LMFDB - Embedded newform 475.2.e.e.26.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [475,2,Mod(26,475)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("475.26"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(475, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.4601315889.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 $ x^8 - x^7 + 6x^6 - 3x^5 + 26x^4 - 14x^3 + 31x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			26.1
Root			$1.07988 + 1.87040i$ of defining polynomial
Character	$\chi$	$=$	475.26
Dual form			475.2.e.e.201.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.832272 - 1.44154i) q^{2} +(-0.579878 - 1.00438i) q^{3} +(-0.385355 + 0.667454i) q^{4} +(-0.965233 + 1.67183i) q^{6} +2.43525 q^{7} -2.04621 q^{8} +(0.827483 - 1.43324i) q^{9} -5.75477 q^{11} +0.893835 q^{12} +(-0.797505 + 1.38132i) q^{13} +(-2.02680 - 3.51051i) q^{14} +(2.47371 + 4.28460i) q^{16} +(-2.99203 - 5.18234i) q^{17} -2.75477 q^{18} +(0.149412 - 4.35634i) q^{19} +(-1.41215 - 2.44592i) q^{21} +(4.78953 + 8.29572i) q^{22} +(-0.470022 + 0.814102i) q^{23} +(1.18655 + 2.05517i) q^{24} +2.65497 q^{26} -5.39862 q^{27} +(-0.938437 + 1.62542i) q^{28} +(-1.30917 + 2.26755i) q^{29} -5.26913 q^{31} +(2.07140 - 3.58777i) q^{32} +(3.33706 + 5.77996i) q^{33} +(-4.98037 + 8.62625i) q^{34} +(0.637749 + 1.10461i) q^{36} +2.89384 q^{37} +(-6.40418 + 3.41028i) q^{38} +1.84982 q^{39} +(3.15767 + 5.46925i) q^{41} +(-2.35059 + 4.07134i) q^{42} +(2.26961 + 3.93108i) q^{43} +(2.21763 - 3.84104i) q^{44} +1.56475 q^{46} +(4.47718 - 7.75471i) q^{47} +(2.86890 - 4.96909i) q^{48} -1.06953 q^{49} +(-3.47002 + 6.01025i) q^{51} +(-0.614645 - 1.06460i) q^{52} +(-1.09819 + 1.90213i) q^{53} +(4.49313 + 7.78232i) q^{54} -4.98304 q^{56} +(-4.46205 + 2.37608i) q^{57} +4.35834 q^{58} +(5.39939 + 9.35202i) q^{59} +(5.26434 - 9.11811i) q^{61} +(4.38535 + 7.59566i) q^{62} +(2.01513 - 3.49031i) q^{63} +2.99898 q^{64} +(5.55469 - 9.62100i) q^{66} +(0.504789 - 0.874320i) q^{67} +4.61197 q^{68} +1.09022 q^{69} +(-4.41694 - 7.65036i) q^{71} +(-1.69320 + 2.93271i) q^{72} +(-5.12499 - 8.87674i) q^{73} +(-2.40846 - 4.17157i) q^{74} +(2.85008 + 1.77846i) q^{76} -14.0143 q^{77} +(-1.53956 - 2.66659i) q^{78} +(-3.80229 - 6.58577i) q^{79} +(0.648093 + 1.12253i) q^{81} +(5.25609 - 9.10381i) q^{82} -3.11355 q^{83} +2.17672 q^{84} +(3.77787 - 6.54346i) q^{86} +3.03663 q^{87} +11.7755 q^{88} +(5.55706 - 9.62511i) q^{89} +(-1.94213 + 3.36387i) q^{91} +(-0.362251 - 0.627436i) q^{92} +(3.05545 + 5.29220i) q^{93} -14.9049 q^{94} -4.80463 q^{96} +(2.02888 + 3.51412i) q^{97} +(0.890144 + 1.54177i) q^{98} +(-4.76197 + 8.24798i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 3 q^{3} - 5 q^{4} - 2 q^{6} + 8 q^{7} - 24 q^{8} - q^{9} - 4 q^{11} - 12 q^{12} + 7 q^{13} + q^{14} - 7 q^{16} - q^{17} + 20 q^{18} + 5 q^{19} + 4 q^{21} + 2 q^{22} + 2 q^{23} - 23 q^{24}+ \cdots - 38 q^{99}+O(q^{100}) $ 8 * q + q^2 + 3 * q^3 - 5 * q^4 - 2 * q^6 + 8 * q^7 - 24 * q^8 - q^9 - 4 * q^11 - 12 * q^12 + 7 * q^13 + q^14 - 7 * q^16 - q^17 + 20 * q^18 + 5 * q^19 + 4 * q^21 + 2 * q^22 + 2 * q^23 - 23 * q^24 + 6 * q^26 - 24 * q^27 - 19 * q^28 + q^29 + 30 * q^32 + 19 * q^33 - 15 * q^34 + 7 * q^36 + 4 * q^37 - 13 * q^38 + 30 * q^39 + 8 * q^41 - 15 * q^42 + q^43 + 12 * q^44 + 24 * q^46 - 12 * q^47 + 23 * q^48 - 20 * q^49 - 22 * q^51 - 3 * q^52 - 5 * q^53 + 34 * q^54 - 82 * q^56 - 7 * q^57 + 54 * q^58 + 5 * q^59 + 37 * q^62 - 3 * q^63 + 112 * q^64 + 31 * q^66 + 4 * q^67 - 32 * q^68 - 18 * q^69 - 20 * q^71 + 17 * q^72 - 20 * q^73 - 25 * q^74 + 63 * q^76 - 28 * q^77 - 18 * q^78 - 17 * q^79 - 12 * q^81 + 21 * q^82 - 2 * q^83 - 40 * q^84 - 8 * q^86 + 32 * q^87 + 14 * q^88 - 11 * q^89 - 6 * q^91 - q^92 - 8 * q^93 - 62 * q^94 + 42 * q^96 + q^97 + 9 * q^98 - 38 * q^99

Character values

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

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

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 $

$2$	−0.832272	−	1.44154i	−0.588506	−	1.01932i	−0.994428	−	0.105414i	$-0.966383\pi$
$2$	−0.832272	−	1.44154i	−0.588506	−	1.01932i	0.405923	−	0.913907i	$-0.366950\pi$
$3$	−0.579878	−	1.00438i	−0.334793	−	0.579878i	0.648652	−	0.761085i	$-0.275333\pi$
$3$	−0.579878	−	1.00438i	−0.334793	−	0.579878i	−0.983445	+	0.181207i	$0.942000\pi$
$4$	−0.385355	+	0.667454i	−0.192677	+	0.333727i
$5$		0			0
$5$		0			0
$6$	−0.965233	+	1.67183i	−0.394055	+	0.682523i
$7$	2.43525			0.920440			0.460220	−	0.887805i	$-0.347771\pi$
$7$	2.43525			0.920440			0.460220	+	0.887805i	$0.347771\pi$
$8$	−2.04621			−0.723444
$9$	0.827483	−	1.43324i	0.275828	−	0.477748i
$10$		0			0
$11$	−5.75477			−1.73513			−0.867564	−	0.497326i	$-0.834315\pi$
$11$	−5.75477			−1.73513			−0.867564	+	0.497326i	$0.834315\pi$
$12$	0.893835			0.258028
$13$	−0.797505	+	1.38132i	−0.221188	+	0.383109i	−0.955169	−	0.296061i	$-0.904327\pi$
$13$	−0.797505	+	1.38132i	−0.221188	+	0.383109i	0.733981	+	0.679170i	$0.237660\pi$
$14$	−2.02680	−	3.51051i	−0.541684	−	0.938224i
$15$		0			0
$16$	2.47371	+	4.28460i	0.618428	+	1.07115i
$17$	−2.99203	−	5.18234i	−0.725673	−	1.25690i	−0.958696	−	0.284432i	$-0.908195\pi$
$17$	−2.99203	−	5.18234i	−0.725673	−	1.25690i	0.233023	−	0.972471i	$-0.425138\pi$
$18$	−2.75477			−0.649305
$19$	0.149412	−	4.35634i	0.0342775	−	0.999412i
$19$	0.149412	−	4.35634i	0.0342775	−	0.999412i
$20$		0			0
$21$	−1.41215	−	2.44592i	−0.308156	−	0.533743i
$22$	4.78953	+	8.29572i	1.02113	+	1.76865i
$23$	−0.470022	+	0.814102i	−0.0980064	+	0.169752i	−0.910859	−	0.412717i	$-0.864580\pi$
$23$	−0.470022	+	0.814102i	−0.0980064	+	0.169752i	0.812853	+	0.582469i	$0.197913\pi$
$24$	1.18655	+	2.05517i	0.242204	+	0.419509i
$25$		0			0
$26$	2.65497			0.520682
$27$	−5.39862			−1.03897
$28$	−0.938437	+	1.62542i	−0.177348	+	0.307176i
$29$	−1.30917	+	2.26755i	−0.243106	+	0.421073i	−0.961598	−	0.274463i	$-0.911500\pi$
$29$	−1.30917	+	2.26755i	−0.243106	+	0.421073i	0.718491	+	0.695536i	$0.244833\pi$
$30$		0			0
$31$	−5.26913			−0.946364			−0.473182	−	0.880965i	$-0.656895\pi$
$31$	−5.26913			−0.946364			−0.473182	+	0.880965i	$0.656895\pi$
$32$	2.07140	−	3.58777i	0.366175	−	0.634233i
$33$	3.33706	+	5.77996i	0.580908	+	1.00616i
$34$	−4.98037	+	8.62625i	−0.854126	+	1.47939i
$35$		0			0
$36$	0.637749	+	1.10461i	0.106292	+	0.184102i
$37$	2.89384			0.475744			0.237872	−	0.971297i	$-0.423550\pi$
$37$	2.89384			0.475744			0.237872	+	0.971297i	$0.423550\pi$
$38$	−6.40418	+	3.41028i	−1.03889	+	0.553220i
$39$	1.84982			0.296209
$40$		0			0
$41$	3.15767	+	5.46925i	0.493145	+	0.854153i	0.999969	−	0.00789701i	$-0.00251372\pi$
$41$	3.15767	+	5.46925i	0.493145	+	0.854153i	−0.506823	+	0.862050i	$0.669180\pi$
$42$	−2.35059	+	4.07134i	−0.362704	+	0.628221i
$43$	2.26961	+	3.93108i	0.346113	+	0.599485i	0.985555	−	0.169354i	$-0.0541682\pi$
$43$	2.26961	+	3.93108i	0.346113	+	0.599485i	−0.639443	+	0.768839i	$0.720835\pi$
$44$	2.21763	−	3.84104i	0.334320	−	0.579059i
$45$		0			0
$46$	1.56475			0.230709
$47$	4.47718	−	7.75471i	0.653064	−	1.13114i	−0.329311	−	0.944221i	$-0.606816\pi$
$47$	4.47718	−	7.75471i	0.653064	−	1.13114i	0.982375	−	0.186919i	$-0.0598502\pi$
$48$	2.86890	−	4.96909i	0.414090	−	0.717226i
$49$	−1.06953			−0.152791
$50$		0			0
$51$	−3.47002	+	6.01025i	−0.485900	+	0.841604i
$52$	−0.614645	−	1.06460i	−0.0852359	−	0.147633i
$53$	−1.09819	+	1.90213i	−0.150848	+	0.261277i	−0.931540	−	0.363640i	$-0.881534\pi$
$53$	−1.09819	+	1.90213i	−0.150848	+	0.261277i	0.780691	+	0.624917i	$0.214867\pi$
$54$	4.49313	+	7.78232i	0.611437	+	1.05904i
$55$		0			0
$56$	−4.98304			−0.665887
$57$	−4.46205	+	2.37608i	−0.591013	+	0.314719i
$58$	4.35834			0.572278
$59$	5.39939	+	9.35202i	0.702941	+	1.21753i	0.967430	+	0.253140i	$0.0814634\pi$
$59$	5.39939	+	9.35202i	0.702941	+	1.21753i	−0.264489	+	0.964389i	$0.585203\pi$
$60$		0			0
