LMFDB - Embedded newform 1950.2.i.bi.601.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(451,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("1950.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.i (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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.1
Root			$-0.780776 + 1.35234i$ of defining polynomial
Character	$\chi$	$=$	1950.601
Dual form			1950.2.i.bi.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.280776 + 0.486319i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.280776 + 0.486319i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.06155 - 3.57071i) q^{11} -1.00000 q^{12} +(-2.84233 + 2.21837i) q^{13} -0.561553 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.56155 + 2.70469i) q^{17} -1.00000 q^{18} +(-0.280776 + 0.486319i) q^{19} -0.561553 q^{21} +(2.06155 - 3.57071i) q^{22} +(2.34233 + 4.05703i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.34233 - 1.35234i) q^{26} -1.00000 q^{27} +(-0.280776 - 0.486319i) q^{28} +(-1.21922 - 2.11176i) q^{29} -6.68466 q^{31} +(0.500000 - 0.866025i) q^{32} +(2.06155 - 3.57071i) q^{33} -3.12311 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-2.06155 - 3.57071i) q^{37} -0.561553 q^{38} +(-3.34233 - 1.35234i) q^{39} +(-6.12311 - 10.6055i) q^{41} +(-0.280776 - 0.486319i) q^{42} +(0.219224 - 0.379706i) q^{43} +4.12311 q^{44} +(-2.34233 + 4.05703i) q^{46} -7.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(3.34233 + 5.78908i) q^{49} -3.12311 q^{51} +(-0.500000 - 3.57071i) q^{52} -8.56155 q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.280776 - 0.486319i) q^{56} -0.561553 q^{57} +(1.21922 - 2.11176i) q^{58} +(-3.21922 + 5.57586i) q^{59} +(-3.00000 + 5.19615i) q^{61} +(-3.34233 - 5.78908i) q^{62} +(-0.280776 - 0.486319i) q^{63} +1.00000 q^{64} +4.12311 q^{66} +(-1.12311 - 1.94528i) q^{67} +(-1.56155 - 2.70469i) q^{68} +(-2.34233 + 4.05703i) q^{69} +(6.56155 - 11.3649i) q^{71} +(0.500000 - 0.866025i) q^{72} -9.36932 q^{73} +(2.06155 - 3.57071i) q^{74} +(-0.280776 - 0.486319i) q^{76} +2.31534 q^{77} +(-0.500000 - 3.57071i) q^{78} +11.5616 q^{79} +(-0.500000 - 0.866025i) q^{81} +(6.12311 - 10.6055i) q^{82} +7.12311 q^{83} +(0.280776 - 0.486319i) q^{84} +0.438447 q^{86} +(1.21922 - 2.11176i) q^{87} +(2.06155 + 3.57071i) q^{88} +(9.40388 + 16.2880i) q^{89} +(-0.280776 - 2.00514i) q^{91} -4.68466 q^{92} +(-3.34233 - 5.78908i) q^{93} +(-3.50000 - 6.06218i) q^{94} +1.00000 q^{96} +(-3.56155 + 6.16879i) q^{97} +(-3.34233 + 5.78908i) q^{98} +4.12311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} + 3 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 + 3 * q^7 - 4 * q^8 - 2 * q^9	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} + 3 q^{7} - 4 q^{8} - 2 q^{9} - 4 q^{12} + q^{13} + 6 q^{14} - 2 q^{16} + 2 q^{17} - 4 q^{18} + 3 q^{19} + 6 q^{21} - 3 q^{23} - 2 q^{24} - q^{26} - 4 q^{27} + 3 q^{28} - 9 q^{29} - 2 q^{31} + 2 q^{32} + 4 q^{34} - 2 q^{36} + 6 q^{38} - q^{39} - 8 q^{41} + 3 q^{42} + 5 q^{43} + 3 q^{46} - 28 q^{47} + 2 q^{48} + q^{49} + 4 q^{51} - 2 q^{52} - 26 q^{53} - 2 q^{54} - 3 q^{56} + 6 q^{57} + 9 q^{58} - 17 q^{59} - 12 q^{61} - q^{62} + 3 q^{63} + 4 q^{64} + 12 q^{67} + 2 q^{68} + 3 q^{69} + 18 q^{71} + 2 q^{72} + 12 q^{73} + 3 q^{76} + 34 q^{77} - 2 q^{78} + 38 q^{79} - 2 q^{81} + 8 q^{82} + 12 q^{83} - 3 q^{84} + 10 q^{86} + 9 q^{87} + 17 q^{89} + 3 q^{91} + 6 q^{92} - q^{93} - 14 q^{94} + 4 q^{96} - 6 q^{97} - q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 + 3 * q^7 - 4 * q^8 - 2 * q^9 - 4 * q^12 + q^13 + 6 * q^14 - 2 * q^16 + 2 * q^17 - 4 * q^18 + 3 * q^19 + 6 * q^21 - 3 * q^23 - 2 * q^24 - q^26 - 4 * q^27 + 3 * q^28 - 9 * q^29 - 2 * q^31 + 2 * q^32 + 4 * q^34 - 2 * q^36 + 6 * q^38 - q^39 - 8 * q^41 + 3 * q^42 + 5 * q^43 + 3 * q^46 - 28 * q^47 + 2 * q^48 + q^49 + 4 * q^51 - 2 * q^52 - 26 * q^53 - 2 * q^54 - 3 * q^56 + 6 * q^57 + 9 * q^58 - 17 * q^59 - 12 * q^61 - q^62 + 3 * q^63 + 4 * q^64 + 12 * q^67 + 2 * q^68 + 3 * q^69 + 18 * q^71 + 2 * q^72 + 12 * q^73 + 3 * q^76 + 34 * q^77 - 2 * q^78 + 38 * q^79 - 2 * q^81 + 8 * q^82 + 12 * q^83 - 3 * q^84 + 10 * q^86 + 9 * q^87 + 17 * q^89 + 3 * q^91 + 6 * q^92 - q^93 - 14 * q^94 + 4 * q^96 - 6 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−0.280776	+	0.486319i	−0.106124	+	0.183811i	−0.914197	−	0.405271i	$-0.867177\pi$
$7$	−0.280776	+	0.486319i	−0.106124	+	0.183811i	0.808073	+	0.589082i	$0.200511\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−2.06155	−	3.57071i	−0.621582	−	1.07661i	−0.989191	−	0.146631i	$-0.953157\pi$
$11$	−2.06155	−	3.57071i	−0.621582	−	1.07661i	0.367610	−	0.929980i	$-0.380176\pi$
$12$	−1.00000			−0.288675
$13$	−2.84233	+	2.21837i	−0.788320	+	0.615265i
$13$	−2.84233	+	2.21837i	−0.788320	+	0.615265i
$14$	−0.561553			−0.150081
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.56155	+	2.70469i	−0.378732	+	0.655983i	−0.990878	−	0.134761i	$-0.956973\pi$
$17$	−1.56155	+	2.70469i	−0.378732	+	0.655983i	0.612146	+	0.790745i	$0.290307\pi$
$18$	−1.00000			−0.235702
$19$	−0.280776	+	0.486319i	−0.0644145	+	0.111569i	−0.896434	−	0.443177i	$-0.853851\pi$
$19$	−0.280776	+	0.486319i	−0.0644145	+	0.111569i	0.832020	+	0.554746i	$0.187185\pi$
$20$		0			0
$21$	−0.561553			−0.122541
$22$	2.06155	−	3.57071i	0.439525	−	0.761279i
$23$	2.34233	+	4.05703i	0.488409	+	0.845950i	0.999911	−	0.0133324i	$-0.00424395\pi$
$23$	2.34233	+	4.05703i	0.488409	+	0.845950i	−0.511502	+	0.859282i	$0.670911\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$		0			0
$26$	−3.34233	−	1.35234i	−0.655485	−	0.265217i
$27$	−1.00000			−0.192450
$28$	−0.280776	−	0.486319i	−0.0530618	−	0.0919057i
$29$	−1.21922	−	2.11176i	−0.226404	−	0.392143i	0.730336	−	0.683088i	$-0.239364\pi$
$29$	−1.21922	−	2.11176i	−0.226404	−	0.392143i	−0.956740	+	0.290945i	$0.906030\pi$
$30$		0			0
$31$	−6.68466			−1.20060			−0.600300	−	0.799775i	$-0.704952\pi$
$31$	−6.68466			−1.20060			−0.600300	+	0.799775i	$0.704952\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.06155	−	3.57071i	0.358870	−	0.621582i
$34$	−3.12311			−0.535608
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−2.06155	−	3.57071i	−0.338917	−	0.587022i	0.645312	−	0.763919i	$-0.276727\pi$
$37$	−2.06155	−	3.57071i	−0.338917	−	0.587022i	−0.984229	+	0.176897i	$0.943394\pi$
$38$	−0.561553			−0.0910959
$39$	−3.34233	−	1.35234i	−0.535201	−	0.216548i
$40$		0			0
$41$	−6.12311	−	10.6055i	−0.956268	−	1.65631i	−0.731438	−	0.681908i	$-0.761151\pi$
$41$	−6.12311	−	10.6055i	−0.956268	−	1.65631i	−0.224830	−	0.974398i	$-0.572183\pi$
$42$	−0.280776	−	0.486319i	−0.0433247	−	0.0750407i
$43$	0.219224	−	0.379706i	0.0334313	−	0.0579047i	−0.848826	−	0.528673i	$-0.822690\pi$
$43$	0.219224	−	0.379706i	0.0334313	−	0.0579047i	0.882257	+	0.470768i	$0.156023\pi$
$44$	4.12311			0.621582
$45$		0			0
$46$	−2.34233	+	4.05703i	−0.345358	+	0.598177i
$47$	−7.00000			−1.02105			−0.510527	−	0.859861i	$-0.670550\pi$
$47$	−7.00000			−1.02105			−0.510527	+	0.859861i	$0.670550\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	3.34233	+	5.78908i	0.477476	+	0.827012i
$50$		0			0
$51$	−3.12311			−0.437322
$52$	−0.500000	−	3.57071i	−0.0693375	−	0.495169i
$53$	−8.56155			−1.17602			−0.588010	−	0.808854i	$-0.700088\pi$
$53$	−8.56155			−1.17602			−0.588010	+	0.808854i	$0.700088\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$	0.280776	−	0.486319i	0.0375203	−	0.0649871i
$57$	−0.561553			−0.0743795
$58$	1.21922	−	2.11176i	0.160092	−	0.277287i
$59$	−3.21922	+	5.57586i	−0.419107	+	0.725915i	−0.995850	−	0.0910109i	$-0.970990\pi$
$59$	−3.21922	+	5.57586i	−0.419107	+	0.725915i	0.576743	+	0.816926i	$0.304324\pi$
$60$		0			0
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	−0.991645	−	0.128994i	$-0.958825\pi$
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	0.607535	+	0.794293i	$0.292159\pi$
$62$	−3.34233	−	5.78908i	−0.424476	−	0.735214i
