LMFDB - Embedded newform 675.2.r.a.46.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(46,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.46"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 18])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			46.23
Character	$\chi$	$=$	675.46
Dual form			675.2.r.a.631.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22593 + 1.36154i) q^{2} +(-0.141814 + 1.34927i) q^{4} +(-1.94663 - 1.10028i) q^{5} +(-2.15924 + 3.73991i) q^{7} +(0.953512 - 0.692767i) q^{8} +(-0.888371 - 3.99929i) q^{10} +(0.605752 + 0.672756i) q^{11} +(-4.13776 + 4.59545i) q^{13} +(-7.73912 + 1.64500i) q^{14} +(4.76628 + 1.01310i) q^{16} +(-4.65336 + 3.38087i) q^{17} +(-2.14825 + 1.56079i) q^{19} +(1.76064 - 2.47050i) q^{20} +(-0.173370 + 1.64951i) q^{22} +(3.44271 - 0.731772i) q^{23} +(2.57876 + 4.28369i) q^{25} -11.3295 q^{26} +(-4.73994 - 3.44377i) q^{28} +(2.08431 - 0.927996i) q^{29} +(-2.13557 - 0.950816i) q^{31} +(3.28516 + 5.69007i) q^{32} +(-10.3079 - 2.19101i) q^{34} +(8.31820 - 4.90447i) q^{35} +(-0.704813 - 2.16919i) q^{37} +(-4.75869 - 1.01149i) q^{38} +(-2.61838 + 0.299432i) q^{40} +(4.04708 - 4.49473i) q^{41} +(-1.16011 + 2.00937i) q^{43} +(-0.993634 + 0.721917i) q^{44} +(5.21688 + 3.79028i) q^{46} +(-5.09769 + 2.26964i) q^{47} +(-5.82462 - 10.0885i) q^{49} +(-2.67101 + 8.76261i) q^{50} +(-5.61371 - 6.23466i) q^{52} +(-3.50455 - 2.54621i) q^{53} +(-0.438957 - 1.97611i) q^{55} +(0.532027 + 5.06190i) q^{56} +(3.81874 + 1.70021i) q^{58} +(8.79570 - 9.76861i) q^{59} +(9.45934 + 10.5057i) q^{61} +(-1.32349 - 4.07330i) q^{62} +(-0.708321 + 2.17999i) q^{64} +(13.1110 - 4.39296i) q^{65} +(6.96006 + 3.09882i) q^{67} +(-3.90179 - 6.75810i) q^{68} +(16.8752 + 5.31299i) q^{70} +(4.21064 + 3.05921i) q^{71} +(0.0260643 - 0.0802177i) q^{73} +(2.08938 - 3.61892i) q^{74} +(-1.80128 - 3.11991i) q^{76} +(-3.82401 + 0.812818i) q^{77} +(-0.815175 + 0.362939i) q^{79} +(-8.16350 - 7.21639i) q^{80} +11.0812 q^{82} +(0.108872 + 1.03584i) q^{83} +(12.7783 - 1.46130i) q^{85} +(-4.15806 + 0.883823i) q^{86} +(1.04365 + 0.221836i) q^{88} +(-1.84560 + 5.68017i) q^{89} +(-8.25216 - 25.3975i) q^{91} +(0.499132 + 4.74893i) q^{92} +(-9.33964 - 4.15827i) q^{94} +(5.89916 - 0.674617i) q^{95} +(-1.49796 + 0.666933i) q^{97} +(6.59533 - 20.2983i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	1.22593	+	1.36154i	0.866867	+	0.962753i	0.999597	−	0.0283992i	$-0.00904097\pi$
$2$	1.22593	+	1.36154i	0.866867	+	0.962753i	−0.132730	+	0.991152i	$0.542374\pi$
$3$		0			0
$3$		0			0
$4$	−0.141814	+	1.34927i	−0.0709070	+	0.674635i
$5$	−1.94663	−	1.10028i	−0.870561	−	0.492061i
$5$	−1.94663	−	1.10028i	−0.870561	−	0.492061i
$6$		0			0
$7$	−2.15924	+	3.73991i	−0.816115	+	1.41355i	0.0924090	+	0.995721i	$0.470543\pi$
$7$	−2.15924	+	3.73991i	−0.816115	+	1.41355i	−0.908524	+	0.417832i	$0.862790\pi$
$8$	0.953512	−	0.692767i	0.337117	−	0.244930i
$9$		0			0
$10$	−0.888371	−	3.99929i	−0.280928	−	1.26469i
$11$	0.605752	+	0.672756i	0.182641	+	0.202844i	0.827512	−	0.561448i	$-0.189756\pi$
$11$	0.605752	+	0.672756i	0.182641	+	0.202844i	−0.644871	+	0.764292i	$0.723089\pi$
$12$		0			0
$13$	−4.13776	+	4.59545i	−1.14761	+	1.27455i	−0.191515	+	0.981490i	$0.561340\pi$
$13$	−4.13776	+	4.59545i	−1.14761	+	1.27455i	−0.956094	+	0.293059i	$0.905327\pi$
$14$	−7.73912	+	1.64500i	−2.06837	+	0.439645i
$15$		0			0
$16$	4.76628	+	1.01310i	1.19157	+	0.253276i
$17$	−4.65336	+	3.38087i	−1.12861	+	0.819981i	−0.985491	−	0.169726i	$-0.945712\pi$
$17$	−4.65336	+	3.38087i	−1.12861	+	0.819981i	−0.143115	+	0.989706i	$0.545712\pi$
$18$		0			0
$19$	−2.14825	+	1.56079i	−0.492842	+	0.358070i	−0.806276	−	0.591539i	$-0.798520\pi$
$19$	−2.14825	+	1.56079i	−0.492842	+	0.358070i	0.313434	+	0.949610i	$0.398520\pi$
$20$	1.76064	−	2.47050i	0.393690	−	0.552421i
$21$		0			0
$22$	−0.173370	+	1.64951i	−0.0369627	+	0.351677i
$23$	3.44271	−	0.731772i	0.717856	−	0.152585i	0.165520	−	0.986206i	$-0.447070\pi$
$23$	3.44271	−	0.731772i	0.717856	−	0.152585i	0.552336	+	0.833622i	$0.313737\pi$
$24$		0			0
$25$	2.57876	+	4.28369i	0.515753	+	0.856737i
$26$	−11.3295			−2.22190
$27$		0			0
$28$	−4.73994	−	3.44377i	−0.895764	−	0.650811i
$29$	2.08431	−	0.927996i	0.387047	−	0.172325i	−0.203982	−	0.978975i	$-0.565388\pi$
$29$	2.08431	−	0.927996i	0.387047	−	0.172325i	0.591029	+	0.806650i	$0.298722\pi$
$30$		0			0
$31$	−2.13557	−	0.950816i	−0.383559	−	0.170772i	0.205893	−	0.978574i	$-0.433990\pi$
$31$	−2.13557	−	0.950816i	−0.383559	−	0.170772i	−0.589453	+	0.807803i	$0.700657\pi$
$32$	3.28516	+	5.69007i	0.580740	+	1.00587i
$33$		0			0
$34$	−10.3079	−	2.19101i	−1.76779	−	0.375755i
$35$	8.31820	−	4.90447i	1.40603	−	0.829006i
$36$		0			0
$37$	−0.704813	−	2.16919i	−0.115871	−	0.356613i	0.876257	−	0.481844i	$-0.160033\pi$
$37$	−0.704813	−	2.16919i	−0.115871	−	0.356613i	−0.992128	+	0.125231i	$0.960033\pi$
$38$	−4.75869	−	1.01149i	−0.771961	−	0.164085i
$39$		0			0
$40$	−2.61838	+	0.299432i	−0.414001	+	0.0473444i
$41$	4.04708	−	4.49473i	0.632047	−	0.701960i	−0.339016	−	0.940780i	$-0.610094\pi$
$41$	4.04708	−	4.49473i	0.632047	−	0.701960i	0.971064	+	0.238821i	$0.0767609\pi$
$42$		0			0
$43$	−1.16011	+	2.00937i	−0.176915	+	0.306427i	−0.940822	−	0.338900i	$-0.889945\pi$
$43$	−1.16011	+	2.00937i	−0.176915	+	0.306427i	0.763907	+	0.645326i	$0.223279\pi$
$44$	−0.993634	+	0.721917i	−0.149796	+	0.108833i
$45$		0			0
$46$	5.21688	+	3.79028i	0.769187	+	0.558847i
$47$	−5.09769	+	2.26964i	−0.743575	+	0.331061i	−0.743317	−	0.668939i	$-0.766749\pi$
$47$	−5.09769	+	2.26964i	−0.743575	+	0.331061i	−0.000257570		1.00000i	$0.500082\pi$
$48$		0			0
$49$	−5.82462	−	10.0885i	−0.832088	−	1.44122i
$50$	−2.67101	+	8.76261i	−0.377738	+	1.23922i
$51$		0			0
$52$	−5.61371	−	6.23466i	−0.778482	−	0.864592i
$53$	−3.50455	−	2.54621i	−0.481387	−	0.349748i	0.320475	−	0.947257i	$-0.396157\pi$
$53$	−3.50455	−	2.54621i	−0.481387	−	0.349748i	−0.801862	+	0.597509i	$0.796157\pi$
$54$		0			0
$55$	−0.438957	−	1.97611i	−0.0591889	−	0.266458i
$56$	0.532027	+	5.06190i	0.0710951	+	0.676424i
$57$		0			0
$58$	3.81874	+	1.70021i	0.501425	+	0.223249i
$59$	8.79570	−	9.76861i	1.14510	−	1.27177i	0.187951	−	0.982178i	$-0.439815\pi$
$59$	8.79570	−	9.76861i	1.14510	−	1.27177i	0.957152	−	0.289587i	$-0.0935179\pi$
$60$		0			0
$61$	9.45934	+	10.5057i	1.21114	+	1.34511i	0.921694	+	0.387918i	$0.126806\pi$
$61$	9.45934	+	10.5057i	1.21114	+	1.34511i	0.289450	+	0.957193i	$0.406528\pi$
$62$	−1.32349	−	4.07330i	−0.168084	−	0.517309i
$63$		0			0
$64$	−0.708321	+	2.17999i	−0.0885401	+	0.272498i
$65$	13.1110	−	4.39296i	1.62622	−	0.544880i
$66$		0			0
$67$	6.96006	+	3.09882i	0.850306	+	0.378581i	0.785158	−	0.619295i	$-0.212581\pi$
$67$	6.96006	+	3.09882i	0.850306	+	0.378581i	0.0651477	+	0.997876i	$0.479248\pi$
$68$	−3.90179	−	6.75810i	−0.473162	−	0.819540i
$69$		0			0
$70$	16.8752	+	5.31299i	2.01697	+	0.635024i
$71$	4.21064	+	3.05921i	0.499711	+	0.363061i	0.808907	−	0.587937i	$-0.200060\pi$
$71$	4.21064	+	3.05921i	0.499711	+	0.363061i	−0.309195	+	0.950999i	$0.600060\pi$
$72$		0			0
$73$	0.0260643	−	0.0802177i	0.00305060	−	0.00938878i	−0.949520	−	0.313708i	$-0.898429\pi$
$73$	0.0260643	−	0.0802177i	0.00305060	−	0.00938878i	0.952570	+	0.304319i	$0.0984288\pi$
$74$	2.08938	−	3.61892i	0.242886	−	0.420691i
$75$		0			0
$76$	−1.80128	−	3.11991i	−0.206621	−	0.357878i
$77$	−3.82401	+	0.812818i	−0.435786	+	0.0926292i
$78$		0			0
$79$	−0.815175	+	0.362939i	−0.0917144	+	0.0408339i	−0.452081	−	0.891977i	$-0.649318\pi$
$79$	−0.815175	+	0.362939i	−0.0917144	+	0.0408339i	0.360367	+	0.932811i	$0.382652\pi$
