LMFDB - Embedded newform 950.2.j.f.349.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(49,950)]

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([3, 4]))

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

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

chi := DirichletCharacter("950.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1731891456.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 $ x^8 - 9x^6 + 65x^4 - 144*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.1
Root			$-1.35234 + 0.780776i$ of defining polynomial
Character	$\chi$	$=$	950.349
Dual form			950.2.j.f.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.35234 + 0.780776i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.780776 - 1.35234i) q^{6} +4.56155i q^{7} +1.00000i q^{8} +(-0.280776 + 0.486319i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.35234 + 0.780776i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.780776 - 1.35234i) q^{6} +4.56155i q^{7} +1.00000i q^{8} +(-0.280776 + 0.486319i) q^{9} +1.00000 q^{11} +1.56155i q^{12} +(-1.73205 - 1.00000i) q^{13} +(-2.28078 - 3.95042i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.70469 + 1.56155i) q^{17} -0.561553i q^{18} +(2.50000 + 3.57071i) q^{19} +(-3.56155 - 6.16879i) q^{21} +(-0.866025 + 0.500000i) q^{22} +(6.65511 + 3.84233i) q^{23} +(-0.780776 - 1.35234i) q^{24} +2.00000 q^{26} -5.56155i q^{27} +(3.95042 + 2.28078i) q^{28} +(1.00000 - 1.73205i) q^{29} -6.24621 q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.35234 + 0.780776i) q^{33} +(1.56155 - 2.70469i) q^{34} +(0.280776 + 0.486319i) q^{36} +7.68466i q^{37} +(-3.95042 - 1.84233i) q^{38} +3.12311 q^{39} +(-1.06155 - 1.83866i) q^{41} +(6.16879 + 3.56155i) q^{42} +(4.43674 - 2.56155i) q^{43} +(0.500000 - 0.866025i) q^{44} -7.68466 q^{46} +(-9.63289 - 5.56155i) q^{47} +(1.35234 + 0.780776i) q^{48} -13.8078 q^{49} +(2.43845 - 4.22351i) q^{51} +(-1.73205 + 1.00000i) q^{52} +(-2.97778 - 1.71922i) q^{53} +(2.78078 + 4.81645i) q^{54} -4.56155 q^{56} +(-6.16879 - 2.87689i) q^{57} +2.00000i q^{58} +(5.21922 + 9.03996i) q^{59} +(1.56155 - 2.70469i) q^{61} +(5.40938 - 3.12311i) q^{62} +(-2.21837 - 1.28078i) q^{63} -1.00000 q^{64} +(0.780776 - 1.35234i) q^{66} +(-11.7446 - 6.78078i) q^{67} +3.12311i q^{68} -12.0000 q^{69} +(0.123106 + 0.213225i) q^{71} +(-0.486319 - 0.280776i) q^{72} +(-9.25319 + 5.34233i) q^{73} +(-3.84233 - 6.65511i) q^{74} +(4.34233 - 0.379706i) q^{76} +4.56155i q^{77} +(-2.70469 + 1.56155i) q^{78} +(-1.43845 - 2.49146i) q^{79} +(3.50000 + 6.06218i) q^{81} +(1.83866 + 1.06155i) q^{82} -9.80776i q^{83} -7.12311 q^{84} +(-2.56155 + 4.43674i) q^{86} +3.12311i q^{87} +1.00000i q^{88} +(4.84233 - 8.38716i) q^{89} +(4.56155 - 7.90084i) q^{91} +(6.65511 - 3.84233i) q^{92} +(8.44703 - 4.87689i) q^{93} +11.1231 q^{94} -1.56155 q^{96} +(-9.25319 + 5.34233i) q^{97} +(11.9579 - 6.90388i) q^{98} +(-0.280776 + 0.486319i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 2 q^{6} + 6 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 - 2 * q^6 + 6 * q^9	$ 8 q + 4 q^{4} - 2 q^{6} + 6 q^{9} + 8 q^{11} - 10 q^{14} - 4 q^{16} + 20 q^{19} - 12 q^{21} + 2 q^{24} + 16 q^{26} + 8 q^{29} + 16 q^{31} - 4 q^{34} - 6 q^{36} - 8 q^{39} + 8 q^{41} + 4 q^{44} - 12 q^{46} - 28 q^{49} + 36 q^{51} + 14 q^{54} - 20 q^{56} + 50 q^{59} - 4 q^{61} - 8 q^{64} - 2 q^{66} - 96 q^{69} - 32 q^{71} - 6 q^{74} + 10 q^{76} - 28 q^{79} + 28 q^{81} - 24 q^{84} - 4 q^{86} + 14 q^{89} + 20 q^{91} + 56 q^{94} + 4 q^{96} + 6 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 - 2 * q^6 + 6 * q^9 + 8 * q^11 - 10 * q^14 - 4 * q^16 + 20 * q^19 - 12 * q^21 + 2 * q^24 + 16 * q^26 + 8 * q^29 + 16 * q^31 - 4 * q^34 - 6 * q^36 - 8 * q^39 + 8 * q^41 + 4 * q^44 - 12 * q^46 - 28 * q^49 + 36 * q^51 + 14 * q^54 - 20 * q^56 + 50 * q^59 - 4 * q^61 - 8 * q^64 - 2 * q^66 - 96 * q^69 - 32 * q^71 - 6 * q^74 + 10 * q^76 - 28 * q^79 + 28 * q^81 - 24 * q^84 - 4 * q^86 + 14 * q^89 + 20 * q^91 + 56 * q^94 + 4 * q^96 + 6 * 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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.35234	+	0.780776i	−0.780776	+	0.450781i	−0.836705	−	0.547653i	$-0.815521\pi$
$3$	−1.35234	+	0.780776i	−0.780776	+	0.450781i	0.0559290	+	0.998435i	$0.482188\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.780776	−	1.35234i	0.318751	−	0.552092i
$7$			4.56155i			1.72410i	0.506819	+	0.862052i	$0.330821\pi$
$7$			4.56155i			1.72410i	−0.506819	+	0.862052i	$0.669179\pi$
$8$			1.00000i			0.353553i
$9$	−0.280776	+	0.486319i	−0.0935921	+	0.162106i
$10$		0			0
$11$	1.00000			0.301511			0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000			0.301511			0.150756	+	0.988571i	$0.451829\pi$
$12$			1.56155i			0.450781i
$13$	−1.73205	−	1.00000i	−0.480384	−	0.277350i	0.240192	−	0.970725i	$-0.422790\pi$
$13$	−1.73205	−	1.00000i	−0.480384	−	0.277350i	−0.720577	+	0.693375i	$0.756123\pi$
$14$	−2.28078	−	3.95042i	−0.609563	−	1.05579i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.70469	+	1.56155i	−0.655983	+	0.378732i	−0.790745	−	0.612146i	$-0.790307\pi$
$17$	−2.70469	+	1.56155i	−0.655983	+	0.378732i	0.134761	+	0.990878i	$0.456973\pi$
$18$		−	0.561553i		−	0.132359i
$19$	2.50000	+	3.57071i	0.573539	+	0.819178i
$19$	2.50000	+	3.57071i	0.573539	+	0.819178i
$20$		0			0
$21$	−3.56155	−	6.16879i	−0.777195	−	1.34614i
$22$	−0.866025	+	0.500000i	−0.184637	+	0.106600i
$23$	6.65511	+	3.84233i	1.38769	+	0.801181i	0.993054	−	0.117658i	$-0.0375387\pi$
$23$	6.65511	+	3.84233i	1.38769	+	0.801181i	0.394632	+	0.918839i	$0.370872\pi$
$24$	−0.780776	−	1.35234i	−0.159375	−	0.276046i
$25$		0			0
$26$	2.00000			0.392232
$27$		−	5.56155i		−	1.07032i
$28$	3.95042	+	2.28078i	0.746559	+	0.431026i
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	−0.758115	−	0.652121i	$-0.773880\pi$
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	0.943811	+	0.330487i	$0.107213\pi$
$30$		0			0
$31$	−6.24621			−1.12185			−0.560926	−	0.827866i	$-0.689555\pi$
$31$	−6.24621			−1.12185			−0.560926	+	0.827866i	$0.689555\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−1.35234	+	0.780776i	−0.235413	+	0.135916i
$34$	1.56155	−	2.70469i	0.267804	−	0.463850i
$35$		0			0
$36$	0.280776	+	0.486319i	0.0467961	+	0.0810532i
$37$			7.68466i			1.26335i	0.775233	+	0.631675i	$0.217632\pi$
$37$			7.68466i			1.26335i	−0.775233	+	0.631675i	$0.782368\pi$
$38$	−3.95042	−	1.84233i	−0.640843	−	0.298865i
$39$	3.12311			0.500097
$40$		0			0
$41$	−1.06155	−	1.83866i	−0.165787	−	0.287151i	0.771148	−	0.636656i	$-0.219683\pi$
$41$	−1.06155	−	1.83866i	−0.165787	−	0.287151i	−0.936934	+	0.349505i	$0.886350\pi$
$42$	6.16879	+	3.56155i	0.951865	+	0.549560i
$43$	4.43674	−	2.56155i	0.676596	−	0.390633i	−0.121975	−	0.992533i	$-0.538923\pi$
$43$	4.43674	−	2.56155i	0.676596	−	0.390633i	0.798571	+	0.601900i	$0.205589\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$		0			0
$46$	−7.68466			−1.13304
$47$	−9.63289	−	5.56155i	−1.40510	−	0.811236i	−0.410191	−	0.911999i	$-0.634538\pi$
$47$	−9.63289	−	5.56155i	−1.40510	−	0.811236i	−0.994910	+	0.100764i	$0.967871\pi$
$48$	1.35234	+	0.780776i	0.195194	+	0.112695i
$49$	−13.8078			−1.97254
$50$		0			0
$51$	2.43845	−	4.22351i	0.341451	−	0.591410i
$52$	−1.73205	+	1.00000i	−0.240192	+	0.138675i
$53$	−2.97778	−	1.71922i	−0.409030	−	0.236154i	0.281343	−	0.959607i	$-0.409220\pi$
$53$	−2.97778	−	1.71922i	−0.409030	−	0.236154i	−0.690373	+	0.723454i	$0.742553\pi$
$54$	2.78078	+	4.81645i	0.378416	+	0.655435i
$55$		0			0
$56$	−4.56155			−0.609563
$57$	−6.16879	−	2.87689i	−0.817076	−	0.381054i
$58$			2.00000i			0.262613i
$59$	5.21922	+	9.03996i	0.679485	+	1.17690i	0.975136	+	0.221607i	$0.0711301\pi$
$59$	5.21922	+	9.03996i	0.679485	+	1.17690i	−0.295651	+	0.955296i	$0.595537\pi$
$60$		0			0
$61$	1.56155	−	2.70469i	0.199936	−	0.346300i	−0.748571	−	0.663054i	$-0.769260\pi$
$61$	1.56155	−	2.70469i	0.199936	−	0.346300i	0.948508	+	0.316754i	$0.102593\pi$
