LMFDB - Embedded newform 950.2.e.l.501.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(201,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("950.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.39075800976.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 12x^{6} - 13x^{5} + 125x^{4} - 116x^{3} + 232x^{2} + 96x + 64 $ x^8 - x^7 + 12x^6 - 13x^5 + 125x^4 - 116x^3 + 232x^2 + 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			501.3
Root			$0.851703 + 1.47519i$ of defining polynomial
Character	$\chi$	$=$	950.501
Dual form			950.2.e.l.201.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.851703 + 1.47519i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.851703 - 1.47519i) q^{6} -3.74324 q^{7} +1.00000 q^{8} +(0.0492032 - 0.0852224i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.851703 + 1.47519i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.851703 - 1.47519i) q^{6} -3.74324 q^{7} +1.00000 q^{8} +(0.0492032 - 0.0852224i) q^{9} +3.64483 q^{11} -1.70341 q^{12} +(3.01991 - 5.23065i) q^{13} +(1.87162 + 3.24174i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.04920 + 3.54932i) q^{17} -0.0984064 q^{18} +(-0.697500 + 4.30273i) q^{19} +(-3.18813 - 5.52200i) q^{21} +(-1.82241 - 3.15651i) q^{22} +(-2.34233 + 4.05703i) q^{23} +(0.851703 + 1.47519i) q^{24} -6.03983 q^{26} +5.27785 q^{27} +(1.87162 - 3.24174i) q^{28} +(3.32241 - 5.75459i) q^{29} +10.8416 q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.10431 + 5.37683i) q^{33} +(2.04920 - 3.54932i) q^{34} +(0.0492032 + 0.0852224i) q^{36} -7.75505 q^{37} +(4.07502 - 1.54731i) q^{38} +10.2883 q^{39} +(3.99653 + 6.92220i) q^{41} +(-3.18813 + 5.52200i) q^{42} +(2.19403 + 3.80018i) q^{43} +(-1.82241 + 3.15651i) q^{44} +4.68466 q^{46} +(-0.871618 + 1.50969i) q^{47} +(0.851703 - 1.47519i) q^{48} +7.01181 q^{49} +(-3.49063 + 6.04594i) q^{51} +(3.01991 + 5.23065i) q^{52} +(0.871618 - 1.50969i) q^{53} +(-2.63892 - 4.57075i) q^{54} -3.74324 q^{56} +(-6.94142 + 2.63570i) q^{57} -6.64483 q^{58} +(3.67412 + 6.36376i) q^{59} +(-1.15420 + 1.99914i) q^{61} +(-5.42082 - 9.38914i) q^{62} +(-0.184179 + 0.319008i) q^{63} +1.00000 q^{64} +(3.10431 - 5.37683i) q^{66} +(3.37162 - 5.83981i) q^{67} -4.09841 q^{68} -7.97988 q^{69} +(0.994093 + 1.72182i) q^{71} +(0.0492032 - 0.0852224i) q^{72} +(4.59494 + 7.95867i) q^{73} +(3.87752 + 6.71607i) q^{74} +(-3.37752 - 2.75542i) q^{76} -13.6435 q^{77} +(-5.14414 - 8.90992i) q^{78} +(-3.07849 - 5.33210i) q^{79} +(4.34755 + 7.53017i) q^{81} +(3.99653 - 6.92220i) q^{82} -5.69159 q^{83} +6.37625 q^{84} +(2.19403 - 3.80018i) q^{86} +11.3188 q^{87} +3.64483 q^{88} +(5.53983 - 9.59527i) q^{89} +(-11.3043 + 19.5795i) q^{91} +(-2.34233 - 4.05703i) q^{92} +(9.23386 + 15.9935i) q^{93} +1.74324 q^{94} -1.70341 q^{96} +(0.752610 + 1.30356i) q^{97} +(-3.50591 - 6.07241i) q^{98} +(0.179337 - 0.310621i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + q^{3} - 4 q^{4} + q^{6} + 12 q^{7} + 8 q^{8} - 11 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + q^3 - 4 * q^4 + q^6 + 12 * q^7 + 8 * q^8 - 11 * q^9	$ 8 q - 4 q^{2} + q^{3} - 4 q^{4} + q^{6} + 12 q^{7} + 8 q^{8} - 11 q^{9} + 10 q^{11} - 2 q^{12} + 9 q^{13} - 6 q^{14} - 4 q^{16} + 5 q^{17} + 22 q^{18} - q^{21} - 5 q^{22} + 6 q^{23} + q^{24} - 18 q^{26} + 16 q^{27} - 6 q^{28} + 17 q^{29} + 22 q^{31} - 4 q^{32} - 4 q^{33} + 5 q^{34} - 11 q^{36} - 8 q^{37} - 36 q^{39} + 7 q^{41} - q^{42} - 13 q^{43} - 5 q^{44} - 12 q^{46} + 14 q^{47} + q^{48} + 44 q^{49} - 9 q^{51} + 9 q^{52} - 14 q^{53} - 8 q^{54} + 12 q^{56} - 48 q^{57} - 34 q^{58} + 14 q^{59} - 9 q^{61} - 11 q^{62} - 45 q^{63} + 8 q^{64} - 4 q^{66} + 6 q^{67} - 10 q^{68} + 54 q^{69} + 14 q^{71} - 11 q^{72} - 11 q^{73} + 4 q^{74} - 10 q^{77} + 18 q^{78} - 17 q^{79} - 36 q^{81} + 7 q^{82} - 46 q^{83} + 2 q^{84} - 13 q^{86} - 2 q^{87} + 10 q^{88} + 14 q^{89} - 25 q^{91} + 6 q^{92} + 13 q^{93} - 28 q^{94} - 2 q^{96} - 17 q^{97} - 22 q^{98} - 60 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 + q^3 - 4 * q^4 + q^6 + 12 * q^7 + 8 * q^8 - 11 * q^9 + 10 * q^11 - 2 * q^12 + 9 * q^13 - 6 * q^14 - 4 * q^16 + 5 * q^17 + 22 * q^18 - q^21 - 5 * q^22 + 6 * q^23 + q^24 - 18 * q^26 + 16 * q^27 - 6 * q^28 + 17 * q^29 + 22 * q^31 - 4 * q^32 - 4 * q^33 + 5 * q^34 - 11 * q^36 - 8 * q^37 - 36 * q^39 + 7 * q^41 - q^42 - 13 * q^43 - 5 * q^44 - 12 * q^46 + 14 * q^47 + q^48 + 44 * q^49 - 9 * q^51 + 9 * q^52 - 14 * q^53 - 8 * q^54 + 12 * q^56 - 48 * q^57 - 34 * q^58 + 14 * q^59 - 9 * q^61 - 11 * q^62 - 45 * q^63 + 8 * q^64 - 4 * q^66 + 6 * q^67 - 10 * q^68 + 54 * q^69 + 14 * q^71 - 11 * q^72 - 11 * q^73 + 4 * q^74 - 10 * q^77 + 18 * q^78 - 17 * q^79 - 36 * q^81 + 7 * q^82 - 46 * q^83 + 2 * q^84 - 13 * q^86 - 2 * q^87 + 10 * q^88 + 14 * q^89 - 25 * q^91 + 6 * q^92 + 13 * q^93 - 28 * q^94 - 2 * q^96 - 17 * q^97 - 22 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.851703	+	1.47519i	0.491731	+	0.851703i	0.999955	−	0.00952194i	$-0.00303097\pi$
$3$	0.851703	+	1.47519i	0.491731	+	0.851703i	−0.508224	+	0.861225i	$0.669698\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.851703	−	1.47519i	0.347706	−	0.602245i
$7$	−3.74324			−1.41481			−0.707405	−	0.706808i	$-0.750134\pi$
$7$	−3.74324			−1.41481			−0.707405	+	0.706808i	$0.750134\pi$
$8$	1.00000			0.353553
$9$	0.0492032	−	0.0852224i	0.0164011	−	0.0284075i
$10$		0			0
$11$	3.64483			1.09896			0.549479	−	0.835508i	$-0.314826\pi$
$11$	3.64483			1.09896			0.549479	+	0.835508i	$0.314826\pi$
$12$	−1.70341			−0.491731
$13$	3.01991	−	5.23065i	0.837574	−	1.45072i	−0.0543441	−	0.998522i	$-0.517307\pi$
$13$	3.01991	−	5.23065i	0.837574	−	1.45072i	0.891918	−	0.452198i	$-0.149360\pi$
$14$	1.87162	+	3.24174i	0.500211	+	0.866391i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.04920	+	3.54932i	0.497005	+	0.860838i	0.999994	−	0.00345514i	$-0.00109981\pi$
$17$	2.04920	+	3.54932i	0.497005	+	0.860838i	−0.502989	+	0.864293i	$0.667766\pi$
$18$	−0.0984064			−0.0231946
$19$	−0.697500	+	4.30273i	−0.160017	+	0.987114i
$19$	−0.697500	+	4.30273i	−0.160017	+	0.987114i
$20$		0			0
$21$	−3.18813	−	5.52200i	−0.695706	−	1.20500i
$22$	−1.82241	−	3.15651i	−0.388540	−	0.672971i
$23$	−2.34233	+	4.05703i	−0.488409	+	0.845950i	−0.999911	−	0.0133324i	$-0.995756\pi$
$23$	−2.34233	+	4.05703i	−0.488409	+	0.845950i	0.511502	+	0.859282i	$0.329089\pi$
$24$	0.851703	+	1.47519i	0.173853	+	0.301123i
$25$		0			0
$26$	−6.03983			−1.18451
$27$	5.27785			1.01572
$28$	1.87162	−	3.24174i	0.353703	−	0.612631i
$29$	3.32241	−	5.75459i	0.616957	−	1.06860i	−0.373081	−	0.927799i	$-0.621699\pi$
$29$	3.32241	−	5.75459i	0.616957	−	1.06860i	0.990038	−	0.140802i	$-0.0449681\pi$
$30$		0			0
$31$	10.8416			1.94722			0.973608	−	0.228226i	$-0.0732925\pi$
$31$	10.8416			1.94722			0.973608	+	0.228226i	$0.0732925\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	3.10431	+	5.37683i	0.540392	+	0.935986i
$34$	2.04920	−	3.54932i	0.351435	−	0.608704i
$35$		0			0
$36$	0.0492032	+	0.0852224i	0.00820053	+	0.0142037i
$37$	−7.75505			−1.27492			−0.637461	−	0.770483i	$-0.720015\pi$
$37$	−7.75505			−1.27492			−0.637461	+	0.770483i	$0.720015\pi$
$38$	4.07502	−	1.54731i	0.661056	−	0.251007i
$39$	10.2883			1.64744
$40$		0			0
$41$	3.99653	+	6.92220i	0.624154	+	1.08107i	0.988704	+	0.149882i	$0.0478894\pi$
$41$	3.99653	+	6.92220i	0.624154	+	1.08107i	−0.364550	+	0.931184i	$0.618777\pi$
$42$	−3.18813	+	5.52200i	−0.491939	+	0.852062i
$43$	2.19403	+	3.80018i	0.334587	+	0.579521i	0.983405	−	0.181422i	$-0.0580699\pi$
$43$	2.19403	+	3.80018i	0.334587	+	0.579521i	−0.648819	+	0.760943i	$0.724737\pi$
$44$	−1.82241	+	3.15651i	−0.274739	+	0.475863i
$45$		0			0
$46$	4.68466			0.690715
$47$	−0.871618	+	1.50969i	−0.127139	+	0.220210i	−0.922567	−	0.385837i	$-0.873913\pi$
$47$	−0.871618	+	1.50969i	−0.127139	+	0.220210i	0.795428	+	0.606048i	$0.207246\pi$
$48$	0.851703	−	1.47519i	0.122933	−	0.212926i
$49$	7.01181			1.00169
$50$		0			0
$51$	−3.49063	+	6.04594i	−0.488785	+	0.846601i
$52$	3.01991	+	5.23065i	0.418787	+	0.725360i
