LMFDB - Embedded newform 475.2.e.e.201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(26,475)]

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([0, 2]))

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

//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);

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: 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:	$8$
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			201.1
Root			$1.07988 - 1.87040i$ of defining polynomial
Character	$\chi$	$=$	475.201
Dual form			475.2.e.e.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.832272 + 1.44154i) q^{2} +(-0.579878 + 1.00438i) q^{3} +(-0.385355 - 0.667454i) q^{4} +(-0.965233 - 1.67183i) q^{6} +2.43525 q^{7} -2.04621 q^{8} +(0.827483 + 1.43324i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 8 * q + q^2 + 3 * q^3 - 5 * q^4 - 2 * q^6 + 8 * q^7 - 24 * q^8 - q^9	$ 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}+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

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 $

$2$	−0.832272	+	1.44154i	−0.588506	+	1.01932i	0.405923	+	0.913907i	$0.366950\pi$
$2$	−0.832272	+	1.44154i	−0.588506	+	1.01932i	−0.994428	+	0.105414i	$0.966383\pi$
$3$	−0.579878	+	1.00438i	−0.334793	+	0.579878i	−0.983445	−	0.181207i	$-0.942000\pi$
$3$	−0.579878	+	1.00438i	−0.334793	+	0.579878i	0.648652	+	0.761085i	$0.275333\pi$
$4$	−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	0.733981	−	0.679170i	$-0.237660\pi$
$13$	−0.797505	−	1.38132i	−0.221188	−	0.383109i	−0.955169	+	0.296061i	$0.904327\pi$
$14$	−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	0.233023	+	0.972471i	$0.425138\pi$
$17$	−2.99203	+	5.18234i	−0.725673	+	1.25690i	−0.958696	+	0.284432i	$0.908195\pi$
$18$	−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	0.812853	−	0.582469i	$-0.197913\pi$
$23$	−0.470022	−	0.814102i	−0.0980064	−	0.169752i	−0.910859	+	0.412717i	$0.864580\pi$
$24$	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	0.718491	−	0.695536i	$-0.244833\pi$
$29$	−1.30917	−	2.26755i	−0.243106	−	0.421073i	−0.961598	+	0.274463i	$0.911500\pi$
$30$		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	−0.506823	−	0.862050i	$-0.669180\pi$
$41$	3.15767	−	5.46925i	0.493145	−	0.854153i	0.999969	+	0.00789701i	$0.00251372\pi$
$42$	−2.35059	−	4.07134i	−0.362704	−	0.628221i
$43$	2.26961	−	3.93108i	0.346113	−	0.599485i	−0.639443	−	0.768839i	$-0.720835\pi$
$43$	2.26961	−	3.93108i	0.346113	−	0.599485i	0.985555	+	0.169354i	$0.0541682\pi$
$44$	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	0.982375	+	0.186919i	$0.0598502\pi$
$47$	4.47718	+	7.75471i	0.653064	+	1.13114i	−0.329311	+	0.944221i	$0.606816\pi$
$48$	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	0.780691	−	0.624917i	$-0.214867\pi$
$53$	−1.09819	−	1.90213i	−0.150848	−	0.261277i	−0.931540	+	0.363640i	$0.881534\pi$
$54$	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	−0.264489	−	0.964389i	$-0.585203\pi$
$59$	5.39939	−	9.35202i	0.702941	−	1.21753i	0.967430	−	0.253140i	$-0.0814634\pi$