$63$	−0.280776	−	0.486319i	−0.0353745	−	0.0612704i
$64$	1.00000			0.125000
$65$		0			0
$66$	4.12311			0.507519
$67$	−1.12311	−	1.94528i	−0.137209	−	0.237653i	0.789230	−	0.614098i	$-0.210480\pi$
$67$	−1.12311	−	1.94528i	−0.137209	−	0.237653i	−0.926439	+	0.376444i	$0.877147\pi$
$68$	−1.56155	−	2.70469i	−0.189366	−	0.327992i
$69$	−2.34233	+	4.05703i	−0.281983	+	0.488409i
$70$		0			0
$71$	6.56155	−	11.3649i	0.778713	−	1.34877i	−0.153971	−	0.988075i	$-0.549206\pi$
$71$	6.56155	−	11.3649i	0.778713	−	1.34877i	0.932684	−	0.360695i	$-0.117461\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−9.36932			−1.09660			−0.548298	−	0.836283i	$-0.684724\pi$
$73$	−9.36932			−1.09660			−0.548298	+	0.836283i	$0.684724\pi$
$74$	2.06155	−	3.57071i	0.239651	−	0.415087i
$75$		0			0
$76$	−0.280776	−	0.486319i	−0.0322073	−	0.0557846i
$77$	2.31534			0.263858
$78$	−0.500000	−	3.57071i	−0.0566139	−	0.404304i
$79$	11.5616			1.30078			0.650388	−	0.759602i	$-0.274606\pi$
$79$	11.5616			1.30078			0.650388	+	0.759602i	$0.274606\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	6.12311	−	10.6055i	0.676184	−	1.17118i
$83$	7.12311			0.781862			0.390931	−	0.920420i	$-0.372153\pi$
$83$	7.12311			0.781862			0.390931	+	0.920420i	$0.372153\pi$
$84$	0.280776	−	0.486319i	0.0306352	−	0.0530618i
$85$		0			0
$86$	0.438447			0.0472790
$87$	1.21922	−	2.11176i	0.130714	−	0.226404i
$88$	2.06155	+	3.57071i	0.219762	+	0.380639i
$89$	9.40388	+	16.2880i	0.996810	+	1.72652i	0.567529	+	0.823354i	$0.307900\pi$
$89$	9.40388	+	16.2880i	0.996810	+	1.72652i	0.429281	+	0.903171i	$0.358767\pi$
$90$		0			0
$91$	−0.280776	−	2.00514i	−0.0294334	−	0.210196i
$92$	−4.68466			−0.488409
$93$	−3.34233	−	5.78908i	−0.346583	−	0.600300i
$94$	−3.50000	−	6.06218i	−0.360997	−	0.625266i
$95$		0			0
$96$	1.00000			0.102062
$97$	−3.56155	+	6.16879i	−0.361621	+	0.626346i	−0.988228	−	0.152990i	$-0.951110\pi$
$97$	−3.56155	+	6.16879i	−0.361621	+	0.626346i	0.626607	+	0.779335i	$0.284443\pi$
$98$	−3.34233	+	5.78908i	−0.337626	+	0.584786i
$99$	4.12311			0.414388
$100$		0			0
$101$	4.43845	+	7.68762i	0.441642	+	0.764946i	0.997812	−	0.0661225i	$-0.0210628\pi$
$101$	4.43845	+	7.68762i	0.441642	+	0.764946i	−0.556170	+	0.831069i	$0.687729\pi$
$102$	−1.56155	−	2.70469i	−0.154617	−	0.267804i
$103$	−4.56155			−0.449463			−0.224732	−	0.974421i	$-0.572151\pi$
$103$	−4.56155			−0.449463			−0.224732	+	0.974421i	$0.572151\pi$
$104$	2.84233	−	2.21837i	0.278713	−	0.217529i
$105$		0			0
$106$	−4.28078	−	7.41452i	−0.415786	−	0.720162i
$107$	1.00000	+	1.73205i	0.0966736	+	0.167444i	0.910306	−	0.413936i	$-0.135846\pi$
$107$	1.00000	+	1.73205i	0.0966736	+	0.167444i	−0.813632	+	0.581380i	$0.802513\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−3.75379			−0.359548			−0.179774	−	0.983708i	$-0.557537\pi$
$109$	−3.75379			−0.359548			−0.179774	+	0.983708i	$0.557537\pi$
$110$		0			0
$111$	2.06155	−	3.57071i	0.195674	−	0.338917i
$112$	0.561553			0.0530618
$113$	4.34233	−	7.52113i	0.408492	−	0.707529i	−0.586229	−	0.810145i	$-0.699388\pi$
$113$	4.34233	−	7.52113i	0.408492	−	0.707529i	0.994721	+	0.102617i	$0.0327215\pi$
$114$	−0.280776	−	0.486319i	−0.0262971	−	0.0455479i
$115$		0			0
$116$	2.43845			0.226404
$117$	−0.500000	−	3.57071i	−0.0462250	−	0.330113i
$118$	−6.43845			−0.592707
$119$	−0.876894	−	1.51883i	−0.0803848	−	0.139231i
$120$		0			0
$121$	−3.00000	+	5.19615i	−0.272727	+	0.472377i
$122$	−6.00000			−0.543214
$123$	6.12311	−	10.6055i	0.552102	−	0.956268i
$124$	3.34233	−	5.78908i	0.300150	−	0.519875i
$125$		0			0
$126$	0.280776	−	0.486319i	0.0250136	−	0.0433247i
$127$	−4.28078	−	7.41452i	−0.379857	−	0.657932i	0.611184	−	0.791489i	$-0.290694\pi$
$127$	−4.28078	−	7.41452i	−0.379857	−	0.657932i	−0.991041	+	0.133556i	$0.957360\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	0.438447			0.0386031
$130$		0			0
$131$	−2.12311			−0.185497			−0.0927483	−	0.995690i	$-0.529565\pi$
$131$	−2.12311			−0.185497			−0.0927483	+	0.995690i	$0.529565\pi$
$132$	2.06155	+	3.57071i	0.179435	+	0.310791i
$133$	−0.157671	−	0.273094i	−0.0136718	−	0.0236802i
$134$	1.12311	−	1.94528i	0.0970215	−	0.168046i
$135$		0			0
$136$	1.56155	−	2.70469i	0.133902	−	0.231925i
$137$	5.90388	−	10.2258i	0.504403	−	0.873651i	−0.495584	−	0.868560i	$-0.665046\pi$
$137$	5.90388	−	10.2258i	0.504403	−	0.873651i	0.999987	−	0.00509126i	$-0.00162061\pi$
$138$	−4.68466			−0.398785
$139$	−6.28078	+	10.8786i	−0.532729	+	0.922713i	0.466541	+	0.884500i	$0.345500\pi$
$139$	−6.28078	+	10.8786i	−0.532729	+	0.922713i	−0.999270	+	0.0382133i	$0.987833\pi$
$140$		0			0
$141$	−3.50000	−	6.06218i	−0.294753	−	0.510527i
$142$	13.1231			1.10127
$143$	13.7808	+	5.57586i	1.15241	+	0.466277i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−4.68466	−	8.11407i	−0.387705	−	0.671525i
$147$	−3.34233	+	5.78908i	−0.275671	+	0.477476i
$148$	4.12311			0.338917
$149$	1.09612	−	1.89853i	0.0897975	−	0.155534i	−0.817628	−	0.575747i	$-0.804711\pi$
$149$	1.09612	−	1.89853i	0.0897975	−	0.155534i	0.907425	+	0.420213i	$0.138045\pi$
$150$		0			0
$151$	−15.3693			−1.25074			−0.625369	−	0.780329i	$-0.715051\pi$
$151$	−15.3693			−1.25074			−0.625369	+	0.780329i	$0.715051\pi$
$152$	0.280776	−	0.486319i	0.0227740	−	0.0394457i
$153$	−1.56155	−	2.70469i	−0.126244	−	0.218661i
$154$	1.15767	+	2.00514i	0.0932878	+	0.161579i
$155$		0			0
$156$	2.84233	−	2.21837i	0.227568	−	0.177612i
$157$	−13.8769			−1.10750			−0.553748	−	0.832684i	$-0.686803\pi$
$157$	−13.8769			−1.10750			−0.553748	+	0.832684i	$0.686803\pi$
$158$	5.78078	+	10.0126i	0.459894	+	0.796560i
$159$	−4.28078	−	7.41452i	−0.339488	−	0.588010i
$160$		0			0
$161$	−2.63068			−0.207327
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−7.21922	+	12.5041i	−0.565453	+	0.979394i	0.431554	+	0.902087i	$0.357965\pi$
$163$	−7.21922	+	12.5041i	−0.565453	+	0.979394i	−0.997007	+	0.0773067i	$0.975368\pi$
$164$	12.2462			0.956268
$165$		0			0
$166$	3.56155	+	6.16879i	0.276430	+	0.478791i
$167$	2.18466	+	3.78394i	0.169054	+	0.292810i	0.938087	−	0.346398i	$-0.112595\pi$
$167$	2.18466	+	3.78394i	0.169054	+	0.292810i	−0.769034	+	0.639208i	$0.779262\pi$
$168$	0.561553			0.0433247
$169$	3.15767	−	12.6107i	0.242898	−	0.970052i
$170$		0			0
$171$	−0.280776	−	0.486319i	−0.0214715	−	0.0371897i
$172$	0.219224	+	0.379706i	0.0167156	+	0.0289523i
$173$	10.0885	−	17.4739i	0.767018	−	1.32851i	−0.172156	−	0.985070i	$-0.555073\pi$
$173$	10.0885	−	17.4739i	0.767018	−	1.32851i	0.939173	−	0.343444i	$-0.111593\pi$
$174$	2.43845			0.184858
$175$		0			0
$176$	−2.06155	+	3.57071i	−0.155395	+	0.269153i
$177$	−6.43845			−0.483943
$178$	−9.40388	+	16.2880i	−0.704851	+	1.22084i
$179$	6.34233	+	10.9852i	0.474048	+	0.821075i	0.999559	−	0.0297120i	$-0.00945900\pi$
$179$	6.34233	+	10.9852i	0.474048	+	0.821075i	−0.525511	+	0.850787i	$0.676126\pi$
$180$		0			0
$181$	2.87689			0.213838			0.106919	−	0.994268i	$-0.465901\pi$
$181$	2.87689			0.213838			0.106919	+	0.994268i	$0.465901\pi$
$182$	1.59612	−	1.24573i	0.118312	−	0.0923398i
$183$	−6.00000			−0.443533
$184$	−2.34233	−	4.05703i	−0.172679	−	0.299088i
$185$		0			0
$186$	3.34233	−	5.78908i	0.245071	−	0.424476i
$187$	12.8769			0.941652
$188$	3.50000	−	6.06218i	0.255264	−	0.442130i
$189$	0.280776	−	0.486319i	0.0204235	−	0.0353745i
$190$		0			0
$191$	−5.43845	+	9.41967i	−0.393512	+	0.681583i	−0.992910	−	0.118868i	$-0.962073\pi$
$191$	−5.43845	+	9.41967i	−0.393512	+	0.681583i	0.599398	+	0.800451i	$0.295407\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$193$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$194$	−7.12311			−0.511409
$195$		0			0
$196$	−6.68466			−0.477476
$197$	6.40388	+	11.0918i	0.456258	+	0.790262i	0.998760	−	0.0497931i	$-0.0158562\pi$
$197$	6.40388	+	11.0918i	0.456258	+	0.790262i	−0.542502	+	0.840055i	$0.682523\pi$
$198$	2.06155	+	3.57071i	0.146508	+	0.253760i
$199$	−1.43845	+	2.49146i	−0.101969	+	0.176615i	−0.912496	−	0.409086i	$-0.865848\pi$
$199$	−1.43845	+	2.49146i	−0.101969	+	0.176615i	0.810527	+	0.585701i	$0.199181\pi$