$80$	−8.16350	−	7.21639i	−0.912708	−	0.806817i
$81$		0			0
$82$	11.0812			1.22371
$83$	0.108872	+	1.03584i	0.0119502	+	0.113699i	0.998871	−	0.0475082i	$-0.0151280\pi$
$83$	0.108872	+	1.03584i	0.0119502	+	0.113699i	−0.986921	+	0.161207i	$0.948461\pi$
$84$		0			0
$85$	12.7783	−	1.46130i	1.38600	−	0.158500i
$86$	−4.15806	+	0.883823i	−0.448375	+	0.0953051i
$87$		0			0
$88$	1.04365	+	0.221836i	0.111254	+	0.0236478i
$89$	−1.84560	+	5.68017i	−0.195633	+	0.602096i	0.804336	+	0.594175i	$0.202521\pi$
$89$	−1.84560	+	5.68017i	−0.195633	+	0.602096i	−0.999969	+	0.00792122i	$0.997479\pi$
$90$		0			0
$91$	−8.25216	−	25.3975i	−0.865062	−	2.66239i
$92$	0.499132	+	4.74893i	0.0520382	+	0.495110i
$93$		0			0
$94$	−9.33964	−	4.15827i	−0.963310	−	0.428893i
$95$	5.89916	−	0.674617i	0.605241	−	0.0692142i
$96$		0			0
$97$	−1.49796	+	0.666933i	−0.152094	+	0.0677168i	−0.481372	−	0.876516i	$-0.659861\pi$
$97$	−1.49796	+	0.666933i	−0.152094	+	0.0677168i	0.329278	+	0.944233i	$0.393195\pi$
$98$	6.59533	−	20.2983i	0.666229	−	2.05044i
$99$		0			0
$100$	−6.14556	+	2.87196i	−0.614556	+	0.287196i
$101$	−3.92357	+	6.79582i	−0.390410	+	0.676209i	−0.992504	−	0.122216i	$-0.961000\pi$
$101$	−3.92357	+	6.79582i	−0.390410	+	0.676209i	0.602094	+	0.798425i	$0.294333\pi$
$102$		0			0
$103$	1.30490	−	12.4153i	0.128576	−	1.22331i	−0.719899	−	0.694079i	$-0.755812\pi$
$103$	1.30490	−	12.4153i	0.128576	−	1.22331i	0.848475	−	0.529236i	$-0.177521\pi$
$104$	−0.761829	+	7.24832i	−0.0747035	+	0.710756i
$105$		0			0
$106$	−0.829594	−	7.89306i	−0.0805773	−	0.766642i
$107$	−6.18859			−0.598273			−0.299137	−	0.954210i	$-0.596699\pi$
$107$	−6.18859			−0.598273			−0.299137	+	0.954210i	$0.596699\pi$
$108$		0			0
$109$	5.35768	+	16.4892i	0.513173	+	1.57938i	0.786582	+	0.617485i	$0.211848\pi$
$109$	5.35768	+	16.4892i	0.513173	+	1.57938i	−0.273410	+	0.961898i	$0.588152\pi$
$110$	2.15241	−	3.02023i	0.205224	−	0.287968i
$111$		0			0
$112$	−14.0805	+	15.6379i	−1.33048	+	1.47765i
$113$	−4.01244	+	4.45627i	−0.377459	+	0.419210i	−0.901702	−	0.432358i	$-0.857682\pi$
$113$	−4.01244	+	4.45627i	−0.377459	+	0.419210i	0.524243	+	0.851569i	$0.324348\pi$
$114$		0			0
$115$	−7.50686	−	2.36346i	−0.700018	−	0.220394i
$116$	0.956533	+	2.94391i	0.0888119	+	0.273335i
$117$		0			0
$118$	24.0833			2.21705
$119$	−2.59642	−	24.7033i	−0.238013	−	2.26454i
$120$		0			0
$121$	1.06415	−	10.1247i	0.0967408	−	0.920427i
$122$	−2.70733	+	25.7585i	−0.245110	+	2.33206i
$123$		0			0
$124$	1.58576	−	2.74662i	0.142406	−	0.246654i
$125$	−0.306650	−	11.1761i	−0.0274276	−	0.999624i
$126$		0			0
$127$	−3.86196	+	11.8859i	−0.342694	+	1.05470i	0.620113	+	0.784512i	$0.287087\pi$
$127$	−3.86196	+	11.8859i	−0.342694	+	1.05470i	−0.962807	+	0.270190i	$0.912913\pi$
$128$	8.16810	−	3.63667i	0.721965	−	0.321439i
$129$		0			0
$130$	22.0544	+	12.4656i	1.93430	+	1.09331i
$131$	−4.74442	−	2.11235i	−0.414522	−	0.184557i	0.188870	−	0.982002i	$-0.439518\pi$
$131$	−4.74442	−	2.11235i	−0.414522	−	0.184557i	−0.603391	+	0.797445i	$0.706184\pi$
$132$		0			0
$133$	−1.19865	−	11.4044i	−0.103936	−	0.988885i
$134$	4.31342	+	13.2753i	0.372622	+	1.14681i
$135$		0			0
$136$	−2.09488	+	6.44739i	−0.179635	+	0.552859i
$137$	9.92347	+	2.10930i	0.847819	+	0.180210i	0.611282	−	0.791413i	$-0.290654\pi$
$137$	9.92347	+	2.10930i	0.847819	+	0.180210i	0.236537	+	0.971622i	$0.423987\pi$
$138$		0			0
$139$	3.34344	−	0.710671i	0.283587	−	0.0602783i	−0.0639220	−	0.997955i	$-0.520361\pi$
$139$	3.34344	−	0.710671i	0.283587	−	0.0602783i	0.347509	+	0.937677i	$0.387028\pi$
$140$	5.43781	+	11.9190i	0.459579	+	1.00734i
$141$		0			0
$142$	0.996739	+	9.48334i	0.0836445	+	0.795824i
$143$	−5.59808			−0.468135
$144$		0			0
$145$	−5.07845	−	0.486862i	−0.421742	−	0.0404317i
$146$	0.141173	−	0.0628541i	0.0116835	−	0.00520184i
$147$		0			0
$148$	3.02678	−	0.643362i	0.248800	−	0.0528840i
$149$	7.01283	+	12.1466i	0.574514	+	0.995087i	0.996094	+	0.0882960i	$0.0281421\pi$
$149$	7.01283	+	12.1466i	0.574514	+	0.995087i	−0.421581	+	0.906791i	$0.638525\pi$
$150$		0			0
$151$	−0.171017	+	0.296210i	−0.0139171	+	0.0241052i	−0.872900	−	0.487899i	$-0.837763\pi$
$151$	−0.171017	+	0.296210i	−0.0139171	+	0.0241052i	0.858983	+	0.512004i	$0.171097\pi$
$152$	−0.967113	+	2.97647i	−0.0784432	+	0.241423i
$153$		0			0
$154$	−5.79467	−	4.21007i	−0.466948	−	0.339257i
$155$	3.11100	+	4.20062i	0.249882	+	0.337402i
$156$		0			0
$157$	6.47430	+	11.2138i	0.516705	+	0.894959i	0.999812	+	0.0193980i	$0.00617496\pi$
$157$	6.47430	+	11.2138i	0.516705	+	0.894959i	−0.483107	+	0.875561i	$0.660492\pi$
$158$	−1.49351	−	0.664953i	−0.118817	−	0.0529008i
$159$		0			0
$160$	−0.134334	−	14.6911i	−0.0106201	−	1.16143i
$161$	−4.69688	+	14.4555i	−0.370166	+	1.13925i
$162$		0			0
$163$	0.350556	+	1.07890i	0.0274577	+	0.0845060i	0.963846	−	0.266459i	$-0.0858536\pi$
$163$	0.350556	+	1.07890i	0.0274577	+	0.0845060i	−0.936389	+	0.350965i	$0.885854\pi$
$164$	5.49068	+	6.09802i	0.428750	+	0.476175i
$165$		0			0
$166$	−1.27687	+	1.41811i	−0.0991046	+	0.110067i
$167$	1.01332	+	0.451160i	0.0784132	+	0.0349118i	0.445569	−	0.895248i	$-0.353002\pi$
$167$	1.01332	+	0.451160i	0.0784132	+	0.0349118i	−0.367155	+	0.930160i	$0.619668\pi$
$168$		0			0
$169$	−2.63822	−	25.1010i	−0.202940	−	1.93085i
$170$	17.6550	+	15.6067i	1.35407	+	1.19698i
$171$		0			0
$172$	−2.54667	−	1.85026i	−0.194182	−	0.141081i
$173$	3.29083	+	3.65484i	0.250197	+	0.277872i	0.855140	−	0.518396i	$-0.173471\pi$
$173$	3.29083	+	3.65484i	0.250197	+	0.277872i	−0.604943	+	0.796269i	$0.706804\pi$
$174$		0			0
$175$	−21.5888	+	0.394845i	−1.63196	+	0.0298475i
$176$	2.20561	+	3.82023i	0.166254	+	0.287961i
$177$		0			0
$178$	−9.99635	+	4.45066i	−0.749258	+	0.333591i
$179$	1.61240	+	1.17148i	0.120516	+	0.0875602i	0.646411	−	0.762990i	$-0.276269\pi$
$179$	1.61240	+	1.17148i	0.120516	+	0.0875602i	−0.525894	+	0.850550i	$0.676269\pi$
$180$		0			0
$181$	7.03514	−	5.11133i	0.522918	−	0.379922i	−0.294784	−	0.955564i	$-0.595248\pi$
$181$	7.03514	−	5.11133i	0.522918	−	0.379922i	0.817702	+	0.575642i	$0.195248\pi$
$182$	24.4631	−	42.3714i	1.81333	−	3.14077i
$183$		0			0
$184$	2.77572	−	3.08275i	0.204629	−	0.227263i
$185$	−1.01471	+	4.99811i	−0.0746028	+	0.367469i
$186$		0			0
$187$	−5.09328	−	1.08261i	−0.372458	−	0.0791683i
$188$	−2.33943	−	7.20003i	−0.170621	−	0.525116i
$189$		0			0
$190$	8.15050	+	7.20490i	0.591300	+	0.522698i
$191$	−22.0101	−	4.67839i	−1.59259	−	0.338516i	−0.675554	−	0.737311i	$-0.736095\pi$
$191$	−22.0101	−	4.67839i	−1.59259	−	0.338516i	−0.917040	+	0.398794i	$0.869429\pi$
$192$		0			0
$193$	−5.49895	−	9.52446i	−0.395823	−	0.685586i	0.597383	−	0.801956i	$-0.296207\pi$
$193$	−5.49895	−	9.52446i	−0.395823	−	0.685586i	−0.993206	+	0.116371i	$0.962874\pi$
$194$	−2.74445	−	1.22191i	−0.197040	−	0.0877279i
$195$		0			0
$196$	14.4382	−	6.42829i	1.03130	−	0.459164i
$197$	4.79140	+	3.48116i	0.341373	+	0.248022i	0.745241	−	0.666795i	$-0.232334\pi$
$197$	4.79140	+	3.48116i	0.341373	+	0.248022i	−0.403868	+	0.914817i	$0.632334\pi$
$198$		0			0
$199$	8.53871			0.605293			0.302646	−	0.953103i	$-0.402130\pi$
$199$	8.53871			0.605293			0.302646	+	0.953103i	$0.402130\pi$
$200$	5.42648	+	2.29806i	0.383710	+	0.162498i
$201$		0			0
$202$	−14.0628	+	2.98914i	−0.989456	+	0.210315i
$203$	−1.02991	+	9.79891i	−0.0722853	+	0.687749i
$204$		0			0
$205$	−12.8236	+	4.29668i	−0.895642	+	0.300093i
$206$	18.5036	−	13.4437i	1.28921	−	0.936664i
$207$		0			0
$208$	−24.3774	+	17.7112i	−1.69027	+	1.22805i
$209$	−2.35134	−	0.499792i	−0.162645	−	0.0345714i
$210$		0			0
$211$	−26.2461	+	5.57878i	−1.80686	+	0.384059i	−0.983127	−	0.182923i	$-0.941444\pi$