$53$	0.871618	−	1.50969i	0.119726	−	0.207371i	−0.799933	−	0.600089i	$-0.795132\pi$
$53$	0.871618	−	1.50969i	0.119726	−	0.207371i	0.919659	+	0.392718i	$0.128465\pi$
$54$	−2.63892	−	4.57075i	−0.359112	−	0.622000i
$55$		0			0
$56$	−3.74324			−0.500211
$57$	−6.94142	+	2.63570i	−0.919414	+	0.349107i
$58$	−6.64483			−0.872509
$59$	3.67412	+	6.36376i	0.478329	+	0.828491i	0.999691	−	0.0248448i	$-0.00790917\pi$
$59$	3.67412	+	6.36376i	0.478329	+	0.828491i	−0.521362	+	0.853336i	$0.674576\pi$
$60$		0			0
$61$	−1.15420	+	1.99914i	−0.147781	+	0.255963i	−0.930407	−	0.366528i	$-0.880546\pi$
$61$	−1.15420	+	1.99914i	−0.147781	+	0.255963i	0.782626	+	0.622492i	$0.213880\pi$
$62$	−5.42082	−	9.38914i	−0.688445	−	1.19242i
$63$	−0.184179	+	0.319008i	−0.0232044	+	0.0401912i
$64$	1.00000			0.125000
$65$		0			0
$66$	3.10431	−	5.37683i	0.382115	−	0.661842i
$67$	3.37162	−	5.83981i	0.411909	−	0.713447i	−0.583190	−	0.812336i	$-0.698196\pi$
$67$	3.37162	−	5.83981i	0.411909	−	0.713447i	0.995098	+	0.0988892i	$0.0315289\pi$
$68$	−4.09841			−0.497005
$69$	−7.97988			−0.960664
$70$		0			0
$71$	0.994093	+	1.72182i	0.117977	+	0.204342i	0.918966	−	0.394337i	$-0.129026\pi$
$71$	0.994093	+	1.72182i	0.117977	+	0.204342i	−0.800989	+	0.598679i	$0.795692\pi$
$72$	0.0492032	−	0.0852224i	0.00579865	−	0.0100436i
$73$	4.59494	+	7.95867i	0.537797	+	0.931492i	0.999022	+	0.0442086i	$0.0140766\pi$
$73$	4.59494	+	7.95867i	0.537797	+	0.931492i	−0.461225	+	0.887283i	$0.652590\pi$
$74$	3.87752	+	6.71607i	0.450753	+	0.780727i
$75$		0			0
$76$	−3.37752	−	2.75542i	−0.387429	−	0.316068i
$77$	−13.6435			−1.55482
$78$	−5.14414	−	8.90992i	−0.582459	−	1.00885i
$79$	−3.07849	−	5.33210i	−0.346357	−	0.599909i	0.639242	−	0.769006i	$-0.279248\pi$
$79$	−3.07849	−	5.33210i	−0.346357	−	0.599909i	−0.985599	+	0.169097i	$0.945915\pi$
$80$		0			0
$81$	4.34755	+	7.53017i	0.483061	+	0.836686i
$82$	3.99653	−	6.92220i	0.441343	−	0.764429i
$83$	−5.69159			−0.624734			−0.312367	−	0.949962i	$-0.601122\pi$
$83$	−5.69159			−0.624734			−0.312367	+	0.949962i	$0.601122\pi$
$84$	6.37625			0.695706
$85$		0			0
$86$	2.19403	−	3.80018i	0.236589	−	0.409783i
$87$	11.3188			1.21351
$88$	3.64483			0.388540
$89$	5.53983	−	9.59527i	0.587221	−	1.01710i	−0.407374	−	0.913261i	$-0.633555\pi$
$89$	5.53983	−	9.59527i	0.587221	−	1.01710i	0.994595	−	0.103835i	$-0.0331113\pi$
$90$		0			0
$91$	−11.3043	+	19.5795i	−1.18501	+	2.05249i
$92$	−2.34233	−	4.05703i	−0.244205	−	0.422975i
$93$	9.23386	+	15.9935i	0.957507	+	1.65845i
$94$	1.74324			0.179801
$95$		0			0
$96$	−1.70341			−0.173853
$97$	0.752610	+	1.30356i	0.0764159	+	0.132356i	0.901701	−	0.432360i	$-0.142319\pi$
$97$	0.752610	+	1.30356i	0.0764159	+	0.132356i	−0.825285	+	0.564716i	$0.808986\pi$
$98$	−3.50591	−	6.07241i	−0.354150	−	0.613406i
$99$	0.179337	−	0.310621i	0.0180241	−	0.0312186i
$100$		0			0
$101$	3.91735	−	6.78506i	0.389791	−	0.675138i	−0.602630	−	0.798021i	$-0.705880\pi$
$101$	3.91735	−	6.78506i	0.389791	−	0.675138i	0.992421	+	0.122883i	$0.0392138\pi$
$102$	6.98125			0.691247
$103$	13.6036			1.34041			0.670203	−	0.742178i	$-0.266207\pi$
$103$	13.6036			1.34041			0.670203	+	0.742178i	$0.266207\pi$
$104$	3.01991	−	5.23065i	0.296127	−	0.512907i
$105$		0			0
$106$	−1.74324			−0.169318
$107$	7.24845			0.700735			0.350367	−	0.936612i	$-0.386057\pi$
$107$	7.24845			0.700735			0.350367	+	0.936612i	$0.386057\pi$
$108$	−2.63892	+	4.57075i	−0.253930	+	0.439820i
$109$	−2.24392	−	3.88659i	−0.214929	−	0.372268i	0.738322	−	0.674449i	$-0.235619\pi$
$109$	−2.24392	−	3.88659i	−0.214929	−	0.372268i	−0.953251	+	0.302181i	$0.902285\pi$
$110$		0			0
$111$	−6.60500	−	11.4402i	−0.626919	−	1.08586i
$112$	1.87162	+	3.24174i	0.176851	+	0.306315i
$113$	−13.2813			−1.24940			−0.624702	−	0.780863i	$-0.714780\pi$
$113$	−13.2813			−1.24940			−0.624702	+	0.780863i	$0.714780\pi$
$114$	5.75330	+	4.69360i	0.538846	+	0.439596i
$115$		0			0
$116$	3.32241	+	5.75459i	0.308478	+	0.534300i
$117$	−0.297179	−	0.514729i	−0.0274742	−	0.0475867i
$118$	3.67412	−	6.36376i	0.338230	−	0.585831i
$119$	−7.67065	−	13.2860i	−0.703167	−	1.21792i
$120$		0			0
$121$	2.28478			0.207707
$122$	2.30841			0.208993
$123$	−6.80772	+	11.7913i	−0.613831	+	1.06319i
$124$	−5.42082	+	9.38914i	−0.486804	+	0.843169i
$125$		0			0
$126$	0.368358			0.0328160
$127$	−1.72332	+	2.98488i	−0.152920	+	0.264865i	−0.932300	−	0.361687i	$-0.882201\pi$
$127$	−1.72332	+	2.98488i	−0.152920	+	0.264865i	0.779380	+	0.626552i	$0.215534\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−3.73733	+	6.47324i	−0.329053	+	0.569937i
$130$		0			0
$131$	−8.26315	−	14.3122i	−0.721955	−	1.25046i	−0.960215	−	0.279261i	$-0.909911\pi$
$131$	−8.26315	−	14.3122i	−0.721955	−	1.25046i	0.238260	−	0.971201i	$-0.423423\pi$
$132$	−6.20863			−0.540392
$133$	2.61091	−	16.1061i	0.226394	−	1.39658i
$134$	−6.74324			−0.582527
$135$		0			0
$136$	2.04920	+	3.54932i	0.175718	+	0.304352i
$137$	11.1560	−	19.3227i	0.953118	−	1.65085i	0.214499	−	0.976724i	$-0.431188\pi$
$137$	11.1560	−	19.3227i	0.953118	−	1.65085i	0.738618	−	0.674124i	$-0.235479\pi$
$138$	3.98994	+	6.91078i	0.339646	+	0.588284i
$139$	0.880992	−	1.52592i	0.0747248	−	0.129427i	−0.826242	−	0.563316i	$-0.809526\pi$
$139$	0.880992	−	1.52592i	0.0747248	−	0.129427i	0.900967	+	0.433889i	$0.142859\pi$
$140$		0			0
$141$	−2.96944			−0.250072
$142$	0.994093	−	1.72182i	0.0834225	−	0.144492i
$143$	11.0071	−	19.0648i	0.920458	−	1.59428i
$144$	−0.0984064			−0.00820053
$145$		0			0
$146$	4.59494	−	7.95867i	0.380280	−	0.658664i
$147$	5.97198	+	10.3438i	0.492561	+	0.853141i
$148$	3.87752	−	6.71607i	0.318731	−	0.552057i
$149$	1.80713	+	3.13005i	0.148046	+	0.256424i	0.930505	−	0.366278i	$-0.119368\pi$
$149$	1.80713	+	3.13005i	0.148046	+	0.256424i	−0.782459	+	0.622702i	$0.786035\pi$
$150$		0			0
$151$	−18.1711			−1.47875			−0.739373	−	0.673296i	$-0.764878\pi$
$151$	−18.1711			−1.47875			−0.739373	+	0.673296i	$0.764878\pi$
$152$	−0.697500	+	4.30273i	−0.0565747	+	0.348998i
$153$	0.403309			0.0326056
$154$	6.82173	+	11.8156i	0.549710	+	0.952126i
$155$		0			0
$156$	−5.14414	+	8.90992i	−0.411861	+	0.713364i
$157$	3.89153	+	6.74033i	0.310578	+	0.537937i	0.978488	−	0.206305i	$-0.0661440\pi$
$157$	3.89153	+	6.74033i	0.310578	+	0.537937i	−0.667910	+	0.744242i	$0.732811\pi$
$158$	−3.07849	+	5.33210i	−0.244912	+	0.424199i
$159$	2.96944			0.235492
$160$		0			0
$161$	8.76789	−	15.1864i	0.691007	−	1.19686i
$162$	4.34755	−	7.53017i	0.341576	−	0.591626i
$163$	5.46539			0.428082			0.214041	−	0.976825i	$-0.431337\pi$
$163$	5.46539			0.428082			0.214041	+	0.976825i	$0.431337\pi$
$164$	−7.99307			−0.624154
$165$		0			0
$166$	2.84580	+	4.92906i	0.220877	+	0.382570i
$167$	9.19994	−	15.9348i	0.711913	−	1.23307i	−0.252226	−	0.967668i	$-0.581163\pi$
$167$	9.19994	−	15.9348i	0.711913	−	1.23307i	0.964138	−	0.265400i	$-0.0855042\pi$
$168$	−3.18813	−	5.52200i	−0.245969	−	0.426031i
$169$	−11.7398	−	20.3339i	−0.903059	−	1.56414i
$170$		0			0
$171$	0.332370	+	0.271151i	0.0254170	+	0.0207354i
$172$	−4.38806			−0.334587
$173$	−9.74914	−	16.8860i	−0.741214	−	1.28382i	−0.951943	−	0.306275i	$-0.900917\pi$
$173$	−9.74914	−	16.8860i	−0.741214	−	1.28382i	0.210729	−	0.977544i	$-0.432416\pi$
$174$	−5.65942	−	9.80241i	−0.429040	−	0.743119i
$175$		0			0
$176$	−1.82241	−	3.15651i	−0.137370	−	0.237931i
$177$	−6.25852	+	10.8401i	−0.470419	+	0.814789i
$178$	−11.0797			−0.830456
$179$	−23.5661			−1.76142			−0.880708	−	0.473660i	$-0.842932\pi$
$179$	−23.5661			−1.76142			−0.880708	+	0.473660i	$0.842932\pi$
$180$		0			0
$181$	−7.86746	+	13.6268i	−0.584784	+	1.01288i	0.410118	+	0.912032i	$0.365487\pi$
$181$	−7.86746	+	13.6268i	−0.584784	+	1.01288i	−0.994902	+	0.100843i	$0.967846\pi$
$182$	22.6085			1.67585
$183$	−3.93215			−0.290673
$184$	−2.34233	+	4.05703i	−0.172679	+	0.299088i
$185$		0			0
$186$	9.23386	−	15.9935i	0.677060	−	1.17270i
$187$	7.46900	+	12.9367i	0.546187	+	0.946024i
$188$	−0.871618	−	1.50969i	−0.0635693	−	0.110105i
$189$	−19.7562			−1.43705
$190$		0			0
$191$	6.64483			0.480803			0.240401	−	0.970674i	$-0.422721\pi$