$61$	5.26434	−	9.11811i	0.674030	−	1.16745i	−0.302721	−	0.953079i	$-0.597895\pi$
$61$	5.26434	−	9.11811i	0.674030	−	1.16745i	0.976751	−	0.214375i	$-0.0687716\pi$
$62$	4.38535	+	7.59566i	0.556941	+	0.964649i
$63$	2.01513	−	3.49031i	0.253883	−	0.439738i
$64$	2.99898			0.374873
$65$		0			0
$66$	5.55469	−	9.62100i	0.683735	−	1.18426i
$67$	0.504789	−	0.874320i	0.0616698	−	0.106815i	−0.833542	−	0.552456i	$-0.813691\pi$
$67$	0.504789	−	0.874320i	0.0616698	−	0.106815i	0.895212	+	0.445641i	$0.147024\pi$
$68$	4.61197			0.559284
$69$	1.09022			0.131247
$70$		0			0
$71$	−4.41694	−	7.65036i	−0.524194	−	0.907931i	−0.999603	−	0.0281662i	$-0.991033\pi$
$71$	−4.41694	−	7.65036i	−0.524194	−	0.907931i	0.475409	−	0.879765i	$-0.342300\pi$
$72$	−1.69320	+	2.93271i	−0.199546	+	0.345624i
$73$	−5.12499	−	8.87674i	−0.599835	−	1.03894i	−0.992845	−	0.119410i	$-0.961900\pi$
$73$	−5.12499	−	8.87674i	−0.599835	−	1.03894i	0.393011	−	0.919534i	$-0.371434\pi$
$74$	−2.40846	−	4.17157i	−0.279978	−	0.484936i
$75$		0			0
$76$	2.85008	+	1.77846i	0.326927	+	0.204004i
$77$	−14.0143			−1.59708
$78$	−1.53956	−	2.66659i	−0.174320	−	0.301932i
$79$	−3.80229	−	6.58577i	−0.427792	−	0.740957i	0.568885	−	0.822417i	$-0.307375\pi$
$79$	−3.80229	−	6.58577i	−0.427792	−	0.740957i	−0.996677	+	0.0814604i	$0.974042\pi$
$80$		0			0
$81$	0.648093	+	1.12253i	0.0720103	+	0.124726i
$82$	5.25609	−	9.10381i	0.580438	−	1.00535i
$83$	−3.11355			−0.341756			−0.170878	−	0.985292i	$-0.554660\pi$
$83$	−3.11355			−0.341756			−0.170878	+	0.985292i	$0.554660\pi$
$84$	2.17672			0.237499
$85$		0			0
$86$	3.77787	−	6.54346i	0.407378	−	0.705600i
$87$	3.03663			0.325561
$88$	11.7755			1.25527
$89$	5.55706	−	9.62511i	0.589047	−	1.02026i	−0.405310	−	0.914179i	$-0.632837\pi$
$89$	5.55706	−	9.62511i	0.589047	−	1.02026i	0.994358	−	0.106081i	$-0.0338302\pi$
$90$		0			0
$91$	−1.94213	+	3.36387i	−0.203590	+	0.352629i
$92$	−0.362251	−	0.627436i	−0.0377672	−	0.0654148i
$93$	3.05545	+	5.29220i	0.316836	+	0.548776i
$94$	−14.9049			−1.53733
$95$		0			0
$96$	−4.80463			−0.490371
$97$	2.02888	+	3.51412i	0.206002	+	0.356805i	0.950451	−	0.310873i	$-0.100621\pi$
$97$	2.02888	+	3.51412i	0.206002	+	0.356805i	−0.744450	+	0.667678i	$0.767288\pi$
$98$	0.890144	+	1.54177i	0.0899181	+	0.155743i
$99$	−4.76197	+	8.24798i	−0.478596	+	0.828953i
$100$		0			0
$101$	5.56503	−	9.63892i	0.553741	−	0.959108i	−0.444259	−	0.895898i	$-0.646533\pi$
$101$	5.56503	−	9.63892i	0.553741	−	0.959108i	0.998000	−	0.0632098i	$-0.0201337\pi$
$102$	11.5520			1.14382
$103$	−11.5791			−1.14092			−0.570460	−	0.821326i	$-0.693235\pi$
$103$	−11.5791			−1.14092			−0.570460	+	0.821326i	$0.693235\pi$
$104$	1.63186	−	2.82647i	0.160017	−	0.277158i
$105$		0			0
$106$	3.65598			0.355101
$107$	−17.9177			−1.73217			−0.866086	−	0.499894i	$-0.833372\pi$
$107$	−17.9177			−1.73217			−0.866086	+	0.499894i	$0.833372\pi$
$108$	2.08039	−	3.60333i	0.200185	−	0.346731i
$109$	−2.81235	−	4.87113i	−0.269374	−	0.466570i	0.699326	−	0.714803i	$-0.253484\pi$
$109$	−2.81235	−	4.87113i	−0.269374	−	0.466570i	−0.968700	+	0.248233i	$0.920150\pi$
$110$		0			0
$111$	−1.67807	−	2.90650i	−0.159275	−	0.275873i
$112$	6.02412	+	10.4341i	0.569226	+	0.985928i
$113$	15.6789			1.47494			0.737472	−	0.675378i	$-0.236019\pi$
$113$	15.6789			1.47494			0.737472	+	0.675378i	$0.236019\pi$
$114$	7.13885	+	4.45467i	0.668614	+	0.417218i
$115$		0			0
$116$	−1.00899	−	1.74762i	−0.0936822	−	0.162262i
$117$	1.31984	+	2.28604i	0.122020	+	0.211344i
$118$	8.98753	−	15.5669i	0.827369	−	1.43304i
$119$	−7.28635	−	12.6203i	−0.667939	−	1.15690i
$120$		0			0
$121$	22.1173			2.01067
$122$	−17.5255			−1.58668
$123$	3.66213	−	6.34299i	0.330203	−	0.571928i
$124$	2.03049	−	3.51691i	0.182343	−	0.315827i
$125$		0			0
$126$	−6.70856			−0.597646
$127$	3.05996	−	5.30000i	0.271527	−	0.470299i	−0.697726	−	0.716365i	$-0.745805\pi$
$127$	3.05996	−	5.30000i	0.271527	−	0.470299i	0.969253	+	0.246066i	$0.0791380\pi$
$128$	−6.63877	−	11.4987i	−0.586790	−	1.01635i
$129$	2.63220	−	4.55910i	0.231752	−	0.401406i
$130$		0			0
$131$	7.44055	+	12.8874i	0.650084	+	1.12598i	0.983102	+	0.183058i	$0.0585997\pi$
$131$	7.44055	+	12.8874i	0.650084	+	1.12598i	−0.333018	+	0.942920i	$0.608067\pi$
$132$	−5.14381			−0.447711
$133$	0.363857	−	10.6088i	0.0315504	−	0.919899i
$134$	−1.68049			−0.145172
$135$		0			0
$136$	6.12231	+	10.6042i	0.524984	+	0.909299i
$137$	8.67518	−	15.0258i	0.741170	−	1.28374i	−0.210793	−	0.977531i	$-0.567604\pi$
$137$	8.67518	−	15.0258i	0.741170	−	1.28374i	0.951963	−	0.306214i	$-0.0990622\pi$
$138$	−0.907361	−	1.57160i	−0.0772397	−	0.133783i
$139$	3.35267	−	5.80700i	0.284370	−	0.492543i	−0.688086	−	0.725629i	$-0.741549\pi$
$139$	3.35267	−	5.80700i	0.284370	−	0.492543i	0.972456	+	0.233086i	$0.0748823\pi$
$140$		0			0
$141$	−10.3849			−0.874564
$142$	−7.35219	+	12.7344i	−0.616982	+	1.06864i
$143$	4.58946	−	7.94917i	0.383790	−	0.664743i
$144$	8.18782			0.682319
$145$		0			0
$146$	−8.53077	+	14.7757i	−0.706012	+	1.22285i
$147$	0.620199	+	1.07422i	0.0511532	+	0.0885999i
$148$	−1.11515	+	1.93150i	−0.0916651	+	0.158769i
$149$	−7.19642	−	12.4646i	−0.589553	−	1.02114i	−0.994291	−	0.106704i	$-0.965970\pi$
$149$	−7.19642	−	12.4646i	−0.589553	−	1.02114i	0.404737	−	0.914433i	$-0.367363\pi$
$150$		0			0
$151$	12.7219			1.03529			0.517645	−	0.855595i	$-0.326809\pi$
$151$	12.7219			1.03529			0.517645	+	0.855595i	$0.326809\pi$
$152$	−0.305729	+	8.91398i	−0.0247979	+	0.723019i
$153$	−9.90341			−0.800644
$154$	11.6637	+	20.2022i	0.939890	+	1.62794i
$155$		0			0
$156$	−0.712838	+	1.23467i	−0.0570727	+	0.0988529i
$157$	−1.68765	−	2.92309i	−0.134689	−	0.233288i	0.790790	−	0.612088i	$-0.209670\pi$
$157$	−1.68765	−	2.92309i	−0.134689	−	0.233288i	−0.925479	+	0.378800i	$0.876337\pi$
$158$	−6.32909	+	10.9623i	−0.503515	+	0.872114i
$159$	2.54727			0.202012
$160$		0			0
$161$	−1.14462	+	1.98255i	−0.0902089	+	0.156246i
$162$	1.07878	−	1.86850i	0.0847569	−	0.146803i
$163$	−0.307960			−0.0241213			−0.0120607	−	0.999927i	$-0.503839\pi$
$163$	−0.307960			−0.0241213			−0.0120607	+	0.999927i	$0.503839\pi$
$164$	−4.86730			−0.380072
$165$		0			0
$166$	2.59132	+	4.48830i	0.201125	+	0.348359i
$167$	7.13215	−	12.3532i	0.551902	−	0.955923i	−0.446235	−	0.894916i	$-0.647235\pi$
$167$	7.13215	−	12.3532i	0.551902	−	0.955923i	0.998137	−	0.0610070i	$-0.0194312\pi$
$168$	2.88955	+	5.00486i	0.222934	+	0.386133i
$169$	5.22797	+	9.05511i	0.402152	+	0.696547i
$170$		0			0
$171$	−6.12005	−	3.81894i	−0.468012	−	0.292042i
$172$	−3.49842			−0.266752
$173$	6.67357	+	11.5590i	0.507382	+	0.878811i	0.999963	+	0.00854514i	$0.00272003\pi$
$173$	6.67357	+	11.5590i	0.507382	+	0.878811i	−0.492581	+	0.870266i	$0.663947\pi$
$174$	−2.52730	−	4.37742i	−0.191594	−	0.331851i
$175$		0			0
$176$	−14.2356	−	24.6569i	−1.07305	−	1.85858i
$177$	6.26197	−	10.8461i	0.470679	−	0.815239i
$178$	−18.5000			−1.38663
$179$	−14.2207			−1.06291			−0.531454	−	0.847087i	$-0.678354\pi$
$179$	−14.2207			−1.06291			−0.531454	+	0.847087i	$0.678354\pi$
$180$		0			0
$181$	−4.94132	+	8.55861i	−0.367285	+	0.636157i	−0.989140	−	0.146976i	$-0.953046\pi$
$181$	−4.94132	+	8.55861i	−0.367285	+	0.636157i	0.621855	+	0.783133i	$0.286379\pi$
$182$	6.46552			0.479256
$183$	−12.2107			−0.902641
$184$	0.961763	−	1.66582i	0.0709021	−	0.122806i
$185$		0			0
$186$	5.08594	−	8.80911i	0.372919	−	0.645915i
$187$	17.2184	+	29.8232i	1.25914	+	2.18089i
$188$	3.45061	+	5.97663i	0.251661	+	0.435891i
$189$	−13.1470			−0.956305
$190$		0			0
$191$	−12.9942			−0.940228			−0.470114	−	0.882606i	$-0.655787\pi$
$191$	−12.9942			−0.940228			−0.470114	+	0.882606i	$0.655787\pi$
$192$	−1.73904	−	3.01211i	−0.125505	−	0.217380i
$193$	7.25795	+	12.5711i	0.522439	+	0.904890i	0.999659	+	0.0261066i	$0.00831094\pi$
$193$	7.25795	+	12.5711i	0.522439	+	0.904890i	−0.477221	+	0.878784i	$0.658356\pi$
$194$	3.37716	−	5.84942i	0.242466	−	0.419964i
$195$		0			0
$196$	0.412150	−	0.713865i	0.0294393	−	0.0509904i
