LMFDB - Embedded newform 450.2.l.c.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(19,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("450.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.l (of order $10$, degree $4$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + \cdots + 11105 $ x^16 - 4x^15 - 24x^14 + 94x^13 + 262x^12 - 936x^11 - 1584x^10 + 4642x^9 + 6259x^8 - 11958x^7 - 15752x^6 + 14670x^5 + 18271x^4 - 10440x^3 + 1135x^2 + 21080*x + 11105
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			379.1
Root			$-0.705457 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	450.379
Dual form			450.2.l.c.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(0.809017 + 0.587785i) q^{4} +(-1.97959 + 1.03982i) q^{5} -0.329315i q^{7} +(-0.587785 - 0.809017i) q^{8} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(0.809017 + 0.587785i) q^{4} +(-1.97959 + 1.03982i) q^{5} -0.329315i q^{7} +(-0.587785 - 0.809017i) q^{8} +(2.20402 - 0.377200i) q^{10} +(1.55540 - 4.78704i) q^{11} +(-0.458554 + 0.148993i) q^{13} +(-0.101764 + 0.313197i) q^{14} +(0.309017 + 0.951057i) q^{16} +(3.98877 + 5.49007i) q^{17} +(4.40115 - 3.19762i) q^{19} +(-2.21271 - 0.322342i) q^{20} +(-2.95855 + 4.07210i) q^{22} +(6.18239 + 2.00878i) q^{23} +(2.83755 - 4.11683i) q^{25} +0.482152 q^{26} +(0.193566 - 0.266421i) q^{28} +(4.87203 + 3.53974i) q^{29} +(-1.06685 + 0.775108i) q^{31} -1.00000i q^{32} +(-2.09702 - 6.45396i) q^{34} +(0.342428 + 0.651908i) q^{35} +(-0.741956 + 0.241076i) q^{37} +(-5.17386 + 1.68109i) q^{38} +(2.00481 + 0.990331i) q^{40} +(-3.86905 - 11.9077i) q^{41} +2.47582i q^{43} +(4.07210 - 2.95855i) q^{44} +(-5.25906 - 3.82093i) q^{46} +(2.57473 - 3.54381i) q^{47} +6.89155 q^{49} +(-3.97084 + 3.03849i) q^{50} +(-0.458554 - 0.148993i) q^{52} +(-0.990953 + 1.36393i) q^{53} +(1.89860 + 11.0937i) q^{55} +(-0.266421 + 0.193566i) q^{56} +(-3.53974 - 4.87203i) q^{58} +(0.313909 + 0.966113i) q^{59} +(1.29419 - 3.98310i) q^{61} +(1.25415 - 0.407499i) q^{62} +(-0.309017 + 0.951057i) q^{64} +(0.752823 - 0.771759i) q^{65} +(-1.84819 - 2.54381i) q^{67} +6.78610i q^{68} +(-0.124218 - 0.725818i) q^{70} +(4.62101 + 3.35736i) q^{71} +(-2.79866 - 0.909340i) q^{73} +0.780139 q^{74} +5.44012 q^{76} +(-1.57644 - 0.512218i) q^{77} +(6.86459 + 4.98742i) q^{79} +(-1.60065 - 1.56138i) q^{80} +12.5205i q^{82} +(-10.1073 - 13.9114i) q^{83} +(-13.6048 - 6.72048i) q^{85} +(0.765070 - 2.35464i) q^{86} +(-4.78704 + 1.55540i) q^{88} +(1.06683 - 3.28336i) q^{89} +(0.0490657 + 0.151009i) q^{91} +(3.82093 + 5.25906i) q^{92} +(-3.54381 + 2.57473i) q^{94} +(-5.38752 + 10.9064i) q^{95} +(-5.58986 + 7.69378i) q^{97} +(-6.55426 - 2.12961i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 4 q^{5}+O(q^{10}) $ 16 * q + 4 * q^4 - 4 * q^5	$ 16 q + 4 q^{4} - 4 q^{5} + 2 q^{10} - 2 q^{11} + 20 q^{13} - 2 q^{14} - 4 q^{16} + 30 q^{17} + 4 q^{20} - 20 q^{22} + 10 q^{23} + 24 q^{25} - 4 q^{26} + 10 q^{29} - 18 q^{31} + 12 q^{34} + 34 q^{35} + 20 q^{37} - 10 q^{38} - 2 q^{40} - 22 q^{41} - 8 q^{44} - 6 q^{46} + 50 q^{47} - 52 q^{49} - 12 q^{50} + 20 q^{52} - 30 q^{53} + 18 q^{55} + 2 q^{56} - 30 q^{58} - 20 q^{59} + 12 q^{61} - 50 q^{62} + 4 q^{64} + 8 q^{65} - 50 q^{67} - 12 q^{70} + 28 q^{71} + 20 q^{73} - 12 q^{74} + 20 q^{76} - 100 q^{77} - 20 q^{79} - 4 q^{80} + 30 q^{83} - 4 q^{85} + 6 q^{86} - 70 q^{89} + 12 q^{91} + 30 q^{92} + 2 q^{94} + 30 q^{95} - 10 q^{97} - 60 q^{98}+O(q^{100}) $ 16 * q + 4 * q^4 - 4 * q^5 + 2 * q^10 - 2 * q^11 + 20 * q^13 - 2 * q^14 - 4 * q^16 + 30 * q^17 + 4 * q^20 - 20 * q^22 + 10 * q^23 + 24 * q^25 - 4 * q^26 + 10 * q^29 - 18 * q^31 + 12 * q^34 + 34 * q^35 + 20 * q^37 - 10 * q^38 - 2 * q^40 - 22 * q^41 - 8 * q^44 - 6 * q^46 + 50 * q^47 - 52 * q^49 - 12 * q^50 + 20 * q^52 - 30 * q^53 + 18 * q^55 + 2 * q^56 - 30 * q^58 - 20 * q^59 + 12 * q^61 - 50 * q^62 + 4 * q^64 + 8 * q^65 - 50 * q^67 - 12 * q^70 + 28 * q^71 + 20 * q^73 - 12 * q^74 + 20 * q^76 - 100 * q^77 - 20 * q^79 - 4 * q^80 + 30 * q^83 - 4 * q^85 + 6 * q^86 - 70 * q^89 + 12 * q^91 + 30 * q^92 + 2 * q^94 + 30 * q^95 - 10 * q^97 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$		0			0
$3$		0			0
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−1.97959	+	1.03982i	−0.885299	+	0.465021i
$5$	−1.97959	+	1.03982i	−0.885299	+	0.465021i
$6$		0			0
$7$		−	0.329315i		−	0.124469i	−0.998062	−	0.0622347i	$-0.980177\pi$
$7$		−	0.329315i		−	0.124469i	0.998062	−	0.0622347i	$-0.0198227\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$		0			0
$10$	2.20402	−	0.377200i	0.696973	−	0.119281i
$11$	1.55540	−	4.78704i	0.468972	−	1.44335i	−0.384946	−	0.922939i	$-0.625780\pi$
$11$	1.55540	−	4.78704i	0.468972	−	1.44335i	0.853918	−	0.520408i	$-0.174220\pi$
$12$		0			0
$13$	−0.458554	+	0.148993i	−0.127180	+	0.0413233i	−0.371915	−	0.928267i	$-0.621299\pi$
$13$	−0.458554	+	0.148993i	−0.127180	+	0.0413233i	0.244735	+	0.969590i	$0.421299\pi$
$14$	−0.101764	+	0.313197i	−0.0271975	+	0.0837054i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	3.98877	+	5.49007i	0.967418	+	1.33154i	0.943340	+	0.331827i	$0.107665\pi$
$17$	3.98877	+	5.49007i	0.967418	+	1.33154i	0.0240779	+	0.999710i	$0.492335\pi$
$18$		0			0
$19$	4.40115	−	3.19762i	1.00969	−	0.733585i	0.0455487	−	0.998962i	$-0.485496\pi$
$19$	4.40115	−	3.19762i	1.00969	−	0.733585i	0.964145	+	0.265377i	$0.0854964\pi$
$20$	−2.21271	−	0.322342i	−0.494778	−	0.0720778i
$21$		0			0
$22$	−2.95855	+	4.07210i	−0.630766	+	0.868175i
$23$	6.18239	+	2.00878i	1.28912	+	0.418860i	0.871783	−	0.489893i	$-0.162964\pi$
$23$	6.18239	+	2.00878i	1.28912	+	0.418860i	0.417335	+	0.908753i	$0.362964\pi$
$24$		0			0
$25$	2.83755	−	4.11683i	0.567510	−	0.823366i
$26$	0.482152			0.0945578
$27$		0			0
$28$	0.193566	−	0.266421i	0.0365806	−	0.0503489i
$29$	4.87203	+	3.53974i	0.904714	+	0.657313i	0.939672	−	0.342076i	$-0.111130\pi$
$29$	4.87203	+	3.53974i	0.904714	+	0.657313i	−0.0349585	+	0.999389i	$0.511130\pi$
$30$		0			0
$31$	−1.06685	+	0.775108i	−0.191611	+	0.139214i	−0.679455	−	0.733717i	$-0.737784\pi$
$31$	−1.06685	+	0.775108i	−0.191611	+	0.139214i	0.487844	+	0.872931i	$0.337784\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−2.09702	−	6.45396i	−0.359636	−	1.10685i
$35$	0.342428	+	0.651908i	0.0578809	+	0.110193i
$36$		0			0
$37$	−0.741956	+	0.241076i	−0.121977	+	0.0396327i	−0.369369	−	0.929283i	$-0.620426\pi$
$37$	−0.741956	+	0.241076i	−0.121977	+	0.0396327i	0.247393	+	0.968915i	$0.420426\pi$
$38$	−5.17386	+	1.68109i	−0.839312	+	0.272709i
$39$		0			0
$40$	2.00481	+	0.990331i	0.316988	+	0.156585i
$41$	−3.86905	−	11.9077i	−0.604245	−	1.85967i	−0.501901	−	0.864925i	$-0.667366\pi$
$41$	−3.86905	−	11.9077i	−0.604245	−	1.85967i	−0.102344	−	0.994749i	$-0.532634\pi$
$42$		0			0
$43$			2.47582i			0.377559i	0.982020	+	0.188779i	$0.0604531\pi$
$43$			2.47582i			0.377559i	−0.982020	+	0.188779i	$0.939547\pi$
$44$	4.07210	−	2.95855i	0.613892	−	0.446019i
$45$		0			0
$46$	−5.25906	−	3.82093i	−0.775405	−	0.563365i
$47$	2.57473	−	3.54381i	0.375563	−	0.516918i	−0.578839	−	0.815442i	$-0.696494\pi$
$47$	2.57473	−	3.54381i	0.375563	−	0.516918i	0.954402	+	0.298523i	$0.0964941\pi$
$48$		0			0
$49$	6.89155			0.984507
$50$	−3.97084	+	3.03849i	−0.561562	+	0.429707i
$51$		0			0
$52$	−0.458554	−	0.148993i	−0.0635900	−	0.0206616i
$53$	−0.990953	+	1.36393i	−0.136118	+	0.187350i	−0.871634	−	0.490157i	$-0.836940\pi$
$53$	−0.990953	+	1.36393i	−0.136118	+	0.187350i	0.735516	+	0.677507i	$0.236940\pi$
$54$		0			0
$55$	1.89860	+	11.0937i	0.256007	+	1.49588i
$56$	−0.266421	+	0.193566i	−0.0356021	+	0.0258664i
$57$		0			0
$58$	−3.53974	−	4.87203i	−0.464791	−	0.639729i
$59$	0.313909	+	0.966113i	0.0408675	+	0.125777i	0.969409	−	0.245452i	$-0.0789364\pi$
$59$	0.313909	+	0.966113i	0.0408675	+	0.125777i	−0.928541	+	0.371229i	$0.878936\pi$
$60$		0			0
