LMFDB - Embedded newform 525.2.r.h.424.8

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			424.8
Root			$2.34074 - 1.35143i$ of defining polynomial
Character	$\chi$	$=$	525.424
Dual form			525.2.r.h.499.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.34074 - 1.35143i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.65271 - 4.59463i) q^{4} -2.70285 q^{6} +(2.06605 - 1.65271i) q^{7} -8.93406i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(2.34074 - 1.35143i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.65271 - 4.59463i) q^{4} -2.70285 q^{6} +(2.06605 - 1.65271i) q^{7} -8.93406i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.41275 + 2.44696i) q^{11} +(-4.59463 + 2.65271i) q^{12} +4.47992i q^{13} +(2.60256 - 6.66067i) q^{14} +(-6.76831 - 11.7231i) q^{16} +(-3.66433 - 2.11560i) q^{17} +(2.34074 + 1.35143i) q^{18} +(1.05014 + 1.81890i) q^{19} +(-2.61560 + 0.398264i) q^{21} +7.63692i q^{22} +(5.72515 - 3.30542i) q^{23} +(-4.46703 + 7.73712i) q^{24} +(6.05428 + 10.4863i) q^{26} -1.00000i q^{27} +(-2.11296 - 13.8769i) q^{28} -4.00000 q^{29} +(-4.66575 + 8.08131i) q^{31} +(-16.2115 - 9.35970i) q^{32} +(2.44696 - 1.41275i) q^{33} -11.4363 q^{34} +5.30542 q^{36} +(3.64175 - 2.10256i) q^{37} +(4.91623 + 2.83839i) q^{38} +(2.23996 - 3.87972i) q^{39} +2.37963 q^{41} +(-5.58422 + 4.46703i) q^{42} +3.13092i q^{43} +(7.49523 + 12.9821i) q^{44} +(8.93406 - 15.4742i) q^{46} +(6.74230 - 3.89267i) q^{47} +13.5366i q^{48} +(1.53710 - 6.82915i) q^{49} +(2.11560 + 3.66433i) q^{51} +(20.5835 + 11.8839i) q^{52} +(2.23452 + 1.29010i) q^{53} +(-1.35143 - 2.34074i) q^{54} +(-14.7654 - 18.4582i) q^{56} -2.10029i q^{57} +(-9.36296 + 5.40571i) q^{58} +(-1.89267 + 3.27820i) q^{59} +(2.50000 + 4.33013i) q^{61} +25.2217i q^{62} +(2.46431 + 0.962895i) q^{63} -23.5225 q^{64} +(3.81846 - 6.61376i) q^{66} +(2.86258 + 1.65271i) q^{67} +(-19.4408 + 11.2242i) q^{68} -6.61084 q^{69} -11.4223 q^{71} +(7.73712 - 4.46703i) q^{72} +(2.29584 + 1.32550i) q^{73} +(5.68292 - 9.84311i) q^{74} +11.1429 q^{76} +(1.12530 + 7.39039i) q^{77} -12.1086i q^{78} +(6.31846 + 10.9439i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(5.57009 - 3.21589i) q^{82} +3.02608i q^{83} +(-5.10856 + 13.0742i) q^{84} +(4.23121 + 7.32867i) q^{86} +(3.46410 + 2.00000i) q^{87} +(21.8613 + 12.6216i) q^{88} +(-4.11560 - 7.12844i) q^{89} +(7.40400 + 9.25572i) q^{91} -35.0733i q^{92} +(8.08131 - 4.66575i) q^{93} +(10.5213 - 18.2234i) q^{94} +(9.35970 + 16.2115i) q^{96} -15.0165i q^{97} +(-5.63114 - 18.0626i) q^{98} -2.82550 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 $

$2$	2.34074	−	1.35143i	1.65515	−	0.955603i	0.680248	−	0.732982i	$-0.261872\pi$
$2$	2.34074	−	1.35143i	1.65515	−	0.955603i	0.974905	−	0.222621i	$-0.0714613\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	2.65271	−	4.59463i	1.32635	−	2.29731i
$5$		0			0
$5$		0			0
$6$	−2.70285			−1.10344
$7$	2.06605	−	1.65271i	0.780893	−	0.624665i
$7$	2.06605	−	1.65271i	0.780893	−	0.624665i
$8$		−	8.93406i		−	3.15867i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−1.41275	+	2.44696i	−0.425960	+	0.737785i	−0.996510	−	0.0834785i	$-0.973397\pi$
$11$	−1.41275	+	2.44696i	−0.425960	+	0.737785i	0.570549	+	0.821263i	$0.306730\pi$
$12$	−4.59463	+	2.65271i	−1.32635	+	0.765771i
$13$			4.47992i			1.24251i	0.783610	+	0.621253i	$0.213376\pi$
$13$			4.47992i			1.24251i	−0.783610	+	0.621253i	$0.786624\pi$
$14$	2.60256	−	6.66067i	0.695565	−	1.78014i
$15$		0			0
$16$	−6.76831	−	11.7231i	−1.69208	−	2.93077i
$17$	−3.66433	−	2.11560i	−0.888732	−	0.513109i	−0.0152042	−	0.999884i	$-0.504840\pi$
$17$	−3.66433	−	2.11560i	−0.888732	−	0.513109i	−0.873527	+	0.486775i	$0.838173\pi$
$18$	2.34074	+	1.35143i	0.551718	+	0.318534i
$19$	1.05014	+	1.81890i	0.240920	+	0.417285i	0.960977	−	0.276630i	$-0.0892176\pi$
$19$	1.05014	+	1.81890i	0.240920	+	0.417285i	−0.720057	+	0.693915i	$0.755884\pi$
$20$		0			0
$21$	−2.61560	+	0.398264i	−0.570772	+	0.0869084i
$22$			7.63692i			1.62820i
$23$	5.72515	−	3.30542i	1.19378	−	0.689227i	0.234616	−	0.972088i	$-0.424617\pi$
$23$	5.72515	−	3.30542i	1.19378	−	0.689227i	0.959161	+	0.282861i	$0.0912835\pi$
$24$	−4.46703	+	7.73712i	−0.911829	+	1.57933i
$25$		0			0
$26$	6.05428	+	10.4863i	1.18734	+	2.05654i
$27$		−	1.00000i		−	0.192450i
$28$	−2.11296	−	13.8769i	−0.399312	−	2.62248i
$29$	−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
$31$	−4.66575	+	8.08131i	−0.837993	+	1.45145i	0.0535767	+	0.998564i	$0.482938\pi$
$31$	−4.66575	+	8.08131i	−0.837993	+	1.45145i	−0.891570	+	0.452883i	$0.850395\pi$
$32$	−16.2115	−	9.35970i	−2.86581	−	1.65458i
$33$	2.44696	−	1.41275i	0.425960	−	0.245928i
$34$	−11.4363			−1.96132
$35$		0			0
$36$	5.30542			0.884236
$37$	3.64175	−	2.10256i	0.598700	−	0.345659i	−0.169830	−	0.985473i	$-0.554322\pi$
$37$	3.64175	−	2.10256i	0.598700	−	0.345659i	0.768530	+	0.639814i	$0.220989\pi$
$38$	4.91623	+	2.83839i	0.797518	+	0.460447i
$39$	2.23996	−	3.87972i	0.358680	−	0.621253i
$40$		0			0
$41$	2.37963			0.371635			0.185818	−	0.982584i	$-0.440507\pi$
$41$	2.37963			0.371635			0.185818	+	0.982584i	$0.440507\pi$
$42$	−5.58422	+	4.46703i	−0.861665	+	0.689278i
$43$			3.13092i			0.477461i	0.971086	+	0.238730i	$0.0767312\pi$
$43$			3.13092i			0.477461i	−0.971086	+	0.238730i	$0.923269\pi$
$44$	7.49523	+	12.9821i	1.12995	+	1.95713i
$45$		0			0
$46$	8.93406	−	15.4742i	1.31726	−	2.28155i
$47$	6.74230	−	3.89267i	0.983465	−	0.567804i	0.0801507	−	0.996783i	$-0.474460\pi$
$47$	6.74230	−	3.89267i	0.983465	−	0.567804i	0.903315	+	0.428979i	$0.141126\pi$
$48$			13.5366i			1.95384i
$49$	1.53710	−	6.82915i	0.219586	−	0.975593i
$50$		0			0
$51$	2.11560	+	3.66433i	0.296244	+	0.513109i
$52$	20.5835	+	11.8839i	2.85442	+	1.64800i
$53$	2.23452	+	1.29010i	0.306936	+	0.177209i	0.645554	−	0.763714i	$-0.276626\pi$
$53$	2.23452	+	1.29010i	0.306936	+	0.177209i	−0.338619	+	0.940924i	$0.609960\pi$
$54$	−1.35143	−	2.34074i	−0.183906	−	0.318534i
$55$		0			0
$56$	−14.7654	−	18.4582i	−1.97311	−	2.46658i
$57$		−	2.10029i		−	0.278190i
$58$	−9.36296	+	5.40571i	−1.22942	+	0.709804i
$59$	−1.89267	+	3.27820i	−0.246404	+	0.426785i	−0.962526	−	0.271191i	$-0.912582\pi$
$59$	−1.89267	+	3.27820i	−0.246404	+	0.426785i	0.716121	+	0.697976i	$0.245916\pi$
$60$		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	$0.729619\pi$
$62$			25.2217i			3.20316i
$63$	2.46431	+	0.962895i	0.310474	+	0.121313i
$64$	−23.5225			−2.94032
$65$		0			0
$66$	3.81846	−	6.61376i	0.470020	−	0.814098i
$67$	2.86258	+	1.65271i	0.349719	+	0.201911i	0.664562	−	0.747233i	$-0.268618\pi$
$67$	2.86258	+	1.65271i	0.349719	+	0.201911i	−0.314842	+	0.949144i	$0.601952\pi$
$68$	−19.4408	+	11.2242i	−2.35755	+	1.36113i
$69$	−6.61084			−0.795851
$70$		0			0
$71$	−11.4223			−1.35557			−0.677786	−	0.735259i	$-0.737060\pi$
$71$	−11.4223			−1.35557			−0.677786	+	0.735259i	$0.737060\pi$
$72$	7.73712	−	4.46703i	0.911829	−	0.526445i
$73$	2.29584	+	1.32550i	0.268707	+	0.155138i	0.628300	−	0.777971i	$-0.283751\pi$
$73$	2.29584	+	1.32550i	0.268707	+	0.155138i	−0.359593	+	0.933109i	$0.617084\pi$
$74$	5.68292	−	9.84311i	0.660627	−	1.14424i
$75$		0			0
$76$	11.1429			1.27818
$77$	1.12530	+	7.39039i	0.128239	+	0.842213i
$78$		−	12.1086i		−	1.37102i
$79$	6.31846	+	10.9439i	0.710882	+	1.23128i	0.964526	+	0.263986i	$0.0850374\pi$
$79$	6.31846	+	10.9439i	0.710882	+	1.23128i	−0.253644	+	0.967298i	$0.581629\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.57009	−	3.21589i	0.615114	−	0.355136i
$83$			3.02608i			0.332155i	0.986113	+	0.166078i	$0.0531102\pi$
$83$			3.02608i			0.332155i	−0.986113	+	0.166078i	$0.946890\pi$
