LMFDB - Embedded newform 225.2.m.b.64.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(19,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, 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("225.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.m (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:	$1.79663404548$
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} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.2
Root			$-0.0898194i$ of defining polynomial
Character	$\chi$	$=$	225.64
Dual form			225.2.m.b.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0527945 - 0.0726655i) q^{2} +(0.615541 - 1.89444i) q^{4} +(1.27125 + 1.83954i) q^{5} +4.36070i q^{7} +(-0.341004 + 0.110799i) q^{8} +O(q^{10})$	\(q+(-0.0527945 - 0.0726655i) q^{2} +(0.615541 - 1.89444i) q^{4} +(1.27125 + 1.83954i) q^{5} +4.36070i q^{7} +(-0.341004 + 0.110799i) q^{8} +(0.0665563 - 0.189494i) q^{10} +(3.55235 - 2.58093i) q^{11} +(1.16479 - 1.60319i) q^{13} +(0.316872 - 0.230221i) q^{14} +(-3.19696 - 2.32273i) q^{16} +(0.948224 - 0.308097i) q^{17} +(-0.417468 - 1.28484i) q^{19} +(4.26741 - 1.27599i) q^{20} +(-0.375089 - 0.121874i) q^{22} +(-1.38512 - 1.90646i) q^{23} +(-1.76785 + 4.67704i) q^{25} -0.177991 q^{26} +(8.26109 + 2.68419i) q^{28} +(-2.46551 + 7.58806i) q^{29} +(-1.13645 - 3.49762i) q^{31} +1.07204i q^{32} +(-0.0724490 - 0.0526373i) q^{34} +(-8.02171 + 5.54354i) q^{35} +(-0.844681 + 1.16260i) q^{37} +(-0.0713231 + 0.0981678i) q^{38} +(-0.637321 - 0.486439i) q^{40} +(-4.83992 - 3.51641i) q^{41} -2.68554i q^{43} +(-2.70280 - 8.31838i) q^{44} +(-0.0654066 + 0.201301i) q^{46} +(-10.4039 - 3.38042i) q^{47} -12.0157 q^{49} +(0.433192 - 0.118461i) q^{50} +(-2.32018 - 3.19345i) q^{52} +(10.5102 + 3.41496i) q^{53} +(9.26366 + 3.25369i) q^{55} +(-0.483161 - 1.48702i) q^{56} +(0.681555 - 0.221451i) q^{58} +(-5.41147 - 3.93167i) q^{59} +(7.64982 - 5.55792i) q^{61} +(-0.194158 + 0.267235i) q^{62} +(-6.31602 + 4.58886i) q^{64} +(4.42988 + 0.104621i) q^{65} +(-12.2894 + 3.99307i) q^{67} -1.98600i q^{68} +(0.826326 + 0.290232i) q^{70} +(-2.26280 + 6.96418i) q^{71} +(-0.249694 - 0.343674i) q^{73} +0.129076 q^{74} -2.69101 q^{76} +(11.2547 + 15.4907i) q^{77} +(1.96390 - 6.04425i) q^{79} +(0.208626 - 8.83372i) q^{80} +0.537343i q^{82} +(-0.700939 + 0.227749i) q^{83} +(1.77219 + 1.35263i) q^{85} +(-0.195146 + 0.141782i) q^{86} +(-0.925401 + 1.27370i) q^{88} +(7.91814 - 5.75286i) q^{89} +(6.99105 + 5.07929i) q^{91} +(-4.46427 + 1.45053i) q^{92} +(0.303628 + 0.934470i) q^{94} +(1.83281 - 2.40130i) q^{95} +(0.0320583 + 0.0104164i) q^{97} +(0.634365 + 0.873128i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 30 q^{8}+O(q^{10}) $ 16 * q + 2 * q^4 + 30 * q^8	$ 16 q + 2 q^{4} + 30 q^{8} + 6 q^{11} + 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} - 20 q^{20} - 30 q^{22} + 20 q^{23} - 10 q^{25} - 12 q^{26} + 30 q^{28} - 16 q^{29} + 6 q^{31} - 36 q^{34} - 10 q^{35} - 10 q^{37} - 30 q^{38} + 10 q^{40} + 14 q^{41} - 26 q^{44} + 16 q^{46} - 40 q^{47} - 20 q^{50} + 40 q^{52} - 10 q^{53} + 10 q^{55} + 10 q^{58} - 12 q^{59} + 10 q^{62} + 8 q^{64} + 70 q^{65} - 40 q^{67} + 30 q^{70} + 8 q^{71} - 20 q^{73} + 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 10 q^{83} - 20 q^{85} + 36 q^{86} - 40 q^{88} - 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} + 40 q^{95} + 40 q^{97} - 60 q^{98}+O(q^{100}) $ 16 * q + 2 * q^4 + 30 * q^8 + 6 * q^11 + 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 - 20 * q^20 - 30 * q^22 + 20 * q^23 - 10 * q^25 - 12 * q^26 + 30 * q^28 - 16 * q^29 + 6 * q^31 - 36 * q^34 - 10 * q^35 - 10 * q^37 - 30 * q^38 + 10 * q^40 + 14 * q^41 - 26 * q^44 + 16 * q^46 - 40 * q^47 - 20 * q^50 + 40 * q^52 - 10 * q^53 + 10 * q^55 + 10 * q^58 - 12 * q^59 + 10 * q^62 + 8 * q^64 + 70 * q^65 - 40 * q^67 + 30 * q^70 + 8 * q^71 - 20 * q^73 + 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 10 * q^83 - 20 * q^85 + 36 * q^86 - 40 * q^88 - 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 + 40 * q^95 + 40 * q^97 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.0527945	−	0.0726655i	−0.0373314	−	0.0513822i	0.789943	−	0.613180i	$-0.210110\pi$
$2$	−0.0527945	−	0.0726655i	−0.0373314	−	0.0513822i	−0.827275	+	0.561798i	$0.810110\pi$
$3$		0			0
$3$		0			0
$4$	0.615541	−	1.89444i	0.307770	−	0.947220i
$5$	1.27125	+	1.83954i	0.568520	+	0.822669i
$5$	1.27125	+	1.83954i	0.568520	+	0.822669i
$6$		0			0
$7$			4.36070i			1.64819i	0.566451	+	0.824095i	$0.308316\pi$
$7$			4.36070i			1.64819i	−0.566451	+	0.824095i	$0.691684\pi$
$8$	−0.341004	+	0.110799i	−0.120563	+	0.0391734i
$9$		0			0
$10$	0.0665563	−	0.189494i	0.0210469	−	0.0599232i
$11$	3.55235	−	2.58093i	1.07107	−	0.778180i	0.0949680	−	0.995480i	$-0.469725\pi$
$11$	3.55235	−	2.58093i	1.07107	−	0.778180i	0.976105	+	0.217300i	$0.0697251\pi$
$12$		0			0
$13$	1.16479	−	1.60319i	0.323054	−	0.444646i	−0.616343	−	0.787478i	$-0.711386\pi$
$13$	1.16479	−	1.60319i	0.323054	−	0.444646i	0.939397	+	0.342832i	$0.111386\pi$
$14$	0.316872	−	0.230221i	0.0846877	−	0.0615292i
$15$		0			0
$16$	−3.19696	−	2.32273i	−0.799240	−	0.580682i
$17$	0.948224	−	0.308097i	0.229978	−	0.0747244i	−0.191761	−	0.981442i	$-0.561420\pi$
$17$	0.948224	−	0.308097i	0.229978	−	0.0747244i	0.421739	+	0.906717i	$0.361420\pi$
$18$		0			0
$19$	−0.417468	−	1.28484i	−0.0957738	−	0.294761i	0.891681	−	0.452665i	$-0.149527\pi$
$19$	−0.417468	−	1.28484i	−0.0957738	−	0.294761i	−0.987455	+	0.157903i	$0.949527\pi$
$20$	4.26741	−	1.27599i	0.954223	−	0.285320i
$21$		0			0
$22$	−0.375089	−	0.121874i	−0.0799692	−	0.0259836i
$23$	−1.38512	−	1.90646i	−0.288818	−	0.397524i	0.639812	−	0.768532i	$-0.279012\pi$
$23$	−1.38512	−	1.90646i	−0.288818	−	0.397524i	−0.928630	+	0.371008i	$0.879012\pi$
$24$		0			0
$25$	−1.76785	+	4.67704i	−0.353570	+	0.935408i
$26$	−0.177991			−0.0349069
$27$		0			0
$28$	8.26109	+	2.68419i	1.56120	+	0.507264i
$29$	−2.46551	+	7.58806i	−0.457834	+	1.40907i	0.409942	+	0.912111i	$0.365549\pi$
$29$	−2.46551	+	7.58806i	−0.457834	+	1.40907i	−0.867776	+	0.496955i	$0.834451\pi$
$30$		0			0
$31$	−1.13645	−	3.49762i	−0.204112	−	0.628191i	−0.999749	−	0.0224173i	$-0.992864\pi$
$31$	−1.13645	−	3.49762i	−0.204112	−	0.628191i	0.795637	−	0.605774i	$-0.207136\pi$
$32$			1.07204i			0.189512i
$33$		0			0
$34$	−0.0724490	−	0.0526373i	−0.0124249	−	0.00902722i
$35$	−8.02171	+	5.54354i	−1.35592	+	0.937029i
$36$		0			0
$37$	−0.844681	+	1.16260i	−0.138865	+	0.191131i	−0.872785	−	0.488105i	$-0.837688\pi$
$37$	−0.844681	+	1.16260i	−0.138865	+	0.191131i	0.733920	+	0.679235i	$0.237688\pi$
$38$	−0.0713231	+	0.0981678i	−0.0115701	+	0.0159249i
$39$		0			0
$40$	−0.637321	−	0.486439i	−0.100769	−	0.0769128i
$41$	−4.83992	−	3.51641i	−0.755869	−	0.549171i	0.141771	−	0.989899i	$-0.454720\pi$
$41$	−4.83992	−	3.51641i	−0.755869	−	0.549171i	−0.897641	+	0.440728i	$0.854720\pi$
$42$		0			0
$43$		−	2.68554i		−	0.409541i	−0.978810	−	0.204770i	$-0.934355\pi$
$43$		−	2.68554i		−	0.409541i	0.978810	−	0.204770i	$-0.0656447\pi$
$44$	−2.70280	−	8.31838i	−0.407463	−	1.25404i
$45$		0			0
$46$	−0.0654066	+	0.201301i	−0.00964368	+	0.0296802i
$47$	−10.4039	−	3.38042i	−1.51756	−	0.493086i	−0.572480	−	0.819919i	$-0.694018\pi$
$47$	−10.4039	−	3.38042i	−1.51756	−	0.493086i	−0.945082	+	0.326833i	$0.894018\pi$
$48$		0			0
$49$	−12.0157			−1.71653
$50$	0.433192	−	0.118461i	0.0612626	−	0.0167529i
$51$		0			0
$52$	−2.32018	−	3.19345i	−0.321751	−	0.442852i
$53$	10.5102	+	3.41496i	1.44368	+	0.469081i	0.923043	−	0.384696i	$-0.125694\pi$
$53$	10.5102	+	3.41496i	1.44368	+	0.469081i	0.520639	+	0.853777i	$0.325694\pi$
$54$		0			0
$55$	9.26366	+	3.25369i	1.24911	+	0.438728i
$56$	−0.483161	−	1.48702i	−0.0645652	−	0.198711i
$57$		0			0
$58$	0.681555	−	0.221451i	0.0894926	−	0.0290779i
$59$	−5.41147	−	3.93167i	−0.704514	−	0.511859i	0.176885	−	0.984231i	$-0.443398\pi$
$59$	−5.41147	−	3.93167i	−0.704514	−	0.511859i	−0.881399	+	0.472372i	$0.843398\pi$
