LMFDB - Embedded newform 460.2.g.c.459.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(459,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("460.459");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.g (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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			459.5
Character	$\chi$	$=$	460.459
Dual form			460.2.g.c.459.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28797 - 0.584066i) q^{2} +2.56426 q^{3} +(1.31773 + 1.50452i) q^{4} +(-0.662839 - 2.13557i) q^{5} +(-3.30269 - 1.49770i) q^{6} -1.62105i q^{7} +(-0.818466 - 2.70742i) q^{8} +3.57544 q^{9} +O(q^{10})$	\(q+(-1.28797 - 0.584066i) q^{2} +2.56426 q^{3} +(1.31773 + 1.50452i) q^{4} +(-0.662839 - 2.13557i) q^{5} +(-3.30269 - 1.49770i) q^{6} -1.62105i q^{7} +(-0.818466 - 2.70742i) q^{8} +3.57544 q^{9} +(-0.393594 + 3.13769i) q^{10} +1.26237 q^{11} +(3.37902 + 3.85798i) q^{12} -3.70421i q^{13} +(-0.946800 + 2.08787i) q^{14} +(-1.69969 - 5.47615i) q^{15} +(-0.527150 + 3.96511i) q^{16} -7.74004 q^{17} +(-4.60507 - 2.08829i) q^{18} +3.73366 q^{19} +(2.33955 - 3.81136i) q^{20} -4.15680i q^{21} +(-1.62590 - 0.737308i) q^{22} +(3.86984 - 2.83273i) q^{23} +(-2.09876 - 6.94253i) q^{24} +(-4.12129 + 2.83107i) q^{25} +(-2.16350 + 4.77091i) q^{26} +1.47559 q^{27} +(2.43890 - 2.13612i) q^{28} +3.07514 q^{29} +(-1.00928 + 8.04586i) q^{30} +7.06240i q^{31} +(2.99484 - 4.79906i) q^{32} +3.23705 q^{33} +(9.96894 + 4.52069i) q^{34} +(-3.46186 + 1.07450i) q^{35} +(4.71149 + 5.37932i) q^{36} +9.94153 q^{37} +(-4.80884 - 2.18070i) q^{38} -9.49856i q^{39} +(-5.23936 + 3.54247i) q^{40} +0.611252 q^{41} +(-2.42784 + 5.35384i) q^{42} +6.59717i q^{43} +(1.66347 + 1.89926i) q^{44} +(-2.36994 - 7.63560i) q^{45} +(-6.63874 + 1.38823i) q^{46} -2.33340 q^{47} +(-1.35175 + 10.1676i) q^{48} +4.37219 q^{49} +(6.96163 - 1.23923i) q^{50} -19.8475 q^{51} +(5.57305 - 4.88116i) q^{52} -0.331215 q^{53} +(-1.90051 - 0.861841i) q^{54} +(-0.836749 - 2.69588i) q^{55} +(-4.38886 + 1.32678i) q^{56} +9.57409 q^{57} +(-3.96068 - 1.79608i) q^{58} -9.13726i q^{59} +(5.99923 - 9.77334i) q^{60} -7.91039i q^{61} +(4.12490 - 9.09616i) q^{62} -5.79598i q^{63} +(-6.66023 + 4.43186i) q^{64} +(-7.91058 + 2.45529i) q^{65} +(-4.16923 - 1.89065i) q^{66} +10.5612i q^{67} +(-10.1993 - 11.6450i) q^{68} +(9.92328 - 7.26386i) q^{69} +(5.08635 + 0.638037i) q^{70} -2.77876i q^{71} +(-2.92638 - 9.68022i) q^{72} -5.23380i q^{73} +(-12.8044 - 5.80651i) q^{74} +(-10.5681 + 7.25961i) q^{75} +(4.91997 + 5.61736i) q^{76} -2.04637i q^{77} +(-5.54778 + 12.2339i) q^{78} -1.62920 q^{79} +(8.81718 - 1.50247i) q^{80} -6.94253 q^{81} +(-0.787274 - 0.357011i) q^{82} +13.2717i q^{83} +(6.25398 - 5.47756i) q^{84} +(5.13040 + 16.5294i) q^{85} +(3.85318 - 8.49696i) q^{86} +7.88546 q^{87} +(-1.03321 - 3.41777i) q^{88} +12.2047i q^{89} +(-1.40727 + 11.2186i) q^{90} -6.00471 q^{91} +(9.36131 + 2.08946i) q^{92} +18.1098i q^{93} +(3.00535 + 1.36286i) q^{94} +(-2.47481 - 7.97348i) q^{95} +(7.67955 - 12.3060i) q^{96} +9.85230 q^{97} +(-5.63125 - 2.55365i) q^{98} +4.51354 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{4} - 8 q^{6} + 16 q^{9}+O(q^{10}) $ 56 * q - 8 * q^4 - 8 * q^6 + 16 * q^9	$ 56 q - 8 q^{4} - 8 q^{6} + 16 q^{9} - 8 q^{16} - 100 q^{24} - 24 q^{25} - 24 q^{26} - 16 q^{29} + 104 q^{41} - 8 q^{46} + 32 q^{49} - 32 q^{50} + 52 q^{54} - 92 q^{64} + 32 q^{69} - 44 q^{70} + 24 q^{81} + 56 q^{85} + 28 q^{94} + 88 q^{96}+O(q^{100}) $ 56 * q - 8 * q^4 - 8 * q^6 + 16 * q^9 - 8 * q^16 - 100 * q^24 - 24 * q^25 - 24 * q^26 - 16 * q^29 + 104 * q^41 - 8 * q^46 + 32 * q^49 - 32 * q^50 + 52 * q^54 - 92 * q^64 + 32 * q^69 - 44 * q^70 + 24 * q^81 + 56 * q^85 + 28 * q^94 + 88 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.28797	−	0.584066i	−0.910733	−	0.412997i
$2$	−1.28797	−	0.584066i	−0.910733	−	0.412997i
$3$	2.56426			1.48048			0.740239	−	0.672344i	$-0.234712\pi$
$3$	2.56426			1.48048			0.740239	+	0.672344i	$0.234712\pi$
$4$	1.31773	+	1.50452i	0.658867	+	0.752259i
$5$	−0.662839	−	2.13557i	−0.296430	−	0.955054i
$5$	−0.662839	−	2.13557i	−0.296430	−	0.955054i
$6$	−3.30269	−	1.49770i	−1.34832	−	0.611432i
$7$		−	1.62105i		−	0.612700i	−0.951919	−	0.306350i	$-0.900892\pi$
$7$		−	1.62105i		−	0.612700i	0.951919	−	0.306350i	$-0.0991078\pi$
$8$	−0.818466	−	2.70742i	−0.289371	−	0.957217i
$9$	3.57544			1.19181
$10$	−0.393594	+	3.13769i	−0.124465	+	0.992224i
$11$	1.26237			0.380619			0.190310	−	0.981724i	$-0.439051\pi$
$11$	1.26237			0.380619			0.190310	+	0.981724i	$0.439051\pi$
$12$	3.37902	+	3.85798i	0.975439	+	1.11370i
$13$		−	3.70421i		−	1.02736i	−0.857981	−	0.513681i	$-0.828281\pi$
$13$		−	3.70421i		−	1.02736i	0.857981	−	0.513681i	$-0.171719\pi$
$14$	−0.946800	+	2.08787i	−0.253043	+	0.558006i
$15$	−1.69969	−	5.47615i	−0.438859	−	1.41394i
$16$	−0.527150	+	3.96511i	−0.131787	+	0.991278i
$17$	−7.74004			−1.87724			−0.938618	−	0.344959i	$-0.887893\pi$
$17$	−7.74004			−1.87724			−0.938618	+	0.344959i	$0.887893\pi$
$18$	−4.60507	−	2.08829i	−1.08542	−	0.492215i
$19$	3.73366			0.856560			0.428280	−	0.903646i	$-0.359120\pi$
$19$	3.73366			0.856560			0.428280	+	0.903646i	$0.359120\pi$
$20$	2.33955	−	3.81136i	0.523140	−	0.852247i
$21$		−	4.15680i		−	0.907089i
$22$	−1.62590	−	0.737308i	−0.346642	−	0.157195i
$23$	3.86984	−	2.83273i	0.806917	−	0.590665i
$23$	3.86984	−	2.83273i	0.806917	−	0.590665i
$24$	−2.09876	−	6.94253i	−0.428408	−	1.41714i
$25$	−4.12129	+	2.83107i	−0.824258	+	0.566214i
$26$	−2.16350	+	4.77091i	−0.424297	+	0.935652i
$27$	1.47559			0.283977
$28$	2.43890	−	2.13612i	0.460909	−	0.403688i
$29$	3.07514			0.571038			0.285519	−	0.958373i	$-0.407834\pi$
$29$	3.07514			0.571038			0.285519	+	0.958373i	$0.407834\pi$
$30$	−1.00928	+	8.04586i	−0.184268	+	1.46897i
$31$			7.06240i			1.26844i	0.773151	+	0.634222i	$0.218679\pi$
$31$			7.06240i			1.26844i	−0.773151	+	0.634222i	$0.781321\pi$
$32$	2.99484	−	4.79906i	0.529418	−	0.848361i
$33$	3.23705			0.563499
$34$	9.96894	+	4.52069i	1.70966	+	0.775292i
$35$	−3.46186	+	1.07450i	−0.585162	+	0.181623i
$36$	4.71149	+	5.37932i	0.785248	+	0.896553i
$37$	9.94153			1.63438			0.817189	−	0.576370i	$-0.195531\pi$
$37$	9.94153			1.63438			0.817189	+	0.576370i	$0.195531\pi$
$38$	−4.80884	−	2.18070i	−0.780097	−	0.353757i
$39$		−	9.49856i		−	1.52099i
$40$	−5.23936	+	3.54247i	−0.828416	+	0.560114i
$41$	0.611252			0.0954615			0.0477308	−	0.998860i	$-0.484801\pi$
$41$	0.611252			0.0954615			0.0477308	+	0.998860i	$0.484801\pi$
$42$	−2.42784	+	5.35384i	−0.374625	+	0.826115i
$43$			6.59717i			1.00606i	0.864269	+	0.503029i	$0.167781\pi$
$43$			6.59717i			1.00606i	−0.864269	+	0.503029i	$0.832219\pi$
$44$	1.66347	+	1.89926i	0.250778	+	0.286324i
$45$	−2.36994	−	7.63560i	−0.353290	−	1.13825i
$46$	−6.63874	+	1.38823i	−0.978828	+	0.204684i
$47$	−2.33340			−0.340361			−0.170180	−	0.985413i	$-0.554435\pi$
$47$	−2.33340			−0.340361			−0.170180	+	0.985413i	$0.554435\pi$
$48$	−1.35175	+	10.1676i	−0.195108	+	1.46757i
$49$	4.37219			0.624599
$50$	6.96163	−	1.23923i	0.984523	−	0.175254i
$51$	−19.8475			−2.77921
$52$	5.57305	−	4.88116i	0.772843	−	0.676896i
$53$	−0.331215			−0.0454959			−0.0227480	−	0.999741i	$-0.507242\pi$
$53$	−0.331215			−0.0454959			−0.0227480	+	0.999741i	$0.507242\pi$
$54$	−1.90051	−	0.861841i	−0.258627	−	0.117282i
$55$	−0.836749	−	2.69588i	−0.112827	−	0.363512i
$56$	−4.38886	+	1.32678i	−0.586487	+	0.177298i
$57$	9.57409			1.26812
$58$	−3.96068	−	1.79608i	−0.520063	−	0.235837i
$59$		−	9.13726i		−	1.18957i	−0.803885	−	0.594785i	$-0.797237\pi$
$59$		−	9.13726i		−	1.18957i	0.803885	−	0.594785i	$-0.202763\pi$
$60$	5.99923	−	9.77334i	0.774497	−	1.26173i
$61$		−	7.91039i		−	1.01282i	−0.862292	−	0.506411i	$-0.830972\pi$
$61$		−	7.91039i		−	1.01282i	0.862292	−	0.506411i	$-0.169028\pi$
$62$	4.12490	−	9.09616i	0.523863	−	1.15521i
$63$		−	5.79598i		−	0.730225i
$64$	−6.66023	+	4.43186i	−0.832528	+	0.553983i
$65$	−7.91058	+	2.45529i	−0.981187	+	0.304542i
$66$	−4.16923	−	1.89065i	−0.513196	−	0.232723i
$67$			10.5612i			1.29026i	0.764073	+	0.645130i	$0.223197\pi$
$67$			10.5612i			1.29026i	−0.764073	+	0.645130i	$0.776803\pi$