$84$	−5.10856	+	13.0742i	−0.557390	+	1.42651i
$85$		0			0
$86$	4.23121	+	7.32867i	0.456263	+	0.790271i
$87$	3.46410	+	2.00000i	0.371391	+	0.214423i
$88$	21.8613	+	12.6216i	2.33042	+	1.34547i
$89$	−4.11560	−	7.12844i	−0.436253	−	0.755613i	0.561144	−	0.827718i	$-0.310361\pi$
$89$	−4.11560	−	7.12844i	−0.436253	−	0.755613i	−0.997397	+	0.0721056i	$0.977028\pi$
$90$		0			0
$91$	7.40400	+	9.25572i	0.776150	+	0.970263i
$92$		−	35.0733i		−	3.65664i
$93$	8.08131	−	4.66575i	0.837993	−	0.483816i
$94$	10.5213	−	18.2234i	1.08519	−	1.87960i
$95$		0			0
$96$	9.35970	+	16.2115i	0.955270	+	1.65458i
$97$		−	15.0165i		−	1.52470i	−0.647166	−	0.762350i	$-0.724046\pi$
$97$		−	15.0165i		−	1.52470i	0.647166	−	0.762350i	$-0.275954\pi$
$98$	−5.63114	−	18.0626i	−0.568831	−	1.82459i
$99$	−2.82550			−0.283974
$100$		0			0
$101$	1.11560	−	1.93228i	0.111007	−	0.192269i	−0.805170	−	0.593045i	$-0.797926\pi$
$101$	1.11560	−	1.93228i	0.111007	−	0.192269i	0.916176	+	0.400775i	$0.131259\pi$
$102$	9.90416	+	5.71817i	0.980658	+	0.566183i
$103$	−6.79141	+	3.92102i	−0.669178	+	0.386350i	−0.795765	−	0.605606i	$-0.792931\pi$
$103$	−6.79141	+	3.92102i	−0.669178	+	0.386350i	0.126587	+	0.991955i	$0.459598\pi$
$104$	40.0239			3.92466
$105$		0			0
$106$	6.97392			0.677367
$107$	−13.5420	+	7.81846i	−1.30915	+	0.755839i	−0.981954	−	0.189117i	$-0.939437\pi$
$107$	−13.5420	+	7.81846i	−1.30915	+	0.755839i	−0.327197	+	0.944956i	$0.606104\pi$
$108$	−4.59463	−	2.65271i	−0.442118	−	0.255257i
$109$	1.53710	−	2.66234i	0.147228	−	0.255006i	−0.782974	−	0.622054i	$-0.786298\pi$
$109$	1.53710	−	2.66234i	0.147228	−	0.255006i	0.930202	+	0.367048i	$0.119632\pi$
$110$		0			0
$111$	−4.20513			−0.399133
$112$	−33.3585	−	13.0344i	−3.15208	−	1.23163i
$113$		−	0.348998i		−	0.0328310i	−0.999865	−	0.0164155i	$-0.994775\pi$
$113$		−	0.348998i		−	0.0328310i	0.999865	−	0.0164155i	$-0.00522545\pi$
$114$	−2.83839	−	4.91623i	−0.265839	−	0.460447i
$115$		0			0
$116$	−10.6108	+	18.3785i	−0.985191	+	1.70640i
$117$	−3.87972	+	2.23996i	−0.358680	+	0.207084i
$118$			10.2312i			0.941859i
$119$	−11.0672	+	1.68514i	−1.01453	+	0.154476i
$120$		0			0
$121$	1.50827	+	2.61240i	0.137116	+	0.237491i
$122$	11.7037	+	6.75713i	1.05960	+	0.611762i
$123$	−2.06082	−	1.18981i	−0.185818	−	0.107282i
$124$	24.7537	+	42.8748i	2.22295	+	3.85027i
$125$		0			0
$126$	7.06960	−	1.07645i	0.629810	−	0.0958978i
$127$		−	2.27137i		−	0.201552i	−0.994909	−	0.100776i	$-0.967867\pi$
$127$		−	2.27137i		−	0.201552i	0.994909	−	0.100776i	$-0.0321325\pi$
$128$	−22.6372	+	13.0696i	−2.00087	+	1.15520i
$129$	1.56546	−	2.71146i	0.137831	−	0.238730i
$130$		0			0
$131$	−9.61084	−	16.6465i	−0.839703	−	1.45441i	−0.890143	−	0.455681i	$-0.849396\pi$
$131$	−9.61084	−	16.6465i	−0.839703	−	1.45441i	0.0504406	−	0.998727i	$-0.483937\pi$
$132$		−	14.9905i		−	1.30475i
$133$	5.17577	+	2.02236i	0.448796	+	0.175361i
$134$	8.93406			0.771785
$135$		0			0
$136$	−18.9009	+	32.7374i	−1.62074	+	2.80721i
$137$	−7.15496	−	4.13092i	−0.611290	−	0.352928i	0.162180	−	0.986761i	$-0.448147\pi$
$137$	−7.15496	−	4.13092i	−0.611290	−	0.352928i	−0.773470	+	0.633833i	$0.781481\pi$
$138$	−15.4742	+	8.93406i	−1.31726	+	0.760518i
$139$	−0.985914			−0.0836241			−0.0418121	−	0.999125i	$-0.513313\pi$
$139$	−0.985914			−0.0836241			−0.0418121	+	0.999125i	$0.513313\pi$
$140$		0			0
$141$	−7.78534			−0.655644
$142$	−26.7365	+	15.4363i	−2.24368	+	1.29539i
$143$	−10.9622	−	6.32901i	−0.916702	−	0.529258i
$144$	6.76831	−	11.7231i	0.564026	−	0.976922i
$145$		0			0
$146$	7.16527			0.593002
$147$	−4.74575	+	5.14567i	−0.391423	+	0.424407i
$148$		−	22.3100i		−	1.83387i
$149$	3.91048	+	6.77314i	0.320359	+	0.554877i	0.980562	−	0.196209i	$-0.0628633\pi$
$149$	3.91048	+	6.77314i	0.320359	+	0.554877i	−0.660203	+	0.751087i	$0.729530\pi$
$150$		0			0
$151$	1.56717	−	2.71441i	0.127534	−	0.220896i	−0.795186	−	0.606365i	$-0.792627\pi$
$151$	1.56717	−	2.71441i	0.127534	−	0.220896i	0.922721	+	0.385469i	$0.125960\pi$
$152$	16.2502	−	9.38206i	1.31807	−	0.760985i
$153$		−	4.23121i		−	0.342073i
$154$	12.6216	+	15.7782i	1.01708	+	1.27145i
$155$		0			0
$156$	−11.8839	−	20.5835i	−0.951475	−	1.64800i
$157$	−20.3334	−	11.7395i	−1.62278	−	0.936913i	−0.986172	−	0.165725i	$-0.947004\pi$
$157$	−20.3334	−	11.7395i	−1.62278	−	0.936913i	−0.636608	−	0.771187i	$-0.719663\pi$
$158$	29.5797	+	17.0779i	2.35324	+	1.35864i
$159$	−1.29010	−	2.23452i	−0.102312	−	0.177209i
$160$		0			0
$161$	6.36554	−	16.2912i	0.501675	−	1.28392i
$162$			2.70285i			0.212356i
$163$	−10.7702	+	6.21817i	−0.843586	+	0.487045i	−0.858482	−	0.512844i	$-0.828592\pi$
$163$	−10.7702	+	6.21817i	−0.843586	+	0.487045i	0.0148956	+	0.999889i	$0.495258\pi$
$164$	6.31246	−	10.9335i	0.492920	−	0.853763i
$165$		0			0
$166$	4.08952	+	7.08326i	0.317409	+	0.549768i
$167$		−	18.4483i		−	1.42757i	−0.700362	−	0.713787i	$-0.746978\pi$
$167$		−	18.4483i		−	1.42757i	0.700362	−	0.713787i	$-0.253022\pi$
$168$	3.55812	+	23.3680i	0.274515	+	1.80288i
$169$	−7.06966			−0.543820
$170$		0			0
$171$	−1.05014	+	1.81890i	−0.0803066	+	0.139095i
$172$	14.3854	+	8.30542i	1.09688	+	0.633282i
$173$	6.62596	−	3.82550i	0.503763	−	0.290847i	−0.226503	−	0.974010i	$-0.572729\pi$
$173$	6.62596	−	3.82550i	0.503763	−	0.290847i	0.730266	+	0.683163i	$0.239396\pi$
$174$	10.8114			0.819611
$175$		0			0
$176$	38.2478			2.88303
$177$	3.27820	−	1.89267i	0.246404	−	0.142262i
$178$	−19.2671	−	11.1239i	−1.44413	−	0.833770i
$179$	−1.20513	+	2.08734i	−0.0900756	+	0.156015i	−0.907543	−	0.419960i	$-0.862044\pi$
$179$	−1.20513	+	2.08734i	−0.0900756	+	0.156015i	0.817467	+	0.575975i	$0.195378\pi$
$180$		0			0
$181$	−13.6970			−1.01809			−0.509046	−	0.860739i	$-0.670002\pi$
$181$	−13.6970			−1.01809			−0.509046	+	0.860739i	$0.670002\pi$
$182$	29.8393	+	11.6593i	2.21183	+	0.864243i
$183$		−	5.00000i		−	0.369611i
$184$	−29.5308	−	51.1489i	−2.17704	−	3.77074i
$185$		0			0
$186$	12.6108	−	21.8426i	0.924671	−	1.60158i
$187$	10.3536	−	5.97764i	0.757129	−	0.437128i
$188$		−	41.3045i		−	3.01244i
$189$	−1.65271	−	2.06605i	−0.120217	−	0.150283i
$190$		0			0
$191$	6.06717	+	10.5086i	0.439005	+	0.760379i	0.997613	−	0.0690531i	$-0.0219978\pi$
$191$	6.06717	+	10.5086i	0.439005	+	0.760379i	−0.558608	+	0.829432i	$0.688664\pi$
$192$	20.3711	+	11.7613i	1.47016	+	0.848797i
$193$	−10.3280	−	5.96290i	−0.743428	−	0.429219i	0.0798861	−	0.996804i	$-0.474544\pi$
$193$	−10.3280	−	5.96290i	−0.743428	−	0.429219i	−0.823315	+	0.567585i	$0.807878\pi$
$194$	−20.2938	−	35.1498i	−1.45701	−	2.52361i
$195$		0			0
$196$	−27.2999	−	25.1782i	−1.94999	−	1.79844i
$197$			5.50258i			0.392043i	0.980600	+	0.196021i	$0.0628022\pi$
$197$			5.50258i			0.392043i	−0.980600	+	0.196021i	$0.937198\pi$
$198$	−6.61376	+	3.81846i	−0.470020	+	0.271366i
$199$	−5.66404	+	9.81041i	−0.401513	+	0.695441i	−0.993909	−	0.110206i	$-0.964849\pi$
$199$	−5.66404	+	9.81041i	−0.401513	+	0.695441i	0.592396	+	0.805647i	$0.298182\pi$
$200$		0			0
$201$	−1.65271	−	2.86258i	−0.116573	−	0.201911i
$202$		−	6.03063i		−	0.424314i
$203$	−8.26419	+	6.61084i	−0.580032	+	0.463990i
$204$	22.4483			1.57170
$205$		0			0
$206$	−10.5980	+	18.3562i	−0.738394	+	1.27894i
$207$	5.72515	+	3.30542i	0.397926	+	0.229742i
$208$	52.5184	−	30.3215i	3.64149	−	2.10242i
$209$	−5.93437			−0.410489
$210$		0			0
$211$	8.82095			0.607259			0.303630	−	0.952790i	$-0.401801\pi$
$211$	8.82095			0.607259			0.303630	+	0.952790i	$0.401801\pi$
$212$	11.8551	−	6.84454i	0.814211	−	0.470085i
$213$	9.89196	+	5.71113i	0.677786	+	0.391320i
$214$	−21.1321	+	36.6020i	−1.44456	+	2.50206i
$215$		0			0
$216$	−8.93406			−0.607886
$217$	3.71640	+	24.4075i	0.252286	+	1.65689i
