LMFDB - Embedded newform 931.2.f.j.704.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(324,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("931.324");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.f (of order $3$, 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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 133)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			704.2
Root			$0.809017 + 1.40126i$ of defining polynomial
Character	$\chi$	$=$	931.704
Dual form			931.2.f.j.324.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30902 + 2.26728i) q^{2} +(-1.30902 + 2.26728i) q^{3} +(-2.42705 + 4.20378i) q^{4} +(1.11803 + 1.93649i) q^{5} -6.85410 q^{6} -7.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +O(q^{10})$	\(q+(1.30902 + 2.26728i) q^{2} +(-1.30902 + 2.26728i) q^{3} +(-2.42705 + 4.20378i) q^{4} +(1.11803 + 1.93649i) q^{5} -6.85410 q^{6} -7.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +(-2.92705 + 5.06980i) q^{10} +(2.80902 - 4.86536i) q^{11} +(-6.35410 - 11.0056i) q^{12} -1.00000 q^{13} -5.85410 q^{15} +(-4.92705 - 8.53390i) q^{16} +(-2.42705 + 4.20378i) q^{17} +(5.04508 - 8.73834i) q^{18} +(-0.500000 - 0.866025i) q^{19} -10.8541 q^{20} +14.7082 q^{22} +(1.50000 + 2.59808i) q^{23} +(9.78115 - 16.9415i) q^{24} +(-1.30902 - 2.26728i) q^{26} +2.23607 q^{27} -5.61803 q^{29} +(-7.66312 - 13.2729i) q^{30} +(-0.427051 + 0.739674i) q^{31} +(5.42705 - 9.39993i) q^{32} +(7.35410 + 12.7377i) q^{33} -12.7082 q^{34} +18.7082 q^{36} +(5.35410 + 9.27358i) q^{37} +(1.30902 - 2.26728i) q^{38} +(1.30902 - 2.26728i) q^{39} +(-8.35410 - 14.4697i) q^{40} -0.381966 q^{41} -2.00000 q^{43} +(13.6353 + 23.6170i) q^{44} +(4.30902 - 7.46344i) q^{45} +(-3.92705 + 6.80185i) q^{46} +(5.59017 + 9.68246i) q^{47} +25.7984 q^{48} +(-6.35410 - 11.0056i) q^{51} +(2.42705 - 4.20378i) q^{52} +(-0.545085 + 0.944115i) q^{53} +(2.92705 + 5.06980i) q^{54} +12.5623 q^{55} +2.61803 q^{57} +(-7.35410 - 12.7377i) q^{58} +(0.354102 - 0.613323i) q^{59} +(14.2082 - 24.6093i) q^{60} +(-3.35410 - 5.80948i) q^{61} -2.23607 q^{62} +8.70820 q^{64} +(-1.11803 - 1.93649i) q^{65} +(-19.2533 + 33.3477i) q^{66} +(-3.28115 + 5.68312i) q^{67} +(-11.7812 - 20.4056i) q^{68} -7.85410 q^{69} +7.47214 q^{71} +(14.3992 + 24.9401i) q^{72} +(2.07295 - 3.59045i) q^{73} +(-14.0172 + 24.2785i) q^{74} +4.85410 q^{76} +6.85410 q^{78} +(5.00000 + 8.66025i) q^{79} +(11.0172 - 19.0824i) q^{80} +(2.85410 - 4.94345i) q^{81} +(-0.500000 - 0.866025i) q^{82} +7.85410 q^{83} -10.8541 q^{85} +(-2.61803 - 4.53457i) q^{86} +(7.35410 - 12.7377i) q^{87} +(-20.9894 + 36.3546i) q^{88} +(1.14590 + 1.98475i) q^{89} +22.5623 q^{90} -14.5623 q^{92} +(-1.11803 - 1.93649i) q^{93} +(-14.6353 + 25.3490i) q^{94} +(1.11803 - 1.93649i) q^{95} +(14.2082 + 24.6093i) q^{96} -14.4164 q^{97} -21.6525 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 14 q^{6} - 12 q^{8} - q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 14 * q^6 - 12 * q^8 - q^9	$ 4 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 14 q^{6} - 12 q^{8} - q^{9} - 5 q^{10} + 9 q^{11} - 12 q^{12} - 4 q^{13} - 10 q^{15} - 13 q^{16} - 3 q^{17} + 9 q^{18} - 2 q^{19} - 30 q^{20} + 32 q^{22} + 6 q^{23} + 19 q^{24} - 3 q^{26} - 18 q^{29} - 15 q^{30} + 5 q^{31} + 15 q^{32} + 16 q^{33} - 24 q^{34} + 48 q^{36} + 8 q^{37} + 3 q^{38} + 3 q^{39} - 20 q^{40} - 6 q^{41} - 8 q^{43} + 21 q^{44} + 15 q^{45} - 9 q^{46} + 54 q^{48} - 12 q^{51} + 3 q^{52} + 9 q^{53} + 5 q^{54} + 10 q^{55} + 6 q^{57} - 16 q^{58} - 12 q^{59} + 30 q^{60} + 8 q^{64} - 39 q^{66} + 7 q^{67} - 27 q^{68} - 18 q^{69} + 12 q^{71} + 33 q^{72} + 15 q^{73} - 27 q^{74} + 6 q^{76} + 14 q^{78} + 20 q^{79} + 15 q^{80} - 2 q^{81} - 2 q^{82} + 18 q^{83} - 30 q^{85} - 6 q^{86} + 16 q^{87} - 37 q^{88} + 18 q^{89} + 50 q^{90} - 18 q^{92} - 25 q^{94} + 30 q^{96} - 4 q^{97} - 24 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 14 * q^6 - 12 * q^8 - q^9 - 5 * q^10 + 9 * q^11 - 12 * q^12 - 4 * q^13 - 10 * q^15 - 13 * q^16 - 3 * q^17 + 9 * q^18 - 2 * q^19 - 30 * q^20 + 32 * q^22 + 6 * q^23 + 19 * q^24 - 3 * q^26 - 18 * q^29 - 15 * q^30 + 5 * q^31 + 15 * q^32 + 16 * q^33 - 24 * q^34 + 48 * q^36 + 8 * q^37 + 3 * q^38 + 3 * q^39 - 20 * q^40 - 6 * q^41 - 8 * q^43 + 21 * q^44 + 15 * q^45 - 9 * q^46 + 54 * q^48 - 12 * q^51 + 3 * q^52 + 9 * q^53 + 5 * q^54 + 10 * q^55 + 6 * q^57 - 16 * q^58 - 12 * q^59 + 30 * q^60 + 8 * q^64 - 39 * q^66 + 7 * q^67 - 27 * q^68 - 18 * q^69 + 12 * q^71 + 33 * q^72 + 15 * q^73 - 27 * q^74 + 6 * q^76 + 14 * q^78 + 20 * q^79 + 15 * q^80 - 2 * q^81 - 2 * q^82 + 18 * q^83 - 30 * q^85 - 6 * q^86 + 16 * q^87 - 37 * q^88 + 18 * q^89 + 50 * q^90 - 18 * q^92 - 25 * q^94 + 30 * q^96 - 4 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.30902	+	2.26728i	0.925615	+	1.60321i	0.790569	+	0.612372i	$0.209785\pi$
$2$	1.30902	+	2.26728i	0.925615	+	1.60321i	0.135045	+	0.990839i	$0.456882\pi$
$3$	−1.30902	+	2.26728i	−0.755761	+	1.30902i	0.189234	+	0.981932i	$0.439400\pi$
$3$	−1.30902	+	2.26728i	−0.755761	+	1.30902i	−0.944995	+	0.327085i	$0.893934\pi$
$4$	−2.42705	+	4.20378i	−1.21353	+	2.10189i
$5$	1.11803	+	1.93649i	0.500000	+	0.866025i	1.00000			$0$
$5$	1.11803	+	1.93649i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$6$	−6.85410			−2.79818
$7$		0			0
$7$		0			0
$8$	−7.47214			−2.64180
$9$	−1.92705	−	3.33775i	−0.642350	−	1.11258i
$10$	−2.92705	+	5.06980i	−0.925615	+	1.60321i
$11$	2.80902	−	4.86536i	0.846950	−	1.46696i	−0.0369660	−	0.999317i	$-0.511769\pi$
$11$	2.80902	−	4.86536i	0.846950	−	1.46696i	0.883917	−	0.467645i	$-0.154897\pi$
$12$	−6.35410	−	11.0056i	−1.83427	−	3.17705i
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$		0			0
$15$	−5.85410			−1.51152
$16$	−4.92705	−	8.53390i	−1.23176	−	2.13348i
$17$	−2.42705	+	4.20378i	−0.588646	+	1.01957i	0.405764	+	0.913978i	$0.367006\pi$
$17$	−2.42705	+	4.20378i	−0.588646	+	1.01957i	−0.994410	+	0.105587i	$0.966328\pi$
$18$	5.04508	−	8.73834i	1.18914	−	2.05965i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$20$	−10.8541			−2.42705
$21$		0			0
$22$	14.7082			3.13580
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$	9.78115	−	16.9415i	1.99657	−	3.45816i
$25$		0			0
$26$	−1.30902	−	2.26728i	−0.256719	−	0.444651i
$27$	2.23607			0.430331
$28$		0			0
$29$	−5.61803			−1.04324			−0.521621	−	0.853177i	$-0.674673\pi$
$29$	−5.61803			−1.04324			−0.521621	+	0.853177i	$0.674673\pi$
$30$	−7.66312	−	13.2729i	−1.39909	−	2.42329i
$31$	−0.427051	+	0.739674i	−0.0767006	+	0.132849i	−0.901825	−	0.432102i	$-0.857772\pi$
$31$	−0.427051	+	0.739674i	−0.0767006	+	0.132849i	0.825124	+	0.564952i	$0.191105\pi$
$32$	5.42705	−	9.39993i	0.959376	−	1.66169i
$33$	7.35410	+	12.7377i	1.28018	+	2.21735i
$34$	−12.7082			−2.17944
$35$		0			0
$36$	18.7082			3.11803
$37$	5.35410	+	9.27358i	0.880209	+	1.52457i	0.851108	+	0.524990i	$0.175931\pi$
$37$	5.35410	+	9.27358i	0.880209	+	1.52457i	0.0291006	+	0.999576i	$0.490736\pi$
$38$	1.30902	−	2.26728i	0.212351	−	0.367802i
$39$	1.30902	−	2.26728i	0.209610	−	0.363056i
$40$	−8.35410	−	14.4697i	−1.32090	−	2.28787i
$41$	−0.381966			−0.0596531			−0.0298265	−	0.999555i	$-0.509495\pi$
$41$	−0.381966			−0.0596531			−0.0298265	+	0.999555i	$0.509495\pi$
$42$		0			0
$43$	−2.00000			−0.304997			−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000			−0.304997			−0.152499	+	0.988304i	$0.548732\pi$
$44$	13.6353	+	23.6170i	2.05559	+	3.56039i
$45$	4.30902	−	7.46344i	0.642350	−	1.11258i
$46$	−3.92705	+	6.80185i	−0.579012	+	1.00288i
$47$	5.59017	+	9.68246i	0.815410	+	1.41233i	0.909033	+	0.416724i	$0.136822\pi$
$47$	5.59017	+	9.68246i	0.815410	+	1.41233i	−0.0936230	+	0.995608i	$0.529845\pi$
$48$	25.7984			3.72367
$49$		0			0
$50$		0			0
$51$	−6.35410	−	11.0056i	−0.889752	−	1.54110i
$52$	2.42705	−	4.20378i	0.336571	−	0.582959i
$53$	−0.545085	+	0.944115i	−0.0748732	+	0.129684i	−0.901031	−	0.433754i	$-0.857189\pi$
$53$	−0.545085	+	0.944115i	−0.0748732	+	0.129684i	0.826158	+	0.563439i	$0.190522\pi$