$60$		0			0
$61$	7.64982	−	5.55792i	0.979460	−	0.711619i	0.0218719	−	0.999761i	$-0.493037\pi$
$61$	7.64982	−	5.55792i	0.979460	−	0.711619i	0.957588	+	0.288142i	$0.0930374\pi$
$62$	−0.194158	+	0.267235i	−0.0246581	+	0.0339389i
$63$		0			0
$64$	−6.31602	+	4.58886i	−0.789502	+	0.573607i
$65$	4.42988	+	0.104621i	0.549459	+	0.0129766i
$66$		0			0
$67$	−12.2894	+	3.99307i	−1.50139	+	0.487831i	−0.940423	−	0.340006i	$-0.889571\pi$
$67$	−12.2894	+	3.99307i	−1.50139	+	0.487831i	−0.560968	+	0.827838i	$0.689571\pi$
$68$		−	1.98600i		−	0.240838i
$69$		0			0
$70$	0.826326	+	0.290232i	0.0987649	+	0.0346894i
$71$	−2.26280	+	6.96418i	−0.268545	+	0.826496i	0.722311	+	0.691569i	$0.243080\pi$
$71$	−2.26280	+	6.96418i	−0.268545	+	0.826496i	−0.990856	+	0.134927i	$0.956920\pi$
$72$		0			0
$73$	−0.249694	−	0.343674i	−0.0292244	−	0.0402240i	0.794155	−	0.607716i	$-0.207914\pi$
$73$	−0.249694	−	0.343674i	−0.0292244	−	0.0402240i	−0.823379	+	0.567492i	$0.807914\pi$
$74$	0.129076			0.0150047
$75$		0			0
$76$	−2.69101			−0.308680
$77$	11.2547	+	15.4907i	1.28259	+	1.76533i
$78$		0			0
$79$	1.96390	−	6.04425i	0.220956	−	0.680032i	−0.777721	−	0.628609i	$-0.783624\pi$
$79$	1.96390	−	6.04425i	0.220956	−	0.680032i	0.998677	−	0.0514225i	$-0.0163755\pi$
$80$	0.208626	−	8.83372i	0.0233251	−	0.987640i
$81$		0			0
$82$			0.537343i			0.0593396i
$83$	−0.700939	+	0.227749i	−0.0769381	+	0.0249987i	−0.347233	−	0.937779i	$-0.612879\pi$
$83$	−0.700939	+	0.227749i	−0.0769381	+	0.0249987i	0.270295	+	0.962778i	$0.412879\pi$
$84$		0			0
$85$	1.77219	+	1.35263i	0.192221	+	0.146714i
$86$	−0.195146	+	0.141782i	−0.0210431	+	0.0152887i
$87$		0			0
$88$	−0.925401	+	1.27370i	−0.0986481	+	0.135777i
$89$	7.91814	−	5.75286i	0.839321	−	0.609802i	−0.0828599	−	0.996561i	$-0.526405\pi$
$89$	7.91814	−	5.75286i	0.839321	−	0.609802i	0.922181	+	0.386759i	$0.126405\pi$
$90$		0			0
$91$	6.99105	+	5.07929i	0.732861	+	0.532455i
$92$	−4.46427	+	1.45053i	−0.465432	+	0.151228i
$93$		0			0
$94$	0.303628	+	0.934470i	0.0313168	+	0.0963833i
$95$	1.83281	−	2.40130i	0.188042	−	0.246368i
$96$		0			0
$97$	0.0320583	+	0.0104164i	0.00325503	+	0.00105762i	0.310644	−	0.950526i	$-0.399455\pi$
$97$	0.0320583	+	0.0104164i	0.00325503	+	0.00105762i	−0.307389	+	0.951584i	$0.599455\pi$
$98$	0.634365	+	0.873128i	0.0640805	+	0.0881992i
$99$		0			0
$100$	7.77219	+	6.22799i	0.777219	+	0.622799i
$101$	−3.19390			−0.317805			−0.158902	−	0.987294i	$-0.550796\pi$
$101$	−3.19390			−0.317805			−0.158902	+	0.987294i	$0.550796\pi$
$102$		0			0
$103$	−8.13479	−	2.64315i	−0.801544	−	0.260438i	−0.120532	−	0.992709i	$-0.538460\pi$
$103$	−8.13479	−	2.64315i	−0.801544	−	0.260438i	−0.681012	+	0.732272i	$0.738460\pi$
$104$	−0.219565	+	0.675753i	−0.0215302	+	0.0662630i
$105$		0			0
$106$	−0.306730	−	0.944017i	−0.0297922	−	0.0916910i
$107$		−	2.22136i		−	0.214747i	−0.994219	−	0.107373i	$-0.965756\pi$
$107$		−	2.22136i		−	0.214747i	0.994219	−	0.107373i	$-0.0342440\pi$
$108$		0			0
$109$	8.90108	+	6.46701i	0.852569	+	0.619427i	0.925853	−	0.377884i	$-0.123348\pi$
$109$	8.90108	+	6.46701i	0.852569	+	0.619427i	−0.0732844	+	0.997311i	$0.523348\pi$
$110$	−0.252639	−	0.844925i	−0.0240882	−	0.0805604i
$111$		0			0
$112$	10.1287	−	13.9410i	0.957074	−	1.31730i
$113$	1.00524	−	1.38359i	0.0945646	−	0.130157i	−0.759113	−	0.650959i	$-0.774367\pi$
$113$	1.00524	−	1.38359i	0.0945646	−	0.130157i	0.853678	+	0.520802i	$0.174367\pi$
$114$		0			0
$115$	1.74618	−	4.97157i	0.162832	−	0.463602i
$116$	12.8575	+	9.34152i	1.19379	+	0.867338i
$117$		0			0
$118$			0.600798i			0.0553079i
$119$	1.34352	+	4.13492i	0.123160	+	0.379048i
$120$		0			0
$121$	2.55877	−	7.87510i	0.232616	−	0.715918i
$122$	−0.807738	−	0.262450i	−0.0731292	−	0.0237611i
$123$		0			0
$124$	−7.32556			−0.657855
$125$	−10.8510	+	2.69365i	−0.970543	+	0.240927i
$126$		0			0
$127$	7.38079	+	10.1588i	0.654939	+	0.901447i	0.999301	−	0.0373905i	$-0.0119046\pi$
$127$	7.38079	+	10.1588i	0.654939	+	0.901447i	−0.344361	+	0.938837i	$0.611905\pi$
$128$	2.70605	+	0.879248i	0.239183	+	0.0777153i
$129$		0			0
$130$	−0.226271	−	0.327423i	−0.0198453	−	0.0287169i
$131$	−5.09006	−	15.6656i	−0.444721	−	1.36871i	−0.882790	−	0.469769i	$-0.844337\pi$
$131$	−5.09006	−	15.6656i	−0.444721	−	1.36871i	0.438069	−	0.898942i	$-0.355663\pi$
$132$		0			0
$133$	5.60278	−	1.82046i	0.485823	−	0.157853i
$134$	0.938972	+	0.682203i	0.0811149	+	0.0589334i
$135$		0			0
$136$	−0.289212	+	0.210125i	−0.0247997	+	0.0180180i
$137$	5.68231	−	7.82102i	0.485472	−	0.668195i	−0.494073	−	0.869421i	$-0.664492\pi$
$137$	5.68231	−	7.82102i	0.485472	−	0.668195i	0.979545	+	0.201225i	$0.0644923\pi$
$138$		0			0
$139$	10.9482	−	7.95430i	0.928611	−	0.674675i	−0.0170416	−	0.999855i	$-0.505425\pi$
$139$	10.9482	−	7.95430i	0.928611	−	0.674675i	0.945652	+	0.325180i	$0.105425\pi$
$140$	5.56422	+	18.6089i	0.470262	+	1.57274i
$141$		0			0
$142$	0.625518	−	0.203243i	0.0524923	−	0.0170558i
$143$		−	8.70133i		−	0.727642i
$144$		0			0
$145$	−17.0928	+	5.11090i	−1.41948	+	0.424437i
$146$	−0.0117907	+	0.0362882i	−0.000975809	+	0.00300323i
$147$		0			0
$148$	1.68255	+	2.31583i	0.138304	+	0.190360i
$149$	13.6843			1.12106			0.560529	−	0.828134i	$-0.310598\pi$
$149$	13.6843			1.12106			0.560529	+	0.828134i	$0.310598\pi$
$150$		0			0
$151$	−11.3204			−0.921237			−0.460619	−	0.887598i	$-0.652372\pi$
$151$	−11.3204			−0.921237			−0.460619	+	0.887598i	$0.652372\pi$
$152$	0.284717	+	0.391879i	0.0230936	+	0.0317856i
$153$		0			0
$154$	0.531455	−	1.63565i	0.0428259	−	0.131805i
$155$	4.98932	−	6.53689i	0.400752	−	0.525055i
$156$		0			0
$157$			8.56070i			0.683219i	0.939842	+	0.341609i	$0.110972\pi$
$157$			8.56070i			0.683219i	−0.939842	+	0.341609i	$0.889028\pi$
$158$	−0.542892	+	0.176396i	−0.0431901	+	0.0140333i
$159$		0			0
$160$	−1.97207	+	1.36283i	−0.155906	+	0.107741i
$161$	8.31349	−	6.04010i	0.655194	−	0.476027i
$162$		0			0
$163$	−2.69505	+	3.70942i	−0.211093	+	0.290544i	−0.901413	−	0.432959i	$-0.857469\pi$
$163$	−2.69505	+	3.70942i	−0.211093	+	0.290544i	0.690321	+	0.723503i	$0.257469\pi$
$164$	−9.64080	+	7.00445i	−0.752820	+	0.546956i
$165$		0			0
$166$	0.0535552	+	0.0389102i	0.00415669	+	0.00302001i
$167$	6.86465	−	2.23046i	0.531203	−	0.172598i	−0.0311206	−	0.999516i	$-0.509908\pi$
$167$	6.86465	−	2.23046i	0.531203	−	0.172598i	0.562323	+	0.826917i	$0.309908\pi$
$168$		0			0
$169$	2.80372	+	8.62898i	0.215671	+	0.663767i
$170$	0.00472785	−	0.200188i	0.000362610	−	0.0153537i
$171$		0			0
$172$	−5.08759	−	1.65306i	−0.387925	−	0.126045i
$173$	2.73326	+	3.76201i	0.207806	+	0.286020i	0.900180	−	0.435519i	$-0.143435\pi$
$173$	2.73326	+	3.76201i	0.207806	+	0.286020i	−0.692374	+	0.721539i	$0.743435\pi$
$174$		0			0
$175$	−20.3952	−	7.70906i	−1.54173	−	0.582750i
$176$	−17.3515			−1.30792
$177$		0			0
$178$	−0.836069	−	0.271655i	−0.0626660	−	0.0203614i
$179$	−2.22597	+	6.85082i	−0.166377	+	0.512055i	−0.999135	−	0.0415819i	$-0.986760\pi$
$179$	−2.22597	+	6.85082i	−0.166377	+	0.512055i	0.832758	+	0.553636i	$0.186760\pi$
$180$		0			0
$181$	−1.17557	−	3.61804i	−0.0873797	−	0.268927i	0.897813	−	0.440376i	$-0.145155\pi$
$181$	−1.17557	−	3.61804i	−0.0873797	−	0.268927i	−0.985193	+	0.171449i	$0.945155\pi$
$182$		−	0.776167i		−	0.0575333i
$183$		0			0
$184$	0.683566	+	0.496640i	0.0503931	+	0.0366128i
$185$	−3.21246	−	0.0758687i	−0.236185	−	0.00557798i
$186$		0			0
$187$	2.57324	−	3.54177i	0.188174	−	0.259000i
$188$	−12.8080	+	17.6287i	−0.934121	+	1.28571i
$189$		0			0
$190$	−0.271254	−	0.00640620i	−0.0196788	−	0.000464755i
$191$	17.4377	+	12.6692i	1.26174	+	0.916711i	0.998842	−	0.0481112i	$-0.0153202\pi$
$191$	17.4377	+	12.6692i	1.26174	+	0.916711i	0.262903	+	0.964822i	$0.415320\pi$
$192$		0			0
$193$		−	3.15029i		−	0.226763i	−0.993552	−	0.113381i	$-0.963832\pi$
$193$		−	3.15029i		−	0.226763i	0.993552	−	0.113381i	$-0.0361682\pi$
$194$	−0.000935592	−	0.00287946i	−6.71716e−5	−	0.000206733i