$197$	25.0010			1.78125			0.890624	−	0.454740i	$-0.150268\pi$
$197$	25.0010			1.78125			0.890624	+	0.454740i	$0.150268\pi$
$198$	15.8530			1.12663
$199$	1.12769	−	1.95322i	0.0799401	−	0.138460i	−0.823284	−	0.567630i	$-0.807860\pi$
$199$	1.12769	−	1.95322i	0.0799401	−	0.138460i	0.903224	+	0.429170i	$0.141194\pi$
$200$		0			0
$201$	−1.17086			−0.0825864
$202$	−18.5265			−1.30352
$203$	−3.18816	+	5.52205i	−0.223765	+	0.387572i
$204$	−2.67438	−	4.63216i	−0.187244	−	0.324316i
$205$		0			0
$206$	9.63694	+	16.6917i	0.671437	+	1.16296i
$207$	0.777871	+	1.34731i	0.0540657	+	0.0936446i
$208$	−7.89120			−0.547156
$209$	−0.859833	+	25.0697i	−0.0594759	+	1.73411i
$210$		0			0
$211$	−11.1081	−	19.2397i	−0.764710	−	1.32452i	−0.940400	−	0.340071i	$-0.889549\pi$
$211$	−11.1081	−	19.2397i	−0.764710	−	1.32452i	0.175689	−	0.984446i	$-0.443785\pi$
$212$	−0.846388	−	1.46599i	−0.0581302	−	0.100684i
$213$	−5.12257	+	8.87255i	−0.350993	+	0.607937i
$214$	14.9124	+	25.8291i	1.01939	+	1.76564i
$215$		0			0
$216$	11.0467			0.751634
$217$	−12.8317			−0.871071
$218$	−4.68128	+	8.10822i	−0.317057	+	0.549158i
$219$	−5.94373	+	10.2949i	−0.401640	+	0.695662i
$220$		0			0
$221$	9.54463			0.642041
$222$	−2.79322	+	4.83801i	−0.187469	+	0.324706i
$223$	5.10799	+	8.84730i	0.342056	+	0.592459i	0.984814	−	0.173610i	$-0.0555432\pi$
$223$	5.10799	+	8.84730i	0.342056	+	0.592459i	−0.642758	+	0.766069i	$0.722210\pi$
$224$	5.04438	−	8.73712i	0.337042	−	0.583774i
$225$		0			0
$226$	−13.0491	−	22.6017i	−0.868012	−	1.50344i
$227$	−4.15180			−0.275565			−0.137782	−	0.990463i	$-0.543997\pi$
$227$	−4.15180			−0.275565			−0.137782	+	0.990463i	$0.543997\pi$
$228$	0.133550	−	3.89385i	0.00884456	−	0.257876i
$229$	6.53286			0.431703			0.215852	−	0.976426i	$-0.430747\pi$
$229$	6.53286			0.431703			0.215852	+	0.976426i	$0.430747\pi$
$230$		0			0
$231$	8.12660	+	14.0757i	0.534691	+	0.926111i
$232$	2.67883	−	4.63987i	0.175874	−	0.304623i
$233$	2.57410	+	4.45848i	0.168635	+	0.292084i	0.937940	−	0.346797i	$-0.112731\pi$
$233$	2.57410	+	4.45848i	0.168635	+	0.292084i	−0.769305	+	0.638882i	$0.779397\pi$
$234$	2.19694	−	3.80521i	0.143618	−	0.248755i
$235$		0			0
$236$	−8.32272			−0.541763
$237$	−4.40973	+	7.63788i	−0.286443	+	0.496134i
$238$	−12.1285	+	21.0071i	−0.786171	+	1.36169i
$239$	13.9962			0.905338			0.452669	−	0.891679i	$-0.350472\pi$
$239$	13.9962			0.905338			0.452669	+	0.891679i	$0.350472\pi$
$240$		0			0
$241$	−7.61285	+	13.1858i	−0.490387	+	0.849375i	−0.999939	−	0.0110652i	$-0.996478\pi$
$241$	−7.61285	+	13.1858i	−0.490387	+	0.849375i	0.509552	+	0.860440i	$0.329811\pi$
$242$	−18.4076	−	31.8830i	−1.18329	−	2.04952i
$243$	−7.34631	+	12.7242i	−0.471266	+	0.816256i
$244$	4.05728	+	7.02742i	0.259741	+	0.449884i
$245$		0			0
$246$	−12.1916			−0.777305
$247$	5.89834	+	3.68059i	0.375302	+	0.234190i
$248$	10.7817			0.684642
$249$	1.80548	+	3.12718i	0.114417	+	0.198177i
$250$		0			0
$251$	3.05630	−	5.29366i	0.192912	−	0.334133i	−0.753302	−	0.657674i	$-0.771540\pi$
$251$	3.05630	−	5.29366i	0.192912	−	0.334133i	0.946214	+	0.323542i	$0.104874\pi$
$252$	1.55308	+	2.69002i	0.0978350	+	0.169455i
$253$	2.70487	−	4.68497i	0.170053	−	0.294541i
$254$	−10.1869			−0.639181
$255$		0			0
$256$	−8.05154	+	13.9457i	−0.503221	+	0.871605i
$257$	0.0613414	−	0.106246i	0.00382637	−	0.00662747i	−0.864106	−	0.503310i	$-0.832115\pi$
$257$	0.0613414	−	0.106246i	0.00382637	−	0.00662747i	0.867932	+	0.496683i	$0.165449\pi$
$258$	−8.76281			−0.545549
$259$	7.04723			0.437893
$260$		0			0
$261$	2.16663	+	3.75271i	0.134111	+	0.232287i
$262$	12.3851	−	21.4517i	0.765156	−	1.32529i
$263$	−5.03027	−	8.71267i	−0.310179	−	0.537247i	0.668222	−	0.743962i	$-0.267056\pi$
$263$	−5.03027	−	8.71267i	−0.310179	−	0.537247i	−0.978401	+	0.206716i	$0.933722\pi$
$264$	−6.82832	−	11.8270i	−0.420254	−	0.727902i
$265$		0			0
$266$	−15.5958	+	8.30489i	−0.956240	+	0.509206i
$267$	−12.8897			−0.788835
$268$	0.389046	+	0.673847i	0.0237648	+	0.0411618i
$269$	−2.85614	−	4.94698i	−0.174142	−	0.301623i	0.765722	−	0.643172i	$-0.222382\pi$
$269$	−2.85614	−	4.94698i	−0.174142	−	0.301623i	−0.939864	+	0.341549i	$0.889049\pi$
$270$		0			0
$271$	6.35560	+	11.0082i	0.386075	+	0.668702i	0.991918	−	0.126883i	$-0.0404972\pi$
$271$	6.35560	+	11.0082i	0.386075	+	0.668702i	−0.605843	+	0.795585i	$0.707164\pi$
$272$	14.8028	−	25.6393i	0.897554	−	1.55461i
$273$	4.50479			0.272642
$274$	−28.8804			−1.74473
$275$		0			0
$276$	−0.420122	+	0.727673i	−0.0252884	+	0.0438008i
$277$	−17.6019			−1.05760			−0.528799	−	0.848747i	$-0.677358\pi$
$277$	−17.6019			−1.05760			−0.528799	+	0.848747i	$0.677358\pi$
$278$	−11.1613			−0.669413
$279$	−4.36012	+	7.55195i	−0.261034	+	0.452123i
$280$		0			0
$281$	10.2502	−	17.7539i	0.611476	−	1.05911i	−0.379516	−	0.925185i	$-0.623910\pi$
$281$	10.2502	−	17.7539i	0.611476	−	1.05911i	0.990992	−	0.133922i	$-0.0427571\pi$
$282$	8.64305	+	14.9702i	0.514686	+	0.891462i
$283$	−5.92805	−	10.2677i	−0.352386	−	0.610350i	0.634281	−	0.773103i	$-0.281296\pi$
$283$	−5.92805	−	10.2677i	−0.352386	−	0.610350i	−0.986667	+	0.162752i	$0.947963\pi$
$284$	6.80836			0.404002
$285$		0			0
$286$	−15.2787			−0.903449
$287$	7.68973	+	13.3190i	0.453911	+	0.786196i
$288$	−3.42809	−	5.93763i	−0.202002	−	0.349878i
$289$	−9.40447	+	16.2890i	−0.553204	+	0.958177i
$290$		0			0
$291$	2.35301	−	4.07552i	0.137936	−	0.238911i
$292$	7.89976			0.462298
$293$	24.9814			1.45943			0.729715	−	0.683751i	$-0.239653\pi$
$293$	24.9814			1.45943			0.729715	+	0.683751i	$0.239653\pi$
$294$	1.03235	−	1.78808i	0.0602079	−	0.104283i
$295$		0			0
$296$	−5.92139			−0.344174
$297$	31.0678			1.80274
$298$	−11.9788	+	20.7478i	−0.693911	+	1.20189i
$299$	−0.749690	−	1.29850i	−0.0433557	−	0.0750943i
$300$		0			0
$301$	5.52708	+	9.57319i	0.318576	+	0.551789i
$302$	−10.5881	−	18.3391i	−0.609274	−	1.05529i
$303$	−12.9082			−0.741554
$304$	19.0348	−	10.1362i	1.09172	−	0.581348i
$305$		0			0
$306$	8.24234	+	14.2761i	0.471183	+	0.816113i
$307$	8.45997	+	14.6531i	0.482836	+	0.836296i	0.999806	−	0.0197074i	$-0.00627348\pi$
$307$	8.45997	+	14.6531i	0.482836	+	0.836296i	−0.516970	+	0.856003i	$0.672940\pi$
$308$	5.40049	−	9.35392i	0.307721	−	0.532989i
$309$	6.71444	+	11.6298i	0.381971	+	0.661594i
$310$		0			0
$311$	−15.2133			−0.862670			−0.431335	−	0.902192i	$-0.641957\pi$
$311$	−15.2133			−0.862670			−0.431335	+	0.902192i	$0.641957\pi$
$312$	−3.78512			−0.214290
$313$	12.4637	−	21.5877i	0.704488	−	1.22021i	−0.262389	−	0.964962i	$-0.584510\pi$
$313$	12.4637	−	21.5877i	0.704488	−	1.22021i	0.966876	−	0.255246i	$-0.0821564\pi$
$314$	−2.80917	+	4.86562i	−0.158531	+	0.274583i
$315$		0			0
$316$	5.86093			0.329703
$317$	−12.6152	+	21.8502i	−0.708541	+	1.22723i	0.256857	+	0.966449i	$0.417313\pi$
$317$	−12.6152	+	21.8502i	−0.708541	+	1.22723i	−0.965398	+	0.260780i	$0.916020\pi$
$318$	−2.12002	−	3.67199i	−0.118885	−	0.205915i
$319$	7.53396	−	13.0492i	0.421821	−	0.730615i
$320$		0			0
$321$	10.3901	+	17.9962i	0.579919	+	1.00445i
$322$	3.81055			0.212354
$323$	−23.0231	+	12.2600i	−1.28104	+	0.682163i
$324$	−0.998983			−0.0554991
$325$		0			0
$326$	0.256307	+	0.443937i	0.0141955	+	0.0245874i
$327$	−3.26164	+	5.64933i	−0.180369	+	0.312408i
$328$	−6.46125	−	11.1912i	−0.356763	−	0.617932i
$329$	10.9031	−	18.8847i	0.601106	−	1.04115i
$330$		0			0
$331$	−20.2063			−1.11064			−0.555320	−	0.831637i	$-0.687404\pi$
$331$	−20.2063			−1.11064			−0.555320	+	0.831637i	$0.687404\pi$
$332$	1.19982	−	2.07815i	0.0658487	−	0.114053i
$333$	2.39460	−	4.14757i	0.131223	−	0.227285i
$334$	−23.7436			−1.29919
$335$		0			0
$336$	6.98651	−	12.1010i	0.381145	−	0.660163i
$337$	−15.9123	−	27.5610i	−0.866800	−	1.50134i	−0.865249	−	0.501342i	$-0.832840\pi$
$337$	−15.9123	−	27.5610i	−0.866800	−	1.50134i	−0.00155051	−	0.999999i	$-0.500494\pi$
$338$	8.70219	−	15.0726i	0.473337	−	0.819843i