$60$		0			0
$61$	5.26434	+	9.11811i	0.674030	+	1.16745i	0.976751	+	0.214375i	$0.0687716\pi$
$61$	5.26434	+	9.11811i	0.674030	+	1.16745i	−0.302721	+	0.953079i	$0.597895\pi$
$62$	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	0.895212	−	0.445641i	$-0.147024\pi$
$67$	0.504789	+	0.874320i	0.0616698	+	0.106815i	−0.833542	+	0.552456i	$0.813691\pi$
$68$	4.61197			0.559284
$69$	1.09022			0.131247
$70$		0			0
$71$	−4.41694	+	7.65036i	−0.524194	+	0.907931i	0.475409	+	0.879765i	$0.342300\pi$
$71$	−4.41694	+	7.65036i	−0.524194	+	0.907931i	−0.999603	+	0.0281662i	$0.991033\pi$
$72$	−1.69320	−	2.93271i	−0.199546	−	0.345624i
$73$	−5.12499	+	8.87674i	−0.599835	+	1.03894i	0.393011	+	0.919534i	$0.371434\pi$
$73$	−5.12499	+	8.87674i	−0.599835	+	1.03894i	−0.992845	+	0.119410i	$0.961900\pi$
$74$	−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	−0.996677	−	0.0814604i	$-0.974042\pi$
$79$	−3.80229	+	6.58577i	−0.427792	+	0.740957i	0.568885	+	0.822417i	$0.307375\pi$
$80$		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	0.994358	+	0.106081i	$0.0338302\pi$
$89$	5.55706	+	9.62511i	0.589047	+	1.02026i	−0.405310	+	0.914179i	$0.632837\pi$
$90$		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	−0.744450	−	0.667678i	$-0.767288\pi$
$97$	2.02888	−	3.51412i	0.206002	−	0.356805i	0.950451	+	0.310873i	$0.100621\pi$
$98$	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	0.998000	+	0.0632098i	$0.0201337\pi$
$101$	5.56503	+	9.63892i	0.553741	+	0.959108i	−0.444259	+	0.895898i	$0.646533\pi$
$102$	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	−0.968700	−	0.248233i	$-0.920150\pi$
$109$	−2.81235	+	4.87113i	−0.269374	+	0.466570i	0.699326	+	0.714803i	$0.253484\pi$
$110$		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	0.969253	−	0.246066i	$-0.0791380\pi$
$127$	3.05996	+	5.30000i	0.271527	+	0.470299i	−0.697726	+	0.716365i	$0.745805\pi$
$128$	−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	−0.333018	−	0.942920i	$-0.608067\pi$
$131$	7.44055	−	12.8874i	0.650084	−	1.12598i	0.983102	−	0.183058i	$-0.0585997\pi$
$132$	−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	0.951963	+	0.306214i	$0.0990622\pi$
$137$	8.67518	+	15.0258i	0.741170	+	1.28374i	−0.210793	+	0.977531i	$0.567604\pi$
$138$	−0.907361	+	1.57160i	−0.0772397	+	0.133783i
$139$	3.35267	+	5.80700i	0.284370	+	0.492543i	0.972456	−	0.233086i	$-0.0748823\pi$
$139$	3.35267	+	5.80700i	0.284370	+	0.492543i	−0.688086	+	0.725629i	$0.741549\pi$
$140$		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	0.404737	+	0.914433i	$0.367363\pi$
$149$	−7.19642	+	12.4646i	−0.589553	+	1.02114i	−0.994291	+	0.106704i	$0.965970\pi$
$150$		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	−0.925479	−	0.378800i	$-0.876337\pi$
$157$	−1.68765	+	2.92309i	−0.134689	+	0.233288i	0.790790	+	0.612088i	$0.209670\pi$
$158$	−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	0.998137	+	0.0610070i	$0.0194312\pi$
$167$	7.13215	+	12.3532i	0.551902	+	0.955923i	−0.446235	+	0.894916i	$0.647235\pi$
