LMFDB - Embedded newform 525.2.r.h.424.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(424,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("525.424");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 15x^{14} + 158x^{12} - 843x^{10} + 3258x^{8} - 4947x^{6} + 5489x^{4} - 1296x^{2} + 256 $ x^16 - 15x^14 + 158x^12 - 843x^10 + 3258x^8 - 4947x^6 + 5489x^4 - 1296*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			424.2
Root			$-2.11082 + 1.21868i$ of defining polynomial
Character	$\chi$	$=$	525.424
Dual form			525.2.r.h.499.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.11082 + 1.21868i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(1.97036 - 3.41277i) q^{4} +2.43736 q^{6} +(-2.46138 - 0.970361i) q^{7} +4.73024i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.11082 + 1.21868i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(1.97036 - 3.41277i) q^{4} +2.43736 q^{6} +(-2.46138 - 0.970361i) q^{7} +4.73024i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.29092 + 3.96799i) q^{11} +(-3.41277 + 1.97036i) q^{12} +1.35888i q^{13} +(6.37808 - 0.951383i) q^{14} +(-1.82392 - 3.15913i) q^{16} +(3.71774 + 2.14644i) q^{17} +(-2.11082 - 1.21868i) q^{18} +(-3.40772 - 5.90235i) q^{19} +(1.64644 + 2.07105i) q^{21} -11.1676i q^{22} +(3.36143 - 1.94072i) q^{23} +(2.36512 - 4.09651i) q^{24} +(-1.65604 - 2.86834i) q^{26} -1.00000i q^{27} +(-8.16142 + 6.48816i) q^{28} -4.00000 q^{29} +(4.05416 - 7.02201i) q^{31} +(-0.493084 - 0.284682i) q^{32} +(3.96799 - 2.29092i) q^{33} -10.4633 q^{34} +3.94072 q^{36} +(10.1811 - 5.87808i) q^{37} +(14.3861 + 8.30584i) q^{38} +(0.679440 - 1.17682i) q^{39} +8.17432 q^{41} +(-5.99927 - 2.36512i) q^{42} +3.52256i q^{43} +(9.02788 + 15.6368i) q^{44} +(-4.73024 + 8.19301i) q^{46} +(2.85754 - 1.64980i) q^{47} +3.64784i q^{48} +(5.11680 + 4.77686i) q^{49} +(-2.14644 - 3.71774i) q^{51} +(4.63754 + 2.67748i) q^{52} +(-8.18962 - 4.72828i) q^{53} +(1.21868 + 2.11082i) q^{54} +(4.59004 - 11.6429i) q^{56} +6.81544i q^{57} +(8.44326 - 4.87472i) q^{58} +(0.350199 - 0.606563i) q^{59} +(2.50000 + 4.33013i) q^{61} +19.7629i q^{62} +(-0.390334 - 2.61680i) q^{63} +8.68344 q^{64} +(-5.58380 + 9.67142i) q^{66} +(1.68071 + 0.970361i) q^{67} +(14.6506 - 8.45852i) q^{68} -3.88144 q^{69} +11.8680 q^{71} +(-4.09651 + 2.36512i) q^{72} +(5.33791 + 3.08184i) q^{73} +(-14.3270 + 24.8151i) q^{74} -26.8578 q^{76} +(9.48921 - 7.54372i) q^{77} +3.31208i q^{78} +(-3.08380 - 5.34130i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-17.2545 + 9.96188i) q^{82} -13.0490i q^{83} +(10.3121 - 1.53820i) q^{84} +(-4.29288 - 7.43548i) q^{86} +(3.46410 + 2.00000i) q^{87} +(-18.7695 - 10.8366i) q^{88} +(0.146439 + 0.253639i) q^{89} +(1.31860 - 3.34472i) q^{91} -15.2957i q^{92} +(-7.02201 + 4.05416i) q^{93} +(-4.02116 + 6.96485i) q^{94} +(0.284682 + 0.493084i) q^{96} -2.00672i q^{97} +(-16.6221 - 3.84732i) q^{98} -4.58184 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 14 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) $ 16 * q + 14 * q^4 - 4 * q^6 + 8 * q^9	$ 16 q + 14 q^{4} - 4 q^{6} + 8 q^{9} - 16 q^{11} + 24 q^{14} - 34 q^{16} + 6 q^{19} + 4 q^{21} - 6 q^{24} + 38 q^{26} - 64 q^{29} - 18 q^{31} - 56 q^{34} + 28 q^{36} + 14 q^{39} + 16 q^{41} + 52 q^{44} + 12 q^{46} + 42 q^{49} - 12 q^{51} - 2 q^{54} - 42 q^{56} + 20 q^{59} + 40 q^{61} - 84 q^{64} - 24 q^{66} + 8 q^{69} + 88 q^{71} - 42 q^{74} - 92 q^{76} + 16 q^{79} - 8 q^{81} + 36 q^{84} - 24 q^{86} - 20 q^{89} + 42 q^{91} + 44 q^{94} + 34 q^{96} - 32 q^{99}+O(q^{100}) $ 16 * q + 14 * q^4 - 4 * q^6 + 8 * q^9 - 16 * q^11 + 24 * q^14 - 34 * q^16 + 6 * q^19 + 4 * q^21 - 6 * q^24 + 38 * q^26 - 64 * q^29 - 18 * q^31 - 56 * q^34 + 28 * q^36 + 14 * q^39 + 16 * q^41 + 52 * q^44 + 12 * q^46 + 42 * q^49 - 12 * q^51 - 2 * q^54 - 42 * q^56 + 20 * q^59 + 40 * q^61 - 84 * q^64 - 24 * q^66 + 8 * q^69 + 88 * q^71 - 42 * q^74 - 92 * q^76 + 16 * q^79 - 8 * q^81 + 36 * q^84 - 24 * q^86 - 20 * q^89 + 42 * q^91 + 44 * q^94 + 34 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.11082	+	1.21868i	−1.49257	+	0.861737i	−0.999964	−	0.00851453i	$-0.997290\pi$
$2$	−2.11082	+	1.21868i	−1.49257	+	0.861737i	−0.492608	+	0.870251i	$0.663956\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	1.97036	−	3.41277i	0.985180	−	1.70638i
$5$		0			0
$5$		0			0
$6$	2.43736			0.995048
$7$	−2.46138	−	0.970361i	−0.930315	−	0.366762i
$7$	−2.46138	−	0.970361i	−0.930315	−	0.366762i
$8$			4.73024i			1.67239i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−2.29092	+	3.96799i	−0.690739	+	1.19639i	0.280858	+	0.959749i	$0.409381\pi$
$11$	−2.29092	+	3.96799i	−0.690739	+	1.19639i	−0.971596	+	0.236645i	$0.923952\pi$
$12$	−3.41277	+	1.97036i	−0.985180	+	0.568794i
$13$			1.35888i			0.376885i	0.982084	+	0.188443i	$0.0603440\pi$
$13$			1.35888i			0.376885i	−0.982084	+	0.188443i	$0.939656\pi$
$14$	6.37808	−	0.951383i	1.70461	−	0.254268i
$15$		0			0
$16$	−1.82392	−	3.15913i	−0.455981	−	0.789782i
$17$	3.71774	+	2.14644i	0.901685	+	0.520588i	0.877746	−	0.479126i	$-0.159046\pi$
$17$	3.71774	+	2.14644i	0.901685	+	0.520588i	0.0239382	+	0.999713i	$0.492379\pi$
$18$	−2.11082	−	1.21868i	−0.497524	−	0.287246i
$19$	−3.40772	−	5.90235i	−0.781785	−	1.35409i	−0.930901	−	0.365271i	$-0.880976\pi$
$19$	−3.40772	−	5.90235i	−0.781785	−	1.35409i	0.149116	−	0.988820i	$-0.452357\pi$
$20$		0			0
$21$	1.64644	+	2.07105i	0.359282	+	0.451940i
$22$		−	11.1676i		−	2.38094i
$23$	3.36143	−	1.94072i	0.700906	−	0.404668i	−0.106779	−	0.994283i	$-0.534054\pi$
$23$	3.36143	−	1.94072i	0.700906	−	0.404668i	0.807685	+	0.589614i	$0.200720\pi$
$24$	2.36512	−	4.09651i	0.482778	−	0.836196i
$25$		0			0
$26$	−1.65604	−	2.86834i	−0.324776	−	0.562529i
$27$		−	1.00000i		−	0.192450i
$28$	−8.16142	+	6.48816i	−1.54236	+	1.22615i
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$		0			0
$31$	4.05416	−	7.02201i	0.728148	−	1.26119i	−0.229516	−	0.973305i	$-0.573714\pi$
$31$	4.05416	−	7.02201i	0.728148	−	1.26119i	0.957665	−	0.287885i	$-0.0929522\pi$
$32$	−0.493084	−	0.284682i	−0.0871658	−	0.0503252i
$33$	3.96799	−	2.29092i	0.690739	−	0.398798i
$34$	−10.4633			−1.79444
$35$		0			0
$36$	3.94072			0.656787
$37$	10.1811	−	5.87808i	1.67377	−	0.966351i	0.708270	−	0.705942i	$-0.249476\pi$
$37$	10.1811	−	5.87808i	1.67377	−	0.966351i	0.965498	−	0.260409i	$-0.0838574\pi$
$38$	14.3861	+	8.30584i	2.33374	+	1.34739i
$39$	0.679440	−	1.17682i	0.108797	−	0.188443i
$40$		0			0
$41$	8.17432			1.27661			0.638307	−	0.769782i	$-0.279635\pi$
$41$	8.17432			1.27661			0.638307	+	0.769782i	$0.279635\pi$
$42$	−5.99927	−	2.36512i	−0.925708	−	0.364946i
$43$			3.52256i			0.537186i	0.963254	+	0.268593i	$0.0865587\pi$
$43$			3.52256i			0.537186i	−0.963254	+	0.268593i	$0.913441\pi$
$44$	9.02788	+	15.6368i	1.36100	+	2.35733i
$45$		0			0
$46$	−4.73024	+	8.19301i	−0.697435	+	1.20799i
$47$	2.85754	−	1.64980i	0.416815	−	0.240648i	−0.276899	−	0.960899i	$-0.589307\pi$
$47$	2.85754	−	1.64980i	0.416815	−	0.240648i	0.693714	+	0.720251i	$0.255973\pi$
$48$			3.64784i			0.526521i
$49$	5.11680	+	4.77686i	0.730971	+	0.682408i
$50$		0			0
$51$	−2.14644	−	3.71774i	−0.300562	−	0.520588i
$52$	4.63754	+	2.67748i	0.643111	+	0.371300i
$53$	−8.18962	−	4.72828i	−1.12493	−	0.649479i	−0.182276	−	0.983247i	$-0.558346\pi$
$53$	−8.18962	−	4.72828i	−1.12493	−	0.649479i	−0.942655	+	0.333768i	$0.891680\pi$
$54$	1.21868	+	2.11082i	0.165841	+	0.287246i
$55$		0			0
$56$	4.59004	−	11.6429i	0.613369	−	1.55585i
$57$			6.81544i			0.902727i
$58$	8.44326	−	4.87472i	1.10865	−	0.640082i
$59$	0.350199	−	0.606563i	0.0455921	−	0.0789678i	−0.842329	−	0.538964i	$-0.818816\pi$
$59$	0.350199	−	0.606563i	0.0455921	−	0.0789678i	0.887921	+	0.459996i	$0.152149\pi$
$60$		0			0
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	0.980507	−	0.196485i	$-0.0629528\pi$
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	−0.660415	+	0.750901i	$0.729619\pi$
$62$			19.7629i			2.50989i