$54$	2.92705	+	5.06980i	0.398321	+	0.689913i
$55$	12.5623			1.69390
$56$		0			0
$57$	2.61803			0.346767
$58$	−7.35410	−	12.7377i	−0.965641	−	1.67254i
$59$	0.354102	−	0.613323i	0.0461001	−	0.0798478i	−0.842055	−	0.539392i	$-0.818654\pi$
$59$	0.354102	−	0.613323i	0.0461001	−	0.0798478i	0.888155	+	0.459545i	$0.151987\pi$
$60$	14.2082	−	24.6093i	1.83427	−	3.17705i
$61$	−3.35410	−	5.80948i	−0.429449	−	0.743827i	0.567376	−	0.823459i	$-0.307959\pi$
$61$	−3.35410	−	5.80948i	−0.429449	−	0.743827i	−0.996824	+	0.0796321i	$0.974625\pi$
$62$	−2.23607			−0.283981
$63$		0			0
$64$	8.70820			1.08853
$65$	−1.11803	−	1.93649i	−0.138675	−	0.240192i
$66$	−19.2533	+	33.3477i	−2.36992	+	4.10481i
$67$	−3.28115	+	5.68312i	−0.400857	+	0.694304i	−0.993830	−	0.110918i	$-0.964621\pi$
$67$	−3.28115	+	5.68312i	−0.400857	+	0.694304i	0.592973	+	0.805222i	$0.297954\pi$
$68$	−11.7812	−	20.4056i	−1.42867	−	2.47454i
$69$	−7.85410			−0.945523
$70$		0			0
$71$	7.47214			0.886779			0.443390	−	0.896329i	$-0.353776\pi$
$71$	7.47214			0.886779			0.443390	+	0.896329i	$0.353776\pi$
$72$	14.3992	+	24.9401i	1.69696	+	2.93922i
$73$	2.07295	−	3.59045i	0.242620	−	0.420231i	−0.718840	−	0.695176i	$-0.755326\pi$
$73$	2.07295	−	3.59045i	0.242620	−	0.420231i	0.961460	+	0.274945i	$0.0886597\pi$
$74$	−14.0172	+	24.2785i	−1.62947	+	2.82232i
$75$		0			0
$76$	4.85410			0.556804
$77$		0			0
$78$	6.85410			0.776074
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$	11.0172	−	19.0824i	1.23176	−	2.13348i
$81$	2.85410	−	4.94345i	0.317122	−	0.549272i
$82$	−0.500000	−	0.866025i	−0.0552158	−	0.0956365i
$83$	7.85410			0.862100			0.431050	−	0.902328i	$-0.358143\pi$
$83$	7.85410			0.862100			0.431050	+	0.902328i	$0.358143\pi$
$84$		0			0
$85$	−10.8541			−1.17729
$86$	−2.61803	−	4.53457i	−0.282310	−	0.488975i
$87$	7.35410	−	12.7377i	0.788442	−	1.36562i
$88$	−20.9894	+	36.3546i	−2.23747	+	3.87542i
$89$	1.14590	+	1.98475i	0.121465	+	0.210383i	0.920346	−	0.391106i	$-0.127907\pi$
$89$	1.14590	+	1.98475i	0.121465	+	0.210383i	−0.798881	+	0.601490i	$0.794574\pi$
$90$	22.5623			2.37828
$91$		0			0
$92$	−14.5623			−1.51823
$93$	−1.11803	−	1.93649i	−0.115935	−	0.200805i
$94$	−14.6353	+	25.3490i	−1.50951	+	2.61455i
$95$	1.11803	−	1.93649i	0.114708	−	0.198680i
$96$	14.2082	+	24.6093i	1.45012	+	2.51168i
$97$	−14.4164			−1.46376			−0.731882	−	0.681431i	$-0.761358\pi$
$97$	−14.4164			−1.46376			−0.731882	+	0.681431i	$0.761358\pi$
$98$		0			0
$99$	−21.6525			−2.17616
$100$		0			0
$101$	6.73607	−	11.6672i	0.670264	−	1.16093i	−0.307565	−	0.951527i	$-0.599514\pi$
$101$	6.73607	−	11.6672i	0.670264	−	1.16093i	0.977829	−	0.209404i	$-0.0671524\pi$
$102$	16.6353	−	28.8131i	1.64714	−	2.85292i
$103$	−2.35410	−	4.07742i	−0.231957	−	0.401761i	0.726427	−	0.687243i	$-0.241179\pi$
$103$	−2.35410	−	4.07742i	−0.231957	−	0.401761i	−0.958384	+	0.285483i	$0.907846\pi$
$104$	7.47214			0.732703
$105$		0			0
$106$	−2.85410			−0.277215
$107$	−0.736068	−	1.27491i	−0.0711584	−	0.123250i	0.828251	−	0.560357i	$-0.189336\pi$
$107$	−0.736068	−	1.27491i	−0.0711584	−	0.123250i	−0.899409	+	0.437108i	$0.856003\pi$
$108$	−5.42705	+	9.39993i	−0.522218	+	0.904508i
$109$	5.20820	−	9.02087i	0.498855	−	0.864043i	−0.501144	−	0.865364i	$-0.667087\pi$
$109$	5.20820	−	9.02087i	0.498855	−	0.864043i	0.999999	+	0.00132109i	$0.000420517\pi$
$110$	16.4443	+	28.4823i	1.56790	+	2.71568i
$111$	−28.0344			−2.66091
$112$		0			0
$113$	−4.14590			−0.390013			−0.195007	−	0.980802i	$-0.562473\pi$
$113$	−4.14590			−0.390013			−0.195007	+	0.980802i	$0.562473\pi$
$114$	3.42705	+	5.93583i	0.320973	+	0.555941i
$115$	−3.35410	+	5.80948i	−0.312772	+	0.541736i
$116$	13.6353	−	23.6170i	1.26600	−	2.19278i
$117$	1.92705	+	3.33775i	0.178156	+	0.308575i
$118$	1.85410			0.170684
$119$		0			0
$120$	43.7426			3.99314
$121$	−10.2812	−	17.8075i	−0.934650	−	1.61886i
$122$	8.78115	−	15.2094i	0.795008	−	1.37699i
$123$	0.500000	−	0.866025i	0.0450835	−	0.0780869i
$124$	−2.07295	−	3.59045i	−0.186156	−	0.322432i
$125$	11.1803			1.00000
$126$		0			0
$127$	6.29180			0.558307			0.279153	−	0.960247i	$-0.409946\pi$
$127$	6.29180			0.558307			0.279153	+	0.960247i	$0.409946\pi$
$128$	0.545085	+	0.944115i	0.0481792	+	0.0834488i
$129$	2.61803	−	4.53457i	0.230505	−	0.399246i
$130$	2.92705	−	5.06980i	0.256719	−	0.444651i
$131$	5.04508	+	8.73834i	0.440791	+	0.763473i	0.997748	−	0.0670685i	$-0.0213646\pi$
$131$	5.04508	+	8.73834i	0.440791	+	0.763473i	−0.556957	+	0.830541i	$0.688031\pi$
$132$	−71.3951			−6.21415
$133$		0			0
$134$	−17.1803			−1.48416
$135$	2.50000	+	4.33013i	0.215166	+	0.372678i
$136$	18.1353	−	31.4112i	1.55509	−	2.69349i
$137$	−8.23607	+	14.2653i	−0.703655	+	1.21877i	0.263520	+	0.964654i	$0.415116\pi$
$137$	−8.23607	+	14.2653i	−0.703655	+	1.21877i	−0.967175	+	0.254112i	$0.918217\pi$
$138$	−10.2812	−	17.8075i	−0.875190	−	1.51587i
$139$	7.29180			0.618482			0.309241	−	0.950984i	$-0.399925\pi$
$139$	7.29180			0.618482			0.309241	+	0.950984i	$0.399925\pi$
$140$		0			0
$141$	−29.2705			−2.46502
$142$	9.78115	+	16.9415i	0.820816	+	1.42170i
$143$	−2.80902	+	4.86536i	−0.234902	+	0.406862i
$144$	−18.9894	+	32.8905i	−1.58245	+	2.74088i
$145$	−6.28115	−	10.8793i	−0.521621	−	0.903475i
$146$	10.8541			0.898292
$147$		0			0
$148$	−51.9787			−4.27262
$149$	7.44427	+	12.8939i	0.609859	+	1.05631i	0.991263	+	0.131898i	$0.0421071\pi$
$149$	7.44427	+	12.8939i	0.609859	+	1.05631i	−0.381405	+	0.924408i	$0.624560\pi$
$150$		0			0
$151$	−0.718847	+	1.24508i	−0.0584989	+	0.101323i	−0.893792	−	0.448482i	$-0.851965\pi$
$151$	−0.718847	+	1.24508i	−0.0584989	+	0.101323i	0.835293	+	0.549805i	$0.185298\pi$
$152$	3.73607	+	6.47106i	0.303035	+	0.524872i
$153$	18.7082			1.51247
$154$		0			0
$155$	−1.90983			−0.153401
$156$	6.35410	+	11.0056i	0.508735	+	0.881155i
$157$	−0.572949	+	0.992377i	−0.0457263	+	0.0792003i	−0.887983	−	0.459877i	$-0.847894\pi$
$157$	−0.572949	+	0.992377i	−0.0457263	+	0.0792003i	0.842256	+	0.539077i	$0.181227\pi$
$158$	−13.0902	+	22.6728i	−1.04140	+	1.80375i
$159$	−1.42705	−	2.47172i	−0.113173	−	0.196021i
$160$	24.2705			1.91875
$161$		0			0
$162$	14.9443			1.17413
$163$	7.92705	+	13.7301i	0.620895	+	1.07542i	0.989319	+	0.145763i	$0.0465638\pi$
$163$	7.92705	+	13.7301i	0.620895	+	1.07542i	−0.368425	+	0.929658i	$0.620103\pi$
$164$	0.927051	−	1.60570i	0.0723905	−	0.125384i
$165$	−16.4443	+	28.4823i	−1.28018	+	2.21735i
$166$	10.2812	+	17.8075i	0.797972	+	1.38213i
$167$	7.47214			0.578211			0.289106	−	0.957297i	$-0.406642\pi$
$167$	7.47214			0.578211			0.289106	+	0.957297i	$0.406642\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$	−14.2082	−	24.6093i	−1.08972	−	1.88745i
$171$	−1.92705	+	3.33775i	−0.147365	+	0.255244i
$172$	4.85410	−	8.40755i	0.370122	−	0.641070i
$173$	−10.0902	−	17.4767i	−0.767141	−	1.32873i	−0.939107	−	0.343625i	$-0.888345\pi$
$173$	−10.0902	−	17.4767i	−0.767141	−	1.32873i	0.171966	−	0.985103i	$-0.444988\pi$
$174$	38.5066			2.91918
$175$		0			0
$176$	−55.3607			−4.17297
$177$	0.927051	+	1.60570i	0.0696814	+	0.120692i
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	5.04508	−	8.73834i	0.377087	−	0.653134i	−0.613550	−	0.789656i	$-0.710259\pi$
$179$	5.04508	−	8.73834i	0.377087	−	0.653134i	0.990637	+	0.136522i	$0.0435923\pi$
$180$	20.9164	+	36.2283i	1.55902	+	2.70030i
$181$	1.43769			0.106863			0.0534315	−	0.998572i	$-0.482984\pi$
$181$	1.43769			0.106863			0.0534315	+	0.998572i	$0.482984\pi$
$182$		0			0
$183$	17.5623			1.29824
$184$	−11.2082	−	19.4132i	−0.826280	−	1.43116i
$185$	−11.9721	+	20.7363i	−0.880209	+	1.52457i
$186$	2.92705	−	5.06980i	0.214622	−	0.371736i
$187$	13.6353	+	23.6170i	0.997109	+	1.72704i
$188$	−54.2705			−3.95808
$189$		0			0
$190$	5.85410			0.424701
$191$	3.16312	+	5.47868i	0.228875	+	0.396424i	0.957475	−	0.288516i	$-0.0931619\pi$
$191$	3.16312	+	5.47868i	0.228875	+	0.396424i	−0.728600	+	0.684940i	$0.759829\pi$
$192$	−11.3992	+	19.7440i	−0.822665	+	1.42490i
$193$	−9.28115	+	16.0754i	−0.668072	+	1.15713i	0.310371	+	0.950616i	$0.399547\pi$
$193$	−9.28115	+	16.0754i	−0.668072	+	1.15713i	−0.978443	+	0.206519i	$0.933786\pi$