$218$		−	8.30914i		−	0.562766i
$219$	−1.32550	−	2.29584i	−0.0895691	−	0.155138i
$220$		0			0
$221$	9.47773	−	16.4159i	0.637541	−	1.10425i
$222$	−9.84311	+	5.68292i	−0.660627	+	0.381413i
$223$			26.4885i			1.77380i	0.461961	+	0.886900i	$0.347146\pi$
$223$			26.4885i			1.77380i	−0.461961	+	0.886900i	$0.652854\pi$
$224$	−48.9625	+	7.45527i	−3.27145	+	0.498126i
$225$		0			0
$226$	−0.471645	−	0.816914i	−0.0313734	−	0.0543403i
$227$	−15.3904	−	8.88562i	−1.02149	−	0.589760i	−0.106957	−	0.994264i	$-0.534111\pi$
$227$	−15.3904	−	8.88562i	−1.02149	−	0.589760i	−0.914536	+	0.404504i	$0.867444\pi$
$228$	−9.65005	−	5.57146i	−0.639090	−	0.368979i
$229$	9.32244	+	16.1469i	0.616044	+	1.06702i	0.990200	+	0.139654i	$0.0445991\pi$
$229$	9.32244	+	16.1469i	0.616044	+	1.06702i	−0.374156	+	0.927366i	$0.622068\pi$
$230$		0			0
$231$	2.72066	−	6.96292i	0.179006	−	0.458126i
$232$			35.7362i			2.34620i
$233$	−8.46002	+	4.88440i	−0.554234	+	0.319987i	−0.750828	−	0.660498i	$-0.770345\pi$
$233$	−8.46002	+	4.88440i	−0.554234	+	0.319987i	0.196594	+	0.980485i	$0.437012\pi$
$234$	−6.05428	+	10.4863i	−0.395781	+	0.685512i
$235$		0			0
$236$	10.0414	+	17.3922i	0.653639	+	1.13214i
$237$		−	12.6369i		−	0.820856i
$238$	−23.6280	+	18.9009i	−1.53158	+	1.22517i
$239$	6.20058			0.401082			0.200541	−	0.979685i	$-0.435730\pi$
$239$	6.20058			0.401082			0.200541	+	0.979685i	$0.435730\pi$
$240$		0			0
$241$	10.1191	−	17.5268i	0.651829	−	1.12900i	−0.330850	−	0.943684i	$-0.607335\pi$
$241$	10.1191	−	17.5268i	0.651829	−	1.12900i	0.982679	−	0.185318i	$-0.0593314\pi$
$242$	7.06095	+	4.07664i	0.453895	+	0.262056i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	26.5271			1.69822
$245$		0			0
$246$	−6.43179			−0.410076
$247$	−8.14854	+	4.70456i	−0.518479	+	0.299344i
$248$	72.1990	+	41.6841i	4.58464	+	2.64694i
$249$	1.51304	−	2.62066i	0.0958850	−	0.166078i
$250$		0			0
$251$	−6.21466			−0.392266			−0.196133	−	0.980577i	$-0.562838\pi$
$251$	−6.21466			−0.392266			−0.196133	+	0.980577i	$0.562838\pi$
$252$	10.9612	−	8.76831i	0.690494	−	0.552352i
$253$			18.6789i			1.17433i
$254$	−3.06960	−	5.31670i	−0.192604	−	0.333599i
$255$		0			0
$256$	−11.8027	+	20.4428i	−0.737667	+	1.27768i
$257$	−4.89604	+	2.82673i	−0.305407	+	0.176327i	−0.644869	−	0.764293i	$-0.723088\pi$
$257$	−4.89604	+	2.82673i	−0.305407	+	0.176327i	0.339463	+	0.940620i	$0.389755\pi$
$258$		−	8.46242i		−	0.526847i
$259$	4.04910	−	10.3627i	0.251599	−	0.643910i
$260$		0			0
$261$	−2.00000	−	3.46410i	−0.123797	−	0.214423i
$262$	−44.9929	−	25.9767i	−2.77967	−	1.60484i
$263$	−21.6610	−	12.5060i	−1.33568	−	0.771153i	−0.349513	−	0.936932i	$-0.613653\pi$
$263$	−21.6610	−	12.5060i	−1.33568	−	0.771153i	−0.986163	+	0.165779i	$0.946986\pi$
$264$	−12.6216	−	21.8613i	−0.776806	−	1.34547i
$265$		0			0
$266$	14.8482	−	2.26086i	0.910401	−	0.138622i
$267$			8.23121i			0.503742i
$268$	15.1872	−	8.76831i	0.927704	−	0.535610i
$269$	−3.94111	+	6.82619i	−0.240293	+	0.416200i	−0.960798	−	0.277250i	$-0.910577\pi$
$269$	−3.94111	+	6.82619i	−0.240293	+	0.416200i	0.720504	+	0.693450i	$0.243910\pi$
$270$		0			0
$271$	−2.37136	−	4.10731i	−0.144050	−	0.249501i	0.784968	−	0.619536i	$-0.212679\pi$
$271$	−2.37136	−	4.10731i	−0.144050	−	0.249501i	−0.929018	+	0.370035i	$0.879346\pi$
$272$			57.2763i			3.47289i
$273$	−1.78419	−	11.7177i	−0.107984	−	0.709187i
$274$	−22.3305			−1.34904
$275$		0			0
$276$	−17.5366	+	30.3743i	−1.05558	+	1.82832i
$277$	6.70062	+	3.86860i	0.402601	+	0.232442i	0.687606	−	0.726084i	$-0.258662\pi$
$277$	6.70062	+	3.86860i	0.402601	+	0.232442i	−0.285005	+	0.958526i	$0.591995\pi$
$278$	−2.30777	+	1.33239i	−0.138411	+	0.0799115i
$279$	−9.33150			−0.558662
$280$		0			0
$281$	2.11779			0.126337			0.0631684	−	0.998003i	$-0.479879\pi$
$281$	2.11779			0.126337			0.0631684	+	0.998003i	$0.479879\pi$
$282$	−18.2234	+	10.5213i	−1.08519	+	0.626535i
$283$	−3.80856	−	2.19887i	−0.226395	−	0.130709i	0.382513	−	0.923950i	$-0.375059\pi$
$283$	−3.80856	−	2.19887i	−0.226395	−	0.130709i	−0.608908	+	0.793241i	$0.708392\pi$
$284$	−30.2999	+	52.4810i	−1.79797	+	3.11417i
$285$		0			0
$286$	−34.2128			−2.02304
$287$	4.91642	−	3.93283i	0.290207	−	0.232148i
$288$		−	18.7194i		−	1.10305i
$289$	0.451563	+	0.782129i	0.0265625	+	0.0460076i
$290$		0			0
$291$	−7.50827	+	13.0047i	−0.440143	+	0.762350i
$292$	12.1804	−	7.03234i	0.712802	−	0.411536i
$293$		−	14.2006i		−	0.829607i	−0.909911	−	0.414803i	$-0.863850\pi$
$293$		−	14.2006i		−	0.829607i	0.909911	−	0.414803i	$-0.136150\pi$
$294$	−4.15457	+	18.4582i	−0.242299	+	1.07650i
$295$		0			0
$296$	−18.7844	−	32.5356i	−1.09182	−	1.89109i
$297$	2.44696	+	1.41275i	0.141987	+	0.0819761i
$298$	18.3068	+	10.5694i	1.06049	+	0.612271i
$299$	14.8080	+	25.6482i	0.856369	+	1.48327i
$300$		0			0
$301$	5.17450	+	6.46863i	0.298253	+	0.372846i
$302$		−	8.47165i		−	0.487488i
$303$	−1.93228	+	1.11560i	−0.111007	+	0.0640898i
$304$	14.2154	−	24.6218i	0.815310	−	1.41216i
$305$		0			0
$306$	−5.71817	−	9.90416i	−0.326886	−	0.566183i
$307$			13.9423i			0.795731i	0.917444	+	0.397866i	$0.130249\pi$
$307$			13.9423i			0.795731i	−0.917444	+	0.397866i	$0.869751\pi$
$308$	36.9412	+	14.4342i	2.10492	+	0.822467i
$309$	7.84205			0.446118
$310$		0			0
$311$	1.89971	−	3.29040i	0.107723	−	0.186581i	−0.807125	−	0.590381i	$-0.798977\pi$
$311$	1.89971	−	3.29040i	0.107723	−	0.186581i	0.914847	+	0.403800i	$0.132311\pi$
$312$	−34.6617	−	20.0119i	−1.96233	−	1.13295i
$313$	24.1600	−	13.9488i	1.36561	−	0.788433i	0.375243	−	0.926926i	$-0.377559\pi$
$313$	24.1600	−	13.9488i	1.36561	−	0.788433i	0.990363	+	0.138493i	$0.0442259\pi$
$314$	−63.4602			−3.58127
$315$		0			0
$316$	67.0441			3.77153
$317$	−29.8740	+	17.2478i	−1.67789	+	0.968730i	−0.714887	+	0.699240i	$0.753522\pi$
$317$	−29.8740	+	17.2478i	−1.67789	+	0.968730i	−0.963003	+	0.269490i	$0.913145\pi$
$318$	−6.03959	−	3.48696i	−0.338684	−	0.195539i
$319$	5.65100	−	9.78782i	0.316395	−	0.548013i
$320$		0			0
$321$	15.6369			0.872768
$322$	−7.11624	−	46.7359i	−0.396572	−	2.60449i
$323$		−	8.88676i		−	0.494473i
$324$	2.65271	+	4.59463i	0.147373	+	0.255257i
$325$		0			0
$326$	−16.8068	+	29.1102i	−0.930843	+	1.61227i
$327$	−2.66234	+	1.53710i	−0.147228	+	0.0850021i
$328$		−	21.2597i		−	1.17387i
$329$	7.49646	−	19.1855i	0.413293	−	1.05773i
$330$		0			0
$331$	14.9471	+	25.8891i	0.821567	+	1.42300i	0.904515	+	0.426442i	$0.140233\pi$
$331$	14.9471	+	25.8891i	0.821567	+	1.42300i	−0.0829479	+	0.996554i	$0.526434\pi$
$332$	13.9037	+	8.02731i	0.763065	+	0.440556i
$333$	3.64175	+	2.10256i	0.199567	+	0.115220i
$334$	−24.9316	−	43.1827i	−1.36419	−	2.36285i
$335$		0			0
$336$	22.3721	+	27.9673i	1.22050	+	1.52574i
$337$		−	19.3480i		−	1.05395i	−0.849879	−	0.526977i	$-0.823325\pi$
$337$		−	19.3480i		−	1.05395i	0.849879	−	0.526977i	$-0.176675\pi$
$338$	−16.5482	+	9.55413i	−0.900105	+	0.519676i
$339$	−0.174499	+	0.302241i	−0.00947748	+	0.0164155i
$340$		0			0
$341$	−13.1831	−	22.8338i	−0.713904	−	1.23652i
$342$			5.67677i			0.306965i
$343$	−8.11087	−	16.6497i	−0.437946	−	0.899001i
$344$	27.9718			1.50814
$345$		0			0
$346$	10.3398	−	17.9090i	0.555869	−	0.962794i
$347$	22.7764	+	13.1500i	1.22270	+	0.705927i	0.965493	−	0.260429i	$-0.0838642\pi$
$347$	22.7764	+	13.1500i	1.22270	+	0.705927i	0.257208	+	0.966356i	$0.417197\pi$
$348$	18.3785	−	10.6108i	0.985191	−	0.568801i
$349$	14.9083			0.798022			0.399011	−	0.916946i	$-0.369353\pi$
$349$	14.9083			0.798022			0.399011	+	0.916946i	$0.369353\pi$
$350$		0			0
$351$	4.47992			0.239120
$352$	45.8055	−	26.4458i	2.44144	−	1.40957i
$353$	13.7013	+	7.91048i	0.729249	+	0.421032i	0.818147	−	0.575009i	$-0.195001\pi$