$191$	6.64483			0.480803			0.240401	+	0.970674i	$0.422721\pi$
$192$	0.851703	+	1.47519i	0.0614664	+	0.106463i
$193$	−3.99931	−	6.92701i	−0.287877	−	0.498617i	0.685426	−	0.728142i	$-0.259616\pi$
$193$	−3.99931	−	6.92701i	−0.287877	−	0.498617i	−0.973303	+	0.229525i	$0.926283\pi$
$194$	0.752610	−	1.30356i	0.0540342	−	0.0935900i
$195$		0			0
$196$	−3.50591	+	6.07241i	−0.250422	+	0.433743i
$197$	0.481593			0.0343121			0.0171560	−	0.999853i	$-0.494539\pi$
$197$	0.481593			0.0343121			0.0171560	+	0.999853i	$0.494539\pi$
$198$	−0.358674			−0.0254899
$199$	−11.6793	+	20.2292i	−0.827926	+	1.43401i	0.0717359	+	0.997424i	$0.477146\pi$
$199$	−11.6793	+	20.2292i	−0.827926	+	1.43401i	−0.899662	+	0.436587i	$0.856187\pi$
$200$		0			0
$201$	11.4865			0.810193
$202$	−7.83471			−0.551248
$203$	−12.4366	+	21.5408i	−0.872877	+	1.51187i
$204$	−3.49063	−	6.04594i	−0.244393	−	0.423301i
$205$		0			0
$206$	−6.80181	−	11.7811i	−0.473905	−	0.820827i
$207$	0.230500	+	0.399238i	0.0160209	+	0.0277490i
$208$	−6.03983			−0.418787
$209$	−2.54227	+	15.6827i	−0.175852	+	1.08480i
$210$		0			0
$211$	2.91491	+	5.04878i	0.200671	+	0.347572i	0.948745	−	0.316043i	$-0.102354\pi$
$211$	2.91491	+	5.04878i	0.200671	+	0.347572i	−0.748074	+	0.663616i	$0.769021\pi$
$212$	0.871618	+	1.50969i	0.0598630	+	0.103686i
$213$	−1.69335	+	2.93296i	−0.116026	+	0.200963i
$214$	−3.62423	−	6.27735i	−0.247747	−	0.429111i
$215$		0			0
$216$	5.27785			0.359112
$217$	−40.5828			−2.75494
$218$	−2.24392	+	3.88659i	−0.151978	+	0.263233i
$219$	−7.82705	+	13.5568i	−0.528903	+	0.916087i
$220$		0			0
$221$	24.7537			1.66511
$222$	−6.60500	+	11.4402i	−0.443299	+	0.767816i
$223$	8.36224	+	14.4838i	0.559977	+	0.969909i	0.997498	+	0.0707005i	$0.0225235\pi$
$223$	8.36224	+	14.4838i	0.559977	+	0.969909i	−0.437520	+	0.899209i	$0.644143\pi$
$224$	1.87162	−	3.24174i	0.125053	−	0.216598i
$225$		0			0
$226$	6.64067	+	11.5020i	0.441731	+	0.765101i
$227$	−4.16186			−0.276232			−0.138116	−	0.990416i	$-0.544105\pi$
$227$	−4.16186			−0.276232			−0.138116	+	0.990416i	$0.544105\pi$
$228$	1.18813	−	7.32930i	0.0786856	−	0.485395i
$229$	−5.49828			−0.363337			−0.181668	−	0.983360i	$-0.558150\pi$
$229$	−5.49828			−0.363337			−0.181668	+	0.983360i	$0.558150\pi$
$230$		0			0
$231$	−11.6202	−	20.1267i	−0.764551	−	1.32424i
$232$	3.32241	−	5.75459i	0.218127	−	0.377807i
$233$	−6.59738	−	11.4270i	−0.432209	−	0.748607i	0.564855	−	0.825190i	$-0.308932\pi$
$233$	−6.59738	−	11.4270i	−0.432209	−	0.748607i	−0.997063	+	0.0765832i	$0.975599\pi$
$234$	−0.297179	+	0.514729i	−0.0194272	+	0.0336489i
$235$		0			0
$236$	−7.34824			−0.478329
$237$	5.24392	−	9.08274i	0.340629	−	0.589987i
$238$	−7.67065	+	13.2860i	−0.497214	+	0.861201i
$239$	8.47720			0.548345			0.274172	−	0.961681i	$-0.411596\pi$
$239$	8.47720			0.548345			0.274172	+	0.961681i	$0.411596\pi$
$240$		0			0
$241$	−10.5146	+	18.2118i	−0.677304	+	1.17313i	0.298485	+	0.954414i	$0.403519\pi$
$241$	−10.5146	+	18.2118i	−0.677304	+	1.17313i	−0.975790	+	0.218711i	$0.929815\pi$
$242$	−1.14239	−	1.97868i	−0.0734356	−	0.127194i
$243$	0.511126	−	0.885296i	0.0327887	−	0.0567918i
$244$	−1.15420	−	1.99914i	−0.0738903	−	0.127982i
$245$		0			0
$246$	13.6154			0.868089
$247$	20.3997	+	16.6423i	1.29800	+	1.05892i
$248$	10.8416			0.688445
$249$	−4.84755	−	8.39620i	−0.307201	−	0.532088i
$250$		0			0
$251$	−13.6183	+	23.5876i	−0.859581	+	1.48884i	0.0127485	+	0.999919i	$0.495942\pi$
$251$	−13.6183	+	23.5876i	−0.859581	+	1.48884i	−0.872329	+	0.488919i	$0.837391\pi$
$252$	−0.184179	−	0.319008i	−0.0116022	−	0.0200956i
$253$	−8.53739	+	14.7872i	−0.536741	+	0.929663i
$254$	3.44664			0.216262
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.32705	+	14.4229i	−0.519427	+	0.899674i	0.480318	+	0.877094i	$0.340521\pi$
$257$	−8.32705	+	14.4229i	−0.519427	+	0.899674i	−0.999745	+	0.0225796i	$0.992812\pi$
$258$	7.47466			0.465352
$259$	29.0290			1.80377
$260$		0			0
$261$	−0.326947	−	0.566288i	−0.0202375	−	0.0350524i
$262$	−8.26315	+	14.3122i	−0.510499	+	0.884210i
$263$	0.994093	+	1.72182i	0.0612984	+	0.106172i	0.895046	−	0.445974i	$-0.147143\pi$
$263$	0.994093	+	1.72182i	0.0612984	+	0.106172i	−0.833748	+	0.552146i	$0.813809\pi$
$264$	3.10431	+	5.37683i	0.191057	+	0.330921i
$265$		0			0
$266$	−15.2538	+	5.79196i	−0.935269	+	0.355128i
$267$	18.8732			1.15502
$268$	3.37162	+	5.83981i	0.205954	+	0.356723i
$269$	−3.57224	−	6.18731i	−0.217804	−	0.377247i	0.736333	−	0.676620i	$-0.236556\pi$
$269$	−3.57224	−	6.18731i	−0.217804	−	0.377247i	−0.954136	+	0.299373i	$0.903223\pi$
$270$		0			0
$271$	−5.47940	−	9.49060i	−0.332850	−	0.576513i	0.650220	−	0.759746i	$-0.274677\pi$
$271$	−5.47940	−	9.49060i	−0.332850	−	0.576513i	−0.983069	+	0.183234i	$0.941344\pi$
$272$	2.04920	−	3.54932i	0.124251	−	0.215209i
$273$	−38.5115			−2.33082
$274$	−22.3119			−1.34791
$275$		0			0
$276$	3.98994	−	6.91078i	0.240166	−	0.415980i
$277$	12.2686			0.737147			0.368574	−	0.929599i	$-0.379846\pi$
$277$	12.2686			0.737147			0.368574	+	0.929599i	$0.379846\pi$
$278$	−1.76198			−0.105677
$279$	0.533443	−	0.923951i	0.0319364	−	0.0553155i
$280$		0			0
$281$	8.53983	−	14.7914i	0.509443	−	0.882382i	−0.490497	−	0.871443i	$-0.663185\pi$
$281$	8.53983	−	14.7914i	0.509443	−	0.882382i	0.999940	−	0.0109390i	$-0.00348205\pi$
$282$	1.48472	+	2.57161i	0.0884138	+	0.153137i
$283$	−15.0064	−	25.9918i	−0.892037	−	1.54505i	−0.837429	−	0.546546i	$-0.815943\pi$
$283$	−15.0064	−	25.9918i	−0.892037	−	1.54505i	−0.0546077	−	0.998508i	$-0.517391\pi$
$284$	−1.98819			−0.117977
$285$		0			0
$286$	−22.0141			−1.30172
$287$	−14.9600	−	25.9114i	−0.883059	−	1.52950i
$288$	0.0492032	+	0.0852224i	0.00289933	+	0.00502178i
$289$	0.101533	−	0.175860i	0.00597251	−	0.0103447i
$290$		0			0
$291$	−1.28200	+	2.22049i	−0.0751522	+	0.130167i
$292$	−9.18988			−0.537797
$293$	22.4677			1.31258			0.656289	−	0.754509i	$-0.272125\pi$
$293$	22.4677			1.31258			0.656289	+	0.754509i	$0.272125\pi$
$294$	5.97198	−	10.3438i	0.348293	−	0.603261i
$295$		0			0
$296$	−7.75505			−0.450753
$297$	19.2368			1.11624
$298$	1.80713	−	3.13005i	0.104684	−	0.181319i
$299$	14.1473	+	24.5038i	0.818158	+	1.41709i
$300$		0			0
$301$	−8.21278	−	14.2250i	−0.473377	−	0.819913i
$302$	9.08556	+	15.7367i	0.522816	+	0.905543i
$303$	13.3457			0.766690
$304$	4.07502	−	1.54731i	0.233719	−	0.0887445i
$305$		0			0
$306$	−0.201655	−	0.349276i	−0.0115278	−	0.0199668i
$307$	−8.19578	−	14.1955i	−0.467758	−	0.810181i	0.531563	−	0.847019i	$-0.321605\pi$
$307$	−8.19578	−	14.1955i	−0.467758	−	0.810181i	−0.999321	+	0.0368378i	$0.988271\pi$
$308$	6.82173	−	11.8156i	0.388704	−	0.673255i
$309$	11.5863	+	20.0680i	0.659119	+	1.14163i
$310$		0			0
$311$	−18.0197			−1.02180			−0.510902	−	0.859639i	$-0.670688\pi$
$311$	−18.0197			−1.02180			−0.510902	+	0.859639i	$0.670688\pi$
$312$	10.2883			0.582459
$313$	−9.00522	+	15.5975i	−0.509005	+	0.881623i	0.490941	+	0.871193i	$0.336653\pi$
$313$	−9.00522	+	15.5975i	−0.509005	+	0.881623i	−0.999946	+	0.0104296i	$0.996680\pi$
$314$	3.89153	−	6.74033i	0.219612	−	0.380379i
$315$		0			0
$316$	6.15698			0.346357
$317$	−11.6277	+	20.1398i	−0.653076	+	1.13116i	0.329296	+	0.944227i	$0.393189\pi$
$317$	−11.6277	+	20.1398i	−0.653076	+	1.13116i	−0.982372	+	0.186935i	$0.940145\pi$
$318$	−1.48472	−	2.57161i	−0.0832589	−	0.144209i
$319$	12.1096	−	20.9745i	0.678009	−	1.17435i
$320$		0			0
$321$	6.17353	+	10.6929i	0.344573	+	0.596818i
$322$	−17.5358			−0.977231
$323$	−16.7011	+	6.34152i	−0.929274	+	0.352851i
$324$	−8.69510			−0.483061
$325$		0			0
$326$	−2.73270	−	4.73317i	−0.151350	−	0.262146i
$327$	3.82231	−	6.62044i	0.211374	−	0.366111i
$328$	3.99653	+	6.92220i	0.220672	+	0.382214i
$329$	3.26267	−	5.65111i	0.179877	−	0.311556i
$330$		0			0
$331$	7.38319			0.405817			0.202908	−	0.979198i	$-0.434961\pi$
$331$	7.38319			0.405817			0.202908	+	0.979198i	$0.434961\pi$
$332$	2.84580	−	4.92906i	0.156183	−	0.270518i
$333$	−0.381573	+	0.660904i	−0.0209101	+	0.0362173i
$334$	−18.3999			−1.00680
$335$		0			0
$336$	−3.18813	+	5.52200i	−0.173927	+	0.301250i
$337$	15.4400	+	26.7429i	0.841073	+	1.45678i	0.888988	+	0.457930i	$0.151409\pi$