$195$		0			0
$196$	−7.39617	+	22.7631i	−0.528298	+	1.62593i
$197$	−24.8071	−	8.06032i	−1.76743	−	0.574274i	−0.769507	−	0.638638i	$-0.779498\pi$
$197$	−24.8071	−	8.06032i	−1.76743	−	0.574274i	−0.997927	+	0.0643637i	$0.979498\pi$
$198$		0			0
$199$	24.2662			1.72018			0.860092	−	0.510139i	$-0.170406\pi$
$199$	24.2662			1.72018			0.860092	+	0.510139i	$0.170406\pi$
$200$	0.0846324	−	1.79077i	0.00598441	−	0.126626i
$201$		0			0
$202$	0.168620	+	0.232086i	0.0118641	+	0.0163295i
$203$	−33.0893	−	10.7514i	−2.32241	−	0.754597i
$204$		0			0
$205$	0.315842	−	13.3735i	0.0220594	−	0.934045i
$206$	0.237406	+	0.730662i	0.0165409	+	0.0509076i
$207$		0			0
$208$	−7.44756	+	2.41986i	−0.516395	+	0.167787i
$209$	−4.79906	−	3.48672i	−0.331958	−	0.241182i
$210$		0			0
$211$	−13.2503	+	9.62694i	−0.912192	+	0.662746i	−0.941568	−	0.336822i	$-0.890648\pi$
$211$	−13.2503	+	9.62694i	−0.912192	+	0.662746i	0.0293766	+	0.999568i	$0.490648\pi$
$212$	12.9389	−	17.8088i	0.888645	−	1.22312i
$213$		0			0
$214$	−0.161416	+	0.117276i	−0.0110342	+	0.00801680i
$215$	4.94017	−	3.41399i	0.336917	−	0.232832i
$216$		0			0
$217$	15.2521	−	4.95570i	1.03538	−	0.336415i
$218$		−	0.988224i		−	0.0669310i
$219$		0			0
$220$	11.8661	−	15.5467i	0.800011	−	1.04816i
$221$	0.610541	−	1.87905i	0.0410695	−	0.126399i
$222$		0			0
$223$	−3.34035	−	4.59760i	−0.223687	−	0.307878i	0.682393	−	0.730985i	$-0.260939\pi$
$223$	−3.34035	−	4.59760i	−0.223687	−	0.307878i	−0.906080	+	0.423107i	$0.860939\pi$
$224$	−4.67486			−0.312352
$225$		0			0
$226$	−0.153610			−0.0102180
$227$	2.14174	+	2.94785i	0.142152	+	0.195656i	0.874157	−	0.485644i	$-0.161415\pi$
$227$	2.14174	+	2.94785i	0.142152	+	0.195656i	−0.732004	+	0.681300i	$0.761415\pi$
$228$		0			0
$229$	−0.513355	+	1.57994i	−0.0339235	+	0.104406i	−0.966584	−	0.256348i	$-0.917481\pi$
$229$	−0.513355	+	1.57994i	−0.0339235	+	0.104406i	0.932661	+	0.360754i	$0.117481\pi$
$230$	−0.453450	+	0.135585i	−0.0298996	+	0.00894023i
$231$		0			0
$232$		−	2.86074i		−	0.187817i
$233$	−7.47434	+	2.42856i	−0.489661	+	0.159100i	−0.543432	−	0.839453i	$-0.682876\pi$
$233$	−7.47434	+	2.42856i	−0.489661	+	0.159100i	0.0537719	+	0.998553i	$0.482876\pi$
$234$		0			0
$235$	−7.00748	−	23.4358i	−0.457118	−	1.52878i
$236$	−10.7793	+	7.83161i	−0.701672	+	0.509795i
$237$		0			0
$238$	0.229536	−	0.315929i	0.0148786	−	0.0204786i
$239$	0.458956	−	0.333451i	0.0296874	−	0.0215691i	−0.572843	−	0.819665i	$-0.694159\pi$
$239$	0.458956	−	0.333451i	0.0296874	−	0.0215691i	0.602530	+	0.798096i	$0.294159\pi$
$240$		0			0
$241$	15.3779	+	11.1727i	0.990578	+	0.719697i	0.960048	−	0.279837i	$-0.0902804\pi$
$241$	15.3779	+	11.1727i	0.990578	+	0.719697i	0.0305304	+	0.999534i	$0.490280\pi$
$242$	−0.707337	+	0.229828i	−0.0454693	+	0.0147739i
$243$		0			0
$244$	−5.82037	−	17.9133i	−0.372611	−	1.14678i
$245$	−15.2750	−	22.1035i	−0.975883	−	1.41214i
$246$		0			0
$247$	−2.54610	−	0.827278i	−0.162005	−	0.0526385i
$248$	0.775065	+	1.06679i	0.0492167	+	0.0677410i
$249$		0			0
$250$	0.768609	+	0.646283i	0.0486111	+	0.0408745i
$251$	−3.02533			−0.190957			−0.0954787	−	0.995431i	$-0.530438\pi$
$251$	−3.02533			−0.190957			−0.0954787	+	0.995431i	$0.530438\pi$
$252$		0			0
$253$	−9.84086	−	3.19749i	−0.618690	−	0.201024i
$254$	0.348527	−	1.07266i	0.0218686	−	0.0673045i
$255$		0			0
$256$	4.74604	+	14.6068i	0.296627	+	0.912925i
$257$			19.8613i			1.23891i	0.785032	+	0.619456i	$0.212647\pi$
$257$			19.8613i			1.23891i	−0.785032	+	0.619456i	$0.787353\pi$
$258$		0			0
$259$	−5.06977	−	3.68340i	−0.315020	−	0.228875i
$260$	2.92497	−	8.32775i	0.181399	−	0.516465i
$261$		0			0
$262$	−0.869621	+	1.19693i	−0.0537253	+	0.0739466i
$263$	13.4191	−	18.4698i	0.827456	−	1.13890i	−0.160935	−	0.986965i	$-0.551451\pi$
$263$	13.4191	−	18.4698i	0.827456	−	1.13890i	0.988391	−	0.151930i	$-0.0485489\pi$
$264$		0			0
$265$	7.07907	+	23.6752i	0.434864	+	1.45435i
$266$	−0.428081	−	0.311019i	−0.0262473	−	0.0190698i
$267$		0			0
$268$			25.7395i			1.57229i
$269$	4.58346	+	14.1065i	0.279459	+	0.860086i	0.988005	+	0.154421i	$0.0493513\pi$
$269$	4.58346	+	14.1065i	0.279459	+	0.860086i	−0.708546	+	0.705664i	$0.750649\pi$
$270$		0			0
$271$	−1.98920	+	6.12214i	−0.120835	+	0.371893i	−0.993119	−	0.117106i	$-0.962638\pi$
$271$	−1.98920	+	6.12214i	−0.120835	+	0.371893i	0.872284	+	0.489000i	$0.162638\pi$
$272$	−3.74706	−	1.21749i	−0.227199	−	0.0738214i
$273$		0			0
$274$	−0.868313			−0.0524567
$275$	5.79111	+	21.1772i	0.349217	+	1.27703i
$276$		0			0
$277$	−3.94390	−	5.42831i	−0.236966	−	0.326155i	0.673927	−	0.738798i	$-0.264606\pi$
$277$	−3.94390	−	5.42831i	−0.236966	−	0.326155i	−0.910893	+	0.412642i	$0.864606\pi$
$278$	−1.15601	−	0.375609i	−0.0693326	−	0.0225275i
$279$		0			0
$280$	2.12122	−	2.77917i	0.126767	−	0.166087i
$281$	6.33074	+	19.4840i	0.377661	+	1.16232i	0.941666	+	0.336549i	$0.109260\pi$
$281$	6.33074	+	19.4840i	0.377661	+	1.16232i	−0.564006	+	0.825771i	$0.690740\pi$
$282$		0			0
$283$	−10.8589	+	3.52828i	−0.645496	+	0.209734i	−0.613427	−	0.789751i	$-0.710210\pi$
$283$	−10.8589	+	3.52828i	−0.645496	+	0.209734i	−0.0320688	+	0.999486i	$0.510210\pi$
$284$	11.8004	+	8.57347i	0.700223	+	0.508742i
$285$		0			0
$286$	−0.632286	+	0.459383i	−0.0373879	+	0.0271639i
$287$	15.3340	−	21.1055i	0.905139	−	1.24582i
$288$		0			0
$289$	−12.9491	+	9.40806i	−0.761711	+	0.553415i
$290$	1.27380	+	0.972232i	0.0747998	+	0.0570914i
$291$		0			0
$292$	−0.804766	+	0.261484i	−0.0470954	+	0.0153022i
$293$			28.5505i			1.66794i	0.551812	+	0.833968i	$0.313937\pi$
$293$			28.5505i			1.66794i	−0.551812	+	0.833968i	$0.686063\pi$
$294$		0			0
$295$	0.353140	−	14.9528i	0.0205606	−	0.870584i
$296$	0.159224	−	0.490042i	0.00925473	−	0.0284831i
$297$		0			0
$298$	−0.722455	−	0.994374i	−0.0418507	−	0.0576025i
$299$	−4.66979			−0.270061
$300$		0			0
$301$	11.7108			0.675001
$302$	0.597653	+	0.822598i	0.0343910	+	0.0473352i
$303$		0			0
$304$	−1.64969	+	5.07723i	−0.0946164	+	0.291199i
$305$	19.9489	+	7.00669i	1.14227	+	0.401202i
$306$		0			0
$307$		−	20.5417i		−	1.17238i	−0.810175	−	0.586188i	$-0.800628\pi$
$307$		−	20.5417i		−	1.17238i	0.810175	−	0.586188i	$-0.199372\pi$
$308$	36.2740	−	11.7861i	2.06690	−	0.671577i
$309$		0			0
$310$	−0.738415	−	0.0174392i	−0.0419391	−	0.000990477i
$311$	14.1979	−	10.3154i	0.805090	−	0.584932i	−0.107313	−	0.994225i	$-0.534225\pi$
$311$	14.1979	−	10.3154i	0.805090	−	0.584932i	0.912403	+	0.409293i	$0.134225\pi$
$312$		0			0
$313$	1.75491	−	2.41543i	0.0991935	−	0.136528i	−0.756535	−	0.653953i	$-0.773109\pi$
$313$	1.75491	−	2.41543i	0.0991935	−	0.136528i	0.855729	+	0.517425i	$0.173109\pi$
$314$	0.622067	−	0.451958i	0.0351053	−	0.0255055i
$315$		0			0
$316$	−10.2416	−	7.44097i	−0.576136	−	0.418587i
$317$	−15.3794	+	4.99706i	−0.863791	+	0.280663i	−0.707211	−	0.707003i	$-0.750047\pi$
$317$	−15.3794	+	4.99706i	−0.863791	+	0.280663i	−0.156580	+	0.987665i	$0.550047\pi$
$318$		0			0
$319$	10.8259	+	33.3187i	0.606134	+	1.86549i
$320$	−16.4706	−	5.78502i	−0.920737	−	0.323392i
$321$		0			0
$322$	−0.877813	−	0.285219i	−0.0489186	−	0.0158946i
$323$	−0.791707	−	1.08969i	−0.0440518	−	0.0606320i
$324$		0			0
$325$	5.43903	+	8.28196i	0.301703	+	0.459401i
$326$	0.411830			0.0228092
$327$		0			0
$328$	2.04005	+	0.662852i	0.112643	+	0.0365999i
$329$	14.7410	−	45.3682i	0.812699	−	2.50123i
$330$		0			0
$331$	−4.03900	−	12.4307i	−0.222003	−	0.683256i	−0.998582	−	0.0532356i	$-0.983047\pi$
$331$	−4.03900	−	12.4307i	−0.222003	−	0.683256i	0.776579	−	0.630020i	$-0.216953\pi$
$332$			1.46808i			0.0805711i
$333$		0			0
$334$	−0.524494	−	0.381067i	−0.0286990	−	0.0208511i
$335$	−22.9683	−	17.5307i	−1.25489	−	0.957806i
$336$		0			0
$337$	15.7555	−	21.6856i	0.858257	−	1.18129i	−0.123725	−	0.992317i	$-0.539484\pi$
$337$	15.7555	−	21.6856i	0.858257	−	1.18129i	0.981982	−	0.188973i	$-0.0605159\pi$
$338$	0.479007	−	0.659297i	0.0260545	−	0.0358610i
$339$		0			0
$340$	3.65334	−	2.52470i	0.198130	−	0.136921i