$194$	−18.8713	−	32.6861i	−1.35488	−	2.34672i
$195$	5.85410			0.419221
$196$		0			0
$197$	15.2705			1.08798			0.543989	−	0.839092i	$-0.316913\pi$
$197$	15.2705			1.08798			0.543989	+	0.839092i	$0.316913\pi$
$198$	−28.3435	−	49.0923i	−2.01428	−	3.48884i
$199$	8.35410	−	14.4697i	0.592207	−	1.02573i	−0.401728	−	0.915759i	$-0.631590\pi$
$199$	8.35410	−	14.4697i	0.592207	−	1.02573i	0.993935	−	0.109973i	$-0.0350764\pi$
$200$		0			0
$201$	−8.59017	−	14.8786i	−0.605904	−	1.04946i
$202$	35.2705			2.48162
$203$		0			0
$204$	61.6869			4.31895
$205$	−0.427051	−	0.739674i	−0.0298265	−	0.0516611i
$206$	6.16312	−	10.6748i	0.429405	−	0.743751i
$207$	5.78115	−	10.0133i	0.401818	−	0.695969i
$208$	4.92705	+	8.53390i	0.341630	+	0.591720i
$209$	−5.61803			−0.388608
$210$		0			0
$211$	13.5623			0.933668			0.466834	−	0.884345i	$-0.345395\pi$
$211$	13.5623			0.933668			0.466834	+	0.884345i	$0.345395\pi$
$212$	−2.64590	−	4.58283i	−0.181721	−	0.314750i
$213$	−9.78115	+	16.9415i	−0.670194	+	1.16081i
$214$	1.92705	−	3.33775i	0.131730	−	0.228164i
$215$	−2.23607	−	3.87298i	−0.152499	−	0.264135i
$216$	−16.7082			−1.13685
$217$		0			0
$218$	27.2705			1.84699
$219$	5.42705	+	9.39993i	0.366726	+	0.635188i
$220$	−30.4894	+	52.8091i	−2.05559	+	3.56039i
$221$	2.42705	−	4.20378i	0.163261	−	0.282777i
$222$	−36.6976	−	63.5620i	−2.46298	−	4.26600i
$223$	−0.416408			−0.0278847			−0.0139424	−	0.999903i	$-0.504438\pi$
$223$	−0.416408			−0.0278847			−0.0139424	+	0.999903i	$0.504438\pi$
$224$		0			0
$225$		0			0
$226$	−5.42705	−	9.39993i	−0.361002	−	0.625274i
$227$	−9.19098	+	15.9192i	−0.610027	+	1.05660i	0.381208	+	0.924489i	$0.375508\pi$
$227$	−9.19098	+	15.9192i	−0.610027	+	1.05660i	−0.991235	+	0.132109i	$0.957825\pi$
$228$	−6.35410	+	11.0056i	−0.420811	+	0.728865i
$229$	8.70820	+	15.0831i	0.575454	+	0.996716i	0.995992	+	0.0894411i	$0.0285081\pi$
$229$	8.70820	+	15.0831i	0.575454	+	0.996716i	−0.420538	+	0.907275i	$0.638159\pi$
$230$	−17.5623			−1.15802
$231$		0			0
$232$	41.9787			2.75604
$233$	−6.51722	−	11.2882i	−0.426957	−	0.739512i	0.569644	−	0.821892i	$-0.307081\pi$
$233$	−6.51722	−	11.2882i	−0.426957	−	0.739512i	−0.996601	+	0.0823800i	$0.973748\pi$
$234$	−5.04508	+	8.73834i	−0.329808	+	0.571243i
$235$	−12.5000	+	21.6506i	−0.815410	+	1.41233i
$236$	1.71885	+	2.97713i	0.111887	+	0.193795i
$237$	−26.1803			−1.70060
$238$		0			0
$239$	4.52786			0.292883			0.146442	−	0.989219i	$-0.453218\pi$
$239$	4.52786			0.292883			0.146442	+	0.989219i	$0.453218\pi$
$240$	28.8435	+	49.9583i	1.86184	+	3.22480i
$241$	−2.14590	+	3.71680i	−0.138229	+	0.239420i	−0.926826	−	0.375490i	$-0.877474\pi$
$241$	−2.14590	+	3.71680i	−0.138229	+	0.239420i	0.788597	+	0.614910i	$0.210808\pi$
$242$	26.9164	−	46.6206i	1.73025	−	2.99688i
$243$	10.8262	+	18.7516i	0.694503	+	1.20292i
$244$	32.5623			2.08459
$245$		0			0
$246$	2.61803			0.166920
$247$	0.500000	+	0.866025i	0.0318142	+	0.0551039i
$248$	3.19098	−	5.52694i	0.202628	−	0.350961i
$249$	−10.2812	+	17.8075i	−0.651542	+	1.12850i
$250$	14.6353	+	25.3490i	0.925615	+	1.60321i
$251$	−25.7984			−1.62838			−0.814189	−	0.580599i	$-0.802818\pi$
$251$	−25.7984			−1.62838			−0.814189	+	0.580599i	$0.802818\pi$
$252$		0			0
$253$	16.8541			1.05961
$254$	8.23607	+	14.2653i	0.516777	+	0.895084i
$255$	14.2082	−	24.6093i	0.889752	−	1.54110i
$256$	7.28115	−	12.6113i	0.455072	−	0.788208i
$257$	−9.48936	−	16.4360i	−0.591930	−	1.02525i	−0.993972	−	0.109632i	$-0.965033\pi$
$257$	−9.48936	−	16.4360i	−0.591930	−	1.02525i	0.402042	−	0.915621i	$-0.368300\pi$
$258$	13.7082			0.853435
$259$		0			0
$260$	10.8541			0.673143
$261$	10.8262	+	18.7516i	0.670127	+	1.16069i
$262$	−13.2082	+	22.8773i	−0.816006	+	1.41336i
$263$	11.7812	−	20.4056i	0.726457	−	1.25826i	−0.231914	−	0.972736i	$-0.574499\pi$
$263$	11.7812	−	20.4056i	0.726457	−	1.25826i	0.958371	−	0.285524i	$-0.0921677\pi$
$264$	−54.9508	−	95.1777i	−3.38199	−	5.85778i
$265$	−2.43769			−0.149746
$266$		0			0
$267$	−6.00000			−0.367194
$268$	−15.9271	−	27.5865i	−0.972899	−	1.68511i
$269$	−2.78115	+	4.81710i	−0.169570	+	0.293704i	−0.938269	−	0.345907i	$-0.887571\pi$
$269$	−2.78115	+	4.81710i	−0.169570	+	0.293704i	0.768699	+	0.639611i	$0.220905\pi$
$270$	−6.54508	+	11.3364i	−0.398321	+	0.689913i
$271$	−7.13525	−	12.3586i	−0.433436	−	0.750733i	0.563731	−	0.825959i	$-0.309366\pi$
$271$	−7.13525	−	12.3586i	−0.433436	−	0.750733i	−0.997167	+	0.0752257i	$0.976032\pi$
$272$	47.8328			2.90029
$273$		0			0
$274$	−43.1246			−2.60525
$275$		0			0
$276$	19.0623	−	33.0169i	1.14742	−	1.98738i
$277$	2.14590	−	3.71680i	0.128935	−	0.223321i	−0.794330	−	0.607487i	$-0.792178\pi$
$277$	2.14590	−	3.71680i	0.128935	−	0.223321i	0.923264	+	0.384166i	$0.125511\pi$
$278$	9.54508	+	16.5326i	0.572476	+	0.991558i
$279$	3.29180			0.197075
$280$		0			0
$281$	26.8885			1.60404			0.802018	−	0.597300i	$-0.203760\pi$
$281$	26.8885			1.60404			0.802018	+	0.597300i	$0.203760\pi$
$282$	−38.3156	−	66.3646i	−2.28166	−	3.95195i
$283$	−5.78115	+	10.0133i	−0.343654	+	0.595226i	−0.985108	−	0.171935i	$-0.944998\pi$
$283$	−5.78115	+	10.0133i	−0.343654	+	0.595226i	0.641454	+	0.767161i	$0.278331\pi$
$284$	−18.1353	+	31.4112i	−1.07613	+	1.86391i
$285$	2.92705	+	5.06980i	0.173384	+	0.300309i
$286$	−14.7082			−0.869714
$287$		0			0
$288$	−41.8328			−2.46502
$289$	−3.28115	−	5.68312i	−0.193009	−	0.334301i
$290$	16.4443	−	28.4823i	0.965641	−	1.67254i
$291$	18.8713	−	32.6861i	1.10626	−	1.91609i
$292$	10.0623	+	17.4284i	0.588852	+	1.01992i
$293$	−0.708204			−0.0413737			−0.0206869	−	0.999786i	$-0.506585\pi$
$293$	−0.708204			−0.0413737			−0.0206869	+	0.999786i	$0.506585\pi$
$294$		0			0
$295$	1.58359			0.0922003
$296$	−40.0066	−	69.2934i	−2.32534	−	4.02760i
$297$	6.28115	−	10.8793i	0.364469	−	0.631280i
$298$	−19.4894	+	33.7566i	−1.12899	+	1.95546i
$299$	−1.50000	−	2.59808i	−0.0867472	−	0.150251i
$300$		0			0
$301$		0			0
$302$	−3.76393			−0.216590
$303$	17.6353	+	30.5452i	1.01312	+	1.75477i
$304$	−4.92705	+	8.53390i	−0.282586	+	0.489453i
$305$	7.50000	−	12.9904i	0.429449	−	0.743827i
$306$	24.4894	+	42.4168i	1.39996	+	2.42481i
$307$	22.5623			1.28770			0.643849	−	0.765152i	$-0.277336\pi$
$307$	22.5623			1.28770			0.643849	+	0.765152i	$0.277336\pi$
$308$		0			0
$309$	12.3262			0.701215
$310$	−2.50000	−	4.33013i	−0.141990	−	0.245935i
$311$	8.04508	−	13.9345i	0.456195	−	0.790153i	−0.542561	−	0.840016i	$-0.682545\pi$
$311$	8.04508	−	13.9345i	0.456195	−	0.790153i	0.998756	+	0.0498636i	$0.0158786\pi$
$312$	−9.78115	+	16.9415i	−0.553749	+	0.959121i
$313$	−7.85410	−	13.6037i	−0.443940	−	0.768927i	0.554038	−	0.832492i	$-0.313086\pi$
$313$	−7.85410	−	13.6037i	−0.443940	−	0.768927i	−0.997978	+	0.0635648i	$0.979753\pi$
$314$	−3.00000			−0.169300
$315$		0			0
$316$	−48.5410			−2.73065
$317$	0.708204	+	1.22665i	0.0397767	+	0.0688953i	0.885228	−	0.465157i	$-0.154002\pi$
$317$	0.708204	+	1.22665i	0.0397767	+	0.0688953i	−0.845452	+	0.534052i	$0.820669\pi$
$318$	3.73607	−	6.47106i	0.209508	−	0.362879i
$319$	−15.7812	+	27.3338i	−0.883575	+	1.53040i
$320$	9.73607	+	16.8634i	0.544263	+	0.942691i
$321$	3.85410			0.215115
$322$		0			0
$323$	4.85410			0.270089
$324$	13.8541	+	23.9960i	0.769672	+	1.33311i
$325$		0			0
$326$	−20.7533	+	35.9458i	−1.14942	+	1.99085i
$327$	13.6353	+	23.6170i	0.754031	+	1.30602i
$328$	2.85410			0.157591
$329$		0			0
$330$	−86.1033			−4.73983
$331$	10.7812	+	18.6735i	0.592586	+	1.02639i	0.993883	+	0.110441i	$0.0352262\pi$
$331$	10.7812	+	18.6735i	0.592586	+	1.02639i	−0.401297	+	0.915948i	$0.631440\pi$
$332$	−19.0623	+	33.0169i	−1.04618	+	1.81204i
$333$	20.6353	−	35.7413i	1.13081	−	1.95861i
$334$	9.78115	+	16.9415i	0.535201	+	0.926995i
$335$	−14.6738			−0.801713
$336$		0			0
$337$	−22.2705			−1.21315			−0.606576	−	0.795026i	$-0.707457\pi$
$337$	−22.2705			−1.21315			−0.606576	+	0.795026i	$0.707457\pi$
$338$	−15.7082	−	27.2074i	−0.854414	−	1.47989i
$339$	5.42705	−	9.39993i	0.294757	−	0.510534i
$340$	26.3435	−	45.6282i	1.42867	−	2.47454i