$339$	−9.09183	−	15.7475i	−0.493800	−	0.855287i
$340$		0			0
$341$	30.3226			1.64206
$342$	−0.411596	+	12.0007i	−0.0222566	+	0.648923i
$343$	−19.6514			−1.06107
$344$	−4.64410	−	8.04382i	−0.250393	−	0.433693i
$345$		0			0
$346$	11.1085	−	19.2404i	0.597194	−	1.03437i
$347$	−1.65128	−	2.86009i	−0.0886451	−	0.153538i	0.818294	−	0.574801i	$-0.194920\pi$
$347$	−1.65128	−	2.86009i	−0.0886451	−	0.153538i	−0.906939	+	0.421263i	$0.861587\pi$
$348$	−1.17018	+	2.02681i	−0.0627283	+	0.108649i
$349$	17.8486			0.955416			0.477708	−	0.878519i	$-0.341468\pi$
$349$	17.8486			0.955416			0.477708	+	0.878519i	$0.341468\pi$
$350$		0			0
$351$	4.30543	−	7.45723i	0.229807	−	0.398037i
$352$	−11.9204	+	20.6468i	−0.635360	+	1.10048i
$353$	8.29523			0.441511			0.220755	−	0.975329i	$-0.429148\pi$
$353$	8.29523			0.441511			0.220755	+	0.975329i	$0.429148\pi$
$354$	−20.8467			−1.10799
$355$		0			0
$356$	4.28288	+	7.41817i	0.226992	+	0.393162i
$357$	−8.45039	+	14.6365i	−0.447242	+	0.774646i
$358$	11.8355	+	20.4997i	0.625527	+	1.08344i
$359$	−4.17511	−	7.23150i	−0.220354	−	0.381664i	0.734562	−	0.678542i	$-0.237388\pi$
$359$	−4.17511	−	7.23150i	−0.220354	−	0.381664i	−0.954915	+	0.296878i	$0.904055\pi$
$360$		0			0
$361$	−18.9554	−	1.30178i	−0.997650	−	0.0685148i
$362$	16.4501			0.864598
$363$	−12.8254	−	22.2142i	−0.673156	−	1.16594i
$364$	−1.49682	−	2.59256i	−0.0784545	−	0.135887i
$365$		0			0
$366$	10.1626	+	17.6022i	0.531209	+	0.920082i
$367$	7.20988	−	12.4879i	0.376353	−	0.651862i	−0.614176	−	0.789169i	$-0.710511\pi$
$367$	7.20988	−	12.4879i	0.376353	−	0.651862i	0.990528	+	0.137307i	$0.0438448\pi$
$368$	−4.65080			−0.242440
$369$	10.4517			0.544093
$370$		0			0
$371$	−2.67438	+	4.63216i	−0.138847	+	0.240490i
$372$	−4.70974			−0.244188
$373$	24.1157			1.24866			0.624332	−	0.781159i	$-0.285371\pi$
$373$	24.1157			1.24866			0.624332	+	0.781159i	$0.285371\pi$
$374$	28.6608	−	49.6420i	1.48202	−	2.56693i
$375$		0			0
$376$	−9.16125	+	15.8678i	−0.472455	+	0.818317i
$377$	−2.08814	−	3.61676i	−0.107545	−	0.186273i
$378$	10.9419	+	18.9519i	0.562791	+	0.974783i
$379$	16.6757			0.856571			0.428285	−	0.903644i	$-0.359118\pi$
$379$	16.6757			0.856571			0.428285	+	0.903644i	$0.359118\pi$
$380$		0			0
$381$	−7.09760			−0.363621
$382$	10.8147	+	18.7316i	0.553329	+	0.958395i
$383$	−5.43895	−	9.42053i	−0.277917	−	0.481367i	0.692950	−	0.720986i	$-0.256311\pi$
$383$	−5.43895	−	9.42053i	−0.277917	−	0.481367i	−0.970867	+	0.239619i	$0.922977\pi$
$384$	−7.69935	+	13.3357i	−0.392906	+	0.680533i
$385$		0			0
$386$	12.0812	−	20.9252i	0.614916	−	1.06507i
$387$	7.51226			0.381870
$388$	−3.12736			−0.158767
$389$	−18.2272	+	31.5704i	−0.924154	+	1.60068i	−0.131237	+	0.991351i	$0.541895\pi$
$389$	−18.2272	+	31.5704i	−0.924154	+	1.60068i	−0.792917	+	0.609330i	$0.791438\pi$
$390$		0			0
$391$	5.62528			0.284482
$392$	2.18849			0.110535
$393$	8.62922	−	14.9463i	0.435287	−	0.753939i
$394$	−20.8077	−	36.0399i	−1.04827	−	1.81566i
$395$		0			0
$396$	−3.67010	−	6.35680i	−0.184429	−	0.319441i
$397$	4.29191	+	7.43380i	0.215405	+	0.373092i	0.953398	−	0.301717i	$-0.0975597\pi$
$397$	4.29191	+	7.43380i	0.215405	+	0.373092i	−0.737993	+	0.674808i	$0.764226\pi$
$398$	−3.75419			−0.188181
$399$	−10.8662	+	5.78635i	−0.543992	+	0.289680i
$400$		0			0
$401$	8.52785	+	14.7707i	0.425860	+	0.737612i	0.996500	−	0.0835885i	$-0.0266381\pi$
$401$	8.52785	+	14.7707i	0.425860	+	0.737612i	−0.570640	+	0.821200i	$0.693305\pi$
$402$	0.974478	+	1.68785i	0.0486026	+	0.0841821i
$403$	4.20216	−	7.27836i	0.209325	−	0.362561i
$404$	4.28903	+	7.42881i	0.213387	+	0.369597i
$405$		0			0
$406$	10.6137			0.526747
$407$	−16.6533			−0.825476
$408$	7.10039	−	12.2982i	0.351522	−	0.608853i
$409$	5.89702	−	10.2139i	0.291589	−	0.505047i	−0.682597	−	0.730795i	$-0.739149\pi$
$409$	5.89702	−	10.2139i	0.291589	−	0.505047i	0.974186	+	0.225749i	$0.0724828\pi$
$410$		0			0
$411$	−20.1222			−0.992553
$412$	4.46205	−	7.72850i	0.219829	−	0.380756i
$413$	13.1489	+	22.7745i	0.647015	+	1.12066i
$414$	1.29480	−	2.24266i	0.0636360	−	0.110221i
$415$		0			0
$416$	3.30390	+	5.72252i	0.161987	+	0.280570i
$417$	−7.77656			−0.380820
$418$	36.8546	−	19.6253i	1.80261	−	0.959907i
$419$	1.14280			0.0558292			0.0279146	−	0.999610i	$-0.491113\pi$
$419$	1.14280			0.0558292			0.0279146	+	0.999610i	$0.491113\pi$
$420$		0			0
$421$	−9.75944	−	16.9039i	−0.475646	−	0.823843i	0.523965	−	0.851740i	$-0.324452\pi$
$421$	−9.75944	−	16.9039i	−0.475646	−	0.823843i	−0.999611	+	0.0278967i	$0.991119\pi$
$422$	−18.4899	+	32.0254i	−0.900072	+	1.55897i
$423$	−7.40959	−	12.8338i	−0.360266	−	0.624000i
$424$	2.24713	−	3.89215i	0.109130	−	0.189019i
$425$		0			0
$426$	17.0535			0.826245
$427$	12.8200	−	22.2049i	0.620404	−	1.07457i
$428$	6.90469	−	11.9593i	0.333751	−	0.578073i
$429$	−10.6453			−0.513960
$430$		0			0
$431$	18.4392	−	31.9377i	0.888187	−	1.53838i	0.0461694	−	0.998934i	$-0.485299\pi$
$431$	18.4392	−	31.9377i	0.888187	−	1.53838i	0.842017	−	0.539451i	$-0.181368\pi$
$432$	−13.3546	−	23.1309i	−0.642526	−	1.11289i
$433$	0.184467	−	0.319506i	0.00886490	−	0.0153545i	−0.861559	−	0.507658i	$-0.830512\pi$
$433$	0.184467	−	0.319506i	0.00886490	−	0.0153545i	0.870424	+	0.492303i	$0.163845\pi$
$434$	10.6795	+	18.4974i	0.512630	+	0.887902i
$435$		0			0
$436$	4.33501			0.207609
$437$	3.47628	+	2.16921i	0.166293	+	0.103767i
$438$	19.7872			0.945470
$439$	1.13220	+	1.96102i	0.0540367	+	0.0935944i	0.891778	−	0.452472i	$-0.149458\pi$
$439$	1.13220	+	1.96102i	0.0540367	+	0.0935944i	−0.837742	+	0.546067i	$0.816125\pi$
$440$		0			0
$441$	−0.885022	+	1.53290i	−0.0421439	+	0.0729954i
$442$	−7.94373	−	13.7590i	−0.377845	−	0.654447i
$443$	−8.23137	+	14.2572i	−0.391084	+	0.677378i	−0.992593	−	0.121488i	$-0.961233\pi$
$443$	−8.23137	+	14.2572i	−0.391084	+	0.677378i	0.601508	+	0.798866i	$0.294567\pi$
$444$	2.58661			0.122755
$445$		0			0
$446$	8.50248	−	14.7267i	0.402604	−	0.697331i
$447$	−8.34609	+	14.4558i	−0.394756	+	0.683738i
$448$	7.30329			0.345048
$449$	14.1613			0.668315			0.334158	−	0.942517i	$-0.391548\pi$
$449$	14.1613			0.668315			0.334158	+	0.942517i	$0.391548\pi$
$450$		0			0
$451$	−18.1717	−	31.4742i	−0.855670	−	1.48206i
$452$	−6.04193	+	10.4649i	−0.284188	+	0.492229i
$453$	−7.37713	−	12.7776i	−0.346608	−	0.600342i
$454$	3.45543	+	5.98498i	0.162171	+	0.280889i
$455$		0			0
$456$	9.13029	−	4.86195i	0.427565	−	0.227682i
$457$	−1.22073			−0.0571033			−0.0285516	−	0.999592i	$-0.509090\pi$
$457$	−1.22073			−0.0571033			−0.0285516	+	0.999592i	$0.509090\pi$
$458$	−5.43712	−	9.41736i	−0.254060	−	0.440045i
$459$	16.1528	+	27.9775i	0.753950	+	1.30588i
$460$		0			0
$461$	4.34580	+	7.52714i	0.202404	+	0.350574i	0.949303	−	0.314364i	$-0.101791\pi$
$461$	4.34580	+	7.52714i	0.202404	+	0.350574i	−0.746898	+	0.664938i	$0.768458\pi$
$462$	13.5271	−	23.4296i	0.629337	−	1.09004i
$463$	19.7149			0.916229			0.458114	−	0.888893i	$-0.348525\pi$
$463$	19.7149			0.916229			0.458114	+	0.888893i	$0.348525\pi$
$464$	−12.9540			−0.601375
$465$		0			0
$466$	4.28471	−	7.42133i	0.198485	−	0.343787i
$467$	11.4795			0.531207			0.265604	−	0.964082i	$-0.414429\pi$
$467$	11.4795			0.531207			0.265604	+	0.964082i	$0.414429\pi$
$468$	−2.03443			−0.0940418
$469$	1.22929	−	2.12919i	0.0567633	−	0.0983170i
$470$		0			0
$471$	−1.95726	+	3.39008i	−0.0901858	+	0.156206i
$472$	−11.0483	−	19.1362i	−0.508538	−	0.880814i
$473$	−13.0611	−	22.6225i	−0.600549	−	1.04018i
$474$	14.6804			0.674293
$475$		0			0
$476$	11.2313			0.514787
$477$	1.81747	+	3.14796i	0.0832164	+	0.144135i
$478$	−11.6486	−	20.1760i	−0.532796	−	0.922830i
$479$	−19.6316	+	34.0029i	−0.896989	+	1.55363i	−0.0656652	+	0.997842i	$0.520917\pi$
$479$	−19.6316	+	34.0029i	−0.896989	+	1.55363i	−0.831324	+	0.555789i	$0.812416\pi$
$480$		0			0
$481$	−2.30785	+	3.99731i	−0.105229	+	0.182262i
$482$	25.3439			1.15438
$483$	2.65497			0.120805
$484$	−8.52302	+	14.7623i	−0.387410	+	0.671014i