$63$	−0.390334	−	2.61680i	−0.0491774	−	0.329686i
$64$	8.68344			1.08543
$65$		0			0
$66$	−5.58380	+	9.67142i	−0.687318	+	1.19047i
$67$	1.68071	+	0.970361i	0.205332	+	0.118548i	0.599140	−	0.800644i	$-0.295509\pi$
$67$	1.68071	+	0.970361i	0.205332	+	0.118548i	−0.393808	+	0.919193i	$0.628843\pi$
$68$	14.6506	−	8.45852i	1.77664	−	1.02575i
$69$	−3.88144			−0.467271
$70$		0			0
$71$	11.8680			1.40847			0.704236	−	0.709966i	$-0.251290\pi$
$71$	11.8680			1.40847			0.704236	+	0.709966i	$0.251290\pi$
$72$	−4.09651	+	2.36512i	−0.482778	+	0.278732i
$73$	5.33791	+	3.08184i	0.624755	+	0.360702i	0.778718	−	0.627374i	$-0.215870\pi$
$73$	5.33791	+	3.08184i	0.624755	+	0.360702i	−0.153963	+	0.988077i	$0.549204\pi$
$74$	−14.3270	+	24.8151i	−1.66548	+	2.88470i
$75$		0			0
$76$	−26.8578			−3.08080
$77$	9.48921	−	7.54372i	1.08140	−	0.859687i
$78$			3.31208i			0.375019i
$79$	−3.08380	−	5.34130i	−0.346954	−	0.600943i	0.638752	−	0.769412i	$-0.279451\pi$
$79$	−3.08380	−	5.34130i	−0.346954	−	0.600943i	−0.985707	+	0.168470i	$0.946117\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−17.2545	+	9.96188i	−1.90544	+	1.10011i
$83$		−	13.0490i		−	1.43232i	−0.697937	−	0.716159i	$-0.745898\pi$
$83$		−	13.0490i		−	1.43232i	0.697937	−	0.716159i	$-0.254102\pi$
$84$	10.3121	−	1.53820i	1.12514	−	0.167831i
$85$		0			0
$86$	−4.29288	−	7.43548i	−0.462913	−	0.801789i
$87$	3.46410	+	2.00000i	0.371391	+	0.214423i
$88$	−18.7695	−	10.8366i	−2.00084	−	1.15519i
$89$	0.146439	+	0.253639i	0.0155225	+	0.0268857i	0.873682	−	0.486497i	$-0.161726\pi$
$89$	0.146439	+	0.253639i	0.0155225	+	0.0268857i	−0.858160	+	0.513383i	$0.828392\pi$
$90$		0			0
$91$	1.31860	−	3.34472i	0.138227	−	0.350622i
$92$		−	15.2957i		−	1.59469i
$93$	−7.02201	+	4.05416i	−0.728148	+	0.420397i
$94$	−4.02116	+	6.96485i	−0.414751	+	0.718369i
$95$		0			0
$96$	0.284682	+	0.493084i	0.0290553	+	0.0503252i
$97$		−	2.00672i		−	0.203752i	−0.994797	−	0.101876i	$-0.967516\pi$
$97$		−	2.00672i		−	0.203752i	0.994797	−	0.101876i	$-0.0324845\pi$
$98$	−16.6221	−	3.84732i	−1.67908	−	0.388638i
$99$	−4.58184			−0.460492
$100$		0			0
$101$	−3.14644	+	5.44979i	−0.313082	+	0.542275i	−0.979028	−	0.203726i	$-0.934695\pi$
$101$	−3.14644	+	5.44979i	−0.313082	+	0.542275i	0.665946	+	0.746000i	$0.268028\pi$
$102$	9.06147	+	5.23164i	0.897219	+	0.518010i
$103$	2.95439	−	1.70572i	0.291105	−	0.168069i	−0.347335	−	0.937741i	$-0.612913\pi$
$103$	2.95439	−	1.70572i	0.291105	−	0.168069i	0.638440	+	0.769672i	$0.279580\pi$
$104$	−6.42782			−0.630300
$105$		0			0
$106$	23.0490			2.23872
$107$	2.74322	−	1.58380i	0.265197	−	0.153112i	−0.361506	−	0.932370i	$-0.617737\pi$
$107$	2.74322	−	1.58380i	0.265197	−	0.153112i	0.626703	+	0.779258i	$0.284404\pi$
$108$	−3.41277	−	1.97036i	−0.328393	−	0.189598i
$109$	5.11680	−	8.86256i	0.490101	−	0.848879i	−0.509835	−	0.860272i	$-0.670293\pi$
$109$	5.11680	−	8.86256i	0.490101	−	0.848879i	0.999935	+	0.0113935i	$0.00362673\pi$
$110$		0			0
$111$	−11.7562			−1.11585
$112$	1.42388	+	9.54568i	0.134544	+	0.901982i
$113$			3.16368i			0.297614i	0.988866	+	0.148807i	$0.0475434\pi$
$113$			3.16368i			0.297614i	−0.988866	+	0.148807i	$0.952457\pi$
$114$	−8.30584	−	14.3861i	−0.777913	−	1.34739i
$115$		0			0
$116$	−7.88144	+	13.6511i	−0.731774	+	1.26747i
$117$	−1.17682	+	0.679440i	−0.108797	+	0.0628142i
$118$			1.70712i			0.157153i
$119$	−7.06796	−	8.89075i	−0.647919	−	0.815014i
$120$		0			0
$121$	−4.99664	−	8.65443i	−0.454240	−	0.786766i
$122$	−10.5541	−	6.09340i	−0.955521	−	0.551670i
$123$	−7.07917	−	4.08716i	−0.638307	−	0.368527i
$124$	−15.9763	−	27.6718i	−1.43472	−	2.48500i
$125$		0			0
$126$	4.01296	+	5.04789i	0.357503	+	0.449702i
$127$			0.0106369i			0.000943870i	1.00000		0.000471935i	$0.000150222\pi$
$127$			0.0106369i			0.000943870i	−1.00000		0.000471935i	$0.999850\pi$
$128$	−17.3430	+	10.0130i	−1.53292	+	0.885029i
$129$	1.76128	−	3.05063i	0.155072	−	0.268593i
$130$		0			0
$131$	−6.88144	−	11.9190i	−0.601235	−	1.04137i	−0.992634	−	0.121148i	$-0.961342\pi$
$131$	−6.88144	−	11.9190i	−0.601235	−	1.04137i	0.391400	−	0.920221i	$-0.371991\pi$
$132$		−	18.0558i		−	1.57155i
$133$	2.66030	+	17.8346i	0.230677	+	1.54646i
$134$	−4.73024			−0.408630
$135$		0			0
$136$	−10.1532	+	17.5858i	−0.870627	+	1.50797i
$137$	−7.83331	−	4.52256i	−0.669245	−	0.386389i	0.126546	−	0.991961i	$-0.459611\pi$
$137$	−7.83331	−	4.52256i	−0.669245	−	0.386389i	−0.795790	+	0.605572i	$0.792944\pi$
$138$	8.19301	−	4.73024i	0.697435	−	0.402664i
$139$	21.3313			1.80930			0.904648	−	0.426160i	$-0.140134\pi$
$139$	21.3313			1.80930			0.904648	+	0.426160i	$0.140134\pi$
$140$		0			0
$141$	−3.29960			−0.277877
$142$	−25.0511	+	14.4633i	−2.10225	+	1.21373i
$143$	−5.39202	−	3.11309i	−0.450904	−	0.260329i
$144$	1.82392	−	3.15913i	0.151994	−	0.263261i
$145$		0			0
$146$	−15.0231			−1.24332
$147$	−2.04285	−	6.69528i	−0.168491	−	0.552217i
$148$		−	46.3278i		−	3.80812i
$149$	−7.90260	−	13.6877i	−0.647406	−	1.12134i	−0.983740	−	0.179598i	$-0.942520\pi$
$149$	−7.90260	−	13.6877i	−0.647406	−	1.12134i	0.336334	−	0.941743i	$-0.390813\pi$
$150$		0			0
$151$	−2.43204	+	4.21242i	−0.197917	+	0.342802i	−0.947853	−	0.318709i	$-0.896751\pi$
$151$	−2.43204	+	4.21242i	−0.197917	+	0.342802i	0.749936	+	0.661510i	$0.230084\pi$
$152$	27.9195	−	16.1193i	2.26457	−	1.30745i
$153$			4.29288i			0.347059i
$154$	−10.8366	+	27.4877i	−0.873238	+	2.21502i
$155$		0			0
$156$	−2.67748	−	4.63754i	−0.214370	−	0.371300i
$157$	5.69761	+	3.28952i	0.454719	+	0.262532i	0.709821	−	0.704382i	$-0.248776\pi$
$157$	5.69761	+	3.28952i	0.454719	+	0.262532i	−0.255102	+	0.966914i	$0.582109\pi$
$158$	13.0187	+	7.51633i	1.03571	+	0.597967i
$159$	4.72828	+	8.18962i	0.374977	+	0.649479i
$160$		0			0
$161$	−10.1570	+	1.51506i	−0.800481	+	0.119403i
$162$		−	2.43736i		−	0.191497i
$163$	−9.92750	+	5.73164i	−0.777582	+	0.448937i	−0.835572	−	0.549380i	$-0.814864\pi$
$163$	−9.92750	+	5.73164i	−0.777582	+	0.448937i	0.0579910	+	0.998317i	$0.481531\pi$
$164$	16.1064	−	27.8970i	1.25770	−	2.17839i
$165$		0			0
$166$	15.9026	+	27.5441i	1.23428	+	2.13784i
$167$			20.9170i			1.61861i	0.587390	+	0.809304i	$0.300156\pi$
$167$			20.9170i			1.61861i	−0.587390	+	0.809304i	$0.699844\pi$
$168$	−9.79655	+	7.78804i	−0.755820	+	0.600861i
$169$	11.1534			0.857957
$170$		0			0
$171$	3.40772	−	5.90235i	0.260595	−	0.451364i
$172$	12.0217	+	6.94072i	0.916645	+	0.529225i
$173$	9.66803	−	5.58184i	0.735047	−	0.424380i	−0.0852187	−	0.996362i	$-0.527159\pi$
$173$	9.66803	−	5.58184i	0.735047	−	0.424380i	0.820266	+	0.571983i	$0.193826\pi$
$174$	−9.74944			−0.739103
$175$		0			0
$176$	16.7138			1.25985
$177$	−0.606563	+	0.350199i	−0.0455921	+	0.0263226i
$178$	−0.618210	−	0.356924i	−0.0463368	−	0.0267526i
$179$	−8.75616	+	15.1661i	−0.654466	+	1.13357i	0.327561	+	0.944830i	$0.393773\pi$
$179$	−8.75616	+	15.1661i	−0.654466	+	1.13357i	−0.982027	+	0.188739i	$0.939560\pi$
$180$		0			0
$181$	20.2653			1.50631			0.753153	−	0.657845i	$-0.228532\pi$
$181$	20.2653			1.50631			0.753153	+	0.657845i	$0.228532\pi$
$182$	1.29282	+	8.66705i	0.0958299	+	0.642444i
$183$		−	5.00000i		−	0.369611i
$184$	9.18007	+	15.9004i	0.676764	+	1.17219i
$185$		0			0
$186$	9.88144	−	17.1152i	0.724543	−	1.25494i
$187$	−17.0341	+	9.83464i	−1.24566	+	0.719180i
$188$		−	13.0028i		−	0.948328i
$189$	−0.970361	+	2.46138i	−0.0705834	+	0.179039i
$190$		0			0
$191$	2.06796	+	3.58181i	0.149632	+	0.259171i	0.931092	−	0.364786i	$-0.118858\pi$
$191$	2.06796	+	3.58181i	0.149632	+	0.259171i	−0.781459	+	0.623956i	$0.785524\pi$
$192$	−7.52008	−	4.34172i	−0.542715	−	0.313336i
$193$	−4.12782	−	2.38320i	−0.297127	−	0.171547i	0.344024	−	0.938961i	$-0.388210\pi$
$193$	−4.12782	−	2.38320i	−0.297127	−	0.171547i	−0.641152	+	0.767414i	$0.721543\pi$
$194$	2.44555	+	4.23582i	0.175581	+	0.304114i
$195$		0			0
$196$	26.3842	−	8.05030i	1.88459	−	0.575022i
$197$		−	5.30351i		−	0.377860i	−0.981991	−	0.188930i	$-0.939498\pi$
$197$		−	5.30351i		−	0.377860i	0.981991	−	0.188930i	$-0.0605019\pi$