$200$		0			0
$201$	1.12311	−	1.94528i	0.0792178	−	0.137209i
$202$	−4.43845	+	7.68762i	−0.312288	+	0.540899i
$203$	1.36932			0.0961072
$204$	1.56155	−	2.70469i	0.109331	−	0.189366i
$205$		0			0
$206$	−2.28078	−	3.95042i	−0.158909	−	0.275239i
$207$	−4.68466			−0.325606
$208$	3.34233	+	1.35234i	0.231749	+	0.0937682i
$209$	2.31534			0.160156
$210$		0			0
$211$	10.9654	+	18.9927i	0.754892	+	1.30751i	0.945428	+	0.325831i	$0.105644\pi$
$211$	10.9654	+	18.9927i	0.754892	+	1.30751i	−0.190536	+	0.981680i	$0.561023\pi$
$212$	4.28078	−	7.41452i	0.294005	−	0.509231i
$213$	13.1231			0.899180
$214$	−1.00000	+	1.73205i	−0.0683586	+	0.118401i
$215$		0			0
$216$	1.00000			0.0680414
$217$	1.87689	−	3.25088i	0.127412	−	0.220684i
$218$	−1.87689	−	3.25088i	−0.127119	−	0.220177i
$219$	−4.68466	−	8.11407i	−0.316560	−	0.548298i
$220$		0			0
$221$	−1.56155	−	11.1517i	−0.105041	−	0.750146i
$222$	4.12311			0.276725
$223$	13.6501	+	23.6427i	0.914078	+	1.58323i	0.808246	+	0.588845i	$0.200417\pi$
$223$	13.6501	+	23.6427i	0.914078	+	1.58323i	0.105832	+	0.994384i	$0.466249\pi$
$224$	0.280776	+	0.486319i	0.0187602	+	0.0324936i
$225$		0			0
$226$	8.68466			0.577695
$227$	−10.0000	+	17.3205i	−0.663723	+	1.14960i	0.315906	+	0.948790i	$0.397691\pi$
$227$	−10.0000	+	17.3205i	−0.663723	+	1.14960i	−0.979630	+	0.200812i	$0.935642\pi$
$228$	0.280776	−	0.486319i	0.0185949	−	0.0322073i
$229$	−24.2462			−1.60223			−0.801117	−	0.598507i	$-0.795761\pi$
$229$	−24.2462			−1.60223			−0.801117	+	0.598507i	$0.795761\pi$
$230$		0			0
$231$	1.15767	+	2.00514i	0.0761691	+	0.131929i
$232$	1.21922	+	2.11176i	0.0800460	+	0.138644i
$233$	5.31534			0.348220			0.174110	−	0.984726i	$-0.444295\pi$
$233$	5.31534			0.348220			0.174110	+	0.984726i	$0.444295\pi$
$234$	2.84233	−	2.21837i	0.185809	−	0.145019i
$235$		0			0
$236$	−3.21922	−	5.57586i	−0.209554	−	0.362957i
$237$	5.78078	+	10.0126i	0.375502	+	0.650388i
$238$	0.876894	−	1.51883i	0.0568406	−	0.0984508i
$239$	−11.3693			−0.735420			−0.367710	−	0.929941i	$-0.619858\pi$
$239$	−11.3693			−0.735420			−0.367710	+	0.929941i	$0.619858\pi$
$240$		0			0
$241$	14.0616	−	24.3553i	0.905784	−	1.56886i	0.0859232	−	0.996302i	$-0.472616\pi$
$241$	14.0616	−	24.3553i	0.905784	−	1.56886i	0.819861	−	0.572563i	$-0.194051\pi$
$242$	−6.00000			−0.385695
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−3.00000	−	5.19615i	−0.192055	−	0.332650i
$245$		0			0
$246$	12.2462			0.780790
$247$	−0.280776	−	2.00514i	−0.0178654	−	0.127584i
$248$	6.68466			0.424476
$249$	3.56155	+	6.16879i	0.225704	+	0.390931i
$250$		0			0
$251$	4.06155	−	7.03482i	0.256363	−	0.444034i	−0.708902	−	0.705307i	$-0.750809\pi$
$251$	4.06155	−	7.03482i	0.256363	−	0.444034i	0.965265	+	0.261273i	$0.0841424\pi$
$252$	0.561553			0.0353745
$253$	9.65767	−	16.7276i	0.607173	−	1.05165i
$254$	4.28078	−	7.41452i	0.268600	−	0.465229i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.78078	−	4.81645i	−0.173460	−	0.300442i	0.766167	−	0.642641i	$-0.222161\pi$
$257$	−2.78078	−	4.81645i	−0.173460	−	0.300442i	−0.939627	+	0.342200i	$0.888828\pi$
$258$	0.219224	+	0.379706i	0.0136483	+	0.0236395i
$259$	2.31534			0.143868
$260$		0			0
$261$	2.43845			0.150936
$262$	−1.06155	−	1.83866i	−0.0655830	−	0.113593i
$263$	−6.50000	−	11.2583i	−0.400807	−	0.694218i	0.593016	−	0.805190i	$-0.297937\pi$
$263$	−6.50000	−	11.2583i	−0.400807	−	0.694218i	−0.993824	+	0.110972i	$0.964604\pi$
$264$	−2.06155	+	3.57071i	−0.126880	+	0.219762i
$265$		0			0
$266$	0.157671	−	0.273094i	0.00966742	−	0.0167445i
$267$	−9.40388	+	16.2880i	−0.575508	+	0.996810i
$268$	2.24621			0.137209
$269$	−10.6847	+	18.5064i	−0.651455	+	1.12835i	0.331315	+	0.943520i	$0.392508\pi$
$269$	−10.6847	+	18.5064i	−0.651455	+	1.12835i	−0.982770	+	0.184833i	$0.940826\pi$
$270$		0			0
$271$	6.58854	+	11.4117i	0.400225	+	0.693211i	0.993753	−	0.111603i	$-0.0355985\pi$
$271$	6.58854	+	11.4117i	0.400225	+	0.693211i	−0.593528	+	0.804814i	$0.702265\pi$
$272$	3.12311			0.189366
$273$	1.59612	−	1.24573i	0.0966015	−	0.0753951i
$274$	11.8078			0.713333
$275$		0			0
$276$	−2.34233	−	4.05703i	−0.140992	−	0.244205i
$277$	−0.500000	+	0.866025i	−0.0300421	+	0.0520344i	−0.880656	−	0.473757i	$-0.842897\pi$
$277$	−0.500000	+	0.866025i	−0.0300421	+	0.0520344i	0.850613	+	0.525792i	$0.176231\pi$
$278$	−12.5616			−0.753392
$279$	3.34233	−	5.78908i	0.200100	−	0.346583i
$280$		0			0
$281$	16.2462			0.969168			0.484584	−	0.874745i	$-0.338971\pi$
$281$	16.2462			0.969168			0.484584	+	0.874745i	$0.338971\pi$
$282$	3.50000	−	6.06218i	0.208422	−	0.360997i
$283$	7.78078	+	13.4767i	0.462519	+	0.801107i	0.999086	−	0.0427513i	$-0.0136123\pi$
$283$	7.78078	+	13.4767i	0.462519	+	0.801107i	−0.536567	+	0.843858i	$0.680279\pi$
$284$	6.56155	+	11.3649i	0.389357	+	0.674385i
$285$		0			0
$286$	2.06155	+	14.7224i	0.121902	+	0.870556i
$287$	6.87689			0.405930
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	3.62311	+	6.27540i	0.213124	+	0.369141i
$290$		0			0
$291$	−7.12311			−0.417564
$292$	4.68466	−	8.11407i	0.274149	−	0.474840i
$293$	1.96543	−	3.40423i	0.114822	−	0.198877i	−0.802887	−	0.596132i	$-0.796704\pi$
$293$	1.96543	−	3.40423i	0.114822	−	0.198877i	0.917709	+	0.397254i	$0.130037\pi$
$294$	−6.68466			−0.389857
$295$		0			0
$296$	2.06155	+	3.57071i	0.119825	+	0.207544i
$297$	2.06155	+	3.57071i	0.119623	+	0.207194i
$298$	2.19224			0.126993
$299$	−15.6577	−	6.33527i	−0.905506	−	0.366378i
$300$		0			0
$301$	0.123106	+	0.213225i	0.00709569	+	0.0122901i
$302$	−7.68466	−	13.3102i	−0.442202	−	0.765917i
$303$	−4.43845	+	7.68762i	−0.254982	+	0.441642i
$304$	0.561553			0.0322073
$305$		0			0
$306$	1.56155	−	2.70469i	0.0892680	−	0.154617i
$307$	−25.6155			−1.46196			−0.730978	−	0.682401i	$-0.760936\pi$
$307$	−25.6155			−1.46196			−0.730978	+	0.682401i	$0.760936\pi$
$308$	−1.15767	+	2.00514i	−0.0659644	+	0.114254i
$309$	−2.28078	−	3.95042i	−0.129749	−	0.224732i
$310$		0			0
$311$	30.7386			1.74303			0.871514	−	0.490371i	$-0.163139\pi$
$311$	30.7386			1.74303			0.871514	+	0.490371i	$0.163139\pi$
$312$	3.34233	+	1.35234i	0.189222	+	0.0765614i
$313$	−31.3693			−1.77310			−0.886549	−	0.462634i	$-0.846904\pi$
$313$	−31.3693			−1.77310			−0.886549	+	0.462634i	$0.846904\pi$
$314$	−6.93845	−	12.0177i	−0.391559	−	0.678200i
$315$		0			0
$316$	−5.78078	+	10.0126i	−0.325194	+	0.563253i
$317$	24.8078			1.39334			0.696671	−	0.717390i	$-0.254664\pi$
$317$	24.8078			1.39334			0.696671	+	0.717390i	$0.254664\pi$
$318$	4.28078	−	7.41452i	0.240054	−	0.415786i
$319$	−5.02699	+	8.70700i	−0.281457	+	0.487498i
$320$		0			0
$321$	−1.00000	+	1.73205i	−0.0558146	+	0.0966736i
$322$	−1.31534	−	2.27824i	−0.0733011	−	0.126961i
$323$	−0.876894	−	1.51883i	−0.0487917	−	0.0845097i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−14.4384			−0.799672
$327$	−1.87689	−	3.25088i	−0.103792	−	0.179774i
$328$	6.12311	+	10.6055i	0.338092	+	0.585592i
$329$	1.96543	−	3.40423i	0.108358	−	0.187681i
$330$		0			0
$331$	−15.3693	+	26.6204i	−0.844774	+	1.46319i	0.0410432	+	0.999157i	$0.486932\pi$
$331$	−15.3693	+	26.6204i	−0.844774	+	1.46319i	−0.885817	+	0.464034i	$0.846401\pi$
$332$	−3.56155	+	6.16879i	−0.195466	+	0.338556i
$333$	4.12311			0.225945
$334$	−2.18466	+	3.78394i	−0.119539	+	0.207048i
$335$		0			0
$336$	0.280776	+	0.486319i	0.0153176	+	0.0265309i
$337$	6.00000			0.326841			0.163420	−	0.986557i	$-0.447747\pi$
$337$	6.00000			0.326841			0.163420	+	0.986557i	$0.447747\pi$
$338$	12.5000	−	3.57071i	0.679910	−	0.194221i
$339$	8.68466			0.471686
$340$		0			0
$341$	13.7808	+	23.8690i	0.746271	+	1.29258i
$342$	0.280776	−	0.486319i	0.0151826	−	0.0262971i
$343$	−7.68466			−0.414933
$344$	−0.219224	+	0.379706i	−0.0118197	+	0.0204724i
$345$		0			0
$346$	20.1771			1.08473
$347$	0.438447	−	0.759413i	0.0235371	−	0.0407674i	−0.854017	−	0.520245i	$-0.825841\pi$
$347$	0.438447	−	0.759413i	0.0235371	−	0.0407674i	0.877554	+	0.479478i	$0.159174\pi$