$337$	15.4400	+	26.7429i	0.841073	+	1.45678i	−0.0479153	+	0.998851i	$0.515258\pi$
$338$	−11.7398	+	20.3339i	−0.638559	+	1.10602i
$339$	−11.3118	−	19.5926i	−0.614371	−	1.06412i
$340$		0			0
$341$	39.5159			2.13991
$342$	0.0686384	−	0.423416i	0.00371154	−	0.0228957i
$343$	−0.0442191			−0.00238761
$344$	2.19403	+	3.80018i	0.118294	+	0.204892i
$345$		0			0
$346$	−9.74914	+	16.8860i	−0.524117	+	0.907797i
$347$	4.55974	+	7.89771i	0.244780	+	0.423971i	0.962070	−	0.272804i	$-0.0879510\pi$
$347$	4.55974	+	7.89771i	0.244780	+	0.423971i	−0.717290	+	0.696775i	$0.754618\pi$
$348$	−5.65942	+	9.80241i	−0.303377	+	0.525464i
$349$	−14.2508			−0.762827			−0.381414	−	0.924404i	$-0.624563\pi$
$349$	−14.2508			−0.762827			−0.381414	+	0.924404i	$0.624563\pi$
$350$		0			0
$351$	15.9386	−	27.6065i	0.850742	−	1.47353i
$352$	−1.82241	+	3.15651i	−0.0971350	+	0.168243i
$353$	7.77613			0.413882			0.206941	−	0.978353i	$-0.433649\pi$
$353$	7.77613			0.413882			0.206941	+	0.978353i	$0.433649\pi$
$354$	12.5170			0.665273
$355$		0			0
$356$	5.53983	+	9.59527i	0.293610	+	0.508548i
$357$	13.0662	−	22.6314i	0.691539	−	1.19778i
$358$	11.7831	+	20.4089i	0.622754	+	1.07864i
$359$	−2.90437	−	5.03052i	−0.153287	−	0.265501i	0.779147	−	0.626841i	$-0.215653\pi$
$359$	−2.90437	−	5.03052i	−0.153287	−	0.265501i	−0.932434	+	0.361340i	$0.882319\pi$
$360$		0			0
$361$	−18.0270	−	6.00231i	−0.948789	−	0.315911i
$362$	15.7349			0.827009
$363$	1.94595	+	3.37049i	0.102136	+	0.176905i
$364$	−11.3043	−	19.5795i	−0.592504	−	1.02625i
$365$		0			0
$366$	1.96608	+	3.40535i	0.102769	+	0.178000i
$367$	−11.1414	+	19.2974i	−0.581574	+	1.00732i	0.413719	+	0.910405i	$0.364230\pi$
$367$	−11.1414	+	19.2974i	−0.581574	+	1.00732i	−0.995293	+	0.0969115i	$0.969104\pi$
$368$	4.68466			0.244205
$369$	0.786568			0.0409471
$370$		0			0
$371$	−3.26267	+	5.65111i	−0.169389	+	0.293391i
$372$	−18.4677			−0.957507
$373$	−17.0609			−0.883380			−0.441690	−	0.897168i	$-0.645621\pi$
$373$	−17.0609			−0.883380			−0.441690	+	0.897168i	$0.645621\pi$
$374$	7.46900	−	12.9367i	0.386213	−	0.668940i
$375$		0			0
$376$	−0.871618	+	1.50969i	−0.0449503	+	0.0778561i
$377$	−20.0668	−	34.7567i	−1.03349	−	1.79006i
$378$	9.87811	+	17.1094i	0.508075	+	0.880012i
$379$	−10.0329			−0.515355			−0.257678	−	0.966231i	$-0.582957\pi$
$379$	−10.0329			−0.515355			−0.257678	+	0.966231i	$0.582957\pi$
$380$		0			0
$381$	−5.87103			−0.300782
$382$	−3.32241	−	5.75459i	−0.169990	−	0.294430i
$383$	0.994093	+	1.72182i	0.0507958	+	0.0879809i	0.890305	−	0.455364i	$-0.150491\pi$
$383$	0.994093	+	1.72182i	0.0507958	+	0.0879809i	−0.839510	+	0.543345i	$0.817158\pi$
$384$	0.851703	−	1.47519i	0.0434633	−	0.0752806i
$385$		0			0
$386$	−3.99931	+	6.92701i	−0.203560	+	0.352576i
$387$	0.431814			0.0219503
$388$	−1.50522			−0.0764159
$389$	−4.43854	+	7.68778i	−0.225043	+	0.389786i	−0.956332	−	0.292282i	$-0.905586\pi$
$389$	−4.43854	+	7.68778i	−0.225043	+	0.389786i	0.731289	+	0.682067i	$0.238919\pi$
$390$		0			0
$391$	−19.1996			−0.970967
$392$	7.01181			0.354150
$393$	14.0755	−	24.3795i	0.710015	−	1.22978i
$394$	−0.240797	−	0.417072i	−0.0121312	−	0.0210118i
$395$		0			0
$396$	0.179337	+	0.310621i	0.00901203	+	0.0156093i
$397$	−10.5563	−	18.2840i	−0.529804	−	0.917648i	−0.999396	−	0.0347640i	$-0.988932\pi$
$397$	−10.5563	−	18.2840i	−0.529804	−	0.917648i	0.469591	−	0.882884i	$-0.344401\pi$
$398$	23.3587			1.17086
$399$	25.9834	−	9.86606i	1.30080	−	0.493921i
$400$		0			0
$401$	−14.9806	−	25.9471i	−0.748094	−	1.29574i	−0.948735	−	0.316072i	$-0.897636\pi$
$401$	−14.9806	−	25.9471i	−0.748094	−	1.29574i	0.200642	−	0.979665i	$-0.435697\pi$
$402$	−5.74324	−	9.94758i	−0.286447	−	0.496140i
$403$	32.7408	−	56.7088i	1.63094	−	2.82487i
$404$	3.91735	+	6.78506i	0.194896	+	0.337569i
$405$		0			0
$406$	24.8732			1.23443
$407$	−28.2658			−1.40109
$408$	−3.49063	+	6.04594i	−0.172812	+	0.299319i
$409$	2.09772	−	3.63336i	0.103726	−	0.179658i	−0.809491	−	0.587132i	$-0.800257\pi$
$409$	2.09772	−	3.63336i	0.103726	−	0.179658i	0.913217	+	0.407474i	$0.133590\pi$
$410$		0			0
$411$	38.0063			1.87471
$412$	−6.80181	+	11.7811i	−0.335101	+	0.580412i
$413$	−13.7531	−	23.8210i	−0.676745	−	1.17216i
$414$	0.230500	−	0.399238i	0.0113285	−	0.0196215i
$415$		0			0
$416$	3.01991	+	5.23065i	0.148063	+	0.256453i
$417$	3.00137			0.146978
$418$	14.8528	−	5.63969i	0.726473	−	0.275846i
$419$	12.5326			0.612255			0.306128	−	0.951990i	$-0.400967\pi$
$419$	12.5326			0.612255			0.306128	+	0.951990i	$0.400967\pi$
$420$		0			0
$421$	13.2883	+	23.0160i	0.647631	+	1.12173i	0.983687	+	0.179888i	$0.0575736\pi$
$421$	13.2883	+	23.0160i	0.647631	+	1.12173i	−0.336056	+	0.941842i	$0.609093\pi$
$422$	2.91491	−	5.04878i	0.141896	−	0.245771i
$423$	0.0857727	+	0.148563i	0.00417041	+	0.00722337i
$424$	0.871618	−	1.50969i	0.0423295	−	0.0733169i
$425$		0			0
$426$	3.38669			0.164086
$427$	4.32045	−	7.48325i	0.209081	−	0.362140i
$428$	−3.62423	+	6.27735i	−0.175184	+	0.303427i
$429$	37.4990			1.81047
$430$		0			0
$431$	0.0903049	−	0.156413i	0.00434983	−	0.00753413i	−0.863842	−	0.503762i	$-0.831949\pi$
$431$	0.0903049	−	0.156413i	0.00434983	−	0.00753413i	0.868192	+	0.496228i	$0.165282\pi$
$432$	−2.63892	−	4.57075i	−0.126965	−	0.219910i
$433$	−6.00522	+	10.4013i	−0.288592	+	0.499857i	−0.973474	−	0.228798i	$-0.926521\pi$
$433$	−6.00522	+	10.4013i	−0.288592	+	0.499857i	0.684882	+	0.728654i	$0.259854\pi$
$434$	20.2914	+	35.1458i	0.974019	+	1.68705i
$435$		0			0
$436$	4.48785			0.214929
$437$	−15.8225	−	12.9082i	−0.756895	−	0.617483i
$438$	15.6541			0.747982
$439$	14.2544	+	24.6893i	0.680324	+	1.17835i	0.974882	+	0.222722i	$0.0714941\pi$
$439$	14.2544	+	24.6893i	0.680324	+	1.17835i	−0.294559	+	0.955633i	$0.595173\pi$
$440$		0			0
$441$	0.345004	−	0.597564i	0.0164287	−	0.0284554i
$442$	−12.3768	−	21.4373i	−0.588706	−	1.01967i
$443$	4.27321	−	7.40142i	0.203026	−	0.351652i	−0.746476	−	0.665413i	$-0.768256\pi$
$443$	4.27321	−	7.40142i	0.203026	−	0.351652i	0.949502	+	0.313761i	$0.101589\pi$
$444$	13.2100			0.626919
$445$		0			0
$446$	8.36224	−	14.4838i	0.395964	−	0.685829i
$447$	−3.07828	+	5.33174i	−0.145598	+	0.252183i
$448$	−3.74324			−0.176851
$449$	−4.24612			−0.200387			−0.100193	−	0.994968i	$-0.531946\pi$
$449$	−4.24612			−0.200387			−0.100193	+	0.994968i	$0.531946\pi$
$450$		0			0
$451$	14.5667	+	25.2302i	0.685918	+	1.18805i
$452$	6.64067	−	11.5020i	0.312351	−	0.541008i
$453$	−15.4764	−	26.8059i	−0.727145	−	1.25945i
$454$	2.08093	+	3.60428i	0.0976629	+	0.169157i
$455$		0			0
$456$	−6.94142	+	2.63570i	−0.325062	+	0.123428i
$457$	−18.2204			−0.852316			−0.426158	−	0.904649i	$-0.640133\pi$
$457$	−18.2204			−0.852316			−0.426158	+	0.904649i	$0.640133\pi$
$458$	2.74914	+	4.76165i	0.128459	+	0.222497i
$459$	10.8154	+	18.7328i	0.504819	+	0.874371i
$460$		0			0
$461$	−15.0140	−	26.0050i	−0.699272	−	1.21117i	−0.968719	−	0.248160i	$-0.920174\pi$
$461$	−15.0140	−	26.0050i	−0.699272	−	1.21117i	0.269447	−	0.963015i	$-0.413159\pi$
$462$	−11.6202	+	20.1267i	−0.540619	+	0.936380i
$463$	10.1656			0.472434			0.236217	−	0.971700i	$-0.424092\pi$
$463$	10.1656			0.472434			0.236217	+	0.971700i	$0.424092\pi$
$464$	−6.64483			−0.308478
$465$		0			0
$466$	−6.59738	+	11.4270i	−0.305618	+	0.529345i
$467$	13.6129			0.629930			0.314965	−	0.949103i	$-0.398007\pi$
$467$	13.6129			0.629930			0.314965	+	0.949103i	$0.398007\pi$
$468$	0.594358			0.0274742
$469$	−12.6208	+	21.8598i	−0.582773	+	1.00939i
$470$		0			0
$471$	−6.62886	+	11.4815i	−0.305442	+	0.529041i
$472$	3.67412	+	6.36376i	0.169115	+	0.292916i
$473$	7.99687	+	13.8510i	0.367697	+	0.636869i
$474$	−10.4878			−0.481723
$475$		0			0
$476$	15.3413			0.703167
$477$	−0.0857727	−	0.148563i	−0.00392726	−	0.00680222i
$478$	−4.23860	−	7.34147i	−0.193869	−	0.335791i
$479$	−2.71463	+	4.70188i	−0.124035	+	0.214835i	−0.921355	−	0.388722i	$-0.872917\pi$
$479$	−2.71463	+	4.70188i	−0.124035	+	0.214835i	0.797320	+	0.603556i	$0.206250\pi$
$480$		0			0
$481$	−23.4196	+	40.5639i	−1.06784	+	1.84956i
$482$	21.0292			0.957853