$341$	−13.0642	−	9.49167i	−0.707464	−	0.514003i
$342$		0			0
$343$		−	21.8721i		−	1.18098i
$344$	0.297555	+	0.915780i	0.0160431	+	0.0493755i
$345$		0			0
$346$	0.129067	−	0.397227i	0.00693867	−	0.0213550i
$347$	24.2385	+	7.87558i	1.30119	+	0.422783i	0.875996	−	0.482318i	$-0.160205\pi$
$347$	24.2385	+	7.87558i	1.30119	+	0.422783i	0.425196	+	0.905101i	$0.360205\pi$
$348$		0			0
$349$	28.0435			1.50113			0.750566	−	0.660795i	$-0.229781\pi$
$349$	28.0435			1.50113			0.750566	+	0.660795i	$0.229781\pi$
$350$	0.516572	+	1.88902i	0.0276119	+	0.100972i
$351$		0			0
$352$	2.76687	+	3.80826i	0.147474	+	0.202981i
$353$	13.9489	+	4.53226i	0.742423	+	0.241228i	0.655718	−	0.755006i	$-0.272366\pi$
$353$	13.9489	+	4.53226i	0.742423	+	0.241228i	0.0867054	+	0.996234i	$0.472366\pi$
$354$		0			0
$355$	−15.6875	+	4.69069i	−0.832606	+	0.248956i
$356$	−6.02452	−	18.5416i	−0.319299	−	0.982701i
$357$		0			0
$358$	0.615337	−	0.199935i	0.0325216	−	0.0105669i
$359$	11.8283	+	8.59373i	0.624272	+	0.453560i	0.854411	−	0.519598i	$-0.173918\pi$
$359$	11.8283	+	8.59373i	0.624272	+	0.453560i	−0.230139	+	0.973158i	$0.573918\pi$
$360$		0			0
$361$	13.8948	−	10.0952i	0.731305	−	0.531324i
$362$	−0.200843	+	0.276437i	−0.0105561	+	0.0145292i
$363$		0			0
$364$	13.9257	−	10.1176i	0.729905	−	0.530307i
$365$	0.314780	−	0.896217i	0.0164763	−	0.0469102i
$366$		0			0
$367$	16.8279	−	5.46773i	0.878412	−	0.285413i	0.165114	−	0.986274i	$-0.447201\pi$
$367$	16.8279	−	5.46773i	0.878412	−	0.285413i	0.713298	+	0.700861i	$0.247201\pi$
$368$			9.31212i			0.485428i
$369$		0			0
$370$	0.164087	+	0.237440i	0.00853049	+	0.0123439i
$371$	−14.8916	+	45.8317i	−0.773134	+	2.37946i
$372$		0			0
$373$	7.18821	+	9.89372i	0.372191	+	0.512278i	0.953495	−	0.301409i	$-0.0974570\pi$
$373$	7.18821	+	9.89372i	0.372191	+	0.512278i	−0.581303	+	0.813687i	$0.697457\pi$
$374$	−0.393217			−0.0203328
$375$		0			0
$376$	3.92231			0.202278
$377$	9.29333	+	12.7912i	0.478631	+	0.658779i
$378$		0			0
$379$	−8.68186	+	26.7200i	−0.445957	+	1.37251i	0.435474	+	0.900201i	$0.356581\pi$
$379$	−8.68186	+	26.7200i	−0.445957	+	1.37251i	−0.881431	+	0.472313i	$0.843419\pi$
$380$	−3.42095	−	4.95024i	−0.175491	−	0.253942i
$381$		0			0
$382$		−	1.93598i		−	0.0990533i
$383$	−32.7481	+	10.6405i	−1.67335	+	0.543705i	−0.983603	−	0.180345i	$-0.942279\pi$
$383$	−32.7481	+	10.6405i	−1.67335	+	0.543705i	−0.689748	+	0.724049i	$0.742279\pi$
$384$		0			0
$385$	−14.1884	+	40.3960i	−0.723107	+	2.05877i
$386$	−0.228917	+	0.166318i	−0.0116516	+	0.00846536i
$387$		0			0
$388$	0.0394664	−	0.0543208i	0.00200360	−	0.00275772i
$389$	−10.9399	+	7.94834i	−0.554677	+	0.402997i	−0.829507	−	0.558496i	$-0.811378\pi$
$389$	−10.9399	+	7.94834i	−0.554677	+	0.402997i	0.274830	+	0.961493i	$0.411378\pi$
$390$		0			0
$391$	−1.90078	−	1.38100i	−0.0961265	−	0.0698400i
$392$	4.09741	−	1.33133i	0.206951	−	0.0672423i
$393$		0			0
$394$	0.723974	+	2.22816i	0.0364733	+	0.112253i
$395$	13.6153	−	4.07108i	0.685059	−	0.204838i
$396$		0			0
$397$	−34.2136	−	11.1167i	−1.71713	−	0.557931i	−0.725639	−	0.688076i	$-0.758456\pi$
$397$	−34.2136	−	11.1167i	−1.71713	−	0.557931i	−0.991495	+	0.130145i	$0.958456\pi$
$398$	−1.28112	−	1.76331i	−0.0642169	−	0.0883869i
$399$		0			0
$400$	16.5152	−	10.8461i	0.825762	−	0.542304i
$401$	−4.35977			−0.217717			−0.108858	−	0.994057i	$-0.534719\pi$
$401$	−4.35977			−0.217717			−0.108858	+	0.994057i	$0.534719\pi$
$402$		0			0
$403$	−6.93108	−	2.25204i	−0.345261	−	0.112182i
$404$	−1.96598	+	6.05065i	−0.0978110	+	0.301031i
$405$		0			0
$406$	0.965680	+	2.97206i	0.0479259	+	0.147501i
$407$			6.31003i			0.312777i
$408$		0			0
$409$	−14.6543	−	10.6470i	−0.724610	−	0.526460i	0.163243	−	0.986586i	$-0.447804\pi$
$409$	−14.6543	−	10.6470i	−0.724610	−	0.526460i	−0.887854	+	0.460126i	$0.847804\pi$
$410$	−0.988466	+	0.683097i	−0.0488168	+	0.0337357i
$411$		0			0
$412$	−10.0146	+	13.7839i	−0.493383	+	0.679084i
$413$	17.1448	−	23.5978i	0.843642	−	1.16117i
$414$		0			0
$415$	−1.31002	−	0.999883i	−0.0643065	−	0.0490823i
$416$	1.71869	+	1.24870i	0.0842657	+	0.0612226i
$417$		0			0
$418$			0.532806i			0.0260604i
$419$	0.163120	+	0.502031i	0.00796892	+	0.0245258i	0.954962	−	0.296728i	$-0.0958956\pi$
$419$	0.163120	+	0.502031i	0.00796892	+	0.0245258i	−0.946993	+	0.321254i	$0.895896\pi$
$420$		0			0
$421$	5.76583	−	17.7454i	0.281009	−	0.864857i	−0.706557	−	0.707656i	$-0.749753\pi$
$421$	5.76583	−	17.7454i	0.281009	−	0.864857i	0.987567	−	0.157201i	$-0.0502472\pi$
$422$	1.39909	+	0.454593i	0.0681067	+	0.0221292i
$423$		0			0
$424$	−3.96239			−0.192430
$425$	−0.235336	+	4.97955i	−0.0114155	+	0.241544i
$426$		0			0
$427$	24.2364	+	33.3586i	1.17288	+	1.61434i
$428$	−4.20823	−	1.36734i	−0.203413	−	0.0660928i
$429$		0			0
$430$	−0.508893	−	0.178739i	−0.0245410	−	0.00861958i
$431$	−6.48668	−	19.9640i	−0.312453	−	0.961630i	−0.976790	−	0.214198i	$-0.931286\pi$
$431$	−6.48668	−	19.9640i	−0.312453	−	0.961630i	0.664338	−	0.747432i	$-0.268714\pi$
$432$		0			0
$433$	−12.9952	+	4.22239i	−0.624508	+	0.202915i	−0.604141	−	0.796877i	$-0.706484\pi$
$433$	−12.9952	+	4.22239i	−0.624508	+	0.202915i	−0.0203675	+	0.999793i	$0.506484\pi$
$434$	−1.16533	−	0.846665i	−0.0559378	−	0.0406412i
$435$		0			0
$436$	17.7303	−	12.8819i	0.849130	−	0.616929i
$437$	−1.87124	+	2.57554i	−0.0895134	+	0.123205i
$438$		0			0
$439$	−3.50578	+	2.54710i	−0.167322	+	0.121567i	−0.668295	−	0.743896i	$-0.732976\pi$
$439$	−3.50578	+	2.54710i	−0.167322	+	0.121567i	0.500973	+	0.865463i	$0.332976\pi$
$440$	−3.51945	−	0.0831190i	−0.167783	−	0.00396254i
$441$		0			0
$442$	−0.168776	+	0.0548385i	−0.00802783	+	0.00260840i
$443$		−	1.60742i		−	0.0763707i	−0.999271	−	0.0381854i	$-0.987842\pi$
$443$		−	1.60742i		−	0.0763707i	0.999271	−	0.0381854i	$-0.0121577\pi$
$444$		0			0
$445$	20.6486	+	7.25244i	0.978837	+	0.343799i
$446$	−0.157734	+	0.485456i	−0.00746894	+	0.0229870i
$447$		0			0
$448$	−20.0106	−	27.5423i	−0.945414	−	1.30125i
$449$	−13.8291			−0.652634			−0.326317	−	0.945260i	$-0.605808\pi$
$449$	−13.8291			−0.652634			−0.326317	+	0.945260i	$0.605808\pi$
$450$		0			0
$451$	−26.2687			−1.23694
$452$	−2.00236	−	2.75601i	−0.0941832	−	0.129632i
$453$		0			0
$454$	0.101135	−	0.311261i	0.00474649	−	0.0146082i
$455$	−0.456219	+	19.3174i	−0.0213879	+	0.905613i
$456$		0			0
$457$			20.1345i			0.941850i	0.882173	+	0.470925i	$0.156080\pi$
$457$			20.1345i			0.941850i	−0.882173	+	0.470925i	$0.843920\pi$
$458$	0.141910	−	0.0461093i	0.00663101	−	0.00215455i
$459$		0			0
$460$	−8.34351	−	6.36823i	−0.389018	−	0.296920i
$461$	25.5054	−	18.5308i	1.18791	−	0.863064i	0.194865	−	0.980830i	$-0.437573\pi$
$461$	25.5054	−	18.5308i	1.18791	−	0.863064i	0.993041	+	0.117766i	$0.0375732\pi$
$462$		0			0
$463$	0.0265501	−	0.0365431i	0.00123389	−	0.00169830i	−0.808400	−	0.588634i	$-0.799666\pi$
$463$	0.0265501	−	0.0365431i	0.00123389	−	0.00169830i	0.809633	+	0.586936i	$0.199666\pi$
$464$	25.5071	−	18.5320i	1.18414	−	0.860327i
$465$		0			0
$466$	0.571077	+	0.414912i	0.0264546	+	0.0192204i
$467$	−31.2278	+	10.1465i	−1.44505	+	0.469525i	−0.923468	−	0.383676i	$-0.874658\pi$
$467$	−31.2278	+	10.1465i	−1.44505	+	0.469525i	−0.521582	+	0.853201i	$0.674658\pi$
$468$		0			0
$469$	−17.4126	−	53.5905i	−0.804039	−	2.47458i
$470$	−1.33301	+	1.74648i	−0.0614873	+	0.0805592i
$471$		0			0
$472$	2.28096	+	0.741129i	0.104990	+	0.0341132i
$473$	−6.93119	−	9.53996i	−0.318696	−	0.438648i
$474$		0			0
$475$	6.74725	+	0.318878i	0.309585	+	0.0146311i
$476$	8.66035			0.396947
$477$		0			0
$478$	−0.0484607	−	0.0157458i	−0.00221654	−	0.000720198i
$479$	2.31323	−	7.11938i	0.105694	−	0.325293i	−0.884199	−	0.467111i	$-0.845295\pi$
$479$	2.31323	−	7.11938i	0.105694	−	0.325293i	0.989893	+	0.141818i	$0.0452948\pi$
$480$		0			0
$481$	0.880003	+	2.70837i	0.0401247	+	0.123491i
$482$		−	1.70730i		−	0.0777654i
$483$		0			0
$484$	−13.3439	−	9.69489i	−0.606540	−	0.440677i
$485$	0.0215927	+	0.0722145i	0.000980475	+	0.00327909i