$353$	13.7013	+	7.91048i	0.729249	+	0.421032i	−0.0888984	+	0.996041i	$0.528335\pi$
$354$	5.11560	−	8.86049i	0.271891	−	0.470930i
$355$		0			0
$356$	−43.6700			−2.31451
$357$	10.4270	+	4.07421i	0.551856	+	0.215630i
$358$			6.51458i			0.344306i
$359$	8.33854	+	14.4428i	0.440091	+	0.762261i	0.997696	−	0.0678462i	$-0.0216127\pi$
$359$	8.33854	+	14.4428i	0.440091	+	0.762261i	−0.557604	+	0.830107i	$0.688279\pi$
$360$		0			0
$361$	7.29439	−	12.6343i	0.383915	−	0.664961i
$362$	−32.0612	+	18.5105i	−1.68510	+	0.972893i
$363$		−	3.01654i		−	0.158328i
$364$	62.1673	−	9.46588i	3.25845	−	0.496147i
$365$		0			0
$366$	−6.75713	−	11.7037i	−0.353201	−	0.611762i
$367$	24.4112	+	14.0938i	1.27425	+	0.735691i	0.975786	−	0.218728i	$-0.0701908\pi$
$367$	24.4112	+	14.0938i	1.27425	+	0.735691i	0.298469	+	0.954419i	$0.403524\pi$
$368$	−77.4993	−	44.7442i	−4.03993	−	2.33245i
$369$	1.18981	+	2.06082i	0.0619392	+	0.107282i
$370$		0			0
$371$	6.74880	−	1.02760i	0.350380	−	0.0533506i
$372$		−	49.5075i		−	2.56684i
$373$	20.7838	−	11.9995i	1.07614	−	0.621312i	0.146290	−	0.989242i	$-0.453267\pi$
$373$	20.7838	−	11.9995i	1.07614	−	0.621312i	0.929853	+	0.367930i	$0.119933\pi$
$374$	16.1567	−	27.9842i	0.835443	−	1.44703i
$375$		0			0
$376$	−34.7773	−	60.2361i	−1.79350	−	3.10644i
$377$		−	17.9197i		−	0.922910i
$378$	−6.66067	−	2.60256i	−0.342588	−	0.133861i
$379$	−13.8550			−0.711683			−0.355842	−	0.934546i	$-0.615806\pi$
$379$	−13.8550			−0.711683			−0.355842	+	0.934546i	$0.615806\pi$
$380$		0			0
$381$	−1.13569	+	1.96707i	−0.0581830	+	0.100776i
$382$	28.4033	+	16.3987i	1.45324	+	0.839029i
$383$	−26.6532	+	15.3882i	−1.36191	+	0.786301i	−0.989878	−	0.141918i	$-0.954673\pi$
$383$	−26.6532	+	15.3882i	−1.36191	+	0.786301i	−0.372034	+	0.928219i	$0.621340\pi$
$384$	26.1392			1.33391
$385$		0			0
$386$	−32.2337			−1.64065
$387$	−2.71146	+	1.56546i	−0.137831	+	0.0795768i
$388$	−68.9954	−	39.8345i	−3.50271	−	2.02229i
$389$	19.2064	−	33.2664i	0.973801	−	1.68667i	0.289965	−	0.957037i	$-0.406356\pi$
$389$	19.2064	−	33.2664i	0.973801	−	1.68667i	0.683836	−	0.729636i	$-0.260310\pi$
$390$		0			0
$391$	−27.9718			−1.41460
$392$	−61.0121	−	13.7326i	−3.08157	−	0.693601i
$393$			19.2217i			0.969605i
$394$	7.43634	+	12.8801i	0.374637	+	0.648891i
$395$		0			0
$396$	−7.49523	+	12.9821i	−0.376650	+	0.652376i
$397$	28.9785	−	16.7307i	1.45439	−	0.839691i	0.455662	−	0.890153i	$-0.349403\pi$
$397$	28.9785	−	16.7307i	1.45439	−	0.839691i	0.998726	+	0.0504616i	$0.0160693\pi$
$398$			30.6182i			1.53475i
$399$	−3.47117	−	4.33930i	−0.173776	−	0.217237i
$400$		0			0
$401$	−7.42102	−	12.8536i	−0.370588	−	0.641878i	0.619068	−	0.785337i	$-0.287511\pi$
$401$	−7.42102	−	12.8536i	−0.370588	−	0.641878i	−0.989656	+	0.143460i	$0.954177\pi$
$402$	−7.73712	−	4.46703i	−0.385893	−	0.222795i
$403$	−36.2036	−	20.9022i	−1.80343	−	1.04121i
$404$	−5.91875	−	10.2516i	−0.294469	−	0.510035i
$405$		0			0
$406$	−10.4103	+	26.6427i	−0.516652	+	1.32225i
$407$			11.8816i			0.588949i
$408$	32.7374	−	18.9009i	1.62074	−	0.935736i
$409$	4.22246	−	7.31351i	0.208787	−	0.361630i	−0.742546	−	0.669796i	$-0.766382\pi$
$409$	4.22246	−	7.31351i	0.208787	−	0.361630i	0.951333	+	0.308166i	$0.0997151\pi$
$410$		0			0
$411$	4.13092	+	7.15496i	0.203763	+	0.352928i
$412$			41.6053i			2.04975i
$413$	1.50756	+	9.90094i	0.0741824	+	0.487193i
$414$	17.8681			0.878170
$415$		0			0
$416$	41.9307	−	72.6261i	2.05582	−	3.56079i
$417$	0.853827	+	0.492957i	0.0418121	+	0.0241402i
$418$	−13.8908	+	8.01987i	−0.679422	+	0.392264i
$419$	18.8427			0.920524			0.460262	−	0.887783i	$-0.347755\pi$
$419$	18.8427			0.920524			0.460262	+	0.887783i	$0.347755\pi$
$420$		0			0
$421$	−9.09687			−0.443355			−0.221677	−	0.975120i	$-0.571153\pi$
$421$	−9.09687			−0.443355			−0.221677	+	0.975120i	$0.571153\pi$
$422$	20.6476	−	11.9209i	1.00511	−	0.580299i
$423$	6.74230	+	3.89267i	0.327822	+	0.189268i
$424$	11.5259	−	19.9634i	0.559745	−	0.969507i
$425$		0			0
$426$	30.8727			1.49579
$427$	12.3216	+	4.81448i	0.596282	+	0.232989i
$428$			82.9604i			4.01004i
$429$	6.32901	+	10.9622i	0.305567	+	0.529258i
$430$		0			0
$431$	2.47992	−	4.29534i	0.119453	−	0.206899i	−0.800098	−	0.599870i	$-0.795219\pi$
$431$	2.47992	−	4.29534i	0.119453	−	0.206899i	0.919551	+	0.392970i	$0.128552\pi$
$432$	−11.7231	+	6.76831i	−0.564026	+	0.325641i
$433$		−	2.61696i		−	0.125763i	−0.998021	−	0.0628815i	$-0.979971\pi$
$433$		−	2.61696i		−	0.125763i	0.998021	−	0.0628815i	$-0.0200290\pi$
$434$	41.6841	+	52.1092i	2.00090	+	2.50132i
$435$		0			0
$436$	−8.15498	−	14.1248i	−0.390553	−	0.676458i
$437$	12.0245	+	6.94233i	0.575209	+	0.332097i
$438$	−6.20531	−	3.58264i	−0.296501	−	0.171185i
$439$	−13.2525	−	22.9540i	−0.632508	−	1.09554i	−0.987037	−	0.160491i	$-0.948692\pi$
$439$	−13.2525	−	22.9540i	−0.632508	−	1.09554i	0.354529	−	0.935045i	$-0.384641\pi$
$440$		0			0
$441$	6.68277	−	2.08340i	0.318227	−	0.0992097i
$442$		−	51.2338i		−	2.43695i
$443$	34.1996	−	19.7452i	1.62487	−	0.938121i	0.639284	−	0.768971i	$-0.279231\pi$
$443$	34.1996	−	19.7452i	1.62487	−	0.938121i	0.985590	−	0.169150i	$-0.0541023\pi$
$444$	−11.1550	+	19.3210i	−0.529392	+	0.916934i
$445$		0			0
$446$	35.7973	+	62.0027i	1.69505	+	2.93591i
$447$		−	7.82095i		−	0.369918i
$448$	−48.5987	+	38.8759i	−2.29607	+	1.83671i
$449$	−21.3045			−1.00542			−0.502710	−	0.864455i	$-0.667664\pi$
$449$	−21.3045			−1.00542			−0.502710	+	0.864455i	$0.667664\pi$
$450$		0			0
$451$	−3.36182	+	5.82284i	−0.158302	+	0.274187i
$452$	−1.60352	−	0.925790i	−0.0754230	−	0.0435455i
$453$	−2.71441	+	1.56717i	−0.127534	+	0.0736319i
$454$	−48.0331			−2.25430
$455$		0			0
$456$	−18.7641			−0.878710
$457$	−24.1449	+	13.9401i	−1.12945	+	0.652088i	−0.943797	−	0.330527i	$-0.892774\pi$
$457$	−24.1449	+	13.9401i	−1.12945	+	0.652088i	−0.185654	+	0.982615i	$0.559440\pi$
$458$	43.6428	+	25.1972i	2.03929	+	1.17739i
$459$	−2.11560	+	3.66433i	−0.0987479	+	0.171036i
$460$		0			0
$461$	22.5237			1.04903			0.524516	−	0.851401i	$-0.324246\pi$
$461$	22.5237			1.04903			0.524516	+	0.851401i	$0.324246\pi$
$462$	−3.04151	−	19.9751i	−0.141504	−	0.929328i
$463$		−	1.69301i		−	0.0786809i	−0.999226	−	0.0393405i	$-0.987474\pi$
$463$		−	1.69301i		−	0.0786809i	0.999226	−	0.0393405i	$-0.0125257\pi$
$464$	27.0733	+	46.8923i	1.25684	+	2.17692i
$465$		0			0
$466$	−13.2018	+	22.8662i	−0.611562	+	1.05926i
$467$	0.0695685	−	0.0401654i	0.00321925	−	0.00185863i	−0.498390	−	0.866953i	$-0.666075\pi$
$467$	0.0695685	−	0.0401654i	0.00321925	−	0.00185863i	0.501609	+	0.865095i	$0.332742\pi$
$468$			23.7678i			1.09867i
$469$	8.64567	−	1.31643i	0.399220	−	0.0607871i
$470$		0			0
$471$	11.7395	+	20.3334i	0.540927	+	0.936913i
$472$	29.2876	+	16.9092i	1.34807	+	0.778310i
$473$	−7.66122	−	4.42321i	−0.352263	−	0.203379i
$474$	−17.0779	−	29.5797i	−0.784412	−	1.35864i
$475$		0			0
$476$	−21.6154	+	55.3197i	−0.990740	+	2.53557i
$477$			2.58021i			0.118140i
$478$	14.5139	−	8.37963i	0.663852	−	0.383275i
$479$	−19.3891	+	33.5830i	−0.885912	+	1.53444i	−0.0412471	+	0.999149i	$0.513133\pi$
$479$	−19.3891	+	33.5830i	−0.885912	+	1.53444i	−0.844665	+	0.535295i	$0.820200\pi$
$480$		0			0
$481$	9.41932	+	16.3147i	0.429484	+	0.743888i
$482$		−	54.7009i		−	2.49156i
$483$	−13.6583	+	10.9258i	−0.621474	+	0.497141i
$484$	16.0040			0.727456
$485$		0			0
$486$	1.35143	−	2.34074i	0.0613020	−	0.106178i
$487$	−23.4961	−	13.5655i	−1.06471	−	0.614710i	−0.137977	−	0.990435i	$-0.544060\pi$
$487$	−23.4961	−	13.5655i	−1.06471	−	0.614710i	−0.926731	+	0.375726i	$0.877393\pi$
$488$	38.6856	−	22.3352i	1.75122	−	1.01106i
$489$	12.4363			0.562391
$490$		0			0
$491$	16.7243			0.754755			0.377378	−	0.926059i	$-0.376826\pi$