$348$	1.21922	+	2.11176i	0.0653572	+	0.113202i
$349$	−4.24621	−	7.35465i	−0.227294	−	0.393686i	0.729711	−	0.683756i	$-0.239655\pi$
$349$	−4.24621	−	7.35465i	−0.227294	−	0.393686i	−0.957005	+	0.290070i	$0.906321\pi$
$350$		0			0
$351$	2.84233	−	2.21837i	0.151712	−	0.118408i
$352$	−4.12311			−0.219762
$353$	−12.9309	−	22.3969i	−0.688241	−	1.19207i	−0.972407	−	0.233293i	$-0.925050\pi$
$353$	−12.9309	−	22.3969i	−0.688241	−	1.19207i	0.284166	−	0.958775i	$-0.408283\pi$
$354$	−3.21922	−	5.57586i	−0.171100	−	0.296354i
$355$		0			0
$356$	−18.8078			−0.996810
$357$	0.876894	−	1.51883i	0.0464102	−	0.0803848i
$358$	−6.34233	+	10.9852i	−0.335203	+	0.580588i
$359$	13.1231			0.692611			0.346306	−	0.938122i	$-0.387436\pi$
$359$	13.1231			0.692611			0.346306	+	0.938122i	$0.387436\pi$
$360$		0			0
$361$	9.34233	+	16.1814i	0.491702	+	0.851652i
$362$	1.43845	+	2.49146i	0.0756031	+	0.130948i
$363$	−6.00000			−0.314918
$364$	1.87689	+	0.759413i	0.0983760	+	0.0398040i
$365$		0			0
$366$	−3.00000	−	5.19615i	−0.156813	−	0.271607i
$367$	6.24621	+	10.8188i	0.326050	+	0.564734i	0.981724	−	0.190309i	$-0.0609490\pi$
$367$	6.24621	+	10.8188i	0.326050	+	0.564734i	−0.655675	+	0.755044i	$0.727616\pi$
$368$	2.34233	−	4.05703i	0.122102	−	0.211487i
$369$	12.2462			0.637512
$370$		0			0
$371$	2.40388	−	4.16365i	0.124803	−	0.216166i
$372$	6.68466			0.346583
$373$	−12.9039	+	22.3502i	−0.668138	+	1.15725i	0.310287	+	0.950643i	$0.399575\pi$
$373$	−12.9039	+	22.3502i	−0.668138	+	1.15725i	−0.978424	+	0.206605i	$0.933758\pi$
$374$	6.43845	+	11.1517i	0.332924	+	0.576642i
$375$		0			0
$376$	7.00000			0.360997
$377$	8.15009	+	3.29762i	0.419751	+	0.169836i
$378$	0.561553			0.0288832
$379$	8.84233	+	15.3154i	0.454200	+	0.786697i	0.998642	−	0.0521012i	$-0.0165918\pi$
$379$	8.84233	+	15.3154i	0.454200	+	0.786697i	−0.544442	+	0.838799i	$0.683259\pi$
$380$		0			0
$381$	4.28078	−	7.41452i	0.219311	−	0.379857i
$382$	−10.8769			−0.556510
$383$	0.0961180	−	0.166481i	0.00491140	−	0.00850679i	−0.863559	−	0.504247i	$-0.831770\pi$
$383$	0.0961180	−	0.166481i	0.00491140	−	0.00850679i	0.868471	+	0.495741i	$0.165103\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$		0			0
$386$		0			0
$387$	0.219224	+	0.379706i	0.0111438	+	0.0193016i
$388$	−3.56155	−	6.16879i	−0.180810	−	0.313173i
$389$	−18.0540			−0.915373			−0.457686	−	0.889114i	$-0.651322\pi$
$389$	−18.0540			−0.915373			−0.457686	+	0.889114i	$0.651322\pi$
$390$		0			0
$391$	−14.6307			−0.739905
$392$	−3.34233	−	5.78908i	−0.168813	−	0.292393i
$393$	−1.06155	−	1.83866i	−0.0535483	−	0.0927483i
$394$	−6.40388	+	11.0918i	−0.322623	+	0.558799i
$395$		0			0
$396$	−2.06155	+	3.57071i	−0.103597	+	0.179435i
$397$	−10.0616	+	17.4271i	−0.504975	+	0.874642i	0.495009	+	0.868888i	$0.335165\pi$
$397$	−10.0616	+	17.4271i	−0.504975	+	0.874642i	−0.999983	+	0.00575403i	$0.998168\pi$
$398$	−2.87689			−0.144206
$399$	0.157671	−	0.273094i	0.00789341	−	0.0136718i
$400$		0			0
$401$	−0.157671	−	0.273094i	−0.00787370	−	0.0136377i	0.862062	−	0.506803i	$-0.169173\pi$
$401$	−0.157671	−	0.273094i	−0.00787370	−	0.0136377i	−0.869935	+	0.493166i	$0.835840\pi$
$402$	2.24621			0.112031
$403$	19.0000	−	14.8290i	0.946457	−	0.738687i
$404$	−8.87689			−0.441642
$405$		0			0
$406$	0.684658	+	1.18586i	0.0339790	+	0.0588534i
$407$	−8.50000	+	14.7224i	−0.421329	+	0.729764i
$408$	3.12311			0.154617
$409$	9.40388	−	16.2880i	0.464992	−	0.805390i	−0.534209	−	0.845352i	$-0.679391\pi$
$409$	9.40388	−	16.2880i	0.464992	−	0.805390i	0.999201	+	0.0399625i	$0.0127239\pi$
$410$		0			0
$411$	11.8078			0.582434
$412$	2.28078	−	3.95042i	0.112366	−	0.194623i
$413$	−1.80776	−	3.13114i	−0.0889543	−	0.154073i
$414$	−2.34233	−	4.05703i	−0.115119	−	0.199392i
$415$		0			0
$416$	0.500000	+	3.57071i	0.0245145	+	0.175069i
$417$	−12.5616			−0.615142
$418$	1.15767	+	2.00514i	0.0566235	+	0.0980748i
$419$	−16.2462	−	28.1393i	−0.793679	−	1.37469i	−0.923674	−	0.383178i	$-0.874829\pi$
$419$	−16.2462	−	28.1393i	−0.793679	−	1.37469i	0.129995	−	0.991515i	$-0.458504\pi$
$420$		0			0
$421$	−32.4924			−1.58358			−0.791792	−	0.610791i	$-0.790852\pi$
$421$	−32.4924			−1.58358			−0.791792	+	0.610791i	$0.790852\pi$
$422$	−10.9654	+	18.9927i	−0.533789	+	0.924550i
$423$	3.50000	−	6.06218i	0.170176	−	0.294753i
$424$	8.56155			0.415786
$425$		0			0
$426$	6.56155	+	11.3649i	0.317908	+	0.550633i
$427$	−1.68466	−	2.91791i	−0.0815263	−	0.141208i
$428$	−2.00000			−0.0966736
$429$	2.06155	+	14.7224i	0.0995327	+	0.710806i
$430$		0			0
$431$	11.3693	+	19.6922i	0.547641	+	0.948542i	0.998436	+	0.0559140i	$0.0178073\pi$
$431$	11.3693	+	19.6922i	0.547641	+	0.948542i	−0.450795	+	0.892628i	$0.648859\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−9.36932	+	16.2281i	−0.450261	+	0.779874i	−0.998402	−	0.0565114i	$-0.982002\pi$
$433$	−9.36932	+	16.2281i	−0.450261	+	0.779874i	0.548141	+	0.836386i	$0.315336\pi$
$434$	3.75379			0.180188
$435$		0			0
$436$	1.87689	−	3.25088i	0.0898869	−	0.155689i
$437$	−2.63068			−0.125843
$438$	4.68466	−	8.11407i	0.223842	−	0.387705i
$439$	−12.5616	−	21.7572i	−0.599530	−	1.03842i	−0.992890	−	0.119032i	$-0.962021\pi$
$439$	−12.5616	−	21.7572i	−0.599530	−	1.03842i	0.393360	−	0.919384i	$-0.371313\pi$
$440$		0			0
$441$	−6.68466			−0.318317
$442$	8.87689	−	6.92820i	0.422231	−	0.329541i
$443$	13.1231			0.623498			0.311749	−	0.950165i	$-0.399085\pi$
$443$	13.1231			0.623498			0.311749	+	0.950165i	$0.399085\pi$
$444$	2.06155	+	3.57071i	0.0978370	+	0.169459i
$445$		0			0
$446$	−13.6501	+	23.6427i	−0.646351	+	1.11951i
$447$	2.19224			0.103689
$448$	−0.280776	+	0.486319i	−0.0132654	+	0.0229764i
$449$	10.0885	−	17.4739i	0.476108	−	0.824643i	−0.523518	−	0.852015i	$-0.675381\pi$
$449$	10.0885	−	17.4739i	0.476108	−	0.824643i	0.999625	+	0.0273722i	$0.00871392\pi$
$450$		0			0
$451$	−25.2462	+	43.7277i	−1.18880	+	2.05906i
$452$	4.34233	+	7.52113i	0.204246	+	0.353764i
$453$	−7.68466	−	13.3102i	−0.361057	−	0.625369i
$454$	−20.0000			−0.938647
$455$		0			0
$456$	0.561553			0.0262971
$457$	10.1231	+	17.5337i	0.473539	+	0.820193i	0.999541	−	0.0302897i	$-0.00964299\pi$
$457$	10.1231	+	17.5337i	0.473539	+	0.820193i	−0.526002	+	0.850483i	$0.676310\pi$
$458$	−12.1231	−	20.9978i	−0.566476	−	0.981164i
$459$	1.56155	−	2.70469i	0.0728870	−	0.126244i
$460$		0			0
$461$	15.0270	−	26.0275i	0.699877	−	1.21222i	−0.268632	−	0.963243i	$-0.586572\pi$
$461$	15.0270	−	26.0275i	0.699877	−	1.21222i	0.968509	−	0.248979i	$-0.0800950\pi$
$462$	−1.15767	+	2.00514i	−0.0538597	+	0.0932878i
$463$	7.61553			0.353924			0.176962	−	0.984218i	$-0.443373\pi$
$463$	7.61553			0.353924			0.176962	+	0.984218i	$0.443373\pi$
$464$	−1.21922	+	2.11176i	−0.0566010	+	0.0980359i
$465$		0			0
$466$	2.65767	+	4.60322i	0.123114	+	0.213240i
$467$	17.8617			0.826543			0.413271	−	0.910608i	$-0.364386\pi$
$467$	17.8617			0.826543			0.413271	+	0.910608i	$0.364386\pi$
$468$	3.34233	+	1.35234i	0.154499	+	0.0625121i
$469$	1.26137			0.0582445
$470$		0			0
$471$	−6.93845	−	12.0177i	−0.319707	−	0.553748i
$472$	3.21922	−	5.57586i	0.148177	−	0.256650i
$473$	−1.80776			−0.0831211
$474$	−5.78078	+	10.0126i	−0.265520	+	0.459894i
$475$		0			0
$476$	1.75379			0.0803848
$477$	4.28078	−	7.41452i	0.196003	−	0.339488i
$478$	−5.68466	−	9.84612i	−0.260010	−	0.450351i
$479$	19.1231	+	33.1222i	0.873757	+	1.51339i	0.858081	+	0.513514i	$0.171657\pi$
$479$	19.1231	+	33.1222i	0.873757	+	1.51339i	0.0156760	+	0.999877i	$0.495010\pi$
$480$		0			0
$481$	13.7808	+	5.57586i	0.628349	+	0.254237i
$482$	28.1231			1.28097
$483$	−1.31534	−	2.27824i	−0.0598501	−	0.103663i
$484$	−3.00000	−	5.19615i	−0.136364	−	0.236189i
$485$		0			0
$486$	1.00000			0.0453609
$487$	6.52699	−	11.3051i	0.295766	−	0.512282i	−0.679397	−	0.733771i	$-0.737758\pi$
$487$	6.52699	−	11.3051i	0.295766	−	0.512282i	0.975163	+	0.221489i	$0.0710918\pi$
$488$	3.00000	−	5.19615i	0.135804	−	0.235219i
$489$	−14.4384			−0.652929
$490$		0			0
$491$	8.71922	+	15.1021i	0.393493	+	0.681550i	0.992908	−	0.118889i	$-0.0379332\pi$
