LMFDB - Embedded newform 950.2.e.m.501.2

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			501.2
Root			$0.851703 + 1.47519i$ of defining polynomial
Character	$\chi$	$=$	950.501
Dual form			950.2.e.m.201.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.851703 - 1.47519i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.851703 - 1.47519i) q^{6} +3.74324 q^{7} -1.00000 q^{8} +(0.0492032 - 0.0852224i) q^{9} +O(q^{10})$	\(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	0.508224	−	0.861225i	$-0.330302\pi$
$3$	−0.851703	−	1.47519i	−0.491731	−	0.851703i	−0.999955	+	0.00952194i	$0.996969\pi$
$4$	−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	$-0.249866\pi$
$7$	3.74324			1.41481			0.707405	+	0.706808i	$0.249866\pi$
$8$	−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	$0.482693\pi$
$13$	−3.01991	+	5.23065i	−0.837574	+	1.45072i	−0.891918	+	0.452198i	$0.850640\pi$
$14$	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	0.502989	−	0.864293i	$-0.332234\pi$
$17$	−2.04920	−	3.54932i	−0.497005	−	0.860838i	−0.999994	+	0.00345514i	$0.998900\pi$
$18$	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	−0.511502	−	0.859282i	$-0.670911\pi$
$23$	2.34233	−	4.05703i	0.488409	−	0.845950i	0.999911	+	0.0133324i	$0.00424395\pi$
$24$	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	$-0.279985\pi$
$37$	7.75505			1.27492			0.637461	+	0.770483i	$0.279985\pi$
$38$	−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	0.648819	−	0.760943i	$-0.275263\pi$
$43$	−2.19403	−	3.80018i	−0.334587	−	0.579521i	−0.983405	+	0.181422i	$0.941930\pi$
$44$	−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	−0.795428	−	0.606048i	$-0.792754\pi$
$47$	0.871618	−	1.50969i	0.127139	−	0.220210i	0.922567	+	0.385837i	$0.126087\pi$
$48$	−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	−0.919659	−	0.392718i	$-0.871535\pi$
$53$	−0.871618	+	1.50969i	−0.119726	+	0.207371i	0.799933	+	0.600089i	$0.204868\pi$
$54$	−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	−0.995098	−	0.0988892i	$-0.968471\pi$
$67$	−3.37162	+	5.83981i	−0.411909	+	0.713447i	0.583190	+	0.812336i	$0.301804\pi$
$68$	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	$-0.985923\pi$
$73$	−4.59494	−	7.95867i	−0.537797	−	0.931492i	0.461225	−	0.887283i	$-0.347410\pi$
$74$	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	$-0.398878\pi$
$83$	5.69159			0.624734			0.312367	+	0.949962i	$0.398878\pi$
$84$	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	0.825285	−	0.564716i	$-0.191014\pi$
$97$	−0.752610	−	1.30356i	−0.0764159	−	0.132356i	−0.901701	+	0.432360i	$0.857681\pi$
$98$	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	$-0.733793\pi$
$103$	−13.6036			−1.34041			−0.670203	+	0.742178i	$0.733793\pi$
$104$	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	$-0.613943\pi$
$107$	−7.24845			−0.700735			−0.350367	+	0.936612i	$0.613943\pi$
$108$	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	$-0.285220\pi$
$113$	13.2813			1.24940			0.624702	+	0.780863i	$0.285220\pi$
$114$	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	−0.779380	−	0.626552i	$-0.784466\pi$
$127$	1.72332	−	2.98488i	0.152920	−	0.264865i	0.932300	+	0.361687i	$0.117799\pi$
$128$	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	$0.568812\pi$
$137$	−11.1560	+	19.3227i	−0.953118	+	1.65085i	−0.738618	+	0.674124i	$0.764521\pi$
$138$	−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	0.667910	−	0.744242i	$-0.267189\pi$
$157$	−3.89153	−	6.74033i	−0.310578	−	0.537937i	−0.978488	+	0.206305i	$0.933856\pi$
$158$	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	$-0.568663\pi$
$163$	−5.46539			−0.428082			−0.214041	+	0.976825i	$0.568663\pi$
$164$	−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	$0.418837\pi$