$491$	16.7243			0.754755			0.377378	+	0.926059i	$0.376826\pi$
$492$	−10.9335	+	6.31246i	−0.492920	+	0.284588i
$493$	14.6573	+	8.46242i	0.660133	+	0.381128i
$494$	−12.7157	+	22.0243i	−0.572108	+	0.990920i
$495$		0			0
$496$	126.317			5.67180
$497$	−23.5989	+	18.8777i	−1.05856	+	0.846779i
$498$		−	8.17905i		−	0.366512i
$499$	9.89219	+	17.1338i	0.442835	+	0.767013i	0.997899	−	0.0647949i	$-0.0206393\pi$
$499$	9.89219	+	17.1338i	0.442835	+	0.767013i	−0.555063	+	0.831808i	$0.687306\pi$
$500$		0			0
$501$	−9.22417	+	15.9767i	−0.412105	+	0.713787i
$502$	−14.5469	+	8.39866i	−0.649261	+	0.374851i
$503$		−	6.75015i		−	0.300975i	−0.988612	−	0.150487i	$-0.951916\pi$
$503$		−	6.75015i		−	0.300975i	0.988612	−	0.150487i	$-0.0480843\pi$
$504$	8.60256	−	22.0163i	0.383189	−	0.980685i
$505$		0			0
$506$	25.2432	+	43.7225i	1.12220	+	1.94370i
$507$	6.12250	+	3.53483i	0.271910	+	0.156987i
$508$	−10.4361	−	6.02529i	−0.463028	−	0.267329i
$509$	−20.1735	−	34.9416i	−0.894177	−	1.54876i	−0.834820	−	0.550522i	$-0.814429\pi$
$509$	−20.1735	−	34.9416i	−0.894177	−	1.54876i	−0.0593561	−	0.998237i	$-0.518905\pi$
$510$		0			0
$511$	6.93397	−	1.05580i	0.306741	−	0.0467058i
$512$			11.5234i			0.509266i
$513$	1.81890	−	1.05014i	0.0803066	−	0.0463650i
$514$	−7.64024	+	13.2333i	−0.336996	+	0.583695i
$515$		0			0
$516$	−8.30542	−	14.3854i	−0.365626	−	0.633282i
$517$			21.9975i			0.967448i
$518$	−4.52661	−	29.7286i	−0.198888	−	1.30620i
$519$	−7.65100			−0.335842
$520$		0			0
$521$	−18.8019	+	32.5658i	−0.823725	+	1.42673i	0.0791643	+	0.996862i	$0.474775\pi$
$521$	−18.8019	+	32.5658i	−0.823725	+	1.42673i	−0.902890	+	0.429872i	$0.858559\pi$
$522$	−9.36296	−	5.40571i	−0.409806	−	0.236601i
$523$	34.0456	−	19.6562i	1.48871	−	0.859506i	0.488792	−	0.872401i	$-0.337438\pi$
$523$	34.0456	−	19.6562i	1.48871	−	0.859506i	0.999917	+	0.0128944i	$0.00410453\pi$
$524$	−101.979			−4.45497
$525$		0			0
$526$	−67.6038			−2.94766
$527$	34.1937	−	19.7418i	1.48950	−	0.859964i
$528$	−33.1235	−	19.1239i	−1.44152	−	0.832260i
$529$	10.3516	−	17.9295i	0.450069	−	0.779542i
$530$		0			0
$531$	−3.78534			−0.164270
$532$	23.0218	−	18.4160i	0.998121	−	0.798435i
$533$			10.6605i			0.461759i
$534$	11.1239	+	19.2671i	0.481377	+	0.833770i
$535$		0			0
$536$	14.7654	−	25.5744i	0.637768	−	1.10465i
$537$	2.08734	−	1.20513i	0.0900756	−	0.0520052i
$538$			21.3045i			0.918501i
$539$	14.5391	+	13.4091i	0.626243	+	0.577571i
$540$		0			0
$541$	−10.7861	−	18.6821i	−0.463732	−	0.803207i	0.535412	−	0.844591i	$-0.320156\pi$
$541$	−10.7861	−	18.6821i	−0.463732	−	0.803207i	−0.999143	+	0.0413846i	$0.986823\pi$
$542$	−11.1015	−	6.40943i	−0.476848	−	0.275309i
$543$	11.8620	+	6.84852i	0.509046	+	0.293898i
$544$	39.6028	+	68.5941i	1.69796	+	2.94095i
$545$		0			0
$546$	−20.0119	−	25.0169i	−0.856432	−	1.07062i
$547$			21.3707i			0.913745i	0.889532	+	0.456873i	$0.151031\pi$
$547$			21.3707i			0.913745i	−0.889532	+	0.456873i	$0.848969\pi$
$548$	−37.9601	+	21.9163i	−1.62157	+	0.936216i
$549$	−2.50000	+	4.33013i	−0.106697	+	0.184805i
$550$		0			0
$551$	−4.20058	−	7.27562i	−0.178951	−	0.309952i
$552$			59.0616i			2.51383i
$553$	31.1413	+	12.1680i	1.32426	+	0.517437i
$554$	20.9125			0.888488
$555$		0			0
$556$	−2.61534	+	4.52991i	−0.110915	+	0.192111i
$557$	12.3511	+	7.13092i	0.523334	+	0.302147i	0.738297	−	0.674475i	$-0.235630\pi$
$557$	12.3511	+	7.13092i	0.523334	+	0.302147i	−0.214964	+	0.976622i	$0.568963\pi$
$558$	−21.8426	+	12.6108i	−0.924671	+	0.533859i
$559$	−14.0263			−0.593248
$560$		0			0
$561$	−11.9553			−0.504752
$562$	4.95719	−	2.86204i	0.209107	−	0.120728i
$563$	2.04649	+	1.18154i	0.0862493	+	0.0497961i	0.542504	−	0.840053i	$-0.317476\pi$
$563$	2.04649	+	1.18154i	0.0862493	+	0.0497961i	−0.456255	+	0.889849i	$0.650810\pi$
$564$	−20.6522	+	35.7707i	−0.869616	+	1.50622i
$565$		0			0
$566$	−11.8865			−0.499625
$567$	0.398264	+	2.61560i	0.0167255	+	0.109845i
$568$			102.047i			4.28180i
$569$	−6.37289	−	11.0382i	−0.267166	−	0.462744i	0.700963	−	0.713197i	$-0.252754\pi$
$569$	−6.37289	−	11.0382i	−0.267166	−	0.462744i	−0.968129	+	0.250453i	$0.919420\pi$
$570$		0			0
$571$	−0.180757	+	0.313080i	−0.00756444	+	0.0131020i	−0.869783	−	0.493435i	$-0.835741\pi$
$571$	−0.180757	+	0.313080i	−0.00756444	+	0.0131020i	0.862218	+	0.506537i	$0.169075\pi$
$572$	−58.1588	+	33.5780i	−2.43174	+	1.40397i
$573$		−	12.1343i		−	0.506919i
$574$	6.19314	−	15.8499i	0.258496	−	0.661563i
$575$		0			0
$576$	−11.7613	−	20.3711i	−0.490053	−	0.848797i
$577$	8.30807	+	4.79667i	0.345870	+	0.199688i	0.662865	−	0.748739i	$-0.269341\pi$
$577$	8.30807	+	4.79667i	0.345870	+	0.199688i	−0.316995	+	0.948427i	$0.602674\pi$
$578$	2.11398	+	1.22051i	0.0879300	+	0.0507664i
$579$	5.96290	+	10.3280i	0.247809	+	0.429219i
$580$		0			0
$581$	5.00123	+	6.25202i	0.207486	+	0.259378i
$582$			40.5875i			1.68241i
$583$	−6.31365	+	3.64519i	−0.261485	+	0.150968i
$584$	11.8421	−	20.5111i	0.490030	−	0.848757i
$585$		0			0
$586$	−19.1910	−	33.2399i	−0.792775	−	1.37313i
$587$		−	19.2217i		−	0.793363i	−0.917956	−	0.396682i	$-0.870162\pi$
$587$		−	19.2217i		−	0.793363i	0.917956	−	0.396682i	$-0.129838\pi$
$588$	11.0533	+	35.4549i	0.455832	+	1.46214i
$589$	−19.5988			−0.807556
$590$		0			0
$591$	2.75129	−	4.76538i	0.113173	−	0.196021i
$592$	−49.2970	−	28.4616i	−2.02609	−	1.16977i
$593$	10.2186	−	5.89971i	0.419628	−	0.242272i	−0.275290	−	0.961361i	$-0.588774\pi$
$593$	10.2186	−	5.89971i	0.419628	−	0.242272i	0.694918	+	0.719089i	$0.255441\pi$
$594$	7.63692			0.313346
$595$		0			0
$596$	41.4934			1.69964
$597$	9.81041	−	5.66404i	0.401513	−	0.231814i
$598$	69.3234	+	40.0239i	2.83484	+	1.63670i
$599$	20.1981	−	34.9841i	0.825271	−	1.42941i	−0.0764403	−	0.997074i	$-0.524355\pi$
$599$	20.1981	−	34.9841i	0.825271	−	1.42941i	0.901712	−	0.432338i	$-0.142311\pi$
$600$		0			0
$601$	−20.9073			−0.852828			−0.426414	−	0.904528i	$-0.640223\pi$
$601$	−20.9073			−0.852828			−0.426414	+	0.904528i	$0.640223\pi$
$602$	20.8540	+	8.14842i	0.849947	+	0.332105i
$603$			3.30542i			0.134607i
$604$	−8.31448	−	14.4011i	−0.338311	−	0.585972i
$605$		0			0
$606$	−3.01532	+	5.22268i	−0.122489	+	0.212157i
$607$	3.64388	−	2.10379i	0.147900	−	0.0853903i	−0.424224	−	0.905557i	$-0.639453\pi$
$607$	3.64388	−	2.10379i	0.147900	−	0.0853903i	0.572124	+	0.820167i	$0.306120\pi$
$608$		−	39.3161i		−	1.59448i
$609$	10.4624	−	1.59306i	0.423959	−	0.0645539i
$610$		0			0
$611$	17.4388	+	30.2049i	0.705500	+	1.22196i
$612$	−19.4408	−	11.2242i	−0.785849	−	0.453710i
$613$	14.2260	+	8.21340i	0.574584	+	0.331736i	0.758978	−	0.651116i	$-0.225699\pi$
$613$	14.2260	+	8.21340i	0.574584	+	0.331736i	−0.184394	+	0.982852i	$0.559032\pi$
$614$	18.8420	+	32.6354i	0.760403	+	1.31706i
$615$		0			0
$616$	66.0262	−	10.0535i	2.66027	−	0.405066i
$617$			21.9037i			0.881811i	0.897553	+	0.440906i	$0.145343\pi$
$617$			21.9037i			0.881811i	−0.897553	+	0.440906i	$0.854657\pi$
$618$	18.3562	−	10.5980i	0.738394	−	0.426312i
$619$	0.159752	−	0.276699i	0.00642098	−	0.0111215i	−0.862797	−	0.505550i	$-0.831289\pi$
$619$	0.159752	−	0.276699i	0.00642098	−	0.0111215i	0.869218	+	0.494429i	$0.164623\pi$
$620$		0			0
$621$	−3.30542	−	5.72515i	−0.132642	−	0.229742i
$622$		−	10.2693i		−	0.411761i
$623$	−20.2843	−	7.92579i	−0.812672	−	0.317540i
$624$	−60.6430			−2.42766
$625$		0			0
$626$	37.7016	−	65.3011i	1.50686	−	2.60996i
$627$	5.13931	+	2.96718i	0.205244	+	0.118498i
$628$	−107.877	+	62.2829i	−4.30476	+	2.48536i
$629$	−17.7928			−0.709445
$630$		0			0
$631$	17.3090			0.689061			0.344530	−	0.938775i	$-0.388038\pi$
$631$	17.3090			0.689061			0.344530	+	0.938775i	$0.388038\pi$
