LMFDB - Embedded newform 539.2.i.e.362.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(362,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("539.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.i (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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			362.15
Character	$\chi$	$=$	539.362
Dual form			539.2.i.e.472.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.25797 + 1.30364i) q^{2} +(-2.44288 + 1.41040i) q^{3} +(2.39897 + 4.15513i) q^{4} +(1.60021 + 0.923880i) q^{5} -7.35461 q^{6} +7.29501i q^{8} +(2.47844 - 4.29278i) q^{9} +O(q^{10})$	\(q+(2.25797 + 1.30364i) q^{2} +(-2.44288 + 1.41040i) q^{3} +(2.39897 + 4.15513i) q^{4} +(1.60021 + 0.923880i) q^{5} -7.35461 q^{6} +7.29501i q^{8} +(2.47844 - 4.29278i) q^{9} +(2.40882 + 4.17219i) q^{10} +(-2.81444 + 1.75469i) q^{11} +(-11.7208 - 6.76699i) q^{12} +4.27619 q^{13} -5.21215 q^{15} +(-4.71215 + 8.16168i) q^{16} +(-1.65135 - 2.86022i) q^{17} +(11.1925 - 6.46199i) q^{18} +(-1.79391 + 3.10715i) q^{19} +8.86542i q^{20} +(-8.64242 + 0.293029i) q^{22} +(2.49368 - 4.31919i) q^{23} +(-10.2889 - 17.8208i) q^{24} +(-0.792893 - 1.37333i) q^{25} +(9.65552 + 5.57462i) q^{26} +5.51994i q^{27} -3.27285i q^{29} +(-11.7689 - 6.79477i) q^{30} +(1.37156 - 0.791873i) q^{31} +(-8.64449 + 4.99090i) q^{32} +(4.40052 - 8.25597i) q^{33} -8.61108i q^{34} +23.7827 q^{36} +(-0.473398 + 0.819949i) q^{37} +(-8.10122 + 4.67724i) q^{38} +(-10.4462 + 6.03112i) q^{39} +(-6.73971 + 11.6735i) q^{40} +1.77125 q^{41} +12.0622i q^{43} +(-14.0427 - 7.48491i) q^{44} +(7.93202 - 4.57955i) q^{45} +(11.2614 - 6.50174i) q^{46} +(7.06076 + 4.07653i) q^{47} -26.5840i q^{48} -4.13460i q^{50} +(8.06809 + 4.65812i) q^{51} +(10.2584 + 17.7681i) q^{52} +(0.435776 + 0.754787i) q^{53} +(-7.19602 + 12.4639i) q^{54} +(-6.12480 + 0.207667i) q^{55} -10.1205i q^{57} +(4.26663 - 7.39001i) q^{58} +(5.79228 - 3.34417i) q^{59} +(-12.5038 - 21.6572i) q^{60} +(-2.33971 + 4.05249i) q^{61} +4.12927 q^{62} -7.17680 q^{64} +(6.84278 + 3.95068i) q^{65} +(20.6991 - 12.9051i) q^{66} +(4.33474 + 7.50799i) q^{67} +(7.92306 - 13.7232i) q^{68} +14.0683i q^{69} +7.09378 q^{71} +(31.3159 + 18.0802i) q^{72} +(-4.67507 - 8.09746i) q^{73} +(-2.13784 + 1.23428i) q^{74} +(3.87388 + 2.23659i) q^{75} -17.2142 q^{76} -31.4497 q^{78} +(-5.61747 - 3.24325i) q^{79} +(-15.0808 + 8.70691i) q^{80} +(-0.349990 - 0.606200i) q^{81} +(3.99945 + 2.30908i) q^{82} -8.55237 q^{83} -6.10259i q^{85} +(-15.7248 + 27.2362i) q^{86} +(4.61602 + 7.99518i) q^{87} +(-12.8005 - 20.5313i) q^{88} +(6.56594 + 3.79085i) q^{89} +23.8804 q^{90} +23.9291 q^{92} +(-2.23371 + 3.86890i) q^{93} +(10.6287 + 18.4094i) q^{94} +(-5.74126 + 3.31472i) q^{95} +(14.0783 - 24.3843i) q^{96} -3.12677i q^{97} +(0.557097 + 16.4307i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} + 16 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 + 16 * q^9	$ 32 q + 32 q^{4} + 16 q^{9} - 32 q^{15} - 16 q^{16} - 64 q^{22} + 16 q^{23} - 48 q^{25} + 192 q^{36} - 64 q^{37} - 48 q^{44} + 32 q^{53} + 80 q^{58} - 112 q^{60} - 64 q^{64} + 112 q^{67} - 96 q^{71} - 32 q^{78} + 16 q^{81} - 16 q^{86} - 96 q^{88} + 32 q^{92} - 32 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 + 16 * q^9 - 32 * q^15 - 16 * q^16 - 64 * q^22 + 16 * q^23 - 48 * q^25 + 192 * q^36 - 64 * q^37 - 48 * q^44 + 32 * q^53 + 80 * q^58 - 112 * q^60 - 64 * q^64 + 112 * q^67 - 96 * q^71 - 32 * q^78 + 16 * q^81 - 16 * q^86 - 96 * q^88 + 32 * q^92 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.25797	+	1.30364i	1.59663	+	0.921814i	0.992130	+	0.125208i	$0.0399599\pi$
$2$	2.25797	+	1.30364i	1.59663	+	0.921814i	0.604499	+	0.796606i	$0.293373\pi$
$3$	−2.44288	+	1.41040i	−1.41040	+	0.814293i	−0.995425	−	0.0955417i	$-0.969542\pi$
$3$	−2.44288	+	1.41040i	−1.41040	+	0.814293i	−0.414971	+	0.909835i	$0.636208\pi$
$4$	2.39897	+	4.15513i	1.19948	+	2.07757i
$5$	1.60021	+	0.923880i	0.715634	+	0.413171i	0.813144	−	0.582063i	$-0.197754\pi$
$5$	1.60021	+	0.923880i	0.715634	+	0.413171i	−0.0975096	+	0.995235i	$0.531088\pi$
$6$	−7.35461			−3.00251
$7$		0			0
$7$		0			0
$8$			7.29501i			2.57917i
$9$	2.47844	−	4.29278i	0.826146	−	1.43093i
$10$	2.40882	+	4.17219i	0.761735	+	1.31936i
$11$	−2.81444	+	1.75469i	−0.848585	+	0.529059i
$11$	−2.81444	+	1.75469i	−0.848585	+	0.529059i
$12$	−11.7208	−	6.76699i	−3.38349	−	1.95346i
$13$	4.27619			1.18600			0.593000	−	0.805202i	$-0.297943\pi$
$13$	4.27619			1.18600			0.593000	+	0.805202i	$0.297943\pi$
$14$		0			0
$15$	−5.21215			−1.34577
$16$	−4.71215	+	8.16168i	−1.17804	+	2.04042i
$17$	−1.65135	−	2.86022i	−0.400511	−	0.693706i	0.593276	−	0.804999i	$-0.297834\pi$
$17$	−1.65135	−	2.86022i	−0.400511	−	0.693706i	−0.993788	+	0.111293i	$0.964501\pi$
$18$	11.1925	−	6.46199i	2.63810	−	1.52311i
$19$	−1.79391	+	3.10715i	−0.411552	+	0.712829i	−0.995060	−	0.0992787i	$-0.968346\pi$
$19$	−1.79391	+	3.10715i	−0.411552	+	0.712829i	0.583508	+	0.812108i	$0.301680\pi$
$20$			8.86542i			1.98237i
$21$		0			0
$22$	−8.64242	+	0.293029i	−1.84257	+	0.0624741i
$23$	2.49368	−	4.31919i	0.519969	−	0.900613i	−0.479761	−	0.877399i	$-0.659277\pi$
$23$	2.49368	−	4.31919i	0.519969	−	0.900613i	0.999731	−	0.0232140i	$-0.00738990\pi$
$24$	−10.2889	−	17.8208i	−2.10020	−	3.63766i
$25$	−0.792893	−	1.37333i	−0.158579	−	0.274666i
$26$	9.65552	+	5.57462i	1.89360	+	1.09327i
$27$			5.51994i			1.06231i
$28$		0			0
$29$		−	3.27285i		−	0.607753i	−0.952711	−	0.303877i	$-0.901719\pi$
$29$		−	3.27285i		−	0.607753i	0.952711	−	0.303877i	$-0.0982811\pi$
$30$	−11.7689	−	6.79477i	−2.14870	−	1.24055i
$31$	1.37156	−	0.791873i	0.246340	−	0.142225i	−0.371747	−	0.928334i	$-0.621241\pi$
$31$	1.37156	−	0.791873i	0.246340	−	0.142225i	0.618087	+	0.786109i	$0.287908\pi$
$32$	−8.64449	+	4.99090i	−1.52814	+	0.882275i
$33$	4.40052	−	8.25597i	0.766032	−	1.43718i
$34$		−	8.61108i		−	1.47679i
$35$		0			0
$36$	23.7827			3.96379
$37$	−0.473398	+	0.819949i	−0.0778261	+	0.134799i	−0.902312	−	0.431084i	$-0.858131\pi$
$37$	−0.473398	+	0.819949i	−0.0778261	+	0.134799i	0.824486	+	0.565883i	$0.191465\pi$
$38$	−8.10122	+	4.67724i	−1.31419	+	0.758749i
$39$	−10.4462	+	6.03112i	−1.67273	+	0.965752i
$40$	−6.73971	+	11.6735i	−1.06564	+	1.84574i
$41$	1.77125			0.276623			0.138312	−	0.990389i	$-0.455832\pi$
$41$	1.77125			0.276623			0.138312	+	0.990389i	$0.455832\pi$
$42$		0			0
$43$			12.0622i			1.83947i	0.392535	+	0.919737i	$0.371598\pi$
$43$			12.0622i			1.83947i	−0.392535	+	0.919737i	$0.628402\pi$
$44$	−14.0427	−	7.48491i	−2.11702	−	1.12839i
$45$	7.93202	−	4.57955i	1.18244	−	0.682680i
$46$	11.2614	−	6.50174i	1.66040	−	0.958630i
$47$	7.06076	+	4.07653i	1.02992	+	0.594624i	0.916961	−	0.398976i	$-0.130634\pi$
$47$	7.06076	+	4.07653i	1.02992	+	0.594624i	0.112957	+	0.993600i	$0.463968\pi$
$48$		−	26.5840i		−	3.83707i
$49$		0			0
$50$		−	4.13460i		−	0.584720i
$51$	8.06809	+	4.65812i	1.12976	+	0.652267i
$52$	10.2584	+	17.7681i	1.42259	+	2.46399i
$53$	0.435776	+	0.754787i	0.0598585	+	0.103678i	0.894402	−	0.447264i	$-0.147602\pi$
$53$	0.435776	+	0.754787i	0.0598585	+	0.103678i	−0.834543	+	0.550942i	$0.814268\pi$
$54$	−7.19602	+	12.4639i	−0.979255	+	1.69612i
$55$	−6.12480	+	0.207667i	−0.825868	+	0.0280018i
$56$		0			0
$57$		−	10.1205i		−	1.34050i
$58$	4.26663	−	7.39001i	0.560236	−	0.970356i
$59$	5.79228	−	3.34417i	0.754091	−	0.435374i	−0.0730794	−	0.997326i	$-0.523283\pi$
$59$	5.79228	−	3.34417i	0.754091	−	0.435374i	0.827170	+	0.561952i	$0.189949\pi$
$60$	−12.5038	−	21.6572i	−1.61423	−	2.79593i
$61$	−2.33971	+	4.05249i	−0.299569	+	0.518869i	−0.976037	−	0.217603i	$-0.930176\pi$
$61$	−2.33971	+	4.05249i	−0.299569	+	0.518869i	0.676468	+	0.736472i	$0.263510\pi$
$62$	4.12927			0.524418
$63$		0			0
$64$	−7.17680			−0.897101
$65$	6.84278	+	3.95068i	0.848742	+	0.490022i
$66$	20.6991	−	12.9051i	2.54788	−	1.58850i
$67$	4.33474	+	7.50799i	0.529573	+	0.917248i	0.999405	+	0.0344916i	$0.0109812\pi$
$67$	4.33474	+	7.50799i	0.529573	+	0.917248i	−0.469832	+	0.882756i	$0.655685\pi$