$62$	5.40938	−	3.12311i	0.686992	−	0.396635i
$63$	−2.21837	−	1.28078i	−0.279488	−	0.161363i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	0.780776	−	1.35234i	0.0961069	−	0.166462i
$67$	−11.7446	−	6.78078i	−1.43484	−	0.828404i	−0.437353	−	0.899290i	$-0.644084\pi$
$67$	−11.7446	−	6.78078i	−1.43484	−	0.828404i	−0.997484	+	0.0708863i	$0.977417\pi$
$68$			3.12311i			0.378732i
$69$	−12.0000			−1.44463
$70$		0			0
$71$	0.123106	+	0.213225i	0.0146099	+	0.0253052i	0.873238	−	0.487294i	$-0.162016\pi$
$71$	0.123106	+	0.213225i	0.0146099	+	0.0253052i	−0.858628	+	0.512599i	$0.828683\pi$
$72$	−0.486319	−	0.280776i	−0.0573132	−	0.0330898i
$73$	−9.25319	+	5.34233i	−1.08300	+	0.625272i	−0.931705	−	0.363216i	$-0.881679\pi$
$73$	−9.25319	+	5.34233i	−1.08300	+	0.625272i	−0.151298	+	0.988488i	$0.548345\pi$
$74$	−3.84233	−	6.65511i	−0.446662	−	0.773641i
$75$		0			0
$76$	4.34233	−	0.379706i	0.498099	−	0.0435553i
$77$			4.56155i			0.519837i
$78$	−2.70469	+	1.56155i	−0.306246	+	0.176811i
$79$	−1.43845	−	2.49146i	−0.161838	−	0.280312i	0.773690	−	0.633564i	$-0.218409\pi$
$79$	−1.43845	−	2.49146i	−0.161838	−	0.280312i	−0.935528	+	0.353253i	$0.885076\pi$
$80$		0			0
$81$	3.50000	+	6.06218i	0.388889	+	0.673575i
$82$	1.83866	+	1.06155i	0.203046	+	0.117229i
$83$		−	9.80776i		−	1.07654i	−0.842772	−	0.538271i	$-0.819078\pi$
$83$		−	9.80776i		−	1.07654i	0.842772	−	0.538271i	$-0.180922\pi$
$84$	−7.12311			−0.777195
$85$		0			0
$86$	−2.56155	+	4.43674i	−0.276219	+	0.478426i
$87$			3.12311i			0.334832i
$88$			1.00000i			0.106600i
$89$	4.84233	−	8.38716i	0.513286	−	0.889037i	−0.486595	−	0.873627i	$-0.661761\pi$
$89$	4.84233	−	8.38716i	0.513286	−	0.889037i	0.999881	−	0.0154098i	$-0.00490527\pi$
$90$		0			0
$91$	4.56155	−	7.90084i	0.478181	−	0.828233i
$92$	6.65511	−	3.84233i	0.693843	−	0.400591i
$93$	8.44703	−	4.87689i	0.875916	−	0.505710i
$94$	11.1231			1.14726
$95$		0			0
$96$	−1.56155			−0.159375
$97$	−9.25319	+	5.34233i	−0.939519	+	0.542431i	−0.889809	−	0.456332i	$-0.849163\pi$
$97$	−9.25319	+	5.34233i	−0.939519	+	0.542431i	−0.0497093	+	0.998764i	$0.515829\pi$
$98$	11.9579	−	6.90388i	1.20793	−	0.697397i
$99$	−0.280776	+	0.486319i	−0.0282191	+	0.0488769i
$100$		0			0
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$			4.87689i			0.482884i
$103$		−	14.8078i		−	1.45905i	−0.683953	−	0.729526i	$-0.739741\pi$
$103$		−	14.8078i		−	1.45905i	0.683953	−	0.729526i	$-0.260259\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$		0			0
$106$	3.43845			0.333972
$107$		−	14.2462i		−	1.37723i	−0.725126	−	0.688617i	$-0.758218\pi$
$107$		−	14.2462i		−	1.37723i	0.725126	−	0.688617i	$-0.241782\pi$
$108$	−4.81645	−	2.78078i	−0.463463	−	0.267580i
$109$	1.12311	+	1.94528i	0.107574	+	0.186324i	0.914787	−	0.403937i	$-0.132358\pi$
$109$	1.12311	+	1.94528i	0.107574	+	0.186324i	−0.807213	+	0.590260i	$0.799025\pi$
$110$		0			0
$111$	−6.00000	−	10.3923i	−0.569495	−	0.986394i
$112$	3.95042	−	2.28078i	0.373280	−	0.215513i
$113$		−	3.80776i		−	0.358204i	−0.983830	−	0.179102i	$-0.942681\pi$
$113$		−	3.80776i		−	0.358204i	0.983830	−	0.179102i	$-0.0573193\pi$
$114$	6.78078	−	0.592932i	0.635078	−	0.0555331i
$115$		0			0
$116$	−1.00000	−	1.73205i	−0.0928477	−	0.160817i
$117$	0.972638	−	0.561553i	0.0899204	−	0.0519156i
$118$	−9.03996	−	5.21922i	−0.832196	−	0.480468i
$119$	−7.12311	−	12.3376i	−0.652974	−	1.13098i
$120$		0			0
$121$	−10.0000			−0.909091
$122$			3.12311i			0.282753i
$123$	2.87117	+	1.65767i	0.258885	+	0.149467i
$124$	−3.12311	+	5.40938i	−0.280463	+	0.485776i
$125$		0			0
$126$	2.56155			0.228201
$127$	9.90599	+	5.71922i	0.879014	+	0.507499i	0.870333	−	0.492463i	$-0.163903\pi$
$127$	9.90599	+	5.71922i	0.879014	+	0.507499i	0.00868089	+	0.999962i	$0.497237\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−4.00000	+	6.92820i	−0.352180	+	0.609994i
$130$		0			0
$131$	3.93845	+	6.82159i	0.344104	+	0.596005i	0.985191	−	0.171463i	$-0.0548495\pi$
$131$	3.93845	+	6.82159i	0.344104	+	0.596005i	−0.641087	+	0.767468i	$0.721516\pi$
$132$			1.56155i			0.135916i
$133$	−16.2880	+	11.4039i	−1.41235	+	0.988842i
$134$	13.5616			1.17154
$135$		0			0
$136$	−1.56155	−	2.70469i	−0.133902	−	0.231925i
$137$	8.28055	+	4.78078i	0.707455	+	0.408449i	0.810118	−	0.586267i	$-0.199403\pi$
$137$	8.28055	+	4.78078i	0.707455	+	0.408449i	−0.102663	+	0.994716i	$0.532736\pi$
$138$	10.3923	−	6.00000i	0.884652	−	0.510754i
$139$	−5.90388	+	10.2258i	−0.500761	+	0.867343i	0.499239	+	0.866464i	$0.333613\pi$
$139$	−5.90388	+	10.2258i	−0.500761	+	0.867343i	−1.00000		0.000878648i	$0.999720\pi$
$140$		0			0
$141$	17.3693			1.46276
$142$	−0.213225	−	0.123106i	−0.0178935	−	0.0103308i
$143$	−1.73205	−	1.00000i	−0.144841	−	0.0836242i
$144$	0.561553			0.0467961
$145$		0			0
$146$	5.34233	−	9.25319i	0.442134	−	0.765799i
$147$	18.6729	−	10.7808i	1.54011	−	0.889183i
$148$	6.65511	+	3.84233i	0.547047	+	0.315838i
$149$	8.00000	+	13.8564i	0.655386	+	1.13516i	0.981797	+	0.189933i	$0.0608272\pi$
$149$	8.00000	+	13.8564i	0.655386	+	1.13516i	−0.326411	+	0.945228i	$0.605840\pi$
$150$		0			0
$151$	−12.4924			−1.01662			−0.508309	−	0.861174i	$-0.669729\pi$
$151$	−12.4924			−1.01662			−0.508309	+	0.861174i	$0.669729\pi$
$152$	−3.57071	+	2.50000i	−0.289623	+	0.202777i
$153$		−	1.75379i		−	0.141785i
$154$	−2.28078	−	3.95042i	−0.183790	−	0.318334i
$155$		0			0
$156$	1.56155	−	2.70469i	0.125024	−	0.216548i
$157$	5.68247	−	3.28078i	0.453511	−	0.261834i	−0.255801	−	0.966729i	$-0.582339\pi$
$157$	5.68247	−	3.28078i	0.453511	−	0.261834i	0.709312	+	0.704895i	$0.249006\pi$
$158$	2.49146	+	1.43845i	0.198210	+	0.114437i
$159$	5.36932			0.425815
$160$		0			0
$161$	−17.5270	+	30.3576i	−1.38132	+	2.39252i
$162$	−6.06218	−	3.50000i	−0.476290	−	0.274986i
$163$			20.0540i			1.57075i	0.619021	+	0.785374i	$0.287529\pi$
$163$			20.0540i			1.57075i	−0.619021	+	0.785374i	$0.712471\pi$
$164$	−2.12311			−0.165787
$165$		0			0
$166$	4.90388	+	8.49377i	0.380615	+	0.659245i
$167$	10.1192	+	5.84233i	0.783048	+	0.452093i	0.837509	−	0.546423i	$-0.184011\pi$
$167$	10.1192	+	5.84233i	0.783048	+	0.452093i	−0.0544614	+	0.998516i	$0.517344\pi$
$168$	6.16879	−	3.56155i	0.475933	−	0.274780i
$169$	−4.50000	−	7.79423i	−0.346154	−	0.599556i
$170$		0			0
$171$	−2.43845	+	0.213225i	−0.186473	+	0.0163057i
$172$		−	5.12311i		−	0.390633i
$173$	−12.8239	+	7.40388i	−0.974983	+	0.562907i	−0.900752	−	0.434334i	$-0.856984\pi$
$173$	−12.8239	+	7.40388i	−0.974983	+	0.562907i	−0.0742313	+	0.997241i	$0.523650\pi$
$174$	−1.56155	−	2.70469i	−0.118381	−	0.205042i
$175$		0			0
$176$	−0.500000	−	0.866025i	−0.0376889	−	0.0652791i
$177$	−14.1164	−	8.15009i	−1.06105	−	0.612599i
$178$			9.68466i			0.725896i
$179$	21.4924			1.60642			0.803210	−	0.595697i	$-0.203124\pi$
$179$	21.4924			1.60642			0.803210	+	0.595697i	$0.203124\pi$
$180$		0			0
$181$	1.68466	−	2.91791i	0.125220	−	0.216887i	−0.796599	−	0.604508i	$-0.793370\pi$
$181$	1.68466	−	2.91791i	0.125220	−	0.216887i	0.921819	+	0.387621i	$0.126703\pi$
$182$			9.12311i			0.676250i
$183$			4.87689i			0.360510i
$184$	−3.84233	+	6.65511i	−0.283260	+	0.490621i
$185$		0			0
$186$	−4.87689	+	8.44703i	−0.357591	+	0.619366i
$187$	−2.70469	+	1.56155i	−0.197786	+	0.114192i
$188$	−9.63289	+	5.56155i	−0.702551	+	0.405618i
$189$	25.3693			1.84535
$190$		0			0
$191$	19.3693			1.40151			0.700757	−	0.713400i	$-0.252846\pi$
$191$	19.3693			1.40151			0.700757	+	0.713400i	$0.252846\pi$
$192$	1.35234	−	0.780776i	0.0975971	−	0.0563477i
$193$	13.5234	−	7.80776i	0.973439	−	0.562015i	0.0731559	−	0.997321i	$-0.476693\pi$
$193$	13.5234	−	7.80776i	0.973439	−	0.562015i	0.900283	+	0.435305i	$0.143360\pi$
$194$	5.34233	−	9.25319i	0.383557	−	0.664340i
$195$		0			0
$196$	−6.90388	+	11.9579i	−0.493134	+	0.854134i
$197$			18.5616i			1.32246i	0.750185	+	0.661228i	$0.229964\pi$
$197$			18.5616i			1.32246i	−0.750185	+	0.661228i	$0.770036\pi$
$198$		−	0.561553i		−	0.0399078i
