LMFDB - Embedded newform 475.2.j.d.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(49,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("475.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.j (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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Character	$\chi$	$=$	475.49
Dual form			475.2.j.d.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87935 - 1.08504i) q^{2} +(2.55640 + 1.47594i) q^{3} +(1.35464 + 2.34630i) q^{4} +(-3.20292 - 5.54761i) q^{6} +0.591620i q^{7} -1.53919i q^{8} +(2.85679 + 4.94811i) q^{9} +O(q^{10})$	\(q+(-1.87935 - 1.08504i) q^{2} +(2.55640 + 1.47594i) q^{3} +(1.35464 + 2.34630i) q^{4} +(-3.20292 - 5.54761i) q^{6} +0.591620i q^{7} -1.53919i q^{8} +(2.85679 + 4.94811i) q^{9} +2.58045 q^{11} +7.99745i q^{12} +(-5.94669 + 3.43332i) q^{13} +(0.641933 - 1.11186i) q^{14} +(1.03919 - 1.79993i) q^{16} +(4.53429 + 2.61787i) q^{17} -12.3990i q^{18} +(2.26423 - 3.72468i) q^{19} +(-0.873195 + 1.51242i) q^{21} +(-4.84957 - 2.79990i) q^{22} +(-2.51271 + 1.45072i) q^{23} +(2.27175 - 3.93478i) q^{24} +14.9012 q^{26} +8.01017i q^{27} +(-1.38812 + 0.801431i) q^{28} +(3.52494 + 6.10538i) q^{29} -6.81421 q^{31} +(-6.57195 + 3.79432i) q^{32} +(6.59667 + 3.80859i) q^{33} +(-5.68101 - 9.83980i) q^{34} +(-7.73984 + 13.4058i) q^{36} -4.82538i q^{37} +(-8.29672 + 4.54320i) q^{38} -20.2695 q^{39} +(-3.11419 + 5.39393i) q^{41} +(3.28208 - 1.89491i) q^{42} +(3.77609 + 2.18013i) q^{43} +(3.49558 + 6.05452i) q^{44} +6.29636 q^{46} +(2.21600 - 1.27941i) q^{47} +(5.31317 - 3.06756i) q^{48} +6.64999 q^{49} +(7.72764 + 13.3847i) q^{51} +(-16.1112 - 9.30181i) q^{52} +(8.30645 - 4.79573i) q^{53} +(8.69138 - 15.0539i) q^{54} +0.910615 q^{56} +(11.2857 - 6.17993i) q^{57} -15.2989i q^{58} +(-1.46221 + 2.53263i) q^{59} +(-1.16586 - 2.01932i) q^{61} +(12.8063 + 7.39371i) q^{62} +(-2.92740 + 1.69013i) q^{63} +12.3112 q^{64} +(-8.26497 - 14.3153i) q^{66} +(3.72603 - 2.15122i) q^{67} +14.1851i q^{68} -8.56468 q^{69} +(6.74645 - 11.6852i) q^{71} +(7.61607 - 4.39714i) q^{72} +(-7.29777 - 4.21337i) q^{73} +(-5.23574 + 9.06858i) q^{74} +(11.8064 + 0.266962i) q^{76} +1.52665i q^{77} +(38.0935 + 21.9933i) q^{78} +(2.93630 - 5.08583i) q^{79} +(-3.25215 + 5.63288i) q^{81} +(11.7053 - 6.75806i) q^{82} +4.02036i q^{83} -4.73145 q^{84} +(-4.73107 - 8.19445i) q^{86} +20.8104i q^{87} -3.97180i q^{88} +(1.85823 + 3.21855i) q^{89} +(-2.03122 - 3.51818i) q^{91} +(-6.80764 - 3.93039i) q^{92} +(-17.4199 - 10.0574i) q^{93} -5.55285 q^{94} -22.4007 q^{96} +(-2.18732 - 1.26285i) q^{97} +(-12.4977 - 7.21552i) q^{98} +(7.37182 + 12.7684i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4} + 2 q^{6} + 14 q^{9}+O(q^{10}) $ 24 * q + 4 * q^4 + 2 * q^6 + 14 * q^9	$ 24 q + 4 q^{4} + 2 q^{6} + 14 q^{9} - 4 q^{11} - 12 q^{14} + 12 q^{16} + 12 q^{19} - 6 q^{21} + 22 q^{24} + 76 q^{26} + 6 q^{29} - 12 q^{31} - 2 q^{34} - 26 q^{36} - 32 q^{39} - 22 q^{41} + 42 q^{44} - 48 q^{46} - 16 q^{49} + 34 q^{51} + 36 q^{54} + 16 q^{56} + 8 q^{59} - 50 q^{61} + 88 q^{64} - 68 q^{66} - 52 q^{69} - 36 q^{71} - 12 q^{74} + 48 q^{76} + 6 q^{79} - 4 q^{81} - 148 q^{84} - 18 q^{86} + 24 q^{89} + 22 q^{91} - 32 q^{94} - 52 q^{96} - 40 q^{99}+O(q^{100}) $ 24 * q + 4 * q^4 + 2 * q^6 + 14 * q^9 - 4 * q^11 - 12 * q^14 + 12 * q^16 + 12 * q^19 - 6 * q^21 + 22 * q^24 + 76 * q^26 + 6 * q^29 - 12 * q^31 - 2 * q^34 - 26 * q^36 - 32 * q^39 - 22 * q^41 + 42 * q^44 - 48 * q^46 - 16 * q^49 + 34 * q^51 + 36 * q^54 + 16 * q^56 + 8 * q^59 - 50 * q^61 + 88 * q^64 - 68 * q^66 - 52 * q^69 - 36 * q^71 - 12 * q^74 + 48 * q^76 + 6 * q^79 - 4 * q^81 - 148 * q^84 - 18 * q^86 + 24 * q^89 + 22 * q^91 - 32 * q^94 - 52 * q^96 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.87935	−	1.08504i	−1.32890	−	0.767241i	−0.343771	−	0.939053i	$-0.611705\pi$
$2$	−1.87935	−	1.08504i	−1.32890	−	0.767241i	−0.985130	+	0.171812i	$0.945038\pi$
$3$	2.55640	+	1.47594i	1.47594	+	0.852134i	0.999632	−	0.0271449i	$-0.00864156\pi$
$3$	2.55640	+	1.47594i	1.47594	+	0.852134i	0.476308	+	0.879279i	$0.341975\pi$
$4$	1.35464	+	2.34630i	0.677319	+	1.17315i
$5$		0			0
$5$		0			0
$6$	−3.20292	−	5.54761i	−1.30758	−	2.26480i
$7$			0.591620i			0.223611i	0.993730	+	0.111806i	$0.0356634\pi$
$7$			0.591620i			0.223611i	−0.993730	+	0.111806i	$0.964337\pi$
$8$		−	1.53919i		−	0.544185i
$9$	2.85679	+	4.94811i	0.952264	+	1.64937i
$10$		0			0
$11$	2.58045			0.778036			0.389018	−	0.921230i	$-0.372814\pi$
$11$	2.58045			0.778036			0.389018	+	0.921230i	$0.372814\pi$
$12$			7.99745i			2.30867i
$13$	−5.94669	+	3.43332i	−1.64931	+	0.952232i	−0.671969	+	0.740579i	$0.734551\pi$
$13$	−5.94669	+	3.43332i	−1.64931	+	0.952232i	−0.977345	+	0.211653i	$0.932115\pi$
$14$	0.641933	−	1.11186i	0.171564	−	0.297157i
$15$		0			0
$16$	1.03919	−	1.79993i	0.259797	−	0.449982i
$17$	4.53429	+	2.61787i	1.09973	+	0.634927i	0.936149	−	0.351603i	$-0.114363\pi$
$17$	4.53429	+	2.61787i	1.09973	+	0.634927i	0.163577	+	0.986531i	$0.447697\pi$
$18$		−	12.3990i		−	2.92247i
$19$	2.26423	−	3.72468i	0.519449	−	0.854501i
$19$	2.26423	−	3.72468i	0.519449	−	0.854501i
$20$		0			0
$21$	−0.873195	+	1.51242i	−0.190547	+	0.330037i
$22$	−4.84957	−	2.79990i	−1.03393	−	0.596941i
$23$	−2.51271	+	1.45072i	−0.523937	+	0.302495i	−0.738544	−	0.674205i	$-0.764486\pi$
$23$	−2.51271	+	1.45072i	−0.523937	+	0.302495i	0.214607	+	0.976701i	$0.431153\pi$
$24$	2.27175	−	3.93478i	0.463719	−	0.803185i
$25$		0			0
$26$	14.9012			2.92237
$27$			8.01017i			1.54156i
$28$	−1.38812	+	0.801431i	−0.262330	+	0.151456i
$29$	3.52494	+	6.10538i	0.654565	+	1.13374i	0.982003	+	0.188867i	$0.0604816\pi$
$29$	3.52494	+	6.10538i	0.654565	+	1.13374i	−0.327438	+	0.944873i	$0.606185\pi$
$30$		0			0
$31$	−6.81421			−1.22387			−0.611934	−	0.790909i	$-0.709608\pi$
$31$	−6.81421			−1.22387			−0.611934	+	0.790909i	$0.709608\pi$
$32$	−6.57195	+	3.79432i	−1.16177	+	0.670747i
$33$	6.59667	+	3.80859i	1.14833	+	0.662990i
$34$	−5.68101	−	9.83980i	−0.974285	−	1.68751i
$35$		0			0
$36$	−7.73984	+	13.4058i	−1.28997	+	2.23430i
$37$		−	4.82538i		−	0.793287i	−0.917973	−	0.396644i	$-0.870175\pi$
$37$		−	4.82538i		−	0.793287i	0.917973	−	0.396644i	$-0.129825\pi$
$38$	−8.29672	+	4.54320i	−1.34591	+	0.737005i
$39$	−20.2695			−3.24572
$40$		0			0
$41$	−3.11419	+	5.39393i	−0.486355	+	0.842391i	−0.999877	−	0.0156852i	$-0.995007\pi$
$41$	−3.11419	+	5.39393i	−0.486355	+	0.842391i	0.513522	+	0.858076i	$0.328340\pi$
$42$	3.28208	−	1.89491i	0.506436	−	0.292391i
$43$	3.77609	+	2.18013i	0.575849	+	0.332467i	0.759482	−	0.650528i	$-0.225452\pi$
$43$	3.77609	+	2.18013i	0.575849	+	0.332467i	−0.183633	+	0.982995i	$0.558786\pi$
$44$	3.49558	+	6.05452i	0.526978	+	0.912753i
$45$		0			0
$46$	6.29636			0.928348
$47$	2.21600	−	1.27941i	0.323237	−	0.186621i	−0.329598	−	0.944121i	$-0.606913\pi$
$47$	2.21600	−	1.27941i	0.323237	−	0.186621i	0.652834	+	0.757501i	$0.273580\pi$
$48$	5.31317	−	3.06756i	0.766890	−	0.442764i
$49$	6.64999			0.949998
$50$		0			0
$51$	7.72764	+	13.3847i	1.08209	+	1.87423i
$52$	−16.1112	−	9.30181i	−2.23422	−	1.28993i
$53$	8.30645	−	4.79573i	1.14098	−	0.658745i	0.194306	−	0.980941i	$-0.437754\pi$
$53$	8.30645	−	4.79573i	1.14098	−	0.658745i	0.946673	+	0.322196i	$0.104421\pi$
$54$	8.69138	−	15.0539i	1.18275	−	2.04858i
$55$		0			0
$56$	0.910615			0.121686
$57$	11.2857	−	6.17993i	1.49483	−	0.818551i
$58$		−	15.2989i		−	2.00884i
$59$	−1.46221	+	2.53263i	−0.190364	+	0.329720i	−0.945371	−	0.325997i	$-0.894300\pi$
$59$	−1.46221	+	2.53263i	−0.190364	+	0.329720i	0.755007	+	0.655717i	$0.227633\pi$
$60$		0			0
$61$	−1.16586	−	2.01932i	−0.149273	−	0.258548i	0.781686	−	0.623672i	$-0.214360\pi$
$61$	−1.16586	−	2.01932i	−0.149273	−	0.258548i	−0.930959	+	0.365124i	$0.881027\pi$
$62$	12.8063	+	7.39371i	1.62640	+	0.939003i
$63$	−2.92740	+	1.69013i	−0.368818	+	0.212937i
$64$	12.3112			1.53891