$68$	7.92306	−	13.7232i	0.960813	−	1.66418i
$69$			14.0683i			1.69363i
$70$		0			0
$71$	7.09378			0.841877			0.420938	−	0.907089i	$-0.361701\pi$
$71$	7.09378			0.841877			0.420938	+	0.907089i	$0.361701\pi$
$72$	31.3159	+	18.0802i	3.69061	+	2.13077i
$73$	−4.67507	−	8.09746i	−0.547176	−	0.947736i	−0.998467	−	0.0553590i	$-0.982370\pi$
$73$	−4.67507	−	8.09746i	−0.547176	−	0.947736i	0.451291	−	0.892377i	$-0.350964\pi$
$74$	−2.13784	+	1.23428i	−0.248519	+	0.143482i
$75$	3.87388	+	2.23659i	0.447318	+	0.258259i
$76$	−17.2142			−1.97460
$77$		0			0
$78$	−31.4497			−3.56098
$79$	−5.61747	−	3.24325i	−0.632014	−	0.364894i	0.149517	−	0.988759i	$-0.452228\pi$
$79$	−5.61747	−	3.24325i	−0.632014	−	0.364894i	−0.781532	+	0.623865i	$0.785561\pi$
$80$	−15.0808	+	8.70691i	−1.68609	+	0.973462i
$81$	−0.349990	−	0.606200i	−0.0388878	−	0.0673556i
$82$	3.99945	+	2.30908i	0.441665	+	0.254995i
$83$	−8.55237			−0.938745			−0.469372	−	0.883000i	$-0.655520\pi$
$83$	−8.55237			−0.938745			−0.469372	+	0.883000i	$0.655520\pi$
$84$		0			0
$85$		−	6.10259i		−	0.661919i
$86$	−15.7248	+	27.2362i	−1.69565	+	2.93696i
$87$	4.61602	+	7.99518i	0.494889	+	0.857173i
$88$	−12.8005	−	20.5313i	−1.36454	−	2.18865i
$89$	6.56594	+	3.79085i	0.695988	+	0.401829i	0.805852	−	0.592118i	$-0.201708\pi$
$89$	6.56594	+	3.79085i	0.695988	+	0.401829i	−0.109863	+	0.993947i	$0.535041\pi$
$90$	23.8804			2.51722
$91$		0			0
$92$	23.9291			2.49478
$93$	−2.23371	+	3.86890i	−0.231625	+	0.401186i
$94$	10.6287	+	18.4094i	1.09627	+	1.89879i
$95$	−5.74126	+	3.31472i	−0.589041	+	0.340083i
$96$	14.0783	−	24.3843i	1.43686	−	2.48871i
$97$		−	3.12677i		−	0.317475i	−0.987321	−	0.158738i	$-0.949258\pi$
$97$		−	3.12677i		−	0.317475i	0.987321	−	0.158738i	$-0.0507424\pi$
$98$		0			0
$99$	0.557097	+	16.4307i	0.0559903	+	1.65134i
$100$	3.80425	−	6.58915i	0.380425	−	0.658915i
$101$	1.85297	+	3.20943i	0.184377	+	0.319350i	0.943366	−	0.331753i	$-0.107640\pi$
$101$	1.85297	+	3.20943i	0.184377	+	0.319350i	−0.758989	+	0.651103i	$0.774307\pi$
$102$	12.1450	+	21.0358i	1.20254	+	2.08286i
$103$	−14.8522	−	8.57490i	−1.46343	−	0.844910i	−0.464260	−	0.885699i	$-0.653680\pi$
$103$	−14.8522	−	8.57490i	−1.46343	−	0.844910i	−0.999168	+	0.0407886i	$0.987013\pi$
$104$			31.1948i			3.05890i
$105$		0			0
$106$			2.27239i			0.220714i
$107$	−10.3949	−	6.00151i	−1.00492	−	0.580188i	−0.0952164	−	0.995457i	$-0.530354\pi$
$107$	−10.3949	−	6.00151i	−1.00492	−	0.580188i	−0.909699	+	0.415269i	$0.863688\pi$
$108$	−22.9361	+	13.2421i	−2.20702	+	1.27423i
$109$	11.8663	−	6.85099i	1.13658	−	0.656206i	0.191001	−	0.981590i	$-0.438827\pi$
$109$	11.8663	−	6.85099i	1.13658	−	0.656206i	0.945582	+	0.325384i	$0.105493\pi$
$110$	−14.1004	−	7.51565i	−1.34442	−	0.716589i
$111$		−	2.67071i		−	0.253493i
$112$		0			0
$113$	9.40320			0.884579			0.442290	−	0.896872i	$-0.354166\pi$
$113$	9.40320			0.884579			0.442290	+	0.896872i	$0.354166\pi$
$114$	13.1935	−	22.8519i	1.23569	−	2.14027i
$115$	7.98082	−	4.60773i	0.744215	−	0.429673i
$116$	13.5991	−	7.85146i	1.26265	−	0.728990i
$117$	10.5983	−	18.3567i	0.979809	−	1.69708i
$118$	17.4384			1.60534
$119$		0			0
$120$		−	38.0226i		−	3.47098i
$121$	4.84212	−	9.87694i	0.440192	−	0.897904i
$122$	−10.5660	+	6.10029i	−0.956601	+	0.552294i
$123$	−4.32696	+	2.49817i	−0.390149	+	0.225252i
$124$	6.58067	+	3.79935i	0.590962	+	0.341192i
$125$		−	12.1689i		−	1.08842i
$126$		0			0
$127$		−	17.0586i		−	1.51370i	−0.653586	−	0.756852i	$-0.726736\pi$
$127$		−	17.0586i		−	1.51370i	0.653586	−	0.756852i	$-0.273264\pi$
$128$	1.08394	+	0.625813i	0.0958076	+	0.0553145i
$129$	−17.0125	−	29.4666i	−1.49787	−	2.59439i
$130$	10.3005	+	17.8411i	0.903418	+	1.56477i
$131$	7.91872	−	13.7156i	0.691862	−	1.19834i	−0.279366	−	0.960185i	$-0.590124\pi$
$131$	7.91872	−	13.7156i	0.691862	−	1.19834i	0.971227	−	0.238155i	$-0.0765425\pi$
$132$	44.8613	−	1.52107i	3.90468	−	0.132392i
$133$		0			0
$134$			22.6038i			1.95267i
$135$	−5.09976	+	8.83304i	−0.438917	+	0.760227i
$136$	20.8653	−	12.0466i	1.78919	−	1.03299i
$137$	6.05663	+	10.4904i	0.517453	+	0.896255i	0.999795	+	0.0202716i	$0.00645309\pi$
$137$	6.05663	+	10.4904i	0.517453	+	0.896255i	−0.482342	+	0.875983i	$0.660214\pi$
$138$	−18.3401	+	31.7659i	−1.56121	+	2.70410i
$139$	−0.679664			−0.0576484			−0.0288242	−	0.999584i	$-0.509176\pi$
$139$	−0.679664			−0.0576484			−0.0288242	+	0.999584i	$0.509176\pi$
$140$		0			0
$141$	−22.9981			−1.93679
$142$	16.0176	+	9.24775i	1.34416	+	0.776054i
$143$	−12.0351	+	7.50339i	−1.00642	+	0.627465i
$144$	23.3575	+	40.4564i	1.94646	+	3.37137i
$145$	3.02372	−	5.23724i	0.251106	−	0.434929i
$146$		−	24.3785i		−	2.01758i
$147$		0			0
$148$	−4.54266			−0.373404
$149$	−7.47412	−	4.31518i	−0.612304	−	0.353514i	0.161563	−	0.986862i	$-0.448347\pi$
$149$	−7.47412	−	4.31518i	−0.612304	−	0.353514i	−0.773867	+	0.633349i	$0.781680\pi$
$150$	5.83142	+	10.1003i	0.476134	+	0.824687i
$151$	−8.17065	+	4.71733i	−0.664918	+	0.383891i	−0.794148	−	0.607724i	$-0.792083\pi$
$151$	−8.17065	+	4.71733i	−0.664918	+	0.383891i	0.129230	+	0.991615i	$0.458749\pi$
$152$	−22.6667	−	13.0866i	−1.83851	−	1.06146i
$153$	−16.3711			−1.32352
$154$		0			0
$155$	2.92638			0.235052
$156$	−50.1202	−	28.9369i	−4.01283	−	2.31681i
$157$	−15.0808	+	8.70691i	−1.20358	+	0.694887i	−0.961349	−	0.275332i	$-0.911212\pi$
$157$	−15.0808	+	8.70691i	−1.20358	+	0.694887i	−0.242231	+	0.970219i	$0.577879\pi$
$158$	−8.45606	−	14.6463i	−0.672728	−	1.16520i
$159$	−2.12910	−	1.22924i	−0.168848	−	0.0974847i
$160$	−18.4440			−1.45812
$161$		0			0
$162$		−	1.82505i		−	0.143389i
$163$	7.90790	−	13.6969i	0.619394	−	1.07282i	−0.370202	−	0.928951i	$-0.620712\pi$
$163$	7.90790	−	13.6969i	0.619394	−	1.07282i	0.989596	−	0.143871i	$-0.0459551\pi$
$164$	4.24918	+	7.35979i	0.331805	+	0.574703i
$165$	14.6693	−	9.14571i	1.14200	−	0.711992i
$166$	−19.3110	−	11.1492i	−1.49883	−	0.865348i
$167$	2.86284			0.221534			0.110767	−	0.993846i	$-0.464669\pi$
$167$	2.86284			0.221534			0.110767	+	0.993846i	$0.464669\pi$
$168$		0			0
$169$	5.28577			0.406597
$170$	7.95560	−	13.7795i	0.610167	−	1.05684i
$171$	8.89220	+	15.4017i	0.680004	+	1.17780i
$172$	−50.1202	+	28.9369i	−3.82163	+	2.20642i
$173$	−10.3193	+	17.8735i	−0.784560	+	1.35890i	0.144701	+	0.989475i	$0.453778\pi$
$173$	−10.3193	+	17.8735i	−0.784560	+	1.35890i	−0.929261	+	0.369423i	$0.879555\pi$
$174$			24.0705i			1.82478i
$175$		0			0
$176$	−1.05918	−	31.2389i	−0.0798390	−	2.35472i
$177$	−9.43322	+	16.3388i	−0.709045	+	1.22810i
$178$	9.88382	+	17.1193i	0.740824	+	1.28314i
$179$	−12.0440	−	20.8608i	−0.900211	−	1.55921i	−0.827220	−	0.561878i	$-0.810079\pi$
$179$	−12.0440	−	20.8608i	−0.900211	−	1.55921i	−0.0729910	−	0.997333i	$-0.523254\pi$
$180$	38.0573	+	21.9724i	2.83662	+	1.63773i
$181$			3.10219i			0.230584i	0.993332	+	0.115292i	$0.0367804\pi$
$181$			3.10219i			0.230584i	−0.993332	+	0.115292i	$0.963220\pi$
$182$		0			0
$183$		−	13.1997i		−	0.975748i
$184$	31.5085	+	18.1914i	2.32284	+	1.34109i
$185$	−1.51507	+	0.874725i	−0.111390	+	0.0643111i
$186$	−10.0873	+	5.82392i	−0.739638	+	0.427030i
$187$	9.66643	+	5.15231i	0.706879	+	0.376774i
$188$			39.1179i			2.85296i
$189$		0			0
$190$	−17.2848			−1.25397
$191$	−3.41421	+	5.91359i	−0.247044	+	0.427892i	−0.962704	−	0.270556i	$-0.912792\pi$
$191$	−3.41421	+	5.91359i	−0.247044	+	0.427892i	0.715660	+	0.698448i	$0.246126\pi$
$192$	17.5321	−	10.1221i	1.26527	−	0.730503i
$193$	−6.31400	+	3.64539i	−0.454491	+	0.262401i	−0.709725	−	0.704479i	$-0.751181\pi$
$193$	−6.31400	+	3.64539i	−0.454491	+	0.262401i	0.255234	+	0.966879i	$0.417848\pi$
$194$	4.07619	−	7.06017i	0.292653	−	0.506890i
$195$	−22.2881			−1.59608
$196$		0			0
$197$			4.62851i			0.329768i	0.986313	+	0.164884i	$0.0527249\pi$
$197$			4.62851i			0.329768i	−0.986313	+	0.164884i	$0.947275\pi$
$198$	−20.1618	+	37.8262i	−1.43284	+	2.68819i
$199$	−7.63693	+	4.40918i	−0.541368	+	0.312559i	−0.745633	−	0.666357i	$-0.767853\pi$
$199$	−7.63693	+	4.40918i	−0.541368	+	0.312559i	0.204265	+	0.978916i	$0.434519\pi$
$200$	10.0185	−	5.78416i	0.708412	−	0.409002i