$199$	−5.56155	+	9.63289i	−0.394248	+	0.682858i	−0.993005	−	0.118073i	$-0.962328\pi$
$199$	−5.56155	+	9.63289i	−0.394248	+	0.682858i	0.598757	+	0.800931i	$0.295662\pi$
$200$		0			0
$201$	21.1771			1.49372
$202$		−	10.0000i		−	0.703598i
$203$	7.90084	+	4.56155i	0.554530	+	0.320158i
$204$	−2.43845	−	4.22351i	−0.170725	−	0.295705i
$205$		0			0
$206$	7.40388	+	12.8239i	0.515853	+	0.893483i
$207$	−3.73720	+	2.15767i	−0.259753	+	0.149968i
$208$			2.00000i			0.138675i
$209$	2.50000	+	3.57071i	0.172929	+	0.246991i
$210$		0			0
$211$	7.84233	+	13.5833i	0.539888	+	0.935114i	0.998909	+	0.0466885i	$0.0148668\pi$
$211$	7.84233	+	13.5833i	0.539888	+	0.935114i	−0.459021	+	0.888425i	$0.651800\pi$
$212$	−2.97778	+	1.71922i	−0.204515	+	0.118077i
$213$	−0.332962	−	0.192236i	−0.0228142	−	0.0131718i
$214$	7.12311	+	12.3376i	0.486925	+	0.843380i
$215$		0			0
$216$	5.56155			0.378416
$217$		−	28.4924i		−	1.93419i
$218$	−1.94528	−	1.12311i	−0.131751	−	0.0760663i
$219$	8.34233	−	14.4493i	0.563722	−	0.976396i
$220$		0			0
$221$	6.24621			0.420166
$222$	10.3923	+	6.00000i	0.697486	+	0.402694i
$223$	−20.5115	+	11.8423i	−1.37355	+	0.793021i	−0.991373	−	0.131067i	$-0.958160\pi$
$223$	−20.5115	+	11.8423i	−1.37355	+	0.793021i	−0.382179	+	0.924088i	$0.624826\pi$
$224$	−2.28078	+	3.95042i	−0.152391	+	0.263949i
$225$		0			0
$226$	1.90388	+	3.29762i	0.126644	+	0.219354i
$227$		−	8.93087i		−	0.592763i	−0.955070	−	0.296381i	$-0.904220\pi$
$227$		−	8.93087i		−	0.592763i	0.955070	−	0.296381i	$-0.0957799\pi$
$228$	−5.57586	+	3.90388i	−0.369270	+	0.258541i
$229$	−21.1231			−1.39585			−0.697927	−	0.716169i	$-0.745894\pi$
$229$	−21.1231			−1.39585			−0.697927	+	0.716169i	$0.745894\pi$
$230$		0			0
$231$	−3.56155	−	6.16879i	−0.234333	−	0.405877i
$232$	1.73205	+	1.00000i	0.113715	+	0.0656532i
$233$	−12.7173	+	7.34233i	−0.833137	+	0.481012i	−0.854926	−	0.518751i	$-0.826397\pi$
$233$	−12.7173	+	7.34233i	−0.833137	+	0.481012i	0.0217884	+	0.999763i	$0.493064\pi$
$234$	−0.561553	+	0.972638i	−0.0367099	+	0.0635833i
$235$		0			0
$236$	10.4384			0.679485
$237$	3.89055	+	2.24621i	0.252719	+	0.145907i
$238$	12.3376	+	7.12311i	0.799727	+	0.461722i
$239$	−1.75379			−0.113443			−0.0567216	−	0.998390i	$-0.518065\pi$
$239$	−1.75379			−0.113443			−0.0567216	+	0.998390i	$0.518065\pi$
$240$		0			0
$241$	2.21922	−	3.84381i	0.142953	−	0.247601i	−0.785655	−	0.618665i	$-0.787674\pi$
$241$	2.21922	−	3.84381i	0.142953	−	0.247601i	0.928607	+	0.371064i	$0.121007\pi$
$242$	8.66025	−	5.00000i	0.556702	−	0.321412i
$243$	4.98293	+	2.87689i	0.319655	+	0.184553i
$244$	−1.56155	−	2.70469i	−0.0999682	−	0.173150i
$245$		0			0
$246$	−3.31534			−0.211378
$247$	−0.759413	−	8.68466i	−0.0483203	−	0.552592i
$248$		−	6.24621i		−	0.396635i
$249$	7.65767	+	13.2635i	0.485285	+	0.840539i
$250$		0			0
$251$	1.46543	−	2.53821i	0.0924974	−	0.160210i	−0.816064	−	0.577962i	$-0.803848\pi$
$251$	1.46543	−	2.53821i	0.0924974	−	0.160210i	0.908561	+	0.417751i	$0.137182\pi$
$252$	−2.21837	+	1.28078i	−0.139744	+	0.0806813i
$253$	6.65511	+	3.84233i	0.418403	+	0.241565i
$254$	−11.4384			−0.717712
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	20.8314	+	12.0270i	1.29942	+	0.750223i	0.980305	−	0.197492i	$-0.0632795\pi$
$257$	20.8314	+	12.0270i	1.29942	+	0.750223i	0.319120	+	0.947714i	$0.396613\pi$
$258$		−	8.00000i		−	0.498058i
$259$	−35.0540			−2.17815
$260$		0			0
$261$	0.561553	+	0.972638i	0.0347592	+	0.0602048i
$262$	−6.82159	−	3.93845i	−0.421439	−	0.243318i
$263$	19.7521	−	11.4039i	1.21797	−	0.703193i	0.253484	−	0.967340i	$-0.418423\pi$
$263$	19.7521	−	11.4039i	1.21797	−	0.703193i	0.964483	+	0.264146i	$0.0850901\pi$
$264$	−0.780776	−	1.35234i	−0.0480535	−	0.0832310i
$265$		0			0
$266$	8.40388	−	18.0201i	0.515275	−	1.10488i
$267$			15.1231i			0.925519i
$268$	−11.7446	+	6.78078i	−0.717419	+	0.414202i
$269$	2.00000	+	3.46410i	0.121942	+	0.211210i	0.920534	−	0.390664i	$-0.127754\pi$
$269$	2.00000	+	3.46410i	0.121942	+	0.211210i	−0.798591	+	0.601874i	$0.794421\pi$
$270$		0			0
$271$	−4.12311	−	7.14143i	−0.250461	−	0.433811i	0.713192	−	0.700969i	$-0.247249\pi$
$271$	−4.12311	−	7.14143i	−0.250461	−	0.433811i	−0.963653	+	0.267158i	$0.913915\pi$
$272$	2.70469	+	1.56155i	0.163996	+	0.0946830i
$273$			14.2462i			0.862220i
$274$	−9.56155			−0.577635
$275$		0			0
$276$	−6.00000	+	10.3923i	−0.361158	+	0.625543i
$277$		−	12.2462i		−	0.735804i	−0.929865	−	0.367902i	$-0.880076\pi$
$277$		−	12.2462i		−	0.735804i	0.929865	−	0.367902i	$-0.119924\pi$
$278$		−	11.8078i		−	0.708183i
$279$	1.75379	−	3.03765i	0.104997	−	0.181859i
$280$		0			0
$281$	8.18466	−	14.1762i	0.488256	−	0.845684i	−0.511653	−	0.859192i	$-0.670967\pi$
$281$	8.18466	−	14.1762i	0.488256	−	0.845684i	0.999909	+	0.0135084i	$0.00429998\pi$
$282$	−15.0423	+	8.68466i	−0.895754	+	0.517164i
$283$	20.4049	−	11.7808i	1.21295	−	0.700294i	0.249546	−	0.968363i	$-0.419719\pi$
$283$	20.4049	−	11.7808i	1.21295	−	0.700294i	0.963400	+	0.268069i	$0.0863854\pi$
$284$	0.246211			0.0146099
$285$		0			0
$286$	2.00000			0.118262
$287$	8.38716	−	4.84233i	0.495078	−	0.285834i
$288$	−0.486319	+	0.280776i	−0.0286566	+	0.0165449i
$289$	−3.62311	+	6.27540i	−0.213124	+	0.369141i
$290$		0			0
$291$	8.34233	−	14.4493i	0.489036	−	0.847035i
$292$			10.6847i			0.625272i
$293$		−	19.4384i		−	1.13561i	−0.823164	−	0.567803i	$-0.807793\pi$
$293$		−	19.4384i		−	1.13561i	0.823164	−	0.567803i	$-0.192207\pi$
$294$	−10.7808	+	18.6729i	−0.628748	+	1.08902i
$295$		0			0
$296$	−7.68466			−0.446662
$297$		−	5.56155i		−	0.322714i
$298$	−13.8564	−	8.00000i	−0.802680	−	0.463428i
$299$	−7.68466	−	13.3102i	−0.444415	−	0.769750i
$300$		0			0
$301$	11.6847	+	20.2384i	0.673493	+	1.16652i
$302$	10.8188	−	6.24621i	0.622549	−	0.359429i
$303$		−	15.6155i		−	0.897089i
$304$	1.84233	−	3.95042i	0.105665	−	0.226572i
$305$		0			0
$306$	0.876894	+	1.51883i	0.0501287	+	0.0868255i
$307$	4.27026	−	2.46543i	0.243717	−	0.140710i	−0.373167	−	0.927764i	$-0.621728\pi$
$307$	4.27026	−	2.46543i	0.243717	−	0.140710i	0.616884	+	0.787054i	$0.288395\pi$
$308$	3.95042	+	2.28078i	0.225096	+	0.129959i
$309$	11.5616	+	20.0252i	0.657714	+	1.13919i
$310$		0			0
$311$	4.00000			0.226819			0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000			0.226819			0.113410	+	0.993548i	$0.463823\pi$
$312$			3.12311i			0.176811i
$313$	14.4493	+	8.34233i	0.816725	+	0.471536i	0.849286	−	0.527933i	$-0.177033\pi$
$313$	14.4493	+	8.34233i	0.816725	+	0.471536i	−0.0325609	+	0.999470i	$0.510366\pi$
$314$	−3.28078	+	5.68247i	−0.185145	+	0.320680i
$315$		0			0
$316$	−2.87689			−0.161838
$317$	−5.46925	−	3.15767i	−0.307183	−	0.177352i	0.338482	−	0.940973i	$-0.390087\pi$
$317$	−5.46925	−	3.15767i	−0.307183	−	0.177352i	−0.645665	+	0.763620i	$0.723420\pi$
$318$	−4.64996	+	2.68466i	−0.260757	+	0.150548i
$319$	1.00000	−	1.73205i	0.0559893	−	0.0969762i
$320$		0			0
$321$	11.1231	+	19.2658i	0.620831	+	1.07531i
$322$		−	35.0540i		−	1.95348i
$323$	−12.3376	−	5.75379i	−0.686481	−	0.320149i
$324$	7.00000			0.388889
$325$		0			0
$326$	−10.0270	−	17.3673i	−0.555343	−	0.961883i
$327$	−3.03765	−	1.75379i	−0.167982	−	0.0969847i
$328$	1.83866	−	1.06155i	0.101523	−	0.0586144i
$329$	25.3693	−	43.9409i	1.39866	−	2.42254i
$330$		0			0
$331$	−9.49242			−0.521751			−0.260875	−	0.965372i	$-0.584011\pi$
$331$	−9.49242			−0.521751			−0.260875	+	0.965372i	$0.584011\pi$
$332$	−8.49377	−	4.90388i	−0.466156	−	0.269135i
$333$	−3.73720	−	2.15767i	−0.204797	−	0.118240i
$334$	−11.6847			−0.639356
$335$		0			0
$336$	−3.56155	+	6.16879i	−0.194299	+	0.336535i
$337$	−13.9032	+	8.02699i	−0.757353	+	0.437258i	−0.828345	−	0.560219i	$-0.810717\pi$
$337$	−13.9032	+	8.02699i	−0.757353	+	0.437258i	0.0709917	+	0.997477i	$0.477384\pi$
$338$	7.79423	+	4.50000i	0.423950	+	0.244768i
$339$	2.97301	+	5.14941i	0.161472	+	0.279677i
$340$		0			0
$341$	−6.24621			−0.338251
$342$	2.00514	−	1.40388i	0.108426	−	0.0759132i
$343$		−	31.0540i		−	1.67676i
$344$	2.56155	+	4.43674i	0.138110	+	0.239213i