$483$	29.8706			1.35916
$484$	−1.14239	+	1.97868i	−0.0519268	+	0.0899399i
$485$		0			0
$486$	−1.02225			−0.0463703
$487$	32.5569			1.47529			0.737646	−	0.675188i	$-0.235937\pi$
$487$	32.5569			1.47529			0.737646	+	0.675188i	$0.235937\pi$
$488$	−1.15420	+	1.99914i	−0.0522483	+	0.0904968i
$489$	4.65489	+	8.06251i	0.210501	+	0.364599i
$490$		0			0
$491$	−15.3410	−	26.5713i	−0.692328	−	1.19915i	−0.971073	−	0.238782i	$-0.923252\pi$
$491$	−15.3410	−	26.5713i	−0.692328	−	1.19915i	0.278746	−	0.960365i	$-0.410081\pi$
$492$	−6.80772	−	11.7913i	−0.306916	−	0.531594i
$493$	27.2332			1.22652
$494$	4.21278	−	25.9878i	0.189542	−	1.16924i
$495$		0			0
$496$	−5.42082	−	9.38914i	−0.243402	−	0.421585i
$497$	−3.72113	−	6.44518i	−0.166915	−	0.289106i
$498$	−4.84755	+	8.39620i	−0.217224	+	0.376243i
$499$	4.91213	+	8.50807i	0.219897	+	0.380873i	0.954776	−	0.297325i	$-0.0960944\pi$
$499$	4.91213	+	8.50807i	0.219897	+	0.380873i	−0.734879	+	0.678198i	$0.762761\pi$
$500$		0			0
$501$	31.3425			1.40028
$502$	27.2366			1.21563
$503$	−7.57502	+	13.1203i	−0.337754	+	0.585006i	−0.984010	−	0.178114i	$-0.943000\pi$
$503$	−7.57502	+	13.1203i	−0.337754	+	0.585006i	0.646256	+	0.763121i	$0.276334\pi$
$504$	−0.184179	+	0.319008i	−0.00820399	+	0.0142097i
$505$		0			0
$506$	17.0748			0.759067
$507$	19.9976	−	34.6369i	0.888124	−	1.53828i
$508$	−1.72332	−	2.98488i	−0.0764600	−	0.132433i
$509$	1.12110	−	1.94180i	0.0496919	−	0.0860690i	−0.840110	−	0.542417i	$-0.817509\pi$
$509$	1.12110	−	1.94180i	0.0496919	−	0.0860690i	0.889801	+	0.456348i	$0.150843\pi$
$510$		0			0
$511$	−17.1999	−	29.7912i	−0.760881	−	1.31788i
$512$	1.00000			0.0441942
$513$	−3.68130	+	22.7091i	−0.162533	+	1.00263i
$514$	16.6541			0.734581
$515$		0			0
$516$	−3.73733	−	6.47324i	−0.164527	−	0.284969i
$517$	−3.17690	+	5.50255i	−0.139720	+	0.242002i
$518$	−14.5145	−	25.1398i	−0.637730	−	1.10458i
$519$	16.6068	−	28.7637i	0.728956	−	1.26259i
$520$		0			0
$521$	−7.06785			−0.309648			−0.154824	−	0.987942i	$-0.549481\pi$
$521$	−7.06785			−0.309648			−0.154824	+	0.987942i	$0.549481\pi$
$522$	−0.326947	+	0.566288i	−0.0143101	+	0.0247858i
$523$	17.4970	−	30.3057i	0.765091	−	1.32518i	−0.175108	−	0.984549i	$-0.556027\pi$
$523$	17.4970	−	30.3057i	0.765091	−	1.32518i	0.940199	−	0.340627i	$-0.110639\pi$
$524$	16.5263			0.721955
$525$		0			0
$526$	0.994093	−	1.72182i	0.0433445	−	0.0750749i
$527$	22.2167	+	38.4805i	0.967776	+	1.67624i
$528$	3.10431	−	5.37683i	0.135098	−	0.233996i
$529$	0.526988	+	0.912769i	0.0229125	+	0.0396856i
$530$		0			0
$531$	0.723113			0.0313804
$532$	12.6429	+	10.3142i	0.548138	+	0.447176i
$533$	48.2767			2.09110
$534$	−9.43658	−	16.3446i	−0.408361	−	0.707302i
$535$		0			0
$536$	3.37162	−	5.83981i	0.145632	−	0.252242i
$537$	−20.0713	−	34.7646i	−0.866143	−	1.50020i
$538$	−3.57224	+	6.18731i	−0.154010	+	0.266754i
$539$	25.5569			1.10081
$540$		0			0
$541$	14.4090	−	24.9571i	0.619492	−	1.07299i	−0.370087	−	0.928997i	$-0.620672\pi$
$541$	14.4090	−	24.9571i	0.619492	−	1.07299i	0.989579	−	0.143994i	$-0.0459946\pi$
$542$	−5.47940	+	9.49060i	−0.235360	+	0.407656i
$543$	−26.8030			−1.15023
$544$	−4.09841			−0.175718
$545$		0			0
$546$	19.2557	+	33.3519i	0.824069	+	1.42733i
$547$	−16.0375	+	27.7778i	−0.685715	+	1.18769i	0.287496	+	0.957782i	$0.407177\pi$
$547$	−16.0375	+	27.7778i	−0.685715	+	1.18769i	−0.973211	+	0.229912i	$0.926156\pi$
$548$	11.1560	+	19.3227i	0.476559	+	0.825424i
$549$	0.113581	+	0.196728i	0.00484752	+	0.00839615i
$550$		0			0
$551$	22.4431	+	18.3093i	0.956107	+	0.780002i
$552$	−7.97988			−0.339646
$553$	11.5235	+	19.9593i	0.490030	+	0.848757i
$554$	−6.13429	−	10.6249i	−0.260621	−	0.451409i
$555$		0			0
$556$	0.880992	+	1.52592i	0.0373624	+	0.0647135i
$557$	5.18813	−	8.98610i	0.219828	−	0.380753i	−0.734927	−	0.678146i	$-0.762784\pi$
$557$	5.18813	−	8.98610i	0.219828	−	0.380753i	0.954755	+	0.297393i	$0.0961171\pi$
$558$	−1.06689			−0.0451649
$559$	26.5032			1.12096
$560$		0			0
$561$	−12.7227	+	22.0364i	−0.537154	+	0.930379i
$562$	−17.0797			−0.720462
$563$	−8.44664			−0.355984			−0.177992	−	0.984032i	$-0.556960\pi$
$563$	−8.44664			−0.355984			−0.177992	+	0.984032i	$0.556960\pi$
$564$	1.48472	−	2.57161i	0.0625180	−	0.108284i
$565$		0			0
$566$	−15.0064	+	25.9918i	−0.630765	+	1.09252i
$567$	−16.2739	−	28.1872i	−0.683440	−	1.18375i
$568$	0.994093	+	1.72182i	0.0417112	+	0.0722460i
$569$	1.80181			0.0755359			0.0377680	−	0.999287i	$-0.487975\pi$
$569$	1.80181			0.0755359			0.0377680	+	0.999287i	$0.487975\pi$
$570$		0			0
$571$	2.70574			0.113232			0.0566158	−	0.998396i	$-0.481969\pi$
$571$	2.70574			0.113232			0.0566158	+	0.998396i	$0.481969\pi$
$572$	11.0071	+	19.0648i	0.460229	+	0.797140i
$573$	5.65942	+	9.80241i	0.236426	+	0.409501i
$574$	−14.9600	+	25.9114i	−0.624417	+	1.08152i
$575$		0			0
$576$	0.0492032	−	0.0852224i	0.00205013	−	0.00355093i
$577$	−6.61544			−0.275404			−0.137702	−	0.990474i	$-0.543972\pi$
$577$	−6.61544			−0.275404			−0.137702	+	0.990474i	$0.543972\pi$
$578$	−0.203065			−0.00844640
$579$	6.81246	−	11.7995i	0.283116	−	0.490371i
$580$		0			0
$581$	21.3050			0.883879
$582$	2.56400			0.106281
$583$	3.17690	−	5.50255i	0.131574	−	0.227892i
$584$	4.59494	+	7.95867i	0.190140	+	0.329332i
$585$		0			0
$586$	−11.2339	−	19.4576i	−0.464067	−	0.803787i
$587$	7.21463	+	12.4961i	0.297780	+	0.515770i	0.975628	−	0.219432i	$-0.0704205\pi$
$587$	7.21463	+	12.4961i	0.297780	+	0.515770i	−0.677848	+	0.735202i	$0.737087\pi$
$588$	−11.9440			−0.492561
$589$	−7.56204	+	46.6487i	−0.311589	+	1.92212i
$590$		0			0
$591$	0.410174	+	0.710443i	0.0168723	+	0.0292237i
$592$	3.87752	+	6.71607i	0.159365	+	0.276029i
$593$	10.3722	−	17.9652i	0.425935	−	0.737742i	−0.570572	−	0.821248i	$-0.693278\pi$
$593$	10.3722	−	17.9652i	0.425935	−	0.737742i	0.996507	+	0.0835060i	$0.0266118\pi$
$594$	−9.61842	−	16.6596i	−0.394649	−	0.683552i
$595$		0			0
$596$	−3.61427			−0.148046
$597$	−39.7893			−1.62847
$598$	14.1473	−	24.5038i	0.578525	−	1.00203i
$599$	9.41389	−	16.3053i	0.384641	−	0.666218i	−0.607078	−	0.794642i	$-0.707659\pi$
$599$	9.41389	−	16.3053i	0.384641	−	0.666218i	0.991719	+	0.128424i	$0.0409919\pi$
$600$		0			0
$601$	−23.0999			−0.942263			−0.471131	−	0.882063i	$-0.656154\pi$
$601$	−23.0999			−0.942263			−0.471131	+	0.882063i	$0.656154\pi$
$602$	−8.21278	+	14.2250i	−0.334728	+	0.579766i
$603$	−0.331789	−	0.574675i	−0.0135115	−	0.0234026i
$604$	9.08556	−	15.7367i	0.369686	−	0.640316i
$605$		0			0
$606$	−6.67285	−	11.5577i	−0.271066	−	0.469500i
$607$	28.6025			1.16094			0.580470	−	0.814281i	$-0.302869\pi$
$607$	28.6025			1.16094			0.580470	+	0.814281i	$0.302869\pi$
$608$	−3.37752	−	2.75542i	−0.136977	−	0.111747i
$609$	−42.3691			−1.71688
$610$		0			0
$611$	5.26442	+	9.11825i	0.212976	+	0.368885i
$612$	−0.201655	+	0.349276i	−0.00815141	+	0.0141186i
$613$	−3.72507	−	6.45202i	−0.150454	−	0.260594i	0.780940	−	0.624606i	$-0.214740\pi$
$613$	−3.72507	−	6.45202i	−0.150454	−	0.260594i	−0.931395	+	0.364011i	$0.881407\pi$
$614$	−8.19578	+	14.1955i	−0.330755	+	0.572884i
$615$		0			0
$616$	−13.6435			−0.549710
$617$	−15.6711	+	27.1432i	−0.630896	+	1.09274i	0.356473	+	0.934306i	$0.383979\pi$
$617$	−15.6711	+	27.1432i	−0.630896	+	1.09274i	−0.987369	+	0.158438i	$0.949354\pi$
$618$	11.5863	−	20.0680i	0.466067	−	0.807252i
$619$	1.60012			0.0643143			0.0321572	−	0.999483i	$-0.489762\pi$
$619$	1.60012			0.0643143			0.0321572	+	0.999483i	$0.489762\pi$
$620$		0			0
$621$	−12.3625	+	21.4124i	−0.496088	+	0.859250i
$622$	9.00985	+	15.6055i	0.361262	+	0.625724i
$623$	−20.7369	+	35.9173i	−0.830806	+	1.43900i
$624$	−5.14414	−	8.90992i	−0.205930	−	0.356682i
$625$		0			0
$626$	18.0104			0.719842
$627$	−25.3003	+	9.60669i	−1.01040	+	0.383654i
$628$	−7.78306			−0.310578
$629$	−15.8917	−	27.5252i	−0.633642	−	1.09750i
$630$		0			0
$631$	6.44386	−	11.1611i	0.256526	−	0.444316i	−0.708783	−	0.705427i	$-0.750755\pi$
$631$	6.44386	−	11.1611i	0.256526	−	0.444316i	0.965309	+	0.261111i	$0.0840887\pi$
$632$	−3.07849	−	5.33210i	−0.122456	−	0.212100i
$633$	−4.96528	+	8.60012i	−0.197352	+	0.341824i