$211$	−26.2461	+	5.57878i	−1.80686	+	0.384059i	−0.823730	+	0.566983i	$0.808111\pi$
$212$	3.93251	−	4.36750i	0.270086	−	0.299961i
$213$		0			0
$214$	−7.58680	−	8.42600i	−0.518623	−	0.575989i
$215$	4.46919	−	2.63506i	0.304796	−	0.179710i
$216$		0			0
$217$	8.16717	−	5.93380i	0.554424	−	0.402812i
$218$	−15.8826	+	27.5094i	−1.07570	+	1.86317i
$219$		0			0
$220$	2.72855	−	0.312032i	0.183959	−	0.0210372i
$221$	3.71791	−	35.3735i	0.250094	−	2.37948i
$222$		0			0
$223$	9.91315	+	11.0097i	0.663834	+	0.737262i	0.977188	−	0.212374i	$-0.0681195\pi$
$223$	9.91315	+	11.0097i	0.663834	+	0.737262i	−0.313355	+	0.949636i	$0.601453\pi$
$224$	−28.3738			−1.89580
$225$		0			0
$226$	−10.9864			−0.730802
$227$	8.29081	+	9.20787i	0.550280	+	0.611148i	0.952553	−	0.304372i	$-0.0984465\pi$
$227$	8.29081	+	9.20787i	0.550280	+	0.611148i	−0.402273	+	0.915520i	$0.631780\pi$
$228$		0			0
$229$	−1.65335	+	15.7306i	−0.109256	+	1.03950i	0.793270	+	0.608870i	$0.208377\pi$
$229$	−1.65335	+	15.7306i	−0.109256	+	1.03950i	−0.902526	+	0.430635i	$0.858290\pi$
$230$	−5.98497	−	13.1183i	−0.394637	−	0.864997i
$231$		0			0
$232$	1.34453	−	2.32880i	0.0882729	−	0.152893i
$233$	10.4851	−	7.61788i	0.686903	−	0.499064i	−0.188738	−	0.982028i	$-0.560440\pi$
$233$	10.4851	−	7.61788i	0.686903	−	0.499064i	0.875640	+	0.482964i	$0.160440\pi$
$234$		0			0
$235$	12.4206	+	1.19074i	0.810229	+	0.0776752i
$236$	11.9331	+	13.2531i	0.776782	+	0.862704i
$237$		0			0
$238$	30.4514	−	33.8197i	1.97387	−	2.19221i
$239$	−4.77002	+	1.01390i	−0.308547	+	0.0655837i	−0.359583	−	0.933113i	$-0.617081\pi$
$239$	−4.77002	+	1.01390i	−0.308547	+	0.0655837i	0.0510358	+	0.998697i	$0.483748\pi$
$240$		0			0
$241$	2.51591	+	0.534773i	0.162064	+	0.0344477i	0.288229	−	0.957562i	$-0.406934\pi$
$241$	2.51591	+	0.534773i	0.162064	+	0.0344477i	−0.126165	+	0.992009i	$0.540267\pi$
$242$	15.0897	−	10.9633i	0.970005	−	0.704750i
$243$		0			0
$244$	−15.5164	+	11.2734i	−0.993338	+	0.721702i
$245$	0.238176	+	26.0474i	0.0152165	+	1.66411i
$246$		0			0
$247$	1.71639	−	16.3304i	0.109211	−	1.03908i
$248$	−2.69498	+	0.572836i	−0.171132	+	0.0363751i
$249$		0			0
$250$	14.8408	−	14.1187i	0.938615	−	0.892947i
$251$	−12.4805			−0.787764			−0.393882	−	0.919161i	$-0.628868\pi$
$251$	−12.4805			−0.787764			−0.393882	+	0.919161i	$0.628868\pi$
$252$		0			0
$253$	2.57774	+	1.87283i	0.162061	+	0.117744i
$254$	−20.9176	+	9.31312i	−1.31249	+	0.584357i
$255$		0			0
$256$	19.1530	+	8.52748i	1.19706	+	0.532967i
$257$	6.11612	+	10.5934i	0.381513	+	0.660800i	0.991279	−	0.131782i	$-0.0420699\pi$
$257$	6.11612	+	10.5934i	0.381513	+	0.660800i	−0.609766	+	0.792582i	$0.708737\pi$
$258$		0			0
$259$	9.63444	+	2.04786i	0.598655	+	0.127248i
$260$	4.06797	+	18.3133i	0.252285	+	1.13574i
$261$		0			0
$262$	−2.94030	−	9.04931i	−0.181652	−	0.559068i
$263$	−10.7842	−	2.29225i	−0.664981	−	0.141346i	−0.136959	−	0.990577i	$-0.543733\pi$
$263$	−10.7842	−	2.29225i	−0.664981	−	0.141346i	−0.528022	+	0.849231i	$0.677066\pi$
$264$		0			0
$265$	4.02054	+	8.81252i	0.246980	+	0.541349i
$266$	14.0580	−	15.6130i	0.861953	−	0.957296i
$267$		0			0
$268$	−5.16817	+	8.95154i	−0.315696	+	0.546802i
$269$	−5.11244	+	3.71441i	−0.311711	+	0.226471i	−0.732630	−	0.680627i	$-0.761708\pi$
$269$	−5.11244	+	3.71441i	−0.311711	+	0.226471i	0.420919	+	0.907098i	$0.361708\pi$
$270$		0			0
$271$	−4.89989	−	3.55998i	−0.297647	−	0.216253i	0.428931	−	0.903337i	$-0.358890\pi$
$271$	−4.89989	−	3.55998i	−0.297647	−	0.216253i	−0.726578	+	0.687084i	$0.758890\pi$
$272$	−25.6044	+	11.3998i	−1.55250	+	0.691216i
$273$		0			0
$274$	9.29363	+	16.0970i	0.561449	+	0.972458i
$275$	−1.31978	+	4.32973i	−0.0795860	+	0.261093i
$276$		0			0
$277$	19.9612	+	22.1692i	1.19935	+	1.33202i	0.929369	+	0.369153i	$0.120352\pi$
$277$	19.9612	+	22.1692i	1.19935	+	1.33202i	0.269985	+	0.962865i	$0.412981\pi$
$278$	5.06645	+	3.68099i	0.303865	+	0.220771i
$279$		0			0
$280$	4.53385	−	10.4390i	0.270949	−	0.623852i
$281$	−2.33067	−	22.1749i	−0.139036	−	1.32284i	−0.812214	−	0.583360i	$-0.801738\pi$
$281$	−2.33067	−	22.1749i	−0.139036	−	1.32284i	0.673178	−	0.739481i	$-0.264929\pi$
$282$		0			0
$283$	23.1782	+	10.3196i	1.37780	+	0.613437i	0.956031	−	0.293266i	$-0.0947422\pi$
$283$	23.1782	+	10.3196i	1.37780	+	0.613437i	0.421770	+	0.906703i	$0.361409\pi$
$284$	−4.72483	+	5.24745i	−0.280367	+	0.311379i
$285$		0			0
$286$	−6.86288	−	7.62199i	−0.405810	−	0.450698i
$287$	8.07130	+	24.8409i	0.476434	+	1.46631i
$288$		0			0
$289$	4.97024	−	15.2968i	0.292367	−	0.899814i
$290$	−5.56297	−	7.51137i	−0.326669	−	0.441083i
$291$		0			0
$292$	0.104539	+	0.0465438i	0.00611769	+	0.00272377i
$293$	−8.32257	−	14.4151i	−0.486210	−	0.842140i	0.513664	−	0.857991i	$-0.328288\pi$
$293$	−8.32257	−	14.4151i	−0.486210	−	0.842140i	−0.999874	+	0.0158509i	$0.994954\pi$
$294$		0			0
$295$	−27.8702	+	9.33817i	−1.62267	+	0.543689i
$296$	−2.17479	−	1.58008i	−0.126407	−	0.0918402i
$297$		0			0
$298$	−7.94076	+	24.4392i	−0.459996	+	1.41572i
$299$	−10.8823	+	18.8487i	−0.629341	+	1.09005i
$300$		0			0
$301$	−5.00992	−	8.67743i	−0.288767	−	0.500159i
$302$	−0.612956	+	0.130288i	−0.0352717	+	0.00749723i
$303$		0			0
$304$	−11.8204	+	5.26278i	−0.677946	+	0.301841i
$305$	−6.85469	−	30.8586i	−0.392498	−	1.76696i
$306$		0			0
$307$	−0.293679			−0.0167612			−0.00838058	−	0.999965i	$-0.502668\pi$
$307$	−0.293679			−0.0167612			−0.00838058	+	0.999965i	$0.502668\pi$
$308$	−0.554413	−	5.27489i	−0.0315906	−	0.300565i
$309$		0			0
$310$	−1.90541	+	9.38543i	−0.108220	+	0.533057i
$311$	−19.6920	+	4.18566i	−1.11663	+	0.237347i	−0.729030	−	0.684481i	$-0.760029\pi$
$311$	−19.6920	+	4.18566i	−1.11663	+	0.237347i	−0.387599	+	0.921828i	$0.626695\pi$
$312$		0			0
$313$	−6.40947	−	1.36237i	−0.362285	−	0.0770060i	0.0231731	−	0.999731i	$-0.492623\pi$
$313$	−6.40947	−	1.36237i	−0.362285	−	0.0770060i	−0.385458	+	0.922725i	$0.625956\pi$
$314$	−7.33097	+	22.5624i	−0.413710	+	1.27327i
$315$		0			0
$316$	−0.374100	−	1.15136i	−0.0210448	−	0.0647692i
$317$	−2.51998	−	23.9760i	−0.141536	−	1.34663i	−0.802698	−	0.596385i	$-0.796603\pi$
$317$	−2.51998	−	23.9760i	−0.141536	−	1.34663i	0.661162	−	0.750243i	$-0.270064\pi$
$318$		0			0
$319$	1.88689	+	0.840099i	0.105646	+	0.0470365i
$320$	3.77744	−	3.46428i	0.211165	−	0.193659i
$321$		0			0
$322$	−25.4398	+	11.3265i	−1.41770	+	0.631203i
$323$	4.71974	−	14.5259i	0.262613	−	0.808241i
$324$		0			0
$325$	−30.3558	−	5.87430i	−1.68384	−	0.325847i
$326$	−1.03921	+	1.79996i	−0.0575563	+	0.0996904i
$327$		0			0
$328$	0.745132	−	7.08946i	0.0411431	−	0.391450i
$329$	2.51889	−	23.9656i	0.138871	−	1.32127i
$330$		0			0
$331$	−1.78479	−	16.9811i	−0.0981008	−	0.933367i	−0.927276	−	0.374378i	$-0.877856\pi$
$331$	−1.78479	−	16.9811i	−0.0981008	−	0.933367i	0.829175	−	0.558989i	$-0.188810\pi$
$332$	−1.41307			−0.0775525
$333$		0			0
$334$	0.627995	+	1.93277i	0.0343624	+	0.105756i
$335$	−10.1391	−	13.6903i	−0.553959	−	0.747980i
$336$		0			0
$337$	17.1186	−	19.0122i	0.932512	−	1.03566i	−0.0667700	−	0.997768i	$-0.521269\pi$
$337$	17.1186	−	19.0122i	0.932512	−	1.03566i	0.999282	−	0.0378910i	$-0.0120640\pi$
$338$	30.9417	−	34.3642i	1.68301	−	1.86917i
$339$		0			0
$340$	0.159549	+	17.4486i	0.00865275	+	0.946284i
$341$	−0.653958	−	2.01268i	−0.0354138	−	0.108992i
$342$		0			0
$343$	20.0776			1.08409
$344$	0.285846	+	2.71965i	0.0154118	+	0.146634i
$345$		0			0
$346$	−0.941859	+	8.96119i	−0.0506347	+	0.481757i
$347$	2.76150	−	26.2739i	0.148245	−	1.41046i	−0.627109	−	0.778932i	$-0.715762\pi$
$347$	2.76150	−	26.2739i	0.148245	−	1.41046i	0.775354	−	0.631527i	$-0.217571\pi$