$61$	1.29419	−	3.98310i	0.165704	−	0.509984i	−0.833384	−	0.552695i	$-0.813599\pi$
$61$	1.29419	−	3.98310i	0.165704	−	0.509984i	0.999087	+	0.0427111i	$0.0135995\pi$
$62$	1.25415	−	0.407499i	0.159277	−	0.0517524i
$63$		0			0
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	0.752823	−	0.771759i	0.0933762	−	0.0957249i
$66$		0			0
$67$	−1.84819	−	2.54381i	−0.225792	−	0.310776i	0.681058	−	0.732230i	$-0.261520\pi$
$67$	−1.84819	−	2.54381i	−0.225792	−	0.310776i	−0.906850	+	0.421453i	$0.861520\pi$
$68$			6.78610i			0.822935i
$69$		0			0
$70$	−0.124218	−	0.725818i	−0.0148469	−	0.0867518i
$71$	4.62101	+	3.35736i	0.548413	+	0.398446i	0.827200	−	0.561907i	$-0.189932\pi$
$71$	4.62101	+	3.35736i	0.548413	+	0.398446i	−0.278787	+	0.960353i	$0.589932\pi$
$72$		0			0
$73$	−2.79866	−	0.909340i	−0.327558	−	0.106430i	0.140621	−	0.990063i	$-0.455090\pi$
$73$	−2.79866	−	0.909340i	−0.327558	−	0.106430i	−0.468180	+	0.883633i	$0.655090\pi$
$74$	0.780139			0.0906893
$75$		0			0
$76$	5.44012			0.624025
$77$	−1.57644	−	0.512218i	−0.179652	−	0.0583726i
$78$		0			0
$79$	6.86459	+	4.98742i	0.772327	+	0.561128i	0.902666	−	0.430341i	$-0.141607\pi$
$79$	6.86459	+	4.98742i	0.772327	+	0.561128i	−0.130339	+	0.991469i	$0.541607\pi$
$80$	−1.60065	−	1.56138i	−0.178959	−	0.174568i
$81$		0			0
$82$			12.5205i			1.38266i
$83$	−10.1073	−	13.9114i	−1.10942	−	1.52698i	−0.822274	−	0.569092i	$-0.807295\pi$
$83$	−10.1073	−	13.9114i	−1.10942	−	1.52698i	−0.287142	−	0.957888i	$-0.592705\pi$
$84$		0			0
$85$	−13.6048	−	6.72048i	−1.47565	−	0.728939i
$86$	0.765070	−	2.35464i	0.0824996	−	0.253908i
$87$		0			0
$88$	−4.78704	+	1.55540i	−0.510300	+	0.165807i
$89$	1.06683	−	3.28336i	0.113084	−	0.348036i	−0.878459	−	0.477818i	$-0.841428\pi$
$89$	1.06683	−	3.28336i	0.113084	−	0.348036i	0.991543	+	0.129782i	$0.0414279\pi$
$90$		0			0
$91$	0.0490657	+	0.151009i	0.00514348	+	0.0158300i
$92$	3.82093	+	5.25906i	0.398359	+	0.548294i
$93$		0			0
$94$	−3.54381	+	2.57473i	−0.365517	+	0.265563i
$95$	−5.38752	+	10.9064i	−0.552748	+	1.11897i
$96$		0			0
$97$	−5.58986	+	7.69378i	−0.567564	+	0.781185i	−0.992264	−	0.124149i	$-0.960380\pi$
$97$	−5.58986	+	7.69378i	−0.567564	+	0.781185i	0.424699	+	0.905334i	$0.360380\pi$
$98$	−6.55426	−	2.12961i	−0.662080	−	0.215123i
$99$		0			0
$100$	4.71544	−	1.66272i	0.471544	−	0.166272i
$101$	−19.2435			−1.91480			−0.957400	−	0.288765i	$-0.906755\pi$
$101$	−19.2435			−1.91480			−0.957400	+	0.288765i	$0.906755\pi$
$102$		0			0
$103$	−3.00175	+	4.13156i	−0.295771	+	0.407095i	−0.930878	−	0.365330i	$-0.880956\pi$
$103$	−3.00175	+	4.13156i	−0.295771	+	0.407095i	0.635107	+	0.772424i	$0.280956\pi$
$104$	0.390069	+	0.283402i	0.0382494	+	0.0277898i
$105$		0			0
$106$	1.36393	−	0.990953i	0.132477	−	0.0962499i
$107$			15.3340i			1.48239i	0.671290	+	0.741194i	$0.265740\pi$
$107$			15.3340i			1.48239i	−0.671290	+	0.741194i	$0.734260\pi$
$108$		0			0
$109$	3.01609	+	9.28257i	0.288889	+	0.889109i	0.985206	+	0.171375i	$0.0548208\pi$
$109$	3.01609	+	9.28257i	0.288889	+	0.889109i	−0.696317	+	0.717735i	$0.745179\pi$
$110$	1.62247	−	11.1374i	0.154697	−	1.06191i
$111$		0			0
$112$	0.313197	−	0.101764i	0.0295943	−	0.00961579i
$113$	−1.44148	+	0.468364i	−0.135603	+	0.0440599i	−0.376032	−	0.926607i	$-0.622712\pi$
$113$	−1.44148	+	0.468364i	−0.135603	+	0.0440599i	0.240429	+	0.970667i	$0.422712\pi$
$114$		0			0
$115$	−14.3274	+	2.45201i	−1.33603	+	0.228651i
$116$	1.86095	+	5.72742i	0.172785	+	0.531778i
$117$		0			0
$118$		−	1.01583i		−	0.0935149i
$119$	1.80796	−	1.31356i	0.165736	−	0.120414i
$120$		0			0
$121$	−11.5973	−	8.42593i	−1.05430	−	0.765993i
$122$	−2.46169	+	3.38823i	−0.222871	+	0.306756i
$123$		0			0
$124$	−1.31869			−0.118422
$125$	−1.33642	+	11.1002i	−0.119533	+	0.992830i
$126$		0			0
$127$	11.9886	+	3.89534i	1.06382	+	0.345656i	0.788077	−	0.615576i	$-0.211077\pi$
$127$	11.9886	+	3.89534i	1.06382	+	0.345656i	0.275741	+	0.961232i	$0.411077\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$		0			0
$130$	−0.954463	+	0.501351i	−0.0837120	+	0.0439714i
$131$	11.3715	−	8.26187i	0.993532	−	0.721843i	0.0328399	−	0.999461i	$-0.489545\pi$
$131$	11.3715	−	8.26187i	0.993532	−	0.721843i	0.960692	+	0.277618i	$0.0895449\pi$
$132$		0			0
$133$	−1.05303	−	1.44936i	−0.0913089	−	0.125676i
$134$	0.971651	+	2.99043i	0.0839378	+	0.258334i
$135$		0			0
$136$	2.09702	−	6.45396i	0.179818	−	0.553423i
$137$	−6.36127	+	2.06690i	−0.543480	+	0.176587i	−0.567874	−	0.823115i	$-0.692234\pi$
$137$	−6.36127	+	2.06690i	−0.543480	+	0.176587i	0.0243949	+	0.999702i	$0.492234\pi$
$138$		0			0
$139$	0.951151	−	2.92734i	0.0806755	−	0.248294i	−0.902581	−	0.430520i	$-0.858330\pi$
$139$	0.951151	−	2.92734i	0.0806755	−	0.248294i	0.983257	+	0.182226i	$0.0583303\pi$
$140$	−0.106152	+	0.728679i	−0.00897148	+	0.0615846i
$141$		0			0
$142$	−3.35736	−	4.62101i	−0.281744	−	0.387787i
$143$			2.42686i			0.202944i
$144$		0			0
$145$	−13.3253	−	1.94120i	−1.10661	−	0.161208i
$146$	2.38068	+	1.72967i	0.197027	+	0.143148i
$147$		0			0
$148$	−0.741956	−	0.241076i	−0.0609884	−	0.0198163i
$149$	5.06465			0.414912			0.207456	−	0.978244i	$-0.433482\pi$
$149$	5.06465			0.414912			0.207456	+	0.978244i	$0.433482\pi$
$150$		0			0
$151$	−16.9581			−1.38003			−0.690015	−	0.723795i	$-0.742396\pi$
$151$	−16.9581			−1.38003			−0.690015	+	0.723795i	$0.742396\pi$
$152$	−5.17386	−	1.68109i	−0.419656	−	0.136354i
$153$		0			0
$154$	1.34100	+	0.974296i	0.108061	+	0.0785110i
$155$	1.30594	−	2.64372i	0.104896	−	0.212349i
$156$		0			0
$157$		−	22.8284i		−	1.82190i	−0.412513	−	0.910952i	$-0.635349\pi$
$157$		−	22.8284i		−	1.82190i	0.412513	−	0.910952i	$-0.364651\pi$
$158$	−4.98742	−	6.86459i	−0.396778	−	0.546118i
$159$		0			0
$160$	1.03982	+	1.97959i	0.0822050	+	0.156500i
$161$	0.661521	−	2.03595i	0.0521352	−	0.160456i
$162$		0			0
$163$	7.56873	−	2.45923i	0.592829	−	0.192622i	0.00278919	−	0.999996i	$-0.499112\pi$
$163$	7.56873	−	2.45923i	0.592829	−	0.192622i	0.590039	+	0.807374i	$0.299112\pi$
$164$	3.86905	−	11.9077i	0.302122	−	0.929837i
$165$		0			0
$166$	5.31370	+	16.3539i	0.412423	+	1.26931i
$167$	8.19979	+	11.2860i	0.634519	+	0.873340i	0.998308	−	0.0581411i	$-0.0185173\pi$
$167$	8.19979	+	11.2860i	0.634519	+	0.873340i	−0.363790	+	0.931481i	$0.618517\pi$
$168$		0			0
$169$	−10.3291	+	7.50457i	−0.794550	+	0.577274i
$170$	10.8622	+	10.5957i	0.833092	+	0.812651i
$171$		0			0
$172$	−1.45525	+	2.00298i	−0.110962	+	0.152726i
$173$	−18.5464	−	6.02610i	−1.41006	−	0.458156i	−0.497629	−	0.867390i	$-0.665796\pi$
$173$	−18.5464	−	6.02610i	−1.41006	−	0.458156i	−0.912430	+	0.409234i	$0.865796\pi$
$174$		0			0
$175$	−1.35573	−	0.934448i	−0.102484	−	0.0706376i
$176$	5.03339			0.379406
$177$		0			0
$178$	−2.02923	+	2.79299i	−0.152097	+	0.209344i
$179$	15.3641	+	11.1627i	1.14837	+	0.834338i	0.988263	−	0.152761i	$-0.0488166\pi$
$179$	15.3641	+	11.1627i	1.14837	+	0.834338i	0.160105	+	0.987100i	$0.448817\pi$
$180$		0			0
$181$	15.3296	−	11.1376i	1.13944	−	0.827850i	0.152397	−	0.988319i	$-0.451301\pi$
$181$	15.3296	−	11.1376i	1.13944	−	0.827850i	0.987041	+	0.160470i	$0.0513008\pi$
$182$		−	0.158780i		−	0.0117695i
$183$		0			0
$184$	−2.00878	−	6.18239i	−0.148089	−	0.455772i
$185$	1.21809	−	1.24873i	0.0895559	−	0.0918086i
$186$		0			0
$187$	32.4853	−	10.5551i	2.37556	−	0.771867i
$188$	4.16600	−	1.35362i	0.303837	−	0.0987226i
$189$		0			0
$190$	8.49410	−	8.70775i	0.616227	−	0.631727i
$191$	3.73703	+	11.5014i	0.270402	+	0.832212i	0.990399	+	0.138235i	$0.0441430\pi$
$191$	3.73703	+	11.5014i	0.270402	+	0.832212i	−0.719997	+	0.693977i	$0.755857\pi$
$192$		0			0
$193$			11.0357i			0.794368i	0.917739	+	0.397184i	$0.130013\pi$
$193$			11.0357i			0.794368i	−0.917739	+	0.397184i	$0.869987\pi$
$194$	7.69378	−	5.58986i	0.552381	−	0.401329i
$195$		0			0
$196$	5.57538	+	4.05075i	0.398242	+	0.289339i