$634$	23.2554			0.923590
$635$		0			0
$636$	−1.48472	+	2.57161i	−0.0588730	+	0.101971i
$637$	21.1751	−	36.6763i	0.838987	−	1.45317i
$638$	−24.2193			−0.958850
$639$	0.195650			0.00773980
$640$		0			0
$641$	13.9086	+	24.0903i	0.549355	+	0.951511i	0.998319	+	0.0579612i	$0.0184600\pi$
$641$	13.9086	+	24.0903i	0.549355	+	0.951511i	−0.448964	+	0.893550i	$0.648207\pi$
$642$	6.17353	−	10.6929i	0.243650	−	0.422014i
$643$	−8.50292	−	14.7275i	−0.335322	−	0.580795i	0.648224	−	0.761449i	$-0.275512\pi$
$643$	−8.50292	−	14.7275i	−0.335322	−	0.580795i	−0.983547	+	0.180654i	$0.942179\pi$
$644$	8.76789	+	15.1864i	0.345503	+	0.598429i
$645$		0			0
$646$	13.8425	+	11.2928i	0.544625	+	0.444310i
$647$	−42.3379			−1.66447			−0.832237	−	0.554420i	$-0.812940\pi$
$647$	−42.3379			−1.66447			−0.832237	+	0.554420i	$0.812940\pi$
$648$	4.34755	+	7.53017i	0.170788	+	0.295813i
$649$	13.3915	+	23.1948i	0.525664	+	0.910476i
$650$		0			0
$651$	−34.5645	−	59.8675i	−1.35469	−	2.34639i
$652$	−2.73270	+	4.73317i	−0.107021	+	0.185365i
$653$	−48.6365			−1.90329			−0.951647	−	0.307194i	$-0.900610\pi$
$653$	−48.6365			−1.90329			−0.951647	+	0.307194i	$0.900610\pi$
$654$	−7.64463			−0.298929
$655$		0			0
$656$	3.99653	−	6.92220i	0.156038	−	0.270266i
$657$	0.904342			0.0352818
$658$	−6.52534			−0.254384
$659$	−5.47593	+	9.48459i	−0.213312	+	0.369467i	−0.952749	−	0.303758i	$-0.901758\pi$
$659$	−5.47593	+	9.48459i	−0.213312	+	0.369467i	0.739437	+	0.673226i	$0.235092\pi$
$660$		0			0
$661$	12.3214	−	21.3413i	0.479246	−	0.830079i	−0.520470	−	0.853880i	$-0.674243\pi$
$661$	12.3214	−	21.3413i	0.479246	−	0.830079i	0.999717	+	0.0238007i	$0.00757670\pi$
$662$	−3.69159	−	6.39403i	−0.143478	−	0.248511i
$663$	21.0828	+	36.5165i	0.818788	+	1.41818i
$664$	−5.69159			−0.220877
$665$		0			0
$666$	0.763146			0.0295713
$667$	15.5644	+	26.9583i	0.602655	+	1.04383i
$668$	9.19994	+	15.9348i	0.355956	+	0.616534i
$669$	−14.2443	+	24.6719i	−0.550716	+	0.953869i
$670$		0			0
$671$	−4.20687	+	7.28652i	−0.162405	+	0.281293i
$672$	6.37625			0.245969
$673$	5.18012			0.199679			0.0998395	−	0.995004i	$-0.468167\pi$
$673$	5.18012			0.199679			0.0998395	+	0.995004i	$0.468167\pi$
$674$	15.4400	−	26.7429i	0.594728	−	1.03010i
$675$		0			0
$676$	23.4795			0.903059
$677$	−45.4548			−1.74697			−0.873485	−	0.486851i	$-0.838146\pi$
$677$	−45.4548			−1.74697			−0.873485	+	0.486851i	$0.838146\pi$
$678$	−11.3118	+	19.5926i	−0.434426	+	0.752448i
$679$	−2.81720	−	4.87953i	−0.108114	−	0.187259i
$680$		0			0
$681$	−3.54467	−	6.13955i	−0.135832	−	0.235268i
$682$	−19.7580	−	34.2218i	−0.756572	−	1.31042i
$683$	3.24495			0.124165			0.0620823	−	0.998071i	$-0.480226\pi$
$683$	3.24495			0.124165			0.0620823	+	0.998071i	$0.480226\pi$
$684$	−0.401008	+	0.152265i	−0.0153329	+	0.00582201i
$685$		0			0
$686$	0.0221096	+	0.0382949i	0.000844147	+	0.00146211i
$687$	−4.68291	−	8.11103i	−0.178664	−	0.309455i
$688$	2.19403	−	3.80018i	0.0836467	−	0.144880i
$689$	−5.26442	−	9.11825i	−0.200559	−	0.347378i
$690$		0			0
$691$	44.0806			1.67691			0.838453	−	0.544974i	$-0.183461\pi$
$691$	44.0806			1.67691			0.838453	+	0.544974i	$0.183461\pi$
$692$	19.4983			0.741214
$693$	−0.671301	+	1.16273i	−0.0255006	+	0.0441684i
$694$	4.55974	−	7.89771i	0.173086	−	0.299793i
$695$		0			0
$696$	11.3188			0.429040
$697$	−16.3794	+	28.3700i	−0.620415	+	1.07459i
$698$	7.12539	+	12.3415i	0.269700	+	0.467134i
$699$	11.2380	−	19.4648i	0.425061	−	0.736227i
$700$		0			0
$701$	−25.7667	−	44.6292i	−0.973193	−	1.68562i	−0.685773	−	0.727815i	$-0.740536\pi$
$701$	−25.7667	−	44.6292i	−0.973193	−	1.68562i	−0.287420	−	0.957805i	$-0.592797\pi$
$702$	−31.8773			−1.20313
$703$	5.40915	−	33.3679i	0.204010	−	1.25849i
$704$	3.64483			0.137370
$705$		0			0
$706$	−3.88806	−	6.73433i	−0.146329	−	0.253450i
$707$	−14.6636	+	25.3981i	−0.551481	+	0.955192i
$708$	−6.25852	−	10.8401i	−0.235209	−	0.407395i
$709$	−4.42556	+	7.66530i	−0.166205	+	0.287876i	−0.937083	−	0.349107i	$-0.886485\pi$
$709$	−4.42556	+	7.66530i	−0.166205	+	0.287876i	0.770877	+	0.636984i	$0.219818\pi$
$710$		0			0
$711$	−0.605886			−0.0227225
$712$	5.53983	−	9.59527i	0.207614	−	0.359598i
$713$	−25.3947	+	43.9849i	−0.951039	+	1.64725i
$714$	−26.1325			−0.977983
$715$		0			0
$716$	11.7831	−	20.4089i	0.440354	−	0.762715i
$717$	7.22006	+	12.5055i	0.269638	+	0.467027i
$718$	−2.90437	+	5.03052i	−0.108390	+	0.187737i
$719$	−23.5785	−	40.8392i	−0.879331	−	1.52305i	−0.852077	−	0.523417i	$-0.824657\pi$
$719$	−23.5785	−	40.8392i	−0.879331	−	1.52305i	−0.0272540	−	0.999629i	$-0.508676\pi$
$720$		0			0
$721$	−50.9216			−1.89642
$722$	3.81534	+	18.6130i	0.141992	+	0.692704i
$723$	−35.8213			−1.33221
$724$	−7.86746	−	13.6268i	−0.292392	−	0.506438i
$725$		0			0
$726$	1.94595	−	3.37049i	0.0722212	−	0.125091i
$727$	−6.52177	−	11.2960i	−0.241879	−	0.418947i	0.719371	−	0.694627i	$-0.244430\pi$
$727$	−6.52177	−	11.2960i	−0.241879	−	0.418947i	−0.961250	+	0.275680i	$0.911097\pi$
$728$	−11.3043	+	19.5795i	−0.418963	+	0.725666i
$729$	27.8266			1.03061
$730$		0			0
$731$	−8.99204	+	15.5747i	−0.332582	+	0.576050i
$732$	1.96608	−	3.40535i	0.0726683	−	0.125865i
$733$	13.9861			0.516590			0.258295	−	0.966066i	$-0.416839\pi$
$733$	13.9861			0.516590			0.258295	+	0.966066i	$0.416839\pi$
$734$	22.2827			0.822470
$735$		0			0
$736$	−2.34233	−	4.05703i	−0.0863394	−	0.149544i
$737$	12.2890	−	21.2851i	0.452670	−	0.784048i
$738$	−0.393284	−	0.681188i	−0.0144770	−	0.0250749i
$739$	−0.534508	−	0.925795i	−0.0196622	−	0.0340559i	0.856027	−	0.516931i	$-0.172926\pi$
$739$	−0.534508	−	0.925795i	−0.0196622	−	0.0340559i	−0.875689	+	0.482875i	$0.839592\pi$
$740$		0			0
$741$	−7.17608	+	44.2677i	−0.263620	+	1.62622i
$742$	6.52534			0.239553
$743$	5.00591	+	8.67048i	0.183649	+	0.318089i	0.943120	−	0.332451i	$-0.107876\pi$
$743$	5.00591	+	8.67048i	0.183649	+	0.318089i	−0.759472	+	0.650541i	$0.774542\pi$
$744$	9.23386	+	15.9935i	0.338530	+	0.586351i
$745$		0			0
$746$	8.53046	+	14.7752i	0.312322	+	0.540958i
$747$	−0.280045	+	0.485051i	−0.0102463	+	0.0177471i
$748$	−14.9380			−0.546187
$749$	−27.1327			−0.991406
$750$		0			0
$751$	−17.3070	+	29.9767i	−0.631543	+	1.09386i	0.355694	+	0.934603i	$0.384245\pi$
$751$	−17.3070	+	29.9767i	−0.631543	+	1.09386i	−0.987236	+	0.159261i	$0.949089\pi$
$752$	1.74324			0.0635693
$753$	−46.3951			−1.69073
$754$	−20.0668	+	34.7567i	−0.730790	+	1.26577i
$755$		0			0
$756$	9.87811	−	17.1094i	0.359263	−	0.622262i
$757$	−1.67642	−	2.90364i	−0.0609305	−	0.105535i	0.833951	−	0.551838i	$-0.186073\pi$
$757$	−1.67642	−	2.90364i	−0.0609305	−	0.105535i	−0.894882	+	0.446304i	$0.852740\pi$
$758$	5.01645	+	8.68874i	0.182206	+	0.315589i
$759$	−29.0853			−1.05573
$760$		0			0
$761$	27.5087			0.997190			0.498595	−	0.866835i	$-0.333849\pi$
$761$	27.5087			0.997190			0.498595	+	0.866835i	$0.333849\pi$
$762$	2.93552	+	5.08446i	0.106343	+	0.184191i
$763$	8.39953	+	14.5484i	0.304083	+	0.526688i
$764$	−3.32241	+	5.75459i	−0.120201	+	0.208194i
$765$		0			0
$766$	0.994093	−	1.72182i	0.0359181	−	0.0622119i
$767$	44.3821			1.60254
$768$	−1.70341			−0.0614664
$769$	17.1306	−	29.6711i	0.617746	−	1.06997i	−0.372150	−	0.928172i	$-0.621379\pi$
$769$	17.1306	−	29.6711i	0.617746	−	1.06997i	0.989896	−	0.141795i	$-0.0452872\pi$
$770$		0			0
$771$	−28.3687			−1.02167
$772$	7.99863			0.287877
$773$	5.98184	−	10.3608i	0.215152	−	0.372654i	−0.738168	−	0.674617i	$-0.764309\pi$
$773$	5.98184	−	10.3608i	0.215152	−	0.372654i	0.953320	+	0.301963i	$0.0976421\pi$
$774$	−0.215907	−	0.373961i	−0.00776061	−	0.0134418i
$775$		0			0
$776$	0.752610	+	1.30356i	0.0270171	+	0.0467950i
$777$	24.7241	+	42.8233i	0.886971	+	1.53628i
$778$	8.87708			0.318259
$779$	−32.5719	+	12.3678i	−1.16701	+	0.443121i
$780$		0			0
$781$	3.62330	+	6.27574i	0.129652	+	0.224564i
$782$	9.59982	+	16.6274i	0.343289	+	0.594594i
$783$	17.5352	−	30.3718i	0.626657	−	1.08540i
$784$	−3.50591	−	6.07241i	−0.125211	−	0.216872i
$785$		0			0
$786$	−28.1510			−1.00411
$787$	32.2277			1.14879			0.574396	−	0.818578i	$-0.305237\pi$
$787$	32.2277			1.14879			0.574396	+	0.818578i	$0.305237\pi$