$68$	−10.1993	−	11.6450i	−1.23685	−	1.41217i
$69$	9.92328	−	7.26386i	1.19462	−	0.874466i
$70$	5.08635	+	0.638037i	0.607935	+	0.0762600i
$71$		−	2.77876i		−	0.329778i	−0.986312	−	0.164889i	$-0.947273\pi$
$71$		−	2.77876i		−	0.329778i	0.986312	−	0.164889i	$-0.0527266\pi$
$72$	−2.92638	−	9.68022i	−0.344877	−	1.14083i
$73$		−	5.23380i		−	0.612569i	−0.951940	−	0.306285i	$-0.900914\pi$
$73$		−	5.23380i		−	0.612569i	0.951940	−	0.306285i	$-0.0990860\pi$
$74$	−12.8044	−	5.80651i	−1.48848	−	0.674993i
$75$	−10.5681	+	7.25961i	−1.22030	+	0.838268i
$76$	4.91997	+	5.61736i	0.564360	+	0.644355i
$77$		−	2.04637i		−	0.233205i
$78$	−5.54778	+	12.2339i	−0.628163	+	1.38521i
$79$	−1.62920			−0.183300			−0.0916498	−	0.995791i	$-0.529214\pi$
$79$	−1.62920			−0.183300			−0.0916498	+	0.995791i	$0.529214\pi$
$80$	8.81718	−	1.50247i	0.985790	−	0.167981i
$81$	−6.94253			−0.771393
$82$	−0.787274	−	0.357011i	−0.0869399	−	0.0394253i
$83$			13.2717i			1.45676i	0.685173	+	0.728381i	$0.259727\pi$
$83$			13.2717i			1.45676i	−0.685173	+	0.728381i	$0.740273\pi$
$84$	6.25398	−	5.47756i	0.682366	−	0.597651i
$85$	5.13040	+	16.5294i	0.556470	+	1.79286i
$86$	3.85318	−	8.49696i	0.415499	−	0.916250i
$87$	7.88546			0.845410
$88$	−1.03321	−	3.41777i	−0.110140	−	0.364335i
$89$			12.2047i			1.29370i	0.762618	+	0.646850i	$0.223914\pi$
$89$			12.2047i			1.29370i	−0.762618	+	0.646850i	$0.776086\pi$
$90$	−1.40727	+	11.2186i	−0.148340	+	1.18255i
$91$	−6.00471			−0.629465
$92$	9.36131	+	2.08946i	0.975984	+	0.217841i
$93$			18.1098i			1.87790i
$94$	3.00535	+	1.36286i	0.309978	+	0.140568i
$95$	−2.47481	−	7.97348i	−0.253911	−	0.818062i
$96$	7.67955	−	12.3060i	0.783791	−	1.25598i
$97$	9.85230			1.00035			0.500175	−	0.865924i	$-0.333269\pi$
$97$	9.85230			1.00035			0.500175	+	0.865924i	$0.333269\pi$
$98$	−5.63125	−	2.55365i	−0.568842	−	0.257957i
$99$	4.51354			0.453628
$100$	−9.69017	−	2.46995i	−0.969017	−	0.246995i
$101$	2.75584			0.274216			0.137108	−	0.990556i	$-0.456219\pi$
$101$	2.75584			0.274216			0.137108	+	0.990556i	$0.456219\pi$
$102$	25.5630	+	11.5922i	2.53111	+	1.14780i
$103$			9.45350i			0.931481i	0.884921	+	0.465740i	$0.154212\pi$
$103$			9.45350i			0.931481i	−0.884921	+	0.465740i	$0.845788\pi$
$104$	−10.0288	+	3.03177i	−0.983409	+	0.297289i
$105$	−8.87713	+	2.75529i	−0.866319	+	0.268889i
$106$	0.426596	+	0.193451i	0.0414346	+	0.0187897i
$107$		−	3.34030i		−	0.322919i	−0.986879	−	0.161460i	$-0.948380\pi$
$107$		−	3.34030i		−	0.322919i	0.986879	−	0.161460i	$-0.0516201\pi$
$108$	1.94443	+	2.22005i	0.187103	+	0.213624i
$109$			12.7148i			1.21785i	0.793227	+	0.608926i	$0.208400\pi$
$109$			12.7148i			1.21785i	−0.793227	+	0.608926i	$0.791600\pi$
$110$	−0.496862	+	3.96093i	−0.0473740	+	0.377660i
$111$	25.4927			2.41966
$112$	6.42765	+	0.854537i	0.607356	+	0.0807461i
$113$	13.7089			1.28963			0.644813	−	0.764341i	$-0.276935\pi$
$113$	13.7089			1.28963			0.644813	+	0.764341i	$0.276935\pi$
$114$	−12.3311	−	5.59189i	−1.15492	−	0.523729i
$115$	−8.61456	−	6.38665i	−0.803312	−	0.595559i
$116$	4.05221	+	4.62660i	0.376239	+	0.429569i
$117$		−	13.2442i		−	1.22443i
$118$	−5.33676	+	11.7685i	−0.491288	+	1.08338i
$119$			12.5470i			1.15018i
$120$	−13.4351	+	9.08383i	−1.22645	+	0.829236i
$121$	−9.40642			−0.855129
$122$	−4.62018	+	10.1883i	−0.418292	+	0.922409i
$123$	1.56741			0.141329
$124$	−10.6255	+	9.30637i	−0.954198	+	0.835736i
$125$	8.77769	+	6.92474i	0.785101	+	0.619368i
$126$	−3.38523	+	7.46505i	−0.301580	+	0.665039i
$127$	−11.9753			−1.06263			−0.531317	−	0.847173i	$-0.678303\pi$
$127$	−11.9753			−1.06263			−0.531317	+	0.847173i	$0.678303\pi$
$128$	11.1667	−	1.81810i	0.987004	−	0.160698i
$129$			16.9169i			1.48945i
$130$	11.6226	+	1.45796i	1.01937	+	0.127871i
$131$			5.21493i			0.455630i	0.973704	+	0.227815i	$0.0731582\pi$
$131$			5.21493i			0.455630i	−0.973704	+	0.227815i	$0.926842\pi$
$132$	4.26558	+	4.87020i	0.371271	+	0.423897i
$133$		−	6.05246i		−	0.524814i
$134$	6.16846	−	13.6026i	0.532873	−	1.17508i
$135$	−0.978077	−	3.15122i	−0.0841795	−	0.271214i
$136$	6.33496	+	20.9555i	0.543218	+	1.79692i
$137$	−12.8474			−1.09762			−0.548812	−	0.835946i	$-0.684920\pi$
$137$	−12.8474			−1.09762			−0.548812	+	0.835946i	$0.684920\pi$
$138$	−17.0235	+	3.55979i	−1.44913	+	0.303030i
$139$		−	6.09860i		−	0.517277i	−0.965974	−	0.258638i	$-0.916726\pi$
$139$		−	6.09860i		−	0.517277i	0.965974	−	0.258638i	$-0.0832738\pi$
$140$	−6.17842	−	3.79254i	−0.522171	−	0.320528i
$141$	−5.98344			−0.503897
$142$	−1.62298	+	3.57896i	−0.136197	+	0.300339i
$143$		−	4.67609i		−	0.391034i
$144$	−1.88479	+	14.1770i	−0.157066	+	1.18142i
$145$	−2.03832	−	6.56716i	−0.169273	−	0.545373i
$146$	−3.05688	+	6.74097i	−0.252989	+	0.557887i
$147$	11.2114			0.924705
$148$	13.1003	+	14.9572i	1.07684	+	1.22948i
$149$		−	10.3256i		−	0.845907i	−0.906151	−	0.422953i	$-0.860993\pi$
$149$		−	10.3256i		−	0.845907i	0.906151	−	0.422953i	$-0.139007\pi$
$150$	17.8515	−	3.17772i	1.45756	−	0.259460i
$151$			11.9160i			0.969711i	0.874594	+	0.484856i	$0.161128\pi$
$151$			11.9160i			0.969711i	−0.874594	+	0.484856i	$0.838872\pi$
$152$	−3.05587	−	10.1086i	−0.247864	−	0.819914i
$153$	−27.6741			−2.23732
$154$	−1.19521	+	2.63566i	−0.0963131	+	0.212388i
$155$	15.0822	−	4.68123i	1.21143	−	0.376005i
$156$	14.2908	−	12.5166i	1.14418	−	1.00213i
$157$	−12.3832			−0.988289			−0.494144	−	0.869380i	$-0.664519\pi$
$157$	−12.3832			−0.988289			−0.494144	+	0.869380i	$0.664519\pi$
$158$	2.09836	+	0.951561i	0.166937	+	0.0757021i
$159$	−0.849323			−0.0673557
$160$	−12.2338	−	3.21468i	−0.967167	−	0.254142i
$161$	−4.59200	−	6.27321i	−0.361900	−	0.494398i
$162$	8.94178	+	4.05489i	0.702532	+	0.318583i
$163$	11.9253			0.934062			0.467031	−	0.884241i	$-0.345324\pi$
$163$	11.9253			0.934062			0.467031	+	0.884241i	$0.345324\pi$
$164$	0.805468	+	0.919639i	0.0628965	+	0.0718118i
$165$	−2.14564	−	6.91294i	−0.167038	−	0.538172i
$166$	7.75156	−	17.0936i	0.601638	−	1.32672i
$167$	10.1226			0.783310			0.391655	−	0.920112i	$-0.371903\pi$
$167$	10.1226			0.783310			0.391655	+	0.920112i	$0.371903\pi$
$168$	−11.2542	+	3.40220i	−0.868280	+	0.262486i
$169$	−0.721160			−0.0554738
$170$	3.04644	−	24.2858i	0.233651	−	1.86264i
$171$	13.3495			1.02086
$172$	−9.92556	+	8.69332i	−0.756817	+	0.662859i
$173$		−	4.77722i		−	0.363205i	−0.983372	−	0.181603i	$-0.941872\pi$
$173$		−	4.77722i		−	0.363205i	0.983372	−	0.181603i	$-0.0581284\pi$
$174$	−10.1562	−	4.60562i	−0.769942	−	0.349151i
$175$	4.58931	+	6.68082i	0.346920	+	0.505023i
$176$	−0.665459	+	5.00545i	−0.0501608	+	0.377300i
$177$		−	23.4303i		−	1.76113i
$178$	7.12837	−	15.7193i	0.534294	−	1.17821i
$179$			25.2785i			1.88941i	0.327925	+	0.944704i	$0.393651\pi$
$179$			25.2785i			1.88941i	−0.327925	+	0.944704i	$0.606349\pi$
$180$	8.36494	−	13.6273i	0.623486	−	1.01572i
$181$			1.32658i			0.0986036i	0.998784	+	0.0493018i	$0.0156996\pi$
$181$			1.32658i			0.0986036i	−0.998784	+	0.0493018i	$0.984300\pi$
$182$	7.73389	+	3.50715i	0.573274	+	0.259967i
$183$		−	20.2843i		−	1.49946i
$184$	−10.8367	−	8.15878i	−0.798893	−	0.601473i
$185$	−6.58963	−	21.2308i	−0.484479	−	1.56092i
$186$	10.5773	−	23.3249i	0.775568	−	1.71027i
$187$	−9.77081			−0.714512
$188$	−3.07480	−	3.51064i	−0.224253	−	0.256040i
$189$		−	2.39201i		−	0.173993i
$190$	−1.46955	+	11.7151i	−0.106612	+	0.849900i
$191$	−17.3904			−1.25832			−0.629162	−	0.777274i	$-0.716602\pi$
$191$	−17.3904			−1.25832			−0.629162	+	0.777274i	$0.716602\pi$
$192$	−17.0786	+	11.3645i	−1.23254	+	0.820159i
$193$			16.0635i			1.15627i	0.815940	+	0.578137i	$0.196220\pi$
$193$			16.0635i			1.15627i	−0.815940	+	0.578137i	$0.803780\pi$
$194$	−12.6895	−	5.75439i	−0.911051	−	0.413141i
$195$	−20.2848	+	6.29602i	−1.45263	+	0.450867i
$196$	5.76139	+	6.57804i	0.411528	+	0.469860i
$197$			13.1841i			0.939328i	0.882845	+	0.469664i	$0.155625\pi$
$197$			13.1841i			0.939328i	−0.882845	+	0.469664i	$0.844375\pi$
$198$	−5.81330	−	2.63620i	−0.413134	−	0.187347i
$199$	4.84781			0.343652			0.171826	−	0.985127i	$-0.445033\pi$
$199$	4.84781			0.343652			0.171826	+	0.985127i	$0.445033\pi$
$200$	11.0380	+	8.84092i	0.780507	+	0.625147i
$201$			27.0818i			1.91020i
$202$	−3.54944	−	1.60959i	−0.249738	−	0.113250i