$197$	12.1208	−	16.6829i	0.863573	−	1.18861i	−0.117133	−	0.993116i	$-0.537370\pi$
$197$	12.1208	−	16.6829i	0.863573	−	1.18861i	0.980706	−	0.195490i	$-0.0626296\pi$
$198$		0			0
$199$	−18.5313			−1.31365			−0.656826	−	0.754042i	$-0.728101\pi$
$199$	−18.5313			−1.31365			−0.656826	+	0.754042i	$0.728101\pi$
$200$	−4.99846	+	0.124187i	−0.353444	+	0.00878136i
$201$		0			0
$202$	18.3017	+	5.94657i	1.28770	+	0.418399i
$203$	1.16569	−	1.60443i	0.0818153	−	0.112609i
$204$		0			0
$205$	20.0410	+	19.5493i	1.39973	+	1.36538i
$206$	4.13156	−	3.00175i	0.287859	−	0.209142i
$207$		0			0
$208$	−0.283402	−	0.390069i	−0.0196504	−	0.0270464i
$209$	−8.46159	−	26.0421i	−0.585300	−	1.80137i
$210$		0			0
$211$	4.87129	−	14.9923i	0.335353	−	1.03211i	−0.631194	−	0.775625i	$-0.717435\pi$
$211$	4.87129	−	14.9923i	0.335353	−	1.03211i	0.966548	−	0.256487i	$-0.0825650\pi$
$212$	−1.60340	+	0.520975i	−0.110122	+	0.0357807i
$213$		0			0
$214$	4.73845	−	14.5835i	0.323914	−	0.996904i
$215$	−2.57440	−	4.90110i	−0.175573	−	0.334253i
$216$		0			0
$217$	0.255255	+	0.351328i	0.0173278	+	0.0238497i
$218$		−	9.76027i		−	0.661049i
$219$		0			0
$220$	−4.98472	+	10.0910i	−0.336070	+	0.680333i
$221$	−2.64705	−	1.92319i	−0.178060	−	0.129368i
$222$		0			0
$223$	21.0928	+	6.85345i	1.41248	+	0.458941i	0.913203	−	0.407504i	$-0.133601\pi$
$223$	21.0928	+	6.85345i	1.41248	+	0.458941i	0.499272	+	0.866445i	$0.333601\pi$
$224$	−0.329315			−0.0220033
$225$		0			0
$226$	1.51566			0.100820
$227$	−10.5538	−	3.42913i	−0.700480	−	0.227600i	−0.0629401	−	0.998017i	$-0.520048\pi$
$227$	−10.5538	−	3.42913i	−0.700480	−	0.227600i	−0.637539	+	0.770418i	$0.720048\pi$
$228$		0			0
$229$	1.45525	+	1.05730i	0.0961658	+	0.0698685i	0.634829	−	0.772653i	$-0.281071\pi$
$229$	1.45525	+	1.05730i	0.0961658	+	0.0698685i	−0.538663	+	0.842521i	$0.681071\pi$
$230$	14.3838	+	2.09540i	0.948443	+	0.138167i
$231$		0			0
$232$		−	6.02216i		−	0.395374i
$233$	−2.17821	−	2.99805i	−0.142699	−	0.196409i	0.731685	−	0.681643i	$-0.238734\pi$
$233$	−2.17821	−	2.99805i	−0.142699	−	0.196409i	−0.874384	+	0.485234i	$0.838734\pi$
$234$		0			0
$235$	−1.41198	+	9.69255i	−0.0921077	+	0.632273i
$236$	−0.313909	+	0.966113i	−0.0204338	+	0.0628886i
$237$		0			0
$238$	−2.12539	+	0.690580i	−0.137768	+	0.0447636i
$239$	−5.21415	+	16.0475i	−0.337275	+	1.03803i	0.628315	+	0.777959i	$0.283745\pi$
$239$	−5.21415	+	16.0475i	−0.337275	+	1.03803i	−0.965590	+	0.260068i	$0.916255\pi$
$240$		0			0
$241$	6.37366	+	19.6161i	0.410564	+	1.26359i	0.916159	+	0.400815i	$0.131273\pi$
$241$	6.37366	+	19.6161i	0.410564	+	1.26359i	−0.505595	+	0.862771i	$0.668727\pi$
$242$	8.42593	+	11.5973i	0.541639	+	0.745502i
$243$		0			0
$244$	3.38823	−	2.46169i	0.216909	−	0.157594i
$245$	−13.6424	+	7.16597i	−0.871584	+	0.457817i
$246$		0			0
$247$	−1.54174	+	2.12202i	−0.0980986	+	0.135021i
$248$	1.25415	+	0.407499i	0.0796387	+	0.0258762i
$249$		0			0
$250$	4.70116	−	10.1439i	0.297327	−	0.641558i
$251$	−8.69615			−0.548896			−0.274448	−	0.961602i	$-0.588495\pi$
$251$	−8.69615			−0.548896			−0.274448	+	0.961602i	$0.588495\pi$
$252$		0			0
$253$	19.2322	−	26.4709i	1.20912	−	1.66421i
$254$	−10.1981	−	7.40938i	−0.639888	−	0.464906i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$		−	7.10714i		−	0.443331i	−0.975123	−	0.221666i	$-0.928851\pi$
$257$		−	7.10714i		−	0.443331i	0.975123	−	0.221666i	$-0.0711493\pi$
$258$		0			0
$259$	0.0793900	+	0.244337i	0.00493305	+	0.0151824i
$260$	1.06267	−	0.181868i	0.0659043	−	0.0112790i
$261$		0			0
$262$	−13.3680	+	4.34352i	−0.825877	+	0.268344i
$263$	15.0847	−	4.90130i	0.930160	−	0.302227i	0.195532	−	0.980697i	$-0.437357\pi$
$263$	15.0847	−	4.90130i	0.930160	−	0.302227i	0.734628	+	0.678470i	$0.237357\pi$
$264$		0			0
$265$	0.543439	−	3.73044i	0.0333832	−	0.229159i
$266$	0.553608	+	1.70383i	0.0339439	+	0.104469i
$267$		0			0
$268$		−	3.14433i		−	0.192070i
$269$	−3.65623	+	2.65641i	−0.222925	+	0.161964i	−0.693642	−	0.720320i	$-0.743995\pi$
$269$	−3.65623	+	2.65641i	−0.222925	+	0.161964i	0.470718	+	0.882284i	$0.343995\pi$
$270$		0			0
$271$	−9.00551	−	6.54289i	−0.547046	−	0.397452i	0.279649	−	0.960102i	$-0.409782\pi$
$271$	−9.00551	−	6.54289i	−0.547046	−	0.397452i	−0.826695	+	0.562650i	$0.809782\pi$
$272$	−3.98877	+	5.49007i	−0.241855	+	0.332884i
$273$		0			0
$274$	6.68863			0.404075
$275$	−15.2939	−	19.9868i	−0.922257	−	1.20525i
$276$		0			0
$277$	−21.7162	−	7.05603i	−1.30480	−	0.423956i	−0.427552	−	0.903991i	$-0.640624\pi$
$277$	−21.7162	−	7.05603i	−1.30480	−	0.423956i	−0.877249	+	0.480035i	$0.840624\pi$
$278$	−1.80920	+	2.49014i	−0.108508	+	0.149349i
$279$		0			0
$280$	0.326131	−	0.660212i	0.0194900	−	0.0394552i
$281$	23.2631	−	16.9016i	1.38776	−	1.00827i	0.391653	−	0.920113i	$-0.371903\pi$
$281$	23.2631	−	16.9016i	1.38776	−	1.00827i	0.996107	−	0.0881540i	$-0.0280968\pi$
$282$		0			0
$283$	−11.3720	−	15.6522i	−0.675992	−	0.930424i	0.323885	−	0.946097i	$-0.395011\pi$
$283$	−11.3720	−	15.6522i	−0.675992	−	0.930424i	−0.999877	+	0.0156727i	$0.995011\pi$
$284$	1.76507	+	5.43233i	0.104738	+	0.322349i
$285$		0			0
$286$	0.749941	−	2.30808i	0.0443450	−	0.136480i
$287$	−3.92139	+	1.27414i	−0.231472	+	0.0752100i
$288$		0			0
$289$	−8.97729	+	27.6292i	−0.528076	+	1.62525i
$290$	12.0733	+	5.96394i	0.708967	+	0.350214i
$291$		0			0
$292$	−1.72967	−	2.38068i	−0.101221	−	0.139319i
$293$			15.0301i			0.878069i	0.898470	+	0.439035i	$0.144679\pi$
$293$			15.0301i			0.878069i	−0.898470	+	0.439035i	$0.855321\pi$
$294$		0			0
$295$	−1.62600	−	1.58610i	−0.0946691	−	0.0923463i
$296$	0.631145	+	0.458554i	0.0366846	+	0.0266529i
$297$		0			0
$298$	−4.81677	−	1.56506i	−0.279028	−	0.0906617i
$299$	−3.13425			−0.181259
$300$		0			0
$301$	0.815324			0.0469945
$302$	16.1281	+	5.24034i	0.928069	+	0.301548i
$303$		0			0
$304$	4.40115	+	3.19762i	0.252423	+	0.183396i
$305$	1.57975	+	9.23063i	0.0904560	+	0.528544i
$306$		0			0
$307$			19.7061i			1.12468i	0.826905	+	0.562342i	$0.190100\pi$
$307$			19.7061i			1.12468i	−0.826905	+	0.562342i	$0.809900\pi$
$308$	−0.974296	−	1.34100i	−0.0555157	−	0.0764108i
$309$		0			0
$310$	−2.05898	+	2.11077i	−0.116942	+	0.119884i
$311$	−8.72642	+	26.8572i	−0.494830	+	1.52293i	0.322392	+	0.946606i	$0.395513\pi$
$311$	−8.72642	+	26.8572i	−0.494830	+	1.52293i	−0.817222	+	0.576323i	$0.804487\pi$
$312$		0			0
$313$	−10.6973	+	3.47577i	−0.604648	+	0.196462i	−0.595312	−	0.803494i	$-0.702972\pi$
$313$	−10.6973	+	3.47577i	−0.604648	+	0.196462i	−0.00933550	+	0.999956i	$0.502972\pi$
$314$	−7.05436	+	21.7111i	−0.398101	+	1.22523i
$315$		0			0
$316$	2.62204	+	8.06981i	0.147501	+	0.453962i
$317$	−13.6905	−	18.8433i	−0.768935	−	1.05835i	−0.996418	−	0.0845658i	$-0.973050\pi$
$317$	−13.6905	−	18.8433i	−0.768935	−	1.05835i	0.227483	−	0.973782i	$-0.426950\pi$
$318$		0			0
$319$	24.5229	−	17.8169i	1.37302	−	0.997555i
$320$	−0.377200	−	2.20402i	−0.0210861	−	0.123209i
$321$		0			0
$322$	−1.25829	+	1.73189i	−0.0701217	+	0.0965142i
$323$	35.1103	+	11.4080i	1.95359	+	0.634760i
$324$		0			0
$325$	−0.687790	+	2.31057i	−0.0381517	+	0.128167i
$326$	−7.95823			−0.440766
$327$		0			0
$328$	−7.35938	+	10.1293i	−0.406354	+	0.559298i
$329$	−1.16703	−	0.847898i	−0.0643405	−	0.0467461i
$330$		0			0
$331$	−0.104633	+	0.0760205i	−0.00575116	+	0.00417847i	−0.590657	−	0.806923i	$-0.701131\pi$
$331$	−0.104633	+	0.0760205i	−0.00575116	+	0.00417847i	0.584906	+	0.811101i	$0.301131\pi$
$332$		−	17.1955i		−	0.943725i
$333$		0			0
$334$	−4.31088	−	13.2675i	−0.235881	−	0.725967i
$335$	6.30376	+	3.11392i	0.344411	+	0.170132i
$336$		0			0
$337$	−0.511734	+	0.166272i	−0.0278759	+	0.00905743i	−0.322922	−	0.946426i	$-0.604665\pi$
$337$	−0.511734	+	0.166272i	−0.0278759	+	0.00905743i	0.295046	+	0.955483i	$0.404665\pi$
$338$	12.1426	−	3.94538i	0.660473	−	0.214601i
$339$		0			0
$340$	−7.05632	−	13.4337i	−0.382683	−	0.728544i
$341$	2.05110	+	6.31264i	0.111073	+	0.341849i