$348$		0			0
$349$	6.45615	−	11.1824i	0.345590	−	0.598579i	−0.639871	−	0.768482i	$-0.721012\pi$
$349$	6.45615	−	11.1824i	0.345590	−	0.598579i	0.985461	+	0.169903i	$0.0543455\pi$
$350$	−27.0040	−	28.9099i	−1.44343	−	1.54530i
$351$		0			0
$352$	−1.83803	+	5.65689i	−0.0979675	+	0.301513i
$353$	−0.971952	+	0.432741i	−0.0517318	+	0.0230325i	−0.432439	−	0.901663i	$-0.642347\pi$
$353$	−0.971952	+	0.432741i	−0.0517318	+	0.0230325i	0.380708	+	0.924695i	$0.375680\pi$
$354$		0			0
$355$	−4.83059	−	10.5880i	−0.256381	−	0.561955i
$356$	−7.40235	−	3.29574i	−0.392324	−	0.174674i
$357$		0			0
$358$	0.381685	+	3.63149i	0.0201727	+	0.191930i
$359$	1.89849	+	5.84296i	0.100199	+	0.308380i	0.988574	−	0.150739i	$-0.0481653\pi$
$359$	1.89849	+	5.84296i	0.100199	+	0.308380i	−0.888375	+	0.459119i	$0.848165\pi$
$360$		0			0
$361$	−3.69243	+	11.3641i	−0.194339	+	0.598112i
$362$	15.5839	+	3.31246i	0.819071	+	0.174099i
$363$		0			0
$364$	35.4384	−	7.53267i	1.85748	−	0.394819i
$365$	−0.139000	+	0.127476i	−0.00727558	+	0.00667242i
$366$		0			0
$367$	1.46186	+	13.9087i	0.0763086	+	0.726028i	0.964056	+	0.265698i	$0.0856024\pi$
$367$	1.46186	+	13.9087i	0.0763086	+	0.726028i	−0.887748	+	0.460330i	$0.847731\pi$
$368$	17.1503			0.894022
$369$		0			0
$370$	−8.04909	+	4.74580i	−0.418452	+	0.246722i
$371$	17.0897	−	7.60884i	0.887255	−	0.395031i
$372$		0			0
$373$	−1.46137	+	0.310623i	−0.0756667	+	0.0160835i	−0.245589	−	0.969374i	$-0.578982\pi$
$373$	−1.46137	+	0.310623i	−0.0756667	+	0.0160835i	0.169923	+	0.985457i	$0.445648\pi$
$374$	−4.77001	−	8.26191i	−0.246652	−	0.427213i
$375$		0			0
$376$	−3.28838	+	5.69564i	−0.169585	+	0.293730i
$377$	−4.35984	+	13.4182i	−0.224543	+	0.691072i
$378$		0			0
$379$	−0.536836	−	0.390034i	−0.0275754	−	0.0200347i	0.573912	−	0.818917i	$-0.305425\pi$
$379$	−0.536836	−	0.390034i	−0.0275754	−	0.0200347i	−0.601488	+	0.798882i	$0.705425\pi$
$380$	0.0736565	+	8.05523i	0.00377850	+	0.413225i
$381$		0			0
$382$	−20.6131	−	35.7030i	−1.05466	−	1.82672i
$383$	−19.2398	−	8.56610i	−0.983106	−	0.437707i	−0.148715	−	0.988880i	$-0.547514\pi$
$383$	−19.2398	−	8.56610i	−0.983106	−	0.437707i	−0.834391	+	0.551173i	$0.814180\pi$
$384$		0			0
$385$	8.33827	+	2.62522i	0.424958	+	0.133794i
$386$	6.22657	−	19.1634i	0.316924	−	0.975391i
$387$		0			0
$388$	−0.687442	−	2.11573i	−0.0348996	−	0.107410i
$389$	10.8617	+	12.0631i	0.550710	+	0.611625i	0.952660	−	0.304036i	$-0.0983344\pi$
$389$	10.8617	+	12.0631i	0.550710	+	0.611625i	−0.401951	+	0.915661i	$0.631668\pi$
$390$		0			0
$391$	−13.5462	+	15.0446i	−0.685060	+	0.760836i
$392$	−12.5428	−	5.58443i	−0.633509	−	0.282056i
$393$		0			0
$394$	1.13422	+	10.7914i	0.0571410	+	0.543660i
$395$	1.98618	+	0.190412i	0.0999357	+	0.00958065i
$396$		0			0
$397$	−13.0288	−	9.46597i	−0.653896	−	0.475083i	0.210700	−	0.977551i	$-0.432426\pi$
$397$	−13.0288	−	9.46597i	−0.653896	−	0.475083i	−0.864596	+	0.502467i	$0.832426\pi$
$398$	10.4679	+	11.6258i	0.524708	+	0.582748i
$399$		0			0
$400$	7.95129	+	23.0298i	0.397565	+	1.15149i
$401$	9.75500	+	16.8962i	0.487142	+	0.843754i	0.999891	−	0.0147845i	$-0.00470621\pi$
$401$	9.75500	+	16.8962i	0.487142	+	0.843754i	−0.512749	+	0.858539i	$0.671373\pi$
$402$		0			0
$403$	13.2059	−	5.87965i	0.657833	−	0.292886i
$404$	−8.61298	−	6.25770i	−0.428512	−	0.311332i
$405$		0			0
$406$	−14.6042	+	10.6106i	−0.724794	+	0.526594i
$407$	1.03239	−	1.78816i	0.0511739	−	0.0886358i
$408$		0			0
$409$	11.4065	−	12.6682i	0.564014	−	0.626401i	−0.391914	−	0.920002i	$-0.628187\pi$
$409$	11.4065	−	12.6682i	0.564014	−	0.626401i	0.955928	+	0.293601i	$0.0948536\pi$
$410$	−21.5710	−	12.1924i	−1.06532	−	0.602142i
$411$		0			0
$412$	16.5665	+	3.52132i	0.816174	+	0.173483i
$413$	17.5417	+	53.9879i	0.863172	+	2.65657i
$414$		0			0
$415$	0.927787	−	2.13620i	0.0455433	−	0.104862i
$416$	−39.7417	−	8.44736i	−1.94850	−	0.414166i
$417$		0			0
$418$	−2.20210	−	3.81415i	−0.107708	−	0.186556i
$419$	28.4147	+	12.6511i	1.38815	+	0.618044i	0.958537	−	0.284969i	$-0.0919832\pi$
$419$	28.4147	+	12.6511i	1.38815	+	0.618044i	0.429613	+	0.903013i	$0.358650\pi$
$420$		0			0
$421$	−23.9324	+	10.6554i	−1.16639	+	0.519311i	−0.896267	−	0.443514i	$-0.853732\pi$
$421$	−23.9324	+	10.6554i	−1.16639	+	0.519311i	−0.270125	+	0.962825i	$0.587065\pi$
$422$	−39.7717	−	28.8959i	−1.93606	−	1.40663i
$423$		0			0
$424$	−5.10556			−0.247948
$425$	−26.4825	−	11.2151i	−1.28459	−	0.544012i
$426$		0			0
$427$	−59.7152	+	12.6929i	−2.88982	+	0.614250i
$428$	0.877628	−	8.35007i	0.0424218	−	0.403616i
$429$		0			0
$430$	9.06667	+	2.85455i	0.437234	+	0.137659i
$431$	−25.1191	+	18.2501i	−1.20995	+	0.879078i	−0.995226	−	0.0975980i	$-0.968884\pi$
$431$	−25.1191	+	18.2501i	−1.20995	+	0.879078i	−0.214721	+	0.976676i	$0.568884\pi$
$432$		0			0
$433$	21.1261	−	15.3490i	1.01526	−	0.737628i	0.0499521	−	0.998752i	$-0.484093\pi$
$433$	21.1261	−	15.3490i	1.01526	−	0.737628i	0.965305	+	0.261124i	$0.0840931\pi$
$434$	18.0915	+	3.84547i	0.868420	+	0.184588i
$435$		0			0
$436$	−23.0082	+	4.89055i	−1.10189	+	0.234215i
$437$	−6.25366	+	6.94539i	−0.299153	+	0.332243i
$438$		0			0
$439$	5.83202	+	6.47712i	0.278347	+	0.309136i	0.866066	−	0.499929i	$-0.166641\pi$
$439$	5.83202	+	6.47712i	0.278347	+	0.309136i	−0.587719	+	0.809065i	$0.699974\pi$
$440$	−1.78753	−	1.58015i	−0.0852172	−	0.0753305i
$441$		0			0
$442$	52.7203	−	38.3036i	2.50765	−	1.82191i
$443$	9.84019	−	17.0437i	0.467521	−	0.809771i	−0.531790	−	0.846876i	$-0.678480\pi$
$443$	9.84019	−	17.0437i	0.467521	−	0.809771i	0.999311	+	0.0371056i	$0.0118138\pi$
$444$		0			0
$445$	9.84248	−	9.02653i	0.466578	−	0.427898i
$446$	−2.83721	+	26.9943i	−0.134346	+	1.27822i
$447$		0			0
$448$	−6.62352	−	7.35617i	−0.312932	−	0.347546i
$449$	4.17634			0.197094			0.0985469	−	0.995132i	$-0.468581\pi$
$449$	4.17634			0.197094			0.0985469	+	0.995132i	$0.468581\pi$
$450$		0			0
$451$	5.47538			0.257826
$452$	−5.44369	−	6.04583i	−0.256050	−	0.284372i
$453$		0			0
$454$	−2.37289	+	22.5765i	−0.111365	+	1.05957i
$455$	−11.8805	+	58.5194i	−0.556966	+	2.74343i
$456$		0			0
$457$	7.74545	−	13.4155i	0.362317	−	0.627551i	−0.626025	−	0.779803i	$-0.715319\pi$
$457$	7.74545	−	13.4155i	0.362317	−	0.627551i	0.988342	+	0.152252i	$0.0486525\pi$
$458$	−23.4447	+	17.0335i	−1.09550	+	0.795925i
$459$		0			0
$460$	4.25353	−	9.79361i	0.198322	−	0.456629i
$461$	−1.52663	−	1.69550i	−0.0711023	−	0.0789671i	0.706544	−	0.707669i	$-0.250253\pi$
$461$	−1.52663	−	1.69550i	−0.0711023	−	0.0789671i	−0.777646	+	0.628702i	$0.783587\pi$
$462$		0			0
$463$	−10.0422	+	11.1530i	−0.466701	+	0.518324i	−0.929841	−	0.367961i	$-0.880056\pi$
$463$	−10.0422	+	11.1530i	−0.466701	+	0.518324i	0.463140	+	0.886285i	$0.346723\pi$
$464$	10.8746	−	2.31146i	0.504840	−	0.107307i
$465$		0			0
$466$	23.2261	+	4.93686i	1.07593	+	0.228696i
$467$	4.68683	−	3.40518i	0.216881	−	0.157573i	−0.474041	−	0.880503i	$-0.657205\pi$
$467$	4.68683	−	3.40518i	0.216881	−	0.157573i	0.690921	+	0.722930i	$0.257205\pi$
$468$		0			0
$469$	−26.6177	+	19.3389i	−1.22909	+	0.892987i
$470$	13.6056	+	18.3709i	0.627579	+	0.847385i
$471$		0			0
$472$	1.61943	−	15.4079i	0.0745403	−	0.709204i
$473$	−2.05456	+	0.436710i	−0.0944687	+	0.0200799i
$474$		0			0
$475$	−12.2258	−	5.17750i	−0.560957	−	0.237560i
$476$	33.6996			1.54462
$477$		0			0
$478$	−7.22820	−	5.25160i	−0.330610	−	0.240202i
$479$	−18.2495	+	8.12520i	−0.833841	+	0.371250i	−0.778830	−	0.627236i	$-0.784186\pi$
$479$	−18.2495	+	8.12520i	−0.833841	+	0.371250i	−0.0550118	+	0.998486i	$0.517520\pi$
$480$		0			0
$481$	12.8848	+	5.73667i	0.587495	+	0.261570i
$482$	2.35623	+	4.08110i	0.107323	+	0.185889i