$486$		0			0
$487$	−14.9471	+	20.5729i	−0.677316	+	0.932246i	−0.999898	−	0.0142956i	$-0.995449\pi$
$487$	−14.9471	+	20.5729i	−0.677316	+	0.932246i	0.322581	+	0.946542i	$0.395449\pi$
$488$	−1.99281	+	2.74287i	−0.0902103	+	0.124164i
$489$		0			0
$490$	−0.799722	+	2.27691i	−0.0361278	+	0.102860i
$491$	−8.95323	−	6.50490i	−0.404053	−	0.293562i	0.367137	−	0.930167i	$-0.380338\pi$
$491$	−8.95323	−	6.50490i	−0.404053	−	0.293562i	−0.771190	+	0.636605i	$0.780338\pi$
$492$		0			0
$493$			7.95479i			0.358266i
$494$	0.0743057	+	0.228689i	0.00334317	+	0.0102892i
$495$		0			0
$496$	−4.49084	+	13.8214i	−0.201645	+	0.620599i
$497$	−30.3687	−	9.86739i	−1.36222	−	0.442613i
$498$		0			0
$499$	−4.68157			−0.209576			−0.104788	−	0.994495i	$-0.533416\pi$
$499$	−4.68157			−0.209576			−0.104788	+	0.994495i	$0.533416\pi$
$500$	−1.57627	+	22.2146i	−0.0704932	+	0.993468i
$501$		0			0
$502$	0.159721	+	0.219837i	0.00712870	+	0.00981182i
$503$	10.2985	+	3.34618i	0.459187	+	0.149199i	0.529471	−	0.848328i	$-0.322391\pi$
$503$	10.2985	+	3.34618i	0.459187	+	0.149199i	−0.0702839	+	0.997527i	$0.522391\pi$
$504$		0			0
$505$	−4.06024	−	5.87532i	−0.180678	−	0.261448i
$506$	0.287197	+	0.883901i	0.0127675	+	0.0392942i
$507$		0			0
$508$	23.7884	−	7.72932i	1.05544	−	0.342933i
$509$	−9.30422	−	6.75991i	−0.412402	−	0.299628i	0.362171	−	0.932112i	$-0.382036\pi$
$509$	−9.30422	−	6.75991i	−0.412402	−	0.299628i	−0.774574	+	0.632484i	$0.782036\pi$
$510$		0			0
$511$	1.49866	−	1.08884i	0.0662967	−	0.0481674i
$512$	4.15570	−	5.71984i	0.183658	−	0.252783i
$513$		0			0
$514$	1.44323	−	1.04857i	0.0636580	−	0.0462503i
$515$	−5.47915	−	18.3244i	−0.241440	−	0.807470i
$516$		0			0
$517$	−45.6828	+	14.8432i	−2.00913	+	0.652805i
$518$			0.562860i			0.0247307i
$519$		0			0
$520$	−1.52220	+	0.455150i	−0.0667529	+	0.0199597i
$521$	−0.246536	+	0.758759i	−0.0108009	+	0.0332418i	−0.956312	−	0.292349i	$-0.905563\pi$
$521$	−0.246536	+	0.758759i	−0.0108009	+	0.0332418i	0.945511	+	0.325591i	$0.105563\pi$
$522$		0			0
$523$	23.5954	+	32.4763i	1.03175	+	1.42009i	0.903622	+	0.428331i	$0.140898\pi$
$523$	23.5954	+	32.4763i	1.03175	+	1.42009i	0.128133	+	0.991757i	$0.459102\pi$
$524$	−32.8107			−1.43334
$525$		0			0
$526$	−2.05057			−0.0894090
$527$	−2.15521	−	2.96639i	−0.0938824	−	0.129218i
$528$		0			0
$529$	5.39138	−	16.5930i	0.234408	−	0.721433i
$530$	1.34663	−	1.76432i	0.0584939	−	0.0766374i
$531$		0			0
$532$		−	11.7347i		−	0.508764i
$533$	−11.2750	+	3.66346i	−0.488373	+	0.158682i
$534$		0			0
$535$	4.08629	−	2.82390i	0.176666	−	0.122088i
$536$	3.74831	−	2.72331i	0.161903	−	0.117629i
$537$		0			0
$538$	0.783070	−	1.07780i	0.0337605	−	0.0464674i
$539$	−42.6840	+	31.0117i	−1.83853	+	1.33577i
$540$		0			0
$541$	−1.14085	−	0.828873i	−0.0490488	−	0.0356360i	0.562991	−	0.826463i	$-0.309651\pi$
$541$	−1.14085	−	0.828873i	−0.0490488	−	0.0356360i	−0.612040	+	0.790827i	$0.709651\pi$
$542$	0.549887	−	0.178669i	0.0236197	−	0.00767449i
$543$		0			0
$544$	0.330293	+	1.01654i	0.0141612	+	0.0435836i
$545$	−0.580863	+	24.5951i	−0.0248815	+	1.05354i
$546$		0			0
$547$	14.7053	+	4.77804i	0.628753	+	0.204294i	0.606023	−	0.795447i	$-0.292764\pi$
$547$	14.7053	+	4.77804i	0.628753	+	0.204294i	0.0227302	+	0.999742i	$0.492764\pi$
$548$	−11.3188	−	15.5790i	−0.483514	−	0.665500i
$549$		0			0
$550$	1.23311	−	1.53885i	0.0525800	−	0.0656169i
$551$	10.7787			0.459187
$552$		0			0
$553$	26.3572	+	8.56397i	1.12082	+	0.364177i
$554$	−0.186234	+	0.573170i	−0.00791234	+	0.0243517i
$555$		0			0
$556$	−8.32991	−	25.6368i	−0.353267	−	1.08724i
$557$			18.0445i			0.764568i	0.924045	+	0.382284i	$0.124862\pi$
$557$			18.0445i			0.764568i	−0.924045	+	0.382284i	$0.875138\pi$
$558$		0			0
$559$	−4.30543	−	3.12808i	−0.182100	−	0.132304i
$560$	38.5212	+	0.909756i	1.62782	+	0.0384442i
$561$		0			0
$562$	1.08159	−	1.48868i	0.0456240	−	0.0627960i
$563$	−16.7711	+	23.0834i	−0.706816	+	0.972849i	0.293043	+	0.956099i	$0.405332\pi$
$563$	−16.7711	+	23.0834i	−0.706816	+	0.972849i	−0.999860	+	0.0167502i	$0.994668\pi$
$564$		0			0
$565$	3.82308	+	0.0902897i	0.160838	+	0.00379852i
$566$	0.829676	+	0.602795i	0.0348739	+	0.0253374i
$567$		0			0
$568$		−	2.62553i		−	0.110165i
$569$	5.07011	+	15.6042i	0.212550	+	0.654162i	0.999318	+	0.0369135i	$0.0117526\pi$
$569$	5.07011	+	15.6042i	0.212550	+	0.654162i	−0.786768	+	0.617248i	$0.788247\pi$
$570$		0			0
$571$	−2.57938	+	7.93852i	−0.107944	+	0.332217i	−0.990410	−	0.138159i	$-0.955882\pi$
$571$	−2.57938	+	7.93852i	−0.107944	+	0.332217i	0.882466	+	0.470376i	$0.155882\pi$
$572$	−16.4842	−	5.35603i	−0.689237	−	0.223947i
$573$		0			0
$574$	−2.34319			−0.0978029
$575$	11.3653	−	3.10794i	0.473964	−	0.129610i
$576$		0			0
$577$	−4.95815	−	6.82431i	−0.206411	−	0.284100i	0.693243	−	0.720704i	$-0.256181\pi$
$577$	−4.95815	−	6.82431i	−0.206411	−	0.284100i	−0.899654	+	0.436604i	$0.856181\pi$
$578$	1.36728	+	0.444257i	0.0568714	+	0.0184786i
$579$		0			0
$580$	−0.839050	+	35.5273i	−0.0348397	+	1.47519i
$581$	−0.993145	−	3.05659i	−0.0412026	−	0.126809i
$582$		0			0
$583$	46.1495	−	14.9949i	1.91132	−	0.621025i
$584$	0.123225	+	0.0895284i	0.00509910	+	0.00370471i
$585$		0			0
$586$	2.07463	−	1.50731i	0.0857023	−	0.0622664i
$587$	14.2745	−	19.6471i	0.589171	−	0.810925i	−0.405492	−	0.914099i	$-0.632900\pi$
$587$	14.2745	−	19.6471i	0.589171	−	0.810925i	0.994663	+	0.103174i	$0.0328998\pi$
$588$		0			0
$589$	−4.01943	+	2.92029i	−0.165618	+	0.120328i
$590$	−1.10519	+	0.763764i	−0.0455001	+	0.0314437i
$591$		0			0
$592$	5.40082	−	1.75483i	0.221972	−	0.0721232i
$593$		−	28.4653i		−	1.16893i	−0.811418	−	0.584466i	$-0.801304\pi$
$593$		−	28.4653i		−	1.16893i	0.811418	−	0.584466i	$-0.198696\pi$
$594$		0			0
$595$	−5.89843	+	7.72798i	−0.241812	+	0.316816i
$596$	8.42323	−	25.9240i	0.345029	−	1.06189i
$597$		0			0
$598$	0.246539	+	0.339332i	0.0100817	+	0.0138763i
$599$	16.0387			0.655323			0.327662	−	0.944795i	$-0.393739\pi$
$599$	16.0387			0.655323			0.327662	+	0.944795i	$0.393739\pi$
$600$		0			0
$601$	−8.09005			−0.330000			−0.165000	−	0.986294i	$-0.552762\pi$
$601$	−8.09005			−0.330000			−0.165000	+	0.986294i	$0.552762\pi$
$602$	−0.618268	−	0.850973i	−0.0251987	−	0.0346831i
$603$		0			0
$604$	−6.96814	+	21.4457i	−0.283530	+	0.872614i
$605$	17.7394	−	5.30424i	0.721211	−	0.215648i
$606$		0			0
$607$		−	0.434608i		−	0.0176402i	−0.999961	−	0.00882010i	$-0.997192\pi$
$607$		−	0.434608i		−	0.0176402i	0.999961	−	0.00882010i	$-0.00280756\pi$
$608$	1.37740	−	0.447544i	0.0558609	−	0.0181503i
$609$		0			0
$610$	−0.544048	−	1.81951i	−0.0220279	−	0.0736698i
$611$	−17.5378	+	12.7419i	−0.709503	+	0.515484i
$612$		0			0
$613$	23.1565	−	31.8722i	0.935282	−	1.28731i	−0.0224808	−	0.999747i	$-0.507156\pi$
$613$	23.1565	−	31.8722i	0.935282	−	1.28731i	0.957763	−	0.287558i	$-0.0928435\pi$
$614$	−1.49267	+	1.08449i	−0.0602393	+	0.0437664i
$615$		0			0
$616$	−5.55425	−	4.03540i	−0.223787	−	0.162591i
$617$	14.6602	−	4.76337i	0.590196	−	0.191766i	0.00133273	−	0.999999i	$-0.499576\pi$
$617$	14.6602	−	4.76337i	0.590196	−	0.191766i	0.588863	+	0.808233i	$0.299576\pi$
$618$		0			0
$619$	3.29776	+	10.1495i	0.132548	+	0.407942i	0.995201	−	0.0978556i	$-0.0311983\pi$
$619$	3.29776	+	10.1495i	0.132548	+	0.407942i	−0.862652	+	0.505797i	$0.831198\pi$
$620$	−9.31261	−	13.4757i	−0.374004	−	0.541197i
$621$		0			0
$622$	−1.49914	−	0.487102i	−0.0601102	−	0.0195310i
$623$	25.0865	+	34.5286i	1.00507	+	1.38336i
$624$		0			0
$625$	−18.7494	−	16.5366i	−0.749977	−	0.661464i
$626$	−0.268168			−0.0107182
$627$		0			0
$628$	16.2177	+	5.26946i	0.647158	+	0.210275i
$629$	−0.442752	+	1.36265i	−0.0176537	+	0.0543325i
$630$		0			0
$631$	−5.69664	−	17.5324i	−0.226780	−	0.697956i	−0.998106	−	0.0615162i	$-0.980406\pi$
$631$	−5.69664	−	17.5324i	−0.226780	−	0.697956i	0.771327	−	0.636440i	$-0.219594\pi$
$632$			2.27871i			0.0906424i
$633$		0			0
$634$	1.17506	+	0.853731i	0.0466676	+	0.0339060i