$65$		0			0
$66$	−8.26497	−	14.3153i	−1.01735	−	1.76210i
$67$	3.72603	−	2.15122i	0.455207	−	0.262814i	−0.254820	−	0.966989i	$-0.582016\pi$
$67$	3.72603	−	2.15122i	0.455207	−	0.262814i	0.710027	+	0.704175i	$0.248683\pi$
$68$			14.1851i			1.72019i
$69$	−8.56468			−1.03107
$70$		0			0
$71$	6.74645	−	11.6852i	0.800656	−	1.38678i	−0.118528	−	0.992951i	$-0.537818\pi$
$71$	6.74645	−	11.6852i	0.800656	−	1.38678i	0.919185	−	0.393827i	$-0.128849\pi$
$72$	7.61607	−	4.39714i	0.897563	−	0.518208i
$73$	−7.29777	−	4.21337i	−0.854139	−	0.493137i	0.00790620	−	0.999969i	$-0.497483\pi$
$73$	−7.29777	−	4.21337i	−0.854139	−	0.493137i	−0.862045	+	0.506831i	$0.830817\pi$
$74$	−5.23574	+	9.06858i	−0.608643	+	1.05420i
$75$		0			0
$76$	11.8064	+	0.266962i	1.35429	+	0.0306226i
$77$			1.52665i			0.173978i
$78$	38.0935	+	21.9933i	4.31324	+	2.49025i
$79$	2.93630	−	5.08583i	0.330360	−	0.572200i	−0.652222	−	0.758028i	$-0.726163\pi$
$79$	2.93630	−	5.08583i	0.330360	−	0.572200i	0.982582	+	0.185827i	$0.0594965\pi$
$80$		0			0
$81$	−3.25215	+	5.63288i	−0.361350	+	0.625876i
$82$	11.7053	−	6.75806i	1.29263	−	0.746303i
$83$			4.02036i			0.441292i	0.975354	+	0.220646i	$0.0708165\pi$
$83$			4.02036i			0.441292i	−0.975354	+	0.220646i	$0.929184\pi$
$84$	−4.73145			−0.516244
$85$		0			0
$86$	−4.73107	−	8.19445i	−0.510164	−	0.883630i
$87$			20.8104i			2.23111i
$88$		−	3.97180i		−	0.423396i
$89$	1.85823	+	3.21855i	0.196972	+	0.341166i	0.947545	−	0.319622i	$-0.103556\pi$
$89$	1.85823	+	3.21855i	0.196972	+	0.341166i	−0.750573	+	0.660787i	$0.770222\pi$
$90$		0			0
$91$	−2.03122	−	3.51818i	−0.212930	−	0.368805i
$92$	−6.80764	−	3.93039i	−0.709745	−	0.409772i
$93$	−17.4199	−	10.0574i	−1.80636	−	1.04290i
$94$	−5.55285			−0.572733
$95$		0			0
$96$	−22.4007			−2.28627
$97$	−2.18732	−	1.26285i	−0.222089	−	0.128223i	0.384828	−	0.922988i	$-0.374261\pi$
$97$	−2.18732	−	1.26285i	−0.222089	−	0.128223i	−0.606917	+	0.794765i	$0.707594\pi$
$98$	−12.4977	−	7.21552i	−1.26245	−	0.728878i
$99$	7.37182	+	12.7684i	0.740895	+	1.28327i
$100$		0			0
$101$	−0.692736	−	1.19985i	−0.0689298	−	0.119390i	0.829501	−	0.558506i	$-0.188625\pi$
$101$	−0.692736	−	1.19985i	−0.0689298	−	0.119390i	−0.898430	+	0.439116i	$0.855292\pi$
$102$		−	33.5393i		−	3.32088i
$103$		−	0.166774i		−	0.0164328i	−0.999966	−	0.00821638i	$-0.997385\pi$
$103$		−	0.166774i		−	0.0164328i	0.999966	−	0.00821638i	$-0.00261539\pi$
$104$	5.28453	+	9.15307i	0.518191	+	0.897533i
$105$		0			0
$106$	−20.8143			−2.02166
$107$		−	4.51729i		−	0.436703i	−0.975870	−	0.218351i	$-0.929932\pi$
$107$		−	4.51729i		−	0.436703i	0.975870	−	0.218351i	$-0.0700679\pi$
$108$	−18.7943	+	10.8509i	−1.80848	+	1.04413i
$109$	−5.35464	+	9.27450i	−0.512881	+	0.888336i	0.487007	+	0.873398i	$0.338089\pi$
$109$	−5.35464	+	9.27450i	−0.512881	+	0.888336i	−0.999888	+	0.0149384i	$0.995245\pi$
$110$		0			0
$111$	7.12196	−	12.3356i	0.675987	−	1.17084i
$112$	1.06487	+	0.614805i	0.100621	+	0.0580936i
$113$		−	13.2065i		−	1.24237i	−0.783665	−	0.621183i	$-0.786652\pi$
$113$		−	13.2065i		−	1.24237i	0.783665	−	0.621183i	$-0.213348\pi$
$114$	−27.9152	−	0.631206i	−2.61450	−	0.0591178i
$115$		0			0
$116$	−9.55004	+	16.5411i	−0.886699	+	1.53581i
$117$	−33.9769	−	19.6166i	−3.14117	−	1.81355i
$118$	5.49602	−	3.17313i	0.505950	−	0.292110i
$119$	−1.54879	+	2.68257i	−0.141977	+	0.245911i
$120$		0			0
$121$	−4.34127			−0.394661
$122$			5.06002i			0.458113i
$123$	−15.9222	+	9.19271i	−1.43566	+	0.828879i
$124$	−9.23079	−	15.9882i	−0.828949	−	1.43578i
$125$		0			0
$126$	7.33548			0.653496
$127$	1.49096	−	0.860805i	0.132301	−	0.0763841i	−0.432389	−	0.901687i	$-0.642329\pi$
$127$	1.49096	−	0.860805i	0.132301	−	0.0763841i	0.564690	+	0.825303i	$0.308996\pi$
$128$	−9.99323	−	5.76959i	−0.883285	−	0.509965i
$129$	6.43548	+	11.1466i	0.566612	+	0.981401i
$130$		0			0
$131$	−1.64201	+	2.84405i	−0.143463	+	0.248486i	−0.928799	−	0.370585i	$-0.879157\pi$
$131$	−1.64201	+	2.84405i	−0.143463	+	0.248486i	0.785335	+	0.619071i	$0.212491\pi$
$132$			20.6370i			1.79622i
$133$	2.20360	+	1.33956i	0.191076	+	0.116155i
$134$	−9.33668			−0.806567
$135$		0			0
$136$	4.02940	−	6.97913i	0.345518	−	0.598455i
$137$	7.05882	−	4.07541i	0.603075	−	0.348186i	−0.167175	−	0.985927i	$-0.553464\pi$
$137$	7.05882	−	4.07541i	0.603075	−	0.348186i	0.770251	+	0.637741i	$0.220131\pi$
$138$	16.0960	+	9.29304i	1.37018	+	0.791076i
$139$	−7.81401	−	13.5343i	−0.662776	−	1.14796i	−0.979883	−	0.199571i	$-0.936045\pi$
$139$	−7.81401	−	13.5343i	−0.662776	−	1.14796i	0.317108	−	0.948390i	$-0.397288\pi$
$140$		0			0
$141$	7.55331			0.636103
$142$	−25.3579	+	14.6404i	−2.12799	+	1.22859i
$143$	−15.3451	+	8.85952i	−1.28323	+	0.740870i
$144$	11.8750			0.989582
$145$		0			0
$146$	9.14337	+	15.8368i	0.756711	+	1.31066i
$147$	17.0000	+	9.81497i	1.40214	+	0.809525i
$148$	11.3218	−	6.53664i	0.930646	−	0.537308i
$149$	1.61005	−	2.78869i	0.131900	−	0.228458i	−0.792509	−	0.609861i	$-0.791225\pi$
$149$	1.61005	−	2.78869i	0.131900	−	0.228458i	0.924409	+	0.381402i	$0.124559\pi$
$150$		0			0
$151$	−11.1226			−0.905142			−0.452571	−	0.891728i	$-0.649493\pi$
$151$	−11.1226			−0.905142			−0.452571	+	0.891728i	$0.649493\pi$
$152$	−5.73299	−	3.48507i	−0.465007	−	0.282677i
$153$			29.9149i			2.41847i
$154$	1.65648	−	2.86910i	0.133483	−	0.231199i
$155$		0			0
$156$	−27.4578	−	47.5583i	−2.19838	−	3.80771i
$157$	−18.5602	−	10.7157i	−1.48127	−	0.855209i	−0.481491	−	0.876451i	$-0.659905\pi$
$157$	−18.5602	−	10.7157i	−1.48127	−	0.855209i	−0.999774	+	0.0212418i	$0.993238\pi$
$158$	−11.0367	+	6.37203i	−0.878032	+	0.506932i
$159$	28.3128			2.24535
$160$		0			0
$161$	−0.858273	−	1.48657i	−0.0676414	−	0.117158i
$162$	12.2238	−	7.05744i	0.960396	−	0.554485i
$163$		−	10.3129i		−	0.807768i	−0.914810	−	0.403884i	$-0.867660\pi$
$163$		−	10.3129i		−	0.807768i	0.914810	−	0.403884i	$-0.132340\pi$
$164$	−16.8744			−1.31767
$165$		0			0
$166$	4.36226	−	7.55566i	0.338577	−	0.586433i
$167$	5.63509	−	3.25342i	0.436056	−	0.251757i	−0.265867	−	0.964010i	$-0.585658\pi$
$167$	5.63509	−	3.25342i	0.436056	−	0.251757i	0.701923	+	0.712252i	$0.252325\pi$
$168$	2.32790	+	1.34401i	0.179601	+	0.103693i
$169$	17.0754	−	29.5754i	1.31349	−	2.27503i
$170$		0			0
$171$	24.8986	+	0.562995i	1.90404	+	0.0430533i
$172$			11.8131i			0.900744i
$173$	5.42179	+	3.13027i	0.412211	+	0.237990i	0.691739	−	0.722147i	$-0.256845\pi$
$173$	5.42179	+	3.13027i	0.412211	+	0.237990i	−0.279528	+	0.960137i	$0.590178\pi$
$174$	22.5802	−	39.1100i	1.71180	−	2.96492i
$175$		0			0
$176$	2.68158	−	4.64463i	0.202131	−	0.350102i
$177$	−7.47601	+	4.31628i	−0.561931	+	0.324431i
$178$		−	8.06505i		−	0.604501i
$179$	−23.1893			−1.73325			−0.866624	−	0.498961i	$-0.833715\pi$
$179$	−23.1893			−1.73325			−0.866624	+	0.498961i	$0.833715\pi$
$180$		0			0
$181$	1.59948	+	2.77039i	0.118889	+	0.205921i	0.919328	−	0.393493i	$-0.128733\pi$
$181$	1.59948	+	2.77039i	0.118889	+	0.205921i	−0.800439	+	0.599414i	$0.795400\pi$
$182$			8.81585i			0.653474i
$183$		−	6.88294i		−	0.508801i
$184$	2.23293	+	3.86754i	0.164614	+	0.285119i
$185$		0			0
$186$	21.8253	+	37.8026i	1.60031	+	2.77182i
$187$	11.7005	+	6.75529i	0.855626	+	0.493996i
$188$	6.00375	+	3.46627i	0.437868	+	0.252803i
$189$	−4.73898			−0.344710
$190$		0			0
$191$	18.9443			1.37076			0.685382	−	0.728184i	$-0.259635\pi$
$191$	18.9443			1.37076			0.685382	+	0.728184i	$0.259635\pi$
$192$	31.4725	+	18.1706i	2.27133	+	1.31135i
$193$	−0.892472	−	0.515269i	−0.0642415	−	0.0370899i	0.467535	−	0.883974i	$-0.345142\pi$
$193$	−0.892472	−	0.515269i	−0.0642415	−	0.0370899i	−0.531777	+	0.846885i	$0.678475\pi$
$194$	2.74049	+	4.74667i	0.196756	+	0.340791i
$195$		0			0
$196$	9.00832	+	15.6029i	0.643452	+	1.11449i
$197$		−	18.5515i		−	1.32174i	−0.750502	−	0.660868i	$-0.770188\pi$
$197$		−	18.5515i		−	1.32174i	0.750502	−	0.660868i	$-0.229812\pi$
$198$		−	31.9950i		−	2.27378i