$203$		−	4.98495i		−	0.349875i
$204$	−26.1537	−	29.8609i	−1.83113	−	2.09068i
$205$	−0.405161	−	1.30537i	−0.0282977	−	0.0911709i
$206$	5.52146	−	12.1758i	0.384699	−	0.848330i
$207$	13.8364	−	10.1283i	0.961695	−	0.703963i
$208$	14.6876	+	1.95267i	1.01840	+	0.135393i
$209$	4.71327			0.326024
$210$	13.0427	+	1.63609i	0.900035	+	0.112901i
$211$		−	22.3882i		−	1.54126i	−0.637280	−	0.770632i	$-0.719941\pi$
$211$		−	22.3882i		−	1.54126i	0.637280	−	0.770632i	$-0.280059\pi$
$212$	−0.436454	−	0.498320i	−0.0299758	−	0.0342247i
$213$		−	7.12546i		−	0.488229i
$214$	−1.95095	+	4.30221i	−0.133364	+	0.294093i
$215$	14.0887	−	4.37286i	0.960841	−	0.298226i
$216$	−1.20772	−	3.99504i	−0.0821749	−	0.271828i
$217$	11.4485			0.777175
$218$	7.42625	−	16.3762i	0.502969	−	1.10914i
$219$		−	13.4208i		−	0.906896i
$220$	2.95339	−	4.81136i	0.199117	−	0.324382i
$221$			28.6707i			1.92860i
$222$	−32.8338	−	14.8894i	−2.20366	−	0.999312i
$223$	−13.4927			−0.903539			−0.451770	−	0.892135i	$-0.649207\pi$
$223$	−13.4927			−0.903539			−0.451770	+	0.892135i	$0.649207\pi$
$224$	−7.77952	−	4.85479i	−0.519791	−	0.324374i
$225$	−14.7354	+	10.1223i	−0.982363	+	0.674823i
$226$	−17.6567	−	8.00690i	−1.17450	−	0.532611i
$227$		−	2.65450i		−	0.176185i	−0.996112	−	0.0880927i	$-0.971923\pi$
$227$		−	2.65450i		−	0.176185i	0.996112	−	0.0880927i	$-0.0280772\pi$
$228$	12.6161	+	14.4044i	0.835522	+	0.953954i
$229$		−	17.5942i		−	1.16266i	−0.813669	−	0.581328i	$-0.802533\pi$
$229$		−	17.5942i		−	1.16266i	0.813669	−	0.581328i	$-0.197467\pi$
$230$	7.36507	+	13.2573i	0.485639	+	0.874160i
$231$		−	5.24743i		−	0.345256i
$232$	−2.51689	−	8.32568i	−0.165242	−	0.546608i
$233$		−	3.11938i		−	0.204357i	−0.994766	−	0.102179i	$-0.967419\pi$
$233$		−	3.11938i		−	0.204357i	0.994766	−	0.102179i	$-0.0325813\pi$
$234$	−7.73547	+	17.0581i	−0.505684	+	1.11512i
$235$	1.54667	+	4.98313i	0.100893	+	0.325063i
$236$	13.7472	−	12.0405i	0.894864	−	0.783769i
$237$	−4.17770			−0.271371
$238$	7.32827	−	16.1602i	0.475021	−	1.04751i
$239$		−	5.17786i		−	0.334928i	−0.985878	−	0.167464i	$-0.946442\pi$
$239$		−	5.17786i		−	0.334928i	0.985878	−	0.167464i	$-0.0535577\pi$
$240$	22.6096	−	3.85272i	1.45944	−	0.248692i
$241$		−	30.9351i		−	1.99270i	−0.0853470	−	0.996351i	$-0.527200\pi$
$241$		−	30.9351i		−	1.99270i	0.0853470	−	0.996351i	$-0.472800\pi$
$242$	12.1152	+	5.49396i	0.778794	+	0.353165i
$243$	−22.2292			−1.42601
$244$	11.9013	−	10.4238i	0.761904	−	0.667315i
$245$	−2.89806	−	9.33711i	−0.185150	−	0.596526i
$246$	−2.01878	−	0.915470i	−0.128713	−	0.0583683i
$247$		−	13.8303i		−	0.879998i
$248$	19.1209	−	5.78033i	1.21418	−	0.367051i
$249$			34.0322i			2.15670i
$250$	−7.26090	−	14.0456i	−0.459220	−	0.888323i
$251$	6.68143			0.421728			0.210864	−	0.977515i	$-0.432372\pi$
$251$	6.68143			0.421728			0.210864	+	0.977515i	$0.432372\pi$
$252$	8.72015	−	7.63756i	0.549318	−	0.481121i
$253$	4.88517	−	3.57596i	0.307128	−	0.224819i
$254$	15.4238	+	6.99434i	0.967775	+	0.438864i
$255$	13.1557	+	42.3856i	0.823841	+	2.65429i
$256$	−15.4442	−	4.18041i	−0.965264	−	0.261276i
$257$			23.9916i			1.49655i	0.663386	+	0.748277i	$0.269119\pi$
$257$			23.9916i			1.49655i	−0.663386	+	0.748277i	$0.730881\pi$
$258$	9.88056	−	21.7884i	0.615137	−	1.35649i
$259$		−	16.1157i		−	1.00138i
$260$	−14.1181	−	8.66619i	−0.875566	−	0.537454i
$261$	10.9950			0.680572
$262$	3.04586	−	6.71667i	0.188174	−	0.414957i
$263$		−	1.22644i		−	0.0756257i	−0.999285	−	0.0378128i	$-0.987961\pi$
$263$		−	1.22644i		−	0.0756257i	0.999285	−	0.0378128i	$-0.0120391\pi$
$264$	−2.64942	−	8.76406i	−0.163060	−	0.539390i
$265$	0.219542	+	0.707332i	0.0134864	+	0.0434511i
$266$	−3.53503	+	7.79538i	−0.216747	+	0.477966i
$267$			31.2961i			1.91529i
$268$	−15.8896	+	13.9169i	−0.970610	+	0.850111i
$269$	−16.6973			−1.01805			−0.509027	−	0.860750i	$-0.669995\pi$
$269$	−16.6973			−1.01805			−0.509027	+	0.860750i	$0.669995\pi$
$270$	−0.580783	+	4.62994i	−0.0353454	+	0.281769i
$271$		−	23.7737i		−	1.44415i	−0.691816	−	0.722074i	$-0.743189\pi$
$271$		−	23.7737i		−	1.44415i	0.691816	−	0.722074i	$-0.256811\pi$
$272$	4.08016	−	30.6901i	0.247396	−	1.86086i
$273$	−15.3977			−0.931909
$274$	16.5470	+	7.50371i	0.999643	+	0.453315i
$275$	−5.20260	+	3.57387i	−0.313729	+	0.215512i
$276$	24.0049	+	5.35791i	1.44492	+	0.322508i
$277$		−	0.193125i		−	0.0116038i	−0.999983	−	0.00580189i	$-0.998153\pi$
$277$		−	0.193125i		−	0.0116038i	0.999983	−	0.00580189i	$-0.00184681\pi$
$278$	−3.56198	+	7.85482i	−0.213634	+	0.471101i
$279$			25.2512i			1.51175i
$280$	5.74253	+	8.49327i	0.343182	+	0.507570i
$281$		−	0.685427i		−	0.0408892i	−0.999791	−	0.0204446i	$-0.993492\pi$
$281$		−	0.685427i		−	0.0408892i	0.999791	−	0.0204446i	$-0.00650816\pi$
$282$	7.70650	+	3.49472i	0.458915	+	0.208108i
$283$			6.29825i			0.374392i	0.982323	+	0.187196i	$0.0599400\pi$
$283$			6.29825i			0.374392i	−0.982323	+	0.187196i	$0.940060\pi$
$284$	4.18069	−	3.66167i	0.248078	−	0.217280i
$285$	−6.34608	−	20.4461i	−0.375909	−	1.21112i
$286$	−2.73114	+	6.02266i	−0.161496	+	0.356127i
$287$		−	0.990871i		−	0.0584892i
$288$	10.7079	−	17.1588i	0.630968	−	1.01109i
$289$	42.9082			2.52401
$290$	−1.21036	+	9.64882i	−0.0710746	+	0.566598i
$291$	25.2639			1.48100
$292$	7.87434	−	6.89676i	0.460811	−	0.403602i
$293$	−25.1421			−1.46882			−0.734408	−	0.678708i	$-0.762540\pi$
$293$	−25.1421			−1.46882			−0.734408	+	0.678708i	$0.762540\pi$
$294$	−14.4400	−	6.54822i	−0.842159	−	0.381900i
$295$	−19.5132	+	6.05653i	−1.13610	+	0.352625i
$296$	−8.13681	−	26.9159i	−0.472942	−	1.56445i
$297$	1.86274			0.108087
$298$	−6.03083	+	13.2991i	−0.349357	+	0.770395i
$299$	−10.4930	−	14.3347i	−0.606827	−	0.828996i
$300$	−24.8481	−	6.33361i	−1.43461	−	0.365671i
$301$	10.6943			0.616412
$302$	6.95973	−	15.3475i	0.400488	−	0.883148i
$303$	7.06669			0.405971
$304$	−1.96820	+	14.8044i	−0.112884	+	0.849090i
$305$	−16.8932	+	5.24331i	−0.967299	+	0.300231i
$306$	35.6434	+	16.1635i	2.03760	+	0.924004i
$307$	−0.393652			−0.0224669			−0.0112334	−	0.999937i	$-0.503576\pi$
$307$	−0.393652			−0.0224669			−0.0112334	+	0.999937i	$0.503576\pi$
$308$	3.07880	−	2.69657i	0.175431	−	0.153651i
$309$			24.2413i			1.37904i
$310$	−22.1596	−	2.77972i	−1.25858	−	0.157877i
$311$			2.70456i			0.153362i	0.997056	+	0.0766808i	$0.0244322\pi$
$311$			2.70456i			0.153362i	−0.997056	+	0.0766808i	$0.975568\pi$
$312$	−25.7166	+	7.77425i	−1.45591	+	0.440130i
$313$	12.4169			0.701843			0.350922	−	0.936405i	$-0.385868\pi$
$313$	12.4169			0.701843			0.350922	+	0.936405i	$0.385868\pi$
$314$	15.9492	+	7.23262i	0.900067	+	0.408160i
$315$	−12.3777	+	3.84180i	−0.697404	+	0.216461i
$316$	−2.14686	−	2.45116i	−0.120770	−	0.137889i
$317$		−	19.2978i		−	1.08387i	−0.840420	−	0.541935i	$-0.817692\pi$
$317$		−	19.2978i		−	1.08387i	0.840420	−	0.541935i	$-0.182308\pi$
$318$	1.09390	+	0.496060i	0.0613430	+	0.0278177i
$319$	3.88196			0.217348
$320$	13.8792	+	11.2857i	0.775870	+	0.630893i
$321$		−	8.56541i		−	0.478074i
$322$	2.25040	+	10.7617i	0.125410	+	0.599728i
$323$	−28.8987			−1.60797
$324$	−9.14842	−	10.4452i	−0.508245	−	0.580287i
$325$	10.4869	+	15.2661i	0.581708	+	0.846812i
$326$	−15.3594	−	6.96516i	−0.850681	−	0.385765i
$327$			32.6040i			1.80300i
$328$	−0.500289	−	1.65491i	−0.0276238	−	0.0913774i
$329$			3.78256i			0.208539i
$330$	−1.27409	+	10.1569i	−0.0701361	+	0.559117i
$331$			24.6944i			1.35733i	0.734449	+	0.678664i	$0.237441\pi$
$331$			24.6944i			1.35733i	−0.734449	+	0.678664i	$0.762559\pi$
$332$	−19.9676	+	17.4886i	−1.09586	+	0.959813i
$333$	35.5454			1.94788
$334$	−13.0376	−	5.91226i	−0.713386	−	0.323505i
$335$	22.5542	−	7.00040i	1.23227	−	0.382473i
$336$	16.4822	+	2.19126i	0.899177	+	0.119543i
$337$	−0.810102			−0.0441291			−0.0220645	−	0.999757i	$-0.507024\pi$
$337$	−0.810102			−0.0441291			−0.0220645	+	0.999757i	$0.507024\pi$
$338$	0.928833	+	0.421205i	0.0505218	+	0.0229105i
$339$	35.1532			1.90926
$340$	−18.1082	+	29.5001i	−0.982057	+	1.59987i
$341$			8.91537i			0.482794i
$342$	−17.1938	−	7.79698i	−0.929732	−	0.421612i
$343$		−	18.4349i		−	0.995392i
$344$	17.8613	−	5.39956i	0.963016	−	0.291125i
$345$	−22.0900	−	16.3771i	−1.18929	−	0.881711i
$346$	−2.79021	+	6.15291i	−0.150002	+	0.330783i