$198$	9.67142	−	5.58380i	0.687318	−	0.396823i
$199$	−1.13916	+	1.97309i	−0.0807532	+	0.139869i	−0.903574	−	0.428433i	$-0.859066\pi$
$199$	−1.13916	+	1.97309i	−0.0807532	+	0.139869i	0.822820	+	0.568301i	$0.192399\pi$
$200$		0			0
$201$	−0.970361	−	1.68071i	−0.0684440	−	0.118548i
$202$		−	15.3380i		−	1.07918i
$203$	9.84553	+	3.88144i	0.691021	+	0.272424i
$204$	−16.9170			−1.18443
$205$		0			0
$206$	−4.15745	+	7.20091i	−0.289663	+	0.501711i
$207$	3.36143	+	1.94072i	0.233635	+	0.134889i
$208$	4.29287	−	2.47849i	0.297657	−	0.171852i
$209$	31.2273			2.16004
$210$		0			0
$211$	−14.8052			−1.01923			−0.509616	−	0.860402i	$-0.670213\pi$
$211$	−14.8052			−1.01923			−0.509616	+	0.860402i	$0.670213\pi$
$212$	−32.2730	+	18.6328i	−2.21652	+	1.27971i
$213$	−10.2780	−	5.93400i	−0.704236	−	0.406591i
$214$	−3.86029	+	6.68621i	−0.263884	+	0.457060i
$215$		0			0
$216$	4.73024			0.321852
$217$	−16.7927	+	13.3498i	−1.13996	+	0.906247i
$218$			24.9430i			1.68935i
$219$	−3.08184	−	5.33791i	−0.208252	−	0.360702i
$220$		0			0
$221$	−2.91675	+	5.05196i	−0.196202	+	0.339832i
$222$	24.8151	−	14.3270i	1.66548	−	0.961565i
$223$		−	6.63479i		−	0.444299i	−0.975013	−	0.222149i	$-0.928693\pi$
$223$		−	6.63479i		−	0.444299i	0.975013	−	0.222149i	$-0.0713073\pi$
$224$	0.937424	+	1.17918i	0.0626343	+	0.0787874i
$225$		0			0
$226$	−3.85552	−	6.67795i	−0.256465	−	0.444211i
$227$	7.82166	+	4.51584i	0.519142	+	0.299727i	0.736584	−	0.676347i	$-0.236438\pi$
$227$	7.82166	+	4.51584i	0.519142	+	0.299727i	−0.217442	+	0.976073i	$0.569771\pi$
$228$	23.2595	+	13.4289i	1.54040	+	0.889349i
$229$	8.41640	+	14.5776i	0.556171	+	0.963317i	0.997811	+	0.0661248i	$0.0210635\pi$
$229$	8.41640	+	14.5776i	0.556171	+	0.963317i	−0.441640	+	0.897192i	$0.645603\pi$
$230$		0			0
$231$	−11.9898	+	1.78845i	−0.788868	+	0.117671i
$232$		−	18.9209i		−	1.24222i
$233$	−15.8421	+	9.14644i	−1.03785	+	0.599203i	−0.919224	−	0.393736i	$-0.871182\pi$
$233$	−15.8421	+	9.14644i	−1.03785	+	0.599203i	−0.118627	+	0.992939i	$0.537849\pi$
$234$	1.65604	−	2.86834i	0.108259	−	0.187510i
$235$		0			0
$236$	−1.38004	−	2.39030i	−0.0898328	−	0.155595i
$237$			6.16760i			0.400628i
$238$	25.7541	+	10.1532i	1.66939	+	0.658132i
$239$	−11.6309			−0.752339			−0.376170	−	0.926551i	$-0.622759\pi$
$239$	−11.6309			−0.752339			−0.376170	+	0.926551i	$0.622759\pi$
$240$		0			0
$241$	0.884806	−	1.53253i	0.0569953	−	0.0987188i	−0.836120	−	0.548547i	$-0.815181\pi$
$241$	0.884806	−	1.53253i	0.0569953	−	0.0987188i	0.893115	+	0.449828i	$0.148515\pi$
$242$	21.0940	+	12.1786i	1.35597	+	0.782870i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	19.7036			1.26139
$245$		0			0
$246$	19.9238			1.27029
$247$	8.02058	−	4.63068i	0.510337	−	0.294643i
$248$	33.2158	+	19.1771i	2.10920	+	1.21775i
$249$	−6.52452	+	11.3008i	−0.413475	+	0.716159i
$250$		0			0
$251$	−10.7004			−0.675403			−0.337702	−	0.941253i	$-0.609649\pi$
$251$	−10.7004			−0.675403			−0.337702	+	0.941253i	$0.609649\pi$
$252$	−9.69962	−	3.82392i	−0.611019	−	0.240884i
$253$			17.7842i			1.11808i
$254$	−0.0129630	−	0.0224525i	−0.000813368	−	0.00140879i
$255$		0			0
$256$	15.7218	−	27.2309i	0.982610	−	1.70193i
$257$	22.6560	−	13.0804i	1.41324	−	0.815935i	0.417549	−	0.908654i	$-0.362889\pi$
$257$	22.6560	−	13.0804i	1.41324	−	0.815935i	0.995692	+	0.0927193i	$0.0295559\pi$
$258$			8.58575i			0.534526i
$259$	−30.7635	+	4.58883i	−1.91155	+	0.285136i
$260$		0			0
$261$	−2.00000	−	3.46410i	−0.123797	−	0.214423i
$262$	29.0509	+	16.7726i	1.79477	+	1.03621i
$263$	11.5877	+	6.69016i	0.714528	+	0.412533i	0.812735	−	0.582633i	$-0.197977\pi$
$263$	11.5877	+	6.69016i	0.714528	+	0.412533i	−0.0982073	+	0.995166i	$0.531311\pi$
$264$	10.8366	+	18.7695i	0.666947	+	1.15519i
$265$		0			0
$266$	−27.3501	−	34.4036i	−1.67694	−	2.10942i
$267$		−	0.292877i		−	0.0179238i
$268$	6.62323	−	3.82392i	0.404578	−	0.233583i
$269$	−1.43540	+	2.48619i	−0.0875181	+	0.151586i	−0.906461	−	0.422289i	$-0.861227\pi$
$269$	−1.43540	+	2.48619i	−0.0875181	+	0.151586i	0.818943	+	0.573874i	$0.194560\pi$
$270$		0			0
$271$	−14.6710	−	25.4108i	−0.891197	−	1.54360i	−0.838442	−	0.544991i	$-0.816533\pi$
$271$	−14.6710	−	25.4108i	−0.891197	−	1.54360i	−0.0527557	−	0.998607i	$-0.516800\pi$
$272$		−	15.6597i		−	0.949512i
$273$	−2.81431	+	2.23731i	−0.170330	+	0.135408i
$274$	22.0462			1.33186
$275$		0			0
$276$	−7.64784	+	13.2465i	−0.460346	+	0.797343i
$277$	−17.3058	−	9.99152i	−1.03981	−	0.600332i	−0.120028	−	0.992771i	$-0.538298\pi$
$277$	−17.3058	−	9.99152i	−1.03981	−	0.600332i	−0.919778	+	0.392438i	$0.871632\pi$
$278$	−45.0264	+	25.9960i	−2.70050	+	1.55914i
$279$	8.10832			0.485432
$280$		0			0
$281$	7.12919			0.425292			0.212646	−	0.977129i	$-0.431792\pi$
$281$	7.12919			0.425292			0.212646	+	0.977129i	$0.431792\pi$
$282$	6.96485	−	4.02116i	0.414751	−	0.239456i
$283$	19.8104	+	11.4376i	1.17761	+	0.679892i	0.955460	−	0.295121i	$-0.0953598\pi$
$283$	19.8104	+	11.4376i	1.17761	+	0.679892i	0.222148	+	0.975013i	$0.428693\pi$
$284$	23.3842	−	40.5027i	1.38760	−	2.40339i
$285$		0			0
$286$	15.1754			0.897341
$287$	−20.1201	−	7.93204i	−1.18765	−	0.468214i
$288$		−	0.569365i		−	0.0335501i
$289$	0.714397	+	1.23737i	0.0420234	+	0.0727866i
$290$		0			0
$291$	−1.00336	+	1.73787i	−0.0588181	+	0.101876i
$292$	21.0352	−	12.1447i	1.23099	−	0.710714i
$293$			3.63088i			0.212118i	0.994360	+	0.106059i	$0.0338233\pi$
$293$			3.63088i			0.212118i	−0.994360	+	0.106059i	$0.966177\pi$
$294$	12.4715	+	11.6429i	0.727352	+	0.679029i
$295$		0			0
$296$	27.8047	+	48.1592i	1.61612	+	2.79920i
$297$	3.96799	+	2.29092i	0.230246	+	0.132933i
$298$	33.3619	+	19.2615i	1.93260	+	1.11579i
$299$	2.63721	+	4.56778i	0.152514	+	0.264161i
$300$		0			0
$301$	3.41816	−	8.67037i	0.197019	−	0.499752i
$302$		−	11.8555i		−	0.682208i
$303$	5.44979	−	3.14644i	0.313082	−	0.180758i
$304$	−12.4308	+	21.5308i	−0.712957	+	1.23488i
$305$		0			0
$306$	−5.23164	−	9.06147i	−0.299073	−	0.518010i
$307$		−	6.22687i		−	0.355387i	−0.984086	−	0.177693i	$-0.943137\pi$
$307$		−	6.22687i		−	0.355387i	0.984086	−	0.177693i	$-0.0568635\pi$
$308$	−7.04777	−	47.2483i	−0.401584	−	2.69222i
$309$	−3.41143			−0.194070
$310$		0			0
$311$	10.8154	−	18.7329i	0.613287	−	1.06224i	−0.377395	−	0.926052i	$-0.623180\pi$
$311$	10.8154	−	18.7329i	0.613287	−	1.06224i	0.990682	−	0.136193i	$-0.0434866\pi$
$312$	5.56666	+	3.21391i	0.315150	+	0.181952i
$313$	−20.6947	+	11.9481i	−1.16973	+	0.675345i	−0.953617	−	0.301022i	$-0.902672\pi$
$313$	−20.6947	+	11.9481i	−1.16973	+	0.675345i	−0.216115	+	0.976368i	$0.569339\pi$
$314$	−16.0355			−0.904933
$315$		0			0
$316$	−24.3048			−1.36725
$317$	7.42383	−	4.28615i	0.416964	−	0.240734i	−0.276813	−	0.960924i	$-0.589278\pi$
$317$	7.42383	−	4.28615i	0.416964	−	0.240734i	0.693778	+	0.720189i	$0.255945\pi$
$318$	−19.9611	−	11.5245i	−1.11936	−	0.646263i
$319$	9.16368	−	15.8720i	0.513068	−	0.888659i
$320$		0			0
$321$	−3.16760			−0.176798
$322$	19.5931	−	15.5761i	1.09188	−	0.868022i
$323$		−	29.2579i		−	1.62795i
$324$	1.97036	+	3.41277i	0.109464	+	0.189598i
$325$		0			0
$326$	13.9701	−	24.1969i	0.773731	−	1.34014i
$327$	−8.86256	+	5.11680i	−0.490101	+	0.282960i
$328$			38.6665i			2.13500i
$329$	−8.63440	+	1.28795i	−0.476030	+	0.0710067i
$330$		0			0
$331$	−6.75476	−	11.6996i	−0.371275	−	0.643067i	0.618487	−	0.785795i	$-0.287746\pi$
$331$	−6.75476	−	11.6996i	−0.371275	−	0.643067i	−0.989762	+	0.142728i	$0.954413\pi$
$332$	−44.5333	−	25.7113i	−2.44408	−	1.41109i
$333$	10.1811	+	5.87808i	0.557923	+	0.322117i
$334$	−25.4912	−	44.1520i	−1.39481	−	2.41589i
$335$		0			0
$336$	3.53973	−	8.97874i	0.193108	−	0.489830i
$337$			11.1016i			0.604742i	0.953190	+	0.302371i	$0.0977782\pi$
$337$			11.1016i			0.604742i	−0.953190	+	0.302371i	$0.902222\pi$
$338$	−23.5429	+	13.5925i	−1.28056	+	0.739333i
$339$	1.58184	−	2.73983i	0.0859139	−	0.148807i
$340$		0			0
$341$	18.5755	+	32.1737i	1.00592	+	1.74231i
$342$			16.6117i			0.898257i
$343$	−7.95912	−	16.7228i	−0.429752	−	0.902947i
$344$	−16.6626			−0.898385