$635$	−9.30471	+	26.4916i	−0.369246	+	1.05129i
$636$		0			0
$637$	−13.9958	+	19.2635i	−0.554533	+	0.763249i
$638$	1.84957	−	2.54572i	0.0732252	−	0.100786i
$639$		0			0
$640$	1.82265	+	6.09564i	0.0720464	+	0.240951i
$641$	10.0546	+	7.30508i	0.397132	+	0.288533i	0.768372	−	0.640004i	$-0.221067\pi$
$641$	10.0546	+	7.30508i	0.397132	+	0.288533i	−0.371240	+	0.928537i	$0.621067\pi$
$642$		0			0
$643$			1.84657i			0.0728218i	0.999337	+	0.0364109i	$0.0115925\pi$
$643$			1.84657i			0.0728218i	−0.999337	+	0.0364109i	$0.988407\pi$
$644$	−6.32532	−	19.4673i	−0.249253	−	0.767120i
$645$		0			0
$646$	−0.0373851	+	0.115059i	−0.00147090	+	0.00452695i
$647$	37.0683	+	12.0442i	1.45731	+	0.473508i	0.927246	−	0.374452i	$-0.122169\pi$
$647$	37.0683	+	12.0442i	1.45731	+	0.473508i	0.530061	+	0.847960i	$0.322169\pi$
$648$		0			0
$649$	−29.3708			−1.15290
$650$	0.314661	−	0.832472i	0.0123420	−	0.0326522i
$651$		0			0
$652$	5.36836	+	7.38891i	0.210241	+	0.289372i
$653$	26.9519	+	8.75719i	1.05471	+	0.342695i	0.784514	−	0.620111i	$-0.212912\pi$
$653$	26.9519	+	8.75719i	1.05471	+	0.342695i	0.270193	+	0.962806i	$0.412912\pi$
$654$		0			0
$655$	22.3468	−	29.2783i	0.873163	−	1.14400i
$656$	7.30538	+	22.4836i	0.285227	+	0.877839i
$657$		0			0
$658$	−4.07495	+	1.32403i	−0.158858	+	0.0516161i
$659$	18.0864	+	13.1406i	0.704547	+	0.511883i	0.881410	−	0.472352i	$-0.156595\pi$
$659$	18.0864	+	13.1406i	0.704547	+	0.511883i	−0.176863	+	0.984236i	$0.556595\pi$
$660$		0			0
$661$	−23.6349	+	17.1717i	−0.919290	+	0.667903i	−0.943347	−	0.331807i	$-0.892342\pi$
$661$	−23.6349	+	17.1717i	−0.919290	+	0.667903i	0.0240570	+	0.999711i	$0.492342\pi$
$662$	−0.690049	+	0.949771i	−0.0268195	+	0.0369139i
$663$		0			0
$664$	0.213789	−	0.155327i	0.00829662	−	0.00602785i
$665$	10.4713	+	7.99232i	0.406061	+	0.309929i
$666$		0			0
$667$	17.8813	−	5.81000i	0.692368	−	0.224964i
$668$		−	14.3776i		−	0.556287i
$669$		0			0
$670$	−0.0612751	+	2.59453i	−0.00236726	+	0.100236i
$671$	12.8302	−	39.4873i	0.495305	−	1.52439i
$672$		0			0
$673$	1.89000	+	2.60136i	0.0728542	+	0.100275i	0.843889	−	0.536518i	$-0.180261\pi$
$673$	1.89000	+	2.60136i	0.0728542	+	0.100275i	−0.771035	+	0.636793i	$0.780261\pi$
$674$	−2.40760			−0.0927372
$675$		0			0
$676$	18.0729			0.695111
$677$	−27.7711	−	38.2236i	−1.06733	−	1.46905i	−0.872751	−	0.488166i	$-0.837666\pi$
$677$	−27.7711	−	38.2236i	−1.06733	−	1.46905i	−0.194579	−	0.980887i	$-0.562334\pi$
$678$		0			0
$679$	−0.0454227	+	0.139797i	−0.00174316	+	0.00536490i
$680$	−0.754194	−	0.264897i	−0.0289220	−	0.0101583i
$681$		0			0
$682$			1.45042i			0.0555395i
$683$	35.4294	−	11.5117i	1.35567	−	0.440483i	0.461074	−	0.887362i	$-0.347464\pi$
$683$	35.4294	−	11.5117i	1.35567	−	0.440483i	0.894595	+	0.446879i	$0.147464\pi$
$684$		0			0
$685$	21.6108	+	0.510382i	0.825705	+	0.0195007i
$686$	−1.58934	+	1.15473i	−0.0606814	+	0.0440876i
$687$		0			0
$688$	−6.23777	+	8.58556i	−0.237813	+	0.327321i
$689$	17.7170	−	12.8721i	0.674962	−	0.490389i
$690$		0			0
$691$	8.88522	+	6.45549i	0.338010	+	0.245578i	0.743822	−	0.668378i	$-0.233011\pi$
$691$	8.88522	+	6.45549i	0.338010	+	0.245578i	−0.405812	+	0.913957i	$0.633011\pi$
$692$	8.80933	−	2.86232i	0.334880	−	0.108809i
$693$		0			0
$694$	−0.707380	−	2.17709i	−0.0268518	−	0.0826412i
$695$	28.5501	+	10.0277i	1.08297	+	0.380373i
$696$		0			0
$697$	−5.67273	−	1.84318i	−0.214870	−	0.0698154i
$698$	−1.48054	−	2.03779i	−0.0560394	−	0.0771316i
$699$		0			0
$700$	−27.1584	+	33.8922i	−1.02649	+	1.28101i
$701$	−22.4086			−0.846361			−0.423180	−	0.906046i	$-0.639086\pi$
$701$	−22.4086			−0.846361			−0.423180	+	0.906046i	$0.639086\pi$
$702$		0			0
$703$	1.84638	+	0.599926i	0.0696376	+	0.0226266i
$704$	−10.5932	+	32.6024i	−0.399245	+	1.22875i
$705$		0			0
$706$	−0.407085	−	1.25288i	−0.0153209	−	0.0471527i
$707$		−	13.9276i		−	0.523803i
$708$		0			0
$709$	−11.8357	−	8.59914i	−0.444499	−	0.322948i	0.342921	−	0.939364i	$-0.388584\pi$
$709$	−11.8357	−	8.59914i	−0.444499	−	0.322948i	−0.787420	+	0.616417i	$0.788584\pi$
$710$	1.16907	+	0.892296i	0.0438742	+	0.0334873i
$711$		0			0
$712$	−2.06271	+	2.83907i	−0.0773032	+	0.106399i
$713$	−5.09394	+	7.01121i	−0.190770	+	0.262572i
$714$		0			0
$715$	16.0065	−	11.0616i	0.598609	−	0.413679i
$716$	11.6083	+	8.43392i	0.433823	+	0.315191i
$717$		0			0
$718$		−	1.31321i		−	0.0490085i
$719$	−8.80627	−	27.1029i	−0.328419	−	1.01077i	−0.969874	−	0.243608i	$-0.921669\pi$
$719$	−8.80627	−	27.1029i	−0.328419	−	1.01077i	0.641455	−	0.767160i	$-0.278331\pi$
$720$		0			0
$721$	11.5260	−	35.4734i	0.429251	−	1.32110i
$722$	−1.46714	−	0.476702i	−0.0546013	−	0.0177410i
$723$		0			0
$724$	−7.57778			−0.281626
$725$	−31.1310	−	24.9458i	−1.15618	−	0.926465i
$726$		0			0
$727$	−25.8663	−	35.6019i	−0.959329	−	1.32040i	−0.947257	−	0.320476i	$-0.896157\pi$
$727$	−25.8663	−	35.6019i	−0.959329	−	1.32040i	−0.0120725	−	0.999927i	$-0.503843\pi$
$728$	−2.94676	−	0.957460i	−0.109214	−	0.0354858i
$729$		0			0
$730$	−0.0817427	+	0.0244417i	−0.00302543	+	0.000904629i
$731$	−0.827405	−	2.54649i	−0.0306027	−	0.0941854i
$732$		0			0
$733$	−25.9854	+	8.44317i	−0.959793	+	0.311856i	−0.746689	−	0.665174i	$-0.768357\pi$
$733$	−25.9854	+	8.44317i	−0.959793	+	0.311856i	−0.213104	+	0.977029i	$0.568357\pi$
$734$	−1.28574	−	0.934144i	−0.0474575	−	0.0344799i
$735$		0			0
$736$	2.04380	−	1.48491i	0.0753355	−	0.0547344i
$737$	−33.3504	+	45.9029i	−1.22848	+	1.69086i
$738$		0			0
$739$	13.3227	−	9.67951i	0.490083	−	0.356066i	−0.315133	−	0.949048i	$-0.602049\pi$
$739$	13.3227	−	9.67951i	0.490083	−	0.356066i	0.805216	+	0.592981i	$0.202049\pi$
$740$	−2.12113	+	6.03911i	−0.0779743	+	0.222002i
$741$		0			0
$742$	4.11658	−	1.33756i	0.151124	−	0.0491033i
$743$		−	35.6012i		−	1.30608i	−0.757322	−	0.653041i	$-0.773493\pi$
$743$		−	35.6012i		−	1.30608i	0.757322	−	0.653041i	$-0.226507\pi$
$744$		0			0
$745$	17.3961	+	25.1728i	0.637345	+	0.922261i
$746$	0.339434	−	1.04467i	0.0124275	−	0.0382481i
$747$		0			0
$748$	−5.12573	−	7.05496i	−0.187415	−	0.257955i
$749$	9.68668			0.353944
$750$		0			0
$751$	46.0748			1.68129			0.840647	−	0.541583i	$-0.182175\pi$
$751$	46.0748			1.68129			0.840647	+	0.541583i	$0.182175\pi$
$752$	25.4090	+	34.9725i	0.926570	+	1.27531i
$753$		0			0
$754$	0.438839	−	1.35061i	0.0159816	−	0.0491862i
$755$	−14.3910	−	20.8243i	−0.523742	−	0.757873i
$756$		0			0
$757$			36.6482i			1.33200i	0.745951	+	0.666000i	$0.231995\pi$
$757$			36.6482i			1.33200i	−0.745951	+	0.666000i	$0.768005\pi$
$758$	2.39998	−	0.779800i	0.0871711	−	0.0283236i
$759$		0			0
$760$	−0.358933	+	1.02193i	−0.0130199	+	0.0370692i
$761$	−22.0116	+	15.9923i	−0.797919	+	0.579722i	−0.910303	−	0.413943i	$-0.864151\pi$
$761$	−22.0116	+	15.9923i	−0.797919	+	0.579722i	0.112384	+	0.993665i	$0.464151\pi$
$762$		0			0
$763$	−28.2007	+	38.8149i	−1.02093	+	1.40520i
$764$	34.7346	−	25.2362i	1.25666	−	0.913013i
$765$		0			0
$766$	2.50212	+	1.81790i	0.0904053	+	0.0656833i
$767$	−12.6064	+	4.09608i	−0.455192	+	0.147901i
$768$		0			0
$769$	−8.19906	−	25.2341i	−0.295666	−	0.909965i	−0.982997	−	0.183621i	$-0.941218\pi$
$769$	−8.19906	−	25.2341i	−0.295666	−	0.909965i	0.687331	−	0.726344i	$-0.258782\pi$
$770$	3.68447	−	1.10169i	0.132779	−	0.0397020i
$771$		0			0
$772$	−5.96803	−	1.93913i	−0.214794	−	0.0697908i
$773$	16.9092	+	23.2736i	0.608183	+	0.837092i	0.996426	−	0.0844651i	$-0.0269181\pi$
$773$	16.9092	+	23.2736i	0.608183	+	0.837092i	−0.388244	+	0.921557i	$0.626918\pi$
$774$		0			0
$775$	18.3676	+	0.868059i	0.659783	+	0.0311816i
$776$	−0.0120861			−0.000433867
$777$		0			0
$778$	1.15514	+	0.375327i	0.0414137	+	0.0134561i
$779$	−2.49749	+	7.68650i	−0.0894820	+	0.275397i
$780$		0			0
$781$	9.93581	+	30.5793i	0.355531	+	1.09421i
$782$			0.211030i			0.00754641i
$783$		0			0
$784$	38.4138	+	27.9092i	1.37192	+	0.996759i
$785$	−15.7478	+	10.8828i	−0.562063	+	0.388424i
$786$		0			0
$787$	14.6160	−	20.1172i	0.521005	−	0.717102i	−0.464721	−	0.885457i	$-0.653845\pi$