$485$		0			0
$486$	24.4565			1.10937
$487$	−31.5943			−1.43168			−0.715838	−	0.698266i	$-0.753955\pi$
$487$	−31.5943			−1.43168			−0.715838	+	0.698266i	$0.753955\pi$
$488$	−10.7719	+	18.6576i	−0.487623	+	0.844588i
$489$	0.178579	+	0.309309i	0.00807564	+	0.0139874i
$490$		0			0
$491$	5.53187	+	9.58148i	0.249650	+	0.432406i	0.963429	−	0.267965i	$-0.0863511\pi$
$491$	5.53187	+	9.58148i	0.249650	+	0.432406i	−0.713779	+	0.700371i	$0.753018\pi$
$492$	2.82244	+	4.88861i	0.127245	+	0.220395i
$493$	15.6683			0.705663
$494$	0.396685	−	11.5659i	0.0178477	−	0.520376i
$495$		0			0
$496$	−13.0343	−	22.5761i	−0.585258	−	1.01370i
$497$	−10.7564	−	18.6306i	−0.482489	−	0.835696i
$498$	3.00530	−	5.20533i	0.134671	−	0.233256i
$499$	10.1868	+	17.6440i	0.456023	+	0.789854i	0.998746	−	0.0500570i	$-0.0159403\pi$
$499$	10.1868	+	17.6440i	0.456023	+	0.789854i	−0.542724	+	0.839911i	$0.682607\pi$
$500$		0			0
$501$	−16.5431			−0.739091
$502$	−10.1747			−0.454118
$503$	−6.83622	+	11.8407i	−0.304812	+	0.527950i	−0.977219	−	0.212231i	$-0.931927\pi$
$503$	−6.83622	+	11.8407i	−0.304812	+	0.527950i	0.672407	+	0.740181i	$0.265260\pi$
$504$	−4.12338	+	7.14191i	−0.183670	+	0.318126i
$505$		0			0
$506$	−9.00474			−0.400310
$507$	6.06317	−	10.5017i	0.269275	−	0.466398i
$508$	2.35834	+	4.08476i	0.104634	+	0.181232i
$509$	3.86196	−	6.68912i	0.171179	−	0.296490i	−0.767654	−	0.640865i	$-0.778576\pi$
$509$	3.86196	−	6.68912i	0.171179	−	0.296490i	0.938832	+	0.344375i	$0.111909\pi$
$510$		0			0
$511$	−12.4807	−	21.6171i	−0.552112	−	0.956285i
$512$	0.249240			0.0110150
$513$	−0.806621	+	23.5182i	−0.0356132	+	1.03836i
$514$	−0.204211			−0.00900736
$515$		0			0
$516$	2.02866	+	3.51374i	0.0893067	+	0.154684i
$517$	−25.7651	+	44.6265i	−1.13315	+	1.96267i
$518$	−5.86521	−	10.1588i	−0.257703	−	0.446354i
$519$	7.73971	−	13.4056i	0.339736	−	0.588439i
$520$		0			0
$521$	−2.16876			−0.0950151			−0.0475075	−	0.998871i	$-0.515128\pi$
$521$	−2.16876			−0.0950151			−0.0475075	+	0.998871i	$0.515128\pi$
$522$	3.60645	−	6.24656i	0.157850	−	0.273404i
$523$	−11.9466	+	20.6921i	−0.522389	+	0.904804i	0.477272	+	0.878756i	$0.341626\pi$
$523$	−11.9466	+	20.6921i	−0.522389	+	0.904804i	−0.999661	+	0.0260485i	$0.991708\pi$
$524$	−11.4690			−0.501026
$525$		0			0
$526$	−8.37310	+	14.5026i	−0.365085	+	0.632345i
$527$	15.7654	+	27.3065i	0.686751	+	1.18949i
$528$	−16.5099	+	28.5959i	−0.718500	+	1.24448i
$529$	11.0582	+	19.1533i	0.480790	+	0.832752i
$530$		0			0
$531$	17.8716			0.775562
$532$	6.94067	+	4.33101i	0.300916	+	0.187773i
$533$	−10.0730			−0.436312
$534$	10.7277	+	18.5809i	0.464234	+	0.804076i
$535$		0			0
$536$	−1.03290	+	1.78904i	−0.0446147	+	0.0772749i
$537$	8.24629	+	14.2830i	0.355854	+	0.616356i
$538$	−4.75418	+	8.23448i	−0.204967	+	0.355013i
$539$	6.15492			0.265111
$540$		0			0
$541$	−21.2275	+	36.7671i	−0.912641	+	1.58074i	−0.102323	+	0.994751i	$0.532627\pi$
$541$	−21.2275	+	36.7671i	−0.912641	+	1.58074i	−0.810319	+	0.585990i	$0.800706\pi$
$542$	10.5792	−	18.3237i	0.454415	−	0.787069i
$543$	11.4614			0.491858
$544$	−24.7907			−1.06289
$545$		0			0
$546$	−3.74921	−	6.49383i	−0.160451	−	0.277910i
$547$	6.01535	−	10.4189i	0.257198	−	0.445480i	−0.708292	−	0.705919i	$-0.750534\pi$
$547$	6.01535	−	10.4189i	0.257198	−	0.445480i	0.965490	+	0.260439i	$0.0838674\pi$
$548$	6.68604	+	11.5806i	0.285614	+	0.494697i
$549$	−8.71231	−	15.0902i	−0.371833	−	0.644033i
$550$		0			0
$551$	9.68259	+	6.04198i	0.412492	+	0.257397i
$552$	−2.23082			−0.0949500
$553$	−9.25956	−	16.0380i	−0.393756	−	0.682006i
$554$	14.6496	+	25.3739i	0.622403	+	1.07803i
$555$		0			0
$556$	2.58394	+	4.47551i	0.109583	+	0.189804i
$557$	−4.37635	+	7.58006i	−0.185432	+	0.321178i	−0.943722	−	0.330740i	$-0.892702\pi$
$557$	−4.37635	+	7.58006i	−0.185432	+	0.321178i	0.758290	+	0.651917i	$0.226035\pi$
$558$	14.5152			0.614479
$559$	−7.24011			−0.306224
$560$		0			0
$561$	19.9692	−	34.5876i	0.843099	−	1.46029i
$562$	−34.1238			−1.43943
$563$	35.9707			1.51598			0.757991	−	0.652265i	$-0.226181\pi$
$563$	35.9707			1.51598			0.757991	+	0.652265i	$0.226181\pi$
$564$	4.00186	−	6.93143i	0.168509	−	0.291866i
$565$		0			0
$566$	−9.86750	+	17.0910i	−0.414762	+	0.718389i
$567$	1.57827	+	2.73365i	0.0662812	+	0.114802i
$568$	9.03798	+	15.6542i	0.379225	+	0.656837i
$569$	−20.3125			−0.851543			−0.425772	−	0.904831i	$-0.639997\pi$
$569$	−20.3125			−0.851543			−0.425772	+	0.904831i	$0.639997\pi$
$570$		0			0
$571$	10.1773			0.425906			0.212953	−	0.977062i	$-0.431692\pi$
$571$	10.1773			0.425906			0.212953	+	0.977062i	$0.431692\pi$
$572$	3.53714	+	6.12650i	0.147895	+	0.256162i
$573$	7.53505	+	13.0511i	0.314781	+	0.545217i
$574$	12.7999	−	22.1701i	0.534258	−	0.925362i
$575$		0			0
$576$	2.48161	−	4.29827i	0.103400	−	0.179095i
$577$	32.7441			1.36316			0.681578	−	0.731745i	$-0.261294\pi$
$577$	32.7441			1.36316			0.681578	+	0.731745i	$0.261294\pi$
$578$	31.3083			1.30225
$579$	8.41745	−	14.5794i	0.349817	−	0.605901i
$580$		0			0
$581$	−7.58228			−0.314566
$582$	−7.83337			−0.324703
$583$	6.31984	−	10.9463i	0.261741	−	0.453349i
$584$	10.4868	+	18.1637i	0.433947	+	0.751618i
$585$		0			0
$586$	−20.7913	−	36.0117i	−0.858883	−	1.48763i
$587$	4.38663	+	7.59786i	0.181056	+	0.313597i	0.942240	−	0.334938i	$-0.108715\pi$
$587$	4.38663	+	7.59786i	0.181056	+	0.313597i	−0.761185	+	0.648535i	$0.775382\pi$
$588$	−0.955987			−0.0394243
$589$	−0.787274	+	22.9541i	−0.0324390	+	0.945808i
$590$		0			0
$591$	−14.4975	−	25.1105i	−0.596349	−	1.03291i
$592$	7.15852	+	12.3989i	0.294213	+	0.509592i
$593$	−16.1603	+	27.9905i	−0.663625	+	1.14943i	0.316031	+	0.948749i	$0.397650\pi$
$593$	−16.1603	+	27.9905i	−0.663625	+	1.14943i	−0.979656	+	0.200684i	$0.935684\pi$
$594$	−25.8569	−	44.7855i	−1.06092	−	1.83757i
$595$		0			0
$596$	11.0927			0.454375
$597$	−2.61570			−0.107053
$598$	−1.24789	+	2.16141i	−0.0510301	+	0.0883868i
$599$	9.77520	−	16.9311i	0.399404	−	0.691787i	−0.594249	−	0.804281i	$-0.702551\pi$
$599$	9.77520	−	16.9311i	0.399404	−	0.691787i	0.993652	+	0.112494i	$0.0358839\pi$
$600$		0			0
$601$	−0.401837			−0.0163913			−0.00819564	−	0.999966i	$-0.502609\pi$
$601$	−0.401837			−0.0163913			−0.00819564	+	0.999966i	$0.502609\pi$
$602$	9.20008	−	15.9350i	0.374967	−	0.649462i
$603$	−0.835409	−	1.44697i	−0.0340205	−	0.0589252i
$604$	−4.90243	+	8.49126i	−0.199477	+	0.345505i
$605$		0			0
$606$	10.7431	+	18.6076i	0.436409	+	0.755882i
$607$	−13.4453			−0.545727			−0.272863	−	0.962053i	$-0.587971\pi$
$607$	−13.4453			−0.545727			−0.272863	+	0.962053i	$0.587971\pi$
$608$	−15.3200	−	9.55976i	−0.621309	−	0.387700i
$609$	7.39497			0.299659
$610$		0			0
$611$	7.14115	+	12.3688i	0.288900	+	0.500390i
$612$	3.81633	−	6.61008i	0.154266	−	0.267196i
$613$	−10.3527	−	17.9313i	−0.418140	−	0.724239i	0.577613	−	0.816311i	$-0.303984\pi$
$613$	−10.3527	−	17.9313i	−0.418140	−	0.724239i	−0.995752	+	0.0920716i	$0.970651\pi$
$614$	14.0820	−	24.3907i	0.568303	−	0.984330i
$615$		0			0
$616$	28.6762			1.15540
$617$	−4.63936	+	8.03560i	−0.186773	+	0.323501i	−0.944173	−	0.329451i	$-0.893136\pi$
$617$	−4.63936	+	8.03560i	−0.186773	+	0.323501i	0.757399	+	0.652952i	$0.226470\pi$
$618$	11.1765	−	19.3583i	0.449585	−	0.778703i
$619$	−2.89129			−0.116211			−0.0581053	−	0.998310i	$-0.518506\pi$
$619$	−2.89129			−0.116211			−0.0581053	+	0.998310i	$0.518506\pi$
$620$		0			0
$621$	2.53747	−	4.39503i	0.101825	−	0.176366i
$622$	12.6616	+	21.9306i	0.507686	+	0.879338i
$623$	13.5329	−	23.4396i	0.542183	−	0.939088i
$624$	4.57593	+	7.92574i	0.183184	+	0.317284i
$625$		0			0
$626$	−41.4926			−1.65838
$627$	25.6781	−	13.6738i	1.02548	−	0.546078i
$628$	2.60138			0.103806
$629$	−8.65844	−	14.9969i	−0.345234	−	0.597964i
$630$		0			0
$631$	−15.2270	+	26.3740i	−0.606178	+	1.04993i	0.385686	+	0.922630i	$0.373965\pi$
$631$	−15.2270	+	26.3740i	−0.606178	+	1.04993i	−0.991864	+	0.127301i	$0.959369\pi$