$341$	2.39919	+	4.15551i	0.129923	+	0.225034i
$342$	−10.0902			−0.545614
$343$		0			0
$344$	14.9443			0.805741
$345$	−8.78115	−	15.2094i	−0.472761	−	0.818847i
$346$	26.4164	−	45.7546i	1.42015	−	2.45978i
$347$	14.7812	−	25.6017i	0.793494	−	1.37437i	−0.130297	−	0.991475i	$-0.541593\pi$
$347$	14.7812	−	25.6017i	0.793494	−	1.37437i	0.923791	−	0.382897i	$-0.125073\pi$
$348$	35.6976	+	61.8300i	1.91359	+	3.31444i
$349$	9.27051			0.496239			0.248120	−	0.968729i	$-0.420187\pi$
$349$	9.27051			0.496239			0.248120	+	0.968729i	$0.420187\pi$
$350$		0			0
$351$	−2.23607			−0.119352
$352$	−30.4894	−	52.8091i	−1.62509	−	2.81474i
$353$	5.80902	−	10.0615i	0.309183	−	0.535520i	−0.669001	−	0.743261i	$-0.733278\pi$
$353$	5.80902	−	10.0615i	0.309183	−	0.535520i	0.978184	+	0.207741i	$0.0666112\pi$
$354$	−2.42705	+	4.20378i	−0.128996	+	0.223428i
$355$	8.35410	+	14.4697i	0.443390	+	0.767973i
$356$	−11.1246			−0.589603
$357$		0			0
$358$	26.4164			1.39615
$359$	−5.37132	−	9.30340i	−0.283488	−	0.491015i	0.688754	−	0.724995i	$-0.258158\pi$
$359$	−5.37132	−	9.30340i	−0.283488	−	0.491015i	−0.972241	+	0.233981i	$0.924825\pi$
$360$	−32.1976	+	55.7678i	−1.69696	+	2.93922i
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$	1.88197	+	3.25966i	0.0989139	+	0.171324i
$363$	53.8328			2.82549
$364$		0			0
$365$	9.27051			0.485241
$366$	22.9894	+	39.8187i	1.20167	+	2.08136i
$367$	−6.50000	+	11.2583i	−0.339297	+	0.587680i	−0.984301	−	0.176500i	$-0.943523\pi$
$367$	−6.50000	+	11.2583i	−0.339297	+	0.587680i	0.645003	+	0.764180i	$0.276856\pi$
$368$	14.7812	−	25.6017i	0.770521	−	1.33458i
$369$	0.736068	+	1.27491i	0.0383182	+	0.0663690i
$370$	−62.6869			−3.25894
$371$		0			0
$372$	10.8541			0.562759
$373$	0.364745	+	0.631757i	0.0188858	+	0.0327111i	0.875314	−	0.483555i	$-0.160655\pi$
$373$	0.364745	+	0.631757i	0.0188858	+	0.0327111i	−0.856428	+	0.516266i	$0.827321\pi$
$374$	−35.6976	+	61.8300i	−1.84588	+	3.19715i
$375$	−14.6353	+	25.3490i	−0.755761	+	1.30902i
$376$	−41.7705	−	72.3486i	−2.15415	−	3.73110i
$377$	5.61803			0.289343
$378$		0			0
$379$	30.7082			1.57737			0.788687	−	0.614795i	$-0.210761\pi$
$379$	30.7082			1.57737			0.788687	+	0.614795i	$0.210761\pi$
$380$	5.42705	+	9.39993i	0.278402	+	0.482206i
$381$	−8.23607	+	14.2653i	−0.421947	+	0.730833i
$382$	−8.28115	+	14.3434i	−0.423701	+	0.733871i
$383$	−10.1180	−	17.5249i	−0.517007	−	0.895483i	−0.999805	−	0.0197511i	$-0.993713\pi$
$383$	−10.1180	−	17.5249i	−0.517007	−	0.895483i	0.482798	−	0.875732i	$-0.339621\pi$
$384$	−2.85410			−0.145648
$385$		0			0
$386$	−48.5967			−2.47351
$387$	3.85410	+	6.67550i	0.195915	+	0.339335i
$388$	34.9894	−	60.6033i	1.77632	−	3.07667i
$389$	6.89919	−	11.9497i	0.349803	−	0.605876i	−0.636412	−	0.771350i	$-0.719582\pi$
$389$	6.89919	−	11.9497i	0.349803	−	0.605876i	0.986214	+	0.165474i	$0.0529153\pi$
$390$	7.66312	+	13.2729i	0.388037	+	0.672100i
$391$	−14.5623			−0.736447
$392$		0			0
$393$	−26.4164			−1.33253
$394$	19.9894	+	34.6226i	1.00705	+	1.74426i
$395$	−11.1803	+	19.3649i	−0.562544	+	0.974355i
$396$	52.5517	−	91.0221i	2.64082	−	4.57404i
$397$	16.2705	+	28.1813i	0.816593	+	1.41438i	0.908178	+	0.418584i	$0.137473\pi$
$397$	16.2705	+	28.1813i	0.816593	+	1.41438i	−0.0915846	+	0.995797i	$0.529193\pi$
$398$	43.7426			2.19262
$399$		0			0
$400$		0			0
$401$	3.19098	+	5.52694i	0.159350	+	0.276002i	0.934634	−	0.355610i	$-0.115727\pi$
$401$	3.19098	+	5.52694i	0.159350	+	0.276002i	−0.775284	+	0.631612i	$0.782393\pi$
$402$	22.4894	−	38.9527i	1.12167	−	1.94278i
$403$	0.427051	−	0.739674i	0.0212729	−	0.0368458i
$404$	32.6976	+	56.6338i	1.62676	+	2.81764i
$405$	12.7639			0.634245
$406$		0			0
$407$	60.1591			2.98197
$408$	47.4787	+	82.2355i	2.35055	+	4.07127i
$409$	−5.92705	+	10.2660i	−0.293074	+	0.507619i	−0.974535	−	0.224236i	$-0.928012\pi$
$409$	−5.92705	+	10.2660i	−0.293074	+	0.507619i	0.681461	+	0.731854i	$0.261345\pi$
$410$	1.11803	−	1.93649i	0.0552158	−	0.0956365i
$411$	−21.5623	−	37.3470i	−1.06359	−	1.84219i
$412$	22.8541			1.12594
$413$		0			0
$414$	30.2705			1.48771
$415$	8.78115	+	15.2094i	0.431050	+	0.746600i
$416$	−5.42705	+	9.39993i	−0.266083	+	0.460869i
$417$	−9.54508	+	16.5326i	−0.467425	+	0.809604i
$418$	−7.35410	−	12.7377i	−0.359701	−	0.623020i
$419$	36.7082			1.79331			0.896657	−	0.442727i	$-0.145989\pi$
$419$	36.7082			1.79331			0.896657	+	0.442727i	$0.145989\pi$
$420$		0			0
$421$	−34.7082			−1.69157			−0.845787	−	0.533520i	$-0.820869\pi$
$421$	−34.7082			−1.69157			−0.845787	+	0.533520i	$0.820869\pi$
$422$	17.7533	+	30.7496i	0.864217	+	1.49687i
$423$	21.5451	−	37.3172i	1.04756	−	1.81442i
$424$	4.07295	−	7.05455i	0.197800	−	0.342599i
$425$		0			0
$426$	−51.2148			−2.48136
$427$		0			0
$428$	7.14590			0.345410
$429$	−7.35410	−	12.7377i	−0.355059	−	0.614981i
$430$	5.85410	−	10.1396i	0.282310	−	0.488975i
$431$	−11.1803	+	19.3649i	−0.538538	+	0.932775i	0.460445	+	0.887688i	$0.347690\pi$
$431$	−11.1803	+	19.3649i	−0.538538	+	0.932775i	−0.998983	+	0.0450870i	$0.985643\pi$
$432$	−11.0172	−	19.0824i	−0.530066	−	0.918102i
$433$	35.5410			1.70799			0.853996	−	0.520279i	$-0.174172\pi$
$433$	35.5410			1.70799			0.853996	+	0.520279i	$0.174172\pi$
$434$		0			0
$435$	32.8885			1.57688
$436$	25.2812	+	43.7882i	1.21075	+	2.09708i
$437$	1.50000	−	2.59808i	0.0717547	−	0.124283i
$438$	−14.2082	+	24.6093i	−0.678894	+	1.17588i
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$	−93.8673			−4.47495
$441$		0			0
$442$	12.7082			0.604468
$443$	7.30902	+	12.6596i	0.347262	+	0.601475i	0.985762	−	0.168146i	$-0.0537782\pi$
$443$	7.30902	+	12.6596i	0.347262	+	0.601475i	−0.638500	+	0.769622i	$0.720445\pi$
$444$	68.0410	−	117.851i	3.22908	−	5.59294i
$445$	−2.56231	+	4.43804i	−0.121465	+	0.210383i
$446$	−0.545085	−	0.944115i	−0.0258105	−	0.0447051i
$447$	−38.9787			−1.84363
$448$		0			0
$449$	−30.3262			−1.43118			−0.715592	−	0.698519i	$-0.753843\pi$
$449$	−30.3262			−1.43118			−0.715592	+	0.698519i	$0.753843\pi$
$450$		0			0
$451$	−1.07295	+	1.85840i	−0.0505232	+	0.0875087i
$452$	10.0623	−	17.4284i	0.473291	−	0.819764i
$453$	−1.88197	−	3.25966i	−0.0884225	−	0.153152i
$454$	−48.1246			−2.25860
$455$		0			0
$456$	−19.5623			−0.916089
$457$	−2.21885	−	3.84316i	−0.103793	−	0.179775i	0.809451	−	0.587187i	$-0.199765\pi$
$457$	−2.21885	−	3.84316i	−0.103793	−	0.179775i	−0.913245	+	0.407412i	$0.866431\pi$
$458$	−22.7984	+	39.4879i	−1.06530	+	1.84515i
$459$	−5.42705	+	9.39993i	−0.253313	+	0.438751i
$460$	−16.2812	−	28.1998i	−0.759113	−	1.31482i
$461$	−22.9098			−1.06702			−0.533509	−	0.845795i	$-0.679127\pi$
$461$	−22.9098			−1.06702			−0.533509	+	0.845795i	$0.679127\pi$
$462$		0			0
$463$	17.2918			0.803618			0.401809	−	0.915724i	$-0.368382\pi$
$463$	17.2918			0.803618			0.401809	+	0.915724i	$0.368382\pi$
$464$	27.6803	+	47.9438i	1.28503	+	2.22573i
$465$	2.50000	−	4.33013i	0.115935	−	0.200805i
$466$	17.0623	−	29.5528i	0.790396	−	1.36901i
$467$	−19.9615	−	34.5743i	−0.923708	−	1.59991i	−0.793626	−	0.608405i	$-0.791809\pi$
$467$	−19.9615	−	34.5743i	−0.923708	−	1.59991i	−0.130081	−	0.991503i	$-0.541524\pi$
$468$	−18.7082			−0.864787
$469$		0			0
$470$	−65.4508			−3.01902
$471$	−1.50000	−	2.59808i	−0.0691164	−	0.119713i
$472$	−2.64590	+	4.58283i	−0.121787	+	0.210942i
$473$	−5.61803	+	9.73072i	−0.258317	+	0.447419i
$474$	−34.2705	−	59.3583i	−1.57410	−	2.72642i
$475$		0			0
$476$		0			0
$477$	4.20163			0.192379
$478$	5.92705	+	10.2660i	0.271097	+	0.469554i
$479$	−7.22542	+	12.5148i	−0.330138	+	0.571816i	−0.982539	−	0.186058i	$-0.940429\pi$
$479$	−7.22542	+	12.5148i	−0.330138	+	0.571816i	0.652401	+	0.757874i	$0.273762\pi$
$480$	−31.7705	+	55.0281i	−1.45012	+	2.51168i
$481$	−5.35410	−	9.27358i	−0.244126	−	0.422839i
$482$	−11.2361			−0.511789
$483$		0			0
$484$	99.8115			4.53689
$485$	−16.1180	−	27.9173i	−0.731882	−	1.26766i
$486$	−28.3435	+	49.0923i	−1.28569	+	2.22687i
$487$	−18.2082	+	31.5375i	−0.825092	+	1.42910i	0.0767561	+	0.997050i	$0.475544\pi$
$487$	−18.2082	+	31.5375i	−0.825092	+	1.42910i	−0.901849	+	0.432052i	$0.857790\pi$