$199$	11.3166	+	19.6010i	0.802215	+	1.38948i	0.918155	+	0.396221i	$0.129679\pi$
$199$	11.3166	+	19.6010i	0.802215	+	1.38948i	−0.115940	+	0.993256i	$0.536988\pi$
$200$		0			0
$201$	12.7003			0.895810
$202$			3.00659i			0.211543i
$203$	−3.61206	+	2.08542i	−0.253517	+	0.146368i
$204$	−20.9363	+	36.2627i	−1.46583	+	2.53890i
$205$		0			0
$206$	−0.180957	+	0.313427i	−0.0126079	+	0.0218375i
$207$	−14.3566	−	8.28879i	−0.997853	−	0.576111i
$208$			14.2715i			0.989549i
$209$	5.84273	−	9.61137i	0.404150	−	0.664832i
$210$		0			0
$211$	−6.21978	+	10.7730i	−0.428187	+	0.741642i	−0.996712	−	0.0810240i	$-0.974181\pi$
$211$	−6.21978	+	10.7730i	−0.428187	+	0.741642i	0.568525	+	0.822666i	$0.307514\pi$
$212$	22.5045	+	12.9930i	1.54561	+	0.892360i
$213$	34.4933	−	19.9147i	2.36344	−	1.36453i
$214$	−4.90145	+	8.48956i	−0.335056	+	0.580335i
$215$		0			0
$216$	12.3292			0.838893
$217$		−	4.03142i		−	0.273671i
$218$	20.1265	−	11.6200i	1.36314	−	0.787008i
$219$	−12.4373	−	21.5421i	−0.840438	−	1.45568i
$220$		0			0
$221$	−35.9520			−2.41839
$222$	−26.7693	+	15.4553i	−1.79664	+	1.03729i
$223$	−16.6044	−	9.58654i	−1.11191	−	0.641962i	−0.172588	−	0.984994i	$-0.555213\pi$
$223$	−16.6044	−	9.58654i	−1.11191	−	0.641962i	−0.939324	+	0.343032i	$0.888546\pi$
$224$	−2.24479	−	3.88810i	−0.149987	−	0.259784i
$225$		0			0
$226$	−14.3297	+	24.8197i	−0.953195	+	1.65098i
$227$		−	26.5208i		−	1.76025i	−0.474745	−	0.880123i	$-0.657460\pi$
$227$		−	26.5208i		−	1.76025i	0.474745	−	0.880123i	$-0.342540\pi$
$228$	29.7880	+	18.1080i	1.97276	+	1.19923i
$229$	8.81023			0.582196			0.291098	−	0.956693i	$-0.405979\pi$
$229$	8.81023			0.582196			0.291098	+	0.956693i	$0.405979\pi$
$230$		0			0
$231$	−2.25324	+	3.90272i	−0.148252	+	0.256780i
$232$	9.39733	−	5.42555i	0.616965	−	0.356205i
$233$	−3.90778	−	2.25616i	−0.256007	−	0.147806i	0.366505	−	0.930416i	$-0.380554\pi$
$233$	−3.90778	−	2.25616i	−0.256007	−	0.147806i	−0.622512	+	0.782610i	$0.713888\pi$
$234$	42.5697	+	73.7328i	2.78287	+	4.82006i
$235$		0			0
$236$	−7.92308			−0.515749
$237$	15.0127	−	8.66761i	0.975182	−	0.563022i
$238$	5.82142	−	3.36100i	0.377347	−	0.217861i
$239$	7.82431			0.506112			0.253056	−	0.967452i	$-0.418564\pi$
$239$	7.82431			0.506112			0.253056	+	0.967452i	$0.418564\pi$
$240$		0			0
$241$	−13.6697	−	23.6766i	−0.880541	−	1.52514i	−0.850740	−	0.525586i	$-0.823846\pi$
$241$	−13.6697	−	23.6766i	−0.880541	−	1.52514i	−0.0298010	−	0.999556i	$-0.509487\pi$
$242$	8.15876	+	4.71046i	0.524465	+	0.302800i
$243$	4.18345	−	2.41531i	0.268368	−	0.154942i
$244$	3.15863	−	5.47091i	0.202210	−	0.350239i
$245$		0			0
$246$	39.8979			2.54380
$247$	−0.676612	+	29.9233i	−0.0430518	+	1.90398i
$248$			10.4884i			0.666011i
$249$	−5.93380	+	10.2777i	−0.376040	+	0.651320i
$250$		0			0
$251$	8.11886	+	14.0623i	0.512458	+	0.887603i	0.999896	+	0.0144451i	$0.00459818\pi$
$251$	8.11886	+	14.0623i	0.512458	+	0.887603i	−0.487438	+	0.873158i	$0.662068\pi$
$252$	−7.93113	−	4.57904i	−0.499614	−	0.288452i
$253$	−6.48394	+	3.74350i	−0.407642	+	0.235352i
$254$	−3.73604			−0.234420
$255$		0			0
$256$	0.209275	+	0.362476i	0.0130797	+	0.0226547i
$257$	−7.91848	+	4.57174i	−0.493941	+	0.285177i	−0.726208	−	0.687475i	$-0.758719\pi$
$257$	−7.91848	+	4.57174i	−0.493941	+	0.285177i	0.232267	+	0.972652i	$0.425386\pi$
$258$		−	27.9311i		−	1.73891i
$259$	2.85479			0.177388
$260$		0			0
$261$	−20.1400	+	34.8836i	−1.24664	+	2.15924i
$262$	6.17183	−	3.56331i	0.381297	−	0.220142i
$263$	−13.2478	−	7.64861i	−0.816894	−	0.471634i	0.0324505	−	0.999473i	$-0.489669\pi$
$263$	−13.2478	−	7.64861i	−0.816894	−	0.471634i	−0.849344	+	0.527840i	$0.823002\pi$
$264$	5.86214	−	10.1535i	0.360790	−	0.624906i
$265$		0			0
$266$	−2.68785	−	4.90850i	−0.164803	−	0.300960i
$267$			10.9705i			0.671386i
$268$	10.0948	+	5.82826i	0.616640	+	0.356017i
$269$	−7.07334	+	12.2514i	−0.431269	+	0.746981i	−0.996983	−	0.0776213i	$-0.975267\pi$
$269$	−7.07334	+	12.2514i	−0.431269	+	0.746981i	0.565714	+	0.824602i	$0.308601\pi$
$270$		0			0
$271$	5.68158	−	9.84078i	0.345131	−	0.597785i	−0.640246	−	0.768170i	$-0.721168\pi$
$271$	5.68158	−	9.84078i	0.345131	−	0.597785i	0.985378	+	0.170385i	$0.0545010\pi$
$272$	9.42396	−	5.44093i	0.571412	−	0.329905i
$273$		−	11.9918i		−	0.725779i
$274$	−17.6880			−1.06857
$275$		0			0
$276$	−11.6020	−	20.0953i	−0.698360	−	1.20960i
$277$			18.9102i			1.13620i	0.822959	+	0.568101i	$0.192322\pi$
$277$			18.9102i			1.13620i	−0.822959	+	0.568101i	$0.807678\pi$
$278$			33.9142i			2.03404i
$279$	−19.4668	−	33.7175i	−1.16545	−	2.01861i
$280$		0			0
$281$	13.9438	+	24.1513i	0.831816	+	1.44075i	0.896596	+	0.442849i	$0.146032\pi$
$281$	13.9438	+	24.1513i	0.831816	+	1.44075i	−0.0647802	+	0.997900i	$0.520635\pi$
$282$	−14.1953	−	8.19567i	−0.845318	−	0.488045i
$283$	12.4673	+	7.19798i	0.741102	+	0.427876i	0.822470	−	0.568809i	$-0.192595\pi$
$283$	12.4673	+	7.19798i	0.741102	+	0.427876i	−0.0813677	+	0.996684i	$0.525929\pi$
$284$	36.5560			2.16920
$285$		0			0
$286$	38.4519			2.27371
$287$	−3.19116	−	1.84242i	−0.188368	−	0.108754i
$288$	−37.5494	−	21.6792i	−2.21262	−	1.27746i
$289$	5.20651	+	9.01794i	0.306265	+	0.530467i
$290$		0			0
$291$	−3.72778	−	6.45670i	−0.218526	−	0.378498i
$292$		−	22.8303i		−	1.33605i
$293$		−	2.63178i		−	0.153750i	−0.997041	−	0.0768752i	$-0.975506\pi$
$293$		−	2.63178i		−	0.153750i	0.997041	−	0.0768752i	$-0.0244943\pi$
$294$	−21.2993	−	36.8915i	−1.24220	−	2.15156i
$295$		0			0
$296$	−7.42717			−0.431695
$297$			20.6699i			1.19939i
$298$	−6.05169	+	3.49395i	−0.350565	+	0.202399i
$299$	9.96155	−	17.2539i	0.576091	−	0.997819i
$300$		0			0
$301$	−1.28981	+	2.23401i	−0.0743433	+	0.128766i
$302$	20.9032	+	12.0685i	1.20284	+	0.694463i
$303$		−	4.08974i		−	0.234950i
$304$	−4.35120	−	7.94610i	−0.249559	−	0.455740i
$305$		0			0
$306$	32.4589	−	56.2205i	1.85555	−	3.21391i
$307$	14.5710	+	8.41257i	0.831611	+	0.480131i	0.854404	−	0.519609i	$-0.173923\pi$
$307$	14.5710	+	8.41257i	0.831611	+	0.480131i	−0.0227929	+	0.999740i	$0.507256\pi$
$308$	−3.58197	+	2.06805i	−0.204102	+	0.117838i
$309$	0.246149	−	0.426342i	0.0140029	−	0.0242538i
$310$		0			0
$311$	−18.3273			−1.03924			−0.519622	−	0.854396i	$-0.673927\pi$
$311$	−18.3273			−1.03924			−0.519622	+	0.854396i	$0.673927\pi$
$312$			31.1986i			1.76627i
$313$	20.3562	−	11.7527i	1.15060	−	0.664299i	0.201567	−	0.979475i	$-0.435397\pi$
$313$	20.3562	−	11.7527i	1.15060	−	0.664299i	0.949033	+	0.315176i	$0.102063\pi$
$314$	23.2541	+	40.2772i	1.31230	+	2.27298i
$315$		0			0
$316$	15.9105			0.895036
$317$	−3.36324	+	1.94177i	−0.188899	+	0.109061i	−0.591467	−	0.806329i	$-0.701451\pi$
$317$	−3.36324	+	1.94177i	−0.188899	+	0.109061i	0.402568	+	0.915390i	$0.368118\pi$
$318$	−53.2097	−	30.7207i	−2.98385	−	1.72273i
$319$	9.09594	+	15.7546i	0.509275	+	0.882090i
$320$		0			0
$321$	6.66724	−	11.5480i	0.372129	−	0.644546i
$322$			3.72505i			0.207589i
$323$	20.0174	−	10.9613i	1.11380	−	0.609905i
$324$	−17.6219			−0.978996
$325$		0			0
$326$	−11.1899	+	19.3815i	−0.619753	+	1.07344i
$327$	−27.3772	+	15.8062i	−1.51396	+	0.874087i
$328$	8.30228	+	4.79333i	0.458417	+	0.264667i
$329$	0.756923	+	1.31103i	0.0417305	+	0.0722793i
$330$		0			0
$331$	3.25821			0.179087			0.0895437	−	0.995983i	$-0.471459\pi$
$331$	3.25821			0.179087			0.0895437	+	0.995983i	$0.471459\pi$
$332$	−9.43297	+	5.44613i	−0.517702	+	0.298895i
$333$	23.8765	−	13.7851i	1.30842	−	0.755419i
$334$	−14.1204			−0.772635
$335$		0			0
$336$	1.81483	+	3.14338i	0.0990070	+	0.171485i
$337$	19.2234	+	11.0987i	1.04717	+	0.604582i	0.921855	−	0.387535i	$-0.126673\pi$
$337$	19.2234	+	11.0987i	1.04717	+	0.604582i	0.125312	+	0.992117i	$0.460007\pi$
$338$	−64.1813	+	37.0551i	−3.49100	+	2.01553i
$339$	19.4921	−	33.7612i	1.05866	−	1.83366i
$340$		0			0
$341$	−17.5837			−0.952213
$342$	−46.1823	−	28.0741i	−2.49725	−	1.51807i
$343$			8.07560i			0.436042i