$345$		0			0
$346$	7.40388	−	12.8239i	0.398035	−	0.689417i
$347$	−9.25319	+	5.34233i	−0.496737	+	0.286791i	−0.727365	−	0.686251i	$-0.759255\pi$
$347$	−9.25319	+	5.34233i	−0.496737	+	0.286791i	0.230628	+	0.973042i	$0.425922\pi$
$348$	2.70469	+	1.56155i	0.144987	+	0.0837080i
$349$	−2.24621			−0.120237			−0.0601185	−	0.998191i	$-0.519148\pi$
$349$	−2.24621			−0.120237			−0.0601185	+	0.998191i	$0.519148\pi$
$350$		0			0
$351$	−5.56155	+	9.63289i	−0.296854	+	0.514166i
$352$	0.866025	+	0.500000i	0.0461593	+	0.0266501i
$353$			21.1771i			1.12714i	0.826068	+	0.563571i	$0.190573\pi$
$353$			21.1771i			1.12714i	−0.826068	+	0.563571i	$0.809427\pi$
$354$	16.3002			0.866345
$355$		0			0
$356$	−4.84233	−	8.38716i	−0.256643	−	0.444519i
$357$	19.2658	+	11.1231i	1.01965	+	0.588697i
$358$	−18.6130	+	10.7462i	−0.983727	+	0.567955i
$359$	3.43845	+	5.95557i	0.181474	+	0.314323i	0.942383	−	0.334536i	$-0.108580\pi$
$359$	3.43845	+	5.95557i	0.181474	+	0.314323i	−0.760908	+	0.648859i	$0.775246\pi$
$360$		0			0
$361$	−6.50000	+	17.8536i	−0.342105	+	0.939662i
$362$			3.36932i			0.177087i
$363$	13.5234	−	7.80776i	0.709797	−	0.409801i
$364$	−4.56155	−	7.90084i	−0.239090	−	0.414117i
$365$		0			0
$366$	−2.43845	−	4.22351i	−0.127460	−	0.220767i
$367$	29.6581	+	17.1231i	1.54814	+	0.893819i	0.998284	+	0.0585592i	$0.0186506\pi$
$367$	29.6581	+	17.1231i	1.54814	+	0.893819i	0.549856	+	0.835260i	$0.314683\pi$
$368$		−	7.68466i		−	0.400591i
$369$	1.19224			0.0620653
$370$		0			0
$371$	7.84233	−	13.5833i	0.407153	−	0.705210i
$372$		−	9.75379i		−	0.505710i
$373$			15.1922i			0.786624i	0.919405	+	0.393312i	$0.128671\pi$
$373$			15.1922i			0.786624i	−0.919405	+	0.393312i	$0.871329\pi$
$374$	1.56155	−	2.70469i	0.0807460	−	0.139856i
$375$		0			0
$376$	5.56155	−	9.63289i	0.286815	−	0.496778i
$377$	−3.46410	+	2.00000i	−0.178410	+	0.103005i
$378$	−21.9705	+	12.6847i	−1.13004	+	0.652428i
$379$	−32.4924			−1.66902			−0.834512	−	0.550990i	$-0.814250\pi$
$379$	−32.4924			−1.66902			−0.834512	+	0.550990i	$0.814250\pi$
$380$		0			0
$381$	−17.8617			−0.915085
$382$	−16.7743	+	9.68466i	−0.858249	+	0.495510i
$383$	2.70469	−	1.56155i	0.138203	−	0.0797916i	−0.429304	−	0.903160i	$-0.641241\pi$
$383$	2.70469	−	1.56155i	0.138203	−	0.0797916i	0.567507	+	0.823368i	$0.307908\pi$
$384$	−0.780776	+	1.35234i	−0.0398438	+	0.0690115i
$385$		0			0
$386$	−7.80776	+	13.5234i	−0.397405	+	0.688325i
$387$			2.87689i			0.146241i
$388$			10.6847i			0.542431i
$389$	−5.43845	+	9.41967i	−0.275740	+	0.477596i	−0.970322	−	0.241818i	$-0.922256\pi$
$389$	−5.43845	+	9.41967i	−0.275740	+	0.477596i	0.694581	+	0.719414i	$0.255590\pi$
$390$		0			0
$391$	−24.0000			−1.21373
$392$		−	13.8078i		−	0.697397i
$393$	−10.6523	−	6.15009i	−0.537336	−	0.310231i
$394$	−9.28078	−	16.0748i	−0.467559	−	0.809836i
$395$		0			0
$396$	0.280776	+	0.486319i	0.0141095	+	0.0244384i
$397$	−21.9106	+	12.6501i	−1.09966	+	0.634890i	−0.936132	−	0.351648i	$-0.885621\pi$
$397$	−21.9106	+	12.6501i	−1.09966	+	0.634890i	−0.163530	+	0.986538i	$0.552288\pi$
$398$		−	11.1231i		−	0.557551i
$399$	13.1231	−	28.1393i	0.656977	−	1.40873i
$400$		0			0
$401$	0.465435	+	0.806157i	0.0232427	+	0.0402575i	0.877413	−	0.479736i	$-0.159268\pi$
$401$	0.465435	+	0.806157i	0.0232427	+	0.0402575i	−0.854170	+	0.519994i	$0.825934\pi$
$402$	−18.3399	+	10.5885i	−0.914711	+	0.528108i
$403$	10.8188	+	6.24621i	0.538921	+	0.311146i
$404$	5.00000	+	8.66025i	0.248759	+	0.430864i
$405$		0			0
$406$	−9.12311			−0.452772
$407$			7.68466i			0.380914i
$408$	4.22351	+	2.43845i	0.209095	+	0.120721i
$409$	10.5000	−	18.1865i	0.519192	−	0.899266i	−0.480560	−	0.876962i	$-0.659566\pi$
$409$	10.5000	−	18.1865i	0.519192	−	0.899266i	0.999751	−	0.0223042i	$-0.00710022\pi$
$410$		0			0
$411$	−14.9309			−0.736485
$412$	−12.8239	−	7.40388i	−0.631788	−	0.364763i
$413$	−41.2363	+	23.8078i	−2.02910	+	1.17150i
$414$	2.15767	−	3.73720i	0.106044	−	0.183673i
$415$		0			0
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$		−	18.4384i		−	0.902935i
$418$	−3.95042	−	1.84233i	−0.193221	−	0.0901113i
$419$	13.4384			0.656511			0.328256	−	0.944589i	$-0.393539\pi$
$419$	13.4384			0.656511			0.328256	+	0.944589i	$0.393539\pi$
$420$		0			0
$421$	0.246211	+	0.426450i	0.0119996	+	0.0207839i	0.871963	−	0.489572i	$-0.162847\pi$
$421$	0.246211	+	0.426450i	0.0119996	+	0.0207839i	−0.859963	+	0.510356i	$0.829514\pi$
$422$	−13.5833	−	7.84233i	−0.661225	−	0.381759i
$423$	5.40938	−	3.12311i	0.263013	−	0.151851i
$424$	1.71922	−	2.97778i	0.0834929	−	0.144614i
$425$		0			0
$426$	0.384472			0.0186277
$427$	12.3376	+	7.12311i	0.597057	+	0.344711i
$428$	−12.3376	−	7.12311i	−0.596359	−	0.344308i
$429$	3.12311			0.150785
$430$		0			0
$431$	−8.68466	+	15.0423i	−0.418325	+	0.724561i	−0.995771	−	0.0918683i	$-0.970716\pi$
$431$	−8.68466	+	15.0423i	−0.418325	+	0.724561i	0.577446	+	0.816429i	$0.304049\pi$
$432$	−4.81645	+	2.78078i	−0.231731	+	0.133790i
$433$	11.0320	+	6.36932i	0.530163	+	0.306090i	0.741083	−	0.671414i	$-0.234313\pi$
$433$	11.0320	+	6.36932i	0.530163	+	0.306090i	−0.210920	+	0.977503i	$0.567646\pi$
$434$	14.2462	+	24.6752i	0.683840	+	1.18445i
$435$		0			0
$436$	2.24621			0.107574
$437$	2.91791	+	33.3693i	0.139583	+	1.59627i
$438$			16.6847i			0.797224i
$439$	8.24621	+	14.2829i	0.393570	+	0.681684i	0.992918	−	0.118806i	$-0.0379065\pi$
$439$	8.24621	+	14.2829i	0.393570	+	0.681684i	−0.599347	+	0.800489i	$0.704573\pi$
$440$		0			0
$441$	3.87689	−	6.71498i	0.184614	−	0.319761i
$442$	−5.40938	+	3.12311i	−0.257298	+	0.148551i
$443$	4.39000	+	2.53457i	0.208575	+	0.120421i	0.600649	−	0.799513i	$-0.294909\pi$
$443$	4.39000	+	2.53457i	0.208575	+	0.120421i	−0.392074	+	0.919934i	$0.628242\pi$
$444$	−12.0000			−0.569495
$445$		0			0
$446$	11.8423	−	20.5115i	0.560751	−	0.971248i
$447$	−21.6375	−	12.4924i	−1.02342	−	0.590871i
$448$		−	4.56155i		−	0.215513i
$449$	−29.0000			−1.36859			−0.684297	−	0.729203i	$-0.739891\pi$
$449$	−29.0000			−1.36859			−0.684297	+	0.729203i	$0.739891\pi$
$450$		0			0
$451$	−1.06155	−	1.83866i	−0.0499866	−	0.0865793i
$452$	−3.29762	−	1.90388i	−0.155107	−	0.0895511i
$453$	16.8941	−	9.75379i	0.793752	−	0.458273i
$454$	4.46543	+	7.73436i	0.209573	+	0.362992i
$455$		0			0
$456$	2.87689	−	6.16879i	0.134723	−	0.288880i
$457$		−	30.0540i		−	1.40587i	−0.711256	−	0.702933i	$-0.751873\pi$
$457$		−	30.0540i		−	1.40587i	0.711256	−	0.702933i	$-0.248127\pi$
$458$	18.2931	−	10.5616i	0.854783	−	0.493509i
$459$	8.68466	+	15.0423i	0.405365	+	0.702113i
$460$		0			0
$461$	−13.4924	−	23.3696i	−0.628405	−	1.08843i	−0.987872	−	0.155271i	$-0.950375\pi$
$461$	−13.4924	−	23.3696i	−0.628405	−	1.08843i	0.359467	−	0.933158i	$-0.382958\pi$
$462$	6.16879	+	3.56155i	0.286998	+	0.165698i
$463$			15.4384i			0.717485i	0.933436	+	0.358743i	$0.116794\pi$
$463$			15.4384i			0.717485i	−0.933436	+	0.358743i	$0.883206\pi$
$464$	−2.00000			−0.0928477
$465$		0			0
$466$	7.34233	−	12.7173i	0.340127	−	0.589117i
$467$			12.4384i			0.575583i	0.957693	+	0.287791i	$0.0929210\pi$
$467$			12.4384i			0.575583i	−0.957693	+	0.287791i	$0.907079\pi$
$468$		−	1.12311i		−	0.0519156i
$469$	30.9309	−	53.5738i	1.42825	−	2.47381i
$470$		0			0
$471$	−5.12311	+	8.87348i	−0.236060	+	0.408868i
$472$	−9.03996	+	5.21922i	−0.416098	+	0.240234i
$473$	4.43674	−	2.56155i	0.204002	−	0.117780i
$474$	−4.49242			−0.206344
$475$		0			0
$476$	−14.2462			−0.652974
$477$	1.67218	−	0.965435i	0.0765640	−	0.0442042i
$478$	1.51883	−	0.876894i	0.0694695	−	0.0401082i
$479$	2.31534	−	4.01029i	0.105791	−	0.183235i	−0.808270	−	0.588812i	$-0.799596\pi$
$479$	2.31534	−	4.01029i	0.105791	−	0.183235i	0.914061	+	0.405577i	$0.132929\pi$
$480$		0			0
$481$	7.68466	−	13.3102i	0.350390	−	0.606894i
$482$			4.43845i			0.202166i
$483$		−	54.7386i		−	2.49069i
$484$	−5.00000	+	8.66025i	−0.227273	+	0.393648i
$485$		0			0
$486$	−5.75379			−0.260997
$487$			21.9309i			0.993783i	0.867813	+	0.496891i	$0.165525\pi$