$491$	8.71922	+	15.1021i	0.393493	+	0.681550i	−0.599415	+	0.800439i	$0.704600\pi$
$492$	6.12311	+	10.6055i	0.276051	+	0.478134i
$493$	7.61553			0.342986
$494$	1.59612	−	1.24573i	0.0718127	−	0.0560481i
$495$		0			0
$496$	3.34233	+	5.78908i	0.150075	+	0.259938i
$497$	3.68466	+	6.38202i	0.165280	+	0.286273i
$498$	−3.56155	+	6.16879i	−0.159597	+	0.276430i
$499$	4.00000			0.179065			0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000			0.179065			0.0895323	+	0.995984i	$0.471463\pi$
$500$		0			0
$501$	−2.18466	+	3.78394i	−0.0976033	+	0.169054i
$502$	8.12311			0.362552
$503$	−21.5270	+	37.2858i	−0.959841	+	1.66249i	−0.236962	+	0.971519i	$0.576152\pi$
$503$	−21.5270	+	37.2858i	−0.959841	+	1.66249i	−0.722879	+	0.690974i	$0.757182\pi$
$504$	0.280776	+	0.486319i	0.0125068	+	0.0216624i
$505$		0			0
$506$	19.3153			0.858672
$507$	12.5000	−	3.57071i	0.555144	−	0.158581i
$508$	8.56155			0.379857
$509$	−20.2732	−	35.1142i	−0.898594	−	1.55641i	−0.829293	−	0.558814i	$-0.811256\pi$
$509$	−20.2732	−	35.1142i	−0.898594	−	1.55641i	−0.0693009	−	0.997596i	$-0.522077\pi$
$510$		0			0
$511$	2.63068	−	4.55648i	0.116375	−	0.201567i
$512$	−1.00000			−0.0441942
$513$	0.280776	−	0.486319i	0.0123966	−	0.0214715i
$514$	2.78078	−	4.81645i	0.122655	−	0.212444i
$515$		0			0
$516$	−0.219224	+	0.379706i	−0.00965078	+	0.0167156i
$517$	14.4309	+	24.9950i	0.634669	+	1.09928i
$518$	1.15767	+	2.00514i	0.0508651	+	0.0881010i
$519$	20.1771			0.885676
$520$		0			0
$521$	−6.31534			−0.276680			−0.138340	−	0.990385i	$-0.544177\pi$
$521$	−6.31534			−0.276680			−0.138340	+	0.990385i	$0.544177\pi$
$522$	1.21922	+	2.11176i	0.0533640	+	0.0924291i
$523$	−14.9039	−	25.8143i	−0.651701	−	1.12878i	−0.982710	−	0.185152i	$-0.940722\pi$
$523$	−14.9039	−	25.8143i	−0.651701	−	1.12878i	0.331009	−	0.943628i	$-0.392611\pi$
$524$	1.06155	−	1.83866i	0.0463741	−	0.0803224i
$525$		0			0
$526$	6.50000	−	11.2583i	0.283413	−	0.490887i
$527$	10.4384	−	18.0799i	0.454706	−	0.787574i
$528$	−4.12311			−0.179435
$529$	0.526988	−	0.912769i	0.0229125	−	0.0396856i
$530$		0			0
$531$	−3.21922	−	5.57586i	−0.139702	−	0.241972i
$532$	0.315342			0.0136718
$533$	40.9309	+	16.5611i	1.77291	+	0.717341i
$534$	−18.8078			−0.813892
$535$		0			0
$536$	1.12311	+	1.94528i	0.0485108	+	0.0840231i
$537$	−6.34233	+	10.9852i	−0.273692	+	0.474048i
$538$	−21.3693			−0.921297
$539$	13.7808	−	23.8690i	0.593580	−	1.02811i
$540$		0			0
$541$	−27.3693			−1.17670			−0.588349	−	0.808607i	$-0.700222\pi$
$541$	−27.3693			−1.17670			−0.588349	+	0.808607i	$0.700222\pi$
$542$	−6.58854	+	11.4117i	−0.283002	+	0.490174i
$543$	1.43845	+	2.49146i	0.0617297	+	0.106919i
$544$	1.56155	+	2.70469i	0.0669510	+	0.115963i
$545$		0			0
$546$	1.87689	+	0.759413i	0.0803237	+	0.0324999i
$547$	5.61553			0.240103			0.120051	−	0.992768i	$-0.461694\pi$
$547$	5.61553			0.240103			0.120051	+	0.992768i	$0.461694\pi$
$548$	5.90388	+	10.2258i	0.252201	+	0.436826i
$549$	−3.00000	−	5.19615i	−0.128037	−	0.221766i
$550$		0			0
$551$	1.36932			0.0583349
$552$	2.34233	−	4.05703i	0.0996962	−	0.172679i
$553$	−3.24621	+	5.62260i	−0.138043	+	0.239097i
$554$	−1.00000			−0.0424859
$555$		0			0
$556$	−6.28078	−	10.8786i	−0.266364	−	0.461356i
$557$	−4.28078	−	7.41452i	−0.181382	−	0.314163i	0.760969	−	0.648788i	$-0.224724\pi$
$557$	−4.28078	−	7.41452i	−0.181382	−	0.314163i	−0.942352	+	0.334625i	$0.891390\pi$
$558$	6.68466			0.282984
$559$	0.219224	+	1.56557i	0.00927217	+	0.0662165i
$560$		0			0
$561$	6.43845	+	11.1517i	0.271831	+	0.470826i
$562$	8.12311	+	14.0696i	0.342653	+	0.593492i
$563$	−16.4924	+	28.5657i	−0.695073	+	1.20390i	0.275083	+	0.961420i	$0.411295\pi$
$563$	−16.4924	+	28.5657i	−0.695073	+	1.20390i	−0.970156	+	0.242481i	$0.922039\pi$
$564$	7.00000			0.294753
$565$		0			0
$566$	−7.78078	+	13.4767i	−0.327050	+	0.566468i
$567$	0.561553			0.0235830
$568$	−6.56155	+	11.3649i	−0.275317	+	0.476862i
$569$	−13.0885	−	22.6700i	−0.548700	−	0.950377i	−0.998364	−	0.0571787i	$-0.981790\pi$
$569$	−13.0885	−	22.6700i	−0.548700	−	0.950377i	0.449664	−	0.893198i	$-0.351544\pi$
$570$		0			0
$571$	23.6847			0.991172			0.495586	−	0.868559i	$-0.334953\pi$
$571$	23.6847			0.991172			0.495586	+	0.868559i	$0.334953\pi$
$572$	−11.7192	+	9.14657i	−0.490005	+	0.382437i
$573$	−10.8769			−0.454389
$574$	3.43845	+	5.95557i	0.143518	+	0.248580i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	40.7386			1.69597			0.847986	−	0.530019i	$-0.177815\pi$
$577$	40.7386			1.69597			0.847986	+	0.530019i	$0.177815\pi$
$578$	−3.62311	+	6.27540i	−0.150701	+	0.261022i
$579$		0			0
$580$		0			0
$581$	−2.00000	+	3.46410i	−0.0829740	+	0.143715i
$582$	−3.56155	−	6.16879i	−0.147631	−	0.255705i
$583$	17.6501	+	30.5709i	0.730992	+	1.26612i
$584$	9.36932			0.387705
$585$		0			0
$586$	3.93087			0.162383
$587$	−20.1231	−	34.8542i	−0.830569	−	1.43859i	−0.897587	−	0.440837i	$-0.854682\pi$
$587$	−20.1231	−	34.8542i	−0.830569	−	1.43859i	0.0670179	−	0.997752i	$-0.478652\pi$
$588$	−3.34233	−	5.78908i	−0.137835	−	0.238738i
$589$	1.87689	−	3.25088i	0.0773361	−	0.133950i
$590$		0			0
$591$	−6.40388	+	11.0918i	−0.263421	+	0.456258i
$592$	−2.06155	+	3.57071i	−0.0847293	+	0.146755i
$593$	−33.1771			−1.36242			−0.681210	−	0.732088i	$-0.738546\pi$
$593$	−33.1771			−1.36242			−0.681210	+	0.732088i	$0.738546\pi$
$594$	−2.06155	+	3.57071i	−0.0845865	+	0.146508i
$595$		0			0
$596$	1.09612	+	1.89853i	0.0448987	+	0.0777669i
$597$	−2.87689			−0.117743
$598$	−2.34233	−	16.7276i	−0.0957850	−	0.684041i
$599$	−14.0000			−0.572024			−0.286012	−	0.958226i	$-0.592330\pi$
$599$	−14.0000			−0.572024			−0.286012	+	0.958226i	$0.592330\pi$
$600$		0			0
$601$	−14.9924	−	25.9676i	−0.611554	−	1.05924i	−0.990979	−	0.134020i	$-0.957212\pi$
$601$	−14.9924	−	25.9676i	−0.611554	−	1.05924i	0.379425	−	0.925222i	$-0.376122\pi$
$602$	−0.123106	+	0.213225i	−0.00501741	+	0.00869041i
$603$	2.24621			0.0914728
$604$	7.68466	−	13.3102i	0.312684	−	0.541585i
$605$		0			0
$606$	−8.87689			−0.360599
$607$	16.2116	−	28.0794i	0.658010	−	1.13971i	−0.323120	−	0.946358i	$-0.604732\pi$
$607$	16.2116	−	28.0794i	0.658010	−	1.13971i	0.981130	−	0.193349i	$-0.0619351\pi$
$608$	0.280776	+	0.486319i	0.0113870	+	0.0197228i
$609$	0.684658	+	1.18586i	0.0277438	+	0.0480536i
$610$		0			0
$611$	19.8963	−	15.5286i	0.804918	−	0.628219i
$612$	3.12311			0.126244
$613$	9.93845	+	17.2139i	0.401410	+	0.695263i	0.993896	−	0.110318i	$-0.0351869\pi$
$613$	9.93845	+	17.2139i	0.401410	+	0.695263i	−0.592486	+	0.805581i	$0.701854\pi$
$614$	−12.8078	−	22.1837i	−0.516879	−	0.895261i
$615$		0			0
$616$	−2.31534			−0.0932878
$617$	−14.6577	+	25.3878i	−0.590096	+	1.02208i	0.404123	+	0.914704i	$0.367577\pi$
$617$	−14.6577	+	25.3878i	−0.590096	+	1.02208i	−0.994219	+	0.107371i	$0.965757\pi$
$618$	2.28078	−	3.95042i	0.0917463	−	0.158909i
$619$	−20.5616			−0.826439			−0.413219	−	0.910632i	$-0.635596\pi$
$619$	−20.5616			−0.826439			−0.413219	+	0.910632i	$0.635596\pi$
$620$		0			0
$621$	−2.34233	−	4.05703i	−0.0939944	−	0.162803i
$622$	15.3693	+	26.6204i	0.616253	+	1.06738i
$623$	−10.5616			−0.423140
$624$	0.500000	+	3.57071i	0.0200160	+	0.142943i
$625$		0			0
$626$	−15.6847	−	27.1666i	−0.626885	−	1.08580i
$627$	1.15767	+	2.00514i	0.0462329	+	0.0800778i
$628$	6.93845	−	12.0177i	0.276874	−	0.479560i
$629$	12.8769			0.513435
$630$		0			0
$631$	6.87689	−	11.9111i	0.273765	−	0.474175i	−0.696058	−	0.717986i	$-0.745064\pi$
$631$	6.87689	−	11.9111i	0.273765	−	0.474175i	0.969823	+	0.243811i	$0.0783977\pi$
$632$	−11.5616			−0.459894
$633$	−10.9654	+	18.9927i	−0.435837	+	0.754892i
$634$	12.4039	+	21.4842i	0.492621	+	0.853245i
$635$		0			0
$636$	8.56155			0.339488
$637$	−22.3423	−	9.03996i	−0.885235	−	0.358176i
$638$	−10.0540			−0.398041
$639$	6.56155	+	11.3649i	0.259571	+	0.449590i
$640$		0			0
$641$	5.71922	−	9.90599i	0.225896	−	0.391263i	−0.730692	−	0.682707i	$-0.760802\pi$
$641$	5.71922	−	9.90599i	0.225896	−	0.391263i	0.956588	+	0.291444i	$0.0941358\pi$
