	0.168173i
$915$			13.4668i			0.445200i
$916$	2.02039	−	4.68937i	0.0667556	−	0.154941i
$917$			7.25178i			0.239475i
$918$	−2.12889	+	10.3215i	−0.0702637	+	0.340660i
$919$	−21.0630			−0.694805			−0.347402	−	0.937716i	$-0.612936\pi$
$919$	−21.0630			−0.694805			−0.347402	+	0.937716i	$0.612936\pi$
$920$	−3.95393	+	5.65460i	−0.130357	+	0.186427i
$921$	3.02852			0.0997932
$922$	−3.45730	+	16.7620i	−0.113860	+	0.552028i
$923$		−	18.7062i		−	0.615724i
$924$	13.5477	+	5.83694i	0.445685	+	0.192021i
$925$		−	6.31548i		−	0.207652i
$926$	42.8502	+	8.83819i	1.40814	+	0.290441i
$927$	−11.5665			−0.379894
$928$	9.21294	−	5.69639i	0.302430	−	0.186993i
$929$	9.36655			0.307307			0.153653	−	0.988125i	$-0.450896\pi$
$929$	9.36655			0.307307			0.153653	+	0.988125i	$0.450896\pi$
$930$	−10.3308	−	2.13080i	−0.338759	−	0.0698718i
$931$			36.0758i			1.18234i
$932$	29.2930	+	12.6207i	0.959524	+	0.413406i
$933$		−	17.6413i		−	0.577549i
$934$	8.17479	−	39.6338i	0.267487	−	1.29686i
$935$	38.2622			1.25131
$936$	−3.02414	+	4.32488i	−0.0988469	+	0.141363i
$937$	41.6393			1.36030			0.680148	−	0.733075i	$-0.261916\pi$
$937$	41.6393			1.36030			0.680148	+	0.733075i	$0.261916\pi$
$938$	5.44919	−	26.4193i	0.177922	−	0.862622i
$939$			2.79695i			0.0912751i
$940$	−0.818087	+	1.89880i	−0.0266831	+	0.0619319i
$941$		−	53.3473i		−	1.73907i	−0.493870	−	0.869536i	$-0.664418\pi$
$941$		−	53.3473i		−	1.73907i	0.493870	−	0.869536i	$-0.335582\pi$
$942$	−28.4226	−	5.86238i	−0.926058	−	0.191007i
$943$	8.85352			0.288310
$944$	−20.0199	+	18.9205i	−0.651591	+	0.615811i
$945$	8.54876			0.278091
$946$	3.87887	+	0.800047i	0.126113	+	0.0260118i
$947$			15.6490i			0.508523i	0.967136	+	0.254261i	$0.0818324\pi$
$947$			15.6490i			0.508523i	−0.967136	+	0.254261i	$0.918168\pi$
$948$	−5.97778	+	13.8745i	−0.194149	+	0.450624i
$949$		−	7.20573i		−	0.233908i
$950$	−1.85611	+	8.99899i	−0.0602202	+	0.291966i
$951$	−29.1832			−0.946331
$952$	60.5325	+	42.3268i	1.96187	+	1.37182i
$953$	3.15311			0.102139			0.0510696	−	0.998695i	$-0.483737\pi$
$953$	3.15311			0.102139			0.0510696	+	0.998695i	$0.483737\pi$
$954$	1.64117	−	7.95691i	0.0531350	−	0.257614i
$955$			30.9975i			1.00306i
$956$	32.0224	+	13.7967i	1.03568	+	0.446217i
$957$		−	4.03018i		−	0.130277i
$958$	30.4983	+	6.29051i	0.985355	+	0.203237i
$959$	45.5556			1.47107
$960$	6.69858	+	18.3301i	0.216196	+	0.591602i
$961$	−21.6516			−0.698438
$962$	17.1616	+	3.53972i	0.553313	+	0.114125i
$963$			17.7588i			0.572270i
$964$	−1.86900	−	0.805248i	−0.0601964	−	0.0259353i
$965$		−	45.6606i		−	1.46987i
$966$	−1.00112	+	4.85374i	−0.0322105	+	0.156166i
$967$	8.52752			0.274227			0.137113	−	0.990555i	$-0.456218\pi$
$967$	8.52752			0.274227			0.137113	+	0.990555i	$0.456218\pi$
$968$	−15.2291	−	10.6488i	−0.489482	−	0.342266i
$969$	−50.9115			−1.63551
$970$	12.5570	−	60.8799i	0.403180	−	1.95474i
$971$		−	20.2389i		−	0.649497i	−0.945800	−	0.324749i	$-0.894720\pi$
$971$		−	20.2389i		−	0.649497i	0.945800	−	0.324749i	$-0.105280\pi$
$972$	−0.791365	+	1.83677i	−0.0253830	+	0.0589146i