$487$			21.9309i			0.993783i	−0.867813	+	0.496891i	$0.834475\pi$
$488$	2.70469	+	1.56155i	0.122436	+	0.0706882i
$489$	−15.6577	−	27.1199i	−0.708064	−	1.22640i
$490$		0			0
$491$	−18.0885	−	31.3303i	−0.816324	−	1.41392i	−0.908373	−	0.418161i	$-0.862675\pi$
$491$	−18.0885	−	31.3303i	−0.816324	−	1.41392i	0.0920486	−	0.995755i	$-0.470658\pi$
$492$	2.87117	−	1.65767i	0.129442	−	0.0747336i
$493$			6.24621i			0.281315i
$494$	5.00000	+	7.14143i	0.224961	+	0.321308i
$495$		0			0
$496$	3.12311	+	5.40938i	0.140232	+	0.242888i
$497$	−0.972638	+	0.561553i	−0.0436288	+	0.0251891i
$498$	−13.2635	−	7.65767i	−0.594351	−	0.343148i
$499$	14.5000	+	25.1147i	0.649109	+	1.12429i	0.983336	+	0.181797i	$0.0581915\pi$
$499$	14.5000	+	25.1147i	0.649109	+	1.12429i	−0.334227	+	0.942493i	$0.608475\pi$
$500$		0			0
$501$	−18.2462			−0.815181
$502$			2.93087i			0.130811i
$503$	−29.8114	−	17.2116i	−1.32923	−	0.767429i	−0.344047	−	0.938953i	$-0.611798\pi$
$503$	−29.8114	−	17.2116i	−1.32923	−	0.767429i	−0.985180	+	0.171523i	$0.945131\pi$
$504$	1.28078	−	2.21837i	0.0570503	−	0.0988140i
$505$		0			0
$506$	−7.68466			−0.341625
$507$	12.1711	+	7.02699i	0.540538	+	0.312079i
$508$	9.90599	−	5.71922i	0.439507	−	0.253750i
$509$	−4.56155	+	7.90084i	−0.202187	+	0.350199i	−0.949233	−	0.314574i	$-0.898138\pi$
$509$	−4.56155	+	7.90084i	−0.202187	+	0.350199i	0.747046	+	0.664773i	$0.231472\pi$
$510$		0			0
$511$	−24.3693	−	42.2089i	−1.07804	−	1.86721i
$512$		−	1.00000i		−	0.0441942i
$513$	19.8587	−	13.9039i	0.876784	−	0.613871i
$514$	−24.0540			−1.06098
$515$		0			0
$516$	4.00000	+	6.92820i	0.176090	+	0.304997i
$517$	−9.63289	−	5.56155i	−0.423654	−	0.244597i
$518$	30.3576	−	17.5270i	1.33384	−	0.770092i
$519$	11.5616	−	20.0252i	0.507496	−	0.879009i
$520$		0			0
$521$	−2.19224			−0.0960436			−0.0480218	−	0.998846i	$-0.515292\pi$
$521$	−2.19224			−0.0960436			−0.0480218	+	0.998846i	$0.515292\pi$
$522$	−0.972638	−	0.561553i	−0.0425712	−	0.0245785i
$523$	34.0948	+	19.6847i	1.49086	+	0.860750i	0.999945	−	0.0104561i	$-0.00332834\pi$
$523$	34.0948	+	19.6847i	1.49086	+	0.860750i	0.490917	+	0.871206i	$0.336662\pi$
$524$	7.87689			0.344104
$525$		0			0
$526$	−11.4039	+	19.7521i	−0.497233	+	0.861233i
$527$	16.8941	−	9.75379i	0.735917	−	0.424882i
$528$	1.35234	+	0.780776i	0.0588532	+	0.0339789i
$529$	18.0270	+	31.2237i	0.783782	+	1.35755i
$530$		0			0
$531$	−5.86174			−0.254378
$532$	1.73205	+	19.8078i	0.0750939	+	0.858775i
$533$			4.24621i			0.183924i
$534$	−7.56155	−	13.0970i	−0.327220	−	0.566762i
$535$		0			0
$536$	6.78078	−	11.7446i	0.292885	−	0.507292i
$537$	−29.0652	+	16.7808i	−1.25425	+	0.724144i
$538$	−3.46410	−	2.00000i	−0.149348	−	0.0862261i
$539$	−13.8078			−0.594743
$540$		0			0
$541$	−2.24621	+	3.89055i	−0.0965722	+	0.167268i	−0.910264	−	0.414029i	$-0.864121\pi$
$541$	−2.24621	+	3.89055i	−0.0965722	+	0.167268i	0.813692	+	0.581297i	$0.197455\pi$
$542$	7.14143	+	4.12311i	0.306751	+	0.177103i
$543$			5.26137i			0.225787i
$544$	−3.12311			−0.133902
$545$		0			0
$546$	−7.12311	−	12.3376i	−0.304841	−	0.528000i
$547$	11.3649	+	6.56155i	0.485930	+	0.280552i	0.722884	−	0.690969i	$-0.242816\pi$
$547$	11.3649	+	6.56155i	0.485930	+	0.280552i	−0.236955	+	0.971521i	$0.576149\pi$
$548$	8.28055	−	4.78078i	0.353727	−	0.204225i
$549$	0.876894	+	1.51883i	0.0374249	+	0.0648219i
$550$		0			0
$551$	8.68466	−	0.759413i	0.369979	−	0.0323521i
$552$		−	12.0000i		−	0.510754i
$553$	11.3649	−	6.56155i	0.483287	−	0.279026i
$554$	6.12311	+	10.6055i	0.260146	+	0.450586i
$555$		0			0
$556$	5.90388	+	10.2258i	0.250380	+	0.433672i
$557$	31.7567	+	18.3348i	1.34558	+	0.776868i	0.987619	−	0.156870i	$-0.0501404\pi$
$557$	31.7567	+	18.3348i	1.34558	+	0.776868i	0.357956	+	0.933738i	$0.383474\pi$
$558$			3.50758i			0.148488i
$559$	−10.2462			−0.433369
$560$		0			0
$561$	2.43845	−	4.22351i	0.102951	−	0.178317i
$562$			16.3693i			0.690498i
$563$			32.3002i			1.36129i	0.732613	+	0.680645i	$0.238300\pi$
$563$			32.3002i			1.36129i	−0.732613	+	0.680645i	$0.761700\pi$
$564$	8.68466	−	15.0423i	0.365690	−	0.633394i
$565$		0			0
$566$	−11.7808	+	20.4049i	−0.495183	+	0.857682i
$567$	−27.6529	+	15.9654i	−1.16131	+	0.670485i
$568$	−0.213225	+	0.123106i	−0.00894673	+	0.00516540i
$569$	−34.1771			−1.43278			−0.716389	−	0.697701i	$-0.754206\pi$
$569$	−34.1771			−1.43278			−0.716389	+	0.697701i	$0.754206\pi$
$570$		0			0
$571$	15.8078			0.661534			0.330767	−	0.943712i	$-0.392693\pi$
$571$	15.8078			0.661534			0.330767	+	0.943712i	$0.392693\pi$
$572$	−1.73205	+	1.00000i	−0.0724207	+	0.0418121i
$573$	−26.1940	+	15.1231i	−1.09427	+	0.631777i
$574$	−4.84233	+	8.38716i	−0.202115	+	0.350073i
$575$		0			0
$576$	0.280776	−	0.486319i	0.0116990	−	0.0202633i
$577$		−	28.6847i		−	1.19416i	−0.802182	−	0.597079i	$-0.796328\pi$
$577$		−	28.6847i		−	1.19416i	0.802182	−	0.597079i	$-0.203672\pi$
$578$		−	7.24621i		−	0.301403i
$579$	−12.1922	+	21.1176i	−0.506692	+	0.877616i
$580$		0			0
$581$	44.7386			1.85607
$582$			16.6847i			0.691601i
$583$	−2.97778	−	1.71922i	−0.123327	−	0.0712030i
$584$	−5.34233	−	9.25319i	−0.221067	−	0.382900i
$585$		0			0
$586$	9.71922	+	16.8342i	0.401497	+	0.695414i
$587$	−19.6922	+	11.3693i	−0.812786	+	0.469262i	−0.847922	−	0.530121i	$-0.822147\pi$
$587$	−19.6922	+	11.3693i	−0.812786	+	0.469262i	0.0351368	+	0.999383i	$0.488813\pi$
$588$		−	21.5616i		−	0.889183i
$589$	−15.6155	−	22.3034i	−0.643427	−	0.918997i
$590$		0			0
$591$	−14.4924	−	25.1016i	−0.596139	−	1.03254i
$592$	6.65511	−	3.84233i	0.273523	−	0.157919i
$593$	−38.5783	−	22.2732i	−1.58422	−	0.914651i	−0.994233	−	0.107239i	$-0.965799\pi$
$593$	−38.5783	−	22.2732i	−1.58422	−	0.914651i	−0.589988	−	0.807412i	$-0.700868\pi$
$594$	2.78078	+	4.81645i	0.114097	+	0.197621i
$595$		0			0
$596$	16.0000			0.655386
$597$		−	17.3693i		−	0.710879i
$598$	13.3102	+	7.68466i	0.544295	+	0.314249i
$599$	0.246211	−	0.426450i	0.0100599	−	0.0174243i	−0.860952	−	0.508687i	$-0.830131\pi$
$599$	0.246211	−	0.426450i	0.0100599	−	0.0174243i	0.871012	+	0.491263i	$0.163464\pi$
$600$		0			0
$601$	−36.3693			−1.48354			−0.741768	−	0.670657i	$-0.766012\pi$
$601$	−36.3693			−1.48354			−0.741768	+	0.670657i	$0.766012\pi$
$602$	−20.2384	−	11.6847i	−0.824857	−	0.476231i
$603$	6.59524	−	3.80776i	0.268579	−	0.155064i
$604$	−6.24621	+	10.8188i	−0.254155	+	0.440209i
$605$		0			0
$606$	7.80776	+	13.5234i	0.317169	+	0.549352i
$607$			30.8078i			1.25045i	0.780445	+	0.625224i	$0.214993\pi$
$607$			30.8078i			1.25045i	−0.780445	+	0.625224i	$0.785007\pi$
$608$	0.379706	+	4.34233i	0.0153991	+	0.176105i
$609$	−14.2462			−0.577286
$610$		0			0
$611$	11.1231	+	19.2658i	0.449993	+	0.779410i
$612$	−1.51883	−	0.876894i	−0.0613949	−	0.0354464i
$613$	−15.8616	+	9.15767i	−0.640642	+	0.369875i	−0.784862	−	0.619671i	$-0.787266\pi$
$613$	−15.8616	+	9.15767i	−0.640642	+	0.369875i	0.144220	+	0.989546i	$0.453933\pi$
$614$	−2.46543	+	4.27026i	−0.0994969	+	0.172334i
$615$		0			0
$616$	−4.56155			−0.183790
$617$	−24.0822	−	13.9039i	−0.969514	−	0.559749i	−0.0704260	−	0.997517i	$-0.522436\pi$
$617$	−24.0822	−	13.9039i	−0.969514	−	0.559749i	−0.899088	+	0.437768i	$0.855769\pi$
$618$	−20.0252	−	11.5616i	−0.805532	−	0.465074i
$619$	11.0540			0.444297			0.222148	−	0.975013i	$-0.428693\pi$
$619$	11.0540			0.444297			0.222148	+	0.975013i	$0.428693\pi$
$620$		0			0
$621$	21.3693	−	37.0127i	0.857521	−	1.48527i
$622$	−3.46410	+	2.00000i	−0.138898	+	0.0801927i
$623$	38.2585	+	22.0885i	1.53279	+	0.884959i
$624$	−1.56155	−	2.70469i	−0.0625121	−	0.108274i
$625$		0			0
$626$	−16.6847			−0.666853
$627$	−6.16879	−	2.87689i	−0.246358	−	0.114892i
$628$		−	6.56155i		−	0.261834i
$629$	−12.0000	−	20.7846i	−0.478471	−	0.828737i
$630$		0			0
$631$	6.12311	−	10.6055i	0.243757	−	0.422199i	−0.718024	−	0.696018i	$-0.754953\pi$
$631$	6.12311	−	10.6055i	0.243757	−	0.422199i	0.961781	+	0.273818i	$0.0882867\pi$
$632$	2.49146	−	1.43845i	0.0991051	−	0.0572184i
$633$	−21.2111	−	12.2462i	−0.843064	−	0.486743i
$634$	6.31534			0.250814