$167$	−9.19994	+	15.9348i	−0.711913	+	1.23307i	−0.964138	+	0.265400i	$0.914496\pi$
$168$	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	$0.0990827\pi$
$173$	9.74914	+	16.8860i	0.741214	+	1.28382i	−0.210729	+	0.977544i	$0.567584\pi$
$174$	−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	0.973303	−	0.229525i	$-0.0737173\pi$
$193$	3.99931	+	6.92701i	0.287877	+	0.498617i	−0.685426	+	0.728142i	$0.740384\pi$
$194$	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	$-0.505461\pi$
$197$	−0.481593			−0.0343121			−0.0171560	+	0.999853i	$0.505461\pi$
$198$	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	$-0.977477\pi$
$223$	−8.36224	−	14.4838i	−0.559977	−	0.969909i	0.437520	−	0.899209i	$-0.355857\pi$
$224$	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	$-0.455895\pi$
$227$	4.16186			0.276232			0.138116	+	0.990416i	$0.455895\pi$
$228$	−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	0.997063	−	0.0765832i	$-0.0244011\pi$
$233$	6.59738	+	11.4270i	0.432209	+	0.748607i	−0.564855	+	0.825190i	$0.691068\pi$
$234$	−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	$-0.659479\pi$
$257$	8.32705	−	14.4229i	0.519427	−	0.899674i	0.999745	−	0.0225796i	$-0.00718792\pi$
$258$	−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	0.833748	−	0.552146i	$-0.186191\pi$
$263$	−0.994093	−	1.72182i	−0.0612984	−	0.106172i	−0.895046	+	0.445974i	$0.852857\pi$
$264$	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	$-0.620154\pi$
$277$	−12.2686			−0.737147			−0.368574	+	0.929599i	$0.620154\pi$
$278$	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	$0.184057\pi$
$283$	15.0064	+	25.9918i	0.892037	+	1.54505i	0.0546077	+	0.998508i	$0.482609\pi$
$284$	−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	$-0.727875\pi$
$293$	−22.4677			−1.31258			−0.656289	+	0.754509i	$0.727875\pi$
$294$	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	0.999321	−	0.0368378i	$-0.0117285\pi$
$307$	8.19578	+	14.1955i	0.467758	+	0.810181i	−0.531563	+	0.847019i	$0.678395\pi$
$308$	−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	$-0.663347\pi$
$313$	9.00522	−	15.5975i	0.509005	−	0.881623i	0.999946	−	0.0104296i	$-0.00331990\pi$
$314$	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	$-0.606811\pi$
$317$	11.6277	−	20.1398i	0.653076	−	1.13116i	0.982372	−	0.186935i	$-0.0598553\pi$
$318$	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	$-0.848591\pi$
$337$	−15.4400	−	26.7429i	−0.841073	−	1.45678i	0.0479153	−	0.998851i	$-0.484742\pi$
$338$	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	0.717290	−	0.696775i	$-0.245382\pi$
$347$	−4.55974	−	7.89771i	−0.244780	−	0.423971i	−0.962070	+	0.272804i	$0.912049\pi$
$348$	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	$-0.566351\pi$
$353$	−7.77613			−0.413882			−0.206941	+	0.978353i	$0.566351\pi$
$354$	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	$-0.635770\pi$
$367$	11.1414	−	19.2974i	0.581574	−	1.00732i	0.995293	−	0.0969115i	$-0.0308964\pi$
$368$	−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	$-0.354379\pi$
$373$	17.0609			0.883380			0.441690	+	0.897168i	$0.354379\pi$
$374$	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	0.839510	−	0.543345i	$-0.182842\pi$
$383$	−0.994093	−	1.72182i	−0.0507958	−	0.0879809i	−0.890305	+	0.455364i	$0.849509\pi$
$384$	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	$0.0110680\pi$
$397$	10.5563	+	18.2840i	0.529804	+	0.917648i	−0.469591	+	0.882884i	$0.655599\pi$
$398$	−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	−0.684882	−	0.728654i	$-0.740146\pi$
$433$	6.00522	−	10.4013i	0.288592	−	0.499857i	0.973474	+	0.228798i	$0.0734794\pi$
$434$	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	−0.949502	−	0.313761i	$-0.898411\pi$