$632$	97.7734	−	56.4495i	3.88922	−	2.24544i
$633$	−7.63917	−	4.41048i	−0.303630	−	0.175301i
$634$	−46.6182	+	80.7450i	−1.85144	+	3.20679i
$635$		0			0
$636$	−13.6891			−0.542807
$637$	30.5940	+	6.88610i	1.21218	+	0.272837i
$638$		−	30.5477i		−	1.20939i
$639$	−5.71113	−	9.89196i	−0.225929	−	0.391320i
$640$		0			0
$641$	−24.1429	+	41.8168i	−0.953588	+	1.65166i	−0.216020	+	0.976389i	$0.569308\pi$
$641$	−24.1429	+	41.8168i	−0.953588	+	1.65166i	−0.737567	+	0.675273i	$0.764026\pi$
$642$	36.6020	−	21.1321i	1.44456	−	0.834019i
$643$		−	12.6460i		−	0.498710i	−0.968412	−	0.249355i	$-0.919781\pi$
$643$		−	12.6460i		−	0.498710i	0.968412	−	0.249355i	$-0.0802186\pi$
$644$	−57.9659	−	72.4630i	−2.28418	−	2.85544i
$645$		0			0
$646$	−12.0098	−	20.8016i	−0.472520	−	0.818428i
$647$	13.7295	+	7.92671i	0.539761	+	0.311631i	0.744982	−	0.667084i	$-0.232458\pi$
$647$	13.7295	+	7.92671i	0.539761	+	0.311631i	−0.205221	+	0.978716i	$0.565791\pi$
$648$	7.73712	+	4.46703i	0.303943	+	0.175482i
$649$	−5.34773	−	9.26255i	−0.209917	−	0.363587i
$650$		0			0
$651$	8.98525	−	22.9957i	0.352160	−	0.901273i
$652$			65.9800i			2.58398i
$653$	−1.00282	+	0.578977i	−0.0392433	+	0.0226571i	−0.519493	−	0.854475i	$-0.673879\pi$
$653$	−1.00282	+	0.578977i	−0.0392433	+	0.0226571i	0.480250	+	0.877132i	$0.340546\pi$
$654$	−4.15457	+	7.19593i	−0.162457	+	0.281383i
$655$		0			0
$656$	−16.1061	−	27.8965i	−0.628836	−	1.08918i
$657$			2.65100i			0.103425i
$658$	−8.38053	−	55.0392i	−0.326707	−	2.14565i
$659$	34.5617			1.34633			0.673167	−	0.739490i	$-0.264933\pi$
$659$	34.5617			1.34633			0.673167	+	0.739490i	$0.264933\pi$
$660$		0			0
$661$	0.640148	−	1.10877i	0.0248989	−	0.0431261i	−0.853307	−	0.521408i	$-0.825407\pi$
$661$	0.640148	−	1.10877i	0.0248989	−	0.0431261i	0.878206	+	0.478282i	$0.158740\pi$
$662$	69.9746	+	40.3998i	2.71964	+	1.57018i
$663$	−16.4159	+	9.47773i	−0.637541	+	0.368085i
$664$	27.0352			1.04917
$665$		0			0
$666$	11.3658			0.440418
$667$	−22.9006	+	13.2217i	−0.886715	+	0.511945i
$668$	−84.7632	−	48.9381i	−3.27959	−	1.89347i
$669$	13.2442	−	22.9397i	0.512052	−	0.886900i
$670$		0			0
$671$	−14.1275			−0.545386
$672$	46.1304	+	18.0248i	1.77952	+	0.695322i
$673$		−	45.9058i		−	1.76954i	−0.466031	−	0.884769i	$-0.654316\pi$
$673$		−	45.9058i		−	1.76954i	0.466031	−	0.884769i	$-0.345684\pi$
$674$	−26.1475	−	45.2887i	−1.00716	−	1.74446i
$675$		0			0
$676$	−18.7537	+	32.4824i	−0.721298	+	1.24932i
$677$	17.0694	−	9.85499i	0.656028	−	0.378758i	−0.134734	−	0.990882i	$-0.543018\pi$
$677$	17.0694	−	9.85499i	0.656028	−	0.378758i	0.790762	+	0.612124i	$0.209685\pi$
$678$			0.943291i			0.0362269i
$679$	−24.8180	−	31.0249i	−0.952427	−	1.19063i
$680$		0			0
$681$	8.88562	+	15.3904i	0.340498	+	0.589760i
$682$	−61.7163	−	35.6319i	−2.36324	−	1.36442i
$683$	1.24982	+	0.721583i	0.0478230	+	0.0276106i	0.523721	−	0.851890i	$-0.324543\pi$
$683$	1.24982	+	0.721583i	0.0478230	+	0.0276106i	−0.475898	+	0.879501i	$0.657877\pi$
$684$	5.57146	+	9.65005i	0.213030	+	0.368979i
$685$		0			0
$686$	−41.4863	−	28.0115i	−1.58396	−	1.06948i
$687$		−	18.6449i		−	0.711347i
$688$	36.7040	−	21.1910i	1.39933	−	0.807901i
$689$	−5.77956	+	10.0105i	−0.220184	+	0.381369i
$690$		0			0
$691$	15.4611	+	26.7793i	0.588167	+	1.01873i	0.994473	+	0.104997i	$0.0334834\pi$
$691$	15.4611	+	26.7793i	0.588167	+	1.01873i	−0.406306	+	0.913737i	$0.633183\pi$
$692$		−	40.5918i		−	1.54307i
$693$	−5.83762	+	4.66973i	−0.221753	+	0.177388i
$694$	71.0848			2.69834
$695$		0			0
$696$	17.8681	−	30.9485i	0.677290	−	1.17310i
$697$	−8.71975	−	5.03435i	−0.330284	−	0.190690i
$698$	34.8964	−	20.1475i	1.32085	−	0.762593i
$699$	9.76879			0.369490
$700$		0			0
$701$	50.6746			1.91395			0.956976	−	0.290168i	$-0.0937111\pi$
$701$	50.6746			1.91395			0.956976	+	0.290168i	$0.0937111\pi$
$702$	10.4863	−	6.05428i	0.395781	−	0.228504i
$703$	7.64873	+	4.41599i	0.288477	+	0.166552i
$704$	33.2315	−	57.5586i	1.25246	−	2.16932i
$705$		0			0
$706$	42.7617			1.60936
$707$	−0.888611	−	5.83596i	−0.0334196	−	0.219484i
$708$		−	20.0828i		−	0.754757i
$709$	−10.0885	−	17.4738i	−0.378881	−	0.656241i	0.612019	−	0.790843i	$-0.290358\pi$
$709$	−10.0885	−	17.4738i	−0.378881	−	0.656241i	−0.990900	+	0.134602i	$0.957024\pi$
$710$		0			0
$711$	−6.31846	+	10.9439i	−0.236961	+	0.410428i
$712$	−63.6859	+	36.7691i	−2.38673	+	1.37798i
$713$			61.6890i			2.31027i
$714$	29.9129	−	4.55469i	1.11946	−	0.170455i
$715$		0			0
$716$	6.39371	+	11.0742i	0.238944	+	0.413864i
$717$	−5.36986	−	3.10029i	−0.200541	−	0.115782i
$718$	39.0367	+	22.5379i	1.45684	+	0.841105i
$719$	22.6639	+	39.2551i	0.845221	+	1.46397i	0.885429	+	0.464775i	$0.153865\pi$
$719$	22.6639	+	39.2551i	0.845221	+	1.46397i	−0.0402072	+	0.999191i	$0.512802\pi$
$720$		0			0
$721$	−7.55107	+	19.3252i	−0.281216	+	0.719710i
$722$		−	39.4314i		−	1.46748i
$723$	−17.5268	+	10.1191i	−0.651829	+	0.376334i
$724$	−36.3343	+	62.9328i	−1.35035	+	2.33888i
$725$		0			0
$726$	−4.07664	−	7.06095i	−0.151298	−	0.262056i
$727$		−	16.9117i		−	0.627220i	−0.949552	−	0.313610i	$-0.898461\pi$
$727$		−	16.9117i		−	0.627220i	0.949552	−	0.313610i	$-0.101539\pi$
$728$	82.6912	−	66.1478i	3.06474	−	2.45160i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	6.62379	−	11.4727i	0.244990	−	0.424334i
$732$	−22.9731	−	13.2635i	−0.849112	−	0.490235i
$733$	6.20557	−	3.58279i	0.229208	−	0.132333i	−0.380999	−	0.924576i	$-0.624420\pi$
$733$	6.20557	−	3.58279i	0.229208	−	0.132333i	0.610207	+	0.792242i	$0.291086\pi$
$734$	76.1870			2.81211
$735$		0			0
$736$	−123.751			−4.56152
$737$	−8.08821	+	4.66973i	−0.297933	+	0.172012i
$738$	5.57009	+	3.21589i	0.205038	+	0.118379i
$739$	−10.1924	+	17.6537i	−0.374933	+	0.649404i	−0.990317	−	0.138824i	$-0.955668\pi$
$739$	−10.1924	+	17.6537i	−0.374933	+	0.649404i	0.615384	+	0.788228i	$0.289001\pi$
$740$		0			0
$741$	9.40912			0.345653
$742$	14.4085	−	11.5259i	0.528951	−	0.423128i
$743$			16.9267i			0.620982i	0.950576	+	0.310491i	$0.100493\pi$
$743$			16.9267i			0.620982i	−0.950576	+	0.310491i	$0.899507\pi$
$744$	−41.6841	−	72.1990i	−1.52821	−	2.64694i
$745$		0			0
$746$	32.4330	−	56.1755i	1.18745	−	2.05673i
$747$	−2.62066	+	1.51304i	−0.0958850	+	0.0553592i
$748$		−	63.4278i		−	2.31915i
$749$	−15.0567	+	38.5342i	−0.550160	+	1.40801i
$750$		0			0
$751$	−19.5439	−	33.8509i	−0.713165	−	1.23524i	−0.963663	−	0.267121i	$-0.913928\pi$
$751$	−19.5439	−	33.8509i	−0.713165	−	1.23524i	0.250498	−	0.968117i	$-0.419406\pi$
$752$	−91.2680	−	52.6936i	−3.32820	−	1.92154i
$753$	5.38206	+	3.10733i	0.196133	+	0.113237i
$754$	−24.2171	−	41.9453i	−0.881936	−	1.52756i
$755$		0			0
$756$	−13.8769	+	2.11296i	−0.504697	+	0.0768476i
$757$			22.6675i			0.823866i	0.911214	+	0.411933i	$0.135146\pi$
$757$			22.6675i			0.823866i	−0.911214	+	0.411933i	$0.864854\pi$
$758$	−32.4309	+	18.7240i	−1.17794	+	0.680087i
$759$	9.33946	−	16.1764i	0.339001	−	0.587167i
$760$		0			0
$761$	−5.16373	−	8.94385i	−0.187185	−	0.324214i	0.757125	−	0.653269i	$-0.226603\pi$
$761$	−5.16373	−	8.94385i	−0.187185	−	0.324214i	−0.944311	+	0.329055i	$0.893270\pi$
$762$			6.13919i			0.222399i
$763$	−1.22435	−	8.04092i	−0.0443244	−	0.291101i
$764$	64.3777			2.32910
$765$		0			0
$766$	−41.5921	+	72.0396i	−1.50278	+	2.60290i
$767$	−14.6861	−	8.47900i	−0.530283	−	0.306159i
$768$	20.4428	−	11.8027i	0.737667	−	0.425892i
$769$	25.8785			0.933204			0.466602	−	0.884467i	$-0.345478\pi$
$769$	25.8785			0.933204			0.466602	+	0.884467i	$0.345478\pi$
$770$		0			0
$771$	5.65346			0.203604
$772$	−54.7946	+	31.6357i	−1.97210	+	1.13859i
$773$	−8.10094	−	4.67708i	−0.291371	−	0.168223i	0.347189	−	0.937795i	$-0.387136\pi$