$344$	3.35563	−	5.81212i	0.180923	−	0.313369i
$345$		0			0
$346$	−6.79296	−	11.7658i	−0.365192	−	0.632531i
$347$	2.59336	+	1.49728i	0.139219	+	0.0803780i	0.567992	−	0.823034i	$-0.307721\pi$
$347$	2.59336	+	1.49728i	0.139219	+	0.0803780i	−0.428773	+	0.903412i	$0.641054\pi$
$348$	−48.8274	+	28.1905i	−2.61743	+	1.51117i
$349$	−15.1407			−0.810461			−0.405230	−	0.914215i	$-0.632809\pi$
$349$	−15.1407			−0.810461			−0.405230	+	0.914215i	$0.632809\pi$
$350$		0			0
$351$	−27.5015	−	47.6340i	−1.46792	−	2.54251i
$352$	−16.9586	+	9.79106i	−0.903897	+	0.521865i
$353$			34.4369i			1.83289i	0.400159	+	0.916446i	$0.368955\pi$
$353$			34.4369i			1.83289i	−0.400159	+	0.916446i	$0.631045\pi$
$354$	18.7334			0.995668
$355$		0			0
$356$	−5.03446	+	8.71994i	−0.266826	+	0.462156i
$357$	−7.91863	+	4.57182i	−0.419098	+	0.241967i
$358$	43.5808	+	25.1614i	2.30332	+	1.32982i
$359$	1.58165	−	2.73950i	0.0834763	−	0.144585i	−0.821265	−	0.570548i	$-0.806731\pi$
$359$	1.58165	−	2.73950i	0.0834763	−	0.144585i	0.904741	+	0.425962i	$0.140064\pi$
$360$		0			0
$361$	−8.74655	−	16.8671i	−0.460345	−	0.887740i
$362$		−	6.94204i		−	0.364865i
$363$	−11.0980	−	6.40744i	−0.582495	−	0.336304i
$364$	5.50314	−	9.53171i	0.288443	−	0.499597i
$365$		0			0
$366$	−7.46829	+	12.9354i	−0.390374	+	0.676147i
$367$	18.5797	−	10.7270i	0.969853	−	0.559945i	0.0706615	−	0.997500i	$-0.477489\pi$
$367$	18.5797	−	10.7270i	0.969853	−	0.559945i	0.899191	+	0.437556i	$0.144156\pi$
$368$			6.03027i			0.314350i
$369$	−35.5864			−1.85255
$370$		0			0
$371$	2.83725	+	4.91426i	0.147303	+	0.255136i
$372$		−	54.4963i		−	2.82550i
$373$			33.1587i			1.71689i	0.512904	+	0.858446i	$0.328570\pi$
$373$			33.1587i			1.71689i	−0.512904	+	0.858446i	$0.671430\pi$
$374$	−14.6596	−	25.3911i	−0.758028	−	1.31294i
$375$		0			0
$376$	−1.96925	−	3.41084i	−0.101556	−	0.175901i
$377$	−41.9234	−	24.2045i	−2.15917	−	1.24660i
$378$	8.90619	+	5.14199i	0.458085	+	0.264476i
$379$	14.1646			0.727589			0.363795	−	0.931479i	$-0.381481\pi$
$379$	14.1646			0.727589			0.363795	+	0.931479i	$0.381481\pi$
$380$		0			0
$381$	5.08198			0.260358
$382$	−35.6030	−	20.5554i	−1.82161	−	1.05171i
$383$	9.37102	+	5.41036i	0.478837	+	0.276457i	0.719932	−	0.694045i	$-0.244173\pi$
$383$	9.37102	+	5.41036i	0.478837	+	0.276457i	−0.241095	+	0.970502i	$0.577506\pi$
$384$	−17.0311	−	29.4988i	−0.869117	−	1.50535i
$385$		0			0
$386$	1.11818	+	1.93674i	0.0569138	+	0.0985775i
$387$			24.9127i			1.26638i
$388$		−	6.84281i		−	0.347391i
$389$	5.38703	+	9.33061i	0.273133	+	0.473081i	0.969662	−	0.244448i	$-0.0786066\pi$
$389$	5.38703	+	9.33061i	0.273133	+	0.473081i	−0.696529	+	0.717529i	$0.745273\pi$
$390$		0			0
$391$	−15.1912			−0.768250
$392$		−	10.2356i		−	0.516975i
$393$	−8.39529	+	4.84702i	−0.423486	+	0.244500i
$394$	−20.1291	+	34.8647i	−1.01409	+	1.75646i
$395$		0			0
$396$	−19.9723	+	34.5930i	−1.00364	+	1.73836i
$397$	2.68653	+	1.55107i	0.134833	+	0.0778461i	0.565899	−	0.824474i	$-0.308529\pi$
$397$	2.68653	+	1.55107i	0.134833	+	0.0778461i	−0.431066	+	0.902320i	$0.641862\pi$
$398$		−	49.1162i		−	2.46197i
$399$	3.65617	+	6.67683i	0.183037	+	0.334260i
$400$		0			0
$401$	5.65671	−	9.79771i	0.282483	−	0.489274i	−0.689513	−	0.724273i	$-0.742175\pi$
$401$	5.65671	−	9.79771i	0.282483	−	0.489274i	0.971996	+	0.234999i	$0.0755088\pi$
$402$	−23.8683	−	13.7804i	−1.19044	−	0.687303i
$403$	40.5220	−	23.3954i	2.01854	−	1.16541i
$404$	1.87681	−	3.25074i	0.0933749	−	0.161730i
$405$		0			0
$406$	9.05110			0.449199
$407$		−	12.4517i		−	0.617206i
$408$	20.6015	−	11.8943i	1.01993	−	0.588855i
$409$	7.11186	+	12.3181i	0.351659	+	0.609091i	0.986540	−	0.163519i	$-0.0522844\pi$
$409$	7.11186	+	12.3181i	0.351659	+	0.609091i	−0.634882	+	0.772609i	$0.718951\pi$
$410$		0			0
$411$	24.0602			1.18680
$412$	0.391303	−	0.225919i	0.0192781	−	0.0111302i
$413$	−1.49835	−	0.865075i	−0.0737291	−	0.0425675i
$414$	17.9874	+	31.1551i	0.884032	+	1.53119i
$415$		0			0
$416$	26.0542	−	45.1272i	1.27741	−	2.21255i
$417$		−	46.1320i		−	2.25909i
$418$	−21.4093	+	11.7235i	−1.04716	+	0.573416i
$419$	11.0053			0.537643			0.268821	−	0.963190i	$-0.413366\pi$
$419$	11.0053			0.537643			0.268821	+	0.963190i	$0.413366\pi$
$420$		0			0
$421$	11.4625	−	19.8536i	0.558646	−	0.967604i	−0.438963	−	0.898505i	$-0.644654\pi$
$421$	11.4625	−	19.8536i	0.558646	−	0.967604i	0.997610	−	0.0690991i	$-0.0220125\pi$
$422$	23.3783	−	13.4975i	1.13804	−	0.657046i
$423$	12.6613	+	7.31000i	0.615613	+	0.355424i
$424$	−7.38154	−	12.7852i	−0.358479	−	0.620904i
$425$		0			0
$426$	−86.4332			−4.18770
$427$	1.19467	−	0.689744i	0.0578142	−	0.0333791i
$428$	10.5989	−	6.11929i	0.512318	−	0.295787i
$429$	−52.3045			−2.52528
$430$		0			0
$431$	8.49811	+	14.7192i	0.409340	+	0.708997i	0.994816	−	0.101693i	$-0.0324258\pi$
$431$	8.49811	+	14.7192i	0.409340	+	0.708997i	−0.585476	+	0.810690i	$0.699092\pi$
$432$	14.4177	+	8.32408i	0.693673	+	0.400492i
$433$	−27.2786	+	15.7493i	−1.31093	+	0.756863i	−0.982249	−	0.187580i	$-0.939936\pi$
$433$	−27.2786	+	15.7493i	−1.31093	+	0.756863i	−0.328676	+	0.944443i	$0.606602\pi$
$434$	−4.37427	+	7.57645i	−0.209972	+	0.363681i
$435$		0			0
$436$	−29.0144			−1.38954
$437$	−0.285896	+	12.6438i	−0.0136763	+	0.604836i
$438$			53.9802i			2.57928i
$439$	1.57963	−	2.73600i	0.0753916	−	0.130582i	−0.825865	−	0.563868i	$-0.809313\pi$
$439$	1.57963	−	2.73600i	0.0753916	−	0.130582i	0.901256	+	0.433286i	$0.142646\pi$
$440$		0			0
$441$	18.9976	+	32.9049i	0.904649	+	1.56690i
$442$	67.5664	+	39.0095i	3.21380	+	1.85549i
$443$	10.3008	−	5.94720i	0.489408	−	0.282560i	−0.234921	−	0.972015i	$-0.575483\pi$
$443$	10.3008	−	5.94720i	0.489408	−	0.282560i	0.724329	+	0.689455i	$0.242150\pi$
$444$	38.5907			1.83143
$445$		0			0
$446$	20.8036	+	36.0329i	0.985080	+	1.70621i
$447$	8.23186	−	4.75267i	0.389354	−	0.224794i
$448$			7.28358i			0.344117i
$449$	−21.2175			−1.00132			−0.500659	−	0.865645i	$-0.666909\pi$
$449$	−21.2175			−1.00132			−0.500659	+	0.865645i	$0.666909\pi$
$450$		0			0
$451$	−8.03602	+	13.9188i	−0.378401	+	0.655410i
$452$	30.9865	−	17.8901i	1.45748	−	0.841479i
$453$	−28.4338	−	16.4162i	−1.33593	−	0.771302i
$454$	−28.7762	+	49.8418i	−1.35053	+	2.33919i
$455$		0			0
$456$	−9.51208	−	17.3708i	−0.445444	−	0.813462i
$457$		−	9.41670i		−	0.440495i	−0.975444	−	0.220247i	$-0.929314\pi$
$457$		−	9.41670i		−	0.440495i	0.975444	−	0.220247i	$-0.0706864\pi$
$458$	−16.5575	−	9.55948i	−0.773682	−	0.446685i
$459$	−20.9696	+	36.3204i	−0.978777	+	1.69529i
$460$		0			0
$461$	−1.16004	+	2.00924i	−0.0540282	+	0.0935797i	−0.891775	−	0.452480i	$-0.850539\pi$
$461$	−1.16004	+	2.00924i	−0.0540282	+	0.0935797i	0.837746	+	0.546060i	$0.183873\pi$
$462$	8.46924	−	4.88972i	0.394025	−	0.227490i
$463$			14.7160i			0.683909i	0.939716	+	0.341955i	$0.111089\pi$
$463$			14.7160i			0.683909i	−0.939716	+	0.341955i	$0.888911\pi$
$464$	14.6523			0.680217
$465$		0			0
$466$	4.89606	+	8.48023i	0.226806	+	0.392839i
$467$			11.7747i			0.544867i	0.962175	+	0.272434i	$0.0878285\pi$
$467$			11.7747i			0.544867i	−0.962175	+	0.272434i	$0.912172\pi$
$468$		−	106.293i		−	4.91341i
$469$	1.27271	+	2.20439i	0.0587681	+	0.101789i
$470$		0			0
$471$	−31.6316	−	54.7875i	−1.45751	−	2.52447i
$472$	3.89819	+	2.25062i	0.179429	+	0.103593i
$473$	9.74403	+	5.62572i	0.448031	+	0.258671i
$474$	−37.6189			−1.72789
$475$		0			0
$476$	−8.39217			−0.384655
$477$	47.4596	+	27.4008i	2.17303	+	1.25460i
$478$	−14.7046	−	8.48971i	−0.672573	−	0.388310i
$479$	5.69219	+	9.85915i	0.260083	+	0.450476i	0.966264	−	0.257555i	$-0.0829169\pi$
$479$	5.69219	+	9.85915i	0.260083	+	0.450476i	−0.706181	+	0.708031i	$0.749584\pi$
$480$		0			0
$481$	16.5671	+	28.6950i	0.755394	+	1.30838i
$482$			59.3288i			2.70235i
$483$		−	5.06703i		−	0.230558i
$484$	−5.88084	−	10.1859i	−0.267311	−	0.462996i
$485$		0			0
$486$	−10.4829			−0.475513
$487$			4.77063i			0.216178i	0.994141	+	0.108089i	$0.0344731\pi$