$973$		−	17.1492i		−	0.549779i
$974$	0.960294	+	0.198068i	0.0307698	+	0.00634651i
$975$	1.77440			0.0568263
$976$	−16.0485	+	15.1672i	−0.513699	+	0.485490i
$977$	−20.8048			−0.665603			−0.332802	−	0.942997i	$-0.607994\pi$
$977$	−20.8048			−0.665603			−0.332802	+	0.942997i	$0.607994\pi$
$978$	18.8385	+	3.88560i	0.602390	+	0.124248i
$979$			0.302703i			0.00967444i
$980$	10.1941	−	23.6606i	0.325637	−	0.755811i
$981$		−	17.4519i		−	0.557198i
$982$	−11.1874	+	54.2400i	−0.357005	+	1.73087i
$983$	−6.00846			−0.191640			−0.0958200	−	0.995399i	$-0.530547\pi$
$983$	−6.00846			−0.191640			−0.0958200	+	0.995399i	$0.530547\pi$
$984$	14.3499	−	20.5221i	0.457459	−	0.654222i
$985$	6.96150			0.221812
$986$	4.07640	−	19.7636i	0.129819	−	0.629402i
$987$			1.48503i			0.0472691i
$988$	−23.4134	−	10.0876i	−0.744881	−	0.320928i
$989$			1.33057i			0.0423095i
$990$	7.11154	+	1.46681i	0.226020	+	0.0466183i
$991$	−27.4949			−0.873404			−0.436702	−	0.899606i	$-0.643853\pi$
$991$	−27.4949			−0.873404			−0.436702	+	0.899606i	$0.643853\pi$
$992$	−9.09589	−	14.7110i	−0.288795	−	0.467076i
$993$	15.1651			0.481249
$994$	−48.6626	−	10.0370i	−1.54348	−	0.318356i
$995$			8.97150i			0.284416i
$996$	−30.0074	−	12.9285i	−0.950820	−	0.409656i
$997$		−	47.1134i		−	1.49210i	−0.665892	−	0.746048i	$-0.731949\pi$
$997$		−	47.1134i		−	1.49210i	0.665892	−	0.746048i	$-0.268051\pi$
$998$	5.32561	−	25.8202i	0.168579	−	0.817323i
$999$	6.64083			0.210107

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.f.d.277.1	✓	20
4.3	odd	2		2208.2.f.d.1105.3		20
8.3	odd	2		2208.2.f.d.1105.18		20
8.5	even	2	inner	552.2.f.d.277.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.f.d.277.1	✓	20	1.1	even	1	trivial
552.2.f.d.277.2	yes	20	8.5	even	2	inner
2208.2.f.d.1105.3		20	4.3	odd	2
2208.2.f.d.1105.18		20	8.3	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38506 - 0.285679i) q^{2} +1.00000i q^{3} +(1.83677 + 0.791365i) q^{4} -2.43947i q^{5} +(0.285679 - 1.38506i) q^{6} -3.50435 q^{7} +(-2.31796 - 1.62082i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.38506 - 0.285679i) q^{2} +1.00000i q^{3} +(1.83677 + 0.791365i) q^{4} -2.43947i q^{5} +(0.285679 - 1.38506i) q^{6} -3.50435 q^{7} +(-2.31796 - 1.62082i) q^{8} -1.00000 q^{9} +(-0.696905 + 3.37881i) q^{10} +2.10475i q^{11} +(-0.791365 + 1.83677i) q^{12} +1.86581i q^{13} +(4.85374 + 1.00112i) q^{14} +2.43947 q^{15} +(2.74748 + 2.90712i) q^{16} +7.45202 q^{17} +(1.38506 + 0.285679i) q^{18} +6.83190i q^{19} +(1.93051 - 4.48075i) q^{20} -3.50435i q^{21} +(0.601283 - 2.91520i) q^{22} +1.00000 q^{23} +(1.62082 - 2.31796i) q^{24} -0.951008 q^{25} +(0.533023 - 2.58426i) q^{26} -1.00000i q^{27} +(-6.43671 - 2.77322i) q^{28} +1.91480i q^{29} +(-3.37881 - 0.696905i) q^{30} +3.05752 q^{31} +(-2.97492 - 4.81143i) q^{32} -2.10475 q^{33} +(-10.3215 - 2.12889i) q^{34} +8.54876i q^{35} +(-1.83677 - 0.791365i) q^{36} +6.64083i q^{37} +(1.95173 - 9.46258i) q^{38} -1.86581 q^{39} +(-3.95393 + 5.65460i) q^{40} +8.85352 q^{41} +(-1.00112 + 