$773$	−8.10094	−	4.67708i	−0.291371	−	0.168223i	−0.638560	+	0.769572i	$0.720470\pi$
$774$	−4.23121	+	7.32867i	−0.152088	+	0.263424i
$775$		0			0
$776$	−134.159			−4.81602
$777$	−8.68800	+	6.94986i	−0.311680	+	0.249325i
$778$		−	103.824i		−	3.72227i
$779$	2.49895	+	4.32831i	0.0895343	+	0.155078i
$780$		0			0
$781$	16.1368	−	27.9497i	0.577420	−	1.00012i
$782$	−65.4748	+	37.8019i	−2.34137	+	1.35179i
$783$			4.00000i			0.142948i
$784$	−90.4622	+	28.2023i	−3.23079	+	1.00722i
$785$		0			0
$786$	25.9767	+	44.9929i	0.926558	+	1.60484i
$787$	−2.42650	−	1.40094i	−0.0864953	−	0.0499381i	0.456128	−	0.889914i	$-0.349236\pi$
$787$	−2.42650	−	1.40094i	−0.0864953	−	0.0499381i	−0.542624	+	0.839976i	$0.682569\pi$
$788$	25.2823	+	14.5968i	0.900645	+	0.519988i
$789$	12.5060	+	21.6610i	0.445225	+	0.771153i
$790$		0			0
$791$	−0.576792	−	0.721046i	−0.0205084	−	0.0256375i
$792$			25.2432i			0.896978i
$793$	−19.3986	+	11.1998i	−0.688865	+	0.397716i
$794$	45.2207	−	78.3246i	1.60482	−	2.77964i
$795$		0			0
$796$	30.0501	+	52.0483i	1.06510	+	1.84480i
$797$		−	13.0211i		−	0.461231i	−0.973045	−	0.230615i	$-0.925926\pi$
$797$		−	13.0211i		−	0.461231i	0.973045	−	0.230615i	$-0.0740739\pi$
$798$	−13.9893	−	5.46614i	−0.495217	−	0.193499i
$799$	−32.9414			−1.16538
$800$		0			0
$801$	4.11560	−	7.12844i	0.145418	−	0.251871i
$802$	−34.7414	−	20.0579i	−1.22676	−	0.708270i
$803$	−6.48688	+	3.74520i	−0.228917	+	0.132165i
$804$	−17.5366			−0.618469
$805$		0			0
$806$	−112.991			−3.97994
$807$	6.82619	−	3.94111i	0.240293	−	0.138733i
$808$	−17.2631	−	9.96688i	−0.607315	−	0.350634i
$809$	10.5105	−	18.2048i	0.369531	−	0.640047i	−0.619961	−	0.784633i	$-0.712852\pi$
$809$	10.5105	−	18.2048i	0.369531	−	0.640047i	0.989492	+	0.144586i	$0.0461850\pi$
$810$		0			0
$811$	−46.2591			−1.62438			−0.812189	−	0.583395i	$-0.801724\pi$
$811$	−46.2591			−1.62438			−0.812189	+	0.583395i	$0.801724\pi$
$812$	8.45184	+	55.5075i	0.296601	+	1.94793i
$813$			4.74271i			0.166334i
$814$	16.0571	+	27.8117i	0.562801	+	0.974801i
$815$		0			0
$816$	28.6381	−	49.6027i	1.00254	−	1.73644i
$817$	−5.69484	+	3.28792i	−0.199237	+	0.115030i
$818$		−	22.8254i		−	0.798070i
$819$	−4.31369	+	11.0399i	−0.150733	+	0.385766i
$820$		0			0
$821$	−8.46915	−	14.6690i	−0.295575	−	0.511952i	0.679543	−	0.733636i	$-0.262178\pi$
$821$	−8.46915	−	14.6690i	−0.295575	−	0.511952i	−0.975119	+	0.221684i	$0.928845\pi$
$822$	19.3388	+	11.1653i	0.674519	+	0.389434i
$823$	−16.0502	−	9.26661i	−0.559476	−	0.323014i	0.193459	−	0.981108i	$-0.438029\pi$
$823$	−16.0502	−	9.26661i	−0.559476	−	0.323014i	−0.752935	+	0.658095i	$0.771363\pi$
$824$	35.0307	+	60.6749i	1.22035	+	2.11371i
$825$		0			0
$826$	16.9092	+	21.1382i	0.588347	+	0.735491i
$827$			32.5496i			1.13186i	0.824453	+	0.565930i	$0.191483\pi$
$827$			32.5496i			1.13186i	−0.824453	+	0.565930i	$0.808517\pi$
$828$	30.3743	−	17.5366i	1.05558	−	0.609440i
$829$	−5.47764	+	9.48755i	−0.190246	+	0.329516i	−0.945332	−	0.326110i	$-0.894262\pi$
$829$	−5.47764	+	9.48755i	−0.190246	+	0.329516i	0.755085	+	0.655626i	$0.227595\pi$
$830$		0			0
$831$	−3.86860	−	6.70062i	−0.134200	−	0.232442i
$832$		−	105.379i		−	3.65336i
$833$	−20.0802	+	21.7724i	−0.695739	+	0.754368i
$834$	2.66478			0.0922738
$835$		0			0
$836$	−15.7422	+	27.2662i	−0.544454	+	0.943022i
$837$	8.08131	+	4.66575i	0.279331	+	0.161272i
$838$	44.1058	−	25.4645i	1.52361	−	0.879656i
$839$	−1.24074			−0.0428352			−0.0214176	−	0.999771i	$-0.506818\pi$
$839$	−1.24074			−0.0428352			−0.0214176	+	0.999771i	$0.506818\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	−21.2934	+	12.2938i	−0.733820	+	0.423671i
$843$	−1.83406	−	1.05889i	−0.0631684	−	0.0364703i
$844$	23.3994	−	40.5290i	0.805441	−	1.39506i
$845$		0			0
$846$	21.0426			0.723460
$847$	7.43371	+	2.90462i	0.255425	+	0.0998038i
$848$		−	34.9273i		−	1.19941i
$849$	2.19887	+	3.80856i	0.0754651	+	0.130709i
$850$		0			0
$851$	13.8997	−	24.0750i	0.476476	−	0.825281i
$852$	52.4810	−	30.2999i	1.79797	−	1.03806i
$853$		−	44.8500i		−	1.53564i	−0.640669	−	0.767818i	$-0.721343\pi$
$853$		−	44.8500i		−	1.53564i	0.640669	−	0.767818i	$-0.278657\pi$
$854$	35.3480	−	5.38225i	1.20958	−	0.184177i
$855$		0			0
$856$	69.8506	+	120.985i	2.38744	+	4.13517i
$857$	−33.4380	−	19.3054i	−1.14222	−	0.659461i	−0.195240	−	0.980756i	$-0.562549\pi$
$857$	−33.4380	−	19.3054i	−1.14222	−	0.659461i	−0.946979	+	0.321295i	$0.895882\pi$
$858$	29.6291	+	17.1064i	1.01152	+	0.584002i
$859$	17.5541	+	30.4046i	0.598939	+	1.03739i	0.992978	+	0.118299i	$0.0377442\pi$
$859$	17.5541	+	30.4046i	0.598939	+	1.03739i	−0.394039	+	0.919094i	$0.628922\pi$
$860$		0			0
$861$	−6.22417	+	0.947721i	−0.212119	+	0.0322982i
$862$		−	13.4057i		−	0.456600i
$863$	−4.28314	+	2.47287i	−0.145800	+	0.0841776i	−0.571125	−	0.820863i	$-0.693493\pi$
$863$	−4.28314	+	2.47287i	−0.145800	+	0.0841776i	0.425325	+	0.905040i	$0.360160\pi$
$864$	−9.35970	+	16.2115i	−0.318423	+	0.551526i
$865$		0			0
$866$	−3.53663	−	6.12562i	−0.120179	−	0.208157i
$867$		−	0.903125i		−	0.0306717i
$868$	122.002	+	47.6705i	4.14101	+	1.61804i
$869$	−35.7056			−1.21123
$870$		0			0
$871$	−7.40400	+	12.8241i	−0.250875	+	0.434528i
$872$	−23.7855	−	13.7326i	−0.805480	−	0.465044i
$873$	13.0047	−	7.50827i	0.440143	−	0.254117i
$874$	37.5282			1.26941
$875$		0			0
$876$	−14.0647			−0.475201
$877$	−9.27709	+	5.35613i	−0.313265	+	0.180864i	−0.648387	−	0.761311i	$-0.724556\pi$
$877$	−9.27709	+	5.35613i	−0.313265	+	0.180864i	0.335122	+	0.942175i	$0.391223\pi$
$878$	−62.0414	−	35.8196i	−2.09380	−	1.20885i
$879$	−7.10029	+	12.2981i	−0.239487	+	0.414803i
$880$		0			0
$881$	40.2527			1.35615			0.678075	−	0.734993i	$-0.262815\pi$
$881$	40.2527			1.35615			0.678075	+	0.734993i	$0.262815\pi$
$882$	12.8271	−	13.9080i	0.431910	−	0.468306i
$883$			26.2228i			0.882468i	0.897392	+	0.441234i	$0.145459\pi$
$883$			26.2228i			0.882468i	−0.897392	+	0.441234i	$0.854541\pi$
$884$	−50.2833	−	87.0933i	−1.69121	−	2.92926i
$885$		0			0
$886$	53.3683	−	92.4366i	1.79294	−	3.10547i
$887$	42.7785	−	24.6982i	1.43636	−	0.829284i	0.438767	−	0.898601i	$-0.355415\pi$
$887$	42.7785	−	24.6982i	1.43636	−	0.829284i	0.997595	+	0.0693174i	$0.0220821\pi$
$888$			37.5689i			1.26073i
$889$	−3.75392	−	4.69277i	−0.125902	−	0.157390i
$890$		0			0
$891$	−1.41275	−	2.44696i	−0.0473289	−	0.0819761i
$892$	121.705	+	70.2663i	4.07498	+	2.35269i
$893$	14.1608	+	8.17573i	0.473872	+	0.273590i
$894$	−10.5694	−	18.3068i	−0.353495	−	0.612271i
$895$		0			0
$896$	−25.1693	+	64.4151i	−0.840847	+	2.15196i
$897$		−	29.6160i		−	0.988850i
$898$	−49.8682	+	28.7914i	−1.66412	+	0.960782i
$899$	18.6630	−	32.3253i	0.622446	−	1.07811i
$900$		0			0
$901$	−5.45870	−	9.45474i	−0.181856	−	0.314983i
$902$			18.1730i			0.605095i
$903$	−1.24693	−	8.18925i	−0.0414953	−	0.272521i
$904$	−3.11797			−0.103702
$905$		0			0
$906$	−4.23582	+	7.33666i	−0.140726	+	0.243744i
$907$	−48.6385	−	28.0814i	−1.61501	−	0.932429i	−0.988184	−	0.153273i	$-0.951019\pi$
$907$	−48.6385	−	28.0814i	−1.61501	−	0.932429i	−0.626830	−	0.779156i	$-0.715648\pi$
$908$	−81.6523	+	47.1420i	−2.70973	+	1.56446i
$909$	2.23121			0.0740045
$910$		0			0
$911$	−35.9981			−1.19267			−0.596335	−	0.802736i	$-0.703377\pi$
$911$	−35.9981			−1.19267			−0.596335	+	0.802736i	$0.703377\pi$
$912$	−24.6218	+	14.2154i	−0.815310	+	0.470719i
$913$	−7.40468	−	4.27510i	−0.245059	−	0.141485i
$914$	−37.6779	+	65.2601i	−1.24628	+	2.15861i
$915$		0			0
$916$	98.9189			3.26837
$917$	−47.3682	−	18.5085i	−1.56424	−	0.611203i
$918$			11.4363i			0.377455i
$919$	−3.77400	−	6.53677i	−0.124493	−	0.215628i	0.797042	−	0.603924i	$-0.206397\pi$
$919$	−3.77400	−	6.53677i	−0.124493	−	0.215628i	−0.921535	+	0.388296i	$0.873064\pi$