$347$	−20.6572			−1.10894			−0.554469	−	0.832204i	$-0.687079\pi$
$347$	−20.6572			−1.10894			−0.554469	+	0.832204i	$0.687079\pi$
$348$	10.3909	+	11.8638i	0.557013	+	0.635967i
$349$	−9.11873			−0.488115			−0.244057	−	0.969761i	$-0.578479\pi$
$349$	−9.11873			−0.488115			−0.244057	+	0.969761i	$0.578479\pi$
$350$	−2.00886	−	11.2852i	−0.107378	−	0.603217i
$351$		−	5.46589i		−	0.291748i
$352$	3.78060	−	6.05819i	0.201507	−	0.322903i
$353$		−	18.5400i		−	0.986783i	−0.869807	−	0.493391i	$-0.835757\pi$
$353$		−	18.5400i		−	0.986783i	0.869807	−	0.493391i	$-0.164243\pi$
$354$	−13.6848	+	30.1776i	−0.727341	+	1.60392i
$355$	−5.93422	+	1.84187i	−0.314956	+	0.0977562i
$356$	−18.3622	+	16.0826i	−0.973197	+	0.852376i
$357$			32.1738i			1.70282i
$358$	14.7643	−	32.5580i	0.780319	−	1.72074i
$359$	24.8931			1.31381			0.656905	−	0.753973i	$-0.271865\pi$
$359$	24.8931			1.31381			0.656905	+	0.753973i	$0.271865\pi$
$360$	−18.7330	+	12.6659i	−0.987318	+	0.667552i
$361$	−5.05978			−0.266304
$362$	0.774807	−	1.70859i	0.0407230	−	0.0898015i
$363$	−24.1205			−1.26600
$364$	−7.91262	−	9.03420i	−0.414734	−	0.473521i
$365$	−11.1771	+	3.46916i	−0.585037	+	0.181584i
$366$	−11.8474	+	26.1256i	−0.619272	+	1.36561i
$367$		−	33.2237i		−	1.73427i	−0.498077	−	0.867133i	$-0.665960\pi$
$367$		−	33.2237i		−	1.73427i	0.498077	−	0.867133i	$-0.334040\pi$
$368$	9.19210	+	16.8376i	0.479172	+	0.877721i
$369$	2.18550			0.113772
$370$	−3.91293	+	31.1934i	−0.203424	+	1.62167i
$371$			0.536917i			0.0278753i
$372$	−27.2466	+	23.8640i	−1.41267	+	1.23729i
$373$	15.0397			0.778727			0.389363	−	0.921084i	$-0.372695\pi$
$373$	15.0397			0.778727			0.389363	+	0.921084i	$0.372695\pi$
$374$	12.5845	+	5.70679i	0.650729	+	0.295091i
$375$	22.5083	+	17.7569i	1.16232	+	0.916961i
$376$	1.90981	+	6.31748i	0.0984908	+	0.325799i
$377$		−	11.3909i		−	0.586663i
$378$	−1.39709	+	3.08083i	−0.0718585	+	0.158461i
$379$	−31.0601			−1.59545			−0.797724	−	0.603023i	$-0.793963\pi$
$379$	−31.0601			−1.59545			−0.797724	+	0.603023i	$0.793963\pi$
$380$	8.73510	−	14.2303i	0.448101	−	0.730001i
$381$	−30.7077			−1.57321
$382$	22.3983	+	10.1571i	1.14600	+	0.519684i
$383$		−	3.54400i		−	0.181090i	−0.995892	−	0.0905449i	$-0.971139\pi$
$383$		−	3.54400i		−	0.181090i	0.995892	−	0.0905449i	$-0.0288609\pi$
$384$	28.6343	−	4.66208i	1.46124	−	0.237911i
$385$	−4.37016	+	1.35641i	−0.222724	+	0.0691292i
$386$	9.38212	−	20.6893i	0.477537	−	1.05306i
$387$			23.5878i			1.19904i
$388$	12.9827	+	14.8230i	0.659098	+	0.752522i
$389$		−	8.58051i		−	0.435049i	−0.976055	−	0.217525i	$-0.930202\pi$
$389$		−	8.58051i		−	0.435049i	0.976055	−	0.217525i	$-0.0697982\pi$
$390$	29.8035	+	3.73858i	1.50916	+	0.189310i
$391$	−29.9527	+	21.9254i	−1.51477	+	1.10882i
$392$	−3.57849	−	11.8374i	−0.180741	−	0.597877i
$393$			13.3724i			0.674550i
$394$	7.70037	−	16.9807i	0.387939	−	0.855476i
$395$	1.07990	+	3.47927i	0.0543356	+	0.175061i
$396$	5.94765	+	6.79070i	0.298881	+	0.341246i
$397$			12.9361i			0.649246i	0.945843	+	0.324623i	$0.105237\pi$
$397$			12.9361i			0.649246i	−0.945843	+	0.324623i	$0.894763\pi$
$398$	−6.24384	−	2.83144i	−0.312975	−	0.141927i
$399$		−	15.5201i		−	0.776976i
$400$	−9.05298	−	17.8338i	−0.452649	−	0.891689i
$401$		−	24.7106i		−	1.23399i	−0.786967	−	0.616995i	$-0.788350\pi$
$401$		−	24.7106i		−	1.23399i	0.786967	−	0.616995i	$-0.211650\pi$
$402$	15.8175	−	34.8805i	0.788907	−	1.73968i
$403$	26.1606			1.30315
$404$	3.63146	+	4.14621i	0.180672	+	0.206282i
$405$	4.60178	+	14.8262i	0.228664	+	0.736722i
$406$	−2.91154	+	6.42047i	−0.144497	+	0.318643i
$407$	12.5499			0.622076
$408$	16.2445	+	53.7355i	0.804223	+	2.66030i
$409$	7.62265			0.376916			0.188458	−	0.982081i	$-0.439651\pi$
$409$	7.62265			0.376916			0.188458	+	0.982081i	$0.439651\pi$
$410$	−0.240585	+	1.91792i	−0.0118817	+	0.0947192i
$411$	−32.9440			−1.62501
$412$	−14.2230	+	12.4572i	−0.700715	+	0.613722i
$413$	−14.8120			−0.728849
$414$	−23.7364	+	4.96355i	−1.16658	+	0.243945i
$415$	28.3427	−	8.79701i	1.39129	−	0.431828i
$416$	−17.7767	−	11.0935i	−0.871575	−	0.543904i
$417$		−	15.6384i		−	0.765817i
$418$	−6.07055	−	2.75286i	−0.296920	−	0.134647i
$419$	−5.55318			−0.271291			−0.135645	−	0.990757i	$-0.543311\pi$
$419$	−5.55318			−0.271291			−0.135645	+	0.990757i	$0.543311\pi$
$420$	−15.8431	−	9.72506i	−0.773063	−	0.474534i
$421$		−	9.55340i		−	0.465604i	−0.972524	−	0.232802i	$-0.925211\pi$
$421$		−	9.55340i		−	0.465604i	0.972524	−	0.232802i	$-0.0747894\pi$
$422$	−13.0762	+	28.8353i	−0.636537	+	1.40368i
$423$	−8.34293			−0.405647
$424$	0.271089	+	0.896738i	0.0131652	+	0.0435495i
$425$	31.8989	−	21.9126i	1.54733	−	1.06292i
$426$	−4.16174	+	9.17739i	−0.201637	+	0.444646i
$427$	−12.8231			−0.620555
$428$	5.02554	−	4.40163i	0.242919	−	0.212761i
$429$		−	11.9907i		−	0.578917i
$430$	−20.6999	−	2.59661i	−0.998236	−	0.125220i
$431$	36.8035			1.77276			0.886381	−	0.462956i	$-0.153211\pi$
$431$	36.8035			1.77276			0.886381	+	0.462956i	$0.153211\pi$
$432$	−0.777856	+	5.85087i	−0.0374246	+	0.281500i
$433$	16.1069			0.774049			0.387025	−	0.922069i	$-0.373503\pi$
$433$	16.1069			0.774049			0.387025	+	0.922069i	$0.373503\pi$
$434$	−14.7453	−	6.68668i	−0.707799	−	0.320971i
$435$	−5.22679	−	16.8399i	−0.250605	−	0.807412i
$436$	−19.1296	+	16.7547i	−0.916141	+	0.802404i
$437$	14.4487	−	10.5764i	0.691173	−	0.505940i
$438$	−7.83864	+	17.2856i	−0.374545	+	0.825939i
$439$		−	30.9144i		−	1.47546i	−0.675095	−	0.737731i	$-0.735897\pi$
$439$		−	30.9144i		−	1.47546i	0.675095	−	0.737731i	$-0.264103\pi$
$440$	−6.61402	+	4.47191i	−0.315311	+	0.213190i
$441$	15.6325			0.744406
$442$	16.7456	−	36.9270i	0.796506	−	1.75644i
$443$	−1.86842			−0.0887711			−0.0443855	−	0.999014i	$-0.514133\pi$
$443$	−1.86842			−0.0887711			−0.0443855	+	0.999014i	$0.514133\pi$
$444$	33.5926	+	38.3542i	1.59424	+	1.82021i
$445$	26.0640	−	8.08977i	1.23555	−	0.383492i
$446$	17.3782	+	7.88063i	0.822883	+	0.373159i
$447$		−	26.4776i		−	1.25235i
$448$	7.18427	+	10.7966i	0.339425	+	0.510090i
$449$	33.1765			1.56570			0.782848	−	0.622213i	$-0.213766\pi$
$449$	33.1765			1.56570			0.782848	+	0.622213i	$0.213766\pi$
$450$	24.8909	−	4.43081i	1.17337	−	0.208870i
$451$	0.771627			0.0363345
$452$	18.0647	+	20.6253i	0.849692	+	0.970132i
$453$			30.5558i			1.43564i
$454$	−1.55040	+	3.41892i	−0.0727640	+	0.160458i
$455$	3.98016	+	12.8235i	0.186593	+	0.601173i
$456$	−7.83607	−	25.9211i	−0.366957	−	1.21386i
$457$	−16.4071			−0.767491			−0.383746	−	0.923439i	$-0.625366\pi$
$457$	−16.4071			−0.767491			−0.383746	+	0.923439i	$0.625366\pi$
$458$	−10.2762	+	22.6608i	−0.480173	+	1.05887i
$459$	−11.4211			−0.533092
$460$	−1.74287	−	21.3767i	−0.0812617	−	0.996693i
$461$	−12.2226			−0.569262			−0.284631	−	0.958637i	$-0.591871\pi$
$461$	−12.2226			−0.569262			−0.284631	+	0.958637i	$0.591871\pi$
$462$	−3.06484	+	6.75853i	−0.142589	+	0.314435i
$463$	38.5395			1.79108			0.895540	−	0.444980i	$-0.146789\pi$
$463$	38.5395			1.79108			0.895540	+	0.444980i	$0.146789\pi$
$464$	−1.62106	+	12.1933i	−0.0752557	+	0.566058i
$465$	38.6748	−	12.0039i	1.79350	−	0.556668i
$466$	−1.82192	+	4.01767i	−0.0843989	+	0.186115i
$467$			9.00046i			0.416492i	0.978077	+	0.208246i	$0.0667754\pi$
$467$			9.00046i			0.416492i	−0.978077	+	0.208246i	$0.933225\pi$
$468$	19.9261	−	17.4523i	0.921085	−	0.806734i
$469$	17.1203			0.790543
$470$	0.918412	−	7.32147i	0.0423632	−	0.337714i
$471$	−31.7538			−1.46314
$472$	−24.7384	+	7.47854i	−1.13868	+	0.344227i
$473$			8.32808i			0.382925i
$474$	5.38076	+	2.44005i	0.247146	+	0.112075i
$475$	−15.3875	+	10.5703i	−0.706027	+	0.484997i
$476$	−18.8772	+	16.5336i	−0.865235	+	0.757817i
$477$	−1.18424			−0.0542227
$478$	−3.02421	+	6.66893i	−0.138324	+	0.305030i
$479$	−20.2212			−0.923929			−0.461965	−	0.886898i	$-0.652855\pi$
$479$	−20.2212			−0.923929			−0.461965	+	0.886898i	$0.652855\pi$
$480$	−31.3707	−	8.24327i	−1.43187	−	0.376252i
$481$		−	36.8255i		−	1.67910i
$482$	−18.0681	+	39.8434i	−0.822980	+	1.81482i
$483$	−11.7751	−	16.0862i	−0.535785	−	0.731945i
$484$	−12.3952	−	14.1521i	−0.563417	−	0.643278i
$485$	−6.53049	−	21.0403i	−0.296534	−	0.955389i
$486$	28.6306	+	12.9833i	1.29871	+	0.588936i