$168$	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	−0.492581	−	0.870266i	$-0.663947\pi$
$173$	6.67357	−	11.5590i	0.507382	−	0.878811i	0.999963	−	0.00854514i	$-0.00272003\pi$
$174$	−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	0.621855	−	0.783133i	$-0.286379\pi$
$181$	−4.94132	−	8.55861i	−0.367285	−	0.636157i	−0.989140	+	0.146976i	$0.953046\pi$
$182$	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	−0.477221	−	0.878784i	$-0.658356\pi$
$193$	7.25795	−	12.5711i	0.522439	−	0.904890i	0.999659	−	0.0261066i	$-0.00831094\pi$
$194$	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	0.903224	−	0.429170i	$-0.141194\pi$
$199$	1.12769	+	1.95322i	0.0799401	+	0.138460i	−0.823284	+	0.567630i	$0.807860\pi$
$200$		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	0.175689	+	0.984446i	$0.443785\pi$
$211$	−11.1081	+	19.2397i	−0.764710	+	1.32452i	−0.940400	+	0.340071i	$0.889549\pi$
$212$	−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	−0.642758	−	0.766069i	$-0.722210\pi$
$223$	5.10799	−	8.84730i	0.342056	−	0.592459i	0.984814	+	0.173610i	$0.0555432\pi$
$224$	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	−0.769305	−	0.638882i	$-0.779397\pi$
$233$	2.57410	−	4.45848i	0.168635	−	0.292084i	0.937940	+	0.346797i	$0.112731\pi$
$234$	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	0.509552	−	0.860440i	$-0.329811\pi$
$241$	−7.61285	−	13.1858i	−0.490387	−	0.849375i	−0.999939	+	0.0110652i	$0.996478\pi$
$242$	−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	0.946214	−	0.323542i	$-0.104874\pi$
$251$	3.05630	+	5.29366i	0.192912	+	0.334133i	−0.753302	+	0.657674i	$0.771540\pi$
$252$	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	0.867932	−	0.496683i	$-0.165449\pi$
$257$	0.0613414	+	0.106246i	0.00382637	+	0.00662747i	−0.864106	+	0.503310i	$0.832115\pi$
$258$	−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	−0.978401	−	0.206716i	$-0.933722\pi$
$263$	−5.03027	+	8.71267i	−0.310179	+	0.537247i	0.668222	+	0.743962i	$0.267056\pi$
$264$	−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	−0.939864	−	0.341549i	$-0.889049\pi$
$269$	−2.85614	+	4.94698i	−0.174142	+	0.301623i	0.765722	+	0.643172i	$0.222382\pi$
$270$		0			0
$271$	6.35560	−	11.0082i	0.386075	−	0.668702i	−0.605843	−	0.795585i	$-0.707164\pi$
$271$	6.35560	−	11.0082i	0.386075	−	0.668702i	0.991918	+	0.126883i	$0.0404972\pi$
$272$	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	0.990992	+	0.133922i	$0.0427571\pi$
$281$	10.2502	+	17.7539i	0.611476	+	1.05911i	−0.379516	+	0.925185i	$0.623910\pi$
$282$	8.64305	−	14.9702i	0.514686	−	0.891462i
$283$	−5.92805	+	10.2677i	−0.352386	+	0.610350i	−0.986667	−	0.162752i	$-0.947963\pi$
$283$	−5.92805	+	10.2677i	−0.352386	+	0.610350i	0.634281	+	0.773103i	$0.281296\pi$
$284$	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	−0.516970	−	0.856003i	$-0.672940\pi$
$307$	8.45997	−	14.6531i	0.482836	−	0.836296i	0.999806	+	0.0197074i	$0.00627348\pi$
$308$	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	0.966876	+	0.255246i	$0.0821564\pi$