$635$		0			0
$636$	2.68466	−	4.64996i	0.106454	−	0.184383i
$637$	23.9157	+	13.8078i	0.947576	+	0.547084i
$638$			2.00000i			0.0791808i
$639$	−0.138261			−0.00546951
$640$		0			0
$641$	−5.78078	−	10.0126i	−0.228327	−	0.395474i	0.728985	−	0.684529i	$-0.239992\pi$
$641$	−5.78078	−	10.0126i	−0.228327	−	0.395474i	−0.957312	+	0.289055i	$0.906659\pi$
$642$	−19.2658	−	11.1231i	−0.760360	−	0.438994i
$643$	15.9682	−	9.21922i	0.629723	−	0.363571i	−0.150922	−	0.988546i	$-0.548224\pi$
$643$	15.9682	−	9.21922i	0.629723	−	0.363571i	0.780645	+	0.624975i	$0.214891\pi$
$644$	17.5270	+	30.3576i	0.690660	+	1.19626i
$645$		0			0
$646$	13.5616	−	1.18586i	0.533572	−	0.0466572i
$647$		−	42.1771i		−	1.65815i	−0.559136	−	0.829076i	$-0.688867\pi$
$647$		−	42.1771i		−	1.65815i	0.559136	−	0.829076i	$-0.311133\pi$
$648$	−6.06218	+	3.50000i	−0.238145	+	0.137493i
$649$	5.21922	+	9.03996i	0.204872	+	0.354849i
$650$		0			0
$651$	22.2462	+	38.5316i	0.871898	+	1.51017i
$652$	17.3673	+	10.0270i	0.680154	+	0.392687i
$653$			33.9309i			1.32782i	0.747814	+	0.663909i	$0.231104\pi$
$653$			33.9309i			1.32782i	−0.747814	+	0.663909i	$0.768896\pi$
$654$	3.50758			0.137157
$655$		0			0
$656$	−1.06155	+	1.83866i	−0.0414467	+	0.0717877i
$657$		−	6.00000i		−	0.234082i
$658$			50.7386i			1.97800i
$659$	−4.96543	+	8.60039i	−0.193426	+	0.335023i	−0.946383	−	0.323046i	$-0.895293\pi$
$659$	−4.96543	+	8.60039i	−0.193426	+	0.335023i	0.752957	+	0.658069i	$0.228627\pi$
$660$		0			0
$661$	−8.93087	+	15.4687i	−0.347371	+	0.601663i	−0.985782	−	0.168032i	$-0.946259\pi$
$661$	−8.93087	+	15.4687i	−0.347371	+	0.601663i	0.638411	+	0.769696i	$0.279592\pi$
$662$	8.22068	−	4.74621i	0.319506	−	0.184467i
$663$	−8.44703	+	4.87689i	−0.328055	+	0.189403i
$664$	9.80776			0.380615
$665$		0			0
$666$	4.31534			0.167216
$667$	13.3102	−	7.68466i	0.515374	−	0.297551i
$668$	10.1192	−	5.84233i	0.391524	−	0.226047i
$669$	18.4924	−	32.0298i	0.714958	−	1.23834i
$670$		0			0
$671$	1.56155	−	2.70469i	0.0602831	−	0.104413i
$672$		−	7.12311i		−	0.274780i
$673$			28.1080i			1.08348i	0.840546	+	0.541741i	$0.182235\pi$
$673$			28.1080i			1.08348i	−0.840546	+	0.541741i	$0.817765\pi$
$674$	8.02699	−	13.9032i	0.309188	−	0.535529i
$675$		0			0
$676$	−9.00000			−0.346154
$677$			22.1771i			0.852334i	0.904644	+	0.426167i	$0.140136\pi$
$677$			22.1771i			0.852334i	−0.904644	+	0.426167i	$0.859864\pi$
$678$	−5.14941	−	2.97301i	−0.197762	−	0.114178i
$679$	−24.3693	−	42.2089i	−0.935209	−	1.61983i
$680$		0			0
$681$	6.97301	+	12.0776i	0.267206	+	0.462815i
$682$	5.40938	−	3.12311i	0.207136	−	0.119590i
$683$		−	28.0000i		−	1.07139i	−0.844411	−	0.535695i	$-0.820050\pi$
$683$		−	28.0000i		−	1.07139i	0.844411	−	0.535695i	$-0.179950\pi$
$684$	−1.03457	+	2.21837i	−0.0395576	+	0.0848215i
$685$		0			0
$686$	15.5270	+	26.8935i	0.592823	+	1.02680i
$687$	28.5657	−	16.4924i	1.08985	−	0.629225i
$688$	−4.43674	−	2.56155i	−0.169149	−	0.0976583i
$689$	3.43845	+	5.95557i	0.130994	+	0.226889i
$690$		0			0
$691$	−49.9309			−1.89946			−0.949730	−	0.313070i	$-0.898642\pi$
$691$	−49.9309			−1.89946			−0.949730	+	0.313070i	$0.898642\pi$
$692$			14.8078i			0.562907i
$693$	−2.21837	−	1.28078i	−0.0842689	−	0.0486527i
$694$	5.34233	−	9.25319i	0.202792	−	0.351246i
$695$		0			0
$696$	−3.12311			−0.118381
$697$	5.74234	+	3.31534i	0.217507	+	0.125578i
$698$	1.94528	−	1.12311i	0.0736298	−	0.0425102i
$699$	11.4654	−	19.8587i	0.433663	−	0.751126i
$700$		0			0
$701$	13.2462	+	22.9431i	0.500302	+	0.866549i	1.00000		0.000349325i	$0.000111194\pi$
$701$	13.2462	+	22.9431i	0.500302	+	0.866549i	−0.499697	+	0.866200i	$0.666555\pi$
$702$		−	11.1231i		−	0.419815i
$703$	−27.4397	+	19.2116i	−1.03491	+	0.724581i
$704$	−1.00000			−0.0376889
$705$		0			0
$706$	−10.5885	−	18.3399i	−0.398505	−	0.690231i
$707$	−39.5042	−	22.8078i	−1.48571	−	0.857774i
$708$	−14.1164	+	8.15009i	−0.530526	+	0.306299i
$709$	−20.0000	+	34.6410i	−0.751116	+	1.30097i	0.196167	+	0.980571i	$0.437151\pi$
$709$	−20.0000	+	34.6410i	−0.751116	+	1.30097i	−0.947282	+	0.320400i	$0.896183\pi$
$710$		0			0
$711$	1.61553			0.0605870
$712$	8.38716	+	4.84233i	0.314322	+	0.181474i
$713$	−41.5692	−	24.0000i	−1.55678	−	0.898807i
$714$	−22.2462			−0.832544
$715$		0			0
$716$	10.7462	−	18.6130i	0.401605	−	0.695600i
$717$	2.37173	−	1.36932i	0.0885737	−	0.0511381i
$718$	−5.95557	−	3.43845i	−0.222260	−	0.128322i
$719$	11.5616	+	20.0252i	0.431173	+	0.746814i	0.996975	−	0.0777277i	$-0.0247665\pi$
$719$	11.5616	+	20.0252i	0.431173	+	0.746814i	−0.565801	+	0.824542i	$0.691433\pi$
$720$		0			0
$721$	67.5464			2.51556
$722$	−3.29762	−	18.7116i	−0.122725	−	0.696375i
$723$			6.93087i			0.257762i
$724$	−1.68466	−	2.91791i	−0.0626098	−	0.108443i
$725$		0			0
$726$	−7.80776	+	13.5234i	−0.289773	+	0.501902i
$727$	−6.92820	+	4.00000i	−0.256953	+	0.148352i	−0.622944	−	0.782267i	$-0.714063\pi$
$727$	−6.92820	+	4.00000i	−0.256953	+	0.148352i	0.365991	+	0.930618i	$0.380730\pi$
$728$	7.90084	+	4.56155i	0.292825	+	0.169062i
$729$	−29.9848			−1.11055
$730$		0			0
$731$	−8.00000	+	13.8564i	−0.295891	+	0.512498i
$732$	4.22351	+	2.43845i	0.156106	+	0.0901276i
$733$		−	1.93087i		−	0.0713183i	−0.999364	−	0.0356591i	$-0.988647\pi$
$733$		−	1.93087i		−	0.0713183i	0.999364	−	0.0356591i	$-0.0113531\pi$
$734$	−34.2462			−1.26405
$735$		0			0
$736$	3.84233	+	6.65511i	0.141630	+	0.245311i
$737$	−11.7446	−	6.78078i	−0.432620	−	0.249773i
$738$	−1.03251	+	0.596118i	−0.0380071	+	0.0219434i
$739$	17.6231	+	30.5241i	0.648276	+	1.12285i	0.983534	+	0.180721i	$0.0578432\pi$
$739$	17.6231	+	30.5241i	0.648276	+	1.12285i	−0.335258	+	0.942126i	$0.608823\pi$
$740$		0			0
$741$	7.80776	+	11.1517i	0.286825	+	0.409669i
$742$			15.6847i			0.575802i
$743$	19.5389	−	11.2808i	0.716812	−	0.413852i	−0.0967662	−	0.995307i	$-0.530850\pi$
$743$	19.5389	−	11.2808i	0.716812	−	0.413852i	0.813578	+	0.581456i	$0.197517\pi$
$744$	4.87689	+	8.44703i	0.178796	+	0.309683i
$745$		0			0
$746$	−7.59612	−	13.1569i	−0.278114	−	0.481707i
$747$	4.76970	+	2.75379i	0.174514	+	0.100756i
$748$			3.12311i			0.114192i
$749$	64.9848			2.37449
$750$		0			0
$751$	21.5616	−	37.3457i	0.786792	−	1.36276i	−0.141130	−	0.989991i	$-0.545074\pi$
$751$	21.5616	−	37.3457i	0.786792	−	1.36276i	0.927923	−	0.372773i	$-0.121593\pi$
$752$			11.1231i			0.405618i
$753$			4.57671i			0.166785i
$754$	2.00000	−	3.46410i	0.0728357	−	0.126155i
$755$		0			0
$756$	12.6847	−	21.9705i	0.461337	−	0.799058i
$757$	−13.3701	+	7.71922i	−0.485944	+	0.280560i	−0.722890	−	0.690963i	$-0.757187\pi$
$757$	−13.3701	+	7.71922i	−0.485944	+	0.280560i	0.236946	+	0.971523i	$0.423853\pi$
$758$	28.1393	−	16.2462i	1.02206	−	0.590089i
$759$	−12.0000			−0.435572
$760$		0			0
$761$	13.9848			0.506950			0.253475	−	0.967342i	$-0.418426\pi$
$761$	13.9848			0.506950			0.253475	+	0.967342i	$0.418426\pi$
$762$	15.4687	−	8.93087i	0.560373	−	0.323531i
$763$	−8.87348	+	5.12311i	−0.321242	+	0.185469i
$764$	9.68466	−	16.7743i	0.350379	−	0.606874i
$765$		0			0
$766$	−1.56155	+	2.70469i	−0.0564212	+	0.0977244i
$767$		−	20.8769i		−	0.753821i
$768$		−	1.56155i		−	0.0563477i
$769$	−3.24621	+	5.62260i	−0.117061	+	0.202756i	−0.918602	−	0.395184i	$-0.870681\pi$
$769$	−3.24621	+	5.62260i	−0.117061	+	0.202756i	0.801541	+	0.597940i	$0.204014\pi$
$770$		0			0
$771$	−37.5616			−1.35275
$772$		−	15.6155i		−	0.562015i
$773$	34.0350	+	19.6501i	1.22415	+	0.706765i	0.965801	−	0.259286i	$-0.0834873\pi$
$773$	34.0350	+	19.6501i	1.22415	+	0.706765i	0.258352	+	0.966051i	$0.416821\pi$
$774$	−1.43845	−	2.49146i	−0.0517039	−	0.0895538i
$775$		0			0
$776$	−5.34233	−	9.25319i	−0.191778	−	0.332170i
$777$	47.4050	−	27.3693i	1.70065	−	0.981869i
$778$		−	10.8769i		−	0.389956i
$779$	3.91146	−	8.38716i	0.140143	−	0.300501i
$780$		0			0
$781$	0.123106	+	0.213225i	0.00440507	+	0.00762980i
$782$	20.7846	−	12.0000i	0.743256	−	0.429119i
$783$	−9.63289	−	5.56155i	−0.344251	−	0.198754i
$784$	6.90388	+	11.9579i	0.246567	+	0.427067i
$785$		0			0