$487$	−21.7271			−0.984547			−0.492274	−	0.870440i	$-0.663834\pi$
$487$	−21.7271			−0.984547			−0.492274	+	0.870440i	$0.663834\pi$
$488$	−21.4167	+	6.47438i	−0.969490	+	0.293082i
$489$	30.5796			1.38286
$490$	−1.72087	+	13.7186i	−0.0777410	+	0.619742i
$491$			11.6459i			0.525572i	0.964854	+	0.262786i	$0.0846413\pi$
$491$			11.6459i			0.525572i	−0.964854	+	0.262786i	$0.915359\pi$
$492$	2.06543	+	2.35820i	0.0931168	+	0.106316i
$493$	−23.8017			−1.07197
$494$	−8.07778	+	17.8130i	−0.363436	+	0.801443i
$495$	−2.99175	−	9.63896i	−0.134469	−	0.433239i
$496$	−28.0032	−	3.72294i	−1.25738	−	0.167165i
$497$	−4.50451			−0.202055
$498$	19.8770	−	43.8325i	0.890711	−	1.96418i
$499$		−	20.6465i		−	0.924263i	−0.886811	−	0.462132i	$-0.847085\pi$
$499$		−	20.6465i		−	0.924263i	0.886811	−	0.462132i	$-0.152915\pi$
$500$	1.14827	+	22.3312i	0.0513522	+	0.998681i
$501$	25.9570			1.15967
$502$	−8.60548	−	3.90239i	−0.384081	−	0.174172i
$503$		−	19.9699i		−	0.890413i	−0.895428	−	0.445207i	$-0.853130\pi$
$503$		−	19.9699i		−	0.890413i	0.895428	−	0.445207i	$-0.146870\pi$
$504$	−15.6921	+	4.74381i	−0.698983	+	0.211306i
$505$	−1.82668	−	5.88528i	−0.0812860	−	0.261891i
$506$	−8.38055	+	1.75246i	−0.372561	+	0.0779066i
$507$	−1.84924			−0.0821278
$508$	−15.7802	−	18.0170i	−0.700135	−	0.799376i
$509$	−21.2795			−0.943197			−0.471598	−	0.881813i	$-0.656323\pi$
$509$	−21.2795			−0.943197			−0.471598	+	0.881813i	$0.656323\pi$
$510$	7.81186	−	62.2752i	0.345915	−	2.75759i
$511$	−8.48425			−0.375321
$512$	17.4501	+	14.4047i	0.771191	+	0.636603i
$513$	5.50935			0.243244
$514$	14.0127	−	30.9005i	0.618072	−	1.36296i
$515$	20.1886	−	6.26615i	0.889615	−	0.276119i
$516$	−25.4517	+	22.2920i	−1.12045	+	0.981349i
$517$	−2.94561			−0.129548
$518$	−9.41265	+	20.7566i	−0.413568	+	0.911992i
$519$		−	12.2500i		−	0.537717i
$520$	13.1220	+	19.4077i	0.575440	+	0.851083i
$521$			6.12734i			0.268444i	0.990951	+	0.134222i	$0.0428535\pi$
$521$			6.12734i			0.268444i	−0.990951	+	0.134222i	$0.957147\pi$
$522$	−14.1612	−	6.42179i	−0.619819	−	0.281074i
$523$			3.52313i			0.154056i	0.997029	+	0.0770278i	$0.0245430\pi$
$523$			3.52313i			0.154056i	−0.997029	+	0.0770278i	$0.975457\pi$
$524$	−7.84595	+	6.87189i	−0.342752	+	0.300200i
$525$	11.7682	+	17.1314i	0.513607	+	0.747675i
$526$	−0.716323	+	1.57962i	−0.0312332	+	0.0688748i
$527$		−	54.6632i		−	2.38117i
$528$	−1.70641	+	12.8353i	−0.0742620	+	0.558584i
$529$	6.95129	−	21.9244i	0.302230	−	0.953235i
$530$	0.130364	−	1.03925i	0.00566267	−	0.0451421i
$531$		−	32.6697i		−	1.41775i
$532$	9.10603	−	7.97553i	0.394796	−	0.345783i
$533$		−	2.26420i		−	0.0980736i
$534$	18.2790	−	40.3085i	0.791010	−	1.74432i
$535$	−7.13343	+	2.21408i	−0.308405	+	0.0957230i
$536$	28.5937	−	8.64402i	1.23506	−	0.373365i
$537$			64.8208i			2.79723i
$538$	21.5057	+	9.75234i	0.927175	+	0.420453i
$539$	5.51933			0.237734
$540$	3.45222	−	5.62401i	0.148560	−	0.242019i
$541$	−21.0618			−0.905518			−0.452759	−	0.891633i	$-0.649560\pi$
$541$	−21.0618			−0.905518			−0.452759	+	0.891633i	$0.649560\pi$
$542$	−13.8854	+	30.6198i	−0.596428	+	1.31523i
$543$			3.40169i			0.145980i
$544$	−23.1802	+	37.1449i	−0.993841	+	1.59257i
$545$	27.1532	−	8.42783i	1.16312	−	0.361009i
$546$	19.8317	+	8.99324i	0.848720	+	0.384875i
$547$	44.2233			1.89085			0.945425	−	0.325839i	$-0.105647\pi$
$547$	44.2233			1.89085			0.945425	+	0.325839i	$0.105647\pi$
$548$	−16.9294	−	19.3291i	−0.723189	−	0.825698i
$549$		−	28.2831i		−	1.20710i
$550$	8.78817	−	1.56437i	0.374729	−	0.0667051i
$551$	11.4815			0.489129
$552$	−27.7882	−	20.9212i	−1.18274	−	0.890467i
$553$			2.64102i			0.112308i
$554$	−0.112798	+	0.248740i	−0.00479232	+	0.0105679i
$555$	−16.8975	−	54.4414i	−0.717261	−	2.31091i
$556$	9.17546	−	8.03634i	0.389126	−	0.340817i
$557$	−11.8698			−0.502938			−0.251469	−	0.967865i	$-0.580914\pi$
$557$	−11.8698			−0.502938			−0.251469	+	0.967865i	$0.580914\pi$
$558$	14.7484	−	32.5228i	0.624348	−	1.37680i
$559$	24.4373			1.03359
$560$	−2.43558	−	14.2931i	−0.102922	−	0.603994i
$561$	−25.0549			−1.05782
$562$	−0.400334	+	0.882810i	−0.0168871	+	0.0372391i
$563$			27.1163i			1.14282i	0.820666	+	0.571408i	$0.193603\pi$
$563$			27.1163i			1.14282i	−0.820666	+	0.571408i	$0.806397\pi$
$564$	−7.88459	−	9.00220i	−0.332001	−	0.379061i
$565$	−9.08679	−	29.2763i	−0.382284	−	1.23166i
$566$	3.67859	−	8.11196i	0.154623	−	0.340971i
$567$			11.2542i			0.472632i
$568$	−7.52326	+	2.27432i	−0.315669	+	0.0954283i
$569$			16.5698i			0.694644i	0.937746	+	0.347322i	$0.112909\pi$
$569$			16.5698i			0.694644i	−0.937746	+	0.347322i	$0.887091\pi$
$570$	−3.76831	+	30.0405i	−0.157837	+	1.25826i
$571$	−26.2174			−1.09717			−0.548583	−	0.836096i	$-0.684833\pi$
$571$	−26.2174			−1.09717			−0.548583	+	0.836096i	$0.684833\pi$
$572$	7.03526	−	6.16184i	0.294159	−	0.257640i
$573$	−44.5935			−1.86292
$574$	−0.578733	+	1.27621i	−0.0241559	+	0.0532681i
$575$	−7.92906	+	22.6303i	−0.330665	+	0.943748i
$576$	−23.8133	+	15.8459i	−0.992219	+	0.660244i
$577$			35.5566i			1.48024i	0.672473	+	0.740121i	$0.265232\pi$
$577$			35.5566i			1.48024i	−0.672473	+	0.740121i	$0.734768\pi$
$578$	−55.2645	−	25.0612i	−2.29870	−	1.04241i
$579$			41.1910i			1.71184i
$580$	7.19444	−	11.7205i	0.298733	−	0.486666i
$581$	21.5142			0.892557
$582$	−32.5391	−	14.7558i	−1.34879	−	0.611646i
$583$	−0.418117			−0.0173166
$584$	−14.1701	+	4.28368i	−0.586362	+	0.177260i
$585$	−28.2838	+	8.77876i	−1.16939	+	0.362957i
$586$	32.3823	+	14.6846i	1.33770	+	0.606616i
$587$	−21.4550			−0.885542			−0.442771	−	0.896635i	$-0.646005\pi$
$587$	−21.4550			−0.885542			−0.442771	+	0.896635i	$0.646005\pi$
$588$	14.7737	+	16.8678i	0.609258	+	0.695618i
$589$			26.3686i			1.08650i
$590$	28.6699	+	3.59637i	1.18032	+	0.148060i
$591$			33.8075i			1.39065i
$592$	−5.24067	+	39.4193i	−0.215390	+	1.62012i
$593$			24.9201i			1.02335i	0.859180	+	0.511673i	$0.170974\pi$
$593$			24.9201i			1.02335i	−0.859180	+	0.511673i	$0.829026\pi$
$594$	−2.39916	−	1.08796i	−0.0984386	−	0.0446397i
$595$	26.7950	−	8.31664i	1.09849	−	0.340949i
$596$	15.5351	−	13.6064i	0.636341	−	0.557340i
$597$	12.4311			0.508770
$598$	5.14230	+	24.5913i	0.210284	+	1.00561i
$599$			42.3392i			1.72993i	0.501831	+	0.864965i	$0.332660\pi$
$599$			42.3392i			1.72993i	−0.501831	+	0.864965i	$0.667340\pi$
$600$	28.3044	+	22.6704i	1.15552	+	0.925517i
$601$	11.3211			0.461796			0.230898	−	0.972978i	$-0.425834\pi$
$601$	11.3211			0.461796			0.230898	+	0.972978i	$0.425834\pi$
$602$	−13.7740	−	6.24620i	−0.561386	−	0.254576i
$603$			37.7611i			1.53775i
$604$	−17.9279	+	15.7021i	−0.729474	+	0.638911i
$605$	6.23494	+	20.0880i	0.253486	+	0.816695i
$606$	−9.10169	−	4.12741i	−0.369731	−	0.167665i
$607$	−44.0794			−1.78913			−0.894564	−	0.446940i	$-0.852514\pi$
$607$	−44.0794			−1.78913			−0.894564	+	0.446940i	$0.852514\pi$
$608$	11.1817	−	17.9180i	0.453478	−	0.726673i
$609$		−	12.7827i		−	0.517982i
$610$	24.8203	+	3.11348i	1.00495	+	0.126061i
$611$			8.64339i			0.349674i
$612$	−36.4671	−	41.6361i	−1.47409	−	1.68304i
$613$	39.7817			1.60677			0.803384	−	0.595462i	$-0.203031\pi$
$613$	39.7817			1.60677			0.803384	+	0.595462i	$0.203031\pi$
$614$	0.507012	+	0.229918i	0.0204613	+	0.00927875i
$615$	−1.03894	−	3.34731i	−0.0418941	−	0.134977i
$616$	−5.54038	+	1.67488i	−0.223228	+	0.0674830i
$617$	1.72131			0.0692972			0.0346486	−	0.999400i	$-0.488969\pi$
$617$	1.72131			0.0692972			0.0346486	+	0.999400i	$0.488969\pi$
$618$	14.1585	−	31.2220i	0.569538	−	1.25593i
$619$	12.8611			0.516933			0.258467	−	0.966020i	$-0.416783\pi$
$619$	12.8611			0.516933			0.258467	+	0.966020i	$0.416783\pi$
$620$	26.9174	+	16.5228i	1.08103	+	0.663574i
$621$	5.71029	−	4.17994i	0.229146	−	0.167735i
$622$	1.57964	−	3.48339i	0.0633378	−	0.139671i
$623$	19.7845			0.792649
$624$	37.6629	+	5.00716i	1.50772	+	0.200447i
$625$	8.97006	−	23.3353i	0.358802	−	0.933414i
$626$	−15.9926	−	7.25227i	−0.639192	−	0.289859i
$627$	12.0861			0.482671
$628$	−16.3178	−	18.6308i	−0.651151	−	0.743449i
$629$	−76.9478			−3.06811
$630$	18.1860	+	2.28126i	0.724546	+	0.0908877i
$631$	7.22744			0.287720			0.143860	−	0.989598i	$-0.454049\pi$
$631$	7.22744			0.287720			0.143860	+	0.989598i	$0.454049\pi$