$632$	7.78029	+	13.4759i	0.309483	+	0.536041i
$633$	−12.8826	+	22.3134i	−0.512039	+	0.886877i
$634$	41.9972			1.66792
$635$		0			0
$636$	−0.981604	+	1.70019i	−0.0389231	+	0.0674168i
$637$	0.852959	−	1.47737i	0.0337955	−	0.0585355i
$638$	−25.0812			−0.992975
$639$	−14.6198			−0.578349
$640$		0			0
$641$	10.0369	+	17.3845i	0.396434	+	0.686645i	0.993283	−	0.115709i	$-0.0369141\pi$
$641$	10.0369	+	17.3845i	0.396434	+	0.686645i	−0.596849	+	0.802354i	$0.703581\pi$
$642$	17.2948	−	29.9554i	0.682571	−	1.18225i
$643$	−1.04457	−	1.80924i	−0.0411937	−	0.0713496i	0.844693	−	0.535250i	$-0.179783\pi$
$643$	−1.04457	−	1.80924i	−0.0411937	−	0.0713496i	−0.885887	+	0.463901i	$0.846449\pi$
$644$	−0.882172	−	1.52797i	−0.0347625	−	0.0602103i
$645$		0			0
$646$	36.8347	+	22.9850i	1.44924	+	0.904334i
$647$	2.10623			0.0828043			0.0414021	−	0.999143i	$-0.486818\pi$
$647$	2.10623			0.0828043			0.0414021	+	0.999143i	$0.486818\pi$
$648$	−1.32613	−	2.29693i	−0.0520954	−	0.0902319i
$649$	−31.0722	−	53.8187i	−1.21969	−	2.11257i
$650$		0			0
$651$	7.44081	+	12.8879i	0.291628	+	0.505115i
$652$	0.118674	−	0.205549i	0.00464763	−	0.00804994i
$653$	−1.83067			−0.0716395			−0.0358197	−	0.999358i	$-0.511404\pi$
$653$	−1.83067			−0.0716395			−0.0358197	+	0.999358i	$0.511404\pi$
$654$	10.8583			0.424593
$655$		0			0
$656$	−15.6223	+	27.0587i	−0.609950	+	1.05646i
$657$	−16.9634			−0.661804
$658$	−36.2973			−1.41502
$659$	−12.0268	+	20.8310i	−0.468497	+	0.811460i	−0.999352	−	0.0360024i	$-0.988538\pi$
$659$	−12.0268	+	20.8310i	−0.468497	+	0.811460i	0.530855	+	0.847463i	$0.321871\pi$
$660$		0			0
$661$	8.72110	−	15.1054i	0.339211	−	0.587531i	−0.645073	−	0.764121i	$-0.723173\pi$
$661$	8.72110	−	15.1054i	0.339211	−	0.587531i	0.984285	+	0.176589i	$0.0565065\pi$
$662$	16.8172	+	29.1282i	0.653617	+	1.13210i
$663$	−5.53472	−	9.58642i	−0.214951	−	0.372306i
$664$	6.37097			0.247241
$665$		0			0
$666$	−7.97184			−0.308902
$667$	−1.23068	−	2.13159i	−0.0476519	−	0.0825356i
$668$	5.49682	+	9.52077i	0.212678	+	0.368370i
$669$	5.92402	−	10.2607i	0.229036	−	0.396702i
$670$		0			0
$671$	−30.2951	+	52.4726i	−1.16953	+	2.02568i
$672$	−11.7005			−0.451357
$673$	−47.5187			−1.83171			−0.915856	−	0.401506i	$-0.868487\pi$
$673$	−47.5187			−1.83171			−0.915856	+	0.401506i	$0.868487\pi$
$674$	−26.4868	+	45.8765i	−1.02023	+	1.76709i
$675$		0			0
$676$	−8.05850			−0.309942
$677$	−14.5531			−0.559321			−0.279661	−	0.960099i	$-0.590222\pi$
$677$	−14.5531			−0.559321			−0.279661	+	0.960099i	$0.590222\pi$
$678$	−15.1338	+	26.2124i	−0.581208	+	1.00668i
$679$	4.94084	+	8.55778i	0.189612	+	0.328418i
$680$		0			0
$681$	2.40754	+	4.16998i	0.0922570	+	0.159794i
$682$	−25.2367	−	43.7112i	−0.966363	−	1.67379i
$683$	−3.33714			−0.127692			−0.0638460	−	0.997960i	$-0.520337\pi$
$683$	−3.33714			−0.127692			−0.0638460	+	0.997960i	$0.520337\pi$
$684$	4.90736	−	2.61321i	0.187638	−	0.0999185i
$685$		0			0
$686$	16.3553	+	28.3282i	0.624448	+	1.08158i
$687$	−3.78826	−	6.56146i	−0.144531	−	0.250335i
$688$	−11.2287	+	19.4487i	−0.428092	+	0.741476i
$689$	−1.75163	−	3.03391i	−0.0667318	−	0.115583i
$690$		0			0
$691$	−19.3318			−0.735415			−0.367708	−	0.929941i	$-0.619857\pi$
$691$	−19.3318			−0.735415			−0.367708	+	0.929941i	$0.619857\pi$
$692$	−10.2868			−0.391044
$693$	−11.5966	+	20.0859i	−0.440519	+	0.763001i
$694$	−2.74862	+	4.76075i	−0.104336	+	0.180716i
$695$		0			0
$696$	−6.21358			−0.235525
$697$	18.8957	−	32.7283i	0.715725	−	1.23967i
$698$	−14.8549	−	25.7295i	−0.562268	−	0.973876i
$699$	2.98533	−	5.17074i	0.112916	−	0.195575i
$700$		0			0
$701$	−4.96892	−	8.60643i	−0.187674	−	0.325060i	0.756801	−	0.653646i	$-0.226761\pi$
$701$	−4.96892	−	8.60643i	−0.187674	−	0.325060i	−0.944474	+	0.328586i	$0.893428\pi$
$702$	−14.3332			−0.540971
$703$	0.432375	−	12.6065i	0.0163073	−	0.475464i
$704$	−17.2584			−0.650452
$705$		0			0
$706$	−6.90389	−	11.9579i	−0.259831	−	0.450041i
$707$	13.5523	−	23.4732i	0.509686	−	0.882801i
$708$	4.82616	+	8.35916i	0.181378	+	0.314157i
$709$	−18.6059	+	32.2264i	−0.698760	+	1.21029i	0.270136	+	0.962822i	$0.412931\pi$
$709$	−18.6059	+	32.2264i	−0.698760	+	1.21029i	−0.968897	+	0.247466i	$0.920402\pi$
$710$		0			0
$711$	−12.5853			−0.471987
$712$	−11.3709	+	19.6950i	−0.426143	+	0.738101i
$713$	2.47661	−	4.28961i	0.0927497	−	0.160647i
$714$	28.1321			1.05282
$715$		0			0
$716$	5.48003	−	9.49169i	0.204798	−	0.354721i
$717$	−8.11608	−	14.0575i	−0.303100	−	0.524985i
$718$	−6.94966	+	12.0372i	−0.259359	+	0.449223i
$719$	1.32109	+	2.28819i	0.0492683	+	0.0853351i	0.889608	−	0.456725i	$-0.150978\pi$
$719$	1.32109	+	2.28819i	0.0492683	+	0.0853351i	−0.840340	+	0.542060i	$0.817644\pi$
$720$		0			0
$721$	−28.1980			−1.05015
$722$	13.8995	+	28.4083i	0.517284	+	1.05725i
$723$	17.6581			0.656711
$724$	−3.80832	−	6.59621i	−0.141535	−	0.245146i
$725$		0			0
$726$	−21.3484	+	36.9765i	−0.792313	+	1.37233i
$727$	−5.08653	−	8.81013i	−0.188649	−	0.326750i	0.756151	−	0.654397i	$-0.227077\pi$
$727$	−5.08653	−	8.81013i	−0.188649	−	0.326750i	−0.944800	+	0.327647i	$0.893744\pi$
$728$	3.97400	−	6.88317i	0.147286	−	0.255107i
$729$	20.9284			0.775126
$730$		0			0
$731$	13.5815	−	23.5238i	0.502329	−	0.870060i
$732$	4.70546	−	8.15009i	0.173919	−	0.301236i
$733$	−14.8222			−0.547472			−0.273736	−	0.961805i	$-0.588259\pi$
$733$	−14.8222			−0.547472			−0.273736	+	0.961805i	$0.588259\pi$
$734$	−24.0023			−0.885942
$735$		0			0
$736$	1.94720	+	3.37266i	0.0717749	+	0.124318i
$737$	−2.90494	+	5.03151i	−0.107005	+	0.185338i
$738$	−8.69865	−	15.0665i	−0.320202	−	0.554605i
$739$	−17.7433	−	30.7323i	−0.652697	−	1.13050i	−0.982466	−	0.186443i	$-0.940304\pi$
$739$	−17.7433	−	30.7323i	−0.652697	−	1.13050i	0.329769	−	0.944062i	$-0.393029\pi$
$740$		0			0
$741$	0.276386	−	8.05845i	0.0101533	−	0.296035i
$742$	8.90325			0.326849
$743$	−4.36941	−	7.56804i	−0.160298	−	0.277645i	0.774677	−	0.632357i	$-0.217912\pi$
$743$	−4.36941	−	7.56804i	−0.160298	−	0.277645i	−0.934976	+	0.354712i	$0.884579\pi$
$744$	−6.25210	−	10.8289i	−0.229213	−	0.397009i
$745$		0			0
$746$	−20.0708	−	34.7637i	−0.734846	−	1.27279i
$747$	−2.57641	+	4.46247i	−0.0942658	+	0.163273i
$748$	−26.5408			−0.970428
$749$	−43.6342			−1.59436
$750$		0			0
$751$	−6.54957	+	11.3442i	−0.238997	+	0.413955i	−0.960427	−	0.278533i	$-0.910152\pi$
$751$	−6.54957	+	11.3442i	−0.238997	+	0.413955i	0.721430	+	0.692488i	$0.243485\pi$
$752$	44.3011			1.61549
$753$	−7.08911			−0.258342
$754$	−3.47580	+	6.02026i	−0.126581	+	0.219245i
$755$		0			0
$756$	5.06627	−	8.77504i	0.184258	−	0.319145i
$757$	−8.21901	−	14.2357i	−0.298725	−	0.517407i	0.677119	−	0.735873i	$-0.263228\pi$
$757$	−8.21901	−	14.2357i	−0.298725	−	0.517407i	−0.975845	+	0.218466i	$0.929895\pi$
$758$	−13.8787	−	24.0386i	−0.504097	−	0.873121i
$759$	−6.27397			−0.227731
$760$		0			0
$761$	16.3918			0.594203			0.297101	−	0.954846i	$-0.403980\pi$
$761$	16.3918			0.594203			0.297101	+	0.954846i	$0.403980\pi$
$762$	5.90714	+	10.2315i	0.213993	+	0.370647i
$763$	−6.84879	−	11.8625i	−0.247943	−	0.429450i
$764$	5.00738	−	8.67304i	0.181161	−	0.313780i
$765$		0			0
$766$	−9.05337	+	15.6809i	−0.327112	+	0.566574i
$767$	−17.2242			−0.621929
$768$	18.6756			0.673899
$769$	25.0210	−	43.3377i	0.902282	−	1.56280i	0.0777564	−	0.996972i	$-0.475224\pi$
$769$	25.0210	−	43.3377i	0.902282	−	1.56280i	0.824525	−	0.565825i	$-0.191442\pi$
$770$		0			0
$771$	−0.142282			−0.00512416
$772$	−11.1875			−0.402649
$773$	24.3436	−	42.1644i	0.875580	−	1.51655i	0.0194356	−	0.999811i	$-0.493813\pi$
$773$	24.3436	−	42.1644i	0.875580	−	1.51655i	0.856144	−	0.516737i	$-0.172854\pi$
$774$	−6.25225	−	10.8292i	−0.224732	−	0.389248i
$775$		0			0
$776$	−4.15151	−	7.19063i	−0.149031	−	0.258129i
$777$	−4.08653	−	7.07808i	−0.146603	−	0.253925i
$778$	60.6799			2.17548
$779$	24.2977	−	12.9387i	0.870555	−	0.463577i
$780$		0			0
$781$	25.4185	+	44.0261i	0.909544	+	1.57538i