$345$		0			0
$346$	−13.6050	+	23.5645i	−0.731407	+	1.26683i
$347$	−23.7154	−	13.6921i	−1.27311	−	0.735031i	−0.297539	−	0.954710i	$-0.596166\pi$
$347$	−23.7154	−	13.6921i	−1.27311	−	0.735031i	−0.975572	+	0.219678i	$0.929499\pi$
$348$	13.6511	−	7.88144i	0.731774	−	0.422490i
$349$	−6.17823			−0.330713			−0.165357	−	0.986234i	$-0.552878\pi$
$349$	−6.17823			−0.330713			−0.165357	+	0.986234i	$0.552878\pi$
$350$		0			0
$351$	1.35888			0.0725316
$352$	2.25923	−	1.30437i	0.120418	−	0.0695231i
$353$	−6.75950	−	3.90260i	−0.359772	−	0.207715i	0.309209	−	0.950994i	$-0.399936\pi$
$353$	−6.75950	−	3.90260i	−0.359772	−	0.207715i	−0.668981	+	0.743280i	$0.733269\pi$
$354$	0.853561	−	1.47841i	0.0453663	−	0.0785767i
$355$		0			0
$356$	1.15415			0.0611697
$357$	1.67565	+	11.2336i	0.0886850	+	0.594545i
$358$		−	42.6838i		−	2.25591i
$359$	2.05732	+	3.56339i	0.108581	+	0.188068i	0.915196	−	0.403010i	$-0.132036\pi$
$359$	2.05732	+	3.56339i	0.108581	+	0.188068i	−0.806614	+	0.591078i	$0.798703\pi$
$360$		0			0
$361$	−13.7251	+	23.7726i	−0.722375	+	1.25119i
$362$	−42.7763	+	24.6969i	−2.24827	+	1.29804i
$363$			9.99328i			0.524511i
$364$	−8.81662	−	11.0904i	−0.462117	−	0.581295i
$365$		0			0
$366$	6.09340	+	10.5541i	0.318507	+	0.551670i
$367$	18.8893	+	10.9058i	0.986015	+	0.569276i	0.904081	−	0.427361i	$-0.140557\pi$
$367$	18.8893	+	10.9058i	0.986015	+	0.569276i	0.0819346	+	0.996638i	$0.473890\pi$
$368$	−12.2620	−	7.07945i	−0.639199	−	0.369042i
$369$	4.08716	+	7.07917i	0.212769	+	0.368527i
$370$		0			0
$371$	15.5696	+	19.5850i	0.808336	+	1.01680i
$372$			31.9526i			1.65667i
$373$	−2.54430	+	1.46895i	−0.131739	+	0.0760596i	−0.564421	−	0.825487i	$-0.690901\pi$
$373$	−2.54430	+	1.46895i	−0.131739	+	0.0760596i	0.432682	+	0.901547i	$0.357567\pi$
$374$	23.9706	−	41.5182i	1.23949	−	2.14686i
$375$		0			0
$376$	7.80395	+	13.5168i	0.402458	+	0.697078i
$377$		−	5.43552i		−	0.279943i
$378$	−0.951383	−	6.37808i	−0.0489339	−	0.328053i
$379$	8.85384			0.454791			0.227396	−	0.973802i	$-0.426979\pi$
$379$	8.85384			0.454791			0.227396	+	0.973802i	$0.426979\pi$
$380$		0			0
$381$	0.00531844	−	0.00921181i	0.000272472	−	0.000471935i
$382$	−8.73016	−	5.04036i	−0.446674	−	0.257887i
$383$	15.2756	−	8.81935i	0.780545	−	0.450648i	−0.0560783	−	0.998426i	$-0.517860\pi$
$383$	15.2756	−	8.81935i	0.780545	−	0.450648i	0.836623	+	0.547778i	$0.184526\pi$
$384$	20.0259			1.02194
$385$		0			0
$386$	11.6174			0.591312
$387$	−3.05063	+	1.76128i	−0.155072	+	0.0895310i
$388$	−6.84848	−	3.95397i	−0.347679	−	0.200732i
$389$	9.09388	−	15.7511i	0.461078	−	0.798611i	−0.537937	−	0.842985i	$-0.680796\pi$
$389$	9.09388	−	15.7511i	0.461078	−	0.798611i	0.999015	+	0.0443743i	$0.0141294\pi$
$390$		0			0
$391$	16.6626			0.842662
$392$	−22.5957	+	24.2037i	−1.14125	+	1.22247i
$393$			13.7629i			0.694246i
$394$	6.46329	+	11.1947i	0.325616	+	0.563983i
$395$		0			0
$396$	−9.02788	+	15.6368i	−0.453668	+	0.785776i
$397$	−9.11376	+	5.26183i	−0.457407	+	0.264084i	−0.710953	−	0.703239i	$-0.751736\pi$
$397$	−9.11376	+	5.26183i	−0.457407	+	0.264084i	0.253547	+	0.967323i	$0.418403\pi$
$398$		−	5.55310i		−	0.278352i
$399$	6.61344	−	16.7754i	0.331086	−	0.839821i
$400$		0			0
$401$	−1.79428	−	3.10779i	−0.0896022	−	0.155196i	0.817741	−	0.575587i	$-0.195226\pi$
$401$	−1.79428	−	3.10779i	−0.0896022	−	0.155196i	−0.907343	+	0.420391i	$0.861893\pi$
$402$	4.09651	+	2.36512i	0.204315	+	0.117961i
$403$	9.54207	+	5.50911i	0.475324	+	0.274429i
$404$	12.3992	+	21.4761i	0.616885	+	1.06848i
$405$		0			0
$406$	−25.5123	+	3.80553i	−1.26616	+	0.188865i
$407$			53.8649i			2.66998i
$408$	17.5858	−	10.1532i	0.870627	−	0.502656i
$409$	−11.2652	+	19.5119i	−0.557028	+	0.964801i	0.440715	+	0.897647i	$0.354725\pi$
$409$	−11.2652	+	19.5119i	−0.557028	+	0.964801i	−0.997743	+	0.0671536i	$0.978608\pi$
$410$		0			0
$411$	4.52256	+	7.83331i	0.223082	+	0.386389i
$412$		−	13.4435i		−	0.662314i
$413$	−1.45056	+	1.15316i	−0.0713773	+	0.0567434i
$414$	−9.46047			−0.464957
$415$		0			0
$416$	0.386849	−	0.670042i	0.0189668	−	0.0328515i
$417$	−18.4734	−	10.6656i	−0.904648	−	0.522299i
$418$	−65.9150	+	38.0560i	−3.22401	+	1.86138i
$419$	−39.4055			−1.92508			−0.962542	−	0.271131i	$-0.912602\pi$
$419$	−39.4055			−1.92508			−0.962542	+	0.271131i	$0.912602\pi$
$420$		0			0
$421$	−8.57121			−0.417735			−0.208867	−	0.977944i	$-0.566978\pi$
$421$	−8.57121			−0.417735			−0.208867	+	0.977944i	$0.566978\pi$
$422$	31.2510	−	18.0428i	1.52128	−	0.878310i
$423$	2.85754	+	1.64980i	0.138938	+	0.0802161i
$424$	22.3659	−	38.7389i	1.08618	−	1.88132i
$425$		0			0
$426$	28.9266			1.40150
$427$	−1.95167	−	13.0840i	−0.0944478	−	0.633179i
$428$		−	12.4826i		−	0.603370i
$429$	3.11309	+	5.39202i	0.150301	+	0.260329i
$430$		0			0
$431$	−0.641120	+	1.11045i	−0.0308817	+	0.0534886i	−0.881053	−	0.473017i	$-0.843165\pi$
$431$	−0.641120	+	1.11045i	−0.0308817	+	0.0534886i	0.850172	+	0.526506i	$0.176498\pi$
$432$	−3.15913	+	1.82392i	−0.151994	+	0.0877535i
$433$		−	5.21233i		−	0.250488i	−0.992126	−	0.125244i	$-0.960029\pi$
$433$		−	5.21233i		−	0.250488i	0.992126	−	0.125244i	$-0.0399714\pi$
$434$	19.1771	−	48.6440i	0.920532	−	2.33499i
$435$		0			0
$436$	−20.1639	−	34.9249i	−0.965675	−	1.67260i
$437$	−22.9096	−	13.2269i	−1.09592	−	0.632727i
$438$	13.0104	+	7.51156i	0.621661	+	0.358916i
$439$	9.81404	+	16.9984i	0.468398	+	0.811290i	0.999348	−	0.0361138i	$-0.0114979\pi$
$439$	9.81404	+	16.9984i	0.468398	+	0.811290i	−0.530949	+	0.847404i	$0.678165\pi$
$440$		0			0
$441$	−1.57848	+	6.81971i	−0.0751657	+	0.324748i
$442$		−	14.2183i		−	0.676298i
$443$	15.6185	−	9.01736i	0.742059	−	0.428428i	−0.0807587	−	0.996734i	$-0.525734\pi$
$443$	15.6185	−	9.01736i	0.742059	−	0.428428i	0.822817	+	0.568306i	$0.192401\pi$
$444$	−23.1639	+	40.1210i	−1.09931	+	1.90406i
$445$		0			0
$446$	8.08569	+	14.0048i	0.382869	+	0.663148i
$447$			15.8052i			0.747560i
$448$	−21.3732	−	8.42607i	−1.00979	−	0.398094i
$449$	6.99719			0.330218			0.165109	−	0.986275i	$-0.447202\pi$
$449$	6.99719			0.330218			0.165109	+	0.986275i	$0.447202\pi$
$450$		0			0
$451$	−18.7267	+	32.4356i	−0.881807	+	1.52733i
$452$	10.7969	+	6.23360i	0.507844	+	0.293204i
$453$	4.21242	−	2.43204i	0.197917	−	0.114267i
$454$	−22.0134			−1.03314
$455$		0			0
$456$	−32.2386			−1.50971
$457$	32.7711	−	18.9204i	1.53297	−	0.885059i	0.533744	−	0.845646i	$-0.320785\pi$
$457$	32.7711	−	18.9204i	1.53297	−	0.885059i	0.999223	−	0.0394126i	$-0.0125487\pi$
$458$	−35.5309	−	20.5138i	−1.66025	−	0.958547i
$459$	2.14644	−	3.71774i	0.100187	−	0.173529i
$460$		0			0
$461$	24.0903			1.12200			0.560998	−	0.827817i	$-0.310418\pi$
$461$	24.0903			1.12200			0.560998	+	0.827817i	$0.310418\pi$
$462$	23.1286	−	18.3868i	1.07604	−	0.855430i
$463$		−	23.1154i		−	1.07427i	−0.843498	−	0.537133i	$-0.819507\pi$
$463$		−	23.1154i		−	1.07427i	0.843498	−	0.537133i	$-0.180493\pi$
$464$	7.29569	+	12.6365i	0.338694	+	0.586635i
$465$		0			0
$466$	22.2932	−	38.6129i	1.03271	−	1.78871i
$467$	10.8812	−	6.28224i	0.503520	−	0.290707i	−0.226646	−	0.973977i	$-0.572776\pi$
$467$	10.8812	−	6.28224i	0.503520	−	0.290707i	0.730166	+	0.683270i	$0.239443\pi$
$468$			5.35497i			0.247533i
$469$	−3.19528	−	4.01933i	−0.147544	−	0.185595i
$470$		0			0
$471$	−3.28952	−	5.69761i	−0.151573	−	0.262532i
$472$	2.86919	+	1.65653i	0.132065	+	0.0762478i
$473$	−13.9775	−	8.06992i	−0.642686	−	0.371055i
$474$	−7.51633	−	13.0187i	−0.345236	−	0.597967i
$475$		0			0
$476$	−44.2685	+	6.60329i	−2.02904	+	0.302661i
$477$		−	9.45656i		−	0.432986i
$478$	24.5506	−	14.1743i	1.12292	−	0.648318i
$479$	−1.01540	+	1.75873i	−0.0463950	+	0.0803586i	−0.888290	−	0.459282i	$-0.848107\pi$
$479$	−1.01540	+	1.75873i	−0.0463950	+	0.0803586i	0.841895	+	0.539641i	$0.181440\pi$
$480$		0			0
$481$	7.98761	+	13.8349i	0.364203	+	0.630819i
$482$			4.31318i			0.196460i
$483$	9.55371	+	3.76640i	0.434709	+	0.171377i
$484$	−39.3807			−1.79003
$485$		0			0
$486$	−1.21868	+	2.11082i	−0.0552804	+	0.0957485i