$632$	1.33345	+	4.41093i	0.0530417	+	0.175457i
$633$		−	57.4091i		−	2.28181i
$634$	−11.2712	+	24.8550i	−0.447635	+	0.987116i
$635$	7.93767	+	25.5740i	0.314997	+	1.01487i
$636$	−1.11918	−	1.27782i	−0.0443785	−	0.0506689i
$637$		−	16.1955i		−	0.641689i
$638$	−4.99986	−	2.26732i	−0.197946	−	0.0897641i
$639$		−	9.93529i		−	0.393034i
$640$	−11.2844	−	22.6421i	−0.446054	−	0.895006i
$641$			6.18142i			0.244151i	0.992521	+	0.122076i	$0.0389551\pi$
$641$			6.18142i			0.244151i	−0.992521	+	0.122076i	$0.961045\pi$
$642$	−5.00276	+	11.0320i	−0.197443	+	0.435398i
$643$		−	1.29026i		−	0.0508828i	−0.999676	−	0.0254414i	$-0.991901\pi$
$643$		−	1.29026i		−	0.0508828i	0.999676	−	0.0254414i	$-0.00809912\pi$
$644$	3.38711	−	15.1752i	0.133471	−	0.597985i
$645$	36.1271	−	11.2132i	1.42250	−	0.441518i
$646$	37.2206	+	16.8787i	1.46443	+	0.664084i
$647$	−6.12824			−0.240926			−0.120463	−	0.992718i	$-0.538438\pi$
$647$	−6.12824			−0.240926			−0.120463	+	0.992718i	$0.538438\pi$
$648$	5.68223	+	18.7963i	0.223219	+	0.738390i
$649$		−	11.5346i		−	0.452773i
$650$	−4.59038	−	25.7873i	−0.180050	−	1.01146i
$651$	29.3570			1.15059
$652$	15.7144	+	17.9418i	0.615423	+	0.702657i
$653$			7.74694i			0.303161i	0.988445	+	0.151581i	$0.0484363\pi$
$653$			7.74694i			0.303161i	−0.988445	+	0.151581i	$0.951564\pi$
$654$	19.0429	−	41.9930i	0.744635	−	1.64205i
$655$	11.1368	−	3.45665i	0.435152	−	0.135063i
$656$	−0.322221	+	2.42368i	−0.0125806	+	0.0946289i
$657$		−	18.7131i		−	0.730069i
$658$	2.20926	−	4.87182i	0.0861260	−	0.189923i
$659$	−36.4649			−1.42047			−0.710235	−	0.703965i	$-0.751411\pi$
$659$	−36.4649			−1.42047			−0.710235	+	0.703965i	$0.751411\pi$
$660$	7.57326	−	12.3376i	0.294789	−	0.480240i
$661$			39.3779i			1.53162i	0.643064	+	0.765812i	$0.277663\pi$
$661$			39.3779i			1.53162i	−0.643064	+	0.765812i	$0.722337\pi$
$662$	14.4232	−	31.8057i	0.560572	−	1.23616i
$663$			73.5193i			2.85525i
$664$	35.9321	−	10.8625i	1.39444	−	0.421545i
$665$	−12.9254	+	4.01180i	−0.501226	+	0.155571i
$666$	−45.7814	−	20.7608i	−1.77399	−	0.804466i
$667$	11.9003	−	8.71103i	0.460781	−	0.337292i
$668$	13.3389	+	15.2296i	0.516098	+	0.589252i
$669$	−34.5989			−1.33767
$670$	−33.1379	−	4.15684i	−1.28023	−	0.160593i
$671$		−	9.98585i		−	0.385499i
$672$	−19.9487	−	12.4489i	−0.769539	−	0.480229i
$673$		−	43.3599i		−	1.67140i	−0.549186	−	0.835700i	$-0.685062\pi$
$673$		−	43.3599i		−	1.67140i	0.549186	−	0.835700i	$-0.314938\pi$
$674$	1.04339	+	0.473153i	0.0401898	+	0.0182252i
$675$	−6.08133	+	4.17750i	−0.234070	+	0.160792i
$676$	−0.950298	−	1.08500i	−0.0365499	−	0.0417307i
$677$	−26.2636			−1.00939			−0.504696	−	0.863297i	$-0.668395\pi$
$677$	−26.2636			−1.00939			−0.504696	+	0.863297i	$0.668395\pi$
$678$	−45.2763	−	20.5318i	−1.73883	−	0.788519i
$679$		−	15.9711i		−	0.612914i
$680$	40.5529	−	27.4189i	1.55513	−	1.05147i
$681$		−	6.80684i		−	0.260838i
$682$	5.20716	−	11.4827i	0.199392	−	0.439696i
$683$	−1.55833			−0.0596279			−0.0298139	−	0.999555i	$-0.509491\pi$
$683$	−1.55833			−0.0596279			−0.0298139	+	0.999555i	$0.509491\pi$
$684$	17.5911	+	20.0846i	0.672612	+	0.767952i
$685$	8.51573	+	27.4364i	0.325369	+	1.04829i
$686$	−10.7672	+	23.7436i	−0.411093	+	0.906535i
$687$		−	45.1161i		−	1.72129i
$688$	−26.1585	−	3.47769i	−0.997284	−	0.132586i
$689$			1.22689i			0.0467408i
$690$	18.8860	+	33.9952i	0.718977	+	1.29417i
$691$			20.9491i			0.796941i	0.917181	+	0.398471i	$0.130459\pi$
$691$			20.9491i			0.796941i	−0.917181	+	0.398471i	$0.869541\pi$
$692$	7.18741	−	6.29511i	0.273224	−	0.239304i
$693$		−	7.31668i		−	0.277938i
$694$	26.6059	+	12.0652i	1.00995	+	0.457988i
$695$	−13.0240	+	4.04239i	−0.494028	+	0.153337i
$696$	−6.45398	−	21.3492i	−0.244637	−	0.809240i
$697$	−4.73111			−0.179204
$698$	11.7447	+	5.32594i	0.444542	+	0.201590i
$699$		−	7.99890i		−	0.302546i
$700$	−4.00392	+	15.7083i	−0.151334	+	0.593716i
$701$			32.8322i			1.24005i	0.784580	+	0.620027i	$0.212879\pi$
$701$			32.8322i			1.24005i	−0.784580	+	0.620027i	$0.787121\pi$
$702$	−3.19244	+	7.03990i	−0.120491	+	0.265704i
$703$	37.1183			1.39994
$704$	−8.40768	+	5.59466i	−0.316876	+	0.210857i
$705$	3.96606	+	12.7780i	0.149370	+	0.481249i
$706$	−10.8286	+	23.8789i	−0.407538	+	0.898695i
$707$		−	4.46736i		−	0.168012i
$708$	35.2514	−	30.8750i	1.32483	−	1.16035i
$709$		−	39.9184i		−	1.49917i	−0.661910	−	0.749584i	$-0.730254\pi$
$709$		−	39.9184i		−	1.49917i	0.661910	−	0.749584i	$-0.269746\pi$
$710$	8.71887	+	1.09370i	0.327213	+	0.0410459i
$711$	−5.82512			−0.218459
$712$	33.0433	−	9.98916i	1.23835	−	0.374360i
$713$	20.0059	+	27.3303i	0.749225	+	1.02353i
$714$	18.7916	−	41.4389i	0.703259	−	1.55081i
$715$	−9.98610	+	3.09949i	−0.373459	+	0.115914i
$716$	−38.0320	+	33.3104i	−1.42132	+	1.24487i
$717$		−	13.2774i		−	0.495853i
$718$	−32.0616	−	14.5392i	−1.19653	−	0.542599i
$719$			24.6272i			0.918438i	0.888323	+	0.459219i	$0.151871\pi$
$719$			24.6272i			0.918438i	−0.888323	+	0.459219i	$0.848129\pi$
$720$	31.5253	−	5.37199i	1.17488	−	0.200202i
$721$	15.3246			0.570718
$722$	6.51684	+	2.95524i	0.242532	+	0.109983i
$723$		−	79.3256i		−	2.95015i
$724$	−1.99586	+	1.74808i	−0.0741755	+	0.0649667i
$725$	−12.6735	+	8.70593i	−0.470683	+	0.323330i
$726$	31.0665	+	14.0880i	1.15299	+	0.522854i
$727$			4.57658i			0.169736i	0.996392	+	0.0848679i	$0.0270468\pi$
$727$			4.57658i			0.169736i	−0.996392	+	0.0848679i	$0.972953\pi$
$728$	4.91465	+	16.2573i	0.182149	+	0.602534i
$729$	−36.1740			−1.33978
$730$	16.4220	+	2.05999i	0.607806	+	0.0762437i
$731$		−	51.0623i		−	1.88861i
$732$	30.5181	−	26.7293i	1.12798	−	0.987945i
$733$	28.9459			1.06914			0.534571	−	0.845123i	$-0.320473\pi$
$733$	28.9459			1.06914			0.534571	+	0.845123i	$0.320473\pi$
$734$	−19.4048	+	42.7912i	−0.716246	+	1.57945i
$735$	−7.43138	−	23.9428i	−0.274111	−	0.883143i
$736$	−2.00489	−	27.0551i	−0.0739012	−	0.997266i
$737$			13.3322i			0.491098i
$738$	−2.81485	−	1.27647i	−0.103616	−	0.0469876i
$739$			40.4785i			1.48903i	0.667608	+	0.744513i	$0.267318\pi$
$739$			40.4785i			1.48903i	−0.667608	+	0.744513i	$0.732682\pi$
$740$	23.2587	−	37.8908i	0.855008	−	1.39289i
$741$		−	35.4644i		−	1.30282i
$742$	0.313595	−	0.691533i	0.0115124	−	0.0253870i
$743$			32.9024i			1.20707i	0.797335	+	0.603537i	$0.206242\pi$
$743$			32.9024i			1.20707i	−0.797335	+	0.603537i	$0.793758\pi$
$744$	49.0309	−	14.8223i	1.79756	−	0.543412i
$745$	−22.0510	+	6.84421i	−0.807887	+	0.250753i
$746$	−19.3707	−	8.78418i	−0.709212	−	0.321612i
$747$			47.4523i			1.73619i
$748$	−12.8753	−	14.7004i	−0.470769	−	0.537498i
$749$	−5.41480			−0.197852
$750$	−18.6189	−	36.0166i	−0.679865	−	1.31514i
$751$	−19.3003			−0.704279			−0.352139	−	0.935948i	$-0.614546\pi$
$751$	−19.3003			−0.704279			−0.352139	+	0.935948i	$0.614546\pi$
$752$	1.23005	−	9.25218i	0.0448553	−	0.337392i
$753$	17.1329			0.624359
$754$	−6.65306	+	14.6712i	−0.242290	+	0.534294i
$755$	25.4474	−	7.89840i	0.926127	−	0.287452i
$756$	3.59882	−	3.15203i	0.130888	−	0.114638i
$757$	−44.6128			−1.62148			−0.810739	−	0.585408i	$-0.800935\pi$
$757$	−44.6128			−1.62148			−0.810739	+	0.585408i	$0.800935\pi$
$758$	40.0044	+	18.1411i	1.45303	+	0.658915i
$759$	12.5269	−	9.16969i	0.454697	−	0.332839i
$760$	−19.5620	+	13.2264i	−0.709588	+	0.479771i
$761$	38.6678			1.40171			0.700854	−	0.713305i	$-0.252803\pi$
$761$	38.6678			1.40171			0.700854	+	0.713305i	$0.252803\pi$
$762$	39.5507	+	17.9353i	1.43277	+	0.649729i
$763$	20.6113			0.746178
$764$	−22.9159	−	26.1642i	−0.829069	−	0.946586i
$765$	18.3434	+	59.0998i	0.663209	+	2.13676i
$766$	−2.06993	+	4.56457i	−0.0747895	+	0.164924i
$767$	−33.8463			−1.22212
$768$	−39.6031	−	10.7197i	−1.42905	−	0.386813i
$769$		−	27.9367i		−	1.00742i	−0.863872	−	0.503711i	$-0.831968\pi$
$769$		−	27.9367i		−	1.00742i	0.863872	−	0.503711i	$-0.168032\pi$
$770$	6.42087	+	0.805439i	0.231392	+	0.0290260i
$771$			61.5208i			2.21562i
$772$	−24.1678	+	21.1674i	−0.869817	+	0.761831i
$773$	9.02065			0.324450			0.162225	−	0.986754i	$-0.448133\pi$
$773$	9.02065			0.324450			0.162225	+	0.986754i	$0.448133\pi$
$774$	13.7768	−	30.3804i	0.495198	−	1.09200i
$775$	−19.9942	−	29.1062i	−0.718211	−	1.04552i
$776$	−8.06378	−	26.6743i	−0.289473	−	0.957552i
$777$		−	41.3250i		−	1.48253i