$642$	−2.00000			−0.0789337
$643$	10.8769	−	18.8393i	0.428943	−	0.742951i	−0.567837	−	0.823141i	$-0.692220\pi$
$643$	10.8769	−	18.8393i	0.428943	−	0.742951i	0.996780	+	0.0801904i	$0.0255528\pi$
$644$	1.31534	−	2.27824i	0.0518317	−	0.0897752i
$645$		0			0
$646$	0.876894	−	1.51883i	0.0345009	−	0.0597574i
$647$	17.5270	+	30.3576i	0.689057	+	1.19348i	0.972143	+	0.234387i	$0.0753084\pi$
$647$	17.5270	+	30.3576i	0.689057	+	1.19348i	−0.283086	+	0.959094i	$0.591358\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	26.5464			1.04204
$650$		0			0
$651$	3.75379			0.147123
$652$	−7.21922	−	12.5041i	−0.282727	−	0.489697i
$653$	−22.2808	−	38.5914i	−0.871914	−	1.51020i	−0.860014	−	0.510270i	$-0.829545\pi$
$653$	−22.2808	−	38.5914i	−0.871914	−	1.51020i	−0.0119002	−	0.999929i	$-0.503788\pi$
$654$	1.87689	−	3.25088i	0.0733924	−	0.127119i
$655$		0			0
$656$	−6.12311	+	10.6055i	−0.239067	+	0.414076i
$657$	4.68466	−	8.11407i	0.182766	−	0.316560i
$658$	3.93087			0.153241
$659$	3.02699	−	5.24290i	0.117915	−	0.204234i	−0.801026	−	0.598629i	$-0.795712\pi$
$659$	3.02699	−	5.24290i	0.117915	−	0.204234i	0.918941	+	0.394395i	$0.129046\pi$
$660$		0			0
$661$	−14.8078	−	25.6478i	−0.575955	−	0.997584i	−0.995937	−	0.0900513i	$-0.971297\pi$
$661$	−14.8078	−	25.6478i	−0.575955	−	0.997584i	0.419982	−	0.907532i	$-0.362036\pi$
$662$	−30.7386			−1.19469
$663$	8.87689	−	6.92820i	0.344750	−	0.269069i
$664$	−7.12311			−0.276430
$665$		0			0
$666$	2.06155	+	3.57071i	0.0798835	+	0.138362i
$667$	5.71165	−	9.89286i	0.221156	−	0.383053i
$668$	−4.36932			−0.169054
$669$	−13.6501	+	23.6427i	−0.527743	+	0.914078i
$670$		0			0
$671$	24.7386			0.955024
$672$	−0.280776	+	0.486319i	−0.0108312	+	0.0187602i
$673$	12.8769	+	22.3034i	0.496368	+	0.859734i	0.999991	−	0.00418904i	$-0.00133342\pi$
$673$	12.8769	+	22.3034i	0.496368	+	0.859734i	−0.503623	+	0.863923i	$0.668000\pi$
$674$	3.00000	+	5.19615i	0.115556	+	0.200148i
$675$		0			0
$676$	9.34233	+	9.03996i	0.359320	+	0.347691i
$677$	37.1231			1.42676			0.713378	−	0.700779i	$-0.247164\pi$
$677$	37.1231			1.42676			0.713378	+	0.700779i	$0.247164\pi$
$678$	4.34233	+	7.52113i	0.166766	+	0.288847i
$679$	−2.00000	−	3.46410i	−0.0767530	−	0.132940i
$680$		0			0
$681$	−20.0000			−0.766402
$682$	−13.7808	+	23.8690i	−0.527693	+	0.913991i
$683$	8.56155	−	14.8290i	0.327599	−	0.567418i	−0.654436	−	0.756117i	$-0.727094\pi$
$683$	8.56155	−	14.8290i	0.327599	−	0.567418i	0.982035	+	0.188700i	$0.0604273\pi$
$684$	0.561553			0.0214715
$685$		0			0
$686$	−3.84233	−	6.65511i	−0.146701	−	0.254093i
$687$	−12.1231	−	20.9978i	−0.462525	−	0.801117i
$688$	−0.438447			−0.0167156
$689$	24.3348	−	18.9927i	0.927080	−	0.723564i
$690$		0			0
$691$	10.2808	+	17.8068i	0.391099	+	0.677404i	0.992595	−	0.121472i	$-0.0387616\pi$
$691$	10.2808	+	17.8068i	0.391099	+	0.677404i	−0.601496	+	0.798876i	$0.705428\pi$
$692$	10.0885	+	17.4739i	0.383509	+	0.664257i
$693$	−1.15767	+	2.00514i	−0.0439763	+	0.0761691i
$694$	0.876894			0.0332865
$695$		0			0
$696$	−1.21922	+	2.11176i	−0.0462146	+	0.0800460i
$697$	38.2462			1.44868
$698$	4.24621	−	7.35465i	0.160721	−	0.278378i
$699$	2.65767	+	4.60322i	0.100522	+	0.174110i
$700$		0			0
$701$	−36.3002			−1.37104			−0.685520	−	0.728054i	$-0.740425\pi$
$701$	−36.3002			−1.37104			−0.685520	+	0.728054i	$0.740425\pi$
$702$	3.34233	+	1.35234i	0.126148	+	0.0510410i
$703$	2.31534			0.0873248
$704$	−2.06155	−	3.57071i	−0.0776977	−	0.134576i
$705$		0			0
$706$	12.9309	−	22.3969i	0.486660	−	0.842919i
$707$	−4.98485			−0.187474
$708$	3.21922	−	5.57586i	0.120986	−	0.209554i
$709$	−17.1231	+	29.6581i	−0.643072	+	1.11383i	0.341672	+	0.939819i	$0.389007\pi$
$709$	−17.1231	+	29.6581i	−0.643072	+	1.11383i	−0.984743	+	0.174013i	$0.944326\pi$
$710$		0			0
$711$	−5.78078	+	10.0126i	−0.216796	+	0.375502i
$712$	−9.40388	−	16.2880i	−0.352425	−	0.610419i
$713$	−15.6577	−	27.1199i	−0.586384	−	1.01565i
$714$	1.75379			0.0656339
$715$		0			0
$716$	−12.6847			−0.474048
$717$	−5.68466	−	9.84612i	−0.212297	−	0.367710i
$718$	6.56155	+	11.3649i	0.244875	+	0.424136i
$719$	−22.4924	+	38.9580i	−0.838826	+	1.45289i	0.0520512	+	0.998644i	$0.483424\pi$
$719$	−22.4924	+	38.9580i	−0.838826	+	1.45289i	−0.890877	+	0.454245i	$0.849909\pi$
$720$		0			0
$721$	1.28078	−	2.21837i	0.0476986	−	0.0826164i
$722$	−9.34233	+	16.1814i	−0.347685	+	0.602209i
$723$	28.1231			1.04591
$724$	−1.43845	+	2.49146i	−0.0534595	+	0.0925945i
$725$		0			0
$726$	−3.00000	−	5.19615i	−0.111340	−	0.192847i
$727$	−38.4233			−1.42504			−0.712521	−	0.701651i	$-0.752446\pi$
$727$	−38.4233			−1.42504			−0.712521	+	0.701651i	$0.752446\pi$
$728$	0.280776	+	2.00514i	0.0104063	+	0.0743156i
$729$	1.00000			0.0370370
$730$		0			0
$731$	0.684658	+	1.18586i	0.0253230	+	0.0438607i
$732$	3.00000	−	5.19615i	0.110883	−	0.192055i
$733$	−20.0691			−0.741270			−0.370635	−	0.928779i	$-0.620860\pi$
$733$	−20.0691			−0.741270			−0.370635	+	0.928779i	$0.620860\pi$
$734$	−6.24621	+	10.8188i	−0.230552	+	0.399328i
$735$		0			0
$736$	4.68466			0.172679
$737$	−4.63068	+	8.02058i	−0.170573	+	0.295442i
$738$	6.12311	+	10.6055i	0.225395	+	0.390395i
$739$	13.7732	+	23.8559i	0.506655	+	0.877553i	0.999970	+	0.00770202i	$0.00245165\pi$
$739$	13.7732	+	23.8559i	0.506655	+	0.877553i	−0.493315	+	0.869851i	$0.664215\pi$
$740$		0			0
$741$	1.59612	−	1.24573i	0.0586349	−	0.0457631i
$742$	4.80776			0.176499
$743$	6.58854	+	11.4117i	0.241710	+	0.418654i	0.961202	−	0.275847i	$-0.0889584\pi$
$743$	6.58854	+	11.4117i	0.241710	+	0.418654i	−0.719491	+	0.694501i	$0.755625\pi$
$744$	3.34233	+	5.78908i	0.122536	+	0.212238i
$745$		0			0
$746$	−25.8078			−0.944889
$747$	−3.56155	+	6.16879i	−0.130310	+	0.225704i
$748$	−6.43845	+	11.1517i	−0.235413	+	0.407747i
$749$	−1.12311			−0.0410374
$750$		0			0
$751$	11.9039	+	20.6181i	0.434379	+	0.752366i	0.997245	−	0.0741820i	$-0.0236346\pi$
$751$	11.9039	+	20.6181i	0.434379	+	0.752366i	−0.562866	+	0.826548i	$0.690301\pi$
$752$	3.50000	+	6.06218i	0.127632	+	0.221065i
$753$	8.12311			0.296022
$754$	1.21922	+	8.70700i	0.0444015	+	0.317090i
$755$		0			0
$756$	0.280776	+	0.486319i	0.0102117	+	0.0176873i
$757$	−14.2116	−	24.6153i	−0.516531	−	0.894658i	−0.999816	−	0.0191948i	$-0.993890\pi$
$757$	−14.2116	−	24.6153i	−0.516531	−	0.894658i	0.483285	−	0.875463i	$-0.339444\pi$
$758$	−8.84233	+	15.3154i	−0.321168	+	0.556279i
$759$	19.3153			0.701102
$760$		0			0
$761$	8.96543	−	15.5286i	0.324997	−	0.562911i	−0.656515	−	0.754313i	$-0.727970\pi$
$761$	8.96543	−	15.5286i	0.324997	−	0.562911i	0.981512	+	0.191402i	$0.0613035\pi$
$762$	8.56155			0.310152
$763$	1.05398	−	1.82554i	0.0381565	−	0.0660889i
$764$	−5.43845	−	9.41967i	−0.196756	−	0.340792i
$765$		0			0
$766$	0.192236			0.00694577
$767$	−3.21922	−	22.9899i	−0.116239	−	0.830116i
$768$	−1.00000			−0.0360844
$769$	16.6577	+	28.8519i	0.600691	+	1.04043i	0.992717	+	0.120473i	$0.0384411\pi$
$769$	16.6577	+	28.8519i	0.600691	+	1.04043i	−0.392026	+	0.919954i	$0.628226\pi$
$770$		0			0
$771$	2.78078	−	4.81645i	0.100147	−	0.173460i
$772$		0			0
$773$	12.0885	−	20.9380i	0.434795	−	0.753086i	−0.562484	−	0.826808i	$-0.690154\pi$
$773$	12.0885	−	20.9380i	0.434795	−	0.753086i	0.997279	+	0.0737217i	$0.0234876\pi$
$774$	−0.219224	+	0.379706i	−0.00787983	+	0.0136483i
$775$		0			0
$776$	3.56155	−	6.16879i	0.127852	−	0.221447i
$777$	1.15767	+	2.00514i	0.0415312	+	0.0719342i
$778$	−9.02699	−	15.6352i	−0.323633	−	0.560549i
$779$	6.87689			0.246390
$780$		0			0
$781$	−54.1080			−1.93613
$782$	−7.31534	−	12.6705i	−0.261596	−	0.453098i
$783$	1.21922	+	2.11176i	0.0435715	+	0.0754680i
$784$	3.34233	−	5.78908i	0.119369	−	0.206753i
$785$		0			0
$786$	1.06155	−	1.83866i	0.0378643	−	0.0655830i
$787$	15.6577	−	27.1199i	0.558136	−	0.966719i	−0.439516	−	0.898235i	$-0.644850\pi$
$787$	15.6577	−	27.1199i	0.558136	−	0.966719i	0.997652	−	0.0684848i	$-0.0218165\pi$
$788$	−12.8078			−0.456258
$789$	6.50000	−	11.2583i	0.231406	−	0.400807i
$790$		0			0