$787$	14.6160	−	20.1172i	0.521005	−	0.717102i	0.985726	+	0.168355i	$0.0538455\pi$
$788$	−30.5396	+	42.0341i	−1.08793	+	1.49740i
$789$		0			0
$790$	−1.01464	−	0.774430i	−0.0360992	−	0.0275530i
$791$	6.03342	+	4.38353i	0.214524	+	0.155861i
$792$		0			0
$793$		−	18.7379i		−	0.665404i
$794$	0.998495	+	3.07305i	0.0354352	+	0.109058i
$795$		0			0
$796$	14.9368	−	45.9708i	0.529422	−	1.62939i
$797$	29.8828	+	9.70951i	1.05850	+	0.343928i	0.786000	−	0.618226i	$-0.212149\pi$
$797$	29.8828	+	9.70951i	1.05850	+	0.343928i	0.272503	+	0.962155i	$0.412149\pi$
$798$		0			0
$799$	−10.9067			−0.385851
$800$	−5.01398	−	1.89521i	−0.177271	−	0.0670057i
$801$		0			0
$802$	0.230172	+	0.316805i	0.00812766	+	0.0111868i
$803$	−1.77400	−	0.576406i	−0.0626030	−	0.0203409i
$804$		0			0
$805$	21.6796	+	7.61455i	0.764104	+	0.268378i
$806$	0.202277	+	0.622545i	0.00712491	+	0.0219282i
$807$		0			0
$808$	1.08913	−	0.353881i	0.0383156	−	0.0124495i
$809$	−40.8575	−	29.6847i	−1.43647	−	1.04366i	−0.988765	−	0.149481i	$-0.952240\pi$
$809$	−40.8575	−	29.6847i	−1.43647	−	1.04366i	−0.447710	−	0.894179i	$-0.647760\pi$
$810$		0			0
$811$	−20.3558	+	14.7894i	−0.714789	+	0.519325i	−0.884715	−	0.466132i	$-0.845647\pi$
$811$	−20.3558	+	14.7894i	−0.714789	+	0.519325i	0.169926	+	0.985457i	$0.445647\pi$
$812$	−40.7356	+	56.0677i	−1.42954	+	1.96759i
$813$		0			0
$814$	0.458521	−	0.333135i	0.0160712	−	0.0116764i
$815$	−10.2497	−	0.242068i	−0.359032	−	0.00847927i
$816$		0			0
$817$	−3.45047	+	1.12113i	−0.120717	+	0.0392233i
$818$			1.62697i			0.0568856i
$819$		0			0
$820$	−25.1409	−	8.83028i	−0.877957	−	0.308367i
$821$	6.37524	−	19.6210i	0.222498	−	0.684777i	−0.776038	−	0.630686i	$-0.782774\pi$
$821$	6.37524	−	19.6210i	0.222498	−	0.684777i	0.998536	−	0.0540914i	$-0.0172262\pi$
$822$		0			0
$823$	−21.0790	−	29.0128i	−0.734769	−	1.01132i	−0.998903	−	0.0468368i	$-0.985086\pi$
$823$	−21.0790	−	29.0128i	−0.734769	−	1.01132i	0.264133	−	0.964486i	$-0.414914\pi$
$824$	3.06686			0.106839
$825$		0			0
$826$	−2.61990			−0.0911580
$827$	2.78400	+	3.83184i	0.0968090	+	0.133246i	0.854674	−	0.519166i	$-0.173757\pi$
$827$	2.78400	+	3.83184i	0.0968090	+	0.133246i	−0.757865	+	0.652412i	$0.773757\pi$
$828$		0			0
$829$	8.79981	−	27.0830i	0.305630	−	0.940632i	−0.673811	−	0.738903i	$-0.735344\pi$
$829$	8.79981	−	27.0830i	0.305630	−	0.940632i	0.979441	−	0.201729i	$-0.0646560\pi$
$830$	−0.00349489	+	0.147982i	−0.000121309	+	0.00513652i
$831$		0			0
$832$			15.4708i			0.536355i
$833$	−11.3936	+	3.70200i	−0.394765	+	0.128267i
$834$		0			0
$835$	12.8297	+	9.79236i	0.443991	+	0.338879i
$836$	−9.55941	+	6.94532i	−0.330619	+	0.240209i
$837$		0			0
$838$	0.0278685	−	0.0383577i	0.000962700	−	0.00132504i
$839$	0.619476	−	0.450076i	0.0213867	−	0.0155383i	−0.577041	−	0.816715i	$-0.695793\pi$
$839$	0.619476	−	0.450076i	0.0213867	−	0.0155383i	0.598427	+	0.801177i	$0.295793\pi$
$840$		0			0
$841$	−28.0384	−	20.3711i	−0.966841	−	0.702451i
$842$	−1.59388	+	0.517883i	−0.0549287	+	0.0178474i
$843$		0			0
$844$	10.0815	+	31.0278i	0.347021	+	1.06802i
$845$	−12.3092	+	16.1272i	−0.423448	+	0.554791i
$846$		0			0
$847$	34.3410	+	11.1581i	1.17997	+	0.383395i
$848$	−25.6686	−	35.3297i	−0.881462	−	1.21323i
$849$		0			0
$850$	0.374266	−	0.245792i	0.0128372	−	0.00843061i
$851$	3.38644			0.116086
$852$		0			0
$853$	−33.0292	−	10.7318i	−1.13090	−	0.367451i	−0.316981	−	0.948432i	$-0.602669\pi$
$853$	−33.0292	−	10.7318i	−1.13090	−	0.367451i	−0.813917	+	0.580981i	$0.802669\pi$
$854$	1.14447	−	3.52230i	0.0391628	−	0.120531i
$855$		0			0
$856$	0.246124	+	0.757493i	0.00841236	+	0.0258906i
$857$		−	54.2561i		−	1.85335i	−0.375860	−	0.926676i	$-0.622653\pi$
$857$		−	54.2561i		−	1.85335i	0.375860	−	0.926676i	$-0.377347\pi$
$858$		0			0
$859$	12.8710	+	9.35134i	0.439154	+	0.319064i	0.785299	−	0.619117i	$-0.212509\pi$
$859$	12.8710	+	9.35134i	0.439154	+	0.319064i	−0.346145	+	0.938181i	$0.612509\pi$
$860$	−3.42672	−	11.4603i	−0.116850	−	0.390793i
$861$		0			0
$862$	−1.10823	+	1.52535i	−0.0377464	+	0.0519535i
$863$	13.2083	−	18.1797i	0.449617	−	0.618845i	−0.522698	−	0.852518i	$-0.675074\pi$
$863$	13.2083	−	18.1797i	0.449617	−	0.618845i	0.972315	+	0.233673i	$0.0750744\pi$
$864$		0			0
$865$	−3.44572	+	9.81040i	−0.117158	+	0.333563i
$866$	0.992896	+	0.721381i	0.0337400	+	0.0245135i
$867$		0			0
$868$		−	31.9446i		−	1.08427i
$869$	−8.62336	−	26.5400i	−0.292527	−	0.900307i
$870$		0			0
$871$	−7.91289	+	24.3534i	−0.268118	+	0.825183i
$872$	−3.75184	−	1.21905i	−0.127053	−	0.0412822i
$873$		0			0
$874$	0.285944			0.00967219
$875$	−11.7462	−	47.3180i	−0.397094	−	1.59964i
$876$		0			0
$877$	−15.9146	−	21.9046i	−0.537399	−	0.739667i	0.450836	−	0.892607i	$-0.351126\pi$
$877$	−15.9146	−	21.9046i	−0.537399	−	0.739667i	−0.988235	+	0.152940i	$0.951126\pi$
$878$	0.370173	+	0.120276i	0.0124927	+	0.00405913i
$879$		0			0
$880$	−22.0581	−	31.9189i	−0.743578	−	1.07598i
$881$	2.41440	+	7.43077i	0.0813433	+	0.250349i	0.983455	−	0.181154i	$-0.0579834\pi$
$881$	2.41440	+	7.43077i	0.0813433	+	0.250349i	−0.902111	+	0.431503i	$0.857983\pi$
$882$		0			0
$883$	−55.4476	+	18.0160i	−1.86596	+	0.606287i	−0.873018	+	0.487688i	$0.837840\pi$
$883$	−55.4476	+	18.0160i	−1.86596	+	0.606287i	−0.992942	+	0.118599i	$0.962160\pi$
$884$	−3.18394	−	2.31327i	−0.107088	−	0.0778036i
$885$		0			0
$886$	−0.116804	+	0.0848629i	−0.00392410	+	0.00285102i
$887$	5.08205	−	6.99484i	0.170638	−	0.234864i	−0.715130	−	0.698992i	$-0.753632\pi$
$887$	5.08205	−	6.99484i	0.170638	−	0.234864i	0.885768	+	0.464128i	$0.153632\pi$
$888$		0			0
$889$	−44.2994	+	32.1854i	−1.48576	+	1.07946i
$890$	−0.563130	−	1.88333i	−0.0188762	−	0.0631293i
$891$		0			0
$892$	−10.7660	+	3.49809i	−0.360472	+	0.117125i
$893$			14.7785i			0.494543i
$894$		0			0
$895$	−15.4322	+	4.61434i	−0.515840	+	0.154240i
$896$	−3.83414	+	11.8003i	−0.128090	+	0.394219i
$897$		0			0
$898$	0.730099	+	1.00490i	0.0243637	+	0.0335338i
$899$	29.3420			0.978612
$900$		0			0
$901$	11.0181			0.367067
$902$	1.38684	+	1.90883i	0.0461769	+	0.0635570i
$903$		0			0
$904$	−0.189490	+	0.583189i	−0.00630233	+	0.0193966i
$905$	5.16111	−	6.76196i	0.171561	−	0.224775i
$906$		0			0
$907$		−	40.4367i		−	1.34268i	−0.741151	−	0.671339i	$-0.765720\pi$
$907$		−	40.4367i		−	1.34268i	0.741151	−	0.671339i	$-0.234280\pi$
$908$	6.90285	−	2.24287i	0.229079	−	0.0744324i
$909$		0			0
$910$	1.42779	−	0.986701i	0.0473309	−	0.0327088i
$911$	−40.9074	+	29.7210i	−1.35532	+	0.984700i	−0.356596	+	0.934259i	$0.616063\pi$
$911$	−40.9074	+	29.7210i	−1.35532	+	0.984700i	−0.998727	+	0.0504407i	$0.983937\pi$
$912$		0			0
$913$	−1.90217	+	2.61812i	−0.0629528	+	0.0866471i
$914$	1.46308	−	1.06299i	0.0483944	−	0.0351606i
$915$		0			0
$916$	2.67712	+	1.94504i	0.0884545	+	0.0642660i
$917$	68.3130	−	22.1962i	2.25590	−	0.732985i
$918$		0			0
$919$	13.3979	+	41.2346i	0.441957	+	1.36020i	0.885787	+	0.464092i	$0.153619\pi$
$919$	13.3979	+	41.2346i	0.441957	+	1.36020i	−0.443831	+	0.896111i	$0.646381\pi$
$920$	−0.0446079	+	1.88880i	−0.00147068	+	0.0622720i
$921$		0			0
$922$	−2.69309	−	0.875039i	−0.0886923	−	0.0288179i
$923$	8.52924	+	11.7395i	0.280743	+	0.386410i
$924$		0			0
$925$	−3.94428	−	6.00591i	−0.129687	−	0.197473i
$926$	−0.00405712			−0.000133325
$927$		0			0
$928$	−8.13472	−	2.64313i	−0.267035	−	0.0867650i
$929$	−10.5605	+	32.5020i	−0.346480	+	1.06636i	0.614307	+	0.789067i	$0.289436\pi$
$929$	−10.5605	+	32.5020i	−0.346480	+	1.06636i	−0.960787	+	0.277289i	$0.910564\pi$
$930$		0			0
$931$	5.01618	+	15.4382i	0.164399	+	0.505967i
$932$			15.6546i			0.512783i
$933$		0			0
$934$	2.38596	+	1.73350i	0.0780710	+	0.0567219i
$935$	9.78647	+	0.231127i	0.320052	+	0.00755867i
$936$		0			0
$937$	16.3990	−	22.5713i	0.535731	−	0.737371i	−0.452259	−	0.891887i	$-0.649382\pi$
$937$	16.3990	−	22.5713i	0.535731	−	0.737371i	0.987990	+	0.154516i	$0.0493817\pi$
$938$	−2.97489	+	4.09458i	−0.0971334	+	0.133693i
$939$		0			0