$488$	25.0623	+	43.4092i	1.13452	+	1.96504i
$489$	−41.5066			−1.87699
$490$		0			0
$491$	−1.52786			−0.0689515			−0.0344758	−	0.999406i	$-0.510976\pi$
$491$	−1.52786			−0.0689515			−0.0344758	+	0.999406i	$0.510976\pi$
$492$	2.42705	+	4.20378i	0.109420	+	0.189521i
$493$	13.6353	−	23.6170i	0.614101	−	1.06365i
$494$	−1.30902	+	2.26728i	−0.0588955	+	0.102010i
$495$	−24.2082	−	41.9298i	−1.08808	−	1.88461i
$496$	8.41641			0.377908
$497$		0			0
$498$	−53.8328			−2.41231
$499$	−4.92705	−	8.53390i	−0.220565	−	0.382030i	0.734415	−	0.678701i	$-0.237457\pi$
$499$	−4.92705	−	8.53390i	−0.220565	−	0.382030i	−0.954980	+	0.296671i	$0.904123\pi$
$500$	−27.1353	+	46.9996i	−1.21353	+	2.10189i
$501$	−9.78115	+	16.9415i	−0.436990	+	0.756888i
$502$	−33.7705	−	58.4922i	−1.50725	−	2.61064i
$503$	17.8885			0.797611			0.398805	−	0.917036i	$-0.369425\pi$
$503$	17.8885			0.797611			0.398805	+	0.917036i	$0.369425\pi$
$504$		0			0
$505$	30.1246			1.34053
$506$	22.0623	+	38.2130i	0.980789	+	1.69878i
$507$	15.7082	−	27.2074i	0.697626	−	1.20832i
$508$	−15.2705	+	26.4493i	−0.677519	+	1.17350i
$509$	15.0000	+	25.9808i	0.664863	+	1.15158i	0.979322	+	0.202306i	$0.0648436\pi$
$509$	15.0000	+	25.9808i	0.664863	+	1.15158i	−0.314459	+	0.949271i	$0.601823\pi$
$510$	74.3951			3.29427
$511$		0			0
$512$	40.3050			1.78124
$513$	−1.11803	−	1.93649i	−0.0493624	−	0.0854982i
$514$	24.8435	−	43.0301i	1.09580	−	1.89798i
$515$	5.26393	−	9.11740i	0.231957	−	0.401761i
$516$	12.7082	+	22.0113i	0.559447	+	0.968991i
$517$	62.8115			2.76245
$518$		0			0
$519$	52.8328			2.31910
$520$	8.35410	+	14.4697i	0.366352	+	0.634540i
$521$	−13.8820	+	24.0443i	−0.608180	+	1.05340i	0.383360	+	0.923599i	$0.374767\pi$
$521$	−13.8820	+	24.0443i	−0.608180	+	1.05340i	−0.991540	+	0.129800i	$0.958567\pi$
$522$	−28.3435	+	49.0923i	−1.24056	+	2.14871i
$523$	20.2082	+	35.0016i	0.883643	+	1.53051i	0.847261	+	0.531177i	$0.178250\pi$
$523$	20.2082	+	35.0016i	0.883643	+	1.53051i	0.0363820	+	0.999338i	$0.488417\pi$
$524$	−48.9787			−2.13965
$525$		0			0
$526$	61.6869			2.68968
$527$	−2.07295	−	3.59045i	−0.0902991	−	0.156403i
$528$	72.4681	−	125.518i	3.15377	−	5.46249i
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	−3.19098	−	5.52694i	−0.138607	−	0.240075i
$531$	−2.72949			−0.118450
$532$		0			0
$533$	0.381966			0.0165448
$534$	−7.85410	−	13.6037i	−0.339880	−	0.588690i
$535$	1.64590	−	2.85078i	0.0711584	−	0.123250i
$536$	24.5172	−	42.4651i	1.05898	−	1.83421i
$537$	13.2082	+	22.8773i	0.569976	+	0.987228i
$538$	−14.5623			−0.627826
$539$		0			0
$540$	−24.2705			−1.04444
$541$	6.70820	+	11.6190i	0.288408	+	0.499538i	0.973430	−	0.228985i	$-0.0735407\pi$
$541$	6.70820	+	11.6190i	0.288408	+	0.499538i	−0.685022	+	0.728523i	$0.740207\pi$
$542$	18.6803	−	32.3553i	0.802389	−	1.38978i
$543$	−1.88197	+	3.25966i	−0.0807629	+	0.139885i
$544$	26.3435	+	45.6282i	1.12947	+	1.95629i
$545$	23.2918			0.997711
$546$		0			0
$547$	−17.2705			−0.738434			−0.369217	−	0.929343i	$-0.620374\pi$
$547$	−17.2705			−0.738434			−0.369217	+	0.929343i	$0.620374\pi$
$548$	−39.9787	−	69.2452i	−1.70781	−	2.95801i
$549$	−12.9271	+	22.3903i	−0.551713	+	0.955595i
$550$		0			0
$551$	2.80902	+	4.86536i	0.119668	+	0.207271i
$552$	58.6869			2.49788
$553$		0			0
$554$	11.2361			0.477375
$555$	−31.3435	−	54.2885i	−1.33046	−	2.30442i
$556$	−17.6976	+	30.6531i	−0.750544	+	1.29998i
$557$	1.33688	−	2.31555i	0.0566455	−	0.0981128i	−0.836312	−	0.548254i	$-0.815293\pi$
$557$	1.33688	−	2.31555i	0.0566455	−	0.0981128i	0.892958	+	0.450141i	$0.148626\pi$
$558$	4.30902	+	7.46344i	0.182415	+	0.315952i
$559$	2.00000			0.0845910
$560$		0			0
$561$	−71.3951			−3.01430
$562$	35.1976	+	60.9640i	1.48472	+	2.57161i
$563$	2.59017	−	4.48631i	0.109163	−	0.189075i	−0.806269	−	0.591550i	$-0.798516\pi$
$563$	2.59017	−	4.48631i	0.109163	−	0.189075i	0.915431	+	0.402474i	$0.131850\pi$
$564$	71.0410	−	123.047i	2.99137	−	5.18120i
$565$	−4.63525	−	8.02850i	−0.195007	−	0.337761i
$566$	−30.2705			−1.27236
$567$		0			0
$568$	−55.8328			−2.34269
$569$	−12.2984	−	21.3014i	−0.515575	−	0.893001i	−0.999837	−	0.0180784i	$-0.994245\pi$
$569$	−12.2984	−	21.3014i	−0.515575	−	0.893001i	0.484262	−	0.874923i	$-0.339088\pi$
$570$	−7.66312	+	13.2729i	−0.320973	+	0.555941i
$571$	−12.0623	+	20.8925i	−0.504792	+	0.874325i	0.495193	+	0.868783i	$0.335097\pi$
$571$	−12.0623	+	20.8925i	−0.504792	+	0.874325i	−0.999985	+	0.00554195i	$0.998236\pi$
$572$	−13.6353	−	23.6170i	−0.570119	−	0.987474i
$573$	−16.5623			−0.691900
$574$		0			0
$575$		0			0
$576$	−16.7812	−	29.0658i	−0.699215	−	1.21108i
$577$	7.07295	−	12.2507i	0.294451	−	0.510004i	−0.680406	−	0.732835i	$-0.738197\pi$
$577$	7.07295	−	12.2507i	0.294451	−	0.510004i	0.974857	+	0.222832i	$0.0715300\pi$
$578$	8.59017	−	14.8786i	0.357304	−	0.618869i
$579$	−24.2984	−	42.0860i	−1.00981	−	1.74904i
$580$	60.9787			2.53200
$581$		0			0
$582$	98.8115			4.09587
$583$	3.06231	+	5.30407i	0.126828	+	0.219672i
$584$	−15.4894	+	26.8284i	−0.640954	+	1.11017i
$585$	−4.30902	+	7.46344i	−0.178156	+	0.308575i
$586$	−0.927051	−	1.60570i	−0.0382961	−	0.0663308i
$587$	−21.0557			−0.869063			−0.434531	−	0.900657i	$-0.643086\pi$
$587$	−21.0557			−0.869063			−0.434531	+	0.900657i	$0.643086\pi$
$588$		0			0
$589$	0.854102			0.0351927
$590$	2.07295	+	3.59045i	0.0853420	+	0.147817i
$591$	−19.9894	+	34.6226i	−0.822252	+	1.42418i
$592$	52.7599	−	91.3828i	2.16842	−	3.75581i
$593$	−7.50000	−	12.9904i	−0.307988	−	0.533451i	0.669934	−	0.742421i	$-0.266322\pi$
$593$	−7.50000	−	12.9904i	−0.307988	−	0.533451i	−0.977922	+	0.208970i	$0.932989\pi$
$594$	32.8885			1.34943
$595$		0			0
$596$	−72.2705			−2.96032
$597$	21.8713	+	37.8822i	0.895134	+	1.55042i
$598$	3.92705	−	6.80185i	0.160589	−	0.278148i
$599$	−3.54508	+	6.14027i	−0.144848	+	0.250885i	−0.929316	−	0.369285i	$-0.879603\pi$
$599$	−3.54508	+	6.14027i	−0.144848	+	0.250885i	0.784468	+	0.620169i	$0.212936\pi$
$600$		0			0
$601$	−5.56231			−0.226891			−0.113446	−	0.993544i	$-0.536189\pi$
$601$	−5.56231			−0.226891			−0.113446	+	0.993544i	$0.536189\pi$
$602$		0			0
$603$	25.2918			1.02996
$604$	−3.48936	−	6.04374i	−0.141980	−	0.245916i
$605$	22.9894	−	39.8187i	0.934650	−	1.61886i
$606$	−46.1697	+	79.9683i	−1.87552	+	3.24849i
$607$	0.0623059	+	0.107917i	0.00252892	+	0.00438022i	0.867287	−	0.497808i	$-0.165862\pi$
$607$	0.0623059	+	0.107917i	0.00252892	+	0.00438022i	−0.864758	+	0.502189i	$0.832528\pi$
$608$	−10.8541			−0.440192
$609$		0			0
$610$	39.2705			1.59002
$611$	−5.59017	−	9.68246i	−0.226154	−	0.391710i
$612$	−45.4058	+	78.6451i	−1.83542	+	3.17904i
$613$	23.3435	−	40.4321i	0.942833	−	1.63304i	0.182801	−	0.983150i	$-0.441483\pi$
$613$	23.3435	−	40.4321i	0.942833	−	1.63304i	0.760032	−	0.649886i	$-0.225183\pi$
$614$	29.5344	+	51.1552i	1.19191	+	2.06445i
$615$	2.23607			0.0901670
$616$		0			0
$617$	−27.2148			−1.09563			−0.547813	−	0.836601i	$-0.684539\pi$
$617$	−27.2148			−1.09563			−0.547813	+	0.836601i	$0.684539\pi$
$618$	16.1353	+	27.9471i	0.649055	+	1.12420i
$619$	16.7812	−	29.0658i	0.674491	−	1.16825i	−0.302126	−	0.953268i	$-0.597696\pi$
$619$	16.7812	−	29.0658i	0.674491	−	1.16825i	0.976617	−	0.214985i	$-0.0689704\pi$
$620$	4.63525	−	8.02850i	0.186156	−	0.322432i
$621$	3.35410	+	5.80948i	0.134595	+	0.233126i
$622$	42.1246			1.68904
$623$		0			0
$624$	−25.7984			−1.03276
$625$	12.5000	+	21.6506i	0.500000	+	0.866025i
$626$	20.5623	−	35.6150i	0.821835	−	1.42346i
$627$	7.35410	−	12.7377i	0.293695	−	0.508694i
$628$	−2.78115	−	4.81710i	−0.110980	−	0.192223i
$629$	−51.9787			−2.07253
$630$		0			0
$631$	−14.7082			−0.585524			−0.292762	−	0.956185i	$-0.594574\pi$
$631$	−14.7082			−0.585524			−0.292762	+	0.956185i	$0.594574\pi$
$632$	−37.3607	−	64.7106i	−1.48613	−	2.57405i
$633$	−17.7533	+	30.7496i	−0.705630	+	1.22219i
$634$	−1.85410	+	3.21140i	−0.0736358	+	0.127541i
$635$	7.03444	+	12.1840i	0.279153	+	0.483508i
$636$	13.8541			0.549351
$637$		0			0
$638$	−82.6312			−3.27140
$639$	−14.3992	−	24.9401i	−0.569623	−	0.986616i
$640$	−1.21885	+	2.11111i	−0.0481792	+	0.0834488i