$342$		0			0
$343$		−	4.57470i		−	0.247010i
$344$	2.00298	−	1.45525i	0.107993	−	0.0784618i
$345$		0			0
$346$	15.7765	+	11.4623i	0.848152	+	0.616218i
$347$	13.3519	−	18.3773i	0.716767	−	0.986546i	−0.282858	−	0.959162i	$-0.591282\pi$
$347$	13.3519	−	18.3773i	0.716767	−	0.986546i	0.999625	−	0.0273838i	$-0.00871761\pi$
$348$		0			0
$349$	−6.84350			−0.366324			−0.183162	−	0.983083i	$-0.558633\pi$
$349$	−6.84350			−0.366324			−0.183162	+	0.983083i	$0.558633\pi$
$350$	1.00062	+	1.30766i	0.0534854	+	0.0698972i
$351$		0			0
$352$	−4.78704	−	1.55540i	−0.255150	−	0.0829033i
$353$	−9.86237	+	13.5744i	−0.524921	+	0.722492i	−0.986346	−	0.164688i	$-0.947338\pi$
$353$	−9.86237	+	13.5744i	−0.524921	+	0.722492i	0.461425	+	0.887179i	$0.347338\pi$
$354$		0			0
$355$	−12.6388	−	1.84118i	−0.670796	−	0.0977197i
$356$	2.79299	−	2.02923i	0.148028	−	0.107549i
$357$		0			0
$358$	−11.1627	−	15.3641i	−0.589966	−	0.812019i
$359$	−2.30639	−	7.09834i	−0.121727	−	0.374636i	0.871564	−	0.490282i	$-0.163106\pi$
$359$	−2.30639	−	7.09834i	−0.121727	−	0.374636i	−0.993291	+	0.115646i	$0.963106\pi$
$360$		0			0
$361$	3.27401	−	10.0764i	0.172317	−	0.530336i
$362$	−18.0210	+	5.85537i	−0.947162	+	0.307752i
$363$		0			0
$364$	−0.0490657	+	0.151009i	−0.00257174	+	0.00791500i
$365$	6.48575	−	1.10998i	0.339480	−	0.0580991i
$366$		0			0
$367$	−3.61766	−	4.97929i	−0.188841	−	0.259917i	0.704090	−	0.710110i	$-0.251355\pi$
$367$	−3.61766	−	4.97929i	−0.188841	−	0.259917i	−0.892931	+	0.450194i	$0.851355\pi$
$368$			6.50055i			0.338865i
$369$		0			0
$370$	−1.54435	+	0.811203i	−0.0802872	+	0.0421725i
$371$	0.449163	+	0.326336i	0.0233194	+	0.0169425i
$372$		0			0
$373$	8.72051	+	2.83346i	0.451531	+	0.146711i	0.525949	−	0.850516i	$-0.323710\pi$
$373$	8.72051	+	2.83346i	0.451531	+	0.146711i	−0.0744187	+	0.997227i	$0.523710\pi$
$374$	−34.1571			−1.76622
$375$		0			0
$376$	−4.38040			−0.225902
$377$	−2.76149	−	0.897262i	−0.142224	−	0.0462113i
$378$		0			0
$379$	−28.0179	−	20.3562i	−1.43918	−	1.04563i	−0.988212	−	0.153090i	$-0.951077\pi$
$379$	−28.0179	−	20.3562i	−1.43918	−	1.04563i	−0.450972	−	0.892538i	$-0.648923\pi$
$380$	−10.7692	+	5.65675i	−0.552449	+	0.290185i
$381$		0			0
$382$		−	12.0933i		−	0.618746i
$383$	5.59597	+	7.70220i	0.285941	+	0.393564i	0.927690	−	0.373350i	$-0.121791\pi$
$383$	5.59597	+	7.70220i	0.285941	+	0.393564i	−0.641749	+	0.766914i	$0.721791\pi$
$384$		0			0
$385$	3.65333	−	0.625237i	0.186191	−	0.0318650i
$386$	3.41022	−	10.4956i	0.173576	−	0.534211i
$387$		0			0
$388$	−9.04458	+	2.93876i	−0.459169	+	0.149193i
$389$	−5.39091	+	16.5915i	−0.273330	+	0.841224i	0.716326	+	0.697766i	$0.245822\pi$
$389$	−5.39091	+	16.5915i	−0.273330	+	0.841224i	−0.989656	+	0.143458i	$0.954178\pi$
$390$		0			0
$391$	13.6318	+	41.9543i	0.689389	+	2.12172i
$392$	−4.05075	−	5.57538i	−0.204594	−	0.281599i
$393$		0			0
$394$	−16.6829	+	12.1208i	−0.840471	+	0.610638i
$395$	−18.7751	−	2.73510i	−0.944677	−	0.137618i
$396$		0			0
$397$	−7.96751	+	10.9663i	−0.399878	+	0.550385i	−0.960713	−	0.277542i	$-0.910480\pi$
$397$	−7.96751	+	10.9663i	−0.399878	+	0.550385i	0.560835	+	0.827927i	$0.310480\pi$
$398$	17.6244	+	5.72650i	0.883429	+	0.287044i
$399$		0			0
$400$	4.79219	+	1.42650i	0.239610	+	0.0713250i
$401$	−14.1105			−0.704642			−0.352321	−	0.935879i	$-0.614608\pi$
$401$	−14.1105			−0.704642			−0.352321	+	0.935879i	$0.614608\pi$
$402$		0			0
$403$	0.373720	−	0.514382i	0.0186163	−	0.0256232i
$404$	−15.5683	−	11.3110i	−0.774553	−	0.562746i
$405$		0			0
$406$	−1.60443	+	1.16569i	−0.0796267	+	0.0578522i
$407$			3.92674i			0.194641i
$408$		0			0
$409$	5.11848	+	15.7531i	0.253092	+	0.778938i	0.994200	+	0.107552i	$0.0343011\pi$
$409$	5.11848	+	15.7531i	0.253092	+	0.778938i	−0.741107	+	0.671387i	$0.765699\pi$
$410$	−13.0191	−	24.7855i	−0.642967	−	1.22407i
$411$		0			0
$412$	−4.85694	+	1.57811i	−0.239284	+	0.0777481i
$413$	0.318156	−	0.103375i	0.0156554	−	0.00508675i
$414$		0			0
$415$	34.4736	+	17.0292i	1.69224	+	0.835932i
$416$	0.148993	+	0.458554i	0.00730499	+	0.0224825i
$417$		0			0
$418$			27.3823i			1.33931i
$419$	−13.7294	+	9.97500i	−0.670725	+	0.487310i	−0.870268	−	0.492579i	$-0.836054\pi$
$419$	−13.7294	+	9.97500i	−0.670725	+	0.487310i	0.199543	+	0.979889i	$0.436054\pi$
$420$		0			0
$421$	5.71360	+	4.15118i	0.278464	+	0.202316i	0.718247	−	0.695788i	$-0.244945\pi$
$421$	5.71360	+	4.15118i	0.278464	+	0.202316i	−0.439783	+	0.898104i	$0.644945\pi$
$422$	−9.26574	+	12.7532i	−0.451049	+	0.620816i
$423$		0			0
$424$	1.68591			0.0818751
$425$	33.9200	−	0.842746i	1.64536	−	0.0408792i
$426$		0			0
$427$	−1.31169	−	0.426195i	−0.0634773	−	0.0206250i
$428$	−9.01307	+	12.4054i	−0.435663	+	0.599639i
$429$		0			0
$430$	0.933880	+	5.45676i	0.0450357	+	0.263148i
$431$	−14.4476	+	10.4968i	−0.695915	+	0.505612i	−0.878599	−	0.477560i	$-0.841521\pi$
$431$	−14.4476	+	10.4968i	−0.695915	+	0.505612i	0.182684	+	0.983172i	$0.441521\pi$
$432$		0			0
$433$	−14.2125	−	19.5618i	−0.683007	−	0.940078i	0.316958	−	0.948440i	$-0.397339\pi$
$433$	−14.2125	−	19.5618i	−0.683007	−	0.940078i	−0.999965	+	0.00836116i	$0.997339\pi$
$434$	−0.134195	−	0.413011i	−0.00644158	−	0.0198252i
$435$		0			0
$436$	−3.01609	+	9.28257i	−0.144445	+	0.444555i
$437$	33.6330	−	10.9280i	1.60888	−	0.522758i
$438$		0			0
$439$	5.84359	−	17.9847i	0.278899	−	0.858364i	−0.709262	−	0.704945i	$-0.750972\pi$
$439$	5.84359	−	17.9847i	0.278899	−	0.858364i	0.988161	−	0.153419i	$-0.0490284\pi$
$440$	7.85904	−	8.05672i	0.374665	−	0.384089i
$441$		0			0
$442$	1.92319	+	2.64705i	0.0914770	+	0.125907i
$443$			4.05769i			0.192787i	0.995343	+	0.0963933i	$0.0307307\pi$
$443$			4.05769i			0.192787i	−0.995343	+	0.0963933i	$0.969269\pi$
$444$		0			0
$445$	1.30222	+	7.60902i	0.0617312	+	0.360702i
$446$	−17.9426	−	13.0360i	−0.849605	−	0.617274i
$447$		0			0
$448$	0.313197	+	0.101764i	0.0147972	+	0.00480789i
$449$	−6.26150			−0.295498			−0.147749	−	0.989025i	$-0.547203\pi$
$449$	−6.26150			−0.295498			−0.147749	+	0.989025i	$0.547203\pi$
$450$		0			0
$451$	−63.0207			−2.96753
$452$	−1.44148	−	0.468364i	−0.0678013	−	0.0220300i
$453$		0			0
$454$	8.97759	+	6.52260i	0.421339	+	0.306121i
$455$	−0.254152	−	0.247916i	−0.0119148	−	0.0116225i
$456$		0			0
$457$			1.94229i			0.0908564i	0.998968	+	0.0454282i	$0.0144652\pi$
$457$			1.94229i			0.0908564i	−0.998968	+	0.0454282i	$0.985535\pi$
$458$	−1.05730	−	1.45525i	−0.0494045	−	0.0679995i
$459$		0			0
$460$	−13.0323	−	6.43770i	−0.607636	−	0.300159i
$461$	−0.965342	+	2.97102i	−0.0449605	+	0.138374i	−0.971017	−	0.239011i	$-0.923177\pi$
$461$	−0.965342	+	2.97102i	−0.0449605	+	0.138374i	0.926056	+	0.377385i	$0.123177\pi$
$462$		0			0
$463$	−7.86182	+	2.55446i	−0.365370	+	0.118716i	−0.485947	−	0.873988i	$-0.661525\pi$
$463$	−7.86182	+	2.55446i	−0.365370	+	0.118716i	0.120578	+	0.992704i	$0.461525\pi$
$464$	−1.86095	+	5.72742i	−0.0863925	+	0.265889i
$465$		0			0
$466$	1.14515	+	3.52442i	0.0530482	+	0.163265i
$467$	−17.9975	−	24.7715i	−0.832827	−	1.14629i	−0.987390	−	0.158305i	$-0.949397\pi$
$467$	−17.9975	−	24.7715i	−0.832827	−	1.14629i	0.154563	−	0.987983i	$-0.450603\pi$
$468$		0			0
$469$	−0.837716	+	0.608636i	−0.0386821	+	0.0281042i
$470$	4.33804	−	8.78184i	0.200099	−	0.405076i
$471$		0			0
$472$	0.597091	−	0.821825i	0.0274833	−	0.0378276i
$473$	11.8518	+	3.85090i	0.544948	+	0.177064i
$474$		0			0
$475$	−0.675593	−	27.1922i	−0.0309983	−	1.24766i
$476$	2.23476			0.102430
$477$		0			0
$478$	9.91790	−	13.6508i	0.453634	−	0.624374i
$479$	0.948887	+	0.689407i	0.0433558	+	0.0314998i	0.609252	−	0.792977i	$-0.291470\pi$
$479$	0.948887	+	0.689407i	0.0433558	+	0.0314998i	−0.565896	+	0.824476i	$0.691470\pi$
$480$		0			0
$481$	0.304308	−	0.221093i	0.0138753	−	0.0100810i
$482$		−	20.6256i		−	0.939471i
$483$		0			0
$484$	−4.42977	−	13.6334i	−0.201353	−	0.619702i
$485$	3.06548	−	21.0430i	0.139196	−	0.955512i