$201$	−21.1785	−	12.2274i	−1.49382	−	0.862455i
$202$			9.66242i			0.679845i
$203$		0			0
$204$			44.6987i			3.12953i
$205$	2.83437	+	1.63643i	0.197961	+	0.114293i
$206$	−22.3572	−	38.7238i	−1.55770	−	2.69802i
$207$	−12.3609	−	21.4097i	−0.859141	−	1.48808i
$208$	−20.1500	+	34.9008i	−1.39715	+	2.41994i
$209$	−0.403231	−	11.8926i	−0.0278921	−	0.822631i
$210$		0			0
$211$		−	9.25702i		−	0.637280i	−0.947876	−	0.318640i	$-0.896774\pi$
$211$		−	9.25702i		−	0.637280i	0.947876	−	0.318640i	$-0.103226\pi$
$212$	−2.09083	+	3.62142i	−0.143599	+	0.248720i
$213$	−17.3292	+	10.0050i	−1.18738	+	0.685534i
$214$	−15.6477	−	27.1025i	−1.06965	−	1.85269i
$215$	−11.1441	+	19.3021i	−0.760018	+	1.31639i
$216$	−40.2680			−2.73989
$217$		0			0
$218$	35.7250			2.41960
$219$	22.8413	+	13.1874i	1.54347	+	0.891122i
$220$	−15.5561	−	24.9512i	−1.04879	−	1.68221i
$221$	−7.06148	−	12.2308i	−0.475006	−	0.822735i
$222$	3.48166	−	6.03040i	0.233673	−	0.404734i
$223$		−	17.3218i		−	1.15996i	−0.814632	−	0.579978i	$-0.803061\pi$
$223$		−	17.3218i		−	1.15996i	0.814632	−	0.579978i	$-0.196939\pi$
$224$		0			0
$225$	−7.86054			−0.524036
$226$	21.2322	+	12.2584i	1.41234	+	0.815418i
$227$	12.8833	+	22.3145i	0.855092	+	1.48106i	0.876560	+	0.481294i	$0.159833\pi$
$227$	12.8833	+	22.3145i	0.855092	+	1.48106i	−0.0214673	+	0.999770i	$0.506834\pi$
$228$	42.0521	−	24.2788i	2.78497	−	1.60790i
$229$	−6.74439	−	3.89387i	−0.445682	−	0.257314i	0.260323	−	0.965522i	$-0.416171\pi$
$229$	−6.74439	−	3.89387i	−0.445682	−	0.257314i	−0.706005	+	0.708207i	$0.749504\pi$
$230$	24.0273			1.58431
$231$		0			0
$232$	23.8755			1.56750
$233$	−10.3085	−	5.95161i	−0.675332	−	0.389903i	0.122762	−	0.992436i	$-0.460825\pi$
$233$	−10.3085	−	5.95161i	−0.675332	−	0.389903i	−0.798094	+	0.602533i	$0.794158\pi$
$234$	47.8612	−	27.6327i	3.12878	−	1.80640i
$235$	7.53245	+	13.0466i	0.491363	+	0.851066i
$236$	27.7910	+	16.0451i	1.80904	+	1.04445i
$237$	18.2970			1.18852
$238$		0			0
$239$		−	6.54570i		−	0.423406i	−0.977334	−	0.211703i	$-0.932099\pi$
$239$		−	6.54570i		−	0.423406i	0.977334	−	0.211703i	$-0.0679010\pi$
$240$	24.5604	−	42.5399i	1.58537	−	2.74594i
$241$	−11.8828	−	20.5816i	−0.765436	−	1.32577i	−0.940016	−	0.341132i	$-0.889190\pi$
$241$	−11.8828	−	20.5816i	−0.765436	−	1.32577i	0.174579	−	0.984643i	$-0.444144\pi$
$242$	23.8094	−	15.9895i	1.53052	−	1.02784i
$243$	−12.6313	−	7.29266i	−0.810295	−	0.467824i
$244$	−22.4515			−1.43731
$245$		0			0
$246$	−13.0269			−0.830564
$247$	−7.67111	+	13.2867i	−0.488101	+	0.845416i
$248$	5.77672	+	10.0056i	0.366822	+	0.635354i
$249$	20.8924	−	12.0622i	1.32400	−	0.764413i
$250$	15.8640	−	27.4772i	1.00332	−	1.73781i
$251$		−	12.6830i		−	0.800542i	−0.916397	−	0.400271i	$-0.868916\pi$
$251$		−	12.6830i		−	0.800542i	0.916397	−	0.400271i	$-0.131084\pi$
$252$		0			0
$253$	0.560524	+	16.5317i	0.0352398	+	1.03934i
$254$	22.2383	−	38.5178i	1.39535	−	2.41682i
$255$	8.60708	+	14.9079i	0.538996	+	0.933569i
$256$	8.80848	+	15.2567i	0.550530	+	0.953546i
$257$	17.1450	+	9.89866i	1.06947	+	0.617462i	0.928038	−	0.372486i	$-0.121494\pi$
$257$	17.1450	+	9.89866i	1.06947	+	0.617462i	0.141437	+	0.989947i	$0.454828\pi$
$258$		−	88.7130i		−	5.52303i
$259$		0			0
$260$			37.9102i			2.35109i
$261$	−14.0496	−	8.11156i	−0.869650	−	0.502093i
$262$	35.7605	−	20.6463i	2.20929	−	1.27554i
$263$	−10.3224	+	5.95964i	−0.636507	+	0.367487i	−0.783268	−	0.621685i	$-0.786449\pi$
$263$	−10.3224	+	5.95964i	−0.636507	+	0.367487i	0.146761	+	0.989172i	$0.453115\pi$
$264$	60.2274	+	32.1018i	3.70674	+	1.97573i
$265$			1.61042i			0.0989273i
$266$		0			0
$267$	−21.3864			−1.30883
$268$	−20.7978	+	36.0229i	−1.27043	+	2.20045i
$269$	23.7565	−	13.7158i	1.44846	−	0.836269i	0.450070	−	0.892993i	$-0.351399\pi$
$269$	23.7565	−	13.7158i	1.44846	−	0.836269i	0.998390	+	0.0567244i	$0.0180656\pi$
$270$	−23.0302	+	13.2965i	−1.40158	+	0.809200i
$271$	−2.61434	+	4.52817i	−0.158810	+	0.275067i	−0.934440	−	0.356121i	$-0.884099\pi$
$271$	−2.61434	+	4.52817i	−0.158810	+	0.275067i	0.775630	+	0.631188i	$0.217432\pi$
$272$	31.1256			1.88727
$273$		0			0
$274$			31.5827i			1.90798i
$275$	4.64132	+	2.47387i	0.279882	+	0.149180i
$276$	−58.4558	+	33.7495i	−3.51862	+	2.03148i
$277$	−16.5060	+	9.52975i	−0.991751	+	0.572587i	−0.905797	−	0.423712i	$-0.860727\pi$
$277$	−16.5060	+	9.52975i	−0.991751	+	0.572587i	−0.0859534	+	0.996299i	$0.527394\pi$
$278$	−1.53466	−	0.886039i	−0.0920430	−	0.0531411i
$279$		−	7.85043i		−	0.469993i
$280$		0			0
$281$		−	7.90136i		−	0.471356i	−0.971831	−	0.235678i	$-0.924269\pi$
$281$		−	7.90136i		−	0.471356i	0.971831	−	0.235678i	$-0.0757310\pi$
$282$	−51.9292	−	29.9813i	−3.09234	−	1.78536i
$283$	−1.71655	−	2.97315i	−0.102038	−	0.176736i	0.810486	−	0.585758i	$-0.199203\pi$
$283$	−1.71655	−	2.97315i	−0.102038	−	0.176736i	−0.912524	+	0.409022i	$0.865870\pi$
$284$	17.0177	+	29.4756i	1.00982	+	1.74905i
$285$	9.35014	−	16.1949i	0.553854	−	0.959304i
$286$	−36.9566	+	1.25305i	−2.18529	+	0.0740943i
$287$		0			0
$288$			49.4785i			2.91555i
$289$	3.04609	−	5.27598i	0.179182	−	0.310352i
$290$	13.6550	−	7.88370i	0.801847	−	0.462947i
$291$	4.40999	+	7.63832i	0.258518	+	0.447766i
$292$	22.4307	−	38.8511i	1.31266	−	2.27359i
$293$	21.1965			1.23831			0.619157	−	0.785267i	$-0.287475\pi$
$293$	21.1965			1.23831			0.619157	+	0.785267i	$0.287475\pi$
$294$		0			0
$295$	12.3585			0.719537
$296$	−5.98153	−	3.45344i	−0.347670	−	0.200727i
$297$	−9.68579	−	15.5355i	−0.562026	−	0.901462i
$298$	−11.2509	−	19.4872i	−0.651748	−	1.12886i
$299$	10.6635	−	18.4697i	0.616684	−	1.06813i
$300$			21.4620i			1.23911i
$301$		0			0
$302$	−24.5988			−1.41550
$303$	−9.05314	−	5.22683i	−0.520089	−	0.300274i
$304$	−16.9064	−	29.2827i	−0.969647	−	1.67948i
$305$	−7.48803	+	4.32322i	−0.428764	+	0.247547i
$306$	−36.9655	−	21.3420i	−2.11317	−	1.22004i
$307$	−14.6969			−0.838798			−0.419399	−	0.907802i	$-0.637759\pi$
$307$	−14.6969			−0.838798			−0.419399	+	0.907802i	$0.637759\pi$
$308$		0			0
$309$	48.3761			2.75202
$310$	6.60769	+	3.81495i	0.375292	+	0.216675i
$311$	7.20415	−	4.15932i	0.408510	−	0.235853i	−0.281639	−	0.959520i	$-0.590878\pi$
$311$	7.20415	−	4.15932i	0.408510	−	0.235853i	0.690149	+	0.723667i	$0.257545\pi$
$312$	−43.9970	−	76.2051i	−2.49084	−	4.31427i
$313$	−13.9181	−	8.03564i	−0.786700	−	0.454201i	0.0520997	−	0.998642i	$-0.483409\pi$
$313$	−13.9181	−	8.03564i	−0.786700	−	0.454201i	−0.838799	+	0.544441i	$0.816742\pi$
$314$	−45.4028			−2.56223
$315$		0			0
$316$		−	31.1217i		−	1.75073i
$317$	−8.37109	+	14.4991i	−0.470167	+	0.814353i	−0.999418	−	0.0341120i	$-0.989140\pi$
$317$	−8.37109	+	14.4991i	−0.470167	+	0.814353i	0.529251	+	0.848465i	$0.322473\pi$
$318$	−3.20497	−	5.55116i	−0.179726	−	0.311294i
$319$	5.74284	+	9.21123i	0.321538	+	0.515730i
$320$	−11.4844	−	6.63050i	−0.641996	−	0.370656i
$321$	33.8581			1.88977
$322$		0			0
$323$	11.8495			0.659325
$324$	1.67923	−	2.90851i	0.0932905	−	0.161584i
$325$	−3.39056	−	5.87262i	−0.188074	−	0.325754i
$326$	35.7117	−	20.6181i	1.97789	−	1.14193i
$327$	−19.3252	+	33.4723i	−1.06869	+	1.85102i
$328$			12.9213i			0.713460i
$329$		0			0
$330$	45.0455	−	1.52731i	2.47968	−	0.0840758i
$331$	−11.3220	+	19.6102i	−0.622312	+	1.07788i	0.366742	+	0.930323i	$0.380473\pi$
$331$	−11.3220	+	19.6102i	−0.622312	+	1.07788i	−0.989054	+	0.147554i	$0.952860\pi$
$332$	−20.5169	−	35.5362i	−1.12601	−	1.95030i
$333$	2.34657	+	4.06438i	0.128591	+	0.222727i
$334$	6.46423	+	3.73212i	0.353707	+	0.204213i
$335$			16.0191i			0.875218i
$336$		0			0
$337$			15.0416i			0.819367i	0.912228	+	0.409684i	$0.134361\pi$
$337$			15.0416i			0.819367i	−0.912228	+	0.409684i	$0.865639\pi$
$338$	11.9351	+	6.89075i	0.649185	+	0.374807i
$339$	−22.9709	+	13.2622i	−1.24761	+	0.720306i
$340$	25.3571	−	14.6399i	1.37518	−	0.793961i
$341$	−2.47069	+	4.63535i	−0.133795	+	0.251018i
$342$			46.3690i			2.50735i
$343$		0			0
$344$	−87.9941			−4.74432
$345$	−12.9974	+	22.5122i	−0.699759	+	1.21202i
$346$	−46.6013	+	26.9053i	−2.50530	+	1.44644i
$347$	18.3905	−	10.6178i	0.987254	−	0.569991i	0.0828015	−	0.996566i	$-0.473613\pi$