$641$	−9.84346	+	17.0494i	−0.388793	+	0.673410i	−0.992288	−	0.123958i	$-0.960441\pi$
$641$	−9.84346	+	17.0494i	−0.388793	+	0.673410i	0.603494	+	0.797367i	$0.293775\pi$
$642$	5.04508	+	8.73834i	0.199114	+	0.344875i
$643$	21.5836			0.851174			0.425587	−	0.904918i	$-0.360068\pi$
$643$	21.5836			0.851174			0.425587	+	0.904918i	$0.360068\pi$
$644$		0			0
$645$	11.7082			0.461010
$646$	6.35410	+	11.0056i	0.249999	+	0.433011i
$647$	20.5344	−	35.5667i	0.807292	−	1.39827i	−0.107440	−	0.994212i	$-0.534265\pi$
$647$	20.5344	−	35.5667i	0.807292	−	1.39827i	0.914733	−	0.404060i	$-0.132401\pi$
$648$	−21.3262	+	36.9381i	−0.837774	+	1.45107i
$649$	−1.98936	−	3.44567i	−0.0780891	−	0.135254i
$650$		0			0
$651$		0			0
$652$	−76.9574			−3.01389
$653$	−15.2984	−	26.4976i	−0.598672	−	1.03693i	−0.993017	−	0.117968i	$-0.962362\pi$
$653$	−15.2984	−	26.4976i	−0.598672	−	1.03693i	0.394346	−	0.918962i	$-0.370971\pi$
$654$	−35.6976	+	61.8300i	−1.39589	+	2.41774i
$655$	−11.2812	+	19.5395i	−0.440791	+	0.763473i
$656$	1.88197	+	3.25966i	0.0734784	+	0.127268i
$657$	−15.9787			−0.623389
$658$		0			0
$659$	−11.5066			−0.448233			−0.224116	−	0.974562i	$-0.571950\pi$
$659$	−11.5066			−0.448233			−0.224116	+	0.974562i	$0.571950\pi$
$660$	−79.8222	−	138.256i	−3.10707	−	5.38161i
$661$	18.4164	−	31.8982i	0.716315	−	1.24069i	−0.246135	−	0.969236i	$-0.579161\pi$
$661$	18.4164	−	31.8982i	0.716315	−	1.24069i	0.962450	−	0.271459i	$-0.0875061\pi$
$662$	−28.2254	+	48.8879i	−1.09701	+	1.90008i
$663$	6.35410	+	11.0056i	0.246773	+	0.427423i
$664$	−58.6869			−2.27749
$665$		0			0
$666$	108.048			4.18676
$667$	−8.42705	−	14.5961i	−0.326297	−	0.565162i
$668$	−18.1353	+	31.4112i	−0.701674	+	1.21534i
$669$	0.545085	−	0.944115i	0.0210742	−	0.0365016i
$670$	−19.2082	−	33.2696i	−0.742078	−	1.28532i
$671$	−37.6869			−1.45489
$672$		0			0
$673$	15.2705			0.588635			0.294317	−	0.955708i	$-0.404908\pi$
$673$	15.2705			0.588635			0.294317	+	0.955708i	$0.404908\pi$
$674$	−29.1525	−	50.4936i	−1.12291	−	1.94494i
$675$		0			0
$676$	29.1246	−	50.4453i	1.12018	−	1.94020i
$677$	3.87132	+	6.70533i	0.148787	+	0.257707i	0.930779	−	0.365581i	$-0.119130\pi$
$677$	3.87132	+	6.70533i	0.148787	+	0.257707i	−0.781992	+	0.623288i	$0.785796\pi$
$678$	28.4164			1.09133
$679$		0			0
$680$	81.1033			3.11017
$681$	−24.0623	−	41.6771i	−0.922070	−	1.59707i
$682$	−6.28115	+	10.8793i	−0.240518	+	0.416589i
$683$	18.7361	−	32.4518i	0.716916	−	1.24173i	−0.245300	−	0.969447i	$-0.578887\pi$
$683$	18.7361	−	32.4518i	0.716916	−	1.24173i	0.962216	−	0.272287i	$-0.0877801\pi$
$684$	−9.35410	−	16.2018i	−0.357663	−	0.619491i
$685$	−36.8328			−1.40731
$686$		0			0
$687$	−45.5967			−1.73962
$688$	9.85410	+	17.0678i	0.375684	+	0.650704i
$689$	0.545085	−	0.944115i	0.0207661	−	0.0359679i
$690$	22.9894	−	39.8187i	0.875190	−	1.51587i
$691$	−15.8541	−	27.4601i	−0.603118	−	1.04463i	−0.992346	−	0.123490i	$-0.960591\pi$
$691$	−15.8541	−	27.4601i	−0.603118	−	1.04463i	0.389227	−	0.921142i	$-0.372742\pi$
$692$	97.9574			3.72378
$693$		0			0
$694$	77.3951			2.93788
$695$	8.15248	+	14.1205i	0.309241	+	0.535621i
$696$	−54.9508	+	95.1777i	−2.08291	+	3.60770i
$697$	0.927051	−	1.60570i	0.0351146	−	0.0608202i
$698$	12.1353	+	21.0189i	0.459326	+	0.795576i
$699$	34.1246			1.29071
$700$		0			0
$701$	−46.4721			−1.75523			−0.877614	−	0.479368i	$-0.840866\pi$
$701$	−46.4721			−1.75523			−0.877614	+	0.479368i	$0.840866\pi$
$702$	−2.92705	−	5.06980i	−0.110474	−	0.191347i
$703$	5.35410	−	9.27358i	0.201934	−	0.349760i
$704$	24.4615	−	42.3685i	0.921927	−	1.59682i
$705$	−32.7254	−	56.6821i	−1.23251	−	2.13477i
$706$	30.4164			1.14474
$707$		0			0
$708$	−9.00000			−0.338241
$709$	−12.3541	−	21.3979i	−0.463968	−	0.803616i	0.535186	−	0.844734i	$-0.320241\pi$
$709$	−12.3541	−	21.3979i	−0.463968	−	0.803616i	−0.999154	+	0.0411179i	$0.986908\pi$
$710$	−21.8713	+	37.8822i	−0.820816	+	1.42170i
$711$	19.2705	−	33.3775i	0.722701	−	1.25175i
$712$	−8.56231	−	14.8303i	−0.320886	−	0.555791i
$713$	−2.56231			−0.0959591
$714$		0			0
$715$	−12.5623			−0.469804
$716$	24.4894	+	42.4168i	0.915210	+	1.58519i
$717$	−5.92705	+	10.2660i	−0.221350	+	0.383389i
$718$	14.0623	−	24.3566i	0.524801	−	0.908981i
$719$	−14.9443	−	25.8842i	−0.557327	−	0.965319i	−0.997718	−	0.0675132i	$-0.978494\pi$
$719$	−14.9443	−	25.8842i	−0.557327	−	0.965319i	0.440391	−	0.897806i	$-0.354840\pi$
$720$	−84.9230			−3.16489
$721$		0			0
$722$	−2.61803			−0.0974331
$723$	−5.61803	−	9.73072i	−0.208937	−	0.361889i
$724$	−3.48936	+	6.04374i	−0.129681	+	0.224614i
$725$		0			0
$726$	70.4681	+	122.054i	2.61532	+	4.52986i
$727$	−43.0000			−1.59478			−0.797391	−	0.603463i	$-0.793787\pi$
$727$	−43.0000			−1.59478			−0.797391	+	0.603463i	$0.793787\pi$
$728$		0			0
$729$	−39.5623			−1.46527
$730$	12.1353	+	21.0189i	0.449146	+	0.777944i
$731$	4.85410	−	8.40755i	0.179535	−	0.310965i
$732$	−42.6246	+	73.8280i	−1.57545	+	2.72876i
$733$	15.4164	+	26.7020i	0.569418	+	0.986261i	0.996624	+	0.0821064i	$0.0261647\pi$
$733$	15.4164	+	26.7020i	0.569418	+	0.986261i	−0.427206	+	0.904155i	$0.640502\pi$
$734$	−34.0344			−1.25623
$735$		0			0
$736$	32.5623			1.20026
$737$	18.4336	+	31.9280i	0.679011	+	1.17608i
$738$	−1.92705	+	3.33775i	−0.0709357	+	0.122864i
$739$	2.20820	−	3.82472i	0.0812301	−	0.140695i	−0.822548	−	0.568695i	$-0.807448\pi$
$739$	2.20820	−	3.82472i	0.0812301	−	0.140695i	0.903779	+	0.428000i	$0.140782\pi$
$740$	−58.1140	−	100.656i	−2.13631	−	3.70020i
$741$	−2.61803			−0.0961759
$742$		0			0
$743$	−20.8885			−0.766326			−0.383163	−	0.923681i	$-0.625165\pi$
$743$	−20.8885			−0.766326			−0.383163	+	0.923681i	$0.625165\pi$
$744$	8.35410	+	14.4697i	0.306276	+	0.530486i
$745$	−16.6459	+	28.8315i	−0.609859	+	1.05631i
$746$	−0.954915	+	1.65396i	−0.0349619	+	0.0605558i
$747$	−15.1353	−	26.2150i	−0.553770	−	0.959158i
$748$	−132.374			−4.84007
$749$		0			0
$750$	−76.6312			−2.79818
$751$	−11.0729	−	19.1789i	−0.404058	−	0.699848i	0.590154	−	0.807291i	$-0.299067\pi$
$751$	−11.0729	−	19.1789i	−0.404058	−	0.699848i	−0.994211	+	0.107443i	$0.965734\pi$
$752$	55.0861	−	95.4119i	2.00878	−	3.47932i
$753$	33.7705	−	58.4922i	1.23067	−	2.13158i
$754$	7.35410	+	12.7377i	0.267821	+	0.463879i
$755$	−3.21478			−0.116998
$756$		0			0
$757$	−21.4164			−0.778393			−0.389196	−	0.921155i	$-0.627247\pi$
$757$	−21.4164			−0.778393			−0.389196	+	0.921155i	$0.627247\pi$
$758$	40.1976	+	69.6242i	1.46004	+	2.52887i
$759$	−22.0623	+	38.2130i	−0.800811	+	1.38705i
$760$	−8.35410	+	14.4697i	−0.303035	+	0.524872i
$761$	9.40983	+	16.2983i	0.341106	+	0.590813i	0.984638	−	0.174606i	$-0.0558651\pi$
$761$	9.40983	+	16.2983i	0.341106	+	0.590813i	−0.643532	+	0.765419i	$0.722532\pi$
$762$	−43.1246			−1.56224
$763$		0			0
$764$	−30.7082			−1.11098
$765$	20.9164	+	36.2283i	0.756234	+	1.30984i
$766$	26.4894	−	45.8809i	0.957099	−	1.65774i
$767$	−0.354102	+	0.613323i	−0.0127859	+	0.0221458i
$768$	19.0623	+	33.0169i	0.687852	+	1.19139i
$769$	42.8328			1.54459			0.772295	−	0.635264i	$-0.219109\pi$
$769$	42.8328			1.54459			0.772295	+	0.635264i	$0.219109\pi$
$770$		0			0
$771$	49.6869			1.78943
$772$	−45.0517	−	78.0318i	−1.62144	−	2.80842i
$773$	−18.3262	+	31.7420i	−0.659149	+	1.14168i	0.321687	+	0.946846i	$0.395750\pi$
$773$	−18.3262	+	31.7420i	−0.659149	+	1.14168i	−0.980836	+	0.194834i	$0.937583\pi$
$774$	−10.0902	+	17.4767i	−0.362684	+	0.628187i
$775$		0			0
$776$	107.721			3.86697
$777$		0			0
$778$	36.1246			1.29513
$779$	0.190983	+	0.330792i	0.00684268	+	0.0118519i
$780$	−14.2082	+	24.6093i	−0.508735	+	0.881155i
$781$	20.9894	−	36.3546i	0.751058	−	1.30087i
$782$	−19.0623	−	33.0169i	−0.681667	−	1.18068i
$783$	−12.5623			−0.448940
$784$		0			0
$785$	−2.56231			−0.0914526
$786$	−34.5795	−	59.8935i	−1.23341	−	2.13633i
$787$	−5.70820	+	9.88690i	−0.203475	+	0.352430i	−0.949646	−	0.313325i	$-0.898557\pi$
$787$	−5.70820	+	9.88690i	−0.203475	+	0.352430i	0.746170	+	0.665755i	$0.231890\pi$
$788$	−37.0623	+	64.1938i	−1.32029	+	2.28681i
$789$	30.8435	+	53.4224i	1.09806	+	1.90189i
$790$	−58.5410			−2.08280