$483$		0			0
$484$	13.5100	+	2.87165i	0.614093	+	0.130529i
$485$	3.64979	+	0.349898i	0.165728	+	0.0158881i
$486$		0			0
$487$	9.06469	+	27.8982i	0.410760	+	1.26419i	0.915988	+	0.401205i	$0.131408\pi$
$487$	9.06469	+	27.8982i	0.410760	+	1.26419i	−0.505228	+	0.862986i	$0.668592\pi$
$488$	16.2976	+	3.46415i	0.737756	+	0.156815i
$489$		0			0
$490$	−35.1725	+	32.2567i	−1.58893	+	1.45721i
$491$	5.37446	−	5.96895i	0.242546	−	0.269375i	−0.609564	−	0.792736i	$-0.708656\pi$
$491$	5.37446	−	5.96895i	0.242546	−	0.269375i	0.852111	+	0.523362i	$0.175322\pi$
$492$		0			0
$493$	−6.56164	+	11.3651i	−0.295521	+	0.511858i
$494$	24.3386	−	17.6830i	1.09505	−	0.795597i
$495$		0			0
$496$	−9.21545	−	6.69541i	−0.413786	−	0.300633i
$497$	−20.5329	+	9.14186i	−0.921029	+	0.410068i
$498$		0			0
$499$	14.0871	+	24.3995i	0.630623	+	1.09227i	0.987425	+	0.158091i	$0.0505339\pi$
$499$	14.0871	+	24.3995i	0.630623	+	1.09227i	−0.356801	+	0.934180i	$0.616133\pi$
$500$	15.1231	+	1.17118i	0.676326	+	0.0523767i
$501$		0			0
$502$	−15.3003	−	16.9927i	−0.682886	−	0.758422i
$503$	4.88620	+	3.55003i	0.217865	+	0.158288i	0.691365	−	0.722506i	$-0.257010\pi$
$503$	4.88620	+	3.55003i	0.217865	+	0.158288i	−0.473500	+	0.880794i	$0.657010\pi$
$504$		0			0
$505$	15.1151	−	8.91194i	0.672611	−	0.396576i
$506$	0.610199	+	5.80566i	0.0271267	+	0.258093i
$507$		0			0
$508$	−15.4896	−	6.89641i	−0.687240	−	0.305979i
$509$	26.8278	−	29.7953i	1.18912	−	1.32065i	0.253632	−	0.967301i	$-0.418375\pi$
$509$	26.8278	−	29.7953i	1.18912	−	1.32065i	0.935490	−	0.353353i	$-0.114958\pi$
$510$		0			0
$511$	0.243728	+	0.270687i	0.0107819	+	0.0119745i
$512$	6.34397	+	19.5247i	0.280367	+	0.862880i
$513$		0			0
$514$	−6.92539	+	21.3142i	−0.305466	+	0.940128i
$515$	−16.2005	+	22.7323i	−0.713878	+	1.00170i
$516$		0			0
$517$	−4.61485	−	2.05466i	−0.202961	−	0.0903640i
$518$	9.02295	+	15.6282i	0.396446	+	0.686664i
$519$		0			0
$520$	9.45819	−	13.2716i	0.414769	−	0.581998i
$521$	23.0314	+	16.7333i	1.00902	+	0.733098i	0.964004	−	0.265888i	$-0.0856652\pi$
$521$	23.0314	+	16.7333i	1.00902	+	0.733098i	0.0450190	+	0.998986i	$0.485665\pi$
$522$		0			0
$523$	9.53164	−	29.3354i	0.416790	−	1.28275i	−0.493851	−	0.869547i	$-0.664411\pi$
$523$	9.53164	−	29.3354i	0.416790	−	1.28275i	0.910640	−	0.413200i	$-0.135589\pi$
$524$	3.52296	−	6.10194i	0.153901	−	0.266564i
$525$		0			0
$526$	−10.0997	−	17.4932i	−0.440368	−	0.762740i
$527$	13.1522	−	2.79558i	0.572917	−	0.121777i
$528$		0			0
$529$	−9.69475	+	4.31638i	−0.421511	+	0.187669i
$530$	−7.06967	+	16.2777i	−0.307087	+	0.707057i
$531$		0			0
$532$	15.5576			0.674506
$533$	3.90949	+	37.1963i	0.169339	+	1.61115i
$534$		0			0
$535$	12.0469	+	6.80918i	0.520833	+	0.294387i
$536$	8.78325	−	1.86694i	0.379379	−	0.0806394i
$537$		0			0
$538$	−11.3248	−	2.40717i	−0.488248	−	0.103780i
$539$	3.25885	−	10.0297i	0.140368	−	0.432010i
$540$		0			0
$541$	−3.48166	−	10.7154i	−0.149688	−	0.460693i	0.847896	−	0.530163i	$-0.177869\pi$
$541$	−3.48166	−	10.7154i	−0.149688	−	0.460693i	−0.997584	+	0.0694700i	$0.977869\pi$
$542$	−1.15990	−	11.0357i	−0.0498219	−	0.474024i
$543$		0			0
$544$	−34.5244	−	15.3713i	−1.48022	−	0.659038i
$545$	7.71336	−	37.9935i	0.330404	−	1.62746i
$546$		0			0
$547$	−24.5114	+	10.9132i	−1.04803	+	0.466615i	−0.857187	−	0.515005i	$-0.827790\pi$
$547$	−24.5114	+	10.9132i	−1.04803	+	0.466615i	−0.190846	+	0.981620i	$0.561123\pi$
$548$	−4.25330	+	13.0903i	−0.181692	+	0.559190i
$549$		0			0
$550$	−7.51306	+	3.51103i	−0.320358	+	0.149711i
$551$	−3.02921	+	5.24675i	−0.129049	+	0.223519i
$552$		0			0
$553$	0.402797	−	3.83236i	0.0171287	−	0.162968i
$554$	−5.71304	+	54.3559i	−0.242724	+	2.30936i
$555$		0			0
$556$	0.484740	+	4.61199i	0.0205575	+	0.195592i
$557$	35.4517			1.50214			0.751069	−	0.660224i	$-0.229539\pi$
$557$	35.4517			1.50214			0.751069	+	0.660224i	$0.229539\pi$
$558$		0			0
$559$	−4.43371	−	13.6456i	−0.187526	−	0.577145i
$560$	44.6156	−	14.9489i	1.88535	−	0.631705i
$561$		0			0
$562$	27.3347	−	30.3582i	1.15304	−	1.28058i
$563$	−26.2620	+	29.1669i	−1.10681	+	1.22924i	−0.135664	+	0.990755i	$0.543317\pi$
$563$	−26.2620	+	29.1669i	−1.10681	+	1.22924i	−0.971147	+	0.238483i	$0.923350\pi$
$564$		0			0
$565$	12.7139	−	4.25991i	0.534878	−	0.179216i
$566$	14.3644	+	44.2092i	0.603782	+	1.85825i
$567$		0			0
$568$	6.13421			0.257386
$569$	−4.29417	−	40.8563i	−0.180021	−	1.71278i	−0.595645	−	0.803248i	$-0.703103\pi$
$569$	−4.29417	−	40.8563i	−0.180021	−	1.71278i	0.415624	−	0.909537i	$-0.363563\pi$
$570$		0			0
$571$	−4.85569	+	46.1988i	−0.203204	+	1.93336i	0.132070	+	0.991240i	$0.457838\pi$
$571$	−4.85569	+	46.1988i	−0.203204	+	1.93336i	−0.335274	+	0.942121i	$0.608829\pi$
$572$	0.793886	−	7.55332i	0.0331940	−	0.315820i
$573$		0			0
$574$	−23.9270	+	41.4427i	−0.998692	+	1.72979i
$575$	12.0126	+	12.8604i	0.500961	+	0.536318i
$576$		0			0
$577$	0.870205	−	2.67822i	0.0362271	−	0.111496i	−0.931308	−	0.364233i	$-0.881331\pi$
$577$	0.870205	−	2.67822i	0.0362271	−	0.111496i	0.967535	+	0.252738i	$0.0813310\pi$
$578$	26.9204	−	11.9857i	1.11974	−	0.498541i
$579$		0			0
$580$	1.37710	−	6.78316i	0.0571811	−	0.281655i
$581$	−4.10905	−	1.82947i	−0.170472	−	0.0758990i
$582$		0			0
$583$	−0.409914	−	3.90008i	−0.0169769	−	0.161525i
$584$	−0.0307195	−	0.0945450i	−0.00127118	−	0.00391230i
$585$		0			0
$586$	9.42381	−	29.0035i	0.389294	−	1.19812i
$587$	−7.32326	−	1.55661i	−0.302263	−	0.0642480i	0.0542834	−	0.998526i	$-0.482713\pi$
$587$	−7.32326	−	1.55661i	−0.302263	−	0.0642480i	−0.356547	+	0.934278i	$0.616046\pi$
$588$		0			0
$589$	6.07176	−	1.29059i	0.250182	−	0.0531779i
$590$	−46.8814	−	26.4984i	−1.93007	−	1.09092i
$591$		0			0
$592$	−1.16172	−	11.0530i	−0.0477464	−	0.454277i
$593$	−14.1652			−0.581694			−0.290847	−	0.956770i	$-0.593937\pi$
$593$	−14.1652			−0.581694			−0.290847	+	0.956770i	$0.593937\pi$
$594$		0			0
$595$	−22.1262	+	50.9450i	−0.907088	+	2.08854i
$596$	−17.3835	+	7.73965i	−0.712058	+	0.317029i
$597$		0			0
$598$	−39.0043	+	8.29062i	−1.59500	+	0.339028i
$599$	−17.7180	−	30.6885i	−0.723939	−	1.25390i	−0.959409	−	0.282018i	$-0.908996\pi$
$599$	−17.7180	−	30.6885i	−0.723939	−	1.25390i	0.235470	−	0.971882i	$-0.424337\pi$
$600$		0			0
$601$	0.756431	−	1.31018i	0.0308555	−	0.0534433i	−0.850185	−	0.526484i	$-0.823510\pi$
$601$	0.756431	−	1.31018i	0.0308555	−	0.0534433i	0.881041	+	0.473040i	$0.156844\pi$
$602$	5.67282	−	17.4592i	0.231207	−	0.711582i
$603$		0			0
$604$	−0.375414	−	0.272755i	−0.0152754	−	0.0110982i
$605$	−13.2115	+	18.5382i	−0.537124	+	0.753685i
$606$		0			0
$607$	−6.39122	−	11.0699i	−0.259412	−	0.449314i	0.706673	−	0.707540i	$-0.250195\pi$
$607$	−6.39122	−	11.0699i	−0.259412	−	0.449314i	−0.966084	+	0.258226i	$0.916862\pi$
$608$	−15.9384	−	7.09622i	−0.646386	−	0.287790i
$609$		0			0
$610$	33.6118	−	47.1635i	1.36090	−	1.90960i
$611$	10.6630	−	32.8174i	0.431380	−	1.32765i
$612$		0			0
$613$	9.49601	+	29.2257i	0.383540	+	1.18042i	0.937534	+	0.347894i	$0.113103\pi$
$613$	9.49601	+	29.2257i	0.383540	+	1.18042i	−0.553994	+	0.832521i	$0.686897\pi$
$614$	−0.360031	−	0.399855i	−0.0145297	−	0.0161369i
$615$		0			0
$616$	−3.08314	+	3.42418i	−0.124223	+	0.137964i
$617$	27.7851	+	12.3707i	1.11859	+	0.498027i	0.880894	−	0.473314i	$-0.156942\pi$
$617$	27.7851	+	12.3707i	1.11859	+	0.498027i	0.237692	+	0.971341i	$0.423609\pi$
$618$		0			0
$619$	−3.00135	−	28.5560i	−0.120635	−	1.14776i	−0.872558	−	0.488510i	$-0.837540\pi$
$619$	−3.00135	−	28.5560i	−0.120635	−	1.14776i	0.751924	−	0.659250i	$-0.229126\pi$
$620$	−6.10895	+	3.60188i	−0.245341	+	0.144655i
$621$		0			0
$622$	−29.8400	−	21.6800i	−1.19648	−	0.869290i