$313$	12.4637	+	21.5877i	0.704488	+	1.22021i	−0.262389	+	0.964962i	$0.584510\pi$
$314$	−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	−0.965398	−	0.260780i	$-0.916020\pi$
$317$	−12.6152	−	21.8502i	−0.708541	−	1.22723i	0.256857	−	0.966449i	$-0.417313\pi$
$318$	−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	−0.00155051	+	0.999999i	$0.500494\pi$
$337$	−15.9123	+	27.5610i	−0.866800	+	1.50134i	−0.865249	+	0.501342i	$0.832840\pi$
$338$	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	−0.906939	−	0.421263i	$-0.861587\pi$
$347$	−1.65128	+	2.86009i	−0.0886451	+	0.153538i	0.818294	+	0.574801i	$0.194920\pi$
$348$	−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	−0.954915	−	0.296878i	$-0.904055\pi$
$359$	−4.17511	+	7.23150i	−0.220354	+	0.381664i	0.734562	+	0.678542i	$0.237388\pi$
$360$		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	0.990528	−	0.137307i	$-0.0438448\pi$
$367$	7.20988	+	12.4879i	0.376353	+	0.651862i	−0.614176	+	0.789169i	$0.710511\pi$
$368$	−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	−0.970867	−	0.239619i	$-0.922977\pi$
$383$	−5.43895	+	9.42053i	−0.277917	+	0.481367i	0.692950	+	0.720986i	$0.256311\pi$
$384$	−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	−0.792917	−	0.609330i	$-0.791438\pi$
$389$	−18.2272	−	31.5704i	−0.924154	−	1.60068i	−0.131237	−	0.991351i	$-0.541895\pi$
$390$		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	−0.737993	−	0.674808i	$-0.764226\pi$
$397$	4.29191	−	7.43380i	0.215405	−	0.373092i	0.953398	+	0.301717i	$0.0975597\pi$
$398$	−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	−0.570640	−	0.821200i	$-0.693305\pi$
$401$	8.52785	−	14.7707i	0.425860	−	0.737612i	0.996500	+	0.0835885i	$0.0266381\pi$
$402$	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	0.974186	−	0.225749i	$-0.0724828\pi$
$409$	5.89702	+	10.2139i	0.291589	+	0.505047i	−0.682597	+	0.730795i	$0.739149\pi$
$410$		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	−0.999611	−	0.0278967i	$-0.991119\pi$
$421$	−9.75944	+	16.9039i	−0.475646	+	0.823843i	0.523965	+	0.851740i	$0.324452\pi$
$422$	−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	0.842017	+	0.539451i	$0.181368\pi$
$431$	18.4392	+	31.9377i	0.888187	+	1.53838i	0.0461694	+	0.998934i	$0.485299\pi$
$432$	−13.3546	+	23.1309i	−0.642526	+	1.11289i
$433$	0.184467	+	0.319506i	0.00886490	+	0.0153545i	0.870424	−	0.492303i	$-0.163845\pi$
$433$	0.184467	+	0.319506i	0.00886490	+	0.0153545i	−0.861559	+	0.507658i	$0.830512\pi$
$434$	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	−0.837742	−	0.546067i	$-0.816125\pi$
$439$	1.13220	−	1.96102i	0.0540367	−	0.0935944i	0.891778	+	0.452472i	$0.149458\pi$
$440$		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	0.601508	−	0.798866i	$-0.294567\pi$
$443$	−8.23137	−	14.2572i	−0.391084	−	0.677378i	−0.992593	+	0.121488i	$0.961233\pi$
$444$	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	−0.746898	−	0.664938i	$-0.768458\pi$
$461$	4.34580	−	7.52714i	0.202404	−	0.350574i	0.949303	+	0.314364i	$0.101791\pi$