$786$	12.3002			0.438733
$787$			4.43845i			0.158214i	0.996866	+	0.0791068i	$0.0252068\pi$
$787$			4.43845i			0.158214i	−0.996866	+	0.0791068i	$0.974793\pi$
$788$	16.0748	+	9.28078i	0.572640	+	0.330614i
$789$	−17.8078	+	30.8440i	−0.633973	+	1.09807i
$790$		0			0
$791$	17.3693			0.617582
$792$	−0.486319	−	0.280776i	−0.0172806	−	0.00997696i
$793$	−5.40938	+	3.12311i	−0.192093	+	0.110905i
$794$	12.6501	−	21.9106i	0.448935	−	0.777578i
$795$		0			0
$796$	5.56155	+	9.63289i	0.197124	+	0.341429i
$797$		−	24.8078i		−	0.878736i	−0.898307	−	0.439368i	$-0.855202\pi$
$797$		−	24.8078i		−	0.878736i	0.898307	−	0.439368i	$-0.144798\pi$
$798$	2.70469	+	30.9309i	0.0957449	+	1.09494i
$799$	34.7386			1.22896
$800$		0			0
$801$	2.71922	+	4.70983i	0.0960790	+	0.166414i
$802$	−0.806157	−	0.465435i	−0.0284664	−	0.0164351i
$803$	−9.25319	+	5.34233i	−0.326538	+	0.188527i
$804$	10.5885	−	18.3399i	0.373429	−	0.646798i
$805$		0			0
$806$	−12.4924			−0.440027
$807$	−5.40938	−	3.12311i	−0.190419	−	0.109939i
$808$	−8.66025	−	5.00000i	−0.304667	−	0.175899i
$809$	−27.5616			−0.969013			−0.484506	−	0.874788i	$-0.661001\pi$
$809$	−27.5616			−0.969013			−0.484506	+	0.874788i	$0.661001\pi$
$810$		0			0
$811$	−18.0885	+	31.3303i	−0.635175	+	1.10015i	0.351304	+	0.936262i	$0.385739\pi$
$811$	−18.0885	+	31.3303i	−0.635175	+	1.10015i	−0.986478	+	0.163893i	$0.947595\pi$
$812$	7.90084	−	4.56155i	0.277265	−	0.160079i
$813$	11.1517	+	6.43845i	0.391108	+	0.225806i
$814$	−3.84233	−	6.65511i	−0.134674	−	0.233261i
$815$		0			0
$816$	−4.87689			−0.170725
$817$	20.2384	+	9.43845i	0.708053	+	0.330209i
$818$			21.0000i			0.734248i
$819$	2.56155	+	4.43674i	0.0895079	+	0.155032i
$820$		0			0
$821$	7.00000	−	12.1244i	0.244302	−	0.423143i	−0.717633	−	0.696421i	$-0.754775\pi$
$821$	7.00000	−	12.1244i	0.244302	−	0.423143i	0.961935	+	0.273278i	$0.0881079\pi$
$822$	12.9305	−	7.46543i	0.451003	−	0.260387i
$823$	15.7418	+	9.08854i	0.548725	+	0.316807i	0.748608	−	0.663013i	$-0.230723\pi$
$823$	15.7418	+	9.08854i	0.548725	+	0.316807i	−0.199883	+	0.979820i	$0.564056\pi$
$824$	14.8078			0.515853
$825$		0			0
$826$	23.8078	−	41.2363i	0.828378	−	1.43479i
$827$	2.65794	+	1.53457i	0.0924258	+	0.0533621i	0.545501	−	0.838110i	$-0.316340\pi$
$827$	2.65794	+	1.53457i	0.0924258	+	0.0533621i	−0.453075	+	0.891473i	$0.649673\pi$
$828$			4.31534i			0.149968i
$829$	22.7386			0.789745			0.394873	−	0.918736i	$-0.370789\pi$
$829$	22.7386			0.789745			0.394873	+	0.918736i	$0.370789\pi$
$830$		0			0
$831$	9.56155	+	16.5611i	0.331687	+	0.574498i
$832$	1.73205	+	1.00000i	0.0600481	+	0.0346688i
$833$	37.3457	−	21.5616i	1.29395	−	0.747064i
$834$	9.21922	+	15.9682i	0.319236	+	0.552932i
$835$		0			0
$836$	4.34233	−	0.379706i	0.150183	−	0.0131324i
$837$			34.7386i			1.20074i
$838$	−11.6380	+	6.71922i	−0.402029	+	0.232112i
$839$	−15.2462	−	26.4072i	−0.526358	−	0.911678i	−0.999528	−	0.0307075i	$-0.990224\pi$
$839$	−15.2462	−	26.4072i	−0.526358	−	0.911678i	0.473171	−	0.880971i	$-0.343109\pi$
$840$		0			0
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$	−0.426450	−	0.246211i	−0.0146965	−	0.00848500i
$843$			25.5616i			0.880387i
$844$	15.6847			0.539888
$845$		0			0
$846$	−3.12311	+	5.40938i	−0.107375	+	0.185978i
$847$		−	45.6155i		−	1.56737i
$848$			3.43845i			0.118077i
$849$	−18.3963	+	31.8633i	−0.631360	+	1.09355i
$850$		0			0
$851$	−29.5270	+	51.1422i	−1.01217	+	1.75313i
$852$	−0.332962	+	0.192236i	−0.0114071	+	0.00658589i
$853$	42.2089	−	24.3693i	1.44521	−	0.834390i	0.447015	−	0.894527i	$-0.352487\pi$
$853$	42.2089	−	24.3693i	1.44521	−	0.834390i	0.998190	+	0.0601370i	$0.0191538\pi$
$854$	−14.2462			−0.487495
$855$		0			0
$856$	14.2462			0.486925
$857$	−49.1838	+	28.3963i	−1.68009	+	0.969999i	−0.718490	+	0.695537i	$0.755166\pi$
$857$	−49.1838	+	28.3963i	−1.68009	+	0.969999i	−0.961598	+	0.274462i	$0.911500\pi$
$858$	−2.70469	+	1.56155i	−0.0923366	+	0.0533105i
$859$	7.25379	−	12.5639i	0.247496	−	0.428676i	−0.715334	−	0.698782i	$-0.753726\pi$
$859$	7.25379	−	12.5639i	0.247496	−	0.428676i	0.962830	+	0.270107i	$0.0870589\pi$
$860$		0			0
$861$	−7.56155	+	13.0970i	−0.257697	+	0.446344i
$862$		−	17.3693i		−	0.591601i
$863$			1.30019i			0.0442589i	0.999755	+	0.0221294i	$0.00704459\pi$
$863$			1.30019i			0.0442589i	−0.999755	+	0.0221294i	$0.992955\pi$
$864$	2.78078	−	4.81645i	0.0946039	−	0.163859i
$865$		0			0
$866$	−12.7386			−0.432876
$867$		−	11.3153i		−	0.384289i
$868$	−24.6752	−	14.2462i	−0.837530	−	0.483548i
$869$	−1.43845	−	2.49146i	−0.0487960	−	0.0845171i
$870$		0			0
$871$	13.5616	+	23.4893i	0.459516	+	0.795905i
$872$	−1.94528	+	1.12311i	−0.0658754	+	0.0380332i
$873$		−	6.00000i		−	0.203069i
$874$	−19.2116	−	27.4397i	−0.649844	−	0.928162i
$875$		0			0
$876$	−8.34233	−	14.4493i	−0.281861	−	0.488198i
$877$	−2.43160	+	1.40388i	−0.0821091	+	0.0474057i	−0.540492	−	0.841349i	$-0.681762\pi$
$877$	−2.43160	+	1.40388i	−0.0821091	+	0.0474057i	0.458383	+	0.888755i	$0.348429\pi$
$878$	−14.2829	−	8.24621i	−0.482023	−	0.278296i
$879$	15.1771	+	26.2875i	0.511910	+	0.886655i
$880$		0			0
$881$	−15.8769			−0.534906			−0.267453	−	0.963571i	$-0.586182\pi$
$881$	−15.8769			−0.534906			−0.267453	+	0.963571i	$0.586182\pi$
$882$			7.75379i			0.261084i
$883$	10.2258	+	5.90388i	0.344126	+	0.198681i	0.662095	−	0.749420i	$-0.269667\pi$
$883$	10.2258	+	5.90388i	0.344126	+	0.198681i	−0.317969	+	0.948101i	$0.603001\pi$
$884$	3.12311	−	5.40938i	0.105041	−	0.181937i
$885$		0			0
$886$	−5.06913			−0.170301
$887$	8.44703	+	4.87689i	0.283623	+	0.163750i	0.635063	−	0.772461i	$-0.280974\pi$
$887$	8.44703	+	4.87689i	0.283623	+	0.163750i	−0.351439	+	0.936211i	$0.614308\pi$
$888$	10.3923	−	6.00000i	0.348743	−	0.201347i
$889$	−26.0885	+	45.1867i	−0.874982	+	1.51551i
$890$		0			0
$891$	3.50000	+	6.06218i	0.117254	+	0.203091i
$892$			23.6847i			0.793021i
$893$	−4.22351	−	48.3002i	−0.141335	−	1.61630i
$894$	24.9848			0.835618
$895$		0			0
$896$	2.28078	+	3.95042i	0.0761954	+	0.131974i
$897$	20.7846	+	12.0000i	0.693978	+	0.400668i
$898$	25.1147	−	14.5000i	0.838090	−	0.483871i
$899$	−6.24621	+	10.8188i	−0.208323	+	0.360826i
$900$		0			0
$901$	10.7386			0.357756
$902$	1.83866	+	1.06155i	0.0612208	+	0.0353458i
$903$	−31.6034	−	18.2462i	−1.05169	−	0.607196i
$904$	3.80776			0.126644
$905$		0			0
$906$	−9.75379	+	16.8941i	−0.324048	+	0.561267i
$907$	−4.17677	+	2.41146i	−0.138687	+	0.0800712i	−0.567738	−	0.823209i	$-0.692181\pi$
$907$	−4.17677	+	2.41146i	−0.138687	+	0.0800712i	0.429051	+	0.903280i	$0.358848\pi$
$908$	−7.73436	−	4.46543i	−0.256674	−	0.148191i
$909$	−2.80776	−	4.86319i	−0.0931277	−	0.161302i
$910$		0			0
$911$	53.6155			1.77636			0.888181	−	0.459494i	$-0.151969\pi$
$911$	53.6155			1.77636			0.888181	+	0.459494i	$0.151969\pi$
$912$	0.592932	+	6.78078i	0.0196339	+	0.224534i
$913$		−	9.80776i		−	0.324590i
$914$	15.0270	+	26.0275i	0.497049	+	0.860913i
$915$		0			0
$916$	−10.5616	+	18.2931i	−0.348964	+	0.604423i
$917$	−31.1170	+	17.9654i	−1.02758	+	0.593271i
$918$	−15.0423	−	8.68466i	−0.496469	−	0.286636i
$919$	−3.75379			−0.123826			−0.0619130	−	0.998082i	$-0.519720\pi$
$919$	−3.75379			−0.123826			−0.0619130	+	0.998082i	$0.519720\pi$
$920$		0			0
$921$	−3.84991	+	6.66823i	−0.126859	+	0.219726i
$922$	23.3696	+	13.4924i	0.769636	+	0.444349i
$923$		−	0.492423i		−	0.0162083i
$924$	−7.12311			−0.234333
$925$		0			0
$926$	−7.71922	−	13.3701i	−0.253669	−	0.439368i
$927$	7.20130	+	4.15767i	0.236522	+	0.136556i
$928$	1.73205	−	1.00000i	0.0568574	−	0.0328266i
$929$	14.9924	+	25.9676i	0.491885	+	0.851971i	0.999956	−	0.00934469i	$-0.00297455\pi$
$929$	14.9924	+	25.9676i	0.491885	+	0.851971i	−0.508071	+	0.861315i	$0.669641\pi$
$930$		0			0
$931$	−34.5194	−	49.3036i	−1.13133	−	1.61586i
$932$			14.6847i			0.481012i
$933$	−5.40938	+	3.12311i	−0.177095	+	0.102246i
$934$	−6.21922	−	10.7720i	−0.203499	−	0.352471i
$935$		0			0
$936$	0.561553	+	0.972638i	0.0183549	+	0.0317917i