4.85374i) q^{42} +1.33057i q^{43} +(-1.66562 + 3.86595i) q^{44} +2.43947i q^{45} +(-1.38506 - 0.285679i) q^{46} -0.423767 q^{47} +(-2.90712 + 2.74748i) q^{48} +5.28050 q^{49} +(1.31720 + 0.271683i) q^{50} +7.45202i q^{51} +(-1.47654 + 3.42708i) q^{52} -5.74482i q^{53} +(-0.285679 + 1.38506i) q^{54} +5.13447 q^{55} +(8.12297 + 5.67991i) q^{56} -6.83190 q^{57} +(0.547020 - 2.65212i) q^{58} +6.88650i q^{59} +(4.48075 + 1.93051i) q^{60} +5.52040i q^{61} +(-4.23485 - 0.873470i) q^{62} +3.50435 q^{63} +(2.74592 + 7.51398i) q^{64} +4.55159 q^{65} +(2.91520 + 0.601283i) q^{66} -5.44309i q^{67} +(13.6877 + 5.89727i) q^{68} +1.00000i q^{69} +(2.44220 - 11.8405i) q^{70} -10.0258 q^{71} +(2.31796 + 1.62082i) q^{72} -3.86198 q^{73} +(1.89715 - 9.19794i) q^{74} -0.951008i q^{75} +(-5.40653 + 12.5487i) q^{76} -7.37579i q^{77} +(2.58426 + 0.533023i) q^{78} +7.55375 q^{79} +(7.09182 - 6.70240i) q^{80} +1.00000 q^{81} +(-12.2626 - 2.52927i) q^{82} +16.3370i q^{83} +(2.77322 - 6.43671i) q^{84} -18.1790i q^{85} +(0.380115 - 1.84291i) q^{86} -1.91480 q^{87} +(3.41141 - 4.87873i) q^{88} +0.143819 q^{89} +(0.696905 - 3.37881i) q^{90} -6.53846i q^{91} +(1.83677 + 0.791365i) q^{92} +3.05752i q^{93} +(0.586943 + 0.121062i) q^{94} +16.6662 q^{95} +(4.81143 - 2.97492i) q^{96} -18.0182 q^{97} +(-7.31380 - 1.50853i) q^{98} -2.10475i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9	\( 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9} - 12 q^{10} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 32 q^{17} + 2 q^{18} + 20 q^{20} + 14 q^{22} + 20 q^{23} + 10 q^{24} - 28 q^{25} + 18 q^{28} - 22 q^{32} + 28 q^{33} - 26 q^{34} + 16 q^{38} + 4 q^{40} - 40 q^{41} + 14 q^{42} + 10 q^{44} - 2 q^{46} + 40 q^{47} + 12 q^{49} - 14 q^{50} + 20 q^{52} - 2 q^{54} - 8 q^{55} + 6 q^{56} - 44 q^{57} - 32 q^{58} - 24 q^{60} + 20 q^{62} + 8 q^{63} - 48 q^{64} + 8 q^{65} + 10 q^{66} + 22 q^{68} + 80 q^{70} - 40 q^{71} + 2 q^{72} - 16 q^{73} - 30 q^{74} + 44 q^{76} - 36 q^{78} - 16 q^{79} + 4 q^{80} + 20 q^{81} - 32 q^{82} + 6 q^{84} - 4 q^{86} + 8 q^{87} - 70 q^{88} - 40 q^{89} + 12 q^{90} + 64 q^{94} - 40 q^{95} + 2 q^{96} + 32 q^{97} - 26 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9 - 12 * q^10 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 32 * q^17 + 2 * q^18 + 20 * q^20 + 14 * q^22 + 20 * q^23 + 10 * q^24 - 28 * q^25 + 18 * q^28 - 22 * q^32 + 28 * q^33 - 26 * q^34 + 16 * q^38 + 4 * q^40 - 40 * q^41 + 14 * q^42 + 10 * q^44 - 2 * q^46 + 40 * q^47 + 12 * q^49 - 14 * q^50 + 20 * q^52 - 2 * q^54 - 8 * q^55 + 6 * q^56 - 44 * q^57 - 32 * q^58 - 24 * q^60 + 20 * q^62 + 8 * q^63 - 48 * q^64 + 8 * q^65 + 10 * q^66 + 22 * q^68 + 80 * q^70 - 40 * q^71 + 2 * q^72 - 16 * q^73 - 30 * q^74 + 44 * q^76 - 36 * q^78 - 16 * q^79 + 4 * q^80 + 20 * q^81 - 32 * q^82 + 6 * q^84 - 4 * q^86 + 8 * q^87 - 70 * q^88 - 40 * q^89 + 12 * q^90 + 64 * q^94 - 40 * q^95 + 2 * q^96 + 32 * q^97 - 26 * q^98

Introduction

L-functions

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