$462$	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	−0.831324	−	0.555789i	$-0.812416\pi$
$479$	−19.6316	−	34.0029i	−0.896989	−	1.55363i	−0.0656652	−	0.997842i	$-0.520917\pi$
$480$		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	−0.713779	−	0.700371i	$-0.753018\pi$
$491$	5.53187	−	9.58148i	0.249650	−	0.432406i	0.963429	+	0.267965i	$0.0863511\pi$
$492$	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	−0.542724	−	0.839911i	$-0.682607\pi$
$499$	10.1868	−	17.6440i	0.456023	−	0.789854i	0.998746	+	0.0500570i	$0.0159403\pi$
$500$		0			0
$501$	−16.5431			−0.739091
$502$	−10.1747			−0.454118
$503$	−6.83622	−	11.8407i	−0.304812	−	0.527950i	0.672407	−	0.740181i	$-0.265260\pi$
$503$	−6.83622	−	11.8407i	−0.304812	−	0.527950i	−0.977219	+	0.212231i	$0.931927\pi$
$504$	−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	0.938832	−	0.344375i	$-0.111909\pi$
$509$	3.86196	+	6.68912i	0.171179	+	0.296490i	−0.767654	+	0.640865i	$0.778576\pi$
$510$		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	−0.999661	−	0.0260485i	$-0.991708\pi$
$523$	−11.9466	−	20.6921i	−0.522389	−	0.904804i	0.477272	−	0.878756i	$-0.341626\pi$
$524$	−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	−0.810319	−	0.585990i	$-0.800706\pi$
$541$	−21.2275	−	36.7671i	−0.912641	−	1.58074i	−0.102323	−	0.994751i	$-0.532627\pi$
$542$	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	0.965490	−	0.260439i	$-0.0838674\pi$
$547$	6.01535	+	10.4189i	0.257198	+	0.445480i	−0.708292	+	0.705919i	$0.750534\pi$
$548$	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	0.758290	−	0.651917i	$-0.226035\pi$
$557$	−4.37635	−	7.58006i	−0.185432	−	0.321178i	−0.943722	+	0.330740i	$0.892702\pi$
$558$	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	−0.761185	−	0.648535i	$-0.775382\pi$
$587$	4.38663	−	7.59786i	0.181056	−	0.313597i	0.942240	+	0.334938i	$0.108715\pi$
$588$	−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	−0.979656	−	0.200684i	$-0.935684\pi$
$593$	−16.1603	−	27.9905i	−0.663625	−	1.14943i	0.316031	−	0.948749i	$-0.397650\pi$
$594$	−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	0.993652	−	0.112494i	$-0.0358839\pi$
$599$	9.77520	+	16.9311i	0.399404	+	0.691787i	−0.594249	+	0.804281i	$0.702551\pi$
$600$		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	−0.995752	−	0.0920716i	$-0.970651\pi$
$613$	−10.3527	+	17.9313i	−0.418140	+	0.724239i	0.577613	+	0.816311i	$0.303984\pi$
$614$	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	0.757399	−	0.652952i	$-0.226470\pi$
$617$	−4.63936	−	8.03560i	−0.186773	−	0.323501i	−0.944173	+	0.329451i	$0.893136\pi$
$618$	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	−0.991864	−	0.127301i	$-0.959369\pi$
$631$	−15.2270	−	26.3740i	−0.606178	−	1.04993i	0.385686	−	0.922630i	$-0.373965\pi$
$632$	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	−0.596849	−	0.802354i	$-0.703581\pi$
$641$	10.0369	−	17.3845i	0.396434	−	0.686645i	0.993283	+	0.115709i	$0.0369141\pi$
$642$	17.2948	+	29.9554i	0.682571	+	1.18225i