$487$			4.77063i			0.216178i	−0.994141	+	0.108089i	$0.965527\pi$
$488$	−3.10812	+	1.79447i	−0.140698	+	0.0812321i
$489$	15.2212	−	26.3639i	0.688326	−	1.19222i
$490$		0			0
$491$	2.50665	−	4.34165i	0.113124	−	0.195936i	−0.803904	−	0.594758i	$-0.797248\pi$
$491$	2.50665	−	4.34165i	0.113124	−	0.195936i	0.917028	+	0.398822i	$0.130581\pi$
$492$	−43.1377	−	24.9056i	−1.94480	−	1.12283i
$493$			36.9114i			1.66240i
$494$	33.7397	−	55.5023i	1.51802	−	2.49717i
$495$		0			0
$496$	−7.08125	+	12.2651i	−0.317958	+	0.550719i
$497$	6.91319	+	3.99133i	0.310099	+	0.179036i
$498$	22.3034	−	12.8769i	0.999439	−	0.577026i
$499$	10.9112	−	18.8987i	0.488450	−	0.846021i	−0.511461	−	0.859306i	$-0.670896\pi$
$499$	10.9112	−	18.8987i	0.488450	−	0.846021i	0.999912	+	0.0132853i	$0.00422897\pi$
$500$		0			0
$501$	19.2074			0.858124
$502$		−	35.2372i		−	1.57272i
$503$	13.1391	−	7.58583i	0.585841	−	0.338236i	−0.177610	−	0.984101i	$-0.556837\pi$
$503$	13.1391	−	7.58583i	0.585841	−	0.338236i	0.763451	+	0.645865i	$0.223503\pi$
$504$	2.60144	+	4.50582i	0.115877	+	0.200705i
$505$		0			0
$506$	16.2475			0.722288
$507$	87.3031	−	50.4045i	3.87727	−	2.23854i
$508$	4.03941	+	2.33216i	0.179220	+	0.103473i
$509$	2.59122	+	4.48812i	0.114854	+	0.198933i	0.917721	−	0.397225i	$-0.130027\pi$
$509$	2.59122	+	4.48812i	0.114854	+	0.198933i	−0.802868	+	0.596157i	$0.796693\pi$
$510$		0			0
$511$	2.49271	−	4.31750i	0.110271	−	0.190995i
$512$			22.1701i			0.979789i
$513$	29.8354	+	18.1368i	1.31726	+	0.800761i
$514$	19.8421			0.875199
$515$		0			0
$516$	−17.4355	+	30.1991i	−0.767554	+	1.32944i
$517$	5.71828	−	3.30145i	0.251490	−	0.145198i
$518$	−5.36515	−	3.09757i	−0.235731	−	0.136099i
$519$	9.24018	+	16.0045i	0.405599	+	0.702518i
$520$		0			0
$521$	11.2091			0.491079			0.245540	−	0.969387i	$-0.421035\pi$
$521$	11.2091			0.491079			0.245540	+	0.969387i	$0.421035\pi$
$522$	75.7004	−	43.7056i	3.31332	−	1.91294i
$523$	−4.71014	+	2.71940i	−0.205960	+	0.118911i	−0.599433	−	0.800425i	$-0.704607\pi$
$523$	−4.71014	+	2.71940i	−0.205960	+	0.118911i	0.393472	+	0.919336i	$0.371274\pi$
$524$	−8.89733			−0.388682
$525$		0			0
$526$	16.5982	+	28.7488i	0.723714	+	1.25351i
$527$	−30.8976	−	17.8387i	−1.34592	−	0.777067i
$528$	13.7104	−	7.91569i	0.596668	−	0.344486i
$529$	−7.29084	+	12.6281i	−0.316993	+	0.549048i
$530$		0			0
$531$	−16.7090			−0.725107
$532$	−0.157940	+	6.98492i	−0.00684756	+	0.302835i
$533$		−	42.7680i		−	1.85249i
$534$	11.9035	−	20.6175i	0.515116	−	0.892206i
$535$		0			0
$536$	−3.31114	−	5.73506i	−0.143019	−	0.247717i
$537$	−59.2811	−	34.2260i	−2.55817	−	1.47696i
$538$	26.5866	−	15.3498i	1.14623	−	0.661776i
$539$	17.1600			0.739132
$540$		0			0
$541$	−7.14111	−	12.3688i	−0.307020	−	0.531775i	0.670689	−	0.741739i	$-0.265999\pi$
$541$	−7.14111	−	12.3688i	−0.307020	−	0.531775i	−0.977709	+	0.209964i	$0.932665\pi$
$542$	−21.3554	+	12.3295i	−0.917291	+	0.529598i
$543$			9.44296i			0.405236i
$544$	−39.7322			−1.70350
$545$		0			0
$546$	−13.0117	+	22.5369i	−0.556848	+	0.964488i
$547$	−21.6717	+	12.5122i	−0.926616	+	0.534982i	−0.885740	−	0.464182i	$-0.846348\pi$
$547$	−21.6717	+	12.5122i	−0.926616	+	0.534982i	−0.0408766	+	0.999164i	$0.513015\pi$
$548$	19.1243	+	11.0414i	0.816949	+	0.471666i
$549$	6.66122	−	11.5376i	0.284294	−	0.492412i
$550$		0			0
$551$	30.7219	+	0.694668i	1.30880	+	0.0295939i
$552$			13.1827i			0.561091i
$553$	3.00888	+	1.73718i	0.127950	+	0.0738722i
$554$	20.5184	−	35.5388i	0.871741	−	1.50990i
$555$		0			0
$556$	21.1703	−	36.6680i	0.897821	−	1.55507i
$557$	−6.19807	+	3.57846i	−0.262621	+	0.151624i	−0.625529	−	0.780201i	$-0.715117\pi$
$557$	−6.19807	+	3.57846i	−0.262621	+	0.151624i	0.362909	+	0.931825i	$0.381784\pi$
$558$			84.4892i			3.57671i
$559$	−29.9403			−1.26634
$560$		0			0
$561$	19.9408	+	34.5385i	0.841901	+	1.45822i
$562$		−	60.5184i		−	2.55282i
$563$		−	28.9386i		−	1.21962i	−0.792548	−	0.609809i	$-0.791246\pi$
$563$		−	28.9386i		−	1.21962i	0.792548	−	0.609809i	$-0.208754\pi$
$564$	10.2320	+	17.7223i	0.430845	+	0.746245i
$565$		0			0
$566$	−15.6202	−	27.0551i	−0.656568	−	1.13721i
$567$	−3.33253	−	1.92403i	−0.139953	−	0.0808019i
$568$	−17.9857	−	10.3841i	−0.754664	−	0.435706i
$569$	−38.8864			−1.63020			−0.815100	−	0.579320i	$-0.803318\pi$
$569$	−38.8864			−1.63020			−0.815100	+	0.579320i	$0.803318\pi$
$570$		0			0
$571$	15.1613			0.634480			0.317240	−	0.948345i	$-0.397244\pi$
$571$	15.1613			0.634480			0.317240	+	0.948345i	$0.397244\pi$
$572$	−41.5742	−	24.0029i	−1.73831	−	1.00361i
$573$	48.4293	+	27.9607i	2.02316	+	1.16807i
$574$	3.99820	+	6.92509i	0.166882	+	0.289048i
$575$		0			0
$576$	35.1707	+	60.9174i	1.46544	+	2.53822i
$577$			20.6412i			0.859303i	0.902995	+	0.429651i	$0.141364\pi$
$577$			20.6412i			0.859303i	−0.902995	+	0.429651i	$0.858636\pi$
$578$		−	22.5972i		−	0.939918i
$579$	−1.52101	−	2.63447i	−0.0632111	−	0.109485i
$580$		0			0
$581$	−2.37852			−0.0986778
$582$			16.1792i			0.670649i
$583$	21.4344	−	12.3752i	0.887723	−	0.512527i
$584$	−6.48517	+	11.2326i	−0.268358	+	0.464810i
$585$		0			0
$586$	−2.85560	+	4.94604i	−0.117964	+	0.204319i
$587$	−6.21706	−	3.58942i	−0.256606	−	0.148151i	0.366180	−	0.930544i	$-0.380666\pi$
$587$	−6.21706	−	3.58942i	−0.256606	−	0.148151i	−0.622785	+	0.782393i	$0.713999\pi$
$588$			53.1829i			2.19323i
$589$	−15.4289	+	25.3808i	−0.635738	+	1.04580i
$590$		0			0
$591$	27.3808	−	47.4250i	1.12630	−	1.95080i
$592$	−8.68533	−	5.01448i	−0.356965	−	0.206094i
$593$	−31.8253	+	18.3743i	−1.30691	+	0.754543i	−0.981579	−	0.191058i	$-0.938808\pi$
$593$	−31.8253	+	18.3743i	−1.30691	+	0.754543i	−0.325328	+	0.945601i	$0.605475\pi$
$594$	22.4277	−	38.8459i	0.920219	−	1.59387i
$595$		0			0
$596$	8.72413			0.357354
$597$			66.8107i			2.73438i
$598$	−37.4425	+	21.6174i	−1.53114	+	0.884002i
$599$	−0.926876	−	1.60540i	−0.0378711	−	0.0655947i	0.846469	−	0.532439i	$-0.178724\pi$
$599$	−0.926876	−	1.60540i	−0.0378711	−	0.0655947i	−0.884340	+	0.466844i	$0.845391\pi$
$600$		0			0
$601$	−38.1633			−1.55671			−0.778356	−	0.627823i	$-0.783946\pi$
$601$	−38.1633			−1.55671			−0.778356	+	0.627823i	$0.783946\pi$
$602$	4.84800	−	2.79899i	0.197590	−	0.114078i
$603$	21.2890	+	12.2912i	0.866954	+	0.500536i
$604$	−15.0671	−	26.0969i	−0.613070	−	1.06187i
$605$		0			0
$606$	−4.43755	+	7.68606i	−0.180263	+	0.312225i
$607$			7.44914i			0.302351i	0.988507	+	0.151176i	$0.0483059\pi$
$607$			7.44914i			0.302351i	−0.988507	+	0.151176i	$0.951694\pi$
$608$	−0.747755	+	33.0696i	−0.0303255	+	1.34115i
$609$	−12.3118			−0.498901
$610$		0			0
$611$	−8.78523	+	15.2165i	−0.355412	+	0.615592i
$612$	−70.1893	+	40.5238i	−2.83723	+	1.63808i
$613$	−18.3682	−	10.6049i	−0.741883	−	0.428326i	0.0808706	−	0.996725i	$-0.474230\pi$
$613$	−18.3682	−	10.6049i	−0.741883	−	0.428326i	−0.822754	+	0.568398i	$0.807563\pi$
$614$	−18.2560	−	31.6203i	−0.736753	−	1.27609i
$615$		0			0
$616$	2.34980			0.0946760
$617$	−26.6868	+	15.4076i	−1.07437	+	0.620287i	−0.929372	−	0.369145i	$-0.879651\pi$
$617$	−26.6868	+	15.4076i	−1.07437	+	0.620287i	−0.144997	+	0.989432i	$0.546317\pi$
$618$	−0.925199	+	0.534164i	−0.0372170	+	0.0214872i
$619$	−7.32036			−0.294230			−0.147115	−	0.989119i	$-0.546999\pi$
$619$	−7.32036			−0.294230			−0.147115	+	0.989119i	$0.546999\pi$
$620$		0			0
$621$	−11.6205	−	20.1273i	−0.466314	−	0.807680i
$622$	34.4434	+	19.8859i	1.38105	+	0.797352i
$623$	−1.90416	+	1.09937i	−0.0762885	+	0.0440452i
$624$	−21.0638	+	36.4836i	−0.843228	+	1.46051i
$625$		0			0
$626$	−51.0086			−2.03871
$627$	29.1222	−	15.9470i	1.16303	−	0.636862i
$628$		−	58.0638i		−	2.31700i
$629$	12.6322	−	21.8797i	0.503680	−	0.872399i
$630$		0			0
$631$	−2.25414	−	3.90429i	−0.0897360	−	0.155427i	0.817664	−	0.575696i	$-0.195269\pi$
$631$	−2.25414	−	3.90429i	−0.0897360	−	0.155427i	−0.907399	+	0.420269i	$0.861936\pi$
$632$	−7.82805	−	4.51953i	−0.311383	−	0.179777i
$633$	−31.8005	+	18.3600i	−1.26396	+	0.729746i