$791$		0			0
$792$	161.790			5.74897
$793$	3.35410	+	5.80948i	0.119108	+	0.206301i
$794$	−42.5967	+	73.7797i	−1.51170	+	2.61834i
$795$	3.19098	−	5.52694i	0.113173	−	0.196021i
$796$	40.5517	+	70.2375i	1.43732	+	2.48950i
$797$	13.6869			0.484815			0.242408	−	0.970174i	$-0.422063\pi$
$797$	13.6869			0.484815			0.242408	+	0.970174i	$0.422063\pi$
$798$		0			0
$799$	−54.2705			−1.91995
$800$		0			0
$801$	4.41641	−	7.64944i	0.156046	−	0.270280i
$802$	−8.35410	+	14.4697i	−0.294994	+	0.510944i
$803$	−11.6459	−	20.1713i	−0.410975	−	0.711829i
$804$	83.3951			2.94112
$805$		0			0
$806$	2.23607			0.0787621
$807$	−7.28115	−	12.6113i	−0.256309	−	0.443940i
$808$	−50.3328	+	87.1790i	−1.77070	+	3.06695i
$809$	15.2426	−	26.4010i	0.535903	−	0.928211i	−0.463216	−	0.886245i	$-0.653305\pi$
$809$	15.2426	−	26.4010i	0.535903	−	0.928211i	0.999119	−	0.0419657i	$-0.0133620\pi$
$810$	16.7082	+	28.9395i	0.587066	+	1.01683i
$811$	−36.2492			−1.27288			−0.636441	−	0.771325i	$-0.719594\pi$
$811$	−36.2492			−1.27288			−0.636441	+	0.771325i	$0.719594\pi$
$812$		0			0
$813$	37.3607			1.31030
$814$	78.7492	+	136.398i	2.76016	+	4.78074i
$815$	−17.7254	+	30.7013i	−0.620895	+	1.07542i
$816$	−62.6140	+	108.451i	−2.19193	+	3.79653i
$817$	1.00000	+	1.73205i	0.0349856	+	0.0605968i
$818$	−31.0344			−1.08509
$819$		0			0
$820$	4.14590			0.144781
$821$	2.29180	+	3.96951i	0.0799842	+	0.138537i	0.903243	−	0.429130i	$-0.141180\pi$
$821$	2.29180	+	3.96951i	0.0799842	+	0.138537i	−0.823259	+	0.567666i	$0.807846\pi$
$822$	56.4508	−	97.7757i	1.96895	−	3.41032i
$823$	−13.5623	+	23.4906i	−0.472752	+	0.818831i	−0.999514	−	0.0311822i	$-0.990073\pi$
$823$	−13.5623	+	23.4906i	−0.472752	+	0.818831i	0.526761	+	0.850013i	$0.323406\pi$
$824$	17.5902	+	30.4671i	0.612783	+	1.06137i
$825$		0			0
$826$		0			0
$827$	29.9443			1.04126			0.520632	−	0.853781i	$-0.325696\pi$
$827$	29.9443			1.04126			0.520632	+	0.853781i	$0.325696\pi$
$828$	28.0623	+	48.6053i	0.975233	+	1.68915i
$829$	−3.41641	+	5.91739i	−0.118657	+	0.205520i	−0.919236	−	0.393708i	$-0.871192\pi$
$829$	−3.41641	+	5.91739i	−0.118657	+	0.205520i	0.800579	+	0.599227i	$0.204525\pi$
$830$	−22.9894	+	39.8187i	−0.797972	+	1.38213i
$831$	5.61803	+	9.73072i	0.194887	+	0.337555i
$832$	−8.70820			−0.301903
$833$		0			0
$834$	−49.9787			−1.73062
$835$	8.35410	+	14.4697i	0.289106	+	0.500746i
$836$	13.6353	−	23.6170i	0.471585	−	0.816809i
$837$	−0.954915	+	1.65396i	−0.0330067	+	0.0571693i
$838$	48.0517	+	83.2279i	1.65992	+	2.87506i
$839$	28.3607			0.979119			0.489560	−	0.871970i	$-0.337158\pi$
$839$	28.3607			0.979119			0.489560	+	0.871970i	$0.337158\pi$
$840$		0			0
$841$	2.56231			0.0883554
$842$	−45.4336	−	78.6934i	−1.56575	−	2.71195i
$843$	−35.1976	+	60.9640i	−1.21227	+	2.09971i
$844$	−32.9164	+	57.0129i	−1.13303	+	1.96246i
$845$	−13.4164	−	23.2379i	−0.461538	−	0.799408i
$846$	112.812			3.87854
$847$		0			0
$848$	10.7426			0.368904
$849$	−15.1353	−	26.2150i	−0.519441	−	0.899698i
$850$		0			0
$851$	−16.0623	+	27.8207i	−0.550609	+	0.953682i
$852$	−47.4787	−	82.2355i	−1.62659	−	2.81734i
$853$	3.56231			0.121971			0.0609855	−	0.998139i	$-0.480576\pi$
$853$	3.56231			0.121971			0.0609855	+	0.998139i	$0.480576\pi$
$854$		0			0
$855$	−8.61803			−0.294731
$856$	5.50000	+	9.52628i	0.187986	+	0.325602i
$857$	13.9336	−	24.1338i	0.475964	−	0.824393i	−0.523657	−	0.851929i	$-0.675433\pi$
$857$	13.9336	−	24.1338i	0.475964	−	0.824393i	0.999621	+	0.0275358i	$0.00876603\pi$
$858$	19.2533	−	33.3477i	0.657296	−	1.13847i
$859$	22.2812	+	38.5921i	0.760223	+	1.31675i	0.942735	+	0.333542i	$0.108244\pi$
$859$	22.2812	+	38.5921i	0.760223	+	1.31675i	−0.182512	+	0.983204i	$0.558423\pi$
$860$	21.7082			0.740244
$861$		0			0
$862$	−58.5410			−1.99392
$863$	−10.3090	−	17.8557i	−0.350923	−	0.607816i	0.635488	−	0.772110i	$-0.280799\pi$
$863$	−10.3090	−	17.8557i	−0.350923	−	0.607816i	−0.986411	+	0.164294i	$0.947465\pi$
$864$	12.1353	−	21.0189i	0.412850	−	0.715077i
$865$	22.5623	−	39.0791i	0.767141	−	1.32873i
$866$	46.5238	+	80.5816i	1.58094	+	2.73827i
$867$	17.1803			0.583475
$868$		0			0
$869$	56.1803			1.90579
$870$	43.0517	+	74.5677i	1.45959	+	2.52808i
$871$	3.28115	−	5.68312i	0.111178	−	0.192565i
$872$	−38.9164	+	67.4052i	−1.31788	+	2.28263i
$873$	27.7812	+	48.1184i	0.940250	+	1.62856i
$874$	7.85410			0.265669
$875$		0			0
$876$	−52.6869			−1.78013
$877$	−28.5623	−	49.4714i	−0.964481	−	1.67053i	−0.711004	−	0.703188i	$-0.751759\pi$
$877$	−28.5623	−	49.4714i	−0.964481	−	1.67053i	−0.253476	−	0.967342i	$-0.581574\pi$
$878$	−10.4721	+	18.1383i	−0.353417	+	0.612137i
$879$	0.927051	−	1.60570i	0.0312687	−	0.0541589i
$880$	−61.8951	−	107.205i	−2.08648	−	3.61390i
$881$	36.1033			1.21635			0.608176	−	0.793802i	$-0.291901\pi$
$881$	36.1033			1.21635			0.608176	+	0.793802i	$0.291901\pi$
$882$		0			0
$883$	1.83282			0.0616792			0.0308396	−	0.999524i	$-0.490182\pi$
$883$	1.83282			0.0616792			0.0308396	+	0.999524i	$0.490182\pi$
$884$	11.7812	+	20.4056i	0.396243	+	0.686313i
$885$	−2.07295	+	3.59045i	−0.0696814	+	0.120692i
$886$	−19.1353	+	33.1432i	−0.642861	+	1.11347i
$887$	−14.2082	−	24.6093i	−0.477065	−	0.826300i	0.522590	−	0.852584i	$-0.324966\pi$
$887$	−14.2082	−	24.6093i	−0.477065	−	0.826300i	−0.999655	+	0.0262838i	$0.991633\pi$
$888$	209.477			7.02959
$889$		0			0
$890$	−13.4164			−0.449719
$891$	−16.0344	−	27.7725i	−0.537174	−	0.930413i
$892$	1.01064	−	1.75049i	0.0338388	−	0.0586106i
$893$	5.59017	−	9.68246i	0.187068	−	0.324011i
$894$	−51.0238	−	88.3758i	−1.70649	−	2.95573i
$895$	22.5623			0.754175
$896$		0			0
$897$	7.85410			0.262241
$898$	−39.6976	−	68.7582i	−1.32472	−	2.29449i
$899$	2.39919	−	4.15551i	0.0800174	−	0.138594i
$900$		0			0
$901$	−2.64590	−	4.58283i	−0.0881476	−	0.152676i
$902$	−5.61803			−0.187060
$903$		0			0
$904$	30.9787			1.03034
$905$	1.60739	+	2.78408i	0.0534315	+	0.0925460i
$906$	4.92705	−	8.53390i	0.163690	−	0.283520i
$907$	−7.06231	+	12.2323i	−0.234500	+	0.406166i	−0.959127	−	0.282975i	$-0.908679\pi$
$907$	−7.06231	+	12.2323i	−0.234500	+	0.406166i	0.724627	+	0.689141i	$0.242012\pi$
$908$	−44.6140	−	77.2737i	−1.48057	−	2.56442i
$909$	−51.9230			−1.72218
$910$		0			0
$911$	−26.9443			−0.892704			−0.446352	−	0.894858i	$-0.647277\pi$
$911$	−26.9443			−0.892704			−0.446352	+	0.894858i	$0.647277\pi$
$912$	−12.8992	−	22.3420i	−0.427135	−	0.739819i
$913$	22.0623	−	38.2130i	0.730156	−	1.26467i
$914$	5.80902	−	10.0615i	0.192145	−	0.332805i
$915$	19.6353	+	34.0093i	0.649122	+	1.12431i
$916$	−84.5410			−2.79331
$917$		0			0
$918$	−28.4164			−0.937881
$919$	15.6459	+	27.0995i	0.516111	+	0.893930i	0.999825	+	0.0187039i	$0.00595397\pi$
$919$	15.6459	+	27.0995i	0.516111	+	0.893930i	−0.483715	+	0.875226i	$0.660713\pi$
$920$	25.0623	−	43.4092i	0.826280	−	1.43116i
$921$	−29.5344	+	51.1552i	−0.973193	+	1.68562i
$922$	−29.9894	−	51.9431i	−0.987647	−	1.71065i
$923$	−7.47214			−0.245948
$924$		0			0
$925$		0			0
$926$	22.6353	+	39.2054i	0.743841	+	1.28837i
$927$	−9.07295	+	15.7148i	−0.297995	+	0.516142i
$928$	−30.4894	+	52.8091i	−1.00086	+	1.73354i
$929$	11.8369	+	20.5021i	0.388355	+	0.672651i	0.992228	−	0.124429i	$-0.0397099\pi$
$929$	11.8369	+	20.5021i	0.388355	+	0.672651i	−0.603873	+	0.797081i	$0.706377\pi$
$930$	13.0902			0.429244
$931$		0			0
$932$	63.2705			2.07249
$933$	21.0623	+	36.4810i	0.689549	+	1.19433i
$934$	52.2599	−	90.5167i	1.71000	−	2.96180i
$935$	−30.4894	+	52.8091i	−0.997109	+	1.72704i
$936$	−14.3992	−	24.9401i	−0.470652	−	0.815193i
$937$	−13.9787			−0.456665			−0.228332	−	0.973583i	$-0.573327\pi$
$937$	−13.9787			−0.456665			−0.228332	+	0.973583i	$0.573327\pi$
$938$		0			0
$939$	41.1246			1.34205
$940$	−60.6763	−	105.094i	−1.97904	−	3.42780i
$941$	29.1803	−	50.5418i	0.951252	−	1.64762i	0.208531	−	0.978016i	$-0.433132\pi$
$941$	29.1803	−	50.5418i	0.951252	−	1.64762i	0.742721	−	0.669601i	$-0.233535\pi$
$942$	3.92705	−	6.80185i	0.127950	−	0.221616i
$943$	−0.572949	−	0.992377i	−0.0186578	−	0.0323162i
$944$	−6.97871			−0.227138
$945$		0			0
$946$	−29.4164			−0.956410