$347$	18.3905	−	10.6178i	0.987254	−	0.569991i	0.904452	+	0.426575i	$0.140280\pi$
$348$	−22.1473	+	38.3603i	−1.18722	+	2.05633i
$349$	27.2440			1.45834			0.729168	−	0.684335i	$-0.239907\pi$
$349$	27.2440			1.45834			0.729168	+	0.684335i	$0.239907\pi$
$350$		0			0
$351$			23.6043i			1.25990i
$352$	15.5719	−	29.2150i	0.829985	−	1.55716i
$353$	21.2351	−	12.2601i	1.13023	−	0.652537i	0.186236	−	0.982505i	$-0.440371\pi$
$353$	21.2351	−	12.2601i	1.13023	−	0.652537i	0.943992	+	0.329968i	$0.107038\pi$
$354$	−42.6000	+	24.5951i	−2.26416	+	1.30721i
$355$	11.3515	+	6.55380i	0.602475	+	0.347839i
$356$			36.3765i			1.92795i
$357$		0			0
$358$		−	62.8043i		−	3.31931i
$359$	14.1873	+	8.19106i	0.748779	+	0.432308i	0.825253	−	0.564764i	$-0.191033\pi$
$359$	14.1873	+	8.19106i	0.748779	+	0.432308i	−0.0764735	+	0.997072i	$0.524366\pi$
$360$	33.4079	+	57.8641i	1.76075	+	3.04971i
$361$	3.06375	+	5.30657i	0.161250	+	0.279293i
$362$	−4.04414	+	7.00466i	−0.212555	+	0.368157i
$363$	2.10170	+	30.9575i	0.110311	+	1.62485i
$364$		0			0
$365$		−	17.2768i		−	0.904309i
$366$	17.2076	−	29.8045i	0.899458	−	1.55791i
$367$	0.468546	−	0.270515i	0.0244579	−	0.0141208i	−0.487721	−	0.872999i	$-0.662172\pi$
$367$	0.468546	−	0.270515i	0.0244579	−	0.0141208i	0.512179	+	0.858879i	$0.328838\pi$
$368$	23.5012	+	40.7053i	1.22509	+	2.12191i
$369$	4.38994	−	7.60360i	0.228531	−	0.395828i
$370$	−4.56131			−0.237131
$371$		0			0
$372$	−21.4344			−1.11132
$373$	−25.1681	−	14.5308i	−1.30315	−	0.752376i	−0.322210	−	0.946668i	$-0.604426\pi$
$373$	−25.1681	−	14.5308i	−1.30315	−	0.752376i	−0.980944	+	0.194292i	$0.937759\pi$
$374$	15.1098	+	24.2353i	0.781308	+	1.25318i
$375$	17.1630	+	29.7273i	0.886296	+	1.53511i
$376$	−29.7383	+	51.5083i	−1.53364	+	2.65634i
$377$		−	13.9953i		−	0.720796i
$378$		0			0
$379$	−0.941949			−0.0483846			−0.0241923	−	0.999707i	$-0.507701\pi$
$379$	−0.941949			−0.0483846			−0.0241923	+	0.999707i	$0.507701\pi$
$380$	−27.5462	−	15.9038i	−1.41309	−	0.815848i
$381$	24.0594	+	41.6720i	1.23260	+	2.13492i
$382$	−15.4184	+	8.90183i	−0.788875	+	0.455457i
$383$	1.26300	+	0.729194i	0.0645363	+	0.0372600i	0.531921	−	0.846794i	$-0.321470\pi$
$383$	1.26300	+	0.729194i	0.0645363	+	0.0372600i	−0.467385	+	0.884054i	$0.654804\pi$
$384$	−3.53058			−0.180169
$385$		0			0
$386$	−19.0091			−0.967539
$387$	51.7805	+	29.8955i	2.63215	+	1.51967i
$388$	12.9921	−	7.50102i	0.659576	−	0.380806i
$389$	−3.41972	−	5.92313i	−0.173387	−	0.300314i	0.766215	−	0.642584i	$-0.222138\pi$
$389$	−3.41972	−	5.92313i	−0.173387	−	0.300314i	−0.939602	+	0.342270i	$0.888804\pi$
$390$	−50.3260	−	29.0557i	−2.54836	−	1.47129i
$391$	−16.4718			−0.833014
$392$		0			0
$393$			44.6741i			2.25351i
$394$	−6.03392	+	10.4511i	−0.303985	+	0.526517i
$395$	−5.99274	−	10.3797i	−0.301527	−	0.522261i
$396$	−66.9351	+	41.7314i	−3.36361	+	2.09708i
$397$	10.7156	+	6.18664i	0.537799	+	0.310499i	0.744187	−	0.667972i	$-0.232837\pi$
$397$	10.7156	+	6.18664i	0.537799	+	0.310499i	−0.206387	+	0.978470i	$0.566171\pi$
$398$	−22.9920			−1.15248
$399$		0			0
$400$	14.9449			0.747246
$401$	9.80088	−	16.9756i	0.489433	−	0.847723i	−0.510493	−	0.859882i	$-0.670537\pi$
$401$	9.80088	−	16.9756i	0.489433	−	0.847723i	0.999926	+	0.0121592i	$0.00387050\pi$
$402$	−31.8803	−	55.2184i	−1.59005	−	2.75404i
$403$	5.86506	−	3.38619i	0.292160	−	0.168678i
$404$	−8.89040	+	15.3986i	−0.442314	+	0.766110i
$405$		−	1.29339i		−	0.0642693i
$406$		0			0
$407$	−0.106409	−	3.13836i	−0.00527450	−	0.155563i
$408$	−33.9810	+	58.8568i	−1.68231	+	2.91385i
$409$	7.41981	+	12.8515i	0.366886	+	0.635465i	0.989077	−	0.147400i	$-0.0470906\pi$
$409$	7.41981	+	12.8515i	0.366886	+	0.635465i	−0.622191	+	0.782866i	$0.713757\pi$
$410$	4.26663	+	7.39001i	0.210714	+	0.364967i
$411$	−29.5912	−	17.0845i	−1.45963	−	0.842717i
$412$		−	82.2836i		−	4.05382i
$413$		0			0
$414$		−	64.4567i		−	3.16787i
$415$	−13.6856	−	7.90136i	−0.671798	−	0.387863i
$416$	−36.9655	+	21.3420i	−1.81238	+	1.04638i
$417$	1.66034	−	0.958596i	0.0813070	−	0.0469426i
$418$	14.5933	−	27.3790i	0.713780	−	1.33915i
$419$		−	10.7644i		−	0.525877i	−0.964813	−	0.262939i	$-0.915308\pi$
$419$		−	10.7644i		−	0.525877i	0.964813	−	0.262939i	$-0.0846917\pi$
$420$		0			0
$421$	−22.4013			−1.09177			−0.545887	−	0.837859i	$-0.683807\pi$
$421$	−22.4013			−1.09177			−0.545887	+	0.837859i	$0.683807\pi$
$422$	12.0678	−	20.9021i	0.587453	−	1.01750i
$423$	34.9993	−	20.2069i	1.70173	−	0.982492i
$424$	−5.50618	+	3.17899i	−0.267404	+	0.154385i
$425$	−2.61869	+	4.53570i	−0.127025	+	0.220014i
$426$	−52.1720			−2.52774
$427$		0			0
$428$		−	57.5897i		−	2.78370i
$429$	18.8174	−	35.3041i	0.908514	−	1.70450i
$430$	−50.3260	+	29.0557i	−2.42693	+	1.40119i
$431$	8.14061	−	4.69999i	0.392120	−	0.226390i	−0.290959	−	0.956736i	$-0.593974\pi$
$431$	8.14061	−	4.69999i	0.392120	−	0.226390i	0.683078	+	0.730345i	$0.260641\pi$
$432$	−45.0519	−	26.0108i	−2.16756	−	1.25144i
$433$			12.0749i			0.580282i	0.956984	+	0.290141i	$0.0937021\pi$
$433$			12.0749i			0.580282i	−0.956984	+	0.290141i	$0.906298\pi$
$434$		0			0
$435$			17.0586i			0.817896i
$436$	56.9336	+	32.8706i	2.72662	+	1.57422i
$437$	8.94691	+	15.4965i	0.427989	+	0.741298i
$438$	34.3833	+	59.5537i	1.64290	+	2.84558i
$439$	−19.3252	+	33.4723i	−0.922343	+	1.59755i	−0.126564	+	0.991958i	$0.540395\pi$
$439$	−19.3252	+	33.4723i	−0.922343	+	1.59755i	−0.795779	+	0.605587i	$0.792938\pi$
$440$	−1.51493	−	44.6805i	−0.0722217	−	2.13006i
$441$		0			0
$442$		−	36.8226i		−	1.75147i
$443$	−6.74816	+	11.6881i	−0.320615	+	0.555321i	−0.980615	−	0.195945i	$-0.937223\pi$
$443$	−6.74816	+	11.6881i	−0.320615	+	0.555321i	0.660000	+	0.751265i	$0.270556\pi$
$444$	11.0972	−	6.40695i	0.526648	−	0.304061i
$445$	7.00457	+	12.1323i	0.332049	+	0.575125i
$446$	22.5815	−	39.1123i	1.06926	−	1.85202i
$447$	24.3445			1.15145
$448$		0			0
$449$	−23.6949			−1.11823			−0.559115	−	0.829090i	$-0.688859\pi$
$449$	−23.6949			−1.11823			−0.559115	+	0.829090i	$0.688859\pi$
$450$	−17.7489	−	10.2473i	−0.836692	−	0.483064i
$451$	−4.98508	+	3.10800i	−0.234738	+	0.146350i
$452$	22.5580	+	39.0716i	1.06104	+	1.83777i
$453$	13.3066	−	23.0477i	0.625199	−	1.08288i
$454$			67.1807i			3.15294i
$455$		0			0
$456$	73.8292			3.45737
$457$	12.3951	+	7.15629i	0.579816	+	0.334757i	0.761060	−	0.648681i	$-0.224679\pi$
$457$	12.3951	+	7.15629i	0.579816	+	0.334757i	−0.181244	+	0.983438i	$0.558012\pi$
$458$	−10.1524	−	17.5845i	−0.474392	−	0.821671i
$459$	15.7882	−	9.11535i	0.736932	−	0.425468i
$460$	38.2914	+	22.1076i	1.78535	+	1.03077i
$461$	25.7002			1.19698			0.598489	−	0.801131i	$-0.295768\pi$
$461$	25.7002			1.19698			0.598489	+	0.801131i	$0.295768\pi$
$462$		0			0
$463$	−30.0222			−1.39525			−0.697624	−	0.716464i	$-0.745759\pi$
$463$	−30.0222			−1.39525			−0.697624	+	0.716464i	$0.745759\pi$
$464$	26.7120	+	15.4222i	1.24007	+	0.715955i
$465$	−7.14879	+	4.12736i	−0.331517	+	0.191402i
$466$	−15.5175	−	26.8772i	−0.718836	−	1.24506i
$467$	26.1555	+	15.1009i	1.21033	+	0.698786i	0.962832	−	0.270102i	$-0.0870575\pi$
$467$	26.1555	+	15.1009i	1.21033	+	0.698786i	0.247500	+	0.968888i	$0.420391\pi$
$468$	101.699			4.70106
$469$		0			0
$470$			39.2785i			1.81178i
$471$	24.5604	−	42.5399i	1.13168	−	1.96013i
$472$	24.3958	+	42.2547i	1.12291	+	1.94493i
$473$	−21.1655	−	33.9484i	−0.973191	−	1.56095i
$474$	41.3143	+	23.8528i	1.89763	+	1.09560i
$475$	5.68953			0.261053
$476$		0			0
$477$	4.32018			0.197807
$478$	8.53325	−	14.7800i	0.390302	−	0.676023i
$479$	−15.2248	−	26.3701i	−0.695638	−	1.20488i	−0.969965	−	0.243243i	$-0.921789\pi$
$479$	−15.2248	−	26.3701i	−0.695638	−	1.20488i	0.274328	−	0.961636i	$-0.411545\pi$
$480$	45.0564	−	26.0133i	2.05653	−	1.18734i
$481$	−2.02434	+	3.50625i	−0.0923018	+	0.159871i
$482$		−	61.9635i		−	2.82236i
$483$		0			0
$484$	52.6561	−	3.57482i	2.39346	−	0.162492i
$485$	2.88876	−	5.00348i	0.131172	−	0.227196i
$486$	−19.0140	−	32.9333i	−0.862494	−	1.49388i
$487$	0.643219	+	1.11409i	0.0291470	+	0.0504842i	0.880231	−	0.474545i	$-0.157388\pi$