$487$	−23.8352	−	13.7613i	−1.08008	−	0.623583i	−0.149160	−	0.988813i	$-0.547657\pi$
$487$	−23.8352	−	13.7613i	−1.08008	−	0.623583i	−0.930917	+	0.365230i	$0.880990\pi$
$488$	−20.4825	+	11.8256i	−0.927200	+	0.535319i
$489$	11.4633			0.518388
$490$		0			0
$491$	0.459373			0.0207312			0.0103656	−	0.999946i	$-0.496700\pi$
$491$	0.459373			0.0207312			0.0103656	+	0.999946i	$0.496700\pi$
$492$	−27.8970	+	16.1064i	−1.25770	+	0.726131i
$493$	−14.8710	−	8.58575i	−0.669754	−	0.386683i
$494$	−11.2866	+	19.5490i	−0.507810	+	0.879553i
$495$		0			0
$496$	−29.5779			−1.32809
$497$	−29.2117	−	11.5162i	−1.31032	−	0.516574i
$498$		−	31.8052i		−	1.42523i
$499$	−5.81915	−	10.0791i	−0.260501	−	0.451201i	0.705874	−	0.708337i	$-0.250554\pi$
$499$	−5.81915	−	10.0791i	−0.260501	−	0.451201i	−0.966375	+	0.257136i	$0.917221\pi$
$500$		0			0
$501$	10.4585	−	18.1147i	0.467252	−	0.809304i
$502$	22.5866	−	13.0404i	1.00809	−	0.582020i
$503$			32.4254i			1.44578i	0.690964	+	0.722890i	$0.257187\pi$
$503$			32.4254i			1.44578i	−0.690964	+	0.722890i	$0.742813\pi$
$504$	12.3781	−	1.84637i	0.551364	−	0.0822439i
$505$		0			0
$506$	−21.6732	−	37.5391i	−0.963491	−	1.66882i
$507$	−9.65917	−	5.57672i	−0.428979	−	0.247671i
$508$	0.0363012	+	0.0209585i	0.00161060	+	0.000929883i
$509$	8.51975	+	14.7566i	0.377631	+	0.654077i	0.990717	−	0.135940i	$-0.0434053\pi$
$509$	8.51975	+	14.7566i	0.377631	+	0.654077i	−0.613086	+	0.790016i	$0.710072\pi$
$510$		0			0
$511$	−10.1481	−	12.7653i	−0.448927	−	0.564703i
$512$			36.5873i			1.61695i
$513$	−5.90235	+	3.40772i	−0.260595	+	0.150455i
$514$	−31.8817	+	55.2208i	−1.40624	+	2.43568i
$515$		0			0
$516$	−6.94072	−	12.0217i	−0.305548	−	0.529225i
$517$			15.1183i			0.664900i
$518$	59.3438	−	47.1770i	2.60742	−	2.07284i
$519$	−11.1637			−0.490031
$520$		0			0
$521$	−1.30633	+	2.26262i	−0.0572312	+	0.0991273i	−0.893222	−	0.449617i	$-0.851561\pi$
$521$	−1.30633	+	2.26262i	−0.0572312	+	0.0991273i	0.835990	+	0.548744i	$0.184894\pi$
$522$	8.44326	+	4.87472i	0.369552	+	0.213361i
$523$	24.2515	−	14.0016i	1.06044	−	0.612247i	0.134889	−	0.990861i	$-0.456932\pi$
$523$	24.2515	−	14.0016i	1.06044	−	0.612247i	0.925555	+	0.378613i	$0.123599\pi$
$524$	−54.2357			−2.36930
$525$		0			0
$526$	−32.6127			−1.42198
$527$	30.1446	−	17.4040i	1.31312	−	0.758130i
$528$	−14.4746	−	8.35692i	−0.629927	−	0.363688i
$529$	−3.96720	+	6.87139i	−0.172487	+	0.298756i
$530$		0			0
$531$	0.700398			0.0303947
$532$	66.1072	+	26.0617i	2.86611	+	1.12992i
$533$			11.1079i			0.481137i
$534$	0.356924	+	0.618210i	0.0154456	+	0.0267526i
$535$		0			0
$536$	−4.59004	+	7.95018i	−0.198259	+	0.343395i
$537$	15.1661	−	8.75616i	0.654466	−	0.377856i
$538$		−	6.99719i		−	0.301670i
$539$	−30.6767	+	9.36002i	−1.32134	+	0.403164i
$540$		0			0
$541$	3.72848	+	6.45792i	0.160300	+	0.277648i	0.934976	−	0.354710i	$-0.115421\pi$
$541$	3.72848	+	6.45792i	0.160300	+	0.277648i	−0.774676	+	0.632358i	$0.782087\pi$
$542$	61.9354	+	35.7584i	2.66035	+	1.53595i
$543$	−17.5502	−	10.1326i	−0.753153	−	0.434833i
$544$	−1.22211	−	2.11675i	−0.0523974	−	0.0907549i
$545$		0			0
$546$	3.21391	−	8.15229i	0.137543	−	0.348886i
$547$		−	16.7640i		−	0.716776i	−0.933573	−	0.358388i	$-0.883326\pi$
$547$		−	16.7640i		−	0.716776i	0.933573	−	0.358388i	$-0.116674\pi$
$548$	−30.8689	+	17.8222i	−1.31865	+	0.761325i
$549$	−2.50000	+	4.33013i	−0.106697	+	0.184805i
$550$		0			0
$551$	13.6309	+	23.6094i	0.580695	+	1.00579i
$552$		−	18.3601i		−	0.781460i
$553$	2.40742	+	16.1394i	0.102374	+	0.686316i
$554$	48.7058			2.06931
$555$		0			0
$556$	42.0303	−	72.7987i	1.78248	−	3.08735i
$557$	13.0295	+	7.52256i	0.552076	+	0.318741i	0.749959	−	0.661484i	$-0.230073\pi$
$557$	13.0295	+	7.52256i	0.552076	+	0.318741i	−0.197883	+	0.980226i	$0.563407\pi$
$558$	−17.1152	+	9.88144i	−0.724543	+	0.418315i
$559$	−4.78674			−0.202458
$560$		0			0
$561$	19.6693			0.830438
$562$	−15.0484	+	8.68820i	−0.634779	+	0.366490i
$563$	18.3317	+	10.5838i	0.772588	+	0.446054i	0.833797	−	0.552071i	$-0.186162\pi$
$563$	18.3317	+	10.5838i	0.772588	+	0.446054i	−0.0612090	+	0.998125i	$0.519496\pi$
$564$	−6.50141	+	11.2608i	−0.273759	+	0.474164i
$565$		0			0
$566$	−55.7549			−2.34355
$567$	2.07105	−	1.64644i	0.0869758	−	0.0691439i
$568$			56.1384i			2.35552i
$569$	22.4884	+	38.9510i	0.942761	+	1.63291i	0.760173	+	0.649720i	$0.225114\pi$
$569$	22.4884	+	38.9510i	0.942761	+	1.63291i	0.182587	+	0.983190i	$0.441553\pi$
$570$		0			0
$571$	−19.6119	+	33.9688i	−0.820732	+	1.42155i	0.0844066	+	0.996431i	$0.473101\pi$
$571$	−19.6119	+	33.9688i	−0.820732	+	1.42155i	−0.905138	+	0.425117i	$0.860233\pi$
$572$	−21.2485	+	12.2678i	−0.888443	+	0.512943i
$573$		−	4.13592i		−	0.172780i
$574$	52.1365	−	7.77691i	2.17613	−	0.324602i
$575$		0			0
$576$	4.34172	+	7.52008i	0.180905	+	0.313336i
$577$	−6.11690	−	3.53160i	−0.254650	−	0.147022i	0.367242	−	0.930126i	$-0.380302\pi$
$577$	−6.11690	−	3.53160i	−0.254650	−	0.147022i	−0.621892	+	0.783103i	$0.713636\pi$
$578$	−3.01592	−	1.74124i	−0.125446	−	0.0724262i
$579$	2.38320	+	4.12782i	0.0990424	+	0.171547i
$580$		0			0
$581$	−12.6623	+	32.1187i	−0.525320	+	1.33251i
$582$		−	4.89111i		−	0.202743i
$583$	37.5236	−	21.6642i	1.55407	−	0.897241i
$584$	−14.5778	+	25.2496i	−0.603235	+	1.04483i
$585$		0			0
$586$	−4.42488	−	7.66412i	−0.182790	−	0.316602i
$587$		−	13.7629i		−	0.568055i	−0.958816	−	0.284028i	$-0.908329\pi$
$587$		−	13.7629i		−	0.568055i	0.958816	−	0.284028i	$-0.0916707\pi$
$588$	−26.8746	−	6.22035i	−1.10829	−	0.256523i
$589$	−55.2618			−2.27702
$590$		0			0
$591$	−2.65176	+	4.59298i	−0.109079	+	0.188930i
$592$	−37.1392	−	21.4423i	−1.52641	−	0.881274i
$593$	25.6611	−	14.8154i	1.05377	−	0.608397i	0.130071	−	0.991505i	$-0.458479\pi$
$593$	25.6611	−	14.8154i	1.05377	−	0.608397i	0.923704	+	0.383107i	$0.125146\pi$
$594$	−11.1676			−0.458212
$595$		0			0
$596$	−62.2839			−2.55125
$597$	1.97309	−	1.13916i	0.0807532	−	0.0466229i
$598$	−11.1333	−	6.42782i	−0.455275	−	0.262853i
$599$	16.5905	−	28.7356i	0.677870	−	1.17411i	−0.297751	−	0.954644i	$-0.596236\pi$
$599$	16.5905	−	28.7356i	0.677870	−	1.17411i	0.975621	−	0.219462i	$-0.0704303\pi$
$600$		0			0
$601$	27.1161			1.10609			0.553045	−	0.833151i	$-0.313466\pi$
$601$	27.1161			1.10609			0.553045	+	0.833151i	$0.313466\pi$
$602$	3.35131	+	22.4672i	0.136589	+	0.915695i
$603$			1.94072i			0.0790323i
$604$	9.58400	+	16.6000i	0.389967	+	0.675443i
$605$		0			0
$606$	−7.66900	+	13.2831i	−0.311532	+	0.539589i
$607$	−20.4108	+	11.7842i	−0.828450	+	0.478306i	−0.853322	−	0.521385i	$-0.825416\pi$
$607$	−20.4108	+	11.7842i	−0.828450	+	0.478306i	0.0248717	+	0.999691i	$0.492082\pi$
$608$			3.88047i			0.157374i
$609$	−6.58575	−	8.28419i	−0.266868	−	0.335692i
$610$		0			0
$611$	2.24188	+	3.88305i	0.0906968	+	0.157091i
$612$	14.6506	+	8.45852i	0.592215	+	0.341915i
$613$	16.0380	+	9.25952i	0.647767	+	0.373989i	0.787600	−	0.616186i	$-0.211323\pi$
$613$	16.0380	+	9.25952i	0.647767	+	0.373989i	−0.139833	+	0.990175i	$0.544657\pi$
$614$	7.58857	+	13.1438i	0.306250	+	0.530440i
$615$		0			0
$616$	35.6836	+	44.8862i	1.43773	+	1.80852i
$617$		−	24.5653i		−	0.988961i	−0.869189	−	0.494480i	$-0.835358\pi$
$617$		−	24.5653i		−	0.988961i	0.869189	−	0.494480i	$-0.164642\pi$
$618$	7.20091	−	4.15745i	0.289663	−	0.167237i
$619$	10.6360	−	18.4221i	0.427497	−	0.740446i	−0.569153	−	0.822232i	$-0.692729\pi$
$619$	10.6360	−	18.4221i	0.427497	−	0.740446i	0.996650	+	0.0817851i	$0.0260621\pi$
$620$		0			0
$621$	−1.94072	−	3.36143i	−0.0778785	−	0.134889i
$622$			52.7222i			2.11397i
$623$	−0.114320	−	0.766401i	−0.00458013	−	0.0307052i
$624$	−4.95698			−0.198438
$625$		0			0
$626$	29.1218	−	50.4404i	1.16394	−	2.01600i
$627$	−27.0436	−	15.6136i	−1.08002	−	0.623549i
$628$	22.4527	−	12.9631i	0.895960	−	0.517283i
$629$	50.4678			2.01228
$630$		0			0
$631$	14.3899			0.572851			0.286426	−	0.958102i	$-0.407533\pi$
$631$	14.3899			0.572851			0.286426	+	0.958102i	$0.407533\pi$
$632$	25.2656	−	14.5871i	1.00501	−	0.580244i
$633$	12.8217	+	7.40260i	0.509616	+	0.294227i