$643$	−1.04457	+	1.80924i	−0.0411937	+	0.0713496i	−0.885887	−	0.463901i	$-0.846449\pi$
$643$	−1.04457	+	1.80924i	−0.0411937	+	0.0713496i	0.844693	+	0.535250i	$0.179783\pi$
$644$	−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	0.530855	−	0.847463i	$-0.321871\pi$
$659$	−12.0268	−	20.8310i	−0.468497	−	0.811460i	−0.999352	+	0.0360024i	$0.988538\pi$
$660$		0			0
$661$	8.72110	+	15.1054i	0.339211	+	0.587531i	0.984285	−	0.176589i	$-0.0565065\pi$
$661$	8.72110	+	15.1054i	0.339211	+	0.587531i	−0.645073	+	0.764121i	$0.723173\pi$
$662$	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	−0.944474	−	0.328586i	$-0.893428\pi$
$701$	−4.96892	+	8.60643i	−0.187674	+	0.325060i	0.756801	+	0.653646i	$0.226761\pi$
$702$	−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	−0.968897	−	0.247466i	$-0.920402\pi$
$709$	−18.6059	−	32.2264i	−0.698760	−	1.21029i	0.270136	−	0.962822i	$-0.412931\pi$
$710$		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	−0.840340	−	0.542060i	$-0.817644\pi$
$719$	1.32109	−	2.28819i	0.0492683	−	0.0853351i	0.889608	+	0.456725i	$0.150978\pi$
$720$		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	−0.944800	−	0.327647i	$-0.893744\pi$
$727$	−5.08653	+	8.81013i	−0.188649	+	0.326750i	0.756151	+	0.654397i	$0.227077\pi$
$728$	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	0.329769	+	0.944062i	$0.393029\pi$
$739$	−17.7433	+	30.7323i	−0.652697	+	1.13050i	−0.982466	+	0.186443i	$0.940304\pi$
$740$		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	−0.934976	−	0.354712i	$-0.884579\pi$
$743$	−4.36941	+	7.56804i	−0.160298	+	0.277645i	0.774677	+	0.632357i	$0.217912\pi$
$744$	−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	0.721430	−	0.692488i	$-0.243485\pi$
$751$	−6.54957	−	11.3442i	−0.238997	−	0.413955i	−0.960427	+	0.278533i	$0.910152\pi$
$752$	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	−0.975845	−	0.218466i	$-0.929895\pi$
$757$	−8.21901	+	14.2357i	−0.298725	+	0.517407i	0.677119	+	0.735873i	$0.263228\pi$
$758$	−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	0.824525	+	0.565825i	$0.191442\pi$
$769$	25.0210	+	43.3377i	0.902282	+	1.56280i	0.0777564	+	0.996972i	$0.475224\pi$
$770$		0			0
$771$	−0.142282			−0.00512416
$772$	−11.1875			−0.402649
$773$	24.3436	+	42.1644i	0.875580	+	1.51655i	0.856144	+	0.516737i	$0.172854\pi$
$773$	24.3436	+	42.1644i	0.875580	+	1.51655i	0.0194356	+	0.999811i	$0.493813\pi$
$774$	−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	0.901626	+	0.432517i	$0.142374\pi$
$811$	23.5053	+	40.7124i	0.825383	+	1.42961i	−0.0762426	+	0.997089i	$0.524292\pi$
$812$	−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	0.985511	−	0.169610i	$-0.0542509\pi$
$821$	9.91021	+	17.1650i	0.345869	+	0.599062i	−0.639642	+	0.768673i	$0.720918\pi$
$822$	16.7471	−	29.0069i	0.584123	−	1.01173i
$823$	−19.6084	−	33.9627i	−0.683505	−	1.18387i	−0.973904	−	0.226960i	$-0.927121\pi$
$823$	−19.6084	−	33.9627i	−0.683505	−	1.18387i	0.290399	−	0.956906i	$-0.406212\pi$
$824$	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	0.744506	−	0.667616i	$-0.232685\pi$