$940$	−48.7110	−	1.15041i	−1.58878	−	0.0375222i
$941$	−43.9507	−	31.9321i	−1.43275	−	1.04096i	−0.989496	−	0.144561i	$-0.953823\pi$
$941$	−43.9507	−	31.9321i	−1.43275	−	1.04096i	−0.443257	−	0.896395i	$-0.646177\pi$
$942$		0			0
$943$			14.0978i			0.459086i
$944$	8.16808	+	25.1388i	0.265848	+	0.818197i
$945$		0			0
$946$	−0.327297	+	1.00732i	−0.0106413	+	0.0327507i
$947$	−4.02460	−	1.30767i	−0.130782	−	0.0424936i	0.242895	−	0.970053i	$-0.421903\pi$
$947$	−4.02460	−	1.30767i	−0.130782	−	0.0424936i	−0.373677	+	0.927559i	$0.621903\pi$
$948$		0			0
$949$	−0.841815			−0.0273265
$950$	−0.333046	−	0.507127i	−0.0108055	−	0.0164534i
$951$		0			0
$952$	−0.916291	−	1.26117i	−0.0296971	−	0.0408746i
$953$	−45.5848	−	14.8114i	−1.47664	−	0.479788i	−0.543531	−	0.839389i	$-0.682913\pi$
$953$	−45.5848	−	14.8114i	−1.47664	−	0.479788i	−0.933106	+	0.359601i	$0.882913\pi$
$954$		0			0
$955$	−1.13794	+	48.1831i	−0.0368229	+	1.55917i
$956$	−0.349197	−	1.07472i	−0.0112938	−	0.0347588i
$957$		0			0
$958$	−0.639459	+	0.207773i	−0.0206600	+	0.00671284i
$959$	34.1052	+	24.7788i	1.10131	+	0.800151i
$960$		0			0
$961$	14.1377	−	10.2716i	0.456055	−	0.331343i
$962$	0.150346	−	0.206933i	0.00484734	−	0.00667179i
$963$		0			0
$964$	30.6318	−	22.2553i	0.986582	−	0.716794i
$965$	5.79509	−	4.00480i	0.186551	−	0.128919i
$966$		0			0
$967$	19.8607	−	6.45312i	0.638676	−	0.207518i	0.0282614	−	0.999601i	$-0.491003\pi$
$967$	19.8607	−	6.45312i	0.638676	−	0.207518i	0.610414	+	0.792082i	$0.291003\pi$
$968$			2.96895i			0.0954257i
$969$		0			0
$970$	0.00410752	−	0.00538157i	0.000131884	−	0.000172792i
$971$	−4.96713	+	15.2872i	−0.159403	+	0.490591i	−0.998580	−	0.0532663i	$-0.983037\pi$
$971$	−4.96713	+	15.2872i	−0.159403	+	0.490591i	0.839178	+	0.543857i	$0.183037\pi$
$972$		0			0
$973$	34.6863	+	47.7417i	1.11199	+	1.53053i
$974$	2.28406			0.0731860
$975$		0			0
$976$	−37.3657			−1.19605
$977$	−20.9055	−	28.7739i	−0.668826	−	0.920560i	0.330907	−	0.943663i	$-0.392645\pi$
$977$	−20.9055	−	28.7739i	−0.668826	−	0.920560i	−0.999733	+	0.0231034i	$0.992645\pi$
$978$		0			0
$979$	13.2802	−	40.8723i	0.424438	−	1.30629i
$980$	−51.2761	+	15.3320i	−1.63795	+	0.489762i
$981$		0			0
$982$			0.994014i			0.0317202i
$983$	−17.5671	+	5.70790i	−0.560303	+	0.182054i	−0.575458	−	0.817832i	$-0.695176\pi$
$983$	−17.5671	+	5.70790i	−0.560303	+	0.182054i	0.0151542	+	0.999885i	$0.495176\pi$
$984$		0			0
$985$	−16.7087	−	55.8805i	−0.532384	−	1.78050i
$986$	0.578039	−	0.419970i	0.0184085	−	0.0133746i
$987$		0			0
$988$	−3.13446	+	4.31421i	−0.0997204	+	0.137253i
$989$	−5.11986	+	3.71979i	−0.162802	+	0.118283i
$990$		0			0
$991$	33.6476	+	24.4464i	1.06885	+	0.776566i	0.975705	−	0.219087i	$-0.0703078\pi$
$991$	33.6476	+	24.4464i	1.06885	+	0.776566i	0.0931455	+	0.995653i	$0.470308\pi$
$992$	3.74959	−	1.21832i	0.119050	−	0.0386816i
$993$		0			0
$994$	0.886283	+	2.72770i	0.0281112	+	0.0865174i
$995$	30.8484	+	44.6387i	0.977959	+	1.41514i
$996$		0			0
$997$	30.2792	+	9.83830i	0.958952	+	0.311582i	0.746348	−	0.665556i	$-0.231806\pi$
$997$	30.2792	+	9.83830i	0.958952	+	0.311582i	0.212604	+	0.977138i	$0.431806\pi$
$998$	0.247161	+	0.340189i	0.00782376	+	0.0107685i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.m.b.64.2		16
3.2	odd	2		75.2.i.a.64.3	yes	16
15.2	even	4		375.2.g.e.301.2		16
15.8	even	4		375.2.g.d.301.3		16
15.14	odd	2		375.2.i.c.199.2		16
25.3	odd	20		5625.2.a.t.1.5		8
25.9	even	10	inner	225.2.m.b.109.2		16
25.22	odd	20		5625.2.a.bd.1.4		8
75.29	odd	10		1875.2.b.h.1249.9		16
75.38	even	20		375.2.g.d.76.3		16
75.41	odd	10		375.2.i.c.49.2		16
75.47	even	20		1875.2.a.m.1.5		8
75.53	even	20		1875.2.a.p.1.4		8
75.59	odd	10		75.2.i.a.34.3	✓	16
75.62	even	20		375.2.g.e.76.2		16
75.71	odd	10		1875.2.b.h.1249.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.34.3	✓	16	75.59	odd	10
75.2.i.a.64.3	yes	16	3.2	odd	2
225.2.m.b.64.2		16	1.1	even	1	trivial
225.2.m.b.109.2		16	25.9	even	10	inner
375.2.g.d.76.3		16	75.38	even	20
375.2.g.d.301.3		16	15.8	even	4
375.2.g.e.76.2		16	75.62	even	20
375.2.g.e.301.2		16	15.2	even	4
375.2.i.c.49.2		16	75.41	odd	10
375.2.i.c.199.2		16	15.14	odd	2
1875.2.a.m.1.5		8	75.47	even	20
1875.2.a.p.1.4		8	75.53	even	20
1875.2.b.h.1249.8		16	75.71	odd	10
1875.2.b.h.1249.9		16	75.29	odd	10
5625.2.a.t.1.5		8	25.3	odd	20
5625.2.a.bd.1.4		8	25.22	odd	20

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0527945 - 0.0726655i) q^{2} +(0.615541 - 1.89444i) q^{4} +(1.27125 + 1.83954i) q^{5} +4.36070i q^{7} +(-0.341004 + 0.110799i) q^{8} +O(q^{10})\)	\(q+(-0.0527945 - 0.0726655i) q^{2} +(0.615541 - 1.89444i) q^{4} +(1.27125 + 1.83954i) q^{5} +4.36070i q^{7} +(-0.341004 + 0.110799i) q^{8} +(0.0665563 - 0.189494i) q^{10} +(3.55235 - 2.58093i) q^{11} +(1.16479 - 1.60319i) q^{13} +(0.316872 - 0.230221i) q^{14} +(-3.19696 - 2.32273i) q^{16} +(0.948224 - 0.308097i) q^{17} +(-0.417468 - 1.28484i) q^{19} +(4.26741 - 1.27599i) q^{20} +(-0.375089 - 0.121874i) q^{22} +(-1.38512 - 1.90646i) q^{23} +(-1.76785 + 4.67704i) q^{25} -0.177991 q^{26} +(8.26109 + 2.68419i) q^{28} +(-2.46551 + 7.58806i) q^{29} +(-1.13645 - 3.49762i) q^{31} +1.07204i q^{32} +(-0.0724490 - 0.0526373i) q^{34} +(-8.02171 + 5.54354i) q^{35} +(-0.844681 + 1.16260i) q^{37} +(-0.0713231 + 0.0981678i) q^{38} +(-0.637321 - 0.486439i) q^{40} +(-4.83992 - 3.51641i) q^{41} -2.68554i q^{43} +(-2.70280 - 8.31838i) q^{44} +(-0.0654066 + 0.201301i) q^{46} +(-10.4039 - 3.38042i) q^{47} -12.0157 q^{49} +(0.433192 - 0.118461i) q^{50} +(-2.32018 - 3.19345i) q^{52} +(10.5102 + 3.41496i) q^{53} +(9.26366 + 3.25369i) q^{55} +(-0.483161 - 1.48702i) q^{56} +(0.681555 - 0.221451i) q^{58} +(-5.41147 - 3.93167i) q^{59} +(7.64982 - 5.55792i) q^{61} +(-0.194158 + 0.267235i) q^{62} +(-6.31602 + 4.58886i) q^{64} +(4.42988 + 0.104621i) q^{65} +(-12.2894 + 3.99307i) q^{67} -1.98600i q^{68} +(0.826326 + 0.290232i) q^{70} +(-2.26280 + 6.96418i) q^{71} +(-0.249694 - 0.343674i) q^{73} +0.129076 q^{74} -2.69101 q^{76} +(11.2547 + 15.4907i) q^{77} +(1.96390 - 6.04425i) q^{79} +(0.208626 - 8.83372i) q^{80} +0.537343i q^{82} +(-0.700939 + 0.227749i) q^{83} +(1.77219 + 1.35263i) q^{85} +(-0.195146 + 0.141782i) q^{86} +(-0.925401 + 1.27370i) q^{88} +(7.91814 - 5.75286i) q^{89} +(6.99105 + 5.07929i) q^{91} +(-4.46427 + 1.45053i) q^{92} +(0.303628 + 0.934470i) q^{94} +(1.83281 - 2.40130i) q^{95} +(0.0320583 + 0.0104164i) q^{97} +(0.634365 + 0.873128i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 30 q^{8}+O(q^{10}) \) 16 * q + 2 * q^4 + 30 * q^8	\( 16 q + 2 q^{4} + 30 q^{8} + 6 q^{11} + 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} - 20 q^{20} - 30 q^{22} + 20 q^{23} - 10 q^{25} - 12 q^{26} + 30 q^{28} - 16 q^{29} + 6 q^{31} - 36 q^{34} - 10 q^{35} - 10 q^{37} - 30 q^{38} + 10 q^{40} + 14 q^{41} - 26 q^{44} + 16 q^{46} - 40 q^{47} - 20 q^{50} + 40 q^{52} - 10 q^{53} + 10 q^{55} + 10 q^{58} - 12 q^{59} + 10 q^{62} + 8 q^{64} + 70 q^{65} - 40 q^{67} + 30 q^{70} + 8 q^{71} - 20 q^{73} + 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 10 q^{83} - 20 q^{85} + 36 q^{86} - 40 q^{88} - 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} + 40 q^{95} + 40 q^{97} - 60 q^{98}+O(q^{100}) \) 16 * q + 2 * q^4 + 30 * q^8 + 6 * q^11 + 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 - 20 * q^20 - 30 * q^22 + 20 * q^23 - 10 * q^25 - 12 * q^26 + 30 * q^28 - 16 * q^29 + 6 * q^31 - 36 * q^34 - 10 * q^35 - 10 * q^37 - 30 * q^38 + 10 * q^40 + 14 * q^41 - 26 * q^44 + 16 * q^46 - 40 * q^47 - 20 * q^50 + 40 * q^52 - 10 * q^53 + 10 * q^55 + 10 * q^58 - 12 * q^59 + 10 * q^62 + 8 * q^64 + 70 * q^65 - 40 * q^67 + 30 * q^70 + 8 * q^71 - 20 * q^73 + 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 10 * q^83 - 20 * q^85 + 36 * q^86 - 40 * q^88 - 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 + 40 * q^95 + 40 * q^97 - 60 * q^98

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