$634$	−10.4469	+	18.0946i	−0.414899	+	0.718627i
$635$		0			0
$636$	37.2657			1.47768
$637$	−6.49117	+	6.95312i	−0.257190	+	0.275492i
$638$			44.6704i			1.76852i
$639$	5.93400	+	10.2780i	0.234745	+	0.406591i
$640$		0			0
$641$	13.8578	−	24.0023i	0.547348	−	0.948035i	−0.451107	−	0.892470i	$-0.648971\pi$
$641$	13.8578	−	24.0023i	0.547348	−	0.948035i	0.998455	−	0.0555653i	$-0.0176961\pi$
$642$	6.68621	−	3.86029i	0.263884	−	0.152353i
$643$		−	44.6065i		−	1.75911i	−0.475799	−	0.879554i	$-0.657841\pi$
$643$		−	44.6065i		−	1.75911i	0.475799	−	0.879554i	$-0.342159\pi$
$644$	−14.8423	+	37.6485i	−0.584870	+	1.48356i
$645$		0			0
$646$	35.6560	+	61.7579i	1.40286	+	2.42983i
$647$	11.4335	+	6.60116i	0.449499	+	0.259518i	0.707619	−	0.706595i	$-0.249770\pi$
$647$	11.4335	+	6.60116i	0.449499	+	0.259518i	−0.258120	+	0.966113i	$0.583103\pi$
$648$	−4.09651	−	2.36512i	−0.160926	−	0.0929106i
$649$	1.60456	+	2.77917i	0.0629844	+	0.109092i
$650$		0			0
$651$	21.2178	−	3.16495i	0.831593	−	0.124044i
$652$			45.1736i			1.76914i
$653$	−10.7486	+	6.20572i	−0.420626	+	0.242848i	−0.695345	−	0.718676i	$-0.744748\pi$
$653$	−10.7486	+	6.20572i	−0.420626	+	0.242848i	0.274719	+	0.961525i	$0.411415\pi$
$654$	12.4715	−	21.6012i	0.487673	−	0.844675i
$655$		0			0
$656$	−14.9093	−	25.8237i	−0.582111	−	1.00825i
$657$			6.16368i			0.240468i
$658$	16.6560	−	13.2412i	0.649319	−	0.516195i
$659$	−18.3391			−0.714390			−0.357195	−	0.934030i	$-0.616267\pi$
$659$	−18.3391			−0.714390			−0.357195	+	0.934030i	$0.616267\pi$
$660$		0			0
$661$	21.4638	−	37.1765i	0.834846	−	1.44600i	−0.0593089	−	0.998240i	$-0.518890\pi$
$661$	21.4638	−	37.1765i	0.834846	−	1.44600i	0.894155	−	0.447757i	$-0.147777\pi$
$662$	28.5161	+	16.4638i	1.10831	+	0.639883i
$663$	5.05196	−	2.91675i	0.196202	−	0.113277i
$664$	61.7250			2.39540
$665$		0			0
$666$	−28.6540			−1.11032
$667$	−13.4457	+	7.76289i	−0.520620	+	0.300580i
$668$	71.3849	+	41.2141i	2.76197	+	1.59462i
$669$	−3.31740	+	5.74590i	−0.128258	+	0.222149i
$670$		0			0
$671$	−22.9092			−0.884400
$672$	−0.222242	−	1.48991i	−0.00857318	−	0.0574747i
$673$		−	17.9400i		−	0.691537i	−0.938320	−	0.345768i	$-0.887618\pi$
$673$		−	17.9400i		−	0.691537i	0.938320	−	0.345768i	$-0.112382\pi$
$674$	−13.5293	−	23.4334i	−0.521129	−	0.902621i
$675$		0			0
$676$	21.9763	−	38.0641i	0.845243	−	1.46400i
$677$	−22.2635	+	12.8538i	−0.855656	+	0.494013i	−0.862555	−	0.505963i	$-0.831137\pi$
$677$	−22.2635	+	12.8538i	−0.855656	+	0.494013i	0.00689904	+	0.999976i	$0.497804\pi$
$678$			7.71104i			0.296141i
$679$	−1.94725	+	4.93931i	−0.0747285	+	0.189553i
$680$		0			0
$681$	−4.51584	−	7.82166i	−0.173047	−	0.299727i
$682$	−78.4190	−	45.2752i	−3.00282	−	1.73368i
$683$	−14.1249	−	8.15500i	−0.540474	−	0.312043i	0.204797	−	0.978804i	$-0.434346\pi$
$683$	−14.1249	−	8.15500i	−0.540474	−	0.312043i	−0.745271	+	0.666762i	$0.767680\pi$
$684$	−13.4289	−	23.2595i	−0.513466	−	0.889349i
$685$		0			0
$686$	37.1800	+	25.5991i	1.41954	+	0.977380i
$687$		−	16.8328i		−	0.642211i
$688$	11.1282	−	6.42488i	0.424260	−	0.244946i
$689$	6.42517	−	11.1287i	0.244779	−	0.423970i
$690$		0			0
$691$	−8.44452	−	14.6263i	−0.321245	−	0.556412i	0.659501	−	0.751704i	$-0.270768\pi$
$691$	−8.44452	−	14.6263i	−0.321245	−	0.556412i	−0.980745	+	0.195292i	$0.937435\pi$
$692$		−	43.9930i		−	1.67236i
$693$	11.2777	+	4.44604i	0.428403	+	0.168891i
$694$	66.7452			2.53361
$695$		0			0
$696$	−9.46047	+	16.3860i	−0.358598	+	0.621111i
$697$	30.3900	+	17.5457i	1.15110	+	0.664590i
$698$	13.0411	−	7.52929i	0.493613	−	0.284988i
$699$	18.2929			0.691900
$700$		0			0
$701$	31.2329			1.17965			0.589825	−	0.807531i	$-0.299197\pi$
$701$	31.2329			1.17965			0.589825	+	0.807531i	$0.299197\pi$
$702$	−2.86834	+	1.65604i	−0.108259	+	0.0625032i
$703$	−69.3889	−	40.0617i	−2.61705	−	1.51096i
$704$	−19.8931	+	34.4558i	−0.749748	+	1.29860i
$705$		0			0
$706$	19.0241			0.715981
$707$	13.0329	−	10.3608i	0.490151	−	0.389659i
$708$			2.76008i			0.103730i
$709$	8.45320	+	14.6414i	0.317467	+	0.549868i	0.979959	−	0.199201i	$-0.0638345\pi$
$709$	8.45320	+	14.6414i	0.317467	+	0.549868i	−0.662492	+	0.749069i	$0.730501\pi$
$710$		0			0
$711$	3.08380	−	5.34130i	0.115651	−	0.200314i
$712$	−1.19977	+	0.692689i	−0.0449634	+	0.0259596i
$713$		−	31.4720i		−	1.17863i
$714$	−17.2272	−	21.6700i	−0.644710	−	0.810978i
$715$		0			0
$716$	34.5056	+	59.7655i	1.28953	+	2.23354i
$717$	10.0726	+	5.81544i	0.376170	+	0.217182i
$718$	−8.68525	−	5.01443i	−0.324131	−	0.187137i
$719$	−6.38188	−	11.0537i	−0.238004	−	0.412235i	0.722138	−	0.691750i	$-0.243160\pi$
$719$	−6.38188	−	11.0537i	−0.238004	−	0.412235i	−0.960141	+	0.279515i	$0.909826\pi$
$720$		0			0
$721$	−8.92704	+	1.33160i	−0.332460	+	0.0495913i
$722$		−	66.9061i		−	2.48999i
$723$	−1.53253	+	0.884806i	−0.0569953	+	0.0329063i
$724$	39.9299	−	69.1606i	1.48398	−	2.57033i
$725$		0			0
$726$	−12.1786	−	21.0940i	−0.451990	−	0.782870i
$727$			12.5649i			0.466006i	0.972476	+	0.233003i	$0.0748551\pi$
$727$			12.5649i			0.466006i	−0.972476	+	0.233003i	$0.925145\pi$
$728$	15.8213	+	6.23731i	0.586377	+	0.231170i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−7.56097	+	13.0960i	−0.279652	+	0.484372i
$732$	−17.0638	−	9.85180i	−0.630697	−	0.364133i
$733$	−33.3594	+	19.2601i	−1.23216	+	0.711387i	−0.967480	−	0.252949i	$-0.918599\pi$
$733$	−33.3594	+	19.2601i	−1.23216	+	0.711387i	−0.264679	+	0.964337i	$0.585266\pi$
$734$	−53.1625			−1.96227
$735$		0			0
$736$	−2.20996			−0.0814601
$737$	−7.70077	+	4.44604i	−0.283661	+	0.163772i
$738$	−17.2545	−	9.96188i	−0.635146	−	0.366702i
$739$	−2.28365	+	3.95539i	−0.0840053	+	0.145501i	−0.904967	−	0.425482i	$-0.860105\pi$
$739$	−2.28365	+	3.95539i	−0.0840053	+	0.145501i	0.820962	+	0.570983i	$0.193438\pi$
$740$		0			0
$741$	−9.26137			−0.340225
$742$	−56.7325	−	22.3659i	−2.08272	−	0.821078i
$743$			36.7043i			1.34655i	0.739392	+	0.673275i	$0.235113\pi$
$743$			36.7043i			1.34655i	−0.739392	+	0.673275i	$0.764887\pi$
$744$	−19.1771	−	33.2158i	−0.703068	−	1.21775i
$745$		0			0
$746$	3.58037	−	6.20139i	0.131087	−	0.227049i
$747$	11.3008	−	6.52452i	0.413475	−	0.238720i
$748$			77.5112i			2.83409i
$749$	−8.28896	+	1.23642i	−0.302872	+	0.0451778i
$750$		0			0
$751$	27.2046	+	47.1197i	0.992710	+	1.71942i	0.600737	+	0.799447i	$0.294874\pi$
$751$	27.2046	+	47.1197i	0.992710	+	1.71942i	0.391973	+	0.919977i	$0.371793\pi$
$752$	−10.4239	−	6.01822i	−0.380119	−	0.219462i
$753$	9.26682	+	5.35020i	0.337702	+	0.194972i
$754$	6.62416	+	11.4734i	0.241238	+	0.417836i
$755$		0			0
$756$	6.48816	+	8.16142i	0.235972	+	0.296828i
$757$			13.1704i			0.478687i	0.970935	+	0.239343i	$0.0769321\pi$
$757$			13.1704i			0.478687i	−0.970935	+	0.239343i	$0.923068\pi$
$758$	−18.6888	+	10.7900i	−0.678809	+	0.391910i
$759$	8.89208	−	15.4015i	0.322762	−	0.559040i
$760$		0			0
$761$	−24.1362	−	41.8051i	−0.874937	−	1.51543i	−0.856830	−	0.515599i	$-0.827570\pi$
$761$	−24.1362	−	41.8051i	−0.874937	−	1.51543i	−0.0181063	−	0.999836i	$-0.505764\pi$
$762$			0.0259259i			0.000939196i
$763$	−21.1943	+	16.8490i	−0.767284	+	0.609974i
$764$	16.2985			0.589659
$765$		0			0
$766$	−21.4959	+	37.2321i	−0.776680	+	1.34525i
$767$	0.824246	+	0.475879i	0.0297618	+	0.0171830i
$768$	−27.2309	+	15.7218i	−0.982610	+	0.567310i
$769$	−19.7846			−0.713452			−0.356726	−	0.934209i	$-0.616107\pi$
$769$	−19.7846			−0.713452			−0.356726	+	0.934209i	$0.616107\pi$
$770$		0			0
$771$	−26.1609			−0.942161
$772$	−16.2666	+	9.39153i	−0.585448	+	0.338009i
$773$	13.6578	+	7.88536i	0.491238	+	0.283617i	0.725088	−	0.688656i	$-0.241799\pi$
$773$	13.6578	+	7.88536i	0.491238	+	0.283617i	−0.233850	+	0.972273i	$0.575132\pi$
$774$	4.29288	−	7.43548i	0.154304	−	0.267263i
$775$		0			0
$776$	9.49228			0.340753
$777$	28.9364	+	11.4077i	1.03809	+	0.409250i
$778$			44.3301i			1.58931i
$779$	−27.8558	−	48.2477i	−0.998038	−	1.72865i
$780$		0			0
$781$	−27.1886	+	47.0921i	−0.972886	+	1.68509i
$782$	−35.1716	+	20.3063i	−1.25773	+	0.726153i