$827$	−5.92176	−	10.2568i	−0.205920	−	0.356663i	−0.950425	+	0.310953i	$0.899352\pi$
$828$	−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	0.113532	−	0.993534i	$-0.463783\pi$
$839$	26.5669	−	46.0153i	0.917192	−	1.58862i	0.803660	−	0.595089i	$-0.202883\pi$
$840$		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	−0.235160	−	0.971957i	$-0.575562\pi$
$853$	21.1499	−	36.6327i	0.724159	−	1.25428i	0.959319	−	0.282324i	$-0.0911052\pi$
$854$	−42.6790			−1.46045
$855$		0			0
$856$	36.6634			1.25313
$857$	11.7692	−	20.3849i	0.402028	−	0.696333i	−0.591942	−	0.805980i	$-0.701639\pi$
$857$	11.7692	−	20.3849i	0.402028	−	0.696333i	0.993971	+	0.109647i	$0.0349720\pi$
$858$	8.85979	−	15.3456i	0.302468	−	0.523890i
$859$	−4.74062	−	8.21099i	−0.161748	−	0.280156i	0.773748	−	0.633494i	$-0.218380\pi$
$859$	−4.74062	−	8.21099i	−0.161748	−	0.280156i	−0.935496	+	0.353338i	$0.885046\pi$
$860$		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	−0.996611	−	0.0822647i	$-0.973785\pi$
$877$	−12.6471	+	21.9054i	−0.427062	+	0.739693i	0.569549	+	0.821958i	$0.307118\pi$
$878$	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	0.707979	−	0.706233i	$-0.249607\pi$
$883$	−7.65544	−	13.2596i	−0.257626	−	0.446222i	−0.965606	+	0.260011i	$0.916274\pi$
$884$	−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	0.958830	+	0.283980i	$0.0916550\pi$
$887$	21.6027	+	37.4171i	0.725349	+	1.25634i	−0.233481	+	0.972361i	$0.575012\pi$
$888$	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	−0.722230	−	0.691653i	$-0.756883\pi$
$907$	7.16392	−	12.4083i	0.237874	−	0.412010i	0.960104	+	0.279643i	$0.0902161\pi$
$908$	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	−0.824364	−	0.566060i	$-0.808467\pi$
$929$	2.37863	−	4.11990i	0.0780402	−	0.135170i	0.902404	+	0.430890i	$0.141800\pi$
$930$		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	0.751916	−	0.659259i	$-0.229130\pi$
$937$	−5.96833	−	10.3375i	−0.194977	−	0.337710i	−0.946893	+	0.321549i	$0.895797\pi$
$938$	−4.09242			−0.133622
$939$	−28.9096			−0.943429
$940$		0			0
$941$	8.99715	+	15.5835i	0.293299	+	0.508008i	0.974588	−	0.224006i	$-0.0719136\pi$
$941$	8.99715	+	15.5835i	0.293299	+	0.508008i	−0.681289	+	0.732015i	$0.738580\pi$
$942$	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	−0.994862	−	0.101239i	$-0.967719\pi$
$947$	−12.6096	+	21.8404i	−0.409755	+	0.709717i	0.585107	+	0.810956i	$0.301053\pi$
$948$	−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	−0.287904	−	0.957659i	$-0.592958\pi$
$953$	21.1589	−	36.6484i	0.685405	−	1.18716i	0.973309	−	0.229498i	$-0.0737083\pi$
$954$	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	−0.954876	−	0.297006i	$-0.904012\pi$
$967$	−6.84820	+	11.8614i	−0.220223	+	0.381438i	0.734652	+	0.678444i	$0.237345\pi$
$968$	−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	−0.370591	−	0.928796i	$-0.620845\pi$
$971$	19.2906	−	33.4123i	0.619065	−	1.07225i	0.989657	−	0.143457i	$-0.0458217\pi$