$778$	−5.01158	+	11.0514i	−0.179674	+	0.396213i
$779$	2.28221			0.0817685
$780$	−36.2025	−	22.2224i	−1.29626	−	0.795689i
$781$		−	3.50782i		−	0.125520i
$782$	51.3841	−	10.7450i	1.83749	−	0.384239i
$783$	4.53764			0.162162
$784$	−2.30480	+	17.3362i	−0.0823143	+	0.619151i
$785$	8.20808	+	26.4452i	0.292959	+	0.943870i
$786$	7.81038	−	17.2233i	0.278587	−	0.614335i
$787$		−	22.2563i		−	0.793352i	−0.917959	−	0.396676i	$-0.870164\pi$
$787$		−	22.2563i		−	0.793352i	0.917959	−	0.396676i	$-0.129836\pi$
$788$	−19.8357	+	17.3731i	−0.706618	+	0.618892i
$789$		−	3.14492i		−	0.111962i
$790$	0.641245	−	5.11193i	0.0228145	−	0.181874i
$791$		−	22.2228i		−	0.790153i
$792$	−3.69418	−	12.2200i	−0.131267	−	0.434220i
$793$	−29.3017			−1.04053
$794$	7.55555	−	16.6614i	0.268137	−	0.591290i
$795$	0.562964	+	1.81379i	0.0199663	+	0.0643284i
$796$	6.38813	+	7.29362i	0.226421	+	0.258516i
$797$	26.3482			0.933300			0.466650	−	0.884442i	$-0.345461\pi$
$797$	26.3482			0.933300			0.466650	+	0.884442i	$0.345461\pi$
$798$	−9.06475	+	19.9894i	−0.320889	+	0.707618i
$799$	18.0606			0.638938
$800$	1.24388	+	28.2569i	0.0439778	+	0.999033i
$801$			43.6373i			1.54185i
$802$	−14.4326	+	31.8266i	−0.509634	+	1.12384i
$803$		−	6.60700i		−	0.233156i
$804$	−40.7450	+	35.6866i	−1.43697	+	1.25857i
$805$	−10.3531	+	13.9646i	−0.364899	+	0.492189i
$806$	−33.6941	−	15.2795i	−1.18682	−	0.538197i
$807$	−42.8164			−1.50721
$808$	−2.25556	−	7.46121i	−0.0793503	−	0.262484i
$809$	−21.6638			−0.761657			−0.380829	−	0.924646i	$-0.624361\pi$
$809$	−21.6638			−0.761657			−0.380829	+	0.924646i	$0.624361\pi$
$810$	2.73254	−	21.7835i	0.0960117	−	0.765394i
$811$		−	0.319681i		−	0.0112255i	−0.999984	−	0.00561275i	$-0.998213\pi$
$811$		−	0.319681i		−	0.0112255i	0.999984	−	0.00561275i	$-0.00178660\pi$
$812$	7.49995	−	6.56885i	0.263197	−	0.230521i
$813$		−	60.9619i		−	2.13803i
$814$	−16.1639	−	7.32997i	−0.566545	−	0.256915i
$815$	−7.90456	−	25.4673i	−0.276885	−	0.892080i
$816$	10.4626	−	78.6975i	0.366264	−	2.75496i
$817$			24.6316i			0.861750i
$818$	−9.81775	−	4.45213i	−0.343270	−	0.155665i
$819$	−21.4695			−0.750205
$820$	1.43006	−	2.32970i	0.0499397	−	0.0813568i
$821$	12.4488			0.434466			0.217233	−	0.976120i	$-0.430297\pi$
$821$	12.4488			0.434466			0.217233	+	0.976120i	$0.430297\pi$
$822$	42.4309	+	19.2415i	1.47995	+	0.671123i
$823$	−24.9542			−0.869850			−0.434925	−	0.900467i	$-0.643225\pi$
$823$	−24.9542			−0.869850			−0.434925	+	0.900467i	$0.643225\pi$
$824$	25.5946	−	7.73737i	0.891629	−	0.269544i
$825$	−13.3408	+	9.16433i	−0.464468	+	0.319061i
$826$	19.0774	+	8.65116i	0.663787	+	0.301012i
$827$			37.0949i			1.28992i	0.764218	+	0.644958i	$0.223125\pi$
$827$			37.0949i			1.28992i	−0.764218	+	0.644958i	$0.776875\pi$
$828$	33.4708	+	7.47073i	1.16319	+	0.259626i
$829$	−30.2201			−1.04959			−0.524794	−	0.851230i	$-0.675858\pi$
$829$	−30.2201			−1.04959			−0.524794	+	0.851230i	$0.675858\pi$
$830$	−41.6425	−	5.22368i	−1.44543	−	0.181316i
$831$		−	0.495224i		−	0.0171791i
$832$	16.4165	+	24.6709i	0.569141	+	0.855308i
$833$	−33.8409			−1.17252
$834$	−9.13386	+	20.1418i	−0.316280	+	0.697454i
$835$	−6.70965	−	21.6175i	−0.232197	−	0.748104i
$836$	6.21084	+	7.09120i	0.214806	+	0.245254i
$837$			10.4212i			0.360209i
$838$	7.15233	+	3.24342i	0.247073	+	0.112042i
$839$	−18.5073			−0.638942			−0.319471	−	0.947596i	$-0.603505\pi$
$839$	−18.5073			−0.638942			−0.319471	+	0.947596i	$0.603505\pi$
$840$	14.7253	+	21.7790i	0.508073	+	0.751446i
$841$	−19.5435			−0.673915
$842$	−5.57981	+	12.3045i	−0.192293	+	0.424041i
$843$		−	1.75762i		−	0.0605355i
$844$	33.6834	−	29.5017i	1.15943	−	1.01549i
$845$	0.478013	+	1.54009i	0.0164441	+	0.0529805i
$846$	10.7454	+	4.87282i	0.369436	+	0.167531i
$847$			15.2483i			0.523937i
$848$	0.174600	−	1.31331i	0.00599579	−	0.0450991i
$849$			16.1504i			0.554280i
$850$	−53.8833	+	9.59172i	−1.84818	+	0.328993i
$851$	38.4721	−	28.1617i	1.31881	−	0.965369i
$852$	10.7204	−	9.38947i	0.367275	−	0.321678i
$853$		−	42.7030i		−	1.46212i	−0.682312	−	0.731061i	$-0.739025\pi$
$853$		−	42.7030i		−	1.46212i	0.682312	−	0.731061i	$-0.260975\pi$
$854$	16.5158	+	7.48956i	0.565160	+	0.256287i
$855$	−8.84856	−	28.5087i	−0.302614	−	0.974978i
$856$	−9.04359	+	2.73392i	−0.309104	+	0.0934436i
$857$		−	20.9362i		−	0.715168i	−0.933881	−	0.357584i	$-0.883601\pi$
$857$		−	20.9362i		−	0.715168i	0.933881	−	0.357584i	$-0.116399\pi$
$858$	−7.00337	+	15.4437i	−0.239091	+	0.527239i
$859$			36.7363i			1.25343i	0.779250	+	0.626714i	$0.215600\pi$
$859$			36.7363i			1.25343i	−0.779250	+	0.626714i	$0.784400\pi$
$860$	25.1442	+	15.4344i	0.857410	+	0.526309i
$861$		−	2.54085i		−	0.0865920i
$862$	−47.4018	−	21.4957i	−1.61451	−	0.732145i
$863$	47.2340			1.60786			0.803932	−	0.594721i	$-0.202737\pi$
$863$	47.2340			1.60786			0.803932	+	0.594721i	$0.202737\pi$
$864$	4.41915	−	7.08143i	0.150343	−	0.240915i
$865$	−10.2021	+	3.16652i	−0.346881	+	0.107665i
$866$	−20.7452	−	9.40750i	−0.704952	−	0.319680i
$867$	110.028			3.73674
$868$	15.0861	+	17.2245i	0.512055	+	0.584637i
$869$	−2.05666			−0.0697673
$870$	−3.10367	+	24.7421i	−0.105224	+	0.838836i
$871$	39.1210			1.32557
$872$	34.4242	−	10.4066i	1.16575	−	0.352412i
$873$	35.2264			1.19223
$874$	−24.7868	+	5.18319i	−0.838426	+	0.175324i
$875$	11.2254	−	14.2291i	0.379487	−	0.481031i
$876$	20.1919	−	17.6851i	0.682220	−	0.597524i
$877$			0.341245i			0.0115230i	0.999983	+	0.00576151i	$0.00183396\pi$
$877$			0.341245i			0.0115230i	−0.999983	+	0.00576151i	$0.998166\pi$
$878$	−18.0560	+	39.8168i	−0.609361	+	1.34375i
$879$	−64.4709			−2.17455
$880$	11.1306	−	1.89667i	0.375211	−	0.0639368i
$881$			37.6366i			1.26801i	0.773329	+	0.634005i	$0.218590\pi$
$881$			37.6366i			1.26801i	−0.773329	+	0.634005i	$0.781410\pi$
$882$	−20.1342	−	9.13042i	−0.677955	−	0.307437i
$883$	−10.8974			−0.366725			−0.183363	−	0.983045i	$-0.558698\pi$
$883$	−10.8974			−0.366725			−0.183363	+	0.983045i	$0.558698\pi$
$884$	−43.1356	+	37.7804i	−1.45081	+	1.27069i
$885$	−50.0370	+	15.5305i	−1.68198	+	0.522053i
$886$	2.40646	+	1.09128i	0.0808467	+	0.0366622i
$887$	−17.9288			−0.601991			−0.300995	−	0.953626i	$-0.597319\pi$
$887$	−17.9288			−0.601991			−0.300995	+	0.953626i	$0.597319\pi$
$888$	−20.8649	−	69.0194i	−0.700181	−	2.31614i
$889$			19.4125i			0.651075i
$890$	−38.2946	−	4.80371i	−1.28364	−	0.161021i
$891$	−8.76406			−0.293607
$892$	−17.7798	−	20.3000i	−0.595313	−	0.679696i
$893$	−8.71211			−0.291540
$894$	−15.4646	+	34.1023i	−0.517215	+	1.14055i
$895$	53.9840	−	16.7556i	1.80449	−	0.560078i
$896$	−2.94723	−	18.1017i	−0.0984599	−	0.604737i
$897$	−26.9069	−	36.7579i	−0.898394	−	1.22731i
$898$	−42.7304	−	19.3773i	−1.42593	−	0.646627i
$899$			21.7178i			0.724330i
$900$	−34.6466	−	8.83117i	−1.15489	−	0.294372i
$901$	2.56362			0.0854066
$902$	−0.993833	−	0.450681i	−0.0330910	−	0.0150060i
$903$	27.4231			0.912584
$904$	−11.2203	−	37.1157i	−0.373181	−	1.23445i
$905$	2.83299	−	0.879306i	0.0941718	−	0.0292291i
$906$	17.8466	−	39.3550i	0.592913	−	1.30748i
$907$		−	56.2830i		−	1.86885i	−0.356164	−	0.934423i	$-0.615916\pi$
$907$		−	56.2830i		−	1.86885i	0.356164	−	0.934423i	$-0.384084\pi$
$908$	3.99374	−	3.49793i	0.132537	−	0.116083i
$909$	9.85334			0.326815
$910$	2.36342	−	18.8409i	0.0783466	−	0.624570i
$911$	26.0399			0.862742			0.431371	−	0.902175i	$-0.358030\pi$
$911$	26.0399			0.862742			0.431371	+	0.902175i	$0.358030\pi$
$912$	−5.04698	+	37.9623i	−0.167122	+	1.25706i
$913$			16.7539i			0.554472i
$914$	21.1318	+	9.58281i	0.698979	+	0.316971i
$915$	−43.3185	+	13.4452i	−1.43207	+	0.444485i
$916$	26.4708	−	23.1845i	0.874619	−	0.766037i
$917$	8.45366			0.279165
$918$	14.7101	+	6.67068i	0.485504	+	0.220165i
$919$	−20.8262			−0.686992			−0.343496	−	0.939154i	$-0.611611\pi$
$919$	−20.8262			−0.686992			−0.343496	+	0.939154i	$0.611611\pi$
$920$	−10.2406	+	28.5505i	−0.337623	+	0.941281i
$921$	−1.00943			−0.0332617
$922$	15.7423	+	7.13879i	0.518446	+	0.235103i
$923$	−10.2931			−0.338801
$924$	7.89485	−	6.91472i	0.259722	−	0.227478i
$925$	−40.9719	+	28.1452i	−1.34715	+	0.925408i
$926$	−49.6377	−	22.5096i	−1.63120	−	0.739711i
$927$			33.8005i			1.11015i
$928$	9.20953	−	14.7578i	0.302318	−	0.484447i