$788$	−0.240797	+	0.417072i	−0.00857802	+	0.0148576i
$789$	−1.69335	+	2.93296i	−0.0602847	+	0.104416i
$790$		0			0
$791$	49.7152			1.76767
$792$	0.179337	−	0.310621i	0.00637247	−	0.0110374i
$793$	6.97119	+	12.0745i	0.247554	+	0.428777i
$794$	−10.5563	+	18.2840i	−0.374628	+	0.648875i
$795$		0			0
$796$	−11.6793	−	20.2292i	−0.413963	−	0.717005i
$797$	39.9120			1.41376			0.706878	−	0.707335i	$-0.250103\pi$
$797$	39.9120			1.41376			0.706878	+	0.707335i	$0.250103\pi$
$798$	−21.5359	−	17.5692i	−0.762364	−	0.621944i
$799$	−7.14449			−0.252754
$800$		0			0
$801$	−0.545154	−	0.944235i	−0.0192621	−	0.0333629i
$802$	−14.9806	+	25.9471i	−0.528982	+	0.916224i
$803$	16.7478	+	29.0080i	0.591016	+	1.02367i
$804$	−5.74324	+	9.94758i	−0.202548	+	0.350824i
$805$		0			0
$806$	−65.4817			−2.30649
$807$	6.08498	−	10.5395i	0.214202	−	0.371008i
$808$	3.91735	−	6.78506i	0.137812	−	0.238697i
$809$	−22.1075			−0.777257			−0.388629	−	0.921394i	$-0.627051\pi$
$809$	−22.1075			−0.777257			−0.388629	+	0.921394i	$0.627051\pi$
$810$		0			0
$811$	−10.5035	+	18.1925i	−0.368827	+	0.638826i	−0.989382	−	0.145336i	$-0.953574\pi$
$811$	−10.5035	+	18.1925i	−0.368827	+	0.638826i	0.620556	+	0.784162i	$0.286907\pi$
$812$	−12.4366	−	21.5408i	−0.436438	−	0.755934i
$813$	9.33364	−	16.1663i	0.327345	−	0.566978i
$814$	14.1329	+	24.4789i	0.495358	+	0.857986i
$815$		0			0
$816$	6.98125			0.244393
$817$	−17.8815	+	6.78971i	−0.625593	+	0.237542i
$818$	−4.19544			−0.146690
$819$	1.11241	+	1.92675i	0.0388708	+	0.0673261i
$820$		0			0
$821$	−19.1593	+	33.1849i	−0.668665	+	1.15816i	0.309613	+	0.950863i	$0.399801\pi$
$821$	−19.1593	+	33.1849i	−0.668665	+	1.15816i	−0.978278	+	0.207299i	$0.933533\pi$
$822$	−19.0031	−	32.9144i	−0.662810	−	1.14802i
$823$	−26.7590	+	46.3479i	−0.932760	+	1.61559i	−0.154179	+	0.988043i	$0.549273\pi$
$823$	−26.7590	+	46.3479i	−0.932760	+	1.61559i	−0.778580	+	0.627545i	$0.784060\pi$
$824$	13.6036			0.473905
$825$		0			0
$826$	−13.7531	+	23.8210i	−0.478531	+	0.828840i
$827$	−10.4410	+	18.0843i	−0.363068	+	0.628853i	−0.988464	−	0.151455i	$-0.951604\pi$
$827$	−10.4410	+	18.0843i	−0.363068	+	0.628853i	0.625396	+	0.780308i	$0.284938\pi$
$828$	−0.461000			−0.0160209
$829$	−57.1594			−1.98523			−0.992614	−	0.121317i	$-0.961288\pi$
$829$	−57.1594			−1.98523			−0.992614	+	0.121317i	$0.961288\pi$
$830$		0			0
$831$	10.4492	+	18.0985i	0.362478	+	0.627831i
$832$	3.01991	−	5.23065i	0.104697	−	0.181340i
$833$	14.3686	+	24.8872i	0.497844	+	0.862290i
$834$	−1.50069	−	2.59927i	−0.0519645	−	0.0900052i
$835$		0			0
$836$	−12.3105	−	10.0430i	−0.425768	−	0.347345i
$837$	57.2205			1.97783
$838$	−6.26628	−	10.8535i	−0.216465	−	0.374928i
$839$	12.4778	+	21.6122i	0.430781	+	0.746135i	0.996941	−	0.0781610i	$-0.0249048\pi$
$839$	12.4778	+	21.6122i	0.430781	+	0.746135i	−0.566160	+	0.824296i	$0.691571\pi$
$840$		0			0
$841$	−7.57688	−	13.1235i	−0.261272	−	0.452536i
$842$	13.2883	−	23.0160i	0.457945	−	0.793183i
$843$	29.0936			1.00204
$844$	−5.82983			−0.200671
$845$		0			0
$846$	0.0857727	−	0.148563i	0.00294893	−	0.00510769i
$847$	−8.55247			−0.293866
$848$	−1.74324			−0.0598630
$849$	25.5620	−	44.2746i	0.877285	−	1.51950i
$850$		0			0
$851$	18.1649	−	31.4625i	0.622684	−	1.07852i
$852$	−1.69335	−	2.93296i	−0.0580131	−	0.100482i
$853$	−13.8375	−	23.9672i	−0.473787	−	0.820622i	0.525763	−	0.850631i	$-0.323780\pi$
$853$	−13.8375	−	23.9672i	−0.473787	−	0.820622i	−0.999550	+	0.0300087i	$0.990447\pi$
$854$	−8.64091			−0.295686
$855$		0			0
$856$	7.24845			0.247747
$857$	−10.5000	−	18.1865i	−0.358673	−	0.621240i	0.629066	−	0.777352i	$-0.283437\pi$
$857$	−10.5000	−	18.1865i	−0.358673	−	0.621240i	−0.987739	+	0.156112i	$0.950104\pi$
$858$	−18.7495	−	32.4751i	−0.640098	−	1.10868i
$859$	−11.0617	+	19.1594i	−0.377420	+	0.653711i	−0.990686	−	0.136165i	$-0.956522\pi$
$859$	−11.0617	+	19.1594i	−0.377420	+	0.653711i	0.613266	+	0.789877i	$0.289856\pi$
$860$		0			0
$861$	25.4829	−	44.1377i	0.868455	−	1.50421i
$862$	−0.180610			−0.00615159
$863$	−31.1716			−1.06109			−0.530547	−	0.847655i	$-0.678013\pi$
$863$	−31.1716			−1.06109			−0.530547	+	0.847655i	$0.678013\pi$
$864$	−2.63892	+	4.57075i	−0.0897780	+	0.155500i
$865$		0			0
$866$	12.0104			0.408131
$867$	0.345903			0.0117475
$868$	20.2914	−	35.1458i	0.688735	−	1.19292i
$869$	−11.2206	−	19.4346i	−0.380632	−	0.659274i
$870$		0			0
$871$	−20.3640	−	35.2715i	−0.690008	−	1.19513i
$872$	−2.24392	−	3.88659i	−0.0759888	−	0.131616i
$873$	0.148123			0.00501321
$874$	−3.26755	+	20.1568i	−0.110526	+	0.681815i
$875$		0			0
$876$	−7.82705	−	13.5568i	−0.264451	−	0.458043i
$877$	10.3314	+	17.8946i	0.348868	+	0.604257i	0.986049	−	0.166457i	$-0.0532328\pi$
$877$	10.3314	+	17.8946i	0.348868	+	0.604257i	−0.637180	+	0.770715i	$0.719899\pi$
$878$	14.2544	−	24.6893i	0.481061	−	0.833223i
$879$	19.1358	+	33.1442i	0.645436	+	1.11793i
$880$		0			0
$881$	35.5613			1.19809			0.599045	−	0.800716i	$-0.295547\pi$
$881$	35.5613			1.19809			0.599045	+	0.800716i	$0.295547\pi$
$882$	−0.690007			−0.0232337
$883$	9.03845	−	15.6551i	0.304168	−	0.526835i	−0.672908	−	0.739727i	$-0.734955\pi$
$883$	9.03845	−	15.6551i	0.304168	−	0.526835i	0.977076	+	0.212892i	$0.0682882\pi$
$884$	−12.3768	+	21.4373i	−0.416278	+	0.721015i
$885$		0			0
$886$	−8.54642			−0.287123
$887$	23.5340	−	40.7620i	0.790193	−	1.36865i	−0.135654	−	0.990756i	$-0.543314\pi$
$887$	23.5340	−	40.7620i	0.790193	−	1.36865i	0.925847	−	0.377898i	$-0.123353\pi$
$888$	−6.60500	−	11.4402i	−0.221649	−	0.383908i
$889$	6.45080	−	11.1731i	0.216353	−	0.374734i
$890$		0			0
$891$	15.8461	+	27.4462i	0.530863	+	0.919482i
$892$	−16.7245			−0.559977
$893$	−5.88782	−	4.80334i	−0.197028	−	0.160738i
$894$	6.15657			0.205906
$895$		0			0
$896$	1.87162	+	3.24174i	0.0625264	+	0.108299i
$897$	−24.0985	+	41.7399i	−0.804627	+	1.39366i
$898$	2.12306	+	3.67725i	0.0708475	+	0.122711i
$899$	36.0204	−	62.3892i	1.20135	−	2.08080i
$900$		0			0
$901$	7.14449			0.238017
$902$	14.5667	−	25.2302i	0.485017	−	0.840075i
$903$	13.9897	−	24.2309i	0.465548	−	0.806353i
$904$	−13.2813			−0.441731
$905$		0			0
$906$	−15.4764	+	26.8059i	−0.514169	+	0.890567i
$907$	10.0383	+	17.3869i	0.333317	+	0.577322i	0.983160	−	0.182746i	$-0.0584987\pi$
$907$	10.0383	+	17.3869i	0.333317	+	0.577322i	−0.649843	+	0.760068i	$0.725165\pi$
$908$	2.08093	−	3.60428i	0.0690581	−	0.119612i
$909$	−0.385493	−	0.667693i	−0.0127860	−	0.0221460i
$910$		0			0
$911$	−29.6273			−0.981595			−0.490797	−	0.871274i	$-0.663294\pi$
$911$	−29.6273			−0.981595			−0.490797	+	0.871274i	$0.663294\pi$
$912$	5.75330	+	4.69360i	0.190511	+	0.155421i
$913$	−20.7449			−0.686556
$914$	9.11022	+	15.7794i	0.301339	+	0.521935i
$915$		0			0
$916$	2.74914	−	4.76165i	0.0908342	−	0.157329i
$917$	30.9309	+	53.5739i	1.02143	+	1.76917i
$918$	10.8154	−	18.7328i	0.356961	−	0.618274i
$919$	−55.4525			−1.82921			−0.914604	−	0.404350i	$-0.867498\pi$
$919$	−55.4525			−1.82921			−0.914604	+	0.404350i	$0.867498\pi$
$920$		0			0
$921$	13.9608	−	24.1807i	0.460022	−	0.796782i
$922$	−15.0140	+	26.0050i	−0.494460	+	0.856430i
$923$	12.0083			0.395258
$924$	23.2403			0.764551
$925$		0			0
$926$	−5.08278	−	8.80364i	−0.167031	−	0.289306i
$927$	0.669342	−	1.15933i	0.0219841	−	0.0380775i
$928$	3.32241	+	5.75459i	0.109064	+	0.188904i
$929$	−3.61925	−	6.26873i	−0.118744	−	0.205670i	0.800526	−	0.599298i	$-0.204553\pi$
$929$	−3.61925	−	6.26873i	−0.118744	−	0.205670i	−0.919270	+	0.393627i	$0.871220\pi$
$930$		0			0
$931$	−4.89074	+	30.1699i	−0.160288	+	0.988780i
$932$	13.1948			0.432209
$933$	−15.3474	−	26.5826i	−0.502453	−	0.870274i
$934$	−6.80645	−	11.7891i	−0.222714	−	0.385752i
$935$		0			0
$936$	−0.297179	−	0.514729i	−0.00971359	−	0.0168244i
$937$	18.8201	−	32.5974i	0.614826	−	1.06491i	−0.375589	−	0.926786i	$-0.622559\pi$
$937$	18.8201	−	32.5974i	0.614826	−	1.06491i	0.990415	−	0.138124i	$-0.0441072\pi$
$938$	25.2415			0.824165
$939$	−30.6791			−1.00117
$940$		0			0
$941$	12.9631	−	22.4527i	0.422585	−	0.731938i	−0.573607	−	0.819131i	$-0.694456\pi$