$486$		0			0
$487$	−11.1802	+	3.63267i	−0.506623	+	0.164612i	−0.551166	−	0.834396i	$-0.685817\pi$
$487$	−11.1802	+	3.63267i	−0.506623	+	0.164612i	0.0445428	+	0.999007i	$0.485817\pi$
$488$	−3.98310	+	1.29419i	−0.180307	+	0.0585851i
$489$		0			0
$490$	15.1891	−	2.59950i	0.686176	−	0.117433i
$491$	−1.27640	−	3.92836i	−0.0576031	−	0.177284i	0.918115	−	0.396314i	$-0.129711\pi$
$491$	−1.27640	−	3.92836i	−0.0576031	−	0.177284i	−0.975718	+	0.219030i	$0.929711\pi$
$492$		0			0
$493$			40.8670i			1.84056i
$494$	2.12202	−	1.54174i	0.0954744	−	0.0693662i
$495$		0			0
$496$	−1.06685	−	0.775108i	−0.0479028	−	0.0348034i
$497$	1.10563	−	1.52177i	0.0495943	−	0.0682606i
$498$		0			0
$499$	−9.59154			−0.429376			−0.214688	−	0.976683i	$-0.568873\pi$
$499$	−9.59154			−0.429376			−0.214688	+	0.976683i	$0.568873\pi$
$500$	−7.60571	+	8.19470i	−0.340138	+	0.366478i
$501$		0			0
$502$	8.27053	+	2.68726i	0.369132	+	0.119938i
$503$	9.96021	−	13.7091i	0.444104	−	0.611257i	−0.527014	−	0.849857i	$-0.676688\pi$
$503$	9.96021	−	13.7091i	0.444104	−	0.611257i	0.971118	+	0.238600i	$0.0766885\pi$
$504$		0			0
$505$	38.0942	−	20.0098i	1.69517	−	0.890423i
$506$	−26.4709	+	19.2322i	−1.17677	+	0.854977i
$507$		0			0
$508$	7.40938	+	10.1981i	0.328738	+	0.452469i
$509$	10.5993	+	32.6213i	0.469805	+	1.44591i	0.852837	+	0.522177i	$0.174880\pi$
$509$	10.5993	+	32.6213i	0.469805	+	1.44591i	−0.383032	+	0.923735i	$0.625120\pi$
$510$		0			0
$511$	−0.299459	+	0.921641i	−0.0132473	+	0.0407710i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$		0			0
$514$	−2.19623	+	6.75929i	−0.0968714	+	0.298140i
$515$	1.64616	−	11.3001i	0.0725386	−	0.497941i
$516$		0			0
$517$	−12.9596	−	17.8374i	−0.569964	−	0.784488i
$518$		−	0.256911i		−	0.0112880i
$519$		0			0
$520$	−1.06686	−	0.155418i	−0.0467851	−	0.00681552i
$521$	17.2185	+	12.5100i	0.754356	+	0.548072i	0.897174	−	0.441677i	$-0.145616\pi$
$521$	17.2185	+	12.5100i	0.754356	+	0.548072i	−0.142818	+	0.989749i	$0.545616\pi$
$522$		0			0
$523$	39.3254	+	12.7776i	1.71958	+	0.558726i	0.991881	−	0.127170i	$-0.0405893\pi$
$523$	39.3254	+	12.7776i	1.71958	+	0.558726i	0.727700	+	0.685896i	$0.240589\pi$
$524$	14.0559			0.614036
$525$		0			0
$526$	−15.8609			−0.691570
$527$	−8.51080	−	2.76533i	−0.370736	−	0.120459i
$528$		0			0
$529$	15.5794	+	11.3191i	0.677364	+	0.492133i
$530$	−1.66961	+	3.37992i	−0.0725232	+	0.146814i
$531$		0			0
$532$		−	1.79151i		−	0.0776720i
$533$	3.54834	+	4.88387i	0.153696	+	0.211544i
$534$		0			0
$535$	−15.9445	−	30.3549i	−0.689343	−	1.31236i
$536$	−0.971651	+	2.99043i	−0.0419689	+	0.129167i
$537$		0			0
$538$	4.29816	−	1.39656i	0.185307	−	0.0602099i
$539$	10.7191	−	32.9901i	0.461706	−	1.42099i
$540$		0			0
$541$	−11.0695	−	34.0685i	−0.475916	−	1.46472i	−0.844719	−	0.535210i	$-0.820232\pi$
$541$	−11.0695	−	34.0685i	−0.475916	−	1.46472i	0.368803	−	0.929507i	$-0.379768\pi$
$542$	6.54289	+	9.00551i	0.281041	+	0.386820i
$543$		0			0
$544$	5.49007	−	3.98877i	0.235385	−	0.171017i
$545$	−15.6228	−	15.2395i	−0.669208	−	0.652788i
$546$		0			0
$547$	4.91537	−	6.76543i	0.210166	−	0.289269i	−0.690900	−	0.722950i	$-0.742786\pi$
$547$	4.91537	−	6.76543i	0.210166	−	0.289269i	0.901066	+	0.433681i	$0.142786\pi$
$548$	−6.36127	−	2.06690i	−0.271740	−	0.0882936i
$549$		0			0
$550$	8.36911	+	23.7347i	0.356860	+	1.01205i
$551$	32.7613			1.39568
$552$		0			0
$553$	1.64243	−	2.26061i	0.0698433	−	0.0961310i
$554$	18.4729	+	13.4214i	0.784840	+	0.570219i
$555$		0			0
$556$	2.49014	−	1.80920i	0.105606	−	0.0767270i
$557$			28.1467i			1.19262i	0.802756	+	0.596308i	$0.203366\pi$
$557$			28.1467i			1.19262i	−0.802756	+	0.596308i	$0.796634\pi$
$558$		0			0
$559$	−0.368880	−	1.13530i	−0.0156020	−	0.0480179i
$560$	−0.514186	+	0.527119i	−0.0217283	+	0.0222749i
$561$		0			0
$562$	−27.3474	+	8.88571i	−1.15358	+	0.374821i
$563$	3.28183	−	1.06633i	0.138313	−	0.0449406i	−0.239043	−	0.971009i	$-0.576834\pi$
$563$	3.28183	−	1.06633i	0.138313	−	0.0449406i	0.377355	+	0.926069i	$0.376834\pi$
$564$		0			0
$565$	2.36652	−	2.42604i	0.0995601	−	0.102064i
$566$	5.97859	+	18.4002i	0.251299	+	0.773418i
$567$		0			0
$568$		−	5.71189i		−	0.239665i
$569$	−14.0801	+	10.2298i	−0.590270	+	0.428856i	−0.842412	−	0.538834i	$-0.818865\pi$
$569$	−14.0801	+	10.2298i	−0.590270	+	0.428856i	0.252142	+	0.967690i	$0.418865\pi$
$570$		0			0
$571$	30.1126	+	21.8781i	1.26017	+	0.915570i	0.998766	−	0.0496580i	$-0.0158131\pi$
$571$	30.1126	+	21.8781i	1.26017	+	0.915570i	0.261408	+	0.965228i	$0.415813\pi$
$572$	−1.42647	+	1.96337i	−0.0596438	+	0.0820927i
$573$		0			0
$574$	4.12320			0.172099
$575$	25.8127	−	19.7519i	1.07646	−	0.823709i
$576$		0			0
$577$	−19.1201	−	6.21250i	−0.795980	−	0.258630i	−0.117332	−	0.993093i	$-0.537434\pi$
$577$	−19.1201	−	6.21250i	−0.795980	−	0.258630i	−0.678649	+	0.734463i	$0.737434\pi$
$578$	17.0758	−	23.5028i	0.710260	−	0.977589i
$579$		0			0
$580$	−9.63940	−	9.40289i	−0.400254	−	0.390434i
$581$	−4.58125	+	3.32847i	−0.190062	+	0.138088i
$582$		0			0
$583$	4.98786	+	6.86520i	0.206576	+	0.284327i
$584$	0.909340	+	2.79866i	0.0376287	+	0.115809i
$585$		0			0
$586$	4.64456	−	14.2945i	0.191865	−	0.590500i
$587$	−5.81892	+	1.89068i	−0.240173	+	0.0780368i	−0.426630	−	0.904426i	$-0.640299\pi$
$587$	−5.81892	+	1.89068i	−0.240173	+	0.0780368i	0.186457	+	0.982463i	$0.440299\pi$
$588$		0			0
$589$	−2.21684	+	6.82274i	−0.0913434	+	0.281126i
$590$	1.05628	+	2.01093i	0.0434864	+	0.0827887i
$591$		0			0
$592$	−0.458554	−	0.631145i	−0.0188465	−	0.0259399i
$593$			24.9458i			1.02440i	0.858866	+	0.512201i	$0.171170\pi$
$593$			24.9458i			1.02440i	−0.858866	+	0.512201i	$0.828830\pi$
$594$		0			0
$595$	−2.21315	+	4.48026i	−0.0907305	+	0.183673i
$596$	4.09739	+	2.97693i	0.167836	+	0.121940i
$597$		0			0
$598$	2.98085	+	0.968538i	0.121896	+	0.0396065i
$599$	−0.941228			−0.0384575			−0.0192288	−	0.999815i	$-0.506121\pi$
$599$	−0.941228			−0.0384575			−0.0192288	+	0.999815i	$0.506121\pi$
$600$		0			0
$601$	10.2333			0.417426			0.208713	−	0.977977i	$-0.433073\pi$
$601$	10.2333			0.417426			0.208713	+	0.977977i	$0.433073\pi$
$602$	−0.775419	−	0.251949i	−0.0316037	−	0.0102687i
$603$		0			0
$604$	−13.7194	−	9.96772i	−0.558234	−	0.405581i
$605$	31.7193	+	4.62078i	1.28957	+	0.187862i
$606$		0			0
$607$			6.80623i			0.276256i	0.990414	+	0.138128i	$0.0441086\pi$
$607$			6.80623i			0.276256i	−0.990414	+	0.138128i	$0.955891\pi$
$608$	−3.19762	−	4.40115i	−0.129681	−	0.178490i
$609$		0			0
$610$	1.34999	−	9.26702i	0.0546596	−	0.375211i
$611$	−0.652649	+	2.00865i	−0.0264034	+	0.0812612i
$612$		0			0
$613$	−1.08367	+	0.352106i	−0.0437690	+	0.0142214i	−0.330820	−	0.943694i	$-0.607325\pi$
$613$	−1.08367	+	0.352106i	−0.0437690	+	0.0142214i	0.287051	+	0.957915i	$0.407325\pi$
$614$	6.08951	−	18.7416i	0.245753	−	0.756349i
$615$		0			0
$616$	0.512218	+	1.57644i	0.0206378	+	0.0635167i
$617$	−8.43925	−	11.6156i	−0.339752	−	0.467628i	0.604617	−	0.796516i	$-0.293326\pi$
$617$	−8.43925	−	11.6156i	−0.339752	−	0.467628i	−0.944369	+	0.328888i	$0.893326\pi$
$618$		0			0
$619$	0.385511	−	0.280090i	0.0154950	−	0.0112578i	−0.580011	−	0.814609i	$-0.696952\pi$
$619$	0.385511	−	0.280090i	0.0154950	−	0.0112578i	0.595506	+	0.803351i	$0.296952\pi$
$620$	2.61047	−	1.37120i	0.104839	−	0.0550688i
$621$		0			0
$622$	16.5986	−	22.8461i	0.665545	−	0.916044i
$623$	−1.08126	−	0.351323i	−0.0433198	−	0.0140754i
$624$		0			0
$625$	−8.89662	−	23.3634i	−0.355865	−	0.934537i
$626$	11.2478			0.449553
$627$		0			0
$628$	13.4182	−	18.4686i	0.535444	−	0.736976i
$629$	−4.28301	−	3.11179i	−0.170775	−	0.124075i
$630$		0			0
$631$	13.7958	−	10.0232i	0.549201	−	0.399018i	−0.278290	−	0.960497i	$-0.589768\pi$
$631$	13.7958	−	10.0232i	0.549201	−	0.399018i	0.827491	+	0.561479i	$0.189768\pi$
$632$		−	8.48510i		−	0.337519i
$633$		0			0
$634$	7.19752	+	22.1517i	0.285850	+	0.879756i