$487$	0.643219	+	1.11409i	0.0291470	+	0.0504842i	−0.851084	+	0.525030i	$0.824054\pi$
$488$	−29.5630	−	17.0682i	−1.33825	−	0.772641i
$489$			44.6131i			2.01747i
$490$		0			0
$491$		−	4.06107i		−	0.183274i	−0.995792	−	0.0916368i	$-0.970790\pi$
$491$		−	4.06107i		−	0.183274i	0.995792	−	0.0916368i	$-0.0292099\pi$
$492$	−20.7605	−	11.9861i	−0.935954	−	0.540373i
$493$	−9.36108	+	5.40462i	−0.421602	+	0.243412i
$494$	−34.6423	+	20.0008i	−1.55863	+	0.899877i
$495$	−14.2885	+	26.8071i	−0.642219	+	1.20489i
$496$			14.9257i			0.670183i
$497$		0			0
$498$	62.8994			2.81859
$499$	9.51802	−	16.4857i	0.426085	−	0.738001i	−0.570436	−	0.821342i	$-0.693226\pi$
$499$	9.51802	−	16.4857i	0.426085	−	0.738001i	0.996521	+	0.0833412i	$0.0265591\pi$
$500$	50.5636	−	29.1929i	2.26127	−	1.30555i
$501$	−6.99358	+	4.03775i	−0.312450	+	0.180393i
$502$	16.5340	−	28.6378i	0.737951	−	1.27817i
$503$	−42.2557			−1.88409			−0.942044	−	0.335489i	$-0.891098\pi$
$503$	−42.2557			−1.88409			−0.942044	+	0.335489i	$0.891098\pi$
$504$		0			0
$505$			6.84767i			0.304717i
$506$	−20.2858	+	38.0590i	−0.901814	+	1.69193i
$507$	−12.9125	+	7.45503i	−0.573464	+	0.331089i
$508$	70.8806	−	40.9230i	3.14482	−	1.81566i
$509$	−32.6852	−	18.8708i	−1.44875	−	0.836434i	−0.450340	−	0.892857i	$-0.648697\pi$
$509$	−32.6852	−	18.8708i	−1.44875	−	0.836434i	−0.998407	+	0.0564228i	$0.982031\pi$
$510$			44.8822i			1.98742i
$511$		0			0
$512$			43.4292i			1.91932i
$513$	−17.1513	−	9.90229i	−0.757247	−	0.437197i
$514$	25.8086	+	44.7019i	1.13837	+	1.97171i
$515$	−15.8444	−	27.4432i	−0.698186	−	1.20929i
$516$	81.6250	−	141.379i	3.59334	−	6.22385i
$517$	−27.0251	+	0.916313i	−1.18856	+	0.0402994i
$518$		0			0
$519$		−	58.2171i		−	2.55545i
$520$	−28.8202	+	49.9181i	−1.26385	+	2.18905i
$521$	−8.04875	+	4.64695i	−0.352622	+	0.203587i	−0.665840	−	0.746095i	$-0.731927\pi$
$521$	−8.04875	+	4.64695i	−0.352622	+	0.203587i	0.313217	+	0.949681i	$0.398593\pi$
$522$	−21.1491	−	36.6314i	−0.925672	−	1.60331i
$523$	1.66185	−	2.87840i	0.0726674	−	0.125864i	−0.827402	−	0.561610i	$-0.810182\pi$
$523$	1.66185	−	2.87840i	0.0726674	−	0.125864i	0.900070	+	0.435746i	$0.143516\pi$
$524$	75.9869			3.31951
$525$		0			0
$526$	−31.0770			−1.35502
$527$	−4.52986	−	2.61532i	−0.197324	−	0.113925i
$528$	46.6467	+	74.8189i	2.03004	+	3.25608i
$529$	−0.936924	−	1.62280i	−0.0407358	−	0.0705565i
$530$	−2.09941	+	3.63629i	−0.0911926	+	0.157950i
$531$		−	33.1533i		−	1.43873i
$532$		0			0
$533$	7.57421			0.328076
$534$	−48.2899	−	27.8802i	−2.08971	−	1.20649i
$535$	−11.0893	−	19.2073i	−0.479434	−	0.830405i
$536$	−54.7709	+	31.6220i	−2.36574	+	1.36586i
$537$	58.8441	+	33.9736i	2.53931	+	1.46607i
$538$	71.5221			3.08354
$539$		0			0
$540$	−48.9366			−2.10590
$541$	−2.44248	−	1.41017i	−0.105010	−	0.0606277i	0.446575	−	0.894746i	$-0.352644\pi$
$541$	−2.44248	−	1.41017i	−0.105010	−	0.0606277i	−0.551585	+	0.834118i	$0.685977\pi$
$542$	−11.8062	+	6.81633i	−0.507121	+	0.292786i
$543$	−4.37532	−	7.57827i	−0.187763	−	0.325215i
$544$	28.5502	+	16.4834i	1.22408	+	0.706722i
$545$	25.3180			1.08450
$546$		0			0
$547$			30.6702i			1.31136i	0.755038	+	0.655681i	$0.227618\pi$
$547$			30.6702i			1.31136i	−0.755038	+	0.655681i	$0.772382\pi$
$548$	−29.0593	+	50.3322i	−1.24135	+	2.15009i
$549$	11.5976	+	20.0877i	0.494975	+	0.857322i
$550$	7.25494	+	11.6366i	0.309352	+	0.496185i
$551$	10.1692	+	5.87121i	0.433224	+	0.250122i
$552$	−102.629			−4.36816
$553$		0			0
$554$	−49.6936			−2.11128
$555$	2.46742	−	4.27369i	0.104736	−	0.181408i
$556$	−1.63049	−	2.82409i	−0.0691482	−	0.119768i
$557$	−26.1832	+	15.1169i	−1.10942	+	0.640522i	−0.938678	−	0.344794i	$-0.887949\pi$
$557$	−26.1832	+	15.1169i	−1.10942	+	0.640522i	−0.170738	+	0.985316i	$0.554615\pi$
$558$	10.2341	−	17.7261i	0.433246	−	0.750404i
$559$			51.5804i			2.18162i
$560$		0			0
$561$	−30.8807	+	1.04704i	−1.30378	+	0.0442060i
$562$	10.3005	−	17.8411i	0.434502	−	0.752580i
$563$	13.5629	+	23.4917i	0.571609	+	0.990056i	0.996401	+	0.0847651i	$0.0270140\pi$
$563$	13.5629	+	23.4917i	0.571609	+	0.990056i	−0.424792	+	0.905291i	$0.639653\pi$
$564$	−55.1717	−	95.5602i	−2.32315	−	4.02381i
$565$	15.0471	+	8.68743i	0.633035	+	0.365483i
$566$		−	8.95107i		−	0.376241i
$567$		0			0
$568$			51.7492i			2.17135i
$569$	−14.3169	−	8.26587i	−0.600196	−	0.346523i	0.168923	−	0.985629i	$-0.445971\pi$
$569$	−14.3169	−	8.26587i	−0.600196	−	0.346523i	−0.769119	+	0.639106i	$0.779304\pi$
$570$	42.2248	−	24.3785i	1.76860	−	1.02110i
$571$	28.8367	−	16.6489i	1.20678	−	0.696734i	0.244724	−	0.969593i	$-0.421303\pi$
$571$	28.8367	−	16.6489i	1.20678	−	0.696734i	0.962054	+	0.272859i	$0.0879692\pi$
$572$	−60.0493	−	32.0069i	−2.51079	−	1.33827i
$573$		−	19.2616i		−	0.804664i
$574$		0			0
$575$	−7.90890			−0.329824
$576$	−17.7873	+	30.8084i	−0.741136	+	1.28368i
$577$	−26.2756	+	15.1702i	−1.09387	+	0.631544i	−0.934603	−	0.355692i	$-0.884245\pi$
$577$	−26.2756	+	15.1702i	−1.09387	+	0.631544i	−0.159263	+	0.987236i	$0.550912\pi$
$578$	13.7560	−	7.94202i	0.572173	−	0.330344i
$579$	10.2829	−	17.8105i	0.427342	−	0.740178i
$580$	29.0152			1.20479
$581$		0			0
$582$			22.9962i			0.953222i
$583$	−2.55088	−	1.35965i	−0.105647	−	0.0563108i
$584$	59.0710	−	34.1047i	2.44438	−	1.41126i
$585$	33.9188	−	19.5830i	1.40237	−	0.809659i
$586$	47.8612	+	27.6327i	1.97713	+	1.14150i
$587$			4.45108i			0.183716i	0.995772	+	0.0918578i	$0.0292805\pi$
$587$			4.45108i			0.183716i	−0.995772	+	0.0918578i	$0.970719\pi$
$588$		0			0
$589$			5.68220i			0.234131i
$590$	27.9051	+	16.1110i	1.14883	+	0.663280i
$591$	−6.52804	−	11.3069i	−0.268527	−	0.465103i
$592$	−4.46144	−	7.72744i	−0.183364	−	0.317596i
$593$	−13.9845	+	24.2218i	−0.574273	+	0.994671i	0.421847	+	0.906667i	$0.361382\pi$
$593$	−13.9845	+	24.2218i	−0.574273	+	0.994671i	−0.996120	+	0.0880035i	$0.971951\pi$
$594$	−1.61750	−	47.7056i	−0.0663670	−	1.95738i
$595$		0			0
$596$		−	41.4079i		−	1.69614i
$597$	12.4374	−	21.5422i	0.509029	−	0.881664i
$598$	48.1556	−	27.8027i	1.96923	−	1.13694i
$599$	−1.36163	−	2.35841i	−0.0556346	−	0.0963619i	0.836867	−	0.547407i	$-0.184385\pi$
$599$	−1.36163	−	2.35841i	−0.0556346	−	0.0963619i	−0.892501	+	0.451045i	$0.851052\pi$
$600$	−16.3159	+	28.2600i	−0.666095	+	1.15371i
$601$	−11.6830			−0.476558			−0.238279	−	0.971197i	$-0.576583\pi$
$601$	−11.6830			−0.476558			−0.238279	+	0.971197i	$0.576583\pi$
$602$		0			0
$603$	42.9735			1.75002
$604$	−39.2022	−	22.6334i	−1.59512	−	0.920941i
$605$	16.8735	−	11.3316i	0.686005	−	0.460695i
$606$	−13.6278	−	23.6041i	−0.553593	−	0.958851i
$607$	−19.1262	+	33.1275i	−0.776307	+	1.34460i	0.157749	+	0.987479i	$0.449576\pi$
$607$	−19.1262	+	33.1275i	−0.776307	+	1.34460i	−0.934057	+	0.357125i	$0.883757\pi$
$608$		−	35.8130i		−	1.45241i
$609$		0			0
$610$	−22.5437			−0.912768
$611$	30.1931	+	17.4320i	1.22148	+	0.705224i
$612$	−39.2736	−	68.0239i	−1.58754	−	2.74970i
$613$	−0.158952	+	0.0917709i	−0.00642001	+	0.00370659i	−0.503207	−	0.864166i	$-0.667847\pi$
$613$	−0.158952	+	0.0917709i	−0.00642001	+	0.00370659i	0.496787	+	0.867873i	$0.334513\pi$
$614$	−33.1853	−	19.1595i	−1.33925	−	0.773216i
$615$	−9.23204			−0.372272
$616$		0			0
$617$	9.73115			0.391761			0.195881	−	0.980628i	$-0.437243\pi$
$617$	9.73115			0.391761			0.195881	+	0.980628i	$0.437243\pi$
$618$	109.232	+	63.0651i	4.39395	+	2.53685i
$619$	9.96081	−	5.75087i	0.400359	−	0.231147i	−0.286280	−	0.958146i	$-0.592419\pi$
$619$	9.96081	−	5.75087i	0.400359	−	0.231147i	0.686639	+	0.726999i	$0.259085\pi$
$620$	7.02029	+	12.1595i	0.281941	+	0.488337i
$621$	23.8416	+	13.7650i	0.956732	+	0.552370i
$622$	21.6890			0.869651
$623$		0			0
$624$		−	113.678i		−	4.55076i
$625$	7.27817	−	12.6062i	0.291127	−	0.504247i
$626$	−20.9512	−	36.2885i	−0.837378	−	1.45038i
$627$	17.7584	+	28.4836i	0.709202	+	1.13752i
$628$	−72.3567	−	41.7752i	−2.88735	−	1.66701i
$629$	3.12698			0.124681
$630$		0			0
$631$	16.1028			0.641042			0.320521	−	0.947241i	$-0.396142\pi$
$631$	16.1028			0.641042			0.320521	+	0.947241i	$0.396142\pi$
$632$	23.6595	−	40.9794i	0.941124	−	1.63007i