$791$	2.43845	+	4.22351i	0.0867012	+	0.150171i
$792$	−4.12311			−0.146508
$793$	−3.00000	−	21.4243i	−0.106533	−	0.760799i
$794$	−20.1231			−0.714142
$795$		0			0
$796$	−1.43845	−	2.49146i	−0.0509844	−	0.0883076i
$797$	6.56155	−	11.3649i	0.232422	−	0.402567i	−0.726098	−	0.687591i	$-0.758668\pi$
$797$	6.56155	−	11.3649i	0.232422	−	0.402567i	0.958520	+	0.285024i	$0.0920016\pi$
$798$	0.315342			0.0111630
$799$	10.9309	−	18.9328i	0.386706	−	0.669795i
$800$		0			0
$801$	−18.8078			−0.664540
$802$	0.157671	−	0.273094i	0.00556755	−	0.00964328i
$803$	19.3153	+	33.4552i	0.681624	+	1.18061i
$804$	1.12311	+	1.94528i	0.0396089	+	0.0686046i
$805$		0			0
$806$	22.3423	+	9.03996i	0.786975	+	0.318419i
$807$	−21.3693			−0.752236
$808$	−4.43845	−	7.68762i	−0.156144	−	0.270449i
$809$	7.24621	+	12.5508i	0.254763	+	0.441263i	0.964831	−	0.262870i	$-0.0846691\pi$
$809$	7.24621	+	12.5508i	0.254763	+	0.441263i	−0.710068	+	0.704133i	$0.751336\pi$
$810$		0			0
$811$	47.5464			1.66958			0.834790	−	0.550569i	$-0.185589\pi$
$811$	47.5464			1.66958			0.834790	+	0.550569i	$0.185589\pi$
$812$	−0.684658	+	1.18586i	−0.0240268	+	0.0416156i
$813$	−6.58854	+	11.4117i	−0.231070	+	0.400225i
$814$	−17.0000			−0.595850
$815$		0			0
$816$	1.56155	+	2.70469i	0.0546653	+	0.0946830i
$817$	0.123106	+	0.213225i	0.00430692	+	0.00745981i
$818$	18.8078			0.657598
$819$	1.87689	+	0.759413i	0.0655840	+	0.0265360i
$820$		0			0
$821$	4.21922	+	7.30791i	0.147252	+	0.255048i	0.930211	−	0.367026i	$-0.119624\pi$
$821$	4.21922	+	7.30791i	0.147252	+	0.255048i	−0.782959	+	0.622073i	$0.786291\pi$
$822$	5.90388	+	10.2258i	0.205922	+	0.356667i
$823$	2.52699	−	4.37687i	0.0880853	−	0.152568i	−0.818616	−	0.574341i	$-0.805259\pi$
$823$	2.52699	−	4.37687i	0.0880853	−	0.152568i	0.906702	+	0.421772i	$0.138592\pi$
$824$	4.56155			0.158909
$825$		0			0
$826$	1.80776	−	3.13114i	0.0629002	−	0.108946i
$827$	28.2462			0.982217			0.491109	−	0.871098i	$-0.336592\pi$
$827$	28.2462			0.982217			0.491109	+	0.871098i	$0.336592\pi$
$828$	2.34233	−	4.05703i	0.0814016	−	0.140992i
$829$	−6.19224	−	10.7253i	−0.215065	−	0.372504i	0.738228	−	0.674552i	$-0.235663\pi$
$829$	−6.19224	−	10.7253i	−0.215065	−	0.372504i	−0.953293	+	0.302048i	$0.902330\pi$
$830$		0			0
$831$	−1.00000			−0.0346896
$832$	−2.84233	+	2.21837i	−0.0985400	+	0.0769081i
$833$	−20.8769			−0.723342
$834$	−6.28078	−	10.8786i	−0.217486	−	0.376696i
$835$		0			0
$836$	−1.15767	+	2.00514i	−0.0400389	+	0.0693494i
$837$	6.68466			0.231056
$838$	16.2462	−	28.1393i	0.561216	−	0.972055i
$839$	−18.3693	+	31.8166i	−0.634179	+	1.09843i	0.352509	+	0.935808i	$0.385329\pi$
$839$	−18.3693	+	31.8166i	−0.634179	+	1.09843i	−0.986688	+	0.162622i	$0.948005\pi$
$840$		0			0
$841$	11.5270	−	19.9653i	0.397482	−	0.688460i
$842$	−16.2462	−	28.1393i	−0.559881	−	0.969743i
$843$	8.12311	+	14.0696i	0.279775	+	0.484584i
$844$	−21.9309			−0.754892
$845$		0			0
$846$	7.00000			0.240665
$847$	−1.68466	−	2.91791i	−0.0578855	−	0.100261i
$848$	4.28078	+	7.41452i	0.147002	+	0.254616i
$849$	−7.78078	+	13.4767i	−0.267036	+	0.462519i
$850$		0			0
$851$	9.65767	−	16.7276i	0.331061	−	0.573414i
$852$	−6.56155	+	11.3649i	−0.224795	+	0.389357i
$853$	−2.30019			−0.0787569			−0.0393784	−	0.999224i	$-0.512538\pi$
$853$	−2.30019			−0.0787569			−0.0393784	+	0.999224i	$0.512538\pi$
$854$	1.68466	−	2.91791i	0.0576478	−	0.0998490i
$855$		0			0
$856$	−1.00000	−	1.73205i	−0.0341793	−	0.0592003i
$857$	6.19224			0.211523			0.105761	−	0.994392i	$-0.466272\pi$
$857$	6.19224			0.211523			0.105761	+	0.994392i	$0.466272\pi$
$858$	−11.7192	+	9.14657i	−0.400088	+	0.312259i
$859$	39.7926			1.35771			0.678853	−	0.734274i	$-0.262477\pi$
$859$	39.7926			1.35771			0.678853	+	0.734274i	$0.262477\pi$
$860$		0			0
$861$	3.43845	+	5.95557i	0.117182	+	0.202965i
$862$	−11.3693	+	19.6922i	−0.387240	+	0.670720i
$863$	−2.43845			−0.0830057			−0.0415029	−	0.999138i	$-0.513215\pi$
$863$	−2.43845			−0.0830057			−0.0415029	+	0.999138i	$0.513215\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$		0			0
$866$	−18.7386			−0.636765
$867$	−3.62311	+	6.27540i	−0.123047	+	0.213124i
$868$	1.87689	+	3.25088i	0.0637059	+	0.110342i
$869$	−23.8348	−	41.2830i	−0.808539	−	1.40043i
$870$		0			0
$871$	7.50758	+	3.03765i	0.254385	+	0.102927i
$872$	3.75379			0.127119
$873$	−3.56155	−	6.16879i	−0.120540	−	0.208782i
$874$	−1.31534	−	2.27824i	−0.0444921	−	0.0770626i
$875$		0			0
$876$	9.36932			0.316560
$877$	4.21922	−	7.30791i	0.142473	−	0.246771i	−0.785954	−	0.618285i	$-0.787828\pi$
$877$	4.21922	−	7.30791i	0.142473	−	0.246771i	0.928427	+	0.371514i	$0.121161\pi$
$878$	12.5616	−	21.7572i	0.423932	−	0.734272i
$879$	3.93087			0.132585
$880$		0			0
$881$	12.2808	+	21.2709i	0.413750	+	0.716636i	0.995296	−	0.0968774i	$-0.0308855\pi$
$881$	12.2808	+	21.2709i	0.413750	+	0.716636i	−0.581546	+	0.813513i	$0.697552\pi$
$882$	−3.34233	−	5.78908i	−0.112542	−	0.194929i
$883$	19.1771			0.645360			0.322680	−	0.946508i	$-0.395416\pi$
$883$	19.1771			0.645360			0.322680	+	0.946508i	$0.395416\pi$
$884$	10.4384	+	4.22351i	0.351083	+	0.142052i
$885$		0			0
$886$	6.56155	+	11.3649i	0.220440	+	0.381813i
$887$	−16.5540	−	28.6723i	−0.555828	−	0.962722i	−0.997839	−	0.0657126i	$-0.979068\pi$
$887$	−16.5540	−	28.6723i	−0.555828	−	0.962722i	0.442010	−	0.897010i	$-0.354265\pi$
$888$	−2.06155	+	3.57071i	−0.0691812	+	0.119825i
$889$	4.80776			0.161247
$890$		0			0
$891$	−2.06155	+	3.57071i	−0.0690646	+	0.119623i
$892$	−27.3002			−0.914078
$893$	1.96543	−	3.40423i	0.0657708	−	0.113918i
$894$	1.09612	+	1.89853i	0.0366597	+	0.0634964i
$895$		0			0
$896$	−0.561553			−0.0187602
$897$	−2.34233	−	16.7276i	−0.0782081	−	0.558518i
$898$	20.1771			0.673318
$899$	8.15009	+	14.1164i	0.271821	+	0.470807i
$900$		0			0
$901$	13.3693	−	23.1563i	0.445397	−	0.771449i
$902$	−50.4924			−1.68121
$903$	−0.123106	+	0.213225i	−0.00409670	+	0.00709569i
$904$	−4.34233	+	7.52113i	−0.144424	+	0.250149i
$905$		0			0
$906$	7.68466	−	13.3102i	0.255306	−	0.442202i
$907$	−26.9579	−	46.6924i	−0.895121	−	1.55039i	−0.833655	−	0.552286i	$-0.813756\pi$
$907$	−26.9579	−	46.6924i	−0.895121	−	1.55039i	−0.0614661	−	0.998109i	$-0.519578\pi$
$908$	−10.0000	−	17.3205i	−0.331862	−	0.574801i
$909$	−8.87689			−0.294428
$910$		0			0
$911$	−18.6307			−0.617262			−0.308631	−	0.951182i	$-0.599871\pi$
$911$	−18.6307			−0.617262			−0.308631	+	0.951182i	$0.599871\pi$
$912$	0.280776	+	0.486319i	0.00929744	+	0.0161036i
$913$	−14.6847	−	25.4346i	−0.485991	−	0.841762i
$914$	−10.1231	+	17.5337i	−0.334843	+	0.579964i
$915$		0			0
$916$	12.1231	−	20.9978i	0.400559	−	0.693788i
$917$	0.596118	−	1.03251i	0.0196855	−	0.0340964i
$918$	3.12311			0.103078
$919$	−8.31534	+	14.4026i	−0.274298	+	0.475098i	−0.969958	−	0.243274i	$-0.921779\pi$
$919$	−8.31534	+	14.4026i	−0.274298	+	0.475098i	0.695660	+	0.718371i	$0.255112\pi$
$920$		0			0
$921$	−12.8078	−	22.1837i	−0.422030	−	0.730978i
$922$	30.0540			0.989775
$923$	6.56155	+	46.8589i	0.215976	+	1.54238i
$924$	−2.31534			−0.0761691
$925$		0			0
$926$	3.80776	+	6.59524i	0.125131	+	0.216733i
$927$	2.28078	−	3.95042i	0.0749105	−	0.129749i
$928$	−2.43845			−0.0800460
$929$	12.5616	−	21.7572i	0.412131	−	0.713832i	−0.582991	−	0.812478i	$-0.698118\pi$
$929$	12.5616	−	21.7572i	0.412131	−	0.713832i	0.995123	+	0.0986462i	$0.0314512\pi$
$930$		0			0
$931$	−3.75379			−0.123025
$932$	−2.65767	+	4.60322i	−0.0870549	+	0.150784i
$933$	15.3693	+	26.6204i	0.503169	+	0.871514i
$934$	8.93087	+	15.4687i	0.292227	+	0.506152i
$935$		0			0
$936$	0.500000	+	3.57071i	0.0163430	+	0.116712i
$937$	−53.2311			−1.73898			−0.869491	−	0.493948i	$-0.835553\pi$
$937$	−53.2311			−1.73898			−0.869491	+	0.493948i	$0.835553\pi$
$938$	0.630683	+	1.09238i	0.0205925	+	0.0356673i
$939$	−15.6847	−	27.1666i	−0.511849	−	0.886549i
$940$		0			0
$941$	−25.3693			−0.827016			−0.413508	−	0.910500i	$-0.635697\pi$
$941$	−25.3693			−0.827016			−0.413508	+	0.910500i	$0.635697\pi$
$942$	6.93845	−	12.0177i	0.226067	−	0.391559i