$941$	12.9631	−	22.4527i	0.422585	−	0.731938i	0.996191	+	0.0871927i	$0.0277896\pi$
$942$	13.2577			0.431960
$943$	−37.4448			−1.21937
$944$	3.67412	−	6.36376i	0.119582	−	0.207123i
$945$		0			0
$946$	7.99687	−	13.8510i	0.260001	−	0.450335i
$947$	−20.5510	−	35.5953i	−0.667816	−	1.15669i	−0.978513	−	0.206183i	$-0.933896\pi$
$947$	−20.5510	−	35.5953i	−0.667816	−	1.15669i	0.310697	−	0.950509i	$-0.399437\pi$
$948$	5.24392	+	9.08274i	0.170315	+	0.294994i
$949$	55.5053			1.80178
$950$		0			0
$951$	−39.6134			−1.28455
$952$	−7.67065	−	13.2860i	−0.248607	−	0.430600i
$953$	6.83584	+	11.8400i	0.221435	+	0.383536i	0.955244	−	0.295820i	$-0.0955927\pi$
$953$	6.83584	+	11.8400i	0.221435	+	0.383536i	−0.733809	+	0.679356i	$0.762259\pi$
$954$	−0.0857727	+	0.148563i	−0.00277700	+	0.00480990i
$955$		0			0
$956$	−4.23860	+	7.34147i	−0.137086	+	0.237440i
$957$	41.2553			1.33359
$958$	5.42927			0.175412
$959$	−41.7594	+	72.3293i	−1.34848	+	2.33564i
$960$		0			0
$961$	86.5412			2.79165
$962$	46.8392			1.51016
$963$	0.356647	−	0.617731i	0.0114928	−	0.0199061i
$964$	−10.5146	−	18.2118i	−0.338652	−	0.586563i
$965$		0			0
$966$	−14.9353	−	25.8687i	−0.480535	−	0.832311i
$967$	−23.7458	−	41.1289i	−0.763614	−	1.32262i	−0.940976	−	0.338472i	$-0.890090\pi$
$967$	−23.7458	−	41.1289i	−0.763614	−	1.32262i	0.177363	−	0.984146i	$-0.443243\pi$
$968$	2.28478			0.0734356
$969$	−23.5793	−	19.2363i	−0.757478	−	0.617958i
$970$		0			0
$971$	−4.83017	−	8.36611i	−0.155008	−	0.268481i	0.778054	−	0.628197i	$-0.216207\pi$
$971$	−4.83017	−	8.36611i	−0.155008	−	0.268481i	−0.933062	+	0.359716i	$0.882874\pi$
$972$	0.511126	+	0.885296i	0.0163944	+	0.0283959i
$973$	−3.29776	+	5.71189i	−0.105721	+	0.183115i
$974$	−16.2784	−	28.1951i	−0.521595	−	0.903428i
$975$		0			0
$976$	2.30841			0.0738903
$977$	38.8232			1.24206			0.621032	−	0.783786i	$-0.286714\pi$
$977$	38.8232			1.24206			0.621032	+	0.783786i	$0.286714\pi$
$978$	4.65489	−	8.06251i	0.148847	−	0.257811i
$979$	20.1917	−	34.9731i	0.645331	−	1.11775i
$980$		0			0
$981$	−0.441633			−0.0141002
$982$	−15.3410	+	26.5713i	−0.489550	+	0.847925i
$983$	−23.8160	−	41.2505i	−0.759611	−	1.31569i	−0.943049	−	0.332654i	$-0.892056\pi$
$983$	−23.8160	−	41.2505i	−0.759611	−	1.31569i	0.183438	−	0.983031i	$-0.441277\pi$
$984$	−6.80772	+	11.7913i	−0.217022	+	0.375893i
$985$		0			0
$986$	−13.6166	−	23.5847i	−0.433641	−	0.751088i
$987$	11.1153			0.353804
$988$	−24.6125	+	9.34551i	−0.783026	+	0.297320i
$989$	−20.5566			−0.653661
$990$		0			0
$991$	3.04886	+	5.28078i	0.0968503	+	0.167750i	0.910379	−	0.413775i	$-0.135790\pi$
$991$	3.04886	+	5.28078i	0.0968503	+	0.167750i	−0.813529	+	0.581524i	$0.802457\pi$
$992$	−5.42082	+	9.38914i	−0.172111	+	0.298105i
$993$	6.28828	+	10.8916i	0.199553	+	0.345635i
$994$	−3.72113	+	6.44518i	−0.118027	+	0.204429i
$995$		0			0
$996$	9.69510			0.307201
$997$	9.24743	−	16.0170i	0.292869	−	0.507264i	−0.681618	−	0.731708i	$-0.738723\pi$
$997$	9.24743	−	16.0170i	0.292869	−	0.507264i	0.974487	+	0.224444i	$0.0720567\pi$
$998$	4.91213	−	8.50807i	0.155491	−	0.269318i
$999$	−40.9299			−1.29497

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.e.l.501.3	yes	8
5.2	odd	4		950.2.j.i.349.7		16
5.3	odd	4		950.2.j.i.349.2		16
5.4	even	2		950.2.e.m.501.2	yes	8
19.11	even	3	inner	950.2.e.l.201.3	✓	8
95.49	even	6		950.2.e.m.201.2	yes	8
95.68	odd	12		950.2.j.i.49.7		16
95.87	odd	12		950.2.j.i.49.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.e.l.201.3	✓	8	19.11	even	3	inner
950.2.e.l.501.3	yes	8	1.1	even	1	trivial
950.2.e.m.201.2	yes	8	95.49	even	6
950.2.e.m.501.2	yes	8	5.4	even	2
950.2.j.i.49.2		16	95.87	odd	12
950.2.j.i.49.7		16	95.68	odd	12
950.2.j.i.349.2		16	5.3	odd	4
950.2.j.i.349.7		16	5.2	odd	4

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.851703 + 1.47519i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.851703 - 1.47519i) q^{6} -3.74324 q^{7} +1.00000 q^{8} +(0.0492032 - 0.0852224i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.851703 + 1.47519i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.851703 - 1.47519i) q^{6} -3.74324 q^{7} +1.00000 q^{8} +(0.0492032 - 0.0852224i) q^{9} +3.64483 q^{11} -1.70341 q^{12} +(3.01991 - 5.23065i) q^{13} +(1.87162 + 3.24174i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.04920 + 3.54932i) q^{17} -0.0984064 q^{18} +(-0.697500 + 4.30273i) q^{19} +(-3.18813 - 5.52200i) q^{21} +(-1.82241 - 3.15651i) q^{22} +(-2.34233 + 4.05703i) q^{23} +(0.851703 + 1.47519i) q^{24} -6.03983 q^{26} +5.27785 q^{27} +(1.87162 - 3.24174i) q^{28} +(3.32241 - 5.75459i) q^{29} +10.8416 q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.10431 + 5.37683i) q^{33} +(2.04920 - 3.54932i) q^{34} +(0.0492032 + 0.0852224i) q^{36} -7.75505 q^{37} +(4.07502 - 1.54731i) q^{38} +10.2883 q^{39} +(3.99653 + 6.92220i) q^{41} +(-3.18813 + 5.52200i) q^{42} +(2.19403 + 3.80018i) q^{43} +(-1.82241 + 3.15651i) q^{44} +4.68466 q^{46} +(-0.871618 + 1.50969i) q^{47} +(0.851703 - 1.47519i) q^{48} +7.01181 q^{49} +(-3.49063 + 6.04594i) q^{51} +(3.01991 + 5.23065i) q^{52} +(0.871618 - 1.50969i) q^{53} +(-2.63892 - 4.57075i) q^{54} -3.74324 q^{56} +(-6.94142 + 2.63570i) q^{57} -6.64483 q^{58} +(3.67412 + 6.36376i) q^{59} +(-1.15420 + 1.99914i) q^{61} +(-5.42082 - 9.38914i) q^{62} +(-0.184179 + 0.319008i) q^{63} +1.00000 q^{64} +(3.10431 - 5.37683i) q^{66} +(3.37162 - 5.83981i) q^{67} -4.09841 q^{68} -7.97988 q^{69} +(0.994093 + 1.72182i) q^{71} +(0.0492032 - 0.0852224i) q^{72} +(4.59494 + 7.95867i) q^{73} +(3.87752 + 6.71607i) q^{74} +(-3.37752 - 2.75542i) q^{76} -13.6435 q^{77} +(-5.14414 - 8.90992i) q^{78} +(-3.07849 - 5.33210i) q^{79} +(4.34755 + 7.53017i) q^{81} +(3.99653 - 6.92220i) q^{82} -5.69159 q^{83} +6.37625 q^{84} +(2.19403 - 3.80018i) q^{86} +11.3188 q^{87} +3.64483 q^{88} +(5.53983 - 9.59527i) q^{89} +(-11.3043 + 19.5795i) q^{91} +(-2.34233 - 4.05703i) q^{92} +(9.23386 + 15.9935i) q^{93} +1.74324 q^{94} -1.70341 q^{96} +(0.752610 + 1.30356i) q^{97} +(-3.50591 - 6.07241i) q^{98} +(0.179337 - 0.310621i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + q^{3} - 4 q^{4} + q^{6} + 12 q^{7} + 8 q^{8} - 11 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + q^3 - 4 * q^4 + q^6 + 12 * q^7 + 8 * q^8 - 11 * q^9	\( 8 q - 4 q^{2} + q^{3} - 4 q^{4} + q^{6} + 12 q^{7} + 8 q^{8} - 11 q^{9} + 10 q^{11} - 2 q^{12} + 9 q^{13} - 6 q^{14} - 4 q^{16} + 5 q^{17} + 22 q^{18} - q^{21} - 5 q^{22} + 6 q^{23} + q^{24} - 18 q^{26} + 16 q^{27} - 6 q^{28} + 17 q^{29} + 22 q^{31} - 4 q^{32} - 4 q^{33} + 5 q^{34} - 11 q^{36} - 8 q^{37} - 36 q^{39} + 7 q^{41} - q^{42} - 13 q^{43} - 5 q^{44} - 12 q^{46} + 14 q^{47} + q^{48} + 44 q^{49} - 9 q^{51} + 9 q^{52} - 14 q^{53} - 8 q^{54} + 12 q^{56} - 48 q^{57} - 34 q^{58} + 14 q^{59} - 9 q^{61} - 11 q^{62} - 45 q^{63} + 8 q^{64} - 4 q^{66} + 6 q^{67} - 10 q^{68} + 54 q^{69} + 14 q^{71} - 11 q^{72} - 11 q^{73} + 4 q^{74} - 10 q^{77} + 18 q^{78} - 17 q^{79} - 36 q^{81} + 7 q^{82} - 46 q^{83} + 2 q^{84} - 13 q^{86} - 2 q^{87} + 10 q^{88} + 14 q^{89} - 25 q^{91} + 6 q^{92} + 13 q^{93} - 28 q^{94} - 2 q^{96} - 17 q^{97} - 22 q^{98} - 60 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + q^3 - 4 * q^4 + q^6 + 12 * q^7 + 8 * q^8 - 11 * q^9 + 10 * q^11 - 2 * q^12 + 9 * q^13 - 6 * q^14 - 4 * q^16 + 5 * q^17 + 22 * q^18 - q^21 - 5 * q^22 + 6 * q^23 + q^24 - 18 * q^26 + 16 * q^27 - 6 * q^28 + 17 * q^29 + 22 * q^31 - 4 * q^32 - 4 * q^33 + 5 * q^34 - 11 * q^36 - 8 * q^37 - 36 * q^39 + 7 * q^41 - q^42 - 13 * q^43 - 5 * q^44 - 12 * q^46 + 14 * q^47 + q^48 + 44 * q^49 - 9 * q^51 + 9 * q^52 - 14 * q^53 - 8 * q^54 + 12 * q^56 - 48 * q^57 - 34 * q^58 + 14 * q^59 - 9 * q^61 - 11 * q^62 - 45 * q^63 + 8 * q^64 - 4 * q^66 + 6 * q^67 - 10 * q^68 + 54 * q^69 + 14 * q^71 - 11 * q^72 - 11 * q^73 + 4 * q^74 - 10 * q^77 + 18 * q^78 - 17 * q^79 - 36 * q^81 + 7 * q^82 - 46 * q^83 + 2 * q^84 - 13 * q^86 - 2 * q^87 + 10 * q^88 + 14 * q^89 - 25 * q^91 + 6 * q^92 + 13 * q^93 - 28 * q^94 - 2 * q^96 - 17 * q^97 - 22 * q^98 - 60 * q^99

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