$633$	13.0561	+	22.6138i	0.518932	+	0.898817i
$634$	−37.8034	+	21.8258i	−1.50137	+	0.866814i
$635$	15.7601	−	27.2972i	0.625419	−	1.08326i
$636$		−	11.7956i		−	0.467725i
$637$		0			0
$638$	0.959041	+	28.2853i	0.0379688	+	1.11983i
$639$	17.5815	−	30.4520i	0.695513	−	1.20466i
$640$	1.15635	+	2.00286i	0.0457088	+	0.0791699i
$641$	3.34657	+	5.79643i	0.132182	+	0.228945i	0.924517	−	0.381140i	$-0.124468\pi$
$641$	3.34657	+	5.79643i	0.132182	+	0.228945i	−0.792336	+	0.610085i	$0.791135\pi$
$642$	76.4506	+	44.1388i	3.01727	+	1.74202i
$643$		−	2.28381i		−	0.0900647i	−0.998986	−	0.0450323i	$-0.985661\pi$
$643$		−	2.28381i		−	0.0900647i	0.998986	−	0.0450323i	$-0.0143391\pi$
$644$		0			0
$645$		−	62.8701i		−	2.47551i
$646$	26.7559	+	15.4475i	1.05270	+	0.607775i
$647$	−11.7866	+	6.80498i	−0.463378	+	0.267531i	−0.713463	−	0.700692i	$-0.752875\pi$
$647$	−11.7866	+	6.80498i	−0.463378	+	0.267531i	0.250086	+	0.968224i	$0.419541\pi$
$648$	4.42224	−	2.55318i	0.173722	−	0.100298i
$649$	−10.4340	+	19.5756i	−0.409571	+	0.768411i
$650$		−	17.6803i		−	0.693479i
$651$		0			0
$652$	75.8831			2.97181
$653$	−6.50019	+	11.2587i	−0.254372	+	0.440586i	−0.964725	−	0.263260i	$-0.915202\pi$
$653$	−6.50019	+	11.2587i	−0.254372	+	0.440586i	0.710353	+	0.703846i	$0.248535\pi$
$654$	−87.2718	+	50.3864i	−3.41260	+	1.97026i
$655$	25.3432	−	14.6319i	0.990239	−	0.571715i
$656$	−8.34641	+	14.4564i	−0.325873	+	0.564428i
$657$	−46.3475			−1.80819
$658$		0			0
$659$		−	12.0622i		−	0.469878i	−0.972010	−	0.234939i	$-0.924511\pi$
$659$		−	12.0622i		−	0.469878i	0.972010	−	0.234939i	$-0.0754890\pi$
$660$	73.1927	+	39.0125i	2.84902	+	1.51856i
$661$	37.8829	−	21.8717i	1.47348	−	0.850712i	0.473922	−	0.880567i	$-0.342838\pi$
$661$	37.8829	−	21.8717i	1.47348	−	0.850712i	0.999554	+	0.0298555i	$0.00950470\pi$
$662$	−51.1295	+	29.5196i	−1.98720	+	1.14731i
$663$	34.5007	+	19.9190i	1.33989	+	0.773589i
$664$		−	62.3896i		−	2.42119i
$665$		0			0
$666$			12.2364i			0.474150i
$667$	−14.1361	−	8.16146i	−0.547350	−	0.316013i
$668$	6.86787	+	11.8955i	0.265726	+	0.460251i
$669$	24.4307	+	42.3152i	0.944544	+	1.63600i
$670$	−20.8832	+	36.1708i	−0.806788	+	1.39740i
$671$	−0.525914	−	15.5110i	−0.0203027	−	0.598794i
$672$		0			0
$673$			24.5449i			0.946135i	0.881026	+	0.473067i	$0.156853\pi$
$673$			24.5449i			0.946135i	−0.881026	+	0.473067i	$0.843147\pi$
$674$	−19.6088	+	33.9635i	−0.755304	+	1.30823i
$675$	7.58070	−	4.37672i	0.291781	−	0.168460i
$676$	12.6804	+	21.9631i	0.487707	+	0.844733i
$677$	17.0169	−	29.4741i	0.654012	−	1.13278i	−0.328129	−	0.944633i	$-0.606418\pi$
$677$	17.0169	−	29.4741i	0.654012	−	1.13278i	0.982141	−	0.188149i	$-0.0602488\pi$
$678$	−69.1569			−2.65596
$679$		0			0
$680$	44.5185			1.70720
$681$	−62.9445	−	36.3410i	−2.41204	−	1.39259i
$682$	−11.6216	+	7.24560i	−0.445013	+	0.277448i
$683$	−8.22839	−	14.2520i	−0.314850	−	0.545337i	0.664555	−	0.747239i	$-0.268621\pi$
$683$	−8.22839	−	14.2520i	−0.314850	−	0.545337i	−0.979406	+	0.201902i	$0.935288\pi$
$684$	−42.6642	+	73.8966i	−1.63131	+	2.82551i
$685$			22.3824i			0.855187i
$686$		0			0
$687$	21.9676			0.838117
$688$	−98.4481	−	56.8390i	−3.75330	−	2.16697i
$689$	1.86346	+	3.22761i	0.0709922	+	0.122962i
$690$	−58.6958	+	33.8880i	−2.23451	+	1.29010i
$691$	−30.7162	−	17.7340i	−1.16850	−	0.674634i	−0.215174	−	0.976576i	$-0.569032\pi$
$691$	−30.7162	−	17.7340i	−1.16850	−	0.674634i	−0.953326	+	0.301942i	$0.902365\pi$
$692$	−99.0224			−3.76427
$693$		0			0
$694$	55.3670			2.10170
$695$	−1.08760	−	0.627928i	−0.0412551	−	0.0238187i
$696$	−58.3249	+	33.6739i	−2.21080	+	1.27641i
$697$	−2.92496	−	5.06618i	−0.110791	−	0.191895i
$698$	61.5162	+	35.5164i	2.32842	+	1.34431i
$699$	33.5765			1.26998
$700$		0			0
$701$			23.7041i			0.895291i	0.894211	+	0.447645i	$0.147737\pi$
$701$			23.7041i			0.895291i	−0.894211	+	0.447645i	$0.852263\pi$
$702$	−30.7715	+	53.2979i	−1.16140	+	2.01160i
$703$	−1.69847	−	2.94183i	−0.0640590	−	0.110953i
$704$	20.1987	−	12.5931i	0.761266	−	0.474620i
$705$	−36.8017	−	21.2475i	−1.38603	−	0.800227i
$706$	63.9310			2.40607
$707$		0			0
$708$	−90.5199			−3.40195
$709$	−11.5557	+	20.0150i	−0.433983	+	0.751681i	−0.997212	−	0.0746201i	$-0.976226\pi$
$709$	−11.5557	+	20.0150i	−0.433983	+	0.751681i	0.563229	+	0.826301i	$0.309559\pi$
$710$	17.0876	+	29.5966i	0.641287	+	1.11074i
$711$	−27.8451	+	16.0764i	−1.04427	+	0.602911i
$712$	−27.6543	+	47.8986i	−1.03639	+	1.79508i
$713$		−	7.89872i		−	0.295809i
$714$		0			0
$715$	−26.1908	+	0.888024i	−0.979480	+	0.0332102i
$716$	57.7863	−	100.089i	2.15958	−	3.74049i
$717$	9.23204	+	15.9904i	0.344777	+	0.597171i
$718$	21.3564	+	36.9904i	0.797015	+	1.38047i
$719$	−25.8440	−	14.9210i	−0.963818	−	0.556461i	−0.0664721	−	0.997788i	$-0.521174\pi$
$719$	−25.8440	−	14.9210i	−0.963818	−	0.556461i	−0.897346	+	0.441328i	$0.854508\pi$
$720$			86.3181i			3.21689i
$721$		0			0
$722$			15.9761i			0.594570i
$723$	58.0563	+	33.5188i	2.15914	+	1.24658i
$724$	−12.8900	+	7.44205i	−0.479053	+	0.276581i
$725$	−4.49471	+	2.59502i	−0.166929	+	0.0963767i
$726$	−35.6119	+	72.6410i	−1.32168	+	2.69596i
$727$			28.5107i			1.05740i	0.848808	+	0.528702i	$0.177321\pi$
$727$			28.5107i			1.05740i	−0.848808	+	0.528702i	$0.822679\pi$
$728$		0			0
$729$	43.2421			1.60156
$730$	22.5228	−	39.0106i	0.833605	−	1.44385i
$731$	34.5007	−	19.9190i	1.27605	−	0.736730i
$732$	54.8464	−	31.6656i	2.02718	−	1.17039i
$733$	19.7875	−	34.2730i	0.730869	−	1.26590i	−0.225644	−	0.974210i	$-0.572448\pi$
$733$	19.7875	−	34.2730i	0.730869	−	1.26590i	0.956512	−	0.291692i	$-0.0942182\pi$
$734$	1.41062			0.0520669
$735$		0			0
$736$			49.7829i			1.83502i
$737$	−25.3741	−	13.5246i	−0.934666	−	0.498187i
$738$	19.8248	−	11.4458i	0.729759	−	0.421327i
$739$	14.7006	−	8.48742i	0.540772	−	0.312215i	−0.204620	−	0.978842i	$-0.565596\pi$
$739$	14.7006	−	8.48742i	0.540772	−	0.312215i	0.745392	+	0.666627i	$0.232262\pi$
$740$	−7.26919	−	4.19687i	−0.267221	−	0.154280i
$741$		−	43.2772i		−	1.58983i
$742$		0			0
$743$		−	39.9272i		−	1.46479i	−0.680882	−	0.732393i	$-0.738403\pi$
$743$		−	39.9272i		−	1.46479i	0.680882	−	0.732393i	$-0.261597\pi$
$744$	−28.2236	−	16.2949i	−1.03473	−	0.597401i
$745$	−7.97342	−	13.8104i	−0.292124	−	0.505973i
$746$	−37.8859	−	65.6204i	−1.38710	−	2.40253i
$747$	−21.1965	+	36.7134i	−0.775540	+	1.34327i
$748$	1.78093	+	52.5255i	0.0651171	+	1.92052i
$749$		0			0
$750$			89.4979i			3.26800i
$751$	−9.70098	+	16.8026i	−0.353994	+	0.613135i	−0.986945	−	0.161056i	$-0.948510\pi$
$751$	−9.70098	+	16.8026i	−0.353994	+	0.613135i	0.632951	+	0.774192i	$0.281843\pi$
$752$	−66.5427	+	38.4184i	−2.42656	+	1.40098i
$753$	17.8880	+	30.9829i	0.651875	+	1.12908i
$754$	18.2449	−	31.6011i	0.664440	−	1.15084i
$755$	−17.4330			−0.634451
$756$		0			0
$757$	−12.9289			−0.469910			−0.234955	−	0.972006i	$-0.575494\pi$
$757$	−12.9289			−0.469910			−0.234955	+	0.972006i	$0.575494\pi$
$758$	−2.12690	−	1.22796i	−0.0772523	−	0.0446017i
$759$	−24.6856	−	39.5945i	−0.896030	−	1.43719i
$760$	−24.1809	−	41.8826i	−0.877134	−	1.51924i
$761$	−4.84464	+	8.39116i	−0.175618	+	0.304179i	−0.940375	−	0.340139i	$-0.889526\pi$
$761$	−4.84464	+	8.39116i	−0.175618	+	0.304179i	0.764757	+	0.644319i	$0.222859\pi$
$762$			125.459i			4.54491i
$763$		0			0
$764$	−32.7623			−1.18530
$765$	−26.1971	−	15.1249i	−0.947158	−	0.546842i
$766$	1.90122	+	3.29300i	0.0686937	+	0.118981i
$767$	24.7689	−	14.3003i	0.894352	−	0.516354i
$768$	−43.0361	−	24.8469i	−1.55293	−	0.896585i
$769$	7.36367			0.265541			0.132770	−	0.991147i	$-0.457613\pi$
$769$	7.36367			0.265541			0.132770	+	0.991147i	$0.457613\pi$
$770$		0			0
$771$	−55.8442			−2.01118
$772$	−30.2941	−	17.4903i	−1.09031	−	0.629491i
$773$	−7.29716	+	4.21302i	−0.262461	+	0.151532i	−0.625457	−	0.780259i	$-0.715087\pi$
$773$	−7.29716	+	4.21302i	−0.262461	+	0.151532i	0.362996	+	0.931791i	$0.381754\pi$
$774$	77.9461	+	135.007i	2.80171	+	4.85271i
$775$	−2.17501	−	1.25574i	−0.0781286	−	0.0451075i
$776$	22.8098			0.818824
$777$		0			0
$778$		−	17.8324i		−	0.639321i