$937$	4.17677	+	2.41146i	0.136449	+	0.0787789i	0.566671	−	0.823944i	$-0.308231\pi$
$937$	4.17677	+	2.41146i	0.136449	+	0.0787789i	−0.430221	+	0.902723i	$0.641565\pi$
$938$			61.8617i			2.01986i
$939$	−26.0540			−0.850239
$940$		0			0
$941$	−0.123106	+	0.213225i	−0.00401313	+	0.00695094i	−0.868025	−	0.496521i	$-0.834611\pi$
$941$	−0.123106	+	0.213225i	−0.00401313	+	0.00695094i	0.864012	+	0.503471i	$0.167944\pi$
$942$		−	10.2462i		−	0.333840i
$943$		−	16.3153i		−	0.531301i
$944$	5.21922	−	9.03996i	0.169871	−	0.294226i
$945$		0			0
$946$	−2.56155	+	4.43674i	−0.0832833	+	0.144251i
$947$	20.3582	−	11.7538i	0.661551	−	0.381947i	−0.131317	−	0.991340i	$-0.541920\pi$
$947$	20.3582	−	11.7538i	0.661551	−	0.381947i	0.792868	+	0.609394i	$0.208587\pi$
$948$	3.89055	−	2.24621i	0.126359	−	0.0729535i
$949$	21.3693			0.693677
$950$		0			0
$951$	9.86174			0.319789
$952$	12.3376	−	7.12311i	0.399863	−	0.230861i
$953$	2.87117	−	1.65767i	0.0930063	−	0.0536972i	−0.452775	−	0.891625i	$-0.649566\pi$
$953$	2.87117	−	1.65767i	0.0930063	−	0.0536972i	0.545782	+	0.837927i	$0.316233\pi$
$954$	−0.965435	+	1.67218i	−0.0312571	+	0.0541389i
$955$		0			0
$956$	−0.876894	+	1.51883i	−0.0283608	+	0.0491223i
$957$			3.12311i			0.100956i
$958$			4.63068i			0.149611i
$959$	−21.8078	+	37.7722i	−0.704209	+	1.21973i
$960$		0			0
$961$	8.01515			0.258553
$962$			15.3693i			0.495527i
$963$	6.92820	+	4.00000i	0.223258	+	0.128898i
$964$	−2.21922	−	3.84381i	−0.0714764	−	0.123801i
$965$		0			0
$966$	27.3693	+	47.4050i	0.880593	+	1.52523i
$967$	18.0799	−	10.4384i	0.581411	−	0.335678i	−0.180283	−	0.983615i	$-0.557701\pi$
$967$	18.0799	−	10.4384i	0.581411	−	0.335678i	0.761694	+	0.647937i	$0.224368\pi$
$968$		−	10.0000i		−	0.321412i
$969$	21.1771	−	1.85179i	0.680306	−	0.0594880i
$970$		0			0
$971$	5.46543	+	9.46641i	0.175394	+	0.303792i	0.940298	−	0.340353i	$-0.110547\pi$
$971$	5.46543	+	9.46641i	0.175394	+	0.303792i	−0.764903	+	0.644145i	$0.777213\pi$
$972$	4.98293	−	2.87689i	0.159827	−	0.0922764i
$973$	−46.6456	−	26.9309i	−1.49539	−	0.863364i
$974$	−10.9654	−	18.9927i	−0.351355	−	0.608565i
$975$		0			0
$976$	−3.12311			−0.0999682
$977$		−	42.6847i		−	1.36560i	−0.730604	−	0.682802i	$-0.760761\pi$
$977$		−	42.6847i		−	1.36560i	0.730604	−	0.682802i	$-0.239239\pi$
$978$	27.1199	+	15.6577i	0.867198	+	0.500677i
$979$	4.84233	−	8.38716i	0.154762	−	0.268055i
$980$		0			0
$981$	−1.26137			−0.0402723
$982$	31.3303	+	18.0885i	0.999789	+	0.577229i
$983$	−32.4226	+	18.7192i	−1.03412	+	0.597051i	−0.918163	−	0.396203i	$-0.870327\pi$
$983$	−32.4226	+	18.7192i	−1.03412	+	0.597051i	−0.115959	+	0.993254i	$0.536994\pi$
$984$	−1.65767	+	2.87117i	−0.0528446	+	0.0915296i
$985$		0			0
$986$	−3.12311	−	5.40938i	−0.0994599	−	0.172270i
$987$			79.2311i			2.52195i
$988$	−7.90084	−	3.68466i	−0.251359	−	0.117225i
$989$	39.3693			1.25187
$990$		0			0
$991$	24.8078	+	42.9683i	0.788045	+	1.36493i	0.927163	+	0.374658i	$0.122240\pi$
$991$	24.8078	+	42.9683i	0.788045	+	1.36493i	−0.139119	+	0.990276i	$0.544427\pi$
$992$	−5.40938	−	3.12311i	−0.171748	−	0.0991587i
$993$	12.8370	−	7.41146i	0.407371	−	0.235196i
$994$	0.561553	−	0.972638i	0.0178114	−	0.0308502i
$995$		0			0
$996$	15.3153			0.485285
$997$	−8.38716	−	4.84233i	−0.265624	−	0.153358i	0.361273	−	0.932460i	$-0.382342\pi$
$997$	−8.38716	−	4.84233i	−0.265624	−	0.153358i	−0.626897	+	0.779102i	$0.715675\pi$
$998$	−25.1147	−	14.5000i	−0.794993	−	0.458989i
$999$	42.7386			1.35219

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.j.f.349.1		8
5.2	odd	4		950.2.e.h.501.2		4
5.3	odd	4		190.2.e.c.121.1	yes	4
5.4	even	2	inner	950.2.j.f.349.4		8
15.8	even	4		1710.2.l.m.1261.2		4
19.11	even	3	inner	950.2.j.f.49.4		8
20.3	even	4		1520.2.q.h.881.2		4
95.49	even	6	inner	950.2.j.f.49.1		8
95.68	odd	12		190.2.e.c.11.1	✓	4
95.83	odd	12		3610.2.a.k.1.2		2
95.87	odd	12		950.2.e.h.201.2		4
95.88	even	12		3610.2.a.u.1.1		2
285.68	even	12		1710.2.l.m.1531.2		4
380.163	even	12		1520.2.q.h.961.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.e.c.11.1	✓	4	95.68	odd	12
190.2.e.c.121.1	yes	4	5.3	odd	4
950.2.e.h.201.2		4	95.87	odd	12
950.2.e.h.501.2		4	5.2	odd	4
950.2.j.f.49.1		8	95.49	even	6	inner
950.2.j.f.49.4		8	19.11	even	3	inner
950.2.j.f.349.1		8	1.1	even	1	trivial
950.2.j.f.349.4		8	5.4	even	2	inner
1520.2.q.h.881.2		4	20.3	even	4
1520.2.q.h.961.2		4	380.163	even	12
1710.2.l.m.1261.2		4	15.8	even	4
1710.2.l.m.1531.2		4	285.68	even	12
3610.2.a.k.1.2		2	95.83	odd	12
3610.2.a.u.1.1		2	95.88	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.35234 + 0.780776i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.780776 - 1.35234i) q^{6} +4.56155i q^{7} +1.00000i q^{8} +(-0.280776 + 0.486319i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.35234 + 0.780776i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.780776 - 1.35234i) q^{6} +4.56155i q^{7} +1.00000i q^{8} +(-0.280776 + 0.486319i) q^{9} +1.00000 q^{11} +1.56155i q^{12} +(-1.73205 - 1.00000i) q^{13} +(-2.28078 - 3.95042i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.70469 + 1.56155i) q^{17} -0.561553i q^{18} +(2.50000 + 3.57071i) q^{19} +(-3.56155 - 6.16879i) q^{21} +(-0.866025 + 0.500000i) q^{22} +(6.65511 + 3.84233i) q^{23} +(-0.780776 - 1.35234i) q^{24} +2.00000 q^{26} -5.56155i q^{27} +(3.95042 + 2.28078i) q^{28} +(1.00000 - 1.73205i) q^{29} -6.24621 q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.35234 + 0.780776i) q^{33} +(1.56155 - 2.70469i) q^{34} +(0.280776 + 0.486319i) q^{36} +7.68466i q^{37} +(-3.95042 - 1.84233i) q^{38} +3.12311 q^{39} +(-1.06155 - 1.83866i) q^{41} +(6.16879 + 3.56155i) q^{42} +(4.43674 - 2.56155i) q^{43} +(0.500000 - 0.866025i) q^{44} -7.68466 q^{46} +(-9.63289 - 5.56155i) q^{47} +(1.35234 + 0.780776i) q^{48} -13.8078 q^{49} +(2.43845 - 4.22351i) q^{51} +(-1.73205 + 1.00000i) q^{52} +(-2.97778 - 1.71922i) q^{53} +(2.78078 + 4.81645i) q^{54} -4.56155 q^{56} +(-6.16879 - 2.87689i) q^{57} +2.00000i q^{58} +(5.21922 + 9.03996i) q^{59} +(1.56155 - 2.70469i) q^{61} +(5.40938 - 3.12311i) q^{62} +(-2.21837 - 1.28078i) q^{63} -1.00000 q^{64} +(0.780776 - 1.35234i) q^{66} +(-11.7446 - 6.78078i) q^{67} +3.12311i q^{68} -12.0000 q^{69} +(0.123106 + 0.213225i) q^{71} +(-0.486319 - 0.280776i) q^{72} +(-9.25319 + 5.34233i) q^{73} +(-3.84233 - 6.65511i) q^{74} +(4.34233 - 0.379706i) q^{76} +4.56155i q^{77} +(-2.70469 + 1.56155i) q^{78} +(-1.43845 - 2.49146i) q^{79} +(3.50000 + 6.06218i) q^{81} +(1.83866 + 1.06155i) q^{82} -9.80776i q^{83} -7.12311 q^{84} +(-2.56155 + 4.43674i) q^{86} +3.12311i q^{87} +1.00000i q^{88} +(4.84233 - 8.38716i) q^{89} +(4.56155 - 7.90084i) q^{91} +(6.65511 - 3.84233i) q^{92} +(8.44703 - 4.87689i) q^{93} +11.1231 q^{94} -1.56155 q^{96} +(-9.25319 + 5.34233i) q^{97} +(11.9579 - 6.90388i) q^{98} +(-0.280776 + 0.486319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 2 q^{6} + 6 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 - 2 * q^6 + 6 * q^9	\( 8 q + 4 q^{4} - 2 q^{6} + 6 q^{9} + 8 q^{11} - 10 q^{14} - 4 q^{16} + 20 q^{19} - 12 q^{21} + 2 q^{24} + 16 q^{26} + 8 q^{29} + 16 q^{31} - 4 q^{34} - 6 q^{36} - 8 q^{39} + 8 q^{41} + 4 q^{44} - 12 q^{46} - 28 q^{49} + 36 q^{51} + 14 q^{54} - 20 q^{56} + 50 q^{59} - 4 q^{61} - 8 q^{64} - 2 q^{66} - 96 q^{69} - 32 q^{71} - 6 q^{74} + 10 q^{76} - 28 q^{79} + 28 q^{81} - 24 q^{84} - 4 q^{86} + 14 q^{89} + 20 q^{91} + 56 q^{94} + 4 q^{96} + 6 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 - 2 * q^6 + 6 * q^9 + 8 * q^11 - 10 * q^14 - 4 * q^16 + 20 * q^19 - 12 * q^21 + 2 * q^24 + 16 * q^26 + 8 * q^29 + 16 * q^31 - 4 * q^34 - 6 * q^36 - 8 * q^39 + 8 * q^41 + 4 * q^44 - 12 * q^46 - 28 * q^49 + 36 * q^51 + 14 * q^54 - 20 * q^56 + 50 * q^59 - 4 * q^61 - 8 * q^64 - 2 * q^66 - 96 * q^69 - 32 * q^71 - 6 * q^74 + 10 * q^76 - 28 * q^79 + 28 * q^81 - 24 * q^84 - 4 * q^86 + 14 * q^89 + 20 * q^91 + 56 * q^94 + 4 * q^96 + 6 * q^99

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