$623$	−17.2582	−	19.1672i	−0.691436	−	0.767918i
$624$		0			0
$625$	−11.7000	+	22.0932i	−0.467998	+	0.883729i
$626$	−6.00266	−	10.3969i	−0.239915	−	0.415545i
$627$		0			0
$628$	−16.0486	+	7.14530i	−0.640409	+	0.285129i
$629$	10.6135	+	7.71116i	0.423188	+	0.307464i
$630$		0			0
$631$	13.4714	−	9.78757i	0.536289	−	0.389637i	−0.286416	−	0.958105i	$-0.592464\pi$
$631$	13.4714	−	9.78757i	0.536289	−	0.389637i	0.822705	+	0.568468i	$0.192464\pi$
$632$	−0.525847	+	0.910793i	−0.0209171	+	0.0362294i
$633$		0			0
$634$	29.5550	−	32.8241i	1.17378	−	1.30361i
$635$	20.5956	−	18.8882i	0.817313	−	0.749557i
$636$		0			0
$637$	70.4623	+	14.9772i	2.79182	+	0.593419i
$638$	1.16938	+	3.59898i	0.0462962	+	0.142485i
$639$		0			0
$640$	−19.9017	−	1.90794i	−0.786682	−	0.0754178i
$641$	−7.45307	−	1.58420i	−0.294379	−	0.0625721i	0.0583550	−	0.998296i	$-0.481414\pi$
$641$	−7.45307	−	1.58420i	−0.294379	−	0.0625721i	−0.352734	+	0.935724i	$0.614748\pi$
$642$		0			0
$643$	−2.09689	−	3.63192i	−0.0826933	−	0.143229i	0.821713	−	0.569902i	$-0.193019\pi$
$643$	−2.09689	−	3.63192i	−0.0826933	−	0.143229i	−0.904406	+	0.426673i	$0.859686\pi$
$644$	−18.8383	−	8.38736i	−0.742333	−	0.330508i
$645$		0			0
$646$	25.5636	−	11.3817i	1.00579	−	0.447805i
$647$	−40.9094	−	29.7224i	−1.60831	−	1.16851i	−0.868492	−	0.495703i	$-0.834910\pi$
$647$	−40.9094	−	29.7224i	−1.60831	−	1.16851i	−0.739821	−	0.672804i	$-0.765090\pi$
$648$		0			0
$649$	11.8999			0.467112
$650$	−29.2161	−	48.5321i	−1.14595	−	1.90359i
$651$		0			0
$652$	−1.50544	+	0.319992i	−0.0589577	+	0.0125318i
$653$	−3.96661	+	37.7398i	−0.155226	+	1.47687i	0.588560	+	0.808454i	$0.299695\pi$
$653$	−3.96661	+	37.7398i	−0.155226	+	1.47687i	−0.743785	+	0.668419i	$0.766972\pi$
$654$		0			0
$655$	6.91146	+	9.33216i	0.270053	+	0.364638i
$656$	23.8431	−	17.3231i	0.930918	−	0.676352i
$657$		0			0
$658$	35.7181	−	25.9507i	1.39244	−	1.01166i
$659$	−13.1783	−	2.80114i	−0.513355	−	0.109117i	−0.0560518	−	0.998428i	$-0.517851\pi$
$659$	−13.1783	−	2.80114i	−0.513355	−	0.109117i	−0.457303	+	0.889311i	$0.651185\pi$
$660$		0			0
$661$	45.5425	−	9.68036i	1.77140	−	0.376522i	0.797467	−	0.603363i	$-0.206173\pi$
$661$	45.5425	−	9.68036i	1.77140	−	0.376522i	0.973932	+	0.226840i	$0.0728396\pi$
$662$	20.9324	−	23.2478i	0.813561	−	0.903551i
$663$		0			0
$664$	0.821409	+	0.912267i	0.0318769	+	0.0354028i
$665$	−10.2147	+	23.5190i	−0.396109	+	0.912027i
$666$		0			0
$667$	6.49662	−	4.72007i	0.251550	−	0.182762i
$668$	−0.752440	+	1.30327i	−0.0291128	+	0.0504248i
$669$		0			0
$670$	6.20995	−	30.5882i	0.239911	−	1.18172i
$671$	−1.33773	+	12.7276i	−0.0516425	+	0.491345i
$672$		0			0
$673$	4.60871	+	5.11849i	0.177653	+	0.197303i	0.825394	−	0.564557i	$-0.190953\pi$
$673$	4.60871	+	5.11849i	0.177653	+	0.197303i	−0.647741	+	0.761860i	$0.724286\pi$
$674$	46.8721			1.80545
$675$		0			0
$676$	34.2422			1.31701
$677$	24.1380	+	26.8080i	0.927699	+	1.03031i	0.999459	+	0.0328921i	$0.0104718\pi$
$677$	24.1380	+	26.8080i	0.927699	+	1.03031i	−0.0717600	+	0.997422i	$0.522862\pi$
$678$		0			0
$679$	0.740175	−	7.04229i	0.0284053	−	0.270258i
$680$	11.1719	−	10.2457i	0.428423	−	0.392906i
$681$		0			0
$682$	1.93862	−	3.35780i	0.0742338	−	0.128577i
$683$	27.9970	−	20.3410i	1.07127	−	0.778326i	0.0951333	−	0.995465i	$-0.469672\pi$
$683$	27.9970	−	20.3410i	1.07127	−	0.778326i	0.976141	+	0.217138i	$0.0696723\pi$
$684$		0			0
$685$	−16.9965	−	15.0246i	−0.649404	−	0.574062i
$686$	24.6139	+	27.3365i	0.939761	+	1.04371i
$687$		0			0
$688$	−7.56513	+	8.40192i	−0.288418	+	0.320320i
$689$	26.2020	−	5.56940i	0.998215	−	0.212177i
$690$		0			0
$691$	47.8971	+	10.1808i	1.82209	+	0.387297i	0.986725	−	0.162398i	$-0.0519228\pi$
$691$	47.8971	+	10.1808i	1.82209	+	0.387297i	0.835365	+	0.549695i	$0.185256\pi$
$692$	−5.39806	+	3.92192i	−0.205203	+	0.149089i
$693$		0			0
$694$	39.1584	−	28.4502i	1.48643	−	1.07996i
$695$	−7.29040	−	2.29531i	−0.276540	−	0.0870661i
$696$		0			0
$697$	−3.63642	+	34.5983i	−0.137739	+	1.31050i
$698$	23.1401	−	4.91857i	0.875864	−	0.186171i
$699$		0			0
$700$	2.52884	−	29.1851i	0.0955811	−	1.10309i
$701$	−6.00618			−0.226850			−0.113425	−	0.993547i	$-0.536182\pi$
$701$	−6.00618			−0.226850			−0.113425	+	0.993547i	$0.536182\pi$
$702$		0			0
$703$	4.89977	+	3.55989i	0.184798	+	0.134264i
$704$	−1.89567	+	0.844005i	−0.0714456	+	0.0318096i
$705$		0			0
$706$	−1.78074	−	0.792838i	−0.0670191	−	0.0298388i
$707$	−16.9438	−	29.3476i	−0.637239	−	1.10373i
$708$		0			0
$709$	37.3871	+	7.94688i	1.40410	+	0.298451i	0.846824	−	0.531874i	$-0.178512\pi$
$709$	37.3871	+	7.94688i	1.40410	+	0.298451i	0.557279	+	0.830325i	$0.311845\pi$
$710$	8.49405	−	19.5573i	0.318776	−	0.733972i
$711$		0			0
$712$	2.17523	+	6.69467i	0.0815202	+	0.250893i
$713$	−8.04793	−	1.71064i	−0.301397	−	0.0640640i
$714$		0			0
$715$	10.8974	+	6.15946i	0.407540	+	0.230351i
$716$	−1.80930	+	2.00943i	−0.0676166	+	0.0750959i
$717$		0			0
$718$	−5.62798	+	9.74795i	−0.210035	+	0.363790i
$719$	18.5111	−	13.4491i	0.690348	−	0.501567i	−0.186426	−	0.982469i	$-0.559691\pi$
$719$	18.5111	−	13.4491i	0.690348	−	0.501567i	0.876775	+	0.480901i	$0.159691\pi$
$720$		0			0
$721$	43.6145	+	31.6878i	1.62429	+	1.18011i
$722$	−19.9994	+	8.90430i	−0.744300	+	0.331384i
$723$		0			0
$724$	5.89888	+	10.2172i	0.219230	+	0.379718i
$725$	9.35020	+	6.53547i	0.347258	+	0.242721i
$726$		0			0
$727$	12.1687	+	13.5147i	0.451311	+	0.501231i	0.925267	−	0.379317i	$-0.123841\pi$
$727$	12.1687	+	13.5147i	0.451311	+	0.501231i	−0.473956	+	0.880549i	$0.657174\pi$
$728$	−25.4631	−	18.5000i	−0.943725	−	0.685657i
$729$		0			0
$730$	−0.343969	−	0.0329756i	−0.0127309	−	0.00122048i
$731$	−1.39500	−	13.2725i	−0.0515959	−	0.490902i
$732$		0			0
$733$	−29.3911	−	13.0857i	−1.08558	−	0.483333i	−0.215634	−	0.976474i	$-0.569182\pi$
$733$	−29.3911	−	13.0857i	−1.08558	−	0.483333i	−0.869949	+	0.493141i	$0.835849\pi$
$734$	−17.1451	+	19.0415i	−0.632836	+	0.702836i
$735$		0			0
$736$	15.4737	+	17.1853i	0.570369	+	0.633459i
$737$	2.13132	+	6.55953i	0.0785082	+	0.241623i
$738$		0			0
$739$	−9.10517	+	28.0228i	−0.334939	+	1.03084i	0.631813	+	0.775121i	$0.282311\pi$
$739$	−9.10517	+	28.0228i	−0.334939	+	1.03084i	−0.966752	+	0.255716i	$0.917689\pi$
$740$	−6.59991	−	2.07792i	−0.242617	−	0.0763857i
$741$		0			0
$742$	31.3106	+	13.9404i	1.14945	+	0.511768i
$743$	−3.85790	−	6.68207i	−0.141533	−	0.245142i	0.786541	−	0.617538i	$-0.211870\pi$
$743$	−3.85790	−	6.68207i	−0.141533	−	0.245142i	−0.928074	+	0.372396i	$0.878536\pi$
$744$		0			0
$745$	−0.286763	−	31.3610i	−0.0105062	−	1.14898i
$746$	−2.21447	−	1.60890i	−0.0810773	−	0.0589061i
$747$		0			0
$748$	2.18303	−	6.71868i	0.0798196	−	0.245659i
$749$	13.3626	−	23.1448i	0.488260	−	0.845691i
$750$		0			0
$751$	−26.7485	−	46.3297i	−0.976066	−	1.69060i	−0.676372	−	0.736560i	$-0.736449\pi$
$751$	−26.7485	−	46.3297i	−0.976066	−	1.69060i	−0.299694	−	0.954035i	$-0.596885\pi$
$752$	−26.5964	+	5.65324i	−0.969871	+	0.206153i
$753$		0			0
$754$	−23.6143	+	10.5137i	−0.859981	+	0.382888i
$755$	0.658821	−	0.388445i	0.0239770	−	0.0141370i
$756$		0			0
$757$	−10.3719			−0.376971			−0.188486	−	0.982076i	$-0.560358\pi$
$757$	−10.3719			−0.376971			−0.188486	+	0.982076i	$0.560358\pi$
$758$	−0.127079	−	1.20908i	−0.00461573	−	0.0439157i
$759$		0			0
$760$	5.15757	−	4.73000i	0.187085	−	0.171575i
$761$	22.3424	−	4.74901i	0.809910	−	0.172152i	0.215698	−	0.976460i	$-0.430797\pi$
$761$	22.3424	−	4.74901i	0.809910	−	0.172152i	0.594212	+	0.804309i	$0.297464\pi$
$762$		0			0
$763$	−73.2368	−	15.5670i	−2.65135	−	0.563562i
$764$	9.43375	−	29.0341i	0.341301	−	1.05042i