$634$	8.42762			0.334704
$635$		0			0
$636$	38.3536	+	66.4305i	1.52082	+	2.63414i
$637$	−39.5454	+	22.8315i	−1.56685	+	0.904618i
$638$		−	39.4780i		−	1.56295i
$639$	77.0928			3.04975
$640$		0			0
$641$	8.48158	−	14.6905i	0.335002	−	0.580241i	−0.648483	−	0.761229i	$-0.724596\pi$
$641$	8.48158	−	14.6905i	0.335002	−	0.580241i	0.983485	+	0.180988i	$0.0579296\pi$
$642$	−25.0602	+	14.4685i	−0.989046	+	0.571026i
$643$	8.04202	+	4.64306i	0.317146	+	0.183104i	0.650120	−	0.759832i	$-0.274719\pi$
$643$	8.04202	+	4.64306i	0.317146	+	0.183104i	−0.332974	+	0.942936i	$0.608052\pi$
$644$	2.32530	−	4.02753i	0.0916295	−	0.158707i
$645$		0			0
$646$	−49.5132	−	1.11957i	−1.94807	−	0.0440489i
$647$			39.2779i			1.54418i	0.635516	+	0.772088i	$0.280787\pi$
$647$			39.2779i			1.54418i	−0.635516	+	0.772088i	$0.719213\pi$
$648$	8.67007	+	5.00567i	0.340593	+	0.196641i
$649$	−3.77317	+	6.53533i	−0.148110	+	0.256534i
$650$		0			0
$651$	5.95013	−	10.3059i	0.233204	−	0.403921i
$652$	24.1972	−	13.9702i	0.947634	−	0.547116i
$653$		−	26.5513i		−	1.03903i	−0.854460	−	0.519517i	$-0.826112\pi$
$653$		−	26.5513i		−	1.03903i	0.854460	−	0.519517i	$-0.173888\pi$
$654$	68.6018			2.68254
$655$		0			0
$656$	6.47246	+	11.2106i	0.252707	+	0.437702i
$657$		−	48.1469i		−	1.87839i
$658$		−	3.28518i		−	0.128069i
$659$	16.3143	+	28.2573i	0.635517	+	1.10075i	0.986405	+	0.164330i	$0.0525463\pi$
$659$	16.3143	+	28.2573i	0.635517	+	1.10075i	−0.350889	+	0.936417i	$0.614120\pi$
$660$		0			0
$661$	−3.13332	−	5.42707i	−0.121872	−	0.211088i	0.798634	−	0.601817i	$-0.205556\pi$
$661$	−3.13332	−	5.42707i	−0.121872	−	0.211088i	−0.920506	+	0.390729i	$0.872223\pi$
$662$	−6.12332	−	3.53530i	−0.237989	−	0.137403i
$663$	−91.9077	−	53.0629i	−3.56940	−	2.06079i
$664$	6.18809			0.240145
$665$		0			0
$666$	−59.8297			−2.31836
$667$	−17.7143	−	10.2274i	−0.685902	−	0.396006i
$668$	15.2670	+	8.81442i	0.590699	+	0.341040i
$669$	−28.2983	−	49.0141i	−1.09408	−	1.89499i
$670$		0			0
$671$	−3.00844	−	5.21077i	−0.116140	−	0.201160i
$672$		−	13.2527i		−	0.511235i
$673$			7.39044i			0.284881i	0.989803	+	0.142440i	$0.0454949\pi$
$673$			7.39044i			0.284881i	−0.989803	+	0.142440i	$0.954505\pi$
$674$	−24.0850	−	41.7165i	−0.927721	−	1.60686i
$675$		0			0
$676$	92.5238			3.55861
$677$		−	20.2751i		−	0.779234i	−0.920977	−	0.389617i	$-0.872607\pi$
$677$		−	20.2751i		−	0.779234i	0.920977	−	0.389617i	$-0.127393\pi$
$678$	−73.2648	+	42.2994i	−2.81372	+	1.62450i
$679$	0.747127	−	1.29406i	0.0286721	−	0.0496615i
$680$		0			0
$681$	39.1431	−	67.7978i	1.49997	−	2.59802i
$682$	33.0460	+	19.0791i	1.26540	+	0.730577i
$683$		−	24.6563i		−	0.943448i	−0.881746	−	0.471724i	$-0.843632\pi$
$683$		−	24.6563i		−	0.943448i	0.881746	−	0.471724i	$-0.156368\pi$
$684$	32.4076	+	59.1822i	1.23914	+	2.26289i
$685$		0			0
$686$	8.76238	−	15.1769i	0.334549	−	0.579456i
$687$	22.5225	+	13.0034i	0.859286	+	0.496109i
$688$	7.84815	−	4.53113i	0.299208	−	0.172748i
$689$	−32.9306	+	57.0374i	−1.25456	+	2.17295i
$690$		0			0
$691$	−41.7299			−1.58748			−0.793739	−	0.608258i	$-0.791869\pi$
$691$	−41.7299			−1.58748			−0.793739	+	0.608258i	$0.791869\pi$
$692$			16.9615i			0.644781i
$693$	−7.55402	+	4.36131i	−0.286953	+	0.165673i
$694$	−3.24922	−	5.62782i	−0.123339	−	0.213629i
$695$		0			0
$696$	32.0311			1.21414
$697$	−28.2413	+	16.3051i	−1.06971	+	0.617600i
$698$	28.4546	+	16.4283i	1.07702	+	0.621819i
$699$	−6.65991	−	11.5353i	−0.251901	−	0.436305i
$700$		0			0
$701$	3.60840	−	6.24993i	0.136287	−	0.236057i	−0.789801	−	0.613363i	$-0.789816\pi$
$701$	3.60840	−	6.24993i	0.136287	−	0.236057i	0.926089	+	0.377306i	$0.123150\pi$
$702$			119.361i			4.50500i
$703$	−17.9730	−	10.9258i	−0.677865	−	0.412073i
$704$	31.7686			1.19732
$705$		0			0
$706$	37.3655	−	64.7190i	1.40627	−	2.43573i
$707$	0.709857	−	0.409836i	0.0266969	−	0.0154135i
$708$	−20.2546	−	11.6940i	−0.761213	−	0.439487i
$709$	−10.3172	−	17.8700i	−0.387472	−	0.671122i	0.604636	−	0.796502i	$-0.293318\pi$
$709$	−10.3172	−	17.8700i	−0.387472	−	0.671122i	−0.992109	+	0.125380i	$0.959985\pi$
$710$		0			0
$711$	33.5536			1.25836
$712$	4.95396	−	2.86017i	0.185657	−	0.107189i
$713$	17.1222	−	9.88549i	0.641230	−	0.370214i
$714$	19.8425			0.742587
$715$		0			0
$716$	−31.4131	−	54.4091i	−1.17396	−	2.03336i
$717$	20.0021	+	11.5482i	0.746991	+	0.431275i
$718$	−5.94495	+	3.43232i	−0.221864	+	0.128093i
$719$	0.748958	−	1.29723i	0.0279314	−	0.0483787i	−0.851722	−	0.523994i	$-0.824441\pi$
$719$	0.748958	−	1.29723i	0.0279314	−	0.0483787i	0.879653	+	0.475616i	$0.157775\pi$
$720$		0			0
$721$	0.0986670			0.00367455
$722$	−1.86367	+	41.1895i	−0.0693585	+	1.53291i
$723$		−	80.7024i		−	3.00136i
$724$	−4.33344	+	7.50574i	−0.161051	+	0.278949i
$725$		0			0
$726$	13.9047	+	24.0837i	0.516052	+	0.893828i
$727$	9.84190	+	5.68222i	0.365016	+	0.210742i	0.671279	−	0.741205i	$-0.265745\pi$
$727$	9.84190	+	5.68222i	0.365016	+	0.210742i	−0.306263	+	0.951947i	$0.599079\pi$
$728$	−5.41514	+	3.12643i	−0.200698	+	0.115873i
$729$	33.7723			1.25083
$730$		0			0
$731$	11.4146	+	19.7707i	0.422184	+	0.731244i
$732$	16.1494	−	9.32389i	0.596901	−	0.344621i
$733$		−	45.6910i		−	1.68764i	−0.536630	−	0.843818i	$-0.680303\pi$
$733$		−	45.6910i		−	1.68764i	0.536630	−	0.843818i	$-0.319697\pi$
$734$	−46.5570			−1.71845
$735$		0			0
$736$	11.0090	−	19.0681i	0.405796	−	0.702859i
$737$	9.61484	−	5.55113i	0.354167	−	0.204479i
$738$	66.8792	+	38.6127i	2.46186	+	1.42135i
$739$	−1.78276	+	3.08783i	−0.0655799	+	0.113588i	−0.896951	−	0.442130i	$-0.854223\pi$
$739$	−1.78276	+	3.08783i	−0.0655799	+	0.113588i	0.831371	+	0.555718i	$0.187556\pi$
$740$		0			0
$741$	−45.8947	+	75.4975i	−1.68599	+	2.77347i
$742$		−	12.3142i		−	0.452067i
$743$	36.8030	+	21.2482i	1.35017	+	0.779522i	0.988273	−	0.152696i	$-0.0487955\pi$
$743$	36.8030	+	21.2482i	1.35017	+	0.779522i	0.361898	+	0.932218i	$0.382129\pi$
$744$	−15.4802	+	26.8125i	−0.567531	+	0.982992i
$745$		0			0
$746$	35.9786	−	62.3168i	1.31727	−	2.28158i
$747$	−19.8932	+	11.4853i	−0.727853	+	0.420226i
$748$			36.6039i			1.33837i
$749$	2.67252			0.0976516
$750$		0			0
$751$	6.38588	+	11.0607i	0.233024	+	0.403610i	0.958697	−	0.284431i	$-0.0918045\pi$
$751$	6.38588	+	11.0607i	0.233024	+	0.403610i	−0.725672	+	0.688040i	$0.758471\pi$
$752$		−	5.31818i		−	0.193934i
$753$			47.9317i			1.74673i
$754$	52.5259	+	90.9775i	1.91288	+	3.31320i
$755$		0			0
$756$	−6.41960	−	11.1191i	−0.233478	−	0.404396i
$757$	9.82603	+	5.67306i	0.357133	+	0.206191i	0.667822	−	0.744321i	$-0.267227\pi$
$757$	9.82603	+	5.67306i	0.357133	+	0.206191i	−0.310689	+	0.950512i	$0.600560\pi$
$758$	−26.6203	−	15.3693i	−0.966894	−	0.558237i
$759$	−22.1007			−0.802206
$760$		0			0
$761$	−36.9214			−1.33840			−0.669199	−	0.743083i	$-0.733363\pi$
$761$	−36.9214			−1.33840			−0.669199	+	0.743083i	$0.733363\pi$
$762$	−9.55082	−	5.51417i	−0.345990	−	0.199757i
$763$	−5.48698	−	3.16791i	−0.198642	−	0.114686i
$764$	25.6627	+	44.4491i	0.928444	+	1.60811i
$765$		0			0
$766$	−11.7410	−	20.3359i	−0.424218	−	0.734767i
$767$		−	20.0810i		−	0.725083i
$768$			1.23551i			0.0445827i
$769$	14.2528	+	24.6866i	0.513971	+	0.890223i	0.999869	+	0.0162076i	$0.00515927\pi$
$769$	14.2528	+	24.6866i	0.513971	+	0.890223i	−0.485898	+	0.874015i	$0.661507\pi$
$770$		0			0
$771$	−26.9904			−0.972036
$772$		−	2.79201i		−	0.100487i
$773$	13.1801	−	7.60956i	0.474057	−	0.273697i	−0.243880	−	0.969805i	$-0.578420\pi$
$773$	13.1801	−	7.60956i	0.474057	−	0.273697i	0.717936	+	0.696109i	$0.245087\pi$
$774$	27.0314	−	46.8197i	0.971622	−	1.68290i
$775$		0			0
$776$	−1.94376	+	3.36670i	−0.0697770	+	0.120857i
$777$	7.29799	+	4.21350i	0.261814	+	0.151158i
$778$		−	23.3807i		−	0.838237i
$779$	13.0395	+	23.8125i	0.467188	+	0.853170i
$780$		0			0
$781$	17.4089	−	30.1531i	0.622939	−	1.07896i
$782$	28.5495	+	16.4831i	1.02093	+	0.589433i
$783$	−48.9051	+	28.2354i	−1.74773	+	1.00905i