$783$			4.00000i			0.142948i
$784$	5.75805	−	24.8772i	0.205645	−	0.888473i
$785$		0			0
$786$	−16.7726	−	29.0509i	−0.598257	−	1.03621i
$787$	12.7251	+	7.34684i	0.453601	+	0.261886i	0.709350	−	0.704857i	$-0.248989\pi$
$787$	12.7251	+	7.34684i	0.453601	+	0.261886i	−0.255749	+	0.966743i	$0.582322\pi$
$788$	−18.0996	−	10.4498i	−0.644773	−	0.372260i
$789$	−6.69016	−	11.5877i	−0.238176	−	0.412533i
$790$		0			0
$791$	3.06992	−	7.78703i	0.109154	−	0.276875i
$792$		−	21.6732i		−	0.770124i
$793$	−5.88412	+	3.39720i	−0.208951	+	0.120638i
$794$	12.8250	−	22.2135i	0.455141	−	0.788328i
$795$		0			0
$796$	4.48913	+	7.77540i	0.159113	+	0.275592i
$797$		−	25.3938i		−	0.899493i	−0.893156	−	0.449747i	$-0.851514\pi$
$797$		−	25.3938i		−	0.899493i	0.893156	−	0.449747i	$-0.148486\pi$
$798$	6.48410	+	43.4694i	0.229535	+	1.53880i
$799$	14.1648			0.501114
$800$		0			0
$801$	−0.146439	+	0.253639i	−0.00517415	+	0.00896190i
$802$	7.57480	+	4.37331i	0.267476	+	0.154427i
$803$	−24.4574	+	14.1205i	−0.863085	+	0.498302i
$804$	−7.64784			−0.269719
$805$		0			0
$806$	−26.8554			−0.945941
$807$	2.48619	−	1.43540i	0.0875181	−	0.0505286i
$808$	−25.7788	−	14.8834i	−0.906895	−	0.523596i
$809$	16.6969	−	28.9199i	0.587031	−	1.01677i	−0.407588	−	0.913166i	$-0.633630\pi$
$809$	16.6969	−	28.9199i	0.587031	−	1.01677i	0.994619	−	0.103602i	$-0.0330367\pi$
$810$		0			0
$811$	−33.3276			−1.17029			−0.585145	−	0.810929i	$-0.698962\pi$
$811$	−33.3276			−1.17029			−0.585145	+	0.810929i	$0.698962\pi$
$812$	32.6457	−	25.9526i	1.14564	−	0.910759i
$813$			29.3419i			1.02907i
$814$	−65.6440	−	113.699i	−2.30082	−	3.98514i
$815$		0			0
$816$	−7.82987	+	13.5617i	−0.274100	+	0.474756i
$817$	20.7914	−	12.0039i	0.727399	−	0.419964i
$818$		−	54.9147i		−	1.92005i
$819$	3.55592	−	0.530417i	0.124254	−	0.0185343i
$820$		0			0
$821$	−26.0769	−	45.1666i	−0.910091	−	1.57632i	−0.813934	−	0.580957i	$-0.802678\pi$
$821$	−26.0769	−	45.1666i	−0.910091	−	1.57632i	−0.0961569	−	0.995366i	$-0.530655\pi$
$822$	−19.0926	−	11.0231i	−0.665931	−	0.384475i
$823$	−14.7523	−	8.51725i	−0.514233	−	0.296893i	0.220339	−	0.975423i	$-0.429284\pi$
$823$	−14.7523	−	8.51725i	−0.514233	−	0.296893i	−0.734572	+	0.678531i	$0.762617\pi$
$824$	8.06844	+	13.9750i	0.281078	+	0.486841i
$825$		0			0
$826$	1.65653	−	4.20188i	0.0576379	−	0.146202i
$827$			11.2054i			0.389651i	0.980838	+	0.194826i	$0.0624141\pi$
$827$			11.2054i			0.389651i	−0.980838	+	0.194826i	$0.937586\pi$
$828$	13.2465	−	7.64784i	0.460346	−	0.265781i
$829$	10.3346	−	17.9001i	0.358937	−	0.621697i	−0.628847	−	0.777529i	$-0.716473\pi$
$829$	10.3346	−	17.9001i	0.358937	−	0.621697i	0.987784	+	0.155832i	$0.0498060\pi$
$830$		0			0
$831$	9.99152	+	17.3058i	0.346602	+	0.600332i
$832$			11.7997i			0.409083i
$833$	8.76970	+	28.7420i	0.303852	+	0.995852i
$834$	51.9920			1.80034
$835$		0			0
$836$	61.5290	−	106.571i	2.12802	−	3.68585i
$837$	−7.02201	−	4.05416i	−0.242716	−	0.140132i
$838$	83.1777	−	48.0227i	2.87333	−	1.65892i
$839$	10.3486			0.357275			0.178637	−	0.983915i	$-0.442831\pi$
$839$	10.3486			0.357275			0.178637	+	0.983915i	$0.442831\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	18.0922	−	10.4456i	0.623499	−	0.359978i
$843$	−6.17406	−	3.56460i	−0.212646	−	0.122771i
$844$	−29.1716	+	50.5267i	−1.00413	+	1.73920i
$845$		0			0
$846$	−8.04232			−0.276501
$847$	3.90071	+	26.1504i	0.134030	+	0.898538i
$848$			34.4961i			1.18460i
$849$	−11.4376	−	19.8104i	−0.392536	−	0.679892i
$850$		0			0
$851$	22.8154	−	39.5175i	0.782103	−	1.35464i
$852$	−40.5027	+	23.3842i	−1.38760	+	0.801131i
$853$		−	50.5890i		−	1.73213i	−0.499929	−	0.866067i	$-0.666640\pi$
$853$		−	50.5890i		−	1.73213i	0.499929	−	0.866067i	$-0.333360\pi$
$854$	20.0648	+	25.2394i	0.686604	+	0.863676i
$855$		0			0
$856$	7.49174	+	12.9761i	0.256062	+	0.443513i
$857$	−31.0742	−	17.9407i	−1.06148	−	0.612843i	−0.135636	−	0.990759i	$-0.543308\pi$
$857$	−31.0742	−	17.9407i	−1.06148	−	0.612843i	−0.925840	+	0.377915i	$0.876641\pi$
$858$	−13.1423	−	7.58771i	−0.448671	−	0.259040i
$859$	21.5925	+	37.3993i	0.736726	+	1.27605i	0.953962	+	0.299928i	$0.0969625\pi$
$859$	21.5925	+	37.3993i	0.736726	+	1.27605i	−0.217236	+	0.976119i	$0.569704\pi$
$860$		0			0
$861$	13.4585	+	16.9294i	0.458665	+	0.576953i
$862$		−	3.12528i		−	0.106447i
$863$	20.4499	−	11.8068i	0.696123	−	0.401907i	−0.109779	−	0.993956i	$-0.535014\pi$
$863$	20.4499	−	11.8068i	0.696123	−	0.401907i	0.805902	+	0.592049i	$0.201681\pi$
$864$	−0.284682	+	0.493084i	−0.00968509	+	0.0167751i
$865$		0			0
$866$	6.35216	+	11.0023i	0.215855	+	0.373872i
$867$		−	1.42879i		−	0.0485244i
$868$	12.4722	+	83.6136i	0.423334	+	2.83803i
$869$	28.2590			0.958619
$870$		0			0
$871$	−1.31860	+	2.28389i	−0.0446792	+	0.0773866i
$872$	41.9220	+	24.2037i	1.41966	+	0.819640i
$873$	1.73787	−	1.00336i	0.0588181	−	0.0339587i
$874$	64.4773			2.18098
$875$		0			0
$876$	−24.2894			−0.820662
$877$	−28.4400	+	16.4198i	−0.960351	+	0.554459i	−0.896281	−	0.443487i	$-0.853741\pi$
$877$	−28.4400	+	16.4198i	−0.960351	+	0.554459i	−0.0640698	+	0.997945i	$0.520408\pi$
$878$	−41.4312	−	23.9203i	−1.39824	−	0.807272i
$879$	1.81544	−	3.14444i	0.0612333	−	0.106059i
$880$		0			0
$881$	−9.72896			−0.327777			−0.163889	−	0.986479i	$-0.552404\pi$
$881$	−9.72896			−0.327777			−0.163889	+	0.986479i	$0.552404\pi$
$882$	−4.97916	−	16.3188i	−0.167657	−	0.549483i
$883$			54.5366i			1.83530i	0.397387	+	0.917651i	$0.369917\pi$
$883$			54.5366i			1.83530i	−0.397387	+	0.917651i	$0.630083\pi$
$884$	11.4941	+	19.9084i	0.386589	+	0.669591i
$885$		0			0
$886$	−21.9786	+	38.0680i	−0.738384	+	1.27892i
$887$	42.4498	−	24.5084i	1.42533	−	0.822912i	0.428578	−	0.903505i	$-0.359015\pi$
$887$	42.4498	−	24.5084i	1.42533	−	0.822912i	0.996747	+	0.0805927i	$0.0256813\pi$
$888$		−	55.6094i		−	1.86613i
$889$	0.0103216	−	0.0261814i	0.000346176	−	0.000878097i
$890$		0			0
$891$	−2.29092	−	3.96799i	−0.0767487	−	0.132933i
$892$	−22.6430	−	13.0729i	−0.758144	−	0.437714i
$893$	−19.4754	−	11.2441i	−0.651719	−	0.376270i
$894$	−19.2615	−	33.3619i	−0.644200	−	1.11579i
$895$		0			0
$896$	52.4038	−	7.81679i	1.75069	−	0.261141i
$897$		−	5.27442i		−	0.176108i
$898$	−14.7698	+	8.52733i	−0.492874	+	0.284561i
$899$	−16.2166	+	28.0880i	−0.540855	+	0.936789i
$900$		0			0
$901$	−20.2979	−	35.1570i	−0.676222	−	1.17125i
$902$		−	91.2875i		−	3.03954i
$903$	−7.29540	+	5.79968i	−0.242776	+	0.193001i
$904$	−14.9650			−0.497728
$905$		0			0
$906$	−5.92776	+	10.2672i	−0.196937	+	0.341104i
$907$	2.80391	+	1.61884i	0.0931024	+	0.0537527i	0.545828	−	0.837897i	$-0.316215\pi$
$907$	2.80391	+	1.61884i	0.0931024	+	0.0537527i	−0.452726	+	0.891650i	$0.649548\pi$
$908$	30.8230	−	17.7957i	1.02290	−	0.590570i
$909$	−6.29288			−0.208722
$910$		0			0
$911$	17.8758			0.592252			0.296126	−	0.955149i	$-0.404305\pi$
$911$	17.8758			0.592252			0.296126	+	0.955149i	$0.404305\pi$
$912$	21.5308	−	12.4308i	0.712957	−	0.411626i
$913$	51.7785	+	29.8943i	1.71362	+	0.989358i
$914$	−46.1158	+	79.8749i	−1.52538	+	2.64203i
$915$		0			0
$916$	66.3334			2.19172
$917$	5.37212	+	36.0147i	0.177403	+	1.18931i
$918$			10.4633i			0.345340i
$919$	−3.13080	−	5.42270i	−0.103276	−	0.178878i	0.809757	−	0.586766i	$-0.199599\pi$
$919$	−3.13080	−	5.42270i	−0.103276	−	0.178878i	−0.913032	+	0.407887i	$0.866266\pi$
$920$		0			0
$921$	−3.11344	+	5.39263i	−0.102591	+	0.177693i
$922$	−50.8501	+	29.3583i	−1.67466	+	0.966864i
$923$			16.1272i			0.530833i
$924$	−17.5206	+	44.4421i	−0.576386	+	1.46204i
$925$		0			0
$926$	28.1703	+	48.7924i	0.925734	+	1.60342i
$927$	2.95439	+	1.70572i	0.0970348	+	0.0560231i
$928$	1.97234	+	1.13873i	0.0647451	+	0.0373806i
$929$	−4.78756	−	8.29230i	−0.157075	−	0.272061i	0.776738	−	0.629824i	$-0.216873\pi$
$929$	−4.78756	−	8.29230i	−0.157075	−	0.272061i	−0.933813	+	0.357763i	$0.883540\pi$
$930$		0			0
$931$	10.7580	−	46.4793i	0.352580	−	1.52330i
$932$			72.0871i			2.36129i
$933$	−18.7329	+	10.8154i	−0.613287	+	0.354082i
$934$	−15.3121	+	26.5213i	−0.501027	+	0.867803i