$635$	−27.7830	+	4.75483i	−1.10254	+	0.188690i
$636$		0			0
$637$	−3.16015	+	1.02679i	−0.125210	+	0.0406831i
$638$	−28.8283	+	9.36690i	−1.14133	+	0.370839i
$639$		0			0
$640$	−0.322342	+	2.21271i	−0.0127417	+	0.0874651i
$641$	10.1127	+	31.1237i	0.399428	+	1.22931i	0.925459	+	0.378848i	$0.123680\pi$
$641$	10.1127	+	31.1237i	0.399428	+	1.22931i	−0.526031	+	0.850465i	$0.676320\pi$
$642$		0			0
$643$			12.5844i			0.496281i	0.968724	+	0.248141i	$0.0798195\pi$
$643$			12.5844i			0.496281i	−0.968724	+	0.248141i	$0.920180\pi$
$644$	1.73189	−	1.25829i	0.0682458	−	0.0495835i
$645$		0			0
$646$	−29.8666	−	21.6994i	−1.17509	−	0.853751i
$647$	−15.0706	+	20.7430i	−0.592488	+	0.815490i	−0.994995	−	0.0999273i	$-0.968139\pi$
$647$	−15.0706	+	20.7430i	−0.592488	+	0.815490i	0.402507	+	0.915417i	$0.368139\pi$
$648$		0			0
$649$	5.11308			0.200706
$650$	1.36813	−	1.98494i	0.0536625	−	0.0778557i
$651$		0			0
$652$	7.56873	+	2.45923i	0.296414	+	0.0963109i
$653$	17.6669	−	24.3165i	0.691361	−	0.951577i	−0.308639	−	0.951179i	$-0.599873\pi$
$653$	17.6669	−	24.3165i	0.691361	−	0.951577i	1.00000		0.000397632i	$-0.000126570\pi$
$654$		0			0
$655$	−13.9200	+	28.1794i	−0.543900	+	1.10106i
$656$	10.1293	−	7.35938i	0.395483	−	0.287335i
$657$		0			0
$658$	0.847898	+	1.16703i	0.0330545	+	0.0454956i
$659$	−2.48706	−	7.65438i	−0.0968821	−	0.298172i	0.890858	−	0.454283i	$-0.150104\pi$
$659$	−2.48706	−	7.65438i	−0.0968821	−	0.298172i	−0.987740	+	0.156110i	$0.950104\pi$
$660$		0			0
$661$	−0.225140	+	0.692909i	−0.00875692	+	0.0269510i	−0.955340	−	0.295510i	$-0.904510\pi$
$661$	−0.225140	+	0.692909i	−0.00875692	+	0.0269510i	0.946583	+	0.322461i	$0.104510\pi$
$662$	0.123004	−	0.0399663i	0.00478068	−	0.00155334i
$663$		0			0
$664$	−5.31370	+	16.3539i	−0.206212	+	0.634654i
$665$	3.59164	+	1.77419i	0.139278	+	0.0688002i
$666$		0			0
$667$	23.0103	+	31.6709i	0.890961	+	1.22630i
$668$			13.9503i			0.539754i
$669$		0			0
$670$	−5.03298	−	4.90949i	−0.194441	−	0.189670i
$671$	−17.0543	−	12.3907i	−0.658373	−	0.478336i
$672$		0			0
$673$	−7.04563	−	2.28926i	−0.271589	−	0.0882446i	0.170056	−	0.985434i	$-0.445605\pi$
$673$	−7.04563	−	2.28926i	−0.271589	−	0.0882446i	−0.441645	+	0.897190i	$0.645605\pi$
$674$	0.538069			0.0207256
$675$		0			0
$676$	−12.7675			−0.491059
$677$	−9.31563	−	3.02683i	−0.358029	−	0.116331i	0.124479	−	0.992222i	$-0.460274\pi$
$677$	−9.31563	−	3.02683i	−0.358029	−	0.116331i	−0.482508	+	0.875892i	$0.660274\pi$
$678$		0			0
$679$	2.53368	+	1.84082i	0.0972336	+	0.0706444i
$680$	2.55972	+	14.9567i	0.0981607	+	0.573564i
$681$		0			0
$682$		−	6.63750i		−	0.254163i
$683$	−19.7406	−	27.1706i	−0.755354	−	1.03966i	−0.997586	−	0.0694369i	$-0.977880\pi$
$683$	−19.7406	−	27.1706i	−0.755354	−	1.03966i	0.242233	−	0.970218i	$-0.422120\pi$
$684$		0			0
$685$	10.4435	−	10.7062i	0.399025	−	0.409062i
$686$	−1.41366	+	4.35079i	−0.0539737	+	0.166114i
$687$		0			0
$688$	−2.35464	+	0.765070i	−0.0897699	+	0.0291680i
$689$	0.251189	−	0.773081i	0.00956955	−	0.0294520i
$690$		0			0
$691$	8.06874	+	24.8330i	0.306950	+	0.944693i	0.978943	+	0.204136i	$0.0654385\pi$
$691$	8.06874	+	24.8330i	0.306950	+	0.944693i	−0.671993	+	0.740557i	$0.734562\pi$
$692$	−11.4623	−	15.7765i	−0.435732	−	0.599734i
$693$		0			0
$694$	−18.3773	+	13.3519i	−0.697593	+	0.506831i
$695$	1.16102	+	6.78396i	0.0440399	+	0.257330i
$696$		0			0
$697$	49.9415	−	68.7385i	1.89167	−	2.60366i
$698$	6.50855	+	2.11476i	0.246352	+	0.0800447i
$699$		0			0
$700$	−0.547558	−	1.55286i	−0.0206957	−	0.0586928i
$701$	−41.8212			−1.57956			−0.789782	−	0.613388i	$-0.789806\pi$
$701$	−41.8212			−1.57956			−0.789782	+	0.613388i	$0.789806\pi$
$702$		0			0
$703$	−2.49459	+	3.43351i	−0.0940852	+	0.129497i
$704$	4.07210	+	2.95855i	0.153473	+	0.111505i
$705$		0			0
$706$	13.5744	−	9.86237i	0.510879	−	0.371175i
$707$			6.33717i			0.238334i
$708$		0			0
$709$	2.74068	+	8.43495i	0.102928	+	0.316781i	0.989239	−	0.146311i	$-0.0467400\pi$
$709$	2.74068	+	8.43495i	0.102928	+	0.316781i	−0.886310	+	0.463092i	$0.846740\pi$
$710$	11.4512	+	5.65666i	0.429757	+	0.212291i
$711$		0			0
$712$	−3.28336	+	1.06683i	−0.123049	+	0.0399811i
$713$	−8.15268	+	2.64897i	−0.305320	+	0.0992045i
$714$		0			0
$715$	−2.52350	−	4.80419i	−0.0943735	−	0.179666i
$716$	5.86857	+	18.0616i	0.219319	+	0.674994i
$717$		0			0
$718$			7.46364i			0.278541i
$719$	2.14802	−	1.56062i	0.0801074	−	0.0582015i	−0.547011	−	0.837126i	$-0.684234\pi$
$719$	2.14802	−	1.56062i	0.0801074	−	0.0582015i	0.627118	+	0.778924i	$0.284234\pi$
$720$		0			0
$721$	1.36058	+	0.988522i	0.0506708	+	0.0368145i
$722$	−6.22755	+	8.57148i	−0.231765	+	0.318998i
$723$		0			0
$724$	18.9484			0.704211
$725$	28.3972	−	10.0132i	1.05464	−	0.371879i
$726$		0			0
$727$	−6.69240	−	2.17449i	−0.248207	−	0.0806475i	0.182271	−	0.983248i	$-0.441655\pi$
$727$	−6.69240	−	2.17449i	−0.248207	−	0.0806475i	−0.430479	+	0.902601i	$0.641655\pi$
$728$	0.0933285	−	0.128456i	0.00345898	−	0.00476088i
$729$		0			0
$730$	−6.51132	−	0.948551i	−0.240995	−	0.0351074i
$731$	−13.5924	+	9.87546i	−0.502733	+	0.365257i
$732$		0			0
$733$	11.9086	+	16.3908i	0.439854	+	0.605407i	0.970180	−	0.242387i	$-0.0779304\pi$
$733$	11.9086	+	16.3908i	0.439854	+	0.605407i	−0.530326	+	0.847794i	$0.677930\pi$
$734$	1.90192	+	5.85350i	0.0702011	+	0.216057i
$735$		0			0
$736$	2.00878	−	6.18239i	0.0740446	−	0.227886i
$737$	−15.0520	+	4.89070i	−0.554448	+	0.180151i
$738$		0			0
$739$	−5.30003	+	16.3118i	−0.194965	+	0.600039i	0.805012	+	0.593258i	$0.202159\pi$
$739$	−5.30003	+	16.3118i	−0.194965	+	0.600039i	−0.999977	+	0.00678134i	$0.997841\pi$
$740$	1.71944	−	0.294269i	0.0632080	−	0.0108175i
$741$		0			0
$742$	−0.326336	−	0.449163i	−0.0119802	−	0.0164893i
$743$		−	9.94252i		−	0.364756i	−0.983229	−	0.182378i	$-0.941621\pi$
$743$		−	9.94252i		−	0.364756i	0.983229	−	0.182378i	$-0.0583794\pi$
$744$		0			0
$745$	−10.0259	+	5.26632i	−0.367322	+	0.192943i
$746$	−7.41811	−	5.38957i	−0.271596	−	0.197326i
$747$		0			0
$748$	32.4853	+	10.5551i	1.18778	+	0.385933i
$749$	5.04970			0.184512
$750$		0			0
$751$	−17.6941			−0.645667			−0.322833	−	0.946456i	$-0.604635\pi$
$751$	−17.6941			−0.645667			−0.322833	+	0.946456i	$0.604635\pi$
$752$	4.16600	+	1.35362i	0.151919	+	0.0493613i
$753$		0			0
$754$	2.34906	+	1.70669i	0.0855478	+	0.0621541i
$755$	33.5701	−	17.6334i	1.22174	−	0.641744i
$756$		0			0
$757$			37.1272i			1.34941i	0.738087	+	0.674706i	$0.235729\pi$
$757$			37.1272i			1.34941i	−0.738087	+	0.674706i	$0.764271\pi$
$758$	20.3562	+	28.0179i	0.739371	+	1.01766i
$759$		0			0
$760$	11.9902	−	2.05202i	0.434929	−	0.0744345i
$761$	15.3161	−	47.1381i	0.555208	−	1.70876i	−0.140184	−	0.990125i	$-0.544770\pi$
$761$	15.3161	−	47.1381i	0.555208	−	1.70876i	0.695393	−	0.718630i	$-0.255230\pi$
$762$		0			0
$763$	3.05689	−	0.993244i	0.110667	−	0.0359578i
$764$	−3.73703	+	11.5014i	−0.135201	+	0.416106i
$765$		0			0
$766$	−2.94198	−	9.05448i	−0.106298	−	0.327152i
$767$	−0.287889	−	0.396245i	−0.0103951	−	0.0143076i
$768$		0			0
$769$	27.8015	−	20.1990i	1.00255	−	0.728393i	0.0399144	−	0.999203i	$-0.487291\pi$
$769$	27.8015	−	20.1990i	1.00255	−	0.728393i	0.962633	+	0.270810i	$0.0872915\pi$
$770$	−3.66773	−	0.534304i	−0.132176	−	0.0192550i
$771$		0			0
$772$	−6.48663	+	8.92808i	−0.233459	+	0.321329i
$773$	−21.8672	−	7.10509i	−0.786510	−	0.255552i	−0.111893	−	0.993720i	$-0.535691\pi$
$773$	−21.8672	−	7.10509i	−0.786510	−	0.255552i	−0.674617	+	0.738168i	$0.735691\pi$
$774$		0			0
$775$	0.163765	+	6.59143i	0.00588260	+	0.236771i
$776$	9.51004			0.341390
$777$		0			0
$778$	10.2541	−	14.1136i	0.367628	−	0.505997i
$779$	−55.1047	−	40.0359i	−1.97433	−	1.43444i
$780$		0			0
$781$	23.2594	−	16.8989i	0.832286	−	0.604691i
$782$		−	44.1134i		−	1.57749i
$783$		0			0
$784$	2.12961	+	6.55426i	0.0760574	+	0.234081i
$785$	23.7374	+	45.1908i	0.847224	+	1.61293i
$786$		0			0