$947$	−0.600813	−	1.04064i	−0.0195238	−	0.0338162i	0.856098	−	0.516813i	$-0.172882\pi$
$947$	−0.600813	−	1.04064i	−0.0195238	−	0.0338162i	−0.875622	+	0.482997i	$0.839548\pi$
$948$	63.5410	−	110.056i	2.06372	−	3.57446i
$949$	−2.07295	+	3.59045i	−0.0672908	+	0.116551i
$950$		0			0
$951$	−3.70820			−0.120247
$952$		0			0
$953$	10.7426			0.347988			0.173994	−	0.984747i	$-0.444333\pi$
$953$	10.7426			0.347988			0.173994	+	0.984747i	$0.444333\pi$
$954$	5.50000	+	9.52628i	0.178069	+	0.308425i
$955$	−7.07295	+	12.2507i	−0.228875	+	0.396424i
$956$	−10.9894	+	19.0341i	−0.355421	+	0.615608i
$957$	−41.3156	−	71.5607i	−1.33554	−	2.31323i
$958$	−37.8328			−1.22232
$959$		0			0
$960$	−50.9787			−1.64533
$961$	15.1353	+	26.2150i	0.488234	+	0.845646i
$962$	14.0172	−	24.2785i	0.451933	−	0.782772i
$963$	−2.83688	+	4.91362i	−0.0914172	+	0.158339i
$964$	−10.4164	−	18.0417i	−0.335490	−	0.581086i
$965$	−41.5066			−1.33614
$966$		0			0
$967$	−26.8541			−0.863570			−0.431785	−	0.901977i	$-0.642116\pi$
$967$	−26.8541			−0.863570			−0.431785	+	0.901977i	$0.642116\pi$
$968$	76.8222	+	133.060i	2.46916	+	4.27671i
$969$	−6.35410	+	11.0056i	−0.204123	+	0.353552i
$970$	42.1976	−	73.0883i	1.35488	−	2.34672i
$971$	−3.40983	−	5.90600i	−0.109427	−	0.189533i	0.806111	−	0.591764i	$-0.201568\pi$
$971$	−3.40983	−	5.90600i	−0.109427	−	0.189533i	−0.915538	+	0.402231i	$0.868235\pi$
$972$	−105.103			−3.37119
$973$		0			0
$974$	−95.3394			−3.05487
$975$		0			0
$976$	−33.0517	+	57.2472i	−1.05796	+	1.83244i
$977$	13.0902	−	22.6728i	0.418792	−	0.725368i	−0.577027	−	0.816725i	$-0.695787\pi$
$977$	13.0902	−	22.6728i	0.418792	−	0.725368i	0.995818	+	0.0913570i	$0.0291204\pi$
$978$	−54.3328	−	94.1072i	−1.73737	−	3.00922i
$979$	12.8754			0.411499
$980$		0			0
$981$	−40.1459			−1.28176
$982$	−2.00000	−	3.46410i	−0.0638226	−	0.110544i
$983$	5.53444	−	9.58593i	0.176521	−	0.305744i	−0.764165	−	0.645020i	$-0.776849\pi$
$983$	5.53444	−	9.58593i	0.176521	−	0.305744i	0.940687	+	0.339276i	$0.110182\pi$
$984$	−3.73607	+	6.47106i	−0.119101	+	0.206290i
$985$	17.0729	+	29.5712i	0.543989	+	0.942217i
$986$	71.3951			2.27368
$987$		0			0
$988$	−4.85410			−0.154430
$989$	−3.00000	−	5.19615i	−0.0953945	−	0.165228i
$990$	63.3779	−	109.774i	2.01428	−	3.48884i
$991$	29.5623	−	51.2034i	0.939078	−	1.62653i	0.171881	−	0.985118i	$-0.445015\pi$
$991$	29.5623	−	51.2034i	0.939078	−	1.62653i	0.767196	−	0.641412i	$-0.221651\pi$
$992$	4.63525	+	8.02850i	0.147169	+	0.254905i
$993$	−56.4508			−1.79141
$994$		0			0
$995$	37.3607			1.18441
$996$	−49.9058	−	86.4393i	−1.58132	−	2.73893i
$997$	−12.0729	+	20.9110i	−0.382354	+	0.662257i	−0.991398	−	0.130880i	$-0.958220\pi$
$997$	−12.0729	+	20.9110i	−0.382354	+	0.662257i	0.609044	+	0.793136i	$0.291553\pi$
$998$	12.8992	−	22.3420i	0.408317	−	0.707225i
$999$	11.9721	+	20.7363i	0.378782	+	0.656069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.f.j.704.2		4
7.2	even	3	inner	931.2.f.j.324.2		4
7.3	odd	6		133.2.a.a.1.1	✓	2
7.4	even	3		931.2.a.d.1.1		2
7.5	odd	6		931.2.f.k.324.2		4
7.6	odd	2		931.2.f.k.704.2		4
21.11	odd	6		8379.2.a.bn.1.2		2
21.17	even	6		1197.2.a.j.1.2		2
28.3	even	6		2128.2.a.o.1.2		2
35.24	odd	6		3325.2.a.q.1.2		2
56.3	even	6		8512.2.a.j.1.1		2
56.45	odd	6		8512.2.a.be.1.2		2
133.94	even	6		2527.2.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.a.a.1.1	✓	2	7.3	odd	6
931.2.a.d.1.1		2	7.4	even	3
931.2.f.j.324.2		4	7.2	even	3	inner
931.2.f.j.704.2		4	1.1	even	1	trivial
931.2.f.k.324.2		4	7.5	odd	6
931.2.f.k.704.2		4	7.6	odd	2
1197.2.a.j.1.2		2	21.17	even	6
2128.2.a.o.1.2		2	28.3	even	6
2527.2.a.e.1.2		2	133.94	even	6
3325.2.a.q.1.2		2	35.24	odd	6
8379.2.a.bn.1.2		2	21.11	odd	6
8512.2.a.j.1.1		2	56.3	even	6
8512.2.a.be.1.2		2	56.45	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.30902 + 2.26728i) q^{2} +(-1.30902 + 2.26728i) q^{3} +(-2.42705 + 4.20378i) q^{4} +(1.11803 + 1.93649i) q^{5} -6.85410 q^{6} -7.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +O(q^{10})\)	\(q+(1.30902 + 2.26728i) q^{2} +(-1.30902 + 2.26728i) q^{3} +(-2.42705 + 4.20378i) q^{4} +(1.11803 + 1.93649i) q^{5} -6.85410 q^{6} -7.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +(-2.92705 + 5.06980i) q^{10} +(2.80902 - 4.86536i) q^{11} +(-6.35410 - 11.0056i) q^{12} -1.00000 q^{13} -5.85410 q^{15} +(-4.92705 - 8.53390i) q^{16} +(-2.42705 + 4.20378i) q^{17} +(5.04508 - 8.73834i) q^{18} +(-0.500000 - 0.866025i) q^{19} -10.8541 q^{20} +14.7082 q^{22} +(1.50000 + 2.59808i) q^{23} +(9.78115 - 16.9415i) q^{24} +(-1.30902 - 2.26728i) q^{26} +2.23607 q^{27} -5.61803 q^{29} +(-7.66312 - 13.2729i) q^{30} +(-0.427051 + 0.739674i) q^{31} +(5.42705 - 9.39993i) q^{32} +(7.35410 + 12.7377i) q^{33} -12.7082 q^{34} +18.7082 q^{36} +(5.35410 + 9.27358i) q^{37} +(1.30902 - 2.26728i) q^{38} +(1.30902 - 2.26728i) q^{39} +(-8.35410 - 14.4697i) q^{40} -0.381966 q^{41} -2.00000 q^{43} +(13.6353 + 23.6170i) q^{44} +(4.30902 - 7.46344i) q^{45} +(-3.92705 + 6.80185i) q^{46} +(5.59017 + 9.68246i) q^{47} +25.7984 q^{48} +(-6.35410 - 11.0056i) q^{51} +(2.42705 - 4.20378i) q^{52} +(-0.545085 + 0.944115i) q^{53} +(2.92705 + 5.06980i) q^{54} +12.5623 q^{55} +2.61803 q^{57} +(-7.35410 - 12.7377i) q^{58} +(0.354102 - 0.613323i) q^{59} +(14.2082 - 24.6093i) q^{60} +(-3.35410 - 5.80948i) q^{61} -2.23607 q^{62} +8.70820 q^{64} +(-1.11803 - 1.93649i) q^{65} +(-19.2533 + 33.3477i) q^{66} +(-3.28115 + 5.68312i) q^{67} +(-11.7812 - 20.4056i) q^{68} -7.85410 q^{69} +7.47214 q^{71} +(14.3992 + 24.9401i) q^{72} +(2.07295 - 3.59045i) q^{73} +(-14.0172 + 24.2785i) q^{74} +4.85410 q^{76} +6.85410 q^{78} +(5.00000 + 8.66025i) q^{79} +(11.0172 - 19.0824i) q^{80} +(2.85410 - 4.94345i) q^{81} +(-0.500000 - 0.866025i) q^{82} +7.85410 q^{83} -10.8541 q^{85} +(-2.61803 - 4.53457i) q^{86} +(7.35410 - 12.7377i) q^{87} +(-20.9894 + 36.3546i) q^{88} +(1.14590 + 1.98475i) q^{89} +22.5623 q^{90} -14.5623 q^{92} +(-1.11803 - 1.93649i) q^{93} +(-14.6353 + 25.3490i) q^{94} +(1.11803 - 1.93649i) q^{95} +(14.2082 + 24.6093i) q^{96} -14.4164 q^{97} -21.6525 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 14 q^{6} - 12 q^{8} - q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 14 * q^6 - 12 * q^8 - q^9	\( 4 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 14 q^{6} - 12 q^{8} - q^{9} - 5 q^{10} + 9 q^{11} - 12 q^{12} - 4 q^{13} - 10 q^{15} - 13 q^{16} - 3 q^{17} + 9 q^{18} - 2 q^{19} - 30 q^{20} + 32 q^{22} + 6 q^{23} + 19 q^{24} - 3 q^{26} - 18 q^{29} - 15 q^{30} + 5 q^{31} + 15 q^{32} + 16 q^{33} - 24 q^{34} + 48 q^{36} + 8 q^{37} + 3 q^{38} + 3 q^{39} - 20 q^{40} - 6 q^{41} - 8 q^{43} + 21 q^{44} + 15 q^{45} - 9 q^{46} + 54 q^{48} - 12 q^{51} + 3 q^{52} + 9 q^{53} + 5 q^{54} + 10 q^{55} + 6 q^{57} - 16 q^{58} - 12 q^{59} + 30 q^{60} + 8 q^{64} - 39 q^{66} + 7 q^{67} - 27 q^{68} - 18 q^{69} + 12 q^{71} + 33 q^{72} + 15 q^{73} - 27 q^{74} + 6 q^{76} + 14 q^{78} + 20 q^{79} + 15 q^{80} - 2 q^{81} - 2 q^{82} + 18 q^{83} - 30 q^{85} - 6 q^{86} + 16 q^{87} - 37 q^{88} + 18 q^{89} + 50 q^{90} - 18 q^{92} - 25 q^{94} + 30 q^{96} - 4 q^{97} - 24 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 14 * q^6 - 12 * q^8 - q^9 - 5 * q^10 + 9 * q^11 - 12 * q^12 - 4 * q^13 - 10 * q^15 - 13 * q^16 - 3 * q^17 + 9 * q^18 - 2 * q^19 - 30 * q^20 + 32 * q^22 + 6 * q^23 + 19 * q^24 - 3 * q^26 - 18 * q^29 - 15 * q^30 + 5 * q^31 + 15 * q^32 + 16 * q^33 - 24 * q^34 + 48 * q^36 + 8 * q^37 + 3 * q^38 + 3 * q^39 - 20 * q^40 - 6 * q^41 - 8 * q^43 + 21 * q^44 + 15 * q^45 - 9 * q^46 + 54 * q^48 - 12 * q^51 + 3 * q^52 + 9 * q^53 + 5 * q^54 + 10 * q^55 + 6 * q^57 - 16 * q^58 - 12 * q^59 + 30 * q^60 + 8 * q^64 - 39 * q^66 + 7 * q^67 - 27 * q^68 - 18 * q^69 + 12 * q^71 + 33 * q^72 + 15 * q^73 - 27 * q^74 + 6 * q^76 + 14 * q^78 + 20 * q^79 + 15 * q^80 - 2 * q^81 - 2 * q^82 + 18 * q^83 - 30 * q^85 - 6 * q^86 + 16 * q^87 - 37 * q^88 + 18 * q^89 + 50 * q^90 - 18 * q^92 - 25 * q^94 + 30 * q^96 - 4 * q^97 - 24 * q^99

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