$920$		0			0
$921$	6.97117	−	12.0744i	0.229708	−	0.397866i
$922$	52.7221	−	30.4391i	1.73631	−	1.00246i
$923$		−	51.1707i		−	1.68431i
$924$	−24.7749	−	30.9710i	−0.815034	−	1.01887i
$925$		0			0
$926$	−2.28798	−	3.96290i	−0.0751877	−	0.130229i
$927$	−6.79141	−	3.92102i	−0.223059	−	0.128783i
$928$	64.8459	+	37.4388i	2.12867	+	1.22899i
$929$	2.59552	+	4.49558i	0.0851563	+	0.147495i	0.905458	−	0.424436i	$-0.139528\pi$
$929$	2.59552	+	4.49558i	0.0851563	+	0.147495i	−0.820302	+	0.571931i	$0.806194\pi$
$930$		0			0
$931$	14.0358	−	4.37575i	0.460003	−	0.143409i
$932$			51.8275i			1.69767i
$933$	−3.29040	+	1.89971i	−0.107723	+	0.0621937i
$934$	0.108561	−	0.188034i	0.00355223	−	0.00615264i
$935$		0			0
$936$	20.0119	+	34.6617i	0.654110	+	1.13295i
$937$		−	5.23690i		−	0.171082i	−0.996335	−	0.0855410i	$-0.972738\pi$
$937$		−	5.23690i		−	0.171082i	0.996335	−	0.0855410i	$-0.0272619\pi$
$938$	18.4582	−	14.7654i	0.602682	−	0.482108i
$939$	−27.8976			−0.910404
$940$		0			0
$941$	6.47195	−	11.2098i	0.210980	−	0.365427i	−0.741042	−	0.671459i	$-0.765668\pi$
$941$	6.47195	−	11.2098i	0.210980	−	0.365427i	0.952021	+	0.306032i	$0.0990013\pi$
$942$	54.9581	+	31.7301i	1.79063	+	1.03382i
$943$	13.6237	−	7.86567i	0.443650	−	0.256141i
$944$	51.2407			1.66774
$945$		0			0
$946$	−23.9106			−0.777400
$947$	−19.9309	+	11.5071i	−0.647669	+	0.373932i	−0.787562	−	0.616235i	$-0.788657\pi$
$947$	−19.9309	+	11.5071i	−0.647669	+	0.373932i	0.139894	+	0.990167i	$0.455324\pi$
$948$	−58.0619	−	33.5221i	−1.88576	−	1.08875i
$949$	−5.93813	+	10.2852i	−0.192760	+	0.333870i
$950$		0			0
$951$	34.4955			1.11859
$952$	15.0551	+	98.8748i	0.487940	+	3.20455i
$953$			15.1560i			0.490952i	0.969403	+	0.245476i	$0.0789443\pi$
$953$			15.1560i			0.490952i	−0.969403	+	0.245476i	$0.921056\pi$
$954$	3.48696	+	6.03959i	0.112895	+	0.195539i
$955$		0			0
$956$	16.4483	−	28.4893i	0.531977	−	0.921411i
$957$	−9.78782	+	5.65100i	−0.316395	+	0.182671i
$958$			104.812i			3.38632i
$959$	−21.6097	+	3.29040i	−0.697814	+	0.106252i
$960$		0			0
$961$	−28.0384	−	48.5640i	−0.904465	−	1.56658i
$962$	44.0963	+	25.4590i	1.42172	+	0.820832i
$963$	−13.5420	−	7.81846i	−0.436384	−	0.251946i
$964$	−53.6861	−	92.9871i	−1.72911	−	2.99491i
$965$		0			0
$966$	−17.2051	+	44.0326i	−0.553566	+	1.41673i
$967$		−	45.5145i		−	1.46365i	−0.681494	−	0.731824i	$-0.738669\pi$
$967$		−	45.5145i		−	1.46365i	0.681494	−	0.731824i	$-0.261331\pi$
$968$	23.3394	−	13.4750i	0.750156	−	0.433103i
$969$	−4.44338	+	7.69616i	−0.142742	+	0.247236i
$970$		0			0
$971$	3.80096	+	6.58345i	0.121979	+	0.211273i	0.920548	−	0.390630i	$-0.127743\pi$
$971$	3.80096	+	6.58345i	0.121979	+	0.211273i	−0.798569	+	0.601903i	$0.794409\pi$
$972$		−	5.30542i		−	0.170171i
$973$	−2.03695	+	1.62943i	−0.0653015	+	0.0522371i
$974$	−73.3309			−2.34967
$975$		0			0
$976$	33.8416	−	58.6153i	1.08324	−	1.87623i
$977$	30.0456	+	17.3468i	0.961243	+	0.554974i	0.896555	−	0.442932i	$-0.146062\pi$
$977$	30.0456	+	17.3468i	0.961243	+	0.554974i	0.0646874	+	0.997906i	$0.479395\pi$
$978$	29.1102	−	16.8068i	0.930843	−	0.537422i
$979$	23.2573			0.743306
$980$		0			0
$981$	3.07421			0.0981520
$982$	39.1471	−	22.6016i	1.24924	−	0.721246i
$983$	13.4909	+	7.78896i	0.430292	+	0.248429i	0.699471	−	0.714661i	$-0.253419\pi$
$983$	13.4909	+	7.78896i	0.430292	+	0.248429i	−0.269179	+	0.963090i	$0.586752\pi$
$984$	−10.6299	+	18.4115i	−0.338868	+	0.586937i
$985$		0			0
$986$	45.7454			1.45683
$987$	−16.0849	+	12.8669i	−0.511987	+	0.409558i
$988$			49.9193i			1.58815i
$989$	10.3490	+	17.9250i	0.329079	+	0.569982i
$990$		0			0
$991$	22.9794	−	39.8016i	0.729966	−	1.26434i	−0.226931	−	0.973911i	$-0.572869\pi$
$991$	22.9794	−	39.8016i	0.729966	−	1.26434i	0.956897	−	0.290427i	$-0.0937974\pi$
$992$	151.277	−	87.3400i	4.80306	−	2.77305i
$993$		−	29.8942i		−	0.948664i
$994$	−29.7271	+	76.0799i	−0.942888	+	2.41311i
$995$		0			0
$996$	−8.02731	−	13.9037i	−0.254355	−	0.440556i
$997$	−35.5665	−	20.5344i	−1.12640	−	0.650329i	−0.183376	−	0.983043i	$-0.558702\pi$
$997$	−35.5665	−	20.5344i	−1.12640	−	0.650329i	−0.943028	+	0.332713i	$0.892036\pi$
$998$	46.3101	+	26.7371i	1.46592	+	0.846349i
$999$	−2.10256	−	3.64175i	−0.0665222	−	0.115220i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.r.h.424.8		16
5.2	odd	4		525.2.i.j.151.4	yes	8
5.3	odd	4		525.2.i.i.151.1	✓	8
5.4	even	2	inner	525.2.r.h.424.1		16
7.2	even	3	inner	525.2.r.h.499.1		16
35.2	odd	12		525.2.i.j.226.4	yes	8
35.3	even	12		3675.2.a.bx.1.4		4
35.9	even	6	inner	525.2.r.h.499.8		16
35.17	even	12		3675.2.a.bq.1.1		4
35.18	odd	12		3675.2.a.bw.1.4		4
35.23	odd	12		525.2.i.i.226.1	yes	8
35.32	odd	12		3675.2.a.br.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.i.i.151.1	✓	8	5.3	odd	4
525.2.i.i.226.1	yes	8	35.23	odd	12
525.2.i.j.151.4	yes	8	5.2	odd	4
525.2.i.j.226.4	yes	8	35.2	odd	12
525.2.r.h.424.1		16	5.4	even	2	inner
525.2.r.h.424.8		16	1.1	even	1	trivial
525.2.r.h.499.1		16	7.2	even	3	inner
525.2.r.h.499.8		16	35.9	even	6	inner
3675.2.a.bq.1.1		4	35.17	even	12
3675.2.a.br.1.1		4	35.32	odd	12
3675.2.a.bw.1.4		4	35.18	odd	12
3675.2.a.bx.1.4		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)

\(f(q)\)	\(=\)	\(q+(2.34074 - 1.35143i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.65271 - 4.59463i) q^{4} -2.70285 q^{6} +(2.06605 - 1.65271i) q^{7} -8.93406i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(2.34074 - 1.35143i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.65271 - 4.59463i) q^{4} -2.70285 q^{6} +(2.06605 - 1.65271i) q^{7} -8.93406i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.41275 + 2.44696i) q^{11} +(-4.59463 + 2.65271i) q^{12} +4.47992i q^{13} +(2.60256 - 6.66067i) q^{14} +(-6.76831 - 11.7231i) q^{16} +(-3.66433 - 2.11560i) q^{17} +(2.34074 + 1.35143i) q^{18} +(1.05014 + 1.81890i) q^{19} +(-2.61560 + 0.398264i) q^{21} +7.63692i q^{22} +(5.72515 - 3.30542i) q^{23} +(-4.46703 + 7.73712i) q^{24} +(6.05428 + 10.4863i) q^{26} -1.00000i q^{27} +(-2.11296 - 13.8769i) q^{28} -4.00000 q^{29} +(-4.66575 + 8.08131i) q^{31} +(-16.2115 - 9.35970i) q^{32} +(2.44696 - 1.41275i) q^{33} -11.4363 q^{34} +5.30542 q^{36} +(3.64175 - 2.10256i) q^{37} +(4.91623 + 2.83839i) q^{38} +(2.23996 - 3.87972i) q^{39} +2.37963 q^{41} +(-5.58422 + 4.46703i) q^{42} +3.13092i q^{43} +(7.49523 + 12.9821i) q^{44} +(8.93406 - 15.4742i) q^{46} +(6.74230 - 3.89267i) q^{47} +13.5366i q^{48} +(1.53710 - 6.82915i) q^{49} +(2.11560 + 3.66433i) q^{51} +(20.5835 + 11.8839i) q^{52} +(2.23452 + 1.29010i) q^{53} +(-1.35143 - 2.34074i) q^{54} +(-14.7654 - 18.4582i) q^{56} -2.10029i q^{57} +(-9.36296 + 5.40571i) q^{58} +(-1.89267 + 3.27820i) q^{59} +(2.50000 + 4.33013i) q^{61} +25.2217i q^{62} +(2.46431 + 0.962895i) q^{63} -23.5225 q^{64} +(3.81846 - 6.61376i) q^{66} +(2.86258 + 1.65271i) q^{67} +(-19.4408 + 11.2242i) q^{68} -6.61084 q^{69} -11.4223 q^{71} +(7.73712 - 4.46703i) q^{72} +(2.29584 + 1.32550i) q^{73} +(5.68292 - 9.84311i) q^{74} +11.1429 q^{76} +(1.12530 + 7.39039i) q^{77} -12.1086i q^{78} +(6.31846 + 10.9439i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(5.57009 - 3.21589i) q^{82} +3.02608i q^{83} +(-5.10856 + 13.0742i) q^{84} +(4.23121 + 7.32867i) q^{86} +(3.46410 + 2.00000i) q^{87} +(21.8613 + 12.6216i) q^{88} +(-4.11560 - 7.12844i) q^{89} +(7.40400 + 9.25572i) q^{91} -35.0733i q^{92} +(8.08131 - 4.66575i) q^{93} +(10.5213 - 18.2234i) q^{94} +(9.35970 + 16.2115i) q^{96} -15.0165i q^{97} +(-5.63114 - 18.0626i) q^{98} -2.82550 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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