$787$	8.00012	−	2.59940i	0.285174	−	0.0926585i	−0.162938	−	0.986636i	$-0.552097\pi$
$787$	8.00012	−	2.59940i	0.285174	−	0.0926585i	0.448111	+	0.893978i	$0.352097\pi$
$788$	19.6119	−	6.37229i	0.698645	−	0.227004i
$789$		0			0
$790$	17.0110	+	8.40306i	0.605223	+	0.298967i
$791$	0.154239	+	0.474699i	0.00548411	+	0.0168784i
$792$		0			0
$793$			2.01929i			0.0717072i
$794$	10.9663	−	7.96751i	0.389181	−	0.282757i
$795$		0			0
$796$	−14.9922	−	10.8925i	−0.531383	−	0.386073i
$797$	−22.4972	+	30.9647i	−0.796890	+	1.09683i	0.196325	+	0.980539i	$0.437099\pi$
$797$	−22.4972	+	30.9647i	−0.796890	+	1.09683i	−0.993216	+	0.116287i	$0.962901\pi$
$798$		0			0
$799$	29.7258			1.05162
$800$	−4.11683	−	2.83755i	−0.145552	−	0.100323i
$801$		0			0
$802$	13.4198	+	4.36037i	0.473871	+	0.153970i
$803$	−8.70609	+	11.9829i	−0.307231	+	0.422868i
$804$		0			0
$805$	0.807484	+	4.71822i	0.0284601	+	0.166295i
$806$	−0.514382	+	0.373720i	−0.0181183	+	0.0131637i
$807$		0			0
$808$	11.3110	+	15.5683i	0.397921	+	0.547692i
$809$	−9.51817	−	29.2939i	−0.334641	−	1.02992i	−0.966899	−	0.255161i	$-0.917872\pi$
$809$	−9.51817	−	29.2939i	−0.334641	−	1.02992i	0.632258	−	0.774758i	$-0.282128\pi$
$810$		0			0
$811$	−0.243268	+	0.748703i	−0.00854230	+	0.0262905i	−0.955237	−	0.295842i	$-0.904400\pi$
$811$	−0.243268	+	0.748703i	−0.00854230	+	0.0262905i	0.946695	+	0.322133i	$0.104400\pi$
$812$	1.88612	−	0.612839i	0.0661900	−	0.0215064i
$813$		0			0
$814$	1.21343	−	3.73456i	0.0425307	−	0.130896i
$815$	−12.4258	+	12.7384i	−0.435258	+	0.446206i
$816$		0			0
$817$	7.91674	+	10.8965i	0.276972	+	0.381219i
$818$		−	16.5637i		−	0.579138i
$819$		0			0
$820$	4.72275	+	27.5955i	0.164925	+	0.963678i
$821$	14.1344	+	10.2692i	0.493293	+	0.358398i	0.806449	−	0.591303i	$-0.201386\pi$
$821$	14.1344	+	10.2692i	0.493293	+	0.358398i	−0.313157	+	0.949702i	$0.601386\pi$
$822$		0			0
$823$	−35.5950	−	11.5655i	−1.24077	−	0.403149i	−0.386162	−	0.922431i	$-0.626199\pi$
$823$	−35.5950	−	11.5655i	−1.24077	−	0.403149i	−0.854603	+	0.519282i	$0.826199\pi$
$824$	5.10689			0.177907
$825$		0			0
$826$	−0.334529			−0.0116397
$827$	11.2147	+	3.64386i	0.389972	+	0.126710i	0.497439	−	0.867499i	$-0.334274\pi$
$827$	11.2147	+	3.64386i	0.389972	+	0.126710i	−0.107467	+	0.994209i	$0.534274\pi$
$828$		0			0
$829$	−28.3388	−	20.5893i	−0.984247	−	0.715098i	−0.0255936	−	0.999672i	$-0.508148\pi$
$829$	−28.3388	−	20.5893i	−0.984247	−	0.715098i	−0.958654	+	0.284575i	$0.908148\pi$
$830$	−27.5240	−	26.8487i	−0.955373	−	0.931932i
$831$		0			0
$832$		−	0.482152i		−	0.0167156i
$833$	27.4888	+	37.8351i	0.952430	+	1.31091i
$834$		0			0
$835$	−27.9677	−	13.8154i	−0.967861	−	0.478103i
$836$	8.46159	−	26.0421i	0.292650	−	0.900684i
$837$		0			0
$838$	16.1399	−	5.24417i	0.557543	−	0.181157i
$839$	0.154094	−	0.474252i	0.00531991	−	0.0163730i	−0.948361	−	0.317192i	$-0.897260\pi$
$839$	0.154094	−	0.474252i	0.00531991	−	0.0163730i	0.953681	+	0.300819i	$0.0972600\pi$
$840$		0			0
$841$	2.24546	+	6.91082i	0.0774297	+	0.238304i
$842$	−4.15118	−	5.71360i	−0.143059	−	0.196904i
$843$		0			0
$844$	12.7532	−	9.26574i	0.438983	−	0.318940i
$845$	12.6441	−	25.5964i	0.434970	−	0.880543i
$846$		0			0
$847$	−2.77478	+	3.81916i	−0.0953427	+	0.131228i
$848$	−1.60340	−	0.520975i	−0.0550609	−	0.0178904i
$849$		0			0
$850$	−32.5203	−	9.68036i	−1.11544	−	0.332034i
$851$	−5.07133			−0.173843
$852$		0			0
$853$	−12.5542	+	17.2793i	−0.429846	+	0.591633i	−0.967918	−	0.251266i	$-0.919153\pi$
$853$	−12.5542	+	17.2793i	−0.429846	+	0.591633i	0.538072	+	0.842899i	$0.319153\pi$
$854$	1.11579	+	0.810672i	0.0381817	+	0.0277406i
$855$		0			0
$856$	12.4054	−	9.01307i	0.424009	−	0.308060i
$857$			33.4831i			1.14376i	0.820337	+	0.571880i	$0.193786\pi$
$857$			33.4831i			1.14376i	−0.820337	+	0.571880i	$0.806214\pi$
$858$		0			0
$859$	−14.0563	−	43.2610i	−0.479596	−	1.47605i	−0.839657	−	0.543117i	$-0.817244\pi$
$859$	−14.0563	−	43.2610i	−0.479596	−	1.47605i	0.360061	−	0.932929i	$-0.382756\pi$
$860$	0.798060	−	5.47827i	0.0272136	−	0.186808i
$861$		0			0
$862$	16.9841	−	5.51848i	0.578482	−	0.187960i
$863$	−13.7608	+	4.47115i	−0.468423	+	0.152200i	−0.533711	−	0.845667i	$-0.679203\pi$
$863$	−13.7608	+	4.47115i	−0.468423	+	0.152200i	0.0652888	+	0.997866i	$0.479203\pi$
$864$		0			0
$865$	42.9804	−	7.35574i	1.46138	−	0.250103i
$866$	7.47193	+	22.9962i	0.253906	+	0.781444i
$867$		0			0
$868$			0.434265i			0.0147399i
$869$	34.5522	−	25.1036i	1.17210	−	0.851582i
$870$		0			0
$871$	1.22651	+	0.891108i	0.0415586	+	0.0301941i
$872$	5.73695	−	7.89623i	0.194277	−	0.267400i
$873$		0			0
$874$	−35.3638			−1.19620
$875$	3.65545	+	0.440103i	0.123577	+	0.0148782i
$876$		0			0
$877$	−42.9869	−	13.9673i	−1.45156	−	0.471641i	−0.526082	−	0.850434i	$-0.676339\pi$
$877$	−42.9869	−	13.9673i	−1.45156	−	0.471641i	−0.925482	+	0.378793i	$0.876339\pi$
$878$	−11.1152	+	15.2987i	−0.375119	+	0.516307i
$879$		0			0
$880$	−9.96405	+	5.23382i	−0.335888	+	0.176432i
$881$	11.3062	−	8.21440i	0.380914	−	0.276750i	−0.380808	−	0.924654i	$-0.624354\pi$
$881$	11.3062	−	8.21440i	0.380914	−	0.276750i	0.761722	+	0.647904i	$0.224354\pi$
$882$		0			0
$883$	−6.89760	−	9.49373i	−0.232123	−	0.319490i	0.677028	−	0.735958i	$-0.263268\pi$
$883$	−6.89760	−	9.49373i	−0.232123	−	0.319490i	−0.909150	+	0.416468i	$0.863268\pi$
$884$	−1.01108	−	3.11179i	−0.0340064	−	0.104661i
$885$		0			0
$886$	1.25389	−	3.85909i	0.0421254	−	0.129649i
$887$	18.7845	−	6.10346i	0.630722	−	0.204934i	0.0238271	−	0.999716i	$-0.492415\pi$
$887$	18.7845	−	6.10346i	0.630722	−	0.204934i	0.606895	+	0.794782i	$0.292415\pi$
$888$		0			0
$889$	1.28279	−	3.94803i	0.0430235	−	0.132413i
$890$	1.11283	−	7.63901i	0.0373022	−	0.256060i
$891$		0			0
$892$	13.0360	+	17.9426i	0.436479	+	0.600762i
$893$		−	23.8299i		−	0.797437i
$894$		0			0
$895$	−42.0218	−	6.12162i	−1.40464	−	0.204623i
$896$	−0.266421	−	0.193566i	−0.00890051	−	0.00646660i
$897$		0			0
$898$	5.95504	+	1.93491i	0.198722	+	0.0645688i
$899$	−7.94139			−0.264860
$900$		0			0
$901$	−11.4408			−0.381147
$902$	59.9363	+	19.4745i	1.99566	+	0.648429i
$903$		0			0
$904$	1.22619	+	0.890881i	0.0407825	+	0.0296302i
$905$	−18.7652	+	37.9878i	−0.623775	+	1.26276i
$906$		0			0
$907$		−	21.0111i		−	0.697661i	−0.937186	−	0.348831i	$-0.886579\pi$
$907$		−	21.0111i		−	0.697661i	0.937186	−	0.348831i	$-0.113421\pi$
$908$	−6.52260	−	8.97759i	−0.216460	−	0.297932i
$909$		0			0
$910$	0.165102	+	0.314319i	0.00547309	+	0.0104196i
$911$	−7.67252	+	23.6136i	−0.254202	+	0.782353i	0.739784	+	0.672844i	$0.234928\pi$
$911$	−7.67252	+	23.6136i	−0.254202	+	0.782353i	−0.993986	+	0.109508i	$0.965072\pi$
$912$		0			0
$913$	−82.3155	+	26.7459i	−2.72425	+	0.885161i
$914$	0.600200	−	1.84723i	0.0198528	−	0.0611008i
$915$		0			0
$916$	0.555857	+	1.71075i	0.0183660	+	0.0565248i
$917$	−2.72076	−	3.74480i	−0.0898473	−	0.123664i
$918$		0			0
$919$	−29.1482	+	21.1774i	−0.961511	+	0.698579i	−0.953501	−	0.301389i	$-0.902550\pi$
$919$	−29.1482	+	21.1774i	−0.961511	+	0.698579i	−0.00801012	+	0.999968i	$0.502550\pi$
$920$	10.4051	+	10.1498i	0.343047	+	0.334630i
$921$		0			0
$922$	1.83619	−	2.52730i	0.0604717	−	0.0832321i
$923$	−2.61921	−	0.851032i	−0.0862123	−	0.0280121i
$924$		0			0
$925$	−1.11287	+	3.73857i	−0.0365908	+	0.122924i
$926$	8.26641			0.271651
$927$		0			0
$928$	3.53974	−	4.87203i	0.116198	−	0.159932i
$929$	46.0844	+	33.4822i	1.51198	+	1.09852i	0.965290	+	0.261181i	$0.0841119\pi$
$929$	46.0844	+	33.4822i	1.51198	+	1.09852i	0.546689	+	0.837336i	$0.315888\pi$
$930$		0			0
$931$	30.3308	−	22.0366i	0.994051	−	0.722220i
$932$		−	3.70579i		−	0.121387i
$933$		0			0
$934$	9.46187	+	29.1206i	0.309602	+	0.952856i
$935$	−53.3322	+	54.6737i	−1.74415	+	1.78802i
$936$		0			0
$937$	−39.7133	+	12.9036i	−1.29738	+	0.421543i	−0.874668	−	0.484723i	$-0.838920\pi$
$937$	−39.7133	+	12.9036i	−1.29738	+	0.421543i	−0.422708	+	0.906266i	$0.638920\pi$