$943$	28.6847	−	49.6833i	0.934101	−	1.61791i
$944$	6.43845			0.209554
$945$		0			0
$946$	−0.903882	−	1.56557i	−0.0293877	−	0.0509011i
$947$	−21.9309	−	37.9854i	−0.712658	−	1.23436i	−0.963856	−	0.266423i	$-0.914158\pi$
$947$	−21.9309	−	37.9854i	−0.712658	−	1.23436i	0.251199	−	0.967936i	$-0.419175\pi$
$948$	−11.5616			−0.375502
$949$	26.6307	−	20.7846i	0.864469	−	0.674697i
$950$		0			0
$951$	12.4039	+	21.4842i	0.402223	+	0.696671i
$952$	0.876894	+	1.51883i	0.0284203	+	0.0492254i
$953$	25.5885	−	44.3207i	0.828894	−	1.43569i	−0.0700123	−	0.997546i	$-0.522304\pi$
$953$	25.5885	−	44.3207i	0.828894	−	1.43569i	0.898906	−	0.438141i	$-0.144363\pi$
$954$	8.56155			0.277191
$955$		0			0
$956$	5.68466	−	9.84612i	0.183855	−	0.318446i
$957$	−10.0540			−0.324999
$958$	−19.1231	+	33.1222i	−0.617839	+	1.07013i
$959$	3.31534	+	5.74234i	0.107058	+	0.185430i
$960$		0			0
$961$	13.6847			0.441441
$962$	2.06155	+	14.7224i	0.0664671	+	0.474670i
$963$	−2.00000			−0.0644491
$964$	14.0616	+	24.3553i	0.452892	+	0.784432i
$965$		0			0
$966$	1.31534	−	2.27824i	0.0423204	−	0.0733011i
$967$	−15.6847			−0.504385			−0.252192	−	0.967677i	$-0.581152\pi$
$967$	−15.6847			−0.504385			−0.252192	+	0.967677i	$0.581152\pi$
$968$	3.00000	−	5.19615i	0.0964237	−	0.167011i
$969$	0.876894	−	1.51883i	0.0281699	−	0.0487917i
$970$		0			0
$971$	2.15767	−	3.73720i	0.0692430	−	0.119932i	−0.829325	−	0.558766i	$-0.811275\pi$
$971$	2.15767	−	3.73720i	0.0692430	−	0.119932i	0.898568	+	0.438834i	$0.144608\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−3.52699	−	6.10892i	−0.113070	−	0.195843i
$974$	13.0540			0.418276
$975$		0			0
$976$	6.00000			0.192055
$977$	−24.1501	−	41.8292i	−0.772630	−	1.33823i	−0.936117	−	0.351689i	$-0.885608\pi$
$977$	−24.1501	−	41.8292i	−0.772630	−	1.33823i	0.163487	−	0.986545i	$-0.447726\pi$
$978$	−7.21922	−	12.5041i	−0.230845	−	0.399836i
$979$	38.7732	−	67.1572i	1.23920	−	2.14635i
$980$		0			0
$981$	1.87689	−	3.25088i	0.0599246	−	0.103792i
$982$	−8.71922	+	15.1021i	−0.278242	+	0.481929i
$983$	−32.1231			−1.02457			−0.512284	−	0.858816i	$-0.671200\pi$
$983$	−32.1231			−1.02457			−0.512284	+	0.858816i	$0.671200\pi$
$984$	−6.12311	+	10.6055i	−0.195197	+	0.338092i
$985$		0			0
$986$	3.80776	+	6.59524i	0.121264	+	0.210035i
$987$	3.93087			0.125121
$988$	1.87689	+	0.759413i	0.0597120	+	0.0241601i
$989$	2.05398			0.0653126
$990$		0			0
$991$	−24.7116	−	42.8018i	−0.784991	−	1.35964i	−0.929004	−	0.370069i	$-0.879334\pi$
$991$	−24.7116	−	42.8018i	−0.784991	−	1.35964i	0.144013	−	0.989576i	$-0.453999\pi$
$992$	−3.34233	+	5.78908i	−0.106119	+	0.183804i
$993$	−30.7386			−0.975461
$994$	−3.68466	+	6.38202i	−0.116870	+	0.202425i
$995$		0			0
$996$	−7.12311			−0.225704
$997$	−18.7732	+	32.5161i	−0.594553	+	1.02980i	0.399057	+	0.916926i	$0.369338\pi$
$997$	−18.7732	+	32.5161i	−0.594553	+	1.02980i	−0.993610	+	0.112870i	$0.963996\pi$
$998$	2.00000	+	3.46410i	0.0633089	+	0.109654i
$999$	2.06155	+	3.57071i	0.0652246	+	0.112972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.i.bi.601.1		4
5.2	odd	4		1950.2.z.n.1849.1		8
5.3	odd	4		1950.2.z.n.1849.4		8
5.4	even	2		390.2.i.g.211.2	yes	4
13.9	even	3	inner	1950.2.i.bi.451.1		4
15.14	odd	2		1170.2.i.o.991.2		4
65.9	even	6		390.2.i.g.61.2	✓	4
65.22	odd	12		1950.2.z.n.1699.4		8
65.24	odd	12		5070.2.b.r.1351.4		4
65.29	even	6		5070.2.a.bi.1.1		2
65.48	odd	12		1950.2.z.n.1699.1		8
65.49	even	6		5070.2.a.bb.1.2		2
65.54	odd	12		5070.2.b.r.1351.1		4
195.74	odd	6		1170.2.i.o.451.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.g.61.2	✓	4	65.9	even	6
390.2.i.g.211.2	yes	4	5.4	even	2
1170.2.i.o.451.2		4	195.74	odd	6
1170.2.i.o.991.2		4	15.14	odd	2
1950.2.i.bi.451.1		4	13.9	even	3	inner
1950.2.i.bi.601.1		4	1.1	even	1	trivial
1950.2.z.n.1699.1		8	65.48	odd	12
1950.2.z.n.1699.4		8	65.22	odd	12
1950.2.z.n.1849.1		8	5.2	odd	4
1950.2.z.n.1849.4		8	5.3	odd	4
5070.2.a.bb.1.2		2	65.49	even	6
5070.2.a.bi.1.1		2	65.29	even	6
5070.2.b.r.1351.1		4	65.54	odd	12
5070.2.b.r.1351.4		4	65.24	odd	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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.280776 + 0.486319i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.280776 + 0.486319i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.06155 - 3.57071i) q^{11} -1.00000 q^{12} +(-2.84233 + 2.21837i) q^{13} -0.561553 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.56155 + 2.70469i) q^{17} -1.00000 q^{18} +(-0.280776 + 0.486319i) q^{19} -0.561553 q^{21} +(2.06155 - 3.57071i) q^{22} +(2.34233 + 4.05703i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.34233 - 1.35234i) q^{26} -1.00000 q^{27} +(-0.280776 - 0.486319i) q^{28} +(-1.21922 - 2.11176i) q^{29} -6.68466 q^{31} +(0.500000 - 0.866025i) q^{32} +(2.06155 - 3.57071i) q^{33} -3.12311 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-2.06155 - 3.57071i) q^{37} -0.561553 q^{38} +(-3.34233 - 1.35234i) q^{39} +(-6.12311 - 10.6055i) q^{41} +(-0.280776 - 0.486319i) q^{42} +(0.219224 - 0.379706i) q^{43} +4.12311 q^{44} +(-2.34233 + 4.05703i) q^{46} -7.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(3.34233 + 5.78908i) q^{49} -3.12311 q^{51} +(-0.500000 - 3.57071i) q^{52} -8.56155 q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.280776 - 0.486319i) q^{56} -0.561553 q^{57} +(1.21922 - 2.11176i) q^{58} +(-3.21922 + 5.57586i) q^{59} +(-3.00000 + 5.19615i) q^{61} +(-3.34233 - 5.78908i) q^{62} +(-0.280776 - 0.486319i) q^{63} +1.00000 q^{64} +4.12311 q^{66} +(-1.12311 - 1.94528i) q^{67} +(-1.56155 - 2.70469i) q^{68} +(-2.34233 + 4.05703i) q^{69} +(6.56155 - 11.3649i) q^{71} +(0.500000 - 0.866025i) q^{72} -9.36932 q^{73} +(2.06155 - 3.57071i) q^{74} +(-0.280776 - 0.486319i) q^{76} +2.31534 q^{77} +(-0.500000 - 3.57071i) q^{78} +11.5616 q^{79} +(-0.500000 - 0.866025i) q^{81} +(6.12311 - 10.6055i) q^{82} +7.12311 q^{83} +(0.280776 - 0.486319i) q^{84} +0.438447 q^{86} +(1.21922 - 2.11176i) q^{87} +(2.06155 + 3.57071i) q^{88} +(9.40388 + 16.2880i) q^{89} +(-0.280776 - 2.00514i) q^{91} -4.68466 q^{92} +(-3.34233 - 5.78908i) q^{93} +(-3.50000 - 6.06218i) q^{94} +1.00000 q^{96} +(-3.56155 + 6.16879i) q^{97} +(-3.34233 + 5.78908i) q^{98} +4.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} + 3 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 + 3 * q^7 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} + 3 q^{7} - 4 q^{8} - 2 q^{9} - 4 q^{12} + q^{13} + 6 q^{14} - 2 q^{16} + 2 q^{17} - 4 q^{18} + 3 q^{19} + 6 q^{21} - 3 q^{23} - 2 q^{24} - q^{26} - 4 q^{27} + 3 q^{28} - 9 q^{29} - 2 q^{31} + 2 q^{32} + 4 q^{34} - 2 q^{36} + 6 q^{38} - q^{39} - 8 q^{41} + 3 q^{42} + 5 q^{43} + 3 q^{46} - 28 q^{47} + 2 q^{48} + q^{49} + 4 q^{51} - 2 q^{52} - 26 q^{53} - 2 q^{54} - 3 q^{56} + 6 q^{57} + 9 q^{58} - 17 q^{59} - 12 q^{61} - q^{62} + 3 q^{63} + 4 q^{64} + 12 q^{67} + 2 q^{68} + 3 q^{69} + 18 q^{71} + 2 q^{72} + 12 q^{73} + 3 q^{76} + 34 q^{77} - 2 q^{78} + 38 q^{79} - 2 q^{81} + 8 q^{82} + 12 q^{83} - 3 q^{84} + 10 q^{86} + 9 q^{87} + 17 q^{89} + 3 q^{91} + 6 q^{92} - q^{93} - 14 q^{94} + 4 q^{96} - 6 q^{97} - q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 + 3 * q^7 - 4 * q^8 - 2 * q^9 - 4 * q^12 + q^13 + 6 * q^14 - 2 * q^16 + 2 * q^17 - 4 * q^18 + 3 * q^19 + 6 * q^21 - 3 * q^23 - 2 * q^24 - q^26 - 4 * q^27 + 3 * q^28 - 9 * q^29 - 2 * q^31 + 2 * q^32 + 4 * q^34 - 2 * q^36 + 6 * q^38 - q^39 - 8 * q^41 + 3 * q^42 + 5 * q^43 + 3 * q^46 - 28 * q^47 + 2 * q^48 + q^49 + 4 * q^51 - 2 * q^52 - 26 * q^53 - 2 * q^54 - 3 * q^56 + 6 * q^57 + 9 * q^58 - 17 * q^59 - 12 * q^61 - q^62 + 3 * q^63 + 4 * q^64 + 12 * q^67 + 2 * q^68 + 3 * q^69 + 18 * q^71 + 2 * q^72 + 12 * q^73 + 3 * q^76 + 34 * q^77 - 2 * q^78 + 38 * q^79 - 2 * q^81 + 8 * q^82 + 12 * q^83 - 3 * q^84 + 10 * q^86 + 9 * q^87 + 17 * q^89 + 3 * q^91 + 6 * q^92 - q^93 - 14 * q^94 + 4 * q^96 - 6 * q^97 - q^98

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