$935$		0			0
$936$	−3.21391	−	5.56666i	−0.105050	−	0.181952i
$937$		−	55.8679i		−	1.82512i	−0.408939	−	0.912562i	$-0.634101\pi$
$937$		−	55.8679i		−	1.82512i	0.408939	−	0.912562i	$-0.365899\pi$
$938$	11.6429	+	4.59004i	0.380155	+	0.149870i
$939$	23.8962			0.779822
$940$		0			0
$941$	−13.6415	+	23.6278i	−0.444701	+	0.770244i	−0.998031	−	0.0627174i	$-0.980023\pi$
$941$	−13.6415	+	23.6278i	−0.444701	+	0.770244i	0.553331	+	0.832962i	$0.313357\pi$
$942$	13.8871	+	8.01773i	0.452467	+	0.261232i
$943$	27.4774	−	15.8641i	0.894787	−	0.516606i
$944$	−2.55494			−0.0831564
$945$		0			0
$946$	39.3386			1.27901
$947$	−45.1780	+	26.0835i	−1.46809	+	0.847601i	−0.999361	−	0.0357424i	$-0.988620\pi$
$947$	−45.1780	+	26.0835i	−1.46809	+	0.847601i	−0.468727	+	0.883343i	$0.655287\pi$
$948$	21.0486	+	12.1524i	0.683625	+	0.394691i
$949$	−4.18785	+	7.25357i	−0.135943	+	0.235461i
$950$		0			0
$951$	−8.57231			−0.277976
$952$	42.0554	−	33.4331i	1.36302	−	1.08357i
$953$		−	27.4644i		−	0.889659i	−0.895615	−	0.444829i	$-0.853264\pi$
$953$		−	27.4644i		−	0.889659i	0.895615	−	0.444829i	$-0.146736\pi$
$954$	11.5245	+	19.9611i	0.373120	+	0.646263i
$955$		0			0
$956$	−22.9170	+	39.6935i	−0.741190	+	1.28378i
$957$	−15.8720	+	9.16368i	−0.513068	+	0.296220i
$958$		−	4.94981i		−	0.159921i
$959$	14.8922	+	18.7329i	0.480896	+	0.604917i
$960$		0			0
$961$	−17.3724	−	30.0899i	−0.560400	−	0.970642i
$962$	−33.7207	−	19.4687i	−1.08720	−	0.627695i
$963$	2.74322	+	1.58380i	0.0883990	+	0.0510372i
$964$	−3.48677	−	6.03927i	−0.112301	−	0.194512i
$965$		0			0
$966$	−24.7562	+	3.69274i	−0.796516	+	0.118812i
$967$			45.8901i			1.47573i	0.674950	+	0.737864i	$0.264165\pi$
$967$			45.8901i			1.47573i	−0.674950	+	0.737864i	$0.735835\pi$
$968$	40.9375	−	23.6353i	1.31578	−	0.759667i
$969$	−14.6289	+	25.3380i	−0.469949	+	0.813975i
$970$		0			0
$971$	−19.5284	−	33.8242i	−0.626697	−	1.08547i	−0.988210	−	0.153104i	$-0.951073\pi$
$971$	−19.5284	−	33.8242i	−0.626697	−	1.08547i	0.361513	−	0.932367i	$-0.382260\pi$
$972$		−	3.94072i		−	0.126399i
$973$	−52.5044	−	20.6990i	−1.68321	−	0.663581i
$974$	67.0824			2.14946
$975$		0			0
$976$	9.11961	−	15.7956i	0.291912	−	0.505606i
$977$	7.89934	+	4.56068i	0.252722	+	0.145909i	0.621010	−	0.783803i	$-0.286723\pi$
$977$	7.89934	+	4.56068i	0.252722	+	0.145909i	−0.368288	+	0.929712i	$0.620056\pi$
$978$	−24.1969	+	13.9701i	−0.773731	+	0.446714i
$979$	−1.34192			−0.0428879
$980$		0			0
$981$	10.2336			0.326734
$982$	−0.969652	+	0.559829i	−0.0309428	+	0.0178648i
$983$	39.5806	+	22.8519i	1.26243	+	0.728862i	0.973543	−	0.228502i	$-0.0733829\pi$
$983$	39.5806	+	22.8519i	1.26243	+	0.728862i	0.288883	+	0.957364i	$0.406716\pi$
$984$	19.3332	−	33.4861i	0.616321	−	1.06750i
$985$		0			0
$986$	41.8531			1.33288
$987$	8.12158	+	3.20180i	0.258513	+	0.101915i
$988$		−	36.4965i		−	1.16111i
$989$	6.83632	+	11.8408i	0.217382	+	0.376517i
$990$		0			0
$991$	6.38992	−	11.0677i	0.202983	−	0.351576i	−0.746505	−	0.665379i	$-0.768270\pi$
$991$	6.38992	−	11.0677i	0.202983	−	0.351576i	0.949488	+	0.313803i	$0.101603\pi$
$992$	−3.99808	+	2.30830i	−0.126939	+	0.0732885i
$993$			13.5095i			0.428711i
$994$	75.6950	−	11.2910i	2.40090	−	0.358129i
$995$		0			0
$996$	25.7113	+	44.5333i	0.814694	+	1.41109i
$997$	3.54322	+	2.04568i	0.112215	+	0.0647873i	0.555057	−	0.831812i	$-0.312696\pi$
$997$	3.54322	+	2.04568i	0.112215	+	0.0647873i	−0.442842	+	0.896600i	$0.646030\pi$
$998$	24.5663	+	14.1834i	0.777633	+	0.448967i
$999$	−5.87808	−	10.1811i	−0.185974	−	0.322117i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.r.h.424.2		16
5.2	odd	4		525.2.i.j.151.1	yes	8
5.3	odd	4		525.2.i.i.151.4	✓	8
5.4	even	2	inner	525.2.r.h.424.7		16
7.2	even	3	inner	525.2.r.h.499.7		16
35.2	odd	12		525.2.i.j.226.1	yes	8
35.3	even	12		3675.2.a.bx.1.1		4
35.9	even	6	inner	525.2.r.h.499.2		16
35.17	even	12		3675.2.a.bq.1.4		4
35.18	odd	12		3675.2.a.bw.1.1		4
35.23	odd	12		525.2.i.i.226.4	yes	8
35.32	odd	12		3675.2.a.br.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.i.i.151.4	✓	8	5.3	odd	4
525.2.i.i.226.4	yes	8	35.23	odd	12
525.2.i.j.151.1	yes	8	5.2	odd	4
525.2.i.j.226.1	yes	8	35.2	odd	12
525.2.r.h.424.2		16	1.1	even	1	trivial
525.2.r.h.424.7		16	5.4	even	2	inner
525.2.r.h.499.2		16	35.9	even	6	inner
525.2.r.h.499.7		16	7.2	even	3	inner
3675.2.a.bq.1.4		4	35.17	even	12
3675.2.a.br.1.4		4	35.32	odd	12
3675.2.a.bw.1.1		4	35.18	odd	12
3675.2.a.bx.1.1		4	35.3	even	12

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.11082 + 1.21868i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(1.97036 - 3.41277i) q^{4} +2.43736 q^{6} +(-2.46138 - 0.970361i) q^{7} +4.73024i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.11082 + 1.21868i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(1.97036 - 3.41277i) q^{4} +2.43736 q^{6} +(-2.46138 - 0.970361i) q^{7} +4.73024i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.29092 + 3.96799i) q^{11} +(-3.41277 + 1.97036i) q^{12} +1.35888i q^{13} +(6.37808 - 0.951383i) q^{14} +(-1.82392 - 3.15913i) q^{16} +(3.71774 + 2.14644i) q^{17} +(-2.11082 - 1.21868i) q^{18} +(-3.40772 - 5.90235i) q^{19} +(1.64644 + 2.07105i) q^{21} -11.1676i q^{22} +(3.36143 - 1.94072i) q^{23} +(2.36512 - 4.09651i) q^{24} +(-1.65604 - 2.86834i) q^{26} -1.00000i q^{27} +(-8.16142 + 6.48816i) q^{28} -4.00000 q^{29} +(4.05416 - 7.02201i) q^{31} +(-0.493084 - 0.284682i) q^{32} +(3.96799 - 2.29092i) q^{33} -10.4633 q^{34} +3.94072 q^{36} +(10.1811 - 5.87808i) q^{37} +(14.3861 + 8.30584i) q^{38} +(0.679440 - 1.17682i) q^{39} +8.17432 q^{41} +(-5.99927 - 2.36512i) q^{42} +3.52256i q^{43} +(9.02788 + 15.6368i) q^{44} +(-4.73024 + 8.19301i) q^{46} +(2.85754 - 1.64980i) q^{47} +3.64784i q^{48} +(5.11680 + 4.77686i) q^{49} +(-2.14644 - 3.71774i) q^{51} +(4.63754 + 2.67748i) q^{52} +(-8.18962 - 4.72828i) q^{53} +(1.21868 + 2.11082i) q^{54} +(4.59004 - 11.6429i) q^{56} +6.81544i q^{57} +(8.44326 - 4.87472i) q^{58} +(0.350199 - 0.606563i) q^{59} +(2.50000 + 4.33013i) q^{61} +19.7629i q^{62} +(-0.390334 - 2.61680i) q^{63} +8.68344 q^{64} +(-5.58380 + 9.67142i) q^{66} +(1.68071 + 0.970361i) q^{67} +(14.6506 - 8.45852i) q^{68} -3.88144 q^{69} +11.8680 q^{71} +(-4.09651 + 2.36512i) q^{72} +(5.33791 + 3.08184i) q^{73} +(-14.3270 + 24.8151i) q^{74} -26.8578 q^{76} +(9.48921 - 7.54372i) q^{77} +3.31208i q^{78} +(-3.08380 - 5.34130i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-17.2545 + 9.96188i) q^{82} -13.0490i q^{83} +(10.3121 - 1.53820i) q^{84} +(-4.29288 - 7.43548i) q^{86} +(3.46410 + 2.00000i) q^{87} +(-18.7695 - 10.8366i) q^{88} +(0.146439 + 0.253639i) q^{89} +(1.31860 - 3.34472i) q^{91} -15.2957i q^{92} +(-7.02201 + 4.05416i) q^{93} +(-4.02116 + 6.96485i) q^{94} +(0.284682 + 0.493084i) q^{96} -2.00672i q^{97} +(-16.6221 - 3.84732i) q^{98} -4.58184 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 14 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) \) 16 * q + 14 * q^4 - 4 * q^6 + 8 * q^9	\( 16 q + 14 q^{4} - 4 q^{6} + 8 q^{9} - 16 q^{11} + 24 q^{14} - 34 q^{16} + 6 q^{19} + 4 q^{21} - 6 q^{24} + 38 q^{26} - 64 q^{29} - 18 q^{31} - 56 q^{34} + 28 q^{36} + 14 q^{39} + 16 q^{41} + 52 q^{44} + 12 q^{46} + 42 q^{49} - 12 q^{51} - 2 q^{54} - 42 q^{56} + 20 q^{59} + 40 q^{61} - 84 q^{64} - 24 q^{66} + 8 q^{69} + 88 q^{71} - 42 q^{74} - 92 q^{76} + 16 q^{79} - 8 q^{81} + 36 q^{84} - 24 q^{86} - 20 q^{89} + 42 q^{91} + 44 q^{94} + 34 q^{96} - 32 q^{99}+O(q^{100}) \) 16 * q + 14 * q^4 - 4 * q^6 + 8 * q^9 - 16 * q^11 + 24 * q^14 - 34 * q^16 + 6 * q^19 + 4 * q^21 - 6 * q^24 + 38 * q^26 - 64 * q^29 - 18 * q^31 - 56 * q^34 + 28 * q^36 + 14 * q^39 + 16 * q^41 + 52 * q^44 + 12 * q^46 + 42 * q^49 - 12 * q^51 - 2 * q^54 - 42 * q^56 + 20 * q^59 + 40 * q^61 - 84 * q^64 - 24 * q^66 + 8 * q^69 + 88 * q^71 - 42 * q^74 - 92 * q^76 + 16 * q^79 - 8 * q^81 + 36 * q^84 - 24 * q^86 - 20 * q^89 + 42 * q^91 + 44 * q^94 + 34 * q^96 - 32 * q^99

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