$929$	34.6067			1.13541			0.567704	−	0.823233i	$-0.307832\pi$
$929$	34.6067			1.13541			0.567704	+	0.823233i	$0.307832\pi$
$930$	−56.8230	−	7.12793i	−1.86330	−	0.233734i
$931$	16.3243			0.535007
$932$	4.69316	−	4.11051i	0.153730	−	0.134644i
$933$			6.93520i			0.227048i
$934$	5.25686	−	11.5923i	0.172010	−	0.379313i
$935$	6.47647	+	20.8662i	0.211803	+	0.682398i
$936$	−35.8576	+	10.8399i	−1.17204	+	0.354314i
$937$	−28.5789			−0.933633			−0.466817	−	0.884354i	$-0.654599\pi$
$937$	−28.5789			−0.933633			−0.466817	+	0.884354i	$0.654599\pi$
$938$	−22.0505	−	9.99938i	−0.719973	−	0.326491i
$939$	31.8401			1.03906
$940$	−5.45911	+	8.89343i	−0.178056	+	0.290072i
$941$			30.7312i			1.00181i	0.865502	+	0.500905i	$0.166999\pi$
$941$			30.7312i			1.00181i	−0.865502	+	0.500905i	$0.833001\pi$
$942$	40.8980	+	18.5463i	1.33253	+	0.604272i
$943$	2.36545	−	1.73151i	0.0770295	−	0.0563858i
$944$	36.2302	+	4.81670i	1.17919	+	0.156770i
$945$	−5.10829	+	1.58551i	−0.166173	+	0.0515768i
$946$	4.86414	−	10.7263i	0.158147	−	0.348743i
$947$	6.09604			0.198095			0.0990474	−	0.995083i	$-0.468420\pi$
$947$	6.09604			0.198095			0.0990474	+	0.995083i	$0.468420\pi$
$948$	−5.50510	−	6.28543i	−0.178797	−	0.204141i
$949$	−19.3871			−0.629331
$950$	25.9924	−	4.62688i	0.843304	−	0.150116i
$951$		−	49.4846i		−	1.60465i
$952$	33.9700	−	10.2693i	1.10097	−	0.332830i
$953$	−14.7724			−0.478526			−0.239263	−	0.970955i	$-0.576906\pi$
$953$	−14.7724			−0.478526			−0.239263	+	0.970955i	$0.576906\pi$
$954$	1.52527	+	0.691675i	0.0493824	+	0.0223938i
$955$	11.5270	+	37.1383i	0.373006	+	1.20177i
$956$	7.79018	−	6.82304i	0.251952	−	0.220673i
$957$	9.95438			0.321779
$958$	26.0443	+	11.8105i	0.841453	+	0.381580i
$959$			20.8262i			0.672515i
$960$	35.5899	+	28.9396i	1.14866	+	0.934022i
$961$	−18.8774			−0.608949
$962$	−21.5085	+	47.4302i	−0.693462	+	1.52921i
$963$		−	11.9431i		−	0.384860i
$964$	46.5424	−	40.7642i	1.49903	−	1.31293i
$965$	34.3046	−	10.6475i	1.10430	−	0.342755i
$966$	5.77061	+	27.5959i	0.185666	+	0.887884i
$967$	−6.31871			−0.203196			−0.101598	−	0.994826i	$-0.532396\pi$
$967$	−6.31871			−0.203196			−0.101598	+	0.994826i	$0.532396\pi$
$968$	7.69883	+	25.4671i	0.247450	+	0.818544i
$969$	−74.1038			−2.38056
$970$	−3.87781	+	30.9135i	−0.124509	+	0.992571i
$971$	1.24147			0.0398407			0.0199204	−	0.999802i	$-0.493659\pi$
$971$	1.24147			0.0398407			0.0199204	+	0.999802i	$0.493659\pi$
$972$	−29.2923	−	33.4443i	−0.939549	−	1.07273i
$973$	−9.88615			−0.316935
$974$	27.9838	+	12.6900i	0.896659	+	0.406615i
$975$	26.8911	+	39.1463i	0.861205	+	1.25369i
$976$	31.3656	+	4.16996i	1.00399	+	0.133477i
$977$	52.9476			1.69394			0.846972	−	0.531637i	$-0.178423\pi$
$977$	52.9476			1.69394			0.846972	+	0.531637i	$0.178423\pi$
$978$	−39.3856	−	17.8605i	−1.25941	−	0.571116i
$979$			15.4069i			0.492407i
$980$	10.2290	−	16.6640i	0.326753	−	0.532312i
$981$			45.4609i			1.45145i
$982$	6.80197	−	14.9996i	0.217059	−	0.478655i
$983$		−	24.3193i		−	0.775664i	−0.921730	−	0.387832i	$-0.873224\pi$
$983$		−	24.3193i		−	0.775664i	0.921730	−	0.387832i	$-0.126776\pi$
$984$	−1.28287	−	4.24364i	−0.0408965	−	0.135282i
$985$	28.1555	−	8.73893i	0.897109	−	0.278445i
$986$	30.6558	+	13.9017i	0.976281	+	0.442722i
$987$			9.69947i			0.308738i
$988$	20.8079	−	18.2246i	0.661987	−	0.579802i
$989$	18.6880	+	25.5300i	0.594244	+	0.811806i
$990$	−1.77650	+	14.1621i	−0.0564610	+	0.450100i
$991$		−	26.9879i		−	0.857299i	−0.903471	−	0.428650i	$-0.858989\pi$
$991$		−	26.9879i		−	0.857299i	0.903471	−	0.428650i	$-0.141011\pi$
$992$	33.8928	+	21.1507i	1.07610	+	0.671536i
$993$			63.3229i			2.00949i
$994$	5.80167	+	2.63093i	0.184018	+	0.0834480i
$995$	−3.21332	−	10.3528i	−0.101869	−	0.328207i
$996$	−51.2021	+	44.8454i	−1.62240	+	1.42098i
$997$		−	1.51921i		−	0.0481140i	−0.999711	−	0.0240570i	$-0.992342\pi$
$997$		−	1.51921i		−	0.0481140i	0.999711	−	0.0240570i	$-0.00765832\pi$
$998$	−12.0589	+	26.5920i	−0.381718	+	0.841756i
$999$	14.6696			0.464126

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.g.c.459.5	✓	56
4.3	odd	2	inner	460.2.g.c.459.49	yes	56
5.4	even	2	inner	460.2.g.c.459.52	yes	56
20.19	odd	2	inner	460.2.g.c.459.8	yes	56
23.22	odd	2	inner	460.2.g.c.459.6	yes	56
92.91	even	2	inner	460.2.g.c.459.50	yes	56
115.114	odd	2	inner	460.2.g.c.459.51	yes	56
460.459	even	2	inner	460.2.g.c.459.7	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.g.c.459.5	✓	56	1.1	even	1	trivial
460.2.g.c.459.6	yes	56	23.22	odd	2	inner
460.2.g.c.459.7	yes	56	460.459	even	2	inner
460.2.g.c.459.8	yes	56	20.19	odd	2	inner
460.2.g.c.459.49	yes	56	4.3	odd	2	inner
460.2.g.c.459.50	yes	56	92.91	even	2	inner
460.2.g.c.459.51	yes	56	115.114	odd	2	inner
460.2.g.c.459.52	yes	56	5.4	even	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28797 - 0.584066i) q^{2} +2.56426 q^{3} +(1.31773 + 1.50452i) q^{4} +(-0.662839 - 2.13557i) q^{5} +(-3.30269 - 1.49770i) q^{6} -1.62105i q^{7} +(-0.818466 - 2.70742i) q^{8} +3.57544 q^{9} +O(q^{10})\)	\(q+(-1.28797 - 0.584066i) q^{2} +2.56426 q^{3} +(1.31773 + 1.50452i) q^{4} +(-0.662839 - 2.13557i) q^{5} +(-3.30269 - 1.49770i) q^{6} -1.62105i q^{7} +(-0.818466 - 2.70742i) q^{8} +3.57544 q^{9} +(-0.393594 + 3.13769i) q^{10} +1.26237 q^{11} +(3.37902 + 3.85798i) q^{12} -3.70421i q^{13} +(-0.946800 + 2.08787i) q^{14} +(-1.69969 - 5.47615i) q^{15} +(-0.527150 + 3.96511i) q^{16} -7.74004 q^{17} +(-4.60507 - 2.08829i) q^{18} +3.73366 q^{19} +(2.33955 - 3.81136i) q^{20} -4.15680i q^{21} +(-1.62590 - 0.737308i) q^{22} +(3.86984 - 2.83273i) q^{23} +(-2.09876 - 6.94253i) q^{24} +(-4.12129 + 2.83107i) q^{25} +(-2.16350 + 4.77091i) q^{26} +1.47559 q^{27} +(2.43890 - 2.13612i) q^{28} +3.07514 q^{29} +(-1.00928 + 8.04586i) q^{30} +7.06240i q^{31} +(2.99484 - 4.79906i) q^{32} +3.23705 q^{33} +(9.96894 + 4.52069i) q^{34} +(-3.46186 + 1.07450i) q^{35} +(4.71149 + 5.37932i) q^{36} +9.94153 q^{37} +(-4.80884 - 2.18070i) q^{38} -9.49856i q^{39} +(-5.23936 + 3.54247i) q^{40} +0.611252 q^{41} +(-2.42784 + 5.35384i) q^{42} +6.59717i q^{43} +(1.66347 + 1.89926i) q^{44} +(-2.36994 - 7.63560i) q^{45} +(-6.63874 + 1.38823i) q^{46} -2.33340 q^{47} +(-1.35175 + 10.1676i) q^{48} +4.37219 q^{49} +(6.96163 - 1.23923i) q^{50} -19.8475 q^{51} +(5.57305 - 4.88116i) q^{52} -0.331215 q^{53} +(-1.90051 - 0.861841i) q^{54} +(-0.836749 - 2.69588i) q^{55} +(-4.38886 + 1.32678i) q^{56} +9.57409 q^{57} +(-3.96068 - 1.79608i) q^{58} -9.13726i q^{59} +(5.99923 - 9.77334i) q^{60} -7.91039i q^{61} +(4.12490 - 9.09616i) q^{62} -5.79598i q^{63} +(-6.66023 + 4.43186i) q^{64} +(-7.91058 + 2.45529i) q^{65} +(-4.16923 - 1.89065i) q^{66} +10.5612i q^{67} +(-10.1993 - 11.6450i) q^{68} +(9.92328 - 7.26386i) q^{69} +(5.08635 + 0.638037i) q^{70} -2.77876i q^{71} +(-2.92638 - 9.68022i) q^{72} -5.23380i q^{73} +(-12.8044 - 5.80651i) q^{74} +(-10.5681 + 7.25961i) q^{75} +(4.91997 + 5.61736i) q^{76} -2.04637i q^{77} +(-5.54778 + 12.2339i) q^{78} -1.62920 q^{79} +(8.81718 - 1.50247i) q^{80} -6.94253 q^{81} +(-0.787274 - 0.357011i) q^{82} +13.2717i q^{83} +(6.25398 - 5.47756i) q^{84} +(5.13040 + 16.5294i) q^{85} +(3.85318 - 8.49696i) q^{86} +7.88546 q^{87} +(-1.03321 - 3.41777i) q^{88} +12.2047i q^{89} +(-1.40727 + 11.2186i) q^{90} -6.00471 q^{91} +(9.36131 + 2.08946i) q^{92} +18.1098i q^{93} +(3.00535 + 1.36286i) q^{94} +(-2.47481 - 7.97348i) q^{95} +(7.67955 - 12.3060i) q^{96} +9.85230 q^{97} +(-5.63125 - 2.55365i) q^{98} +4.51354 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{4} - 8 q^{6} + 16 q^{9}+O(q^{10}) \) 56 * q - 8 * q^4 - 8 * q^6 + 16 * q^9	\( 56 q - 8 q^{4} - 8 q^{6} + 16 q^{9} - 8 q^{16} - 100 q^{24} - 24 q^{25} - 24 q^{26} - 16 q^{29} + 104 q^{41} - 8 q^{46} + 32 q^{49} - 32 q^{50} + 52 q^{54} - 92 q^{64} + 32 q^{69} - 44 q^{70} + 24 q^{81} + 56 q^{85} + 28 q^{94} + 88 q^{96}+O(q^{100}) \) 56 * q - 8 * q^4 - 8 * q^6 + 16 * q^9 - 8 * q^16 - 100 * q^24 - 24 * q^25 - 24 * q^26 - 16 * q^29 + 104 * q^41 - 8 * q^46 + 32 * q^49 - 32 * q^50 + 52 * q^54 - 92 * q^64 + 32 * q^69 - 44 * q^70 + 24 * q^81 + 56 * q^85 + 28 * q^94 + 88 * q^96

Introduction

L-functions

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