$443$	−4.27321	+	7.40142i	−0.203026	+	0.351652i	0.746476	+	0.665413i	$0.231744\pi$
$444$	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	$-0.359867\pi$
$457$	18.2204			0.852316			0.426158	+	0.904649i	$0.359867\pi$
$458$	−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	$-0.575908\pi$
$463$	−10.1656			−0.472434			−0.236217	+	0.971700i	$0.575908\pi$
$464$	−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	$-0.601993\pi$
$467$	−13.6129			−0.629930			−0.314965	+	0.949103i	$0.601993\pi$
$468$	−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	$-0.764063\pi$
$487$	−32.5569			−1.47529			−0.737646	+	0.675188i	$0.764063\pi$
$488$	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	−0.646256	−	0.763121i	$-0.723666\pi$
$503$	7.57502	−	13.1203i	0.337754	−	0.585006i	0.984010	+	0.178114i	$0.0569996\pi$
$504$	−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	$0.443973\pi$
$523$	−17.4970	+	30.3057i	−0.765091	+	1.32518i	−0.940199	+	0.340627i	$0.889361\pi$
$524$	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	$-0.592823\pi$
$547$	16.0375	−	27.7778i	0.685715	−	1.18769i	0.973211	−	0.229912i	$-0.0738438\pi$
$548$	−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	−0.954755	−	0.297393i	$-0.903883\pi$
$557$	−5.18813	+	8.98610i	−0.219828	+	0.380753i	0.734927	+	0.678146i	$0.237216\pi$
$558$	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	$-0.443040\pi$
$563$	8.44664			0.355984			0.177992	+	0.984032i	$0.443040\pi$
$564$	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	$-0.456028\pi$
$577$	6.61544			0.275404			0.137702	+	0.990474i	$0.456028\pi$
$578$	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	0.677848	−	0.735202i	$-0.262913\pi$
$587$	−7.21463	−	12.4961i	−0.297780	−	0.515770i	−0.975628	+	0.219432i	$0.929579\pi$
$588$	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	−0.996507	−	0.0835060i	$-0.973388\pi$
$593$	−10.3722	+	17.9652i	−0.425935	+	0.737742i	0.570572	+	0.821248i	$0.306722\pi$
$594$	−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	$-0.697131\pi$
$607$	−28.6025			−1.16094			−0.580470	+	0.814281i	$0.697131\pi$
$608$	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	0.931395	−	0.364011i	$-0.118593\pi$
$613$	3.72507	+	6.45202i	0.150454	+	0.260594i	−0.780940	+	0.624606i	$0.785260\pi$
$614$	−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	$-0.616021\pi$
$617$	15.6711	−	27.1432i	0.630896	−	1.09274i	0.987369	−	0.158438i	$-0.0506459\pi$
$618$	−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	0.983547	−	0.180654i	$-0.0578214\pi$
$643$	8.50292	+	14.7275i	0.335322	+	0.580795i	−0.648224	+	0.761449i	$0.724488\pi$
$644$	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	$-0.187060\pi$
$647$	42.3379			1.66447			0.832237	+	0.554420i	$0.187060\pi$
$648$	−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	$-0.0993899\pi$
$653$	48.6365			1.90329			0.951647	+	0.307194i	$0.0993899\pi$
$654$	−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	$-0.531833\pi$
$673$	−5.18012			−0.199679			−0.0998395	+	0.995004i	$0.531833\pi$
$674$	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	$-0.161854\pi$
$677$	45.4548			1.74697			0.873485	+	0.486851i	$0.161854\pi$
$678$	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	$-0.519774\pi$
$683$	−3.24495			−0.124165			−0.0620823	+	0.998071i	$0.519774\pi$
$684$	−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	0.961250	−	0.275680i	$-0.0889030\pi$
$727$	6.52177	+	11.2960i	0.241879	+	0.418947i	−0.719371	+	0.694627i	$0.755570\pi$
$728$	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	$-0.583161\pi$
$733$	−13.9861			−0.516590			−0.258295	+	0.966066i	$0.583161\pi$
$734$	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	0.759472	−	0.650541i	$-0.225458\pi$
$743$	−5.00591	−	8.67048i	−0.183649	−	0.318089i	−0.943120	+	0.332451i	$0.892124\pi$