$765$		0			0
$766$	−11.9236	−	36.6972i	−0.430818	−	1.32592i
$767$	8.49667	+	80.8404i	0.306797	+	2.91898i
$768$		0			0
$769$	17.1427	+	7.63243i	0.618182	+	0.275232i	0.691840	−	0.722051i	$-0.256800\pi$
$769$	17.1427	+	7.63243i	0.618182	+	0.275232i	−0.0736574	+	0.997284i	$0.523467\pi$
$770$	6.64783	+	14.5712i	0.239571	+	0.525111i
$771$		0			0
$772$	13.6309	−	6.06887i	0.490587	−	0.218423i
$773$	−11.9727	+	36.8481i	−0.430627	+	1.32533i	0.466875	+	0.884323i	$0.345380\pi$
$773$	−11.9727	+	36.8481i	−0.430627	+	1.32533i	−0.897502	+	0.441010i	$0.854620\pi$
$774$		0			0
$775$	−1.43413	−	11.6000i	−0.0515154	−	0.416686i
$776$	−0.966290	+	1.67366i	−0.0346878	+	0.0600810i
$777$		0			0
$778$	−3.10869	+	29.5772i	−0.111452	+	1.06039i
$779$	−1.67877	+	15.9724i	−0.0601482	+	0.572272i
$780$		0			0
$781$	0.492503	+	4.68586i	0.0176232	+	0.167673i
$782$	−37.0905			−1.32635
$783$		0			0
$784$	−17.5410	−	53.9858i	−0.626466	−	1.92806i
$785$	−0.264742	−	28.9527i	−0.00944904	−	1.03337i
$786$		0			0
$787$	5.79895	−	6.44039i	0.206710	−	0.229575i	−0.630871	−	0.775888i	$-0.717302\pi$
$787$	5.79895	−	6.44039i	0.206710	−	0.229575i	0.837581	+	0.546313i	$0.183969\pi$
$788$	−5.37651	+	5.97122i	−0.191530	+	0.212716i
$789$		0			0
$790$	2.17568	+	2.93770i	0.0774071	+	0.104519i
$791$	−8.00222	−	24.6283i	−0.284526	−	0.875682i
$792$		0			0
$793$	−87.4187			−3.10433
$794$	−3.08416	−	29.3439i	−0.109453	−	1.04137i
$795$		0			0
$796$	−1.21091	+	11.5210i	−0.0429195	+	0.408352i
$797$	−1.80598	+	17.1828i	−0.0639712	+	0.608645i	0.914831	+	0.403837i	$0.132324\pi$
$797$	−1.80598	+	17.1828i	−0.0639712	+	0.608645i	−0.978802	+	0.204808i	$0.934343\pi$
$798$		0			0
$799$	16.0481	−	27.7961i	0.567740	−	0.983354i
$800$	−15.9028	+	28.7460i	−0.562250	+	1.01632i
$801$		0			0
$802$	−11.0458	+	33.9954i	−0.390040	+	1.20042i
$803$	0.0697555	−	0.0310571i	0.00246162	−	0.00109598i
$804$		0			0
$805$	25.0482	−	22.9717i	0.882834	−	0.809646i
$806$	24.1950	+	10.7723i	0.852231	+	0.379438i
$807$		0			0
$808$	0.966750	+	9.19801i	0.0340101	+	0.323585i
$809$	7.51279	+	23.1220i	0.264136	+	0.812925i	0.991891	+	0.127089i	$0.0405634\pi$
$809$	7.51279	+	23.1220i	0.264136	+	0.812925i	−0.727756	+	0.685836i	$0.759437\pi$
$810$		0			0
$811$	−6.22416	+	19.1560i	−0.218560	+	0.672658i	0.780322	+	0.625378i	$0.215055\pi$
$811$	−6.22416	+	19.1560i	−0.218560	+	0.672658i	−0.998882	+	0.0472798i	$0.984945\pi$
$812$	−13.0753	−	2.77925i	−0.458854	−	0.0975324i
$813$		0			0
$814$	3.70030	−	0.786522i	0.129695	−	0.0275676i
$815$	0.504689	−	2.48593i	0.0176785	−	0.0870785i
$816$		0			0
$817$	−0.644008	−	6.12733i	−0.0225310	−	0.214368i
$818$	31.2318			1.09199
$819$		0			0
$820$	−3.97881	−	17.9119i	−0.138946	−	0.625510i
$821$	28.4737	−	12.6773i	0.993739	−	0.442441i	0.155554	−	0.987827i	$-0.450284\pi$
$821$	28.4737	−	12.6773i	0.993739	−	0.442441i	0.838185	+	0.545386i	$0.183617\pi$
$822$		0			0
$823$	7.36472	−	1.56542i	0.256718	−	0.0545671i	−0.0777548	−	0.996973i	$-0.524775\pi$
$823$	7.36472	−	1.56542i	0.256718	−	0.0545671i	0.334473	+	0.942405i	$0.391442\pi$
$824$	−7.35666	−	12.7421i	−0.256281	−	0.443892i
$825$		0			0
$826$	−52.0016	+	90.0694i	−1.80937	+	3.13391i
$827$	11.4110	−	35.1194i	0.396798	−	1.22122i	−0.530754	−	0.847526i	$-0.678091\pi$
$827$	11.4110	−	35.1194i	0.396798	−	1.22122i	0.927552	−	0.373694i	$-0.121909\pi$
$828$		0			0
$829$	37.5208	+	27.2605i	1.30315	+	0.946796i	0.999981	−	0.00614051i	$-0.00195460\pi$
$829$	37.5208	+	27.2605i	1.30315	+	0.946796i	0.303171	+	0.952936i	$0.401955\pi$
$830$	4.04592	−	1.35562i	0.140436	−	0.0470544i
$831$		0			0
$832$	−7.08716	−	12.2753i	−0.245703	−	0.425570i
$833$	61.2121	+	27.2534i	2.12087	+	0.944273i
$834$		0			0
$835$	−1.47616	−	1.99318i	−0.0510848	−	0.0689769i
$836$	1.00781	−	3.10171i	0.0348558	−	0.107275i
$837$		0			0
$838$	17.6097	+	54.1971i	0.608317	+	1.87221i
$839$	1.71729	+	1.90725i	0.0592875	+	0.0658454i	0.772059	−	0.635551i	$-0.219227\pi$
$839$	1.71729	+	1.90725i	0.0592875	+	0.0658454i	−0.712771	+	0.701396i	$0.752560\pi$
$840$		0			0
$841$	−15.9216	+	17.6827i	−0.549021	+	0.609749i
$842$	−43.8472	−	19.5220i	−1.51107	−	0.672774i
$843$		0			0
$844$	−3.80522	−	36.2043i	−0.130981	−	1.24620i
$845$	−22.4825	+	51.7652i	−0.773422	+	1.78078i
$846$		0			0
$847$	35.5677	+	25.8414i	1.22212	+	0.887923i
$848$	−14.1241	−	15.6864i	−0.485024	−	0.538673i
$849$		0			0
$850$	−17.1960	−	49.8059i	−0.589819	−	1.70833i
$851$	−4.01382	−	6.95215i	−0.137592	−	0.238316i
$852$		0			0
$853$	0.319722	−	0.142349i	0.0109471	−	0.00487395i	−0.401256	−	0.915966i	$-0.631426\pi$
$853$	0.319722	−	0.142349i	0.0109471	−	0.00487395i	0.412203	+	0.911092i	$0.364759\pi$
$854$	−90.4887	−	65.7439i	−3.09646	−	2.24971i
$855$		0			0
$856$	−5.90089	+	4.28725i	−0.201688	+	0.146535i
$857$	−0.706787	+	1.22419i	−0.0241434	+	0.0418175i	−0.877845	−	0.478945i	$-0.841019\pi$
$857$	−0.706787	+	1.22419i	−0.0241434	+	0.0418175i	0.853701	+	0.520763i	$0.174352\pi$
$858$		0			0
$859$	16.3422	−	18.1499i	0.557589	−	0.619265i	−0.396773	−	0.917917i	$-0.629870\pi$
$859$	16.3422	−	18.1499i	0.557589	−	0.619265i	0.954362	+	0.298651i	$0.0965368\pi$
$860$	2.92162	+	6.40383i	0.0996264	+	0.218369i
$861$		0			0
$862$	−55.6427	−	11.8272i	−1.89520	−	0.402837i
$863$	−11.4015	−	35.0901i	−0.388111	−	1.19448i	−0.934198	−	0.356754i	$-0.883883\pi$
$863$	−11.4015	−	35.0901i	−0.388111	−	1.19448i	0.546087	−	0.837728i	$-0.316117\pi$
$864$		0			0
$865$	−2.38470	−	10.7355i	−0.0810821	−	0.365017i
$866$	46.7976	+	9.94713i	1.59025	+	0.338017i
$867$		0			0
$868$	6.84808	+	11.8612i	0.232439	+	0.402596i
$869$	−0.737964	−	0.328563i	−0.0250337	−	0.0111457i
$870$		0			0
$871$	−43.0395	+	19.1624i	−1.45834	+	0.649294i
$872$	16.5318	+	12.0111i	0.559838	+	0.406746i
$873$		0			0
$874$	−17.1230			−0.579194
$875$	42.4599	+	22.9851i	1.43541	+	0.777038i
$876$		0			0
$877$	37.1903	−	7.90505i	1.25583	−	0.266934i	0.468497	−	0.883465i	$-0.344796\pi$
$877$	37.1903	−	7.90505i	1.25583	−	0.266934i	0.787331	+	0.616531i	$0.211462\pi$
$878$	−1.66916	+	15.8810i	−0.0563316	+	0.535959i
$879$		0			0
$880$	−0.0901901	−	9.86339i	−0.00304031	−	0.332495i
$881$	−34.5989	+	25.1376i	−1.16567	+	0.846907i	−0.990484	−	0.137629i	$-0.956052\pi$
$881$	−34.5989	+	25.1376i	−1.16567	+	0.846907i	−0.175183	+	0.984536i	$0.556052\pi$
$882$		0			0
$883$	−33.9890	+	24.6945i	−1.14382	+	0.831036i	−0.987647	−	0.156694i	$-0.949916\pi$
$883$	−33.9890	+	24.6945i	−1.14382	+	0.831036i	−0.156175	+	0.987729i	$0.549916\pi$
$884$	47.2012	+	10.0329i	1.58755	+	0.337444i
$885$		0			0
$886$	35.2691	−	7.49667i	1.18489	−	0.251856i
$887$	18.3209	−	20.3474i	0.615155	−	0.683199i	−0.352402	−	0.935849i	$-0.614635\pi$
$887$	18.3209	−	20.3474i	0.615155	−	0.683199i	0.967558	+	0.252649i	$0.0813018\pi$
$888$		0			0
$889$	−36.1133	−	40.1079i	−1.21120	−	1.34517i
$890$	24.3562	+	2.33498i	0.816422	+	0.0782689i
$891$		0			0
$892$	−16.2608	+	11.8142i	−0.544453	+	0.395569i
$893$	7.40867	−	12.8322i	0.247922	−	0.429413i
$894$		0			0
$895$	−1.84980	−	4.05452i	−0.0618319	−	0.135528i
$896$	−4.03604	+	38.4004i	−0.134835	+	1.28287i
$897$		0			0
$898$	5.11992	+	5.68625i	0.170854	+	0.189753i
$899$	−5.33355			−0.177884
$900$		0			0
$901$	24.9163			0.830083
$902$	6.71246	+	7.45494i	0.223501	+	0.248223i
$903$		0			0
$904$	−0.738755	+	7.02879i	−0.0245706	+	0.233774i
$905$	−19.3187	+	2.20925i	−0.642176	+	0.0734381i
$906$		0			0
$907$	−1.09709	+	1.90022i	−0.0364283	+	0.0630956i	−0.883665	−	0.468120i	$-0.844931\pi$
$907$	−1.09709	+	1.90022i	−0.0364283	+	0.0630956i	0.847236	+	0.531216i	$0.178265\pi$
$908$	−13.5997	+	9.88073i	−0.451321	+	0.327904i
$909$		0			0