$784$	6.91059	−	11.9695i	0.246807	−	0.427482i
$785$		0			0
$786$	21.0369			0.750362
$787$		−	46.5712i		−	1.66008i	−0.557700	−	0.830042i	$-0.688316\pi$
$787$		−	46.5712i		−	1.66008i	0.557700	−	0.830042i	$-0.311684\pi$
$788$	43.5273	−	25.1305i	1.55060	−	0.895237i
$789$	−22.5778	−	39.1059i	−0.803790	−	1.39221i
$790$		0			0
$791$	7.81325			0.277807
$792$	19.6529	−	11.3466i	0.698336	−	0.403184i
$793$	13.8660	+	8.00553i	0.492395	+	0.284285i
$794$	−3.36596	−	5.83001i	−0.119453	−	0.206899i
$795$		0			0
$796$	−30.6599	+	53.1045i	−1.08671	+	1.88224i
$797$		−	8.32080i		−	0.294738i	−0.989082	−	0.147369i	$-0.952920\pi$
$797$		−	8.32080i		−	0.294738i	0.989082	−	0.147369i	$-0.0470805\pi$
$798$	0.373434	−	16.5152i	0.0132194	−	0.584632i
$799$	13.3973			0.473962
$800$		0			0
$801$	−10.6172	+	18.3895i	−0.375139	+	0.649760i
$802$	−21.2619	+	12.2755i	−0.750783	+	0.433465i
$803$	−18.8315	−	10.8724i	−0.664551	−	0.383678i
$804$	17.2043	+	29.7987i	0.606749	+	1.05092i
$805$		0			0
$806$	−101.540			−3.57659
$807$	−36.1646	+	20.8796i	−1.27305	+	0.734998i
$808$	−1.84680	+	1.06625i	−0.0649703	+	0.0375106i
$809$	14.2469			0.500893			0.250447	−	0.968130i	$-0.419423\pi$
$809$	14.2469			0.500893			0.250447	+	0.968130i	$0.419423\pi$
$810$		0			0
$811$	16.4331	+	28.4630i	0.577045	+	0.999471i	0.995816	+	0.0913794i	$0.0291276\pi$
$811$	16.4331	+	28.4630i	0.577045	+	0.999471i	−0.418771	+	0.908092i	$0.637539\pi$
$812$	−9.78607	−	5.64999i	−0.343424	−	0.198276i
$813$	29.0488	−	16.7713i	1.01879	−	0.588196i
$814$	−13.5106	+	23.4010i	−0.473546	+	0.820206i
$815$		0			0
$816$	32.1219			1.12449
$817$	16.6702	−	9.12845i	0.583218	−	0.319364i
$818$		−	30.8667i		−	1.07923i
$819$	11.6056	−	20.1014i	0.405531	−	0.702400i
$820$		0			0
$821$	−6.58734	−	11.4096i	−0.229900	−	0.398198i	0.727878	−	0.685706i	$-0.240507\pi$
$821$	−6.58734	−	11.4096i	−0.229900	−	0.398198i	−0.957778	+	0.287508i	$0.907173\pi$
$822$	−45.2176	−	26.1064i	−1.57714	−	0.910565i
$823$	−26.8545	+	15.5045i	−0.936090	+	0.540452i	−0.888732	−	0.458426i	$-0.848413\pi$
$823$	−26.8545	+	15.5045i	−0.936090	+	0.540452i	−0.0473572	+	0.998878i	$0.515080\pi$
$824$	−0.256697			−0.00894247
$825$		0			0
$826$	1.87729	+	3.25156i	0.0653192	+	0.113136i
$827$	16.9649	−	9.79469i	0.589927	−	0.340595i	−0.175141	−	0.984543i	$-0.556038\pi$
$827$	16.9649	−	9.79469i	0.589927	−	0.340595i	0.765069	+	0.643949i	$0.222705\pi$
$828$		−	44.9132i		−	1.56084i
$829$	14.9634			0.519699			0.259850	−	0.965649i	$-0.416327\pi$
$829$	14.9634			0.519699			0.259850	+	0.965649i	$0.416327\pi$
$830$		0			0
$831$	−27.9103	+	48.3420i	−0.968196	+	1.67697i
$832$	−73.2111	+	42.2685i	−2.53814	+	1.46539i
$833$	30.1529	+	17.4088i	1.04474	+	0.603180i
$834$	−50.0552	+	86.6982i	−1.73327	+	3.00211i
$835$		0			0
$836$	30.4660	+	0.688881i	1.05369	+	0.0238255i
$837$		−	54.5830i		−	1.88666i
$838$	−20.6828	−	11.9412i	−0.714474	−	0.412502i
$839$	−13.2661	+	22.9776i	−0.457997	+	0.793274i	−0.998855	−	0.0478399i	$-0.984766\pi$
$839$	−13.2661	+	22.9776i	−0.457997	+	0.793274i	0.540858	+	0.841114i	$0.318100\pi$
$840$		0			0
$841$	−10.3504	+	17.9274i	−0.356911	+	0.618188i
$842$	−43.0840	+	24.8745i	−1.48477	+	0.857233i
$843$			82.3207i			2.83528i
$844$	−33.7022			−1.16008
$845$		0			0
$846$	−15.8633	−	27.4761i	−0.545393	−	0.944648i
$847$		−	2.56838i		−	0.0882505i
$848$		−	19.9347i		−	0.684560i
$849$	21.2476	+	36.8019i	0.729215	+	1.26304i
$850$		0			0
$851$	7.00026	+	12.1248i	0.239966	+	0.415633i
$852$	93.4518	+	53.9544i	3.20160	+	1.84845i
$853$	−5.38226	−	3.10745i	−0.184285	−	0.106397i	0.405019	−	0.914308i	$-0.367265\pi$
$853$	−5.38226	−	3.10745i	−0.184285	−	0.106397i	−0.589304	+	0.807911i	$0.700598\pi$
$854$	−2.99361			−0.102439
$855$		0			0
$856$	−6.95296			−0.237647
$857$	−32.3832	−	18.6965i	−1.10619	−	0.638659i	−0.168350	−	0.985727i	$-0.553844\pi$
$857$	−32.3832	−	18.6965i	−1.10619	−	0.638659i	−0.937840	+	0.347068i	$0.887177\pi$
$858$	98.2984	+	56.7526i	3.35585	+	1.93750i
$859$	−21.4745	−	37.1950i	−0.732701	−	1.26908i	−0.955725	−	0.294263i	$-0.904926\pi$
$859$	−21.4745	−	37.1950i	−0.732701	−	1.26908i	0.223023	−	0.974813i	$-0.428407\pi$
$860$		0			0
$861$	−5.43859	−	9.41991i	−0.185347	−	0.321030i
$862$		−	36.8833i		−	1.25625i
$863$			37.3005i			1.26972i	0.772625	+	0.634862i	$0.218943\pi$
$863$			37.3005i			1.26972i	−0.772625	+	0.634862i	$0.781057\pi$
$864$	−30.3931	−	52.6425i	−1.03400	−	1.79093i
$865$		0			0
$866$	68.3547			2.32279
$867$			30.7380i			1.04392i
$868$	9.45893	−	5.46112i	0.321057	−	0.185362i
$869$	7.57699	−	13.1237i	0.257032	−	0.445192i
$870$		0			0
$871$	−14.7717	+	25.5853i	−0.500519	+	0.866925i
$872$	14.2752	+	8.24180i	0.483420	+	0.279103i
$873$		−	14.4308i		−	0.488408i
$874$	14.2564	−	23.4520i	0.482230	−	0.793274i
$875$		0			0
$876$	33.6962	−	58.3635i	1.13849	−	1.97192i
$877$	32.5073	+	18.7681i	1.09769	+	0.633754i	0.935614	−	0.353024i	$-0.114847\pi$
$877$	32.5073	+	18.7681i	1.09769	+	0.633754i	0.162079	+	0.986778i	$0.448180\pi$
$878$	−5.93735	+	3.42793i	−0.200376	+	0.115687i
$879$	3.88435	−	6.72789i	0.131016	−	0.226926i
$880$		0			0
$881$	24.1432			0.813404			0.406702	−	0.913561i	$-0.366679\pi$
$881$	24.1432			0.813404			0.406702	+	0.913561i	$0.366679\pi$
$882$		−	82.4530i		−	2.77634i
$883$	−26.8575	+	15.5062i	−0.903827	+	0.521825i	−0.878440	−	0.477853i	$-0.841415\pi$
$883$	−26.8575	+	15.5062i	−0.903827	+	0.521825i	−0.0253873	+	0.999678i	$0.508082\pi$
$884$	−48.7019	−	84.3542i	−1.63802	−	2.83714i
$885$		0			0
$886$	−25.8119			−0.867167
$887$	32.2276	−	18.6066i	1.08210	−	0.624750i	0.150637	−	0.988589i	$-0.451868\pi$
$887$	32.2276	−	18.6066i	1.08210	−	0.624750i	0.931462	+	0.363839i	$0.118534\pi$
$888$	−18.9868	−	10.9620i	−0.637156	−	0.367862i
$889$	0.509269	+	0.882080i	0.0170803	+	0.0295840i
$890$		0			0
$891$	−8.39201	+	14.5354i	−0.281143	+	0.486954i
$892$		−	51.9452i		−	1.73925i
$893$	0.252136	−	11.1508i	0.00843740	−	0.373146i
$894$	−20.6274			−0.689884
$895$		0			0
$896$	3.41341	−	5.91219i	0.114034	−	0.197513i
$897$	50.9314	−	29.4053i	1.70055	−	0.981814i
$898$	39.8752	+	23.0219i	1.33065	+	0.768252i
$899$	−24.0197	−	41.6033i	−0.801102	−	1.38755i
$900$		0			0
$901$	50.2185			1.67302
$902$	30.2050	−	17.4389i	1.00572	−	0.580650i
$903$	−6.59453	+	3.80735i	−0.219452	+	0.126701i
$904$	−20.3274			−0.676078
$905$		0			0
$906$	35.6247	+	61.7037i	1.18355	+	2.04997i
$907$	−7.69168	−	4.44080i	−0.255398	−	0.147454i	0.366835	−	0.930286i	$-0.380441\pi$
$907$	−7.69168	−	4.44080i	−0.255398	−	0.147454i	−0.622234	+	0.782832i	$0.713775\pi$
$908$	62.2258	−	35.9261i	2.06503	−	1.19225i
$909$	3.95801	−	6.85547i	0.131279	−	0.227382i
$910$		0			0
$911$	−7.31703			−0.242424			−0.121212	−	0.992627i	$-0.538678\pi$
$911$	−7.31703			−0.242424			−0.121212	+	0.992627i	$0.538678\pi$
$912$	0.604531	−	26.7355i	0.0200180	−	0.885302i
$913$			10.3743i			0.343341i
$914$	−10.2175	+	17.6973i	−0.337966	+	0.585374i
$915$		0			0
$916$	11.9347	+	20.6715i	0.394333	+	0.683004i
$917$	−1.68260	−	0.971448i	−0.0555642	−	0.0320800i
$918$	78.8184	−	45.5059i	2.60140	−	1.50192i
$919$	18.1725			0.599454			0.299727	−	0.954025i	$-0.403104\pi$
$919$	18.1725			0.599454			0.299727	+	0.954025i	$0.403104\pi$
$920$		0			0
$921$	24.8329	+	43.0118i	0.818271	+	1.41729i
$922$	4.36023	−	2.51738i	0.143596	−	0.0829054i
$923$			92.6509i			3.04964i
$924$	−12.2093			−0.401656
$925$		0			0
$926$	15.9675	−	27.6565i	0.524724	−	0.908848i
$927$	0.825218	−	0.476440i	0.0271037	−	0.0156483i
$928$	−46.3315	−	26.7495i	−1.52091	−	0.878095i
$929$	3.62348	−	6.27605i	0.118882	−	0.205910i	−0.800443	−	0.599409i	$-0.795402\pi$
$929$	3.62348	−	6.27605i	0.118882	−	0.205910i	0.919325	+	0.393499i	$0.128735\pi$
$930$		0			0
$931$	15.0571	−	24.7691i	0.493476	−	0.811774i
$932$		−	12.2251i		−	0.400447i
$933$	−46.8519	−	27.0500i	−1.53386	−	0.885576i
$934$	12.7760	−	22.1287i	0.418045	−	0.724074i
$935$		0			0