$972$	−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	−0.267989	−	0.963422i	$-0.586359\pi$
$983$	21.9581	−	38.0325i	0.700353	−	1.21305i	0.968342	−	0.249625i	$-0.0803075\pi$
$984$	−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	0.218112	+	0.975924i	$0.430010\pi$
$991$	−23.1731	+	40.1370i	−0.736118	+	1.27499i	−0.954231	+	0.299071i	$0.903323\pi$
$992$	−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	0.943866	−	0.330329i	$-0.107160\pi$
$997$	5.86857	+	10.1647i	0.185859	+	0.321918i	−0.758006	+	0.652247i	$0.773826\pi$
$998$	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.201.1		8
5.2	odd	4		475.2.j.c.49.2		16
5.3	odd	4		475.2.j.c.49.7		16
5.4	even	2		95.2.e.c.11.4	✓	8
15.14	odd	2		855.2.k.h.676.1		8
19.7	even	3	inner	475.2.e.e.26.1		8
19.8	odd	6		9025.2.a.bp.1.1		4
19.11	even	3		9025.2.a.bg.1.4		4
20.19	odd	2		1520.2.q.o.961.1		8
95.7	odd	12		475.2.j.c.349.7		16
95.49	even	6		1805.2.a.o.1.1		4
95.64	even	6		95.2.e.c.26.4	yes	8
95.83	odd	12		475.2.j.c.349.2		16
95.84	odd	6		1805.2.a.i.1.4		4
285.254	odd	6		855.2.k.h.406.1		8
380.159	odd	6		1520.2.q.o.881.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.c.11.4	✓	8	5.4	even	2
95.2.e.c.26.4	yes	8	95.64	even	6
475.2.e.e.26.1		8	19.7	even	3	inner
475.2.e.e.201.1		8	1.1	even	1	trivial
475.2.j.c.49.2		16	5.2	odd	4
475.2.j.c.49.7		16	5.3	odd	4
475.2.j.c.349.2		16	95.83	odd	12
475.2.j.c.349.7		16	95.7	odd	12
855.2.k.h.406.1		8	285.254	odd	6
855.2.k.h.676.1		8	15.14	odd	2
1520.2.q.o.881.1		8	380.159	odd	6
1520.2.q.o.961.1		8	20.19	odd	2
1805.2.a.i.1.4		4	95.84	odd	6
1805.2.a.o.1.1		4	95.49	even	6
9025.2.a.bg.1.4		4	19.11	even	3
9025.2.a.bp.1.1		4	19.8	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.832272 + 1.44154i) q^{2} +(-0.579878 + 1.00438i) q^{3} +(-0.385355 - 0.667454i) q^{4} +(-0.965233 - 1.67183i) q^{6} +2.43525 q^{7} -2.04621 q^{8} +(0.827483 + 1.43324i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 3 q^{3} - 5 q^{4} - 2 q^{6} + 8 q^{7} - 24 q^{8} - q^{9}+O(q^{10}) \) 8 * q + q^2 + 3 * q^3 - 5 * q^4 - 2 * q^6 + 8 * q^7 - 24 * q^8 - q^9	\( 8 q + q^{2} + 3 q^{3} - 5 q^{4} - 2 q^{6} + 8 q^{7} - 24 q^{8} - q^{9} - 4 q^{11} - 12 q^{12} + 7 q^{13} + q^{14} - 7 q^{16} - q^{17} + 20 q^{18} + 5 q^{19} + 4 q^{21} + 2 q^{22} + 2 q^{23} - 23 q^{24} + 6 q^{26} - 24 q^{27} - 19 q^{28} + q^{29} + 30 q^{32} + 19 q^{33} - 15 q^{34} + 7 q^{36} + 4 q^{37} - 13 q^{38} + 30 q^{39} + 8 q^{41} - 15 q^{42} + q^{43} + 12 q^{44} + 24 q^{46} - 12 q^{47} + 23 q^{48} - 20 q^{49} - 22 q^{51} - 3 q^{52} - 5 q^{53} + 34 q^{54} - 82 q^{56} - 7 q^{57} + 54 q^{58} + 5 q^{59} + 37 q^{62} - 3 q^{63} + 112 q^{64} + 31 q^{66} + 4 q^{67} - 32 q^{68} - 18 q^{69} - 20 q^{71} + 17 q^{72} - 20 q^{73} - 25 q^{74} + 63 q^{76} - 28 q^{77} - 18 q^{78} - 17 q^{79} - 12 q^{81} + 21 q^{82} - 2 q^{83} - 40 q^{84} - 8 q^{86} + 32 q^{87} + 14 q^{88} - 11 q^{89} - 6 q^{91} - q^{92} - 8 q^{93} - 62 q^{94} + 42 q^{96} + q^{97} + 9 q^{98} - 38 q^{99}+O(q^{100}) \) 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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