$938$	0.984794	−	0.319979i	0.0321547	−	0.0104477i
$939$		0			0
$940$	−6.83946	+	7.01150i	−0.223079	+	0.228690i
$941$	7.05275	+	21.7061i	0.229913	+	0.707599i	0.997756	+	0.0669608i	$0.0213302\pi$
$941$	7.05275	+	21.7061i	0.229913	+	0.707599i	−0.767843	+	0.640638i	$0.778670\pi$
$942$		0			0
$943$		−	81.3903i		−	2.65043i
$944$	−0.821825	+	0.597091i	−0.0267481	+	0.0194337i
$945$		0			0
$946$	−10.0818	−	7.32484i	−0.327787	−	0.238151i
$947$	4.97703	−	6.85030i	0.161732	−	0.222605i	−0.720458	−	0.693498i	$-0.756068\pi$
$947$	4.97703	−	6.85030i	0.161732	−	0.222605i	0.882190	+	0.470894i	$0.156068\pi$
$948$		0			0
$949$	1.41882			0.0460569
$950$	−7.76033	+	26.0701i	−0.251778	+	0.845826i
$951$		0			0
$952$	−2.12539	−	0.690580i	−0.0688841	−	0.0223818i
$953$	14.6287	−	20.1346i	0.473869	−	0.652225i	−0.503443	−	0.864028i	$-0.667934\pi$
$953$	14.6287	−	20.1346i	0.473869	−	0.652225i	0.977312	+	0.211803i	$0.0679336\pi$
$954$		0			0
$955$	−19.3572	−	18.8822i	−0.626383	−	0.611014i
$956$	−13.6508	+	9.91790i	−0.441499	+	0.320768i
$957$		0			0
$958$	−0.689407	−	0.948887i	−0.0222737	−	0.0306571i
$959$	0.680661	+	2.09486i	0.0219797	+	0.0676465i
$960$		0			0
$961$	−9.04216	+	27.8289i	−0.291683	+	0.897707i
$962$	−0.357736	+	0.116235i	−0.0115339	+	0.00374758i
$963$		0			0
$964$	−6.37366	+	19.6161i	−0.205282	+	0.631793i
$965$	−11.4751	−	21.8462i	−0.369398	−	0.703253i
$966$		0			0
$967$	13.0046	+	17.8993i	0.418199	+	0.575602i	0.965194	−	0.261534i	$-0.0842283\pi$
$967$	13.0046	+	17.8993i	0.418199	+	0.575602i	−0.546995	+	0.837136i	$0.684228\pi$
$968$			14.3350i			0.460746i
$969$		0			0
$970$	−9.41809	+	19.0658i	−0.302397	+	0.612165i
$971$	−13.7573	−	9.99529i	−0.441494	−	0.320764i	0.344734	−	0.938700i	$-0.387969\pi$
$971$	−13.7573	−	9.99529i	−0.441494	−	0.320764i	−0.786228	+	0.617936i	$0.787969\pi$
$972$		0			0
$973$	−0.964017	−	0.313228i	−0.0309050	−	0.0100416i
$974$	11.7556			0.376672
$975$		0			0
$976$	4.18808			0.134057
$977$	−39.2815	−	12.7633i	−1.25673	−	0.408335i	−0.396400	−	0.918078i	$-0.629741\pi$
$977$	−39.2815	−	12.7633i	−1.25673	−	0.408335i	−0.860327	+	0.509742i	$0.829741\pi$
$978$		0			0
$979$	−14.0582	−	10.2139i	−0.449303	−	0.326438i
$980$	−15.2490	−	2.22144i	−0.487112	−	0.0709611i
$981$		0			0
$982$			4.13052i			0.131810i
$983$	−36.3933	−	50.0911i	−1.16077	−	1.59766i	−0.708369	−	0.705842i	$-0.750569\pi$
$983$	−36.3933	−	50.0911i	−1.16077	−	1.59766i	−0.452398	−	0.891816i	$-0.649431\pi$
$984$		0			0
$985$	−6.64707	+	45.6287i	−0.211793	+	1.45385i
$986$	12.6286	−	38.8668i	0.402176	−	1.23777i
$987$		0			0
$988$	−2.49459	+	0.810541i	−0.0793635	+	0.0257868i
$989$	−4.97338	+	15.3065i	−0.158144	+	0.486718i
$990$		0			0
$991$	1.52376	+	4.68964i	0.0484037	+	0.148971i	0.972337	−	0.233582i	$-0.0750448\pi$
$991$	1.52376	+	4.68964i	0.0484037	+	0.148971i	−0.923933	+	0.382553i	$0.875045\pi$
$992$	0.775108	+	1.06685i	0.0246097	+	0.0338724i
$993$		0			0
$994$	−1.52177	+	1.10563i	−0.0482676	+	0.0350684i
$995$	36.6845	−	19.2693i	1.16298	−	0.610876i
$996$		0			0
$997$	−29.1304	+	40.0946i	−0.922569	+	1.26981i	0.0401195	+	0.999195i	$0.487226\pi$
$997$	−29.1304	+	40.0946i	−0.922569	+	1.26981i	−0.962688	+	0.270612i	$0.912774\pi$
$998$	9.12209	+	2.96395i	0.288755	+	0.0938221i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.l.c.379.1		16
3.2	odd	2		150.2.h.b.79.4	yes	16
15.2	even	4		750.2.g.g.601.3		16
15.8	even	4		750.2.g.f.601.2		16
15.14	odd	2		750.2.h.d.649.2		16
25.19	even	10	inner	450.2.l.c.19.1		16
75.8	even	20		750.2.g.f.151.2		16
75.17	even	20		750.2.g.g.151.3		16
75.38	even	20		3750.2.a.v.1.4		8
75.41	odd	10		3750.2.c.k.1249.12		16
75.44	odd	10		150.2.h.b.19.4	✓	16
75.56	odd	10		750.2.h.d.349.1		16
75.59	odd	10		3750.2.c.k.1249.5		16
75.62	even	20		3750.2.a.u.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.19.4	✓	16	75.44	odd	10
150.2.h.b.79.4	yes	16	3.2	odd	2
450.2.l.c.19.1		16	25.19	even	10	inner
450.2.l.c.379.1		16	1.1	even	1	trivial
750.2.g.f.151.2		16	75.8	even	20
750.2.g.f.601.2		16	15.8	even	4
750.2.g.g.151.3		16	75.17	even	20
750.2.g.g.601.3		16	15.2	even	4
750.2.h.d.349.1		16	75.56	odd	10
750.2.h.d.649.2		16	15.14	odd	2
3750.2.a.u.1.5		8	75.62	even	20
3750.2.a.v.1.4		8	75.38	even	20
3750.2.c.k.1249.5		16	75.59	odd	10
3750.2.c.k.1249.12		16	75.41	odd	10

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.809017 + 0.587785i) q^{4} +(-1.97959 + 1.03982i) q^{5} -0.329315i q^{7} +(-0.587785 - 0.809017i) q^{8} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.809017 + 0.587785i) q^{4} +(-1.97959 + 1.03982i) q^{5} -0.329315i q^{7} +(-0.587785 - 0.809017i) q^{8} +(2.20402 - 0.377200i) q^{10} +(1.55540 - 4.78704i) q^{11} +(-0.458554 + 0.148993i) q^{13} +(-0.101764 + 0.313197i) q^{14} +(0.309017 + 0.951057i) q^{16} +(3.98877 + 5.49007i) q^{17} +(4.40115 - 3.19762i) q^{19} +(-2.21271 - 0.322342i) q^{20} +(-2.95855 + 4.07210i) q^{22} +(6.18239 + 2.00878i) q^{23} +(2.83755 - 4.11683i) q^{25} +0.482152 q^{26} +(0.193566 - 0.266421i) q^{28} +(4.87203 + 3.53974i) q^{29} +(-1.06685 + 0.775108i) q^{31} -1.00000i q^{32} +(-2.09702 - 6.45396i) q^{34} +(0.342428 + 0.651908i) q^{35} +(-0.741956 + 0.241076i) q^{37} +(-5.17386 + 1.68109i) q^{38} +(2.00481 + 0.990331i) q^{40} +(-3.86905 - 11.9077i) q^{41} +2.47582i q^{43} +(4.07210 - 2.95855i) q^{44} +(-5.25906 - 3.82093i) q^{46} +(2.57473 - 3.54381i) q^{47} +6.89155 q^{49} +(-3.97084 + 3.03849i) q^{50} +(-0.458554 - 0.148993i) q^{52} +(-0.990953 + 1.36393i) q^{53} +(1.89860 + 11.0937i) q^{55} +(-0.266421 + 0.193566i) q^{56} +(-3.53974 - 4.87203i) q^{58} +(0.313909 + 0.966113i) q^{59} +(1.29419 - 3.98310i) q^{61} +(1.25415 - 0.407499i) q^{62} +(-0.309017 + 0.951057i) q^{64} +(0.752823 - 0.771759i) q^{65} +(-1.84819 - 2.54381i) q^{67} +6.78610i q^{68} +(-0.124218 - 0.725818i) q^{70} +(4.62101 + 3.35736i) q^{71} +(-2.79866 - 0.909340i) q^{73} +0.780139 q^{74} +5.44012 q^{76} +(-1.57644 - 0.512218i) q^{77} +(6.86459 + 4.98742i) q^{79} +(-1.60065 - 1.56138i) q^{80} +12.5205i q^{82} +(-10.1073 - 13.9114i) q^{83} +(-13.6048 - 6.72048i) q^{85} +(0.765070 - 2.35464i) q^{86} +(-4.78704 + 1.55540i) q^{88} +(1.06683 - 3.28336i) q^{89} +(0.0490657 + 0.151009i) q^{91} +(3.82093 + 5.25906i) q^{92} +(-3.54381 + 2.57473i) q^{94} +(-5.38752 + 10.9064i) q^{95} +(-5.58986 + 7.69378i) q^{97} +(-6.55426 - 2.12961i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 4 q^{5}+O(q^{10}) \) 16 * q + 4 * q^4 - 4 * q^5	\( 16 q + 4 q^{4} - 4 q^{5} + 2 q^{10} - 2 q^{11} + 20 q^{13} - 2 q^{14} - 4 q^{16} + 30 q^{17} + 4 q^{20} - 20 q^{22} + 10 q^{23} + 24 q^{25} - 4 q^{26} + 10 q^{29} - 18 q^{31} + 12 q^{34} + 34 q^{35} + 20 q^{37} - 10 q^{38} - 2 q^{40} - 22 q^{41} - 8 q^{44} - 6 q^{46} + 50 q^{47} - 52 q^{49} - 12 q^{50} + 20 q^{52} - 30 q^{53} + 18 q^{55} + 2 q^{56} - 30 q^{58} - 20 q^{59} + 12 q^{61} - 50 q^{62} + 4 q^{64} + 8 q^{65} - 50 q^{67} - 12 q^{70} + 28 q^{71} + 20 q^{73} - 12 q^{74} + 20 q^{76} - 100 q^{77} - 20 q^{79} - 4 q^{80} + 30 q^{83} - 4 q^{85} + 6 q^{86} - 70 q^{89} + 12 q^{91} + 30 q^{92} + 2 q^{94} + 30 q^{95} - 10 q^{97} - 60 q^{98}+O(q^{100}) \) 16 * q + 4 * q^4 - 4 * q^5 + 2 * q^10 - 2 * q^11 + 20 * q^13 - 2 * q^14 - 4 * q^16 + 30 * q^17 + 4 * q^20 - 20 * q^22 + 10 * q^23 + 24 * q^25 - 4 * q^26 + 10 * q^29 - 18 * q^31 + 12 * q^34 + 34 * q^35 + 20 * q^37 - 10 * q^38 - 2 * q^40 - 22 * q^41 - 8 * q^44 - 6 * q^46 + 50 * q^47 - 52 * q^49 - 12 * q^50 + 20 * q^52 - 30 * q^53 + 18 * q^55 + 2 * q^56 - 30 * q^58 - 20 * q^59 + 12 * q^61 - 50 * q^62 + 4 * q^64 + 8 * q^65 - 50 * q^67 - 12 * q^70 + 28 * q^71 + 20 * q^73 - 12 * q^74 + 20 * q^76 - 100 * q^77 - 20 * q^79 - 4 * q^80 + 30 * q^83 - 4 * q^85 + 6 * q^86 - 70 * q^89 + 12 * q^91 + 30 * q^92 + 2 * q^94 + 30 * q^95 - 10 * q^97 - 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more