$910$	−94.2411	+	55.5652i	−3.12406	+	1.84197i
$911$	7.31104	+	8.11974i	0.242226	+	0.269019i	0.851983	−	0.523569i	$-0.175400\pi$
$911$	7.31104	+	8.11974i	0.242226	+	0.269019i	−0.609757	+	0.792588i	$0.708733\pi$
$912$		0			0
$913$	−0.630921	+	0.700709i	−0.0208805	+	0.0231901i
$914$	27.7612	−	5.90082i	0.918257	−	0.195182i
$915$		0			0
$916$	−20.9903	−	4.46163i	−0.693539	−	0.147416i
$917$	18.1443	−	13.1826i	0.599178	−	0.435329i
$918$		0			0
$919$	−13.1150	+	9.52858i	−0.432623	+	0.314319i	−0.782697	−	0.622403i	$-0.786156\pi$
$919$	−13.1150	+	9.52858i	−0.432623	+	0.314319i	0.350074	+	0.936722i	$0.386156\pi$
$920$	−8.79520	+	2.94691i	−0.289969	+	0.0971568i
$921$		0			0
$922$	0.436932	−	4.15713i	0.0143896	−	0.136908i
$923$	−31.4811	+	6.69151i	−1.03621	+	0.220254i
$924$		0			0
$925$	7.47459	−	8.61303i	0.245763	−	0.283195i
$926$	−27.4963			−0.903586
$927$		0			0
$928$	12.1277	+	8.81128i	0.398111	+	0.289244i
$929$	10.7595	−	4.79042i	0.353007	−	0.157169i	−0.222570	−	0.974917i	$-0.571444\pi$
$929$	10.7595	−	4.79042i	0.353007	−	0.157169i	0.575576	+	0.817748i	$0.304778\pi$
$930$		0			0
$931$	28.2588	+	12.5816i	0.926146	+	0.412347i
$932$	8.79165	+	15.2276i	0.287980	+	0.498796i
$933$		0			0
$934$	10.3820	+	2.20677i	0.339710	+	0.0722077i
$935$	8.72358	+	7.71149i	0.285291	+	0.252193i
$936$		0			0
$937$	−18.1426	−	55.8372i	−0.592693	−	1.82412i	−0.565888	−	0.824482i	$-0.691466\pi$
$937$	−18.1426	−	55.8372i	−0.592693	−	1.82412i	−0.0268057	−	0.999641i	$-0.508534\pi$
$938$	−58.9622	−	12.5328i	−1.92518	−	0.409211i
$939$		0			0
$940$	−3.36804	+	16.5899i	−0.109853	+	0.541101i
$941$	−36.2928	+	40.3072i	−1.18311	+	1.31398i	−0.244238	+	0.969715i	$0.578538\pi$
$941$	−36.2928	+	40.3072i	−1.18311	+	1.31398i	−0.938873	+	0.344262i	$0.888129\pi$
$942$		0			0
$943$	10.6438	−	18.4356i	0.346610	−	0.600346i
$944$	51.8194	−	37.6490i	1.68658	−	1.22537i
$945$		0			0
$946$	−3.11335	−	2.26198i	−0.101224	−	0.0735434i
$947$	6.86583	−	3.05687i	0.223110	−	0.0993348i	−0.292138	−	0.956376i	$-0.594367\pi$
$947$	6.86583	−	3.05687i	0.223110	−	0.0993348i	0.515248	+	0.857041i	$0.327700\pi$
$948$		0			0
$949$	0.260789	+	0.451699i	0.00846556	+	0.0146628i
$950$	−7.93863	−	22.9931i	−0.257563	−	0.745996i
$951$		0			0
$952$	−19.5893	−	21.7561i	−0.634893	−	0.705120i
$953$	−23.0950	−	16.7795i	−0.748119	−	0.543540i	0.147124	−	0.989118i	$-0.452998\pi$
$953$	−23.0950	−	16.7795i	−0.748119	−	0.543540i	−0.895243	+	0.445578i	$0.852998\pi$
$954$		0			0
$955$	37.6980	+	33.3244i	1.21988	+	1.07835i
$956$	−0.691569	−	6.57984i	−0.0223669	−	0.212807i
$957$		0			0
$958$	−33.4355	−	14.8864i	−1.08025	−	0.480959i
$959$	−29.3157	+	32.5584i	−0.946654	+	1.05137i
$960$		0			0
$961$	−17.0864	−	18.9764i	−0.551176	−	0.612143i
$962$	7.98519	+	24.5759i	0.257453	+	0.792358i
$963$		0			0
$964$	−1.07834	+	3.31880i	−0.0347311	+	0.106891i
$965$	0.224859	+	24.5910i	0.00723846	+	0.791613i
$966$		0			0
$967$	23.8286	+	10.6092i	0.766277	+	0.341168i	0.752375	−	0.658735i	$-0.228908\pi$
$967$	23.8286	+	10.6092i	0.766277	+	0.341168i	0.0139016	+	0.999903i	$0.495575\pi$
$968$	−5.99937	−	10.3912i	−0.192827	−	0.333986i
$969$		0			0
$970$	3.99800	+	5.39828i	0.128368	+	0.173328i
$971$	−45.5475	−	33.0922i	−1.46169	−	1.06198i	−0.982919	−	0.184037i	$-0.941083\pi$
$971$	−45.5475	−	33.0922i	−1.46169	−	1.06198i	−0.478769	−	0.877941i	$-0.658917\pi$
$972$		0			0
$973$	−4.56144	+	14.0387i	−0.146233	+	0.450060i
$974$	−26.8718	+	46.5434i	−0.861029	+	1.49135i
$975$		0			0
$976$	34.4425	+	59.6562i	1.10248	+	1.90955i
$977$	−11.7376	+	2.49491i	−0.375520	+	0.0798193i	−0.391805	−	0.920048i	$-0.628149\pi$
$977$	−11.7376	+	2.49491i	−0.375520	+	0.0798193i	0.0162853	+	0.999867i	$0.494816\pi$
$978$		0			0
$979$	−4.93934	+	2.19914i	−0.157862	+	0.0702847i
$980$	−35.1788	−	3.37252i	−1.12374	−	0.107731i
$981$		0			0
$982$	14.7157			0.469597
$983$	−4.33583	−	41.2526i	−0.138291	−	1.31575i	−0.814982	−	0.579487i	$-0.803253\pi$
$983$	−4.33583	−	41.2526i	−0.138291	−	1.31575i	0.676690	−	0.736268i	$-0.263414\pi$
$984$		0			0
$985$	−5.49685	−	12.0484i	−0.175144	−	0.383895i
$986$	−23.5181	+	4.99894i	−0.748970	+	0.159199i
$987$		0			0
$988$	21.7907	+	4.63175i	0.693253	+	0.147356i
$989$	−2.52353	+	7.76664i	−0.0802437	+	0.246965i
$990$		0			0
$991$	−13.7209	−	42.2286i	−0.435858	−	1.34143i	−0.892204	−	0.451632i	$-0.850842\pi$
$991$	−13.7209	−	42.2286i	−0.435858	−	1.34143i	0.456346	−	0.889802i	$-0.349158\pi$
$992$	−1.60548	−	15.2751i	−0.0509741	−	0.484986i
$993$		0			0
$994$	−37.6190	−	16.7491i	−1.19320	−	0.531248i
$995$	−16.6217	−	9.39498i	−0.526944	−	0.297841i
$996$		0			0
$997$	−27.3540	+	12.1788i	−0.866310	+	0.385706i	−0.791264	−	0.611474i	$-0.790577\pi$
$997$	−27.3540	+	12.1788i	−0.866310	+	0.385706i	−0.0750454	+	0.997180i	$0.523910\pi$
$998$	−15.9510	+	49.0922i	−0.504921	+	1.55399i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.46.23		224
3.2	odd	2		225.2.q.a.196.6	yes	224
9.4	even	3	inner	675.2.r.a.496.6		224
9.5	odd	6		225.2.q.a.121.23	yes	224
25.6	even	5	inner	675.2.r.a.181.6		224
75.56	odd	10		225.2.q.a.106.23	yes	224
225.31	even	15	inner	675.2.r.a.631.23		224
225.131	odd	30		225.2.q.a.31.6	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.6	✓	224	225.131	odd	30
225.2.q.a.106.23	yes	224	75.56	odd	10
225.2.q.a.121.23	yes	224	9.5	odd	6
225.2.q.a.196.6	yes	224	3.2	odd	2
675.2.r.a.46.23		224	1.1	even	1	trivial
675.2.r.a.181.6		224	25.6	even	5	inner
675.2.r.a.496.6		224	9.4	even	3	inner
675.2.r.a.631.23		224	225.31	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22593 + 1.36154i) q^{2} +(-0.141814 + 1.34927i) q^{4} +(-1.94663 - 1.10028i) q^{5} +(-2.15924 + 3.73991i) q^{7} +(0.953512 - 0.692767i) q^{8} +(-0.888371 - 3.99929i) q^{10} +(0.605752 + 0.672756i) q^{11} +(-4.13776 + 4.59545i) q^{13} +(-7.73912 + 1.64500i) q^{14} +(4.76628 + 1.01310i) q^{16} +(-4.65336 + 3.38087i) q^{17} +(-2.14825 + 1.56079i) q^{19} +(1.76064 - 2.47050i) q^{20} +(-0.173370 + 1.64951i) q^{22} +(3.44271 - 0.731772i) q^{23} +(2.57876 + 4.28369i) q^{25} -11.3295 q^{26} +(-4.73994 - 3.44377i) q^{28} +(2.08431 - 0.927996i) q^{29} +(-2.13557 - 0.950816i) q^{31} +(3.28516 + 5.69007i) q^{32} +(-10.3079 - 2.19101i) q^{34} +(8.31820 - 4.90447i) q^{35} +(-0.704813 - 2.16919i) q^{37} +(-4.75869 - 1.01149i) q^{38} +(-2.61838 + 0.299432i) q^{40} +(4.04708 - 4.49473i) q^{41} +(-1.16011 + 2.00937i) q^{43} +(-0.993634 + 0.721917i) q^{44} +(5.21688 + 3.79028i) q^{46} +(-5.09769 + 2.26964i) q^{47} +(-5.82462 - 10.0885i) q^{49} +(-2.67101 + 8.76261i) q^{50} +(-5.61371 - 6.23466i) q^{52} +(-3.50455 - 2.54621i) q^{53} +(-0.438957 - 1.97611i) q^{55} +(0.532027 + 5.06190i) q^{56} +(3.81874 + 1.70021i) q^{58} +(8.79570 - 9.76861i) q^{59} +(9.45934 + 10.5057i) q^{61} +(-1.32349 - 4.07330i) q^{62} +(-0.708321 + 2.17999i) q^{64} +(13.1110 - 4.39296i) q^{65} +(6.96006 + 3.09882i) q^{67} +(-3.90179 - 6.75810i) q^{68} +(16.8752 + 5.31299i) q^{70} +(4.21064 + 3.05921i) q^{71} +(0.0260643 - 0.0802177i) q^{73} +(2.08938 - 3.61892i) q^{74} +(-1.80128 - 3.11991i) q^{76} +(-3.82401 + 0.812818i) q^{77} +(-0.815175 + 0.362939i) q^{79} +(-8.16350 - 7.21639i) q^{80} +11.0812 q^{82} +(0.108872 + 1.03584i) q^{83} +(12.7783 - 1.46130i) q^{85} +(-4.15806 + 0.883823i) q^{86} +(1.04365 + 0.221836i) q^{88} +(-1.84560 + 5.68017i) q^{89} +(-8.25216 - 25.3975i) q^{91} +(0.499132 + 4.74893i) q^{92} +(-9.33964 - 4.15827i) q^{94} +(5.89916 - 0.674617i) q^{95} +(-1.49796 + 0.666933i) q^{97} +(6.59533 - 20.2983i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

L-functions

Modular forms

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