$779$	−3.17748	+	5.50355i	−0.113845	+	0.197185i
$780$	−53.4684	−	92.6100i	−1.91448	−	3.31597i
$781$	−19.9650	+	12.4474i	−0.714404	+	0.445403i
$782$	−37.1929	−	21.4733i	−1.33001	−	0.767884i
$783$	18.0659			0.645624
$784$		0			0
$785$	−32.1765			−1.14843
$786$	−58.2391	+	100.873i	−2.07732	+	3.59802i
$787$	1.73921	+	3.01240i	0.0619961	+	0.107380i	0.895358	−	0.445348i	$-0.146920\pi$
$787$	1.73921	+	3.01240i	0.0619961	+	0.107380i	−0.833361	+	0.552728i	$0.813587\pi$
$788$	−19.2321	+	11.1036i	−0.685114	+	0.395551i
$789$	16.8109	−	29.1174i	0.598485	−	1.03661i
$790$		−	31.2495i		−	1.11181i
$791$		0			0
$792$	−119.862	+	4.06402i	−4.25910	+	0.144409i
$793$	−10.0050	+	17.3292i	−0.355289	+	0.615379i
$794$	16.1303	+	27.9386i	0.572444	+	0.991502i
$795$	−2.27133	−	3.93406i	−0.0805558	−	0.139527i
$796$	−36.6415	−	21.1550i	−1.29872	−	0.749818i
$797$			26.1007i			0.924535i	0.886741	+	0.462267i	$0.152964\pi$
$797$			26.1007i			0.924535i	−0.886741	+	0.462267i	$0.847036\pi$
$798$		0			0
$799$		−	26.9271i		−	0.952614i
$800$	13.7083	+	7.91450i	0.484662	+	0.279820i
$801$	32.5465	−	18.7908i	1.14998	−	0.663939i
$802$	44.2603	−	25.5537i	1.56289	−	0.902332i
$803$	27.3662	+	14.5865i	0.965733	+	0.514746i
$804$		−	117.333i		−	4.13800i
$805$		0			0
$806$	17.6575			0.621961
$807$	−38.6895	+	67.0122i	−1.36194	+	2.35894i
$808$	−23.4128	+	13.5174i	−0.823660	+	0.475540i
$809$	39.6015	−	22.8639i	1.39231	−	0.803852i	0.398742	−	0.917063i	$-0.369447\pi$
$809$	39.6015	−	22.8639i	1.39231	−	0.803852i	0.993571	+	0.113211i	$0.0361135\pi$
$810$	1.68612	−	2.92045i	0.0592443	−	0.102614i
$811$	−4.50370			−0.158146			−0.0790731	−	0.996869i	$-0.525196\pi$
$811$	−4.50370			−0.158146			−0.0790731	+	0.996869i	$0.525196\pi$
$812$		0			0
$813$		−	14.7490i		−	0.517271i
$814$	3.85103	−	7.22506i	0.134979	−	0.253238i
$815$	25.3085	−	14.6119i	0.886519	−	0.511832i
$816$	−76.0361	+	43.8994i	−2.66180	+	1.53679i
$817$	−37.4792	−	21.6386i	−1.31123	−	0.757039i
$818$			38.6911i			1.35280i
$819$		0			0
$820$			15.7029i			0.548370i
$821$	−5.93602	−	3.42716i	−0.207168	−	0.119609i	0.392826	−	0.919613i	$-0.371497\pi$
$821$	−5.93602	−	3.42716i	−0.207168	−	0.119609i	−0.599995	+	0.800004i	$0.704831\pi$
$822$	−44.5442	−	77.1528i	−1.55366	−	2.69101i
$823$	−16.8656	−	29.2120i	−0.587897	−	1.01827i	−0.994507	−	0.104666i	$-0.966623\pi$
$823$	−16.8656	−	29.2120i	−0.587897	−	1.01827i	0.406611	−	0.913602i	$-0.366711\pi$
$824$	62.5540	−	108.347i	2.17917	−	3.77444i
$825$	−14.8273	+	0.502734i	−0.516221	+	0.0175030i
$826$		0			0
$827$			4.06107i			0.141217i	0.997504	+	0.0706086i	$0.0224941\pi$
$827$			4.06107i			0.141217i	−0.997504	+	0.0706086i	$0.977506\pi$
$828$	59.3067	−	102.722i	2.06105	−	3.56984i
$829$	−40.0146	+	23.1024i	−1.38976	+	0.802381i	−0.993288	−	0.115664i	$-0.963100\pi$
$829$	−40.0146	+	23.1024i	−1.38976	+	0.802381i	−0.396476	+	0.918045i	$0.629767\pi$
$830$	−20.6011	−	35.6821i	−0.715075	−	1.23855i
$831$	26.8815	−	46.5601i	0.932508	−	1.61515i
$832$	−30.6894			−1.06396
$833$		0			0
$834$	4.99866			0.173090
$835$	4.58114	+	2.64492i	0.158537	+	0.0915313i
$836$	48.4482	−	30.2055i	1.67561	−	1.04468i
$837$	4.37109	+	7.57095i	0.151087	+	0.261690i
$838$	14.0330	−	24.3058i	0.484761	−	0.839631i
$839$			2.39354i			0.0826343i	0.999146	+	0.0413171i	$0.0131554\pi$
$839$			2.39354i			0.0826343i	−0.999146	+	0.0413171i	$0.986845\pi$
$840$		0			0
$841$	18.2884			0.630636
$842$	−50.5816	−	29.2033i	−1.74316	−	1.00641i
$843$	11.1441	+	19.3021i	0.383822	+	0.664798i
$844$	38.4641	−	22.2073i	1.32399	−	0.764406i
$845$	8.45832	+	4.88341i	0.290975	+	0.167994i
$846$	105.370			3.62270
$847$		0			0
$848$	−8.21377			−0.282062
$849$	8.38665	+	4.84203i	0.287829	+	0.166178i
$850$	−11.8259	+	6.82766i	−0.405624	+	0.234187i
$851$	2.36101	+	4.08939i	0.0809343	+	0.140182i
$852$	−83.1445	−	48.0035i	−2.84848	−	1.64457i
$853$	−20.2353			−0.692844			−0.346422	−	0.938079i	$-0.612604\pi$
$853$	−20.2353			−0.692844			−0.346422	+	0.938079i	$0.612604\pi$
$854$		0			0
$855$			32.8613i			1.12383i
$856$	43.7811	−	75.8310i	1.49641	−	2.59185i
$857$	−10.2037	−	17.6734i	−0.348552	−	0.603711i	0.637440	−	0.770500i	$-0.279993\pi$
$857$	−10.2037	−	17.6734i	−0.348552	−	0.603711i	−0.985993	+	0.166789i	$0.946660\pi$
$858$	88.5132	−	55.1845i	3.02179	−	1.88397i
$859$	−11.9756	−	6.91410i	−0.408601	−	0.235906i	0.281587	−	0.959536i	$-0.409139\pi$
$859$	−11.9756	−	6.91410i	−0.408601	−	0.235906i	−0.690188	+	0.723630i	$0.742472\pi$
$860$	−106.937			−3.64652
$861$		0			0
$862$	24.5084			0.834759
$863$	22.2605	−	38.5563i	0.757756	−	1.31247i	−0.186236	−	0.982505i	$-0.559629\pi$
$863$	22.2605	−	38.5563i	0.757756	−	1.31247i	0.943992	−	0.329967i	$-0.107038\pi$
$864$	−27.5495	−	47.7171i	−0.937251	−	1.62337i
$865$	−33.0259	+	19.0675i	−1.12292	+	0.648316i
$866$	−15.7413	+	27.2648i	−0.534912	+	0.926494i
$867$			17.1848i			0.583625i
$868$		0			0
$869$	21.5009	−	0.729008i	0.729368	−	0.0247299i
$870$	−22.2383	+	38.5178i	−0.753948	+	1.30588i
$871$	18.5362	+	32.1056i	0.628074	+	1.08786i
$872$	49.9781	+	86.5645i	1.69247	+	2.93144i
$873$	−13.4225	−	7.74950i	−0.454284	−	0.262281i
$874$			46.6543i			1.57810i
$875$		0			0
$876$			126.545i			4.27554i
$877$	19.2378	+	11.1070i	0.649615	+	0.375056i	0.788309	−	0.615280i	$-0.210957\pi$
$877$	19.2378	+	11.1070i	0.649615	+	0.375056i	−0.138693	+	0.990335i	$0.544290\pi$
$878$	−87.2718	+	50.3864i	−2.94528	+	1.70046i
$879$	−51.7805	+	29.8955i	−1.74651	+	1.00835i
$880$	27.1661	−	50.9672i	0.915768	−	1.71810i
$881$			44.2943i			1.49231i	0.665771	+	0.746157i	$0.268103\pi$
$881$			44.2943i			1.49231i	−0.665771	+	0.746157i	$0.731897\pi$
$882$		0			0
$883$	21.3173			0.717385			0.358692	−	0.933456i	$-0.383223\pi$
$883$	21.3173			0.717385			0.358692	+	0.933456i	$0.383223\pi$
$884$	33.8805	−	58.6827i	1.13952	−	1.97371i
$885$	−30.1902	+	17.4303i	−1.01483	+	0.585914i
$886$	−30.4743	+	17.5944i	−1.02381	+	0.591094i
$887$	−18.1650	+	31.4627i	−0.609920	+	1.05641i	0.381333	+	0.924438i	$0.375465\pi$
$887$	−18.1650	+	31.4627i	−0.609920	+	1.05641i	−0.991253	+	0.131975i	$0.957868\pi$
$888$	19.4829			0.653803
$889$		0			0
$890$			36.5258i			1.22435i
$891$	2.04872	+	1.09199i	0.0686347	+	0.0365830i
$892$	71.9745	−	41.5545i	2.40989	−	1.39135i
$893$	−25.3328	+	14.6259i	−0.847730	+	0.489437i
$894$	54.9692	+	31.7365i	1.83845	+	1.06143i
$895$		−	44.5088i		−	1.48777i
$896$		0			0
$897$			60.1588i			2.00864i
$898$	−53.5024	−	30.8896i	−1.78540	−	1.03080i
$899$	−2.59168	−	4.48892i	−0.0864374	−	0.149714i
$900$	−18.8572	−	32.6616i	−0.628573	−	1.08872i
$901$	1.43924	−	2.49283i	0.0479480	−	0.0830484i
$902$	−15.3079	+	0.519030i	−0.509698	+	0.0172818i
$903$		0			0
$904$			68.5964i			2.28148i
$905$	−2.86605	+	4.96414i	−0.0952707	+	0.165014i
$906$	60.0920	−	34.6941i	1.99642	−	1.15263i
$907$	0.623061	+	1.07917i	0.0206884	+	0.0358334i	0.876184	−	0.481976i	$-0.160081\pi$
$907$	0.623061	+	1.07917i	0.0206884	+	0.0358334i	−0.855496	+	0.517810i	$0.826748\pi$
$908$	−61.8130	+	107.063i	−2.05134	+	3.55302i
$909$	18.3698			0.609289
$910$		0			0
$911$	12.1914			0.403920			0.201960	−	0.979394i	$-0.435269\pi$
$911$	12.1914			0.403920			0.201960	+	0.979394i	$0.435269\pi$
$912$	82.6004	+	47.6894i	2.73517	+	1.57915i
$913$	24.0701	−	15.0068i	0.796605	−	0.496652i
$914$	18.6585	+	32.3174i	0.617168	+	1.06897i
$915$	12.1949	−	21.1222i	0.403151	−	0.698278i
$916$		−	37.3651i		−	1.23458i
$917$		0			0
$918$	47.5326			1.56881
$919$	25.6301	+	14.7976i	0.845459	+	0.488126i	0.859116	−	0.511781i	$-0.171014\pi$
$919$	25.6301	+	14.7976i	0.845459	+	0.488126i	−0.0136568	+	0.999907i	$0.504347\pi$
$920$	33.6134	+	58.2201i	1.10820	+	1.91946i
$921$	35.9028	−	20.7285i	1.18304	−	0.683027i
$922$	58.0304	+	33.5039i	1.91113	+	1.10339i
$923$	30.3343			0.998466
$924$		0			0
$925$	1.50142			0.0493662
$926$	−67.7893	−	39.1382i	−2.22769	−	1.28616i
$927$	−73.6203	+	42.5047i	−2.41801	+	1.39604i
$928$	16.3345	+	28.2921i	0.536205	+	0.928735i
$929$	9.08740	+	5.24661i	0.298148	+	0.172136i	0.641611	−	0.767031i	$-0.278267\pi$
$929$	9.08740	+	5.24661i	0.298148	+	0.172136i	−0.343463	+	0.939166i	$0.611600\pi$