$936$	−30.1936	+	52.2969i	−0.986909	+	1.70938i
$937$	−1.51431	+	0.874288i	−0.0494704	+	0.0285618i	−0.524531	−	0.851391i	$-0.675759\pi$
$937$	−1.51431	+	0.874288i	−0.0494704	+	0.0285618i	0.475061	+	0.879953i	$0.342426\pi$
$938$		−	5.52377i		−	0.180357i
$939$	69.3848			2.26429
$940$		0			0
$941$	−14.2280	−	24.6436i	−0.463819	−	0.803359i	0.535328	−	0.844644i	$-0.320188\pi$
$941$	−14.2280	−	24.6436i	−0.463819	−	0.803359i	−0.999147	+	0.0412856i	$0.986855\pi$
$942$			137.286i			4.47303i
$943$		−	18.0712i		−	0.588480i
$944$	3.03903	+	5.26376i	0.0989121	+	0.171321i
$945$		0			0
$946$	−12.2083	−	21.1454i	−0.396926	−	0.687496i
$947$	−9.58793	−	5.53560i	−0.311566	−	0.179883i	0.336061	−	0.941840i	$-0.390905\pi$
$947$	−9.58793	−	5.53560i	−0.311566	−	0.179883i	−0.647627	+	0.761957i	$0.724238\pi$
$948$	40.6737	+	23.4829i	1.32102	+	0.762691i
$949$	57.8634			1.87832
$950$		0			0
$951$	−11.4637			−0.371737
$952$	4.12899	+	2.38387i	0.133821	+	0.0772618i
$953$	−45.4464	−	26.2385i	−1.47215	−	0.849949i	−0.472644	−	0.881253i	$-0.656701\pi$
$953$	−45.4464	−	26.2385i	−1.47215	−	0.849949i	−0.999510	+	0.0313045i	$0.990034\pi$
$954$	−59.4622	−	102.992i	−1.92516	−	3.33447i
$955$		0			0
$956$	10.5991	+	18.3582i	0.342799	+	0.593746i
$957$			53.7002i			1.73588i
$958$		−	24.7051i		−	0.798185i
$959$	2.41109	+	4.17614i	0.0778583	+	0.134854i
$960$		0			0
$961$	15.4335			0.497854
$962$		−	71.9040i		−	2.31828i
$963$	22.3520	−	12.9050i	0.720284	−	0.415856i
$964$	37.0349	−	64.1464i	1.19281	−	2.06602i
$965$		0			0
$966$	−5.49795	+	9.52273i	−0.176894	+	0.306389i
$967$	−13.2278	−	7.63706i	−0.425376	−	0.245591i	0.271999	−	0.962298i	$-0.412315\pi$
$967$	−13.2278	−	7.63706i	−0.425376	−	0.245591i	−0.697375	+	0.716707i	$0.745649\pi$
$968$			6.68203i			0.214769i
$969$	67.3508	+	1.52290i	2.16362	+	0.0489227i
$970$		0			0
$971$	−26.3376	+	45.6181i	−0.845215	+	1.46396i	0.0402194	+	0.999191i	$0.487194\pi$
$971$	−26.3376	+	45.6181i	−0.845215	+	1.46396i	−0.885434	+	0.464764i	$0.846139\pi$
$972$	11.3341	+	6.54375i	0.363542	+	0.209891i
$973$	8.00714	−	4.62292i	0.256697	−	0.148204i
$974$	5.17634	−	8.96568i	0.165861	−	0.287279i
$975$		0			0
$976$	−4.84618			−0.155123
$977$			56.5695i			1.80982i	0.425605	+	0.904909i	$0.360061\pi$
$977$			56.5695i			1.80982i	−0.425605	+	0.904909i	$0.639939\pi$
$978$	−57.2119	+	33.0313i	−1.82944	+	1.05623i
$979$	4.79508	+	8.30532i	0.153251	+	0.265439i
$980$		0			0
$981$	−61.1883			−1.95359
$982$	−9.42176	+	5.43965i	−0.300660	+	0.173586i
$983$	53.4806	+	30.8770i	1.70577	+	0.984825i	0.939659	+	0.342111i	$0.111142\pi$
$983$	53.4806	+	30.8770i	1.70577	+	0.984825i	0.766107	+	0.642713i	$0.222191\pi$
$984$	14.1493	+	24.5073i	0.451064	+	0.781265i
$985$		0			0
$986$	40.0504	−	69.3694i	1.27547	−	2.20917i
$987$			4.46869i			0.142240i
$988$	−71.1258	+	38.9478i	−2.26281	+	1.23909i
$989$	−12.6510			−0.402278
$990$		0			0
$991$	28.5967	−	49.5310i	0.908404	−	1.57340i	0.0921233	−	0.995748i	$-0.470635\pi$
$991$	28.5967	−	49.5310i	0.908404	−	1.57340i	0.816281	−	0.577655i	$-0.196032\pi$
$992$	44.7827	−	25.8553i	1.42185	−	0.820906i
$993$	8.32929	+	4.80892i	0.264322	+	0.152606i
$994$	−8.66154	−	15.0022i	−0.274727	−	0.475842i
$995$		0			0
$996$	−32.1526			−1.01879
$997$	−26.7761	+	15.4592i	−0.848007	+	0.489597i	−0.859978	−	0.510332i	$-0.829523\pi$
$997$	−26.7761	+	15.4592i	−0.848007	+	0.489597i	0.0119712	+	0.999928i	$0.496189\pi$
$998$	−41.0118	+	23.6782i	−1.29820	+	0.749519i
$999$	38.6521			1.22290

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.j.d.49.2		24
5.2	odd	4		475.2.e.h.201.6	yes	12
5.3	odd	4		475.2.e.f.201.1	yes	12
5.4	even	2	inner	475.2.j.d.49.11		24
19.7	even	3	inner	475.2.j.d.349.11		24
95.7	odd	12		475.2.e.h.26.6	yes	12
95.8	even	12		9025.2.a.bs.1.1		6
95.27	even	12		9025.2.a.by.1.6		6
95.64	even	6	inner	475.2.j.d.349.2		24
95.68	odd	12		9025.2.a.bz.1.6		6
95.83	odd	12		475.2.e.f.26.1	✓	12
95.87	odd	12		9025.2.a.br.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.e.f.26.1	✓	12	95.83	odd	12
475.2.e.f.201.1	yes	12	5.3	odd	4
475.2.e.h.26.6	yes	12	95.7	odd	12
475.2.e.h.201.6	yes	12	5.2	odd	4
475.2.j.d.49.2		24	1.1	even	1	trivial
475.2.j.d.49.11		24	5.4	even	2	inner
475.2.j.d.349.2		24	95.64	even	6	inner
475.2.j.d.349.11		24	19.7	even	3	inner
9025.2.a.br.1.1		6	95.87	odd	12
9025.2.a.bs.1.1		6	95.8	even	12
9025.2.a.by.1.6		6	95.27	even	12
9025.2.a.bz.1.6		6	95.68	odd	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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.87935 - 1.08504i) q^{2} +(2.55640 + 1.47594i) q^{3} +(1.35464 + 2.34630i) q^{4} +(-3.20292 - 5.54761i) q^{6} +0.591620i q^{7} -1.53919i q^{8} +(2.85679 + 4.94811i) q^{9} +O(q^{10})\)	\(q+(-1.87935 - 1.08504i) q^{2} +(2.55640 + 1.47594i) q^{3} +(1.35464 + 2.34630i) q^{4} +(-3.20292 - 5.54761i) q^{6} +0.591620i q^{7} -1.53919i q^{8} +(2.85679 + 4.94811i) q^{9} +2.58045 q^{11} +7.99745i q^{12} +(-5.94669 + 3.43332i) q^{13} +(0.641933 - 1.11186i) q^{14} +(1.03919 - 1.79993i) q^{16} +(4.53429 + 2.61787i) q^{17} -12.3990i q^{18} +(2.26423 - 3.72468i) q^{19} +(-0.873195 + 1.51242i) q^{21} +(-4.84957 - 2.79990i) q^{22} +(-2.51271 + 1.45072i) q^{23} +(2.27175 - 3.93478i) q^{24} +14.9012 q^{26} +8.01017i q^{27} +(-1.38812 + 0.801431i) q^{28} +(3.52494 + 6.10538i) q^{29} -6.81421 q^{31} +(-6.57195 + 3.79432i) q^{32} +(6.59667 + 3.80859i) q^{33} +(-5.68101 - 9.83980i) q^{34} +(-7.73984 + 13.4058i) q^{36} -4.82538i q^{37} +(-8.29672 + 4.54320i) q^{38} -20.2695 q^{39} +(-3.11419 + 5.39393i) q^{41} +(3.28208 - 1.89491i) q^{42} +(3.77609 + 2.18013i) q^{43} +(3.49558 + 6.05452i) q^{44} +6.29636 q^{46} +(2.21600 - 1.27941i) q^{47} +(5.31317 - 3.06756i) q^{48} +6.64999 q^{49} +(7.72764 + 13.3847i) q^{51} +(-16.1112 - 9.30181i) q^{52} +(8.30645 - 4.79573i) q^{53} +(8.69138 - 15.0539i) q^{54} +0.910615 q^{56} +(11.2857 - 6.17993i) q^{57} -15.2989i q^{58} +(-1.46221 + 2.53263i) q^{59} +(-1.16586 - 2.01932i) q^{61} +(12.8063 + 7.39371i) q^{62} +(-2.92740 + 1.69013i) q^{63} +12.3112 q^{64} +(-8.26497 - 14.3153i) q^{66} +(3.72603 - 2.15122i) q^{67} +14.1851i q^{68} -8.56468 q^{69} +(6.74645 - 11.6852i) q^{71} +(7.61607 - 4.39714i) q^{72} +(-7.29777 - 4.21337i) q^{73} +(-5.23574 + 9.06858i) q^{74} +(11.8064 + 0.266962i) q^{76} +1.52665i q^{77} +(38.0935 + 21.9933i) q^{78} +(2.93630 - 5.08583i) q^{79} +(-3.25215 + 5.63288i) q^{81} +(11.7053 - 6.75806i) q^{82} +4.02036i q^{83} -4.73145 q^{84} +(-4.73107 - 8.19445i) q^{86} +20.8104i q^{87} -3.97180i q^{88} +(1.85823 + 3.21855i) q^{89} +(-2.03122 - 3.51818i) q^{91} +(-6.80764 - 3.93039i) q^{92} +(-17.4199 - 10.0574i) q^{93} -5.55285 q^{94} -22.4007 q^{96} +(-2.18732 - 1.26285i) q^{97} +(-12.4977 - 7.21552i) q^{98} +(7.37182 + 12.7684i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} + 2 q^{6} + 14 q^{9}+O(q^{10}) \) 24 * q + 4 * q^4 + 2 * q^6 + 14 * q^9	\( 24 q + 4 q^{4} + 2 q^{6} + 14 q^{9} - 4 q^{11} - 12 q^{14} + 12 q^{16} + 12 q^{19} - 6 q^{21} + 22 q^{24} + 76 q^{26} + 6 q^{29} - 12 q^{31} - 2 q^{34} - 26 q^{36} - 32 q^{39} - 22 q^{41} + 42 q^{44} - 48 q^{46} - 16 q^{49} + 34 q^{51} + 36 q^{54} + 16 q^{56} + 8 q^{59} - 50 q^{61} + 88 q^{64} - 68 q^{66} - 52 q^{69} - 36 q^{71} - 12 q^{74} + 48 q^{76} + 6 q^{79} - 4 q^{81} - 148 q^{84} - 18 q^{86} + 24 q^{89} + 22 q^{91} - 32 q^{94} - 52 q^{96} - 40 q^{99}+O(q^{100}) \) 24 * q + 4 * q^4 + 2 * q^6 + 14 * q^9 - 4 * q^11 - 12 * q^14 + 12 * q^16 + 12 * q^19 - 6 * q^21 + 22 * q^24 + 76 * q^26 + 6 * q^29 - 12 * q^31 - 2 * q^34 - 26 * q^36 - 32 * q^39 - 22 * q^41 + 42 * q^44 - 48 * q^46 - 16 * q^49 + 34 * q^51 + 36 * q^54 + 16 * q^56 + 8 * q^59 - 50 * q^61 + 88 * q^64 - 68 * q^66 - 52 * q^69 - 36 * q^71 - 12 * q^74 + 48 * q^76 + 6 * q^79 - 4 * q^81 - 148 * q^84 - 18 * q^86 + 24 * q^89 + 22 * q^91 - 32 * q^94 - 52 * q^96 - 40 * q^99

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