$782$	−4.68176	−	8.10905i	−0.167419	−	0.289979i
$783$	7.06771	−	12.2416i	0.252579	−	0.437480i
$784$	−2.64572	−	4.58252i	−0.0944900	−	0.163662i
$785$		0			0
$786$	−28.7275			−1.02467
$787$	−6.51678			−0.232298			−0.116149	−	0.993232i	$-0.537055\pi$
$787$	−6.51678			−0.232298			−0.116149	+	0.993232i	$0.537055\pi$
$788$	−9.63426	+	16.6870i	−0.343206	+	0.594451i
$789$	−5.83388	+	10.1046i	−0.207692	+	0.359732i
$790$		0			0
$791$	38.1820			1.35760
$792$	9.74399	−	16.8771i	0.346238	−	0.599701i
$793$	8.39668	+	14.5435i	0.298175	+	0.516454i
$794$	7.14407	−	12.3739i	0.253534	−	0.439133i
$795$		0			0
$796$	0.869124	+	1.50537i	0.0308053	+	0.0533563i
$797$	−38.3796			−1.35947			−0.679737	−	0.733456i	$-0.737906\pi$
$797$	−38.3796			−1.35947			−0.679737	+	0.733456i	$0.737906\pi$
$798$	17.3849	+	10.8483i	0.615419	+	0.384024i
$799$	−53.5834			−1.89565
$800$		0			0
$801$	−9.19675	−	15.9292i	−0.324951	−	0.562832i
$802$	14.1950	−	24.5864i	0.501242	−	0.868177i
$803$	29.4931	+	51.0836i	1.04079	+	1.80270i
$804$	0.451198	−	0.781498i	0.0159125	−	0.0275613i
$805$		0			0
$806$	−13.9894			−0.492755
$807$	−3.31243	+	5.73729i	−0.116603	+	0.201962i
$808$	−11.3872	+	19.7232i	−0.400601	+	0.693861i
$809$	25.1409			0.883906			0.441953	−	0.897038i	$-0.354286\pi$
$809$	25.1409			0.883906			0.441953	+	0.897038i	$0.354286\pi$
$810$		0			0
$811$	23.5053	−	40.7124i	0.825383	−	1.42961i	−0.0762426	−	0.997089i	$-0.524292\pi$
$811$	23.5053	−	40.7124i	0.825383	−	1.42961i	0.901626	−	0.432517i	$-0.142374\pi$
$812$	−2.45714	−	4.25590i	−0.0862289	−	0.149353i
$813$	7.37094	−	12.7668i	0.258510	−	0.447753i
$814$	13.8601	+	24.0064i	0.485797	+	0.841425i
$815$		0			0
$816$	−34.3354			−1.20198
$817$	17.4642	−	9.29984i	0.610996	−	0.325360i
$818$	−19.6317			−0.686406
$819$	3.21416	+	5.56708i	0.112312	+	0.194530i
$820$		0			0
$821$	9.91021	−	17.1650i	0.345869	−	0.599062i	−0.639642	−	0.768673i	$-0.720918\pi$
$821$	9.91021	−	17.1650i	0.345869	−	0.599062i	0.985511	+	0.169610i	$0.0542509\pi$
$822$	16.7471	+	29.0069i	0.584123	+	1.01173i
$823$	−19.6084	+	33.9627i	−0.683505	+	1.18387i	0.290399	+	0.956906i	$0.406212\pi$
$823$	−19.6084	+	33.9627i	−0.683505	+	1.18387i	−0.973904	+	0.226960i	$0.927121\pi$
$824$	23.6932			0.825391
$825$		0			0
$826$	21.8869	−	37.9092i	0.761543	−	1.31903i
$827$	−5.92176	+	10.2568i	−0.205920	+	0.356663i	−0.950425	−	0.310953i	$-0.899352\pi$
$827$	−5.92176	+	10.2568i	−0.205920	+	0.356663i	0.744506	+	0.667616i	$0.232685\pi$
$828$	−1.19903			−0.0416690
$829$	46.9321			1.63002			0.815010	−	0.579447i	$-0.196731\pi$
$829$	46.9321			1.63002			0.815010	+	0.579447i	$0.196731\pi$
$830$		0			0
$831$	10.2070	+	17.6790i	0.354076	+	0.613278i
$832$	−2.39170	+	4.14255i	−0.0829174	+	0.143617i
$833$	3.20008	+	5.54270i	0.110876	+	0.192043i
$834$	6.47222	+	11.2102i	0.224115	+	0.388178i
$835$		0			0
$836$	−16.4015	−	10.2346i	−0.567259	−	0.353972i
$837$	28.4461			0.983240
$838$	−0.951117	−	1.64738i	−0.0328558	−	0.0569079i
$839$	26.5669	+	46.0153i	0.917192	+	1.58862i	0.803660	+	0.595089i	$0.202883\pi$
$839$	26.5669	+	46.0153i	0.917192	+	1.58862i	0.113532	+	0.993534i	$0.463783\pi$
$840$		0			0
$841$	11.0722	+	19.1775i	0.381799	+	0.661294i
$842$	−16.2450	+	28.1372i	−0.559841	+	0.969673i
$843$	−23.7755			−0.818870
$844$	17.1222			0.589370
$845$		0			0
$846$	−12.3336	+	21.3624i	−0.424038	+	0.734455i
$847$	53.8613			1.85070
$848$	−10.8665			−0.373156
$849$	−6.87509	+	11.9080i	−0.235952	+	0.408682i
$850$		0			0
$851$	−1.36017	+	2.35588i	−0.0466259	+	0.0807584i
$852$	−3.94802	−	6.83816i	−0.135257	−	0.234272i
$853$	21.1499	+	36.6327i	0.724159	+	1.25428i	0.959319	+	0.282324i	$0.0911052\pi$
$853$	21.1499	+	36.6327i	0.724159	+	1.25428i	−0.235160	+	0.971957i	$0.575562\pi$
$854$	−42.6790			−1.46045
$855$		0			0
$856$	36.6634			1.25313
$857$	11.7692	+	20.3849i	0.402028	+	0.696333i	0.993971	−	0.109647i	$-0.0349720\pi$
$857$	11.7692	+	20.3849i	0.402028	+	0.696333i	−0.591942	+	0.805980i	$0.701639\pi$
$858$	8.85979	+	15.3456i	0.302468	+	0.523890i
$859$	−4.74062	+	8.21099i	−0.161748	+	0.280156i	−0.935496	−	0.353338i	$-0.885046\pi$
$859$	−4.74062	+	8.21099i	−0.161748	+	0.280156i	0.773748	+	0.633494i	$0.218380\pi$
$860$		0			0
$861$	8.91821	−	15.4468i	0.303932	−	0.526425i
$862$	−61.3859			−2.09081
$863$	−22.8204			−0.776816			−0.388408	−	0.921487i	$-0.626975\pi$
$863$	−22.8204			−0.776816			−0.388408	+	0.921487i	$0.626975\pi$
$864$	−11.1827	+	19.3690i	−0.380443	+	0.658947i
$865$		0			0
$866$	−0.614106			−0.0208682
$867$	21.8138			0.740834
$868$	4.94475	−	8.56456i	0.167836	−	0.290700i
$869$	21.8813	+	37.8996i	0.742273	+	1.28565i
$870$		0			0
$871$	0.805144	+	1.39455i	0.0272813	+	0.0472525i
$872$	5.75466	+	9.96736i	0.194877	+	0.337537i
$873$	6.71546			0.227284
$874$	0.233792	−	6.81656i	0.00790814	−	0.230574i
$875$		0			0
$876$	−4.58089	−	7.93434i	−0.154774	−	0.268077i
$877$	−12.6471	−	21.9054i	−0.427062	−	0.739693i	0.569549	−	0.821958i	$-0.307118\pi$
$877$	−12.6471	−	21.9054i	−0.427062	−	0.739693i	−0.996611	+	0.0822647i	$0.973785\pi$
$878$	1.88459	−	3.26421i	0.0636018	−	0.110162i
$879$	−14.4862	−	25.0908i	−0.488606	−	0.846291i
$880$		0			0
$881$	−33.2871			−1.12147			−0.560736	−	0.827995i	$-0.689482\pi$
$881$	−33.2871			−1.12147			−0.560736	+	0.827995i	$0.689482\pi$
$882$	2.94632			0.0992077
$883$	−7.65544	+	13.2596i	−0.257626	+	0.446222i	−0.965606	−	0.260011i	$-0.916274\pi$
$883$	−7.65544	+	13.2596i	−0.257626	+	0.446222i	0.707979	+	0.706233i	$0.249607\pi$
$884$	−3.67807	+	6.37061i	−0.123707	+	0.214267i
$885$		0			0
$886$	27.4030			0.920621
$887$	21.6027	−	37.4171i	0.725349	−	1.25634i	−0.233481	−	0.972361i	$-0.575012\pi$
$887$	21.6027	−	37.4171i	0.725349	−	1.25634i	0.958830	−	0.283980i	$-0.0916550\pi$
$888$	3.43368	+	5.94731i	0.115227	+	0.199579i
$889$	7.45177	−	12.9068i	0.249924	−	0.432882i
$890$		0			0
$891$	−3.72962	−	6.45990i	−0.124947	−	0.216415i
$892$	−7.87356			−0.263626
$893$	−33.1132	−	20.6628i	−1.10809	−	0.691453i
$894$	27.7849			0.929265
$895$		0			0
$896$	−16.1671	−	28.0022i	−0.540104	−	0.935488i
$897$	−0.869457	+	1.50594i	−0.0290303	+	0.0502820i
$898$	−11.7861	−	20.4141i	−0.393307	−	0.681228i
$899$	6.89818	−	11.9480i	0.230067	−	0.398488i
$900$		0			0
$901$	13.1433			0.437867
$902$	−30.2475	+	52.3903i	−1.00713	+	1.74441i
$903$	6.41007	−	11.1026i	0.213314	−	0.369470i
$904$	−32.0822			−1.06704
$905$		0			0
$906$	−12.2796	+	21.2688i	−0.407961	+	0.706609i
$907$	7.16392	+	12.4083i	0.237874	+	0.412010i	0.960104	−	0.279643i	$-0.0902161\pi$
$907$	7.16392	+	12.4083i	0.237874	+	0.412010i	−0.722230	+	0.691653i	$0.756883\pi$
$908$	1.59992	−	2.77114i	0.0530951	−	0.0919634i
$909$	−9.20994	−	15.9521i	−0.305475	−	0.529097i
$910$		0			0
$911$	−4.61162			−0.152790			−0.0763949	−	0.997078i	$-0.524341\pi$
$911$	−4.61162			−0.152790			−0.0763949	+	0.997078i	$0.524341\pi$
$912$	−21.2184	−	13.2404i	−0.702610	−	0.438432i
$913$	17.9177			0.592990
$914$	1.01598	+	1.75973i	0.0336056	+	0.0582066i
$915$		0			0
$916$	−2.51747	+	4.36038i	−0.0831795	+	0.144071i
$917$	18.1196	+	31.3841i	0.598363	+	1.03640i
$918$	26.8871	−	46.5699i	0.887407	−	1.53703i
$919$	26.4921			0.873892			0.436946	−	0.899488i	$-0.356060\pi$
$919$	26.4921			0.873892			0.436946	+	0.899488i	$0.356060\pi$
$920$		0			0
$921$	9.81149	−	16.9940i	0.323300	−	0.559972i
$922$	7.23378	−	12.5293i	0.238232	−	0.412630i
$923$	14.0901			0.463782
$924$	−12.5265			−0.412091
$925$		0			0
$926$	−16.4082	−	28.4198i	−0.539206	−	0.933932i
$927$	−9.58148	+	16.5956i	−0.314697	+	0.545072i
$928$	5.42362	+	9.39398i	0.178039	+	0.308372i
$929$	2.37863	+	4.11990i	0.0780402	+	0.135170i	0.902404	−	0.430890i	$-0.141800\pi$
$929$	2.37863	+	4.11990i	0.0780402	+	0.135170i	−0.824364	+	0.566060i	$0.808467\pi$
$930$		0			0
$931$	−0.159802	+	4.65925i	−0.00523729	+	0.152701i
$932$	−3.96777			−0.129969
$933$	8.82188	+	15.2799i	0.288815	+	0.500243i
$934$	−9.55406	−	16.5481i	−0.312619	−	0.541471i
$935$		0			0