$744$	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	0.894882	−	0.446304i	$-0.147260\pi$
$757$	1.67642	+	2.90364i	0.0609305	+	0.105535i	−0.833951	+	0.551838i	$0.813927\pi$
$758$	−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	−0.953320	−	0.301963i	$-0.902358\pi$
$773$	−5.98184	+	10.3608i	−0.215152	+	0.372654i	0.738168	+	0.674617i	$0.235691\pi$
$774$	−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	$-0.694763\pi$
$787$	−32.2277			−1.14879			−0.574396	+	0.818578i	$0.694763\pi$
$788$	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	$-0.749897\pi$
$797$	−39.9120			−1.41376			−0.706878	+	0.707335i	$0.749897\pi$
$798$	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	$-0.450727\pi$
$823$	26.7590	−	46.3479i	0.932760	−	1.61559i	0.778580	−	0.627545i	$-0.215940\pi$
$824$	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	−0.625396	−	0.780308i	$-0.715062\pi$
$827$	10.4410	−	18.0843i	0.363068	−	0.628853i	0.988464	+	0.151455i	$0.0483958\pi$
$828$	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	0.999550	−	0.0300087i	$-0.00955349\pi$
$853$	13.8375	+	23.9672i	0.473787	+	0.820622i	−0.525763	+	0.850631i	$0.676220\pi$
$854$	−8.64091			−0.295686
$855$		0			0
$856$	7.24845			0.247747
$857$	10.5000	+	18.1865i	0.358673	+	0.621240i	0.987739	−	0.156112i	$-0.0498959\pi$
$857$	10.5000	+	18.1865i	0.358673	+	0.621240i	−0.629066	+	0.777352i	$0.716563\pi$
$858$	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	$-0.321987\pi$
$863$	31.1716			1.06109			0.530547	+	0.847655i	$0.321987\pi$
$864$	−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	0.637180	−	0.770715i	$-0.280101\pi$
$877$	−10.3314	−	17.8946i	−0.348868	−	0.604257i	−0.986049	+	0.166457i	$0.946767\pi$
$878$	−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	−0.977076	−	0.212892i	$-0.931712\pi$
$883$	−9.03845	+	15.6551i	−0.304168	+	0.526835i	0.672908	+	0.739727i	$0.265045\pi$
$884$	−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	$0.456686\pi$
$887$	−23.5340	+	40.7620i	−0.790193	+	1.36865i	−0.925847	+	0.377898i	$0.876647\pi$
$888$	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	0.649843	−	0.760068i	$-0.274835\pi$
$907$	−10.0383	−	17.3869i	−0.333317	−	0.577322i	−0.983160	+	0.182746i	$0.941501\pi$
$908$	−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	$0.377441\pi$
$937$	−18.8201	+	32.5974i	−0.614826	+	1.06491i	−0.990415	+	0.138124i	$0.955893\pi$
$938$	−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	$0.0661042\pi$
$947$	20.5510	+	35.5953i	0.667816	+	1.15669i	−0.310697	+	0.950509i	$0.600563\pi$
$948$	−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	0.733809	−	0.679356i	$-0.237741\pi$
$953$	−6.83584	−	11.8400i	−0.221435	−	0.383536i	−0.955244	+	0.295820i	$0.904407\pi$
$954$	−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	$0.109910\pi$
$967$	23.7458	+	41.1289i	0.763614	+	1.32262i	−0.177363	+	0.984146i	$0.556757\pi$
$968$	−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	$-0.713286\pi$
$977$	−38.8232			−1.24206			−0.621032	+	0.783786i	$0.713286\pi$
$978$	−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	$0.107944\pi$
$983$	23.8160	+	41.2505i	0.759611	+	1.31569i	−0.183438	+	0.983031i	$0.558723\pi$
$984$	−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	−0.974487	−	0.224444i	$-0.927943\pi$
$997$	−9.24743	+	16.0170i	−0.292869	+	0.507264i	0.681618	+	0.731708i	$0.261277\pi$
$998$	−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.m.501.2	yes	8
5.2	odd	4		950.2.j.i.349.2		16
5.3	odd	4		950.2.j.i.349.7		16
5.4	even	2		950.2.e.l.501.3	yes	8
19.11	even	3	inner	950.2.e.m.201.2	yes	8
95.49	even	6		950.2.e.l.201.3	✓	8
95.68	odd	12		950.2.j.i.49.2		16
95.87	odd	12		950.2.j.i.49.7		16

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