$930$	−21.5224			−0.705747
$931$		0			0
$932$		−	57.1109i		−	1.87073i
$933$	−11.7326	+	20.3214i	−0.384107	+	0.665293i
$934$	39.3723	+	68.1948i	1.28830	+	2.23140i
$935$	10.7082	+	17.1754i	0.350195	+	0.561695i
$936$	133.912	+	77.3144i	4.37706	+	2.52710i
$937$	−22.1577			−0.723861			−0.361930	−	0.932205i	$-0.617882\pi$
$937$	−22.1577			−0.723861			−0.361930	+	0.932205i	$0.617882\pi$
$938$		0			0
$939$	45.3338			1.47941
$940$	−36.1402	+	62.5967i	−1.17876	+	2.04168i
$941$	−5.19386	−	8.99603i	−0.169315	−	0.293262i	0.768864	−	0.639412i	$-0.220822\pi$
$941$	−5.19386	−	8.99603i	−0.169315	−	0.293262i	−0.938179	+	0.346150i	$0.887489\pi$
$942$	110.913	−	64.0359i	3.61376	−	2.08640i
$943$	4.41695	−	7.65038i	0.143836	−	0.249131i
$944$			63.0330i			2.05155i
$945$		0			0
$946$	−3.53459	−	104.247i	−0.114919	−	3.38936i
$947$	−19.2238	+	33.2967i	−0.624691	+	1.08200i	0.363909	+	0.931434i	$0.381442\pi$
$947$	−19.2238	+	33.2967i	−0.624691	+	1.08200i	−0.988601	+	0.150562i	$0.951892\pi$
$948$	43.8940	+	76.0266i	1.42561	+	2.46923i
$949$	−19.9915	−	34.6262i	−0.648951	−	1.12402i
$950$	12.8468	+	7.41711i	0.416806	+	0.240643i
$951$		−	47.2262i		−	1.53141i
$952$		0			0
$953$			1.18153i			0.0382735i	0.999817	+	0.0191367i	$0.00609178\pi$
$953$			1.18153i			0.0382735i	−0.999817	+	0.0191367i	$0.993908\pi$
$954$	9.75485	+	5.63197i	0.315825	+	0.182342i
$955$	−10.9269	+	6.30864i	−0.353586	+	0.204143i
$956$	27.1983	−	15.7029i	0.879654	−	0.507869i
$957$	−27.0206	−	14.4022i	−0.873451	−	0.465558i
$958$		−	79.3906i		−	2.56499i
$959$		0			0
$960$	37.4066			1.20729
$961$	−14.2459	+	24.6746i	−0.459544	+	0.795954i
$962$	−9.14180	+	5.27802i	−0.294744	+	0.170170i
$963$	−51.5263	+	29.7487i	−1.66041	+	0.958640i
$964$	57.0127	−	98.7489i	1.83626	−	3.18049i
$965$	−13.4716			−0.433666
$966$		0			0
$967$		−	38.1782i		−	1.22773i	−0.789411	−	0.613865i	$-0.789614\pi$
$967$		−	38.1782i		−	1.22773i	0.789411	−	0.613865i	$-0.210386\pi$
$968$	72.0523	+	35.3233i	2.31585	+	1.13533i
$969$	−28.9469	+	16.7125i	−0.929909	+	0.536883i
$970$	13.0455	−	7.53182i	0.418865	−	0.241832i
$971$	25.5626	+	14.7586i	0.820342	+	0.473625i	0.850535	−	0.525919i	$-0.176279\pi$
$971$	25.5626	+	14.7586i	0.820342	+	0.473625i	−0.0301922	+	0.999544i	$0.509612\pi$
$972$		−	69.9794i		−	2.24459i
$973$		0			0
$974$			3.35411i			0.107473i
$975$	16.5654	+	9.56407i	0.530519	+	0.306295i
$976$	−22.0501	−	38.1919i	−0.705806	−	1.22249i
$977$	1.22250	+	2.11743i	0.0391112	+	0.0677425i	0.884918	−	0.465746i	$-0.154214\pi$
$977$	1.22250	+	2.11743i	0.0391112	+	0.0677425i	−0.845807	+	0.533489i	$0.820881\pi$
$978$	−58.1595	+	100.735i	−1.85974	+	3.22116i
$979$	−25.1312	+	0.852097i	−0.803197	+	0.0272331i
$980$		0			0
$981$		−	67.9190i		−	2.16849i
$982$	5.29418	−	9.16980i	0.168944	−	0.292620i
$983$	−5.73767	+	3.31265i	−0.183003	+	0.105657i	−0.588703	−	0.808349i	$-0.700361\pi$
$983$	−5.73767	+	3.31265i	−0.183003	+	0.105657i	0.405700	+	0.914006i	$0.367028\pi$
$984$	−18.2242	−	31.5652i	−0.580965	−	1.00626i
$985$	−4.27619	+	7.40657i	−0.136251	+	0.235993i
$986$	−28.1828			−0.897522
$987$		0			0
$988$	−73.6109			−2.34188
$989$	52.0991	+	30.0794i	1.65665	+	0.956470i
$990$	−67.2099	+	41.9027i	−2.13607	+	1.33176i
$991$	−4.48884	−	7.77489i	−0.142593	−	0.246978i	0.785880	−	0.618380i	$-0.212211\pi$
$991$	−4.48884	−	7.77489i	−0.142593	−	0.246978i	−0.928472	+	0.371402i	$0.878877\pi$
$992$	−7.90431	+	13.6907i	−0.250962	+	0.434679i
$993$		−	63.8739i		−	2.02698i
$994$		0			0
$995$	−16.2942			−0.516562
$996$	100.240	+	57.8738i	3.17624	+	1.83380i
$997$	−18.5412	−	32.1143i	−0.587206	−	1.01707i	−0.994596	−	0.103816i	$-0.966895\pi$
$997$	−18.5412	−	32.1143i	−0.587206	−	1.01707i	0.407391	−	0.913254i	$-0.366439\pi$
$998$	42.9829	−	24.8162i	1.36060	−	0.785542i
$999$	−4.52607	−	2.61313i	−0.143198	−	0.0826756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.i.e.362.15		32
7.2	even	3		539.2.b.c.538.1	✓	16
7.3	odd	6	inner	539.2.i.e.472.1		32
7.4	even	3	inner	539.2.i.e.472.2		32
7.5	odd	6		539.2.b.c.538.2	yes	16
7.6	odd	2	inner	539.2.i.e.362.16		32
11.10	odd	2	inner	539.2.i.e.362.1		32
77.10	even	6	inner	539.2.i.e.472.15		32
77.32	odd	6	inner	539.2.i.e.472.16		32
77.54	even	6		539.2.b.c.538.16	yes	16
77.65	odd	6		539.2.b.c.538.15	yes	16
77.76	even	2	inner	539.2.i.e.362.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
539.2.b.c.538.1	✓	16	7.2	even	3
539.2.b.c.538.2	yes	16	7.5	odd	6
539.2.b.c.538.15	yes	16	77.65	odd	6
539.2.b.c.538.16	yes	16	77.54	even	6
539.2.i.e.362.1		32	11.10	odd	2	inner
539.2.i.e.362.2		32	77.76	even	2	inner
539.2.i.e.362.15		32	1.1	even	1	trivial
539.2.i.e.362.16		32	7.6	odd	2	inner
539.2.i.e.472.1		32	7.3	odd	6	inner
539.2.i.e.472.2		32	7.4	even	3	inner
539.2.i.e.472.15		32	77.10	even	6	inner
539.2.i.e.472.16		32	77.32	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.25797 + 1.30364i) q^{2} +(-2.44288 + 1.41040i) q^{3} +(2.39897 + 4.15513i) q^{4} +(1.60021 + 0.923880i) q^{5} -7.35461 q^{6} +7.29501i q^{8} +(2.47844 - 4.29278i) q^{9} +O(q^{10})\)	\(q+(2.25797 + 1.30364i) q^{2} +(-2.44288 + 1.41040i) q^{3} +(2.39897 + 4.15513i) q^{4} +(1.60021 + 0.923880i) q^{5} -7.35461 q^{6} +7.29501i q^{8} +(2.47844 - 4.29278i) q^{9} +(2.40882 + 4.17219i) q^{10} +(-2.81444 + 1.75469i) q^{11} +(-11.7208 - 6.76699i) q^{12} +4.27619 q^{13} -5.21215 q^{15} +(-4.71215 + 8.16168i) q^{16} +(-1.65135 - 2.86022i) q^{17} +(11.1925 - 6.46199i) q^{18} +(-1.79391 + 3.10715i) q^{19} +8.86542i q^{20} +(-8.64242 + 0.293029i) q^{22} +(2.49368 - 4.31919i) q^{23} +(-10.2889 - 17.8208i) q^{24} +(-0.792893 - 1.37333i) q^{25} +(9.65552 + 5.57462i) q^{26} +5.51994i q^{27} -3.27285i q^{29} +(-11.7689 - 6.79477i) q^{30} +(1.37156 - 0.791873i) q^{31} +(-8.64449 + 4.99090i) q^{32} +(4.40052 - 8.25597i) q^{33} -8.61108i q^{34} +23.7827 q^{36} +(-0.473398 + 0.819949i) q^{37} +(-8.10122 + 4.67724i) q^{38} +(-10.4462 + 6.03112i) q^{39} +(-6.73971 + 11.6735i) q^{40} +1.77125 q^{41} +12.0622i q^{43} +(-14.0427 - 7.48491i) q^{44} +(7.93202 - 4.57955i) q^{45} +(11.2614 - 6.50174i) q^{46} +(7.06076 + 4.07653i) q^{47} -26.5840i q^{48} -4.13460i q^{50} +(8.06809 + 4.65812i) q^{51} +(10.2584 + 17.7681i) q^{52} +(0.435776 + 0.754787i) q^{53} +(-7.19602 + 12.4639i) q^{54} +(-6.12480 + 0.207667i) q^{55} -10.1205i q^{57} +(4.26663 - 7.39001i) q^{58} +(5.79228 - 3.34417i) q^{59} +(-12.5038 - 21.6572i) q^{60} +(-2.33971 + 4.05249i) q^{61} +4.12927 q^{62} -7.17680 q^{64} +(6.84278 + 3.95068i) q^{65} +(20.6991 - 12.9051i) q^{66} +(4.33474 + 7.50799i) q^{67} +(7.92306 - 13.7232i) q^{68} +14.0683i q^{69} +7.09378 q^{71} +(31.3159 + 18.0802i) q^{72} +(-4.67507 - 8.09746i) q^{73} +(-2.13784 + 1.23428i) q^{74} +(3.87388 + 2.23659i) q^{75} -17.2142 q^{76} -31.4497 q^{78} +(-5.61747 - 3.24325i) q^{79} +(-15.0808 + 8.70691i) q^{80} +(-0.349990 - 0.606200i) q^{81} +(3.99945 + 2.30908i) q^{82} -8.55237 q^{83} -6.10259i q^{85} +(-15.7248 + 27.2362i) q^{86} +(4.61602 + 7.99518i) q^{87} +(-12.8005 - 20.5313i) q^{88} +(6.56594 + 3.79085i) q^{89} +23.8804 q^{90} +23.9291 q^{92} +(-2.23371 + 3.86890i) q^{93} +(10.6287 + 18.4094i) q^{94} +(-5.74126 + 3.31472i) q^{95} +(14.0783 - 24.3843i) q^{96} -3.12677i q^{97} +(0.557097 + 16.4307i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} + 16 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 + 16 * q^9	\( 32 q + 32 q^{4} + 16 q^{9} - 32 q^{15} - 16 q^{16} - 64 q^{22} + 16 q^{23} - 48 q^{25} + 192 q^{36} - 64 q^{37} - 48 q^{44} + 32 q^{53} + 80 q^{58} - 112 q^{60} - 64 q^{64} + 112 q^{67} - 96 q^{71} - 32 q^{78} + 16 q^{81} - 16 q^{86} - 96 q^{88} + 32 q^{92} - 32 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 + 16 * q^9 - 32 * q^15 - 16 * q^16 - 64 * q^22 + 16 * q^23 - 48 * q^25 + 192 * q^36 - 64 * q^37 - 48 * q^44 + 32 * q^53 + 80 * q^58 - 112 * q^60 - 64 * q^64 + 112 * q^67 - 96 * q^71 - 32 * q^78 + 16 * q^81 - 16 * q^86 - 96 * q^88 + 32 * q^92 - 32 * q^99

Introduction

L-functions

Modular forms

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