$936$	−2.70068	−	4.67771i	−0.0882744	−	0.152896i
$937$	−5.96833	+	10.3375i	−0.194977	+	0.337710i	−0.946893	−	0.321549i	$-0.895797\pi$
$937$	−5.96833	+	10.3375i	−0.194977	+	0.337710i	0.751916	+	0.659259i	$0.229130\pi$
$938$	−4.09242			−0.133622
$939$	−28.9096			−0.943429
$940$		0			0
$941$	8.99715	−	15.5835i	0.293299	−	0.508008i	−0.681289	−	0.732015i	$-0.738580\pi$
$941$	8.99715	−	15.5835i	0.293299	−	0.508008i	0.974588	+	0.224006i	$0.0719136\pi$
$942$	6.51590			0.212299
$943$	−5.93670			−0.193326
$944$	−26.7131	+	46.2684i	−0.869437	+	1.50591i
$945$		0			0
$946$	−21.7408	+	37.6561i	−0.706853	+	1.22431i
$947$	−12.6096	−	21.8404i	−0.409755	−	0.709717i	0.585107	−	0.810956i	$-0.301053\pi$
$947$	−12.6096	−	21.8404i	−0.409755	−	0.709717i	−0.994862	+	0.101239i	$0.967719\pi$
$948$	−3.39862	−	5.88659i	−0.110382	−	0.191188i
$949$	16.3488			0.530705
$950$		0			0
$951$	29.2611			0.948858
$952$	14.9094	+	25.8238i	0.483216	+	0.836955i
$953$	21.1589	+	36.6484i	0.685405	+	1.18716i	0.973309	+	0.229498i	$0.0737083\pi$
$953$	21.1589	+	36.6484i	0.685405	+	1.18716i	−0.287904	+	0.957659i	$0.592958\pi$
$954$	3.02527	−	5.23991i	0.0979466	−	0.169648i
$955$		0			0
$956$	−5.39350	+	9.34181i	−0.174438	+	0.302136i
$957$	−17.4751			−0.564890
$958$	65.3552			2.11153
$959$	21.1263	−	36.5918i	0.682203	−	1.18161i
$960$		0			0
$961$	−3.23623			−0.104395
$962$	7.68304			0.247711
$963$	−14.8266	+	25.6805i	−0.477781	+	0.827542i
$964$	−5.86730	−	10.1625i	−0.188973	−	0.327311i
$965$		0			0
$966$	−2.20966	−	3.82724i	−0.0710945	−	0.123139i
$967$	−6.84820	−	11.8614i	−0.220223	−	0.381438i	0.734652	−	0.678444i	$-0.237345\pi$
$967$	−6.84820	−	11.8614i	−0.220223	−	0.381438i	−0.954876	+	0.297006i	$0.904012\pi$
$968$	−45.2567			−1.45460
$969$	25.6642	+	16.0146i	0.824454	+	0.514463i
$970$		0			0
$971$	19.2906	+	33.4123i	0.619065	+	1.07225i	0.989657	+	0.143457i	$0.0458217\pi$
$971$	19.2906	+	33.4123i	0.619065	+	1.07225i	−0.370591	+	0.928796i	$0.620845\pi$
$972$	−5.66187	−	9.80665i	−0.181605	−	0.314548i
$973$	8.16461	−	14.1415i	0.261745	−	0.453356i
$974$	26.2951	+	45.5445i	0.842549	+	1.45934i
$975$		0			0
$976$	52.0899			1.66736
$977$	17.4592			0.558568			0.279284	−	0.960209i	$-0.409903\pi$
$977$	17.4592			0.558568			0.279284	+	0.960209i	$0.409903\pi$
$978$	0.297253	−	0.514858i	0.00950512	−	0.0164633i
$979$	−31.9796	+	55.3903i	−1.02207	+	1.77028i
$980$		0			0
$981$	−9.30869			−0.297204
$982$	9.20805	−	15.9488i	0.293841	−	0.508947i
$983$	21.9581	+	38.0325i	0.700353	+	1.21305i	0.968342	+	0.249625i	$0.0803075\pi$
$983$	21.9581	+	38.0325i	0.700353	+	1.21305i	−0.267989	+	0.963422i	$0.586359\pi$
$984$	−7.49348	+	12.9791i	−0.238883	+	0.413758i
$985$		0			0
$986$	−13.0403	−	22.5864i	−0.415287	−	0.719298i
$987$	−25.2898			−0.804984
$988$	−4.72958	+	2.51854i	−0.150468	+	0.0801254i
$989$	−4.26707			−0.135685
$990$		0			0
$991$	−23.1731	−	40.1370i	−0.736118	−	1.27499i	−0.954231	−	0.299071i	$-0.903323\pi$
$991$	−23.1731	−	40.1370i	−0.736118	−	1.27499i	0.218112	−	0.975924i	$-0.430010\pi$
$992$	−10.9145	+	18.9044i	−0.346535	+	0.600216i
$993$	11.7172	+	20.2948i	0.371834	+	0.644035i
$994$	−17.9045	+	31.0114i	−0.567895	+	0.983623i
$995$		0			0
$996$	−2.78300			−0.0881827
$997$	5.86857	−	10.1647i	0.185859	−	0.321918i	−0.758006	−	0.652247i	$-0.773826\pi$
$997$	5.86857	−	10.1647i	0.185859	−	0.321918i	0.943866	+	0.330329i	$0.107160\pi$
$998$	16.9563	−	29.3692i	0.536744	−	0.929667i
$999$	−15.6227			−0.494281

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.e.e.26.1		8
5.2	odd	4		475.2.j.c.349.7		16
5.3	odd	4		475.2.j.c.349.2		16
5.4	even	2		95.2.e.c.26.4	yes	8
15.14	odd	2		855.2.k.h.406.1		8
19.7	even	3		9025.2.a.bg.1.4		4
19.11	even	3	inner	475.2.e.e.201.1		8
19.12	odd	6		9025.2.a.bp.1.1		4
20.19	odd	2		1520.2.q.o.881.1		8
95.49	even	6		95.2.e.c.11.4	✓	8
95.64	even	6		1805.2.a.o.1.1		4
95.68	odd	12		475.2.j.c.49.7		16
95.69	odd	6		1805.2.a.i.1.4		4
95.87	odd	12		475.2.j.c.49.2		16
285.239	odd	6		855.2.k.h.676.1		8
380.239	odd	6		1520.2.q.o.961.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.c.11.4	✓	8	95.49	even	6
95.2.e.c.26.4	yes	8	5.4	even	2
475.2.e.e.26.1		8	1.1	even	1	trivial
475.2.e.e.201.1		8	19.11	even	3	inner
475.2.j.c.49.2		16	95.87	odd	12
475.2.j.c.49.7		16	95.68	odd	12
475.2.j.c.349.2		16	5.3	odd	4
475.2.j.c.349.7		16	5.2	odd	4
855.2.k.h.406.1		8	15.14	odd	2
855.2.k.h.676.1		8	285.239	odd	6
1520.2.q.o.881.1		8	20.19	odd	2
1520.2.q.o.961.1		8	380.239	odd	6
1805.2.a.i.1.4		4	95.69	odd	6
1805.2.a.o.1.1		4	95.64	even	6
9025.2.a.bg.1.4		4	19.7	even	3
9025.2.a.bp.1.1		4	19.12	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.832272 - 1.44154i) q^{2} +(-0.579878 - 1.00438i) q^{3} +(-0.385355 + 0.667454i) q^{4} +(-0.965233 + 1.67183i) q^{6} +2.43525 q^{7} -2.04621 q^{8} +(0.827483 - 1.43324i) q^{9} -5.75477 q^{11} +0.893835 q^{12} +(-0.797505 + 1.38132i) q^{13} +(-2.02680 - 3.51051i) q^{14} +(2.47371 + 4.28460i) q^{16} +(-2.99203 - 5.18234i) q^{17} -2.75477 q^{18} +(0.149412 - 4.35634i) q^{19} +(-1.41215 - 2.44592i) q^{21} +(4.78953 + 8.29572i) q^{22} +(-0.470022 + 0.814102i) q^{23} +(1.18655 + 2.05517i) q^{24} +2.65497 q^{26} -5.39862 q^{27} +(-0.938437 + 1.62542i) q^{28} +(-1.30917 + 2.26755i) q^{29} -5.26913 q^{31} +(2.07140 - 3.58777i) q^{32} +(3.33706 + 5.77996i) q^{33} +(-4.98037 + 8.62625i) q^{34} +(0.637749 + 1.10461i) q^{36} +2.89384 q^{37} +(-6.40418 + 3.41028i) q^{38} +1.84982 q^{39} +(3.15767 + 5.46925i) q^{41} +(-2.35059 + 4.07134i) q^{42} +(2.26961 + 3.93108i) q^{43} +(2.21763 - 3.84104i) q^{44} +1.56475 q^{46} +(4.47718 - 7.75471i) q^{47} +(2.86890 - 4.96909i) q^{48} -1.06953 q^{49} +(-3.47002 + 6.01025i) q^{51} +(-0.614645 - 1.06460i) q^{52} +(-1.09819 + 1.90213i) q^{53} +(4.49313 + 7.78232i) q^{54} -4.98304 q^{56} +(-4.46205 + 2.37608i) q^{57} +4.35834 q^{58} +(5.39939 + 9.35202i) q^{59} +(5.26434 - 9.11811i) q^{61} +(4.38535 + 7.59566i) q^{62} +(2.01513 - 3.49031i) q^{63} +2.99898 q^{64} +(5.55469 - 9.62100i) q^{66} +(0.504789 - 0.874320i) q^{67} +4.61197 q^{68} +1.09022 q^{69} +(-4.41694 - 7.65036i) q^{71} +(-1.69320 + 2.93271i) q^{72} +(-5.12499 - 8.87674i) q^{73} +(-2.40846 - 4.17157i) q^{74} +(2.85008 + 1.77846i) q^{76} -14.0143 q^{77} +(-1.53956 - 2.66659i) q^{78} +(-3.80229 - 6.58577i) q^{79} +(0.648093 + 1.12253i) q^{81} +(5.25609 - 9.10381i) q^{82} -3.11355 q^{83} +2.17672 q^{84} +(3.77787 - 6.54346i) q^{86} +3.03663 q^{87} +11.7755 q^{88} +(5.55706 - 9.62511i) q^{89} +(-1.94213 + 3.36387i) q^{91} +(-0.362251 - 0.627436i) q^{92} +(3.05545 + 5.29220i) q^{93} -14.9049 q^{94} -4.80463 q^{96} +(2.02888 + 3.51412i) q^{97} +(0.890144 + 1.54177i) q^{98} +(-4.76197 + 8.24798i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 3 q^{3} - 5 q^{4} - 2 q^{6} + 8 q^{7} - 24 q^{8} - q^{9} - 4 q^{11} - 12 q^{12} + 7 q^{13} + q^{14} - 7 q^{16} - q^{17} + 20 q^{18} + 5 q^{19} + 4 q^{21} + 2 q^{22} + 2 q^{23} - 23 q^{24}+ \cdots - 38 q^{99}+O(q^{100}) \) 8 * q + q^2 + 3 * q^3 - 5 * q^4 - 2 * q^6 + 8 * q^7 - 24 * q^8 - q^9 - 4 * q^11 - 12 * q^12 + 7 * q^13 + q^14 - 7 * q^16 - q^17 + 20 * q^18 + 5 * q^19 + 4 * q^21 + 2 * q^22 + 2 * q^23 - 23 * q^24 + 6 * q^26 - 24 * q^27 - 19 * q^28 + q^29 + 30 * q^32 + 19 * q^33 - 15 * q^34 + 7 * q^36 + 4 * q^37 - 13 * q^38 + 30 * q^39 + 8 * q^41 - 15 * q^42 + q^43 + 12 * q^44 + 24 * q^46 - 12 * q^47 + 23 * q^48 - 20 * q^49 - 22 * q^51 - 3 * q^52 - 5 * q^53 + 34 * q^54 - 82 * q^56 - 7 * q^57 + 54 * q^58 + 5 * q^59 + 37 * q^62 - 3 * q^63 + 112 * q^64 + 31 * q^66 + 4 * q^67 - 32 * q^68 - 18 * q^69 - 20 * q^71 + 17 * q^72 - 20 * q^73 - 25 * q^74 + 63 * q^76 - 28 * q^77 - 18 * q^78 - 17 * q^79 - 12 * q^81 + 21 * q^82 - 2 * q^83 - 40 * q^84 - 8 * q^86 + 32 * q^87 + 14 * q^88 - 11 * q^89 - 6 * q^91 - q^92 - 8 * q^93 - 62 * q^94 + 42 * q^96 + q^97 + 9 * q^98 - 38 * q^99

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